LMFDB - Embedded newform 304.2.u.d.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [304,2,Mod(17,304)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("304.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(304, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	304.81
Dual form			304.2.u.d.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0603074 - 0.342020i) q^{3} +(1.17365 + 0.984808i) q^{5} +(-0.152704 - 0.264490i) q^{7} +(2.70574 + 0.984808i) q^{9} +(0.152704 - 0.264490i) q^{11} +(0.0603074 + 0.342020i) q^{13} +(0.407604 - 0.342020i) q^{15} +(1.76604 - 0.642788i) q^{17} +(3.06418 + 3.10013i) q^{19} +(-0.0996702 + 0.0362770i) q^{21} +(2.17365 - 1.82391i) q^{23} +(-0.460637 - 2.61240i) q^{25} +(1.02094 - 1.76833i) q^{27} +(-3.29813 - 1.20042i) q^{29} +(2.91147 + 5.04282i) q^{31} +(-0.0812519 - 0.0681784i) q^{33} +(0.0812519 - 0.460802i) q^{35} -8.12836 q^{37} +0.120615 q^{39} +(0.429892 - 2.43804i) q^{41} +(0.890530 + 0.747243i) q^{43} +(2.20574 + 3.82045i) q^{45} +(-5.87211 - 2.13727i) q^{47} +(3.45336 - 5.98140i) q^{49} +(-0.113341 - 0.642788i) q^{51} +(-5.52094 + 4.63262i) q^{53} +(0.439693 - 0.160035i) q^{55} +(1.24510 - 0.861050i) q^{57} +(-10.7096 + 3.89798i) q^{59} +(-8.71348 + 7.31148i) q^{61} +(-0.152704 - 0.866025i) q^{63} +(-0.266044 + 0.460802i) q^{65} +(0.340022 + 0.123758i) q^{67} +(-0.492726 - 0.853427i) q^{69} +(-9.93242 - 8.33429i) q^{71} +(1.04071 - 5.90214i) q^{73} -0.921274 q^{75} -0.0932736 q^{77} +(-1.57011 + 8.90452i) q^{79} +(6.07398 + 5.09667i) q^{81} +(-8.28106 - 14.3432i) q^{83} +(2.70574 + 0.984808i) q^{85} +(-0.609470 + 1.05563i) q^{87} +(-0.180922 - 1.02606i) q^{89} +(0.0812519 - 0.0681784i) q^{91} +(1.90033 - 0.691663i) q^{93} +(0.543233 + 6.65609i) q^{95} +(8.83022 - 3.21394i) q^{97} +(0.673648 - 0.565258i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 6 q^{5} - 3 q^{7} + 6 q^{9} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 6 q^{17} - 15 q^{21} + 12 q^{23} + 6 q^{25} + 3 q^{27} - 6 q^{29} - 3 q^{31} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 12 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 6 * q^5 - 3 * q^7 + 6 * q^9 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 6 * q^17 - 15 * q^21 + 12 * q^23 + 6 * q^25 + 3 * q^27 - 6 * q^29 - 3 * q^31 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 12 * q^39 - 6 * q^41 - 12 * q^43 + 3 * q^45 - 6 * q^47 - 6 * q^49 + 6 * q^51 - 30 * q^53 - 3 * q^55 + 6 * q^57 - 30 * q^59 + 6 * q^61 - 3 * q^63 + 3 * q^65 - 18 * q^67 + 15 * q^69 - 36 * q^71 + 6 * q^73 + 12 * q^75 - 54 * q^77 - 18 * q^79 + 21 * q^81 - 15 * q^83 + 6 * q^85 - 21 * q^87 - 18 * q^89 + 3 * q^91 - 3 * q^93 - 12 * q^95 + 30 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0603074	−	0.342020i	0.0348185	−	0.197465i	−0.962437	−	0.271506i	$-0.912478\pi$
$3$	0.0603074	−	0.342020i	0.0348185	−	0.197465i	0.997255	+	0.0740406i	$0.0235894\pi$
$4$		0			0
$5$	1.17365	+	0.984808i	0.524871	+	0.440419i	0.866326	−	0.499479i	$-0.166475\pi$
$5$	1.17365	+	0.984808i	0.524871	+	0.440419i	−0.341455	+	0.939898i	$0.610920\pi$
$6$		0			0
$7$	−0.152704	−	0.264490i	−0.0577166	−	0.0999680i	0.835723	−	0.549151i	$-0.185049\pi$
$7$	−0.152704	−	0.264490i	−0.0577166	−	0.0999680i	−0.893440	+	0.449183i	$0.851715\pi$
$8$		0			0
$9$	2.70574	+	0.984808i	0.901912	+	0.328269i
$10$		0			0
$11$	0.152704	−	0.264490i	0.0460419	−	0.0797469i	−0.842086	−	0.539343i	$-0.818673\pi$
$11$	0.152704	−	0.264490i	0.0460419	−	0.0797469i	0.888128	+	0.459596i	$0.152006\pi$
$12$		0			0
$13$	0.0603074	+	0.342020i	0.0167263	+	0.0948593i	0.992028	−	0.126017i	$-0.0402194\pi$
$13$	0.0603074	+	0.342020i	0.0167263	+	0.0948593i	−0.975302	+	0.220876i	$0.929108\pi$
$14$		0			0
$15$	0.407604	−	0.342020i	0.105243	−	0.0883092i
$16$		0			0
$17$	1.76604	−	0.642788i	0.428329	−	0.155899i	−0.118855	−	0.992912i	$-0.537922\pi$
$17$	1.76604	−	0.642788i	0.428329	−	0.155899i	0.547183	+	0.837013i	$0.315700\pi$
$18$		0			0
$19$	3.06418	+	3.10013i	0.702971	+	0.711219i
$19$	3.06418	+	3.10013i	0.702971	+	0.711219i
$20$		0			0
$21$	−0.0996702	+	0.0362770i	−0.0217498	+	0.00791629i
$22$		0			0
$23$	2.17365	−	1.82391i	0.453237	−	0.380311i	−0.387398	−	0.921912i	$-0.626626\pi$
$23$	2.17365	−	1.82391i	0.453237	−	0.380311i	0.840635	+	0.541601i	$0.182182\pi$
$24$		0			0
$25$	−0.460637	−	2.61240i	−0.0921274	−	0.522481i
$26$		0			0
$27$	1.02094	−	1.76833i	0.196481	−	0.340315i
$28$		0			0
$29$	−3.29813	−	1.20042i	−0.612448	−	0.222913i	0.0171260	−	0.999853i	$-0.494548\pi$
$29$	−3.29813	−	1.20042i	−0.612448	−	0.222913i	−0.629574	+	0.776941i	$0.716771\pi$
$30$		0			0
$31$	2.91147	+	5.04282i	0.522916	+	0.905717i	0.999644	+	0.0266667i	$0.00848927\pi$
$31$	2.91147	+	5.04282i	0.522916	+	0.905717i	−0.476728	+	0.879051i	$0.658177\pi$
$32$		0			0
$33$	−0.0812519	−	0.0681784i	−0.0141441	−	0.0118683i
$34$		0			0
$35$	0.0812519	−	0.460802i	0.0137341	−	0.0778898i
$36$		0			0
$37$	−8.12836			−1.33629			−0.668147	−	0.744030i	$-0.732912\pi$
$37$	−8.12836			−1.33629			−0.668147	+	0.744030i	$0.732912\pi$
$38$		0			0
$39$	0.120615			0.0193138
$40$		0			0
$41$	0.429892	−	2.43804i	0.0671379	−	0.380758i	−0.932662	−	0.360752i	$-0.882520\pi$
$41$	0.429892	−	2.43804i	0.0671379	−	0.380758i	0.999800	−	0.0200065i	$-0.00636868\pi$
$42$		0			0
$43$	0.890530	+	0.747243i	0.135804	+	0.113953i	0.708160	−	0.706052i	$-0.249526\pi$
$43$	0.890530	+	0.747243i	0.135804	+	0.113953i	−0.572355	+	0.820006i	$0.693970\pi$
$44$		0			0
$45$	2.20574	+	3.82045i	0.328812	+	0.569519i
$46$		0			0
$47$	−5.87211	−	2.13727i	−0.856535	−	0.311753i	−0.123833	−	0.992303i	$-0.539519\pi$
$47$	−5.87211	−	2.13727i	−0.856535	−	0.311753i	−0.732702	+	0.680550i	$0.761741\pi$
$48$		0			0
$49$	3.45336	−	5.98140i	0.493338	−	0.854486i
$50$		0			0
$51$	−0.113341	−	0.642788i	−0.0158709	−	0.0900083i
$52$		0			0
$53$	−5.52094	+	4.63262i	−0.758360	+	0.636340i	−0.937699	−	0.347448i	$-0.887048\pi$
$53$	−5.52094	+	4.63262i	−0.758360	+	0.636340i	0.179339	+	0.983787i	$0.442604\pi$
$54$		0			0
$55$	0.439693	−	0.160035i	0.0592881	−	0.0215791i
$56$		0			0
$57$	1.24510	−	0.861050i	0.164918	−	0.114049i
$58$		0			0
$59$	−10.7096	+	3.89798i	−1.39427	+	0.507474i	−0.926473	−	0.376361i	$-0.877175\pi$
$59$	−10.7096	+	3.89798i	−1.39427	+	0.507474i	−0.467799	+	0.883835i	$0.654953\pi$
$60$		0			0
$61$	−8.71348	+	7.31148i	−1.11565	+	0.936139i	−0.998376	−	0.0569615i	$-0.981859\pi$
$61$	−8.71348	+	7.31148i	−1.11565	+	0.936139i	−0.117270	+	0.993100i	$0.537414\pi$
$62$		0			0
$63$	−0.152704	−	0.866025i	−0.0192389	−	0.109109i
$64$		0			0
$65$	−0.266044	+	0.460802i	−0.0329988	+	0.0571555i
$66$		0			0
$67$	0.340022	+	0.123758i	0.0415403	+	0.0151194i	0.362707	−	0.931903i	$-0.381853\pi$
$67$	0.340022	+	0.123758i	0.0415403	+	0.0151194i	−0.321166	+	0.947023i	$0.604075\pi$
$68$		0			0
$69$	−0.492726	−	0.853427i	−0.0593172	−	0.102740i
$70$		0			0
$71$	−9.93242	−	8.33429i	−1.17876	−	0.989098i	−0.999986	−	0.00520809i	$-0.998342\pi$
$71$	−9.93242	−	8.33429i	−1.17876	−	0.989098i	−0.178775	−	0.983890i	$-0.557213\pi$
$72$		0			0
$73$	1.04071	−	5.90214i	0.121806	−	0.690794i	−0.861348	−	0.508015i	$-0.830380\pi$
$73$	1.04071	−	5.90214i	0.121806	−	0.690794i	0.983154	−	0.182779i	$-0.0585093\pi$
$74$		0			0
$75$	−0.921274			−0.106380
$76$		0			0
$77$	−0.0932736			−0.0106295
$78$		0			0
$79$	−1.57011	+	8.90452i	−0.176651	+	1.00184i	0.759570	+	0.650425i	$0.225409\pi$
$79$	−1.57011	+	8.90452i	−0.176651	+	1.00184i	−0.936221	+	0.351412i	$0.885702\pi$
$80$		0			0
$81$	6.07398	+	5.09667i	0.674886	+	0.566297i
$82$		0			0
$83$	−8.28106	−	14.3432i	−0.908964	−	1.57437i	−0.815506	−	0.578749i	$-0.803541\pi$
$83$	−8.28106	−	14.3432i	−0.908964	−	1.57437i	−0.0934588	−	0.995623i	$-0.529792\pi$
$84$		0			0
$85$	2.70574	+	0.984808i	0.293478	+	0.106817i
$86$		0			0
$87$	−0.609470	+	1.05563i	−0.0653421	+	0.113176i
$88$		0			0
$89$	−0.180922	−	1.02606i	−0.0191777	−	0.108762i	0.973716	−	0.227764i	$-0.0731416\pi$
$89$	−0.180922	−	1.02606i	−0.0191777	−	0.108762i	−0.992894	+	0.119002i	$0.962030\pi$
$90$		0			0
$91$	0.0812519	−	0.0681784i	0.00851751	−	0.00714704i
$92$		0			0
$93$	1.90033	−	0.691663i	0.197055	−	0.0717222i
$94$		0			0
$95$	0.543233	+	6.65609i	0.0557346	+	0.682900i
$96$		0			0
$97$	8.83022	−	3.21394i	0.896573	−	0.326326i	0.147694	−	0.989033i	$-0.452815\pi$
$97$	8.83022	−	3.21394i	0.896573	−	0.326326i	0.748879	+	0.662707i	$0.230593\pi$
$98$		0			0
$99$	0.673648	−	0.565258i	0.0677042	−	0.0568106i
$100$		0			0
$101$	0.429892	+	2.43804i	0.0427759	+	0.242594i	0.998697	−	0.0510289i	$-0.0162501\pi$
$101$	0.429892	+	2.43804i	0.0427759	+	0.242594i	−0.955921	+	0.293623i	$0.905139\pi$
$102$		0			0
$103$	8.36484	−	14.4883i	0.824212	−	1.42758i	−0.0783082	−	0.996929i	$-0.524952\pi$
$103$	8.36484	−	14.4883i	0.824212	−	1.42758i	0.902520	−	0.430648i	$-0.141715\pi$
$104$		0			0
$105$	−0.152704	−	0.0555796i	−0.0149023	−	0.00542401i
$106$		0			0
$107$	3.60607	+	6.24589i	0.348612	+	0.603813i	0.986003	−	0.166727i	$-0.0533199\pi$
$107$	3.60607	+	6.24589i	0.348612	+	0.603813i	−0.637391	+	0.770540i	$0.719987\pi$
$108$		0			0
$109$	−4.95471	−	4.15749i	−0.474575	−	0.398216i	0.373885	−	0.927475i	$-0.378025\pi$
$109$	−4.95471	−	4.15749i	−0.474575	−	0.398216i	−0.848460	+	0.529259i	$0.822470\pi$
$110$		0			0
$111$	−0.490200	+	2.78006i	−0.0465277	+	0.263872i
$112$		0			0
$113$	−13.5175			−1.27162			−0.635812	−	0.771844i	$-0.719334\pi$
$113$	−13.5175			−1.27162			−0.635812	+	0.771844i	$0.719334\pi$
$114$		0			0
$115$	4.34730			0.405387
$116$		0			0
$117$	−0.173648	+	0.984808i	−0.0160538	+	0.0910455i
$118$		0			0
$119$	−0.439693	−	0.368946i	−0.0403066	−	0.0338212i
$120$		0			0
$121$	5.45336	+	9.44550i	0.495760	+	0.858682i
$122$		0			0
$123$	−0.807934	−	0.294064i	−0.0728489	−	0.0265148i
$124$		0			0
$125$	5.86231	−	10.1538i	0.524341	−	0.908185i
$126$		0			0
$127$	1.72756	+	9.79747i	0.153296	+	0.869385i	0.960327	+	0.278876i	$0.0899619\pi$
$127$	1.72756	+	9.79747i	0.153296	+	0.869385i	−0.807031	+	0.590509i	$0.798927\pi$
$128$		0			0
$129$	0.309278	−	0.259515i	0.0272304	−	0.0228490i
$130$		0			0
$131$	9.78833	−	3.56266i	0.855211	−	0.311271i	0.123048	−	0.992401i	$-0.460733\pi$
$131$	9.78833	−	3.56266i	0.855211	−	0.311271i	0.732163	+	0.681130i	$0.238511\pi$
$132$		0			0
$133$	0.352044	−	1.28385i	0.0305261	−	0.111324i
$134$		0			0
$135$	2.93969	−	1.06996i	0.253008	−	0.0920875i
$136$		0			0
$137$	−14.1472	+	11.8709i	−1.20868	+	1.01420i	−0.209342	+	0.977843i	$0.567132\pi$
$137$	−14.1472	+	11.8709i	−1.20868	+	1.01420i	−0.999339	+	0.0363607i	$0.988423\pi$
$138$		0			0
$139$	2.95929	+	16.7830i	0.251004	+	1.42351i	0.806125	+	0.591745i	$0.201561\pi$
$139$	2.95929	+	16.7830i	0.251004	+	1.42351i	−0.555121	+	0.831769i	$0.687328\pi$
$140$		0			0
$141$	−1.08512	+	1.87949i	−0.0913838	+	0.158281i
$142$		0			0
$143$	0.0996702	+	0.0362770i	0.00833484	+	0.00303363i
$144$		0			0
$145$	−2.68866	−	4.65690i	−0.223281	−	0.386735i
$146$		0			0
$147$	−1.83750	−	1.54184i	−0.151554	−	0.127169i
$148$		0			0
$149$	2.75490	−	15.6238i	0.225690	−	1.27995i	−0.635671	−	0.771960i	$-0.719277\pi$
$149$	2.75490	−	15.6238i	0.225690	−	1.27995i	0.861361	−	0.507993i	$-0.169612\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	5.41147			0.437492
$154$		0			0
$155$	−1.54916	+	8.78574i	−0.124432	+	0.705688i
$156$		0			0
$157$	8.93242	+	7.49519i	0.712885	+	0.598181i	0.925407	−	0.378975i	$-0.123723\pi$
$157$	8.93242	+	7.49519i	0.712885	+	0.598181i	−0.212522	+	0.977156i	$0.568168\pi$
$158$		0			0
$159$	1.25150	+	2.16766i	0.0992501	+	0.171906i
$160$		0			0
$161$	−0.814330	−	0.296392i	−0.0641782	−	0.0233590i
$162$		0			0
$163$	8.03983	−	13.9254i	0.629728	−	1.09072i	−0.357878	−	0.933768i	$-0.616500\pi$
$163$	8.03983	−	13.9254i	0.629728	−	1.09072i	0.987606	−	0.156953i	$-0.0501670\pi$
$164$		0			0
$165$	−0.0282185	−	0.160035i	−0.00219681	−	0.0124587i
$166$		0			0
$167$	4.49866	−	3.77482i	0.348116	−	0.292104i	−0.451917	−	0.892060i	$-0.649260\pi$
$167$	4.49866	−	3.77482i	0.348116	−	0.292104i	0.800033	+	0.599956i	$0.204815\pi$
$168$		0			0
$169$	12.1027	−	4.40501i	0.930974	−	0.338847i
$170$		0			0
$171$	5.23783	+	11.4058i	0.400547	+	0.872221i
$172$		0			0
$173$	7.28359	−	2.65101i	0.553761	−	0.201552i	−0.0499559	−	0.998751i	$-0.515908\pi$
$173$	7.28359	−	2.65101i	0.553761	−	0.201552i	0.603717	+	0.797199i	$0.293686\pi$
$174$		0			0
$175$	−0.620615	+	0.520758i	−0.0469141	+	0.0393656i
$176$		0			0
$177$	0.687319	+	3.89798i	0.0516620	+	0.292990i
$178$		0			0
$179$	7.91147	−	13.7031i	0.591331	−	1.02422i	−0.402722	−	0.915322i	$-0.631936\pi$
$179$	7.91147	−	13.7031i	0.591331	−	1.02422i	0.994053	−	0.108894i	$-0.0347308\pi$
$180$		0			0
$181$	3.52481	+	1.28293i	0.261997	+	0.0953593i	0.469679	−	0.882837i	$-0.344370\pi$
$181$	3.52481	+	1.28293i	0.261997	+	0.0953593i	−0.207682	+	0.978196i	$0.566592\pi$
$182$		0			0
$183$	1.97519	+	3.42112i	0.146010	+	0.252897i
$184$		0			0
$185$	−9.53983	−	8.00487i	−0.701382	−	0.588530i
$186$		0			0
$187$	0.0996702	−	0.565258i	0.00728861	−	0.0413358i
$188$		0			0
$189$	−0.623608			−0.0453608
$190$		0			0
$191$	−4.73917			−0.342914			−0.171457	−	0.985192i	$-0.554848\pi$
$191$	−4.73917			−0.342914			−0.171457	+	0.985192i	$0.554848\pi$
$192$		0			0
$193$	−1.72756	+	9.79747i	−0.124352	+	0.705238i	0.857338	+	0.514754i	$0.172117\pi$
$193$	−1.72756	+	9.79747i	−0.124352	+	0.705238i	−0.981690	+	0.190484i	$0.938994\pi$
$194$		0			0
$195$	0.141559	+	0.118782i	0.0101373	+	0.00850618i
$196$		0			0
$197$	6.86959	+	11.8985i	0.489438	+	0.847731i	0.999926	−	0.0121537i	$-0.00386873\pi$
$197$	6.86959	+	11.8985i	0.489438	+	0.847731i	−0.510488	+	0.859885i	$0.670535\pi$
$198$		0			0
$199$	−14.2417	−	5.18355i	−1.00957	−	0.367452i	−0.216300	−	0.976327i	$-0.569399\pi$
$199$	−14.2417	−	5.18355i	−1.00957	−	0.367452i	−0.793267	+	0.608874i	$0.791621\pi$
$200$		0			0
$201$	0.0628336	−	0.108831i	0.00443194	−	0.00767635i
$202$		0			0
$203$	0.186137	+	1.05563i	0.0130642	+	0.0740910i
$204$		0			0
$205$	2.90554	−	2.43804i	0.202932	−	0.170280i
$206$		0			0
$207$	7.67752	−	2.79439i	0.533624	−	0.194223i
$208$		0			0
$209$	1.28787	−	0.337044i	0.0890836	−	0.0233139i
$210$		0			0
$211$	−11.4042	+	4.15079i	−0.785098	+	0.285752i	−0.703297	−	0.710897i	$-0.748289\pi$
$211$	−11.4042	+	4.15079i	−0.785098	+	0.285752i	−0.0818009	+	0.996649i	$0.526067\pi$
$212$		0			0
$213$	−3.44949	+	2.89447i	−0.236355	+	0.198326i
$214$		0			0
$215$	0.309278	+	1.75400i	0.0210926	+	0.119622i
$216$		0			0
$217$	0.889185	−	1.54011i	0.0603618	−	0.104550i
$218$		0			0
$219$	−1.95589	−	0.711886i	−0.132167	−	0.0481048i
$220$		0			0
$221$	0.326352	+	0.565258i	0.0219528	+	0.0380234i
$222$		0			0
$223$	−18.3858	−	15.4275i	−1.23120	−	1.03310i	−0.998160	−	0.0606356i	$-0.980687\pi$
$223$	−18.3858	−	15.4275i	−1.23120	−	1.03310i	−0.233043	−	0.972466i	$-0.574868\pi$
$224$		0			0
$225$	1.32635	−	7.52211i	0.0884235	−	0.501474i
$226$		0			0
$227$	−15.3500			−1.01881			−0.509407	−	0.860526i	$-0.670135\pi$
$227$	−15.3500			−1.01881			−0.509407	+	0.860526i	$0.670135\pi$
$228$		0			0
$229$	6.90673			0.456409			0.228205	−	0.973613i	$-0.426714\pi$
$229$	6.90673			0.456409			0.228205	+	0.973613i	$0.426714\pi$
$230$		0			0
$231$	−0.00562509	+	0.0319015i	−0.000370104	+	0.00209896i
$232$		0			0
$233$	1.17365	+	0.984808i	0.0768882	+	0.0645169i	0.680422	−	0.732821i	$-0.261797\pi$
$233$	1.17365	+	0.984808i	0.0768882	+	0.0645169i	−0.603534	+	0.797338i	$0.706241\pi$
$234$		0			0
$235$	−4.78699	−	8.29131i	−0.312269	−	0.540865i
$236$		0			0
$237$	2.95084	+	1.07402i	0.191677	+	0.0697649i
$238$		0			0
$239$	−10.3007	+	17.8413i	−0.666294	+	1.15406i	0.312638	+	0.949872i	$0.398787\pi$
$239$	−10.3007	+	17.8413i	−0.666294	+	1.15406i	−0.978933	+	0.204183i	$0.934546\pi$
$240$		0			0
$241$	3.33662	+	18.9229i	0.214931	+	1.21893i	0.881027	+	0.473066i	$0.156853\pi$
$241$	3.33662	+	18.9229i	0.214931	+	1.21893i	−0.666097	+	0.745866i	$0.732036\pi$
$242$		0			0
$243$	6.80200	−	5.70756i	0.436349	−	0.366140i
$244$		0			0
$245$	9.94356	−	3.61916i	0.635271	−	0.231220i
$246$		0			0
$247$	−0.875515	+	1.23497i	−0.0557077	+	0.0785793i
$248$		0			0
$249$	−5.40508	+	1.96729i	−0.342533	+	0.124672i
$250$		0			0
$251$	−10.2797	+	8.62571i	−0.648850	+	0.544450i	−0.906722	−	0.421729i	$-0.861423\pi$
$251$	−10.2797	+	8.62571i	−0.648850	+	0.544450i	0.257872	+	0.966179i	$0.416979\pi$
$252$		0			0
$253$	−0.150482	−	0.853427i	−0.00946073	−	0.0536545i
$254$		0			0
$255$	0.500000	−	0.866025i	0.0313112	−	0.0542326i
$256$		0			0
$257$	−18.1211	−	6.59553i	−1.13036	−	0.411418i	−0.291938	−	0.956437i	$-0.594300\pi$
$257$	−18.1211	−	6.59553i	−1.13036	−	0.411418i	−0.838424	+	0.545019i	$0.816522\pi$
$258$		0			0
$259$	1.24123	+	2.14987i	0.0771262	+	0.133587i
$260$		0			0
$261$	−7.74170	−	6.49605i	−0.479199	−	0.402096i
$262$		0			0
$263$	4.79948	−	27.2192i	0.295948	−	1.67841i	−0.367374	−	0.930073i	$-0.619743\pi$
$263$	4.79948	−	27.2192i	0.295948	−	1.67841i	0.663322	−	0.748334i	$-0.269146\pi$
$264$		0			0
$265$	−11.0419			−0.678298
$266$		0			0
$267$	−0.361844			−0.0221445
$268$		0			0
$269$	1.33662	−	7.58034i	0.0814951	−	0.462182i	−0.916563	−	0.399890i	$-0.869048\pi$
$269$	1.33662	−	7.58034i	0.0814951	−	0.462182i	0.998058	−	0.0622911i	$-0.0198407\pi$
$270$		0			0
$271$	3.78177	+	3.17329i	0.229726	+	0.192763i	0.750384	−	0.661002i	$-0.229869\pi$
$271$	3.78177	+	3.17329i	0.229726	+	0.192763i	−0.520657	+	0.853766i	$0.674313\pi$
$272$		0			0
$273$	−0.0184183	−	0.0319015i	−0.00111473	−	0.00193076i
$274$		0			0
$275$	−0.761297	−	0.277089i	−0.0459079	−	0.0167091i
$276$		0			0
$277$	−0.889185	+	1.54011i	−0.0534260	+	0.0925365i	−0.891502	−	0.453018i	$-0.850347\pi$
$277$	−0.889185	+	1.54011i	−0.0534260	+	0.0925365i	0.838076	+	0.545554i	$0.183681\pi$
$278$		0			0
$279$	2.91147	+	16.5118i	0.174305	+	0.988535i
$280$		0			0
$281$	−16.1027	+	13.5117i	−0.960604	+	0.806043i	−0.981051	−	0.193748i	$-0.937936\pi$
$281$	−16.1027	+	13.5117i	−0.960604	+	0.806043i	0.0204469	+	0.999791i	$0.493491\pi$
$282$		0			0
$283$	−4.95084	+	1.80196i	−0.294297	+	0.107115i	−0.484949	−	0.874542i	$-0.661162\pi$
$283$	−4.95084	+	1.80196i	−0.294297	+	0.107115i	0.190652	+	0.981658i	$0.438940\pi$
$284$		0			0
$285$	2.30928	+	0.215615i	0.136790	+	0.0127719i
$286$		0			0
$287$	−0.710485	+	0.258595i	−0.0419386	+	0.0152644i
$288$		0			0
$289$	−10.3170	+	8.65701i	−0.606883	+	0.509236i
$290$		0			0
$291$	−0.566704	−	3.21394i	−0.0332208	−	0.188404i
$292$		0			0
$293$	13.3229	−	23.0760i	0.778335	−	1.34812i	−0.154566	−	0.987982i	$-0.549398\pi$
$293$	13.3229	−	23.0760i	0.778335	−	1.34812i	0.932901	−	0.360133i	$-0.117269\pi$
$294$		0			0
$295$	−16.4081	−	5.97205i	−0.955315	−	0.347706i
$296$		0			0
$297$	−0.311804	−	0.540060i	−0.0180927	−	0.0313375i
$298$		0			0
$299$	0.754900	+	0.633436i	0.0436570	+	0.0366326i
$300$		0			0
$301$	0.0616516	−	0.349643i	0.00355354	−	0.0201531i
$302$		0			0
$303$	0.859785			0.0493934
$304$		0			0
$305$	−17.4270			−0.997865
$306$		0			0
$307$	0.385315	−	2.18523i	0.0219911	−	0.124718i	−0.971836	−	0.235659i	$-0.924275\pi$
$307$	0.385315	−	2.18523i	0.0219911	−	0.124718i	0.993827	+	0.110941i	$0.0353864\pi$
$308$		0			0
$309$	−4.45084	−	3.73470i	−0.253199	−	0.212459i
$310$		0			0
$311$	7.84730	+	13.5919i	0.444979	+	0.770727i	0.998051	−	0.0624070i	$-0.0198777\pi$
$311$	7.84730	+	13.5919i	0.444979	+	0.770727i	−0.553071	+	0.833134i	$0.686544\pi$
$312$		0			0
$313$	−7.75150	−	2.82131i	−0.438140	−	0.159470i	0.113526	−	0.993535i	$-0.463786\pi$
$313$	−7.75150	−	2.82131i	−0.438140	−	0.159470i	−0.551666	+	0.834065i	$0.686008\pi$
$314$		0			0
$315$	0.673648	−	1.16679i	0.0379558	−	0.0657413i
$316$		0			0
$317$	1.04071	+	5.90214i	0.0584519	+	0.331497i	0.999985	−	0.00542238i	$-0.00172601\pi$
$317$	1.04071	+	5.90214i	0.0584519	+	0.331497i	−0.941533	+	0.336920i	$0.890615\pi$
$318$		0			0
$319$	−0.821137	+	0.689016i	−0.0459749	+	0.0385775i
$320$		0			0
$321$	2.35369	−	0.856674i	0.131370	−	0.0478149i
$322$		0			0
$323$	7.40420	+	3.50535i	0.411981	+	0.195043i
$324$		0			0
$325$	0.865715	−	0.315094i	0.0480212	−	0.0174783i
$326$		0			0
$327$	−1.72075	+	1.44388i	−0.0951578	+	0.0798469i
$328$		0			0
$329$	0.331404	+	1.87949i	0.0182709	+	0.103619i
$330$		0			0
$331$	2.47771	−	4.29152i	0.136187	−	0.235883i	−0.789863	−	0.613283i	$-0.789848\pi$
$331$	2.47771	−	4.29152i	0.136187	−	0.235883i	0.926050	+	0.377400i	$0.123182\pi$
$332$		0			0
$333$	−21.9932	−	8.00487i	−1.20522	−	0.438664i
$334$		0			0
$335$	0.277189	+	0.480105i	0.0151444	+	0.0262309i
$336$		0			0
$337$	−5.71760	−	4.79763i	−0.311457	−	0.261344i	0.473637	−	0.880720i	$-0.342941\pi$
$337$	−5.71760	−	4.79763i	−0.311457	−	0.261344i	−0.785094	+	0.619377i	$0.787385\pi$
$338$		0			0
$339$	−0.815207	+	4.62327i	−0.0442760	+	0.251102i
$340$		0			0
$341$	1.77837			0.0963042
$342$		0			0
$343$	−4.24722			−0.229328
$344$		0			0
$345$	0.262174	−	1.48686i	0.0141150	−	0.0800500i
$346$		0			0
$347$	20.1668	+	16.9220i	1.08261	+	0.908420i	0.996135	−	0.0878338i	$-0.0279945\pi$
$347$	20.1668	+	16.9220i	1.08261	+	0.908420i	0.0864776	+	0.996254i	$0.472439\pi$
$348$		0			0
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	0.680439	−	0.732805i	$-0.261789\pi$
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	−0.974847	+	0.222875i	$0.928456\pi$
$350$		0			0
$351$	0.666374	+	0.242540i	0.0355684	+	0.0129458i
$352$		0			0
$353$	−1.58378	+	2.74318i	−0.0842960	+	0.146005i	−0.905091	−	0.425218i	$-0.860197\pi$
$353$	−1.58378	+	2.74318i	−0.0842960	+	0.146005i	0.820795	+	0.571223i	$0.193531\pi$
$354$		0			0
$355$	−3.44949	−	19.5630i	−0.183080	−	1.03830i
$356$		0			0
$357$	−0.152704	+	0.128134i	−0.00808193	+	0.00678155i
$358$		0			0
$359$	23.6018	−	8.59035i	1.24565	−	0.453381i	0.366724	−	0.930330i	$-0.380480\pi$
$359$	23.6018	−	8.59035i	1.24565	−	0.453381i	0.878931	+	0.476949i	$0.158257\pi$
$360$		0			0
$361$	−0.221629	+	18.9987i	−0.0116647	+	0.999932i
$362$		0			0
$363$	3.55943	−	1.29553i	0.186822	−	0.0679975i
$364$		0			0
$365$	7.03390	−	5.90214i	0.368171	−	0.308932i
$366$		0			0
$367$	3.61468	+	20.4999i	0.188685	+	1.07009i	0.921129	+	0.389258i	$0.127269\pi$
$367$	3.61468	+	20.4999i	0.188685	+	1.07009i	−0.732444	+	0.680828i	$0.761620\pi$
$368$		0			0
$369$	3.56418	−	6.17334i	0.185544	−	0.321371i
$370$		0			0
$371$	2.06835	+	0.752819i	0.107384	+	0.0390844i
$372$		0			0
$373$	0.953363	+	1.65127i	0.0493633	+	0.0854997i	0.889651	−	0.456641i	$-0.150947\pi$
$373$	0.953363	+	1.65127i	0.0493633	+	0.0854997i	−0.840288	+	0.542140i	$0.817614\pi$
$374$		0			0
$375$	−3.11927	−	2.61738i	−0.161078	−	0.135161i
$376$		0			0
$377$	0.211667	−	1.20042i	0.0109014	−	0.0618249i
$378$		0			0
$379$	−23.7743			−1.22120			−0.610601	−	0.791939i	$-0.709072\pi$
$379$	−23.7743			−1.22120			−0.610601	+	0.791939i	$0.709072\pi$
$380$		0			0
$381$	3.45512			0.177011
$382$		0			0
$383$	0.346114	−	1.96291i	0.0176856	−	0.100300i	−0.974687	−	0.223573i	$-0.928228\pi$
$383$	0.346114	−	1.96291i	0.0176856	−	0.100300i	0.992373	+	0.123273i	$0.0393390\pi$
$384$		0			0
$385$	−0.109470	−	0.0918566i	−0.00557913	−	0.00468144i
$386$		0			0
$387$	1.67365	+	2.89884i	0.0850763	+	0.147357i
$388$		0			0
$389$	−1.29813	−	0.472482i	−0.0658180	−	0.0239558i	0.308901	−	0.951094i	$-0.400039\pi$
$389$	−1.29813	−	0.472482i	−0.0658180	−	0.0239558i	−0.374719	+	0.927138i	$0.622261\pi$
$390$		0			0
$391$	2.66637	−	4.61830i	0.134844	−	0.233557i
$392$		0			0
$393$	−0.628193	−	3.56266i	−0.0316882	−	0.179713i
$394$		0			0
$395$	−10.6120	+	8.90452i	−0.533947	+	0.448035i
$396$		0			0
$397$	15.0424	−	5.47497i	0.754954	−	0.274781i	0.0642653	−	0.997933i	$-0.479530\pi$
$397$	15.0424	−	5.47497i	0.754954	−	0.274781i	0.690689	+	0.723152i	$0.257307\pi$
$398$		0			0
$399$	−0.417871	−	0.197832i	−0.0209197	−	0.00990397i
$400$		0			0
$401$	−7.66772	+	2.79082i	−0.382908	+	0.139367i	−0.526300	−	0.850299i	$-0.676421\pi$
$401$	−7.66772	+	2.79082i	−0.382908	+	0.139367i	0.143392	+	0.989666i	$0.454199\pi$
$402$		0			0
$403$	−1.54916	+	1.29990i	−0.0771693	+	0.0647527i
$404$		0			0
$405$	2.10947	+	11.9634i	0.104820	+	0.594466i
$406$		0			0
$407$	−1.24123	+	2.14987i	−0.0615255	+	0.106565i
$408$		0			0
$409$	18.9586	+	6.90036i	0.937441	+	0.341201i	0.765155	−	0.643846i	$-0.222662\pi$
$409$	18.9586	+	6.90036i	0.937441	+	0.341201i	0.172286	+	0.985047i	$0.444885\pi$
$410$		0			0
$411$	3.20692	+	5.55455i	0.158186	+	0.273986i
$412$		0			0
$413$	2.66637	+	2.23735i	0.131204	+	0.110093i
$414$		0			0
$415$	4.40626	−	24.9891i	0.216295	−	1.22667i
$416$		0			0
$417$	5.91859			0.289834
$418$		0			0
$419$	10.7784			0.526558			0.263279	−	0.964720i	$-0.415196\pi$
$419$	10.7784			0.526558			0.263279	+	0.964720i	$0.415196\pi$
$420$		0			0
$421$	−3.64378	+	20.6649i	−0.177587	+	1.00715i	0.757528	+	0.652802i	$0.226407\pi$
$421$	−3.64378	+	20.6649i	−0.177587	+	1.00715i	−0.935115	+	0.354344i	$0.884704\pi$
$422$		0			0
$423$	−13.7836	−	11.5658i	−0.670181	−	0.562349i
$424$		0			0
$425$	−2.49273	−	4.31753i	−0.120915	−	0.209431i
$426$		0			0
$427$	3.26440	+	1.18814i	0.157975	+	0.0574983i
$428$		0			0
$429$	0.0184183	−	0.0319015i	0.000889245	−	0.00154022i
$430$		0			0
$431$	3.16132	+	17.9287i	0.152276	+	0.863597i	0.961234	+	0.275732i	$0.0889203\pi$
$431$	3.16132	+	17.9287i	0.152276	+	0.863597i	−0.808959	+	0.587865i	$0.799969\pi$
$432$		0			0
$433$	27.2729	−	22.8847i	1.31065	−	1.09977i	0.322454	−	0.946585i	$-0.395492\pi$
$433$	27.2729	−	22.8847i	1.31065	−	1.09977i	0.988198	−	0.153183i	$-0.0489524\pi$
$434$		0			0
$435$	−1.75490	+	0.638731i	−0.0841410	+	0.0306248i
$436$		0			0
$437$	12.3148	+	1.14982i	0.589097	+	0.0550033i
$438$		0			0
$439$	12.0005	−	4.36781i	0.572751	−	0.208464i	−0.0393751	−	0.999225i	$-0.512537\pi$
$439$	12.0005	−	4.36781i	0.572751	−	0.208464i	0.612126	+	0.790760i	$0.290314\pi$
$440$		0			0
$441$	15.2344	−	12.7832i	0.725449	−	0.608724i
$442$		0			0
$443$	−4.42989	−	25.1232i	−0.210471	−	1.19364i	−0.888596	−	0.458691i	$-0.848318\pi$
$443$	−4.42989	−	25.1232i	−0.210471	−	1.19364i	0.678125	−	0.734946i	$-0.262793\pi$
$444$		0			0
$445$	0.798133	−	1.38241i	0.0378351	−	0.0655324i
$446$		0			0
$447$	−5.17752	−	1.88446i	−0.244888	−	0.0891320i
$448$		0			0
$449$	15.2392	+	26.3950i	0.719181	+	1.24566i	0.961325	+	0.275417i	$0.0888161\pi$
$449$	15.2392	+	26.3950i	0.719181	+	1.24566i	−0.242144	+	0.970240i	$0.577851\pi$
$450$		0			0
$451$	−0.579193	−	0.486000i	−0.0272731	−	0.0228849i
$452$		0			0
$453$	0.964918	−	5.47232i	0.0453358	−	0.257112i
$454$		0			0
$455$	0.162504			0.00761830
$456$		0			0
$457$	17.2608			0.807428			0.403714	−	0.914885i	$-0.367719\pi$
$457$	17.2608			0.807428			0.403714	+	0.914885i	$0.367719\pi$
$458$		0			0
$459$	0.666374	−	3.77920i	0.0311037	−	0.176398i
$460$		0			0
$461$	23.7108	+	19.8957i	1.10432	+	0.926636i	0.997708	−	0.0676647i	$-0.0215548\pi$
$461$	23.7108	+	19.8957i	1.10432	+	0.926636i	0.106613	+	0.994301i	$0.465999\pi$
$462$		0			0
$463$	15.1236	+	26.1949i	0.702854	+	1.21738i	0.967461	+	0.253022i	$0.0814245\pi$
$463$	15.1236	+	26.1949i	0.702854	+	1.21738i	−0.264607	+	0.964356i	$0.585242\pi$
$464$		0			0
$465$	2.91147	+	1.05969i	0.135016	+	0.0491419i
$466$		0			0
$467$	11.0885	−	19.2059i	0.513116	−	0.888743i	−0.486769	−	0.873531i	$-0.661824\pi$
$467$	11.0885	−	19.2059i	0.513116	−	0.888743i	0.999884	−	0.0152116i	$-0.00484219\pi$
$468$		0			0
$469$	−0.0191898	−	0.108831i	−0.000886104	−	0.00502535i
$470$		0			0
$471$	3.10220	−	2.60305i	0.142942	−	0.119942i
$472$		0			0
$473$	0.333626	−	0.121430i	0.0153401	−	0.00558335i
$474$		0			0
$475$	6.68732	−	9.43290i	0.306835	−	0.432811i
$476$		0			0
$477$	−19.5005	+	7.09759i	−0.892865	+	0.324976i
$478$		0			0
$479$	−14.9060	+	12.5076i	−0.681073	+	0.571488i	−0.916320	−	0.400448i	$-0.868855\pi$
$479$	−14.9060	+	12.5076i	−0.681073	+	0.571488i	0.235247	+	0.971936i	$0.424410\pi$
$480$		0			0
$481$	−0.490200	−	2.78006i	−0.0223512	−	0.126760i
$482$		0			0
$483$	−0.150482	+	0.260643i	−0.00684717	+	0.0118597i
$484$		0			0
$485$	13.5287	+	4.92404i	0.614306	+	0.223589i
$486$		0			0
$487$	−15.1432	−	26.2288i	−0.686204	−	1.18854i	−0.973057	−	0.230566i	$-0.925942\pi$
$487$	−15.1432	−	26.2288i	−0.686204	−	1.18854i	0.286852	−	0.957975i	$-0.407391\pi$
$488$		0			0
$489$	−4.27790	−	3.58959i	−0.193454	−	0.162327i
$490$		0			0
$491$	−4.60519	+	26.1173i	−0.207829	+	1.17866i	0.685096	+	0.728453i	$0.259760\pi$
$491$	−4.60519	+	26.1173i	−0.207829	+	1.17866i	−0.892925	+	0.450205i	$0.851351\pi$
$492$		0			0
$493$	−6.59627			−0.297081
$494$		0			0
$495$	1.34730			0.0605565
$496$		0			0
$497$	−0.687623	+	3.89971i	−0.0308441	+	0.174926i
$498$		0			0
$499$	17.1027	+	14.3508i	0.765620	+	0.642432i	0.939583	−	0.342320i	$-0.111213\pi$
$499$	17.1027	+	14.3508i	0.765620	+	0.642432i	−0.173963	+	0.984752i	$0.555657\pi$
$500$		0			0
$501$	−1.01976	−	1.76628i	−0.0455596	−	0.0789116i
$502$		0			0
$503$	14.7096	+	5.35386i	0.655869	+	0.238717i	0.648452	−	0.761256i	$-0.275417\pi$
$503$	14.7096	+	5.35386i	0.655869	+	0.238717i	0.00741717	+	0.999972i	$0.497639\pi$
$504$		0			0
$505$	−1.89646	+	3.28476i	−0.0843913	+	0.146170i
$506$		0			0
$507$	−0.776722	−	4.40501i	−0.0344954	−	0.195633i
$508$		0			0
$509$	3.00072	−	2.51790i	0.133004	−	0.111604i	−0.573859	−	0.818954i	$-0.694554\pi$
$509$	3.00072	−	2.51790i	0.133004	−	0.111604i	0.706863	+	0.707350i	$0.250110\pi$
$510$		0			0
$511$	−1.71998	+	0.626022i	−0.0760874	+	0.0276936i
$512$		0			0
$513$	8.61040	−	2.25341i	0.380159	−	0.0994904i
$514$		0			0
$515$	24.0856	−	8.76644i	1.06134	−	0.386295i
$516$		0			0
$517$	−1.46198	+	1.22675i	−0.0642979	+	0.0539523i
$518$		0			0
$519$	−0.467444	−	2.65101i	−0.0205185	−	0.116366i
$520$		0			0
$521$	10.2588	−	17.7687i	0.449445	−	0.778461i	−0.548905	−	0.835885i	$-0.684955\pi$
$521$	10.2588	−	17.7687i	0.449445	−	0.778461i	0.998350	+	0.0574233i	$0.0182885\pi$
$522$		0			0
$523$	−4.56670	−	1.66214i	−0.199688	−	0.0726805i	0.240240	−	0.970714i	$-0.422774\pi$
$523$	−4.56670	−	1.66214i	−0.199688	−	0.0726805i	−0.439928	+	0.898033i	$0.644996\pi$
$524$		0			0
$525$	0.140682	+	0.243668i	0.00613986	+	0.0106346i
$526$		0			0
$527$	8.38326	+	7.03439i	0.365180	+	0.306423i
$528$		0			0
$529$	−2.59580	+	14.7215i	−0.112861	+	0.640066i
$530$		0			0
$531$	−32.8161			−1.42410
$532$		0			0
$533$	0.859785			0.0372414
$534$		0			0
$535$	−1.91875	+	10.8818i	−0.0829547	+	0.470460i
$536$		0			0
$537$	−4.20961	−	3.53228i	−0.181658	−	0.152429i
$538$		0			0
$539$	−1.05468	−	1.82676i	−0.0454284	−	0.0786843i
$540$		0			0
$541$	−32.0082	−	11.6500i	−1.37614	−	0.500874i	−0.455134	−	0.890423i	$-0.650409\pi$
$541$	−32.0082	−	11.6500i	−1.37614	−	0.500874i	−0.921006	+	0.389549i	$0.872631\pi$
$542$		0			0
$543$	0.651359	−	1.12819i	0.0279525	−	0.0484152i
$544$		0			0
$545$	−1.72075	−	9.75887i	−0.0737089	−	0.418024i
$546$		0			0
$547$	−30.8169	+	25.8584i	−1.31763	+	1.10563i	−0.330832	+	0.943690i	$0.607329\pi$
$547$	−30.8169	+	25.8584i	−1.31763	+	1.10563i	−0.986801	+	0.161936i	$0.948226\pi$
$548$		0			0
$549$	−30.7768	+	11.2018i	−1.31352	+	0.478083i
$550$		0			0
$551$	−6.38460	−	13.9030i	−0.271993	−	0.592286i
$552$		0			0
$553$	2.59492	−	0.944475i	0.110347	−	0.0401631i
$554$		0			0
$555$	−3.31315	+	2.78006i	−0.140635	+	0.118007i
$556$		0			0
$557$	3.46497	+	19.6508i	0.146816	+	0.832633i	0.965891	+	0.258948i	$0.0833757\pi$
$557$	3.46497	+	19.6508i	0.146816	+	0.832633i	−0.819076	+	0.573685i	$0.805513\pi$
$558$		0			0
$559$	−0.201867	+	0.349643i	−0.00853805	+	0.0147883i
$560$		0			0
$561$	−0.187319	−	0.0681784i	−0.00790860	−	0.00287850i
$562$		0			0
$563$	7.15270	+	12.3888i	0.301451	+	0.522128i	0.976465	−	0.215677i	$-0.0691959\pi$
$563$	7.15270	+	12.3888i	0.301451	+	0.522128i	−0.675014	+	0.737805i	$0.735863\pi$
$564$		0			0
$565$	−15.8648	−	13.3122i	−0.667439	−	0.560048i
$566$		0			0
$567$	0.420503	−	2.38479i	0.0176595	−	0.100152i
$568$		0			0
$569$	20.3851			0.854586			0.427293	−	0.904113i	$-0.359467\pi$
$569$	20.3851			0.854586			0.427293	+	0.904113i	$0.359467\pi$
$570$		0			0
$571$	32.9377			1.37840			0.689200	−	0.724571i	$-0.257962\pi$
$571$	32.9377			1.37840			0.689200	+	0.724571i	$0.257962\pi$
$572$		0			0
$573$	−0.285807	+	1.62089i	−0.0119398	+	0.0677137i
$574$		0			0
$575$	−5.76604	−	4.83829i	−0.240461	−	0.201770i
$576$		0			0
$577$	−22.0526	−	38.1963i	−0.918063	−	1.59013i	−0.802354	−	0.596848i	$-0.796420\pi$
$577$	−22.0526	−	38.1963i	−0.918063	−	1.59013i	−0.115708	−	0.993283i	$-0.536914\pi$
$578$		0			0
$579$	3.24675	+	1.18172i	0.134930	+	0.0491106i
$580$		0			0
$581$	−2.52910	+	4.38052i	−0.104925	+	0.181735i
$582$		0			0
$583$	0.382216	+	2.16766i	0.0158298	+	0.0897751i
$584$		0			0
$585$	−1.17365	+	0.984808i	−0.0485244	+	0.0407168i
$586$		0			0
$587$	6.11334	−	2.22507i	0.252325	−	0.0918386i	−0.212761	−	0.977104i	$-0.568246\pi$
$587$	6.11334	−	2.22507i	0.252325	−	0.0918386i	0.465086	+	0.885266i	$0.346023\pi$
$588$		0			0
$589$	−6.71213	+	24.4781i	−0.276569	+	1.00860i
$590$		0			0
$591$	4.48380	−	1.63197i	0.184439	−	0.0671303i
$592$		0			0
$593$	9.79994	−	8.22313i	0.402435	−	0.337683i	−0.418999	−	0.907987i	$-0.637619\pi$
$593$	9.79994	−	8.22313i	0.402435	−	0.337683i	0.821434	+	0.570303i	$0.193174\pi$
$594$		0			0
$595$	−0.152704	−	0.866025i	−0.00626024	−	0.0355036i
$596$		0			0
$597$	−2.63176	+	4.55834i	−0.107711	+	0.186560i
$598$		0			0
$599$	17.1630	+	6.24681i	0.701260	+	0.255238i	0.667949	−	0.744207i	$-0.267173\pi$
$599$	17.1630	+	6.24681i	0.701260	+	0.255238i	0.0333112	+	0.999445i	$0.489395\pi$
$600$		0			0
$601$	−9.95336	−	17.2397i	−0.406006	−	0.703223i	0.588432	−	0.808547i	$-0.299746\pi$
$601$	−9.95336	−	17.2397i	−0.406006	−	0.703223i	−0.994438	+	0.105324i	$0.966412\pi$
$602$		0			0
$603$	0.798133	+	0.669713i	0.0325025	+	0.0272728i
$604$		0			0
$605$	−2.90167	+	16.4562i	−0.117970	+	0.669040i
$606$		0			0
$607$	22.5526			0.915383			0.457691	−	0.889111i	$-0.348676\pi$
$607$	22.5526			0.915383			0.457691	+	0.889111i	$0.348676\pi$
$608$		0			0
$609$	0.372273			0.0150853
$610$		0			0
$611$	0.376859	−	2.13727i	0.0152461	−	0.0864648i
$612$		0			0
$613$	−34.3148	−	28.7935i	−1.38596	−	1.16296i	−0.966946	−	0.254981i	$-0.917931\pi$
$613$	−34.3148	−	28.7935i	−1.38596	−	1.16296i	−0.419015	−	0.907979i	$-0.637625\pi$
$614$		0			0
$615$	−0.658633	−	1.14079i	−0.0265587	−	0.0460010i
$616$		0			0
$617$	−23.7224	−	8.63425i	−0.955028	−	0.347602i	−0.182945	−	0.983123i	$-0.558563\pi$
$617$	−23.7224	−	8.63425i	−0.955028	−	0.347602i	−0.772083	+	0.635521i	$0.780785\pi$
$618$		0			0
$619$	17.5574	−	30.4103i	0.705690	−	1.22229i	−0.260752	−	0.965406i	$-0.583970\pi$
$619$	17.5574	−	30.4103i	0.705690	−	1.22229i	0.966442	−	0.256886i	$-0.0826963\pi$
$620$		0			0
$621$	−1.00609	−	5.70583i	−0.0403731	−	0.228967i
$622$		0			0
$623$	−0.243756	+	0.204535i	−0.00976587	+	0.00819454i
$624$		0			0
$625$	4.41622	−	1.60737i	0.176649	−	0.0642949i
$626$		0			0
$627$	−0.0376082	−	0.460802i	−0.00150192	−	0.0184027i
$628$		0			0
$629$	−14.3550	+	5.22481i	−0.572373	+	0.208327i
$630$		0			0
$631$	−25.9256	+	21.7542i	−1.03208	+	0.866020i	−0.991097	−	0.133140i	$-0.957494\pi$
$631$	−25.9256	+	21.7542i	−1.03208	+	0.866020i	−0.0409850	+	0.999160i	$0.513050\pi$
$632$		0			0
$633$	0.731896	+	4.15079i	0.0290903	+	0.164979i
$634$		0			0
$635$	−7.62108	+	13.2001i	−0.302433	+	0.523830i
$636$		0			0
$637$	2.25402	+	0.820397i	0.0893076	+	0.0325053i
$638$		0			0
$639$	−18.6668	−	32.3319i	−0.738449	−	1.27903i
$640$		0			0
$641$	17.7108	+	14.8611i	0.699534	+	0.586979i	0.921641	−	0.388043i	$-0.126849\pi$
$641$	17.7108	+	14.8611i	0.699534	+	0.586979i	−0.222107	+	0.975022i	$0.571293\pi$
$642$		0			0
$643$	−2.61880	+	14.8520i	−0.103276	+	0.585705i	0.888620	+	0.458645i	$0.151665\pi$
$643$	−2.61880	+	14.8520i	−0.103276	+	0.585705i	−0.991895	+	0.127060i	$0.959446\pi$
$644$		0			0
$645$	0.618555			0.0243556
$646$		0			0
$647$	−25.4783			−1.00166			−0.500828	−	0.865547i	$-0.666971\pi$
$647$	−25.4783			−1.00166			−0.500828	+	0.865547i	$0.666971\pi$
$648$		0			0
$649$	−0.604418	+	3.42782i	−0.0237255	+	0.134554i
$650$		0			0
$651$	−0.473126	−	0.397000i	−0.0185433	−	0.0155596i
$652$		0			0
$653$	−17.0175	−	29.4752i	−0.665948	−	1.15346i	−0.979027	−	0.203729i	$-0.934694\pi$
$653$	−17.0175	−	29.4752i	−0.665948	−	1.15346i	0.313080	−	0.949727i	$-0.398639\pi$
$654$		0			0
$655$	14.9966	+	5.45831i	0.585966	+	0.213274i
$656$		0			0
$657$	8.62836	−	14.9448i	0.336624	−	0.583050i
$658$		0			0
$659$	−4.38532	−	24.8704i	−0.170828	−	0.968812i	−0.942850	−	0.333217i	$-0.891866\pi$
$659$	−4.38532	−	24.8704i	−0.170828	−	0.968812i	0.772023	−	0.635595i	$-0.219245\pi$
$660$		0			0
$661$	−2.95471	+	2.47929i	−0.114925	+	0.0964334i	−0.698439	−	0.715670i	$-0.746122\pi$
$661$	−2.95471	+	2.47929i	−0.114925	+	0.0964334i	0.583514	+	0.812103i	$0.301677\pi$
$662$		0			0
$663$	0.213011	−	0.0775297i	0.00827266	−	0.00301100i
$664$		0			0
$665$	1.67752	−	1.16009i	0.0650514	−	0.0449863i
$666$		0			0
$667$	−9.35844	+	3.40619i	−0.362360	+	0.131888i
$668$		0			0
$669$	−6.38532	+	5.35792i	−0.246871	+	0.207149i
$670$		0			0
$671$	0.603236	+	3.42112i	0.0232877	+	0.132071i
$672$		0			0
$673$	2.62836	−	4.55245i	0.101316	−	0.175484i	−0.810911	−	0.585169i	$-0.801028\pi$
$673$	2.62836	−	4.55245i	0.101316	−	0.175484i	0.912227	+	0.409685i	$0.134361\pi$
$674$		0			0
$675$	−5.08987	−	1.85256i	−0.195909	−	0.0713051i
$676$		0			0
$677$	20.5993	+	35.6790i	0.791694	+	1.37125i	0.924917	+	0.380168i	$0.124134\pi$
$677$	20.5993	+	35.6790i	0.791694	+	1.37125i	−0.133224	+	0.991086i	$0.542533\pi$
$678$		0			0
$679$	−2.19846	−	1.84473i	−0.0843693	−	0.0707942i
$680$		0			0
$681$	−0.925717	+	5.25000i	−0.0354736	+	0.201181i
$682$		0			0
$683$	−45.6459			−1.74659			−0.873296	−	0.487190i	$-0.838022\pi$
$683$	−45.6459			−1.74659			−0.873296	+	0.487190i	$0.838022\pi$
$684$		0			0
$685$	−28.2945			−1.08108
$686$		0			0
$687$	0.416527	−	2.36224i	0.0158915	−	0.0901251i
$688$		0			0
$689$	−1.91740	−	1.60889i	−0.0730473	−	0.0612939i
$690$		0			0
$691$	7.49319	+	12.9786i	0.285054	+	0.493729i	0.972622	−	0.232391i	$-0.0746550\pi$
$691$	7.49319	+	12.9786i	0.285054	+	0.493729i	−0.687568	+	0.726120i	$0.741322\pi$
$692$		0			0
$693$	−0.252374	−	0.0918566i	−0.00958689	−	0.00348934i
$694$		0			0
$695$	−13.0548	+	22.6117i	−0.495198	+	0.857709i
$696$		0			0
$697$	−0.807934	−	4.58202i	−0.0306027	−	0.173556i
$698$		0			0
$699$	0.407604	−	0.342020i	0.0154170	−	0.0129364i
$700$		0			0
$701$	−3.14068	+	1.14311i	−0.118622	+	0.0431748i	−0.400649	−	0.916232i	$-0.631215\pi$
$701$	−3.14068	+	1.14311i	−0.118622	+	0.0431748i	0.282027	+	0.959406i	$0.408993\pi$
$702$		0			0
$703$	−24.9067	−	25.1990i	−0.939375	−	0.950397i
$704$		0			0
$705$	−3.12449	+	1.13722i	−0.117675	+	0.0428302i
$706$		0			0
$707$	0.579193	−	0.486000i	0.0217828	−	0.0182779i
$708$		0			0
$709$	−3.26058	−	18.4917i	−0.122454	−	0.694469i	−0.982788	−	0.184739i	$-0.940856\pi$
$709$	−3.26058	−	18.4917i	−0.122454	−	0.694469i	0.860334	−	0.509731i	$-0.170255\pi$
$710$		0			0
$711$	−13.0175	+	22.5470i	−0.488196	+	0.845580i
$712$		0			0
$713$	15.5262	+	5.65106i	0.581459	+	0.211634i
$714$		0			0
$715$	0.0812519	+	0.140732i	0.00303865	+	0.00526309i
$716$		0			0
$717$	5.48087	+	4.59899i	0.204687	+	0.171753i
$718$		0			0
$719$	5.50418	−	31.2157i	0.205271	−	1.16415i	−0.691741	−	0.722145i	$-0.743156\pi$
$719$	5.50418	−	31.2157i	0.205271	−	1.16415i	0.897013	−	0.442005i	$-0.145733\pi$
$720$		0			0
$721$	−5.10936			−0.190283
$722$		0			0
$723$	6.67324			0.248180
$724$		0			0
$725$	−1.61674	+	9.16901i	−0.0600444	+	0.340529i
$726$		0			0
$727$	15.5168	+	13.0202i	0.575487	+	0.482891i	0.883462	−	0.468504i	$-0.155207\pi$
$727$	15.5168	+	13.0202i	0.575487	+	0.482891i	−0.307974	+	0.951395i	$0.599651\pi$
$728$		0			0
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$		0			0
$731$	2.05303	+	0.747243i	0.0759342	+	0.0276378i
$732$		0			0
$733$	−0.406726	+	0.704471i	−0.0150228	+	0.0260202i	−0.873439	−	0.486933i	$-0.838115\pi$
$733$	−0.406726	+	0.704471i	−0.0150228	+	0.0260202i	0.858416	+	0.512954i	$0.171449\pi$
$734$		0			0
$735$	−0.638156	−	3.61916i	−0.0235387	−	0.133495i
$736$		0			0
$737$	0.0846555	−	0.0710344i	0.00311832	−	0.00261659i
$738$		0			0
$739$	−37.5581	+	13.6700i	−1.38160	+	0.502861i	−0.922662	−	0.385609i	$-0.873992\pi$
$739$	−37.5581	+	13.6700i	−1.38160	+	0.502861i	−0.458936	+	0.888469i	$0.651769\pi$
$740$		0			0
$741$	0.369585	+	0.373922i	0.0135770	+	0.0137364i
$742$		0			0
$743$	7.41875	−	2.70020i	0.272167	−	0.0990609i	−0.202331	−	0.979317i	$-0.564852\pi$
$743$	7.41875	−	2.70020i	0.272167	−	0.0990609i	0.474498	+	0.880256i	$0.342629\pi$
$744$		0			0
$745$	18.6197	−	15.6238i	0.682174	−	0.572412i
$746$		0			0
$747$	−8.28106	−	46.9642i	−0.302988	−	1.71833i
$748$		0			0
$749$	1.10132	−	1.90754i	0.0402413	−	0.0697000i
$750$		0			0
$751$	−19.3606	−	7.04667i	−0.706477	−	0.257137i	−0.0363031	−	0.999341i	$-0.511558\pi$
$751$	−19.3606	−	7.04667i	−0.706477	−	0.257137i	−0.670174	+	0.742204i	$0.733780\pi$
$752$		0			0
$753$	2.33022	+	4.03606i	0.0849180	+	0.147082i
$754$		0			0
$755$	18.7784	+	15.7569i	0.683415	+	0.573453i
$756$		0			0
$757$	−4.67886	+	26.5351i	−0.170056	+	0.964436i	0.773641	+	0.633625i	$0.218434\pi$
$757$	−4.67886	+	26.5351i	−0.170056	+	0.964436i	−0.943697	+	0.330812i	$0.892677\pi$
$758$		0			0
$759$	−0.300964			−0.0109243
$760$		0			0
$761$	7.38919			0.267858			0.133929	−	0.990991i	$-0.457241\pi$
$761$	7.38919			0.267858			0.133929	+	0.990991i	$0.457241\pi$
$762$		0			0
$763$	−0.343015	+	1.94534i	−0.0124180	+	0.0704259i
$764$		0			0
$765$	6.35117	+	5.32926i	0.229627	+	0.192680i
$766$		0			0
$767$	−1.97906	−	3.42782i	−0.0714596	−	0.123772i
$768$		0			0
$769$	14.8011	+	5.38717i	0.533742	+	0.194266i	0.594809	−	0.803867i	$-0.297228\pi$
$769$	14.8011	+	5.38717i	0.533742	+	0.194266i	−0.0610663	+	0.998134i	$0.519450\pi$
$770$		0			0
$771$	−3.34864	+	5.80002i	−0.120598	+	0.208882i
$772$		0			0
$773$	−0.309278	−	1.75400i	−0.0111239	−	0.0630870i	0.978740	−	0.205103i	$-0.0657528\pi$
$773$	−0.309278	−	1.75400i	−0.0111239	−	0.0630870i	−0.989864	+	0.142016i	$0.954642\pi$
$774$		0			0
$775$	11.8327	−	9.92885i	0.425045	−	0.356655i
$776$		0			0
$777$	0.810155	−	0.294872i	0.0290641	−	0.0105785i
$778$		0			0
$779$	8.87551	−	6.13787i	0.317998	−	0.219912i
$780$		0			0
$781$	−3.72106	+	1.35435i	−0.133150	+	0.0484626i
$782$		0			0
$783$	−5.48995	+	4.60662i	−0.196195	+	0.164627i
$784$		0			0
$785$	3.10220	+	17.5934i	0.110722	+	0.627936i
$786$		0			0
$787$	−14.3844	+	24.9146i	−0.512750	+	0.888109i	0.487141	+	0.873323i	$0.338040\pi$
$787$	−14.3844	+	24.9146i	−0.512750	+	0.888109i	−0.999891	+	0.0147853i	$0.995294\pi$
$788$		0			0
$789$	−9.02007	−	3.28304i	−0.321123	−	0.116879i
$790$		0			0
$791$	2.06418	+	3.57526i	0.0733937	+	0.127122i
$792$		0			0
$793$	−3.02616	−	2.53925i	−0.107462	−	0.0901714i
$794$		0			0
$795$	−0.665907	+	3.77655i	−0.0236173	+	0.133940i
$796$		0			0
$797$	44.4944			1.57607			0.788037	−	0.615628i	$-0.211098\pi$
$797$	44.4944			1.57607			0.788037	+	0.615628i	$0.211098\pi$
$798$		0			0
$799$	−11.7442			−0.415481
$800$		0			0
$801$	0.520945	−	2.95442i	0.0184067	−	0.104389i
$802$		0			0
$803$	−1.40214	−	1.17654i	−0.0494805	−	0.0415190i
$804$		0			0
$805$	−0.663848	−	1.14982i	−0.0233976	−	0.0405258i
$806$		0			0
$807$	−2.51202	−	0.914301i	−0.0884274	−	0.0321849i
$808$		0			0
$809$	−17.1168	+	29.6472i	−0.601795	+	1.04234i	0.390755	+	0.920495i	$0.372214\pi$
$809$	−17.1168	+	29.6472i	−0.601795	+	1.04234i	−0.992549	+	0.121844i	$0.961119\pi$
$810$		0			0
$811$	−7.93733	−	45.0148i	−0.278717	−	1.58068i	−0.726901	−	0.686743i	$-0.759040\pi$
$811$	−7.93733	−	45.0148i	−0.278717	−	1.58068i	0.448183	−	0.893942i	$-0.352071\pi$
$812$		0			0
$813$	1.31340	−	1.10207i	0.0460628	−	0.0386513i
$814$		0			0
$815$	23.1498	−	8.42583i	0.810901	−	0.295144i
$816$		0			0
$817$	0.412189	+	5.05044i	0.0144207	+	0.176693i
$818$		0			0
$819$	0.286989	−	0.104455i	0.0100282	−	0.00364997i
$820$		0			0
$821$	34.0959	−	28.6098i	1.18995	−	0.998490i	0.190093	−	0.981766i	$-0.439121\pi$
$821$	34.0959	−	28.6098i	1.18995	−	0.998490i	0.999860	−	0.0167236i	$-0.00532354\pi$
$822$		0			0
$823$	8.24098	+	46.7369i	0.287263	+	1.62915i	0.697090	+	0.716984i	$0.254478\pi$
$823$	8.24098	+	46.7369i	0.287263	+	1.62915i	−0.409827	+	0.912163i	$0.634411\pi$
$824$		0			0
$825$	−0.140682	+	0.243668i	−0.00489792	+	0.00848344i
$826$		0			0
$827$	36.5967	+	13.3201i	1.27259	+	0.463186i	0.887976	−	0.459890i	$-0.152111\pi$
$827$	36.5967	+	13.3201i	1.27259	+	0.463186i	0.384617	+	0.923076i	$0.374333\pi$
$828$		0			0
$829$	−9.86959	−	17.0946i	−0.342785	−	0.593721i	0.642164	−	0.766567i	$-0.278037\pi$
$829$	−9.86959	−	17.0946i	−0.342785	−	0.593721i	−0.984949	+	0.172847i	$0.944704\pi$
$830$		0			0
$831$	0.473126	+	0.397000i	0.0164125	+	0.0137718i
$832$		0			0
$833$	2.25402	−	12.7832i	0.0780973	−	0.442912i
$834$		0			0
$835$	8.99731			0.311365
$836$		0			0
$837$	11.8898			0.410972
$838$		0			0
$839$	8.89874	−	50.4672i	0.307219	−	1.74232i	−0.305655	−	0.952142i	$-0.598876\pi$
$839$	8.89874	−	50.4672i	0.307219	−	1.74232i	0.612874	−	0.790181i	$-0.290013\pi$
$840$		0			0
$841$	−12.7786	−	10.7225i	−0.440642	−	0.369743i
$842$		0			0
$843$	3.65018	+	6.32229i	0.125719	+	0.217751i
$844$		0			0
$845$	18.5424	+	6.74887i	0.637876	+	0.232168i
$846$		0			0
$847$	1.66550	−	2.88473i	0.0572271	−	0.0991203i
$848$		0			0
$849$	0.317734	+	1.80196i	0.0109046	+	0.0618430i
$850$		0			0
$851$	−17.6682	+	14.8254i	−0.605658	+	0.508207i
$852$		0			0
$853$	−2.92855	+	1.06590i	−0.100272	+	0.0364959i	−0.391669	−	0.920106i	$-0.628102\pi$
$853$	−2.92855	+	1.06590i	−0.100272	+	0.0364959i	0.291397	+	0.956602i	$0.405880\pi$
$854$		0			0
$855$	−5.08512	+	18.5446i	−0.173908	+	0.634212i
$856$		0			0
$857$	−15.8062	+	5.75298i	−0.539929	+	0.196518i	−0.597566	−	0.801820i	$-0.703865\pi$
$857$	−15.8062	+	5.75298i	−0.539929	+	0.196518i	0.0576374	+	0.998338i	$0.481643\pi$
$858$		0			0
$859$	30.7708	−	25.8198i	1.04989	−	0.880960i	0.0568060	−	0.998385i	$-0.481908\pi$
$859$	30.7708	−	25.8198i	1.04989	−	0.880960i	0.993082	+	0.117425i	$0.0374639\pi$
$860$		0			0
$861$	0.0455973	+	0.258595i	0.00155395	+	0.00881290i
$862$		0			0
$863$	−0.743918	+	1.28850i	−0.0253233	+	0.0438612i	−0.878409	−	0.477909i	$-0.841395\pi$
$863$	−0.743918	+	1.28850i	−0.0253233	+	0.0438612i	0.853086	+	0.521770i	$0.174728\pi$
$864$		0			0
$865$	11.1591	+	4.06158i	0.379421	+	0.138098i
$866$		0			0
$867$	2.33868	+	4.05071i	0.0794257	+	0.137569i
$868$		0			0
$869$	2.11540	+	1.77503i	0.0717600	+	0.0602138i
$870$		0			0
$871$	−0.0218219	+	0.123758i	−0.000739406	+	0.00419338i
$872$		0			0
$873$	27.0574			0.915753
$874$		0			0
$875$	−3.58079			−0.121053
$876$		0			0
$877$	2.45899	−	13.9456i	0.0830341	−	0.470910i	−0.914729	−	0.404067i	$-0.867596\pi$
$877$	2.45899	−	13.9456i	0.0830341	−	0.470910i	0.997764	−	0.0668429i	$-0.0212926\pi$
$878$		0			0
$879$	−7.08899	−	5.94837i	−0.239106	−	0.200634i
$880$		0			0
$881$	−8.84998	−	15.3286i	−0.298164	−	0.516434i	0.677552	−	0.735475i	$-0.263041\pi$
$881$	−8.84998	−	15.3286i	−0.298164	−	0.516434i	−0.975716	+	0.219040i	$0.929707\pi$
$882$		0			0
$883$	15.4779	+	5.63349i	0.520872	+	0.189582i	0.589058	−	0.808091i	$-0.299499\pi$
$883$	15.4779	+	5.63349i	0.520872	+	0.189582i	−0.0681861	+	0.997673i	$0.521721\pi$
$884$		0			0
$885$	−3.03209	+	5.25173i	−0.101923	+	0.176535i
$886$		0			0
$887$	8.53503	+	48.4045i	0.286578	+	1.62527i	0.699593	+	0.714541i	$0.253364\pi$
$887$	8.53503	+	48.4045i	0.286578	+	1.62527i	−0.413015	+	0.910724i	$0.635524\pi$
$888$		0			0
$889$	2.32753	−	1.95303i	0.0780630	−	0.0655026i
$890$		0			0
$891$	2.27554	−	0.828229i	0.0762335	−	0.0277467i
$892$		0			0
$893$	−11.3674	−	24.7533i	−0.380394	−	0.828338i
$894$		0			0
$895$	22.7802	−	8.29131i	0.761458	−	0.277148i
$896$		0			0
$897$	0.262174	−	0.219990i	0.00875374	−	0.00734526i
$898$		0			0
$899$	−3.54891	−	20.1269i	−0.118363	−	0.671270i
$900$		0			0
$901$	−6.77244	+	11.7302i	−0.225623	+	0.390790i
$902$		0			0
$903$	−0.115867	−	0.0421721i	−0.00385581	−	0.00140340i
$904$		0			0
$905$	2.87346	+	4.97697i	0.0955169	+	0.165440i
$906$		0			0
$907$	19.6243	+	16.4668i	0.651615	+	0.546770i	0.907561	−	0.419921i	$-0.137942\pi$
$907$	19.6243	+	16.4668i	0.651615	+	0.546770i	−0.255946	+	0.966691i	$0.582387\pi$
$908$		0			0
$909$	−1.23783	+	7.02006i	−0.0410561	+	0.232841i
$910$		0			0
$911$	39.3809			1.30475			0.652375	−	0.757897i	$-0.273773\pi$
$911$	39.3809			1.30475			0.652375	+	0.757897i	$0.273773\pi$
$912$		0			0
$913$	−5.05819			−0.167402
$914$		0			0
$915$	−1.05097	+	5.96037i	−0.0347441	+	0.197044i
$916$		0			0
$917$	−2.43700	−	2.04489i	−0.0804770	−	0.0675282i
$918$		0			0
$919$	21.6061	+	37.4228i	0.712718	+	1.23446i	0.963833	+	0.266507i	$0.0858696\pi$
$919$	21.6061	+	37.4228i	0.712718	+	1.23446i	−0.251115	+	0.967957i	$0.580797\pi$
$920$		0			0
$921$	−0.724155	−	0.263571i	−0.0238617	−	0.00868496i
$922$		0			0
$923$	2.25150	−	3.89971i	0.0741089	−	0.128360i
$924$		0			0
$925$	3.74422	+	21.2345i	0.123109	+	0.698187i
$926$		0			0
$927$	36.9013	−	30.9638i	1.21200	−	1.01699i
$928$		0			0
$929$	−14.0664	+	5.11975i	−0.461504	+	0.167974i	−0.562300	−	0.826934i	$-0.690083\pi$
$929$	−14.0664	+	5.11975i	−0.461504	+	0.167974i	0.100796	+	0.994907i	$0.467861\pi$
$930$		0			0
$931$	29.1248	−	7.62219i	0.954528	−	0.249807i
$932$		0			0
$933$	5.12196	−	1.86424i	0.167685	−	0.0610325i
$934$		0			0
$935$	0.673648	−	0.565258i	0.0220307	−	0.0184859i
$936$		0			0
$937$	−9.05855	−	51.3736i	−0.295930	−	1.67830i	−0.663398	−	0.748266i	$-0.730886\pi$
$937$	−9.05855	−	51.3736i	−0.295930	−	1.67830i	0.367468	−	0.930036i	$-0.380225\pi$
$938$		0			0
$939$	−1.43242	+	2.48102i	−0.0467452	+	0.0809651i
$940$		0			0
$941$	6.61809	+	2.40879i	0.215744	+	0.0785242i	0.447631	−	0.894218i	$-0.352268\pi$
$941$	6.61809	+	2.40879i	0.215744	+	0.0785242i	−0.231887	+	0.972743i	$0.574490\pi$
$942$		0			0
$943$	−3.51233	−	6.08353i	−0.114377	−	0.198107i
$944$		0			0
$945$	−0.731896	−	0.614134i	−0.0238086	−	0.0199778i
$946$		0			0
$947$	−2.75726	+	15.6372i	−0.0895990	+	0.508141i	0.906670	+	0.421840i	$0.138616\pi$
$947$	−2.75726	+	15.6372i	−0.0895990	+	0.508141i	−0.996269	+	0.0863010i	$0.972495\pi$
$948$		0			0
$949$	2.08141			0.0675656
$950$		0			0
$951$	2.08141			0.0674945
$952$		0			0
$953$	1.35023	−	7.65755i	0.0437383	−	0.248052i	−0.955097	−	0.296292i	$-0.904250\pi$
$953$	1.35023	−	7.65755i	0.0437383	−	0.248052i	0.998836	+	0.0482394i	$0.0153610\pi$
$954$		0			0
$955$	−5.56212	−	4.66717i	−0.179986	−	0.151026i
$956$		0			0
$957$	0.186137	+	0.322398i	0.00601695	+	0.0104217i
$958$		0			0
$959$	5.30009	+	1.92907i	0.171149	+	0.0622930i
$960$		0			0
$961$	−1.45336	+	2.51730i	−0.0468827	+	0.0812032i
$962$		0			0
$963$	3.60607	+	20.4510i	0.116204	+	0.659025i
$964$		0			0
$965$	−11.6762	+	9.79747i	−0.375869	+	0.315392i
$966$		0			0
$967$	−44.6960	+	16.2680i	−1.43733	+	0.523144i	−0.939022	−	0.343858i	$-0.888266\pi$
$967$	−44.6960	+	16.2680i	−1.43733	+	0.523144i	−0.498305	+	0.867002i	$0.666044\pi$
$968$		0			0
$969$	1.64543	−	2.32099i	0.0528588	−	0.0745608i
$970$		0			0
$971$	5.41875	−	1.97226i	0.173896	−	0.0632929i	−0.253605	−	0.967308i	$-0.581616\pi$
$971$	5.41875	−	1.97226i	0.173896	−	0.0632929i	0.427501	+	0.904015i	$0.359394\pi$
$972$		0			0
$973$	3.98704	−	3.34553i	0.127819	−	0.107253i
$974$		0			0
$975$	−0.0555596	−	0.315094i	−0.00177933	−	0.0100911i
$976$		0			0
$977$	−9.78581	+	16.9495i	−0.313076	+	0.542263i	−0.979027	−	0.203733i	$-0.934693\pi$
$977$	−9.78581	+	16.9495i	−0.313076	+	0.542263i	0.665951	+	0.745996i	$0.268026\pi$
$978$		0			0
$979$	−0.299011	−	0.108831i	−0.00955642	−	0.00347825i
$980$		0			0
$981$	−9.31180	−	16.1285i	−0.297303	−	0.514944i
$982$		0			0
$983$	30.1668	+	25.3130i	0.962173	+	0.807359i	0.981305	−	0.192458i	$-0.0616460\pi$
$983$	30.1668	+	25.3130i	0.962173	+	0.807359i	−0.0191324	+	0.999817i	$0.506090\pi$
$984$		0			0
$985$	−3.65523	+	20.7298i	−0.116465	+	0.660508i
$986$		0			0
$987$	0.662809			0.0210974
$988$		0			0
$989$	3.29860			0.104889
$990$		0			0
$991$	5.59146	−	31.7108i	0.177619	−	1.00733i	−0.757459	−	0.652883i	$-0.773559\pi$
$991$	5.59146	−	31.7108i	0.177619	−	1.00733i	0.935078	−	0.354443i	$-0.115329\pi$
$992$		0			0
$993$	−1.31836	−	1.10624i	−0.0418370	−	0.0351054i
$994$		0			0
$995$	−11.6099	−	20.1090i	−0.368060	−	0.637498i
$996$		0			0
$997$	11.9491	+	4.34911i	0.378431	+	0.137738i	0.524230	−	0.851577i	$-0.324353\pi$
$997$	11.9491	+	4.34911i	0.378431	+	0.137738i	−0.145799	+	0.989314i	$0.546575\pi$
$998$		0			0
$999$	−8.29860	+	14.3736i	−0.262556	+	0.454760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.d.81.1		6
4.3	odd	2		152.2.q.a.81.1	✓	6
19.2	odd	18		5776.2.a.bm.1.2		3
19.4	even	9	inner	304.2.u.d.289.1		6
19.17	even	9		5776.2.a.bl.1.2		3
76.23	odd	18		152.2.q.a.137.1	yes	6
76.55	odd	18		2888.2.a.q.1.2		3
76.59	even	18		2888.2.a.p.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.a.81.1	✓	6	4.3	odd	2
152.2.q.a.137.1	yes	6	76.23	odd	18
304.2.u.d.81.1		6	1.1	even	1	trivial
304.2.u.d.289.1		6	19.4	even	9	inner
2888.2.a.p.1.2		3	76.59	even	18
2888.2.a.q.1.2		3	76.55	odd	18
5776.2.a.bl.1.2		3	19.17	even	9
5776.2.a.bm.1.2		3	19.2	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0603074 - 0.342020i) q^{3} +(1.17365 + 0.984808i) q^{5} +(-0.152704 - 0.264490i) q^{7} +(2.70574 + 0.984808i) q^{9} +(0.152704 - 0.264490i) q^{11} +(0.0603074 + 0.342020i) q^{13} +(0.407604 - 0.342020i) q^{15} +(1.76604 - 0.642788i) q^{17} +(3.06418 + 3.10013i) q^{19} +(-0.0996702 + 0.0362770i) q^{21} +(2.17365 - 1.82391i) q^{23} +(-0.460637 - 2.61240i) q^{25} +(1.02094 - 1.76833i) q^{27} +(-3.29813 - 1.20042i) q^{29} +(2.91147 + 5.04282i) q^{31} +(-0.0812519 - 0.0681784i) q^{33} +(0.0812519 - 0.460802i) q^{35} -8.12836 q^{37} +0.120615 q^{39} +(0.429892 - 2.43804i) q^{41} +(0.890530 + 0.747243i) q^{43} +(2.20574 + 3.82045i) q^{45} +(-5.87211 - 2.13727i) q^{47} +(3.45336 - 5.98140i) q^{49} +(-0.113341 - 0.642788i) q^{51} +(-5.52094 + 4.63262i) q^{53} +(0.439693 - 0.160035i) q^{55} +(1.24510 - 0.861050i) q^{57} +(-10.7096 + 3.89798i) q^{59} +(-8.71348 + 7.31148i) q^{61} +(-0.152704 - 0.866025i) q^{63} +(-0.266044 + 0.460802i) q^{65} +(0.340022 + 0.123758i) q^{67} +(-0.492726 - 0.853427i) q^{69} +(-9.93242 - 8.33429i) q^{71} +(1.04071 - 5.90214i) q^{73} -0.921274 q^{75} -0.0932736 q^{77} +(-1.57011 + 8.90452i) q^{79} +(6.07398 + 5.09667i) q^{81} +(-8.28106 - 14.3432i) q^{83} +(2.70574 + 0.984808i) q^{85} +(-0.609470 + 1.05563i) q^{87} +(-0.180922 - 1.02606i) q^{89} +(0.0812519 - 0.0681784i) q^{91} +(1.90033 - 0.691663i) q^{93} +(0.543233 + 6.65609i) q^{95} +(8.83022 - 3.21394i) q^{97} +(0.673648 - 0.565258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 6 q^{5} - 3 q^{7} + 6 q^{9} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 6 q^{17} - 15 q^{21} + 12 q^{23} + 6 q^{25} + 3 q^{27} - 6 q^{29} - 3 q^{31} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 12 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 6 * q^5 - 3 * q^7 + 6 * q^9 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 6 * q^17 - 15 * q^21 + 12 * q^23 + 6 * q^25 + 3 * q^27 - 6 * q^29 - 3 * q^31 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 12 * q^39 - 6 * q^41 - 12 * q^43 + 3 * q^45 - 6 * q^47 - 6 * q^49 + 6 * q^51 - 30 * q^53 - 3 * q^55 + 6 * q^57 - 30 * q^59 + 6 * q^61 - 3 * q^63 + 3 * q^65 - 18 * q^67 + 15 * q^69 - 36 * q^71 + 6 * q^73 + 12 * q^75 - 54 * q^77 - 18 * q^79 + 21 * q^81 - 15 * q^83 + 6 * q^85 - 21 * q^87 - 18 * q^89 + 3 * q^91 - 3 * q^93 - 12 * q^95 + 30 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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