LMFDB - Embedded newform 315.2.r.b.184.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			184.14
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.08755i q^{2} +(-0.137009 + 1.72662i) q^{3} +0.817229 q^{4} +(-0.940709 + 2.02856i) q^{5} +(1.87779 + 0.149005i) q^{6} +(-1.34619 + 2.27767i) q^{7} -3.06389i q^{8} +(-2.96246 - 0.473127i) q^{9} +O(q^{10})$	\(q-1.08755i q^{2} +(-0.137009 + 1.72662i) q^{3} +0.817229 q^{4} +(-0.940709 + 2.02856i) q^{5} +(1.87779 + 0.149005i) q^{6} +(-1.34619 + 2.27767i) q^{7} -3.06389i q^{8} +(-2.96246 - 0.473127i) q^{9} +(2.20617 + 1.02307i) q^{10} +(-0.449548 + 0.778641i) q^{11} +(-0.111968 + 1.41105i) q^{12} +(4.10888 + 2.37226i) q^{13} +(2.47708 + 1.46405i) q^{14} +(-3.37368 - 1.90218i) q^{15} -1.69768 q^{16} +(-4.82187 + 2.78391i) q^{17} +(-0.514551 + 3.22183i) q^{18} +(-1.83472 + 3.17783i) q^{19} +(-0.768775 + 1.65780i) q^{20} +(-3.74823 - 2.63643i) q^{21} +(0.846813 + 0.488908i) q^{22} +(4.32806 - 2.49880i) q^{23} +(5.29018 + 0.419781i) q^{24} +(-3.23013 - 3.81657i) q^{25} +(2.57996 - 4.46862i) q^{26} +(1.22280 - 5.05022i) q^{27} +(-1.10015 + 1.86138i) q^{28} +(2.42600 + 4.20195i) q^{29} +(-2.06872 + 3.66905i) q^{30} +5.92329 q^{31} -4.28146i q^{32} +(-1.28283 - 0.882882i) q^{33} +(3.02765 + 5.24404i) q^{34} +(-3.35402 - 4.87345i) q^{35} +(-2.42101 - 0.386653i) q^{36} +(7.91515 + 4.56982i) q^{37} +(3.45606 + 1.99536i) q^{38} +(-4.65896 + 6.76946i) q^{39} +(6.21528 + 2.88222i) q^{40} +(1.70982 - 2.96149i) q^{41} +(-2.86725 + 4.07640i) q^{42} +(4.49284 - 2.59394i) q^{43} +(-0.367384 + 0.636328i) q^{44} +(3.74658 - 5.56446i) q^{45} +(-2.71758 - 4.70699i) q^{46} -9.17076i q^{47} +(0.232598 - 2.93125i) q^{48} +(-3.37554 - 6.13235i) q^{49} +(-4.15072 + 3.51294i) q^{50} +(-4.14612 - 8.70697i) q^{51} +(3.35789 + 1.93868i) q^{52} +(-4.50327 + 2.59996i) q^{53} +(-5.49239 - 1.32986i) q^{54} +(-1.15663 - 1.64441i) q^{55} +(6.97851 + 4.12457i) q^{56} +(-5.23554 - 3.60327i) q^{57} +(4.56985 - 2.63840i) q^{58} +1.20627 q^{59} +(-2.75707 - 1.55452i) q^{60} -2.78377 q^{61} -6.44189i q^{62} +(5.06566 - 6.11057i) q^{63} -8.05166 q^{64} +(-8.67753 + 6.10351i) q^{65} +(-0.960180 + 1.39514i) q^{66} -0.197198i q^{67} +(-3.94057 + 2.27509i) q^{68} +(3.72151 + 7.81528i) q^{69} +(-5.30014 + 3.64767i) q^{70} -8.28511 q^{71} +(-1.44961 + 9.07663i) q^{72} +(6.62001 - 3.82206i) q^{73} +(4.96992 - 8.60815i) q^{74} +(7.03234 - 5.05432i) q^{75} +(-1.49939 + 2.59702i) q^{76} +(-1.16831 - 2.07212i) q^{77} +(7.36214 + 5.06686i) q^{78} +3.14682 q^{79} +(1.59702 - 3.44385i) q^{80} +(8.55230 + 2.80324i) q^{81} +(-3.22078 - 1.85952i) q^{82} +(9.96810 - 5.75509i) q^{83} +(-3.06317 - 2.15456i) q^{84} +(-1.11136 - 12.4003i) q^{85} +(-2.82105 - 4.88620i) q^{86} +(-7.58758 + 3.61308i) q^{87} +(2.38567 + 1.37736i) q^{88} +(0.723450 - 1.25305i) q^{89} +(-6.05164 - 4.07460i) q^{90} +(-10.9346 + 6.16514i) q^{91} +(3.53701 - 2.04210i) q^{92} +(-0.811546 + 10.2273i) q^{93} -9.97369 q^{94} +(-4.72049 - 6.71126i) q^{95} +(7.39246 + 0.586599i) q^{96} +(-13.8177 + 7.97765i) q^{97} +(-6.66925 + 3.67108i) q^{98} +(1.70016 - 2.09400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.08755i		−	0.769016i	−0.923122	−	0.384508i	$-0.874371\pi$
$2$		−	1.08755i		−	0.769016i	0.923122	−	0.384508i	$-0.125629\pi$
$3$	−0.137009	+	1.72662i	−0.0791024	+	0.996866i
$3$	−0.137009	+	1.72662i	−0.0791024	+	0.996866i
$4$	0.817229			0.408615
$5$	−0.940709	+	2.02856i	−0.420698	+	0.907201i
$5$	−0.940709	+	2.02856i	−0.420698	+	0.907201i
$6$	1.87779	+	0.149005i	0.766606	+	0.0608310i
$7$	−1.34619	+	2.27767i	−0.508812	+	0.860878i
$7$	−1.34619	+	2.27767i	−0.508812	+	0.860878i
$8$		−	3.06389i		−	1.08325i
$9$	−2.96246	−	0.473127i	−0.987486	−	0.157709i
$10$	2.20617	+	1.02307i	0.697652	+	0.323523i
$11$	−0.449548	+	0.778641i	−0.135544	+	0.234769i	−0.925805	−	0.378001i	$-0.876612\pi$
$11$	−0.449548	+	0.778641i	−0.135544	+	0.234769i	0.790261	+	0.612770i	$0.209945\pi$
$12$	−0.111968	+	1.41105i	−0.0323224	+	0.407334i
$13$	4.10888	+	2.37226i	1.13960	+	0.657947i	0.946331	−	0.323200i	$-0.104759\pi$
$13$	4.10888	+	2.37226i	1.13960	+	0.657947i	0.193266	+	0.981146i	$0.438092\pi$
$14$	2.47708	+	1.46405i	0.662029	+	0.391285i
$15$	−3.37368	−	1.90218i	−0.871080	−	0.491141i
$16$	−1.69768			−0.424419
$17$	−4.82187	+	2.78391i	−1.16947	+	0.675197i	−0.953556	−	0.301215i	$-0.902608\pi$
$17$	−4.82187	+	2.78391i	−1.16947	+	0.675197i	−0.215918	+	0.976411i	$0.569275\pi$
$18$	−0.514551	+	3.22183i	−0.121281	+	0.759392i
$19$	−1.83472	+	3.17783i	−0.420914	+	0.729044i	−0.996029	−	0.0890281i	$-0.971624\pi$
$19$	−1.83472	+	3.17783i	−0.420914	+	0.729044i	0.575115	+	0.818072i	$0.304957\pi$
$20$	−0.768775	+	1.65780i	−0.171903	+	0.370696i
$21$	−3.74823	−	2.63643i	−0.817932	−	0.575315i
$22$	0.846813	+	0.488908i	0.180541	+	0.104235i
$23$	4.32806	−	2.49880i	0.902462	−	0.521037i	0.0244639	−	0.999701i	$-0.492212\pi$
$23$	4.32806	−	2.49880i	0.902462	−	0.521037i	0.877998	+	0.478664i	$0.158879\pi$
$24$	5.29018	+	0.419781i	1.07985	+	0.0856874i
$25$	−3.23013	−	3.81657i	−0.646027	−	0.763315i
$26$	2.57996	−	4.46862i	0.505971	−	0.876368i
$27$	1.22280	−	5.05022i	0.235327	−	0.971916i
$28$	−1.10015	+	1.86138i	−0.207908	+	0.351767i
$29$	2.42600	+	4.20195i	0.450497	+	0.780283i	0.998417	−	0.0562474i	$-0.0179136\pi$
$29$	2.42600	+	4.20195i	0.450497	+	0.780283i	−0.547920	+	0.836531i	$0.684580\pi$
$30$	−2.06872	+	3.66905i	−0.377695	+	0.669874i
$31$	5.92329			1.06385			0.531927	−	0.846790i	$-0.321468\pi$
$31$	5.92329			1.06385			0.531927	+	0.846790i	$0.321468\pi$
$32$		−	4.28146i		−	0.756862i
$33$	−1.28283	−	0.882882i	−0.223312	−	0.153690i
$34$	3.02765	+	5.24404i	0.519237	+	0.899345i
$35$	−3.35402	−	4.87345i	−0.566933	−	0.823764i
$36$	−2.42101	−	0.386653i	−0.403501	−	0.0644422i
$37$	7.91515	+	4.56982i	1.30124	+	0.751273i	0.980617	−	0.195933i	$-0.0627734\pi$
$37$	7.91515	+	4.56982i	1.30124	+	0.751273i	0.320626	+	0.947206i	$0.396107\pi$
$38$	3.45606	+	1.99536i	0.560647	+	0.323689i
$39$	−4.65896	+	6.76946i	−0.746030	+	1.08398i
$40$	6.21528	+	2.88222i	0.982723	+	0.455719i
$41$	1.70982	−	2.96149i	0.267029	−	0.462508i	−0.701064	−	0.713098i	$-0.747291\pi$
$41$	1.70982	−	2.96149i	0.267029	−	0.462508i	0.968093	+	0.250590i	$0.0806247\pi$
$42$	−2.86725	+	4.07640i	−0.442426	+	0.629003i
$43$	4.49284	−	2.59394i	0.685152	−	0.395573i	−0.116642	−	0.993174i	$-0.537213\pi$
$43$	4.49284	−	2.59394i	0.685152	−	0.395573i	0.801793	+	0.597602i	$0.203880\pi$
$44$	−0.367384	+	0.636328i	−0.0553852	+	0.0959301i
$45$	3.74658	−	5.56446i	0.558507	−	0.829500i
$46$	−2.71758	−	4.70699i	−0.400686	−	0.694008i
$47$		−	9.17076i		−	1.33769i	−0.743400	−	0.668847i	$-0.766788\pi$
$47$		−	9.17076i		−	1.33769i	0.743400	−	0.668847i	$-0.233212\pi$
$48$	0.232598	−	2.93125i	0.0335726	−	0.423090i
$49$	−3.37554	−	6.13235i	−0.482221	−	0.876050i
$50$	−4.15072	+	3.51294i	−0.587001	+	0.496805i
$51$	−4.14612	−	8.70697i	−0.580573	−	1.21922i
$52$	3.35789	+	1.93868i	0.465656	+	0.268847i
$53$	−4.50327	+	2.59996i	−0.618571	+	0.357132i	−0.776313	−	0.630348i	$-0.782912\pi$
$53$	−4.50327	+	2.59996i	−0.618571	+	0.357132i	0.157741	+	0.987480i	$0.449579\pi$
$54$	−5.49239	−	1.32986i	−0.747419	−	0.180970i
$55$	−1.15663	−	1.64441i	−0.155960	−	0.221732i
$56$	6.97851	+	4.12457i	0.932543	+	0.551169i
$57$	−5.23554	−	3.60327i	−0.693465	−	0.477264i
$58$	4.56985	−	2.63840i	0.600050	−	0.346439i
$59$	1.20627			0.157043			0.0785215	−	0.996912i	$-0.474980\pi$
$59$	1.20627			0.157043			0.0785215	+	0.996912i	$0.474980\pi$
$60$	−2.75707	−	1.55452i	−0.355936	−	0.200687i
$61$	−2.78377			−0.356425			−0.178213	−	0.983992i	$-0.557032\pi$
$61$	−2.78377			−0.356425			−0.178213	+	0.983992i	$0.557032\pi$
$62$		−	6.44189i		−	0.818120i
$63$	5.06566	−	6.11057i	0.638213	−	0.769860i
$64$	−8.05166			−1.00646
$65$	−8.67753	+	6.10351i	−1.07632	+	0.757047i
$66$	−0.960180	+	1.39514i	−0.118190	+	0.171730i
$67$		−	0.197198i		−	0.0240916i	−0.999927	−	0.0120458i	$-0.996166\pi$
$67$		−	0.197198i		−	0.0240916i	0.999927	−	0.0120458i	$-0.00383439\pi$
$68$	−3.94057	+	2.27509i	−0.477865	+	0.275895i
$69$	3.72151	+	7.81528i	0.448017	+	0.940849i
$70$	−5.30014	+	3.64767i	−0.633488	+	0.435980i
$71$	−8.28511			−0.983262			−0.491631	−	0.870804i	$-0.663599\pi$
$71$	−8.28511			−0.983262			−0.491631	+	0.870804i	$0.663599\pi$
$72$	−1.44961	+	9.07663i	−0.170838	+	1.06969i
$73$	6.62001	−	3.82206i	0.774813	−	0.447339i	−0.0597758	−	0.998212i	$-0.519039\pi$
$73$	6.62001	−	3.82206i	0.774813	−	0.447339i	0.834589	+	0.550873i	$0.185705\pi$
$74$	4.96992	−	8.60815i	0.577741	−	1.00068i
$75$	7.03234	−	5.05432i	0.812025	−	0.583623i
$76$	−1.49939	+	2.59702i	−0.171992	+	0.297898i
$77$	−1.16831	−	2.07212i	−0.133141	−	0.236140i
$78$	7.36214	+	5.06686i	0.833599	+	0.573709i
$79$	3.14682			0.354045			0.177023	−	0.984207i	$-0.443353\pi$
$79$	3.14682			0.354045			0.177023	+	0.984207i	$0.443353\pi$
$80$	1.59702	−	3.44385i	0.178552	−	0.385034i
$81$	8.55230	+	2.80324i	0.950256	+	0.311471i
$82$	−3.22078	−	1.85952i	−0.355676	−	0.205350i
$83$	9.96810	−	5.75509i	1.09414	−	0.631703i	0.159466	−	0.987203i	$-0.449023\pi$
$83$	9.96810	−	5.75509i	1.09414	−	0.631703i	0.934676	+	0.355501i	$0.115690\pi$
$84$	−3.06317	−	2.15456i	−0.334219	−	0.235082i
$85$	−1.11136	−	12.4003i	−0.120544	−	1.34500i
$86$	−2.82105	−	4.88620i	−0.304202	−	0.526893i
$87$	−7.58758	+	3.61308i	−0.813474	+	0.387363i
$88$	2.38567	+	1.37736i	0.254313	+	0.146828i
$89$	0.723450	−	1.25305i	0.0766856	−	0.132823i	−0.825132	−	0.564939i	$-0.808900\pi$
$89$	0.723450	−	1.25305i	0.0766856	−	0.132823i	0.901818	+	0.432116i	$0.142233\pi$
$90$	−6.05164	−	4.07460i	−0.637899	−	0.429500i
$91$	−10.9346	+	6.16514i	−1.14625	+	0.646282i
$92$	3.53701	−	2.04210i	0.368759	−	0.212903i
$93$	−0.811546	+	10.2273i	−0.0841534	+	1.06052i
$94$	−9.97369			−1.02871
$95$	−4.72049	−	6.71126i	−0.484312	−	0.688561i
$96$	7.39246	+	0.586599i	0.754490	+	0.0598696i
$97$	−13.8177	+	7.97765i	−1.40297	+	0.810008i	−0.994697	−	0.102850i	$-0.967204\pi$
$97$	−13.8177	+	7.97765i	−1.40297	+	0.810008i	−0.408278	+	0.912858i	$0.633870\pi$
$98$	−6.66925	+	3.67108i	−0.673696	+	0.370835i
$99$	1.70016	−	2.09400i	0.170873	−	0.210455i
$100$	−2.63976	−	3.11902i	−0.263976	−	0.311902i
$101$	−4.31602	+	7.47556i	−0.429460	+	0.743846i	−0.996825	−	0.0796200i	$-0.974629\pi$
$101$	−4.31602	+	7.47556i	−0.429460	+	0.743846i	0.567366	+	0.823466i	$0.307963\pi$
$102$	−9.46929	+	4.50912i	−0.937599	+	0.446470i
$103$	−2.14502	+	1.23843i	−0.211355	+	0.122026i	−0.601941	−	0.798541i	$-0.705606\pi$
$103$	−2.14502	+	1.23843i	−0.211355	+	0.122026i	0.390586	+	0.920567i	$0.372272\pi$
$104$	7.26833	−	12.5891i	0.712719	−	1.23447i
$105$	8.87415	−	5.12342i	0.866028	−	0.499995i
$106$	2.82760	+	4.89754i	0.274640	+	0.475691i
$107$	12.2855	+	7.09301i	1.18768	+	0.685707i	0.957779	−	0.287507i	$-0.0928263\pi$
$107$	12.2855	+	7.09301i	1.18768	+	0.685707i	0.229901	+	0.973214i	$0.426160\pi$
$108$	0.999305	−	4.12719i	0.0961582	−	0.397139i
$109$	−8.86242	−	15.3502i	−0.848866	−	1.47028i	−0.882221	−	0.470836i	$-0.843952\pi$
$109$	−8.86242	−	15.3502i	−0.848866	−	1.47028i	0.0333544	−	0.999444i	$-0.489381\pi$
$110$	−1.78838	+	1.25789i	−0.170516	+	0.119935i
$111$	−8.97480	+	13.0404i	−0.851850	+	1.23774i
$112$	2.28540	−	3.86675i	0.215950	−	0.365373i
$113$	9.26695	+	5.35028i	0.871761	+	0.503312i	0.867933	−	0.496681i	$-0.165448\pi$
$113$	9.26695	+	5.35028i	0.871761	+	0.503312i	0.00382807	+	0.999993i	$0.498781\pi$
$114$	−3.91874	+	5.69393i	−0.367024	+	0.533285i
$115$	0.997543	+	11.1304i	0.0930213	+	1.03791i
$116$	1.98260	+	3.43396i	0.184080	+	0.318835i
$117$	−11.0500	−	8.97174i	−1.02157	−	0.829438i
$118$		−	1.31188i		−	0.120769i
$119$	0.150336	−	14.7303i	0.0137813	−	1.35032i
$120$	−5.82807	+	10.3366i	−0.532027	+	0.943595i
$121$	5.09581	+	8.82621i	0.463256	+	0.802382i
$122$			3.02750i			0.274097i
$123$	4.87913	+	3.35797i	0.439936	+	0.302778i
$124$	4.84068			0.434706
$125$	10.7808	−	2.96225i	0.964262	−	0.264952i
$126$	−6.64557	−	5.50917i	−0.592035	−	0.490796i
$127$		−	11.4930i		−	1.01984i	−0.860222	−	0.509919i	$-0.829675\pi$
$127$		−	11.4930i		−	1.01984i	0.860222	−	0.509919i	$-0.170325\pi$
$128$			0.193696i			0.0171205i
$129$	3.86320	+	8.11284i	0.340136	+	0.714296i
$130$	6.63789	+	9.43728i	0.582181	+	0.827704i
$131$	2.11637	+	3.66567i	0.184908	+	0.320271i	0.943546	−	0.331243i	$-0.107468\pi$
$131$	2.11637	+	3.66567i	0.184908	+	0.320271i	−0.758637	+	0.651513i	$0.774134\pi$
$132$	−1.04836	−	0.721517i	−0.0912483	−	0.0628000i
$133$	−4.76816	−	8.45685i	−0.413452	−	0.733302i
$134$	−0.214464			−0.0185268
$135$	9.09440	+	7.23131i	0.782722	+	0.622372i
$136$	8.52957	+	14.7736i	0.731405	+	1.26683i
$137$	−7.57113	−	4.37120i	−0.646845	−	0.373456i	0.140401	−	0.990095i	$-0.455161\pi$
$137$	−7.57113	−	4.37120i	−0.646845	−	0.373456i	−0.787247	+	0.616638i	$0.788494\pi$
$138$	8.49953	−	4.04734i	0.723528	−	0.344532i
$139$	3.23489	−	5.60299i	0.274379	−	0.475239i	−0.695599	−	0.718430i	$-0.744861\pi$
$139$	3.23489	−	5.60299i	0.274379	−	0.475239i	0.969978	+	0.243191i	$0.0781942\pi$
$140$	−2.74100	−	3.98273i	−0.231657	−	0.336602i
$141$	15.8345	+	1.25648i	1.33350	+	0.105815i
$142$			9.01050i			0.756144i
$143$	−3.69428	+	2.13289i	−0.308931	+	0.178361i
$144$	5.02930	+	0.803217i	0.419108	+	0.0669348i
$145$	−10.8061	+	0.968478i	−0.897397	+	0.0804277i
$146$	−4.15669	−	7.19961i	−0.344010	−	0.595844i
$147$	11.0507	−	4.98810i	0.911450	−	0.411412i
$148$	6.46850	+	3.73459i	0.531707	+	0.306981i
$149$	8.24920	+	14.2880i	0.675801	+	1.17052i	0.976234	+	0.216718i	$0.0695353\pi$
$149$	8.24920	+	14.2880i	0.675801	+	1.17052i	−0.300433	+	0.953803i	$0.597131\pi$
$150$	−5.49684	−	7.64804i	−0.448815	−	0.624460i
$151$	4.00545	−	6.93764i	0.325959	−	0.564577i	−0.655747	−	0.754981i	$-0.727646\pi$
$151$	4.00545	−	6.93764i	0.325959	−	0.564577i	0.981706	+	0.190403i	$0.0609796\pi$
$152$	9.73651	+	5.62138i	0.789735	+	0.455954i
$153$	15.6017	−	5.96585i	1.26132	−	0.482310i
$154$	−2.25354	+	1.27060i	−0.181595	+	0.102388i
$155$	−5.57209	+	12.0158i	−0.447561	+	0.965129i
$156$	−3.80743	+	5.53220i	−0.304839	+	0.442931i
$157$			3.12095i			0.249079i	0.992215	+	0.124539i	$0.0397453\pi$
$157$			3.12095i			0.249079i	−0.992215	+	0.124539i	$0.960255\pi$
$158$		−	3.42233i		−	0.272266i
$159$	−3.87217	−	8.13167i	−0.307083	−	0.644883i
$160$	8.68520	+	4.02760i	0.686626	+	0.318410i
$161$	−0.134940	+	13.2217i	−0.0106348	+	1.04202i
$162$	3.04867	−	9.30108i	0.239526	−	0.730762i
$163$	−16.5250	−	9.54073i	−1.29434	−	0.747288i	−0.314920	−	0.949118i	$-0.601978\pi$
$163$	−16.5250	−	9.54073i	−1.29434	−	0.747288i	−0.979421	+	0.201830i	$0.935311\pi$
$164$	1.39731	−	2.42022i	0.109112	−	0.188987i
$165$	2.99775	−	1.77176i	0.233374	−	0.137931i
$166$	−6.25896	−	10.8408i	−0.485790	−	0.841412i
$167$	8.91914	+	5.14947i	0.690184	+	0.398478i	0.803681	−	0.595060i	$-0.202872\pi$
$167$	8.91914	+	5.14947i	0.690184	+	0.398478i	−0.113497	+	0.993538i	$0.536205\pi$
$168$	−8.07770	+	11.4842i	−0.623208	+	0.886022i
$169$	4.75524	+	8.23632i	0.365788	+	0.633563i
$170$	−13.4860	+	1.20866i	−1.03433	+	0.0927000i
$171$	6.93880	−	8.54613i	0.530623	−	0.653539i
$172$	3.67168	−	2.11985i	0.279963	−	0.161637i
$173$			17.6048i			1.33847i	0.743052	+	0.669234i	$0.233377\pi$
$173$			17.6048i			1.33847i	−0.743052	+	0.669234i	$0.766623\pi$
$174$	3.92942	+	8.25189i	0.297888	+	0.625574i
$175$	13.0413	−	2.21934i	0.985827	−	0.167766i
$176$	0.763188	−	1.32188i	0.0575275	−	0.0996405i
$177$	−0.165270	+	2.08277i	−0.0124225	+	0.156551i
$178$	−1.36276	−	0.786790i	−0.102143	−	0.0589724i
$179$	1.55582	+	2.69476i	0.116288	+	0.201416i	0.918294	−	0.395900i	$-0.129567\pi$
$179$	1.55582	+	2.69476i	0.116288	+	0.201416i	−0.802006	+	0.597316i	$0.796234\pi$
$180$	3.06181	−	4.54744i	0.228214	−	0.338946i
$181$	21.6100			1.60626			0.803130	−	0.595803i	$-0.203166\pi$
$181$	21.6100			1.60626			0.803130	+	0.595803i	$0.203166\pi$
$182$	6.70492	+	11.8919i	0.497001	+	0.881486i
$183$	0.381403	−	4.80653i	0.0281941	−	0.355309i
$184$	−7.65605	−	13.2607i	−0.564411	−	0.977589i
$185$	−16.7160	+	11.7575i	−1.22899	+	0.864430i
$186$	11.1227	+	0.882599i	0.815557	+	0.0647153i
$187$		−	5.00600i		−	0.366075i
$188$		−	7.49462i		−	0.546601i
$189$	9.85662	+	9.58369i	0.716964	+	0.697111i
$190$	−7.29885	+	5.13378i	−0.529514	+	0.372444i
$191$	−5.55741			−0.402120			−0.201060	−	0.979579i	$-0.564439\pi$
$191$	−5.55741			−0.402120			−0.201060	+	0.979579i	$0.564439\pi$
$192$	1.10315	−	13.9022i	0.0796132	−	1.00330i
$193$			8.02088i			0.577356i	0.957426	+	0.288678i	$0.0932157\pi$
$193$			8.02088i			0.577356i	−0.957426	+	0.288678i	$0.906784\pi$
$194$	8.67611	+	15.0275i	0.622909	+	1.07891i
$195$	−9.34956	−	15.8191i	−0.669536	−	1.13283i
$196$	−2.75859	−	5.01154i	−0.197042	−	0.357967i
$197$			1.41139i			0.100557i	0.998735	+	0.0502786i	$0.0160109\pi$
$197$			1.41139i			0.100557i	−0.998735	+	0.0502786i	$0.983989\pi$
$198$	−2.27733	−	1.84902i	−0.161843	−	0.131404i
$199$	−12.2848	−	21.2779i	−0.870845	−	1.50835i	−0.861124	−	0.508395i	$-0.830239\pi$
$199$	−12.2848	−	21.2779i	−0.870845	−	1.50835i	−0.00972071	−	0.999953i	$-0.503094\pi$
$200$	−11.6935	+	9.89676i	−0.826858	+	0.699807i
$201$	0.340487	+	0.0270180i	0.0240161	+	0.00190570i
$202$	8.13007	+	4.69390i	0.572029	+	0.330261i
$203$	−12.8365	−	0.131009i	−0.900947	−	0.00919500i
$204$	−3.38833	−	7.11559i	−0.237230	−	0.498191i
$205$	4.39914	+	6.25438i	0.307249	+	0.436825i
$206$	1.34686	+	2.33282i	0.0938399	+	0.162536i
$207$	−14.0039	+	5.35488i	−0.973341	+	0.372190i
$208$	−6.97555	−	4.02733i	−0.483667	−	0.279245i
$209$	−1.64959	−	2.85718i	−0.114105	−	0.197635i
$210$	−5.57199	−	9.65111i	−0.384504	−	0.665990i
$211$	6.68390	−	11.5769i	0.460139	−	0.796983i	−0.538829	−	0.842415i	$-0.681133\pi$
$211$	6.68390	−	11.5769i	0.460139	−	0.796983i	0.998967	+	0.0454319i	$0.0144664\pi$
$212$	−3.68020	+	2.12477i	−0.252757	+	0.145930i
$213$	1.13514	−	14.3053i	0.0777784	−	0.980181i
$214$	7.71402	−	13.3611i	0.527320	−	0.913345i
$215$	1.03552	+	11.5542i	0.0706220	+	0.787987i
$216$	−15.4733	−	3.74651i	−1.05283	−	0.254918i
$217$	−7.97387	+	13.4913i	−0.541302	+	0.915848i
$218$	−16.6941	+	9.63835i	−1.13067	+	0.652792i
$219$	5.69226	+	11.9539i	0.384647	+	0.807771i
$220$	−0.945230	−	1.34386i	−0.0637274	−	0.0906031i
$221$	−26.4166			−1.77697
$222$	14.1821	+	9.76057i	0.951840	+	0.655086i
$223$	−21.3419	+	12.3217i	−1.42916	+	0.825125i	−0.997054	−	0.0766985i	$-0.975562\pi$
$223$	−21.3419	+	12.3217i	−1.42916	+	0.825125i	−0.432104	+	0.901824i	$0.642229\pi$
$224$	9.75174	+	5.76365i	0.651565	+	0.385100i
$225$	7.76341	+	12.8347i	0.517561	+	0.855646i
$226$	5.81871	−	10.0783i	0.387055	−	0.670398i
$227$	−11.8033	−	6.81464i	−0.783413	−	0.452304i	0.0542254	−	0.998529i	$-0.482731\pi$
$227$	−11.8033	−	6.81464i	−0.783413	−	0.452304i	−0.837639	+	0.546225i	$0.816064\pi$
$228$	−4.27864	−	2.94469i	−0.283360	−	0.195017i
$229$	−1.06655	−	1.84732i	−0.0704798	−	0.122075i	0.828632	−	0.559794i	$-0.189120\pi$
$229$	−1.06655	−	1.84732i	−0.0704798	−	0.122075i	−0.899112	+	0.437719i	$0.855786\pi$
$230$	12.1049	−	1.08488i	0.798172	−	0.0715349i
$231$	3.73784	−	1.73333i	0.245932	−	0.114045i
$232$	12.8743	−	7.43298i	0.845240	−	0.487999i
$233$	20.8864	+	12.0588i	1.36831	+	0.789995i	0.990712	−	0.135974i	$-0.0434163\pi$
$233$	20.8864	+	12.0588i	1.36831	+	0.789995i	0.377600	+	0.925969i	$0.376750\pi$
$234$	−9.75724	+	12.0174i	−0.637851	+	0.785605i
$235$	18.6035	+	8.62701i	1.21356	+	0.562764i
$236$	0.985799			0.0641701
$237$	−0.431144	+	5.43338i	−0.0280058	+	0.352936i
$238$	−16.0200	−	0.163499i	−1.03842	−	0.0105980i
$239$	8.06114	−	13.9623i	0.521432	−	0.903147i	−0.478257	−	0.878220i	$-0.658731\pi$
$239$	8.06114	−	13.9623i	0.521432	−	0.903147i	0.999689	−	0.0249270i	$-0.00793532\pi$
$240$	5.72742	+	3.22929i	0.369703	+	0.208450i
$241$	−2.28069	+	3.95028i	−0.146912	+	0.254460i	−0.930085	−	0.367345i	$-0.880267\pi$
$241$	−2.28069	+	3.95028i	−0.146912	+	0.254460i	0.783172	+	0.621805i	$0.213600\pi$
$242$	9.59896	−	5.54196i	0.617045	−	0.356251i
$243$	−6.01188	+	14.3825i	−0.385662	+	0.922640i
$244$	−2.27498			−0.145641
$245$	15.6153	−	1.07875i	0.997622	−	0.0689188i
$246$	3.65197	−	5.30631i	0.232841	−	0.338318i
$247$	−15.0773	+	8.70488i	−0.959345	+	0.553878i
$248$		−	18.1483i		−	1.15242i
$249$	8.57115	+	17.9997i	0.543174	+	1.14068i
$250$	−3.22160	−	11.7247i	−0.203752	−	0.741533i
$251$	−16.9101			−1.06736			−0.533679	−	0.845687i	$-0.679191\pi$
$251$	−16.9101			−1.06736			−0.533679	+	0.845687i	$0.679191\pi$
$252$	4.13980	−	4.99374i	0.260783	−	0.314576i
$253$			4.49333i			0.282493i
$254$	−12.4992			−0.784272
$255$	21.5629	−	0.219939i	1.35032	−	0.0137731i
$256$	−15.8927			−0.993292
$257$	−18.5311	+	10.6989i	−1.15594	+	0.667380i	−0.950327	−	0.311254i	$-0.899251\pi$
$257$	−18.5311	+	10.6989i	−1.15594	+	0.667380i	−0.205610	+	0.978634i	$0.565918\pi$
$258$	8.82314	−	4.20143i	0.549305	−	0.261570i
$259$	−21.0638	+	11.8763i	−1.30884	+	0.737954i
$260$	−7.09154	+	4.98797i	−0.439798	+	0.309340i
$261$	−5.19886	−	13.5959i	−0.321801	−	0.841566i
$262$	3.98660	−	2.30167i	0.246293	−	0.142197i
$263$	3.17450	+	1.83280i	0.195748	+	0.113015i	0.594671	−	0.803969i	$-0.297282\pi$
$263$	3.17450	+	1.83280i	0.195748	+	0.113015i	−0.398922	+	0.916985i	$0.630616\pi$
$264$	−2.70505	+	3.93043i	−0.166484	+	0.241902i
$265$	−1.03793	−	11.5810i	−0.0637593	−	0.711413i
$266$	−9.19727	+	5.18562i	−0.563921	+	0.317951i
$267$	2.06443	+	1.42081i	0.126341	+	0.0869519i
$268$		−	0.161156i		−	0.00984419i
$269$	−11.2715	−	19.5228i	−0.687235	−	1.19033i	−0.972729	−	0.231945i	$-0.925491\pi$
$269$	−11.2715	−	19.5228i	−0.687235	−	1.19033i	0.285494	−	0.958381i	$-0.407842\pi$
$270$	7.86443	−	9.89064i	0.478614	−	0.601925i
$271$	1.89382	−	3.28019i	0.115041	−	0.199257i	−0.802755	−	0.596309i	$-0.796633\pi$
$271$	1.89382	−	3.28019i	0.115041	−	0.199257i	0.917796	+	0.397052i	$0.129967\pi$
$272$	8.18598	−	4.72618i	0.496348	−	0.286567i
$273$	−9.14674	−	19.7245i	−0.553586	−	1.19378i
$274$	−4.75390	+	8.23400i	−0.287194	+	0.497434i
$275$	4.42384	−	0.799380i	0.266768	−	0.0482044i
$276$	3.04133	+	6.38688i	0.183066	+	0.384445i
$277$	−14.7886	−	8.53818i	−0.888558	−	0.513009i	−0.0150875	−	0.999886i	$-0.504803\pi$
$277$	−14.7886	−	8.53818i	−0.888558	−	0.513009i	−0.873471	+	0.486877i	$0.838136\pi$
$278$	−6.09354	−	3.51811i	−0.365466	−	0.211002i
$279$	−17.5475	−	2.80247i	−1.05054	−	0.167779i
$280$	−14.9317	+	10.2763i	−0.892340	+	0.614128i
$281$	5.22118	+	9.04336i	0.311470	+	0.539481i	0.978681	−	0.205387i	$-0.0658454\pi$
$281$	5.22118	+	9.04336i	0.311470	+	0.539481i	−0.667211	+	0.744869i	$0.732512\pi$
$282$	1.36649	−	17.2208i	0.0813732	−	1.02548i
$283$			1.24168i			0.0738102i	0.999319	+	0.0369051i	$0.0117499\pi$
$283$			1.24168i			0.0738102i	−0.999319	+	0.0369051i	$0.988250\pi$
$284$	−6.77084			−0.401775
$285$	12.2346	−	7.23101i	0.724713	−	0.428328i
$286$	2.31963	+	4.01772i	0.137163	+	0.237573i
$287$	4.44356	+	7.88114i	0.262295	+	0.465209i
$288$	−2.02567	+	12.6836i	−0.119364	+	0.747390i
$289$	7.00027	−	12.1248i	0.411781	−	0.713225i
$290$	1.05327	+	11.7522i	0.0618502	+	0.690112i
$291$	−11.8812	−	24.9510i	−0.696491	−	1.46265i
$292$	5.41006	−	3.12350i	0.316600	−	0.182789i
$293$	−3.00614	−	1.73559i	−0.175620	−	0.101394i	0.409613	−	0.912259i	$-0.365664\pi$
$293$	−3.00614	−	1.73559i	−0.175620	−	0.101394i	−0.585233	+	0.810865i	$0.698997\pi$
$294$	−5.42483	−	12.0183i	−0.316382	−	0.700919i
$295$	−1.13475	+	2.44699i	−0.0660676	+	0.142470i
$296$	14.0014	−	24.2511i	0.813814	−	1.40957i
$297$	3.38260	+	3.22244i	0.196279	+	0.186985i
$298$	15.5390	−	8.97144i	0.900149	−	0.519701i
$299$	23.7113			1.37126
$300$	5.74704	−	4.13054i	0.331805	−	0.238477i
$301$	−0.140078	+	13.7251i	−0.00807395	+	0.791104i
$302$	−7.54505	−	4.35614i	−0.434169	−	0.250668i
$303$	−12.3161	−	8.47636i	−0.707544	−	0.486954i
$304$	3.11477	−	5.39493i	0.178644	−	0.309421i
$305$	2.61872	−	5.64706i	0.149947	−	0.323350i
$306$	−6.48817	−	16.9677i	−0.370904	−	0.969978i
$307$		−	5.08997i		−	0.290500i	−0.989395	−	0.145250i	$-0.953601\pi$
$307$		−	5.08997i		−	0.290500i	0.989395	−	0.145250i	$-0.0463986\pi$
$308$	−0.954775	−	1.69340i	−0.0544034	−	0.0964903i
$309$	−1.84441	−	3.87332i	−0.104925	−	0.220346i
$310$	13.0678	+	6.05994i	0.742200	+	0.344181i
$311$	14.4791			0.821032			0.410516	−	0.911853i	$-0.365349\pi$
$311$	14.4791			0.821032			0.410516	+	0.911853i	$0.365349\pi$
$312$	20.7408	+	14.2745i	1.17422	+	0.808135i
$313$			11.6328i			0.657526i	0.944412	+	0.328763i	$0.106632\pi$
$313$			11.6328i			0.657526i	−0.944412	+	0.328763i	$0.893368\pi$
$314$	3.39419			0.191545
$315$	7.63038	+	16.0243i	0.429923	+	0.902866i
$316$	2.57168			0.144668
$317$		−	18.7219i		−	1.05153i	−0.850631	−	0.525763i	$-0.823780\pi$
$317$		−	18.7219i		−	1.05153i	0.850631	−	0.525763i	$-0.176220\pi$
$318$	−8.84362	+	4.21119i	−0.495925	+	0.236152i
$319$	−4.36242			−0.244248
$320$	7.57427	−	16.3333i	0.423415	−	0.913060i
$321$	−13.9302	+	20.2406i	−0.777507	+	1.12972i
$322$	14.3793	+	0.146755i	0.801329	+	0.00817831i
$323$		−	20.4308i		−	1.13680i
$324$	6.98919	+	2.29089i	0.388288	+	0.127272i
$325$	−4.21832	−	23.3445i	−0.233990	−	1.29492i
$326$	−10.3761	+	17.9718i	−0.574676	+	0.995369i
$327$	27.7182	−	13.1990i	1.53282	−	0.729904i
$328$	−9.07368	−	5.23869i	−0.501010	−	0.289258i
$329$	20.8880	+	12.3456i	1.15159	+	0.680634i
$330$	−1.92688	−	3.26021i	−0.106071	−	0.179469i
$331$	15.7205			0.864079			0.432039	−	0.901855i	$-0.357794\pi$
$331$	15.7205			0.864079			0.432039	+	0.901855i	$0.357794\pi$
$332$	8.14623	−	4.70323i	0.447082	−	0.258123i
$333$	−21.2862	−	17.2828i	−1.16648	−	0.947089i
$334$	5.60032	−	9.70004i	0.306436	−	0.530762i
$335$	0.400029	+	0.185506i	0.0218559	+	0.0101353i
$336$	6.36329	+	4.47580i	0.347146	+	0.244175i
$337$	−6.28248	−	3.62719i	−0.342229	−	0.197586i	0.319029	−	0.947745i	$-0.396643\pi$
$337$	−6.28248	−	3.62719i	−0.342229	−	0.197586i	−0.661257	+	0.750159i	$0.729977\pi$
$338$	8.95743	−	5.17158i	0.487220	−	0.281297i
$339$	−10.5076	+	15.2675i	−0.570693	+	0.829216i
$340$	−0.908234	−	10.1339i	−0.0492559	−	0.549588i
$341$	−2.66280	+	4.61211i	−0.144199	+	0.249760i
$342$	−9.29437	−	7.54631i	−0.502582	−	0.408058i
$343$	18.5116	+	0.566941i	0.999531	+	0.0306119i
$344$	−7.94754	−	13.7655i	−0.428503	−	0.742189i
$345$	−19.3546	+	0.197414i	−1.04202	+	0.0106284i
$346$	19.1461			1.02930
$347$			4.09429i			0.219793i	0.993943	+	0.109896i	$0.0350519\pi$
$347$			4.09429i			0.219793i	−0.993943	+	0.109896i	$0.964948\pi$
$348$	−6.20079	+	2.95272i	−0.332397	+	0.158282i
$349$	3.70073	+	6.40985i	0.198095	+	0.343111i	0.947911	−	0.318536i	$-0.103191\pi$
$349$	3.70073	+	6.40985i	0.198095	+	0.343111i	−0.749816	+	0.661647i	$0.769858\pi$
$350$	−2.41365	−	14.1831i	−0.129015	−	0.758116i
$351$	17.0048	−	17.8500i	0.907647	−	0.952760i
$352$	3.33372	+	1.92472i	0.177688	+	0.102588i
$353$	−0.809472	−	0.467349i	−0.0430839	−	0.0248745i	0.478303	−	0.878195i	$-0.341252\pi$
$353$	−0.809472	−	0.467349i	−0.0430839	−	0.0248745i	−0.521387	+	0.853320i	$0.674585\pi$
$354$	2.26513	+	0.179740i	0.120390	+	0.00955308i
$355$	7.79388	−	16.8069i	0.413656	−	0.892016i
$356$	0.591225	−	1.02403i	0.0313349	−	0.0542736i
$357$	25.4131	+	2.27776i	1.34500	+	0.120552i
$358$	2.93070	−	1.69204i	0.154892	−	0.0894270i
$359$	−10.1911	+	17.6515i	−0.537867	+	0.931613i	0.461152	+	0.887321i	$0.347436\pi$
$359$	−10.1911	+	17.6515i	−0.537867	+	0.931613i	−0.999019	+	0.0442913i	$0.985897\pi$
$360$	−17.0489	−	11.4791i	−0.898553	−	0.605001i
$361$	2.76759	+	4.79361i	0.145663	+	0.252296i
$362$		−	23.5020i		−	1.23524i
$363$	−15.9377	+	7.58928i	−0.836513	+	0.398334i
$364$	−8.93604	+	5.03833i	−0.468376	+	0.264080i
$365$	1.52580	+	17.0245i	0.0798639	+	0.891105i
$366$	−5.22735	−	0.414796i	−0.273238	−	0.0216817i
$367$	7.00713	+	4.04557i	0.365769	+	0.211177i	0.671609	−	0.740906i	$-0.265604\pi$
$367$	7.00713	+	4.04557i	0.365769	+	0.211177i	−0.305839	+	0.952083i	$0.598937\pi$
$368$	−7.34764	+	4.24216i	−0.383022	+	0.221138i
$369$	−6.46643	+	7.96434i	−0.336629	+	0.414607i
$370$	12.7869	+	18.1795i	0.664761	+	0.945109i
$371$	0.140403	−	13.7570i	0.00728936	−	0.714228i
$372$	−0.663219	+	8.35804i	−0.0343863	+	0.433344i
$373$	20.0512	−	11.5766i	1.03821	−	0.599413i	0.118887	−	0.992908i	$-0.462068\pi$
$373$	20.0512	−	11.5766i	1.03821	−	0.599413i	0.919327	+	0.393495i	$0.128734\pi$
$374$	−5.44429			−0.281518
$375$	3.63762	+	19.0202i	0.187846	+	0.982198i
$376$	−28.0982			−1.44905
$377$			23.0204i			1.18561i
$378$	10.4228	−	10.7196i	0.536089	−	0.551356i
$379$	−19.6139			−1.00750			−0.503748	−	0.863851i	$-0.668046\pi$
$379$	−19.6139			−1.00750			−0.503748	+	0.863851i	$0.668046\pi$
$380$	−3.85772	−	5.48464i	−0.197897	−	0.281356i
$381$	19.8441	+	1.57465i	1.01664	+	0.0806717i
$382$			6.04397i			0.309237i
$383$	−5.80615	+	3.35218i	−0.296680	+	0.171289i	−0.640951	−	0.767582i	$-0.721460\pi$
$383$	−5.80615	+	3.35218i	−0.296680	+	0.171289i	0.344270	+	0.938871i	$0.388126\pi$
$384$	−0.334440	−	0.0265382i	−0.0170668	−	0.00135427i
$385$	5.30246	−	0.420723i	0.270239	−	0.0214421i
$386$	8.72313			0.443996
$387$	−14.5371	+	5.55876i	−0.738963	+	0.282568i
$388$	−11.2922	+	6.51957i	−0.573276	+	0.330981i
$389$	−2.84525	+	4.92812i	−0.144260	+	0.249865i	−0.929097	−	0.369837i	$-0.879413\pi$
$389$	−2.84525	+	4.92812i	−0.144260	+	0.249865i	0.784837	+	0.619703i	$0.212747\pi$
$390$	−17.2041	+	10.1681i	−0.871162	+	0.514884i
$391$	−13.9129	+	24.0978i	−0.703604	+	1.21868i
$392$	−18.7888	+	10.3423i	−0.948978	+	0.522364i
$393$	−6.61919	+	3.15195i	−0.333894	+	0.158995i
$394$	1.53496			0.0773301
$395$	−2.96024	+	6.38353i	−0.148946	+	0.321190i
$396$	1.38942	−	1.71127i	0.0698212	−	0.0859948i
$397$	−23.8918	−	13.7939i	−1.19909	−	0.692297i	−0.238741	−	0.971083i	$-0.576735\pi$
$397$	−23.8918	−	13.7939i	−1.19909	−	0.692297i	−0.960353	+	0.278786i	$0.910068\pi$
$398$	−23.1408	+	13.3603i	−1.15994	+	0.669693i
$399$	15.2551	−	7.07415i	0.763709	−	0.354150i
$400$	5.48373	+	6.47931i	0.274186	+	0.323966i
$401$	−7.40146	−	12.8197i	−0.369611	−	0.640185i	0.619893	−	0.784686i	$-0.287176\pi$
$401$	−7.40146	−	12.8197i	−0.369611	−	0.640185i	−0.989505	+	0.144501i	$0.953842\pi$
$402$	0.0293835	−	0.370298i	0.00146552	−	0.0184688i
$403$	24.3381	+	14.0516i	1.21236	+	0.699959i
$404$	−3.52718	+	6.10925i	−0.175484	+	0.303946i
$405$	−13.7318	+	14.7119i	−0.682337	+	0.731038i
$406$	−0.142479	+	13.9604i	−0.00707110	+	0.692842i
$407$	−7.11649	+	4.10871i	−0.352751	+	0.203661i
$408$	−26.6772	+	12.7032i	−1.32072	+	0.628904i
$409$	17.4502			0.862855			0.431428	−	0.902148i	$-0.358010\pi$
$409$	17.4502			0.862855			0.431428	+	0.902148i	$0.358010\pi$
$410$	6.80197	−	4.78429i	0.335925	−	0.236279i
$411$	8.58472	−	12.4736i	0.423453	−	0.615277i
$412$	−1.75297	+	1.01208i	−0.0863629	+	0.0498616i
$413$	−1.62387	+	2.74748i	−0.0799054	+	0.135195i
$414$	5.82371	+	15.2300i	0.286220	+	0.748514i
$415$	2.29748	+	25.6348i	0.112779	+	1.25836i
$416$	10.1567	−	17.5920i	0.497975	−	0.862517i
$417$	9.23104	+	6.35309i	0.452046	+	0.311112i
$418$	−3.10733	+	1.79402i	−0.151985	+	0.0877483i
$419$	9.28876	−	16.0886i	0.453786	−	0.785980i	−0.544832	−	0.838545i	$-0.683406\pi$
$419$	9.28876	−	16.0886i	0.453786	−	0.785980i	0.998617	+	0.0525654i	$0.0167398\pi$
$420$	7.25222	−	4.18701i	0.353872	−	0.204305i
$421$	−14.5746	−	25.2440i	−0.710323	−	1.23032i	−0.964736	−	0.263221i	$-0.915215\pi$
$421$	−14.5746	−	25.2440i	−0.710323	−	1.23032i	0.254412	−	0.967096i	$-0.418118\pi$
$422$	−12.5904	−	7.26909i	−0.612893	−	0.353854i
$423$	−4.33894	+	27.1680i	−0.210966	+	1.32095i
$424$	7.96599	+	13.7975i	0.386863	+	0.670066i
$425$	26.2003	+	9.41062i	1.27090	+	0.456482i
$426$	−15.5577	−	1.23452i	−0.753775	−	0.0598128i
$427$	3.74749	−	6.34051i	0.181354	−	0.306839i
$428$	10.0400	+	5.79662i	0.485303	+	0.280190i
$429$	−3.17655	−	6.67085i	−0.153365	−	0.322072i
$430$	12.5657	−	1.12619i	0.605974	−	0.0543095i
$431$	−1.29565	−	2.24413i	−0.0624093	−	0.108096i	0.833133	−	0.553073i	$-0.186545\pi$
$431$	−1.29565	−	2.24413i	−0.0624093	−	0.108096i	−0.895542	+	0.444977i	$0.853212\pi$
$432$	−2.07591	+	8.57365i	−0.0998775	+	0.412500i
$433$			30.7769i			1.47904i	0.673133	+	0.739522i	$0.264948\pi$
$433$			30.7769i			1.47904i	−0.673133	+	0.739522i	$0.735052\pi$
$434$	14.6725	+	8.67200i	0.704302	+	0.416270i
$435$	−0.191663	−	18.7907i	−0.00918952	−	0.900947i
$436$	−7.24263	−	12.5446i	−0.346859	−	0.600778i
$437$			18.3384i			0.877247i
$438$	13.0005	−	6.19063i	0.621189	−	0.295800i
$439$	−33.8865			−1.61731			−0.808656	−	0.588281i	$-0.799805\pi$
$439$	−33.8865			−1.61731			−0.808656	+	0.588281i	$0.799805\pi$
$440$	−5.03829	+	3.54377i	−0.240191	+	0.168943i
$441$	7.09852	+	19.7639i	0.338025	+	0.941137i
$442$			28.7295i			1.36652i
$443$		−	27.6935i		−	1.31576i	−0.753124	−	0.657879i	$-0.771454\pi$
$443$		−	27.6935i		−	1.31576i	0.753124	−	0.657879i	$-0.228546\pi$
$444$	−7.33447	+	10.6570i	−0.348079	+	0.505758i
$445$	1.86134	+	2.64632i	0.0882360	+	0.125448i
$446$	13.4005	+	23.2104i	0.634534	+	1.09905i
$447$	−25.8003	+	12.2857i	−1.22031	+	0.581092i
$448$	10.8391	−	18.3390i	0.512098	−	0.866437i
$449$	26.7298			1.26146			0.630728	−	0.776004i	$-0.282756\pi$
$449$	26.7298			1.26146			0.630728	+	0.776004i	$0.282756\pi$
$450$	13.9584	−	8.44312i	0.658006	−	0.398012i
$451$	1.53729	+	2.66267i	0.0723883	+	0.125380i
$452$	7.57322	+	4.37240i	0.356214	+	0.205660i
$453$	11.4299	+	7.86643i	0.537024	+	0.369597i
$454$	−7.41128	+	12.8367i	−0.347829	+	0.602457i
$455$	−2.22015	−	27.9810i	−0.104082	−	1.31177i
$456$	−11.0400	+	16.0411i	−0.516995	+	0.751193i
$457$		−	27.6155i		−	1.29180i	−0.763423	−	0.645899i	$-0.776483\pi$
$457$		−	27.6155i		−	1.29180i	0.763423	−	0.645899i	$-0.223517\pi$
$458$	−2.00906	+	1.15993i	−0.0938772	+	0.0542001i
$459$	8.16319	+	27.7557i	0.381025	+	1.29552i
$460$	0.815221	+	9.09607i	0.0380099	+	0.424107i
$461$	−7.84817	−	13.5934i	−0.365526	−	0.633109i	0.623335	−	0.781955i	$-0.285778\pi$
$461$	−7.84817	−	13.5934i	−0.365526	−	0.633109i	−0.988860	+	0.148846i	$0.952444\pi$
$462$	−1.88508	−	4.06510i	−0.0877021	−	0.189126i
$463$	−32.3670	−	18.6871i	−1.50422	−	0.868463i	−0.999988	−	0.00489558i	$-0.998442\pi$
$463$	−32.3670	−	18.6871i	−1.50422	−	0.868463i	−0.504234	−	0.863567i	$-0.668225\pi$
$464$	−4.11857	−	7.13356i	−0.191200	−	0.331167i
$465$	−19.9833	−	11.2672i	−0.926702	−	0.522502i
$466$	13.1145	−	22.7150i	0.607519	−	1.05225i
$467$	−5.47692	−	3.16210i	−0.253442	−	0.146325i	0.367897	−	0.929866i	$-0.380078\pi$
$467$	−5.47692	−	3.16210i	−0.253442	−	0.146325i	−0.621339	+	0.783542i	$0.713411\pi$
$468$	−9.03037	−	7.33197i	−0.417429	−	0.338920i
$469$	0.449153	+	0.265467i	0.0207399	+	0.0122581i
$470$	9.38233	−	20.2323i	0.432775	−	0.933244i
$471$	−5.38870	−	0.427599i	−0.248298	−	0.0197027i
$472$		−	3.69587i		−	0.170116i
$473$			4.66441i			0.214470i
$474$	5.90908	+	0.468892i	0.271413	+	0.0215369i
$475$	18.0548	−	3.26247i	0.828412	−	0.149693i
$476$	0.122859	−	12.0380i	0.00563124	−	0.551762i
$477$	14.5709	−	5.57166i	0.667153	−	0.255109i
$478$	−15.1847	−	8.76692i	−0.694534	−	0.400989i
$479$	4.16121	−	7.20742i	0.190130	−	0.329316i	−0.755163	−	0.655537i	$-0.772442\pi$
$479$	4.16121	−	7.20742i	0.190130	−	0.329316i	0.945293	+	0.326222i	$0.105776\pi$
$480$	−8.14411	+	14.4443i	−0.371726	+	0.659287i
$481$	21.6816	+	37.5536i	0.988595	+	1.71230i
$482$	4.29613	+	2.48037i	0.195684	+	0.112978i
$483$	−22.8105	−	2.04449i	−1.03791	−	0.0930276i
$484$	4.16445	+	7.21303i	0.189293	+	0.327865i
$485$	−3.18474	−	35.5347i	−0.144612	−	1.61355i
$486$	15.6418	+	6.53824i	0.709525	+	0.296580i
$487$	24.9182	−	14.3865i	1.12915	−	0.651917i	0.185431	−	0.982657i	$-0.440632\pi$
$487$	24.9182	−	14.3865i	1.12915	−	0.651917i	0.943722	+	0.330740i	$0.107298\pi$
$488$			8.52916i			0.386097i
$489$	18.7373	−	27.2253i	0.847332	−	1.23117i
$490$	−1.17320	−	16.9824i	−0.0529996	−	0.767187i
$491$	−1.15384	+	1.99851i	−0.0520721	+	0.0901915i	−0.890887	−	0.454226i	$-0.849916\pi$
$491$	−1.15384	+	1.99851i	−0.0520721	+	0.0901915i	0.838814	+	0.544417i	$0.183249\pi$
$492$	3.98736	+	2.74423i	0.179764	+	0.123719i
$493$	−23.3957	−	13.5075i	−1.05369	−	0.608348i
$494$	9.46701	+	16.3973i	0.425941	+	0.737751i
$495$	2.64844	+	5.41873i	0.119039	+	0.243554i
$496$	−10.0558			−0.451520
$497$	11.1533	−	18.8707i	0.500296	−	0.846468i
$498$	19.5756	−	9.32157i	0.877203	−	0.417710i
$499$	5.44126	+	9.42453i	0.243584	+	0.421900i	0.961733	−	0.273990i	$-0.0883435\pi$
$499$	5.44126	+	9.42453i	0.243584	+	0.421900i	−0.718148	+	0.695890i	$0.755010\pi$
$500$	8.81036	−	2.42084i	0.394011	−	0.108263i
$501$	−10.1132	+	14.6945i	−0.451825	+	0.656501i
$502$			18.3906i			0.820815i
$503$		−	20.8217i		−	0.928393i	−0.885732	−	0.464197i	$-0.846343\pi$
$503$		−	20.8217i		−	0.928393i	0.885732	−	0.464197i	$-0.153657\pi$
$504$	−18.7221	−	15.5206i	−0.833949	−	0.691342i
$505$	−11.1045	−	15.7876i	−0.494145	−	0.702541i
$506$	4.88674			0.217242
$507$	−14.8725	+	7.08206i	−0.660513	+	0.314525i
$508$		−	9.39241i		−	0.416721i
$509$	−15.4876	−	26.8252i	−0.686474	−	1.18901i	−0.972971	−	0.230927i	$-0.925824\pi$
$509$	−15.4876	−	26.8252i	−0.686474	−	1.18901i	0.286497	−	0.958081i	$-0.407509\pi$
$510$	−0.239195	−	23.4508i	−0.0105917	−	1.03842i
$511$	−0.206399	+	20.2234i	−0.00913054	+	0.894631i
$512$			17.6715i			0.780978i
$513$	13.8053	+	13.1516i	0.609517	+	0.580657i
$514$	11.6356	+	20.1535i	0.513226	+	0.888934i
$515$	−0.494391	−	5.51631i	−0.0217855	−	0.243078i
$516$	3.15712	+	6.63005i	0.138984	+	0.291872i
$517$	7.14073	+	4.12270i	0.314049	+	0.181316i
$518$	12.9160	+	22.9080i	0.567499	+	1.00652i
$519$	−30.3968	−	2.41202i	−1.33427	−	0.105876i
$520$	18.7004	+	26.5870i	0.820069	+	1.16592i
$521$	20.3164	+	35.1891i	0.890080	+	1.54166i	0.839778	+	0.542929i	$0.182685\pi$
$521$	20.3164	+	35.1891i	0.890080	+	1.54166i	0.0503015	+	0.998734i	$0.483982\pi$
$522$	−14.7863	+	5.65403i	−0.647178	+	0.247470i
$523$	22.8709	+	13.2045i	1.00007	+	0.577393i	0.908270	−	0.418384i	$-0.137404\pi$
$523$	22.8709	+	13.2045i	1.00007	+	0.577393i	0.0918035	+	0.995777i	$0.470737\pi$
$524$	1.72956	+	2.99569i	0.0755563	+	0.130867i
$525$	2.04519	+	22.8214i	0.0892596	+	0.996008i
$526$	1.99327	−	3.45244i	0.0869106	−	0.150534i
$527$	−28.5613	+	16.4899i	−1.24415	+	0.718310i
$528$	2.17783	+	1.49885i	0.0947777	+	0.0652290i
$529$	0.988047	−	1.71135i	0.0429586	−	0.0744064i
$530$	−12.5949	+	1.12880i	−0.547088	+	0.0490319i
$531$	−3.57352	−	0.570719i	−0.155078	−	0.0247671i
$532$	−3.89668	−	6.91119i	−0.168942	−	0.299638i
$533$	14.0509	−	8.11228i	0.608611	−	0.351382i
$534$	1.54520	−	2.24518i	0.0668674	−	0.0971583i
$535$	−25.9457	+	18.2494i	−1.12173	+	0.788989i
$536$	−0.604193			−0.0260972
$537$	−4.86600	+	2.31711i	−0.209984	+	0.0999907i
$538$	−21.2321	+	12.2583i	−0.915379	+	0.528495i
$539$	6.29237	+	0.128452i	0.271031	+	0.00553283i
$540$	7.43221	+	5.90964i	0.319832	+	0.254310i
$541$	5.26850	−	9.12530i	0.226510	−	0.392327i	−0.730261	−	0.683168i	$-0.760602\pi$
$541$	5.26850	−	9.12530i	0.226510	−	0.392327i	0.956772	+	0.290841i	$0.0939350\pi$
$542$	−3.56738	−	2.05963i	−0.153232	−	0.0884686i
$543$	−2.96078	+	37.3124i	−0.127059	+	1.60123i
$544$	11.9192	+	20.6446i	0.511030	+	0.885131i
$545$	39.4757	−	3.53795i	1.69096	−	0.151549i
$546$	−21.4515	+	9.94756i	−0.918038	+	0.425716i
$547$	12.9372	−	7.46928i	0.553154	−	0.319363i	−0.197239	−	0.980355i	$-0.563198\pi$
$547$	12.9372	−	7.46928i	0.553154	−	0.319363i	0.750393	+	0.660992i	$0.229864\pi$
$548$	−6.18735	−	3.57227i	−0.264311	−	0.152600i
$549$	8.24680	+	1.31708i	0.351965	+	0.0562115i
$550$	−0.869368	−	4.81116i	−0.0370700	−	0.205149i
$551$	−17.8041			−0.758482
$552$	23.9451	−	11.4023i	1.01917	−	0.485313i
$553$	−4.23622	+	7.16742i	−0.180142	+	0.304790i
$554$	−9.28572	+	16.0833i	−0.394512	+	0.683315i
$555$	−18.0106	−	30.4731i	−0.764506	−	1.29351i
$556$	2.64364	−	4.57893i	0.112115	−	0.194190i
$557$	28.4420	−	16.4210i	1.20513	−	0.695779i	0.243435	−	0.969917i	$-0.421726\pi$
$557$	28.4420	−	16.4210i	1.20513	−	0.695779i	0.961690	+	0.274138i	$0.0883925\pi$
$558$	−3.04783	+	19.0838i	−0.129025	+	0.807882i
$559$	24.6140			1.04106
$560$	5.69405	+	8.27355i	0.240617	+	0.349621i
$561$	8.64348	+	0.685869i	0.364928	+	0.0289574i
$562$	9.83512	−	5.67831i	0.414870	−	0.239525i
$563$		−	33.3400i		−	1.40512i	−0.711627	−	0.702558i	$-0.752041\pi$
$563$		−	33.3400i		−	1.40512i	0.711627	−	0.702558i	$-0.247959\pi$
$564$	12.9404	+	1.02683i	0.544888	+	0.0432374i
$565$	−19.5709	+	13.7655i	−0.823353	+	0.579121i
$566$	1.35039			0.0567612
$567$	−17.8979	+	15.7056i	−0.751640	+	0.659574i
$568$			25.3846i			1.06512i
$569$	19.8152			0.830698			0.415349	−	0.909662i	$-0.363660\pi$
$569$	19.8152			0.830698			0.415349	+	0.909662i	$0.363660\pi$
$570$	−7.86410	−	13.3057i	−0.329391	−	0.557316i
$571$	−10.2362			−0.428372			−0.214186	−	0.976793i	$-0.568710\pi$
$571$	−10.2362			−0.428372			−0.214186	+	0.976793i	$0.568710\pi$
$572$	−3.01907	+	1.74306i	−0.126234	+	0.0728811i
$573$	0.761417	−	9.59555i	0.0318086	−	0.400860i
$574$	8.57115	−	4.83260i	0.357753	−	0.201709i
$575$	−23.5171	−	8.44687i	−0.980730	−	0.352259i
$576$	23.8527	+	3.80946i	0.993863	+	0.158728i
$577$	−20.8977	+	12.0653i	−0.869981	+	0.502284i	−0.867342	−	0.497713i	$-0.834173\pi$
$577$	−20.8977	+	12.0653i	−0.869981	+	0.502284i	−0.00263902	+	0.999997i	$0.500840\pi$
$578$	−13.1864	−	7.61317i	−0.548482	−	0.316666i
$579$	−13.8490	−	1.09894i	−0.575547	−	0.0456702i
$580$	−8.83105	+	0.791469i	−0.366689	+	0.0328640i
$581$	−0.310786	+	30.4515i	−0.0128936	+	1.26334i
$582$	−27.1355	+	12.9215i	−1.12480	+	0.535613i
$583$		−	4.67524i		−	0.193629i
$584$	−11.7104	−	20.2829i	−0.484578	−	0.839314i
$585$	28.5946	−	13.9758i	1.18224	−	0.577828i
$586$	−1.88755	+	3.26933i	−0.0779739	+	0.135055i
$587$	3.21570	−	1.85658i	0.132726	−	0.0766295i	−0.432167	−	0.901794i	$-0.642251\pi$
$587$	3.21570	−	1.85658i	0.132726	−	0.0766295i	0.564893	+	0.825164i	$0.308917\pi$
$588$	9.03099	−	4.07642i	0.372432	−	0.168109i
$589$	−10.8676	+	18.8232i	−0.447791	+	0.775597i
$590$	2.66124	+	1.23410i	0.109561	+	0.0508070i
$591$	−2.43694	−	0.193373i	−0.100242	−	0.00795432i
$592$	−13.4374	−	7.75807i	−0.552273	−	0.318855i
$593$	−24.6121	−	14.2098i	−1.01070	−	0.583526i	−0.0993007	−	0.995057i	$-0.531661\pi$
$593$	−24.6121	−	14.2098i	−1.01070	−	0.583526i	−0.911395	+	0.411532i	$0.864994\pi$
$594$	3.50457	−	3.67876i	0.143794	−	0.150941i
$595$	29.7399	+	14.1619i	1.21922	+	0.580580i
$596$	6.74149	+	11.6766i	0.276142	+	0.478292i
$597$	38.4220	−	18.2959i	1.57251	−	0.748802i
$598$		−	25.7872i		−	1.05452i
$599$	−12.6921			−0.518586			−0.259293	−	0.965799i	$-0.583489\pi$
$599$	−12.6921			−0.518586			−0.259293	+	0.965799i	$0.583489\pi$
$600$	−15.4859	−	21.5463i	−0.632207	−	0.879624i
$601$	−5.41542	−	9.37979i	−0.220900	−	0.382610i	0.734182	−	0.678953i	$-0.237566\pi$
$601$	−5.41542	−	9.37979i	−0.220900	−	0.382610i	−0.955081	+	0.296343i	$0.904233\pi$
$602$	14.9268	+	0.152342i	0.608371	+	0.00620900i
$603$	−0.0932999	+	0.584192i	−0.00379947	+	0.0237901i
$604$	3.27337	−	5.66965i	0.133192	−	0.230695i
$605$	−22.6982	+	2.03429i	−0.922813	+	0.0827056i
$606$	−9.21848	+	13.3945i	−0.374475	+	0.544113i
$607$	22.2259	−	12.8321i	0.902123	−	0.520841i	0.0242344	−	0.999706i	$-0.492285\pi$
$607$	22.2259	−	12.8321i	0.902123	−	0.520841i	0.877888	+	0.478866i	$0.158952\pi$
$608$	13.6057	+	7.85528i	0.551786	+	0.318574i
$609$	1.98492	−	22.1459i	0.0804332	−	0.897396i
$610$	−6.14147	−	2.84799i	−0.248661	−	0.115312i
$611$	21.7554	−	37.6815i	0.880131	−	1.52443i
$612$	12.7502	−	4.87547i	0.515396	−	0.197079i
$613$	13.6135	−	7.85974i	0.549843	−	0.317452i	−0.199216	−	0.979956i	$-0.563839\pi$
$613$	13.6135	−	7.85974i	0.549843	−	0.317452i	0.749059	+	0.662504i	$0.230506\pi$
$614$	−5.53561			−0.223399
$615$	−11.4017	+	6.73874i	−0.459760	+	0.271732i
$616$	−6.34874	+	3.57956i	−0.255798	+	0.144225i
$617$	−26.3219	−	15.1969i	−1.05968	−	0.611806i	−0.134335	−	0.990936i	$-0.542890\pi$
$617$	−26.3219	−	15.1969i	−1.05968	−	0.611806i	−0.925343	+	0.379130i	$0.876223\pi$
$618$	−4.21244	+	2.00590i	−0.169449	+	0.0806889i
$619$	16.4071	−	28.4180i	0.659458	−	1.14221i	−0.321298	−	0.946978i	$-0.604119\pi$
$619$	16.4071	−	28.4180i	0.659458	−	1.14221i	0.980756	−	0.195237i	$-0.0625475\pi$
$620$	−4.55367	+	9.81963i	−0.182880	+	0.394366i
$621$	−7.32719	−	24.9132i	−0.294030	−	0.999732i
$622$		−	15.7467i		−	0.631386i
$623$	1.88014	+	3.33463i	0.0753261	+	0.133599i
$624$	7.90940	−	11.4924i	0.316630	−	0.460063i
$625$	−4.13246	+	24.6561i	−0.165298	+	0.986244i
$626$	12.6513			0.505648
$627$	5.15928	−	2.45676i	0.206042	−	0.0981137i
$628$			2.55053i			0.101777i
$629$	−50.8878			−2.02903
$630$	17.4272	−	8.29844i	0.694318	−	0.330618i
$631$	19.4885			0.775826			0.387913	−	0.921696i	$-0.373196\pi$
$631$	19.4885			0.775826			0.387913	+	0.921696i	$0.373196\pi$
$632$		−	9.64150i		−	0.383518i
$633$	19.0731	+	13.1267i	0.758088	+	0.521740i
$634$	−20.3611			−0.808641
$635$	23.3143	+	10.8116i	0.925199	+	0.429044i
$636$	−3.16445	−	6.64544i	−0.125479	−	0.263509i
$637$	0.677841	−	33.2047i	0.0268570	−	1.31562i
$638$			4.74436i			0.187831i
$639$	24.5443	+	3.91991i	0.970957	+	0.155069i
$640$	−0.392925	−	0.182212i	−0.0155317	−	0.00720255i
$641$	6.92467	−	11.9939i	0.273508	−	0.473730i	−0.696250	−	0.717800i	$-0.745149\pi$
$641$	6.92467	−	11.9939i	0.273508	−	0.473730i	0.969758	+	0.244070i	$0.0784826\pi$
$642$	22.0127	+	15.1498i	0.868771	+	0.597915i
$643$	38.3905	+	22.1647i	1.51397	+	0.874092i	0.999866	+	0.0163656i	$0.00520955\pi$
$643$	38.3905	+	22.1647i	1.51397	+	0.874092i	0.514106	+	0.857727i	$0.328124\pi$
$644$	−0.110277	+	10.8052i	−0.00434553	+	0.425784i
$645$	−20.0915	+	0.204931i	−0.791104	+	0.00806914i
$646$	−22.2195			−0.874216
$647$	6.32230	−	3.65018i	0.248555	−	0.143503i	−0.370547	−	0.928814i	$-0.620830\pi$
$647$	6.32230	−	3.65018i	0.248555	−	0.143503i	0.619103	+	0.785310i	$0.287497\pi$
$648$	8.58880	−	26.2033i	0.337400	−	1.02936i
$649$	−0.542277	+	0.939251i	−0.0212862	+	0.0368688i
$650$	−25.3884	+	4.58764i	−0.995816	+	0.179942i
$651$	−22.2019	−	15.6163i	−0.870160	−	0.612051i
$652$	−13.5047	−	7.79697i	−0.528887	−	0.305353i
$653$	10.4027	−	6.00603i	0.407091	−	0.235034i	−0.282448	−	0.959283i	$-0.591147\pi$
$653$	10.4027	−	6.00603i	0.407091	−	0.235034i	0.689539	+	0.724249i	$0.257813\pi$
$654$	−14.3546	−	30.1450i	−0.561308	−	1.17876i
$655$	−9.42692	+	0.844873i	−0.368340	+	0.0330119i
$656$	−2.90272	+	5.02766i	−0.113332	+	0.196297i
$657$	−21.4198	+	8.19059i	−0.835666	+	0.319545i
$658$	13.4265	−	22.7167i	0.523419	−	0.885591i
$659$	10.4638	+	18.1239i	0.407612	+	0.706005i	0.994622	−	0.103575i	$-0.0330281\pi$
$659$	10.4638	+	18.1239i	0.407612	+	0.706005i	−0.587009	+	0.809580i	$0.699695\pi$
$660$	2.44985	−	1.44793i	0.0953602	−	0.0563608i
$661$	−27.9730			−1.08803			−0.544013	−	0.839077i	$-0.683096\pi$
$661$	−27.9730			−1.08803			−0.544013	+	0.839077i	$0.683096\pi$
$662$		−	17.0969i		−	0.664490i
$663$	3.61932	−	45.6115i	0.140563	−	1.77141i
$664$	−17.6329	−	30.5411i	−0.684290	−	1.18523i
$665$	21.6407	−	1.71708i	0.839190	−	0.0665855i
$666$	−18.7959	+	23.1499i	−0.728327	+	0.897039i
$667$	20.9997	+	12.1242i	0.813113	+	0.469451i
$668$	7.28899	+	4.20830i	0.282019	+	0.162824i
$669$	−18.3510	−	38.5376i	−0.709490	−	1.48995i
$670$	0.201748	−	0.435053i	0.00779420	−	0.0168076i
$671$	1.25144	−	2.16756i	0.0483113	−	0.0836776i
$672$	−11.2877	+	16.0479i	−0.435434	+	0.619061i
$673$	16.2514	−	9.38274i	0.626444	−	0.361678i	−0.152929	−	0.988237i	$-0.548871\pi$
$673$	16.2514	−	9.38274i	0.626444	−	0.361678i	0.779374	+	0.626559i	$0.215537\pi$
$674$	−3.94476	+	6.83253i	−0.151947	+	0.263179i
$675$	−23.2243	+	11.6460i	−0.893906	+	0.448255i
$676$	3.88612	+	6.73096i	0.149466	+	0.258883i
$677$			45.5985i			1.75249i	0.481862	+	0.876247i	$0.339961\pi$
$677$			45.5985i			1.75249i	−0.481862	+	0.876247i	$0.660039\pi$
$678$	16.6042	+	11.4275i	0.637681	+	0.438872i
$679$	0.430808	−	42.2116i	0.0165329	−	1.61993i
$680$	−37.9931	+	3.40507i	−1.45697	+	0.130579i
$681$	13.3835	−	19.4462i	0.512856	−	0.745180i
$682$	5.01591	+	2.89594i	0.192069	+	0.110891i
$683$	−34.1296	+	19.7047i	−1.30593	+	0.753980i	−0.981415	−	0.191899i	$-0.938535\pi$
$683$	−34.1296	+	19.7047i	−1.30593	+	0.753980i	−0.324518	+	0.945880i	$0.605202\pi$
$684$	5.67059	−	6.98415i	0.216820	−	0.267046i
$685$	15.9895	−	11.2465i	0.610926	−	0.429707i
$686$	0.616578	−	20.1323i	0.0235411	−	0.768655i
$687$	3.33576	−	1.58843i	0.127267	−	0.0606025i
$688$	−7.62739	+	4.40368i	−0.290792	+	0.167889i
$689$	−24.6712			−0.939896
$690$	0.214699	+	21.0492i	0.00817344	+	0.801329i
$691$	20.8027			0.791370			0.395685	−	0.918386i	$-0.370507\pi$
$691$	20.8027			0.791370			0.395685	+	0.918386i	$0.370507\pi$
$692$			14.3871i			0.546917i
$693$	2.48068	+	6.69133i	0.0942334	+	0.254182i
$694$	4.45276			0.169024
$695$	8.32293	+	11.8329i	0.315707	+	0.448849i
$696$	11.0701	+	23.2475i	0.419610	+	0.881193i
$697$			19.0399i			0.721188i
$698$	6.97104	−	4.02473i	0.263858	−	0.152338i
$699$	−23.6826	+	34.4107i	−0.895757	+	1.30153i
$700$	10.6577	−	1.81371i	0.402823	−	0.0685518i
$701$	3.57398			0.134987			0.0674936	−	0.997720i	$-0.478500\pi$
$701$	3.57398			0.134987			0.0674936	+	0.997720i	$0.478500\pi$
$702$	−19.4128	−	18.4936i	−0.732688	−	0.697995i
$703$	−29.0442	+	16.7687i	−1.09542	+	0.632443i
$704$	3.61961	−	6.26935i	0.136419	−	0.236285i
$705$	−17.4445	+	30.9392i	−0.656996	+	1.16524i
$706$	−0.508267	+	0.880344i	−0.0191289	+	0.0331322i
$707$	−11.2167	−	19.8940i	−0.421846	−	0.748190i
$708$	−0.135064	+	1.70210i	−0.00507600	+	0.0639690i
$709$	−33.7904			−1.26903			−0.634513	−	0.772912i	$-0.718799\pi$
$709$	−33.7904			−1.26903			−0.634513	+	0.772912i	$0.718799\pi$
$710$	−18.2784	−	8.47625i	−0.685975	−	0.318108i
$711$	−9.32232	−	1.48885i	−0.349614	−	0.0558361i
$712$	−3.83921	−	2.21657i	−0.143880	−	0.0830694i
$713$	25.6363	−	14.8011i	0.960088	−	0.554307i
$714$	2.47718	−	27.6380i	0.0927063	−	1.03433i
$715$	−0.851467	−	9.50050i	−0.0318431	−	0.355299i
$716$	1.27146	+	2.20224i	0.0475168	+	0.0823015i
$717$	23.0032	+	15.8315i	0.859070	+	0.591239i
$718$	19.1970	+	11.0834i	0.716425	+	0.413628i
$719$	13.9199	−	24.1100i	0.519126	−	0.899153i	−0.480627	−	0.876925i	$-0.659591\pi$
$719$	13.9199	−	24.1100i	0.519126	−	0.899153i	0.999753	−	0.0222275i	$-0.00707582\pi$
$720$	−6.36048	+	9.44665i	−0.237041	+	0.352056i
$721$	0.0668775	−	6.55281i	0.00249065	−	0.244039i
$722$	5.21331	−	3.00991i	0.194019	−	0.112017i
$723$	−6.50816	−	4.47912i	−0.242041	−	0.166580i
$724$	17.6603			0.656342
$725$	8.20076	−	22.8319i	0.304569	−	0.847955i
$726$	8.25374	+	17.3331i	0.306325	+	0.643292i
$727$	4.20007	−	2.42491i	0.155772	−	0.0899350i	−0.420088	−	0.907483i	$-0.638001\pi$
$727$	4.20007	−	2.42491i	0.155772	−	0.0899350i	0.575860	+	0.817548i	$0.304667\pi$
$728$	18.8893	+	33.5022i	0.700083	+	1.24167i
$729$	−24.0095	−	12.3508i	−0.889242	−	0.457437i
$730$	18.5151	−	1.65939i	0.685274	−	0.0614166i
$731$	−14.4426	+	25.0153i	−0.534178	+	0.925224i
$732$	0.311693	−	3.92803i	0.0115205	−	0.145184i
$733$	6.23853	−	3.60182i	0.230425	−	0.133036i	−0.380343	−	0.924846i	$-0.624194\pi$
$733$	6.23853	−	3.60182i	0.230425	−	0.133036i	0.610768	+	0.791809i	$0.290861\pi$
$734$	4.39977	−	7.62062i	0.162398	−	0.281282i
$735$	−0.276842	+	27.1095i	−0.0102115	+	0.999948i
$736$	−10.6985	−	18.5304i	−0.394353	−	0.683039i
$737$	0.153547	+	0.0886502i	0.00565597	+	0.00326547i
$738$	8.66164	+	7.03258i	0.318839	+	0.258873i
$739$	10.4815	+	18.1544i	0.385567	+	0.667822i	0.991848	−	0.127429i	$-0.0406725\pi$
$739$	10.4815	+	18.1544i	0.385567	+	0.667822i	−0.606281	+	0.795251i	$0.707339\pi$
$740$	−13.6608	+	9.60859i	−0.502182	+	0.353219i
$741$	−12.9643	−	27.2254i	−0.476256	−	1.00015i
$742$	−14.9615	−	0.152696i	−0.549252	−	0.00560563i
$743$	−22.7236	−	13.1195i	−0.833649	−	0.481307i	0.0214515	−	0.999770i	$-0.493171\pi$
$743$	−22.7236	−	13.1195i	−0.833649	−	0.481307i	−0.855100	+	0.518462i	$0.826505\pi$
$744$	31.3352	+	2.48648i	1.14881	+	0.0911589i
$745$	−36.7443	+	3.29315i	−1.34621	+	0.120652i
$746$	−12.5901	−	21.8068i	−0.460958	−	0.798402i
$747$	−32.2530	+	12.3330i	−1.18007	+	0.451242i
$748$		−	4.09105i		−	0.149584i
$749$	−32.6941	+	18.4337i	−1.19462	+	0.673551i
$750$	20.6855	−	3.95611i	0.755326	−	0.144457i
$751$	−6.23584	−	10.8008i	−0.227549	−	0.394127i	0.729532	−	0.683947i	$-0.239738\pi$
$751$	−6.23584	−	10.8008i	−0.227549	−	0.394127i	−0.957081	+	0.289820i	$0.906405\pi$
$752$			15.5690i			0.567743i
$753$	2.31684	−	29.1974i	0.0844305	−	1.06401i
$754$	25.0359			0.911754
$755$	10.3055	+	14.6516i	0.375055	+	0.533227i
$756$	8.05512	+	7.83207i	0.292962	+	0.284850i
$757$			16.1928i			0.588536i	0.955723	+	0.294268i	$0.0950758\pi$
$757$			16.1928i			0.588536i	−0.955723	+	0.294268i	$0.904924\pi$
$758$			21.3311i			0.774780i
$759$	−7.75830	−	0.615629i	−0.281608	−	0.0223459i
$760$	−20.5625	+	14.4630i	−0.745881	+	0.524630i
$761$	−26.5462	−	45.9794i	−0.962299	−	1.66675i	−0.716702	−	0.697380i	$-0.754349\pi$
$761$	−26.5462	−	45.9794i	−0.962299	−	1.66675i	−0.245598	−	0.969372i	$-0.578984\pi$
$762$	1.71251	−	21.5815i	0.0620378	−	0.781815i
$763$	46.8931	+	0.478588i	1.69764	+	0.0173260i
$764$	−4.54168			−0.164312
$765$	−2.57457	+	37.2612i	−0.0930838	+	1.34718i
$766$	3.64567	+	6.31449i	0.131724	+	0.228152i
$767$	4.95641	+	2.86159i	0.178966	+	0.103326i
$768$	2.17744	−	27.4407i	0.0785718	−	0.990180i
$769$	11.7274	−	20.3125i	0.422902	−	0.732487i	−0.573320	−	0.819331i	$-0.694345\pi$
$769$	11.7274	−	20.3125i	0.422902	−	0.732487i	0.996222	+	0.0868442i	$0.0276782\pi$
$770$	−0.457559	−	5.76671i	−0.0164893	−	0.207818i
$771$	−15.9341	−	33.4620i	−0.573852	−	1.20511i
$772$			6.55490i			0.235916i
$773$	20.1696	−	11.6449i	0.725451	−	0.418839i	−0.0913047	−	0.995823i	$-0.529104\pi$
$773$	20.1696	−	11.6449i	0.725451	−	0.418839i	0.816756	+	0.576984i	$0.195770\pi$
$774$	6.04544	+	15.8099i	0.217299	+	0.568274i
$775$	−19.1330	−	22.6067i	−0.687278	−	0.812055i
$776$	24.4426	+	42.3358i	0.877438	+	1.51977i
$777$	−17.6199	−	37.9965i	−0.632109	−	1.36312i
$778$	5.35959	+	3.09436i	0.192150	+	0.110938i
$779$	6.27409	+	10.8670i	0.224792	+	0.389352i
$780$	−7.64073	−	12.9278i	−0.273582	−	0.462890i
$781$	3.72456	−	6.45113i	0.133275	−	0.230839i
$782$	26.2076	+	15.1310i	0.937183	+	0.541083i
$783$	24.1873	−	7.11371i	0.864384	−	0.254223i
$784$	5.73058	+	10.4108i	0.204664	+	0.371813i
$785$	−6.33103	−	2.93590i	−0.225964	−	0.104787i
$786$	3.42791	+	7.19871i	0.122270	+	0.256770i
$787$		−	38.1460i		−	1.35976i	−0.733324	−	0.679879i	$-0.762032\pi$
$787$		−	38.1460i		−	1.35976i	0.733324	−	0.679879i	$-0.237968\pi$
$788$			1.15343i			0.0410892i
$789$	−3.59949	+	5.23006i	−0.128145	+	0.186195i
$790$	6.94242	+	3.21942i	0.247000	+	0.114542i
$791$	−24.6612	+	13.9045i	−0.876852	+	0.494389i
$792$	−6.41576	−	5.20911i	−0.227974	−	0.185098i
$793$	−11.4382	−	6.60383i	−0.406181	−	0.234509i
$794$	−15.0016	+	25.9836i	−0.532388	+	0.922122i
$795$	20.1382	−	0.205406i	0.714228	−	0.00728501i
$796$	−10.0395	−	17.3889i	−0.355840	−	0.616333i
$797$	−12.1001	−	6.98598i	−0.428607	−	0.247456i	0.270146	−	0.962819i	$-0.412928\pi$
$797$	−12.1001	−	6.98598i	−0.428607	−	0.247456i	−0.698753	+	0.715363i	$0.746261\pi$
$798$	−7.69351	−	16.5907i	−0.272347	−	0.587304i
$799$	25.5305	+	44.2202i	0.903206	+	1.56440i
$800$	−16.3405	+	13.8297i	−0.577724	+	0.488953i
$801$	−2.73604	+	3.36983i	−0.0966733	+	0.119067i
$802$	−13.9421	+	8.04948i	−0.492313	+	0.284237i
$803$			6.87281i			0.242536i
$804$	0.278256	+	0.0220799i	0.00981334	+	0.000778699i
$805$	−26.6942	−	12.7115i	−0.940847	−	0.448023i
$806$	15.2818	−	26.4689i	0.538280	−	0.932328i
$807$	35.2528	−	16.7868i	1.24096	−	0.590924i
$808$	22.9043	+	13.2238i	0.805769	+	0.465211i
$809$	−5.54651	−	9.60684i	−0.195005	−	0.337758i	0.751897	−	0.659280i	$-0.229139\pi$
$809$	−5.54651	−	9.60684i	−0.195005	−	0.337758i	−0.946902	+	0.321522i	$0.895806\pi$
$810$	15.9999	+	14.9340i	0.562180	+	0.524728i
$811$	−16.2762			−0.571534			−0.285767	−	0.958299i	$-0.592248\pi$
$811$	−16.2762			−0.571534			−0.285767	+	0.958299i	$0.592248\pi$
$812$	−10.4904	−	0.107064i	−0.368140	−	0.00375721i
$813$	5.40418	+	3.71933i	0.189533	+	0.130443i
$814$	4.46844	+	7.73956i	0.156619	+	0.271271i
$815$	34.8992	−	24.5470i	1.22247	−	0.859845i
$816$	7.03877	+	14.7816i	0.246406	+	0.517461i
$817$			19.0366i			0.666008i
$818$		−	18.9780i		−	0.663549i
$819$	35.3100	−	13.0905i	1.23383	−	0.457420i
$820$	3.59510	+	5.11126i	0.125546	+	0.178493i
$821$	−41.9201			−1.46302			−0.731512	−	0.681829i	$-0.761185\pi$
$821$	−41.9201			−1.46302			−0.731512	+	0.681829i	$0.761185\pi$
$822$	−13.5657	−	9.33634i	−0.473158	−	0.325642i
$823$			44.7737i			1.56071i	0.625334	+	0.780357i	$0.284963\pi$
$823$			44.7737i			1.56071i	−0.625334	+	0.780357i	$0.715037\pi$
$824$	3.79440	+	6.57210i	0.132184	+	0.228950i
$825$	0.774121	+	7.74783i	0.0269514	+	0.269745i
$826$	2.98803	+	1.76604i	0.103967	+	0.0614485i
$827$			28.3554i			0.986015i	0.870025	+	0.493007i	$0.164102\pi$
$827$			28.3554i			0.986015i	−0.870025	+	0.493007i	$0.835898\pi$
$828$	−11.4444	+	4.37616i	−0.397721	+	0.152082i
$829$	−6.94632	−	12.0314i	−0.241256	−	0.417867i	0.719817	−	0.694164i	$-0.244226\pi$
$829$	−6.94632	−	12.0314i	−0.241256	−	0.417867i	−0.961072	+	0.276297i	$0.910893\pi$
$830$	27.8792	−	2.49863i	0.967700	−	0.0867286i
$831$	16.7684	−	24.3645i	0.581689	−	0.845194i
$832$	−33.0833	−	19.1006i	−1.14696	−	0.662196i
$833$	33.3483	+	20.1722i	1.15545	+	0.698925i
$834$	6.90932	−	10.0392i	0.239250	−	0.347631i
$835$	−18.8363	+	13.2489i	−0.651858	+	0.458497i
$836$	−1.34810	−	2.33497i	−0.0466248	−	0.0807566i
$837$	7.24297	−	29.9139i	0.250354	−	1.03398i
$838$	−17.4972	−	10.1020i	−0.604431	−	0.348968i
$839$	6.97311	+	12.0778i	0.240739	+	0.416971i	0.960925	−	0.276809i	$-0.0892770\pi$
$839$	6.97311	+	12.0778i	0.240739	+	0.416971i	−0.720186	+	0.693781i	$0.755944\pi$
$840$	−15.6976	−	27.1894i	−0.541618	−	0.938123i
$841$	2.72905	−	4.72686i	0.0941053	−	0.162995i
$842$	−27.4542	+	15.8507i	−0.946133	+	0.546250i
$843$	−16.3298	+	7.77599i	−0.562429	+	0.267819i
$844$	5.46228	−	9.46094i	0.188019	−	0.325659i
$845$	−21.1812	+	1.89833i	−0.728655	+	0.0653046i
$846$	29.5466	+	4.71882i	1.01583	+	0.162236i
$847$	−26.9631	−	0.275184i	−0.926463	−	0.00945542i
$848$	7.64510	−	4.41390i	0.262534	−	0.151574i
$849$	−2.14391	−	0.170122i	−0.0735789	−	0.00583856i
$850$	10.2345	−	28.4942i	0.351042	−	0.977342i
$851$	45.6763			1.56576
$852$	0.927668	−	11.6907i	0.0317814	−	0.400516i
$853$	−13.5450	+	7.82023i	−0.463773	+	0.267760i	−0.713629	−	0.700523i	$-0.752950\pi$
$853$	−13.5450	+	7.82023i	−0.463773	+	0.267760i	0.249856	+	0.968283i	$0.419617\pi$
$854$	−6.89564	−	4.07559i	−0.235964	−	0.139464i
$855$	10.8090	+	22.1152i	0.369659	+	0.756324i
$856$	21.7322	−	37.6412i	0.742790	−	1.28655i
$857$	−7.63203	−	4.40635i	−0.260705	−	0.150518i	0.363951	−	0.931418i	$-0.381428\pi$
$857$	−7.63203	−	4.40635i	−0.260705	−	0.150518i	−0.624656	+	0.780900i	$0.714761\pi$
$858$	−7.25490	+	3.45467i	−0.247678	+	0.117940i
$859$	16.3647	+	28.3445i	0.558356	+	0.967101i	0.997634	+	0.0687500i	$0.0219011\pi$
$859$	16.3647	+	28.3445i	0.558356	+	0.967101i	−0.439278	+	0.898351i	$0.644766\pi$
$860$	0.846259	+	9.44239i	0.0288572	+	0.321983i
$861$	−14.2166	+	6.59256i	−0.484499	+	0.224674i
$862$	−2.44061	+	1.40909i	−0.0831276	+	0.0479937i
$863$	41.7889	+	24.1268i	1.42251	+	0.821287i	0.996513	−	0.0834379i	$-0.0265900\pi$
$863$	41.7889	+	24.1268i	1.42251	+	0.821287i	0.425997	+	0.904725i	$0.359923\pi$
$864$	−21.6223	−	5.23535i	−0.735606	−	0.178110i
$865$	−35.7124	−	16.5610i	−1.21426	−	0.563090i
$866$	33.4715			1.13741
$867$	19.9759	+	13.7481i	0.678418	+	0.466908i
$868$	−6.51648	+	11.0255i	−0.221184	+	0.374229i
$869$	−1.41465	+	2.45024i	−0.0479887	+	0.0831188i
$870$	−20.4359	+	0.208443i	−0.692842	+	0.00706689i
$871$	0.467806	−	0.810264i	0.0158510	−	0.0274547i
$872$	−47.0312	+	27.1535i	−1.59268	+	0.919532i
$873$	44.7088	−	17.0959i	1.51316	−	0.578609i
$874$	19.9440			0.674616
$875$	−7.76595	+	28.5428i	−0.262537	+	0.964922i
$876$	4.65188	+	9.76909i	0.157173	+	0.330067i
$877$	−40.0692	+	23.1340i	−1.35304	+	0.781179i	−0.988674	−	0.150077i	$-0.952048\pi$
$877$	−40.0692	+	23.1340i	−1.35304	+	0.781179i	−0.364367	+	0.931255i	$0.618715\pi$
$878$			36.8533i			1.24374i
$879$	3.40858	−	4.95267i	0.114969	−	0.167049i
$880$	1.96358	+	2.79168i	0.0661923	+	0.0941075i
$881$	2.96913			0.100032			0.0500162	−	0.998748i	$-0.484073\pi$
$881$	2.96913			0.100032			0.0500162	+	0.998748i	$0.484073\pi$
$882$	21.4943	−	7.72002i	0.723749	−	0.259946i
$883$		−	1.66096i		−	0.0558956i	−0.999609	−	0.0279478i	$-0.991103\pi$
$883$		−	1.66096i		−	0.0558956i	0.999609	−	0.0279478i	$-0.00889722\pi$
$884$	−21.5884			−0.726097
$885$	−4.06957	−	2.29454i	−0.136797	−	0.0771303i
$886$	−30.1181			−1.01184
$887$	15.6505	−	9.03581i	0.525492	−	0.303393i	−0.213687	−	0.976902i	$-0.568547\pi$
$887$	15.6505	−	9.03581i	0.525492	−	0.303393i	0.739179	+	0.673509i	$0.235214\pi$
$888$	39.9542	+	27.4978i	1.34078	+	0.922764i
$889$	26.1772	+	15.4718i	0.877956	+	0.518906i
$890$	2.87801	−	2.02431i	0.0964713	−	0.0678549i
$891$	−6.02739	+	5.39898i	−0.201925	+	0.180873i
$892$	−17.4412	+	10.0697i	−0.583975	+	0.337158i
$893$	29.1431	+	16.8258i	0.975238	+	0.563054i
$894$	13.3613	+	28.0591i	0.446869	+	0.938438i
$895$	−6.93007	+	0.621097i	−0.231647	+	0.0207610i
$896$	−0.441176	−	0.260752i	−0.0147386	−	0.00871111i
$897$	−3.24866	+	40.9404i	−0.108470	+	1.36696i
$898$		−	29.0700i		−	0.970080i
$899$	14.3699	+	24.8894i	0.479263	+	0.830107i
$900$	6.34449	+	10.4889i	0.211483	+	0.349630i
$901$	14.4761	−	25.0734i	0.482269	−	0.835315i
$902$	2.89579	−	1.67189i	0.0964194	−	0.0556678i
$903$	−23.6790	−	2.12233i	−0.787986	−	0.0706268i
$904$	16.3926	−	28.3929i	0.545211	−	0.944333i
$905$	−20.3287	+	43.8373i	−0.675750	+	1.45720i
$906$	8.55515	−	12.4306i	0.284226	−	0.412980i
$907$	−8.97440	−	5.18137i	−0.297990	−	0.172045i	0.343550	−	0.939135i	$-0.388371\pi$
$907$	−8.97440	−	5.18137i	−0.297990	−	0.172045i	−0.641540	+	0.767090i	$0.721704\pi$
$908$	−9.64601	−	5.56913i	−0.320114	−	0.184818i
$909$	16.3229	−	20.1040i	0.541397	−	0.666808i
$910$	−30.4308	+	2.41453i	−1.00877	+	0.0800409i
$911$	−1.97637	−	3.42317i	−0.0654800	−	0.113415i	0.831427	−	0.555634i	$-0.187525\pi$
$911$	−1.97637	−	3.42317i	−0.0654800	−	0.113415i	−0.896907	+	0.442220i	$0.854191\pi$
$912$	8.88826	+	6.11718i	0.294320	+	0.202560i
$913$			10.3488i			0.342494i
$914$	−30.0333			−0.993413
$915$	9.39155	+	5.29524i	0.310475	+	0.175055i
$916$	−0.871618	−	1.50969i	−0.0287991	−	0.0498814i
$917$	−11.1982	−	0.114288i	−0.369797	−	0.00377413i
$918$	30.1857	−	8.87790i	0.996278	−	0.293014i
$919$	−29.5683	+	51.2138i	−0.975368	+	1.68939i	−0.296655	+	0.954985i	$0.595871\pi$
$919$	−29.5683	+	51.2138i	−0.975368	+	1.68939i	−0.678714	+	0.734403i	$0.737462\pi$
$920$	34.1022	−	3.05636i	1.12432	−	0.100765i
$921$	8.78846	+	0.697373i	0.289590	+	0.0229792i
$922$	−14.7836	+	8.53530i	−0.486871	+	0.281095i
$923$	−34.0425	−	19.6545i	−1.12052	−	0.646934i
$924$	3.05467	−	1.41653i	0.100491	−	0.0466003i
$925$	−8.12598	−	44.9699i	−0.267181	−	1.47860i
$926$	−20.3232	+	35.2008i	−0.667862	+	1.15677i
$927$	6.94047	−	2.65392i	0.227955	−	0.0871663i
$928$	17.9905	−	10.3868i	0.590567	−	0.340964i
$929$	−53.7469			−1.76338			−0.881689	−	0.471831i	$-0.843593\pi$
$929$	−53.7469			−1.76338			−0.881689	+	0.471831i	$0.843593\pi$
$930$	−12.2536	+	21.7329i	−0.401813	+	0.712648i
$931$	25.6807	+	0.524246i	0.841653	+	0.0171815i
$932$	17.0690	+	9.85477i	0.559112	+	0.322804i
$933$	−1.98376	+	24.9999i	−0.0649455	+	0.818459i
$934$	−3.43895	+	5.95644i	−0.112526	+	0.194901i
$935$	10.1550	+	4.70919i	0.332104	+	0.154007i
$936$	−27.4884	+	33.8559i	−0.898486	+	1.10661i
$937$		−	25.3844i		−	0.829274i	−0.909987	−	0.414637i	$-0.863909\pi$
$937$		−	25.3844i		−	0.829274i	0.909987	−	0.414637i	$-0.136091\pi$
$938$	0.288709	−	0.488477i	0.00942668	−	0.0159493i
$939$	−20.0855	−	1.59381i	−0.655466	−	0.0520119i
$940$	15.2033	+	7.05025i	0.495877	+	0.229954i
$941$	25.8044			0.841200			0.420600	−	0.907246i	$-0.361820\pi$
$941$	25.8044			0.841200			0.420600	+	0.907246i	$0.361820\pi$
$942$	−0.465036	+	5.86049i	−0.0151517	+	0.190945i
$943$		−	17.0900i		−	0.556528i
$944$	−2.04786			−0.0666521
$945$	−28.7133	+	10.9793i	−0.934044	+	0.357157i
$946$	5.07279			0.164931
$947$		−	23.2482i		−	0.755463i	−0.925915	−	0.377732i	$-0.876704\pi$
$947$		−	23.2482i		−	0.755463i	0.925915	−	0.377732i	$-0.123296\pi$
$948$	−0.352343	+	4.44031i	−0.0114436	+	0.144215i
$949$	36.2677			1.17730
$950$	−3.54811	−	19.6356i	−0.115116	−	0.637062i
$951$	32.3257	+	2.56508i	1.04823	+	0.0831783i
$952$	−45.1319	−	0.460613i	−1.46273	−	0.0149286i
$953$		−	14.0065i		−	0.453715i	−0.973928	−	0.226858i	$-0.927155\pi$
$953$		−	14.0065i		−	0.453715i	0.973928	−	0.226858i	$-0.0728452\pi$
$954$	−6.05947	−	15.8466i	−0.196183	−	0.513052i
$955$	5.22790	−	11.2736i	0.169171	−	0.364804i
$956$	6.58780	−	11.4104i	0.213065	−	0.369039i
$957$	0.597692	−	7.53225i	0.0193206	−	0.243483i
$958$	−7.83845	−	4.52553i	−0.253249	−	0.146213i
$959$	20.1483	−	11.3601i	0.650623	−	0.366836i
$960$	27.1637	+	15.3157i	0.876706	+	0.494313i
$961$	4.08533			0.131785
$962$	40.8415	−	23.5799i	1.31678	−	0.760246i
$963$	−33.0392	−	26.8253i	−1.06467	−	0.864434i
$964$	−1.86385	+	3.22828i	−0.0600305	+	0.103976i
$965$	−16.2709	−	7.54531i	−0.523778	−	0.242892i
$966$	−2.22349	+	24.8076i	−0.0715397	+	0.798171i
$967$	1.23131	+	0.710899i	0.0395964	+	0.0228610i	0.519668	−	0.854369i	$-0.326056\pi$
$967$	1.23131	+	0.710899i	0.0395964	+	0.0228610i	−0.480071	+	0.877230i	$0.659389\pi$
$968$	27.0425	−	15.6130i	0.869178	−	0.501820i
$969$	35.2763	+	2.79921i	1.13324	+	0.0899235i
$970$	−38.6459	+	3.46357i	−1.24084	+	0.111209i
$971$	−7.59134	+	13.1486i	−0.243618	+	0.421958i	−0.961742	−	0.273957i	$-0.911668\pi$
$971$	−7.59134	+	13.1486i	−0.243618	+	0.421958i	0.718124	+	0.695915i	$0.245001\pi$
$972$	−4.91308	+	11.7538i	−0.157587	+	0.377004i
$973$	8.40697	+	14.9107i	0.269515	+	0.478015i
$974$	−15.6461	−	27.0999i	−0.501334	−	0.868336i
$975$	40.8852	−	4.08503i	1.30937	−	0.130826i
$976$	4.72595			0.151274
$977$			27.2304i			0.871178i	0.900146	+	0.435589i	$0.143460\pi$
$977$			27.2304i			0.871178i	−0.900146	+	0.435589i	$0.856540\pi$
$978$	−29.6090	−	20.3778i	−0.946791	−	0.651612i
$979$	0.650452	+	1.12662i	0.0207885	+	0.0360068i
$980$	12.7612	−	0.881586i	0.407643	−	0.0281612i
$981$	18.9920	+	49.6673i	0.606367	+	1.58575i
$982$	2.17348	+	1.25486i	0.0693587	+	0.0400442i
$983$	−5.26985	−	3.04255i	−0.168082	−	0.0970423i	0.413599	−	0.910459i	$-0.364272\pi$
$983$	−5.26985	−	3.04255i	−0.168082	−	0.0970423i	−0.581681	+	0.813417i	$0.697605\pi$
$984$	10.2884	−	14.9491i	0.327983	−	0.476559i
$985$	−2.86309	−	1.32770i	−0.0912256	−	0.0423042i
$986$	−14.6901	+	25.4441i	−0.467829	+	0.810304i
$987$	−24.1780	+	34.3742i	−0.769595	+	1.09414i
$988$	−12.3216	+	7.11388i	−0.392002	+	0.226323i
$989$	12.9635	−	22.4535i	0.412216	−	0.713978i
$990$	5.89315	−	2.88032i	0.187297	−	0.0915427i
$991$	10.7998	+	18.7057i	0.343066	+	0.594207i	0.985000	−	0.172552i	$-0.0552013\pi$
$991$	10.7998	+	18.7057i	0.343066	+	0.594207i	−0.641935	+	0.766759i	$0.721868\pi$
$992$		−	25.3603i		−	0.805190i
$993$	−2.15386	+	27.1434i	−0.0683507	+	0.861371i
$994$	−20.5229	−	12.1298i	−0.650948	−	0.384735i
$995$	54.7199	−	4.90418i	1.73474	−	0.155473i
$996$	7.00459	+	14.7099i	0.221949	+	0.466099i
$997$	49.9166	+	28.8194i	1.58087	+	0.912718i	0.994732	+	0.102511i	$0.0326876\pi$
$997$	49.9166	+	28.8194i	1.58087	+	0.912718i	0.586143	+	0.810208i	$0.300646\pi$
$998$	10.2497	−	5.91765i	0.324448	−	0.187320i
$999$	32.7572	−	34.3853i	1.03639	−	1.08790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.14	✓	84
3.2	odd	2		945.2.r.b.604.29		84
5.4	even	2	inner	315.2.r.b.184.29	yes	84
7.4	even	3		315.2.bo.b.4.29	yes	84
9.2	odd	6		945.2.bo.b.289.29		84
9.7	even	3		315.2.bo.b.79.14	yes	84
15.14	odd	2		945.2.r.b.604.14		84
21.11	odd	6		945.2.bo.b.739.14		84
35.4	even	6		315.2.bo.b.4.14	yes	84
45.29	odd	6		945.2.bo.b.289.14		84
45.34	even	6		315.2.bo.b.79.29	yes	84
63.11	odd	6		945.2.r.b.424.29		84
63.25	even	3	inner	315.2.r.b.214.14	yes	84
105.74	odd	6		945.2.bo.b.739.29		84
315.74	odd	6		945.2.r.b.424.14		84
315.214	even	6	inner	315.2.r.b.214.29	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.14	✓	84	1.1	even	1	trivial
315.2.r.b.184.29	yes	84	5.4	even	2	inner
315.2.r.b.214.14	yes	84	63.25	even	3	inner
315.2.r.b.214.29	yes	84	315.214	even	6	inner
315.2.bo.b.4.14	yes	84	35.4	even	6
315.2.bo.b.4.29	yes	84	7.4	even	3
315.2.bo.b.79.14	yes	84	9.7	even	3
315.2.bo.b.79.29	yes	84	45.34	even	6
945.2.r.b.424.14		84	315.74	odd	6
945.2.r.b.424.29		84	63.11	odd	6
945.2.r.b.604.14		84	15.14	odd	2
945.2.r.b.604.29		84	3.2	odd	2
945.2.bo.b.289.14		84	45.29	odd	6
945.2.bo.b.289.29		84	9.2	odd	6
945.2.bo.b.739.14		84	21.11	odd	6
945.2.bo.b.739.29		84	105.74	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.08755i q^{2} +(-0.137009 + 1.72662i) q^{3} +0.817229 q^{4} +(-0.940709 + 2.02856i) q^{5} +(1.87779 + 0.149005i) q^{6} +(-1.34619 + 2.27767i) q^{7} -3.06389i q^{8} +(-2.96246 - 0.473127i) q^{9} +O(q^{10})\)	\(q-1.08755i q^{2} +(-0.137009 + 1.72662i) q^{3} +0.817229 q^{4} +(-0.940709 + 2.02856i) q^{5} +(1.87779 + 0.149005i) q^{6} +(-1.34619 + 2.27767i) q^{7} -3.06389i q^{8} +(-2.96246 - 0.473127i) q^{9} +(2.20617 + 1.02307i) q^{10} +(-0.449548 + 0.778641i) q^{11} +(-0.111968 + 1.41105i) q^{12} +(4.10888 + 2.37226i) q^{13} +(2.47708 + 1.46405i) q^{14} +(-3.37368 - 1.90218i) q^{15} -1.69768 q^{16} +(-4.82187 + 2.78391i) q^{17} +(-0.514551 + 3.22183i) q^{18} +(-1.83472 + 3.17783i) q^{19} +(-0.768775 + 1.65780i) q^{20} +(-3.74823 - 2.63643i) q^{21} +(0.846813 + 0.488908i) q^{22} +(4.32806 - 2.49880i) q^{23} +(5.29018 + 0.419781i) q^{24} +(-3.23013 - 3.81657i) q^{25} +(2.57996 - 4.46862i) q^{26} +(1.22280 - 5.05022i) q^{27} +(-1.10015 + 1.86138i) q^{28} +(2.42600 + 4.20195i) q^{29} +(-2.06872 + 3.66905i) q^{30} +5.92329 q^{31} -4.28146i q^{32} +(-1.28283 - 0.882882i) q^{33} +(3.02765 + 5.24404i) q^{34} +(-3.35402 - 4.87345i) q^{35} +(-2.42101 - 0.386653i) q^{36} +(7.91515 + 4.56982i) q^{37} +(3.45606 + 1.99536i) q^{38} +(-4.65896 + 6.76946i) q^{39} +(6.21528 + 2.88222i) q^{40} +(1.70982 - 2.96149i) q^{41} +(-2.86725 + 4.07640i) q^{42} +(4.49284 - 2.59394i) q^{43} +(-0.367384 + 0.636328i) q^{44} +(3.74658 - 5.56446i) q^{45} +(-2.71758 - 4.70699i) q^{46} -9.17076i q^{47} +(0.232598 - 2.93125i) q^{48} +(-3.37554 - 6.13235i) q^{49} +(-4.15072 + 3.51294i) q^{50} +(-4.14612 - 8.70697i) q^{51} +(3.35789 + 1.93868i) q^{52} +(-4.50327 + 2.59996i) q^{53} +(-5.49239 - 1.32986i) q^{54} +(-1.15663 - 1.64441i) q^{55} +(6.97851 + 4.12457i) q^{56} +(-5.23554 - 3.60327i) q^{57} +(4.56985 - 2.63840i) q^{58} +1.20627 q^{59} +(-2.75707 - 1.55452i) q^{60} -2.78377 q^{61} -6.44189i q^{62} +(5.06566 - 6.11057i) q^{63} -8.05166 q^{64} +(-8.67753 + 6.10351i) q^{65} +(-0.960180 + 1.39514i) q^{66} -0.197198i q^{67} +(-3.94057 + 2.27509i) q^{68} +(3.72151 + 7.81528i) q^{69} +(-5.30014 + 3.64767i) q^{70} -8.28511 q^{71} +(-1.44961 + 9.07663i) q^{72} +(6.62001 - 3.82206i) q^{73} +(4.96992 - 8.60815i) q^{74} +(7.03234 - 5.05432i) q^{75} +(-1.49939 + 2.59702i) q^{76} +(-1.16831 - 2.07212i) q^{77} +(7.36214 + 5.06686i) q^{78} +3.14682 q^{79} +(1.59702 - 3.44385i) q^{80} +(8.55230 + 2.80324i) q^{81} +(-3.22078 - 1.85952i) q^{82} +(9.96810 - 5.75509i) q^{83} +(-3.06317 - 2.15456i) q^{84} +(-1.11136 - 12.4003i) q^{85} +(-2.82105 - 4.88620i) q^{86} +(-7.58758 + 3.61308i) q^{87} +(2.38567 + 1.37736i) q^{88} +(0.723450 - 1.25305i) q^{89} +(-6.05164 - 4.07460i) q^{90} +(-10.9346 + 6.16514i) q^{91} +(3.53701 - 2.04210i) q^{92} +(-0.811546 + 10.2273i) q^{93} -9.97369 q^{94} +(-4.72049 - 6.71126i) q^{95} +(7.39246 + 0.586599i) q^{96} +(-13.8177 + 7.97765i) q^{97} +(-6.66925 + 3.67108i) q^{98} +(1.70016 - 2.09400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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