LMFDB - Embedded newform 465.2.bg.c.76.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(76,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 22]))

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

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

chi := DirichletCharacter("465.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			76.6
Character	$\chi$	$=$	465.76
Dual form			465.2.bg.c.361.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.863191 - 2.65663i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-4.69455 - 3.41079i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.39667 - 2.41911i) q^{6} +(0.217892 - 2.07310i) q^{7} +(-8.59378 + 6.24374i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.863191 - 2.65663i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-4.69455 - 3.41079i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.39667 - 2.41911i) q^{6} +(0.217892 - 2.07310i) q^{7} +(-8.59378 + 6.24374i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.86911 - 2.07586i) q^{10} +(-0.221024 + 0.0984060i) q^{11} +(-5.67598 + 1.20647i) q^{12} +(5.89916 + 1.25391i) q^{13} +(-5.31938 - 2.36834i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(5.58293 + 17.1825i) q^{16} +(3.73506 + 1.66296i) q^{17} +(-2.73230 - 0.580769i) q^{18} +(-5.99568 + 1.27442i) q^{19} +(-5.30111 + 2.36020i) q^{20} +(-1.39482 - 1.54910i) q^{21} +(0.0706428 + 0.672121i) q^{22} +(3.35565 - 2.43802i) q^{23} +(-1.11035 + 10.5643i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(8.42327 - 14.5895i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-8.09382 + 8.98910i) q^{28} +(0.0933165 - 0.287199i) q^{29} -2.79335 q^{30} +(-5.34927 + 1.54444i) q^{31} +29.2216 q^{32} +(-0.0747637 + 0.230099i) q^{33} +(7.64193 - 8.48722i) q^{34} +(-1.68641 - 1.22525i) q^{35} +(-2.90139 + 5.02536i) q^{36} +(-1.81399 - 3.14192i) q^{37} +(-1.78975 + 17.0284i) q^{38} +(4.87914 - 3.54490i) q^{39} +(1.11035 + 10.5643i) q^{40} +(1.00273 + 1.11364i) q^{41} +(-5.31938 + 2.36834i) q^{42} +(-4.65960 + 0.990430i) q^{43} +(1.37325 + 0.291893i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(-3.58035 - 11.0192i) q^{46} +(0.282199 + 0.868520i) q^{47} +(16.5048 + 7.34840i) q^{48} +(2.59676 + 0.551958i) q^{49} +(-2.73230 + 0.580769i) q^{50} +(3.73506 - 1.66296i) q^{51} +(-23.4171 - 26.0073i) q^{52} +(-0.974765 - 9.27427i) q^{53} +(-2.25986 + 1.64189i) q^{54} +(-0.0252897 + 0.240615i) q^{55} +(11.0714 + 19.1762i) q^{56} +(-3.06481 + 5.30841i) q^{57} +(-0.682431 - 0.495815i) q^{58} +(6.93049 - 7.69709i) q^{59} +(-1.79316 + 5.51877i) q^{60} +12.0137 q^{61} +(-0.514438 + 15.5442i) q^{62} -2.08452 q^{63} +(14.0580 - 43.2661i) q^{64} +(4.03549 - 4.48187i) q^{65} +(0.546753 + 0.397239i) q^{66} +(-4.18241 + 7.24414i) q^{67} +(-11.8624 - 20.5463i) q^{68} +(0.433564 - 4.12509i) q^{69} +(-4.71074 + 3.42255i) q^{70} +(-0.425363 - 4.04706i) q^{71} +(7.10783 + 7.89405i) q^{72} +(-5.94760 + 2.64804i) q^{73} +(-9.91273 + 2.10702i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(32.4938 + 14.4672i) q^{76} +(0.155847 + 0.479646i) q^{77} +(-5.20587 - 16.0220i) q^{78} +(-0.456107 - 0.203072i) q^{79} +(17.6719 + 3.75628i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(3.82407 - 1.70259i) q^{82} +(7.58303 + 8.42180i) q^{83} +(1.26438 + 12.0298i) q^{84} +(3.30769 - 2.40318i) q^{85} +(-1.39093 + 13.2338i) q^{86} +(-0.150989 - 0.261521i) q^{87} +(1.28500 - 2.22569i) q^{88} +(11.0539 + 8.03113i) q^{89} +(-1.86911 + 2.07586i) q^{90} +(3.88485 - 11.9564i) q^{91} -24.0688 q^{92} +(-2.43162 + 5.00872i) q^{93} +2.55093 q^{94} +(-1.89416 + 5.82962i) q^{95} +(19.5531 - 21.7159i) q^{96} +(-13.7142 - 9.96396i) q^{97} +(3.70784 - 6.42218i) q^{98} +(0.120970 + 0.209527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{2} + 6 q^{3} - 10 q^{4} + 24 q^{5} - 4 q^{6} - 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 48 * q - 2 * q^2 + 6 * q^3 - 10 * q^4 + 24 * q^5 - 4 * q^6 - 5 * q^7 - 6 * q^8 + 6 * q^9	\( 48 q - 2 q^{2} + 6 q^{3} - 10 q^{4} + 24 q^{5} - 4 q^{6} - 5 q^{7} - 6 q^{8} + 6 q^{9} - q^{10} + 17 q^{11} - 5 q^{12} + 7 q^{13} - 9 q^{14} + 12 q^{15} - 26 q^{16} + 24 q^{17} + q^{18} - 2 q^{19} - 5 q^{20} + 10 q^{21} + q^{22} - 6 q^{23} + 3 q^{24} - 24 q^{25} - 15 q^{26} - 12 q^{27} + 95 q^{28} - 32 q^{29} - 8 q^{30} - 13 q^{31} + 56 q^{32} - 14 q^{33} - 66 q^{34} - 10 q^{35} - 30 q^{36} + 14 q^{37} - 4 q^{38} + 21 q^{39} - 3 q^{40} - 20 q^{41} - 9 q^{42} - 28 q^{43} + 74 q^{44} - 6 q^{45} - 53 q^{46} - 45 q^{47} + 53 q^{48} + 61 q^{49} + q^{50} + 24 q^{51} - 78 q^{52} + 7 q^{53} - 2 q^{54} + 13 q^{55} - 11 q^{56} - 7 q^{57} - 73 q^{58} + 56 q^{59} + 20 q^{60} + 26 q^{61} + 26 q^{62} + 20 q^{63} - 80 q^{64} - 7 q^{65} + 13 q^{66} - 46 q^{67} - 66 q^{68} + 3 q^{69} - 48 q^{70} + 72 q^{71} + 3 q^{72} + 23 q^{73} - 64 q^{74} + 6 q^{75} - 74 q^{76} - 60 q^{77} - 20 q^{78} + 34 q^{79} + 17 q^{80} + 6 q^{81} + 108 q^{82} - 25 q^{83} + 15 q^{84} + 18 q^{85} + 130 q^{86} - 4 q^{87} - 25 q^{88} - 18 q^{89} - q^{90} + 33 q^{91} + 52 q^{92} - 22 q^{93} - 72 q^{94} + 11 q^{95} + 32 q^{96} - 79 q^{97} - 37 q^{98} - 18 q^{99}+O(q^{100}) \) 48 * q - 2 * q^2 + 6 * q^3 - 10 * q^4 + 24 * q^5 - 4 * q^6 - 5 * q^7 - 6 * q^8 + 6 * q^9 - q^10 + 17 * q^11 - 5 * q^12 + 7 * q^13 - 9 * q^14 + 12 * q^15 - 26 * q^16 + 24 * q^17 + q^18 - 2 * q^19 - 5 * q^20 + 10 * q^21 + q^22 - 6 * q^23 + 3 * q^24 - 24 * q^25 - 15 * q^26 - 12 * q^27 + 95 * q^28 - 32 * q^29 - 8 * q^30 - 13 * q^31 + 56 * q^32 - 14 * q^33 - 66 * q^34 - 10 * q^35 - 30 * q^36 + 14 * q^37 - 4 * q^38 + 21 * q^39 - 3 * q^40 - 20 * q^41 - 9 * q^42 - 28 * q^43 + 74 * q^44 - 6 * q^45 - 53 * q^46 - 45 * q^47 + 53 * q^48 + 61 * q^49 + q^50 + 24 * q^51 - 78 * q^52 + 7 * q^53 - 2 * q^54 + 13 * q^55 - 11 * q^56 - 7 * q^57 - 73 * q^58 + 56 * q^59 + 20 * q^60 + 26 * q^61 + 26 * q^62 + 20 * q^63 - 80 * q^64 - 7 * q^65 + 13 * q^66 - 46 * q^67 - 66 * q^68 + 3 * q^69 - 48 * q^70 + 72 * q^71 + 3 * q^72 + 23 * q^73 - 64 * q^74 + 6 * q^75 - 74 * q^76 - 60 * q^77 - 20 * q^78 + 34 * q^79 + 17 * q^80 + 6 * q^81 + 108 * q^82 - 25 * q^83 + 15 * q^84 + 18 * q^85 + 130 * q^86 - 4 * q^87 - 25 * q^88 - 18 * q^89 - q^90 + 33 * q^91 + 52 * q^92 - 22 * q^93 - 72 * q^94 + 11 * q^95 + 32 * q^96 - 79 * q^97 - 37 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.863191	−	2.65663i	0.610369	−	1.87852i	0.155859	−	0.987779i	$-0.450185\pi$
$2$	0.863191	−	2.65663i	0.610369	−	1.87852i	0.454509	−	0.890742i	$-0.349815\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−4.69455	−	3.41079i	−2.34728	−	1.70540i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.39667	−	2.41911i	−0.570189	−	0.987597i
$7$	0.217892	−	2.07310i	0.0823554	−	0.783559i	−0.872924	−	0.487856i	$-0.837779\pi$
$7$	0.217892	−	2.07310i	0.0823554	−	0.783559i	0.955280	−	0.295704i	$-0.0955541\pi$
$8$	−8.59378	+	6.24374i	−3.03836	+	2.20750i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−1.86911	−	2.07586i	−0.591066	−	0.656445i
$11$	−0.221024	+	0.0984060i	−0.0666411	+	0.0296705i	−0.439787	−	0.898102i	$-0.644946\pi$
$11$	−0.221024	+	0.0984060i	−0.0666411	+	0.0296705i	0.373145	+	0.927773i	$0.378279\pi$
$12$	−5.67598	+	1.20647i	−1.63851	+	0.348277i
$13$	5.89916	+	1.25391i	1.63613	+	0.347771i	0.932045	−	0.362342i	$-0.118023\pi$
$13$	5.89916	+	1.25391i	1.63613	+	0.347771i	0.704088	+	0.710113i	$0.251356\pi$
$14$	−5.31938	−	2.36834i	−1.42167	−	0.632966i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	5.58293	+	17.1825i	1.39573	+	4.29562i
$17$	3.73506	+	1.66296i	0.905885	+	0.403326i	0.806166	−	0.591690i	$-0.201539\pi$
$17$	3.73506	+	1.66296i	0.905885	+	0.403326i	0.0997190	+	0.995016i	$0.468206\pi$
$18$	−2.73230	−	0.580769i	−0.644010	−	0.136889i
$19$	−5.99568	+	1.27442i	−1.37550	+	0.292372i	−0.835593	−	0.549350i	$-0.814875\pi$
$19$	−5.99568	+	1.27442i	−1.37550	+	0.292372i	−0.539911	+	0.841722i	$0.681542\pi$
$20$	−5.30111	+	2.36020i	−1.18536	+	0.527758i
$21$	−1.39482	−	1.54910i	−0.304374	−	0.338042i
$22$	0.0706428	+	0.672121i	0.0150611	+	0.143297i
$23$	3.35565	−	2.43802i	0.699701	−	0.508363i	−0.180134	−	0.983642i	$-0.557653\pi$
$23$	3.35565	−	2.43802i	0.699701	−	0.508363i	0.879835	+	0.475280i	$0.157653\pi$
$24$	−1.11035	+	10.5643i	−0.226650	+	2.15643i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	8.42327	−	14.5895i	1.65194	−	2.86124i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−8.09382	+	8.98910i	−1.52959	+	1.69878i
$29$	0.0933165	−	0.287199i	0.0173284	−	0.0533315i	−0.942018	−	0.335561i	$-0.891074\pi$
$29$	0.0933165	−	0.287199i	0.0173284	−	0.0533315i	0.959347	+	0.282230i	$0.0910741\pi$
$30$	−2.79335			−0.509993
$31$	−5.34927	+	1.54444i	−0.960757	+	0.277390i
$31$	−5.34927	+	1.54444i	−0.960757	+	0.277390i
$32$	29.2216			5.16571
$33$	−0.0747637	+	0.230099i	−0.0130147	+	0.0400551i
$34$	7.64193	−	8.48722i	1.31058	−	1.45555i
$35$	−1.68641	−	1.22525i	−0.285056	−	0.207105i
$36$	−2.90139	+	5.02536i	−0.483565	+	0.837560i
$37$	−1.81399	−	3.14192i	−0.298218	−	0.516528i	0.677511	−	0.735513i	$-0.263059\pi$
$37$	−1.81399	−	3.14192i	−0.298218	−	0.516528i	−0.975728	+	0.218985i	$0.929725\pi$
$38$	−1.78975	+	17.0284i	−0.290337	+	2.76237i
$39$	4.87914	−	3.54490i	0.781288	−	0.567639i
$40$	1.11035	+	10.5643i	0.175562	+	1.67036i
$41$	1.00273	+	1.11364i	0.156599	+	0.173921i	0.816339	−	0.577573i	$-0.196000\pi$
$41$	1.00273	+	1.11364i	0.156599	+	0.173921i	−0.659740	+	0.751494i	$0.729333\pi$
$42$	−5.31938	+	2.36834i	−0.820799	+	0.365443i
$43$	−4.65960	+	0.990430i	−0.710583	+	0.151039i	−0.549003	−	0.835820i	$-0.684992\pi$
$43$	−4.65960	+	0.990430i	−0.710583	+	0.151039i	−0.161580	+	0.986860i	$0.551659\pi$
$44$	1.37325	+	0.291893i	0.207025	+	0.0440045i
$45$	−0.913545	−	0.406737i	−0.136183	−	0.0606327i
$46$	−3.58035	−	11.0192i	−0.527894	−	1.62469i
$47$	0.282199	+	0.868520i	0.0411630	+	0.126687i	0.969526	−	0.244987i	$-0.0787839\pi$
$47$	0.282199	+	0.868520i	0.0411630	+	0.126687i	−0.928363	+	0.371674i	$0.878784\pi$
$48$	16.5048	+	7.34840i	2.38226	+	1.06065i
$49$	2.59676	+	0.551958i	0.370965	+	0.0788511i
$50$	−2.73230	+	0.580769i	−0.386406	+	0.0821332i
$51$	3.73506	−	1.66296i	0.523013	−	0.232860i
$52$	−23.4171	−	26.0073i	−3.24737	−	3.60657i
$53$	−0.974765	−	9.27427i	−0.133894	−	1.27392i	−0.830725	−	0.556683i	$-0.812074\pi$
$53$	−0.974765	−	9.27427i	−0.133894	−	1.27392i	0.696831	−	0.717236i	$-0.254593\pi$
$54$	−2.25986	+	1.64189i	−0.307529	+	0.223433i
$55$	−0.0252897	+	0.240615i	−0.00341006	+	0.0324445i
$56$	11.0714	+	19.1762i	1.47948	+	2.56253i
$57$	−3.06481	+	5.30841i	−0.405945	+	0.703117i
$58$	−0.682431	−	0.495815i	−0.0896075	−	0.0651037i
$59$	6.93049	−	7.69709i	0.902273	−	1.00208i	−0.0977037	−	0.995216i	$-0.531150\pi$
$59$	6.93049	−	7.69709i	0.902273	−	1.00208i	0.999976	−	0.00685990i	$-0.00218359\pi$
$60$	−1.79316	+	5.51877i	−0.231496	+	0.712471i
$61$	12.0137			1.53819			0.769097	−	0.639132i	$-0.220706\pi$
$61$	12.0137			1.53819			0.769097	+	0.639132i	$0.220706\pi$
$62$	−0.514438	+	15.5442i	−0.0653337	+	1.97411i
$63$	−2.08452			−0.262625
$64$	14.0580	−	43.2661i	1.75725	−	5.40827i
$65$	4.03549	−	4.48187i	0.500541	−	0.555908i
$66$	0.546753	+	0.397239i	0.0673006	+	0.0488967i
$67$	−4.18241	+	7.24414i	−0.510962	+	0.885013i	0.488957	+	0.872308i	$0.337377\pi$
$67$	−4.18241	+	7.24414i	−0.510962	+	0.885013i	−0.999919	+	0.0127047i	$0.995956\pi$
$68$	−11.8624	−	20.5463i	−1.43853	−	2.49161i
$69$	0.433564	−	4.12509i	0.0521950	−	0.496602i
$70$	−4.71074	+	3.42255i	−0.563041	+	0.409073i
$71$	−0.425363	−	4.04706i	−0.0504813	−	0.480298i	−0.990333	−	0.138714i	$-0.955703\pi$
$71$	−0.425363	−	4.04706i	−0.0504813	−	0.480298i	0.939851	−	0.341584i	$-0.110963\pi$
$72$	7.10783	+	7.89405i	0.837666	+	0.930323i
$73$	−5.94760	+	2.64804i	−0.696114	+	0.309930i	−0.724116	−	0.689678i	$-0.757752\pi$
$73$	−5.94760	+	2.64804i	−0.696114	+	0.309930i	0.0280023	+	0.999608i	$0.491085\pi$
$74$	−9.91273	+	2.10702i	−1.15233	+	0.244936i
$75$	−0.978148	−	0.207912i	−0.112947	−	0.0240076i
$76$	32.4938	+	14.4672i	3.72730	+	1.65950i
$77$	0.155847	+	0.479646i	0.0177604	+	0.0546608i
$78$	−5.20587	−	16.0220i	−0.589448	−	1.81414i
$79$	−0.456107	−	0.203072i	−0.0513160	−	0.0228474i	0.380918	−	0.924609i	$-0.375608\pi$
$79$	−0.456107	−	0.203072i	−0.0513160	−	0.0228474i	−0.432234	+	0.901761i	$0.642275\pi$
$80$	17.6719	+	3.75628i	1.97578	+	0.419965i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	3.82407	−	1.70259i	0.422298	−	0.188019i
$83$	7.58303	+	8.42180i	0.832345	+	0.924413i	0.998091	−	0.0617554i	$-0.0196699\pi$
$83$	7.58303	+	8.42180i	0.832345	+	0.924413i	−0.165746	+	0.986168i	$0.553003\pi$
$84$	1.26438	+	12.0298i	0.137955	+	1.31255i
$85$	3.30769	−	2.40318i	0.358769	−	0.260661i
$86$	−1.39093	+	13.2338i	−0.149987	+	1.42703i
$87$	−0.150989	−	0.261521i	−0.0161878	−	0.0280380i
$88$	1.28500	−	2.22569i	0.136982	−	0.237260i
$89$	11.0539	+	8.03113i	1.17171	+	0.851298i	0.991213	−	0.132277i	$-0.0422287\pi$
$89$	11.0539	+	8.03113i	1.17171	+	0.851298i	0.180499	+	0.983575i	$0.442229\pi$
$90$	−1.86911	+	2.07586i	−0.197022	+	0.218815i
$91$	3.88485	−	11.9564i	0.407243	−	1.25337i
$92$	−24.0688			−2.50935
$93$	−2.43162	+	5.00872i	−0.252147	+	0.519380i
$94$	2.55093			0.263108
$95$	−1.89416	+	5.82962i	−0.194337	+	0.598107i
$96$	19.5531	−	21.7159i	1.99563	−	2.21637i
$97$	−13.7142	−	9.96396i	−1.39247	−	1.01169i	−0.995590	−	0.0938149i	$-0.970094\pi$
$97$	−13.7142	−	9.96396i	−1.39247	−	1.01169i	−0.396877	−	0.917872i	$-0.629906\pi$
$98$	3.70784	−	6.42218i	0.374549	−	0.648738i
$99$	0.120970	+	0.209527i	0.0121580	+	0.0210582i
$100$	−0.606556	+	5.77100i	−0.0606556	+	0.577100i
$101$	−5.84514	+	4.24675i	−0.581613	+	0.422567i	−0.839305	−	0.543660i	$-0.817038\pi$
$101$	−5.84514	+	4.24675i	−0.581613	+	0.422567i	0.257692	+	0.966227i	$0.417038\pi$
$102$	−1.19379	−	11.3581i	−0.118202	−	1.12462i
$103$	9.04933	+	10.0503i	0.891657	+	0.990286i	0.999993	−	0.00382850i	$-0.00121865\pi$
$103$	9.04933	+	10.0503i	0.891657	+	0.990286i	−0.108335	+	0.994114i	$0.534552\pi$
$104$	−58.5251	+	26.0571i	−5.73886	+	2.55511i
$105$	−2.03897	+	0.433396i	−0.198983	+	0.0422952i
$106$	−25.4797	−	5.41588i	−2.47481	−	0.526037i
$107$	0.289207	+	0.128763i	0.0279587	+	0.0124480i	0.420668	−	0.907214i	$-0.361796\pi$
$107$	0.289207	+	0.128763i	0.0279587	+	0.0124480i	−0.392710	+	0.919663i	$0.628462\pi$
$108$	1.79316	+	5.51877i	0.172547	+	0.531044i
$109$	−5.08667	−	15.6552i	−0.487215	−	1.49949i	−0.828747	−	0.559624i	$-0.810946\pi$
$109$	−5.08667	−	15.6552i	−0.487215	−	1.49949i	0.341532	−	0.939870i	$-0.389054\pi$
$110$	0.617395	+	0.274882i	0.0588663	+	0.0262090i
$111$	−3.54869	−	0.754298i	−0.336827	−	0.0715948i
$112$	36.8375	−	7.83006i	3.48082	−	0.739871i
$113$	1.36216	−	0.606473i	0.128141	−	0.0570522i	−0.341664	−	0.939822i	$-0.610991\pi$
$113$	1.36216	−	0.606473i	0.128141	−	0.0570522i	0.469806	+	0.882770i	$0.344324\pi$
$114$	11.4570	+	12.7243i	1.07304	+	1.19174i
$115$	−0.433564	−	4.12509i	−0.0404301	−	0.384666i
$116$	−1.41765	+	1.02999i	−0.131626	+	0.0956318i
$117$	0.630406	−	5.99791i	0.0582811	−	0.554507i
$118$	−14.4660	−	25.0558i	−1.33170	−	2.30657i
$119$	4.26132	−	7.38081i	0.390634	−	0.676598i
$120$	8.59378	+	6.24374i	0.784501	+	0.569973i
$121$	−7.32127	+	8.13109i	−0.665570	+	0.739190i
$122$	10.3701	−	31.9159i	0.938865	−	2.88953i
$123$	1.49855			0.135120
$124$	30.3802	+	10.9948i	2.72822	+	0.987361i
$125$	−1.00000			−0.0894427
$126$	−1.79934	+	5.53780i	−0.160298	+	0.493347i
$127$	−10.9613	+	12.1738i	−0.972661	+	1.08025i	0.0240900	+	0.999710i	$0.492331\pi$
$127$	−10.9613	+	12.1738i	−0.972661	+	1.08025i	−0.996751	+	0.0805401i	$0.974335\pi$
$128$	−55.5258	−	40.3418i	−4.90783	−	3.56575i
$129$	−2.38185	+	4.12549i	−0.209710	+	0.363229i
$130$	−8.42327	−	14.5895i	−0.738770	−	1.27959i
$131$	−0.594889	+	5.65999i	−0.0519757	+	0.494515i	0.937307	+	0.348504i	$0.113310\pi$
$131$	−0.594889	+	5.65999i	−0.0519757	+	0.494515i	−0.989283	+	0.146011i	$0.953356\pi$
$132$	1.13580	−	0.825208i	0.0988588	−	0.0718251i
$133$	1.33560	+	12.7073i	0.115811	+	1.10187i
$134$	15.6348	+	17.3642i	1.35064	+	1.50004i
$135$	−0.913545	+	0.406737i	−0.0786255	+	0.0350063i
$136$	−42.4813	+	9.02968i	−3.64274	+	0.774289i
$137$	8.54308	+	1.81589i	0.729885	+	0.155142i	0.557841	−	0.829948i	$-0.311630\pi$
$137$	8.54308	+	1.81589i	0.729885	+	0.155142i	0.172043	+	0.985089i	$0.444963\pi$
$138$	−10.5846	−	4.71256i	−0.901020	−	0.401160i
$139$	2.43903	+	7.50656i	0.206876	+	0.636698i	0.999631	+	0.0271580i	$0.00864572\pi$
$139$	2.43903	+	7.50656i	0.206876	+	0.636698i	−0.792756	+	0.609540i	$0.791354\pi$
$140$	3.73788	+	11.5040i	0.315908	+	0.972266i
$141$	0.834264	+	0.371438i	0.0702577	+	0.0312808i
$142$	−11.1187	−	2.36335i	−0.933061	−	0.198328i
$143$	−1.42725	+	0.303370i	−0.119352	+	0.0253691i
$144$	16.5048	−	7.34840i	1.37540	−	0.612367i
$145$	−0.202063	−	0.224414i	−0.0167804	−	0.0186366i
$146$	1.90095	+	18.0863i	0.157324	+	1.49684i
$147$	2.14775	−	1.56043i	0.177144	−	0.128702i
$148$	−2.20057	+	20.9370i	−0.180886	+	1.72101i
$149$	9.64300	+	16.7022i	0.789986	+	1.36830i	0.925975	+	0.377585i	$0.123245\pi$
$149$	9.64300	+	16.7022i	0.789986	+	1.36830i	−0.135989	+	0.990710i	$0.543421\pi$
$150$	−1.39667	+	2.41911i	−0.114038	+	0.197519i
$151$	−6.02666	−	4.37863i	−0.490443	−	0.356328i	0.314912	−	0.949121i	$-0.398025\pi$
$151$	−6.02666	−	4.37863i	−0.490443	−	0.356328i	−0.805355	+	0.592793i	$0.798025\pi$
$152$	43.5684	−	48.3876i	3.53386	−	3.92475i
$153$	1.26343	−	3.88842i	0.102142	−	0.314360i
$154$	1.40877			0.113522
$155$	−1.33711	+	5.40483i	−0.107399	+	0.434126i
$156$	−34.9963			−2.80195
$157$	−2.09906	+	6.46024i	−0.167523	+	0.515584i	−0.999213	−	0.0396565i	$-0.987374\pi$
$157$	−2.09906	+	6.46024i	−0.167523	+	0.515584i	0.831690	+	0.555240i	$0.187374\pi$
$158$	−0.933194	+	1.03642i	−0.0742410	+	0.0824529i
$159$	−7.54437	−	5.48131i	−0.598307	−	0.434696i
$160$	14.6108	−	25.3067i	1.15509	−	2.00067i
$161$	−4.32310	−	7.48783i	−0.340708	−	0.590124i
$162$	−0.291984	+	2.77804i	−0.0229404	+	0.218264i
$163$	−3.88524	+	2.82279i	−0.304316	+	0.221098i	−0.729454	−	0.684030i	$-0.760226\pi$
$163$	−3.88524	+	2.82279i	−0.304316	+	0.221098i	0.425138	+	0.905129i	$0.360226\pi$
$164$	−0.908955	−	8.64813i	−0.0709774	−	0.675305i
$165$	0.161890	+	0.179797i	0.0126031	+	0.0139972i
$166$	28.9192	−	12.8757i	2.24457	−	0.999346i
$167$	8.03599	−	1.70810i	0.621844	−	0.132177i	0.113794	−	0.993504i	$-0.463700\pi$
$167$	8.03599	−	1.70810i	0.621844	−	0.132177i	0.508050	+	0.861327i	$0.330366\pi$
$168$	21.6589	+	4.60375i	1.67102	+	0.355187i
$169$	21.3517	+	9.50640i	1.64244	+	0.731262i
$170$	−3.52918	−	10.8617i	−0.270676	−	0.833055i
$171$	1.89416	+	5.82962i	0.144850	+	0.445802i
$172$	25.2529	+	11.2433i	1.92552	+	0.857295i
$173$	16.2106	+	3.44567i	1.23247	+	0.261969i	0.777697	−	0.628639i	$-0.216388\pi$
$173$	16.2106	+	3.44567i	1.23247	+	0.261969i	0.454771	+	0.890609i	$0.349721\pi$
$174$	−0.825098	+	0.175380i	−0.0625505	+	0.0132955i
$175$	−1.90431	+	0.847851i	−0.143952	+	0.0640915i
$176$	−2.92482	−	3.24834i	−0.220466	−	0.244853i
$177$	−1.08265	−	10.3007i	−0.0813769	−	0.774249i
$178$	30.8774	−	22.4337i	2.31436	−	1.68148i
$179$	1.28509	−	12.2268i	0.0960520	−	0.913874i	−0.835310	−	0.549779i	$-0.814712\pi$
$179$	1.28509	−	12.2268i	0.0960520	−	0.913874i	0.931362	−	0.364094i	$-0.118621\pi$
$180$	2.90139	+	5.02536i	0.216257	+	0.374568i
$181$	3.35955	−	5.81891i	0.249713	−	0.432516i	−0.713733	−	0.700418i	$-0.752997\pi$
$181$	3.35955	−	5.81891i	0.249713	−	0.432516i	0.963446	+	0.267902i	$0.0863303\pi$
$182$	−28.4102	−	20.6412i	−2.10591	−	1.53003i
$183$	8.03872	−	8.92790i	0.594239	−	0.659970i
$184$	−13.6153	+	41.9036i	−1.00373	+	3.08918i
$185$	−3.62797			−0.266734
$186$	11.2074	+	10.7834i	0.821763	+	0.790677i
$187$	−0.989181			−0.0723361
$188$	1.63754	−	5.03983i	0.119430	−	0.367568i
$189$	−1.39482	+	1.54910i	−0.101458	+	0.112681i
$190$	13.8521	+	10.0642i	1.00494	+	0.730131i
$191$	4.34771	−	7.53045i	0.314589	−	0.544884i	−0.664761	−	0.747056i	$-0.731467\pi$
$191$	4.34771	−	7.53045i	0.314589	−	0.544884i	0.979350	+	0.202172i	$0.0648000\pi$
$192$	−22.7464	−	39.3979i	−1.64158	−	2.84329i
$193$	1.80077	−	17.1332i	0.129622	−	1.23327i	−0.715466	−	0.698648i	$-0.753786\pi$
$193$	1.80077	−	17.1332i	0.129622	−	1.23327i	0.845088	−	0.534627i	$-0.179548\pi$
$194$	−38.3085	+	27.8328i	−2.75039	+	1.99828i
$195$	−0.630406	−	5.99791i	−0.0451443	−	0.429520i
$196$	−10.3080	−	11.4482i	−0.736285	−	0.817727i
$197$	−12.8757	+	5.73262i	−0.917353	+	0.408432i	−0.810430	−	0.585835i	$-0.800767\pi$
$197$	−12.8757	+	5.73262i	−0.917353	+	0.408432i	−0.106923	+	0.994267i	$0.534100\pi$
$198$	0.661055	−	0.140512i	0.0469791	−	0.00998572i
$199$	5.95022	+	1.26476i	0.421800	+	0.0896563i	0.413921	−	0.910313i	$-0.364159\pi$
$199$	5.95022	+	1.26476i	0.421800	+	0.0896563i	0.00787840	+	0.999969i	$0.497492\pi$
$200$	9.70413	+	4.32056i	0.686185	+	0.305509i
$201$	2.58487	+	7.95541i	0.182323	+	0.561131i
$202$	6.23655	+	19.1941i	0.438802	+	1.35049i
$203$	−0.575059	−	0.256033i	−0.0403613	−	0.0179700i
$204$	−23.2064	−	4.93268i	−1.62477	−	0.345356i
$205$	1.46580	−	0.311566i	0.102376	−	0.0217607i
$206$	34.5113	−	15.3654i	2.40451	−	1.07056i
$207$	−2.77543	−	3.08242i	−0.192905	−	0.214243i
$208$	11.3894	+	108.363i	0.789711	+	7.51360i
$209$	1.19978	−	0.871688i	0.0829903	−	0.0602959i
$210$	−0.608647	+	5.79089i	−0.0420007	+	0.399610i
$211$	4.41872	+	7.65346i	0.304198	+	0.526886i	0.977082	−	0.212862i	$-0.0682784\pi$
$211$	4.41872	+	7.65346i	0.304198	+	0.526886i	−0.672885	+	0.739747i	$0.734945\pi$
$212$	−27.0565	+	46.8632i	−1.85825	+	3.21858i
$213$	−3.29217	−	2.39190i	−0.225576	−	0.163891i
$214$	0.591717	−	0.657169i	0.0404490	−	0.0449231i
$215$	−1.47207	+	4.53055i	−0.100394	+	0.308981i
$216$	10.6225			0.722769
$217$	2.03622	+	11.4261i	0.138228	+	0.775655i
$218$	−45.9808			−3.11421
$219$	−2.01184	+	6.19181i	−0.135948	+	0.418404i
$220$	0.939411	−	1.04332i	0.0633351	−	0.0703407i
$221$	19.9485	+	14.4935i	1.34188	+	0.974935i
$222$	−5.06709	+	8.77646i	−0.340081	+	0.589038i
$223$	10.3996	+	18.0127i	0.696411	+	1.20622i	0.969703	+	0.244289i	$0.0785544\pi$
$223$	10.3996	+	18.0127i	0.696411	+	1.20622i	−0.273291	+	0.961931i	$0.588112\pi$
$224$	6.36716	−	60.5795i	0.425424	−	4.04764i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−0.435369	−	4.14226i	−0.0289603	−	0.275539i
$227$	−9.69452	−	10.7669i	−0.643448	−	0.714621i	0.329885	−	0.944021i	$-0.392990\pi$
$227$	−9.69452	−	10.7669i	−0.643448	−	0.714621i	−0.973332	+	0.229400i	$0.926324\pi$
$228$	32.4938	−	14.4672i	2.15196	−	0.958112i
$229$	17.4738	−	3.71417i	1.15470	−	0.245439i	0.409519	−	0.912301i	$-0.365696\pi$
$229$	17.4738	−	3.71417i	1.15470	−	0.245439i	0.745181	+	0.666862i	$0.232363\pi$
$230$	−11.3331	−	2.40892i	−0.747281	−	0.158840i
$231$	0.460728	+	0.205130i	0.0303137	+	0.0134965i
$232$	0.991254	+	3.05077i	0.0650790	+	0.200293i
$233$	6.81454	+	20.9730i	0.446435	+	1.37399i	0.880902	+	0.473298i	$0.156937\pi$
$233$	6.81454	+	20.9730i	0.446435	+	1.37399i	−0.434467	+	0.900688i	$0.643063\pi$
$234$	−15.3901	−	6.85210i	−1.00608	−	0.447936i
$235$	0.893260	+	0.189868i	0.0582699	+	0.0123856i
$236$	−58.7887	+	12.4959i	−3.82682	+	0.813415i
$237$	−0.456107	+	0.203072i	−0.0296273	+	0.0131909i
$238$	−15.9298	−	17.6918i	−1.03257	−	1.14679i
$239$	−1.34986	−	12.8430i	−0.0873151	−	0.830748i	−0.947283	−	0.320399i	$-0.896183\pi$
$239$	−1.34986	−	12.8430i	−0.0873151	−	0.830748i	0.859968	−	0.510349i	$-0.170484\pi$
$240$	14.6163	−	10.6194i	0.943477	−	0.685476i
$241$	−0.385948	+	3.67205i	−0.0248611	+	0.236538i	0.975034	+	0.222056i	$0.0712766\pi$
$241$	−0.385948	+	3.67205i	−0.0248611	+	0.236538i	−0.999895	+	0.0144821i	$0.995390\pi$
$242$	15.2816	+	26.4686i	0.982342	+	1.70147i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−56.3988	−	40.9761i	−3.61056	−	2.62323i
$245$	1.77639	−	1.97288i	0.113489	−	0.126043i
$246$	1.29354	−	3.98109i	0.0824728	−	0.253825i
$247$	−36.9675			−2.35219
$248$	36.3273	−	46.6721i	2.30679	−	2.96368i
$249$	11.3327			0.718178
$250$	−0.863191	+	2.65663i	−0.0545930	+	0.168020i
$251$	−12.0829	+	13.4194i	−0.762664	+	0.847024i	−0.991989	−	0.126326i	$-0.959682\pi$
$251$	−12.0829	+	13.4194i	−0.762664	+	0.847024i	0.229325	+	0.973350i	$0.426348\pi$
$252$	9.78589	+	7.10987i	0.616453	+	0.447880i
$253$	−0.501761	+	0.869076i	−0.0315455	+	0.0546384i
$254$	22.8795	+	39.6285i	1.43559	+	2.48652i
$255$	0.427368	−	4.06613i	0.0267628	−	0.254631i
$256$	−81.4939	+	59.2088i	−5.09337	+	3.70055i
$257$	−0.319167	−	3.03667i	−0.0199091	−	0.189422i	0.980047	−	0.198765i	$-0.0636929\pi$
$257$	−0.319167	−	3.03667i	−0.0199091	−	0.189422i	−0.999956	+	0.00934216i	$0.997026\pi$
$258$	8.90390	+	9.88878i	0.554333	+	0.615649i
$259$	−6.90877	+	3.07598i	−0.429290	+	0.191132i
$260$	−34.2316	+	7.27614i	−2.12295	+	0.451247i
$261$	−0.295380	−	0.0627849i	−0.0182835	−	0.00388629i
$262$	14.5230	+	6.46605i	0.897233	+	0.399474i
$263$	2.51475	+	7.73961i	0.155066	+	0.477245i	0.998168	−	0.0605099i	$-0.0192727\pi$
$263$	2.51475	+	7.73961i	0.155066	+	0.477245i	−0.843101	+	0.537755i	$0.819273\pi$
$264$	−0.794177	−	2.44422i	−0.0488782	−	0.150432i
$265$	−8.51914	−	3.79296i	−0.523326	−	0.233000i
$266$	34.9116	+	7.42069i	2.14057	+	0.454992i
$267$	13.3648	−	2.84078i	0.817913	−	0.173853i
$268$	44.3428	−	19.7427i	2.70867	−	1.20598i
$269$	2.28448	+	2.53717i	0.139287	+	0.154694i	0.808752	−	0.588149i	$-0.200143\pi$
$269$	2.28448	+	2.53717i	0.139287	+	0.154694i	−0.669465	+	0.742844i	$0.733477\pi$
$270$	0.291984	+	2.77804i	0.0177696	+	0.169066i
$271$	−0.311388	+	0.226237i	−0.0189155	+	0.0137429i	−0.597203	−	0.802090i	$-0.703721\pi$
$271$	−0.311388	+	0.226237i	−0.0189155	+	0.0137429i	0.578287	+	0.815833i	$0.303721\pi$
$272$	−7.72114	+	73.4617i	−0.468163	+	4.45427i
$273$	−6.28583	−	10.8874i	−0.380435	−	0.658934i
$274$	12.1985	−	21.1283i	0.736936	−	1.27641i
$275$	0.195734	+	0.142209i	0.0118032	+	0.00857553i
$276$	−16.1052	+	17.8866i	−0.969419	+	1.07665i
$277$	−8.21715	+	25.2898i	−0.493721	+	1.51952i	0.325220	+	0.945638i	$0.394562\pi$
$277$	−8.21715	+	25.2898i	−0.493721	+	1.51952i	−0.818941	+	0.573878i	$0.805438\pi$
$278$	22.0475			1.32232
$279$	2.09513	+	5.15853i	0.125432	+	0.308833i
$280$	22.1428			1.32329
$281$	2.80058	−	8.61930i	0.167069	−	0.514185i	−0.832114	−	0.554604i	$-0.812870\pi$
$281$	2.80058	−	8.61930i	0.167069	−	0.514185i	0.999183	+	0.0404200i	$0.0128696\pi$
$282$	1.70690	−	1.89571i	0.101645	−	0.112888i
$283$	−15.4601	−	11.2324i	−0.919006	−	0.667697i	0.0242708	−	0.999705i	$-0.492274\pi$
$283$	−15.4601	−	11.2324i	−0.919006	−	0.667697i	−0.943276	+	0.332009i	$0.892274\pi$
$284$	−11.8068	+	20.4499i	−0.700604	+	1.21348i
$285$	3.06481	+	5.30841i	0.181544	+	0.314443i
$286$	−0.426043	+	4.05353i	−0.0251925	+	0.239690i
$287$	2.52718	−	1.83610i	0.149174	−	0.108382i
$288$	−3.05449	−	29.0616i	−0.179988	−	1.71247i
$289$	−0.189979	−	0.210993i	−0.0111752	−	0.0124113i
$290$	−0.770604	+	0.343095i	−0.0452514	+	0.0201472i
$291$	−16.5813	+	3.52446i	−0.972011	+	0.206607i
$292$	36.9532	+	7.85465i	2.16252	+	0.459659i
$293$	15.6092	+	6.94968i	0.911901	+	0.406004i	0.808406	−	0.588626i	$-0.200331\pi$
$293$	15.6092	+	6.94968i	0.911901	+	0.406004i	0.103495	+	0.994630i	$0.466997\pi$
$294$	−2.29157	−	7.05274i	−0.133647	−	0.411324i
$295$	−3.20063	−	9.85052i	−0.186348	−	0.573520i
$296$	35.2063	+	15.6749i	2.04633	+	0.911083i
$297$	0.236653	+	0.0503022i	0.0137320	+	0.00291883i
$298$	52.6953	−	11.2007i	3.05255	−	0.648840i
$299$	22.8526	−	10.1746i	1.32160	−	0.588413i
$300$	3.88282	+	4.31231i	0.224175	+	0.248971i
$301$	1.03797	+	9.87565i	0.0598277	+	0.569223i
$302$	−16.8346	+	12.2310i	−0.968720	+	0.703816i
$303$	−0.755218	+	7.18542i	−0.0433861	+	0.412791i
$304$	−55.3712	−	95.9057i	−3.17575	−	5.50057i
$305$	6.00684	−	10.4042i	0.343951	−	0.595740i
$306$	−9.23953	−	6.71291i	−0.528189	−	0.383751i
$307$	2.81838	−	3.13012i	0.160853	−	0.178646i	−0.657331	−	0.753602i	$-0.728314\pi$
$307$	2.81838	−	3.13012i	0.160853	−	0.178646i	0.818184	+	0.574957i	$0.194981\pi$
$308$	0.904344	−	2.78328i	0.0515298	−	0.158592i
$309$	13.5240			0.769355
$310$	13.2044	+	8.21761i	0.749962	+	0.466729i
$311$	−26.7043			−1.51426			−0.757130	−	0.653264i	$-0.773399\pi$
$311$	−26.7043			−1.51426			−0.757130	+	0.653264i	$0.773399\pi$
$312$	−19.7968	+	60.9282i	−1.12077	+	3.44938i
$313$	−11.9956	+	13.3224i	−0.678031	+	0.753029i	−0.979719	−	0.200377i	$-0.935783\pi$
$313$	−11.9956	+	13.3224i	−0.678031	+	0.753029i	0.301688	+	0.953407i	$0.402450\pi$
$314$	15.3506	+	11.1529i	0.866284	+	0.629392i
$315$	−1.04226	+	1.80525i	−0.0587247	+	0.101714i
$316$	1.44858	+	2.50902i	0.0814890	+	0.141143i
$317$	−0.318470	+	3.03004i	−0.0178871	+	0.170184i	−0.999818	−	0.0190531i	$-0.993935\pi$
$317$	−0.318470	+	3.03004i	−0.0178871	+	0.170184i	0.981931	+	0.189237i	$0.0606015\pi$
$318$	−21.0740	+	15.3112i	−1.18177	+	0.858609i
$319$	0.00763694	+	0.0726606i	0.000427586	+	0.00406821i
$320$	−30.4406	−	33.8077i	−1.70168	−	1.88991i
$321$	0.289207	−	0.128763i	0.0161420	−	0.00718687i
$322$	−23.6241	+	5.02145i	−1.31652	+	0.279834i
$323$	−24.5135	−	5.21051i	−1.36397	−	0.289921i
$324$	5.30111	+	2.36020i	0.294506	+	0.131122i
$325$	−1.86367	−	5.73578i	−0.103378	−	0.318164i
$326$	4.14541	+	12.7583i	0.229593	+	0.706615i
$327$	−15.0377	−	6.69522i	−0.831587	−	0.370247i
$328$	−15.5705	−	3.30961i	−0.859736	−	0.182743i
$329$	1.86202	−	0.395785i	0.102657	−	0.0218203i
$330$	0.617395	−	0.274882i	0.0339865	−	0.0151318i
$331$	−9.37540	−	10.4124i	−0.515319	−	0.572319i	0.428181	−	0.903693i	$-0.359155\pi$
$331$	−9.37540	−	10.4124i	−0.515319	−	0.572319i	−0.943500	+	0.331374i	$0.892488\pi$
$332$	−6.87389	−	65.4007i	−0.377254	−	3.58933i
$333$	−2.93509	+	2.13247i	−0.160842	+	0.116859i
$334$	2.39880	−	22.8231i	0.131257	−	1.24882i
$335$	4.18241	+	7.24414i	0.228509	+	0.395790i
$336$	18.8302	−	32.6149i	1.02727	−	1.77929i
$337$	1.46991	+	1.06795i	0.0800711	+	0.0581750i	0.627101	−	0.778938i	$-0.284241\pi$
$337$	1.46991	+	1.06795i	0.0800711	+	0.0581750i	−0.547030	+	0.837113i	$0.684241\pi$
$338$	43.6856	−	48.5178i	2.37619	−	2.63902i
$339$	0.460766	−	1.41809i	0.0250254	−	0.0770202i
$340$	−23.7249			−1.28666
$341$	1.03033	−	0.867758i	0.0557956	−	0.0469917i
$342$	17.1222			0.925861
$343$	6.21915	−	19.1406i	0.335802	−	1.03349i
$344$	33.8596	−	37.6049i	1.82559	−	2.02752i
$345$	−3.35565	−	2.43802i	−0.180662	−	0.131259i
$346$	23.1467	−	40.0912i	1.24437	−	2.15532i
$347$	−7.16433	−	12.4090i	−0.384602	−	0.666150i	0.607112	−	0.794616i	$-0.292328\pi$
$347$	−7.16433	−	12.4090i	−0.384602	−	0.666150i	−0.991714	+	0.128467i	$0.958995\pi$
$348$	−0.183167	+	1.74272i	−0.00981878	+	0.0934194i
$349$	−22.7758	+	16.5476i	−1.21916	+	0.885774i	−0.996030	−	0.0890142i	$-0.971628\pi$
$349$	−22.7758	+	16.5476i	−1.21916	+	0.885774i	−0.223133	+	0.974788i	$0.571628\pi$
$350$	0.608647	+	5.79089i	0.0325336	+	0.309536i
$351$	−4.03549	−	4.48187i	−0.215399	−	0.239225i
$352$	−6.45867	+	2.87559i	−0.344248	+	0.153269i
$353$	0.210489	−	0.0447407i	0.0112032	−	0.00238131i	−0.202307	−	0.979322i	$-0.564844\pi$
$353$	0.210489	−	0.0447407i	0.0112032	−	0.00238131i	0.213510	+	0.976941i	$0.431510\pi$
$354$	−28.2997	−	6.01529i	−1.50411	−	0.319709i
$355$	−3.71754	−	1.65515i	−0.197306	−	0.0878465i
$356$	−24.5006	−	75.4051i	−1.29853	−	3.99646i
$357$	−2.63364	−	8.10550i	−0.139387	−	0.428989i
$358$	−31.3728	−	13.9681i	−1.65810	−	0.738235i
$359$	25.1539	+	5.34663i	1.32757	+	0.282184i	0.816496	−	0.577351i	$-0.195914\pi$
$359$	25.1539	+	5.34663i	1.32757	+	0.282184i	0.511077	+	0.859535i	$0.329247\pi$
$360$	10.3904	−	2.20854i	0.547620	−	0.116400i
$361$	16.9667	−	7.55405i	0.892983	−	0.397582i
$362$	−12.5588	−	13.9479i	−0.660073	−	0.733086i
$363$	1.14369	+	10.8815i	0.0600284	+	0.571132i
$364$	−59.0182	+	42.8793i	−3.09340	+	2.24748i
$365$	−0.680528	+	6.47479i	−0.0356205	+	0.338906i
$366$	−16.7792	−	29.0624i	−0.877062	−	1.51912i
$367$	−10.2801	+	17.8057i	−0.536618	+	0.929449i	0.462466	+	0.886637i	$0.346965\pi$
$367$	−10.2801	+	17.8057i	−0.536618	+	0.929449i	−0.999083	+	0.0428117i	$0.986368\pi$
$368$	60.6256	+	44.0471i	3.16033	+	2.29611i
$369$	1.00273	−	1.11364i	0.0521998	−	0.0579738i
$370$	−3.13164	+	9.63818i	−0.162806	+	0.501065i
$371$	−19.4389			−1.00922
$372$	28.4990	−	15.2199i	1.47761	−	0.789117i
$373$	−3.37774			−0.174893			−0.0874463	−	0.996169i	$-0.527871\pi$
$373$	−3.37774			−0.174893			−0.0874463	+	0.996169i	$0.527871\pi$
$374$	−0.853852	+	2.62789i	−0.0441517	+	0.135885i
$375$	−0.669131	+	0.743145i	−0.0345538	+	0.0383758i
$376$	−7.84797	−	5.70189i	−0.404728	−	0.294052i
$377$	0.910609	−	1.57722i	0.0468988	−	0.0812310i
$378$	2.91140	+	5.04269i	0.149746	+	0.259368i
$379$	−0.0364702	+	0.346991i	−0.00187335	+	0.0178237i	−0.995419	−	0.0956124i	$-0.969519\pi$
$379$	−0.0364702	+	0.346991i	−0.00187335	+	0.0178237i	0.993545	+	0.113436i	$0.0361857\pi$
$380$	28.7758	−	20.9069i	1.47617	−	1.07250i
$381$	1.71233	+	16.2917i	0.0877253	+	0.834650i
$382$	−16.2527	−	18.0505i	−0.831561	−	0.923542i
$383$	13.6387	−	6.07232i	0.696903	−	0.310281i	−0.0275355	−	0.999621i	$-0.508766\pi$
$383$	13.6387	−	6.07232i	0.696903	−	0.310281i	0.724438	+	0.689340i	$0.242099\pi$
$384$	−67.1338	+	14.2697i	−3.42591	+	0.728199i
$385$	0.493309	+	0.104856i	0.0251414	+	0.00534396i
$386$	−43.9622	−	19.5732i	−2.23761	−	0.996250i
$387$	1.47207	+	4.53055i	0.0748293	+	0.230301i
$388$	30.3971	+	93.5526i	1.54318	+	4.74941i
$389$	−13.2781	−	5.91180i	−0.673227	−	0.299740i	0.0415048	−	0.999138i	$-0.486785\pi$
$389$	−13.2781	−	5.91180i	−0.673227	−	0.299740i	−0.714732	+	0.699398i	$0.753451\pi$
$390$	−16.4784	−	3.50259i	−0.834416	−	0.177361i
$391$	16.5879	−	3.52586i	0.838884	−	0.178310i
$392$	−25.7622	+	11.4701i	−1.30119	+	0.579326i
$393$	3.80813	+	4.22936i	0.192095	+	0.213343i
$394$	4.11527	+	39.1542i	0.207325	+	1.97256i
$395$	−0.403919	+	0.293464i	−0.0203234	+	0.0147658i
$396$	0.146750	−	1.39624i	0.00737449	−	0.0701635i
$397$	−13.7371	−	23.7934i	−0.689448	−	1.19416i	−0.972017	−	0.234912i	$-0.924520\pi$
$397$	−13.7371	−	23.7934i	−0.689448	−	1.19416i	0.282569	−	0.959247i	$-0.408813\pi$
$398$	8.49617	−	14.7158i	0.425875	−	0.737636i
$399$	10.3371	+	7.51033i	0.517502	+	0.375987i
$400$	12.0890	−	13.4262i	0.604450	−	0.671310i
$401$	−0.335375	+	1.03218i	−0.0167478	+	0.0515445i	−0.959081	−	0.283131i	$-0.908627\pi$
$401$	−0.335375	+	1.03218i	−0.0167478	+	0.0515445i	0.942333	+	0.334676i	$0.108627\pi$
$402$	23.3658			1.16538
$403$	−33.4928	+	2.40342i	−1.66840	+	0.119723i
$404$	41.9251			2.08585
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	−1.17657	+	1.30671i	−0.0583923	+	0.0648512i
$407$	0.710117	+	0.515930i	0.0351992	+	0.0255737i
$408$	−21.7152	+	37.6118i	−1.07506	+	1.86206i
$409$	−6.09355	−	10.5543i	−0.301307	−	0.521878i	0.675126	−	0.737703i	$-0.264089\pi$
$409$	−6.09355	−	10.5543i	−0.301307	−	0.521878i	−0.976432	+	0.215824i	$0.930756\pi$
$410$	0.437553	−	4.16304i	0.0216092	−	0.205598i
$411$	7.06591	−	5.13368i	0.348535	−	0.253226i
$412$	−8.20307	−	78.0470i	−0.404136	−	3.84510i
$413$	−14.4468	−	16.0447i	−0.710878	−	0.789510i
$414$	−10.5846	+	4.71256i	−0.520204	+	0.231610i
$415$	11.0850	−	2.35619i	0.544142	−	0.115661i
$416$	172.383	+	36.6412i	8.45178	+	1.79648i
$417$	7.21049	+	3.21032i	0.353099	+	0.157210i
$418$	−1.28012	−	3.93980i	−0.0626126	−	0.192702i
$419$	−10.5615	−	32.5050i	−0.515964	−	1.58797i	−0.781521	−	0.623879i	$-0.785556\pi$
$419$	−10.5615	−	32.5050i	−0.515964	−	1.58797i	0.265557	−	0.964095i	$-0.414444\pi$
$420$	11.0503	+	4.91990i	0.539198	+	0.240066i
$421$	27.3280	+	5.80874i	1.33188	+	0.283100i	0.818227	−	0.574896i	$-0.194957\pi$
$421$	27.3280	+	5.80874i	1.33188	+	0.283100i	0.513656	+	0.857996i	$0.328291\pi$
$422$	24.1466	−	5.13252i	1.17544	−	0.249847i
$423$	0.834264	−	0.371438i	0.0405633	−	0.0180600i
$424$	66.2831	+	73.6148i	3.21899	+	3.57505i
$425$	−0.427368	−	4.06613i	−0.0207304	−	0.197236i
$426$	−9.19618	+	6.68142i	−0.445557	+	0.323716i
$427$	2.61768	−	24.9056i	0.126679	−	1.20527i
$428$	−0.918513	−	1.59091i	−0.0443980	−	0.0768996i
$429$	−0.729566	+	1.26364i	−0.0352238	+	0.0610093i
$430$	10.7653	+	7.82147i	0.519150	+	0.377185i
$431$	−22.5116	+	25.0017i	−1.08435	+	1.20429i	−0.106645	+	0.994297i	$0.534011\pi$
$431$	−22.5116	+	25.0017i	−1.08435	+	1.20429i	−0.977703	+	0.209993i	$0.932656\pi$
$432$	5.58293	−	17.1825i	0.268609	−	0.826692i
$433$	9.14483			0.439472			0.219736	−	0.975559i	$-0.429480\pi$
$433$	9.14483			0.439472			0.219736	+	0.975559i	$0.429480\pi$
$434$	32.1126	+	4.45343i	1.54145	+	0.213772i
$435$	−0.301979			−0.0144788
$436$	−29.5169	+	90.8436i	−1.41360	+	4.35062i
$437$	−17.0123	+	18.8941i	−0.813810	+	0.903828i
$438$	14.7128	+	10.6894i	0.703003	+	0.510761i
$439$	−8.04178	+	13.9288i	−0.383813	+	0.664784i	−0.991604	−	0.129313i	$-0.958723\pi$
$439$	−8.04178	+	13.9288i	−0.383813	+	0.664784i	0.607791	+	0.794097i	$0.292056\pi$
$440$	−1.28500	−	2.22569i	−0.0612602	−	0.106106i
$441$	0.277499	−	2.64023i	0.0132142	−	0.125725i
$442$	55.7231	−	40.4852i	2.65048	−	1.92569i
$443$	0.653247	+	6.21523i	0.0310367	+	0.295295i	0.999019	+	0.0442772i	$0.0140985\pi$
$443$	0.653247	+	6.21523i	0.0310367	+	0.295295i	−0.967983	+	0.251017i	$0.919235\pi$
$444$	14.0868	+	15.6449i	0.668528	+	0.742476i
$445$	12.4821	−	5.55740i	0.591709	−	0.263446i
$446$	56.8300	−	12.0796i	2.69098	−	0.571985i
$447$	18.8646	+	4.00979i	0.892263	+	0.189656i
$448$	−86.6320	−	38.5711i	−4.09298	−	1.82231i
$449$	−2.65805	−	8.18063i	−0.125441	−	0.386068i	0.868540	−	0.495619i	$-0.165059\pi$
$449$	−2.65805	−	8.18063i	−0.125441	−	0.386068i	−0.993981	+	0.109551i	$0.965059\pi$
$450$	0.863191	+	2.65663i	0.0406912	+	0.125235i
$451$	−0.331215	−	0.147466i	−0.0155963	−	0.00694392i
$452$	−8.46328	−	1.79893i	−0.398079	−	0.0846144i
$453$	−7.28658	+	1.54881i	−0.342353	+	0.0727694i
$454$	−36.9718	+	16.4609i	−1.73517	+	0.772548i
$455$	−8.41208	−	9.34256i	−0.394364	−	0.437986i
$456$	−6.80605	−	64.7552i	−0.318722	−	3.03244i
$457$	−3.75276	+	2.72654i	−0.175547	+	0.127542i	−0.672089	−	0.740470i	$-0.734603\pi$
$457$	−3.75276	+	2.72654i	−0.175547	+	0.127542i	0.496542	+	0.868013i	$0.334603\pi$
$458$	5.21605	−	49.6274i	0.243730	−	2.31894i
$459$	−2.04427	−	3.54077i	−0.0954181	−	0.165269i
$460$	−12.0344	+	20.8442i	−0.561108	+	0.971867i
$461$	−22.6060	−	16.4242i	−1.05287	−	0.764953i	−0.0801121	−	0.996786i	$-0.525528\pi$
$461$	−22.6060	−	16.4242i	−1.05287	−	0.764953i	−0.972756	+	0.231833i	$0.925528\pi$
$462$	0.942650	−	1.04692i	0.0438561	−	0.0487071i
$463$	0.944857	−	2.90797i	0.0439112	−	0.135145i	−0.926697	−	0.375808i	$-0.877365\pi$
$463$	0.944857	−	2.90797i	0.0439112	−	0.135145i	0.970609	+	0.240664i	$0.0773651\pi$
$464$	5.45577			0.253278
$465$	3.12187	+	4.61020i	0.144773	+	0.213793i
$466$	61.5997			2.85355
$467$	2.08107	−	6.40487i	0.0963003	−	0.296382i	−0.891290	−	0.453434i	$-0.850199\pi$
$467$	2.08107	−	6.40487i	0.0963003	−	0.296382i	0.987590	+	0.157052i	$0.0501989\pi$
$468$	−23.4171	+	26.0073i	−1.08246	+	1.20219i
$469$	14.1065	+	10.2490i	0.651379	+	0.473255i
$470$	1.27546	−	2.20917i	0.0588328	−	0.101901i
$471$	3.39635	+	5.88265i	0.156496	+	0.271058i
$472$	−11.5004	+	109.419i	−0.529350	+	5.03643i
$473$	0.932418	−	0.677442i	0.0428726	−	0.0311488i
$474$	0.145779	+	1.38700i	0.00669586	+	0.0637069i
$475$	4.10152	+	4.55520i	0.188191	+	0.209007i
$476$	−45.1794	+	20.1152i	−2.07079	+	0.921977i
$477$	−9.12157	+	1.93885i	−0.417648	+	0.0887739i
$478$	−35.2844	−	7.49993i	−1.61387	−	0.343039i
$479$	−11.5741	−	5.15311i	−0.528833	−	0.235452i	0.124910	−	0.992168i	$-0.460136\pi$
$479$	−11.5741	−	5.15311i	−0.528833	−	0.235452i	−0.653743	+	0.756716i	$0.726802\pi$
$480$	−9.02999	−	27.7914i	−0.412161	−	1.26850i
$481$	−6.76133	−	20.8092i	−0.308290	−	0.948820i
$482$	9.42214	+	4.19501i	0.429167	+	0.191077i
$483$	−8.45726	−	1.79765i	−0.384819	−	0.0817957i
$484$	62.1035	−	13.2005i	2.82289	−	0.600023i
$485$	−15.4861	+	6.89488i	−0.703190	+	0.313080i
$486$	1.86911	+	2.07586i	0.0847847	+	0.0941630i
$487$	−0.711239	−	6.76699i	−0.0322293	−	0.306642i	−0.998747	−	0.0500420i	$-0.984064\pi$
$487$	−0.711239	−	6.76699i	−0.0322293	−	0.306642i	0.966518	−	0.256600i	$-0.0826022\pi$
$488$	−103.243	+	75.0103i	−4.67358	+	3.39556i
$489$	−0.501990	+	4.77611i	−0.0227008	+	0.215983i
$490$	−3.70784	−	6.42218i	−0.167503	−	0.290124i
$491$	0.534935	−	0.926535i	0.0241413	−	0.0418140i	−0.853702	−	0.520761i	$-0.825648\pi$
$491$	0.534935	−	0.926535i	0.0241413	−	0.0418140i	0.877844	+	0.478947i	$0.158982\pi$
$492$	−7.03502	−	5.11124i	−0.317163	−	0.230433i
$493$	0.826141	−	0.917523i	0.0372075	−	0.0413231i
$494$	−31.9100	+	98.2090i	−1.43570	+	4.41863i
$495$	0.241940			0.0108744
$496$	−56.4019	−	83.2912i	−2.53252	−	3.73989i
$497$	−8.48265			−0.380499
$498$	9.78225	−	30.1067i	0.438353	−	1.34911i
$499$	14.8713	−	16.5162i	0.665730	−	0.739368i	−0.311804	−	0.950146i	$-0.600933\pi$
$499$	14.8713	−	16.5162i	0.665730	−	0.739368i	0.977534	+	0.210778i	$0.0675999\pi$
$500$	4.69455	+	3.41079i	0.209947	+	0.152535i
$501$	4.10776	−	7.11485i	0.183521	−	0.317868i
$502$	25.2205	+	43.6832i	1.12565	+	1.94968i
$503$	−1.89638	+	18.0428i	−0.0845554	+	0.804491i	0.867268	+	0.497842i	$0.165874\pi$
$503$	−1.89638	+	18.0428i	−0.0845554	+	0.804491i	−0.951823	+	0.306648i	$0.900792\pi$
$504$	17.9139	−	13.0152i	0.797949	−	0.579744i
$505$	0.755218	+	7.18542i	0.0336067	+	0.319747i
$506$	1.87570	+	2.08317i	0.0833849	+	0.0926084i
$507$	21.3517	−	9.50640i	0.948264	−	0.422194i
$508$	92.9808	−	19.7637i	4.12536	−	0.876872i
$509$	−39.5028	−	8.39657i	−1.75093	−	0.372171i	−0.782731	−	0.622360i	$-0.786174\pi$
$509$	−39.5028	−	8.39657i	−1.75093	−	0.372171i	−0.968197	+	0.250188i	$0.919508\pi$
$510$	−10.4333	−	4.64521i	−0.461995	−	0.205693i
$511$	4.19373	+	12.9070i	0.185520	+	0.570971i
$512$	44.5331	+	137.059i	1.96810	+	6.05720i
$513$	5.59969	+	2.49314i	0.247233	+	0.110075i
$514$	−8.34282	−	1.77332i	−0.367986	−	0.0782178i
$515$	13.2285	−	2.81180i	0.582917	−	0.123903i
$516$	25.2529	−	11.2433i	1.11170	−	0.494959i
$517$	−0.147840	−	0.164193i	−0.00650201	−	0.00722121i
$518$	2.20816	+	21.0092i	0.0970208	+	0.923091i
$519$	13.4076	−	9.74121i	0.588529	−	0.427592i
$520$	−6.69648	+	63.7128i	−0.293660	+	2.79399i
$521$	−6.03968	−	10.4610i	−0.264603	−	0.458306i	0.702856	−	0.711332i	$-0.251908\pi$
$521$	−6.03968	−	10.4610i	−0.264603	−	0.458306i	−0.967460	+	0.253025i	$0.918574\pi$
$522$	−0.421765	+	0.730519i	−0.0184602	+	0.0319740i
$523$	−33.1010	−	24.0493i	−1.44741	−	1.05160i	−0.986428	−	0.164192i	$-0.947498\pi$
$523$	−33.1010	−	24.0493i	−1.44741	−	1.05160i	−0.460979	−	0.887411i	$-0.652502\pi$
$524$	22.0978	−	24.5421i	0.965345	−	1.07212i
$525$	−0.644153	+	1.98250i	−0.0281131	+	0.0865233i
$526$	22.7320			0.991162
$527$	−22.5482	−	3.12702i	−0.982214	−	0.136215i
$528$	−4.37107			−0.190226
$529$	−1.79096	+	5.51201i	−0.0778679	+	0.239653i
$530$	−17.4301	+	19.3581i	−0.757117	+	0.840864i
$531$	−8.37936	−	6.08796i	−0.363633	−	0.264195i
$532$	37.0721	−	64.2107i	1.60728	−	2.78389i
$533$	4.51884	+	7.82687i	0.195733	+	0.339019i
$534$	3.98949	−	37.9575i	0.172642	−	1.64258i
$535$	0.256116	−	0.186079i	0.0110729	−	0.00804490i
$536$	−9.28789	−	88.3684i	−0.401176	−	3.81693i
$537$	−8.22639	−	9.13633i	−0.354995	−	0.394262i
$538$	8.71228	−	3.87896i	0.375613	−	0.167234i
$539$	−0.628260	+	0.133541i	−0.0270611	+	0.00575201i
$540$	5.67598	+	1.20647i	0.244255	+	0.0519181i
$541$	19.3770	+	8.62720i	0.833083	+	0.370912i	0.778537	−	0.627599i	$-0.215962\pi$
$541$	19.3770	+	8.62720i	0.833083	+	0.370912i	0.0545461	+	0.998511i	$0.482629\pi$
$542$	0.332240	+	1.02253i	0.0142709	+	0.0439214i
$543$	−2.07631	−	6.39024i	−0.0891032	−	0.274231i
$544$	109.145	+	48.5943i	4.67953	+	2.08346i
$545$	−16.1011	−	3.42240i	−0.689696	−	0.146599i
$546$	−34.3496	+	7.30123i	−1.47003	+	0.312464i
$547$	9.36496	−	4.16955i	0.400417	−	0.178277i	−0.196641	−	0.980476i	$-0.563003\pi$
$547$	9.36496	−	4.16955i	0.400417	−	0.178277i	0.597057	+	0.802199i	$0.296337\pi$
$548$	−33.9123	−	37.6634i	−1.44866	−	1.60890i
$549$	−1.25577	−	11.9479i	−0.0535950	−	0.509923i
$550$	0.546753	−	0.397239i	0.0233136	−	0.0169383i
$551$	−0.193484	+	1.84088i	−0.00824269	+	0.0784240i
$552$	22.0300	+	38.1571i	0.937661	+	1.62408i
$553$	−0.520371	+	0.901309i	−0.0221284	+	0.0383275i
$554$	60.0927	+	43.6599i	2.55309	+	1.85493i
$555$	−2.42759	+	2.69611i	−0.103045	+	0.114443i
$556$	14.1531	−	43.5589i	0.600227	−	1.84731i
$557$	−3.64108			−0.154277			−0.0771387	−	0.997020i	$-0.524578\pi$
$557$	−3.64108			−0.154277			−0.0771387	+	0.997020i	$0.524578\pi$
$558$	15.5128	−	1.11319i	0.656709	−	0.0471251i
$559$	−28.7297			−1.21514
$560$	11.6377	−	35.8173i	0.491784	−	1.51356i
$561$	−0.661891	+	0.735105i	−0.0279451	+	0.0310361i
$562$	−20.4809	−	14.8802i	−0.863933	−	0.627684i
$563$	7.35427	−	12.7380i	0.309946	−	0.536841i	−0.668405	−	0.743798i	$-0.733022\pi$
$563$	7.35427	−	12.7380i	0.309946	−	0.536841i	0.978350	+	0.206956i	$0.0663558\pi$
$564$	−2.64960	−	4.58924i	−0.111568	−	0.193242i
$565$	0.155859	−	1.48290i	0.00655705	−	0.0623862i
$566$	−43.1853	+	31.3760i	−1.81521	+	1.31883i
$567$	0.217892	+	2.07310i	0.00915060	+	0.0870621i
$568$	28.9243	+	32.1237i	1.21364	+	1.34788i
$569$	8.81501	−	3.92469i	0.369544	−	0.164532i	−0.213558	−	0.976930i	$-0.568505\pi$
$569$	8.81501	−	3.92469i	0.369544	−	0.164532i	0.583102	+	0.812399i	$0.301839\pi$
$570$	16.7480	−	3.55990i	0.701497	−	0.149108i
$571$	−16.2023	−	3.44391i	−0.678046	−	0.144123i	−0.143999	−	0.989578i	$-0.545996\pi$
$571$	−16.2023	−	3.44391i	−0.678046	−	0.144123i	−0.534047	+	0.845455i	$0.679329\pi$
$572$	7.73501	+	3.44385i	0.323417	+	0.143995i
$573$	−2.68703	−	8.26983i	−0.112252	−	0.345477i
$574$	−2.69640	−	8.29868i	−0.112546	−	0.346380i
$575$	−3.78921	−	1.68707i	−0.158021	−	0.0703555i
$576$	−44.4986	−	9.45847i	−1.85411	−	0.394103i
$577$	−1.10467	+	0.234805i	−0.0459880	+	0.00977506i	−0.230848	−	0.972990i	$-0.574150\pi$
$577$	−1.10467	+	0.234805i	−0.0459880	+	0.00977506i	0.184860	+	0.982765i	$0.440817\pi$
$578$	−0.724518	+	0.322576i	−0.0301360	+	0.0134174i
$579$	−11.5275	−	12.8026i	−0.479066	−	0.532057i
$580$	0.183167	+	1.74272i	0.00760559	+	0.0723624i
$581$	19.1115	−	13.8853i	0.792880	−	0.576061i
$582$	−4.94963	+	47.0926i	−0.205169	+	1.95205i
$583$	1.12809	+	1.95391i	0.0467207	+	0.0809227i
$584$	34.5786	−	59.8920i	1.43087	−	2.47835i
$585$	−4.87914	−	3.54490i	−0.201728	−	0.146564i
$586$	31.9365	−	35.4690i	1.31928	−	1.46521i
$587$	8.98992	−	27.6681i	0.371054	−	1.14199i	−0.575049	−	0.818119i	$-0.695017\pi$
$587$	8.98992	−	27.6681i	0.371054	−	1.14199i	0.946103	−	0.323867i	$-0.104983\pi$
$588$	−15.4050			−0.635294
$589$	30.1043	−	16.0772i	1.24042	−	0.662449i
$590$	−28.9320			−1.19111
$591$	−4.35534	+	13.4044i	−0.179155	+	0.551381i
$592$	43.8586	−	48.7099i	1.80258	−	2.00196i
$593$	−21.5408	−	15.6503i	−0.884575	−	0.642681i	0.0498832	−	0.998755i	$-0.484115\pi$
$593$	−21.5408	−	15.6503i	−0.884575	−	0.642681i	−0.934458	+	0.356074i	$0.884115\pi$
$594$	0.337912	−	0.585280i	0.0138647	−	0.0240143i
$595$	−4.26132	−	7.38081i	−0.174697	−	0.302584i
$596$	11.6980	−	111.299i	0.479171	−	4.55900i
$597$	4.92137	−	3.57558i	0.201418	−	0.146339i
$598$	−7.30406	−	69.4934i	−0.298685	−	2.84180i
$599$	−4.32957	−	4.80847i	−0.176901	−	0.196469i	0.648173	−	0.761493i	$-0.275533\pi$
$599$	−4.32957	−	4.80847i	−0.176901	−	0.196469i	−0.825074	+	0.565024i	$0.808867\pi$
$600$	9.70413	−	4.32056i	0.396169	−	0.176386i
$601$	20.7856	−	4.41811i	0.847862	−	0.180219i	0.236561	−	0.971617i	$-0.423980\pi$
$601$	20.7856	−	4.41811i	0.847862	−	0.180219i	0.611301	+	0.791398i	$0.290646\pi$
$602$	27.1319	+	5.76706i	1.10581	+	0.235048i
$603$	7.64164	+	3.40228i	0.311191	+	0.138551i
$604$	13.3579	+	41.1114i	0.543525	+	1.67280i
$605$	3.38110	+	10.4060i	0.137461	+	0.423062i
$606$	18.4371	+	8.20872i	0.748956	+	0.333457i
$607$	9.25105	+	1.96637i	0.375489	+	0.0798126i	0.391790	−	0.920055i	$-0.371856\pi$
$607$	9.25105	+	1.96637i	0.375489	+	0.0798126i	−0.0163017	+	0.999867i	$0.505189\pi$
$608$	−175.204	+	37.2407i	−7.10545	+	1.51031i
$609$	−0.575059	+	0.256033i	−0.0233026	+	0.0103750i
$610$	−22.4549	−	24.9387i	−0.909174	−	1.00974i
$611$	0.575697	+	5.47739i	0.0232902	+	0.221592i
$612$	−19.1938	+	13.9451i	−0.775864	+	0.563698i
$613$	−2.30819	+	21.9610i	−0.0932271	+	0.886996i	0.843546	+	0.537058i	$0.180464\pi$
$613$	−2.30819	+	21.9610i	−0.0932271	+	0.886996i	−0.936773	+	0.349939i	$0.886202\pi$
$614$	−5.88278	−	10.1893i	−0.237410	−	0.411206i
$615$	0.749275	−	1.29778i	0.0302137	−	0.0523317i
$616$	−4.33410	−	3.14891i	−0.174626	−	0.126873i
$617$	−3.19711	+	3.55075i	−0.128711	+	0.142948i	−0.804055	−	0.594555i	$-0.797328\pi$
$617$	−3.19711	+	3.55075i	−0.128711	+	0.142948i	0.675344	+	0.737503i	$0.263995\pi$
$618$	11.6738	−	35.9283i	0.469590	−	1.44525i
$619$	−32.6591			−1.31268			−0.656340	−	0.754465i	$-0.727896\pi$
$619$	−32.6591			−1.31268			−0.656340	+	0.754465i	$0.727896\pi$
$620$	24.7119	−	20.8126i	0.992452	−	0.835855i
$621$	−4.14781			−0.166446
$622$	−23.0509	+	70.9434i	−0.924257	+	2.84457i
$623$	19.0579	−	21.1660i	0.763539	−	0.847996i
$624$	88.1501	+	64.0448i	3.52883	+	2.56384i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	25.0383	+	43.3677i	1.00073	+	1.73332i
$627$	0.155016	−	1.47488i	0.00619075	−	0.0589011i
$628$	31.8887	−	23.1685i	1.27250	−	0.924523i
$629$	−1.55048	−	14.7518i	−0.0618216	−	0.588194i
$630$	3.89621	+	4.32718i	0.155229	+	0.172399i
$631$	−21.5918	+	9.61327i	−0.859555	+	0.382698i	−0.788693	−	0.614788i	$-0.789242\pi$
$631$	−21.5918	+	9.61327i	−0.859555	+	0.382698i	−0.0708620	+	0.997486i	$0.522575\pi$
$632$	5.18761	−	1.10266i	0.206352	−	0.0438615i
$633$	8.64433	+	1.83741i	0.343581	+	0.0730305i
$634$	7.77480	+	3.46156i	0.308777	+	0.137476i
$635$	5.06215	+	15.5797i	0.200885	+	0.618261i
$636$	16.7218	+	51.4645i	0.663064	+	2.04070i
$637$	14.6266	+	6.51217i	0.579526	+	0.258022i
$638$	0.199624	+	0.0424315i	0.00790321	+	0.00167988i
$639$	−3.98043	+	0.846066i	−0.157463	+	0.0334698i
$640$	−62.6999	+	27.9158i	−2.47843	+	1.10347i
$641$	26.8809	+	29.8543i	1.06173	+	1.17917i	0.983251	+	0.182259i	$0.0583408\pi$
$641$	26.8809	+	29.8543i	1.06173	+	1.17917i	0.0784825	+	0.996915i	$0.474993\pi$
$642$	−0.0924353	−	0.879464i	−0.00364813	−	0.0347097i
$643$	−16.0390	+	11.6530i	−0.632516	+	0.459550i	−0.857271	−	0.514866i	$-0.827842\pi$
$643$	−16.0390	+	11.6530i	−0.632516	+	0.459550i	0.224755	+	0.974415i	$0.427842\pi$
$644$	−5.24440	+	49.8972i	−0.206658	+	1.96622i
$645$	2.38185	+	4.12549i	0.0937853	+	0.162441i
$646$	−35.0023	+	60.6257i	−1.37715	+	2.38529i
$647$	34.1613	+	24.8196i	1.34302	+	0.975760i	0.999327	+	0.0366775i	$0.0116774\pi$
$647$	34.1613	+	24.8196i	1.34302	+	0.975760i	0.343691	+	0.939083i	$0.388323\pi$
$648$	7.10783	−	7.89405i	0.279222	−	0.310108i
$649$	−0.774362	+	2.38324i	−0.0303963	+	0.0935503i
$650$	−16.8465			−0.660776
$651$	9.85375	+	6.13235i	0.386199	+	0.240346i
$652$	27.8674			1.09137
$653$	−7.58770	+	23.3525i	−0.296930	+	0.913856i	0.685637	+	0.727944i	$0.259524\pi$
$653$	−7.58770	+	23.3525i	−0.296930	+	0.913856i	−0.982566	+	0.185912i	$0.940476\pi$
$654$	−30.7671	+	34.1704i	−1.20309	+	1.33617i
$655$	4.60425	+	3.34518i	0.179903	+	0.130707i
$656$	−13.5370	+	23.4467i	−0.528529	+	0.915439i
$657$	3.25523	+	5.63822i	0.126999	+	0.219968i
$658$	0.555827	−	5.28834i	0.0216684	−	0.206161i
$659$	0.0959190	−	0.0696892i	0.00373647	−	0.00271471i	−0.585915	−	0.810372i	$-0.699265\pi$
$659$	0.0959190	−	0.0696892i	0.00373647	−	0.00271471i	0.589652	+	0.807657i	$0.299265\pi$
$660$	−0.146750	−	1.39624i	−0.00571225	−	0.0543485i
$661$	14.8535	+	16.4965i	0.577735	+	0.641640i	0.959195	−	0.282745i	$-0.0912452\pi$
$661$	14.8535	+	16.4965i	0.577735	+	0.641640i	−0.381460	+	0.924385i	$0.624579\pi$
$662$	−35.7548	+	15.9190i	−1.38965	+	0.618711i
$663$	24.1189	−	5.12663i	0.936700	−	0.199102i
$664$	−117.750	−	25.0286i	−4.56960	−	0.971299i
$665$	11.6727	+	5.19701i	0.452647	+	0.201532i
$666$	3.13164	+	9.63818i	0.121348	+	0.373472i
$667$	−0.387059	−	1.19125i	−0.0149870	−	0.0461252i
$668$	−43.5513	−	19.3903i	−1.68505	−	0.750234i
$669$	20.3448	+	4.32441i	0.786574	+	0.167191i
$670$	22.8552	−	4.85803i	0.882974	−	0.187682i
$671$	−2.65531	+	1.18222i	−0.102507	+	0.0456390i
$672$	−40.7589	−	45.2673i	−1.57231	−	1.74622i
$673$	2.95307	+	28.0966i	0.113832	+	1.08304i	0.891079	+	0.453848i	$0.149949\pi$
$673$	2.95307	+	28.0966i	0.113832	+	1.08304i	−0.777247	+	0.629196i	$0.783384\pi$
$674$	4.10597	−	2.98316i	0.158156	−	0.114907i
$675$	−0.104528	+	0.994522i	−0.00402330	+	0.0382792i
$676$	−67.8124	−	117.455i	−2.60817	−	4.51748i
$677$	−6.69296	+	11.5926i	−0.257231	+	0.445538i	−0.965499	−	0.260406i	$-0.916144\pi$
$677$	−6.69296	+	11.5926i	−0.257231	+	0.445538i	0.708268	+	0.705944i	$0.249477\pi$
$678$	−3.36962	−	2.44817i	−0.129409	−	0.0940214i
$679$	−23.6445	+	26.2599i	−0.907393	+	1.00776i
$680$	−13.4207	+	41.3047i	−0.514661	+	1.58396i
$681$	−14.4882			−0.555190
$682$	−1.41594	−	3.48625i	−0.0542191	−	0.133496i
$683$	−50.2255			−1.92182			−0.960912	−	0.276854i	$-0.910708\pi$
$683$	−50.2255			−1.92182			−0.960912	+	0.276854i	$0.910708\pi$
$684$	10.9914	−	33.8280i	0.420267	−	1.29345i
$685$	5.84415	−	6.49058i	0.223293	−	0.247992i
$686$	−45.4811	−	33.0439i	−1.73648	−	1.26162i
$687$	8.93208	−	15.4708i	0.340780	−	0.590248i
$688$	−43.0323	−	74.5341i	−1.64059	−	2.84158i
$689$	5.87876	−	55.9327i	0.223963	−	2.13087i
$690$	−9.37349	+	6.81024i	−0.356843	+	0.259261i
$691$	−1.64003	−	15.6038i	−0.0623896	−	0.593597i	−0.980397	−	0.197034i	$-0.936869\pi$
$691$	−1.64003	−	15.6038i	−0.0623896	−	0.593597i	0.918007	−	0.396564i	$-0.129797\pi$
$692$	−64.3489	−	71.4667i	−2.44618	−	2.71676i
$693$	0.460728	−	0.205130i	0.0175016	−	0.00779223i
$694$	−39.1503	+	8.32165i	−1.48612	+	0.315886i
$695$	7.72038	+	1.64102i	0.292851	+	0.0622473i
$696$	2.93044	+	1.30472i	0.111078	+	0.0494551i
$697$	1.89331	+	5.82700i	0.0717141	+	0.220713i
$698$	24.3010	+	74.7908i	0.919806	+	2.83087i
$699$	20.1458	+	8.96948i	0.761983	+	0.339257i
$700$	11.8317	+	2.51491i	0.447196	+	0.0950545i
$701$	11.9145	−	2.53251i	0.450006	−	0.0956517i	0.0226666	−	0.999743i	$-0.492784\pi$
$701$	11.9145	−	2.53251i	0.450006	−	0.0956517i	0.427339	+	0.904091i	$0.359451\pi$
$702$	−15.3901	+	6.85210i	−0.580861	+	0.258616i
$703$	14.8802	+	16.5261i	0.561218	+	0.623296i
$704$	1.15050	+	10.9462i	0.0433609	+	0.412552i
$705$	0.738807	−	0.536775i	0.0278251	−	0.0202161i
$706$	0.0628324	−	0.597810i	0.00236473	−	0.0224989i
$707$	7.53033	+	13.0429i	0.283207	+	0.490529i
$708$	−30.0510	+	52.0499i	−1.12939	+	1.95616i
$709$	2.82123	+	2.04975i	0.105954	+	0.0769798i	0.639500	−	0.768791i	$-0.279141\pi$
$709$	2.82123	+	2.04975i	0.105954	+	0.0769798i	−0.533547	+	0.845771i	$0.679141\pi$
$710$	−7.60608	+	8.44741i	−0.285451	+	0.317026i
$711$	−0.154283	+	0.474835i	−0.00578607	+	0.0178077i
$712$	−145.139			−5.43932
$713$	−14.1849	+	18.2242i	−0.531229	+	0.682503i
$714$	−23.8067			−0.890942
$715$	−0.450896	+	1.38772i	−0.0168626	+	0.0518976i
$716$	−47.7359	+	53.0161i	−1.78398	+	1.98131i
$717$	−10.4475	−	7.59054i	−0.390168	−	0.283474i
$718$	35.9167	−	62.2095i	1.34040	−	2.32164i
$719$	−24.7071	−	42.7939i	−0.921418	−	1.59594i	−0.797223	−	0.603684i	$-0.793699\pi$
$719$	−24.7071	−	42.7939i	−0.921418	−	1.59594i	−0.124194	−	0.992258i	$-0.539635\pi$
$720$	1.88849	−	17.9678i	0.0703798	−	0.669619i
$721$	22.8071	−	16.5703i	0.849380	−	0.617111i
$722$	−5.42283	−	51.5948i	−0.201817	−	1.92016i
$723$	2.47062	+	2.74390i	0.0918832	+	0.102047i
$724$	−35.6186	+	15.8584i	−1.32376	+	0.589374i
$725$	−0.295380	+	0.0627849i	−0.0109701	+	0.00233177i
$726$	29.8954	+	6.35447i	1.10952	+	0.235836i
$727$	23.0214	+	10.2498i	0.853816	+	0.380143i	0.786502	−	0.617588i	$-0.211890\pi$
$727$	23.0214	+	10.2498i	0.853816	+	0.380143i	0.0673147	+	0.997732i	$0.478557\pi$
$728$	41.2668	+	127.006i	1.52945	+	4.70716i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	16.6137	+	7.39690i	0.614901	+	0.273771i
$731$	−19.0509	−	4.04940i	−0.704624	−	0.149773i
$732$	−68.1894	+	14.4941i	−2.52035	+	0.535717i
$733$	−17.2098	+	7.66230i	−0.635659	+	0.283014i	−0.699157	−	0.714968i	$-0.746441\pi$
$733$	−17.2098	+	7.66230i	−0.635659	+	0.283014i	0.0634979	+	0.997982i	$0.479774\pi$
$734$	38.4294	+	42.6802i	1.41846	+	1.57535i
$735$	−0.277499	−	2.64023i	−0.0102357	−	0.0973862i
$736$	98.0576	−	71.2430i	3.61445	−	2.62605i
$737$	0.211543	−	2.01270i	0.00779230	−	0.0741387i
$738$	−2.09299	−	3.62516i	−0.0770438	−	0.133444i
$739$	16.6168	−	28.7812i	0.611260	−	1.05873i	−0.379769	−	0.925081i	$-0.623996\pi$
$739$	16.6168	−	28.7812i	0.611260	−	1.05873i	0.991028	−	0.133651i	$-0.0426702\pi$
$740$	17.0317	+	12.3743i	0.626098	+	0.454887i
$741$	−24.7361	+	27.4722i	−0.908703	+	1.00922i
$742$	−16.7795	+	51.6420i	−0.615995	+	1.89584i
$743$	−36.3183			−1.33239			−0.666195	−	0.745778i	$-0.732078\pi$
$743$	−36.3183			−1.33239			−0.666195	+	0.745778i	$0.732078\pi$
$744$	−10.3764	−	58.2262i	−0.380416	−	2.13468i
$745$	19.2860			0.706585
$746$	−2.91563	+	8.97340i	−0.106749	+	0.328539i
$747$	7.58303	−	8.42180i	0.277448	−	0.308138i
$748$	4.64376	+	3.37389i	0.169793	+	0.123362i
$749$	0.329955	−	0.571499i	0.0120563	−	0.0208821i
$750$	1.39667	+	2.41911i	0.0509993	+	0.0883334i
$751$	−1.24297	+	11.8260i	−0.0453565	+	0.431538i	0.948155	+	0.317808i	$0.102947\pi$
$751$	−1.24297	+	11.8260i	−0.0453565	+	0.431538i	−0.993512	+	0.113731i	$0.963720\pi$
$752$	−13.3478	+	9.69777i	−0.486745	+	0.353641i
$753$	1.88753	+	17.9586i	0.0687854	+	0.654449i
$754$	−3.40406	−	3.78060i	−0.123969	−	0.137681i
$755$	−6.80533	+	3.02993i	−0.247671	+	0.110270i
$756$	11.8317	−	2.51491i	0.430315	−	0.0914662i
$757$	−41.0668	−	8.72902i	−1.49260	−	0.317262i	−0.611899	−	0.790936i	$-0.709594\pi$
$757$	−41.0668	−	8.72902i	−1.49260	−	0.317262i	−0.880700	+	0.473674i	$0.842927\pi$
$758$	0.890346	+	0.396408i	0.0323388	+	0.0143982i
$759$	0.310106	+	0.954407i	0.0112561	+	0.0346428i
$760$	−20.1207	−	61.9251i	−0.729854	−	2.24626i
$761$	−30.7207	−	13.6777i	−1.11362	−	0.495818i	−0.234359	−	0.972150i	$-0.575299\pi$
$761$	−30.7207	−	13.6777i	−1.11362	−	0.495818i	−0.879265	+	0.476332i	$0.841966\pi$
$762$	44.7591	+	9.51385i	1.62145	+	0.344650i
$763$	−33.5631	+	7.13406i	−1.21507	+	0.258270i
$764$	−46.0953	+	20.5229i	−1.66767	+	0.742494i
$765$	−2.73576	−	3.03837i	−0.0989116	−	0.109853i
$766$	−4.35914	−	41.4744i	−0.157502	−	1.49853i
$767$	50.5355	−	36.7162i	1.82473	−	1.32574i
$768$	−10.5294	+	100.180i	−0.379946	+	3.61494i
$769$	18.5594	+	32.1459i	0.669271	+	1.15921i	0.978108	+	0.208096i	$0.0667267\pi$
$769$	18.5594	+	32.1459i	0.669271	+	1.15921i	−0.308838	+	0.951115i	$0.599940\pi$
$770$	0.704384	−	1.22003i	0.0253842	−	0.0439668i
$771$	−2.47025	−	1.79474i	−0.0889640	−	0.0646361i
$772$	−66.8916	+	74.2906i	−2.40748	+	2.67378i
$773$	9.31703	−	28.6749i	0.335110	−	1.03136i	−0.631557	−	0.775329i	$-0.717584\pi$
$773$	9.31703	−	28.6749i	0.335110	−	1.03136i	0.966668	−	0.256034i	$-0.0824160\pi$
$774$	13.3067			0.478298
$775$	4.01216	+	3.86038i	0.144121	+	0.138669i
$776$	180.069			6.46411
$777$	−2.33697	+	7.19245i	−0.0838383	+	0.258028i
$778$	−27.1670	+	30.1720i	−0.973985	+	1.08172i
$779$	−7.43127	−	5.39914i	−0.266253	−	0.193444i
$780$	−17.4982	+	30.3077i	−0.626534	+	1.08519i
$781$	0.492270	+	0.852637i	0.0176148	+	0.0305098i
$782$	4.95160	−	47.1113i	0.177069	−	1.68470i
$783$	−0.244306	+	0.177499i	−0.00873078	+	0.00634328i
$784$	5.01350	+	47.7002i	0.179053	+	1.70358i
$785$	4.54520	+	5.04796i	0.162225	+	0.180169i
$786$	14.5230	−	6.46605i	0.518018	−	0.230636i
$787$	24.3348	−	5.17251i	0.867441	−	0.184380i	0.247365	−	0.968922i	$-0.420435\pi$
$787$	24.3348	−	5.17251i	0.867441	−	0.184380i	0.620075	+	0.784542i	$0.287102\pi$
$788$	79.9982	+	17.0041i	2.84982	+	0.605748i
$789$	7.43435	+	3.30998i	0.264670	+	0.117839i
$790$	0.430967	+	1.32638i	0.0153331	+	0.0471904i
$791$	−0.960477	−	2.95604i	−0.0341506	−	0.105105i
$792$	−2.34782	−	1.04532i	−0.0834262	−	0.0371437i
$793$	70.8706	+	15.0640i	2.51669	+	0.534939i
$794$	−75.0682	+	15.9562i	−2.66407	+	0.566265i
$795$	−8.51914	+	3.79296i	−0.302143	+	0.134523i
$796$	−23.6198	−	26.2324i	−0.837181	−	0.929783i
$797$	2.29940	+	21.8773i	0.0814488	+	0.774933i	0.956663	+	0.291198i	$0.0940538\pi$
$797$	2.29940	+	21.8773i	0.0814488	+	0.774933i	−0.875214	+	0.483736i	$0.839280\pi$
$798$	28.8751	−	20.9790i	1.02217	−	0.742647i
$799$	−0.390279	+	3.71326i	−0.0138071	+	0.131366i
$800$	−14.6108	−	25.3067i	−0.516571	−	0.894727i
$801$	6.83169	−	11.8328i	0.241386	−	0.418093i
$802$	2.45262	+	1.78193i	0.0866051	+	0.0629223i
$803$	1.05398	−	1.17056i	0.0371940	−	0.0413081i
$804$	14.9994	−	46.1635i	0.528989	−	1.62806i
$805$	−8.64620			−0.304738
$806$	−22.5257	+	91.0526i	−0.793434	+	3.20719i
$807$	3.41411			0.120182
$808$	23.7163	−	72.9911i	0.834335	−	2.56782i
$809$	−16.5493	+	18.3798i	−0.581841	+	0.646200i	−0.960152	−	0.279478i	$-0.909838\pi$
$809$	−16.5493	+	18.3798i	−0.581841	+	0.646200i	0.378311	+	0.925679i	$0.376505\pi$
$810$	2.25986	+	1.64189i	0.0794035	+	0.0576901i
$811$	17.7623	−	30.7652i	0.623719	−	1.08031i	−0.365068	−	0.930981i	$-0.618954\pi$
$811$	17.7623	−	30.7652i	0.623719	−	1.08031i	0.988787	−	0.149333i	$-0.0477125\pi$
$812$	1.82637	+	3.16337i	0.0640931	+	0.111012i
$813$	−0.0402327	+	0.382788i	−0.00141102	+	0.0134250i
$814$	1.98360	−	1.44117i	0.0695253	−	0.0505131i
$815$	0.501990	+	4.77611i	0.0175839	+	0.167300i
$816$	49.4262	+	54.8934i	1.73026	+	1.92165i
$817$	26.6753	−	11.8766i	0.933250	−	0.415510i
$818$	−33.2989	+	7.07789i	−1.16427	+	0.247473i
$819$	−12.2969	−	2.61379i	−0.429690	−	0.0913333i
$820$	−7.94398	−	3.53689i	−0.277416	−	0.123513i
$821$	12.4052	+	38.1794i	0.432946	+	1.33247i	0.895177	+	0.445711i	$0.147049\pi$
$821$	12.4052	+	38.1794i	0.432946	+	1.33247i	−0.462231	+	0.886759i	$0.652951\pi$
$822$	−7.53906	−	23.2028i	−0.262955	−	0.809292i
$823$	28.2352	+	12.5711i	0.984218	+	0.438202i	0.834789	−	0.550570i	$-0.185590\pi$
$823$	28.2352	+	12.5711i	0.984218	+	0.438202i	0.149430	+	0.988772i	$0.452256\pi$
$824$	−140.519	−	29.8683i	−4.89523	−	1.04051i
$825$	0.236653	−	0.0503022i	0.00823922	−	0.00175130i
$826$	−55.0953	+	24.5300i	−1.91701	+	0.853508i
$827$	22.2673	+	24.7303i	0.774308	+	0.859957i	0.993275	−	0.115776i	$-0.0369353\pi$
$827$	22.2673	+	24.7303i	0.774308	+	0.859957i	−0.218967	+	0.975732i	$0.570269\pi$
$828$	2.51588	+	23.9370i	0.0874328	+	0.831868i
$829$	31.3304	−	22.7629i	1.08815	−	0.790587i	0.109064	−	0.994035i	$-0.465215\pi$
$829$	31.3304	−	22.7629i	1.08815	−	0.790587i	0.979086	+	0.203448i	$0.0652148\pi$
$830$	3.30896	−	31.4826i	0.114856	−	1.09278i
$831$	13.2956	+	23.0287i	0.461220	+	0.798857i
$832$	137.182	−	237.607i	4.75594	−	8.23752i
$833$	8.78115	+	6.37988i	0.304249	+	0.221050i
$834$	14.7526	−	16.3845i	0.510842	−	0.567348i
$835$	2.53874	−	7.81342i	0.0878566	−	0.270395i
$836$	−8.60556			−0.297629
$837$	5.23545	+	1.89474i	0.180964	+	0.0654919i
$838$	−95.4704			−3.29797
$839$	−12.9143	+	39.7461i	−0.445851	+	1.37219i	0.435698	+	0.900093i	$0.356502\pi$
$839$	−12.9143	+	39.7461i	−0.445851	+	1.37219i	−0.881548	+	0.472094i	$0.843498\pi$
$840$	14.8164	−	16.4553i	0.511216	−	0.567762i
$841$	23.3877	+	16.9922i	0.806473	+	0.585937i
$842$	39.0209	−	67.5862i	1.34475	−	2.32917i
$843$	−4.53144	−	7.84868i	−0.156071	−	0.270323i
$844$	5.36041	−	51.0009i	0.184513	−	1.75552i
$845$	18.9087	−	13.7379i	0.650477	−	0.472600i
$846$	−0.266645	−	2.53695i	−0.00916743	−	0.0872223i
$847$	15.2613	+	16.9494i	0.524386	+	0.582390i
$848$	153.913	−	68.5264i	5.28539	−	2.35321i
$849$	−18.6921	+	3.97313i	−0.641511	+	0.136357i
$850$	−11.1711	−	2.37449i	−0.383166	−	0.0814444i
$851$	−13.7472	−	6.12063i	−0.471247	−	0.209813i
$852$	7.29699	+	22.4578i	0.249991	+	0.769393i
$853$	−11.8258	−	36.3962i	−0.404909	−	1.24618i	−0.920971	−	0.389630i	$-0.872603\pi$
$853$	−11.8258	−	36.3962i	−0.404909	−	1.24618i	0.516062	−	0.856551i	$-0.327397\pi$
$854$	−63.9054	−	28.4525i	−2.18680	−	0.973625i
$855$	5.99568	+	1.27442i	0.205048	+	0.0435843i
$856$	−3.28935	+	0.699172i	−0.112428	+	0.0238972i
$857$	−19.4134	+	8.64340i	−0.663149	+	0.295253i	−0.710575	−	0.703622i	$-0.751565\pi$
$857$	−19.4134	+	8.64340i	−0.663149	+	0.295253i	0.0474259	+	0.998875i	$0.484898\pi$
$858$	2.72728	+	3.02895i	0.0931079	+	0.103407i
$859$	−0.310167	−	2.95105i	−0.0105828	−	0.100688i	0.987955	−	0.154739i	$-0.0494536\pi$
$859$	−0.310167	−	2.95105i	−0.0105828	−	0.100688i	−0.998538	+	0.0540502i	$0.982787\pi$
$860$	22.3634	−	16.2480i	0.762587	−	0.554052i
$861$	0.326522	−	3.10665i	0.0111278	−	0.105874i
$862$	46.9885	+	81.3864i	1.60043	+	2.77203i
$863$	−23.0981	+	40.0071i	−0.786269	+	1.36186i	0.141968	+	0.989871i	$0.454657\pi$
$863$	−23.0981	+	40.0071i	−0.786269	+	1.36186i	−0.928238	+	0.371987i	$0.878676\pi$
$864$	−23.6408	−	17.1761i	−0.804277	−	0.584341i
$865$	11.0893	−	12.3159i	0.377048	−	0.418755i
$866$	7.89374	−	24.2944i	0.268240	−	0.825558i
$867$	−0.283919			−0.00964239
$868$	29.4129	−	60.5856i	0.998340	−	2.05641i
$869$	0.120794			0.00409765
$870$	−0.260665	+	0.802245i	−0.00883738	+	0.0271987i
$871$	−33.7562	+	37.4900i	−1.14378	+	1.27030i
$872$	141.461	+	102.777i	4.79046	+	3.48047i
$873$	−8.47585	+	14.6806i	−0.286864	+	0.496863i
$874$	35.5098	+	61.5047i	1.20114	+	2.08043i
$875$	−0.217892	+	2.07310i	−0.00736609	+	0.0700837i
$876$	30.5637	−	22.2058i	1.03265	−	0.750265i
$877$	4.79637	+	45.6344i	0.161962	+	1.54097i	0.709813	+	0.704390i	$0.248779\pi$
$877$	4.79637	+	45.6344i	0.161962	+	1.54097i	−0.547851	+	0.836576i	$0.684554\pi$
$878$	30.0620	+	33.3872i	1.01454	+	1.12676i
$879$	15.6092	−	6.94968i	0.526486	−	0.234407i
$880$	−4.27555	+	0.908797i	−0.144129	+	0.0306355i
$881$	1.64665	+	0.350006i	0.0554770	+	0.0117920i	0.235567	−	0.971858i	$-0.424305\pi$
$881$	1.64665	+	0.350006i	0.0554770	+	0.0117920i	−0.180090	+	0.983650i	$0.557639\pi$
$882$	−6.77457	−	3.01623i	−0.228112	−	0.101562i
$883$	4.31462	+	13.2790i	0.145199	+	0.446875i	0.997036	−	0.0769301i	$-0.0245118\pi$
$883$	4.31462	+	13.2790i	0.145199	+	0.446875i	−0.851838	+	0.523806i	$0.824512\pi$
$884$	−44.2152	−	136.080i	−1.48712	−	4.57688i
$885$	−9.46200	−	4.21276i	−0.318062	−	0.141610i
$886$	17.0754	+	3.62950i	0.573661	+	0.121935i
$887$	47.9687	−	10.1961i	1.61063	−	0.342350i	0.687305	−	0.726369i	$-0.258794\pi$
$887$	47.9687	−	10.1961i	1.61063	−	0.342350i	0.923325	+	0.384019i	$0.125460\pi$
$888$	35.2063	−	15.6749i	1.18145	−	0.526014i
$889$	22.8491	+	25.3765i	0.766336	+	0.851102i
$890$	−3.98949	−	37.9575i	−0.133728	−	1.27234i
$891$	0.195734	−	0.142209i	0.00655733	−	0.00476418i
$892$	12.6159	−	120.033i	0.422413	−	4.01899i
$893$	−2.79884	−	4.84773i	−0.0936595	−	0.162223i
$894$	26.9362	−	46.6549i	0.900883	−	1.56037i
$895$	−9.94617	−	7.22632i	−0.332464	−	0.241549i
$896$	−95.7314	+	106.320i	−3.19816	+	3.55192i
$897$	7.73013	−	23.7909i	0.258102	−	0.794355i
$898$	−24.0273			−0.801801
$899$	−0.0556140	+	1.68043i	−0.00185483	+	0.0560453i
$900$	5.80278			0.193426
$901$	11.7819	−	36.2609i	0.392512	−	1.20803i
$902$	−0.677666	+	0.752624i	−0.0225638	+	0.0250596i
$903$	8.03357	+	5.83673i	0.267341	+	0.194234i
$904$	−7.91944	+	13.7169i	−0.263397	+	0.456216i
$905$	−3.35955	−	5.81891i	−0.111675	−	0.193427i
$906$	−2.17510	+	20.6947i	−0.0722627	+	0.687534i
$907$	−2.99420	+	2.17541i	−0.0994207	+	0.0722333i	−0.636385	−	0.771372i	$-0.719571\pi$
$907$	−2.99420	+	2.17541i	−0.0994207	+	0.0722333i	0.536964	+	0.843605i	$0.319571\pi$
$908$	8.78792	+	83.6115i	0.291637	+	2.77474i
$909$	4.83446	+	5.36922i	0.160349	+	0.178086i
$910$	−32.0810	+	14.2834i	−1.06347	+	0.473489i
$911$	15.9714	−	3.39483i	0.529156	−	0.112476i	0.0644168	−	0.997923i	$-0.479481\pi$
$911$	15.9714	−	3.39483i	0.529156	−	0.112476i	0.464740	+	0.885447i	$0.346148\pi$
$912$	−108.322	−	23.0246i	−3.58691	−	0.762422i
$913$	−2.50478	−	1.11520i	−0.0828962	−	0.0369078i
$914$	4.00406	+	12.3232i	0.132442	+	0.407616i
$915$	−3.71243	−	11.4257i	−0.122729	−	0.377722i
$916$	−94.6998	−	42.1631i	−3.12897	−	1.39311i
$917$	11.6041	+	2.46653i	0.383202	+	0.0814520i
$918$	−11.1711	+	2.37449i	−0.368702	+	0.0783700i
$919$	−7.95328	+	3.54103i	−0.262354	+	0.116808i	−0.533699	−	0.845675i	$-0.679198\pi$
$919$	−7.95328	+	3.54103i	−0.262354	+	0.116808i	0.271344	+	0.962482i	$0.412532\pi$
$920$	29.4819	+	32.7430i	0.971991	+	1.07951i
$921$	−0.440274	−	4.18892i	−0.0145075	−	0.138030i
$922$	−63.1465	+	45.8786i	−2.07962	+	1.51093i
$923$	2.56534	−	24.4076i	0.0844393	−	0.803387i
$924$	−1.46326	−	2.53444i	−0.0481377	−	0.0833769i
$925$	−1.81399	+	3.14192i	−0.0596435	+	0.103306i
$926$	−6.90981	−	5.02027i	−0.227070	−	0.164976i
$927$	9.04933	−	10.0503i	0.297219	−	0.330095i
$928$	2.72686	−	8.39242i	0.0895136	−	0.275495i
$929$	−30.0814			−0.986938			−0.493469	−	0.869763i	$-0.664271\pi$
$929$	−30.0814			−0.986938			−0.493469	+	0.869763i	$0.664271\pi$
$930$	14.9424	−	4.31416i	0.489980	−	0.141467i
$931$	−16.2727			−0.533318
$932$	39.5433	−	121.702i	1.29528	−	3.98647i
$933$	−17.8686	+	19.8451i	−0.584993	+	0.649701i
$934$	−15.2190	−	11.0573i	−0.497981	−	0.361804i
$935$	−0.494590	+	0.856656i	−0.0161748	+	0.0280156i
$936$	32.0319	+	55.4808i	1.04699	+	1.81345i
$937$	2.42323	−	23.0555i	0.0791634	−	0.753189i	−0.880880	−	0.473339i	$-0.843049\pi$
$937$	2.42323	−	23.0555i	0.0791634	−	0.753189i	0.960044	−	0.279850i	$-0.0902848\pi$
$938$	39.4044	−	28.6290i	1.28660	−	0.934770i
$939$	1.87389	+	17.8289i	0.0611522	+	0.581825i
$940$	−3.54585	−	3.93807i	−0.115653	−	0.128446i
$941$	−24.3914	+	10.8597i	−0.795135	+	0.354017i	−0.763768	−	0.645491i	$-0.776653\pi$
$941$	−24.3914	+	10.8597i	−0.795135	+	0.354017i	−0.0313674	+	0.999508i	$0.509986\pi$
$942$	18.5597	−	3.94499i	0.604709	−	0.128535i
$943$	6.07987	+	1.29232i	0.197988	+	0.0420836i
$944$	170.947	+	76.1107i	5.56387	+	2.47719i
$945$	0.644153	+	1.98250i	0.0209543	+	0.0644907i
$946$	−0.994856	−	3.06185i	−0.0323456	−	0.0995494i
$947$	21.2095	+	9.44310i	0.689218	+	0.306859i	0.721297	−	0.692626i	$-0.243546\pi$
$947$	21.2095	+	9.44310i	0.689218	+	0.306859i	−0.0320794	+	0.999485i	$0.510213\pi$
$948$	2.83385	+	0.602354i	0.0920392	+	0.0195635i
$949$	−38.4062	+	8.16350i	−1.24672	+	0.264998i
$950$	15.6419	−	6.96422i	0.507490	−	0.225949i
$951$	2.03866	+	2.26416i	0.0661081	+	0.0734205i
$952$	9.46313	+	90.0356i	0.306702	+	2.91807i
$953$	21.7059	−	15.7703i	0.703124	−	0.510850i	−0.177824	−	0.984062i	$-0.556906\pi$
$953$	21.7059	−	15.7703i	0.703124	−	0.510850i	0.880948	+	0.473213i	$0.156906\pi$
$954$	−2.72286	+	25.9062i	−0.0881557	+	0.838746i
$955$	−4.34771	−	7.53045i	−0.140688	−	0.243680i
$956$	−37.4680	+	64.8964i	−1.21180	+	2.09890i
$957$	0.0591075	+	0.0429441i	0.00191067	+	0.00138818i
$958$	−23.6806	+	26.2999i	−0.765084	+	0.849712i
$959$	5.62599	−	17.3150i	0.181673	−	0.559131i
$960$	−45.4927			−1.46827
$961$	26.2294	−	16.5233i	0.846110	−	0.533008i
$962$	−61.1188			−1.97055
$963$	0.0978275	−	0.301082i	0.00315245	−	0.00970224i
$964$	14.3365	−	15.9222i	0.461746	−	0.512821i
$965$	−13.9374	−	10.1261i	−0.448661	−	0.325971i
$966$	−12.0759	+	20.9161i	−0.388536	+	0.672964i
$967$	−4.82197	−	8.35190i	−0.155064	−	0.268579i	0.778018	−	0.628242i	$-0.216225\pi$
$967$	−4.82197	−	8.35190i	−0.155064	−	0.268579i	−0.933082	+	0.359663i	$0.882892\pi$
$968$	12.1489	−	115.589i	0.390480	−	3.71517i
$969$	−20.2749	+	14.7306i	−0.651324	+	0.473215i
$970$	4.94963	+	47.0926i	0.158923	+	1.51205i
$971$	34.0728	+	37.8417i	1.09345	+	1.21440i	0.975179	+	0.221418i	$0.0710684\pi$
$971$	34.0728	+	37.8417i	1.09345	+	1.21440i	0.118271	+	0.992981i	$0.462265\pi$
$972$	5.30111	−	2.36020i	0.170033	−	0.0757036i
$973$	16.0933	−	3.42074i	0.515928	−	0.109664i
$974$	−18.5913	−	3.95171i	−0.595705	−	0.126621i
$975$	−5.50955	−	2.45301i	−0.176447	−	0.0785592i
$976$	67.0715	+	206.425i	2.14691	+	6.60750i
$977$	−0.507558	−	1.56210i	−0.0162382	−	0.0499761i	0.942609	−	0.333898i	$-0.108364\pi$
$977$	−0.507558	−	1.56210i	−0.0162382	−	0.0499761i	−0.958847	+	0.283922i	$0.908364\pi$
$978$	12.2551	+	5.45630i	0.391873	+	0.174473i
$979$	−3.23349	−	0.687299i	−0.103343	−	0.0219662i
$980$	−15.0684	+	3.20289i	−0.481343	+	0.102313i
$981$	−15.0377	+	6.69522i	−0.480117	+	0.213762i
$982$	−1.99971	−	2.22090i	−0.0638133	−	0.0708719i
$983$	2.95809	+	28.1443i	0.0943483	+	0.897664i	0.934656	+	0.355554i	$0.115708\pi$
$983$	2.95809	+	28.1443i	0.0943483	+	0.897664i	−0.840307	+	0.542110i	$0.817626\pi$
$984$	−12.8782	+	9.35656i	−0.410542	+	0.298276i
$985$	−1.47324	+	14.0170i	−0.0469414	+	0.446618i
$986$	−1.72440	−	2.98675i	−0.0549161	−	0.0951175i
$987$	0.951809	−	1.64858i	0.0302964	−	0.0524750i
$988$	173.546	+	126.088i	5.52123	+	4.01141i
$989$	−13.2213	+	14.6837i	−0.420413	+	0.466916i
$990$	0.208841	−	0.642746i	0.00663740	−	0.0204278i
$991$	18.1458			0.576419			0.288210	−	0.957567i	$-0.406940\pi$
$991$	18.1458			0.576419			0.288210	+	0.957567i	$0.406940\pi$
$992$	−156.315	+	45.1311i	−4.96299	+	1.43291i
$993$	−14.0113			−0.444636
$994$	−7.32215	+	22.5353i	−0.232245	+	0.714775i
$995$	4.07042	−	4.52066i	0.129041	−	0.143315i
$996$	−53.2017	−	38.6533i	−1.68576	−	1.22478i
$997$	−19.5402	+	33.8447i	−0.618846	+	1.07187i	0.370851	+	0.928692i	$0.379066\pi$
$997$	−19.5402	+	33.8447i	−0.618846	+	1.07187i	−0.989697	+	0.143180i	$0.954267\pi$
$998$	−31.0408	−	53.7642i	−0.982578	−	1.70187i
$999$	−0.379226	+	3.60810i	−0.0119982	+	0.114155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.bg.c.76.6	✓	48
31.20	even	15	inner	465.2.bg.c.361.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.bg.c.76.6	✓	48	1.1	even	1	trivial
465.2.bg.c.361.6	yes	48	31.20	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.863191 - 2.65663i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-4.69455 - 3.41079i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.39667 - 2.41911i) q^{6} +(0.217892 - 2.07310i) q^{7} +(-8.59378 + 6.24374i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.863191 - 2.65663i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-4.69455 - 3.41079i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.39667 - 2.41911i) q^{6} +(0.217892 - 2.07310i) q^{7} +(-8.59378 + 6.24374i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.86911 - 2.07586i) q^{10} +(-0.221024 + 0.0984060i) q^{11} +(-5.67598 + 1.20647i) q^{12} +(5.89916 + 1.25391i) q^{13} +(-5.31938 - 2.36834i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(5.58293 + 17.1825i) q^{16} +(3.73506 + 1.66296i) q^{17} +(-2.73230 - 0.580769i) q^{18} +(-5.99568 + 1.27442i) q^{19} +(-5.30111 + 2.36020i) q^{20} +(-1.39482 - 1.54910i) q^{21} +(0.0706428 + 0.672121i) q^{22} +(3.35565 - 2.43802i) q^{23} +(-1.11035 + 10.5643i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(8.42327 - 14.5895i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-8.09382 + 8.98910i) q^{28} +(0.0933165 - 0.287199i) q^{29} -2.79335 q^{30} +(-5.34927 + 1.54444i) q^{31} +29.2216 q^{32} +(-0.0747637 + 0.230099i) q^{33} +(7.64193 - 8.48722i) q^{34} +(-1.68641 - 1.22525i) q^{35} +(-2.90139 + 5.02536i) q^{36} +(-1.81399 - 3.14192i) q^{37} +(-1.78975 + 17.0284i) q^{38} +(4.87914 - 3.54490i) q^{39} +(1.11035 + 10.5643i) q^{40} +(1.00273 + 1.11364i) q^{41} +(-5.31938 + 2.36834i) q^{42} +(-4.65960 + 0.990430i) q^{43} +(1.37325 + 0.291893i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(-3.58035 - 11.0192i) q^{46} +(0.282199 + 0.868520i) q^{47} +(16.5048 + 7.34840i) q^{48} +(2.59676 + 0.551958i) q^{49} +(-2.73230 + 0.580769i) q^{50} +(3.73506 - 1.66296i) q^{51} +(-23.4171 - 26.0073i) q^{52} +(-0.974765 - 9.27427i) q^{53} +(-2.25986 + 1.64189i) q^{54} +(-0.0252897 + 0.240615i) q^{55} +(11.0714 + 19.1762i) q^{56} +(-3.06481 + 5.30841i) q^{57} +(-0.682431 - 0.495815i) q^{58} +(6.93049 - 7.69709i) q^{59} +(-1.79316 + 5.51877i) q^{60} +12.0137 q^{61} +(-0.514438 + 15.5442i) q^{62} -2.08452 q^{63} +(14.0580 - 43.2661i) q^{64} +(4.03549 - 4.48187i) q^{65} +(0.546753 + 0.397239i) q^{66} +(-4.18241 + 7.24414i) q^{67} +(-11.8624 - 20.5463i) q^{68} +(0.433564 - 4.12509i) q^{69} +(-4.71074 + 3.42255i) q^{70} +(-0.425363 - 4.04706i) q^{71} +(7.10783 + 7.89405i) q^{72} +(-5.94760 + 2.64804i) q^{73} +(-9.91273 + 2.10702i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(32.4938 + 14.4672i) q^{76} +(0.155847 + 0.479646i) q^{77} +(-5.20587 - 16.0220i) q^{78} +(-0.456107 - 0.203072i) q^{79} +(17.6719 + 3.75628i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(3.82407 - 1.70259i) q^{82} +(7.58303 + 8.42180i) q^{83} +(1.26438 + 12.0298i) q^{84} +(3.30769 - 2.40318i) q^{85} +(-1.39093 + 13.2338i) q^{86} +(-0.150989 - 0.261521i) q^{87} +(1.28500 - 2.22569i) q^{88} +(11.0539 + 8.03113i) q^{89} +(-1.86911 + 2.07586i) q^{90} +(3.88485 - 11.9564i) q^{91} -24.0688 q^{92} +(-2.43162 + 5.00872i) q^{93} +2.55093 q^{94} +(-1.89416 + 5.82962i) q^{95} +(19.5531 - 21.7159i) q^{96} +(-13.7142 - 9.96396i) q^{97} +(3.70784 - 6.42218i) q^{98} +(0.120970 + 0.209527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 6 q^{3} - 10 q^{4} + 24 q^{5} - 4 q^{6} - 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 48 * q - 2 * q^2 + 6 * q^3 - 10 * q^4 + 24 * q^5 - 4 * q^6 - 5 * q^7 - 6 * q^8 + 6 * q^9	\( 48 q - 2 q^{2} + 6 q^{3} - 10 q^{4} + 24 q^{5} - 4 q^{6} - 5 q^{7} - 6 q^{8} + 6 q^{9} - q^{10} + 17 q^{11} - 5 q^{12} + 7 q^{13} - 9 q^{14} + 12 q^{15} - 26 q^{16} + 24 q^{17} + q^{18} - 2 q^{19} - 5 q^{20} + 10 q^{21} + q^{22} - 6 q^{23} + 3 q^{24} - 24 q^{25} - 15 q^{26} - 12 q^{27} + 95 q^{28} - 32 q^{29} - 8 q^{30} - 13 q^{31} + 56 q^{32} - 14 q^{33} - 66 q^{34} - 10 q^{35} - 30 q^{36} + 14 q^{37} - 4 q^{38} + 21 q^{39} - 3 q^{40} - 20 q^{41} - 9 q^{42} - 28 q^{43} + 74 q^{44} - 6 q^{45} - 53 q^{46} - 45 q^{47} + 53 q^{48} + 61 q^{49} + q^{50} + 24 q^{51} - 78 q^{52} + 7 q^{53} - 2 q^{54} + 13 q^{55} - 11 q^{56} - 7 q^{57} - 73 q^{58} + 56 q^{59} + 20 q^{60} + 26 q^{61} + 26 q^{62} + 20 q^{63} - 80 q^{64} - 7 q^{65} + 13 q^{66} - 46 q^{67} - 66 q^{68} + 3 q^{69} - 48 q^{70} + 72 q^{71} + 3 q^{72} + 23 q^{73} - 64 q^{74} + 6 q^{75} - 74 q^{76} - 60 q^{77} - 20 q^{78} + 34 q^{79} + 17 q^{80} + 6 q^{81} + 108 q^{82} - 25 q^{83} + 15 q^{84} + 18 q^{85} + 130 q^{86} - 4 q^{87} - 25 q^{88} - 18 q^{89} - q^{90} + 33 q^{91} + 52 q^{92} - 22 q^{93} - 72 q^{94} + 11 q^{95} + 32 q^{96} - 79 q^{97} - 37 q^{98} - 18 q^{99}+O(q^{100}) \) 48 * q - 2 * q^2 + 6 * q^3 - 10 * q^4 + 24 * q^5 - 4 * q^6 - 5 * q^7 - 6 * q^8 + 6 * q^9 - q^10 + 17 * q^11 - 5 * q^12 + 7 * q^13 - 9 * q^14 + 12 * q^15 - 26 * q^16 + 24 * q^17 + q^18 - 2 * q^19 - 5 * q^20 + 10 * q^21 + q^22 - 6 * q^23 + 3 * q^24 - 24 * q^25 - 15 * q^26 - 12 * q^27 + 95 * q^28 - 32 * q^29 - 8 * q^30 - 13 * q^31 + 56 * q^32 - 14 * q^33 - 66 * q^34 - 10 * q^35 - 30 * q^36 + 14 * q^37 - 4 * q^38 + 21 * q^39 - 3 * q^40 - 20 * q^41 - 9 * q^42 - 28 * q^43 + 74 * q^44 - 6 * q^45 - 53 * q^46 - 45 * q^47 + 53 * q^48 + 61 * q^49 + q^50 + 24 * q^51 - 78 * q^52 + 7 * q^53 - 2 * q^54 + 13 * q^55 - 11 * q^56 - 7 * q^57 - 73 * q^58 + 56 * q^59 + 20 * q^60 + 26 * q^61 + 26 * q^62 + 20 * q^63 - 80 * q^64 - 7 * q^65 + 13 * q^66 - 46 * q^67 - 66 * q^68 + 3 * q^69 - 48 * q^70 + 72 * q^71 + 3 * q^72 + 23 * q^73 - 64 * q^74 + 6 * q^75 - 74 * q^76 - 60 * q^77 - 20 * q^78 + 34 * q^79 + 17 * q^80 + 6 * q^81 + 108 * q^82 - 25 * q^83 + 15 * q^84 + 18 * q^85 + 130 * q^86 - 4 * q^87 - 25 * q^88 - 18 * q^89 - q^90 + 33 * q^91 + 52 * q^92 - 22 * q^93 - 72 * q^94 + 11 * q^95 + 32 * q^96 - 79 * q^97 - 37 * q^98 - 18 * q^99

Introduction

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