LMFDB - Embedded newform 300.2.x.a.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			77.2
Character	$\chi$	$=$	300.77
Dual form			300.2.x.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50650 - 0.854667i) q^{3} +(-2.22337 + 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(1.53909 + 2.57511i) q^{9} +O(q^{10})$	\(q+(-1.50650 - 0.854667i) q^{3} +(-2.22337 + 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(1.53909 + 2.57511i) q^{9} +(-0.626305 - 0.862035i) q^{11} +(4.64256 - 0.735309i) q^{13} +(3.55289 + 1.54175i) q^{15} +(5.63490 + 2.87112i) q^{17} +(-2.86859 + 0.932063i) q^{19} +(-1.59299 - 5.77036i) q^{21} +(4.44376 + 0.703822i) q^{23} +(4.88675 - 1.05817i) q^{25} +(-0.117773 - 5.19482i) q^{27} +(-2.43550 + 7.49571i) q^{29} +(-0.586924 - 1.80637i) q^{31} +(0.206776 + 1.83394i) q^{33} +(-6.01516 - 4.85205i) q^{35} +(0.993131 + 6.27038i) q^{37} +(-7.62246 - 2.86010i) q^{39} +(-1.22959 + 1.69238i) q^{41} +(-8.27416 + 8.27416i) q^{43} +(-4.03475 - 5.35918i) q^{45} +(-4.80234 - 9.42512i) q^{47} +4.94490i q^{49} +(-6.03512 - 9.14131i) q^{51} +(9.25431 - 4.71531i) q^{53} +(1.59764 + 1.76758i) q^{55} +(5.11814 + 1.04754i) q^{57} +(3.79924 + 2.76031i) q^{59} +(2.42074 - 1.75877i) q^{61} +(-2.53190 + 10.0545i) q^{63} +(-10.1471 + 2.73963i) q^{65} +(2.94083 - 5.77171i) q^{67} +(-6.09299 - 4.85824i) q^{69} +(0.855266 + 0.277893i) q^{71} +(-0.277586 + 1.75261i) q^{73} +(-8.26627 - 2.58241i) q^{75} +(0.576091 - 3.63730i) q^{77} +(-8.30052 - 2.69700i) q^{79} +(-4.26241 + 7.92665i) q^{81} +(2.42816 - 4.76553i) q^{83} +(-13.2117 - 5.04266i) q^{85} +(10.0754 - 9.21074i) q^{87} +(-1.94640 + 1.41415i) q^{89} +(13.1428 + 9.54877i) q^{91} +(-0.659641 + 3.22292i) q^{93} +(6.15615 - 2.75494i) q^{95} +(-4.23366 + 2.15716i) q^{97} +(1.25590 - 2.93956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{20}\right)$

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
$3$	−1.50650	−	0.854667i	−0.869779	−	0.493442i
$3$	−1.50650	−	0.854667i	−0.869779	−	0.493442i
$4$		0			0
$5$	−2.22337	+	0.237965i	−0.994321	+	0.106421i
$5$	−2.22337	+	0.237965i	−0.994321	+	0.106421i
$6$		0			0
$7$	2.44386	+	2.44386i	0.923692	+	0.923692i	0.997288	−	0.0735960i	$-0.0234475\pi$
$7$	2.44386	+	2.44386i	0.923692	+	0.923692i	−0.0735960	+	0.997288i	$0.523448\pi$
$8$		0			0
$9$	1.53909	+	2.57511i	0.513029	+	0.858371i
$10$		0			0
$11$	−0.626305	−	0.862035i	−0.188838	−	0.259913i	0.704092	−	0.710109i	$-0.251354\pi$
$11$	−0.626305	−	0.862035i	−0.188838	−	0.259913i	−0.892930	+	0.450195i	$0.851354\pi$
$12$		0			0
$13$	4.64256	−	0.735309i	1.28761	−	0.203938i	0.525173	−	0.850996i	$-0.324001\pi$
$13$	4.64256	−	0.735309i	1.28761	−	0.203938i	0.762441	+	0.647058i	$0.224001\pi$
$14$		0			0
$15$	3.55289	+	1.54175i	0.917352	+	0.398077i
$16$		0			0
$17$	5.63490	+	2.87112i	1.36666	+	0.696350i	0.974676	−	0.223621i	$-0.0717877\pi$
$17$	5.63490	+	2.87112i	1.36666	+	0.696350i	0.391987	+	0.919971i	$0.371788\pi$
$18$		0			0
$19$	−2.86859	+	0.932063i	−0.658101	+	0.213830i	−0.618983	−	0.785405i	$-0.712455\pi$
$19$	−2.86859	+	0.932063i	−0.658101	+	0.213830i	−0.0391181	+	0.999235i	$0.512455\pi$
$20$		0			0
$21$	−1.59299	−	5.77036i	−0.347619	−	1.25920i
$22$		0			0
$23$	4.44376	+	0.703822i	0.926588	+	0.146757i	0.601451	−	0.798910i	$-0.294590\pi$
$23$	4.44376	+	0.703822i	0.926588	+	0.146757i	0.325137	+	0.945667i	$0.394590\pi$
$24$		0			0
$25$	4.88675	−	1.05817i	0.977349	−	0.211633i
$26$		0			0
$27$	−0.117773	−	5.19482i	−0.0226654	−	0.999743i
$28$		0			0
$29$	−2.43550	+	7.49571i	−0.452261	+	1.39192i	0.422059	+	0.906568i	$0.361307\pi$
$29$	−2.43550	+	7.49571i	−0.452261	+	1.39192i	−0.874320	+	0.485349i	$0.838693\pi$
$30$		0			0
$31$	−0.586924	−	1.80637i	−0.105415	−	0.324433i	0.884413	−	0.466705i	$-0.154559\pi$
$31$	−0.586924	−	1.80637i	−0.105415	−	0.324433i	−0.989828	+	0.142272i	$0.954559\pi$
$32$		0			0
$33$	0.206776	+	1.83394i	0.0359951	+	0.319248i
$34$		0			0
$35$	−6.01516	−	4.85205i	−1.01675	−	0.820146i
$36$		0			0
$37$	0.993131	+	6.27038i	0.163270	+	1.03084i	0.924172	+	0.381977i	$0.124757\pi$
$37$	0.993131	+	6.27038i	0.163270	+	1.03084i	−0.760902	+	0.648867i	$0.775243\pi$
$38$		0			0
$39$	−7.62246	−	2.86010i	−1.22057	−	0.457982i
$40$		0			0
$41$	−1.22959	+	1.69238i	−0.192029	+	0.264306i	−0.894165	−	0.447737i	$-0.852230\pi$
$41$	−1.22959	+	1.69238i	−0.192029	+	0.264306i	0.702136	+	0.712043i	$0.252230\pi$
$42$		0			0
$43$	−8.27416	+	8.27416i	−1.26180	+	1.26180i	−0.311576	+	0.950221i	$0.600857\pi$
$43$	−8.27416	+	8.27416i	−1.26180	+	1.26180i	−0.950221	+	0.311576i	$0.899143\pi$
$44$		0			0
$45$	−4.03475	−	5.35918i	−0.601465	−	0.798899i
$46$		0			0
$47$	−4.80234	−	9.42512i	−0.700493	−	1.37480i	−0.917148	−	0.398547i	$-0.869515\pi$
$47$	−4.80234	−	9.42512i	−0.700493	−	1.37480i	0.216655	−	0.976248i	$-0.430485\pi$
$48$		0			0
$49$			4.94490i			0.706414i
$50$		0			0
$51$	−6.03512	−	9.14131i	−0.845086	−	1.28004i
$52$		0			0
$53$	9.25431	−	4.71531i	1.27118	−	0.647697i	0.317423	−	0.948284i	$-0.397183\pi$
$53$	9.25431	−	4.71531i	1.27118	−	0.647697i	0.953754	+	0.300587i	$0.0971825\pi$
$54$		0			0
$55$	1.59764	+	1.76758i	0.215426	+	0.238341i
$56$		0			0
$57$	5.11814	+	1.04754i	0.677915	+	0.138750i
$58$		0			0
$59$	3.79924	+	2.76031i	0.494619	+	0.359362i	0.806958	−	0.590609i	$-0.201112\pi$
$59$	3.79924	+	2.76031i	0.494619	+	0.359362i	−0.312339	+	0.949971i	$0.601112\pi$
$60$		0			0
$61$	2.42074	−	1.75877i	0.309944	−	0.225188i	−0.421928	−	0.906629i	$-0.638647\pi$
$61$	2.42074	−	1.75877i	0.309944	−	0.225188i	0.731873	+	0.681441i	$0.238647\pi$
$62$		0			0
$63$	−2.53190	+	10.0545i	−0.318989	+	1.26675i
$64$		0			0
$65$	−10.1471	+	2.73963i	−1.25860	+	0.339809i
$66$		0			0
$67$	2.94083	−	5.77171i	0.359280	−	0.705126i	−0.638646	−	0.769501i	$-0.720505\pi$
$67$	2.94083	−	5.77171i	0.359280	−	0.705126i	0.997926	+	0.0643744i	$0.0205052\pi$
$68$		0			0
$69$	−6.09299	−	4.85824i	−0.733510	−	0.584864i
$70$		0			0
$71$	0.855266	+	0.277893i	0.101501	+	0.0329798i	0.359327	−	0.933212i	$-0.383006\pi$
$71$	0.855266	+	0.277893i	0.101501	+	0.0329798i	−0.257826	+	0.966191i	$0.583006\pi$
$72$		0			0
$73$	−0.277586	+	1.75261i	−0.0324890	+	0.205127i	−0.998593	−	0.0530251i	$-0.983114\pi$
$73$	−0.277586	+	1.75261i	−0.0324890	+	0.205127i	0.966104	+	0.258152i	$0.0831137\pi$
$74$		0			0
$75$	−8.26627	−	2.58241i	−0.954506	−	0.298191i
$76$		0			0
$77$	0.576091	−	3.63730i	0.0656517	−	0.414508i
$78$		0			0
$79$	−8.30052	−	2.69700i	−0.933882	−	0.303437i	−0.197733	−	0.980256i	$-0.563358\pi$
$79$	−8.30052	−	2.69700i	−0.933882	−	0.303437i	−0.736149	+	0.676819i	$0.763358\pi$
$80$		0			0
$81$	−4.26241	+	7.92665i	−0.473602	+	0.880739i
$82$		0			0
$83$	2.42816	−	4.76553i	0.266525	−	0.523085i	−0.718493	−	0.695534i	$-0.755168\pi$
$83$	2.42816	−	4.76553i	0.266525	−	0.523085i	0.985018	+	0.172449i	$0.0551679\pi$
$84$		0			0
$85$	−13.2117	−	5.04266i	−1.43301	−	0.546954i
$86$		0			0
$87$	10.0754	−	9.21074i	1.08020	−	0.987495i
$88$		0			0
$89$	−1.94640	+	1.41415i	−0.206318	+	0.149899i	−0.686146	−	0.727463i	$-0.740699\pi$
$89$	−1.94640	+	1.41415i	−0.206318	+	0.149899i	0.479828	+	0.877363i	$0.340699\pi$
$90$		0			0
$91$	13.1428	+	9.54877i	1.37773	+	1.00098i
$92$		0			0
$93$	−0.659641	+	3.22292i	−0.0684016	+	0.334201i
$94$		0			0
$95$	6.15615	−	2.75494i	0.631607	−	0.282651i
$96$		0			0
$97$	−4.23366	+	2.15716i	−0.429864	+	0.219026i	−0.655516	−	0.755182i	$-0.727549\pi$
$97$	−4.23366	+	2.15716i	−0.429864	+	0.219026i	0.225652	+	0.974208i	$0.427549\pi$
$98$		0			0
$99$	1.25590	−	2.93956i	0.126223	−	0.295436i
$100$		0			0
$101$		−	19.4515i		−	1.93550i	−0.251916	−	0.967749i	$-0.581061\pi$
$101$		−	19.4515i		−	1.93550i	0.251916	−	0.967749i	$-0.418939\pi$
$102$		0			0
$103$	2.61006	+	5.12254i	0.257177	+	0.504738i	0.983107	−	0.183030i	$-0.0585905\pi$
$103$	2.61006	+	5.12254i	0.257177	+	0.504738i	−0.725930	+	0.687768i	$0.758591\pi$
$104$		0			0
$105$	4.91495	+	12.4506i	0.479650	+	1.21505i
$106$		0			0
$107$	−7.71479	+	7.71479i	−0.745817	+	0.745817i	−0.973691	−	0.227874i	$-0.926823\pi$
$107$	−7.71479	+	7.71479i	−0.745817	+	0.745817i	0.227874	+	0.973691i	$0.426823\pi$
$108$		0			0
$109$	6.10072	−	8.39692i	0.584343	−	0.804279i	−0.409820	−	0.912166i	$-0.634409\pi$
$109$	6.10072	−	8.39692i	0.584343	−	0.804279i	0.994163	+	0.107887i	$0.0344086\pi$
$110$		0			0
$111$	3.86294	−	10.2951i	0.366654	−	0.977171i
$112$		0			0
$113$	0.703338	+	4.44070i	0.0661645	+	0.417746i	0.998432	+	0.0559766i	$0.0178272\pi$
$113$	0.703338	+	4.44070i	0.0661645	+	0.417746i	−0.932268	+	0.361769i	$0.882173\pi$
$114$		0			0
$115$	−10.0476	−	0.507399i	−0.936944	−	0.0473152i
$116$		0			0
$117$	9.03881	+	10.8234i	0.835638	+	1.00062i
$118$		0			0
$119$	6.75428	+	20.7875i	0.619163	+	1.90559i
$120$		0			0
$121$	3.04834	−	9.38183i	0.277122	−	0.852893i
$122$		0			0
$123$	3.29880	−	1.49869i	0.297443	−	0.135132i
$124$		0			0
$125$	−10.6132	+	3.51557i	−0.949277	+	0.314442i
$126$		0			0
$127$	9.50331	+	1.50518i	0.843283	+	0.133563i	0.563105	−	0.826385i	$-0.309607\pi$
$127$	9.50331	+	1.50518i	0.843283	+	0.133563i	0.280178	+	0.959948i	$0.409607\pi$
$128$		0			0
$129$	19.5367	−	5.39337i	1.72011	−	0.474860i
$130$		0			0
$131$	15.2113	−	4.94246i	1.32902	−	0.431825i	0.443436	−	0.896306i	$-0.353759\pi$
$131$	15.2113	−	4.94246i	1.32902	−	0.431825i	0.885583	+	0.464481i	$0.153759\pi$
$132$		0			0
$133$	−9.28827	−	4.73261i	−0.805395	−	0.410369i
$134$		0			0
$135$	1.49804	+	11.5220i	0.128930	+	0.991654i
$136$		0			0
$137$	−7.60492	+	1.20450i	−0.649732	+	0.102907i	−0.472596	−	0.881279i	$-0.656683\pi$
$137$	−7.60492	+	1.20450i	−0.649732	+	0.102907i	−0.177136	+	0.984186i	$0.556683\pi$
$138$		0			0
$139$	5.03690	+	6.93270i	0.427224	+	0.588024i	0.967313	−	0.253584i	$-0.0816094\pi$
$139$	5.03690	+	6.93270i	0.427224	+	0.588024i	−0.540089	+	0.841608i	$0.681609\pi$
$140$		0			0
$141$	−0.820614	+	18.3034i	−0.0691082	+	1.54142i
$142$		0			0
$143$	−3.54152	−	3.54152i	−0.296157	−	0.296157i
$144$		0			0
$145$	3.63131	−	17.2453i	0.301564	−	1.43214i
$146$		0			0
$147$	4.22624	−	7.44949i	0.348575	−	0.614424i
$148$		0			0
$149$	−5.42628			−0.444538			−0.222269	−	0.974985i	$-0.571346\pi$
$149$	−5.42628			−0.444538			−0.222269	+	0.974985i	$0.571346\pi$
$150$		0			0
$151$	−15.4523			−1.25749			−0.628745	−	0.777611i	$-0.716431\pi$
$151$	−15.4523			−1.25749			−0.628745	+	0.777611i	$0.716431\pi$
$152$		0			0
$153$	1.27914	+	18.9294i	0.103412	+	1.53035i
$154$		0			0
$155$	1.73480	+	3.87656i	0.139343	+	0.311372i
$156$		0			0
$157$	−5.46444	−	5.46444i	−0.436110	−	0.436110i	0.454591	−	0.890700i	$-0.349786\pi$
$157$	−5.46444	−	5.46444i	−0.436110	−	0.436110i	−0.890700	+	0.454591i	$0.849786\pi$
$158$		0			0
$159$	−17.9716	−	0.805743i	−1.42524	−	0.0638995i
$160$		0			0
$161$	9.13988	+	12.5800i	0.720324	+	0.991440i
$162$		0			0
$163$	12.1195	−	1.91953i	0.949270	−	0.150350i	0.337447	−	0.941344i	$-0.390437\pi$
$163$	12.1195	−	1.91953i	0.949270	−	0.150350i	0.611823	+	0.790995i	$0.290437\pi$
$164$		0			0
$165$	−0.896152	−	4.02832i	−0.0697654	−	0.313604i
$166$		0			0
$167$	−8.67164	−	4.41842i	−0.671032	−	0.341908i	0.0850576	−	0.996376i	$-0.472893\pi$
$167$	−8.67164	−	4.41842i	−0.671032	−	0.341908i	−0.756090	+	0.654468i	$0.772893\pi$
$168$		0			0
$169$	8.64893	−	2.81021i	0.665302	−	0.216170i
$170$		0			0
$171$	−6.81519	−	5.95243i	−0.521170	−	0.455194i
$172$		0			0
$173$	16.7643	+	2.65520i	1.27456	+	0.201871i	0.756797	−	0.653650i	$-0.226763\pi$
$173$	16.7643	+	2.65520i	1.27456	+	0.201871i	0.517767	+	0.855522i	$0.326763\pi$
$174$		0			0
$175$	14.5285	+	9.35651i	1.09825	+	0.707286i
$176$		0			0
$177$	−3.36441	−	7.40550i	−0.252885	−	0.556631i
$178$		0			0
$179$	−3.51696	+	10.8241i	−0.262870	+	0.809031i	0.729306	+	0.684187i	$0.239843\pi$
$179$	−3.51696	+	10.8241i	−0.262870	+	0.809031i	−0.992176	+	0.124843i	$0.960157\pi$
$180$		0			0
$181$	0.864359	+	2.66022i	0.0642473	+	0.197733i	0.978027	−	0.208476i	$-0.0668504\pi$
$181$	0.864359	+	2.66022i	0.0642473	+	0.197733i	−0.913780	+	0.406209i	$0.866850\pi$
$182$		0			0
$183$	−5.15002	+	0.580663i	−0.380700	+	0.0429238i
$184$		0			0
$185$	−3.70023	−	13.7050i	−0.272046	−	1.00762i
$186$		0			0
$187$	−1.05416	−	6.65568i	−0.0770875	−	0.486712i
$188$		0			0
$189$	12.4076	−	12.9832i	0.902519	−	0.944391i
$190$		0			0
$191$	−7.23129	+	9.95302i	−0.523238	+	0.720175i	−0.986081	−	0.166265i	$-0.946829\pi$
$191$	−7.23129	+	9.95302i	−0.523238	+	0.720175i	0.462843	+	0.886440i	$0.346829\pi$
$192$		0			0
$193$	−2.46367	+	2.46367i	−0.177339	+	0.177339i	−0.790195	−	0.612856i	$-0.790021\pi$
$193$	−2.46367	+	2.46367i	−0.177339	+	0.177339i	0.612856	+	0.790195i	$0.290021\pi$
$194$		0			0
$195$	17.6281	+	4.54518i	1.26238	+	0.325487i
$196$		0			0
$197$	4.60438	+	9.03661i	0.328049	+	0.643832i	0.994845	−	0.101408i	$-0.0323349\pi$
$197$	4.60438	+	9.03661i	0.328049	+	0.643832i	−0.666796	+	0.745240i	$0.732335\pi$
$198$		0			0
$199$		−	13.8104i		−	0.978994i	−0.872005	−	0.489497i	$-0.837180\pi$
$199$		−	13.8104i		−	0.978994i	0.872005	−	0.489497i	$-0.162820\pi$
$200$		0			0
$201$	−9.36325	+	6.18165i	−0.660433	+	0.436020i
$202$		0			0
$203$	−24.2705	+	12.3664i	−1.70345	+	0.867953i
$204$		0			0
$205$	2.33110	−	4.05539i	0.162811	−	0.283241i
$206$		0			0
$207$	5.02692	+	12.5264i	0.349395	+	0.870647i
$208$		0			0
$209$	2.60009	+	1.88907i	0.179852	+	0.130670i
$210$		0			0
$211$	−4.04500	+	2.93886i	−0.278469	+	0.202320i	−0.718249	−	0.695786i	$-0.755056\pi$
$211$	−4.04500	+	2.93886i	−0.278469	+	0.202320i	0.439780	+	0.898105i	$0.355056\pi$
$212$		0			0
$213$	−1.05095	−	1.14961i	−0.0720101	−	0.0787702i
$214$		0			0
$215$	16.4276	−	20.3655i	1.12035	−	1.38891i
$216$		0			0
$217$	2.98015	−	5.84887i	0.202306	−	0.397047i
$218$		0			0
$219$	1.91608	−	2.40306i	0.129477	−	0.162384i
$220$		0			0
$221$	28.2715	+	9.18597i	1.90175	+	0.617915i
$222$		0			0
$223$	2.86335	−	18.0785i	0.191744	−	1.21063i	−0.684592	−	0.728926i	$-0.740020\pi$
$223$	2.86335	−	18.0785i	0.191744	−	1.21063i	0.876337	−	0.481699i	$-0.159980\pi$
$224$		0			0
$225$	10.2460	+	10.9553i	0.683069	+	0.730354i
$226$		0			0
$227$	0.316481	−	1.99819i	0.0210056	−	0.132624i	−0.974957	−	0.222394i	$-0.928613\pi$
$227$	0.316481	−	1.99819i	0.0210056	−	0.132624i	0.995963	+	0.0897694i	$0.0286130\pi$
$228$		0			0
$229$	−25.7555	−	8.36847i	−1.70197	−	0.553004i	−0.713007	−	0.701157i	$-0.752667\pi$
$229$	−25.7555	−	8.36847i	−1.70197	−	0.553004i	−0.988965	+	0.148153i	$0.952667\pi$
$230$		0			0
$231$	−3.97656	+	4.98722i	−0.261638	+	0.328135i
$232$		0			0
$233$	13.3461	−	26.1931i	0.874329	−	1.71597i	0.196838	−	0.980436i	$-0.436933\pi$
$233$	13.3461	−	26.1931i	0.874329	−	1.71597i	0.677491	−	0.735531i	$-0.263067\pi$
$234$		0			0
$235$	12.9202	+	19.8127i	0.842822	+	1.29244i
$236$		0			0
$237$	10.1997	+	11.1572i	0.662542	+	0.724740i
$238$		0			0
$239$	−3.18910	+	2.31702i	−0.206286	+	0.149875i	−0.686132	−	0.727477i	$-0.740693\pi$
$239$	−3.18910	+	2.31702i	−0.206286	+	0.149875i	0.479846	+	0.877353i	$0.340693\pi$
$240$		0			0
$241$	−8.48908	−	6.16768i	−0.546830	−	0.397295i	0.279786	−	0.960063i	$-0.409737\pi$
$241$	−8.48908	−	6.16768i	−0.546830	−	0.397295i	−0.826615	+	0.562768i	$0.809737\pi$
$242$		0			0
$243$	13.1960	−	8.29856i	0.846523	−	0.532353i
$244$		0			0
$245$	−1.17671	−	10.9943i	−0.0751774	−	0.702403i
$246$		0			0
$247$	−12.6323	+	6.43646i	−0.803772	+	0.409542i
$248$		0			0
$249$	−7.73097	+	5.10401i	−0.489930	+	0.323453i
$250$		0			0
$251$		−	1.17570i		−	0.0742098i	−0.999311	−	0.0371049i	$-0.988186\pi$
$251$		−	1.17570i		−	0.0742098i	0.999311	−	0.0371049i	$-0.0118136\pi$
$252$		0			0
$253$	−2.17643	−	4.27149i	−0.136831	−	0.268546i
$254$		0			0
$255$	15.5936	+	18.8884i	0.976510	+	1.18284i
$256$		0			0
$257$	−18.9675	+	18.9675i	−1.18316	+	1.18316i	−0.204237	+	0.978921i	$0.565471\pi$
$257$	−18.9675	+	18.9675i	−1.18316	+	1.18316i	−0.978921	+	0.204237i	$0.934529\pi$
$258$		0			0
$259$	−12.8969	+	17.7510i	−0.801372	+	1.10299i
$260$		0			0
$261$	−23.0507	+	5.26486i	−1.42681	+	0.325887i
$262$		0			0
$263$	−3.31659	−	20.9401i	−0.204510	−	1.29122i	−0.849726	−	0.527224i	$-0.823233\pi$
$263$	−3.31659	−	20.9401i	−0.204510	−	1.29122i	0.645216	−	0.764000i	$-0.276767\pi$
$264$		0			0
$265$	−19.4537	+	12.6861i	−1.19503	+	0.779299i
$266$		0			0
$267$	4.14088	−	0.466883i	0.253418	−	0.0285728i
$268$		0			0
$269$	−6.34707	−	19.5343i	−0.386988	−	1.19103i	−0.935028	−	0.354574i	$-0.884626\pi$
$269$	−6.34707	−	19.5343i	−0.386988	−	1.19103i	0.548040	−	0.836452i	$-0.315374\pi$
$270$		0			0
$271$	8.54780	−	26.3074i	0.519242	−	1.59806i	−0.256187	−	0.966627i	$-0.582466\pi$
$271$	8.54780	−	26.3074i	0.519242	−	1.59806i	0.775429	−	0.631435i	$-0.217534\pi$
$272$		0			0
$273$	−11.6385	−	25.6179i	−0.704397	−	1.55047i
$274$		0			0
$275$	−3.97277	−	3.54981i	−0.239567	−	0.214062i
$276$		0			0
$277$	−17.2867	−	2.73795i	−1.03866	−	0.164507i	−0.386265	−	0.922388i	$-0.626235\pi$
$277$	−17.2867	−	2.73795i	−1.03866	−	0.164507i	−0.652393	+	0.757880i	$0.726235\pi$
$278$		0			0
$279$	3.74827	−	4.29156i	0.224403	−	0.256929i
$280$		0			0
$281$	−22.5521	+	7.32761i	−1.34534	+	0.437129i	−0.891123	−	0.453761i	$-0.850082\pi$
$281$	−22.5521	+	7.32761i	−1.34534	+	0.437129i	−0.454220	+	0.890890i	$0.650082\pi$
$282$		0			0
$283$	−22.7567	−	11.5951i	−1.35275	−	0.689258i	−0.380843	−	0.924640i	$-0.624366\pi$
$283$	−22.7567	−	11.5951i	−1.35275	−	0.689258i	−0.971903	+	0.235382i	$0.924366\pi$
$284$		0			0
$285$	−11.6288	−	1.11113i	−0.688831	−	0.0658178i
$286$		0			0
$287$	−7.14088	+	1.13100i	−0.421513	+	0.0667611i
$288$		0			0
$289$	13.5164	+	18.6037i	0.795081	+	1.09433i
$290$		0			0
$291$	8.22167	+	0.368611i	0.481963	+	0.0216084i
$292$		0			0
$293$	−14.6342	−	14.6342i	−0.854941	−	0.854941i	0.135796	−	0.990737i	$-0.456641\pi$
$293$	−14.6342	−	14.6342i	−0.854941	−	0.854941i	−0.990737	+	0.135796i	$0.956641\pi$
$294$		0			0
$295$	−9.10398	−	5.23311i	−0.530054	−	0.304683i
$296$		0			0
$297$	−4.40435	+	3.35507i	−0.255567	+	0.194681i
$298$		0			0
$299$	21.1479			1.22302
$300$		0			0
$301$	−40.4418			−2.33102
$302$		0			0
$303$	−16.6246	+	29.3037i	−0.955057	+	1.68345i
$304$		0			0
$305$	−4.96368	+	4.48645i	−0.284219	+	0.256894i
$306$		0			0
$307$	−0.692742	−	0.692742i	−0.0395369	−	0.0395369i	0.687062	−	0.726599i	$-0.258900\pi$
$307$	−0.692742	−	0.692742i	−0.0395369	−	0.0395369i	−0.726599	+	0.687062i	$0.758900\pi$
$308$		0			0
$309$	0.446002	−	9.94784i	0.0253722	−	0.565913i
$310$		0			0
$311$	8.16369	+	11.2364i	0.462920	+	0.637155i	0.975111	−	0.221716i	$-0.0711659\pi$
$311$	8.16369	+	11.2364i	0.462920	+	0.637155i	−0.512191	+	0.858872i	$0.671166\pi$
$312$		0			0
$313$	24.8253	−	3.93194i	1.40321	−	0.222246i	0.591498	−	0.806306i	$-0.298537\pi$
$313$	24.8253	−	3.93194i	1.40321	−	0.222246i	0.811711	+	0.584060i	$0.198537\pi$
$314$		0			0
$315$	3.23672	−	22.9574i	0.182369	−	1.29351i
$316$		0			0
$317$	−0.679335	−	0.346138i	−0.0381552	−	0.0194411i	0.434809	−	0.900523i	$-0.356816\pi$
$317$	−0.679335	−	0.346138i	−0.0381552	−	0.0194411i	−0.472964	+	0.881082i	$0.656816\pi$
$318$		0			0
$319$	7.98693	−	2.59511i	0.447182	−	0.145298i
$320$		0			0
$321$	18.2159	−	5.02876i	1.01671	−	0.280678i
$322$		0			0
$323$	−18.8403	−	2.98401i	−1.04830	−	0.166035i
$324$		0			0
$325$	21.9089	−	8.50587i	1.21529	−	0.471821i
$326$		0			0
$327$	−16.3673	+	7.43588i	−0.905114	+	0.411205i
$328$		0			0
$329$	11.2974	−	34.7699i	0.622848	−	1.91693i
$330$		0			0
$331$	10.5348	+	32.4227i	0.579043	+	1.78211i	0.621979	+	0.783034i	$0.286329\pi$
$331$	10.5348	+	32.4227i	0.579043	+	1.78211i	−0.0429352	+	0.999078i	$0.513671\pi$
$332$		0			0
$333$	−14.6184	+	12.2081i	−0.801085	+	0.668999i
$334$		0			0
$335$	−5.16509	+	13.5325i	−0.282199	+	0.739357i
$336$		0			0
$337$	1.01297	+	6.39561i	0.0551797	+	0.348391i	0.999796	+	0.0202133i	$0.00643454\pi$
$337$	1.01297	+	6.39561i	0.0551797	+	0.348391i	−0.944616	+	0.328178i	$0.893565\pi$
$338$		0			0
$339$	2.73574	−	7.29104i	0.148585	−	0.395995i
$340$		0			0
$341$	−1.18956	+	1.63729i	−0.0644182	+	0.0886641i
$342$		0			0
$343$	5.02238	−	5.02238i	0.271183	−	0.271183i
$344$		0			0
$345$	14.7031	+	9.35176i	0.791587	+	0.503482i
$346$		0			0
$347$	1.98524	+	3.89625i	0.106573	+	0.209162i	0.938134	−	0.346272i	$-0.112552\pi$
$347$	1.98524	+	3.89625i	0.106573	+	0.209162i	−0.831561	+	0.555433i	$0.812552\pi$
$348$		0			0
$349$		−	1.78658i		−	0.0956333i	−0.998856	−	0.0478167i	$-0.984774\pi$
$349$		−	1.78658i		−	0.0956333i	0.998856	−	0.0478167i	$-0.0152263\pi$
$350$		0			0
$351$	−4.36656	−	24.0306i	−0.233070	−	1.28266i
$352$		0			0
$353$	21.0739	−	10.7377i	1.12165	−	0.571511i	0.208050	−	0.978118i	$-0.433288\pi$
$353$	21.0739	−	10.7377i	1.12165	−	0.571511i	0.913603	+	0.406607i	$0.133288\pi$
$354$		0			0
$355$	−1.96770	−	0.414335i	−0.104435	−	0.0219906i
$356$		0			0
$357$	7.59109	−	37.0891i	0.401763	−	1.96296i
$358$		0			0
$359$	0.704752	+	0.512032i	0.0371954	+	0.0270240i	0.606228	−	0.795291i	$-0.292682\pi$
$359$	0.704752	+	0.512032i	0.0371954	+	0.0270240i	−0.569032	+	0.822315i	$0.692682\pi$
$360$		0			0
$361$	−8.01123	+	5.82050i	−0.421644	+	0.306342i
$362$		0			0
$363$	−12.6107	+	11.5284i	−0.661888	+	0.605085i
$364$		0			0
$365$	0.200117	−	3.96275i	0.0104746	−	0.207420i
$366$		0			0
$367$	−4.22786	+	8.29765i	−0.220693	+	0.433134i	−0.974633	−	0.223809i	$-0.928151\pi$
$367$	−4.22786	+	8.29765i	−0.220693	+	0.433134i	0.753940	+	0.656943i	$0.228151\pi$
$368$		0			0
$369$	−6.25052	−	0.561602i	−0.325389	−	0.0292358i
$370$		0			0
$371$	34.1398	+	11.0927i	1.77245	+	0.575904i
$372$		0			0
$373$	−1.84063	+	11.6213i	−0.0953042	+	0.601727i	0.893097	+	0.449864i	$0.148527\pi$
$373$	−1.84063	+	11.6213i	−0.0953042	+	0.601727i	−0.988401	+	0.151864i	$0.951473\pi$
$374$		0			0
$375$	18.9935	+	3.77458i	0.980819	+	0.194918i
$376$		0			0
$377$	−5.79530	+	36.5901i	−0.298473	+	1.88449i
$378$		0			0
$379$	33.6144	+	10.9220i	1.72666	+	0.561024i	0.992960	−	0.118453i	$-0.0377936\pi$
$379$	33.6144	+	10.9220i	1.72666	+	0.561024i	0.733696	+	0.679478i	$0.237794\pi$
$380$		0			0
$381$	−13.0303	−	10.3897i	−0.667564	−	0.532281i
$382$		0			0
$383$	−0.430527	+	0.844956i	−0.0219989	+	0.0431753i	−0.901744	−	0.432270i	$-0.857713\pi$
$383$	−0.430527	+	0.844956i	−0.0219989	+	0.0431753i	0.879746	+	0.475445i	$0.157713\pi$
$384$		0			0
$385$	−0.415315	+	8.22414i	−0.0211664	+	0.419141i
$386$		0			0
$387$	−34.0415	−	8.57223i	−1.73043	−	0.435751i
$388$		0			0
$389$	−11.4768	+	8.33838i	−0.581897	+	0.422773i	−0.839407	−	0.543503i	$-0.817098\pi$
$389$	−11.4768	+	8.33838i	−0.581897	+	0.422773i	0.257511	+	0.966275i	$0.417098\pi$
$390$		0			0
$391$	23.0194	+	16.7246i	1.16414	+	0.845797i
$392$		0			0
$393$	−27.1400	−	5.55480i	−1.36903	−	0.280203i
$394$		0			0
$395$	19.0969	+	4.02120i	0.960871	+	0.202329i
$396$		0			0
$397$	15.5654	−	7.93097i	0.781205	−	0.398044i	−0.0174386	−	0.999848i	$-0.505551\pi$
$397$	15.5654	−	7.93097i	0.781205	−	0.398044i	0.798644	+	0.601804i	$0.205551\pi$
$398$		0			0
$399$	9.94798	+	15.0681i	0.498022	+	0.754347i
$400$		0			0
$401$			25.5008i			1.27345i	0.771092	+	0.636724i	$0.219711\pi$
$401$			25.5008i			1.27345i	−0.771092	+	0.636724i	$0.780289\pi$
$402$		0			0
$403$	−4.05307	−	7.95459i	−0.201898	−	0.396247i
$404$		0			0
$405$	7.59066	−	18.6382i	0.377183	−	0.926139i
$406$		0			0
$407$	4.78329	−	4.78329i	0.237099	−	0.237099i
$408$		0			0
$409$	14.7468	−	20.2972i	0.729183	−	1.00363i	−0.269985	−	0.962864i	$-0.587019\pi$
$409$	14.7468	−	20.2972i	0.729183	−	1.00363i	0.999169	−	0.0407700i	$-0.0129811\pi$
$410$		0			0
$411$	12.4863	+	4.68509i	0.615902	+	0.231099i
$412$		0			0
$413$	2.53900	+	16.0306i	0.124936	+	0.788816i
$414$		0			0
$415$	−4.26467	+	11.1734i	−0.209344	+	0.548478i
$416$		0			0
$417$	−1.66294	−	14.7490i	−0.0814347	−	0.722261i
$418$		0			0
$419$	−0.988493	−	3.04227i	−0.0482910	−	0.148625i	0.924003	−	0.382385i	$-0.124897\pi$
$419$	−0.988493	−	3.04227i	−0.0482910	−	0.148625i	−0.972294	+	0.233760i	$0.924897\pi$
$420$		0			0
$421$	5.67396	−	17.4626i	0.276532	−	0.851077i	−0.712278	−	0.701897i	$-0.752337\pi$
$421$	5.67396	−	17.4626i	0.276532	−	0.851077i	0.988810	−	0.149180i	$-0.0476634\pi$
$422$		0			0
$423$	16.8795	−	26.8727i	0.820711	−	1.30659i
$424$		0			0
$425$	30.5744	+	8.06779i	1.48308	+	0.391345i
$426$		0			0
$427$	10.2141	+	1.61776i	0.494297	+	0.0782890i
$428$		0			0
$429$	2.30848	+	8.36212i	0.111455	+	0.403727i
$430$		0			0
$431$	−1.65426	+	0.537501i	−0.0796828	+	0.0258905i	−0.348587	−	0.937276i	$-0.613338\pi$
$431$	−1.65426	+	0.537501i	−0.0796828	+	0.0258905i	0.268904	+	0.963167i	$0.413338\pi$
$432$		0			0
$433$	23.5980	+	12.0238i	1.13405	+	0.577825i	0.917218	−	0.398385i	$-0.130429\pi$
$433$	23.5980	+	12.0238i	1.13405	+	0.577825i	0.216827	+	0.976210i	$0.430429\pi$
$434$		0			0
$435$	−20.2095	+	22.8765i	−0.968974	+	1.09684i
$436$		0			0
$437$	−13.4034	+	2.12288i	−0.641169	+	0.101551i
$438$		0			0
$439$	−5.66588	−	7.79842i	−0.270418	−	0.372198i	0.652113	−	0.758122i	$-0.273883\pi$
$439$	−5.66588	−	7.79842i	−0.270418	−	0.372198i	−0.922531	+	0.385924i	$0.873883\pi$
$440$		0			0
$441$	−12.7337	+	7.61064i	−0.606366	+	0.362411i
$442$		0			0
$443$	2.72820	+	2.72820i	0.129621	+	0.129621i	0.768941	−	0.639320i	$-0.220784\pi$
$443$	2.72820	+	2.72820i	0.129621	+	0.129621i	−0.639320	+	0.768941i	$0.720784\pi$
$444$		0			0
$445$	3.99106	−	3.60734i	0.189194	−	0.171004i
$446$		0			0
$447$	8.17469	+	4.63766i	0.386650	+	0.219354i
$448$		0			0
$449$	−21.4808			−1.01374			−0.506870	−	0.862022i	$-0.669198\pi$
$449$	−21.4808			−1.01374			−0.506870	+	0.862022i	$0.669198\pi$
$450$		0			0
$451$	2.22899			0.104959
$452$		0			0
$453$	23.2789	+	13.2066i	1.09374	+	0.620499i
$454$		0			0
$455$	−31.4935	−	18.1029i	−1.47644	−	0.848678i
$456$		0			0
$457$	−4.66772	−	4.66772i	−0.218347	−	0.218347i	0.589455	−	0.807801i	$-0.299343\pi$
$457$	−4.66772	−	4.66772i	−0.218347	−	0.218347i	−0.807801	+	0.589455i	$0.799343\pi$
$458$		0			0
$459$	14.2513	−	29.6104i	0.665195	−	1.38210i
$460$		0			0
$461$	−8.79509	−	12.1054i	−0.409628	−	0.563805i	0.553499	−	0.832850i	$-0.313292\pi$
$461$	−8.79509	−	12.1054i	−0.409628	−	0.563805i	−0.963128	+	0.269045i	$0.913292\pi$
$462$		0			0
$463$	25.9007	−	4.10227i	1.20371	−	0.190648i	0.477817	−	0.878459i	$-0.341428\pi$
$463$	25.9007	−	4.10227i	1.20371	−	0.190648i	0.725890	+	0.687811i	$0.241428\pi$
$464$		0			0
$465$	0.699685	−	7.32271i	0.0324471	−	0.339583i
$466$		0			0
$467$	−15.6353	−	7.96659i	−0.723516	−	0.368650i	0.0531298	−	0.998588i	$-0.483080\pi$
$467$	−15.6353	−	7.96659i	−0.723516	−	0.368650i	−0.776645	+	0.629938i	$0.783080\pi$
$468$		0			0
$469$	21.2922	−	6.91826i	0.983184	−	0.319456i
$470$		0			0
$471$	3.56190	+	12.9025i	0.164124	+	0.594514i
$472$		0			0
$473$	12.3148	+	1.95047i	0.566233	+	0.0896825i
$474$		0			0
$475$	−13.0318	+	7.59021i	−0.597941	+	0.348263i
$476$		0			0
$477$	26.3857	+	16.5736i	1.20812	+	0.758854i
$478$		0			0
$479$	−4.12695	+	12.7015i	−0.188565	+	0.580345i	−0.999992	−	0.00411038i	$-0.998692\pi$
$479$	−4.12695	+	12.7015i	−0.188565	+	0.580345i	0.811426	+	0.584455i	$0.198692\pi$
$480$		0			0
$481$	9.22133	+	28.3804i	0.420457	+	1.29403i
$482$		0			0
$483$	−3.01755	−	26.7633i	−0.137303	−	1.21777i
$484$		0			0
$485$	8.89967	−	5.80363i	0.404113	−	0.263529i
$486$		0			0
$487$	−3.73244	−	23.5657i	−0.169133	−	1.06786i	−0.915497	−	0.402325i	$-0.868202\pi$
$487$	−3.73244	−	23.5657i	−0.169133	−	1.06786i	0.746364	−	0.665538i	$-0.231798\pi$
$488$		0			0
$489$	−19.8985	−	7.46633i	−0.899843	−	0.337639i
$490$		0			0
$491$	2.44616	−	3.36685i	0.110393	−	0.151944i	−0.750245	−	0.661160i	$-0.770065\pi$
$491$	2.44616	−	3.36685i	0.110393	−	0.151944i	0.860639	+	0.509216i	$0.170065\pi$
$492$		0			0
$493$	−35.2449	+	35.2449i	−1.58735	+	1.58735i
$494$		0			0
$495$	−2.09282	+	6.83458i	−0.0940652	+	0.307191i
$496$		0			0
$497$	1.41102	+	2.76928i	0.0632928	+	0.124219i
$498$		0			0
$499$		−	3.23858i		−	0.144979i	−0.997369	−	0.0724894i	$-0.976906\pi$
$499$		−	3.23858i		−	0.144979i	0.997369	−	0.0724894i	$-0.0230943\pi$
$500$		0			0
$501$	9.28755	+	14.0677i	0.414937	+	0.628500i
$502$		0			0
$503$	−16.4890	+	8.40155i	−0.735207	+	0.374607i	−0.781155	−	0.624337i	$-0.785369\pi$
$503$	−16.4890	+	8.40155i	−0.735207	+	0.374607i	0.0459478	+	0.998944i	$0.485369\pi$
$504$		0			0
$505$	4.62878	+	43.2479i	0.205978	+	1.92451i
$506$		0			0
$507$	−15.4314	−	3.15838i	−0.685333	−	0.140268i
$508$		0			0
$509$	5.30145	+	3.85173i	0.234982	+	0.170725i	0.699045	−	0.715078i	$-0.253609\pi$
$509$	5.30145	+	3.85173i	0.234982	+	0.170725i	−0.464063	+	0.885802i	$0.653609\pi$
$510$		0			0
$511$	−4.96151	+	3.60475i	−0.219484	+	0.159465i
$512$		0			0
$513$	5.17974	+	14.7921i	0.228691	+	0.653085i
$514$		0			0
$515$	−7.02212	−	10.7682i	−0.309431	−	0.474503i
$516$		0			0
$517$	−5.11706	+	10.0428i	−0.225048	+	0.441681i
$518$		0			0
$519$	−22.9861	−	18.3279i	−1.00898	−	0.804507i
$520$		0			0
$521$	−5.03678	−	1.63655i	−0.220666	−	0.0716986i	0.196598	−	0.980484i	$-0.437011\pi$
$521$	−5.03678	−	1.63655i	−0.220666	−	0.0716986i	−0.417263	+	0.908786i	$0.637011\pi$
$522$		0			0
$523$	−3.33523	+	21.0578i	−0.145839	+	0.920794i	0.800901	+	0.598797i	$0.204354\pi$
$523$	−3.33523	+	21.0578i	−0.145839	+	0.920794i	−0.946741	+	0.321997i	$0.895646\pi$
$524$		0			0
$525$	−13.8905	−	26.5126i	−0.606233	−	1.15711i
$526$		0			0
$527$	1.87905	−	11.8638i	0.0818525	−	0.516797i
$528$		0			0
$529$	−2.62266	−	0.852155i	−0.114029	−	0.0370502i
$530$		0			0
$531$	−1.26074	+	14.0318i	−0.0547117	+	0.608930i
$532$		0			0
$533$	−4.46401	+	8.76111i	−0.193358	+	0.379486i
$534$		0			0
$535$	15.3170	−	18.9887i	0.662211	−	0.820952i
$536$		0			0
$537$	14.5493	−	13.3007i	0.627849	−	0.573966i
$538$		0			0
$539$	4.26268	−	3.09702i	0.183607	−	0.133398i
$540$		0			0
$541$	23.2705	+	16.9070i	1.00048	+	0.726890i	0.962191	−	0.272376i	$-0.0878096\pi$
$541$	23.2705	+	16.9070i	1.00048	+	0.726890i	0.0382880	+	0.999267i	$0.487810\pi$
$542$		0			0
$543$	0.971449	−	4.74637i	0.0416888	−	0.203686i
$544$		0			0
$545$	−11.5660	+	20.1212i	−0.495432	+	0.861898i
$546$		0			0
$547$	20.6603	−	10.5270i	0.883372	−	0.450100i	0.0474020	−	0.998876i	$-0.484906\pi$
$547$	20.6603	−	10.5270i	0.883372	−	0.450100i	0.835970	+	0.548776i	$0.184906\pi$
$548$		0			0
$549$	8.25477	+	3.52678i	0.352305	+	0.150519i
$550$		0			0
$551$		−	23.7722i		−	1.01273i
$552$		0			0
$553$	−13.6942	−	26.8764i	−0.582337	−	1.14290i
$554$		0			0
$555$	−6.13886	+	23.8091i	−0.260580	+	1.01064i
$556$		0			0
$557$	29.9868	−	29.9868i	1.27058	−	1.27058i	0.324797	−	0.945784i	$-0.394704\pi$
$557$	29.9868	−	29.9868i	1.27058	−	1.27058i	0.945784	−	0.324797i	$-0.105296\pi$
$558$		0			0
$559$	−32.3292	+	44.4973i	−1.36738	+	1.88204i
$560$		0			0
$561$	−4.10030	+	10.9277i	−0.173115	+	0.461370i
$562$		0			0
$563$	5.14467	+	32.4822i	0.216822	+	1.36896i	0.820461	+	0.571702i	$0.193717\pi$
$563$	5.14467	+	32.4822i	0.216822	+	1.36896i	−0.603639	+	0.797258i	$0.706283\pi$
$564$		0			0
$565$	−2.62051	−	9.70595i	−0.110246	−	0.408332i
$566$		0			0
$567$	−29.7884	+	8.95488i	−1.25099	+	0.376070i
$568$		0			0
$569$	−4.11085	−	12.6519i	−0.172336	−	0.530395i	0.827166	−	0.561958i	$-0.189952\pi$
$569$	−4.11085	−	12.6519i	−0.172336	−	0.530395i	−0.999502	+	0.0315628i	$0.989952\pi$
$570$		0			0
$571$	3.97739	−	12.2411i	0.166449	−	0.512276i	−0.832692	−	0.553737i	$-0.813201\pi$
$571$	3.97739	−	12.2411i	0.166449	−	0.512276i	0.999140	+	0.0414611i	$0.0132013\pi$
$572$		0			0
$573$	19.4005	−	8.81389i	0.810466	−	0.368205i
$574$		0			0
$575$	22.4603	−	1.26284i	0.936659	−	0.0526641i
$576$		0			0
$577$	8.34723	+	1.32207i	0.347500	+	0.0550386i	0.327745	−	0.944766i	$-0.393711\pi$
$577$	8.34723	+	1.32207i	0.347500	+	0.0550386i	0.0197550	+	0.999805i	$0.493711\pi$
$578$		0			0
$579$	5.81714	−	1.60590i	0.241752	−	0.0667390i
$580$		0			0
$581$	17.5804	−	5.71221i	0.729357	−	0.236982i
$582$		0			0
$583$	−9.86078	−	5.02432i	−0.408392	−	0.208086i
$584$		0			0
$585$	−22.6722	−	21.9135i	−0.937380	−	0.906012i
$586$		0			0
$587$	22.1842	−	3.51364i	0.915641	−	0.145023i	0.319207	−	0.947685i	$-0.396584\pi$
$587$	22.1842	−	3.51364i	0.915641	−	0.145023i	0.596434	+	0.802662i	$0.296584\pi$
$588$		0			0
$589$	3.36730	+	4.63469i	0.138747	+	0.190969i
$590$		0			0
$591$	0.786788	−	17.5489i	0.0323641	−	0.721864i
$592$		0			0
$593$	−12.6961	−	12.6961i	−0.521368	−	0.521368i	0.396616	−	0.917984i	$-0.370184\pi$
$593$	−12.6961	−	12.6961i	−0.521368	−	0.521368i	−0.917984	+	0.396616i	$0.870184\pi$
$594$		0			0
$595$	−19.9639	−	44.6111i	−0.818442	−	1.82888i
$596$		0			0
$597$	−11.8033	+	20.8054i	−0.483077	+	0.851508i
$598$		0			0
$599$	20.3237			0.830405			0.415202	−	0.909729i	$-0.363711\pi$
$599$	20.3237			0.830405			0.415202	+	0.909729i	$0.363711\pi$
$600$		0			0
$601$	−19.3802			−0.790537			−0.395268	−	0.918566i	$-0.629348\pi$
$601$	−19.3802			−0.790537			−0.395268	+	0.918566i	$0.629348\pi$
$602$		0			0
$603$	19.3890	−	1.31019i	0.789581	−	0.0533552i
$604$		0			0
$605$	−4.54504	+	21.5847i	−0.184782	+	0.877542i
$606$		0			0
$607$	−4.21561	−	4.21561i	−0.171106	−	0.171106i	0.616359	−	0.787465i	$-0.288607\pi$
$607$	−4.21561	−	4.21561i	−0.171106	−	0.171106i	−0.787465	+	0.616359i	$0.788607\pi$
$608$		0			0
$609$	47.1327	+	2.11315i	1.90991	+	0.0856292i
$610$		0			0
$611$	−29.2255	−	40.2255i	−1.18234	−	1.62735i
$612$		0			0
$613$	26.2327	−	4.15485i	1.05953	−	0.167813i	0.397736	−	0.917500i	$-0.369796\pi$
$613$	26.2327	−	4.15485i	1.05953	−	0.167813i	0.661793	+	0.749687i	$0.269796\pi$
$614$		0			0
$615$	−6.97781	+	4.11713i	−0.281372	+	0.166019i
$616$		0			0
$617$	−21.7016	−	11.0575i	−0.873673	−	0.445159i	−0.0411527	−	0.999153i	$-0.513103\pi$
$617$	−21.7016	−	11.0575i	−0.873673	−	0.445159i	−0.832521	+	0.553994i	$0.813103\pi$
$618$		0			0
$619$	−1.60460	+	0.521366i	−0.0644943	+	0.0209555i	−0.341086	−	0.940032i	$-0.610795\pi$
$619$	−1.60460	+	0.521366i	−0.0644943	+	0.0209555i	0.276592	+	0.960987i	$0.410795\pi$
$620$		0			0
$621$	3.13287	−	23.1674i	0.125718	−	0.929676i
$622$		0			0
$623$	−8.21271	−	1.30077i	−0.329035	−	0.0521141i
$624$		0			0
$625$	22.7606	−	10.3420i	0.910423	−	0.413679i
$626$		0			0
$627$	−2.30250	−	5.06810i	−0.0919531	−	0.202400i
$628$		0			0
$629$	−12.4069	+	38.1844i	−0.494694	+	1.52251i
$630$		0			0
$631$	−12.4398	−	38.2857i	−0.495219	−	1.52413i	−0.816615	−	0.577183i	$-0.804152\pi$
$631$	−12.4398	−	38.2857i	−0.495219	−	1.52413i	0.321395	−	0.946945i	$-0.395848\pi$
$632$		0			0
$633$	8.60554	−	0.970272i	0.342040	−	0.0385649i
$634$		0			0
$635$	−21.4876	−	1.08511i	−0.852708	−	0.0430613i
$636$		0			0
$637$	3.63603	+	22.9570i	0.144065	+	0.909589i
$638$		0			0
$639$	0.600724	+	2.63011i	0.0237643	+	0.104045i
$640$		0			0
$641$	2.73450	−	3.76371i	0.108006	−	0.148658i	−0.751592	−	0.659628i	$-0.770714\pi$
$641$	2.73450	−	3.76371i	0.108006	−	0.148658i	0.859598	+	0.510970i	$0.170714\pi$
$642$		0			0
$643$	−23.9228	+	23.9228i	−0.943425	+	0.943425i	−0.998483	−	0.0550581i	$-0.982466\pi$
$643$	−23.9228	+	23.9228i	−0.943425	+	0.943425i	0.0550581	+	0.998483i	$0.482466\pi$
$644$		0			0
$645$	−42.1538	+	16.6405i	−1.65980	+	0.655219i
$646$		0			0
$647$	7.38947	+	14.5027i	0.290510	+	0.570158i	0.989425	−	0.145047i	$-0.0463333\pi$
$647$	7.38947	+	14.5027i	0.290510	+	0.570158i	−0.698915	+	0.715205i	$0.746333\pi$
$648$		0			0
$649$		−	5.00388i		−	0.196419i
$650$		0			0
$651$	−9.48843	+	6.26429i	−0.371881	+	0.245517i
$652$		0			0
$653$	−5.02081	+	2.55823i	−0.196479	+	0.100111i	−0.549462	−	0.835519i	$-0.685167\pi$
$653$	−5.02081	+	2.55823i	−0.196479	+	0.100111i	0.352983	+	0.935630i	$0.385167\pi$
$654$		0			0
$655$	−32.6443	+	14.6087i	−1.27552	+	0.570808i
$656$		0			0
$657$	−4.94039	+	1.98260i	−0.192743	+	0.0773487i
$658$		0			0
$659$	−13.2174	−	9.60298i	−0.514875	−	0.374079i	0.299794	−	0.954004i	$-0.403082\pi$
$659$	−13.2174	−	9.60298i	−0.514875	−	0.374079i	−0.814670	+	0.579925i	$0.803082\pi$
$660$		0			0
$661$	31.5545	−	22.9257i	1.22733	−	0.891706i	0.230641	−	0.973039i	$-0.425918\pi$
$661$	31.5545	−	22.9257i	1.22733	−	0.891706i	0.996687	+	0.0813326i	$0.0259176\pi$
$662$		0			0
$663$	−34.7401	−	38.0014i	−1.34919	−	1.47585i
$664$		0			0
$665$	21.7775	+	8.31206i	0.844494	+	0.322328i
$666$		0			0
$667$	−16.0984	+	31.5950i	−0.623334	+	1.22336i
$668$		0			0
$669$	−19.7647	+	24.7880i	−0.764149	+	0.958361i
$670$		0			0
$671$	−3.03225	−	0.985237i	−0.117059	−	0.0380347i
$672$		0			0
$673$	−2.05812	+	12.9944i	−0.0793346	+	0.500899i	0.915740	+	0.401771i	$0.131605\pi$
$673$	−2.05812	+	12.9944i	−0.0793346	+	0.500899i	−0.995075	+	0.0991277i	$0.968395\pi$
$674$		0			0
$675$	−6.07251	−	25.2611i	−0.233731	−	0.972301i
$676$		0			0
$677$	−1.37035	+	8.65208i	−0.0526670	+	0.332526i	0.947260	+	0.320465i	$0.103839\pi$
$677$	−1.37035	+	8.65208i	−0.0526670	+	0.332526i	−0.999927	+	0.0120611i	$0.996161\pi$
$678$		0			0
$679$	−15.6183	−	5.07469i	−0.599375	−	0.194749i
$680$		0			0
$681$	−2.18456	+	2.73978i	−0.0837126	+	0.104989i
$682$		0			0
$683$	−0.144185	+	0.282980i	−0.00551710	+	0.0108279i	−0.893749	−	0.448568i	$-0.851934\pi$
$683$	−0.144185	+	0.282980i	−0.00551710	+	0.0108279i	0.888232	+	0.459396i	$0.151934\pi$
$684$		0			0
$685$	16.6219	−	4.48775i	0.635091	−	0.171468i
$686$		0			0
$687$	31.6484	+	34.6195i	1.20746	+	1.32082i
$688$		0			0
$689$	39.4965	−	28.6959i	1.50470	−	1.09323i
$690$		0			0
$691$	−24.5745	−	17.8544i	−0.934857	−	0.679214i	0.0123200	−	0.999924i	$-0.496078\pi$
$691$	−24.5745	−	17.8544i	−0.934857	−	0.679214i	−0.947177	+	0.320711i	$0.896078\pi$
$692$		0			0
$693$	10.2531	−	4.11462i	0.389483	−	0.156301i
$694$		0			0
$695$	−12.8486	−	14.2154i	−0.487376	−	0.539219i
$696$		0			0
$697$	−11.7876	+	6.00610i	−0.446489	+	0.227497i
$698$		0			0
$699$	−42.4922	+	28.0535i	−1.60720	+	1.06108i
$700$		0			0
$701$		−	35.6884i		−	1.34793i	−0.738763	−	0.673965i	$-0.764590\pi$
$701$		−	35.6884i		−	1.34793i	0.738763	−	0.673965i	$-0.235410\pi$
$702$		0			0
$703$	−8.69328	−	17.0615i	−0.327873	−	0.643488i
$704$		0			0
$705$	−2.53102	−	40.8904i	−0.0953238	−	1.54002i
$706$		0			0
$707$	47.5368	−	47.5368i	1.78780	−	1.78780i
$708$		0			0
$709$	−16.4858	+	22.6908i	−0.619137	+	0.852169i	−0.997290	−	0.0735741i	$-0.976559\pi$
$709$	−16.4858	+	22.6908i	−0.619137	+	0.852169i	0.378153	+	0.925743i	$0.376559\pi$
$710$		0			0
$711$	−5.83015	−	25.5257i	−0.218648	−	0.957289i
$712$		0			0
$713$	−1.33679	−	8.44015i	−0.0500631	−	0.316086i
$714$		0			0
$715$	8.71687	+	7.03135i	0.325992	+	0.262958i
$716$		0			0
$717$	6.78466	−	0.764969i	0.253378	−	0.0285683i
$718$		0			0
$719$	15.8013	+	48.6313i	0.589288	+	1.81364i	0.581324	+	0.813672i	$0.302535\pi$
$719$	15.8013	+	48.6313i	0.589288	+	1.81364i	0.00796379	+	0.999968i	$0.497465\pi$
$720$		0			0
$721$	−6.14013	+	18.8974i	−0.228670	+	0.703775i
$722$		0			0
$723$	7.51749	+	16.5469i	0.279579	+	0.615388i
$724$		0			0
$725$	−3.96997	+	39.2068i	−0.147441	+	1.45610i
$726$		0			0
$727$	−28.2055	−	4.46731i	−1.04608	−	0.165684i	−0.390343	−	0.920669i	$-0.627644\pi$
$727$	−28.2055	−	4.46731i	−1.04608	−	0.165684i	−0.655741	+	0.754986i	$0.727644\pi$
$728$		0			0
$729$	−26.9723	+	1.22362i	−0.998973	+	0.0453191i
$730$		0			0
$731$	−70.3802	+	22.8679i	−2.60310	+	0.845800i
$732$		0			0
$733$	−9.46545	−	4.82289i	−0.349615	−	0.178138i	0.270360	−	0.962759i	$-0.412857\pi$
$733$	−9.46545	−	4.82289i	−0.349615	−	0.178138i	−0.619975	+	0.784622i	$0.712857\pi$
$734$		0			0
$735$	−7.62378	+	17.5687i	−0.281208	+	0.648030i
$736$		0			0
$737$	−6.81727	+	1.07975i	−0.251117	+	0.0397731i
$738$		0			0
$739$	−22.5311	−	31.0114i	−0.828820	−	1.14077i	−0.988141	−	0.153547i	$-0.950930\pi$
$739$	−22.5311	−	31.0114i	−0.828820	−	1.14077i	0.159321	−	0.987227i	$-0.449070\pi$
$740$		0			0
$741$	24.5315	+	1.09985i	0.901189	+	0.0404040i
$742$		0			0
$743$	21.5734	+	21.5734i	0.791451	+	0.791451i	0.981730	−	0.190279i	$-0.0609394\pi$
$743$	21.5734	+	21.5734i	0.791451	+	0.791451i	−0.190279	+	0.981730i	$0.560939\pi$
$744$		0			0
$745$	12.0646	−	1.29126i	0.442014	−	0.0473082i
$746$		0			0
$747$	16.0089	−	1.08179i	0.585736	−	0.0395805i
$748$		0			0
$749$	−37.7077			−1.37781
$750$		0			0
$751$	18.5240			0.675951			0.337975	−	0.941155i	$-0.390258\pi$
$751$	18.5240			0.675951			0.337975	+	0.941155i	$0.390258\pi$
$752$		0			0
$753$	−1.00484	+	1.77120i	−0.0366182	+	0.0645461i
$754$		0			0
$755$	34.3562	−	3.67710i	1.25035	−	0.133824i
$756$		0			0
$757$	26.4091	+	26.4091i	0.959855	+	0.959855i	0.999225	−	0.0393695i	$-0.0125349\pi$
$757$	26.4091	+	26.4091i	0.959855	+	0.959855i	−0.0393695	+	0.999225i	$0.512535\pi$
$758$		0			0
$759$	−0.371904	+	8.29512i	−0.0134993	+	0.301094i
$760$		0			0
$761$	−6.87014	−	9.45593i	−0.249042	−	0.342777i	0.666133	−	0.745833i	$-0.267948\pi$
$761$	−6.87014	−	9.45593i	−0.249042	−	0.342777i	−0.915176	+	0.403055i	$0.867948\pi$
$762$		0			0
$763$	35.4302	−	5.61159i	1.28266	−	0.203153i
$764$		0			0
$765$	−7.34853	−	41.7827i	−0.265686	−	1.51066i
$766$		0			0
$767$	19.6679	+	10.0213i	0.710166	+	0.361848i
$768$		0			0
$769$	−27.7100	+	9.00353i	−0.999249	+	0.324676i	−0.762565	−	0.646911i	$-0.776060\pi$
$769$	−27.7100	+	9.00353i	−0.999249	+	0.324676i	−0.236683	+	0.971587i	$0.576060\pi$
$770$		0			0
$771$	44.7854	−	12.3636i	1.61291	−	0.445266i
$772$		0			0
$773$	31.5458	+	4.99637i	1.13462	+	0.179707i	0.695368	−	0.718654i	$-0.255242\pi$
$773$	31.5458	+	4.99637i	1.13462	+	0.179707i	0.439257	+	0.898361i	$0.355242\pi$
$774$		0			0
$775$	−4.77959	−	8.20619i	−0.171688	−	0.294775i
$776$		0			0
$777$	34.6003	−	15.7194i	1.24128	−	0.563930i
$778$		0			0
$779$	1.94978	−	6.00081i	0.0698582	−	0.215001i
$780$		0			0
$781$	−0.296104	−	0.911315i	−0.0105954	−	0.0326094i
$782$		0			0
$783$	39.2257	+	11.7692i	1.40181	+	0.420597i
$784$		0			0
$785$	13.4498	+	10.8491i	0.480044	+	0.387222i
$786$		0			0
$787$	0.919135	+	5.80319i	0.0327636	+	0.206861i	0.998640	−	0.0521437i	$-0.0166054\pi$
$787$	0.919135	+	5.80319i	0.0327636	+	0.206861i	−0.965876	+	0.259005i	$0.916605\pi$
$788$		0			0
$789$	−12.9004	+	34.3809i	−0.459266	+	1.22399i
$790$		0			0
$791$	−9.13359	+	12.5713i	−0.324753	+	0.446984i
$792$		0			0
$793$	9.94520	−	9.94520i	0.353164	−	0.353164i
$794$		0			0
$795$	40.1493	−	2.48515i	1.42395	−	0.0881393i
$796$		0			0
$797$	−16.5621	−	32.5049i	−0.586658	−	1.15138i	−0.973383	−	0.229187i	$-0.926393\pi$
$797$	−16.5621	−	32.5049i	−0.586658	−	1.15138i	0.386724	−	0.922196i	$-0.373607\pi$
$798$		0			0
$799$		−	66.8977i		−	2.36667i
$800$		0			0
$801$	−6.63727	−	2.83572i	−0.234516	−	0.100195i
$802$		0			0
$803$	1.68466	−	0.858379i	0.0594505	−	0.0302915i
$804$		0			0
$805$	−23.3149	−	25.7950i	−0.821743	−	0.909153i
$806$		0			0
$807$	−7.13344	+	34.8530i	−0.251109	+	1.22688i
$808$		0			0
$809$	−9.33253	−	6.78048i	−0.328114	−	0.238389i	0.411516	−	0.911403i	$-0.364999\pi$
$809$	−9.33253	−	6.78048i	−0.328114	−	0.238389i	−0.739630	+	0.673014i	$0.764999\pi$
$810$		0			0
$811$	−31.9194	+	23.1908i	−1.12084	+	0.814339i	−0.984336	−	0.176300i	$-0.943587\pi$
$811$	−31.9194	+	23.1908i	−1.12084	+	0.814339i	−0.136505	+	0.990639i	$0.543587\pi$
$812$		0			0
$813$	−35.3613	+	32.3266i	−1.24018	+	1.13374i
$814$		0			0
$815$	−26.4893	+	7.15184i	−0.927879	+	0.250518i
$816$		0			0
$817$	16.0232	−	31.4472i	0.560580	−	1.10020i
$818$		0			0
$819$	−4.36130	+	48.5405i	−0.152396	+	1.69614i
$820$		0			0
$821$	−37.1920	−	12.0844i	−1.29801	−	0.421749i	−0.423121	−	0.906073i	$-0.639066\pi$
$821$	−37.1920	−	12.0844i	−1.29801	−	0.421749i	−0.874889	+	0.484324i	$0.839066\pi$
$822$		0			0
$823$	1.55960	−	9.84694i	0.0543643	−	0.343243i	−0.945481	−	0.325676i	$-0.894408\pi$
$823$	1.55960	−	9.84694i	0.0543643	−	0.343243i	0.999846	−	0.0175667i	$-0.00559193\pi$
$824$		0			0
$825$	2.95108	+	8.74319i	0.102743	+	0.304399i
$826$		0			0
$827$	6.65765	−	42.0348i	0.231509	−	1.46169i	−0.548619	−	0.836072i	$-0.684846\pi$
$827$	6.65765	−	42.0348i	0.231509	−	1.46169i	0.780128	−	0.625620i	$-0.215154\pi$
$828$		0			0
$829$	−24.5774	−	7.98569i	−0.853610	−	0.277355i	−0.150652	−	0.988587i	$-0.548137\pi$
$829$	−24.5774	−	7.98569i	−0.853610	−	0.277355i	−0.702957	+	0.711232i	$0.748137\pi$
$830$		0			0
$831$	23.7024	+	18.8991i	0.822228	+	0.655603i
$832$		0			0
$833$	−14.1974	+	27.8640i	−0.491911	+	0.965431i
$834$		0			0
$835$	20.3317	+	7.76024i	0.703607	+	0.268554i
$836$		0			0
$837$	−9.31463	+	3.26171i	−0.321961	+	0.112741i
$838$		0			0
$839$	−1.53562	+	1.11569i	−0.0530154	+	0.0385180i	−0.613977	−	0.789324i	$-0.710431\pi$
$839$	−1.53562	+	1.11569i	−0.0530154	+	0.0385180i	0.560962	+	0.827842i	$0.310431\pi$
$840$		0			0
$841$	−26.7924	−	19.4658i	−0.923877	−	0.671236i
$842$		0			0
$843$	40.2374	+	8.23546i	1.38585	+	0.283644i
$844$		0			0
$845$	−18.5610	+	8.30627i	−0.638519	+	0.285744i
$846$		0			0
$847$	30.3776	−	15.4782i	1.04379	−	0.531836i
$848$		0			0
$849$	24.3730	+	36.9175i	0.836480	+	1.26700i
$850$		0			0
$851$			28.5631i			0.979129i
$852$		0			0
$853$	−1.47079	−	2.88659i	−0.0503589	−	0.0988348i	0.864456	−	0.502709i	$-0.167663\pi$
$853$	−1.47079	−	2.88659i	−0.0503589	−	0.0988348i	−0.914814	+	0.403874i	$0.867663\pi$
$854$		0			0
$855$	16.5691	+	11.6127i	0.566653	+	0.397145i
$856$		0			0
$857$	−8.33034	+	8.33034i	−0.284559	+	0.284559i	−0.834924	−	0.550365i	$-0.814489\pi$
$857$	−8.33034	+	8.33034i	−0.284559	+	0.284559i	0.550365	+	0.834924i	$0.314489\pi$
$858$		0			0
$859$	−6.01185	+	8.27460i	−0.205122	+	0.282326i	−0.899167	−	0.437605i	$-0.855827\pi$
$859$	−6.01185	+	8.27460i	−0.205122	+	0.282326i	0.694045	+	0.719931i	$0.255827\pi$
$860$		0			0
$861$	11.7244	+	4.39922i	0.399566	+	0.149925i
$862$		0			0
$863$	−0.387244	−	2.44496i	−0.0131819	−	0.0832274i	0.980220	−	0.197909i	$-0.0634151\pi$
$863$	−0.387244	−	2.44496i	−0.0131819	−	0.0832274i	−0.993402	+	0.114682i	$0.963415\pi$
$864$		0			0
$865$	−37.9050	−	1.91418i	−1.28881	−	0.0650842i
$866$		0			0
$867$	−4.46246	−	39.5785i	−0.151553	−	1.34416i
$868$		0			0
$869$	2.87375	+	8.84449i	0.0974853	+	0.300029i
$870$		0			0
$871$	9.40899	−	28.9579i	0.318812	−	0.981201i
$872$		0			0
$873$	−12.0709	−	7.58211i	−0.408539	−	0.256615i
$874$		0			0
$875$	−34.5288	−	17.3457i	−1.16729	−	0.586392i
$876$		0			0
$877$	25.9412	+	4.10868i	0.875972	+	0.138740i	0.578198	−	0.815896i	$-0.303756\pi$
$877$	25.9412	+	4.10868i	0.875972	+	0.138740i	0.297774	+	0.954637i	$0.403756\pi$
$878$		0			0
$879$	9.53909	+	34.5539i	0.321745	+	1.16547i
$880$		0			0
$881$	10.1224	−	3.28897i	0.341033	−	0.110808i	−0.133493	−	0.991050i	$-0.542619\pi$
$881$	10.1224	−	3.28897i	0.341033	−	0.110808i	0.474526	+	0.880241i	$0.342619\pi$
$882$		0			0
$883$	−18.4301	−	9.39060i	−0.620222	−	0.316019i	0.115495	−	0.993308i	$-0.463155\pi$
$883$	−18.4301	−	9.39060i	−0.620222	−	0.316019i	−0.735717	+	0.677289i	$0.763155\pi$
$884$		0			0
$885$	9.24259	+	15.6646i	0.310686	+	0.526558i
$886$		0			0
$887$	46.5615	−	7.37461i	1.56338	−	0.247615i	0.686070	−	0.727536i	$-0.259335\pi$
$887$	46.5615	−	7.37461i	1.56338	−	0.247615i	0.877312	+	0.479921i	$0.159335\pi$
$888$		0			0
$889$	19.5463	+	26.9032i	0.655563	+	0.902304i
$890$		0			0
$891$	9.50263	−	1.29015i	0.318350	−	0.0432217i
$892$		0			0
$893$	22.5608	+	22.5608i	0.754967	+	0.754967i
$894$		0			0
$895$	5.24375	−	24.9029i	0.175279	−	0.832411i
$896$		0			0
$897$	−31.8594	−	18.0744i	−1.06375	−	0.603488i
$898$		0			0
$899$	14.9695			0.499259
$900$		0			0
$901$	65.6853			2.18830
$902$		0			0
$903$	60.9255	+	34.5642i	2.02747	+	1.15023i
$904$		0			0
$905$	−2.55483	−	5.70898i	−0.0849254	−	0.189773i
$906$		0			0
$907$	20.5525	+	20.5525i	0.682436	+	0.682436i	0.960548	−	0.278113i	$-0.0897089\pi$
$907$	20.5525	+	20.5525i	0.682436	+	0.682436i	−0.278113	+	0.960548i	$0.589709\pi$
$908$		0			0
$909$	50.0899	−	29.9376i	1.66138	−	0.992968i
$910$		0			0
$911$	23.4595	+	32.2893i	0.777249	+	1.06979i	0.995580	+	0.0939170i	$0.0299388\pi$
$911$	23.4595	+	32.2893i	0.777249	+	1.06979i	−0.218331	+	0.975875i	$0.570061\pi$
$912$		0			0
$913$	−5.62882	+	0.891518i	−0.186287	+	0.0295049i
$914$		0			0
$915$	11.3122	−	2.51655i	0.373970	−	0.0831946i
$916$		0			0
$917$	49.2530	+	25.0957i	1.62648	+	0.828732i
$918$		0			0
$919$	36.5522	−	11.8765i	1.20574	−	0.391770i	0.363873	−	0.931448i	$-0.381454\pi$
$919$	36.5522	−	11.8765i	1.20574	−	0.391770i	0.841871	+	0.539678i	$0.181454\pi$
$920$		0			0
$921$	0.451553	+	1.63568i	0.0148792	+	0.0538975i
$922$		0			0
$923$	4.17496	+	0.661248i	0.137420	+	0.0217652i
$924$		0			0
$925$	11.4883	+	29.5909i	0.377733	+	0.972942i
$926$		0			0
$927$	−9.17399	+	14.6052i	−0.301313	+	0.479699i
$928$		0			0
$929$	13.4033	−	41.2512i	0.439749	−	1.35341i	−0.448391	−	0.893837i	$-0.648003\pi$
$929$	13.4033	−	41.2512i	0.439749	−	1.35341i	0.888141	−	0.459572i	$-0.151997\pi$
$930$		0			0
$931$	−4.60896	−	14.1849i	−0.151052	−	0.464892i
$932$		0			0
$933$	−2.69526	−	23.9048i	−0.0882389	−	0.782608i
$934$		0			0
$935$	3.92760	+	14.5472i	0.128446	+	0.475744i
$936$		0			0
$937$	−1.98787	−	12.5509i	−0.0649409	−	0.410021i	−0.998648	−	0.0519830i	$-0.983446\pi$
$937$	−1.98787	−	12.5509i	−0.0649409	−	0.410021i	0.933707	−	0.358038i	$-0.116554\pi$
$938$		0			0
$939$	−40.7598	−	15.2939i	−1.33015	−	0.499097i
$940$		0			0
$941$	8.76171	−	12.0595i	0.285623	−	0.393127i	−0.641963	−	0.766736i	$-0.721880\pi$
$941$	8.76171	−	12.0595i	0.285623	−	0.393127i	0.927586	+	0.373609i	$0.121880\pi$
$942$		0			0
$943$	−6.65513	+	6.65513i	−0.216721	+	0.216721i
$944$		0			0
$945$	−24.4971	+	31.8191i	−0.796891	+	1.03507i
$946$		0			0
$947$	22.4410	+	44.0430i	0.729235	+	1.43120i	0.895472	+	0.445118i	$0.146838\pi$
$947$	22.4410	+	44.0430i	0.729235	+	1.43120i	−0.166237	+	0.986086i	$0.553162\pi$
$948$		0			0
$949$			8.34069i			0.270750i
$950$		0			0
$951$	0.727585	+	1.10206i	0.0235936	+	0.0357368i
$952$		0			0
$953$	5.03167	−	2.56376i	0.162992	−	0.0830484i	−0.370592	−	0.928796i	$-0.620845\pi$
$953$	5.03167	−	2.56376i	0.162992	−	0.0830484i	0.533583	+	0.845747i	$0.320845\pi$
$954$		0			0
$955$	13.7094	−	23.8500i	0.443625	−	0.771769i
$956$		0			0
$957$	−14.2503	−	2.91663i	−0.460646	−	0.0942813i
$958$		0			0
$959$	−21.5290	−	15.6417i	−0.695207	−	0.505098i
$960$		0			0
$961$	22.1610	−	16.1009i	0.714872	−	0.519385i
$962$		0			0
$963$	−31.7402	−	7.99271i	−1.02281	−	0.257562i
$964$		0			0
$965$	4.89138	−	6.06392i	0.157459	−	0.195204i
$966$		0			0
$967$	−0.988454	+	1.93995i	−0.0317865	+	0.0623846i	−0.906354	−	0.422520i	$-0.861146\pi$
$967$	−0.988454	+	1.93995i	−0.0317865	+	0.0623846i	0.874567	+	0.484905i	$0.161146\pi$
$968$		0			0
$969$	25.8326	+	20.5976i	0.829863	+	0.661690i
$970$		0			0
$971$	−47.8773	−	15.5563i	−1.53646	−	0.499225i	−0.586061	−	0.810267i	$-0.699322\pi$
$971$	−47.8773	−	15.5563i	−1.53646	−	0.499225i	−0.950396	+	0.311042i	$0.899322\pi$
$972$		0			0
$973$	−4.63307	+	29.2520i	−0.148529	+	0.937777i
$974$		0			0
$975$	−40.2755	−	5.91073i	−1.28985	−	0.189295i
$976$		0			0
$977$	6.17988	−	39.0183i	0.197712	−	1.24830i	−0.666626	−	0.745393i	$-0.732262\pi$
$977$	6.17988	−	39.0183i	0.197712	−	1.24830i	0.864338	−	0.502912i	$-0.167738\pi$
$978$		0			0
$979$	2.43809	+	0.792182i	0.0779216	+	0.0253182i
$980$		0			0
$981$	31.0126	+	2.78644i	0.990155	+	0.0889642i
$982$		0			0
$983$	0.0192554	−	0.0377908i	0.000614152	−	0.00120534i	−0.890699	−	0.454593i	$-0.849785\pi$
$983$	0.0192554	−	0.0377908i	0.000614152	−	0.00120534i	0.891313	+	0.453388i	$0.149785\pi$
$984$		0			0
$985$	−12.3876	−	18.9960i	−0.394703	−	0.605264i
$986$		0			0
$987$	−46.7363	+	42.7254i	−1.48763	+	1.35996i
$988$		0			0
$989$	−42.5919	+	30.9448i	−1.35434	+	0.983988i
$990$		0			0
$991$	4.35016	+	3.16057i	0.138187	+	0.100399i	0.654731	−	0.755862i	$-0.272782\pi$
$991$	4.35016	+	3.16057i	0.138187	+	0.100399i	−0.516544	+	0.856261i	$0.672782\pi$
$992$		0			0
$993$	11.8400	−	57.8485i	0.375730	−	1.83577i
$994$		0			0
$995$	3.28639	+	30.7056i	0.104186	+	0.973434i
$996$		0			0
$997$	−27.4689	+	13.9961i	−0.869947	+	0.443260i	−0.831190	−	0.555988i	$-0.812340\pi$
$997$	−27.4689	+	13.9961i	−0.869947	+	0.443260i	−0.0387573	+	0.999249i	$0.512340\pi$
$998$		0			0
$999$	32.4565	−	5.89761i	1.02688	−	0.186592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.77.2	✓	80
3.2	odd	2	inner	300.2.x.a.77.5	yes	80
25.13	odd	20	inner	300.2.x.a.113.5	yes	80
75.38	even	20	inner	300.2.x.a.113.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.77.2	✓	80	1.1	even	1	trivial
300.2.x.a.77.5	yes	80	3.2	odd	2	inner
300.2.x.a.113.2	yes	80	75.38	even	20	inner
300.2.x.a.113.5	yes	80	25.13	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50650 - 0.854667i) q^{3} +(-2.22337 + 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(1.53909 + 2.57511i) q^{9} +O(q^{10})\)	\(q+(-1.50650 - 0.854667i) q^{3} +(-2.22337 + 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(1.53909 + 2.57511i) q^{9} +(-0.626305 - 0.862035i) q^{11} +(4.64256 - 0.735309i) q^{13} +(3.55289 + 1.54175i) q^{15} +(5.63490 + 2.87112i) q^{17} +(-2.86859 + 0.932063i) q^{19} +(-1.59299 - 5.77036i) q^{21} +(4.44376 + 0.703822i) q^{23} +(4.88675 - 1.05817i) q^{25} +(-0.117773 - 5.19482i) q^{27} +(-2.43550 + 7.49571i) q^{29} +(-0.586924 - 1.80637i) q^{31} +(0.206776 + 1.83394i) q^{33} +(-6.01516 - 4.85205i) q^{35} +(0.993131 + 6.27038i) q^{37} +(-7.62246 - 2.86010i) q^{39} +(-1.22959 + 1.69238i) q^{41} +(-8.27416 + 8.27416i) q^{43} +(-4.03475 - 5.35918i) q^{45} +(-4.80234 - 9.42512i) q^{47} +4.94490i q^{49} +(-6.03512 - 9.14131i) q^{51} +(9.25431 - 4.71531i) q^{53} +(1.59764 + 1.76758i) q^{55} +(5.11814 + 1.04754i) q^{57} +(3.79924 + 2.76031i) q^{59} +(2.42074 - 1.75877i) q^{61} +(-2.53190 + 10.0545i) q^{63} +(-10.1471 + 2.73963i) q^{65} +(2.94083 - 5.77171i) q^{67} +(-6.09299 - 4.85824i) q^{69} +(0.855266 + 0.277893i) q^{71} +(-0.277586 + 1.75261i) q^{73} +(-8.26627 - 2.58241i) q^{75} +(0.576091 - 3.63730i) q^{77} +(-8.30052 - 2.69700i) q^{79} +(-4.26241 + 7.92665i) q^{81} +(2.42816 - 4.76553i) q^{83} +(-13.2117 - 5.04266i) q^{85} +(10.0754 - 9.21074i) q^{87} +(-1.94640 + 1.41415i) q^{89} +(13.1428 + 9.54877i) q^{91} +(-0.659641 + 3.22292i) q^{93} +(6.15615 - 2.75494i) q^{95} +(-4.23366 + 2.15716i) q^{97} +(1.25590 - 2.93956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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