LMFDB - Embedded newform 810.2.s.a.557.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.7
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.730092 + 2.11352i) q^{5} +(0.512056 + 1.09811i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.730092 + 2.11352i) q^{5} +(0.512056 + 1.09811i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.614209 - 2.15006i) q^{10} +(0.131652 + 0.156897i) q^{11} +(1.17604 + 1.67956i) q^{13} +(0.210397 - 1.19322i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.232092 - 0.866178i) q^{17} +(-0.760464 + 0.439054i) q^{19} +(-1.73635 + 1.40893i) q^{20} +(-0.0178508 - 0.204035i) q^{22} +(5.70966 + 2.66246i) q^{23} +(-3.93393 + 3.08613i) q^{25} -2.05036i q^{26} +(-0.856750 + 0.856750i) q^{28} +(-0.321053 - 1.82078i) q^{29} +(-7.59799 + 2.76544i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-0.306701 + 0.842654i) q^{34} +(-1.94702 + 1.88396i) q^{35} +(-2.05840 + 0.551547i) q^{37} +(0.874767 + 0.0765322i) q^{38} +(2.23047 - 0.158195i) q^{40} +(0.641136 + 0.113050i) q^{41} +(-1.12279 + 12.8336i) q^{43} +(-0.102407 + 0.177375i) q^{44} +(-3.14995 - 5.45588i) q^{46} +(-8.41431 + 3.92366i) q^{47} +(3.55587 - 4.23773i) q^{49} +(4.99262 - 0.271595i) q^{50} +(-1.17604 + 1.67956i) q^{52} +(4.82344 + 4.82344i) q^{53} +(-0.235487 + 0.392799i) q^{55} +(1.19322 - 0.210397i) q^{56} +(-0.781366 + 1.67564i) q^{58} +(3.62459 + 3.04139i) q^{59} +(-1.71537 - 0.624344i) q^{61} +(7.81010 + 2.09271i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-2.69117 + 3.71182i) q^{65} +(6.81694 - 4.77327i) q^{67} +(0.734561 - 0.514345i) q^{68} +(2.67550 - 0.426482i) q^{70} +(-2.96211 - 1.71017i) q^{71} +(12.5459 + 3.36167i) q^{73} +(2.00250 + 0.728850i) q^{74} +(-0.672670 - 0.564437i) q^{76} +(-0.104877 + 0.224909i) q^{77} +(-13.9602 + 2.46157i) q^{79} +(-1.91783 - 1.14976i) q^{80} +(-0.460346 - 0.460346i) q^{82} +(6.90097 - 9.85560i) q^{83} +(1.66124 - 1.12292i) q^{85} +(8.28078 - 9.86864i) q^{86} +(0.185625 - 0.0865584i) q^{88} +(8.58613 + 14.8716i) q^{89} +(-1.24214 + 2.15145i) q^{91} +(-0.549073 + 6.27594i) q^{92} +(9.14312 + 1.61218i) q^{94} +(-1.48316 - 1.28671i) q^{95} +(10.1255 + 0.885866i) q^{97} +(-5.34346 + 1.43178i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	0.730092	+	2.11352i	0.326507	+	0.945195i
$5$	0.730092	+	2.11352i	0.326507	+	0.945195i
$6$		0			0
$7$	0.512056	+	1.09811i	0.193539	+	0.415046i	0.978999	−	0.203867i	$-0.0653511\pi$
$7$	0.512056	+	1.09811i	0.193539	+	0.415046i	−0.785460	+	0.618913i	$0.787573\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	0.614209	−	2.15006i	0.194230	−	0.679908i
$11$	0.131652	+	0.156897i	0.0396947	+	0.0473063i	0.785527	−	0.618828i	$-0.212392\pi$
$11$	0.131652	+	0.156897i	0.0396947	+	0.0473063i	−0.745832	+	0.666134i	$0.767948\pi$
$12$		0			0
$13$	1.17604	+	1.67956i	0.326175	+	0.465826i	0.948429	−	0.316989i	$-0.102672\pi$
$13$	1.17604	+	1.67956i	0.326175	+	0.465826i	−0.622254	+	0.782815i	$0.713783\pi$
$14$	0.210397	−	1.19322i	0.0562310	−	0.318902i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.232092	−	0.866178i	−0.0562905	−	0.210079i	0.932052	−	0.362324i	$-0.118016\pi$
$17$	−0.232092	−	0.866178i	−0.0562905	−	0.210079i	−0.988343	+	0.152245i	$0.951350\pi$
$18$		0			0
$19$	−0.760464	+	0.439054i	−0.174462	+	0.100726i	−0.584688	−	0.811258i	$-0.698783\pi$
$19$	−0.760464	+	0.439054i	−0.174462	+	0.100726i	0.410226	+	0.911984i	$0.365450\pi$
$20$	−1.73635	+	1.40893i	−0.388260	+	0.315046i
$21$		0			0
$22$	−0.0178508	−	0.204035i	−0.00380580	−	0.0435005i
$23$	5.70966	+	2.66246i	1.19055	+	0.555161i	0.913950	−	0.405826i	$-0.133016\pi$
$23$	5.70966	+	2.66246i	1.19055	+	0.555161i	0.276595	+	0.960986i	$0.410794\pi$
$24$		0			0
$25$	−3.93393	+	3.08613i	−0.786787	+	0.617225i
$26$		−	2.05036i		−	0.402109i
$27$		0			0
$28$	−0.856750	+	0.856750i	−0.161911	+	0.161911i
$29$	−0.321053	−	1.82078i	−0.0596180	−	0.338110i	0.940380	−	0.340126i	$-0.110470\pi$
$29$	−0.321053	−	1.82078i	−0.0596180	−	0.338110i	−0.999998	+	0.00201529i	$0.999359\pi$
$30$		0			0
$31$	−7.59799	+	2.76544i	−1.36464	+	0.496688i	−0.917486	−	0.397769i	$-0.869785\pi$
$31$	−7.59799	+	2.76544i	−1.36464	+	0.496688i	−0.447154	+	0.894457i	$0.647562\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$		0			0
$34$	−0.306701	+	0.842654i	−0.0525988	+	0.144514i
$35$	−1.94702	+	1.88396i	−0.329107	+	0.318447i
$36$		0			0
$37$	−2.05840	+	0.551547i	−0.338399	+	0.0906738i	−0.424017	−	0.905654i	$-0.639380\pi$
$37$	−2.05840	+	0.551547i	−0.338399	+	0.0906738i	0.0856178	+	0.996328i	$0.472714\pi$
$38$	0.874767	+	0.0765322i	0.141906	+	0.0124152i
$39$		0			0
$40$	2.23047	−	0.158195i	0.352667	−	0.0250128i
$41$	0.641136	+	0.113050i	0.100129	+	0.0176554i	0.223488	−	0.974707i	$-0.428256\pi$
$41$	0.641136	+	0.113050i	0.100129	+	0.0176554i	−0.123359	+	0.992362i	$0.539367\pi$
$42$		0			0
$43$	−1.12279	+	12.8336i	−0.171224	+	1.95710i	0.101046	+	0.994882i	$0.467781\pi$
$43$	−1.12279	+	12.8336i	−0.171224	+	1.95710i	−0.272271	+	0.962221i	$0.587775\pi$
$44$	−0.102407	+	0.177375i	−0.0154385	+	0.0267402i
$45$		0			0
$46$	−3.14995	−	5.45588i	−0.464435	−	0.804426i
$47$	−8.41431	+	3.92366i	−1.22735	+	0.572324i	−0.924671	−	0.380767i	$-0.875660\pi$
$47$	−8.41431	+	3.92366i	−1.22735	+	0.572324i	−0.302683	+	0.953091i	$0.597882\pi$
$48$		0			0
$49$	3.55587	−	4.23773i	0.507982	−	0.605389i
$50$	4.99262	−	0.271595i	0.706063	−	0.0384094i
$51$		0			0
$52$	−1.17604	+	1.67956i	−0.163087	+	0.232913i
$53$	4.82344	+	4.82344i	0.662550	+	0.662550i	0.955980	−	0.293430i	$-0.0947968\pi$
$53$	4.82344	+	4.82344i	0.662550	+	0.662550i	−0.293430	+	0.955980i	$0.594797\pi$
$54$		0			0
$55$	−0.235487	+	0.392799i	−0.0317531	+	0.0529650i
$56$	1.19322	−	0.210397i	0.159451	−	0.0281155i
$57$		0			0
$58$	−0.781366	+	1.67564i	−0.102598	+	0.220023i
$59$	3.62459	+	3.04139i	0.471882	+	0.395956i	0.847480	−	0.530827i	$-0.178118\pi$
$59$	3.62459	+	3.04139i	0.471882	+	0.395956i	−0.375599	+	0.926782i	$0.622563\pi$
$60$		0			0
$61$	−1.71537	−	0.624344i	−0.219631	−	0.0799391i	0.229861	−	0.973223i	$-0.426173\pi$
$61$	−1.71537	−	0.624344i	−0.219631	−	0.0799391i	−0.449492	+	0.893284i	$0.648395\pi$
$62$	7.81010	+	2.09271i	0.991884	+	0.265774i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−2.69117	+	3.71182i	−0.333798	+	0.460394i
$66$		0			0
$67$	6.81694	−	4.77327i	0.832822	−	0.583148i	−0.0775268	−	0.996990i	$-0.524702\pi$
$67$	6.81694	−	4.77327i	0.832822	−	0.583148i	0.910349	+	0.413842i	$0.135813\pi$
$68$	0.734561	−	0.514345i	0.0890786	−	0.0623735i
$69$		0			0
$70$	2.67550	−	0.426482i	0.319784	−	0.0509743i
$71$	−2.96211	−	1.71017i	−0.351537	−	0.202960i	0.313825	−	0.949481i	$-0.398390\pi$
$71$	−2.96211	−	1.71017i	−0.351537	−	0.202960i	−0.665362	+	0.746521i	$0.731723\pi$
$72$		0			0
$73$	12.5459	+	3.36167i	1.46839	+	0.393454i	0.902379	−	0.430943i	$-0.141819\pi$
$73$	12.5459	+	3.36167i	1.46839	+	0.393454i	0.566011	+	0.824397i	$0.308486\pi$
$74$	2.00250	+	0.728850i	0.232786	+	0.0847271i
$75$		0			0
$76$	−0.672670	−	0.564437i	−0.0771606	−	0.0647454i
$77$	−0.104877	+	0.224909i	−0.0119518	+	0.0256307i
$78$		0			0
$79$	−13.9602	+	2.46157i	−1.57065	+	0.276948i	−0.890104	−	0.455757i	$-0.849369\pi$
$79$	−13.9602	+	2.46157i	−1.57065	+	0.276948i	−0.680546	+	0.732705i	$0.738257\pi$
$80$	−1.91783	−	1.14976i	−0.214420	−	0.128547i
$81$		0			0
$82$	−0.460346	−	0.460346i	−0.0508367	−	0.0508367i
$83$	6.90097	−	9.85560i	0.757479	−	1.08179i	−0.236436	−	0.971647i	$-0.575979\pi$
$83$	6.90097	−	9.85560i	0.757479	−	1.08179i	0.993915	−	0.110146i	$-0.0351317\pi$
$84$		0			0
$85$	1.66124	−	1.12292i	0.180186	−	0.121798i
$86$	8.28078	−	9.86864i	0.892939	−	1.06416i
$87$		0			0
$88$	0.185625	−	0.0865584i	0.0197877	−	0.00922716i
$89$	8.58613	+	14.8716i	0.910128	+	1.57639i	0.813882	+	0.581031i	$0.197350\pi$
$89$	8.58613	+	14.8716i	0.910128	+	1.57639i	0.0962464	+	0.995358i	$0.469316\pi$
$90$		0			0
$91$	−1.24214	+	2.15145i	−0.130212	+	0.225533i
$92$	−0.549073	+	6.27594i	−0.0572448	+	0.654312i
$93$		0			0
$94$	9.14312	+	1.61218i	0.943041	+	0.166284i
$95$	−1.48316	−	1.28671i	−0.152169	−	0.132013i
$96$		0			0
$97$	10.1255	+	0.885866i	1.02809	+	0.0899460i	0.588700	−	0.808351i	$-0.299640\pi$
$97$	10.1255	+	0.885866i	1.02809	+	0.0899460i	0.439388	+	0.898297i	$0.355195\pi$
$98$	−5.34346	+	1.43178i	−0.539771	+	0.144631i
$99$		0			0
$100$	−4.24549	−	2.64117i	−0.424549	−	0.264117i
$101$	0.608139	−	1.67085i	0.0605121	−	0.166256i	−0.905752	−	0.423807i	$-0.860693\pi$
$101$	0.608139	−	1.67085i	0.0605121	−	0.166256i	0.966265	+	0.257551i	$0.0829157\pi$
$102$		0			0
$103$	12.5997	−	1.10233i	1.24148	−	0.108616i	0.552574	−	0.833464i	$-0.313646\pi$
$103$	12.5997	−	1.10233i	1.24148	−	0.108616i	0.688908	+	0.724849i	$0.258090\pi$
$104$	1.92671	−	0.701266i	0.188930	−	0.0687648i
$105$		0			0
$106$	−1.18452	−	6.71774i	−0.115051	−	0.652485i
$107$	−9.84729	+	9.84729i	−0.951973	+	0.951973i	−0.998898	−	0.0469251i	$-0.985058\pi$
$107$	−9.84729	+	9.84729i	−0.951973	+	0.951973i	0.0469251	+	0.998898i	$0.485058\pi$
$108$		0			0
$109$		−	12.5667i		−	1.20367i	−0.798620	−	0.601836i	$-0.794436\pi$
$109$		−	12.5667i		−	1.20367i	0.798620	−	0.601836i	$-0.205564\pi$
$110$	0.418200	−	0.186692i	0.0398738	−	0.0178004i
$111$		0			0
$112$	−1.09811	−	0.512056i	−0.103761	−	0.0483847i
$113$	0.897508	+	10.2586i	0.0844305	+	0.965045i	0.913752	+	0.406273i	$0.133172\pi$
$113$	0.897508	+	10.2586i	0.0844305	+	0.965045i	−0.829321	+	0.558772i	$0.811273\pi$
$114$		0			0
$115$	−1.45858	+	14.0113i	−0.136014	+	1.30656i
$116$	1.60117	−	0.924434i	0.148665	−	0.0858316i
$117$		0			0
$118$	−1.22462	−	4.57034i	−0.112735	−	0.420734i
$119$	0.832313	−	0.698393i	0.0762980	−	0.0640216i
$120$		0			0
$121$	1.90285	−	10.7916i	0.172986	−	0.981052i
$122$	1.04704	+	1.49533i	0.0947946	+	0.135381i
$123$		0			0
$124$	−5.19733	−	6.19394i	−0.466734	−	0.556232i
$125$	−9.39472	−	6.06129i	−0.840289	−	0.542138i
$126$		0			0
$127$	−2.60620	+	9.72646i	−0.231262	+	0.863083i	0.748536	+	0.663095i	$0.230757\pi$
$127$	−2.60620	+	9.72646i	−0.231262	+	0.863083i	−0.979798	+	0.199989i	$0.935909\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$		0			0
$130$	4.33349	−	1.49695i	0.380072	−	0.131292i
$131$	−7.53635	−	20.7060i	−0.658454	−	1.80909i	−0.583829	−	0.811877i	$-0.698446\pi$
$131$	−7.53635	−	20.7060i	−0.658454	−	1.80909i	−0.0746258	−	0.997212i	$-0.523776\pi$
$132$		0			0
$133$	−0.871529	−	0.610251i	−0.0755712	−	0.0529155i
$134$	−8.32195			−0.718907
$135$		0			0
$136$	−0.896733			−0.0768942
$137$	−18.4594	−	12.9254i	−1.57709	−	1.10429i	−0.943868	−	0.330324i	$-0.892842\pi$
$137$	−18.4594	−	12.9254i	−1.57709	−	1.10429i	−0.633224	−	0.773968i	$-0.718269\pi$
$138$		0			0
$139$	1.92493	+	5.28871i	0.163271	+	0.448582i	0.994168	−	0.107844i	$-0.0343946\pi$
$139$	1.92493	+	5.28871i	0.163271	+	0.448582i	−0.830897	+	0.556426i	$0.812172\pi$
$140$	−2.43626	−	1.18525i	−0.205902	−	0.100172i
$141$		0			0
$142$	1.44550	+	3.09989i	0.121304	+	0.260137i
$143$	−0.108690	+	0.405635i	−0.00908909	+	0.0339209i
$144$		0			0
$145$	3.61386	−	2.00789i	0.300115	−	0.166746i
$146$	−8.34885	−	9.94977i	−0.690956	−	0.823449i
$147$		0			0
$148$	−1.22230	−	1.74562i	−0.100472	−	0.143489i
$149$	0.358581	−	2.03361i	0.0293761	−	0.166600i	−0.966590	−	0.256326i	$-0.917488\pi$
$149$	0.358581	−	2.03361i	0.0293761	−	0.166600i	0.995966	+	0.0897259i	$0.0285991\pi$
$150$		0			0
$151$	0.0759710	−	0.0637473i	0.00618244	−	0.00518768i	−0.639691	−	0.768632i	$-0.720938\pi$
$151$	0.0759710	−	0.0637473i	0.00618244	−	0.00518768i	0.645874	+	0.763444i	$0.276493\pi$
$152$	0.227271	+	0.848188i	0.0184341	+	0.0687971i
$153$		0			0
$154$	0.214912	−	0.124080i	0.0173181	−	0.00999862i
$155$	−11.3920	−	14.0395i	−0.915031	−	1.12768i
$156$		0			0
$157$	1.03453	+	11.8247i	0.0825643	+	0.943714i	0.918639	+	0.395098i	$0.129289\pi$
$157$	1.03453	+	11.8247i	0.0825643	+	0.943714i	−0.836075	+	0.548616i	$0.815155\pi$
$158$	12.8475	+	5.99087i	1.02209	+	0.476608i
$159$		0			0
$160$	0.911519	+	2.04185i	0.0720619	+	0.161422i
$161$			7.63314i			0.601576i
$162$		0			0
$163$	8.19206	−	8.19206i	0.641651	−	0.641651i	−0.309310	−	0.950961i	$-0.600098\pi$
$163$	8.19206	−	8.19206i	0.641651	−	0.641651i	0.950961	+	0.309310i	$0.100098\pi$
$164$	0.113050	+	0.641136i	0.00882769	+	0.0500643i
$165$		0			0
$166$	−11.3059	+	4.11500i	−0.877506	+	0.319386i
$167$	−5.12778	+	0.448623i	−0.396800	+	0.0347155i	−0.283810	−	0.958881i	$-0.591598\pi$
$167$	−5.12778	+	0.448623i	−0.396800	+	0.0347155i	−0.112990	+	0.993596i	$0.536043\pi$
$168$		0			0
$169$	3.00841	−	8.26554i	0.231416	−	0.635811i
$170$	−2.00489	−	0.0330040i	−0.153768	−	0.00253129i
$171$		0			0
$172$	−12.4436	+	3.33426i	−0.948818	+	0.254235i
$173$	−13.3418	−	1.16726i	−1.01436	−	0.0887451i	−0.432166	−	0.901794i	$-0.642251\pi$
$173$	−13.3418	−	1.16726i	−1.01436	−	0.0887451i	−0.582195	+	0.813049i	$0.697806\pi$
$174$		0			0
$175$	−5.40329	−	2.73961i	−0.408451	−	0.207095i
$176$	−0.201703	−	0.0355657i	−0.0152039	−	0.00268086i
$177$		0			0
$178$	1.49666	−	17.1069i	0.112180	−	1.28222i
$179$	2.05790	−	3.56438i	0.153814	−	0.266414i	−0.778812	−	0.627257i	$-0.784178\pi$
$179$	2.05790	−	3.56438i	0.153814	−	0.266414i	0.932627	+	0.360843i	$0.117511\pi$
$180$		0			0
$181$	0.0854873	+	0.148068i	0.00635422	+	0.0110058i	0.869185	−	0.494487i	$-0.164644\pi$
$181$	0.0854873	+	0.148068i	0.00635422	+	0.0110058i	−0.862831	+	0.505493i	$0.831311\pi$
$182$	2.25152	−	1.04990i	0.166894	−	0.0778239i
$183$		0			0
$184$	4.04950	−	4.82601i	0.298533	−	0.355778i
$185$	−2.66853	−	3.94779i	−0.196194	−	0.290247i
$186$		0			0
$187$	0.105345	−	0.150449i	0.00770362	−	0.0110019i
$188$	−6.56490	−	6.56490i	−0.478794	−	0.478794i
$189$		0			0
$190$	0.476908	+	1.90471i	0.0345985	+	0.138182i
$191$	13.7059	−	2.41673i	0.991727	−	0.174868i	0.345834	−	0.938296i	$-0.387596\pi$
$191$	13.7059	−	2.41673i	0.991727	−	0.174868i	0.645894	+	0.763427i	$0.276485\pi$
$192$		0			0
$193$	7.57475	−	16.2441i	0.545242	−	1.16928i	−0.419905	−	0.907568i	$-0.637937\pi$
$193$	7.57475	−	16.2441i	0.545242	−	1.16928i	0.965147	−	0.261708i	$-0.0842857\pi$
$194$	−7.78621	−	6.53340i	−0.559017	−	0.469071i
$195$		0			0
$196$	5.19834	+	1.89204i	0.371310	+	0.135146i
$197$	26.1569	+	7.00872i	1.86360	+	0.499351i	0.999988	−	0.00480456i	$-0.00152934\pi$
$197$	26.1569	+	7.00872i	1.86360	+	0.499351i	0.863613	+	0.504155i	$0.168196\pi$
$198$		0			0
$199$	−14.8330	−	8.56386i	−1.05149	−	0.607076i	−0.128421	−	0.991720i	$-0.540991\pi$
$199$	−14.8330	−	8.56386i	−1.05149	−	0.607076i	−0.923065	+	0.384644i	$0.874324\pi$
$200$	1.96279	+	4.59864i	0.138790	+	0.325173i
$201$		0			0
$202$	−1.45652	+	1.01986i	−0.102480	+	0.0717574i
$203$	1.83502	−	1.28489i	0.128793	−	0.0901817i
$204$		0			0
$205$	0.229156	+	1.43759i	0.0160049	+	0.100406i
$206$	−10.9533	−	6.32390i	−0.763153	−	0.440607i
$207$		0			0
$208$	−1.98050	−	0.530673i	−0.137323	−	0.0367956i
$209$	−0.169003	−	0.0615122i	−0.0116902	−	0.00425488i
$210$		0			0
$211$	−3.84507	−	3.22639i	−0.264705	−	0.222114i	0.500768	−	0.865581i	$-0.333051\pi$
$211$	−3.84507	−	3.22639i	−0.264705	−	0.222114i	−0.765474	+	0.643467i	$0.777495\pi$
$212$	−2.88284	+	6.18226i	−0.197994	+	0.424600i
$213$		0			0
$214$	13.7146	−	2.41825i	0.937511	−	0.165308i
$215$	−27.9438	+	6.99664i	−1.90575	+	0.477167i
$216$		0			0
$217$	−6.92735	−	6.92735i	−0.470259	−	0.470259i
$218$	−7.20796	+	10.2940i	−0.488185	+	0.697200i
$219$		0			0
$220$	−0.449652	−	0.0869402i	−0.0303155	−	0.00586150i
$221$	1.18185	−	1.40847i	0.0794997	−	0.0947441i
$222$		0			0
$223$	−11.0879	+	5.17037i	−0.742500	+	0.346234i	−0.756785	−	0.653664i	$-0.773231\pi$
$223$	−11.0879	+	5.17037i	−0.742500	+	0.346234i	0.0142843	+	0.999898i	$0.495453\pi$
$224$	0.605814	+	1.04930i	0.0404776	+	0.0701093i
$225$		0			0
$226$	5.14888	−	8.91811i	0.342498	−	0.593224i
$227$	0.990889	−	11.3259i	0.0657676	−	0.751728i	−0.889683	−	0.456578i	$-0.849075\pi$
$227$	0.990889	−	11.3259i	0.0657676	−	0.751728i	0.955451	−	0.295150i	$-0.0953695\pi$
$228$		0			0
$229$	1.63845	+	0.288903i	0.108272	+	0.0190912i	0.227522	−	0.973773i	$-0.426938\pi$
$229$	1.63845	+	0.288903i	0.108272	+	0.0190912i	−0.119250	+	0.992864i	$0.538049\pi$
$230$	9.23136	−	10.6408i	0.608698	−	0.701633i
$231$		0			0
$232$	−1.84183	−	0.161140i	−0.120922	−	0.0105793i
$233$	16.0876	−	4.31066i	1.05393	−	0.282401i	0.310057	−	0.950718i	$-0.399652\pi$
$233$	16.0876	−	4.31066i	1.05393	−	0.282401i	0.743876	+	0.668317i	$0.232985\pi$
$234$		0			0
$235$	−14.4360	−	14.9192i	−0.941698	−	0.973221i
$236$	−1.61829	+	4.44622i	−0.105342	+	0.289424i
$237$		0			0
$238$	−1.08237	+	0.0946953i	−0.0701598	+	0.00613819i
$239$	−11.0137	+	4.00867i	−0.712419	+	0.259299i	−0.672704	−	0.739912i	$-0.734867\pi$
$239$	−11.0137	+	4.00867i	−0.712419	+	0.259299i	−0.0397151	+	0.999211i	$0.512645\pi$
$240$		0			0
$241$	−1.83616	−	10.4134i	−0.118277	−	0.670785i	−0.985075	−	0.172125i	$-0.944937\pi$
$241$	−1.83616	−	10.4134i	−0.118277	−	0.670785i	0.866798	−	0.498660i	$-0.166174\pi$
$242$	−7.74851	+	7.74851i	−0.498093	+	0.498093i
$243$		0			0
$244$		−	1.82546i		−	0.116863i
$245$	11.5526	+	4.42148i	0.738071	+	0.282478i
$246$		0			0
$247$	−1.63175	−	0.760900i	−0.103826	−	0.0484149i
$248$	0.704707	+	8.05484i	0.0447490	+	0.511483i
$249$		0			0
$250$	4.21909	+	10.3537i	0.266839	+	0.654826i
$251$	18.0016	−	10.3933i	1.13625	−	0.656016i	0.190753	−	0.981638i	$-0.438907\pi$
$251$	18.0016	−	10.3933i	1.13625	−	0.656016i	0.945500	+	0.325622i	$0.105574\pi$
$252$		0			0
$253$	0.333958	+	1.24635i	0.0209957	+	0.0783572i
$254$	7.71374	−	6.47259i	0.484003	−	0.406127i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.24740	−	4.63777i	−0.202567	−	0.289296i	0.704996	−	0.709211i	$-0.250949\pi$
$257$	−3.24740	−	4.63777i	−0.202567	−	0.289296i	−0.907563	+	0.419915i	$0.862060\pi$
$258$		0			0
$259$	−1.65967	−	1.97792i	−0.103127	−	0.122902i
$260$	−4.40840	−	1.25935i	−0.273397	−	0.0781017i
$261$		0			0
$262$	−5.70303	+	21.2840i	−0.352335	+	1.31493i
$263$	−3.88915	−	8.34031i	−0.239815	−	0.514286i	0.749156	−	0.662394i	$-0.230459\pi$
$263$	−3.88915	−	8.34031i	−0.239815	−	0.514286i	−0.988971	+	0.148108i	$0.952682\pi$
$264$		0			0
$265$	−6.67288	+	13.7160i	−0.409912	+	0.842566i
$266$	0.363889	+	0.999777i	0.0223115	+	0.0613003i
$267$		0			0
$268$	6.81694	+	4.77327i	0.416411	+	0.291574i
$269$	11.5982			0.707152			0.353576	−	0.935406i	$-0.384966\pi$
$269$	11.5982			0.707152			0.353576	+	0.935406i	$0.384966\pi$
$270$		0			0
$271$	7.56470			0.459523			0.229761	−	0.973247i	$-0.426205\pi$
$271$	7.56470			0.459523			0.229761	+	0.973247i	$0.426205\pi$
$272$	0.734561	+	0.514345i	0.0445393	+	0.0311868i
$273$		0			0
$274$	7.70734	+	21.1757i	0.465617	+	1.27927i
$275$	−1.00212	−	0.210927i	−0.0604298	−	0.0127194i
$276$		0			0
$277$	−10.5123	−	22.5437i	−0.631623	−	1.35452i	−0.918068	−	0.396423i	$-0.870251\pi$
$277$	−10.5123	−	22.5437i	−0.631623	−	1.35452i	0.286445	−	0.958097i	$-0.407526\pi$
$278$	1.45667	−	5.43635i	0.0873650	−	0.326051i
$279$		0			0
$280$	1.31584	+	2.36829i	0.0786364	+	0.141532i
$281$	7.22854	+	8.61464i	0.431218	+	0.513906i	0.937273	−	0.348595i	$-0.113341\pi$
$281$	7.22854	+	8.61464i	0.431218	+	0.513906i	−0.506055	+	0.862501i	$0.668897\pi$
$282$		0			0
$283$	−9.01180	−	12.8702i	−0.535696	−	0.765053i	0.456502	−	0.889722i	$-0.349102\pi$
$283$	−9.01180	−	12.8702i	−0.535696	−	0.765053i	−0.992198	+	0.124669i	$0.960213\pi$
$284$	0.593937	−	3.36838i	0.0352437	−	0.199877i
$285$		0			0
$286$	0.321696	−	0.269935i	0.0190223	−	0.0159616i
$287$	0.204157	+	0.761924i	0.0120510	+	0.0449750i
$288$		0			0
$289$	14.0260	−	8.09793i	0.825061	−	0.476349i
$290$	−4.11198	−	0.428058i	−0.241464	−	0.0251364i
$291$		0			0
$292$	1.13202	+	12.9391i	0.0662466	+	0.757202i
$293$	11.9170	+	5.55697i	0.696196	+	0.324642i	0.738301	−	0.674472i	$-0.235628\pi$
$293$	11.9170	+	5.55697i	0.696196	+	0.324642i	−0.0421046	+	0.999113i	$0.513406\pi$
$294$		0			0
$295$	−3.78176	+	9.88114i	−0.220183	+	0.575302i
$296$			2.13101i			0.123863i
$297$		0			0
$298$	−1.46016	+	1.46016i	−0.0845850	+	0.0845850i
$299$	2.24303	+	12.7209i	0.129718	+	0.735667i
$300$		0			0
$301$	−14.6676	+	5.33856i	−0.845425	+	0.307710i
$302$	−0.0987958	+	0.00864351i	−0.00568506	+	0.000497378i
$303$		0			0
$304$	0.300331	−	0.825152i	0.0172252	−	0.0473257i
$305$	0.0671855	−	4.08130i	0.00384703	−	0.233695i
$306$		0			0
$307$	7.23597	−	1.93887i	0.412979	−	0.110657i	−0.0463465	−	0.998925i	$-0.514758\pi$
$307$	7.23597	−	1.93887i	0.412979	−	0.110657i	0.459325	+	0.888268i	$0.348091\pi$
$308$	−0.247215	−	0.0216285i	−0.0140864	−	0.00123240i
$309$		0			0
$310$	1.27910	+	18.0347i	0.0726482	+	1.02430i
$311$	−15.2177	−	2.68330i	−0.862918	−	0.152156i	−0.275364	−	0.961340i	$-0.588798\pi$
$311$	−15.2177	−	2.68330i	−0.862918	−	0.152156i	−0.587555	+	0.809184i	$0.699909\pi$
$312$		0			0
$313$	−2.02080	+	23.0978i	−0.114222	+	1.30557i	0.695404	+	0.718619i	$0.255226\pi$
$313$	−2.02080	+	23.0978i	−0.114222	+	1.30557i	−0.809626	+	0.586946i	$0.800330\pi$
$314$	5.93493	−	10.2796i	0.334928	−	0.580112i
$315$		0			0
$316$	−7.08780	−	12.2764i	−0.398720	−	0.690603i
$317$	25.2300	−	11.7649i	1.41706	−	0.660784i	0.445000	−	0.895530i	$-0.353204\pi$
$317$	25.2300	−	11.7649i	1.41706	−	0.660784i	0.972057	+	0.234746i	$0.0754258\pi$
$318$		0			0
$319$	0.243408	−	0.290082i	0.0136282	−	0.0162415i
$320$	0.424482	−	2.19541i	0.0237293	−	0.122727i
$321$		0			0
$322$	4.37819	−	6.25271i	0.243987	−	0.348450i
$323$	0.556797	+	0.556797i	0.0309810	+	0.0309810i
$324$		0			0
$325$	−9.80980	−	2.97787i	−0.544150	−	0.165182i
$326$	−11.4093	+	2.01177i	−0.631903	+	0.111422i
$327$		0			0
$328$	0.275136	−	0.590031i	0.0151918	−	0.0325790i
$329$	−8.61720	−	7.23069i	−0.475082	−	0.398641i
$330$		0			0
$331$	0.921531	+	0.335410i	0.0506519	+	0.0184358i	0.367222	−	0.930133i	$-0.380309\pi$
$331$	0.921531	+	0.335410i	0.0506519	+	0.0184358i	−0.316570	+	0.948569i	$0.602531\pi$
$332$	11.6215	+	3.11397i	0.637813	+	0.170901i
$333$		0			0
$334$	4.45775	+	2.57368i	0.243917	+	0.140826i
$335$	15.0654	+	10.9228i	0.823111	+	0.596777i
$336$		0			0
$337$	12.7075	−	8.89789i	0.692222	−	0.484699i	−0.173751	−	0.984790i	$-0.555589\pi$
$337$	12.7075	−	8.89789i	0.692222	−	0.484699i	0.865973	+	0.500090i	$0.166700\pi$
$338$	−7.20527	+	5.04518i	−0.391915	+	0.274422i
$339$		0			0
$340$	1.62338	+	1.17699i	0.0880399	+	0.0638313i
$341$	−1.43418	−	0.828026i	−0.0776654	−	0.0448401i
$342$		0			0
$343$	14.6667	+	3.92993i	0.791926	+	0.212196i
$344$	12.1057	+	4.40611i	0.652695	+	0.237561i
$345$		0			0
$346$	10.2595	+	8.60873i	0.551553	+	0.462808i
$347$	0.815565	−	1.74898i	0.0437818	−	0.0938904i	−0.883200	−	0.468996i	$-0.844616\pi$
$347$	0.815565	−	1.74898i	0.0437818	−	0.0938904i	0.926982	+	0.375106i	$0.122394\pi$
$348$		0			0
$349$	20.9374	−	3.69184i	1.12076	−	0.197620i	0.417583	−	0.908639i	$-0.362877\pi$
$349$	20.9374	−	3.69184i	1.12076	−	0.197620i	0.703173	+	0.711019i	$0.251766\pi$
$350$	2.85474	+	5.34336i	0.152592	+	0.285615i
$351$		0			0
$352$	0.144826	+	0.144826i	0.00771924	+	0.00771924i
$353$	−6.19741	+	8.85082i	−0.329855	+	0.471082i	−0.949485	−	0.313812i	$-0.898394\pi$
$353$	−6.19741	+	8.85082i	−0.329855	+	0.471082i	0.619630	+	0.784894i	$0.287283\pi$
$354$		0			0
$355$	1.45188	−	7.50905i	0.0770575	−	0.398539i
$356$	−11.0381	+	13.1547i	−0.585019	+	0.697199i
$357$		0			0
$358$	−3.73018	+	1.73941i	−0.197146	+	0.0919306i
$359$	3.91189	+	6.77560i	0.206462	+	0.357602i	0.950598	−	0.310426i	$-0.100472\pi$
$359$	3.91189	+	6.77560i	0.206462	+	0.357602i	−0.744136	+	0.668029i	$0.767138\pi$
$360$		0			0
$361$	−9.11446	+	15.7867i	−0.479709	+	0.830880i
$362$	0.0149014	−	0.170324i	0.000783201	−	0.00895203i
$363$		0			0
$364$	−2.44654	−	0.431390i	−0.128233	−	0.0226110i
$365$	2.05472	+	28.9704i	0.107549	+	1.51638i
$366$		0			0
$367$	−3.38287	−	0.295963i	−0.176585	−	0.0154491i	−0.00147952	−	0.999999i	$-0.500471\pi$
$367$	−3.38287	−	0.295963i	−0.176585	−	0.0154491i	−0.175105	+	0.984550i	$0.556027\pi$
$368$	−6.08524	+	1.63054i	−0.317215	+	0.0849976i
$369$		0			0
$370$	−0.0784314	+	4.76445i	−0.00407745	+	0.247692i
$371$	−2.82678	+	7.76653i	−0.146759	+	0.403218i
$372$		0			0
$373$	1.34109	−	0.117330i	0.0694392	−	0.00607514i	−0.0523832	−	0.998627i	$-0.516682\pi$
$373$	1.34109	−	0.117330i	0.0694392	−	0.00607514i	0.121822	+	0.992552i	$0.461126\pi$
$374$	−0.172588	+	0.0628168i	−0.00892430	+	0.00324818i
$375$		0			0
$376$	1.61218	+	9.14312i	0.0831418	+	0.471520i
$377$	2.68054	−	2.68054i	0.138055	−	0.138055i
$378$		0			0
$379$			22.9013i			1.17636i	0.808730	+	0.588180i	$0.200155\pi$
$379$			22.9013i			1.17636i	−0.808730	+	0.588180i	$0.799845\pi$
$380$	0.701839	−	1.83379i	0.0360036	−	0.0940716i
$381$		0			0
$382$	−12.6134	−	5.88174i	−0.645359	−	0.300936i
$383$	0.843973	+	9.64665i	0.0431250	+	0.492921i	0.986788	+	0.162014i	$0.0517990\pi$
$383$	0.843973	+	9.64665i	0.0431250	+	0.492921i	−0.943663	+	0.330907i	$0.892645\pi$
$384$		0			0
$385$	−0.551918	−	0.0574549i	−0.0281284	−	0.00292817i
$386$	−15.5221	+	8.96169i	−0.790054	+	0.456138i
$387$		0			0
$388$	2.63068	+	9.81783i	0.133553	+	0.498425i
$389$	16.0316	−	13.4521i	0.812836	−	0.682050i	−0.138447	−	0.990370i	$-0.544211\pi$
$389$	16.0316	−	13.4521i	0.812836	−	0.682050i	0.951283	+	0.308320i	$0.0997666\pi$
$390$		0			0
$391$	0.980997	−	5.56351i	0.0496112	−	0.281359i
$392$	−3.17300	−	4.53151i	−0.160261	−	0.228876i
$393$		0			0
$394$	−17.4064	−	20.7442i	−0.876924	−	1.04508i
$395$	−15.3948	−	27.7081i	−0.774598	−	1.39415i
$396$		0			0
$397$	−0.519764	+	1.93978i	−0.0260862	+	0.0973550i	−0.977742	−	0.209813i	$-0.932715\pi$
$397$	−0.519764	+	1.93978i	−0.0260862	+	0.0973550i	0.951655	+	0.307168i	$0.0993813\pi$
$398$	7.23849	+	15.5230i	0.362833	+	0.778097i
$399$		0			0
$400$	1.02984	−	4.89279i	0.0514922	−	0.244640i
$401$	1.89007	+	5.19294i	0.0943858	+	0.259323i	0.977897	−	0.209087i	$-0.0670492\pi$
$401$	1.89007	+	5.19294i	0.0943858	+	0.259323i	−0.883511	+	0.468410i	$0.844827\pi$
$402$		0			0
$403$	−13.5803	−	9.50901i	−0.676481	−	0.473677i
$404$	1.77808			0.0884628
$405$		0			0
$406$	−2.24014			−0.111176
$407$	−0.357529	−	0.250345i	−0.0177221	−	0.0124091i
$408$		0			0
$409$	11.0834	+	30.4515i	0.548041	+	1.50573i	0.836351	+	0.548194i	$0.184684\pi$
$409$	11.0834	+	30.4515i	0.548041	+	1.50573i	−0.288310	+	0.957537i	$0.593093\pi$
$410$	0.636855	−	1.30904i	0.0314520	−	0.0646491i
$411$		0			0
$412$	5.34519	+	11.4628i	0.263339	+	0.564731i
$413$	−1.48378	+	5.53755i	−0.0730122	+	0.272485i
$414$		0			0
$415$	25.8683	+	7.38984i	1.26983	+	0.362753i
$416$	1.31795	+	1.57067i	0.0646177	+	0.0770084i
$417$		0			0
$418$	0.103157	+	0.147324i	0.00504560	+	0.00720586i
$419$	0.408570	−	2.31711i	0.0199599	−	0.113198i	−0.973200	−	0.229960i	$-0.926140\pi$
$419$	0.408570	−	2.31711i	0.0199599	−	0.113198i	0.993160	+	0.116762i	$0.0372515\pi$
$420$		0			0
$421$	13.7299	−	11.5207i	0.669153	−	0.561486i	−0.243662	−	0.969860i	$-0.578349\pi$
$421$	13.7299	−	11.5207i	0.669153	−	0.561486i	0.912814	+	0.408375i	$0.133904\pi$
$422$	1.29911	+	4.84835i	0.0632397	+	0.236014i
$423$		0			0
$424$	5.90748	−	3.41069i	0.286893	−	0.165638i
$425$	3.58617	+	2.69122i	0.173955	+	0.130543i
$426$		0			0
$427$	−0.192769	−	2.20336i	−0.00932875	−	0.106628i
$428$	−12.6214	−	5.88545i	−0.610078	−	0.284484i
$429$		0			0
$430$	26.9033	+	10.2966i	1.29739	+	0.496545i
$431$			28.2435i			1.36044i	0.733007	+	0.680221i	$0.238116\pi$
$431$			28.2435i			1.36044i	−0.733007	+	0.680221i	$0.761884\pi$
$432$		0			0
$433$	−14.9342	+	14.9342i	−0.717690	+	0.717690i	−0.968132	−	0.250441i	$-0.919424\pi$
$433$	−14.9342	+	14.9342i	−0.717690	+	0.717690i	0.250441	+	0.968132i	$0.419424\pi$
$434$	1.70119	+	9.64792i	0.0816596	+	0.463115i
$435$		0			0
$436$	11.8088	−	4.29806i	0.565541	−	0.205840i
$437$	−5.51095	+	0.482146i	−0.263625	+	0.0230642i
$438$		0			0
$439$	2.75826	−	7.57827i	0.131645	−	0.361691i	−0.856304	−	0.516472i	$-0.827245\pi$
$439$	2.75826	−	7.57827i	0.131645	−	0.361691i	0.987949	+	0.154781i	$0.0494672\pi$
$440$	0.318466	+	0.329127i	0.0151823	+	0.0156905i
$441$		0			0
$442$	−1.77598	+	0.475872i	−0.0844748	+	0.0226349i
$443$	−10.4807	−	0.916946i	−0.497955	−	0.0435654i	−0.164588	−	0.986362i	$-0.552629\pi$
$443$	−10.4807	−	0.916946i	−0.497955	−	0.0435654i	−0.333367	+	0.942797i	$0.608185\pi$
$444$		0			0
$445$	−25.1628	+	29.0046i	−1.19283	+	1.37495i
$446$	12.0483	+	2.12444i	0.570502	+	0.100595i
$447$		0			0
$448$	0.105600	−	1.20702i	0.00498915	−	0.0570262i
$449$	10.1216	−	17.5311i	0.477666	−	0.827342i	−0.522006	−	0.852942i	$-0.674816\pi$
$449$	10.1216	−	17.5311i	0.477666	−	0.827342i	0.999672	+	0.0255999i	$0.00814959\pi$
$450$		0			0
$451$	0.0666699	+	0.115476i	0.00313936	+	0.00543754i
$452$	−9.33293	+	4.35202i	−0.438984	+	0.204702i
$453$		0			0
$454$	−7.30797	+	8.70930i	−0.342980	+	0.408748i
$455$	−5.45400	−	1.05453i	−0.255688	−	0.0494372i
$456$		0			0
$457$	13.4904	−	19.2663i	0.631055	−	0.901240i	−0.368542	−	0.929611i	$-0.620143\pi$
$457$	13.4904	−	19.2663i	0.631055	−	0.901240i	0.999597	+	0.0283709i	$0.00903196\pi$
$458$	−1.17643	−	1.17643i	−0.0549710	−	0.0549710i
$459$		0			0
$460$	−13.6652	+	3.42153i	−0.637143	+	0.159530i
$461$	7.64593	−	1.34818i	0.356107	−	0.0627912i	0.00726687	−	0.999974i	$-0.497687\pi$
$461$	7.64593	−	1.34818i	0.356107	−	0.0627912i	0.348840	+	0.937182i	$0.386576\pi$
$462$		0			0
$463$	14.9585	−	32.0785i	0.695179	−	1.49082i	−0.167931	−	0.985799i	$-0.553709\pi$
$463$	14.9585	−	32.0785i	0.695179	−	1.49082i	0.863110	−	0.505017i	$-0.168514\pi$
$464$	1.41632	+	1.18843i	0.0657508	+	0.0551715i
$465$		0			0
$466$	−15.6507	−	5.69638i	−0.725004	−	0.263880i
$467$	−12.1883	−	3.26586i	−0.564009	−	0.151126i	−0.0344615	−	0.999406i	$-0.510972\pi$
$467$	−12.1883	−	3.26586i	−0.564009	−	0.151126i	−0.529548	+	0.848280i	$0.677638\pi$
$468$		0			0
$469$	8.73222	+	5.04155i	0.403217	+	0.232797i
$470$	3.26794	+	20.5012i	0.150739	+	0.945650i
$471$		0			0
$472$	3.87587	−	2.71392i	0.178402	−	0.124918i
$473$	−2.16137	+	1.51341i	−0.0993799	+	0.0695866i
$474$		0			0
$475$	1.63664	−	4.07410i	0.0750941	−	0.186932i
$476$	0.940943	+	0.543253i	0.0431280	+	0.0249000i
$477$		0			0
$478$	11.3212	+	3.03351i	0.517820	+	0.138749i
$479$	10.3375	+	3.76253i	0.472331	+	0.171914i	0.567208	−	0.823575i	$-0.308024\pi$
$479$	10.3375	+	3.76253i	0.472331	+	0.171914i	−0.0948770	+	0.995489i	$0.530246\pi$
$480$		0			0
$481$	−3.34712	−	2.80857i	−0.152616	−	0.128060i
$482$	−4.46877	+	9.58332i	−0.203547	+	0.436508i
$483$		0			0
$484$	10.7916	−	1.90285i	0.490526	−	0.0864930i
$485$	5.52024	+	22.0472i	0.250661	+	1.00111i
$486$		0			0
$487$	28.8664	+	28.8664i	1.30806	+	1.30806i	0.922812	+	0.385250i	$0.125885\pi$
$487$	28.8664	+	28.8664i	1.30806	+	1.30806i	0.385250	+	0.922812i	$0.374115\pi$
$488$	−1.04704	+	1.49533i	−0.0473973	+	0.0676904i
$489$		0			0
$490$	−6.92730	−	10.2482i	−0.312944	−	0.462966i
$491$	14.3448	−	17.0954i	0.647371	−	0.771506i	−0.338144	−	0.941094i	$-0.609799\pi$
$491$	14.3448	−	17.0954i	0.647371	−	0.771506i	0.985515	+	0.169588i	$0.0542437\pi$
$492$		0			0
$493$	−1.50261	+	0.700677i	−0.0676740	+	0.0315569i
$494$	0.900221	+	1.55923i	0.0405029	+	0.0701530i
$495$		0			0
$496$	4.04281	−	7.00235i	0.181527	−	0.314415i
$497$	0.361190	−	4.12842i	0.0162016	−	0.185185i
$498$		0			0
$499$	−17.8528	−	3.14793i	−0.799202	−	0.140921i	−0.240891	−	0.970552i	$-0.577439\pi$
$499$	−17.8528	−	3.14793i	−0.799202	−	0.140921i	−0.558311	+	0.829631i	$0.688551\pi$
$500$	2.48257	−	10.9012i	0.111024	−	0.487518i
$501$		0			0
$502$	−20.7074	−	1.81166i	−0.924217	−	0.0808585i
$503$	29.5490	−	7.91764i	1.31753	−	0.353030i	0.469476	−	0.882945i	$-0.344443\pi$
$503$	29.5490	−	7.91764i	1.31753	−	0.353030i	0.848051	+	0.529915i	$0.177776\pi$
$504$		0			0
$505$	3.97537	+	0.0654417i	0.176902	+	0.00291212i
$506$	0.441313	−	1.21250i	0.0196188	−	0.0539021i
$507$		0			0
$508$	−10.0313	+	0.877621i	−0.445065	+	0.0389381i
$509$	−36.7004	+	13.3579i	−1.62672	+	0.592077i	−0.984645	−	0.174566i	$-0.944148\pi$
$509$	−36.7004	+	13.3579i	−1.62672	+	0.592077i	−0.642073	+	0.766644i	$0.721925\pi$
$510$		0			0
$511$	2.73274	+	15.4982i	0.120889	+	0.685598i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			5.66167i			0.249726i
$515$	11.5287	+	25.8248i	0.508015	+	1.13798i
$516$		0			0
$517$	−1.72337	−	0.803623i	−0.0757939	−	0.0353433i
$518$	0.225036	+	2.57217i	0.00988750	+	0.113015i
$519$		0			0
$520$	2.88882	+	3.56016i	0.126683	+	0.156123i
$521$	22.2362	−	12.8381i	0.974186	−	0.562447i	0.0736765	−	0.997282i	$-0.476527\pi$
$521$	22.2362	−	12.8381i	0.974186	−	0.562447i	0.900510	+	0.434835i	$0.143193\pi$
$522$		0			0
$523$	5.40063	+	20.1554i	0.236153	+	0.881336i	0.977626	+	0.210353i	$0.0674612\pi$
$523$	5.40063	+	20.1554i	0.236153	+	0.881336i	−0.741472	+	0.670983i	$0.765872\pi$
$524$	16.8797	−	14.1637i	0.737391	−	0.618745i
$525$		0			0
$526$	−1.59800	+	9.06271i	−0.0696761	+	0.395153i
$527$	4.15879	+	5.93937i	0.181160	+	0.258723i
$528$		0			0
$529$	10.7274	+	12.7844i	0.466408	+	0.555844i
$530$	13.3333	−	7.40807i	0.579160	−	0.321786i
$531$		0			0
$532$	0.275368	−	1.02769i	0.0119387	−	0.0445559i
$533$	0.564129	+	1.20978i	0.0244351	+	0.0524013i
$534$		0			0
$535$	−28.0019	−	13.6230i	−1.21063	−	0.588974i
$536$	−2.84627	−	7.82007i	−0.122940	−	0.337776i
$537$		0			0
$538$	−9.50065	−	6.65243i	−0.409602	−	0.286806i
$539$	1.13303			0.0488029
$540$		0			0
$541$	−7.30965			−0.314267			−0.157133	−	0.987577i	$-0.550225\pi$
$541$	−7.30965			−0.314267			−0.157133	+	0.987577i	$0.550225\pi$
$542$	−6.19664	−	4.33893i	−0.266169	−	0.186373i
$543$		0			0
$544$	−0.306701	−	0.842654i	−0.0131497	−	0.0361285i
$545$	26.5600	−	9.17484i	1.13770	−	0.393007i
$546$		0			0
$547$	−14.4758	−	31.0435i	−0.618941	−	1.32732i	−0.926679	−	0.375853i	$-0.877350\pi$
$547$	−14.4758	−	31.0435i	−0.618941	−	1.32732i	0.307738	−	0.951471i	$-0.400428\pi$
$548$	5.83242	−	21.7669i	0.249149	−	0.929836i
$549$		0			0
$550$	0.699902	+	0.747571i	0.0298439	+	0.0318765i
$551$	1.04357	+	1.24368i	0.0444576	+	0.0529825i
$552$		0			0
$553$	−9.85149	−	14.0694i	−0.418928	−	0.598291i
$554$	−4.31936	+	24.4963i	−0.183512	+	1.04075i
$555$		0			0
$556$	−4.31139	+	3.61769i	−0.182844	+	0.153424i
$557$	−9.69273	−	36.1738i	−0.410694	−	1.53273i	−0.793306	−	0.608823i	$-0.791642\pi$
$557$	−9.69273	−	36.1738i	−0.410694	−	1.53273i	0.382612	−	0.923909i	$-0.375025\pi$
$558$		0			0
$559$	−22.8752	+	13.2070i	−0.967518	+	0.558597i
$560$	0.280521	−	2.69472i	0.0118542	−	0.113873i
$561$		0			0
$562$	−0.980119	−	11.2028i	−0.0413438	−	0.472562i
$563$	20.5463	+	9.58091i	0.865924	+	0.403787i	0.804237	−	0.594308i	$-0.202574\pi$
$563$	20.5463	+	9.58091i	0.865924	+	0.403787i	0.0616871	+	0.998096i	$0.480352\pi$
$564$		0			0
$565$	−21.0264	+	9.38659i	−0.884588	+	0.394897i
$566$			15.7116i			0.660408i
$567$		0			0
$568$	−2.41855	+	2.41855i	−0.101480	+	0.101480i
$569$	−3.47879	−	19.7292i	−0.145839	−	0.827092i	−0.966690	−	0.255950i	$-0.917612\pi$
$569$	−3.47879	−	19.7292i	−0.145839	−	0.827092i	0.820851	−	0.571142i	$-0.193499\pi$
$570$		0			0
$571$	−37.9524	+	13.8136i	−1.58826	+	0.578080i	−0.976979	−	0.213334i	$-0.931568\pi$
$571$	−37.9524	+	13.8136i	−1.58826	+	0.578080i	−0.611281	+	0.791414i	$0.709346\pi$
$572$	−0.418347	+	0.0366006i	−0.0174920	+	0.00153035i
$573$		0			0
$574$	0.269786	−	0.741232i	0.0112607	−	0.0309384i
$575$	−30.6781	+	7.14680i	−1.27936	+	0.298042i
$576$		0			0
$577$	0.250804	−	0.0672027i	0.0104411	−	0.00279769i	−0.253595	−	0.967311i	$-0.581613\pi$
$577$	0.250804	−	0.0672027i	0.0104411	−	0.00279769i	0.264036	+	0.964513i	$0.414946\pi$
$578$	−16.1342	−	1.41156i	−0.671096	−	0.0587133i
$579$		0			0
$580$	3.12281	+	2.70918i	0.129668	+	0.112492i
$581$	14.3562	+	2.53138i	0.595595	+	0.105019i
$582$		0			0
$583$	−0.121767	+	1.39180i	−0.00504306	+	0.0576425i
$584$	6.49425	−	11.2484i	0.268734	−	0.465461i
$585$		0			0
$586$	−6.57446	−	11.3873i	−0.271588	−	0.470405i
$587$	24.4223	−	11.3883i	1.00802	−	0.470046i	0.152767	−	0.988262i	$-0.451182\pi$
$587$	24.4223	−	11.3883i	1.00802	−	0.470046i	0.855249	+	0.518217i	$0.173404\pi$
$588$		0			0
$589$	4.56382	−	5.43895i	0.188049	−	0.224108i
$590$	8.76543	−	5.92503i	0.360867	−	0.243930i
$591$		0			0
$592$	1.22230	−	1.74562i	0.0502362	−	0.0717447i
$593$	−20.0504	−	20.0504i	−0.823370	−	0.823370i	0.163220	−	0.986590i	$-0.447812\pi$
$593$	−20.0504	−	20.0504i	−0.823370	−	0.823370i	−0.986590	+	0.163220i	$0.947812\pi$
$594$		0			0
$595$	2.08373	+	1.24922i	0.0854247	+	0.0512130i
$596$	2.03361	−	0.358581i	0.0833000	−	0.0146880i
$597$		0			0
$598$	5.45901	−	11.7069i	0.223235	−	0.478730i
$599$	−27.1271	−	22.7623i	−1.10838	−	0.930043i	−0.110422	−	0.993885i	$-0.535220\pi$
$599$	−27.1271	−	22.7623i	−1.10838	−	0.930043i	−0.997960	+	0.0638421i	$0.979665\pi$
$600$		0			0
$601$	38.8010	+	14.1224i	1.58273	+	0.576065i	0.975794	−	0.218690i	$-0.0701783\pi$
$601$	38.8010	+	14.1224i	1.58273	+	0.576065i	0.606931	+	0.794755i	$0.292401\pi$
$602$	15.0771	+	4.03988i	0.614495	+	0.164653i
$603$		0			0
$604$	0.0858865	+	0.0495866i	0.00349467	+	0.00201765i
$605$	24.1975	−	3.85713i	0.983767	−	0.156815i
$606$		0			0
$607$	6.72972	−	4.71220i	0.273151	−	0.191262i	−0.428973	−	0.903318i	$-0.641124\pi$
$607$	6.72972	−	4.71220i	0.273151	−	0.191262i	0.702124	+	0.712055i	$0.252235\pi$
$608$	−0.719304	+	0.503662i	−0.0291716	+	0.0204262i
$609$		0			0
$610$	−2.39597	+	3.30467i	−0.0970101	+	0.133802i
$611$	−16.4856	−	9.51796i	−0.666936	−	0.385056i
$612$		0			0
$613$	2.46287	+	0.659923i	0.0994743	+	0.0266541i	0.308213	−	0.951317i	$-0.400269\pi$
$613$	2.46287	+	0.659923i	0.0994743	+	0.0266541i	−0.208739	+	0.977971i	$0.566936\pi$
$614$	−7.03946	−	2.56215i	−0.284089	−	0.103400i
$615$		0			0
$616$	0.190101	+	0.159514i	0.00765938	+	0.00642699i
$617$	−8.07120	+	17.3087i	−0.324934	+	0.696824i	−0.999129	−	0.0417299i	$-0.986713\pi$
$617$	−8.07120	+	17.3087i	−0.324934	+	0.696824i	0.674195	+	0.738554i	$0.264491\pi$
$618$		0			0
$619$	−21.7107	+	3.82818i	−0.872626	+	0.153867i	−0.591988	−	0.805946i	$-0.701657\pi$
$619$	−21.7107	+	3.82818i	−0.872626	+	0.153867i	−0.280637	+	0.959814i	$0.590546\pi$
$620$	9.29648	−	15.5068i	0.373356	−	0.622768i
$621$		0			0
$622$	10.9266	+	10.9266i	0.438115	+	0.438115i
$623$	−11.9341	+	17.0436i	−0.478128	+	0.682837i
$624$		0			0
$625$	5.95165	−	24.2812i	0.238066	−	0.971249i
$626$	14.9037	−	17.7615i	0.595672	−	0.709894i
$627$		0			0
$628$	−10.7578	+	5.01642i	−0.429281	+	0.200177i
$629$	0.955476	+	1.65493i	0.0380973	+	0.0659865i
$630$		0			0
$631$	−5.47963	+	9.49099i	−0.218140	+	0.377830i	−0.954239	−	0.299044i	$-0.903332\pi$
$631$	−5.47963	+	9.49099i	−0.218140	+	0.377830i	0.736099	+	0.676874i	$0.236666\pi$
$632$	−1.23549	+	14.1217i	−0.0491450	+	0.561730i
$633$		0			0
$634$	−27.4153	−	4.83405i	−1.08880	−	0.191985i
$635$	−22.4598	+	1.59296i	−0.891291	+	0.0632145i
$636$		0			0
$637$	11.2994	+	0.988566i	0.447697	+	0.0391684i
$638$	−0.365772	+	0.0980084i	−0.0144811	+	0.00388019i
$639$		0			0
$640$	−1.60695	+	1.55490i	−0.0635203	+	0.0614628i
$641$	−10.1359	+	27.8483i	−0.400345	+	1.09994i	0.561769	+	0.827294i	$0.310121\pi$
$641$	−10.1359	+	27.8483i	−0.400345	+	1.09994i	−0.962114	+	0.272646i	$0.912101\pi$
$642$		0			0
$643$	−24.8490	+	2.17400i	−0.979947	+	0.0857343i	−0.565859	−	0.824502i	$-0.691455\pi$
$643$	−24.8490	+	2.17400i	−0.979947	+	0.0857343i	−0.414089	+	0.910237i	$0.635900\pi$
$644$	−7.17281	+	2.61069i	−0.282648	+	0.102876i
$645$		0			0
$646$	−0.136736	−	0.775466i	−0.00537979	−	0.0305103i
$647$	−6.38157	+	6.38157i	−0.250885	+	0.250885i	−0.821334	−	0.570448i	$-0.806770\pi$
$647$	−6.38157	+	6.38157i	−0.250885	+	0.250885i	0.570448	+	0.821334i	$0.306770\pi$
$648$		0			0
$649$			0.969094i			0.0380403i
$650$	6.32768	+	8.06599i	0.248192	+	0.316374i
$651$		0			0
$652$	10.4999	+	4.89617i	0.411206	+	0.191749i
$653$	−1.17337	−	13.4117i	−0.0459175	−	0.524840i	−0.983969	−	0.178342i	$-0.942927\pi$
$653$	−1.17337	−	13.4117i	−0.0459175	−	0.524840i	0.938051	−	0.346497i	$-0.112629\pi$
$654$		0			0
$655$	38.2602	−	31.0455i	1.49495	−	1.21305i
$656$	−0.563806	+	0.325513i	−0.0220129	+	0.0127092i
$657$		0			0
$658$	2.91144	+	10.8657i	0.113500	+	0.423587i
$659$	−15.7592	+	13.2235i	−0.613891	+	0.515116i	−0.895877	−	0.444303i	$-0.853451\pi$
$659$	−15.7592	+	13.2235i	−0.613891	+	0.515116i	0.281985	+	0.959419i	$0.409007\pi$
$660$		0			0
$661$	−5.60715	+	31.7997i	−0.218093	+	1.23687i	0.657366	+	0.753572i	$0.271671\pi$
$661$	−5.60715	+	31.7997i	−0.218093	+	1.23687i	−0.875458	+	0.483294i	$0.839440\pi$
$662$	−0.562491	−	0.803320i	−0.0218618	−	0.0312219i
$663$		0			0
$664$	−7.73368	−	9.21664i	−0.300125	−	0.357675i
$665$	0.653482	−	2.28753i	0.0253410	−	0.0887068i
$666$		0			0
$667$	3.01465	−	11.2508i	0.116728	−	0.435633i
$668$	−2.17537	−	4.66510i	−0.0841677	−	0.180498i
$669$		0			0
$670$	−6.07578	−	17.5886i	−0.234728	−	0.679507i
$671$	−0.127875	−	0.351333i	−0.00493655	−	0.0135631i
$672$		0			0
$673$	−2.28431	−	1.59949i	−0.0880538	−	0.0616559i	0.528720	−	0.848796i	$-0.322672\pi$
$673$	−2.28431	−	1.59949i	−0.0880538	−	0.0616559i	−0.616774	+	0.787140i	$0.711561\pi$
$674$	−15.5130			−0.597539
$675$		0			0
$676$	8.79601			0.338308
$677$	−27.2385	−	19.0726i	−1.04686	−	0.733019i	−0.0822260	−	0.996614i	$-0.526203\pi$
$677$	−27.2385	−	19.0726i	−1.04686	−	0.733019i	−0.964633	+	0.263595i	$0.915092\pi$
$678$		0			0
$679$	4.21204	+	11.5725i	0.161643	+	0.444112i
$680$	−0.654697	−	1.89526i	−0.0251065	−	0.0726800i
$681$		0			0
$682$	0.699878	+	1.50089i	0.0267997	+	0.0574721i
$683$	9.05115	−	33.7793i	0.346333	−	1.29253i	−0.544715	−	0.838621i	$-0.683362\pi$
$683$	9.05115	−	33.7793i	0.346333	−	1.29253i	0.891048	−	0.453910i	$-0.149971\pi$
$684$		0			0
$685$	13.8411	−	48.4510i	0.528839	−	1.85122i
$686$	−9.76013	−	11.6317i	−0.372644	−	0.444099i
$687$		0			0
$688$	−7.38916	−	10.5528i	−0.281709	−	0.402322i
$689$	−2.42870	+	13.7738i	−0.0925259	+	0.524741i
$690$		0			0
$691$	−8.59664	+	7.21344i	−0.327032	+	0.274412i	−0.791489	−	0.611183i	$-0.790694\pi$
$691$	−8.59664	+	7.21344i	−0.327032	+	0.274412i	0.464457	+	0.885595i	$0.346249\pi$
$692$	−3.46631	−	12.9365i	−0.131769	−	0.491770i
$693$		0			0
$694$	−1.67125	+	0.964896i	−0.0634397	+	0.0366269i
$695$	−9.77241	+	7.92962i	−0.370689	+	0.300788i
$696$		0			0
$697$	−0.0508813	−	0.581576i	−0.00192727	−	0.0220288i
$698$	−19.2685	−	8.98505i	−0.729324	−	0.340089i
$699$		0			0
$700$	0.726358	−	6.01444i	0.0274538	−	0.227324i
$701$		−	30.0692i		−	1.13570i	−0.823132	−	0.567849i	$-0.807776\pi$
$701$		−	30.0692i		−	1.13570i	0.823132	−	0.567849i	$-0.192224\pi$
$702$		0			0
$703$	1.32318	−	1.32318i	0.0499047	−	0.0499047i
$704$	−0.0355657	−	0.201703i	−0.00134043	−	0.00760197i
$705$		0			0
$706$	10.1532	−	3.69548i	0.382123	−	0.139081i
$707$	2.14617	−	0.187766i	0.0807151	−	0.00706166i
$708$		0			0
$709$	15.5993	−	42.8588i	0.585845	−	1.60960i	−0.192177	−	0.981360i	$-0.561555\pi$
$709$	15.5993	−	42.8588i	0.585845	−	1.60960i	0.778022	−	0.628237i	$-0.216223\pi$
$710$	−5.49632	+	5.31829i	−0.206273	+	0.199592i
$711$		0			0
$712$	16.5871	−	4.44451i	0.621629	−	0.166565i
$713$	−50.7448	−	4.43959i	−1.90041	−	0.166264i
$714$		0			0
$715$	−0.936672	+	0.0664332i	−0.0350295	+	0.00248446i
$716$	4.05327	+	0.714700i	0.151478	+	0.0267096i
$717$		0			0
$718$	0.681888	−	7.79401i	0.0254478	−	0.290870i
$719$	−2.51235	+	4.35151i	−0.0936947	+	0.162284i	−0.909063	−	0.416658i	$-0.863201\pi$
$719$	−2.51235	+	4.35151i	−0.0936947	+	0.162284i	0.815368	+	0.578943i	$0.196534\pi$
$720$		0			0
$721$	7.66221	+	13.2713i	0.285356	+	0.494250i
$722$	16.5210	−	7.70388i	0.614849	−	0.286709i
$723$		0			0
$724$	−0.109900	+	0.130974i	−0.00408442	+	0.00486762i
$725$	6.88216	+	6.17202i	0.255597	+	0.229223i
$726$		0			0
$727$	−27.2940	+	38.9798i	−1.01228	+	1.44568i	−0.120766	+	0.992681i	$0.538535\pi$
$727$	−27.2940	+	38.9798i	−1.01228	+	1.44568i	−0.891511	+	0.453000i	$0.850354\pi$
$728$	1.75665	+	1.75665i	0.0651058	+	0.0651058i
$729$		0			0
$730$	14.9336	−	24.9097i	0.552718	−	0.921950i
$731$	11.3768	−	2.00603i	0.420784	−	0.0741956i
$732$		0			0
$733$	7.39404	−	15.8566i	0.273105	−	0.585676i	−0.721142	−	0.692787i	$-0.756382\pi$
$733$	7.39404	−	15.8566i	0.273105	−	0.585676i	0.994247	+	0.107111i	$0.0341602\pi$
$734$	2.60133	+	2.18278i	0.0960169	+	0.0805677i
$735$		0			0
$736$	5.91998	+	2.15470i	0.218213	+	0.0794231i
$737$	1.64638	+	0.441146i	0.0606452	+	0.0162498i
$738$		0			0
$739$	−16.4332	−	9.48774i	−0.604507	−	0.349012i	0.166306	−	0.986074i	$-0.446816\pi$
$739$	−16.4332	−	9.48774i	−0.604507	−	0.349012i	−0.770812	+	0.637062i	$0.780149\pi$
$740$	2.79702	−	3.85782i	0.102821	−	0.141816i
$741$		0			0
$742$	6.77026	−	4.74059i	0.248544	−	0.174032i
$743$	12.3738	−	8.66423i	0.453951	−	0.317860i	−0.324143	−	0.946008i	$-0.605076\pi$
$743$	12.3738	−	8.66423i	0.453951	−	0.317860i	0.778094	+	0.628148i	$0.216187\pi$
$744$		0			0
$745$	4.55987	−	0.726855i	0.167061	−	0.0266299i
$746$	−1.16586	−	0.673108i	−0.0426851	−	0.0246442i
$747$		0			0
$748$	0.177406	+	0.0475358i	0.00648660	+	0.00173808i
$749$	−15.8557	−	5.77102i	−0.579356	−	0.210868i
$750$		0			0
$751$	11.4253	+	9.58698i	0.416916	+	0.349834i	0.826988	−	0.562219i	$-0.190052\pi$
$751$	11.4253	+	9.58698i	0.416916	+	0.349834i	−0.410073	+	0.912053i	$0.634497\pi$
$752$	3.92366	−	8.41431i	0.143081	−	0.306838i
$753$		0			0
$754$	−3.73326	+	0.658275i	−0.135957	+	0.0239730i
$755$	0.190197	+	0.114025i	0.00692198	+	0.00414979i
$756$		0			0
$757$	−12.2668	−	12.2668i	−0.445843	−	0.445843i	0.448127	−	0.893970i	$-0.352091\pi$
$757$	−12.2668	−	12.2668i	−0.445843	−	0.445843i	−0.893970	+	0.448127i	$0.852091\pi$
$758$	13.1356	−	18.7596i	0.477108	−	0.681381i
$759$		0			0
$760$	−1.62673	+	1.09960i	−0.0590078	+	0.0398866i
$761$	−16.6045	+	19.7885i	−0.601913	+	0.717332i	−0.977848	−	0.209314i	$-0.932877\pi$
$761$	−16.6045	+	19.7885i	−0.601913	+	0.717332i	0.375936	+	0.926646i	$0.377321\pi$
$762$		0			0
$763$	13.7996	−	6.43485i	0.499579	−	0.232957i
$764$	6.95869	+	12.0528i	0.251757	+	0.436055i
$765$		0			0
$766$	4.84175	−	8.38616i	0.174940	−	0.303004i
$767$	−0.845536	+	9.66452i	−0.0305305	+	0.348966i
$768$		0			0
$769$	−17.2526	−	3.04209i	−0.622144	−	0.109701i	−0.146314	−	0.989238i	$-0.546741\pi$
$769$	−17.2526	−	3.04209i	−0.622144	−	0.109701i	−0.475830	+	0.879538i	$0.657852\pi$
$770$	0.419150	+	0.363632i	0.0151051	+	0.0131044i
$771$		0			0
$772$	17.8552	+	1.56213i	0.642622	+	0.0562221i
$773$	−16.9577	+	4.54381i	−0.609927	+	0.163429i	−0.550544	−	0.834806i	$-0.685580\pi$
$773$	−16.9577	+	4.54381i	−0.609927	+	0.163429i	−0.0593824	+	0.998235i	$0.518913\pi$
$774$		0			0
$775$	21.3555	−	34.3274i	0.767111	−	1.23308i
$776$	3.47635	−	9.55120i	0.124794	−	0.342868i
$777$		0			0
$778$	−20.8482	+	1.82398i	−0.747443	+	0.0653928i
$779$	−0.537196	+	0.195523i	−0.0192471	+	0.00700535i
$780$		0			0
$781$	−0.121647	−	0.689894i	−0.00435287	−	0.0246864i
$782$	−3.99469	+	3.99469i	−0.142850	+	0.142850i
$783$		0			0
$784$			5.53196i			0.197570i
$785$	−24.2364	+	10.8196i	−0.865036	+	0.386168i
$786$		0			0
$787$	4.10799	+	1.91559i	0.146434	+	0.0682833i	0.494454	−	0.869204i	$-0.335368\pi$
$787$	4.10799	+	1.91559i	0.146434	+	0.0682833i	−0.348020	+	0.937487i	$0.613146\pi$
$788$	2.36014	+	26.9766i	0.0840766	+	0.961000i
$789$		0			0
$790$	−3.28200	+	31.5272i	−0.116768	+	1.12169i
$791$	−10.8054	+	6.23852i	−0.384197	+	0.221816i
$792$		0			0
$793$	−0.968723	−	3.61532i	−0.0344004	−	0.128384i
$794$	1.53838	−	1.29085i	0.0545951	−	0.0458107i
$795$		0			0
$796$	2.97420	−	16.8675i	0.105418	−	0.597853i
$797$	1.80840	+	2.58266i	0.0640567	+	0.0914825i	0.849902	−	0.526940i	$-0.176661\pi$
$797$	1.80840	+	2.58266i	0.0640567	+	0.0914825i	−0.785846	+	0.618423i	$0.787772\pi$
$798$		0			0
$799$	5.35148	+	6.37764i	0.189322	+	0.225625i
$800$	−3.64999	+	3.41725i	−0.129047	+	0.120818i
$801$		0			0
$802$	1.43029	−	5.33791i	0.0505052	−	0.188488i
$803$	1.12426	+	2.41099i	0.0396744	+	0.0850821i
$804$		0			0
$805$	−16.1328	+	5.57289i	−0.568607	+	0.196419i
$806$	5.67016	+	15.5786i	0.199723	+	0.548734i
$807$		0			0
$808$	−1.45652	−	1.01986i	−0.0512401	−	0.0358787i
$809$	−13.7303			−0.482731			−0.241366	−	0.970434i	$-0.577595\pi$
$809$	−13.7303			−0.482731			−0.241366	+	0.970434i	$0.577595\pi$
$810$		0			0
$811$	37.3334			1.31095			0.655477	−	0.755215i	$-0.272468\pi$
$811$	37.3334			1.31095			0.655477	+	0.755215i	$0.272468\pi$
$812$	1.83502	+	1.28489i	0.0643964	+	0.0450909i
$813$		0			0
$814$	0.149279	+	0.410141i	0.00523223	+	0.0143754i
$815$	23.2950	+	11.3331i	0.815989	+	0.396982i
$816$		0			0
$817$	−4.78079	−	10.2524i	−0.167259	−	0.358688i
$818$	8.38725	−	31.3016i	0.293253	−	1.09444i
$819$		0			0
$820$	−1.27252	+	0.707021i	−0.0444382	+	0.0246902i
$821$	11.6201	+	13.8483i	0.405544	+	0.483309i	0.929702	−	0.368312i	$-0.120064\pi$
$821$	11.6201	+	13.8483i	0.405544	+	0.483309i	−0.524158	+	0.851621i	$0.675620\pi$
$822$		0			0
$823$	26.7341	+	38.1803i	0.931893	+	1.33088i	0.943648	+	0.330950i	$0.107369\pi$
$823$	26.7341	+	38.1803i	0.931893	+	1.33088i	−0.0117552	+	0.999931i	$0.503742\pi$
$824$	2.19627	−	12.4556i	0.0765106	−	0.433913i
$825$		0			0
$826$	4.39166	−	3.68504i	0.152805	−	0.128219i
$827$	3.94411	+	14.7196i	0.137150	+	0.511851i	0.999980	+	0.00635656i	$0.00202337\pi$
$827$	3.94411	+	14.7196i	0.137150	+	0.511851i	−0.862830	+	0.505495i	$0.831310\pi$
$828$		0			0
$829$	−36.1429	+	20.8671i	−1.25530	+	0.724746i	−0.972156	−	0.234333i	$-0.924709\pi$
$829$	−36.1429	+	20.8671i	−1.25530	+	0.724746i	−0.283140	+	0.959079i	$0.591376\pi$
$830$	−16.9515	−	20.8909i	−0.588394	−	0.725133i
$831$		0			0
$832$	−0.178701	−	2.04256i	−0.00619534	−	0.0708131i
$833$	−4.49591	−	2.09648i	−0.155774	−	0.0726387i
$834$		0			0
$835$	−4.69192	−	10.5101i	−0.162371	−	0.363718i
$836$		−	0.179850i		−	0.00622023i
$837$		0			0
$838$	−1.66372	+	1.66372i	−0.0574723	+	0.0574723i
$839$	6.98603	+	39.6197i	0.241185	+	1.36783i	0.829189	+	0.558968i	$0.188803\pi$
$839$	6.98603	+	39.6197i	0.241185	+	1.36783i	−0.588005	+	0.808858i	$0.700086\pi$
$840$		0			0
$841$	24.0389	−	8.74945i	0.828928	−	0.301705i
$842$	−17.8549	+	1.56210i	−0.615319	+	0.0538334i
$843$		0			0
$844$	1.71673	−	4.71667i	0.0590922	−	0.162355i
$845$	19.6658	+	0.323735i	0.676524	+	0.0111368i
$846$		0			0
$847$	12.8247	−	3.43636i	0.440661	−	0.118075i
$848$	−6.79542	−	0.594522i	−0.233356	−	0.0204160i
$849$		0			0
$850$	−1.39399	−	4.26146i	−0.0478136	−	0.146167i
$851$	−13.2212	−	2.33126i	−0.453218	−	0.0799146i
$852$		0			0
$853$	−2.06130	+	23.5607i	−0.0705775	+	0.806704i	0.875596	+	0.483044i	$0.160469\pi$
$853$	−2.06130	+	23.5607i	−0.0705775	+	0.806704i	−0.946173	+	0.323660i	$0.895087\pi$
$854$	−1.10589	+	1.91546i	−0.0378427	+	0.0655455i
$855$		0			0
$856$	6.96308	+	12.0604i	0.237993	+	0.412217i
$857$	−1.65214	+	0.770407i	−0.0564361	+	0.0263166i	−0.450631	−	0.892710i	$-0.648801\pi$
$857$	−1.65214	+	0.770407i	−0.0564361	+	0.0263166i	0.394195	+	0.919027i	$0.371023\pi$
$858$		0			0
$859$	34.6572	−	41.3029i	1.18249	−	1.40924i	0.290682	−	0.956820i	$-0.406118\pi$
$859$	34.6572	−	41.3029i	1.18249	−	1.40924i	0.891807	−	0.452416i	$-0.149438\pi$
$860$	−16.1320	−	23.8656i	−0.550097	−	0.813809i
$861$		0			0
$862$	16.1998	−	23.1357i	0.551768	−	0.788006i
$863$	−12.9123	−	12.9123i	−0.439540	−	0.439540i	0.452317	−	0.891857i	$-0.350598\pi$
$863$	−12.9123	−	12.9123i	−0.439540	−	0.439540i	−0.891857	+	0.452317i	$0.850598\pi$
$864$		0			0
$865$	−7.27374	−	29.0505i	−0.247315	−	0.987745i
$866$	20.7992	−	3.66747i	0.706787	−	0.124626i
$867$		0			0
$868$	4.14029	−	8.87887i	0.140530	−	0.301369i
$869$	−2.22411	−	1.86625i	−0.0754478	−	0.0633082i
$870$		0			0
$871$	16.0340	+	5.83590i	0.543291	+	0.197742i
$872$	−12.1385	−	3.25250i	−0.411061	−	0.110144i
$873$		0			0
$874$	4.79086	+	2.76600i	0.162053	+	0.0935614i
$875$	1.84533	−	13.4201i	0.0623834	−	0.453683i
$876$		0			0
$877$	12.4115	−	8.69061i	0.419106	−	0.293461i	−0.344938	−	0.938625i	$-0.612100\pi$
$877$	12.4115	−	8.69061i	0.419106	−	0.293461i	0.764044	+	0.645165i	$0.223211\pi$
$878$	−6.60616	+	4.62568i	−0.222947	+	0.156109i
$879$		0			0
$880$	−0.0720929	−	0.452270i	−0.00243025	−	0.0152460i
$881$	4.03571	+	2.33002i	0.135967	+	0.0785004i	0.566440	−	0.824103i	$-0.308320\pi$
$881$	4.03571	+	2.33002i	0.135967	+	0.0785004i	−0.430474	+	0.902603i	$0.641653\pi$
$882$		0			0
$883$	−27.1020	−	7.26197i	−0.912056	−	0.244385i	−0.227869	−	0.973692i	$-0.573176\pi$
$883$	−27.1020	−	7.26197i	−0.912056	−	0.244385i	−0.684187	+	0.729307i	$0.739843\pi$
$884$	1.72775	+	0.628848i	0.0581104	+	0.0211505i
$885$		0			0
$886$	8.05938	+	6.76262i	0.270760	+	0.227195i
$887$	7.58519	−	16.2665i	0.254686	−	0.546176i	−0.736843	−	0.676064i	$-0.763684\pi$
$887$	7.58519	−	16.2665i	0.254686	−	0.546176i	0.991529	+	0.129889i	$0.0414620\pi$
$888$		0			0
$889$	−12.0152	+	2.11861i	−0.402977	+	0.0710558i
$890$	37.2485	−	9.32639i	1.24857	−	0.312621i
$891$		0			0
$892$	−8.65084	−	8.65084i	−0.289652	−	0.289652i
$893$	4.67609	−	6.67814i	0.156479	−	0.223476i
$894$		0			0
$895$	9.03584	+	1.74708i	0.302035	+	0.0583985i
$896$	−0.778819	+	0.928161i	−0.0260185	+	0.0310077i
$897$		0			0
$898$	−18.3465	+	8.55511i	−0.612231	+	0.285488i
$899$	7.47462	+	12.9464i	0.249292	+	0.431787i
$900$		0			0
$901$	3.05848	−	5.29744i	0.101893	−	0.176483i
$902$	0.0116213	−	0.132832i	0.000386948	−	0.00442284i
$903$		0			0
$904$	10.1413	+	1.78819i	0.337295	+	0.0594742i
$905$	−0.250532	+	0.288783i	−0.00832796	+	0.00959946i
$906$		0			0
$907$	−28.2315	−	2.46994i	−0.937412	−	0.0820129i	−0.391800	−	0.920051i	$-0.628147\pi$
$907$	−28.2315	−	2.46994i	−0.937412	−	0.0820129i	−0.545612	+	0.838038i	$0.683703\pi$
$908$	10.9818	−	2.94256i	0.364443	−	0.0976523i
$909$		0			0
$910$	3.86280	+	3.99211i	0.128051	+	0.132337i
$911$	−16.4035	+	45.0683i	−0.543473	+	1.49318i	0.298901	+	0.954284i	$0.403380\pi$
$911$	−16.4035	+	45.0683i	−0.543473	+	1.49318i	−0.842373	+	0.538894i	$0.818842\pi$
$912$		0			0
$913$	2.45484	−	0.214771i	0.0812435	−	0.00710788i
$914$	−22.1014	+	8.04425i	−0.731049	+	0.266080i
$915$		0			0
$916$	0.288903	+	1.63845i	0.00954562	+	0.0541359i
$917$	18.8783	−	18.8783i	0.623418	−	0.623418i
$918$		0			0
$919$			21.8235i			0.719892i	0.932973	+	0.359946i	$0.117205\pi$
$919$			21.8235i			0.719892i	−0.932973	+	0.359946i	$0.882795\pi$
$920$	13.1564	+	5.03528i	0.433753	+	0.166008i
$921$		0			0
$922$	−7.03647	−	3.28116i	−0.231734	−	0.108059i
$923$	−0.611219	−	6.98627i	−0.0201185	−	0.229956i
$924$		0			0
$925$	6.39547	−	8.52224i	0.210282	−	0.280209i
$926$	−30.6527	+	17.6974i	−1.00731	+	0.581572i
$927$		0			0
$928$	−0.478522	−	1.78587i	−0.0157083	−	0.0586241i
$929$	15.6214	−	13.1080i	0.512523	−	0.430058i	−0.349493	−	0.936939i	$-0.613646\pi$
$929$	15.6214	−	13.1080i	0.512523	−	0.430058i	0.862016	+	0.506881i	$0.169202\pi$
$930$		0			0
$931$	−0.843524	+	4.78386i	−0.0276454	+	0.156785i
$932$	9.55298	+	13.6431i	0.312918	+	0.446893i
$933$		0			0
$934$	8.11088	+	9.66618i	0.265396	+	0.316287i
$935$	0.394888	+	0.112808i	0.0129142	+	0.00368922i
$936$		0			0
$937$	−1.64111	+	6.12469i	−0.0536126	+	0.200085i	−0.987537	−	0.157385i	$-0.949694\pi$
$937$	−1.64111	+	6.12469i	−0.0536126	+	0.200085i	0.933925	+	0.357470i	$0.116360\pi$
$938$	−4.26130	−	9.13840i	−0.139137	−	0.298379i
$939$		0			0
$940$	9.08207	−	18.6680i	0.296224	−	0.608884i
$941$	3.41430	+	9.38071i	0.111303	+	0.305802i	0.982821	−	0.184561i	$-0.0590863\pi$
$941$	3.41430	+	9.38071i	0.111303	+	0.305802i	−0.871518	+	0.490363i	$0.836864\pi$
$942$		0			0
$943$	3.35968	+	2.35247i	0.109406	+	0.0766070i
$944$	−4.73157			−0.153999
$945$		0			0
$946$	2.63855			0.0857865
$947$	12.2790	+	8.59784i	0.399013	+	0.279392i	0.755811	−	0.654789i	$-0.227243\pi$
$947$	12.2790	+	8.59784i	0.399013	+	0.279392i	−0.356798	+	0.934182i	$0.616132\pi$
$948$		0			0
$949$	9.10840	+	25.0251i	0.295671	+	0.812349i
$950$	−3.67746	+	2.39857i	−0.119313	+	0.0778199i
$951$		0			0
$952$	−0.459178	−	0.984710i	−0.0148820	−	0.0319146i
$953$	1.34190	−	5.00803i	0.0434684	−	0.162226i	−0.940780	−	0.339018i	$-0.889905\pi$
$953$	1.34190	−	5.00803i	0.0434684	−	0.162226i	0.984248	+	0.176792i	$0.0565719\pi$
$954$		0			0
$955$	15.1144	+	27.2034i	0.489090	+	0.880280i
$956$	−7.53384	−	8.97848i	−0.243662	−	0.290385i
$957$		0			0
$958$	−6.30986	−	9.01141i	−0.203862	−	0.291146i
$959$	4.74124	−	26.8889i	0.153103	−	0.868289i
$960$		0			0
$961$	26.3344	−	22.0972i	0.849497	−	0.712812i
$962$	1.13087	+	4.22047i	0.0364608	+	0.136073i
$963$		0			0
$964$	9.15737	−	5.28701i	0.294939	−	0.170283i
$965$	39.8625	+	4.14970i	1.28322	+	0.133584i
$966$		0			0
$967$	3.24871	+	37.1330i	0.104472	+	1.19412i	0.849685	+	0.527290i	$0.176792\pi$
$967$	3.24871	+	37.1330i	0.104472	+	1.19412i	−0.745214	+	0.666826i	$0.767653\pi$
$968$	−9.93137	−	4.63107i	−0.319206	−	0.148848i
$969$		0			0
$970$	8.12383	−	21.2263i	0.260841	−	0.681535i
$971$			0.0917099i			0.00294311i	0.999999	+	0.00147156i	$0.000468411\pi$
$971$			0.0917099i			0.00294311i	−0.999999	+	0.00147156i	$0.999532\pi$
$972$		0			0
$973$	−4.82190	+	4.82190i	−0.154583	+	0.154583i
$974$	−7.08889	−	40.2031i	−0.227143	−	1.28819i
$975$		0			0
$976$	1.71537	−	0.624344i	0.0549077	−	0.0199848i
$977$	−24.1813	+	2.11559i	−0.773629	+	0.0676837i	−0.467131	−	0.884188i	$-0.654713\pi$
$977$	−24.1813	+	2.11559i	−0.773629	+	0.0676837i	−0.306497	+	0.951872i	$0.599157\pi$
$978$		0			0
$979$	−1.20293	+	3.30502i	−0.0384458	+	0.105629i
$980$	−0.203602	+	12.3682i	−0.00650383	+	0.395086i
$981$		0			0
$982$	−21.5561	+	5.77594i	−0.687883	+	0.184318i
$983$	−12.9503	−	1.13300i	−0.413051	−	0.0361372i	−0.121263	−	0.992620i	$-0.538694\pi$
$983$	−12.9503	−	1.13300i	−0.413051	−	0.0361372i	−0.291788	+	0.956483i	$0.594250\pi$
$984$		0			0
$985$	4.28386	+	60.4001i	0.136495	+	1.92451i
$986$	1.63275	+	0.287899i	0.0519975	+	0.00916856i
$987$		0			0
$988$	0.156919	−	1.79359i	0.00499225	−	0.0570617i
$989$	−40.5796	+	70.2859i	−1.29036	+	2.23496i
$990$		0			0
$991$	−1.82976	−	3.16924i	−0.0581243	−	0.100674i	0.835499	−	0.549492i	$-0.185179\pi$
$991$	−1.82976	−	3.16924i	−0.0581243	−	0.100674i	−0.893623	+	0.448818i	$0.851845\pi$
$992$	−7.32805	+	3.41713i	−0.232666	+	0.108494i
$993$		0			0
$994$	−2.66383	+	3.17463i	−0.0844916	+	0.100693i
$995$	7.27041	−	37.6023i	0.230488	−	1.19207i
$996$		0			0
$997$	3.32110	−	4.74303i	0.105180	−	0.150213i	−0.763111	−	0.646267i	$-0.776329\pi$
$997$	3.32110	−	4.74303i	0.105180	−	0.150213i	0.868292	+	0.496054i	$0.165218\pi$
$998$	12.8186	+	12.8186i	0.405765	+	0.405765i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.7		216
3.2	odd	2		270.2.r.a.257.17	yes	216
5.3	odd	4	inner	810.2.s.a.233.2		216
15.8	even	4		270.2.r.a.203.15	yes	216
27.2	odd	18	inner	810.2.s.a.737.2		216
27.25	even	9		270.2.r.a.137.15	yes	216
135.83	even	36	inner	810.2.s.a.413.7		216
135.133	odd	36		270.2.r.a.83.17	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.17	✓	216	135.133	odd	36
270.2.r.a.137.15	yes	216	27.25	even	9
270.2.r.a.203.15	yes	216	15.8	even	4
270.2.r.a.257.17	yes	216	3.2	odd	2
810.2.s.a.233.2		216	5.3	odd	4	inner
810.2.s.a.413.7		216	135.83	even	36	inner
810.2.s.a.557.7		216	1.1	even	1	trivial
810.2.s.a.737.2		216	27.2	odd	18	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.730092 + 2.11352i) q^{5} +(0.512056 + 1.09811i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.730092 + 2.11352i) q^{5} +(0.512056 + 1.09811i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.614209 - 2.15006i) q^{10} +(0.131652 + 0.156897i) q^{11} +(1.17604 + 1.67956i) q^{13} +(0.210397 - 1.19322i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.232092 - 0.866178i) q^{17} +(-0.760464 + 0.439054i) q^{19} +(-1.73635 + 1.40893i) q^{20} +(-0.0178508 - 0.204035i) q^{22} +(5.70966 + 2.66246i) q^{23} +(-3.93393 + 3.08613i) q^{25} -2.05036i q^{26} +(-0.856750 + 0.856750i) q^{28} +(-0.321053 - 1.82078i) q^{29} +(-7.59799 + 2.76544i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-0.306701 + 0.842654i) q^{34} +(-1.94702 + 1.88396i) q^{35} +(-2.05840 + 0.551547i) q^{37} +(0.874767 + 0.0765322i) q^{38} +(2.23047 - 0.158195i) q^{40} +(0.641136 + 0.113050i) q^{41} +(-1.12279 + 12.8336i) q^{43} +(-0.102407 + 0.177375i) q^{44} +(-3.14995 - 5.45588i) q^{46} +(-8.41431 + 3.92366i) q^{47} +(3.55587 - 4.23773i) q^{49} +(4.99262 - 0.271595i) q^{50} +(-1.17604 + 1.67956i) q^{52} +(4.82344 + 4.82344i) q^{53} +(-0.235487 + 0.392799i) q^{55} +(1.19322 - 0.210397i) q^{56} +(-0.781366 + 1.67564i) q^{58} +(3.62459 + 3.04139i) q^{59} +(-1.71537 - 0.624344i) q^{61} +(7.81010 + 2.09271i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-2.69117 + 3.71182i) q^{65} +(6.81694 - 4.77327i) q^{67} +(0.734561 - 0.514345i) q^{68} +(2.67550 - 0.426482i) q^{70} +(-2.96211 - 1.71017i) q^{71} +(12.5459 + 3.36167i) q^{73} +(2.00250 + 0.728850i) q^{74} +(-0.672670 - 0.564437i) q^{76} +(-0.104877 + 0.224909i) q^{77} +(-13.9602 + 2.46157i) q^{79} +(-1.91783 - 1.14976i) q^{80} +(-0.460346 - 0.460346i) q^{82} +(6.90097 - 9.85560i) q^{83} +(1.66124 - 1.12292i) q^{85} +(8.28078 - 9.86864i) q^{86} +(0.185625 - 0.0865584i) q^{88} +(8.58613 + 14.8716i) q^{89} +(-1.24214 + 2.15145i) q^{91} +(-0.549073 + 6.27594i) q^{92} +(9.14312 + 1.61218i) q^{94} +(-1.48316 - 1.28671i) q^{95} +(10.1255 + 0.885866i) q^{97} +(-5.34346 + 1.43178i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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