LMFDB - Embedded newform 378.2.bf.a.101.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.21
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(1.36829 - 1.06197i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.52794 + 1.28209i) q^{5} +(0.0660042 - 1.73079i) q^{6} +(2.53168 - 0.768505i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.744440 - 2.90617i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(1.36829 - 1.06197i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.52794 + 1.28209i) q^{5} +(0.0660042 - 1.73079i) q^{6} +(2.53168 - 0.768505i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.744440 - 2.90617i) q^{9} +1.99458i q^{10} +(-0.382485 + 0.455827i) q^{11} +(-1.28344 - 1.16309i) q^{12} +(1.84331 - 5.06446i) q^{13} +(1.03862 - 2.43336i) q^{14} +(-0.729119 + 3.37690i) q^{15} +(-0.939693 + 0.342020i) q^{16} -0.401268 q^{17} +(-1.74774 - 2.43832i) q^{18} +0.671957i q^{19} +(1.52794 + 1.28209i) q^{20} +(2.64794 - 3.74011i) q^{21} +(0.103328 + 0.586000i) q^{22} +(-0.520211 + 1.42927i) q^{23} +(-1.71596 + 0.235548i) q^{24} +(-0.177408 + 1.00613i) q^{25} +(-2.69474 - 4.66743i) q^{26} +(-2.06765 - 4.76705i) q^{27} +(-1.19645 - 2.35977i) q^{28} +(2.27212 + 6.24260i) q^{29} +(2.11818 + 2.72916i) q^{30} +(-2.61731 + 0.461502i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.0392752 + 1.02989i) q^{33} +(-0.257930 + 0.307389i) q^{34} +(-2.88295 + 4.42007i) q^{35} +(-2.99129 - 0.228479i) q^{36} +(-3.13338 + 5.42718i) q^{37} +(0.514749 + 0.431926i) q^{38} +(-2.85612 - 8.88719i) q^{39} +(1.96428 - 0.346355i) q^{40} +(5.17669 + 1.88416i) q^{41} +(-1.16302 - 4.43254i) q^{42} +(-0.883954 + 5.01315i) q^{43} +(0.515320 + 0.297520i) q^{44} +(2.58851 + 5.39488i) q^{45} +(0.760498 + 1.31722i) q^{46} +(-1.48049 + 8.39629i) q^{47} +(-0.922558 + 1.46591i) q^{48} +(5.81880 - 3.89122i) q^{49} +(0.656707 + 0.782633i) q^{50} +(-0.549051 + 0.426135i) q^{51} +(-5.30761 - 0.935874i) q^{52} +(3.91397 + 2.25973i) q^{53} +(-4.98084 - 1.48029i) q^{54} -1.18685i q^{55} +(-2.57675 - 0.600295i) q^{56} +(0.713598 + 0.919433i) q^{57} +(6.24260 + 2.27212i) q^{58} +(-11.1527 - 4.05925i) q^{59} +(3.45220 + 0.131651i) q^{60} +(-5.87906 - 1.03664i) q^{61} +(-1.32884 + 2.30162i) q^{62} +(-0.348723 - 7.92959i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.67663 + 10.1015i) q^{65} +(0.763697 + 0.692088i) q^{66} +(7.47548 - 6.27267i) q^{67} +(0.0696795 + 0.395172i) q^{68} +(0.806040 + 2.50810i) q^{69} +(1.53284 + 5.04963i) q^{70} +(6.48140 - 3.74204i) q^{71} +(-2.09779 + 2.14460i) q^{72} +(10.7027 - 6.17922i) q^{73} +(2.14336 + 5.88883i) q^{74} +(0.825737 + 1.56509i) q^{75} +(0.661749 - 0.116684i) q^{76} +(-0.618022 + 1.44795i) q^{77} +(-8.64386 - 3.52467i) q^{78} +(2.76496 + 2.32008i) q^{79} +(0.997290 - 1.72736i) q^{80} +(-7.89162 - 4.32693i) q^{81} +(4.77086 - 2.75446i) q^{82} +(6.67653 - 2.43006i) q^{83} +(-4.14310 - 1.95825i) q^{84} +(0.613112 - 0.514462i) q^{85} +(3.27210 + 3.89954i) q^{86} +(9.73838 + 6.12877i) q^{87} +(0.559155 - 0.203516i) q^{88} -16.8147 q^{89} +(5.79658 + 1.48484i) q^{90} +(0.774612 - 14.2382i) q^{91} +(1.49789 + 0.264118i) q^{92} +(-3.09113 + 3.41097i) q^{93} +(5.48029 + 6.53115i) q^{94} +(-0.861510 - 1.02671i) q^{95} +(0.529942 + 1.64899i) q^{96} +(-5.55525 - 0.979540i) q^{97} +(0.759407 - 6.95869i) q^{98} +(1.03997 + 1.45090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) $ 144 * q + 18 * q^6 - 12 * q^9	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	1.36829	−	1.06197i	0.789983	−	0.613129i
$3$	1.36829	−	1.06197i	0.789983	−	0.613129i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	−1.52794	+	1.28209i	−0.683314	+	0.573368i	−0.916973	−	0.398950i	$-0.869375\pi$
$5$	−1.52794	+	1.28209i	−0.683314	+	0.573368i	0.233659	+	0.972319i	$0.424930\pi$
$6$	0.0660042	−	1.73079i	0.0269461	−	0.706593i
$7$	2.53168	−	0.768505i	0.956885	−	0.290468i
$7$	2.53168	−	0.768505i	0.956885	−	0.290468i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.744440	−	2.90617i	0.248147	−	0.968723i
$10$			1.99458i			0.630741i
$11$	−0.382485	+	0.455827i	−0.115323	+	0.137437i	−0.820618	−	0.571478i	$-0.806370\pi$
$11$	−0.382485	+	0.455827i	−0.115323	+	0.137437i	0.705294	+	0.708915i	$0.250815\pi$
$12$	−1.28344	−	1.16309i	−0.370496	−	0.335756i
$13$	1.84331	−	5.06446i	0.511243	−	1.40463i	−0.368700	−	0.929548i	$-0.620197\pi$
$13$	1.84331	−	5.06446i	0.511243	−	1.40463i	0.879943	−	0.475080i	$-0.157581\pi$
$14$	1.03862	−	2.43336i	0.277584	−	0.650344i
$15$	−0.729119	+	3.37690i	−0.188258	+	0.871911i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.401268			−0.0973218			−0.0486609	−	0.998815i	$-0.515495\pi$
$17$	−0.401268			−0.0973218			−0.0486609	+	0.998815i	$0.515495\pi$
$18$	−1.74774	−	2.43832i	−0.411946	−	0.574718i
$19$			0.671957i			0.154158i	0.997025	+	0.0770788i	$0.0245593\pi$
$19$			0.671957i			0.154158i	−0.997025	+	0.0770788i	$0.975441\pi$
$20$	1.52794	+	1.28209i	0.341657	+	0.286684i
$21$	2.64794	−	3.74011i	0.577829	−	0.816158i
$22$	0.103328	+	0.586000i	0.0220295	+	0.124936i
$23$	−0.520211	+	1.42927i	−0.108472	+	0.298023i	−0.982038	−	0.188681i	$-0.939579\pi$
$23$	−0.520211	+	1.42927i	−0.108472	+	0.298023i	0.873567	+	0.486704i	$0.161801\pi$
$24$	−1.71596	+	0.235548i	−0.350269	+	0.0480809i
$25$	−0.177408	+	1.00613i	−0.0354817	+	0.201227i
$26$	−2.69474	−	4.66743i	−0.528482	−	0.915358i
$27$	−2.06765	−	4.76705i	−0.397920	−	0.917420i
$28$	−1.19645	−	2.35977i	−0.226108	−	0.445954i
$29$	2.27212	+	6.24260i	0.421922	+	1.15922i	0.950605	+	0.310403i	$0.100464\pi$
$29$	2.27212	+	6.24260i	0.421922	+	1.15922i	−0.528683	+	0.848819i	$0.677314\pi$
$30$	2.11818	+	2.72916i	0.386726	+	0.498275i
$31$	−2.61731	+	0.461502i	−0.470082	+	0.0828881i	−0.403671	−	0.914904i	$-0.632266\pi$
$31$	−2.61731	+	0.461502i	−0.470082	+	0.0828881i	−0.0664110	+	0.997792i	$0.521155\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−0.0392752	+	1.02989i	−0.00683693	+	0.179281i
$34$	−0.257930	+	0.307389i	−0.0442347	+	0.0527168i
$35$	−2.88295	+	4.42007i	−0.487308	+	0.747128i
$36$	−2.99129	−	0.228479i	−0.498548	−	0.0380799i
$37$	−3.13338	+	5.42718i	−0.515125	+	0.892222i	0.484721	+	0.874669i	$0.338921\pi$
$37$	−3.13338	+	5.42718i	−0.515125	+	0.892222i	−0.999846	+	0.0175536i	$0.994412\pi$
$38$	0.514749	+	0.431926i	0.0835033	+	0.0700676i
$39$	−2.85612	−	8.88719i	−0.457345	−	1.42309i
$40$	1.96428	−	0.346355i	0.310579	−	0.0547635i
$41$	5.17669	+	1.88416i	0.808463	+	0.294257i	0.712989	−	0.701175i	$-0.247341\pi$
$41$	5.17669	+	1.88416i	0.808463	+	0.294257i	0.0954744	+	0.995432i	$0.469563\pi$
$42$	−1.16302	−	4.43254i	−0.179458	−	0.683955i
$43$	−0.883954	+	5.01315i	−0.134802	+	0.764498i	0.840196	+	0.542283i	$0.182440\pi$
$43$	−0.883954	+	5.01315i	−0.134802	+	0.764498i	−0.974998	+	0.222215i	$0.928671\pi$
$44$	0.515320	+	0.297520i	0.0776874	+	0.0448528i
$45$	2.58851	+	5.39488i	0.385873	+	0.804221i
$46$	0.760498	+	1.31722i	0.112129	+	0.194214i
$47$	−1.48049	+	8.39629i	−0.215952	+	1.22472i	0.663295	+	0.748358i	$0.269157\pi$
$47$	−1.48049	+	8.39629i	−0.215952	+	1.22472i	−0.879247	+	0.476366i	$0.841954\pi$
$48$	−0.922558	+	1.46591i	−0.133160	+	0.211586i
$49$	5.81880	−	3.89122i	0.831257	−	0.555888i
$50$	0.656707	+	0.782633i	0.0928724	+	0.110681i
$51$	−0.549051	+	0.426135i	−0.0768826	+	0.0596708i
$52$	−5.30761	−	0.935874i	−0.736032	−	0.129782i
$53$	3.91397	+	2.25973i	0.537624	+	0.310398i	0.744116	−	0.668051i	$-0.232871\pi$
$53$	3.91397	+	2.25973i	0.537624	+	0.310398i	−0.206491	+	0.978448i	$0.566204\pi$
$54$	−4.98084	−	1.48029i	−0.677806	−	0.201442i
$55$		−	1.18685i		−	0.160035i
$56$	−2.57675	−	0.600295i	−0.344333	−	0.0802177i
$57$	0.713598	+	0.919433i	0.0945184	+	0.121782i
$58$	6.24260	+	2.27212i	0.819694	+	0.298344i
$59$	−11.1527	−	4.05925i	−1.45196	−	0.528469i	−0.508820	−	0.860873i	$-0.669918\pi$
$59$	−11.1527	−	4.05925i	−1.45196	−	0.528469i	−0.943137	+	0.332403i	$0.892140\pi$
$60$	3.45220	+	0.131651i	0.445677	+	0.0169960i
$61$	−5.87906	−	1.03664i	−0.752736	−	0.132728i	−0.215901	−	0.976415i	$-0.569269\pi$
$61$	−5.87906	−	1.03664i	−0.752736	−	0.132728i	−0.536835	+	0.843687i	$0.680380\pi$
$62$	−1.32884	+	2.30162i	−0.168763	+	0.292306i
$63$	−0.348723	−	7.92959i	−0.0439349	−	0.999034i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	3.67663	+	10.1015i	0.456030	+	1.25293i
$66$	0.763697	+	0.692088i	0.0940046	+	0.0851901i
$67$	7.47548	−	6.27267i	0.913275	−	0.766329i	−0.0594643	−	0.998230i	$-0.518939\pi$
$67$	7.47548	−	6.27267i	0.913275	−	0.766329i	0.972739	+	0.231902i	$0.0744948\pi$
$68$	0.0696795	+	0.395172i	0.00844988	+	0.0479216i
$69$	0.806040	+	2.50810i	0.0970359	+	0.301940i
$70$	1.53284	+	5.04963i	0.183210	+	0.603547i
$71$	6.48140	−	3.74204i	0.769201	−	0.444098i	−0.0633886	−	0.997989i	$-0.520191\pi$
$71$	6.48140	−	3.74204i	0.769201	−	0.444098i	0.832589	+	0.553891i	$0.186857\pi$
$72$	−2.09779	+	2.14460i	−0.247227	+	0.252743i
$73$	10.7027	−	6.17922i	1.25266	−	0.723223i	0.281022	−	0.959701i	$-0.409327\pi$
$73$	10.7027	−	6.17922i	1.25266	−	0.723223i	0.971637	+	0.236479i	$0.0759934\pi$
$74$	2.14336	+	5.88883i	0.249160	+	0.684563i
$75$	0.825737	+	1.56509i	0.0953479	+	0.180720i
$76$	0.661749	−	0.116684i	0.0759078	−	0.0133846i
$77$	−0.618022	+	1.44795i	−0.0704302	+	0.165009i
$78$	−8.64386	−	3.52467i	−0.978725	−	0.399090i
$79$	2.76496	+	2.32008i	0.311083	+	0.261030i	0.784939	−	0.619573i	$-0.212694\pi$
$79$	2.76496	+	2.32008i	0.311083	+	0.261030i	−0.473857	+	0.880602i	$0.657138\pi$
$80$	0.997290	−	1.72736i	0.111500	−	0.193124i
$81$	−7.89162	−	4.32693i	−0.876847	−	0.480770i
$82$	4.77086	−	2.75446i	0.526854	−	0.304179i
$83$	6.67653	−	2.43006i	0.732844	−	0.266734i	0.0514760	−	0.998674i	$-0.483607\pi$
$83$	6.67653	−	2.43006i	0.732844	−	0.266734i	0.681368	+	0.731941i	$0.261385\pi$
$84$	−4.14310	−	1.95825i	−0.452049	−	0.213663i
$85$	0.613112	−	0.514462i	0.0665013	−	0.0558012i
$86$	3.27210	+	3.89954i	0.352840	+	0.420498i
$87$	9.73838	+	6.12877i	1.04406	+	0.657073i
$88$	0.559155	−	0.203516i	0.0596061	−	0.0216949i
$89$	−16.8147			−1.78235			−0.891175	−	0.453660i	$-0.850118\pi$
$89$	−16.8147			−1.78235			−0.891175	+	0.453660i	$0.850118\pi$
$90$	5.79658	+	1.48484i	0.611013	+	0.156516i
$91$	0.774612	−	14.2382i	0.0812014	−	1.49257i
$92$	1.49789	+	0.264118i	0.156166	+	0.0275362i
$93$	−3.09113	+	3.41097i	−0.320536	+	0.353701i
$94$	5.48029	+	6.53115i	0.565248	+	0.673637i
$95$	−0.861510	−	1.02671i	−0.0883891	−	0.105338i
$96$	0.529942	+	1.64899i	0.0540870	+	0.168299i
$97$	−5.55525	−	0.979540i	−0.564050	−	0.0994572i	−0.115650	−	0.993290i	$-0.536895\pi$
$97$	−5.55525	−	0.979540i	−0.564050	−	0.0994572i	−0.448400	+	0.893833i	$0.648006\pi$
$98$	0.759407	−	6.95869i	0.0767117	−	0.702933i
$99$	1.03997	+	1.45090i	0.104521	+	0.145821i
$100$	1.02165			0.102165
$101$	2.74255	−	0.998207i	0.272894	−	0.0993253i	−0.201948	−	0.979396i	$-0.564727\pi$
$101$	2.74255	−	0.998207i	0.272894	−	0.0993253i	0.474842	+	0.880071i	$0.342505\pi$
$102$	−0.0264854	+	0.694512i	−0.00262244	+	0.0687669i
$103$	9.58028	+	11.4173i	0.943973	+	1.12498i	0.992013	+	0.126138i	$0.0402581\pi$
$103$	9.58028	+	11.4173i	0.943973	+	1.12498i	−0.0480399	+	0.998845i	$0.515297\pi$
$104$	−4.12858	+	3.46429i	−0.404841	+	0.339702i
$105$	0.749266	+	9.10955i	0.0731208	+	0.889001i
$106$	4.24690	−	1.54575i	0.412495	−	0.150136i
$107$	−8.35505	+	4.82379i	−0.807713	+	0.466333i	−0.846161	−	0.532927i	$-0.821092\pi$
$107$	−8.35505	+	4.82379i	−0.807713	+	0.466333i	0.0384482	+	0.999261i	$0.487759\pi$
$108$	−4.33559	+	2.86403i	−0.417192	+	0.275592i
$109$	−8.57185	+	14.8469i	−0.821034	+	1.42207i	0.0838785	+	0.996476i	$0.473269\pi$
$109$	−8.57185	+	14.8469i	−0.821034	+	1.42207i	−0.904913	+	0.425597i	$0.860064\pi$
$110$	−0.909184	−	0.762896i	−0.0866873	−	0.0727392i
$111$	1.47612	+	10.7535i	0.140107	+	1.02068i
$112$	−2.11616	+	1.58804i	−0.199958	+	0.150056i
$113$	−17.6143	+	3.10588i	−1.65702	+	0.292177i	−0.922380	−	0.386283i	$-0.873759\pi$
$113$	−17.6143	+	3.10588i	−1.65702	+	0.292177i	−0.734637	+	0.678460i	$0.762648\pi$
$114$	1.16302	+	0.0443520i	0.108927	+	0.00415394i
$115$	−1.03760	−	2.85079i	−0.0967570	−	0.265838i
$116$	5.75321	−	3.32162i	0.534172	−	0.308405i
$117$	−13.3459	−	9.12716i	−1.23383	−	0.843806i
$118$	−10.2784	+	5.93423i	−0.946202	+	0.546290i
$119$	−1.01588	+	0.308377i	−0.0931258	+	0.0282688i
$120$	2.31988	−	2.55992i	0.211775	−	0.233687i
$121$	1.84865	+	10.4842i	0.168059	+	0.953108i
$122$	−4.57309	+	3.83728i	−0.414029	+	0.347411i
$123$	9.08414	−	2.91941i	0.819089	−	0.263234i
$124$	0.908981	+	2.49740i	0.0816289	+	0.224274i
$125$	−6.00533	−	10.4015i	−0.537133	−	0.930342i
$126$	−6.29857	−	4.82990i	−0.561121	−	0.430282i
$127$	5.27029	−	9.12841i	0.467663	−	0.810016i	−0.531654	−	0.846961i	$-0.678430\pi$
$127$	5.27029	−	9.12841i	0.467663	−	0.810016i	0.999317	+	0.0369456i	$0.0117628\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	4.11431	+	7.79818i	0.362245	+	0.686591i
$130$	10.1015	+	3.67663i	0.885957	+	0.322462i
$131$	−9.65684	−	3.51480i	−0.843722	−	0.307090i	−0.116244	−	0.993221i	$-0.537086\pi$
$131$	−9.65684	−	3.51480i	−0.843722	−	0.307090i	−0.727478	+	0.686131i	$0.759308\pi$
$132$	1.02107	−	0.140160i	0.0888723	−	0.0121994i
$133$	0.516403	+	1.70118i	0.0447778	+	0.147511i
$134$		−	9.75854i		−	0.843010i
$135$	9.27104	+	4.63284i	0.797924	+	0.398731i
$136$	0.347508	+	0.200634i	0.0297986	+	0.0172042i
$137$	12.0205	+	2.11953i	1.02698	+	0.181084i	0.661664	−	0.749800i	$-0.269850\pi$
$137$	12.0205	+	2.11953i	1.02698	+	0.181084i	0.365314	+	0.930884i	$0.380962\pi$
$138$	2.43943	+	0.994716i	0.207658	+	0.0846758i
$139$	−11.9727	−	14.2685i	−1.01551	−	1.21024i	−0.977494	−	0.210962i	$-0.932340\pi$
$139$	−11.9727	−	14.2685i	−1.01551	−	1.21024i	−0.0380171	−	0.999277i	$-0.512104\pi$
$140$	4.85354	+	2.07162i	0.410199	+	0.175083i
$141$	6.89086	+	13.0608i	0.580315	+	1.09992i
$142$	1.29960	−	7.37038i	0.109060	−	0.618508i
$143$	1.60348	+	2.77731i	0.134090	+	0.232250i
$144$	0.294423	+	2.98552i	0.0245353	+	0.248793i
$145$	−11.4752	−	6.62523i	−0.952967	−	0.550196i
$146$	2.14602	−	12.1707i	0.177606	−	1.00725i
$147$	3.82945	−	11.5037i	0.315848	−	0.948810i
$148$	5.88883	+	2.14336i	0.484059	+	0.176183i
$149$	−0.0629334	+	0.0110969i	−0.00515571	+	0.000909090i	−0.176225	−	0.984350i	$-0.556389\pi$
$149$	−0.0629334	+	0.0110969i	−0.00515571	+	0.000909090i	0.171070	+	0.985259i	$0.445278\pi$
$150$	1.72970	+	0.373466i	0.141229	+	0.0304934i
$151$	13.6538	+	11.4569i	1.11113	+	0.932347i	0.998123	−	0.0612469i	$-0.0195077\pi$
$151$	13.6538	+	11.4569i	1.11113	+	0.932347i	0.113006	+	0.993594i	$0.463952\pi$
$152$	0.335979	−	0.581932i	0.0272515	−	0.0472009i
$153$	−0.298720	+	1.16615i	−0.0241501	+	0.0942778i
$154$	0.711937	+	1.40416i	0.0573695	+	0.113150i
$155$	3.40739	−	4.06077i	0.273688	−	0.326169i
$156$	−8.25622	+	4.35597i	−0.661026	+	0.348757i
$157$	−1.31583	+	3.61520i	−0.105014	+	0.288525i	−0.981060	−	0.193703i	$-0.937950\pi$
$157$	−1.31583	+	3.61520i	−0.105014	+	0.288525i	0.876046	+	0.482228i	$0.160172\pi$
$158$	3.55457	−	0.626767i	0.282786	−	0.0498629i
$159$	7.75521	−	1.06455i	0.615028	−	0.0844241i
$160$	−0.682186	−	1.87429i	−0.0539316	−	0.148176i
$161$	−0.218608	+	4.01824i	−0.0172287	+	0.316681i
$162$	−8.38726	+	3.26403i	−0.658965	+	0.256447i
$163$	−5.20887	−	9.02203i	−0.407990	−	0.706660i	0.586674	−	0.809823i	$-0.300437\pi$
$163$	−5.20887	−	9.02203i	−0.407990	−	0.706660i	−0.994664	+	0.103163i	$0.967104\pi$
$164$	0.956614	−	5.42523i	0.0746990	−	0.423639i
$165$	−1.26040	−	1.62396i	−0.0981223	−	0.126425i
$166$	2.43006	−	6.67653i	0.188609	−	0.518199i
$167$	−2.32854	−	13.2058i	−0.180188	−	1.02190i	−0.931984	−	0.362500i	$-0.881923\pi$
$167$	−2.32854	−	13.2058i	−0.180188	−	1.02190i	0.751796	−	0.659396i	$-0.229188\pi$
$168$	−4.16324	+	1.91505i	−0.321201	+	0.147750i
$169$	−12.2924	−	10.3145i	−0.945566	−	0.793424i
$170$		−	0.800361i		−	0.0613849i
$171$	1.95282	+	0.500231i	0.149336	+	0.0382537i
$172$	5.09049			0.388146
$173$	10.5080	−	3.82459i	0.798907	−	0.290778i	0.0898732	−	0.995953i	$-0.471354\pi$
$173$	10.5080	−	3.82459i	0.798907	−	0.290778i	0.709033	+	0.705175i	$0.249132\pi$
$174$	10.9546	−	3.52053i	0.830468	−	0.266891i
$175$	0.324077	+	2.68355i	0.0244979	+	0.202857i
$176$	0.203516	−	0.559155i	0.0153406	−	0.0421479i
$177$	−19.5709	+	6.28960i	−1.47104	+	0.472755i
$178$	−10.8082	+	12.8808i	−0.810113	+	0.965455i
$179$		−	20.7730i		−	1.55264i	−0.630336	−	0.776322i	$-0.717083\pi$
$179$		−	20.7730i		−	1.55264i	0.630336	−	0.776322i	$-0.282917\pi$
$180$	4.86343	−	3.48600i	0.362498	−	0.259831i
$181$	−9.02537	−	5.21080i	−0.670850	−	0.387316i	0.125548	−	0.992087i	$-0.459931\pi$
$181$	−9.02537	−	5.21080i	−0.670850	−	0.387316i	−0.796399	+	0.604772i	$0.793264\pi$
$182$	−10.4092	−	9.74551i	−0.771579	−	0.722385i
$183$	−9.14514	+	4.82496i	−0.676028	+	0.356671i
$184$	1.16515	−	0.977678i	0.0858961	−	0.0720754i
$185$	−2.17053	−	12.3097i	−0.159580	−	0.905024i
$186$	0.626010	+	4.56047i	0.0459013	+	0.334390i
$187$	0.153479	−	0.182909i	0.0112235	−	0.0133756i
$188$	8.52581			0.621809
$189$	−8.89814	−	10.4797i	−0.647244	−	0.762282i
$190$	−1.34027			−0.0972335
$191$	−3.06050	+	3.64736i	−0.221450	+	0.263914i	−0.865319	−	0.501222i	$-0.832884\pi$
$191$	−3.06050	+	3.64736i	−0.221450	+	0.263914i	0.643869	+	0.765136i	$0.277328\pi$
$192$	1.60384	+	0.653990i	0.115747	+	0.0471976i
$193$	−0.818095	−	4.63965i	−0.0588878	−	0.333969i	0.941104	−	0.338118i	$-0.109790\pi$
$193$	−0.818095	−	4.63965i	−0.0588878	−	0.333969i	−0.999991	+	0.00414908i	$0.998679\pi$
$194$	−4.32122	+	3.62593i	−0.310245	+	0.260327i
$195$	15.7582	+	9.91727i	1.12846	+	0.710190i
$196$	−4.84253	−	5.05470i	−0.345895	−	0.361050i
$197$	19.3931	+	11.1966i	1.38170	+	0.797725i	0.992361	−	0.123370i	$-0.0393702\pi$
$197$	19.3931	+	11.1966i	1.38170	+	0.797725i	0.389339	+	0.921095i	$0.372704\pi$
$198$	1.77994	+	0.135954i	0.126495	+	0.00966185i
$199$		−	23.5588i		−	1.67004i	−0.550220	−	0.835020i	$-0.685456\pi$
$199$		−	23.5588i		−	1.67004i	0.550220	−	0.835020i	$-0.314544\pi$
$200$	0.656707	−	0.782633i	0.0464362	−	0.0553405i
$201$	3.56724	−	16.5216i	0.251614	−	1.16534i
$202$	0.998207	−	2.74255i	0.0702336	−	0.192965i
$203$	10.5498	+	14.0581i	0.740448	+	0.986687i
$204$	0.515003	+	0.466713i	0.0360574	+	0.0326764i
$205$	−10.3253	+	3.75811i	−0.721152	+	0.262478i
$206$	14.9043			1.03843
$207$	3.76643	+	2.57583i	0.261785	+	0.179032i
$208$			5.38948i			0.373693i
$209$	−0.306296	−	0.257013i	−0.0211870	−	0.0177780i
$210$	7.45994	+	5.28153i	0.514785	+	0.364460i
$211$	−2.10004	−	11.9099i	−0.144573	−	0.819911i	−0.967709	−	0.252068i	$-0.918889\pi$
$211$	−2.10004	−	11.9099i	−0.144573	−	0.819911i	0.823137	−	0.567843i	$-0.192222\pi$
$212$	1.54575	−	4.24690i	0.106162	−	0.291678i
$213$	4.89451	−	12.0033i	0.335366	−	0.822449i
$214$	−1.67528	+	9.50101i	−0.114520	+	0.649476i
$215$	−5.07669	−	8.79308i	−0.346227	−	0.599683i
$216$	−0.592888	+	5.16222i	−0.0403409	+	0.351244i
$217$	−6.27151	+	3.17979i	−0.425738	+	0.215858i
$218$	5.86349	+	16.1098i	0.397126	+	1.09109i
$219$	8.08229	−	19.8209i	0.546150	−	1.33937i
$220$	−1.16882	+	0.206095i	−0.0788021	+	0.0138949i
$221$	−0.739662	+	2.03221i	−0.0497551	+	0.136701i
$222$	9.18650	+	5.78145i	0.616558	+	0.388026i
$223$	−9.22125	+	10.9895i	−0.617500	+	0.735908i	−0.980638	−	0.195827i	$-0.937261\pi$
$223$	−9.22125	+	10.9895i	−0.617500	+	0.735908i	0.363138	+	0.931735i	$0.381705\pi$
$224$	−0.143727	+	2.64184i	−0.00960314	+	0.176516i
$225$	2.79192	+	1.26458i	0.186128	+	0.0843056i
$226$	−8.94303	+	15.4898i	−0.594882	+	1.03037i
$227$	−17.1471	−	14.3881i	−1.13809	−	0.954971i	−0.138716	−	0.990332i	$-0.544297\pi$
$227$	−17.1471	−	14.3881i	−1.13809	−	0.954971i	−0.999375	+	0.0353610i	$0.988742\pi$
$228$	0.781550	−	0.862415i	0.0517594	−	0.0571148i
$229$	−6.93959	+	1.22364i	−0.458581	+	0.0808603i	−0.398167	−	0.917313i	$-0.630353\pi$
$229$	−6.93959	+	1.22364i	−0.458581	+	0.0808603i	−0.0604147	+	0.998173i	$0.519242\pi$
$230$	−2.85079	−	1.03760i	−0.187976	−	0.0684175i
$231$	0.692045	+	2.63754i	0.0455332	+	0.173537i
$232$	1.15359	−	6.54231i	0.0757367	−	0.429524i
$233$	−7.08185	−	4.08871i	−0.463948	−	0.267860i	0.249755	−	0.968309i	$-0.419650\pi$
$233$	−7.08185	−	4.08871i	−0.463948	−	0.267860i	−0.713703	+	0.700449i	$0.752983\pi$
$234$	−15.5704	+	4.35675i	−1.01787	+	0.284810i
$235$	−8.50270	−	14.7271i	−0.554655	−	0.960691i
$236$	−2.06094	+	11.6881i	−0.134155	+	0.760833i
$237$	6.24713	+	0.238236i	0.405795	+	0.0154751i
$238$	−0.416766	+	0.976432i	−0.0270149	+	0.0632927i
$239$	4.44960	+	5.30283i	0.287821	+	0.343011i	0.890509	−	0.454965i	$-0.150348\pi$
$239$	4.44960	+	5.30283i	0.287821	+	0.343011i	−0.602689	+	0.797977i	$0.705904\pi$
$240$	−0.469818	−	3.42262i	−0.0303266	−	0.220929i
$241$	20.0285	+	3.53157i	1.29015	+	0.227488i	0.776285	−	0.630382i	$-0.217102\pi$
$241$	20.0285	+	3.53157i	1.29015	+	0.227488i	0.513866	+	0.857871i	$0.328213\pi$
$242$	9.21964	+	5.32296i	0.592661	+	0.342173i
$243$	−15.3931	+	2.46016i	−0.987468	+	0.157819i
$244$			5.96975i			0.382174i
$245$	−3.90186	+	13.4058i	−0.249281	+	0.856463i
$246$	3.60278	−	8.83542i	0.229705	−	0.563326i
$247$	3.40310	+	1.23863i	0.216534	+	0.0788119i
$248$	2.49740	+	0.908981i	0.158585	+	0.0577203i
$249$	6.55479	−	10.4153i	0.415393	−	0.660043i
$250$	−11.8282	−	2.08563i	−0.748081	−	0.131907i
$251$	−1.05243	+	1.82287i	−0.0664291	+	0.115059i	−0.897327	−	0.441366i	$-0.854494\pi$
$251$	−1.05243	+	1.82287i	−0.0664291	+	0.115059i	0.830898	+	0.556425i	$0.187827\pi$
$252$	−7.74857	+	1.72038i	−0.488114	+	0.108374i
$253$	−0.452527	−	0.783800i	−0.0284501	−	0.0492771i
$254$	−3.60509	−	9.90491i	−0.226204	−	0.621489i
$255$	0.292572	−	1.35504i	0.0183216	−	0.0848559i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−2.48107	−	14.0709i	−0.154765	−	0.877716i	−0.959000	−	0.283405i	$-0.908536\pi$
$257$	−2.48107	−	14.0709i	−0.154765	−	0.877716i	0.804235	−	0.594311i	$-0.202575\pi$
$258$	8.61838	+	1.86083i	0.536557	+	0.115850i
$259$	−3.76190	+	16.1479i	−0.233753	+	1.00338i
$260$	9.30956	−	5.37488i	0.577354	−	0.333336i
$261$	19.8335	−	1.95593i	1.22766	−	0.121069i
$262$	−8.89980	+	5.13830i	−0.549831	+	0.317445i
$263$	−5.48914	−	15.0813i	−0.338475	−	0.929953i	−0.985828	−	0.167762i	$-0.946346\pi$
$263$	−5.48914	−	15.0813i	−0.338475	−	0.929953i	0.647353	−	0.762191i	$-0.275876\pi$
$264$	0.548959	−	0.872275i	0.0337861	−	0.0536848i
$265$	−8.87747	+	1.56534i	−0.545338	+	0.0961579i
$266$	1.63512	+	0.697910i	0.100255	+	0.0427916i
$267$	−23.0073	+	17.8567i	−1.40803	+	1.09281i
$268$	−7.47548	−	6.27267i	−0.456637	−	0.383164i
$269$	−6.85306	+	11.8698i	−0.417838	+	0.723717i	−0.995722	−	0.0924021i	$-0.970545\pi$
$269$	−6.85306	+	11.8698i	−0.417838	+	0.723717i	0.577883	+	0.816119i	$0.303879\pi$
$270$	9.50827	−	4.12410i	0.578655	−	0.250985i
$271$	9.52665	−	5.50022i	0.578703	−	0.334114i	−0.181915	−	0.983314i	$-0.558229\pi$
$271$	9.52665	−	5.50022i	0.578703	−	0.334114i	0.760618	+	0.649200i	$0.224896\pi$
$272$	0.377069	−	0.137242i	0.0228631	−	0.00832150i
$273$	−14.0606	−	20.3046i	−0.850988	−	1.22889i
$274$	9.35027	−	7.84581i	0.564871	−	0.473983i
$275$	−0.390767	−	0.465698i	−0.0235641	−	0.0280826i
$276$	2.33003	−	1.22932i	0.140252	−	0.0739965i
$277$	−20.4381	+	7.43884i	−1.22800	+	0.446957i	−0.872913	−	0.487875i	$-0.837772\pi$
$277$	−20.4381	+	7.43884i	−1.22800	+	0.446957i	−0.355090	+	0.934832i	$0.615550\pi$
$278$	−18.6262			−1.11713
$279$	−0.607225	+	7.94989i	−0.0363536	+	0.475947i
$280$	4.70674	−	2.38642i	0.281282	−	0.142616i
$281$	28.9353	+	5.10208i	1.72614	+	0.304365i	0.946700	−	0.322115i	$-0.104394\pi$
$281$	28.9353	+	5.10208i	1.72614	+	0.304365i	0.779438	+	0.626480i	$0.215505\pi$
$282$	14.4345	+	3.11661i	0.859563	+	0.185592i
$283$	15.7511	+	18.7715i	0.936308	+	1.11585i	0.993078	+	0.117461i	$0.0374755\pi$
$283$	15.7511	+	18.7715i	0.936308	+	1.11585i	−0.0567697	+	0.998387i	$0.518080\pi$
$284$	−4.81067	−	5.73314i	−0.285461	−	0.340199i
$285$	−2.26913	−	0.489937i	−0.134412	−	0.0290214i
$286$	3.15824	+	0.556883i	0.186751	+	0.0329292i
$287$	14.5537	+	0.791778i	0.859078	+	0.0467372i
$288$	2.47629	+	1.69351i	0.145917	+	0.0997912i
$289$	−16.8390			−0.990528
$290$	−12.4514	+	4.53193i	−0.731169	+	0.266124i
$291$	−8.64144	+	4.55921i	−0.506570	+	0.267266i
$292$	−7.94385	−	9.46711i	−0.464879	−	0.554021i
$293$	6.67571	−	5.60159i	0.389999	−	0.327248i	−0.426614	−	0.904434i	$-0.640294\pi$
$293$	6.67571	−	5.60159i	0.389999	−	0.327248i	0.816613	+	0.577186i	$0.195849\pi$
$294$	−6.35083	−	10.3280i	−0.370388	−	0.602340i
$295$	22.2449	−	8.09649i	1.29515	−	0.471396i
$296$	5.42718	−	3.13338i	0.315448	−	0.182124i
$297$	2.96380	+	0.880832i	0.171977	+	0.0511111i
$298$	−0.0319521	+	0.0553427i	−0.00185094	+	0.00320592i
$299$	6.27956	+	5.26918i	0.363156	+	0.304724i
$300$	1.39792	−	1.08497i	0.0807090	−	0.0626406i
$301$	1.61474	+	13.3710i	0.0930724	+	0.770692i
$302$	17.5530	−	3.09506i	1.01006	−	0.178101i
$303$	2.69254	−	4.27834i	0.154682	−	0.245784i
$304$	−0.229823	−	0.631433i	−0.0131812	−	0.0362152i
$305$	10.3119	−	5.95357i	0.590457	−	0.340900i
$306$	0.701311	+	0.978421i	0.0400913	+	0.0559326i
$307$	−0.100880	+	0.0582430i	−0.00575752	+	0.00332410i	−0.502876	−	0.864359i	$-0.667725\pi$
$307$	−0.100880	+	0.0582430i	−0.00575752	+	0.00332410i	0.497118	+	0.867683i	$0.334391\pi$
$308$	1.53327	+	0.357199i	0.0873662	+	0.0203533i
$309$	25.2335	+	5.44826i	1.43548	+	0.309941i
$310$	−0.920501	−	5.22042i	−0.0522810	−	0.296500i
$311$	24.1551	−	20.2685i	1.36971	−	1.14932i	0.396860	−	0.917879i	$-0.370100\pi$
$311$	24.1551	−	20.2685i	1.36971	−	1.14932i	0.972849	−	0.231443i	$-0.0743446\pi$
$312$	−1.97013	+	9.12459i	−0.111537	+	0.516578i
$313$	7.96678	+	21.8885i	0.450309	+	1.23721i	0.932507	+	0.361152i	$0.117616\pi$
$313$	7.96678	+	21.8885i	0.450309	+	1.23721i	−0.482198	+	0.876062i	$0.660161\pi$
$314$	1.92361	+	3.33179i	0.108556	+	0.188024i
$315$	10.6993	+	11.6688i	0.602836	+	0.657463i
$316$	1.80470	−	3.12584i	0.101522	−	0.175842i
$317$	13.1959	+	2.32680i	0.741157	+	0.130686i	0.531463	−	0.847081i	$-0.321642\pi$
$317$	13.1959	+	2.32680i	0.741157	+	0.130686i	0.209693	+	0.977767i	$0.432753\pi$
$318$	4.16946	−	6.62511i	0.233812	−	0.371518i
$319$	−3.71460	−	1.35200i	−0.207978	−	0.0756977i
$320$	−1.87429	−	0.682186i	−0.104776	−	0.0381354i
$321$	−6.30941	+	15.4732i	−0.352157	+	0.863627i
$322$	2.93763	+	2.75034i	0.163708	+	0.153270i
$323$		−	0.269635i		−	0.0150029i
$324$	−2.89083	+	8.52309i	−0.160602	+	0.473505i
$325$	4.76850	+	2.75309i	0.264509	+	0.152714i
$326$	−10.2595	−	1.80902i	−0.568220	−	0.100192i
$327$	4.03816	+	29.4179i	0.223311	+	1.62681i
$328$	−3.54106	−	4.22008i	−0.195523	−	0.233015i
$329$	2.70446	+	22.3945i	0.149102	+	1.23465i
$330$	−2.05420	−	0.0783374i	−0.113080	−	0.00431233i
$331$	3.23087	−	18.3232i	0.177585	−	1.00713i	−0.757533	−	0.652797i	$-0.773596\pi$
$331$	3.23087	−	18.3232i	0.177585	−	1.00713i	0.935118	−	0.354337i	$-0.115293\pi$
$332$	−3.55251	−	6.15312i	−0.194969	−	0.337697i
$333$	13.4397	+	13.1463i	0.736490	+	0.720415i
$334$	−11.6130	−	6.70476i	−0.635434	−	0.366868i
$335$	−3.37992	+	19.1685i	−0.184665	+	1.04729i
$336$	−1.20906	+	4.42020i	−0.0659597	+	0.241142i
$337$	−29.6933	−	10.8075i	−1.61750	−	0.588722i	−0.634596	−	0.772844i	$-0.718833\pi$
$337$	−29.6933	−	10.8075i	−1.61750	−	0.588722i	−0.982903	+	0.184123i	$0.941056\pi$
$338$	−15.8028	+	2.78645i	−0.859557	+	0.151563i
$339$	−20.8032	+	22.9557i	−1.12987	+	1.24678i
$340$	−0.613112	−	0.514462i	−0.0332507	−	0.0279006i
$341$	0.790714	−	1.36956i	0.0428196	−	0.0741656i
$342$	1.63845	−	1.17440i	0.0885971	−	0.0635045i
$343$	11.7409	−	14.3231i	0.633950	−	0.773374i
$344$	3.27210	−	3.89954i	0.176420	−	0.210249i
$345$	−4.44720	−	2.79881i	−0.239429	−	0.150683i
$346$	3.82459	−	10.5080i	0.205611	−	0.564912i
$347$	−34.6105	+	6.10277i	−1.85799	+	0.327614i	−0.986623	−	0.163018i	$-0.947877\pi$
$347$	−34.6105	+	6.10277i	−1.85799	+	0.327614i	−0.871367	+	0.490631i	$0.836766\pi$
$348$	4.34461	−	10.6547i	0.232896	−	0.571151i
$349$	2.20301	+	6.05271i	0.117924	+	0.323994i	0.984586	−	0.174902i	$-0.0559610\pi$
$349$	2.20301	+	6.05271i	0.117924	+	0.323994i	−0.866662	+	0.498897i	$0.833739\pi$
$350$	2.26403	+	1.47669i	0.121017	+	0.0789325i
$351$	−27.9539	+	1.68437i	−1.49207	+	0.0899051i
$352$	−0.297520	−	0.515320i	−0.0158579	−	0.0274666i
$353$	3.07443	−	17.4359i	0.163635	−	0.928022i	−0.786825	−	0.617176i	$-0.788277\pi$
$353$	3.07443	−	17.4359i	0.163635	−	0.928022i	0.950460	−	0.310846i	$-0.100612\pi$
$354$	−7.76184	+	19.0351i	−0.412537	+	1.01170i
$355$	−5.10553	+	14.0273i	−0.270974	+	0.744494i
$356$	2.91983	+	16.5592i	0.154751	+	0.877636i
$357$	−1.06254	+	1.50079i	−0.0562353	+	0.0794300i
$358$	−15.9130	−	13.3526i	−0.841029	−	0.705707i
$359$		−	16.0483i		−	0.846996i	−0.905897	−	0.423498i	$-0.860802\pi$
$359$		−	16.0483i		−	0.846996i	0.905897	−	0.423498i	$-0.139198\pi$
$360$	0.455720	−	5.96636i	0.0240185	−	0.314455i
$361$	18.5485			0.976235
$362$	−9.79310	+	3.56440i	−0.514714	+	0.187340i
$363$	13.6634	+	12.3822i	0.717142	+	0.649898i
$364$	−14.1564	+	1.70959i	−0.741996	+	0.0896069i
$365$	−8.43075	+	23.1633i	−0.441286	+	1.21242i
$366$	−2.18225	+	10.1070i	−0.114068	+	0.528302i
$367$	−21.1295	+	25.1812i	−1.10295	+	1.31445i	−0.157928	+	0.987451i	$0.550481\pi$
$367$	−21.1295	+	25.1812i	−1.10295	+	1.31445i	−0.945025	+	0.326998i	$0.893963\pi$
$368$		−	1.52100i		−	0.0792874i
$369$	9.32942	−	13.6417i	0.485670	−	0.710158i
$370$	−10.8249	−	6.24978i	−0.562762	−	0.324911i
$371$	11.6455	+	2.71301i	0.604605	+	0.140852i
$372$	3.89592	+	2.45186i	0.201994	+	0.127123i
$373$	−27.3613	+	22.9589i	−1.41672	+	1.18877i	−0.463645	+	0.886021i	$0.653459\pi$
$373$	−27.3613	+	22.9589i	−1.41672	+	1.18877i	−0.953071	+	0.302746i	$0.902097\pi$
$374$	−0.0414621	−	0.235143i	−0.00214395	−	0.0121590i
$375$	−19.2632	−	7.85485i	−0.994746	−	0.405623i
$376$	5.48029	−	6.53115i	0.282624	−	0.336818i
$377$	35.8036			1.84398
$378$	−13.7475	+	0.0801807i	−0.707095	+	0.00412405i
$379$	15.2080			0.781183			0.390592	−	0.920564i	$-0.372270\pi$
$379$	15.2080			0.781183			0.390592	+	0.920564i	$0.372270\pi$
$380$	−0.861510	+	1.02671i	−0.0441945	+	0.0526690i
$381$	−2.48281	−	18.0872i	−0.127198	−	0.926636i
$382$	0.826790	+	4.68896i	0.0423022	+	0.239908i
$383$	16.5107	−	13.8541i	0.843657	−	0.707912i	−0.114727	−	0.993397i	$-0.536599\pi$
$383$	16.5107	−	13.8541i	0.843657	−	0.707912i	0.958383	+	0.285485i	$0.0921547\pi$
$384$	1.53191	−	0.808235i	0.0781751	−	0.0412451i
$385$	−0.912104	−	3.00474i	−0.0464851	−	0.153136i
$386$	−4.08004	−	2.35561i	−0.207669	−	0.119897i
$387$	13.9110	+	6.30090i	0.707136	+	0.320293i
$388$			5.64095i			0.286376i
$389$	2.19559	−	2.61660i	0.111321	−	0.132667i	−0.707507	−	0.706707i	$-0.750180\pi$
$389$	2.19559	−	2.61660i	0.111321	−	0.132667i	0.818827	+	0.574040i	$0.194625\pi$
$390$	17.7262	−	5.69675i	0.897602	−	0.288466i
$391$	0.208744	−	0.573520i	0.0105566	−	0.0290042i
$392$	−6.98484	+	0.460494i	−0.352788	+	0.0232584i
$393$	−16.9460	+	5.44600i	−0.854812	+	0.274715i
$394$	21.0427	−	7.65892i	1.06012	−	0.385851i
$395$	−7.19924			−0.362233
$396$	1.24827	−	1.27612i	0.0627278	−	0.0641275i
$397$			29.5615i			1.48365i	0.670595	+	0.741824i	$0.266039\pi$
$397$			29.5615i			1.48365i	−0.670595	+	0.741824i	$0.733961\pi$
$398$	−18.0471	−	15.1433i	−0.904619	−	0.759066i
$399$	2.51319	+	1.77930i	0.125817	+	0.0890767i
$400$	−0.177408	−	1.00613i	−0.00887042	−	0.0503067i
$401$	−0.590364	+	1.62201i	−0.0294814	+	0.0809994i	−0.953560	−	0.301203i	$-0.902612\pi$
$401$	−0.590364	+	1.62201i	−0.0294814	+	0.0809994i	0.924079	+	0.382202i	$0.124834\pi$
$402$	−10.3633	−	13.3525i	−0.516873	−	0.665963i
$403$	−2.48726	+	14.1059i	−0.123899	+	0.702666i
$404$	−1.45928	−	2.52755i	−0.0726019	−	0.125750i
$405$	17.6054	−	3.50650i	0.874820	−	0.174239i
$406$	17.5504	+	0.954810i	0.871012	+	0.0473864i
$407$	−1.27539	−	3.50409i	−0.0632185	−	0.173691i
$408$	0.688560	−	0.0945177i	0.0340888	−	0.00467932i
$409$	2.97675	−	0.524882i	0.147191	−	0.0259537i	−0.0995671	−	0.995031i	$-0.531746\pi$
$409$	2.97675	−	0.524882i	0.147191	−	0.0259537i	0.246758	+	0.969077i	$0.420635\pi$
$410$	−3.75811	+	10.3253i	−0.185600	+	0.509931i
$411$	18.6984	−	9.86525i	0.922324	−	0.486617i
$412$	9.58028	−	11.4173i	0.471986	−	0.562491i
$413$	−31.3546	−	1.70581i	−1.54286	−	0.0839375i
$414$	4.39421	−	1.22954i	0.215964	−	0.0604288i
$415$	−7.08576	+	12.2729i	−0.347826	+	0.602453i
$416$	4.12858	+	3.46429i	0.202420	+	0.169851i
$417$	−31.5349	−	6.80882i	−1.54427	−	0.333429i
$418$	−0.393767	+	0.0694318i	−0.0192598	+	0.00339602i
$419$	−11.3810	−	4.14233i	−0.555996	−	0.202366i	0.0487126	−	0.998813i	$-0.484488\pi$
$419$	−11.3810	−	4.14233i	−0.555996	−	0.202366i	−0.604708	+	0.796447i	$0.706710\pi$
$420$	8.84104	−	2.31974i	0.431399	−	0.113192i
$421$	2.11999	−	12.0231i	0.103322	−	0.585968i	−0.888555	−	0.458770i	$-0.848290\pi$
$421$	2.11999	−	12.0231i	0.103322	−	0.585968i	0.991877	−	0.127199i	$-0.0405986\pi$
$422$	−10.4734	−	6.04682i	−0.509837	−	0.294354i
$423$	23.2989	+	10.5531i	1.13283	+	0.513109i
$424$	−2.25973	−	3.91397i	−0.109742	−	0.190079i
$425$	0.0711883	−	0.403729i	0.00345314	−	0.0195837i
$426$	−6.04889	−	11.4650i	−0.293070	−	0.555479i
$427$	−15.6805	+	1.89366i	−0.758835	+	0.0916404i
$428$	6.20134	+	7.39047i	0.299753	+	0.357232i
$429$	5.14345	+	2.09732i	0.248328	+	0.101259i
$430$	−9.99912	−	1.76312i	−0.482201	−	0.0850250i
$431$	−7.36706	−	4.25338i	−0.354859	−	0.204878i	0.311964	−	0.950094i	$-0.399013\pi$
$431$	−7.36706	−	4.25338i	−0.354859	−	0.204878i	−0.666823	+	0.745216i	$0.732346\pi$
$432$	3.57339	+	3.77239i	0.171925	+	0.181499i
$433$			14.7055i			0.706702i	0.935491	+	0.353351i	$0.114958\pi$
$433$			14.7055i			0.706702i	−0.935491	+	0.353351i	$0.885042\pi$
$434$	−1.59539	+	6.84818i	−0.0765813	+	0.328723i
$435$	−22.7373	+	3.12111i	−1.09017	+	0.149646i
$436$	16.1098	+	5.86349i	0.771520	+	0.280810i
$437$	−0.960408	−	0.349560i	−0.0459425	−	0.0167217i
$438$	−9.98852	−	18.9320i	−0.477270	−	0.904608i
$439$	31.0489	+	5.47475i	1.48188	+	0.261296i	0.855329	−	0.518084i	$-0.173355\pi$
$439$	31.0489	+	5.47475i	1.48188	+	0.261296i	0.626551	+	0.779380i	$0.284466\pi$
$440$	−0.593427	+	1.02785i	−0.0282905	+	0.0490007i
$441$	−6.97679	−	19.8072i	−0.332228	−	0.943199i
$442$	1.08131	+	1.87289i	0.0514329	+	0.0890843i
$443$	1.13815	+	3.12704i	0.0540751	+	0.148570i	0.963789	−	0.266665i	$-0.0859216\pi$
$443$	1.13815	+	3.12704i	0.0540751	+	0.148570i	−0.909714	+	0.415235i	$0.863699\pi$
$444$	10.3338	−	3.32102i	0.490421	−	0.157609i
$445$	25.6917	−	21.5579i	1.21790	−	1.02194i
$446$	2.49111	+	14.1278i	0.117957	+	0.668969i
$447$	−0.0743267	+	0.0820172i	−0.00351553	+	0.00387928i
$448$	1.93138	+	1.80825i	0.0912493	+	0.0854316i
$449$	−30.3913	+	17.5464i	−1.43425	+	0.828067i	−0.997442	−	0.0714850i	$-0.977226\pi$
$449$	−30.3913	+	17.5464i	−1.43425	+	0.828067i	−0.436813	+	0.899552i	$0.643893\pi$
$450$	2.76334	−	1.32588i	0.130265	−	0.0625024i
$451$	−2.83886	+	1.63901i	−0.133677	+	0.0771782i
$452$	6.11740	+	16.8074i	0.287738	+	0.790554i
$453$	30.8492	+	1.17644i	1.44942	+	0.0552740i
$454$	−22.0438	+	3.88692i	−1.03457	+	0.182422i
$455$	17.0711	+	22.7482i	0.800305	+	1.06645i
$456$	−0.158278	−	1.15305i	−0.00741204	−	0.0539966i
$457$	9.37061	+	7.86287i	0.438339	+	0.367810i	0.835087	−	0.550118i	$-0.185417\pi$
$457$	9.37061	+	7.86287i	0.438339	+	0.367810i	−0.396749	+	0.917927i	$0.629862\pi$
$458$	−3.52332	+	6.10258i	−0.164634	+	0.285155i
$459$	0.829683	+	1.91287i	0.0387263	+	0.0892850i
$460$	−2.62730	+	1.51687i	−0.122499	+	0.0707246i
$461$	3.14982	−	1.14644i	0.146702	−	0.0533951i	−0.267626	−	0.963523i	$-0.586239\pi$
$461$	3.14982	−	1.14644i	0.146702	−	0.0533951i	0.414327	+	0.910128i	$0.364017\pi$
$462$	2.46531	+	1.16524i	0.114697	+	0.0542118i
$463$	−6.83592	+	5.73602i	−0.317692	+	0.266575i	−0.787663	−	0.616107i	$-0.788709\pi$
$463$	−6.83592	+	5.73602i	−0.317692	+	0.266575i	0.469971	+	0.882682i	$0.344265\pi$
$464$	−4.27019	−	5.08902i	−0.198239	−	0.236252i
$465$	0.349885	−	9.17486i	0.0162255	−	0.425474i
$466$	−7.68426	+	2.79684i	−0.355966	+	0.129561i
$467$	−2.74618			−0.127078			−0.0635389	−	0.997979i	$-0.520239\pi$
$467$	−2.74618			−0.127078			−0.0635389	+	0.997979i	$0.520239\pi$
$468$	−6.67100	+	14.7281i	−0.308367	+	0.680806i
$469$	14.1049	−	21.6253i	0.651305	−	0.998565i
$470$	−16.7471	−	2.95296i	−0.772484	−	0.136210i
$471$	2.03881	+	6.34402i	0.0939432	+	0.292317i
$472$	7.62889	+	9.09176i	0.351148	+	0.418482i
$473$	−1.94703	−	2.32038i	−0.0895246	−	0.106691i
$474$	4.19808	−	4.63245i	0.192824	−	0.212775i
$475$	−0.676078	−	0.119211i	−0.0310206	−	0.00546977i
$476$	0.480098	+	0.946900i	0.0220052	+	0.0434011i
$477$	9.48086	−	9.69241i	0.434099	−	0.443785i
$478$	6.92235			0.316621
$479$	−13.3507	+	4.85927i	−0.610011	+	0.222026i	−0.628508	−	0.777803i	$-0.716334\pi$
$479$	−13.3507	+	4.85927i	−0.610011	+	0.222026i	0.0184973	+	0.999829i	$0.494112\pi$
$480$	−2.92387	−	1.84011i	−0.133456	−	0.0839893i
$481$	21.7099	+	25.8729i	0.989887	+	1.17970i
$482$	15.5794	−	13.0727i	0.709623	−	0.595445i
$483$	3.96813	+	5.73027i	0.180556	+	0.260736i
$484$	10.0039	−	3.64112i	0.454723	−	0.165506i
$485$	9.74393	−	5.62566i	0.442449	−	0.255448i
$486$	−8.00990	+	13.3732i	−0.363337	+	0.606619i
$487$	1.64943	−	2.85690i	0.0747429	−	0.129459i	−0.826232	−	0.563331i	$-0.809520\pi$
$487$	1.64943	−	2.85690i	0.0747429	−	0.129459i	0.900974	+	0.433872i	$0.142853\pi$
$488$	4.57309	+	3.83728i	0.207014	+	0.173706i
$489$	−16.7084	−	6.81309i	−0.755579	−	0.308099i
$490$	7.76134	+	11.6061i	0.350622	+	0.524308i
$491$	−1.97357	+	0.347994i	−0.0890662	+	0.0157048i	−0.218004	−	0.975948i	$-0.569954\pi$
$491$	−1.97357	+	0.347994i	−0.0890662	+	0.0157048i	0.128937	+	0.991653i	$0.458843\pi$
$492$	−4.45250	−	8.43918i	−0.200734	−	0.380468i
$493$	−0.911730	−	2.50496i	−0.0410622	−	0.112818i
$494$	3.13631	−	1.81075i	0.141109	−	0.0814695i
$495$	−3.44920	−	0.883542i	−0.155030	−	0.0397122i
$496$	2.30162	−	1.32884i	0.103346	−	0.0596667i
$497$	13.5331	−	14.4546i	0.607040	−	0.648379i
$498$	−3.76525	−	11.7161i	−0.168725	−	0.525010i
$499$	−4.68556	−	26.5731i	−0.209754	−	1.18958i	−0.889781	−	0.456388i	$-0.849143\pi$
$499$	−4.68556	−	26.5731i	−0.209754	−	1.18958i	0.680026	−	0.733188i	$-0.261968\pi$
$500$	−9.20070	+	7.72031i	−0.411468	+	0.345263i
$501$	−17.2103	−	15.5965i	−0.768899	−	0.696802i
$502$	0.719907	+	1.97793i	0.0321310	+	0.0882793i
$503$	−7.22578	−	12.5154i	−0.322181	−	0.558035i	0.658756	−	0.752356i	$-0.271083\pi$
$503$	−7.22578	−	12.5154i	−0.322181	−	0.558035i	−0.980938	+	0.194322i	$0.937749\pi$
$504$	−3.66279	+	7.04159i	−0.163154	+	0.313657i
$505$	−2.91065	+	5.04139i	−0.129522	+	0.224339i
$506$	−0.891304	−	0.157161i	−0.0396233	−	0.00698666i
$507$	−27.7732	−	1.05914i	−1.23345	−	0.0470380i
$508$	−9.90491	−	3.60509i	−0.439459	−	0.159950i
$509$	−2.11810	−	0.770924i	−0.0938830	−	0.0341706i	0.294652	−	0.955605i	$-0.404796\pi$
$509$	−2.11810	−	0.770924i	−0.0938830	−	0.0341706i	−0.388535	+	0.921434i	$0.627019\pi$
$510$	−0.849959	−	1.09513i	−0.0376368	−	0.0484930i
$511$	22.3471	−	23.8689i	0.988577	−	1.05590i
$512$		−	1.00000i		−	0.0441942i
$513$	3.20326	−	1.38937i	0.141427	−	0.0613424i
$514$	−12.3737	−	7.14396i	−0.545781	−	0.315107i
$515$	−29.2761	−	5.16217i	−1.29006	−	0.227472i
$516$	6.96526	−	5.40594i	0.306629	−	0.237983i
$517$	−3.26099	−	3.88630i	−0.143418	−	0.170919i
$518$	9.95190	+	13.2615i	0.437261	+	0.582675i
$519$	10.3164	−	16.3923i	0.452838	−	0.719542i
$520$	1.86667	−	10.5864i	0.0818591	−	0.464246i
$521$	15.2425	+	26.4008i	0.667786	+	1.15664i	0.978522	+	0.206143i	$0.0660913\pi$
$521$	15.2425	+	26.4008i	0.667786	+	1.15664i	−0.310736	+	0.950496i	$0.600575\pi$
$522$	11.2504	−	16.4506i	0.492417	−	0.720023i
$523$	33.0408	+	19.0761i	1.44478	+	0.834141i	0.998163	−	0.0605863i	$-0.0192970\pi$
$523$	33.0408	+	19.0761i	1.44478	+	0.834141i	0.446612	+	0.894728i	$0.352630\pi$
$524$	−1.78451	+	10.1205i	−0.0779568	+	0.442115i
$525$	3.29328	+	3.32771i	0.143730	+	0.145233i
$526$	−15.0813	−	5.48914i	−0.657576	−	0.239338i
$527$	1.05024	−	0.185186i	0.0457492	−	0.00806682i
$528$	−0.315337	−	0.981214i	−0.0137233	−	0.0427019i
$529$	15.8468	+	13.2971i	0.688993	+	0.578134i
$530$	−4.50721	+	7.80671i	−0.195781	+	0.339102i
$531$	−20.0994	+	29.3897i	−0.872238	+	1.27541i
$532$	1.58566	−	0.803964i	0.0687472	−	0.0348563i
$533$	19.0845	−	22.7440i	0.826642	−	0.985154i
$534$	−1.10984	+	29.1027i	−0.0480274	+	1.25940i
$535$	6.58144	−	18.0824i	0.284541	−	0.781769i
$536$	−9.61029	+	1.69455i	−0.415101	+	0.0731935i
$537$	−22.0603	−	28.4235i	−0.951971	−	1.22656i
$538$	4.68777	+	12.8795i	0.202104	+	0.555276i
$539$	−0.451878	+	4.14070i	−0.0194637	+	0.178352i
$540$	2.95256	−	9.93467i	0.127058	−	0.427520i
$541$	−15.9930	−	27.7006i	−0.687592	−	1.19094i	−0.972615	−	0.232423i	$-0.925335\pi$
$541$	−15.9930	−	27.7006i	−0.687592	−	1.19094i	0.285023	−	0.958521i	$-0.407999\pi$
$542$	1.91021	−	10.8333i	0.0820503	−	0.465331i
$543$	−17.8830	+	2.45478i	−0.767435	+	0.105345i
$544$	0.137242	−	0.377069i	0.00588419	−	0.0161667i
$545$	−5.93781	−	33.6750i	−0.254348	−	1.44248i
$546$	−24.5922	−	2.28047i	−1.05245	−	0.0975952i
$547$	−17.9068	−	15.0256i	−0.765639	−	0.642448i	0.173949	−	0.984755i	$-0.444347\pi$
$547$	−17.9068	−	15.0256i	−0.765639	−	0.642448i	−0.939588	+	0.342307i	$0.888792\pi$
$548$		−	12.2059i		−	0.521411i
$549$	−7.38924	+	16.3138i	−0.315365	+	0.696257i
$550$	−0.607925			−0.0259220
$551$	−4.19476	+	1.52677i	−0.178703	+	0.0650425i
$552$	0.556001	−	2.57510i	0.0236650	−	0.109604i
$553$	8.78300	+	3.74881i	0.373491	+	0.159416i
$554$	−7.43884	+	20.4381i	−0.316046	+	0.868330i
$555$	−16.0424	−	14.5382i	−0.680962	−	0.617111i
$556$	−11.9727	+	14.2685i	−0.507756	+	0.605120i
$557$			26.9996i			1.14401i	0.820250	+	0.572006i	$0.193834\pi$
$557$			26.9996i			1.14401i	−0.820250	+	0.572006i	$0.806166\pi$
$558$	5.69965	+	5.57525i	0.241285	+	0.236019i
$559$	23.7595	+	13.7175i	1.00492	+	0.580190i
$560$	1.19733	−	5.13953i	0.0505966	−	0.217185i
$561$	0.0157599	−	0.413263i	0.000665382	−	0.0174480i
$562$	22.5077	−	18.8862i	0.949430	−	0.796666i
$563$	−1.59008	−	9.01776i	−0.0670137	−	0.380053i	−0.999807	−	0.0196419i	$-0.993747\pi$
$563$	−1.59008	−	9.01776i	−0.0670137	−	0.380053i	0.932793	−	0.360412i	$-0.117364\pi$
$564$	11.6658	−	9.05416i	0.491218	−	0.381249i
$565$	22.9316	−	27.3288i	0.964738	−	1.14973i
$566$	24.5044			1.03000
$567$	−23.3043	−	4.88965i	−0.978689	−	0.205346i
$568$	−7.48408			−0.314025
$569$	17.8550	−	21.2787i	0.748519	−	0.892051i	−0.248545	−	0.968620i	$-0.579952\pi$
$569$	17.8550	−	21.2787i	0.748519	−	0.892051i	0.997064	+	0.0765698i	$0.0243968\pi$
$570$	−1.83388	+	1.42333i	−0.0768128	+	0.0596167i
$571$	−2.63887	−	14.9658i	−0.110433	−	0.626298i	−0.988910	−	0.148514i	$-0.952551\pi$
$571$	−2.63887	−	14.9658i	−0.110433	−	0.626298i	0.878477	−	0.477784i	$-0.158560\pi$
$572$	2.45667	−	2.06139i	0.102719	−	0.0861912i
$573$	−0.314265	+	8.24081i	−0.0131286	+	0.344265i
$574$	9.96148	−	10.6398i	0.415784	−	0.444098i
$575$	−1.34575	−	0.776966i	−0.0561214	−	0.0324017i
$576$	2.88903	−	0.808380i	0.120376	−	0.0336825i
$577$		−	9.97852i		−	0.415411i	−0.978191	−	0.207706i	$-0.933400\pi$
$577$		−	9.97852i		−	0.415411i	0.978191	−	0.207706i	$-0.0665996\pi$
$578$	−10.8239	+	12.8994i	−0.450214	+	0.536545i
$579$	−6.04656	−	5.47960i	−0.251286	−	0.227724i
$580$	−4.53193	+	12.4514i	−0.188178	+	0.517015i
$581$	15.0353	−	11.2831i	0.623770	−	0.468101i
$582$	−2.06205	+	9.55033i	−0.0854748	+	0.395874i
$583$	−2.52708	+	0.919781i	−0.104661	+	0.0380934i
$584$	−12.3584			−0.511396
$585$	32.0936	−	3.16498i	1.32691	−	0.130856i
$586$		−	8.71452i		−	0.359994i
$587$	−10.7885	−	9.05266i	−0.445291	−	0.373643i	0.392394	−	0.919797i	$-0.371647\pi$
$587$	−10.7885	−	9.05266i	−0.445291	−	0.373643i	−0.837685	+	0.546154i	$0.816091\pi$
$588$	−11.9939	−	1.77368i	−0.494621	−	0.0731452i
$589$	−0.310109	−	1.75872i	−0.0127778	−	0.0724667i
$590$	8.09649	−	22.2449i	0.333327	−	0.915810i
$591$	38.4258	−	5.27466i	1.58063	−	0.216971i
$592$	1.08821	−	6.17156i	0.0447252	−	0.253649i
$593$	3.26912	+	5.66229i	0.134247	+	0.232522i	0.925309	−	0.379213i	$-0.123805\pi$
$593$	3.26912	+	5.66229i	0.134247	+	0.232522i	−0.791063	+	0.611735i	$0.790472\pi$
$594$	2.57985	−	1.70421i	0.105853	−	0.0699247i
$595$	1.15684	−	1.77363i	0.0474257	−	0.0727119i
$596$	0.0218566	+	0.0600504i	0.000895279	+	0.00245976i
$597$	−25.0188	−	32.2353i	−1.02395	−	1.31930i
$598$	8.07285	−	1.42346i	0.330123	−	0.0582097i
$599$	−2.27979	+	6.26366i	−0.0931496	+	0.255926i	−0.977514	−	0.210871i	$-0.932370\pi$
$599$	−2.27979	+	6.26366i	−0.0931496	+	0.255926i	0.884364	+	0.466797i	$0.154592\pi$
$600$	0.0674335	−	1.76827i	0.00275296	−	0.0721894i
$601$	−8.49583	+	10.1249i	−0.346552	+	0.413005i	−0.910962	−	0.412490i	$-0.864659\pi$
$601$	−8.49583	+	10.1249i	−0.346552	+	0.413005i	0.564410	+	0.825494i	$0.309104\pi$
$602$	11.2807	+	7.35775i	0.459768	+	0.299880i
$603$	−12.6644	−	26.3946i	−0.515734	−	1.07487i
$604$	8.91187	−	15.4358i	0.362619	−	0.628074i
$605$	−16.2663	−	13.6490i	−0.661319	−	0.554913i
$606$	−1.54667	−	4.81267i	−0.0628291	−	0.195501i
$607$	−31.6163	+	5.57480i	−1.28327	+	0.226274i	−0.773366	−	0.633960i	$-0.781428\pi$
$607$	−31.6163	+	5.57480i	−1.28327	+	0.226274i	−0.509899	+	0.860234i	$0.670317\pi$
$608$	−0.631433	−	0.229823i	−0.0256080	−	0.00932055i
$609$	29.3644	+	8.03209i	1.18991	+	0.325477i
$610$	2.06765	−	11.7262i	0.0837168	−	0.474782i
$611$	39.7936	+	22.9749i	1.60988	+	0.929464i
$612$	1.20031	+	0.0916814i	0.0485196	+	0.00370600i
$613$	7.17489	+	12.4273i	0.289791	+	0.501933i	0.973760	−	0.227578i	$-0.0730808\pi$
$613$	7.17489	+	12.4273i	0.289791	+	0.501933i	−0.683969	+	0.729511i	$0.739747\pi$
$614$	−0.0202276	+	0.114716i	−0.000816319	+	0.00462957i
$615$	−10.1370	+	16.1074i	−0.408765	+	0.649512i
$616$	1.25920	−	0.944950i	0.0507345	−	0.0380731i
$617$	−7.14938	−	8.52029i	−0.287823	−	0.343014i	0.602687	−	0.797978i	$-0.294097\pi$
$617$	−7.14938	−	8.52029i	−0.287823	−	0.343014i	−0.890510	+	0.454964i	$0.849652\pi$
$618$	20.3934	−	15.8279i	0.820342	−	0.636691i
$619$	−3.77914	−	0.666364i	−0.151896	−	0.0267834i	0.0971828	−	0.995267i	$-0.469017\pi$
$619$	−3.77914	−	0.666364i	−0.151896	−	0.0267834i	−0.249079	+	0.968483i	$0.580128\pi$
$620$	−4.59076	−	2.65048i	−0.184369	−	0.106446i
$621$	7.88902	−	0.475356i	0.316575	−	0.0190754i
$622$		−	31.5322i		−	1.26433i
$623$	−42.5693	+	12.9221i	−1.70550	+	0.517715i
$624$	5.72347	+	7.37438i	0.229122	+	0.295212i
$625$	17.7113	+	6.44638i	0.708451	+	0.257855i
$626$	21.8885	+	7.96678i	0.874842	+	0.318417i
$627$	−0.692043	−	0.0263912i	−0.0276375	−	0.00105396i
$628$	3.78877	+	0.668063i	0.151188	+	0.0266586i
$629$	1.25733	−	2.17775i	0.0501329	−	0.0868327i
$630$	15.8162	−	0.695555i	0.630132	−	0.0277116i
$631$	18.5421	+	32.1159i	0.738150	+	1.27851i	0.953328	+	0.301938i	$0.0976335\pi$
$631$	18.5421	+	32.1159i	0.738150	+	1.27851i	−0.215178	+	0.976575i	$0.569033\pi$
$632$	−1.23449	−	3.39173i	−0.0491053	−	0.134916i
$633$	−15.5214	−	14.0660i	−0.616921	−	0.559075i
$634$	10.2646	−	8.61303i	0.407660	−	0.342067i
$635$	3.65078	+	20.7046i	0.144877	+	0.821638i
$636$	−2.39505	−	7.45253i	−0.0949700	−	0.295512i
$637$	−8.98105	−	36.6418i	−0.355842	−	1.45180i
$638$	−3.42339	+	1.97650i	−0.135533	+	0.0782503i
$639$	−6.04998	−	21.6218i	−0.239334	−	0.855344i
$640$	−1.72736	+	0.997290i	−0.0682797	+	0.0394213i
$641$	4.57963	+	12.5824i	0.180885	+	0.496976i	0.996685	−	0.0813572i	$-0.0259254\pi$
$641$	4.57963	+	12.5824i	0.180885	+	0.496976i	−0.815800	+	0.578334i	$0.803703\pi$
$642$	7.79751	+	14.7792i	0.307743	+	0.583290i
$643$	23.6344	−	4.16738i	0.932050	−	0.164346i	0.313050	−	0.949737i	$-0.398649\pi$
$643$	23.6344	−	4.16738i	0.932050	−	0.164346i	0.619000	+	0.785391i	$0.287538\pi$
$644$	3.99515	−	0.482473i	0.157431	−	0.0190121i
$645$	−16.2844	−	6.64020i	−0.641197	−	0.261458i
$646$	−0.206552	−	0.173318i	−0.00812669	−	0.00681911i
$647$	−10.7513	+	18.6218i	−0.422677	+	0.732097i	−0.996200	−	0.0870916i	$-0.972243\pi$
$647$	−10.7513	+	18.6218i	−0.422677	+	0.732097i	0.573524	+	0.819189i	$0.305576\pi$
$648$	4.67088	+	7.69304i	0.183489	+	0.302211i
$649$	6.11605	−	3.53110i	0.240076	−	0.138608i
$650$	5.17413	−	1.88323i	0.202946	−	0.0738663i
$651$	−5.20441	+	11.0110i	−0.203977	+	0.431556i
$652$	−7.98045	+	6.69639i	−0.312539	+	0.262251i
$653$	−11.8745	−	14.1515i	−0.464685	−	0.553789i	0.481908	−	0.876222i	$-0.339944\pi$
$653$	−11.8745	−	14.1515i	−0.464685	−	0.553789i	−0.946592	+	0.322432i	$0.895500\pi$
$654$	25.1311	+	15.8161i	0.982703	+	0.618457i
$655$	19.2613	−	7.01055i	0.752603	−	0.273925i
$656$	−5.50892			−0.215087
$657$	−9.99031	−	35.7039i	−0.389759	−	1.39294i
$658$	18.8936	+	12.3232i	0.736547	+	0.480406i
$659$	0.0707308	+	0.0124718i	0.00275528	+	0.000485831i	0.175026	−	0.984564i	$-0.443999\pi$
$659$	0.0707308	+	0.0124718i	0.00275528	+	0.000485831i	−0.172270	+	0.985050i	$0.555110\pi$
$660$	−1.38042	+	1.52325i	−0.0537329	+	0.0592926i
$661$	6.15052	+	7.32991i	0.239228	+	0.285100i	0.872278	−	0.489010i	$-0.162642\pi$
$661$	6.15052	+	7.32991i	0.239228	+	0.285100i	−0.633051	+	0.774110i	$0.718197\pi$
$662$	−11.9596	−	14.2529i	−0.464824	−	0.553955i
$663$	1.14607	+	3.56615i	0.0445096	+	0.138498i
$664$	−6.99707	−	1.23377i	−0.271539	−	0.0478797i
$665$	−2.97010	−	1.93722i	−0.115175	−	0.0751222i
$666$	18.7095	−	1.84508i	0.724980	−	0.0714955i
$667$	−10.1043			−0.391242
$668$	−12.6008	+	4.58633i	−0.487541	+	0.177450i
$669$	−0.946877	+	24.8295i	−0.0366084	+	0.959962i
$670$	12.5113	+	14.9104i	0.483355	+	0.576040i
$671$	2.72118	−	2.28334i	0.105050	−	0.0881473i
$672$	2.60890	+	3.76744i	0.100640	+	0.145332i
$673$	45.6643	−	16.6204i	1.76023	−	0.640671i	0.760268	−	0.649609i	$-0.225067\pi$
$673$	45.6643	−	16.6204i	1.76023	−	0.640671i	0.999960	+	0.00893840i	$0.00284522\pi$
$674$	−27.3655	+	15.7995i	−1.05408	+	0.608574i
$675$	5.16311	−	1.23462i	0.198728	−	0.0475205i
$676$	−8.02327	+	13.8967i	−0.308587	+	0.534489i
$677$	−36.7615	−	30.8465i	−1.41286	−	1.18553i	−0.955038	−	0.296484i	$-0.904186\pi$
$677$	−36.7615	−	30.8465i	−1.41286	−	1.18553i	−0.457821	−	0.889045i	$-0.651370\pi$
$678$	4.21302	+	30.6918i	0.161800	+	1.17871i
$679$	−14.8169	+	1.78936i	−0.568620	+	0.0686692i
$680$	−0.788202	+	0.138981i	−0.0302262	+	0.00532969i
$681$	−38.7419	−	1.47743i	−1.48459	−	0.0566153i
$682$	−0.540880	−	1.48606i	−0.0207114	−	0.0569040i
$683$	13.5587	−	7.82813i	0.518810	−	0.299535i	−0.217638	−	0.976030i	$-0.569835\pi$
$683$	13.5587	−	7.82813i	0.518810	−	0.299535i	0.736448	+	0.676495i	$0.236502\pi$
$684$	0.153528	−	2.01002i	0.00587030	−	0.0768549i
$685$	−21.0840	+	12.1728i	−0.805577	+	0.465100i
$686$	−3.42521	−	18.2008i	−0.130775	−	0.694909i
$687$	−8.19592	+	9.04393i	−0.312694	+	0.345048i
$688$	−0.883954	−	5.01315i	−0.0337004	−	0.191125i
$689$	18.6590	−	15.6567i	0.710850	−	0.596474i
$690$	−5.00261	+	1.60771i	−0.190446	+	0.0612045i
$691$	6.56204	+	18.0291i	0.249632	+	0.685858i	0.999700	+	0.0244972i	$0.00779847\pi$
$691$	6.56204	+	18.0291i	0.249632	+	0.685858i	−0.750068	+	0.661361i	$0.769979\pi$
$692$	−5.59118	−	9.68420i	−0.212545	−	0.368138i
$693$	3.74790	+	2.87399i	0.142371	+	0.109174i
$694$	−17.5722	+	30.4360i	−0.667033	+	1.15533i
$695$	36.5870	+	6.45128i	1.38783	+	0.244711i
$696$	−5.36930	−	10.1769i	−0.203523	−	0.385753i
$697$	−2.07724	−	0.756054i	−0.0786811	−	0.0286376i
$698$	6.05271	+	2.20301i	0.229099	+	0.0833850i
$699$	−14.0321	+	1.92617i	−0.530743	+	0.0728545i
$700$	2.58650	−	0.785147i	0.0977605	−	0.0296758i
$701$			15.5312i			0.586604i	0.956020	+	0.293302i	$0.0947542\pi$
$701$			15.5312i			0.586604i	−0.956020	+	0.293302i	$0.905246\pi$
$702$	−16.6781	+	22.4966i	−0.629474	+	0.849080i
$703$	−3.64683	−	2.10550i	−0.137543	−	0.0794104i
$704$	−0.586000	−	0.103328i	−0.0220857	−	0.00389431i
$705$	−27.2739	−	11.1214i	−1.02720	−	0.418855i
$706$	−11.3805	−	13.5628i	−0.428311	−	0.510441i
$707$	6.17613	−	4.63480i	0.232277	−	0.174310i
$708$	9.59250	+	18.1814i	0.360508	+	0.683300i
$709$	3.65351	−	20.7201i	0.137210	−	0.778159i	−0.836084	−	0.548601i	$-0.815161\pi$
$709$	3.65351	−	20.7201i	0.137210	−	0.778159i	0.973295	−	0.229558i	$-0.0737282\pi$
$710$	7.46379	+	12.9277i	0.280111	+	0.485167i
$711$	8.80089	−	6.30829i	0.330059	−	0.236579i
$712$	14.5619	+	8.40733i	0.545731	+	0.315078i
$713$	0.701942	−	3.98091i	0.0262879	−	0.149086i
$714$	0.466684	+	1.77864i	0.0174652	+	0.0665638i
$715$	−6.01078	−	2.18774i	−0.224790	−	0.0818170i
$716$	−20.4574	+	3.60719i	−0.764528	+	0.134807i
$717$	11.7198	+	2.53047i	0.437684	+	0.0945021i
$718$	−12.2937	−	10.3156i	−0.458797	−	0.384976i
$719$	−5.52185	+	9.56412i	−0.205930	+	0.356681i	−0.950429	−	0.310943i	$-0.899355\pi$
$719$	−5.52185	+	9.56412i	−0.205930	+	0.356681i	0.744499	+	0.667624i	$0.232689\pi$
$720$	−4.27756	−	4.18420i	−0.159415	−	0.155936i
$721$	33.0285	+	21.5425i	1.23004	+	0.802286i
$722$	11.9227	−	14.2090i	0.443718	−	0.528803i
$723$	31.1553	−	16.4375i	1.15868	−	0.611316i
$724$	−3.56440	+	9.79310i	−0.132470	+	0.363958i
$725$	−6.68398	+	1.17857i	−0.248237	+	0.0437709i
$726$	18.2680	−	2.50762i	0.677988	−	0.0930666i
$727$	−7.32567	−	20.1271i	−0.271694	−	0.746474i	−0.998237	−	0.0593525i	$-0.981096\pi$
$727$	−7.32567	−	20.1271i	−0.271694	−	0.746474i	0.726543	−	0.687121i	$-0.241126\pi$
$728$	−7.78992	+	11.9433i	−0.288714	+	0.442649i
$729$	−18.4496	+	19.7132i	−0.683319	+	0.730120i
$730$	12.3249	+	21.3474i	0.456166	+	0.790103i
$731$	0.354702	−	2.01162i	0.0131191	−	0.0744023i
$732$	6.33970	+	8.16836i	0.234322	+	0.301911i
$733$	−4.15168	+	11.4066i	−0.153346	+	0.421314i	−0.992449	−	0.122658i	$-0.960858\pi$
$733$	−4.15168	+	11.4066i	−0.153346	+	0.421314i	0.839103	+	0.543972i	$0.183080\pi$
$734$	5.70812	+	32.3723i	0.210690	+	1.19488i
$735$	8.89764	+	22.4866i	0.328194	+	0.829432i
$736$	−1.16515	−	0.977678i	−0.0429480	−	0.0360377i
$737$			5.80673i			0.213893i
$738$	−4.45330	−	15.9155i	−0.163928	−	0.585856i
$739$	−35.5154			−1.30646			−0.653228	−	0.757161i	$-0.726586\pi$
$739$	−35.5154			−1.30646			−0.653228	+	0.757161i	$0.726586\pi$
$740$	−11.7457	+	4.27510i	−0.431782	+	0.157156i
$741$	5.97181	−	1.91919i	0.219380	−	0.0705031i
$742$	9.56388	−	7.17710i	0.351101	−	0.263480i
$743$	2.80594	−	7.70925i	0.102940	−	0.282825i	−0.877521	−	0.479538i	$-0.840804\pi$
$743$	2.80594	−	7.70925i	0.102940	−	0.282825i	0.980461	+	0.196713i	$0.0630266\pi$
$744$	4.38249	−	1.40842i	0.160670	−	0.0516351i
$745$	0.0819311	−	0.0976417i	0.00300172	−	0.00357731i
$746$			35.7177i			1.30772i
$747$	−2.09188	−	21.2121i	−0.0765380	−	0.776112i
$748$	−0.206781	−	0.119385i	−0.00756068	−	0.00436516i
$749$	−17.4452	+	18.6332i	−0.637433	+	0.680842i
$750$	−18.3993	+	9.70744i	−0.671847	+	0.354466i
$751$	−6.17232	+	5.17919i	−0.225231	+	0.188991i	−0.748419	−	0.663226i	$-0.769187\pi$
$751$	−6.17232	+	5.17919i	−0.225231	+	0.188991i	0.523188	+	0.852217i	$0.324742\pi$
$752$	−1.48049	−	8.39629i	−0.0539880	−	0.306181i
$753$	0.495797	+	3.61187i	0.0180678	+	0.131624i
$754$	23.0141	−	27.4272i	0.838125	−	0.998839i
$755$	−35.5509			−1.29383
$756$	−8.77530	+	10.5827i	−0.319154	+	0.384890i
$757$	1.61976			0.0588711			0.0294355	−	0.999567i	$-0.490629\pi$
$757$	1.61976			0.0588711			0.0294355	+	0.999567i	$0.490629\pi$
$758$	9.77553	−	11.6500i	0.355063	−	0.423148i
$759$	−1.45156	−	0.591896i	−0.0526883	−	0.0214845i
$760$	0.232736	+	1.31991i	0.00844221	+	0.0478782i
$761$	11.7224	−	9.83623i	0.424935	−	0.356563i	−0.405101	−	0.914272i	$-0.632764\pi$
$761$	11.7224	−	9.83623i	0.424935	−	0.356563i	0.830037	+	0.557709i	$0.188319\pi$
$762$	−15.4515	−	9.72430i	−0.559750	−	0.352274i
$763$	−10.2913	+	44.1750i	−0.372569	+	1.59924i
$764$	4.12340	+	2.38065i	0.149179	+	0.0861287i
$765$	−1.03869	−	2.16479i	−0.0375539	−	0.0782682i
$766$		−	21.5532i		−	0.778748i
$767$	−41.1158	+	48.9999i	−1.48461	+	1.76928i
$768$	0.365550	−	1.69304i	0.0131907	−	0.0610922i
$769$	−2.78234	+	7.64441i	−0.100334	+	0.275665i	−0.979696	−	0.200489i	$-0.935747\pi$
$769$	−2.78234	+	7.64441i	−0.100334	+	0.275665i	0.879362	+	0.476153i	$0.157969\pi$
$770$	−2.88805	−	1.23269i	−0.104078	−	0.0444232i
$771$	−18.3377	−	16.6182i	−0.660415	−	0.598490i
$772$	−4.42710	+	1.61133i	−0.159335	+	0.0579932i
$773$	10.5191			0.378347			0.189174	−	0.981944i	$-0.439419\pi$
$773$	10.5191			0.378347			0.189174	+	0.981944i	$0.439419\pi$
$774$	13.7686	−	6.60630i	0.494902	−	0.237459i
$775$		−	2.71523i		−	0.0975340i
$776$	4.32122	+	3.62593i	0.155123	+	0.130163i
$777$	12.0012	+	26.0900i	0.430541	+	0.935975i
$778$	−0.593135	−	3.36384i	−0.0212649	−	0.120599i
$779$	−1.26608	+	3.47851i	−0.0453619	+	0.124631i
$780$	7.03023	−	17.2409i	0.251722	−	0.617322i
$781$	−0.773312	+	4.38567i	−0.0276713	+	0.156932i
$782$	−0.305164	−	0.528559i	−0.0109126	−	0.0189012i
$783$	25.0609	−	23.7389i	0.895602	−	0.848358i
$784$	−4.13701	+	5.64669i	−0.147750	+	0.201668i
$785$	−2.62452	−	7.21081i	−0.0936732	−	0.257365i
$786$	−6.72079	+	16.4820i	−0.239723	+	0.587894i
$787$	−15.4224	+	2.71938i	−0.549749	+	0.0969355i	−0.441621	−	0.897202i	$-0.645597\pi$
$787$	−15.4224	+	2.71938i	−0.549749	+	0.0969355i	−0.108127	+	0.994137i	$0.534485\pi$
$788$	7.65892	−	21.0427i	0.272838	−	0.749616i
$789$	−23.5266	−	14.8063i	−0.837570	−	0.527118i
$790$	−4.62758	+	5.51494i	−0.164642	+	0.196213i
$791$	−42.2070	+	21.3998i	−1.50071	+	0.760890i
$792$	−0.175194	−	1.77650i	−0.00622524	−	0.0631253i
$793$	−16.0869	+	27.8634i	−0.571264	+	0.989458i
$794$	22.6454	+	19.0018i	0.803655	+	0.674347i
$795$	−10.4846	+	11.5694i	−0.371851	+	0.410326i
$796$	−23.2009	+	4.09094i	−0.822334	+	0.145000i
$797$	14.8946	+	5.42119i	0.527593	+	0.192028i	0.592063	−	0.805891i	$-0.298313\pi$
$797$	14.8946	+	5.42119i	0.527593	+	0.192028i	−0.0644701	+	0.997920i	$0.520536\pi$
$798$	2.97847	−	0.781501i	0.105437	−	0.0276648i
$799$	0.594074	−	3.36916i	0.0210168	−	0.119192i
$800$	−0.884779	−	0.510827i	−0.0312816	−	0.0180605i
$801$	−12.5175	+	48.8662i	−0.442284	+	1.72660i
$802$	0.863055	+	1.49485i	0.0304755	+	0.0527852i
$803$	−1.27697	+	7.24205i	−0.0450632	+	0.255566i
$804$	−16.8900	−	0.644105i	−0.595665	−	0.0227158i
$805$	−4.81772	−	6.41988i	−0.169802	−	0.226271i
$806$	9.20699	+	10.9725i	0.324302	+	0.386489i
$807$	3.22844	+	23.5191i	0.113647	+	0.827913i
$808$	−2.87422	−	0.506803i	−0.101115	−	0.0178293i
$809$	44.8033	+	25.8672i	1.57520	+	0.909443i	0.995515	+	0.0946029i	$0.0301582\pi$
$809$	44.8033	+	25.8672i	1.57520	+	0.909443i	0.579686	+	0.814840i	$0.303175\pi$
$810$	8.63041	−	15.7405i	0.303242	−	0.553063i
$811$		−	22.8393i		−	0.801997i	−0.916079	−	0.400999i	$-0.868663\pi$
$811$		−	22.8393i		−	0.801997i	0.916079	−	0.400999i	$-0.131337\pi$
$812$	12.0126	−	12.8306i	0.421560	−	0.450268i
$813$	7.19417	−	17.6429i	0.252311	−	0.618764i
$814$	−3.50409	−	1.27539i	−0.122818	−	0.0447022i
$815$	19.5259	+	7.10684i	0.683962	+	0.248942i
$816$	0.370193	−	0.588222i	0.0129593	−	0.0205919i
$817$	−3.36862	−	0.593979i	−0.117853	−	0.0207807i
$818$	1.51134	−	2.61771i	0.0528427	−	0.0915262i
$819$	−40.8019	−	12.8506i	−1.42573	−	0.449037i
$820$	5.49399	+	9.51587i	0.191858	+	0.332308i
$821$	10.4496	+	28.7099i	0.364692	+	1.00198i	0.977349	+	0.211634i	$0.0678785\pi$
$821$	10.4496	+	28.7099i	0.364692	+	1.00198i	−0.612657	+	0.790349i	$0.709899\pi$
$822$	4.46188	−	20.6651i	0.155626	−	0.720777i
$823$	−33.4879	+	28.0997i	−1.16732	+	0.979494i	−0.999979	−	0.00640611i	$-0.997961\pi$
$823$	−33.4879	+	28.0997i	−1.16732	+	0.979494i	−0.167336	+	0.985900i	$0.553516\pi$
$824$	−2.58810	−	14.6778i	−0.0901607	−	0.511327i
$825$	−1.02924	−	0.222227i	−0.0358335	−	0.00773697i
$826$	−21.4611	+	22.9225i	−0.746726	+	0.797577i
$827$	−11.3252	+	6.53859i	−0.393814	+	0.227369i	−0.683812	−	0.729659i	$-0.739679\pi$
$827$	−11.3252	+	6.53859i	−0.393814	+	0.227369i	0.289997	+	0.957028i	$0.406346\pi$
$828$	1.88266	−	4.15650i	0.0654270	−	0.144448i
$829$	−9.00647	+	5.19989i	−0.312807	+	0.180599i	−0.648182	−	0.761485i	$-0.724470\pi$
$829$	−9.00647	+	5.19989i	−0.312807	+	0.180599i	0.335375	+	0.942085i	$0.391137\pi$
$830$	4.84694	+	13.3169i	0.168240	+	0.462235i
$831$	−20.0654	+	31.8831i	−0.696060	+	1.10601i
$832$	5.30761	−	0.935874i	0.184008	−	0.0324456i
$833$	−2.33490	+	1.56142i	−0.0808994	+	0.0541000i
$834$	−25.4861	+	19.7805i	−0.882511	+	0.684942i
$835$	20.4889	+	17.1922i	0.709048	+	0.594962i
$836$	−0.199921	+	0.346273i	−0.00691440	+	0.0119761i
$837$	7.61168	+	11.5226i	0.263098	+	0.398280i
$838$	−10.4887	+	6.05568i	−0.362328	+	0.209190i
$839$	10.1190	−	3.68300i	0.349345	−	0.127151i	−0.161387	−	0.986891i	$-0.551597\pi$
$839$	10.1190	−	3.68300i	0.349345	−	0.127151i	0.510732	+	0.859740i	$0.329374\pi$
$840$	3.90589	−	8.26373i	0.134766	−	0.285126i
$841$	−11.5923	+	9.72706i	−0.399733	+	0.335416i
$842$	−7.84750	−	9.35229i	−0.270443	−	0.322301i
$843$	45.0102	−	23.7473i	1.55023	−	0.817902i
$844$	−11.3643	+	4.13627i	−0.391175	+	0.142376i
$845$	32.0061			1.10104
$846$	23.0604	−	11.0646i	0.792832	−	0.380408i
$847$	12.7373	+	25.1219i	0.437660	+	0.863199i
$848$	−4.45080	−	0.784796i	−0.152841	−	0.0269500i
$849$	41.4869	+	8.95760i	1.42383	+	0.307424i
$850$	−0.263515	−	0.314045i	−0.00903851	−	0.0107717i
$851$	−6.12688	−	7.30173i	−0.210027	−	0.250300i
$852$	−12.6708	−	2.73581i	−0.434095	−	0.0937272i
$853$	−32.5761	−	5.74404i	−1.11538	−	0.196672i	−0.414570	−	0.910017i	$-0.636068\pi$
$853$	−32.5761	−	5.74404i	−1.11538	−	0.196672i	−0.700813	+	0.713345i	$0.747179\pi$
$854$	−8.62864	+	13.2292i	−0.295266	+	0.452694i
$855$	−3.62513	+	1.73937i	−0.123977	+	0.0594852i
$856$	9.64758			0.329747
$857$	−44.3260	+	16.1333i	−1.51415	+	0.551105i	−0.959679	−	0.281100i	$-0.909301\pi$
$857$	−44.3260	+	16.1333i	−1.51415	+	0.551105i	−0.554469	+	0.832204i	$0.687079\pi$
$858$	4.91278	−	2.59198i	0.167720	−	0.0884887i
$859$	−11.4118	−	13.6001i	−0.389367	−	0.464029i	0.535380	−	0.844611i	$-0.320168\pi$
$859$	−11.4118	−	13.6001i	−0.389367	−	0.464029i	−0.924747	+	0.380582i	$0.875724\pi$
$860$	−7.77794	+	6.52646i	−0.265225	+	0.222551i
$861$	20.7545	−	14.3722i	0.707313	−	0.489804i
$862$	−7.99373	+	2.90948i	−0.272268	+	0.0990973i
$863$	−6.80308	+	3.92776i	−0.231580	+	0.133703i	−0.611301	−	0.791398i	$-0.709353\pi$
$863$	−6.80308	+	3.92776i	−0.231580	+	0.133703i	0.379721	+	0.925101i	$0.376020\pi$
$864$	5.18675	−	0.312529i	0.176457	−	0.0106325i
$865$	−11.1520	+	19.3159i	−0.379181	+	0.656761i
$866$	11.2651	+	9.45252i	0.382803	+	0.321210i
$867$	−23.0406	+	17.8825i	−0.782501	+	0.607321i
$868$	4.22052	+	5.62407i	0.143254	+	0.190893i
$869$	−2.11511	+	0.372951i	−0.0717503	+	0.0126515i
$870$	−12.2243	+	19.4240i	−0.414443	+	0.658534i
$871$	−17.9880	−	49.4217i	−0.609501	−	1.67459i
$872$	14.8469	−	8.57185i	0.502779	−	0.290279i
$873$	−6.98225	+	15.4153i	−0.236314	+	0.521728i
$874$	−0.885116	+	0.511022i	−0.0299395	+	0.0172856i
$875$	−23.1972	−	21.7182i	−0.784209	−	0.734210i
$876$	−20.9233	−	4.51763i	−0.706932	−	0.152637i
$877$	−5.41149	−	30.6901i	−0.182733	−	1.03633i	−0.928834	−	0.370497i	$-0.879187\pi$
$877$	−5.41149	−	30.6901i	−0.182733	−	1.03633i	0.746101	−	0.665833i	$-0.231924\pi$
$878$	24.1517	−	20.2657i	0.815081	−	0.683934i
$879$	3.18560	−	14.7540i	0.107448	−	0.497640i
$880$	0.405928	+	1.11528i	0.0136838	+	0.0375960i
$881$	2.88180	+	4.99142i	0.0970902	+	0.168165i	0.910479	−	0.413555i	$-0.135713\pi$
$881$	2.88180	+	4.99142i	0.0970902	+	0.168165i	−0.813389	+	0.581720i	$0.802380\pi$
$882$	−19.6578	−	7.38728i	−0.661912	−	0.248743i
$883$	−5.42873	+	9.40283i	−0.182691	+	0.316430i	−0.942796	−	0.333370i	$-0.891814\pi$
$883$	−5.42873	+	9.40283i	−0.182691	+	0.316430i	0.760105	+	0.649800i	$0.225148\pi$
$884$	2.12977	+	0.375536i	0.0716320	+	0.0126307i
$885$	21.8393	−	34.7018i	0.734120	−	1.16649i
$886$	3.12704	+	1.13815i	0.105055	+	0.0382369i
$887$	46.8208	+	17.0414i	1.57209	+	0.572193i	0.973465	−	0.228837i	$-0.0734924\pi$
$887$	46.8208	+	17.0414i	1.57209	+	0.572193i	0.598623	+	0.801031i	$0.295715\pi$
$888$	4.09840	−	10.0509i	0.137533	−	0.337285i
$889$	6.32746	−	27.1605i	0.212216	−	0.910933i
$890$		−	33.5382i		−	1.12420i
$891$	4.99076	−	1.94223i	0.167197	−	0.0650672i
$892$	12.4238	+	7.17286i	0.415978	+	0.240165i
$893$	−5.64194	−	0.994827i	−0.188800	−	0.0332906i
$894$	0.0150525	+	0.109657i	0.000503431	+	0.00366748i
$895$	26.6328	+	31.7398i	0.890237	+	1.06094i
$896$	2.62667	−	0.317208i	0.0877508	−	0.0105972i
$897$	14.1880	+	0.541062i	0.473723	+	0.0180655i
$898$	−6.09381	+	34.5597i	−0.203353	+	1.15327i
$899$	−8.82781	−	15.2902i	−0.294424	−	0.509957i
$900$	0.760560	−	2.96910i	0.0253520	−	0.0989700i
$901$	−1.57055	−	0.906757i	−0.0523226	−	0.0302085i
$902$	−0.569224	+	3.22823i	−0.0189531	+	0.107488i
$903$	16.4091	+	16.5806i	0.546059	+	0.551768i
$904$	16.8074	+	6.11740i	0.559006	+	0.203462i
$905$	20.4709	−	3.60957i	0.680476	−	0.119986i
$906$	20.7307	−	22.8757i	0.688731	−	0.759993i
$907$	22.2815	+	18.6964i	0.739844	+	0.620803i	0.932796	−	0.360406i	$-0.117362\pi$
$907$	22.2815	+	18.6964i	0.739844	+	0.620803i	−0.192952	+	0.981208i	$0.561806\pi$
$908$	−11.1919	+	19.3850i	−0.371418	+	0.643315i
$909$	−0.859293	−	8.71341i	−0.0285009	−	0.289006i
$910$	28.3992	+	1.54503i	0.941423	+	0.0512171i
$911$	29.6831	−	35.3750i	0.983445	−	1.17202i	−0.00164715	−	0.999999i	$-0.500524\pi$
$911$	29.6831	−	35.3750i	0.983445	−	1.17202i	0.985092	−	0.172026i	$-0.0550312\pi$
$912$	−0.985028	−	0.619919i	−0.0326175	−	0.0205276i
$913$	−1.44598	+	3.97280i	−0.0478550	+	0.131481i
$914$	12.0466	−	2.12414i	0.398467	−	0.0702604i
$915$	7.78715	−	19.0971i	0.257435	−	0.631332i
$916$	2.41010	+	6.62168i	0.0796318	+	0.218787i
$917$	−27.1492	−	1.47702i	−0.896545	−	0.0487755i
$918$	1.99865	+	0.593993i	0.0659653	+	0.0196047i
$919$	15.7061	+	27.2038i	0.518098	+	0.897371i	0.999779	+	0.0210248i	$0.00669291\pi$
$919$	15.7061	+	27.2038i	0.518098	+	0.897371i	−0.481681	+	0.876346i	$0.659974\pi$
$920$	−0.526805	+	2.98766i	−0.0173682	+	0.0985002i
$921$	−0.0761806	+	0.186825i	−0.00251024	+	0.00615608i
$922$	1.14644	−	3.14982i	0.0377560	−	0.103734i
$923$	−7.00415	−	39.7225i	−0.230545	−	1.30748i
$924$	2.47730	−	1.13953i	0.0814970	−	0.0374879i
$925$	−4.90457	−	4.11543i	−0.161261	−	0.135314i
$926$			8.92366i			0.293250i
$927$	40.3126	−	19.3424i	1.32404	−	0.635287i
$928$	−6.64324			−0.218075
$929$	36.3304	−	13.2232i	1.19196	−	0.433839i	0.331550	−	0.943438i	$-0.392428\pi$
$929$	36.3304	−	13.2232i	1.19196	−	0.433839i	0.860412	+	0.509599i	$0.170206\pi$
$930$	−6.80345	−	6.16551i	−0.223094	−	0.202175i
$931$	2.61473	+	3.90998i	0.0856944	+	0.128145i
$932$	−2.79684	+	7.68426i	−0.0916136	+	0.251706i
$933$	11.5266	−	53.3852i	0.377364	−	1.74775i
$934$	−1.76521	+	2.10369i	−0.0577594	+	0.0688349i
$935$			0.476247i			0.0155749i
$936$	6.99434	+	14.5773i	0.228617	+	0.476474i
$937$	15.1097	+	8.72360i	0.493613	+	0.284988i	0.726072	−	0.687619i	$-0.241344\pi$
$937$	15.1097	+	8.72360i	0.493613	+	0.284988i	−0.232459	+	0.972606i	$0.574677\pi$
$938$	−7.49949	−	24.7055i	−0.244867	−	0.806663i
$939$	34.1459	+	21.4894i	1.11431	+	0.701281i
$940$	−13.0269	+	10.9309i	−0.424891	+	0.356525i
$941$	5.18854	+	29.4257i	0.169142	+	0.959249i	0.944691	+	0.327962i	$0.106362\pi$
$941$	5.18854	+	29.4257i	0.169142	+	0.959249i	−0.775549	+	0.631287i	$0.782527\pi$
$942$	6.17032	+	2.51604i	0.201040	+	0.0819771i
$943$	−5.38595	+	6.41872i	−0.175391	+	0.209022i
$944$	11.8685			0.386285
$945$	27.0317	+	4.60402i	0.879340	+	0.149769i
$946$	−3.02904			−0.0984827
$947$	9.26108	−	11.0369i	0.300945	−	0.358652i	−0.594287	−	0.804253i	$-0.702566\pi$
$947$	9.26108	−	11.0369i	0.300945	−	0.358652i	0.895232	+	0.445601i	$0.147010\pi$
$948$	−0.850187	−	6.19359i	−0.0276128	−	0.201159i
$949$	−11.5659	−	65.5937i	−0.375446	−	2.12926i
$950$	−0.525896	+	0.441279i	−0.0170623	+	0.0143170i
$951$	20.5269	−	10.8299i	0.665629	−	0.351185i
$952$	1.03397	+	0.240879i	0.0335111	+	0.00780693i
$953$	−8.62879	−	4.98184i	−0.279514	−	0.161377i	0.353689	−	0.935363i	$-0.384927\pi$
$953$	−8.62879	−	4.98184i	−0.279514	−	0.161377i	−0.633203	+	0.773985i	$0.718260\pi$
$954$	−1.33063	−	13.4929i	−0.0430809	−	0.436849i
$955$		−	9.49677i		−	0.307308i
$956$	4.44960	−	5.30283i	0.143910	−	0.171506i
$957$	−6.51844	+	2.09486i	−0.210711	+	0.0677172i
$958$	−4.85927	+	13.3507i	−0.156996	+	0.431343i
$959$	32.0609	−	3.87182i	1.03530	−	0.125028i
$960$	−3.28904	+	1.05701i	−0.106153	+	0.0341149i
$961$	−22.4932	+	8.18684i	−0.725586	+	0.264092i
$962$	33.7746			1.08894
$963$	7.79891	+	27.8722i	0.251316	+	0.898168i
$964$		−	20.3375i		−	0.655027i
$965$	7.19845	+	6.04022i	0.231726	+	0.194441i
$966$	6.94030	+	0.643585i	0.223301	+	0.0207070i
$967$	−9.03747	−	51.2540i	−0.290625	−	1.64822i	−0.684470	−	0.729041i	$-0.739966\pi$
$967$	−9.03747	−	51.2540i	−0.290625	−	1.64822i	0.393845	−	0.919177i	$-0.371145\pi$
$968$	3.64112	−	10.0039i	0.117030	−	0.321537i
$969$	−0.286344	−	0.368939i	−0.00919870	−	0.0118520i
$970$	1.95377	−	11.0804i	0.0627318	−	0.355770i
$971$	−26.7263	−	46.2914i	−0.857689	−	1.48556i	−0.874128	−	0.485696i	$-0.838566\pi$
$971$	−26.7263	−	46.2914i	−0.857689	−	1.48556i	0.0164383	−	0.999865i	$-0.494767\pi$
$972$	5.09577	+	14.7320i	0.163447	+	0.472531i
$973$	−41.2765	−	26.9222i	−1.32326	−	0.863086i
$974$	−1.12828	−	3.09992i	−0.0361524	−	0.0993278i
$975$	9.44840	−	1.29697i	0.302591	−	0.0415363i
$976$	5.87906	−	1.03664i	0.188184	−	0.0331819i
$977$	14.3299	−	39.3711i	0.458454	−	1.25959i	−0.468182	−	0.883632i	$-0.655091\pi$
$977$	14.3299	−	39.3711i	0.458454	−	1.25959i	0.926636	−	0.375960i	$-0.122687\pi$
$978$	−15.9591	+	8.41998i	−0.510315	+	0.269241i
$979$	6.43134	−	7.66458i	0.205547	−	0.244961i
$980$	13.8796	+	1.51470i	0.443369	+	0.0483852i
$981$	36.7663	+	35.9638i	1.17386	+	1.14824i
$982$	−1.00201	+	1.73553i	−0.0319754	+	0.0553831i
$983$	−12.3391	−	10.3537i	−0.393556	−	0.330233i	0.424441	−	0.905456i	$-0.360471\pi$
$983$	−12.3391	−	10.3537i	−0.393556	−	0.330233i	−0.817997	+	0.575223i	$0.804915\pi$
$984$	−9.32680	−	2.01379i	−0.297328	−	0.0641972i
$985$	−43.9864	+	7.75600i	−1.40152	+	0.247127i
$986$	−2.50496	−	0.911730i	−0.0797741	−	0.0290354i
$987$	27.4827	+	27.7701i	0.874785	+	0.883932i
$988$	0.628867	−	3.56648i	0.0200069	−	0.113465i
$989$	−6.70530	−	3.87131i	−0.213216	−	0.123100i
$990$	−2.89393	+	2.07431i	−0.0919753	+	0.0659259i
$991$	−8.72806	−	15.1174i	−0.277256	−	0.480221i	0.693446	−	0.720509i	$-0.256092\pi$
$991$	−8.72806	−	15.1174i	−0.277256	−	0.480221i	−0.970702	+	0.240287i	$0.922758\pi$
$992$	0.461502	−	2.61731i	0.0146527	−	0.0830995i
$993$	−15.0379	−	28.5025i	−0.477213	−	0.904501i
$994$	−2.37401	−	19.6582i	−0.0752991	−	0.623520i
$995$	30.2045	+	35.9964i	0.957548	+	1.14116i
$996$	−11.3953	−	4.64661i	−0.361074	−	0.147233i
$997$	−54.6690	−	9.63963i	−1.73139	−	0.305290i	−0.782909	−	0.622136i	$-0.786265\pi$
$997$	−54.6690	−	9.63963i	−1.73139	−	0.305290i	−0.948477	+	0.316846i	$0.897376\pi$
$998$	−23.3680	−	13.4915i	−0.739701	−	0.427067i
$999$	32.3504	+	3.71549i	1.02352	+	0.117553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.21	yes	144
7.5	odd	6		378.2.ba.a.47.5	✓	144
27.23	odd	18		378.2.ba.a.185.5	yes	144
189.131	even	18	inner	378.2.bf.a.131.21	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.5	✓	144	7.5	odd	6
378.2.ba.a.185.5	yes	144	27.23	odd	18
378.2.bf.a.101.21	yes	144	1.1	even	1	trivial
378.2.bf.a.131.21	yes	144	189.131	even	18	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.36829 - 1.06197i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.52794 + 1.28209i) q^{5} +(0.0660042 - 1.73079i) q^{6} +(2.53168 - 0.768505i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.744440 - 2.90617i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.36829 - 1.06197i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.52794 + 1.28209i) q^{5} +(0.0660042 - 1.73079i) q^{6} +(2.53168 - 0.768505i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.744440 - 2.90617i) q^{9} +1.99458i q^{10} +(-0.382485 + 0.455827i) q^{11} +(-1.28344 - 1.16309i) q^{12} +(1.84331 - 5.06446i) q^{13} +(1.03862 - 2.43336i) q^{14} +(-0.729119 + 3.37690i) q^{15} +(-0.939693 + 0.342020i) q^{16} -0.401268 q^{17} +(-1.74774 - 2.43832i) q^{18} +0.671957i q^{19} +(1.52794 + 1.28209i) q^{20} +(2.64794 - 3.74011i) q^{21} +(0.103328 + 0.586000i) q^{22} +(-0.520211 + 1.42927i) q^{23} +(-1.71596 + 0.235548i) q^{24} +(-0.177408 + 1.00613i) q^{25} +(-2.69474 - 4.66743i) q^{26} +(-2.06765 - 4.76705i) q^{27} +(-1.19645 - 2.35977i) q^{28} +(2.27212 + 6.24260i) q^{29} +(2.11818 + 2.72916i) q^{30} +(-2.61731 + 0.461502i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.0392752 + 1.02989i) q^{33} +(-0.257930 + 0.307389i) q^{34} +(-2.88295 + 4.42007i) q^{35} +(-2.99129 - 0.228479i) q^{36} +(-3.13338 + 5.42718i) q^{37} +(0.514749 + 0.431926i) q^{38} +(-2.85612 - 8.88719i) q^{39} +(1.96428 - 0.346355i) q^{40} +(5.17669 + 1.88416i) q^{41} +(-1.16302 - 4.43254i) q^{42} +(-0.883954 + 5.01315i) q^{43} +(0.515320 + 0.297520i) q^{44} +(2.58851 + 5.39488i) q^{45} +(0.760498 + 1.31722i) q^{46} +(-1.48049 + 8.39629i) q^{47} +(-0.922558 + 1.46591i) q^{48} +(5.81880 - 3.89122i) q^{49} +(0.656707 + 0.782633i) q^{50} +(-0.549051 + 0.426135i) q^{51} +(-5.30761 - 0.935874i) q^{52} +(3.91397 + 2.25973i) q^{53} +(-4.98084 - 1.48029i) q^{54} -1.18685i q^{55} +(-2.57675 - 0.600295i) q^{56} +(0.713598 + 0.919433i) q^{57} +(6.24260 + 2.27212i) q^{58} +(-11.1527 - 4.05925i) q^{59} +(3.45220 + 0.131651i) q^{60} +(-5.87906 - 1.03664i) q^{61} +(-1.32884 + 2.30162i) q^{62} +(-0.348723 - 7.92959i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.67663 + 10.1015i) q^{65} +(0.763697 + 0.692088i) q^{66} +(7.47548 - 6.27267i) q^{67} +(0.0696795 + 0.395172i) q^{68} +(0.806040 + 2.50810i) q^{69} +(1.53284 + 5.04963i) q^{70} +(6.48140 - 3.74204i) q^{71} +(-2.09779 + 2.14460i) q^{72} +(10.7027 - 6.17922i) q^{73} +(2.14336 + 5.88883i) q^{74} +(0.825737 + 1.56509i) q^{75} +(0.661749 - 0.116684i) q^{76} +(-0.618022 + 1.44795i) q^{77} +(-8.64386 - 3.52467i) q^{78} +(2.76496 + 2.32008i) q^{79} +(0.997290 - 1.72736i) q^{80} +(-7.89162 - 4.32693i) q^{81} +(4.77086 - 2.75446i) q^{82} +(6.67653 - 2.43006i) q^{83} +(-4.14310 - 1.95825i) q^{84} +(0.613112 - 0.514462i) q^{85} +(3.27210 + 3.89954i) q^{86} +(9.73838 + 6.12877i) q^{87} +(0.559155 - 0.203516i) q^{88} -16.8147 q^{89} +(5.79658 + 1.48484i) q^{90} +(0.774612 - 14.2382i) q^{91} +(1.49789 + 0.264118i) q^{92} +(-3.09113 + 3.41097i) q^{93} +(5.48029 + 6.53115i) q^{94} +(-0.861510 - 1.02671i) q^{95} +(0.529942 + 1.64899i) q^{96} +(-5.55525 - 0.979540i) q^{97} +(0.759407 - 6.95869i) q^{98} +(1.03997 + 1.45090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) 144 * q + 18 * q^6 - 12 * q^9	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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