LMFDB - Embedded newform 925.2.o.d.174.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("925.174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (of order $6$, degree $2$, not 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.13
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.193739 - 0.111855i) q^{2} +(1.82447 + 1.05336i) q^{3} +(-0.974977 + 1.68871i) q^{4} +0.471293 q^{6} +(-1.18597 - 0.684718i) q^{7} +0.883645i q^{8} +(0.719118 + 1.24555i) q^{9} +O(q^{10})$	\(q+(0.193739 - 0.111855i) q^{2} +(1.82447 + 1.05336i) q^{3} +(-0.974977 + 1.68871i) q^{4} +0.471293 q^{6} +(-1.18597 - 0.684718i) q^{7} +0.883645i q^{8} +(0.719118 + 1.24555i) q^{9} -6.06122 q^{11} +(-3.55762 + 2.05400i) q^{12} +(-2.36167 - 1.36351i) q^{13} -0.306357 q^{14} +(-1.85111 - 3.20622i) q^{16} +(-2.74767 + 1.58637i) q^{17} +(0.278642 + 0.160874i) q^{18} +(-3.83912 + 6.64955i) q^{19} +(-1.44250 - 2.49849i) q^{21} +(-1.17429 + 0.677978i) q^{22} +5.25584i q^{23} +(-0.930792 + 1.61218i) q^{24} -0.610063 q^{26} -3.29019i q^{27} +(2.31258 - 1.33517i) q^{28} +8.70325 q^{29} +2.28851 q^{31} +(-2.24778 - 1.29776i) q^{32} +(-11.0585 - 6.38462i) q^{33} +(-0.354887 + 0.614682i) q^{34} -2.80449 q^{36} +(5.41761 + 2.76577i) q^{37} +1.71770i q^{38} +(-2.87253 - 4.97536i) q^{39} +(2.78826 - 4.82940i) q^{41} +(-0.558937 - 0.322702i) q^{42} +10.6635i q^{43} +(5.90955 - 10.2356i) q^{44} +(0.587892 + 1.01826i) q^{46} +4.35223i q^{47} -7.79953i q^{48} +(-2.56232 - 4.43808i) q^{49} -6.68405 q^{51} +(4.60515 - 2.65879i) q^{52} +(-6.18394 + 3.57030i) q^{53} +(-0.368024 - 0.637437i) q^{54} +(0.605047 - 1.04797i) q^{56} +(-14.0087 + 8.08791i) q^{57} +(1.68616 - 0.973502i) q^{58} +(2.55710 + 4.42903i) q^{59} +(1.52416 - 2.63992i) q^{61} +(0.443374 - 0.255982i) q^{62} -1.96957i q^{63} +6.82381 q^{64} -2.85661 q^{66} +(-0.0815677 - 0.0470931i) q^{67} -6.18670i q^{68} +(-5.53627 + 9.58910i) q^{69} +(1.98787 - 3.44308i) q^{71} +(-1.10062 + 0.635444i) q^{72} +9.76975i q^{73} +(1.35897 - 0.0701508i) q^{74} +(-7.48610 - 12.9663i) q^{76} +(7.18839 + 4.15022i) q^{77} +(-1.11304 - 0.642613i) q^{78} +(1.40843 - 2.43947i) q^{79} +(5.62309 - 9.73948i) q^{81} -1.24752i q^{82} +(-9.71449 + 5.60866i) q^{83} +5.62563 q^{84} +(1.19277 + 2.06594i) q^{86} +(15.8788 + 9.16762i) q^{87} -5.35596i q^{88} +(-4.04287 - 7.00246i) q^{89} +(1.86724 + 3.23416i) q^{91} +(-8.87559 - 5.12432i) q^{92} +(4.17532 + 2.41062i) q^{93} +(0.486820 + 0.843196i) q^{94} +(-2.73400 - 4.73543i) q^{96} -9.94455i q^{97} +(-0.992842 - 0.573218i) q^{98} +(-4.35873 - 7.54954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) $ 48 * q + 22 * q^4 + 20 * q^9	$ 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.193739	−	0.111855i	0.136994	−	0.0790935i	−0.429937	−	0.902859i	$-0.641464\pi$
$2$	0.193739	−	0.111855i	0.136994	−	0.0790935i	0.566931	+	0.823766i	$0.308131\pi$
$3$	1.82447	+	1.05336i	1.05336	+	0.608155i	0.923587	−	0.383389i	$-0.125243\pi$
$3$	1.82447	+	1.05336i	1.05336	+	0.608155i	0.129769	+	0.991544i	$0.458576\pi$
$4$	−0.974977	+	1.68871i	−0.487488	+	0.844355i
$5$		0			0
$5$		0			0
$6$	0.471293			0.192404
$7$	−1.18597	−	0.684718i	−0.448253	−	0.258799i	0.258839	−	0.965920i	$-0.416660\pi$
$7$	−1.18597	−	0.684718i	−0.448253	−	0.258799i	−0.707092	+	0.707122i	$0.749993\pi$
$8$			0.883645i			0.312416i
$9$	0.719118	+	1.24555i	0.239706	+	0.415183i
$10$		0			0
$11$	−6.06122			−1.82753			−0.913763	−	0.406248i	$-0.866837\pi$
$11$	−6.06122			−1.82753			−0.913763	+	0.406248i	$0.866837\pi$
$12$	−3.55762	+	2.05400i	−1.02700	+	0.592937i
$13$	−2.36167	−	1.36351i	−0.655010	−	0.378170i	0.135363	−	0.990796i	$-0.456780\pi$
$13$	−2.36167	−	1.36351i	−0.655010	−	0.378170i	−0.790373	+	0.612626i	$0.790113\pi$
$14$	−0.306357			−0.0818772
$15$		0			0
$16$	−1.85111	−	3.20622i	−0.462778	−	0.801556i
$17$	−2.74767	+	1.58637i	−0.666409	+	0.384751i	−0.794714	−	0.606983i	$-0.792379\pi$
$17$	−2.74767	+	1.58637i	−0.666409	+	0.384751i	0.128306	+	0.991735i	$0.459046\pi$
$18$	0.278642	+	0.160874i	0.0656765	+	0.0379183i
$19$	−3.83912	+	6.64955i	−0.880754	+	1.52551i	−0.0302494	+	0.999542i	$0.509630\pi$
$19$	−3.83912	+	6.64955i	−0.880754	+	1.52551i	−0.850504	+	0.525968i	$0.823703\pi$
$20$		0			0
$21$	−1.44250	−	2.49849i	−0.314780	−	0.545215i
$22$	−1.17429	+	0.677978i	−0.250360	+	0.144545i
$23$			5.25584i			1.09592i	0.836505	+	0.547959i	$0.184595\pi$
$23$			5.25584i			1.09592i	−0.836505	+	0.547959i	$0.815405\pi$
$24$	−0.930792	+	1.61218i	−0.189997	+	0.329085i
$25$		0			0
$26$	−0.610063			−0.119643
$27$		−	3.29019i		−	0.633197i
$28$	2.31258	−	1.33517i	0.437036	−	0.252323i
$29$	8.70325			1.61615			0.808076	−	0.589078i	$-0.200509\pi$
$29$	8.70325			1.61615			0.808076	+	0.589078i	$0.200509\pi$
$30$		0			0
$31$	2.28851			0.411029			0.205515	−	0.978654i	$-0.434113\pi$
$31$	2.28851			0.411029			0.205515	+	0.978654i	$0.434113\pi$
$32$	−2.24778	−	1.29776i	−0.397356	−	0.229413i
$33$	−11.0585	−	6.38462i	−1.92503	−	1.11142i
$34$	−0.354887	+	0.614682i	−0.0608626	+	0.105417i
$35$		0			0
$36$	−2.80449			−0.467415
$37$	5.41761	+	2.76577i	0.890650	+	0.454690i
$37$	5.41761	+	2.76577i	0.890650	+	0.454690i
$38$			1.71770i			0.278648i
$39$	−2.87253	−	4.97536i	−0.459972	−	0.796696i
$40$		0			0
$41$	2.78826	−	4.82940i	0.435452	−	0.754226i	−0.561880	−	0.827219i	$-0.689922\pi$
$41$	2.78826	−	4.82940i	0.435452	−	0.754226i	0.997332	+	0.0729930i	$0.0232551\pi$
$42$	−0.558937	−	0.322702i	−0.0862459	−	0.0497941i
$43$			10.6635i			1.62617i	0.582144	+	0.813086i	$0.302214\pi$
$43$			10.6635i			1.62617i	−0.582144	+	0.813086i	$0.697786\pi$
$44$	5.90955	−	10.2356i	0.890897	−	1.54308i
$45$		0			0
$46$	0.587892	+	1.01826i	0.0866800	+	0.150134i
$47$			4.35223i			0.634839i	0.948285	+	0.317419i	$0.102816\pi$
$47$			4.35223i			0.634839i	−0.948285	+	0.317419i	$0.897184\pi$
$48$		−	7.79953i		−	1.12576i
$49$	−2.56232	−	4.43808i	−0.366046	−	0.634011i
$50$		0			0
$51$	−6.68405			−0.935954
$52$	4.60515	−	2.65879i	0.638620	−	0.368707i
$53$	−6.18394	+	3.57030i	−0.849429	+	0.490418i	−0.860458	−	0.509521i	$-0.829823\pi$
$53$	−6.18394	+	3.57030i	−0.849429	+	0.490418i	0.0110292	+	0.999939i	$0.496489\pi$
$54$	−0.368024	−	0.637437i	−0.0500818	−	0.0867442i
$55$		0			0
$56$	0.605047	−	1.04797i	0.0808528	−	0.140041i
$57$	−14.0087	+	8.08791i	−1.85549	+	1.07127i
$58$	1.68616	−	0.973502i	0.221403	−	0.127827i
$59$	2.55710	+	4.42903i	0.332907	+	0.576611i	0.983080	−	0.183174i	$-0.0586373\pi$
$59$	2.55710	+	4.42903i	0.332907	+	0.576611i	−0.650174	+	0.759786i	$0.725304\pi$
$60$		0			0
$61$	1.52416	−	2.63992i	0.195149	−	0.338008i	−0.751801	−	0.659391i	$-0.770814\pi$
$61$	1.52416	−	2.63992i	0.195149	−	0.338008i	0.946949	+	0.321383i	$0.104148\pi$
$62$	0.443374	−	0.255982i	0.0563085	−	0.0325097i
$63$		−	1.96957i		−	0.248142i
$64$	6.82381			0.852976
$65$		0			0
$66$	−2.85661			−0.351624
$67$	−0.0815677	−	0.0470931i	−0.00996508	−	0.00575334i	0.495009	−	0.868888i	$-0.335165\pi$
$67$	−0.0815677	−	0.0470931i	−0.00996508	−	0.00575334i	−0.504974	+	0.863134i	$0.668498\pi$
$68$		−	6.18670i		−	0.750247i
$69$	−5.53627	+	9.58910i	−0.666489	+	1.15439i
$70$		0			0
$71$	1.98787	−	3.44308i	0.235916	−	0.408619i	−0.723622	−	0.690196i	$-0.757524\pi$
$71$	1.98787	−	3.44308i	0.235916	−	0.408619i	0.959539	+	0.281577i	$0.0908576\pi$
$72$	−1.10062	+	0.635444i	−0.129710	+	0.0748879i
$73$			9.76975i			1.14346i	0.820441	+	0.571732i	$0.193728\pi$
$73$			9.76975i			1.14346i	−0.820441	+	0.571732i	$0.806272\pi$
$74$	1.35897	−	0.0701508i	0.157977	−	0.00815486i
$75$		0			0
$76$	−7.48610	−	12.9663i	−0.858715	−	1.48734i
$77$	7.18839	+	4.15022i	0.819193	+	0.472962i
$78$	−1.11304	−	0.642613i	−0.126027	−	0.0727616i
$79$	1.40843	−	2.43947i	0.158461	−	0.274462i	−0.775853	−	0.630914i	$-0.782680\pi$
$79$	1.40843	−	2.43947i	0.158461	−	0.274462i	0.934314	+	0.356452i	$0.116014\pi$
$80$		0			0
$81$	5.62309	−	9.73948i	0.624788	−	1.08216i
$82$		−	1.24752i		−	0.137766i
$83$	−9.71449	+	5.60866i	−1.06630	+	0.615631i	−0.927169	−	0.374643i	$-0.877765\pi$
$83$	−9.71449	+	5.60866i	−1.06630	+	0.615631i	−0.139134	+	0.990274i	$0.544432\pi$
$84$	5.62563			0.613806
$85$		0			0
$86$	1.19277	+	2.06594i	0.128620	+	0.222776i
$87$	15.8788	+	9.16762i	1.70238	+	0.982872i
$88$		−	5.35596i		−	0.570947i
$89$	−4.04287	−	7.00246i	−0.428543	−	0.742259i	0.568201	−	0.822890i	$-0.307640\pi$
$89$	−4.04287	−	7.00246i	−0.428543	−	0.742259i	−0.996744	+	0.0806312i	$0.974306\pi$
$90$		0			0
$91$	1.86724	+	3.23416i	0.195740	+	0.339032i
$92$	−8.87559	−	5.12432i	−0.925344	−	0.534248i
$93$	4.17532	+	2.41062i	0.432960	+	0.249970i
$94$	0.486820	+	0.843196i	0.0502116	+	0.0869690i
$95$		0			0
$96$	−2.73400	−	4.73543i	−0.279038	−	0.483308i
$97$		−	9.94455i		−	1.00972i	−0.863202	−	0.504858i	$-0.831545\pi$
$97$		−	9.94455i		−	1.00972i	0.863202	−	0.504858i	$-0.168455\pi$
$98$	−0.992842	−	0.573218i	−0.100292	−	0.0579037i
$99$	−4.35873	−	7.54954i	−0.438069	−	0.758757i
$100$		0			0
$101$	−4.75480			−0.473121			−0.236560	−	0.971617i	$-0.576020\pi$
$101$	−4.75480			−0.473121			−0.236560	+	0.971617i	$0.576020\pi$
$102$	−1.29496	+	0.747645i	−0.128220	+	0.0740279i
$103$		−	0.981145i		−	0.0966751i	−0.998831	−	0.0483376i	$-0.984608\pi$
$103$		−	0.981145i		−	0.0966751i	0.998831	−	0.0483376i	$-0.0153923\pi$
$104$	1.20486	−	2.08688i	0.118146	−	0.204635i
$105$		0			0
$106$	−0.798712	+	1.38341i	−0.0775777	+	0.134369i
$107$	−2.19051	−	1.26469i	−0.211764	−	0.122262i	0.390367	−	0.920659i	$-0.372348\pi$
$107$	−2.19051	−	1.26469i	−0.211764	−	0.122262i	−0.602131	+	0.798397i	$0.705682\pi$
$108$	5.55617	+	3.20786i	0.534643	+	0.308676i
$109$	5.46888	+	9.47239i	0.523824	+	0.907290i	0.999615	+	0.0277318i	$0.00882845\pi$
$109$	5.46888	+	9.47239i	0.523824	+	0.907290i	−0.475791	+	0.879558i	$0.657838\pi$
$110$		0			0
$111$	6.97091	+	10.7527i	0.661649	+	1.02060i
$112$			5.06996i			0.479066i
$113$	−2.90152	+	1.67519i	−0.272952	+	0.157589i	−0.630228	−	0.776410i	$-0.717039\pi$
$113$	−2.90152	+	1.67519i	−0.272952	+	0.157589i	0.357276	+	0.933999i	$0.383705\pi$
$114$	−1.80935	+	3.13388i	−0.169461	+	0.293515i
$115$		0			0
$116$	−8.48546	+	14.6973i	−0.787855	+	1.36461i
$117$		−	3.92210i		−	0.362598i
$118$	0.990820	+	0.572050i	0.0912124	+	0.0526615i
$119$	4.34486			0.398293
$120$		0			0
$121$	25.7383			2.33985
$122$		−	0.681940i		−	0.0617400i
$123$	10.1742	−	5.87405i	0.917373	−	0.529645i
$124$	−2.23125	+	3.86464i	−0.200372	+	0.347055i
$125$		0			0
$126$	−0.220306	−	0.381582i	−0.0196265	−	0.0339940i
$127$	7.68261	−	4.43556i	0.681721	−	0.393592i	−0.118782	−	0.992920i	$-0.537899\pi$
$127$	7.68261	−	4.43556i	0.681721	−	0.393592i	0.800503	+	0.599328i	$0.204566\pi$
$128$	5.81760	−	3.35879i	0.514208	−	0.296878i
$129$	−11.2325	+	19.4552i	−0.988965	+	1.71294i
$130$		0			0
$131$	3.80480	+	6.59011i	0.332427	+	0.575781i	0.982987	−	0.183674i	$-0.0587991\pi$
$131$	3.80480	+	6.59011i	0.332427	+	0.575781i	−0.650560	+	0.759455i	$0.725466\pi$
$132$	21.5635	−	12.4497i	1.87686	−	1.08361i
$133$	9.10612	−	5.25742i	0.789601	−	0.455876i
$134$	−0.0210704			−0.00182021
$135$		0			0
$136$	−1.40179	−	2.42797i	−0.120202	−	0.208196i
$137$			16.8213i			1.43714i	0.695454	+	0.718571i	$0.255203\pi$
$137$			16.8213i			1.43714i	−0.695454	+	0.718571i	$0.744797\pi$
$138$			2.47704i			0.210860i
$139$	−3.09201	−	5.35552i	−0.262261	−	0.454249i	0.704581	−	0.709623i	$-0.251135\pi$
$139$	−3.09201	−	5.35552i	−0.262261	−	0.454249i	−0.966842	+	0.255374i	$0.917801\pi$
$140$		0			0
$141$	−4.58445	+	7.94050i	−0.386081	+	0.668711i
$142$		−	0.889411i		−	0.0746377i
$143$	14.3146	+	8.26454i	1.19705	+	0.691116i
$144$	2.66234	−	4.61130i	0.221861	−	0.384275i
$145$		0			0
$146$	1.09280	+	1.89278i	0.0904405	+	0.156647i
$147$		−	10.7962i		−	0.890452i
$148$	−9.95263	+	6.45221i	−0.818101	+	0.530368i
$149$	−18.1225			−1.48465			−0.742327	−	0.670037i	$-0.766278\pi$
$149$	−18.1225			−1.48465			−0.742327	+	0.670037i	$0.766278\pi$
$150$		0			0
$151$	−7.83821	+	13.5762i	−0.637865	+	1.10481i	0.348036	+	0.937481i	$0.386849\pi$
$151$	−7.83821	+	13.5762i	−0.637865	+	1.10481i	−0.985900	+	0.167333i	$0.946485\pi$
$152$	−5.87584	−	3.39242i	−0.476593	−	0.275161i
$153$	−3.95180	−	2.28157i	−0.319484	−	0.184454i
$154$	1.85689			0.149633
$155$		0			0
$156$	11.2026			0.896925
$157$	−14.9803	+	8.64886i	−1.19556	+	0.690254i	−0.959561	−	0.281500i	$-0.909168\pi$
$157$	−14.9803	+	8.64886i	−1.19556	+	0.690254i	−0.235994	+	0.971754i	$0.575835\pi$
$158$		−	0.630160i		−	0.0501329i
$159$	−15.0432			−1.19300
$160$		0			0
$161$	3.59877	−	6.23325i	0.283622	−	0.491249i
$162$		−	2.51589i		−	0.197667i
$163$	4.11283	−	2.37454i	0.322142	−	0.185989i	−0.330205	−	0.943909i	$-0.607118\pi$
$163$	4.11283	−	2.37454i	0.322142	−	0.185989i	0.652347	+	0.757921i	$0.273785\pi$
$164$	5.43697	+	9.41711i	0.424556	+	0.735353i
$165$		0			0
$166$	−1.25471	+	2.17323i	−0.0973847	+	0.168675i
$167$	−19.7560	−	11.4061i	−1.52877	−	0.882634i	−0.999414	−	0.0342329i	$-0.989101\pi$
$167$	−19.7560	−	11.4061i	−1.52877	−	0.882634i	−0.529354	−	0.848401i	$-0.677565\pi$
$168$	2.20778	−	1.27466i	0.170334	−	0.0983421i
$169$	−2.78167	−	4.81800i	−0.213975	−	0.370615i
$170$		0			0
$171$	−11.0431			−0.844487
$172$	−18.0076	−	10.3967i	−1.37307	−	0.792740i
$173$	12.0270	−	6.94380i	0.914397	−	0.527927i	0.0325537	−	0.999470i	$-0.489636\pi$
$173$	12.0270	−	6.94380i	0.914397	−	0.527927i	0.881843	+	0.471543i	$0.156303\pi$
$174$	4.10178			0.310955
$175$		0			0
$176$	11.2200	+	19.4336i	0.845739	+	1.46486i
$177$			10.7742i			0.809836i
$178$	−1.56652	−	0.904431i	−0.117416	−	0.0677900i
$179$	10.5636			0.789557			0.394779	−	0.918776i	$-0.370821\pi$
$179$	10.5636			0.789557			0.394779	+	0.918776i	$0.370821\pi$
$180$		0			0
$181$	−2.04799	+	3.54722i	−0.152226	+	0.263663i	−0.932045	−	0.362341i	$-0.881977\pi$
$181$	−2.04799	+	3.54722i	−0.152226	+	0.263663i	0.779820	+	0.626004i	$0.215311\pi$
$182$	0.723514	+	0.417721i	0.0536304	+	0.0309635i
$183$	5.56156	−	3.21097i	0.411122	−	0.237362i
$184$	−4.64430			−0.342382
$185$		0			0
$186$	1.07856			0.0790839
$187$	16.6542	−	9.61533i	1.21788	−	0.703143i
$188$	−7.34966	−	4.24333i	−0.536029	−	0.309477i
$189$	−2.25285	+	3.90205i	−0.163871	+	0.283832i
$190$		0			0
$191$	−21.2024			−1.53415			−0.767075	−	0.641558i	$-0.778288\pi$
$191$	−21.2024			−1.53415			−0.767075	+	0.641558i	$0.778288\pi$
$192$	12.4498	+	7.18790i	0.898488	+	0.518742i
$193$		−	11.7664i		−	0.846964i	−0.905905	−	0.423482i	$-0.860808\pi$
$193$		−	11.7664i		−	0.846964i	0.905905	−	0.423482i	$-0.139192\pi$
$194$	−1.11235	−	1.92664i	−0.0798619	−	0.138325i
$195$		0			0
$196$	9.99283			0.713773
$197$	1.42618	−	0.823404i	0.101611	−	0.0586651i	−0.448333	−	0.893866i	$-0.647982\pi$
$197$	1.42618	−	0.823404i	0.101611	−	0.0586651i	0.549944	+	0.835201i	$0.314649\pi$
$198$	−1.68891	−	0.975091i	−0.120025	−	0.0692967i
$199$	0.133836			0.00948740			0.00474370	−	0.999989i	$-0.498490\pi$
$199$	0.133836			0.00948740			0.00474370	+	0.999989i	$0.498490\pi$
$200$		0			0
$201$	−0.0992117	−	0.171840i	−0.00699785	−	0.0121206i
$202$	−0.921189	+	0.531849i	−0.0648146	+	0.0374208i
$203$	−10.3217	−	5.95926i	−0.724445	−	0.418258i
$204$	6.51679	−	11.2874i	0.456267	−	0.790277i
$205$		0			0
$206$	−0.109746	−	0.190086i	−0.00764637	−	0.0132439i
$207$	−6.54640	+	3.77957i	−0.455006	+	0.262698i
$208$			10.0961i			0.700036i
$209$	23.2697	−	40.3043i	1.60960	−	2.78791i
$210$		0			0
$211$	15.2034			1.04664			0.523321	−	0.852135i	$-0.324693\pi$
$211$	15.2034			1.04664			0.523321	+	0.852135i	$0.324693\pi$
$212$		−	13.9238i		−	0.956293i
$213$	7.25358	−	4.18786i	0.497007	−	0.286947i
$214$	−0.565847			−0.0386805
$215$		0			0
$216$	2.90736			0.197821
$217$	−2.71410	−	1.56699i	−0.184245	−	0.106374i
$218$	2.11907	+	1.22345i	0.143521	+	0.0828622i
$219$	−10.2910	+	17.8246i	−0.695403	+	1.20447i
$220$		0			0
$221$	8.65214			0.582006
$222$	2.55328	+	1.30349i	0.171365	+	0.0874844i
$223$			25.6769i			1.71945i	0.510757	+	0.859725i	$0.329365\pi$
$223$			25.6769i			1.71945i	−0.510757	+	0.859725i	$0.670635\pi$
$224$	1.77719	+	3.07819i	0.118744	+	0.205670i
$225$		0			0
$226$	−0.374758	+	0.649099i	−0.0249285	+	0.0431775i
$227$	−0.334932	−	0.193373i	−0.0222302	−	0.0128346i	0.488844	−	0.872371i	$-0.337419\pi$
$227$	−0.334932	−	0.193373i	−0.0222302	−	0.0128346i	−0.511074	+	0.859537i	$0.670752\pi$
$228$		−	31.5421i		−	2.08893i
$229$	8.52971	−	14.7739i	0.563659	−	0.976286i	−0.433514	−	0.901147i	$-0.642727\pi$
$229$	8.52971	−	14.7739i	0.563659	−	0.976286i	0.997173	−	0.0751393i	$-0.0239401\pi$
$230$		0			0
$231$	8.74332	+	15.1439i	0.575268	+	0.996394i
$232$			7.69058i			0.504911i
$233$			22.4209i			1.46884i	0.678693	+	0.734422i	$0.262547\pi$
$233$			22.4209i			1.46884i	−0.678693	+	0.734422i	$0.737453\pi$
$234$	−0.438707	−	0.759863i	−0.0286792	−	0.0496738i
$235$		0			0
$236$	−9.97247			−0.649153
$237$	5.13927	−	2.96716i	0.333831	−	0.192738i
$238$	0.841768	−	0.485995i	0.0545637	−	0.0315024i
$239$	−4.59485	−	7.95852i	−0.297216	−	0.514794i	0.678282	−	0.734802i	$-0.262725\pi$
$239$	−4.59485	−	7.95852i	−0.297216	−	0.514794i	−0.975498	+	0.220008i	$0.929392\pi$
$240$		0			0
$241$	−0.513306	+	0.889072i	−0.0330649	+	0.0572702i	−0.882084	−	0.471092i	$-0.843860\pi$
$241$	−0.513306	+	0.889072i	−0.0330649	+	0.0572702i	0.849019	+	0.528362i	$0.177193\pi$
$242$	4.98651	−	2.87896i	0.320545	−	0.185067i
$243$	11.9701	−	6.91095i	0.767884	−	0.443338i
$244$	2.97204	+	5.14773i	0.190266	+	0.329550i
$245$		0			0
$246$	1.31409	−	2.27606i	0.0837830	−	0.145116i
$247$	18.1335	−	10.4694i	1.15380	−	0.666150i
$248$			2.02223i			0.128412i
$249$	−23.6317			−1.49760
$250$		0			0
$251$	6.10655			0.385442			0.192721	−	0.981254i	$-0.438269\pi$
$251$	6.10655			0.385442			0.192721	+	0.981254i	$0.438269\pi$
$252$	3.32603	+	1.92028i	0.209520	+	0.120967i
$253$		−	31.8568i		−	2.00282i
$254$	0.992279	−	1.71868i	0.0622611	−	0.107839i
$255$		0			0
$256$	−6.07242	+	10.5177i	−0.379526	+	0.657358i
$257$	11.5232	−	6.65294i	0.718799	−	0.414999i	−0.0955113	−	0.995428i	$-0.530449\pi$
$257$	11.5232	−	6.65294i	0.718799	−	0.414999i	0.814311	+	0.580429i	$0.197115\pi$
$258$			5.02564i			0.312883i
$259$	−4.53133	−	6.98964i	−0.281563	−	0.434315i
$260$		0			0
$261$	6.25866	+	10.8403i	0.387401	+	0.670998i
$262$	1.47428	+	0.851173i	0.0910810	+	0.0525857i
$263$	−9.80423	−	5.66048i	−0.604555	−	0.349040i	0.166276	−	0.986079i	$-0.446826\pi$
$263$	−9.80423	−	5.66048i	−0.604555	−	0.349040i	−0.770831	+	0.637039i	$0.780159\pi$
$264$	5.64173	−	9.77177i	0.347225	−	0.601411i
$265$		0			0
$266$	1.17614	−	2.03713i	0.0721137	−	0.124905i
$267$		−	17.0343i		−	1.04248i
$268$	0.159053	−	0.0918295i	0.00971573	−	0.00560938i
$269$	−6.30917			−0.384677			−0.192338	−	0.981329i	$-0.561607\pi$
$269$	−6.30917			−0.384677			−0.192338	+	0.981329i	$0.561607\pi$
$270$		0			0
$271$	5.32922	+	9.23048i	0.323727	+	0.560712i	0.981254	−	0.192719i	$-0.0617307\pi$
$271$	5.32922	+	9.23048i	0.323727	+	0.560712i	−0.657527	+	0.753431i	$0.728397\pi$
$272$	10.1725	+	5.87310i	0.616799	+	0.356109i
$273$			7.86748i			0.476161i
$274$	1.88155	+	3.25894i	0.113669	+	0.196880i
$275$		0			0
$276$	−10.7955	−	18.6983i	−0.649811	−	1.12551i
$277$	23.4573	+	13.5431i	1.40941	+	0.813724i	0.995331	−	0.0965160i	$-0.0307699\pi$
$277$	23.4573	+	13.5431i	1.40941	+	0.813724i	0.414080	+	0.910240i	$0.364103\pi$
$278$	−1.19808	−	0.691714i	−0.0718563	−	0.0414863i
$279$	1.64571	+	2.85046i	0.0985262	+	0.170652i
$280$		0			0
$281$	7.20850	+	12.4855i	0.430023	+	0.744822i	0.996875	−	0.0789977i	$-0.0251720\pi$
$281$	7.20850	+	12.4855i	0.430023	+	0.744822i	−0.566851	+	0.823820i	$0.691839\pi$
$282$			2.05118i			0.122146i
$283$	12.8129	+	7.39753i	0.761648	+	0.439737i	0.829887	−	0.557931i	$-0.188405\pi$
$283$	12.8129	+	7.39753i	0.761648	+	0.439737i	−0.0682393	+	0.997669i	$0.521738\pi$
$284$	3.87625	+	6.71385i	0.230013	+	0.398394i
$285$		0			0
$286$	3.69772			0.218651
$287$	−6.61355	+	3.81834i	−0.390386	+	0.225389i
$288$		−	3.73296i		−	0.219967i
$289$	−3.46686	+	6.00478i	−0.203933	+	0.353222i
$290$		0			0
$291$	10.4751	−	18.1435i	0.614064	−	1.06359i
$292$	−16.4983	−	9.52528i	−0.965488	−	0.557425i
$293$	−17.8983	−	10.3336i	−1.04563	−	0.603694i	−0.124206	−	0.992256i	$-0.539638\pi$
$293$	−17.8983	−	10.3336i	−1.04563	−	0.603694i	−0.921422	+	0.388563i	$0.872972\pi$
$294$	−1.20760	−	2.09163i	−0.0704289	−	0.121987i
$295$		0			0
$296$	−2.44396	+	4.78724i	−0.142052	+	0.278253i
$297$			19.9425i			1.15718i
$298$	−3.51103	+	2.02710i	−0.203389	+	0.117427i
$299$	7.16640	−	12.4126i	0.414444	−	0.717837i
$300$		0			0
$301$	7.30150	−	12.6466i	0.420851	−	0.728936i
$302$			3.50698i			0.201804i
$303$	−8.67498	−	5.00850i	−0.498364	−	0.287731i
$304$	28.4266			1.63038
$305$		0			0
$306$	−1.02082			−0.0583565
$307$			27.2825i			1.55709i	0.627586	+	0.778547i	$0.284043\pi$
$307$			27.2825i			1.55709i	−0.627586	+	0.778547i	$0.715957\pi$
$308$	−14.0170	+	8.09274i	−0.798695	+	0.461127i
$309$	1.03350	−	1.79007i	0.0587935	−	0.101833i
$310$		0			0
$311$	−9.14961	−	15.8476i	−0.518827	−	0.898634i	−0.999761	−	0.0218775i	$-0.993036\pi$
$311$	−9.14961	−	15.8476i	−0.518827	−	0.898634i	0.480934	−	0.876757i	$-0.340298\pi$
$312$	4.39645	−	2.53829i	0.248900	−	0.143703i
$313$	16.4105	−	9.47461i	0.927577	−	0.535537i	0.0415323	−	0.999137i	$-0.486776\pi$
$313$	16.4105	−	9.47461i	0.927577	−	0.535537i	0.886044	+	0.463601i	$0.153443\pi$
$314$	−1.93484	+	3.35124i	−0.109189	+	0.189121i
$315$		0			0
$316$	2.74637	+	4.75686i	0.154496	+	0.267594i
$317$	−1.88556	+	1.08863i	−0.105904	+	0.0611435i	−0.552016	−	0.833833i	$-0.686141\pi$
$317$	−1.88556	+	1.08863i	−0.105904	+	0.0611435i	0.446113	+	0.894977i	$0.352808\pi$
$318$	−2.91444	+	1.68266i	−0.163434	+	0.0943586i
$319$	−52.7522			−2.95356
$320$		0			0
$321$	−2.66434	−	4.61476i	−0.148709	−	0.257571i
$322$		−	1.61016i		−	0.0897308i
$323$		−	24.3610i		−	1.35548i
$324$	10.9648	+	18.9915i	0.609154	+	1.05509i
$325$		0			0
$326$	0.531210	−	0.920082i	0.0294210	−	0.0509586i
$327$			23.0427i			1.27427i
$328$	4.26747	+	2.46383i	0.235632	+	0.136042i
$329$	2.98005	−	5.16160i	0.164296	−	0.284568i
$330$		0			0
$331$	−14.1648	−	24.5341i	−0.778566	−	1.34852i	−0.932768	−	0.360477i	$-0.882614\pi$
$331$	−14.1648	−	24.5341i	−0.778566	−	1.34852i	0.154202	−	0.988039i	$-0.450719\pi$
$332$		−	21.8733i		−	1.20045i
$333$	0.451000	+	8.73681i	0.0247147	+	0.478774i
$334$	−5.10334			−0.279242
$335$		0			0
$336$	−5.34047	+	9.24997i	−0.291347	+	0.504627i
$337$	−1.51233	−	0.873146i	−0.0823820	−	0.0475633i	0.458243	−	0.888827i	$-0.348479\pi$
$337$	−1.51233	−	0.873146i	−0.0823820	−	0.0475633i	−0.540625	+	0.841264i	$0.681812\pi$
$338$	−1.07783	−	0.622288i	−0.0586265	−	0.0338480i
$339$	−7.05830			−0.383354
$340$		0			0
$341$	−13.8712			−0.751167
$342$	−2.13948	+	1.23523i	−0.115690	+	0.0667935i
$343$			16.6039i			0.896527i
$344$	−9.42276			−0.508041
$345$		0			0
$346$	1.55340	−	2.69057i	0.0835112	−	0.144646i
$347$		−	13.5735i		−	0.728665i	−0.931269	−	0.364333i	$-0.881297\pi$
$347$		−	13.5735i		−	0.728665i	0.931269	−	0.364333i	$-0.118703\pi$
$348$	−30.9629	+	17.8764i	−1.65978	+	0.958277i
$349$	16.5706	+	28.7012i	0.887005	+	1.53634i	0.843398	+	0.537289i	$0.180551\pi$
$349$	16.5706	+	28.7012i	0.887005	+	1.53634i	0.0436065	+	0.999049i	$0.486115\pi$
$350$		0			0
$351$	−4.48621	+	7.77035i	−0.239456	+	0.414750i
$352$	13.6243	+	7.86599i	0.726177	+	0.419259i
$353$	−13.2818	+	7.66823i	−0.706917	+	0.408138i	−0.809918	−	0.586543i	$-0.800489\pi$
$353$	−13.2818	+	7.66823i	−0.706917	+	0.408138i	0.103002	+	0.994681i	$0.467155\pi$
$354$	1.20515	+	2.08737i	0.0640527	+	0.110943i
$355$		0			0
$356$	15.7668			0.835640
$357$	7.92705	+	4.57669i	0.419544	+	0.242224i
$358$	2.04657	−	1.18159i	0.108165	−	0.0624488i
$359$	10.2666			0.541849			0.270924	−	0.962601i	$-0.412671\pi$
$359$	10.2666			0.541849			0.270924	+	0.962601i	$0.412671\pi$
$360$		0			0
$361$	−19.9776	−	34.6023i	−1.05145	−	1.82117i
$362$			0.916312i			0.0481603i
$363$	46.9587	+	27.1116i	2.46469	+	1.42299i
$364$	−7.28207			−0.381684
$365$		0			0
$366$	0.718326	−	1.24418i	0.0375475	−	0.0650342i
$367$	32.1694	+	18.5730i	1.67923	+	0.969504i	0.962153	+	0.272511i	$0.0878542\pi$
$367$	32.1694	+	18.5730i	1.67923	+	0.969504i	0.717078	+	0.696993i	$0.245479\pi$
$368$	16.8514	−	9.72916i	0.878440	−	0.507167i
$369$	8.02034			0.417522
$370$		0			0
$371$	9.77858			0.507679
$372$	−8.14168	+	4.70060i	−0.422126	+	0.243715i
$373$	9.93260	+	5.73459i	0.514290	+	0.296926i	0.734596	−	0.678505i	$-0.237372\pi$
$373$	9.93260	+	5.73459i	0.514290	+	0.296926i	−0.220305	+	0.975431i	$0.570705\pi$
$374$	2.15105	−	3.72572i	0.111228	−	0.192653i
$375$		0			0
$376$	−3.84583			−0.198333
$377$	−20.5542	−	11.8670i	−1.05860	−	0.611180i
$378$			1.00797i			0.0518444i
$379$	0.671855	+	1.16369i	0.0345109	+	0.0597746i	0.882765	−	0.469815i	$-0.155679\pi$
$379$	0.671855	+	1.16369i	0.0345109	+	0.0597746i	−0.848254	+	0.529589i	$0.822346\pi$
$380$		0			0
$381$	18.6889			0.957460
$382$	−4.10772	+	2.37159i	−0.210169	+	0.121341i
$383$	−21.5672	−	12.4519i	−1.10203	−	0.636260i	−0.165280	−	0.986247i	$-0.552853\pi$
$383$	−21.5672	−	12.4519i	−1.10203	−	0.636260i	−0.936755	+	0.349987i	$0.886186\pi$
$384$	14.1520			0.722192
$385$		0			0
$386$	−1.31613	−	2.27961i	−0.0669893	−	0.116029i
$387$	−13.2819	+	7.66832i	−0.675158	+	0.389803i
$388$	16.7935	+	9.69570i	0.852558	+	0.492225i
$389$	−6.46405	+	11.1961i	−0.327741	+	0.567663i	−0.982063	−	0.188552i	$-0.939621\pi$
$389$	−6.46405	+	11.1961i	−0.327741	+	0.567663i	0.654323	+	0.756216i	$0.272954\pi$
$390$		0			0
$391$	−8.33771	−	14.4413i	−0.421656	−	0.730330i
$392$	3.92168	−	2.26418i	0.198075	−	0.114359i
$393$			16.0313i			0.808670i
$394$	0.184204	−	0.319050i	0.00928005	−	0.0160735i
$395$		0			0
$396$	16.9986			0.854213
$397$		−	7.29210i		−	0.365980i	−0.983115	−	0.182990i	$-0.941422\pi$
$397$		−	7.29210i		−	0.365980i	0.983115	−	0.182990i	$-0.0585776\pi$
$398$	0.0259293	−	0.0149703i	0.00129972	−	0.000750391i
$399$	22.1517			1.10897
$400$		0			0
$401$	5.51474			0.275393			0.137696	−	0.990474i	$-0.456030\pi$
$401$	5.51474			0.275393			0.137696	+	0.990474i	$0.456030\pi$
$402$	−0.0384423	−	0.0221947i	−0.00191733	−	0.00110697i
$403$	−5.40472	−	3.12042i	−0.269228	−	0.155439i
$404$	4.63582	−	8.02948i	0.230641	−	0.399482i
$405$		0			0
$406$	−2.66630			−0.132326
$407$	−32.8373	−	16.7639i	−1.62769	−	0.830957i
$408$		−	5.90632i		−	0.292407i
$409$	11.9196	+	20.6454i	0.589387	+	1.02085i	0.994313	+	0.106499i	$0.0339641\pi$
$409$	11.9196	+	20.6454i	0.589387	+	1.02085i	−0.404926	+	0.914350i	$0.632703\pi$
$410$		0			0
$411$	−17.7188	+	30.6899i	−0.874006	+	1.51382i
$412$	1.65687	+	0.956594i	0.0816281	+	0.0471280i
$413$		−	7.00358i		−	0.344623i
$414$	−0.845528	+	1.46450i	−0.0415554	+	0.0719761i
$415$		0			0
$416$	3.53902	+	6.12976i	0.173515	+	0.300536i
$417$		−	13.0280i		−	0.637981i
$418$		−	10.4113i		−	0.509235i
$419$	−19.8879	−	34.4469i	−0.971589	−	1.68284i	−0.690761	−	0.723083i	$-0.742724\pi$
$419$	−19.8879	−	34.4469i	−0.971589	−	1.68284i	−0.280828	−	0.959758i	$-0.590609\pi$
$420$		0			0
$421$	1.66044			0.0809251			0.0404625	−	0.999181i	$-0.487117\pi$
$421$	1.66044			0.0809251			0.0404625	+	0.999181i	$0.487117\pi$
$422$	2.94548	−	1.70057i	0.143384	−	0.0827826i
$423$	−5.42092	+	3.12977i	−0.263574	+	0.152175i
$424$	−3.15487	−	5.46440i	−0.153214	−	0.265375i
$425$		0			0
$426$	0.936867	−	1.62270i	0.0453913	−	0.0786201i
$427$	−3.61520	+	2.08724i	−0.174952	+	0.101009i
$428$	4.27138	−	2.46608i	0.206465	−	0.119203i
$429$	17.4110	+	30.1567i	0.840611	+	1.45598i
$430$		0			0
$431$	5.27976	−	9.14481i	0.254317	−	0.440490i	−0.710393	−	0.703805i	$-0.751483\pi$
$431$	5.27976	−	9.14481i	0.254317	−	0.440490i	0.964710	+	0.263316i	$0.0848161\pi$
$432$	−10.5491	+	6.09051i	−0.507543	+	0.293030i
$433$			22.3065i			1.07198i	0.844223	+	0.535992i	$0.180062\pi$
$433$			22.3065i			1.07198i	−0.844223	+	0.535992i	$0.819938\pi$
$434$	−0.701101			−0.0336539
$435$		0			0
$436$	−21.3281			−1.02143
$437$	−34.9489	−	20.1778i	−1.67183	−	0.965234i
$438$			4.60441i			0.220007i
$439$	−16.6320	+	28.8075i	−0.793804	+	1.37491i	0.129792	+	0.991541i	$0.458569\pi$
$439$	−16.6320	+	28.8075i	−0.793804	+	1.37491i	−0.923596	+	0.383367i	$0.874764\pi$
$440$		0			0
$441$	3.68522	−	6.38300i	0.175487	−	0.303952i
$442$	1.67625	−	0.967785i	0.0797313	−	0.0460329i
$443$			21.3560i			1.01465i	0.861754	+	0.507326i	$0.169366\pi$
$443$			21.3560i			1.01465i	−0.861754	+	0.507326i	$0.830634\pi$
$444$	−24.9547	+	1.28818i	−1.18430	+	0.0611343i
$445$		0			0
$446$	2.87209	+	4.97460i	0.135997	+	0.235554i
$447$	−33.0639	−	19.0895i	−1.56387	−	0.902901i
$448$	−8.09281	−	4.67238i	−0.382349	−	0.220749i
$449$	19.2410	−	33.3263i	0.908037	−	1.57277i	0.0912489	−	0.995828i	$-0.470914\pi$
$449$	19.2410	−	33.3263i	0.908037	−	1.57277i	0.816788	−	0.576938i	$-0.195753\pi$
$450$		0			0
$451$	−16.9002	+	29.2720i	−0.795800	+	1.37837i
$452$		−	6.53310i		−	0.307291i
$453$	−28.6011	+	16.5129i	−1.34380	+	0.775842i
$454$	−0.0865191			−0.00406054
$455$		0			0
$456$	−7.14684	−	12.3787i	−0.334682	−	0.579685i
$457$	−15.7563	−	9.09691i	−0.737049	−	0.425535i	0.0839464	−	0.996470i	$-0.473248\pi$
$457$	−15.7563	−	9.09691i	−0.737049	−	0.425535i	−0.820995	+	0.570935i	$0.806581\pi$
$458$		−	3.81637i		−	0.178327i
$459$	5.21946	+	9.04036i	0.243623	+	0.421968i
$460$		0			0
$461$	3.17765	+	5.50386i	0.147998	+	0.256340i	0.930487	−	0.366324i	$-0.119384\pi$
$461$	3.17765	+	5.50386i	0.147998	+	0.256340i	−0.782489	+	0.622664i	$0.786050\pi$
$462$	3.38784	+	1.95597i	0.157617	+	0.0909999i
$463$	−19.2540	−	11.1163i	−0.894810	−	0.516619i	−0.0192974	−	0.999814i	$-0.506143\pi$
$463$	−19.2540	−	11.1163i	−0.894810	−	0.516619i	−0.875513	+	0.483195i	$0.839476\pi$
$464$	−16.1107	−	27.9045i	−0.747920	−	1.29544i
$465$		0			0
$466$	2.50789	+	4.34380i	0.116176	+	0.201223i
$467$			25.7761i			1.19277i	0.802697	+	0.596387i	$0.203398\pi$
$467$			25.7761i			1.19277i	−0.802697	+	0.596387i	$0.796602\pi$
$468$	6.62329	+	3.82396i	0.306162	+	0.176763i
$469$	0.0644910	+	0.111702i	0.00297792	+	0.00515791i
$470$		0			0
$471$	−36.4413			−1.67913
$472$	−3.91369	+	2.25957i	−0.180142	+	0.104005i
$473$		−	64.6339i		−	2.97187i
$474$	0.663783	−	1.14971i	0.0304886	−	0.0528077i
$475$		0			0
$476$	−4.23614	+	7.33721i	−0.194163	+	0.336300i
$477$	−8.89395	−	5.13493i	−0.407226	−	0.235112i
$478$	−1.78040	−	1.02792i	−0.0814337	−	0.0470158i
$479$	−1.29374	−	2.24082i	−0.0591125	−	0.102386i	0.834955	−	0.550319i	$-0.185494\pi$
$479$	−1.29374	−	2.24082i	−0.0591125	−	0.102386i	−0.894067	+	0.447933i	$0.852160\pi$
$480$		0			0
$481$	−9.02346	−	13.9188i	−0.411434	−	0.634644i
$482$			0.229663i			0.0104609i
$483$	13.1317	−	7.58156i	0.597511	−	0.344973i
$484$	−25.0943	+	43.4646i	−1.14065	+	1.97566i
$485$		0			0
$486$	1.54605	−	2.67784i	0.0701303	−	0.121469i
$487$			38.7207i			1.75460i	0.479940	+	0.877301i	$0.340658\pi$
$487$			38.7207i			1.75460i	−0.479940	+	0.877301i	$0.659342\pi$
$488$	2.33275	+	1.34682i	0.105599	+	0.0609675i
$489$	10.0050			0.452440
$490$		0			0
$491$	−2.19394			−0.0990112			−0.0495056	−	0.998774i	$-0.515765\pi$
$491$	−2.19394			−0.0990112			−0.0495056	+	0.998774i	$0.515765\pi$
$492$			22.9083i			1.03278i
$493$	−23.9137	+	13.8066i	−1.07702	+	0.621817i
$494$	2.34210	−	4.05664i	0.105376	−	0.182517i
$495$		0			0
$496$	−4.23630	−	7.33749i	−0.190216	−	0.329463i
$497$	−4.71508	+	2.72225i	−0.211500	+	0.122110i
$498$	−4.57837	+	2.64332i	−0.205162	+	0.118450i
$499$	−0.224669	+	0.389137i	−0.0100575	+	0.0174202i	−0.871010	−	0.491265i	$-0.836535\pi$
$499$	−0.224669	+	0.389137i	−0.0100575	+	0.0174202i	0.860953	+	0.508685i	$0.169868\pi$
$500$		0			0
$501$	−24.0295	−	41.6203i	−1.07356	−	1.85946i
$502$	1.18308	−	0.683049i	0.0528032	−	0.0304860i
$503$	−13.1783	+	7.60851i	−0.587593	+	0.339247i	−0.764145	−	0.645044i	$-0.776839\pi$
$503$	−13.1783	+	7.60851i	−0.587593	+	0.339247i	0.176552	+	0.984291i	$0.443506\pi$
$504$	1.74040			0.0775236
$505$		0			0
$506$	−3.56334	−	6.17189i	−0.158410	−	0.274374i
$507$		−	11.7204i		−	0.520519i
$508$			17.2983i			0.767486i
$509$	14.8791	+	25.7714i	0.659506	+	1.14230i	0.980744	+	0.195300i	$0.0625679\pi$
$509$	14.8791	+	25.7714i	0.659506	+	1.14230i	−0.321237	+	0.946999i	$0.604099\pi$
$510$		0			0
$511$	6.68952	−	11.5866i	0.295927	−	0.512561i
$512$			16.1521i			0.713828i
$513$	21.8783	+	12.6314i	0.965949	+	0.557691i
$514$	1.48833	−	2.57786i	0.0656474	−	0.113705i
$515$		0			0
$516$	−21.9028	−	37.9368i	−0.964218	−	1.67007i
$517$		−	26.3798i		−	1.16018i
$518$	−1.65972	−	0.847312i	−0.0729239	−	0.0372287i
$519$	29.2572			1.28425
$520$		0			0
$521$	9.16401	−	15.8725i	0.401483	−	0.695388i	−0.592422	−	0.805627i	$-0.701828\pi$
$521$	9.16401	−	15.8725i	0.401483	−	0.695388i	0.993905	+	0.110239i	$0.0351617\pi$
$522$	2.42509	+	1.40013i	0.106143	+	0.0612818i
$523$	−7.17391	−	4.14186i	−0.313693	−	0.181111i	0.334885	−	0.942259i	$-0.391303\pi$
$523$	−7.17391	−	4.14186i	−0.313693	−	0.181111i	−0.648578	+	0.761148i	$0.724636\pi$
$524$	−14.8384			−0.648218
$525$		0			0
$526$	−2.53261			−0.110427
$527$	−6.28809	+	3.63043i	−0.273914	+	0.158144i
$528$			47.2746i			2.05736i
$529$	−4.62386			−0.201037
$530$		0			0
$531$	−3.67772	+	6.36999i	−0.159599	+	0.276434i
$532$			20.5035i			0.888938i
$533$	−13.1699	+	7.60364i	−0.570451	+	0.329350i
$534$	−1.90538	−	3.30021i	−0.0824537	−	0.142814i
$535$		0			0
$536$	0.0416136	−	0.0720769i	0.00179743	−	0.00311325i
$537$	19.2728	+	11.1272i	0.831685	+	0.480173i
$538$	−1.22233	+	0.705713i	−0.0526984	+	0.0304254i
$539$	15.5308	+	26.9001i	0.668959	+	1.15867i
$540$		0			0
$541$	−13.1983			−0.567437			−0.283719	−	0.958908i	$-0.591568\pi$
$541$	−13.1983			−0.567437			−0.283719	+	0.958908i	$0.591568\pi$
$542$	2.06495	+	1.19220i	0.0886973	+	0.0512094i
$543$	−7.47298	+	4.31452i	−0.320696	+	0.185154i
$544$	8.23490			0.353068
$545$		0			0
$546$	0.880017	+	1.52423i	0.0376613	+	0.0652312i
$547$		−	43.3722i		−	1.85446i	−0.374492	−	0.927230i	$-0.622183\pi$
$547$		−	43.3722i		−	1.85446i	0.374492	−	0.927230i	$-0.377817\pi$
$548$	−28.4063	−	16.4004i	−1.21346	−	0.700590i
$549$	4.38420			0.187113
$550$		0			0
$551$	−33.4128	+	57.8726i	−1.42343	+	2.46546i
$552$	−8.47336	−	4.89210i	−0.360650	−	0.208221i
$553$	−3.34070	+	1.92875i	−0.142061	+	0.0820189i
$554$	6.05945			0.257441
$555$		0			0
$556$	12.0586			0.511397
$557$	−28.4067	+	16.4006i	−1.20363	+	0.694917i	−0.961361	−	0.275292i	$-0.911226\pi$
$557$	−28.4067	+	16.4006i	−1.20363	+	0.694917i	−0.242271	+	0.970209i	$0.577892\pi$
$558$	0.637676	+	0.368162i	0.0269950	+	0.0155856i
$559$	14.5398	−	25.1837i	0.614969	−	1.06516i
$560$		0			0
$561$	40.5135			1.71048
$562$	2.79313	+	1.61262i	0.117821	+	0.0680241i
$563$			18.4068i			0.775754i	0.921711	+	0.387877i	$0.126791\pi$
$563$			18.4068i			0.775754i	−0.921711	+	0.387877i	$0.873209\pi$
$564$	−8.93947	−	15.4836i	−0.376420	−	0.651978i
$565$		0			0
$566$	3.30980			0.139121
$567$	−13.3376	+	7.70046i	−0.560126	+	0.323389i
$568$	3.04246	+	1.75657i	0.127659	+	0.0737039i
$569$	−3.64317			−0.152730			−0.0763648	−	0.997080i	$-0.524331\pi$
$569$	−3.64317			−0.152730			−0.0763648	+	0.997080i	$0.524331\pi$
$570$		0			0
$571$	12.1334	+	21.0157i	0.507767	+	0.879478i	0.999960	+	0.00899174i	$0.00286220\pi$
$571$	12.1334	+	21.0157i	0.507767	+	0.879478i	−0.492193	+	0.870486i	$0.663804\pi$
$572$	−27.9128	+	16.1155i	−1.16709	+	0.673822i
$573$	−38.6830	−	22.3336i	−1.61601	−	0.933001i
$574$	−0.854200	+	1.47952i	−0.0356536	+	0.0617539i
$575$		0			0
$576$	4.90712	+	8.49939i	0.204463	+	0.354141i
$577$	−27.8994	+	16.1077i	−1.16147	+	0.670573i	−0.951655	−	0.307169i	$-0.900618\pi$
$577$	−27.8994	+	16.1077i	−1.16147	+	0.670573i	−0.209811	+	0.977742i	$0.567285\pi$
$578$			1.55114i			0.0645191i
$579$	12.3942	−	21.4674i	0.515086	−	0.892155i
$580$		0			0
$581$	15.3614			0.637298
$582$		−	4.68679i		−	0.194274i
$583$	37.4822	−	21.6403i	1.55235	−	0.896251i
$584$	−8.63299			−0.357236
$585$		0			0
$586$	−4.62345			−0.190993
$587$	15.0255	+	8.67496i	0.620168	+	0.358054i	0.776934	−	0.629582i	$-0.216774\pi$
$587$	15.0255	+	8.67496i	0.620168	+	0.358054i	−0.156767	+	0.987636i	$0.550107\pi$
$588$	18.2316	+	10.5260i	0.751857	+	0.434085i
$589$	−8.78588	+	15.2176i	−0.362016	+	0.627030i
$590$		0			0
$591$	3.46935			0.142710
$592$	−1.16094	−	22.4898i	−0.0477144	−	0.924326i
$593$		−	6.48625i		−	0.266358i	−0.991092	−	0.133179i	$-0.957481\pi$
$593$		−	6.48625i		−	0.266358i	0.991092	−	0.133179i	$-0.0425186\pi$
$594$	2.23067	+	3.86364i	0.0915257	+	0.158527i
$595$		0			0
$596$	17.6690	−	30.6037i	0.723752	−	1.25358i
$597$	0.244180	+	0.140977i	0.00999361	+	0.00576981i
$598$		−	3.20639i		−	0.131119i
$599$	6.38920	−	11.0664i	0.261056	−	0.452162i	−0.705467	−	0.708743i	$-0.749263\pi$
$599$	6.38920	−	11.0664i	0.261056	−	0.452162i	0.966523	+	0.256581i	$0.0825961\pi$
$600$		0			0
$601$	−0.0159615	−	0.0276461i	−0.000651082	−	0.00112771i	0.865700	−	0.500564i	$-0.166874\pi$
$601$	−0.0159615	−	0.0276461i	−0.000651082	−	0.00112771i	−0.866351	+	0.499436i	$0.833541\pi$
$602$		−	3.26684i		−	0.133146i
$603$		−	0.135462i		−	0.00551644i
$604$	−15.2842	−	26.4729i	−0.621903	−	1.07717i
$605$		0			0
$606$	−2.24090			−0.0910305
$607$	21.6443	−	12.4963i	0.878514	−	0.507210i	0.00834578	−	0.999965i	$-0.497343\pi$
$607$	21.6443	−	12.4963i	0.878514	−	0.507210i	0.870168	+	0.492755i	$0.164010\pi$
$608$	17.2590	−	9.96449i	0.699945	−	0.404113i
$609$	−12.5545	−	21.7450i	−0.508732	−	0.881150i
$610$		0			0
$611$	5.93432	−	10.2785i	0.240077	−	0.415826i
$612$	7.70583	−	4.44896i	0.311490	−	0.179839i
$613$	−0.193713	+	0.111840i	−0.00782398	+	0.00451717i	−0.503907	−	0.863758i	$-0.668105\pi$
$613$	−0.193713	+	0.111840i	−0.00782398	+	0.00451717i	0.496083	+	0.868275i	$0.334771\pi$
$614$	3.05169	+	5.28568i	0.123156	+	0.213312i
$615$		0			0
$616$	−3.66732	+	6.35199i	−0.147761	+	0.255929i
$617$	34.4977	−	19.9172i	1.38882	−	0.801838i	0.395642	−	0.918405i	$-0.370522\pi$
$617$	34.4977	−	19.9172i	1.38882	−	0.801838i	0.993183	+	0.116567i	$0.0371889\pi$
$618$		−	0.462407i		−	0.0186007i
$619$	45.4294			1.82596			0.912981	−	0.408002i	$-0.133774\pi$
$619$	45.4294			1.82596			0.912981	+	0.408002i	$0.133774\pi$
$620$		0			0
$621$	17.2927			0.693932
$622$	−3.54527	−	2.04686i	−0.142152	−	0.0820716i
$623$			11.0729i			0.443626i
$624$	−10.6347	+	18.4199i	−0.425731	+	0.737387i
$625$		0			0
$626$	2.11957	−	3.67120i	0.0847149	−	0.146731i
$627$	84.9096	−	49.0226i	3.39096	−	1.95777i
$628$		−	33.7298i		−	1.34596i
$629$	−19.2734	+	0.994904i	−0.768479	+	0.0396694i
$630$		0			0
$631$	5.98428	+	10.3651i	0.238230	+	0.412627i	0.960207	−	0.279291i	$-0.0900993\pi$
$631$	5.98428	+	10.3651i	0.238230	+	0.412627i	−0.721976	+	0.691918i	$0.756766\pi$
$632$	2.15563	+	1.24455i	0.0857462	+	0.0495056i
$633$	27.7380	+	16.0145i	1.10249	+	0.636521i
$634$	−0.243537	+	0.421819i	−0.00967210	+	0.0167526i
$635$		0			0
$636$	14.6667	−	25.4036i	0.581574	−	1.00732i
$637$			13.9750i			0.553711i
$638$	−10.2202	+	5.90061i	−0.404620	+	0.233607i
$639$	5.71804			0.226202
$640$		0			0
$641$	−13.1254	−	22.7339i	−0.518424	−	0.897936i	−0.999771	−	0.0214063i	$-0.993186\pi$
$641$	−13.1254	−	22.7339i	−0.518424	−	0.897936i	0.481347	−	0.876530i	$-0.340148\pi$
$642$	−1.03237	−	0.596039i	−0.0407444	−	0.0235238i
$643$		−	13.7647i		−	0.542827i	−0.962463	−	0.271413i	$-0.912509\pi$
$643$		−	13.7647i		−	0.542827i	0.962463	−	0.271413i	$-0.0874910\pi$
$644$	7.01743	+	12.1545i	0.276525	+	0.478956i
$645$		0			0
$646$	−2.72491	−	4.71968i	−0.107210	−	0.185693i
$647$	30.6515	+	17.6966i	1.20503	+	0.695727i	0.961670	−	0.274208i	$-0.0884158\pi$
$647$	30.6515	+	17.6966i	1.20503	+	0.695727i	0.243364	+	0.969935i	$0.421749\pi$
$648$	8.60624	+	4.96882i	0.338085	+	0.195194i
$649$	−15.4992	−	26.8453i	−0.608395	−	1.05377i
$650$		0			0
$651$	−3.30119	−	5.71783i	−0.129384	−	0.224099i
$652$			9.26051i			0.362669i
$653$	−39.5051	−	22.8083i	−1.54595	−	0.892557i	−0.998444	−	0.0557569i	$-0.982243\pi$
$653$	−39.5051	−	22.8083i	−1.54595	−	0.892557i	−0.547509	−	0.836800i	$-0.684424\pi$
$654$	2.57745	+	4.46427i	0.100786	+	0.174567i
$655$		0			0
$656$	−20.6455			−0.806072
$657$	−12.1687	+	7.02560i	−0.474746	+	0.274095i
$658$		−	1.33334i		−	0.0519788i
$659$	1.92370	−	3.33195i	0.0749367	−	0.129794i	−0.826122	−	0.563491i	$-0.809458\pi$
$659$	1.92370	−	3.33195i	0.0749367	−	0.129794i	0.901059	+	0.433697i	$0.142791\pi$
$660$		0			0
$661$	−3.84761	+	6.66425i	−0.149655	+	0.259209i	−0.931100	−	0.364764i	$-0.881150\pi$
$661$	−3.84761	+	6.66425i	−0.149655	+	0.259209i	0.781445	+	0.623974i	$0.214483\pi$
$662$	−5.48853	−	3.16880i	−0.213318	−	0.123159i
$663$	15.7855	+	9.11378i	0.613059	+	0.353950i
$664$	−4.95606	−	8.58416i	−0.192333	−	0.333130i
$665$		0			0
$666$	1.06463	+	1.64221i	0.0412537	+	0.0636344i
$667$			45.7429i			1.77117i
$668$	38.5233	−	22.2415i	1.49051	−	0.860548i
$669$	−27.0469	+	46.8466i	−1.04569	+	1.81119i
$670$		0			0
$671$	−9.23827	+	16.0011i	−0.356639	+	0.617717i
$672$			7.48808i			0.288859i
$673$	−5.09978	−	2.94436i	−0.196582	−	0.113497i	0.398478	−	0.917178i	$-0.369538\pi$
$673$	−5.09978	−	2.94436i	−0.196582	−	0.113497i	−0.595060	+	0.803681i	$0.702872\pi$
$674$	−0.390663			−0.0150478
$675$		0			0
$676$	10.8483			0.417241
$677$			14.5967i			0.560998i	0.959854	+	0.280499i	$0.0904999\pi$
$677$			14.5967i			0.560998i	−0.959854	+	0.280499i	$0.909500\pi$
$678$	−1.36747	+	0.789507i	−0.0525172	+	0.0303208i
$679$	−6.80921	+	11.7939i	−0.261313	+	0.452608i
$680$		0			0
$681$	−0.407381	−	0.705605i	−0.0156109	−	0.0270389i
$682$	−2.68738	+	1.55156i	−0.102905	+	0.0594124i
$683$	9.89573	−	5.71330i	0.378649	−	0.218613i	−0.298581	−	0.954384i	$-0.596513\pi$
$683$	9.89573	−	5.71330i	0.378649	−	0.218613i	0.677231	+	0.735771i	$0.263180\pi$
$684$	10.7668	−	18.6486i	0.411678	−	0.713047i
$685$		0			0
$686$	1.85723	+	3.21682i	0.0709095	+	0.122819i
$687$	31.1243	−	17.9696i	1.18747	−	0.685585i
$688$	34.1896	−	19.7394i	1.30347	−	0.752557i
$689$	19.4726			0.741846
$690$		0			0
$691$	−4.90404	−	8.49405i	−0.186559	−	0.323129i	0.757542	−	0.652786i	$-0.226400\pi$
$691$	−4.90404	−	8.49405i	−0.186559	−	0.323129i	−0.944101	+	0.329657i	$0.893067\pi$
$692$			27.0802i			1.02943i
$693$			11.9380i			0.453487i
$694$	−1.51827	−	2.62972i	−0.0576327	−	0.0998227i
$695$		0			0
$696$	−8.10092	+	14.0312i	−0.307064	+	0.531851i
$697$			17.6928i			0.670163i
$698$	6.42074	+	3.70702i	0.243029	+	0.140313i
$699$	−23.6172	+	40.9062i	−0.893285	+	1.54722i
$700$		0			0
$701$	−5.18495	−	8.98060i	−0.195833	−	0.339193i	0.751340	−	0.659915i	$-0.229408\pi$
$701$	−5.18495	−	8.98060i	−0.195833	−	0.339193i	−0.947173	+	0.320722i	$0.896074\pi$
$702$			2.00722i			0.0757577i
$703$	−39.1900	+	25.4065i	−1.47808	+	0.958226i
$704$	−41.3606			−1.55884
$705$		0			0
$706$	−1.71546	+	2.97126i	−0.0645622	+	0.111825i
$707$	5.63903	+	3.25570i	0.212078	+	0.122443i
$708$	−18.1944	−	10.5046i	−0.683789	−	0.394786i
$709$	29.3510			1.10230			0.551151	−	0.834406i	$-0.314189\pi$
$709$	29.3510			1.10230			0.551151	+	0.834406i	$0.314189\pi$
$710$		0			0
$711$	4.05131			0.151936
$712$	6.18768	−	3.57246i	0.231893	−	0.133884i
$713$			12.0281i			0.450455i
$714$	2.04770			0.0766333
$715$		0			0
$716$	−10.2992	+	17.8388i	−0.384900	+	0.666666i
$717$		−	19.3601i		−	0.723015i
$718$	1.98903	−	1.14837i	0.0742300	−	0.0428567i
$719$	−11.3957	−	19.7379i	−0.424987	−	0.736099i	0.571432	−	0.820649i	$-0.306388\pi$
$719$	−11.3957	−	19.7379i	−0.424987	−	0.736099i	−0.996419	+	0.0845500i	$0.973055\pi$
$720$		0			0
$721$	−0.671807	+	1.16360i	−0.0250194	+	0.0433349i
$722$	−7.74088	−	4.46920i	−0.288086	−	0.166326i
$723$	−1.87302	+	1.08139i	−0.0696583	+	0.0402172i
$724$	−3.99349	−	6.91692i	−0.148417	−	0.257065i
$725$		0			0
$726$	12.1303			0.450197
$727$	14.0233	+	8.09635i	0.520095	+	0.300277i	0.736974	−	0.675922i	$-0.236254\pi$
$727$	14.0233	+	8.09635i	0.520095	+	0.300277i	−0.216879	+	0.976199i	$0.569588\pi$
$728$	−2.85785	+	1.64998i	−0.105919	+	0.0611522i
$729$	−4.61978			−0.171103
$730$		0			0
$731$	−16.9163	−	29.2999i	−0.625671	−	1.08369i
$732$			12.5225i			0.462844i
$733$	−31.0850	−	17.9470i	−1.14815	−	0.662886i	−0.199716	−	0.979854i	$-0.564002\pi$
$733$	−31.0850	−	17.9470i	−1.14815	−	0.662886i	−0.948436	+	0.316968i	$0.897335\pi$
$734$	8.30995			0.306726
$735$		0			0
$736$	6.82081	−	11.8140i	0.251418	−	0.435469i
$737$	0.494400	+	0.285442i	0.0182114	+	0.0105144i
$738$	1.55385	−	0.897115i	0.0571980	−	0.0330233i
$739$	−12.1252			−0.446033			−0.223017	−	0.974815i	$-0.571590\pi$
$739$	−12.1252			−0.446033			−0.223017	+	0.974815i	$0.571590\pi$
$740$		0			0
$741$	44.1119			1.62049
$742$	1.89449	−	1.09378i	0.0695489	−	0.0401541i
$743$	44.0282	+	25.4197i	1.61524	+	0.932559i	0.988129	+	0.153628i	$0.0490959\pi$
$743$	44.0282	+	25.4197i	1.61524	+	0.932559i	0.627110	+	0.778930i	$0.284237\pi$
$744$	−2.13013	+	3.68950i	−0.0780944	+	0.135264i
$745$		0			0
$746$	2.56577			0.0939396
$747$	−13.9717	−	8.06658i	−0.511198	−	0.295141i
$748$			37.4989i			1.37110i
$749$	1.73191	+	2.99975i	0.0632826	+	0.109609i
$750$		0			0
$751$	18.2535			0.666081			0.333041	−	0.942913i	$-0.391925\pi$
$751$	18.2535			0.666081			0.333041	+	0.942913i	$0.391925\pi$
$752$	13.9542	−	8.05648i	0.508859	−	0.293790i
$753$	11.1412	+	6.43237i	0.406008	+	0.234409i
$754$	−5.30953			−0.193362
$755$		0			0
$756$	−4.39295	−	7.60882i	−0.159770	−	0.276730i
$757$	0.0991719	−	0.0572569i	0.00360446	−	0.00208104i	−0.498197	−	0.867064i	$-0.666004\pi$
$757$	0.0991719	−	0.0572569i	0.00360446	−	0.00208104i	0.501801	+	0.864983i	$0.332671\pi$
$758$	0.260329	+	0.150301i	0.00945556	+	0.00545917i
$759$	33.5565	−	58.1216i	1.21802	−	2.10968i
$760$		0			0
$761$	−17.1513	−	29.7069i	−0.621733	−	1.07687i	−0.989163	−	0.146822i	$-0.953096\pi$
$761$	−17.1513	−	29.7069i	−0.621733	−	1.07687i	0.367430	−	0.930051i	$-0.380238\pi$
$762$	3.62076	−	2.09045i	0.131166	−	0.0757289i
$763$		−	14.9786i		−	0.542260i
$764$	20.6718	−	35.8046i	0.747880	−	1.29537i
$765$		0			0
$766$	−5.57121			−0.201296
$767$		−	13.9466i		−	0.503581i
$768$	−22.1578	+	12.7928i	−0.799552	+	0.461621i
$769$	17.5240			0.631933			0.315966	−	0.948770i	$-0.397671\pi$
$769$	17.5240			0.631933			0.315966	+	0.948770i	$0.397671\pi$
$770$		0			0
$771$	28.0317			1.00954
$772$	19.8700	+	11.4720i	0.715138	+	0.412885i
$773$	−23.8965	−	13.7967i	−0.859499	−	0.496232i	0.00434571	−	0.999991i	$-0.498617\pi$
$773$	−23.8965	−	13.7967i	−0.859499	−	0.496232i	−0.863844	+	0.503759i	$0.831950\pi$
$774$	−1.71548	+	2.97130i	−0.0616617	+	0.106801i
$775$		0			0
$776$	8.78745			0.315451
$777$	−0.904677	−	17.5255i	−0.0324551	−	0.628723i
$778$			2.89215i			0.103689i
$779$	21.4089	+	37.0813i	0.767053	+	1.32857i
$780$		0			0
$781$	−12.0489	+	20.8693i	−0.431143	+	0.746761i
$782$	−3.23067	−	1.86523i	−0.115529	−	0.0667005i
$783$		−	28.6353i		−	1.02334i
$784$	−9.48630	+	16.4308i	−0.338797	+	0.586813i
$785$		0			0
$786$	1.79318	+	3.10587i	0.0639605	+	0.110783i
$787$			9.45983i			0.337207i	0.985684	+	0.168603i	$0.0539257\pi$
$787$			9.45983i			0.337207i	−0.985684	+	0.168603i	$0.946074\pi$
$788$			3.21120i			0.114394i
$789$	−11.9250	−	20.6547i	−0.424541	−	0.735327i
$790$		0			0
$791$	4.58814			0.163135
$792$	6.67111	−	3.85157i	0.237048	−	0.136859i
$793$	−7.19913	+	4.15642i	−0.255649	+	0.147599i
$794$	−0.815658	−	1.41276i	−0.0289466	−	0.0501370i
$795$		0			0
$796$	−0.130487	+	0.226011i	−0.00462500	+	0.00801073i
$797$	20.0855	−	11.5964i	0.711465	−	0.410764i	−0.100138	−	0.994974i	$-0.531929\pi$
$797$	20.0855	−	11.5964i	0.711465	−	0.410764i	0.811603	+	0.584209i	$0.198595\pi$
$798$	4.29165	−	2.47778i	0.151923	−	0.0877126i
$799$	−6.90425	−	11.9585i	−0.244255	−	0.423062i
$800$		0			0
$801$	5.81460	−	10.0712i	0.205449	−	0.355848i
$802$	1.06842	−	0.616851i	0.0377272	−	0.0217818i
$803$		−	59.2166i		−	2.08971i
$804$	0.386916			0.0136455
$805$		0			0
$806$	−1.39614			−0.0491769
$807$	−11.5109	−	6.64580i	−0.405202	−	0.233943i
$808$		−	4.20156i		−	0.147810i
$809$	−22.2150	+	38.4775i	−0.781037	+	1.35280i	0.150302	+	0.988640i	$0.451976\pi$
$809$	−22.2150	+	38.4775i	−0.781037	+	1.35280i	−0.931338	+	0.364155i	$0.881358\pi$
$810$		0			0
$811$	−26.2576	+	45.4796i	−0.922030	+	1.59700i	−0.125762	+	0.992060i	$0.540138\pi$
$811$	−26.2576	+	45.4796i	−0.922030	+	1.59700i	−0.796269	+	0.604943i	$0.793196\pi$
$812$	20.1269	−	11.6203i	0.706317	−	0.407792i
$813$			22.4543i			0.787506i
$814$	−8.23699	+	0.425199i	−0.288706	+	0.0149032i
$815$		0			0
$816$	12.3729	+	21.4306i	0.433139	+	0.750219i
$817$	−70.9076	−	40.9385i	−2.48074	−	1.43226i
$818$	4.61858	+	2.66654i	0.161485	+	0.0932334i
$819$	−2.68553	+	4.65148i	−0.0938401	+	0.162536i
$820$		0			0
$821$	−8.55929	+	14.8251i	−0.298721	+	0.517401i	−0.975844	−	0.218470i	$-0.929893\pi$
$821$	−8.55929	+	14.8251i	−0.298721	+	0.517401i	0.677122	+	0.735870i	$0.263227\pi$
$822$			7.92777i			0.276513i
$823$	37.2109	−	21.4837i	1.29709	−	0.748875i	0.317189	−	0.948362i	$-0.397261\pi$
$823$	37.2109	−	21.4837i	1.29709	−	0.748875i	0.979900	+	0.199487i	$0.0639277\pi$
$824$	0.866984			0.0302028
$825$		0			0
$826$	−0.783386	−	1.35686i	−0.0272575	−	0.0472113i
$827$	35.8573	+	20.7022i	1.24688	+	0.719887i	0.970486	−	0.241157i	$-0.0775270\pi$
$827$	35.8573	+	20.7022i	1.24688	+	0.719887i	0.276395	+	0.961044i	$0.410860\pi$
$828$		−	14.7400i		−	0.512249i
$829$	−22.0715	−	38.2290i	−0.766576	−	1.32775i	−0.939409	−	0.342798i	$-0.888625\pi$
$829$	−22.0715	−	38.2290i	−0.766576	−	1.32775i	0.172833	−	0.984951i	$-0.444708\pi$
$830$		0			0
$831$	28.5314	+	49.4177i	0.989742	+	1.71428i
$832$	−16.1156	−	9.30435i	−0.558708	−	0.322570i
$833$	14.0809	+	8.12959i	0.487873	+	0.281673i
$834$	−1.45724	−	2.52402i	−0.0504602	−	0.0873996i
$835$		0			0
$836$	45.3749	+	78.5916i	1.56932	+	2.71815i
$837$		−	7.52965i		−	0.260263i
$838$	−7.70612	−	4.44913i	−0.266204	−	0.153693i
$839$	−10.7059	−	18.5432i	−0.369609	−	0.640181i	0.619896	−	0.784684i	$-0.287175\pi$
$839$	−10.7059	−	18.5432i	−0.369609	−	0.640181i	−0.989504	+	0.144503i	$0.953842\pi$
$840$		0			0
$841$	46.7465			1.61195
$842$	0.321692	−	0.185729i	0.0110862	−	0.00640065i
$843$			30.3725i			1.04608i
$844$	−14.8229	+	25.6741i	−0.510226	+	0.883738i
$845$		0			0
$846$	−0.700161	+	1.21271i	−0.0240720	+	0.0416940i
$847$	−30.5248	−	17.6235i	−1.04884	−	0.605550i
$848$	22.8943	+	13.2181i	0.786195	+	0.453910i
$849$	15.5845	+	26.9931i	0.534857	+	0.926400i
$850$		0			0
$851$	−14.5364	+	28.4741i	−0.498303	+	0.976080i
$852$			16.3323i			0.559534i
$853$	2.64359	−	1.52628i	0.0905149	−	0.0522588i	−0.454059	−	0.890971i	$-0.650025\pi$
$853$	2.64359	−	1.52628i	0.0905149	−	0.0522588i	0.544574	+	0.838713i	$0.316691\pi$
$854$	−0.466936	+	0.808758i	−0.0159782	+	0.0276751i
$855$		0			0
$856$	1.11754	−	1.93563i	0.0381966	−	0.0661584i
$857$		−	31.3537i		−	1.07102i	−0.844529	−	0.535510i	$-0.820119\pi$
$857$		−	31.3537i		−	1.07102i	0.844529	−	0.535510i	$-0.179881\pi$
$858$	6.74637	+	3.89502i	0.230317	+	0.132974i
$859$	37.7129			1.28675			0.643374	−	0.765552i	$-0.277534\pi$
$859$	37.7129			1.28675			0.643374	+	0.765552i	$0.277534\pi$
$860$		0			0
$861$	−16.0883			−0.548287
$862$		−	2.36227i		−	0.0804592i
$863$	14.7260	−	8.50207i	0.501280	−	0.289414i	−0.227962	−	0.973670i	$-0.573206\pi$
$863$	14.7260	−	8.50207i	0.501280	−	0.289414i	0.729242	+	0.684256i	$0.239873\pi$
$864$	−4.26987	+	7.39563i	−0.145264	+	0.251604i
$865$		0			0
$866$	2.49510	+	4.32164i	0.0847869	+	0.146855i
$867$	−12.6503	+	7.30368i	−0.429628	+	0.248046i
$868$	5.29237	−	3.05555i	0.179635	−	0.103712i
$869$	−8.53680	+	14.7862i	−0.289591	+	0.501586i
$870$		0			0
$871$	0.128424	+	0.222437i	0.00435149	+	0.00753699i
$872$	−8.37022	+	4.83255i	−0.283452	+	0.163651i
$873$	12.3864	−	7.15130i	0.419217	−	0.242035i
$874$	−9.02795			−0.305375
$875$		0			0
$876$	−20.0670	−	34.7571i	−0.678002	−	1.17433i
$877$		−	18.2065i		−	0.614790i	−0.951582	−	0.307395i	$-0.900543\pi$
$877$		−	18.2065i		−	0.614790i	0.951582	−	0.307395i	$-0.0994573\pi$
$878$			7.44151i			0.251139i
$879$	−21.7699	−	37.7065i	−0.734279	−	1.27181i
$880$		0			0
$881$	−0.139401	+	0.241449i	−0.00469652	+	0.00813462i	−0.868364	−	0.495927i	$-0.834828\pi$
$881$	−0.139401	+	0.241449i	−0.00469652	+	0.00813462i	0.863668	+	0.504062i	$0.168162\pi$
$882$		−	1.64884i		−	0.0555195i
$883$	−1.50222	−	0.867309i	−0.0505539	−	0.0291873i	0.474510	−	0.880250i	$-0.342625\pi$
$883$	−1.50222	−	0.867309i	−0.0505539	−	0.0291873i	−0.525064	+	0.851063i	$0.675959\pi$
$884$	−8.43563	+	14.6109i	−0.283721	+	0.491419i
$885$		0			0
$886$	2.38877	+	4.13748i	0.0802524	+	0.139001i
$887$			5.67679i			0.190608i	0.995448	+	0.0953040i	$0.0303823\pi$
$887$			5.67679i			0.190608i	−0.995448	+	0.0953040i	$0.969618\pi$
$888$	−9.50159	+	6.15981i	−0.318853	+	0.206710i
$889$	−12.1484			−0.407445
$890$		0			0
$891$	−34.0828	+	59.0331i	−1.14182	+	1.97768i
$892$	−43.3608	−	25.0344i	−1.45183	−	0.838212i
$893$	−28.9404	−	16.7087i	−0.968453	−	0.559137i
$894$	−8.54101			−0.285654
$895$		0			0
$896$	−9.19930			−0.307327
$897$	26.1497	−	15.0975i	0.873113	−	0.504092i
$898$		−	8.60879i		−	0.287279i
$899$	19.9175			0.664286
$900$		0			0
$901$	11.3276	−	19.6200i	0.377378	−	0.653638i
$902$			7.56150i			0.251770i
$903$	26.6427	−	15.3822i	0.886613	−	0.511886i
$904$	−1.48028	−	2.56391i	−0.0492332	−	0.0852745i
$905$		0			0
$906$	−3.69409	+	6.39836i	−0.122728	+	0.212571i
$907$	29.9569	+	17.2956i	0.994703	+	0.574292i	0.906677	−	0.421826i	$-0.138611\pi$
$907$	29.9569	+	17.2956i	0.994703	+	0.574292i	0.0880261	+	0.996118i	$0.471944\pi$
$908$	0.653102	−	0.377069i	0.0216740	−	0.0125135i
$909$	−3.41926	−	5.92234i	−0.113410	−	0.196431i
$910$		0			0
$911$	7.53582			0.249673			0.124836	−	0.992177i	$-0.460159\pi$
$911$	7.53582			0.249673			0.124836	+	0.992177i	$0.460159\pi$
$912$	51.8633	+	29.9433i	1.71737	+	0.991522i
$913$	58.8816	−	33.9953i	1.94870	−	1.12508i
$914$	−4.07014			−0.134628
$915$		0			0
$916$	16.6325	+	28.8084i	0.549555	+	0.951856i
$917$		−	10.4209i		−	0.344127i
$918$	2.02242	+	1.16765i	0.0667498	+	0.0385380i
$919$	7.50061			0.247422			0.123711	−	0.992318i	$-0.460520\pi$
$919$	7.50061			0.247422			0.123711	+	0.992318i	$0.460520\pi$
$920$		0			0
$921$	−28.7382	+	49.7760i	−0.946955	+	1.64017i
$922$	1.23127	+	0.710873i	0.0405497	+	0.0234114i
$923$	−9.38937	+	5.42096i	−0.309055	+	0.178433i
$924$	−34.0981			−1.12175
$925$		0			0
$926$	−4.97366			−0.163445
$927$	1.22206	−	0.705559i	0.0401378	−	0.0231736i
$928$	−19.5630	−	11.2947i	−0.642187	−	0.370767i
$929$	17.0962	−	29.6116i	0.560910	−	0.971524i	−0.436508	−	0.899700i	$-0.643785\pi$
$929$	17.0962	−	29.6116i	0.560910	−	0.971524i	0.997417	−	0.0718234i	$-0.0228818\pi$
$930$		0			0
$931$	39.3482			1.28959
$932$	−37.8624	−	21.8599i	−1.24023	−	0.716044i
$933$		−	38.5512i		−	1.26211i
$934$	2.88318	+	4.99382i	0.0943407	+	0.163403i
$935$		0			0
$936$	3.46574			0.113281
$937$	31.1800	−	18.0018i	1.01861	−	0.588092i	0.104906	−	0.994482i	$-0.466546\pi$
$937$	31.1800	−	18.0018i	1.01861	−	0.588092i	0.913700	+	0.406390i	$0.133213\pi$
$938$	0.0249888	+	0.0144273i	0.000815913	+	0.000471068i
$939$	39.9206			1.30276
$940$		0			0
$941$	−0.481538	−	0.834048i	−0.0156977	−	0.0271892i	0.858070	−	0.513533i	$-0.171664\pi$
$941$	−0.481538	−	0.834048i	−0.0156977	−	0.0271892i	−0.873768	+	0.486344i	$0.838330\pi$
$942$	−7.06009	+	4.07615i	−0.230030	+	0.132808i
$943$	25.3826	+	14.6546i	0.826570	+	0.477220i
$944$	9.46698	−	16.3973i	0.308124	−	0.533686i
$945$		0			0
$946$	−7.22963	−	12.5221i	−0.235056	−	0.407128i
$947$	−24.7243	+	14.2746i	−0.803431	+	0.463861i	−0.844669	−	0.535288i	$-0.820203\pi$
$947$	−24.7243	+	14.2746i	−0.803431	+	0.463861i	0.0412387	+	0.999149i	$0.486870\pi$
$948$			11.5716i			0.375829i
$949$	13.3212	−	23.0729i	0.432424	−	0.748980i
$950$		0			0
$951$	−4.58685			−0.148739
$952$			3.83931i			0.124433i
$953$	0.719990	−	0.415686i	0.0233228	−	0.0134654i	−0.488293	−	0.872680i	$-0.662380\pi$
$953$	0.719990	−	0.415686i	0.0233228	−	0.0134654i	0.511616	+	0.859214i	$0.329047\pi$
$954$	−2.29747			−0.0743834
$955$		0			0
$956$	17.9195			0.579558
$957$	−96.2447	−	55.5669i	−3.11115	−	1.79622i
$958$	−0.501295	−	0.289423i	−0.0161961	−	0.00935083i
$959$	11.5178	−	19.9495i	0.371931	−	0.644203i
$960$		0			0
$961$	−25.7627			−0.831055
$962$	−3.30508	−	1.68729i	−0.106560	−	0.0544005i
$963$		−	3.63784i		−	0.117228i
$964$	−1.00092	−	1.73365i	−0.0322376	−	0.0558371i
$965$		0			0
$966$	1.69607	−	2.93768i	0.0545702	−	0.0945184i
$967$	−12.5261	−	7.23192i	−0.402811	−	0.232563i	0.284885	−	0.958562i	$-0.408044\pi$
$967$	−12.5261	−	7.23192i	−0.402811	−	0.232563i	−0.687696	+	0.725999i	$0.741378\pi$
$968$			22.7435i			0.731005i
$969$	25.6608	−	44.4459i	0.824345	−	1.42781i
$970$		0			0
$971$	12.5432	+	21.7255i	0.402532	+	0.697205i	0.994031	−	0.109100i	$-0.0347970\pi$
$971$	12.5432	+	21.7255i	0.402532	+	0.697205i	−0.591499	+	0.806306i	$0.701464\pi$
$972$			26.9521i			0.864488i
$973$			8.46861i			0.271491i
$974$	4.33111	+	7.50170i	0.138778	+	0.240370i
$975$		0			0
$976$	−11.2856			−0.361243
$977$	0.799438	−	0.461556i	0.0255763	−	0.0147665i	−0.487157	−	0.873314i	$-0.661966\pi$
$977$	0.799438	−	0.461556i	0.0255763	−	0.0147665i	0.512734	+	0.858548i	$0.328633\pi$
$978$	1.93835	−	1.11911i	0.0619815	−	0.0357851i
$979$	24.5047	+	42.4434i	0.783174	+	1.35650i
$980$		0			0
$981$	−7.86554	+	13.6235i	−0.251127	+	0.434966i
$982$	−0.425051	+	0.245403i	−0.0135639	+	0.00783114i
$983$	−23.4898	+	13.5618i	−0.749207	+	0.432555i	−0.825407	−	0.564538i	$-0.809054\pi$
$983$	−23.4898	+	13.5618i	−0.749207	+	0.432555i	0.0762005	+	0.997093i	$0.475721\pi$
$984$	5.19058	+	8.99034i	0.165469	+	0.286602i
$985$		0			0
$986$	−3.08867	+	5.34973i	−0.0983633	+	0.170370i
$987$	10.8740	−	6.27811i	0.346123	−	0.199834i
$988$			40.8295i			1.29896i
$989$	−56.0458			−1.78215
$990$		0			0
$991$	12.9186			0.410373			0.205186	−	0.978723i	$-0.434220\pi$
$991$	12.9186			0.410373			0.205186	+	0.978723i	$0.434220\pi$
$992$	−5.14408	−	2.96994i	−0.163325	−	0.0942956i
$993$		−	59.6822i		−	1.89396i
$994$	−0.608995	+	1.05481i	−0.0193162	+	0.0334566i
$995$		0			0
$996$	23.0403	−	39.9070i	0.730061	−	1.26450i
$997$	29.4442	−	16.9996i	0.932507	−	0.538383i	0.0449034	−	0.998991i	$-0.485702\pi$
$997$	29.4442	−	16.9996i	0.932507	−	0.538383i	0.887604	+	0.460608i	$0.152369\pi$
$998$			0.100521i			0.00318194i
$999$	9.09990	−	17.8250i	0.287908	−	0.563957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.13		48
5.2	odd	4		925.2.e.e.26.6	yes	24
5.3	odd	4		925.2.e.d.26.7	✓	24
5.4	even	2	inner	925.2.o.d.174.12		48
37.10	even	3	inner	925.2.o.d.824.12		48
185.47	odd	12		925.2.e.e.676.6	yes	24
185.84	even	6	inner	925.2.o.d.824.13		48
185.158	odd	12		925.2.e.d.676.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.7	✓	24	5.3	odd	4
925.2.e.d.676.7	yes	24	185.158	odd	12
925.2.e.e.26.6	yes	24	5.2	odd	4
925.2.e.e.676.6	yes	24	185.47	odd	12
925.2.o.d.174.12		48	5.4	even	2	inner
925.2.o.d.174.13		48	1.1	even	1	trivial
925.2.o.d.824.12		48	37.10	even	3	inner
925.2.o.d.824.13		48	185.84	even	6	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.193739 - 0.111855i) q^{2} +(1.82447 + 1.05336i) q^{3} +(-0.974977 + 1.68871i) q^{4} +0.471293 q^{6} +(-1.18597 - 0.684718i) q^{7} +0.883645i q^{8} +(0.719118 + 1.24555i) q^{9} +O(q^{10})\)	\(q+(0.193739 - 0.111855i) q^{2} +(1.82447 + 1.05336i) q^{3} +(-0.974977 + 1.68871i) q^{4} +0.471293 q^{6} +(-1.18597 - 0.684718i) q^{7} +0.883645i q^{8} +(0.719118 + 1.24555i) q^{9} -6.06122 q^{11} +(-3.55762 + 2.05400i) q^{12} +(-2.36167 - 1.36351i) q^{13} -0.306357 q^{14} +(-1.85111 - 3.20622i) q^{16} +(-2.74767 + 1.58637i) q^{17} +(0.278642 + 0.160874i) q^{18} +(-3.83912 + 6.64955i) q^{19} +(-1.44250 - 2.49849i) q^{21} +(-1.17429 + 0.677978i) q^{22} +5.25584i q^{23} +(-0.930792 + 1.61218i) q^{24} -0.610063 q^{26} -3.29019i q^{27} +(2.31258 - 1.33517i) q^{28} +8.70325 q^{29} +2.28851 q^{31} +(-2.24778 - 1.29776i) q^{32} +(-11.0585 - 6.38462i) q^{33} +(-0.354887 + 0.614682i) q^{34} -2.80449 q^{36} +(5.41761 + 2.76577i) q^{37} +1.71770i q^{38} +(-2.87253 - 4.97536i) q^{39} +(2.78826 - 4.82940i) q^{41} +(-0.558937 - 0.322702i) q^{42} +10.6635i q^{43} +(5.90955 - 10.2356i) q^{44} +(0.587892 + 1.01826i) q^{46} +4.35223i q^{47} -7.79953i q^{48} +(-2.56232 - 4.43808i) q^{49} -6.68405 q^{51} +(4.60515 - 2.65879i) q^{52} +(-6.18394 + 3.57030i) q^{53} +(-0.368024 - 0.637437i) q^{54} +(0.605047 - 1.04797i) q^{56} +(-14.0087 + 8.08791i) q^{57} +(1.68616 - 0.973502i) q^{58} +(2.55710 + 4.42903i) q^{59} +(1.52416 - 2.63992i) q^{61} +(0.443374 - 0.255982i) q^{62} -1.96957i q^{63} +6.82381 q^{64} -2.85661 q^{66} +(-0.0815677 - 0.0470931i) q^{67} -6.18670i q^{68} +(-5.53627 + 9.58910i) q^{69} +(1.98787 - 3.44308i) q^{71} +(-1.10062 + 0.635444i) q^{72} +9.76975i q^{73} +(1.35897 - 0.0701508i) q^{74} +(-7.48610 - 12.9663i) q^{76} +(7.18839 + 4.15022i) q^{77} +(-1.11304 - 0.642613i) q^{78} +(1.40843 - 2.43947i) q^{79} +(5.62309 - 9.73948i) q^{81} -1.24752i q^{82} +(-9.71449 + 5.60866i) q^{83} +5.62563 q^{84} +(1.19277 + 2.06594i) q^{86} +(15.8788 + 9.16762i) q^{87} -5.35596i q^{88} +(-4.04287 - 7.00246i) q^{89} +(1.86724 + 3.23416i) q^{91} +(-8.87559 - 5.12432i) q^{92} +(4.17532 + 2.41062i) q^{93} +(0.486820 + 0.843196i) q^{94} +(-2.73400 - 4.73543i) q^{96} -9.94455i q^{97} +(-0.992842 - 0.573218i) q^{98} +(-4.35873 - 7.54954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) \) 48 * q + 22 * q^4 + 20 * q^9	\( 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Introduction

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