LMFDB - Embedded newform 441.2.u.e.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.8
Character	$\chi$	$=$	441.127
Dual form			441.2.u.e.316.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23234 + 0.593462i) q^{2} +(-0.0805240 - 0.100974i) q^{4} +(-0.303726 - 1.33071i) q^{5} +(-0.112387 - 2.64336i) q^{7} +(-0.648032 - 2.83922i) q^{8} +O(q^{10})$	\(q+(1.23234 + 0.593462i) q^{2} +(-0.0805240 - 0.100974i) q^{4} +(-0.303726 - 1.33071i) q^{5} +(-0.112387 - 2.64336i) q^{7} +(-0.648032 - 2.83922i) q^{8} +(0.415434 - 1.82013i) q^{10} +(-2.76798 - 1.33299i) q^{11} +(-0.877440 - 0.422553i) q^{13} +(1.43024 - 3.32421i) q^{14} +(0.828895 - 3.63163i) q^{16} +(-1.45310 + 1.82214i) q^{17} +2.66550 q^{19} +(-0.109910 + 0.137823i) q^{20} +(-2.62000 - 3.28538i) q^{22} +(3.32581 + 4.17043i) q^{23} +(2.82630 - 1.36108i) q^{25} +(-0.830532 - 1.04145i) q^{26} +(-0.257861 + 0.224202i) q^{28} +(0.334746 - 0.419759i) q^{29} +7.03525 q^{31} +(-0.454784 + 0.570282i) q^{32} +(-2.87208 + 1.38312i) q^{34} +(-3.48342 + 0.952412i) q^{35} +(2.59779 - 3.25752i) q^{37} +(3.28480 + 1.58187i) q^{38} +(-3.58135 + 1.72469i) q^{40} +(1.82428 + 7.99268i) q^{41} +(1.75602 - 7.69362i) q^{43} +(0.0882916 + 0.386831i) q^{44} +(1.62352 + 7.11312i) q^{46} +(5.08378 + 2.44822i) q^{47} +(-6.97474 + 0.594157i) q^{49} +4.29070 q^{50} +(0.0279882 + 0.122624i) q^{52} +(-6.36693 - 7.98388i) q^{53} +(-0.933114 + 4.08824i) q^{55} +(-7.43225 + 2.03207i) q^{56} +(0.661631 - 0.318625i) q^{58} +(-2.38335 + 10.4421i) q^{59} +(-2.10460 + 2.63908i) q^{61} +(8.66979 + 4.17515i) q^{62} +(-7.61114 + 3.66533i) q^{64} +(-0.295794 + 1.29596i) q^{65} +5.63728 q^{67} +0.300998 q^{68} +(-4.85796 - 0.893583i) q^{70} +(-7.53046 - 9.44290i) q^{71} +(0.0447399 - 0.0215456i) q^{73} +(5.13456 - 2.47268i) q^{74} +(-0.214637 - 0.269146i) q^{76} +(-3.21249 + 7.46658i) q^{77} +7.11287 q^{79} -5.08440 q^{80} +(-2.49523 + 10.9323i) q^{82} +(-2.91100 + 1.40187i) q^{83} +(2.86608 + 1.38023i) q^{85} +(6.72987 - 8.43900i) q^{86} +(-1.99090 + 8.72270i) q^{88} +(13.7790 - 6.63562i) q^{89} +(-1.01835 + 2.36688i) q^{91} +(0.153297 - 0.671640i) q^{92} +(4.81200 + 6.03406i) q^{94} +(-0.809583 - 3.54701i) q^{95} -14.2452 q^{97} +(-8.94783 - 3.40704i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) $ 60 * q - 12 * q^4 - 2 * q^7	$ 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) $ 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	1.23234	+	0.593462i	0.871393	+	0.419641i	0.815474	−	0.578794i	$-0.196477\pi$
$2$	1.23234	+	0.593462i	0.871393	+	0.419641i	0.0559198	+	0.998435i	$0.482191\pi$
$3$		0			0
$3$		0			0
$4$	−0.0805240	−	0.100974i	−0.0402620	−	0.0504870i
$5$	−0.303726	−	1.33071i	−0.135830	−	0.595112i	−0.996325	−	0.0856525i	$-0.972703\pi$
$5$	−0.303726	−	1.33071i	−0.135830	−	0.595112i	0.860495	−	0.509459i	$-0.170155\pi$
$6$		0			0
$7$	−0.112387	−	2.64336i	−0.0424782	−	0.999097i
$7$	−0.112387	−	2.64336i	−0.0424782	−	0.999097i
$8$	−0.648032	−	2.83922i	−0.229114	−	1.00381i
$9$		0			0
$10$	0.415434	−	1.82013i	0.131372	−	0.575577i
$11$	−2.76798	−	1.33299i	−0.834576	−	0.401911i	−0.0327469	−	0.999464i	$-0.510426\pi$
$11$	−2.76798	−	1.33299i	−0.834576	−	0.401911i	−0.801830	+	0.597553i	$0.796140\pi$
$12$		0			0
$13$	−0.877440	−	0.422553i	−0.243358	−	0.117195i	0.308230	−	0.951312i	$-0.400264\pi$
$13$	−0.877440	−	0.422553i	−0.243358	−	0.117195i	−0.551588	+	0.834117i	$0.685978\pi$
$14$	1.43024	−	3.32421i	0.382247	−	0.888432i
$15$		0			0
$16$	0.828895	−	3.63163i	0.207224	−	0.907906i
$17$	−1.45310	+	1.82214i	−0.352430	+	0.441933i	−0.926171	−	0.377104i	$-0.876920\pi$
$17$	−1.45310	+	1.82214i	−0.352430	+	0.441933i	0.573741	+	0.819036i	$0.305491\pi$
$18$		0			0
$19$	2.66550			0.611508			0.305754	−	0.952110i	$-0.401091\pi$
$19$	2.66550			0.611508			0.305754	+	0.952110i	$0.401091\pi$
$20$	−0.109910	+	0.137823i	−0.0245766	+	0.0308181i
$21$		0			0
$22$	−2.62000	−	3.28538i	−0.558586	−	0.700445i
$23$	3.32581	+	4.17043i	0.693479	+	0.869596i	0.996518	−	0.0833828i	$-0.0265724\pi$
$23$	3.32581	+	4.17043i	0.693479	+	0.869596i	−0.303038	+	0.952978i	$0.598001\pi$
$24$		0			0
$25$	2.82630	−	1.36108i	0.565260	−	0.272215i
$26$	−0.830532	−	1.04145i	−0.162881	−	0.204246i
$27$		0			0
$28$	−0.257861	+	0.224202i	−0.0487311	+	0.0423703i
$29$	0.334746	−	0.419759i	0.0621609	−	0.0779473i	−0.749779	−	0.661688i	$-0.769840\pi$
$29$	0.334746	−	0.419759i	0.0621609	−	0.0779473i	0.811940	+	0.583741i	$0.198412\pi$
$30$		0			0
$31$	7.03525			1.26357			0.631784	−	0.775145i	$-0.282323\pi$
$31$	7.03525			1.26357			0.631784	+	0.775145i	$0.282323\pi$
$32$	−0.454784	+	0.570282i	−0.0803953	+	0.100812i
$33$		0			0
$34$	−2.87208	+	1.38312i	−0.492558	+	0.237203i
$35$	−3.48342	+	0.952412i	−0.588805	+	0.160987i
$36$		0			0
$37$	2.59779	−	3.25752i	0.427074	−	0.535534i	−0.521012	−	0.853550i	$-0.674445\pi$
$37$	2.59779	−	3.25752i	0.427074	−	0.535534i	0.948085	+	0.318016i	$0.103017\pi$
$38$	3.28480	+	1.58187i	0.532864	+	0.256614i
$39$		0			0
$40$	−3.58135	+	1.72469i	−0.566261	+	0.272697i
$41$	1.82428	+	7.99268i	0.284904	+	1.24825i	0.891421	+	0.453176i	$0.149709\pi$
$41$	1.82428	+	7.99268i	0.284904	+	1.24825i	−0.606517	+	0.795070i	$0.707434\pi$
$42$		0			0
$43$	1.75602	−	7.69362i	0.267790	−	1.17327i	−0.644787	−	0.764362i	$-0.723054\pi$
$43$	1.75602	−	7.69362i	0.267790	−	1.17327i	0.912577	−	0.408904i	$-0.134089\pi$
$44$	0.0882916	+	0.386831i	0.0133105	+	0.0583170i
$45$		0			0
$46$	1.62352	+	7.11312i	0.239375	+	1.04877i
$47$	5.08378	+	2.44822i	0.741545	+	0.357109i	0.766213	−	0.642586i	$-0.222139\pi$
$47$	5.08378	+	2.44822i	0.741545	+	0.357109i	−0.0246682	+	0.999696i	$0.507853\pi$
$48$		0			0
$49$	−6.97474	+	0.594157i	−0.996391	+	0.0848796i
$50$	4.29070			0.606797
$51$		0			0
$52$	0.0279882	+	0.122624i	0.00388126	+	0.0170049i
$53$	−6.36693	−	7.98388i	−0.874565	−	1.09667i	−0.994588	−	0.103899i	$-0.966868\pi$
$53$	−6.36693	−	7.98388i	−0.874565	−	1.09667i	0.120023	−	0.992771i	$-0.461703\pi$
$54$		0			0
$55$	−0.933114	+	4.08824i	−0.125821	+	0.551258i
$56$	−7.43225	+	2.03207i	−0.993176	+	0.271547i
$57$		0			0
$58$	0.661631	−	0.318625i	0.0868764	−	0.0418375i
$59$	−2.38335	+	10.4421i	−0.310286	+	1.35945i	0.543755	+	0.839244i	$0.317002\pi$
$59$	−2.38335	+	10.4421i	−0.310286	+	1.35945i	−0.854041	+	0.520206i	$0.825855\pi$
$60$		0			0
$61$	−2.10460	+	2.63908i	−0.269466	+	0.337900i	−0.898092	−	0.439808i	$-0.855046\pi$
$61$	−2.10460	+	2.63908i	−0.269466	+	0.337900i	0.628626	+	0.777708i	$0.283618\pi$
$62$	8.66979	+	4.17515i	1.10106	+	0.530245i
$63$		0			0
$64$	−7.61114	+	3.66533i	−0.951393	+	0.458166i
$65$	−0.295794	+	1.29596i	−0.0366888	+	0.160744i
$66$		0			0
$67$	5.63728			0.688704			0.344352	−	0.938841i	$-0.388099\pi$
$67$	5.63728			0.688704			0.344352	+	0.938841i	$0.388099\pi$
$68$	0.300998			0.0365014
$69$		0			0
$70$	−4.85796	−	0.893583i	−0.580638	−	0.106804i
$71$	−7.53046	−	9.44290i	−0.893702	−	1.12067i	−0.992091	−	0.125518i	$-0.959941\pi$
$71$	−7.53046	−	9.44290i	−0.893702	−	1.12067i	0.0983897	−	0.995148i	$-0.468631\pi$
$72$		0			0
$73$	0.0447399	−	0.0215456i	0.00523641	−	0.00252172i	−0.431264	−	0.902226i	$-0.641932\pi$
$73$	0.0447399	−	0.0215456i	0.00523641	−	0.00252172i	0.436500	+	0.899704i	$0.356218\pi$
$74$	5.13456	−	2.47268i	0.596881	−	0.287443i
$75$		0			0
$76$	−0.214637	−	0.269146i	−0.0246206	−	0.0308732i
$77$	−3.21249	+	7.46658i	−0.366097	+	0.850896i
$78$		0			0
$79$	7.11287			0.800261			0.400130	−	0.916458i	$-0.368965\pi$
$79$	7.11287			0.800261			0.400130	+	0.916458i	$0.368965\pi$
$80$	−5.08440			−0.568453
$81$		0			0
$82$	−2.49523	+	10.9323i	−0.275552	+	1.20727i
$83$	−2.91100	+	1.40187i	−0.319524	+	0.153875i	−0.586770	−	0.809754i	$-0.699601\pi$
$83$	−2.91100	+	1.40187i	−0.319524	+	0.153875i	0.267246	+	0.963628i	$0.413886\pi$
$84$		0			0
$85$	2.86608	+	1.38023i	0.310870	+	0.149707i
$86$	6.72987	−	8.43900i	0.725701	−	0.910000i
$87$		0			0
$88$	−1.99090	+	8.72270i	−0.212231	+	0.929843i
$89$	13.7790	−	6.63562i	1.46057	−	0.703374i	0.476176	−	0.879350i	$-0.342022\pi$
$89$	13.7790	−	6.63562i	1.46057	−	0.703374i	0.984394	+	0.175976i	$0.0563081\pi$
$90$		0			0
$91$	−1.01835	+	2.36688i	−0.106752	+	0.248117i
$92$	0.153297	−	0.671640i	0.0159824	−	0.0700233i
$93$		0			0
$94$	4.81200	+	6.03406i	0.496320	+	0.622365i
$95$	−0.809583	−	3.54701i	−0.0830614	−	0.363916i
$96$		0			0
$97$	−14.2452			−1.44638			−0.723191	−	0.690648i	$-0.757325\pi$
$97$	−14.2452			−1.44638			−0.723191	+	0.690648i	$0.757325\pi$
$98$	−8.94783	−	3.40704i	−0.903868	−	0.344163i
$99$		0			0
$100$	−0.365018	−	0.175784i	−0.0365018	−	0.0175784i
$101$	−2.83594	−	12.4251i	−0.282186	−	1.23634i	−0.894984	−	0.446099i	$-0.852813\pi$
$101$	−2.83594	−	12.4251i	−0.282186	−	1.23634i	0.612797	−	0.790240i	$-0.290044\pi$
$102$		0			0
$103$	4.04138	+	17.7064i	0.398209	+	1.74467i	0.634442	+	0.772971i	$0.281230\pi$
$103$	4.04138	+	17.7064i	0.398209	+	1.74467i	−0.236233	+	0.971696i	$0.575913\pi$
$104$	−0.631109	+	2.76507i	−0.0618853	+	0.271137i
$105$		0			0
$106$	−3.10807	−	13.6174i	−0.301883	−	1.32263i
$107$	3.19285	−	1.53760i	0.308664	−	0.148645i	−0.273139	−	0.961975i	$-0.588062\pi$
$107$	3.19285	−	1.53760i	0.308664	−	0.148645i	0.581803	+	0.813330i	$0.302347\pi$
$108$		0			0
$109$	8.51670	+	4.10142i	0.815752	+	0.392845i	0.794752	−	0.606934i	$-0.207601\pi$
$109$	8.51670	+	4.10142i	0.815752	+	0.392845i	0.0209995	+	0.999779i	$0.493315\pi$
$110$	−3.57612	+	4.48432i	−0.340970	+	0.427563i
$111$		0			0
$112$	−9.69286	−	1.78292i	−0.915889	−	0.168470i
$113$	1.73782	−	0.836891i	0.163481	−	0.0787281i	−0.350354	−	0.936617i	$-0.613939\pi$
$113$	1.73782	−	0.836891i	0.163481	−	0.0787281i	0.513835	+	0.857889i	$0.328224\pi$
$114$		0			0
$115$	4.53951	−	5.69236i	0.423311	−	0.530815i
$116$	−0.0693398			−0.00643804
$117$		0			0
$118$	−9.13409	+	11.4538i	−0.840861	+	1.05441i
$119$	4.97987	+	3.63630i	0.456504	+	0.333339i
$120$		0			0
$121$	−0.973547	−	1.22079i	−0.0885043	−	0.110981i
$122$	−4.15977	+	2.00324i	−0.376608	+	0.181365i
$123$		0			0
$124$	−0.566506	−	0.710377i	−0.0508738	−	0.0637937i
$125$	−6.92473	−	8.68333i	−0.619366	−	0.776661i
$126$		0			0
$127$	0.185249	−	0.232295i	0.0164382	−	0.0206128i	−0.773544	−	0.633742i	$-0.781518\pi$
$127$	0.185249	−	0.232295i	0.0164382	−	0.0206128i	0.789983	+	0.613129i	$0.210090\pi$
$128$	−10.0959			−0.892358
$129$		0			0
$130$	−1.13362	+	1.42152i	−0.0994251	+	0.124675i
$131$	2.72299	−	11.9302i	0.237909	−	1.04235i	−0.704977	−	0.709230i	$-0.749043\pi$
$131$	2.72299	−	11.9302i	0.237909	−	1.04235i	0.942886	−	0.333116i	$-0.108100\pi$
$132$		0			0
$133$	−0.299567	−	7.04589i	−0.0259757	−	0.610956i
$134$	6.94703	+	3.34551i	0.600132	+	0.289008i
$135$		0			0
$136$	6.11509	+	2.94487i	0.524365	+	0.252521i
$137$	−1.22580	+	5.37058i	−0.104727	+	0.458839i	0.895186	+	0.445692i	$0.147042\pi$
$137$	−1.22580	+	5.37058i	−0.104727	+	0.458839i	−0.999914	+	0.0131476i	$0.995815\pi$
$138$		0			0
$139$	2.72649	+	11.9455i	0.231257	+	1.01321i	0.948598	+	0.316483i	$0.102502\pi$
$139$	2.72649	+	11.9455i	0.231257	+	1.01321i	−0.717341	+	0.696722i	$0.754641\pi$
$140$	0.376668	+	0.275042i	0.0318342	+	0.0232453i
$141$		0			0
$142$	−3.67606	−	16.1059i	−0.308488	−	1.35157i
$143$	1.86548	+	2.33923i	0.155999	+	0.195617i
$144$		0			0
$145$	−0.660249	−	0.317959i	−0.0548307	−	0.0264051i
$146$	0.0679211			0.00562119
$147$		0			0
$148$	−0.538109			−0.0442323
$149$	10.4075	+	5.01201i	0.852619	+	0.410600i	0.808549	−	0.588429i	$-0.200253\pi$
$149$	10.4075	+	5.01201i	0.852619	+	0.410600i	0.0440698	+	0.999028i	$0.485968\pi$
$150$		0			0
$151$	5.62196	+	7.04972i	0.457509	+	0.573698i	0.956063	−	0.293161i	$-0.0947071\pi$
$151$	5.62196	+	7.04972i	0.457509	+	0.573698i	−0.498555	+	0.866858i	$0.666136\pi$
$152$	−1.72733	−	7.56794i	−0.140105	−	0.613841i
$153$		0			0
$154$	−8.38999	+	7.29485i	−0.676085	+	0.587836i
$155$	−2.13679	−	9.36188i	−0.171631	−	0.751964i
$156$		0			0
$157$	2.07773	−	9.10314i	0.165821	−	0.726510i	−0.821816	−	0.569753i	$-0.807039\pi$
$157$	2.07773	−	9.10314i	0.165821	−	0.726510i	0.987637	−	0.156757i	$-0.0501039\pi$
$158$	8.76545	+	4.22122i	0.697342	+	0.335822i
$159$		0			0
$160$	0.897010	+	0.431977i	0.0709149	+	0.0341508i
$161$	10.6502	−	9.26003i	0.839353	−	0.729792i
$162$		0			0
$163$	0.106797	−	0.467907i	0.00836496	−	0.0366493i	−0.970573	−	0.240806i	$-0.922588\pi$
$163$	0.106797	−	0.467907i	0.00836496	−	0.0366493i	0.978938	+	0.204157i	$0.0654453\pi$
$164$	0.660154	−	0.827807i	0.0515494	−	0.0646408i
$165$		0			0
$166$	−4.41929			−0.343003
$167$	−3.32042	+	4.16367i	−0.256942	+	0.322195i	−0.893525	−	0.449013i	$-0.851776\pi$
$167$	−3.32042	+	4.16367i	−0.256942	+	0.322195i	0.636584	+	0.771208i	$0.280347\pi$
$168$		0			0
$169$	−7.51402	−	9.42228i	−0.578001	−	0.724791i
$170$	2.71286	+	3.40182i	0.208067	+	0.260908i
$171$		0			0
$172$	−0.918257	+	0.442209i	−0.0700164	+	0.0337181i
$173$	13.0539	+	16.3690i	0.992466	+	1.24451i	0.969580	+	0.244775i	$0.0787142\pi$
$173$	13.0539	+	16.3690i	0.992466	+	1.24451i	0.0228864	+	0.999738i	$0.492714\pi$
$174$		0			0
$175$	−3.91546	−	7.31798i	−0.295981	−	0.553187i
$176$	−7.13527	+	8.94735i	−0.537841	+	0.674432i
$177$		0			0
$178$	20.9183			1.56790
$179$	−15.2024	+	19.0633i	−1.13628	+	1.42486i	−0.246106	+	0.969243i	$0.579151\pi$
$179$	−15.2024	+	19.0633i	−1.13628	+	1.42486i	−0.890178	+	0.455613i	$0.849420\pi$
$180$		0			0
$181$	−3.86873	+	1.86308i	−0.287561	+	0.138482i	−0.572104	−	0.820181i	$-0.693872\pi$
$181$	−3.86873	+	1.86308i	−0.287561	+	0.138482i	0.284543	+	0.958663i	$0.408158\pi$
$182$	−2.65960	+	2.31244i	−0.197143	+	0.171410i
$183$		0			0
$184$	9.68553	−	12.1453i	0.714027	−	0.895361i
$185$	−5.12384	−	2.46751i	−0.376712	−	0.181415i
$186$		0			0
$187$	6.45104	−	3.10666i	0.471747	−	0.227181i
$188$	−0.162160	−	0.710469i	−0.0118267	−	0.0518163i
$189$		0			0
$190$	1.10734	−	4.85157i	0.0803348	−	0.351970i
$191$	−1.25887	−	5.51549i	−0.0910889	−	0.399087i	0.908744	−	0.417353i	$-0.137042\pi$
$191$	−1.25887	−	5.51549i	−0.0910889	−	0.399087i	−0.999833	+	0.0182668i	$0.994185\pi$
$192$		0			0
$193$	−0.230142	−	1.00832i	−0.0165660	−	0.0725803i	0.965969	−	0.258657i	$-0.0832799\pi$
$193$	−0.230142	−	1.00832i	−0.0165660	−	0.0725803i	−0.982535	+	0.186077i	$0.940423\pi$
$194$	−17.5549	−	8.45399i	−1.26037	−	0.606961i
$195$		0			0
$196$	0.621628	+	0.656423i	0.0444020	+	0.0468873i
$197$	12.3062			0.876782			0.438391	−	0.898784i	$-0.355549\pi$
$197$	12.3062			0.876782			0.438391	+	0.898784i	$0.355549\pi$
$198$		0			0
$199$	4.56312	+	19.9923i	0.323471	+	1.41722i	0.831330	+	0.555779i	$0.187580\pi$
$199$	4.56312	+	19.9923i	0.323471	+	1.41722i	−0.507859	+	0.861440i	$0.669563\pi$
$200$	−5.69592	−	7.14246i	−0.402762	−	0.505048i
$201$		0			0
$202$	3.87897	−	16.9949i	0.272923	−	1.19575i
$203$	−1.14720	−	0.837681i	−0.0805174	−	0.0587937i
$204$		0			0
$205$	10.0819	−	4.85517i	0.704148	−	0.339100i
$206$	−5.52776	+	24.2187i	−0.385137	+	1.68740i
$207$		0			0
$208$	−2.26186	+	2.83628i	−0.156832	+	0.196661i
$209$	−7.37805	−	3.55308i	−0.510351	−	0.245772i
$210$		0			0
$211$	6.10427	−	2.93966i	0.420235	−	0.202375i	−0.211802	−	0.977313i	$-0.567933\pi$
$211$	6.10427	−	2.93966i	0.420235	−	0.202375i	0.632037	+	0.774938i	$0.282219\pi$
$212$	−0.293473	+	1.28579i	−0.0201558	+	0.0883083i
$213$		0			0
$214$	4.84717			0.331346
$215$	−10.7713			−0.734599
$216$		0			0
$217$	−0.790668	−	18.5967i	−0.0536740	−	1.26243i
$218$	8.06139	+	10.1087i	0.545986	+	0.684645i
$219$		0			0
$220$	0.487944	−	0.234981i	0.0328972	−	0.0158424i
$221$	2.04496	−	0.984801i	0.137559	−	0.0662449i
$222$		0			0
$223$	−7.68070	−	9.63129i	−0.514338	−	0.644959i	0.455058	−	0.890462i	$-0.349618\pi$
$223$	−7.68070	−	9.63129i	−0.514338	−	0.644959i	−0.969396	+	0.245503i	$0.921047\pi$
$224$	1.55857	+	1.13807i	0.104137	+	0.0760404i
$225$		0			0
$226$	2.63825			0.175493
$227$	27.1475			1.80184			0.900922	−	0.433982i	$-0.142892\pi$
$227$	27.1475			1.80184			0.900922	+	0.433982i	$0.142892\pi$
$228$		0			0
$229$	−1.51835	+	6.65234i	−0.100336	+	0.439599i	0.899660	+	0.436591i	$0.143814\pi$
$229$	−1.51835	+	6.65234i	−0.100336	+	0.439599i	−0.999995	+	0.00300754i	$0.999043\pi$
$230$	8.97240	−	4.32088i	0.591622	−	0.284910i
$231$		0			0
$232$	−1.40871	−	0.678400i	−0.0924865	−	0.0445391i
$233$	−7.67894	+	9.62909i	−0.503064	+	0.630823i	−0.966917	−	0.255089i	$-0.917895\pi$
$233$	−7.67894	+	9.62909i	−0.503064	+	0.630823i	0.463853	+	0.885912i	$0.346467\pi$
$234$		0			0
$235$	1.71379	−	7.50862i	0.111796	−	0.489809i
$236$	1.24630	−	0.600186i	0.0811272	−	0.0390688i
$237$		0			0
$238$	3.97888	+	7.43651i	0.257912	+	0.482037i
$239$	−2.02375	+	8.86663i	−0.130906	+	0.573535i	0.866346	+	0.499444i	$0.166462\pi$
$239$	−2.02375	+	8.86663i	−0.130906	+	0.573535i	−0.997252	+	0.0740905i	$0.976395\pi$
$240$		0			0
$241$	−17.1799	−	21.5429i	−1.10665	−	1.38770i	−0.913650	−	0.406501i	$-0.866749\pi$
$241$	−17.1799	−	21.5429i	−1.10665	−	1.38770i	−0.193003	−	0.981198i	$-0.561823\pi$
$242$	−0.475245	−	2.08219i	−0.0305499	−	0.133848i
$243$		0			0
$244$	0.435949			0.0279088
$245$	2.90906	+	9.10090i	0.185853	+	0.581435i
$246$		0			0
$247$	−2.33882	−	1.12632i	−0.148816	−	0.0716658i
$248$	−4.55907	−	19.9746i	−0.289501	−	1.26839i
$249$		0			0
$250$	−3.38037	−	14.8103i	−0.213793	−	0.936689i
$251$	4.93000	−	21.5998i	0.311179	−	1.36336i	−0.541399	−	0.840766i	$-0.682105\pi$
$251$	4.93000	−	21.5998i	0.311179	−	1.36336i	0.852579	−	0.522599i	$-0.175038\pi$
$252$		0			0
$253$	−3.64663	−	15.9769i	−0.229262	−	1.00446i
$254$	0.366147	−	0.176327i	0.0229741	−	0.0110637i
$255$		0			0
$256$	2.78076	+	1.33914i	0.173797	+	0.0836964i
$257$	−16.8137	+	21.0837i	−1.04881	+	1.31516i	−0.101500	+	0.994836i	$0.532364\pi$
$257$	−16.8137	+	21.0837i	−1.04881	+	1.31516i	−0.947307	+	0.320327i	$0.896207\pi$
$258$		0			0
$259$	−8.90277	−	6.50080i	−0.553191	−	0.403940i
$260$	0.154677	−	0.0744884i	0.00959264	−	0.00461957i
$261$		0			0
$262$	10.4358	−	13.0860i	0.644723	−	0.808457i
$263$	28.9304			1.78392			0.891962	−	0.452110i	$-0.149328\pi$
$263$	28.9304			1.78392			0.891962	+	0.452110i	$0.149328\pi$
$264$		0			0
$265$	−8.69043	+	10.8975i	−0.533849	+	0.669425i
$266$	3.81230	−	8.86069i	0.233747	−	0.543284i
$267$		0			0
$268$	−0.453937	−	0.569219i	−0.0277286	−	0.0347706i
$269$	−1.45752	+	0.701905i	−0.0888666	+	0.0427959i	−0.477789	−	0.878475i	$-0.658562\pi$
$269$	−1.45752	+	0.701905i	−0.0888666	+	0.0427959i	0.388922	+	0.921270i	$0.372847\pi$
$270$		0			0
$271$	13.1231	+	16.4558i	0.797171	+	0.999621i	0.999793	+	0.0203638i	$0.00648246\pi$
$271$	13.1231	+	16.4558i	0.797171	+	0.999621i	−0.202622	+	0.979257i	$0.564946\pi$
$272$	5.41284	+	6.78749i	0.328202	+	0.411552i
$273$		0			0
$274$	−4.69783	+	5.89089i	−0.283806	+	0.355882i
$275$	−9.63744			−0.581159
$276$		0			0
$277$	6.01381	−	7.54108i	0.361335	−	0.453099i	−0.567621	−	0.823290i	$-0.692136\pi$
$277$	6.01381	−	7.54108i	0.361335	−	0.453099i	0.928956	+	0.370190i	$0.120708\pi$
$278$	−3.72926	+	16.3390i	−0.223666	+	0.979945i
$279$		0			0
$280$	4.96147	+	9.27298i	0.296505	+	0.554166i
$281$	−10.9308	−	5.26397i	−0.652074	−	0.314022i	0.0784411	−	0.996919i	$-0.475006\pi$
$281$	−10.9308	−	5.26397i	−0.652074	−	0.314022i	−0.730515	+	0.682896i	$0.760720\pi$
$282$		0			0
$283$	−2.51800	−	1.21260i	−0.149679	−	0.0720817i	0.357545	−	0.933896i	$-0.383614\pi$
$283$	−2.51800	−	1.21260i	−0.149679	−	0.0720817i	−0.507224	+	0.861814i	$0.669328\pi$
$284$	−0.347104	+	1.52076i	−0.0205968	+	0.0902406i
$285$		0			0
$286$	0.910649	+	3.98981i	0.0538478	+	0.235923i
$287$	20.9225	−	5.72049i	1.23502	−	0.337670i
$288$		0			0
$289$	2.57419	+	11.2783i	0.151423	+	0.663428i
$290$	−0.624952	−	0.783665i	−0.0366984	−	0.0460184i
$291$		0			0
$292$	−0.00577818	−	0.00278263i	−0.000338142	−	0.000162841i
$293$	−13.6034			−0.794718			−0.397359	−	0.917663i	$-0.630073\pi$
$293$	−13.6034			−0.794718			−0.397359	+	0.917663i	$0.630073\pi$
$294$		0			0
$295$	14.6193			0.851171
$296$	−10.9323	−	5.26470i	−0.635425	−	0.306004i
$297$		0			0
$298$	9.85115	+	12.3530i	0.570662	+	0.715587i
$299$	−1.15597	−	5.06464i	−0.0668515	−	0.292896i
$300$		0			0
$301$	−20.5344	−	3.77713i	−1.18358	−	0.217710i
$302$	2.74441	+	12.0240i	0.157923	+	0.691906i
$303$		0			0
$304$	2.20942	−	9.68011i	0.126719	−	0.555192i
$305$	4.15108	+	1.99905i	0.237690	+	0.114465i
$306$		0			0
$307$	0.0745615	+	0.0359069i	0.00425545	+	0.00204932i	0.436010	−	0.899942i	$-0.356391\pi$
$307$	0.0745615	+	0.0359069i	0.00425545	+	0.00204932i	−0.431755	+	0.901991i	$0.642105\pi$
$308$	1.01261	−	0.276862i	0.0576989	−	0.0157756i
$309$		0			0
$310$	2.92268	−	12.8051i	0.165997	−	0.727280i
$311$	15.2796	−	19.1600i	0.866427	−	1.08647i	−0.129066	−	0.991636i	$-0.541198\pi$
$311$	15.2796	−	19.1600i	0.866427	−	1.08647i	0.995494	−	0.0948296i	$-0.0302306\pi$
$312$		0			0
$313$	−1.80986			−0.102300			−0.0511498	−	0.998691i	$-0.516289\pi$
$313$	−1.80986			−0.102300			−0.0511498	+	0.998691i	$0.516289\pi$
$314$	7.96283	−	9.98508i	0.449369	−	0.563490i
$315$		0			0
$316$	−0.572757	−	0.718215i	−0.0322201	−	0.0404027i
$317$	−15.6694	−	19.6488i	−0.880080	−	1.10359i	−0.993922	−	0.110087i	$-0.964887\pi$
$317$	−15.6694	−	19.6488i	−0.880080	−	1.10359i	0.113842	−	0.993499i	$-0.463684\pi$
$318$		0			0
$319$	−1.48610	+	0.715670i	−0.0832058	+	0.0400698i
$320$	7.18920	+	9.01497i	0.401888	+	0.503952i
$321$		0			0
$322$	18.6201	−	5.09098i	1.03766	−	0.283709i
$323$	−3.87325	+	4.85691i	−0.215514	+	0.270246i
$324$		0			0
$325$	−3.05504			−0.169463
$326$	0.409294	−	0.513239i	0.0226687	−	0.0284257i
$327$		0			0
$328$	21.5107	−	10.3590i	1.18773	−	0.571981i
$329$	5.90018	−	13.7134i	0.325287	−	0.756045i
$330$		0			0
$331$	−12.5175	+	15.6965i	−0.688025	+	0.862756i	−0.996066	−	0.0886170i	$-0.971755\pi$
$331$	−12.5175	+	15.6965i	−0.688025	+	0.862756i	0.308041	+	0.951373i	$0.400327\pi$
$332$	0.375958	+	0.181052i	0.0206334	+	0.00993650i
$333$		0			0
$334$	−6.56285	+	3.16050i	−0.359103	+	0.172935i
$335$	−1.71219	−	7.50160i	−0.0935469	−	0.409856i
$336$		0			0
$337$	1.98651	−	8.70346i	0.108212	−	0.474108i	−0.891563	−	0.452897i	$-0.850391\pi$
$337$	1.98651	−	8.70346i	0.108212	−	0.474108i	0.999775	−	0.0212111i	$-0.00675221\pi$
$338$	−3.66803	−	16.0707i	−0.199515	−	0.874131i
$339$		0			0
$340$	−0.0914209	−	0.400541i	−0.00495800	−	0.0217224i
$341$	−19.4734	−	9.37790i	−1.05454	−	0.507842i
$342$		0			0
$343$	2.35444	+	18.3700i	0.127128	+	0.991886i
$344$	−22.9818			−1.23910
$345$		0			0
$346$	6.37235	+	27.9191i	0.342580	+	1.50094i
$347$	−12.1600	−	15.2482i	−0.652784	−	0.818566i	0.339752	−	0.940515i	$-0.389657\pi$
$347$	−12.1600	−	15.2482i	−0.652784	−	0.818566i	−0.992536	+	0.121950i	$0.961085\pi$
$348$		0			0
$349$	−3.39280	+	14.8648i	−0.181612	+	0.795696i	0.799251	+	0.600998i	$0.205230\pi$
$349$	−3.39280	+	14.8648i	−0.181612	+	0.795696i	−0.980863	+	0.194698i	$0.937627\pi$
$350$	−0.482217	−	11.3419i	−0.0257756	−	0.606249i
$351$		0			0
$352$	2.01901	−	0.972304i	0.107614	−	0.0518240i
$353$	6.67458	−	29.2433i	0.355252	−	1.55646i	−0.409606	−	0.912263i	$-0.634334\pi$
$353$	6.67458	−	29.2433i	0.355252	−	1.55646i	0.764858	−	0.644199i	$-0.222809\pi$
$354$		0			0
$355$	−10.2786	+	12.8889i	−0.545530	+	0.684073i
$356$	−1.77956	−	0.856993i	−0.0943167	−	0.0454205i
$357$		0			0
$358$	−30.0479	+	14.4703i	−1.58808	+	0.764778i
$359$	−5.62056	+	24.6253i	−0.296642	+	1.29967i	0.578451	+	0.815717i	$0.303657\pi$
$359$	−5.62056	+	24.6253i	−0.296642	+	1.29967i	−0.875093	+	0.483956i	$0.839200\pi$
$360$		0			0
$361$	−11.8951			−0.626057
$362$	−5.87325			−0.308691
$363$		0			0
$364$	0.320995	−	0.0877643i	0.0168247	−	0.00460010i
$365$	−0.0422596	−	0.0529919i	−0.00221197	−	0.00277372i
$366$		0			0
$367$	−18.0209	+	8.67839i	−0.940681	+	0.453008i	−0.840410	−	0.541952i	$-0.817686\pi$
$367$	−18.0209	+	8.67839i	−0.940681	+	0.453008i	−0.100272	+	0.994960i	$0.531971\pi$
$368$	17.9022	−	8.62125i	0.933217	−	0.449413i
$369$		0			0
$370$	−4.84992	−	6.08160i	−0.252135	−	0.316168i
$371$	−20.3887	+	17.7274i	−1.05853	+	0.920360i
$372$		0			0
$373$	−19.6193			−1.01585			−0.507925	−	0.861401i	$-0.669587\pi$
$373$	−19.6193			−1.01585			−0.507925	+	0.861401i	$0.669587\pi$
$374$	9.79354			0.506412
$375$		0			0
$376$	3.65657	−	16.0205i	0.188573	−	0.826192i
$377$	−0.471090	+	0.226865i	−0.0242624	+	0.0116842i
$378$		0			0
$379$	29.2165	+	14.0699i	1.50075	+	0.722724i	0.990527	−	0.137317i	$-0.0438478\pi$
$379$	29.2165	+	14.0699i	1.50075	+	0.722724i	0.510225	+	0.860041i	$0.329562\pi$
$380$	−0.292965	+	0.367367i	−0.0150288	+	0.0188455i
$381$		0			0
$382$	1.72188	−	7.54403i	0.0880988	−	0.385986i
$383$	18.8818	−	9.09302i	0.964817	−	0.464632i	0.115960	−	0.993254i	$-0.463005\pi$
$383$	18.8818	−	9.09302i	0.964817	−	0.464632i	0.848857	+	0.528622i	$0.177291\pi$
$384$		0			0
$385$	10.9116	+	2.00710i	0.556105	+	0.102291i
$386$	0.314786	−	1.37917i	0.0160222	−	0.0701978i
$387$		0			0
$388$	1.14708	+	1.43840i	0.0582343	+	0.0730234i
$389$	2.02434	+	8.86919i	0.102638	+	0.449686i	0.999965	+	0.00832058i	$0.00264855\pi$
$389$	2.02434	+	8.86919i	0.102638	+	0.449686i	−0.897328	+	0.441365i	$0.854494\pi$
$390$		0			0
$391$	−12.4318			−0.628705
$392$	6.20680	+	19.4177i	0.313491	+	0.980744i
$393$		0			0
$394$	15.1654	+	7.30327i	0.764022	+	0.367933i
$395$	−2.16037	−	9.46518i	−0.108700	−	0.476245i
$396$		0			0
$397$	−3.26493	−	14.3046i	−0.163862	−	0.717928i	−0.988369	−	0.152075i	$-0.951404\pi$
$397$	−3.26493	−	14.3046i	−0.163862	−	0.717928i	0.824507	−	0.565852i	$-0.191453\pi$
$398$	−6.24139	+	27.3453i	−0.312853	+	1.37070i
$399$		0			0
$400$	−2.60021	−	11.3923i	−0.130010	−	0.569613i
$401$	−0.403551	+	0.194340i	−0.0201524	+	0.00970488i	−0.443933	−	0.896060i	$-0.646417\pi$
$401$	−0.403551	+	0.194340i	−0.0201524	+	0.00970488i	0.423780	+	0.905765i	$0.360703\pi$
$402$		0			0
$403$	−6.17301	−	2.97277i	−0.307500	−	0.148084i
$404$	−1.02625	+	1.28687i	−0.0510576	+	0.0640242i
$405$		0			0
$406$	−0.916599	−	1.71312i	−0.0454901	−	0.0850208i
$407$	−11.5329	+	5.55393i	−0.571662	+	0.275298i
$408$		0			0
$409$	−21.9849	+	27.5681i	−1.08708	+	1.36316i	−0.160512	+	0.987034i	$0.551314\pi$
$409$	−21.9849	+	27.5681i	−1.08708	+	1.36316i	−0.926570	+	0.376123i	$0.877257\pi$
$410$	15.3056			0.755890
$411$		0			0
$412$	1.46246	−	1.83387i	0.0720502	−	0.0903481i
$413$	27.8702	+	5.12650i	1.37140	+	0.252259i
$414$		0			0
$415$	2.74963	+	3.44792i	0.134974	+	0.169252i
$416$	0.640020	−	0.308218i	0.0313796	−	0.0151116i
$417$		0			0
$418$	−6.98362	−	8.75718i	−0.341580	−	0.428328i
$419$	4.36285	+	5.47085i	0.213139	+	0.267268i	0.876896	−	0.480680i	$-0.159610\pi$
$419$	4.36285	+	5.47085i	0.213139	+	0.267268i	−0.663756	+	0.747949i	$0.731039\pi$
$420$		0			0
$421$	−22.7217	+	28.4921i	−1.10739	+	1.38862i	−0.194260	+	0.980950i	$0.562231\pi$
$421$	−22.7217	+	28.4921i	−1.10739	+	1.38862i	−0.913128	+	0.407672i	$0.866341\pi$
$422$	9.26709			0.451115
$423$		0			0
$424$	−18.5420	+	23.2509i	−0.900478	+	1.12916i
$425$	−1.62685	+	7.12769i	−0.0789138	+	0.345744i
$426$		0			0
$427$	7.21258	+	5.26662i	0.349041	+	0.254870i
$428$	−0.412358	−	0.198581i	−0.0199321	−	0.00959879i
$429$		0			0
$430$	−13.2739	−	6.39237i	−0.640124	−	0.308268i
$431$	−9.09444	+	39.8453i	−0.438064	+	1.91928i	−0.0470626	+	0.998892i	$0.514986\pi$
$431$	−9.09444	+	39.8453i	−0.438064	+	1.91928i	−0.391001	+	0.920390i	$0.627871\pi$
$432$		0			0
$433$	1.80181	+	7.89427i	0.0865897	+	0.379374i	0.999591	−	0.0285813i	$-0.00909896\pi$
$433$	1.80181	+	7.89427i	0.0865897	+	0.379374i	−0.913002	+	0.407956i	$0.866242\pi$
$434$	10.0621	−	23.3866i	0.482995	−	1.12259i
$435$		0			0
$436$	−0.271662	−	1.19023i	−0.0130102	−	0.0570015i
$437$	8.86496	+	11.1163i	0.424068	+	0.531765i
$438$		0			0
$439$	15.5540	+	7.49041i	0.742351	+	0.357498i	0.766529	−	0.642210i	$-0.221982\pi$
$439$	15.5540	+	7.49041i	0.742351	+	0.357498i	−0.0241772	+	0.999708i	$0.507697\pi$
$440$	12.2121			0.582188
$441$		0			0
$442$	3.10452			0.147667
$443$	−7.85071	−	3.78070i	−0.372999	−	0.179627i	0.237987	−	0.971268i	$-0.423512\pi$
$443$	−7.85071	−	3.78070i	−0.372999	−	0.179627i	−0.610986	+	0.791642i	$0.709227\pi$
$444$		0			0
$445$	−13.0151	−	16.3205i	−0.616976	−	0.773664i
$446$	−3.74940	−	16.4272i	−0.177539	−	0.777850i
$447$		0			0
$448$	10.5442	+	19.7071i	0.498166	+	0.931072i
$449$	4.09699	+	17.9501i	0.193349	+	0.847116i	0.974788	+	0.223134i	$0.0716289\pi$
$449$	4.09699	+	17.9501i	0.193349	+	0.847116i	−0.781439	+	0.623982i	$0.785514\pi$
$450$		0			0
$451$	5.60458	−	24.5553i	0.263909	−	1.15626i
$452$	−0.224441	−	0.108085i	−0.0105568	−	0.00508389i
$453$		0			0
$454$	33.4549	+	16.1110i	1.57011	+	0.756127i
$455$	3.45894	+	0.636243i	0.162157	+	0.0298276i
$456$		0			0
$457$	−4.09147	+	17.9259i	−0.191391	+	0.838539i	0.784474	+	0.620162i	$0.212933\pi$
$457$	−4.09147	+	17.9259i	−0.191391	+	0.838539i	−0.975865	+	0.218377i	$0.929924\pi$
$458$	−5.81903	+	7.29684i	−0.271905	+	0.340959i
$459$		0			0
$460$	−0.940319			−0.0438426
$461$	−9.24568	+	11.5937i	−0.430614	+	0.539973i	−0.949043	−	0.315148i	$-0.897946\pi$
$461$	−9.24568	+	11.5937i	−0.430614	+	0.539973i	0.518428	+	0.855121i	$0.326517\pi$
$462$		0			0
$463$	22.3950	+	28.0825i	1.04079	+	1.30510i	0.951016	+	0.309142i	$0.100042\pi$
$463$	22.3950	+	28.0825i	1.04079	+	1.30510i	0.0897702	+	0.995963i	$0.471387\pi$
$464$	−1.24694	−	1.56361i	−0.0578876	−	0.0725888i
$465$		0			0
$466$	−15.1775	+	7.30912i	−0.703086	+	0.338588i
$467$	17.5831	+	22.0485i	0.813647	+	1.02028i	0.999290	+	0.0376636i	$0.0119915\pi$
$467$	17.5831	+	22.0485i	0.813647	+	1.02028i	−0.185644	+	0.982617i	$0.559437\pi$
$468$		0			0
$469$	−0.633555	−	14.9014i	−0.0292549	−	0.688082i
$470$	6.56805	−	8.23608i	0.302962	−	0.379902i
$471$		0			0
$472$	31.1919			1.43573
$473$	−15.1161	+	18.9550i	−0.695040	+	0.871552i
$474$		0			0
$475$	7.53352	−	3.62795i	0.345662	−	0.166462i
$476$	−0.0338281	−	0.795647i	−0.00155051	−	0.0364684i
$477$		0			0
$478$	−7.75595	+	9.72566i	−0.354749	+	0.444841i
$479$	−27.8491	−	13.4114i	−1.27246	−	0.612783i	−0.329016	−	0.944324i	$-0.606717\pi$
$479$	−27.8491	−	13.4114i	−1.27246	−	0.612783i	−0.943441	+	0.331542i	$0.892431\pi$
$480$		0			0
$481$	−3.65588	+	1.76058i	−0.166694	+	0.0802755i
$482$	−8.38651	−	36.7437i	−0.381995	−	1.67363i
$483$		0			0
$484$	−0.0448740	+	0.196606i	−0.00203973	+	0.00893662i
$485$	4.32664	+	18.9563i	0.196463	+	0.860759i
$486$		0			0
$487$	−1.70289	−	7.46087i	−0.0771655	−	0.338084i	0.921578	−	0.388193i	$-0.126900\pi$
$487$	−1.70289	−	7.46087i	−0.0771655	−	0.338084i	−0.998744	+	0.0501084i	$0.984043\pi$
$488$	8.85677	+	4.26520i	0.400927	+	0.193076i
$489$		0			0
$490$	−1.81609	+	12.9418i	−0.0820428	+	0.584650i
$491$	−4.29477			−0.193820			−0.0969100	−	0.995293i	$-0.530896\pi$
$491$	−4.29477			−0.193820			−0.0969100	+	0.995293i	$0.530896\pi$
$492$		0			0
$493$	0.278436	+	1.21991i	0.0125401	+	0.0549418i
$494$	−2.21379	−	2.77600i	−0.0996030	−	0.124898i
$495$		0			0
$496$	5.83148	−	25.5494i	0.261841	−	1.14720i
$497$	−24.1147	+	20.9670i	−1.08169	+	0.940499i
$498$		0			0
$499$	−24.6474	+	11.8696i	−1.10337	+	0.531355i	−0.894717	−	0.446634i	$-0.852623\pi$
$499$	−24.6474	+	11.8696i	−1.10337	+	0.531355i	−0.208654	+	0.977989i	$0.566908\pi$
$500$	−0.319183	+	1.39843i	−0.0142743	+	0.0625399i
$501$		0			0
$502$	18.8941	−	23.6924i	0.843283	−	1.05744i
$503$	−19.5969	−	9.43736i	−0.873781	−	0.420791i	−0.0574320	−	0.998349i	$-0.518291\pi$
$503$	−19.5969	−	9.43736i	−0.873781	−	0.420791i	−0.816349	+	0.577559i	$0.804006\pi$
$504$		0			0
$505$	−15.6728	+	7.54762i	−0.697431	+	0.335865i
$506$	4.98782	−	21.8531i	0.221736	−	0.971488i
$507$		0			0
$508$	−0.0383727			−0.00170251
$509$	−18.9541			−0.840126			−0.420063	−	0.907495i	$-0.637992\pi$
$509$	−18.9541			−0.840126			−0.420063	+	0.907495i	$0.637992\pi$
$510$		0			0
$511$	−0.0619810	−	0.115842i	−0.00274188	−	0.00512457i
$512$	15.2215	+	19.0871i	0.672700	+	0.843539i
$513$		0			0
$514$	−33.2324	+	16.0039i	−1.46582	+	0.705901i
$515$	22.3347	−	10.7558i	0.984183	−	0.473958i
$516$		0			0
$517$	−10.8083	−	13.5532i	−0.475350	−	0.596070i
$518$	−7.11324	−	13.2946i	−0.312538	−	0.584132i
$519$		0			0
$520$	3.87119			0.169763
$521$	17.6678			0.774042			0.387021	−	0.922071i	$-0.373504\pi$
$521$	17.6678			0.774042			0.387021	+	0.922071i	$0.373504\pi$
$522$		0			0
$523$	3.50381	−	15.3512i	0.153211	−	0.671261i	−0.838729	−	0.544550i	$-0.816701\pi$
$523$	3.50381	−	15.3512i	0.153211	−	0.671261i	0.991940	−	0.126711i	$-0.0404422\pi$
$524$	−1.42391	+	0.685717i	−0.0622036	+	0.0299557i
$525$		0			0
$526$	35.6520	+	17.1691i	1.55450	+	0.748608i
$527$	−10.2230	+	12.8192i	−0.445319	+	0.558412i
$528$		0			0
$529$	−1.21353	+	5.31680i	−0.0527620	+	0.231165i
$530$	−17.1768	+	8.27189i	−0.746111	+	0.359308i
$531$		0			0
$532$	−0.687329	+	0.597612i	−0.0297995	+	0.0259098i
$533$	1.77664	−	7.78395i	0.0769546	−	0.337160i
$534$		0			0
$535$	−3.01585	−	3.78175i	−0.130386	−	0.163499i
$536$	−3.65314	−	16.0055i	−0.157792	−	0.691331i
$537$		0			0
$538$	−2.21271			−0.0953967
$539$	20.0979	+	7.65262i	0.865679	+	0.329622i
$540$		0			0
$541$	0.0621748	+	0.0299418i	0.00267310	+	0.00128730i	0.435220	−	0.900324i	$-0.356671\pi$
$541$	0.0621748	+	0.0299418i	0.00267310	+	0.00128730i	−0.432547	+	0.901612i	$0.642385\pi$
$542$	6.40615	+	28.0672i	0.275168	+	1.20559i
$543$		0			0
$544$	−0.378281	−	1.65736i	−0.0162187	−	0.0710586i
$545$	2.87107	−	12.5790i	0.122983	−	0.538824i
$546$		0			0
$547$	−8.04313	−	35.2393i	−0.343899	−	1.50672i	−0.790765	−	0.612120i	$-0.790317\pi$
$547$	−8.04313	−	35.2393i	−0.343899	−	1.50672i	0.446865	−	0.894601i	$-0.352540\pi$
$548$	0.640995	−	0.308687i	0.0273819	−	0.0131864i
$549$		0			0
$550$	−11.8766	−	5.71945i	−0.506418	−	0.243878i
$551$	0.892268	−	1.11887i	0.0380119	−	0.0476654i
$552$		0			0
$553$	−0.799392	−	18.8019i	−0.0339936	−	0.799539i
$554$	11.8864	−	5.72418i	0.505004	−	0.243197i
$555$		0			0
$556$	0.986638	−	1.23720i	0.0418428	−	0.0524692i
$557$	2.13155			0.0903168			0.0451584	−	0.998980i	$-0.485621\pi$
$557$	2.13155			0.0903168			0.0451584	+	0.998980i	$0.485621\pi$
$558$		0			0
$559$	−4.79176	+	6.00868i	−0.202670	+	0.254140i
$560$	0.571419	+	13.4399i	0.0241468	+	0.567940i
$561$		0			0
$562$	−10.3464	−	12.9740i	−0.436436	−	0.547274i
$563$	−31.2599	+	15.0540i	−1.31745	+	0.634450i	−0.954737	−	0.297452i	$-0.903863\pi$
$563$	−31.2599	+	15.0540i	−1.31745	+	0.634450i	−0.362712	+	0.931901i	$0.618149\pi$
$564$		0			0
$565$	−1.64148	−	2.05835i	−0.0690577	−	0.0865956i
$566$	−2.38338	−	2.98867i	−0.100181	−	0.125623i
$567$		0			0
$568$	−21.9304	+	27.4999i	−0.920181	+	1.15387i
$569$	19.9857			0.837846			0.418923	−	0.908022i	$-0.362408\pi$
$569$	19.9857			0.837846			0.418923	+	0.908022i	$0.362408\pi$
$570$		0			0
$571$	25.9512	−	32.5418i	1.08602	−	1.36183i	0.158805	−	0.987310i	$-0.449236\pi$
$571$	25.9512	−	32.5418i	1.08602	−	1.36183i	0.927219	−	0.374520i	$-0.122193\pi$
$572$	0.0859859	−	0.376729i	0.00359525	−	0.0157518i
$573$		0			0
$574$	29.1785	+	5.36715i	1.21789	+	0.224020i
$575$	15.0760	+	7.26023i	0.628714	+	0.302772i
$576$		0			0
$577$	−38.1943	−	18.3934i	−1.59005	−	0.765728i	−0.590893	−	0.806750i	$-0.701224\pi$
$577$	−38.1943	−	18.3934i	−1.59005	−	0.765728i	−0.999158	+	0.0410216i	$0.986939\pi$
$578$	−3.52095	+	15.4263i	−0.146452	+	0.641650i
$579$		0			0
$580$	0.0210603	+	0.0922713i	0.000874482	+	0.00383136i
$581$	4.03280	+	7.53729i	0.167309	+	0.312699i
$582$		0			0
$583$	6.98111	+	30.5862i	0.289128	+	1.26675i
$584$	−0.0901655	−	0.113064i	−0.00373108	−	0.00467862i
$585$		0			0
$586$	−16.7639	−	8.07308i	−0.692512	−	0.333496i
$587$	19.7402			0.814766			0.407383	−	0.913257i	$-0.366441\pi$
$587$	19.7402			0.814766			0.407383	+	0.913257i	$0.366441\pi$
$588$		0			0
$589$	18.7525			0.772682
$590$	18.0159	+	8.67602i	0.741705	+	0.357186i
$591$		0			0
$592$	−9.67681	−	12.1343i	−0.397714	−	0.498718i
$593$	−8.24385	−	36.1187i	−0.338534	−	1.48322i	−0.802119	−	0.597164i	$-0.796294\pi$
$593$	−8.24385	−	36.1187i	−0.338534	−	1.48322i	0.463585	−	0.886052i	$-0.346563\pi$
$594$		0			0
$595$	3.32634	−	7.73121i	0.136367	−	0.316949i
$596$	−0.331975	−	1.45448i	−0.0135982	−	0.0595777i
$597$		0			0
$598$	1.58113	−	6.92736i	0.0646570	−	0.283281i
$599$	−10.9740	−	5.28478i	−0.448384	−	0.215930i	0.196045	−	0.980595i	$-0.437190\pi$
$599$	−10.9740	−	5.28478i	−0.448384	−	0.215930i	−0.644428	+	0.764665i	$0.722905\pi$
$600$		0			0
$601$	8.79677	+	4.23630i	0.358828	+	0.172802i	0.604608	−	0.796523i	$-0.293330\pi$
$601$	8.79677	+	4.23630i	0.358828	+	0.172802i	−0.245780	+	0.969326i	$0.579044\pi$
$602$	−23.0637	−	16.8411i	−0.940005	−	0.686391i
$603$		0			0
$604$	0.259135	−	1.13534i	0.0105440	−	0.0461964i
$605$	−1.32883	+	1.66629i	−0.0540245	+	0.0677445i
$606$		0			0
$607$	6.64364			0.269657			0.134828	−	0.990869i	$-0.456952\pi$
$607$	6.64364			0.269657			0.134828	+	0.990869i	$0.456952\pi$
$608$	−1.21223	+	1.52009i	−0.0491624	+	0.0616477i
$609$		0			0
$610$	3.92916	+	4.92701i	0.159087	+	0.199489i
$611$	−3.42621	−	4.29633i	−0.138610	−	0.173811i
$612$		0			0
$613$	30.8612	−	14.8620i	1.24647	−	0.600269i	0.309907	−	0.950767i	$-0.399702\pi$
$613$	30.8612	−	14.8620i	1.24647	−	0.600269i	0.936563	+	0.350498i	$0.113988\pi$
$614$	0.0705754	+	0.0884988i	0.00284819	+	0.00357152i
$615$		0			0
$616$	23.2810	+	4.28236i	0.938019	+	0.172541i
$617$	28.1392	−	35.2854i	1.13284	−	1.42054i	0.239648	−	0.970860i	$-0.422968\pi$
$617$	28.1392	−	35.2854i	1.13284	−	1.42054i	0.893192	−	0.449676i	$-0.148461\pi$
$618$		0			0
$619$	6.50579			0.261490			0.130745	−	0.991416i	$-0.458263\pi$
$619$	6.50579			0.261490			0.130745	+	0.991416i	$0.458263\pi$
$620$	−0.773243	+	0.969616i	−0.0310542	+	0.0389407i
$621$		0			0
$622$	30.2004	−	14.5437i	1.21092	−	0.583150i
$623$	−19.0889	−	35.6771i	−0.764781	−	1.42937i
$624$		0			0
$625$	0.327523	−	0.410701i	0.0131009	−	0.0164280i
$626$	−2.23036	−	1.07409i	−0.0891431	−	0.0429291i
$627$		0			0
$628$	−1.08649	+	0.523225i	−0.0433556	+	0.0208789i
$629$	2.16079	+	9.46704i	0.0861564	+	0.377476i
$630$		0			0
$631$	−0.544022	+	2.38351i	−0.0216572	+	0.0948862i	−0.984601	−	0.174814i	$-0.944068\pi$
$631$	−0.544022	+	2.38351i	−0.0216572	+	0.0948862i	0.962944	+	0.269700i	$0.0869247\pi$
$632$	−4.60937	−	20.1950i	−0.183351	−	0.803313i
$633$		0			0
$634$	−7.64914	−	33.5131i	−0.303786	−	1.33097i
$635$	−0.365382	−	0.175959i	−0.0144997	−	0.00698270i
$636$		0			0
$637$	6.37098	+	2.42586i	0.252427	+	0.0961160i
$638$	−2.25610			−0.0893199
$639$		0			0
$640$	3.06638	+	13.4347i	0.121209	+	0.531053i
$641$	−20.6318	−	25.8714i	−0.814906	−	1.02186i	−0.999239	−	0.0389959i	$-0.987584\pi$
$641$	−20.6318	−	25.8714i	−0.814906	−	1.02186i	0.184333	−	0.982864i	$-0.440987\pi$
$642$		0			0
$643$	9.81691	−	43.0107i	0.387141	−	1.69618i	−0.287295	−	0.957842i	$-0.592756\pi$
$643$	9.81691	−	43.0107i	0.387141	−	1.69618i	0.674436	−	0.738333i	$-0.264387\pi$
$644$	−1.79262	−	0.329738i	−0.0706390	−	0.0129935i
$645$		0			0
$646$	−7.65554	+	3.68671i	−0.301203	+	0.145052i
$647$	−4.42883	+	19.4040i	−0.174115	+	0.762849i	0.810160	+	0.586209i	$0.199380\pi$
$647$	−4.42883	+	19.4040i	−0.174115	+	0.762849i	−0.984275	+	0.176640i	$0.943477\pi$
$648$		0			0
$649$	20.5163	−	25.7266i	0.805335	−	1.00986i
$650$	−3.76483	−	1.81305i	−0.147669	−	0.0711136i
$651$		0			0
$652$	−0.0558461	+	0.0268941i	−0.00218710	+	0.00105325i
$653$	0.0455981	−	0.199778i	0.00178439	−	0.00781793i	−0.974028	−	0.226428i	$-0.927295\pi$
$653$	0.0455981	−	0.199778i	0.00178439	−	0.00781793i	0.975812	+	0.218610i	$0.0701523\pi$
$654$		0			0
$655$	−16.7027			−0.652628
$656$	30.5385			1.19233
$657$		0			0
$658$	15.4094	−	13.3980i	0.600721	−	0.522309i
$659$	−10.7159	−	13.4373i	−0.417432	−	0.523444i	0.528008	−	0.849240i	$-0.322939\pi$
$659$	−10.7159	−	13.4373i	−0.417432	−	0.523444i	−0.945440	+	0.325796i	$0.894368\pi$
$660$		0			0
$661$	−42.2869	+	20.3643i	−1.64477	+	0.792080i	−0.645164	+	0.764044i	$0.723211\pi$
$661$	−42.2869	+	20.3643i	−1.64477	+	0.792080i	−0.999607	+	0.0280354i	$0.991075\pi$
$662$	−24.7411	+	11.9147i	−0.961588	+	0.463076i
$663$		0			0
$664$	5.86662	+	7.35651i	0.227669	+	0.285488i
$665$	−9.28506	+	2.53866i	−0.360059	+	0.0984450i
$666$		0			0
$667$	2.86388			0.110890
$668$	0.687796			0.0266116
$669$		0			0
$670$	2.34192	−	10.2606i	0.0904761	−	0.396402i
$671$	9.34334	−	4.49952i	0.360696	−	0.173702i
$672$		0			0
$673$	37.8113	+	18.2090i	1.45752	+	0.701904i	0.983883	−	0.178816i	$-0.0572266\pi$
$673$	37.8113	+	18.2090i	1.45752	+	0.701904i	0.473637	+	0.880720i	$0.342941\pi$
$674$	7.61322	−	9.54667i	0.293250	−	0.367724i
$675$		0			0
$676$	−0.346346	+	1.51744i	−0.0133210	+	0.0583631i
$677$	39.2998	−	18.9258i	1.51041	−	0.727377i	0.518594	−	0.855021i	$-0.326456\pi$
$677$	39.2998	−	18.9258i	1.51041	−	0.727377i	0.991820	+	0.127644i	$0.0407414\pi$
$678$		0			0
$679$	1.60097	+	37.6553i	0.0614397	+	1.44508i
$680$	2.06146	−	9.03185i	0.0790535	−	0.346356i
$681$		0			0
$682$	−18.4324	−	23.1134i	−0.705812	−	0.885060i
$683$	−4.69196	−	20.5568i	−0.179533	−	0.786585i	−0.981846	−	0.189681i	$-0.939255\pi$
$683$	−4.69196	−	20.5568i	−0.179533	−	0.786585i	0.802313	−	0.596904i	$-0.203603\pi$
$684$		0			0
$685$	7.51899			0.287286
$686$	−8.00043	+	24.0353i	−0.305458	+	0.917671i
$687$		0			0
$688$	−26.4848	−	12.7544i	−1.00972	−	0.486257i
$689$	2.21299	+	9.69574i	0.0843082	+	0.369378i
$690$		0			0
$691$	−0.0774778	−	0.339452i	−0.00294739	−	0.0129134i	0.973433	−	0.228973i	$-0.0735367\pi$
$691$	−0.0774778	−	0.339452i	−0.00294739	−	0.0129134i	−0.976380	+	0.216059i	$0.930680\pi$
$692$	0.601695	−	2.63620i	0.0228730	−	0.100213i
$693$		0			0
$694$	−5.93602	−	26.0074i	−0.225328	−	0.987227i
$695$	15.0679	−	7.25633i	0.571559	−	0.275248i
$696$		0			0
$697$	−17.2146	−	8.29011i	−0.652049	−	0.314010i
$698$	−13.0028	+	16.3050i	−0.492162	+	0.617152i
$699$		0			0
$700$	−0.423637	+	0.984632i	−0.0160120	+	0.0372156i
$701$	7.45026	−	3.58785i	0.281392	−	0.135511i	−0.287865	−	0.957671i	$-0.592945\pi$
$701$	7.45026	−	3.58785i	0.281392	−	0.135511i	0.569257	+	0.822160i	$0.307231\pi$
$702$		0			0
$703$	6.92441	−	8.68294i	0.261159	−	0.327483i
$704$	25.9533			0.978152
$705$		0			0
$706$	25.5801	−	32.0764i	0.962719	−	1.20721i
$707$	−32.5252	+	8.89282i	−1.22324	+	0.334449i
$708$		0			0
$709$	21.7610	+	27.2874i	0.817252	+	1.02480i	0.999139	+	0.0414821i	$0.0132080\pi$
$709$	21.7610	+	27.2874i	0.817252	+	1.02480i	−0.181887	+	0.983319i	$0.558221\pi$
$710$	−20.3157	+	9.78355i	−0.762436	+	0.367170i
$711$		0			0
$712$	−27.7692	−	34.8214i	−1.04069	−	1.30499i
$713$	23.3979	+	29.3400i	0.876258	+	1.09879i
$714$		0			0
$715$	2.54625	−	3.19290i	0.0952244	−	0.119408i
$716$	3.14906			0.117686
$717$		0			0
$718$	−21.5406	+	27.0110i	−0.803888	+	1.00804i
$719$	6.95956	−	30.4918i	0.259548	−	1.13715i	−0.662189	−	0.749337i	$-0.730372\pi$
$719$	6.95956	−	30.4918i	0.259548	−	1.13715i	0.921737	−	0.387816i	$-0.126770\pi$
$720$		0			0
$721$	46.3503	−	12.6728i	1.72618	−	0.471960i
$722$	−14.6588	−	7.05928i	−0.545542	−	0.262719i
$723$		0			0
$724$	0.499649	+	0.240618i	0.0185693	+	0.00894250i
$725$	0.374771	−	1.64198i	0.0139187	−	0.0609816i
$726$		0			0
$727$	2.42932	+	10.6435i	0.0900983	+	0.394747i	0.999789	−	0.0205399i	$-0.00653850\pi$
$727$	2.42932	+	10.6435i	0.0900983	+	0.394747i	−0.909691	+	0.415286i	$0.863681\pi$
$728$	7.38001	+	1.35749i	0.273521	+	0.0503121i
$729$		0			0
$730$	−0.0206294	−	0.0903833i	−0.000763529	−	0.00334524i
$731$	11.4671	+	14.3793i	0.424127	+	0.531839i
$732$		0			0
$733$	−14.5759	−	7.01938i	−0.538373	−	0.259267i	0.144879	−	0.989449i	$-0.453721\pi$
$733$	−14.5759	−	7.01938i	−0.538373	−	0.259267i	−0.683252	+	0.730183i	$0.739435\pi$
$734$	−27.3581			−1.00980
$735$		0			0
$736$	−3.89085			−0.143419
$737$	−15.6039	−	7.51443i	−0.574776	−	0.276798i
$738$		0			0
$739$	−24.0593	−	30.1694i	−0.885037	−	1.10980i	−0.993287	−	0.115677i	$-0.963096\pi$
$739$	−24.0593	−	30.1694i	−0.885037	−	1.10980i	0.108250	−	0.994124i	$-0.465475\pi$
$740$	0.163438	+	0.716068i	0.00600809	+	0.0263232i
$741$		0			0
$742$	−35.6463	+	9.74617i	−1.30862	+	0.357793i
$743$	0.788165	+	3.45318i	0.0289150	+	0.126685i	0.987326	−	0.158708i	$-0.0507330\pi$
$743$	0.788165	+	3.45318i	0.0289150	+	0.126685i	−0.958411	+	0.285393i	$0.907876\pi$
$744$		0			0
$745$	3.50849	−	15.3717i	0.128541	−	0.563176i
$746$	−24.1776	−	11.6433i	−0.885205	−	0.426292i
$747$		0			0
$748$	−0.833155	−	0.401226i	−0.0304632	−	0.0146703i
$749$	−4.42326	−	8.26706i	−0.161622	−	0.302072i
$750$		0			0
$751$	−3.21027	+	14.0651i	−0.117144	+	0.513243i	0.881975	+	0.471295i	$0.156213\pi$
$751$	−3.21027	+	14.0651i	−0.117144	+	0.513243i	−0.999120	+	0.0419476i	$0.986644\pi$
$752$	13.1049	−	16.4331i	0.477887	−	0.599252i
$753$		0			0
$754$	−0.715178			−0.0260452
$755$	7.67360	−	9.62239i	0.279271	−	0.350194i
$756$		0			0
$757$	2.98420	+	3.74206i	0.108462	+	0.136008i	0.833100	−	0.553123i	$-0.186564\pi$
$757$	2.98420	+	3.74206i	0.108462	+	0.136008i	−0.724637	+	0.689131i	$0.757993\pi$
$758$	27.6546	+	34.6778i	1.00446	+	1.25955i
$759$		0			0
$760$	−9.54610	+	4.59716i	−0.346273	+	0.166757i
$761$	12.7722	+	16.0158i	0.462990	+	0.580572i	0.957439	−	0.288635i	$-0.0932015\pi$
$761$	12.7722	+	16.0158i	0.462990	+	0.580572i	−0.494449	+	0.869207i	$0.664630\pi$
$762$		0			0
$763$	9.88439	−	22.9737i	0.357839	−	0.831703i
$764$	−0.455551	+	0.571243i	−0.0164812	+	0.0206668i
$765$		0			0
$766$	28.6651			1.03571
$767$	6.50360	−	8.15526i	0.234831	−	0.294469i
$768$		0			0
$769$	20.4061	−	9.82708i	0.735864	−	0.354374i	−0.0281233	−	0.999604i	$-0.508953\pi$
$769$	20.4061	−	9.82708i	0.735864	−	0.354374i	0.763988	+	0.645231i	$0.223239\pi$
$770$	12.2556	+	8.94902i	0.441661	+	0.322500i
$771$		0			0
$772$	−0.0832818	+	0.104432i	−0.00299738	+	0.00375859i
$773$	−29.1120	−	14.0196i	−1.04709	−	0.504251i	−0.170432	−	0.985369i	$-0.554516\pi$
$773$	−29.1120	−	14.0196i	−1.04709	−	0.504251i	−0.876655	+	0.481119i	$0.840231\pi$
$774$		0			0
$775$	19.8837	−	9.57550i	0.714245	−	0.343962i
$776$	9.23136	+	40.4452i	0.331386	+	1.45190i
$777$		0			0
$778$	−2.76887	+	12.1312i	−0.0992686	+	0.434924i
$779$	4.86261	+	21.3045i	0.174221	+	0.763313i
$780$		0			0
$781$	8.25688	+	36.1758i	0.295454	+	1.29447i
$782$	−15.3202	−	7.37783i	−0.547850	−	0.263830i
$783$		0			0
$784$	−3.62357	+	25.8221i	−0.129413	+	0.922219i
$785$	−12.7447			−0.454878
$786$		0			0
$787$	7.85332	+	34.4076i	0.279941	+	1.22650i	0.897868	+	0.440265i	$0.145115\pi$
$787$	7.85332	+	34.4076i	0.279941	+	1.22650i	−0.617927	+	0.786235i	$0.712027\pi$
$788$	−0.990946	−	1.24261i	−0.0353010	−	0.0442660i
$789$		0			0
$790$	2.95493	−	12.9464i	0.105132	−	0.460611i
$791$	−2.40752	−	4.49964i	−0.0856014	−	0.159989i
$792$		0			0
$793$	2.96181	−	1.42633i	0.105177	−	0.0506506i
$794$	4.46574	−	19.5657i	0.158483	−	0.694361i
$795$		0			0
$796$	1.65126	−	2.07062i	0.0585275	−	0.0733912i
$797$	18.1781	+	8.75413i	0.643903	+	0.310087i	0.727188	−	0.686438i	$-0.240827\pi$
$797$	18.1781	+	8.75413i	0.643903	+	0.310087i	−0.0832850	+	0.996526i	$0.526541\pi$
$798$		0			0
$799$	−11.8482	+	5.70581i	−0.419161	+	0.201857i
$800$	−0.509162	+	2.23078i	−0.0180016	+	0.0788701i
$801$		0			0
$802$	−0.612644			−0.0216332
$803$	−0.152559			−0.00538369
$804$		0			0
$805$	−15.5572	−	11.3598i	−0.548318	−	0.400381i
$806$	−5.84300	−	7.32689i	−0.205811	−	0.258079i
$807$		0			0
$808$	−33.4396	+	16.1037i	−1.17640	+	0.566525i
$809$	−11.3346	+	5.45847i	−0.398504	+	0.191909i	−0.622392	−	0.782705i	$-0.713839\pi$
$809$	−11.3346	+	5.45847i	−0.398504	+	0.191909i	0.223888	+	0.974615i	$0.428125\pi$
$810$		0			0
$811$	−7.84887	−	9.84218i	−0.275611	−	0.345606i	0.624690	−	0.780873i	$-0.285225\pi$
$811$	−7.84887	−	9.84218i	−0.275611	−	0.345606i	−0.900301	+	0.435267i	$0.856654\pi$
$812$	0.00779287	+	0.183290i	0.000273476	+	0.00643223i
$813$		0			0
$814$	−17.5084			−0.613669
$815$	−0.655086			−0.0229466
$816$		0			0
$817$	4.68067	−	20.5074i	0.163756	−	0.717462i
$818$	−43.4534	+	20.9260i	−1.51931	+	0.731662i
$819$		0			0
$820$	−1.30208	−	0.627047i	−0.0454705	−	0.0218974i
$821$	15.7150	−	19.7060i	0.548456	−	0.687743i	−0.427921	−	0.903816i	$-0.640754\pi$
$821$	15.7150	−	19.7060i	0.548456	−	0.687743i	0.976377	+	0.216074i	$0.0693251\pi$
$822$		0			0
$823$	5.43595	−	23.8165i	0.189485	−	0.830190i	−0.787403	−	0.616439i	$-0.788575\pi$
$823$	5.43595	−	23.8165i	0.189485	−	0.830190i	0.976888	−	0.213751i	$-0.0685681\pi$
$824$	47.6534	−	22.9487i	1.66009	−	0.799455i
$825$		0			0
$826$	31.3031	+	22.8575i	1.08917	+	0.795313i
$827$	2.60450	−	11.4111i	0.0905673	−	0.396801i	−0.909243	−	0.416265i	$-0.863339\pi$
$827$	2.60450	−	11.4111i	0.0905673	−	0.396801i	0.999811	+	0.0194639i	$0.00619594\pi$
$828$		0			0
$829$	−26.7167	−	33.5017i	−0.927909	−	1.16356i	−0.986249	−	0.165264i	$-0.947152\pi$
$829$	−26.7167	−	33.5017i	−0.927909	−	1.16356i	0.0583403	−	0.998297i	$-0.481419\pi$
$830$	1.34225	+	5.88080i	0.0465903	+	0.204125i
$831$		0			0
$832$	8.22712			0.285224
$833$	9.05239	−	13.5723i	0.313647	−	0.470252i
$834$		0			0
$835$	6.54914	+	3.15390i	0.226642	+	0.109145i
$836$	0.235342	+	1.03110i	0.00813946	+	0.0356613i
$837$		0			0
$838$	2.12977	+	9.33111i	0.0735715	+	0.322338i
$839$	−11.7286	+	51.3864i	−0.404917	+	1.77406i	0.202099	+	0.979365i	$0.435224\pi$
$839$	−11.7286	+	51.3864i	−0.404917	+	1.77406i	−0.607015	+	0.794690i	$0.707633\pi$
$840$		0			0
$841$	6.38896	+	27.9919i	0.220309	+	0.965237i
$842$	−44.9098	+	21.6274i	−1.54769	+	0.745330i
$843$		0			0
$844$	−0.788370	−	0.379659i	−0.0271368	−	0.0130684i
$845$	−10.2561	+	12.8608i	−0.352821	+	0.442424i
$846$		0			0
$847$	−3.11758	+	2.71064i	−0.107121	+	0.0931386i
$848$	−34.2720	+	16.5045i	−1.17690	+	0.566767i
$849$		0			0
$850$	−6.23484	+	7.81824i	−0.213853	+	0.268163i
$851$	22.2250			0.761864
$852$		0			0
$853$	−32.6804	+	40.9800i	−1.11896	+	1.40313i	−0.214415	+	0.976743i	$0.568785\pi$
$853$	−32.6804	+	40.9800i	−1.11896	+	1.40313i	−0.904542	+	0.426385i	$0.859787\pi$
$854$	5.76279	+	10.7706i	0.197199	+	0.368564i
$855$		0			0
$856$	−6.43463	−	8.06878i	−0.219931	−	0.275785i
$857$	5.83518	−	2.81007i	0.199326	−	0.0959903i	−0.331558	−	0.943435i	$-0.607574\pi$
$857$	5.83518	−	2.81007i	0.199326	−	0.0959903i	0.530884	+	0.847445i	$0.321860\pi$
$858$		0			0
$859$	16.0885	+	20.1744i	0.548934	+	0.688342i	0.976469	−	0.215657i	$-0.0691894\pi$
$859$	16.0885	+	20.1744i	0.548934	+	0.688342i	−0.427535	+	0.903999i	$0.640618\pi$
$860$	0.867351	+	1.08762i	0.0295764	+	0.0370877i
$861$		0			0
$862$	−34.8541	+	43.7056i	−1.18714	+	1.48862i
$863$	30.6376			1.04292			0.521459	−	0.853276i	$-0.325388\pi$
$863$	30.6376			1.04292			0.521459	+	0.853276i	$0.325388\pi$
$864$		0			0
$865$	17.8176	−	22.3426i	0.605818	−	0.759671i
$866$	−2.46450	+	10.7977i	−0.0837473	+	0.366921i
$867$		0			0
$868$	−1.81412	+	1.57732i	−0.0615751	+	0.0535377i
$869$	−19.6883	−	9.48137i	−0.667879	−	0.321634i
$870$		0			0
$871$	−4.94638	−	2.38205i	−0.167602	−	0.0807127i
$872$	6.12573	−	26.8386i	0.207443	−	0.908869i
$873$		0			0
$874$	4.32751	+	18.9600i	0.146380	+	0.641333i
$875$	−22.1750	+	19.2805i	−0.749650	+	0.651799i
$876$		0			0
$877$	−2.84514	−	12.4654i	−0.0960736	−	0.420926i	0.903903	−	0.427737i	$-0.140689\pi$
$877$	−2.84514	−	12.4654i	−0.0960736	−	0.420926i	−0.999977	+	0.00681115i	$0.997832\pi$
$878$	14.7225	+	18.4614i	0.496859	+	0.623042i
$879$		0			0
$880$	14.0735	+	6.77744i	0.474418	+	0.228468i
$881$	28.3450			0.954968			0.477484	−	0.878640i	$-0.341549\pi$
$881$	28.3450			0.954968			0.477484	+	0.878640i	$0.341549\pi$
$882$		0			0
$883$	34.4175			1.15824			0.579120	−	0.815242i	$-0.303396\pi$
$883$	34.4175			1.15824			0.579120	+	0.815242i	$0.303396\pi$
$884$	−0.264108	−	0.127188i	−0.00888290	−	0.00427778i
$885$		0			0
$886$	−7.43101	−	9.31819i	−0.249650	−	0.313051i
$887$	5.44504	+	23.8563i	0.182826	+	0.801015i	0.980277	+	0.197630i	$0.0633245\pi$
$887$	5.44504	+	23.8563i	0.182826	+	0.801015i	−0.797450	+	0.603385i	$0.793818\pi$
$888$		0			0
$889$	−0.634858	−	0.463573i	−0.0212925	−	0.0155477i
$890$	−6.35345	−	27.8363i	−0.212968	−	0.933074i
$891$		0			0
$892$	−0.354029	+	1.55110i	−0.0118538	+	0.0519347i
$893$	13.5508	+	6.52573i	0.453461	+	0.218375i
$894$		0			0
$895$	29.9851	+	14.4401i	1.00229	+	0.482678i
$896$	1.13464	+	26.6871i	0.0379057	+	0.891553i
$897$		0			0
$898$	−5.60382	+	24.5519i	−0.187002	+	0.819308i
$899$	2.35502	−	2.95311i	0.0785445	−	0.0984917i
$900$		0			0
$901$	23.7995			0.792877
$902$	21.4794	−	26.9343i	0.715184	−	0.896813i
$903$		0			0
$904$	−3.50228	−	4.39172i	−0.116484	−	0.146066i
$905$	3.65426	+	4.58230i	0.121472	+	0.152321i
$906$		0			0
$907$	−11.0794	+	5.33556i	−0.367885	+	0.177164i	−0.608688	−	0.793410i	$-0.708304\pi$
$907$	−11.0794	+	5.33556i	−0.367885	+	0.177164i	0.240802	+	0.970574i	$0.422589\pi$
$908$	−2.18603	−	2.74119i	−0.0725458	−	0.0909696i
$909$		0			0
$910$	3.88499	+	2.83681i	0.128786	+	0.0940394i
$911$	−2.20136	+	2.76042i	−0.0729343	+	0.0914567i	−0.816960	−	0.576694i	$-0.804342\pi$
$911$	−2.20136	+	2.76042i	−0.0729343	+	0.0914567i	0.744026	+	0.668151i	$0.232914\pi$
$912$		0			0
$913$	9.92626			0.328511
$914$	−15.6804	+	19.6626i	−0.518662	+	0.650382i
$915$		0			0
$916$	0.793977	−	0.382359i	0.0262337	−	0.0126335i
$917$	−31.8419	−	5.85706i	−1.05151	−	0.193417i
$918$		0			0
$919$	−27.6441	+	34.6646i	−0.911894	+	1.14348i	0.0773206	+	0.997006i	$0.475363\pi$
$919$	−27.6441	+	34.6646i	−0.911894	+	1.14348i	−0.989215	+	0.146473i	$0.953208\pi$
$920$	−19.1036	−	9.19980i	−0.629827	−	0.303308i
$921$		0			0
$922$	−18.2742	+	8.80039i	−0.601829	+	0.289826i
$923$	2.61741	+	11.4676i	0.0861530	+	0.377461i
$924$		0			0
$925$	2.90840	−	12.7425i	0.0956276	−	0.418972i
$926$	10.9323	+	47.8977i	0.359259	+	1.57402i
$927$		0			0
$928$	0.0871432	+	0.381800i	0.00286062	+	0.0125332i
$929$	13.4229	+	6.46411i	0.440390	+	0.212081i	0.640921	−	0.767607i	$-0.278553\pi$
$929$	13.4229	+	6.46411i	0.440390	+	0.212081i	−0.200531	+	0.979687i	$0.564267\pi$
$930$		0			0
$931$	−18.5912	+	1.58373i	−0.609302	+	0.0519046i
$932$	1.59063			0.0521027
$933$		0			0
$934$	8.58332	+	37.6060i	0.280855	+	1.23051i
$935$	−6.09341	−	7.64090i	−0.199276	−	0.249884i
$936$		0			0
$937$	2.91799	−	12.7846i	0.0953266	−	0.417653i	−0.904637	−	0.426183i	$-0.859858\pi$
$937$	2.91799	−	12.7846i	0.0953266	−	0.417653i	0.999964	+	0.00852975i	$0.00271514\pi$
$938$	8.06265	−	18.7395i	0.263255	−	0.611867i
$939$		0			0
$940$	−0.896177	+	0.431576i	−0.0292301	+	0.0140765i
$941$	−9.29324	+	40.7163i	−0.302951	+	1.32731i	0.562698	+	0.826663i	$0.309763\pi$
$941$	−9.29324	+	40.7163i	−0.302951	+	1.32731i	−0.865649	+	0.500652i	$0.833094\pi$
$942$		0			0
$943$	−27.2657	+	34.1901i	−0.887894	+	1.11338i
$944$	35.9464	+	17.3109i	1.16995	+	0.563420i
$945$		0			0
$946$	−29.8772	+	14.3881i	−0.971392	+	0.467798i
$947$	3.78332	−	16.5758i	0.122941	−	0.538642i	−0.875520	−	0.483183i	$-0.839481\pi$
$947$	3.78332	−	16.5758i	0.122941	−	0.538642i	0.998461	−	0.0554590i	$-0.0176622\pi$
$948$		0			0
$949$	−0.0483608			−0.00156986
$950$	11.4369			0.371061
$951$		0			0
$952$	7.09712	−	16.4954i	0.230019	−	0.534618i
$953$	2.41533	+	3.02873i	0.0782402	+	0.0981101i	0.819411	−	0.573206i	$-0.194301\pi$
$953$	2.41533	+	3.02873i	0.0782402	+	0.0981101i	−0.741171	+	0.671316i	$0.765729\pi$
$954$		0			0
$955$	−6.95717	+	3.35039i	−0.225129	+	0.108416i
$956$	1.05826	−	0.509631i	0.0342266	−	0.0164826i
$957$		0			0
$958$	−26.3603	−	33.0547i	−0.851661	−	1.06795i
$959$	14.3342	+	2.63665i	0.462874	+	0.0851419i
$960$		0			0
$961$	18.4947			0.596604
$962$	−5.55011			−0.178943
$963$		0			0
$964$	−0.791877	+	3.46944i	−0.0255046	+	0.111743i
$965$	−1.27188	+	0.612505i	−0.0409432	+	0.0197172i
$966$		0			0
$967$	43.8950	+	21.1387i	1.41157	+	0.679775i	0.975472	−	0.220126i	$-0.0706467\pi$
$967$	43.8950	+	21.1387i	1.41157	+	0.679775i	0.436095	+	0.899900i	$0.356361\pi$
$968$	−2.83519	+	3.55522i	−0.0911266	+	0.114269i
$969$		0			0
$970$	−5.91794	+	25.9282i	−0.190014	+	0.832504i
$971$	−18.7160	+	9.01317i	−0.600626	+	0.289246i	−0.709384	−	0.704822i	$-0.751027\pi$
$971$	−18.7160	+	9.01317i	−0.600626	+	0.289246i	0.108758	+	0.994068i	$0.465313\pi$
$972$		0			0
$973$	31.2699	−	8.54961i	1.00247	−	0.274088i
$974$	2.32920	−	10.2049i	0.0746324	−	0.326986i
$975$		0			0
$976$	7.83967	+	9.83063i	0.250942	+	0.314671i
$977$	−13.5624	−	59.4207i	−0.433899	−	1.90104i	−0.433744	−	0.901036i	$-0.642808\pi$
$977$	−13.5624	−	59.4207i	−0.433899	−	1.90104i	−0.000155196	−	1.00000i	$-0.500049\pi$
$978$		0			0
$979$	−46.9851			−1.50165
$980$	0.684704	−	1.02658i	0.0218721	−	0.0327929i
$981$		0			0
$982$	−5.29260	−	2.54878i	−0.168894	−	0.0813348i
$983$	−0.777261	−	3.40540i	−0.0247908	−	0.108615i	0.961019	−	0.276483i	$-0.0891690\pi$
$983$	−0.777261	−	3.40540i	−0.0247908	−	0.108615i	−0.985810	+	0.167868i	$0.946312\pi$
$984$		0			0
$985$	−3.73772	−	16.3760i	−0.119094	−	0.521783i
$986$	−0.380842	+	1.66858i	−0.0121285	+	0.0531383i
$987$		0			0
$988$	0.0746026	+	0.326855i	0.00237343	+	0.0103987i
$989$	37.9259	−	18.2642i	1.20597	−	0.580766i
$990$		0			0
$991$	−23.6157	−	11.3727i	−0.750178	−	0.361266i	0.0194068	−	0.999812i	$-0.493822\pi$
$991$	−23.6157	−	11.3727i	−0.750178	−	0.361266i	−0.769584	+	0.638545i	$0.779537\pi$
$992$	−3.19952	+	4.01207i	−0.101585	+	0.127383i
$993$		0			0
$994$	−42.1605	+	11.5272i	−1.33725	+	0.365622i
$995$	25.2181	−	12.1444i	0.799467	−	0.385003i
$996$		0			0
$997$	9.09482	−	11.4045i	0.288036	−	0.361186i	−0.616670	−	0.787221i	$-0.711519\pi$
$997$	9.09482	−	11.4045i	0.288036	−	0.361186i	0.904706	+	0.426036i	$0.140090\pi$
$998$	−37.4181			−1.18445
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.e.127.8	yes	60
3.2	odd	2	inner	441.2.u.e.127.3	✓	60
49.22	even	7	inner	441.2.u.e.316.8	yes	60
147.71	odd	14	inner	441.2.u.e.316.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.u.e.127.3	✓	60	3.2	odd	2	inner
441.2.u.e.127.8	yes	60	1.1	even	1	trivial
441.2.u.e.316.3	yes	60	147.71	odd	14	inner
441.2.u.e.316.8	yes	60	49.22	even	7	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23234 + 0.593462i) q^{2} +(-0.0805240 - 0.100974i) q^{4} +(-0.303726 - 1.33071i) q^{5} +(-0.112387 - 2.64336i) q^{7} +(-0.648032 - 2.83922i) q^{8} +O(q^{10})\)	\(q+(1.23234 + 0.593462i) q^{2} +(-0.0805240 - 0.100974i) q^{4} +(-0.303726 - 1.33071i) q^{5} +(-0.112387 - 2.64336i) q^{7} +(-0.648032 - 2.83922i) q^{8} +(0.415434 - 1.82013i) q^{10} +(-2.76798 - 1.33299i) q^{11} +(-0.877440 - 0.422553i) q^{13} +(1.43024 - 3.32421i) q^{14} +(0.828895 - 3.63163i) q^{16} +(-1.45310 + 1.82214i) q^{17} +2.66550 q^{19} +(-0.109910 + 0.137823i) q^{20} +(-2.62000 - 3.28538i) q^{22} +(3.32581 + 4.17043i) q^{23} +(2.82630 - 1.36108i) q^{25} +(-0.830532 - 1.04145i) q^{26} +(-0.257861 + 0.224202i) q^{28} +(0.334746 - 0.419759i) q^{29} +7.03525 q^{31} +(-0.454784 + 0.570282i) q^{32} +(-2.87208 + 1.38312i) q^{34} +(-3.48342 + 0.952412i) q^{35} +(2.59779 - 3.25752i) q^{37} +(3.28480 + 1.58187i) q^{38} +(-3.58135 + 1.72469i) q^{40} +(1.82428 + 7.99268i) q^{41} +(1.75602 - 7.69362i) q^{43} +(0.0882916 + 0.386831i) q^{44} +(1.62352 + 7.11312i) q^{46} +(5.08378 + 2.44822i) q^{47} +(-6.97474 + 0.594157i) q^{49} +4.29070 q^{50} +(0.0279882 + 0.122624i) q^{52} +(-6.36693 - 7.98388i) q^{53} +(-0.933114 + 4.08824i) q^{55} +(-7.43225 + 2.03207i) q^{56} +(0.661631 - 0.318625i) q^{58} +(-2.38335 + 10.4421i) q^{59} +(-2.10460 + 2.63908i) q^{61} +(8.66979 + 4.17515i) q^{62} +(-7.61114 + 3.66533i) q^{64} +(-0.295794 + 1.29596i) q^{65} +5.63728 q^{67} +0.300998 q^{68} +(-4.85796 - 0.893583i) q^{70} +(-7.53046 - 9.44290i) q^{71} +(0.0447399 - 0.0215456i) q^{73} +(5.13456 - 2.47268i) q^{74} +(-0.214637 - 0.269146i) q^{76} +(-3.21249 + 7.46658i) q^{77} +7.11287 q^{79} -5.08440 q^{80} +(-2.49523 + 10.9323i) q^{82} +(-2.91100 + 1.40187i) q^{83} +(2.86608 + 1.38023i) q^{85} +(6.72987 - 8.43900i) q^{86} +(-1.99090 + 8.72270i) q^{88} +(13.7790 - 6.63562i) q^{89} +(-1.01835 + 2.36688i) q^{91} +(0.153297 - 0.671640i) q^{92} +(4.81200 + 6.03406i) q^{94} +(-0.809583 - 3.54701i) q^{95} -14.2452 q^{97} +(-8.94783 - 3.40704i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) \) 60 * q - 12 * q^4 - 2 * q^7	\( 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) \) 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more