LMFDB - Embedded newform 69.7.f.a.34.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.24
Character	$\chi$	$=$	69.34
Dual form			69.7.f.a.67.24

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.6885 - 8.15441i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(67.9173 - 148.718i) q^{4} +(-11.0967 - 37.7918i) q^{5} +(97.6718 + 213.871i) q^{6} +(105.851 - 91.7206i) q^{7} +(-213.563 - 1485.36i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})$	\(q+(12.6885 - 8.15441i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(67.9173 - 148.718i) q^{4} +(-11.0967 - 37.7918i) q^{5} +(97.6718 + 213.871i) q^{6} +(105.851 - 91.7206i) q^{7} +(-213.563 - 1485.36i) q^{8} +(-233.157 - 68.4610i) q^{9} +(-448.970 - 389.035i) q^{10} +(684.941 - 1065.79i) q^{11} +(2144.02 + 1377.88i) q^{12} +(281.824 - 325.242i) q^{13} +(595.167 - 2026.95i) q^{14} +(607.737 - 87.3794i) q^{15} +(-7969.88 - 9197.73i) q^{16} +(-2159.53 + 986.225i) q^{17} +(-3516.67 + 1032.59i) q^{18} +(-2913.85 - 1330.71i) q^{19} +(-6373.99 - 916.441i) q^{20} +(1180.40 + 1836.74i) q^{21} -19108.6i q^{22} +(10098.6 + 6786.39i) q^{23} +23392.6 q^{24} +(11839.5 - 7608.79i) q^{25} +(923.769 - 6424.95i) q^{26} +(1573.59 - 3445.68i) q^{27} +(-6451.40 - 21971.4i) q^{28} +(3038.31 + 6652.97i) q^{29} +(6998.76 - 6064.46i) q^{30} +(2797.32 + 19455.8i) q^{31} +(-83977.6 - 24658.0i) q^{32} +(14925.4 + 12932.9i) q^{33} +(-19359.2 + 30123.4i) q^{34} +(-4640.89 - 2982.52i) q^{35} +(-26016.8 + 30025.0i) q^{36} +(-20746.7 + 70656.8i) q^{37} +(-47823.5 + 6875.98i) q^{38} +(4393.20 + 5070.03i) q^{39} +(-53764.7 + 24553.5i) q^{40} +(-94350.8 + 27703.9i) q^{41} +(29955.1 + 13680.0i) q^{42} +(114372. + 16444.3i) q^{43} +(-111983. - 174249. i) q^{44} +9571.11i q^{45} +(183475. + 3761.43i) q^{46} +106186. q^{47} +(159600. - 102569. i) q^{48} +(-13951.4 + 97034.0i) q^{49} +(88180.5 - 193088. i) q^{50} +(-10426.4 - 35509.0i) q^{51} +(-29228.7 - 64002.0i) q^{52} +(107749. - 93365.4i) q^{53} +(-8130.99 - 56552.3i) q^{54} +(-47878.7 - 14058.4i) q^{55} +(-158844. - 137639. i) q^{56} +(26996.8 - 42007.9i) q^{57} +(92802.7 + 59640.7i) q^{58} +(-227798. + 262893. i) q^{59} +(28281.0 - 96316.2i) q^{60} +(339977. - 48881.3i) q^{61} +(194144. + 224054. i) q^{62} +(-30959.2 + 14138.6i) q^{63} +(-519272. + 152472. i) q^{64} +(-15418.8 - 7041.54i) q^{65} +(294841. + 42391.8i) q^{66} +(-83151.3 - 129386. i) q^{67} +388144. i q^{68} +(-127116. + 140763. i) q^{69} -83206.6 q^{70} +(396281. - 254674. i) q^{71} +(-51895.7 + 360943. i) q^{72} +(-150992. + 330627. i) q^{73} +(312920. + 1.06571e6i) q^{74} +(91136.4 + 199561. i) q^{75} +(-395801. + 342964. i) q^{76} +(-25253.0 - 175638. i) q^{77} +(97086.3 + 28507.1i) q^{78} +(-517694. - 448585. i) q^{79} +(-259160. + 403260. i) q^{80} +(49675.2 + 31924.3i) q^{81} +(-971262. + 1.12090e6i) q^{82} +(84725.9 - 288550. i) q^{83} +(353327. - 50800.7i) q^{84} +(61234.9 + 70668.8i) q^{85} +(1.58531e6 - 723986. i) q^{86} +(-109394. + 32121.1i) q^{87} +(-1.72936e6 - 789772. i) q^{88} +(-306660. - 44091.1i) q^{89} +(78046.8 + 121443. i) q^{90} -60276.4i q^{91} +(1.69513e6 - 1.04093e6i) q^{92} -306404. q^{93} +(1.34734e6 - 865883. i) q^{94} +(-17955.9 + 124886. i) q^{95} +(566770. - 1.24105e6i) q^{96} +(-137865. - 469526. i) q^{97} +(614233. + 1.34498e6i) q^{98} +(-232664. + 201604. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	12.6885	−	8.15441i	1.58606	−	1.01930i	0.612619	−	0.790378i	$-0.290116\pi$
$2$	12.6885	−	8.15441i	1.58606	−	1.01930i	0.973444	−	0.228923i	$-0.0735205\pi$
$3$	−2.21847	+	15.4298i	−0.0821655	+	0.571474i
$3$	−2.21847	+	15.4298i	−0.0821655	+	0.571474i
$4$	67.9173	−	148.718i	1.06121	−	2.32372i
$5$	−11.0967	−	37.7918i	−0.0887734	−	0.302335i	0.903123	−	0.429381i	$-0.141268\pi$
$5$	−11.0967	−	37.7918i	−0.0887734	−	0.302335i	−0.991897	+	0.127047i	$0.959450\pi$
$6$	97.6718	+	213.871i	0.452184	+	0.990145i
$7$	105.851	−	91.7206i	0.308604	−	0.267407i	−0.486764	−	0.873533i	$-0.661823\pi$
$7$	105.851	−	91.7206i	0.308604	−	0.267407i	0.795368	+	0.606126i	$0.207277\pi$
$8$	−213.563	−	1485.36i	−0.417115	−	2.90110i
$9$	−233.157	−	68.4610i	−0.319831	−	0.0939109i
$10$	−448.970	−	389.035i	−0.448970	−	0.389035i
$11$	684.941	−	1065.79i	0.514606	−	0.800743i	−0.482569	−	0.875858i	$-0.660296\pi$
$11$	684.941	−	1065.79i	0.514606	−	0.800743i	0.997175	+	0.0751152i	$0.0239325\pi$
$12$	2144.02	+	1377.88i	1.24075	+	0.797382i
$13$	281.824	−	325.242i	0.128277	−	0.148039i	−0.687978	−	0.725732i	$-0.741501\pi$
$13$	281.824	−	325.242i	0.128277	−	0.148039i	0.816254	+	0.577693i	$0.196047\pi$
$14$	595.167	−	2026.95i	0.216898	−	0.738686i
$15$	607.737	−	87.3794i	0.180070	−	0.0258902i
$16$	−7969.88	−	9197.73i	−1.94577	−	2.24554i
$17$	−2159.53	+	986.225i	−0.439555	+	0.200738i	−0.622885	−	0.782314i	$-0.714040\pi$
$17$	−2159.53	+	986.225i	−0.439555	+	0.200738i	0.183330	+	0.983051i	$0.441312\pi$
$18$	−3516.67	+	1032.59i	−0.602996	+	0.177056i
$19$	−2913.85	−	1330.71i	−0.424821	−	0.194009i	0.191520	−	0.981489i	$-0.438658\pi$
$19$	−2913.85	−	1330.71i	−0.424821	−	0.194009i	−0.616341	+	0.787480i	$0.711386\pi$
$20$	−6373.99	−	916.441i	−0.796749	−	0.114555i
$21$	1180.40	+	1836.74i	0.127460	+	0.198331i
$22$		−	19108.6i		−	1.79457i
$23$	10098.6	+	6786.39i	0.829995	+	0.557770i
$23$	10098.6	+	6786.39i	0.829995	+	0.557770i
$24$	23392.6			1.69217
$25$	11839.5	−	7608.79i	0.757728	−	0.486962i
$26$	923.769	−	6424.95i	0.0525585	−	0.365553i
$27$	1573.59	−	3445.68i	0.0799467	−	0.175059i
$28$	−6451.40	−	21971.4i	−0.293886	−	1.00089i
$29$	3038.31	+	6652.97i	0.124577	+	0.272786i	0.961637	−	0.274326i	$-0.0884546\pi$
$29$	3038.31	+	6652.97i	0.124577	+	0.272786i	−0.837060	+	0.547111i	$0.815727\pi$
$30$	6998.76	−	6064.46i	0.259213	−	0.224609i
$31$	2797.32	+	19455.8i	0.0938982	+	0.653076i	0.981358	+	0.192190i	$0.0615591\pi$
$31$	2797.32	+	19455.8i	0.0938982	+	0.653076i	−0.887460	+	0.460886i	$0.847532\pi$
$32$	−83977.6	−	24658.0i	−2.56279	−	0.752504i
$33$	14925.4	+	12932.9i	0.415321	+	0.359877i
$34$	−19359.2	+	30123.4i	−0.492549	+	0.766422i
$35$	−4640.89	−	2982.52i	−0.108242	−	0.0695631i
$36$	−26016.8	+	30025.0i	−0.557630	+	0.643539i
$37$	−20746.7	+	70656.8i	−0.409585	+	1.39492i	0.454130	+	0.890936i	$0.349950\pi$
$37$	−20746.7	+	70656.8i	−0.409585	+	1.39492i	−0.863714	+	0.503982i	$0.831868\pi$
$38$	−47823.5	+	6875.98i	−0.871547	+	0.125309i
$39$	4393.20	+	5070.03i	0.0740607	+	0.0854706i
$40$	−53764.7	+	24553.5i	−0.840073	+	0.383648i
$41$	−94350.8	+	27703.9i	−1.36897	+	0.401966i	−0.881916	−	0.471406i	$-0.843747\pi$
$41$	−94350.8	+	27703.9i	−1.36897	+	0.401966i	−0.487053	+	0.873372i	$0.661928\pi$
$42$	29955.1	+	13680.0i	0.404318	+	0.184646i
$43$	114372.	+	16444.3i	1.43852	+	0.206828i	0.817030	−	0.576595i	$-0.195619\pi$
$43$	114372.	+	16444.3i	1.43852	+	0.206828i	0.621489	+	0.783423i	$0.286528\pi$
$44$	−111983.	−	174249.i	−1.31460	−	2.04556i
$45$			9571.11i			0.105033i
$46$	183475.	+	3761.43i	1.88496	+	0.0386438i
$47$	106186.			1.02276			0.511379	−	0.859355i	$-0.329135\pi$
$47$	106186.			1.02276			0.511379	+	0.859355i	$0.329135\pi$
$48$	159600.	−	102569.i	1.44314	−	0.927451i
$49$	−13951.4	+	97034.0i	−0.118585	+	0.824775i
$50$	88180.5	−	193088.i	0.705444	−	1.54471i
$51$	−10426.4	−	35509.0i	−0.0786002	−	0.267688i
$52$	−29228.7	−	64002.0i	−0.207874	−	0.455180i
$53$	107749.	−	93365.4i	0.723748	−	0.627131i	−0.213034	−	0.977045i	$-0.568334\pi$
$53$	107749.	−	93365.4i	0.723748	−	0.627131i	0.936782	+	0.349914i	$0.113789\pi$
$54$	−8130.99	−	56552.3i	−0.0516371	−	0.359144i
$55$	−47878.7	−	14058.4i	−0.287776	−	0.0844985i
$56$	−158844.	−	137639.i	−0.904497	−	0.783751i
$57$	26996.8	−	42007.9i	0.145777	−	0.226833i
$58$	92802.7	+	59640.7i	0.475638	+	0.305674i
$59$	−227798.	+	262893.i	−1.10916	+	1.28004i	−0.152669	+	0.988277i	$0.548787\pi$
$59$	−227798.	+	262893.i	−1.10916	+	1.28004i	−0.956491	+	0.291762i	$0.905759\pi$
$60$	28281.0	−	96316.2i	0.130931	−	0.445908i
$61$	339977.	−	48881.3i	1.49782	−	0.215354i	0.655856	−	0.754886i	$-0.272308\pi$
$61$	339977.	−	48881.3i	1.49782	−	0.215354i	0.841965	+	0.539532i	$0.181399\pi$
$62$	194144.	+	224054.i	0.814610	+	0.940110i
$63$	−30959.2	+	14138.6i	−0.123814	+	0.0565438i
$64$	−519272.	+	152472.i	−1.98086	+	0.581634i
$65$	−15418.8	−	7041.54i	−0.0561450	−	0.0256406i
$66$	294841.	+	42391.8i	1.02555	+	0.147452i
$67$	−83151.3	−	129386.i	−0.276468	−	0.430193i	0.675056	−	0.737766i	$-0.264119\pi$
$67$	−83151.3	−	129386.i	−0.276468	−	0.430193i	−0.951524	+	0.307574i	$0.900483\pi$
$68$			388144.i			1.23443i
$69$	−127116.	+	140763.i	−0.386948	+	0.428491i
$70$	−83206.6			−0.242585
$71$	396281.	−	254674.i	1.10720	−	0.711557i	0.146523	−	0.989207i	$-0.453192\pi$
$71$	396281.	−	254674.i	1.10720	−	0.711557i	0.960682	+	0.277650i	$0.0895555\pi$
$72$	−51895.7	+	360943.i	−0.139038	+	0.967032i
$73$	−150992.	+	330627.i	−0.388138	+	0.849903i	0.610199	+	0.792248i	$0.291089\pi$
$73$	−150992.	+	330627.i	−0.388138	+	0.849903i	−0.998337	+	0.0576545i	$0.981638\pi$
$74$	312920.	+	1.06571e6i	0.772214	+	2.62992i
$75$	91136.4	+	199561.i	0.216027	+	0.473033i
$76$	−395801.	+	342964.i	−0.901647	+	0.781281i
$77$	−25253.0	−	175638.i	−0.0553147	−	0.384722i
$78$	97086.3	+	28507.1i	0.204585	+	0.0600716i
$79$	−517694.	−	448585.i	−1.05001	−	0.909836i	−0.0539488	−	0.998544i	$-0.517181\pi$
$79$	−517694.	−	448585.i	−1.05001	−	0.909836i	−0.996058	+	0.0887079i	$0.971726\pi$
$80$	−259160.	+	403260.i	−0.506171	+	0.787618i
$81$	49675.2	+	31924.3i	0.0934726	+	0.0600712i
$82$	−971262.	+	1.12090e6i	−1.76155	+	2.03294i
$83$	84725.9	−	288550.i	0.148177	−	0.504646i	−0.851633	−	0.524139i	$-0.824387\pi$
$83$	84725.9	−	288550.i	0.148177	−	0.504646i	0.999810	+	0.0194934i	$0.00620534\pi$
$84$	353327.	−	50800.7i	0.596127	−	0.0857101i
$85$	61234.9	+	70668.8i	0.0997108	+	0.115072i
$86$	1.58531e6	−	723986.i	2.49240	−	1.13824i
$87$	−109394.	+	32121.1i	−0.166126	+	0.0487789i
$88$	−1.72936e6	−	789772.i	−2.53768	−	1.15892i
$89$	−306660.	−	44091.1i	−0.434998	−	0.0625433i	−0.0786624	−	0.996901i	$-0.525065\pi$
$89$	−306660.	−	44091.1i	−0.434998	−	0.0625433i	−0.356336	+	0.934358i	$0.615974\pi$
$90$	78046.8	+	121443.i	0.107060	+	0.166589i
$91$		−	60276.4i		−	0.0799877i
$92$	1.69513e6	−	1.04093e6i	2.17690	−	1.33677i
$93$	−306404.			−0.380931
$94$	1.34734e6	−	865883.i	1.62216	−	1.04250i
$95$	−17955.9	+	124886.i	−0.0209429	+	0.145661i
$96$	566770.	−	1.24105e6i	0.640609	−	1.40274i
$97$	−137865.	−	469526.i	−0.151056	−	0.514451i	0.848843	−	0.528645i	$-0.177300\pi$
$97$	−137865.	−	469526.i	−0.151056	−	0.514451i	−0.999899	+	0.0141943i	$0.995482\pi$
$98$	614233.	+	1.34498e6i	0.652612	+	1.42902i
$99$	−232664.	+	201604.i	−0.239785	+	0.207775i
$100$	−327458.	−	2.27752e6i	−0.327458	−	2.27752i
$101$	1.43100e6	+	420180.i	1.38892	+	0.407822i	0.888863	−	0.458173i	$-0.151496\pi$
$101$	1.43100e6	+	420180.i	1.38892	+	0.407822i	0.500052	+	0.865995i	$0.333314\pi$
$102$	−421851.	−	365536.i	−0.397519	−	0.344452i
$103$	−865869.	+	1.34732e6i	−0.792393	+	1.23299i	0.176205	+	0.984354i	$0.443618\pi$
$103$	−865869.	+	1.34732e6i	−0.792393	+	1.23299i	−0.968598	+	0.248634i	$0.920018\pi$
$104$	−543290.	−	349151.i	−0.482982	−	0.310394i
$105$	56315.3	−	64991.3i	0.0486473	−	0.0561419i
$106$	605840.	−	2.06330e6i	0.508675	−	1.73239i
$107$	−1.43244e6	+	205954.i	−1.16930	+	0.168120i	−0.699485	−	0.714647i	$-0.746587\pi$
$107$	−1.43244e6	+	205954.i	−1.16930	+	0.168120i	−0.469812	+	0.882767i	$0.655678\pi$
$108$	−405562.	−	468043.i	−0.321948	−	0.371548i
$109$	−563555.	+	257367.i	−0.435168	+	0.198735i	−0.620940	−	0.783858i	$-0.713249\pi$
$109$	−563555.	+	257367.i	−0.435168	+	0.198735i	0.185772	+	0.982593i	$0.440522\pi$
$110$	−722147.	+	212042.i	−0.542560	+	0.159310i
$111$	−1.04419e6	−	476867.i	−0.763505	−	0.348681i
$112$	−1.68724e6	−	242589.i	−1.20095	−	0.172670i
$113$	−1.13809e6	−	1.77090e6i	−0.788751	−	1.22732i	−0.969813	−	0.243849i	$-0.921590\pi$
$113$	−1.13809e6	−	1.77090e6i	−0.788751	−	1.22732i	0.181062	−	0.983472i	$-0.442046\pi$
$114$		−	753161.i		−	0.508362i
$115$	144410.	−	456949.i	0.0949517	−	0.300451i
$116$	1.19577e6			0.766081
$117$	−87975.6	+	56538.5i	−0.0549294	+	0.0353010i
$118$	−746681.	+	5.19328e6i	−0.454453	+	3.16079i
$119$	−138132.	+	302467.i	−0.0819697	+	0.179489i
$120$	−259580.	−	884048.i	−0.150220	−	0.511602i
$121$	69171.2	+	151464.i	0.0390453	+	0.0854974i
$122$	3.91520e6	−	3.39254e6i	2.15613	−	1.86830i
$123$	−218151.	−	1.51727e6i	−0.117231	−	0.815358i
$124$	3.08342e6	+	905373.i	1.61721	+	0.474856i
$125$	−884037.	−	766023.i	−0.452627	−	0.392204i
$126$	−277535.	+	431852.i	−0.138741	+	0.215885i
$127$	−68695.7	−	44148.0i	−0.0335365	−	0.0215526i	0.523765	−	0.851863i	$-0.324527\pi$
$127$	−68695.7	−	44148.0i	−0.0335365	−	0.0215526i	−0.557302	+	0.830310i	$0.688163\pi$
$128$	−1.67729e6	+	1.93569e6i	−0.799793	+	0.923011i
$129$	−507463.	+	1.72826e6i	−0.236393	+	0.805082i
$130$	−253061.	+	36384.7i	−0.115185	+	0.0165611i
$131$	−1.62259e6	−	1.87256e6i	−0.721762	−	0.832958i	0.269756	−	0.962929i	$-0.413057\pi$
$131$	−1.62259e6	−	1.87256e6i	−0.721762	−	0.832958i	−0.991518	+	0.129971i	$0.958512\pi$
$132$	2.93705e6	−	1.34131e6i	1.27700	−	0.583185i
$133$	−430488.	+	126403.i	−0.182981	+	0.0537280i
$134$	−2.11013e6	−	963666.i	−0.876992	−	0.400509i
$135$	−147680.	−	21233.2i	−0.0600234	−	0.00863007i
$136$	1.92610e6	+	2.99706e6i	0.765704	+	1.19146i
$137$			240641.i			0.0935855i	0.998905	+	0.0467927i	$0.0149000\pi$
$137$			240641.i			0.0935855i	−0.998905	+	0.0467927i	$0.985100\pi$
$138$	−465071.	+	2.82263e6i	−0.176963	+	1.07403i
$139$	−2.21749e6			−0.825690			−0.412845	−	0.910801i	$-0.635465\pi$
$139$	−2.21749e6			−0.825690			−0.412845	+	0.910801i	$0.635465\pi$
$140$	−758751.	+	487620.i	−0.276513	+	0.177704i
$141$	−235570.	+	1.63843e6i	−0.0840355	+	0.584480i
$142$	2.95150e6	−	6.46287e6i	1.03081	−	2.25715i
$143$	−153607.	−	523137.i	−0.0525294	−	0.178899i
$144$	1.22855e6	+	2.69014e6i	0.411437	+	0.900922i
$145$	217713.	−	188649.i	0.0714134	−	0.0618801i
$146$	780200.	+	5.42641e6i	0.250696	+	1.74363i
$147$	−1.46626e6	−	430534.i	−0.461594	−	0.135536i
$148$	9.09889e6	+	7.88423e6i	2.80675	+	2.43206i
$149$	2.62794e6	−	4.08916e6i	0.794433	−	1.23616i	−0.173470	−	0.984839i	$-0.555498\pi$
$149$	2.62794e6	−	4.08916e6i	0.794433	−	1.23616i	0.967903	−	0.251323i	$-0.0808656\pi$
$150$	2.78369e6	+	1.78897e6i	0.824796	+	0.530064i
$151$	−3.15780e6	+	3.64430e6i	−0.917179	+	1.05848i	0.0809122	+	0.996721i	$0.474217\pi$
$151$	−3.15780e6	+	3.64430e6i	−0.917179	+	1.05848i	−0.998091	+	0.0617596i	$0.980329\pi$
$152$	−1.35429e6	+	4.61230e6i	−0.385640	+	1.31337i
$153$	571027.	−	82101.4i	0.159435	−	0.0229232i
$154$	−1.75265e6	−	2.02267e6i	−0.479880	−	0.553811i
$155$	704229.	−	321610.i	0.189112	−	0.0863645i
$156$	1.05238e6	−	309007.i	0.277204	−	0.0813943i
$157$	−4.43356e6	−	2.02474e6i	−1.14565	−	0.523203i	−0.250129	−	0.968213i	$-0.580473\pi$
$157$	−4.43356e6	−	2.02474e6i	−1.14565	−	0.523203i	−0.895526	+	0.445009i	$0.853200\pi$
$158$	−1.02267e7	−	1.47038e6i	−2.59277	−	0.372785i
$159$	1.20157e6	+	1.86968e6i	0.298922	+	0.465132i
$160$			3.44729e6i			0.841623i
$161$	1.69140e6	−	207898.i	0.405292	−	0.0498164i
$162$	890628.			0.209484
$163$	1.00547e6	−	646178.i	0.232171	−	0.149207i	−0.419383	−	0.907809i	$-0.637754\pi$
$163$	1.00547e6	−	646178.i	0.232171	−	0.149207i	0.651554	+	0.758602i	$0.274117\pi$
$164$	−2.28798e6	+	1.59132e7i	−0.518705	+	3.60767i
$165$	323136.	−	707570.i	0.0719339	−	0.157513i
$166$	−1.27791e6	−	4.35216e6i	−0.279367	−	0.951438i
$167$	−778473.	−	1.70462e6i	−0.167145	−	0.365997i	0.807462	−	0.589920i	$-0.200841\pi$
$167$	−778473.	−	1.70462e6i	−0.167145	−	0.365997i	−0.974607	+	0.223923i	$0.928114\pi$
$168$	2.47614e6	−	2.14558e6i	0.522212	−	0.452499i
$169$	660569.	+	4.59436e6i	0.136854	+	0.951841i
$170$	1.35324e6	+	397348.i	0.275441	+	0.0808768i
$171$	588281.	+	509749.i	0.117651	+	0.101945i
$172$	1.02134e7	−	1.58924e7i	2.00718	−	3.12323i
$173$	3.46288e6	+	2.22546e6i	0.668804	+	0.429814i	0.830494	−	0.557027i	$-0.188058\pi$
$173$	3.46288e6	+	2.22546e6i	0.668804	+	0.429814i	−0.161690	+	0.986842i	$0.551695\pi$
$174$	−1.12612e6	+	1.29962e6i	−0.213766	+	0.246699i
$175$	555344.	−	1.89133e6i	0.103621	−	0.352901i
$176$	−1.52617e7	+	2.19431e6i	−2.79941	+	0.402494i
$177$	−3.55102e6	−	4.09810e6i	−0.640374	−	0.739031i
$178$	−4.25060e6	+	1.94118e6i	−0.753685	+	0.344196i
$179$	3.19863e6	−	939204.i	0.557706	−	0.163757i	0.00928105	−	0.999957i	$-0.497046\pi$
$179$	3.19863e6	−	939204.i	0.557706	−	0.163757i	0.548425	+	0.836200i	$0.315228\pi$
$180$	1.42340e6	+	650044.i	0.244067	+	0.111462i
$181$	−7.08787e6	−	1.01908e6i	−1.19531	−	0.171859i	−0.484210	−	0.874952i	$-0.660893\pi$
$181$	−7.08787e6	−	1.01908e6i	−1.19531	−	0.171859i	−0.711099	+	0.703092i	$0.751802\pi$
$182$	−491519.	−	764818.i	−0.0815316	−	0.126866i
$183$			5.35421e6i			0.873660i
$184$	7.92356e6	−	1.64493e7i	1.27194	−	2.64055i
$185$	2.90047e6			0.458092
$186$	−3.88782e6	+	2.49855e6i	−0.604181	+	0.388283i
$187$	−428044.	+	2.97711e6i	−0.0654581	+	0.455271i
$188$	7.21186e6	−	1.57918e7i	1.08536	−	2.37661i
$189$	−149474.	−	509060.i	−0.0221401	−	0.0754022i
$190$	790538.	+	1.73104e6i	0.115256	+	0.252374i
$191$	4.11767e6	−	3.56798e6i	0.590950	−	0.512061i	−0.307261	−	0.951625i	$-0.599412\pi$
$191$	4.11767e6	−	3.56798e6i	0.590950	−	0.512061i	0.898211	+	0.439564i	$0.144867\pi$
$192$	−1.20062e6	−	8.35051e6i	−0.169630	−	1.17980i
$193$	9.22262e6	+	2.70800e6i	1.28287	+	0.376684i	0.850959	−	0.525232i	$-0.176022\pi$
$193$	9.22262e6	+	2.70800e6i	1.28287	+	0.376684i	0.431910	+	0.901917i	$0.357840\pi$
$194$	−5.57801e6	−	4.83337e6i	−0.763966	−	0.661980i
$195$	142856.	−	222288.i	0.0192661	−	0.0299786i
$196$	1.34832e7	+	8.66512e6i	1.79071	+	1.15082i
$197$	6.37097e6	−	7.35249e6i	0.833311	−	0.961692i	−0.166392	−	0.986060i	$-0.553212\pi$
$197$	6.37097e6	−	7.35249e6i	0.833311	−	0.961692i	0.999703	+	0.0243678i	$0.00775728\pi$
$198$	−1.30819e6	+	4.45529e6i	−0.168529	+	0.573959i
$199$	−1.92492e6	+	276761.i	−0.244260	+	0.0351193i	−0.263357	−	0.964698i	$-0.584830\pi$
$199$	−1.92492e6	+	276761.i	−0.244260	+	0.0351193i	0.0190973	+	0.999818i	$0.493921\pi$
$200$	−1.38303e7	−	1.59610e7i	−1.72878	−	1.99512i
$201$	2.18087e6	−	995969.i	0.268560	−	0.122647i
$202$	2.15836e7	−	6.33751e6i	2.61860	−	0.768891i
$203$	931824.	+	425550.i	0.111390	+	0.0508700i
$204$	−5.98897e6	−	861084.i	−0.705443	−	0.101427i
$205$	2.09396e6	+	3.25827e6i	0.243056	+	0.378203i
$206$			2.41561e7i			2.76328i
$207$	−1.88994e6	−	2.27365e6i	−0.213078	−	0.256338i
$208$	−5.23760e6			−0.582025
$209$	−3.41407e6	+	2.19409e6i	−0.373967	+	0.240334i
$210$	184591.	−	1.28386e6i	0.0199321	−	0.138631i
$211$	−5.55649e6	+	1.21670e7i	−0.591497	+	1.29520i	0.343036	+	0.939322i	$0.388545\pi$
$211$	−5.55649e6	+	1.21670e7i	−0.591497	+	1.29520i	−0.934533	+	0.355876i	$0.884182\pi$
$212$	−6.56708e6	−	2.23654e7i	−0.689231	−	2.34731i
$213$	3.05043e6	+	6.67952e6i	0.315662	+	0.691204i
$214$	−1.64961e7	+	1.42939e7i	−1.68322	+	1.45851i
$215$	−647695.	−	4.50482e6i	−0.0651711	−	0.453275i
$216$	−5.45414e6	−	1.60148e6i	−0.541209	−	0.158913i
$217$	2.08060e6	+	1.80285e6i	0.203615	+	0.176433i
$218$	−5.05200e6	+	7.86107e6i	−0.487634	+	0.758773i
$219$	−4.76653e6	−	3.06326e6i	−0.453805	−	0.291643i
$220$	−5.34254e6	+	6.16562e6i	−0.501741	+	0.579040i
$221$	−287846.	+	980313.i	−0.0266676	+	0.0908214i
$222$	−1.71378e7	+	2.46405e6i	−1.56638	+	0.225211i
$223$	1.05128e7	+	1.21324e7i	0.947990	+	1.09404i	0.995461	+	0.0951664i	$0.0303383\pi$
$223$	1.05128e7	+	1.21324e7i	0.947990	+	1.09404i	−0.0474711	+	0.998873i	$0.515116\pi$
$224$	−1.11508e7	+	5.09239e6i	−0.992114	+	0.453083i
$225$	−3.28137e6	+	963496.i	−0.288076	+	0.0845867i
$226$	−2.88812e7	−	1.31896e7i	−2.50202	−	1.14263i
$227$	1.46230e7	+	2.10247e6i	1.25014	+	0.179743i	0.735418	−	0.677614i	$-0.236986\pi$
$227$	1.46230e7	+	2.10247e6i	1.25014	+	0.179743i	0.514723	+	0.857357i	$0.327895\pi$
$228$	−4.41379e6	−	6.86798e6i	−0.372397	−	0.579462i
$229$			7.55215e6i			0.628875i	0.949278	+	0.314437i	$0.101816\pi$
$229$			7.55215e6i			0.628875i	−0.949278	+	0.314437i	$0.898184\pi$
$230$	−1.89381e6	−	6.97558e6i	−0.155651	−	0.573320i
$231$	2.76609e6			0.224403
$232$	9.23319e6	−	5.93381e6i	0.739415	−	0.475193i
$233$	−624807.	+	4.34563e6i	−0.0493944	+	0.343546i	0.950106	+	0.311928i	$0.100975\pi$
$233$	−624807.	+	4.34563e6i	−0.0493944	+	0.343546i	−0.999500	+	0.0316174i	$0.989934\pi$
$234$	−655242.	+	1.43478e6i	−0.0511392	+	0.111979i
$235$	−1.17831e6	−	4.01296e6i	−0.0907938	−	0.309215i
$236$	2.36256e7	+	5.17327e7i	1.79740	+	3.93577i
$237$	8.07005e6	−	6.99274e6i	0.606222	−	0.525294i
$238$	713750.	+	4.96424e6i	0.0529438	+	0.368232i
$239$	8.01100e6	+	2.35224e6i	0.586804	+	0.172301i	0.561639	−	0.827382i	$-0.310171\pi$
$239$	8.01100e6	+	2.35224e6i	0.586804	+	0.172301i	0.0251645	+	0.999683i	$0.491989\pi$
$240$	−5.64728e6	−	4.89340e6i	−0.408513	−	0.353979i
$241$	8.05259e6	−	1.25301e7i	0.575287	−	0.895164i	−0.424661	−	0.905352i	$-0.639607\pi$
$241$	8.05259e6	−	1.25301e7i	0.575287	−	0.895164i	0.999948	+	0.0101882i	$0.00324306\pi$
$242$	2.11278e6	+	1.35780e6i	0.149076	+	0.0958053i
$243$	−602788.	+	695654.i	−0.0420093	+	0.0484814i
$244$	1.58208e7	−	5.38806e7i	1.08908	−	3.70906i
$245$	3.82191e6	−	549507.i	0.259885	−	0.0373659i
$246$	−1.51405e7	−	1.74730e7i	−1.01703	−	1.17372i
$247$	−1.25399e6	+	572680.i	−0.0832156	+	0.0380033i
$248$	2.83015e7	−	8.31006e6i	1.85547	−	0.544815i
$249$	4.26430e6	+	1.94744e6i	0.276217	+	0.126144i
$250$	−1.74636e7	−	2.51088e6i	−1.11767	−	0.160697i
$251$	7.61666e6	+	1.18518e7i	0.481663	+	0.749482i	0.994009	−	0.109297i	$-0.0348599\pi$
$251$	7.61666e6	+	1.18518e7i	0.481663	+	0.749482i	−0.512346	+	0.858779i	$0.671224\pi$
$252$			5.56446e6i			0.347713i
$253$	1.41498e7	−	6.11465e6i	0.873751	−	0.377581i
$254$	−1.23165e6			−0.0751597
$255$	−1.22625e6	+	788065.i	−0.0739536	+	0.0475271i
$256$	−568571.	+	3.95450e6i	−0.0338895	+	0.235706i
$257$	9.67929e6	−	2.11947e7i	0.570222	−	1.24861i	−0.376457	−	0.926434i	$-0.622858\pi$
$257$	9.67929e6	−	2.11947e7i	0.570222	−	1.24861i	0.946679	−	0.322178i	$-0.104415\pi$
$258$	7.65400e6	+	2.60671e7i	0.445686	+	1.51787i
$259$	4.28462e6	+	9.38201e6i	0.246611	+	0.540003i
$260$	−2.09441e6	+	1.81482e6i	−0.119163	+	0.103255i
$261$	−252934.	−	1.75919e6i	−0.0142261	−	0.0989445i
$262$	−3.58579e7	−	1.05288e7i	−1.99380	−	0.585431i
$263$	−1.32906e7	−	1.15164e7i	−0.730596	−	0.633065i	0.207982	−	0.978133i	$-0.433310\pi$
$263$	−1.32906e7	−	1.15164e7i	−0.730596	−	0.633065i	−0.938578	+	0.345068i	$0.887856\pi$
$264$	1.60225e7	−	2.49316e7i	0.870802	−	1.35499i
$265$	−4.72411e6	−	3.03600e6i	−0.253853	−	0.163141i
$266$	−4.43151e6	+	5.11423e6i	−0.235454	+	0.271729i
$267$	1.36063e6	−	4.63389e6i	0.0714837	−	0.243451i
$268$	−2.48895e7	+	3.57857e6i	−1.29304	+	0.185911i
$269$	1.09691e6	+	1.26590e6i	0.0563526	+	0.0650344i	0.783226	−	0.621737i	$-0.213573\pi$
$269$	1.09691e6	+	1.26590e6i	0.0563526	+	0.0650344i	−0.726873	+	0.686771i	$0.759027\pi$
$270$	−2.04699e6	+	934827.i	−0.103998	+	0.0474941i
$271$	−1.27731e7	+	3.75052e6i	−0.641784	+	0.188445i	−0.586402	−	0.810020i	$-0.699456\pi$
$271$	−1.27731e7	+	3.75052e6i	−0.641784	+	0.188445i	−0.0553822	+	0.998465i	$0.517638\pi$
$272$	2.62822e7	+	1.20027e7i	1.30604	+	0.596447i
$273$	930052.	+	133721.i	0.0457109	+	0.00657223i
$274$	1.96229e6	+	3.05338e6i	0.0953918	+	0.148433i
$275$		−	1.78300e7i		−	0.857339i
$276$	1.23007e7	+	2.84647e7i	0.585062	+	1.35388i
$277$	−3.26439e6			−0.153590			−0.0767950	−	0.997047i	$-0.524469\pi$
$277$	−3.26439e6			−0.153590			−0.0767950	+	0.997047i	$0.524469\pi$
$278$	−2.81366e7	+	1.80823e7i	−1.30960	+	0.841627i
$279$	679749.	−	4.72776e6i	0.0312994	−	0.217692i
$280$	−3.43899e6	+	7.53035e6i	−0.156660	+	0.343037i
$281$	1.16968e6	+	3.98356e6i	0.0527166	+	0.179536i	0.981643	−	0.190729i	$-0.0610851\pi$
$281$	1.16968e6	+	3.98356e6i	0.0527166	+	0.179536i	−0.928926	+	0.370265i	$0.879267\pi$
$282$	1.03714e7	+	2.27101e7i	0.462475	+	1.01268i
$283$	−8.48379e6	+	7.35124e6i	−0.374309	+	0.324341i	−0.821618	−	0.570039i	$-0.806928\pi$
$283$	−8.48379e6	+	7.35124e6i	−0.374309	+	0.324341i	0.447308	+	0.894380i	$0.352383\pi$
$284$	−1.09604e7	−	7.62310e7i	−0.478487	−	3.32795i
$285$	−1.88713e6	−	554111.i	−0.0815206	−	0.0239366i
$286$	−6.21492e6	−	5.38526e6i	−0.265667	−	0.230202i
$287$	−7.44613e6	+	1.15864e7i	−0.314981	+	0.490121i
$288$	1.78918e7	+	1.14984e7i	0.748992	+	0.481348i
$289$	−1.21158e7	+	1.39824e7i	−0.501948	+	0.579279i
$290$	1.22413e6	−	4.16900e6i	0.0501918	−	0.170938i
$291$	7.55053e6	−	1.08560e6i	0.306407	−	0.0440547i
$292$	3.89152e7	+	4.49106e7i	1.56304	+	1.80385i
$293$	−1.73411e7	+	7.91939e6i	−0.689402	+	0.314839i	−0.729134	−	0.684371i	$-0.760077\pi$
$293$	−1.73411e7	+	7.91939e6i	−0.689402	+	0.314839i	0.0397319	+	0.999210i	$0.487350\pi$
$294$	−2.21155e7	+	6.49368e6i	−0.870270	+	0.255534i
$295$	1.24630e7	+	5.69167e6i	0.485464	+	0.221704i
$296$	1.09382e8	+	1.57267e7i	4.21763	+	0.606404i
$297$	−2.59455e6	−	4.03720e6i	−0.0990360	−	0.154103i
$298$		−	7.33147e7i		−	2.77040i
$299$	5.05324e6	−	1.37191e6i	0.189041	−	0.0513230i
$300$	3.58681e7			1.32845
$301$	1.36147e7	−	8.74966e6i	0.499241	−	0.320842i
$302$	−1.03507e7	+	7.19907e7i	−0.375793	+	2.61370i
$303$	−9.65792e6	+	2.11479e7i	−0.347181	+	0.760220i
$304$	1.09835e7	+	3.74063e7i	0.390949	+	1.33145i
$305$	−5.61993e6	−	1.23059e7i	−0.198076	−	0.433725i
$306$	6.57600e6	−	5.69814e6i	0.229508	−	0.198870i
$307$	4.98175e6	+	3.46489e7i	0.172174	+	1.19750i	0.874280	+	0.485423i	$0.161334\pi$
$307$	4.98175e6	+	3.46489e7i	0.172174	+	1.19750i	−0.702106	+	0.712073i	$0.747757\pi$
$308$	−2.78357e7	−	8.17331e6i	−0.952688	−	0.279734i
$309$	−1.88679e7	−	1.63492e7i	−0.639513	−	0.554141i
$310$	6.31307e6	−	9.82333e6i	0.211912	−	0.329741i
$311$	−9.53020e6	−	6.12469e6i	−0.316826	−	0.203612i	0.372556	−	0.928010i	$-0.378481\pi$
$311$	−9.53020e6	−	6.12469e6i	−0.316826	−	0.203612i	−0.689382	+	0.724398i	$0.742118\pi$
$312$	6.59260e6	−	7.60826e6i	0.217066	−	0.250508i
$313$	1.23480e7	−	4.20535e7i	0.402684	−	1.37141i	−0.469801	−	0.882772i	$-0.655674\pi$
$313$	1.23480e7	−	4.20535e7i	0.402684	−	1.37141i	0.872484	−	0.488642i	$-0.162508\pi$
$314$	−7.27659e7	+	1.04622e7i	−2.35038	+	0.337934i
$315$	877868.	+	1.01311e6i	0.0280865	+	0.0324136i
$316$	−1.01873e8	+	4.65239e7i	−3.22848	+	1.47440i
$317$	−4.12729e7	+	1.21188e7i	−1.29565	+	0.380437i	−0.855647	−	0.517559i	$-0.826841\pi$
$317$	−4.12729e7	+	1.21188e7i	−1.29565	+	0.380437i	−0.440003	+	0.897997i	$0.645022\pi$
$318$	3.04923e7	+	1.39254e7i	0.948218	+	0.433037i
$319$	9.17173e6	+	1.31870e6i	0.282539	+	0.0406230i
$320$	1.15244e7	+	1.79323e7i	0.351696	+	0.547250i
$321$		−	2.25591e7i		−	0.682036i
$322$	1.97660e7	−	1.64303e7i	0.592041	−	0.492127i
$323$	7.60492e6			0.225677
$324$	8.12153e6	−	5.21939e6i	0.238783	−	0.153456i
$325$	861958.	−	5.99505e6i	0.0251094	−	0.174640i
$326$	7.48875e6	−	1.63981e7i	0.216151	−	0.473304i
$327$	−2.72089e6	−	9.26650e6i	−0.0778158	−	0.265016i
$328$	6.13001e7	+	1.34228e8i	1.73716	+	3.80385i
$329$	1.12399e7	−	9.73944e6i	0.315628	−	0.273493i
$330$	−1.66970e6	−	1.16130e7i	−0.0464617	−	0.323149i
$331$	−2.44134e7	−	7.16843e6i	−0.673201	−	0.197670i	−0.0727731	−	0.997349i	$-0.523185\pi$
$331$	−2.44134e7	−	7.16843e6i	−0.673201	−	0.197670i	−0.600428	+	0.799679i	$0.705003\pi$
$332$	−3.71583e7	−	3.21978e7i	−1.01541	−	0.879857i
$333$	9.67447e6	−	1.50538e7i	0.261996	−	0.407673i
$334$	−2.37778e7	−	1.52811e7i	−0.638164	−	0.410123i
$335$	−3.96703e6	+	4.57820e6i	−0.105519	+	0.121775i
$336$	7.48619e6	−	2.54956e7i	0.197353	−	0.672122i
$337$	−1.84509e7	+	2.65284e6i	−0.482090	+	0.0693141i	−0.379076	−	0.925366i	$-0.623758\pi$
$337$	−1.84509e7	+	2.65284e6i	−0.482090	+	0.0693141i	−0.103015	+	0.994680i	$0.532849\pi$
$338$	4.58459e7	+	5.29090e7i	1.18727	+	1.37019i
$339$	2.98494e7	−	1.36318e7i	0.766189	−	0.349907i
$340$	1.46686e7	−	4.30710e6i	0.373210	−	0.109584i
$341$	2.26518e7	+	1.03447e7i	0.571267	+	0.260889i
$342$	1.16211e7	+	1.67086e6i	0.290516	+	0.0417698i
$343$	1.63320e7	+	2.54130e7i	0.404721	+	0.629759i
$344$		−	1.73396e8i		−	4.25955i
$345$	6.73026e6	+	3.24194e6i	0.163898	+	0.0789491i
$346$	6.20860e7			1.49888
$347$	−6.17192e7	+	3.96645e7i	−1.47718	+	0.949323i	−0.479765	+	0.877397i	$0.659278\pi$
$347$	−6.17192e7	+	3.96645e7i	−1.47718	+	0.949323i	−0.997410	+	0.0719258i	$0.977086\pi$
$348$	−2.65278e6	+	1.84505e7i	−0.0629454	+	0.437795i
$349$	−5.16727e6	+	1.13147e7i	−0.121558	+	0.266176i	−0.960623	−	0.277857i	$-0.910376\pi$
$349$	−5.16727e6	+	1.13147e7i	−0.121558	+	0.266176i	0.839064	+	0.544033i	$0.183103\pi$
$350$	−8.37617e6	−	2.85266e7i	−0.195363	−	0.665344i
$351$	−677206.	−	1.48287e6i	−0.0156603	−	0.0342912i
$352$	−8.38000e7	+	7.26131e7i	−1.92139	+	1.66490i
$353$	−5.89182e6	−	4.09785e7i	−0.133945	−	0.931606i	−0.940342	−	0.340232i	$-0.889495\pi$
$353$	−5.89182e6	−	4.09785e7i	−0.133945	−	0.931606i	0.806397	−	0.591375i	$-0.201415\pi$
$354$	−7.84748e7	−	2.30423e7i	−1.76897	−	0.519416i
$355$	−1.40220e7	−	1.21501e7i	−0.313419	−	0.271579i
$356$	−2.73847e7	+	4.26114e7i	−0.606957	+	0.944443i
$357$	−4.36056e6	−	2.80236e6i	−0.0958379	−	0.0615913i
$358$	3.29273e7	−	3.80001e7i	0.717640	−	0.828200i
$359$	−273349.	+	930942.i	−0.00590792	+	0.0201205i	−0.962394	−	0.271657i	$-0.912428\pi$
$359$	−273349.	+	930942.i	−0.00590792	+	0.0201205i	0.956486	+	0.291777i	$0.0942466\pi$
$360$	1.42166e7	−	2.04403e6i	0.304710	−	0.0438107i
$361$	−2.40888e7	−	2.77999e7i	−0.512028	−	0.590911i
$362$	−9.82446e7	+	4.48668e7i	−2.07101	+	0.945800i
$363$	−2.49051e6	+	731279.i	−0.0520677	+	0.0152885i
$364$	−8.96420e6	−	4.09381e6i	−0.185869	−	0.0848836i
$365$	1.41705e7	+	2.03741e6i	0.291411	+	0.0418986i
$366$	4.36605e7	+	6.79370e7i	0.890523	+	1.38568i
$367$		−	9.10755e6i		−	0.184248i	−0.995748	−	0.0921241i	$-0.970634\pi$
$367$		−	9.10755e6i		−	0.184248i	0.995748	−	0.0921241i	$-0.0293657\pi$
$368$	−1.80649e7	−	1.46970e8i	−0.362486	−	2.94908i
$369$	2.38952e7			0.475588
$370$	3.68026e7	−	2.36516e7i	0.726563	−	0.466934i
$371$	2.84188e6	−	1.97657e7i	0.0556524	−	0.387071i
$372$	−2.08102e7	+	4.55679e7i	−0.404247	+	0.885178i
$373$	2.61247e7	+	8.89726e7i	0.503414	+	1.71447i	0.682723	+	0.730677i	$0.260795\pi$
$373$	2.61247e7	+	8.89726e7i	0.503414	+	1.71447i	−0.179310	+	0.983793i	$0.557386\pi$
$374$	1.88453e7	+	4.12655e7i	0.360238	+	0.788811i
$375$	1.37808e7	−	1.19411e7i	0.261324	−	0.226439i
$376$	−2.26773e7	−	1.57724e8i	−0.426608	−	2.96712i
$377$	3.02010e6	+	886781.i	0.0563634	+	0.0165498i
$378$	−6.04769e6	−	5.24035e6i	−0.111973	−	0.0970253i
$379$	5.47805e6	−	8.52402e6i	0.100626	−	0.156577i	−0.787290	−	0.616583i	$-0.788517\pi$
$379$	5.47805e6	−	8.52402e6i	0.100626	−	0.156577i	0.887916	+	0.460006i	$0.152153\pi$
$380$	1.73533e7	+	1.11523e7i	0.316251	+	0.203242i
$381$	833594.	−	962019.i	0.0150723	−	0.0173944i
$382$	2.31523e7	−	7.88495e7i	0.415340	−	1.41452i
$383$	−5.28511e7	+	7.59885e6i	−0.940715	+	0.135254i	−0.595578	−	0.803298i	$-0.703077\pi$
$383$	−5.28511e7	+	7.59885e6i	−0.940715	+	0.135254i	−0.345137	+	0.938552i	$0.612168\pi$
$384$	−2.61463e7	−	3.01745e7i	−0.461761	−	0.532900i
$385$	−6.35747e6	+	2.90336e6i	−0.111404	+	0.0508766i
$386$	1.39103e8	−	4.08445e7i	2.41867	−	0.710185i
$387$	−2.55409e7	−	1.16641e7i	−0.440660	−	0.201243i
$388$	−7.91904e7	−	1.13859e7i	−1.35574	−	0.194927i
$389$	−4.56310e7	−	7.10032e7i	−0.775195	−	1.20623i	−0.974080	−	0.226204i	$-0.927368\pi$
$389$	−4.56310e7	−	7.10032e7i	−0.775195	−	1.20623i	0.198885	−	0.980023i	$-0.436268\pi$
$390$		−	3.98540e6i		−	0.0671859i
$391$	−2.85011e7	−	4.69598e6i	−0.476794	−	0.0785590i
$392$	1.47110e8			2.44222
$393$	3.24929e7	−	2.08819e7i	0.535317	−	0.344028i
$394$	2.08829e7	−	1.45244e8i	0.341430	−	2.37470i
$395$	−1.12081e7	+	2.45424e7i	−0.181862	+	0.398222i
$396$	1.41803e7	+	4.82937e7i	0.228350	+	0.777688i
$397$	−8.39716e6	−	1.83872e7i	−0.134203	−	0.293863i	0.830586	−	0.556891i	$-0.188006\pi$
$397$	−8.39716e6	−	1.83872e7i	−0.134203	−	0.293863i	−0.964788	+	0.263029i	$0.915279\pi$
$398$	−2.21675e7	+	1.92082e7i	−0.351615	+	0.304676i
$399$	−995342.	−	6.92275e6i	−0.0156694	−	0.108983i
$400$	−1.64343e8	−	4.82554e7i	−2.56786	−	0.753991i
$401$	7.05506e6	+	6.11324e6i	0.109413	+	0.0948066i	0.707849	−	0.706364i	$-0.249666\pi$
$401$	7.05506e6	+	6.11324e6i	0.109413	+	0.0948066i	−0.598436	+	0.801170i	$0.704211\pi$
$402$	1.95504e7	−	3.04211e7i	0.300939	−	0.468270i
$403$	7.11620e6	+	4.57330e6i	0.108726	+	0.0698739i
$404$	1.59678e8	−	1.84278e8i	2.42159	−	2.79467i
$405$	655248.	−	2.23157e6i	0.00986371	−	0.0335927i
$406$	1.52936e7	−	2.19888e6i	0.228523	−	0.0328567i
$407$	6.10949e7	+	7.05073e7i	0.906195	+	1.04581i
$408$	−5.05170e7	+	2.30704e7i	−0.743802	+	0.339683i
$409$	9.84328e7	−	2.89025e7i	1.43870	−	0.422440i	0.532911	−	0.846171i	$-0.321098\pi$
$409$	9.84328e7	−	2.89025e7i	1.43870	−	0.422440i	0.905788	+	0.423731i	$0.139280\pi$
$410$	5.31385e7	+	2.42675e7i	0.771005	+	0.352106i
$411$	−3.71304e6	−	533855.i	−0.0534816	−	0.00768950i
$412$	1.41563e8	+	2.20277e8i	2.02423	+	3.14976i
$413$			4.87214e7i			0.691623i
$414$	−4.25208e7	−	1.34379e7i	−0.599240	−	0.189378i
$415$	−1.18450e7			−0.165726
$416$	−3.16868e7	+	2.03638e7i	−0.440147	+	0.282865i
$417$	4.91943e6	−	3.42154e7i	0.0678433	−	0.471860i
$418$	−2.54279e7	+	5.56794e7i	−0.348163	+	0.762370i
$419$	3.01416e7	+	1.02653e8i	0.409754	+	1.39549i	0.863493	+	0.504360i	$0.168272\pi$
$419$	3.01416e7	+	1.02653e8i	0.409754	+	1.39549i	−0.453739	+	0.891135i	$0.649910\pi$
$420$	−5.84061e6	−	1.27891e7i	−0.0788334	−	0.172621i
$421$	−6.00123e6	+	5.20009e6i	−0.0804255	+	0.0696891i	−0.694146	−	0.719834i	$-0.744218\pi$
$421$	−6.00123e6	+	5.20009e6i	−0.0804255	+	0.0696891i	0.613720	+	0.789524i	$0.289672\pi$
$422$	2.87112e7	+	1.99691e8i	0.382045	+	2.65718i
$423$	−2.47580e7	−	7.26959e6i	−0.327110	−	0.0960481i
$424$	−1.61693e8	−	1.40107e8i	−2.12125	−	1.83808i
$425$	−1.80638e7	+	2.81078e7i	−0.235311	+	0.366151i
$426$	9.31730e7	+	5.98786e7i	1.20521	+	0.774539i
$427$	3.15036e7	−	3.63570e7i	0.404647	−	0.466987i
$428$	−6.66584e7	+	2.27018e8i	−0.850205	+	2.89553i
$429$	8.41266e6	−	1.20956e6i	0.106552	−	0.0153199i
$430$	−4.49524e7	−	5.18778e7i	−0.565389	−	0.652494i
$431$	−1.11625e8	+	5.09775e7i	−1.39422	+	0.636718i	−0.963974	−	0.265995i	$-0.914300\pi$
$431$	−1.11625e8	+	5.09775e7i	−1.39422	+	0.636718i	−0.430243	+	0.902713i	$0.641572\pi$
$432$	−4.42338e7	+	1.29882e7i	−0.548659	+	0.161101i
$433$	−2.57787e7	−	1.17727e7i	−0.317539	−	0.145015i	0.250269	−	0.968176i	$-0.419481\pi$
$433$	−2.57787e7	−	1.17727e7i	−0.317539	−	0.145015i	−0.567808	+	0.823161i	$0.692208\pi$
$434$	4.11008e7	+	5.90941e6i	0.502784	+	0.0722894i
$435$	2.42783e6	+	3.77777e6i	0.0294951	+	0.0458953i
$436$			1.01291e8i			1.22211i
$437$	−2.03949e7	−	3.32127e7i	−0.244387	−	0.397979i
$438$	−8.54592e7			−1.01704
$439$	−7.47266e7	+	4.80239e7i	−0.883246	+	0.567628i	−0.901778	−	0.432200i	$-0.857737\pi$
$439$	−7.47266e7	+	4.80239e7i	−0.883246	+	0.567628i	0.0185314	+	0.999828i	$0.494101\pi$
$440$	−1.06568e7	+	7.41195e7i	−0.125103	+	0.870110i
$441$	9.89591e6	−	2.16690e7i	0.115382	−	0.252652i
$442$	4.34154e6	+	1.47859e7i	0.0502779	+	0.171231i
$443$	9.90095e6	+	2.16801e7i	0.113885	+	0.249373i	0.957988	−	0.286807i	$-0.0925940\pi$
$443$	9.90095e6	+	2.16801e7i	0.113885	+	0.249373i	−0.844103	+	0.536180i	$0.819867\pi$
$444$	−1.41838e8	+	1.22903e8i	−1.62048	+	1.40415i
$445$	1.73663e6	+	1.20785e7i	0.0197073	+	0.137067i
$446$	2.32325e8	+	6.82166e7i	2.61873	+	0.768928i
$447$	5.72649e7	+	4.96203e7i	0.641159	+	0.555567i
$448$	−4.09808e7	+	6.37673e7i	−0.455770	+	0.709192i
$449$	−7.06802e7	−	4.54234e7i	−0.780834	−	0.501812i	0.0884760	−	0.996078i	$-0.471800\pi$
$449$	−7.06802e7	−	4.54234e7i	−0.780834	−	0.501812i	−0.869310	+	0.494266i	$0.835437\pi$
$450$	−3.37789e7	+	3.89829e7i	−0.370688	+	0.427796i
$451$	−3.50982e7	+	1.19533e8i	−0.382609	+	1.30305i
$452$	−3.40660e8	+	4.89796e7i	−3.68898	+	0.530395i
$453$	−4.92253e7	−	5.68090e7i	−0.529533	−	0.611114i
$454$	2.02688e8	−	9.25647e7i	2.16602	−	0.989186i
$455$	−2.27796e6	+	668868.i	−0.0241830	+	0.00710078i
$456$	−6.81624e7	−	3.11287e7i	−0.718870	−	0.328297i
$457$	6.73357e7	+	9.68141e6i	0.705499	+	0.101435i	0.485720	−	0.874114i	$-0.338557\pi$
$457$	6.73357e7	+	9.68141e6i	0.705499	+	0.101435i	0.219779	+	0.975550i	$0.429466\pi$
$458$	6.15833e7	+	9.58255e7i	0.641013	+	0.997435i
$459$			8.99297e6i			0.0929962i
$460$	−5.81487e7	−	5.25111e7i	−0.597402	−	0.539483i
$461$	1.16300e8			1.18707			0.593537	−	0.804807i	$-0.297731\pi$
$461$	1.16300e8			1.18707			0.593537	+	0.804807i	$0.297731\pi$
$462$	3.50975e7	−	2.25558e7i	0.355918	−	0.228735i
$463$	−1.19874e7	+	8.33744e7i	−0.120777	+	0.840020i	0.835903	+	0.548877i	$0.184945\pi$
$463$	−1.19874e7	+	8.33744e7i	−0.120777	+	0.840020i	−0.956680	+	0.291143i	$0.905964\pi$
$464$	3.69773e7	−	8.09689e7i	0.370153	−	0.810521i
$465$	3.40007e6	+	1.15796e7i	0.0338165	+	0.115169i
$466$	2.75082e7	+	6.02345e7i	0.271834	+	0.595233i
$467$	1.11935e8	−	9.69923e7i	1.09905	−	0.952328i	0.0999560	−	0.994992i	$-0.468130\pi$
$467$	1.11935e8	−	9.69923e7i	1.09905	−	0.952328i	0.999089	+	0.0426635i	$0.0135843\pi$
$468$	2.43324e6	+	1.69235e7i	0.0237381	+	0.165102i
$469$	−2.06690e7	−	6.06898e6i	−0.200356	−	0.0588298i
$470$	−4.76743e7	−	4.13100e7i	−0.459188	−	0.397889i
$471$	4.10770e7	−	6.39171e7i	0.393130	−	0.611722i
$472$	4.39140e8	+	2.82218e8i	4.17616	+	2.68386i
$473$	9.58644e7	−	1.10633e8i	0.905887	−	1.04545i
$474$	4.53753e7	−	1.54534e8i	0.426073	−	1.45107i
$475$	−4.46236e7	+	6.41590e6i	−0.416374	+	0.0598655i
$476$	3.56008e7	+	4.10855e7i	0.330095	+	0.380950i
$477$	−3.15144e7	+	1.43921e7i	−0.290372	+	0.132608i
$478$	1.20829e8	−	3.54785e7i	1.10634	−	0.324849i
$479$	−4.76654e7	−	2.17680e7i	−0.433707	−	0.198067i	0.186584	−	0.982439i	$-0.440258\pi$
$479$	−4.76654e7	−	2.17680e7i	−0.433707	−	0.198067i	−0.620291	+	0.784372i	$0.712986\pi$
$480$	−5.31909e7	−	7.64770e6i	−0.480965	−	0.0691524i
$481$	1.71337e7	+	2.66605e7i	0.153962	+	0.239570i
$482$		−	2.24652e8i		−	2.00618i
$483$	−544491.	+	2.65591e7i	−0.00483225	+	0.235707i
$484$	2.72234e7			0.240107
$485$	−1.62144e7	+	1.04203e7i	−0.142127	+	0.0913392i
$486$	−1.97583e6	+	1.37422e7i	−0.0172124	+	0.119715i
$487$	−1.35934e7	+	2.97653e7i	−0.117690	+	0.257706i	−0.959305	−	0.282373i	$-0.908878\pi$
$487$	−1.35934e7	+	2.97653e7i	−0.117690	+	0.257706i	0.841614	+	0.540079i	$0.181606\pi$
$488$	−1.45213e8	−	4.94549e8i	−1.24953	−	4.25549i
$489$	7.73979e6	+	1.69478e7i	0.0661915	+	0.144939i
$490$	4.40134e7	−	3.81378e7i	0.374108	−	0.324166i
$491$	1.98192e7	+	1.37845e8i	0.167433	+	1.16452i	0.884165	+	0.467174i	$0.154728\pi$
$491$	1.98192e7	+	1.37845e8i	0.167433	+	1.16452i	−0.716732	+	0.697349i	$0.754363\pi$
$492$	−2.40462e8	−	7.06061e7i	−2.01907	−	0.592853i
$493$	−1.31227e7	−	1.13708e7i	−0.109517	−	0.0948969i
$494$	−1.12415e7	+	1.74921e7i	−0.0932485	+	0.145097i
$495$	1.02008e7	+	6.55564e6i	0.0841042	+	0.0540505i
$496$	1.56655e8	−	1.80789e8i	1.28380	−	1.48159i
$497$	1.85879e7	−	6.33047e7i	0.151413	−	0.515664i
$498$	6.99879e7	−	1.00627e7i	0.566676	−	0.0814757i
$499$	−8.41102e7	−	9.70683e7i	−0.676935	−	0.781225i	0.308510	−	0.951221i	$-0.400170\pi$
$499$	−8.41102e7	−	9.70683e7i	−0.676935	−	0.781225i	−0.985445	+	0.169996i	$0.945624\pi$
$500$	−1.73963e8	+	7.94462e7i	−1.39170	+	0.635570i
$501$	2.80289e7	−	8.23003e6i	0.222891	−	0.0654468i
$502$	1.93288e8	+	8.82717e7i	1.52790	+	0.697767i
$503$	−1.64843e8	−	2.37008e7i	−1.29529	−	0.186234i	−0.540020	−	0.841652i	$-0.681583\pi$
$503$	−1.64843e8	−	2.37008e7i	−1.29529	−	0.186234i	−0.755266	+	0.655419i	$0.772492\pi$
$504$	2.76127e7	+	4.29662e7i	0.215683	+	0.335610i
$505$		−	5.87427e7i		−	0.456121i
$506$	1.29678e8	−	1.92969e8i	1.00096	−	1.48948i
$507$	−7.23554e7			−0.555197
$508$	−1.12312e7	+	7.21788e6i	−0.0856716	+	0.0550578i
$509$	−3.22069e6	+	2.24004e7i	−0.0244228	+	0.169864i	−0.998382	−	0.0568578i	$-0.981892\pi$
$509$	−3.22069e6	+	2.24004e7i	−0.0244228	+	0.169864i	0.973959	+	0.226722i	$0.0728009\pi$
$510$	−9.13312e6	+	1.99987e7i	−0.0688507	+	0.150762i
$511$	1.43426e7	+	4.88463e7i	0.107489	+	0.366074i
$512$	−4.30636e7	−	9.42961e7i	−0.320849	−	0.702561i
$513$	−9.17040e6	+	7.94619e6i	−0.0679260	+	0.0588582i
$514$	−5.00144e7	−	3.47858e8i	−0.368304	−	2.56161i
$515$	6.05259e7	+	1.77720e7i	0.443118	+	0.130111i
$516$	2.22558e8	+	1.92848e8i	1.61992	+	1.40367i
$517$	7.27310e7	−	1.13172e8i	0.526318	−	0.818967i
$518$	1.30870e8	+	8.41052e7i	0.941567	+	0.605109i
$519$	−4.20206e7	+	4.84944e7i	−0.300580	+	0.346888i
$520$	−7.16634e6	+	2.44063e7i	−0.0509668	+	0.173577i
$521$	−1.63304e8	+	2.34795e7i	−1.15473	+	0.166026i	−0.692963	−	0.720973i	$-0.743695\pi$
$521$	−1.63304e8	+	2.34795e7i	−1.15473	+	0.166026i	−0.461772	+	0.886999i	$0.652786\pi$
$522$	−1.75545e7	−	2.02590e7i	−0.123418	−	0.142432i
$523$	1.91427e8	−	8.74219e7i	1.33813	−	0.611104i	0.387628	−	0.921816i	$-0.373295\pi$
$523$	1.91427e8	−	8.74219e7i	1.33813	−	0.611104i	0.950504	+	0.310712i	$0.100567\pi$
$524$	−3.88686e8	+	1.14129e8i	−2.70150	+	0.793233i
$525$	2.79508e7	+	1.27647e7i	0.193159	+	0.0882129i
$526$	−2.62547e8	−	3.77486e7i	−1.80406	−	0.259384i
$527$	−2.52287e7	−	3.92566e7i	−0.172370	−	0.268214i
$528$		−	2.40353e8i		−	1.63286i
$529$	5.59257e7	+	1.37065e8i	0.377785	+	0.925893i
$530$	−8.46987e7			−0.568917
$531$	7.11106e7	−	4.57000e7i	0.474953	−	0.305234i
$532$	−1.04392e7	+	7.26063e7i	−0.0693318	+	0.482213i
$533$	−1.75798e7	+	3.84945e7i	−0.116100	+	0.254224i
$534$	−2.05222e7	−	6.98923e7i	−0.134772	−	0.458992i
$535$	2.36787e7	+	5.18491e7i	0.154631	+	0.338594i
$536$	−1.74427e8	+	1.51142e8i	−1.13271	+	0.981500i
$537$	7.39565e6	+	5.14379e7i	0.0477588	+	0.332170i
$538$	2.42408e7	+	7.11775e6i	0.155669	+	0.0457084i
$539$	9.38619e7	+	8.13318e7i	0.599409	+	0.519391i
$540$	−1.31878e7	+	2.05206e7i	−0.0837513	+	0.130320i
$541$	−6.22601e7	−	4.00121e7i	−0.393204	−	0.252697i	0.329068	−	0.944306i	$-0.393266\pi$
$541$	−6.22601e7	−	4.00121e7i	−0.393204	−	0.252697i	−0.722272	+	0.691610i	$0.756902\pi$
$542$	−1.31488e8	+	1.51746e8i	−0.825828	+	0.953057i
$543$	3.14484e7	−	1.07104e8i	0.196426	−	0.668967i
$544$	2.05671e8	−	2.95710e7i	1.27754	−	0.183683i
$545$	1.59800e7	+	1.84419e7i	0.0987157	+	0.113924i
$546$	1.28914e7	−	5.88731e6i	0.0791994	−	0.0361692i
$547$	−2.96316e8	+	8.70064e7i	−1.81048	+	0.531605i	−0.998633	−	0.0522655i	$-0.983356\pi$
$547$	−2.96316e8	+	8.70064e7i	−1.81048	+	0.531605i	−0.811847	+	0.583870i	$0.801538\pi$
$548$	3.57877e7	+	1.63437e7i	0.217467	+	0.0993137i
$549$	−8.26144e7	−	1.18782e7i	−0.499274	−	0.0717847i
$550$	−1.45393e8	−	2.26236e8i	−0.873887	−	1.35979i
$551$		−	2.34288e7i		−	0.140054i
$552$	2.36231e8	+	1.58751e8i	1.40450	+	0.943843i
$553$	−9.59430e7			−0.567333
$554$	−4.14203e7	+	2.66192e7i	−0.243604	+	0.156555i
$555$	−6.43459e6	+	4.47536e7i	−0.0376394	+	0.261788i
$556$	−1.50606e8	+	3.29781e8i	−0.876230	+	1.91868i
$557$	−7.96008e7	−	2.71095e8i	−0.460629	−	1.56876i	−0.782922	−	0.622120i	$-0.786272\pi$
$557$	−7.96008e7	−	2.71095e8i	−0.460629	−	1.56876i	0.322293	−	0.946640i	$-0.395547\pi$
$558$	−2.99271e7	−	6.55311e7i	−0.172251	−	0.377177i
$559$	3.75813e7	−	3.25644e7i	0.215147	−	0.186426i
$560$	9.55492e6	+	6.64559e7i	0.0544080	+	0.378416i
$561$	−4.49866e7	−	1.32093e7i	−0.254797	−	0.0748152i
$562$	4.73251e7	+	4.10074e7i	0.266614	+	0.231022i
$563$	−6.48342e7	+	1.00884e8i	−0.363312	+	0.565324i	−0.974000	−	0.226547i	$-0.927256\pi$
$563$	−6.48342e7	+	1.00884e8i	−0.363312	+	0.565324i	0.610689	+	0.791871i	$0.290893\pi$
$564$	2.27664e8	+	1.46311e8i	1.26899	+	0.815530i
$565$	−5.42964e7	+	6.26614e7i	−0.301041	+	0.347420i
$566$	−4.77016e7	+	1.62457e8i	−0.263077	+	0.895959i
$567$	8.18630e6	−	1.17701e6i	0.0449095	−	0.00645701i
$568$	−4.62914e8	−	5.34231e8i	−2.52613	−	2.91531i
$569$	1.74505e8	−	7.96936e7i	0.947263	−	0.432600i	0.118971	−	0.992898i	$-0.462040\pi$
$569$	1.74505e8	−	7.96936e7i	0.947263	−	0.432600i	0.828292	+	0.560297i	$0.189313\pi$
$570$	−2.84633e7	+	8.35758e6i	−0.153695	+	0.0451290i
$571$	−1.50343e7	−	6.86592e6i	−0.0807559	−	0.0368800i	0.374628	−	0.927175i	$-0.377771\pi$
$571$	−1.50343e7	−	6.86592e6i	−0.0807559	−	0.0368800i	−0.455383	+	0.890295i	$0.650498\pi$
$572$	−8.82326e7	−	1.26859e7i	−0.471456	−	0.0677851i
$573$	4.59182e7	+	7.14502e7i	0.244074	+	0.379786i
$574$			2.07733e8i			1.09842i
$575$	1.71198e8	+	3.50975e6i	0.900524	+	0.0184617i
$576$	1.31510e8			0.688164
$577$	7.52319e7	−	4.83486e7i	0.391629	−	0.251685i	−0.329977	−	0.943989i	$-0.607041\pi$
$577$	7.52319e7	−	4.83486e7i	0.391629	−	0.251685i	0.721605	+	0.692305i	$0.243404\pi$
$578$	−3.97134e7	+	2.76213e8i	−0.205662	+	1.43041i
$579$	−6.22440e7	+	1.36295e8i	−0.320673	+	0.702175i
$580$	−1.32691e7	−	4.51904e7i	−0.0680076	−	0.231613i
$581$	−1.74976e7	−	3.83145e7i	−0.0892177	−	0.195360i
$582$	8.69525e7	−	7.53448e7i	0.441076	−	0.382194i
$583$	−2.57058e7	−	1.78788e8i	−0.129726	−	0.902262i
$584$	5.23346e8	+	1.53668e8i	2.62755	+	0.771517i
$585$	3.11293e6	+	2.69737e6i	0.0155490	+	0.0134733i
$586$	−1.55454e8	+	2.41891e8i	−0.772519	+	1.20206i
$587$	−2.24982e8	−	1.44587e8i	−1.11233	−	0.714852i	−0.150531	−	0.988605i	$-0.548098\pi$
$587$	−2.24982e8	−	1.44587e8i	−1.11233	−	0.714852i	−0.961800	+	0.273754i	$0.911735\pi$
$588$	−1.63613e8	+	1.88819e8i	−0.804796	+	0.928784i
$589$	1.77390e7	−	6.04136e7i	0.0868128	−	0.295657i
$590$	2.04549e8	−	2.94097e7i	0.995960	−	0.143197i
$591$	9.93136e7	+	1.14614e8i	0.481112	+	0.555233i
$592$	8.15230e8	−	3.72303e8i	3.92930	−	1.79445i
$593$	3.08959e8	−	9.07185e7i	1.48162	−	0.435043i	0.561763	−	0.827298i	$-0.310123\pi$
$593$	3.08959e8	−	9.07185e7i	1.48162	−	0.435043i	0.919856	+	0.392256i	$0.128305\pi$
$594$	−6.58420e7	−	3.00690e7i	−0.314155	−	0.143470i
$595$	1.29636e7	+	1.86388e6i	0.0615423	+	0.00884845i
$596$	−4.29650e8	−	6.68548e8i	−2.02944	−	3.15787i
$597$		−	3.03150e7i		−	0.142474i
$598$	5.29310e7	−	5.86137e7i	0.247518	−	0.274091i
$599$	−2.24575e8			−1.04491			−0.522457	−	0.852666i	$-0.674984\pi$
$599$	−2.24575e8			−1.04491			−0.522457	+	0.852666i	$0.674984\pi$
$600$	2.76957e8	−	1.77989e8i	1.28221	−	0.824024i
$601$	8.08418e6	−	5.62267e7i	0.0372403	−	0.259012i	−0.962693	−	0.270597i	$-0.912779\pi$
$601$	8.08418e6	−	5.62267e7i	0.0372403	−	0.259012i	0.999933	+	0.0115856i	$0.00368789\pi$
$602$	1.01402e8	−	2.22040e8i	0.464792	−	1.01775i
$603$	1.05294e7	+	3.58599e7i	0.0480233	+	0.163552i
$604$	3.27504e8	+	7.17134e8i	1.48630	+	3.25454i
$605$	4.95652e6	−	4.29485e6i	0.0223826	−	0.0193947i
$606$	4.99040e7	+	3.47090e8i	0.224242	+	1.55964i
$607$	2.02704e8	+	5.95192e7i	0.906349	+	0.266128i	0.701503	−	0.712666i	$-0.252513\pi$
$607$	2.02704e8	+	5.95192e7i	0.906349	+	0.266128i	0.204846	+	0.978794i	$0.434331\pi$
$608$	2.11885e8	+	1.83599e8i	0.942735	+	0.816884i
$609$	−8.63336e6	+	1.34338e7i	−0.0382233	+	0.0594766i
$610$	−1.71656e8	−	1.10317e8i	−0.756258	−	0.486017i
$611$	2.99257e7	−	3.45362e7i	0.131196	−	0.151409i
$612$	2.65727e7	−	9.04983e7i	0.115926	−	0.394808i
$613$	−4.50228e7	+	6.47330e6i	−0.195457	+	0.0281024i	−0.239348	−	0.970934i	$-0.576934\pi$
$613$	−4.50228e7	+	6.47330e6i	−0.195457	+	0.0281024i	0.0438911	+	0.999036i	$0.486025\pi$
$614$	3.45752e8	+	3.99019e8i	1.49369	+	1.72381i
$615$	−5.49197e7	+	2.50810e7i	−0.236104	+	0.107825i
$616$	−2.55493e8	+	7.50196e7i	−1.09304	+	0.320946i
$617$	−1.58627e8	−	7.24427e7i	−0.675340	−	0.308418i	0.0480619	−	0.998844i	$-0.484696\pi$
$617$	−1.58627e8	−	7.24427e7i	−0.675340	−	0.308418i	−0.723402	+	0.690427i	$0.757423\pi$
$618$	−3.72724e8	−	5.35896e7i	−1.57914	−	0.227047i
$619$	−9.85085e7	−	1.53282e8i	−0.415338	−	0.646279i	0.569047	−	0.822305i	$-0.307312\pi$
$619$	−9.85085e7	−	1.53282e8i	−0.415338	−	0.646279i	−0.984386	+	0.176026i	$0.943676\pi$
$620$		−	1.26575e8i		−	0.531094i
$621$	3.92747e7	−	2.41174e7i	0.163998	−	0.100706i
$622$	−1.70867e8			−0.710048
$623$	−3.65044e7	+	2.34600e7i	−0.150967	+	0.0970204i
$624$	1.16194e7	−	8.08150e7i	0.0478224	−	0.332612i
$625$	7.22105e7	−	1.58119e8i	0.295774	−	0.647655i
$626$	−1.86243e8	−	6.34287e8i	−0.759203	−	2.58561i
$627$	−2.62803e7	−	5.75458e7i	−0.106617	−	0.233459i
$628$	−6.02231e8	+	5.21836e8i	−2.43156	+	2.10696i
$629$	−2.48803e7	−	1.73046e8i	−0.0999779	−	0.695362i
$630$	1.94002e7	+	5.69641e6i	0.0775862	+	0.0227814i
$631$	−3.18492e8	−	2.75975e8i	−1.26768	−	1.09845i	−0.990482	−	0.137639i	$-0.956048\pi$
$631$	−3.18492e8	−	2.75975e8i	−1.26768	−	1.09845i	−0.277199	−	0.960813i	$-0.589406\pi$
$632$	−5.55750e8	+	8.64764e8i	−2.20155	+	3.42567i
$633$	−1.75407e8	−	1.12728e8i	−0.691571	−	0.444446i
$634$	−4.24870e8	+	4.90326e8i	−1.66720	+	1.92406i
$635$	−906141.	+	3.08603e6i	−0.00353895	+	0.0120526i
$636$	3.59663e8	−	5.17117e7i	1.39805	−	0.201010i
$637$	2.76277e7	+	3.18841e7i	0.106888	+	0.123355i
$638$	1.27129e8	−	5.80577e7i	0.489533	−	0.223562i
$639$	−1.09831e8	+	3.22492e7i	−0.420941	+	0.123600i
$640$	9.17657e7	+	4.19080e7i	0.350058	+	0.159866i
$641$	3.69339e8	+	5.31029e7i	1.40233	+	0.201625i	0.801617	−	0.597838i	$-0.203973\pi$
$641$	3.69339e8	+	5.31029e7i	1.40233	+	0.201625i	0.600715	+	0.799463i	$0.294883\pi$
$642$	−1.83956e8	−	2.86242e8i	−0.695200	−	1.08175i
$643$			4.99894e8i			1.88038i	0.340652	+	0.940190i	$0.389352\pi$
$643$			4.99894e8i			1.88038i	−0.340652	+	0.940190i	$0.610648\pi$
$644$	8.39570e7	−	2.65661e8i	0.314340	−	0.994651i
$645$	7.09453e7			0.264390
$646$	9.64951e7	−	6.20136e7i	0.357938	−	0.230033i
$647$	−2.93671e7	+	2.04253e8i	−0.108430	+	0.754146i	0.860970	+	0.508657i	$0.169858\pi$
$647$	−2.93671e7	+	2.04253e8i	−0.108430	+	0.754146i	−0.969399	+	0.245489i	$0.921051\pi$
$648$	3.68103e7	−	8.06034e7i	0.135284	−	0.296230i
$649$	1.24160e8	+	4.22851e8i	0.454201	+	1.54687i
$650$	−3.79491e7	−	8.30970e7i	−0.138185	−	0.302583i
$651$	−3.24333e7	+	2.81036e7i	−0.117557	+	0.101864i
$652$	−2.78094e7	−	1.93419e8i	−0.100334	−	0.697840i
$653$	3.40176e8	+	9.98846e7i	1.22170	+	0.358723i	0.828111	−	0.560565i	$-0.189416\pi$
$653$	3.40176e8	+	9.98846e7i	1.22170	+	0.358723i	0.393587	+	0.919287i	$0.371234\pi$
$654$	−1.10087e8	−	9.53908e7i	−0.393552	−	0.341015i
$655$	−5.27623e7	+	8.20998e7i	−0.187759	+	0.292158i
$656$	1.00678e9	+	6.47016e8i	3.56633	+	2.29194i
$657$	5.78399e7	−	6.67508e7i	0.203954	−	0.235375i
$658$	6.31983e7	−	2.15234e8i	0.221834	−	0.755497i
$659$	4.55473e8	−	6.54872e7i	1.59150	−	0.228823i	0.711113	−	0.703078i	$-0.248191\pi$
$659$	4.55473e8	−	6.54872e7i	1.59150	−	0.228823i	0.880388	+	0.474255i	$0.157282\pi$
$660$	−8.32819e7	−	9.61125e7i	−0.289680	−	0.334309i
$661$	5.17863e8	−	2.36500e8i	1.79312	−	0.818892i	0.826394	−	0.563092i	$-0.190389\pi$
$661$	5.17863e8	−	2.36500e8i	1.79312	−	0.818892i	0.966730	−	0.255800i	$-0.0823388\pi$
$662$	−3.68224e8	+	1.08120e8i	−1.26922	+	0.372678i
$663$	−1.44875e7	−	6.61620e6i	−0.0497109	−	0.0227022i
$664$	−4.46695e8	−	6.42250e7i	−1.52583	−	0.219382i
$665$	9.55397e6	+	1.48663e7i	0.0324877	+	0.0505518i
$666$		−	2.69899e8i		−	0.913649i
$667$	−1.44671e7	+	8.78046e7i	−0.0487534	+	0.295896i
$668$	−3.06379e8			−1.02785
$669$	−2.10523e8	+	1.35295e8i	−0.703107	+	0.451859i
$670$	−1.30032e7	+	9.04393e7i	−0.0432341	+	0.300699i
$671$	1.80767e8	−	3.95824e8i	0.598345	−	1.31019i
$672$	−5.38369e7	−	1.83352e8i	−0.177408	−	0.604195i
$673$	−8.73374e7	−	1.91242e8i	−0.286520	−	0.627391i	0.710570	−	0.703627i	$-0.248437\pi$
$673$	−8.73374e7	−	1.91242e8i	−0.286520	−	0.627391i	−0.997090	+	0.0762353i	$0.975710\pi$
$674$	−2.12482e8	+	1.84117e8i	−0.693974	+	0.601332i
$675$	−7.58693e6	−	5.27683e7i	−0.0246692	−	0.171578i
$676$	7.28129e8	+	2.13798e8i	2.35705	+	0.692091i
$677$	1.69276e8	+	1.46679e8i	0.545544	+	0.472717i	0.883491	−	0.468448i	$-0.155187\pi$
$677$	1.69276e8	+	1.46679e8i	0.545544	+	0.472717i	−0.337946	+	0.941165i	$0.609732\pi$
$678$	2.67585e8	−	4.16371e8i	0.858565	−	1.33595i
$679$	−5.76584e7	−	3.70548e7i	−0.184185	−	0.118368i
$680$	9.18912e7	−	1.06048e8i	0.292245	−	0.337269i
$681$	−6.48813e7	+	2.20966e8i	−0.205437	+	0.699654i
$682$	3.71772e8	−	5.34528e7i	1.17199	−	0.168507i
$683$	−4.93145e7	−	5.69119e7i	−0.154779	−	0.178625i	0.673064	−	0.739584i	$-0.264978\pi$
$683$	−4.93145e7	−	5.69119e7i	−0.154779	−	0.178625i	−0.827843	+	0.560960i	$0.810432\pi$
$684$	1.15763e8	−	5.28674e7i	0.361745	−	0.165204i
$685$	9.09427e6	−	2.67032e6i	0.0282941	−	0.00830790i
$686$	4.14457e8	+	1.89276e8i	1.28383	+	0.586305i
$687$	−1.16528e8	−	1.67542e7i	−0.359385	−	0.0516718i
$688$	−7.60284e8	−	1.18302e9i	−2.33459	−	3.63269i
$689$		−	6.13573e7i		−	0.187590i
$690$	1.11833e8	−	1.37459e7i	0.340426	−	0.0418434i
$691$	6.85438e7			0.207747			0.103873	−	0.994591i	$-0.466876\pi$
$691$	6.85438e7			0.207747			0.103873	+	0.994591i	$0.466876\pi$
$692$	5.66155e8	−	3.63846e8i	1.70851	−	1.09799i
$693$	−6.13647e6	+	4.26801e7i	−0.0184382	+	0.128241i
$694$	−4.59684e8	+	1.00657e9i	−1.37525	+	3.01137i
$695$	2.46068e7	+	8.38030e7i	0.0732994	+	0.249635i
$696$	7.10739e7	+	1.55630e8i	0.210806	+	0.461600i
$697$	1.76431e8	−	1.52878e8i	0.521047	−	0.451490i
$698$	2.67001e7	+	1.85703e8i	0.0785139	+	0.546076i
$699$	−6.56660e7	−	1.92813e7i	−0.192269	−	0.0564552i
$700$	−2.43557e8	−	2.11044e8i	−0.710079	−	0.615287i
$701$	−1.55840e7	+	2.42492e7i	−0.0452403	+	0.0703953i	−0.863137	−	0.504970i	$-0.831504\pi$
$701$	−1.55840e7	+	2.42492e7i	−0.0452403	+	0.0703953i	0.817897	+	0.575365i	$0.195140\pi$
$702$	−2.06847e7	−	1.32933e7i	−0.0597913	−	0.0384255i
$703$	1.54476e8	−	1.78275e8i	0.444627	−	0.513127i
$704$	−1.93168e8	+	6.57868e8i	−0.553626	+	1.88548i
$705$	6.45331e7	−	9.27846e6i	0.184169	−	0.0264794i
$706$	−4.08914e8	−	4.71912e8i	−1.16203	−	1.34106i
$707$	1.90012e8	−	8.67758e7i	0.537680	−	0.245550i
$708$	−8.50638e8	+	2.49770e8i	−2.39687	+	0.703785i
$709$	3.14582e8	+	1.43665e8i	0.882663	+	0.403099i	0.804577	−	0.593848i	$-0.202392\pi$
$709$	3.14582e8	+	1.43665e8i	0.882663	+	0.403099i	0.0780858	+	0.996947i	$0.475119\pi$
$710$	−2.76996e8	−	3.98259e7i	−0.773923	−	0.111273i
$711$	8.99934e7	+	1.40032e8i	0.250381	+	0.389601i
$712$			4.64917e8i			1.28806i
$713$	−1.03786e8	+	2.15459e8i	−0.286331	+	0.594424i
$714$	−7.81806e7			−0.214785
$715$	−1.80658e7	+	1.16102e7i	−0.0494240	+	0.0317629i
$716$	7.75660e7	−	5.39483e8i	0.211316	−	1.46974i
$717$	−5.40667e7	+	1.18390e8i	−0.146681	+	0.321186i
$718$	4.12289e6	+	1.40413e7i	0.0111385	+	0.0379344i
$719$	1.54463e8	+	3.38227e8i	0.415564	+	0.909959i	0.995452	+	0.0952627i	$0.0303691\pi$
$719$	1.54463e8	+	3.38227e8i	0.415564	+	0.909959i	−0.579888	+	0.814696i	$0.696904\pi$
$720$	8.80325e7	−	7.62806e7i	0.235855	−	0.204370i
$721$	3.19236e7	+	2.22033e8i	0.0851738	+	0.592397i
$722$	−5.32343e8	−	1.56310e8i	−1.41443	−	0.415313i
$723$	1.75472e8	+	1.52047e8i	0.464294	+	0.402313i
$724$	−6.32945e8	+	9.84882e8i	−1.66783	+	2.59519i
$725$	8.65931e7	+	5.56500e7i	0.227232	+	0.146033i
$726$	−2.56377e7	+	2.95875e7i	−0.0669991	+	0.0773211i
$727$	3.56838e7	−	1.21528e8i	0.0928683	−	0.316280i	−0.899937	−	0.436020i	$-0.856388\pi$
$727$	3.56838e7	−	1.21528e8i	0.0928683	−	0.316280i	0.992805	+	0.119739i	$0.0382059\pi$
$728$	−8.95322e7	+	1.28728e7i	−0.232052	+	0.0333640i
$729$	−9.39654e6	−	1.08442e7i	−0.0242541	−	0.0279907i
$730$	1.96416e8	−	8.97003e7i	0.504904	−	0.230582i
$731$	−2.63209e8	+	7.72850e7i	−0.673826	+	0.197853i
$732$	7.96269e8	+	3.63644e8i	2.03014	+	0.927135i
$733$	−6.02934e8	−	8.66889e7i	−1.53094	−	0.220116i	−0.675244	−	0.737595i	$-0.735961\pi$
$733$	−6.02934e8	−	8.66889e7i	−1.53094	−	0.220116i	−0.855696	+	0.517479i	$0.826871\pi$
$734$	−7.42667e7	−	1.15561e8i	−0.187805	−	0.292230i
$735$			6.01903e7i			0.151588i
$736$	−6.80713e8	−	8.18915e8i	−1.70738	−	2.05402i
$737$	−1.94852e8			−0.486746
$738$	3.03194e8	−	1.94851e8i	0.754313	−	0.484767i
$739$	−6.17297e6	+	4.29340e7i	−0.0152954	+	0.106382i	−0.996039	−	0.0889183i	$-0.971659\pi$
$739$	−6.17297e6	+	4.29340e7i	−0.0152954	+	0.106382i	0.980744	+	0.195300i	$0.0625681\pi$
$740$	1.96992e8	−	4.31352e8i	0.486131	−	1.06448i
$741$	−6.05439e6	−	2.06194e7i	−0.0148804	−	0.0506781i
$742$	−1.25118e8	−	2.73971e8i	−0.306274	−	0.670646i
$743$	3.00402e8	−	2.60300e8i	0.732380	−	0.634611i	−0.206662	−	0.978412i	$-0.566260\pi$
$743$	3.00402e8	−	2.60300e8i	0.732380	−	0.634611i	0.939042	+	0.343801i	$0.111715\pi$
$744$	6.54365e7	+	4.55121e8i	0.158892	+	1.10512i
$745$	−1.83698e8	−	5.39387e7i	−0.444259	−	0.130446i
$746$	1.05700e9	+	9.15898e8i	2.54601	+	2.20613i
$747$	−3.95088e7	+	6.14769e7i	−0.0947834	+	0.147486i
$748$	4.13679e8	+	2.65855e8i	0.988459	+	0.635244i
$749$	−1.32735e8	+	1.53185e8i	−0.315894	+	0.364561i
$750$	7.74848e7	−	2.63889e8i	0.183668	−	0.625515i
$751$	4.27126e6	−	614114.i	0.0100841	−	0.00144987i	−0.137271	−	0.990534i	$-0.543833\pi$
$751$	4.27126e6	−	614114.i	0.0100841	−	0.00144987i	0.147355	+	0.989084i	$0.452924\pi$
$752$	−8.46288e8	−	9.76669e8i	−1.99005	−	2.29664i
$753$	−1.99767e8	+	9.12307e7i	−0.467885	+	0.213676i
$754$	4.55517e7	−	1.33752e7i	0.106265	−	0.0312023i
$755$	1.72766e8	+	7.88995e7i	0.401436	+	0.183330i
$756$	−8.58584e7	−	1.23446e7i	−0.198709	−	0.0285700i
$757$	3.03410e8	+	4.72115e8i	0.699426	+	1.08833i	0.991268	+	0.131862i	$0.0420955\pi$
$757$	3.03410e8	+	4.72115e8i	0.699426	+	1.08833i	−0.291842	+	0.956467i	$0.594268\pi$
$758$		−	1.52827e8i		−	0.350908i
$759$	6.29569e7	+	2.31893e8i	0.143985	+	0.530350i
$760$	1.89335e8			0.431312
$761$	2.02262e8	−	1.29986e8i	0.458945	−	0.294946i	−0.290666	−	0.956825i	$-0.593877\pi$
$761$	2.02262e8	−	1.29986e8i	0.458945	−	0.294946i	0.749611	+	0.661878i	$0.230240\pi$
$762$	2.73237e6	−	1.90041e7i	0.00617554	−	0.0429518i
$763$	−3.60472e7	+	7.89323e7i	−0.0811517	+	0.177697i
$764$	−2.50962e8	−	8.54699e8i	−0.562767	−	1.91661i
$765$	−9.43927e6	−	2.06691e7i	−0.0210840	−	0.0461676i
$766$	−6.08638e8	+	5.27388e8i	−1.35417	+	1.17339i
$767$	2.13050e7	+	1.48179e8i	0.0472166	+	0.328399i
$768$	−5.97557e7	−	1.75459e7i	−0.131915	−	0.0387339i
$769$	2.56283e8	+	2.22071e8i	0.563561	+	0.488328i	0.889421	−	0.457090i	$-0.151108\pi$
$769$	2.56283e8	+	2.22071e8i	0.563561	+	0.488328i	−0.325860	+	0.945418i	$0.605654\pi$
$770$	−5.69916e7	+	8.86807e7i	−0.124836	+	0.194248i
$771$	3.05556e8	+	1.96369e8i	0.666697	+	0.428460i
$772$	1.02911e9	−	1.18765e9i	2.23670	−	2.58129i
$773$	−1.30477e8	+	4.44364e8i	−0.282485	+	0.962057i	0.688961	+	0.724798i	$0.258067\pi$
$773$	−1.30477e8	+	4.44364e8i	−0.282485	+	0.962057i	−0.971447	+	0.237259i	$0.923751\pi$
$774$	−4.19190e8	+	6.02705e7i	−0.904041	+	0.129982i
$775$	1.81154e8	+	2.09063e8i	0.389173	+	0.449129i
$776$	−6.67972e8	+	3.05053e8i	−1.42946	+	0.652814i
$777$	−1.54268e8	+	4.52971e7i	−0.328861	+	0.0965622i
$778$	−1.15798e9	−	5.28831e8i	−2.45902	−	1.12300i
$779$	3.11789e8	+	4.48285e7i	0.659552	+	0.0948292i
$780$	−2.33559e7	−	3.63424e7i	−0.0492166	−	0.0765826i
$781$		−	5.96788e8i		−	1.25276i
$782$	−3.99929e8	+	1.72824e8i	−0.836301	+	0.361397i
$783$	2.77051e7			0.0577131
$784$	1.00368e9	−	6.45028e8i	2.08280	−	1.33854i
$785$	−2.73208e7	+	1.90020e8i	−0.0564786	+	0.392818i
$786$	2.42007e8	−	5.29922e8i	0.498380	−	1.09130i
$787$	−1.68366e8	−	5.73403e8i	−0.345407	−	1.17635i	−0.930779	−	0.365583i	$-0.880870\pi$
$787$	−1.68366e8	−	5.73403e8i	−0.345407	−	1.17635i	0.585372	−	0.810765i	$-0.300948\pi$
$788$	−6.60750e8	−	1.44684e9i	−1.35039	−	2.95694i
$789$	2.07180e8	−	1.79522e8i	0.421810	−	0.365500i
$790$	5.79142e7	+	4.02802e8i	0.117464	+	0.816979i
$791$	−2.82896e8	−	8.30657e7i	−0.571606	−	0.167839i
$792$	3.49143e8	+	3.02534e8i	0.702794	+	0.608974i
$793$	7.99154e7	−	1.24351e8i	0.160255	−	0.249361i
$794$	−2.56484e8	−	1.64832e8i	−0.512388	−	0.329292i
$795$	5.73252e7	−	6.61568e7i	0.114089	−	0.131666i
$796$	−8.95758e7	+	3.05067e8i	−0.177603	+	0.604862i
$797$	−9.28917e8	+	1.33558e8i	−1.83486	+	0.263812i	−0.970853	−	0.239676i	$-0.922959\pi$
$797$	−9.28917e8	+	1.33558e8i	−1.83486	+	0.263812i	−0.864002	+	0.503488i	$0.832050\pi$
$798$	−6.90804e7	−	7.97230e7i	−0.135940	−	0.156883i
$799$	−2.29312e8	+	1.04723e8i	−0.449558	+	0.205306i
$800$	−1.18187e9	+	3.47029e8i	−2.30834	+	0.677790i
$801$	6.84814e7	+	3.12744e7i	0.133252	+	0.0608543i
$802$	1.39368e8	+	2.00381e7i	0.270172	+	0.0388448i
$803$	2.48957e8	+	3.87385e8i	0.480816	+	0.748164i
$804$		−	3.91978e8i		−	0.754213i
$805$	−2.66257e7	−	6.16140e7i	−0.0510404	−	0.118111i
$806$	1.27587e8			0.243669
$807$	−2.19661e7	+	1.41167e7i	−0.0417957	+	0.0268605i
$808$	3.18510e8	−	2.21529e9i	0.603795	−	4.19948i
$809$	−5.53185e7	+	1.21131e8i	−0.104478	+	0.228775i	−0.954650	−	0.297730i	$-0.903771\pi$
$809$	−5.53185e7	+	1.21131e8i	−0.104478	+	0.228775i	0.850172	+	0.526505i	$0.176498\pi$
$810$	−9.88301e6	−	3.36584e7i	−0.0185966	−	0.0633343i
$811$	−2.76933e8	−	6.06398e8i	−0.519172	−	1.13683i	−0.969752	−	0.244093i	$-0.921510\pi$
$811$	−2.76933e8	−	6.06398e8i	−0.519172	−	1.13683i	0.450580	−	0.892736i	$-0.351217\pi$
$812$	1.26574e8	−	1.09677e8i	0.236416	−	0.204855i
$813$	−2.95330e7	−	2.05407e8i	−0.0549587	−	0.382246i
$814$	1.35015e9	+	3.96440e8i	2.50327	+	0.735028i
$815$	−3.55777e7	−	3.08282e7i	−0.0657211	−	0.0569476i
$816$	−2.43505e8	+	3.78902e8i	−0.448165	+	0.697358i
$817$	−3.11381e8	−	2.00112e8i	−0.570986	−	0.366951i
$818$	1.01328e9	−	1.16939e9i	1.85128	−	2.13649i
$819$	−4.12658e6	+	1.40539e7i	−0.00751171	+	0.0255825i
$820$	6.26780e8	−	9.01173e7i	1.13677	−	0.163443i
$821$	−2.40271e8	−	2.77288e8i	−0.434182	−	0.501073i	0.495923	−	0.868367i	$-0.334830\pi$
$821$	−2.40271e8	−	2.77288e8i	−0.434182	−	0.501073i	−0.930105	+	0.367293i	$0.880284\pi$
$822$	−5.14663e7	+	2.35039e7i	−0.0926632	+	0.0423179i
$823$	7.58369e8	−	2.22677e8i	1.36044	−	0.399463i	0.481525	−	0.876432i	$-0.340083\pi$
$823$	7.58369e8	−	2.22677e8i	1.36044	−	0.399463i	0.878920	+	0.476970i	$0.158265\pi$
$824$	2.18617e9	+	9.98391e8i	3.90753	+	1.78451i
$825$	2.75113e8	+	3.95552e7i	0.489947	+	0.0704437i
$826$	3.97294e8	+	6.18202e8i	0.704972	+	1.09696i
$827$		−	3.54806e8i		−	0.627299i	−0.949539	−	0.313649i	$-0.898448\pi$
$827$		−	3.54806e8i		−	0.627299i	0.949539	−	0.313649i	$-0.101552\pi$
$828$	−4.66493e8	+	1.26649e8i	−0.821777	+	0.223105i
$829$	−6.36329e8			−1.11691			−0.558455	−	0.829535i	$-0.688606\pi$
$829$	−6.36329e8			−1.11691			−0.558455	+	0.829535i	$0.688606\pi$
$830$	−1.50295e8	+	9.65890e7i	−0.262852	+	0.168925i
$831$	7.24195e6	−	5.03689e7i	0.0126198	−	0.0877727i
$832$	−9.67530e7	+	2.11860e8i	−0.167994	+	0.367856i
$833$	−6.55689e7	−	2.23307e8i	−0.113439	−	0.386338i
$834$	−2.16586e8	−	4.74258e8i	−0.373364	−	0.817553i
$835$	−5.57821e7	+	4.83355e7i	−0.0958155	+	0.0830246i
$836$	9.44265e7	+	6.56750e8i	0.161612	+	1.12404i
$837$	7.14403e7	+	2.09768e7i	0.121834	+	0.0357735i
$838$	1.21952e9	+	1.05672e9i	2.07233	+	1.79568i
$839$	−3.16055e7	+	4.91792e7i	−0.0535152	+	0.0832713i	−0.866980	−	0.498343i	$-0.833942\pi$
$839$	−3.16055e7	+	4.91792e7i	−0.0535152	+	0.0832713i	0.813465	+	0.581614i	$0.197579\pi$
$840$	−1.08562e8	−	6.97688e7i	−0.183165	−	0.117713i
$841$	3.54496e8	−	4.09110e8i	0.595968	−	0.687784i
$842$	−3.37430e7	+	1.14918e8i	−0.0565258	+	0.192509i
$843$	−6.40604e7	+	9.21049e6i	−0.106932	+	0.0153745i
$844$	1.43207e9	+	1.65270e9i	2.38198	+	2.74895i
$845$	1.66299e8	−	7.59462e7i	0.275626	−	0.125874i
$846$	−3.73421e8	+	1.09646e8i	−0.616719	+	0.181085i
$847$	2.12142e7	+	9.68821e6i	0.0349122	+	0.0159439i
$848$	−1.71750e9	−	2.46939e8i	−2.81650	−	0.404951i
$849$	−9.46071e7	−	1.47212e8i	−0.154597	−	0.240557i
$850$			5.03946e8i			0.820592i
$851$	−6.89016e8	+	5.72736e8i	−1.11800	+	0.929321i
$852$	1.20054e9			1.94115
$853$	−3.57929e8	+	2.30027e8i	−0.576700	+	0.370623i	−0.796240	−	0.604981i	$-0.793181\pi$
$853$	−3.57929e8	+	2.30027e8i	−0.576700	+	0.370623i	0.219540	+	0.975604i	$0.429544\pi$
$854$	1.03263e8	−	7.18210e8i	0.165795	−	1.15313i
$855$	1.27364e7	−	2.78887e7i	0.0203773	−	0.0446201i
$856$	6.11831e8	+	2.08371e9i	0.975462	+	3.32212i
$857$	−2.22237e8	−	4.86631e8i	−0.353081	−	0.773139i	−0.999945	−	0.0105334i	$-0.996647\pi$
$857$	−2.22237e8	−	4.86631e8i	−0.353081	−	0.773139i	0.646864	−	0.762606i	$-0.276080\pi$
$858$	9.68809e7	−	8.39478e7i	0.153383	−	0.132907i
$859$	−1.03017e8	−	7.16501e8i	−0.162529	−	1.13041i	−0.893845	−	0.448375i	$-0.852003\pi$
$859$	−1.03017e8	−	7.16501e8i	−0.162529	−	1.13041i	0.731316	−	0.682038i	$-0.238906\pi$
$860$	−7.13938e8	−	2.09631e8i	−1.12245	−	0.329580i
$861$	−1.62257e8	−	1.40596e8i	−0.254210	−	0.220275i
$862$	−1.00067e9	+	1.55707e9i	−1.56231	+	2.43100i
$863$	−5.45949e8	−	3.50860e8i	−0.849415	−	0.545886i	0.0419771	−	0.999119i	$-0.486634\pi$
$863$	−5.45949e8	−	3.50860e8i	−0.849415	−	0.545886i	−0.891392	+	0.453233i	$0.850271\pi$
$864$	−2.17110e8	+	2.50558e8i	−0.336619	+	0.388479i
$865$	4.56776e7	−	1.55564e8i	0.0705757	−	0.240359i
$866$	−4.23093e8	+	6.08316e7i	−0.651452	+	0.0936646i
$867$	−1.88867e8	−	2.17964e8i	−0.289800	−	0.334447i
$868$	4.09425e8	−	1.86978e8i	0.626059	−	0.285911i
$869$	−8.32686e8	+	2.44499e8i	−1.26888	+	0.372578i
$870$	6.16110e7	+	2.81368e7i	0.0935623	+	0.0427285i
$871$	−6.55159e7	−	9.41976e6i	−0.0991499	−	0.0142556i
$872$	5.02637e8	+	7.82119e8i	0.758063	+	1.17957i
$873$			1.18911e8i			0.178723i
$874$	−5.29611e8	−	2.55111e8i	−0.793274	−	0.382116i
$875$	−1.63837e8			−0.244561
$876$	−7.79293e8	+	5.00821e8i	−1.15928	+	0.745024i
$877$	−7.07896e7	+	4.92353e8i	−0.104947	+	0.729924i	0.867608	+	0.497250i	$0.165657\pi$
$877$	−7.07896e7	+	4.92353e8i	−0.104947	+	0.729924i	−0.972555	+	0.232674i	$0.925252\pi$
$878$	−5.56563e8	+	1.21870e9i	−0.822301	+	1.80059i
$879$	−8.37240e7	−	2.85138e8i	−0.123277	−	0.419844i
$880$	2.52281e8	+	5.52419e8i	0.370201	+	0.810626i
$881$	−8.90109e7	+	7.71284e7i	−0.130171	+	0.112794i	−0.717513	−	0.696545i	$-0.754720\pi$
$881$	−8.90109e7	+	7.71284e7i	−0.130171	+	0.112794i	0.587342	+	0.809339i	$0.300174\pi$
$882$	−5.11337e7	−	3.55643e8i	−0.0745249	−	0.518332i
$883$	3.00611e8	+	8.82673e7i	0.436639	+	0.128209i	0.492662	−	0.870221i	$-0.336024\pi$
$883$	3.00611e8	+	8.82673e7i	0.436639	+	0.128209i	−0.0560232	+	0.998429i	$0.517842\pi$
$884$	1.26241e8	+	1.09388e8i	0.182744	+	0.158348i
$885$	−1.15470e8	+	1.79675e8i	−0.166586	+	0.259213i
$886$	3.02416e8	+	1.94351e8i	0.434815	+	0.279438i
$887$	3.15426e8	−	3.64021e8i	0.451987	−	0.521621i	−0.483327	−	0.875440i	$-0.660572\pi$
$887$	3.15426e8	−	3.64021e8i	0.451987	−	0.521621i	0.935314	+	0.353819i	$0.115117\pi$
$888$	−4.85319e8	+	1.65284e9i	−0.693088	+	2.36044i
$889$	−1.13208e7	+	1.62769e6i	−0.0161128	+	0.00231668i
$890$	1.20528e8	+	1.39097e8i	0.170970	+	0.197310i
$891$	6.80491e7	−	3.10770e7i	0.0962032	−	0.0439345i
$892$	2.51831e9	−	7.39443e8i	3.54826	−	1.04186i
$893$	−3.09409e8	−	1.41302e8i	−0.434489	−	0.198425i
$894$	1.13123e9	+	1.62646e8i	1.58321	+	0.227631i
$895$	−7.09884e7	−	1.10460e8i	−0.0990190	−	0.154077i
$896$			3.58738e8i			0.498715i
$897$	9.95782e6	+	8.10139e7i	0.0137971	+	0.112249i
$898$	−1.26723e9			−1.74995
$899$	−1.20940e8	+	7.77232e7i	−0.166452	+	0.106972i
$900$	−7.95722e7	+	5.53437e8i	−0.109153	+	0.759173i
$901$	−1.40609e8	+	3.07891e8i	−0.192238	+	0.420942i
$902$	5.29381e8	+	1.80291e9i	0.721355	+	2.45671i
$903$	1.04802e8	+	2.29483e8i	0.142333	+	0.311665i
$904$	−2.38737e9	+	2.06867e9i	−3.23157	+	2.80017i
$905$	4.01389e7	+	2.79172e8i	0.0541526	+	0.376640i
$906$	−1.08784e9	−	3.19418e8i	−1.46278	−	0.429512i
$907$	−1.60810e6	−	1.39342e6i	−0.00215521	−	0.00186750i	0.653782	−	0.756683i	$-0.273181\pi$
$907$	−1.60810e6	−	1.39342e6i	−0.00215521	−	0.00186750i	−0.655938	+	0.754815i	$0.727727\pi$
$908$	1.30583e9	−	2.03191e9i	1.74433	−	2.71423i
$909$	−3.04882e8	−	1.95936e8i	−0.405919	−	0.260868i
$910$	−2.34496e7	+	2.70623e7i	−0.0311180	+	0.0359121i
$911$	1.23707e8	−	4.21306e8i	0.163621	−	0.557241i	−0.836339	−	0.548213i	$-0.815308\pi$
$911$	1.23707e8	−	4.21306e8i	0.163621	−	0.557241i	0.999959	−	0.00902756i	$-0.00287360\pi$
$912$	−6.01538e8	+	8.64882e7i	−0.793010	+	0.114018i
$913$	−2.49501e8	−	2.87940e8i	−0.327839	−	0.378346i
$914$	9.33336e8	−	4.26240e8i	1.22236	−	0.558233i
$915$	2.02345e8	−	5.94140e7i	0.264138	−	0.0775578i
$916$	1.12314e9	+	5.12922e8i	1.46133	+	0.667367i
$917$	−3.43506e8	−	4.93887e7i	−0.445478	−	0.0640500i
$918$	7.33324e7	+	1.14107e8i	0.0947912	+	0.147498i
$919$		−	1.17844e9i		−	1.51831i	−0.650909	−	0.759156i	$-0.725612\pi$
$919$		−	1.17844e9i		−	1.51831i	0.650909	−	0.759156i	$-0.274388\pi$
$920$	−7.09575e8	−	1.16913e8i	−0.911244	−	0.150141i
$921$	−5.45677e8			−0.698484
$922$	1.47568e9	−	9.48360e8i	1.88278	−	1.20999i
$923$	2.88507e7	−	2.00661e8i	0.0366902	−	0.255186i
$924$	1.87865e8	−	4.11367e8i	0.238139	−	0.521451i
$925$	2.91982e8	+	9.94398e8i	0.368918	+	1.25642i
$926$	5.27767e8	+	1.15565e9i	0.664674	+	1.45543i
$927$	2.94122e8	−	2.54858e8i	0.369223	−	0.319933i
$928$	−9.11007e7	−	6.33619e8i	−0.113993	−	0.792838i
$929$	−4.31492e8	−	1.26697e8i	−0.538177	−	0.158023i	0.00133787	−	0.999999i	$-0.499574\pi$
$929$	−4.31492e8	−	1.26697e8i	−0.538177	−	0.158023i	−0.539515	+	0.841976i	$0.681392\pi$
$930$	1.37567e8	+	1.19202e8i	0.171027	+	0.148195i
$931$	1.69776e8	−	2.64177e8i	0.210391	−	0.327375i
$932$	6.03839e8	+	3.88064e8i	0.745887	+	0.479353i
$933$	1.15645e8	−	1.33462e8i	0.142391	−	0.164328i
$934$	6.29375e8	−	2.14345e9i	0.772447	−	2.63071i
$935$	1.17260e8	−	1.68595e7i	0.143455	−	0.0206257i
$936$	1.02768e8	+	1.18601e8i	0.125323	+	0.144631i
$937$	−3.75738e8	+	1.71594e8i	−0.456737	+	0.208585i	−0.630479	−	0.776207i	$-0.717141\pi$
$937$	−3.75738e8	+	1.71594e8i	−0.456737	+	0.208585i	0.173742	+	0.984791i	$0.444414\pi$
$938$	−3.11748e8	+	9.15376e7i	−0.377742	+	0.110915i
$939$	6.21482e8	+	2.83821e8i	0.750641	+	0.342806i
$940$	−6.76828e8	−	9.73131e7i	−0.814882	−	0.117162i
$941$	6.08293e8	+	9.46523e8i	0.730036	+	1.13596i	0.985588	+	0.169163i	$0.0541063\pi$
$941$	6.08293e8	+	9.46523e8i	0.730036	+	1.13596i	−0.255552	+	0.966795i	$0.582257\pi$
$942$		−	1.14597e9i		−	1.37095i
$943$	−1.14082e9	−	3.60532e8i	−1.36044	−	0.429941i
$944$	4.23354e9			5.03255
$945$	−1.75797e7	+	1.12978e7i	−0.0208312	+	0.0133874i
$946$	3.14226e8	−	2.18549e9i	0.371167	−	2.58152i
$947$	−5.70452e8	+	1.24911e9i	−0.671690	+	1.47080i	0.199524	+	0.979893i	$0.436060\pi$
$947$	−5.70452e8	+	1.24911e9i	−0.671690	+	1.47080i	−0.871214	+	0.490903i	$0.836667\pi$
$948$	−4.91851e8	−	1.67509e9i	−0.577310	−	1.96614i
$949$	6.49806e7	+	1.42288e8i	0.0760300	+	0.166482i
$950$	−5.13889e8	+	4.45287e8i	−0.599374	+	0.519361i
$951$	−9.54282e7	−	6.63718e8i	−0.110952	−	0.771689i
$952$	4.78772e8	+	1.40580e8i	0.554904	+	0.162935i
$953$	−9.39058e8	−	8.13698e8i	−1.08496	−	0.940123i	−0.0865363	−	0.996249i	$-0.527580\pi$
$953$	−9.39058e8	−	8.13698e8i	−1.08496	−	0.940123i	−0.998424	+	0.0561255i	$0.982125\pi$
$954$	−2.82511e8	+	4.39596e8i	−0.325380	+	0.506301i
$955$	−1.80533e8	−	1.16021e8i	−0.207275	−	0.133207i
$956$	8.93907e8	−	1.03162e9i	1.02310	−	1.18072i
$957$	−4.06944e7	+	1.38592e8i	−0.0464300	+	0.158126i
$958$	−7.82308e8	+	1.12479e8i	−0.889777	+	0.127931i
$959$	2.20718e7	+	2.54722e7i	0.0250254	+	0.0288809i
$960$	−3.02258e8	+	1.38037e8i	−0.341636	+	0.156020i
$961$	4.80851e8	−	1.41191e8i	0.541802	−	0.159087i
$962$	4.34801e8	+	1.98567e8i	0.488389	+	0.223040i
$963$	3.48083e8	+	5.00467e7i	0.389766	+	0.0560398i
$964$	−1.31654e9	−	2.04858e9i	−1.46961	−	2.28676i
$965$		−	3.78589e8i		−	0.421295i
$966$	2.09665e8	+	3.41436e8i	0.232592	+	0.378772i
$967$	−1.66536e9			−1.84174			−0.920869	−	0.389873i	$-0.872519\pi$
$967$	−1.66536e9			−1.84174			−0.920869	+	0.389873i	$0.872519\pi$
$968$	2.10206e8	−	1.35091e8i	0.231750	−	0.148936i
$969$	−1.68713e7	+	1.17342e8i	−0.0185429	+	0.128968i
$970$	−1.20765e8	+	2.64437e8i	−0.132320	+	0.289740i
$971$	3.53425e8	+	1.20365e9i	0.386046	+	1.31475i	0.891939	+	0.452156i	$0.149345\pi$
$971$	3.53425e8	+	1.20365e9i	0.386046	+	1.31475i	−0.505892	+	0.862597i	$0.668837\pi$
$972$	6.25167e7	+	1.36893e8i	0.0680765	+	0.149067i
$973$	−2.34724e8	+	2.03390e8i	−0.254812	+	0.220796i
$974$	7.02391e7	+	4.88524e8i	0.0760155	+	0.528700i
$975$	9.05901e7	+	2.65997e7i	0.0977388	+	0.0286987i
$976$	−3.15917e9	−	2.73744e9i	−3.39800	−	2.94439i
$977$	−6.59269e8	+	1.02584e9i	−0.706934	+	1.10001i	0.283087	+	0.959094i	$0.408641\pi$
$977$	−6.59269e8	+	1.02584e9i	−0.706934	+	1.10001i	−0.990021	+	0.140917i	$0.954995\pi$
$978$	2.36405e8	+	1.51929e8i	0.252721	+	0.162414i
$979$	−2.57036e8	+	2.96635e8i	−0.273934	+	0.316136i
$980$	1.77852e8	−	6.05708e8i	0.188965	−	0.643554i
$981$	1.49016e8	−	2.14253e7i	0.157844	−	0.0226945i
$982$	1.37552e9	+	1.58744e9i	1.45256	+	1.67634i
$983$	5.82708e8	−	2.66114e8i	0.613465	−	0.280160i	−0.0843519	−	0.996436i	$-0.526882\pi$
$983$	5.82708e8	−	2.66114e8i	0.613465	−	0.280160i	0.697817	+	0.716276i	$0.254155\pi$
$984$	−2.20711e9	+	6.48065e8i	−2.31653	+	0.680195i
$985$	−3.48561e8	−	1.59182e8i	−0.364729	−	0.166566i
$986$	−2.59230e8	−	3.72716e7i	−0.270429	−	0.0388819i
$987$	1.25342e8	+	1.95036e8i	0.130360	+	0.202845i
$988$			2.25387e8i			0.233699i
$989$	1.04340e9	+	9.42239e8i	1.07860	+	0.974030i
$990$	1.82890e8			0.188488
$991$	1.90203e8	−	1.22236e8i	0.195433	−	0.125597i	−0.439265	−	0.898358i	$-0.644761\pi$
$991$	1.90203e8	−	1.22236e8i	0.195433	−	0.125597i	0.634698	+	0.772761i	$0.281125\pi$
$992$	2.44830e8	−	1.70283e9i	0.250801	−	1.74436i
$993$	1.64768e8	−	3.60791e8i	0.168277	−	0.368475i
$994$	−2.80359e8	−	9.54816e8i	−0.285467	−	0.972211i
$995$	3.18195e7	+	6.96750e7i	0.0323016	+	0.0707306i
$996$	5.79240e8	−	5.01914e8i	0.586247	−	0.507986i
$997$	−2.13524e8	−	1.48509e9i	−0.215457	−	1.49854i	−0.754524	−	0.656272i	$-0.772132\pi$
$997$	−2.13524e8	−	1.48509e9i	−0.215457	−	1.49854i	0.539067	−	0.842263i	$-0.318777\pi$
$998$	−1.85877e9	−	5.45784e8i	−1.86997	−	0.549071i
$999$	2.10814e8	+	1.82671e8i	0.211448	+	0.183220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.34.24	✓	240
23.21	odd	22	inner	69.7.f.a.67.24	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.34.24	✓	240	1.1	even	1	trivial
69.7.f.a.67.24	yes	240	23.21	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(12.6885 - 8.15441i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(67.9173 - 148.718i) q^{4} +(-11.0967 - 37.7918i) q^{5} +(97.6718 + 213.871i) q^{6} +(105.851 - 91.7206i) q^{7} +(-213.563 - 1485.36i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})\)	\(q+(12.6885 - 8.15441i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(67.9173 - 148.718i) q^{4} +(-11.0967 - 37.7918i) q^{5} +(97.6718 + 213.871i) q^{6} +(105.851 - 91.7206i) q^{7} +(-213.563 - 1485.36i) q^{8} +(-233.157 - 68.4610i) q^{9} +(-448.970 - 389.035i) q^{10} +(684.941 - 1065.79i) q^{11} +(2144.02 + 1377.88i) q^{12} +(281.824 - 325.242i) q^{13} +(595.167 - 2026.95i) q^{14} +(607.737 - 87.3794i) q^{15} +(-7969.88 - 9197.73i) q^{16} +(-2159.53 + 986.225i) q^{17} +(-3516.67 + 1032.59i) q^{18} +(-2913.85 - 1330.71i) q^{19} +(-6373.99 - 916.441i) q^{20} +(1180.40 + 1836.74i) q^{21} -19108.6i q^{22} +(10098.6 + 6786.39i) q^{23} +23392.6 q^{24} +(11839.5 - 7608.79i) q^{25} +(923.769 - 6424.95i) q^{26} +(1573.59 - 3445.68i) q^{27} +(-6451.40 - 21971.4i) q^{28} +(3038.31 + 6652.97i) q^{29} +(6998.76 - 6064.46i) q^{30} +(2797.32 + 19455.8i) q^{31} +(-83977.6 - 24658.0i) q^{32} +(14925.4 + 12932.9i) q^{33} +(-19359.2 + 30123.4i) q^{34} +(-4640.89 - 2982.52i) q^{35} +(-26016.8 + 30025.0i) q^{36} +(-20746.7 + 70656.8i) q^{37} +(-47823.5 + 6875.98i) q^{38} +(4393.20 + 5070.03i) q^{39} +(-53764.7 + 24553.5i) q^{40} +(-94350.8 + 27703.9i) q^{41} +(29955.1 + 13680.0i) q^{42} +(114372. + 16444.3i) q^{43} +(-111983. - 174249. i) q^{44} +9571.11i q^{45} +(183475. + 3761.43i) q^{46} +106186. q^{47} +(159600. - 102569. i) q^{48} +(-13951.4 + 97034.0i) q^{49} +(88180.5 - 193088. i) q^{50} +(-10426.4 - 35509.0i) q^{51} +(-29228.7 - 64002.0i) q^{52} +(107749. - 93365.4i) q^{53} +(-8130.99 - 56552.3i) q^{54} +(-47878.7 - 14058.4i) q^{55} +(-158844. - 137639. i) q^{56} +(26996.8 - 42007.9i) q^{57} +(92802.7 + 59640.7i) q^{58} +(-227798. + 262893. i) q^{59} +(28281.0 - 96316.2i) q^{60} +(339977. - 48881.3i) q^{61} +(194144. + 224054. i) q^{62} +(-30959.2 + 14138.6i) q^{63} +(-519272. + 152472. i) q^{64} +(-15418.8 - 7041.54i) q^{65} +(294841. + 42391.8i) q^{66} +(-83151.3 - 129386. i) q^{67} +388144. i q^{68} +(-127116. + 140763. i) q^{69} -83206.6 q^{70} +(396281. - 254674. i) q^{71} +(-51895.7 + 360943. i) q^{72} +(-150992. + 330627. i) q^{73} +(312920. + 1.06571e6i) q^{74} +(91136.4 + 199561. i) q^{75} +(-395801. + 342964. i) q^{76} +(-25253.0 - 175638. i) q^{77} +(97086.3 + 28507.1i) q^{78} +(-517694. - 448585. i) q^{79} +(-259160. + 403260. i) q^{80} +(49675.2 + 31924.3i) q^{81} +(-971262. + 1.12090e6i) q^{82} +(84725.9 - 288550. i) q^{83} +(353327. - 50800.7i) q^{84} +(61234.9 + 70668.8i) q^{85} +(1.58531e6 - 723986. i) q^{86} +(-109394. + 32121.1i) q^{87} +(-1.72936e6 - 789772. i) q^{88} +(-306660. - 44091.1i) q^{89} +(78046.8 + 121443. i) q^{90} -60276.4i q^{91} +(1.69513e6 - 1.04093e6i) q^{92} -306404. q^{93} +(1.34734e6 - 865883. i) q^{94} +(-17955.9 + 124886. i) q^{95} +(566770. - 1.24105e6i) q^{96} +(-137865. - 469526. i) q^{97} +(614233. + 1.34498e6i) q^{98} +(-232664. + 201604. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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