LMFDB - Embedded newform 603.2.v.a.8.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(8,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("603.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.v (of order $22$, degree $10$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			8.16
Character	$\chi$	$=$	603.8
Dual form			603.2.v.a.377.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.121792 - 0.847083i) q^{2} +(1.21627 + 0.357129i) q^{4} +(3.41791 + 2.19655i) q^{5} +(-1.09217 - 0.157030i) q^{7} +(1.16167 - 2.54370i) q^{8} +O(q^{10})$	\(q+(0.121792 - 0.847083i) q^{2} +(1.21627 + 0.357129i) q^{4} +(3.41791 + 2.19655i) q^{5} +(-1.09217 - 0.157030i) q^{7} +(1.16167 - 2.54370i) q^{8} +(2.27694 - 2.62773i) q^{10} +(-2.71676 - 1.74596i) q^{11} +(3.01791 - 1.37823i) q^{13} +(-0.266035 + 0.906032i) q^{14} +(0.119531 + 0.0768181i) q^{16} +(-2.27564 - 7.75013i) q^{17} +(1.06184 + 7.38523i) q^{19} +(3.37264 + 3.89224i) q^{20} +(-1.80985 + 2.08868i) q^{22} +(0.135513 - 0.117423i) q^{23} +(4.78015 + 10.4671i) q^{25} +(-0.799920 - 2.72428i) q^{26} +(-1.27229 - 0.581036i) q^{28} +5.59354i q^{29} +(3.60752 + 1.64750i) q^{31} +(3.74214 - 4.31866i) q^{32} +(-6.84216 + 0.983753i) q^{34} +(-3.38800 - 2.93572i) q^{35} -1.32326 q^{37} +6.38522 q^{38} +(9.55785 - 6.14246i) q^{40} +(-4.91442 + 1.44300i) q^{41} +(-0.886797 - 3.02015i) q^{43} +(-2.68078 - 3.09379i) q^{44} +(-0.0829626 - 0.129092i) q^{46} +(-6.55807 + 5.68260i) q^{47} +(-5.54828 - 1.62912i) q^{49} +(9.44866 - 2.77438i) q^{50} +(4.16280 - 0.598520i) q^{52} +(11.2948 + 3.31645i) q^{53} +(-5.45055 - 11.9350i) q^{55} +(-1.66818 + 2.59573i) q^{56} +(4.73820 + 0.681250i) q^{58} +(-11.3584 - 5.18722i) q^{59} +(-0.430753 - 0.670265i) q^{61} +(1.83493 - 2.85521i) q^{62} +(-3.01641 - 3.48112i) q^{64} +(13.3423 + 1.91833i) q^{65} +(-8.04600 - 1.50397i) q^{67} -10.2389i q^{68} +(-2.89943 + 2.51237i) q^{70} +(3.05819 - 10.4152i) q^{71} +(3.63244 - 2.33443i) q^{73} +(-0.161162 + 1.12091i) q^{74} +(-1.34600 + 9.36164i) q^{76} +(2.69300 + 2.33349i) q^{77} +(-6.31825 + 2.88545i) q^{79} +(0.239811 + 0.525114i) q^{80} +(0.623807 + 4.33867i) q^{82} +(1.91111 - 2.97375i) q^{83} +(9.24564 - 31.4878i) q^{85} +(-2.66632 + 0.383360i) q^{86} +(-7.59717 + 4.88241i) q^{88} +(-3.35742 - 2.90922i) q^{89} +(-3.51249 + 1.03136i) q^{91} +(0.206756 - 0.0944223i) q^{92} +(4.01491 + 6.24732i) q^{94} +(-12.5928 + 27.5744i) q^{95} +0.341393i q^{97} +(-2.05574 + 4.50144i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 28 q^{4}+O(q^{10}) $ 240 * q - 28 * q^4	$ 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) $ 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.121792	−	0.847083i	0.0861201	−	0.598978i	−0.900366	−	0.435133i	$-0.856701\pi$
$2$	0.121792	−	0.847083i	0.0861201	−	0.598978i	0.986486	−	0.163845i	$-0.0523897\pi$
$3$		0			0
$3$		0			0
$4$	1.21627	+	0.357129i	0.608135	+	0.178564i
$5$	3.41791	+	2.19655i	1.52853	+	0.982329i	0.990209	+	0.139591i	$0.0445789\pi$
$5$	3.41791	+	2.19655i	1.52853	+	0.982329i	0.538324	+	0.842738i	$0.319058\pi$
$6$		0			0
$7$	−1.09217	−	0.157030i	−0.412801	−	0.0593518i	−0.0672141	−	0.997739i	$-0.521411\pi$
$7$	−1.09217	−	0.157030i	−0.412801	−	0.0593518i	−0.345587	+	0.938387i	$0.612320\pi$
$8$	1.16167	−	2.54370i	0.410712	−	0.899334i
$9$		0			0
$10$	2.27694	−	2.62773i	0.720031	−	0.830960i
$11$	−2.71676	−	1.74596i	−0.819135	−	0.526426i	0.0626735	−	0.998034i	$-0.480037\pi$
$11$	−2.71676	−	1.74596i	−0.819135	−	0.526426i	−0.881808	+	0.471608i	$0.843674\pi$
$12$		0			0
$13$	3.01791	−	1.37823i	0.837017	−	0.382253i	0.0496723	−	0.998766i	$-0.484182\pi$
$13$	3.01791	−	1.37823i	0.837017	−	0.382253i	0.787345	+	0.616513i	$0.211455\pi$
$14$	−0.266035	+	0.906032i	−0.0711009	+	0.242147i
$15$		0			0
$16$	0.119531	+	0.0768181i	0.0298828	+	0.0192045i
$17$	−2.27564	−	7.75013i	−0.551924	−	1.87968i	−0.469162	−	0.883112i	$-0.655444\pi$
$17$	−2.27564	−	7.75013i	−0.551924	−	1.87968i	−0.0827626	−	0.996569i	$-0.526374\pi$
$18$		0			0
$19$	1.06184	+	7.38523i	0.243602	+	1.69429i	0.633752	+	0.773536i	$0.281514\pi$
$19$	1.06184	+	7.38523i	0.243602	+	1.69429i	−0.390150	+	0.920751i	$0.627577\pi$
$20$	3.37264	+	3.89224i	0.754145	+	0.870330i
$21$		0			0
$22$	−1.80985	+	2.08868i	−0.385862	+	0.445308i
$23$	0.135513	−	0.117423i	0.0282565	−	0.0244844i	−0.640618	−	0.767860i	$-0.721322\pi$
$23$	0.135513	−	0.117423i	0.0282565	−	0.0244844i	0.668875	+	0.743375i	$0.266776\pi$
$24$		0			0
$25$	4.78015	+	10.4671i	0.956030	+	2.09341i
$26$	−0.799920	−	2.72428i	−0.156877	−	0.534275i
$27$		0			0
$28$	−1.27229	−	0.581036i	−0.240441	−	0.109805i
$29$			5.59354i			1.03869i	0.854563	+	0.519347i	$0.173825\pi$
$29$			5.59354i			1.03869i	−0.854563	+	0.519347i	$0.826175\pi$
$30$		0			0
$31$	3.60752	+	1.64750i	0.647929	+	0.295899i	0.712140	−	0.702037i	$-0.247726\pi$
$31$	3.60752	+	1.64750i	0.647929	+	0.295899i	−0.0642113	+	0.997936i	$0.520453\pi$
$32$	3.74214	−	4.31866i	0.661524	−	0.763439i
$33$		0			0
$34$	−6.84216	+	0.983753i	−1.17342	+	0.168712i
$35$	−3.38800	−	2.93572i	−0.572677	−	0.496228i
$36$		0			0
$37$	−1.32326			−0.217542			−0.108771	−	0.994067i	$-0.534692\pi$
$37$	−1.32326			−0.217542			−0.108771	+	0.994067i	$0.534692\pi$
$38$	6.38522			1.03582
$39$		0			0
$40$	9.55785	−	6.14246i	1.51123	−	0.971208i
$41$	−4.91442	+	1.44300i	−0.767504	+	0.225359i	−0.641970	−	0.766730i	$-0.721883\pi$
$41$	−4.91442	+	1.44300i	−0.767504	+	0.225359i	−0.125534	+	0.992089i	$0.540064\pi$
$42$		0			0
$43$	−0.886797	−	3.02015i	−0.135235	−	0.460569i	0.863831	−	0.503782i	$-0.168059\pi$
$43$	−0.886797	−	3.02015i	−0.135235	−	0.460569i	−0.999066	+	0.0432135i	$0.986240\pi$
$44$	−2.68078	−	3.09379i	−0.404143	−	0.466406i
$45$		0			0
$46$	−0.0829626	−	0.129092i	−0.0122322	−	0.0190336i
$47$	−6.55807	+	5.68260i	−0.956592	+	0.828892i	−0.985324	−	0.170695i	$-0.945399\pi$
$47$	−6.55807	+	5.68260i	−0.956592	+	0.828892i	0.0287315	+	0.999587i	$0.490853\pi$
$48$		0			0
$49$	−5.54828	−	1.62912i	−0.792611	−	0.232732i
$50$	9.44866	−	2.77438i	1.33624	−	0.392356i
$51$		0			0
$52$	4.16280	−	0.598520i	0.577276	−	0.0829998i
$53$	11.2948	+	3.31645i	1.55146	+	0.455550i	0.941537	−	0.336910i	$-0.109382\pi$
$53$	11.2948	+	3.31645i	1.55146	+	0.455550i	0.609924	+	0.792460i	$0.291200\pi$
$54$		0			0
$55$	−5.45055	−	11.9350i	−0.734952	−	1.60932i
$56$	−1.66818	+	2.59573i	−0.222919	+	0.346869i
$57$		0			0
$58$	4.73820	+	0.681250i	0.622156	+	0.0894525i
$59$	−11.3584	−	5.18722i	−1.47874	−	0.675318i	−0.497387	−	0.867529i	$-0.665707\pi$
$59$	−11.3584	−	5.18722i	−1.47874	−	0.675318i	−0.981354	+	0.192211i	$0.938434\pi$
$60$		0			0
$61$	−0.430753	−	0.670265i	−0.0551523	−	0.0858186i	0.812582	−	0.582846i	$-0.198061\pi$
$61$	−0.430753	−	0.670265i	−0.0551523	−	0.0858186i	−0.867735	+	0.497028i	$0.834425\pi$
$62$	1.83493	−	2.85521i	0.233037	−	0.362613i
$63$		0			0
$64$	−3.01641	−	3.48112i	−0.377051	−	0.435140i
$65$	13.3423	+	1.91833i	1.65491	+	0.237940i
$66$		0			0
$67$	−8.04600	−	1.50397i	−0.982975	−	0.183739i
$67$	−8.04600	−	1.50397i	−0.982975	−	0.183739i
$68$		−	10.2389i		−	1.24165i
$69$		0			0
$70$	−2.89943	+	2.51237i	−0.346548	+	0.300286i
$71$	3.05819	−	10.4152i	0.362940	−	1.23606i	−0.552468	−	0.833534i	$-0.686314\pi$
$71$	3.05819	−	10.4152i	0.362940	−	1.23606i	0.915408	−	0.402527i	$-0.131868\pi$
$72$		0			0
$73$	3.63244	−	2.33443i	0.425145	−	0.273224i	−0.310524	−	0.950566i	$-0.600504\pi$
$73$	3.63244	−	2.33443i	0.425145	−	0.273224i	0.735669	+	0.677341i	$0.236868\pi$
$74$	−0.161162	+	1.12091i	−0.0187347	+	0.130303i
$75$		0			0
$76$	−1.34600	+	9.36164i	−0.154397	+	1.07385i
$77$	2.69300	+	2.33349i	0.306895	+	0.265926i
$78$		0			0
$79$	−6.31825	+	2.88545i	−0.710858	+	0.324638i	−0.737819	−	0.674998i	$-0.764144\pi$
$79$	−6.31825	+	2.88545i	−0.710858	+	0.324638i	0.0269610	+	0.999636i	$0.491417\pi$
$80$	0.239811	+	0.525114i	0.0268117	+	0.0587095i
$81$		0			0
$82$	0.623807	+	4.33867i	0.0688879	+	0.479126i
$83$	1.91111	−	2.97375i	0.209772	−	0.326411i	−0.720385	−	0.693575i	$-0.756035\pi$
$83$	1.91111	−	2.97375i	0.209772	−	0.326411i	0.930156	+	0.367164i	$0.119671\pi$
$84$		0			0
$85$	9.24564	−	31.4878i	1.00283	−	3.41533i
$86$	−2.66632	+	0.383360i	−0.287517	+	0.0413387i
$87$		0			0
$88$	−7.59717	+	4.88241i	−0.809861	+	0.520466i
$89$	−3.35742	−	2.90922i	−0.355886	−	0.308377i	0.458507	−	0.888691i	$-0.348384\pi$
$89$	−3.35742	−	2.90922i	−0.355886	−	0.308377i	−0.814393	+	0.580314i	$0.802930\pi$
$90$		0			0
$91$	−3.51249	+	1.03136i	−0.368209	+	0.108116i
$92$	0.206756	−	0.0944223i	0.0215558	−	0.00984421i
$93$		0			0
$94$	4.01491	+	6.24732i	0.414106	+	0.644362i
$95$	−12.5928	+	27.5744i	−1.29199	+	2.82907i
$96$		0			0
$97$			0.341393i			0.0346633i	0.999850	+	0.0173316i	$0.00551710\pi$
$97$			0.341393i			0.0346633i	−0.999850	+	0.0173316i	$0.994483\pi$
$98$	−2.05574	+	4.50144i	−0.207661	+	0.454714i
$99$		0			0
$100$	2.07586	+	14.4379i	0.207586	+	1.44379i
$101$	−0.430445	−	2.99381i	−0.0428309	−	0.297896i	−0.999966	−	0.00825350i	$-0.997373\pi$
$101$	−0.430445	−	2.99381i	−0.0428309	−	0.297896i	0.957135	−	0.289642i	$-0.0935363\pi$
$102$		0			0
$103$	−7.83731	+	17.1613i	−0.772234	+	1.69096i	−0.0505611	+	0.998721i	$0.516101\pi$
$103$	−7.83731	+	17.1613i	−0.772234	+	1.69096i	−0.721672	+	0.692235i	$0.756626\pi$
$104$		−	9.27771i		−	0.909754i
$105$		0			0
$106$	4.18493	−	9.16372i	0.406476	−	0.890059i
$107$	−1.47225	−	2.29086i	−0.142328	−	0.221466i	0.762770	−	0.646670i	$-0.223839\pi$
$107$	−1.47225	−	2.29086i	−0.142328	−	0.221466i	−0.905098	+	0.425204i	$0.860202\pi$
$108$		0			0
$109$	5.80681	−	2.65188i	0.556191	−	0.254004i	−0.117429	−	0.993081i	$-0.537465\pi$
$109$	5.80681	−	2.65188i	0.556191	−	0.254004i	0.673621	+	0.739077i	$0.264738\pi$
$110$	−10.7738	+	3.16347i	−1.02724	+	0.301625i
$111$		0			0
$112$	−0.118486	−	0.102668i	−0.0111958	−	0.00970124i
$113$	−8.83234	+	5.67620i	−0.830877	+	0.533972i	−0.885556	−	0.464532i	$-0.846223\pi$
$113$	−8.83234	+	5.67620i	−0.830877	+	0.533972i	0.0546797	+	0.998504i	$0.482586\pi$
$114$		0			0
$115$	0.721098	−	0.103678i	0.0672428	−	0.00966805i
$116$	−1.99762	+	6.80326i	−0.185474	+	0.631667i
$117$		0			0
$118$	−5.77737	+	8.98976i	−0.531850	+	0.827575i
$119$	1.26838	+	8.82179i	0.116272	+	0.808692i
$120$		0			0
$121$	−0.237133	−	0.519248i	−0.0215575	−	0.0472044i
$122$	−0.620232	+	0.283251i	−0.0561532	+	0.0256443i
$123$		0			0
$124$	3.79934	+	3.29215i	0.341191	+	0.295644i
$125$	−3.76235	+	26.1677i	−0.336515	+	2.34051i
$126$		0			0
$127$	0.869213	−	6.04551i	0.0771302	−	0.536452i	−0.914221	−	0.405216i	$-0.867196\pi$
$127$	0.869213	−	6.04551i	0.0771302	−	0.536452i	0.991351	−	0.131236i	$-0.0418946\pi$
$128$	6.29836	−	4.04771i	0.556702	−	0.357771i
$129$		0			0
$130$	3.24997	−	11.0684i	0.285041	−	0.970762i
$131$	−11.3741	+	9.85570i	−0.993759	+	0.861097i	−0.990307	−	0.138897i	$-0.955644\pi$
$131$	−11.3741	+	9.85570i	−0.993759	+	0.861097i	−0.00345187	+	0.999994i	$0.501099\pi$
$132$		0			0
$133$		−	8.23265i		−	0.713862i
$134$	−2.25392	+	6.63246i	−0.194709	+	0.572957i
$135$		0			0
$136$	−22.3575	−	3.21453i	−1.91714	−	0.275644i
$137$	−9.34794	−	10.7881i	−0.798648	−	0.921689i	0.199658	−	0.979866i	$-0.436017\pi$
$137$	−9.34794	−	10.7881i	−0.798648	−	0.921689i	−0.998306	+	0.0581764i	$0.981471\pi$
$138$		0			0
$139$	1.88790	−	2.93763i	0.160129	−	0.249166i	−0.751913	−	0.659263i	$-0.770869\pi$
$139$	1.88790	−	2.93763i	0.160129	−	0.249166i	0.912042	+	0.410096i	$0.134505\pi$
$140$	−3.07229	−	4.78058i	−0.259656	−	0.404033i
$141$		0			0
$142$	−8.45011	−	3.85903i	−0.709117	−	0.323843i
$143$	−10.6053	−	1.52481i	−0.886858	−	0.127511i
$144$		0			0
$145$	−12.2865	+	19.1182i	−1.02034	+	1.58768i
$146$	−1.53505	−	3.36130i	−0.127042	−	0.278183i
$147$		0			0
$148$	−1.60944	−	0.472574i	−0.132295	−	0.0388453i
$149$	13.9835	−	2.01053i	1.14558	−	0.164709i	0.456723	−	0.889609i	$-0.349023\pi$
$149$	13.9835	−	2.01053i	1.14558	−	0.164709i	0.688854	+	0.724900i	$0.258114\pi$
$150$		0			0
$151$	5.64401	−	1.65723i	0.459303	−	0.134864i	−0.0438923	−	0.999036i	$-0.513976\pi$
$151$	5.64401	−	1.65723i	0.459303	−	0.134864i	0.503195	+	0.864173i	$0.332158\pi$
$152$	20.0193	+	5.87820i	1.62378	+	0.476785i
$153$		0			0
$154$	2.30465	−	1.99699i	0.185714	−	0.160922i
$155$	8.71133	+	13.5551i	0.699711	+	1.08877i
$156$		0			0
$157$	−9.14093	−	10.5492i	−0.729525	−	0.841917i	0.262893	−	0.964825i	$-0.415323\pi$
$157$	−9.14093	−	10.5492i	−0.729525	−	0.841917i	−0.992418	+	0.122908i	$0.960778\pi$
$158$	1.67470	+	5.70350i	0.133232	+	0.453746i
$159$		0			0
$160$	22.2765	−	6.54096i	1.76111	−	0.517108i
$161$	−0.166442	+	0.106966i	−0.0131175	+	0.00843011i
$162$		0			0
$163$	0.878709			0.0688258			0.0344129	−	0.999408i	$-0.489044\pi$
$163$	0.878709			0.0688258			0.0344129	+	0.999408i	$0.489044\pi$
$164$	−6.49260			−0.506987
$165$		0			0
$166$	−2.28625	−	1.98105i	−0.177448	−	0.153759i
$167$	0.406582	−	0.0584577i	0.0314623	−	0.00452359i	−0.126566	−	0.991958i	$-0.540395\pi$
$167$	0.406582	−	0.0584577i	0.0314623	−	0.00452359i	0.158028	+	0.987435i	$0.449486\pi$
$168$		0			0
$169$	−1.30494	+	1.50598i	−0.100380	+	0.115845i
$170$	−25.5467	−	11.6668i	−1.95934	−	0.894802i
$171$		0			0
$172$		−	3.99002i		−	0.304236i
$173$	9.31485	+	4.25395i	0.708195	+	0.323422i	0.736745	−	0.676171i	$-0.236362\pi$
$173$	9.31485	+	4.25395i	0.708195	+	0.323422i	−0.0285501	+	0.999592i	$0.509089\pi$
$174$		0			0
$175$	−3.57708	−	12.1824i	−0.270402	−	0.920905i
$176$	−0.190617	−	0.417393i	−0.0143683	−	0.0314622i
$177$		0			0
$178$	−2.87326	+	2.48969i	−0.215360	+	0.186610i
$179$	−1.00953	+	1.16506i	−0.0754561	+	0.0870810i	−0.792222	−	0.610233i	$-0.791076\pi$
$179$	−1.00953	+	1.16506i	−0.0754561	+	0.0870810i	0.716766	+	0.697314i	$0.245621\pi$
$180$		0			0
$181$	11.0482	+	12.7503i	0.821204	+	0.947720i	0.999341	−	0.0362857i	$-0.0115526\pi$
$181$	11.0482	+	12.7503i	0.821204	+	0.947720i	−0.178137	+	0.984006i	$0.557007\pi$
$182$	0.445854	+	3.10098i	0.0330489	+	0.229860i
$183$		0			0
$184$	−0.141267	−	0.481112i	−0.0104144	−	0.0354681i
$185$	−4.52277	−	2.90661i	−0.332521	−	0.213698i
$186$		0			0
$187$	−7.34901	+	25.0284i	−0.537413	+	1.83026i
$188$	−10.0058	+	4.56949i	−0.729748	+	0.333265i
$189$		0			0
$190$	21.8241	+	14.0255i	1.58329	+	1.01752i
$191$	−5.42905	+	6.26546i	−0.392833	+	0.453353i	−0.917371	−	0.398034i	$-0.869693\pi$
$191$	−5.42905	+	6.26546i	−0.392833	+	0.453353i	0.524538	+	0.851387i	$0.324238\pi$
$192$		0			0
$193$	5.18835	−	11.3609i	0.373466	−	0.817776i	−0.625819	−	0.779968i	$-0.715235\pi$
$193$	5.18835	−	11.3609i	0.373466	−	0.817776i	0.999285	−	0.0378077i	$-0.0120374\pi$
$194$	0.289189	+	0.0415790i	0.0207625	+	0.00298520i
$195$		0			0
$196$	−6.16639	−	3.96290i	−0.440457	−	0.283064i
$197$	15.8677	+	4.65919i	1.13053	+	0.331954i	0.792916	−	0.609331i	$-0.208562\pi$
$197$	15.8677	+	4.65919i	1.13053	+	0.331954i	0.337614	+	0.941285i	$0.390380\pi$
$198$		0			0
$199$	3.37795	−	23.4941i	0.239456	−	1.66546i	−0.415353	−	0.909661i	$-0.636342\pi$
$199$	3.37795	−	23.4941i	0.239456	−	1.66546i	0.654809	−	0.755795i	$-0.272749\pi$
$200$	32.1780			2.27533
$201$		0			0
$202$	−2.58843			−0.182122
$203$	0.878355	−	6.10909i	0.0616484	−	0.428774i
$204$		0			0
$205$	−19.9667	−	5.86274i	−1.39453	−	0.409472i
$206$	13.5825	+	8.72897i	0.946341	+	0.608176i
$207$		0			0
$208$	0.466608	+	0.0670881i	0.0323534	+	0.00465172i
$209$	10.0095	−	21.9178i	0.692374	−	1.51609i
$210$		0			0
$211$	17.0075	−	19.6277i	1.17085	−	1.35123i	0.246746	−	0.969080i	$-0.420639\pi$
$211$	17.0075	−	19.6277i	1.17085	−	1.35123i	0.924101	−	0.382149i	$-0.124816\pi$
$212$	12.5531	+	8.06740i	0.862152	+	0.554071i
$213$		0			0
$214$	−2.11986	+	0.968107i	−0.144911	+	0.0661785i
$215$	3.60294	−	12.2705i	0.245719	−	0.836840i
$216$		0			0
$217$	−3.68131	−	2.36583i	−0.249904	−	0.160603i
$218$	−1.53914	−	5.24183i	−0.104244	−	0.355021i
$219$		0			0
$220$	−2.36699	−	16.4628i	−0.159582	−	1.10992i
$221$	−17.5492	−	20.2528i	−1.18048	−	1.36235i
$222$		0			0
$223$	−5.42083	+	6.25597i	−0.363006	+	0.418931i	−0.907644	−	0.419740i	$-0.862121\pi$
$223$	−5.42083	+	6.25597i	−0.363006	+	0.418931i	0.544639	+	0.838671i	$0.316667\pi$
$224$	−4.76521	+	4.12908i	−0.318389	+	0.275886i
$225$		0			0
$226$	3.73250	+	8.17304i	0.248282	+	0.543663i
$227$	2.58940	+	8.81870i	0.171865	+	0.585318i	0.999703	+	0.0243516i	$0.00775211\pi$
$227$	2.58940	+	8.81870i	0.171865	+	0.585318i	−0.827839	+	0.560966i	$0.810430\pi$
$228$		0			0
$229$	20.1393	+	9.19730i	1.33084	+	0.607775i	0.948656	−	0.316310i	$-0.102444\pi$
$229$	20.1393	+	9.19730i	1.33084	+	0.607775i	0.382186	+	0.924085i	$0.375171\pi$
$230$		−	0.623457i		−	0.0411096i
$231$		0			0
$232$	14.2283	+	6.49785i	0.934134	+	0.426605i
$233$	−3.20625	+	3.70021i	−0.210048	+	0.242409i	−0.850991	−	0.525180i	$-0.823998\pi$
$233$	−3.20625	+	3.70021i	−0.210048	+	0.242409i	0.640943	+	0.767589i	$0.278544\pi$
$234$		0			0
$235$	−34.8970	+	5.01743i	−2.27643	+	0.327301i
$236$	−11.9624	−	10.3655i	−0.778686	−	0.674735i
$237$		0			0
$238$	7.62727			0.494402
$239$	−9.15208			−0.591999			−0.295999	−	0.955188i	$-0.595653\pi$
$239$	−9.15208			−0.591999			−0.295999	+	0.955188i	$0.595653\pi$
$240$		0			0
$241$	−5.59878	+	3.59812i	−0.360649	+	0.231775i	−0.708399	−	0.705812i	$-0.750582\pi$
$241$	−5.59878	+	3.59812i	−0.360649	+	0.231775i	0.347750	+	0.937587i	$0.386946\pi$
$242$	−0.468727	+	0.137631i	−0.0301309	+	0.00884724i
$243$		0			0
$244$	−0.284541	−	0.969057i	−0.0182159	−	0.0620375i
$245$	−15.3850	−	17.7553i	−0.982914	−	1.13434i
$246$		0			0
$247$	13.3831	+	20.8245i	0.851545	+	1.32503i
$248$	8.38148	−	7.26260i	0.532225	−	0.461175i
$249$		0			0
$250$	21.7080	+	6.37405i	1.37293	+	0.403130i
$251$	−23.6780	+	6.95249i	−1.49454	+	0.438837i	−0.923988	−	0.382422i	$-0.875090\pi$
$251$	−23.6780	+	6.95249i	−1.49454	+	0.438837i	−0.570555	+	0.821259i	$0.693272\pi$
$252$		0			0
$253$	−0.573173	+	0.0824099i	−0.0360351	+	0.00518107i
$254$	−5.01518	−	1.47259i	−0.314681	−	0.0923986i
$255$		0			0
$256$	−6.48861	−	14.2081i	−0.405538	−	0.888005i
$257$	0.202235	−	0.314684i	0.0126151	−	0.0196295i	−0.834889	−	0.550419i	$-0.814468\pi$
$257$	0.202235	−	0.314684i	0.0126151	−	0.0196295i	0.847504	+	0.530789i	$0.178104\pi$
$258$		0			0
$259$	1.44522	+	0.207791i	0.0898016	+	0.0129115i
$260$	15.5427	+	7.09813i	0.963919	+	0.440207i
$261$		0			0
$262$	6.96332	+	10.8351i	0.430196	+	0.669397i
$263$	−0.0989639	+	0.153991i	−0.00610237	+	0.00949548i	−0.844291	−	0.535884i	$-0.819978\pi$
$263$	−0.0989639	+	0.153991i	−0.00610237	+	0.00949548i	0.838189	+	0.545380i	$0.183615\pi$
$264$		0			0
$265$	31.3198	+	36.1450i	1.92396	+	2.22037i
$266$	−6.97374	−	1.00267i	−0.427587	−	0.0614778i
$267$		0			0
$268$	−9.24899	−	4.70269i	−0.564972	−	0.287262i
$269$			9.40599i			0.573494i	0.958006	+	0.286747i	$0.0925738\pi$
$269$			9.40599i			0.573494i	−0.958006	+	0.286747i	$0.907426\pi$
$270$		0			0
$271$	3.25441	−	2.81996i	0.197691	−	0.171300i	−0.550390	−	0.834908i	$-0.685521\pi$
$271$	3.25441	−	2.81996i	0.197691	−	0.171300i	0.748081	+	0.663607i	$0.230975\pi$
$272$	0.323339	−	1.10119i	0.0196053	−	0.0667696i
$273$		0			0
$274$	−10.2769	+	6.60457i	−0.620851	+	0.398997i
$275$	5.28852	−	36.7825i	0.318910	−	2.21807i
$276$		0			0
$277$	−3.93202	+	27.3478i	−0.236252	+	1.64317i	0.433910	+	0.900956i	$0.357134\pi$
$277$	−3.93202	+	27.3478i	−0.236252	+	1.64317i	−0.670162	+	0.742215i	$0.733776\pi$
$278$	−2.25848	−	1.95699i	−0.135455	−	0.117372i
$279$		0			0
$280$	−11.4033	+	5.20773i	−0.681480	+	0.311221i
$281$	2.09363	+	4.58442i	0.124896	+	0.273483i	0.961743	−	0.273953i	$-0.0883312\pi$
$281$	2.09363	+	4.58442i	0.124896	+	0.273483i	−0.836848	+	0.547436i	$0.815604\pi$
$282$		0			0
$283$	−0.671239	−	4.66857i	−0.0399010	−	0.277517i	0.960097	−	0.279668i	$-0.0902245\pi$
$283$	−0.671239	−	4.66857i	−0.0399010	−	0.277517i	−0.999998	+	0.00215077i	$0.999315\pi$
$284$	7.43917	−	11.5756i	0.441433	−	0.686884i
$285$		0			0
$286$	−2.58328	+	8.79784i	−0.152753	+	0.520227i
$287$	5.59397	−	0.804292i	0.330202	−	0.0474758i
$288$		0			0
$289$	−40.5846	+	26.0821i	−2.38733	+	1.53424i
$290$	14.6983	+	12.7361i	0.863114	+	0.747892i
$291$		0			0
$292$	5.25172	−	1.54204i	0.307334	−	0.0902413i
$293$	3.98614	−	1.82041i	0.232873	−	0.106349i	−0.295561	−	0.955324i	$-0.595507\pi$
$293$	3.98614	−	1.82041i	0.232873	−	0.106349i	0.528434	+	0.848974i	$0.322779\pi$
$294$		0			0
$295$	−27.4280	−	42.6788i	−1.59692	−	2.48486i
$296$	−1.53719	+	3.36597i	−0.0893472	+	0.195643i
$297$		0			0
$298$		−	12.0901i		−	0.700360i
$299$	0.247131	−	0.541141i	0.0142920	−	0.0312950i
$300$		0			0
$301$	0.494277	+	3.43777i	0.0284896	+	0.198150i
$302$	−0.716416	−	4.98278i	−0.0412251	−	0.286727i
$303$		0			0
$304$	−0.440396	+	0.964334i	−0.0252585	+	0.0553083i
$305$		−	3.23707i		−	0.185354i
$306$		0			0
$307$	6.49058	−	14.2124i	0.370437	−	0.811144i	−0.628994	−	0.777410i	$-0.716533\pi$
$307$	6.49058	−	14.2124i	0.370437	−	0.811144i	0.999431	−	0.0337336i	$-0.0107398\pi$
$308$	2.44205	+	3.79990i	0.139149	+	0.216520i
$309$		0			0
$310$	12.5433	−	5.72832i	0.712410	−	0.325347i
$311$	21.5352	−	6.32330i	1.22115	−	0.358562i	0.393246	−	0.919433i	$-0.371352\pi$
$311$	21.5352	−	6.32330i	1.22115	−	0.358562i	0.827903	+	0.560872i	$0.189534\pi$
$312$		0			0
$313$	−15.9179	−	13.7929i	−0.899734	−	0.779624i	0.0763360	−	0.997082i	$-0.475678\pi$
$313$	−15.9179	−	13.7929i	−0.899734	−	0.779624i	−0.976070	+	0.217459i	$0.930223\pi$
$314$	−10.0493	+	6.45831i	−0.567117	+	0.364464i
$315$		0			0
$316$	−8.71517	+	1.25305i	−0.490266	+	0.0704897i
$317$	0.730099	−	2.48649i	0.0410064	−	0.139655i	−0.936446	−	0.350813i	$-0.885905\pi$
$317$	0.730099	−	2.48649i	0.0410064	−	0.139655i	0.977452	+	0.211158i	$0.0677234\pi$
$318$		0			0
$319$	9.76609	−	15.1963i	0.546796	−	0.850831i
$320$	−2.66333	−	18.5238i	−0.148884	−	1.03551i
$321$		0			0
$322$	0.0703378	+	0.154018i	0.00391977	+	0.00858310i
$323$	54.8201	−	25.0355i	3.05027	−	1.39301i
$324$		0			0
$325$	28.8521	+	25.0005i	1.60043	+	1.38678i
$326$	0.107020	−	0.744339i	0.00592728	−	0.0412251i
$327$		0			0
$328$	−2.03836	+	14.1771i	−0.112550	+	0.782800i
$329$	8.05485	−	5.17654i	0.444078	−	0.285392i
$330$		0			0
$331$	4.79549	−	16.3319i	0.263584	−	0.897684i	−0.716246	−	0.697848i	$-0.754141\pi$
$331$	4.79549	−	16.3319i	0.263584	−	0.897684i	0.979829	−	0.199836i	$-0.0640409\pi$
$332$	3.38644	−	2.93436i	0.185855	−	0.161044i
$333$		0			0
$334$		−	0.351528i		−	0.0192348i
$335$	−24.1969	−	22.8139i	−1.32202	−	1.24646i
$336$		0			0
$337$	0.517701	+	0.0744342i	0.0282010	+	0.00405469i	0.156401	−	0.987694i	$-0.450011\pi$
$337$	0.517701	+	0.0744342i	0.0282010	+	0.00405469i	−0.128200	+	0.991748i	$0.540920\pi$
$338$	1.11676	+	1.28881i	0.0607437	+	0.0701019i
$339$		0			0
$340$	22.4904	−	34.9957i	1.21971	−	1.89791i
$341$	−6.92431	−	10.7744i	−0.374972	−	0.583468i
$342$		0			0
$343$	12.8296	+	5.85910i	0.692736	+	0.316362i
$344$	−8.71253	−	1.25267i	−0.469748	−	0.0675396i
$345$		0			0
$346$	4.73792	−	7.37235i	0.254712	−	0.396340i
$347$	9.16565	+	20.0700i	0.492038	+	1.07741i	0.978976	+	0.203976i	$0.0653866\pi$
$347$	9.16565	+	20.0700i	0.492038	+	1.07741i	−0.486938	+	0.873437i	$0.661886\pi$
$348$		0			0
$349$	9.58176	+	2.81346i	0.512900	+	0.150601i	0.527933	−	0.849286i	$-0.322967\pi$
$349$	9.58176	+	2.81346i	0.512900	+	0.150601i	−0.0150331	+	0.999887i	$0.504785\pi$
$350$	−10.7552	+	1.54636i	−0.574889	+	0.0826566i
$351$		0			0
$352$	−17.7067	+	5.19916i	−0.943771	+	0.277116i
$353$	17.6689	+	5.18805i	0.940420	+	0.276132i	0.715793	−	0.698313i	$-0.246065\pi$
$353$	17.6689	+	5.18805i	0.940420	+	0.276132i	0.224627	+	0.974445i	$0.427884\pi$
$354$		0			0
$355$	33.3302	−	28.8808i	1.76899	−	1.53283i
$356$	−3.04456	−	4.73743i	−0.161361	−	0.251083i
$357$		0			0
$358$	0.863953	+	0.997055i	0.0456613	+	0.0526960i
$359$	3.93133	+	13.3889i	0.207488	+	0.706638i	0.995816	+	0.0913829i	$0.0291287\pi$
$359$	3.93133	+	13.3889i	0.207488	+	0.706638i	−0.788328	+	0.615255i	$0.789053\pi$
$360$		0			0
$361$	−35.1837	+	10.3309i	−1.85177	+	0.543730i
$362$	12.1461	−	7.80583i	0.638386	−	0.410266i
$363$		0			0
$364$	−4.64046			−0.243226
$365$	17.5430			0.918245
$366$		0			0
$367$	15.6808	+	13.5875i	0.818533	+	0.709263i	0.959793	−	0.280709i	$-0.0905697\pi$
$367$	15.6808	+	13.5875i	0.818533	+	0.709263i	−0.141259	+	0.989973i	$0.545115\pi$
$368$	0.0252183	−	0.00362584i	0.00131459	−	0.000189010i
$369$		0			0
$370$	−3.01297	+	3.47716i	−0.156637	+	0.180769i
$371$	−11.8150	−	5.39575i	−0.613407	−	0.280133i
$372$		0			0
$373$		−	34.7907i		−	1.80140i	−0.434446	−	0.900698i	$-0.643056\pi$
$373$		−	34.7907i		−	1.80140i	0.434446	−	0.900698i	$-0.356944\pi$
$374$	20.3061	+	9.27349i	1.05000	+	0.479521i
$375$		0			0
$376$	6.83652	+	23.2831i	0.352567	+	1.20073i
$377$	7.70921	+	16.8808i	0.397044	+	0.869406i
$378$		0			0
$379$	−10.9923	+	9.52490i	−0.564638	+	0.489261i	−0.889771	−	0.456407i	$-0.849136\pi$
$379$	−10.9923	+	9.52490i	−0.564638	+	0.489261i	0.325134	+	0.945668i	$0.394591\pi$
$380$	−25.1639	+	29.0406i	−1.29088	+	1.48975i
$381$		0			0
$382$	4.64615	+	5.36194i	0.237718	+	0.274341i
$383$	3.48335	+	24.2272i	0.177991	+	1.23795i	0.861403	+	0.507922i	$0.169586\pi$
$383$	3.48335	+	24.2272i	0.177991	+	1.23795i	−0.683412	+	0.730033i	$0.739505\pi$
$384$		0			0
$385$	4.07876	+	13.8910i	0.207873	+	0.707949i
$386$	−8.99173	−	5.77863i	−0.457667	−	0.294125i
$387$		0			0
$388$	−0.121922	+	0.415227i	−0.00618963	+	0.0210799i
$389$	17.0294	−	7.77709i	0.863427	−	0.394314i	0.0660651	−	0.997815i	$-0.478956\pi$
$389$	17.0294	−	7.77709i	0.863427	−	0.394314i	0.797362	+	0.603501i	$0.206228\pi$
$390$		0			0
$391$	−1.21842	−	0.783033i	−0.0616183	−	0.0395997i
$392$	−10.5893	+	12.2207i	−0.534838	+	0.617236i
$393$		0			0
$394$	5.87929	−	12.8738i	0.296194	−	0.648575i
$395$	−27.9332	−	4.01619i	−1.40547	−	0.202076i
$396$		0			0
$397$	13.9266	+	8.95011i	0.698958	+	0.449193i	0.841260	−	0.540630i	$-0.181814\pi$
$397$	13.9266	+	8.95011i	0.698958	+	0.449193i	−0.142302	+	0.989823i	$0.545450\pi$
$398$	−19.4901	−	5.72280i	−0.976949	−	0.286858i
$399$		0			0
$400$	−0.232683	+	1.61834i	−0.0116341	+	0.0809172i
$401$	−18.8264			−0.940146			−0.470073	−	0.882628i	$-0.655772\pi$
$401$	−18.8264			−0.940146			−0.470073	+	0.882628i	$0.655772\pi$
$402$		0			0
$403$	13.1578			0.655436
$404$	0.545640	−	3.79501i	0.0271466	−	0.188809i
$405$		0			0
$406$	−5.06793	−	1.48808i	−0.251517	−	0.0738521i
$407$	3.59498	+	2.31035i	0.178196	+	0.114520i
$408$		0			0
$409$	−20.5055	−	2.94825i	−1.01393	−	0.145782i	−0.384736	−	0.923027i	$-0.625707\pi$
$409$	−20.5055	−	2.94825i	−1.01393	−	0.145782i	−0.629198	+	0.777245i	$0.716616\pi$
$410$	−7.39801	+	16.1994i	−0.365362	+	0.800031i
$411$		0			0
$412$	−15.6611	+	18.0739i	−0.771567	+	0.890436i
$413$	11.5908	+	7.44893i	0.570344	+	0.366538i
$414$		0			0
$415$	13.0640	−	5.96613i	0.641286	−	0.292866i
$416$	5.34132	−	18.1909i	0.261880	−	0.891881i
$417$		0			0
$418$	−17.3471	−	11.1483i	−0.848476	−	0.545283i
$419$	7.52266	+	25.6198i	0.367506	+	1.25161i	0.911073	+	0.412245i	$0.135255\pi$
$419$	7.52266	+	25.6198i	0.367506	+	1.25161i	−0.543567	+	0.839366i	$0.682927\pi$
$420$		0			0
$421$	2.58744	+	17.9960i	0.126104	+	0.877073i	0.950426	+	0.310951i	$0.100648\pi$
$421$	2.58744	+	17.9960i	0.126104	+	0.877073i	−0.824322	+	0.566121i	$0.808443\pi$
$422$	−14.5549	−	16.7973i	−0.708524	−	0.817680i
$423$		0			0
$424$	21.5569	−	24.8780i	1.04689	−	1.20818i
$425$	70.2432	−	60.8661i	3.40729	−	2.95244i
$426$		0			0
$427$	0.365203	+	0.799684i	0.0176734	+	0.0386994i
$428$	−0.972517	−	3.31209i	−0.0470084	−	0.160096i
$429$		0			0
$430$	−9.95531	−	4.54644i	−0.480088	−	0.219249i
$431$		−	10.1110i		−	0.487028i	−0.969897	−	0.243514i	$-0.921700\pi$
$431$		−	10.1110i		−	0.487028i	0.969897	−	0.243514i	$-0.0783002\pi$
$432$		0			0
$433$	23.5787	+	10.7680i	1.13312	+	0.517478i	0.891558	−	0.452907i	$-0.149613\pi$
$433$	23.5787	+	10.7680i	1.13312	+	0.517478i	0.241562	+	0.970385i	$0.422340\pi$
$434$	−2.45241	+	2.83023i	−0.117720	+	0.135856i
$435$		0			0
$436$	8.00971	−	1.15162i	0.383595	−	0.0551527i
$437$	1.01109	+	0.876114i	0.0483669	+	0.0419102i
$438$		0			0
$439$	6.07559			0.289972			0.144986	−	0.989434i	$-0.453686\pi$
$439$	6.07559			0.289972			0.144986	+	0.989434i	$0.453686\pi$
$440$	−36.6909			−1.74917
$441$		0			0
$442$	−19.2932	+	12.3990i	−0.917682	+	0.589759i
$443$	−11.2957	+	3.31673i	−0.536677	+	0.157583i	−0.538829	−	0.842415i	$-0.681133\pi$
$443$	−11.2957	+	3.31673i	−0.536677	+	0.157583i	0.00215211	+	0.999998i	$0.499315\pi$
$444$		0			0
$445$	−5.08508	−	17.3182i	−0.241056	−	0.820961i
$446$	4.63911	+	5.35382i	0.219668	+	0.253511i
$447$		0			0
$448$	2.74779	+	4.27564i	0.129821	+	0.202005i
$449$	−8.55816	+	7.41569i	−0.403885	+	0.349968i	−0.832992	−	0.553286i	$-0.813374\pi$
$449$	−8.55816	+	7.41569i	−0.403885	+	0.349968i	0.429107	+	0.903254i	$0.358828\pi$
$450$		0			0
$451$	15.8707	+	4.66007i	0.747324	+	0.219434i
$452$	−12.7696	+	3.74951i	−0.600633	+	0.176362i
$453$		0			0
$454$	7.78554	−	1.11939i	0.365394	−	0.0525357i
$455$	−14.2708	−	4.19028i	−0.669025	−	0.196444i
$456$		0			0
$457$	2.69893	+	5.90983i	0.126251	+	0.276450i	0.962194	−	0.272366i	$-0.0878060\pi$
$457$	2.69893	+	5.90983i	0.126251	+	0.276450i	−0.835943	+	0.548816i	$0.815079\pi$
$458$	10.2437	−	15.9395i	0.478656	−	0.744803i
$459$		0			0
$460$	0.914076	+	0.131424i	0.0426190	+	0.00612769i
$461$	−34.8136	−	15.8988i	−1.62143	−	0.740482i	−0.622324	−	0.782760i	$-0.713811\pi$
$461$	−34.8136	−	15.8988i	−1.62143	−	0.740482i	−0.999106	+	0.0422773i	$0.986539\pi$
$462$		0			0
$463$	4.22586	+	6.57557i	0.196392	+	0.305592i	0.925457	−	0.378852i	$-0.123681\pi$
$463$	4.22586	+	6.57557i	0.196392	+	0.305592i	−0.729065	+	0.684445i	$0.760045\pi$
$464$	−0.429685	+	0.668603i	−0.0199476	+	0.0310391i
$465$		0			0
$466$	2.74389	+	3.16662i	0.127108	+	0.146691i
$467$	14.5088	+	2.08605i	0.671387	+	0.0965309i	0.469574	−	0.882893i	$-0.344408\pi$
$467$	14.5088	+	2.08605i	0.671387	+	0.0965309i	0.201813	+	0.979424i	$0.435317\pi$
$468$		0			0
$469$	8.55142	+	2.90605i	0.394868	+	0.134189i
$470$			30.1717i			1.39172i
$471$		0			0
$472$	−26.3895	+	22.8666i	−1.21467	+	1.05252i
$473$	−2.86384	+	9.75334i	−0.131680	+	0.448459i
$474$		0			0
$475$	−72.2259	+	46.4168i	−3.31395	+	2.12975i
$476$	−1.60782	+	11.1826i	−0.0736944	+	0.512556i
$477$		0			0
$478$	−1.11465	+	7.75257i	−0.0509830	+	0.354594i
$479$	5.59027	+	4.84400i	0.255426	+	0.221328i	0.773156	−	0.634216i	$-0.218677\pi$
$479$	5.59027	+	4.84400i	0.255426	+	0.221328i	−0.517730	+	0.855544i	$0.673223\pi$
$480$		0			0
$481$	−3.99347	+	1.82376i	−0.182087	+	0.0831562i
$482$	2.36602	+	5.18086i	0.107769	+	0.235982i
$483$		0			0
$484$	−0.102979	−	0.716233i	−0.00468085	−	0.0325561i
$485$	−0.749889	+	1.16685i	−0.0340507	+	0.0529840i
$486$		0			0
$487$	−0.666176	+	2.26879i	−0.0301873	+	0.102809i	−0.973209	−	0.229924i	$-0.926152\pi$
$487$	−0.666176	+	2.26879i	−0.0301873	+	0.102809i	0.943021	+	0.332732i	$0.107971\pi$
$488$	−2.20535	+	0.317081i	−0.0998313	+	0.0143536i
$489$		0			0
$490$	−16.9140	+	10.8699i	−0.764095	+	0.491054i
$491$	15.1323	+	13.1122i	0.682910	+	0.591745i	0.925666	−	0.378342i	$-0.123506\pi$
$491$	15.1323	+	13.1122i	0.682910	+	0.591745i	−0.242756	+	0.970088i	$0.578051\pi$
$492$		0			0
$493$	43.3507	−	12.7289i	1.95242	−	0.573281i
$494$	19.2700	−	8.80033i	0.866999	−	0.395945i
$495$		0			0
$496$	0.304653	+	0.474050i	0.0136793	+	0.0212855i
$497$	−4.97557	+	10.8950i	−0.223185	+	0.488706i
$498$		0			0
$499$		−	3.71100i		−	0.166127i	−0.996544	−	0.0830636i	$-0.973530\pi$
$499$		−	3.71100i		−	0.166127i	0.996544	−	0.0830636i	$-0.0264705\pi$
$500$	−13.9213	+	30.4834i	−0.622579	+	1.36326i
$501$		0			0
$502$	3.00554	+	20.9040i	0.134144	+	0.932991i
$503$	−0.599178	−	4.16738i	−0.0267160	−	0.185814i	0.972094	−	0.234594i	$-0.0753759\pi$
$503$	−0.599178	−	4.16738i	−0.0267160	−	0.185814i	−0.998810	+	0.0487795i	$0.984467\pi$
$504$		0			0
$505$	5.10485	−	11.1781i	0.227163	−	0.497418i
$506$			0.495562i			0.0220304i
$507$		0			0
$508$	3.21622	−	7.04255i	0.142697	−	0.312463i
$509$	2.31010	+	3.59458i	0.102393	+	0.159327i	0.888670	−	0.458548i	$-0.151630\pi$
$509$	2.31010	+	3.59458i	0.102393	+	0.159327i	−0.786276	+	0.617875i	$0.787994\pi$
$510$		0			0
$511$	−4.33382	+	1.97919i	−0.191717	+	0.0875541i
$512$	1.54153	−	0.452634i	0.0681267	−	0.0200038i
$513$		0			0
$514$	−0.241933	−	0.209636i	−0.0106712	−	0.00924666i
$515$	−64.4830	+	41.4407i	−2.84146	+	1.82610i
$516$		0			0
$517$	27.7383	−	3.98816i	1.21993	−	0.175399i
$518$	0.352033	−	1.19891i	0.0154674	−	0.0526773i
$519$		0			0
$520$	20.3790	−	31.7103i	0.893678	−	1.39059i
$521$	−1.31194	−	9.12475i	−0.0574772	−	0.399763i	−0.998168	−	0.0604984i	$-0.980731\pi$
$521$	−1.31194	−	9.12475i	−0.0574772	−	0.399763i	0.940691	−	0.339264i	$-0.110178\pi$
$522$		0			0
$523$	−4.87811	−	10.6816i	−0.213305	−	0.467072i	0.772490	−	0.635027i	$-0.219011\pi$
$523$	−4.87811	−	10.6816i	−0.213305	−	0.467072i	−0.985795	+	0.167955i	$0.946284\pi$
$524$	−17.3537	+	7.92518i	−0.758101	+	0.346213i
$525$		0			0
$526$	0.118390	+	0.102585i	0.00516205	+	0.00447294i
$527$	4.55890	−	31.7078i	0.198589	−	1.38121i
$528$		0			0
$529$	−3.26867	+	22.7341i	−0.142116	+	0.988438i
$530$	34.4323	−	22.1283i	1.49564	−	0.961191i
$531$		0			0
$532$	2.94012	−	10.0131i	0.127470	−	0.434124i
$533$	−12.8425	+	11.1281i	−0.556270	+	0.482010i
$534$		0			0
$535$		−	11.0638i		−	0.478331i
$536$	−13.1724	+	18.7195i	−0.568962	+	0.808559i
$537$		0			0
$538$	7.96766	+	1.14558i	0.343510	+	0.0493893i
$539$	12.2290	+	14.1130i	0.526739	+	0.607890i
$540$		0			0
$541$	8.62249	−	13.4168i	0.370710	−	0.576835i	−0.604913	−	0.796292i	$-0.706792\pi$
$541$	8.62249	−	13.4168i	0.370710	−	0.576835i	0.975622	+	0.219456i	$0.0704284\pi$
$542$	−1.99238	−	3.10020i	−0.0855800	−	0.133165i
$543$		0			0
$544$	−41.9860	−	19.1743i	−1.80013	−	0.822093i
$545$	25.6721	+	3.69109i	1.09967	+	0.158109i
$546$		0			0
$547$	19.8913	−	30.9514i	0.850490	−	1.32339i	−0.0942442	−	0.995549i	$-0.530043\pi$
$547$	19.8913	−	30.9514i	0.850490	−	1.32339i	0.944734	−	0.327838i	$-0.106320\pi$
$548$	−7.51687	−	16.4597i	−0.321105	−	0.703122i
$549$		0			0
$550$	−30.5137	−	8.95963i	−1.30111	−	0.382040i
$551$	−41.3096	+	5.93942i	−1.75985	+	0.253028i
$552$		0			0
$553$	7.35369	−	2.15924i	0.312711	−	0.0918202i
$554$	22.6870	+	6.66150i	0.963877	+	0.283020i
$555$		0			0
$556$	3.34530	−	2.89872i	0.141873	−	0.122933i
$557$	−12.0814	−	18.7990i	−0.511904	−	0.796537i	0.485054	−	0.874484i	$-0.338800\pi$
$557$	−12.0814	−	18.7990i	−0.511904	−	0.796537i	−0.996958	+	0.0779467i	$0.975164\pi$
$558$		0			0
$559$	−6.83874	−	7.89233i	−0.289248	−	0.333810i
$560$	−0.179456	−	0.611170i	−0.00758339	−	0.0258267i
$561$		0			0
$562$	4.13837	−	1.21513i	0.174567	−	0.0512574i
$563$	−33.2048	+	21.3394i	−1.39941	+	0.899349i	−0.999849	−	0.0173559i	$-0.994475\pi$
$563$	−33.2048	+	21.3394i	−1.39941	+	0.899349i	−0.399565	+	0.916705i	$0.630839\pi$
$564$		0			0
$565$	−42.6562			−1.79456
$566$	−4.03642			−0.169663
$567$		0			0
$568$	−22.9406	−	19.8782i	−0.962568	−	0.834070i
$569$	12.1488	−	1.74673i	0.509303	−	0.0732266i	0.117127	−	0.993117i	$-0.462632\pi$
$569$	12.1488	−	1.74673i	0.509303	−	0.0732266i	0.392176	+	0.919890i	$0.371723\pi$
$570$		0			0
$571$	8.02770	−	9.26446i	0.335949	−	0.387706i	−0.562490	−	0.826804i	$-0.690157\pi$
$571$	8.02770	−	9.26446i	0.335949	−	0.387706i	0.898439	+	0.439098i	$0.144702\pi$
$572$	−12.3543	−	5.64203i	−0.516560	−	0.235905i
$573$		0			0
$574$		−	4.83652i		−	0.201872i
$575$	1.87685	+	0.857129i	0.0782700	+	0.0357447i
$576$		0			0
$577$	−5.94921	−	20.2612i	−0.247669	−	0.843483i	−0.985670	−	0.168684i	$-0.946048\pi$
$577$	−5.94921	−	20.2612i	−0.247669	−	0.843483i	0.738001	−	0.674799i	$-0.235770\pi$
$578$	17.1508	+	37.5551i	0.713381	+	1.56209i
$579$		0			0
$580$	−21.7714	+	18.8650i	−0.904008	+	0.783327i
$581$	−2.55422	+	2.94773i	−0.105967	+	0.122292i
$582$		0			0
$583$	−24.8949	−	28.7303i	−1.03104	−	1.18989i
$584$	−1.71839	−	11.9517i	−0.0711076	−	0.494564i
$585$		0			0
$586$	−1.05656	−	3.59830i	−0.0436459	−	0.148644i
$587$	31.3352	+	20.1379i	1.29334	+	0.831181i	0.992471	−	0.122484i	$-0.0390860\pi$
$587$	31.3352	+	20.1379i	1.29334	+	0.831181i	0.300872	+	0.953665i	$0.402722\pi$
$588$		0			0
$589$	−8.33656	+	28.3917i	−0.343502	+	1.16986i
$590$	−39.4930	+	18.0359i	−1.62590	+	0.742524i
$591$		0			0
$592$	−0.158171	−	0.101650i	−0.00650077	−	0.00417779i
$593$	10.4451	−	12.0543i	0.428929	−	0.495010i	−0.499607	−	0.866252i	$-0.666522\pi$
$593$	10.4451	−	12.0543i	0.428929	−	0.495010i	0.928536	+	0.371242i	$0.121068\pi$
$594$		0			0
$595$	−15.0423	+	32.9381i	−0.616675	+	1.35033i
$596$	17.7258	+	2.54858i	0.726076	+	0.104394i
$597$		0			0
$598$	−0.428293	−	0.275247i	−0.0175142	−	0.0112557i
$599$	10.2818	+	3.01900i	0.420102	+	0.123353i	0.484950	−	0.874542i	$-0.338838\pi$
$599$	10.2818	+	3.01900i	0.420102	+	0.123353i	−0.0648477	+	0.997895i	$0.520656\pi$
$600$		0			0
$601$	4.42355	−	30.7664i	0.180440	−	1.25499i	−0.675284	−	0.737557i	$-0.735979\pi$
$601$	4.42355	−	30.7664i	0.180440	−	1.25499i	0.855725	−	0.517432i	$-0.173112\pi$
$602$	2.97227			0.121141
$603$		0			0
$604$	7.45648			0.303400
$605$	0.330060	−	2.29562i	0.0134188	−	0.0933301i
$606$		0			0
$607$	2.81414	+	0.826306i	0.114222	+	0.0335387i	0.338344	−	0.941022i	$-0.390133\pi$
$607$	2.81414	+	0.826306i	0.114222	+	0.0335387i	−0.224122	+	0.974561i	$0.571951\pi$
$608$	35.8678	+	23.0509i	1.45463	+	0.934836i
$609$		0			0
$610$	−2.74207	−	0.394250i	−0.111023	−	0.0159627i
$611$	−11.9597	+	26.1881i	−0.483838	+	1.05946i
$612$		0			0
$613$	21.5134	−	24.8278i	0.868920	−	1.00279i	−0.131015	−	0.991380i	$-0.541824\pi$
$613$	21.5134	−	24.8278i	0.868920	−	1.00279i	0.999935	−	0.0114065i	$-0.00363089\pi$
$614$	−11.2486	−	7.22902i	−0.453955	−	0.291739i
$615$		0			0
$616$	9.06408	−	4.13943i	0.365202	−	0.166782i
$617$	6.72738	−	22.9114i	0.270834	−	0.922377i	−0.705970	−	0.708242i	$-0.749489\pi$
$617$	6.72738	−	22.9114i	0.270834	−	0.922377i	0.976804	−	0.214135i	$-0.0686933\pi$
$618$		0			0
$619$	28.1787	+	18.1093i	1.13260	+	0.727876i	0.966100	−	0.258166i	$-0.0831183\pi$
$619$	28.1787	+	18.1093i	1.13260	+	0.727876i	0.166496	+	0.986042i	$0.446755\pi$
$620$	5.75441	+	19.5977i	0.231103	+	0.787063i
$621$		0			0
$622$	−2.73354	−	19.0122i	−0.109605	−	0.762321i
$623$	3.21003	+	3.70457i	0.128607	+	0.148421i
$624$		0			0
$625$	−32.6610	+	37.6928i	−1.30644	+	1.50771i
$626$	−13.6224	+	11.8039i	−0.544463	+	0.471779i
$627$		0			0
$628$	−7.35041	−	16.0951i	−0.293313	−	0.642266i
$629$	3.01126	+	10.2554i	0.120067	+	0.408910i
$630$		0			0
$631$	14.6210	+	6.67717i	0.582051	+	0.265814i	0.684606	−	0.728914i	$-0.259974\pi$
$631$	14.6210	+	6.67717i	0.582051	+	0.265814i	−0.102555	+	0.994727i	$0.532702\pi$
$632$			19.4237i			0.772632i
$633$		0			0
$634$	−2.01734	−	0.921289i	−0.0801189	−	0.0365891i
$635$	16.2502	−	18.7537i	0.644868	−	0.744218i
$636$		0			0
$637$	−18.9895	+	2.73028i	−0.752392	+	0.108178i
$638$	−11.6831	−	10.1235i	−0.462539	−	0.400792i
$639$		0			0
$640$	30.4182			1.20239
$641$	−9.73249			−0.384410			−0.192205	−	0.981355i	$-0.561564\pi$
$641$	−9.73249			−0.384410			−0.192205	+	0.981355i	$0.561564\pi$
$642$		0			0
$643$	8.19887	−	5.26909i	0.323332	−	0.207793i	−0.368898	−	0.929470i	$-0.620265\pi$
$643$	8.19887	−	5.26909i	0.323332	−	0.207793i	0.692230	+	0.721677i	$0.256628\pi$
$644$	−0.240640	+	0.0706582i	−0.00948253	+	0.00278432i
$645$		0			0
$646$	−14.5305	−	49.4863i	−0.571694	−	1.94701i
$647$	18.1395	+	20.9340i	0.713135	+	0.823002i	0.990464	−	0.137773i	$-0.0439945\pi$
$647$	18.1395	+	20.9340i	0.713135	+	0.823002i	−0.277328	+	0.960775i	$0.589449\pi$
$648$		0			0
$649$	21.8015	+	33.9238i	0.855783	+	1.33162i
$650$	24.6915	−	21.3953i	0.968479	−	0.839192i
$651$		0			0
$652$	1.06875	+	0.313812i	0.0418554	+	0.0122898i
$653$	5.76302	−	1.69218i	0.225525	−	0.0662200i	−0.167018	−	0.985954i	$-0.553414\pi$
$653$	5.76302	−	1.69218i	0.225525	−	0.0662200i	0.392543	+	0.919734i	$0.371596\pi$
$654$		0			0
$655$	−60.5241	+	8.70206i	−2.36487	+	0.340018i
$656$	−0.698276	−	0.205032i	−0.0272631	−	0.00800517i
$657$		0			0
$658$	−3.40394	−	7.45359i	−0.132699	−	0.290571i
$659$	6.64149	−	10.3344i	0.258716	−	0.402569i	−0.687460	−	0.726222i	$-0.741274\pi$
$659$	6.64149	−	10.3344i	0.258716	−	0.402569i	0.946176	+	0.323652i	$0.104911\pi$
$660$		0			0
$661$	−17.8434	−	2.56550i	−0.694030	−	0.0997864i	−0.213732	−	0.976892i	$-0.568562\pi$
$661$	−17.8434	−	2.56550i	−0.694030	−	0.0997864i	−0.480297	+	0.877106i	$0.659471\pi$
$662$	−13.2504	−	6.05128i	−0.514993	−	0.235190i
$663$		0			0
$664$	−5.34424	−	8.31580i	−0.207397	−	0.322716i
$665$	18.0835	−	28.1384i	0.701247	−	1.09116i
$666$		0			0
$667$	0.656811	+	0.758000i	0.0254318	+	0.0293499i
$668$	0.515390	+	0.0741019i	0.0199410	+	0.00286709i
$669$		0			0
$670$	−22.2723	+	17.7182i	−0.860452	+	0.684515i
$671$			2.57303i			0.0993306i
$672$		0			0
$673$	−29.3120	+	25.3990i	−1.12989	+	0.979058i	−0.999922	−	0.0124601i	$-0.996034\pi$
$673$	−29.3120	+	25.3990i	−1.12989	+	0.979058i	−0.129970	+	0.991518i	$0.541488\pi$
$674$	0.126104	−	0.429470i	0.00485734	−	0.0165426i
$675$		0			0
$676$	−2.12499	+	1.36565i	−0.0817303	+	0.0525248i
$677$	0.732606	−	5.09538i	0.0281563	−	0.195832i	−0.970888	−	0.239533i	$-0.923006\pi$
$677$	0.732606	−	5.09538i	0.0281563	−	0.195832i	0.999045	+	0.0437010i	$0.0139149\pi$
$678$		0			0
$679$	0.0536091	−	0.372859i	0.00205733	−	0.0143090i
$680$	−69.3551	−	60.0965i	−2.65965	−	2.30460i
$681$		0			0
$682$	−9.97016	+	4.55322i	−0.381777	+	0.174352i
$683$	−9.91544	−	21.7118i	−0.379404	−	0.830778i	−0.998950	−	0.0458180i	$-0.985411\pi$
$683$	−9.91544	−	21.7118i	−0.379404	−	0.830778i	0.619546	−	0.784960i	$-0.287317\pi$
$684$		0			0
$685$	−8.25373	−	57.4059i	−0.315359	−	2.19337i
$686$	6.52570	−	10.1542i	0.249152	−	0.387688i
$687$		0			0
$688$	0.126002	−	0.429124i	0.00480379	−	0.0163602i
$689$	38.6575	−	5.55811i	1.47273	−	0.211747i
$690$		0			0
$691$	28.1523	−	18.0924i	1.07096	−	0.688266i	0.118510	−	0.992953i	$-0.462188\pi$
$691$	28.1523	−	18.0924i	1.07096	−	0.688266i	0.952453	+	0.304687i	$0.0985519\pi$
$692$	9.81016	+	8.50055i	0.372926	+	0.323143i
$693$		0			0
$694$	18.1172	−	5.31970i	0.687721	−	0.201933i
$695$	12.9053	−	5.89366i	0.489526	−	0.223559i
$696$		0			0
$697$	22.3669	+	34.8036i	0.847208	+	1.31828i
$698$	3.55022	−	7.77389i	0.134378	−	0.294246i
$699$		0			0
$700$		−	16.0946i		−	0.608319i
$701$	−19.4621	+	42.6161i	−0.735074	+	1.60959i	0.0564182	+	0.998407i	$0.482032\pi$
$701$	−19.4621	+	42.6161i	−0.735074	+	1.60959i	−0.791492	+	0.611180i	$0.790695\pi$
$702$		0			0
$703$	−1.40508	−	9.77256i	−0.0529936	−	0.368579i
$704$	2.11698	+	14.7239i	0.0797866	+	0.554928i
$705$		0			0
$706$	6.54664	−	14.3351i	0.246386	−	0.539510i
$707$			3.33734i			0.125514i
$708$		0			0
$709$	−12.2394	+	26.8006i	−0.459661	+	1.00652i	0.527903	+	0.849305i	$0.322978\pi$
$709$	−12.2394	+	26.8006i	−0.459661	+	1.00652i	−0.987565	+	0.157214i	$0.949749\pi$
$710$	−20.4051	−	31.7509i	−0.765789	−	1.19159i
$711$		0			0
$712$	−11.3004	+	5.16072i	−0.423500	+	0.193406i
$713$	0.682321	−	0.200348i	0.0255531	−	0.00750308i
$714$		0			0
$715$	−32.8985	−	28.5067i	−1.23033	−	1.06609i
$716$	−1.64394	+	1.05650i	−0.0614371	+	0.0394832i
$717$		0			0
$718$	11.8203	−	1.69950i	0.441129	−	0.0634248i
$719$	6.46285	−	22.0104i	0.241024	−	0.820851i	−0.746770	−	0.665082i	$-0.768396\pi$
$719$	6.46285	−	22.0104i	0.241024	−	0.820851i	0.987794	−	0.155769i	$-0.0497854\pi$
$720$		0			0
$721$	11.2545	−	17.5124i	0.419140	−	0.652195i
$722$	4.46601	+	31.0617i	0.166207	+	1.15600i
$723$		0			0
$724$	8.88406	+	19.4534i	0.330174	+	0.722979i
$725$	−58.5480	+	26.7380i	−2.17442	+	0.993023i
$726$		0			0
$727$	22.8240	+	19.7771i	0.846496	+	0.733493i	0.965779	−	0.259368i	$-0.0835141\pi$
$727$	22.8240	+	19.7771i	0.846496	+	0.733493i	−0.119283	+	0.992860i	$0.538060\pi$
$728$	−1.45688	+	10.1328i	−0.0539956	+	0.375547i
$729$		0			0
$730$	2.13660	−	14.8604i	0.0790793	−	0.550009i
$731$	−21.3885	+	13.7456i	−0.791083	+	0.508398i
$732$		0			0
$733$	−8.18233	+	27.8665i	−0.302221	+	1.02927i	0.658690	+	0.752414i	$0.271111\pi$
$733$	−8.18233	+	27.8665i	−0.302221	+	1.02927i	−0.960911	+	0.276857i	$0.910707\pi$
$734$	13.4196	−	11.6281i	0.495325	−	0.429202i
$735$		0			0
$736$		−	1.02465i		−	0.0377691i
$737$	19.2332	+	18.1339i	0.708464	+	0.667971i
$738$		0			0
$739$	−45.0701	−	6.48010i	−1.65793	−	0.238374i	−0.751196	−	0.660080i	$-0.770523\pi$
$739$	−45.0701	−	6.48010i	−1.65793	−	0.238374i	−0.906733	+	0.421705i	$0.861432\pi$
$740$	−4.46287	−	5.15043i	−0.164058	−	0.189334i
$741$		0			0
$742$	−6.00963	+	9.35116i	−0.220620	+	0.343292i
$743$	−20.1193	−	31.3062i	−0.738104	−	1.14851i	−0.983818	−	0.179170i	$-0.942659\pi$
$743$	−20.1193	−	31.3062i	−0.738104	−	1.14851i	0.245714	−	0.969342i	$-0.420978\pi$
$744$		0			0
$745$	52.2107	+	23.8438i	1.91285	+	0.873570i
$746$	−29.4706	−	4.23724i	−1.07900	−	0.155136i
$747$		0			0
$748$	−17.8768	+	27.8168i	−0.653639	+	1.01708i
$749$	1.24821	+	2.73320i	0.0456086	+	0.0998688i
$750$		0			0
$751$	15.5496	+	4.56577i	0.567413	+	0.166607i	0.552842	−	0.833286i	$-0.313543\pi$
$751$	15.5496	+	4.56577i	0.567413	+	0.166607i	0.0145713	+	0.999894i	$0.495362\pi$
$752$	−1.22042	+	0.175470i	−0.0445041	+	0.00639873i
$753$		0			0
$754$	15.2384	−	4.47439i	0.554949	−	0.162948i
$755$	22.9309	+	6.73312i	0.834540	+	0.245043i
$756$		0			0
$757$	−12.0524	+	10.4435i	−0.438052	+	0.379574i	−0.845782	−	0.533528i	$-0.820866\pi$
$757$	−12.0524	+	10.4435i	−0.438052	+	0.379574i	0.407730	+	0.913102i	$0.366320\pi$
$758$	6.72960	+	10.4715i	0.244430	+	0.380341i
$759$		0			0
$760$	55.5123	+	64.0646i	2.01364	+	2.32387i
$761$	−8.90126	−	30.3149i	−0.322670	−	1.09891i	−0.947925	−	0.318494i	$-0.896823\pi$
$761$	−8.90126	−	30.3149i	−0.322670	−	1.09891i	0.625255	−	0.780421i	$-0.284995\pi$
$762$		0			0
$763$	−6.75844	+	1.98446i	−0.244672	+	0.0718422i
$764$	−8.84077	+	5.68162i	−0.319848	+	0.205554i
$765$		0			0
$766$	20.9467			0.756836
$767$	−41.4279			−1.49587
$768$		0			0
$769$	30.2417	+	26.2046i	1.09054	+	0.944961i	0.998708	−	0.0508132i	$-0.0161813\pi$
$769$	30.2417	+	26.2046i	1.09054	+	0.944961i	0.0918350	+	0.995774i	$0.470727\pi$
$770$	12.2636	−	1.76323i	0.441948	−	0.0635426i
$771$		0			0
$772$	10.3677	−	11.9650i	0.373143	−	0.430630i
$773$	−19.9311	−	9.10223i	−0.716872	−	0.327385i	0.0233682	−	0.999727i	$-0.492561\pi$
$773$	−19.9311	−	9.10223i	−0.716872	−	0.327385i	−0.740240	+	0.672342i	$0.765288\pi$
$774$		0			0
$775$			45.6354i			1.63927i
$776$	0.868403	+	0.396586i	0.0311738	+	0.0142366i
$777$		0			0
$778$	−4.51378	−	15.3725i	−0.161827	−	0.551132i
$779$	−15.8752	−	34.7619i	−0.568789	−	1.24547i
$780$		0			0
$781$	−26.4929	+	22.9563i	−0.947992	+	0.821440i
$782$	−0.811689	+	0.936739i	−0.0290259	+	0.0334977i
$783$		0			0
$784$	−0.538047	−	0.620939i	−0.0192159	−	0.0221764i
$785$	−8.07095	−	56.1347i	−0.288064	−	2.00353i
$786$		0			0
$787$	−10.0209	−	34.1279i	−0.357205	−	1.21653i	−0.920655	−	0.390378i	$-0.872344\pi$
$787$	−10.0209	−	34.1279i	−0.357205	−	1.21653i	0.563450	−	0.826150i	$-0.309474\pi$
$788$	17.6355	+	11.3337i	0.628240	+	0.403745i
$789$		0			0
$790$	−6.80409	+	23.1726i	−0.242079	+	0.824444i
$791$	10.5377	−	4.81242i	0.374679	−	0.171110i
$792$		0			0
$793$	−2.22376	−	1.42912i	−0.0789679	−	0.0507496i
$794$	9.27764	−	10.7070i	0.329251	−	0.379976i
$795$		0			0
$796$	12.4989	−	27.3688i	0.443013	−	0.970063i
$797$	23.1728	+	3.33175i	0.820824	+	0.118017i	0.539917	−	0.841718i	$-0.318456\pi$
$797$	23.1728	+	3.33175i	0.820824	+	0.118017i	0.280907	+	0.959735i	$0.409365\pi$
$798$		0			0
$799$	58.9647	+	37.8943i	2.08602	+	1.34060i
$800$	63.0917	+	18.5254i	2.23063	+	0.654972i
$801$		0			0
$802$	−2.29291	+	15.9475i	−0.0809654	+	0.563127i
$803$	−13.9443			−0.492084
$804$		0			0
$805$	−0.803841			−0.0283317
$806$	1.60252	−	11.1457i	0.0564462	−	0.392592i
$807$		0			0
$808$	−8.11540	−	2.38290i	−0.285499	−	0.0838300i
$809$	−5.52474	−	3.55053i	−0.194239	−	0.124830i	0.439906	−	0.898044i	$-0.355012\pi$
$809$	−5.52474	−	3.55053i	−0.194239	−	0.124830i	−0.634146	+	0.773214i	$0.718648\pi$
$810$		0			0
$811$	49.7521	+	7.15328i	1.74703	+	0.251186i	0.940450	−	0.339933i	$-0.110404\pi$
$811$	49.7521	+	7.15328i	1.74703	+	0.251186i	0.806585	+	0.591119i	$0.201314\pi$
$812$	3.25005	−	7.11662i	0.114054	−	0.249744i
$813$		0			0
$814$	2.39490	−	2.76386i	0.0839412	−	0.0968733i
$815$	3.00334	+	1.93013i	0.105203	+	0.0676096i
$816$		0			0
$817$	21.3629	−	9.75610i	0.747392	−	0.341323i
$818$	−4.99483	+	17.0108i	−0.174640	+	0.594769i
$819$		0			0
$820$	−22.1911	−	14.2613i	−0.774947	−	0.498028i
$821$	11.6451	+	39.6596i	0.406417	+	1.38413i	0.867794	+	0.496924i	$0.165537\pi$
$821$	11.6451	+	39.6596i	0.406417	+	1.38413i	−0.461377	+	0.887204i	$0.652644\pi$
$822$		0			0
$823$	2.50581	+	17.4283i	0.0873469	+	0.607511i	0.985735	+	0.168308i	$0.0538302\pi$
$823$	2.50581	+	17.4283i	0.0873469	+	0.607511i	−0.898388	+	0.439204i	$0.855261\pi$
$824$	34.5489	+	39.8716i	1.20357	+	1.38899i
$825$		0			0
$826$	7.72153	−	8.91112i	0.268666	−	0.310057i
$827$	41.4212	−	35.8917i	1.44036	−	1.24808i	0.521636	−	0.853168i	$-0.325322\pi$
$827$	41.4212	−	35.8917i	1.44036	−	1.24808i	0.918721	−	0.394908i	$-0.129223\pi$
$828$		0			0
$829$	−8.33167	−	18.2438i	−0.289371	−	0.633634i	0.707991	−	0.706221i	$-0.249602\pi$
$829$	−8.33167	−	18.2438i	−0.289371	−	0.633634i	−0.997362	+	0.0725873i	$0.976874\pi$
$830$	−3.46271	−	11.7929i	−0.120192	−	0.409338i
$831$		0			0
$832$	−13.9010	−	6.34839i	−0.481932	−	0.220091i
$833$			46.7071i			1.61831i
$834$		0			0
$835$	1.51806	+	0.693277i	0.0525348	+	0.0239918i
$836$	20.0018	−	23.0833i	0.691776	−	0.798352i
$837$		0			0
$838$	22.6183	−	3.25202i	0.781337	−	0.112339i
$839$	−12.2838	−	10.6440i	−0.424084	−	0.367471i	0.416515	−	0.909129i	$-0.363251\pi$
$839$	−12.2838	−	10.6440i	−0.424084	−	0.367471i	−0.840599	+	0.541658i	$0.817797\pi$
$840$		0			0
$841$	−2.28772			−0.0788871
$842$	15.5593			0.536207
$843$		0			0
$844$	27.6954	−	17.7987i	0.953314	−	0.612658i
$845$	−7.76812	+	2.28093i	−0.267232	+	0.0784663i
$846$		0			0
$847$	0.177451	+	0.604344i	0.00609730	+	0.0207655i
$848$	1.09532	+	1.26406i	0.0376134	+	0.0434082i
$849$		0			0
$850$	−43.0035	−	66.9148i	−1.47501	−	2.29516i
$851$	−0.179319	+	0.155381i	−0.00614698	+	0.00532639i
$852$		0			0
$853$	−2.25972	−	0.663513i	−0.0773713	−	0.0227183i	0.242818	−	0.970072i	$-0.421928\pi$
$853$	−2.25972	−	0.663513i	−0.0773713	−	0.0227183i	−0.320189	+	0.947354i	$0.603746\pi$
$854$	0.721877	−	0.211962i	0.0247021	−	0.00725320i
$855$		0			0
$856$	−7.53754	+	1.08373i	−0.257628	+	0.0370413i
$857$	20.7629	+	6.09653i	0.709246	+	0.208253i	0.616407	−	0.787428i	$-0.288588\pi$
$857$	20.7629	+	6.09653i	0.709246	+	0.208253i	0.0928389	+	0.995681i	$0.470406\pi$
$858$		0			0
$859$	0.789191	+	1.72809i	0.0269269	+	0.0589616i	0.922618	−	0.385716i	$-0.126046\pi$
$859$	0.789191	+	1.72809i	0.0269269	+	0.0589616i	−0.895691	+	0.444678i	$0.853318\pi$
$860$	8.76429	−	13.6375i	0.298860	−	0.465035i
$861$		0			0
$862$	−8.56483	−	1.23144i	−0.291719	−	0.0419429i
$863$	−0.0474356	−	0.0216631i	−0.00161473	−	0.000737421i	0.414607	−	0.910000i	$-0.363919\pi$
$863$	−0.0474356	−	0.0216631i	−0.00161473	−	0.000737421i	−0.416222	+	0.909263i	$0.636646\pi$
$864$		0			0
$865$	22.4932	+	35.0002i	0.764793	+	1.19004i
$866$	11.9931	−	18.6616i	0.407543	−	0.634149i
$867$		0			0
$868$	−3.63256	−	4.19219i	−0.123297	−	0.142292i
$869$	22.2030	+	3.19231i	0.753186	+	0.108292i
$870$		0			0
$871$	−26.3549	+	6.55042i	−0.893002	+	0.221953i
$872$		−	17.8514i		−	0.604524i
$873$		0			0
$874$	0.865284	−	0.749772i	0.0292687	−	0.0253614i
$875$	8.21824	−	27.9888i	0.277827	−	0.946193i
$876$		0			0
$877$	15.3910	−	9.89120i	0.519717	−	0.334002i	−0.254343	−	0.967114i	$-0.581859\pi$
$877$	15.3910	−	9.89120i	0.519717	−	0.334002i	0.774060	+	0.633112i	$0.218223\pi$
$878$	0.739959	−	5.14653i	0.0249724	−	0.173687i
$879$		0			0
$880$	0.265316	−	1.84531i	0.00894378	−	0.0622054i
$881$	32.2822	+	27.9727i	1.08762	+	0.942424i	0.998562	−	0.0536031i	$-0.0170706\pi$
$881$	32.2822	+	27.9727i	1.08762	+	0.942424i	0.0890528	+	0.996027i	$0.471616\pi$
$882$		0			0
$883$	40.2684	−	18.3900i	1.35514	−	0.618872i	0.400408	−	0.916337i	$-0.368868\pi$
$883$	40.2684	−	18.3900i	1.35514	−	0.618872i	0.954733	+	0.297465i	$0.0961411\pi$
$884$	−14.1116	−	30.9002i	−0.474626	−	1.03929i
$885$		0			0
$886$	1.43381	+	9.97238i	0.0481699	+	0.335029i
$887$	26.7718	−	41.6577i	0.898909	−	1.39873i	−0.0180885	−	0.999836i	$-0.505758\pi$
$887$	26.7718	−	41.6577i	0.898909	−	1.39873i	0.916997	−	0.398893i	$-0.130606\pi$
$888$		0			0
$889$	−1.89865	+	6.46622i	−0.0636788	+	0.216870i
$890$	−15.2893	+	2.19826i	−0.512497	+	0.0736860i
$891$		0			0
$892$	−8.82738	+	5.67301i	−0.295563	+	0.189946i
$893$	−48.9309	−	42.3988i	−1.63741	−	1.41882i
$894$		0			0
$895$	−6.00962	+	1.76458i	−0.200879	+	0.0589835i
$896$	−7.51449	+	3.43175i	−0.251041	+	0.114647i
$897$		0			0
$898$	5.23939	+	8.15265i	0.174841	+	0.272057i
$899$	−9.21535	+	20.1788i	−0.307349	+	0.673001i
$900$		0			0
$901$		−	95.0832i		−	3.16768i
$902$	5.88040	−	12.8763i	0.195796	−	0.428733i
$903$		0			0
$904$	4.17830	+	29.0607i	0.138968	+	0.966544i
$905$	9.75494	+	67.8471i	0.324265	+	2.25531i
$906$		0			0
$907$	13.5077	−	29.5776i	0.448514	−	0.982110i	−0.541442	−	0.840738i	$-0.682122\pi$
$907$	13.5077	−	29.5776i	0.448514	−	0.982110i	0.989957	−	0.141372i	$-0.0451512\pi$
$908$			11.6507i			0.386641i
$909$		0			0
$910$	−5.28759	+	11.5782i	−0.175282	+	0.383814i
$911$	13.9108	+	21.6456i	0.460885	+	0.717151i	0.991449	−	0.130494i	$-0.0416563\pi$
$911$	13.9108	+	21.6456i	0.460885	+	0.717151i	−0.530564	+	0.847645i	$0.678020\pi$
$912$		0			0
$913$	−10.3841	+	4.74225i	−0.343663	+	0.156945i
$914$	5.33483	−	1.56645i	0.176460	−	0.0518134i
$915$		0			0
$916$	21.2102	+	18.3787i	0.700804	+	0.607250i
$917$	13.9701	−	8.97802i	0.461332	−	0.296480i
$918$		0			0
$919$	−21.6490	+	3.11265i	−0.714134	+	0.102677i	−0.489799	−	0.871835i	$-0.662930\pi$
$919$	−21.6490	+	3.11265i	−0.714134	+	0.102677i	−0.224335	+	0.974512i	$0.572021\pi$
$920$	0.573951	−	1.95470i	0.0189226	−	0.0644445i
$921$		0			0
$922$	−17.7076	+	27.5536i	−0.583170	+	0.907431i
$923$	−5.12529	−	35.6471i	−0.168701	−	1.17334i
$924$		0			0
$925$	−6.32537	−	13.8506i	−0.207977	−	0.455406i
$926$	6.08473	−	2.77880i	0.199957	−	0.0913171i
$927$		0			0
$928$	24.1566	+	20.9318i	0.792980	+	0.687121i
$929$	1.66041	−	11.5484i	0.0544762	−	0.378890i	−0.944285	−	0.329129i	$-0.893245\pi$
$929$	1.66041	−	11.5484i	0.0544762	−	0.378890i	0.998761	−	0.0497611i	$-0.0158460\pi$
$930$		0			0
$931$	6.14007	−	42.7051i	0.201233	−	1.39960i
$932$	−5.22112	+	3.35541i	−0.171023	+	0.109910i
$933$		0			0
$934$	3.53412	−	12.0361i	0.115640	−	0.393833i
$935$	−80.0945	+	69.4023i	−2.61937	+	2.26970i
$936$		0			0
$937$		−	9.25243i		−	0.302264i	−0.988514	−	0.151132i	$-0.951708\pi$
$937$		−	9.25243i		−	0.302264i	0.988514	−	0.151132i	$-0.0482918\pi$
$938$	3.50316	−	6.88983i	0.114382	−	0.224961i
$939$		0			0
$940$	−44.2360	−	6.36018i	−1.44282	−	0.207446i
$941$	−26.3923	−	30.4583i	−0.860364	−	0.992913i	−0.999996	−	0.00270971i	$-0.999137\pi$
$941$	−26.3923	−	30.4583i	−0.860364	−	0.992913i	0.139632	−	0.990203i	$-0.455408\pi$
$942$		0			0
$943$	−0.496528	+	0.772613i	−0.0161692	+	0.0251597i
$944$	−0.959214	−	1.49257i	−0.0312198	−	0.0485789i
$945$		0			0
$946$	7.91310	+	3.61379i	0.257277	+	0.117494i
$947$	−4.94733	−	0.711319i	−0.160767	−	0.0231148i	0.0614614	−	0.998109i	$-0.480424\pi$
$947$	−4.94733	−	0.711319i	−0.160767	−	0.0231148i	−0.222228	+	0.974995i	$0.571333\pi$
$948$		0			0
$949$	7.74499	−	12.0514i	0.251413	−	0.391207i
$950$	30.5223	+	66.8346i	0.990275	+	2.16840i
$951$		0			0
$952$	23.9134	+	7.02162i	0.775039	+	0.227572i
$953$	−8.06972	+	1.16025i	−0.261404	+	0.0375842i	−0.271771	−	0.962362i	$-0.587609\pi$
$953$	−8.06972	+	1.16025i	−0.261404	+	0.0375842i	0.0103668	+	0.999946i	$0.496700\pi$
$954$		0			0
$955$	−32.3184	+	9.48954i	−1.04580	+	0.307074i
$956$	−11.1314	−	3.26847i	−0.360015	−	0.105710i
$957$		0			0
$958$	4.78412	−	4.14546i	0.154568	−	0.133934i
$959$	8.51547	+	13.2503i	0.274979	+	0.427875i
$960$		0			0
$961$	−10.0008	−	11.5415i	−0.322605	−	0.372306i
$962$	1.05850	+	3.60492i	0.0341274	+	0.116227i
$963$		0			0
$964$	−8.09462	+	2.37680i	−0.260710	+	0.0765514i
$965$	42.6881	−	27.4340i	1.37418	−	0.883132i
$966$		0			0
$967$	−14.8781			−0.478448			−0.239224	−	0.970964i	$-0.576893\pi$
$967$	−14.8781			−0.478448			−0.239224	+	0.970964i	$0.576893\pi$
$968$	−1.59628			−0.0513065
$969$		0			0
$970$	0.897089	+	0.777332i	0.0288038	+	0.0249586i
$971$	−24.0348	+	3.45568i	−0.771313	+	0.110898i	−0.516725	−	0.856151i	$-0.672849\pi$
$971$	−24.0348	+	3.45568i	−0.771313	+	0.110898i	−0.254588	+	0.967050i	$0.581940\pi$
$972$		0			0
$973$	−2.52320	+	2.91193i	−0.0808900	+	0.0933521i
$974$	1.84072	+	0.840627i	0.0589804	+	0.0269354i
$975$		0			0
$976$		−	0.113207i		−	0.00362368i
$977$	28.3758	+	12.9588i	0.907821	+	0.414588i	0.813909	−	0.580993i	$-0.197335\pi$
$977$	28.3758	+	12.9588i	0.907821	+	0.414588i	0.0939120	+	0.995581i	$0.470063\pi$
$978$		0			0
$979$	4.04193	+	13.7656i	0.129181	+	0.439949i
$980$	−12.3714	−	27.0896i	−0.395191	−	0.865347i
$981$		0			0
$982$	12.9501	−	11.2213i	0.413255	−	0.358087i
$983$	−9.94740	+	11.4799i	−0.317273	+	0.366152i	−0.891876	−	0.452280i	$-0.850611\pi$
$983$	−9.94740	+	11.4799i	−0.317273	+	0.366152i	0.574603	+	0.818432i	$0.305156\pi$
$984$		0			0
$985$	44.0003	+	50.7790i	1.40197	+	1.61795i
$986$	−5.50267	−	38.2719i	−0.175241	−	1.21883i
$987$		0			0
$988$	8.84041	+	30.1077i	0.281251	+	0.957853i
$989$	−0.474808	−	0.305141i	−0.0150980	−	0.00970291i
$990$		0			0
$991$	10.5718	−	36.0041i	0.335823	−	1.14371i	−0.602549	−	0.798082i	$-0.705848\pi$
$991$	10.5718	−	36.0041i	0.335823	−	1.14371i	0.938372	−	0.345626i	$-0.112334\pi$
$992$	20.6148	−	9.41448i	0.654521	−	0.298910i
$993$		0			0
$994$	8.62296	+	5.54164i	0.273504	+	0.175770i
$995$	63.1516	−	72.8809i	2.00204	−	2.31048i
$996$		0			0
$997$	0.487875	−	1.06830i	0.0154512	−	0.0338333i	−0.901749	−	0.432260i	$-0.857716\pi$
$997$	0.487875	−	1.06830i	0.0154512	−	0.0338333i	0.917200	+	0.398427i	$0.130444\pi$
$998$	−3.14353	−	0.451971i	−0.0995065	−	0.0143069i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.v.a.8.16	yes	240
3.2	odd	2	inner	603.2.v.a.8.9	✓	240
67.42	odd	22	inner	603.2.v.a.377.9	yes	240
201.176	even	22	inner	603.2.v.a.377.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.v.a.8.9	✓	240	3.2	odd	2	inner
603.2.v.a.8.16	yes	240	1.1	even	1	trivial
603.2.v.a.377.9	yes	240	67.42	odd	22	inner
603.2.v.a.377.16	yes	240	201.176	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.121792 - 0.847083i) q^{2} +(1.21627 + 0.357129i) q^{4} +(3.41791 + 2.19655i) q^{5} +(-1.09217 - 0.157030i) q^{7} +(1.16167 - 2.54370i) q^{8} +O(q^{10})\)	\(q+(0.121792 - 0.847083i) q^{2} +(1.21627 + 0.357129i) q^{4} +(3.41791 + 2.19655i) q^{5} +(-1.09217 - 0.157030i) q^{7} +(1.16167 - 2.54370i) q^{8} +(2.27694 - 2.62773i) q^{10} +(-2.71676 - 1.74596i) q^{11} +(3.01791 - 1.37823i) q^{13} +(-0.266035 + 0.906032i) q^{14} +(0.119531 + 0.0768181i) q^{16} +(-2.27564 - 7.75013i) q^{17} +(1.06184 + 7.38523i) q^{19} +(3.37264 + 3.89224i) q^{20} +(-1.80985 + 2.08868i) q^{22} +(0.135513 - 0.117423i) q^{23} +(4.78015 + 10.4671i) q^{25} +(-0.799920 - 2.72428i) q^{26} +(-1.27229 - 0.581036i) q^{28} +5.59354i q^{29} +(3.60752 + 1.64750i) q^{31} +(3.74214 - 4.31866i) q^{32} +(-6.84216 + 0.983753i) q^{34} +(-3.38800 - 2.93572i) q^{35} -1.32326 q^{37} +6.38522 q^{38} +(9.55785 - 6.14246i) q^{40} +(-4.91442 + 1.44300i) q^{41} +(-0.886797 - 3.02015i) q^{43} +(-2.68078 - 3.09379i) q^{44} +(-0.0829626 - 0.129092i) q^{46} +(-6.55807 + 5.68260i) q^{47} +(-5.54828 - 1.62912i) q^{49} +(9.44866 - 2.77438i) q^{50} +(4.16280 - 0.598520i) q^{52} +(11.2948 + 3.31645i) q^{53} +(-5.45055 - 11.9350i) q^{55} +(-1.66818 + 2.59573i) q^{56} +(4.73820 + 0.681250i) q^{58} +(-11.3584 - 5.18722i) q^{59} +(-0.430753 - 0.670265i) q^{61} +(1.83493 - 2.85521i) q^{62} +(-3.01641 - 3.48112i) q^{64} +(13.3423 + 1.91833i) q^{65} +(-8.04600 - 1.50397i) q^{67} -10.2389i q^{68} +(-2.89943 + 2.51237i) q^{70} +(3.05819 - 10.4152i) q^{71} +(3.63244 - 2.33443i) q^{73} +(-0.161162 + 1.12091i) q^{74} +(-1.34600 + 9.36164i) q^{76} +(2.69300 + 2.33349i) q^{77} +(-6.31825 + 2.88545i) q^{79} +(0.239811 + 0.525114i) q^{80} +(0.623807 + 4.33867i) q^{82} +(1.91111 - 2.97375i) q^{83} +(9.24564 - 31.4878i) q^{85} +(-2.66632 + 0.383360i) q^{86} +(-7.59717 + 4.88241i) q^{88} +(-3.35742 - 2.90922i) q^{89} +(-3.51249 + 1.03136i) q^{91} +(0.206756 - 0.0944223i) q^{92} +(4.01491 + 6.24732i) q^{94} +(-12.5928 + 27.5744i) q^{95} +0.341393i q^{97} +(-2.05574 + 4.50144i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 28 q^{4}+O(q^{10}) \) 240 * q - 28 * q^4	\( 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) \) 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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