LMFDB - Embedded newform 21.7.f.b.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.f (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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.4
Root			$-7.08935 - 12.2791i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.7.f.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.58935 + 11.4131i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-54.8390 + 94.9839i) q^{4} +(-68.9069 + 39.7834i) q^{5} +205.435i q^{6} +(284.244 - 191.975i) q^{7} -601.976 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(6.58935 + 11.4131i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-54.8390 + 94.9839i) q^{4} +(-68.9069 + 39.7834i) q^{5} +205.435i q^{6} +(284.244 - 191.975i) q^{7} -601.976 q^{8} +(121.500 + 210.444i) q^{9} +(-908.103 - 524.293i) q^{10} +(-411.119 + 712.080i) q^{11} +(-1480.65 + 854.855i) q^{12} -2429.15i q^{13} +(4064.01 + 1979.11i) q^{14} -1240.32 q^{15} +(-456.932 - 791.429i) q^{16} +(6751.11 + 3897.76i) q^{17} +(-1601.21 + 2773.38i) q^{18} +(5786.98 - 3341.12i) q^{19} -8726.73i q^{20} +(5333.59 - 376.196i) q^{21} -10836.0 q^{22} +(-9416.30 - 16309.5i) q^{23} +(-8126.67 - 4691.94i) q^{24} +(-4647.06 + 8048.94i) q^{25} +(27724.0 - 16006.5i) q^{26} +3788.00i q^{27} +(2646.85 + 37526.3i) q^{28} +13888.2 q^{29} +(-8172.93 - 14155.9i) q^{30} +(-24131.1 - 13932.1i) q^{31} +(-13241.5 + 22934.9i) q^{32} +(-11100.2 + 6408.72i) q^{33} +102735. i q^{34} +(-11949.0 + 24536.6i) q^{35} -26651.7 q^{36} +(-39837.6 - 69000.8i) q^{37} +(76264.9 + 44031.5i) q^{38} +(18933.3 - 32793.5i) q^{39} +(41480.3 - 23948.6i) q^{40} -59196.1i q^{41} +(39438.4 + 58393.8i) q^{42} -91825.9 q^{43} +(-45090.7 - 78099.4i) q^{44} +(-16744.4 - 9667.37i) q^{45} +(124095. - 214938. i) q^{46} +(-4347.44 + 2509.99i) q^{47} -14245.7i q^{48} +(43940.4 - 109135. i) q^{49} -122484. q^{50} +(60760.0 + 105239. i) q^{51} +(230730. + 133212. i) q^{52} +(-93194.8 + 161418. i) q^{53} +(-43232.7 + 24960.4i) q^{54} -65422.9i q^{55} +(-171108. + 115564. i) q^{56} +104166. q^{57} +(91514.3 + 158507. i) q^{58} +(195032. + 112602. i) q^{59} +(68018.1 - 117811. i) q^{60} +(-125018. + 72179.1i) q^{61} -367214. i q^{62} +(74935.6 + 36492.6i) q^{63} -407497. q^{64} +(96639.7 + 167385. i) q^{65} +(-146286. - 84458.5i) q^{66} +(117740. - 203932. i) q^{67} +(-740448. + 427498. i) q^{68} -293571. i q^{69} +(-358774. + 25305.5i) q^{70} +96269.3 q^{71} +(-73140.0 - 126682. i) q^{72} +(238634. + 137775. i) q^{73} +(525008. - 909340. i) q^{74} +(-125471. + 72440.5i) q^{75} +732893. i q^{76} +(19843.1 + 281329. i) q^{77} +499033. q^{78} +(340667. + 590052. i) q^{79} +(62971.5 + 36356.6i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(675610. - 390064. i) q^{82} +128019. i q^{83} +(-256756. + 527235. i) q^{84} -620264. q^{85} +(-605073. - 1.04802e6i) q^{86} +(187491. + 108248. i) q^{87} +(247484. - 428655. i) q^{88} +(-322756. + 186343. i) q^{89} -254807. i q^{90} +(-466335. - 690470. i) q^{91} +2.06552e6 q^{92} +(-217180. - 376167. i) q^{93} +(-57293.5 - 33078.4i) q^{94} +(-265842. + 460452. i) q^{95} +(-357519. + 206414. i) q^{96} -620049. i q^{97} +(1.53511e6 - 217635. i) q^{98} -199804. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	6.58935	+	11.4131i	0.823668	+	1.42664i	0.902933	+	0.429782i	$0.141409\pi$
$2$	6.58935	+	11.4131i	0.823668	+	1.42664i	−0.0792645	+	0.996854i	$0.525257\pi$
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$4$	−54.8390	+	94.9839i	−0.856859	+	1.48412i
$5$	−68.9069	+	39.7834i	−0.551255	+	0.318267i	−0.749628	−	0.661859i	$-0.769768\pi$
$5$	−68.9069	+	39.7834i	−0.551255	+	0.318267i	0.198373	+	0.980127i	$0.436434\pi$
$6$			205.435i			0.951090i
$7$	284.244	−	191.975i	0.828700	−	0.559693i
$7$	284.244	−	191.975i	0.828700	−	0.559693i
$8$	−601.976			−1.17573
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$	−908.103	−	524.293i	−0.908103	−	0.524293i
$11$	−411.119	+	712.080i	−0.308880	+	0.534996i	−0.978118	−	0.208052i	$-0.933288\pi$
$11$	−411.119	+	712.080i	−0.308880	+	0.534996i	0.669238	+	0.743049i	$0.266621\pi$
$12$	−1480.65	+	854.855i	−0.856859	+	0.494708i
$13$		−	2429.15i		−	1.10567i	−0.833292	−	0.552833i	$-0.813547\pi$
$13$		−	2429.15i		−	1.10567i	0.833292	−	0.552833i	$-0.186453\pi$
$14$	4064.01	+	1979.11i	1.48105	+	0.721251i
$15$	−1240.32			−0.367503
$16$	−456.932	−	791.429i	−0.111556	−	0.193220i
$17$	6751.11	+	3897.76i	1.37413	+	0.793355i	0.991445	−	0.130523i	$-0.0416656\pi$
$17$	6751.11	+	3897.76i	1.37413	+	0.793355i	0.382687	+	0.923878i	$0.374999\pi$
$18$	−1601.21	+	2773.38i	−0.274556	+	0.475545i
$19$	5786.98	−	3341.12i	0.843706	−	0.487114i	−0.0148160	−	0.999890i	$-0.504716\pi$
$19$	5786.98	−	3341.12i	0.843706	−	0.487114i	0.858522	+	0.512776i	$0.171383\pi$
$20$		−	8726.73i		−	1.09084i
$21$	5333.59	−	376.196i	0.575919	−	0.0406215i
$22$	−10836.0			−1.01766
$23$	−9416.30	−	16309.5i	−0.773921	−	1.34047i	−0.935399	−	0.353594i	$-0.884959\pi$
$23$	−9416.30	−	16309.5i	−0.773921	−	1.34047i	0.161478	−	0.986876i	$-0.448374\pi$
$24$	−8126.67	−	4691.94i	−0.587867	−	0.339405i
$25$	−4647.06	+	8048.94i	−0.297412	+	0.515132i
$26$	27724.0	−	16006.5i	1.57738	−	0.910701i
$27$			3788.00i			0.192450i
$28$	2646.85	+	37526.3i	0.120575	+	1.70947i
$29$	13888.2			0.569446			0.284723	−	0.958610i	$-0.408098\pi$
$29$	13888.2			0.569446			0.284723	+	0.958610i	$0.408098\pi$
$30$	−8172.93	−	14155.9i	−0.302701	−	0.524293i
$31$	−24131.1	−	13932.1i	−0.810014	−	0.467662i	0.0369467	−	0.999317i	$-0.488237\pi$
$31$	−24131.1	−	13932.1i	−0.810014	−	0.467662i	−0.846961	+	0.531655i	$0.821570\pi$
$32$	−13241.5	+	22934.9i	−0.404097	+	0.699917i
$33$	−11100.2	+	6408.72i	−0.308880	+	0.178332i
$34$			102735.i			2.61385i
$35$	−11949.0	+	24536.6i	−0.278693	+	0.572282i
$36$	−26651.7			−0.571239
$37$	−39837.6	−	69000.8i	−0.786481	−	1.36223i	−0.928110	−	0.372305i	$-0.878567\pi$
$37$	−39837.6	−	69000.8i	−0.786481	−	1.36223i	0.141629	−	0.989920i	$-0.454766\pi$
$38$	76264.9	+	44031.5i	1.38987	+	0.802441i
$39$	18933.3	−	32793.5i	0.319178	−	0.552833i
$40$	41480.3	−	23948.6i	0.648129	−	0.374198i
$41$		−	59196.1i		−	0.858898i	−0.903091	−	0.429449i	$-0.858708\pi$
$41$		−	59196.1i		−	0.858898i	0.903091	−	0.429449i	$-0.141292\pi$
$42$	39438.4	+	58393.8i	0.532319	+	0.788168i
$43$	−91825.9			−1.15494			−0.577471	−	0.816411i	$-0.695960\pi$
$43$	−91825.9			−1.15494			−0.577471	+	0.816411i	$0.695960\pi$
$44$	−45090.7	−	78099.4i	−0.529333	−	0.916832i
$45$	−16744.4	−	9667.37i	−0.183752	−	0.106089i
$46$	124095.	−	214938.i	1.27491	−	2.20821i
$47$	−4347.44	+	2509.99i	−0.0418735	+	0.0241757i	−0.520791	−	0.853684i	$-0.674363\pi$
$47$	−4347.44	+	2509.99i	−0.0418735	+	0.0241757i	0.478917	+	0.877860i	$0.341029\pi$
$48$		−	14245.7i		−	0.128813i
$49$	43940.4	−	109135.i	0.373487	−	0.927635i
$50$	−122484.			−0.979875
$51$	60760.0	+	105239.i	0.458044	+	0.793355i
$52$	230730.	+	133212.i	1.64094	+	0.947399i
$53$	−93194.8	+	161418.i	−0.625985	+	1.08424i	0.362365	+	0.932036i	$0.381970\pi$
$53$	−93194.8	+	161418.i	−0.625985	+	1.08424i	−0.988350	+	0.152201i	$0.951364\pi$
$54$	−43232.7	+	24960.4i	−0.274556	+	0.158515i
$55$		−	65422.9i		−	0.393226i
$56$	−171108.	+	115564.i	−0.974330	+	0.658050i
$57$	104166.			0.562471
$58$	91514.3	+	158507.i	0.469035	+	0.812392i
$59$	195032.	+	112602.i	0.949618	+	0.548262i	0.892962	−	0.450132i	$-0.148623\pi$
$59$	195032.	+	112602.i	0.949618	+	0.548262i	0.0566558	+	0.998394i	$0.481956\pi$
$60$	68018.1	−	117811.i	0.314899	−	0.545420i
$61$	−125018.	+	72179.1i	−0.550786	+	0.317996i	−0.749439	−	0.662074i	$-0.769677\pi$
$61$	−125018.	+	72179.1i	−0.550786	+	0.317996i	0.198653	+	0.980070i	$0.436343\pi$
$62$		−	367214.i		−	1.54079i
$63$	74935.6	+	36492.6i	0.299686	+	0.145943i
$64$	−407497.			−1.55448
$65$	96639.7	+	167385.i	0.351897	+	0.609504i
$66$	−146286.	−	84458.5i	−0.508830	−	0.293773i
$67$	117740.	−	203932.i	0.391471	−	0.678048i	−0.601173	−	0.799119i	$-0.705300\pi$
$67$	117740.	−	203932.i	0.391471	−	0.678048i	0.992644	+	0.121071i	$0.0386329\pi$
$68$	−740448.	+	427498.i	−2.35487	+	1.35959i
$69$		−	293571.i		−	0.893647i
$70$	−358774.	+	25305.5i	−1.04599	+	0.0737770i
$71$	96269.3			0.268975			0.134488	−	0.990915i	$-0.457061\pi$
$71$	96269.3			0.268975			0.134488	+	0.990915i	$0.457061\pi$
$72$	−73140.0	−	126682.i	−0.195956	−	0.339405i
$73$	238634.	+	137775.i	0.613428	+	0.354163i	0.774306	−	0.632812i	$-0.218099\pi$
$73$	238634.	+	137775.i	0.613428	+	0.354163i	−0.160878	+	0.986974i	$0.551433\pi$
$74$	525008.	−	909340.i	1.29560	−	2.24404i
$75$	−125471.	+	72440.5i	−0.297412	+	0.171711i
$76$			732893.i			1.66955i
$77$	19843.1	+	281329.i	0.0434647	+	0.616229i
$78$	499033.			1.05159
$79$	340667.	+	590052.i	0.690953	+	1.19677i	0.971526	+	0.236933i	$0.0761423\pi$
$79$	340667.	+	590052.i	0.690953	+	1.19677i	−0.280573	+	0.959833i	$0.590524\pi$
$80$	62971.5	+	36356.6i	0.122991	+	0.0710090i
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$	675610.	−	390064.i	1.22533	−	0.707447i
$83$			128019.i			0.223893i	0.993714	+	0.111946i	$0.0357085\pi$
$83$			128019.i			0.223893i	−0.993714	+	0.111946i	$0.964291\pi$
$84$	−256756.	+	527235.i	−0.433194	+	0.889542i
$85$	−620264.			−1.01000
$86$	−605073.	−	1.04802e6i	−0.951288	−	1.64768i
$87$	187491.	+	108248.i	0.284723	+	0.164385i
$88$	247484.	−	428655.i	0.363161	−	0.629013i
$89$	−322756.	+	186343.i	−0.457829	+	0.264328i	−0.711131	−	0.703059i	$-0.751817\pi$
$89$	−322756.	+	186343.i	−0.457829	+	0.264328i	0.253302	+	0.967387i	$0.418483\pi$
$90$		−	254807.i		−	0.349529i
$91$	−466335.	−	690470.i	−0.618833	−	0.916265i
$92$	2.06552e6			2.65257
$93$	−217180.	−	376167.i	−0.270005	−	0.467662i
$94$	−57293.5	−	33078.4i	−0.0689798	−	0.0398255i
$95$	−265842.	+	460452.i	−0.310065	+	0.537048i
$96$	−357519.	+	206414.i	−0.404097	+	0.233306i
$97$		−	620049.i		−	0.679377i	−0.940538	−	0.339688i	$-0.889678\pi$
$97$		−	620049.i		−	0.679377i	0.940538	−	0.339688i	$-0.110322\pi$
$98$	1.53511e6	−	217635.i	1.63103	−	0.231234i
$99$	−199804.			−0.205920
$100$	−509680.	−	882792.i	−0.509680	−	0.882792i
$101$	−578698.	−	334111.i	−0.561678	−	0.324285i	0.192141	−	0.981367i	$-0.438457\pi$
$101$	−578698.	−	334111.i	−0.561678	−	0.324285i	−0.753819	+	0.657082i	$0.771790\pi$
$102$	−800737.	+	1.38692e6i	−0.754553	+	1.30692i
$103$	1.34180e6	−	774691.i	1.22794	−	0.708952i	0.261342	−	0.965246i	$-0.415835\pi$
$103$	1.34180e6	−	774691.i	1.22794	−	0.708952i	0.966599	+	0.256294i	$0.0825016\pi$
$104$			1.46229e6i			1.29997i
$105$	−352555.	+	238111.i	−0.304550	+	0.205689i
$106$	−2.45637e6			−2.06242
$107$	477948.	+	827829.i	0.390148	+	0.675755i	0.992469	−	0.122498i	$-0.0390906\pi$
$107$	477948.	+	827829.i	0.390148	+	0.675755i	−0.602321	+	0.798254i	$0.705757\pi$
$108$	−359799.	−	207730.i	−0.285620	−	0.164903i
$109$	−785863.	+	1.36115e6i	−0.606830	+	1.05106i	0.384929	+	0.922946i	$0.374226\pi$
$109$	−785863.	+	1.36115e6i	−0.606830	+	1.05106i	−0.991759	+	0.128115i	$0.959107\pi$
$110$	746677.	−	431094.i	0.560990	−	0.323888i
$111$		−	1.24201e6i		−	0.908150i
$112$	−281814.	−	137240.i	−0.200590	−	0.0976845i
$113$	−2.47576e6			−1.71582			−0.857912	−	0.513797i	$-0.828238\pi$
$113$	−2.47576e6			−1.71582			−0.857912	+	0.513797i	$0.828238\pi$
$114$	686384.	+	1.18885e6i	0.463289	+	0.802441i
$115$	1.29770e6	+	749225.i	0.853256	+	0.492628i
$116$	−761615.	+	1.31916e6i	−0.487935	+	0.845128i
$117$	511200.	−	295141.i	0.319178	−	0.184278i
$118$			2.96788e6i			1.80634i
$119$	2.66723e6	−	188129.i	1.58278	−	0.111639i
$120$	746645.			0.432086
$121$	547742.	+	948717.i	0.309186	+	0.535526i
$122$	−1.64757e6	−	951226.i	−0.907329	−	0.523847i
$123$	461388.	−	799148.i	0.247943	−	0.429449i
$124$	2.64665e6	−	1.52805e6i	1.38814	−	0.801441i
$125$		−	1.98274e6i		−	1.01516i
$126$	77283.9	+	1.09571e6i	0.0386347	+	0.547751i
$127$	292592.			0.142840			0.0714202	−	0.997446i	$-0.477247\pi$
$127$	292592.			0.142840			0.0714202	+	0.997446i	$0.477247\pi$
$128$	−1.83769e6	−	3.18297e6i	−0.876278	−	1.51776i
$129$	−1.23965e6	−	715712.i	−0.577471	−	0.333403i
$130$	−1.27359e6	+	2.20591e6i	−0.579693	+	1.00406i
$131$	−2.36324e6	+	1.36442e6i	−1.05122	+	0.606924i	−0.922991	−	0.384820i	$-0.874263\pi$
$131$	−2.36324e6	+	1.36442e6i	−1.05122	+	0.606924i	−0.128231	+	0.991744i	$0.540930\pi$
$132$		−	1.40579e6i		−	0.611222i
$133$	1.00351e6	−	2.06065e6i	0.426545	−	0.875888i
$134$	3.10332e6			1.28977
$135$	−150699.	−	261019.i	−0.0612506	−	0.106089i
$136$	−4.06400e6	−	2.34635e6i	−1.61561	−	0.932775i
$137$	453922.	−	786216.i	0.176530	−	0.305760i	−0.764159	−	0.645027i	$-0.776846\pi$
$137$	453922.	−	786216.i	0.176530	−	0.305760i	0.940690	+	0.339268i	$0.110179\pi$
$138$	3.35055e6	−	1.93444e6i	1.27491	−	0.736069i
$139$			4640.07i			0.00172775i	1.00000		0.000863874i	$0.000274980\pi$
$139$			4640.07i			0.00172775i	−1.00000		0.000863874i	$0.999725\pi$
$140$	−1.67531e6	−	2.48052e6i	−0.610536	−	0.903980i
$141$	−78253.8			−0.0279157
$142$	634352.	+	1.09873e6i	0.221547	+	0.383730i
$143$	1.72975e6	+	998669.i	0.591526	+	0.341518i
$144$	111034.	−	192317.i	0.0371852	−	0.0644066i
$145$	−956994.	+	552521.i	−0.313910	+	0.181236i
$146$			3.63140e6i			1.16685i
$147$	1.44382e6	−	1.13085e6i	0.454529	−	0.356001i
$148$	8.73862e6			2.69561
$149$	823601.	+	1.42652e6i	0.248976	+	0.431240i	0.963242	−	0.268635i	$-0.0865725\pi$
$149$	823601.	+	1.42652e6i	0.248976	+	0.431240i	−0.714266	+	0.699875i	$0.753239\pi$
$150$	−1.65354e6	−	954671.i	−0.489937	−	0.282865i
$151$	1.22295e6	−	2.11820e6i	0.355203	−	0.615229i	−0.631950	−	0.775009i	$-0.717745\pi$
$151$	1.22295e6	−	2.11820e6i	0.355203	−	0.615229i	0.987153	+	0.159780i	$0.0510785\pi$
$152$	−3.48362e6	+	2.01127e6i	−0.991974	+	0.572716i
$153$			1.89431e6i			0.528904i
$154$	−3.08008e6	+	2.08024e6i	−0.843334	+	0.569577i
$155$	2.21707e6			0.595366
$156$	2.07657e6	+	3.59672e6i	0.546981	+	0.947399i
$157$	−2.43822e6	−	1.40771e6i	−0.630049	−	0.363759i	0.150722	−	0.988576i	$-0.451840\pi$
$157$	−2.43822e6	−	1.40771e6i	−0.630049	−	0.363759i	−0.780771	+	0.624817i	$0.785174\pi$
$158$	−4.48954e6	+	7.77612e6i	−1.13823	+	1.97148i
$159$	−2.51626e6	+	1.45276e6i	−0.625985	+	0.361413i
$160$		−	2.10716e6i		−	0.514444i
$161$	−5.80754e6	−	2.82819e6i	−1.39160	−	0.677690i
$162$	−778189.			−0.183037
$163$	781407.	+	1.35344e6i	0.180432	+	0.312518i	0.942028	−	0.335535i	$-0.108917\pi$
$163$	781407.	+	1.35344e6i	0.180432	+	0.312518i	−0.761596	+	0.648053i	$0.775584\pi$
$164$	5.62268e6	+	3.24625e6i	1.27471	+	0.735955i
$165$	509921.	−	883210.i	0.113515	−	0.196613i
$166$	−1.46109e6	+	843562.i	−0.319414	+	0.184414i
$167$		−	1.15538e6i		−	0.248070i	−0.992278	−	0.124035i	$-0.960416\pi$
$167$		−	1.15538e6i		−	0.248070i	0.992278	−	0.124035i	$-0.0395835\pi$
$168$	−3.21069e6	+	226461.i	−0.677128	+	0.0477600i
$169$	−1.07394e6			−0.222495
$170$	−4.08713e6	−	7.07913e6i	−0.831902	−	1.44090i
$171$	1.40624e6	+	811891.i	0.281235	+	0.162371i
$172$	5.03564e6	−	8.72198e6i	0.989622	−	1.71408i
$173$	−4.98920e6	+	2.88052e6i	−0.963591	+	0.556330i	−0.897277	−	0.441469i	$-0.854458\pi$
$173$	−4.98920e6	+	2.88052e6i	−0.963591	+	0.556330i	−0.0663149	+	0.997799i	$0.521124\pi$
$174$			2.85313e6i			0.541594i
$175$	224295.	+	3.17998e6i	0.0418509	+	0.593350i
$176$	751414.			0.137829
$177$	1.75528e6	+	3.04024e6i	0.316539	+	0.548262i
$178$	−4.25350e6	−	2.45576e6i	−0.754199	−	0.435437i
$179$	597801.	−	1.03542e6i	0.104231	−	0.180534i	−0.809193	−	0.587543i	$-0.800095\pi$
$179$	597801.	−	1.03542e6i	0.104231	−	0.180534i	0.913424	+	0.407010i	$0.133429\pi$
$180$	1.83649e6	−	1.06030e6i	0.314899	−	0.181807i
$181$		−	1.00030e7i		−	1.68692i	−0.537191	−	0.843461i	$-0.680514\pi$
$181$		−	1.00030e7i		−	1.68692i	0.537191	−	0.843461i	$-0.319486\pi$
$182$	4.80756e6	−	9.87207e6i	0.797462	−	1.63755i
$183$	−2.25032e6			−0.367190
$184$	5.66838e6	+	9.81793e6i	0.909925	+	1.57604i
$185$	5.49017e6	+	3.16975e6i	0.867104	+	0.500622i
$186$	2.86215e6	−	4.95739e6i	0.444789	−	0.770397i
$187$	−5.55102e6	+	3.20489e6i	−0.848884	+	0.490103i
$188$		−	550582.i		−	0.0828606i
$189$	727199.	+	1.07672e6i	0.107713	+	0.159483i
$190$	−7.00690e6			−1.02156
$191$	3.79135e6	+	6.56682e6i	0.544120	+	0.942443i	0.998662	+	0.0517175i	$0.0164695\pi$
$191$	3.79135e6	+	6.56682e6i	0.544120	+	0.942443i	−0.454542	+	0.890725i	$0.650197\pi$
$192$	−5.50122e6	−	3.17613e6i	−0.777240	−	0.448740i
$193$	−3.54806e6	+	6.14542e6i	−0.493537	+	0.854830i	−0.999972	−	0.00744730i	$-0.997629\pi$
$193$	−3.54806e6	+	6.14542e6i	−0.493537	+	0.854830i	0.506436	+	0.862278i	$0.330963\pi$
$194$	7.07667e6	−	4.08572e6i	0.969223	−	0.559581i
$195$			3.01293e6i			0.406336i
$196$	7.95645e6	+	1.01585e7i	1.05670	+	1.34915i
$197$	2.00096e6			0.261722			0.130861	−	0.991401i	$-0.458226\pi$
$197$	2.00096e6			0.261722			0.130861	+	0.991401i	$0.458226\pi$
$198$	−1.31658e6	−	2.28038e6i	−0.169610	−	0.293773i
$199$	−3.76381e6	−	2.17304e6i	−0.477605	−	0.275745i	0.241813	−	0.970323i	$-0.422258\pi$
$199$	−3.76381e6	−	2.17304e6i	−0.477605	−	0.275745i	−0.719418	+	0.694578i	$0.755591\pi$
$200$	2.79742e6	−	4.84527e6i	0.349677	−	0.605658i
$201$	3.17898e6	−	1.83539e6i	0.391471	−	0.226016i
$202$		−	8.80630e6i		−	1.06841i
$203$	3.94764e6	−	2.66619e6i	0.471900	−	0.318715i
$204$	−1.33281e7			−1.56992
$205$	2.35502e6	+	4.07902e6i	0.273359	+	0.473472i
$206$	1.76832e7	+	1.02094e7i	2.02283	+	1.16788i
$207$	2.28816e6	−	3.96321e6i	0.257974	−	0.446824i
$208$	−1.92250e6	+	1.10995e6i	−0.213637	+	0.123343i
$209$			5.49439e6i			0.601839i
$210$	−5.04069e6	−	2.45474e6i	−0.544292	−	0.265062i
$211$	1.03642e7			1.10328			0.551641	−	0.834082i	$-0.314002\pi$
$211$	1.03642e7			1.10328			0.551641	+	0.834082i	$0.314002\pi$
$212$	−1.02214e7	−	1.77040e7i	−1.07276	−	1.85808i
$213$	1.29964e6	+	750345.i	0.134488	+	0.0776465i
$214$	−6.29872e6	+	1.09097e7i	−0.642704	+	1.11320i
$215$	6.32744e6	−	3.65315e6i	0.636667	−	0.367580i
$216$		−	2.28028e6i		−	0.226270i
$217$	−9.53375e6	+	672446.i	−0.933006	+	0.0658079i
$218$	−2.07133e7			−1.99931
$219$	2.14770e6	+	3.71993e6i	0.204476	+	0.354163i
$220$	6.21413e6	+	3.58773e6i	0.583596	+	0.336939i
$221$	9.46822e6	−	1.63994e7i	0.877185	−	1.51933i
$222$	1.41752e7	−	8.18406e6i	1.29560	−	0.748014i
$223$			4.84791e6i			0.437159i	0.975819	+	0.218580i	$0.0701424\pi$
$223$			4.84791e6i			0.437159i	−0.975819	+	0.218580i	$0.929858\pi$
$224$	639111.	+	9.06113e6i	0.0568633	+	0.806192i
$225$	−2.25847e6			−0.198275
$226$	−1.63136e7	−	2.82560e7i	−1.41327	−	2.44785i
$227$	−1.30838e7	−	7.55396e6i	−1.11856	−	0.645798i	−0.177524	−	0.984117i	$-0.556809\pi$
$227$	−1.30838e7	−	7.55396e6i	−1.11856	−	0.645798i	−0.941032	+	0.338318i	$0.890142\pi$
$228$	−5.71234e6	+	9.89406e6i	−0.481958	+	0.834776i
$229$	−3.68382e6	+	2.12685e6i	−0.306755	+	0.177105i	−0.645474	−	0.763783i	$-0.723340\pi$
$229$	−3.68382e6	+	2.12685e6i	−0.306755	+	0.177105i	0.338718	+	0.940888i	$0.390007\pi$
$230$			1.97476e7i			1.62305i
$231$	−1.92486e6	+	3.95260e6i	−0.156158	+	0.320662i
$232$	−8.36037e6			−0.669517
$233$	−6.29087e6	−	1.08961e7i	−0.497328	−	0.861397i	0.502667	−	0.864480i	$-0.332352\pi$
$233$	−6.29087e6	−	1.08961e7i	−0.497328	−	0.861397i	−0.999995	+	0.00308269i	$0.999019\pi$
$234$	6.73694e6	+	3.88958e6i	0.525794	+	0.303567i
$235$	199712.	−	345912.i	0.0153887	−	0.0266540i
$236$	−2.13907e7	+	1.23499e7i	−1.62738	+	0.939567i
$237$			1.06209e7i			0.797844i
$238$	1.97225e7	+	2.92017e7i	1.46295	+	2.16609i
$239$	7.54342e6			0.552554			0.276277	−	0.961078i	$-0.410899\pi$
$239$	7.54342e6			0.552554			0.276277	+	0.961078i	$0.410899\pi$
$240$	566743.	+	981628.i	0.0409971	+	0.0710090i
$241$	1.69553e7	+	9.78914e6i	1.21131	+	0.699348i	0.963044	−	0.269345i	$-0.0868071\pi$
$241$	1.69553e7	+	9.78914e6i	1.21131	+	0.699348i	0.248262	+	0.968693i	$0.420140\pi$
$242$	−7.21853e6	+	1.25029e7i	−0.509334	+	0.882192i
$243$	−797162.	+	460241.i	−0.0555556	+	0.0320750i
$244$		−	1.58329e7i		−	1.08991i
$245$	1.31398e6	+	9.26828e6i	0.0893492	+	0.630233i
$246$	1.21610e7			0.816890
$247$	−8.11606e6	−	1.40574e7i	−0.538585	−	0.932857i
$248$	1.45264e7	+	8.38679e6i	0.952361	+	0.549846i
$249$	−997810.	+	1.72826e6i	−0.0646323	+	0.111946i
$250$	2.26291e7	−	1.30649e7i	1.44826	−	0.836156i
$251$			1.39590e7i			0.882743i	0.897324	+	0.441372i	$0.145508\pi$
$251$			1.39590e7i			0.882743i	−0.897324	+	0.441372i	$0.854492\pi$
$252$	−7.57560e6	+	5.11646e6i	−0.473386	+	0.319719i
$253$	1.54849e7			0.956195
$254$	1.92799e6	+	3.33938e6i	0.117653	+	0.203781i
$255$	−8.37356e6	−	4.83448e6i	−0.504998	−	0.291561i
$256$	1.11784e7	−	1.93616e7i	0.666285	−	1.15404i
$257$	−567649.	+	327732.i	−0.0334411	+	0.0193072i	−0.516627	−	0.856210i	$-0.672813\pi$
$257$	−567649.	+	327732.i	−0.0334411	+	0.0193072i	0.483186	+	0.875518i	$0.339479\pi$
$258$		−	1.88643e7i		−	1.09845i
$259$	−2.45700e7	−	1.19652e7i	−1.41418	−	0.688688i
$260$	−2.11985e7			−1.20610
$261$	1.68742e6	+	2.92269e6i	0.0949076	+	0.164385i
$262$	−3.11445e7	−	1.79813e7i	−1.73172	−	0.999808i
$263$	7.46998e6	−	1.29384e7i	0.410632	−	0.711235i	−0.584327	−	0.811518i	$-0.698642\pi$
$263$	7.46998e6	−	1.29384e7i	0.410632	−	0.711235i	0.994959	+	0.100283i	$0.0319749\pi$
$264$	6.68206e6	−	3.85789e6i	0.363161	−	0.209671i
$265$		−	1.48304e7i		−	0.796922i
$266$	3.01308e7	−	2.12522e6i	1.60090	−	0.112917i
$267$	−5.80960e6			−0.305220
$268$	1.29135e7	+	2.23668e7i	0.670871	+	1.16198i
$269$	−2.72017e7	−	1.57049e7i	−1.39746	−	0.806825i	−0.403335	−	0.915052i	$-0.632149\pi$
$269$	−2.72017e7	−	1.57049e7i	−1.39746	−	0.806825i	−0.994126	+	0.108227i	$0.965483\pi$
$270$	1.98602e6	−	3.43989e6i	0.100900	−	0.174764i
$271$	−1.29500e6	+	747670.i	−0.0650673	+	0.0375666i	−0.532181	−	0.846631i	$-0.678627\pi$
$271$	−1.29500e6	+	747670.i	−0.0650673	+	0.0375666i	0.467113	+	0.884197i	$0.345294\pi$
$272$		−	7.12403e6i		−	0.354013i
$273$	−913834.	−	1.29561e7i	−0.0449138	−	0.636774i
$274$	1.19642e7			0.581610
$275$	−3.82099e6	−	6.61815e6i	−0.183729	−	0.318228i
$276$	2.78845e7	+	1.60991e7i	1.32628	+	0.765730i
$277$	991747.	−	1.71776e6i	0.0466618	−	0.0808207i	−0.841751	−	0.539866i	$-0.818475\pi$
$277$	991747.	−	1.71776e6i	0.0466618	−	0.0808207i	0.888413	+	0.459045i	$0.151808\pi$
$278$	−52957.5	+	30575.1i	−0.00246487	+	0.00142309i
$279$		−	6.77101e6i		−	0.311775i
$280$	7.19299e6	−	1.47704e7i	0.327669	−	0.672851i
$281$	−3.50353e6			−0.157902			−0.0789508	−	0.996879i	$-0.525157\pi$
$281$	−3.50353e6			−0.157902			−0.0789508	+	0.996879i	$0.525157\pi$
$282$	−515642.	−	893117.i	−0.0229933	−	0.0398255i
$283$	2.82715e7	+	1.63226e7i	1.24736	+	0.720161i	0.970581	−	0.240774i	$-0.0774012\pi$
$283$	2.82715e7	+	1.63226e7i	1.24736	+	0.720161i	0.276774	+	0.960935i	$0.410735\pi$
$284$	−5.27931e6	+	9.14403e6i	−0.230474	+	0.399193i
$285$	−7.17773e6	+	4.14407e6i	−0.310065	+	0.179016i
$286$			2.63223e7i			1.12519i
$287$	−1.13642e7	−	1.68261e7i	−0.480719	−	0.711769i
$288$	−6.43535e6			−0.269398
$289$	1.83162e7	+	3.17246e7i	0.758826	+	1.31432i
$290$	−1.26119e7	−	7.28150e6i	−0.517115	−	0.298557i
$291$	4.83280e6	−	8.37066e6i	0.196119	−	0.339688i
$292$	−2.61729e7	+	1.51109e7i	−1.05124	+	0.606935i
$293$		−	2.57653e7i		−	1.02431i	−0.858892	−	0.512156i	$-0.828847\pi$
$293$		−	2.57653e7i		−	1.02431i	0.858892	−	0.512156i	$-0.171153\pi$
$294$	2.24203e7	+	9.02692e6i	0.882265	+	0.355220i
$295$	−1.79187e7			−0.697976
$296$	2.39813e7	+	4.15368e7i	0.924692	+	1.60161i
$297$	−2.69735e6	−	1.55732e6i	−0.102960	−	0.0594440i
$298$	−1.08540e7	+	1.87996e7i	−0.410148	+	0.710397i
$299$	−3.96182e7	+	2.28736e7i	−1.48211	+	0.855698i
$300$		−	1.58902e7i		−	0.588528i
$301$	−2.61010e7	+	1.76283e7i	−0.957100	+	0.646413i
$302$	3.22336e7			1.17028
$303$	−5.20828e6	−	9.02100e6i	−0.187226	−	0.324285i
$304$	−5.28851e6	−	3.05332e6i	−0.188240	−	0.108681i
$305$	5.74306e6	−	9.94727e6i	0.202416	−	0.350594i
$306$	−2.16199e7	+	1.24823e7i	−0.754553	+	0.435641i
$307$			1.89894e7i			0.656289i	0.944628	+	0.328145i	$0.106423\pi$
$307$			1.89894e7i			0.656289i	−0.944628	+	0.328145i	$0.893577\pi$
$308$	−2.78099e7	−	1.35430e7i	−0.951803	−	0.463515i
$309$	2.41525e7			0.818627
$310$	1.46090e7	+	2.53036e7i	0.490384	+	0.849370i
$311$	2.80365e7	+	1.61869e7i	0.932057	+	0.538124i	0.887462	−	0.460881i	$-0.152467\pi$
$311$	2.80365e7	+	1.61869e7i	0.932057	+	0.538124i	0.0445958	+	0.999005i	$0.485800\pi$
$312$	−1.13974e7	+	1.97409e7i	−0.375268	+	0.649984i
$313$	2.81397e7	−	1.62465e7i	0.917671	−	0.529818i	0.0347798	−	0.999395i	$-0.488927\pi$
$313$	2.81397e7	−	1.62465e7i	0.917671	−	0.529818i	0.882891	+	0.469577i	$0.155594\pi$
$314$		−	3.71035e7i		−	1.19847i
$315$	−6.61538e6	+	466604.i	−0.211652	+	0.0149285i
$316$	−7.47273e7			−2.36820
$317$	8.17142e6	+	1.41533e7i	0.256519	+	0.444304i	0.965307	−	0.261118i	$-0.0840910\pi$
$317$	8.17142e6	+	1.41533e7i	0.256519	+	0.444304i	−0.708788	+	0.705422i	$0.750758\pi$
$318$	−3.31610e7	−	1.91455e7i	−1.03121	−	0.595368i
$319$	−5.70972e6	+	9.88952e6i	−0.175891	+	0.304651i
$320$	2.80794e7	−	1.62116e7i	0.856915	−	0.494740i
$321$			1.49009e7i			0.450504i
$322$	−5.98953e6	−	8.49179e7i	−0.179401	−	2.54350i
$323$	5.20914e7			1.54582
$324$	−3.23819e6	−	5.60870e6i	−0.0952065	−	0.164903i
$325$	1.95521e7	+	1.12884e7i	0.569564	+	0.328838i
$326$	−1.02979e7	+	1.78365e7i	−0.297233	+	0.514822i
$327$	−2.12183e7	+	1.22504e7i	−0.606830	+	0.350354i
$328$			3.56346e7i			1.00984i
$329$	−753878.	+	1.54805e6i	−0.0211696	+	0.0434707i
$330$	1.34402e7			0.373993
$331$	−2.58785e7	−	4.48229e7i	−0.713601	−	1.23599i	−0.963497	−	0.267720i	$-0.913730\pi$
$331$	−2.58785e7	−	4.48229e7i	−0.713601	−	1.23599i	0.249896	−	0.968273i	$-0.419604\pi$
$332$	−1.21598e7	−	7.02044e6i	−0.332285	−	0.191845i
$333$	9.68054e6	−	1.67672e7i	0.262160	−	0.454075i
$334$	1.31864e7	−	7.61318e6i	0.353905	−	0.204327i
$335$			1.87364e7i			0.498370i
$336$	−2.73482e6	−	4.04926e6i	−0.0720959	−	0.106748i
$337$	6.13986e7			1.60424			0.802119	−	0.597164i	$-0.203706\pi$
$337$	6.13986e7			1.60424			0.802119	+	0.597164i	$0.203706\pi$
$338$	−7.07658e6	−	1.22570e7i	−0.183262	−	0.317420i
$339$	−3.34227e7	−	1.92966e7i	−0.857912	−	0.495316i
$340$	3.40146e7	−	5.89151e7i	0.865424	−	1.49896i
$341$	1.98416e7	−	1.14555e7i	0.500395	−	0.288903i
$342$			2.13993e7i			0.534961i
$343$	−8.46143e6	−	3.94565e7i	−0.209682	−	0.977770i
$344$	5.52770e7			1.35790
$345$	1.16793e7	+	2.02291e7i	0.284419	+	0.492628i
$346$	−6.57512e7	−	3.79615e7i	−1.58736	−	0.916462i
$347$	−1.77833e7	+	3.08017e7i	−0.425623	+	0.737200i	−0.996478	−	0.0838501i	$-0.973278\pi$
$347$	−1.77833e7	+	3.08017e7i	−0.425623	+	0.737200i	0.570855	+	0.821051i	$0.306612\pi$
$348$	−2.05636e7	+	1.18724e7i	−0.487935	+	0.281709i
$349$			5.17156e7i			1.21659i	0.793710	+	0.608297i	$0.208147\pi$
$349$			5.17156e7i			1.21659i	−0.793710	+	0.608297i	$0.791853\pi$
$350$	−3.48154e7	+	2.35139e7i	−0.812022	+	0.548429i
$351$	9.20159e6			0.212785
$352$	−1.08876e7	−	1.88579e7i	−0.249635	−	0.432381i
$353$	−669058.	−	386281.i	−0.0152104	−	0.00878171i	0.492376	−	0.870383i	$-0.336129\pi$
$353$	−669058.	−	386281.i	−0.0152104	−	0.00878171i	−0.507586	+	0.861601i	$0.669462\pi$
$354$	−2.31324e7	+	4.00664e7i	−0.521447	+	0.903172i
$355$	−6.63362e6	+	3.82992e6i	−0.148274	+	0.0856061i
$356$		−	4.08754e7i		−	0.905967i
$357$	3.74740e7	+	1.82493e7i	0.823617	+	0.401090i
$358$	1.57565e7			0.343407
$359$	2.08340e7	+	3.60856e7i	0.450287	+	0.779920i	0.998404	−	0.0564819i	$-0.0179883\pi$
$359$	2.08340e7	+	3.60856e7i	0.450287	+	0.779920i	−0.548117	+	0.836402i	$0.684655\pi$
$360$	1.00797e7	+	5.81952e6i	0.216043	+	0.124733i
$361$	−1.19684e6	+	2.07298e6i	−0.0254398	+	0.0440630i
$362$	1.14165e8	−	6.59133e7i	2.40662	−	1.38946i
$363$			1.70769e7i			0.357017i
$364$	9.11569e7	−	6.42959e6i	1.89010	−	0.133315i
$365$	−2.19247e7			−0.450874
$366$	−1.48281e7	−	2.56831e7i	−0.302443	−	0.523847i
$367$	5.71734e6	+	3.30091e6i	0.115663	+	0.0667783i	0.556716	−	0.830703i	$-0.312061\pi$
$367$	5.71734e6	+	3.30091e6i	0.115663	+	0.0667783i	−0.441052	+	0.897481i	$0.645395\pi$
$368$	−8.60521e6	+	1.49047e7i	−0.172670	+	0.299074i
$369$	1.24575e7	−	7.19233e6i	0.247943	−	0.143150i
$370$			8.35464e7i			1.64939i
$371$	4.49813e6	+	6.37732e7i	0.0880867	+	1.24887i
$372$	4.76398e7			0.925424
$373$	2.47581e6	+	4.28823e6i	0.0477080	+	0.0826326i	0.888893	−	0.458114i	$-0.151475\pi$
$373$	2.47581e6	+	4.28823e6i	0.0477080	+	0.0826326i	−0.841185	+	0.540747i	$0.818142\pi$
$374$	−7.31553e7	−	4.22362e7i	−1.39840	−	0.807365i
$375$	1.54539e7	−	2.67669e7i	0.293052	−	0.507580i
$376$	2.61705e6	−	1.51095e6i	0.0492321	−	0.0284242i
$377$		−	3.37365e7i		−	0.629616i
$378$	−7.49687e6	+	1.53944e7i	−0.138805	+	0.285029i
$379$	−1.05876e8			−1.94482			−0.972409	−	0.233282i	$-0.925053\pi$
$379$	−1.05876e8			−1.94482			−0.972409	+	0.233282i	$0.925053\pi$
$380$	−2.91570e7	−	5.05014e7i	−0.531364	−	0.920349i
$381$	3.94999e6	+	2.28053e6i	0.0714202	+	0.0412345i
$382$	−4.99651e7	+	8.65421e7i	−0.896348	+	1.55252i
$383$	−4.26092e7	+	2.46004e7i	−0.758414	+	0.437871i	−0.828726	−	0.559654i	$-0.810934\pi$
$383$	−4.26092e7	+	2.46004e7i	−0.758414	+	0.437871i	0.0703117	+	0.997525i	$0.477601\pi$
$384$		−	5.72935e7i		−	1.01184i
$385$	−1.25596e7	−	1.85961e7i	−0.220086	−	0.325866i
$386$	−9.35177e7			−1.62604
$387$	−1.11568e7	−	1.93242e7i	−0.192490	−	0.333403i
$388$	5.88947e7	+	3.40028e7i	1.00828	+	0.582130i
$389$	−3.33099e7	+	5.76945e7i	−0.565880	+	0.980134i	0.431087	+	0.902310i	$0.358130\pi$
$389$	−3.33099e7	+	5.76945e7i	−0.565880	+	0.980134i	−0.996967	+	0.0778231i	$0.975203\pi$
$390$	−3.43868e7	+	1.98532e7i	−0.579693	+	0.334686i
$391$		−	1.46810e8i		−	2.45598i
$392$	−2.64511e7	+	6.56968e7i	−0.439122	+	1.09065i
$393$	−4.25384e7			−0.700815
$394$	1.31850e7	+	2.28372e7i	0.215572	+	0.373382i
$395$	−4.69486e7	−	2.71058e7i	−0.761783	−	0.439816i
$396$	1.09570e7	−	1.89782e7i	0.176444	−	0.305611i
$397$	4.16040e7	−	2.40201e7i	0.664911	−	0.383887i	−0.129234	−	0.991614i	$-0.541252\pi$
$397$	4.16040e7	−	2.40201e7i	0.664911	−	0.383887i	0.794146	+	0.607727i	$0.207919\pi$
$398$		−	5.72756e7i		−	0.908491i
$399$	2.96085e7	−	1.99972e7i	0.466120	−	0.314811i
$400$	8.49355e6			0.132712
$401$	−6.97156e6	−	1.20751e7i	−0.108118	−	0.187265i	0.806890	−	0.590702i	$-0.201149\pi$
$401$	−6.97156e6	−	1.20751e7i	−0.108118	−	0.187265i	−0.915008	+	0.403436i	$0.867816\pi$
$402$	4.18948e7	+	2.41880e7i	0.644885	+	0.372324i
$403$	−3.38431e7	+	5.86180e7i	−0.517077	+	0.895604i
$404$	6.34704e7	−	3.66446e7i	0.962558	−	0.555733i
$405$		−	4.69834e6i		−	0.0707261i
$406$	5.64418e7	+	2.74864e7i	0.843379	+	0.410714i
$407$	6.55121e7			0.971713
$408$	−3.65760e7	−	6.33515e7i	−0.538538	−	0.932775i
$409$	1.93849e7	+	1.11919e7i	0.283331	+	0.163581i	0.634931	−	0.772569i	$-0.281029\pi$
$409$	1.93849e7	+	1.11919e7i	0.283331	+	0.163581i	−0.351599	+	0.936151i	$0.614362\pi$
$410$	−3.10361e7	+	5.37562e7i	−0.450315	+	0.779968i
$411$	1.22559e7	−	7.07594e6i	0.176530	−	0.101920i
$412$			1.69933e8i			2.42989i
$413$	7.70532e7	−	5.43482e6i	1.09381	−	0.0771498i
$414$	6.03099e7			0.849939
$415$	−5.09304e6	−	8.82140e6i	−0.0712578	−	0.123422i
$416$	5.57122e7	+	3.21654e7i	0.773874	+	0.446796i
$417$	−36165.8	+	62641.0i	−0.000498758	+	0.000863874i
$418$	−6.27079e7	+	3.62044e7i	−0.858605	+	0.495716i
$419$			5.41233e7i			0.735770i	0.929871	+	0.367885i	$0.119918\pi$
$419$			5.41233e7i			0.735770i	−0.929871	+	0.367885i	$0.880082\pi$
$420$	−3.28296e6	−	4.65448e7i	−0.0443116	−	0.628236i
$421$	−1.30034e8			−1.74265			−0.871323	−	0.490709i	$-0.836738\pi$
$421$	−1.30034e8			−1.74265			−0.871323	+	0.490709i	$0.836738\pi$
$422$	6.82930e7	+	1.18287e8i	0.908738	+	1.57398i
$423$	−1.05643e6	−	609928.i	−0.0139578	−	0.00805856i
$424$	5.61010e7	−	9.71697e7i	0.735992	−	1.27477i
$425$	−6.27456e7	+	3.62262e7i	−0.817366	+	0.471907i
$426$			1.97771e7i			0.255820i
$427$	−2.16790e7	+	4.45167e7i	−0.278456	+	0.571794i
$428$	−1.04841e8			−1.33721
$429$	1.55677e7	+	2.69641e7i	0.197175	+	0.341518i
$430$	8.33874e7	+	4.81437e7i	1.04881	+	0.605528i
$431$	5.99710e7	−	1.03873e8i	0.749047	−	1.29739i	−0.199233	−	0.979952i	$-0.563845\pi$
$431$	5.99710e7	−	1.03873e8i	0.749047	−	1.29739i	0.948280	−	0.317436i	$-0.102822\pi$
$432$	2.99793e6	−	1.73085e6i	0.0371852	−	0.0214689i
$433$		−	1.11549e8i		−	1.37404i	−0.726636	−	0.687022i	$-0.758917\pi$
$433$		−	1.11549e8i		−	1.37404i	0.726636	−	0.687022i	$-0.241083\pi$
$434$	−7.04958e7	−	1.04378e8i	−0.862371	−	1.27686i
$435$	−1.72259e7			−0.209273
$436$	−8.61918e7	−	1.49289e8i	−1.03994	−	1.80122i
$437$	−1.08984e8	−	6.29219e7i	−1.30592	−	0.753976i
$438$	−2.83039e7	+	4.90239e7i	−0.336841	+	0.583425i
$439$	1.06743e8	−	6.16284e7i	1.26168	−	0.728429i	0.288277	−	0.957547i	$-0.406918\pi$
$439$	1.06743e8	−	6.16284e7i	1.26168	−	0.728429i	0.973399	+	0.229118i	$0.0735842\pi$
$440$			3.93830e7i			0.462329i
$441$	2.83057e7	−	4.01295e6i	0.330033	−	0.0467894i
$442$	2.49557e8			2.89004
$443$	3.55708e7	+	6.16104e7i	0.409150	+	0.708669i	0.994795	−	0.101899i	$-0.0324919\pi$
$443$	3.55708e7	+	6.16104e7i	0.409150	+	0.708669i	−0.585645	+	0.810568i	$0.699159\pi$
$444$	1.17971e8	+	6.81108e7i	1.34781	+	0.778157i
$445$	1.48267e7	−	2.56806e7i	0.168254	−	0.291424i
$446$	−5.53296e7	+	3.19445e7i	−0.623667	+	0.360074i
$447$			2.56773e7i			0.287493i
$448$	−1.15829e8	+	7.82292e7i	−1.28820	+	0.870031i
$449$	−1.07566e8			−1.18833			−0.594165	−	0.804343i	$-0.702517\pi$
$449$	−1.07566e8			−1.18833			−0.594165	+	0.804343i	$0.702517\pi$
$450$	−1.48818e7	−	2.57761e7i	−0.163312	−	0.282865i
$451$	4.21524e7	+	2.43367e7i	0.459507	+	0.265297i
$452$	1.35768e8	−	2.35157e8i	1.47022	−	2.54649i
$453$	3.30195e7	−	1.90638e7i	0.355203	−	0.205076i
$454$		−	1.99103e8i		−	2.12769i
$455$	5.96030e7	+	2.90258e7i	0.632752	+	0.308141i
$456$	−6.27052e7			−0.661316
$457$	−6.43381e6	−	1.11437e7i	−0.0674093	−	0.116756i	0.830351	−	0.557241i	$-0.188140\pi$
$457$	−6.43381e6	−	1.11437e7i	−0.0674093	−	0.116756i	−0.897760	+	0.440485i	$0.854807\pi$
$458$	−4.85479e7	−	2.80292e7i	−0.505329	−	0.291752i
$459$	−1.47647e7	+	2.55732e7i	−0.152681	+	0.264452i
$460$	−1.42329e8	+	8.21735e7i	−1.46224	+	0.844225i
$461$			7.08717e6i			0.0723386i	0.999346	+	0.0361693i	$0.0115156\pi$
$461$			7.08717e6i			0.0723386i	−0.999346	+	0.0361693i	$0.988484\pi$
$462$	−5.77950e7	+	4.07647e6i	−0.586090	+	0.0413388i
$463$	1.44698e8			1.45788			0.728938	−	0.684580i	$-0.240014\pi$
$463$	1.44698e8			1.45788			0.728938	+	0.684580i	$0.240014\pi$
$464$	−6.34596e6	−	1.09915e7i	−0.0635249	−	0.110028i
$465$	2.99304e7	+	1.72803e7i	0.297683	+	0.171867i
$466$	8.29054e7	−	1.43596e8i	0.819267	−	1.41901i
$467$	7.34759e7	−	4.24214e7i	0.721431	−	0.416518i	−0.0938485	−	0.995586i	$-0.529917\pi$
$467$	7.34759e7	−	4.24214e7i	0.721431	−	0.416518i	0.815279	+	0.579068i	$0.196584\pi$
$468$			6.47410e7i			0.631599i
$469$	−5.68283e6	−	8.05695e7i	−0.0550866	−	0.781002i
$470$	5.26389e6			0.0507006
$471$	−2.19440e7	−	3.80082e7i	−0.210016	−	0.363759i
$472$	−1.17404e8	−	6.77834e7i	−1.11650	−	0.644610i
$473$	3.77514e7	−	6.53874e7i	0.356738	−	0.617889i
$474$	−1.21218e8	+	6.99851e7i	−1.13823	+	0.657159i
$475$			6.21054e7i			0.579494i
$476$	−1.28399e8	+	2.63661e8i	−1.19053	+	2.44470i
$477$	−4.52927e7			−0.417323
$478$	4.97062e7	+	8.60937e7i	0.455121	+	0.788293i
$479$	1.38250e8	+	7.98185e7i	1.25793	+	0.726268i	0.972672	−	0.232182i	$-0.0745864\pi$
$479$	1.38250e8	+	7.98185e7i	1.25793	+	0.726268i	0.285261	+	0.958450i	$0.407920\pi$
$480$	1.64237e7	−	2.84467e7i	0.148507	−	0.257222i
$481$	−1.67613e8	+	9.67714e7i	−1.50616	+	0.869585i
$482$			2.58016e8i			2.30412i
$483$	−5.63582e7	−	8.34459e7i	−0.500168	−	0.740565i
$484$	−1.20150e8			−1.05972
$485$	2.46677e7	+	4.27256e7i	0.216223	+	0.374510i
$486$	−1.05055e7	−	6.06538e6i	−0.0915187	−	0.0528383i
$487$	−6.90017e7	+	1.19515e8i	−0.597411	+	1.03475i	0.395791	+	0.918341i	$0.370471\pi$
$487$	−6.90017e7	+	1.19515e8i	−0.597411	+	1.03475i	−0.993202	+	0.116405i	$0.962863\pi$
$488$	7.52577e7	−	4.34501e7i	0.647577	−	0.373879i
$489$			2.43619e7i			0.208345i
$490$	−9.71214e7	+	7.60685e7i	−0.825518	+	0.646571i
$491$	−3.91824e7			−0.331014			−0.165507	−	0.986209i	$-0.552926\pi$
$491$	−3.91824e7			−0.331014			−0.165507	+	0.986209i	$0.552926\pi$
$492$	5.06041e7	+	8.76489e7i	0.424904	+	0.735955i
$493$	9.37609e7	+	5.41329e7i	0.782494	+	0.451773i
$494$	1.06959e8	−	1.85258e8i	0.887231	−	1.53673i
$495$	1.37679e7	−	7.94889e6i	0.113515	−	0.0655376i
$496$			2.54641e7i			0.208681i
$497$	2.73640e7	−	1.84813e7i	0.222900	−	0.150544i
$498$	−2.62997e7			−0.212942
$499$	−1.14482e7	−	1.98288e7i	−0.0921370	−	0.159586i	0.816273	−	0.577666i	$-0.196036\pi$
$499$	−1.14482e7	−	1.98288e7i	−0.0921370	−	0.159586i	−0.908410	+	0.418080i	$0.862703\pi$
$500$	1.88328e8	+	1.08731e8i	1.50662	+	0.869849i
$501$	9.00527e6	−	1.55976e7i	0.0716116	−	0.124035i
$502$	−1.59316e8	+	9.19810e7i	−1.25935	+	0.727088i
$503$		−	1.38751e8i		−	1.09027i	−0.838349	−	0.545133i	$-0.816479\pi$
$503$		−	1.38751e8i		−	1.09027i	0.838349	−	0.545133i	$-0.183521\pi$
$504$	−4.51094e7	−	2.19676e7i	−0.352351	−	0.171590i
$505$	5.31683e7			0.412837
$506$	1.02035e8	+	1.76730e8i	0.787588	+	1.36414i
$507$	−1.44982e7	−	8.37055e6i	−0.111248	−	0.0642289i
$508$	−1.60454e7	+	2.77915e7i	−0.122394	+	0.211993i
$509$	−5.07588e7	+	2.93056e7i	−0.384909	+	0.222227i	−0.679952	−	0.733257i	$-0.737999\pi$
$509$	−5.07588e7	+	2.93056e7i	−0.384909	+	0.222227i	0.295043	+	0.955484i	$0.404666\pi$
$510$		−	1.27424e8i		−	0.960598i
$511$	9.42796e7	−	6.64985e6i	0.706570	−	0.0498367i
$512$	5.94097e7			0.442636
$513$	1.26561e7	+	2.19211e7i	0.0937451	+	0.162371i
$514$	−7.48087e6	−	4.31908e6i	−0.0550888	−	0.0318055i
$515$	−6.16397e7	+	1.06763e8i	−0.451272	+	0.781627i
$516$	1.35962e8	−	7.84978e7i	0.989622	−	0.571358i
$517$		−	4.12763e6i		−	0.0298696i
$518$	−2.53400e7	−	3.59263e8i	−0.182313	−	2.58478i
$519$	−8.98057e7			−0.642394
$520$	−5.81748e7	−	1.00762e8i	−0.413737	−	0.716614i
$521$	−1.88084e8	−	1.08590e8i	−1.32996	−	0.767853i	−0.344668	−	0.938725i	$-0.612008\pi$
$521$	−1.88084e8	−	1.08590e8i	−1.32996	−	0.767853i	−0.985293	+	0.170872i	$0.945342\pi$
$522$	−2.22380e7	+	3.85173e7i	−0.156345	+	0.270797i
$523$	1.64929e7	−	9.52217e6i	0.115290	−	0.0665627i	−0.441246	−	0.897386i	$-0.645463\pi$
$523$	1.64929e7	−	9.52217e6i	0.115290	−	0.0665627i	0.556536	+	0.830823i	$0.312130\pi$
$524$		−	2.99294e8i		−	2.08019i
$525$	−2.17575e7	+	4.46780e7i	−0.150360	+	0.308756i
$526$	1.96889e8			1.35290
$527$	−1.08608e8	−	1.88114e8i	−0.742044	−	1.28526i
$528$	1.01441e7	+	5.85669e6i	0.0689146	+	0.0397879i
$529$	−1.03315e8	+	1.78948e8i	−0.697908	+	1.20881i
$530$	1.69261e8	−	9.77228e7i	1.13692	−	0.656400i
$531$			5.47244e7i			0.365508i
$532$	1.40697e8	+	2.08321e8i	0.934437	+	1.38356i
$533$	−1.43796e8			−0.949654
$534$	−3.82815e7	−	6.63054e7i	−0.251400	−	0.435437i
$535$	−6.58678e7	−	3.80288e7i	−0.430142	−	0.248342i
$536$	−7.08766e7	+	1.22762e8i	−0.460266	+	0.797204i
$537$	1.61406e7	−	9.31879e6i	0.104231	−	0.0601778i
$538$		−	4.13941e8i		−	2.65822i
$539$	5.96483e7	+	7.61567e7i	0.380918	+	0.486342i
$540$	3.30568e7			0.209932
$541$	5.05360e7	+	8.75310e7i	0.319161	+	0.552803i	0.980313	−	0.197449i	$-0.0632657\pi$
$541$	5.05360e7	+	8.75310e7i	0.319161	+	0.552803i	−0.661152	+	0.750252i	$0.729932\pi$
$542$	−1.70664e7	−	9.85332e6i	−0.107188	−	0.0618849i
$543$	7.79657e7	−	1.35041e8i	0.486972	−	0.843461i
$544$	−1.78789e8	+	1.03224e8i	−1.11057	+	0.641185i
$545$		−	1.25057e8i		−	0.772537i
$546$	1.41847e8	−	9.58017e7i	0.871450	−	0.588566i
$547$	−2.29198e7			−0.140039			−0.0700196	−	0.997546i	$-0.522306\pi$
$547$	−2.29198e7			−0.140039			−0.0700196	+	0.997546i	$0.522306\pi$
$548$	4.97852e7	+	8.62305e7i	0.302523	+	0.523986i
$549$	−3.03793e7	−	1.75395e7i	−0.183595	−	0.105999i
$550$	5.03557e7	−	8.72186e7i	0.302664	−	0.524229i
$551$	8.03708e7	−	4.64021e7i	0.480445	−	0.277385i
$552$			1.76723e8i			1.05069i
$553$	2.10108e8	+	1.02319e8i	1.24241	+	0.605038i
$554$	2.61399e7			0.153735
$555$	4.94116e7	+	8.55834e7i	0.289035	+	0.500622i
$556$	−440732.	−	254457.i	−0.00256419	−	0.00148044i
$557$	−6.91655e7	+	1.19798e8i	−0.400243	+	0.693242i	−0.993755	−	0.111584i	$-0.964408\pi$
$557$	−6.91655e7	+	1.19798e8i	−0.400243	+	0.693242i	0.593512	+	0.804825i	$0.297741\pi$
$558$	7.72781e7	−	4.46165e7i	0.444789	−	0.256799i
$559$			2.23059e8i			1.27698i
$560$	2.48788e7	−	1.75478e6i	0.141666	−	0.00999217i
$561$	−9.99184e7			−0.565923
$562$	−2.30859e7	−	3.99860e7i	−0.130059	−	0.225268i
$563$	1.95097e8	+	1.12639e8i	1.09326	+	0.631195i	0.934443	−	0.356112i	$-0.115898\pi$
$563$	1.95097e8	+	1.12639e8i	1.09326	+	0.631195i	0.158819	+	0.987308i	$0.449231\pi$
$564$	4.29136e6	−	7.43285e6i	0.0239198	−	0.0414303i
$565$	1.70597e8	−	9.84941e7i	0.945857	−	0.546091i
$566$			4.30221e8i			2.37270i
$567$	1.42503e6	+	2.02036e7i	0.00781761	+	0.110836i
$568$	−5.79518e7			−0.316244
$569$	−1.10276e8	−	1.91003e8i	−0.598609	−	1.03682i	−0.993027	−	0.117890i	$-0.962387\pi$
$569$	−1.10276e8	−	1.91003e8i	−0.598609	−	1.03682i	0.394417	−	0.918931i	$-0.370946\pi$
$570$	−9.45931e7	−	5.46134e7i	−0.510781	−	0.294900i
$571$	3.36594e7	−	5.82999e7i	0.180800	−	0.313155i	−0.761353	−	0.648337i	$-0.775465\pi$
$571$	3.36594e7	−	5.82999e7i	0.180800	−	0.313155i	0.942153	+	0.335182i	$0.108798\pi$
$572$	−1.89715e8	+	1.09532e8i	−1.01371	+	0.585265i
$573$			1.18203e8i			0.628295i
$574$	1.17156e8	−	2.40573e8i	0.619481	−	1.27207i
$575$	1.75032e8			0.920693
$576$	−4.95109e7	−	8.57555e7i	−0.259080	−	0.448740i
$577$	−9.29650e6	−	5.36734e6i	−0.0483941	−	0.0279403i	0.475608	−	0.879657i	$-0.342228\pi$
$577$	−9.29650e6	−	5.36734e6i	−0.0483941	−	0.0279403i	−0.524002	+	0.851717i	$0.675562\pi$
$578$	−2.41384e8	+	4.18089e8i	−1.25004	+	2.16513i
$579$	−9.57977e7	+	5.53088e7i	−0.493537	+	0.284943i
$580$		−	1.21199e8i		−	0.621175i
$581$	2.45764e7	+	3.63887e7i	0.125311	+	0.185540i
$582$	1.27380e8			0.646149
$583$	−7.66284e7	−	1.32724e8i	−0.386709	−	0.669799i
$584$	−1.43652e8	−	8.29374e7i	−0.721228	−	0.416401i
$585$	−2.34835e7	+	4.06745e7i	−0.117299	+	0.203168i
$586$	2.94062e8	−	1.69777e8i	1.46132	−	0.843694i
$587$			2.34143e8i			1.15762i	0.815461	+	0.578812i	$0.196484\pi$
$587$			2.34143e8i			1.15762i	−0.815461	+	0.578812i	$0.803516\pi$
$588$	2.82345e7	+	1.99154e8i	0.138882	+	0.979620i
$589$	−1.86195e8			−0.911219
$590$	−1.18073e8	−	2.04508e8i	−0.574901	−	0.995757i
$591$	2.70130e7	+	1.55960e7i	0.130861	+	0.0755527i
$592$	−3.64061e7	+	6.30573e7i	−0.175473	+	0.303928i
$593$	1.45328e8	−	8.39054e7i	0.696926	−	0.402370i	−0.109275	−	0.994012i	$-0.534853\pi$
$593$	1.45328e8	−	8.39054e7i	0.696926	−	0.402370i	0.806202	+	0.591641i	$0.201520\pi$
$594$		−	4.10468e7i		−	0.195849i
$595$	−1.76306e8	+	1.19075e8i	−0.836984	+	0.565288i
$596$	−1.80662e8			−0.853350
$597$	−3.38743e7	−	5.86720e7i	−0.159202	−	0.275745i
$598$	−5.22116e8	−	3.01444e8i	−2.44154	−	1.40962i
$599$	−2.72137e7	+	4.71356e7i	−0.126622	+	0.219315i	−0.922366	−	0.386318i	$-0.873747\pi$
$599$	−2.72137e7	+	4.71356e7i	−0.126622	+	0.219315i	0.795744	+	0.605633i	$0.207080\pi$
$600$	7.55302e7	−	4.36074e7i	0.349677	−	0.201886i
$601$			1.02729e7i			0.0473226i	0.999720	+	0.0236613i	$0.00753233\pi$
$601$			1.02729e7i			0.0473226i	−0.999720	+	0.0236613i	$0.992468\pi$
$602$	−3.73181e8	−	1.81734e8i	−1.71053	−	0.833003i
$603$	5.72217e7			0.260981
$604$	1.34130e8	+	2.32320e8i	0.608717	+	1.05433i
$605$	−7.54864e7	−	4.35821e7i	−0.340881	−	0.196808i
$606$	6.86383e7	−	1.18885e8i	0.308424	−	0.534207i
$607$	3.20092e8	−	1.84805e8i	1.43123	−	0.826319i	0.434012	−	0.900907i	$-0.357098\pi$
$607$	3.20092e8	−	1.84805e8i	1.43123	−	0.826319i	0.997214	+	0.0745880i	$0.0237642\pi$
$608$			1.76965e8i			0.787366i
$609$	7.40740e7	−	5.22468e6i	0.327955	−	0.0231317i
$610$	1.51372e8			0.666893
$611$	6.09714e6	+	1.05606e7i	0.0267302	+	0.0462981i
$612$	−1.79929e8	−	1.03882e8i	−0.784958	−	0.453196i
$613$	−2.33412e7	+	4.04282e7i	−0.101331	+	0.175510i	−0.912233	−	0.409671i	$-0.865643\pi$
$613$	−2.33412e7	+	4.04282e7i	−0.101331	+	0.175510i	0.810902	+	0.585182i	$0.198977\pi$
$614$	−2.16727e8	+	1.25127e8i	−0.936285	+	0.540565i
$615$			7.34224e7i			0.315648i
$616$	−1.19450e7	−	1.69353e8i	−0.0511029	−	0.724521i
$617$	4.39158e8			1.86967			0.934836	−	0.355080i	$-0.115546\pi$
$617$	4.39158e8			1.86967			0.934836	+	0.355080i	$0.115546\pi$
$618$	1.59149e8	+	2.75654e8i	0.674277	+	1.16788i
$619$	−1.84752e8	−	1.06666e8i	−0.778962	−	0.449734i	0.0571005	−	0.998368i	$-0.481814\pi$
$619$	−1.84752e8	−	1.06666e8i	−0.778962	−	0.449734i	−0.836062	+	0.548635i	$0.815148\pi$
$620$	−1.21582e8	+	2.10586e8i	−0.510145	+	0.883596i
$621$	6.17803e7	−	3.56689e7i	0.257974	−	0.148941i
$622$			4.26644e8i			1.77294i
$623$	−5.59682e7	+	1.14928e8i	−0.231461	+	0.475292i
$624$	−3.46049e7			−0.142424
$625$	6.26968e6	+	1.08594e7i	0.0256806	+	0.0444801i
$626$	3.70845e8	+	2.14107e8i	1.51171	+	0.872788i
$627$	−4.28245e7	+	7.41743e7i	−0.173736	+	0.300920i
$628$	2.67419e8	−	1.54395e8i	1.07973	−	0.623381i
$629$		−	6.21109e8i		−	2.49584i
$630$	−4.89164e7	−	7.24273e7i	−0.195629	−	0.289655i
$631$	2.58817e8			1.03016			0.515080	−	0.857142i	$-0.327762\pi$
$631$	2.58817e8			1.03016			0.515080	+	0.857142i	$0.327762\pi$
$632$	−2.05073e8	−	3.55197e8i	−0.812377	−	1.40708i
$633$	1.39916e8	+	8.07806e7i	0.551641	+	0.318490i
$634$	−1.07689e8	+	1.86522e8i	−0.422573	+	0.731918i
$635$	−2.01616e7	+	1.16403e7i	−0.0787415	+	0.0454614i
$636$		−	3.18672e8i		−	1.23872i
$637$	−2.65106e8	−	1.06738e8i	−1.02565	−	0.412952i
$638$	−1.50493e8			−0.579502
$639$	1.16967e7	+	2.02593e7i	0.0448292	+	0.0776465i
$640$	2.53259e8	+	1.46219e8i	0.966106	+	0.557781i
$641$	−6.64356e7	+	1.15070e8i	−0.252247	+	0.436905i	−0.964144	−	0.265379i	$-0.914503\pi$
$641$	−6.64356e7	+	1.15070e8i	−0.252247	+	0.436905i	0.711897	+	0.702284i	$0.247836\pi$
$642$	−1.70066e8	+	9.81874e7i	−0.642704	+	0.371066i
$643$			1.84168e8i			0.692757i	0.938095	+	0.346378i	$0.112589\pi$
$643$			1.84168e8i			0.692757i	−0.938095	+	0.346378i	$0.887411\pi$
$644$	5.87112e8	−	3.96528e8i	2.19818	−	1.48462i
$645$	1.13894e8			0.424445
$646$	3.43248e8	+	5.94523e8i	1.27324	+	2.20532i
$647$	−2.88189e8	−	1.66386e8i	−1.06405	−	0.614332i	−0.137504	−	0.990501i	$-0.543908\pi$
$647$	−2.88189e8	−	1.66386e8i	−1.06405	−	0.614332i	−0.926551	+	0.376169i	$0.877241\pi$
$648$	1.77730e7	−	3.07838e7i	0.0653185	−	0.113135i
$649$	−1.60363e8	+	9.25854e7i	−0.586636	+	0.338695i
$650$			2.97532e8i			1.08341i
$651$	−1.33947e8	−	6.52302e7i	−0.485500	−	0.236432i
$652$	−1.71406e8			−0.618420
$653$	−1.28291e8	−	2.22206e8i	−0.460741	−	0.798026i	0.538257	−	0.842780i	$-0.319083\pi$
$653$	−1.28291e8	−	2.22206e8i	−0.460741	−	0.798026i	−0.998998	+	0.0447544i	$0.985749\pi$
$654$	−2.79629e8	−	1.61444e8i	−0.999654	−	0.577150i
$655$	1.08563e8	−	1.88036e8i	0.386328	−	0.669140i
$656$	−4.68495e7	+	2.70486e7i	−0.165956	+	0.0958149i
$657$			6.69588e7i			0.236108i
$658$	−2.26356e7	+	1.59656e6i	−0.0794536	+	0.00560412i
$659$	1.84717e8			0.645431			0.322715	−	0.946496i	$-0.395404\pi$
$659$	1.84717e8			0.645431			0.322715	+	0.946496i	$0.395404\pi$
$660$	5.59271e7	+	9.68686e7i	0.194532	+	0.336939i
$661$	1.74480e8	+	1.00736e8i	0.604144	+	0.348803i	0.770670	−	0.637234i	$-0.219922\pi$
$661$	1.74480e8	+	1.00736e8i	0.604144	+	0.348803i	−0.166526	+	0.986037i	$0.553255\pi$
$662$	3.41045e8	−	5.90707e8i	1.17554	−	2.03610i
$663$	2.55642e8	−	1.47595e8i	0.877185	−	0.506443i
$664$		−	7.70644e7i		−	0.263239i
$665$	1.28311e7	+	1.81916e8i	0.0436314	+	0.618593i
$666$	2.55154e8			0.863733
$667$	−1.30776e8	−	2.26510e8i	−0.440706	−	0.763326i
$668$	1.09742e8	+	6.33597e7i	0.368166	+	0.212561i
$669$	−3.77857e7	+	6.54468e7i	−0.126197	+	0.218580i
$670$	−2.13840e8	+	1.23461e8i	−0.710992	+	0.410492i
$671$		−	1.18697e8i		−	0.392891i
$672$	−6.19965e7	+	1.27307e8i	−0.204296	+	0.419511i
$673$	−4.93893e8			−1.62027			−0.810135	−	0.586243i	$-0.800606\pi$
$673$	−4.93893e8			−1.62027			−0.810135	+	0.586243i	$0.800606\pi$
$674$	4.04577e8	+	7.00747e8i	1.32136	+	2.28866i
$675$	−3.04894e7	−	1.76030e7i	−0.0991373	−	0.0572369i
$676$	5.88939e7	−	1.02007e8i	0.190647	−	0.330211i
$677$	−2.71512e8	+	1.56758e8i	−0.875030	+	0.505199i	−0.869017	−	0.494783i	$-0.835248\pi$
$677$	−2.71512e8	+	1.56758e8i	−0.875030	+	0.505199i	−0.00601364	+	0.999982i	$0.501914\pi$
$678$		−	5.08608e8i		−	1.63190i
$679$	−1.19034e8	−	1.76245e8i	−0.380243	−	0.563000i
$680$	3.73384e8			1.18749
$681$	−1.17755e8	−	2.03957e8i	−0.372852	−	0.645798i
$682$	2.61486e8	+	1.50969e8i	0.824318	+	0.475920i
$683$	7.42502e7	−	1.28605e8i	0.233043	−	0.403642i	−0.725659	−	0.688054i	$-0.758465\pi$
$683$	7.42502e7	−	1.28605e8i	0.233043	−	0.403642i	0.958702	+	0.284412i	$0.0917984\pi$
$684$	−1.54233e8	+	8.90465e7i	−0.481958	+	0.278259i
$685$			7.22343e7i			0.224735i
$686$	3.94565e8	−	3.56564e8i	1.22221	−	1.10450i
$687$	−6.63087e7			−0.204503
$688$	4.19582e7	+	7.26737e7i	0.128840	+	0.223158i
$689$	3.92108e8	+	2.26384e8i	1.19880	+	0.692130i
$690$	−1.53917e8	+	2.66593e8i	−0.468533	+	0.811524i
$691$	−3.35862e8	+	1.93910e8i	−1.01795	+	0.587714i	−0.913510	−	0.406817i	$-0.866639\pi$
$691$	−3.35862e8	+	1.93910e8i	−1.01795	+	0.587714i	−0.104441	+	0.994531i	$0.533305\pi$
$692$		−	6.31859e8i		−	1.90678i
$693$	−5.67931e7	+	3.83573e7i	−0.170646	+	0.115252i
$694$	−4.68722e8			−1.40229
$695$	−184598.	−	319733.i	−0.000549886	−	0.000952430i
$696$	−1.12865e8	−	6.51626e7i	−0.334758	−	0.193273i
$697$	2.30732e8	−	3.99640e8i	0.681412	−	1.18024i
$698$	−5.90235e8	+	3.40772e8i	−1.73564	+	1.00207i
$699$		−	1.96130e8i		−	0.574265i
$700$	−3.14347e8	−	1.53083e8i	−0.916464	−	0.446305i
$701$	4.86782e7			0.141312			0.0706562	−	0.997501i	$-0.477491\pi$
$701$	4.86782e7			0.141312			0.0706562	+	0.997501i	$0.477491\pi$
$702$	6.06325e7	+	1.05019e8i	0.175265	+	0.303567i
$703$	−4.61079e8	−	2.66204e8i	−1.32712	−	0.766212i
$704$	1.67530e8	−	2.90171e8i	0.480148	−	0.831640i
$705$	5.39223e6	−	3.11320e6i	0.0153887	−	0.00888465i
$706$		−	1.01814e7i		−	0.0289329i
$707$	−2.28632e8	+	1.61262e7i	−0.646963	+	0.0456324i
$708$	−3.85032e8			−1.08492
$709$	1.58977e8	+	2.75357e8i	0.446064	+	0.772605i	0.998126	−	0.0611981i	$-0.0194921\pi$
$709$	1.58977e8	+	2.75357e8i	0.446064	+	0.772605i	−0.552062	+	0.833803i	$0.686159\pi$
$710$	−8.74224e7	−	5.04734e7i	−0.244257	−	0.141022i
$711$	−8.27820e7	+	1.43383e8i	−0.230318	+	0.398922i
$712$	1.94291e8	−	1.12174e8i	0.538285	−	0.310779i
$713$			5.24756e8i			1.44773i
$714$	3.86483e7	+	5.47944e8i	0.106178	+	1.50537i
$715$	−1.58922e8			−0.434776
$716$	6.55655e7	+	1.13563e8i	0.178623	+	0.309384i
$717$	1.01836e8	+	5.87951e7i	0.276277	+	0.159509i
$718$	−2.74565e8	+	4.75561e8i	−0.741774	+	1.28479i
$719$	−1.50536e8	+	8.69119e7i	−0.404998	+	0.233826i	−0.688638	−	0.725105i	$-0.741791\pi$
$719$	−1.50536e8	+	8.69119e7i	−0.404998	+	0.233826i	0.283640	+	0.958931i	$0.408458\pi$
$720$			1.76693e7i			0.0473393i
$721$	2.32679e8	−	4.77794e8i	0.620799	−	1.27478i
$722$	−3.15455e7			−0.0838157
$723$	1.52598e8	+	2.64307e8i	0.403769	+	0.699348i
$724$	9.50125e8	+	5.48555e8i	2.50360	+	1.44545i
$725$	−6.45394e7	+	1.11785e8i	−0.169360	+	0.293340i
$726$	−1.94900e8	+	1.12526e8i	−0.509334	+	0.294064i
$727$			4.58803e8i			1.19405i	0.802222	+	0.597026i	$0.203651\pi$
$727$			4.58803e8i			1.19405i	−0.802222	+	0.597026i	$0.796349\pi$
$728$	2.80722e8	+	4.15646e8i	0.727583	+	1.07728i
$729$	−1.43489e7			−0.0370370
$730$	−1.44469e8	−	2.50228e8i	−0.371370	−	0.643232i
$731$	−6.19927e8	−	3.57915e8i	−1.58704	−	0.916279i
$732$	1.23405e8	−	2.13744e8i	0.314630	−	0.544956i
$733$	5.55746e8	−	3.20860e8i	1.41112	−	0.814711i	0.415627	−	0.909535i	$-0.363562\pi$
$733$	5.55746e8	−	3.20860e8i	1.41112	−	0.814711i	0.995494	+	0.0948235i	$0.0302287\pi$
$734$			8.70033e7i			0.220013i
$735$	−5.45003e7	+	1.35363e8i	−0.137258	+	0.340909i
$736$	4.98742e8			1.25096
$737$	9.68105e7	+	1.67681e8i	0.241835	+	0.418871i
$738$	1.64173e8	+	9.47855e7i	0.408445	+	0.235816i
$739$	1.70001e8	−	2.94450e8i	0.421229	−	0.729590i	−0.574831	−	0.818272i	$-0.694932\pi$
$739$	1.70001e8	−	2.94450e8i	0.421229	−	0.729590i	0.996060	+	0.0886823i	$0.0282656\pi$
$740$	−6.02151e8	+	3.47652e8i	−1.48597	+	0.857926i
$741$		−	2.53034e8i		−	0.621904i
$742$	−6.98209e8	+	4.71561e8i	−1.70912	+	1.15432i
$743$	6.08554e8			1.48365			0.741827	−	0.670591i	$-0.233960\pi$
$743$	6.08554e8			1.48365			0.741827	+	0.670591i	$0.233960\pi$
$744$	1.30737e8	+	2.26443e8i	0.317454	+	0.549846i
$745$	−1.13504e8	−	6.55313e7i	−0.274499	−	0.158482i
$746$	−3.26280e7	+	5.65133e7i	−0.0785911	+	0.136124i
$747$	−2.69409e7	+	1.55543e7i	−0.0646323	+	0.0373155i
$748$		−	7.03011e8i		−	1.67980i
$749$	2.94776e8	+	1.43552e8i	0.701531	+	0.341636i
$750$	4.07324e8			0.965509
$751$	−8.06132e7	−	1.39626e8i	−0.190321	−	0.329645i	0.755036	−	0.655684i	$-0.227619\pi$
$751$	−8.06132e7	−	1.39626e8i	−0.190321	−	0.329645i	−0.945357	+	0.326038i	$0.894286\pi$
$752$	3.97296e6	+	2.29379e6i	0.00934245	+	0.00539387i
$753$	−1.08800e8	+	1.88447e8i	−0.254826	+	0.441372i
$754$	3.85038e8	−	2.22302e8i	0.898233	−	0.518595i
$755$			1.94612e8i			0.452198i
$756$	−1.42149e8	+	1.00263e7i	−0.328988	+	0.0232046i
$757$	1.60953e8			0.371031			0.185516	−	0.982641i	$-0.440604\pi$
$757$	1.60953e8			0.371031			0.185516	+	0.982641i	$0.440604\pi$
$758$	−6.97652e8	−	1.20837e9i	−1.60189	−	2.77455i
$759$	2.09046e8	+	1.20693e8i	0.478098	+	0.276030i
$760$	1.60030e8	−	2.77181e8i	0.364554	−	0.631426i
$761$	−3.75605e8	+	2.16856e8i	−0.852271	+	0.492059i	−0.861416	−	0.507899i	$-0.830422\pi$
$761$	−3.75605e8	+	2.16856e8i	−0.852271	+	0.492059i	0.00914540	+	0.999958i	$0.497089\pi$
$762$			6.01088e7i			0.135854i
$763$	3.79304e7	+	5.37766e8i	0.0853913	+	1.21065i
$764$	−8.31656e8			−1.86493
$765$	−7.53621e7	−	1.30531e8i	−0.168333	−	0.291561i
$766$	−5.61533e8	−	3.24201e8i	−1.24936	−	0.721321i
$767$	2.73526e8	−	4.73760e8i	0.606194	−	1.04996i
$768$	3.01817e8	−	1.74254e8i	0.666285	−	0.384680i
$769$			3.73405e8i			0.821110i	0.911836	+	0.410555i	$0.134665\pi$
$769$			3.73405e8i			0.821110i	−0.911836	+	0.410555i	$0.865335\pi$
$770$	1.29479e8	−	2.65879e8i	0.283615	−	0.582388i
$771$	−1.02177e7			−0.0222941
$772$	−3.89144e8	−	6.74018e8i	−0.845782	−	1.46494i
$773$	5.92885e8	+	3.42302e8i	1.28361	+	0.741090i	0.977506	−	0.210909i	$-0.0676423\pi$
$773$	5.92885e8	+	3.42302e8i	1.28361	+	0.741090i	0.306100	+	0.951999i	$0.400976\pi$
$774$	1.47033e8	−	2.54668e8i	0.317096	−	0.549227i
$775$	2.24278e8	−	1.29487e8i	0.481816	−	0.278176i
$776$			3.73254e8i			0.798766i
$777$	−2.38435e8	−	3.53035e8i	−0.508285	−	0.752584i
$778$	−8.77962e8			−1.86439
$779$	−1.97781e8	−	3.42567e8i	−0.418381	−	0.724658i
$780$	−2.86180e8	−	1.65226e8i	−0.603052	−	0.348172i
$781$	−3.95782e7	+	6.85514e7i	−0.0830812	+	0.143901i
$782$	1.67555e9	−	9.67380e8i	3.50379	−	2.02291i
$783$			5.26085e7i			0.109590i
$784$	−1.06451e8	+	1.50917e7i	−0.220902	+	0.0313177i
$785$	2.24014e8			0.463091
$786$	−2.80300e8	−	4.85494e8i	−0.577239	−	0.999808i
$787$	6.27494e8	+	3.62284e8i	1.28732	+	0.743233i	0.978175	−	0.207783i	$-0.0666247\pi$
$787$	6.27494e8	+	3.62284e8i	1.28732	+	0.743233i	0.309142	+	0.951016i	$0.399958\pi$
$788$	−1.09731e8	+	1.90059e8i	−0.224259	+	0.388428i
$789$	2.01690e8	−	1.16446e8i	0.410632	−	0.237078i
$790$		−	7.14438e8i		−	1.44905i
$791$	−7.03719e8	+	4.75283e8i	−1.42190	+	0.960335i
$792$	1.20277e8			0.242107
$793$	1.75334e8	+	3.03687e8i	0.351597	+	0.608984i
$794$	5.48287e8	+	3.16553e8i	1.09533	+	0.632391i
$795$	1.15592e8	−	2.00211e8i	0.230052	−	0.398461i
$796$	4.12807e8	−	2.38334e8i	0.818480	−	0.472550i
$797$		−	5.85510e7i		−	0.115654i	−0.998327	−	0.0578268i	$-0.981583\pi$
$797$		−	5.85510e7i		−	0.115654i	0.998327	−	0.0578268i	$-0.0184171\pi$
$798$	4.23330e8	+	2.06156e8i	0.833049	+	0.405683i
$799$	−3.91334e7			−0.0767197
$800$	−1.23068e8	−	2.13159e8i	−0.240367	−	0.416327i
$801$	−7.84296e7	−	4.52813e7i	−0.152610	−	0.0881093i
$802$	9.18761e7	−	1.59134e8i	0.178106	−	0.308489i
$803$	−1.96214e8	+	1.13284e8i	−0.378951	+	0.218788i
$804$			4.02603e8i			0.774655i
$805$	5.12695e8	−	3.61620e7i	0.982814	−	0.0693211i
$806$	−8.92017e8			−1.70360
$807$	−2.44816e8	−	4.24033e8i	−0.465821	−	0.806825i
$808$	3.48362e8	+	2.01127e8i	0.660384	+	0.381273i
$809$	−2.55763e8	+	4.42994e8i	−0.483049	+	0.836666i	−0.999811	−	0.0194637i	$-0.993804\pi$
$809$	−2.55763e8	+	4.42994e8i	−0.483049	+	0.836666i	0.516761	+	0.856129i	$0.327137\pi$
$810$	5.36226e7	−	3.09590e7i	0.100900	−	0.0582548i
$811$			7.81509e8i			1.46511i	0.680706	+	0.732557i	$0.261673\pi$
$811$			7.81509e8i			1.46511i	−0.680706	+	0.732557i	$0.738327\pi$
$812$	3.67601e7	+	5.21173e8i	0.0686607	+	0.973451i
$813$	−2.33101e7			−0.0433782
$814$	4.31682e8	+	7.47695e8i	0.800370	+	1.38628i
$815$	−1.07689e8	−	6.21741e7i	−0.198929	−	0.114851i
$816$	5.55263e7	−	9.61744e7i	0.102195	−	0.177006i
$817$	−5.31395e8	+	3.06801e8i	−0.974431	+	0.562588i
$818$			2.94989e8i			0.538947i
$819$	8.86458e7	−	1.82030e8i	0.161364	−	0.331353i
$820$	−5.16588e8			−0.936921
$821$	2.75815e8	+	4.77726e8i	0.498412	+	0.863275i	0.999998	−	0.00183255i	$-0.000583318\pi$
$821$	2.75815e8	+	4.77726e8i	0.498412	+	0.863275i	−0.501586	+	0.865108i	$0.667250\pi$
$822$	1.61517e8	+	9.32517e7i	0.290805	+	0.167896i
$823$	1.78646e8	−	3.09423e8i	0.320474	−	0.555077i	−0.660112	−	0.751167i	$-0.729491\pi$
$823$	1.78646e8	−	3.09423e8i	0.320474	−	0.555077i	0.980586	+	0.196090i	$0.0628245\pi$
$824$	−8.07733e8	+	4.66345e8i	−1.44373	+	0.833539i
$825$		−	1.19127e8i		−	0.212152i
$826$	5.69758e8	+	8.43603e8i	1.01100	+	1.49692i
$827$	−4.42420e8			−0.782201			−0.391101	−	0.920348i	$-0.627906\pi$
$827$	−4.42420e8			−0.782201			−0.391101	+	0.920348i	$0.627906\pi$
$828$	2.50961e8	+	4.34677e8i	0.442094	+	0.765730i
$829$	−1.02602e8	−	5.92376e7i	−0.180092	−	0.103976i	0.407244	−	0.913319i	$-0.366490\pi$
$829$	−1.02602e8	−	5.92376e7i	−0.180092	−	0.103976i	−0.587336	+	0.809343i	$0.699823\pi$
$830$	6.71196e7	−	1.16255e8i	0.117386	−	0.203318i
$831$	2.67772e7	−	1.54598e7i	0.0466618	−	0.0269402i
$832$			9.89871e8i			1.71873i
$833$	7.22029e8	−	5.65516e8i	1.24917	−	0.978385i
$834$	−953236.			−0.00164324
$835$	4.59648e7	+	7.96134e7i	0.0789526	+	0.136750i
$836$	−5.21878e8	−	3.01307e8i	−0.893204	−	0.515691i
$837$	5.27748e7	−	9.14086e7i	0.0900016	−	0.155887i
$838$	−6.17714e8	+	3.56637e8i	−1.04968	+	0.606031i
$839$		−	1.02452e9i		−	1.73474i	−0.497660	−	0.867372i	$-0.665807\pi$
$839$		−	1.02452e9i		−	1.73474i	0.497660	−	0.867372i	$-0.334193\pi$
$840$	2.12229e8	−	1.43337e8i	0.358070	−	0.241836i
$841$	−4.01941e8			−0.675731
$842$	−8.56837e8	−	1.48408e9i	−1.43536	−	2.48612i
$843$	−4.72976e7	−	2.73073e7i	−0.0789508	−	0.0455823i
$844$	−5.68359e8	+	9.84427e8i	−0.945357	+	1.63741i
$845$	7.40021e7	−	4.27251e7i	0.122652	−	0.0708130i
$846$		−	1.60761e7i		−	0.0265503i
$847$	3.37822e8	+	1.64515e8i	0.555953	+	0.270741i
$848$	1.70335e8			0.279328
$849$	2.54444e8	+	4.40710e8i	0.415785	+	0.720161i
$850$	−8.26905e8	−	4.77414e8i	−1.34648	−	0.777389i
$851$	−7.50246e8	+	1.29946e9i	−1.21735	+	2.10851i
$852$	−1.42541e8	+	8.22963e7i	−0.230474	+	0.133064i
$853$		−	1.03709e9i		−	1.67097i	−0.549517	−	0.835483i	$-0.685188\pi$
$853$		−	1.03709e9i		−	1.67097i	0.549517	−	0.835483i	$-0.314812\pi$
$854$	−6.50924e8	+	4.59118e7i	−1.04510	+	0.0737141i
$855$	−1.29199e8			−0.206710
$856$	−2.87713e8	−	4.98333e8i	−0.458710	−	0.794508i
$857$	4.76107e8	+	2.74881e8i	0.756419	+	0.436719i	0.828009	−	0.560715i	$-0.189474\pi$
$857$	4.76107e8	+	2.74881e8i	0.756419	+	0.436719i	−0.0715895	+	0.997434i	$0.522807\pi$
$858$	−2.05162e8	+	3.55351e8i	−0.324814	+	0.562595i
$859$	1.23390e8	−	7.12392e7i	0.194671	−	0.112393i	−0.399497	−	0.916735i	$-0.630815\pi$
$859$	1.23390e8	−	7.12392e7i	0.194671	−	0.112393i	0.594167	+	0.804342i	$0.297482\pi$
$860$			8.01340e8i			1.25986i
$861$	−2.22693e7	−	3.15728e8i	−0.0348897	−	0.494656i
$862$	1.58068e9			2.46787
$863$	2.00417e8	+	3.47132e8i	0.311818	+	0.540085i	0.978756	−	0.205028i	$-0.0657287\pi$
$863$	2.00417e8	+	3.47132e8i	0.311818	+	0.540085i	−0.666938	+	0.745113i	$0.732395\pi$
$864$	−8.68772e7	−	5.01586e7i	−0.134699	−	0.0777685i
$865$	2.29194e8	−	3.96975e8i	0.354123	−	0.613359i
$866$	1.27311e9	−	7.35033e8i	1.96026	−	1.13176i
$867$			5.71043e8i			0.876216i
$868$	4.58949e8	−	9.42428e8i	0.701787	−	1.44108i
$869$	−5.60219e8			−0.853687
$870$	−1.13507e8	−	1.96601e8i	−0.172372	−	0.298557i
$871$	−4.95380e8	−	2.86008e8i	−0.749694	−	0.432836i
$872$	4.73070e8	−	8.19382e8i	0.713471	−	1.23577i
$873$	1.30486e8	−	7.53359e7i	0.196119	−	0.113229i
$874$		−	1.65846e9i		−	2.48410i
$875$	−3.80635e8	−	5.63581e8i	−0.568178	−	0.841263i
$876$	−4.71112e8			−0.700828
$877$	1.80269e8	+	3.12235e8i	0.267252	+	0.462895i	0.968151	−	0.250366i	$-0.0805509\pi$
$877$	1.80269e8	+	3.12235e8i	0.267252	+	0.462895i	−0.700899	+	0.713261i	$0.747218\pi$
$878$	1.40674e9	+	8.12181e8i	2.07840	+	1.19997i
$879$	2.00821e8	−	3.47832e8i	0.295694	−	0.512156i
$880$	−5.17776e7	+	2.98938e7i	−0.0759791	+	0.0438665i
$881$		−	1.27541e9i		−	1.86519i	−0.360924	−	0.932595i	$-0.617539\pi$
$881$		−	1.27541e9i		−	1.86519i	0.360924	−	0.932595i	$-0.382461\pi$
$882$	2.32316e8	+	2.96612e8i	0.338589	+	0.432298i
$883$	−2.92638e8			−0.425058			−0.212529	−	0.977155i	$-0.568170\pi$
$883$	−2.92638e8			−0.425058			−0.212529	+	0.977155i	$0.568170\pi$
$884$	1.03845e9	+	1.79866e9i	1.50325	+	2.60370i
$885$	−2.41902e8	−	1.39662e8i	−0.348988	−	0.201488i
$886$	−4.68777e8	+	8.11945e8i	−0.674008	+	1.16742i
$887$	−7.14682e8	+	4.12622e8i	−1.02410	+	0.591264i	−0.915289	−	0.402798i	$-0.868038\pi$
$887$	−7.14682e8	+	4.12622e8i	−1.02410	+	0.591264i	−0.108811	+	0.994062i	$0.534704\pi$
$888$			7.47662e8i			1.06774i
$889$	8.31675e7	−	5.61703e7i	0.118372	−	0.0799468i
$890$	3.90794e8			0.554342
$891$	−2.42762e7	−	4.20476e7i	−0.0343200	−	0.0594440i
$892$	−4.60473e8	−	2.65854e8i	−0.648798	−	0.374584i
$893$	−1.67724e7	+	2.90506e7i	−0.0235526	+	0.0407944i
$894$	−2.93058e8	+	1.69197e8i	−0.410148	+	0.236799i
$895$			9.51302e7i			0.132693i
$896$	−1.13340e9	−	5.51951e8i	−1.57565	−	0.767319i
$897$	−7.13127e8			−0.988075
$898$	−7.08792e8	−	1.22766e9i	−0.978790	−	1.69531i
$899$	−3.35138e8	−	1.93492e8i	−0.461259	−	0.266308i
$900$	1.23852e8	−	2.14518e8i	0.169893	−	0.294264i
$901$	−1.25834e9	+	7.26501e8i	−1.72037	+	0.993257i
$902$			6.41451e8i			0.874065i
$903$	−4.89762e8	+	3.45445e7i	−0.665153	+	0.0469154i
$904$	1.49035e9			2.01735
$905$	3.97954e8	+	6.89276e8i	0.536892	+	0.929924i
$906$	4.35154e8	+	2.51236e8i	0.585138	+	0.337830i
$907$	4.80348e8	−	8.31987e8i	0.643775	−	1.11505i	−0.340808	−	0.940133i	$-0.610700\pi$
$907$	4.80348e8	−	8.31987e8i	0.643775	−	1.11505i	0.984583	−	0.174918i	$-0.0559662\pi$
$908$	1.43501e9	−	8.28502e8i	1.91689	−	1.10672i
$909$		−	1.62378e8i		−	0.216190i
$910$	6.14708e7	+	8.71514e8i	0.0815726	+	1.15651i
$911$	1.01677e9			1.34483			0.672413	−	0.740176i	$-0.265258\pi$
$911$	1.01677e9			1.34483			0.672413	+	0.740176i	$0.265258\pi$
$912$	−4.75966e7	−	8.24397e7i	−0.0627468	−	0.108681i
$913$	−9.11598e7	−	5.26311e7i	−0.119782	−	0.0691561i
$914$	8.47892e7	−	1.46859e8i	0.111046	−	0.192337i
$915$	1.55063e8	−	8.95255e7i	0.202416	−	0.116865i
$916$		−	4.66538e8i		−	0.607017i
$917$	−4.09804e8	+	8.41512e8i	−0.531457	+	1.09132i
$918$	−3.89158e8			−0.503035
$919$	2.43093e8	+	4.21050e8i	0.313203	+	0.542484i	0.979054	−	0.203601i	$-0.0652646\pi$
$919$	2.43093e8	+	4.21050e8i	0.313203	+	0.542484i	−0.665851	+	0.746085i	$0.731931\pi$
$920$	−7.81181e8	−	4.51015e8i	−1.00320	−	0.579199i
$921$	−1.48007e8	+	2.56356e8i	−0.189454	+	0.328145i
$922$	−8.08865e7	+	4.66998e7i	−0.103201	+	0.0595830i
$923$		−	2.33852e8i		−	0.297397i
$924$	−2.69876e8	−	3.99587e8i	−0.342096	−	0.506519i
$925$	7.40511e8			0.935635
$926$	9.53467e8	+	1.65145e9i	1.20081	+	2.07986i
$927$	3.26058e8	+	1.88250e8i	0.409314	+	0.236317i
$928$	−1.83900e8	+	3.18525e8i	−0.230112	+	0.398565i
$929$	7.80354e8	−	4.50538e8i	0.973295	−	0.561932i	0.0730561	−	0.997328i	$-0.476725\pi$
$929$	7.80354e8	−	4.50538e8i	0.973295	−	0.561932i	0.900239	+	0.435395i	$0.143391\pi$
$930$			4.55465e8i			0.566247i
$931$	−1.10352e8	−	7.78374e8i	−0.136751	−	0.964583i
$932$	1.37994e9			1.70456
$933$	2.52329e8	+	4.37046e8i	0.310686	+	0.538124i
$934$	9.68317e8	+	5.59058e8i	1.18844	+	0.686146i
$935$	2.55003e8	−	4.41677e8i	0.311968	−	0.540344i
$936$	−3.07730e8	+	1.77668e8i	−0.375268	+	0.216661i
$937$		−	6.19442e8i		−	0.752977i	−0.926421	−	0.376489i	$-0.877131\pi$
$937$		−	6.19442e8i		−	0.752977i	0.926421	−	0.376489i	$-0.122869\pi$
$938$	8.82100e8	−	5.95759e8i	1.06883	−	0.721875i
$939$	5.06515e8			0.611781
$940$	2.19040e7	+	3.79389e7i	0.0263718	+	0.0456774i
$941$	−4.29312e8	−	2.47863e8i	−0.515234	−	0.297470i	0.219749	−	0.975557i	$-0.429476\pi$
$941$	−4.29312e8	−	2.47863e8i	−0.515234	−	0.297470i	−0.734982	+	0.678086i	$0.762810\pi$
$942$	2.89193e8	−	5.00898e8i	0.345968	−	0.599234i
$943$	−9.65460e8	+	5.57408e8i	−1.15133	+	0.664720i
$944$		−	2.05805e8i		−	0.244647i
$945$	−9.29445e7	−	4.52626e7i	−0.110136	−	0.0536345i
$946$	9.95029e8			1.17534
$947$	−5.84700e8	−	1.01273e9i	−0.688467	−	1.19246i	−0.972334	−	0.233597i	$-0.924950\pi$
$947$	−5.84700e8	−	1.01273e9i	−0.688467	−	1.19246i	0.283866	−	0.958864i	$-0.408383\pi$
$948$	−1.00882e9	−	5.82442e8i	−1.18410	−	0.683640i
$949$	3.34676e8	−	5.79677e8i	0.391585	−	0.678246i
$950$	−7.08815e8	+	4.09234e8i	−0.826726	+	0.477311i
$951$			2.54760e8i			0.296203i
$952$	−1.60561e9	+	1.13249e8i	−1.86093	+	0.131257i
$953$	−2.23017e8			−0.257667			−0.128834	−	0.991666i	$-0.541123\pi$
$953$	−2.23017e8			−0.257667			−0.128834	+	0.991666i	$0.541123\pi$
$954$	−2.98449e8	−	5.16929e8i	−0.343736	−	0.595368i
$955$	−5.22501e8	−	3.01666e8i	−0.599897	−	0.346351i
$956$	−4.13673e8	+	7.16503e8i	−0.473461	+	0.820058i
$957$	−1.54162e8	+	8.90057e7i	−0.175891	+	0.101550i
$958$			2.10381e9i			2.39282i
$959$	−2.19089e7	−	3.10619e8i	−0.0248408	−	0.352186i
$960$	5.05429e8			0.571277
$961$	−5.55442e7	−	9.62054e7i	−0.0625847	−	0.108400i
$962$	−2.20892e9	−	1.27532e9i	−2.48116	−	1.43250i
$963$	−1.16141e8	+	2.01163e8i	−0.130049	+	0.225252i
$964$	−1.85962e9	+	1.07365e9i	−2.07584	+	1.19849i
$965$		−	5.64616e8i		−	0.628306i
$966$	5.81011e8	−	1.19308e9i	0.644544	−	1.32354i
$967$	4.77842e8			0.528451			0.264226	−	0.964461i	$-0.414884\pi$
$967$	4.77842e8			0.528451			0.264226	+	0.964461i	$0.414884\pi$
$968$	−3.29727e8	−	5.71105e8i	−0.363521	−	0.629636i
$969$	7.03234e8	+	4.06012e8i	0.772909	+	0.446239i
$970$	−3.25088e8	+	5.63068e8i	−0.356193	+	0.616944i
$971$	8.66630e8	−	5.00349e8i	0.946621	−	0.546532i	0.0545914	−	0.998509i	$-0.482614\pi$
$971$	8.66630e8	−	5.00349e8i	0.946621	−	0.546532i	0.892030	+	0.451977i	$0.149281\pi$
$972$		−	1.00957e8i		−	0.109935i
$973$	890777.	+	1.31891e6i	0.000967009	+	0.00143178i
$974$	−1.81871e9			−1.96827
$975$	1.75969e8	+	3.04786e8i	0.189855	+	0.328838i
$976$	1.14249e8	+	6.59618e7i	0.122886	+	0.0709485i
$977$	2.65667e8	−	4.60149e8i	0.284875	−	0.493417i	−0.687704	−	0.725991i	$-0.741381\pi$
$977$	2.65667e8	−	4.60149e8i	0.284875	−	0.493417i	0.972579	+	0.232574i	$0.0747147\pi$
$978$	−2.78044e8	+	1.60529e8i	−0.297233	+	0.171607i
$979$		−	3.06437e8i		−	0.326583i
$980$	−9.52395e8	−	3.83456e8i	−1.01190	−	0.407415i
$981$	−3.81929e8			−0.404554
$982$	−2.58186e8	−	4.47192e8i	−0.272646	−	0.472236i
$983$	6.03725e8	+	3.48561e8i	0.635592	+	0.366959i	0.782915	−	0.622129i	$-0.213732\pi$
$983$	6.03725e8	+	3.48561e8i	0.635592	+	0.366959i	−0.147322	+	0.989089i	$0.547065\pi$
$984$	−2.77744e8	+	4.81067e8i	−0.291514	+	0.504918i
$985$	−1.37880e8	+	7.96052e7i	−0.144276	+	0.0832976i
$986$			1.42680e9i			1.48844i
$987$	−2.22432e7	+	1.50228e7i	−0.0231337	+	0.0156242i
$988$	1.78031e9			1.84597
$989$	8.64660e8	+	1.49764e9i	0.893833	+	1.54816i
$990$	1.81443e8	+	1.04756e8i	0.186997	+	0.107963i
$991$	−3.67589e8	+	6.36684e8i	−0.377696	+	0.654188i	−0.990727	−	0.135871i	$-0.956617\pi$
$991$	−3.67589e8	+	6.36684e8i	−0.377696	+	0.654188i	0.613031	+	0.790059i	$0.289950\pi$
$992$	6.39063e8	−	3.68963e8i	0.654649	−	0.377962i
$993$		−	8.06812e8i		−	0.823995i
$994$	3.91239e8	+	1.90528e8i	0.398367	+	0.193999i
$995$	3.45803e8			0.351043
$996$	−1.09438e8	−	1.89552e8i	−0.110762	−	0.191845i
$997$	−4.85470e8	−	2.80286e8i	−0.489866	−	0.282824i	0.234653	−	0.972079i	$-0.424605\pi$
$997$	−4.85470e8	−	2.80286e8i	−0.489866	−	0.282824i	−0.724519	+	0.689255i	$0.757938\pi$
$998$	1.50872e8	−	2.61318e8i	0.151781	−	0.262892i
$999$	2.61375e8	−	1.50905e8i	0.262160	−	0.151358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.b.10.4	✓	8
3.2	odd	2		63.7.m.c.10.1		8
4.3	odd	2		336.7.bh.b.241.2		8
7.2	even	3		147.7.f.a.19.4		8
7.3	odd	6		147.7.d.a.97.2		8
7.4	even	3		147.7.d.a.97.1		8
7.5	odd	6	inner	21.7.f.b.19.4	yes	8
7.6	odd	2		147.7.f.a.31.4		8
21.5	even	6		63.7.m.c.19.1		8
21.11	odd	6		441.7.d.d.244.8		8
21.17	even	6		441.7.d.d.244.7		8
28.19	even	6		336.7.bh.b.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.4	✓	8	1.1	even	1	trivial
21.7.f.b.19.4	yes	8	7.5	odd	6	inner
63.7.m.c.10.1		8	3.2	odd	2
63.7.m.c.19.1		8	21.5	even	6
147.7.d.a.97.1		8	7.4	even	3
147.7.d.a.97.2		8	7.3	odd	6
147.7.f.a.19.4		8	7.2	even	3
147.7.f.a.31.4		8	7.6	odd	2
336.7.bh.b.145.2		8	28.19	even	6
336.7.bh.b.241.2		8	4.3	odd	2
441.7.d.d.244.7		8	21.17	even	6
441.7.d.d.244.8		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.58935 + 11.4131i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-54.8390 + 94.9839i) q^{4} +(-68.9069 + 39.7834i) q^{5} +205.435i q^{6} +(284.244 - 191.975i) q^{7} -601.976 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(6.58935 + 11.4131i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-54.8390 + 94.9839i) q^{4} +(-68.9069 + 39.7834i) q^{5} +205.435i q^{6} +(284.244 - 191.975i) q^{7} -601.976 q^{8} +(121.500 + 210.444i) q^{9} +(-908.103 - 524.293i) q^{10} +(-411.119 + 712.080i) q^{11} +(-1480.65 + 854.855i) q^{12} -2429.15i q^{13} +(4064.01 + 1979.11i) q^{14} -1240.32 q^{15} +(-456.932 - 791.429i) q^{16} +(6751.11 + 3897.76i) q^{17} +(-1601.21 + 2773.38i) q^{18} +(5786.98 - 3341.12i) q^{19} -8726.73i q^{20} +(5333.59 - 376.196i) q^{21} -10836.0 q^{22} +(-9416.30 - 16309.5i) q^{23} +(-8126.67 - 4691.94i) q^{24} +(-4647.06 + 8048.94i) q^{25} +(27724.0 - 16006.5i) q^{26} +3788.00i q^{27} +(2646.85 + 37526.3i) q^{28} +13888.2 q^{29} +(-8172.93 - 14155.9i) q^{30} +(-24131.1 - 13932.1i) q^{31} +(-13241.5 + 22934.9i) q^{32} +(-11100.2 + 6408.72i) q^{33} +102735. i q^{34} +(-11949.0 + 24536.6i) q^{35} -26651.7 q^{36} +(-39837.6 - 69000.8i) q^{37} +(76264.9 + 44031.5i) q^{38} +(18933.3 - 32793.5i) q^{39} +(41480.3 - 23948.6i) q^{40} -59196.1i q^{41} +(39438.4 + 58393.8i) q^{42} -91825.9 q^{43} +(-45090.7 - 78099.4i) q^{44} +(-16744.4 - 9667.37i) q^{45} +(124095. - 214938. i) q^{46} +(-4347.44 + 2509.99i) q^{47} -14245.7i q^{48} +(43940.4 - 109135. i) q^{49} -122484. q^{50} +(60760.0 + 105239. i) q^{51} +(230730. + 133212. i) q^{52} +(-93194.8 + 161418. i) q^{53} +(-43232.7 + 24960.4i) q^{54} -65422.9i q^{55} +(-171108. + 115564. i) q^{56} +104166. q^{57} +(91514.3 + 158507. i) q^{58} +(195032. + 112602. i) q^{59} +(68018.1 - 117811. i) q^{60} +(-125018. + 72179.1i) q^{61} -367214. i q^{62} +(74935.6 + 36492.6i) q^{63} -407497. q^{64} +(96639.7 + 167385. i) q^{65} +(-146286. - 84458.5i) q^{66} +(117740. - 203932. i) q^{67} +(-740448. + 427498. i) q^{68} -293571. i q^{69} +(-358774. + 25305.5i) q^{70} +96269.3 q^{71} +(-73140.0 - 126682. i) q^{72} +(238634. + 137775. i) q^{73} +(525008. - 909340. i) q^{74} +(-125471. + 72440.5i) q^{75} +732893. i q^{76} +(19843.1 + 281329. i) q^{77} +499033. q^{78} +(340667. + 590052. i) q^{79} +(62971.5 + 36356.6i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(675610. - 390064. i) q^{82} +128019. i q^{83} +(-256756. + 527235. i) q^{84} -620264. q^{85} +(-605073. - 1.04802e6i) q^{86} +(187491. + 108248. i) q^{87} +(247484. - 428655. i) q^{88} +(-322756. + 186343. i) q^{89} -254807. i q^{90} +(-466335. - 690470. i) q^{91} +2.06552e6 q^{92} +(-217180. - 376167. i) q^{93} +(-57293.5 - 33078.4i) q^{94} +(-265842. + 460452. i) q^{95} +(-357519. + 206414. i) q^{96} -620049. i q^{97} +(1.53511e6 - 217635. i) q^{98} -199804. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Introduction

L-functions

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