LMFDB - Embedded newform 349.3.d.a.136.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,3,Mod(136,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("349.136");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	349.d (of order $4$, 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:	$9.50956122617$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			136.18
Character	$\chi$	$=$	349.136
Dual form			349.3.d.a.213.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16521 + 1.16521i) q^{2} +2.72727i q^{3} +1.28457i q^{4} -6.62972i q^{5} +(-3.17784 - 3.17784i) q^{6} +(-3.22846 - 3.22846i) q^{7} +(-6.15764 - 6.15764i) q^{8} +1.56202 q^{9} +O(q^{10})$	\(q+(-1.16521 + 1.16521i) q^{2} +2.72727i q^{3} +1.28457i q^{4} -6.62972i q^{5} +(-3.17784 - 3.17784i) q^{6} +(-3.22846 - 3.22846i) q^{7} +(-6.15764 - 6.15764i) q^{8} +1.56202 q^{9} +(7.72501 + 7.72501i) q^{10} +(5.84711 - 5.84711i) q^{11} -3.50338 q^{12} +(11.8737 + 11.8737i) q^{13} +7.52366 q^{14} +18.0810 q^{15} +9.21157 q^{16} +19.6237i q^{17} +(-1.82008 + 1.82008i) q^{18} +37.8417 q^{19} +8.51637 q^{20} +(8.80486 - 8.80486i) q^{21} +13.6262i q^{22} -36.4156 q^{23} +(16.7935 - 16.7935i) q^{24} -18.9532 q^{25} -27.6706 q^{26} +28.8054i q^{27} +(4.14719 - 4.14719i) q^{28} -29.6365i q^{29} +(-21.0682 + 21.0682i) q^{30} +31.3687 q^{31} +(13.8971 - 13.8971i) q^{32} +(15.9466 + 15.9466i) q^{33} +(-22.8657 - 22.8657i) q^{34} +(-21.4038 + 21.4038i) q^{35} +2.00653i q^{36} +6.74412i q^{37} +(-44.0935 + 44.0935i) q^{38} +(-32.3827 + 32.3827i) q^{39} +(-40.8234 + 40.8234i) q^{40} -2.21657 q^{41} +20.5190i q^{42} +(5.27136 - 5.27136i) q^{43} +(7.51105 + 7.51105i) q^{44} -10.3557i q^{45} +(42.4318 - 42.4318i) q^{46} +(11.0916 + 11.0916i) q^{47} +25.1224i q^{48} -28.1541i q^{49} +(22.0845 - 22.0845i) q^{50} -53.5190 q^{51} +(-15.2526 + 15.2526i) q^{52} +(9.34438 + 9.34438i) q^{53} +(-33.5644 - 33.5644i) q^{54} +(-38.7647 - 38.7647i) q^{55} +39.7593i q^{56} +103.204i q^{57} +(34.5327 + 34.5327i) q^{58} +(43.9329 + 43.9329i) q^{59} +23.2264i q^{60} +(56.8451 + 56.8451i) q^{61} +(-36.5511 + 36.5511i) q^{62} +(-5.04291 - 5.04291i) q^{63} +69.2324i q^{64} +(78.7192 - 78.7192i) q^{65} -37.1623 q^{66} +123.072 q^{67} -25.2081 q^{68} -99.3151i q^{69} -49.8798i q^{70} +(64.2380 - 64.2380i) q^{71} +(-9.61833 - 9.61833i) q^{72} +19.4765i q^{73} +(-7.85831 - 7.85831i) q^{74} -51.6904i q^{75} +48.6105i q^{76} -37.7543 q^{77} -75.4652i q^{78} +(-29.8848 - 29.8848i) q^{79} -61.0701i q^{80} -64.5019 q^{81} +(2.58276 - 2.58276i) q^{82} -16.7381i q^{83} +(11.3105 + 11.3105i) q^{84} +130.099 q^{85} +12.2845i q^{86} +80.8265 q^{87} -72.0087 q^{88} +(-109.891 + 109.891i) q^{89} +(12.0666 + 12.0666i) q^{90} -76.6673i q^{91} -46.7786i q^{92} +85.5508i q^{93} -25.8481 q^{94} -250.880i q^{95} +(37.9012 + 37.9012i) q^{96} +(-39.2467 - 39.2467i) q^{97} +(32.8054 + 32.8054i) q^{98} +(9.13329 - 9.13329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9}+O(q^{10}) $ 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9	$ 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9} - 16 q^{10} + 8 q^{11} + 32 q^{12} + 22 q^{13} + 56 q^{14} + 32 q^{15} - 436 q^{16} - 112 q^{18} - 52 q^{19} - 72 q^{20} + 50 q^{21} + 200 q^{23} + 144 q^{24} - 408 q^{25} + 72 q^{26} - 84 q^{28} - 6 q^{30} + 68 q^{31} - 130 q^{32} + 146 q^{33} + 62 q^{34} - 60 q^{35} + 2 q^{38} + 64 q^{39} - 218 q^{40} + 144 q^{41} - 180 q^{43} + 32 q^{44} + 122 q^{46} - 100 q^{47} + 56 q^{50} - 172 q^{51} + 296 q^{52} - 188 q^{53} - 540 q^{54} + 160 q^{55} - 140 q^{58} + 202 q^{59} + 62 q^{61} + 424 q^{62} + 362 q^{63} + 206 q^{65} - 268 q^{66} + 252 q^{67} - 404 q^{68} + 12 q^{71} + 664 q^{72} - 68 q^{74} - 884 q^{77} + 50 q^{79} + 1284 q^{81} - 666 q^{82} - 742 q^{84} + 1240 q^{85} + 220 q^{87} + 60 q^{88} + 48 q^{89} + 298 q^{90} + 940 q^{94} - 1588 q^{96} + 180 q^{97} + 704 q^{98} - 26 q^{99}+O(q^{100}) $ 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9 - 16 * q^10 + 8 * q^11 + 32 * q^12 + 22 * q^13 + 56 * q^14 + 32 * q^15 - 436 * q^16 - 112 * q^18 - 52 * q^19 - 72 * q^20 + 50 * q^21 + 200 * q^23 + 144 * q^24 - 408 * q^25 + 72 * q^26 - 84 * q^28 - 6 * q^30 + 68 * q^31 - 130 * q^32 + 146 * q^33 + 62 * q^34 - 60 * q^35 + 2 * q^38 + 64 * q^39 - 218 * q^40 + 144 * q^41 - 180 * q^43 + 32 * q^44 + 122 * q^46 - 100 * q^47 + 56 * q^50 - 172 * q^51 + 296 * q^52 - 188 * q^53 - 540 * q^54 + 160 * q^55 - 140 * q^58 + 202 * q^59 + 62 * q^61 + 424 * q^62 + 362 * q^63 + 206 * q^65 - 268 * q^66 + 252 * q^67 - 404 * q^68 + 12 * q^71 + 664 * q^72 - 68 * q^74 - 884 * q^77 + 50 * q^79 + 1284 * q^81 - 666 * q^82 - 742 * q^84 + 1240 * q^85 + 220 * q^87 + 60 * q^88 + 48 * q^89 + 298 * q^90 + 940 * q^94 - 1588 * q^96 + 180 * q^97 + 704 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.16521	+	1.16521i	−0.582605	+	0.582605i	−0.935618	−	0.353014i	$-0.885157\pi$
$2$	−1.16521	+	1.16521i	−0.582605	+	0.582605i	0.353014	+	0.935618i	$0.385157\pi$
$3$			2.72727i			0.909089i	0.890724	+	0.454544i	$0.150198\pi$
$3$			2.72727i			0.909089i	−0.890724	+	0.454544i	$0.849802\pi$
$4$			1.28457i			0.321144i
$5$		−	6.62972i		−	1.32594i	−0.748644	−	0.662972i	$-0.769295\pi$
$5$		−	6.62972i		−	1.32594i	0.748644	−	0.662972i	$-0.230705\pi$
$6$	−3.17784	−	3.17784i	−0.529639	−	0.529639i
$7$	−3.22846	−	3.22846i	−0.461208	−	0.461208i	0.437843	−	0.899051i	$-0.355743\pi$
$7$	−3.22846	−	3.22846i	−0.461208	−	0.461208i	−0.899051	+	0.437843i	$0.855743\pi$
$8$	−6.15764	−	6.15764i	−0.769704	−	0.769704i
$9$	1.56202			0.173557
$10$	7.72501	+	7.72501i	0.772501	+	0.772501i
$11$	5.84711	−	5.84711i	0.531555	−	0.531555i	−0.389480	−	0.921035i	$-0.627345\pi$
$11$	5.84711	−	5.84711i	0.531555	−	0.531555i	0.921035	+	0.389480i	$0.127345\pi$
$12$	−3.50338			−0.291948
$13$	11.8737	+	11.8737i	0.913360	+	0.913360i	0.996535	−	0.0831751i	$-0.0265061\pi$
$13$	11.8737	+	11.8737i	0.913360	+	0.913360i	−0.0831751	+	0.996535i	$0.526506\pi$
$14$	7.52366			0.537404
$15$	18.0810			1.20540
$16$	9.21157			0.575723
$17$			19.6237i			1.15433i	0.816626	+	0.577167i	$0.195842\pi$
$17$			19.6237i			1.15433i	−0.816626	+	0.577167i	$0.804158\pi$
$18$	−1.82008	+	1.82008i	−0.101115	+	0.101115i
$19$	37.8417			1.99167			0.995834	−	0.0911871i	$-0.0290661\pi$
$19$	37.8417			1.99167			0.995834	+	0.0911871i	$0.0290661\pi$
$20$	8.51637			0.425819
$21$	8.80486	−	8.80486i	0.419279	−	0.419279i
$22$			13.6262i			0.619373i
$23$	−36.4156			−1.58329			−0.791644	−	0.610982i	$-0.790775\pi$
$23$	−36.4156			−1.58329			−0.791644	+	0.610982i	$0.790775\pi$
$24$	16.7935	−	16.7935i	0.699730	−	0.699730i
$25$	−18.9532			−0.758128
$26$	−27.6706			−1.06426
$27$			28.8054i			1.06687i
$28$	4.14719	−	4.14719i	0.148114	−	0.148114i
$29$		−	29.6365i		−	1.02195i	−0.859597	−	0.510973i	$-0.829285\pi$
$29$		−	29.6365i		−	1.02195i	0.859597	−	0.510973i	$-0.170715\pi$
$30$	−21.0682	+	21.0682i	−0.702272	+	0.702272i
$31$	31.3687			1.01189			0.505947	−	0.862565i	$-0.331143\pi$
$31$	31.3687			1.01189			0.505947	+	0.862565i	$0.331143\pi$
$32$	13.8971	−	13.8971i	0.434285	−	0.434285i
$33$	15.9466	+	15.9466i	0.483231	+	0.483231i
$34$	−22.8657	−	22.8657i	−0.672520	−	0.672520i
$35$	−21.4038	+	21.4038i	−0.611536	+	0.611536i
$36$			2.00653i			0.0557369i
$37$			6.74412i			0.182273i	0.995838	+	0.0911367i	$0.0290500\pi$
$37$			6.74412i			0.182273i	−0.995838	+	0.0911367i	$0.970950\pi$
$38$	−44.0935	+	44.0935i	−1.16035	+	1.16035i
$39$	−32.3827	+	32.3827i	−0.830325	+	0.830325i
$40$	−40.8234	+	40.8234i	−1.02059	+	1.02059i
$41$	−2.21657			−0.0540626			−0.0270313	−	0.999635i	$-0.508605\pi$
$41$	−2.21657			−0.0540626			−0.0270313	+	0.999635i	$0.508605\pi$
$42$			20.5190i			0.488548i
$43$	5.27136	−	5.27136i	0.122590	−	0.122590i	−0.643150	−	0.765740i	$-0.722373\pi$
$43$	5.27136	−	5.27136i	0.122590	−	0.122590i	0.765740	+	0.643150i	$0.222373\pi$
$44$	7.51105	+	7.51105i	0.170706	+	0.170706i
$45$		−	10.3557i		−	0.230128i
$46$	42.4318	−	42.4318i	0.922431	−	0.922431i
$47$	11.0916	+	11.0916i	0.235992	+	0.235992i	0.815188	−	0.579196i	$-0.196634\pi$
$47$	11.0916	+	11.0916i	0.235992	+	0.235992i	−0.579196	+	0.815188i	$0.696634\pi$
$48$			25.1224i			0.523384i
$49$		−	28.1541i		−	0.574574i
$50$	22.0845	−	22.0845i	0.441689	−	0.441689i
$51$	−53.5190			−1.04939
$52$	−15.2526	+	15.2526i	−0.293320	+	0.293320i
$53$	9.34438	+	9.34438i	0.176309	+	0.176309i	0.789745	−	0.613436i	$-0.210213\pi$
$53$	9.34438	+	9.34438i	0.176309	+	0.176309i	−0.613436	+	0.789745i	$0.710213\pi$
$54$	−33.5644	−	33.5644i	−0.621562	−	0.621562i
$55$	−38.7647	−	38.7647i	−0.704813	−	0.704813i
$56$			39.7593i			0.709988i
$57$			103.204i			1.81060i
$58$	34.5327	+	34.5327i	0.595391	+	0.595391i
$59$	43.9329	+	43.9329i	0.744626	+	0.744626i	0.973464	−	0.228839i	$-0.0734928\pi$
$59$	43.9329	+	43.9329i	0.744626	+	0.744626i	−0.228839	+	0.973464i	$0.573493\pi$
$60$			23.2264i			0.387107i
$61$	56.8451	+	56.8451i	0.931887	+	0.931887i	0.997824	−	0.0659371i	$-0.0210037\pi$
$61$	56.8451	+	56.8451i	0.931887	+	0.931887i	−0.0659371	+	0.997824i	$0.521004\pi$
$62$	−36.5511	+	36.5511i	−0.589534	+	0.589534i
$63$	−5.04291	−	5.04291i	−0.0800461	−	0.0800461i
$64$			69.2324i			1.08176i
$65$	78.7192	−	78.7192i	1.21106	−	1.21106i
$66$	−37.1623			−0.563065
$67$	123.072			1.83690			0.918448	−	0.395542i	$-0.129443\pi$
$67$	123.072			1.83690			0.918448	+	0.395542i	$0.129443\pi$
$68$	−25.2081			−0.370707
$69$		−	99.3151i		−	1.43935i
$70$		−	49.8798i		−	0.712568i
$71$	64.2380	−	64.2380i	0.904761	−	0.904761i	−0.0910827	−	0.995843i	$-0.529033\pi$
$71$	64.2380	−	64.2380i	0.904761	−	0.904761i	0.995843	+	0.0910827i	$0.0290328\pi$
$72$	−9.61833	−	9.61833i	−0.133588	−	0.133588i
$73$			19.4765i			0.266802i	0.991062	+	0.133401i	$0.0425898\pi$
$73$			19.4765i			0.266802i	−0.991062	+	0.133401i	$0.957410\pi$
$74$	−7.85831	−	7.85831i	−0.106193	−	0.106193i
$75$		−	51.6904i		−	0.689206i
$76$			48.6105i			0.639611i
$77$	−37.7543			−0.490315
$78$		−	75.4652i		−	0.967503i
$79$	−29.8848	−	29.8848i	−0.378289	−	0.378289i	0.492196	−	0.870484i	$-0.336194\pi$
$79$	−29.8848	−	29.8848i	−0.378289	−	0.378289i	−0.870484	+	0.492196i	$0.836194\pi$
$80$		−	61.0701i		−	0.763377i
$81$	−64.5019			−0.796320
$82$	2.58276	−	2.58276i	0.0314971	−	0.0314971i
$83$		−	16.7381i		−	0.201664i	−0.994903	−	0.100832i	$-0.967850\pi$
$83$		−	16.7381i		−	0.201664i	0.994903	−	0.100832i	$-0.0321505\pi$
$84$	11.3105	+	11.3105i	0.134649	+	0.134649i
$85$	130.099			1.53058
$86$			12.2845i			0.142843i
$87$	80.8265			0.929040
$88$	−72.0087			−0.818281
$89$	−109.891	+	109.891i	−1.23473	+	1.23473i	−0.272599	+	0.962128i	$0.587883\pi$
$89$	−109.891	+	109.891i	−1.23473	+	1.23473i	−0.962128	+	0.272599i	$0.912117\pi$
$90$	12.0666	+	12.0666i	0.134073	+	0.134073i
$91$		−	76.6673i		−	0.842498i
$92$		−	46.7786i		−	0.508463i
$93$			85.5508i			0.919901i
$94$	−25.8481			−0.274980
$95$		−	250.880i		−	2.64084i
$96$	37.9012	+	37.9012i	0.394804	+	0.394804i
$97$	−39.2467	−	39.2467i	−0.404605	−	0.404605i	0.475247	−	0.879852i	$-0.342359\pi$
$97$	−39.2467	−	39.2467i	−0.404605	−	0.404605i	−0.879852	+	0.475247i	$0.842359\pi$
$98$	32.8054	+	32.8054i	0.334749	+	0.334749i
$99$	9.13329	−	9.13329i	0.0922554	−	0.0922554i
$100$		−	24.3468i		−	0.243468i
$101$	−71.7621	+	71.7621i	−0.710516	+	0.710516i	−0.966643	−	0.256127i	$-0.917553\pi$
$101$	−71.7621	+	71.7621i	−0.710516	+	0.710516i	0.256127	+	0.966643i	$0.417553\pi$
$102$	62.3608	−	62.3608i	0.611380	−	0.611380i
$103$	−57.3864	+	57.3864i	−0.557150	+	0.557150i	−0.928495	−	0.371345i	$-0.878897\pi$
$103$	−57.3864	+	57.3864i	−0.557150	+	0.557150i	0.371345	+	0.928495i	$0.378897\pi$
$104$		−	146.228i		−	1.40603i
$105$	−58.3738	−	58.3738i	−0.555941	−	0.555941i
$106$	−21.7763			−0.205437
$107$	96.1198	−	96.1198i	0.898316	−	0.898316i	−0.0969710	−	0.995287i	$-0.530915\pi$
$107$	96.1198	−	96.1198i	0.898316	−	0.898316i	0.995287	+	0.0969710i	$0.0309154\pi$
$108$	−37.0027			−0.342618
$109$		−	45.3473i		−	0.416030i	−0.978126	−	0.208015i	$-0.933300\pi$
$109$		−	45.3473i		−	0.416030i	0.978126	−	0.208015i	$-0.0667003\pi$
$110$	90.3380			0.821254
$111$	−18.3930			−0.165703
$112$	−29.7392	−	29.7392i	−0.265528	−	0.265528i
$113$	66.2008	+	66.2008i	0.585848	+	0.585848i	0.936504	−	0.350656i	$-0.114042\pi$
$113$	66.2008	+	66.2008i	0.585848	+	0.585848i	−0.350656	+	0.936504i	$0.614042\pi$
$114$	−120.255	−	120.255i	−1.05487	−	1.05487i
$115$			241.425i			2.09935i
$116$	38.0702			0.328192
$117$	18.5469	+	18.5469i	0.158520	+	0.158520i
$118$	−102.382			−0.867645
$119$	63.3542	−	63.3542i	0.532388	−	0.532388i
$120$	−111.336	−	111.336i	−0.927803	−	0.927803i
$121$			52.6226i			0.434898i
$122$	−132.473			−1.08584
$123$		−	6.04517i		−	0.0491477i
$124$			40.2954i			0.324963i
$125$		−	40.0886i		−	0.320709i
$126$	11.7521			0.0932705
$127$	−78.1675	−	78.1675i	−0.615492	−	0.615492i	0.328880	−	0.944372i	$-0.393329\pi$
$127$	−78.1675	−	78.1675i	−0.615492	−	0.615492i	−0.944372	+	0.328880i	$0.893329\pi$
$128$	−25.0817	−	25.0817i	−0.195951	−	0.195951i
$129$	14.3764	+	14.3764i	0.111445	+	0.111445i
$130$			183.449i			1.41114i
$131$	177.805	−	177.805i	1.35729	−	1.35729i	0.480040	−	0.877247i	$-0.340622\pi$
$131$	177.805	−	177.805i	1.35729	−	1.35729i	0.877247	−	0.480040i	$-0.159378\pi$
$132$	−20.4846	+	20.4846i	−0.155187	+	0.155187i
$133$	−122.170	−	122.170i	−0.918574	−	0.918574i
$134$	−143.405	+	143.405i	−1.07018	+	1.07018i
$135$	190.972			1.41461
$136$	120.835	−	120.835i	0.888495	−	0.888495i
$137$	−101.129	−	101.129i	−0.738166	−	0.738166i	0.234057	−	0.972223i	$-0.424800\pi$
$137$	−101.129	−	101.129i	−0.738166	−	0.738166i	−0.972223	+	0.234057i	$0.924800\pi$
$138$	115.723	+	115.723i	0.838572	+	0.838572i
$139$			26.5181i			0.190778i	0.995440	+	0.0953890i	$0.0304095\pi$
$139$			26.5181i			0.190778i	−0.995440	+	0.0953890i	$0.969590\pi$
$140$	−27.4947	−	27.4947i	−0.196391	−	0.196391i
$141$	−30.2498	+	30.2498i	−0.214538	+	0.214538i
$142$			149.701i			1.05424i
$143$	138.853			0.971003
$144$	14.3886			0.0999211
$145$	−196.481			−1.35504
$146$	−22.6942	−	22.6942i	−0.155440	−	0.155440i
$147$	76.7838			0.522339
$148$	−8.66332			−0.0585360
$149$	−130.222	+	130.222i	−0.873972	+	0.873972i	−0.992903	−	0.118931i	$-0.962053\pi$
$149$	−130.222	+	130.222i	−0.873972	+	0.873972i	0.118931	+	0.992903i	$0.462053\pi$
$150$	60.2302	+	60.2302i	0.401535	+	0.401535i
$151$	−89.2957			−0.591362			−0.295681	−	0.955287i	$-0.595547\pi$
$151$	−89.2957			−0.591362			−0.295681	+	0.955287i	$0.595547\pi$
$152$	−233.015	−	233.015i	−1.53300	−	1.53300i
$153$			30.6525i			0.200343i
$154$	43.9916	−	43.9916i	0.285660	−	0.285660i
$155$		−	207.966i		−	1.34171i
$156$	−41.5980	−	41.5980i	−0.266654	−	0.266654i
$157$			24.0064i			0.152907i	0.997073	+	0.0764536i	$0.0243597\pi$
$157$			24.0064i			0.152907i	−0.997073	+	0.0764536i	$0.975640\pi$
$158$	69.6441			0.440785
$159$	−25.4846	+	25.4846i	−0.160281	+	0.160281i
$160$	−92.1341	−	92.1341i	−0.575838	−	0.575838i
$161$	117.566	+	117.566i	0.730226	+	0.730226i
$162$	75.1583	−	75.1583i	0.463940	−	0.463940i
$163$	119.546	−	119.546i	0.733413	−	0.733413i	−0.237881	−	0.971294i	$-0.576453\pi$
$163$	119.546	−	119.546i	0.733413	−	0.733413i	0.971294	+	0.237881i	$0.0764528\pi$
$164$		−	2.84734i		−	0.0173619i
$165$	105.722	−	105.722i	0.640737	−	0.640737i
$166$	19.5034	+	19.5034i	0.117491	+	0.117491i
$167$	156.357	−	156.357i	0.936268	−	0.936268i	−0.0618198	−	0.998087i	$-0.519690\pi$
$167$	156.357	−	156.357i	0.936268	−	0.936268i	0.998087	+	0.0618198i	$0.0196904\pi$
$168$	−108.434			−0.645442
$169$			112.968i			0.668452i
$170$	−151.593	+	151.593i	−0.891724	+	0.891724i
$171$	59.1094			0.345669
$172$	6.77145	+	6.77145i	0.0393689	+	0.0393689i
$173$	67.2763	+	67.2763i	0.388880	+	0.388880i	0.874288	−	0.485408i	$-0.161329\pi$
$173$	67.2763	+	67.2763i	0.388880	+	0.388880i	−0.485408	+	0.874288i	$0.661329\pi$
$174$	−94.1798	+	94.1798i	−0.541263	+	0.541263i
$175$	61.1896	+	61.1896i	0.349655	+	0.349655i
$176$	53.8611	−	53.8611i	0.306029	−	0.306029i
$177$	−119.817	+	119.817i	−0.676931	+	0.676931i
$178$		−	256.091i		−	1.43872i
$179$	−132.164	−	132.164i	−0.738347	−	0.738347i	0.233911	−	0.972258i	$-0.424848\pi$
$179$	−132.164	−	132.164i	−0.738347	−	0.738347i	−0.972258	+	0.233911i	$0.924848\pi$
$180$	13.3027			0.0739040
$181$		−	100.696i		−	0.556333i	−0.960533	−	0.278166i	$-0.910273\pi$
$181$		−	100.696i		−	0.556333i	0.960533	−	0.278166i	$-0.0897266\pi$
$182$	89.3335	+	89.3335i	0.490843	+	0.490843i
$183$	−155.032	+	155.032i	−0.847168	+	0.847168i
$184$	224.234	+	224.234i	1.21866	+	1.21866i
$185$	44.7116			0.241684
$186$	−99.6846	−	99.6846i	−0.535939	−	0.535939i
$187$	114.742	+	114.742i	0.613592	+	0.613592i
$188$	−14.2480	+	14.2480i	−0.0757873	+	0.0757873i
$189$	92.9971	−	92.9971i	0.492048	−	0.492048i
$190$	292.328	+	292.328i	1.53857	+	1.53857i
$191$		−	42.3334i		−	0.221641i	−0.993840	−	0.110820i	$-0.964652\pi$
$191$		−	42.3334i		−	0.221641i	0.993840	−	0.110820i	$-0.0353478\pi$
$192$	−188.815			−0.983413
$193$	−63.8282	+	63.8282i	−0.330716	+	0.330716i	−0.852858	−	0.522142i	$-0.825133\pi$
$193$	−63.8282	+	63.8282i	−0.330716	+	0.330716i	0.522142	+	0.852858i	$0.325133\pi$
$194$	91.4612			0.471449
$195$	214.688	+	214.688i	1.10096	+	1.10096i
$196$	36.1661			0.184521
$197$	75.0434	−	75.0434i	0.380931	−	0.380931i	−0.490507	−	0.871437i	$-0.663188\pi$
$197$	75.0434	−	75.0434i	0.380931	−	0.380931i	0.871437	+	0.490507i	$0.163188\pi$
$198$			21.2844i			0.107497i
$199$	−261.898	+	261.898i	−1.31607	+	1.31607i	−0.399208	+	0.916861i	$0.630715\pi$
$199$	−261.898	+	261.898i	−1.31607	+	1.31607i	−0.916861	+	0.399208i	$0.869285\pi$
$200$	116.707	+	116.707i	0.583535	+	0.583535i
$201$			335.650i			1.66990i
$202$		−	167.236i		−	0.827900i
$203$	−95.6801	+	95.6801i	−0.471330	+	0.471330i
$204$		−	68.7491i		−	0.337005i
$205$			14.6952i			0.0716840i
$206$		−	133.734i		−	0.649196i
$207$	−56.8818			−0.274792
$208$	109.375	+	109.375i	0.525842	+	0.525842i
$209$	221.264	−	221.264i	1.05868	−	1.05868i
$210$	136.035			0.647788
$211$	−101.808	+	101.808i	−0.482501	+	0.482501i	−0.905930	−	0.423428i	$-0.860827\pi$
$211$	−101.808	+	101.808i	−0.482501	+	0.482501i	0.423428	+	0.905930i	$0.360827\pi$
$212$	−12.0035	+	12.0035i	−0.0566205	+	0.0566205i
$213$	175.194	+	175.194i	0.822508	+	0.822508i
$214$			223.999i			1.04673i
$215$	−34.9477	−	34.9477i	−0.162547	−	0.162547i
$216$	177.373	−	177.373i	0.821173	−	0.821173i
$217$	−101.273	−	101.273i	−0.466694	−	0.466694i
$218$	52.8391	+	52.8391i	0.242381	+	0.242381i
$219$	−53.1177			−0.242546
$220$	49.7961	−	49.7961i	0.226346	−	0.226346i
$221$	−233.005	+	233.005i	−1.05432	+	1.05432i
$222$	21.4317	−	21.4317i	0.0965392	−	0.0965392i
$223$		−	286.169i		−	1.28327i	−0.767011	−	0.641634i	$-0.778257\pi$
$223$		−	286.169i		−	1.28327i	0.767011	−	0.641634i	$-0.221743\pi$
$224$	−89.7326			−0.400592
$225$	−29.6052			−0.131579
$226$	−154.276			−0.682635
$227$			428.016i			1.88553i	0.333451	+	0.942767i	$0.391787\pi$
$227$			428.016i			1.88553i	−0.333451	+	0.942767i	$0.608213\pi$
$228$	−132.574			−0.581463
$229$	155.783	−	155.783i	0.680276	−	0.680276i	−0.279787	−	0.960062i	$-0.590264\pi$
$229$	155.783	−	155.783i	0.680276	−	0.680276i	0.960062	+	0.279787i	$0.0902637\pi$
$230$	−281.311	−	281.311i	−1.22309	−	1.22309i
$231$		−	102.966i		−	0.445740i
$232$	−182.491	+	182.491i	−0.786597	+	0.786597i
$233$			187.430i			0.804419i	0.915548	+	0.402210i	$0.131758\pi$
$233$			187.430i			0.804419i	−0.915548	+	0.402210i	$0.868242\pi$
$234$	−43.2220			−0.184709
$235$	73.5343	−	73.5343i	0.312912	−	0.312912i
$236$	−56.4351	+	56.4351i	−0.239132	+	0.239132i
$237$	81.5038	−	81.5038i	0.343898	−	0.343898i
$238$			147.642i			0.620344i
$239$		−	382.238i		−	1.59932i	−0.600453	−	0.799660i	$-0.705013\pi$
$239$		−	382.238i		−	1.59932i	0.600453	−	0.799660i	$-0.294987\pi$
$240$	166.555			0.693977
$241$		−	20.5132i		−	0.0851169i	−0.999094	−	0.0425585i	$-0.986449\pi$
$241$		−	20.5132i		−	0.0851169i	0.999094	−	0.0425585i	$-0.0135509\pi$
$242$	−61.3164	−	61.3164i	−0.253374	−	0.253374i
$243$			83.3349i			0.342942i
$244$	−73.0217	+	73.0217i	−0.299269	+	0.299269i
$245$	−186.654			−0.761853
$246$	7.04389	+	7.04389i	0.0286337	+	0.0286337i
$247$	449.320	+	449.320i	1.81911	+	1.81911i
$248$	−193.157	−	193.157i	−0.778859	−	0.778859i
$249$	45.6493			0.183331
$250$	46.7116	+	46.7116i	0.186846	+	0.186846i
$251$	−5.81857	+	5.81857i	−0.0231815	+	0.0231815i	−0.718603	−	0.695421i	$-0.755218\pi$
$251$	−5.81857	+	5.81857i	−0.0231815	+	0.0231815i	0.695421	+	0.718603i	$0.255218\pi$
$252$	6.47799	−	6.47799i	0.0257063	−	0.0257063i
$253$	−212.926	+	212.926i	−0.841605	+	0.841605i
$254$	182.163			0.717177
$255$			354.816i			1.39143i
$256$	−218.479			−0.853433
$257$	−319.565			−1.24344			−0.621722	−	0.783238i	$-0.713567\pi$
$257$	−319.565			−1.24344			−0.621722	+	0.783238i	$0.713567\pi$
$258$	−33.5030			−0.129857
$259$	21.7731	−	21.7731i	0.0840660	−	0.0840660i
$260$	101.121	+	101.121i	0.388926	+	0.388926i
$261$		−	46.2927i		−	0.177367i
$262$			414.359i			1.58152i
$263$	−27.4548			−0.104391			−0.0521954	−	0.998637i	$-0.516622\pi$
$263$	−27.4548			−0.104391			−0.0521954	+	0.998637i	$0.516622\pi$
$264$		−	196.387i		−	0.743890i
$265$	61.9506	−	61.9506i	0.233776	−	0.233776i
$266$	284.708			1.07033
$267$	−299.701	−	299.701i	−1.12248	−	1.12248i
$268$			158.095i			0.589907i
$269$	249.899			0.928992			0.464496	−	0.885575i	$-0.346236\pi$
$269$	249.899			0.928992			0.464496	+	0.885575i	$0.346236\pi$
$270$	−222.522	+	222.522i	−0.824157	+	0.824157i
$271$	−297.350			−1.09723			−0.548616	−	0.836074i	$-0.684845\pi$
$271$	−297.350			−1.09723			−0.548616	+	0.836074i	$0.684845\pi$
$272$			180.765i			0.664576i
$273$	209.092			0.765906
$274$	235.672			0.860117
$275$	−110.821	+	110.821i	−0.402987	+	0.402987i
$276$	127.578			0.462238
$277$	−358.783	+	358.783i	−1.29524	+	1.29524i	−0.363747	+	0.931498i	$0.618503\pi$
$277$	−358.783	+	358.783i	−1.29524	+	1.29524i	−0.931498	+	0.363747i	$0.881497\pi$
$278$	−30.8992	−	30.8992i	−0.111148	−	0.111148i
$279$	48.9985			0.175622
$280$	263.593			0.941405
$281$		−	250.284i		−	0.890692i	−0.895359	−	0.445346i	$-0.853081\pi$
$281$		−	250.284i		−	0.890692i	0.895359	−	0.445346i	$-0.146919\pi$
$282$		−	70.4947i		−	0.249981i
$283$		−	76.2107i		−	0.269296i	−0.990894	−	0.134648i	$-0.957010\pi$
$283$		−	76.2107i		−	0.269296i	0.990894	−	0.134648i	$-0.0429903\pi$
$284$	82.5185	+	82.5185i	0.290558	+	0.290558i
$285$	684.216			2.40076
$286$	−161.793	+	161.793i	−0.565711	+	0.565711i
$287$	7.15609	+	7.15609i	0.0249341	+	0.0249341i
$288$	21.7076	−	21.7076i	0.0753735	−	0.0753735i
$289$	−96.0883			−0.332485
$290$	228.942	−	228.942i	0.789455	−	0.789455i
$291$	107.036	−	107.036i	0.367822	−	0.367822i
$292$	−25.0190			−0.0856817
$293$	−34.3601			−0.117270			−0.0586350	−	0.998279i	$-0.518675\pi$
$293$	−34.3601			−0.117270			−0.0586350	+	0.998279i	$0.518675\pi$
$294$	−89.4692	+	89.4692i	−0.304317	+	0.304317i
$295$	291.263	−	291.263i	0.987332	−	0.987332i
$296$	41.5278	−	41.5278i	0.140297	−	0.140297i
$297$	168.429	+	168.429i	0.567099	+	0.567099i
$298$		−	303.471i		−	1.01836i
$299$	−432.387	−	432.387i	−1.44611	−	1.44611i
$300$	66.4002			0.221334
$301$	−34.0367			−0.113079
$302$	104.048	−	104.048i	0.344530	−	0.344530i
$303$	−195.714	−	195.714i	−0.645922	−	0.645922i
$304$	348.581			1.14665
$305$	376.867	−	376.867i	1.23563	−	1.23563i
$306$	−35.7166	−	35.7166i	−0.116721	−	0.116721i
$307$	−107.215			−0.349233			−0.174617	−	0.984636i	$-0.555869\pi$
$307$	−107.215			−0.349233			−0.174617	+	0.984636i	$0.555869\pi$
$308$		−	48.4982i		−	0.157462i
$309$	−156.508	−	156.508i	−0.506499	−	0.506499i
$310$	242.324	+	242.324i	0.781689	+	0.781689i
$311$	159.752	+	159.752i	0.513673	+	0.513673i	0.915650	−	0.401977i	$-0.131677\pi$
$311$	159.752	+	159.752i	0.513673	+	0.513673i	−0.401977	+	0.915650i	$0.631677\pi$
$312$	398.802			1.27821
$313$	−212.888			−0.680155			−0.340077	−	0.940397i	$-0.610453\pi$
$313$	−212.888			−0.680155			−0.340077	+	0.940397i	$0.610453\pi$
$314$	−27.9725	−	27.9725i	−0.0890844	−	0.0890844i
$315$	−33.4331	+	33.4331i	−0.106137	+	0.106137i
$316$	38.3893	−	38.3893i	0.121485	−	0.121485i
$317$	−396.460	−	396.460i	−1.25066	−	1.25066i	−0.955423	−	0.295241i	$-0.904600\pi$
$317$	−396.460	−	396.460i	−1.25066	−	1.25066i	−0.295241	−	0.955423i	$-0.595400\pi$
$318$		−	59.3898i		−	0.186760i
$319$	−173.288	−	173.288i	−0.543221	−	0.543221i
$320$	458.992			1.43435
$321$	262.144	+	262.144i	0.816649	+	0.816649i
$322$	−273.979			−0.850866
$323$			742.593i			2.29905i
$324$		−	82.8575i		−	0.255733i
$325$	−225.044	−	225.044i	−0.692444	−	0.692444i
$326$			278.593i			0.854580i
$327$	123.674			0.378208
$328$	13.6488	+	13.6488i	0.0416122	+	0.0416122i
$329$		−	71.6176i		−	0.217683i
$330$			246.376i			0.746593i
$331$	−404.779	−	404.779i	−1.22290	−	1.22290i	−0.966597	−	0.256301i	$-0.917496\pi$
$331$	−404.779	−	404.779i	−1.22290	−	1.22290i	−0.256301	−	0.966597i	$-0.582504\pi$
$332$	21.5014			0.0647632
$333$			10.5344i			0.0316349i
$334$			364.377i			1.09095i
$335$		−	815.933i		−	2.43562i
$336$	81.1066	−	81.1066i	0.241389	−	0.241389i
$337$		−	113.695i		−	0.337375i	−0.985670	−	0.168688i	$-0.946047\pi$
$337$		−	113.695i		−	0.337375i	0.985670	−	0.168688i	$-0.0539529\pi$
$338$	−131.632	−	131.632i	−0.389443	−	0.389443i
$339$	−180.547	+	180.547i	−0.532588	+	0.532588i
$340$			167.122i			0.491536i
$341$	183.416	−	183.416i	0.537877	−	0.537877i
$342$	−68.8748	+	68.8748i	−0.201388	+	0.201388i
$343$	−249.089	+	249.089i	−0.726206	+	0.726206i
$344$	−64.9182			−0.188716
$345$	−658.432			−1.90850
$346$	−156.782			−0.453127
$347$	−80.3110	−	80.3110i	−0.231444	−	0.231444i	0.581851	−	0.813295i	$-0.302329\pi$
$347$	−80.3110	−	80.3110i	−0.231444	−	0.231444i	−0.813295	+	0.581851i	$0.802329\pi$
$348$			103.828i			0.298355i
$349$	−105.420	−	332.697i	−0.302064	−	0.953288i
$349$	−105.420	−	332.697i	−0.302064	−	0.953288i
$350$	−142.597			−0.407421
$351$	−342.026	+	342.026i	−0.974434	+	0.974434i
$352$		−	162.516i		−	0.461693i
$353$			698.436i			1.97857i	0.145994	+	0.989286i	$0.453362\pi$
$353$			698.436i			1.97857i	−0.145994	+	0.989286i	$0.546638\pi$
$354$		−	279.223i		−	0.788766i
$355$	−425.880	−	425.880i	−1.19966	−	1.19966i
$356$	−141.163	−	141.163i	−0.396525	−	0.396525i
$357$	172.784	+	172.784i	0.483988	+	0.483988i
$358$	307.998			0.860329
$359$	−82.6978	−	82.6978i	−0.230356	−	0.230356i	0.582485	−	0.812841i	$-0.302080\pi$
$359$	−82.6978	−	82.6978i	−0.230356	−	0.230356i	−0.812841	+	0.582485i	$0.802080\pi$
$360$	−63.7669	+	63.7669i	−0.177130	+	0.177130i
$361$	1070.99			2.96674
$362$	117.332	+	117.332i	0.324122	+	0.324122i
$363$	−143.516			−0.395361
$364$	98.4849			0.270563
$365$	129.124			0.353764
$366$		−	361.289i		−	0.987128i
$367$	240.622	−	240.622i	0.655647	−	0.655647i	−0.298700	−	0.954347i	$-0.596553\pi$
$367$	240.622	−	240.622i	0.655647	−	0.655647i	0.954347	+	0.298700i	$0.0965531\pi$
$368$	−335.445			−0.911536
$369$	−3.46232			−0.00938297
$370$	−52.0984	+	52.0984i	−0.140807	+	0.140807i
$371$		−	60.3358i		−	0.162630i
$372$	−109.896			−0.295420
$373$	−271.514	+	271.514i	−0.727919	+	0.727919i	−0.970205	−	0.242286i	$-0.922103\pi$
$373$	−271.514	+	271.514i	−0.727919	+	0.727919i	0.242286	+	0.970205i	$0.422103\pi$
$374$	−267.396			−0.714963
$375$	109.332			0.291553
$376$		−	136.596i		−	0.363288i
$377$	351.894	−	351.894i	0.933405	−	0.933405i
$378$			216.722i			0.573339i
$379$	244.091	−	244.091i	0.644039	−	0.644039i	−0.307507	−	0.951546i	$-0.599495\pi$
$379$	244.091	−	244.091i	0.644039	−	0.644039i	0.951546	+	0.307507i	$0.0994947\pi$
$380$	322.274			0.848089
$381$	213.184	−	213.184i	0.559537	−	0.559537i
$382$	49.3273	+	49.3273i	0.129129	+	0.129129i
$383$	−154.337	−	154.337i	−0.402968	−	0.402968i	0.476310	−	0.879277i	$-0.341974\pi$
$383$	−154.337	−	154.337i	−0.402968	−	0.402968i	−0.879277	+	0.476310i	$0.841974\pi$
$384$	68.4046	−	68.4046i	0.178137	−	0.178137i
$385$			250.300i			0.650131i
$386$		−	148.746i		−	0.385354i
$387$	8.23396	−	8.23396i	0.0212764	−	0.0212764i
$388$	50.4153	−	50.4153i	0.129936	−	0.129936i
$389$	14.7916	−	14.7916i	0.0380246	−	0.0380246i	−0.687839	−	0.725863i	$-0.741440\pi$
$389$	14.7916	−	14.7916i	0.0380246	−	0.0380246i	0.725863	+	0.687839i	$0.241440\pi$
$390$	−500.313			−1.28285
$391$		−	714.608i		−	1.82764i
$392$	−173.363	+	173.363i	−0.442252	+	0.442252i
$393$	484.920	+	484.920i	1.23389	+	1.23389i
$394$			174.883i			0.443864i
$395$	−198.128	+	198.128i	−0.501590	+	0.501590i
$396$	11.7324	+	11.7324i	0.0296272	+	0.0296272i
$397$			161.639i			0.407152i	0.979059	+	0.203576i	$0.0652564\pi$
$397$			161.639i			0.407152i	−0.979059	+	0.203576i	$0.934744\pi$
$398$		−	610.331i		−	1.53349i
$399$	333.191	−	333.191i	0.835065	−	0.835065i
$400$	−174.589			−0.436472
$401$	−555.983	+	555.983i	−1.38649	+	1.38649i	−0.553925	+	0.832567i	$0.686871\pi$
$401$	−555.983	+	555.983i	−1.38649	+	1.38649i	−0.832567	+	0.553925i	$0.813129\pi$
$402$	−391.103	−	391.103i	−0.972892	−	0.972892i
$403$	372.462	+	372.462i	0.924223	+	0.924223i
$404$	−92.1838	−	92.1838i	−0.228178	−	0.228178i
$405$			427.630i			1.05588i
$406$		−	222.975i		−	0.549198i
$407$	39.4336	+	39.4336i	0.0968884	+	0.0968884i
$408$	329.550	+	329.550i	0.807721	+	0.807721i
$409$		−	211.332i		−	0.516705i	−0.966051	−	0.258353i	$-0.916820\pi$
$409$		−	211.332i		−	0.516705i	0.966051	−	0.258353i	$-0.0831796\pi$
$410$	−17.1230	−	17.1230i	−0.0417634	−	0.0417634i
$411$	275.805	−	275.805i	0.671058	−	0.671058i
$412$	−73.7171	−	73.7171i	−0.178925	−	0.178925i
$413$		−	283.671i		−	0.686855i
$414$	66.2793	−	66.2793i	0.160095	−	0.160095i
$415$	−110.969			−0.267396
$416$	330.020			0.793318
$417$	−72.3221			−0.173434
$418$			515.639i			1.23359i
$419$			637.327i			1.52107i	0.649299	+	0.760533i	$0.275062\pi$
$419$			637.327i			1.52107i	−0.649299	+	0.760533i	$0.724938\pi$
$420$	74.9855	−	74.9855i	0.178537	−	0.178537i
$421$	25.9249	+	25.9249i	0.0615793	+	0.0615793i	0.737226	−	0.675646i	$-0.236135\pi$
$421$	25.9249	+	25.9249i	0.0615793	+	0.0615793i	−0.675646	+	0.737226i	$0.736135\pi$
$422$		−	237.255i		−	0.562215i
$423$	17.3253	+	17.3253i	0.0409582	+	0.0409582i
$424$		−	115.079i		−	0.271412i
$425$		−	371.931i		−	0.875133i
$426$	−408.276			−0.958394
$427$		−	367.044i		−	0.859588i
$428$	123.473	+	123.473i	0.288489	+	0.288489i
$429$			378.690i			0.882728i
$430$	81.4427			0.189402
$431$	−343.935	+	343.935i	−0.797993	+	0.797993i	−0.982779	−	0.184786i	$-0.940841\pi$
$431$	−343.935	+	343.935i	−0.797993	+	0.797993i	0.184786	+	0.982779i	$0.440841\pi$
$432$			265.343i			0.614221i
$433$	−367.307	−	367.307i	−0.848285	−	0.848285i	0.141634	−	0.989919i	$-0.454764\pi$
$433$	−367.307	−	367.307i	−0.848285	−	0.848285i	−0.989919	+	0.141634i	$0.954764\pi$
$434$	236.007			0.543796
$435$		−	535.857i		−	1.23186i
$436$	58.2520			0.133605
$437$	−1378.03			−3.15338
$438$	61.8932	−	61.8932i	0.141309	−	0.141309i
$439$	487.430	+	487.430i	1.11032	+	1.11032i	0.993107	+	0.117211i	$0.0373954\pi$
$439$	487.430	+	487.430i	1.11032	+	1.11032i	0.117211	+	0.993107i	$0.462605\pi$
$440$			477.398i			1.08499i
$441$		−	43.9772i		−	0.0997216i
$442$		−	542.999i		−	1.22851i
$443$	347.715			0.784909			0.392455	−	0.919771i	$-0.371626\pi$
$443$	347.715			0.784909			0.392455	+	0.919771i	$0.371626\pi$
$444$		−	23.6272i		−	0.0532144i
$445$	728.545	+	728.545i	1.63718	+	1.63718i
$446$	333.447	+	333.447i	0.747638	+	0.747638i
$447$	−355.150	−	355.150i	−0.794518	−	0.794518i
$448$	223.514	−	223.514i	0.498915	−	0.498915i
$449$			10.2978i			0.0229349i	0.999934	+	0.0114675i	$0.00365029\pi$
$449$			10.2978i			0.0229349i	−0.999934	+	0.0114675i	$0.996350\pi$
$450$	34.4963	−	34.4963i	0.0766584	−	0.0766584i
$451$	−12.9605	+	12.9605i	−0.0287373	+	0.0287373i
$452$	−85.0398	+	85.0398i	−0.188141	+	0.188141i
$453$		−	243.533i		−	0.537601i
$454$	−498.729	−	498.729i	−1.09852	−	1.09852i
$455$	−508.283			−1.11711
$456$	635.495	−	635.495i	1.39363	−	1.39363i
$457$	59.3013			0.129762			0.0648811	−	0.997893i	$-0.479333\pi$
$457$	59.3013			0.129762			0.0648811	+	0.997893i	$0.479333\pi$
$458$			363.040i			0.792664i
$459$	−565.268			−1.23152
$460$	−310.129			−0.674193
$461$	−10.2947	−	10.2947i	−0.0223313	−	0.0223313i	0.695853	−	0.718184i	$-0.255027\pi$
$461$	−10.2947	−	10.2947i	−0.0223313	−	0.0223313i	−0.718184	+	0.695853i	$0.755027\pi$
$462$	119.977	+	119.977i	0.259690	+	0.259690i
$463$	267.539	+	267.539i	0.577838	+	0.577838i	0.934307	−	0.356469i	$-0.116020\pi$
$463$	267.539	+	267.539i	0.577838	+	0.577838i	−0.356469	+	0.934307i	$0.616020\pi$
$464$		−	272.998i		−	0.588358i
$465$	567.178			1.21974
$466$	−218.395	−	218.395i	−0.468658	−	0.468658i
$467$	−64.7978			−0.138753			−0.0693767	−	0.997591i	$-0.522101\pi$
$467$	−64.7978			−0.138753			−0.0693767	+	0.997591i	$0.522101\pi$
$468$	−23.8249	+	23.8249i	−0.0509078	+	0.0509078i
$469$	−397.333	−	397.333i	−0.847191	−	0.847191i
$470$			171.366i			0.364608i
$471$	−65.4719			−0.139006
$472$		−	541.046i		−	1.14628i
$473$		−	61.6444i		−	0.130327i
$474$			189.938i			0.400713i
$475$	−717.221			−1.50994
$476$	81.3832	+	81.3832i	0.170973	+	0.170973i
$477$	14.5961	+	14.5961i	0.0305997	+	0.0305997i
$478$	445.387	+	445.387i	0.931772	+	0.931772i
$479$		−	736.957i		−	1.53853i	−0.638928	−	0.769267i	$-0.720622\pi$
$479$		−	736.957i		−	1.53853i	0.638928	−	0.769267i	$-0.279378\pi$
$480$	251.274	−	251.274i	0.523488	−	0.523488i
$481$	−80.0775	+	80.0775i	−0.166481	+	0.166481i
$482$	23.9021	+	23.9021i	0.0495895	+	0.0495895i
$483$	−320.635	+	320.635i	−0.663840	+	0.663840i
$484$	−67.5977			−0.139665
$485$	−260.194	+	260.194i	−0.536483	+	0.536483i
$486$	−97.1026	−	97.1026i	−0.199800	−	0.199800i
$487$	−310.555	−	310.555i	−0.637689	−	0.637689i	0.312296	−	0.949985i	$-0.398902\pi$
$487$	−310.555	−	310.555i	−0.637689	−	0.637689i	−0.949985	+	0.312296i	$0.898902\pi$
$488$		−	700.063i		−	1.43455i
$489$	326.035	+	326.035i	0.666738	+	0.666738i
$490$	217.491	−	217.491i	0.443859	−	0.443859i
$491$			698.383i			1.42237i	0.703006	+	0.711184i	$0.251841\pi$
$491$			698.383i			1.42237i	−0.703006	+	0.711184i	$0.748159\pi$
$492$	7.76547			0.0157835
$493$	581.576			1.17967
$494$	−1047.10			−2.11964
$495$	−60.5511	−	60.5511i	−0.122326	−	0.122326i
$496$	288.955			0.582571
$497$	−414.779			−0.834566
$498$	−53.1910	+	53.1910i	−0.106809	+	0.106809i
$499$	314.942	+	314.942i	0.631145	+	0.631145i	0.948355	−	0.317210i	$-0.102746\pi$
$499$	314.942	+	314.942i	0.631145	+	0.631145i	−0.317210	+	0.948355i	$0.602746\pi$
$500$	51.4968			0.102994
$501$	426.426	+	426.426i	0.851150	+	0.851150i
$502$		−	13.5597i		−	0.0270114i
$503$	−250.735	+	250.735i	−0.498478	+	0.498478i	−0.910964	−	0.412486i	$-0.864661\pi$
$503$	−250.735	+	250.735i	−0.498478	+	0.498478i	0.412486	+	0.910964i	$0.364661\pi$
$504$			62.1048i			0.123224i
$505$	475.763	+	475.763i	0.942105	+	0.942105i
$506$		−	496.207i		−	0.980646i
$507$	−308.095			−0.607683
$508$	100.412	−	100.412i	0.197661	−	0.197661i
$509$	176.446	+	176.446i	0.346652	+	0.346652i	0.858861	−	0.512209i	$-0.171173\pi$
$509$	176.446	+	176.446i	0.346652	+	0.346652i	−0.512209	+	0.858861i	$0.671173\pi$
$510$	−413.435	−	413.435i	−0.810656	−	0.810656i
$511$	62.8791	−	62.8791i	0.123051	−	0.123051i
$512$	354.900	−	354.900i	0.693165	−	0.693165i
$513$			1090.05i			2.12485i
$514$	372.360	−	372.360i	0.724436	−	0.724436i
$515$	380.456	+	380.456i	0.738750	+	0.738750i
$516$	−18.4676	+	18.4676i	−0.0357898	+	0.0357898i
$517$	129.708			0.250885
$518$			50.7404i			0.0979545i
$519$	−183.480	+	183.480i	−0.353527	+	0.353527i
$520$	−969.448			−1.86432
$521$	402.079	+	402.079i	0.771744	+	0.771744i	0.978411	−	0.206667i	$-0.0662617\pi$
$521$	402.079	+	402.079i	0.771744	+	0.771744i	−0.206667	+	0.978411i	$0.566262\pi$
$522$	53.9406	+	53.9406i	0.103335	+	0.103335i
$523$	−78.0699	+	78.0699i	−0.149273	+	0.149273i	−0.777793	−	0.628520i	$-0.783661\pi$
$523$	−78.0699	+	78.0699i	−0.149273	+	0.149273i	0.628520	+	0.777793i	$0.283661\pi$
$524$	228.403	+	228.403i	0.435884	+	0.435884i
$525$	−166.880	+	166.880i	−0.317867	+	0.317867i
$526$	31.9906	−	31.9906i	0.0608186	−	0.0608186i
$527$			615.569i			1.16806i
$528$	146.893	+	146.893i	0.278207	+	0.278207i
$529$	797.098			1.50680
$530$			144.371i			0.272398i
$531$	68.6240	+	68.6240i	0.129235	+	0.129235i
$532$	156.937	−	156.937i	0.294994	−	0.294994i
$533$	−26.3188	−	26.3188i	−0.0493786	−	0.0493786i
$534$	698.429			1.30792
$535$	−637.248	−	637.248i	−1.19112	−	1.19112i
$536$	−757.833	−	757.833i	−1.41387	−	1.41387i
$537$	360.447	−	360.447i	0.671223	−	0.671223i
$538$	−291.184	+	291.184i	−0.541235	+	0.541235i
$539$	−164.620	−	164.620i	−0.305418	−	0.305418i
$540$			245.318i			0.454292i
$541$	−75.9762			−0.140437			−0.0702183	−	0.997532i	$-0.522370\pi$
$541$	−75.9762			−0.140437			−0.0702183	+	0.997532i	$0.522370\pi$
$542$	346.475	−	346.475i	0.639253	−	0.639253i
$543$	274.625			0.505756
$544$	272.713	+	272.713i	0.501310	+	0.501310i
$545$	−300.640			−0.551633
$546$	−243.636	+	243.636i	−0.446220	+	0.446220i
$547$		−	626.757i		−	1.14581i	−0.819623	−	0.572904i	$-0.805817\pi$
$547$		−	626.757i		−	1.14581i	0.819623	−	0.572904i	$-0.194183\pi$
$548$	129.907	−	129.907i	0.237057	−	0.237057i
$549$	88.7930	+	88.7930i	0.161736	+	0.161736i
$550$		−	258.260i		−	0.469564i
$551$		−	1121.49i		−	2.03538i
$552$	−611.546	+	611.546i	−1.10787	+	1.10787i
$553$			192.964i			0.348940i
$554$		−	836.114i		−	1.50923i
$555$			121.941i			0.219713i
$556$	−34.0645			−0.0612672
$557$	−732.689	−	732.689i	−1.31542	−	1.31542i	−0.917359	−	0.398062i	$-0.869683\pi$
$557$	−732.689	−	732.689i	−1.31542	−	1.31542i	−0.398062	−	0.917359i	$-0.630317\pi$
$558$	−57.0935	+	57.0935i	−0.102318	+	0.102318i
$559$	125.181			0.223937
$560$	−197.162	+	197.162i	−0.352076	+	0.352076i
$561$	−312.931	+	312.931i	−0.557810	+	0.557810i
$562$	291.634	+	291.634i	0.518921	+	0.518921i
$563$			978.093i			1.73729i	0.495437	+	0.868644i	$0.335008\pi$
$563$			978.093i			1.73729i	−0.495437	+	0.868644i	$0.664992\pi$
$564$	−38.8581	−	38.8581i	−0.0688974	−	0.0688974i
$565$	438.893	−	438.893i	0.776801	−	0.776801i
$566$	88.8014	+	88.8014i	0.156893	+	0.156893i
$567$	208.242	+	208.242i	0.367270	+	0.367270i
$568$	−791.108			−1.39280
$569$	−306.948	+	306.948i	−0.539452	+	0.539452i	−0.923368	−	0.383916i	$-0.874575\pi$
$569$	−306.948	+	306.948i	−0.539452	+	0.539452i	0.383916	+	0.923368i	$0.374575\pi$
$570$	−797.255	+	797.255i	−1.39869	+	1.39869i
$571$	−715.846	+	715.846i	−1.25367	+	1.25367i	−0.299608	+	0.954062i	$0.596856\pi$
$571$	−715.846	+	715.846i	−1.25367	+	1.25367i	−0.954062	+	0.299608i	$0.903144\pi$
$572$			178.367i			0.311831i
$573$	115.454			0.201491
$574$	−16.6767			−0.0290535
$575$	690.193			1.20034
$576$			108.142i			0.187747i
$577$	973.291			1.68681			0.843406	−	0.537277i	$-0.180547\pi$
$577$	973.291			1.68681			0.843406	+	0.537277i	$0.180547\pi$
$578$	111.963	−	111.963i	0.193708	−	0.193708i
$579$	−174.077	−	174.077i	−0.300650	−	0.300650i
$580$		−	252.395i		−	0.435164i
$581$	−54.0384	+	54.0384i	−0.0930092	+	0.0930092i
$582$			249.439i			0.428589i
$583$	109.275			0.187436
$584$	119.929	−	119.929i	0.205358	−	0.205358i
$585$	122.961	−	122.961i	0.210189	−	0.210189i
$586$	40.0367	−	40.0367i	0.0683221	−	0.0683221i
$587$			70.0808i			0.119388i	0.998217	+	0.0596940i	$0.0190125\pi$
$587$			70.0808i			0.119388i	−0.998217	+	0.0596940i	$0.980987\pi$
$588$			98.6345i			0.167746i
$589$	1187.04			2.01536
$590$			678.765i			1.15045i
$591$	204.663	+	204.663i	0.346300	+	0.346300i
$592$			62.1239i			0.104939i
$593$	−396.936	+	396.936i	−0.669370	+	0.669370i	−0.957570	−	0.288200i	$-0.906943\pi$
$593$	−396.936	+	396.936i	−0.669370	+	0.669370i	0.288200	+	0.957570i	$0.406943\pi$
$594$	−392.509			−0.660789
$595$	−420.021	−	420.021i	−0.705917	−	0.705917i
$596$	−167.280	−	167.280i	−0.280671	−	0.280671i
$597$	−714.264	−	714.264i	−1.19642	−	1.19642i
$598$	1007.64			1.68502
$599$	−327.788	−	327.788i	−0.547225	−	0.547225i	0.378412	−	0.925637i	$-0.376470\pi$
$599$	−327.788	−	327.788i	−0.547225	−	0.547225i	−0.925637	+	0.378412i	$0.876470\pi$
$600$	−318.291	+	318.291i	−0.530485	+	0.530485i
$601$	−635.830	+	635.830i	−1.05795	+	1.05795i	−0.0597391	+	0.998214i	$0.519027\pi$
$601$	−635.830	+	635.830i	−1.05795	+	1.05795i	−0.998214	+	0.0597391i	$0.980973\pi$
$602$	39.6599	−	39.6599i	0.0658803	−	0.0658803i
$603$	192.241			0.318807
$604$		−	114.707i		−	0.189912i
$605$	348.873			0.576650
$606$	456.096			0.752634
$607$	343.964			0.566662			0.283331	−	0.959022i	$-0.408561\pi$
$607$	343.964			0.566662			0.283331	+	0.959022i	$0.408561\pi$
$608$	525.891	−	525.891i	0.864952	−	0.864952i
$609$	−260.945	−	260.945i	−0.428481	−	0.428481i
$610$			878.258i			1.43977i
$611$			263.397i			0.431091i
$612$	−39.3754			−0.0643389
$613$		−	522.159i		−	0.851809i	−0.904768	−	0.425905i	$-0.859956\pi$
$613$		−	522.159i		−	0.851809i	0.904768	−	0.425905i	$-0.140044\pi$
$614$	124.927	−	124.927i	0.203465	−	0.203465i
$615$	−40.0778			−0.0651671
$616$	232.477	+	232.477i	0.377398	+	0.377398i
$617$			339.268i			0.549867i	0.961463	+	0.274934i	$0.0886559\pi$
$617$			339.268i			0.549867i	−0.961463	+	0.274934i	$0.911344\pi$
$618$	364.729			0.590177
$619$	744.770	−	744.770i	1.20318	−	1.20318i	0.229989	−	0.973193i	$-0.426131\pi$
$619$	744.770	−	744.770i	1.20318	−	1.20318i	0.973193	−	0.229989i	$-0.0738691\pi$
$620$	267.147			0.430883
$621$		−	1048.97i		−	1.68916i
$622$	−372.289			−0.598536
$623$	709.555			1.13893
$624$	−298.295	+	298.295i	−0.478037	+	0.478037i
$625$	−739.606			−1.18337
$626$	248.060	−	248.060i	0.396261	−	0.396261i
$627$	603.447	+	603.447i	0.962436	+	0.962436i
$628$	−30.8380			−0.0491052
$629$	−132.344			−0.210404
$630$		−	77.9130i		−	0.123672i
$631$			295.722i			0.468656i	0.972158	+	0.234328i	$0.0752890\pi$
$631$			295.722i			0.468656i	−0.972158	+	0.234328i	$0.924711\pi$
$632$			368.039i			0.582341i
$633$	−277.657	−	277.657i	−0.438636	−	0.438636i
$634$	923.919			1.45729
$635$	−518.229	+	518.229i	−0.816108	+	0.816108i
$636$	−32.7369	−	32.7369i	−0.0514731	−	0.0514731i
$637$	334.293	−	334.293i	0.524793	−	0.524793i
$638$	403.833			0.632967
$639$	100.341	−	100.341i	0.157028	−	0.157028i
$640$	−166.285	+	166.285i	−0.259820	+	0.259820i
$641$	1179.12			1.83950			0.919750	−	0.392505i	$-0.128391\pi$
$641$	1179.12			1.83950			0.919750	+	0.392505i	$0.128391\pi$
$642$	−610.906			−0.951567
$643$	−308.686	+	308.686i	−0.480071	+	0.480071i	−0.905154	−	0.425083i	$-0.860245\pi$
$643$	−308.686	+	308.686i	−0.480071	+	0.480071i	0.425083	+	0.905154i	$0.360245\pi$
$644$	−151.023	+	151.023i	−0.234507	+	0.234507i
$645$	95.3116	−	95.3116i	0.147770	−	0.147770i
$646$	−865.276	−	865.276i	−1.33944	−	1.33944i
$647$		−	0.227669i		−	0.000351884i	−1.00000		0.000175942i	$-0.999944\pi$
$647$		−	0.227669i		−	0.000351884i	1.00000		0.000175942i	$-5.60041e-5\pi$
$648$	397.179	+	397.179i	0.612931	+	0.612931i
$649$	513.761			0.791620
$650$	524.447			0.806842
$651$	276.197	−	276.197i	0.424266	−	0.424266i
$652$	153.566	+	153.566i	0.235531	+	0.235531i
$653$	461.962			0.707445			0.353723	−	0.935350i	$-0.384916\pi$
$653$	461.962			0.707445			0.353723	+	0.935350i	$0.384916\pi$
$654$	−144.106	+	144.106i	−0.220346	+	0.220346i
$655$	−1178.79	−	1178.79i	−1.79969	−	1.79969i
$656$	−20.4181			−0.0311251
$657$			30.4227i			0.0463054i
$658$	83.4495	+	83.4495i	0.126823	+	0.126823i
$659$	263.530	+	263.530i	0.399894	+	0.399894i	0.878196	−	0.478301i	$-0.158747\pi$
$659$	263.530	+	263.530i	0.399894	+	0.399894i	−0.478301	+	0.878196i	$0.658747\pi$
$660$	135.807	+	135.807i	0.205769	+	0.205769i
$661$	77.4631			0.117191			0.0585954	−	0.998282i	$-0.481338\pi$
$661$	77.4631			0.117191			0.0585954	+	0.998282i	$0.481338\pi$
$662$	943.305			1.42493
$663$	−635.467	−	635.467i	−0.958472	−	0.958472i
$664$	−103.067	+	103.067i	−0.155222	+	0.155222i
$665$	−809.955	+	809.955i	−1.21798	+	1.21798i
$666$	−12.2748	−	12.2748i	−0.0184307	−	0.0184307i
$667$			1079.23i			1.61804i
$668$	200.852	+	200.852i	0.300676	+	0.300676i
$669$	780.459			1.16660
$670$	950.733	+	950.733i	1.41900	+	1.41900i
$671$	664.759			0.990699
$672$		−	244.725i		−	0.364174i
$673$			440.564i			0.654627i	0.944916	+	0.327313i	$0.106143\pi$
$673$			440.564i			0.654627i	−0.944916	+	0.327313i	$0.893857\pi$
$674$	132.479	+	132.479i	0.196556	+	0.196556i
$675$		−	545.955i		−	0.808823i
$676$	−145.116			−0.214669
$677$	99.9794	+	99.9794i	0.147680	+	0.147680i	0.777081	−	0.629401i	$-0.216700\pi$
$677$	99.9794	+	99.9794i	0.147680	+	0.147680i	−0.629401	+	0.777081i	$0.716700\pi$
$678$		−	420.751i		−	0.620576i
$679$			253.412i			0.373214i
$680$	−801.105	−	801.105i	−1.17810	−	1.17810i
$681$	−1167.31			−1.71412
$682$			427.437i			0.626740i
$683$			320.465i			0.469202i	0.972092	+	0.234601i	$0.0753783\pi$
$683$			320.465i			0.469202i	−0.972092	+	0.234601i	$0.924622\pi$
$684$			75.9304i			0.111009i
$685$	−670.455	+	670.455i	−0.978766	+	0.978766i
$686$		−	580.481i		−	0.846183i
$687$	424.862	+	424.862i	0.618431	+	0.618431i
$688$	48.5575	−	48.5575i	0.0705778	−	0.0705778i
$689$			221.904i			0.322067i
$690$	767.211	−	767.211i	1.11190	−	1.11190i
$691$	−28.9213	+	28.9213i	−0.0418543	+	0.0418543i	−0.727724	−	0.685870i	$-0.759422\pi$
$691$	−28.9213	+	28.9213i	−0.0418543	+	0.0418543i	0.685870	+	0.727724i	$0.259422\pi$
$692$	−86.4214	+	86.4214i	−0.124886	+	0.124886i
$693$	−58.9729			−0.0850979
$694$	187.158			0.269680
$695$	175.808			0.252961
$696$	−497.700	−	497.700i	−0.715087	−	0.715087i
$697$		−	43.4972i		−	0.0624063i
$698$	510.499	+	264.825i	0.731374	+	0.379406i
$699$	−511.171			−0.731289
$700$	−78.6026	+	78.6026i	−0.112289	+	0.112289i
$701$		−	823.154i		−	1.17426i	−0.809494	−	0.587129i	$-0.800258\pi$
$701$		−	823.154i		−	1.17426i	0.809494	−	0.587129i	$-0.199742\pi$
$702$		−	797.065i		−	1.13542i
$703$			255.209i			0.363028i
$704$	404.810	+	404.810i	0.575013	+	0.575013i
$705$	200.548	+	200.548i	0.284465	+	0.284465i
$706$	−813.824	−	813.824i	−1.15272	−	1.15272i
$707$	463.362			0.655392
$708$	−153.914	−	153.914i	−0.217392	−	0.217392i
$709$	125.150	−	125.150i	0.176516	−	0.176516i	−0.613319	−	0.789835i	$-0.710166\pi$
$709$	125.150	−	125.150i	0.176516	−	0.176516i	0.789835	+	0.613319i	$0.210166\pi$
$710$	992.479			1.39786
$711$	−46.6806	−	46.6806i	−0.0656548	−	0.0656548i
$712$	1353.33			1.90075
$713$	−1142.31			−1.60212
$714$	−402.658			−0.563947
$715$		−	920.559i		−	1.28750i
$716$	169.775	−	169.775i	0.237115	−	0.237115i
$717$	1042.46			1.45392
$718$	192.720			0.268413
$719$	643.952	−	643.952i	0.895621	−	0.895621i	−0.0994239	−	0.995045i	$-0.531700\pi$
$719$	643.952	−	643.952i	0.895621	−	0.895621i	0.995045	+	0.0994239i	$0.0317000\pi$
$720$		−	95.3926i		−	0.132490i
$721$	370.539			0.513924
$722$	−1247.93	+	1247.93i	−1.72844	+	1.72844i
$723$	55.9449			0.0773788
$724$	129.352			0.178663
$725$			561.706i			0.774767i
$726$	167.226	−	167.226i	0.230339	−	0.230339i
$727$		−	513.000i		−	0.705639i	−0.935691	−	0.352820i	$-0.885223\pi$
$727$		−	513.000i		−	0.705639i	0.935691	−	0.352820i	$-0.114777\pi$
$728$	−472.090	+	472.090i	−0.648475	+	0.648475i
$729$	−807.794			−1.10809
$730$	−150.456	+	150.456i	−0.206105	+	0.206105i
$731$	103.443	+	103.443i	0.141509	+	0.141509i
$732$	−199.150	−	199.150i	−0.272062	−	0.272062i
$733$	−883.739	+	883.739i	−1.20565	+	1.20565i	−0.233223	+	0.972423i	$0.574927\pi$
$733$	−883.739	+	883.739i	−1.20565	+	1.20565i	−0.972423	+	0.233223i	$0.925073\pi$
$734$			560.751i			0.763966i
$735$		−	509.055i		−	0.692592i
$736$	−506.073	+	506.073i	−0.687599	+	0.687599i
$737$	719.615	−	719.615i	0.976412	−	0.976412i
$738$	4.03432	−	4.03432i	0.00546656	−	0.00546656i
$739$	−909.352			−1.23052			−0.615259	−	0.788325i	$-0.710948\pi$
$739$	−909.352			−1.23052			−0.615259	+	0.788325i	$0.710948\pi$
$740$			57.4354i			0.0776154i
$741$	−1225.42	+	1225.42i	−1.65373	+	1.65373i
$742$	70.3039	+	70.3039i	0.0947492	+	0.0947492i
$743$			1037.94i			1.39696i	0.715631	+	0.698478i	$0.246139\pi$
$743$			1037.94i			1.39696i	−0.715631	+	0.698478i	$0.753861\pi$
$744$	526.791	−	526.791i	0.708052	−	0.708052i
$745$	863.335	+	863.335i	1.15884	+	1.15884i
$746$		−	632.741i		−	0.848178i
$747$		−	26.1453i		−	0.0350003i
$748$	−147.394	+	147.394i	−0.197051	+	0.197051i
$749$	−620.638			−0.828622
$750$	−127.395	+	127.395i	−0.169860	+	0.169860i
$751$	−393.160	−	393.160i	−0.523516	−	0.523516i	0.395116	−	0.918631i	$-0.370705\pi$
$751$	−393.160	−	393.160i	−0.523516	−	0.523516i	−0.918631	+	0.395116i	$0.870705\pi$
$752$	102.171	+	102.171i	0.135866	+	0.135866i
$753$	−15.8688	−	15.8688i	−0.0210741	−	0.0210741i
$754$			820.060i			1.08761i
$755$			592.005i			0.784113i
$756$	119.462	+	119.462i	0.158018	+	0.158018i
$757$	2.57729	+	2.57729i	0.00340461	+	0.00340461i	0.708807	−	0.705402i	$-0.249234\pi$
$757$	2.57729	+	2.57729i	0.00340461	+	0.00340461i	−0.705402	+	0.708807i	$0.749234\pi$
$758$			568.834i			0.750440i
$759$	−580.706	−	580.706i	−0.765094	−	0.765094i
$760$	−1544.83	+	1544.83i	−2.03267	+	2.03267i
$761$	−29.1039	−	29.1039i	−0.0382442	−	0.0382442i	0.687726	−	0.725970i	$-0.258609\pi$
$761$	−29.1039	−	29.1039i	−0.0382442	−	0.0382442i	−0.725970	+	0.687726i	$0.758609\pi$
$762$			496.807i			0.651977i
$763$	−146.402	+	146.402i	−0.191877	+	0.191877i
$764$	54.3804			0.0711785
$765$	203.218			0.265644
$766$	359.669			0.469542
$767$			1043.29i			1.36022i
$768$		−	595.850i		−	0.775846i
$769$	−436.844	+	436.844i	−0.568068	+	0.568068i	−0.931587	−	0.363519i	$-0.881575\pi$
$769$	−436.844	+	436.844i	−0.568068	+	0.568068i	0.363519	+	0.931587i	$0.381575\pi$
$770$	−291.652	−	291.652i	−0.378769	−	0.378769i
$771$		−	871.539i		−	1.13040i
$772$	−81.9921	−	81.9921i	−0.106207	−	0.106207i
$773$		−	327.292i		−	0.423404i	−0.977334	−	0.211702i	$-0.932099\pi$
$773$		−	327.292i		−	0.423404i	0.977334	−	0.211702i	$-0.0679007\pi$
$774$			19.1886i			0.0247914i
$775$	−594.537			−0.767145
$776$			483.333i			0.622852i
$777$	59.3811	+	59.3811i	0.0764235	+	0.0764235i
$778$			34.4705i			0.0443066i
$779$	−83.8786			−0.107675
$780$	−275.783	+	275.783i	−0.353568	+	0.353568i
$781$		−	751.213i		−	0.961861i
$782$	832.668	+	832.668i	1.06479	+	1.06479i
$783$	853.691			1.09028
$784$		−	259.344i		−	0.330796i
$785$	159.156			0.202746
$786$	−1130.07			−1.43774
$787$	962.397	−	962.397i	1.22287	−	1.22287i	0.256260	−	0.966608i	$-0.417510\pi$
$787$	962.397	−	962.397i	1.22287	−	1.22287i	0.966608	−	0.256260i	$-0.0824904\pi$
$788$	96.3988	+	96.3988i	0.122334	+	0.122334i
$789$		−	74.8766i		−	0.0949006i
$790$		−	461.721i		−	0.584457i
$791$		−	427.453i		−	0.540396i
$792$	−112.479			−0.142019
$793$			1349.92i			1.70230i
$794$	−188.344	−	188.344i	−0.237209	−	0.237209i
$795$	168.956	+	168.956i	0.212523	+	0.212523i
$796$	−336.427	−	336.427i	−0.422647	−	0.422647i
$797$	641.688	−	641.688i	0.805130	−	0.805130i	−0.178763	−	0.983892i	$-0.557209\pi$
$797$	641.688	−	641.688i	0.805130	−	0.805130i	0.983892	+	0.178763i	$0.0572094\pi$
$798$			776.474i			0.973025i
$799$	−217.658	+	217.658i	−0.272413	+	0.272413i
$800$	−263.395	+	263.395i	−0.329244	+	0.329244i
$801$	−171.651	+	171.651i	−0.214296	+	0.214296i
$802$		−	1295.67i		−	1.61555i
$803$	113.881	+	113.881i	0.141820	+	0.141820i
$804$	−431.168			−0.536278
$805$	779.432	−	779.432i	0.968238	−	0.968238i
$806$	−867.992			−1.07691
$807$			681.541i			0.844536i
$808$	883.770			1.09377
$809$	−775.138			−0.958144			−0.479072	−	0.877776i	$-0.659027\pi$
$809$	−775.138			−0.958144			−0.479072	+	0.877776i	$0.659027\pi$
$810$	−498.278	−	498.278i	−0.615158	−	0.615158i
$811$	−823.239	−	823.239i	−1.01509	−	1.01509i	−0.999884	−	0.0152064i	$-0.995159\pi$
$811$	−823.239	−	823.239i	−1.01509	−	1.01509i	−0.0152064	−	0.999884i	$-0.504841\pi$
$812$	−122.908	−	122.908i	−0.151365	−	0.151365i
$813$		−	810.952i		−	0.997481i
$814$	−91.8968			−0.112895
$815$	−792.559	−	792.559i	−0.972465	−	0.972465i
$816$	−492.994			−0.604159
$817$	199.477	−	199.477i	0.244158	−	0.244158i
$818$	246.246	+	246.246i	0.301035	+	0.301035i
$819$		−	119.756i		−	0.146222i
$820$	−18.8771			−0.0230209
$821$			209.288i			0.254918i	0.991844	+	0.127459i	$0.0406821\pi$
$821$			209.288i			0.254918i	−0.991844	+	0.127459i	$0.959318\pi$
$822$			642.741i			0.781923i
$823$		−	797.862i		−	0.969456i	−0.874665	−	0.484728i	$-0.838919\pi$
$823$		−	797.862i		−	0.969456i	0.874665	−	0.484728i	$-0.161081\pi$
$824$	706.729			0.857681
$825$	−302.240	−	302.240i	−0.366351	−	0.366351i
$826$	330.536	+	330.536i	0.400165	+	0.400165i
$827$	−906.360	−	906.360i	−1.09596	−	1.09596i	−0.994878	−	0.101083i	$-0.967769\pi$
$827$	−906.360	−	906.360i	−1.09596	−	1.09596i	−0.101083	−	0.994878i	$-0.532231\pi$
$828$		−	73.0690i		−	0.0882475i
$829$	−618.358	+	618.358i	−0.745908	+	0.745908i	−0.973708	−	0.227800i	$-0.926847\pi$
$829$	−618.358	+	618.358i	−0.745908	+	0.745908i	0.227800	+	0.973708i	$0.426847\pi$
$830$	129.302	−	129.302i	0.155786	−	0.155786i
$831$	−978.496	−	978.496i	−1.17749	−	1.17749i
$832$	−822.043	+	822.043i	−0.988033	+	0.988033i
$833$	552.487			0.663250
$834$	84.2703	−	84.2703i	0.101044	−	0.101044i
$835$	−1036.60	−	1036.60i	−1.24144	−	1.24144i
$836$	284.231	+	284.231i	0.339989	+	0.339989i
$837$			903.589i			1.07956i
$838$	−742.619	−	742.619i	−0.886180	−	0.886180i
$839$	400.022	−	400.022i	0.476785	−	0.476785i	−0.427317	−	0.904102i	$-0.640541\pi$
$839$	400.022	−	400.022i	0.476785	−	0.476785i	0.904102	+	0.427317i	$0.140541\pi$
$840$			718.889i			0.855820i
$841$	−37.3196			−0.0443753
$842$	−60.4158			−0.0717527
$843$	682.592			0.809718
$844$	−130.780	−	130.780i	−0.154952	−	0.154952i
$845$	748.949			0.886331
$846$	−40.3752			−0.0477248
$847$	169.890	−	169.890i	0.200578	−	0.200578i
$848$	86.0764	+	86.0764i	0.101505	+	0.101505i
$849$	207.847			0.244814
$850$	433.378	+	433.378i	0.509856	+	0.509856i
$851$		−	245.591i		−	0.288591i
$852$	−225.050	+	225.050i	−0.264143	+	0.264143i
$853$		−	318.902i		−	0.373860i	−0.982373	−	0.186930i	$-0.940146\pi$
$853$		−	318.902i		−	0.373860i	0.982373	−	0.186930i	$-0.0598537\pi$
$854$	427.683	+	427.683i	0.500800	+	0.500800i
$855$		−	391.879i		−	0.458338i
$856$	−1183.74			−1.38288
$857$	599.942	−	599.942i	0.700049	−	0.700049i	−0.264372	−	0.964421i	$-0.585165\pi$
$857$	599.942	−	599.942i	0.700049	−	0.700049i	0.964421	+	0.264372i	$0.0851647\pi$
$858$	−441.253	−	441.253i	−0.514281	−	0.514281i
$859$	−100.239	−	100.239i	−0.116692	−	0.116692i	0.646349	−	0.763042i	$-0.276295\pi$
$859$	−100.239	−	100.239i	−0.116692	−	0.116692i	−0.763042	+	0.646349i	$0.776295\pi$
$860$	44.8929	−	44.8929i	0.0522010	−	0.0522010i
$861$	−19.5166	+	19.5166i	−0.0226673	+	0.0226673i
$862$		−	801.513i		−	0.929829i
$863$	304.638	−	304.638i	0.352999	−	0.352999i	−0.508225	−	0.861224i	$-0.669698\pi$
$863$	304.638	−	304.638i	0.352999	−	0.352999i	0.861224	+	0.508225i	$0.169698\pi$
$864$	400.313	+	400.313i	0.463325	+	0.463325i
$865$	446.023	−	446.023i	0.515634	−	0.515634i
$866$	855.980			0.988429
$867$		−	262.058i		−	0.302259i
$868$	130.092	−	130.092i	0.149876	−	0.149876i
$869$	−349.479			−0.402163
$870$	624.386	+	624.386i	0.717685	+	0.717685i
$871$	1461.32	+	1461.32i	1.67775	+	1.67775i
$872$	−279.232	+	279.232i	−0.320220	+	0.320220i
$873$	−61.3040	−	61.3040i	−0.0702222	−	0.0702222i
$874$	1605.69	−	1605.69i	1.83718	−	1.83718i
$875$	−129.424	+	129.424i	−0.147913	+	0.147913i
$876$		−	68.2336i		−	0.0778922i
$877$	−947.983	−	947.983i	−1.08094	−	1.08094i	−0.996422	−	0.0845158i	$-0.973066\pi$
$877$	−947.983	−	947.983i	−1.08094	−	1.08094i	−0.0845158	−	0.996422i	$-0.526934\pi$
$878$	−1135.92			−1.29375
$879$		−	93.7092i		−	0.106609i
$880$	−357.084	−	357.084i	−0.405777	−	0.405777i
$881$	330.380	−	330.380i	0.375006	−	0.375006i	−0.494291	−	0.869297i	$-0.664572\pi$
$881$	330.380	−	330.380i	0.375006	−	0.375006i	0.869297	+	0.494291i	$0.164572\pi$
$882$	51.2427	+	51.2427i	0.0580983	+	0.0580983i
$883$	−236.615			−0.267967			−0.133983	−	0.990984i	$-0.542777\pi$
$883$	−236.615			−0.267967			−0.133983	+	0.990984i	$0.542777\pi$
$884$	−299.312	−	299.312i	−0.338589	−	0.338589i
$885$	794.352	+	794.352i	0.897573	+	0.897573i
$886$	−405.161	+	405.161i	−0.457292	+	0.457292i
$887$	−712.057	+	712.057i	−0.802770	+	0.802770i	−0.983528	−	0.180758i	$-0.942145\pi$
$887$	−712.057	+	712.057i	−0.802770	+	0.802770i	0.180758	+	0.983528i	$0.442145\pi$
$888$	113.257	+	113.257i	0.127542	+	0.127542i
$889$			504.721i			0.567740i
$890$	−1697.81			−1.90766
$891$	−377.150	+	377.150i	−0.423288	+	0.423288i
$892$	367.605			0.412113
$893$	419.725	+	419.725i	0.470017	+	0.470017i
$894$	827.647			0.925780
$895$	−876.211	+	876.211i	−0.979007	+	0.979007i
$896$			161.951i			0.180748i
$897$	1179.24	−	1179.24i	1.31464	−	1.31464i
$898$	−11.9991	−	11.9991i	−0.0133620	−	0.0133620i
$899$		−	929.657i		−	1.03410i
$900$		−	38.0301i		−	0.0422557i
$901$	−183.371	+	183.371i	−0.203519	+	0.203519i
$902$		−	30.2034i		−	0.0334849i
$903$		−	92.8272i		−	0.102799i
$904$		−	815.281i		−	0.901859i
$905$	−667.588			−0.737666
$906$	283.767	+	283.767i	0.313209	+	0.313209i
$907$	665.605	−	665.605i	0.733853	−	0.733853i	−0.237528	−	0.971381i	$-0.576337\pi$
$907$	665.605	−	665.605i	0.733853	−	0.733853i	0.971381	+	0.237528i	$0.0763370\pi$
$908$	−549.819			−0.605527
$909$	−112.094	+	112.094i	−0.123315	+	0.123315i
$910$	592.256	−	592.256i	0.650831	−	0.650831i
$911$	−148.791	−	148.791i	−0.163327	−	0.163327i	0.620712	−	0.784039i	$-0.286844\pi$
$911$	−148.791	−	148.791i	−0.163327	−	0.163327i	−0.784039	+	0.620712i	$0.786844\pi$
$912$			950.674i			1.04241i
$913$	−97.8697	−	97.8697i	−0.107196	−	0.107196i
$914$	−69.0985	+	69.0985i	−0.0756001	+	0.0756001i
$915$	1027.82	+	1027.82i	1.12330	+	1.12330i
$916$	200.115	+	200.115i	0.218466	+	0.218466i
$917$	−1148.07			−1.25198
$918$	658.656	−	658.656i	0.717490	−	0.717490i
$919$	739.322	−	739.322i	0.804485	−	0.804485i	−0.179308	−	0.983793i	$-0.557386\pi$
$919$	739.322	−	739.322i	0.804485	−	0.804485i	0.983793	+	0.179308i	$0.0573858\pi$
$920$	1486.61	−	1486.61i	1.61588	−	1.61588i
$921$		−	292.403i		−	0.317484i
$922$	23.9910			0.0260206
$923$	1525.48			1.65274
$924$	132.267			0.143147
$925$		−	127.823i		−	0.138187i
$926$	−623.478			−0.673302
$927$	−89.6386	+	89.6386i	−0.0966975	+	0.0966975i
$928$	−411.862	−	411.862i	−0.443817	−	0.443817i
$929$		−	1168.76i		−	1.25809i	−0.777370	−	0.629043i	$-0.783447\pi$
$929$		−	1168.76i		−	1.25809i	0.777370	−	0.629043i	$-0.216553\pi$
$930$	−660.881	+	660.881i	−0.710625	+	0.710625i
$931$		−	1065.40i		−	1.14436i
$932$	−240.767			−0.258334
$933$	−435.687	+	435.687i	−0.466974	+	0.466974i
$934$	75.5030	−	75.5030i	0.0808383	−	0.0808383i
$935$	760.706	−	760.706i	0.813589	−	0.813589i
$936$		−	228.410i		−	0.244028i
$937$		−	1018.26i		−	1.08672i	−0.839498	−	0.543362i	$-0.817151\pi$
$937$		−	1018.26i		−	1.08672i	0.839498	−	0.543362i	$-0.182849\pi$
$938$	925.952			0.987155
$939$		−	580.604i		−	0.618321i
$940$	94.4603	+	94.4603i	0.100490	+	0.100490i
$941$			414.634i			0.440631i	0.975429	+	0.220316i	$0.0707088\pi$
$941$			414.634i			0.440631i	−0.975429	+	0.220316i	$0.929291\pi$
$942$	76.2885	−	76.2885i	0.0809857	−	0.0809857i
$943$	80.7177			0.0855967
$944$	404.691	+	404.691i	0.428698	+	0.428698i
$945$	−616.545	−	616.545i	−0.652429	−	0.652429i
$946$	71.8287	+	71.8287i	0.0759288	+	0.0759288i
$947$	1150.04			1.21440			0.607202	−	0.794548i	$-0.292292\pi$
$947$	1150.04			1.21440			0.607202	+	0.794548i	$0.292292\pi$
$948$	104.698	+	104.698i	0.110441	+	0.110441i
$949$	−231.258	+	231.258i	−0.243686	+	0.243686i
$950$	835.713	−	835.713i	0.879698	−	0.879698i
$951$	1081.25	−	1081.25i	1.13696	−	1.13696i
$952$	−780.224			−0.819563
$953$		−	149.422i		−	0.156791i	−0.996922	−	0.0783957i	$-0.975020\pi$
$953$		−	149.422i		−	0.156791i	0.996922	−	0.0783957i	$-0.0249798\pi$
$954$	−34.0150			−0.0356551
$955$	−280.659			−0.293883
$956$	491.013			0.513612
$957$	472.601	−	472.601i	0.493836	−	0.493836i
$958$	858.710	+	858.710i	0.896357	+	0.896357i
$959$			652.979i			0.680896i
$960$			1251.79i			1.30395i
$961$	22.9952			0.0239284
$962$		−	186.614i		−	0.193986i
$963$	150.141	−	150.141i	0.155910	−	0.155910i
$964$	26.3507			0.0273348
$965$	423.163	+	423.163i	0.438511	+	0.438511i
$966$		−	747.213i		−	0.773513i
$967$	−650.551			−0.672752			−0.336376	−	0.941728i	$-0.609201\pi$
$967$	−650.551			−0.672752			−0.336376	+	0.941728i	$0.609201\pi$
$968$	324.031	−	324.031i	0.334743	−	0.334743i
$969$	−2025.25			−2.09004
$970$		−	606.362i		−	0.625115i
$971$	−1504.04			−1.54896			−0.774481	−	0.632597i	$-0.781989\pi$
$971$	−1504.04			−1.54896			−0.774481	+	0.632597i	$0.781989\pi$
$972$	−107.050			−0.110134
$973$	85.6127	−	85.6127i	0.0879884	−	0.0879884i
$974$	723.723			0.743042
$975$	613.756	−	613.756i	0.629493	−	0.629493i
$976$	523.633	+	523.633i	0.536509	+	0.536509i
$977$	195.195			0.199790			0.0998950	−	0.994998i	$-0.468149\pi$
$977$	195.195			0.199790			0.0998950	+	0.994998i	$0.468149\pi$
$978$	−759.798			−0.776889
$979$			1285.09i			1.31265i
$980$		−	239.771i		−	0.244664i
$981$		−	70.8332i		−	0.0722051i
$982$	−813.762	−	813.762i	−0.828678	−	0.828678i
$983$	912.117			0.927891			0.463946	−	0.885864i	$-0.346433\pi$
$983$	912.117			0.927891			0.463946	+	0.885864i	$0.346433\pi$
$984$	−37.2239	+	37.2239i	−0.0378292	+	0.0378292i
$985$	−497.517	−	497.517i	−0.505093	−	0.505093i
$986$	−677.658	+	677.658i	−0.687280	+	0.687280i
$987$	195.320			0.197893
$988$	−577.185	+	577.185i	−0.584195	+	0.584195i
$989$	−191.960	+	191.960i	−0.194095	+	0.194095i
$990$	141.109			0.142535
$991$	1083.73			1.09357			0.546784	−	0.837274i	$-0.315852\pi$
$991$	1083.73			1.09357			0.546784	+	0.837274i	$0.315852\pi$
$992$	435.935	−	435.935i	0.439451	−	0.439451i
$993$	1103.94	−	1103.94i	1.11172	−	1.11172i
$994$	483.305	−	483.305i	0.486222	−	0.486222i
$995$	1736.31	+	1736.31i	1.74503	+	1.74503i
$996$			58.6400i			0.0588755i
$997$	−566.884	−	566.884i	−0.568590	−	0.568590i	0.363143	−	0.931733i	$-0.381704\pi$
$997$	−566.884	−	566.884i	−0.568590	−	0.568590i	−0.931733	+	0.363143i	$0.881704\pi$
$998$	−733.946			−0.735417
$999$	−194.267			−0.194462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.3.d.a.136.18	✓	116
349.213	odd	4	inner	349.3.d.a.213.18	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.3.d.a.136.18	✓	116	1.1	even	1	trivial
349.3.d.a.213.18	yes	116	349.213	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	349.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16521 + 1.16521i) q^{2} +2.72727i q^{3} +1.28457i q^{4} -6.62972i q^{5} +(-3.17784 - 3.17784i) q^{6} +(-3.22846 - 3.22846i) q^{7} +(-6.15764 - 6.15764i) q^{8} +1.56202 q^{9} +O(q^{10})\)	\(q+(-1.16521 + 1.16521i) q^{2} +2.72727i q^{3} +1.28457i q^{4} -6.62972i q^{5} +(-3.17784 - 3.17784i) q^{6} +(-3.22846 - 3.22846i) q^{7} +(-6.15764 - 6.15764i) q^{8} +1.56202 q^{9} +(7.72501 + 7.72501i) q^{10} +(5.84711 - 5.84711i) q^{11} -3.50338 q^{12} +(11.8737 + 11.8737i) q^{13} +7.52366 q^{14} +18.0810 q^{15} +9.21157 q^{16} +19.6237i q^{17} +(-1.82008 + 1.82008i) q^{18} +37.8417 q^{19} +8.51637 q^{20} +(8.80486 - 8.80486i) q^{21} +13.6262i q^{22} -36.4156 q^{23} +(16.7935 - 16.7935i) q^{24} -18.9532 q^{25} -27.6706 q^{26} +28.8054i q^{27} +(4.14719 - 4.14719i) q^{28} -29.6365i q^{29} +(-21.0682 + 21.0682i) q^{30} +31.3687 q^{31} +(13.8971 - 13.8971i) q^{32} +(15.9466 + 15.9466i) q^{33} +(-22.8657 - 22.8657i) q^{34} +(-21.4038 + 21.4038i) q^{35} +2.00653i q^{36} +6.74412i q^{37} +(-44.0935 + 44.0935i) q^{38} +(-32.3827 + 32.3827i) q^{39} +(-40.8234 + 40.8234i) q^{40} -2.21657 q^{41} +20.5190i q^{42} +(5.27136 - 5.27136i) q^{43} +(7.51105 + 7.51105i) q^{44} -10.3557i q^{45} +(42.4318 - 42.4318i) q^{46} +(11.0916 + 11.0916i) q^{47} +25.1224i q^{48} -28.1541i q^{49} +(22.0845 - 22.0845i) q^{50} -53.5190 q^{51} +(-15.2526 + 15.2526i) q^{52} +(9.34438 + 9.34438i) q^{53} +(-33.5644 - 33.5644i) q^{54} +(-38.7647 - 38.7647i) q^{55} +39.7593i q^{56} +103.204i q^{57} +(34.5327 + 34.5327i) q^{58} +(43.9329 + 43.9329i) q^{59} +23.2264i q^{60} +(56.8451 + 56.8451i) q^{61} +(-36.5511 + 36.5511i) q^{62} +(-5.04291 - 5.04291i) q^{63} +69.2324i q^{64} +(78.7192 - 78.7192i) q^{65} -37.1623 q^{66} +123.072 q^{67} -25.2081 q^{68} -99.3151i q^{69} -49.8798i q^{70} +(64.2380 - 64.2380i) q^{71} +(-9.61833 - 9.61833i) q^{72} +19.4765i q^{73} +(-7.85831 - 7.85831i) q^{74} -51.6904i q^{75} +48.6105i q^{76} -37.7543 q^{77} -75.4652i q^{78} +(-29.8848 - 29.8848i) q^{79} -61.0701i q^{80} -64.5019 q^{81} +(2.58276 - 2.58276i) q^{82} -16.7381i q^{83} +(11.3105 + 11.3105i) q^{84} +130.099 q^{85} +12.2845i q^{86} +80.8265 q^{87} -72.0087 q^{88} +(-109.891 + 109.891i) q^{89} +(12.0666 + 12.0666i) q^{90} -76.6673i q^{91} -46.7786i q^{92} +85.5508i q^{93} -25.8481 q^{94} -250.880i q^{95} +(37.9012 + 37.9012i) q^{96} +(-39.2467 - 39.2467i) q^{97} +(32.8054 + 32.8054i) q^{98} +(9.13329 - 9.13329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9}+O(q^{10}) \) 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9	\( 116 q + 32 q^{6} - 18 q^{7} - 30 q^{8} - 352 q^{9} - 16 q^{10} + 8 q^{11} + 32 q^{12} + 22 q^{13} + 56 q^{14} + 32 q^{15} - 436 q^{16} - 112 q^{18} - 52 q^{19} - 72 q^{20} + 50 q^{21} + 200 q^{23} + 144 q^{24} - 408 q^{25} + 72 q^{26} - 84 q^{28} - 6 q^{30} + 68 q^{31} - 130 q^{32} + 146 q^{33} + 62 q^{34} - 60 q^{35} + 2 q^{38} + 64 q^{39} - 218 q^{40} + 144 q^{41} - 180 q^{43} + 32 q^{44} + 122 q^{46} - 100 q^{47} + 56 q^{50} - 172 q^{51} + 296 q^{52} - 188 q^{53} - 540 q^{54} + 160 q^{55} - 140 q^{58} + 202 q^{59} + 62 q^{61} + 424 q^{62} + 362 q^{63} + 206 q^{65} - 268 q^{66} + 252 q^{67} - 404 q^{68} + 12 q^{71} + 664 q^{72} - 68 q^{74} - 884 q^{77} + 50 q^{79} + 1284 q^{81} - 666 q^{82} - 742 q^{84} + 1240 q^{85} + 220 q^{87} + 60 q^{88} + 48 q^{89} + 298 q^{90} + 940 q^{94} - 1588 q^{96} + 180 q^{97} + 704 q^{98} - 26 q^{99}+O(q^{100}) \) 116 * q + 32 * q^6 - 18 * q^7 - 30 * q^8 - 352 * q^9 - 16 * q^10 + 8 * q^11 + 32 * q^12 + 22 * q^13 + 56 * q^14 + 32 * q^15 - 436 * q^16 - 112 * q^18 - 52 * q^19 - 72 * q^20 + 50 * q^21 + 200 * q^23 + 144 * q^24 - 408 * q^25 + 72 * q^26 - 84 * q^28 - 6 * q^30 + 68 * q^31 - 130 * q^32 + 146 * q^33 + 62 * q^34 - 60 * q^35 + 2 * q^38 + 64 * q^39 - 218 * q^40 + 144 * q^41 - 180 * q^43 + 32 * q^44 + 122 * q^46 - 100 * q^47 + 56 * q^50 - 172 * q^51 + 296 * q^52 - 188 * q^53 - 540 * q^54 + 160 * q^55 - 140 * q^58 + 202 * q^59 + 62 * q^61 + 424 * q^62 + 362 * q^63 + 206 * q^65 - 268 * q^66 + 252 * q^67 - 404 * q^68 + 12 * q^71 + 664 * q^72 - 68 * q^74 - 884 * q^77 + 50 * q^79 + 1284 * q^81 - 666 * q^82 - 742 * q^84 + 1240 * q^85 + 220 * q^87 + 60 * q^88 + 48 * q^89 + 298 * q^90 + 940 * q^94 - 1588 * q^96 + 180 * q^97 + 704 * q^98 - 26 * q^99

Introduction

L-functions

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