LMFDB - Embedded newform 828.2.u.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(19,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 15]))

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

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

chi := DirichletCharacter("828.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.u (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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	828.19
Dual form			828.2.u.c.523.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37328 + 0.337778i) q^{2} +(1.77181 - 0.927729i) q^{4} +(-0.802068 + 1.24804i) q^{5} +(0.333353 + 2.31852i) q^{7} +(-2.11983 + 1.87251i) q^{8} +O(q^{10})$	\(q+(-1.37328 + 0.337778i) q^{2} +(1.77181 - 0.927729i) q^{4} +(-0.802068 + 1.24804i) q^{5} +(0.333353 + 2.31852i) q^{7} +(-2.11983 + 1.87251i) q^{8} +(0.679905 - 1.98484i) q^{10} +(1.33517 - 2.92362i) q^{11} +(0.940564 - 6.54177i) q^{13} +(-1.24093 - 3.07139i) q^{14} +(2.27864 - 3.28752i) q^{16} +(3.20986 - 2.78136i) q^{17} +(-1.25613 + 1.44965i) q^{19} +(-0.263269 + 2.95540i) q^{20} +(-0.846036 + 4.46595i) q^{22} +(3.89006 + 2.80489i) q^{23} +(1.16278 + 2.54613i) q^{25} +(0.918003 + 9.30140i) q^{26} +(2.74160 + 3.79872i) q^{28} +(-4.91811 - 5.67580i) q^{29} +(-1.40691 + 4.79150i) q^{31} +(-2.01876 + 5.28437i) q^{32} +(-3.46856 + 4.90381i) q^{34} +(-3.16098 - 1.44357i) q^{35} +(3.15377 + 4.90737i) q^{37} +(1.23536 - 2.41508i) q^{38} +(-0.636724 - 4.14752i) q^{40} +(6.60126 + 4.24238i) q^{41} +(5.91571 - 1.73701i) q^{43} +(-0.346652 - 6.41878i) q^{44} +(-6.28959 - 2.53793i) q^{46} -4.95230i q^{47} +(1.45204 - 0.426357i) q^{49} +(-2.45685 - 3.10380i) q^{50} +(-4.40248 - 12.4634i) q^{52} +(8.67435 - 1.24718i) q^{53} +(2.57790 + 4.01129i) q^{55} +(-5.04811 - 4.29067i) q^{56} +(8.67112 + 6.13325i) q^{58} +(8.23768 + 1.18440i) q^{59} +(-1.16902 + 3.98132i) q^{61} +(0.313626 - 7.05532i) q^{62} +(0.987389 - 7.93883i) q^{64} +(7.41000 + 6.42080i) q^{65} +(-3.55277 - 7.77948i) q^{67} +(3.10692 - 7.90592i) q^{68} +(4.82853 + 0.914724i) q^{70} +(-3.24835 + 1.48347i) q^{71} +(1.59896 - 1.84530i) q^{73} +(-5.98862 - 5.67393i) q^{74} +(-0.880744 + 3.73386i) q^{76} +(7.22356 + 2.12103i) q^{77} +(-1.28775 + 8.95651i) q^{79} +(2.27534 + 5.48065i) q^{80} +(-10.4984 - 3.59622i) q^{82} +(-8.10326 + 5.20765i) q^{83} +(0.896727 + 6.23688i) q^{85} +(-7.53722 + 4.38360i) q^{86} +(2.64417 + 8.69772i) q^{88} +(3.71385 + 12.6482i) q^{89} +15.4808 q^{91} +(9.49464 + 1.36081i) q^{92} +(1.67278 + 6.80091i) q^{94} +(-0.801724 - 2.73042i) q^{95} +(1.20320 - 1.87221i) q^{97} +(-1.85005 + 1.07598i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{2} + 4 q^{8}+O(q^{10}) $ 240 * q + 4 * q^2 + 4 * q^8	$ 240 q + 4 q^{2} + 4 q^{8} - 8 q^{16} + 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} - 22 q^{34} + 110 q^{38} - 22 q^{40} + 16 q^{41} + 154 q^{44} - 88 q^{46} - 40 q^{49} + 142 q^{50} - 70 q^{52} + 110 q^{56} - 46 q^{58} - 40 q^{62} - 48 q^{64} - 72 q^{70} - 22 q^{74} + 110 q^{76} + 192 q^{77} - 198 q^{80} + 172 q^{82} - 200 q^{85} - 220 q^{86} + 176 q^{88} + 88 q^{89} - 154 q^{92} + 126 q^{94} - 88 q^{97} - 228 q^{98}+O(q^{100}) $ 240 * q + 4 * q^2 + 4 * q^8 - 8 * q^16 + 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 - 22 * q^34 + 110 * q^38 - 22 * q^40 + 16 * q^41 + 154 * q^44 - 88 * q^46 - 40 * q^49 + 142 * q^50 - 70 * q^52 + 110 * q^56 - 46 * q^58 - 40 * q^62 - 48 * q^64 - 72 * q^70 - 22 * q^74 + 110 * q^76 + 192 * q^77 - 198 * q^80 + 172 * q^82 - 200 * q^85 - 220 * q^86 + 176 * q^88 + 88 * q^89 - 154 * q^92 + 126 * q^94 - 88 * q^97 - 228 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$1$	$e\left(\frac{15}{22}\right)$

Coefficient data

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

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

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

$2$	−1.37328	+	0.337778i	−0.971058	+	0.238845i
$2$	−1.37328	+	0.337778i	−0.971058	+	0.238845i
$3$		0			0
$3$		0			0
$4$	1.77181	−	0.927729i	0.885906	−	0.463864i
$5$	−0.802068	+	1.24804i	−0.358696	+	0.558141i	−0.972964	−	0.230956i	$-0.925815\pi$
$5$	−0.802068	+	1.24804i	−0.358696	+	0.558141i	0.614269	+	0.789097i	$0.289451\pi$
$6$		0			0
$7$	0.333353	+	2.31852i	0.125996	+	0.876318i	0.950558	+	0.310547i	$0.100512\pi$
$7$	0.333353	+	2.31852i	0.125996	+	0.876318i	−0.824562	+	0.565771i	$0.808579\pi$
$8$	−2.11983	+	1.87251i	−0.749474	+	0.662033i
$9$		0			0
$10$	0.679905	−	1.98484i	0.215005	−	0.627660i
$11$	1.33517	−	2.92362i	0.402570	−	0.881505i	−0.594434	−	0.804145i	$-0.702624\pi$
$11$	1.33517	−	2.92362i	0.402570	−	0.881505i	0.997003	−	0.0773599i	$-0.0246491\pi$
$12$		0			0
$13$	0.940564	−	6.54177i	0.260866	−	1.81436i	−0.265511	−	0.964108i	$-0.585541\pi$
$13$	0.940564	−	6.54177i	0.260866	−	1.81436i	0.526376	−	0.850252i	$-0.323550\pi$
$14$	−1.24093	−	3.07139i	−0.331653	−	0.820862i
$15$		0			0
$16$	2.27864	−	3.28752i	0.569660	−	0.821881i
$17$	3.20986	−	2.78136i	0.778505	−	0.674579i	−0.172066	−	0.985085i	$-0.555044\pi$
$17$	3.20986	−	2.78136i	0.778505	−	0.674579i	0.950571	+	0.310507i	$0.100499\pi$
$18$		0			0
$19$	−1.25613	+	1.44965i	−0.288176	+	0.332573i	−0.881317	−	0.472526i	$-0.843342\pi$
$19$	−1.25613	+	1.44965i	−0.288176	+	0.332573i	0.593141	+	0.805099i	$0.297888\pi$
$20$	−0.263269	+	2.95540i	−0.0588688	+	0.660847i
$21$		0			0
$22$	−0.846036	+	4.46595i	−0.180375	+	0.952144i
$23$	3.89006	+	2.80489i	0.811134	+	0.584860i
$23$	3.89006	+	2.80489i	0.811134	+	0.584860i
$24$		0			0
$25$	1.16278	+	2.54613i	0.232556	+	0.509226i
$26$	0.918003	+	9.30140i	0.180035	+	1.82415i
$27$		0			0
$28$	2.74160	+	3.79872i	0.518113	+	0.717891i
$29$	−4.91811	−	5.67580i	−0.913270	−	1.05397i	−0.998340	−	0.0575950i	$-0.981657\pi$
$29$	−4.91811	−	5.67580i	−0.913270	−	1.05397i	0.0850698	−	0.996375i	$-0.472889\pi$
$30$		0			0
$31$	−1.40691	+	4.79150i	−0.252689	+	0.860580i	0.731255	+	0.682104i	$0.238935\pi$
$31$	−1.40691	+	4.79150i	−0.252689	+	0.860580i	−0.983944	+	0.178476i	$0.942883\pi$
$32$	−2.01876	+	5.28437i	−0.356870	+	0.934154i
$33$		0			0
$34$	−3.46856	+	4.90381i	−0.594854	+	0.840997i
$35$	−3.16098	−	1.44357i	−0.534304	−	0.244008i
$36$		0			0
$37$	3.15377	+	4.90737i	0.518477	+	0.806766i	0.997473	−	0.0710510i	$-0.0226353\pi$
$37$	3.15377	+	4.90737i	0.518477	+	0.806766i	−0.478995	+	0.877817i	$0.658999\pi$
$38$	1.23536	−	2.41508i	0.200402	−	0.391777i
$39$		0			0
$40$	−0.636724	−	4.14752i	−0.100675	−	0.655781i
$41$	6.60126	+	4.24238i	1.03094	+	0.662548i	0.942731	−	0.333554i	$-0.108248\pi$
$41$	6.60126	+	4.24238i	1.03094	+	0.662548i	0.0882133	+	0.996102i	$0.471884\pi$
$42$		0			0
$43$	5.91571	−	1.73701i	0.902137	−	0.264891i	0.202410	−	0.979301i	$-0.435123\pi$
$43$	5.91571	−	1.73701i	0.902137	−	0.264891i	0.699728	+	0.714409i	$0.253305\pi$
$44$	−0.346652	−	6.41878i	−0.0522597	−	0.967668i
$45$		0			0
$46$	−6.28959	−	2.53793i	−0.927349	−	0.374197i
$47$		−	4.95230i		−	0.722367i	−0.932495	−	0.361184i	$-0.882373\pi$
$47$		−	4.95230i		−	0.722367i	0.932495	−	0.361184i	$-0.117627\pi$
$48$		0			0
$49$	1.45204	−	0.426357i	0.207434	−	0.0609081i
$50$	−2.45685	−	3.10380i	−0.347451	−	0.438943i
$51$		0			0
$52$	−4.40248	−	12.4634i	−0.610515	−	1.72836i
$53$	8.67435	−	1.24718i	1.19151	−	0.171314i	0.482107	−	0.876113i	$-0.339872\pi$
$53$	8.67435	−	1.24718i	1.19151	−	0.171314i	0.709407	+	0.704799i	$0.248963\pi$
$54$		0			0
$55$	2.57790	+	4.01129i	0.347604	+	0.540883i
$56$	−5.04811	−	4.29067i	−0.674582	−	0.573365i
$57$		0			0
$58$	8.67112	+	6.13325i	1.13857	+	0.805336i
$59$	8.23768	+	1.18440i	1.07245	+	0.154196i	0.655849	−	0.754892i	$-0.272311\pi$
$59$	8.23768	+	1.18440i	1.07245	+	0.154196i	0.416605	+	0.909088i	$0.363220\pi$
$60$		0			0
$61$	−1.16902	+	3.98132i	−0.149678	+	0.509756i	−0.999860	−	0.0167328i	$-0.994674\pi$
$61$	−1.16902	+	3.98132i	−0.149678	+	0.509756i	0.850182	+	0.526489i	$0.176492\pi$
$62$	0.313626	−	7.05532i	0.0398305	−	0.896026i
$63$		0			0
$64$	0.987389	−	7.93883i	0.123424	−	0.992354i
$65$	7.41000	+	6.42080i	0.919098	+	0.796403i
$66$		0			0
$67$	−3.55277	−	7.77948i	−0.434040	−	0.950415i	−0.992654	−	0.120987i	$-0.961394\pi$
$67$	−3.55277	−	7.77948i	−0.434040	−	0.950415i	0.558614	−	0.829428i	$-0.311333\pi$
$68$	3.10692	−	7.90592i	0.376770	−	0.958734i
$69$		0			0
$70$	4.82853	+	0.914724i	0.577120	+	0.109330i
$71$	−3.24835	+	1.48347i	−0.385509	+	0.176056i	−0.598735	−	0.800947i	$-0.704330\pi$
$71$	−3.24835	+	1.48347i	−0.385509	+	0.176056i	0.213227	+	0.977003i	$0.431603\pi$
$72$		0			0
$73$	1.59896	−	1.84530i	0.187144	−	0.215975i	−0.654423	−	0.756129i	$-0.727088\pi$
$73$	1.59896	−	1.84530i	0.187144	−	0.215975i	0.841567	+	0.540153i	$0.181634\pi$
$74$	−5.98862	−	5.67393i	−0.696163	−	0.659581i
$75$		0			0
$76$	−0.880744	+	3.73386i	−0.101028	+	0.428303i
$77$	7.22356	+	2.12103i	0.823201	+	0.241714i
$78$		0			0
$79$	−1.28775	+	8.95651i	−0.144883	+	1.00769i	0.779549	+	0.626341i	$0.215448\pi$
$79$	−1.28775	+	8.95651i	−0.144883	+	1.00769i	−0.924433	+	0.381345i	$0.875461\pi$
$80$	2.27534	+	5.48065i	0.254391	+	0.612756i
$81$		0			0
$82$	−10.4984	−	3.59622i	−1.15935	−	0.397136i
$83$	−8.10326	+	5.20765i	−0.889448	+	0.571614i	−0.903643	−	0.428286i	$-0.859118\pi$
$83$	−8.10326	+	5.20765i	−0.889448	+	0.571614i	0.0141952	+	0.999899i	$0.495481\pi$
$84$		0			0
$85$	0.896727	+	6.23688i	0.0972638	+	0.676484i
$86$	−7.53722	+	4.38360i	−0.812760	+	0.472696i
$87$		0			0
$88$	2.64417	+	8.69772i	0.281870	+	0.927180i
$89$	3.71385	+	12.6482i	0.393667	+	1.34071i	0.883312	+	0.468786i	$0.155308\pi$
$89$	3.71385	+	12.6482i	0.393667	+	1.34071i	−0.489644	+	0.871922i	$0.662873\pi$
$90$		0			0
$91$	15.4808			1.62282
$92$	9.49464	+	1.36081i	0.989885	+	0.141875i
$93$		0			0
$94$	1.67278	+	6.80091i	0.172534	+	0.701460i
$95$	−0.801724	−	2.73042i	−0.0822552	−	0.280135i
$96$		0			0
$97$	1.20320	−	1.87221i	0.122166	−	0.190094i	−0.774784	−	0.632226i	$-0.782141\pi$
$97$	1.20320	−	1.87221i	0.122166	−	0.190094i	0.896950	+	0.442132i	$0.145778\pi$
$98$	−1.85005	+	1.07598i	−0.186883	+	0.108690i
$99$		0			0
$100$	4.42235	+	3.43252i	0.442235	+	0.343252i
$101$	−4.81693	+	3.09565i	−0.479302	+	0.308029i	−0.757891	−	0.652382i	$-0.773770\pi$
$101$	−4.81693	+	3.09565i	−0.479302	+	0.308029i	0.278588	+	0.960411i	$0.410134\pi$
$102$		0			0
$103$	7.88059	−	17.2561i	0.776498	−	1.70029i	0.0647037	−	0.997905i	$-0.479390\pi$
$103$	7.88059	−	17.2561i	0.776498	−	1.70029i	0.711794	−	0.702388i	$-0.247883\pi$
$104$	10.2557	+	15.6287i	1.00565	+	1.53252i
$105$		0			0
$106$	−11.4911	+	4.64274i	−1.11611	+	0.450943i
$107$	3.86248	+	1.13413i	0.373400	+	0.109640i	0.463048	−	0.886333i	$-0.346756\pi$
$107$	3.86248	+	1.13413i	0.373400	+	0.109640i	−0.0896474	+	0.995974i	$0.528574\pi$
$108$		0			0
$109$	3.66872	−	3.17897i	0.351400	−	0.304490i	−0.461218	−	0.887287i	$-0.652587\pi$
$109$	3.66872	−	3.17897i	0.351400	−	0.304490i	0.812618	+	0.582797i	$0.198042\pi$
$110$	−4.89511	−	4.63788i	−0.466731	−	0.442205i
$111$		0			0
$112$	8.38178	+	4.18716i	0.792004	+	0.395650i
$113$	13.1111	−	5.98765i	1.23339	−	0.563271i	0.311326	−	0.950303i	$-0.399227\pi$
$113$	13.1111	−	5.98765i	1.23339	−	0.563271i	0.922066	+	0.387032i	$0.126500\pi$
$114$		0			0
$115$	−6.62071	+	2.60525i	−0.617385	+	0.242941i
$116$	−13.9796	−	5.49378i	−1.29797	−	0.510085i
$117$		0			0
$118$	−11.7127	+	1.15599i	−1.07824	+	0.106417i
$119$	7.51865	+	6.51495i	0.689234	+	0.597224i
$120$		0			0
$121$	0.438599	+	0.506170i	0.0398726	+	0.0460155i
$122$	0.260595	−	5.86235i	0.0235932	−	0.530752i
$123$		0			0
$124$	1.95243	+	9.79488i	0.175334	+	0.879606i
$125$	−11.4526	−	1.64663i	−1.02435	−	0.147279i
$126$		0			0
$127$	−14.6002	−	6.66769i	−1.29556	−	0.591662i	−0.356140	−	0.934433i	$-0.615907\pi$
$127$	−14.6002	−	6.66769i	−1.29556	−	0.591662i	−0.939419	+	0.342771i	$0.888635\pi$
$128$	1.32560	+	11.2358i	0.117167	+	0.993112i
$129$		0			0
$130$	−12.3448	−	6.31465i	−1.08271	−	0.553831i
$131$	9.70906	−	1.39595i	0.848285	−	0.121965i	0.295555	−	0.955326i	$-0.404495\pi$
$131$	9.70906	−	1.39595i	0.848285	−	0.121965i	0.552730	+	0.833361i	$0.313586\pi$
$132$		0			0
$133$	−3.77978	−	2.42912i	−0.327749	−	0.210631i
$134$	7.50669	+	9.48338i	0.648479	+	0.819239i
$135$		0			0
$136$	−1.59624	+	11.9065i	−0.136876	+	1.02098i
$137$		−	8.56001i		−	0.731331i	−0.930746	−	0.365666i	$-0.880841\pi$
$137$		−	8.56001i		−	0.731331i	0.930746	−	0.365666i	$-0.119159\pi$
$138$		0			0
$139$		−	16.2957i		−	1.38219i	−0.722766	−	0.691093i	$-0.757130\pi$
$139$		−	16.2957i		−	1.38219i	0.722766	−	0.691093i	$-0.242870\pi$
$140$	−6.93991	+	0.374795i	−0.586530	+	0.0316760i
$141$		0			0
$142$	3.95982	−	3.13445i	0.332301	−	0.263037i
$143$	−17.8698	−	11.4842i	−1.49435	−	0.960360i
$144$		0			0
$145$	11.0283	−	1.58563i	0.915850	−	0.131679i
$146$	−1.57252	+	3.07421i	−0.130143	+	0.254423i
$147$		0			0
$148$	10.1406	+	5.76909i	0.833553	+	0.474216i
$149$	0.444193	+	0.202856i	0.0363897	+	0.0166186i	0.433527	−	0.901141i	$-0.357269\pi$
$149$	0.444193	+	0.202856i	0.0363897	+	0.0166186i	−0.397137	+	0.917759i	$0.629996\pi$
$150$		0			0
$151$	−2.22176	−	0.319441i	−0.180805	−	0.0259958i	0.0513177	−	0.998682i	$-0.483658\pi$
$151$	−2.22176	−	0.319441i	−0.180805	−	0.0259958i	−0.232122	+	0.972687i	$0.574567\pi$
$152$	−0.0517044	−	5.42514i	−0.00419378	−	0.440037i
$153$		0			0
$154$	−10.6364	−	0.472814i	−0.857107	−	0.0381005i
$155$	−4.85156	−	5.59900i	−0.389687	−	0.449722i
$156$		0			0
$157$	16.9652	+	14.7004i	1.35397	+	1.17322i	0.968069	+	0.250683i	$0.0806553\pi$
$157$	16.9652	+	14.7004i	1.35397	+	1.17322i	0.385902	+	0.922540i	$0.373890\pi$
$158$	−1.25686	−	12.7348i	−0.0999906	−	1.01313i
$159$		0			0
$160$	−4.97593	−	6.75793i	−0.393382	−	0.534261i
$161$	−5.20643	+	9.95421i	−0.410324	+	0.784502i
$162$		0			0
$163$	−4.19833	+	1.91731i	−0.328839	+	0.150176i	−0.572992	−	0.819561i	$-0.694217\pi$
$163$	−4.19833	+	1.91731i	−0.328839	+	0.150176i	0.244153	+	0.969737i	$0.421490\pi$
$164$	15.6320	+	1.39251i	1.22065	+	0.108737i
$165$		0			0
$166$	9.36904	−	9.88868i	0.727179	−	0.767510i
$167$	−11.8188	+	10.2410i	−0.914565	+	0.792475i	−0.978664	−	0.205468i	$-0.934128\pi$
$167$	−11.8188	+	10.2410i	−0.914565	+	0.792475i	0.0640985	+	0.997944i	$0.479583\pi$
$168$		0			0
$169$	−29.4366	−	8.64338i	−2.26436	−	0.664875i
$170$	−3.33814	−	8.26210i	−0.256024	−	0.633674i
$171$		0			0
$172$	8.87006	−	8.56583i	0.676335	−	0.653138i
$173$	−0.948594	+	2.07713i	−0.0721203	+	0.157921i	−0.942259	−	0.334886i	$-0.891302\pi$
$173$	−0.948594	+	2.07713i	−0.0721203	+	0.157921i	0.870138	+	0.492808i	$0.164029\pi$
$174$		0			0
$175$	−5.51564	+	3.54469i	−0.416943	+	0.267953i
$176$	−6.56909	−	11.0513i	−0.495164	−	0.833022i
$177$		0			0
$178$	−9.37246	−	16.1151i	−0.702495	−	1.20788i
$179$	−3.22329	+	5.01554i	−0.240920	+	0.374879i	−0.940566	−	0.339610i	$-0.889705\pi$
$179$	−3.22329	+	5.01554i	−0.240920	+	0.374879i	0.699646	+	0.714490i	$0.253341\pi$
$180$		0			0
$181$	−3.80130	−	12.9460i	−0.282548	−	0.962271i	−0.971416	−	0.237384i	$-0.923710\pi$
$181$	−3.80130	−	12.9460i	−0.282548	−	0.962271i	0.688868	−	0.724887i	$-0.258108\pi$
$182$	−21.2595	+	5.22906i	−1.57586	+	0.387603i
$183$		0			0
$184$	−13.4985	+	1.33830i	−0.995121	+	0.0986605i
$185$	−8.65414			−0.636265
$186$		0			0
$187$	−3.84592	−	13.0980i	−0.281242	−	0.957821i
$188$	−4.59439	−	8.77455i	−0.335080	−	0.639949i
$189$		0			0
$190$	2.02327	+	3.47884i	0.146783	+	0.252381i
$191$	2.09139	+	14.5459i	0.151328	+	1.05251i	0.913997	+	0.405720i	$0.132979\pi$
$191$	2.09139	+	14.5459i	0.151328	+	1.05251i	−0.762670	+	0.646788i	$0.776112\pi$
$192$		0			0
$193$	11.4643	−	7.36767i	0.825220	−	0.530337i	−0.0585355	−	0.998285i	$-0.518643\pi$
$193$	11.4643	−	7.36767i	0.825220	−	0.530337i	0.883756	+	0.467949i	$0.155007\pi$
$194$	−1.01994	+	2.97749i	−0.0732274	+	0.213771i
$195$		0			0
$196$	2.17720	−	2.10252i	0.155514	−	0.150180i
$197$	0.930114	−	6.46908i	0.0662679	−	0.460903i	−0.929487	−	0.368855i	$-0.879750\pi$
$197$	0.930114	−	6.46908i	0.0662679	−	0.460903i	0.995755	−	0.0920476i	$-0.0293412\pi$
$198$		0			0
$199$	−15.6363	−	4.59125i	−1.10843	−	0.325465i	−0.324234	−	0.945977i	$-0.605107\pi$
$199$	−15.6363	−	4.59125i	−1.10843	−	0.325465i	−0.784197	+	0.620512i	$0.786925\pi$
$200$	−7.23256	−	3.22006i	−0.511419	−	0.227692i
$201$		0			0
$202$	5.56936	−	5.87826i	0.391859	−	0.413593i
$203$	11.5200	−	13.2948i	0.808545	−	0.933111i
$204$		0			0
$205$	−10.5893	+	4.83598i	−0.739590	+	0.337760i
$206$	−4.99356	+	26.3594i	−0.347918	+	1.83655i
$207$		0			0
$208$	−19.3630	−	17.9984i	−1.34258	−	1.24797i
$209$	2.56108	+	5.60798i	0.177154	+	0.387912i
$210$		0			0
$211$	14.7755	+	12.8031i	1.01719	+	0.881400i	0.992977	−	0.118307i	$-0.0377466\pi$
$211$	14.7755	+	12.8031i	1.01719	+	0.881400i	0.0242129	+	0.999707i	$0.492292\pi$
$212$	14.2123	−	10.2572i	0.976103	−	0.704469i
$213$		0			0
$214$	−5.68737	−	0.252817i	−0.388780	−	0.0172822i
$215$	−2.57694	+	8.77625i	−0.175746	+	0.598536i
$216$		0			0
$217$	−11.5782	−	1.66469i	−0.785979	−	0.113007i
$218$	−3.96441	+	5.60483i	−0.268504	+	0.379607i
$219$		0			0
$220$	8.28895	+	4.71566i	0.558841	+	0.317930i
$221$	−15.1759	−	23.6142i	−1.02084	−	1.58846i
$222$		0			0
$223$	0.775713	−	0.111531i	0.0519456	−	0.00746864i	−0.116293	−	0.993215i	$-0.537101\pi$
$223$	0.775713	−	0.111531i	0.0519456	−	0.00746864i	0.168239	+	0.985746i	$0.446192\pi$
$224$	−12.9249	−	2.91898i	−0.863580	−	0.195033i
$225$		0			0
$226$	−15.9828	+	12.6514i	−1.06316	+	0.841558i
$227$	−11.5255	+	3.38418i	−0.764971	+	0.224616i	−0.640865	−	0.767653i	$-0.721424\pi$
$227$	−11.5255	+	3.38418i	−0.764971	+	0.224616i	−0.124106	+	0.992269i	$0.539606\pi$
$228$		0			0
$229$			20.6268i			1.36306i	0.731790	+	0.681530i	$0.238685\pi$
$229$			20.6268i			1.36306i	−0.731790	+	0.681530i	$0.761315\pi$
$230$	8.21212	−	5.81408i	0.541491	−	0.383369i
$231$		0			0
$232$	21.0536	+	2.82253i	1.38224	+	0.185308i
$233$	−0.806856	+	0.236914i	−0.0528589	+	0.0155208i	−0.308055	−	0.951369i	$-0.599678\pi$
$233$	−0.806856	+	0.236914i	−0.0528589	+	0.0155208i	0.255196	+	0.966889i	$0.417860\pi$
$234$		0			0
$235$	6.18068	+	3.97208i	0.403183	+	0.259110i
$236$	15.6944	−	5.54380i	1.02162	−	0.360871i
$237$		0			0
$238$	−12.5258	−	6.40724i	−0.811930	−	0.415319i
$239$	−3.82127	−	5.94601i	−0.247177	−	0.384616i	0.695389	−	0.718633i	$-0.255232\pi$
$239$	−3.82127	−	5.94601i	−0.247177	−	0.384616i	−0.942567	+	0.334018i	$0.891596\pi$
$240$		0			0
$241$	−12.6028	−	5.75550i	−0.811817	−	0.370744i	−0.0341466	−	0.999417i	$-0.510871\pi$
$241$	−12.6028	−	5.75550i	−0.811817	−	0.370744i	−0.777670	+	0.628673i	$0.783599\pi$
$242$	−0.773294	−	0.546966i	−0.0497092	−	0.0351603i
$243$		0			0
$244$	1.62230	+	8.13869i	0.103857	+	0.521026i
$245$	−0.632522	+	2.15417i	−0.0404103	+	0.137625i
$246$		0			0
$247$	8.30181	+	9.58080i	0.528232	+	0.609612i
$248$	−5.98973	−	12.7917i	−0.380349	−	0.812271i
$249$		0			0
$250$	16.2838	−	1.60713i	1.02988	−	0.101644i
$251$	−5.17112	−	11.3232i	−0.326398	−	0.714712i	0.673298	−	0.739371i	$-0.264877\pi$
$251$	−5.17112	−	11.3232i	−0.326398	−	0.714712i	−0.999696	+	0.0246591i	$0.992150\pi$
$252$		0			0
$253$	13.3943	−	7.62806i	0.842095	−	0.479572i
$254$	22.3024	+	4.22500i	1.39938	+	0.265100i
$255$		0			0
$256$	−5.61562	−	14.9822i	−0.350976	−	0.936384i
$257$	−13.1329	+	15.1561i	−0.819205	+	0.945413i	−0.999268	−	0.0382422i	$-0.987824\pi$
$257$	−13.1329	+	15.1561i	−0.819205	+	0.945413i	0.180064	+	0.983655i	$0.442370\pi$
$258$		0			0
$259$	−10.3265	+	8.94798i	−0.641658	+	0.556000i
$260$	19.0859	+	4.50199i	1.18366	+	0.279201i
$261$		0			0
$262$	−12.8618	+	5.19654i	−0.794603	+	0.321044i
$263$	3.67852	−	25.5847i	0.226827	−	1.57762i	−0.484521	−	0.874780i	$-0.661006\pi$
$263$	3.67852	−	25.5847i	0.226827	−	1.57762i	0.711348	−	0.702840i	$-0.248085\pi$
$264$		0			0
$265$	−5.40088	+	11.8263i	−0.331774	+	0.726483i
$266$	6.01121	+	2.05914i	0.368571	+	0.126254i
$267$		0			0
$268$	−13.5121	−	10.4878i	−0.825382	−	0.640643i
$269$	−2.09888	−	14.5980i	−0.127971	−	0.890057i	−0.948121	−	0.317909i	$-0.897019\pi$
$269$	−2.09888	−	14.5980i	−0.127971	−	0.890057i	0.820150	−	0.572148i	$-0.193890\pi$
$270$		0			0
$271$	−13.8554	+	21.5595i	−0.841658	+	1.30965i	0.107295	+	0.994227i	$0.465781\pi$
$271$	−13.8554	+	21.5595i	−0.841658	+	1.30965i	−0.948953	+	0.315418i	$0.897855\pi$
$272$	−1.82967	−	16.8902i	−0.110940	−	1.02412i
$273$		0			0
$274$	2.89138	+	11.7553i	0.174675	+	0.710165i
$275$	8.99643			0.542505
$276$		0			0
$277$	−23.1742			−1.39240			−0.696202	−	0.717846i	$-0.745128\pi$
$277$	−23.1742			−1.39240			−0.696202	+	0.717846i	$0.745128\pi$
$278$	5.50433	+	22.3786i	0.330128	+	1.34218i
$279$		0			0
$280$	9.40386	−	2.85885i	0.561988	−	0.170849i
$281$	6.64531	−	10.3403i	0.396426	−	0.616851i	−0.584463	−	0.811421i	$-0.698695\pi$
$281$	6.64531	−	10.3403i	0.396426	−	0.616851i	0.980889	+	0.194570i	$0.0623311\pi$
$282$		0			0
$283$	0.148711	+	1.03431i	0.00883995	+	0.0614832i	0.993764	−	0.111505i	$-0.0355670\pi$
$283$	0.148711	+	1.03431i	0.00883995	+	0.0614832i	−0.984924	+	0.172988i	$0.944658\pi$
$284$	−4.37921	+	5.64203i	−0.259858	+	0.334793i
$285$		0			0
$286$	28.4194	+	9.73508i	1.68048	+	0.575647i
$287$	−7.63548	+	16.7194i	−0.450708	+	0.986913i
$288$		0			0
$289$	0.147886	−	1.02857i	0.00869920	−	0.0605043i
$290$	−14.6094	+	5.90263i	−0.857892	+	0.346614i
$291$		0			0
$292$	1.12112	−	4.75292i	0.0656085	−	0.278143i
$293$	6.31293	−	5.47019i	0.368805	−	0.319572i	−0.450665	−	0.892693i	$-0.648813\pi$
$293$	6.31293	−	5.47019i	0.368805	−	0.319572i	0.819470	+	0.573121i	$0.194268\pi$
$294$		0			0
$295$	−8.08536	+	9.33100i	−0.470748	+	0.543272i
$296$	−15.8746	−	4.49732i	−0.922692	−	0.261402i
$297$		0			0
$298$	−0.678522	−	0.128540i	−0.0393058	−	0.00744614i
$299$	22.0078	−	22.8097i	1.27274	−	1.31912i
$300$		0			0
$301$	5.99931	+	13.1367i	0.345795	+	0.757184i
$302$	3.15901	−	0.311779i	0.181781	−	0.0179409i
$303$		0			0
$304$	1.90350	+	7.43279i	0.109173	+	0.426300i
$305$	−4.03122	−	4.65228i	−0.230827	−	0.266389i
$306$		0			0
$307$	4.82371	−	16.4280i	0.275304	−	0.937598i	−0.699519	−	0.714614i	$-0.746602\pi$
$307$	4.82371	−	16.4280i	0.275304	−	0.937598i	0.974822	−	0.222984i	$-0.0715796\pi$
$308$	14.7665	−	2.94344i	0.841401	−	0.167718i
$309$		0			0
$310$	8.55378	+	6.05026i	0.485822	+	0.343632i
$311$	−0.540564	−	0.246867i	−0.0306526	−	0.0139986i	0.400030	−	0.916502i	$-0.369000\pi$
$311$	−0.540564	−	0.246867i	−0.0306526	−	0.0139986i	−0.430682	+	0.902504i	$0.641727\pi$
$312$		0			0
$313$	−0.703275	−	1.09432i	−0.0397515	−	0.0618545i	0.820809	−	0.571203i	$-0.193523\pi$
$313$	−0.703275	−	1.09432i	−0.0397515	−	0.0618545i	−0.860561	+	0.509348i	$0.829887\pi$
$314$	−28.2635	−	14.4574i	−1.59500	−	0.815878i
$315$		0			0
$316$	6.02756	+	17.0639i	0.339077	+	0.959922i
$317$	−7.32365	−	4.70662i	−0.411337	−	0.264350i	0.318566	−	0.947901i	$-0.396799\pi$
$317$	−7.32365	−	4.70662i	−0.411337	−	0.264350i	−0.729903	+	0.683550i	$0.760435\pi$
$318$		0			0
$319$	−23.1604	+	6.80051i	−1.29673	+	0.380756i
$320$	9.11604	+	7.59979i	0.509602	+	0.424841i
$321$		0			0
$322$	3.78759	−	15.4286i	0.211074	−	0.859800i
$323$			8.14693i			0.453307i
$324$		0			0
$325$	17.7499	−	5.21183i	0.984585	−	0.289100i
$326$	5.11787	−	4.05112i	0.283453	−	0.224371i
$327$		0			0
$328$	−21.9375	+	3.36782i	−1.21130	+	0.185957i
$329$	11.4820	−	1.65086i	0.633024	−	0.0910150i
$330$		0			0
$331$	−1.67581	−	2.60760i	−0.0921106	−	0.143327i	0.792140	−	0.610339i	$-0.208967\pi$
$331$	−1.67581	−	2.60760i	−0.0921106	−	0.143327i	−0.884251	+	0.467012i	$0.845330\pi$
$332$	−9.52617	+	16.7446i	−0.522816	+	0.918980i
$333$		0			0
$334$	12.7713	−	18.0560i	0.698817	−	0.987979i
$335$	12.5587	+	1.80567i	0.686154	+	0.0986540i
$336$		0			0
$337$	5.57815	−	18.9974i	0.303861	−	1.03486i	−0.656088	−	0.754684i	$-0.727790\pi$
$337$	5.57815	−	18.9974i	0.303861	−	1.03486i	0.959950	−	0.280172i	$-0.0903916\pi$
$338$	43.3444	+	1.92676i	2.35762	+	0.104802i
$339$		0			0
$340$	7.37496	+	10.2187i	0.399964	+	0.554184i
$341$	12.1301	+	10.5108i	0.656880	+	0.569190i
$342$		0			0
$343$	8.28393	+	18.1393i	0.447290	+	0.979428i
$344$	−9.28775	+	14.7594i	−0.500762	+	0.795774i
$345$		0			0
$346$	0.601080	−	3.17290i	0.0323142	−	0.170576i
$347$	8.63193	−	3.94207i	0.463386	−	0.211621i	−0.170020	−	0.985441i	$-0.554383\pi$
$347$	8.63193	−	3.94207i	0.463386	−	0.211621i	0.633407	+	0.773819i	$0.281656\pi$
$348$		0			0
$349$	−2.67061	+	3.08204i	−0.142954	+	0.164978i	−0.822711	−	0.568459i	$-0.807540\pi$
$349$	−2.67061	+	3.08204i	−0.142954	+	0.164978i	0.679757	+	0.733437i	$0.262085\pi$
$350$	6.37722	−	6.73092i	0.340877	−	0.359783i
$351$		0			0
$352$	12.7541	+	12.9576i	0.679796	+	0.690645i
$353$	−19.1996	−	5.63752i	−1.02189	−	0.300055i	−0.272483	−	0.962161i	$-0.587845\pi$
$353$	−19.1996	−	5.63752i	−1.02189	−	0.300055i	−0.749411	+	0.662106i	$0.769663\pi$
$354$		0			0
$355$	0.753963	−	5.24393i	0.0400162	−	0.278319i
$356$	18.3144	+	18.9648i	0.970659	+	1.00513i
$357$		0			0
$358$	2.73236	−	7.97652i	0.144409	−	0.421572i
$359$	−0.418363	+	0.268865i	−0.0220803	+	0.0141902i	−0.551634	−	0.834086i	$-0.685996\pi$
$359$	−0.418363	+	0.268865i	−0.0220803	+	0.0141902i	0.529554	+	0.848276i	$0.322359\pi$
$360$		0			0
$361$	2.18036	+	15.1647i	0.114756	+	0.798142i
$362$	9.59314	+	16.4946i	0.504204	+	0.866936i
$363$		0			0
$364$	27.4290	−	14.3619i	1.43767	−	0.752771i
$365$	1.02053	+	3.47562i	0.0534172	+	0.181922i
$366$		0			0
$367$	25.3143			1.32139			0.660697	−	0.750653i	$-0.270261\pi$
$367$	25.3143			1.32139			0.660697	+	0.750653i	$0.270261\pi$
$368$	18.0852	−	6.39735i	0.942756	−	0.333485i
$369$		0			0
$370$	11.8846	−	2.92318i	0.617850	−	0.151969i
$371$	5.78324	+	19.6959i	0.300251	+	1.02256i
$372$		0			0
$373$	12.2054	−	18.9920i	0.631972	−	0.983368i	−0.366622	−	0.930370i	$-0.619486\pi$
$373$	12.2054	−	18.9920i	0.631972	−	0.983368i	0.998595	−	0.0529982i	$-0.0168778\pi$
$374$	9.70575	+	16.6882i	0.501872	+	0.862926i
$375$		0			0
$376$	9.27325	+	10.4981i	0.478231	+	0.541396i
$377$	−41.7556	+	26.8347i	−2.15052	+	1.38206i
$378$		0			0
$379$	7.99190	−	17.4998i	0.410516	−	0.898905i	−0.585579	−	0.810616i	$-0.699133\pi$
$379$	7.99190	−	17.4998i	0.410516	−	0.898905i	0.996095	−	0.0882894i	$-0.0281400\pi$
$380$	−3.95360	−	4.09401i	−0.202815	−	0.210018i
$381$		0			0
$382$	−7.78537	−	19.2693i	−0.398334	−	0.985902i
$383$	4.14308	+	1.21652i	0.211701	+	0.0621611i	0.385864	−	0.922556i	$-0.373904\pi$
$383$	4.14308	+	1.21652i	0.211701	+	0.0621611i	−0.174162	+	0.984717i	$0.555722\pi$
$384$		0			0
$385$	−8.44091	+	7.31409i	−0.430189	+	0.372761i
$386$	−13.2551	+	13.9903i	−0.674668	+	0.712087i
$387$		0			0
$388$	0.394935	−	4.43345i	0.0200498	−	0.225074i
$389$	−26.0578	+	11.9002i	−1.32118	+	0.603364i	−0.946174	−	0.323657i	$-0.895088\pi$
$389$	−26.0578	+	11.9002i	−1.32118	+	0.603364i	−0.375009	+	0.927021i	$0.622360\pi$
$390$		0			0
$391$	20.2880	−	1.81636i	1.02601	−	0.0918574i
$392$	−2.27972	+	3.62277i	−0.115143	+	0.182977i
$393$		0			0
$394$	0.907803	+	9.19805i	0.0457345	+	0.463391i
$395$	−10.1452	−	8.79090i	−0.510462	−	0.442318i
$396$		0			0
$397$	24.9065	+	28.7436i	1.25002	+	1.44260i	0.850582	+	0.525842i	$0.176250\pi$
$397$	24.9065	+	28.7436i	1.25002	+	1.44260i	0.399440	+	0.916760i	$0.369205\pi$
$398$	23.0239	+	1.02347i	1.15409	+	0.0513019i
$399$		0			0
$400$	11.0200	+	1.97905i	0.551001	+	0.0989524i
$401$	−8.14559	−	1.17116i	−0.406772	−	0.0584849i	−0.0641077	−	0.997943i	$-0.520420\pi$
$401$	−8.14559	−	1.17116i	−0.406772	−	0.0584849i	−0.342664	+	0.939458i	$0.611329\pi$
$402$		0			0
$403$	30.0216	+	13.7104i	1.49548	+	0.682964i
$404$	−5.66277	+	9.95372i	−0.281733	+	0.495216i
$405$		0			0
$406$	−11.3295	+	22.1487i	−0.562275	+	1.09922i
$407$	18.5581	−	2.66825i	0.919892	−	0.132260i
$408$		0			0
$409$	−23.9160	−	15.3699i	−1.18257	−	0.759993i	−0.206715	−	0.978401i	$-0.566277\pi$
$409$	−23.9160	−	15.3699i	−1.18257	−	0.759993i	−0.975858	+	0.218408i	$0.929914\pi$
$410$	12.9087	−	10.2180i	0.637513	−	0.504632i
$411$		0			0
$412$	−2.04604	−	37.8856i	−0.100801	−	1.86649i
$413$			19.4940i			0.959239i
$414$		0			0
$415$		−	14.2901i		−	0.701473i
$416$	32.6704	+	18.1766i	1.60180	+	0.891180i
$417$		0			0
$418$	−5.41134	−	6.83627i	−0.264677	−	0.334373i
$419$	16.6999	+	10.7324i	0.815843	+	0.524311i	0.880750	−	0.473581i	$-0.157039\pi$
$419$	16.6999	+	10.7324i	0.815843	+	0.524311i	−0.0649072	+	0.997891i	$0.520675\pi$
$420$		0			0
$421$	3.20665	−	0.461046i	0.156282	−	0.0224700i	−0.0637295	−	0.997967i	$-0.520299\pi$
$421$	3.20665	−	0.461046i	0.156282	−	0.0224700i	0.220012	+	0.975497i	$0.429390\pi$
$422$	−24.6156	−	12.5914i	−1.19827	−	0.612940i
$423$		0			0
$424$	−16.0528	+	18.8867i	−0.779594	+	0.917217i
$425$	10.8141	+	4.93862i	0.524559	+	0.239558i
$426$		0			0
$427$	−9.62047	−	1.38321i	−0.465567	−	0.0669384i
$428$	7.89576	−	1.57388i	0.381656	−	0.0760762i
$429$		0			0
$430$	0.574446	−	12.9227i	0.0277022	−	0.623189i
$431$	−2.18370	−	2.52012i	−0.105185	−	0.121390i	0.700716	−	0.713440i	$-0.252864\pi$
$431$	−2.18370	−	2.52012i	−0.105185	−	0.121390i	−0.805901	+	0.592050i	$0.798319\pi$
$432$		0			0
$433$	−24.8040	−	21.4928i	−1.19200	−	1.03288i	−0.998660	−	0.0517449i	$-0.983522\pi$
$433$	−24.8040	−	21.4928i	−1.19200	−	1.03288i	−0.193342	−	0.981131i	$-0.561933\pi$
$434$	16.4624	−	1.62476i	0.790222	−	0.0779911i
$435$		0			0
$436$	3.55107	−	9.03611i	0.170065	−	0.432751i
$437$	−8.95254	+	2.11593i	−0.428258	+	0.101219i
$438$		0			0
$439$	−27.0531	+	12.3548i	−1.29118	+	0.589660i	−0.938239	−	0.345987i	$-0.887544\pi$
$439$	−27.0531	+	12.3548i	−1.29118	+	0.589660i	−0.352937	+	0.935647i	$0.614817\pi$
$440$	−12.9759	−	3.67612i	−0.618603	−	0.175252i
$441$		0			0
$442$	28.8172	+	27.3029i	1.37069	+	1.29867i
$443$	−30.7999	+	26.6882i	−1.46335	+	1.26800i	−0.567695	+	0.823239i	$0.692165\pi$
$443$	−30.7999	+	26.6882i	−1.46335	+	1.26800i	−0.895651	+	0.444757i	$0.853290\pi$
$444$		0			0
$445$	−18.7643	−	5.50969i	−0.889512	−	0.261184i
$446$	−1.02760	+	0.415182i	−0.0486583	+	0.0196594i
$447$		0			0
$448$	18.7355	−	0.357150i	0.885169	−	0.0168738i
$449$	13.2847	−	29.0894i	0.626943	−	1.37281i	−0.283416	−	0.958997i	$-0.591468\pi$
$449$	13.2847	−	29.0894i	0.626943	−	1.37281i	0.910360	−	0.413818i	$-0.135805\pi$
$450$		0			0
$451$	21.2169	−	13.6353i	0.999066	−	0.642061i
$452$	17.6756	−	22.7726i	0.831388	−	1.07113i
$453$		0			0
$454$	14.6846	−	8.54048i	0.689183	−	0.400824i
$455$	−12.4166	+	19.3206i	−0.582100	+	0.905765i
$456$		0			0
$457$	2.38748	+	8.13101i	0.111682	+	0.380353i	0.996298	−	0.0859668i	$-0.0273979\pi$
$457$	2.38748	+	8.13101i	0.111682	+	0.380353i	−0.884616	+	0.466319i	$0.845580\pi$
$458$	−6.96729	−	28.3265i	−0.325560	−	1.32361i
$459$		0			0
$460$	−9.31370	+	10.7582i	−0.434253	+	0.501606i
$461$	2.08733			0.0972167			0.0486084	−	0.998818i	$-0.484521\pi$
$461$	2.08733			0.0972167			0.0486084	+	0.998818i	$0.484521\pi$
$462$		0			0
$463$	2.50950	+	8.54657i	0.116626	+	0.397193i	0.997028	−	0.0770352i	$-0.0245454\pi$
$463$	2.50950	+	8.54657i	0.116626	+	0.397193i	−0.880402	+	0.474228i	$0.842727\pi$
$464$	−29.8659	+	3.23530i	−1.38649	+	0.150195i
$465$		0			0
$466$	1.02802	−	0.597888i	0.0476220	−	0.0276966i
$467$	−4.28273	−	29.7871i	−0.198181	−	1.37838i	−0.809558	−	0.587040i	$-0.800293\pi$
$467$	−4.28273	−	29.7871i	−0.198181	−	1.37838i	0.611376	−	0.791340i	$-0.290616\pi$
$468$		0			0
$469$	16.8526	−	10.8305i	0.778179	−	0.500105i
$470$	−9.82950	−	3.36709i	−0.453401	−	0.155312i
$471$		0			0
$472$	−19.6803	+	12.9144i	−0.905860	+	0.594435i
$473$	2.82014	−	19.6145i	0.129670	−	0.901876i
$474$		0			0
$475$	−5.15161	−	1.51265i	−0.236372	−	0.0694051i
$476$	19.3657	+	4.56800i	0.887628	+	0.209374i
$477$		0			0
$478$	7.25612	+	6.87482i	0.331887	+	0.314447i
$479$	−12.1092	+	13.9748i	−0.553283	+	0.638523i	−0.961645	−	0.274297i	$-0.911555\pi$
$479$	−12.1092	+	13.9748i	−0.553283	+	0.638523i	0.408362	+	0.912820i	$0.366100\pi$
$480$		0			0
$481$	35.0692	−	16.0156i	1.59902	−	0.730247i
$482$	19.2513	+	3.64699i	0.876871	+	0.166116i
$483$		0			0
$484$	1.24670	+	0.489938i	0.0566684	+	0.0222699i
$485$	1.37155	+	3.00328i	0.0622790	+	0.136372i
$486$		0			0
$487$	32.0873	+	27.8038i	1.45401	+	1.25991i	0.905891	+	0.423511i	$0.139203\pi$
$487$	32.0873	+	27.8038i	1.45401	+	1.25991i	0.548122	+	0.836398i	$0.315343\pi$
$488$	−4.97694	−	10.6287i	−0.225296	−	0.481141i
$489$		0			0
$490$	0.141000	−	3.17194i	0.00636974	−	0.143294i
$491$	−0.265637	+	0.904677i	−0.0119880	+	0.0408275i	−0.965270	−	0.261255i	$-0.915864\pi$
$491$	−0.265637	+	0.904677i	−0.0119880	+	0.0408275i	0.953282	+	0.302083i	$0.0976818\pi$
$492$		0			0
$493$	−31.5729	−	4.53950i	−1.42197	−	0.204449i
$494$	−14.6369	−	10.3530i	−0.658546	−	0.465803i
$495$		0			0
$496$	12.5463	+	15.5434i	0.563347	+	0.697918i
$497$	−4.52231	−	7.03685i	−0.202853	−	0.315646i
$498$		0			0
$499$	−7.31712	+	1.05204i	−0.327559	+	0.0470959i	−0.304133	−	0.952630i	$-0.598367\pi$
$499$	−7.31712	+	1.05204i	−0.327559	+	0.0470959i	−0.0234265	+	0.999726i	$0.507458\pi$
$500$	−21.8194	+	7.70735i	−0.975793	+	0.344683i
$501$		0			0
$502$	10.9261	+	13.8032i	0.487657	+	0.616068i
$503$	−15.5934	+	4.57863i	−0.695274	+	0.204151i	−0.610228	−	0.792226i	$-0.708922\pi$
$503$	−15.5934	+	4.57863i	−0.695274	+	0.204151i	−0.0850466	+	0.996377i	$0.527104\pi$
$504$		0			0
$505$		−	8.49465i		−	0.378007i
$506$	−15.8176	+	14.9998i	−0.703179	+	0.666822i
$507$		0			0
$508$	−32.0546	+	1.73114i	−1.42219	+	0.0768068i
$509$	−14.8241	+	4.35275i	−0.657067	+	0.192932i	−0.593236	−	0.805029i	$-0.702150\pi$
$509$	−14.8241	+	4.35275i	−0.657067	+	0.192932i	−0.0638305	+	0.997961i	$0.520332\pi$
$510$		0			0
$511$	4.81137	+	3.09208i	0.212843	+	0.136786i
$512$	12.7725	+	18.6779i	0.564469	+	0.825455i
$513$		0			0
$514$	12.9157	−	25.2496i	0.569688	−	1.11371i
$515$	15.2156	+	23.6759i	0.670477	+	1.04328i
$516$		0			0
$517$	−14.4786	−	6.61217i	−0.636770	−	0.290803i
$518$	11.1588	−	15.7762i	0.490290	−	0.693165i
$519$		0			0
$520$	−27.7310	+	0.264291i	−1.21609	+	0.0115899i
$521$	1.35323	−	4.60869i	0.0592862	−	0.201910i	−0.924524	−	0.381124i	$-0.875537\pi$
$521$	1.35323	−	4.60869i	0.0592862	−	0.201910i	0.983810	+	0.179214i	$0.0573553\pi$
$522$		0			0
$523$	−25.8296	−	29.8090i	−1.12945	−	1.30346i	−0.947359	−	0.320174i	$-0.896259\pi$
$523$	−25.8296	−	29.8090i	−1.12945	−	1.30346i	−0.182092	−	0.983281i	$-0.558287\pi$
$524$	15.9076	−	11.4807i	0.694926	−	0.501539i
$525$		0			0
$526$	3.59028	+	36.3775i	0.156544	+	1.58614i
$527$	8.81090	+	19.2932i	0.383809	+	0.840424i
$528$		0			0
$529$	7.26519	+	21.8224i	0.315878	+	0.948800i
$530$	3.42228	−	18.0651i	0.148655	−	0.784699i
$531$		0			0
$532$	−8.95063	−	0.797329i	−0.388059	−	0.0345686i
$533$	33.9615	−	39.1937i	1.47104	−	1.69767i
$534$		0			0
$535$	−4.51341	+	3.91089i	−0.195132	+	0.169083i
$536$	22.0985	+	9.83859i	0.954508	+	0.424963i
$537$		0			0
$538$	7.81324	+	19.3383i	0.336853	+	0.833732i
$539$	0.692216	−	4.81447i	0.0298159	−	0.207374i
$540$		0			0
$541$	16.1367	−	35.3345i	0.693773	−	1.51915i	−0.153589	−	0.988135i	$-0.549083\pi$
$541$	16.1367	−	35.3345i	0.693773	−	1.51915i	0.847362	−	0.531016i	$-0.178190\pi$
$542$	11.7451	−	34.2873i	0.504496	−	1.47277i
$543$		0			0
$544$	8.21779	+	22.5770i	0.352335	+	0.967981i
$545$	1.02492	+	7.12847i	0.0439027	+	0.305350i
$546$		0			0
$547$	12.7705	−	19.8712i	0.546025	−	0.849632i	−0.453100	−	0.891460i	$-0.649682\pi$
$547$	12.7705	−	19.8712i	0.546025	−	0.849632i	0.999125	+	0.0418280i	$0.0133182\pi$
$548$	−7.94137	−	15.1667i	−0.339239	−	0.647891i
$549$		0			0
$550$	−12.3546	+	3.03879i	−0.526804	+	0.129575i
$551$	14.4057			0.613705
$552$		0			0
$553$	−21.1951			−0.901309
$554$	31.8248	−	7.82774i	1.35210	−	0.332569i
$555$		0			0
$556$	−15.1180	−	28.8730i	−0.641147	−	1.22449i
$557$	−16.9850	+	26.4291i	−0.719676	+	1.11984i	0.268014	+	0.963415i	$0.413633\pi$
$557$	−16.9850	+	26.4291i	−0.719676	+	1.11984i	−0.987690	+	0.156423i	$0.950004\pi$
$558$		0			0
$559$	−5.79901	−	40.3330i	−0.245272	−	1.70590i
$560$	−11.9485	+	7.10242i	−0.504917	+	0.300132i
$561$		0			0
$562$	−5.63317	+	16.4448i	−0.237621	+	0.693682i
$563$	10.3325	−	22.6250i	0.435462	−	0.953528i	−0.556947	−	0.830548i	$-0.688027\pi$
$563$	10.3325	−	22.6250i	0.435462	−	0.953528i	0.992409	−	0.122980i	$-0.0392452\pi$
$564$		0			0
$565$	−3.04318	+	21.1658i	−0.128027	+	0.890450i
$566$	−0.553588	−	1.37017i	−0.0232690	−	0.0575924i
$567$		0			0
$568$	4.10814	−	9.22730i	0.172374	−	0.387169i
$569$	28.5953	−	24.7779i	1.19878	−	1.03874i	0.200521	−	0.979689i	$-0.435737\pi$
$569$	28.5953	−	24.7779i	1.19878	−	1.03874i	0.998255	−	0.0590552i	$-0.0188088\pi$
$570$		0			0
$571$	−14.7611	+	17.0352i	−0.617731	+	0.712900i	−0.975275	−	0.220997i	$-0.929069\pi$
$571$	−14.7611	+	17.0352i	−0.617731	+	0.712900i	0.357543	+	0.933897i	$0.383614\pi$
$572$	−42.3162	−	3.76956i	−1.76933	−	0.157613i
$573$		0			0
$574$	4.83825	−	25.5395i	0.201944	−	1.06600i
$575$	−2.61833	+	13.1661i	−0.109192	+	0.549064i
$576$		0			0
$577$	9.64730	+	21.1246i	0.401623	+	0.879431i	0.997103	+	0.0760610i	$0.0242344\pi$
$577$	9.64730	+	21.1246i	0.401623	+	0.879431i	−0.595481	+	0.803370i	$0.703038\pi$
$578$	0.144339	+	1.46247i	0.00600371	+	0.0608309i
$579$		0			0
$580$	18.0690	−	13.0407i	0.750276	−	0.541486i
$581$	−14.7753	−	17.0516i	−0.612982	−	0.707419i
$582$		0			0
$583$	7.93547	−	27.0257i	0.328653	−	1.11929i
$584$	0.0658157	+	6.90579i	0.00272347	+	0.285764i
$585$		0			0
$586$	−6.82173	+	9.64448i	−0.281803	+	0.398410i
$587$	−4.58670	−	2.09468i	−0.189314	−	0.0864566i	0.318503	−	0.947922i	$-0.396820\pi$
$587$	−4.58670	−	2.09468i	−0.189314	−	0.0864566i	−0.507816	+	0.861465i	$0.669547\pi$
$588$		0			0
$589$	−5.17875	−	8.05829i	−0.213387	−	0.332036i
$590$	7.95168	−	15.5452i	0.327365	−	0.639984i
$591$		0			0
$592$	23.3194	+	0.814012i	0.958421	+	0.0334557i
$593$	−4.27509	−	2.74744i	−0.175557	−	0.112824i	0.449911	−	0.893073i	$-0.351456\pi$
$593$	−4.27509	−	2.74744i	−0.175557	−	0.112824i	−0.625468	+	0.780250i	$0.715092\pi$
$594$		0			0
$595$	−14.1614	+	4.15816i	−0.580561	+	0.170468i
$596$	0.975221	−	0.0526676i	0.0399466	−	0.00215735i
$597$		0			0
$598$	−22.5183	+	38.7579i	−0.920842	+	1.58493i
$599$			6.47662i			0.264628i	0.991208	+	0.132314i	$0.0422406\pi$
$599$			6.47662i			0.264628i	−0.991208	+	0.132314i	$0.957759\pi$
$600$		0			0
$601$	−32.9152	+	9.66478i	−1.34264	+	0.394235i	−0.872611	−	0.488416i	$-0.837575\pi$
$601$	−32.9152	+	9.66478i	−1.34264	+	0.394235i	−0.470029	+	0.882651i	$0.655757\pi$
$602$	−12.6760	−	16.0139i	−0.516636	−	0.652679i
$603$		0			0
$604$	−4.23290	+	1.49520i	−0.172234	+	0.0608390i
$605$	−0.983508	+	0.141407i	−0.0399853	+	0.00574902i
$606$		0			0
$607$	14.4425	+	22.4729i	0.586201	+	0.912147i	0.999998	+	0.00177799i	$0.000565952\pi$
$607$	14.4425	+	22.4729i	0.586201	+	0.912147i	−0.413797	+	0.910369i	$0.635798\pi$
$608$	−5.12467	−	9.56437i	−0.207833	−	0.387886i
$609$		0			0
$610$	7.10744	+	5.02723i	0.287772	+	0.203547i
$611$	−32.3968	−	4.65795i	−1.31063	−	0.188441i
$612$		0			0
$613$	−2.12363	+	7.23241i	−0.0857725	+	0.292114i	−0.991197	−	0.132392i	$-0.957734\pi$
$613$	−2.12363	+	7.23241i	−0.0857725	+	0.292114i	0.905425	+	0.424506i	$0.139552\pi$
$614$	−1.07529	+	24.1897i	−0.0433952	+	0.976217i
$615$		0			0
$616$	−19.2844	+	9.02998i	−0.776990	+	0.363828i
$617$	18.4862	+	16.0184i	0.744225	+	0.644875i	0.942092	−	0.335354i	$-0.108856\pi$
$617$	18.4862	+	16.0184i	0.744225	+	0.644875i	−0.197867	+	0.980229i	$0.563401\pi$
$618$		0			0
$619$	11.4620	+	25.0982i	0.460696	+	1.00878i	0.987328	+	0.158691i	$0.0507272\pi$
$619$	11.4620	+	25.0982i	0.460696	+	1.00878i	−0.526632	+	0.850093i	$0.676546\pi$
$620$	−13.7904	−	5.41944i	−0.553836	−	0.217650i
$621$		0			0
$622$	0.825734	+	0.156428i	0.0331089	+	0.00627220i
$623$	−28.0871	+	12.8270i	−1.12529	+	0.513901i
$624$		0			0
$625$	2.07576	−	2.39555i	0.0830302	−	0.0958220i
$626$	1.33543	+	1.26526i	0.0533746	+	0.0505699i
$627$		0			0
$628$	43.6972	+	10.3073i	1.74371	+	0.411306i
$629$	23.7723	+	6.98018i	0.947865	+	0.278318i
$630$		0			0
$631$	−4.81613	+	33.4969i	−0.191727	+	1.33349i	0.635708	+	0.771930i	$0.280708\pi$
$631$	−4.81613	+	33.4969i	−0.191727	+	1.33349i	−0.827435	+	0.561562i	$0.810201\pi$
$632$	−14.0414	−	21.3976i	−0.558535	−	0.851153i
$633$		0			0
$634$	11.6472	+	3.98976i	0.462571	+	0.158454i
$635$	20.0319	−	12.8737i	0.794942	−	0.510879i
$636$		0			0
$637$	−1.42339	−	9.89991i	−0.0563969	−	0.392249i
$638$	29.5087	−	17.1621i	1.16826	−	0.679454i
$639$		0			0
$640$	−15.0859	−	7.35746i	−0.596324	−	0.290829i
$641$	10.5557	+	35.9493i	0.416923	+	1.41991i	0.853900	+	0.520438i	$0.174231\pi$
$641$	10.5557	+	35.9493i	0.416923	+	1.41991i	−0.436976	+	0.899473i	$0.643951\pi$
$642$		0			0
$643$	−0.709360			−0.0279744			−0.0139872	−	0.999902i	$-0.504452\pi$
$643$	−0.709360			−0.0279744			−0.0139872	+	0.999902i	$0.504452\pi$
$644$	0.00999282	+	22.4671i	0.000393772	+	0.885330i
$645$		0			0
$646$	−2.75185	−	11.1880i	−0.108270	−	0.440187i
$647$	−2.16146	−	7.36124i	−0.0849756	−	0.289400i	0.906031	−	0.423211i	$-0.139097\pi$
$647$	−2.16146	−	7.36124i	−0.0849756	−	0.289400i	−0.991007	+	0.133810i	$0.957279\pi$
$648$		0			0
$649$	14.4615	−	22.5025i	0.567662	−	0.883299i
$650$	−22.6152	+	13.1528i	−0.887039	+	0.515896i
$651$		0			0
$652$	−5.65991	+	7.29203i	−0.221659	+	0.285578i
$653$	−30.8430	+	19.8216i	−1.20698	+	0.775678i	−0.980150	−	0.198257i	$-0.936472\pi$
$653$	−30.8430	+	19.8216i	−1.20698	+	0.775678i	−0.226828	+	0.973935i	$0.572836\pi$
$654$		0			0
$655$	−6.04512	+	13.2370i	−0.236202	+	0.517211i
$656$	28.9888	−	12.0350i	1.13182	−	0.469887i
$657$		0			0
$658$	−15.2104	+	6.14547i	−0.592964	+	0.239575i
$659$	−28.8153	−	8.46092i	−1.12248	−	0.329591i	−0.332734	−	0.943021i	$-0.607971\pi$
$659$	−28.8153	−	8.46092i	−1.12248	−	0.329591i	−0.789749	+	0.613430i	$0.789789\pi$
$660$		0			0
$661$	−29.2698	+	25.3625i	−1.13846	+	0.986485i	−0.999992	−	0.00388108i	$-0.998765\pi$
$661$	−29.2698	+	25.3625i	−1.13846	+	0.986485i	−0.138472	+	0.990366i	$0.544219\pi$
$662$	3.18215	+	3.01493i	0.123678	+	0.117179i
$663$		0			0
$664$	7.42617	−	26.2128i	0.288191	−	1.01725i
$665$	6.06328	−	2.76901i	0.235124	−	0.107378i
$666$		0			0
$667$	−3.21177	−	35.8740i	−0.124360	−	1.38905i
$668$	−11.4398	+	29.1098i	−0.442618	+	1.12629i
$669$		0			0
$670$	−17.8565	+	1.76235i	−0.689858	+	0.0680856i
$671$	10.0790	+	8.73352i	0.389096	+	0.337154i
$672$		0			0
$673$	24.5372	+	28.3174i	0.945838	+	1.09156i	0.995685	+	0.0927983i	$0.0295812\pi$
$673$	24.5372	+	28.3174i	0.945838	+	1.09156i	−0.0498470	+	0.998757i	$0.515873\pi$
$674$	−1.24347	+	27.9730i	−0.0478966	+	1.07748i
$675$		0			0
$676$	−60.1749	+	11.9948i	−2.31442	+	0.461338i
$677$	28.1900	+	4.05311i	1.08343	+	0.155774i	0.660825	−	0.750540i	$-0.270207\pi$
$677$	28.1900	+	4.05311i	1.08343	+	0.155774i	0.422605	+	0.906314i	$0.361116\pi$
$678$		0			0
$679$	4.74185	+	2.16553i	0.181976	+	0.0831055i
$680$	−13.5795	−	11.5420i	−0.520752	−	0.442616i
$681$		0			0
$682$	−20.2083	−	10.3370i	−0.773817	−	0.395824i
$683$	−32.5597	+	4.68138i	−1.24586	+	0.179128i	−0.733528	−	0.679659i	$-0.762128\pi$
$683$	−32.5597	+	4.68138i	−1.24586	+	0.179128i	−0.512333	+	0.858787i	$0.671219\pi$
$684$		0			0
$685$	10.6833	+	6.86571i	0.408186	+	0.262325i
$686$	−17.5032	−	22.1122i	−0.668276	−	0.844249i
$687$		0			0
$688$	7.76931	−	23.4061i	0.296202	−	0.892347i
$689$		−	57.9186i		−	2.20652i
$690$		0			0
$691$		−	6.61192i		−	0.251529i	−0.992060	−	0.125765i	$-0.959862\pi$
$691$		−	6.61192i		−	0.251529i	0.992060	−	0.125765i	$-0.0401384\pi$
$692$	0.246284	+	4.56033i	0.00936231	+	0.173358i
$693$		0			0
$694$	−10.5225	+	8.32925i	−0.399430	+	0.316174i
$695$	20.3377	+	13.0703i	0.771455	+	0.495784i
$696$		0			0
$697$	32.9887	−	4.74306i	1.24954	−	0.179656i
$698$	2.62645	−	5.13459i	0.0994127	−	0.194347i
$699$		0			0
$700$	−6.48417	+	11.3975i	−0.245079	+	0.430787i
$701$	30.2597	+	13.8191i	1.14289	+	0.521941i	0.894655	−	0.446758i	$-0.147422\pi$
$701$	30.2597	+	13.8191i	1.14289	+	0.521941i	0.248237	+	0.968699i	$0.420149\pi$
$702$		0			0
$703$	−11.0755	−	1.59242i	−0.417722	−	0.0600593i
$704$	−21.8918	−	13.4865i	−0.825078	−	0.508290i
$705$		0			0
$706$	28.2708	+	1.25670i	1.06398	+	0.0472966i
$707$	−8.78307	−	10.1362i	−0.330321	−	0.381211i
$708$		0			0
$709$	11.1559	+	9.66668i	0.418970	+	0.363040i	0.838685	−	0.544616i	$-0.183325\pi$
$709$	11.1559	+	9.66668i	0.418970	+	0.363040i	−0.419715	+	0.907656i	$0.637870\pi$
$710$	0.735877	+	7.45607i	0.0276170	+	0.279821i
$711$		0			0
$712$	−31.5567	−	19.8579i	−1.18264	−	0.744206i
$713$	−18.9126	+	14.6930i	−0.708283	+	0.550258i
$714$		0			0
$715$	28.6656	−	13.0912i	1.07203	−	0.489581i
$716$	−1.05801	+	11.8769i	−0.0395396	+	0.443862i
$717$		0			0
$718$	0.483714	−	0.510542i	0.0180520	−	0.0190533i
$719$	25.7131	−	22.2805i	0.958937	−	0.830923i	−0.0267275	−	0.999643i	$-0.508509\pi$
$719$	25.7131	−	22.2805i	0.958937	−	0.830923i	0.985664	+	0.168719i	$0.0539632\pi$
$720$		0			0
$721$	42.6356	+	12.5189i	1.58783	+	0.466230i
$722$	−8.11654	−	20.0890i	−0.302066	−	0.747633i
$723$		0			0
$724$	−18.7456	−	19.4114i	−0.696675	−	0.721418i
$725$	8.73266	−	19.1219i	0.324323	−	0.710168i
$726$		0			0
$727$	−7.65889	+	4.92207i	−0.284052	+	0.182549i	−0.674906	−	0.737903i	$-0.735816\pi$
$727$	−7.65889	+	4.92207i	−0.284052	+	0.182549i	0.390854	+	0.920453i	$0.372180\pi$
$728$	−32.8166	+	28.9879i	−1.21627	+	1.07436i
$729$		0			0
$730$	−2.57547	−	4.42829i	−0.0953223	−	0.163899i
$731$	14.1574	−	22.0293i	0.523629	−	0.814782i
$732$		0			0
$733$	−10.6247	−	36.1844i	−0.392432	−	1.33650i	−0.884742	−	0.466080i	$-0.845666\pi$
$733$	−10.6247	−	36.1844i	−0.392432	−	1.33650i	0.492310	−	0.870420i	$-0.336152\pi$
$734$	−34.7636	+	8.55059i	−1.28315	+	0.315608i
$735$		0			0
$736$	−22.6752	+	14.8941i	−0.835819	+	0.549005i
$737$	−27.4878			−1.01253
$738$		0			0
$739$	−4.03568	−	13.7443i	−0.148455	−	0.505591i	0.851365	−	0.524574i	$-0.175775\pi$
$739$	−4.03568	−	13.7443i	−0.148455	−	0.505591i	−0.999820	+	0.0189831i	$0.993957\pi$
$740$	−15.3335	+	8.02870i	−0.563671	+	0.295141i
$741$		0			0
$742$	−14.5949	−	25.0946i	−0.535794	−	0.921252i
$743$	−2.96137	−	20.5968i	−0.108642	−	0.755623i	−0.969201	−	0.246271i	$-0.920795\pi$
$743$	−2.96137	−	20.5968i	−0.108642	−	0.755623i	0.860559	−	0.509351i	$-0.170115\pi$
$744$		0			0
$745$	−0.609445	+	0.391667i	−0.0223284	+	0.0143496i
$746$	−10.3464	+	30.2041i	−0.378809	+	1.10585i
$747$		0			0
$748$	−18.9656	−	19.6392i	−0.693453	−	0.718081i
$749$	−1.34193	+	9.33331i	−0.0490330	+	0.341032i
$750$		0			0
$751$	−14.6850	−	4.31190i	−0.535862	−	0.157343i	0.00259431	−	0.999997i	$-0.499174\pi$
$751$	−14.6850	−	4.31190i	−0.535862	−	0.157343i	−0.538457	+	0.842653i	$0.680992\pi$
$752$	−16.2808	−	11.2845i	−0.593700	−	0.411503i
$753$		0			0
$754$	48.2781	−	50.9557i	1.75818	−	1.85570i
$755$	2.18068	−	2.51664i	0.0793631	−	0.0915899i
$756$		0			0
$757$	−41.0138	+	18.7304i	−1.49067	+	0.680766i	−0.983472	−	0.181063i	$-0.942046\pi$
$757$	−41.0138	+	18.7304i	−1.49067	+	0.680766i	−0.507199	+	0.861829i	$0.669319\pi$
$758$	−5.06409	+	26.7317i	−0.183936	+	0.970938i
$759$		0			0
$760$	6.81228	+	4.28680i	0.247107	+	0.155499i
$761$	12.5944	+	27.5780i	0.456548	+	0.999701i	0.988261	+	0.152776i	$0.0488213\pi$
$761$	12.5944	+	27.5780i	0.456548	+	0.999701i	−0.531713	+	0.846925i	$0.678451\pi$
$762$		0			0
$763$	8.59348	+	7.44629i	0.311105	+	0.269574i
$764$	17.2003	+	23.8324i	0.622283	+	0.862228i
$765$		0			0
$766$	−6.10053	−	0.271183i	−0.220421	−	0.00979825i
$767$	15.4961	−	52.7750i	0.559533	−	1.90559i
$768$		0			0
$769$	4.75286	+	0.683358i	0.171392	+	0.0246425i	0.227477	−	0.973784i	$-0.426952\pi$
$769$	4.75286	+	0.683358i	0.171392	+	0.0246425i	−0.0560842	+	0.998426i	$0.517862\pi$
$770$	9.12123	−	12.8955i	0.328706	−	0.464721i
$771$		0			0
$772$	13.4774	−	23.6899i	0.485063	−	0.852619i
$773$	−8.51370	−	13.2476i	−0.306217	−	0.476482i	0.653706	−	0.756749i	$-0.273213\pi$
$773$	−8.51370	−	13.2476i	−0.306217	−	0.476482i	−0.959922	+	0.280267i	$0.909577\pi$
$774$		0			0
$775$	−13.8357	+	1.98928i	−0.496994	+	0.0714570i
$776$	0.955163	+	6.22178i	0.0342884	+	0.223349i
$777$		0			0
$778$	31.7651	−	25.1441i	1.13883	−	0.901459i
$779$	−14.4420	+	4.24056i	−0.517439	+	0.151934i
$780$		0			0
$781$			11.4776i			0.410702i
$782$	−27.2476	+	9.34720i	−0.974372	+	0.334255i
$783$		0			0
$784$	1.90701	−	5.74512i	0.0681076	−	0.205183i
$785$	−31.9540	+	9.38255i	−1.14049	+	0.334877i
$786$		0			0
$787$	−39.1720	−	25.1743i	−1.39633	−	0.897368i	−0.396545	−	0.918015i	$-0.629791\pi$
$787$	−39.1720	−	25.1743i	−1.39633	−	0.897368i	−0.999787	+	0.0206472i	$0.993427\pi$
$788$	−4.35357	−	12.3249i	−0.155089	−	0.439056i
$789$		0			0
$790$	16.9017	+	8.64555i	0.601334	+	0.307595i
$791$	18.2531	+	28.4024i	0.649007	+	1.00987i
$792$		0			0
$793$	24.9453	+	11.3921i	0.885834	+	0.404547i
$794$	−43.9126	−	31.0603i	−1.55840	−	1.10229i
$795$		0			0
$796$	−31.9641	+	6.37146i	−1.13294	+	0.225831i
$797$	−1.97863	+	6.73859i	−0.0700866	+	0.238693i	−0.987085	−	0.160198i	$-0.948787\pi$
$797$	−1.97863	+	6.73859i	−0.0700866	+	0.238693i	0.916998	+	0.398891i	$0.130605\pi$
$798$		0			0
$799$	−13.7741	−	15.8962i	−0.487293	−	0.562366i
$800$	−15.8021	+	1.00452i	−0.558688	+	0.0355153i
$801$		0			0
$802$	11.5818	−	1.14307i	0.408967	−	0.0403631i
$803$	−3.26006	−	7.13853i	−0.115045	−	0.251913i
$804$		0			0
$805$	−8.24736	−	14.4818i	−0.290681	−	0.510416i
$806$	−45.8592	−	8.68764i	−1.61532	−	0.306009i
$807$		0			0
$808$	4.41444	−	15.5820i	0.155299	−	0.548174i
$809$	18.3259	−	21.1492i	0.644303	−	0.743565i	−0.335827	−	0.941924i	$-0.609016\pi$
$809$	18.3259	−	21.1492i	0.644303	−	0.743565i	0.980129	+	0.198359i	$0.0635611\pi$
$810$		0			0
$811$	−6.48576	+	5.61994i	−0.227746	+	0.197343i	−0.761257	−	0.648450i	$-0.775418\pi$
$811$	−6.48576	+	5.61994i	−0.227746	+	0.197343i	0.533512	+	0.845793i	$0.320872\pi$
$812$	8.07732	−	34.2433i	0.283458	−	1.20170i
$813$		0			0
$814$	−24.5843	+	9.93279i	−0.861678	+	0.348144i
$815$	0.974458	−	6.77751i	0.0341338	−	0.237406i
$816$		0			0
$817$	−4.91285	+	10.7576i	−0.171879	+	0.376362i
$818$	38.0351	+	13.0289i	1.32987	+	0.455546i
$819$		0			0
$820$	−14.2758	+	18.3925i	−0.498533	+	0.642293i
$821$	2.47783	+	17.2337i	0.0864767	+	0.601459i	0.986270	+	0.165142i	$0.0528082\pi$
$821$	2.47783	+	17.2337i	0.0864767	+	0.601459i	−0.899793	+	0.436317i	$0.856283\pi$
$822$		0			0
$823$	−18.2879	+	28.4565i	−0.637475	+	0.991931i	0.360766	+	0.932656i	$0.382515\pi$
$823$	−18.2879	+	28.4565i	−0.637475	+	0.991931i	−0.998242	+	0.0592748i	$0.981121\pi$
$824$	15.6067	+	51.3365i	0.543685	+	1.78839i
$825$		0			0
$826$	−6.58466	−	26.7708i	−0.229109	−	0.931477i
$827$	24.6584			0.857455			0.428727	−	0.903434i	$-0.358962\pi$
$827$	24.6584			0.857455			0.428727	+	0.903434i	$0.358962\pi$
$828$		0			0
$829$	14.1948			0.493004			0.246502	−	0.969142i	$-0.420719\pi$
$829$	14.1948			0.493004			0.246502	+	0.969142i	$0.420719\pi$
$830$	4.82688	+	19.6243i	0.167543	+	0.681171i
$831$		0			0
$832$	−51.0053	−	13.9263i	−1.76829	−	0.482806i
$833$	3.47499	−	5.40719i	0.120401	−	0.187348i
$834$		0			0
$835$	−3.30178	−	22.9644i	−0.114263	−	0.794714i
$836$	9.74044	+	7.56031i	0.336880	+	0.261479i
$837$		0			0
$838$	−26.5588	−	9.09773i	−0.917460	−	0.314276i
$839$	20.6654	−	45.2509i	0.713449	−	1.56223i	−0.109415	−	0.993996i	$-0.534898\pi$
$839$	20.6654	−	45.2509i	0.713449	−	1.56223i	0.822864	−	0.568238i	$-0.192375\pi$
$840$		0			0
$841$	−3.89979	+	27.1236i	−0.134475	+	0.935297i
$842$	−4.24790	+	1.71628i	−0.146392	+	0.0591470i
$843$		0			0
$844$	38.0573	+	8.97696i	1.30999	+	0.309000i
$845$	34.3975	−	29.8056i	1.18331	−	1.02534i
$846$		0			0
$847$	−1.02736	+	1.18563i	−0.0353004	+	0.0407389i
$848$	15.6656	−	31.3590i	0.537958	−	1.07687i
$849$		0			0
$850$	−16.5189	−	3.12937i	−0.566594	−	0.107336i
$851$	−1.49624	+	27.9360i	−0.0512905	+	0.957633i
$852$		0			0
$853$	−1.80785	−	3.95863i	−0.0618994	−	0.135541i	0.876154	−	0.482031i	$-0.160101\pi$
$853$	−1.80785	−	3.95863i	−0.0618994	−	0.135541i	−0.938054	+	0.346490i	$0.887373\pi$
$854$	13.6788	−	1.35003i	0.468080	−	0.0461972i
$855$		0			0
$856$	−10.3115	+	4.82839i	−0.352439	+	0.165031i
$857$	31.3414	+	36.1699i	1.07060	+	1.23554i	0.970637	+	0.240550i	$0.0773276\pi$
$857$	31.3414	+	36.1699i	1.07060	+	1.23554i	0.0999650	+	0.994991i	$0.468127\pi$
$858$		0			0
$859$	−0.884899	+	3.01369i	−0.0301924	+	0.102826i	−0.973211	−	0.229915i	$-0.926155\pi$
$859$	−0.884899	+	3.01369i	−0.0301924	+	0.102826i	0.943018	+	0.332741i	$0.107973\pi$
$860$	3.57613	+	17.9406i	0.121945	+	0.611769i
$861$		0			0
$862$	3.85008	+	2.72324i	0.131134	+	0.0927539i
$863$	−3.32092	−	1.51661i	−0.113045	−	0.0516261i	0.358090	−	0.933687i	$-0.383428\pi$
$863$	−3.32092	−	1.51661i	−0.113045	−	0.0516261i	−0.471135	+	0.882061i	$0.656156\pi$
$864$		0			0
$865$	−1.83151	−	2.84989i	−0.0622732	−	0.0968990i
$866$	41.3226	+	21.1374i	1.40420	+	0.718279i
$867$		0			0
$868$	−22.0588	+	7.79191i	−0.748724	+	0.264475i
$869$	24.4661	+	15.7234i	0.829954	+	0.533379i
$870$		0			0
$871$	−54.2331	+	15.9243i	−1.83762	+	0.539574i
$872$	−1.82443	+	13.6086i	−0.0617828	+	0.460846i
$873$		0			0
$874$	11.5797	−	5.92974i	0.391688	−	0.200577i
$875$		−	27.1019i		−	0.916211i
$876$		0			0
$877$	19.7803	−	5.80801i	0.667932	−	0.196123i	0.0698502	−	0.997557i	$-0.477748\pi$
$877$	19.7803	−	5.80801i	0.667932	−	0.196123i	0.598082	+	0.801435i	$0.295930\pi$
$878$	32.9785	−	26.1045i	1.11297	−	0.880985i
$879$		0			0
$880$	19.0613	+	0.665375i	0.642557	+	0.0224298i
$881$	−37.8699	+	5.44487i	−1.27587	+	0.183442i	−0.746750	−	0.665105i	$-0.768387\pi$
$881$	−37.8699	+	5.44487i	−1.27587	+	0.183442i	−0.529119	+	0.848547i	$0.677478\pi$
$882$		0			0
$883$	24.3069	+	37.8223i	0.817993	+	1.27282i	0.959168	+	0.282838i	$0.0912758\pi$
$883$	24.3069	+	37.8223i	0.817993	+	1.27282i	−0.141174	+	0.989985i	$0.545088\pi$
$884$	−48.7965	−	27.7608i	−1.64120	−	0.933696i
$885$		0			0
$886$	33.2822	−	47.0540i	1.11814	−	1.58081i
$887$	−29.2498	−	4.20549i	−0.982113	−	0.141207i	−0.367490	−	0.930027i	$-0.619783\pi$
$887$	−29.2498	−	4.20549i	−0.982113	−	0.141207i	−0.614623	+	0.788821i	$0.710692\pi$
$888$		0			0
$889$	10.5922	−	36.0736i	0.355250	−	1.20987i
$890$	27.6297	+	1.22821i	0.926150	+	0.0411696i
$891$		0			0
$892$	1.27095	−	0.917262i	0.0425545	−	0.0307122i
$893$	7.17911	+	6.22073i	0.240240	+	0.208169i
$894$		0			0
$895$	−3.67431	−	8.04561i	−0.122819	−	0.268935i
$896$	−25.6085	+	6.81890i	−0.855520	+	0.227804i
$897$		0			0
$898$	−8.41788	+	44.4353i	−0.280908	+	1.48282i
$899$	34.1150	−	15.5798i	1.13780	−	0.519615i
$900$		0			0
$901$	24.3746	−	28.1298i	0.812035	−	0.937138i
$902$	−24.5311	+	25.8917i	−0.816798	+	0.862100i
$903$		0			0
$904$	−16.5815	+	37.2436i	−0.551491	+	1.23870i
$905$	19.2061	+	5.63942i	0.638432	+	0.187461i
$906$		0			0
$907$	6.46214	−	44.9452i	0.214572	−	1.49238i	−0.543058	−	0.839695i	$-0.682734\pi$
$907$	6.46214	−	44.9452i	0.214572	−	1.49238i	0.757630	−	0.652685i	$-0.226357\pi$
$908$	−17.2813	+	16.6886i	−0.573501	+	0.553831i
$909$		0			0
$910$	10.5255	−	30.7268i	0.348915	−	1.01858i
$911$	−24.7627	+	15.9140i	−0.820426	+	0.527256i	−0.882222	−	0.470833i	$-0.843953\pi$
$911$	−24.7627	+	15.9140i	−0.820426	+	0.527256i	0.0617963	+	0.998089i	$0.480317\pi$
$912$		0			0
$913$	4.40594	+	30.6440i	0.145815	+	1.01417i
$914$	−6.02516	−	10.3597i	−0.199295	−	0.342670i
$915$		0			0
$916$	19.1361	+	36.5469i	0.632275	+	1.20754i
$917$	6.47309	+	22.0453i	0.213760	+	0.728001i
$918$		0			0
$919$	−8.22567			−0.271340			−0.135670	−	0.990754i	$-0.543319\pi$
$919$	−8.22567			−0.271340			−0.135670	+	0.990754i	$0.543319\pi$
$920$	9.15645	−	17.9201i	0.301879	−	0.590807i
$921$		0			0
$922$	−2.86650	+	0.705054i	−0.0944031	+	0.0232197i
$923$	6.64925	+	22.6453i	0.218863	+	0.745378i
$924$		0			0
$925$	−8.82766	+	13.7361i	−0.290252	+	0.451641i
$926$	−6.33310	−	10.8892i	−0.208118	−	0.357842i
$927$		0			0
$928$	39.9216	−	14.5310i	1.31049	−	0.477004i
$929$	−24.1395	+	15.5135i	−0.791991	+	0.508982i	−0.872993	−	0.487732i	$-0.837824\pi$
$929$	−24.1395	+	15.5135i	−0.791991	+	0.508982i	0.0810020	+	0.996714i	$0.474188\pi$
$930$		0			0
$931$	−1.20588	+	2.64051i	−0.0395211	+	0.0865392i
$932$	−1.20981	+	1.16831i	−0.0396285	+	0.0382693i
$933$		0			0
$934$	15.9428	+	39.4594i	0.521665	+	1.29115i
$935$	19.4315	+	5.70562i	0.635479	+	0.186594i
$936$		0			0
$937$	−4.63396	+	4.01535i	−0.151385	+	0.131176i	−0.727260	−	0.686362i	$-0.759207\pi$
$937$	−4.63396	+	4.01535i	−0.151385	+	0.131176i	0.575876	+	0.817537i	$0.304661\pi$
$938$	−19.4850	+	20.5657i	−0.636209	+	0.671495i
$939$		0			0
$940$	14.6360	+	1.30379i	0.477374	+	0.0425249i
$941$	−18.4114	+	8.40821i	−0.600195	+	0.274100i	−0.692254	−	0.721654i	$-0.743382\pi$
$941$	−18.4114	+	8.40821i	−0.600195	+	0.274100i	0.0920595	+	0.995754i	$0.470655\pi$
$942$		0			0
$943$	13.7799	+	35.0189i	0.448737	+	1.14037i
$944$	22.6644	−	24.3827i	0.737664	−	0.793591i
$945$		0			0
$946$	2.75249	+	27.8888i	0.0894912	+	0.906744i
$947$	26.0664	+	22.5867i	0.847044	+	0.733968i	0.965892	−	0.258944i	$-0.0833746\pi$
$947$	26.0664	+	22.5867i	0.847044	+	0.733968i	−0.118848	+	0.992912i	$0.537920\pi$
$948$		0			0
$949$	−10.5676	−	12.1956i	−0.343038	−	0.395887i
$950$	7.58555	+	0.337196i	0.246108	+	0.0109401i
$951$		0			0
$952$	−28.1376	+	0.268166i	−0.911945	+	0.00869131i
$953$	35.4453	+	5.09627i	1.14819	+	0.165084i	0.690026	−	0.723785i	$-0.257599\pi$
$953$	35.4453	+	5.09627i	1.14819	+	0.165084i	0.458161	+	0.888869i	$0.348508\pi$
$954$		0			0
$955$	−19.8314	−	9.05669i	−0.641729	−	0.293068i
$956$	−12.2869	−	6.99012i	−0.397385	−	0.226076i
$957$		0			0
$958$	11.9090	−	23.2815i	0.384762	−	0.752191i
$959$	19.8466	−	2.85351i	0.640879	−	0.0921445i
$960$		0			0
$961$	5.09974	+	3.27741i	0.164508	+	0.105723i
$962$	−42.7502	+	33.8395i	−1.37832	+	1.09103i
$963$		0			0
$964$	−27.6693	+	1.49430i	−0.891169	+	0.0481283i
$965$			20.2173i			0.650819i
$966$		0			0
$967$		−	18.9238i		−	0.608547i	−0.952585	−	0.304274i	$-0.901586\pi$
$967$		−	18.9238i		−	0.608547i	0.952585	−	0.304274i	$-0.0984137\pi$
$968$	−1.87757	−	0.251714i	−0.0603473	−	0.00809041i
$969$		0			0
$970$	−2.89797	−	3.66108i	−0.0930483	−	0.117550i
$971$	−31.6354	−	20.3308i	−1.01523	−	0.652448i	−0.0764871	−	0.997071i	$-0.524370\pi$
$971$	−31.6354	−	20.3308i	−1.01523	−	0.652448i	−0.938741	+	0.344623i	$0.888007\pi$
$972$		0			0
$973$	37.7820	−	5.43223i	1.21123	−	0.174149i
$974$	−53.4564	−	27.3441i	−1.71285	−	0.876161i
$975$		0			0
$976$	10.4249	+	12.9152i	0.333693	+	0.413405i
$977$	21.6175	+	9.87239i	0.691606	+	0.315846i	0.730029	−	0.683416i	$-0.239506\pi$
$977$	21.6175	+	9.87239i	0.691606	+	0.315846i	−0.0384235	+	0.999262i	$0.512234\pi$
$978$		0			0
$979$	41.9372	+	6.02966i	1.34032	+	0.192709i
$980$	0.877777	+	4.40360i	0.0280396	+	0.140668i
$981$		0			0
$982$	0.0592152	−	1.33210i	0.00188963	−	0.0425091i
$983$	−39.0723	−	45.0919i	−1.24621	−	1.43821i	−0.855587	−	0.517658i	$-0.826804\pi$
$983$	−39.0723	−	45.0919i	−1.24621	−	1.43821i	−0.390627	−	0.920549i	$-0.627742\pi$
$984$		0			0
$985$	7.32767	+	6.34946i	0.233479	+	0.202311i
$986$	44.8918	−	4.43061i	1.42965	−	0.141099i
$987$		0			0
$988$	23.5976	+	9.27355i	0.750741	+	0.295031i
$989$	27.8846	+	9.83584i	0.886679	+	0.312761i
$990$		0			0
$991$	−14.6872	+	6.70741i	−0.466554	+	0.213068i	−0.634799	−	0.772677i	$-0.718917\pi$
$991$	−14.6872	+	6.70741i	−0.466554	+	0.213068i	0.168245	+	0.985745i	$0.446190\pi$
$992$	−22.4799	−	17.1076i	−0.713737	−	0.543166i
$993$		0			0
$994$	8.58730	+	8.13605i	0.272373	+	0.258060i
$995$	18.2715	−	15.8323i	0.579245	−	0.501918i
$996$		0			0
$997$	−22.7004	−	6.66543i	−0.718928	−	0.211096i	−0.0982500	−	0.995162i	$-0.531324\pi$
$997$	−22.7004	−	6.66543i	−0.718928	−	0.211096i	−0.620678	+	0.784065i	$0.713143\pi$
$998$	9.69312	−	3.91631i	0.306830	−	0.123969i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.u.c.19.2		240
3.2	odd	2		276.2.m.a.19.23	yes	240
4.3	odd	2	inner	828.2.u.c.19.19		240
12.11	even	2		276.2.m.a.19.6	✓	240
23.17	odd	22	inner	828.2.u.c.523.19		240
69.17	even	22		276.2.m.a.247.6	yes	240
92.63	even	22	inner	828.2.u.c.523.2		240
276.155	odd	22		276.2.m.a.247.23	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.m.a.19.6	✓	240	12.11	even	2
276.2.m.a.19.23	yes	240	3.2	odd	2
276.2.m.a.247.6	yes	240	69.17	even	22
276.2.m.a.247.23	yes	240	276.155	odd	22
828.2.u.c.19.2		240	1.1	even	1	trivial
828.2.u.c.19.19		240	4.3	odd	2	inner
828.2.u.c.523.2		240	92.63	even	22	inner
828.2.u.c.523.19		240	23.17	odd	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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37328 + 0.337778i) q^{2} +(1.77181 - 0.927729i) q^{4} +(-0.802068 + 1.24804i) q^{5} +(0.333353 + 2.31852i) q^{7} +(-2.11983 + 1.87251i) q^{8} +O(q^{10})\)	\(q+(-1.37328 + 0.337778i) q^{2} +(1.77181 - 0.927729i) q^{4} +(-0.802068 + 1.24804i) q^{5} +(0.333353 + 2.31852i) q^{7} +(-2.11983 + 1.87251i) q^{8} +(0.679905 - 1.98484i) q^{10} +(1.33517 - 2.92362i) q^{11} +(0.940564 - 6.54177i) q^{13} +(-1.24093 - 3.07139i) q^{14} +(2.27864 - 3.28752i) q^{16} +(3.20986 - 2.78136i) q^{17} +(-1.25613 + 1.44965i) q^{19} +(-0.263269 + 2.95540i) q^{20} +(-0.846036 + 4.46595i) q^{22} +(3.89006 + 2.80489i) q^{23} +(1.16278 + 2.54613i) q^{25} +(0.918003 + 9.30140i) q^{26} +(2.74160 + 3.79872i) q^{28} +(-4.91811 - 5.67580i) q^{29} +(-1.40691 + 4.79150i) q^{31} +(-2.01876 + 5.28437i) q^{32} +(-3.46856 + 4.90381i) q^{34} +(-3.16098 - 1.44357i) q^{35} +(3.15377 + 4.90737i) q^{37} +(1.23536 - 2.41508i) q^{38} +(-0.636724 - 4.14752i) q^{40} +(6.60126 + 4.24238i) q^{41} +(5.91571 - 1.73701i) q^{43} +(-0.346652 - 6.41878i) q^{44} +(-6.28959 - 2.53793i) q^{46} -4.95230i q^{47} +(1.45204 - 0.426357i) q^{49} +(-2.45685 - 3.10380i) q^{50} +(-4.40248 - 12.4634i) q^{52} +(8.67435 - 1.24718i) q^{53} +(2.57790 + 4.01129i) q^{55} +(-5.04811 - 4.29067i) q^{56} +(8.67112 + 6.13325i) q^{58} +(8.23768 + 1.18440i) q^{59} +(-1.16902 + 3.98132i) q^{61} +(0.313626 - 7.05532i) q^{62} +(0.987389 - 7.93883i) q^{64} +(7.41000 + 6.42080i) q^{65} +(-3.55277 - 7.77948i) q^{67} +(3.10692 - 7.90592i) q^{68} +(4.82853 + 0.914724i) q^{70} +(-3.24835 + 1.48347i) q^{71} +(1.59896 - 1.84530i) q^{73} +(-5.98862 - 5.67393i) q^{74} +(-0.880744 + 3.73386i) q^{76} +(7.22356 + 2.12103i) q^{77} +(-1.28775 + 8.95651i) q^{79} +(2.27534 + 5.48065i) q^{80} +(-10.4984 - 3.59622i) q^{82} +(-8.10326 + 5.20765i) q^{83} +(0.896727 + 6.23688i) q^{85} +(-7.53722 + 4.38360i) q^{86} +(2.64417 + 8.69772i) q^{88} +(3.71385 + 12.6482i) q^{89} +15.4808 q^{91} +(9.49464 + 1.36081i) q^{92} +(1.67278 + 6.80091i) q^{94} +(-0.801724 - 2.73042i) q^{95} +(1.20320 - 1.87221i) q^{97} +(-1.85005 + 1.07598i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{2} + 4 q^{8}+O(q^{10}) \) 240 * q + 4 * q^2 + 4 * q^8	\( 240 q + 4 q^{2} + 4 q^{8} - 8 q^{16} + 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} - 22 q^{34} + 110 q^{38} - 22 q^{40} + 16 q^{41} + 154 q^{44} - 88 q^{46} - 40 q^{49} + 142 q^{50} - 70 q^{52} + 110 q^{56} - 46 q^{58} - 40 q^{62} - 48 q^{64} - 72 q^{70} - 22 q^{74} + 110 q^{76} + 192 q^{77} - 198 q^{80} + 172 q^{82} - 200 q^{85} - 220 q^{86} + 176 q^{88} + 88 q^{89} - 154 q^{92} + 126 q^{94} - 88 q^{97} - 228 q^{98}+O(q^{100}) \) 240 * q + 4 * q^2 + 4 * q^8 - 8 * q^16 + 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 - 22 * q^34 + 110 * q^38 - 22 * q^40 + 16 * q^41 + 154 * q^44 - 88 * q^46 - 40 * q^49 + 142 * q^50 - 70 * q^52 + 110 * q^56 - 46 * q^58 - 40 * q^62 - 48 * q^64 - 72 * q^70 - 22 * q^74 + 110 * q^76 + 192 * q^77 - 198 * q^80 + 172 * q^82 - 200 * q^85 - 220 * q^86 + 176 * q^88 + 88 * q^89 - 154 * q^92 + 126 * q^94 - 88 * q^97 - 228 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more