LMFDB - Embedded newform 43.7.d.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.0830i q^{2} +(-28.7233 - 16.5834i) q^{3} -134.330 q^{4} +(147.495 + 85.1564i) q^{5} +(-233.544 + 404.510i) q^{6} +(-245.226 + 141.581i) q^{7} +990.457i q^{8} +(185.520 + 321.330i) q^{9} +O(q^{10})$	\(q-14.0830i q^{2} +(-28.7233 - 16.5834i) q^{3} -134.330 q^{4} +(147.495 + 85.1564i) q^{5} +(-233.544 + 404.510i) q^{6} +(-245.226 + 141.581i) q^{7} +990.457i q^{8} +(185.520 + 321.330i) q^{9} +(1199.26 - 2077.17i) q^{10} -907.989 q^{11} +(3858.41 + 2227.65i) q^{12} +(1023.00 + 1771.88i) q^{13} +(1993.89 + 3453.51i) q^{14} +(-2824.37 - 4891.95i) q^{15} +5351.46 q^{16} +(-3803.60 - 6588.04i) q^{17} +(4525.28 - 2612.67i) q^{18} +(5714.09 + 3299.03i) q^{19} +(-19813.1 - 11439.1i) q^{20} +9391.61 q^{21} +12787.2i q^{22} +(-8931.65 + 15470.1i) q^{23} +(16425.2 - 28449.2i) q^{24} +(6690.73 + 11588.7i) q^{25} +(24953.4 - 14406.8i) q^{26} +11872.4i q^{27} +(32941.2 - 19018.6i) q^{28} +(19886.7 - 11481.6i) q^{29} +(-68893.2 + 39775.5i) q^{30} +(-23828.4 + 41272.1i) q^{31} -11975.2i q^{32} +(26080.5 + 15057.6i) q^{33} +(-92779.1 + 53566.1i) q^{34} -48226.2 q^{35} +(-24920.9 - 43164.3i) q^{36} +(44454.8 + 25666.0i) q^{37} +(46460.2 - 80471.4i) q^{38} -67859.1i q^{39} +(-84343.8 + 146088. i) q^{40} -57173.8 q^{41} -132262. i q^{42} +(-24225.9 - 75726.3i) q^{43} +121970. q^{44} +63192.8i q^{45} +(217865. + 125784. i) q^{46} -146686. q^{47} +(-153712. - 88745.5i) q^{48} +(-18734.0 + 32448.2i) q^{49} +(163203. - 94225.4i) q^{50} +252307. i q^{51} +(-137419. - 238017. i) q^{52} +(57188.6 - 99053.6i) q^{53} +167199. q^{54} +(-133924. - 77321.1i) q^{55} +(-140230. - 242886. i) q^{56} +(-109418. - 189518. i) q^{57} +(-161695. - 280063. i) q^{58} -93833.8 q^{59} +(379398. + 657137. i) q^{60} +(-171840. + 99211.9i) q^{61} +(581233. + 335575. i) q^{62} +(-90988.6 - 52532.3i) q^{63} +173848. q^{64} +348459. i q^{65} +(212055. - 367291. i) q^{66} +(82442.2 - 142794. i) q^{67} +(510939. + 884972. i) q^{68} +(513093. - 296235. i) q^{69} +679168. i q^{70} +(-593710. + 342779. i) q^{71} +(-318264. + 183750. i) q^{72} +(-9402.34 + 5428.44i) q^{73} +(361454. - 626056. i) q^{74} -443821. i q^{75} +(-767575. - 443159. i) q^{76} +(222663. - 128554. i) q^{77} -955658. q^{78} +(201033. + 348199. i) q^{79} +(789314. + 455711. i) q^{80} +(332129. - 575265. i) q^{81} +805177. i q^{82} +(134493. - 232949. i) q^{83} -1.26158e6 q^{84} -1.29561e6i q^{85} +(-1.06645e6 + 341173. i) q^{86} -761615. q^{87} -899325. i q^{88} +(341386. + 197099. i) q^{89} +889943. q^{90} +(-501730. - 289674. i) q^{91} +(1.19979e6 - 2.07810e6i) q^{92} +(1.36886e6 - 790314. i) q^{93} +2.06577e6i q^{94} +(561867. + 973183. i) q^{95} +(-198589. + 343966. i) q^{96} -1.75894e6 q^{97} +(456968. + 263830. i) q^{98} +(-168450. - 291764. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	14.0830i		−	1.76037i	−0.474629	−	0.880186i	$-0.657418\pi$
$2$		−	14.0830i		−	1.76037i	0.474629	−	0.880186i	$-0.342582\pi$
$3$	−28.7233	−	16.5834i	−1.06383	−	0.614201i	−0.137339	−	0.990524i	$-0.543855\pi$
$3$	−28.7233	−	16.5834i	−1.06383	−	0.614201i	−0.926488	+	0.376323i	$0.877188\pi$
$4$	−134.330			−2.09891
$5$	147.495	+	85.1564i	1.17996	+	0.681251i	0.956006	−	0.293348i	$-0.0947694\pi$
$5$	147.495	+	85.1564i	1.17996	+	0.681251i	0.223956	+	0.974599i	$0.428103\pi$
$6$	−233.544	+	404.510i	−1.08122	+	1.87273i
$7$	−245.226	+	141.581i	−0.714944	+	0.412773i	−0.812889	−	0.582419i	$-0.802107\pi$
$7$	−245.226	+	141.581i	−0.714944	+	0.412773i	0.0979447	+	0.995192i	$0.468773\pi$
$8$			990.457i			1.93449i
$9$	185.520	+	321.330i	0.254485	+	0.440782i
$10$	1199.26	−	2077.17i	1.19926	−	2.07717i
$11$	−907.989			−0.682186			−0.341093	−	0.940030i	$-0.610797\pi$
$11$	−907.989			−0.682186			−0.341093	+	0.940030i	$0.610797\pi$
$12$	3858.41	+	2227.65i	2.23288	+	1.28915i
$13$	1023.00	+	1771.88i	0.465633	+	0.806500i	0.999230	−	0.0392388i	$-0.0124933\pi$
$13$	1023.00	+	1771.88i	0.465633	+	0.806500i	−0.533597	+	0.845739i	$0.679160\pi$
$14$	1993.89	+	3453.51i	0.726634	+	1.25857i
$15$	−2824.37	−	4891.95i	−0.836850	−	1.44947i
$16$	5351.46			1.30651
$17$	−3803.60	−	6588.04i	−0.774192	−	1.34094i	−0.935248	−	0.353994i	$-0.884823\pi$
$17$	−3803.60	−	6588.04i	−0.774192	−	1.34094i	0.161056	−	0.986945i	$-0.448510\pi$
$18$	4525.28	−	2612.67i	0.775940	−	0.447989i
$19$	5714.09	+	3299.03i	0.833079	+	0.480979i	0.854906	−	0.518783i	$-0.173615\pi$
$19$	5714.09	+	3299.03i	0.833079	+	0.480979i	−0.0218265	+	0.999762i	$0.506948\pi$
$20$	−19813.1	−	11439.1i	−2.47663	−	1.42988i
$21$	9391.61			1.01410
$22$			12787.2i			1.20090i
$23$	−8931.65	+	15470.1i	−0.734088	+	1.27148i	0.221034	+	0.975266i	$0.429057\pi$
$23$	−8931.65	+	15470.1i	−0.734088	+	1.27148i	−0.955122	+	0.296212i	$0.904277\pi$
$24$	16425.2	−	28449.2i	1.18816	−	2.05796i
$25$	6690.73	+	11588.7i	0.428207	+	0.741676i
$26$	24953.4	−	14406.8i	1.41974	−	0.819687i
$27$			11872.4i			0.603181i
$28$	32941.2	−	19018.6i	1.50060	−	0.866373i
$29$	19886.7	−	11481.6i	0.815395	−	0.470769i	−0.0334308	−	0.999441i	$-0.510643\pi$
$29$	19886.7	−	11481.6i	0.815395	−	0.470769i	0.848826	+	0.528672i	$0.177310\pi$
$30$	−68893.2	+	39775.5i	−2.55160	+	1.47317i
$31$	−23828.4	+	41272.1i	−0.799853	+	1.38539i	0.119858	+	0.992791i	$0.461756\pi$
$31$	−23828.4	+	41272.1i	−0.799853	+	1.38539i	−0.919711	+	0.392596i	$0.871577\pi$
$32$		−	11975.2i		−	0.365453i
$33$	26080.5	+	15057.6i	0.725728	+	0.418999i
$34$	−92779.1	+	53566.1i	−2.36055	+	1.36287i
$35$	−48226.2			−1.12481
$36$	−24920.9	−	43164.3i	−0.534142	−	0.925160i
$37$	44454.8	+	25666.0i	0.877635	+	0.506703i	0.869878	−	0.493267i	$-0.164197\pi$
$37$	44454.8	+	25666.0i	0.877635	+	0.506703i	0.00775705	+	0.999970i	$0.497531\pi$
$38$	46460.2	−	80471.4i	0.846701	−	1.46653i
$39$		−	67859.1i		−	1.14397i
$40$	−84343.8	+	146088.i	−1.31787	+	2.28262i
$41$	−57173.8			−0.829555			−0.414778	−	0.909923i	$-0.636141\pi$
$41$	−57173.8			−0.829555			−0.414778	+	0.909923i	$0.636141\pi$
$42$		−	132262.i		−	1.78520i
$43$	−24225.9	−	75726.3i	−0.304702	−	0.952448i
$43$	−24225.9	−	75726.3i	−0.304702	−	0.952448i
$44$	121970.			1.43185
$45$			63192.8i			0.693474i
$46$	217865.	+	125784.i	2.23827	+	1.29227i
$47$	−146686.			−1.41284			−0.706422	−	0.707791i	$-0.749692\pi$
$47$	−146686.			−1.41284			−0.706422	+	0.707791i	$0.749692\pi$
$48$	−153712.	−	88745.5i	−1.38990	−	0.802458i
$49$	−18734.0	+	32448.2i	−0.159236	+	0.275805i
$50$	163203.	−	94225.4i	1.30563	−	0.753803i
$51$			252307.i			1.90204i
$52$	−137419.	−	238017.i	−0.977321	−	1.69277i
$53$	57188.6	−	99053.6i	0.384133	−	0.665338i	−0.607515	−	0.794308i	$-0.707834\pi$
$53$	57188.6	−	99053.6i	0.384133	−	0.665338i	0.991649	+	0.128970i	$0.0411670\pi$
$54$	167199.			1.06182
$55$	−133924.	−	77321.1i	−0.804953	−	0.464740i
$56$	−140230.	−	242886.i	−0.798505	−	1.38305i
$57$	−109418.	−	189518.i	−0.590835	−	1.02336i
$58$	−161695.	−	280063.i	−0.828728	−	1.43540i
$59$	−93833.8			−0.456881			−0.228440	−	0.973558i	$-0.573363\pi$
$59$	−93833.8			−0.456881			−0.228440	+	0.973558i	$0.573363\pi$
$60$	379398.	+	657137.i	1.75647	+	3.04230i
$61$	−171840.	+	99211.9i	−0.757068	+	0.437093i	−0.828242	−	0.560371i	$-0.810659\pi$
$61$	−171840.	+	99211.9i	−0.757068	+	0.437093i	0.0711742	+	0.997464i	$0.477325\pi$
$62$	581233.	+	335575.i	2.43880	+	1.40804i
$63$	−90988.6	−	52532.3i	−0.363886	−	0.210090i
$64$	173848.			0.663176
$65$			348459.i			1.26885i
$66$	212055.	−	367291.i	0.737594	−	1.27755i
$67$	82442.2	−	142794.i	0.274110	−	0.474773i	−0.695800	−	0.718236i	$-0.744950\pi$
$67$	82442.2	−	142794.i	0.274110	−	0.474773i	0.969910	+	0.243463i	$0.0782833\pi$
$68$	510939.	+	884972.i	1.62496	+	2.81451i
$69$	513093.	−	296235.i	1.56189	−	0.901755i
$70$			679168.i			1.98008i
$71$	−593710.	+	342779.i	−1.65882	+	0.957720i	−0.685560	+	0.728017i	$0.740442\pi$
$71$	−593710.	+	342779.i	−1.65882	+	0.957720i	−0.973261	+	0.229704i	$0.926224\pi$
$72$	−318264.	+	183750.i	−0.852687	+	0.492299i
$73$	−9402.34	+	5428.44i	−0.0241695	+	0.0139543i	−0.512036	−	0.858964i	$-0.671109\pi$
$73$	−9402.34	+	5428.44i	−0.0241695	+	0.0139543i	0.487867	+	0.872918i	$0.337775\pi$
$74$	361454.	−	626056.i	0.891985	−	1.54496i
$75$		−	443821.i		−	1.05202i
$76$	−767575.	−	443159.i	−1.74856	−	1.00953i
$77$	222663.	−	128554.i	0.487725	−	0.281588i
$78$	−955658.			−2.01381
$79$	201033.	+	348199.i	0.407742	+	0.706229i	0.994636	−	0.103434i	$-0.0329831\pi$
$79$	201033.	+	348199.i	0.407742	+	0.706229i	−0.586895	+	0.809663i	$0.699650\pi$
$80$	789314.	+	455711.i	1.54163	+	0.890060i
$81$	332129.	−	575265.i	0.624960	−	1.08246i
$82$			805177.i			1.46033i
$83$	134493.	−	232949.i	0.235215	−	0.407405i	−0.724120	−	0.689674i	$-0.757754\pi$
$83$	134493.	−	232949.i	0.235215	−	0.407405i	0.959335	+	0.282269i	$0.0910872\pi$
$84$	−1.26158e6			−2.12851
$85$		−	1.29561e6i		−	2.10968i
$86$	−1.06645e6	+	341173.i	−1.67666	+	0.536389i
$87$	−761615.			−1.15659
$88$		−	899325.i		−	1.31968i
$89$	341386.	+	197099.i	0.484257	+	0.279586i	0.722189	−	0.691696i	$-0.243136\pi$
$89$	341386.	+	197099.i	0.484257	+	0.279586i	−0.237932	+	0.971282i	$0.576469\pi$
$90$	889943.			1.22077
$91$	−501730.	−	289674.i	−0.665804	−	0.384402i
$92$	1.19979e6	−	2.07810e6i	1.54078	−	2.66872i
$93$	1.36886e6	−	790314.i	1.70181	−	0.982541i
$94$			2.06577e6i			2.48713i
$95$	561867.	+	973183.i	0.655335	+	1.13507i
$96$	−198589.	+	343966.i	−0.224461	+	0.388778i
$97$	−1.75894e6			−1.92724			−0.963620	−	0.267277i	$-0.913876\pi$
$97$	−1.75894e6			−1.92724			−0.963620	+	0.267277i	$0.913876\pi$
$98$	456968.	+	263830.i	0.485520	+	0.280315i
$99$	−168450.	−	291764.i	−0.173606	−	0.300695i
$100$	−898767.	−	1.55671e6i	−0.898767	−	1.55671i
$101$	173349.	+	300249.i	0.168251	+	0.291419i	0.937805	−	0.347163i	$-0.112855\pi$
$101$	173349.	+	300249.i	0.168251	+	0.291419i	−0.769554	+	0.638581i	$0.779522\pi$
$102$	3.55323e6			3.34829
$103$	−538377.	−	932496.i	−0.492691	−	0.853366i	0.507273	−	0.861785i	$-0.330653\pi$
$103$	−538377.	−	932496.i	−0.492691	−	0.853366i	−0.999965	+	0.00841907i	$0.997320\pi$
$104$	−1.75497e6	+	1.01323e6i	−1.56016	+	0.900761i
$105$	1.38522e6	+	799756.i	1.19660	+	0.690859i
$106$	−1.39497e6	−	805386.i	−1.17124	−	0.676217i
$107$	−54696.5			−0.0446486			−0.0223243	−	0.999751i	$-0.507107\pi$
$107$	−54696.5			−0.0446486			−0.0223243	+	0.999751i	$0.507107\pi$
$108$		−	1.59482e6i		−	1.26602i
$109$	−1.01099e6	+	1.75109e6i	−0.780670	+	1.35216i	0.150882	+	0.988552i	$0.451788\pi$
$109$	−1.01099e6	+	1.75109e6i	−0.780670	+	1.35216i	−0.931552	+	0.363608i	$0.881545\pi$
$110$	−1.08891e6	+	1.88605e6i	−0.818115	+	1.41702i
$111$	−851261.	−	1.47443e6i	−0.622435	−	1.07809i
$112$	−1.31232e6	+	757666.i	−0.934081	+	0.539292i
$113$		−	53410.1i		−	0.0370159i	−0.999829	−	0.0185080i	$-0.994108\pi$
$113$		−	53410.1i		−	0.0370159i	0.999829	−	0.0185080i	$-0.00589160\pi$
$114$	−2.66898e6	+	1.54094e6i	−1.80149	+	1.04009i
$115$	−2.63475e6	+	1.52117e6i	−1.73239	+	1.00020i
$116$	−2.67138e6	+	1.54232e6i	−1.71144	+	0.988100i
$117$	−379572.	+	657438.i	−0.236994	+	0.410485i
$118$			1.32146e6i			0.804280i
$119$	1.86548e6	+	1.07704e6i	1.10701	+	0.639131i
$120$	4.84527e6	−	2.79742e6i	2.80398	−	1.61888i
$121$	−947116.			−0.534622
$122$	1.39720e6	+	2.42002e6i	0.769447	+	1.33272i
$123$	1.64222e6	+	948137.i	0.882503	+	0.509514i
$124$	3.20088e6	−	5.54408e6i	1.67882	−	2.90780i
$125$		−	382104.i		−	0.195637i
$126$	−739811.	+	1.28139e6i	−0.369836	+	0.640574i
$127$	3.53436e6			1.72544			0.862719	−	0.505684i	$-0.168760\pi$
$127$	3.53436e6			1.72544			0.862719	+	0.505684i	$0.168760\pi$
$128$		−	3.21470e6i		−	1.53289i
$129$	−559951.	+	2.57686e6i	−0.260844	+	1.20039i
$130$	4.90733e6			2.23365
$131$		−	345718.i		−	0.153783i	−0.997039	−	0.0768916i	$-0.975500\pi$
$131$		−	345718.i		−	0.153783i	0.997039	−	0.0768916i	$-0.0244995\pi$
$132$	−3.50339e6	−	2.02269e6i	−1.52324	−	0.879441i
$133$	−1.86832e6			−0.794140
$134$	−2.01097e6	−	1.16103e6i	−0.835777	−	0.482536i
$135$	−1.01101e6	+	1.75112e6i	−0.410918	+	0.711731i
$136$	6.52517e6	−	3.76731e6i	2.59403	−	1.49766i
$137$		−	1.21745e6i		−	0.473467i	−0.971575	−	0.236733i	$-0.923923\pi$
$137$		−	1.21745e6i		−	0.473467i	0.971575	−	0.236733i	$-0.0760768\pi$
$138$	−4.17186e6	−	7.22588e6i	−1.58742	−	2.74950i
$139$	−669754.	+	1.16005e6i	−0.249385	+	0.431948i	−0.963355	−	0.268228i	$-0.913562\pi$
$139$	−669754.	+	1.16005e6i	−0.249385	+	0.431948i	0.713970	+	0.700176i	$0.246895\pi$
$140$	6.47823e6			2.36087
$141$	4.21330e6	+	2.43255e6i	1.50302	+	0.867770i
$142$	4.82734e6	+	8.36120e6i	1.68594	+	2.92014i
$143$	−928870.	−	1.60885e6i	−0.317648	−	0.550183i
$144$	992802.	+	1.71958e6i	0.332487	+	0.575885i
$145$	3.91092e6			1.28285
$146$	76448.6	+	132413.i	0.0245647	+	0.0425473i
$147$	1.07621e6	−	621348.i	0.338800	−	0.195606i
$148$	−5.97163e6	−	3.44772e6i	−1.84208	−	1.06352i
$149$	−1.54250e6	−	890560.i	−0.466300	−	0.269218i	0.248390	−	0.968660i	$-0.420099\pi$
$149$	−1.54250e6	−	890560.i	−0.466300	−	0.269218i	−0.714689	+	0.699442i	$0.753432\pi$
$150$	−6.25032e6			−1.85195
$151$		−	3.15162e6i		−	0.915384i	−0.889111	−	0.457692i	$-0.848676\pi$
$151$		−	3.15162e6i		−	0.915384i	0.889111	−	0.457692i	$-0.151324\pi$
$152$	−3.26755e6	+	5.65956e6i	−0.930447	+	1.61158i
$153$	1.41129e6	−	2.44442e6i	0.394041	−	0.682499i
$154$	−1.81043e6	−	3.13575e6i	−0.495700	−	0.858577i
$155$	−7.02916e6	+	4.05829e6i	−1.88759	+	1.08980i
$156$			9.11552e6i			2.40109i
$157$	−1.70149e6	+	982356.i	−0.439674	+	0.253846i	−0.703459	−	0.710736i	$-0.748362\pi$
$157$	−1.70149e6	+	982356.i	−0.439674	+	0.253846i	0.263785	+	0.964581i	$0.415029\pi$
$158$	4.90367e6	−	2.83114e6i	1.24323	−	0.717777i
$159$	−3.28530e6	+	1.89677e6i	−0.817303	+	0.471870i
$160$	1.01976e6	−	1.76628e6i	0.248965	−	0.431220i
$161$		−	5.05822e6i		−	1.21205i
$162$	−8.10144e6	−	4.67737e6i	−1.90554	−	1.10016i
$163$	3.19760e6	−	1.84614e6i	0.738349	−	0.426286i	−0.0831199	−	0.996540i	$-0.526488\pi$
$163$	3.19760e6	−	1.84614e6i	0.738349	−	0.426286i	0.821469	+	0.570254i	$0.193155\pi$
$164$	7.68016e6			1.74116
$165$	2.56450e6	+	4.44184e6i	0.570887	+	0.988806i
$166$	−3.28061e6	−	1.89406e6i	−0.717184	−	0.414066i
$167$	3.37967e6	−	5.85375e6i	0.725645	−	1.25685i	−0.233063	−	0.972462i	$-0.574875\pi$
$167$	3.37967e6	−	5.85375e6i	0.725645	−	1.25685i	0.958708	−	0.284393i	$-0.0917919\pi$
$168$			9.30199e6i			1.96177i
$169$	320363.	−	554884.i	0.0663715	−	0.114959i
$170$	−1.82460e7			−3.71381
$171$			2.44814e6i			0.489608i
$172$	3.25427e6	+	1.01723e7i	0.639541	+	1.99910i
$173$	7.24589e6			1.39944			0.699719	−	0.714418i	$-0.253309\pi$
$173$	7.24589e6			1.39944			0.699719	+	0.714418i	$0.253309\pi$
$174$			1.07258e7i			2.03602i
$175$	−3.28148e6	−	1.89456e6i	−0.612288	−	0.353505i
$176$	−4.85907e6			−0.891281
$177$	2.69522e6	+	1.55609e6i	0.486042	+	0.280617i
$178$	2.77575e6	−	4.80773e6i	0.492175	−	0.852472i
$179$	818613.	−	472626.i	0.142731	−	0.0824060i	−0.426934	−	0.904283i	$-0.640406\pi$
$179$	818613.	−	472626.i	0.142731	−	0.0824060i	0.569665	+	0.821877i	$0.307073\pi$
$180$		−	8.48870e6i		−	1.45554i
$181$	1.84184e6	+	3.19016e6i	0.310610	+	0.537992i	0.978495	−	0.206272i	$-0.0661333\pi$
$181$	1.84184e6	+	3.19016e6i	0.310610	+	0.537992i	−0.667884	+	0.744265i	$0.732800\pi$
$182$	−4.07947e6	+	7.06585e6i	−0.676690	+	1.17206i
$183$	6.58109e6			1.07385
$184$	−1.53224e7	−	8.84642e6i	−2.45966	−	1.42008i
$185$	4.37125e6	+	7.57123e6i	0.690384	+	1.19578i
$186$	−1.11300e7	−	1.92777e7i	−1.72964	−	2.99582i
$187$	3.45363e6	+	5.98187e6i	0.528143	+	0.914770i
$188$	1.97043e7			2.96543
$189$	−1.68091e6	−	2.91142e6i	−0.248977	−	0.431241i
$190$	1.37053e7	−	7.91276e6i	1.99815	−	1.15363i
$191$	−1.76482e6	−	1.01892e6i	−0.253280	−	0.146231i	0.367985	−	0.929832i	$-0.380048\pi$
$191$	−1.76482e6	−	1.01892e6i	−0.253280	−	0.146231i	−0.621265	+	0.783600i	$0.713381\pi$
$192$	−4.99348e6	−	2.88299e6i	−0.705504	−	0.407323i
$193$	−5.79058e6			−0.805471			−0.402736	−	0.915316i	$-0.631941\pi$
$193$	−5.79058e6			−0.805471			−0.402736	+	0.915316i	$0.631941\pi$
$194$			2.47711e7i			3.39266i
$195$	5.77864e6	−	1.00089e7i	0.779331	−	1.34984i
$196$	2.51654e6	−	4.35878e6i	0.334222	−	0.578890i
$197$	−671430.	−	1.16295e6i	−0.0878218	−	0.152112i	0.818768	−	0.574124i	$-0.194657\pi$
$197$	−671430.	−	1.16295e6i	−0.0878218	−	0.152112i	−0.906590	+	0.422012i	$0.861324\pi$
$198$	−4.10891e6	+	2.37228e6i	−0.529335	+	0.305612i
$199$		−	8.49116e6i		−	1.07748i	−0.842473	−	0.538738i	$-0.818901\pi$
$199$		−	8.49116e6i		−	1.07748i	0.842473	−	0.538738i	$-0.181099\pi$
$200$	−1.14781e7	+	6.62688e6i	−1.43476	+	0.828360i
$201$	−4.73603e6	+	2.73435e6i	−0.583212	+	0.336718i
$202$	4.22840e6	−	2.44127e6i	0.513005	−	0.296184i
$203$	−3.25115e6	+	5.63116e6i	−0.388641	+	0.673147i
$204$		−	3.38924e7i		−	3.99220i
$205$	−8.43286e6	−	4.86871e6i	−0.978844	−	0.565136i
$206$	−1.31323e7	+	7.58195e6i	−1.50224	+	0.867320i
$207$	−6.62799e6			−0.747259
$208$	5.47452e6	+	9.48215e6i	0.608353	+	1.05370i
$209$	−5.18833e6	−	2.99549e6i	−0.568315	−	0.328117i
$210$	1.12629e7	−	1.95080e7i	1.21617	−	2.10647i
$211$			3.61400e6i			0.384717i	0.981325	+	0.192358i	$0.0616136\pi$
$211$			3.61400e6i			0.384717i	−0.981325	+	0.192358i	$0.938386\pi$
$212$	−7.68215e6	+	1.33059e7i	−0.806261	+	1.39648i
$213$	2.27378e7			2.35293
$214$			770289.i			0.0785981i
$215$	2.87537e6	−	1.32323e7i	0.289320	−	1.33143i
$216$	−1.17591e7			−1.16685
$217$		−	1.34946e7i		−	1.32063i
$218$	2.46605e7	+	1.42377e7i	2.38030	+	1.37427i
$219$	360089.			0.0342829
$220$	1.79900e7	+	1.03866e7i	1.68952	+	0.975447i
$221$	7.78214e6	−	1.34791e7i	0.720979	−	1.24877i
$222$	−2.07643e7	+	1.19883e7i	−1.89784	+	1.09572i
$223$			6.63689e6i			0.598480i	0.954178	+	0.299240i	$0.0967331\pi$
$223$			6.63689e6i			0.598480i	−0.954178	+	0.299240i	$0.903267\pi$
$224$	1.69546e6	+	2.93662e6i	0.150849	+	0.261278i
$225$	−2.48253e6	+	4.29986e6i	−0.217945	+	0.377491i
$226$	−752174.			−0.0651618
$227$	−2.38739e6	−	1.37836e6i	−0.204101	−	0.117838i	0.394466	−	0.918911i	$-0.370930\pi$
$227$	−2.38739e6	−	1.37836e6i	−0.204101	−	0.117838i	−0.598567	+	0.801073i	$0.704263\pi$
$228$	1.46982e7	+	2.54580e7i	1.24011	+	2.14793i
$229$	1.05828e7	+	1.83300e7i	0.881242	+	1.52636i	0.849961	+	0.526845i	$0.176625\pi$
$229$	1.05828e7	+	1.83300e7i	0.881242	+	1.52636i	0.0312804	+	0.999511i	$0.490042\pi$
$230$	2.14227e7	+	3.71051e7i	1.76072	+	3.04965i
$231$	−8.52748e6			−0.691807
$232$	1.13720e7	+	1.96969e7i	0.910696	+	1.57737i
$233$	−5.02056e6	+	2.89862e6i	−0.396903	+	0.229152i	−0.685147	−	0.728405i	$-0.740262\pi$
$233$	−5.02056e6	+	2.89862e6i	−0.396903	+	0.229152i	0.288244	+	0.957557i	$0.406929\pi$
$234$	9.25869e6	+	5.34551e6i	0.722606	+	0.417197i
$235$	−2.16354e7	−	1.24912e7i	−1.66710	−	0.962502i
$236$	1.26047e7			0.958951
$237$		−	1.33352e7i		−	1.00174i
$238$	1.51679e7	−	2.62716e7i	1.12511	−	1.94875i
$239$	7.08410e6	−	1.22700e7i	0.518909	−	0.898777i	−0.480850	−	0.876803i	$-0.659672\pi$
$239$	7.08410e6	−	1.22700e7i	0.518909	−	0.898777i	0.999759	−	0.0219736i	$-0.00699499\pi$
$240$	−1.51145e7	−	2.61791e7i	−1.09335	−	1.89374i
$241$	−1.47331e7	+	8.50617e6i	−1.05255	+	0.607691i	−0.923363	−	0.383928i	$-0.874571\pi$
$241$	−1.47331e7	+	8.50617e6i	−1.05255	+	0.607691i	−0.129190	+	0.991620i	$0.541238\pi$
$242$			1.33382e7i			0.941134i
$243$	−1.15843e7	+	6.68819e6i	−0.807328	+	0.466111i
$244$	2.30833e7	−	1.33271e7i	1.58902	−	0.917419i
$245$	−5.52635e6	+	3.19064e6i	−0.375786	+	0.216960i
$246$	1.33526e7	−	2.31274e7i	0.896933	−	1.55353i
$247$			1.34996e7i			0.895838i
$248$	−4.08782e7	−	2.36010e7i	−2.68001	−	1.54731i
$249$	−7.72617e6	+	4.46071e6i	−0.500457	+	0.288939i
$250$	−5.38115e6			−0.344394
$251$	6.64795e6	+	1.15146e7i	0.420404	+	0.728161i	0.995979	−	0.0895881i	$-0.0285551\pi$
$251$	6.64795e6	+	1.15146e7i	0.420404	+	0.728161i	−0.575575	+	0.817749i	$0.695222\pi$
$252$	1.22225e7	+	7.05667e6i	0.763763	+	0.440959i
$253$	8.10984e6	−	1.40467e7i	0.500785	−	0.867384i
$254$		−	4.97742e7i		−	3.03741i
$255$	−2.14856e7	+	3.72141e7i	−1.29577	+	2.24433i
$256$	−3.41463e7			−2.03528
$257$			2.87939e7i			1.69629i	0.529763	+	0.848146i	$0.322281\pi$
$257$			2.87939e7i			1.69629i	−0.529763	+	0.848146i	$0.677719\pi$
$258$	3.62898e7	+	7.88578e6i	2.11313	+	0.459183i
$259$	−1.45353e7			−0.836614
$260$		−	4.68085e7i		−	2.66321i
$261$	7.37875e6	+	4.26012e6i	0.415012	+	0.239607i
$262$	−4.86874e6			−0.270715
$263$	3.78969e6	+	2.18798e6i	0.208322	+	0.120275i	0.600532	−	0.799601i	$-0.294956\pi$
$263$	3.78969e6	+	2.18798e6i	0.208322	+	0.120275i	−0.392209	+	0.919876i	$0.628289\pi$
$264$	−1.49139e7	+	2.58316e7i	−0.810549	+	1.40391i
$265$	1.68701e7	−	9.73996e6i	0.906525	−	0.523383i
$266$			2.63116e7i			1.39798i
$267$	−6.53717e6	−	1.13227e7i	−0.343444	−	0.594862i
$268$	−1.10745e7	+	1.91816e7i	−0.575332	+	0.996505i
$269$	−1.36480e7			−0.701154			−0.350577	−	0.936534i	$-0.614015\pi$
$269$	−1.36480e7			−0.701154			−0.350577	+	0.936534i	$0.614015\pi$
$270$	2.46610e7	+	1.42381e7i	1.25291	+	0.723368i
$271$	3.38080e6	+	5.85572e6i	0.169868	+	0.294220i	0.938373	−	0.345623i	$-0.112332\pi$
$271$	3.38080e6	+	5.85572e6i	0.169868	+	0.294220i	−0.768505	+	0.639844i	$0.778999\pi$
$272$	−2.03548e7	−	3.52556e7i	−1.01149	−	1.75195i
$273$	9.60758e6	+	1.66408e7i	0.472200	+	0.817874i
$274$	−1.71453e7			−0.833477
$275$	−6.07511e6	−	1.05224e7i	−0.292117	−	0.505961i
$276$	−6.89239e7	+	3.97932e7i	−3.27825	+	1.89270i
$277$	6.82908e6	+	3.94277e6i	0.321309	+	0.185508i	0.651976	−	0.758240i	$-0.273940\pi$
$277$	6.82908e6	+	3.94277e6i	0.321309	+	0.185508i	−0.330667	+	0.943748i	$0.607274\pi$
$278$	1.63369e7	+	9.43213e6i	0.760390	+	0.439011i
$279$	−1.76826e7			−0.814204
$280$		−	4.77660e7i		−	2.17593i
$281$	4.10719e6	−	7.11386e6i	0.185108	−	0.320617i	−0.758505	−	0.651668i	$-0.774070\pi$
$281$	4.10719e6	−	7.11386e6i	0.185108	−	0.320617i	0.943613	+	0.331051i	$0.107403\pi$
$282$	3.42575e7	−	5.93358e7i	1.52760	−	2.64588i
$283$	−1.10085e7	−	1.90673e7i	−0.485701	−	0.841259i	0.514164	−	0.857692i	$-0.328102\pi$
$283$	−1.10085e7	−	1.90673e7i	−0.485701	−	0.841259i	−0.999865	+	0.0164329i	$0.994769\pi$
$284$	7.97531e7	−	4.60455e7i	3.48171	−	2.01017i
$285$		−	3.72707e7i		−	1.61003i
$286$	−2.26574e7	+	1.30812e7i	−0.968527	+	0.559179i
$287$	1.40205e7	−	8.09474e6i	0.593086	−	0.342418i
$288$	3.84797e6	−	2.22163e6i	0.161085	−	0.0930024i
$289$	−1.68660e7	+	2.92128e7i	−0.698746	+	1.21026i
$290$		−	5.50774e7i		−	2.25829i
$291$	5.05226e7	+	2.91692e7i	2.05025	+	1.18371i
$292$	1.26302e6	−	729203.i	0.0507295	−	0.0292887i
$293$	9.03522e6			0.359200			0.179600	−	0.983740i	$-0.442520\pi$
$293$	9.03522e6			0.359200			0.179600	+	0.983740i	$0.442520\pi$
$294$	−8.75042e6	−	1.51562e7i	−0.344340	−	0.596414i
$295$	−1.38400e7	−	7.99055e6i	−0.539102	−	0.311251i
$296$	−2.54211e7	+	4.40306e7i	−0.980210	+	1.69777i
$297$		−	1.07800e7i		−	0.411482i
$298$	−1.25417e7	+	2.17229e7i	−0.473924	+	0.820861i
$299$	−3.65482e7			−1.36726
$300$			5.96185e7i			2.20809i
$301$	1.66622e7	+	1.51401e7i	0.610990	+	0.555174i
$302$	−4.43842e7			−1.61142
$303$		−	1.14989e7i		−	0.413359i
$304$	3.05787e7	+	1.76546e7i	1.08842	+	0.628402i
$305$	−3.37941e7			−1.19108
$306$	−3.44247e7	−	1.98751e7i	−1.20145	−	0.693659i
$307$	−5.29128e6	+	9.16477e6i	−0.182871	+	0.316742i	−0.942857	−	0.333197i	$-0.891873\pi$
$307$	−5.29128e6	+	9.16477e6i	−0.182871	+	0.316742i	0.759986	+	0.649940i	$0.225206\pi$
$308$	−2.99103e7	+	1.72687e7i	−1.02369	+	0.591028i
$309$			3.57125e7i			1.21045i
$310$	5.71528e7	+	9.89915e7i	1.91846	+	3.32287i
$311$	1.26179e7	−	2.18549e7i	0.419476	−	0.726553i	−0.576411	−	0.817160i	$-0.695547\pi$
$311$	1.26179e7	−	2.18549e7i	0.419476	−	0.726553i	0.995887	+	0.0906068i	$0.0288807\pi$
$312$	6.72116e7			2.21299
$313$	−1.70090e7	−	9.82013e6i	−0.554683	−	0.320246i	0.196326	−	0.980539i	$-0.437099\pi$
$313$	−1.70090e7	−	9.82013e6i	−0.554683	−	0.320246i	−0.751009	+	0.660292i	$0.770432\pi$
$314$	1.38345e7	+	2.39621e7i	0.446863	+	0.773990i
$315$	−8.94692e6	−	1.54965e7i	−0.286248	−	0.495795i
$316$	−2.70047e7	−	4.67736e7i	−0.855812	−	1.48231i
$317$	3.29909e7			1.03566			0.517830	−	0.855484i	$-0.326740\pi$
$317$	3.29909e7			1.03566			0.517830	+	0.855484i	$0.326740\pi$
$318$	2.67121e7	+	4.62667e7i	0.830667	+	1.43876i
$319$	−1.80569e7	+	1.04251e7i	−0.556251	+	0.321152i
$320$	2.56417e7	+	1.48042e7i	0.782522	+	0.451789i
$321$	1.57106e6	+	907055.i	0.0474984	+	0.0274232i
$322$	−7.12347e7			−2.13365
$323$		−	5.01928e7i		−	1.48948i
$324$	−4.46150e7	+	7.72754e7i	−1.31173	+	2.27199i
$325$	−1.36892e7	+	2.37104e7i	−0.398775	+	0.690698i
$326$	−2.59991e7	−	4.50317e7i	−0.750421	−	1.29977i
$327$	5.80780e7	−	3.35313e7i	1.66100	−	0.958976i
$328$		−	5.66282e7i		−	1.60476i
$329$	3.59711e7	−	2.07679e7i	1.01010	−	0.583184i
$330$	6.25543e7	−	3.61158e7i	1.74067	−	1.00497i
$331$	−3.17877e7	+	1.83526e7i	−0.876546	+	0.506074i	−0.869518	−	0.493901i	$-0.835570\pi$
$331$	−3.17877e7	+	1.83526e7i	−0.876546	+	0.506074i	−0.00702805	+	0.999975i	$0.502237\pi$
$332$	−1.80665e7	+	3.12920e7i	−0.493695	+	0.855105i
$333$			1.90462e7i			0.515794i
$334$	−8.24382e7	−	4.75957e7i	−2.21253	−	1.27741i
$335$	2.43197e7	−	1.40410e7i	0.646880	−	0.373476i
$336$	5.02588e7			1.32493
$337$	1.93373e7	+	3.34931e7i	0.505249	+	0.875117i	0.999982	+	0.00607192i	$0.00193277\pi$
$337$	1.93373e7	+	3.34931e7i	0.505249	+	0.875117i	−0.494732	+	0.869045i	$0.664734\pi$
$338$	−7.81442e6	−	4.51166e6i	−0.202370	−	0.116839i
$339$	−885723.	+	1.53412e6i	−0.0227352	+	0.0393785i
$340$			1.74039e8i			4.42802i
$341$	2.16360e7	−	3.74746e7i	0.545649	−	0.945091i
$342$	3.44771e7			0.861892
$343$		−	4.39233e7i		−	1.08846i
$344$	7.50036e7	−	2.39948e7i	1.84250	−	0.589442i
$345$	1.00905e8			2.45729
$346$		−	1.02044e8i		−	2.46353i
$347$	−4.84180e7	−	2.79542e7i	−1.15883	−	0.669049i	−0.207805	−	0.978170i	$-0.566632\pi$
$347$	−4.84180e7	−	2.79542e7i	−1.15883	−	0.669049i	−0.951023	+	0.309121i	$0.899965\pi$
$348$	1.02308e8			2.42757
$349$	3.93228e7	+	2.27030e7i	0.925055	+	0.534081i	0.885244	−	0.465126i	$-0.153991\pi$
$349$	3.93228e7	+	2.27030e7i	0.925055	+	0.534081i	0.0398109	+	0.999207i	$0.487324\pi$
$350$	−2.66811e7	+	4.62130e7i	−0.622300	+	1.07785i
$351$	−2.10365e7	+	1.21454e7i	−0.486466	+	0.280861i
$352$			1.08733e7i			0.249307i
$353$	−1.10551e7	−	1.91481e7i	−0.251328	−	0.435312i	0.712564	−	0.701607i	$-0.247534\pi$
$353$	−1.10551e7	−	1.91481e7i	−0.251328	−	0.435312i	−0.963892	+	0.266295i	$0.914200\pi$
$354$	2.19143e7	−	3.79567e7i	0.493990	−	0.855615i
$355$	−1.16759e8			−2.60979
$356$	−4.58585e7	−	2.64764e7i	−1.01641	−	0.586825i
$357$	−3.57220e7	−	6.18722e7i	−0.785110	−	1.35985i
$358$	−6.65598e6	−	1.15285e7i	−0.145065	−	0.251260i
$359$	3.02968e7	+	5.24755e7i	0.654806	+	1.13416i	0.981942	+	0.189181i	$0.0605831\pi$
$359$	3.02968e7	+	5.24755e7i	0.654806	+	1.13416i	−0.327136	+	0.944977i	$0.606084\pi$
$360$	−6.25898e7			−1.34152
$361$	−1.75572e6	−	3.04099e6i	−0.0373193	−	0.0646389i
$362$	4.49269e7	−	2.59385e7i	0.947067	−	0.546789i
$363$	2.72043e7	+	1.57064e7i	0.568746	+	0.328366i
$364$	6.73975e7	+	3.89120e7i	1.39746	+	0.806824i
$365$	−1.84907e6			−0.0380254
$366$		−	9.26813e7i		−	1.89038i
$367$	−3.58199e7	+	6.20418e7i	−0.724646	+	1.25512i	0.234474	+	0.972122i	$0.424663\pi$
$367$	−3.58199e7	+	6.20418e7i	−0.724646	+	1.25512i	−0.959120	+	0.283001i	$0.908670\pi$
$368$	−4.77973e7	+	8.27874e7i	−0.959092	+	1.66120i
$369$	−1.06069e7	−	1.83716e7i	−0.211110	−	0.365653i
$370$	1.06625e8	−	6.15602e7i	2.10502	−	1.21533i
$371$			3.23873e7i			0.634240i
$372$	−1.83880e8	+	1.06163e8i	−3.57195	+	2.06226i
$373$	7.82604e7	−	4.51836e7i	1.50805	−	0.870672i	0.508093	−	0.861302i	$-0.330351\pi$
$373$	7.82604e7	−	4.51836e7i	1.50805	−	0.870672i	0.999956	−	0.00937000i	$-0.00298261\pi$
$374$	8.42425e7	−	4.86374e7i	1.61034	−	0.929727i
$375$	−6.33658e6	+	1.09753e7i	−0.120160	+	0.208124i
$376$		−	1.45286e8i		−	2.73313i
$377$	4.06880e7	+	2.34912e7i	0.759350	+	0.438411i
$378$	−4.10015e7	+	2.36722e7i	−0.759144	+	0.438292i
$379$	−8.65122e7			−1.58913			−0.794565	−	0.607179i	$-0.792301\pi$
$379$	−8.65122e7			−1.58913			−0.794565	+	0.607179i	$0.792301\pi$
$380$	−7.54757e7	−	1.30728e8i	−1.37549	−	2.38241i
$381$	−1.01518e8	−	5.86117e7i	−1.83557	−	1.05977i
$382$	−1.43494e7	+	2.48540e7i	−0.257422	+	0.445867i
$383$		−	2.79970e7i		−	0.498328i	−0.968461	−	0.249164i	$-0.919844\pi$
$383$		−	2.79970e7i		−	0.498328i	0.968461	−	0.249164i	$-0.0801557\pi$
$384$	−5.33107e7	+	9.23369e7i	−0.941501	+	1.63073i
$385$	4.37889e7			0.767329
$386$			8.15486e7i			1.41793i
$387$	1.98387e7	−	2.18332e7i	0.342279	−	0.376691i
$388$	2.36279e8			4.04510
$389$			8.21146e7i			1.39499i	0.716589	+	0.697496i	$0.245702\pi$
$389$			8.21146e7i			1.39499i	−0.716589	+	0.697496i	$0.754298\pi$
$390$	−1.40955e8	−	8.13804e7i	−2.37622	−	1.37191i
$391$	1.35890e8			2.27330
$392$	−3.21386e7	−	1.85552e7i	−0.533542	−	0.308041i
$393$	−5.73320e6	+	9.93019e6i	−0.0944537	+	0.163599i
$394$	−1.63778e7	+	9.45574e6i	−0.267773	+	0.154599i
$395$			6.84768e7i			1.11110i
$396$	2.26279e7	+	3.91927e7i	0.364384	+	0.631131i
$397$	−2.58987e7	+	4.48578e7i	−0.413910	+	0.716913i	−0.995313	−	0.0967024i	$-0.969170\pi$
$397$	−2.58987e7	+	4.48578e7i	−0.413910	+	0.716913i	0.581403	+	0.813615i	$0.302504\pi$
$398$	−1.19581e8			−1.89676
$399$	5.36645e7	+	3.09832e7i	0.844828	+	0.487762i
$400$	3.58052e7	+	6.20164e7i	0.559456	+	0.969005i
$401$	−1.36021e7	−	2.35595e7i	−0.210947	−	0.365370i	0.741064	−	0.671434i	$-0.234321\pi$
$401$	−1.36021e7	−	2.35595e7i	−0.210947	−	0.365370i	−0.952011	+	0.306064i	$0.900988\pi$
$402$	3.85078e7	+	6.66974e7i	0.592748	+	1.02667i
$403$	−9.75056e7			−1.48975
$404$	−2.32860e7	−	4.03325e7i	−0.353143	−	0.611661i
$405$	9.79750e7	−	5.65659e7i	1.47486	−	0.851509i
$406$	7.93035e7	+	4.57859e7i	1.18499	+	0.684153i
$407$	−4.03645e7	−	2.33045e7i	−0.598710	−	0.345665i
$408$	−2.49899e8			−3.67947
$409$		−	2.14296e7i		−	0.313216i	−0.987661	−	0.156608i	$-0.949944\pi$
$409$		−	2.14296e7i		−	0.313216i	0.987661	−	0.156608i	$-0.0500559\pi$
$410$	−6.85660e7	+	1.18760e8i	−0.994849	+	1.72313i
$411$	−2.01895e7	+	3.49692e7i	−0.290804	+	0.503687i
$412$	7.23202e7	+	1.25262e8i	1.03411	+	1.79114i
$413$	2.30105e7	−	1.32851e7i	0.326645	−	0.188588i
$414$			9.33419e7i			1.31545i
$415$	3.96742e7	−	2.29059e7i	0.555090	−	0.320481i
$416$	2.12185e7	−	1.22505e7i	0.294738	−	0.170167i
$417$	3.84752e7	−	2.22136e7i	0.530606	−	0.306346i
$418$	−4.21853e7	+	7.30672e7i	−0.577607	+	1.00045i
$419$			8.20658e7i			1.11563i	0.829965	+	0.557815i	$0.188360\pi$
$419$			8.20658e7i			1.11563i	−0.829965	+	0.557815i	$0.811640\pi$
$420$	−1.86076e8	−	1.07431e8i	−2.51156	−	1.45005i
$421$	141325.	−	81594.2i	0.00189397	−	0.00109349i	−0.499053	−	0.866572i	$-0.666319\pi$
$421$	141325.	−	81594.2i	0.00189397	−	0.00109349i	0.500947	+	0.865478i	$0.332985\pi$
$422$	5.08959e7			0.677244
$423$	−2.72131e7	−	4.71345e7i	−0.359548	−	0.622756i
$424$	9.81084e7	+	5.66429e7i	1.28709	+	0.743101i
$425$	5.08978e7	−	8.81575e7i	0.663028	−	1.14840i
$426$		−	3.20215e8i		−	4.14203i
$427$	2.80931e7	−	4.86586e7i	0.360841	−	0.624995i
$428$	7.34738e6			0.0937133
$429$			6.16154e7i			0.780400i
$430$	−1.86350e8	−	4.04937e7i	−2.34381	−	0.509310i
$431$	8.86033e7			1.10667			0.553335	−	0.832959i	$-0.313355\pi$
$431$	8.86033e7			1.10667			0.553335	+	0.832959i	$0.313355\pi$
$432$			6.35347e7i			0.788061i
$433$	−4.15534e7	−	2.39909e7i	−0.511851	−	0.295517i	0.221743	−	0.975105i	$-0.428825\pi$
$433$	−4.15534e7	−	2.39909e7i	−0.511851	−	0.295517i	−0.733594	+	0.679588i	$0.762159\pi$
$434$	−1.90045e8			−2.32480
$435$	−1.12335e8	−	6.48564e7i	−1.36473	−	0.787926i
$436$	1.35806e8	−	2.35224e8i	1.63855	−	2.83806i
$437$	−1.02073e8	+	5.89316e7i	−1.22311	+	0.706161i
$438$		−	5.07112e6i		−	0.0603506i
$439$	1.65111e6	+	2.85980e6i	0.0195156	+	0.0338020i	0.875618	−	0.483004i	$-0.160454\pi$
$439$	1.65111e6	+	2.85980e6i	0.0195156	+	0.0338020i	−0.856103	+	0.516806i	$0.827121\pi$
$440$	7.65833e7	−	1.32646e8i	0.899034	−	1.55717i
$441$	−1.39021e7			−0.162093
$442$	−1.89825e8	−	1.09596e8i	−2.19830	−	1.26919i
$443$	1.80243e7	+	3.12191e7i	0.207323	+	0.359095i	0.950871	−	0.309589i	$-0.100191\pi$
$443$	1.80243e7	+	3.12191e7i	0.207323	+	0.359095i	−0.743547	+	0.668684i	$0.766858\pi$
$444$	1.14350e8	+	1.98060e8i	1.30643	+	2.26281i
$445$	3.35686e7	+	5.81425e7i	0.380937	+	0.659802i
$446$	9.34671e7			1.05355
$447$	2.95371e7	+	5.11597e7i	0.330708	+	0.572803i
$448$	−4.26319e7	+	2.46136e7i	−0.474134	+	0.273741i
$449$	5.69002e7	+	3.28514e7i	0.628601	+	0.362923i	0.780210	−	0.625518i	$-0.215112\pi$
$449$	5.69002e7	+	3.28514e7i	0.628601	+	0.362923i	−0.151609	+	0.988441i	$0.548445\pi$
$450$	6.05549e7	+	3.49614e7i	0.664525	+	0.383664i
$451$	5.19132e7			0.565911
$452$			7.17459e6i			0.0776930i
$453$	−5.22647e7	+	9.05251e7i	−0.562230	+	0.973810i
$454$	−1.94114e7	+	3.36215e7i	−0.207438	+	0.359293i
$455$	−4.93352e7	−	8.54511e7i	−0.523749	−	0.907159i
$456$	1.87710e8	−	1.08374e8i	1.97967	−	1.14296i
$457$			4.05831e7i			0.425203i	0.977139	+	0.212601i	$0.0681936\pi$
$457$			4.05831e7i			0.425203i	−0.977139	+	0.212601i	$0.931806\pi$
$458$	2.58141e8	−	1.49038e8i	2.68695	−	1.55131i
$459$	7.82159e7	−	4.51580e7i	0.808829	−	0.466978i
$460$	3.53927e8	−	2.04340e8i	3.63613	−	2.09932i
$461$	4.76026e6	−	8.24501e6i	0.0485879	−	0.0841567i	−0.840709	−	0.541488i	$-0.817861\pi$
$461$	4.76026e6	−	8.24501e6i	0.0485879	−	0.0841567i	0.889296	+	0.457331i	$0.151195\pi$
$462$			1.20092e8i			1.21784i
$463$	−6.62323e7	−	3.82392e7i	−0.667309	−	0.385271i	0.127747	−	0.991807i	$-0.459225\pi$
$463$	−6.62323e7	−	3.82392e7i	−0.667309	−	0.385271i	−0.795056	+	0.606536i	$0.792559\pi$
$464$	1.06423e8	−	6.14432e7i	1.06532	−	0.615063i
$465$	2.69201e8			2.67743
$466$	4.08212e7	+	7.07044e7i	0.403393	+	0.698696i
$467$	5.72154e7	+	3.30333e7i	0.561774	+	0.324341i	0.753857	−	0.657038i	$-0.228191\pi$
$467$	5.72154e7	+	3.30333e7i	0.561774	+	0.324341i	−0.192083	+	0.981379i	$0.561524\pi$
$468$	5.09880e7	−	8.83138e7i	0.497428	−	0.861571i
$469$			4.66891e7i			0.452582i
$470$	−1.75914e8	+	3.04691e8i	−1.69436	+	2.93472i
$471$	6.51633e7			0.623649
$472$		−	9.29383e7i		−	0.883830i
$473$	2.19969e7	+	6.87586e7i	0.207863	+	0.649746i
$474$	−1.87800e8			−1.76344
$475$			8.82917e7i			0.823833i
$476$	−2.50591e8	−	1.44679e8i	−2.32351	−	1.34148i
$477$	4.24385e7			0.391025
$478$	−1.72798e8	−	9.97652e7i	−1.58218	−	0.913473i
$479$	2.63590e7	−	4.56552e7i	0.239841	−	0.415417i	−0.720828	−	0.693114i	$-0.756238\pi$
$479$	2.63590e7	−	4.56552e7i	0.239841	−	0.415417i	0.960668	+	0.277698i	$0.0895714\pi$
$480$	−5.85819e7	+	3.38223e7i	−0.529712	+	0.305829i
$481$			1.05025e8i			0.943750i
$482$	1.19792e8	+	2.07486e8i	1.06976	+	1.85288i
$483$	−8.38825e7	+	1.45289e8i	−0.744441	+	1.28941i
$484$	1.27226e8			1.12212
$485$	−2.59435e8	−	1.49785e8i	−2.27407	−	1.31293i
$486$	9.41895e7	+	1.63141e8i	0.820529	+	1.42120i
$487$	8.56781e7	+	1.48399e8i	0.741794	+	1.28482i	0.951678	+	0.307098i	$0.0993579\pi$
$487$	8.56781e7	+	1.48399e8i	0.741794	+	1.28482i	−0.209884	+	0.977726i	$0.567309\pi$
$488$	−9.82651e7	−	1.70200e8i	−0.845551	−	1.46454i
$489$	−1.22461e8			−1.04730
$490$	4.49337e7	+	7.78274e7i	0.381930	+	0.661522i
$491$	−6.18762e7	+	3.57242e7i	−0.522732	+	0.301799i	−0.738052	−	0.674744i	$-0.764254\pi$
$491$	−6.18762e7	+	3.57242e7i	−0.522732	+	0.301799i	0.215320	+	0.976544i	$0.430921\pi$
$492$	−2.20600e8	−	1.27363e8i	−1.85229	−	1.06942i
$493$	−1.51282e8	−	8.73427e7i	−1.26254	−	0.728930i
$494$	1.90114e8			1.57701
$495$		−	5.73784e7i		−	0.473078i
$496$	−1.27517e8	+	2.20866e8i	−1.04501	+	1.81002i
$497$	9.70621e7	−	1.68116e8i	0.790643	−	1.36943i
$498$	6.28200e7	+	1.08808e8i	0.508640	+	0.880990i
$499$	2.56246e7	−	1.47944e7i	0.206232	−	0.119068i	−0.393327	−	0.919399i	$-0.628676\pi$
$499$	2.56246e7	−	1.47944e7i	0.206232	−	0.119068i	0.599559	+	0.800331i	$0.295343\pi$
$500$			5.13280e7i			0.410624i
$501$	−1.94151e8	+	1.12093e8i	−1.54392	+	0.891384i
$502$	1.62160e8	−	9.36229e7i	1.28183	−	0.740067i
$503$	−1.64720e8	+	9.51011e7i	−1.29432	+	0.747277i	−0.979417	−	0.201847i	$-0.935306\pi$
$503$	−1.64720e8	+	9.51011e7i	−1.29432	+	0.747277i	−0.314904	+	0.949123i	$0.601972\pi$
$504$	5.20310e7	−	9.01203e7i	0.406416	−	0.703933i
$505$			5.90470e7i			0.458484i
$506$	−1.97819e8	−	1.14211e8i	−1.52692	−	0.881567i
$507$	−1.84038e7	+	1.06254e7i	−0.141216	+	0.0815309i
$508$	−4.74771e8			−3.62153
$509$	−2.87007e7	−	4.97111e7i	−0.217640	−	0.376964i	0.736446	−	0.676497i	$-0.236503\pi$
$509$	−2.87007e7	−	4.97111e7i	−0.217640	−	0.376964i	−0.954086	+	0.299532i	$0.903169\pi$
$510$	5.24085e8	+	3.02581e8i	3.95086	+	2.28103i
$511$	1.53713e6	−	2.66239e6i	0.0115199	−	0.0199530i
$512$			2.75140e8i			2.04996i
$513$	−3.91675e7	+	6.78400e7i	−0.290117	+	0.502498i
$514$	4.05503e8			2.98610
$515$		−	1.83385e8i		−	1.34259i
$516$	7.52183e7	−	3.46150e8i	0.547488	−	2.51950i
$517$	1.33189e8			0.963822
$518$			2.04700e8i			1.47275i
$519$	−2.08126e8	−	1.20162e8i	−1.48876	−	0.859536i
$520$	−3.45134e8			−2.45458
$521$	7.88970e6	+	4.55512e6i	0.0557889	+	0.0322097i	0.527635	−	0.849471i	$-0.323079\pi$
$521$	7.88970e6	+	4.55512e6i	0.0557889	+	0.0322097i	−0.471846	+	0.881681i	$0.656412\pi$
$522$	5.99952e7	−	1.03915e8i	0.421798	−	0.730576i
$523$	−5.64368e7	+	3.25838e7i	−0.394509	+	0.227770i	−0.684112	−	0.729377i	$-0.739810\pi$
$523$	−5.64368e7	+	3.25838e7i	−0.394509	+	0.227770i	0.289603	+	0.957147i	$0.406477\pi$
$524$			4.64404e7i			0.322777i
$525$	6.28367e7	+	1.08836e8i	0.434246	+	0.752136i
$526$	3.08132e7	−	5.33700e7i	0.211729	−	0.366725i
$527$	3.62536e8			2.47696
$528$	1.39569e8	+	8.05800e7i	0.948169	+	0.547426i
$529$	−8.55308e7	−	1.48144e8i	−0.577770	−	1.00073i
$530$	−1.37168e8	−	2.37581e8i	−0.921348	−	1.59582i
$531$	−1.74080e7	−	3.01516e7i	−0.116270	−	0.201385i
$532$	2.50972e8			1.66683
$533$	−5.84886e7	−	1.01305e8i	−0.386268	−	0.669037i
$534$	−1.59457e8	+	9.20627e7i	−1.04718	+	0.604589i
$535$	−8.06747e6	−	4.65775e6i	−0.0526837	−	0.0304169i
$536$	1.41432e8	+	8.16555e7i	0.918442	+	0.530263i
$537$	−3.13510e7			−0.202455
$538$			1.92205e8i			1.23429i
$539$	1.70103e7	−	2.94627e7i	0.108629	−	0.188151i
$540$	1.35809e8	−	2.35229e8i	0.862479	−	1.49386i
$541$	−7.35142e7	−	1.27330e8i	−0.464279	−	0.804155i	0.534889	−	0.844922i	$-0.320353\pi$
$541$	−7.35142e7	−	1.27330e8i	−0.464279	−	0.804155i	−0.999169	+	0.0407668i	$0.987020\pi$
$542$	8.24660e7	−	4.76118e7i	0.517937	−	0.299031i
$543$		−	1.22176e8i		−	0.763108i
$544$	−7.88927e7	+	4.55487e7i	−0.490050	+	0.282930i
$545$	−2.98232e8	+	1.72185e8i	−1.84232	+	1.06366i
$546$	2.34352e8	−	1.35303e8i	1.43976	−	0.831247i
$547$	1.20188e8	−	2.08172e8i	0.734345	−	1.27192i	−0.220665	−	0.975350i	$-0.570823\pi$
$547$	1.20188e8	−	2.08172e8i	0.734345	−	1.27192i	0.955010	−	0.296573i	$-0.0958439\pi$
$548$			1.63540e8i			0.993763i
$549$	−6.37595e7	−	3.68115e7i	−0.385325	−	0.222468i
$550$	−1.48187e8	+	8.55556e7i	−0.890679	+	0.514234i
$551$	1.51512e8			0.905718
$552$	2.93408e8	+	5.08197e8i	1.74443	+	3.02145i
$553$	−9.85968e7	−	5.69249e7i	−0.583025	−	0.336610i
$554$	5.55259e7	−	9.61737e7i	0.326563	−	0.565623i
$555$		−	2.89961e8i		−	1.69614i
$556$	8.99682e7	−	1.55830e8i	0.523437	−	0.906620i
$557$	−3.05594e8			−1.76839			−0.884196	−	0.467116i	$-0.845293\pi$
$557$	−3.05594e8			−1.76839			−0.884196	+	0.467116i	$0.845293\pi$
$558$			2.49023e8i			1.43330i
$559$	1.09395e8	−	1.20393e8i	0.626270	−	0.689233i
$560$	−2.58080e8			−1.46957
$561$		−	2.29092e8i		−	1.29754i
$562$	−1.00184e8	−	5.78415e7i	−0.564405	−	0.325859i
$563$	3.11950e8			1.74808			0.874038	−	0.485857i	$-0.161492\pi$
$563$	3.11950e8			1.74808			0.874038	+	0.485857i	$0.161492\pi$
$564$	−5.65973e8	−	3.26765e8i	−3.15470	−	1.82137i
$565$	4.54822e6	−	7.87774e6i	0.0252171	−	0.0436774i
$566$	−2.68524e8	+	1.55033e8i	−1.48093	+	0.855015i
$567$			1.88093e8i			1.03187i
$568$	−3.39508e8	−	5.88044e8i	−1.85270	−	3.20897i
$569$	−8.88647e7	+	1.53918e8i	−0.482384	+	0.835513i	−0.999795	−	0.0202235i	$-0.993562\pi$
$569$	−8.88647e7	+	1.53918e8i	−0.482384	+	0.835513i	0.517412	+	0.855737i	$0.326896\pi$
$570$	−5.24883e8			−2.83425
$571$	3.89256e7	+	2.24737e7i	0.209087	+	0.120716i	0.600887	−	0.799334i	$-0.294814\pi$
$571$	3.89256e7	+	2.24737e7i	0.209087	+	0.120716i	−0.391800	+	0.920050i	$0.628147\pi$
$572$	1.24775e8	+	2.16117e8i	0.666715	+	1.15478i
$573$	3.37944e7	+	5.85336e7i	0.179631	+	0.311130i
$574$	−1.13998e8	−	1.97450e8i	−0.602783	−	1.04405i
$575$	−2.39037e8			−1.25737
$576$	3.22522e7	+	5.58624e7i	0.168769	+	0.292316i
$577$	2.29657e8	−	1.32592e8i	1.19551	−	0.690226i	0.235956	−	0.971764i	$-0.424178\pi$
$577$	2.29657e8	−	1.32592e8i	1.19551	−	0.690226i	0.959550	+	0.281538i	$0.0908444\pi$
$578$	4.11403e8	+	2.37524e8i	2.13051	+	1.23005i
$579$	1.66325e8	+	9.60276e7i	0.856882	+	0.494721i
$580$	−5.25354e8			−2.69258
$581$			7.61668e7i			0.388362i
$582$	4.10790e8	−	7.11509e8i	2.08377	−	3.60920i
$583$	−5.19267e7	+	8.99396e7i	−0.262050	+	0.453884i
$584$	−5.37664e6	−	9.31261e6i	−0.0269943	−	0.0467555i
$585$	−1.11970e8	+	6.46460e7i	−0.559287	+	0.322905i
$586$		−	1.27243e8i		−	0.632325i
$587$	2.23222e8	−	1.28877e8i	1.10363	−	0.637179i	0.166455	−	0.986049i	$-0.446768\pi$
$587$	2.23222e8	−	1.28877e8i	1.10363	−	0.637179i	0.937171	+	0.348870i	$0.113435\pi$
$588$	−1.44567e8	+	8.34657e7i	−0.711110	+	0.410559i
$589$	−2.72316e8	+	1.57222e8i	−1.33268	+	0.769425i
$590$	−1.12531e8	+	1.94909e8i	−0.547917	+	0.949020i
$591$			4.45385e7i			0.215761i
$592$	2.37898e8	+	1.37351e8i	1.14664	+	0.662011i
$593$	2.75721e8	−	1.59188e8i	1.32223	−	0.763387i	0.338142	−	0.941095i	$-0.390201\pi$
$593$	2.75721e8	−	1.59188e8i	1.32223	−	0.763387i	0.984083	+	0.177708i	$0.0568681\pi$
$594$	−1.51815e8			−0.724361
$595$	1.83433e8	+	3.17716e8i	0.870818	+	1.50830i
$596$	2.07204e8	+	1.19629e8i	0.978720	+	0.565064i
$597$	−1.40813e8	+	2.43894e8i	−0.661787	+	1.14625i
$598$			5.14707e8i			2.40689i
$599$	2.24525e7	−	3.88889e7i	0.104468	−	0.180944i	−0.809053	−	0.587736i	$-0.800019\pi$
$599$	2.24525e7	−	3.88889e7i	0.104468	−	0.180944i	0.913521	+	0.406792i	$0.133353\pi$
$600$	4.39586e8			2.03512
$601$			2.34530e8i			1.08038i	0.841545	+	0.540188i	$0.181647\pi$
$601$			2.34530e8i			1.08038i	−0.841545	+	0.540188i	$0.818353\pi$
$602$	2.13218e8	−	2.34654e8i	0.977313	−	1.07557i
$603$	6.11787e7			0.279028
$604$			4.23358e8i			1.92131i
$605$	−1.39695e8	−	8.06530e7i	−0.630834	−	0.364212i
$606$	−1.61938e8			−0.727665
$607$	1.29928e8	+	7.50138e7i	0.580946	+	0.335409i	0.761509	−	0.648154i	$-0.224459\pi$
$607$	1.29928e8	+	7.50138e7i	0.580946	+	0.335409i	−0.180563	+	0.983563i	$0.557792\pi$
$608$	3.95064e7	−	6.84271e7i	0.175775	−	0.304451i
$609$	1.86768e8	−	1.07830e8i	0.826895	−	0.477408i
$610$			4.75922e8i			2.09675i
$611$	−1.50059e8	−	2.59910e8i	−0.657867	−	1.13946i
$612$	−1.89579e8	+	3.28360e8i	−0.827056	+	1.43250i
$613$	−1.88110e8			−0.816640			−0.408320	−	0.912839i	$-0.633885\pi$
$613$	−1.88110e8			−0.816640			−0.408320	+	0.912839i	$0.633885\pi$
$614$	1.29067e8	+	7.45170e7i	0.557584	+	0.321922i
$615$	1.61480e8	+	2.79691e8i	0.694214	+	1.20241i
$616$	1.27328e8	+	2.20538e8i	0.544729	+	0.943498i
$617$	−2.51365e7	−	4.35376e7i	−0.107016	−	0.185357i	0.807544	−	0.589807i	$-0.200796\pi$
$617$	−2.51365e7	−	4.35376e7i	−0.107016	−	0.185357i	−0.914560	+	0.404450i	$0.867463\pi$
$618$	5.02939e8			2.13083
$619$	−1.20001e8	−	2.07847e8i	−0.505955	−	0.876340i	−0.999976	−	0.00688978i	$-0.997807\pi$
$619$	−1.20001e8	−	2.07847e8i	−0.505955	−	0.876340i	0.494021	−	0.869450i	$-0.335526\pi$
$620$	9.44228e8	−	5.45150e8i	3.96188	−	2.28740i
$621$	−1.83667e8	−	1.06040e8i	−0.766931	−	0.442788i
$622$	−3.07782e8	−	1.77698e8i	−1.27900	−	0.738433i
$623$	−1.11622e8			−0.461622
$624$		−	3.63145e8i		−	1.49460i
$625$	1.37081e8	−	2.37432e8i	0.561485	−	0.972520i
$626$	−1.38297e8	+	2.39537e8i	−0.563753	+	0.976449i
$627$	9.93508e7	+	1.72081e8i	0.403059	+	0.698119i
$628$	2.28562e8	−	1.31960e8i	0.922835	−	0.532799i
$629$		−	3.90493e8i		−	1.56914i
$630$	−2.18237e8	+	1.25999e8i	−0.872784	+	0.503902i
$631$	1.32376e8	−	7.64276e7i	0.526893	−	0.304202i	−0.212857	−	0.977083i	$-0.568277\pi$
$631$	1.32376e8	−	7.64276e7i	0.526893	−	0.304202i	0.739750	+	0.672881i	$0.234944\pi$
$632$	−3.44876e8	+	1.99114e8i	−1.36619	+	0.788771i
$633$	5.99325e7	−	1.03806e8i	0.236293	−	0.409272i
$634$		−	4.64610e8i		−	1.82314i
$635$	5.21301e8	+	3.00973e8i	2.03595	+	1.17546i
$636$	4.41314e8	−	2.54793e8i	1.71544	−	0.990412i
$637$	−7.66592e7			−0.296583
$638$	1.46817e8	+	2.54295e8i	0.565346	+	0.979209i
$639$	−2.20290e8	−	1.27184e8i	−0.844291	−	0.487452i
$640$	2.73752e8	−	4.74153e8i	1.04428	−	1.80875i
$641$			4.14525e8i			1.57390i	0.617017	+	0.786950i	$0.288341\pi$
$641$			4.14525e8i			1.57390i	−0.617017	+	0.786950i	$0.711659\pi$
$642$	1.27740e7	−	2.21253e7i	0.0482750	−	0.0836148i
$643$	−2.08554e8			−0.784487			−0.392244	−	0.919861i	$-0.628301\pi$
$643$	−2.08554e8			−0.784487			−0.392244	+	0.919861i	$0.628301\pi$
$644$			6.79471e8i			2.54398i
$645$	−3.02026e8	+	3.32391e8i	−1.12555	+	1.23871i
$646$	−7.06864e8			−2.62204
$647$		−	2.12551e8i		−	0.784783i	−0.919798	−	0.392391i	$-0.871648\pi$
$647$		−	2.12551e8i		−	0.784783i	0.919798	−	0.392391i	$-0.128352\pi$
$648$	5.69775e8	+	3.28960e8i	2.09401	+	1.20898i
$649$	8.52001e7			0.311678
$650$	3.33912e8	+	1.92784e8i	1.21588	+	0.701991i
$651$	−2.23787e8	+	3.87611e8i	−0.811134	+	1.40492i
$652$	−4.29534e8	+	2.47992e8i	−1.54973	+	0.894735i
$653$		−	3.38070e8i		−	1.21413i	−0.794651	−	0.607067i	$-0.792346\pi$
$653$		−	3.38070e8i		−	1.21413i	0.794651	−	0.607067i	$-0.207654\pi$
$654$	−4.72221e8	−	8.17911e8i	−1.68815	−	2.92397i
$655$	2.94401e7	−	5.09918e7i	0.104765	−	0.181458i
$656$	−3.05963e8			−1.08382
$657$	−3.48864e6	−	2.01417e6i	−0.0123016	−	0.00710231i
$658$	−2.92474e8	−	5.06580e8i	−1.02662	−	1.77816i
$659$	−7.95195e6	−	1.37732e7i	−0.0277854	−	0.0481258i	0.851798	−	0.523870i	$-0.175512\pi$
$659$	−7.95195e6	−	1.37732e7i	−0.0277854	−	0.0481258i	−0.879584	+	0.475744i	$0.842179\pi$
$660$	−3.44489e8	−	5.96673e8i	−1.19824	−	2.07541i
$661$	5.53539e8			1.91665			0.958327	−	0.285674i	$-0.0922174\pi$
$661$	5.53539e8			1.91665			0.958327	+	0.285674i	$0.0922174\pi$
$662$	2.58459e8	+	4.47665e8i	0.890879	+	1.54305i
$663$	−4.47058e8	+	2.58109e8i	−1.53399	+	0.885651i
$664$	2.30726e8	+	1.33210e8i	0.788119	+	0.455021i
$665$	−2.75569e8	−	1.59100e8i	−0.937056	−	0.541009i
$666$	2.68227e8			0.907989
$667$			4.10198e8i			1.38234i
$668$	−4.53991e8	+	7.86335e8i	−1.52306	+	2.63802i
$669$	1.10062e8	−	1.90633e8i	0.367587	−	0.636679i
$670$	−1.97739e8	−	3.42493e8i	−0.657457	−	1.13875i
$671$	1.56029e8	−	9.00833e7i	0.516461	−	0.298179i
$672$		−	1.12466e8i		−	0.370607i
$673$	−2.32916e8	+	1.34474e8i	−0.764107	+	0.441157i	−0.830768	−	0.556618i	$-0.812099\pi$
$673$	−2.32916e8	+	1.34474e8i	−0.764107	+	0.441157i	0.0666616	+	0.997776i	$0.478765\pi$
$674$	4.71683e8	−	2.72326e8i	1.54053	−	0.889426i
$675$	−1.37586e8	+	7.94351e7i	−0.447365	+	0.258286i
$676$	−4.30344e7	+	7.45377e7i	−0.139308	+	0.241288i
$677$		−	2.76854e8i		−	0.892247i	−0.894971	−	0.446123i	$-0.852804\pi$
$677$		−	2.76854e8i		−	0.892247i	0.894971	−	0.446123i	$-0.147196\pi$
$678$	2.16049e7	+	1.24736e7i	0.0693208	+	0.0400224i
$679$	4.31338e8	−	2.49033e8i	1.37787	−	0.795513i
$680$	1.28324e9			4.08114
$681$	4.57158e7	+	7.91820e7i	0.144752	+	0.250718i
$682$	−5.27754e8	−	3.04699e8i	−1.66371	−	0.960544i
$683$	−1.99451e8	+	3.45459e8i	−0.625999	+	1.08426i	0.362347	+	0.932043i	$0.381975\pi$
$683$	−1.99451e8	+	3.45459e8i	−0.625999	+	1.08426i	−0.988347	+	0.152219i	$0.951358\pi$
$684$		−	3.28860e8i		−	1.02764i
$685$	1.03674e8	−	1.79568e8i	0.322550	−	0.558673i
$686$	−6.18571e8			−1.91610
$687$		−	7.01998e8i		−	2.16504i
$688$	−1.29644e8	−	4.05246e8i	−0.398096	−	1.24438i
$689$	2.34015e8			0.715461
$690$		−	1.42104e9i		−	4.32574i
$691$	2.64597e8	+	1.52765e8i	0.801956	+	0.463009i	0.844155	−	0.536100i	$-0.180103\pi$
$691$	2.64597e8	+	1.52765e8i	0.801956	+	0.463009i	−0.0421988	+	0.999109i	$0.513436\pi$
$692$	−9.73342e8			−2.93729
$693$	8.26167e7	+	4.76987e7i	0.248238	+	0.143320i
$694$	−3.93678e8	+	6.81870e8i	−1.17778	+	2.03997i
$695$	−1.97571e8	+	1.14068e8i	−0.588531	+	0.339788i
$696$		−	7.54348e8i		−	2.23740i
$697$	2.17466e8	+	3.76663e8i	0.642235	+	1.11238i
$698$	3.19726e8	−	5.53781e8i	0.940181	−	1.62844i
$699$	1.92276e8			0.562981
$700$	4.40802e8	+	2.54497e8i	1.28514	+	0.741974i
$701$	1.14283e8	+	1.97943e8i	0.331762	+	0.574628i	0.982857	−	0.184367i	$-0.0590236\pi$
$701$	1.14283e8	+	1.97943e8i	0.331762	+	0.574628i	−0.651096	+	0.758996i	$0.725690\pi$
$702$	1.71044e8	+	2.96257e8i	0.494420	+	0.856360i
$703$	1.69346e8	+	2.93316e8i	0.487426	+	0.844247i
$704$	−1.57852e8			−0.452409
$705$	4.14295e8	+	7.17579e8i	1.18234	+	2.04787i
$706$	−2.69662e8	+	1.55689e8i	−0.766311	+	0.442430i
$707$	−8.50192e7	−	4.90859e7i	−0.240580	−	0.138899i
$708$	−3.62049e8	−	2.09029e8i	−1.02016	−	0.588989i
$709$	1.02910e8			0.288747			0.144373	−	0.989523i	$-0.453883\pi$
$709$	1.02910e8			0.288747			0.144373	+	0.989523i	$0.453883\pi$
$710$			1.64432e9i			4.59421i
$711$	−7.45911e7	+	1.29196e8i	−0.207529	+	0.359450i
$712$	−1.95219e8	+	3.38129e8i	−0.540855	+	0.936789i
$713$	−4.25654e8	−	7.37255e8i	−1.17433	−	2.03399i
$714$	−8.71345e8	+	5.03071e8i	−2.39384	+	1.38209i
$715$		−	3.16397e8i		−	0.865594i
$716$	−1.09964e8	+	6.34879e7i	−0.299580	+	0.172963i
$717$	−4.06958e8	+	2.34957e8i	−1.10406	+	0.637429i
$718$	7.39011e8	−	4.26668e8i	1.99654	−	1.15270i
$719$	−3.51601e8	+	6.08992e8i	−0.945941	+	1.63842i	−0.192085	+	0.981378i	$0.561525\pi$
$719$	−3.51601e8	+	6.08992e8i	−0.945941	+	1.63842i	−0.753856	+	0.657040i	$0.771808\pi$
$720$			3.38174e8i			0.906030i
$721$	2.64048e8	+	1.52448e8i	0.704494	+	0.406740i
$722$	−4.28262e7	+	2.47257e7i	−0.113788	+	0.0656958i
$723$	5.64246e8			1.49298
$724$	−2.47414e8	−	4.28534e8i	−0.651942	−	1.12920i
$725$	2.66113e8	+	1.53640e8i	0.698315	+	0.403173i
$726$	2.21193e8	−	3.83118e8i	0.578045	−	1.00120i
$727$		−	1.72729e8i		−	0.449534i	−0.974413	−	0.224767i	$-0.927838\pi$
$727$		−	1.72729e8i		−	0.449534i	0.974413	−	0.224767i	$-0.0721621\pi$
$728$	2.86910e8	−	4.96943e8i	0.743621	−	1.28799i
$729$	−4.05924e7			−0.104776
$730$			2.60404e7i			0.0669388i
$731$	−4.06741e8	+	4.47634e8i	−1.04128	+	1.14596i
$732$	−8.84039e8			−2.25392
$733$			4.34687e8i			1.10374i	0.833932	+	0.551868i	$0.186085\pi$
$733$			4.34687e8i			1.10374i	−0.833932	+	0.551868i	$0.813915\pi$
$734$	8.73734e8	+	5.04450e8i	2.20948	+	1.27565i
$735$	2.11647e8			0.533028
$736$	1.85256e8	+	1.06958e8i	0.464665	+	0.268274i
$737$	−7.48567e7	+	1.29656e8i	−0.186994	+	0.323883i
$738$	−2.58727e8	+	1.49376e8i	−0.643685	+	0.371632i
$739$			3.36824e8i			0.834585i	0.908772	+	0.417292i	$0.137021\pi$
$739$			3.36824e8i			0.834585i	−0.908772	+	0.417292i	$0.862979\pi$
$740$	−5.87191e8	−	1.01704e9i	−1.44905	−	2.50983i
$741$	2.23869e8	−	3.87753e8i	0.550225	−	0.953017i
$742$	4.56110e8			1.11650
$743$	−6.13956e8	−	3.54467e8i	−1.49682	−	0.864191i	−0.496830	−	0.867848i	$-0.665503\pi$
$743$	−6.13956e8	−	3.54467e8i	−1.49682	−	0.864191i	−0.999993	+	0.00365652i	$0.998836\pi$
$744$	7.82772e8	+	1.35580e9i	1.90071	+	3.29213i
$745$	−1.51674e8	−	2.62707e8i	−0.366811	−	0.635334i
$746$	−6.36320e8	−	1.10214e9i	−1.53271	−	2.65473i
$747$	9.98045e7			0.239435
$748$	−4.63927e8	−	8.03545e8i	−1.10852	−	1.92002i
$749$	1.34130e7	−	7.74399e6i	0.0319213	−	0.0184298i
$750$	1.54565e8	+	8.92379e7i	0.366375	+	0.211527i
$751$	2.54164e8	+	1.46742e8i	0.600060	+	0.346445i	0.769065	−	0.639170i	$-0.220722\pi$
$751$	2.54164e8	+	1.46742e8i	0.600060	+	0.346445i	−0.169005	+	0.985615i	$0.554055\pi$
$752$	−7.84982e8			−1.84589
$753$		−	4.40983e8i		−	1.03285i
$754$	3.30826e8	−	5.73008e8i	0.771766	−	1.33674i
$755$	2.68381e8	−	4.64849e8i	0.623607	−	1.08012i
$756$	2.25797e8	+	3.91092e8i	0.522580	+	0.905135i
$757$	−2.56382e8	+	1.48022e8i	−0.591017	+	0.341224i	−0.765499	−	0.643437i	$-0.777508\pi$
$757$	−2.56382e8	+	1.48022e8i	−0.591017	+	0.341224i	0.174483	+	0.984660i	$0.444175\pi$
$758$			1.21835e9i			2.79746i
$759$	−4.65883e8	+	2.68978e8i	−1.06550	+	0.615165i
$760$	−9.63896e8	+	5.56506e8i	−2.19578	+	1.26774i
$761$	9.29462e7	−	5.36625e7i	0.210901	−	0.121764i	−0.390829	−	0.920463i	$-0.627812\pi$
$761$	9.29462e7	−	5.36625e7i	0.210901	−	0.121764i	0.601730	+	0.798700i	$0.294478\pi$
$762$	−8.25427e8	+	1.42968e9i	−1.86558	+	3.23128i
$763$		−	5.72549e8i		−	1.28896i
$764$	2.37069e8	+	1.36872e8i	0.531612	+	0.306926i
$765$	4.16317e8	−	2.40360e8i	0.929907	−	0.536882i
$766$	−3.94281e8			−0.877242
$767$	−9.59916e7	−	1.66262e8i	−0.212739	−	0.368475i
$768$	9.80795e8	+	5.66262e8i	2.16518	+	1.25007i
$769$	−5.51740e7	+	9.55642e7i	−0.121326	+	0.210144i	−0.920291	−	0.391235i	$-0.872048\pi$
$769$	−5.51740e7	+	9.55642e7i	−0.121326	+	0.210144i	0.798965	+	0.601378i	$0.205381\pi$
$770$		−	6.16678e8i		−	1.35078i
$771$	4.77501e8	−	8.27056e8i	1.04186	−	1.80456i
$772$	7.77849e8			1.69061
$773$			5.44529e8i			1.17892i	0.807799	+	0.589458i	$0.200659\pi$
$773$			5.44529e8i			1.17892i	−0.807799	+	0.589458i	$0.799341\pi$
$774$	−3.07477e8	−	2.79388e8i	−0.663116	−	0.602539i
$775$	−6.37718e8			−1.37001
$776$		−	1.74215e9i		−	3.72822i
$777$	4.17502e8	+	2.41045e8i	0.890012	+	0.513849i
$778$	1.15642e9			2.45570
$779$	−3.26696e8	−	1.88618e8i	−0.691085	−	0.398998i
$780$	−7.76245e8	+	1.34450e9i	−1.63574	+	2.83319i
$781$	5.39082e8	−	3.11239e8i	1.13162	−	0.653343i
$782$		−	1.91373e9i		−	4.00185i
$783$	1.36314e8	+	2.36103e8i	0.283959	+	0.491831i
$784$	−1.00254e8	+	1.73645e8i	−0.208044	+	0.360342i
$785$	−3.34616e8			−0.691731
$786$	1.39847e8	+	8.07404e7i	0.287994	+	0.166274i
$787$	4.93073e7	+	8.54028e7i	0.101155	+	0.175206i	0.912161	−	0.409833i	$-0.134413\pi$
$787$	4.93073e7	+	8.54028e7i	0.101155	+	0.175206i	−0.811006	+	0.585038i	$0.801080\pi$
$788$	9.01933e7	+	1.56219e8i	0.184330	+	0.319269i
$789$	−7.25683e7	−	1.25692e8i	−0.147746	−	0.255904i
$790$	9.64358e8			1.95595
$791$	7.56187e6	+	1.30976e7i	0.0152792	+	0.0264643i
$792$	2.88980e8	−	1.66843e8i	0.581691	−	0.335839i
$793$	−3.51583e8	−	2.02987e8i	−0.705032	−	0.407050i
$794$	6.31731e8	+	3.64730e8i	1.26203	+	0.728635i
$795$	−6.46087e8			−1.28585
$796$			1.14062e9i			2.26152i
$797$	1.93714e8	−	3.35523e8i	0.382636	−	0.662746i	−0.608802	−	0.793322i	$-0.708350\pi$
$797$	1.93714e8	−	3.35523e8i	0.382636	−	0.662746i	0.991438	+	0.130577i	$0.0416829\pi$
$798$	4.36336e8	−	7.55756e8i	0.858642	−	1.48721i
$799$	5.57934e8	+	9.66370e8i	1.09381	+	1.89454i
$800$	1.38776e8	−	8.01225e7i	0.271047	−	0.156489i
$801$			1.46263e8i			0.284602i
$802$	−3.31788e8	+	1.91558e8i	−0.643187	+	0.371344i
$803$	8.53722e6	−	4.92897e6i	0.0164881	−	0.00951939i
$804$	6.36192e8	−	3.67306e8i	1.22411	−	0.706739i
$805$	4.30740e8	−	7.46063e8i	0.825709	−	1.43017i
$806$			1.37317e9i			2.62252i
$807$	3.92017e8	+	2.26331e8i	0.745907	+	0.430649i
$808$	−2.97384e8	+	1.71695e8i	−0.563745	+	0.325479i
$809$	4.87240e7			0.0920232			0.0460116	−	0.998941i	$-0.485349\pi$
$809$	4.87240e7			0.0920232			0.0460116	+	0.998941i	$0.485349\pi$
$810$	−7.96616e8	−	1.37978e9i	−1.49897	−	2.59630i
$811$	−6.01652e8	−	3.47364e8i	−1.12793	−	0.651212i	−0.184518	−	0.982829i	$-0.559072\pi$
$811$	−6.01652e8	−	3.47364e8i	−1.12793	−	0.651212i	−0.943414	+	0.331617i	$0.892406\pi$
$812$	4.36728e8	−	7.56434e8i	0.815723	−	1.41287i
$813$		−	2.24261e8i		−	0.417333i
$814$	−3.28196e8	+	5.68453e8i	−0.608500	+	1.05395i
$815$	6.28841e8			1.16163
$816$			1.35021e9i			2.48503i
$817$	1.11394e8	−	5.12629e8i	0.204266	−	0.940020i
$818$	−3.01792e8			−0.551376
$819$		−	2.14961e8i		−	0.391299i
$820$	1.13279e9	+	6.54015e8i	2.05450	+	1.18617i
$821$	−6.15511e8			−1.11226			−0.556130	−	0.831095i	$-0.687715\pi$
$821$	−6.15511e8			−1.11226			−0.556130	+	0.831095i	$0.687715\pi$
$822$	4.92470e8	+	2.84328e8i	0.886676	+	0.511922i
$823$	−1.49018e8	+	2.58107e8i	−0.267325	+	0.463020i	−0.968170	−	0.250293i	$-0.919473\pi$
$823$	−1.49018e8	+	2.58107e8i	−0.267325	+	0.463020i	0.700845	+	0.713313i	$0.252806\pi$
$824$	9.23598e8	−	5.33239e8i	1.65083	−	0.953105i
$825$			4.02985e8i			0.717673i
$826$	−1.87094e8	−	3.24056e8i	−0.331985	−	0.575016i
$827$	1.09915e8	−	1.90379e8i	0.194331	−	0.336591i	−0.752350	−	0.658764i	$-0.771080\pi$
$827$	1.09915e8	−	1.90379e8i	0.194331	−	0.336591i	0.946681	+	0.322172i	$0.104413\pi$
$828$	8.90339e8			1.56843
$829$	−8.33206e8	−	4.81052e8i	−1.46248	−	0.844361i	−0.463351	−	0.886175i	$-0.653353\pi$
$829$	−8.33206e8	−	4.81052e8i	−1.46248	−	0.844361i	−0.999125	+	0.0418133i	$0.986687\pi$
$830$	−3.22583e8	−	5.58730e8i	−0.564166	−	0.977165i
$831$	−1.30769e8	−	2.26499e8i	−0.227878	−	0.394696i
$832$	1.77845e8	+	3.08037e8i	0.308797	+	0.534851i
$833$	2.85027e8			0.493118
$834$	−3.12834e8	−	5.41845e8i	−0.539282	−	0.934064i
$835$	9.96969e8	−	5.75600e8i	1.71247	−	0.988694i
$836$	6.96950e8	+	4.02384e8i	1.19284	+	0.688687i
$837$	−4.89999e8	−	2.82901e8i	−0.835639	−	0.482456i
$838$	1.15573e9			1.96392
$839$		−	5.53943e8i		−	0.937950i	−0.883212	−	0.468975i	$-0.844623\pi$
$839$		−	5.53943e8i		−	0.937950i	0.883212	−	0.468975i	$-0.155377\pi$
$840$	−7.92124e8	+	1.37200e9i	−1.33646	+	2.31481i
$841$	−3.37585e7	+	5.84715e7i	−0.0567539	+	0.0983006i
$842$	−1.14909e6	−	1.99028e6i	−0.00192494	−	0.00333410i
$843$	−2.35944e8	+	1.36223e8i	−0.393847	+	0.227387i
$844$		−	4.85469e8i		−	0.807485i
$845$	9.45039e7	−	5.45619e7i	0.156632	−	0.0904314i
$846$	−6.63794e8	+	3.83241e8i	−1.09628	+	0.632938i
$847$	2.32257e8	−	1.34094e8i	0.382225	−	0.220678i
$848$	3.06042e8	−	5.30081e8i	0.501873	−	0.869270i
$849$			7.30235e8i			1.19327i
$850$	−1.24152e9	−	7.16792e8i	−2.02161	−	1.16718i
$851$	−7.94110e8	+	4.58480e8i	−1.28852	+	0.743929i
$852$	−3.05437e9			−4.93859
$853$	5.38087e8	+	9.31995e8i	0.866973	+	1.50164i	0.865074	+	0.501643i	$0.167271\pi$
$853$	5.38087e8	+	9.31995e8i	0.866973	+	1.50164i	0.00189876	+	0.999998i	$0.499396\pi$
$854$	−6.85258e8	−	3.95634e8i	−1.10022	−	0.635214i
$855$	−2.08475e8	+	3.61090e8i	−0.333546	+	0.577719i
$856$		−	5.41745e7i		−	0.0863722i
$857$	3.44529e8	−	5.96742e8i	0.547373	−	0.948078i	−0.451080	−	0.892483i	$-0.648961\pi$
$857$	3.44529e8	−	5.96742e8i	0.547373	−	0.948078i	0.998453	−	0.0555946i	$-0.0177055\pi$
$858$	8.67727e8			1.37379
$859$			1.71471e8i			0.270528i	0.990810	+	0.135264i	$0.0431882\pi$
$859$			1.71471e8i			0.270528i	−0.990810	+	0.135264i	$0.956812\pi$
$860$	−3.86248e8	+	1.77749e9i	−0.607255	+	2.79455i
$861$	−5.36954e8			−0.841254
$862$		−	1.24780e9i		−	1.94815i
$863$	−2.92838e8	−	1.69070e8i	−0.455612	−	0.263048i	0.254585	−	0.967050i	$-0.418061\pi$
$863$	−2.92838e8	−	1.69070e8i	−0.455612	−	0.263048i	−0.710198	+	0.704002i	$0.751394\pi$
$864$	1.42174e8			0.220434
$865$	1.06873e9	+	6.17034e8i	1.65128	+	0.953369i
$866$	−3.37863e8	+	5.85196e8i	−0.520220	+	0.901047i
$867$	9.68897e8	−	5.59393e8i	1.48669	−	0.858340i
$868$			1.81274e9i			2.77189i
$869$	−1.82535e8	−	3.16161e8i	−0.278156	−	0.481780i
$870$	−9.13371e8	+	1.58201e9i	−1.38704	+	2.40243i
$871$	3.37352e8			0.510539
$872$	−1.73438e9	−	1.00134e9i	−2.61574	−	1.51020i
$873$	−3.26318e8	−	5.65200e8i	−0.490454	−	0.849492i
$874$	8.29932e8	+	1.43748e9i	1.24311	+	2.15312i
$875$	5.40987e7	+	9.37017e7i	0.0807537	+	0.139870i
$876$	−4.83707e7			−0.0719566
$877$	−3.20715e8	−	5.55495e8i	−0.475467	−	0.823533i	0.524138	−	0.851633i	$-0.324388\pi$
$877$	−3.20715e8	−	5.55495e8i	−0.475467	−	0.823533i	−0.999605	+	0.0281001i	$0.991054\pi$
$878$	4.02745e7	−	2.32525e7i	0.0595040	−	0.0343547i
$879$	−2.59522e8	−	1.49835e8i	−0.382127	−	0.220621i
$880$	−7.16689e8	−	4.13781e8i	−1.05168	−	0.607187i
$881$	−2.34400e8			−0.342791			−0.171395	−	0.985202i	$-0.554828\pi$
$881$	−2.34400e8			−0.342791			−0.171395	+	0.985202i	$0.554828\pi$
$882$			1.95783e8i			0.285344i
$883$	4.36708e8	−	7.56401e8i	0.634321	−	1.09868i	−0.352337	−	0.935873i	$-0.614613\pi$
$883$	4.36708e8	−	7.56401e8i	0.634321	−	1.09868i	0.986658	−	0.162804i	$-0.0520537\pi$
$884$	−1.04538e9	+	1.81065e9i	−1.51327	+	2.62106i
$885$	2.65021e8	+	4.59030e8i	0.382341	+	0.662234i
$886$	4.39658e8	−	2.53836e8i	0.632140	−	0.364966i
$887$			1.04993e9i			1.50449i	0.658882	+	0.752246i	$0.271030\pi$
$887$			1.04993e9i			1.50449i	−0.658882	+	0.752246i	$0.728970\pi$
$888$	1.46036e9	−	8.43138e8i	2.08555	−	1.20409i
$889$	−8.66716e8	+	5.00399e8i	−1.23359	+	0.712214i
$890$	8.18819e8	−	4.72745e8i	1.16150	−	0.670590i
$891$	−3.01570e8	+	5.22334e8i	−0.426339	+	0.738440i
$892$		−	8.91534e8i		−	1.25615i
$893$	−8.38175e8	−	4.83921e8i	−1.17701	−	0.679547i
$894$	7.20481e8	−	4.15970e8i	1.00835	−	0.582169i
$895$	1.60989e8			0.224557
$896$	4.55141e8	+	7.88328e8i	0.632735	+	1.09593i
$897$	1.04979e9	+	6.06094e8i	1.45453	+	0.839774i
$898$	4.62645e8	−	8.01325e8i	0.638879	−	1.10657i
$899$			1.09435e9i			1.50618i
$900$	3.33478e8	−	5.77601e8i	0.457446	−	0.792320i
$901$	−8.70091e8			−1.18957
$902$		−	7.31092e8i		−	0.996214i
$903$	−2.27520e8	−	7.11191e8i	−0.308999	−	0.965880i
$904$	5.29005e7			0.0716068
$905$			6.27377e8i			0.846414i
$906$	1.27486e9	+	7.36042e8i	1.71427	+	0.989733i
$907$	8.31684e8			1.11464			0.557322	−	0.830296i	$-0.311829\pi$
$907$	8.31684e8			1.11464			0.557322	+	0.830296i	$0.311829\pi$
$908$	3.20698e8	+	1.85155e8i	0.428389	+	0.247331i
$909$	−6.43193e7	+	1.11404e8i	−0.0856346	+	0.148324i
$910$	−1.20341e9	+	6.94787e8i	−1.59694	+	0.921992i
$911$		−	8.95127e8i		−	1.18394i	−0.805960	−	0.591970i	$-0.798350\pi$
$911$		−	8.95127e8i		−	1.18394i	0.805960	−	0.591970i	$-0.201650\pi$
$912$	−5.85548e8	−	1.01420e9i	−0.771931	−	1.33702i
$913$	−1.22118e8	+	2.11515e8i	−0.160461	+	0.277926i
$914$	5.71530e8			0.748515
$915$	9.70679e8	+	5.60422e8i	1.26710	+	0.731563i
$916$	−1.42159e9	−	2.46227e9i	−1.84965	−	3.20368i
$917$	4.89473e7	+	8.47791e7i	0.0634776	+	0.109946i
$918$	−6.35958e8	−	1.10151e9i	−0.822054	−	1.42384i
$919$	−1.20081e9			−1.54714			−0.773568	−	0.633713i	$-0.781530\pi$
$919$	−1.20081e9			−1.54714			−0.773568	+	0.633713i	$0.781530\pi$
$920$	−1.50666e9	−	2.60961e9i	−1.93487	−	3.35129i
$921$	3.03966e8	−	1.75495e8i	0.389087	−	0.224639i
$922$	−1.16114e8	−	6.70386e7i	−0.148147	−	0.0855327i
$923$	−1.21473e9	−	7.01322e8i	−1.54480	−	0.891893i
$924$	1.14550e9			1.45204
$925$			6.86898e8i			0.867894i
$926$	−5.38522e8	+	9.32747e8i	−0.678220	+	1.17471i
$927$	1.99759e8	−	3.45993e8i	0.250765	−	0.434338i
$928$	−1.37494e8	−	2.38146e8i	−0.172044	−	0.297988i
$929$	−2.91522e8	+	1.68310e8i	−0.363600	+	0.209925i	−0.670659	−	0.741766i	$-0.733989\pi$
$929$	−2.91522e8	+	1.68310e8i	−0.363600	+	0.209925i	0.307059	+	0.951691i	$0.400655\pi$
$930$		−	3.79115e9i		−	4.71327i
$931$	−2.14096e8	+	1.23608e8i	−0.265313	+	0.153179i
$932$	6.74412e8	−	3.89372e8i	0.833063	−	0.480969i
$933$	−7.24858e8	+	4.18497e8i	−0.892499	+	0.515285i
$934$	4.65207e8	−	8.05762e8i	0.570960	−	0.988932i
$935$			1.17640e9i			1.43919i
$936$	−6.51165e8	−	3.75950e8i	−0.794078	−	0.458461i
$937$	−7.33171e8	+	4.23296e8i	−0.891223	+	0.514548i	−0.874342	−	0.485310i	$-0.838707\pi$
$937$	−7.33171e8	+	4.23296e8i	−0.891223	+	0.514548i	−0.0168804	+	0.999858i	$0.505373\pi$
$938$	6.57521e8			0.796712
$939$	3.25703e8	+	5.64134e8i	0.393391	+	0.681374i
$940$	2.90629e9	+	1.67795e9i	3.49909	+	2.02020i
$941$	−5.92047e8	+	1.02546e9i	−0.710538	+	1.23069i	0.254117	+	0.967174i	$0.418215\pi$
$941$	−5.92047e8	+	1.02546e9i	−0.710538	+	1.23069i	−0.964655	+	0.263515i	$0.915118\pi$
$942$		−	9.17693e8i		−	1.09785i
$943$	5.10656e8	−	8.84482e8i	0.608967	−	1.05476i
$944$	−5.02147e8			−0.596919
$945$		−	5.72561e8i		−	0.678464i
$946$	9.68326e8	−	3.09782e8i	1.14380	−	0.365917i
$947$	2.71770e8			0.320002			0.160001	−	0.987117i	$-0.448850\pi$
$947$	2.71770e8			0.320002			0.160001	+	0.987117i	$0.448850\pi$
$948$			1.79132e9i			2.10256i
$949$	−1.92371e7	−	1.11065e7i	−0.0225082	−	0.0129951i
$950$	1.24341e9			1.45025
$951$	−9.47610e8	−	5.47103e8i	−1.10176	−	0.636103i
$952$	−1.06676e9	+	1.84768e9i	−1.23639	+	2.14149i
$953$	2.00356e8	−	1.15675e8i	0.231485	−	0.133648i	−0.379772	−	0.925080i	$-0.623998\pi$
$953$	2.00356e8	−	1.15675e8i	0.231485	−	0.133648i	0.611257	+	0.791432i	$0.290664\pi$
$954$		−	5.97660e8i		−	0.688350i
$955$	−1.73535e8	−	3.00572e8i	−0.199241	−	0.345095i
$956$	−9.51609e8	+	1.64823e9i	−1.08914	+	1.88645i
$957$	6.91539e8			0.789007
$958$	−6.42961e8	−	3.71214e8i	−0.731287	−	0.422209i
$959$	1.72368e8	+	2.98550e8i	0.195434	+	0.338502i
$960$	−4.91010e8	−	8.50454e8i	−0.554979	−	0.961251i
$961$	−6.91836e8	−	1.19830e9i	−0.779531	−	1.35019i
$962$	1.47906e9			1.66135
$963$	−1.01473e7	−	1.75756e7i	−0.0113624	−	0.0196803i
$964$	1.97910e9	−	1.14264e9i	2.20921	−	1.27549i
$965$	−8.54083e8	−	4.93105e8i	−0.950425	−	0.548728i
$966$	2.04610e9	+	1.18132e9i	2.26984	+	1.31049i
$967$	−1.44955e9			−1.60307			−0.801536	−	0.597946i	$-0.795984\pi$
$967$	−1.44955e9			−1.60307			−0.801536	+	0.597946i	$0.795984\pi$
$968$		−	9.38078e8i		−	1.03422i
$969$	−8.32369e8	+	1.44171e9i	−0.914839	+	1.58455i
$970$	−2.10942e9	+	3.65362e9i	−2.31125	+	4.00321i
$971$	2.89094e8	+	5.00726e8i	0.315778	+	0.546944i	0.979603	−	0.200945i	$-0.0644012\pi$
$971$	2.89094e8	+	5.00726e8i	0.315778	+	0.546944i	−0.663825	+	0.747888i	$0.731068\pi$
$972$	1.55612e9	−	8.98425e8i	1.69451	−	0.978325i
$973$		−	3.79299e8i		−	0.411759i
$974$	2.08990e9	−	1.20660e9i	2.26177	−	1.30583i
$975$	7.86398e8	−	4.54027e8i	0.848454	−	0.489855i
$976$	−9.19594e8	+	5.30928e8i	−0.989115	+	0.571066i
$977$	5.91888e8	−	1.02518e9i	0.634682	−	1.09930i	−0.351901	−	0.936037i	$-0.614465\pi$
$977$	5.91888e8	−	1.02518e9i	0.634682	−	1.09930i	0.986583	−	0.163263i	$-0.0522020\pi$
$978$			1.72462e9i			1.84364i
$979$	−3.09975e8	−	1.78964e8i	−0.330353	−	0.190730i
$980$	7.42355e8	−	4.28599e8i	0.788740	−	0.455379i
$981$	−7.50235e8			−0.794676
$982$	5.03103e8	+	8.71400e8i	0.531279	+	0.920202i
$983$	7.54710e8	+	4.35732e8i	0.794547	+	0.458732i	0.841561	−	0.540162i	$-0.181637\pi$
$983$	7.54710e8	+	4.35732e8i	0.794547	+	0.458732i	−0.0470140	+	0.998894i	$0.514971\pi$
$984$	−9.39089e8	+	1.62655e9i	−0.985648	+	1.70719i
$985$		−	2.28706e8i		−	0.239315i
$986$	−1.23005e9	+	2.13050e9i	−1.28319	+	2.22255i
$987$	−1.37761e9			−1.43277
$988$		−	1.81340e9i		−	1.88028i
$989$	1.38787e9	+	3.01583e8i	1.43469	+	0.311759i
$990$	−8.08059e8			−0.832794
$991$			1.08084e9i			1.11055i	0.831666	+	0.555276i	$0.187387\pi$
$991$			1.08084e9i			1.11055i	−0.831666	+	0.555276i	$0.812613\pi$
$992$	4.94239e8	+	2.85349e8i	0.506293	+	0.292308i
$993$	1.21740e9			1.24332
$994$	−2.36758e9	−	1.36692e9i	−2.41071	−	1.39183i
$995$	7.23077e8	−	1.25241e9i	0.734032	−	1.27138i
$996$	1.03786e9	−	5.99208e8i	1.05041	−	0.606456i
$997$			8.91890e7i			0.0899966i	0.998987	+	0.0449983i	$0.0143282\pi$
$997$			8.91890e7i			0.0899966i	−0.998987	+	0.0449983i	$0.985672\pi$
$998$	−2.08349e8	−	3.60870e8i	−0.209604	−	0.363044i
$999$	−3.04718e8	+	5.27786e8i	−0.305634	+	0.529373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.2	yes	42
43.7	odd	6	inner	43.7.d.a.7.20	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.20	✓	42	43.7	odd	6	inner
43.7.d.a.37.2	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-14.0830i q^{2} +(-28.7233 - 16.5834i) q^{3} -134.330 q^{4} +(147.495 + 85.1564i) q^{5} +(-233.544 + 404.510i) q^{6} +(-245.226 + 141.581i) q^{7} +990.457i q^{8} +(185.520 + 321.330i) q^{9} +O(q^{10})\)	\(q-14.0830i q^{2} +(-28.7233 - 16.5834i) q^{3} -134.330 q^{4} +(147.495 + 85.1564i) q^{5} +(-233.544 + 404.510i) q^{6} +(-245.226 + 141.581i) q^{7} +990.457i q^{8} +(185.520 + 321.330i) q^{9} +(1199.26 - 2077.17i) q^{10} -907.989 q^{11} +(3858.41 + 2227.65i) q^{12} +(1023.00 + 1771.88i) q^{13} +(1993.89 + 3453.51i) q^{14} +(-2824.37 - 4891.95i) q^{15} +5351.46 q^{16} +(-3803.60 - 6588.04i) q^{17} +(4525.28 - 2612.67i) q^{18} +(5714.09 + 3299.03i) q^{19} +(-19813.1 - 11439.1i) q^{20} +9391.61 q^{21} +12787.2i q^{22} +(-8931.65 + 15470.1i) q^{23} +(16425.2 - 28449.2i) q^{24} +(6690.73 + 11588.7i) q^{25} +(24953.4 - 14406.8i) q^{26} +11872.4i q^{27} +(32941.2 - 19018.6i) q^{28} +(19886.7 - 11481.6i) q^{29} +(-68893.2 + 39775.5i) q^{30} +(-23828.4 + 41272.1i) q^{31} -11975.2i q^{32} +(26080.5 + 15057.6i) q^{33} +(-92779.1 + 53566.1i) q^{34} -48226.2 q^{35} +(-24920.9 - 43164.3i) q^{36} +(44454.8 + 25666.0i) q^{37} +(46460.2 - 80471.4i) q^{38} -67859.1i q^{39} +(-84343.8 + 146088. i) q^{40} -57173.8 q^{41} -132262. i q^{42} +(-24225.9 - 75726.3i) q^{43} +121970. q^{44} +63192.8i q^{45} +(217865. + 125784. i) q^{46} -146686. q^{47} +(-153712. - 88745.5i) q^{48} +(-18734.0 + 32448.2i) q^{49} +(163203. - 94225.4i) q^{50} +252307. i q^{51} +(-137419. - 238017. i) q^{52} +(57188.6 - 99053.6i) q^{53} +167199. q^{54} +(-133924. - 77321.1i) q^{55} +(-140230. - 242886. i) q^{56} +(-109418. - 189518. i) q^{57} +(-161695. - 280063. i) q^{58} -93833.8 q^{59} +(379398. + 657137. i) q^{60} +(-171840. + 99211.9i) q^{61} +(581233. + 335575. i) q^{62} +(-90988.6 - 52532.3i) q^{63} +173848. q^{64} +348459. i q^{65} +(212055. - 367291. i) q^{66} +(82442.2 - 142794. i) q^{67} +(510939. + 884972. i) q^{68} +(513093. - 296235. i) q^{69} +679168. i q^{70} +(-593710. + 342779. i) q^{71} +(-318264. + 183750. i) q^{72} +(-9402.34 + 5428.44i) q^{73} +(361454. - 626056. i) q^{74} -443821. i q^{75} +(-767575. - 443159. i) q^{76} +(222663. - 128554. i) q^{77} -955658. q^{78} +(201033. + 348199. i) q^{79} +(789314. + 455711. i) q^{80} +(332129. - 575265. i) q^{81} +805177. i q^{82} +(134493. - 232949. i) q^{83} -1.26158e6 q^{84} -1.29561e6i q^{85} +(-1.06645e6 + 341173. i) q^{86} -761615. q^{87} -899325. i q^{88} +(341386. + 197099. i) q^{89} +889943. q^{90} +(-501730. - 289674. i) q^{91} +(1.19979e6 - 2.07810e6i) q^{92} +(1.36886e6 - 790314. i) q^{93} +2.06577e6i q^{94} +(561867. + 973183. i) q^{95} +(-198589. + 343966. i) q^{96} -1.75894e6 q^{97} +(456968. + 263830. i) q^{98} +(-168450. - 291764. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

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