LMFDB - Embedded newform 702.2.bc.a.557.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(305,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("702.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.12
Character	$\chi$	$=$	702.557
Dual form			702.2.bc.a.305.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.179629 + 0.670386i) q^{5} +(3.24572 - 3.24572i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.601052 + 0.347017i) q^{10} +(2.17356 - 0.582403i) q^{11} +(-1.78196 - 3.13442i) q^{13} +(3.97518 + 2.29507i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.32181 - 4.02149i) q^{17} +(-2.81042 + 0.753050i) q^{19} +(-0.490757 - 0.490757i) q^{20} +(1.12512 + 1.94876i) q^{22} -4.74503 q^{23} +(3.91298 - 2.25916i) q^{25} +(2.56642 - 2.53249i) q^{26} +(-1.18802 + 4.43374i) q^{28} +(4.22816 + 2.44113i) q^{29} +(6.51808 - 1.74651i) q^{31} +(0.965926 + 0.258819i) q^{32} +(4.48539 + 1.20186i) q^{34} +(2.75891 + 1.59286i) q^{35} +(3.44953 + 0.924299i) q^{37} +(-1.45478 - 2.51976i) q^{38} +(0.347017 - 0.601052i) q^{40} +(-4.05999 + 4.05999i) q^{41} +5.30657i q^{43} +(-1.59115 + 1.59115i) q^{44} +(-1.22810 - 4.58334i) q^{46} +(-3.12430 + 11.6601i) q^{47} -14.0694i q^{49} +(3.19493 + 3.19493i) q^{50} +(3.11043 + 1.82351i) q^{52} +5.06576i q^{53} +(0.780869 + 1.35250i) q^{55} -4.59014 q^{56} +(-1.26362 + 4.71590i) q^{58} +(1.38984 - 5.18694i) q^{59} +3.12110 q^{61} +(3.37401 + 5.84395i) q^{62} +1.00000i q^{64} +(1.78118 - 1.75764i) q^{65} +(9.25140 + 9.25140i) q^{67} +4.64361i q^{68} +(-0.824524 + 3.07717i) q^{70} +(-4.16970 - 15.5615i) q^{71} +(-5.55110 + 5.55110i) q^{73} +3.57122i q^{74} +(2.05737 - 2.05737i) q^{76} +(5.16444 - 8.94507i) q^{77} +(-1.55400 - 2.69161i) q^{79} +(0.670386 + 0.179629i) q^{80} +(-4.97245 - 2.87085i) q^{82} +(-9.17998 - 2.45977i) q^{83} +(3.11301 + 0.834129i) q^{85} +(-5.12575 + 1.37344i) q^{86} +(-1.94876 - 1.12512i) q^{88} +(-0.648204 + 2.41913i) q^{89} +(-15.9572 - 4.38972i) q^{91} +(4.10931 - 2.37251i) q^{92} -12.0714 q^{94} +(-1.00967 - 1.74880i) q^{95} +(-0.868150 - 0.868150i) q^{97} +(13.5900 - 3.64143i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.179629	+	0.670386i	0.0803327	+	0.299806i	0.994390	−	0.105780i	$-0.0337341\pi$
$5$	0.179629	+	0.670386i	0.0803327	+	0.299806i	−0.914057	+	0.405586i	$0.867067\pi$
$6$		0			0
$7$	3.24572	−	3.24572i	1.22677	−	1.22677i	0.261587	−	0.965180i	$-0.415754\pi$
$7$	3.24572	−	3.24572i	1.22677	−	1.22677i	0.965180	−	0.261587i	$-0.0842458\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.601052	+	0.347017i	−0.190069	+	0.109736i
$11$	2.17356	−	0.582403i	0.655352	−	0.175601i	0.0842044	−	0.996449i	$-0.473165\pi$
$11$	2.17356	−	0.582403i	0.655352	−	0.175601i	0.571147	+	0.820848i	$0.306498\pi$
$12$		0			0
$13$	−1.78196	−	3.13442i	−0.494227	−	0.869333i
$13$	−1.78196	−	3.13442i	−0.494227	−	0.869333i
$14$	3.97518	+	2.29507i	1.06241	+	0.613383i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.32181	−	4.02149i	0.563121	−	0.975354i	−0.434101	−	0.900864i	$-0.642934\pi$
$17$	2.32181	−	4.02149i	0.563121	−	0.975354i	0.997222	−	0.0744895i	$-0.0237327\pi$
$18$		0			0
$19$	−2.81042	+	0.753050i	−0.644755	+	0.172762i	−0.566356	−	0.824160i	$-0.691647\pi$
$19$	−2.81042	+	0.753050i	−0.644755	+	0.172762i	−0.0783988	+	0.996922i	$0.524981\pi$
$20$	−0.490757	−	0.490757i	−0.109736	−	0.109736i
$21$		0			0
$22$	1.12512	+	1.94876i	0.239875	+	0.415476i
$23$	−4.74503			−0.989407			−0.494703	−	0.869062i	$-0.664723\pi$
$23$	−4.74503			−0.989407			−0.494703	+	0.869062i	$0.664723\pi$
$24$		0			0
$25$	3.91298	−	2.25916i	0.782595	−	0.451832i
$26$	2.56642	−	2.53249i	0.503316	−	0.496662i
$27$		0			0
$28$	−1.18802	+	4.43374i	−0.224514	+	0.837897i
$29$	4.22816	+	2.44113i	0.785150	+	0.453307i	0.838252	−	0.545282i	$-0.183578\pi$
$29$	4.22816	+	2.44113i	0.785150	+	0.453307i	−0.0531023	+	0.998589i	$0.516911\pi$
$30$		0			0
$31$	6.51808	−	1.74651i	1.17068	−	0.313683i	0.379457	−	0.925209i	$-0.376111\pi$
$31$	6.51808	−	1.74651i	1.17068	−	0.313683i	0.791224	+	0.611526i	$0.209444\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	4.48539	+	1.20186i	0.769237	+	0.206116i
$35$	2.75891	+	1.59286i	0.466341	+	0.269242i
$36$		0			0
$37$	3.44953	+	0.924299i	0.567099	+	0.151954i	0.530966	−	0.847393i	$-0.321829\pi$
$37$	3.44953	+	0.924299i	0.567099	+	0.151954i	0.0361333	+	0.999347i	$0.488496\pi$
$38$	−1.45478	−	2.51976i	−0.235997	−	0.408758i
$39$		0			0
$40$	0.347017	−	0.601052i	0.0548682	−	0.0950346i
$41$	−4.05999	+	4.05999i	−0.634064	+	0.634064i	−0.949085	−	0.315021i	$-0.897988\pi$
$41$	−4.05999	+	4.05999i	−0.634064	+	0.634064i	0.315021	+	0.949085i	$0.397988\pi$
$42$		0			0
$43$			5.30657i			0.809244i	0.914484	+	0.404622i	$0.132597\pi$
$43$			5.30657i			0.809244i	−0.914484	+	0.404622i	$0.867403\pi$
$44$	−1.59115	+	1.59115i	−0.239875	+	0.239875i
$45$		0			0
$46$	−1.22810	−	4.58334i	−0.181074	−	0.675777i
$47$	−3.12430	+	11.6601i	−0.455727	+	1.70080i	0.230216	+	0.973140i	$0.426057\pi$
$47$	−3.12430	+	11.6601i	−0.455727	+	1.70080i	−0.685943	+	0.727656i	$0.740610\pi$
$48$		0			0
$49$		−	14.0694i		−	2.00991i
$50$	3.19493	+	3.19493i	0.451832	+	0.451832i
$51$		0			0
$52$	3.11043	+	1.82351i	0.431340	+	0.252876i
$53$			5.06576i			0.695835i	0.937525	+	0.347918i	$0.113111\pi$
$53$			5.06576i			0.695835i	−0.937525	+	0.347918i	$0.886889\pi$
$54$		0			0
$55$	0.780869	+	1.35250i	0.105292	+	0.182372i
$56$	−4.59014			−0.613383
$57$		0			0
$58$	−1.26362	+	4.71590i	−0.165922	+	0.619228i
$59$	1.38984	−	5.18694i	0.180941	−	0.675282i	−0.814522	−	0.580133i	$-0.803001\pi$
$59$	1.38984	−	5.18694i	0.180941	−	0.675282i	0.995463	−	0.0951492i	$-0.0303328\pi$
$60$		0			0
$61$	3.12110			0.399616			0.199808	−	0.979835i	$-0.435968\pi$
$61$	3.12110			0.399616			0.199808	+	0.979835i	$0.435968\pi$
$62$	3.37401	+	5.84395i	0.428499	+	0.742182i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	1.78118	−	1.75764i	0.220928	−	0.218008i
$66$		0			0
$67$	9.25140	+	9.25140i	1.13024	+	1.13024i	0.990137	+	0.140102i	$0.0447429\pi$
$67$	9.25140	+	9.25140i	1.13024	+	1.13024i	0.140102	+	0.990137i	$0.455257\pi$
$68$			4.64361i			0.563121i
$69$		0			0
$70$	−0.824524	+	3.07717i	−0.0985495	+	0.367792i
$71$	−4.16970	−	15.5615i	−0.494852	−	1.84681i	−0.530857	−	0.847461i	$-0.678130\pi$
$71$	−4.16970	−	15.5615i	−0.494852	−	1.84681i	0.0360054	−	0.999352i	$-0.488537\pi$
$72$		0			0
$73$	−5.55110	+	5.55110i	−0.649707	+	0.649707i	−0.952922	−	0.303215i	$-0.901940\pi$
$73$	−5.55110	+	5.55110i	−0.649707	+	0.649707i	0.303215	+	0.952922i	$0.401940\pi$
$74$			3.57122i			0.415145i
$75$		0			0
$76$	2.05737	−	2.05737i	0.235997	−	0.235997i
$77$	5.16444	−	8.94507i	0.588542	−	1.01939i
$78$		0			0
$79$	−1.55400	−	2.69161i	−0.174839	−	0.302829i	0.765267	−	0.643713i	$-0.222607\pi$
$79$	−1.55400	−	2.69161i	−0.174839	−	0.302829i	−0.940105	+	0.340884i	$0.889274\pi$
$80$	0.670386	+	0.179629i	0.0749514	+	0.0200832i
$81$		0			0
$82$	−4.97245	−	2.87085i	−0.549115	−	0.317032i
$83$	−9.17998	−	2.45977i	−1.00763	−	0.269995i	−0.282993	−	0.959122i	$-0.591327\pi$
$83$	−9.17998	−	2.45977i	−1.00763	−	0.269995i	−0.724640	+	0.689127i	$0.757994\pi$
$84$		0			0
$85$	3.11301	+	0.834129i	0.337654	+	0.0904740i
$86$	−5.12575	+	1.37344i	−0.552724	+	0.148102i
$87$		0			0
$88$	−1.94876	−	1.12512i	−0.207738	−	0.119938i
$89$	−0.648204	+	2.41913i	−0.0687095	+	0.256427i	−0.991733	−	0.128315i	$-0.959043\pi$
$89$	−0.648204	+	2.41913i	−0.0687095	+	0.256427i	0.923024	+	0.384743i	$0.125710\pi$
$90$		0			0
$91$	−15.9572	−	4.38972i	−1.67277	−	0.460168i
$92$	4.10931	−	2.37251i	0.428426	−	0.247352i
$93$		0			0
$94$	−12.0714			−1.24507
$95$	−1.00967	−	1.74880i	−0.103590	−	0.179423i
$96$		0			0
$97$	−0.868150	−	0.868150i	−0.0881473	−	0.0881473i	0.661658	−	0.749806i	$-0.269853\pi$
$97$	−0.868150	−	0.868150i	−0.0881473	−	0.0881473i	−0.749806	+	0.661658i	$0.769853\pi$
$98$	13.5900	−	3.64143i	1.37280	−	0.367840i
$99$		0			0
$100$	−2.25916	+	3.91298i	−0.225916	+	0.391298i
$101$	1.88220	−	3.26007i	0.187286	−	0.324389i	−0.757058	−	0.653347i	$-0.773364\pi$
$101$	1.88220	−	3.26007i	0.187286	−	0.324389i	0.944345	+	0.328958i	$0.106698\pi$
$102$		0			0
$103$	−13.1567	−	7.59604i	−1.29637	−	0.748460i	−0.316596	−	0.948561i	$-0.602540\pi$
$103$	−13.1567	−	7.59604i	−1.29637	−	0.748460i	−0.979775	+	0.200100i	$0.935873\pi$
$104$	−0.956337	+	3.47641i	−0.0937766	+	0.340890i
$105$		0			0
$106$	−4.89315	+	1.31111i	−0.475264	+	0.127347i
$107$	−4.73458	+	2.73351i	−0.457709	+	0.264259i	−0.711081	−	0.703111i	$-0.751794\pi$
$107$	−4.73458	+	2.73351i	−0.457709	+	0.264259i	0.253371	+	0.967369i	$0.418461\pi$
$108$		0			0
$109$	5.10130	+	5.10130i	0.488616	+	0.488616i	0.907869	−	0.419253i	$-0.137708\pi$
$109$	5.10130	+	5.10130i	0.488616	+	0.488616i	−0.419253	+	0.907869i	$0.637708\pi$
$110$	−1.10432	+	1.10432i	−0.105292	+	0.105292i
$111$		0			0
$112$	−1.18802	−	4.43374i	−0.112257	−	0.418949i
$113$	−0.409538	+	0.236447i	−0.0385261	+	0.0222430i	−0.519139	−	0.854690i	$-0.673747\pi$
$113$	−0.409538	+	0.236447i	−0.0385261	+	0.0222430i	0.480613	+	0.876933i	$0.340414\pi$
$114$		0			0
$115$	−0.852346	−	3.18100i	−0.0794817	−	0.296630i
$116$	−4.88226			−0.453307
$117$		0			0
$118$	5.36992			0.494341
$119$	−5.51668	−	20.5885i	−0.505714	−	1.88735i
$120$		0			0
$121$	−5.14113	+	2.96823i	−0.467375	+	0.269839i
$122$	0.807800	+	3.01475i	0.0731348	+	0.272943i
$123$		0			0
$124$	−4.77157	+	4.77157i	−0.428499	+	0.428499i
$125$	4.67118	+	4.67118i	0.417803	+	0.417803i
$126$		0			0
$127$	−0.377096	+	0.217716i	−0.0334618	+	0.0193192i	−0.516638	−	0.856204i	$-0.672817\pi$
$127$	−0.377096	+	0.217716i	−0.0334618	+	0.0193192i	0.483176	+	0.875523i	$0.339483\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	2.15875	+	1.26558i	0.189335	+	0.110999i
$131$	9.02321	+	5.20955i	0.788361	+	0.455161i	0.839385	−	0.543537i	$-0.182915\pi$
$131$	9.02321	+	5.20955i	0.788361	+	0.455161i	−0.0510241	+	0.998697i	$0.516249\pi$
$132$		0			0
$133$	−6.67765	+	11.5660i	−0.579026	+	1.00290i
$134$	−6.54173	+	11.3306i	−0.565119	+	0.978815i
$135$		0			0
$136$	−4.48539	+	1.20186i	−0.384619	+	0.103058i
$137$	5.40791	+	5.40791i	0.462029	+	0.462029i	0.899320	−	0.437291i	$-0.144062\pi$
$137$	5.40791	+	5.40791i	0.462029	+	0.462029i	−0.437291	+	0.899320i	$0.644062\pi$
$138$		0			0
$139$	−5.58662	−	9.67631i	−0.473851	−	0.820734i	0.525701	−	0.850670i	$-0.323803\pi$
$139$	−5.58662	−	9.67631i	−0.473851	−	0.820734i	−0.999552	+	0.0299353i	$0.990470\pi$
$140$	−3.18572			−0.269242
$141$		0			0
$142$	13.9521	−	8.05524i	1.17083	−	0.675980i
$143$	−5.69869	−	5.77503i	−0.476548	−	0.482932i
$144$		0			0
$145$	−0.876997	+	3.27300i	−0.0728307	+	0.271808i
$146$	−6.79868	−	3.92522i	−0.562663	−	0.324853i
$147$		0			0
$148$	−3.44953	+	0.924299i	−0.283550	+	0.0759769i
$149$	7.14709	+	1.91506i	0.585513	+	0.156888i	0.539401	−	0.842049i	$-0.318651\pi$
$149$	7.14709	+	1.91506i	0.585513	+	0.156888i	0.0461110	+	0.998936i	$0.485317\pi$
$150$		0			0
$151$	13.8415	+	3.70881i	1.12640	+	0.301818i	0.773471	−	0.633831i	$-0.218519\pi$
$151$	13.8415	+	3.70881i	1.12640	+	0.301818i	0.352930	+	0.935650i	$0.385185\pi$
$152$	2.51976	+	1.45478i	0.204379	+	0.117998i
$153$		0			0
$154$	9.97693	+	2.67331i	0.803964	+	0.215421i
$155$	2.34168	+	4.05590i	0.188088	+	0.325778i
$156$		0			0
$157$	−2.86104	+	4.95546i	−0.228336	+	0.395489i	−0.957315	−	0.289047i	$-0.906662\pi$
$157$	−2.86104	+	4.95546i	−0.228336	+	0.395489i	0.728979	+	0.684536i	$0.239995\pi$
$158$	2.19769	−	2.19769i	0.174839	−	0.174839i
$159$		0			0
$160$			0.694035i			0.0548682i
$161$	−15.4010	+	15.4010i	−1.21377	+	1.21377i
$162$		0			0
$163$	−1.44621	−	5.39731i	−0.113276	−	0.422750i	0.885877	−	0.463921i	$-0.153558\pi$
$163$	−1.44621	−	5.39731i	−0.113276	−	0.422750i	−0.999152	+	0.0411708i	$0.986891\pi$
$164$	1.48606	−	5.54605i	0.116042	−	0.433074i
$165$		0			0
$166$		−	9.50381i		−	0.737639i
$167$	−17.3166	−	17.3166i	−1.34000	−	1.34000i	−0.896054	−	0.443945i	$-0.853579\pi$
$167$	−17.3166	−	17.3166i	−1.34000	−	1.34000i	−0.443945	−	0.896054i	$-0.646421\pi$
$168$		0			0
$169$	−6.64924	+	11.1708i	−0.511480	+	0.859295i
$170$			3.22283i			0.247180i
$171$		0			0
$172$	−2.65328	−	4.59562i	−0.202311	−	0.350413i
$173$	10.5940			0.805445			0.402722	−	0.915322i	$-0.368064\pi$
$173$	10.5940			0.805445			0.402722	+	0.915322i	$0.368064\pi$
$174$		0			0
$175$	5.36783	−	20.0330i	0.405770	−	1.51435i
$176$	0.582403	−	2.17356i	0.0439002	−	0.163838i
$177$		0			0
$178$	−2.50447			−0.187718
$179$	−6.22591	−	10.7836i	−0.465346	−	0.806003i	0.533871	−	0.845566i	$-0.320737\pi$
$179$	−6.22591	−	10.7836i	−0.465346	−	0.806003i	−0.999217	+	0.0395630i	$0.987403\pi$
$180$		0			0
$181$			18.4465i			1.37112i	0.728018	+	0.685558i	$0.240442\pi$
$181$			18.4465i			1.37112i	−0.728018	+	0.685558i	$0.759558\pi$
$182$	0.110118	−	16.5496i	0.00816251	−	1.22674i
$183$		0			0
$184$	3.35524	+	3.35524i	0.247352	+	0.247352i
$185$			2.47855i			0.182226i
$186$		0			0
$187$	2.70445	−	10.0932i	0.197769	−	0.738084i
$188$	−3.12430	−	11.6601i	−0.227863	−	0.850398i
$189$		0			0
$190$	1.42789	−	1.42789i	0.103590	−	0.103590i
$191$			8.51565i			0.616171i	0.951359	+	0.308085i	$0.0996883\pi$
$191$			8.51565i			0.616171i	−0.951359	+	0.308085i	$0.900312\pi$
$192$		0			0
$193$	−13.3856	+	13.3856i	−0.963516	+	0.963516i	−0.999358	−	0.0358411i	$-0.988589\pi$
$193$	−13.3856	+	13.3856i	−0.963516	+	0.963516i	0.0358411	+	0.999358i	$0.488589\pi$
$194$	0.613875	−	1.06326i	0.0440736	−	0.0763378i
$195$		0			0
$196$	7.03470	+	12.1845i	0.502478	+	0.870318i
$197$	−16.8453	−	4.51369i	−1.20018	−	0.321587i	−0.397278	−	0.917698i	$-0.630045\pi$
$197$	−16.8453	−	4.51369i	−1.20018	−	0.321587i	−0.802902	+	0.596111i	$0.796712\pi$
$198$		0			0
$199$	20.0170	+	11.5568i	1.41897	+	0.819243i	0.996208	−	0.0869986i	$-0.0277276\pi$
$199$	20.0170	+	11.5568i	1.41897	+	0.819243i	0.422761	+	0.906241i	$0.361061\pi$
$200$	−4.36436	−	1.16943i	−0.308607	−	0.0826909i
$201$		0			0
$202$	3.63614	+	0.974300i	0.255838	+	0.0685515i
$203$	21.6467	−	5.80020i	1.51930	−	0.407095i
$204$		0			0
$205$	−3.45105	−	1.99247i	−0.241032	−	0.139160i
$206$	3.93200	−	14.6744i	0.273955	−	1.02242i
$207$		0			0
$208$	−3.60547	−	0.0239902i	−0.249994	−	0.00166342i
$209$	−5.67003	+	3.27359i	−0.392204	+	0.226439i
$210$		0			0
$211$	−10.3885			−0.715172			−0.357586	−	0.933880i	$-0.616400\pi$
$211$	−10.3885			−0.715172			−0.357586	+	0.933880i	$0.616400\pi$
$212$	−2.53288	−	4.38707i	−0.173959	−	0.301306i
$213$		0			0
$214$	−3.86577	−	3.86577i	−0.264259	−	0.264259i
$215$	−3.55745	+	0.953215i	−0.242616	+	0.0650087i
$216$		0			0
$217$	15.4872	−	26.8246i	1.05134	−	1.82097i
$218$	−3.60717	+	6.24779i	−0.244308	+	0.423154i
$219$		0			0
$220$	−1.35250	−	0.780869i	−0.0911858	−	0.0526462i
$221$	−16.7424	−	0.111401i	−1.12622	−	0.00749365i
$222$		0			0
$223$	−15.3255	+	4.10646i	−1.02627	+	0.274989i	−0.732414	−	0.680860i	$-0.761606\pi$
$223$	−15.3255	+	4.10646i	−1.02627	+	0.274989i	−0.293859	+	0.955849i	$0.594940\pi$
$224$	3.97518	−	2.29507i	0.265603	−	0.153346i
$225$		0			0
$226$	−0.334386	−	0.334386i	−0.0222430	−	0.0222430i
$227$	−4.50740	+	4.50740i	−0.299167	+	0.299167i	−0.840687	−	0.541521i	$-0.817849\pi$
$227$	−4.50740	+	4.50740i	−0.299167	+	0.299167i	0.541521	+	0.840687i	$0.317849\pi$
$228$		0			0
$229$	−3.31118	−	12.3575i	−0.218809	−	0.816606i	−0.984791	−	0.173744i	$-0.944414\pi$
$229$	−3.31118	−	12.3575i	−0.218809	−	0.816606i	0.765982	−	0.642862i	$-0.222253\pi$
$230$	2.85201	−	1.64661i	0.188056	−	0.108574i
$231$		0			0
$232$	−1.26362	−	4.71590i	−0.0829609	−	0.309614i
$233$	18.2644			1.19654			0.598271	−	0.801294i	$-0.295855\pi$
$233$	18.2644			1.19654			0.598271	+	0.801294i	$0.295855\pi$
$234$		0			0
$235$	−8.37796			−0.546518
$236$	1.38984	+	5.18694i	0.0904707	+	0.337641i
$237$		0			0
$238$	18.4592	−	10.6574i	1.19653	−	0.690818i
$239$	−5.17656	−	19.3192i	−0.334844	−	1.24965i	−0.904039	−	0.427451i	$-0.859412\pi$
$239$	−5.17656	−	19.3192i	−0.334844	−	1.24965i	0.569195	−	0.822203i	$-0.307255\pi$
$240$		0			0
$241$	10.6459	−	10.6459i	0.685762	−	0.685762i	−0.275530	−	0.961292i	$-0.588853\pi$
$241$	10.6459	−	10.6459i	0.685762	−	0.685762i	0.961292	+	0.275530i	$0.0888534\pi$
$242$	−4.19771	−	4.19771i	−0.269839	−	0.269839i
$243$		0			0
$244$	−2.70295	+	1.56055i	−0.173039	+	0.0999040i
$245$	9.43192	−	2.52728i	0.602583	−	0.161462i
$246$		0			0
$247$	7.36844	+	7.46715i	0.468843	+	0.475124i
$248$	−5.84395	−	3.37401i	−0.371091	−	0.214250i
$249$		0			0
$250$	−3.30302	+	5.72100i	−0.208901	+	0.361828i
$251$	−13.1431	+	22.7645i	−0.829586	+	1.43689i	0.0687771	+	0.997632i	$0.478090\pi$
$251$	−13.1431	+	22.7645i	−0.829586	+	1.43689i	−0.898363	+	0.439253i	$0.855243\pi$
$252$		0			0
$253$	−10.3136	+	2.76352i	−0.648409	+	0.173741i
$254$	−0.307897	−	0.307897i	−0.0193192	−	0.0193192i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.6658			−0.852450			−0.426225	−	0.904617i	$-0.640157\pi$
$257$	−13.6658			−0.852450			−0.426225	+	0.904617i	$0.640157\pi$
$258$		0			0
$259$	14.1962	−	8.19619i	0.882110	−	0.509286i
$260$	−0.663731	+	2.41275i	−0.0411629	+	0.149632i
$261$		0			0
$262$	−2.69666	+	10.0641i	−0.166600	+	0.621761i
$263$	4.15346	+	2.39800i	0.256113	+	0.147867i	0.622560	−	0.782572i	$-0.286093\pi$
$263$	4.15346	+	2.39800i	0.256113	+	0.147867i	−0.366447	+	0.930439i	$0.619426\pi$
$264$		0			0
$265$	−3.39601	+	0.909959i	−0.208615	+	0.0558983i
$266$	−12.9002	−	3.45661i	−0.790964	−	0.211938i
$267$		0			0
$268$	−12.6377	−	3.38625i	−0.771967	−	0.206848i
$269$	21.5499	+	12.4418i	1.31392	+	0.758591i	0.982743	−	0.184978i	$-0.0592214\pi$
$269$	21.5499	+	12.4418i	1.31392	+	0.758591i	0.331176	+	0.943569i	$0.392555\pi$
$270$		0			0
$271$	−0.766787	−	0.205460i	−0.0465790	−	0.0124808i	0.235454	−	0.971885i	$-0.424342\pi$
$271$	−0.766787	−	0.205460i	−0.0465790	−	0.0124808i	−0.282033	+	0.959405i	$0.591009\pi$
$272$	−2.32181	−	4.02149i	−0.140780	−	0.243838i
$273$		0			0
$274$	−3.82397	+	6.62331i	−0.231015	+	0.400129i
$275$	7.18933	−	7.18933i	0.433533	−	0.433533i
$276$		0			0
$277$			32.9502i			1.97979i	0.141813	+	0.989893i	$0.454707\pi$
$277$			32.9502i			1.97979i	−0.141813	+	0.989893i	$0.545293\pi$
$278$	7.90068	−	7.90068i	0.473851	−	0.473851i
$279$		0			0
$280$	−0.824524	−	3.07717i	−0.0492747	−	0.183896i
$281$	4.70802	−	17.5706i	0.280857	−	1.04817i	−0.670957	−	0.741496i	$-0.734117\pi$
$281$	4.70802	−	17.5706i	0.280857	−	1.04817i	0.951814	−	0.306676i	$-0.0992168\pi$
$282$		0			0
$283$			24.4025i			1.45058i	0.688446	+	0.725288i	$0.258293\pi$
$283$			24.4025i			1.45058i	−0.688446	+	0.725288i	$0.741707\pi$
$284$	11.3918	+	11.3918i	0.675980	+	0.675980i
$285$		0			0
$286$	4.10332	−	6.99920i	0.242635	−	0.413871i
$287$			26.3552i			1.55570i
$288$		0			0
$289$	−2.28157	−	3.95179i	−0.134210	−	0.232458i
$290$	−3.38846			−0.198977
$291$		0			0
$292$	2.03184	−	7.58294i	0.118905	−	0.443758i
$293$	0.941471	−	3.51362i	0.0550013	−	0.205268i	−0.932957	−	0.359988i	$-0.882781\pi$
$293$	0.941471	−	3.51362i	0.0550013	−	0.205268i	0.987958	+	0.154720i	$0.0494475\pi$
$294$		0			0
$295$	3.72691			0.216989
$296$	−1.78561	−	3.09276i	−0.103786	−	0.179763i
$297$		0			0
$298$			7.39921i			0.428625i
$299$	8.45545	+	14.8729i	0.488991	+	0.860124i
$300$		0			0
$301$	17.2236	+	17.2236i	0.992754	+	0.992754i
$302$			14.3297i			0.824583i
$303$		0			0
$304$	−0.753050	+	2.81042i	−0.0431904	+	0.161189i
$305$	0.560641	+	2.09234i	0.0321022	+	0.119807i
$306$		0			0
$307$	10.8993	−	10.8993i	0.622055	−	0.622055i	−0.324001	−	0.946057i	$-0.605028\pi$
$307$	10.8993	−	10.8993i	0.622055	−	0.622055i	0.946057	+	0.324001i	$0.105028\pi$
$308$			10.3289i			0.588542i
$309$		0			0
$310$	−3.31163	+	3.31163i	−0.188088	+	0.188088i
$311$	−5.37895	+	9.31661i	−0.305012	+	0.528296i	−0.977264	−	0.212026i	$-0.931994\pi$
$311$	−5.37895	+	9.31661i	−0.305012	+	0.528296i	0.672252	+	0.740322i	$0.265327\pi$
$312$		0			0
$313$	6.34655	+	10.9926i	0.358728	+	0.621336i	0.987749	−	0.156053i	$-0.0498771\pi$
$313$	6.34655	+	10.9926i	0.358728	+	0.621336i	−0.629020	+	0.777389i	$0.716544\pi$
$314$	−5.52710	−	1.48098i	−0.311912	−	0.0835766i
$315$		0			0
$316$	2.69161	+	1.55400i	0.151415	+	0.0874193i
$317$	25.1552	+	6.74033i	1.41286	+	0.378574i	0.882945	−	0.469477i	$-0.155557\pi$
$317$	25.1552	+	6.74033i	1.41286	+	0.378574i	0.529914	+	0.848051i	$0.322224\pi$
$318$		0			0
$319$	10.6119	+	2.84344i	0.594151	+	0.159202i
$320$	−0.670386	+	0.179629i	−0.0374757	+	0.0100416i
$321$		0			0
$322$	−18.8623	−	10.8902i	−1.05116	−	0.606886i
$323$	−3.49687	+	13.0505i	−0.194571	+	0.726150i
$324$		0			0
$325$	−14.0539	−	8.23920i	−0.779572	−	0.457029i
$326$	4.83910	−	2.79386i	0.268013	−	0.154737i
$327$		0			0
$328$	5.74169			0.317032
$329$	27.7047	+	47.9859i	1.52741	+	2.64555i
$330$		0			0
$331$	−14.3286	−	14.3286i	−0.787571	−	0.787571i	0.193525	−	0.981095i	$-0.438008\pi$
$331$	−14.3286	−	14.3286i	−0.787571	−	0.787571i	−0.981095	+	0.193525i	$0.938008\pi$
$332$	9.17998	−	2.45977i	0.503817	−	0.134997i
$333$		0			0
$334$	12.2447	−	21.2084i	0.670000	−	1.16047i
$335$	−4.54019	+	7.86383i	−0.248057	+	0.429647i
$336$		0			0
$337$	6.82932	+	3.94291i	0.372017	+	0.214784i	0.674339	−	0.738422i	$-0.264429\pi$
$337$	6.82932	+	3.94291i	0.372017	+	0.214784i	−0.302322	+	0.953206i	$0.597762\pi$
$338$	−12.5112	−	3.53145i	−0.680517	−	0.192085i
$339$		0			0
$340$	−3.11301	+	0.834129i	−0.168827	+	0.0452370i
$341$	13.1502	−	7.59229i	0.712125	−	0.411146i
$342$		0			0
$343$	−22.9453	−	22.9453i	−1.23893	−	1.23893i
$344$	3.75231	−	3.75231i	0.202311	−	0.202311i
$345$		0			0
$346$	2.74192	+	10.2330i	0.147407	+	0.550129i
$347$	14.7186	−	8.49778i	0.790135	−	0.456185i	−0.0498748	−	0.998755i	$-0.515882\pi$
$347$	14.7186	−	8.49778i	0.790135	−	0.456185i	0.840010	+	0.542571i	$0.182549\pi$
$348$		0			0
$349$	−3.76269	−	14.0426i	−0.201412	−	0.751681i	−0.990513	−	0.137418i	$-0.956120\pi$
$349$	−3.76269	−	14.0426i	−0.201412	−	0.751681i	0.789101	−	0.614264i	$-0.210547\pi$
$350$	20.7397			1.10858
$351$		0			0
$352$	2.25023			0.119938
$353$	−2.20358	−	8.22389i	−0.117285	−	0.437713i	0.882163	−	0.470945i	$-0.156087\pi$
$353$	−2.20358	−	8.22389i	−0.117285	−	0.437713i	−0.999448	+	0.0332313i	$0.989420\pi$
$354$		0			0
$355$	9.68322	−	5.59061i	0.513932	−	0.296719i
$356$	−0.648204	−	2.41913i	−0.0343548	−	0.128214i
$357$		0			0
$358$	8.80476	−	8.80476i	0.465346	−	0.465346i
$359$	2.80645	+	2.80645i	0.148119	+	0.148119i	0.777277	−	0.629158i	$-0.216600\pi$
$359$	2.80645	+	2.80645i	0.148119	+	0.148119i	−0.629158	+	0.777277i	$0.716600\pi$
$360$		0			0
$361$	−9.12309	+	5.26722i	−0.480163	+	0.277222i
$362$	−17.8179	+	4.77430i	−0.936489	+	0.250932i
$363$		0			0
$364$	16.0142	−	4.17699i	0.839373	−	0.218934i
$365$	−4.71852	−	2.72424i	−0.246979	−	0.142593i
$366$		0			0
$367$	12.1791	−	21.0948i	0.635742	−	1.10114i	−0.350615	−	0.936520i	$-0.614027\pi$
$367$	12.1791	−	21.0948i	0.635742	−	1.10114i	0.986357	−	0.164618i	$-0.0526392\pi$
$368$	−2.37251	+	4.10931i	−0.123676	+	0.214213i
$369$		0			0
$370$	−2.39409	+	0.641495i	−0.124463	+	0.0333497i
$371$	16.4420	+	16.4420i	0.853628	+	0.853628i
$372$		0			0
$373$	4.62903	+	8.01772i	0.239682	+	0.415142i	0.960623	−	0.277855i	$-0.0896234\pi$
$373$	4.62903	+	8.01772i	0.239682	+	0.415142i	−0.720941	+	0.692997i	$0.756290\pi$
$374$	10.4492			0.540315
$375$		0			0
$376$	10.4541	−	6.03569i	0.539130	−	0.311267i
$377$	0.117126	−	17.6029i	0.00603231	−	0.906593i
$378$		0			0
$379$	−3.58050	+	13.3626i	−0.183918	+	0.686391i	0.810942	+	0.585127i	$0.198955\pi$
$379$	−3.58050	+	13.3626i	−0.183918	+	0.686391i	−0.994860	+	0.101264i	$0.967711\pi$
$380$	1.74880	+	1.00967i	0.0897114	+	0.0517949i
$381$		0			0
$382$	−8.22549	+	2.20401i	−0.420853	+	0.112767i
$383$	−17.2004	−	4.60883i	−0.878898	−	0.235500i	−0.208967	−	0.977923i	$-0.567010\pi$
$383$	−17.2004	−	4.60883i	−0.878898	−	0.235500i	−0.669932	+	0.742423i	$0.733677\pi$
$384$		0			0
$385$	6.92433	+	1.85537i	0.352897	+	0.0945584i
$386$	−16.3939	−	9.46505i	−0.834430	−	0.481758i
$387$		0			0
$388$	1.18591	+	0.317765i	0.0602057	+	0.0161321i
$389$	7.46970	+	12.9379i	0.378729	+	0.655978i	0.990878	−	0.134765i	$-0.0430279\pi$
$389$	7.46970	+	12.9379i	0.378729	+	0.655978i	−0.612149	+	0.790743i	$0.709695\pi$
$390$		0			0
$391$	−11.0170	+	19.0821i	−0.557155	+	0.965021i
$392$	−9.94856	+	9.94856i	−0.502478	+	0.502478i
$393$		0			0
$394$		−	17.4396i		−	0.878593i
$395$	1.52527	−	1.52527i	0.0767447	−	0.0767447i
$396$		0			0
$397$	0.691339	+	2.58011i	0.0346973	+	0.129492i	0.981102	−	0.193491i	$-0.0619810\pi$
$397$	0.691339	+	2.58011i	0.0346973	+	0.129492i	−0.946405	+	0.322983i	$0.895314\pi$
$398$	−5.98226	+	22.3261i	−0.299864	+	1.11911i
$399$		0			0
$400$		−	4.51832i		−	0.225916i
$401$	0.0475983	+	0.0475983i	0.00237694	+	0.00237694i	0.708294	−	0.705917i	$-0.249465\pi$
$401$	0.0475983	+	0.0475983i	0.00237694	+	0.00237694i	−0.705917	+	0.708294i	$0.749465\pi$
$402$		0			0
$403$	−17.0893	−	17.3182i	−0.851277	−	0.862682i
$404$			3.76440i			0.187286i
$405$		0			0
$406$	11.2051	+	19.4079i	0.556101	+	0.963196i
$407$	8.03606			0.398333
$408$		0			0
$409$	−5.28660	+	19.7298i	−0.261405	+	0.975578i	0.703009	+	0.711181i	$0.251840\pi$
$409$	−5.28660	+	19.7298i	−0.261405	+	0.975578i	−0.964414	+	0.264397i	$0.914827\pi$
$410$	1.03138	−	3.84915i	0.0509361	−	0.190096i
$411$		0			0
$412$	15.1921			0.748460
$413$	−12.3243	−	21.3464i	−0.606441	−	1.05039i
$414$		0			0
$415$		−	6.59597i		−	0.323784i
$416$	−0.909992	−	3.48883i	−0.0446160	−	0.171054i
$417$		0			0
$418$	−4.62956	−	4.62956i	−0.226439	−	0.226439i
$419$			22.9596i			1.12165i	0.827934	+	0.560826i	$0.189516\pi$
$419$			22.9596i			1.12165i	−0.827934	+	0.560826i	$0.810484\pi$
$420$		0			0
$421$	−2.92242	+	10.9066i	−0.142430	+	0.531556i	0.857426	+	0.514607i	$0.172062\pi$
$421$	−2.92242	+	10.9066i	−0.142430	+	0.531556i	−0.999856	+	0.0169495i	$0.994605\pi$
$422$	−2.68874	−	10.0345i	−0.130886	−	0.488472i
$423$		0			0
$424$	3.58203	−	3.58203i	0.173959	−	0.173959i
$425$		−	20.9813i		−	1.01774i
$426$		0			0
$427$	10.1302	−	10.1302i	0.490236	−	0.490236i
$428$	2.73351	−	4.73458i	0.132129	−	0.228855i
$429$		0			0
$430$	−1.84147	−	3.18952i	−0.0888036	−	0.153812i
$431$	8.79469	+	2.35653i	0.423625	+	0.113510i	0.464332	−	0.885661i	$-0.346294\pi$
$431$	8.79469	+	2.35653i	0.423625	+	0.113510i	−0.0407069	+	0.999171i	$0.512961\pi$
$432$		0			0
$433$	19.6096	+	11.3216i	0.942379	+	0.544083i	0.890705	−	0.454581i	$-0.150211\pi$
$433$	19.6096	+	11.3216i	0.942379	+	0.544083i	0.0516737	+	0.998664i	$0.483544\pi$
$434$	29.9189	+	8.01675i	1.43615	+	0.384816i
$435$		0			0
$436$	−6.96851	−	1.86721i	−0.333731	−	0.0894230i
$437$	13.3355	−	3.57325i	0.637925	−	0.170931i
$438$		0			0
$439$	−18.5237	−	10.6947i	−0.884090	−	0.510430i	−0.0120853	−	0.999927i	$-0.503847\pi$
$439$	−18.5237	−	10.6947i	−0.884090	−	0.510430i	−0.872005	+	0.489497i	$0.837180\pi$
$440$	0.404207	−	1.50852i	0.0192698	−	0.0719160i
$441$		0			0
$442$	−4.22565	−	16.2008i	−0.200994	−	0.770592i
$443$	−27.1059	+	15.6496i	−1.28784	+	0.743535i	−0.978269	−	0.207341i	$-0.933519\pi$
$443$	−27.1059	+	15.6496i	−1.28784	+	0.743535i	−0.309571	+	0.950876i	$0.600186\pi$
$444$		0			0
$445$	−1.73819			−0.0823980
$446$	−7.93307	−	13.7405i	−0.375642	−	0.650631i
$447$		0			0
$448$	3.24572	+	3.24572i	0.153346	+	0.153346i
$449$	12.7731	−	3.42254i	0.602800	−	0.161520i	0.0555034	−	0.998458i	$-0.482324\pi$
$449$	12.7731	−	3.42254i	0.602800	−	0.161520i	0.547297	+	0.836939i	$0.315657\pi$
$450$		0			0
$451$	−6.46007	+	11.1892i	−0.304193	+	0.526877i
$452$	0.236447	−	0.409538i	0.0111215	−	0.0192630i
$453$		0			0
$454$	−5.52042	−	3.18721i	−0.259086	−	0.149583i
$455$	0.0764259	−	11.4860i	0.00358290	−	0.538472i
$456$		0			0
$457$	−11.3132	+	3.03137i	−0.529210	+	0.141801i	−0.513523	−	0.858076i	$-0.671660\pi$
$457$	−11.3132	+	3.03137i	−0.529210	+	0.141801i	−0.0156865	+	0.999877i	$0.504993\pi$
$458$	11.0794	−	6.39671i	0.517707	−	0.298898i
$459$		0			0
$460$	2.32865	+	2.32865i	0.108574	+	0.108574i
$461$	−5.18033	+	5.18033i	−0.241272	+	0.241272i	−0.817376	−	0.576104i	$-0.804572\pi$
$461$	−5.18033	+	5.18033i	−0.241272	+	0.241272i	0.576104	+	0.817376i	$0.304572\pi$
$462$		0			0
$463$	3.79457	+	14.1615i	0.176349	+	0.658142i	0.996318	+	0.0857346i	$0.0273237\pi$
$463$	3.79457	+	14.1615i	0.176349	+	0.658142i	−0.819969	+	0.572407i	$0.806010\pi$
$464$	4.22816	−	2.44113i	0.196288	−	0.113327i
$465$		0			0
$466$	4.72718	+	17.6421i	0.218982	+	0.817253i
$467$	−18.0118			−0.833488			−0.416744	−	0.909024i	$-0.636829\pi$
$467$	−18.0118			−0.833488			−0.416744	+	0.909024i	$0.636829\pi$
$468$		0			0
$469$	60.0549			2.77308
$470$	−2.16838	−	8.09249i	−0.100020	−	0.373279i
$471$		0			0
$472$	−4.65048	+	2.68496i	−0.214056	+	0.123585i
$473$	3.09056	+	11.5341i	0.142104	+	0.530339i
$474$		0			0
$475$	−9.29586	+	9.29586i	−0.426523	+	0.426523i
$476$	15.0719	+	15.0719i	0.690818	+	0.690818i
$477$		0			0
$478$	17.3211	−	10.0003i	0.792249	−	0.457405i
$479$	6.94673	−	1.86137i	0.317404	−	0.0850482i	−0.0965997	−	0.995323i	$-0.530797\pi$
$479$	6.94673	−	1.86137i	0.317404	−	0.0850482i	0.414004	+	0.910275i	$0.364130\pi$
$480$		0			0
$481$	−3.24978	−	12.4594i	−0.148177	−	0.568098i
$482$	13.0385	+	7.52778i	0.593887	+	0.342881i
$483$		0			0
$484$	2.96823	−	5.14113i	0.134920	−	0.233688i
$485$	0.426050	−	0.737940i	0.0193459	−	0.0335082i
$486$		0			0
$487$	0.324094	−	0.0868407i	0.0146861	−	0.00393513i	−0.251469	−	0.967865i	$-0.580913\pi$
$487$	0.324094	−	0.0868407i	0.0146861	−	0.00393513i	0.266155	+	0.963930i	$0.414247\pi$
$488$	−2.20695	−	2.20695i	−0.0999040	−	0.0999040i
$489$		0			0
$490$	4.88232	+	8.45643i	0.220561	+	0.382023i
$491$	3.92764			0.177252			0.0886260	−	0.996065i	$-0.471752\pi$
$491$	3.92764			0.177252			0.0886260	+	0.996065i	$0.471752\pi$
$492$		0			0
$493$	19.6339	−	11.3357i	0.884269	−	0.510533i
$494$	−5.30562	+	9.05001i	−0.238711	+	0.407179i
$495$		0			0
$496$	1.74651	−	6.51808i	0.0784208	−	0.292670i
$497$	−64.0420	−	36.9747i	−2.87268	−	1.65854i
$498$		0			0
$499$	19.6072	−	5.25372i	0.877737	−	0.235189i	0.208307	−	0.978064i	$-0.433205\pi$
$499$	19.6072	−	5.25372i	0.877737	−	0.235189i	0.669431	+	0.742875i	$0.266538\pi$
$500$	−6.38094	−	1.70977i	−0.285365	−	0.0764632i
$501$		0			0
$502$	−25.3906	−	6.80338i	−1.13324	−	0.303650i
$503$	24.7833	+	14.3086i	1.10503	+	0.637991i	0.937538	−	0.347882i	$-0.113099\pi$
$503$	24.7833	+	14.3086i	1.10503	+	0.637991i	0.167494	+	0.985873i	$0.446432\pi$
$504$		0			0
$505$	2.52360	+	0.676198i	0.112299	+	0.0300904i
$506$	−5.33870	−	9.24691i	−0.237334	−	0.411075i
$507$		0			0
$508$	0.217716	−	0.377096i	0.00965960	−	0.0167309i
$509$	−11.3503	+	11.3503i	−0.503091	+	0.503091i	−0.912397	−	0.409306i	$-0.865771\pi$
$509$	−11.3503	+	11.3503i	−0.503091	+	0.503091i	0.409306	+	0.912397i	$0.365771\pi$
$510$		0			0
$511$			36.0346i			1.59408i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−3.53697	−	13.2002i	−0.156009	−	0.582235i
$515$	2.72894	−	10.1846i	0.120252	−	0.448785i
$516$		0			0
$517$			27.1634i			1.19465i
$518$	11.5912	+	11.5912i	0.509286	+	0.509286i
$519$		0			0
$520$	−2.50232	−	0.0166500i	−0.109734	−	0.000730151i
$521$		−	19.3205i		−	0.846448i	−0.906025	−	0.423224i	$-0.860898\pi$
$521$		−	19.3205i		−	0.846448i	0.906025	−	0.423224i	$-0.139102\pi$
$522$		0			0
$523$	4.17667	+	7.23421i	0.182633	+	0.316330i	0.942776	−	0.333426i	$-0.108205\pi$
$523$	4.17667	+	7.23421i	0.182633	+	0.316330i	−0.760143	+	0.649755i	$0.774871\pi$
$524$	−10.4191			−0.455161
$525$		0			0
$526$	−1.24130	+	4.63258i	−0.0541231	+	0.201990i
$527$	8.11013	−	30.2674i	0.353283	−	1.31847i
$528$		0			0
$529$	−0.484713			−0.0210745
$530$	−1.75791	−	3.04478i	−0.0763585	−	0.132257i
$531$		0			0
$532$		−	13.3553i		−	0.579026i
$533$	19.9605	+	5.49100i	0.864584	+	0.237841i
$534$		0			0
$535$	−2.68298	−	2.68298i	−0.115995	−	0.115995i
$536$		−	13.0835i		−	0.565119i
$537$		0			0
$538$	−6.44036	+	24.0358i	−0.277664	+	1.03625i
$539$	−8.19405	−	30.5806i	−0.352943	−	1.31720i
$540$		0			0
$541$	18.5480	−	18.5480i	0.797443	−	0.797443i	−0.185249	−	0.982692i	$-0.559309\pi$
$541$	18.5480	−	18.5480i	0.797443	−	0.797443i	0.982692	+	0.185249i	$0.0593092\pi$
$542$		−	0.793836i		−	0.0340982i
$543$		0			0
$544$	3.28353	−	3.28353i	0.140780	−	0.140780i
$545$	−2.50350	+	4.33618i	−0.107238	+	0.185742i
$546$		0			0
$547$	−11.1826	−	19.3688i	−0.478133	−	0.828151i	0.521552	−	0.853219i	$-0.325353\pi$
$547$	−11.1826	−	19.3688i	−0.478133	−	0.828151i	−0.999686	+	0.0250681i	$0.992020\pi$
$548$	−7.38734	−	1.97943i	−0.315572	−	0.0845572i
$549$		0			0
$550$	8.80510	+	5.08363i	0.375451	+	0.216767i
$551$	−13.7212	−	3.67659i	−0.584544	−	0.156628i
$552$		0			0
$553$	−13.7800	−	3.69235i	−0.585987	−	0.157015i
$554$	−31.8275	+	8.52814i	−1.35222	+	0.362326i
$555$		0			0
$556$	9.67631	+	5.58662i	0.410367	+	0.236926i
$557$	−3.13004	+	11.6815i	−0.132624	+	0.494959i	−0.999996	−	0.00270033i	$-0.999140\pi$
$557$	−3.13004	+	11.6815i	−0.132624	+	0.494959i	0.867372	+	0.497660i	$0.165807\pi$
$558$		0			0
$559$	16.6330	−	9.45609i	0.703503	−	0.399950i
$560$	2.75891	−	1.59286i	0.116585	−	0.0673105i
$561$		0			0
$562$	18.1904			0.767315
$563$	−17.5904	−	30.4674i	−0.741345	−	1.28405i	−0.951883	−	0.306462i	$-0.900855\pi$
$563$	−17.5904	−	30.4674i	−0.741345	−	1.28405i	0.210538	−	0.977586i	$-0.432479\pi$
$564$		0			0
$565$	−0.232075	−	0.232075i	−0.00976349	−	0.00976349i
$566$	−23.5710	+	6.31582i	−0.990761	+	0.265474i
$567$		0			0
$568$	−8.05524	+	13.9521i	−0.337990	+	0.585416i
$569$	5.63117	−	9.75346i	0.236071	−	0.408886i	−0.723513	−	0.690311i	$-0.757474\pi$
$569$	5.63117	−	9.75346i	0.236071	−	0.408886i	0.959583	+	0.281425i	$0.0908070\pi$
$570$		0			0
$571$	−27.0909	−	15.6409i	−1.13372	−	0.654553i	−0.188852	−	0.982006i	$-0.560477\pi$
$571$	−27.0909	−	15.6409i	−1.13372	−	0.654553i	−0.944868	+	0.327452i	$0.893810\pi$
$572$	7.82272	+	2.15198i	0.327084	+	0.0899788i
$573$		0			0
$574$	−25.4571	+	6.82122i	−1.06256	+	0.284712i
$575$	−18.5672	+	10.7198i	−0.774305	+	0.447045i
$576$		0			0
$577$	−26.9790	−	26.9790i	−1.12315	−	1.12315i	−0.991265	−	0.131887i	$-0.957897\pi$
$577$	−26.9790	−	26.9790i	−1.12315	−	1.12315i	−0.131887	−	0.991265i	$-0.542103\pi$
$578$	3.22662	−	3.22662i	0.134210	−	0.134210i
$579$		0			0
$580$	−0.876997	−	3.27300i	−0.0364153	−	0.135904i
$581$	−37.7793	+	21.8119i	−1.56735	+	0.904911i
$582$		0			0
$583$	2.95031	+	11.0107i	0.122189	+	0.456017i
$584$	7.85044			0.324853
$585$		0			0
$586$	3.63756			0.150266
$587$	0.590896	+	2.20525i	0.0243889	+	0.0910205i	0.977048	−	0.213021i	$-0.0683304\pi$
$587$	0.590896	+	2.20525i	0.0243889	+	0.0910205i	−0.952659	+	0.304042i	$0.901664\pi$
$588$		0			0
$589$	−17.0033	+	9.81688i	−0.700611	+	0.404498i
$590$	0.964595	+	3.59992i	0.0397117	+	0.148206i
$591$		0			0
$592$	2.52523	−	2.52523i	0.103786	−	0.103786i
$593$	−21.4122	−	21.4122i	−0.879295	−	0.879295i	0.114166	−	0.993462i	$-0.463580\pi$
$593$	−21.4122	−	21.4122i	−0.879295	−	0.879295i	−0.993462	+	0.114166i	$0.963580\pi$
$594$		0			0
$595$	12.8113	−	7.39662i	0.525213	−	0.303232i
$596$	−7.14709	+	1.91506i	−0.292756	+	0.0784438i
$597$		0			0
$598$	−12.1777	+	12.0167i	−0.497984	+	0.491401i
$599$	27.0669	+	15.6271i	1.10593	+	0.638506i	0.937771	−	0.347255i	$-0.112886\pi$
$599$	27.0669	+	15.6271i	1.10593	+	0.638506i	0.168154	+	0.985761i	$0.446219\pi$
$600$		0			0
$601$	13.9378	−	24.1409i	0.568533	−	0.984728i	−0.428179	−	0.903694i	$-0.640845\pi$
$601$	13.9378	−	24.1409i	0.568533	−	0.984728i	0.996711	−	0.0810336i	$-0.0258221\pi$
$602$	−12.1789	+	21.0946i	−0.496377	+	0.859750i
$603$		0			0
$604$	−13.8415	+	3.70881i	−0.563201	+	0.150909i
$605$	−2.91336	−	2.91336i	−0.118445	−	0.118445i
$606$		0			0
$607$	1.42278	+	2.46433i	0.0577490	+	0.100024i	0.893455	−	0.449153i	$-0.148274\pi$
$607$	1.42278	+	2.46433i	0.0577490	+	0.100024i	−0.835706	+	0.549178i	$0.814941\pi$
$608$	−2.90956			−0.117998
$609$		0			0
$610$	−1.87594	+	1.08308i	−0.0759547	+	0.0438525i
$611$	42.1150	−	10.9849i	1.70379	−	0.444400i
$612$		0			0
$613$	0.202550	−	0.755928i	0.00818093	−	0.0305316i	−0.961715	−	0.274053i	$-0.911636\pi$
$613$	0.202550	−	0.755928i	0.00818093	−	0.0305316i	0.969896	+	0.243521i	$0.0783024\pi$
$614$	13.3488	+	7.70696i	0.538716	+	0.311028i
$615$		0			0
$616$	−9.97693	+	2.67331i	−0.401982	+	0.107711i
$617$	26.7737	+	7.17399i	1.07787	+	0.288814i	0.753723	−	0.657193i	$-0.228256\pi$
$617$	26.7737	+	7.17399i	1.07787	+	0.288814i	0.324147	+	0.946007i	$0.394923\pi$
$618$		0			0
$619$	−6.46639	−	1.73266i	−0.259906	−	0.0696417i	0.126513	−	0.991965i	$-0.459621\pi$
$619$	−6.46639	−	1.73266i	−0.259906	−	0.0696417i	−0.386419	+	0.922323i	$0.626288\pi$
$620$	−4.05590	−	2.34168i	−0.162889	−	0.0940440i
$621$		0			0
$622$	−10.3913	−	2.78435i	−0.416654	−	0.111642i
$623$	5.74793	+	9.95571i	0.230286	+	0.398867i
$624$		0			0
$625$	9.00338	−	15.5943i	0.360135	−	0.623772i
$626$	−8.97538	+	8.97538i	−0.358728	+	0.358728i
$627$		0			0
$628$		−	5.72207i		−	0.228336i
$629$	11.7262	−	11.7262i	0.467554	−	0.467554i
$630$		0			0
$631$	−1.16111	−	4.33331i	−0.0462230	−	0.172506i	0.938956	−	0.344038i	$-0.111795\pi$
$631$	−1.16111	−	4.33331i	−0.0462230	−	0.172506i	−0.985179	+	0.171532i	$0.945128\pi$
$632$	−0.804409	+	3.00210i	−0.0319977	+	0.119417i
$633$		0			0
$634$			26.0426i			1.03428i
$635$	−0.213691	−	0.213691i	−0.00848008	−	0.00848008i
$636$		0			0
$637$	−44.0995	+	25.0711i	−1.74728	+	0.993353i
$638$			10.9862i			0.434948i
$639$		0			0
$640$	−0.347017	−	0.601052i	−0.0137171	−	0.0237586i
$641$	−42.9821			−1.69769			−0.848845	−	0.528642i	$-0.822702\pi$
$641$	−42.9821			−1.69769			−0.848845	+	0.528642i	$0.822702\pi$
$642$		0			0
$643$	5.91017	−	22.0571i	0.233074	−	0.869845i	−0.745933	−	0.666021i	$-0.767996\pi$
$643$	5.91017	−	22.0571i	0.233074	−	0.869845i	0.979007	−	0.203824i	$-0.0653372\pi$
$644$	5.63717	−	21.0382i	0.222136	−	0.829021i
$645$		0			0
$646$	−13.5109			−0.531579
$647$	−18.2315	−	31.5780i	−0.716756	−	1.24146i	−0.962278	−	0.272067i	$-0.912293\pi$
$647$	−18.2315	−	31.5780i	−0.716756	−	1.24146i	0.245523	−	0.969391i	$-0.421040\pi$
$648$		0			0
$649$		−	12.0836i		−	0.474321i
$650$	4.32103	−	15.7075i	0.169485	−	0.616099i
$651$		0			0
$652$	3.95111	+	3.95111i	0.154737	+	0.154737i
$653$			3.39452i			0.132838i	0.997792	+	0.0664190i	$0.0211574\pi$
$653$			3.39452i			0.132838i	−0.997792	+	0.0664190i	$0.978843\pi$
$654$		0			0
$655$	−1.87158	+	6.98482i	−0.0731285	+	0.272919i
$656$	1.48606	+	5.54605i	0.0580209	+	0.216537i
$657$		0			0
$658$	−39.1803	+	39.1803i	−1.52741	+	1.52741i
$659$		−	27.3904i		−	1.06698i	−0.845806	−	0.533490i	$-0.820880\pi$
$659$		−	27.3904i		−	1.06698i	0.845806	−	0.533490i	$-0.179120\pi$
$660$		0			0
$661$	32.4505	−	32.4505i	1.26218	−	1.26218i	0.312144	−	0.950035i	$-0.398953\pi$
$661$	32.4505	−	32.4505i	1.26218	−	1.26218i	0.950035	−	0.312144i	$-0.101047\pi$
$662$	10.1318	−	17.5489i	0.393785	−	0.682056i
$663$		0			0
$664$	4.75191	+	8.23054i	0.184410	+	0.319407i
$665$	−8.95321	−	2.39900i	−0.347191	−	0.0930294i
$666$		0			0
$667$	−20.0627	−	11.5832i	−0.776833	−	0.448505i
$668$	23.6549	+	6.33832i	0.915236	+	0.245237i
$669$		0			0
$670$	−8.77097	−	2.35017i	−0.338852	−	0.0907951i
$671$	6.78389	−	1.81774i	0.261889	−	0.0701730i
$672$		0			0
$673$	−17.9179	−	10.3449i	−0.690685	−	0.398767i	0.113183	−	0.993574i	$-0.463895\pi$
$673$	−17.9179	−	10.3449i	−0.690685	−	0.398767i	−0.803869	+	0.594807i	$0.797229\pi$
$674$	−2.04100	+	7.61712i	−0.0786164	+	0.293401i
$675$		0			0
$676$	0.172992	−	12.9988i	0.00665353	−	0.499956i
$677$	−6.49755	+	3.75136i	−0.249721	+	0.144176i	−0.619636	−	0.784889i	$-0.712720\pi$
$677$	−6.49755	+	3.75136i	−0.249721	+	0.144176i	0.369916	+	0.929065i	$0.379387\pi$
$678$		0			0
$679$	−5.63554			−0.216272
$680$	−1.61141	−	2.79105i	−0.0617949	−	0.107032i
$681$		0			0
$682$	10.7371	+	10.7371i	0.411146	+	0.411146i
$683$	−39.9739	+	10.7110i	−1.52956	+	0.409844i	−0.922875	−	0.385100i	$-0.874167\pi$
$683$	−39.9739	+	10.7110i	−1.52956	+	0.409844i	−0.606683	+	0.794944i	$0.707500\pi$
$684$		0			0
$685$	−2.65397	+	4.59681i	−0.101403	+	0.175635i
$686$	16.2248	−	28.1021i	0.619464	−	1.07294i
$687$		0			0
$688$	4.59562	+	2.65328i	0.175206	+	0.101155i
$689$	15.8782	−	9.02698i	0.604913	−	0.343900i
$690$		0			0
$691$	−5.45974	+	1.46293i	−0.207698	+	0.0556526i	−0.361168	−	0.932501i	$-0.617622\pi$
$691$	−5.45974	+	1.46293i	−0.207698	+	0.0556526i	0.153470	+	0.988153i	$0.450955\pi$
$692$	−9.17465	+	5.29699i	−0.348768	+	0.201361i
$693$		0			0
$694$	12.0177	+	12.0177i	0.456185	+	0.456185i
$695$	5.48334	−	5.48334i	0.207995	−	0.207995i
$696$		0			0
$697$	6.90068	+	25.7537i	0.261382	+	0.975491i
$698$	12.5902	−	7.26897i	0.476547	−	0.275134i
$699$		0			0
$700$	5.36783	+	20.0330i	0.202885	+	0.757177i
$701$	40.7022			1.53730			0.768651	−	0.639669i	$-0.220928\pi$
$701$	40.7022			1.53730			0.768651	+	0.639669i	$0.220928\pi$
$702$		0			0
$703$	−10.3907			−0.391892
$704$	0.582403	+	2.17356i	0.0219501	+	0.0819190i
$705$		0			0
$706$	7.37333	−	4.25700i	0.277499	−	0.160214i
$707$	−4.47217	−	16.6904i	−0.168193	−	0.627706i
$708$		0			0
$709$	−1.21373	+	1.21373i	−0.0455824	+	0.0455824i	−0.729531	−	0.683948i	$-0.760261\pi$
$709$	−1.21373	+	1.21373i	−0.0455824	+	0.0455824i	0.683948	+	0.729531i	$0.260261\pi$
$710$	7.90632	+	7.90632i	0.296719	+	0.296719i
$711$		0			0
$712$	2.16893	−	1.25223i	0.0812843	−	0.0469295i
$713$	−30.9285	+	8.28726i	−1.15828	+	0.310360i
$714$		0			0
$715$	2.84785	−	4.85768i	0.106503	−	0.181667i
$716$	10.7836	+	6.22591i	0.403001	+	0.232673i
$717$		0			0
$718$	−1.98446	+	3.43719i	−0.0740594	+	0.128275i
$719$	−10.3528	+	17.9315i	−0.386093	+	0.668732i	−0.991920	−	0.126864i	$-0.959509\pi$
$719$	−10.3528	+	17.9315i	−0.386093	+	0.668732i	0.605827	+	0.795596i	$0.292842\pi$
$720$		0			0
$721$	−67.3577	+	18.0484i	−2.50853	+	0.672159i
$722$	−7.44897	−	7.44897i	−0.277222	−	0.277222i
$723$		0			0
$724$	−9.22324	−	15.9751i	−0.342779	−	0.593711i
$725$	22.0596			0.819273
$726$		0			0
$727$	−38.1761	+	22.0410i	−1.41587	+	0.817455i	−0.995933	−	0.0900971i	$-0.971282\pi$
$727$	−38.1761	+	22.0410i	−1.41587	+	0.817455i	−0.419940	+	0.907552i	$0.637949\pi$
$728$	8.17945	+	14.3875i	0.303150	+	0.533234i
$729$		0			0
$730$	1.41017	−	5.26282i	0.0521927	−	0.194786i
$731$	21.3403	+	12.3208i	0.789299	+	0.455702i
$732$		0			0
$733$	19.6173	−	5.25644i	0.724582	−	0.194151i	0.122367	−	0.992485i	$-0.460952\pi$
$733$	19.6173	−	5.25644i	0.724582	−	0.194151i	0.602215	+	0.798334i	$0.294285\pi$
$734$	23.5282	+	6.30435i	0.868440	+	0.232698i
$735$		0			0
$736$	−4.58334	−	1.22810i	−0.168944	−	0.0452685i
$737$	25.4965	+	14.7204i	0.939175	+	0.542233i
$738$		0			0
$739$	37.8060	+	10.1301i	1.39072	+	0.372642i	0.875002	−	0.484118i	$-0.160860\pi$
$739$	37.8060	+	10.1301i	1.39072	+	0.372642i	0.515715	+	0.856760i	$0.327526\pi$
$740$	−1.23927	−	2.14648i	−0.0455566	−	0.0789063i
$741$		0			0
$742$	−11.6263	+	20.1373i	−0.426814	+	0.739263i
$743$	−37.3133	+	37.3133i	−1.36889	+	1.36889i	−0.506867	+	0.862024i	$0.669197\pi$
$743$	−37.3133	+	37.3133i	−1.36889	+	1.36889i	−0.862024	+	0.506867i	$0.830803\pi$
$744$		0			0
$745$			5.13531i			0.188143i
$746$	−6.54644	+	6.54644i	−0.239682	+	0.239682i
$747$		0			0
$748$	2.70445	+	10.0932i	0.0988845	+	0.369042i
$749$	−6.49491	+	24.2393i	−0.237319	+	0.885686i
$750$		0			0
$751$			28.3546i			1.03467i	0.855782	+	0.517336i	$0.173076\pi$
$751$			28.3546i			1.03467i	−0.855782	+	0.517336i	$0.826924\pi$
$752$	8.53576	+	8.53576i	0.311267	+	0.311267i
$753$		0			0
$754$	17.0334	−	4.44282i	0.620319	−	0.161798i
$755$			9.94532i			0.361947i
$756$		0			0
$757$	24.6271	+	42.6555i	0.895089	+	1.55034i	0.833694	+	0.552226i	$0.186221\pi$
$757$	24.6271	+	42.6555i	0.895089	+	1.55034i	0.0613944	+	0.998114i	$0.480445\pi$
$758$	−13.8340			−0.502473
$759$		0			0
$760$	−0.522643	+	1.95053i	−0.0189583	+	0.0707532i
$761$	−6.93919	+	25.8974i	−0.251545	+	0.938780i	0.718435	+	0.695595i	$0.244859\pi$
$761$	−6.93919	+	25.8974i	−0.251545	+	0.938780i	−0.969980	+	0.243185i	$0.921808\pi$
$762$		0			0
$763$	33.1148			1.19884
$764$	−4.25783	−	7.37477i	−0.154043	−	0.266810i
$765$		0			0
$766$		−	17.8071i		−	0.643398i
$767$	−18.7347	+	4.88658i	−0.676471	+	0.176444i
$768$		0			0
$769$	−30.3153	−	30.3153i	−1.09320	−	1.09320i	−0.995185	−	0.0980127i	$-0.968751\pi$
$769$	−30.3153	−	30.3153i	−1.09320	−	1.09320i	−0.0980127	−	0.995185i	$-0.531249\pi$
$770$			7.16860i			0.258338i
$771$		0			0
$772$	4.89947	−	18.2851i	0.176336	−	0.658094i
$773$	1.46006	+	5.44904i	0.0525149	+	0.195988i	0.987200	−	0.159490i	$-0.0509848\pi$
$773$	1.46006	+	5.44904i	0.0525149	+	0.195988i	−0.934685	+	0.355478i	$0.884318\pi$
$774$		0			0
$775$	21.5594	−	21.5594i	0.774438	−	0.774438i
$776$			1.22775i			0.0440736i
$777$		0			0
$778$	−10.5638	+	10.5638i	−0.378729	+	0.378729i
$779$	8.35291	−	14.4677i	0.299274	−	0.518358i
$780$		0			0
$781$	−18.1261	−	31.3954i	−0.648604	−	1.12342i
$782$	−21.2833	−	5.70284i	−0.761088	−	0.203933i
$783$		0			0
$784$	−12.1845	−	7.03470i	−0.435159	−	0.251239i
$785$	−3.83600	−	1.02785i	−0.136913	−	0.0366856i
$786$		0			0
$787$	−42.8409	−	11.4792i	−1.52711	−	0.409189i	−0.605036	−	0.796198i	$-0.706841\pi$
$787$	−42.8409	−	11.4792i	−1.52711	−	0.409189i	−0.922076	+	0.387009i	$0.873508\pi$
$788$	16.8453	−	4.51369i	0.600090	−	0.160794i
$789$		0			0
$790$	1.86807	+	1.07853i	0.0664629	+	0.0383723i
$791$	−0.561805	+	2.09668i	−0.0199755	+	0.0745495i
$792$		0			0
$793$	−5.56168	−	9.78286i	−0.197501	−	0.347399i
$794$	−2.31327	+	1.33556i	−0.0820947	+	0.0473974i
$795$		0			0
$796$	−23.1137			−0.819243
$797$	−0.0239676	−	0.0415131i	−0.000848975	−	0.00147047i	0.865601	−	0.500735i	$-0.166937\pi$
$797$	−0.0239676	−	0.0415131i	−0.000848975	−	0.00147047i	−0.866450	+	0.499265i	$0.833604\pi$
$798$		0			0
$799$	39.6368	+	39.6368i	1.40225	+	1.40225i
$800$	4.36436	−	1.16943i	0.154303	−	0.0413455i
$801$		0			0
$802$	−0.0336571	+	0.0582957i	−0.00118847	+	0.00205849i
$803$	−8.83265	+	15.2986i	−0.311697	+	0.539876i
$804$		0			0
$805$	−13.0911	−	7.55816i	−0.461401	−	0.266390i
$806$	12.3051	−	20.9893i	0.433428	−	0.739315i
$807$		0			0
$808$	−3.63614	+	0.974300i	−0.127919	+	0.0342757i
$809$	11.0405	−	6.37425i	0.388164	−	0.224107i	−0.293200	−	0.956051i	$-0.594720\pi$
$809$	11.0405	−	6.37425i	0.388164	−	0.224107i	0.681364	+	0.731944i	$0.261387\pi$
$810$		0			0
$811$	8.60363	+	8.60363i	0.302114	+	0.302114i	0.841841	−	0.539726i	$-0.181472\pi$
$811$	8.60363	+	8.60363i	0.302114	+	0.302114i	−0.539726	+	0.841841i	$0.681472\pi$
$812$	−15.8465	+	15.8465i	−0.556101	+	0.556101i
$813$		0			0
$814$	2.07988	+	7.76224i	0.0728999	+	0.272066i
$815$	3.35850	−	1.93903i	0.117643	−	0.0679213i
$816$		0			0
$817$	−3.99611	−	14.9137i	−0.139806	−	0.521764i
$818$	−20.4258			−0.714173
$819$		0			0
$820$	3.98493			0.139160
$821$	−5.06925	−	18.9187i	−0.176918	−	0.660267i	−0.996217	−	0.0869005i	$-0.972304\pi$
$821$	−5.06925	−	18.9187i	−0.176918	−	0.660267i	0.819299	−	0.573367i	$-0.194363\pi$
$822$		0			0
$823$	2.77266	−	1.60080i	0.0966489	−	0.0558003i	−0.450897	−	0.892576i	$-0.648896\pi$
$823$	2.77266	−	1.60080i	0.0966489	−	0.0558003i	0.547545	+	0.836776i	$0.315562\pi$
$824$	3.93200	+	14.6744i	0.136978	+	0.511208i
$825$		0			0
$826$	17.4292	−	17.4292i	0.606441	−	0.606441i
$827$	−35.9697	−	35.9697i	−1.25079	−	1.25079i	−0.955367	−	0.295423i	$-0.904539\pi$
$827$	−35.9697	−	35.9697i	−1.25079	−	1.25079i	−0.295423	−	0.955367i	$-0.595461\pi$
$828$		0			0
$829$	−19.7591	+	11.4079i	−0.686263	+	0.396214i	−0.802211	−	0.597041i	$-0.796343\pi$
$829$	−19.7591	+	11.4079i	−0.686263	+	0.396214i	0.115947	+	0.993255i	$0.463010\pi$
$830$	6.37122	−	1.70716i	0.221148	−	0.0592565i
$831$		0			0
$832$	3.13442	−	1.78196i	0.108667	−	0.0617783i
$833$	−56.5799	−	32.6664i	−1.96038	−	1.13182i
$834$		0			0
$835$	8.49824	−	14.7194i	0.294094	−	0.509385i
$836$	3.27359	−	5.67003i	0.113220	−	0.196102i
$837$		0			0
$838$	−22.1773	+	5.94239i	−0.766102	+	0.205276i
$839$	−6.32004	−	6.32004i	−0.218192	−	0.218192i	0.589544	−	0.807736i	$-0.299307\pi$
$839$	−6.32004	−	6.32004i	−0.218192	−	0.218192i	−0.807736	+	0.589544i	$0.799307\pi$
$840$		0			0
$841$	−2.58176	−	4.47174i	−0.0890262	−	0.154198i
$842$	−11.2914			−0.389126
$843$		0			0
$844$	8.99669	−	5.19424i	0.309679	−	0.178793i
$845$	−8.68317	−	2.45095i	−0.298710	−	0.0843151i
$846$		0			0
$847$	−7.05261	+	26.3207i	−0.242331	+	0.904390i
$848$	4.38707	+	2.53288i	0.150653	+	0.0869794i
$849$		0			0
$850$	20.2664	−	5.43036i	0.695131	−	0.186260i
$851$	−16.3681	−	4.38582i	−0.561092	−	0.150344i
$852$		0			0
$853$	−1.39540	−	0.373895i	−0.0477774	−	0.0128019i	0.234851	−	0.972031i	$-0.424540\pi$
$853$	−1.39540	−	0.373895i	−0.0477774	−	0.0128019i	−0.282629	+	0.959229i	$0.591206\pi$
$854$	12.4069	+	7.16315i	0.424557	+	0.245118i
$855$		0			0
$856$	5.28074	+	1.41497i	0.180492	+	0.0483627i
$857$	14.4133	+	24.9645i	0.492347	+	0.852770i	0.999961	−	0.00881420i	$-0.00280568\pi$
$857$	14.4133	+	24.9645i	0.492347	+	0.852770i	−0.507614	+	0.861585i	$0.669472\pi$
$858$		0			0
$859$	7.53374	−	13.0488i	0.257048	−	0.445220i	−0.708402	−	0.705809i	$-0.750584\pi$
$859$	7.53374	−	13.0488i	0.257048	−	0.445220i	0.965450	+	0.260589i	$0.0839169\pi$
$860$	2.60423	−	2.60423i	0.0888036	−	0.0888036i
$861$		0			0
$862$			9.10494i			0.310115i
$863$	6.35047	−	6.35047i	0.216173	−	0.216173i	−0.590711	−	0.806883i	$-0.701153\pi$
$863$	6.35047	−	6.35047i	0.216173	−	0.216173i	0.806883	+	0.590711i	$0.201153\pi$
$864$		0			0
$865$	1.90299	+	7.10205i	0.0647036	+	0.241477i
$866$	−5.86051	+	21.8717i	−0.199148	+	0.743231i
$867$		0			0
$868$			30.9743i			1.05134i
$869$	−4.94530	−	4.94530i	−0.167758	−	0.167758i
$870$		0			0
$871$	12.5122	−	45.4835i	0.423960	−	1.54115i
$872$		−	7.21433i		−	0.244308i
$873$		0			0
$874$	6.90298	+	11.9563i	0.233497	+	0.404428i
$875$	30.3227			1.02509
$876$		0			0
$877$	8.20836	−	30.6340i	0.277177	−	1.03444i	−0.677192	−	0.735806i	$-0.736803\pi$
$877$	8.20836	−	30.6340i	0.277177	−	1.03444i	0.954369	−	0.298631i	$-0.0965299\pi$
$878$	5.53598	−	20.6606i	0.186830	−	0.697260i
$879$		0			0
$880$	1.56174			0.0526462
$881$	25.4661	+	44.1086i	0.857975	+	1.48606i	0.873858	+	0.486182i	$0.161611\pi$
$881$	25.4661	+	44.1086i	0.857975	+	1.48606i	−0.0158827	+	0.999874i	$0.505056\pi$
$882$		0			0
$883$		−	3.78144i		−	0.127256i	−0.997974	−	0.0636278i	$-0.979733\pi$
$883$		−	3.78144i		−	0.127256i	0.997974	−	0.0636278i	$-0.0202671\pi$
$884$	14.5551	−	8.27473i	0.489539	−	0.278309i
$885$		0			0
$886$	−22.1319	−	22.1319i	−0.743535	−	0.743535i
$887$		−	16.2551i		−	0.545792i	−0.962043	−	0.272896i	$-0.912018\pi$
$887$		−	16.2551i		−	0.545792i	0.962043	−	0.272896i	$-0.0879816\pi$
$888$		0			0
$889$	−0.517301	+	1.93059i	−0.0173497	+	0.0647500i
$890$	−0.449876	−	1.67896i	−0.0150799	−	0.0562789i
$891$		0			0
$892$	11.2191	−	11.2191i	0.375642	−	0.375642i
$893$		−	35.1225i		−	1.17533i
$894$		0			0
$895$	6.11081	−	6.11081i	0.204262	−	0.204262i
$896$	−2.29507	+	3.97518i	−0.0766729	+	0.132801i
$897$		0			0
$898$	6.61184	+	11.4520i	0.220640	+	0.382160i
$899$	31.8230	+	8.52694i	1.06136	+	0.284389i
$900$		0			0
$901$	20.3719	+	11.7617i	0.678685	+	0.391839i
$902$	−12.4799	−	3.34398i	−0.415535	−	0.111342i
$903$		0			0
$904$	0.456780	+	0.122394i	0.0151923	+	0.00407076i
$905$	−12.3663	+	3.31353i	−0.411068	+	0.110145i
$906$		0			0
$907$	9.30188	+	5.37044i	0.308864	+	0.178323i	0.646418	−	0.762984i	$-0.276266\pi$
$907$	9.30188	+	5.37044i	0.308864	+	0.178323i	−0.337554	+	0.941306i	$0.609600\pi$
$908$	1.64982	−	6.15723i	0.0547513	−	0.204335i
$909$		0			0
$910$	11.1144	−	2.89898i	0.368439	−	0.0961001i
$911$	51.7103	−	29.8550i	1.71324	−	0.989139i	0.783130	−	0.621858i	$-0.213622\pi$
$911$	51.7103	−	29.8550i	1.71324	−	0.989139i	0.930110	−	0.367281i	$-0.119711\pi$
$912$		0			0
$913$	−21.3858			−0.707766
$914$	−5.85615	−	10.1432i	−0.193704	−	0.335506i
$915$		0			0
$916$	9.04631	+	9.04631i	0.298898	+	0.298898i
$917$	46.1955	−	12.3781i	1.52551	−	0.408759i
$918$		0			0
$919$	−9.50921	+	16.4704i	−0.313680	+	0.543310i	−0.979156	−	0.203110i	$-0.934895\pi$
$919$	−9.50921	+	16.4704i	−0.313680	+	0.543310i	0.665476	+	0.746419i	$0.268229\pi$
$920$	−1.64661	+	2.85201i	−0.0542870	+	0.0940279i
$921$		0			0
$922$	−6.34459	−	3.66305i	−0.208948	−	0.120636i
$923$	−41.3462	+	40.7996i	−1.36093	+	1.34294i
$924$		0			0
$925$	15.5861	−	4.17627i	0.512467	−	0.137315i
$926$	−12.6969	+	7.33055i	−0.417245	+	0.240897i
$927$		0			0
$928$	3.45228	+	3.45228i	0.113327	+	0.113327i
$929$	−1.83688	+	1.83688i	−0.0602660	+	0.0602660i	−0.736597	−	0.676331i	$-0.763569\pi$
$929$	−1.83688	+	1.83688i	−0.0602660	+	0.0602660i	0.676331	+	0.736597i	$0.263569\pi$
$930$		0			0
$931$	10.5950	+	39.5409i	0.347236	+	1.29590i
$932$	−15.8174	+	9.13221i	−0.518118	+	0.299135i
$933$		0			0
$934$	−4.66180	−	17.3981i	−0.152539	−	0.569283i
$935$	7.25210			0.237169
$936$		0			0
$937$	−11.7808			−0.384863			−0.192431	−	0.981310i	$-0.561637\pi$
$937$	−11.7808			−0.384863			−0.192431	+	0.981310i	$0.561637\pi$
$938$	15.5434	+	58.0086i	0.507509	+	1.89405i
$939$		0			0
$940$	7.25552	−	4.18898i	0.236649	−	0.136629i
$941$	−11.8964	−	44.3981i	−0.387813	−	1.44734i	−0.833684	−	0.552241i	$-0.813773\pi$
$941$	−11.8964	−	44.3981i	−0.387813	−	1.44734i	0.445871	−	0.895097i	$-0.352894\pi$
$942$		0			0
$943$	19.2648	−	19.2648i	0.627347	−	0.627347i
$944$	−3.79710	−	3.79710i	−0.123585	−	0.123585i
$945$		0			0
$946$	−10.3412	+	5.97050i	−0.336222	+	0.194118i
$947$	4.27109	−	1.14443i	0.138792	−	0.0371891i	−0.188754	−	0.982024i	$-0.560445\pi$
$947$	4.27109	−	1.14443i	0.138792	−	0.0371891i	0.327546	+	0.944835i	$0.393778\pi$
$948$		0			0
$949$	27.2913	+	7.50767i	0.885914	+	0.243709i
$950$	−11.3851	−	6.57316i	−0.369380	−	0.213262i
$951$		0			0
$952$	−10.6574	+	18.4592i	−0.345409	+	0.598266i
$953$	−15.6177	+	27.0507i	−0.505908	+	0.876258i	0.494069	+	0.869423i	$0.335509\pi$
$953$	−15.6177	+	27.0507i	−0.505908	+	0.876258i	−0.999977	+	0.00683493i	$0.997824\pi$
$954$		0			0
$955$	−5.70877	+	1.52966i	−0.184732	+	0.0494987i
$956$	14.1426	+	14.1426i	0.457405	+	0.457405i
$957$		0			0
$958$	3.59589	+	6.22827i	0.116178	+	0.201226i
$959$	35.1051			1.13360
$960$		0			0
$961$	12.5883	−	7.26783i	0.406073	−	0.234446i
$962$	11.1937	−	6.36376i	0.360900	−	0.205176i
$963$		0			0
$964$	−3.89667	+	14.5426i	−0.125503	+	0.468384i
$965$	−11.3780	−	6.56907i	−0.366270	−	0.211466i
$966$		0			0
$967$	4.87497	−	1.30625i	0.156769	−	0.0420060i	−0.179581	−	0.983743i	$-0.557474\pi$
$967$	4.87497	−	1.30625i	0.156769	−	0.0420060i	0.336350	+	0.941737i	$0.390808\pi$
$968$	5.73418	+	1.53647i	0.184304	+	0.0493840i
$969$		0			0
$970$	0.823066	+	0.220540i	0.0264270	+	0.00708111i
$971$	−44.8178	−	25.8756i	−1.43827	−	0.830387i	−0.440543	−	0.897732i	$-0.645214\pi$
$971$	−44.8178	−	25.8756i	−1.43827	−	0.830387i	−0.997730	+	0.0673446i	$0.978547\pi$
$972$		0			0
$973$	−49.5392	−	13.2740i	−1.58815	−	0.425545i
$974$	0.167763	+	0.290575i	0.00537549	+	0.00931061i
$975$		0			0
$976$	1.56055	−	2.70295i	0.0499520	−	0.0865194i
$977$	−15.1413	+	15.1413i	−0.484415	+	0.484415i	−0.906538	−	0.422124i	$-0.861285\pi$
$977$	−15.1413	+	15.1413i	−0.484415	+	0.484415i	0.422124	+	0.906538i	$0.361285\pi$
$978$		0			0
$979$			5.63563i			0.180116i
$980$	−6.90465	+	6.90465i	−0.220561	+	0.220561i
$981$		0			0
$982$	1.01655	+	3.79381i	0.0324394	+	0.121065i
$983$	12.5292	−	46.7595i	0.399618	−	1.49140i	−0.414151	−	0.910208i	$-0.635922\pi$
$983$	12.5292	−	46.7595i	0.399618	−	1.49140i	0.813769	−	0.581188i	$-0.197412\pi$
$984$		0			0
$985$		−	12.1037i		−	0.385655i
$986$	16.0311	+	16.0311i	0.510533	+	0.510533i
$987$		0			0
$988$	−10.1148	−	2.78252i	−0.321796	−	0.0885239i
$989$		−	25.1798i		−	0.800671i
$990$		0			0
$991$	18.5761	+	32.1748i	0.590090	+	1.02207i	0.994220	+	0.107364i	$0.0342409\pi$
$991$	18.5761	+	32.1748i	0.590090	+	1.02207i	−0.404130	+	0.914701i	$0.632426\pi$
$992$	6.74801			0.214250
$993$		0			0
$994$	19.1395	−	71.4296i	0.607068	−	2.26561i
$995$	−4.15189	+	15.4951i	−0.131624	+	0.491227i
$996$		0			0
$997$	53.0118			1.67890			0.839451	−	0.543436i	$-0.182877\pi$
$997$	53.0118			1.67890			0.839451	+	0.543436i	$0.182877\pi$
$998$	10.1494	+	17.5793i	0.321274	+	0.556463i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.557.12		56
3.2	odd	2		234.2.z.a.167.4	yes	56
9.2	odd	6		702.2.bb.a.89.5		56
9.7	even	3		234.2.y.a.11.9	✓	56
13.6	odd	12		702.2.bb.a.71.5		56
39.32	even	12		234.2.y.a.149.9	yes	56
117.97	odd	12		234.2.z.a.227.4	yes	56
117.110	even	12	inner	702.2.bc.a.305.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.9	✓	56	9.7	even	3
234.2.y.a.149.9	yes	56	39.32	even	12
234.2.z.a.167.4	yes	56	3.2	odd	2
234.2.z.a.227.4	yes	56	117.97	odd	12
702.2.bb.a.71.5		56	13.6	odd	12
702.2.bb.a.89.5		56	9.2	odd	6
702.2.bc.a.305.12		56	117.110	even	12	inner
702.2.bc.a.557.12		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.179629 + 0.670386i) q^{5} +(3.24572 - 3.24572i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.601052 + 0.347017i) q^{10} +(2.17356 - 0.582403i) q^{11} +(-1.78196 - 3.13442i) q^{13} +(3.97518 + 2.29507i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.32181 - 4.02149i) q^{17} +(-2.81042 + 0.753050i) q^{19} +(-0.490757 - 0.490757i) q^{20} +(1.12512 + 1.94876i) q^{22} -4.74503 q^{23} +(3.91298 - 2.25916i) q^{25} +(2.56642 - 2.53249i) q^{26} +(-1.18802 + 4.43374i) q^{28} +(4.22816 + 2.44113i) q^{29} +(6.51808 - 1.74651i) q^{31} +(0.965926 + 0.258819i) q^{32} +(4.48539 + 1.20186i) q^{34} +(2.75891 + 1.59286i) q^{35} +(3.44953 + 0.924299i) q^{37} +(-1.45478 - 2.51976i) q^{38} +(0.347017 - 0.601052i) q^{40} +(-4.05999 + 4.05999i) q^{41} +5.30657i q^{43} +(-1.59115 + 1.59115i) q^{44} +(-1.22810 - 4.58334i) q^{46} +(-3.12430 + 11.6601i) q^{47} -14.0694i q^{49} +(3.19493 + 3.19493i) q^{50} +(3.11043 + 1.82351i) q^{52} +5.06576i q^{53} +(0.780869 + 1.35250i) q^{55} -4.59014 q^{56} +(-1.26362 + 4.71590i) q^{58} +(1.38984 - 5.18694i) q^{59} +3.12110 q^{61} +(3.37401 + 5.84395i) q^{62} +1.00000i q^{64} +(1.78118 - 1.75764i) q^{65} +(9.25140 + 9.25140i) q^{67} +4.64361i q^{68} +(-0.824524 + 3.07717i) q^{70} +(-4.16970 - 15.5615i) q^{71} +(-5.55110 + 5.55110i) q^{73} +3.57122i q^{74} +(2.05737 - 2.05737i) q^{76} +(5.16444 - 8.94507i) q^{77} +(-1.55400 - 2.69161i) q^{79} +(0.670386 + 0.179629i) q^{80} +(-4.97245 - 2.87085i) q^{82} +(-9.17998 - 2.45977i) q^{83} +(3.11301 + 0.834129i) q^{85} +(-5.12575 + 1.37344i) q^{86} +(-1.94876 - 1.12512i) q^{88} +(-0.648204 + 2.41913i) q^{89} +(-15.9572 - 4.38972i) q^{91} +(4.10931 - 2.37251i) q^{92} -12.0714 q^{94} +(-1.00967 - 1.74880i) q^{95} +(-0.868150 - 0.868150i) q^{97} +(13.5900 - 3.64143i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

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