LMFDB - Embedded newform 300.2.x.a.77.5

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			77.5
Character	$\chi$	$=$	300.77
Dual form			300.2.x.a.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.194059 - 1.72115i) q^{3} +(2.22337 - 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(-2.92468 - 0.668006i) q^{9} +O(q^{10})$	\(q+(0.194059 - 1.72115i) q^{3} +(2.22337 - 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(-2.92468 - 0.668006i) q^{9} +(0.626305 + 0.862035i) q^{11} +(4.64256 - 0.735309i) q^{13} +(0.0218922 - 3.87292i) q^{15} +(-5.63490 - 2.87112i) q^{17} +(-2.86859 + 0.932063i) q^{19} +(4.68049 - 3.73199i) q^{21} +(-4.44376 - 0.703822i) q^{23} +(4.88675 - 1.05817i) q^{25} +(-1.71730 + 4.90417i) q^{27} +(2.43550 - 7.49571i) q^{29} +(-0.586924 - 1.80637i) q^{31} +(1.60523 - 0.910677i) q^{33} +(6.01516 + 4.85205i) q^{35} +(0.993131 + 6.27038i) q^{37} +(-0.364645 - 8.13321i) q^{39} +(1.22959 - 1.69238i) q^{41} +(-8.27416 + 8.27416i) q^{43} +(-6.66161 - 0.789253i) q^{45} +(4.80234 + 9.42512i) q^{47} +4.94490i q^{49} +(-6.03512 + 9.14131i) q^{51} +(-9.25431 + 4.71531i) q^{53} +(1.59764 + 1.76758i) q^{55} +(1.04754 + 5.11814i) q^{57} +(-3.79924 - 2.76031i) q^{59} +(2.42074 - 1.75877i) q^{61} +(-5.51500 - 8.78003i) q^{63} +(10.1471 - 2.73963i) q^{65} +(2.94083 - 5.77171i) q^{67} +(-2.07373 + 7.51177i) q^{69} +(-0.855266 - 0.277893i) q^{71} +(-0.277586 + 1.75261i) q^{73} +(-0.872944 - 8.61615i) q^{75} +(-0.576091 + 3.63730i) q^{77} +(-8.30052 - 2.69700i) q^{79} +(8.10754 + 3.90741i) q^{81} +(-2.42816 + 4.76553i) q^{83} +(-13.2117 - 5.04266i) q^{85} +(-12.4286 - 5.64646i) q^{87} +(1.94640 - 1.41415i) q^{89} +(13.1428 + 9.54877i) q^{91} +(-3.22292 + 0.659641i) q^{93} +(-6.15615 + 2.75494i) q^{95} +(-4.23366 + 2.15716i) q^{97} +(-1.25590 - 2.93956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.194059	−	1.72115i	0.112040	−	0.993704i
$3$	0.194059	−	1.72115i	0.112040	−	0.993704i
$4$		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
$9$	−2.92468	−	0.668006i	−0.974894	−	0.222669i
$10$		0			0
$11$	0.626305	+	0.862035i	0.188838	+	0.259913i	0.892930	−	0.450195i	$-0.148646\pi$
$11$	0.626305	+	0.862035i	0.188838	+	0.259913i	−0.704092	+	0.710109i	$0.748646\pi$
$12$		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
$15$	0.0218922	−	3.87292i	0.00565253	−	0.999984i
$16$		0			0
$17$	−5.63490	−	2.87112i	−1.36666	−	0.696350i	−0.391987	−	0.919971i	$-0.628212\pi$
$17$	−5.63490	−	2.87112i	−1.36666	−	0.696350i	−0.974676	+	0.223621i	$0.928212\pi$
$18$		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
$21$	4.68049	−	3.73199i	1.02137	−	0.814386i
$22$		0			0
$23$	−4.44376	−	0.703822i	−0.926588	−	0.146757i	−0.325137	−	0.945667i	$-0.605410\pi$
$23$	−4.44376	−	0.703822i	−0.926588	−	0.146757i	−0.601451	+	0.798910i	$0.705410\pi$
$24$		0			0
$25$	4.88675	−	1.05817i	0.977349	−	0.211633i
$26$		0			0
$27$	−1.71730	+	4.90417i	−0.330494	+	0.943808i
$28$		0			0
$29$	2.43550	−	7.49571i	0.452261	−	1.39192i	−0.422059	−	0.906568i	$-0.638693\pi$
$29$	2.43550	−	7.49571i	0.452261	−	1.39192i	0.874320	−	0.485349i	$-0.161307\pi$
$30$		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
$33$	1.60523	−	0.910677i	0.279434	−	0.158529i
$34$		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
$39$	−0.364645	−	8.13321i	−0.0583900	−	1.30236i
$40$		0			0
$41$	1.22959	−	1.69238i	0.192029	−	0.264306i	−0.702136	−	0.712043i	$-0.747770\pi$
$41$	1.22959	−	1.69238i	0.192029	−	0.264306i	0.894165	+	0.447737i	$0.147770\pi$
$42$		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
$45$	−6.66161	−	0.789253i	−0.993055	−	0.117655i
$46$		0			0
$47$	4.80234	+	9.42512i	0.700493	+	1.37480i	0.917148	+	0.398547i	$0.130485\pi$
$47$	4.80234	+	9.42512i	0.700493	+	1.37480i	−0.216655	+	0.976248i	$0.569515\pi$
$48$		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	−0.953754	−	0.300587i	$-0.902817\pi$
$53$	−9.25431	+	4.71531i	−1.27118	+	0.647697i	−0.317423	+	0.948284i	$0.602817\pi$
$54$		0			0
$55$	1.59764	+	1.76758i	0.215426	+	0.238341i
$56$		0			0
$57$	1.04754	+	5.11814i	0.138750	+	0.677915i
$58$		0			0
$59$	−3.79924	−	2.76031i	−0.494619	−	0.359362i	0.312339	−	0.949971i	$-0.398888\pi$
$59$	−3.79924	−	2.76031i	−0.494619	−	0.359362i	−0.806958	+	0.590609i	$0.798888\pi$
$60$		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
$63$	−5.51500	−	8.78003i	−0.694825	−	1.10618i
$64$		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
$69$	−2.07373	+	7.51177i	−0.249648	+	0.904311i
$70$		0			0
$71$	−0.855266	−	0.277893i	−0.101501	−	0.0329798i	0.257826	−	0.966191i	$-0.416994\pi$
$71$	−0.855266	−	0.277893i	−0.101501	−	0.0329798i	−0.359327	+	0.933212i	$0.616994\pi$
$72$		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
$75$	−0.872944	−	8.61615i	−0.100799	−	0.994907i
$76$		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
$81$	8.10754	+	3.90741i	0.900837	+	0.434157i
$82$		0			0
$83$	−2.42816	+	4.76553i	−0.266525	+	0.523085i	−0.985018	−	0.172449i	$-0.944832\pi$
$83$	−2.42816	+	4.76553i	−0.266525	+	0.523085i	0.718493	+	0.695534i	$0.244832\pi$
$84$		0			0
$85$	−13.2117	−	5.04266i	−1.43301	−	0.546954i
$86$		0			0
$87$	−12.4286	−	5.64646i	−1.33248	−	0.605364i
$88$		0			0
$89$	1.94640	−	1.41415i	0.206318	−	0.149899i	−0.479828	−	0.877363i	$-0.659301\pi$
$89$	1.94640	−	1.41415i	0.206318	−	0.149899i	0.686146	+	0.727463i	$0.259301\pi$
$90$		0			0
$91$	13.1428	+	9.54877i	1.37773	+	1.00098i
$92$		0			0
$93$	−3.22292	+	0.659641i	−0.334201	+	0.0684016i
$94$		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	$0.418939\pi$
$101$			19.4515i			1.93550i	−0.251916	+	0.967749i	$0.581061\pi$
$102$		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
$105$	9.51838	−	9.41137i	0.928899	−	0.918456i
$106$		0			0
$107$	7.71479	−	7.71479i	0.745817	−	0.745817i	−0.227874	−	0.973691i	$-0.573177\pi$
$107$	7.71479	−	7.71479i	0.745817	−	0.745817i	0.973691	+	0.227874i	$0.0731774\pi$
$108$		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
$111$	10.9850	−	0.492501i	1.04265	−	0.0467461i
$112$		0			0
$113$	−0.703338	−	4.44070i	−0.0661645	−	0.417746i	−0.998432	−	0.0559766i	$-0.982173\pi$
$113$	−0.703338	−	4.44070i	−0.0661645	−	0.417746i	0.932268	−	0.361769i	$-0.117827\pi$
$114$		0			0
$115$	−10.0476	−	0.507399i	−0.936944	−	0.0473152i
$116$		0			0
$117$	−14.0692	−	0.950712i	−1.30070	−	0.0878934i
$118$		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
$123$	−2.67422	−	2.44472i	−0.241127	−	0.220433i
$124$		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
$129$	12.6354	+	15.8467i	1.11248	+	1.39522i
$130$		0			0
$131$	−15.2113	+	4.94246i	−1.32902	+	0.431825i	−0.885583	−	0.464481i	$-0.846241\pi$
$131$	−15.2113	+	4.94246i	−1.32902	+	0.431825i	−0.443436	+	0.896306i	$0.646241\pi$
$132$		0			0
$133$	−9.28827	−	4.73261i	−0.805395	−	0.410369i
$134$		0			0
$135$	−2.65116	+	11.3124i	−0.228176	+	0.973620i
$136$		0			0
$137$	7.60492	−	1.20450i	0.649732	−	0.102907i	0.177136	−	0.984186i	$-0.443317\pi$
$137$	7.60492	−	1.20450i	0.649732	−	0.102907i	0.472596	+	0.881279i	$0.343317\pi$
$138$		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
$141$	17.1539	−	6.43650i	1.44462	−	0.542051i
$142$		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
$147$	8.51089	+	0.959600i	0.701966	+	0.0791465i
$148$		0			0
$149$	5.42628			0.444538			0.222269	−	0.974985i	$-0.428654\pi$
$149$	5.42628			0.444538			0.222269	+	0.974985i	$0.428654\pi$
$150$		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
$153$	14.5624	+	12.1613i	1.17730	+	0.983181i
$154$		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
$159$	6.31985	+	16.8431i	0.501197	+	1.33574i
$160$		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
$165$	3.35231	−	2.40676i	0.260977	−	0.187366i
$166$		0			0
$167$	8.67164	+	4.41842i	0.671032	+	0.341908i	0.756090	−	0.654468i	$-0.227107\pi$
$167$	8.67164	+	4.41842i	0.671032	+	0.341908i	−0.0850576	+	0.996376i	$0.527107\pi$
$168$		0			0
$169$	8.64893	−	2.81021i	0.665302	−	0.216170i
$170$		0			0
$171$	9.01235	−	0.809749i	0.689192	−	0.0619231i
$172$		0			0
$173$	−16.7643	−	2.65520i	−1.27456	−	0.201871i	−0.517767	−	0.855522i	$-0.673237\pi$
$173$	−16.7643	−	2.65520i	−1.27456	−	0.201871i	−0.756797	+	0.653650i	$0.773237\pi$
$174$		0			0
$175$	14.5285	+	9.35651i	1.09825	+	0.707286i
$176$		0			0
$177$	−5.48817	+	6.00339i	−0.412516	+	0.451242i
$178$		0			0
$179$	3.51696	−	10.8241i	0.262870	−	0.809031i	−0.729306	−	0.684187i	$-0.760157\pi$
$179$	3.51696	−	10.8241i	0.262870	−	0.809031i	0.992176	−	0.124843i	$-0.0398429\pi$
$180$		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
$183$	−2.55734	−	4.50775i	−0.189044	−	0.333223i
$184$		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
$189$	−16.1819	+	7.78828i	−1.17706	+	0.566514i
$190$		0			0
$191$	7.23129	−	9.95302i	0.523238	−	0.720175i	−0.462843	−	0.886440i	$-0.653171\pi$
$191$	7.23129	−	9.95302i	0.523238	−	0.720175i	0.986081	+	0.166265i	$0.0531707\pi$
$192$		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
$195$	−2.74616	−	17.9964i	−0.196656	−	1.28875i
$196$		0			0
$197$	−4.60438	−	9.03661i	−0.328049	−	0.643832i	0.666796	−	0.745240i	$-0.267665\pi$
$197$	−4.60438	−	9.03661i	−0.328049	−	0.643832i	−0.994845	+	0.101408i	$0.967665\pi$
$198$		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
$207$	12.5264	+	5.02692i	0.870647	+	0.349395i
$208$		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
$213$	−0.644265	+	1.41811i	−0.0441443	+	0.0971672i
$214$		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
$219$	2.96262	+	0.817874i	0.200196	+	0.0552668i
$220$		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
$225$	−14.9990	−	0.169573i	−0.999936	−	0.0113049i
$226$		0			0
$227$	−0.316481	+	1.99819i	−0.0210056	+	0.132624i	−0.995963	−	0.0897694i	$-0.971387\pi$
$227$	−0.316481	+	1.99819i	−0.0210056	+	0.132624i	0.974957	+	0.222394i	$0.0713870\pi$
$228$		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
$231$	6.14852	+	1.69738i	0.404543	+	0.111680i
$232$		0			0
$233$	−13.3461	+	26.1931i	−0.874329	+	1.71597i	−0.196838	+	0.980436i	$0.563067\pi$
$233$	−13.3461	+	26.1931i	−0.874329	+	1.71597i	−0.677491	+	0.735531i	$0.736933\pi$
$234$		0			0
$235$	12.9202	+	19.8127i	0.842822	+	1.29244i
$236$		0			0
$237$	−6.25272	+	13.7630i	−0.406158	+	0.894005i
$238$		0			0
$239$	3.18910	−	2.31702i	0.206286	−	0.149875i	−0.479846	−	0.877353i	$-0.659307\pi$
$239$	3.18910	−	2.31702i	0.206286	−	0.149875i	0.686132	+	0.727477i	$0.259307\pi$
$240$		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
$243$	8.29856	−	13.1960i	0.532353	−	0.846523i
$244$		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	$0.0118136\pi$
$251$			1.17570i			0.0742098i	−0.999311	+	0.0371049i	$0.988186\pi$
$252$		0			0
$253$	−2.17643	−	4.27149i	−0.136831	−	0.268546i
$254$		0			0
$255$	−11.2430	+	21.7607i	−0.704064	+	1.36271i
$256$		0			0
$257$	18.9675	−	18.9675i	1.18316	−	1.18316i	0.204237	−	0.978921i	$-0.434529\pi$
$257$	18.9675	−	18.9675i	1.18316	−	1.18316i	0.978921	−	0.204237i	$-0.0654714\pi$
$258$		0			0
$259$	−12.8969	+	17.7510i	−0.801372	+	1.10299i
$260$		0			0
$261$	−12.1302	+	20.2956i	−0.750843	+	1.25627i
$262$		0			0
$263$	3.31659	+	20.9401i	0.204510	+	1.29122i	0.849726	+	0.527224i	$0.176767\pi$
$263$	3.31659	+	20.9401i	0.204510	+	1.29122i	−0.645216	+	0.764000i	$0.723233\pi$
$264$		0			0
$265$	−19.4537	+	12.6861i	−1.19503	+	0.779299i
$266$		0			0
$267$	−2.05623	−	3.62447i	−0.125839	−	0.221814i
$268$		0			0
$269$	6.34707	+	19.5343i	0.386988	+	1.19103i	0.935028	+	0.354574i	$0.115374\pi$
$269$	6.34707	+	19.5343i	0.386988	+	1.19103i	−0.548040	+	0.836452i	$0.684626\pi$
$270$		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
$273$	18.9853	−	20.7676i	1.14904	−	1.25691i
$274$		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
$279$	0.509903	+	5.67512i	0.0305271	+	0.339761i
$280$		0			0
$281$	22.5521	−	7.32761i	1.34534	−	0.437129i	0.454220	−	0.890890i	$-0.349918\pi$
$281$	22.5521	−	7.32761i	1.34534	−	0.437129i	0.891123	+	0.453761i	$0.149918\pi$
$282$		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
$285$	3.54701	+	11.1302i	0.210107	+	0.659299i
$286$		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
$291$	2.89121	+	7.70537i	0.169486	+	0.451697i
$292$		0			0
$293$	14.6342	+	14.6342i	0.854941	+	0.854941i	0.990737	−	0.135796i	$-0.0433590\pi$
$293$	14.6342	+	14.6342i	0.854941	+	0.854941i	−0.135796	+	0.990737i	$0.543359\pi$
$294$		0			0
$295$	−9.10398	−	5.23311i	−0.530054	−	0.304683i
$296$		0			0
$297$	−5.30312	+	1.59114i	−0.307718	+	0.0923272i
$298$		0			0
$299$	−21.1479			−1.22302
$300$		0			0
$301$	−40.4418			−2.33102
$302$		0			0
$303$	33.4789	+	3.77473i	1.92331	+	0.216853i
$304$		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
$309$	9.32313	−	3.49822i	0.530375	−	0.199007i
$310$		0			0
$311$	−8.16369	−	11.2364i	−0.462920	−	0.637155i	0.512191	−	0.858872i	$-0.328834\pi$
$311$	−8.16369	−	11.2364i	−0.462920	−	0.637155i	−0.975111	+	0.221716i	$0.928834\pi$
$312$		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
$315$	−14.3512	−	18.2089i	−0.808600	−	1.02595i
$316$		0			0
$317$	0.679335	+	0.346138i	0.0381552	+	0.0194411i	0.472964	−	0.881082i	$-0.343184\pi$
$317$	0.679335	+	0.346138i	0.0381552	+	0.0194411i	−0.434809	+	0.900523i	$0.643184\pi$
$318$		0			0
$319$	7.98693	−	2.59511i	0.447182	−	0.145298i
$320$		0			0
$321$	−11.7812	−	14.7754i	−0.657560	−	0.824682i
$322$		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
$327$	−13.2684	−	12.1297i	−0.733745	−	0.670775i
$328$		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
$333$	1.28406	−	19.0023i	0.0703661	−	1.04132i
$334$		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
$339$	−7.77958	+	0.348791i	−0.422529	+	0.0189437i
$340$		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
$345$	−2.82313	+	17.1949i	−0.151992	+	0.925744i
$346$		0			0
$347$	−1.98524	−	3.89625i	−0.106573	−	0.209162i	0.831561	−	0.555433i	$-0.187448\pi$
$347$	−1.98524	−	3.89625i	−0.106573	−	0.209162i	−0.938134	+	0.346272i	$0.887448\pi$
$348$		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	−0.913603	−	0.406607i	$-0.866712\pi$
$353$	−21.0739	+	10.7377i	−1.12165	+	0.571511i	−0.208050	+	0.978118i	$0.566712\pi$
$354$		0			0
$355$	−1.96770	−	0.414335i	−0.104435	−	0.0219906i
$356$		0			0
$357$	−37.0891	+	7.59109i	−1.96296	+	0.401763i
$358$		0			0
$359$	−0.704752	−	0.512032i	−0.0371954	−	0.0270240i	0.569032	−	0.822315i	$-0.307318\pi$
$359$	−0.704752	−	0.512032i	−0.0371954	−	0.0270240i	−0.606228	+	0.795291i	$0.707318\pi$
$360$		0			0
$361$	−8.01123	+	5.82050i	−0.421644	+	0.306342i
$362$		0			0
$363$	−15.5559	−	7.06726i	−0.816475	−	0.370935i
$364$		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
$369$	−4.72667	+	4.12831i	−0.246061	+	0.214911i
$370$		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
$375$	−3.99122	−	18.9491i	−0.206106	−	0.978530i
$376$		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
$381$	4.43483	−	16.0645i	0.227203	−	0.823009i
$382$		0			0
$383$	0.430527	−	0.844956i	0.0219989	−	0.0431753i	−0.879746	−	0.475445i	$-0.842287\pi$
$383$	0.430527	−	0.844956i	0.0219989	−	0.0431753i	0.901744	+	0.432270i	$0.142287\pi$
$384$		0			0
$385$	−0.415315	+	8.22414i	−0.0211664	+	0.419141i
$386$		0			0
$387$	29.7265	−	18.6721i	1.51108	−	0.949156i
$388$		0			0
$389$	11.4768	−	8.33838i	0.581897	−	0.422773i	−0.257511	−	0.966275i	$-0.582902\pi$
$389$	11.4768	−	8.33838i	0.581897	−	0.422773i	0.839407	+	0.543503i	$0.182902\pi$
$390$		0			0
$391$	23.0194	+	16.7246i	1.16414	+	0.845797i
$392$		0			0
$393$	5.55480	+	27.1400i	0.280203	+	1.36903i
$394$		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	$-0.780289\pi$
$401$		−	25.5008i		−	1.27345i	0.771092	−	0.636724i	$-0.219711\pi$
$402$		0			0
$403$	−4.05307	−	7.95459i	−0.201898	−	0.396247i
$404$		0			0
$405$	18.9559	+	6.75831i	0.941925	+	0.335823i
$406$		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
$411$	−0.597321	−	13.3229i	−0.0294637	−	0.657171i
$412$		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
$417$	12.9096	−	7.32389i	0.632188	−	0.358652i
$418$		0			0
$419$	0.988493	+	3.04227i	0.0482910	+	0.148625i	0.972294	−	0.233760i	$-0.0751030\pi$
$419$	0.988493	+	3.04227i	0.0482910	+	0.148625i	−0.924003	+	0.382385i	$0.875103\pi$
$420$		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
$423$	−7.74928	−	30.7735i	−0.376783	−	1.49626i
$424$		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
$429$	6.78273	−	5.40821i	0.327473	−	0.261111i
$430$		0			0
$431$	1.65426	−	0.537501i	0.0796828	−	0.0258905i	−0.268904	−	0.963167i	$-0.586662\pi$
$431$	1.65426	−	0.537501i	0.0796828	−	0.0258905i	0.348587	+	0.937276i	$0.386662\pi$
$432$		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
$435$	−28.9770	−	9.59661i	−1.38934	−	0.460122i
$436$		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
$441$	3.30322	−	14.4623i	0.157296	−	0.688679i
$442$		0			0
$443$	−2.72820	−	2.72820i	−0.129621	−	0.129621i	0.639320	−	0.768941i	$-0.279216\pi$
$443$	−2.72820	−	2.72820i	−0.129621	−	0.129621i	−0.768941	+	0.639320i	$0.779216\pi$
$444$		0			0
$445$	3.99106	−	3.60734i	0.189194	−	0.171004i
$446$		0			0
$447$	1.05302	−	9.33941i	0.0498059	−	0.441739i
$448$		0			0
$449$	21.4808			1.01374			0.506870	−	0.862022i	$-0.330802\pi$
$449$	21.4808			1.01374			0.506870	+	0.862022i	$0.330802\pi$
$450$		0			0
$451$	2.22899			0.104959
$452$		0			0
$453$	−2.99865	+	26.5957i	−0.140889	+	1.24957i
$454$		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
$459$	23.7573	−	22.7039i	1.10889	−	1.05973i
$460$		0			0
$461$	8.79509	+	12.1054i	0.409628	+	0.563805i	0.963128	−	0.269045i	$-0.0867079\pi$
$461$	8.79509	+	12.1054i	0.409628	+	0.563805i	−0.553499	+	0.832850i	$0.686708\pi$
$462$		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
$465$	−7.00877	+	2.23357i	−0.325024	+	0.103579i
$466$		0			0
$467$	15.6353	+	7.96659i	0.723516	+	0.368650i	0.776645	−	0.629938i	$-0.216920\pi$
$467$	15.6353	+	7.96659i	0.723516	+	0.368650i	−0.0531298	+	0.998588i	$0.516920\pi$
$468$		0			0
$469$	21.2922	−	6.91826i	0.983184	−	0.319456i
$470$		0			0
$471$	−10.4655	+	8.34467i	−0.482226	+	0.384502i
$472$		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
$477$	30.2158	−	7.60884i	1.38349	−	0.348385i
$478$		0			0
$479$	4.12695	−	12.7015i	0.188565	−	0.580345i	−0.811426	−	0.584455i	$-0.801308\pi$
$479$	4.12695	−	12.7015i	0.188565	−	0.580345i	0.999992	+	0.00411038i	$0.00130838\pi$
$480$		0			0
$481$	9.22133	+	28.3804i	0.420457	+	1.29403i
$482$		0			0
$483$	−23.4256	+	13.2898i	−1.06590	+	0.604707i
$484$		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
$489$	−0.951912	−	21.2319i	−0.0430469	−	0.960138i
$490$		0			0
$491$	−2.44616	+	3.36685i	−0.110393	+	0.151944i	−0.860639	−	0.509216i	$-0.829935\pi$
$491$	−2.44616	+	3.36685i	−0.110393	+	0.151944i	0.750245	+	0.661160i	$0.229935\pi$
$492$		0			0
$493$	−35.2449	+	35.2449i	−1.58735	+	1.58735i
$494$		0			0
$495$	−3.49184	−	6.23686i	−0.156946	−	0.280326i
$496$		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	−0.0459478	−	0.998944i	$-0.514631\pi$
$503$	16.4890	−	8.40155i	0.735207	−	0.374607i	0.781155	+	0.624337i	$0.214631\pi$
$504$		0			0
$505$	4.62878	+	43.2479i	0.205978	+	1.92451i
$506$		0			0
$507$	−3.15838	−	15.4314i	−0.140268	−	0.685333i
$508$		0			0
$509$	−5.30145	−	3.85173i	−0.234982	−	0.170725i	0.464063	−	0.885802i	$-0.346391\pi$
$509$	−5.30145	−	3.85173i	−0.234982	−	0.170725i	−0.699045	+	0.715078i	$0.746391\pi$
$510$		0			0
$511$	−4.96151	+	3.60475i	−0.219484	+	0.159465i
$512$		0			0
$513$	0.355229	−	15.6687i	0.0156837	−	0.691790i
$514$		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
$519$	−7.82323	+	28.3385i	−0.343402	+	1.24392i
$520$		0			0
$521$	5.03678	+	1.63655i	0.220666	+	0.0716986i	0.417263	−	0.908786i	$-0.362989\pi$
$521$	5.03678	+	1.63655i	0.220666	+	0.0716986i	−0.196598	+	0.980484i	$0.562989\pi$
$522$		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
$525$	18.9233	−	23.1900i	0.825880	−	1.01209i
$526$		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
$531$	9.26768	+	10.6110i	0.402183	+	0.460476i
$532$		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
$537$	−17.9473	−	8.15371i	−0.774485	−	0.351859i
$538$		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
$543$	4.74637	−	0.971449i	0.203686	−	0.0416888i
$544$		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
$555$	24.3064	−	3.70905i	1.03175	−	0.157440i
$556$		0			0
$557$	−29.9868	+	29.9868i	−1.27058	+	1.27058i	−0.324797	+	0.945784i	$0.605296\pi$
$557$	−29.9868	+	29.9868i	−1.27058	+	1.27058i	−0.945784	+	0.324797i	$0.894704\pi$
$558$		0			0
$559$	−32.3292	+	44.4973i	−1.36738	+	1.88204i
$560$		0			0
$561$	−11.6600	+	0.522764i	−0.492284	+	0.0220711i
$562$		0			0
$563$	−5.14467	−	32.4822i	−0.216822	−	1.36896i	−0.820461	−	0.571702i	$-0.806283\pi$
$563$	−5.14467	−	32.4822i	−0.216822	−	1.36896i	0.603639	−	0.797258i	$-0.293717\pi$
$564$		0			0
$565$	−2.62051	−	9.70595i	−0.110246	−	0.408332i
$566$		0			0
$567$	10.2645	+	29.3628i	0.431069	+	1.23312i
$568$		0			0
$569$	4.11085	+	12.6519i	0.172336	+	0.530395i	0.999502	−	0.0315628i	$-0.0100484\pi$
$569$	4.11085	+	12.6519i	0.172336	+	0.530395i	−0.827166	+	0.561958i	$0.810048\pi$
$570$		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
$573$	−15.7273	−	14.3776i	−0.657018	−	0.600632i
$574$		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
$579$	3.76224	+	4.71843i	0.156353	+	0.196091i
$580$		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
$585$	−31.5073	+	1.23419i	−1.30267	+	0.0510274i
$586$		0			0
$587$	−22.1842	+	3.51364i	−0.915641	+	0.145023i	−0.596434	−	0.802662i	$-0.703416\pi$
$587$	−22.1842	+	3.51364i	−0.915641	+	0.145023i	−0.319207	+	0.947685i	$0.603416\pi$
$588$		0			0
$589$	3.36730	+	4.63469i	0.138747	+	0.190969i
$590$		0			0
$591$	−16.4468	+	6.17118i	−0.676532	+	0.253848i
$592$		0			0
$593$	12.6961	+	12.6961i	0.521368	+	0.521368i	0.917984	−	0.396616i	$-0.129816\pi$
$593$	12.6961	+	12.6961i	0.521368	+	0.521368i	−0.396616	+	0.917984i	$0.629816\pi$
$594$		0			0
$595$	−19.9639	−	44.6111i	−0.818442	−	1.82888i
$596$		0			0
$597$	−23.7697	−	2.68003i	−0.972830	−	0.109686i
$598$		0			0
$599$	−20.3237			−0.830405			−0.415202	−	0.909729i	$-0.636289\pi$
$599$	−20.3237			−0.830405			−0.415202	+	0.909729i	$0.636289\pi$
$600$		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
$603$	−12.4565	+	14.9159i	−0.507269	+	0.607423i
$604$		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
$609$	−16.5745	−	44.1728i	−0.671633	−	1.78997i
$610$		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
$615$	−6.52754	−	4.79915i	−0.263216	−	0.193520i
$616$		0			0
$617$	21.7016	+	11.0575i	0.873673	+	0.445159i	0.832521	−	0.553994i	$-0.186897\pi$
$617$	21.7016	+	11.0575i	0.873673	+	0.445159i	0.0411527	+	0.999153i	$0.486897\pi$
$618$		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
$621$	11.0829	−	20.5843i	0.444742	−	0.826019i
$622$		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
$627$	−3.75594	+	4.10854i	−0.149998	+	0.164079i
$628$		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
$633$	4.27324	+	7.53234i	0.169846	+	0.299384i
$634$		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
$639$	2.31575	+	1.38407i	0.0916095	+	0.0547530i
$640$		0			0
$641$	−2.73450	+	3.76371i	−0.108006	+	0.148658i	−0.859598	−	0.510970i	$-0.829286\pi$
$641$	−2.73450	+	3.76371i	−0.108006	+	0.148658i	0.751592	+	0.659628i	$0.229286\pi$
$642$		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
$645$	31.8640	+	32.2263i	1.25464	+	1.26891i
$646$		0			0
$647$	−7.38947	−	14.5027i	−0.290510	−	0.570158i	0.698915	−	0.715205i	$-0.253667\pi$
$647$	−7.38947	−	14.5027i	−0.290510	−	0.570158i	−0.989425	+	0.145047i	$0.953667\pi$
$648$		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	−0.352983	−	0.935630i	$-0.614833\pi$
$653$	5.02081	−	2.55823i	0.196479	−	0.100111i	0.549462	+	0.835519i	$0.314833\pi$
$654$		0			0
$655$	−32.6443	+	14.6087i	−1.27552	+	0.570808i
$656$		0			0
$657$	1.98260	−	4.94039i	0.0773487	−	0.192743i
$658$		0			0
$659$	13.2174	+	9.60298i	0.514875	+	0.374079i	0.814670	−	0.579925i	$-0.196918\pi$
$659$	13.2174	+	9.60298i	0.514875	+	0.374079i	−0.299794	+	0.954004i	$0.596918\pi$
$660$		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
$663$	−21.2967	+	46.8767i	−0.827096	+	1.82054i
$664$		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
$669$	−30.5600	−	8.43653i	−1.18152	−	0.326175i
$670$		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
$675$	−3.20255	+	25.7826i	−0.123266	+	0.992374i
$676$		0			0
$677$	1.37035	−	8.65208i	0.0526670	−	0.332526i	−0.947260	−	0.320465i	$-0.896161\pi$
$677$	1.37035	−	8.65208i	0.0526670	−	0.332526i	0.999927	−	0.0120611i	$-0.00383925\pi$
$678$		0			0
$679$	−15.6183	−	5.07469i	−0.599375	−	0.194749i
$680$		0			0
$681$	3.37775	+	0.932476i	0.129436	+	0.0357325i
$682$		0			0
$683$	0.144185	−	0.282980i	0.00551710	−	0.0108279i	−0.888232	−	0.459396i	$-0.848066\pi$
$683$	0.144185	−	0.282980i	0.00551710	−	0.0108279i	0.893749	+	0.448568i	$0.148066\pi$
$684$		0			0
$685$	16.6219	−	4.48775i	0.635091	−	0.171468i
$686$		0			0
$687$	−19.4014	+	42.7050i	−0.740211	+	1.62930i
$688$		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
$693$	4.11462	−	10.2531i	0.156301	−	0.389483i
$694$		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	$0.235410\pi$
$701$			35.6884i			1.34793i	−0.738763	+	0.673965i	$0.764590\pi$
$702$		0			0
$703$	−8.69328	−	17.0615i	−0.327873	−	0.643488i
$704$		0			0
$705$	36.6079	−	18.3927i	1.37873	−	0.692711i
$706$		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
$711$	22.4748	+	13.4327i	0.842870	+	0.503765i
$712$		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
$717$	−3.36905	−	5.93854i	−0.125820	−	0.221779i
$718$		0			0
$719$	−15.8013	−	48.6313i	−0.589288	−	1.81364i	−0.581324	−	0.813672i	$-0.697465\pi$
$719$	−15.8013	−	48.6313i	−0.589288	−	1.81364i	−0.00796379	−	0.999968i	$-0.502535\pi$
$720$		0			0
$721$	−6.14013	+	18.8974i	−0.228670	+	0.703775i
$722$		0			0
$723$	−12.2628	+	13.4140i	−0.456060	+	0.498874i
$724$		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
$729$	−21.1018	−	16.8438i	−0.781548	−	0.623845i
$730$		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
$735$	19.1512	+	0.108255i	0.706403	+	0.00399303i
$736$		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
$741$	8.62668	+	22.9910i	0.316909	+	0.844596i
$742$		0			0
$743$	−21.5734	−	21.5734i	−0.791451	−	0.791451i	0.190279	−	0.981730i	$-0.439061\pi$
$743$	−21.5734	−	21.5734i	−0.791451	−	0.791451i	−0.981730	+	0.190279i	$0.939061\pi$
$744$		0			0
$745$	12.0646	−	1.29126i	0.442014	−	0.0473082i
$746$		0			0
$747$	10.2850	−	12.3156i	0.376308	−	0.450606i
$748$		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
$753$	2.02356	+	0.228155i	0.0737425	+	0.00831445i
$754$		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
$759$	−7.77420	+	2.91703i	−0.282186	+	0.105882i
$760$		0			0
$761$	6.87014	+	9.45593i	0.249042	+	0.342777i	0.915176	−	0.403055i	$-0.132052\pi$
$761$	6.87014	+	9.45593i	0.249042	+	0.342777i	−0.666133	+	0.745833i	$0.732052\pi$
$762$		0			0
$763$	35.4302	−	5.61159i	1.28266	−	0.203153i
$764$		0			0
$765$	35.2715	+	23.5737i	1.27524	+	0.852308i
$766$		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
$771$	−28.9650	−	36.3266i	−1.04315	−	1.30827i
$772$		0			0
$773$	−31.5458	−	4.99637i	−1.13462	−	0.179707i	−0.439257	−	0.898361i	$-0.644758\pi$
$773$	−31.5458	−	4.99637i	−1.13462	−	0.179707i	−0.695368	+	0.718654i	$0.744758\pi$
$774$		0			0
$775$	−4.77959	−	8.20619i	−0.171688	−	0.294775i
$776$		0			0
$777$	28.0493	+	25.6421i	1.00626	+	0.919905i
$778$		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
$783$	32.5777	+	24.8165i	1.16423	+	0.886868i
$784$		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
$789$	36.6846	−	1.64472i	1.30601	−	0.0585537i
$790$		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
$795$	18.0594	+	35.9444i	0.640502	+	1.27482i
$796$		0			0
$797$	16.5621	+	32.5049i	0.586658	+	1.15138i	0.973383	+	0.229187i	$0.0736066\pi$
$797$	16.5621	+	32.5049i	0.586658	+	1.15138i	−0.386724	+	0.922196i	$0.626393\pi$
$798$		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
$807$	34.8530	−	7.13344i	1.22688	−	0.251109i
$808$		0			0
$809$	9.33253	+	6.78048i	0.328114	+	0.238389i	0.739630	−	0.673014i	$-0.235001\pi$
$809$	9.33253	+	6.78048i	0.328114	+	0.238389i	−0.411516	+	0.911403i	$0.635001\pi$
$810$		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
$813$	−43.6201	−	19.8172i	−1.52982	−	0.695019i
$814$		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
$819$	−32.0597	−	36.7066i	−1.12026	−	1.28263i
$820$		0			0
$821$	37.1920	+	12.0844i	1.29801	+	0.421749i	0.874889	−	0.484324i	$-0.160934\pi$
$821$	37.1920	+	12.0844i	1.29801	+	0.421749i	0.423121	+	0.906073i	$0.360934\pi$
$822$		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
$825$	6.88069	−	6.14885i	0.239555	−	0.214075i
$826$		0			0
$827$	−6.65765	+	42.0348i	−0.231509	+	1.46169i	0.548619	+	0.836072i	$0.315154\pi$
$827$	−6.65765	+	42.0348i	−0.231509	+	1.46169i	−0.780128	+	0.625620i	$0.784846\pi$
$828$		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
$831$	−8.06704	+	29.2216i	−0.279843	+	1.01369i
$832$		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
$837$	9.86666	+	0.223689i	0.341042	+	0.00773183i
$838$		0			0
$839$	1.53562	−	1.11569i	0.0530154	−	0.0385180i	−0.560962	−	0.827842i	$-0.689569\pi$
$839$	1.53562	−	1.11569i	0.0530154	−	0.0385180i	0.613977	+	0.789324i	$0.289569\pi$
$840$		0			0
$841$	−26.7924	−	19.4658i	−0.923877	−	0.671236i
$842$		0			0
$843$	−8.23546	−	40.2374i	−0.283644	−	1.38585i
$844$		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
$855$	19.8451	−	3.94499i	0.678688	−	0.134916i
$856$		0			0
$857$	8.33034	−	8.33034i	0.284559	−	0.284559i	−0.550365	−	0.834924i	$-0.685511\pi$
$857$	8.33034	−	8.33034i	0.284559	−	0.284559i	0.834924	+	0.550365i	$0.185511\pi$
$858$		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
$861$	−0.560874	−	12.5100i	−0.0191145	−	0.426339i
$862$		0			0
$863$	0.387244	+	2.44496i	0.0131819	+	0.0832274i	0.993402	−	0.114682i	$-0.0365849\pi$
$863$	0.387244	+	2.44496i	0.0131819	+	0.0832274i	−0.980220	+	0.197909i	$0.936585\pi$
$864$		0			0
$865$	−37.9050	−	1.91418i	−1.28881	−	0.0650842i
$866$		0			0
$867$	34.6426	−	19.6534i	1.17653	−	0.667466i
$868$		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
$873$	13.8231	−	3.48089i	0.467842	−	0.117810i
$874$		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
$879$	28.0276	−	22.3478i	0.945346	−	0.753771i
$880$		0			0
$881$	−10.1224	+	3.28897i	−0.341033	+	0.110808i	−0.474526	−	0.880241i	$-0.657381\pi$
$881$	−10.1224	+	3.28897i	−0.341033	+	0.110808i	0.133493	+	0.991050i	$0.457381\pi$
$882$		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
$885$	−10.7736	+	14.6537i	−0.362152	+	0.492580i
$886$		0			0
$887$	−46.5615	+	7.37461i	−1.56338	+	0.247615i	−0.877312	−	0.479921i	$-0.840665\pi$
$887$	−46.5615	+	7.37461i	−1.56338	+	0.247615i	−0.686070	+	0.727536i	$0.740665\pi$
$888$		0			0
$889$	19.5463	+	26.9032i	0.655563	+	0.902304i
$890$		0			0
$891$	1.70947	+	9.43621i	0.0572692	+	0.316125i
$892$		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
$897$	−4.10394	+	36.3987i	−0.137027	+	1.21532i
$898$		0			0
$899$	−14.9695			−0.499259
$900$		0			0
$901$	65.6853			2.18830
$902$		0			0
$903$	−7.84807	+	69.6061i	−0.261167	+	2.31635i
$904$		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
$909$	12.9937	−	56.8895i	0.430975	−	1.88691i
$910$		0			0
$911$	−23.4595	−	32.2893i	−0.777249	−	1.06979i	−0.995580	−	0.0939170i	$-0.970061\pi$
$911$	−23.4595	−	32.2893i	−0.777249	−	1.06979i	0.218331	−	0.975875i	$-0.429939\pi$
$912$		0			0
$913$	−5.62882	+	0.891518i	−0.186287	+	0.0295049i
$914$		0			0
$915$	−6.75859	−	9.41385i	−0.223432	−	0.311212i
$916$		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
$921$	−1.32674	+	1.05788i	−0.0437177	+	0.0348582i
$922$		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
$927$	−4.21172	−	16.7253i	−0.138331	−	0.549332i
$928$		0			0
$929$	−13.4033	+	41.2512i	−0.439749	+	1.35341i	0.448391	+	0.893837i	$0.351997\pi$
$929$	−13.4033	+	41.2512i	−0.439749	+	1.35341i	−0.888141	+	0.459572i	$0.848003\pi$
$930$		0			0
$931$	−4.60896	−	14.1849i	−0.151052	−	0.464892i
$932$		0			0
$933$	−20.9236	+	11.8704i	−0.685009	+	0.388619i
$934$		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
$939$	−1.94988	−	43.4910i	−0.0636319	−	1.41927i
$940$		0			0
$941$	−8.76171	+	12.0595i	−0.285623	+	0.393127i	−0.927586	−	0.373609i	$-0.878120\pi$
$941$	−8.76171	+	12.0595i	−0.285623	+	0.393127i	0.641963	+	0.766736i	$0.278120\pi$
$942$		0			0
$943$	−6.65513	+	6.65513i	−0.216721	+	0.216721i
$944$		0			0
$945$	−34.1251	+	21.1669i	−1.11009	+	0.688561i
$946$		0			0
$947$	−22.4410	−	44.0430i	−0.729235	−	1.43120i	−0.895472	−	0.445118i	$-0.853162\pi$
$947$	−22.4410	−	44.0430i	−0.729235	−	1.43120i	0.166237	−	0.986086i	$-0.446838\pi$
$948$		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	−0.533583	−	0.845747i	$-0.679155\pi$
$953$	−5.03167	+	2.56376i	−0.162992	+	0.0830484i	0.370592	+	0.928796i	$0.379155\pi$
$954$		0			0
$955$	13.7094	−	23.8500i	0.443625	−	0.771769i
$956$		0			0
$957$	−2.91663	−	14.2503i	−0.0942813	−	0.460646i
$958$		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
$963$	−27.7168	+	17.4098i	−0.893162	+	0.561022i
$964$		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
$969$	8.79204	−	31.8478i	0.282441	−	1.02310i
$970$		0			0
$971$	47.8773	+	15.5563i	1.53646	+	0.499225i	0.950396	−	0.311042i	$-0.100678\pi$
$971$	47.8773	+	15.5563i	1.53646	+	0.499225i	0.586061	+	0.810267i	$0.300678\pi$
$972$		0			0
$973$	−4.63307	+	29.2520i	−0.148529	+	0.937777i
$974$		0			0
$975$	−10.3882	−	39.3591i	−0.332689	−	1.26050i
$976$		0			0
$977$	−6.17988	+	39.0183i	−0.197712	+	1.24830i	0.666626	+	0.745393i	$0.267738\pi$
$977$	−6.17988	+	39.0183i	−0.197712	+	1.24830i	−0.864338	+	0.502912i	$0.832262\pi$
$978$		0			0
$979$	2.43809	+	0.792182i	0.0779216	+	0.0253182i
$980$		0			0
$981$	−23.4519	+	20.4830i	−0.748760	+	0.653972i
$982$		0			0
$983$	−0.0192554	+	0.0377908i	−0.000614152	+	0.00120534i	−0.891313	−	0.453388i	$-0.850215\pi$
$983$	−0.0192554	+	0.0377908i	−0.000614152	+	0.00120534i	0.890699	+	0.454593i	$0.150215\pi$
$984$		0			0
$985$	−12.3876	−	18.9960i	−0.394703	−	0.605264i
$986$		0			0
$987$	57.6517	+	26.1919i	1.83507	+	0.833698i
$988$		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
$993$	57.8485	−	11.8400i	1.83577	−	0.375730i
$994$		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.77.5	yes	80
3.2	odd	2	inner	300.2.x.a.77.2	✓	80
25.13	odd	20	inner	300.2.x.a.113.2	yes	80
75.38	even	20	inner	300.2.x.a.113.5	yes	80

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

\(f(q)\)	\(=\)	\(q+(0.194059 - 1.72115i) q^{3} +(2.22337 - 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(-2.92468 - 0.668006i) q^{9} +O(q^{10})\)	\(q+(0.194059 - 1.72115i) q^{3} +(2.22337 - 0.237965i) q^{5} +(2.44386 + 2.44386i) q^{7} +(-2.92468 - 0.668006i) q^{9} +(0.626305 + 0.862035i) q^{11} +(4.64256 - 0.735309i) q^{13} +(0.0218922 - 3.87292i) q^{15} +(-5.63490 - 2.87112i) q^{17} +(-2.86859 + 0.932063i) q^{19} +(4.68049 - 3.73199i) q^{21} +(-4.44376 - 0.703822i) q^{23} +(4.88675 - 1.05817i) q^{25} +(-1.71730 + 4.90417i) q^{27} +(2.43550 - 7.49571i) q^{29} +(-0.586924 - 1.80637i) q^{31} +(1.60523 - 0.910677i) q^{33} +(6.01516 + 4.85205i) q^{35} +(0.993131 + 6.27038i) q^{37} +(-0.364645 - 8.13321i) q^{39} +(1.22959 - 1.69238i) q^{41} +(-8.27416 + 8.27416i) q^{43} +(-6.66161 - 0.789253i) q^{45} +(4.80234 + 9.42512i) q^{47} +4.94490i q^{49} +(-6.03512 + 9.14131i) q^{51} +(-9.25431 + 4.71531i) q^{53} +(1.59764 + 1.76758i) q^{55} +(1.04754 + 5.11814i) q^{57} +(-3.79924 - 2.76031i) q^{59} +(2.42074 - 1.75877i) q^{61} +(-5.51500 - 8.78003i) q^{63} +(10.1471 - 2.73963i) q^{65} +(2.94083 - 5.77171i) q^{67} +(-2.07373 + 7.51177i) q^{69} +(-0.855266 - 0.277893i) q^{71} +(-0.277586 + 1.75261i) q^{73} +(-0.872944 - 8.61615i) q^{75} +(-0.576091 + 3.63730i) q^{77} +(-8.30052 - 2.69700i) q^{79} +(8.10754 + 3.90741i) q^{81} +(-2.42816 + 4.76553i) q^{83} +(-13.2117 - 5.04266i) q^{85} +(-12.4286 - 5.64646i) q^{87} +(1.94640 - 1.41415i) q^{89} +(13.1428 + 9.54877i) q^{91} +(-3.22292 + 0.659641i) q^{93} +(-6.15615 + 2.75494i) q^{95} +(-4.23366 + 2.15716i) q^{97} +(-1.25590 - 2.93956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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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