LMFDB - Embedded newform 936.2.w.j.307.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(307,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Character	$\chi$	$=$	936.307
Dual form			936.2.w.j.811.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.849559 - 1.13060i) q^{2} +(-0.556500 + 1.92102i) q^{4} +(1.67211 - 1.67211i) q^{5} +(-1.16012 - 1.16012i) q^{7} +(2.64468 - 1.00284i) q^{8} +(-3.31105 - 0.469928i) q^{10} +(0.391951 - 0.391951i) q^{11} +(-3.59209 + 0.311317i) q^{13} +(-0.326039 + 2.29722i) q^{14} +(-3.38062 - 2.13809i) q^{16} -2.95889i q^{17} +(-0.785637 - 0.785637i) q^{19} +(2.28163 + 4.14269i) q^{20} +(-0.776123 - 0.110153i) q^{22} -2.14814 q^{23} -0.591934i q^{25} +(3.40366 + 3.79672i) q^{26} +(2.87422 - 1.58301i) q^{28} -9.69684i q^{29} +(1.16012 - 1.16012i) q^{31} +(0.454711 + 5.63855i) q^{32} +(-3.34531 + 2.51375i) q^{34} -3.87971 q^{35} +(1.87575 + 1.87575i) q^{37} +(-0.220794 + 1.55568i) q^{38} +(2.74534 - 6.09907i) q^{40} +(1.21870 + 1.21870i) q^{41} +6.64295i q^{43} +(0.534823 + 0.971064i) q^{44} +(1.82497 + 2.42868i) q^{46} +(-5.19778 - 5.19778i) q^{47} -4.30823i q^{49} +(-0.669239 + 0.502883i) q^{50} +(1.40095 - 7.07371i) q^{52} -13.9505i q^{53} -1.31077i q^{55} +(-4.23156 - 1.90473i) q^{56} +(-10.9632 + 8.23804i) q^{58} +(-8.86339 + 8.86339i) q^{59} -5.77916i q^{61} +(-2.29722 - 0.326039i) q^{62} +(5.98862 - 5.30437i) q^{64} +(-5.48582 + 6.52694i) q^{65} +(-5.85732 - 5.85732i) q^{67} +(5.68407 + 1.64662i) q^{68} +(3.29604 + 4.38639i) q^{70} +(-5.33062 + 5.33062i) q^{71} +(-5.90017 + 5.90017i) q^{73} +(0.527158 - 3.71428i) q^{74} +(1.94643 - 1.07202i) q^{76} -0.909421 q^{77} +1.82465i q^{79} +(-9.22791 + 2.07764i) q^{80} +(0.342502 - 2.41322i) q^{82} +(-3.29212 - 3.29212i) q^{83} +(-4.94759 - 4.94759i) q^{85} +(7.51051 - 5.64358i) q^{86} +(0.643519 - 1.42965i) q^{88} +(7.48582 - 7.48582i) q^{89} +(4.52842 + 3.80609i) q^{91} +(1.19544 - 4.12661i) q^{92} +(-1.46078 + 10.2924i) q^{94} -2.62735 q^{95} +(4.94128 + 4.94128i) q^{97} +(-4.87088 + 3.66010i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) $ 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.849559	−	1.13060i	−0.600729	−	0.799453i
$2$	−0.849559	−	1.13060i	−0.600729	−	0.799453i
$3$		0			0
$3$		0			0
$4$	−0.556500	+	1.92102i	−0.278250	+	0.960509i
$5$	1.67211	−	1.67211i	0.747792	−	0.747792i	−0.226272	−	0.974064i	$-0.572654\pi$
$5$	1.67211	−	1.67211i	0.747792	−	0.747792i	0.974064	+	0.226272i	$0.0726538\pi$
$6$		0			0
$7$	−1.16012	−	1.16012i	−0.438485	−	0.438485i	0.453017	−	0.891502i	$-0.350348\pi$
$7$	−1.16012	−	1.16012i	−0.438485	−	0.438485i	−0.891502	+	0.453017i	$0.850348\pi$
$8$	2.64468	−	1.00284i	0.935034	−	0.354557i
$9$		0			0
$10$	−3.31105	−	0.469928i	−1.04705	−	0.148604i
$11$	0.391951	−	0.391951i	0.118178	−	0.118178i	−0.645545	−	0.763722i	$-0.723370\pi$
$11$	0.391951	−	0.391951i	0.118178	−	0.118178i	0.763722	+	0.645545i	$0.223370\pi$
$12$		0			0
$13$	−3.59209	+	0.311317i	−0.996265	+	0.0863438i
$13$	−3.59209	+	0.311317i	−0.996265	+	0.0863438i
$14$	−0.326039	+	2.29722i	−0.0871375	+	0.613958i
$15$		0			0
$16$	−3.38062	−	2.13809i	−0.845154	−	0.534523i
$17$		−	2.95889i		−	0.717635i	−0.933408	−	0.358818i	$-0.883180\pi$
$17$		−	2.95889i		−	0.717635i	0.933408	−	0.358818i	$-0.116820\pi$
$18$		0			0
$19$	−0.785637	−	0.785637i	−0.180238	−	0.180238i	0.611222	−	0.791459i	$-0.290678\pi$
$19$	−0.785637	−	0.785637i	−0.180238	−	0.180238i	−0.791459	+	0.611222i	$0.790678\pi$
$20$	2.28163	+	4.14269i	0.510188	+	0.926334i
$21$		0			0
$22$	−0.776123	−	0.110153i	−0.165470	−	0.0234847i
$23$	−2.14814			−0.447918			−0.223959	−	0.974599i	$-0.571898\pi$
$23$	−2.14814			−0.447918			−0.223959	+	0.974599i	$0.571898\pi$
$24$		0			0
$25$		−	0.591934i		−	0.118387i
$26$	3.40366	+	3.79672i	0.667513	+	0.744598i
$27$		0			0
$28$	2.87422	−	1.58301i	0.543177	−	0.299160i
$29$		−	9.69684i		−	1.80066i	−0.435210	−	0.900329i	$-0.643326\pi$
$29$		−	9.69684i		−	1.80066i	0.435210	−	0.900329i	$-0.356674\pi$
$30$		0			0
$31$	1.16012	−	1.16012i	0.208364	−	0.208364i	−0.595208	−	0.803572i	$-0.702930\pi$
$31$	1.16012	−	1.16012i	0.208364	−	0.208364i	0.803572	+	0.595208i	$0.202930\pi$
$32$	0.454711	+	5.63855i	0.0803824	+	0.996764i
$33$		0			0
$34$	−3.34531	+	2.51375i	−0.573715	+	0.431104i
$35$	−3.87971			−0.655791
$36$		0			0
$37$	1.87575	+	1.87575i	0.308372	+	0.308372i	0.844278	−	0.535906i	$-0.180030\pi$
$37$	1.87575	+	1.87575i	0.308372	+	0.308372i	−0.535906	+	0.844278i	$0.680030\pi$
$38$	−0.220794	+	1.55568i	−0.0358176	+	0.252365i
$39$		0			0
$40$	2.74534	−	6.09907i	0.434076	−	0.964347i
$41$	1.21870	+	1.21870i	0.190329	+	0.190329i	0.795838	−	0.605509i	$-0.207030\pi$
$41$	1.21870	+	1.21870i	0.190329	+	0.190329i	−0.605509	+	0.795838i	$0.707030\pi$
$42$		0			0
$43$			6.64295i			1.01304i	0.862228	+	0.506521i	$0.169069\pi$
$43$			6.64295i			1.01304i	−0.862228	+	0.506521i	$0.830931\pi$
$44$	0.534823	+	0.971064i	0.0806277	+	0.146393i
$45$		0			0
$46$	1.82497	+	2.42868i	0.269077	+	0.358089i
$47$	−5.19778	−	5.19778i	−0.758174	−	0.758174i	0.217816	−	0.975990i	$-0.430107\pi$
$47$	−5.19778	−	5.19778i	−0.758174	−	0.758174i	−0.975990	+	0.217816i	$0.930107\pi$
$48$		0			0
$49$		−	4.30823i		−	0.615462i
$50$	−0.669239	+	0.502883i	−0.0946447	+	0.0711184i
$51$		0			0
$52$	1.40095	−	7.07371i	0.194277	−	0.980947i
$53$		−	13.9505i		−	1.91625i	−0.286355	−	0.958124i	$-0.592444\pi$
$53$		−	13.9505i		−	1.91625i	0.286355	−	0.958124i	$-0.407556\pi$
$54$		0			0
$55$		−	1.31077i		−	0.176745i
$56$	−4.23156	−	1.90473i	−0.565466	−	0.254530i
$57$		0			0
$58$	−10.9632	+	8.23804i	−1.43954	+	1.08171i
$59$	−8.86339	+	8.86339i	−1.15392	+	1.15392i	−0.168155	+	0.985761i	$0.553781\pi$
$59$	−8.86339	+	8.86339i	−1.15392	+	1.15392i	−0.985761	+	0.168155i	$0.946219\pi$
$60$		0			0
$61$		−	5.77916i		−	0.739945i	−0.929043	−	0.369972i	$-0.879367\pi$
$61$		−	5.77916i		−	0.739945i	0.929043	−	0.369972i	$-0.120633\pi$
$62$	−2.29722	−	0.326039i	−0.291748	−	0.0414070i
$63$		0			0
$64$	5.98862	−	5.30437i	0.748578	−	0.663047i
$65$	−5.48582	+	6.52694i	−0.680432	+	0.809567i
$66$		0			0
$67$	−5.85732	−	5.85732i	−0.715585	−	0.715585i	0.252113	−	0.967698i	$-0.418875\pi$
$67$	−5.85732	−	5.85732i	−0.715585	−	0.715585i	−0.967698	+	0.252113i	$0.918875\pi$
$68$	5.68407	+	1.64662i	0.689295	+	0.199682i
$69$		0			0
$70$	3.29604	+	4.38639i	0.393953	+	0.524274i
$71$	−5.33062	+	5.33062i	−0.632629	+	0.632629i	−0.948727	−	0.316098i	$-0.897627\pi$
$71$	−5.33062	+	5.33062i	−0.632629	+	0.632629i	0.316098	+	0.948727i	$0.397627\pi$
$72$		0			0
$73$	−5.90017	+	5.90017i	−0.690563	+	0.690563i	−0.962356	−	0.271793i	$-0.912383\pi$
$73$	−5.90017	+	5.90017i	−0.690563	+	0.690563i	0.271793	+	0.962356i	$0.412383\pi$
$74$	0.527158	−	3.71428i	0.0612809	−	0.431777i
$75$		0			0
$76$	1.94643	−	1.07202i	0.223271	−	0.122969i
$77$	−0.909421			−0.103638
$78$		0			0
$79$			1.82465i			0.205289i	0.994718	+	0.102644i	$0.0327304\pi$
$79$			1.82465i			0.205289i	−0.994718	+	0.102644i	$0.967270\pi$
$80$	−9.22791	+	2.07764i	−1.03171	+	0.232288i
$81$		0			0
$82$	0.342502	−	2.41322i	0.0378230	−	0.266496i
$83$	−3.29212	−	3.29212i	−0.361357	−	0.361357i	0.502955	−	0.864312i	$-0.332246\pi$
$83$	−3.29212	−	3.29212i	−0.361357	−	0.361357i	−0.864312	+	0.502955i	$0.832246\pi$
$84$		0			0
$85$	−4.94759	−	4.94759i	−0.536642	−	0.536642i
$86$	7.51051	−	5.64358i	0.809879	−	0.608563i
$87$		0			0
$88$	0.643519	−	1.42965i	0.0685993	−	0.152401i
$89$	7.48582	−	7.48582i	0.793496	−	0.793496i	−0.188565	−	0.982061i	$-0.560384\pi$
$89$	7.48582	−	7.48582i	0.793496	−	0.793496i	0.982061	+	0.188565i	$0.0603837\pi$
$90$		0			0
$91$	4.52842	+	3.80609i	0.474708	+	0.398987i
$92$	1.19544	−	4.12661i	0.124633	−	0.430229i
$93$		0			0
$94$	−1.46078	+	10.2924i	−0.150667	+	1.06158i
$95$	−2.62735			−0.269561
$96$		0			0
$97$	4.94128	+	4.94128i	0.501711	+	0.501711i	0.911969	−	0.410258i	$-0.134561\pi$
$97$	4.94128	+	4.94128i	0.501711	+	0.501711i	−0.410258	+	0.911969i	$0.634561\pi$
$98$	−4.87088	+	3.66010i	−0.492033	+	0.369726i
$99$		0			0
$100$	1.13712	+	0.329411i	0.113712	+	0.0329411i
$101$	−2.09896			−0.208854			−0.104427	−	0.994533i	$-0.533301\pi$
$101$	−2.09896			−0.208854			−0.104427	+	0.994533i	$0.533301\pi$
$102$		0			0
$103$	−15.6849			−1.54548			−0.772741	−	0.634722i	$-0.781115\pi$
$103$	−15.6849			−1.54548			−0.772741	+	0.634722i	$0.781115\pi$
$104$	−9.18770	+	4.42562i	−0.900928	+	0.433968i
$105$		0			0
$106$	−15.7724	+	11.8518i	−1.53195	+	1.15114i
$107$	11.8062			1.14134			0.570672	−	0.821178i	$-0.306683\pi$
$107$	11.8062			1.14134			0.570672	+	0.821178i	$0.306683\pi$
$108$		0			0
$109$	9.84874	−	9.84874i	0.943338	−	0.943338i	−0.0551405	−	0.998479i	$-0.517561\pi$
$109$	9.84874	−	9.84874i	0.943338	−	0.943338i	0.998479	+	0.0551405i	$0.0175607\pi$
$110$	−1.48196	+	1.11358i	−0.141299	+	0.106176i
$111$		0			0
$112$	1.44148	+	6.40237i	0.136207	+	0.604967i
$113$	−9.39629			−0.883929			−0.441964	−	0.897033i	$-0.645718\pi$
$113$	−9.39629			−0.883929			−0.441964	+	0.897033i	$0.645718\pi$
$114$		0			0
$115$	−3.59193	+	3.59193i	−0.334950	+	0.334950i
$116$	18.6278	+	5.39629i	1.72955	+	0.501033i
$117$		0			0
$118$	17.5509	+	2.49095i	1.61569	+	0.229311i
$119$	−3.43267	+	3.43267i	−0.314672	+	0.314672i
$120$		0			0
$121$			10.6927i			0.972068i
$122$	−6.53390	+	4.90973i	−0.591551	+	0.444506i
$123$		0			0
$124$	1.58301	+	2.87422i	0.142158	+	0.258113i
$125$	7.37079	+	7.37079i	0.659264	+	0.659264i
$126$		0			0
$127$	−4.36241			−0.387101			−0.193551	−	0.981090i	$-0.562000\pi$
$127$	−4.36241			−0.387101			−0.193551	+	0.981090i	$0.562000\pi$
$128$	−11.0848	−	2.26434i	−0.979767	−	0.200142i
$129$		0			0
$130$	12.0399	+	0.657238i	1.05597	+	0.0576436i
$131$	20.5049			1.79152			0.895759	−	0.444540i	$-0.146633\pi$
$131$	20.5049			1.79152			0.895759	+	0.444540i	$0.146633\pi$
$132$		0			0
$133$			1.82287i			0.158063i
$134$	−1.64613	+	11.5984i	−0.142204	+	1.00195i
$135$		0			0
$136$	−2.96729	−	7.82529i	−0.254443	−	0.671013i
$137$	−9.80009	+	9.80009i	−0.837278	+	0.837278i	−0.988500	−	0.151222i	$-0.951679\pi$
$137$	−9.80009	+	9.80009i	−0.837278	+	0.837278i	0.151222	+	0.988500i	$0.451679\pi$
$138$		0			0
$139$	−3.50388			−0.297195			−0.148598	−	0.988898i	$-0.547476\pi$
$139$	−3.50388			−0.297195			−0.148598	+	0.988898i	$0.547476\pi$
$140$	2.15906	−	7.45300i	0.182474	−	0.629893i
$141$		0			0
$142$	10.5555	+	1.49811i	0.885795	+	0.125719i
$143$	−1.28590	+	1.52994i	−0.107532	+	0.127940i
$144$		0			0
$145$	−16.2142	−	16.2142i	−1.34652	−	1.34652i
$146$	11.6833	+	1.65817i	0.966913	+	0.137231i
$147$		0			0
$148$	−4.64721	+	2.55950i	−0.381998	+	0.210389i
$149$	−3.27548	+	3.27548i	−0.268338	+	0.268338i	−0.828430	−	0.560092i	$-0.810766\pi$
$149$	−3.27548	+	3.27548i	−0.268338	+	0.268338i	0.560092	+	0.828430i	$0.310766\pi$
$150$		0			0
$151$	7.01121	+	7.01121i	0.570564	+	0.570564i	0.932286	−	0.361722i	$-0.117811\pi$
$151$	7.01121	+	7.01121i	0.570564	+	0.570564i	−0.361722	+	0.932286i	$0.617811\pi$
$152$	−2.86562	−	1.28989i	−0.232433	−	0.104624i
$153$		0			0
$154$	0.772606	+	1.02819i	0.0622584	+	0.0828538i
$155$		−	3.87971i		−	0.311626i
$156$		0			0
$157$		−	23.5918i		−	1.88283i	−0.337252	−	0.941414i	$-0.609497\pi$
$157$		−	23.5918i		−	1.88283i	0.337252	−	0.941414i	$-0.390503\pi$
$158$	2.06294	−	1.55015i	0.164119	−	0.123323i
$159$		0			0
$160$	10.1886	+	8.66797i	0.805482	+	0.685263i
$161$	2.49210	+	2.49210i	0.196405	+	0.196405i
$162$		0			0
$163$	14.2947	−	14.2947i	1.11965	−	1.11965i	0.127856	−	0.991793i	$-0.459190\pi$
$163$	14.2947	−	14.2947i	1.11965	−	1.11965i	0.991793	−	0.127856i	$-0.0408097\pi$
$164$	−3.01936	+	1.66294i	−0.235772	+	0.129854i
$165$		0			0
$166$	−0.925212	+	6.51891i	−0.0718104	+	0.505965i
$167$	9.66616	+	9.66616i	0.747990	+	0.747990i	0.974101	−	0.226111i	$-0.0726013\pi$
$167$	9.66616	+	9.66616i	0.747990	+	0.747990i	−0.226111	+	0.974101i	$0.572601\pi$
$168$		0			0
$169$	12.8062	−	2.23655i	0.985090	−	0.172043i
$170$	−1.39046	+	9.79701i	−0.106644	+	0.751396i
$171$		0			0
$172$	−12.7612	−	3.69680i	−0.973035	−	0.281879i
$173$	4.90900			0.373224			0.186612	−	0.982434i	$-0.440249\pi$
$173$	4.90900			0.373224			0.186612	+	0.982434i	$0.440249\pi$
$174$		0			0
$175$	−0.686716	+	0.686716i	−0.0519109	+	0.0519109i
$176$	−2.16306	+	0.487008i	−0.163047	+	0.0367096i
$177$		0			0
$178$	−14.8231	−	2.10380i	−1.11104	−	0.157687i
$179$		−	15.4884i		−	1.15766i	−0.815448	−	0.578830i	$-0.803510\pi$
$179$		−	15.4884i		−	1.15766i	0.815448	−	0.578830i	$-0.196490\pi$
$180$		0			0
$181$	13.7660			1.02322			0.511610	−	0.859217i	$-0.329049\pi$
$181$	13.7660			1.02322			0.511610	+	0.859217i	$0.329049\pi$
$182$	0.455995	−	8.35332i	0.0338006	−	0.619189i
$183$		0			0
$184$	−5.68113	+	2.15424i	−0.418819	+	0.158813i
$185$	6.27295			0.461196
$186$		0			0
$187$	−1.15974	−	1.15974i	−0.0848083	−	0.0848083i
$188$	12.8776	−	7.09246i	0.939195	−	0.517271i
$189$		0			0
$190$	2.23209	+	2.97048i	0.161933	+	0.215501i
$191$		−	9.49269i		−	0.686867i	−0.939177	−	0.343433i	$-0.888410\pi$
$191$		−	9.49269i		−	0.686867i	0.939177	−	0.343433i	$-0.111590\pi$
$192$		0			0
$193$	−4.70473	+	4.70473i	−0.338654	+	0.338654i	−0.855861	−	0.517207i	$-0.826972\pi$
$193$	−4.70473	+	4.70473i	−0.338654	+	0.338654i	0.517207	+	0.855861i	$0.326972\pi$
$194$	1.38869	−	9.78451i	0.0997022	−	0.702487i
$195$		0			0
$196$	8.27619	+	2.39753i	0.591157	+	0.171252i
$197$	13.2304	−	13.2304i	0.942629	−	0.942629i	−0.0558125	−	0.998441i	$-0.517775\pi$
$197$	13.2304	−	13.2304i	0.942629	−	0.942629i	0.998441	+	0.0558125i	$0.0177749\pi$
$198$		0			0
$199$	2.89962			0.205549			0.102774	−	0.994705i	$-0.467228\pi$
$199$	2.89962			0.205549			0.102774	+	0.994705i	$0.467228\pi$
$200$	−0.593616	−	1.56547i	−0.0419750	−	0.110696i
$201$		0			0
$202$	1.78319	+	2.37308i	0.125465	+	0.166969i
$203$	−11.2495	+	11.2495i	−0.789561	+	0.789561i
$204$		0			0
$205$	4.07562			0.284654
$206$	13.3253	+	17.7333i	0.928415	+	1.23554i
$207$		0			0
$208$	12.8091	+	6.62777i	0.888150	+	0.459553i
$209$	−0.615862			−0.0426001
$210$		0			0
$211$	23.3268			1.60588			0.802942	−	0.596057i	$-0.203267\pi$
$211$	23.3268			1.60588			0.802942	+	0.596057i	$0.203267\pi$
$212$	26.7991	+	7.76345i	1.84057	+	0.533196i
$213$		0			0
$214$	−10.0300	−	13.3480i	−0.685639	−	0.912452i
$215$	11.1078	+	11.1078i	0.757544	+	0.757544i
$216$		0			0
$217$	−2.69177			−0.182729
$218$	−19.5020	−	2.76787i	−1.32084	−	0.187464i
$219$		0			0
$220$	2.51802	+	0.729445i	0.169765	+	0.0491791i
$221$	0.921151	+	10.6286i	0.0619633	+	0.714955i
$222$		0			0
$223$	−18.2336	+	18.2336i	−1.22101	+	1.22101i	−0.253736	+	0.967274i	$0.581659\pi$
$223$	−18.2336	+	18.2336i	−1.22101	+	1.22101i	−0.967274	+	0.253736i	$0.918341\pi$
$224$	6.01388	−	7.06893i	0.401820	−	0.472312i
$225$		0			0
$226$	7.98270	+	10.6234i	0.531001	+	0.706659i
$227$	−2.94277	−	2.94277i	−0.195319	−	0.195319i	0.602671	−	0.797990i	$-0.294103\pi$
$227$	−2.94277	−	2.94277i	−0.195319	−	0.195319i	−0.797990	+	0.602671i	$0.794103\pi$
$228$		0			0
$229$	2.08468	+	2.08468i	0.137759	+	0.137759i	0.772624	−	0.634864i	$-0.218944\pi$
$229$	2.08468	+	2.08468i	0.137759	+	0.137759i	−0.634864	+	0.772624i	$0.718944\pi$
$230$	7.11259	+	1.00947i	0.468990	+	0.0665626i
$231$		0			0
$232$	−9.72438	−	25.6450i	−0.638437	−	1.68368i
$233$		−	16.1555i		−	1.05838i	−0.848502	−	0.529191i	$-0.822495\pi$
$233$		−	16.1555i		−	1.05838i	0.848502	−	0.529191i	$-0.177505\pi$
$234$		0			0
$235$	−17.3826			−1.13391
$236$	−12.0943	−	21.9592i	−0.787269	−	1.42942i
$237$		0			0
$238$	6.79722	+	0.964711i	0.440598	+	0.0625329i
$239$	11.3906	−	11.3906i	0.736799	−	0.736799i	−0.235158	−	0.971957i	$-0.575561\pi$
$239$	11.3906	−	11.3906i	0.736799	−	0.736799i	0.971957	+	0.235158i	$0.0755607\pi$
$240$		0			0
$241$	8.56378	−	8.56378i	0.551642	−	0.551642i	−0.375273	−	0.926914i	$-0.622451\pi$
$241$	8.56378	−	8.56378i	0.551642	−	0.551642i	0.926914	+	0.375273i	$0.122451\pi$
$242$	12.0892	−	9.08412i	0.777123	−	0.583949i
$243$		0			0
$244$	11.1019	+	3.21610i	0.710724	+	0.205890i
$245$	−7.20386	−	7.20386i	−0.460238	−	0.460238i
$246$		0			0
$247$	3.06666	+	2.57749i	0.195127	+	0.164002i
$248$	1.90473	−	4.23156i	0.120950	−	0.268705i
$249$		0			0
$250$	2.07148	−	14.5953i	0.131012	−	0.923089i
$251$			1.13387i			0.0715692i	0.999360	+	0.0357846i	$0.0113930\pi$
$251$			1.13387i			0.0715692i	−0.999360	+	0.0357846i	$0.988607\pi$
$252$		0			0
$253$	−0.841964	+	0.841964i	−0.0529338	+	0.0529338i
$254$	3.70612	+	4.93213i	0.232543	+	0.309469i
$255$		0			0
$256$	6.85713	+	14.4561i	0.428570	+	0.903508i
$257$		−	11.6824i		−	0.728728i	−0.931257	−	0.364364i	$-0.881286\pi$
$257$		−	11.6824i		−	0.728728i	0.931257	−	0.364364i	$-0.118714\pi$
$258$		0			0
$259$		−	4.35220i		−	0.270433i
$260$	−9.48550	−	14.1706i	−0.588266	−	0.878823i
$261$		0			0
$262$	−17.4201	−	23.1827i	−1.07622	−	1.43223i
$263$		−	2.49816i		−	0.154043i	−0.997029	−	0.0770214i	$-0.975459\pi$
$263$		−	2.49816i		−	0.154043i	0.997029	−	0.0770214i	$-0.0245410\pi$
$264$		0			0
$265$	−23.3268	−	23.3268i	−1.43296	−	1.43296i
$266$	2.06093	−	1.54864i	0.126364	−	0.0949529i
$267$		0			0
$268$	14.5116	−	7.99241i	0.886437	−	0.488214i
$269$			17.3767i			1.05948i	0.848161	+	0.529739i	$0.177710\pi$
$269$			17.3767i			1.05948i	−0.848161	+	0.529739i	$0.822290\pi$
$270$		0			0
$271$	19.5790	+	19.5790i	1.18934	+	1.18934i	0.977250	+	0.212089i	$0.0680266\pi$
$271$	19.5790	+	19.5790i	1.18934	+	1.18934i	0.212089	+	0.977250i	$0.431973\pi$
$272$	−6.32637	+	10.0029i	−0.383592	+	0.606512i
$273$		0			0
$274$	19.4057	+	2.75420i	1.17234	+	0.166387i
$275$	−0.232009	−	0.232009i	−0.0139907	−	0.0139907i
$276$		0			0
$277$	28.2035			1.69459			0.847293	−	0.531126i	$-0.178231\pi$
$277$	28.2035			1.69459			0.847293	+	0.531126i	$0.178231\pi$
$278$	2.97675	+	3.96147i	0.178534	+	0.237593i
$279$		0			0
$280$	−10.2606	+	3.89073i	−0.613187	+	0.232516i
$281$	6.00608	−	6.00608i	0.358292	−	0.358292i	−0.504891	−	0.863183i	$-0.668467\pi$
$281$	6.00608	−	6.00608i	0.358292	−	0.358292i	0.863183	+	0.504891i	$0.168467\pi$
$282$		0			0
$283$			29.1306i			1.73164i	0.500359	+	0.865818i	$0.333201\pi$
$283$			29.1306i			1.73164i	−0.500359	+	0.865818i	$0.666799\pi$
$284$	−7.27373	−	13.2067i	−0.431616	−	0.783674i
$285$		0			0
$286$	2.82219	+	0.154059i	0.166880	+	0.00910972i
$287$		−	2.82769i		−	0.166913i
$288$		0			0
$289$	8.24500			0.485000
$290$	−4.55682	+	32.1067i	−0.267586	+	1.88537i
$291$		0			0
$292$	−8.05088	−	14.6178i	−0.471142	−	0.855440i
$293$	−5.43420	−	5.43420i	−0.317469	−	0.317469i	0.530325	−	0.847794i	$-0.322070\pi$
$293$	−5.43420	−	5.43420i	−0.317469	−	0.317469i	−0.847794	+	0.530325i	$0.822070\pi$
$294$		0			0
$295$			29.6412i			1.72578i
$296$	6.84184	+	3.07968i	0.397674	+	0.179003i
$297$		0			0
$298$	6.48596	+	0.920536i	0.375722	+	0.0533252i
$299$	7.71630	−	0.668752i	0.446245	−	0.0386749i
$300$		0			0
$301$	7.70664	−	7.70664i	0.444203	−	0.444203i
$302$	1.97042	−	13.8833i	0.113385	−	0.798894i
$303$		0			0
$304$	0.976173	+	4.33570i	0.0559874	+	0.248670i
$305$	−9.66341	−	9.66341i	−0.553325	−	0.553325i
$306$		0			0
$307$	11.4314	−	11.4314i	0.652427	−	0.652427i	−0.301150	−	0.953577i	$-0.597370\pi$
$307$	11.4314	−	11.4314i	0.652427	−	0.652427i	0.953577	+	0.301150i	$0.0973704\pi$
$308$	0.506093	−	1.74701i	0.0288373	−	0.0995453i
$309$		0			0
$310$	−4.38639	+	3.29604i	−0.249130	+	0.187203i
$311$	−16.2544			−0.921700			−0.460850	−	0.887478i	$-0.652455\pi$
$311$	−16.2544			−0.921700			−0.460850	+	0.887478i	$0.652455\pi$
$312$		0			0
$313$	19.1736			1.08376			0.541878	−	0.840457i	$-0.317713\pi$
$313$	19.1736			1.08376			0.541878	+	0.840457i	$0.317713\pi$
$314$	−26.6728	+	20.0426i	−1.50523	+	1.13107i
$315$		0			0
$316$	−3.50518	−	1.01542i	−0.197182	−	0.0571216i
$317$	−6.77764	+	6.77764i	−0.380670	+	0.380670i	−0.871344	−	0.490673i	$-0.836751\pi$
$317$	−6.77764	+	6.77764i	−0.380670	+	0.380670i	0.490673	+	0.871344i	$0.336751\pi$
$318$		0			0
$319$	−3.80068	−	3.80068i	−0.212797	−	0.212797i
$320$	1.14414	−	18.8832i	0.0639596	−	1.05560i
$321$		0			0
$322$	0.700377	−	4.93475i	0.0390305	−	0.275003i
$323$	−2.32461	+	2.32461i	−0.129345	+	0.129345i
$324$		0			0
$325$	0.184279	+	2.12628i	0.0102220	+	0.117945i
$326$	−28.3058	−	4.01737i	−1.56771	−	0.222501i
$327$		0			0
$328$	4.44524	+	2.00091i	0.245447	+	0.110482i
$329$			12.0601i			0.664896i
$330$		0			0
$331$	−13.9517	−	13.9517i	−0.766855	−	0.766855i	0.210697	−	0.977551i	$-0.432427\pi$
$331$	−13.9517	−	13.9517i	−0.766855	−	0.766855i	−0.977551	+	0.210697i	$0.932427\pi$
$332$	8.15628	−	4.49215i	0.447634	−	0.246539i
$333$		0			0
$334$	2.71656	−	19.1405i	0.148644	−	1.04732i
$335$	−19.5882			−1.07022
$336$		0			0
$337$			20.3092i			1.10631i	0.833077	+	0.553157i	$0.186577\pi$
$337$			20.3092i			1.10631i	−0.833077	+	0.553157i	$0.813423\pi$
$338$	−13.4082	−	12.5785i	−0.729312	−	0.684182i
$339$		0			0
$340$	12.2578	−	6.75108i	0.664770	−	0.366129i
$341$		−	0.909421i		−	0.0492479i
$342$		0			0
$343$	−13.1189	+	13.1189i	−0.708356	+	0.708356i
$344$	6.66182	+	17.5685i	0.359181	+	0.947228i
$345$		0			0
$346$	−4.17048	−	5.55010i	−0.224206	−	0.298375i
$347$	−18.8537			−1.01212			−0.506060	−	0.862498i	$-0.668899\pi$
$347$	−18.8537			−1.01212			−0.506060	+	0.862498i	$0.668899\pi$
$348$		0			0
$349$	4.93319	+	4.93319i	0.264068	+	0.264068i	0.826704	−	0.562637i	$-0.190213\pi$
$349$	4.93319	+	4.93319i	0.264068	+	0.264068i	−0.562637	+	0.826704i	$0.690213\pi$
$350$	1.35981	+	0.192994i	0.0726846	+	0.0103159i
$351$		0			0
$352$	2.38826	+	2.03181i	0.127295	+	0.108296i
$353$	15.4858	+	15.4858i	0.824227	+	0.824227i	0.986711	−	0.162484i	$-0.0519506\pi$
$353$	15.4858	+	15.4858i	0.824227	+	0.824227i	−0.162484	+	0.986711i	$0.551951\pi$
$354$		0			0
$355$			17.8268i			0.946150i
$356$	10.2145	+	18.5463i	0.541369	+	0.982949i
$357$		0			0
$358$	−17.5112	+	13.1583i	−0.925494	+	0.695439i
$359$	12.6928	+	12.6928i	0.669902	+	0.669902i	0.957693	−	0.287791i	$-0.0929210\pi$
$359$	12.6928	+	12.6928i	0.669902	+	0.669902i	−0.287791	+	0.957693i	$0.592921\pi$
$360$		0			0
$361$		−	17.7655i		−	0.935029i
$362$	−11.6951	−	15.5638i	−0.614678	−	0.818017i
$363$		0			0
$364$	−9.83164	+	6.58109i	−0.515318	+	0.344943i
$365$			19.7315i			1.03279i
$366$		0			0
$367$			1.60603i			0.0838342i	0.999121	+	0.0419171i	$0.0133465\pi$
$367$			1.60603i			0.0838342i	−0.999121	+	0.0419171i	$0.986653\pi$
$368$	7.26203	+	4.59292i	0.378560	+	0.239422i
$369$		0			0
$370$	−5.32924	−	7.09217i	−0.277054	−	0.368705i
$371$	−16.1843	+	16.1843i	−0.840245	+	0.840245i
$372$		0			0
$373$			12.5988i			0.652341i	0.945311	+	0.326170i	$0.105758\pi$
$373$			12.5988i			0.652341i	−0.945311	+	0.326170i	$0.894242\pi$
$374$	−0.325930	+	2.29646i	−0.0168535	+	0.118747i
$375$		0			0
$376$	−18.9590	−	8.53390i	−0.977735	−	0.440102i
$377$	3.01879	+	34.8319i	0.155476	+	1.79393i
$378$		0			0
$379$	3.97178	+	3.97178i	0.204017	+	0.204017i	0.801718	−	0.597702i	$-0.203919\pi$
$379$	3.97178	+	3.97178i	0.204017	+	0.204017i	−0.597702	+	0.801718i	$0.703919\pi$
$380$	1.46212	−	5.04719i	0.0750052	−	0.258915i
$381$		0			0
$382$	−10.7324	+	8.06459i	−0.549118	+	0.412621i
$383$	24.1673	−	24.1673i	1.23489	−	1.23489i	0.272832	−	0.962062i	$-0.412040\pi$
$383$	24.1673	−	24.1673i	1.23489	−	1.23489i	0.962062	−	0.272832i	$-0.0879604\pi$
$384$		0			0
$385$	−1.52066	+	1.52066i	−0.0774998	+	0.0774998i
$386$	9.31610	+	1.32221i	0.474177	+	0.0672987i
$387$		0			0
$388$	−12.2421	+	6.74247i	−0.621499	+	0.342297i
$389$	−19.5120			−0.989298			−0.494649	−	0.869093i	$-0.664703\pi$
$389$	−19.5120			−0.989298			−0.494649	+	0.869093i	$0.664703\pi$
$390$		0			0
$391$			6.35610i			0.321442i
$392$	−4.32047	−	11.3939i	−0.218217	−	0.575478i
$393$		0			0
$394$	−26.1983	−	3.71826i	−1.31985	−	0.187323i
$395$	3.05102	+	3.05102i	0.153513	+	0.153513i
$396$		0			0
$397$	−12.4820	−	12.4820i	−0.626454	−	0.626454i	0.320720	−	0.947174i	$-0.396075\pi$
$397$	−12.4820	−	12.4820i	−0.626454	−	0.626454i	−0.947174	+	0.320720i	$0.896075\pi$
$398$	−2.46340	−	3.27831i	−0.123479	−	0.164327i
$399$		0			0
$400$	−1.26561	+	2.00110i	−0.0632805	+	0.100055i
$401$	5.08810	−	5.08810i	0.254088	−	0.254088i	−0.568557	−	0.822644i	$-0.692498\pi$
$401$	5.08810	−	5.08810i	0.254088	−	0.254088i	0.822644	+	0.568557i	$0.192498\pi$
$402$		0			0
$403$	−3.80609	+	4.52842i	−0.189595	+	0.225577i
$404$	1.16807	−	4.03214i	0.0581137	−	0.200607i
$405$		0			0
$406$	22.2758	+	3.16155i	1.10553	+	0.156905i
$407$	1.47040			0.0728852
$408$		0			0
$409$	18.2904	+	18.2904i	0.904403	+	0.904403i	0.995813	−	0.0914099i	$-0.0291373\pi$
$409$	18.2904	+	18.2904i	0.904403	+	0.904403i	−0.0914099	+	0.995813i	$0.529137\pi$
$410$	−3.46248	−	4.60789i	−0.171000	−	0.227567i
$411$		0			0
$412$	8.72866	−	30.1310i	0.430030	−	1.48445i
$413$	20.5652			1.01195
$414$		0			0
$415$	−11.0096			−0.540440
$416$	−3.38874	−	20.1126i	−0.166147	−	0.986101i
$417$		0			0
$418$	0.523211	+	0.696292i	0.0255911	+	0.0340567i
$419$	19.2388			0.939875			0.469938	−	0.882700i	$-0.344276\pi$
$419$	19.2388			0.939875			0.469938	+	0.882700i	$0.344276\pi$
$420$		0			0
$421$	−22.4944	+	22.4944i	−1.09631	+	1.09631i	−0.101471	+	0.994839i	$0.532355\pi$
$421$	−22.4944	+	22.4944i	−1.09631	+	1.09631i	−0.994839	+	0.101471i	$0.967645\pi$
$422$	−19.8175	−	26.3732i	−0.964701	−	1.28383i
$423$		0			0
$424$	−13.9901	−	36.8945i	−0.679420	−	1.79176i
$425$	−1.75147			−0.0849586
$426$		0			0
$427$	−6.70452	+	6.70452i	−0.324455	+	0.324455i
$428$	−6.57013	+	22.6798i	−0.317579	+	1.09627i
$429$		0			0
$430$	3.12171	−	21.9951i	0.150542	−	1.06070i
$431$	−23.8969	+	23.8969i	−1.15107	+	1.15107i	−0.164735	+	0.986338i	$0.552677\pi$
$431$	−23.8969	+	23.8969i	−1.15107	+	1.15107i	−0.986338	+	0.164735i	$0.947323\pi$
$432$		0			0
$433$			33.4534i			1.60767i	0.594854	+	0.803834i	$0.297210\pi$
$433$			33.4534i			1.60767i	−0.594854	+	0.803834i	$0.702790\pi$
$434$	2.28681	+	3.04330i	0.109771	+	0.146083i
$435$		0			0
$436$	13.4388	+	24.4004i	0.643601	+	1.16857i
$437$	1.68766	+	1.68766i	0.0807316	+	0.0807316i
$438$		0			0
$439$	−2.89421			−0.138133			−0.0690665	−	0.997612i	$-0.522002\pi$
$439$	−2.89421			−0.138133			−0.0690665	+	0.997612i	$0.522002\pi$
$440$	−1.31449	−	3.46657i	−0.0626661	−	0.165262i
$441$		0			0
$442$	11.2341	−	10.0710i	0.534350	−	0.479031i
$443$	19.6887			0.935440			0.467720	−	0.883877i	$-0.345076\pi$
$443$	19.6887			0.935440			0.467720	+	0.883877i	$0.345076\pi$
$444$		0			0
$445$		−	25.0343i		−	1.18674i
$446$	36.1053	+	5.12433i	1.70964	+	0.242644i
$447$		0			0
$448$	−13.1013	−	0.793813i	−0.618976	−	0.0375041i
$449$	13.5405	−	13.5405i	0.639017	−	0.639017i	−0.311296	−	0.950313i	$-0.600763\pi$
$449$	13.5405	−	13.5405i	0.639017	−	0.639017i	0.950313	+	0.311296i	$0.100763\pi$
$450$		0			0
$451$	0.955342			0.0449853
$452$	5.22903	−	18.0504i	0.245953	−	0.849021i
$453$		0			0
$454$	−0.827031	+	5.82714i	−0.0388145	+	0.273481i
$455$	13.9363	−	1.20782i	0.653342	−	0.0566235i
$456$		0			0
$457$	−3.88236	−	3.88236i	−0.181609	−	0.181609i	0.610447	−	0.792057i	$-0.290990\pi$
$457$	−3.88236	−	3.88236i	−0.181609	−	0.181609i	−0.792057	+	0.610447i	$0.790990\pi$
$458$	0.585875	−	4.12799i	0.0273761	−	0.192888i
$459$		0			0
$460$	−4.90126	−	8.89908i	−0.228522	−	0.414922i
$461$	−17.4455	+	17.4455i	−0.812517	+	0.812517i	−0.985011	−	0.172494i	$-0.944818\pi$
$461$	−17.4455	+	17.4455i	−0.812517	+	0.812517i	0.172494	+	0.985011i	$0.444818\pi$
$462$		0			0
$463$	−30.0459	−	30.0459i	−1.39635	−	1.39635i	−0.810210	−	0.586140i	$-0.800647\pi$
$463$	−30.0459	−	30.0459i	−1.39635	−	1.39635i	−0.586140	−	0.810210i	$-0.699353\pi$
$464$	−20.7327	+	32.7813i	−0.962493	+	1.52183i
$465$		0			0
$466$	−18.2654	+	13.7251i	−0.846127	+	0.635801i
$467$		−	8.61820i		−	0.398803i	−0.979918	−	0.199401i	$-0.936100\pi$
$467$		−	8.61820i		−	0.398803i	0.979918	−	0.199401i	$-0.0638998\pi$
$468$		0			0
$469$			13.5904i			0.627547i
$470$	14.7675	+	19.6527i	0.681174	+	0.906510i
$471$		0			0
$472$	−14.5522	+	32.3294i	−0.669821	+	1.48808i
$473$	2.60371	+	2.60371i	0.119719	+	0.119719i
$474$		0			0
$475$	−0.465046	+	0.465046i	−0.0213378	+	0.0213378i
$476$	−4.68394	−	8.50449i	−0.214688	−	0.389803i
$477$		0			0
$478$	−22.5552	−	3.20121i	−1.03165	−	0.146420i
$479$	4.53008	+	4.53008i	0.206985	+	0.206985i	0.802984	−	0.596000i	$-0.203244\pi$
$479$	4.53008	+	4.53008i	0.206985	+	0.206985i	−0.596000	+	0.802984i	$0.703244\pi$
$480$		0			0
$481$	−7.32182	−	6.15391i	−0.333846	−	0.280594i
$482$	−16.9576	−	2.40675i	−0.772399	−	0.109625i
$483$		0			0
$484$	−20.5410	−	5.95051i	−0.933680	−	0.270478i
$485$	16.5248			0.750352
$486$		0			0
$487$	14.1789	−	14.1789i	0.642507	−	0.642507i	−0.308664	−	0.951171i	$-0.599882\pi$
$487$	14.1789	−	14.1789i	0.642507	−	0.642507i	0.951171	+	0.308664i	$0.0998820\pi$
$488$	−5.79557	−	15.2840i	−0.262353	−	0.691874i
$489$		0			0
$490$	−2.02456	+	14.2648i	−0.0914604	+	0.644417i
$491$		−	19.7677i		−	0.892104i	−0.895007	−	0.446052i	$-0.852830\pi$
$491$		−	19.7677i		−	0.892104i	0.895007	−	0.446052i	$-0.147170\pi$
$492$		0			0
$493$	−28.6918			−1.29222
$494$	0.308801	−	5.65689i	0.0138936	−	0.254515i
$495$		0			0
$496$	−6.40237	+	1.44148i	−0.287475	+	0.0647243i
$497$	12.3683			0.554796
$498$		0			0
$499$	−14.8709	−	14.8709i	−0.665713	−	0.665713i	0.291008	−	0.956721i	$-0.406009\pi$
$499$	−14.8709	−	14.8709i	−0.665713	−	0.665713i	−0.956721	+	0.291008i	$0.906009\pi$
$500$	−18.2613	+	10.0576i	−0.816668	+	0.449788i
$501$		0			0
$502$	1.28195	−	0.963288i	0.0572162	−	0.0429937i
$503$			30.0549i			1.34008i	0.742324	+	0.670041i	$0.233724\pi$
$503$			30.0549i			1.34008i	−0.742324	+	0.670041i	$0.766276\pi$
$504$		0			0
$505$	−3.50970	+	3.50970i	−0.156180	+	0.156180i
$506$	1.66722	+	0.236624i	0.0741170	+	0.0105192i
$507$		0			0
$508$	2.42768	−	8.38026i	0.107711	−	0.371814i
$509$	0.547453	−	0.547453i	0.0242654	−	0.0242654i	−0.694870	−	0.719135i	$-0.744538\pi$
$509$	0.547453	−	0.547453i	0.0242654	−	0.0242654i	0.719135	+	0.694870i	$0.244538\pi$
$510$		0			0
$511$	13.6898			0.605602
$512$	10.5185	−	20.0340i	0.464858	−	0.885385i
$513$		0			0
$514$	−13.2081	+	9.92489i	−0.582584	+	0.437768i
$515$	−26.2270	+	26.2270i	−1.15570	+	1.15570i
$516$		0			0
$517$	−4.07454			−0.179198
$518$	−4.92059	+	3.69745i	−0.216198	+	0.162457i
$519$		0			0
$520$	−7.96275	+	22.7630i	−0.349190	+	0.998225i
$521$	−10.9111			−0.478025			−0.239012	−	0.971017i	$-0.576824\pi$
$521$	−10.9111			−0.478025			−0.239012	+	0.971017i	$0.576824\pi$
$522$		0			0
$523$	36.6897			1.60433			0.802165	−	0.597103i	$-0.203682\pi$
$523$	36.6897			1.60433			0.802165	+	0.597103i	$0.203682\pi$
$524$	−11.4110	+	39.3902i	−0.498490	+	1.72077i
$525$		0			0
$526$	−2.82441	+	2.12233i	−0.123150	+	0.0925380i
$527$	−3.43267	−	3.43267i	−0.149529	−	0.149529i
$528$		0			0
$529$	−18.3855			−0.799370
$530$	−6.55573	+	46.1907i	−0.284763	+	2.00640i
$531$		0			0
$532$	−3.50176	−	1.01443i	−0.151821	−	0.0439810i
$533$	−4.75709	−	3.99828i	−0.206052	−	0.173185i
$534$		0			0
$535$	19.7413	−	19.7413i	0.853489	−	0.853489i
$536$	−21.3647	−	9.61676i	−0.922813	−	0.415381i
$537$		0			0
$538$	19.6461	−	14.7626i	0.847003	−	0.636459i
$539$	−1.68861	−	1.68861i	−0.0727338	−	0.0727338i
$540$		0			0
$541$	−2.29349	−	2.29349i	−0.0986047	−	0.0986047i	0.656084	−	0.754688i	$-0.272212\pi$
$541$	−2.29349	−	2.29349i	−0.0986047	−	0.0986047i	−0.754688	+	0.656084i	$0.772212\pi$
$542$	5.50245	−	38.7695i	0.236350	−	1.66529i
$543$		0			0
$544$	16.6838	−	1.34544i	0.715313	−	0.0576852i
$545$		−	32.9364i		−	1.41084i
$546$		0			0
$547$	−29.3860			−1.25646			−0.628228	−	0.778029i	$-0.716220\pi$
$547$	−29.3860			−1.25646			−0.628228	+	0.778029i	$0.716220\pi$
$548$	−13.3724	−	24.2799i	−0.571240	−	1.03719i
$549$		0			0
$550$	−0.0652034	+	0.459414i	−0.00278028	+	0.0195895i
$551$	−7.61820	+	7.61820i	−0.324546	+	0.324546i
$552$		0			0
$553$	2.11681	−	2.11681i	0.0900161	−	0.0900161i
$554$	−23.9606	−	31.8868i	−1.01799	−	1.35474i
$555$		0			0
$556$	1.94991	−	6.73101i	0.0826945	−	0.285458i
$557$	−15.4424	−	15.4424i	−0.654316	−	0.654316i	0.299713	−	0.954029i	$-0.403109\pi$
$557$	−15.4424	−	15.4424i	−0.654316	−	0.654316i	−0.954029	+	0.299713i	$0.903109\pi$
$558$		0			0
$559$	−2.06806	−	23.8621i	−0.0874698	−	1.00926i
$560$	13.1158	+	8.29518i	0.554245	+	0.350536i
$561$		0			0
$562$	−11.8930	−	1.68794i	−0.501675	−	0.0712014i
$563$		−	28.2354i		−	1.18998i	−0.803733	−	0.594990i	$-0.797156\pi$
$563$		−	28.2354i		−	1.18998i	0.803733	−	0.594990i	$-0.202844\pi$
$564$		0			0
$565$	−15.7117	+	15.7117i	−0.660995	+	0.660995i
$566$	32.9350	−	24.7482i	1.38436	−	1.04024i
$567$		0			0
$568$	−8.75201	+	19.4435i	−0.367226	+	0.815832i
$569$		−	8.54680i		−	0.358301i	−0.983822	−	0.179150i	$-0.942665\pi$
$569$		−	8.54680i		−	0.358301i	0.983822	−	0.179150i	$-0.0573348\pi$
$570$		0			0
$571$		−	37.8236i		−	1.58287i	−0.611254	−	0.791435i	$-0.709335\pi$
$571$		−	37.8236i		−	1.58287i	0.611254	−	0.791435i	$-0.290665\pi$
$572$	−2.22344	−	3.32165i	−0.0929667	−	0.138885i
$573$		0			0
$574$	−3.19698	+	2.40229i	−0.133439	+	0.100270i
$575$			1.27156i			0.0530276i
$576$		0			0
$577$	−14.3094	−	14.3094i	−0.595709	−	0.595709i	0.343459	−	0.939168i	$-0.388401\pi$
$577$	−14.3094	−	14.3094i	−0.595709	−	0.595709i	−0.939168	+	0.343459i	$0.888401\pi$
$578$	−7.00461	−	9.32177i	−0.291353	−	0.387735i
$579$		0			0
$580$	40.1710	−	22.1246i	1.66801	−	0.918674i
$581$			7.63852i			0.316899i
$582$		0			0
$583$	−5.46790	−	5.46790i	−0.226457	−	0.226457i
$584$	−9.68711	+	21.5210i	−0.400855	+	0.890544i
$585$		0			0
$586$	−1.52722	+	10.7606i	−0.0630888	+	0.444515i
$587$	−5.61673	−	5.61673i	−0.231827	−	0.231827i	0.581628	−	0.813455i	$-0.302416\pi$
$587$	−5.61673	−	5.61673i	−0.231827	−	0.231827i	−0.813455	+	0.581628i	$0.802416\pi$
$588$		0			0
$589$	−1.82287			−0.0751100
$590$	33.5123	−	25.1820i	1.37968	−	1.03672i
$591$		0			0
$592$	−2.33067	−	10.3517i	−0.0957898	−	0.425453i
$593$	−9.10077	+	9.10077i	−0.373724	+	0.373724i	−0.868832	−	0.495108i	$-0.835129\pi$
$593$	−9.10077	+	9.10077i	−0.373724	+	0.373724i	0.495108	+	0.868832i	$0.335129\pi$
$594$		0			0
$595$			11.4796i			0.470619i
$596$	−4.46945	−	8.11506i	−0.183076	−	0.332406i
$597$		0			0
$598$	−7.31154	−	8.15588i	−0.298991	−	0.333519i
$599$			22.5156i			0.919962i	0.887929	+	0.459981i	$0.152144\pi$
$599$			22.5156i			0.919962i	−0.887929	+	0.459981i	$0.847856\pi$
$600$		0			0
$601$	6.23544			0.254349			0.127174	−	0.991880i	$-0.459409\pi$
$601$	6.23544			0.254349			0.127174	+	0.991880i	$0.459409\pi$
$602$	−15.2603	−	2.16586i	−0.621965	−	0.0882739i
$603$		0			0
$604$	−17.3704	+	9.56692i	−0.706792	+	0.389273i
$605$	17.8795	+	17.8795i	0.726905	+	0.726905i
$606$		0			0
$607$		−	46.7547i		−	1.89772i	−0.315704	−	0.948858i	$-0.602241\pi$
$607$		−	46.7547i		−	1.89772i	0.315704	−	0.948858i	$-0.397759\pi$
$608$	4.07262	−	4.78709i	0.165166	−	0.194142i
$609$		0			0
$610$	−2.71579	+	19.1351i	−0.109959	+	0.774756i
$611$	20.2890	+	17.0527i	0.820806	+	0.689879i
$612$		0			0
$613$	−13.4628	+	13.4628i	−0.543757	+	0.543757i	−0.924628	−	0.380871i	$-0.875624\pi$
$613$	−13.4628	+	13.4628i	−0.543757	+	0.543757i	0.380871	+	0.924628i	$0.375624\pi$
$614$	−22.6360	−	3.21268i	−0.913516	−	0.129653i
$615$		0			0
$616$	−2.40512	+	0.912004i	−0.0969052	+	0.0367457i
$617$	−13.6695	−	13.6695i	−0.550313	−	0.550313i	0.376218	−	0.926531i	$-0.377224\pi$
$617$	−13.6695	−	13.6695i	−0.550313	−	0.550313i	−0.926531	+	0.376218i	$0.877224\pi$
$618$		0			0
$619$	11.8988	−	11.8988i	0.478255	−	0.478255i	−0.426318	−	0.904573i	$-0.640190\pi$
$619$	11.8988	−	11.8988i	0.478255	−	0.478255i	0.904573	+	0.426318i	$0.140190\pi$
$620$	7.45300	+	2.15906i	0.299320	+	0.0867099i
$621$		0			0
$622$	13.8090	+	18.3771i	0.553691	+	0.736855i
$623$	−17.3689			−0.695872
$624$		0			0
$625$	27.6093			1.10437
$626$	−16.2891	−	21.6776i	−0.651044	−	0.866412i
$627$		0			0
$628$	45.3202	+	13.1288i	1.80847	+	0.523897i
$629$	5.55014	−	5.55014i	0.221298	−	0.221298i
$630$		0			0
$631$	11.8137	+	11.8137i	0.470295	+	0.470295i	0.902010	−	0.431715i	$-0.142091\pi$
$631$	11.8137	+	11.8137i	0.470295	+	0.470295i	−0.431715	+	0.902010i	$0.642091\pi$
$632$	1.82983	+	4.82560i	0.0727867	+	0.191952i
$633$		0			0
$634$	13.4208	+	1.90478i	0.533008	+	0.0756484i
$635$	−7.29445	+	7.29445i	−0.289471	+	0.289471i
$636$		0			0
$637$	1.34123	+	15.4755i	0.0531413	+	0.613164i
$638$	−1.06814	+	7.52594i	−0.0422880	+	0.297955i
$639$		0			0
$640$	−22.3213	+	14.7488i	−0.882327	+	0.582998i
$641$			12.0489i			0.475902i	0.971277	+	0.237951i	$0.0764757\pi$
$641$			12.0489i			0.475902i	−0.971277	+	0.237951i	$0.923524\pi$
$642$		0			0
$643$	−28.4624	−	28.4624i	−1.12245	−	1.12245i	−0.991372	−	0.131076i	$-0.958157\pi$
$643$	−28.4624	−	28.4624i	−1.12245	−	1.12245i	−0.131076	−	0.991372i	$-0.541843\pi$
$644$	−6.17423	+	3.40052i	−0.243299	+	0.133999i
$645$		0			0
$646$	4.60309	+	0.653305i	0.181106	+	0.0257039i
$647$	−9.55223			−0.375537			−0.187768	−	0.982213i	$-0.560125\pi$
$647$	−9.55223			−0.375537			−0.187768	+	0.982213i	$0.560125\pi$
$648$		0			0
$649$			6.94802i			0.272734i
$650$	2.24741	−	2.01474i	0.0881507	−	0.0790248i
$651$		0			0
$652$	19.5054	+	35.4154i	0.763890	+	1.38698i
$653$			21.6730i			0.848130i	0.905632	+	0.424065i	$0.139397\pi$
$653$			21.6730i			0.848130i	−0.905632	+	0.424065i	$0.860603\pi$
$654$		0			0
$655$	34.2865	−	34.2865i	1.33968	−	1.33968i
$656$	−1.51427	−	6.72566i	−0.0591222	−	0.262593i
$657$		0			0
$658$	13.6351	−	10.2458i	0.531553	−	0.399422i
$659$	12.1786			0.474409			0.237205	−	0.971460i	$-0.423769\pi$
$659$	12.1786			0.474409			0.237205	+	0.971460i	$0.423769\pi$
$660$		0			0
$661$	−16.9361	−	16.9361i	−0.658738	−	0.658738i	0.296343	−	0.955082i	$-0.404233\pi$
$661$	−16.9361	−	16.9361i	−0.658738	−	0.658738i	−0.955082	+	0.296343i	$0.904233\pi$
$662$	−3.92096	+	27.6265i	−0.152393	+	1.07374i
$663$		0			0
$664$	−12.0081	−	5.40512i	−0.466003	−	0.209759i
$665$	3.04805	+	3.04805i	0.118198	+	0.118198i
$666$		0			0
$667$			20.8302i			0.806547i
$668$	−23.9481	+	13.1896i	−0.926579	+	0.510323i
$669$		0			0
$670$	16.6413	+	22.1464i	0.642911	+	0.855589i
$671$	−2.26514	−	2.26514i	−0.0874449	−	0.0874449i
$672$		0			0
$673$		−	31.5099i		−	1.21462i	−0.794466	−	0.607308i	$-0.792249\pi$
$673$		−	31.5099i		−	1.21462i	0.794466	−	0.607308i	$-0.207751\pi$
$674$	22.9615	−	17.2539i	0.884446	−	0.664594i
$675$		0			0
$676$	−2.83017	+	25.8455i	−0.108853	+	0.994058i
$677$		−	32.9475i		−	1.26627i	−0.774040	−	0.633137i	$-0.781767\pi$
$677$		−	32.9475i		−	1.26627i	0.774040	−	0.633137i	$-0.218233\pi$
$678$		0			0
$679$		−	11.4650i		−	0.439986i
$680$	−18.0464	−	8.12314i	−0.692049	−	0.311508i
$681$		0			0
$682$	−1.02819	+	0.772606i	−0.0393714	+	0.0295846i
$683$	12.5106	−	12.5106i	0.478704	−	0.478704i	−0.426013	−	0.904717i	$-0.640082\pi$
$683$	12.5106	−	12.5106i	0.478704	−	0.478704i	0.904717	+	0.426013i	$0.140082\pi$
$684$		0			0
$685$			32.7737i			1.25222i
$686$	25.9775	+	3.68692i	0.991827	+	0.140767i
$687$		0			0
$688$	14.2032	−	22.4573i	0.541494	−	0.856176i
$689$	4.34302	+	50.1114i	0.165456	+	1.90909i
$690$		0			0
$691$	36.4803	+	36.4803i	1.38777	+	1.38777i	0.829978	+	0.557797i	$0.188353\pi$
$691$	36.4803	+	36.4803i	1.38777	+	1.38777i	0.557797	+	0.829978i	$0.311647\pi$
$692$	−2.73186	+	9.43027i	−0.103850	+	0.358485i
$693$		0			0
$694$	16.0173	+	21.3160i	0.608010	+	0.809142i
$695$	−5.85889	+	5.85889i	−0.222240	+	0.222240i
$696$		0			0
$697$	3.60600	−	3.60600i	0.136587	−	0.136587i
$698$	1.38642	−	9.76849i	0.0524767	−	0.369743i
$699$		0			0
$700$	−0.937036	−	1.70135i	−0.0354166	−	0.0643050i
$701$	41.5365			1.56881			0.784407	−	0.620247i	$-0.212967\pi$
$701$	41.5365			1.56881			0.784407	+	0.620247i	$0.212967\pi$
$702$		0			0
$703$		−	2.94732i		−	0.111160i
$704$	0.268192	−	4.42630i	0.0101079	−	0.166822i
$705$		0			0
$706$	4.35211	−	30.6643i	0.163794	−	1.15407i
$707$	2.43505	+	2.43505i	0.0915795	+	0.0915795i
$708$		0			0
$709$	26.1966	+	26.1966i	0.983834	+	0.983834i	0.999871	−	0.0160378i	$-0.00510519\pi$
$709$	26.1966	+	26.1966i	0.983834	+	0.983834i	−0.0160378	+	0.999871i	$0.505105\pi$
$710$	20.1550	−	15.1449i	0.756402	−	0.568379i
$711$		0			0
$712$	12.2905	−	27.3047i	0.460606	−	1.02329i
$713$	−2.49210	+	2.49210i	−0.0933300	+	0.0933300i
$714$		0			0
$715$	0.408066	+	4.70841i	0.0152608	+	0.176084i
$716$	29.7535	+	8.61931i	1.11194	+	0.322119i
$717$		0			0
$718$	3.56717	−	25.1338i	0.133126	−	0.937984i
$719$	−1.99265			−0.0743134			−0.0371567	−	0.999309i	$-0.511830\pi$
$719$	−1.99265			−0.0743134			−0.0371567	+	0.999309i	$0.511830\pi$
$720$		0			0
$721$	18.1964	+	18.1964i	0.677670	+	0.677670i
$722$	−20.0857	+	15.0929i	−0.747512	+	0.561699i
$723$		0			0
$724$	−7.66079	+	26.4448i	−0.284711	+	0.982813i
$725$	−5.73989			−0.213174
$726$		0			0
$727$	18.2357			0.676325			0.338162	−	0.941088i	$-0.390195\pi$
$727$	18.2357			0.676325			0.338162	+	0.941088i	$0.390195\pi$
$728$	15.7931	+	5.52460i	0.585332	+	0.204755i
$729$		0			0
$730$	22.3084	−	16.7631i	0.825671	−	0.620430i
$731$	19.6557			0.726994
$732$		0			0
$733$	−18.4701	+	18.4701i	−0.682209	+	0.682209i	−0.960497	−	0.278289i	$-0.910233\pi$
$733$	−18.4701	+	18.4701i	−0.682209	+	0.682209i	0.278289	+	0.960497i	$0.410233\pi$
$734$	1.81578	−	1.36442i	0.0670215	−	0.0503616i
$735$		0			0
$736$	−0.976783	−	12.1124i	−0.0360047	−	0.446469i
$737$	−4.59156			−0.169132
$738$		0			0
$739$	−17.9656	+	17.9656i	−0.660876	+	0.660876i	−0.955587	−	0.294710i	$-0.904777\pi$
$739$	−17.9656	+	17.9656i	−0.660876	+	0.660876i	0.294710	+	0.955587i	$0.404777\pi$
$740$	−3.49089	+	12.0504i	−0.128328	+	0.442983i
$741$		0			0
$742$	32.0474	+	4.54840i	1.17650	+	0.166977i
$743$	18.0076	−	18.0076i	0.660635	−	0.660635i	−0.294895	−	0.955530i	$-0.595285\pi$
$743$	18.0076	−	18.0076i	0.660635	−	0.660635i	0.955530	+	0.294895i	$0.0952845\pi$
$744$		0			0
$745$			10.9540i			0.401322i
$746$	14.2442	−	10.7034i	0.521516	−	0.391880i
$747$		0			0
$748$	2.87327	−	1.58248i	0.105057	−	0.0578612i
$749$	−13.6966	−	13.6966i	−0.500462	−	0.500462i
$750$		0			0
$751$	42.4965			1.55072			0.775359	−	0.631521i	$-0.217569\pi$
$751$	42.4965			1.55072			0.775359	+	0.631521i	$0.217569\pi$
$752$	6.45836	+	28.6850i	0.235512	+	1.04604i
$753$		0			0
$754$	36.8162	−	33.0048i	1.34077	−	1.20196i
$755$	23.4471			0.853328
$756$		0			0
$757$			16.7233i			0.607817i	0.952701	+	0.303908i	$0.0982917\pi$
$757$			16.7233i			0.607817i	−0.952701	+	0.303908i	$0.901708\pi$
$758$	1.11622	−	7.86474i	0.0405430	−	0.285660i
$759$		0			0
$760$	−6.94849	+	2.63481i	−0.252048	+	0.0955747i
$761$	1.74539	−	1.74539i	0.0632703	−	0.0632703i	−0.674764	−	0.738034i	$-0.735754\pi$
$761$	1.74539	−	1.74539i	0.0632703	−	0.0632703i	0.738034	+	0.674764i	$0.235754\pi$
$762$		0			0
$763$	−22.8515			−0.827279
$764$	18.2356	+	5.28268i	0.659741	+	0.191121i
$765$		0			0
$766$	−47.8551	−	6.79195i	−1.72908	−	0.245403i
$767$	29.0787	−	34.5974i	1.04997	−	1.24924i
$768$		0			0
$769$	−6.50326	−	6.50326i	−0.234514	−	0.234514i	0.580060	−	0.814574i	$-0.303029\pi$
$769$	−6.50326	−	6.50326i	−0.234514	−	0.234514i	−0.814574	+	0.580060i	$0.803029\pi$
$770$	3.01114	+	0.427363i	0.108514	+	0.0154011i
$771$		0			0
$772$	−6.41969	−	11.6560i	−0.231050	−	0.419510i
$773$	10.4555	−	10.4555i	0.376058	−	0.376058i	−0.493620	−	0.869678i	$-0.664326\pi$
$773$	10.4555	−	10.4555i	0.376058	−	0.376058i	0.869678	+	0.493620i	$0.164326\pi$
$774$		0			0
$775$	−0.686716	−	0.686716i	−0.0246676	−	0.0246676i
$776$	18.0234	+	8.11278i	0.647003	+	0.291232i
$777$		0			0
$778$	16.5766	+	22.0602i	0.594300	+	0.790897i
$779$		−	1.91492i		−	0.0686090i
$780$		0			0
$781$			4.17868i			0.149525i
$782$	7.18618	−	5.39988i	0.256977	−	0.193099i
$783$		0			0
$784$	−9.21140	+	14.5645i	−0.328979	+	0.520160i
$785$	−39.4482	−	39.4482i	−1.40797	−	1.40797i
$786$		0			0
$787$	5.07056	−	5.07056i	0.180746	−	0.180746i	−0.610935	−	0.791681i	$-0.709206\pi$
$787$	5.07056	−	5.07056i	0.180746	−	0.180746i	0.791681	+	0.610935i	$0.209206\pi$
$788$	18.0531	+	32.7786i	0.643117	+	1.16769i
$789$		0			0
$790$	0.857454	−	6.04150i	0.0305068	−	0.214947i
$791$	10.9008	+	10.9008i	0.387589	+	0.387589i
$792$		0			0
$793$	1.79915	+	20.7592i	0.0638896	+	0.737182i
$794$	−3.50793	+	24.7163i	−0.124492	+	0.877150i
$795$		0			0
$796$	−1.61364	+	5.57023i	−0.0571940	+	0.197432i
$797$	−24.5139			−0.868327			−0.434163	−	0.900834i	$-0.642956\pi$
$797$	−24.5139			−0.868327			−0.434163	+	0.900834i	$0.642956\pi$
$798$		0			0
$799$	−15.3796	+	15.3796i	−0.544092	+	0.544092i
$800$	3.33765	−	0.269159i	0.118004	−	0.00951622i
$801$		0			0
$802$	−10.0752	−	1.42995i	−0.355769	−	0.0504934i
$803$			4.62515i			0.163218i
$804$		0			0
$805$	8.33416			0.293741
$806$	8.35332	+	0.455995i	0.294233	+	0.0160618i
$807$		0			0
$808$	−5.55107	+	2.10492i	−0.195286	+	0.0740509i
$809$	−25.7049			−0.903738			−0.451869	−	0.892084i	$-0.649242\pi$
$809$	−25.7049			−0.903738			−0.451869	+	0.892084i	$0.649242\pi$
$810$		0			0
$811$	5.86079	+	5.86079i	0.205800	+	0.205800i	0.802480	−	0.596679i	$-0.203514\pi$
$811$	5.86079	+	5.86079i	0.205800	+	0.205800i	−0.596679	+	0.802480i	$0.703514\pi$
$812$	−15.3502	−	27.8709i	−0.538685	−	0.978076i
$813$		0			0
$814$	−1.24919	−	1.66243i	−0.0437843	−	0.0582683i
$815$		−	47.8048i		−	1.67453i
$816$		0			0
$817$	5.21895	−	5.21895i	0.182588	−	0.182588i
$818$	5.14031	−	36.2179i	0.179727	−	1.26633i
$819$		0			0
$820$	−2.26808	+	7.82934i	−0.0792049	+	0.273412i
$821$	−4.28711	+	4.28711i	−0.149621	+	0.149621i	−0.777949	−	0.628328i	$-0.783740\pi$
$821$	−4.28711	+	4.28711i	−0.149621	+	0.149621i	0.628328	+	0.777949i	$0.283740\pi$
$822$		0			0
$823$	7.17762			0.250196			0.125098	−	0.992144i	$-0.460075\pi$
$823$	7.17762			0.250196			0.125098	+	0.992144i	$0.460075\pi$
$824$	−41.4815	+	15.7295i	−1.44508	+	0.547962i
$825$		0			0
$826$	−17.4714	−	23.2510i	−0.607907	−	0.809006i
$827$	−29.8057	+	29.8057i	−1.03644	+	1.03644i	−0.0371341	+	0.999310i	$0.511823\pi$
$827$	−29.8057	+	29.8057i	−1.03644	+	1.03644i	−0.999310	+	0.0371341i	$0.988177\pi$
$828$		0			0
$829$	−16.9928			−0.590184			−0.295092	−	0.955469i	$-0.595350\pi$
$829$	−16.9928			−0.590184			−0.295092	+	0.955469i	$0.595350\pi$
$830$	9.35330	+	12.4474i	0.324658	+	0.432056i
$831$		0			0
$832$	−19.8603	+	20.9181i	−0.688532	+	0.725206i
$833$	−12.7476			−0.441677
$834$		0			0
$835$	32.3259			1.11868
$836$	0.342727	−	1.18308i	0.0118535	−	0.0409177i
$837$		0			0
$838$	−16.3445	−	21.7513i	−0.564610	−	0.751386i
$839$	7.08206	+	7.08206i	0.244500	+	0.244500i	0.818709	−	0.574209i	$-0.194690\pi$
$839$	7.08206	+	7.08206i	0.244500	+	0.244500i	−0.574209	+	0.818709i	$0.694690\pi$
$840$		0			0
$841$	−65.0287			−2.24237
$842$	44.5424	+	6.32178i	1.53503	+	0.217863i
$843$		0			0
$844$	−12.9814	+	44.8112i	−0.446837	+	1.54247i
$845$	17.6736	−	25.1531i	0.607990	−	0.865295i
$846$		0			0
$847$	12.4049	−	12.4049i	0.426237	−	0.426237i
$848$	−29.8274	+	47.1613i	−1.02428	+	1.61952i
$849$		0			0
$850$	1.48797	+	1.98020i	0.0510371	+	0.0679204i
$851$	−4.02938	−	4.02938i	−0.138125	−	0.138125i
$852$		0			0
$853$	27.2045	+	27.2045i	0.931464	+	0.931464i	0.997797	−	0.0663337i	$-0.0211302\pi$
$853$	27.2045	+	27.2045i	0.931464	+	0.931464i	−0.0663337	+	0.997797i	$0.521130\pi$
$854$	13.2760	+	1.88423i	0.454296	+	0.0644770i
$855$		0			0
$856$	31.2235	−	11.8397i	1.06720	−	0.404672i
$857$		−	28.0509i		−	0.958202i	−0.877760	−	0.479101i	$-0.840963\pi$
$857$		−	28.0509i		−	0.958202i	0.877760	−	0.479101i	$-0.159037\pi$
$858$		0			0
$859$	−13.4573			−0.459158			−0.229579	−	0.973290i	$-0.573735\pi$
$859$	−13.4573			−0.459158			−0.229579	+	0.973290i	$0.573735\pi$
$860$	−27.5197	+	15.1568i	−0.938415	+	0.516841i
$861$		0			0
$862$	47.3196	+	6.71594i	1.61171	+	0.228746i
$863$	−7.81239	+	7.81239i	−0.265937	+	0.265937i	−0.827461	−	0.561524i	$-0.810215\pi$
$863$	−7.81239	+	7.81239i	−0.265937	+	0.265937i	0.561524	+	0.827461i	$0.310215\pi$
$864$		0			0
$865$	8.20840	−	8.20840i	0.279094	−	0.279094i
$866$	37.8223	−	28.4206i	1.28525	−	0.965772i
$867$		0			0
$868$	1.49797	−	5.17093i	0.0508443	−	0.175513i
$869$	0.715172	+	0.715172i	0.0242605	+	0.0242605i
$870$		0			0
$871$	22.8635	+	19.2165i	0.774699	+	0.651126i
$872$	16.1700	−	35.9234i	0.547586	−	1.21652i
$873$		0			0
$874$	0.474297	−	3.34183i	0.0160433	−	0.113039i
$875$		−	17.1020i		−	0.578154i
$876$		0			0
$877$	11.8817	−	11.8817i	0.401216	−	0.401216i	−0.477445	−	0.878661i	$-0.658437\pi$
$877$	11.8817	−	11.8817i	0.401216	−	0.401216i	0.878661	+	0.477445i	$0.158437\pi$
$878$	2.45880	+	3.27218i	0.0829805	+	0.110431i
$879$		0			0
$880$	−2.80255	+	4.43122i	−0.0944740	+	0.149376i
$881$			20.0497i			0.675493i	0.941237	+	0.337746i	$0.109665\pi$
$881$			20.0497i			0.675493i	−0.941237	+	0.337746i	$0.890335\pi$
$882$		0			0
$883$		−	32.1521i		−	1.08201i	−0.841021	−	0.541003i	$-0.818045\pi$
$883$		−	32.1521i		−	1.08201i	0.841021	−	0.541003i	$-0.181955\pi$
$884$	−20.9303	−	4.14525i	−0.703962	−	0.139420i
$885$		0			0
$886$	−16.7267	−	22.2600i	−0.561946	−	0.747840i
$887$		−	36.2082i		−	1.21575i	−0.794032	−	0.607876i	$-0.792022\pi$
$887$		−	36.2082i		−	1.21575i	0.794032	−	0.607876i	$-0.207978\pi$
$888$		0			0
$889$	5.06093	+	5.06093i	0.169738	+	0.169738i
$890$	−28.3037	+	21.2681i	−0.948743	+	0.712909i
$891$		0			0
$892$	−24.8800	−	45.1740i	−0.833044	−	1.51254i
$893$			8.16714i			0.273303i
$894$		0			0
$895$	−25.8984	−	25.8984i	−0.865689	−	0.865689i
$896$	10.2328	+	15.4866i	0.341854	+	0.517372i
$897$		0			0
$898$	−26.8123	−	3.80541i	−0.894739	−	0.126988i
$899$	−11.2495	−	11.2495i	−0.375192	−	0.375192i
$900$		0			0
$901$	−41.2779			−1.37517
$902$	−0.811619	−	1.08011i	−0.0270240	−	0.0359636i
$903$		0			0
$904$	−24.8501	+	9.42298i	−0.826504	+	0.313404i
$905$	23.0184	−	23.0184i	0.765157	−	0.765157i
$906$		0			0
$907$		−	22.5108i		−	0.747460i	−0.927538	−	0.373730i	$-0.878079\pi$
$907$		−	22.5108i		−	0.747460i	0.927538	−	0.373730i	$-0.121921\pi$
$908$	7.29076	−	4.01546i	0.241952	−	0.133258i
$909$		0			0
$910$	−13.2052	−	14.7302i	−0.437749	−	0.488301i
$911$		−	42.8030i		−	1.41813i	−0.705146	−	0.709063i	$-0.749118\pi$
$911$		−	42.8030i		−	1.41813i	0.705146	−	0.709063i	$-0.250882\pi$
$912$		0			0
$913$	−2.58070			−0.0854086
$914$	−1.09109	+	7.68768i	−0.0360901	+	0.254286i
$915$		0			0
$916$	−5.16483	+	2.84458i	−0.170651	+	0.0939876i
$917$	−23.7881	−	23.7881i	−0.785554	−	0.785554i
$918$		0			0
$919$		−	3.91723i		−	0.129218i	−0.997911	−	0.0646088i	$-0.979420\pi$
$919$		−	3.91723i		−	0.129218i	0.997911	−	0.0646088i	$-0.0205800\pi$
$920$	−5.89737	+	13.1016i	−0.194430	+	0.431948i
$921$		0			0
$922$	34.5448	+	4.90285i	1.13767	+	0.161467i
$923$	17.4885	−	20.8076i	0.575642	−	0.684889i
$924$		0			0
$925$	1.11032	−	1.11032i	0.0365072	−	0.0365072i
$926$	−8.44404	+	59.4955i	−0.277488	+	1.95514i
$927$		0			0
$928$	54.6761	−	4.40926i	1.79483	−	0.144741i
$929$	16.9835	+	16.9835i	0.557212	+	0.557212i	0.928513	−	0.371301i	$-0.121088\pi$
$929$	16.9835	+	16.9835i	0.557212	+	0.557212i	−0.371301	+	0.928513i	$0.621088\pi$
$930$		0			0
$931$	−3.38471	+	3.38471i	−0.110929	+	0.110929i
$932$	31.0350	+	8.99054i	1.01659	+	0.294495i
$933$		0			0
$934$	−9.74372	+	7.32167i	−0.318824	+	0.239572i
$935$	−3.87842			−0.126838
$936$		0			0
$937$	16.7414			0.546919			0.273459	−	0.961884i	$-0.411832\pi$
$937$	16.7414			0.546919			0.273459	+	0.961884i	$0.411832\pi$
$938$	15.3653	−	11.5458i	0.501694	−	0.376985i
$939$		0			0
$940$	9.67339	−	33.3922i	0.315511	−	1.08913i
$941$	−30.5678	+	30.5678i	−0.996481	+	0.996481i	−0.999994	−	0.00351291i	$-0.998882\pi$
$941$	−30.5678	+	30.5678i	−0.996481	+	0.996481i	0.00351291	+	0.999994i	$0.498882\pi$
$942$		0			0
$943$	−2.61794	−	2.61794i	−0.0852519	−	0.0852519i
$944$	48.9145	−	11.0130i	1.59203	−	0.358442i
$945$		0			0
$946$	0.731742	−	5.15575i	0.0237910	−	0.167628i
$947$	−34.2563	+	34.2563i	−1.11318	+	1.11318i	−0.120461	+	0.992718i	$0.538437\pi$
$947$	−34.2563	+	34.2563i	−1.11318	+	1.11318i	−0.992718	+	0.120461i	$0.961563\pi$
$948$		0			0
$949$	19.3571	−	23.0307i	0.628358	−	0.747609i
$950$	0.920863	+	0.130696i	0.0298767	+	0.00424033i
$951$		0			0
$952$	−5.63588	+	12.5207i	−0.182660	+	0.405799i
$953$			14.8870i			0.482236i	0.970496	+	0.241118i	$0.0775141\pi$
$953$			14.8870i			0.482236i	−0.970496	+	0.241118i	$0.922486\pi$
$954$		0			0
$955$	−15.8729	−	15.8729i	−0.513634	−	0.513634i
$956$	15.5427	+	28.2205i	0.502688	+	0.912717i
$957$		0			0
$958$	1.27313	−	8.97026i	0.0411328	−	0.289816i
$959$	22.7386			0.734267
$960$		0			0
$961$			28.3082i			0.913169i
$962$	−0.737280	+	13.5061i	−0.0237709	+	0.435455i
$963$		0			0
$964$	11.6854	+	21.2169i	0.376362	+	0.683351i
$965$			15.7337i			0.506486i
$966$		0			0
$967$	−3.08494	+	3.08494i	−0.0992049	+	0.0992049i	−0.754967	−	0.655762i	$-0.772347\pi$
$967$	−3.08494	+	3.08494i	−0.0992049	+	0.0992049i	0.655762	+	0.754967i	$0.272347\pi$
$968$	10.7231	+	28.2789i	0.344654	+	0.908917i
$969$		0			0
$970$	−14.0388	−	18.6829i	−0.450758	−	0.599871i
$971$	−40.4168			−1.29704			−0.648519	−	0.761199i	$-0.724611\pi$
$971$	−40.4168			−1.29704			−0.648519	+	0.761199i	$0.724611\pi$
$972$		0			0
$973$	4.06493	+	4.06493i	0.130316	+	0.130316i
$974$	−28.0764	−	3.98481i	−0.899626	−	0.127682i
$975$		0			0
$976$	−12.3564	+	19.5371i	−0.395518	+	0.625367i
$977$	40.2981	+	40.2981i	1.28925	+	1.28925i	0.935242	+	0.354008i	$0.115182\pi$
$977$	40.2981	+	40.2981i	1.28925	+	1.28925i	0.354008	+	0.935242i	$0.384818\pi$
$978$		0			0
$979$		−	5.86814i		−	0.187547i
$980$	17.8477	−	9.82980i	0.570124	−	0.314001i
$981$		0			0
$982$	−22.3493	+	16.7938i	−0.713195	+	0.535912i
$983$	−4.02628	−	4.02628i	−0.128418	−	0.128418i	0.639976	−	0.768395i	$-0.278944\pi$
$983$	−4.02628	−	4.02628i	−0.128418	−	0.128418i	−0.768395	+	0.639976i	$0.778944\pi$
$984$		0			0
$985$		−	44.2456i		−	1.40978i
$986$	24.3754	+	32.4389i	0.776271	+	1.03307i
$987$		0			0
$988$	−6.65801	+	4.45673i	−0.211819	+	0.141787i
$989$		−	14.2700i		−	0.453759i
$990$		0			0
$991$		−	17.6322i		−	0.560104i	−0.959985	−	0.280052i	$-0.909648\pi$
$991$		−	17.6322i		−	0.560104i	0.959985	−	0.280052i	$-0.0903517\pi$
$992$	7.06893	+	6.01388i	0.224439	+	0.190941i
$993$		0			0
$994$	−10.5076	−	13.9836i	−0.333282	−	0.443533i
$995$	4.84850	−	4.84850i	0.153708	−	0.153708i
$996$		0			0
$997$			0.131010i			0.00414912i	0.999998	+	0.00207456i	$0.000660353\pi$
$997$			0.131010i			0.00414912i	−0.999998	+	0.00207456i	$0.999340\pi$
$998$	−4.17929	+	29.4467i	−0.132293	+	0.932119i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.j.307.4		24
3.2	odd	2		312.2.t.e.307.9	yes	24
8.3	odd	2	inner	936.2.w.j.307.3		24
12.11	even	2		1248.2.bb.f.463.3		24
13.5	odd	4	inner	936.2.w.j.811.3		24
24.5	odd	2		1248.2.bb.f.463.10		24
24.11	even	2		312.2.t.e.307.10	yes	24
39.5	even	4		312.2.t.e.187.10	yes	24
104.83	even	4	inner	936.2.w.j.811.4		24
156.83	odd	4		1248.2.bb.f.655.10		24
312.5	even	4		1248.2.bb.f.655.3		24
312.83	odd	4		312.2.t.e.187.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.9	✓	24	312.83	odd	4
312.2.t.e.187.10	yes	24	39.5	even	4
312.2.t.e.307.9	yes	24	3.2	odd	2
312.2.t.e.307.10	yes	24	24.11	even	2
936.2.w.j.307.3		24	8.3	odd	2	inner
936.2.w.j.307.4		24	1.1	even	1	trivial
936.2.w.j.811.3		24	13.5	odd	4	inner
936.2.w.j.811.4		24	104.83	even	4	inner
1248.2.bb.f.463.3		24	12.11	even	2
1248.2.bb.f.463.10		24	24.5	odd	2
1248.2.bb.f.655.3		24	312.5	even	4
1248.2.bb.f.655.10		24	156.83	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.849559 - 1.13060i) q^{2} +(-0.556500 + 1.92102i) q^{4} +(1.67211 - 1.67211i) q^{5} +(-1.16012 - 1.16012i) q^{7} +(2.64468 - 1.00284i) q^{8} +(-3.31105 - 0.469928i) q^{10} +(0.391951 - 0.391951i) q^{11} +(-3.59209 + 0.311317i) q^{13} +(-0.326039 + 2.29722i) q^{14} +(-3.38062 - 2.13809i) q^{16} -2.95889i q^{17} +(-0.785637 - 0.785637i) q^{19} +(2.28163 + 4.14269i) q^{20} +(-0.776123 - 0.110153i) q^{22} -2.14814 q^{23} -0.591934i q^{25} +(3.40366 + 3.79672i) q^{26} +(2.87422 - 1.58301i) q^{28} -9.69684i q^{29} +(1.16012 - 1.16012i) q^{31} +(0.454711 + 5.63855i) q^{32} +(-3.34531 + 2.51375i) q^{34} -3.87971 q^{35} +(1.87575 + 1.87575i) q^{37} +(-0.220794 + 1.55568i) q^{38} +(2.74534 - 6.09907i) q^{40} +(1.21870 + 1.21870i) q^{41} +6.64295i q^{43} +(0.534823 + 0.971064i) q^{44} +(1.82497 + 2.42868i) q^{46} +(-5.19778 - 5.19778i) q^{47} -4.30823i q^{49} +(-0.669239 + 0.502883i) q^{50} +(1.40095 - 7.07371i) q^{52} -13.9505i q^{53} -1.31077i q^{55} +(-4.23156 - 1.90473i) q^{56} +(-10.9632 + 8.23804i) q^{58} +(-8.86339 + 8.86339i) q^{59} -5.77916i q^{61} +(-2.29722 - 0.326039i) q^{62} +(5.98862 - 5.30437i) q^{64} +(-5.48582 + 6.52694i) q^{65} +(-5.85732 - 5.85732i) q^{67} +(5.68407 + 1.64662i) q^{68} +(3.29604 + 4.38639i) q^{70} +(-5.33062 + 5.33062i) q^{71} +(-5.90017 + 5.90017i) q^{73} +(0.527158 - 3.71428i) q^{74} +(1.94643 - 1.07202i) q^{76} -0.909421 q^{77} +1.82465i q^{79} +(-9.22791 + 2.07764i) q^{80} +(0.342502 - 2.41322i) q^{82} +(-3.29212 - 3.29212i) q^{83} +(-4.94759 - 4.94759i) q^{85} +(7.51051 - 5.64358i) q^{86} +(0.643519 - 1.42965i) q^{88} +(7.48582 - 7.48582i) q^{89} +(4.52842 + 3.80609i) q^{91} +(1.19544 - 4.12661i) q^{92} +(-1.46078 + 10.2924i) q^{94} -2.62735 q^{95} +(4.94128 + 4.94128i) q^{97} +(-4.87088 + 3.66010i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) \) 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

Introduction

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