LMFDB - Embedded newform 603.2.z.c.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(10,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("603.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.z (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	603.10
Dual form			603.2.z.c.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38159 - 1.31734i) q^{2} +(0.0782330 + 1.64231i) q^{4} +(1.09559 - 2.39900i) q^{5} +(-0.489299 + 2.01692i) q^{7} +(-0.444821 + 0.513350i) q^{8} +O(q^{10})$	\(q+(-1.38159 - 1.31734i) q^{2} +(0.0782330 + 1.64231i) q^{4} +(1.09559 - 2.39900i) q^{5} +(-0.489299 + 2.01692i) q^{7} +(-0.444821 + 0.513350i) q^{8} +(-4.67395 + 1.87117i) q^{10} +(3.08119 + 4.32693i) q^{11} +(-1.07027 + 3.09234i) q^{13} +(3.33298 - 2.14198i) q^{14} +(4.56428 - 0.435836i) q^{16} +(-0.0614384 + 1.28975i) q^{17} +(0.549248 + 2.26403i) q^{19} +(4.02562 + 1.61161i) q^{20} +(1.44310 - 10.0370i) q^{22} +(-6.06274 + 4.76779i) q^{23} +(-1.28058 - 1.47787i) q^{25} +(5.55234 - 2.86243i) q^{26} +(-3.35069 - 0.645793i) q^{28} +(-0.104691 + 0.181330i) q^{29} +(2.00833 + 5.80270i) q^{31} +(-5.81223 - 4.57079i) q^{32} +(1.78392 - 1.70097i) q^{34} +(4.30252 + 3.38354i) q^{35} +(-3.39001 - 5.87167i) q^{37} +(2.22367 - 3.85151i) q^{38} +(0.744188 + 1.62954i) q^{40} +(-1.03936 + 0.535829i) q^{41} +(-5.08167 - 3.26579i) q^{43} +(-6.86512 + 5.39879i) q^{44} +(14.6570 + 1.39958i) q^{46} +(8.27339 + 3.31217i) q^{47} +(2.39330 + 1.23383i) q^{49} +(-0.177624 + 3.72878i) q^{50} +(-5.16232 - 1.51580i) q^{52} +(5.11758 - 3.28887i) q^{53} +(13.7560 - 2.65125i) q^{55} +(-0.817736 - 1.14835i) q^{56} +(0.383514 - 0.112610i) q^{58} +(1.78199 - 2.05652i) q^{59} +(-1.50949 + 2.11978i) q^{61} +(4.86945 - 10.6626i) q^{62} +(0.703780 + 4.89489i) q^{64} +(6.24595 + 5.95551i) q^{65} +(3.67942 + 7.31176i) q^{67} -2.12298 q^{68} +(-1.48703 - 10.3425i) q^{70} +(-0.634636 - 13.3226i) q^{71} +(3.40776 - 4.78553i) q^{73} +(-3.05140 + 12.5780i) q^{74} +(-3.67528 + 1.07916i) q^{76} +(-10.2347 + 4.09735i) q^{77} +(-0.226263 + 0.0436086i) q^{79} +(3.95499 - 11.4272i) q^{80} +(2.14184 + 0.628902i) q^{82} +(-5.05885 + 0.483062i) q^{83} +(3.02680 + 1.56042i) q^{85} +(2.71861 + 11.2063i) q^{86} +(-3.59181 - 0.342976i) q^{88} +(1.05386 - 7.32975i) q^{89} +(-5.71332 - 3.67173i) q^{91} +(-8.30451 - 9.58392i) q^{92} +(-7.06717 - 15.4749i) q^{94} +(6.03316 + 1.16280i) q^{95} +(-2.11201 - 3.65811i) q^{97} +(-1.68118 - 4.85744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{8}{33}\right)$	$1$

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 $

$2$	−1.38159	−	1.31734i	−0.976930	−	0.931501i	0.0207356	−	0.999785i	$-0.493399\pi$
$2$	−1.38159	−	1.31734i	−0.976930	−	0.931501i	−0.997666	+	0.0682838i	$0.978248\pi$
$3$		0			0
$3$		0			0
$4$	0.0782330	+	1.64231i	0.0391165	+	0.821156i
$5$	1.09559	−	2.39900i	0.489961	−	1.07287i	−0.489642	−	0.871923i	$-0.662873\pi$
$5$	1.09559	−	2.39900i	0.489961	−	1.07287i	0.979603	−	0.200942i	$-0.0644002\pi$
$6$		0			0
$7$	−0.489299	+	2.01692i	−0.184938	+	0.762324i	0.801474	+	0.598030i	$0.204050\pi$
$7$	−0.489299	+	2.01692i	−0.184938	+	0.762324i	−0.986411	+	0.164294i	$0.947466\pi$
$8$	−0.444821	+	0.513350i	−0.157268	+	0.181497i
$9$		0			0
$10$	−4.67395	+	1.87117i	−1.47803	+	0.591715i
$11$	3.08119	+	4.32693i	0.929014	+	1.30462i	0.952387	+	0.304891i	$0.0986199\pi$
$11$	3.08119	+	4.32693i	0.929014	+	1.30462i	−0.0233736	+	0.999727i	$0.507441\pi$
$12$		0			0
$13$	−1.07027	+	3.09234i	−0.296840	+	0.857662i	0.693679	+	0.720284i	$0.255989\pi$
$13$	−1.07027	+	3.09234i	−0.296840	+	0.857662i	−0.990519	+	0.137377i	$0.956133\pi$
$14$	3.33298	−	2.14198i	0.890777	−	0.572467i
$15$		0			0
$16$	4.56428	−	0.435836i	1.14107	−	0.108959i
$17$	−0.0614384	+	1.28975i	−0.0149010	+	0.312810i	0.979096	+	0.203400i	$0.0651992\pi$
$17$	−0.0614384	+	1.28975i	−0.0149010	+	0.312810i	−0.993997	+	0.109410i	$0.965104\pi$
$18$		0			0
$19$	0.549248	+	2.26403i	0.126006	+	0.519405i	0.999471	+	0.0325176i	$0.0103525\pi$
$19$	0.549248	+	2.26403i	0.126006	+	0.519405i	−0.873465	+	0.486887i	$0.838132\pi$
$20$	4.02562	+	1.61161i	0.900156	+	0.360368i
$21$		0			0
$22$	1.44310	−	10.0370i	0.307671	−	2.13990i
$23$	−6.06274	+	4.76779i	−1.26417	+	0.994153i	−0.264613	+	0.964355i	$0.585244\pi$
$23$	−6.06274	+	4.76779i	−1.26417	+	0.994153i	−0.999556	+	0.0297984i	$0.990513\pi$
$24$		0			0
$25$	−1.28058	−	1.47787i	−0.256117	−	0.295575i
$26$	5.55234	−	2.86243i	1.08890	−	0.561369i
$27$		0			0
$28$	−3.35069	−	0.645793i	−0.633221	−	0.122043i
$29$	−0.104691	+	0.181330i	−0.0194406	+	0.0336722i	−0.875582	−	0.483069i	$-0.839522\pi$
$29$	−0.104691	+	0.181330i	−0.0194406	+	0.0336722i	0.856141	+	0.516742i	$0.172855\pi$
$30$		0			0
$31$	2.00833	+	5.80270i	0.360707	+	1.04220i	0.968696	+	0.248250i	$0.0798554\pi$
$31$	2.00833	+	5.80270i	0.360707	+	1.04220i	−0.607989	+	0.793946i	$0.708023\pi$
$32$	−5.81223	−	4.57079i	−1.02747	−	0.808008i
$33$		0			0
$34$	1.78392	−	1.70097i	0.305940	−	0.291714i
$35$	4.30252	+	3.38354i	0.727258	+	0.571922i
$36$		0			0
$37$	−3.39001	−	5.87167i	−0.557314	−	0.965297i	−0.997719	−	0.0674975i	$-0.978499\pi$
$37$	−3.39001	−	5.87167i	−0.557314	−	0.965297i	0.440405	−	0.897799i	$-0.354835\pi$
$38$	2.22367	−	3.85151i	0.360727	−	0.624797i
$39$		0			0
$40$	0.744188	+	1.62954i	0.117666	+	0.257654i
$41$	−1.03936	+	0.535829i	−0.162321	+	0.0836825i	−0.537473	−	0.843281i	$-0.680621\pi$
$41$	−1.03936	+	0.535829i	−0.162321	+	0.0836825i	0.375152	+	0.926963i	$0.377591\pi$
$42$		0			0
$43$	−5.08167	−	3.26579i	−0.774948	−	0.498029i	0.0924056	−	0.995721i	$-0.470544\pi$
$43$	−5.08167	−	3.26579i	−0.774948	−	0.498029i	−0.867353	+	0.497693i	$0.834181\pi$
$44$	−6.86512	+	5.39879i	−1.03496	+	0.813898i
$45$		0			0
$46$	14.6570	+	1.39958i	2.16106	+	0.206356i
$47$	8.27339	+	3.31217i	1.20680	+	0.483129i	0.885852	−	0.463968i	$-0.153575\pi$
$47$	8.27339	+	3.31217i	1.20680	+	0.483129i	0.320947	+	0.947097i	$0.395999\pi$
$48$		0			0
$49$	2.39330	+	1.23383i	0.341900	+	0.176262i
$50$	−0.177624	+	3.72878i	−0.0251198	+	0.527329i
$51$		0			0
$52$	−5.16232	−	1.51580i	−0.715886	−	0.210203i
$53$	5.11758	−	3.28887i	0.702954	−	0.451761i	−0.139716	−	0.990192i	$-0.544619\pi$
$53$	5.11758	−	3.28887i	0.702954	−	0.451761i	0.842670	+	0.538431i	$0.180983\pi$
$54$		0			0
$55$	13.7560	−	2.65125i	1.85486	−	0.357495i
$56$	−0.817736	−	1.14835i	−0.109275	−	0.153455i
$57$		0			0
$58$	0.383514	−	0.112610i	0.0503578	−	0.0147864i
$59$	1.78199	−	2.05652i	0.231995	−	0.267736i	−0.627802	−	0.778373i	$-0.716045\pi$
$59$	1.78199	−	2.05652i	0.231995	−	0.267736i	0.859796	+	0.510637i	$0.170590\pi$
$60$		0			0
$61$	−1.50949	+	2.11978i	−0.193270	+	0.271410i	−0.899828	−	0.436246i	$-0.856308\pi$
$61$	−1.50949	+	2.11978i	−0.193270	+	0.271410i	0.706557	+	0.707656i	$0.250247\pi$
$62$	4.86945	−	10.6626i	0.618420	−	1.35415i
$63$		0			0
$64$	0.703780	+	4.89489i	0.0879724	+	0.611862i
$65$	6.24595	+	5.95551i	0.774715	+	0.738690i
$66$		0			0
$67$	3.67942	+	7.31176i	0.449512	+	0.893274i
$67$	3.67942	+	7.31176i	0.449512	+	0.893274i
$68$	−2.12298			−0.257449
$69$		0			0
$70$	−1.48703	−	10.3425i	−0.177734	−	1.23617i
$71$	−0.634636	−	13.3226i	−0.0753174	−	1.58111i	−0.648200	−	0.761470i	$-0.724478\pi$
$71$	−0.634636	−	13.3226i	−0.0753174	−	1.58111i	0.572883	−	0.819637i	$-0.305825\pi$
$72$		0			0
$73$	3.40776	−	4.78553i	0.398848	−	0.560104i	−0.565497	−	0.824750i	$-0.691316\pi$
$73$	3.40776	−	4.78553i	0.398848	−	0.560104i	0.964346	+	0.264646i	$0.0852552\pi$
$74$	−3.05140	+	12.5780i	−0.354718	+	1.46217i
$75$		0			0
$76$	−3.67528	+	1.07916i	−0.421584	+	0.123788i
$77$	−10.2347	+	4.09735i	−1.16635	+	0.466936i
$78$		0			0
$79$	−0.226263	+	0.0436086i	−0.0254566	+	0.00490635i	−0.201964	−	0.979393i	$-0.564732\pi$
$79$	−0.226263	+	0.0436086i	−0.0254566	+	0.00490635i	0.176507	+	0.984299i	$0.443520\pi$
$80$	3.95499	−	11.4272i	0.442181	−	1.27760i
$81$		0			0
$82$	2.14184	+	0.628902i	0.236527	+	0.0694506i
$83$	−5.05885	+	0.483062i	−0.555281	+	0.0530229i	−0.368925	−	0.929459i	$-0.620274\pi$
$83$	−5.05885	+	0.483062i	−0.555281	+	0.0530229i	−0.186357	+	0.982482i	$0.559668\pi$
$84$		0			0
$85$	3.02680	+	1.56042i	0.328302	+	0.169252i
$86$	2.71861	+	11.2063i	0.293156	+	1.20840i
$87$		0			0
$88$	−3.59181	−	0.342976i	−0.382888	−	0.0365614i
$89$	1.05386	−	7.32975i	0.111709	−	0.776952i	−0.854548	−	0.519372i	$-0.826166\pi$
$89$	1.05386	−	7.32975i	0.111709	−	0.776952i	0.966257	−	0.257580i	$-0.0829251\pi$
$90$		0			0
$91$	−5.71332	−	3.67173i	−0.598919	−	0.384902i
$92$	−8.30451	−	9.58392i	−0.865805	−	0.999192i
$93$		0			0
$94$	−7.06717	−	15.4749i	−0.728923	−	1.59612i
$95$	6.03316	+	1.16280i	0.618989	+	0.119300i
$96$		0			0
$97$	−2.11201	−	3.65811i	−0.214442	−	0.371425i	0.738658	−	0.674081i	$-0.235460\pi$
$97$	−2.11201	−	3.65811i	−0.214442	−	0.371425i	−0.953100	+	0.302656i	$0.902127\pi$
$98$	−1.68118	−	4.85744i	−0.169825	−	0.490676i
$99$		0			0
$100$	2.32695	−	2.21874i	0.232695	−	0.221874i
$101$	−2.13706	+	2.03768i	−0.212645	+	0.202757i	−0.788914	−	0.614503i	$-0.789356\pi$
$101$	−2.13706	+	2.03768i	−0.212645	+	0.202757i	0.576269	+	0.817260i	$0.304508\pi$
$102$		0			0
$103$	−0.348941	−	1.00820i	−0.0343822	−	0.0993408i	0.926503	−	0.376286i	$-0.122799\pi$
$103$	−0.348941	−	1.00820i	−0.0343822	−	0.0993408i	−0.960886	+	0.276945i	$0.910678\pi$
$104$	−1.11138	−	1.92496i	−0.108979	−	0.188758i
$105$		0			0
$106$	−11.4030	−	2.19774i	−1.10755	−	0.213463i
$107$	6.66606	+	14.5966i	0.644432	+	1.41111i	0.896344	+	0.443360i	$0.146214\pi$
$107$	6.66606	+	14.5966i	0.644432	+	1.41111i	−0.251911	+	0.967750i	$0.581059\pi$
$108$		0			0
$109$	3.47335	+	4.00846i	0.332687	+	0.383941i	0.897305	−	0.441411i	$-0.145522\pi$
$109$	3.47335	+	4.00846i	0.332687	+	0.383941i	−0.564618	+	0.825352i	$0.690977\pi$
$110$	−22.4977	−	14.4584i	−2.14508	−	1.37856i
$111$		0			0
$112$	−1.35425	+	9.41903i	−0.127965	+	0.890015i
$113$	−7.19567	−	0.687103i	−0.676911	−	0.0646372i	−0.249062	−	0.968487i	$-0.580122\pi$
$113$	−7.19567	−	0.687103i	−0.676911	−	0.0646372i	−0.427849	+	0.903850i	$0.640728\pi$
$114$		0			0
$115$	4.79567	+	19.7680i	0.447199	+	1.84338i
$116$	−0.305991	−	0.157749i	−0.0284106	−	0.0146467i
$117$		0			0
$118$	−5.17111	+	0.493781i	−0.476039	+	0.0454562i
$119$	−2.57126	−	0.754990i	−0.235707	−	0.0692098i
$120$		0			0
$121$	−5.63081	+	16.2692i	−0.511892	+	1.47901i
$122$	4.87796	−	0.940150i	0.441630	−	0.0851172i
$123$		0			0
$124$	−9.37273	+	3.75227i	−0.841696	+	0.336964i
$125$	7.70409	−	2.26212i	0.689074	−	0.202331i
$126$		0			0
$127$	1.30086	−	5.36223i	0.115433	−	0.475821i	−0.884524	−	0.466495i	$-0.845516\pi$
$127$	1.30086	−	5.36223i	0.115433	−	0.475821i	0.999957	−	0.00932557i	$-0.00296847\pi$
$128$	−3.10219	+	4.35642i	−0.274197	+	0.385056i
$129$		0			0
$130$	−0.783901	−	16.4561i	−0.0687527	−	1.44330i
$131$	3.24689	+	22.5826i	0.283682	+	1.97305i	0.222548	+	0.974922i	$0.428563\pi$
$131$	3.24689	+	22.5826i	0.283682	+	1.97305i	0.0611341	+	0.998130i	$0.480528\pi$
$132$		0			0
$133$	−4.83512			−0.419258
$134$	4.54865	−	14.9489i	0.392944	−	1.29139i
$135$		0			0
$136$	−0.634765	−	0.605247i	−0.0544306	−	0.0518995i
$137$	0.252348	+	1.75512i	0.0215595	+	0.149950i	0.997758	−	0.0669311i	$-0.0213208\pi$
$137$	0.252348	+	1.75512i	0.0215595	+	0.149950i	−0.976198	+	0.216881i	$0.930412\pi$
$138$		0			0
$139$	2.56455	−	5.61558i	0.217522	−	0.476307i	−0.769142	−	0.639078i	$-0.779316\pi$
$139$	2.56455	−	5.61558i	0.217522	−	0.476307i	0.986664	+	0.162771i	$0.0520432\pi$
$140$	−5.22023	+	7.33078i	−0.441190	+	0.619564i
$141$		0			0
$142$	−16.6737	+	19.2424i	−1.39922	+	1.61479i
$143$	−16.6780	+	4.89712i	−1.39469	+	0.409517i
$144$		0			0
$145$	0.320313	+	0.449817i	0.0266006	+	0.0373553i
$146$	−11.0123	+	2.12245i	−0.911384	+	0.175655i
$147$		0			0
$148$	9.37791	−	6.02682i	0.770859	−	0.495401i
$149$	−19.1834	−	5.63274i	−1.57156	−	0.461452i	−0.624107	−	0.781339i	$-0.714537\pi$
$149$	−19.1834	−	5.63274i	−1.57156	−	0.461452i	−0.947456	+	0.319887i	$0.896355\pi$
$150$		0			0
$151$	0.0616476	−	1.29414i	0.00501681	−	0.105316i	−0.994970	−	0.100174i	$-0.968060\pi$
$151$	0.0616476	−	1.29414i	0.00501681	−	0.105316i	0.999987	−	0.00514215i	$-0.00163680\pi$
$152$	−1.40656	−	0.725131i	−0.114087	−	0.0588159i
$153$		0			0
$154$	19.5377	+	7.82173i	1.57439	+	0.630293i
$155$	16.1210	+	1.53937i	1.29487	+	0.123645i
$156$		0			0
$157$	−11.2013	+	8.80882i	−0.893963	+	0.703021i	−0.955471	−	0.295086i	$-0.904652\pi$
$157$	−11.2013	+	8.80882i	−0.893963	+	0.703021i	0.0615072	+	0.998107i	$0.480409\pi$
$158$	0.370050	+	0.237816i	0.0294396	+	0.0189197i
$159$		0			0
$160$	−17.3331	+	8.93584i	−1.37030	+	0.706440i
$161$	−6.64975	−	14.5609i	−0.524074	−	1.14756i
$162$		0			0
$163$	2.41252	−	4.17861i	0.188963	−	0.327294i	−0.755942	−	0.654639i	$-0.772821\pi$
$163$	2.41252	−	4.17861i	0.188963	−	0.327294i	0.944905	+	0.327345i	$0.106154\pi$
$164$	−0.961312	−	1.66504i	−0.0750658	−	0.130018i
$165$		0			0
$166$	7.62561	+	5.99685i	0.591862	+	0.465446i
$167$	−5.68017	+	5.41603i	−0.439545	+	0.419105i	−0.877265	−	0.480006i	$-0.840634\pi$
$167$	−5.68017	+	5.41603i	−0.439545	+	0.419105i	0.437720	+	0.899111i	$0.355786\pi$
$168$		0			0
$169$	1.80159	+	1.41678i	0.138583	+	0.108983i
$170$	−2.12618	−	6.14319i	−0.163070	−	0.471161i
$171$		0			0
$172$	4.96590	−	8.60119i	0.378646	−	0.655834i
$173$	−3.22624	−	0.621807i	−0.245286	−	0.0472751i	0.0651261	−	0.997877i	$-0.479255\pi$
$173$	−3.22624	−	0.621807i	−0.245286	−	0.0472751i	−0.310412	+	0.950602i	$0.600467\pi$
$174$		0			0
$175$	3.60734	−	1.85971i	0.272689	−	0.140581i
$176$	15.9492	+	18.4064i	1.20222	+	1.38743i
$177$		0			0
$178$	−11.1118	+	8.73841i	−0.832864	+	0.654971i
$179$	−0.844664	+	5.87477i	−0.0631332	+	0.439101i	0.933599	+	0.358320i	$0.116650\pi$
$179$	−0.844664	+	5.87477i	−0.0631332	+	0.439101i	−0.996732	+	0.0807805i	$0.974259\pi$
$180$		0			0
$181$	−0.754117	−	0.301903i	−0.0560531	−	0.0224403i	0.343467	−	0.939165i	$-0.388399\pi$
$181$	−0.754117	−	0.301903i	−0.0560531	−	0.0224403i	−0.399520	+	0.916725i	$0.630823\pi$
$182$	3.05654	+	12.5992i	0.226566	+	0.933916i
$183$		0			0
$184$	0.249284	−	5.23312i	0.0183775	−	0.385791i
$185$	−17.8002	+	1.69971i	−1.30870	+	0.124965i
$186$		0			0
$187$	−5.76996	+	3.70813i	−0.421941	+	0.271165i
$188$	−4.79236	+	13.8466i	−0.349519	+	1.00987i
$189$		0			0
$190$	−6.80354	−	9.55424i	−0.493581	−	0.693137i
$191$	18.9124	−	7.57140i	1.36846	−	0.547847i	0.433033	−	0.901378i	$-0.357443\pi$
$191$	18.9124	−	7.57140i	1.36846	−	0.547847i	0.935423	+	0.353531i	$0.115019\pi$
$192$		0			0
$193$	−2.04204	+	2.35665i	−0.146990	+	0.169635i	−0.824470	−	0.565906i	$-0.808527\pi$
$193$	−2.04204	+	2.35665i	−0.146990	+	0.169635i	0.677480	+	0.735541i	$0.263072\pi$
$194$	−1.90105	+	7.83624i	−0.136487	+	0.562609i
$195$		0			0
$196$	−1.83910	+	4.02707i	−0.131365	+	0.287648i
$197$	0.0534554	+	1.12217i	0.00380854	+	0.0799511i	0.999971	−	0.00756824i	$-0.00240907\pi$
$197$	0.0534554	+	1.12217i	0.00380854	+	0.0799511i	−0.996163	+	0.0875194i	$0.972106\pi$
$198$		0			0
$199$	−6.81457	−	6.49768i	−0.483072	−	0.460608i	0.408978	−	0.912544i	$-0.365885\pi$
$199$	−6.81457	−	6.49768i	−0.483072	−	0.460608i	−0.892050	+	0.451936i	$0.850734\pi$
$200$	1.32830			0.0939248
$201$		0			0
$202$	5.63686			0.396608
$203$	−0.314503	−	0.299878i	−0.0220738	−	0.0210473i
$204$		0			0
$205$	0.146741	+	3.08048i	0.0102489	+	0.215150i
$206$	−0.846050	+	1.85259i	−0.0589471	+	0.129076i
$207$		0			0
$208$	−3.53726	+	14.5808i	−0.245265	+	1.01099i
$209$	−8.10396	+	9.35247i	−0.560563	+	0.646924i
$210$		0			0
$211$	10.8840	−	4.35728i	0.749282	−	0.299967i	0.0345854	−	0.999402i	$-0.488989\pi$
$211$	10.8840	−	4.35728i	0.749282	−	0.299967i	0.714697	+	0.699434i	$0.246565\pi$
$212$	5.80172	+	8.14737i	0.398463	+	0.559564i
$213$		0			0
$214$	10.0190	−	28.9480i	0.684885	−	1.97885i
$215$	−13.4020	+	8.61297i	−0.914012	+	0.587400i
$216$		0			0
$217$	−12.6862	+	1.21139i	−0.861199	+	0.0822345i
$218$	0.481772	−	10.1136i	0.0326297	−	0.684982i
$219$		0			0
$220$	5.43036	+	22.3842i	0.366115	+	1.50915i
$221$	−3.92259	−	1.57037i	−0.263862	−	0.105634i
$222$		0			0
$223$	4.02969	−	28.0271i	0.269848	−	1.87683i	−0.179913	−	0.983683i	$-0.557582\pi$
$223$	4.02969	−	28.0271i	0.269848	−	1.87683i	0.449760	−	0.893149i	$-0.351509\pi$
$224$	12.0628	−	9.48631i	0.805981	−	0.633831i
$225$		0			0
$226$	9.03630	+	10.4284i	0.601086	+	0.693690i
$227$	−0.227384	+	0.117225i	−0.0150920	+	0.00778048i	−0.465756	−	0.884913i	$-0.654218\pi$
$227$	−0.227384	+	0.117225i	−0.0150920	+	0.00778048i	0.450664	+	0.892694i	$0.351187\pi$
$228$		0			0
$229$	5.25142	+	1.01213i	0.347024	+	0.0668833i	0.359785	−	0.933035i	$-0.382850\pi$
$229$	5.25142	+	1.01213i	0.347024	+	0.0668833i	−0.0127614	+	0.999919i	$0.504062\pi$
$230$	19.4156	−	33.6288i	1.28023	−	2.21742i
$231$		0			0
$232$	−0.0465172	−	0.134403i	−0.00305400	−	0.00882397i
$233$	13.5265	+	10.6373i	0.886148	+	0.696874i	0.953674	−	0.300843i	$-0.0972681\pi$
$233$	13.5265	+	10.6373i	0.886148	+	0.696874i	−0.0675259	+	0.997718i	$0.521511\pi$
$234$		0			0
$235$	17.0101	−	16.2191i	1.10962	−	1.05802i
$236$	3.51686	+	2.76569i	0.228928	+	0.180031i
$237$		0			0
$238$	2.55784	+	4.43031i	0.165800	+	0.287174i
$239$	0.621027	−	1.07565i	0.0401709	−	0.0695780i	−0.845241	−	0.534385i	$-0.820543\pi$
$239$	0.621027	−	1.07565i	0.0401709	−	0.0695780i	0.885412	+	0.464807i	$0.153876\pi$
$240$		0			0
$241$	0.991243	+	2.17052i	0.0638515	+	0.139815i	0.938867	−	0.344279i	$-0.111877\pi$
$241$	0.991243	+	2.17052i	0.0638515	+	0.139815i	−0.875016	+	0.484094i	$0.839149\pi$
$242$	29.2115	−	15.0596i	1.87779	−	0.968066i
$243$		0			0
$244$	−3.59943	−	2.31321i	−0.230430	−	0.148088i
$245$	5.58203	−	4.38976i	0.356623	−	0.280451i
$246$		0			0
$247$	−7.58901	−	0.724662i	−0.482877	−	0.0461092i
$248$	−3.87217	−	1.55018i	−0.245883	−	0.0984366i
$249$		0			0
$250$	−13.6239	−	7.02359i	−0.861649	−	0.444211i
$251$	0.985774	−	20.6940i	0.0622215	−	1.30619i	−0.724669	−	0.689098i	$-0.758007\pi$
$251$	0.985774	−	20.6940i	0.0622215	−	1.30619i	0.786890	−	0.617093i	$-0.211690\pi$
$252$		0			0
$253$	−39.3103	−	11.5426i	−2.47142	−	0.725674i
$254$	−8.86115	+	5.69471i	−0.555998	+	0.357318i
$255$		0			0
$256$	19.7366	−	3.80391i	1.23354	−	0.237744i
$257$	−11.2023	−	15.7314i	−0.698777	−	0.981295i	−0.999618	−	0.0276211i	$-0.991207\pi$
$257$	−11.2023	−	15.7314i	−0.698777	−	0.981295i	0.300841	−	0.953674i	$-0.402733\pi$
$258$		0			0
$259$	13.5014	−	3.96437i	0.838937	−	0.246334i
$260$	−9.29216	+	10.7237i	−0.576276	+	0.665057i
$261$		0			0
$262$	25.2631	−	35.4771i	1.56076	−	2.19178i
$263$	7.09723	−	15.5408i	0.437634	−	0.958284i	−0.554393	−	0.832255i	$-0.687049\pi$
$263$	7.09723	−	15.5408i	0.437634	−	0.958284i	0.992027	−	0.126029i	$-0.0402233\pi$
$264$		0			0
$265$	−2.28324	−	15.8803i	−0.140259	−	0.975520i
$266$	6.68014	+	6.36950i	0.409586	+	0.390539i
$267$		0			0
$268$	−11.7204	+	6.61478i	−0.715934	+	0.404062i
$269$	8.39240			0.511694			0.255847	−	0.966717i	$-0.417646\pi$
$269$	8.39240			0.511694			0.255847	+	0.966717i	$0.417646\pi$
$270$		0			0
$271$	2.52358	+	17.5519i	0.153297	+	1.06620i	0.910645	+	0.413190i	$0.135586\pi$
$271$	2.52358	+	17.5519i	0.153297	+	1.06620i	−0.757348	+	0.653011i	$0.773505\pi$
$272$	0.281697	+	5.91355i	0.0170804	+	0.358562i
$273$		0			0
$274$	1.96345	−	2.75728i	0.118616	−	0.166573i
$275$	2.44893	−	10.0946i	0.147676	−	0.608728i
$276$		0			0
$277$	12.4693	−	3.66132i	0.749208	−	0.219987i	0.115231	−	0.993339i	$-0.463239\pi$
$277$	12.4693	−	3.66132i	0.749208	−	0.219987i	0.633978	+	0.773351i	$0.281421\pi$
$278$	−10.9408	+	4.38003i	−0.656185	+	0.262697i
$279$		0			0
$280$	−3.65079	+	0.703632i	−0.218176	+	0.0420500i
$281$	0.929622	−	2.68597i	0.0554566	−	0.160231i	−0.913870	−	0.406006i	$-0.866921\pi$
$281$	0.929622	−	2.68597i	0.0554566	−	0.160231i	0.969327	+	0.245775i	$0.0790424\pi$
$282$		0			0
$283$	−28.2269	−	8.28816i	−1.67791	−	0.492680i	−0.702246	−	0.711934i	$-0.747820\pi$
$283$	−28.2269	−	8.28816i	−1.67791	−	0.492680i	−0.975668	+	0.219254i	$0.929638\pi$
$284$	21.8303	−	2.08454i	1.29539	−	0.123695i
$285$		0			0
$286$	29.4934	+	15.2049i	1.74398	+	0.899084i
$287$	−0.572164	−	2.35849i	−0.0337738	−	0.139217i
$288$		0			0
$289$	15.2633	+	1.45747i	0.897844	+	0.0857337i
$290$	0.150022	−	1.04342i	0.00880957	−	0.0612719i
$291$		0			0
$292$	8.12593	+	5.22222i	0.475534	+	0.305607i
$293$	11.5440	+	13.3225i	0.674407	+	0.778307i	0.985059	−	0.172217i	$-0.0550930\pi$
$293$	11.5440	+	13.3225i	0.674407	+	0.778307i	−0.310653	+	0.950524i	$0.600548\pi$
$294$		0			0
$295$	−2.98127	−	6.52808i	−0.173576	−	0.380079i
$296$	4.52217	+	0.871577i	0.262846	+	0.0506594i
$297$		0			0
$298$	19.0833	+	33.0532i	1.10546	+	1.91472i
$299$	−8.25487	−	23.8509i	−0.477392	−	1.37933i
$300$		0			0
$301$	9.07330	−	8.65137i	0.522976	−	0.498657i
$302$	−1.79000	+	1.70676i	−0.103003	+	0.0982130i
$303$		0			0
$304$	3.49367	+	10.0943i	0.200376	+	0.578947i
$305$	3.43157	+	5.94366i	0.196491	+	0.340333i
$306$		0			0
$307$	26.6665	+	5.13956i	1.52194	+	0.293330i	0.880575	−	0.473906i	$-0.157156\pi$
$307$	26.6665	+	5.13956i	1.52194	+	0.293330i	0.641365	+	0.767236i	$0.278368\pi$
$308$	−7.52982	−	16.4880i	−0.429051	−	0.939491i
$309$		0			0
$310$	−20.2447	−	23.3636i	−1.14982	−	1.32696i
$311$	5.64362	+	3.62694i	0.320020	+	0.205665i	0.690781	−	0.723064i	$-0.257267\pi$
$311$	5.64362	+	3.62694i	0.320020	+	0.205665i	−0.370761	+	0.928728i	$0.620903\pi$
$312$		0			0
$313$	−3.36312	+	23.3910i	−0.190095	+	1.32214i	0.641657	+	0.766992i	$0.278247\pi$
$313$	−3.36312	+	23.3910i	−0.190095	+	1.32214i	−0.831752	+	0.555147i	$0.812662\pi$
$314$	27.0799	+	2.58581i	1.52820	+	0.145926i
$315$		0			0
$316$	−0.0893202	−	0.368183i	−0.00502465	−	0.0207119i
$317$	−18.6109	−	9.59457i	−1.04529	−	0.538885i	−0.152008	−	0.988379i	$-0.548574\pi$
$317$	−18.6109	−	9.59457i	−1.04529	−	0.538885i	−0.893283	+	0.449494i	$0.851604\pi$
$318$		0			0
$319$	−1.10718	+	0.105722i	−0.0619900	+	0.00591932i
$320$	12.5139	+	3.67441i	0.699548	+	0.205406i
$321$		0			0
$322$	−9.99450	+	28.8772i	−0.556972	+	1.60926i
$323$	−2.95378	+	0.569294i	−0.164353	+	0.0316764i
$324$		0			0
$325$	5.94066	−	2.37828i	0.329529	−	0.131923i
$326$	−8.83777	+	2.59500i	−0.489479	+	0.143724i
$327$		0			0
$328$	0.187262	−	0.771906i	0.0103398	−	0.0426214i
$329$	−10.7285	+	15.0661i	−0.591483	+	0.830622i
$330$		0			0
$331$	−0.184653	−	3.87635i	−0.0101495	−	0.213064i	−0.998245	−	0.0592213i	$-0.981138\pi$
$331$	−0.184653	−	3.87635i	−0.0101495	−	0.213064i	0.988095	−	0.153842i	$-0.0491648\pi$
$332$	−1.18911	−	8.27043i	−0.0652608	−	0.453899i
$333$		0			0
$334$	14.9824			0.819802
$335$	21.5720	−	0.816253i	1.17861	−	0.0445966i
$336$		0			0
$337$	23.3616	+	22.2752i	1.27259	+	1.21341i	0.965108	+	0.261854i	$0.0843338\pi$
$337$	23.3616	+	22.2752i	1.27259	+	1.21341i	0.307479	+	0.951555i	$0.400515\pi$
$338$	−0.622663	−	4.33071i	−0.0338684	−	0.235560i
$339$		0			0
$340$	−2.32591	+	5.09303i	−0.126140	+	0.276208i
$341$	−18.9198	+	26.5691i	−1.02456	+	1.43880i
$342$		0			0
$343$	−13.1734	+	15.2029i	−0.711295	+	0.820878i
$344$	3.93693	−	1.15599i	0.212265	−	0.0623266i
$345$		0			0
$346$	3.63820	+	5.10914i	0.195591	+	0.274669i
$347$	34.0194	−	6.55671i	1.82626	−	0.351983i	0.843537	−	0.537071i	$-0.180469\pi$
$347$	34.0194	−	6.55671i	1.82626	−	0.351983i	0.982722	+	0.185088i	$0.0592570\pi$
$348$		0			0
$349$	−16.9483	+	10.8920i	−0.907222	+	0.583036i	−0.908924	−	0.416963i	$-0.863095\pi$
$349$	−16.9483	+	10.8920i	−0.907222	+	0.583036i	0.00170210	+	0.999999i	$0.499458\pi$
$350$	−7.43374	−	2.18274i	−0.397350	−	0.116672i
$351$		0			0
$352$	1.86888	−	39.2325i	0.0996114	−	2.09110i
$353$	7.96168	+	4.10453i	0.423758	+	0.218462i	0.656896	−	0.753981i	$-0.271869\pi$
$353$	7.96168	+	4.10453i	0.423758	+	0.218462i	−0.233138	+	0.972444i	$0.574899\pi$
$354$		0			0
$355$	−32.6563	−	13.0736i	−1.73322	−	0.693875i
$356$	12.1202	+	1.15734i	0.642369	+	0.0613388i
$357$		0			0
$358$	8.90605	−	7.00380i	0.470700	−	0.370162i
$359$	4.89945	+	3.14869i	0.258583	+	0.166181i	0.663509	−	0.748168i	$-0.269066\pi$
$359$	4.89945	+	3.14869i	0.258583	+	0.166181i	−0.404926	+	0.914349i	$0.632703\pi$
$360$		0			0
$361$	12.0637	−	6.21927i	0.634932	−	0.327330i
$362$	0.644170	+	1.41054i	0.0338568	+	0.0741361i
$363$		0			0
$364$	5.58316	−	9.67031i	0.292637	−	0.506862i
$365$	−7.74699	−	13.4182i	−0.405496	−	0.702339i
$366$		0			0
$367$	7.64718	+	6.01381i	0.399179	+	0.313918i	0.797490	−	0.603333i	$-0.206161\pi$
$367$	7.64718	+	6.01381i	0.399179	+	0.313918i	−0.398310	+	0.917251i	$0.630403\pi$
$368$	−25.5941	+	24.4039i	−1.33418	+	1.27214i
$369$		0			0
$370$	26.8316	+	21.1006i	1.39491	+	1.09697i
$371$	4.12935	+	11.9310i	0.214385	+	0.619426i
$372$		0			0
$373$	6.83604	−	11.8404i	0.353957	−	0.613071i	−0.632982	−	0.774167i	$-0.718169\pi$
$373$	6.83604	−	11.8404i	0.353957	−	0.613071i	0.986939	+	0.161095i	$0.0515026\pi$
$374$	12.8566	+	2.47790i	0.664797	+	0.128129i
$375$		0			0
$376$	−5.38048	+	2.77383i	−0.277477	+	0.143049i
$377$	−0.448688	−	0.517813i	−0.0231086	−	0.0266687i
$378$		0			0
$379$	−17.7618	+	13.9680i	−0.912362	+	0.717489i	−0.959592	−	0.281395i	$-0.909203\pi$
$379$	−17.7618	+	13.9680i	−0.912362	+	0.717489i	0.0472305	+	0.998884i	$0.484960\pi$
$380$	−1.43768	+	9.99931i	−0.0737516	+	0.512954i
$381$		0			0
$382$	−36.1033	−	14.4536i	−1.84721	−	0.739510i
$383$	4.19512	+	17.2925i	0.214361	+	0.883606i	0.972760	+	0.231816i	$0.0744667\pi$
$383$	4.19512	+	17.2925i	0.214361	+	0.883606i	−0.758399	+	0.651790i	$0.774018\pi$
$384$		0			0
$385$	−1.38344	+	29.0420i	−0.0705067	+	1.48012i
$386$	5.92577	−	0.565843i	0.301614	−	0.0288006i
$387$		0			0
$388$	5.84253	−	3.75477i	0.296609	−	0.190619i
$389$	−7.64238	+	22.0812i	−0.387484	+	1.11956i	0.567620	+	0.823291i	$0.307864\pi$
$389$	−7.64238	+	22.0812i	−0.387484	+	1.11956i	−0.955104	+	0.296271i	$0.904257\pi$
$390$		0			0
$391$	−5.77677	−	8.11234i	−0.292144	−	0.410259i
$392$	−1.69798	+	0.679768i	−0.0857608	+	0.0343335i
$393$		0			0
$394$	1.40442	−	1.62079i	0.0707539	−	0.0816543i
$395$	−0.143274	+	0.590582i	−0.00720887	+	0.0297154i
$396$		0			0
$397$	6.24983	−	13.6852i	0.313670	−	0.686841i	−0.685479	−	0.728092i	$-0.740407\pi$
$397$	6.24983	−	13.6852i	0.313670	−	0.686841i	0.999149	+	0.0412513i	$0.0131344\pi$
$398$	0.855266	+	17.9542i	0.0428706	+	0.899964i
$399$		0			0
$400$	−6.48905	−	6.18730i	−0.324453	−	0.309365i
$401$	29.3366			1.46500			0.732501	−	0.680766i	$-0.238353\pi$
$401$	29.3366			1.46500			0.732501	+	0.680766i	$0.238353\pi$
$402$		0			0
$403$	−20.0934			−1.00092
$404$	−3.51370	−	3.35030i	−0.174813	−	0.166684i
$405$		0			0
$406$	0.0394719	+	0.828616i	0.00195896	+	0.0411235i
$407$	14.9610	−	32.7601i	0.741590	−	1.62386i
$408$		0			0
$409$	5.58204	−	23.0095i	0.276014	−	1.13774i	−0.649903	−	0.760017i	$-0.725190\pi$
$409$	5.58204	−	23.0095i	0.276014	−	1.13774i	0.925917	−	0.377728i	$-0.123294\pi$
$410$	3.85531	−	4.44926i	0.190400	−	0.219733i
$411$		0			0
$412$	1.62848	−	0.651945i	0.0802294	−	0.0321190i
$413$	3.27591	+	4.60037i	0.161197	+	0.226370i
$414$		0			0
$415$	−4.38355	+	12.6654i	−0.215180	+	0.621721i
$416$	20.3551	−	13.0814i	0.997990	−	0.641369i
$417$		0			0
$418$	23.5167	−	2.24558i	1.15024	−	0.109835i
$419$	1.62241	−	34.0586i	0.0792600	−	1.66387i	−0.513198	−	0.858270i	$-0.671539\pi$
$419$	1.62241	−	34.0586i	0.0792600	−	1.66387i	0.592458	−	0.805601i	$-0.298158\pi$
$420$		0			0
$421$	1.94987	+	8.03748i	0.0950309	+	0.391723i	0.999385	−	0.0350598i	$-0.0111622\pi$
$421$	1.94987	+	8.03748i	0.0950309	+	0.391723i	−0.904354	+	0.426782i	$0.859647\pi$
$422$	−20.7772	−	8.31792i	−1.01142	−	0.404910i
$423$		0			0
$424$	−0.588063	+	4.09007i	−0.0285589	+	0.198631i
$425$	1.98476	−	1.56084i	0.0962752	−	0.0757117i
$426$		0			0
$427$	−3.53683	−	4.08172i	−0.171159	−	0.197528i
$428$	−23.4507	+	12.0897i	−1.13353	+	0.584377i
$429$		0			0
$430$	29.8623	+	5.75549i	1.44009	+	0.277555i
$431$	1.09845	−	1.90257i	0.0529106	−	0.0916438i	−0.838357	−	0.545122i	$-0.816484\pi$
$431$	1.09845	−	1.90257i	0.0529106	−	0.0916438i	0.891268	+	0.453478i	$0.149817\pi$
$432$		0			0
$433$	−6.50222	−	18.7869i	−0.312477	−	0.902842i	−0.986446	−	0.164083i	$-0.947533\pi$
$433$	−6.50222	−	18.7869i	−0.312477	−	0.902842i	0.673970	−	0.738759i	$-0.264588\pi$
$434$	19.1230	+	15.0385i	0.917933	+	0.721870i
$435$		0			0
$436$	−6.31142	+	6.01793i	−0.302262	+	0.288206i
$437$	−14.1244	−	11.1075i	−0.675661	−	0.531346i
$438$		0			0
$439$	−17.0959	−	29.6110i	−0.815944	−	1.41326i	−0.908648	−	0.417562i	$-0.862885\pi$
$439$	−17.0959	−	29.6110i	−0.815944	−	1.41326i	0.0927048	−	0.995694i	$-0.470449\pi$
$440$	−4.75793	+	8.24098i	−0.226826	+	0.392873i
$441$		0			0
$442$	3.35070	+	7.33700i	0.159376	+	0.348985i
$443$	−22.2998	+	11.4964i	−1.05950	+	0.546209i	−0.897696	−	0.440614i	$-0.854761\pi$
$443$	−22.2998	+	11.4964i	−1.05950	+	0.546209i	−0.161801	+	0.986823i	$0.551730\pi$
$444$		0			0
$445$	−16.4295	−	10.5586i	−0.778832	−	0.500525i
$446$	−42.4886	+	33.4134i	−2.01189	+	1.58217i
$447$		0			0
$448$	−10.2170	−	0.975602i	−0.482706	−	0.0460928i
$449$	−6.41806	−	2.56940i	−0.302887	−	0.121258i	0.215240	−	0.976561i	$-0.430946\pi$
$449$	−6.41806	−	2.56940i	−0.302887	−	0.121258i	−0.518127	+	0.855303i	$0.673371\pi$
$450$		0			0
$451$	−5.52097	−	2.84626i	−0.259972	−	0.134025i
$452$	0.565499	−	11.8713i	0.0265988	−	0.558378i
$453$		0			0
$454$	0.468577	+	0.137587i	0.0219914	+	0.00645726i
$455$	−15.0679	+	9.68356i	−0.706395	+	0.453972i
$456$		0			0
$457$	−28.8746	+	5.56513i	−1.35070	+	0.260326i	−0.812731	−	0.582639i	$-0.802020\pi$
$457$	−28.8746	+	5.56513i	−1.35070	+	0.260326i	−0.537968	+	0.842965i	$0.680808\pi$
$458$	−5.92198	−	8.31626i	−0.276716	−	0.388593i
$459$		0			0
$460$	−32.0901	+	9.42251i	−1.49621	+	0.439327i
$461$	2.99213	−	3.45310i	0.139357	−	0.160827i	−0.681781	−	0.731557i	$-0.738794\pi$
$461$	2.99213	−	3.45310i	0.139357	−	0.160827i	0.821138	+	0.570730i	$0.193340\pi$
$462$		0			0
$463$	−3.41523	+	4.79603i	−0.158719	+	0.222890i	−0.886276	−	0.463157i	$-0.846716\pi$
$463$	−3.41523	+	4.79603i	−0.158719	+	0.222890i	0.727557	+	0.686048i	$0.240656\pi$
$464$	−0.398809	+	0.873270i	−0.0185142	+	0.0405405i
$465$		0			0
$466$	−4.67500	−	32.5154i	−0.216565	−	1.50625i
$467$	−6.87996	−	6.56003i	−0.318366	−	0.303562i	0.513997	−	0.857792i	$-0.328164\pi$
$467$	−6.87996	−	6.56003i	−0.318366	−	0.303562i	−0.832363	+	0.554230i	$0.813013\pi$
$468$		0			0
$469$	−16.5476	+	3.84345i	−0.764096	+	0.177474i
$470$	−44.8671			−2.06956
$471$		0			0
$472$	0.263052	+	1.82957i	0.0121079	+	0.0842126i
$473$	−1.52676	−	32.0505i	−0.0702003	−	1.47369i
$474$		0			0
$475$	2.64259	−	3.71101i	0.121251	−	0.170273i
$476$	1.03877	−	4.28188i	0.0476120	−	0.196259i
$477$		0			0
$478$	−2.27500	+	0.668001i	−0.104056	+	0.0305537i
$479$	−23.2521	+	9.30875i	−1.06242	+	0.425328i	−0.836015	−	0.548706i	$-0.815120\pi$
$479$	−23.2521	+	9.30875i	−1.06242	+	0.425328i	−0.226402	+	0.974034i	$0.572696\pi$
$480$		0			0
$481$	21.7854	−	4.19880i	0.993331	−	0.191449i
$482$	1.48983	−	4.30457i	0.0678597	−	0.196068i
$483$		0			0
$484$	−27.1596	−	7.97477i	−1.23453	−	0.362489i
$485$	−11.0897	+	1.05894i	−0.503557	+	0.0480838i
$486$		0			0
$487$	20.5813	+	10.6104i	0.932626	+	0.480802i	0.856414	−	0.516290i	$-0.172687\pi$
$487$	20.5813	+	10.6104i	0.932626	+	0.480802i	0.0762116	+	0.997092i	$0.475718\pi$
$488$	−0.416738	−	1.71782i	−0.0188648	−	0.0777620i
$489$		0			0
$490$	−13.4949	−	1.28860i	−0.609636	−	0.0582132i
$491$	4.43304	−	30.8325i	0.200060	−	1.39145i	−0.604038	−	0.796955i	$-0.706443\pi$
$491$	4.43304	−	30.8325i	0.200060	−	1.39145i	0.804099	−	0.594496i	$-0.202648\pi$
$492$		0			0
$493$	−0.227439	−	0.146166i	−0.0102433	−	0.00658298i
$494$	9.53026	+	10.9985i	0.428786	+	0.494846i
$495$		0			0
$496$	11.6956	+	25.6098i	0.525149	+	1.14992i
$497$	27.1812	+	5.23875i	1.21924	+	0.234990i
$498$		0			0
$499$	19.8313	+	34.3489i	0.887773	+	1.53767i	0.842502	+	0.538693i	$0.181082\pi$
$499$	19.8313	+	34.3489i	0.887773	+	1.53767i	0.0452711	+	0.998975i	$0.485585\pi$
$500$	4.31783	+	12.4755i	0.193099	+	0.557923i
$501$		0			0
$502$	−28.6229	+	27.2919i	−1.27750	+	1.21810i
$503$	13.5036	−	12.8757i	0.602098	−	0.574099i	−0.326495	−	0.945199i	$-0.605868\pi$
$503$	13.5036	−	12.8757i	0.602098	−	0.574099i	0.928593	+	0.371100i	$0.121019\pi$
$504$		0			0
$505$	2.54706	+	7.35926i	0.113343	+	0.327483i
$506$	39.1052	+	67.7322i	1.73844	+	3.01106i
$507$		0			0
$508$	8.90823	+	1.71692i	0.395239	+	0.0761760i
$509$	−13.7355	−	30.0765i	−0.608814	−	1.33312i	−0.923382	−	0.383882i	$-0.874587\pi$
$509$	−13.7355	−	30.0765i	−0.608814	−	1.33312i	0.314568	−	0.949235i	$-0.398140\pi$
$510$		0			0
$511$	7.98461	+	9.21473i	0.353218	+	0.407636i
$512$	−23.2807	−	14.9616i	−1.02887	−	0.661215i
$513$		0			0
$514$	−5.24668	+	36.4915i	−0.231421	+	1.60957i
$515$	−2.80096	−	0.267460i	−0.123425	−	0.0117857i
$516$		0			0
$517$	11.1604	+	46.0038i	0.490834	+	2.02324i
$518$	−23.8758	−	12.3088i	−1.04904	−	0.540819i
$519$		0			0
$520$	−5.83559	+	0.557231i	−0.255908	+	0.0244362i
$521$	26.8679	+	7.88911i	1.17710	+	0.345628i	0.811056	−	0.584968i	$-0.198893\pi$
$521$	26.8679	+	7.88911i	1.17710	+	0.345628i	0.366046	+	0.930597i	$0.380711\pi$
$522$		0			0
$523$	11.2421	−	32.4820i	0.491584	−	1.42034i	−0.377654	−	0.925947i	$-0.623269\pi$
$523$	11.2421	−	32.4820i	0.491584	−	1.42034i	0.869239	−	0.494393i	$-0.164610\pi$
$524$	−36.8337	+	7.09911i	−1.60909	+	0.310126i
$525$		0			0
$526$	−30.2779	+	12.1215i	−1.32018	+	0.528521i
$527$	−7.60742	+	2.23374i	−0.331384	+	0.0973032i
$528$		0			0
$529$	8.60252	−	35.4601i	0.374023	−	1.54174i
$530$	−17.7653	+	24.9479i	−0.771675	+	1.08367i
$531$		0			0
$532$	−0.378266	−	7.94077i	−0.0163999	−	0.344276i
$533$	−0.544568	−	3.78755i	−0.0235878	−	0.164057i
$534$		0			0
$535$	42.3206			1.82968
$536$	−5.39018	−	1.36359i	−0.232820	−	0.0588982i
$537$		0			0
$538$	−11.5948	−	11.0557i	−0.499889	−	0.476643i
$539$	2.03551	+	14.1573i	0.0876758	+	0.609798i
$540$		0			0
$541$	18.9939	−	41.5909i	0.816612	−	1.78813i	0.240742	−	0.970589i	$-0.422609\pi$
$541$	18.9939	−	41.5909i	0.816612	−	1.78813i	0.575870	−	0.817541i	$-0.304664\pi$
$542$	19.6353	−	27.5739i	0.843408	−	1.18440i
$543$		0			0
$544$	6.25226	−	7.21550i	0.268064	−	0.309362i
$545$	13.4217	−	3.94095i	0.574921	−	0.168812i
$546$		0			0
$547$	−14.7224	−	20.6747i	−0.629485	−	0.883988i	0.369491	−	0.929234i	$-0.379532\pi$
$547$	−14.7224	−	20.6747i	−0.629485	−	0.883988i	−0.998976	+	0.0452467i	$0.985593\pi$
$548$	−2.86271	+	0.551742i	−0.122289	+	0.0235693i
$549$		0			0
$550$	−16.6815	+	10.7205i	−0.711300	+	0.457124i
$551$	−0.468039	−	0.137429i	−0.0199391	−	0.00585466i
$552$		0			0
$553$	0.0227553	−	0.477692i	0.000967652	−	0.0203135i
$554$	−22.0507	−	11.3679i	−0.936843	−	0.482976i
$555$		0			0
$556$	9.42318	+	3.77247i	0.399632	+	0.159988i
$557$	−24.0098	−	2.29266i	−1.01733	−	0.0971432i	−0.426955	−	0.904273i	$-0.640414\pi$
$557$	−24.0098	−	2.29266i	−1.01733	−	0.0971432i	−0.590375	+	0.807129i	$0.701020\pi$
$558$		0			0
$559$	15.5377	−	12.2190i	0.657175	−	0.516808i
$560$	21.1125	+	13.5682i	0.892168	+	0.573362i
$561$		0			0
$562$	−4.82269	+	2.48627i	−0.203433	+	0.104877i
$563$	2.49513	+	5.46358i	0.105157	+	0.230262i	0.954895	−	0.296943i	$-0.0959671\pi$
$563$	2.49513	+	5.46358i	0.105157	+	0.230262i	−0.849738	+	0.527205i	$0.823240\pi$
$564$		0			0
$565$	−9.53183	+	16.5096i	−0.401007	+	0.694565i
$566$	28.0796	+	48.6353i	1.18027	+	2.04429i
$567$		0			0
$568$	7.12148	+	5.60040i	0.298811	+	0.234987i
$569$	−4.82538	+	4.60099i	−0.202290	+	0.192884i	−0.784452	−	0.620190i	$-0.787056\pi$
$569$	−4.82538	+	4.60099i	−0.202290	+	0.192884i	0.582161	+	0.813073i	$0.302207\pi$
$570$		0			0
$571$	22.0849	+	17.3678i	0.924226	+	0.726819i	0.962167	−	0.272461i	$-0.0878374\pi$
$571$	22.0849	+	17.3678i	0.924226	+	0.726819i	−0.0379409	+	0.999280i	$0.512080\pi$
$572$	−9.34737	−	27.0075i	−0.390833	−	1.12924i
$573$		0			0
$574$	−2.31645	+	4.01220i	−0.0966866	+	0.167466i
$575$	14.8100	+	2.85440i	0.617622	+	0.119037i
$576$		0			0
$577$	−13.4647	+	6.94154i	−0.560543	+	0.288980i	−0.715121	−	0.699000i	$-0.753629\pi$
$577$	−13.4647	+	6.94154i	−0.560543	+	0.288980i	0.154578	+	0.987981i	$0.450598\pi$
$578$	−19.1677	−	22.1207i	−0.797270	−	0.920098i
$579$		0			0
$580$	−0.713681	+	0.561245i	−0.0296340	+	0.0233044i
$581$	1.50100	−	10.4397i	0.0622718	−	0.433110i
$582$		0			0
$583$	29.9989	+	12.0098i	1.24243	+	0.497393i
$584$	0.940811	+	3.87808i	0.0389310	+	0.160476i
$585$		0			0
$586$	1.60121	−	33.6135i	0.0661454	−	1.38856i
$587$	31.8376	−	3.04012i	1.31408	−	0.125479i	0.585630	−	0.810579i	$-0.300847\pi$
$587$	31.8376	−	3.04012i	1.31408	−	0.125479i	0.728450	+	0.685099i	$0.240241\pi$
$588$		0			0
$589$	−12.0344	+	7.73406i	−0.495870	+	0.318676i
$590$	−4.48082	+	12.9465i	−0.184472	+	0.532998i
$591$		0			0
$592$	−18.0320	−	25.3224i	−0.741112	−	1.04075i
$593$	−8.58984	+	3.43885i	−0.352743	+	0.141217i	−0.541265	−	0.840852i	$-0.682054\pi$
$593$	−8.58984	+	3.43885i	−0.352743	+	0.141217i	0.188522	+	0.982069i	$0.439630\pi$
$594$		0			0
$595$	−4.62826	+	5.34129i	−0.189740	+	0.218972i
$596$	7.74996	−	31.9458i	0.317451	−	1.30855i
$597$		0			0
$598$	−20.0149	+	43.8266i	−0.818472	+	1.79220i
$599$	0.416363	+	8.74053i	0.0170121	+	0.357128i	0.991283	+	0.131749i	$0.0420592\pi$
$599$	0.416363	+	8.74053i	0.0170121	+	0.357128i	−0.974271	+	0.225380i	$0.927638\pi$
$600$		0			0
$601$	−3.70582	−	3.53349i	−0.151164	−	0.144134i	0.610724	−	0.791844i	$-0.290879\pi$
$601$	−3.70582	−	3.53349i	−0.151164	−	0.144134i	−0.761887	+	0.647710i	$0.775727\pi$
$602$	−23.9324			−0.975411
$603$		0			0
$604$	2.13021			0.0866770
$605$	32.8607	+	31.3326i	1.33598	+	1.27385i
$606$		0			0
$607$	0.476155	+	9.99573i	0.0193265	+	0.405714i	0.987715	+	0.156267i	$0.0499459\pi$
$607$	0.476155	+	9.99573i	0.0193265	+	0.405714i	−0.968388	+	0.249447i	$0.919751\pi$
$608$	7.15605	−	15.6696i	0.290216	−	0.635485i
$609$		0			0
$610$	3.08881	−	12.7322i	0.125062	−	0.515514i
$611$	−19.0971	+	22.0393i	−0.772587	+	0.891613i
$612$		0			0
$613$	−41.9757	+	16.8045i	−1.69538	+	0.678728i	−0.999233	−	0.0391696i	$-0.987529\pi$
$613$	−41.9757	+	16.8045i	−1.69538	+	0.678728i	−0.696149	+	0.717898i	$0.745104\pi$
$614$	−30.0716	−	42.2297i	−1.21359	−	1.70425i
$615$		0			0
$616$	2.44922	−	7.07656i	0.0986820	−	0.285123i
$617$	−36.7857	+	23.6407i	−1.48094	+	0.951739i	−0.483874	+	0.875138i	$0.660771\pi$
$617$	−36.7857	+	23.6407i	−1.48094	+	0.951739i	−0.997062	+	0.0766014i	$0.975593\pi$
$618$		0			0
$619$	−22.0518	+	2.10569i	−0.886337	+	0.0846349i	−0.528285	−	0.849067i	$-0.677165\pi$
$619$	−22.0518	+	2.10569i	−0.886337	+	0.0846349i	−0.358052	+	0.933702i	$0.616559\pi$
$620$	−1.26693	+	26.5961i	−0.0508811	+	1.06813i
$621$		0			0
$622$	−3.01925	−	12.4455i	−0.121061	−	0.499020i
$623$	14.2679	+	5.71199i	0.571630	+	0.228846i
$624$		0			0
$625$	4.40515	−	30.6385i	0.176206	−	1.22554i
$626$	35.4604	−	27.8864i	1.41728	−	1.11456i
$627$		0			0
$628$	−15.3432	−	17.7069i	−0.612259	−	0.706584i
$629$	7.78126	−	4.01152i	0.310259	−	0.159950i
$630$		0			0
$631$	−16.5921	−	3.19787i	−0.660522	−	0.127305i	−0.152036	−	0.988375i	$-0.548583\pi$
$631$	−16.5921	−	3.19787i	−0.660522	−	0.127305i	−0.508487	+	0.861070i	$0.669795\pi$
$632$	0.0782599	−	0.135550i	0.00311301	−	0.00539190i
$633$		0			0
$634$	13.0732	+	37.7726i	0.519204	+	1.50014i
$635$	−11.4388	−	8.99556i	−0.453934	−	0.356978i
$636$		0			0
$637$	−6.37691	+	6.08037i	−0.252662	+	0.240913i
$638$	1.66893	+	1.31246i	0.0660737	+	0.0519609i
$639$		0			0
$640$	7.05232	+	12.2150i	0.278767	+	0.482839i
$641$	−18.2813	+	31.6642i	−0.722069	+	1.25066i	0.238100	+	0.971241i	$0.423475\pi$
$641$	−18.2813	+	31.6642i	−0.722069	+	1.25066i	−0.960169	+	0.279419i	$0.909858\pi$
$642$		0			0
$643$	−4.05399	−	8.87701i	−0.159874	−	0.350075i	0.812695	−	0.582689i	$-0.197999\pi$
$643$	−4.05399	−	8.87701i	−0.159874	−	0.350075i	−0.972569	+	0.232614i	$0.925272\pi$
$644$	23.3934	−	12.0601i	0.921828	−	0.475235i
$645$		0			0
$646$	4.83086	+	3.10461i	0.190068	+	0.122149i
$647$	−5.89581	+	4.63652i	−0.231788	+	0.182280i	−0.727297	−	0.686322i	$-0.759224\pi$
$647$	−5.89581	+	4.63652i	−0.231788	+	0.182280i	0.495509	+	0.868603i	$0.334982\pi$
$648$		0			0
$649$	14.3890	+	1.37399i	0.564820	+	0.0539337i
$650$	−11.3406	−	4.54008i	−0.444813	−	0.178076i
$651$		0			0
$652$	7.05133	+	3.63521i	0.276151	+	0.142366i
$653$	1.91252	−	40.1486i	0.0748425	−	1.57114i	−0.579521	−	0.814957i	$-0.696760\pi$
$653$	1.91252	−	40.1486i	0.0748425	−	1.57114i	0.654363	−	0.756180i	$-0.272937\pi$
$654$		0			0
$655$	57.7329	+	16.9519i	2.25581	+	0.662366i
$656$	−4.51041	+	2.89867i	−0.176102	+	0.113174i
$657$		0			0
$658$	34.6697	−	6.68203i	1.35156	−	0.260493i
$659$	7.33166	+	10.2959i	0.285601	+	0.401070i	0.932306	−	0.361670i	$-0.117793\pi$
$659$	7.33166	+	10.2959i	0.285601	+	0.401070i	−0.646706	+	0.762740i	$0.723854\pi$
$660$		0			0
$661$	20.1166	−	5.90678i	0.782447	−	0.229747i	0.133974	−	0.990985i	$-0.457226\pi$
$661$	20.1166	−	5.90678i	0.782447	−	0.229747i	0.648473	+	0.761238i	$0.275408\pi$
$662$	−4.85137	+	5.59877i	−0.188554	+	0.217603i
$663$		0			0
$664$	2.00230	−	2.81184i	0.0777044	−	0.109121i
$665$	−5.29729	+	11.5994i	−0.205420	+	0.449807i
$666$		0			0
$667$	−0.229830	−	1.59850i	−0.00889906	−	0.0618943i
$668$	−9.33920	−	8.90491i	−0.361344	−	0.344541i
$669$		0			0
$670$	−30.8790	−	27.2900i	−1.19296	−	1.05431i
$671$	−13.8231			−0.533637
$672$		0			0
$673$	−4.21036	−	29.2837i	−0.162298	−	1.12880i	−0.894289	−	0.447490i	$-0.852318\pi$
$673$	−4.21036	−	29.2837i	−0.162298	−	1.12880i	0.731991	−	0.681314i	$-0.238591\pi$
$674$	−2.93201	−	61.5504i	−0.112937	−	2.37083i
$675$		0			0
$676$	−2.18586	+	3.06961i	−0.0840714	+	0.118062i
$677$	5.59389	−	23.0583i	0.214991	−	0.886204i	−0.757420	−	0.652928i	$-0.773540\pi$
$677$	5.59389	−	23.0583i	0.214991	−	0.886204i	0.972411	−	0.233276i	$-0.0749445\pi$
$678$		0			0
$679$	8.41151	−	2.46984i	0.322804	−	0.0947839i
$680$	−2.14743	+	0.859700i	−0.0823500	+	0.0329680i
$681$		0			0
$682$	61.1400	−	11.7838i	2.34117	−	0.451224i
$683$	5.49774	−	15.8847i	0.210365	−	0.607811i	−0.789618	−	0.613599i	$-0.789721\pi$
$683$	5.49774	−	15.8847i	0.210365	−	0.607811i	0.999983	+	0.00578812i	$0.00184243\pi$
$684$		0			0
$685$	4.48699	+	1.31750i	0.171439	+	0.0503391i
$686$	38.2275	−	3.65029i	1.45953	−	0.139369i
$687$		0			0
$688$	−24.6175	−	12.6912i	−0.938534	−	0.483848i
$689$	4.69312	+	19.3453i	0.178793	+	0.736997i
$690$		0			0
$691$	−17.9253	−	1.71166i	−0.681910	−	0.0651145i	−0.251648	−	0.967819i	$-0.580973\pi$
$691$	−17.9253	−	1.71166i	−0.681910	−	0.0651145i	−0.430261	+	0.902704i	$0.641579\pi$
$692$	0.768803	−	5.34714i	0.0292255	−	0.203268i
$693$		0			0
$694$	−55.6383	−	35.7566i	−2.11200	−	1.35730i
$695$	−10.6621	−	12.3047i	−0.404436	−	0.466744i
$696$		0			0
$697$	−0.627229	−	1.37344i	−0.0237580	−	0.0520227i
$698$	37.7641	+	7.27843i	1.42939	+	0.275493i
$699$		0			0
$700$	3.33644	+	5.77889i	0.126106	+	0.218422i
$701$	−3.94235	−	11.3907i	−0.148901	−	0.430220i	0.845742	−	0.533592i	$-0.179158\pi$
$701$	−3.94235	−	11.3907i	−0.148901	−	0.430220i	−0.994643	+	0.103372i	$0.967037\pi$
$702$		0			0
$703$	11.4317	−	10.9001i	0.431154	−	0.411105i
$704$	−19.0114	+	18.1273i	−0.716518	+	0.683198i
$705$		0			0
$706$	−5.59270	−	16.1590i	−0.210484	−	0.608153i
$707$	−3.06418	−	5.30731i	−0.115240	−	0.199602i
$708$		0			0
$709$	−6.78133	−	1.30699i	−0.254678	−	0.0490852i	0.0603140	−	0.998179i	$-0.480790\pi$
$709$	−6.78133	−	1.30699i	−0.254678	−	0.0490852i	−0.314992	+	0.949094i	$0.602002\pi$
$710$	27.8952	+	61.0819i	1.04689	+	2.29236i
$711$		0			0
$712$	3.29395	+	3.80142i	0.123446	+	0.142464i
$713$	−39.8421	−	25.6049i	−1.49210	−	0.958913i
$714$		0			0
$715$	−6.52406	+	45.3758i	−0.243986	+	1.69696i
$716$	−9.71429	−	0.927602i	−0.363040	−	0.0346661i
$717$		0			0
$718$	−2.62113	−	10.8044i	−0.0978196	−	0.403218i
$719$	8.48557	+	4.37462i	0.316458	+	0.163146i	0.609137	−	0.793065i	$-0.291516\pi$
$719$	8.48557	+	4.37462i	0.316458	+	0.163146i	−0.292678	+	0.956211i	$0.594546\pi$
$720$		0			0
$721$	2.20419	−	0.210475i	0.0820884	−	0.00783849i
$722$	−24.8600	−	7.29955i	−0.925193	−	0.271661i
$723$		0			0
$724$	0.436822	−	1.26211i	0.0162344	−	0.0469061i
$725$	0.402049	−	0.0774886i	0.0149317	−	0.00287785i
$726$		0			0
$727$	28.2974	−	11.3286i	1.04949	−	0.420154i	0.218152	−	0.975915i	$-0.429997\pi$
$727$	28.2974	−	11.3286i	1.04949	−	0.420154i	0.831342	+	0.555761i	$0.187573\pi$
$728$	4.42629	−	1.29968i	0.164049	−	0.0481692i
$729$		0			0
$730$	−6.97317	+	28.7438i	−0.258089	+	1.06386i
$731$	4.52426	−	6.35344i	0.167336	−	0.234991i
$732$		0			0
$733$	−0.649217	−	13.6287i	−0.0239794	−	0.503389i	−0.978626	−	0.205648i	$-0.934070\pi$
$733$	−0.649217	−	13.6287i	−0.0239794	−	0.503389i	0.954647	−	0.297741i	$-0.0962333\pi$
$734$	−2.64301	−	18.3825i	−0.0975553	−	0.678512i
$735$		0			0
$736$	57.0306			2.10217
$737$	−20.3005	+	38.4495i	−0.747778	+	1.41631i
$738$		0			0
$739$	26.6522	+	25.4128i	0.980415	+	0.934824i	0.997884	−	0.0650233i	$-0.0207122\pi$
$739$	26.6522	+	25.4128i	0.980415	+	0.934824i	−0.0174684	+	0.999847i	$0.505561\pi$
$740$	−4.18402	−	29.1005i	−0.153808	−	1.06976i
$741$		0			0
$742$	10.0121	−	21.9235i	0.367556	−	0.804836i
$743$	11.4850	−	16.1284i	0.421343	−	0.591694i	−0.548281	−	0.836294i	$-0.684717\pi$
$743$	11.4850	−	16.1284i	0.421343	−	0.591694i	0.969624	+	0.244600i	$0.0786568\pi$
$744$		0			0
$745$	−34.5300	+	39.8497i	−1.26508	+	1.45998i
$746$	−25.0424	+	7.35312i	−0.916868	+	0.269217i
$747$		0			0
$748$	−6.54130	−	9.18597i	−0.239174	−	0.335872i
$749$	−32.7019	+	6.30278i	−1.19490	+	0.230299i
$750$		0			0
$751$	3.39240	−	2.18017i	0.123791	−	0.0795554i	−0.477280	−	0.878751i	$-0.658377\pi$
$751$	3.39240	−	2.18017i	0.123791	−	0.0795554i	0.601071	+	0.799196i	$0.294741\pi$
$752$	39.2056	+	11.5118i	1.42968	+	0.419793i
$753$		0			0
$754$	−0.0622353	+	1.30648i	−0.00226648	+	0.0475792i
$755$	−3.03711	−	1.56574i	−0.110532	−	0.0569830i
$756$		0			0
$757$	−22.9663	−	9.19434i	−0.834726	−	0.334174i	−0.0853767	−	0.996349i	$-0.527209\pi$
$757$	−22.9663	−	9.19434i	−0.834726	−	0.334174i	−0.749349	+	0.662175i	$0.769634\pi$
$758$	42.9401	+	4.10029i	1.55966	+	0.148929i
$759$		0			0
$760$	−3.28060	+	2.57989i	−0.119000	+	0.0935824i
$761$	3.30552	+	2.12433i	0.119825	+	0.0770068i	0.599180	−	0.800614i	$-0.295493\pi$
$761$	3.30552	+	2.12433i	0.119825	+	0.0770068i	−0.479356	+	0.877621i	$0.659130\pi$
$762$		0			0
$763$	−9.78425	+	5.04413i	−0.354214	+	0.182610i
$764$	13.9142	+	30.4678i	0.503397	+	1.10229i
$765$		0			0
$766$	16.9842	−	29.4175i	0.613665	−	1.06290i
$767$	4.45226	+	7.71154i	0.160762	+	0.278448i
$768$		0			0
$769$	29.4167	+	23.1336i	1.06079	+	0.834218i	0.986622	−	0.163027i	$-0.0521259\pi$
$769$	29.4167	+	23.1336i	1.06079	+	0.834218i	0.0741730	+	0.997245i	$0.476368\pi$
$770$	40.1696	−	38.3016i	1.44761	−	1.38029i
$771$		0			0
$772$	−4.03010	−	3.16931i	−0.145047	−	0.114066i
$773$	−5.29047	−	15.2858i	−0.190285	−	0.549793i	0.808992	−	0.587820i	$-0.200014\pi$
$773$	−5.29047	−	15.2858i	−0.190285	−	0.549793i	−0.999277	+	0.0380275i	$0.987893\pi$
$774$		0			0
$775$	6.00382	−	10.3989i	0.215663	−	0.373540i
$776$	2.81736	+	0.543001i	0.101137	+	0.0194926i
$777$		0			0
$778$	39.6471	−	20.4395i	1.42142	−	0.732792i
$779$	−1.78400	−	2.05885i	−0.0639186	−	0.0737660i
$780$		0			0
$781$	55.6907	−	43.7956i	1.99277	−	1.56713i
$782$	−2.70561	+	18.8179i	−0.0967523	+	0.672927i
$783$		0			0
$784$	11.4614	+	4.58847i	0.409337	+	0.163874i
$785$	8.86034	+	36.5228i	0.316239	+	1.30356i
$786$		0			0
$787$	0.868517	−	18.2324i	0.0309593	−	0.649915i	−0.929051	−	0.369951i	$-0.879374\pi$
$787$	0.868517	−	18.2324i	0.0309593	−	0.649915i	0.960010	−	0.279964i	$-0.0903226\pi$
$788$	−1.83877	+	0.175581i	−0.0655034	+	0.00625482i
$789$		0			0
$790$	0.975943	−	0.627200i	0.0347225	−	0.0223148i
$791$	4.90666	−	14.1769i	0.174461	−	0.504072i
$792$		0			0
$793$	−4.93952	−	6.93659i	−0.175408	−	0.246326i
$794$	−26.6628	+	10.6742i	−0.946227	+	0.378812i
$795$		0			0
$796$	10.1381	−	11.7000i	0.359335	−	0.414695i
$797$	7.11866	−	29.3435i	0.252156	−	1.03940i	−0.695098	−	0.718915i	$-0.744639\pi$
$797$	7.11866	−	29.3435i	0.252156	−	1.03940i	0.947253	−	0.320485i	$-0.103846\pi$
$798$		0			0
$799$	−4.78017	+	10.4671i	−0.169110	+	0.370300i
$800$	0.688006	+	14.4430i	0.0243247	+	0.510638i
$801$		0			0
$802$	−40.5311	−	38.6464i	−1.43120	−	1.36465i
$803$	31.2066			1.10126
$804$		0			0
$805$	−42.2170			−1.48796
$806$	27.7608	+	26.4699i	0.977832	+	0.932361i
$807$		0			0
$808$	−0.0954366	−	2.00346i	−0.00335745	−	0.0704815i
$809$	3.18839	−	6.98159i	0.112098	−	0.245460i	−0.845266	−	0.534346i	$-0.820558\pi$
$809$	3.18839	−	6.98159i	0.112098	−	0.245460i	0.957363	+	0.288887i	$0.0932851\pi$
$810$		0			0
$811$	−7.45111	+	30.7139i	−0.261644	+	1.07851i	0.677646	+	0.735388i	$0.263000\pi$
$811$	−7.45111	+	30.7139i	−0.261644	+	1.07851i	−0.939290	+	0.343123i	$0.888515\pi$
$812$	0.467889	−	0.539973i	0.0164197	−	0.0189493i
$813$		0			0
$814$	−63.8262	+	25.5521i	−2.23711	+	0.895602i
$815$	−7.38136	−	10.3657i	−0.258558	−	0.363094i
$816$		0			0
$817$	4.60276	−	13.2988i	0.161030	−	0.465266i
$818$	−38.0234	+	24.4362i	−1.32946	+	0.854390i
$819$		0			0
$820$	−5.04763	+	0.481990i	−0.176271	+	0.0168318i
$821$	−0.180704	+	3.79344i	−0.00630660	+	0.132392i	0.993518	+	0.113673i	$0.0362617\pi$
$821$	−0.180704	+	3.79344i	−0.00630660	+	0.132392i	−0.999825	+	0.0187186i	$0.994041\pi$
$822$		0			0
$823$	6.84028	+	28.1960i	0.238437	+	0.982852i	0.957621	+	0.288032i	$0.0930009\pi$
$823$	6.84028	+	28.1960i	0.238437	+	0.982852i	−0.719184	+	0.694820i	$0.755484\pi$
$824$	0.672776	+	0.269339i	0.0234373	+	0.00938286i
$825$		0			0
$826$	1.53430	−	10.6713i	0.0533852	−	0.371303i
$827$	−20.6342	+	16.2269i	−0.717520	+	0.564264i	−0.908780	−	0.417275i	$-0.862985\pi$
$827$	−20.6342	+	16.2269i	−0.717520	+	0.564264i	0.191260	+	0.981539i	$0.438743\pi$
$828$		0			0
$829$	−30.6956	−	35.4246i	−1.06610	−	1.23035i	−0.972048	−	0.234782i	$-0.924563\pi$
$829$	−30.6956	−	35.4246i	−1.06610	−	1.23035i	−0.0940549	−	0.995567i	$-0.529983\pi$
$830$	22.7409	−	11.7238i	0.789350	−	0.406938i
$831$		0			0
$832$	−15.8899	−	3.06253i	−0.550884	−	0.106174i
$833$	−1.73838	+	3.01095i	−0.0602311	+	0.104323i
$834$		0			0
$835$	6.76994	+	19.5605i	0.234283	+	0.676918i
$836$	−15.9937	−	12.5776i	−0.553153	−	0.435004i
$837$		0			0
$838$	−47.1083	+	44.9177i	−1.62733	+	1.55166i
$839$	−29.8523	−	23.4761i	−1.03062	−	0.810486i	−0.0485128	−	0.998823i	$-0.515448\pi$
$839$	−29.8523	−	23.4761i	−1.03062	−	0.810486i	−0.982105	+	0.188336i	$0.939691\pi$
$840$		0			0
$841$	14.4781	+	25.0768i	0.499244	+	0.864716i
$842$	7.89419	−	13.6731i	0.272052	−	0.471207i
$843$		0			0
$844$	8.00750	+	17.5340i	0.275629	+	0.603544i
$845$	5.37265	−	2.76979i	0.184825	−	0.0952838i
$846$		0			0
$847$	−30.0584	−	19.3174i	−1.03282	−	0.663753i
$848$	21.9246	−	17.2417i	0.752895	−	0.592084i
$849$		0			0
$850$	−4.79828	−	0.458180i	−0.164580	−	0.0157155i
$851$	48.5476	+	19.4355i	1.66419	+	0.666242i
$852$		0			0
$853$	28.8912	+	14.8945i	0.989217	+	0.509977i	0.875335	−	0.483518i	$-0.160641\pi$
$853$	28.8912	+	14.8945i	0.989217	+	0.509977i	0.113882	+	0.993494i	$0.463671\pi$
$854$	−0.490577	+	10.2985i	−0.0167872	+	0.352406i
$855$		0			0
$856$	−10.4584	−	3.07086i	−0.357460	−	0.104960i
$857$	29.9146	−	19.2250i	1.02186	−	0.656712i	0.0814270	−	0.996679i	$-0.474052\pi$
$857$	29.9146	−	19.2250i	1.02186	−	0.656712i	0.940437	+	0.339967i	$0.110416\pi$
$858$		0			0
$859$	−35.2109	+	6.78635i	−1.20138	+	0.231547i	−0.750399	−	0.660986i	$-0.770138\pi$
$859$	−35.2109	+	6.78635i	−1.20138	+	0.231547i	−0.450982	+	0.892533i	$0.648926\pi$
$860$	−15.1937	−	21.3365i	−0.518100	−	0.727570i
$861$		0			0
$862$	−4.02395	+	1.18154i	−0.137056	+	0.0402433i
$863$	25.0034	−	28.8554i	0.851125	−	0.982251i	−0.148853	−	0.988859i	$-0.547558\pi$
$863$	25.0034	−	28.8554i	0.851125	−	0.982251i	0.999978	+	0.00660856i	$0.00210358\pi$
$864$		0			0
$865$	−5.02634	+	7.05850i	−0.170901	+	0.239996i
$866$	−15.7654	+	34.5214i	−0.535731	+	1.17309i
$867$		0			0
$868$	−2.98196	−	20.7400i	−0.101214	−	0.703962i
$869$	−0.885850	−	0.844657i	−0.0300504	−	0.0286530i
$870$		0			0
$871$	−26.5484	+	3.55246i	−0.899560	+	0.120370i
$872$	−3.60276			−0.122005
$873$		0			0
$874$	4.88166	+	33.9527i	0.165125	+	1.14847i
$875$	0.792917	+	16.6454i	0.0268055	+	0.562716i
$876$		0			0
$877$	−15.9749	+	22.4336i	−0.539433	+	0.757528i	−0.990877	−	0.134772i	$-0.956970\pi$
$877$	−15.9749	+	22.4336i	−0.539433	+	0.757528i	0.451444	+	0.892300i	$0.350909\pi$
$878$	−15.3883	+	63.4314i	−0.519329	+	2.14070i
$879$		0			0
$880$	61.6307	−	18.0964i	2.07757	−	0.610030i
$881$	13.2808	−	5.31685i	0.447443	−	0.179129i	−0.136988	−	0.990573i	$-0.543742\pi$
$881$	13.2808	−	5.31685i	0.447443	−	0.179129i	0.584431	+	0.811444i	$0.301318\pi$
$882$		0			0
$883$	−31.3747	+	6.04698i	−1.05584	+	0.203497i	−0.687494	−	0.726190i	$-0.741289\pi$
$883$	−31.3747	+	6.04698i	−1.05584	+	0.203497i	−0.368349	+	0.929687i	$0.620077\pi$
$884$	2.27216	−	6.56498i	0.0764211	−	0.220804i
$885$		0			0
$886$	45.9538	+	13.4933i	1.54385	+	0.453315i
$887$	−45.1359	+	4.30995i	−1.51551	+	0.144714i	−0.819402	−	0.573219i	$-0.805694\pi$
$887$	−45.1359	+	4.30995i	−1.51551	+	0.144714i	−0.696112	+	0.717933i	$0.745088\pi$
$888$		0			0
$889$	10.1787	+	5.24747i	0.341382	+	0.175995i
$890$	8.78951	+	36.2309i	0.294625	+	1.21446i
$891$		0			0
$892$	46.3445	+	4.42536i	1.55173	+	0.148172i
$893$	−2.95471	+	20.5504i	−0.0988755	+	0.687694i
$894$		0			0
$895$	13.1682	+	8.46266i	0.440163	+	0.282876i
$896$	−7.26864	−	8.38845i	−0.242828	−	0.280239i
$897$		0			0
$898$	5.48233	+	12.0046i	0.182948	+	0.400600i
$899$	−1.26246	−	0.243319i	−0.0421054	−	0.00811515i
$900$		0			0
$901$	3.92740	+	6.80246i	0.130841	+	0.226623i
$902$	3.87821	+	11.2054i	0.129130	+	0.373098i
$903$		0			0
$904$	3.55351	−	3.38826i	0.118188	−	0.112692i
$905$	−1.55047	+	1.47837i	−0.0515392	+	0.0491425i
$906$		0			0
$907$	−1.33332	−	3.85239i	−0.0442723	−	0.127916i	0.920698	−	0.390276i	$-0.127620\pi$
$907$	−1.33332	−	3.85239i	−0.0442723	−	0.127916i	−0.964970	+	0.262360i	$0.915499\pi$
$908$	−0.210309	−	0.364266i	−0.00697934	−	0.0120886i
$909$		0			0
$910$	33.5742	+	6.47090i	1.11297	+	0.214508i
$911$	6.42252	+	14.0634i	0.212788	+	0.465940i	0.985686	−	0.168590i	$-0.0539213\pi$
$911$	6.42252	+	14.0634i	0.212788	+	0.465940i	−0.772899	+	0.634529i	$0.781194\pi$
$912$		0			0
$913$	−17.6775	−	20.4009i	−0.585039	−	0.675171i
$914$	47.2240	+	30.3491i	1.56203	+	1.00386i
$915$		0			0
$916$	−1.25140	+	8.70366i	−0.0413473	+	0.287577i
$917$	−47.1360	−	4.50094i	−1.55657	−	0.148634i
$918$		0			0
$919$	−4.91498	−	20.2598i	−0.162130	−	0.668310i	−0.993621	−	0.112771i	$-0.964027\pi$
$919$	−4.91498	−	20.2598i	−0.162130	−	0.668310i	0.831491	−	0.555539i	$-0.187488\pi$
$920$	−12.2811	−	6.33137i	−0.404897	−	0.208739i
$921$		0			0
$922$	−8.68281	+	0.829108i	−0.285953	+	0.0273052i
$923$	41.8774	+	12.2963i	1.37841	+	0.404738i
$924$		0			0
$925$	−4.33639	+	12.5292i	−0.142580	+	0.411957i
$926$	11.0365	−	2.12710i	0.362680	−	0.0699009i
$927$		0			0
$928$	1.43731	−	0.575412i	0.0471820	−	0.0188888i
$929$	−35.2307	+	10.3447i	−1.15588	+	0.339397i	−0.802831	−	0.596207i	$-0.796674\pi$
$929$	−35.2307	+	10.3447i	−1.15588	+	0.339397i	−0.353051	+	0.935604i	$0.614856\pi$
$930$		0			0
$931$	−1.47892	+	6.09619i	−0.0484696	+	0.199795i
$932$	−16.4116	+	23.0469i	−0.537580	+	0.754925i
$933$		0			0
$934$	0.863472	+	18.1265i	0.0282537	+	0.593118i
$935$	2.57431	+	17.9047i	0.0841888	+	0.585546i
$936$		0			0
$937$	20.7133			0.676672			0.338336	−	0.941025i	$-0.390136\pi$
$937$	20.7133			0.676672			0.338336	+	0.941025i	$0.390136\pi$
$938$	27.9251	+	16.4887i	0.911785	+	0.538377i
$939$		0			0
$940$	27.9676	+	26.6670i	0.912202	+	0.869783i
$941$	−0.0219305	−	0.152530i	−0.000714913	−	0.00497233i	0.989461	−	0.144801i	$-0.0462541\pi$
$941$	−0.0219305	−	0.152530i	−0.000714913	−	0.00497233i	−0.990176	+	0.139828i	$0.955345\pi$
$942$		0			0
$943$	3.74667	−	8.20406i	0.122008	−	0.267161i
$944$	7.23717	−	10.1632i	0.235550	−	0.330783i
$945$		0			0
$946$	−40.1122	+	46.2919i	−1.30416	+	1.50508i
$947$	37.8509	−	11.1140i	1.22999	−	0.361157i	0.398744	−	0.917062i	$-0.369446\pi$
$947$	37.8509	−	11.1140i	1.22999	−	0.361157i	0.831246	+	0.555905i	$0.187628\pi$
$948$		0			0
$949$	11.1513	+	15.6598i	0.361986	+	0.508338i
$950$	−8.53964	+	1.64588i	−0.277063	+	0.0533994i
$951$		0			0
$952$	1.53132	−	0.984122i	0.0496305	−	0.0318956i
$953$	31.2864	+	9.18653i	1.01347	+	0.297581i	0.745971	−	0.665978i	$-0.231986\pi$
$953$	31.2864	+	9.18653i	1.01347	+	0.297581i	0.267496	+	0.963559i	$0.413804\pi$
$954$		0			0
$955$	2.55643	−	53.6661i	0.0827241	−	1.73659i
$956$	1.81514	+	0.935769i	0.0587058	+	0.0302649i
$957$		0			0
$958$	44.3877	+	17.7701i	1.43410	+	0.574127i
$959$	−3.66340	−	0.349813i	−0.118297	−	0.0112960i
$960$		0			0
$961$	−5.27027	+	4.14459i	−0.170009	+	0.133696i
$962$	−35.6298	−	22.8979i	−1.14875	−	0.738257i
$963$		0			0
$964$	−3.48712	+	1.79774i	−0.112313	+	0.0579012i
$965$	3.41635	+	7.48077i	0.109976	+	0.240815i
$966$		0			0
$967$	−17.7217	+	30.6948i	−0.569891	+	0.987080i	0.426686	+	0.904400i	$0.359681\pi$
$967$	−17.7217	+	30.6948i	−0.569891	+	0.987080i	−0.996576	+	0.0826795i	$0.973652\pi$
$968$	−5.84708	−	10.1274i	−0.187932	−	0.325508i
$969$		0			0
$970$	16.7164	+	13.1459i	0.536730	+	0.422089i
$971$	22.8049	−	21.7444i	0.731845	−	0.697812i	−0.229454	−	0.973319i	$-0.573694\pi$
$971$	22.8049	−	21.7444i	0.731845	−	0.697812i	0.961299	+	0.275507i	$0.0888457\pi$
$972$		0			0
$973$	10.0713	+	7.92019i	0.322872	+	0.253910i
$974$	−14.4573	−	41.7717i	−0.463243	−	1.33845i
$975$		0			0
$976$	−5.96585	+	10.3331i	−0.190962	+	0.330756i
$977$	1.21133	+	0.233464i	0.0387538	+	0.00746919i	0.208591	−	0.978003i	$-0.433112\pi$
$977$	1.21133	+	0.233464i	0.0387538	+	0.00746919i	−0.169837	+	0.985472i	$0.554324\pi$
$978$		0			0
$979$	34.9624	−	18.0244i	1.11740	−	0.576062i
$980$	7.64605	+	8.82402i	0.244244	+	0.281873i
$981$		0			0
$982$	−46.7416	+	36.7580i	−1.49158	+	1.17299i
$983$	−7.31130	+	50.8512i	−0.233194	+	1.62190i	0.450945	+	0.892551i	$0.351087\pi$
$983$	−7.31130	+	50.8512i	−0.233194	+	1.62190i	−0.684140	+	0.729351i	$0.739822\pi$
$984$		0			0
$985$	2.75064	+	1.10119i	0.0876428	+	0.0350869i
$986$	0.121676	+	0.501556i	0.00387496	+	0.0159728i
$987$		0			0
$988$	0.596411	−	12.5202i	0.0189744	−	0.398321i
$989$	46.3795	−	4.42870i	1.47478	−	0.140825i
$990$		0			0
$991$	−30.9200	+	19.8711i	−0.982207	+	0.631226i	−0.930058	−	0.367414i	$-0.880243\pi$
$991$	−30.9200	+	19.8711i	−0.982207	+	0.631226i	−0.0521488	+	0.998639i	$0.516607\pi$
$992$	14.8500	−	42.9063i	0.471488	−	1.36228i
$993$		0			0
$994$	−30.6520	−	43.0447i	−0.972223	−	1.36530i
$995$	−23.0539	+	9.22938i	−0.730857	+	0.292591i
$996$		0			0
$997$	12.3596	−	14.2637i	0.391433	−	0.451737i	−0.525492	−	0.850799i	$-0.676119\pi$
$997$	12.3596	−	14.2637i	0.391433	−	0.451737i	0.916924	+	0.399062i	$0.130664\pi$
$998$	17.8505	−	73.5807i	0.565047	−	2.32916i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.10.1		100
3.2	odd	2		67.2.g.a.10.5	✓	100
67.47	even	33	inner	603.2.z.c.181.1		100
201.47	odd	66		67.2.g.a.47.5	yes	100
201.95	even	66		4489.2.a.q.1.9		50
201.173	odd	66		4489.2.a.p.1.42		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.10.5	✓	100	3.2	odd	2
67.2.g.a.47.5	yes	100	201.47	odd	66
603.2.z.c.10.1		100	1.1	even	1	trivial
603.2.z.c.181.1		100	67.47	even	33	inner
4489.2.a.p.1.42		50	201.173	odd	66
4489.2.a.q.1.9		50	201.95	even	66

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.z (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38159 - 1.31734i) q^{2} +(0.0782330 + 1.64231i) q^{4} +(1.09559 - 2.39900i) q^{5} +(-0.489299 + 2.01692i) q^{7} +(-0.444821 + 0.513350i) q^{8} +O(q^{10})\)	\(q+(-1.38159 - 1.31734i) q^{2} +(0.0782330 + 1.64231i) q^{4} +(1.09559 - 2.39900i) q^{5} +(-0.489299 + 2.01692i) q^{7} +(-0.444821 + 0.513350i) q^{8} +(-4.67395 + 1.87117i) q^{10} +(3.08119 + 4.32693i) q^{11} +(-1.07027 + 3.09234i) q^{13} +(3.33298 - 2.14198i) q^{14} +(4.56428 - 0.435836i) q^{16} +(-0.0614384 + 1.28975i) q^{17} +(0.549248 + 2.26403i) q^{19} +(4.02562 + 1.61161i) q^{20} +(1.44310 - 10.0370i) q^{22} +(-6.06274 + 4.76779i) q^{23} +(-1.28058 - 1.47787i) q^{25} +(5.55234 - 2.86243i) q^{26} +(-3.35069 - 0.645793i) q^{28} +(-0.104691 + 0.181330i) q^{29} +(2.00833 + 5.80270i) q^{31} +(-5.81223 - 4.57079i) q^{32} +(1.78392 - 1.70097i) q^{34} +(4.30252 + 3.38354i) q^{35} +(-3.39001 - 5.87167i) q^{37} +(2.22367 - 3.85151i) q^{38} +(0.744188 + 1.62954i) q^{40} +(-1.03936 + 0.535829i) q^{41} +(-5.08167 - 3.26579i) q^{43} +(-6.86512 + 5.39879i) q^{44} +(14.6570 + 1.39958i) q^{46} +(8.27339 + 3.31217i) q^{47} +(2.39330 + 1.23383i) q^{49} +(-0.177624 + 3.72878i) q^{50} +(-5.16232 - 1.51580i) q^{52} +(5.11758 - 3.28887i) q^{53} +(13.7560 - 2.65125i) q^{55} +(-0.817736 - 1.14835i) q^{56} +(0.383514 - 0.112610i) q^{58} +(1.78199 - 2.05652i) q^{59} +(-1.50949 + 2.11978i) q^{61} +(4.86945 - 10.6626i) q^{62} +(0.703780 + 4.89489i) q^{64} +(6.24595 + 5.95551i) q^{65} +(3.67942 + 7.31176i) q^{67} -2.12298 q^{68} +(-1.48703 - 10.3425i) q^{70} +(-0.634636 - 13.3226i) q^{71} +(3.40776 - 4.78553i) q^{73} +(-3.05140 + 12.5780i) q^{74} +(-3.67528 + 1.07916i) q^{76} +(-10.2347 + 4.09735i) q^{77} +(-0.226263 + 0.0436086i) q^{79} +(3.95499 - 11.4272i) q^{80} +(2.14184 + 0.628902i) q^{82} +(-5.05885 + 0.483062i) q^{83} +(3.02680 + 1.56042i) q^{85} +(2.71861 + 11.2063i) q^{86} +(-3.59181 - 0.342976i) q^{88} +(1.05386 - 7.32975i) q^{89} +(-5.71332 - 3.67173i) q^{91} +(-8.30451 - 9.58392i) q^{92} +(-7.06717 - 15.4749i) q^{94} +(6.03316 + 1.16280i) q^{95} +(-2.11201 - 3.65811i) q^{97} +(-1.68118 - 4.85744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Introduction

L-functions

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