LMFDB - Embedded newform 368.2.m.e.353.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(49,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("368.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			353.3
Character	$\chi$	$=$	368.353
Dual form			368.2.m.e.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.693988 + 1.51962i) q^{3} +(2.16159 + 2.49461i) q^{5} +(-1.24823 - 0.802191i) q^{7} +(0.136950 - 0.158049i) q^{9} +O(q^{10})$	\(q+(0.693988 + 1.51962i) q^{3} +(2.16159 + 2.49461i) q^{5} +(-1.24823 - 0.802191i) q^{7} +(0.136950 - 0.158049i) q^{9} +(0.394823 + 2.74605i) q^{11} +(2.87580 - 1.84816i) q^{13} +(-2.29075 + 5.01604i) q^{15} +(-3.61375 + 1.06109i) q^{17} +(-0.493516 - 0.144909i) q^{19} +(0.352768 - 2.45355i) q^{21} +(-4.43676 - 1.82077i) q^{23} +(-0.839030 + 5.83558i) q^{25} +(5.14397 + 1.51041i) q^{27} +(-6.96116 + 2.04398i) q^{29} +(3.18081 - 6.96501i) q^{31} +(-3.89896 + 2.50571i) q^{33} +(-0.697019 - 4.84787i) q^{35} +(2.15089 - 2.48226i) q^{37} +(4.80428 + 3.08752i) q^{39} +(7.05404 + 8.14079i) q^{41} +(2.54669 + 5.57647i) q^{43} +0.690301 q^{45} +8.93322 q^{47} +(-1.99333 - 4.36478i) q^{49} +(-4.12036 - 4.75514i) q^{51} +(-9.56994 - 6.15023i) q^{53} +(-5.99689 + 6.92079i) q^{55} +(-0.122287 - 0.850523i) q^{57} +(1.71119 - 1.09972i) q^{59} +(4.41429 - 9.66594i) q^{61} +(-0.297731 + 0.0874217i) q^{63} +(10.8268 + 3.17902i) q^{65} +(0.850132 - 5.91280i) q^{67} +(-0.312182 - 8.00578i) q^{69} +(1.85954 - 12.9334i) q^{71} +(-9.62258 - 2.82545i) q^{73} +(-9.45015 + 2.77481i) q^{75} +(1.71003 - 3.74444i) q^{77} +(-6.38435 + 4.10297i) q^{79} +(1.18532 + 8.24410i) q^{81} +(5.26805 - 6.07965i) q^{83} +(-10.4585 - 6.72125i) q^{85} +(-7.93705 - 9.15984i) q^{87} +(6.54409 + 14.3296i) q^{89} -5.07224 q^{91} +12.7916 q^{93} +(-0.705289 - 1.54437i) q^{95} +(-4.67830 - 5.39904i) q^{97} +(0.488082 + 0.313671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.693988	+	1.51962i	0.400674	+	0.877354i	0.997201	+	0.0747614i	$0.0238195\pi$
$3$	0.693988	+	1.51962i	0.400674	+	0.877354i	−0.596527	+	0.802593i	$0.703453\pi$
$4$		0			0
$5$	2.16159	+	2.49461i	0.966695	+	1.11562i	0.993252	+	0.115978i	$0.0370001\pi$
$5$	2.16159	+	2.49461i	0.966695	+	1.11562i	−0.0265573	+	0.999647i	$0.508454\pi$
$6$		0			0
$7$	−1.24823	−	0.802191i	−0.471788	−	0.303200i	0.283057	−	0.959103i	$-0.408651\pi$
$7$	−1.24823	−	0.802191i	−0.471788	−	0.303200i	−0.754845	+	0.655903i	$0.772288\pi$
$8$		0			0
$9$	0.136950	−	0.158049i	0.0456500	−	0.0526830i
$10$		0			0
$11$	0.394823	+	2.74605i	0.119044	+	0.827966i	0.958613	+	0.284713i	$0.0918984\pi$
$11$	0.394823	+	2.74605i	0.119044	+	0.827966i	−0.839569	+	0.543253i	$0.817192\pi$
$12$		0			0
$13$	2.87580	−	1.84816i	0.797602	−	0.512588i	−0.0772303	−	0.997013i	$-0.524608\pi$
$13$	2.87580	−	1.84816i	0.797602	−	0.512588i	0.874833	+	0.484425i	$0.160971\pi$
$14$		0			0
$15$	−2.29075	+	5.01604i	−0.591469	+	1.29514i
$16$		0			0
$17$	−3.61375	+	1.06109i	−0.876462	+	0.257353i	−0.688862	−	0.724893i	$-0.741889\pi$
$17$	−3.61375	+	1.06109i	−0.876462	+	0.257353i	−0.187601	+	0.982245i	$0.560071\pi$
$18$		0			0
$19$	−0.493516	−	0.144909i	−0.113220	−	0.0332445i	0.224632	−	0.974444i	$-0.427882\pi$
$19$	−0.493516	−	0.144909i	−0.113220	−	0.0332445i	−0.337852	+	0.941199i	$0.609700\pi$
$20$		0			0
$21$	0.352768	−	2.45355i	0.0769803	−	0.535409i
$22$		0			0
$23$	−4.43676	−	1.82077i	−0.925128	−	0.379656i
$23$	−4.43676	−	1.82077i	−0.925128	−	0.379656i
$24$		0			0
$25$	−0.839030	+	5.83558i	−0.167806	+	1.16712i
$26$		0			0
$27$	5.14397	+	1.51041i	0.989958	+	0.290678i
$28$		0			0
$29$	−6.96116	+	2.04398i	−1.29266	+	0.379558i	−0.854552	−	0.519366i	$-0.826168\pi$
$29$	−6.96116	+	2.04398i	−1.29266	+	0.379558i	−0.438104	+	0.898924i	$0.644350\pi$
$30$		0			0
$31$	3.18081	−	6.96501i	0.571291	−	1.25095i	−0.374817	−	0.927099i	$-0.622294\pi$
$31$	3.18081	−	6.96501i	0.571291	−	1.25095i	0.946107	−	0.323853i	$-0.104978\pi$
$32$		0			0
$33$	−3.89896	+	2.50571i	−0.678722	+	0.436188i
$34$		0			0
$35$	−0.697019	−	4.84787i	−0.117818	−	0.819440i
$36$		0			0
$37$	2.15089	−	2.48226i	0.353604	−	0.408081i	−0.550883	−	0.834583i	$-0.685709\pi$
$37$	2.15089	−	2.48226i	0.353604	−	0.408081i	0.904487	+	0.426502i	$0.140254\pi$
$38$		0			0
$39$	4.80428	+	3.08752i	0.769300	+	0.494399i
$40$		0			0
$41$	7.05404	+	8.14079i	1.10166	+	1.27138i	0.959553	+	0.281527i	$0.0908407\pi$
$41$	7.05404	+	8.14079i	1.10166	+	1.27138i	0.142102	+	0.989852i	$0.454614\pi$
$42$		0			0
$43$	2.54669	+	5.57647i	0.388366	+	0.850403i	0.998319	+	0.0579651i	$0.0184612\pi$
$43$	2.54669	+	5.57647i	0.388366	+	0.850403i	−0.609953	+	0.792438i	$0.708811\pi$
$44$		0			0
$45$	0.690301			0.102904
$46$		0			0
$47$	8.93322			1.30304			0.651522	−	0.758630i	$-0.274131\pi$
$47$	8.93322			1.30304			0.651522	+	0.758630i	$0.274131\pi$
$48$		0			0
$49$	−1.99333	−	4.36478i	−0.284761	−	0.623540i
$50$		0			0
$51$	−4.12036	−	4.75514i	−0.576965	−	0.665853i
$52$		0			0
$53$	−9.56994	−	6.15023i	−1.31453	−	0.844798i	−0.319818	−	0.947479i	$-0.603622\pi$
$53$	−9.56994	−	6.15023i	−1.31453	−	0.844798i	−0.994714	+	0.102681i	$0.967258\pi$
$54$		0			0
$55$	−5.99689	+	6.92079i	−0.808621	+	0.933198i
$56$		0			0
$57$	−0.122287	−	0.850523i	−0.0161973	−	0.112655i
$58$		0			0
$59$	1.71119	−	1.09972i	0.222779	−	0.143171i	−0.424491	−	0.905432i	$-0.639547\pi$
$59$	1.71119	−	1.09972i	0.222779	−	0.143171i	0.647270	+	0.762261i	$0.275911\pi$
$60$		0			0
$61$	4.41429	−	9.66594i	0.565191	−	1.23760i	−0.384127	−	0.923280i	$-0.625497\pi$
$61$	4.41429	−	9.66594i	0.565191	−	1.23760i	0.949318	−	0.314316i	$-0.101775\pi$
$62$		0			0
$63$	−0.297731	+	0.0874217i	−0.0375106	+	0.0110141i
$64$		0			0
$65$	10.8268	+	3.17902i	1.34289	+	0.394309i
$66$		0			0
$67$	0.850132	−	5.91280i	0.103860	−	0.722363i	−0.869642	−	0.493684i	$-0.835650\pi$
$67$	0.850132	−	5.91280i	0.103860	−	0.722363i	0.973502	−	0.228680i	$-0.0734408\pi$
$68$		0			0
$69$	−0.312182	−	8.00578i	−0.0375823	−	0.963783i
$70$		0			0
$71$	1.85954	−	12.9334i	0.220687	−	1.53491i	−0.514761	−	0.857334i	$-0.672119\pi$
$71$	1.85954	−	12.9334i	0.220687	−	1.53491i	0.735448	−	0.677581i	$-0.236972\pi$
$72$		0			0
$73$	−9.62258	−	2.82545i	−1.12624	−	0.330693i	−0.335010	−	0.942215i	$-0.608740\pi$
$73$	−9.62258	−	2.82545i	−1.12624	−	0.330693i	−0.791228	+	0.611521i	$0.790558\pi$
$74$		0			0
$75$	−9.45015	+	2.77481i	−1.09121	+	0.320408i
$76$		0			0
$77$	1.71003	−	3.74444i	0.194876	−	0.426718i
$78$		0			0
$79$	−6.38435	+	4.10297i	−0.718296	+	0.461621i	−0.848044	−	0.529926i	$-0.822220\pi$
$79$	−6.38435	+	4.10297i	−0.718296	+	0.461621i	0.129748	+	0.991547i	$0.458583\pi$
$80$		0			0
$81$	1.18532	+	8.24410i	0.131703	+	0.916011i
$82$		0			0
$83$	5.26805	−	6.07965i	0.578244	−	0.667329i	−0.388983	−	0.921245i	$-0.627173\pi$
$83$	5.26805	−	6.07965i	0.578244	−	0.667329i	0.967226	+	0.253917i	$0.0817188\pi$
$84$		0			0
$85$	−10.4585	−	6.72125i	−1.13438	−	0.729022i
$86$		0			0
$87$	−7.93705	−	9.15984i	−0.850941	−	0.982038i
$88$		0			0
$89$	6.54409	+	14.3296i	0.693673	+	1.51893i	0.847478	+	0.530830i	$0.178120\pi$
$89$	6.54409	+	14.3296i	0.693673	+	1.51893i	−0.153806	+	0.988101i	$0.549153\pi$
$90$		0			0
$91$	−5.07224			−0.531716
$92$		0			0
$93$	12.7916			1.32643
$94$		0			0
$95$	−0.705289	−	1.54437i	−0.0723611	−	0.158449i
$96$		0			0
$97$	−4.67830	−	5.39904i	−0.475009	−	0.548190i	0.466789	−	0.884369i	$-0.345411\pi$
$97$	−4.67830	−	5.39904i	−0.475009	−	0.548190i	−0.941798	+	0.336179i	$0.890865\pi$
$98$		0			0
$99$	0.488082	+	0.313671i	0.0490541	+	0.0315251i
$100$		0			0
$101$	4.28795	−	4.94856i	0.426667	−	0.492400i	−0.501189	−	0.865338i	$-0.667104\pi$
$101$	4.28795	−	4.94856i	0.426667	−	0.492400i	0.927856	+	0.372938i	$0.121649\pi$
$102$		0			0
$103$	1.82022	+	12.6599i	0.179352	+	1.24742i	0.858267	+	0.513203i	$0.171541\pi$
$103$	1.82022	+	12.6599i	0.179352	+	1.24742i	−0.678916	+	0.734216i	$0.737550\pi$
$104$		0			0
$105$	6.88321	−	4.42357i	0.671733	−	0.431696i
$106$		0			0
$107$	−2.36693	+	5.18286i	−0.228820	+	0.501046i	−0.988863	−	0.148826i	$-0.952450\pi$
$107$	−2.36693	+	5.18286i	−0.228820	+	0.501046i	0.760043	+	0.649873i	$0.225178\pi$
$108$		0			0
$109$	1.43685	−	0.421897i	0.137625	−	0.0404104i	−0.212195	−	0.977227i	$-0.568061\pi$
$109$	1.43685	−	0.421897i	0.137625	−	0.0404104i	0.349820	+	0.936817i	$0.386243\pi$
$110$		0			0
$111$	5.26479	+	1.54588i	0.499712	+	0.146729i
$112$		0			0
$113$	1.50819	−	10.4897i	0.141879	−	0.986789i	−0.787145	−	0.616768i	$-0.788442\pi$
$113$	1.50819	−	10.4897i	0.141879	−	0.986789i	0.929024	−	0.370020i	$-0.120649\pi$
$114$		0			0
$115$	−5.04837	−	15.0037i	−0.470763	−	1.39911i
$116$		0			0
$117$	0.101741	−	0.707622i	0.00940593	−	0.0654197i
$118$		0			0
$119$	5.36200	+	1.57442i	0.491534	+	0.144327i
$120$		0			0
$121$	3.16950	−	0.930649i	0.288136	−	0.0846044i
$122$		0			0
$123$	−7.47551	+	16.3691i	−0.674044	+	1.47595i
$124$		0			0
$125$	−2.48691	+	1.59824i	−0.222436	+	0.142951i
$126$		0			0
$127$	−1.61459	−	11.2297i	−0.143272	−	0.996479i	−0.926916	−	0.375269i	$-0.877550\pi$
$127$	−1.61459	−	11.2297i	−0.143272	−	0.996479i	0.783644	−	0.621210i	$-0.213359\pi$
$128$		0			0
$129$	−6.70675	+	7.74000i	−0.590497	+	0.681469i
$130$		0			0
$131$	−1.31374	−	0.844286i	−0.114782	−	0.0737657i	0.481990	−	0.876176i	$-0.339914\pi$
$131$	−1.31374	−	0.844286i	−0.114782	−	0.0737657i	−0.596772	+	0.802411i	$0.703550\pi$
$132$		0			0
$133$	0.499778	+	0.576775i	0.0433363	+	0.0500127i
$134$		0			0
$135$	7.35131	+	16.0971i	0.632700	+	1.38542i
$136$		0			0
$137$	−10.3690			−0.885885			−0.442942	−	0.896550i	$-0.646065\pi$
$137$	−10.3690			−0.885885			−0.442942	+	0.896550i	$0.646065\pi$
$138$		0			0
$139$	−19.2890			−1.63607			−0.818034	−	0.575169i	$-0.804936\pi$
$139$	−19.2890			−1.63607			−0.818034	+	0.575169i	$0.804936\pi$
$140$		0			0
$141$	6.19955	+	13.5751i	0.522096	+	1.14323i
$142$		0			0
$143$	6.21058	+	7.16739i	0.519355	+	0.599367i
$144$		0			0
$145$	−20.1462	−	12.9471i	−1.67305	−	1.07520i
$146$		0			0
$147$	5.24947	−	6.05821i	0.432969	−	0.499673i
$148$		0			0
$149$	1.74896	+	12.1643i	0.143280	+	0.996535i	0.926904	+	0.375299i	$0.122460\pi$
$149$	1.74896	+	12.1643i	0.143280	+	0.996535i	−0.783624	+	0.621236i	$0.786631\pi$
$150$		0			0
$151$	−0.112654	+	0.0723984i	−0.00916766	+	0.00589169i	−0.545217	−	0.838295i	$-0.683553\pi$
$151$	−0.112654	+	0.0723984i	−0.00916766	+	0.00589169i	0.536049	+	0.844187i	$0.319916\pi$
$152$		0			0
$153$	−0.327199	+	0.716465i	−0.0264524	+	0.0579228i
$154$		0			0
$155$	24.2506	−	7.12063i	1.94786	−	0.571942i
$156$		0			0
$157$	0.281739	+	0.0827259i	0.0224852	+	0.00660225i	0.292956	−	0.956126i	$-0.405361\pi$
$157$	0.281739	+	0.0827259i	0.0224852	+	0.00660225i	−0.270471	+	0.962728i	$0.587179\pi$
$158$		0			0
$159$	2.70460	−	18.8109i	0.214488	−	1.49180i
$160$		0			0
$161$	4.07751	+	5.83187i	0.321353	+	0.459615i
$162$		0			0
$163$	−0.876633	+	6.09712i	−0.0686632	+	0.477563i	0.926257	+	0.376893i	$0.123008\pi$
$163$	−0.876633	+	6.09712i	−0.0686632	+	0.477563i	−0.994920	+	0.100670i	$0.967901\pi$
$164$		0			0
$165$	−14.6788	−	4.31007i	−1.14274	−	0.335539i
$166$		0			0
$167$	−14.4077	+	4.23050i	−1.11490	+	0.327366i	−0.786758	−	0.617261i	$-0.788242\pi$
$167$	−14.4077	+	4.23050i	−1.11490	+	0.327366i	−0.328146	+	0.944627i	$0.606424\pi$
$168$		0			0
$169$	−0.545896	+	1.19535i	−0.0419920	+	0.0919496i
$170$		0			0
$171$	−0.0904899	+	0.0581543i	−0.00691993	+	0.00444717i
$172$		0			0
$173$	0.176963	+	1.23081i	0.0134543	+	0.0935765i	0.995442	−	0.0953675i	$-0.0304026\pi$
$173$	0.176963	+	1.23081i	0.0134543	+	0.0935765i	−0.981988	+	0.188944i	$0.939494\pi$
$174$		0			0
$175$	5.72855	−	6.61110i	0.433038	−	0.499752i
$176$		0			0
$177$	2.85870	+	1.83718i	0.214873	+	0.138091i
$178$		0			0
$179$	11.3483	+	13.0967i	0.848216	+	0.978893i	0.999955	−	0.00952771i	$-0.00303281\pi$
$179$	11.3483	+	13.0967i	0.848216	+	0.978893i	−0.151739	+	0.988421i	$0.548487\pi$
$180$		0			0
$181$	8.51103	+	18.6366i	0.632620	+	1.38524i	0.905975	+	0.423331i	$0.139139\pi$
$181$	8.51103	+	18.6366i	0.632620	+	1.38524i	−0.273355	+	0.961913i	$0.588134\pi$
$182$		0			0
$183$	17.7520			1.31227
$184$		0			0
$185$	10.8416			0.797092
$186$		0			0
$187$	−4.34060	−	9.50460i	−0.317416	−	0.695045i
$188$		0			0
$189$	−5.20925	−	6.01179i	−0.378917	−	0.437293i
$190$		0			0
$191$	6.06685	+	3.89893i	0.438982	+	0.282117i	0.741406	−	0.671057i	$-0.234159\pi$
$191$	6.06685	+	3.89893i	0.438982	+	0.282117i	−0.302424	+	0.953174i	$0.597796\pi$
$192$		0			0
$193$	−3.05146	+	3.52157i	−0.219649	+	0.253488i	−0.854870	−	0.518842i	$-0.826363\pi$
$193$	−3.05146	+	3.52157i	−0.219649	+	0.253488i	0.635221	+	0.772330i	$0.280909\pi$
$194$		0			0
$195$	2.68273	+	18.6588i	0.192114	+	1.33618i
$196$		0			0
$197$	−0.954666	+	0.613527i	−0.0680171	+	0.0437120i	−0.574207	−	0.818710i	$-0.694690\pi$
$197$	−0.954666	+	0.613527i	−0.0680171	+	0.0437120i	0.506190	+	0.862422i	$0.331053\pi$
$198$		0			0
$199$	−6.58668	+	14.4228i	−0.466917	+	1.02241i	0.518939	+	0.854811i	$0.326327\pi$
$199$	−6.58668	+	14.4228i	−0.466917	+	1.02241i	−0.985856	+	0.167595i	$0.946400\pi$
$200$		0			0
$201$	9.57520	−	2.81153i	0.675383	−	0.198310i
$202$		0			0
$203$	10.3288	+	3.03282i	0.724941	+	0.212862i
$204$		0			0
$205$	−5.06016	+	35.1942i	−0.353417	+	2.45807i
$206$		0			0
$207$	−0.895384	+	0.451870i	−0.0622335	+	0.0314072i
$208$		0			0
$209$	0.203078	−	1.41244i	0.0140472	−	0.0977002i
$210$		0			0
$211$	18.7387	+	5.50219i	1.29003	+	0.378786i	0.853589	−	0.520948i	$-0.174421\pi$
$211$	18.7387	+	5.50219i	1.29003	+	0.378786i	0.436439	+	0.899734i	$0.356240\pi$
$212$		0			0
$213$	20.9444	−	6.14983i	1.43509	−	0.421380i
$214$		0			0
$215$	−8.40622	+	18.4071i	−0.573300	+	1.25535i
$216$		0			0
$217$	−9.55766	+	6.14234i	−0.648816	+	0.416969i
$218$		0			0
$219$	−2.38435	−	16.5835i	−0.161119	−	1.12061i
$220$		0			0
$221$	−8.43133	+	9.73027i	−0.567152	+	0.654529i
$222$		0			0
$223$	−17.6126	−	11.3189i	−1.17943	−	0.757972i	−0.204147	−	0.978940i	$-0.565442\pi$
$223$	−17.6126	−	11.3189i	−1.17943	−	0.757972i	−0.975281	+	0.220968i	$0.929078\pi$
$224$		0			0
$225$	0.807401	+	0.931791i	0.0538268	+	0.0621194i
$226$		0			0
$227$	−9.58300	−	20.9838i	−0.636046	−	1.39275i	−0.903254	−	0.429107i	$-0.858828\pi$
$227$	−9.58300	−	20.9838i	−0.636046	−	1.39275i	0.267208	−	0.963639i	$-0.413899\pi$
$228$		0			0
$229$	7.93760			0.524532			0.262266	−	0.964996i	$-0.415530\pi$
$229$	7.93760			0.524532			0.262266	+	0.964996i	$0.415530\pi$
$230$		0			0
$231$	6.87687			0.452465
$232$		0			0
$233$	−5.72720	−	12.5408i	−0.375201	−	0.821576i	−0.999194	−	0.0401461i	$-0.987218\pi$
$233$	−5.72720	−	12.5408i	−0.375201	−	0.821576i	0.623992	−	0.781430i	$-0.285510\pi$
$234$		0			0
$235$	19.3100	+	22.2849i	1.25965	+	1.45371i
$236$		0			0
$237$	−10.6656	−	6.85439i	−0.692807	−	0.445240i
$238$		0			0
$239$	−8.26670	+	9.54028i	−0.534728	+	0.617109i	−0.957256	−	0.289240i	$-0.906597\pi$
$239$	−8.26670	+	9.54028i	−0.534728	+	0.617109i	0.422528	+	0.906350i	$0.361143\pi$
$240$		0			0
$241$	1.30173	+	9.05373i	0.0838518	+	0.583202i	0.987820	+	0.155602i	$0.0497317\pi$
$241$	1.30173	+	9.05373i	0.0838518	+	0.583202i	−0.903968	+	0.427600i	$0.859359\pi$
$242$		0			0
$243$	1.82491	−	1.17280i	0.117068	−	0.0752350i
$244$		0			0
$245$	6.57967	−	14.4075i	0.420360	−	0.920460i
$246$		0			0
$247$	−1.68707	+	0.495368i	−0.107346	+	0.0315195i
$248$		0			0
$249$	12.8947	+	3.78624i	0.817171	+	0.239943i
$250$		0			0
$251$	−1.32530	+	9.21770i	−0.0836525	+	0.581816i	0.904281	+	0.426938i	$0.140408\pi$
$251$	−1.32530	+	9.21770i	−0.0836525	+	0.581816i	−0.987934	+	0.154878i	$0.950501\pi$
$252$		0			0
$253$	3.24819	−	12.9025i	0.204212	−	0.811170i
$254$		0			0
$255$	2.95571	−	20.5574i	0.185094	−	1.28735i
$256$		0			0
$257$	22.1295	+	6.49781i	1.38040	+	0.405322i	0.885909	−	0.463860i	$-0.153536\pi$
$257$	22.1295	+	6.49781i	1.38040	+	0.405322i	0.494492	+	0.869182i	$0.335354\pi$
$258$		0			0
$259$	−4.67606	+	1.37301i	−0.290556	+	0.0853150i
$260$		0			0
$261$	−0.630283	+	1.38013i	−0.0390135	+	0.0854277i
$262$		0			0
$263$	−22.4697	+	14.4404i	−1.38554	+	0.890433i	−0.999486	−	0.0320439i	$-0.989798\pi$
$263$	−22.4697	+	14.4404i	−1.38554	+	0.890433i	−0.386054	+	0.922476i	$0.626162\pi$
$264$		0			0
$265$	−5.34389	−	37.1676i	−0.328273	−	2.28319i
$266$		0			0
$267$	−17.2340	+	19.8891i	−1.05470	+	1.21719i
$268$		0			0
$269$	−6.60662	−	4.24582i	−0.402813	−	0.258872i	0.323512	−	0.946224i	$-0.395137\pi$
$269$	−6.60662	−	4.24582i	−0.402813	−	0.258872i	−0.726324	+	0.687352i	$0.758773\pi$
$270$		0			0
$271$	−11.5987	−	13.3857i	−0.704574	−	0.813121i	0.284789	−	0.958590i	$-0.408076\pi$
$271$	−11.5987	−	13.3857i	−0.704574	−	0.813121i	−0.989363	+	0.145469i	$0.953531\pi$
$272$		0			0
$273$	−3.52008	−	7.70789i	−0.213045	−	0.466503i
$274$		0			0
$275$	−16.3561			−0.986309
$276$		0			0
$277$	−2.46981			−0.148396			−0.0741982	−	0.997244i	$-0.523640\pi$
$277$	−2.46981			−0.148396			−0.0741982	+	0.997244i	$0.523640\pi$
$278$		0			0
$279$	−0.665199	−	1.45658i	−0.0398244	−	0.0872033i
$280$		0			0
$281$	−7.50679	−	8.66330i	−0.447818	−	0.516809i	0.486291	−	0.873797i	$-0.338349\pi$
$281$	−7.50679	−	8.66330i	−0.447818	−	0.516809i	−0.934109	+	0.356987i	$0.883804\pi$
$282$		0			0
$283$	−19.2772	−	12.3887i	−1.14591	−	0.736433i	−0.177091	−	0.984195i	$-0.556669\pi$
$283$	−19.2772	−	12.3887i	−1.14591	−	0.736433i	−0.968821	+	0.247762i	$0.920305\pi$
$284$		0			0
$285$	1.85739	−	2.14355i	0.110022	−	0.126973i
$286$		0			0
$287$	−2.27462	−	15.8203i	−0.134266	−	0.933843i
$288$		0			0
$289$	−2.36806	+	1.52186i	−0.139298	+	0.0895212i
$290$		0			0
$291$	4.95782	−	10.8561i	0.290633	−	0.636397i
$292$		0			0
$293$	−29.6060	+	8.69310i	−1.72960	+	0.507856i	−0.986840	−	0.161701i	$-0.948302\pi$
$293$	−29.6060	+	8.69310i	−1.72960	+	0.507856i	−0.742761	+	0.669557i	$0.766484\pi$
$294$		0			0
$295$	6.44228	+	1.89162i	0.375084	+	0.110135i
$296$		0			0
$297$	−2.11670	+	14.7220i	−0.122823	+	0.854256i
$298$		0			0
$299$	−16.1243	+	2.96370i	−0.932491	+	0.171395i
$300$		0			0
$301$	1.29453	−	9.00366i	0.0746155	−	0.518962i
$302$		0			0
$303$	10.4957	+	3.08182i	0.602964	+	0.177046i
$304$		0			0
$305$	33.6547	−	9.88191i	1.92706	−	0.565836i
$306$		0			0
$307$	−3.38302	+	7.40778i	−0.193079	+	0.422784i	−0.981268	−	0.192650i	$-0.938292\pi$
$307$	−3.38302	+	7.40778i	−0.193079	+	0.422784i	0.788188	+	0.615434i	$0.211019\pi$
$308$		0			0
$309$	−17.9751	+	11.5519i	−1.02257	+	0.657164i
$310$		0			0
$311$	−2.06169	−	14.3394i	−0.116908	−	0.813110i	−0.960928	−	0.276799i	$-0.910726\pi$
$311$	−2.06169	−	14.3394i	−0.116908	−	0.813110i	0.844020	−	0.536311i	$-0.180183\pi$
$312$		0			0
$313$	−1.77523	+	2.04872i	−0.100342	+	0.115801i	−0.803699	−	0.595036i	$-0.797138\pi$
$313$	−1.77523	+	2.04872i	−0.100342	+	0.115801i	0.703357	+	0.710836i	$0.251683\pi$
$314$		0			0
$315$	−0.861657	−	0.553754i	−0.0485489	−	0.0312005i
$316$		0			0
$317$	9.31198	+	10.7466i	0.523013	+	0.603589i	0.954383	−	0.298586i	$-0.0965151\pi$
$317$	9.31198	+	10.7466i	0.523013	+	0.603589i	−0.431370	+	0.902175i	$0.641970\pi$
$318$		0			0
$319$	−8.36131	−	18.3087i	−0.468143	−	1.02509i
$320$		0			0
$321$	−9.51862			−0.531277
$322$		0			0
$323$	1.93720			0.107789
$324$		0			0
$325$	8.37221	+	18.3326i	0.464407	+	1.01691i
$326$		0			0
$327$	1.63828	+	1.89068i	0.0905971	+	0.104555i
$328$		0			0
$329$	−11.1507	−	7.16615i	−0.614760	−	0.395082i
$330$		0			0
$331$	19.3990	−	22.3876i	1.06627	−	1.23054i	0.0942669	−	0.995547i	$-0.469949\pi$
$331$	19.3990	−	22.3876i	1.06627	−	1.23054i	0.971998	−	0.234989i	$-0.0755053\pi$
$332$		0			0
$333$	−0.0977536	−	0.679891i	−0.00535687	−	0.0372578i
$334$		0			0
$335$	16.5878	−	10.6603i	0.906287	−	0.582436i
$336$		0			0
$337$	9.13044	−	19.9929i	0.497367	−	1.08908i	−0.479950	−	0.877296i	$-0.659345\pi$
$337$	9.13044	−	19.9929i	0.497367	−	1.08908i	0.977316	−	0.211785i	$-0.0679277\pi$
$338$		0			0
$339$	16.9871	−	4.98785i	0.922610	−	0.270903i
$340$		0			0
$341$	20.3821	+	5.98474i	1.10375	+	0.324092i
$342$		0			0
$343$	−2.49139	+	17.3280i	−0.134523	+	0.935625i
$344$		0			0
$345$	19.2965	−	18.0840i	1.03889	−	0.973612i
$346$		0			0
$347$	−1.24061	+	8.62864i	−0.0665995	+	0.463209i	0.929044	+	0.369969i	$0.120632\pi$
$347$	−1.24061	+	8.62864i	−0.0665995	+	0.463209i	−0.995644	+	0.0932405i	$0.970277\pi$
$348$		0			0
$349$	−2.27303	−	0.667423i	−0.121673	−	0.0357263i	0.220329	−	0.975426i	$-0.429287\pi$
$349$	−2.27303	−	0.667423i	−0.121673	−	0.0357263i	−0.342002	+	0.939699i	$0.611105\pi$
$350$		0			0
$351$	17.5845	−	5.16327i	0.938591	−	0.275595i
$352$		0			0
$353$	2.88483	−	6.31690i	0.153544	−	0.336215i	−0.817191	−	0.576367i	$-0.804470\pi$
$353$	2.88483	−	6.31690i	0.153544	−	0.336215i	0.970735	+	0.240152i	$0.0771972\pi$
$354$		0			0
$355$	36.2835	−	23.3180i	1.92573	−	1.23759i
$356$		0			0
$357$	1.32863	+	9.24084i	0.0703187	+	0.489077i
$358$		0			0
$359$	−8.40045	+	9.69464i	−0.443359	+	0.511664i	−0.932811	−	0.360367i	$-0.882652\pi$
$359$	−8.40045	+	9.69464i	−0.443359	+	0.511664i	0.489452	+	0.872030i	$0.337197\pi$
$360$		0			0
$361$	−15.7613	−	10.1291i	−0.829540	−	0.533113i
$362$		0			0
$363$	3.61383	+	4.17058i	0.189677	+	0.218899i
$364$		0			0
$365$	−13.7517	−	30.1121i	−0.719798	−	1.57614i
$366$		0			0
$367$	−16.5274			−0.862724			−0.431362	−	0.902179i	$-0.641967\pi$
$367$	−16.5274			−0.862724			−0.431362	+	0.902179i	$0.641967\pi$
$368$		0			0
$369$	2.25269			0.117271
$370$		0			0
$371$	7.01186	+	15.3538i	0.364038	+	0.797131i
$372$		0			0
$373$	6.70607	+	7.73922i	0.347227	+	0.400722i	0.902320	−	0.431067i	$-0.141863\pi$
$373$	6.70607	+	7.73922i	0.347227	+	0.400722i	−0.555093	+	0.831789i	$0.687317\pi$
$374$		0			0
$375$	−4.15461	−	2.67000i	−0.214543	−	0.137878i
$376$		0			0
$377$	−16.2413	+	18.7434i	−0.836468	+	0.965336i
$378$		0			0
$379$	3.39889	+	23.6398i	0.174589	+	1.21429i	0.869036	+	0.494749i	$0.164740\pi$
$379$	3.39889	+	23.6398i	0.174589	+	1.21429i	−0.694447	+	0.719544i	$0.744351\pi$
$380$		0			0
$381$	15.9445	−	10.2469i	0.816859	−	0.524964i
$382$		0			0
$383$	−5.79010	+	12.6785i	−0.295860	+	0.647844i	−0.997933	−	0.0642615i	$-0.979531\pi$
$383$	−5.79010	+	12.6785i	−0.295860	+	0.647844i	0.702073	+	0.712105i	$0.252258\pi$
$384$		0			0
$385$	13.0373	−	3.82810i	0.664443	−	0.195098i
$386$		0			0
$387$	1.23012	+	0.361197i	0.0625307	+	0.0183607i
$388$		0			0
$389$	1.52593	−	10.6131i	0.0773680	−	0.538106i	−0.913869	−	0.406009i	$-0.866920\pi$
$389$	1.52593	−	10.6131i	0.0773680	−	0.538106i	0.991237	−	0.132097i	$-0.0421709\pi$
$390$		0			0
$391$	17.9653	+	1.87198i	0.908545	+	0.0946700i
$392$		0			0
$393$	0.371280	−	2.58231i	0.0187286	−	0.130260i
$394$		0			0
$395$	−24.0357	−	7.05752i	−1.20937	−	0.355102i
$396$		0			0
$397$	−12.2869	+	3.60776i	−0.616662	+	0.181068i	−0.575121	−	0.818069i	$-0.695045\pi$
$397$	−12.2869	+	3.60776i	−0.616662	+	0.181068i	−0.0415410	+	0.999137i	$0.513227\pi$
$398$		0			0
$399$	−0.529640	+	1.15975i	−0.0265152	+	0.0580601i
$400$		0			0
$401$	−22.7409	+	14.6147i	−1.13563	+	0.729823i	−0.966727	−	0.255810i	$-0.917658\pi$
$401$	−22.7409	+	14.6147i	−1.13563	+	0.729823i	−0.168900	+	0.985633i	$0.554022\pi$
$402$		0			0
$403$	−3.72509	−	25.9086i	−0.185560	−	1.29060i
$404$		0			0
$405$	−18.0037	+	20.7773i	−0.894609	+	1.03243i
$406$		0			0
$407$	7.66564	+	4.92641i	0.379972	+	0.244193i
$408$		0			0
$409$	−4.94965	−	5.71220i	−0.244744	−	0.282450i	0.620065	−	0.784550i	$-0.287106\pi$
$409$	−4.94965	−	5.71220i	−0.244744	−	0.282450i	−0.864809	+	0.502100i	$0.832561\pi$
$410$		0			0
$411$	−7.19598	−	15.7570i	−0.354951	−	0.777235i
$412$		0			0
$413$	−3.01815			−0.148514
$414$		0			0
$415$	26.5538			1.30347
$416$		0			0
$417$	−13.3863	−	29.3119i	−0.655531	−	1.43541i
$418$		0			0
$419$	0.778603	+	0.898555i	0.0380372	+	0.0438973i	0.774449	−	0.632636i	$-0.218027\pi$
$419$	0.778603	+	0.898555i	0.0380372	+	0.0438973i	−0.736412	+	0.676533i	$0.763482\pi$
$420$		0			0
$421$	24.8232	+	15.9529i	1.20981	+	0.777497i	0.980627	−	0.195887i	$-0.0627585\pi$
$421$	24.8232	+	15.9529i	1.20981	+	0.777497i	0.229182	+	0.973384i	$0.426395\pi$
$422$		0			0
$423$	1.22341	−	1.41188i	0.0594840	−	0.0686482i
$424$		0			0
$425$	−3.16004	−	21.9786i	−0.153285	−	1.06612i
$426$		0			0
$427$	−13.2640	+	8.52425i	−0.641889	+	0.412517i
$428$		0			0
$429$	−6.58166	+	14.4118i	−0.317765	+	0.695809i
$430$		0			0
$431$	16.0710	−	4.71888i	0.774115	−	0.227301i	0.129265	−	0.991610i	$-0.458738\pi$
$431$	16.0710	−	4.71888i	0.774115	−	0.227301i	0.644850	+	0.764310i	$0.276920\pi$
$432$		0			0
$433$	−28.9576	−	8.50272i	−1.39161	−	0.408615i	−0.501818	−	0.864973i	$-0.667335\pi$
$433$	−28.9576	−	8.50272i	−1.39161	−	0.408615i	−0.889796	+	0.456358i	$0.849154\pi$
$434$		0			0
$435$	5.69358	−	39.5997i	0.272986	−	1.89866i
$436$		0			0
$437$	1.92577	+	1.54150i	0.0921218	+	0.0737402i
$438$		0			0
$439$	2.70705	−	18.8279i	0.129200	−	0.898608i	−0.817371	−	0.576112i	$-0.804569\pi$
$439$	2.70705	−	18.8279i	0.129200	−	0.898608i	0.946571	−	0.322496i	$-0.104522\pi$
$440$		0			0
$441$	−0.962835	−	0.282714i	−0.0458493	−	0.0134626i
$442$		0			0
$443$	32.7272	−	9.60959i	1.55492	−	0.456565i	0.612352	−	0.790585i	$-0.290223\pi$
$443$	32.7272	−	9.60959i	1.55492	−	0.456565i	0.942566	+	0.334020i	$0.108405\pi$
$444$		0			0
$445$	−21.6011	+	47.2997i	−1.02399	+	2.24222i
$446$		0			0
$447$	−17.2713	+	11.0996i	−0.816905	+	0.524993i
$448$		0			0
$449$	−1.10434	−	7.68088i	−0.0521172	−	0.362483i	−0.999145	−	0.0413328i	$-0.986840\pi$
$449$	−1.10434	−	7.68088i	−0.0521172	−	0.362483i	0.947028	−	0.321150i	$-0.104069\pi$
$450$		0			0
$451$	−19.5700	+	22.5849i	−0.921513	+	1.06348i
$452$		0			0
$453$	−0.188199	−	0.120948i	−0.00884235	−	0.00568263i
$454$		0			0
$455$	−10.9641	−	12.6533i	−0.514007	−	0.593195i
$456$		0			0
$457$	0.940775	+	2.06001i	0.0440076	+	0.0963632i	0.930359	−	0.366650i	$-0.119495\pi$
$457$	0.940775	+	2.06001i	0.0440076	+	0.0963632i	−0.886351	+	0.463013i	$0.846768\pi$
$458$		0			0
$459$	−20.1917			−0.942468
$460$		0			0
$461$	21.3135			0.992668			0.496334	−	0.868132i	$-0.334679\pi$
$461$	21.3135			0.992668			0.496334	+	0.868132i	$0.334679\pi$
$462$		0			0
$463$	0.204871	+	0.448605i	0.00952116	+	0.0208484i	0.914333	−	0.404964i	$-0.132716\pi$
$463$	0.204871	+	0.448605i	0.00952116	+	0.0208484i	−0.904812	+	0.425812i	$0.859989\pi$
$464$		0			0
$465$	27.6503	+	31.9102i	1.28225	+	1.47980i
$466$		0			0
$467$	−16.8769	−	10.8461i	−0.780968	−	0.501897i	0.0883870	−	0.996086i	$-0.471829\pi$
$467$	−16.8769	−	10.8461i	−0.780968	−	0.501897i	−0.869355	+	0.494189i	$0.835465\pi$
$468$		0			0
$469$	−5.80436	+	6.69858i	−0.268020	+	0.309312i
$470$		0			0
$471$	0.0698112	+	0.485547i	0.00321673	+	0.0223728i
$472$		0			0
$473$	−14.3078	+	9.19505i	−0.657873	+	0.422789i
$474$		0			0
$475$	1.25970	−	2.75837i	0.0577992	−	0.126563i
$476$		0			0
$477$	−2.28264	+	0.670244i	−0.104515	+	0.0306883i
$478$		0			0
$479$	−3.56305	−	1.04620i	−0.162800	−	0.0478023i	0.199317	−	0.979935i	$-0.436128\pi$
$479$	−3.56305	−	1.04620i	−0.162800	−	0.0478023i	−0.362117	+	0.932133i	$0.617946\pi$
$480$		0			0
$481$	1.59790	−	11.1137i	0.0728581	−	0.506739i
$482$		0			0
$483$	−6.03249	+	10.2435i	−0.274488	+	0.466096i
$484$		0			0
$485$	3.35594	−	23.3411i	0.152385	−	1.05986i
$486$		0			0
$487$	17.7880	+	5.22303i	0.806052	+	0.236678i	0.658700	−	0.752406i	$-0.271107\pi$
$487$	17.7880	+	5.22303i	0.806052	+	0.236678i	0.147352	+	0.989084i	$0.452925\pi$
$488$		0			0
$489$	−9.87369	+	2.89918i	−0.446504	+	0.131105i
$490$		0			0
$491$	−14.9691	+	32.7777i	−0.675545	+	1.47924i	0.191751	+	0.981444i	$0.438583\pi$
$491$	−14.9691	+	32.7777i	−0.675545	+	1.47924i	−0.867296	+	0.497793i	$0.834144\pi$
$492$		0			0
$493$	22.9870	−	14.7729i	1.03528	−	0.665336i
$494$		0			0
$495$	0.272547	+	1.89560i	0.0122501	+	0.0852011i
$496$		0			0
$497$	−12.6962	+	14.6522i	−0.569503	+	0.657242i
$498$		0			0
$499$	−15.7374	−	10.1138i	−0.704504	−	0.452757i	0.138711	−	0.990333i	$-0.455704\pi$
$499$	−15.7374	−	10.1138i	−0.704504	−	0.452757i	−0.843216	+	0.537575i	$0.819340\pi$
$500$		0			0
$501$	−16.4276	−	18.9584i	−0.733929	−	0.846999i
$502$		0			0
$503$	14.0889	+	30.8504i	0.628194	+	1.37555i	0.909407	+	0.415907i	$0.136536\pi$
$503$	14.0889	+	30.8504i	0.628194	+	1.37555i	−0.281214	+	0.959645i	$0.590737\pi$
$504$		0			0
$505$	21.6135			0.961790
$506$		0			0
$507$	−2.19532			−0.0974975
$508$		0			0
$509$	−12.4899	−	27.3491i	−0.553606	−	1.21223i	−0.955077	−	0.296357i	$-0.904228\pi$
$509$	−12.4899	−	27.3491i	−0.553606	−	1.21223i	0.401471	−	0.915872i	$-0.368499\pi$
$510$		0			0
$511$	9.74468	+	11.2460i	0.431079	+	0.497492i
$512$		0			0
$513$	−2.31976	−	1.49082i	−0.102420	−	0.0658213i
$514$		0			0
$515$	−27.6470	+	31.9064i	−1.21827	+	1.40596i
$516$		0			0
$517$	3.52704	+	24.5311i	0.155119	+	1.07888i
$518$		0			0
$519$	−1.74755	+	1.12308i	−0.0767089	+	0.0492978i
$520$		0			0
$521$	4.72921	−	10.3555i	0.207191	−	0.453684i	−0.777298	−	0.629132i	$-0.783410\pi$
$521$	4.72921	−	10.3555i	0.207191	−	0.453684i	0.984489	+	0.175449i	$0.0561376\pi$
$522$		0			0
$523$	8.97084	−	2.63408i	0.392267	−	0.115180i	−0.0796500	−	0.996823i	$-0.525380\pi$
$523$	8.97084	−	2.63408i	0.392267	−	0.115180i	0.471917	+	0.881643i	$0.343562\pi$
$524$		0			0
$525$	14.0219	+	4.11721i	0.611967	+	0.179690i
$526$		0			0
$527$	−4.10414	+	28.5449i	−0.178779	+	1.24344i
$528$		0			0
$529$	16.3696	+	16.1566i	0.711723	+	0.702460i
$530$		0			0
$531$	0.0605391	−	0.421059i	0.00262717	−	0.0182724i
$532$		0			0
$533$	35.3315	+	10.3743i	1.53038	+	0.449359i
$534$		0			0
$535$	−18.0456	+	5.29866i	−0.780179	+	0.229081i
$536$		0			0
$537$	−12.0264	+	26.3342i	−0.518978	+	1.13640i
$538$		0			0
$539$	11.1989	−	7.19710i	0.482371	−	0.310001i
$540$		0			0
$541$	−0.143855	−	1.00054i	−0.00618482	−	0.0430164i	0.986495	−	0.163789i	$-0.0523718\pi$
$541$	−0.143855	−	1.00054i	−0.00618482	−	0.0430164i	−0.992680	+	0.120773i	$0.961463\pi$
$542$		0			0
$543$	−22.4140	+	25.8671i	−0.961875	+	1.11006i
$544$		0			0
$545$	4.15835	+	2.67241i	0.178124	+	0.114474i
$546$		0			0
$547$	−7.17243	−	8.27743i	−0.306671	−	0.353917i	0.581405	−	0.813615i	$-0.302503\pi$
$547$	−7.17243	−	8.27743i	−0.306671	−	0.353917i	−0.888076	+	0.459697i	$0.847958\pi$
$548$		0			0
$549$	−0.923154	−	2.02142i	−0.0393992	−	0.0862723i
$550$		0			0
$551$	3.73164			0.158973
$552$		0			0
$553$	11.2605			0.478846
$554$		0			0
$555$	7.52396	+	16.4752i	0.319374	+	0.699332i
$556$		0			0
$557$	−1.92001	−	2.21580i	−0.0813532	−	0.0938866i	0.713614	−	0.700540i	$-0.247057\pi$
$557$	−1.92001	−	2.21580i	−0.0813532	−	0.0938866i	−0.794967	+	0.606653i	$0.792512\pi$
$558$		0			0
$559$	17.6300	+	11.3301i	0.745668	+	0.479212i
$560$		0			0
$561$	11.4311	−	13.1922i	0.482620	−	0.556973i
$562$		0			0
$563$	−2.43880	−	16.9622i	−0.102783	−	0.714872i	−0.974422	−	0.224724i	$-0.927852\pi$
$563$	−2.43880	−	16.9622i	−0.102783	−	0.714872i	0.871639	−	0.490148i	$-0.163057\pi$
$564$		0			0
$565$	29.4279	−	18.9121i	1.23804	−	0.795640i
$566$		0			0
$567$	5.13379	−	11.2414i	0.215599	−	0.472095i
$568$		0			0
$569$	36.8195	−	10.8112i	1.54355	−	0.453229i	0.604388	−	0.796690i	$-0.293418\pi$
$569$	36.8195	−	10.8112i	1.54355	−	0.453229i	0.939167	+	0.343462i	$0.111600\pi$
$570$		0			0
$571$	16.2300	+	4.76556i	0.679205	+	0.199432i	0.603098	−	0.797667i	$-0.293933\pi$
$571$	16.2300	+	4.76556i	0.679205	+	0.199432i	0.0761067	+	0.997100i	$0.475751\pi$
$572$		0			0
$573$	−1.71458	+	11.9251i	−0.0716274	+	0.498180i
$574$		0			0
$575$	14.3478	−	24.3634i	0.598344	−	1.01602i
$576$		0			0
$577$	−2.45746	+	17.0920i	−0.102305	+	0.711549i	0.872520	+	0.488578i	$0.162484\pi$
$577$	−2.45746	+	17.0920i	−0.102305	+	0.711549i	−0.974825	+	0.222970i	$0.928425\pi$
$578$		0			0
$579$	−7.46914	−	2.19314i	−0.310407	−	0.0911437i
$580$		0			0
$581$	−11.4528	+	3.36284i	−0.475142	+	0.139514i
$582$		0			0
$583$	13.1104	−	28.7078i	0.542978	−	1.18896i
$584$		0			0
$585$	1.98517	−	1.27579i	0.0820765	−	0.0527474i
$586$		0			0
$587$	4.56136	+	31.7250i	0.188267	+	1.30943i	0.836492	+	0.547980i	$0.184603\pi$
$587$	4.56136	+	31.7250i	0.188267	+	1.30943i	−0.648224	+	0.761450i	$0.724488\pi$
$588$		0			0
$589$	−2.57908	+	2.97641i	−0.106269	+	0.122641i
$590$		0			0
$591$	−1.59486	−	1.02495i	−0.0656036	−	0.0421609i
$592$		0			0
$593$	2.00343	+	2.31209i	0.0822712	+	0.0949460i	0.795393	−	0.606094i	$-0.207265\pi$
$593$	2.00343	+	2.31209i	0.0822712	+	0.0949460i	−0.713121	+	0.701040i	$0.752719\pi$
$594$		0			0
$595$	7.66289	+	16.7794i	0.314148	+	0.687887i
$596$		0			0
$597$	−26.4883			−1.08409
$598$		0			0
$599$	20.8858			0.853370			0.426685	−	0.904400i	$-0.359681\pi$
$599$	20.8858			0.853370			0.426685	+	0.904400i	$0.359681\pi$
$600$		0			0
$601$	13.5502	+	29.6708i	0.552724	+	1.21030i	0.955498	+	0.294997i	$0.0953186\pi$
$601$	13.5502	+	29.6708i	0.552724	+	1.21030i	−0.402775	+	0.915299i	$0.631954\pi$
$602$		0			0
$603$	−0.818085	−	0.944121i	−0.0333150	−	0.0384476i
$604$		0			0
$605$	9.17278	+	5.89499i	0.372926	+	0.239665i
$606$		0			0
$607$	−25.3700	+	29.2786i	−1.02974	+	1.18838i	−0.0478627	+	0.998854i	$0.515241\pi$
$607$	−25.3700	+	29.2786i	−1.02974	+	1.18838i	−0.981875	+	0.189527i	$0.939304\pi$
$608$		0			0
$609$	2.55935	+	17.8006i	0.103710	+	0.721318i
$610$		0			0
$611$	25.6901	−	16.5100i	1.03931	−	0.667924i
$612$		0			0
$613$	7.26983	−	15.9187i	0.293626	−	0.642950i	−0.704118	−	0.710083i	$-0.748658\pi$
$613$	7.26983	−	15.9187i	0.293626	−	0.642950i	0.997744	+	0.0671321i	$0.0213849\pi$
$614$		0			0
$615$	−56.9936	+	16.7348i	−2.29820	+	0.674813i
$616$		0			0
$617$	−13.0260	−	3.82479i	−0.524408	−	0.153980i	0.00880470	−	0.999961i	$-0.497197\pi$
$617$	−13.0260	−	3.82479i	−0.524408	−	0.153980i	−0.533213	+	0.845981i	$0.679016\pi$
$618$		0			0
$619$	−5.83479	+	40.5819i	−0.234520	+	1.63112i	0.443638	+	0.896206i	$0.353688\pi$
$619$	−5.83479	+	40.5819i	−0.234520	+	1.63112i	−0.678158	+	0.734916i	$0.737221\pi$
$620$		0			0
$621$	−20.0725	−	16.0673i	−0.805480	−	0.644758i
$622$		0			0
$623$	3.32649	−	23.1363i	0.133273	−	0.926935i
$624$		0			0
$625$	18.9212	+	5.55576i	0.756848	+	0.222231i
$626$		0			0
$627$	2.28730	−	0.671612i	0.0913460	−	0.0268216i
$628$		0			0
$629$	−5.13887	+	11.2525i	−0.204900	+	0.448668i
$630$		0			0
$631$	−4.82543	+	3.10111i	−0.192097	+	0.123453i	−0.633154	−	0.774026i	$-0.718240\pi$
$631$	−4.82543	+	3.10111i	−0.192097	+	0.123453i	0.441057	+	0.897479i	$0.354604\pi$
$632$		0			0
$633$	4.64321	+	32.2942i	0.184551	+	1.28358i
$634$		0			0
$635$	24.5238	−	28.3019i	0.973196	−	1.12313i
$636$		0			0
$637$	−13.7992	−	8.86822i	−0.546745	−	0.351372i
$638$		0			0
$639$	−1.78945	−	2.06513i	−0.0707894	−	0.0816954i
$640$		0			0
$641$	7.60286	+	16.6479i	0.300295	+	0.657554i	0.998284	−	0.0585538i	$-0.0186489\pi$
$641$	7.60286	+	16.6479i	0.300295	+	0.657554i	−0.697989	+	0.716108i	$0.745922\pi$
$642$		0			0
$643$	14.0965			0.555913			0.277957	−	0.960594i	$-0.410343\pi$
$643$	14.0965			0.555913			0.277957	+	0.960594i	$0.410343\pi$
$644$		0			0
$645$	−33.8056			−1.33109
$646$		0			0
$647$	−12.9929	−	28.4506i	−0.510805	−	1.11851i	−0.972805	−	0.231627i	$-0.925595\pi$
$647$	−12.9929	−	28.4506i	−0.510805	−	1.11851i	0.462000	−	0.886880i	$-0.347132\pi$
$648$		0			0
$649$	3.69550	+	4.26484i	0.145061	+	0.167410i
$650$		0			0
$651$	−15.9669	−	10.2613i	−0.625794	−	0.402173i
$652$		0			0
$653$	0.0592343	−	0.0683600i	0.00231802	−	0.00267514i	−0.754589	−	0.656197i	$-0.772164\pi$
$653$	0.0592343	−	0.0683600i	0.00231802	−	0.00267514i	0.756907	+	0.653522i	$0.226709\pi$
$654$		0			0
$655$	−0.733595	−	5.10227i	−0.0286639	−	0.199362i
$656$		0			0
$657$	−1.76437	+	1.13389i	−0.0688347	+	0.0442374i
$658$		0			0
$659$	11.4949	−	25.1703i	0.447778	−	0.980496i	−0.542327	−	0.840167i	$-0.682457\pi$
$659$	11.4949	−	25.1703i	0.447778	−	0.980496i	0.990105	−	0.140329i	$-0.0448160\pi$
$660$		0			0
$661$	11.2677	−	3.30849i	0.438262	−	0.128685i	−0.0551559	−	0.998478i	$-0.517566\pi$
$661$	11.2677	−	3.30849i	0.438262	−	0.128685i	0.493418	+	0.869792i	$0.335747\pi$
$662$		0			0
$663$	−20.6376	−	6.05974i	−0.801497	−	0.235341i
$664$		0			0
$665$	−0.358512	+	2.49351i	−0.0139025	+	0.0966941i
$666$		0			0
$667$	34.6066	+	3.60599i	1.33997	+	0.139625i
$668$		0			0
$669$	4.97757	−	34.6197i	0.192444	−	1.33848i
$670$		0			0
$671$	28.2860	+	8.30553i	1.09197	+	0.320632i
$672$		0			0
$673$	−27.4177	+	8.05055i	−1.05687	+	0.310326i	−0.763591	−	0.645700i	$-0.776566\pi$
$673$	−27.4177	+	8.05055i	−1.05687	+	0.310326i	−0.293282	+	0.956026i	$0.594747\pi$
$674$		0			0
$675$	−13.1300	+	28.7508i	−0.505376	+	1.10662i
$676$		0			0
$677$	24.0687	−	15.4680i	0.925037	−	0.594485i	0.0109217	−	0.999940i	$-0.496523\pi$
$677$	24.0687	−	15.4680i	0.925037	−	0.594485i	0.914115	+	0.405455i	$0.132887\pi$
$678$		0			0
$679$	1.50854	+	10.4922i	0.0578926	+	0.402652i
$680$		0			0
$681$	25.2370	−	29.1251i	0.967085	−	1.11608i
$682$		0			0
$683$	−9.39901	−	6.04038i	−0.359643	−	0.231129i	0.348324	−	0.937374i	$-0.386751\pi$
$683$	−9.39901	−	6.04038i	−0.359643	−	0.231129i	−0.707967	+	0.706246i	$0.750387\pi$
$684$		0			0
$685$	−22.4136	−	25.8667i	−0.856380	−	0.988315i
$686$		0			0
$687$	5.50860	+	12.0622i	0.210166	+	0.460200i
$688$		0			0
$689$	−38.8878			−1.48151
$690$		0			0
$691$	26.1688			0.995509			0.497755	−	0.867318i	$-0.334158\pi$
$691$	26.1688			0.995509			0.497755	+	0.867318i	$0.334158\pi$
$692$		0			0
$693$	−0.357616	−	0.783069i	−0.0135847	−	0.0297463i
$694$		0			0
$695$	−41.6949	−	48.1185i	−1.58158	−	1.82524i
$696$		0			0
$697$	−34.1296	−	21.9338i	−1.29275	−	0.830801i
$698$		0			0
$699$	15.0827	−	17.4064i	0.570480	−	0.658369i
$700$		0			0
$701$	0.0593912	+	0.413075i	0.00224318	+	0.0156016i	0.990912	−	0.134510i	$-0.0429459\pi$
$701$	0.0593912	+	0.413075i	0.00224318	+	0.0156016i	−0.988669	+	0.150111i	$0.952037\pi$
$702$		0			0
$703$	−1.42120	+	0.913351i	−0.0536016	+	0.0344477i
$704$		0			0
$705$	−20.4638	+	44.8094i	−0.770709	+	1.68762i
$706$		0			0
$707$	−9.32205	+	2.73720i	−0.350592	+	0.102943i
$708$		0			0
$709$	2.45837	+	0.721843i	0.0923260	+	0.0271094i	0.327569	−	0.944827i	$-0.393771\pi$
$709$	2.45837	+	0.721843i	0.0923260	+	0.0271094i	−0.235243	+	0.971937i	$0.575589\pi$
$710$		0			0
$711$	−0.225867	+	1.57094i	−0.00847069	+	0.0589149i
$712$		0			0
$713$	−26.7941	+	25.1105i	−1.00345	+	0.940397i
$714$		0			0
$715$	−4.45511	+	30.9860i	−0.166612	+	1.15881i
$716$		0			0
$717$	−20.2346	−	5.94142i	−0.755675	−	0.221886i
$718$		0			0
$719$	28.7133	−	8.43100i	1.07083	−	0.314423i	0.301623	−	0.953427i	$-0.402471\pi$
$719$	28.7133	−	8.43100i	1.07083	−	0.314423i	0.769203	+	0.639004i	$0.220653\pi$
$720$		0			0
$721$	7.88361	−	17.2627i	0.293601	−	0.642897i
$722$		0			0
$723$	−12.8549	+	8.26132i	−0.478077	+	0.307242i
$724$		0			0
$725$	−6.08720	−	42.3374i	−0.226073	−	1.57237i
$726$		0			0
$727$	8.29715	−	9.57543i	0.307724	−	0.355133i	−0.580731	−	0.814095i	$-0.697233\pi$
$727$	8.29715	−	9.57543i	0.307724	−	0.355133i	0.888456	+	0.458962i	$0.151779\pi$
$728$		0			0
$729$	24.0688	+	15.4681i	0.891436	+	0.572891i
$730$		0			0
$731$	−15.1202	−	17.4497i	−0.559242	−	0.645399i
$732$		0			0
$733$	2.28738	+	5.00866i	0.0844863	+	0.184999i	0.947160	−	0.320762i	$-0.103939\pi$
$733$	2.28738	+	5.00866i	0.0844863	+	0.184999i	−0.862674	+	0.505761i	$0.831212\pi$
$734$		0			0
$735$	26.4601			0.975997
$736$		0			0
$737$	16.5725			0.610456
$738$		0			0
$739$	−13.6086	−	29.7986i	−0.500599	−	1.09616i	−0.976274	−	0.216539i	$-0.930523\pi$
$739$	−13.6086	−	29.7986i	−0.500599	−	1.09616i	0.475675	−	0.879621i	$-0.342204\pi$
$740$		0			0
$741$	−1.92358	−	2.21993i	−0.0706644	−	0.0815510i
$742$		0			0
$743$	−22.4994	−	14.4595i	−0.825422	−	0.530467i	0.0583978	−	0.998293i	$-0.481401\pi$
$743$	−22.4994	−	14.4595i	−0.825422	−	0.530467i	−0.883820	+	0.467827i	$0.845037\pi$
$744$		0			0
$745$	−26.5646	+	30.6572i	−0.973251	+	1.12319i
$746$		0			0
$747$	−0.239422	−	1.66522i	−0.00876000	−	0.0609272i
$748$		0			0
$749$	7.11213	−	4.57069i	0.259872	−	0.167009i
$750$		0			0
$751$	14.1293	−	30.9388i	0.515585	−	1.12897i	−0.455499	−	0.890236i	$-0.650539\pi$
$751$	14.1293	−	30.9388i	0.515585	−	1.12897i	0.971084	−	0.238737i	$-0.0767335\pi$
$752$		0			0
$753$	−14.9272	+	4.38301i	−0.543976	+	0.159726i
$754$		0			0
$755$	−0.424118	−	0.124532i	−0.0154352	−	0.00453220i
$756$		0			0
$757$	6.35134	−	44.1746i	0.230844	−	1.60555i	−0.463627	−	0.886031i	$-0.653452\pi$
$757$	6.35134	−	44.1746i	0.230844	−	1.60555i	0.694470	−	0.719521i	$-0.255639\pi$
$758$		0			0
$759$	21.8611	−	4.01814i	0.793506	−	0.145849i
$760$		0			0
$761$	−2.53451	+	17.6279i	−0.0918758	+	0.639010i	0.890899	+	0.454202i	$0.150075\pi$
$761$	−2.53451	+	17.6279i	−0.0918758	+	0.639010i	−0.982775	+	0.184808i	$0.940834\pi$
$762$		0			0
$763$	−2.13196	−	0.626001i	−0.0771823	−	0.0226628i
$764$		0			0
$765$	−2.49457	+	0.732473i	−0.0901915	+	0.0264826i
$766$		0			0
$767$	2.88859	−	6.32513i	0.104301	−	0.228387i
$768$		0			0
$769$	26.9080	−	17.2927i	0.970326	−	0.623591i	0.0434889	−	0.999054i	$-0.486153\pi$
$769$	26.9080	−	17.2927i	0.970326	−	0.623591i	0.926837	+	0.375463i	$0.122516\pi$
$770$		0			0
$771$	5.48340	+	38.1379i	0.197480	+	1.37350i
$772$		0			0
$773$	−13.2482	+	15.2893i	−0.476506	+	0.549917i	−0.942210	−	0.335024i	$-0.891256\pi$
$773$	−13.2482	+	15.2893i	−0.476506	+	0.549917i	0.465704	+	0.884941i	$0.345801\pi$
$774$		0			0
$775$	37.9760	+	24.4057i	1.36414	+	0.876679i
$776$		0			0
$777$	−5.33159	−	6.15299i	−0.191270	−	0.220737i
$778$		0			0
$779$	−2.30160	−	5.03981i	−0.0824635	−	0.180570i
$780$		0			0
$781$	36.2500			1.29713
$782$		0			0
$783$	−38.8953			−1.39000
$784$		0			0
$785$	0.402636	+	0.881649i	0.0143707	+	0.0314674i
$786$		0			0
$787$	17.8726	+	20.6261i	0.637091	+	0.735242i	0.978858	−	0.204543i	$-0.0655707\pi$
$787$	17.8726	+	20.6261i	0.637091	+	0.735242i	−0.341767	+	0.939785i	$0.611025\pi$
$788$		0			0
$789$	−37.5376	−	24.1240i	−1.33638	−	0.858836i
$790$		0			0
$791$	−10.2973	+	11.8837i	−0.366131	+	0.422537i
$792$		0			0
$793$	−5.16963	−	35.9556i	−0.183579	−	1.27682i
$794$		0			0
$795$	52.7721	−	33.9146i	1.87163	−	1.20283i
$796$		0			0
$797$	−21.2445	+	46.5190i	−0.752519	+	1.64779i	0.00926492	+	0.999957i	$0.497051\pi$
$797$	−21.2445	+	46.5190i	−0.752519	+	1.64779i	−0.761784	+	0.647831i	$0.775676\pi$
$798$		0			0
$799$	−32.2824	+	9.47896i	−1.14207	+	0.335342i
$800$		0			0
$801$	3.16099	+	0.928149i	0.111688	+	0.0327945i
$802$		0			0
$803$	3.95961	−	27.5397i	0.139732	−	0.971854i
$804$		0			0
$805$	−5.73433	+	22.7779i	−0.202109	+	0.802817i
$806$		0			0
$807$	1.86712	−	12.9861i	0.0657258	−	0.457133i
$808$		0			0
$809$	−0.662682	−	0.194581i	−0.0232987	−	0.00684111i	0.270062	−	0.962843i	$-0.412956\pi$
$809$	−0.662682	−	0.194581i	−0.0232987	−	0.00684111i	−0.293361	+	0.956002i	$0.594774\pi$
$810$		0			0
$811$	−31.0212	+	9.10866i	−1.08930	+	0.319848i	−0.776594	−	0.630001i	$-0.783054\pi$
$811$	−31.0212	+	9.10866i	−1.08930	+	0.319848i	−0.312709	+	0.949849i	$0.601236\pi$
$812$		0			0
$813$	12.2918	−	26.9152i	0.431091	−	0.943957i
$814$		0			0
$815$	−17.1049	+	10.9926i	−0.599158	+	0.385055i
$816$		0			0
$817$	−0.448749	−	3.12111i	−0.0156997	−	0.109194i
$818$		0			0
$819$	−0.694644	+	0.801662i	−0.0242728	+	0.0280123i
$820$		0			0
$821$	5.13003	+	3.29687i	0.179039	+	0.115062i	0.627091	−	0.778946i	$-0.284246\pi$
$821$	5.13003	+	3.29687i	0.179039	+	0.115062i	−0.448051	+	0.894008i	$0.647882\pi$
$822$		0			0
$823$	18.1101	+	20.9001i	0.631277	+	0.728532i	0.977807	−	0.209506i	$-0.0671857\pi$
$823$	18.1101	+	20.9001i	0.631277	+	0.728532i	−0.346531	+	0.938039i	$0.612640\pi$
$824$		0			0
$825$	−11.3509	−	24.8551i	−0.395189	−	0.865342i
$826$		0			0
$827$	−17.5955			−0.611857			−0.305929	−	0.952054i	$-0.598967\pi$
$827$	−17.5955			−0.611857			−0.305929	+	0.952054i	$0.598967\pi$
$828$		0			0
$829$	26.7911			0.930494			0.465247	−	0.885181i	$-0.345965\pi$
$829$	26.7911			0.930494			0.465247	+	0.885181i	$0.345965\pi$
$830$		0			0
$831$	−1.71402	−	3.75318i	−0.0594586	−	0.130196i
$832$		0			0
$833$	11.8348	+	13.6581i	0.410052	+	0.473225i
$834$		0			0
$835$	−41.6972	−	26.7971i	−1.44299	−	0.927353i
$836$		0			0
$837$	26.8820	−	31.0235i	0.929178	−	1.07233i
$838$		0			0
$839$	−0.800873	−	5.57020i	−0.0276492	−	0.192304i	0.971316	−	0.237794i	$-0.0764243\pi$
$839$	−0.800873	−	5.57020i	−0.0276492	−	0.192304i	−0.998965	+	0.0454895i	$0.985515\pi$
$840$		0			0
$841$	19.8836	−	12.7784i	0.685640	−	0.440634i
$842$		0			0
$843$	7.95532	−	17.4197i	0.273996	−	0.599967i
$844$		0			0
$845$	−4.16193	+	1.22205i	−0.143175	+	0.0420399i
$846$		0			0
$847$	−4.70283	−	1.38088i	−0.161591	−	0.0474475i
$848$		0			0
$849$	5.44801	−	37.8917i	0.186975	−	1.30044i
$850$		0			0
$851$	−14.0626	+	7.09692i	−0.482059	+	0.243279i
$852$		0			0
$853$	−1.84561	+	12.8365i	−0.0631924	+	0.439512i	0.933522	+	0.358519i	$0.116718\pi$
$853$	−1.84561	+	12.8365i	−0.0631924	+	0.439512i	−0.996715	+	0.0809931i	$0.974191\pi$
$854$		0			0
$855$	−0.340675	−	0.100031i	−0.0116508	−	0.00342099i
$856$		0			0
$857$	−11.1973	+	3.28783i	−0.382493	+	0.112310i	−0.467326	−	0.884085i	$-0.654783\pi$
$857$	−11.1973	+	3.28783i	−0.382493	+	0.112310i	0.0848328	+	0.996395i	$0.472964\pi$
$858$		0			0
$859$	17.1397	−	37.5306i	0.584797	−	1.28053i	−0.353738	−	0.935345i	$-0.615090\pi$
$859$	17.1397	−	37.5306i	0.584797	−	1.28053i	0.938535	−	0.345183i	$-0.112183\pi$
$860$		0			0
$861$	22.4623	−	14.4357i	0.765514	−	0.491966i
$862$		0			0
$863$	0.807279	+	5.61475i	0.0274801	+	0.191128i	0.998937	−	0.0460859i	$-0.0146748\pi$
$863$	0.807279	+	5.61475i	0.0274801	+	0.191128i	−0.971457	+	0.237214i	$0.923766\pi$
$864$		0			0
$865$	−2.68786	+	3.10196i	−0.0913901	+	0.105470i
$866$		0			0
$867$	−3.95606	−	2.54240i	−0.134355	−	0.0863446i
$868$		0			0
$869$	−13.7877	−	15.9118i	−0.467715	−	0.539772i
$870$		0			0
$871$	−8.48300	−	18.5752i	−0.287435	−	0.629396i
$872$		0			0
$873$	−1.49401			−0.0505644
$874$		0			0
$875$	4.38634			0.148285
$876$		0			0
$877$	8.90815	+	19.5061i	0.300807	+	0.658675i	0.998323	−	0.0578941i	$-0.0184386\pi$
$877$	8.90815	+	19.5061i	0.300807	+	0.658675i	−0.697516	+	0.716569i	$0.745711\pi$
$878$		0			0
$879$	−33.7564	−	38.9570i	−1.13858	−	1.31399i
$880$		0			0
$881$	−7.46135	−	4.79512i	−0.251379	−	0.161552i	0.408883	−	0.912587i	$-0.365918\pi$
$881$	−7.46135	−	4.79512i	−0.251379	−	0.161552i	−0.660262	+	0.751035i	$0.729555\pi$
$882$		0			0
$883$	30.8589	−	35.6131i	1.03848	−	1.19848i	0.0587301	−	0.998274i	$-0.481295\pi$
$883$	30.8589	−	35.6131i	1.03848	−	1.19848i	0.979755	−	0.200202i	$-0.0641597\pi$
$884$		0			0
$885$	1.59631	+	11.1026i	0.0536595	+	0.373210i
$886$		0			0
$887$	−5.68147	+	3.65126i	−0.190765	+	0.122597i	−0.632537	−	0.774530i	$-0.717986\pi$
$887$	−5.68147	+	3.65126i	−0.190765	+	0.122597i	0.441772	+	0.897127i	$0.354350\pi$
$888$		0			0
$889$	−6.99301	+	15.3126i	−0.234538	+	0.513567i
$890$		0			0
$891$	−22.1708	+	6.50992i	−0.742748	+	0.218091i
$892$		0			0
$893$	−4.40869	−	1.29451i	−0.147531	−	0.0433190i
$894$		0			0
$895$	−8.14065	+	56.6195i	−0.272112	+	1.89258i
$896$		0			0
$897$	−15.6938	−	22.4460i	−0.523999	−	0.749451i
$898$		0			0
$899$	−7.90580	+	54.9861i	−0.263673	+	1.83389i
$900$		0			0
$901$	41.1093	+	12.0708i	1.36955	+	0.402136i
$902$		0			0
$903$	14.5806	−	4.28124i	0.485210	−	0.142471i
$904$		0			0
$905$	−28.0936	+	61.5164i	−0.933863	+	2.04487i
$906$		0			0
$907$	−14.3349	+	9.21246i	−0.475981	+	0.305895i	−0.756546	−	0.653940i	$-0.773115\pi$
$907$	−14.3349	+	9.21246i	−0.475981	+	0.305895i	0.280565	+	0.959835i	$0.409478\pi$
$908$		0			0
$909$	−0.194879	−	1.35541i	−0.00646372	−	0.0449561i
$910$		0			0
$911$	−7.96025	+	9.18662i	−0.263735	+	0.304366i	−0.872136	−	0.489263i	$-0.837266\pi$
$911$	−7.96025	+	9.18662i	−0.263735	+	0.304366i	0.608401	+	0.793630i	$0.291811\pi$
$912$		0			0
$913$	18.7750	+	12.0660i	0.621362	+	0.399325i
$914$		0			0
$915$	38.3727	+	44.2845i	1.26856	+	1.46400i
$916$		0			0
$917$	0.962570	+	2.10773i	0.0317868	+	0.0696035i
$918$		0			0
$919$	−1.52112			−0.0501772			−0.0250886	−	0.999685i	$-0.507987\pi$
$919$	−1.52112			−0.0501772			−0.0250886	+	0.999685i	$0.507987\pi$
$920$		0			0
$921$	−13.6048			−0.448293
$922$		0			0
$923$	−18.5554	−	40.6306i	−0.610758	−	1.33737i
$924$		0			0
$925$	12.6808	+	14.6344i	0.416941	+	0.481175i
$926$		0			0
$927$	2.25017	+	1.44609i	0.0739051	+	0.0474960i
$928$		0			0
$929$	2.64936	−	3.05753i	0.0869227	−	0.100314i	−0.710622	−	0.703574i	$-0.751586\pi$
$929$	2.64936	−	3.05753i	0.0869227	−	0.100314i	0.797545	+	0.603260i	$0.206132\pi$
$930$		0			0
$931$	0.351242	+	2.44294i	0.0115115	+	0.0800642i
$932$		0			0
$933$	20.3596	−	13.0843i	0.666544	−	0.428362i
$934$		0			0
$935$	14.3277	−	31.3732i	0.468565	−	1.02601i
$936$		0			0
$937$	35.2747	−	10.3576i	1.15237	−	0.338367i	0.350908	−	0.936410i	$-0.385873\pi$
$937$	35.2747	−	10.3576i	1.15237	−	0.338367i	0.801464	+	0.598043i	$0.204055\pi$
$938$		0			0
$939$	−4.34528	−	1.27589i	−0.141803	−	0.0416370i
$940$		0			0
$941$	1.43349	−	9.97016i	0.0467305	−	0.325018i	−0.953025	−	0.302893i	$-0.902048\pi$
$941$	1.43349	−	9.97016i	0.0467305	−	0.325018i	0.999755	−	0.0221253i	$-0.00704326\pi$
$942$		0			0
$943$	−16.4746	−	48.9625i	−0.536486	−	1.59444i
$944$		0			0
$945$	3.73681	−	25.9901i	0.121559	−	0.845458i
$946$		0			0
$947$	−17.6526	−	5.18327i	−0.573632	−	0.168434i	−0.0179651	−	0.999839i	$-0.505719\pi$
$947$	−17.6526	−	5.18327i	−0.573632	−	0.168434i	−0.555667	+	0.831405i	$0.687537\pi$
$948$		0			0
$949$	−32.8945	+	9.65869i	−1.06780	+	0.313534i
$950$		0			0
$951$	−9.86836	+	21.6087i	−0.320004	+	0.700710i
$952$		0			0
$953$	27.2193	−	17.4928i	0.881718	−	0.566646i	−0.0195979	−	0.999808i	$-0.506239\pi$
$953$	27.2193	−	17.4928i	0.881718	−	0.566646i	0.901316	+	0.433162i	$0.142602\pi$
$954$		0			0
$955$	3.38776	+	23.5624i	0.109625	+	0.762460i
$956$		0			0
$957$	22.0197	−	25.4121i	0.711795	−	0.821455i
$958$		0			0
$959$	12.9430	+	8.31793i	0.417950	+	0.268600i
$960$		0			0
$961$	−18.0931	−	20.8805i	−0.583647	−	0.673565i
$962$		0			0
$963$	0.494994	+	1.08388i	0.0159509	+	0.0349277i
$964$		0			0
$965$	−15.3810			−0.495131
$966$		0			0
$967$	52.5187			1.68889			0.844443	−	0.535645i	$-0.179932\pi$
$967$	52.5187			1.68889			0.844443	+	0.535645i	$0.179932\pi$
$968$		0			0
$969$	1.34440	+	2.94382i	0.0431883	+	0.0945691i
$970$		0			0
$971$	14.5394	+	16.7794i	0.466591	+	0.538475i	0.939460	−	0.342658i	$-0.111327\pi$
$971$	14.5394	+	16.7794i	0.466591	+	0.538475i	−0.472869	+	0.881133i	$0.656782\pi$
$972$		0			0
$973$	24.0771	+	15.4734i	0.771877	+	0.496055i
$974$		0			0
$975$	−22.0484	+	25.4452i	−0.706114	+	0.814899i
$976$		0			0
$977$	1.22218	+	8.50046i	0.0391011	+	0.271954i	0.999988	−	0.00498865i	$-0.00158794\pi$
$977$	1.22218	+	8.50046i	0.0391011	+	0.271954i	−0.960887	+	0.276942i	$0.910679\pi$
$978$		0			0
$979$	−36.7660	+	23.6281i	−1.17505	+	0.755157i
$980$		0			0
$981$	0.130096	−	0.284871i	0.00415366	−	0.00909524i
$982$		0			0
$983$	17.3050	−	5.08122i	0.551945	−	0.162066i	0.00614492	−	0.999981i	$-0.498044\pi$
$983$	17.3050	−	5.08122i	0.551945	−	0.162066i	0.545800	+	0.837915i	$0.316226\pi$
$984$		0			0
$985$	−3.59411	−	1.05533i	−0.114518	−	0.0336255i
$986$		0			0
$987$	3.15135	−	21.9181i	0.100309	−	0.697662i
$988$		0			0
$989$	−1.14560	−	29.3783i	−0.0364278	−	0.934177i
$990$		0			0
$991$	−4.59379	+	31.9505i	−0.145927	+	1.01494i	0.776872	+	0.629658i	$0.216805\pi$
$991$	−4.59379	+	31.9505i	−0.145927	+	1.01494i	−0.922799	+	0.385283i	$0.874104\pi$
$992$		0			0
$993$	47.4834	+	13.9424i	1.50684	+	0.442448i
$994$		0			0
$995$	−50.2171	+	14.7451i	−1.59199	+	0.467450i
$996$		0			0
$997$	16.6671	−	36.4959i	0.527854	−	1.15584i	−0.438526	−	0.898719i	$-0.644499\pi$
$997$	16.6671	−	36.4959i	0.527854	−	1.15584i	0.966380	−	0.257120i	$-0.0827735\pi$
$998$		0			0
$999$	14.8133	−	9.51996i	0.468674	−	0.301198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.353.3		30
4.3	odd	2		184.2.i.b.169.1	yes	30
23.3	even	11	inner	368.2.m.e.49.3		30
23.7	odd	22		8464.2.a.ch.1.11		15
23.16	even	11		8464.2.a.cg.1.11		15
92.3	odd	22		184.2.i.b.49.1	✓	30
92.7	even	22		4232.2.a.ba.1.5		15
92.39	odd	22		4232.2.a.bb.1.5		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.49.1	✓	30	92.3	odd	22
184.2.i.b.169.1	yes	30	4.3	odd	2
368.2.m.e.49.3		30	23.3	even	11	inner
368.2.m.e.353.3		30	1.1	even	1	trivial
4232.2.a.ba.1.5		15	92.7	even	22
4232.2.a.bb.1.5		15	92.39	odd	22
8464.2.a.cg.1.11		15	23.16	even	11
8464.2.a.ch.1.11		15	23.7	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.693988 + 1.51962i) q^{3} +(2.16159 + 2.49461i) q^{5} +(-1.24823 - 0.802191i) q^{7} +(0.136950 - 0.158049i) q^{9} +O(q^{10})\)	\(q+(0.693988 + 1.51962i) q^{3} +(2.16159 + 2.49461i) q^{5} +(-1.24823 - 0.802191i) q^{7} +(0.136950 - 0.158049i) q^{9} +(0.394823 + 2.74605i) q^{11} +(2.87580 - 1.84816i) q^{13} +(-2.29075 + 5.01604i) q^{15} +(-3.61375 + 1.06109i) q^{17} +(-0.493516 - 0.144909i) q^{19} +(0.352768 - 2.45355i) q^{21} +(-4.43676 - 1.82077i) q^{23} +(-0.839030 + 5.83558i) q^{25} +(5.14397 + 1.51041i) q^{27} +(-6.96116 + 2.04398i) q^{29} +(3.18081 - 6.96501i) q^{31} +(-3.89896 + 2.50571i) q^{33} +(-0.697019 - 4.84787i) q^{35} +(2.15089 - 2.48226i) q^{37} +(4.80428 + 3.08752i) q^{39} +(7.05404 + 8.14079i) q^{41} +(2.54669 + 5.57647i) q^{43} +0.690301 q^{45} +8.93322 q^{47} +(-1.99333 - 4.36478i) q^{49} +(-4.12036 - 4.75514i) q^{51} +(-9.56994 - 6.15023i) q^{53} +(-5.99689 + 6.92079i) q^{55} +(-0.122287 - 0.850523i) q^{57} +(1.71119 - 1.09972i) q^{59} +(4.41429 - 9.66594i) q^{61} +(-0.297731 + 0.0874217i) q^{63} +(10.8268 + 3.17902i) q^{65} +(0.850132 - 5.91280i) q^{67} +(-0.312182 - 8.00578i) q^{69} +(1.85954 - 12.9334i) q^{71} +(-9.62258 - 2.82545i) q^{73} +(-9.45015 + 2.77481i) q^{75} +(1.71003 - 3.74444i) q^{77} +(-6.38435 + 4.10297i) q^{79} +(1.18532 + 8.24410i) q^{81} +(5.26805 - 6.07965i) q^{83} +(-10.4585 - 6.72125i) q^{85} +(-7.93705 - 9.15984i) q^{87} +(6.54409 + 14.3296i) q^{89} -5.07224 q^{91} +12.7916 q^{93} +(-0.705289 - 1.54437i) q^{95} +(-4.67830 - 5.39904i) q^{97} +(0.488082 + 0.313671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

L-functions

Modular forms

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