LMFDB - Embedded newform 425.2.m.e.76.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			76.6
Character	$\chi$	$=$	425.76
Dual form			425.2.m.e.151.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.63043 - 1.63043i) q^{2} +(0.718554 - 1.73474i) q^{3} -3.31660i q^{4} +(-1.65683 - 3.99993i) q^{6} +(-1.42808 + 0.591528i) q^{7} +(-2.14663 - 2.14663i) q^{8} +(-0.371694 - 0.371694i) q^{9} +(-1.76717 - 4.26632i) q^{11} +(-5.75346 - 2.38316i) q^{12} +3.51782i q^{13} +(-1.36393 + 3.29282i) q^{14} -0.366652 q^{16} +(-1.14190 + 3.96182i) q^{17} -1.21204 q^{18} +(4.68326 - 4.68326i) q^{19} +2.90239i q^{21} +(-9.83718 - 4.07469i) q^{22} +(0.993477 + 2.39846i) q^{23} +(-5.26632 + 2.18138i) q^{24} +(5.73556 + 5.73556i) q^{26} +(4.29235 - 1.77795i) q^{27} +(1.96187 + 4.73636i) q^{28} +(0.904478 + 0.374647i) q^{29} +(-0.468546 + 1.13117i) q^{31} +(3.69546 - 3.69546i) q^{32} -8.67078 q^{33} +(4.59768 + 8.32127i) q^{34} +(-1.23276 + 1.23276i) q^{36} +(-0.156011 + 0.376644i) q^{37} -15.2714i q^{38} +(6.10251 + 2.52774i) q^{39} +(-9.45483 + 3.91632i) q^{41} +(4.73214 + 4.73214i) q^{42} +(3.00290 + 3.00290i) q^{43} +(-14.1497 + 5.86100i) q^{44} +(5.53032 + 2.29073i) q^{46} +3.99531i q^{47} +(-0.263460 + 0.636048i) q^{48} +(-3.26025 + 3.26025i) q^{49} +(6.05223 + 4.82770i) q^{51} +11.6672 q^{52} +(1.24288 - 1.24288i) q^{53} +(4.09956 - 9.89721i) q^{54} +(4.33534 + 1.79576i) q^{56} +(-4.75907 - 11.4894i) q^{57} +(2.08552 - 0.863853i) q^{58} +(1.10431 + 1.10431i) q^{59} +(12.9280 - 5.35497i) q^{61} +(1.08036 + 2.60823i) q^{62} +(0.750675 + 0.310940i) q^{63} -12.7837i q^{64} +(-14.1371 + 14.1371i) q^{66} -8.84212 q^{67} +(13.1398 + 3.78724i) q^{68} +4.87459 q^{69} +(-0.495735 + 1.19681i) q^{71} +1.59578i q^{72} +(-9.03279 - 3.74150i) q^{73} +(0.359726 + 0.868456i) q^{74} +(-15.5325 - 15.5325i) q^{76} +(5.04730 + 5.04730i) q^{77} +(14.0710 - 5.82841i) q^{78} +(-4.17760 - 10.0856i) q^{79} -10.3007i q^{81} +(-9.03016 + 21.8007i) q^{82} +(-8.97341 + 8.97341i) q^{83} +9.62608 q^{84} +9.79203 q^{86} +(1.29983 - 1.29983i) q^{87} +(-5.36476 + 12.9517i) q^{88} +8.62631i q^{89} +(-2.08089 - 5.02371i) q^{91} +(7.95476 - 3.29497i) q^{92} +(1.62561 + 1.62561i) q^{93} +(6.51407 + 6.51407i) q^{94} +(-3.75529 - 9.06606i) q^{96} +(5.47747 + 2.26884i) q^{97} +10.6312i q^{98} +(-0.928920 + 2.24261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	1.63043	−	1.63043i	1.15289	−	1.15289i	0.166917	−	0.985971i	$-0.446619\pi$
$2$	1.63043	−	1.63043i	1.15289	−	1.15289i	0.985971	−	0.166917i	$-0.0533812\pi$
$3$	0.718554	−	1.73474i	0.414857	−	1.00155i	−0.568957	−	0.822367i	$-0.692653\pi$
$3$	0.718554	−	1.73474i	0.414857	−	1.00155i	0.983815	−	0.179188i	$-0.0573469\pi$
$4$		−	3.31660i		−	1.65830i
$5$		0			0
$5$		0			0
$6$	−1.65683	−	3.99993i	−0.676396	−	1.63296i
$7$	−1.42808	+	0.591528i	−0.539762	+	0.223577i	−0.635873	−	0.771794i	$-0.719360\pi$
$7$	−1.42808	+	0.591528i	−0.539762	+	0.223577i	0.0961108	+	0.995371i	$0.469360\pi$
$8$	−2.14663	−	2.14663i	−0.758948	−	0.758948i
$9$	−0.371694	−	0.371694i	−0.123898	−	0.123898i
$10$		0			0
$11$	−1.76717	−	4.26632i	−0.532821	−	1.28634i	−0.929647	−	0.368451i	$-0.879888\pi$
$11$	−1.76717	−	4.26632i	−0.532821	−	1.28634i	0.396826	−	0.917894i	$-0.370112\pi$
$12$	−5.75346	−	2.38316i	−1.66088	−	0.687959i
$13$			3.51782i			0.975667i	0.872937	+	0.487834i	$0.162213\pi$
$13$			3.51782i			0.975667i	−0.872937	+	0.487834i	$0.837787\pi$
$14$	−1.36393	+	3.29282i	−0.364526	+	0.880044i
$15$		0			0
$16$	−0.366652			−0.0916631
$17$	−1.14190	+	3.96182i	−0.276952	+	0.960884i
$17$	−1.14190	+	3.96182i	−0.276952	+	0.960884i
$18$	−1.21204			−0.285681
$19$	4.68326	−	4.68326i	1.07441	−	1.07441i	0.0774135	−	0.996999i	$-0.475334\pi$
$19$	4.68326	−	4.68326i	1.07441	−	1.07441i	0.996999	−	0.0774135i	$-0.0246662\pi$
$20$		0			0
$21$			2.90239i			0.633353i
$22$	−9.83718	−	4.07469i	−2.09729	−	0.868728i
$23$	0.993477	+	2.39846i	0.207154	+	0.500114i	0.992973	−	0.118343i	$-0.0377581\pi$
$23$	0.993477	+	2.39846i	0.207154	+	0.500114i	−0.785819	+	0.618457i	$0.787758\pi$
$24$	−5.26632	+	2.18138i	−1.07498	+	0.445273i
$25$		0			0
$26$	5.73556	+	5.73556i	1.12483	+	1.12483i
$27$	4.29235	−	1.77795i	0.826064	−	0.342167i
$28$	1.96187	+	4.73636i	0.370758	+	0.895088i
$29$	0.904478	+	0.374647i	0.167957	+	0.0695702i	0.465078	−	0.885270i	$-0.346026\pi$
$29$	0.904478	+	0.374647i	0.167957	+	0.0695702i	−0.297120	+	0.954840i	$0.596026\pi$
$30$		0			0
$31$	−0.468546	+	1.13117i	−0.0841534	+	0.203164i	−0.960355	−	0.278781i	$-0.910070\pi$
$31$	−0.468546	+	1.13117i	−0.0841534	+	0.203164i	0.876201	+	0.481945i	$0.160070\pi$
$32$	3.69546	−	3.69546i	0.653271	−	0.653271i
$33$	−8.67078			−1.50939
$34$	4.59768	+	8.32127i	0.788496	+	1.42709i
$35$		0			0
$36$	−1.23276	+	1.23276i	−0.205460	+	0.205460i
$37$	−0.156011	+	0.376644i	−0.0256480	+	0.0619198i	−0.936185	−	0.351509i	$-0.885669\pi$
$37$	−0.156011	+	0.376644i	−0.0256480	+	0.0619198i	0.910537	+	0.413428i	$0.135669\pi$
$38$		−	15.2714i		−	2.47735i
$39$	6.10251	+	2.52774i	0.977184	+	0.404763i
$40$		0			0
$41$	−9.45483	+	3.91632i	−1.47660	+	0.611626i	−0.968353	−	0.249586i	$-0.919705\pi$
$41$	−9.45483	+	3.91632i	−1.47660	+	0.611626i	−0.508244	+	0.861213i	$0.669705\pi$
$42$	4.73214	+	4.73214i	0.730186	+	0.730186i
$43$	3.00290	+	3.00290i	0.457938	+	0.457938i	0.897978	−	0.440040i	$-0.145036\pi$
$43$	3.00290	+	3.00290i	0.457938	+	0.457938i	−0.440040	+	0.897978i	$0.645036\pi$
$44$	−14.1497	+	5.86100i	−2.13315	+	0.883579i
$45$		0			0
$46$	5.53032	+	2.29073i	0.815402	+	0.337750i
$47$			3.99531i			0.582776i	0.956605	+	0.291388i	$0.0941171\pi$
$47$			3.99531i			0.582776i	−0.956605	+	0.291388i	$0.905883\pi$
$48$	−0.263460	+	0.636048i	−0.0380271	+	0.0918056i
$49$	−3.26025	+	3.26025i	−0.465750	+	0.465750i
$50$		0			0
$51$	6.05223	+	4.82770i	0.847482	+	0.676013i
$52$	11.6672			1.61795
$53$	1.24288	−	1.24288i	0.170723	−	0.170723i	−0.616574	−	0.787297i	$-0.711480\pi$
$53$	1.24288	−	1.24288i	0.170723	−	0.170723i	0.787297	+	0.616574i	$0.211480\pi$
$54$	4.09956	−	9.89721i	0.557879	−	1.34684i
$55$		0			0
$56$	4.33534	+	1.79576i	0.579335	+	0.239968i
$57$	−4.75907	−	11.4894i	−0.630355	−	1.52181i
$58$	2.08552	−	0.863853i	0.273843	−	0.113429i
$59$	1.10431	+	1.10431i	0.143769	+	0.143769i	0.775328	−	0.631559i	$-0.217585\pi$
$59$	1.10431	+	1.10431i	0.143769	+	0.143769i	−0.631559	+	0.775328i	$0.717585\pi$
$60$		0			0
$61$	12.9280	−	5.35497i	1.65527	−	0.685634i	0.657566	−	0.753397i	$-0.271586\pi$
$61$	12.9280	−	5.35497i	1.65527	−	0.685634i	0.997701	+	0.0677633i	$0.0215863\pi$
$62$	1.08036	+	2.60823i	0.137206	+	0.331245i
$63$	0.750675	+	0.310940i	0.0945761	+	0.0391747i
$64$		−	12.7837i		−	1.59796i
$65$		0			0
$66$	−14.1371	+	14.1371i	−1.74016	+	1.74016i
$67$	−8.84212			−1.08024			−0.540119	−	0.841589i	$-0.681621\pi$
$67$	−8.84212			−1.08024			−0.540119	+	0.841589i	$0.681621\pi$
$68$	13.1398	+	3.78724i	1.59344	+	0.459271i
$69$	4.87459			0.586831
$70$		0			0
$71$	−0.495735	+	1.19681i	−0.0588329	+	0.142035i	−0.950562	−	0.310534i	$-0.899492\pi$
$71$	−0.495735	+	1.19681i	−0.0588329	+	0.142035i	0.891730	+	0.452569i	$0.149492\pi$
$72$			1.59578i			0.188064i
$73$	−9.03279	−	3.74150i	−1.05721	−	0.437910i	−0.214748	−	0.976669i	$-0.568893\pi$
$73$	−9.03279	−	3.74150i	−1.05721	−	0.437910i	−0.842460	+	0.538760i	$0.818893\pi$
$74$	0.359726	+	0.868456i	0.0418173	+	0.100956i
$75$		0			0
$76$	−15.5325	−	15.5325i	−1.78170	−	1.78170i
$77$	5.04730	+	5.04730i	0.575193	+	0.575193i
$78$	14.0710	−	5.82841i	1.59323	−	0.659937i
$79$	−4.17760	−	10.0856i	−0.470017	−	1.13472i	−0.964155	−	0.265338i	$-0.914516\pi$
$79$	−4.17760	−	10.0856i	−0.470017	−	1.13472i	0.494139	−	0.869383i	$-0.335484\pi$
$80$		0			0
$81$		−	10.3007i		−	1.14452i
$82$	−9.03016	+	21.8007i	−0.997214	+	2.40749i
$83$	−8.97341	+	8.97341i	−0.984959	+	0.984959i	−0.999889	−	0.0149292i	$-0.995248\pi$
$83$	−8.97341	+	8.97341i	−0.984959	+	0.984959i	0.0149292	+	0.999889i	$0.495248\pi$
$84$	9.62608			1.05029
$85$		0			0
$86$	9.79203			1.05590
$87$	1.29983	−	1.29983i	0.139357	−	0.139357i
$88$	−5.36476	+	12.9517i	−0.571885	+	1.38065i
$89$			8.62631i			0.914387i	0.889367	+	0.457193i	$0.151145\pi$
$89$			8.62631i			0.914387i	−0.889367	+	0.457193i	$0.848855\pi$
$90$		0			0
$91$	−2.08089	−	5.02371i	−0.218136	−	0.526628i
$92$	7.95476	−	3.29497i	0.829341	−	0.343524i
$93$	1.62561	+	1.62561i	0.168568	+	0.168568i
$94$	6.51407	+	6.51407i	0.671875	+	0.671875i
$95$		0			0
$96$	−3.75529	−	9.06606i	−0.383272	−	0.925301i
$97$	5.47747	+	2.26884i	0.556152	+	0.230366i	0.643014	−	0.765855i	$-0.277684\pi$
$97$	5.47747	+	2.26884i	0.556152	+	0.230366i	−0.0868615	+	0.996220i	$0.527684\pi$
$98$			10.6312i			1.07392i
$99$	−0.928920	+	2.24261i	−0.0933600	+	0.225391i
$100$		0			0
$101$	5.79390			0.576515			0.288257	−	0.957553i	$-0.406924\pi$
$101$	5.79390			0.576515			0.288257	+	0.957553i	$0.406924\pi$
$102$	17.7390	−	1.99652i	1.75642	−	0.197685i
$103$	6.99141			0.688885			0.344442	−	0.938807i	$-0.388068\pi$
$103$	6.99141			0.688885			0.344442	+	0.938807i	$0.388068\pi$
$104$	7.55145	−	7.55145i	0.740481	−	0.740481i
$105$		0			0
$106$		−	4.05286i		−	0.393649i
$107$	−1.29113	−	0.534802i	−0.124818	−	0.0517013i	0.319400	−	0.947620i	$-0.396519\pi$
$107$	−1.29113	−	0.534802i	−0.124818	−	0.0517013i	−0.444218	+	0.895919i	$0.646519\pi$
$108$	−5.89676	−	14.2360i	−0.567416	−	1.36986i
$109$	−10.0234	+	4.15183i	−0.960068	+	0.397673i	−0.807006	−	0.590543i	$-0.798914\pi$
$109$	−10.0234	+	4.15183i	−0.960068	+	0.397673i	−0.153062	+	0.988217i	$0.548914\pi$
$110$		0			0
$111$	0.541278	+	0.541278i	0.0513758	+	0.0513758i
$112$	0.523607	−	0.216885i	0.0494762	−	0.0204937i
$113$	−1.52342	−	3.67787i	−0.143312	−	0.345985i	0.835883	−	0.548907i	$-0.184956\pi$
$113$	−1.52342	−	3.67787i	−0.143312	−	0.345985i	−0.979195	+	0.202923i	$0.934956\pi$
$114$	−26.4920	−	10.9734i	−2.48121	−	1.02775i
$115$		0			0
$116$	1.24256	−	2.99980i	0.115368	−	0.278524i
$117$	1.30755	−	1.30755i	0.120883	−	0.120883i
$118$	3.60100			0.331499
$119$	−0.712807	−	6.33325i	−0.0653429	−	0.580568i
$120$		0			0
$121$	−7.30044	+	7.30044i	−0.663677	+	0.663677i
$122$	12.3474	−	29.8092i	1.11788	−	2.69880i
$123$			19.2158i			1.73263i
$124$	3.75164	+	1.55398i	0.336908	+	0.139552i
$125$		0			0
$126$	1.73089	−	0.716957i	0.154200	−	0.0638716i
$127$	8.82196	+	8.82196i	0.782822	+	0.782822i	0.980306	−	0.197484i	$-0.0632770\pi$
$127$	8.82196	+	8.82196i	0.782822	+	0.782822i	−0.197484	+	0.980306i	$0.563277\pi$
$128$	−13.4520	−	13.4520i	−1.18900	−	1.18900i
$129$	7.36700	−	3.05151i	0.648629	−	0.268671i
$130$		0			0
$131$	−7.19402	−	2.97986i	−0.628544	−	0.260352i	0.0455901	−	0.998960i	$-0.485483\pi$
$131$	−7.19402	−	2.97986i	−0.628544	−	0.260352i	−0.674134	+	0.738609i	$0.735483\pi$
$132$			28.7575i			2.50302i
$133$	−3.91777	+	9.45832i	−0.339713	+	0.820141i
$134$	−14.4165	+	14.4165i	−1.24539	+	1.24539i
$135$		0			0
$136$	10.9558	−	6.05333i	0.939454	−	0.519069i
$137$	−15.2375			−1.30182			−0.650912	−	0.759153i	$-0.725613\pi$
$137$	−15.2375			−1.30182			−0.650912	+	0.759153i	$0.725613\pi$
$138$	7.94767	−	7.94767i	0.676551	−	0.676551i
$139$	0.0176413	−	0.0425899i	0.00149632	−	0.00361243i	−0.923130	−	0.384489i	$-0.874378\pi$
$139$	0.0176413	−	0.0425899i	0.00149632	−	0.00361243i	0.924626	+	0.380876i	$0.124378\pi$
$140$		0			0
$141$	6.93084	+	2.87085i	0.583682	+	0.241769i
$142$	1.14305	+	2.75957i	0.0959229	+	0.231578i
$143$	15.0081	−	6.21658i	1.25504	−	0.519856i
$144$	0.136282	+	0.136282i	0.0113569	+	0.0113569i
$145$		0			0
$146$	−20.8276	+	8.62707i	−1.72370	+	0.713981i
$147$	3.31303	+	7.99837i	0.273254	+	0.659694i
$148$	1.24918	+	0.517426i	0.102682	+	0.0425322i
$149$			1.49474i			0.122454i	0.998124	+	0.0612268i	$0.0195013\pi$
$149$			1.49474i			0.122454i	−0.998124	+	0.0612268i	$0.980499\pi$
$150$		0			0
$151$	3.73457	−	3.73457i	0.303915	−	0.303915i	−0.538629	−	0.842543i	$-0.681057\pi$
$151$	3.73457	−	3.73457i	0.303915	−	0.303915i	0.842543	+	0.538629i	$0.181057\pi$
$152$	−20.1064			−1.63085
$153$	1.89702	−	1.04815i	0.153365	−	0.0847377i
$154$	16.4585			1.32627
$155$		0			0
$156$	8.38352	−	20.2396i	0.671219	−	1.62047i
$157$		−	12.6990i		−	1.01349i	−0.862096	−	0.506745i	$-0.830848\pi$
$157$		−	12.6990i		−	1.01349i	0.862096	−	0.506745i	$-0.169152\pi$
$158$	−23.2552	−	9.63261i	−1.85008	−	0.766329i
$159$	−1.26300	−	3.04916i	−0.100163	−	0.241814i
$160$		0			0
$161$	−2.83752	−	2.83752i	−0.223628	−	0.223628i
$162$	−16.7945	−	16.7945i	−1.31950	−	1.31950i
$163$	−3.75157	+	1.55395i	−0.293846	+	0.121715i	−0.524736	−	0.851265i	$-0.675836\pi$
$163$	−3.75157	+	1.55395i	−0.293846	+	0.121715i	0.230890	+	0.972980i	$0.425836\pi$
$164$	12.9889	+	31.3579i	1.01426	+	2.44864i
$165$		0			0
$166$			29.2610i			2.27110i
$167$	−6.18724	+	14.9373i	−0.478783	+	1.15589i	0.481397	+	0.876503i	$0.340130\pi$
$167$	−6.18724	+	14.9373i	−0.478783	+	1.15589i	−0.960180	+	0.279382i	$0.909870\pi$
$168$	6.23036	−	6.23036i	0.480683	−	0.480683i
$169$	0.624957			0.0480736
$170$		0			0
$171$	−3.48148			−0.266235
$172$	9.95942	−	9.95942i	0.759399	−	0.759399i
$173$	0.603220	−	1.45630i	0.0458620	−	0.110721i	−0.899288	−	0.437356i	$-0.855915\pi$
$173$	0.603220	−	1.45630i	0.0458620	−	0.110721i	0.945150	+	0.326635i	$0.105915\pi$
$174$		−	4.23857i		−	0.321326i
$175$		0			0
$176$	0.647936	+	1.56426i	0.0488400	+	0.117910i
$177$	2.70920	−	1.12219i	0.203636	−	0.0843489i
$178$	14.0646	+	14.0646i	1.05419	+	1.05419i
$179$	−2.43803	−	2.43803i	−0.182227	−	0.182227i	0.610099	−	0.792325i	$-0.291130\pi$
$179$	−2.43803	−	2.43803i	−0.182227	−	0.182227i	−0.792325	+	0.610099i	$0.791130\pi$
$180$		0			0
$181$	5.63559	+	13.6055i	0.418890	+	1.01129i	0.982670	+	0.185365i	$0.0593466\pi$
$181$	5.63559	+	13.6055i	0.418890	+	1.01129i	−0.563780	+	0.825925i	$0.690653\pi$
$182$	−11.5836	−	4.79806i	−0.858630	−	0.355656i
$183$		−	26.2747i		−	1.94228i
$184$	3.01599	−	7.28124i	0.222342	−	0.536780i
$185$		0			0
$186$	5.30090			0.388681
$187$	18.9204	−	2.12948i	1.38359	−	0.155723i
$188$	13.2509			0.966418
$189$	−5.07810	+	5.07810i	−0.369377	+	0.369377i
$190$		0			0
$191$			15.5715i			1.12671i	0.826214	+	0.563356i	$0.190490\pi$
$191$			15.5715i			1.12671i	−0.826214	+	0.563356i	$0.809510\pi$
$192$	−22.1764	−	9.18577i	−1.60044	−	0.662926i
$193$	0.0405694	+	0.0979433i	0.00292025	+	0.00705011i	0.925333	−	0.379156i	$-0.123785\pi$
$193$	0.0405694	+	0.0979433i	0.00292025	+	0.00705011i	−0.922413	+	0.386206i	$0.873785\pi$
$194$	12.6298	−	5.23144i	0.906768	−	0.375595i
$195$		0			0
$196$	10.8130	+	10.8130i	0.772355	+	0.772355i
$197$	−9.74194	+	4.03524i	−0.694085	+	0.287499i	−0.701701	−	0.712472i	$-0.747576\pi$
$197$	−9.74194	+	4.03524i	−0.694085	+	0.287499i	0.00761621	+	0.999971i	$0.497576\pi$
$198$	2.14188	+	5.17096i	0.152217	+	0.367484i
$199$	−1.06359	−	0.440552i	−0.0753957	−	0.0312299i	0.344667	−	0.938725i	$-0.387992\pi$
$199$	−1.06359	−	0.440552i	−0.0753957	−	0.0312299i	−0.420063	+	0.907495i	$0.637992\pi$
$200$		0			0
$201$	−6.35355	+	15.3388i	−0.448145	+	1.08192i
$202$	9.44655	−	9.44655i	0.664657	−	0.664657i
$203$	−1.51328			−0.106211
$204$	16.0116	−	20.0728i	1.12103	−	1.40538i
$205$		0			0
$206$	11.3990	−	11.3990i	0.794207	−	0.794207i
$207$	0.522226	−	1.26076i	0.0362972	−	0.0876291i
$208$		−	1.28982i		−	0.0894327i
$209$	−28.2564	−	11.7042i	−1.95453	−	0.809595i
$210$		0			0
$211$	−3.86883	+	1.60252i	−0.266341	+	0.110322i	−0.511858	−	0.859070i	$-0.671042\pi$
$211$	−3.86883	+	1.60252i	−0.266341	+	0.110322i	0.245516	+	0.969392i	$0.421042\pi$
$212$	−4.12214	−	4.12214i	−0.283110	−	0.283110i
$213$	1.71994	+	1.71994i	0.117849	+	0.117849i
$214$	−2.97705	+	1.23313i	−0.203507	+	0.0842954i
$215$		0			0
$216$	−13.0307	−	5.39749i	−0.886627	−	0.367253i
$217$		−	1.89256i		−	0.128475i
$218$	−9.57319	+	23.1117i	−0.648378	+	1.56532i
$219$	−12.9811	+	12.9811i	−0.877181	+	0.877181i
$220$		0			0
$221$	−13.9370	−	4.01701i	−0.937503	−	0.270213i
$222$	1.76503			0.118461
$223$	−5.40538	+	5.40538i	−0.361971	+	0.361971i	−0.864538	−	0.502567i	$-0.832389\pi$
$223$	−5.40538	+	5.40538i	−0.361971	+	0.361971i	0.502567	+	0.864538i	$0.332389\pi$
$224$	−3.09143	+	7.46336i	−0.206555	+	0.498667i
$225$		0			0
$226$	−8.48034	−	3.51267i	−0.564104	−	0.233660i
$227$	−9.13285	−	22.0487i	−0.606169	−	1.46342i	−0.867135	−	0.498073i	$-0.834041\pi$
$227$	−9.13285	−	22.0487i	−0.606169	−	1.46342i	0.260967	−	0.965348i	$-0.415959\pi$
$228$	−38.1059	+	15.7840i	−2.52362	+	1.04532i
$229$	9.73973	+	9.73973i	0.643620	+	0.643620i	0.951443	−	0.307824i	$-0.0996007\pi$
$229$	9.73973	+	9.73973i	0.643620	+	0.643620i	−0.307824	+	0.951443i	$0.599601\pi$
$230$		0			0
$231$	12.3825	−	5.12901i	0.814711	−	0.337464i
$232$	−1.13735	−	2.74581i	−0.0746708	−	0.180271i
$233$	5.37022	+	2.22442i	0.351815	+	0.145727i	0.551590	−	0.834115i	$-0.314021\pi$
$233$	5.37022	+	2.22442i	0.351815	+	0.145727i	−0.199775	+	0.979842i	$0.564021\pi$
$234$		−	4.26374i		−	0.278730i
$235$		0			0
$236$	3.66256	−	3.66256i	0.238412	−	0.238412i
$237$	−20.4978			−1.33147
$238$	−11.4881	−	9.16375i	−0.744663	−	0.593997i
$239$	−5.09183			−0.329363			−0.164682	−	0.986347i	$-0.552660\pi$
$239$	−5.09183			−0.329363			−0.164682	+	0.986347i	$0.552660\pi$
$240$		0			0
$241$	−2.03293	+	4.90792i	−0.130952	+	0.316147i	−0.975732	−	0.218967i	$-0.929731\pi$
$241$	−2.03293	+	4.90792i	−0.130952	+	0.316147i	0.844780	+	0.535114i	$0.179731\pi$
$242$			23.8057i			1.53029i
$243$	−4.99192	−	2.06772i	−0.320232	−	0.132644i
$244$	−17.7603	−	42.8772i	−1.13699	−	2.74493i
$245$		0			0
$246$	31.3300	+	31.3300i	1.99753	+	1.99753i
$247$	16.4748	+	16.4748i	1.04827	+	1.04827i
$248$	3.43400	−	1.42241i	0.218059	−	0.0903231i
$249$	9.11868	+	22.0144i	0.577873	+	1.39511i
$250$		0			0
$251$		−	28.2032i		−	1.78017i	−0.455797	−	0.890084i	$-0.650646\pi$
$251$		−	28.2032i		−	1.78017i	0.455797	−	0.890084i	$-0.349354\pi$
$252$	1.03126	−	2.48969i	0.0649635	−	0.156836i
$253$	8.47698	−	8.47698i	0.532943	−	0.532943i
$254$	28.7672			1.80501
$255$		0			0
$256$	−18.2976			−1.14360
$257$	−2.32880	+	2.32880i	−0.145267	+	0.145267i	−0.776000	−	0.630733i	$-0.782754\pi$
$257$	−2.32880	+	2.32880i	−0.145267	+	0.145267i	0.630733	+	0.776000i	$0.282754\pi$
$258$	7.03611	−	16.9867i	0.438049	−	1.05754i
$259$		−	0.630161i		−	0.0391563i
$260$		0			0
$261$	−0.196935	−	0.475443i	−0.0121900	−	0.0294292i
$262$	−16.5878	+	6.87089i	−1.02480	+	0.424485i
$263$	−19.6841	−	19.6841i	−1.21377	−	1.21377i	−0.969776	−	0.243997i	$-0.921541\pi$
$263$	−19.6841	−	19.6841i	−1.21377	−	1.21377i	−0.243997	−	0.969776i	$-0.578459\pi$
$264$	18.6130	+	18.6130i	1.14555	+	1.14555i
$265$		0			0
$266$	9.03349	+	21.8088i	0.553879	+	1.33718i
$267$	14.9644	+	6.19847i	0.915808	+	0.379340i
$268$			29.3258i			1.79136i
$269$	5.61079	−	13.5456i	0.342096	−	0.825892i	−0.655408	−	0.755275i	$-0.727503\pi$
$269$	5.61079	−	13.5456i	0.342096	−	0.825892i	0.997504	−	0.0706169i	$-0.0224968\pi$
$270$		0			0
$271$	−2.50962			−0.152449			−0.0762244	−	0.997091i	$-0.524287\pi$
$271$	−2.50962			−0.152449			−0.0762244	+	0.997091i	$0.524287\pi$
$272$	0.418682	−	1.45261i	0.0253863	−	0.0880776i
$273$	−10.2101			−0.617942
$274$	−24.8436	+	24.8436i	−1.50086	+	1.50086i
$275$		0			0
$276$		−	16.1671i		−	0.973144i
$277$	−22.1415	−	9.17130i	−1.33035	−	0.551050i	−0.399596	−	0.916691i	$-0.630850\pi$
$277$	−22.1415	−	9.17130i	−1.33035	−	0.551050i	−0.930756	+	0.365641i	$0.880850\pi$
$278$	−0.0406769	−	0.0982028i	−0.00243964	−	0.00588981i
$279$	0.594605	−	0.246293i	0.0355981	−	0.0147452i
$280$		0			0
$281$	−10.0556	−	10.0556i	−0.599865	−	0.599865i	0.340411	−	0.940277i	$-0.389434\pi$
$281$	−10.0556	−	10.0556i	−0.599865	−	0.599865i	−0.940277	+	0.340411i	$0.889434\pi$
$282$	15.9810	−	6.61953i	0.951652	−	0.394187i
$283$	3.83106	+	9.24901i	0.227733	+	0.549796i	0.995901	−	0.0904523i	$-0.0288313\pi$
$283$	3.83106	+	9.24901i	0.227733	+	0.549796i	−0.768168	+	0.640249i	$0.778831\pi$
$284$	3.96934	+	1.64416i	0.235537	+	0.0975627i
$285$		0			0
$286$	14.3340	−	34.6054i	0.847589	−	2.04626i
$287$	11.1856	−	11.1856i	0.660265	−	0.660265i
$288$	−2.74716			−0.161878
$289$	−14.3921	−	9.04804i	−0.846595	−	0.532238i
$290$		0			0
$291$	7.87171	−	7.87171i	0.461448	−	0.461448i
$292$	−12.4091	+	29.9582i	−0.726187	+	1.75317i
$293$		−	11.2943i		−	0.659821i	−0.944012	−	0.329910i	$-0.892981\pi$
$293$		−	11.2943i		−	0.659821i	0.944012	−	0.329910i	$-0.107019\pi$
$294$	18.4425	+	7.63911i	1.07559	+	0.445522i
$295$		0			0
$296$	1.14341	−	0.473617i	0.0664595	−	0.0275284i
$297$	−15.1706	−	15.1706i	−0.880289	−	0.880289i
$298$	2.43706	+	2.43706i	0.141175	+	0.141175i
$299$	−8.43736	+	3.49487i	−0.487945	+	0.202114i
$300$		0			0
$301$	−6.06467	−	2.51207i	−0.349562	−	0.144793i
$302$		−	12.1779i		−	0.700759i
$303$	4.16323	−	10.0509i	0.239171	−	0.577411i
$304$	−1.71713	+	1.71713i	−0.0984840	+	0.0984840i
$305$		0			0
$306$	1.38403	−	4.80190i	0.0791200	−	0.274506i
$307$	25.1396			1.43479			0.717397	−	0.696664i	$-0.245333\pi$
$307$	25.1396			1.43479			0.717397	+	0.696664i	$0.245333\pi$
$308$	16.7399	−	16.7399i	0.953844	−	0.953844i
$309$	5.02371	−	12.1283i	0.285789	−	0.689955i
$310$		0			0
$311$	−20.6277	−	8.54428i	−1.16969	−	0.484502i	−0.288600	−	0.957450i	$-0.593190\pi$
$311$	−20.6277	−	8.54428i	−1.16969	−	0.484502i	−0.881090	+	0.472948i	$0.843190\pi$
$312$	−7.67370	−	18.5260i	−0.434438	−	1.04883i
$313$	27.4658	−	11.3767i	1.55246	−	0.643049i	0.568699	−	0.822546i	$-0.307447\pi$
$313$	27.4658	−	11.3767i	1.55246	−	0.643049i	0.983759	+	0.179496i	$0.0574469\pi$
$314$	−20.7048	−	20.7048i	−1.16844	−	1.16844i
$315$		0			0
$316$	−33.4500	+	13.8554i	−1.88171	+	0.779430i
$317$	−4.55229	−	10.9902i	−0.255682	−	0.617271i	0.742962	−	0.669334i	$-0.233420\pi$
$317$	−4.55229	−	10.9902i	−0.255682	−	0.617271i	−0.998644	+	0.0520626i	$0.983420\pi$
$318$	−7.03067	−	2.91220i	−0.394261	−	0.163308i
$319$		−	4.52086i		−	0.253120i
$320$		0			0
$321$	−1.85549	+	1.85549i	−0.103563	+	0.103563i
$322$	−9.25275			−0.515636
$323$	13.2064	+	23.9021i	0.734824	+	1.32995i
$324$	−34.1632			−1.89795
$325$		0			0
$326$	−3.58307	+	8.65029i	−0.198448	+	0.479095i
$327$			20.3714i			1.12654i
$328$	28.7029	+	11.8891i	1.58485	+	0.656468i
$329$	−2.36334	−	5.70561i	−0.130295	−	0.314560i
$330$		0			0
$331$	6.46861	+	6.46861i	0.355547	+	0.355547i	0.862169	−	0.506621i	$-0.169106\pi$
$331$	6.46861	+	6.46861i	0.355547	+	0.355547i	−0.506621	+	0.862169i	$0.669106\pi$
$332$	29.7612	+	29.7612i	1.63336	+	1.63336i
$333$	0.197984	−	0.0820079i	0.0108495	−	0.00449400i
$334$	14.2664	+	34.4421i	0.780623	+	1.88459i
$335$		0			0
$336$		−	1.06417i		−	0.0580551i
$337$	8.23886	−	19.8904i	0.448799	−	1.08350i	−0.523973	−	0.851735i	$-0.675551\pi$
$337$	8.23886	−	19.8904i	0.448799	−	1.08350i	0.972772	−	0.231763i	$-0.0744493\pi$
$338$	1.01895	−	1.01895i	0.0554235	−	0.0554235i
$339$	−7.47482			−0.405977
$340$		0			0
$341$	5.65394			0.306178
$342$	−5.67630	+	5.67630i	−0.306939	+	0.306939i
$343$	6.86805	−	16.5810i	0.370840	−	0.895287i
$344$		−	12.8922i		−	0.695102i
$345$		0			0
$346$	−1.39089	−	3.35791i	−0.0747748	−	0.180522i
$347$	5.04551	−	2.08992i	0.270857	−	0.112193i	−0.243121	−	0.969996i	$-0.578171\pi$
$347$	5.04551	−	2.08992i	0.270857	−	0.112193i	0.513978	+	0.857803i	$0.328171\pi$
$348$	−4.31103	−	4.31103i	−0.231096	−	0.231096i
$349$	23.3519	+	23.3519i	1.25000	+	1.25000i	0.955719	+	0.294280i	$0.0950800\pi$
$349$	23.3519	+	23.3519i	1.25000	+	1.25000i	0.294280	+	0.955719i	$0.404920\pi$
$350$		0			0
$351$	6.25451	+	15.0997i	0.333841	+	0.805963i
$352$	−22.2965	−	9.23552i	−1.18841	−	0.492255i
$353$		−	12.4962i		−	0.665103i	−0.943085	−	0.332552i	$-0.892090\pi$
$353$		−	12.4962i		−	0.665103i	0.943085	−	0.332552i	$-0.107910\pi$
$354$	2.58752	−	6.24682i	0.137525	−	0.332015i
$355$		0			0
$356$	28.6100			1.51633
$357$	−11.4988	−	3.31425i	−0.608579	−	0.175409i
$358$	−7.95007			−0.420174
$359$	12.8609	−	12.8609i	0.678775	−	0.678775i	−0.280948	−	0.959723i	$-0.590649\pi$
$359$	12.8609	−	12.8609i	0.678775	−	0.678775i	0.959723	+	0.280948i	$0.0906489\pi$
$360$		0			0
$361$		−	24.8658i		−	1.30872i
$362$	31.3713	+	12.9944i	1.64884	+	0.682971i
$363$	7.41863	+	17.9102i	0.389377	+	0.940040i
$364$	−16.6617	+	6.90148i	−0.873308	+	0.361736i
$365$		0			0
$366$	−42.8390	−	42.8390i	−2.23923	−	2.23923i
$367$	21.0350	−	8.71298i	1.09802	−	0.454814i	0.241222	−	0.970470i	$-0.422452\pi$
$367$	21.0350	−	8.71298i	1.09802	−	0.454814i	0.856796	+	0.515656i	$0.172452\pi$
$368$	−0.364260	−	0.879403i	−0.0189884	−	0.0458420i
$369$	4.96998	+	2.05863i	0.258727	+	0.107168i
$370$		0			0
$371$	−1.03973	+	2.51013i	−0.0539800	+	0.130319i
$372$	5.39152	−	5.39152i	0.279537	−	0.279537i
$373$	−24.5550			−1.27141			−0.635705	−	0.771932i	$-0.719291\pi$
$373$	−24.5550			−1.27141			−0.635705	+	0.771932i	$0.719291\pi$
$374$	27.3763	−	34.3203i	1.41560	−	1.77466i
$375$		0			0
$376$	8.57645	−	8.57645i	0.442297	−	0.442297i
$377$	−1.31794	+	3.18179i	−0.0678774	+	0.163871i
$378$			16.5590i			0.851701i
$379$	17.2403	+	7.14115i	0.885573	+	0.366816i	0.778656	−	0.627451i	$-0.215902\pi$
$379$	17.2403	+	7.14115i	0.885573	+	0.366816i	0.106918	+	0.994268i	$0.465902\pi$
$380$		0			0
$381$	21.6429	−	8.96478i	1.10880	−	0.459280i
$382$	25.3882	+	25.3882i	1.29897	+	1.29897i
$383$	18.1834	+	18.1834i	0.929126	+	0.929126i	0.997650	−	0.0685233i	$-0.0218288\pi$
$383$	18.1834	+	18.1834i	0.929126	+	0.929126i	−0.0685233	+	0.997650i	$0.521829\pi$
$384$	−33.0017	+	13.6698i	−1.68411	+	0.697582i
$385$		0			0
$386$	0.225835	+	0.0935440i	0.0114947	+	0.00476127i
$387$		−	2.23232i		−	0.113475i
$388$	7.52485	−	18.1666i	0.382016	−	0.922269i
$389$	16.9576	−	16.9576i	0.859782	−	0.859782i	−0.131530	−	0.991312i	$-0.541989\pi$
$389$	16.9576	−	16.9576i	0.859782	−	0.859782i	0.991312	+	0.131530i	$0.0419890\pi$
$390$		0			0
$391$	−10.6368	+	1.19716i	−0.537924	+	0.0605432i
$392$	13.9971			0.706961
$393$	−10.3386	+	10.3386i	−0.521513	+	0.521513i
$394$	−9.30437	+	22.4627i	−0.468747	+	1.13166i
$395$		0			0
$396$	7.43785	+	3.08086i	0.373766	+	0.154819i
$397$	5.47839	+	13.2260i	0.274953	+	0.663794i	0.999681	−	0.0252400i	$-0.00803499\pi$
$397$	5.47839	+	13.2260i	0.274953	+	0.663794i	−0.724729	+	0.689034i	$0.758035\pi$
$398$	−2.45239	+	1.01581i	−0.122927	+	0.0509182i
$399$	13.5926	+	13.5926i	0.680483	+	0.680483i
$400$		0			0
$401$	−2.72816	+	1.13004i	−0.136238	+	0.0564316i	−0.449761	−	0.893149i	$-0.648491\pi$
$401$	−2.72816	+	1.13004i	−0.136238	+	0.0564316i	0.313523	+	0.949581i	$0.398491\pi$
$402$	14.6499	+	35.3679i	0.730668	+	1.76399i
$403$	−3.97925	−	1.64826i	−0.198221	−	0.0821057i
$404$		−	19.2161i		−	0.956036i
$405$		0			0
$406$	−2.46729	+	2.46729i	−0.122450	+	0.122450i
$407$	1.88258			0.0933161
$408$	−2.62862	−	23.3552i	−0.130136	−	1.15625i
$409$	−2.54353			−0.125769			−0.0628846	−	0.998021i	$-0.520030\pi$
$409$	−2.54353			−0.125769			−0.0628846	+	0.998021i	$0.520030\pi$
$410$		0			0
$411$	−10.9489	+	26.4331i	−0.540072	+	1.30385i
$412$		−	23.1878i		−	1.14238i
$413$	−2.23027	−	0.923809i	−0.109744	−	0.0454576i
$414$	−1.20414	−	2.90704i	−0.0591800	−	0.142873i
$415$		0			0
$416$	13.0000	+	13.0000i	0.637375	+	0.637375i
$417$	−0.0612063	−	0.0612063i	−0.00299729	−	0.00299729i
$418$	−65.1529	+	26.9872i	−3.18673	+	1.31999i
$419$	−2.20082	−	5.31324i	−0.107517	−	0.259569i	0.860960	−	0.508673i	$-0.169864\pi$
$419$	−2.20082	−	5.31324i	−0.107517	−	0.259569i	−0.968477	+	0.249104i	$0.919864\pi$
$420$		0			0
$421$		−	19.5960i		−	0.955050i	−0.878618	−	0.477525i	$-0.841534\pi$
$421$		−	19.5960i		−	0.955050i	0.878618	−	0.477525i	$-0.158466\pi$
$422$	−3.69506	+	8.92065i	−0.179873	+	0.434251i
$423$	1.48503	−	1.48503i	0.0722048	−	0.0722048i
$424$	−5.33601			−0.259140
$425$		0			0
$426$	5.60850			0.271733
$427$	−15.2946	+	15.2946i	−0.740158	+	0.740158i
$428$	−1.77373	+	4.28216i	−0.0857364	+	0.206986i
$429$		−	30.5022i		−	1.47266i
$430$		0			0
$431$	9.87988	+	23.8521i	0.475897	+	1.14892i	0.961517	+	0.274747i	$0.0885940\pi$
$431$	9.87988	+	23.8521i	0.475897	+	1.14892i	−0.485620	+	0.874170i	$0.661406\pi$
$432$	−1.57380	+	0.651890i	−0.0757196	+	0.0313641i
$433$	27.4660	+	27.4660i	1.31993	+	1.31993i	0.913826	+	0.406105i	$0.133113\pi$
$433$	27.4660	+	27.4660i	1.31993	+	1.31993i	0.406105	+	0.913826i	$0.366887\pi$
$434$	−3.08568	−	3.08568i	−0.148117	−	0.148117i
$435$		0			0
$436$	13.7700	+	33.2437i	0.659462	+	1.59208i
$437$	15.8853	+	6.57992i	0.759898	+	0.314760i
$438$			42.3295i			2.02258i
$439$	1.30810	−	3.15802i	0.0624320	−	0.150724i	−0.889585	−	0.456770i	$-0.849006\pi$
$439$	1.30810	−	3.15802i	0.0624320	−	0.150724i	0.952017	+	0.306046i	$0.0990061\pi$
$440$		0			0
$441$	2.42363			0.115411
$442$	−29.2727	+	16.1738i	−1.39236	+	0.769310i
$443$	−19.8457			−0.942899			−0.471449	−	0.881893i	$-0.656269\pi$
$443$	−19.8457			−0.942899			−0.471449	+	0.881893i	$0.656269\pi$
$444$	1.79520	−	1.79520i	0.0851966	−	0.0851966i
$445$		0			0
$446$			17.6262i			0.834624i
$447$	2.59299	+	1.07405i	0.122644	+	0.0508008i
$448$	7.56191	+	18.2561i	0.357267	+	0.862518i
$449$	5.56173	−	2.30374i	0.262474	−	0.108720i	−0.247566	−	0.968871i	$-0.579631\pi$
$449$	5.56173	−	2.30374i	0.262474	−	0.108720i	0.510040	+	0.860151i	$0.329631\pi$
$450$		0			0
$451$	33.4166	+	33.4166i	1.57352	+	1.57352i
$452$	−12.1980	+	5.05259i	−0.573747	+	0.237654i
$453$	−3.79502	−	9.16200i	−0.178306	−	0.430468i
$454$	−50.8393	−	21.0583i	−2.38600	−	0.988316i
$455$		0			0
$456$	−14.4476	+	34.8795i	−0.676569	+	1.63338i
$457$	−20.2147	+	20.2147i	−0.945603	+	0.945603i	−0.998595	−	0.0529924i	$-0.983124\pi$
$457$	−20.2147	+	20.2147i	−0.945603	+	0.945603i	0.0529924	+	0.998595i	$0.483124\pi$
$458$	31.7599			1.48404
$459$	2.14248	+	19.0358i	0.100002	+	0.888515i
$460$		0			0
$461$	−5.44426	+	5.44426i	−0.253565	+	0.253565i	−0.822430	−	0.568866i	$-0.807382\pi$
$461$	−5.44426	+	5.44426i	−0.253565	+	0.253565i	0.568866	+	0.822430i	$0.307382\pi$
$462$	11.8264	−	28.5513i	0.550212	−	1.32833i
$463$		−	26.7823i		−	1.24468i	−0.782748	−	0.622339i	$-0.786183\pi$
$463$		−	26.7823i		−	1.24468i	0.782748	−	0.622339i	$-0.213817\pi$
$464$	−0.331629	−	0.137365i	−0.0153955	−	0.00637702i
$465$		0			0
$466$	12.3825	−	5.12901i	0.573610	−	0.237597i
$467$	7.30998	+	7.30998i	0.338266	+	0.338266i	0.855714	−	0.517449i	$-0.173118\pi$
$467$	7.30998	+	7.30998i	0.338266	+	0.338266i	−0.517449	+	0.855714i	$0.673118\pi$
$468$	−4.33663	−	4.33663i	−0.200461	−	0.200461i
$469$	12.6272	−	5.23037i	0.583071	−	0.241516i
$470$		0			0
$471$	−22.0295	−	9.12492i	−1.01507	−	0.420454i
$472$		−	4.74109i		−	0.218227i
$473$	7.50470	−	18.1180i	0.345067	−	0.833065i
$474$	−33.4202	+	33.4202i	−1.53504	+	1.53504i
$475$		0			0
$476$	−21.0049	+	2.36410i	−0.962758	+	0.108358i
$477$	−0.923943			−0.0423044
$478$	−8.30188	+	8.30188i	−0.379719	+	0.379719i
$479$	−9.90265	+	23.9071i	−0.452464	+	1.09234i	0.518919	+	0.854823i	$0.326335\pi$
$479$	−9.90265	+	23.9071i	−0.452464	+	1.09234i	−0.971383	+	0.237520i	$0.923665\pi$
$480$		0			0
$481$	−1.32496	−	0.548818i	−0.0604132	−	0.0250239i
$482$	4.68748	+	11.3166i	0.213509	+	0.515456i
$483$	−6.96128	+	2.88346i	−0.316749	+	0.131202i
$484$	24.2127	+	24.2127i	1.10058	+	1.10058i
$485$		0			0
$486$	−11.5103	+	4.76770i	−0.522116	+	0.216267i
$487$	−9.08625	−	21.9361i	−0.411737	−	0.994021i	−0.984671	−	0.174420i	$-0.944195\pi$
$487$	−9.08625	−	21.9361i	−0.411737	−	0.994021i	0.572934	−	0.819601i	$-0.305805\pi$
$488$	−39.2469	−	16.2566i	−1.77662	−	0.735901i
$489$			7.62461i			0.344797i
$490$		0			0
$491$	28.3186	−	28.3186i	1.27800	−	1.27800i	0.336213	−	0.941786i	$-0.390854\pi$
$491$	28.3186	−	28.3186i	1.27800	−	1.27800i	0.941786	−	0.336213i	$-0.109146\pi$
$492$	63.7312			2.87322
$493$	−2.51711	+	3.15557i	−0.113365	+	0.142120i
$494$	53.7221			2.41707
$495$		0			0
$496$	0.171794	−	0.414746i	0.00771376	−	0.0186227i
$497$		−	2.00238i		−	0.0898188i
$498$	50.7604	+	21.0256i	2.27463	+	0.942181i
$499$	−1.39163	−	3.35969i	−0.0622979	−	0.150400i	0.889665	−	0.456614i	$-0.150938\pi$
$499$	−1.39163	−	3.35969i	−0.0622979	−	0.150400i	−0.951963	+	0.306213i	$0.900938\pi$
$500$		0			0
$501$	21.4666	+	21.4666i	0.959055	+	0.959055i
$502$	−45.9833	−	45.9833i	−2.05233	−	2.05233i
$503$	32.6193	−	13.5113i	1.45442	−	0.602441i	0.491175	−	0.871061i	$-0.336568\pi$
$503$	32.6193	−	13.5113i	1.45442	−	0.602441i	0.963246	+	0.268620i	$0.0865676\pi$
$504$	−0.943948	−	2.27889i	−0.0420468	−	0.101510i
$505$		0			0
$506$		−	27.6423i		−	1.22885i
$507$	0.449066	−	1.08414i	0.0199437	−	0.0481484i
$508$	29.2589	−	29.2589i	1.29816	−	1.29816i
$509$	8.67454			0.384492			0.192246	−	0.981347i	$-0.438423\pi$
$509$	8.67454			0.384492			0.192246	+	0.981347i	$0.438423\pi$
$510$		0			0
$511$	15.1127			0.668547
$512$	−2.92908	+	2.92908i	−0.129448	+	0.129448i
$513$	11.7756	−	28.4288i	0.519905	−	1.25516i
$514$			7.59390i			0.334953i
$515$		0			0
$516$	−10.1207	−	24.4334i	−0.445537	−	1.07562i
$517$	17.0453	−	7.06039i	0.749651	−	0.310515i
$518$	−1.02743	−	1.02743i	−0.0451428	−	0.0451428i
$519$	−2.09286	−	2.09286i	−0.0918666	−	0.0918666i
$520$		0			0
$521$	−5.43328	−	13.1171i	−0.238036	−	0.574670i	0.759043	−	0.651040i	$-0.225667\pi$
$521$	−5.43328	−	13.1171i	−0.238036	−	0.574670i	−0.997080	+	0.0763698i	$0.975667\pi$
$522$	−1.09627	−	0.454088i	−0.0479822	−	0.0198749i
$523$		−	28.1516i		−	1.23098i	−0.788143	−	0.615492i	$-0.788957\pi$
$523$		−	28.1516i		−	1.23098i	0.788143	−	0.615492i	$-0.211043\pi$
$524$	−9.88301	+	23.8597i	−0.431742	+	1.04232i
$525$		0			0
$526$	−64.1871			−2.79869
$527$	−3.94647	−	3.14799i	−0.171911	−	0.137128i
$528$	3.17916			0.138355
$529$	11.4978	−	11.4978i	0.499905	−	0.499905i
$530$		0			0
$531$		−	0.820931i		−	0.0356254i
$532$	31.3695	+	12.9937i	1.36004	+	0.563347i
$533$	−13.7769	−	33.2604i	−0.596744	−	1.44067i
$534$	34.5046	−	14.2923i	1.49316	−	0.618488i
$535$		0			0
$536$	18.9808	+	18.9808i	0.819844	+	0.819844i
$537$	−5.98121	+	2.47750i	−0.258108	+	0.106912i
$538$	−12.9372	−	31.2332i	−0.557763	−	1.34656i
$539$	19.6707	+	8.14787i	0.847277	+	0.350954i
$540$		0			0
$541$	−7.68568	+	18.5549i	−0.330433	+	0.797736i	0.668125	+	0.744049i	$0.267097\pi$
$541$	−7.68568	+	18.5549i	−0.330433	+	0.797736i	−0.998558	+	0.0536867i	$0.982903\pi$
$542$	−4.09177	+	4.09177i	−0.175756	+	0.175756i
$543$	27.6515			1.18664
$544$	10.4209	+	18.8606i	0.446793	+	0.808642i
$545$		0			0
$546$	−16.6468	+	16.6468i	−0.712418	+	0.712418i
$547$	−0.767610	+	1.85317i	−0.0328206	+	0.0792360i	−0.939440	−	0.342713i	$-0.888654\pi$
$547$	−0.767610	+	1.85317i	−0.0328206	+	0.0792360i	0.906619	+	0.421949i	$0.138654\pi$
$548$			50.5366i			2.15882i
$549$	−6.79569	−	2.81487i	−0.290033	−	0.120136i
$550$		0			0
$551$	5.99047	−	2.48133i	0.255203	−	0.105708i
$552$	−10.4639	−	10.4639i	−0.445375	−	0.445375i
$553$	11.9319	+	11.9319i	0.507394	+	0.507394i
$554$	−51.0533	+	21.1470i	−2.16905	+	0.898448i
$555$		0			0
$556$	−0.141254	−	0.0585092i	−0.00599050	−	0.00248134i
$557$		−	16.9217i		−	0.716994i	−0.933531	−	0.358497i	$-0.883289\pi$
$557$		−	16.9217i		−	0.716994i	0.933531	−	0.358497i	$-0.116711\pi$
$558$	0.567898	−	1.37103i	0.0240410	−	0.0580402i
$559$	−10.5637	+	10.5637i	−0.446795	+	0.446795i
$560$		0			0
$561$	9.90120	−	34.3521i	0.418029	−	1.45035i
$562$	−32.7898			−1.38316
$563$	−29.9664	+	29.9664i	−1.26293	+	1.26293i	−0.313271	+	0.949664i	$0.601425\pi$
$563$	−29.9664	+	29.9664i	−1.26293	+	1.26293i	−0.949664	+	0.313271i	$0.898575\pi$
$564$	9.52146	−	22.9868i	0.400926	−	0.967921i
$565$		0			0
$566$	21.3261	+	8.83358i	0.896404	+	0.371303i
$567$	6.09313	+	14.7101i	0.255887	+	0.617767i
$568$	3.63327	−	1.50495i	0.152448	−	0.0631462i
$569$	−29.3744	−	29.3744i	−1.23144	−	1.23144i	−0.963411	−	0.268030i	$-0.913627\pi$
$569$	−29.3744	−	29.3744i	−1.23144	−	1.23144i	−0.268030	−	0.963411i	$-0.586373\pi$
$570$		0			0
$571$	−17.6451	+	7.30885i	−0.738426	+	0.305866i	−0.720009	−	0.693964i	$-0.755862\pi$
$571$	−17.6451	+	7.30885i	−0.738426	+	0.305866i	−0.0184165	+	0.999830i	$0.505862\pi$
$572$	−20.6179	−	49.7761i	−0.862079	−	2.08124i
$573$	27.0125	+	11.1889i	1.12846	+	0.467425i
$574$		−	36.4747i		−	1.52242i
$575$		0			0
$576$	−4.75162	+	4.75162i	−0.197984	+	0.197984i
$577$	3.81985			0.159023			0.0795113	−	0.996834i	$-0.474664\pi$
$577$	3.81985			0.159023			0.0795113	+	0.996834i	$0.474664\pi$
$578$	−38.2175	+	8.71313i	−1.58964	+	0.362418i
$579$	0.199058			0.00827256
$580$		0			0
$581$	7.50668	−	18.1227i	0.311430	−	0.751857i
$582$		−	25.6686i		−	1.06400i
$583$	−7.49891	−	3.10615i	−0.310573	−	0.128644i
$584$	11.3584	+	27.4217i	0.470015	+	1.13472i
$585$		0			0
$586$	−18.4146	−	18.4146i	−0.760700	−	0.760700i
$587$	−4.90654	−	4.90654i	−0.202514	−	0.202514i	0.598562	−	0.801076i	$-0.295739\pi$
$587$	−4.90654	−	4.90654i	−0.202514	−	0.202514i	−0.801076	+	0.598562i	$0.795739\pi$
$588$	26.5274	−	10.9880i	1.09397	−	0.453138i
$589$	3.10324	+	7.49188i	0.127867	+	0.308698i
$590$		0			0
$591$			19.7993i			0.814435i
$592$	0.0572018	−	0.138097i	0.00235098	−	0.00567576i
$593$	−26.3112	+	26.3112i	−1.08047	+	1.08047i	−0.0840076	+	0.996465i	$0.526772\pi$
$593$	−26.3112	+	26.3112i	−1.08047	+	1.08047i	−0.996465	+	0.0840076i	$0.973228\pi$
$594$	−49.4693			−2.02975
$595$		0			0
$596$	4.95745			0.203065
$597$	−1.52849	+	1.52849i	−0.0625569	+	0.0625569i
$598$	−8.05839	+	19.4547i	−0.329532	+	0.795561i
$599$			20.3199i			0.830249i	0.909765	+	0.415124i	$0.136262\pi$
$599$			20.3199i			0.830249i	−0.909765	+	0.415124i	$0.863738\pi$
$600$		0			0
$601$	9.23333	+	22.2912i	0.376636	+	0.909279i	0.992592	+	0.121498i	$0.0387699\pi$
$601$	9.23333	+	22.2912i	0.376636	+	0.909279i	−0.615956	+	0.787780i	$0.711230\pi$
$602$	−13.9838	+	5.79226i	−0.569936	+	0.236075i
$603$	3.28656	+	3.28656i	0.133839	+	0.133839i
$604$	−12.3861	−	12.3861i	−0.503982	−	0.503982i
$605$		0			0
$606$	−9.59948	−	23.1752i	−0.389952	−	0.941428i
$607$	1.47684	+	0.611728i	0.0599432	+	0.0248293i	0.412454	−	0.910979i	$-0.364672\pi$
$607$	1.47684	+	0.611728i	0.0599432	+	0.0248293i	−0.352510	+	0.935808i	$0.614672\pi$
$608$		−	34.6136i		−	1.40377i
$609$	−1.08737	+	2.62515i	−0.0440625	+	0.106376i
$610$		0			0
$611$	−14.0548			−0.568595
$612$	−3.47629	−	6.29168i	−0.140521	−	0.254326i
$613$	−29.2631			−1.18192			−0.590962	−	0.806699i	$-0.701252\pi$
$613$	−29.2631			−1.18192			−0.590962	+	0.806699i	$0.701252\pi$
$614$	40.9884	−	40.9884i	1.65416	−	1.65416i
$615$		0			0
$616$		−	21.6694i		−	0.873084i
$617$	16.5320	+	6.84778i	0.665553	+	0.275681i	0.689773	−	0.724025i	$-0.257710\pi$
$617$	16.5320	+	6.84778i	0.665553	+	0.275681i	−0.0242199	+	0.999707i	$0.507710\pi$
$618$	−11.5836	−	27.9652i	−0.465959	−	1.12492i
$619$	−2.87805	+	1.19213i	−0.115678	+	0.0479156i	−0.439772	−	0.898109i	$-0.644941\pi$
$619$	−2.87805	+	1.19213i	−0.115678	+	0.0479156i	0.324094	+	0.946025i	$0.394941\pi$
$620$		0			0
$621$	8.52871	+	8.52871i	0.342245	+	0.342245i
$622$	−47.5629	+	19.7012i	−1.90710	+	0.789946i
$623$	−5.10271	−	12.3190i	−0.204436	−	0.493551i
$624$	−2.23750	−	0.926803i	−0.0895717	−	0.0371018i
$625$		0			0
$626$	26.2321	−	63.3299i	1.04845	−	2.53117i
$627$	−40.6075	+	40.6075i	−1.62171	+	1.62171i
$628$	−42.1175			−1.68067
$629$	−1.31405	−	1.04818i	−0.0523945	−	0.0417936i
$630$		0			0
$631$	25.7673	−	25.7673i	1.02578	−	1.02578i	0.0261195	−	0.999659i	$-0.491685\pi$
$631$	25.7673	−	25.7673i	1.02578	−	1.02578i	0.999659	−	0.0261195i	$-0.00831503\pi$
$632$	−12.6823	+	30.6179i	−0.504476	+	1.21791i
$633$			7.86292i			0.312523i
$634$	−25.3410	−	10.4966i	−1.00642	−	0.416872i
$635$		0			0
$636$	−10.1128	+	4.18888i	−0.401000	+	0.166100i
$637$	−11.4690	−	11.4690i	−0.454417	−	0.454417i
$638$	−7.37095	−	7.37095i	−0.291819	−	0.291819i
$639$	0.629108	−	0.260585i	0.0248871	−	0.0103086i
$640$		0			0
$641$	3.63772	+	1.50679i	0.143681	+	0.0595147i	0.453365	−	0.891325i	$-0.350223\pi$
$641$	3.63772	+	1.50679i	0.143681	+	0.0595147i	−0.309684	+	0.950840i	$0.600223\pi$
$642$			6.05049i			0.238794i
$643$	5.70294	−	13.7681i	0.224902	−	0.542962i	−0.770641	−	0.637270i	$-0.780064\pi$
$643$	5.70294	−	13.7681i	0.224902	−	0.542962i	0.995543	+	0.0943078i	$0.0300638\pi$
$644$	−9.41093	+	9.41093i	−0.370843	+	0.370843i
$645$		0			0
$646$	60.5028	+	17.4385i	2.38045	+	0.686109i
$647$	−28.8503			−1.13422			−0.567110	−	0.823642i	$-0.691939\pi$
$647$	−28.8503			−1.13422			−0.567110	+	0.823642i	$0.691939\pi$
$648$	−22.1117	+	22.1117i	−0.868629	+	0.868629i
$649$	2.75984	−	6.66285i	0.108333	−	0.261540i
$650$		0			0
$651$	−3.28310	−	1.35990i	−0.128675	−	0.0532988i
$652$	5.15384	+	12.4425i	0.201840	+	0.487285i
$653$	−13.0606	+	5.40988i	−0.511101	+	0.211705i	−0.623303	−	0.781980i	$-0.714210\pi$
$653$	−13.0606	+	5.40988i	−0.511101	+	0.211705i	0.112202	+	0.993685i	$0.464210\pi$
$654$	33.2141	+	33.2141i	1.29877	+	1.29877i
$655$		0			0
$656$	3.46664	−	1.43593i	0.135349	−	0.0560636i
$657$	1.96674	+	4.74813i	0.0767298	+	0.185242i
$658$	−13.1559	−	5.44933i	−0.512868	−	0.212437i
$659$		−	38.8064i		−	1.51168i	−0.654756	−	0.755840i	$-0.727229\pi$
$659$		−	38.8064i		−	1.51168i	0.654756	−	0.755840i	$-0.272771\pi$
$660$		0			0
$661$	−12.4897	+	12.4897i	−0.485794	+	0.485794i	−0.906976	−	0.421182i	$-0.861615\pi$
$661$	−12.4897	+	12.4897i	−0.485794	+	0.485794i	0.421182	+	0.906976i	$0.361615\pi$
$662$	21.0932			0.819812
$663$	−16.9830	+	21.2906i	−0.659563	+	0.826860i
$664$	38.5252			1.49507
$665$		0			0
$666$	0.189092	−	0.456508i	0.00732716	−	0.0176893i
$667$			2.54156i			0.0984097i
$668$	49.5412	+	20.5206i	1.91681	+	0.793967i
$669$	5.49289	+	13.2610i	0.212367	+	0.512700i
$670$		0			0
$671$	−45.6921	−	45.6921i	−1.76392	−	1.76392i
$672$	10.7257	+	10.7257i	0.413751	+	0.413751i
$673$	−36.0132	+	14.9171i	−1.38821	+	0.575014i	−0.946663	−	0.322227i	$-0.895569\pi$
$673$	−36.0132	+	14.9171i	−1.38821	+	0.575014i	−0.441543	+	0.897240i	$0.645569\pi$
$674$	−18.9970	−	45.8627i	−0.731736	−	1.76657i
$675$		0			0
$676$		−	2.07274i		−	0.0797206i
$677$	17.7215	−	42.7835i	0.681094	−	1.64431i	−0.0809013	−	0.996722i	$-0.525780\pi$
$677$	17.7215	−	42.7835i	0.681094	−	1.64431i	0.761995	−	0.647583i	$-0.224220\pi$
$678$	−12.1872	+	12.1872i	−0.468046	+	0.468046i
$679$	−9.16432			−0.351694
$680$		0			0
$681$	−44.8112			−1.71717
$682$	9.21835	−	9.21835i	0.352989	−	0.352989i
$683$	−11.1344	+	26.8809i	−0.426048	+	1.02857i	0.554482	+	0.832196i	$0.312917\pi$
$683$	−11.1344	+	26.8809i	−0.426048	+	1.02857i	−0.980529	+	0.196374i	$0.937083\pi$
$684$			11.5467i			0.441498i
$685$		0			0
$686$	−15.8362	−	38.2320i	−0.604629	−	1.45970i
$687$	23.8945	−	9.89741i	0.911631	−	0.377610i
$688$	−1.10102	−	1.10102i	−0.0419760	−	0.0419760i
$689$	4.37223	+	4.37223i	0.166569	+	0.166569i
$690$		0			0
$691$	−2.96838	−	7.16631i	−0.112923	−	0.272619i	0.857307	−	0.514805i	$-0.172136\pi$
$691$	−2.96838	−	7.16631i	−0.112923	−	0.272619i	−0.970230	+	0.242186i	$0.922136\pi$
$692$	−4.82998	−	2.00064i	−0.183608	−	0.0760530i
$693$		−	3.75210i		−	0.142531i
$694$	4.81889	−	11.6338i	0.182922	−	0.441614i
$695$		0			0
$696$	−5.58052			−0.211529
$697$	−4.71927	−	41.9305i	−0.178755	−	1.58823i
$698$	76.1473			2.88222
$699$	7.71759	−	7.71759i	0.291906	−	0.291906i
$700$		0			0
$701$			4.74948i			0.179386i	0.995969	+	0.0896928i	$0.0285885\pi$
$701$			4.74948i			0.179386i	−0.995969	+	0.0896928i	$0.971411\pi$
$702$	34.8166	+	14.4215i	1.31407	+	0.544304i
$703$	1.03328	+	2.49456i	0.0389709	+	0.0940840i
$704$	−54.5393	+	22.5909i	−2.05553	+	0.851427i
$705$		0			0
$706$	−20.3741	−	20.3741i	−0.766790	−	0.766790i
$707$	−8.27413	+	3.42726i	−0.311181	+	0.128895i
$708$	−3.72186	−	8.98535i	−0.139876	−	0.337690i
$709$	−40.1605	−	16.6350i	−1.50826	−	0.624741i	−0.533061	−	0.846077i	$-0.678958\pi$
$709$	−40.1605	−	16.6350i	−1.50826	−	0.624741i	−0.975198	+	0.221336i	$0.928958\pi$
$710$		0			0
$711$	−2.19597	+	5.30155i	−0.0823555	+	0.198824i
$712$	18.5175	−	18.5175i	0.693972	−	0.693972i
$713$	−3.17856			−0.119038
$714$	−24.1516	+	13.3443i	−0.903850	+	0.499397i
$715$		0			0
$716$	−8.08597	+	8.08597i	−0.302187	+	0.302187i
$717$	−3.65876	+	8.83302i	−0.136639	+	0.329875i
$718$		−	41.9377i		−	1.56510i
$719$	35.1404	+	14.5556i	1.31052	+	0.542833i	0.925035	−	0.379883i	$-0.124036\pi$
$719$	35.1404	+	14.5556i	1.31052	+	0.542833i	0.385481	+	0.922716i	$0.374036\pi$
$720$		0			0
$721$	−9.98427	+	4.13562i	−0.371834	+	0.154019i
$722$	−40.5419	−	40.5419i	−1.50881	−	1.50881i
$723$	7.05322	+	7.05322i	0.262312	+	0.262312i
$724$	45.1241	−	18.6910i	1.67702	−	0.694646i
$725$		0			0
$726$	41.2968	+	17.1057i	1.53267	+	0.634852i
$727$		−	32.4604i		−	1.20389i	−0.798538	−	0.601944i	$-0.794393\pi$
$727$		−	32.4604i		−	1.20389i	0.798538	−	0.601944i	$-0.205607\pi$
$728$	−6.31715	+	15.2509i	−0.234129	+	0.565238i
$729$	14.6770	−	14.6770i	0.543594	−	0.543594i
$730$		0			0
$731$	−15.3260	+	8.46794i	−0.566852	+	0.313198i
$732$	−87.1427			−3.22089
$733$	27.9059	−	27.9059i	1.03073	−	1.03073i	0.0312144	−	0.999513i	$-0.490063\pi$
$733$	27.9059	−	27.9059i	1.03073	−	1.03073i	0.999513	−	0.0312144i	$-0.00993745\pi$
$734$	20.0902	−	48.5020i	0.741543	−	1.79024i
$735$		0			0
$736$	12.5348	+	5.19208i	0.462038	+	0.191382i
$737$	15.6255	+	37.7234i	0.575574	+	1.38956i
$738$	11.4597	−	4.74674i	0.421836	−	0.174730i
$739$	6.57694	+	6.57694i	0.241937	+	0.241937i	0.817651	−	0.575714i	$-0.195276\pi$
$739$	6.57694	+	6.57694i	0.241937	+	0.241937i	−0.575714	+	0.817651i	$0.695276\pi$
$740$		0			0
$741$	40.4177	−	16.7416i	1.48478	−	0.615016i
$742$	2.39738	+	5.78779i	0.0880107	+	0.212477i
$743$	38.4742	+	15.9365i	1.41148	+	0.584655i	0.952705	−	0.303896i	$-0.0982877\pi$
$743$	38.4742	+	15.9365i	1.41148	+	0.584655i	0.458777	+	0.888551i	$0.348288\pi$
$744$		−	6.97919i		−	0.255869i
$745$		0			0
$746$	−40.0352	+	40.0352i	−1.46579	+	1.46579i
$747$	6.67072			0.244069
$748$	−7.06265	−	62.7513i	−0.258236	−	2.29442i
$749$	2.16018			0.0789312
$750$		0			0
$751$	5.95174	−	14.3688i	0.217182	−	0.524324i	−0.777312	−	0.629115i	$-0.783417\pi$
$751$	5.95174	−	14.3688i	0.217182	−	0.524324i	0.994494	+	0.104791i	$0.0334174\pi$
$752$		−	1.46489i		−	0.0534190i
$753$	−48.9252	−	20.2655i	−1.78293	−	0.738516i
$754$	3.03888	+	7.33650i	0.110669	+	0.267179i
$755$		0			0
$756$	16.8420	+	16.8420i	0.612539	+	0.612539i
$757$	29.1872	+	29.1872i	1.06083	+	1.06083i	0.998026	+	0.0627989i	$0.0200027\pi$
$757$	29.1872	+	29.1872i	1.06083	+	1.06083i	0.0627989	+	0.998026i	$0.479997\pi$
$758$	39.7522	−	16.4659i	1.44387	−	0.598069i
$759$	−8.61422	−	20.7966i	−0.312676	−	0.754867i
$760$		0			0
$761$			42.6707i			1.54681i	0.633910	+	0.773407i	$0.281449\pi$
$761$			42.6707i			1.54681i	−0.633910	+	0.773407i	$0.718551\pi$
$762$	20.6708	−	49.9037i	0.748823	−	1.80782i
$763$	11.8583	−	11.8583i	0.429298	−	0.429298i
$764$	51.6444			1.86843
$765$		0			0
$766$	59.2934			2.14236
$767$	−3.88477	+	3.88477i	−0.140271	+	0.140271i
$768$	−13.1479	+	31.7417i	−0.474432	+	1.14538i
$769$		−	8.29133i		−	0.298993i	−0.988762	−	0.149497i	$-0.952235\pi$
$769$		−	8.29133i		−	0.298993i	0.988762	−	0.149497i	$-0.0477653\pi$
$770$		0			0
$771$	2.36650	+	5.71325i	0.0852276	+	0.205758i
$772$	0.324839	−	0.134553i	0.0116912	−	0.00484266i
$773$	0.168240	+	0.168240i	0.00605117	+	0.00605117i	0.710126	−	0.704075i	$-0.248638\pi$
$773$	0.168240	+	0.168240i	0.00605117	+	0.00605117i	−0.704075	+	0.710126i	$0.748638\pi$
$774$	−3.63964	−	3.63964i	−0.130824	−	0.130824i
$775$		0			0
$776$	−6.88773	−	16.6285i	−0.247255	−	0.596927i
$777$	−1.09317	−	0.452805i	−0.0392171	−	0.0162443i
$778$		−	55.2962i		−	1.98246i
$779$	−25.9383	+	62.6205i	−0.929335	+	2.24361i
$780$		0			0
$781$	5.98202			0.214054
$782$	−15.3906	+	19.2944i	−0.550366	+	0.689965i
$783$	4.54845			0.162548
$784$	1.19538	−	1.19538i	0.0426921	−	0.0426921i
$785$		0			0
$786$			33.7127i			1.20249i
$787$	1.37415	+	0.569193i	0.0489833	+	0.0202895i	0.407041	−	0.913410i	$-0.366561\pi$
$787$	1.37415	+	0.569193i	0.0489833	+	0.0202895i	−0.358057	+	0.933700i	$0.616561\pi$
$788$	13.3833	+	32.3102i	0.476761	+	1.15100i
$789$	−48.2909	+	20.0028i	−1.71920	+	0.712117i
$790$		0			0
$791$	4.35113	+	4.35113i	0.154708	+	0.154708i
$792$	6.80811	−	2.82001i	0.241915	−	0.100205i
$793$	18.8378	+	45.4785i	0.668951	+	1.61499i
$794$	30.4962	+	12.6319i	1.08227	+	0.448291i
$795$		0			0
$796$	−1.46114	+	3.52750i	−0.0517886	+	0.125029i
$797$	−0.399266	+	0.399266i	−0.0141427	+	0.0141427i	−0.714143	−	0.700000i	$-0.753183\pi$
$797$	−0.399266	+	0.399266i	−0.0141427	+	0.0141427i	0.700000	+	0.714143i	$0.253183\pi$
$798$	44.3237			1.56904
$799$	−15.8287	−	4.56226i	−0.559980	−	0.161401i
$800$		0			0
$801$	3.20635	−	3.20635i	0.113291	−	0.113291i
$802$	−2.60563	+	6.29054i	−0.0920078	+	0.222127i
$803$			45.1486i			1.59326i
$804$	50.8728	+	21.0722i	1.79414	+	0.743159i
$805$		0			0
$806$	−9.17526	+	3.80052i	−0.323185	+	0.133868i
$807$	−19.4666	−	19.4666i	−0.685255	−	0.685255i
$808$	−12.4374	−	12.4374i	−0.437545	−	0.437545i
$809$	−43.3268	+	17.9466i	−1.52329	+	0.630967i	−0.978247	−	0.207442i	$-0.933486\pi$
$809$	−43.3268	+	17.9466i	−1.52329	+	0.630967i	−0.545042	+	0.838409i	$0.683486\pi$
$810$		0			0
$811$	5.97603	+	2.47535i	0.209847	+	0.0869215i	0.485131	−	0.874441i	$-0.338772\pi$
$811$	5.97603	+	2.47535i	0.209847	+	0.0869215i	−0.275284	+	0.961363i	$0.588772\pi$
$812$			5.01894i			0.176130i
$813$	−1.80330	+	4.35355i	−0.0632445	+	0.152686i
$814$	3.06942	−	3.06942i	0.107583	−	0.107583i
$815$		0			0
$816$	−2.21906	−	1.77009i	−0.0776828	−	0.0619654i
$817$	28.1267			0.984028
$818$	−4.14704	+	4.14704i	−0.144998	+	0.144998i
$819$	−1.09383	+	2.64074i	−0.0382215	+	0.0922748i
$820$		0			0
$821$	10.8492	+	4.49387i	0.378638	+	0.156837i	0.563882	−	0.825856i	$-0.309307\pi$
$821$	10.8492	+	4.49387i	0.378638	+	0.156837i	−0.185244	+	0.982693i	$0.559307\pi$
$822$	25.2458	+	60.9488i	0.880549	+	2.12583i
$823$	22.3851	−	9.27219i	0.780294	−	0.323208i	0.0432598	−	0.999064i	$-0.486226\pi$
$823$	22.3851	−	9.27219i	0.780294	−	0.323208i	0.737034	+	0.675855i	$0.236226\pi$
$824$	−15.0080	−	15.0080i	−0.522828	−	0.522828i
$825$		0			0
$826$	−5.14251	+	2.13010i	−0.178931	+	0.0741155i
$827$	3.17168	+	7.65712i	0.110290	+	0.266264i	0.969382	−	0.245557i	$-0.0789710\pi$
$827$	3.17168	+	7.65712i	0.110290	+	0.266264i	−0.859092	+	0.511821i	$0.828971\pi$
$828$	−4.18145	−	1.73202i	−0.145316	−	0.0601917i
$829$			42.2364i			1.46693i	0.679726	+	0.733466i	$0.262098\pi$
$829$			42.2364i			1.46693i	−0.679726	+	0.733466i	$0.737902\pi$
$830$		0			0
$831$	−31.8197	+	31.8197i	−1.10381	+	1.10381i
$832$	44.9707			1.55908
$833$	−9.19366	−	16.6394i	−0.318541	−	0.576523i
$834$	−0.199585			−0.00691107
$835$		0			0
$836$	−38.8181	+	93.7152i	−1.34255	+	3.24121i
$837$			5.68844i			0.196621i
$838$	−12.2511	−	5.07459i	−0.423209	−	0.175299i
$839$	−2.83865	−	6.85310i	−0.0980009	−	0.236595i	0.867274	−	0.497831i	$-0.165870\pi$
$839$	−2.83865	−	6.85310i	−0.0980009	−	0.236595i	−0.965275	+	0.261236i	$0.915870\pi$
$840$		0			0
$841$	−19.8284	−	19.8284i	−0.683737	−	0.683737i
$842$	−31.9499	−	31.9499i	−1.10107	−	1.10107i
$843$	−24.6693	+	10.2184i	−0.849656	+	0.351939i
$844$	5.31493	+	12.8314i	0.182947	+	0.441674i
$845$		0			0
$846$		−	4.84248i		−	0.166488i
$847$	6.10717	−	14.7440i	0.209845	−	0.506610i
$848$	−0.455705	+	0.455705i	−0.0156490	+	0.0156490i
$849$	18.7975			0.645128
$850$		0			0
$851$	−1.05836			−0.0362801
$852$	5.70437	−	5.70437i	0.195429	−	0.195429i
$853$	−5.50010	+	13.2784i	−0.188320	+	0.454644i	−0.989636	−	0.143596i	$-0.954133\pi$
$853$	−5.50010	+	13.2784i	−0.188320	+	0.454644i	0.801317	+	0.598241i	$0.204133\pi$
$854$			49.8736i			1.70664i
$855$		0			0
$856$	1.62355	+	3.91960i	0.0554918	+	0.133969i
$857$	−40.0122	+	16.5736i	−1.36679	+	0.566143i	−0.940916	−	0.338640i	$-0.890033\pi$
$857$	−40.0122	+	16.5736i	−1.36679	+	0.566143i	−0.425873	+	0.904783i	$0.640033\pi$
$858$	−49.7317	−	49.7317i	−1.69781	−	1.69781i
$859$	−9.67814	−	9.67814i	−0.330214	−	0.330214i	0.522454	−	0.852668i	$-0.325017\pi$
$859$	−9.67814	−	9.67814i	−0.330214	−	0.330214i	−0.852668	+	0.522454i	$0.825017\pi$
$860$		0			0
$861$	−11.3667	−	27.4416i	−0.387376	−	0.935208i
$862$	54.9977	+	22.7808i	1.87323	+	0.775917i
$863$		−	6.87984i		−	0.234192i	−0.993121	−	0.117096i	$-0.962641\pi$
$863$		−	6.87984i		−	0.234192i	0.993121	−	0.117096i	$-0.0373586\pi$
$864$	9.29187	−	22.4326i	0.316116	−	0.763171i
$865$		0			0
$866$	89.5628			3.04347
$867$	−26.0375	+	18.4651i	−0.884281	+	0.627108i
$868$	−6.27686			−0.213050
$869$	−35.6460	+	35.6460i	−1.20921	+	1.20921i
$870$		0			0
$871$		−	31.1050i		−	1.05395i
$872$	30.4290	+	12.6041i	1.03046	+	0.426829i
$873$	−1.19263	−	2.87925i	−0.0403643	−	0.0974480i
$874$	36.6280	−	15.1718i	1.23896	−	0.513194i
$875$		0			0
$876$	43.0531	+	43.0531i	1.45463	+	1.45463i
$877$	−26.2792	+	10.8852i	−0.887385	+	0.367567i	−0.779356	−	0.626581i	$-0.784454\pi$
$877$	−26.2792	+	10.8852i	−0.887385	+	0.367567i	−0.108029	+	0.994148i	$0.534454\pi$
$878$	−3.01618	−	7.28169i	−0.101791	−	0.245745i
$879$	−19.5927	−	8.11558i	−0.660847	−	0.273732i
$880$		0			0
$881$	−8.01474	+	19.3493i	−0.270023	+	0.651894i	−0.999484	−	0.0321289i	$-0.989771\pi$
$881$	−8.01474	+	19.3493i	−0.270023	+	0.651894i	0.729460	+	0.684023i	$0.239771\pi$
$882$	3.95156	−	3.95156i	0.133056	−	0.133056i
$883$	7.88825			0.265461			0.132730	−	0.991152i	$-0.457626\pi$
$883$	7.88825			0.265461			0.132730	+	0.991152i	$0.457626\pi$
$884$	−13.3228	+	46.2234i	−0.448095	+	1.55466i
$885$		0			0
$886$	−32.3571	+	32.3571i	−1.08706	+	1.08706i
$887$	−2.09077	+	5.04757i	−0.0702013	+	0.169481i	−0.955086	−	0.296330i	$-0.904237\pi$
$887$	−2.09077	+	5.04757i	−0.0702013	+	0.169481i	0.884884	+	0.465811i	$0.154237\pi$
$888$		−	2.32385i		−	0.0779832i
$889$	−17.8169	−	7.37999i	−0.597559	−	0.247517i
$890$		0			0
$891$	−43.9459	+	18.2030i	−1.47224	+	0.609823i
$892$	17.9275	+	17.9275i	0.600257	+	0.600257i
$893$	18.7111	+	18.7111i	0.626142	+	0.626142i
$894$	5.97884	−	2.47652i	0.199962	−	0.0828272i
$895$		0			0
$896$	27.1677	+	11.2532i	0.907608	+	0.375944i
$897$			17.1479i			0.572552i
$898$	5.31191	−	12.8241i	0.177261	−	0.427946i
$899$	−0.847580	+	0.847580i	−0.0282684	+	0.0282684i
$900$		0			0
$901$	3.50483	+	6.34333i	0.116763	+	0.211327i
$902$	108.967			3.62820
$903$	−8.71558	+	8.71558i	−0.290036	+	0.290036i
$904$	−4.62480	+	11.1653i	−0.153819	+	0.371351i
$905$		0			0
$906$	−21.1255	−	8.75048i	−0.701848	−	0.290715i
$907$	5.49369	+	13.2629i	0.182415	+	0.440388i	0.988463	−	0.151461i	$-0.0483979\pi$
$907$	5.49369	+	13.2629i	0.182415	+	0.440388i	−0.806048	+	0.591850i	$0.798398\pi$
$908$	−73.1267	+	30.2901i	−2.42679	+	1.00521i
$909$	−2.15356	−	2.15356i	−0.0714290	−	0.0714290i
$910$		0			0
$911$	21.5527	−	8.92744i	0.714074	−	0.295779i	0.00408474	−	0.999992i	$-0.498700\pi$
$911$	21.5527	−	8.92744i	0.714074	−	0.295779i	0.709989	+	0.704213i	$0.248700\pi$
$912$	1.74493	+	4.21262i	0.0577803	+	0.139494i
$913$	54.1410	+	22.4259i	1.79180	+	0.742190i
$914$			65.9172i			2.18035i
$915$		0			0
$916$	32.3028	−	32.3028i	1.06732	−	1.06732i
$917$	12.0363			0.397473
$918$	34.5297	+	27.5434i	1.13965	+	0.909067i
$919$	−27.6524			−0.912170			−0.456085	−	0.889936i	$-0.650749\pi$
$919$	−27.6524			−0.912170			−0.456085	+	0.889936i	$0.650749\pi$
$920$		0			0
$921$	18.0642	−	43.6108i	0.595235	−	1.43703i
$922$			17.7530i			0.584663i
$923$	−4.21016	−	1.74390i	−0.138579	−	0.0574013i
$924$	−17.0109	−	41.0679i	−0.559618	−	1.35104i
$925$		0			0
$926$	−43.6666	−	43.6666i	−1.43497	−	1.43497i
$927$	−2.59867	−	2.59867i	−0.0853514	−	0.0853514i
$928$	4.72696	−	1.95797i	0.155170	−	0.0642735i
$929$	−0.372470	−	0.899221i	−0.0122203	−	0.0295025i	0.917652	−	0.397386i	$-0.130083\pi$
$929$	−0.372470	−	0.899221i	−0.0122203	−	0.0295025i	−0.929872	+	0.367883i	$0.880083\pi$
$930$		0			0
$931$			30.5372i			1.00082i
$932$	7.37752	−	17.8109i	0.241659	−	0.583415i
$933$	−29.6443	+	29.6443i	−0.970510	+	0.970510i
$934$	23.8368			0.779965
$935$		0			0
$936$	−5.61366			−0.183488
$937$	2.88720	−	2.88720i	0.0943206	−	0.0943206i	−0.658372	−	0.752693i	$-0.728755\pi$
$937$	2.88720	−	2.88720i	0.0943206	−	0.0943206i	0.752693	+	0.658372i	$0.228755\pi$
$938$	12.0601	−	29.1156i	0.393775	−	0.950656i
$939$		−	55.8209i		−	1.82164i
$940$		0			0
$941$	6.25311	+	15.0963i	0.203846	+	0.492127i	0.992432	−	0.122798i	$-0.0391866\pi$
$941$	6.25311	+	15.0963i	0.203846	+	0.492127i	−0.788586	+	0.614924i	$0.789187\pi$
$942$	−50.7951	+	21.0400i	−1.65499	+	0.685521i
$943$	−18.7863	−	18.7863i	−0.611767	−	0.611767i
$944$	−0.404898	−	0.404898i	−0.0131783	−	0.0131783i
$945$		0			0
$946$	−17.3042	−	41.7760i	−0.562607	−	1.35825i
$947$	−15.3016	−	6.33813i	−0.497235	−	0.205961i	0.119950	−	0.992780i	$-0.461727\pi$
$947$	−15.3016	−	6.33813i	−0.497235	−	0.205961i	−0.617184	+	0.786819i	$0.711727\pi$
$948$			67.9831i			2.20799i
$949$	13.1619	−	31.7757i	0.427254	−	1.03148i
$950$		0			0
$951$	−22.3363			−0.724303
$952$	−12.0650	+	15.1253i	−0.391030	+	0.490213i
$953$	−57.0108			−1.84676			−0.923380	−	0.383887i	$-0.874585\pi$
$953$	−57.0108			−1.84676			−0.923380	+	0.383887i	$0.874585\pi$
$954$	−1.50642	+	1.50642i	−0.0487723	+	0.0487723i
$955$		0			0
$956$			16.8876i			0.546184i
$957$	−7.84253	−	3.24848i	−0.253513	−	0.105009i
$958$	22.8333	+	55.1244i	0.737710	+	1.78099i
$959$	21.7603	−	9.01339i	0.702675	−	0.291058i
$960$		0			0
$961$	20.8603	+	20.8603i	0.672913	+	0.672913i
$962$	−3.05507	+	1.26545i	−0.0984994	+	0.0407998i
$963$	0.281121	+	0.678687i	0.00905901	+	0.0218704i
$964$	16.2776	+	6.74242i	0.524267	+	0.217159i
$965$		0			0
$966$	−6.64861	+	16.0512i	−0.213915	+	0.516437i
$967$	7.19460	−	7.19460i	0.231363	−	0.231363i	−0.581899	−	0.813261i	$-0.697690\pi$
$967$	7.19460	−	7.19460i	0.231363	−	0.231363i	0.813261	+	0.581899i	$0.197690\pi$
$968$	31.3427			1.00739
$969$	50.9535	−	5.73480i	1.63686	−	0.184228i
$970$		0			0
$971$	10.6541	−	10.6541i	0.341905	−	0.341905i	−0.515178	−	0.857083i	$-0.672274\pi$
$971$	10.6541	−	10.6541i	0.341905	−	0.341905i	0.857083	+	0.515178i	$0.172274\pi$
$972$	−6.85781	+	16.5562i	−0.219965	+	0.531041i
$973$			0.0712569i			0.00228439i
$974$	−50.5798	−	20.9508i	−1.62068	−	0.671309i
$975$		0			0
$976$	−4.74010	+	1.96341i	−0.151727	+	0.0628473i
$977$	12.7437	+	12.7437i	0.407708	+	0.407708i	0.880939	−	0.473231i	$-0.156912\pi$
$977$	12.7437	+	12.7437i	0.407708	+	0.407708i	−0.473231	+	0.880939i	$0.656912\pi$
$978$	12.4314	+	12.4314i	0.397512	+	0.397512i
$979$	36.8026	−	15.2441i	1.17622	−	0.487205i
$980$		0			0
$981$	5.26885	+	2.18243i	0.168221	+	0.0696796i
$982$		−	92.3429i		−	2.94678i
$983$	−9.17720	+	22.1557i	−0.292707	+	0.706658i	−1.00000		0.000262992i	$-0.999916\pi$
$983$	−9.17720	+	22.1557i	−0.292707	+	0.706658i	0.707293	+	0.706921i	$0.249916\pi$
$984$	41.2492	−	41.2492i	1.31498	−	1.31498i
$985$		0			0
$986$	1.04096	+	9.24892i	0.0331511	+	0.294546i
$987$	−11.5960			−0.369103
$988$	54.6405	−	54.6405i	1.73835	−	1.73835i
$989$	−4.21904	+	10.1857i	−0.134158	+	0.323885i
$990$		0			0
$991$	32.6010	+	13.5038i	1.03560	+	0.428961i	0.834732	−	0.550656i	$-0.185622\pi$
$991$	32.6010	+	13.5038i	1.03560	+	0.428961i	0.200872	+	0.979617i	$0.435622\pi$
$992$	2.44870	+	5.91169i	0.0777463	+	0.187696i
$993$	15.8694	−	6.57333i	0.503601	−	0.208598i
$994$	−3.26473	−	3.26473i	−0.103551	−	0.103551i
$995$		0			0
$996$	73.0132	−	30.2430i	2.31351	−	0.958287i
$997$	19.6247	+	47.3783i	0.621522	+	1.50049i	0.849916	+	0.526918i	$0.176652\pi$
$997$	19.6247	+	47.3783i	0.621522	+	1.50049i	−0.228394	+	0.973569i	$0.573348\pi$
$998$	−7.74670	−	3.20879i	−0.245217	−	0.101572i
$999$			1.89407i			0.0599257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.e.76.6		24
5.2	odd	4		85.2.m.a.59.6	yes	24
5.3	odd	4		85.2.m.a.59.1	yes	24
5.4	even	2	inner	425.2.m.e.76.1		24
15.2	even	4		765.2.bh.b.739.1		24
15.8	even	4		765.2.bh.b.739.6		24
17.7	odd	16		7225.2.a.by.1.1		24
17.10	odd	16		7225.2.a.by.1.2		24
17.15	even	8	inner	425.2.m.e.151.6		24
85.7	even	16		1445.2.b.i.579.2		24
85.24	odd	16		7225.2.a.by.1.24		24
85.27	even	16		1445.2.b.i.579.1		24
85.32	odd	8		85.2.m.a.49.1	✓	24
85.44	odd	16		7225.2.a.by.1.23		24
85.49	even	8	inner	425.2.m.e.151.1		24
85.58	even	16		1445.2.b.i.579.23		24
85.78	even	16		1445.2.b.i.579.24		24
85.83	odd	8		85.2.m.a.49.6	yes	24
255.32	even	8		765.2.bh.b.559.6		24
255.83	even	8		765.2.bh.b.559.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.49.1	✓	24	85.32	odd	8
85.2.m.a.49.6	yes	24	85.83	odd	8
85.2.m.a.59.1	yes	24	5.3	odd	4
85.2.m.a.59.6	yes	24	5.2	odd	4
425.2.m.e.76.1		24	5.4	even	2	inner
425.2.m.e.76.6		24	1.1	even	1	trivial
425.2.m.e.151.1		24	85.49	even	8	inner
425.2.m.e.151.6		24	17.15	even	8	inner
765.2.bh.b.559.1		24	255.83	even	8
765.2.bh.b.559.6		24	255.32	even	8
765.2.bh.b.739.1		24	15.2	even	4
765.2.bh.b.739.6		24	15.8	even	4
1445.2.b.i.579.1		24	85.27	even	16
1445.2.b.i.579.2		24	85.7	even	16
1445.2.b.i.579.23		24	85.58	even	16
1445.2.b.i.579.24		24	85.78	even	16
7225.2.a.by.1.1		24	17.7	odd	16
7225.2.a.by.1.2		24	17.10	odd	16
7225.2.a.by.1.23		24	85.44	odd	16
7225.2.a.by.1.24		24	85.24	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63043 - 1.63043i) q^{2} +(0.718554 - 1.73474i) q^{3} -3.31660i q^{4} +(-1.65683 - 3.99993i) q^{6} +(-1.42808 + 0.591528i) q^{7} +(-2.14663 - 2.14663i) q^{8} +(-0.371694 - 0.371694i) q^{9} +(-1.76717 - 4.26632i) q^{11} +(-5.75346 - 2.38316i) q^{12} +3.51782i q^{13} +(-1.36393 + 3.29282i) q^{14} -0.366652 q^{16} +(-1.14190 + 3.96182i) q^{17} -1.21204 q^{18} +(4.68326 - 4.68326i) q^{19} +2.90239i q^{21} +(-9.83718 - 4.07469i) q^{22} +(0.993477 + 2.39846i) q^{23} +(-5.26632 + 2.18138i) q^{24} +(5.73556 + 5.73556i) q^{26} +(4.29235 - 1.77795i) q^{27} +(1.96187 + 4.73636i) q^{28} +(0.904478 + 0.374647i) q^{29} +(-0.468546 + 1.13117i) q^{31} +(3.69546 - 3.69546i) q^{32} -8.67078 q^{33} +(4.59768 + 8.32127i) q^{34} +(-1.23276 + 1.23276i) q^{36} +(-0.156011 + 0.376644i) q^{37} -15.2714i q^{38} +(6.10251 + 2.52774i) q^{39} +(-9.45483 + 3.91632i) q^{41} +(4.73214 + 4.73214i) q^{42} +(3.00290 + 3.00290i) q^{43} +(-14.1497 + 5.86100i) q^{44} +(5.53032 + 2.29073i) q^{46} +3.99531i q^{47} +(-0.263460 + 0.636048i) q^{48} +(-3.26025 + 3.26025i) q^{49} +(6.05223 + 4.82770i) q^{51} +11.6672 q^{52} +(1.24288 - 1.24288i) q^{53} +(4.09956 - 9.89721i) q^{54} +(4.33534 + 1.79576i) q^{56} +(-4.75907 - 11.4894i) q^{57} +(2.08552 - 0.863853i) q^{58} +(1.10431 + 1.10431i) q^{59} +(12.9280 - 5.35497i) q^{61} +(1.08036 + 2.60823i) q^{62} +(0.750675 + 0.310940i) q^{63} -12.7837i q^{64} +(-14.1371 + 14.1371i) q^{66} -8.84212 q^{67} +(13.1398 + 3.78724i) q^{68} +4.87459 q^{69} +(-0.495735 + 1.19681i) q^{71} +1.59578i q^{72} +(-9.03279 - 3.74150i) q^{73} +(0.359726 + 0.868456i) q^{74} +(-15.5325 - 15.5325i) q^{76} +(5.04730 + 5.04730i) q^{77} +(14.0710 - 5.82841i) q^{78} +(-4.17760 - 10.0856i) q^{79} -10.3007i q^{81} +(-9.03016 + 21.8007i) q^{82} +(-8.97341 + 8.97341i) q^{83} +9.62608 q^{84} +9.79203 q^{86} +(1.29983 - 1.29983i) q^{87} +(-5.36476 + 12.9517i) q^{88} +8.62631i q^{89} +(-2.08089 - 5.02371i) q^{91} +(7.95476 - 3.29497i) q^{92} +(1.62561 + 1.62561i) q^{93} +(6.51407 + 6.51407i) q^{94} +(-3.75529 - 9.06606i) q^{96} +(5.47747 + 2.26884i) q^{97} +10.6312i q^{98} +(-0.928920 + 2.24261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Introduction

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