LMFDB - Embedded newform 184.2.i.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [184,2,Mod(9,184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(184, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("184.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	184.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.46924739719$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	184.49
Dual form			184.2.i.b.169.1

$q$-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 $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.693988	+	1.51962i	−0.400674	+	0.877354i	0.596527	+	0.802593i	$0.296547\pi$
$3$	−0.693988	+	1.51962i	−0.400674	+	0.877354i	−0.997201	+	0.0747614i	$0.976180\pi$
$4$		0			0
$5$	2.16159	−	2.49461i	0.966695	−	1.11562i	−0.0265573	−	0.999647i	$-0.508454\pi$
$5$	2.16159	−	2.49461i	0.966695	−	1.11562i	0.993252	−	0.115978i	$-0.0370001\pi$
$6$		0			0
$7$	1.24823	−	0.802191i	0.471788	−	0.303200i	−0.283057	−	0.959103i	$-0.591349\pi$
$7$	1.24823	−	0.802191i	0.471788	−	0.303200i	0.754845	+	0.655903i	$0.227712\pi$
$8$		0			0
$9$	0.136950	+	0.158049i	0.0456500	+	0.0526830i
$10$		0			0
$11$	−0.394823	+	2.74605i	−0.119044	+	0.827966i	0.839569	+	0.543253i	$0.182808\pi$
$11$	−0.394823	+	2.74605i	−0.119044	+	0.827966i	−0.958613	+	0.284713i	$0.908102\pi$
$12$		0			0
$13$	2.87580	+	1.84816i	0.797602	+	0.512588i	0.874833	−	0.484425i	$-0.160971\pi$
$13$	2.87580	+	1.84816i	0.797602	+	0.512588i	−0.0772303	+	0.997013i	$0.524608\pi$
$14$		0			0
$15$	2.29075	+	5.01604i	0.591469	+	1.29514i
$16$		0			0
$17$	−3.61375	−	1.06109i	−0.876462	−	0.257353i	−0.187601	−	0.982245i	$-0.560071\pi$
$17$	−3.61375	−	1.06109i	−0.876462	−	0.257353i	−0.688862	+	0.724893i	$0.741889\pi$
$18$		0			0
$19$	0.493516	−	0.144909i	0.113220	−	0.0332445i	−0.224632	−	0.974444i	$-0.572118\pi$
$19$	0.493516	−	0.144909i	0.113220	−	0.0332445i	0.337852	+	0.941199i	$0.390300\pi$
$20$		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	−0.438104	−	0.898924i	$-0.644350\pi$
$29$	−6.96116	−	2.04398i	−1.29266	−	0.379558i	−0.854552	+	0.519366i	$0.826168\pi$
$30$		0			0
$31$	−3.18081	−	6.96501i	−0.571291	−	1.25095i	−0.946107	−	0.323853i	$-0.895022\pi$
$31$	−3.18081	−	6.96501i	−0.571291	−	1.25095i	0.374817	−	0.927099i	$-0.377706\pi$
$32$		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	0.904487	−	0.426502i	$-0.140254\pi$
$37$	2.15089	+	2.48226i	0.353604	+	0.408081i	−0.550883	+	0.834583i	$0.685709\pi$
$38$		0			0
$39$	−4.80428	+	3.08752i	−0.769300	+	0.494399i
$40$		0			0
$41$	7.05404	−	8.14079i	1.10166	−	1.27138i	0.142102	−	0.989852i	$-0.454614\pi$
$41$	7.05404	−	8.14079i	1.10166	−	1.27138i	0.959553	−	0.281527i	$-0.0908407\pi$
$42$		0			0
$43$	−2.54669	+	5.57647i	−0.388366	+	0.850403i	0.609953	+	0.792438i	$0.291189\pi$
$43$	−2.54669	+	5.57647i	−0.388366	+	0.850403i	−0.998319	+	0.0579651i	$0.981539\pi$
$44$		0			0
$45$	0.690301			0.102904
$46$		0			0
$47$	−8.93322			−1.30304			−0.651522	−	0.758630i	$-0.725869\pi$
$47$	−8.93322			−1.30304			−0.651522	+	0.758630i	$0.725869\pi$
$48$		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	−0.994714	−	0.102681i	$-0.967258\pi$
$53$	−9.56994	+	6.15023i	−1.31453	+	0.844798i	−0.319818	+	0.947479i	$0.603622\pi$
$54$		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	$-0.360453\pi$
$59$	−1.71119	−	1.09972i	−0.222779	−	0.143171i	−0.647270	+	0.762261i	$0.724089\pi$
$60$		0			0
$61$	4.41429	+	9.66594i	0.565191	+	1.23760i	0.949318	+	0.314316i	$0.101775\pi$
$61$	4.41429	+	9.66594i	0.565191	+	1.23760i	−0.384127	+	0.923280i	$0.625497\pi$
$62$		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	−0.973502	−	0.228680i	$-0.926559\pi$
$67$	−0.850132	−	5.91280i	−0.103860	−	0.722363i	0.869642	−	0.493684i	$-0.164350\pi$
$68$		0			0
$69$	−0.312182	+	8.00578i	−0.0375823	+	0.963783i
$70$		0			0
$71$	−1.85954	−	12.9334i	−0.220687	−	1.53491i	−0.735448	−	0.677581i	$-0.763028\pi$
$71$	−1.85954	−	12.9334i	−0.220687	−	1.53491i	0.514761	−	0.857334i	$-0.327881\pi$
$72$		0			0
$73$	−9.62258	+	2.82545i	−1.12624	+	0.330693i	−0.791228	−	0.611521i	$-0.790558\pi$
$73$	−9.62258	+	2.82545i	−1.12624	+	0.330693i	−0.335010	+	0.942215i	$0.608740\pi$
$74$		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	$-0.177780\pi$
$79$	6.38435	+	4.10297i	0.718296	+	0.461621i	−0.129748	+	0.991547i	$0.541417\pi$
$80$		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	$-0.372827\pi$
$83$	−5.26805	−	6.07965i	−0.578244	−	0.667329i	−0.967226	+	0.253917i	$0.918281\pi$
$84$		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	−0.153806	−	0.988101i	$-0.549153\pi$
$89$	6.54409	−	14.3296i	0.693673	−	1.51893i	0.847478	−	0.530830i	$-0.178120\pi$
$90$		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	−0.941798	−	0.336179i	$-0.890865\pi$
$97$	−4.67830	+	5.39904i	−0.475009	+	0.548190i	0.466789	+	0.884369i	$0.345411\pi$
$98$		0			0
$99$	−0.488082	+	0.313671i	−0.0490541	+	0.0315251i
$100$		0			0
$101$	4.28795	+	4.94856i	0.426667	+	0.492400i	0.927856	−	0.372938i	$-0.121649\pi$
$101$	4.28795	+	4.94856i	0.426667	+	0.492400i	−0.501189	+	0.865338i	$0.667104\pi$
$102$		0			0
$103$	−1.82022	+	12.6599i	−0.179352	+	1.24742i	0.678916	+	0.734216i	$0.262450\pi$
$103$	−1.82022	+	12.6599i	−0.179352	+	1.24742i	−0.858267	+	0.513203i	$0.828459\pi$
$104$		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	$-0.0475495\pi$
$107$	2.36693	+	5.18286i	0.228820	+	0.501046i	−0.760043	+	0.649873i	$0.774822\pi$
$108$		0			0
$109$	1.43685	+	0.421897i	0.137625	+	0.0404104i	0.349820	−	0.936817i	$-0.386243\pi$
$109$	1.43685	+	0.421897i	0.137625	+	0.0404104i	−0.212195	+	0.977227i	$0.568061\pi$
$110$		0			0
$111$	−5.26479	+	1.54588i	−0.499712	+	0.146729i
$112$		0			0
$113$	1.50819	+	10.4897i	0.141879	+	0.986789i	0.929024	+	0.370020i	$0.120649\pi$
$113$	1.50819	+	10.4897i	0.141879	+	0.986789i	−0.787145	+	0.616768i	$0.788442\pi$
$114$		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	−0.783644	−	0.621210i	$-0.786641\pi$
$127$	1.61459	−	11.2297i	0.143272	−	0.996479i	0.926916	−	0.375269i	$-0.122450\pi$
$128$		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	$-0.660086\pi$
$131$	1.31374	−	0.844286i	0.114782	−	0.0737657i	0.596772	+	0.802411i	$0.296450\pi$
$132$		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	$-0.195064\pi$
$139$	19.2890			1.63607			0.818034	+	0.575169i	$0.195064\pi$
$140$		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	−0.783624	−	0.621236i	$-0.786631\pi$
$149$	1.74896	−	12.1643i	0.143280	−	0.996535i	0.926904	−	0.375299i	$-0.122460\pi$
$150$		0			0
$151$	0.112654	+	0.0723984i	0.00916766	+	0.00589169i	0.545217	−	0.838295i	$-0.316447\pi$
$151$	0.112654	+	0.0723984i	0.00916766	+	0.00589169i	−0.536049	+	0.844187i	$0.680084\pi$
$152$		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	−0.270471	−	0.962728i	$-0.587179\pi$
$157$	0.281739	−	0.0827259i	0.0224852	−	0.00660225i	0.292956	+	0.956126i	$0.405361\pi$
$158$		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	0.994920	+	0.100670i	$0.0320986\pi$
$163$	0.876633	+	6.09712i	0.0686632	+	0.477563i	−0.926257	+	0.376893i	$0.876992\pi$
$164$		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	$-0.211758\pi$
$167$	14.4077	+	4.23050i	1.11490	+	0.327366i	0.328146	+	0.944627i	$0.393576\pi$
$168$		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	−0.981988	−	0.188944i	$-0.939494\pi$
$173$	0.176963	−	1.23081i	0.0134543	−	0.0935765i	0.995442	+	0.0953675i	$0.0304026\pi$
$174$		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	$-0.996967\pi$
$179$	−11.3483	+	13.0967i	−0.848216	+	0.978893i	0.151739	+	0.988421i	$0.451513\pi$
$180$		0			0
$181$	8.51103	−	18.6366i	0.632620	−	1.38524i	−0.273355	−	0.961913i	$-0.588134\pi$
$181$	8.51103	−	18.6366i	0.632620	−	1.38524i	0.905975	−	0.423331i	$-0.139139\pi$
$182$		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	$-0.765841\pi$
$191$	−6.06685	+	3.89893i	−0.438982	+	0.282117i	0.302424	+	0.953174i	$0.402204\pi$
$192$		0			0
$193$	−3.05146	−	3.52157i	−0.219649	−	0.253488i	0.635221	−	0.772330i	$-0.280909\pi$
$193$	−3.05146	−	3.52157i	−0.219649	−	0.253488i	−0.854870	+	0.518842i	$0.826363\pi$
$194$		0			0
$195$	−2.68273	+	18.6588i	−0.192114	+	1.33618i
$196$		0			0
$197$	−0.954666	−	0.613527i	−0.0680171	−	0.0437120i	0.506190	−	0.862422i	$-0.331053\pi$
$197$	−0.954666	−	0.613527i	−0.0680171	−	0.0437120i	−0.574207	+	0.818710i	$0.694690\pi$
$198$		0			0
$199$	6.58668	+	14.4228i	0.466917	+	1.02241i	0.985856	+	0.167595i	$0.0536000\pi$
$199$	6.58668	+	14.4228i	0.466917	+	1.02241i	−0.518939	+	0.854811i	$0.673673\pi$
$200$		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	$-0.825579\pi$
$211$	−18.7387	+	5.50219i	−1.29003	+	0.378786i	−0.436439	+	0.899734i	$0.643760\pi$
$212$		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	$-0.434558\pi$
$223$	17.6126	−	11.3189i	1.17943	−	0.757972i	0.975281	+	0.220968i	$0.0709216\pi$
$224$		0			0
$225$	0.807401	−	0.931791i	0.0538268	−	0.0621194i
$226$		0			0
$227$	9.58300	−	20.9838i	0.636046	−	1.39275i	−0.267208	−	0.963639i	$-0.586101\pi$
$227$	9.58300	−	20.9838i	0.636046	−	1.39275i	0.903254	−	0.429107i	$-0.141172\pi$
$228$		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	0.623992	+	0.781430i	$0.285510\pi$
$233$	−5.72720	+	12.5408i	−0.375201	+	0.821576i	−0.999194	+	0.0401461i	$0.987218\pi$
$234$		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	$-0.0934027\pi$
$239$	8.26670	+	9.54028i	0.534728	+	0.617109i	−0.422528	+	0.906350i	$0.638857\pi$
$240$		0			0
$241$	1.30173	−	9.05373i	0.0838518	−	0.583202i	−0.903968	−	0.427600i	$-0.859359\pi$
$241$	1.30173	−	9.05373i	0.0838518	−	0.583202i	0.987820	−	0.155602i	$-0.0497317\pi$
$242$		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	0.987934	+	0.154878i	$0.0494985\pi$
$251$	1.32530	+	9.21770i	0.0836525	+	0.581816i	−0.904281	+	0.426938i	$0.859592\pi$
$252$		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	0.494492	−	0.869182i	$-0.335354\pi$
$257$	22.1295	−	6.49781i	1.38040	−	0.405322i	0.885909	+	0.463860i	$0.153536\pi$
$258$		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	$-0.0102016\pi$
$263$	22.4697	+	14.4404i	1.38554	+	0.890433i	0.386054	+	0.922476i	$0.373838\pi$
$264$		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	−0.726324	−	0.687352i	$-0.758773\pi$
$269$	−6.60662	+	4.24582i	−0.402813	+	0.258872i	0.323512	+	0.946224i	$0.395137\pi$
$270$		0			0
$271$	11.5987	−	13.3857i	0.704574	−	0.813121i	−0.284789	−	0.958590i	$-0.591924\pi$
$271$	11.5987	−	13.3857i	0.704574	−	0.813121i	0.989363	+	0.145469i	$0.0464691\pi$
$272$		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	−0.934109	−	0.356987i	$-0.883804\pi$
$281$	−7.50679	+	8.66330i	−0.447818	+	0.516809i	0.486291	+	0.873797i	$0.338349\pi$
$282$		0			0
$283$	19.2772	−	12.3887i	1.14591	−	0.736433i	0.177091	−	0.984195i	$-0.443331\pi$
$283$	19.2772	−	12.3887i	1.14591	−	0.736433i	0.968821	+	0.247762i	$0.0796951\pi$
$284$		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	−0.742761	−	0.669557i	$-0.766484\pi$
$293$	−29.6060	−	8.69310i	−1.72960	−	0.507856i	−0.986840	+	0.161701i	$0.948302\pi$
$294$		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	$-0.0617081\pi$
$307$	3.38302	+	7.40778i	0.193079	+	0.422784i	−0.788188	+	0.615434i	$0.788981\pi$
$308$		0			0
$309$	−17.9751	−	11.5519i	−1.02257	−	0.657164i
$310$		0			0
$311$	2.06169	−	14.3394i	0.116908	−	0.813110i	−0.844020	−	0.536311i	$-0.819817\pi$
$311$	2.06169	−	14.3394i	0.116908	−	0.813110i	0.960928	−	0.276799i	$-0.0892736\pi$
$312$		0			0
$313$	−1.77523	−	2.04872i	−0.100342	−	0.115801i	0.703357	−	0.710836i	$-0.251683\pi$
$313$	−1.77523	−	2.04872i	−0.100342	−	0.115801i	−0.803699	+	0.595036i	$0.797138\pi$
$314$		0			0
$315$	0.861657	−	0.553754i	0.0485489	−	0.0312005i
$316$		0			0
$317$	9.31198	−	10.7466i	0.523013	−	0.603589i	−0.431370	−	0.902175i	$-0.641970\pi$
$317$	9.31198	−	10.7466i	0.523013	−	0.603589i	0.954383	+	0.298586i	$0.0965151\pi$
$318$		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	−0.971998	−	0.234989i	$-0.924495\pi$
$331$	−19.3990	−	22.3876i	−1.06627	−	1.23054i	−0.0942669	−	0.995547i	$-0.530051\pi$
$332$		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	0.977316	+	0.211785i	$0.0679277\pi$
$337$	9.13044	+	19.9929i	0.497367	+	1.08908i	−0.479950	+	0.877296i	$0.659345\pi$
$338$		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	0.995644	+	0.0932405i	$0.0297226\pi$
$347$	1.24061	+	8.62864i	0.0665995	+	0.463209i	−0.929044	+	0.369969i	$0.879368\pi$
$348$		0			0
$349$	−2.27303	+	0.667423i	−0.121673	+	0.0357263i	−0.342002	−	0.939699i	$-0.611105\pi$
$349$	−2.27303	+	0.667423i	−0.121673	+	0.0357263i	0.220329	+	0.975426i	$0.429287\pi$
$350$		0			0
$351$	−17.5845	−	5.16327i	−0.938591	−	0.275595i
$352$		0			0
$353$	2.88483	+	6.31690i	0.153544	+	0.336215i	0.970735	−	0.240152i	$-0.0771972\pi$
$353$	2.88483	+	6.31690i	0.153544	+	0.336215i	−0.817191	+	0.576367i	$0.804470\pi$
$354$		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	$-0.117348\pi$
$359$	8.40045	+	9.69464i	0.443359	+	0.511664i	−0.489452	+	0.872030i	$0.662803\pi$
$360$		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	$-0.358033\pi$
$367$	16.5274			0.862724			0.431362	+	0.902179i	$0.358033\pi$
$368$		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	−0.555093	−	0.831789i	$-0.687317\pi$
$373$	6.70607	−	7.73922i	0.347227	−	0.400722i	0.902320	+	0.431067i	$0.141863\pi$
$374$		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	0.694447	+	0.719544i	$0.255649\pi$
$379$	−3.39889	+	23.6398i	−0.174589	+	1.21429i	−0.869036	+	0.494749i	$0.835260\pi$
$380$		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	$-0.0204692\pi$
$383$	5.79010	+	12.6785i	0.295860	+	0.647844i	−0.702073	+	0.712105i	$0.747742\pi$
$384$		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	0.991237	+	0.132097i	$0.0421709\pi$
$389$	1.52593	+	10.6131i	0.0773680	+	0.538106i	−0.913869	+	0.406009i	$0.866920\pi$
$390$		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	−0.0415410	−	0.999137i	$-0.513227\pi$
$397$	−12.2869	−	3.60776i	−0.616662	−	0.181068i	−0.575121	+	0.818069i	$0.695045\pi$
$398$		0			0
$399$	0.529640	+	1.15975i	0.0265152	+	0.0580601i
$400$		0			0
$401$	−22.7409	−	14.6147i	−1.13563	−	0.729823i	−0.168900	−	0.985633i	$-0.554022\pi$
$401$	−22.7409	−	14.6147i	−1.13563	−	0.729823i	−0.966727	+	0.255810i	$0.917658\pi$
$402$		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	−0.864809	−	0.502100i	$-0.832561\pi$
$409$	−4.94965	+	5.71220i	−0.244744	+	0.282450i	0.620065	+	0.784550i	$0.287106\pi$
$410$		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	$-0.781973\pi$
$419$	−0.778603	+	0.898555i	−0.0380372	+	0.0438973i	0.736412	+	0.676533i	$0.236518\pi$
$420$		0			0
$421$	24.8232	−	15.9529i	1.20981	−	0.777497i	0.229182	−	0.973384i	$-0.426395\pi$
$421$	24.8232	−	15.9529i	1.20981	−	0.777497i	0.980627	+	0.195887i	$0.0627585\pi$
$422$		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	$-0.541262\pi$
$431$	−16.0710	−	4.71888i	−0.774115	−	0.227301i	−0.644850	+	0.764310i	$0.723080\pi$
$432$		0			0
$433$	−28.9576	+	8.50272i	−1.39161	+	0.408615i	−0.889796	−	0.456358i	$-0.849154\pi$
$433$	−28.9576	+	8.50272i	−1.39161	+	0.408615i	−0.501818	+	0.864973i	$0.667335\pi$
$434$		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	−0.946571	−	0.322496i	$-0.895478\pi$
$439$	−2.70705	−	18.8279i	−0.129200	−	0.898608i	0.817371	−	0.576112i	$-0.195431\pi$
$440$		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	$-0.709777\pi$
$443$	−32.7272	−	9.60959i	−1.55492	−	0.456565i	−0.942566	+	0.334020i	$0.891595\pi$
$444$		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	0.947028	+	0.321150i	$0.104069\pi$
$449$	−1.10434	+	7.68088i	−0.0521172	+	0.362483i	−0.999145	+	0.0413328i	$0.986840\pi$
$450$		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	−0.886351	−	0.463013i	$-0.846768\pi$
$457$	0.940775	−	2.06001i	0.0440076	−	0.0963632i	0.930359	+	0.366650i	$0.119495\pi$
$458$		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	$-0.867284\pi$
$463$	−0.204871	+	0.448605i	−0.00952116	+	0.0208484i	0.904812	+	0.425812i	$0.140011\pi$
$464$		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	$-0.528171\pi$
$467$	16.8769	−	10.8461i	0.780968	−	0.501897i	0.869355	+	0.494189i	$0.164535\pi$
$468$		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	$-0.563872\pi$
$479$	3.56305	−	1.04620i	0.162800	−	0.0478023i	0.362117	+	0.932133i	$0.382054\pi$
$480$		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	$-0.728893\pi$
$487$	−17.7880	+	5.22303i	−0.806052	+	0.236678i	−0.147352	+	0.989084i	$0.547075\pi$
$488$		0			0
$489$	−9.87369	−	2.89918i	−0.446504	−	0.131105i
$490$		0			0
$491$	14.9691	+	32.7777i	0.675545	+	1.47924i	0.867296	+	0.497793i	$0.165856\pi$
$491$	14.9691	+	32.7777i	0.675545	+	1.47924i	−0.191751	+	0.981444i	$0.561417\pi$
$492$		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	$-0.544296\pi$
$499$	15.7374	−	10.1138i	0.704504	−	0.452757i	0.843216	+	0.537575i	$0.180660\pi$
$500$		0			0
$501$	−16.4276	+	18.9584i	−0.733929	+	0.846999i
$502$		0			0
$503$	−14.0889	+	30.8504i	−0.628194	+	1.37555i	0.281214	+	0.959645i	$0.409263\pi$
$503$	−14.0889	+	30.8504i	−0.628194	+	1.37555i	−0.909407	+	0.415907i	$0.863464\pi$
$504$		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	0.401471	+	0.915872i	$0.368499\pi$
$509$	−12.4899	+	27.3491i	−0.553606	+	1.21223i	−0.955077	+	0.296357i	$0.904228\pi$
$510$		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	0.984489	−	0.175449i	$-0.0561376\pi$
$521$	4.72921	+	10.3555i	0.207191	+	0.453684i	−0.777298	+	0.629132i	$0.783410\pi$
$522$		0			0
$523$	−8.97084	−	2.63408i	−0.392267	−	0.115180i	0.0796500	−	0.996823i	$-0.474620\pi$
$523$	−8.97084	−	2.63408i	−0.392267	−	0.115180i	−0.471917	+	0.881643i	$0.656438\pi$
$524$		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	−0.992680	−	0.120773i	$-0.961463\pi$
$541$	−0.143855	+	1.00054i	−0.00618482	+	0.0430164i	0.986495	+	0.163789i	$0.0523718\pi$
$542$		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	$-0.697497\pi$
$547$	7.17243	−	8.27743i	0.306671	−	0.353917i	0.888076	+	0.459697i	$0.152042\pi$
$548$		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	−0.794967	−	0.606653i	$-0.792512\pi$
$557$	−1.92001	+	2.21580i	−0.0813532	+	0.0938866i	0.713614	+	0.700540i	$0.247057\pi$
$558$		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	−0.871639	−	0.490148i	$-0.836943\pi$
$563$	2.43880	−	16.9622i	0.102783	−	0.714872i	0.974422	−	0.224724i	$-0.0721481\pi$
$564$		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	0.939167	−	0.343462i	$-0.111600\pi$
$569$	36.8195	+	10.8112i	1.54355	+	0.453229i	0.604388	+	0.796690i	$0.293418\pi$
$570$		0			0
$571$	−16.2300	+	4.76556i	−0.679205	+	0.199432i	−0.603098	−	0.797667i	$-0.706067\pi$
$571$	−16.2300	+	4.76556i	−0.679205	+	0.199432i	−0.0761067	+	0.997100i	$0.524249\pi$
$572$		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	−0.974825	−	0.222970i	$-0.928425\pi$
$577$	−2.45746	−	17.0920i	−0.102305	−	0.711549i	0.872520	−	0.488578i	$-0.162484\pi$
$578$		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	0.648224	+	0.761450i	$0.275512\pi$
$587$	−4.56136	+	31.7250i	−0.188267	+	1.30943i	−0.836492	+	0.547980i	$0.815397\pi$
$588$		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	−0.713121	−	0.701040i	$-0.752719\pi$
$593$	2.00343	−	2.31209i	0.0822712	−	0.0949460i	0.795393	+	0.606094i	$0.207265\pi$
$594$		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	$-0.640319\pi$
$599$	−20.8858			−0.853370			−0.426685	+	0.904400i	$0.640319\pi$
$600$		0			0
$601$	13.5502	−	29.6708i	0.552724	−	1.21030i	−0.402775	−	0.915299i	$-0.631954\pi$
$601$	13.5502	−	29.6708i	0.552724	−	1.21030i	0.955498	−	0.294997i	$-0.0953186\pi$
$602$		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	0.981875	+	0.189527i	$0.0606955\pi$
$607$	25.3700	+	29.2786i	1.02974	+	1.18838i	0.0478627	+	0.998854i	$0.484759\pi$
$608$		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	0.997744	−	0.0671321i	$-0.0213849\pi$
$613$	7.26983	+	15.9187i	0.293626	+	0.642950i	−0.704118	+	0.710083i	$0.748658\pi$
$614$		0			0
$615$	56.9936	+	16.7348i	2.29820	+	0.674813i
$616$		0			0
$617$	−13.0260	+	3.82479i	−0.524408	+	0.153980i	−0.533213	−	0.845981i	$-0.679016\pi$
$617$	−13.0260	+	3.82479i	−0.524408	+	0.153980i	0.00880470	+	0.999961i	$0.497197\pi$
$618$		0			0
$619$	5.83479	+	40.5819i	0.234520	+	1.63112i	0.678158	+	0.734916i	$0.262779\pi$
$619$	5.83479	+	40.5819i	0.234520	+	1.63112i	−0.443638	+	0.896206i	$0.646312\pi$
$620$		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	$-0.281760\pi$
$631$	4.82543	+	3.10111i	0.192097	+	0.123453i	−0.441057	+	0.897479i	$0.645396\pi$
$632$		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	−0.697989	−	0.716108i	$-0.745922\pi$
$641$	7.60286	−	16.6479i	0.300295	−	0.657554i	0.998284	+	0.0585538i	$0.0186489\pi$
$642$		0			0
$643$	−14.0965			−0.555913			−0.277957	−	0.960594i	$-0.589657\pi$
$643$	−14.0965			−0.555913			−0.277957	+	0.960594i	$0.589657\pi$
$644$		0			0
$645$	−33.8056			−1.33109
$646$		0			0
$647$	12.9929	−	28.4506i	0.510805	−	1.11851i	−0.462000	−	0.886880i	$-0.652868\pi$
$647$	12.9929	−	28.4506i	0.510805	−	1.11851i	0.972805	−	0.231627i	$-0.0744048\pi$
$648$		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	0.756907	−	0.653522i	$-0.226709\pi$
$653$	0.0592343	+	0.0683600i	0.00231802	+	0.00267514i	−0.754589	+	0.656197i	$0.772164\pi$
$654$		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	−0.990105	−	0.140329i	$-0.955184\pi$
$659$	−11.4949	−	25.1703i	−0.447778	−	0.980496i	0.542327	−	0.840167i	$-0.317543\pi$
$660$		0			0
$661$	11.2677	+	3.30849i	0.438262	+	0.128685i	0.493418	−	0.869792i	$-0.335747\pi$
$661$	11.2677	+	3.30849i	0.438262	+	0.128685i	−0.0551559	+	0.998478i	$0.517566\pi$
$662$		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	−0.293282	−	0.956026i	$-0.594747\pi$
$673$	−27.4177	−	8.05055i	−1.05687	−	0.310326i	−0.763591	+	0.645700i	$0.776566\pi$
$674$		0			0
$675$	13.1300	+	28.7508i	0.505376	+	1.10662i
$676$		0			0
$677$	24.0687	+	15.4680i	0.925037	+	0.594485i	0.914115	−	0.405455i	$-0.132887\pi$
$677$	24.0687	+	15.4680i	0.925037	+	0.594485i	0.0109217	+	0.999940i	$0.496523\pi$
$678$		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	$-0.613249\pi$
$683$	9.39901	−	6.04038i	0.359643	−	0.231129i	0.707967	+	0.706246i	$0.249613\pi$
$684$		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	$-0.665842\pi$
$691$	−26.1688			−0.995509			−0.497755	+	0.867318i	$0.665842\pi$
$692$		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	−0.988669	−	0.150111i	$-0.952037\pi$
$701$	0.0593912	−	0.413075i	0.00224318	−	0.0156016i	0.990912	+	0.134510i	$0.0429459\pi$
$702$		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	−0.235243	−	0.971937i	$-0.575589\pi$
$709$	2.45837	−	0.721843i	0.0923260	−	0.0271094i	0.327569	+	0.944827i	$0.393771\pi$
$710$		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	$-0.597529\pi$
$719$	−28.7133	−	8.43100i	−1.07083	−	0.314423i	−0.769203	+	0.639004i	$0.779347\pi$
$720$		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	$-0.302767\pi$
$727$	−8.29715	−	9.57543i	−0.307724	−	0.355133i	−0.888456	+	0.458962i	$0.848221\pi$
$728$		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	−0.862674	−	0.505761i	$-0.831212\pi$
$733$	2.28738	−	5.00866i	0.0844863	−	0.184999i	0.947160	+	0.320762i	$0.103939\pi$
$734$		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	−0.475675	−	0.879621i	$-0.657796\pi$
$739$	13.6086	−	29.7986i	0.500599	−	1.09616i	0.976274	−	0.216539i	$-0.0694767\pi$
$740$		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	$-0.518599\pi$
$743$	22.4994	−	14.4595i	0.825422	−	0.530467i	0.883820	+	0.467827i	$0.154963\pi$
$744$		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	−0.971084	−	0.238737i	$-0.923267\pi$
$751$	−14.1293	−	30.9388i	−0.515585	−	1.12897i	0.455499	−	0.890236i	$-0.349461\pi$
$752$		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	0.694470	+	0.719521i	$0.255639\pi$
$757$	6.35134	+	44.1746i	0.230844	+	1.60555i	−0.463627	+	0.886031i	$0.653452\pi$
$758$		0			0
$759$	−21.8611	−	4.01814i	−0.793506	−	0.145849i
$760$		0			0
$761$	−2.53451	−	17.6279i	−0.0918758	−	0.639010i	−0.982775	−	0.184808i	$-0.940834\pi$
$761$	−2.53451	−	17.6279i	−0.0918758	−	0.639010i	0.890899	−	0.454202i	$-0.150075\pi$
$762$		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	0.926837	−	0.375463i	$-0.122516\pi$
$769$	26.9080	+	17.2927i	0.970326	+	0.623591i	0.0434889	+	0.999054i	$0.486153\pi$
$770$		0			0
$771$	−5.48340	+	38.1379i	−0.197480	+	1.37350i
$772$		0			0
$773$	−13.2482	−	15.2893i	−0.476506	−	0.549917i	0.465704	−	0.884941i	$-0.345801\pi$
$773$	−13.2482	−	15.2893i	−0.476506	−	0.549917i	−0.942210	+	0.335024i	$0.891256\pi$
$774$		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	$-0.934429\pi$
$787$	−17.8726	+	20.6261i	−0.637091	+	0.735242i	0.341767	+	0.939785i	$0.388975\pi$
$788$		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	−0.761784	−	0.647831i	$-0.775676\pi$
$797$	−21.2445	−	46.5190i	−0.752519	−	1.64779i	0.00926492	−	0.999957i	$-0.497051\pi$
$798$		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	−0.293361	−	0.956002i	$-0.594774\pi$
$809$	−0.662682	+	0.194581i	−0.0232987	+	0.00684111i	0.270062	+	0.962843i	$0.412956\pi$
$810$		0			0
$811$	31.0212	+	9.10866i	1.08930	+	0.319848i	0.776594	−	0.630001i	$-0.216946\pi$
$811$	31.0212	+	9.10866i	1.08930	+	0.319848i	0.312709	+	0.949849i	$0.398764\pi$
$812$		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	−0.448051	−	0.894008i	$-0.647882\pi$
$821$	5.13003	−	3.29687i	0.179039	−	0.115062i	0.627091	+	0.778946i	$0.284246\pi$
$822$		0			0
$823$	−18.1101	+	20.9001i	−0.631277	+	0.728532i	−0.977807	−	0.209506i	$-0.932814\pi$
$823$	−18.1101	+	20.9001i	−0.631277	+	0.728532i	0.346531	+	0.938039i	$0.387360\pi$
$824$		0			0
$825$	−11.3509	+	24.8551i	−0.395189	+	0.865342i
$826$		0			0
$827$	17.5955			0.611857			0.305929	−	0.952054i	$-0.401033\pi$
$827$	17.5955			0.611857			0.305929	+	0.952054i	$0.401033\pi$
$828$		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	$-0.923576\pi$
$839$	0.800873	−	5.57020i	0.0276492	−	0.192304i	0.998965	+	0.0454895i	$0.0144848\pi$
$840$		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	−0.996715	−	0.0809931i	$-0.974191\pi$
$853$	−1.84561	−	12.8365i	−0.0631924	−	0.439512i	0.933522	−	0.358519i	$-0.116718\pi$
$854$		0			0
$855$	0.340675	−	0.100031i	0.0116508	−	0.00342099i
$856$		0			0
$857$	−11.1973	−	3.28783i	−0.382493	−	0.112310i	0.0848328	−	0.996395i	$-0.472964\pi$
$857$	−11.1973	−	3.28783i	−0.382493	−	0.112310i	−0.467326	+	0.884085i	$0.654783\pi$
$858$		0			0
$859$	−17.1397	−	37.5306i	−0.584797	−	1.28053i	−0.938535	−	0.345183i	$-0.887817\pi$
$859$	−17.1397	−	37.5306i	−0.584797	−	1.28053i	0.353738	−	0.935345i	$-0.384910\pi$
$860$		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	$-0.985325\pi$
$863$	−0.807279	+	5.61475i	−0.0274801	+	0.191128i	0.971457	+	0.237214i	$0.0762343\pi$
$864$		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	−0.697516	−	0.716569i	$-0.745711\pi$
$877$	8.90815	−	19.5061i	0.300807	−	0.658675i	0.998323	+	0.0578941i	$0.0184386\pi$
$878$		0			0
$879$	33.7564	−	38.9570i	1.13858	−	1.31399i
$880$		0			0
$881$	−7.46135	+	4.79512i	−0.251379	+	0.161552i	−0.660262	−	0.751035i	$-0.729555\pi$
$881$	−7.46135	+	4.79512i	−0.251379	+	0.161552i	0.408883	+	0.912587i	$0.365918\pi$
$882$		0			0
$883$	−30.8589	−	35.6131i	−1.03848	−	1.19848i	−0.979755	−	0.200202i	$-0.935840\pi$
$883$	−30.8589	−	35.6131i	−1.03848	−	1.19848i	−0.0587301	−	0.998274i	$-0.518705\pi$
$884$		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	$-0.282014\pi$
$887$	5.68147	+	3.65126i	0.190765	+	0.122597i	−0.441772	+	0.897127i	$0.645650\pi$
$888$		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	$-0.226885\pi$
$907$	14.3349	+	9.21246i	0.475981	+	0.305895i	−0.280565	+	0.959835i	$0.590522\pi$
$908$		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	$-0.162734\pi$
$911$	7.96025	+	9.18662i	0.263735	+	0.304366i	−0.608401	+	0.793630i	$0.708189\pi$
$912$		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	$-0.492013\pi$
$919$	1.52112			0.0501772			0.0250886	+	0.999685i	$0.492013\pi$
$920$		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	0.797545	−	0.603260i	$-0.206132\pi$
$929$	2.64936	+	3.05753i	0.0869227	+	0.100314i	−0.710622	+	0.703574i	$0.751586\pi$
$930$		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	0.801464	−	0.598043i	$-0.204055\pi$
$937$	35.2747	+	10.3576i	1.15237	+	0.338367i	0.350908	+	0.936410i	$0.385873\pi$
$938$		0			0
$939$	4.34528	−	1.27589i	0.141803	−	0.0416370i
$940$		0			0
$941$	1.43349	+	9.97016i	0.0467305	+	0.325018i	0.999755	+	0.0221253i	$0.00704326\pi$
$941$	1.43349	+	9.97016i	0.0467305	+	0.325018i	−0.953025	+	0.302893i	$0.902048\pi$
$942$		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	$-0.494281\pi$
$947$	17.6526	−	5.18327i	0.573632	−	0.168434i	0.555667	+	0.831405i	$0.312463\pi$
$948$		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	0.901316	−	0.433162i	$-0.142602\pi$
$953$	27.2193	+	17.4928i	0.881718	+	0.566646i	−0.0195979	+	0.999808i	$0.506239\pi$
$954$		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	$-0.820068\pi$
$967$	−52.5187			−1.68889			−0.844443	+	0.535645i	$0.820068\pi$
$968$		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	$-0.888673\pi$
$971$	−14.5394	+	16.7794i	−0.466591	+	0.538475i	0.472869	+	0.881133i	$0.343218\pi$
$972$		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	−0.960887	−	0.276942i	$-0.910679\pi$
$977$	1.22218	−	8.50046i	0.0391011	−	0.271954i	0.999988	+	0.00498865i	$0.00158794\pi$
$978$		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	$-0.501956\pi$
$983$	−17.3050	−	5.08122i	−0.551945	−	0.162066i	−0.545800	+	0.837915i	$0.683774\pi$
$984$		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	0.922799	+	0.385283i	$0.125896\pi$
$991$	4.59379	+	31.9505i	0.145927	+	1.01494i	−0.776872	+	0.629658i	$0.783195\pi$
$992$		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	0.966380	+	0.257120i	$0.0827735\pi$
$997$	16.6671	+	36.4959i	0.527854	+	1.15584i	−0.438526	+	0.898719i	$0.644499\pi$
$998$		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	184.2.i.b.49.1	✓	30
4.3	odd	2		368.2.m.e.49.3		30
23.8	even	11	inner	184.2.i.b.169.1	yes	30
23.10	odd	22		4232.2.a.ba.1.5		15
23.13	even	11		4232.2.a.bb.1.5		15
92.31	odd	22		368.2.m.e.353.3		30
92.59	odd	22		8464.2.a.cg.1.11		15
92.79	even	22		8464.2.a.ch.1.11		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.49.1	✓	30	1.1	even	1	trivial
184.2.i.b.169.1	yes	30	23.8	even	11	inner
368.2.m.e.49.3		30	4.3	odd	2
368.2.m.e.353.3		30	92.31	odd	22
4232.2.a.ba.1.5		15	23.10	odd	22
4232.2.a.bb.1.5		15	23.13	even	11
8464.2.a.cg.1.11		15	92.59	odd	22
8464.2.a.ch.1.11		15	92.79	even	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:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.i (of order \(11\), degree \(10\), 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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