LMFDB - Embedded newform 378.2.v.a.67.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, 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:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.11
Character	$\chi$	$=$	378.67
Dual form			378.2.v.a.79.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(1.59651 + 0.671670i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.153204 + 0.868862i) q^{5} +(-1.65474 + 0.511691i) q^{6} +(0.258184 + 2.63312i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.09772 + 2.14466i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(1.59651 + 0.671670i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.153204 + 0.868862i) q^{5} +(-1.65474 + 0.511691i) q^{6} +(0.258184 + 2.63312i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.09772 + 2.14466i) q^{9} +(-0.441133 - 0.764065i) q^{10} +(-0.774572 - 4.39282i) q^{11} +(0.938697 - 1.45563i) q^{12} +(-1.01265 + 5.74304i) q^{13} +(-1.89032 - 1.85113i) q^{14} +(-0.828181 + 1.28425i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.137765 + 0.238617i) q^{17} +(-2.98551 - 0.294518i) q^{18} +(0.413891 - 0.716881i) q^{19} +(0.829059 + 0.301753i) q^{20} +(-1.35639 + 4.37724i) q^{21} +(3.41700 + 2.86721i) q^{22} +(0.534541 + 0.448533i) q^{23} +(0.216574 + 1.71846i) q^{24} +(3.96701 + 1.44387i) q^{25} +(-2.91582 - 5.05034i) q^{26} +(1.90854 + 4.83296i) q^{27} +(2.63795 + 0.202975i) q^{28} +(-0.781152 - 4.43013i) q^{29} +(-0.191076 - 1.51614i) q^{30} +(-0.512775 + 2.90809i) q^{31} +(0.939693 - 0.342020i) q^{32} +(1.71391 - 7.53345i) q^{33} +(-0.258914 - 0.0942371i) q^{34} +(-2.32738 - 0.179078i) q^{35} +(2.47634 - 1.69343i) q^{36} -4.50782 q^{37} +(0.143743 + 0.815207i) q^{38} +(-5.47414 + 8.48868i) q^{39} +(-0.829059 + 0.301753i) q^{40} +(0.487212 - 2.76311i) q^{41} +(-1.77457 - 4.22503i) q^{42} +(8.27783 - 6.94593i) q^{43} -4.46058 q^{44} +(-2.18479 + 1.49406i) q^{45} -0.697794 q^{46} +(1.15690 + 6.56113i) q^{47} +(-1.27051 - 1.17720i) q^{48} +(-6.86668 + 1.35966i) q^{49} +(-3.96701 + 1.44387i) q^{50} +(0.0596729 + 0.473488i) q^{51} +(5.47994 + 1.99454i) q^{52} +(-1.99907 + 3.46249i) q^{53} +(-4.56859 - 2.47548i) q^{54} +3.93542 q^{55} +(-2.15126 + 1.54016i) q^{56} +(1.14229 - 0.866513i) q^{57} +(3.44603 + 2.89156i) q^{58} +(-4.51775 + 1.64433i) q^{59} +(1.12093 + 1.03861i) q^{60} +(-2.30913 - 13.0957i) q^{61} +(-1.47648 - 2.55733i) q^{62} +(-5.10556 + 6.07727i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.83477 - 1.75971i) q^{65} +(3.52948 + 6.87264i) q^{66} +(3.60874 + 3.02809i) q^{67} +(0.258914 - 0.0942371i) q^{68} +(0.552137 + 1.07513i) q^{69} +(1.89798 - 1.35883i) q^{70} +(4.51335 - 7.81735i) q^{71} +(-0.808471 + 2.88901i) q^{72} +5.73418 q^{73} +(3.45319 - 2.89757i) q^{74} +(5.36359 + 4.96969i) q^{75} +(-0.634118 - 0.532088i) q^{76} +(11.3668 - 3.17370i) q^{77} +(-1.26298 - 10.0214i) q^{78} +(10.3882 - 8.71672i) q^{79} +(0.441133 - 0.764065i) q^{80} +(-0.199145 + 8.99780i) q^{81} +(1.40287 + 2.42984i) q^{82} +(-1.62387 - 9.20943i) q^{83} +(4.07520 + 2.09589i) q^{84} +(-0.228431 + 0.0831422i) q^{85} +(-1.87643 + 10.6418i) q^{86} +(1.72846 - 7.59745i) q^{87} +(3.41700 - 2.86721i) q^{88} +(8.69998 - 15.0688i) q^{89} +(0.713287 - 2.54887i) q^{90} +(-15.3836 - 1.18368i) q^{91} +(0.534541 - 0.448533i) q^{92} +(-2.77193 + 4.29839i) q^{93} +(-5.10365 - 4.28247i) q^{94} +(0.559461 + 0.469444i) q^{95} +(1.72996 + 0.0851228i) q^{96} +(-5.48553 + 4.60290i) q^{97} +(4.38621 - 5.45538i) q^{98} +(7.79627 - 10.8761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	1.59651	+	0.671670i	0.921748	+	0.387789i
$3$	1.59651	+	0.671670i	0.921748	+	0.387789i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.153204	+	0.868862i	−0.0685149	+	0.388567i	0.931196	+	0.364519i	$0.118767\pi$
$5$	−0.153204	+	0.868862i	−0.0685149	+	0.388567i	−0.999711	+	0.0240481i	$0.992345\pi$
$6$	−1.65474	+	0.511691i	−0.675546	+	0.208897i
$7$	0.258184	+	2.63312i	0.0975845	+	0.995227i
$7$	0.258184	+	2.63312i	0.0975845	+	0.995227i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.09772	+	2.14466i	0.699240	+	0.714887i
$10$	−0.441133	−	0.764065i	−0.139499	−	0.241619i
$11$	−0.774572	−	4.39282i	−0.233542	−	1.32448i	−0.845662	−	0.533719i	$-0.820794\pi$
$11$	−0.774572	−	4.39282i	−0.233542	−	1.32448i	0.612120	−	0.790765i	$-0.290317\pi$
$12$	0.938697	−	1.45563i	0.270979	−	0.420203i
$13$	−1.01265	+	5.74304i	−0.280859	+	1.59283i	0.438853	+	0.898559i	$0.355385\pi$
$13$	−1.01265	+	5.74304i	−0.280859	+	1.59283i	−0.719712	+	0.694273i	$0.755726\pi$
$14$	−1.89032	−	1.85113i	−0.505209	−	0.494736i
$15$	−0.828181	+	1.28425i	−0.213835	+	0.331592i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.137765	+	0.238617i	0.0334130	+	0.0578730i	0.882248	−	0.470784i	$-0.156029\pi$
$17$	0.137765	+	0.238617i	0.0334130	+	0.0578730i	−0.848835	+	0.528657i	$0.822696\pi$
$18$	−2.98551	−	0.294518i	−0.703691	−	0.0694185i
$19$	0.413891	−	0.716881i	0.0949532	−	0.164464i	−0.814636	−	0.579973i	$-0.803063\pi$
$19$	0.413891	−	0.716881i	0.0949532	−	0.164464i	0.909589	+	0.415509i	$0.136397\pi$
$20$	0.829059	+	0.301753i	0.185383	+	0.0674740i
$21$	−1.35639	+	4.37724i	−0.295989	+	0.955191i
$22$	3.41700	+	2.86721i	0.728508	+	0.611291i
$23$	0.534541	+	0.448533i	0.111460	+	0.0935257i	0.696814	−	0.717252i	$-0.254600\pi$
$23$	0.534541	+	0.448533i	0.111460	+	0.0935257i	−0.585355	+	0.810777i	$0.699045\pi$
$24$	0.216574	+	1.71846i	0.0442081	+	0.350779i
$25$	3.96701	+	1.44387i	0.793403	+	0.288775i
$26$	−2.91582	−	5.05034i	−0.571839	−	0.990454i
$27$	1.90854	+	4.83296i	0.367298	+	0.930103i
$28$	2.63795	+	0.202975i	0.498526	+	0.0383587i
$29$	−0.781152	−	4.43013i	−0.145056	−	0.822655i	−0.967322	−	0.253551i	$-0.918401\pi$
$29$	−0.781152	−	4.43013i	−0.145056	−	0.822655i	0.822266	−	0.569104i	$-0.192710\pi$
$30$	−0.191076	−	1.51614i	−0.0348856	−	0.276807i
$31$	−0.512775	+	2.90809i	−0.0920970	+	0.522308i	0.903501	+	0.428585i	$0.140988\pi$
$31$	−0.512775	+	2.90809i	−0.0920970	+	0.522308i	−0.995598	+	0.0937228i	$0.970123\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	1.71391	−	7.53345i	0.298353	−	1.31141i
$34$	−0.258914	−	0.0942371i	−0.0444034	−	0.0161615i
$35$	−2.32738	−	0.179078i	−0.393399	−	0.0302697i
$36$	2.47634	−	1.69343i	0.412724	−	0.282239i
$37$	−4.50782			−0.741080			−0.370540	−	0.928816i	$-0.620827\pi$
$37$	−4.50782			−0.741080			−0.370540	+	0.928816i	$0.620827\pi$
$38$	0.143743	+	0.815207i	0.0233182	+	0.132244i
$39$	−5.47414	+	8.48868i	−0.876564	+	1.35928i
$40$	−0.829059	+	0.301753i	−0.131086	+	0.0477113i
$41$	0.487212	−	2.76311i	0.0760897	−	0.431526i	−0.922836	−	0.385192i	$-0.874135\pi$
$41$	0.487212	−	2.76311i	0.0760897	−	0.431526i	0.998926	−	0.0463337i	$-0.0147537\pi$
$42$	−1.77457	−	4.22503i	−0.273823	−	0.651936i
$43$	8.27783	−	6.94593i	1.26236	−	1.05924i	0.266931	−	0.963716i	$-0.413990\pi$
$43$	8.27783	−	6.94593i	1.26236	−	1.05924i	0.995427	−	0.0955283i	$-0.0304540\pi$
$44$	−4.46058			−0.672458
$45$	−2.18479	+	1.49406i	−0.325690	+	0.222721i
$46$	−0.697794			−0.102884
$47$	1.15690	+	6.56113i	0.168752	+	0.957039i	0.945111	+	0.326748i	$0.105953\pi$
$47$	1.15690	+	6.56113i	0.168752	+	0.957039i	−0.776360	+	0.630290i	$0.782936\pi$
$48$	−1.27051	−	1.17720i	−0.183382	−	0.169915i
$49$	−6.86668	+	1.35966i	−0.980955	+	0.194238i
$50$	−3.96701	+	1.44387i	−0.561020	+	0.204195i
$51$	0.0596729	+	0.473488i	0.00835588	+	0.0663016i
$52$	5.47994	+	1.99454i	0.759931	+	0.276592i
$53$	−1.99907	+	3.46249i	−0.274593	+	0.475609i	−0.970032	−	0.242976i	$-0.921876\pi$
$53$	−1.99907	+	3.46249i	−0.274593	+	0.475609i	0.695439	+	0.718585i	$0.255210\pi$
$54$	−4.56859	−	2.47548i	−0.621706	−	0.336870i
$55$	3.93542			0.530652
$56$	−2.15126	+	1.54016i	−0.287474	+	0.205812i
$57$	1.14229	−	0.866513i	0.151300	−	0.114772i
$58$	3.44603	+	2.89156i	0.452486	+	0.379681i
$59$	−4.51775	+	1.64433i	−0.588161	+	0.214073i	−0.618921	−	0.785454i	$-0.712430\pi$
$59$	−4.51775	+	1.64433i	−0.588161	+	0.214073i	0.0307592	+	0.999527i	$0.490208\pi$
$60$	1.12093	+	1.03861i	0.144711	+	0.134084i
$61$	−2.30913	−	13.0957i	−0.295654	−	1.67674i	−0.664532	−	0.747260i	$-0.731369\pi$
$61$	−2.30913	−	13.0957i	−0.295654	−	1.67674i	0.368878	−	0.929478i	$-0.379742\pi$
$62$	−1.47648	−	2.55733i	−0.187513	−	0.324781i
$63$	−5.10556	+	6.07727i	−0.643240	+	0.765664i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.83477	−	1.75971i	−0.599679	−	0.218265i
$66$	3.52948	+	6.87264i	0.434449	+	0.845963i
$67$	3.60874	+	3.02809i	0.440878	+	0.369940i	0.836038	−	0.548672i	$-0.184866\pi$
$67$	3.60874	+	3.02809i	0.440878	+	0.369940i	−0.395160	+	0.918612i	$0.629311\pi$
$68$	0.258914	−	0.0942371i	0.0313980	−	0.0114279i
$69$	0.552137	+	1.07513i	0.0664695	+	0.129430i
$70$	1.89798	−	1.35883i	0.226852	−	0.162411i
$71$	4.51335	−	7.81735i	0.535636	−	0.927748i	−0.463496	−	0.886099i	$-0.653405\pi$
$71$	4.51335	−	7.81735i	0.535636	−	0.927748i	0.999132	−	0.0416496i	$-0.0132613\pi$
$72$	−0.808471	+	2.88901i	−0.0952793	+	0.340473i
$73$	5.73418			0.671135			0.335568	−	0.942016i	$-0.391072\pi$
$73$	5.73418			0.671135			0.335568	+	0.942016i	$0.391072\pi$
$74$	3.45319	−	2.89757i	0.401425	−	0.336835i
$75$	5.36359	+	4.96969i	0.619334	+	0.573850i
$76$	−0.634118	−	0.532088i	−0.0727384	−	0.0610347i
$77$	11.3668	−	3.17370i	1.29537	−	0.361677i
$78$	−1.26298	−	10.0214i	−0.143005	−	1.13470i
$79$	10.3882	−	8.71672i	1.16876	−	0.980707i	0.168773	−	0.985655i	$-0.446019\pi$
$79$	10.3882	−	8.71672i	1.16876	−	0.980707i	0.999988	+	0.00494777i	$0.00157493\pi$
$80$	0.441133	−	0.764065i	0.0493202	−	0.0854250i
$81$	−0.199145	+	8.99780i	−0.0221272	+	0.999755i
$82$	1.40287	+	2.42984i	0.154921	+	0.268331i
$83$	−1.62387	−	9.20943i	−0.178243	−	1.01087i	−0.934334	−	0.356399i	$-0.884004\pi$
$83$	−1.62387	−	9.20943i	−0.178243	−	1.01087i	0.756091	−	0.654467i	$-0.227107\pi$
$84$	4.07520	+	2.09589i	0.444641	+	0.228680i
$85$	−0.228431	+	0.0831422i	−0.0247768	+	0.00901804i
$86$	−1.87643	+	10.6418i	−0.202341	+	1.14753i
$87$	1.72846	−	7.59745i	0.185311	−	0.814532i
$88$	3.41700	−	2.86721i	0.364254	−	0.305645i
$89$	8.69998	−	15.0688i	0.922196	−	1.59729i	0.126186	−	0.992007i	$-0.459726\pi$
$89$	8.69998	−	15.0688i	0.922196	−	1.59729i	0.796010	−	0.605284i	$-0.206940\pi$
$90$	0.713287	−	2.54887i	0.0751870	−	0.268675i
$91$	−15.3836	−	1.18368i	−1.61264	−	0.124083i
$92$	0.534541	−	0.448533i	0.0557298	−	0.0467628i
$93$	−2.77193	+	4.29839i	−0.287435	+	0.445723i
$94$	−5.10365	−	4.28247i	−0.526401	−	0.441703i
$95$	0.559461	+	0.469444i	0.0573995	+	0.0481639i
$96$	1.72996	+	0.0851228i	0.176563	+	0.00868781i
$97$	−5.48553	+	4.60290i	−0.556971	+	0.467354i	−0.877293	−	0.479954i	$-0.840653\pi$
$97$	−5.48553	+	4.60290i	−0.556971	+	0.467354i	0.320322	+	0.947309i	$0.396209\pi$
$98$	4.38621	−	5.45538i	0.443074	−	0.551077i
$99$	7.79627	−	10.8761i	0.783554	−	1.09309i
$100$	2.11080	−	3.65602i	0.211080	−	0.365602i
$101$	0.279153	−	0.234237i	0.0277767	−	0.0233074i	−0.628794	−	0.777572i	$-0.716451\pi$
$101$	0.279153	−	0.234237i	0.0277767	−	0.0233074i	0.656570	+	0.754265i	$0.272007\pi$
$102$	−0.350064	−	0.324356i	−0.0346615	−	0.0321160i
$103$	1.41441	−	8.02150i	0.139366	−	0.790382i	−0.832354	−	0.554244i	$-0.813007\pi$
$103$	1.41441	−	8.02150i	0.139366	−	0.790382i	0.971720	−	0.236137i	$-0.0758816\pi$
$104$	−5.47994	+	1.99454i	−0.537353	+	0.195580i
$105$	−3.59541	−	1.84913i	−0.350876	−	0.180457i
$106$	−0.694269	−	3.93739i	−0.0674333	−	0.382433i
$107$	−6.69049	−	11.5883i	−0.646794	−	1.12028i	−0.983884	−	0.178808i	$-0.942776\pi$
$107$	−6.69049	−	11.5883i	−0.646794	−	1.12028i	0.337090	−	0.941473i	$-0.390557\pi$
$108$	5.09095	−	1.04031i	0.489877	−	0.100104i
$109$	2.48589	−	4.30569i	0.238105	−	0.412411i	−0.722065	−	0.691825i	$-0.756807\pi$
$109$	2.48589	−	4.30569i	0.238105	−	0.412411i	0.960171	+	0.279414i	$0.0901403\pi$
$110$	−3.01471	+	2.52964i	−0.287441	+	0.241192i
$111$	−7.19680	−	3.02776i	−0.683090	−	0.287383i
$112$	0.657967	−	2.56263i	0.0621721	−	0.242146i
$113$	0.948298	+	0.795717i	0.0892084	+	0.0748547i	0.686301	−	0.727317i	$-0.259233\pi$
$113$	0.948298	+	0.795717i	0.0892084	+	0.0748547i	−0.597093	+	0.802172i	$0.703678\pi$
$114$	−0.318062	+	1.39804i	−0.0297892	+	0.130938i
$115$	−0.471608	+	0.395726i	−0.0439776	+	0.0369016i
$116$	−4.49847			−0.417673
$117$	−14.4411	+	9.87549i	−1.33508	+	0.912989i
$118$	2.40385	−	4.16358i	0.221292	−	0.383289i
$119$	−0.592738	+	0.424360i	−0.0543362	+	0.0389011i
$120$	−1.52628	−	0.0751010i	−0.139330	−	0.00685575i
$121$	−8.36025	+	3.04288i	−0.760023	+	0.276626i
$122$	10.1867	+	8.54764i	0.922258	+	0.773867i
$123$	2.63374	−	4.08411i	0.237476	−	0.368252i
$124$	2.77487	+	1.00997i	0.249190	+	0.0906979i
$125$	−4.06796	+	7.04591i	−0.363849	+	0.630205i
$126$	0.00468999	−	7.93725i	0.000417817	−	0.707107i
$127$	2.60913	+	4.51914i	0.231523	+	0.401009i	0.958256	−	0.285910i	$-0.0922959\pi$
$127$	2.60913	+	4.51914i	0.231523	+	0.401009i	−0.726734	+	0.686919i	$0.758963\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	17.8811	−	5.52931i	1.57434	−	0.486828i
$130$	4.83477	−	1.75971i	0.424037	−	0.154337i
$131$	15.6291	+	13.1144i	1.36552	+	1.14581i	0.974233	+	0.225544i	$0.0724161\pi$
$131$	15.6291	+	13.1144i	1.36552	+	1.14581i	0.391292	+	0.920267i	$0.372028\pi$
$132$	−7.12139	−	2.99604i	−0.619837	−	0.260772i
$133$	1.99450	+	0.904740i	0.172945	+	0.0784509i
$134$	−4.71087			−0.406958
$135$	−4.49157	+	0.917828i	−0.386573	+	0.0789940i
$136$	−0.137765	+	0.238617i	−0.0118133	+	0.0204612i
$137$	−17.5708	−	6.39526i	−1.50118	−	0.546384i	−0.544813	−	0.838558i	$-0.683399\pi$
$137$	−17.5708	−	6.39526i	−1.50118	−	0.546384i	−0.956365	+	0.292173i	$0.905622\pi$
$138$	−1.11404	−	0.468687i	−0.0948333	−	0.0398973i
$139$	14.9591	−	5.44467i	1.26881	−	0.461811i	0.382097	−	0.924122i	$-0.375202\pi$
$139$	14.9591	−	5.44467i	1.26881	−	0.461811i	0.886717	+	0.462312i	$0.152980\pi$
$140$	−0.580502	+	2.26092i	−0.0490614	+	0.191083i
$141$	−2.55990	+	11.2520i	−0.215582	+	0.947589i
$142$	1.56747	+	8.88956i	0.131539	+	0.745995i
$143$	26.0125			2.17527
$144$	−1.23769	−	2.73278i	−0.103141	−	0.227732i
$145$	3.96885			0.329595
$146$	−4.39264	+	3.68586i	−0.363537	+	0.305044i
$147$	−11.8760	−	2.44142i	−0.979516	−	0.201365i
$148$	−0.782774	+	4.43933i	−0.0643436	+	0.364911i
$149$	−1.60950	+	0.585809i	−0.131855	+	0.0479914i	−0.407105	−	0.913381i	$-0.633462\pi$
$149$	−1.60950	+	0.585809i	−0.131855	+	0.0479914i	0.275250	+	0.961373i	$0.411239\pi$
$150$	−7.30320	−	0.359355i	−0.596304	−	0.0293412i
$151$	0.0132478	+	0.0751320i	0.00107809	+	0.00611416i	0.985342	−	0.170590i	$-0.0545674\pi$
$151$	0.0132478	+	0.0751320i	0.00107809	+	0.00611416i	−0.984264	+	0.176704i	$0.943456\pi$
$152$	0.827783			0.0671420
$153$	−0.222759	+	0.796011i	−0.0180090	+	0.0643537i
$154$	−6.66749	+	9.73766i	−0.537282	+	0.784683i
$155$	−2.44817	−	0.891061i	−0.196642	−	0.0715717i
$156$	7.40914	+	6.86502i	0.593206	+	0.549641i
$157$	−21.7090	+	7.90142i	−1.73256	+	0.630602i	−0.998808	−	0.0488115i	$-0.984457\pi$
$157$	−21.7090	+	7.90142i	−1.73256	+	0.630602i	−0.733756	+	0.679413i	$0.762234\pi$
$158$	−2.35481	+	13.3548i	−0.187339	+	1.06245i
$159$	−5.51719	+	4.18520i	−0.437541	+	0.331908i
$160$	0.153204	+	0.868862i	0.0121118	+	0.0686896i
$161$	−1.04303	+	1.52332i	−0.0822026	+	0.120054i
$162$	−5.63112	−	7.02072i	−0.442422	−	0.551600i
$163$	−9.47704	−	16.4147i	−0.742299	−	1.28570i	−0.951446	−	0.307815i	$-0.900402\pi$
$163$	−9.47704	−	16.4147i	−0.742299	−	1.28570i	0.209147	−	0.977884i	$-0.432931\pi$
$164$	−2.63653	−	0.959619i	−0.205879	−	0.0749337i
$165$	6.28296	+	2.64330i	0.489128	+	0.205781i
$166$	7.16367	+	6.01103i	0.556008	+	0.466546i
$167$	9.60067	+	8.05592i	0.742922	+	0.623385i	0.933621	−	0.358263i	$-0.116631\pi$
$167$	9.60067	+	8.05592i	0.742922	+	0.623385i	−0.190699	+	0.981649i	$0.561075\pi$
$168$	−4.46899	+	1.01395i	−0.344790	+	0.0782276i
$169$	−19.7410	−	7.18514i	−1.51854	−	0.552703i
$170$	0.121546	−	0.210523i	0.00932213	−	0.0161464i
$171$	2.40569	−	0.616158i	0.183968	−	0.0471188i
$172$	−5.40297	−	9.35822i	−0.411973	−	0.713558i
$173$	8.12881	+	2.95865i	0.618022	+	0.224942i	0.632010	−	0.774961i	$-0.282230\pi$
$173$	8.12881	+	2.95865i	0.618022	+	0.224942i	−0.0139876	+	0.999902i	$0.504453\pi$
$174$	3.55946	+	6.93102i	0.269842	+	0.525439i
$175$	−2.77768	+	10.8184i	−0.209973	+	0.817796i
$176$	−0.774572	+	4.39282i	−0.0583856	+	0.331121i
$177$	−8.31711	−	0.409244i	−0.625152	−	0.0307607i
$178$	3.02147	+	17.1356i	0.226469	+	1.28437i
$179$	5.57428	+	9.65493i	0.416641	+	0.721644i	0.995599	−	0.0937138i	$-0.0298739\pi$
$179$	5.57428	+	9.65493i	0.416641	+	0.721644i	−0.578958	+	0.815357i	$0.696541\pi$
$180$	1.09198	+	2.41104i	0.0813911	+	0.179709i
$181$	6.77495	+	11.7346i	0.503578	+	0.872223i	0.999991	+	0.00413682i	$0.00131679\pi$
$181$	6.77495	+	11.7346i	0.503578	+	0.872223i	−0.496413	+	0.868086i	$0.665350\pi$
$182$	12.5454	−	8.98163i	0.929924	−	0.665762i
$183$	5.10945	−	22.4585i	0.377701	−	1.66018i
$184$	−0.121171	+	0.687193i	−0.00893282	+	0.0506605i
$185$	0.690615	−	3.91667i	0.0507750	−	0.287959i
$186$	−0.639534	−	5.07452i	−0.0468929	−	0.372082i
$187$	0.941490	−	0.790004i	0.0688486	−	0.0577708i
$188$	6.66234			0.485901
$189$	−12.2330	+	6.27321i	−0.889822	+	0.456309i
$190$	−0.730324			−0.0529833
$191$	−17.4749	+	14.6632i	−1.26444	+	1.06099i	−0.269244	+	0.963072i	$0.586774\pi$
$191$	−17.4749	+	14.6632i	−1.26444	+	1.06099i	−0.995195	+	0.0979176i	$0.968782\pi$
$192$	−1.37994	+	1.04679i	−0.0995886	+	0.0755454i
$193$	−4.13025	+	23.4238i	−0.297302	+	1.68608i	0.360396	+	0.932799i	$0.382642\pi$
$193$	−4.13025	+	23.4238i	−0.297302	+	1.68608i	−0.657698	+	0.753282i	$0.728470\pi$
$194$	1.24347	−	7.05206i	0.0892758	−	0.506308i
$195$	−6.53683	−	6.05677i	−0.468112	−	0.433734i
$196$	0.146620	+	6.99846i	0.0104729	+	0.499890i
$197$	0.0332154	+	0.0575308i	0.00236650	+	0.00409890i	0.867206	−	0.497949i	$-0.165913\pi$
$197$	0.0332154	+	0.0575308i	0.00236650	+	0.00409890i	−0.864840	+	0.502048i	$0.832580\pi$
$198$	1.01873	+	13.3429i	0.0723979	+	0.948240i
$199$	−1.86870	−	3.23668i	−0.132468	−	0.229442i	0.792159	−	0.610315i	$-0.208957\pi$
$199$	−1.86870	−	3.23668i	−0.132468	−	0.229442i	−0.924628	+	0.380873i	$0.875624\pi$
$200$	0.733074	+	4.15747i	0.0518362	+	0.293978i
$201$	3.72753	+	7.25827i	0.262920	+	0.511959i
$202$	−0.0632787	+	0.358872i	−0.00445228	+	0.0252501i
$203$	11.4634	−	3.20066i	0.804573	−	0.224642i
$204$	0.476657	+	0.0234540i	0.0333726	+	0.00164211i
$205$	2.32612	+	0.846640i	0.162463	+	0.0591319i
$206$	4.07262	+	7.05399i	0.283753	+	0.491475i
$207$	0.159365	+	2.08731i	0.0110767	+	0.145078i
$208$	2.91582	−	5.05034i	0.202176	−	0.350178i
$209$	−3.46971	−	1.26287i	−0.240005	−	0.0873547i
$210$	3.94284	−	0.894570i	0.272082	−	0.0617312i
$211$	−15.0979	−	12.6686i	−1.03938	−	0.872143i	−0.0474425	−	0.998874i	$-0.515107\pi$
$211$	−15.0979	−	12.6686i	−1.03938	−	0.872143i	−0.991937	+	0.126731i	$0.959552\pi$
$212$	3.06275	+	2.56995i	0.210350	+	0.176505i
$213$	12.4563	−	9.44903i	0.853492	−	0.647437i
$214$	12.5740	+	4.57657i	0.859542	+	0.312848i
$215$	4.76686	+	8.25644i	0.325097	+	0.563085i
$216$	−3.23120	+	4.06932i	−0.219855	+	0.276882i
$217$	−7.78975	−	0.599376i	−0.528803	−	0.0406883i
$218$	0.863341	+	4.89625i	0.0584729	+	0.331616i
$219$	9.15471	+	3.85148i	0.618618	+	0.260259i
$220$	0.683379	−	3.87563i	0.0460734	−	0.261295i
$221$	−1.50989	+	0.549556i	−0.101566	+	0.0369671i
$222$	7.45927	−	2.30661i	0.500634	−	0.154810i
$223$	14.0745	+	5.12270i	0.942498	+	0.343041i	0.767152	−	0.641466i	$-0.221673\pi$
$223$	14.0745	+	5.12270i	0.942498	+	0.343041i	0.175346	+	0.984507i	$0.443896\pi$
$224$	1.14320	+	2.38602i	0.0763830	+	0.159423i
$225$	5.22506	+	11.5367i	0.348337	+	0.769116i
$226$	−1.23792			−0.0823449
$227$	2.69204	+	15.2673i	0.178677	+	1.01333i	0.933813	+	0.357760i	$0.116460\pi$
$227$	2.69204	+	15.2673i	0.178677	+	1.01333i	−0.755136	+	0.655568i	$0.772429\pi$
$228$	−0.654992	−	1.27541i	−0.0433779	−	0.0844658i
$229$	−12.2753	+	4.46786i	−0.811178	+	0.295245i	−0.714110	−	0.700033i	$-0.753168\pi$
$229$	−12.2753	+	4.46786i	−0.811178	+	0.295245i	−0.0970674	+	0.995278i	$0.530946\pi$
$230$	0.106905	−	0.606287i	0.00704909	−	0.0399774i
$231$	20.2790	+	2.56791i	1.33426	+	0.168956i
$232$	3.44603	−	2.89156i	0.226243	−	0.189840i
$233$	−28.8855			−1.89235			−0.946177	−	0.323650i	$-0.895090\pi$
$233$	−28.8855			−1.89235			−0.946177	+	0.323650i	$0.895090\pi$
$234$	4.71471	−	16.8476i	0.308210	−	1.10136i
$235$	−5.87796			−0.383436
$236$	0.834847	+	4.73465i	0.0543439	+	0.308200i
$237$	22.4396	−	6.93894i	1.45761	−	0.450733i
$238$	0.181290	−	0.706084i	0.0117513	−	0.0457686i
$239$	−20.1559	+	7.33614i	−1.30378	+	0.474535i	−0.898224	−	0.439537i	$-0.855143\pi$
$239$	−20.1559	+	7.33614i	−1.30378	+	0.474535i	−0.405551	+	0.914072i	$0.632920\pi$
$240$	1.21747	−	0.923545i	0.0785876	−	0.0596146i
$241$	−22.2770	−	8.10815i	−1.43499	−	0.522292i	−0.496629	−	0.867963i	$-0.665429\pi$
$241$	−22.2770	−	8.10815i	−1.43499	−	0.522292i	−0.938356	+	0.345671i	$0.887651\pi$
$242$	4.44840	−	7.70485i	0.285954	−	0.495287i
$243$	−6.36149	+	14.2314i	−0.408089	+	0.912942i
$244$	−13.2978			−0.851302
$245$	−0.129358	−	6.17451i	−0.00826437	−	0.394475i
$246$	0.607651	+	4.82154i	0.0387424	+	0.307410i
$247$	3.69795	+	3.10294i	0.235295	+	0.197436i
$248$	−2.77487	+	1.00997i	−0.176204	+	0.0641331i
$249$	3.59316	−	15.7937i	0.227707	−	1.00088i
$250$	−1.41279	−	8.01231i	−0.0893524	−	0.506743i
$251$	4.00465	+	6.93625i	0.252771	+	0.437813i	0.964288	−	0.264857i	$-0.0853247\pi$
$251$	4.00465	+	6.93625i	0.252771	+	0.437813i	−0.711517	+	0.702669i	$0.751991\pi$
$252$	5.09837	+	6.08330i	0.321167	+	0.383212i
$253$	1.55628	−	2.69556i	0.0978428	−	0.169469i
$254$	−4.90356	−	1.78475i	−0.307676	−	0.111985i
$255$	−0.420538	−	0.0206926i	−0.0263351	−	0.00129582i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−17.6364	+	6.41912i	−1.10013	+	0.400414i	−0.827363	−	0.561667i	$-0.810160\pi$
$257$	−17.6364	+	6.41912i	−1.10013	+	0.400414i	−0.272764	+	0.962081i	$0.587938\pi$
$258$	−10.1435	+	15.7294i	−0.631507	+	0.979270i
$259$	−1.16385	−	11.8696i	−0.0723180	−	0.737543i
$260$	−2.57253	+	4.45575i	−0.159541	+	0.276334i
$261$	7.86249	−	10.9685i	0.486676	−	0.678932i
$262$	−20.4024			−1.26046
$263$	18.6391	−	15.6400i	1.14933	−	0.964405i	0.149630	−	0.988742i	$-0.452192\pi$
$263$	18.6391	−	15.6400i	1.14933	−	0.964405i	0.999704	+	0.0243369i	$0.00774745\pi$
$264$	7.38111	−	2.28244i	0.454276	−	0.140475i
$265$	−2.70216	−	2.26738i	−0.165992	−	0.139284i
$266$	−2.10943	+	0.588967i	−0.129337	+	0.0361119i
$267$	24.0109	−	18.2141i	1.46944	−	1.11468i
$268$	3.60874	−	3.02809i	0.220439	−	0.184970i
$269$	4.24620	−	7.35464i	0.258895	−	0.448420i	−0.707051	−	0.707163i	$-0.749975\pi$
$269$	4.24620	−	7.35464i	0.258895	−	0.448420i	0.965946	+	0.258743i	$0.0833082\pi$
$270$	2.85078	−	3.59022i	0.173493	−	0.218494i
$271$	−0.505870	−	0.876192i	−0.0307294	−	0.0532249i	0.850252	−	0.526376i	$-0.176450\pi$
$271$	−0.505870	−	0.876192i	−0.0307294	−	0.0532249i	−0.880981	+	0.473151i	$0.843116\pi$
$272$	−0.0478454	−	0.271345i	−0.00290105	−	0.0164527i
$273$	−23.7651	−	12.2224i	−1.43833	−	0.739736i
$274$	17.5708	−	6.39526i	1.06149	−	0.386352i
$275$	3.26994	−	18.5447i	0.197185	−	1.11829i
$276$	1.15467	−	0.357055i	0.0695029	−	0.0214922i
$277$	16.1426	−	13.5452i	0.969915	−	0.813855i	−0.0126226	−	0.999920i	$-0.504018\pi$
$277$	16.1426	−	13.5452i	0.969915	−	0.813855i	0.982537	+	0.186065i	$0.0595736\pi$
$278$	−7.95957	+	13.7864i	−0.477383	+	0.826852i
$279$	−7.31252	+	5.00063i	−0.437789	+	0.299380i
$280$	−1.00860	−	2.10511i	−0.0602755	−	0.125804i
$281$	−14.1454	+	11.8694i	−0.843844	+	0.708069i	−0.958425	−	0.285345i	$-0.907892\pi$
$281$	−14.1454	+	11.8694i	−0.843844	+	0.708069i	0.114581	+	0.993414i	$0.463448\pi$
$282$	−5.27165	−	10.2650i	−0.313922	−	0.611272i
$283$	−11.0003	−	9.23033i	−0.653899	−	0.548686i	0.254353	−	0.967112i	$-0.418138\pi$
$283$	−11.0003	−	9.23033i	−0.653899	−	0.548686i	−0.908251	+	0.418425i	$0.862582\pi$
$284$	−6.91485	−	5.80225i	−0.410321	−	0.344300i
$285$	0.577877	+	1.12525i	0.0342305	+	0.0666539i
$286$	−19.9267	+	16.7205i	−1.17829	+	0.988704i
$287$	7.40141	+	0.569495i	0.436892	+	0.0336162i
$288$	2.70473	+	1.29786i	0.159378	+	0.0764771i
$289$	8.46204	−	14.6567i	0.497767	−	0.862158i
$290$	−3.04032	+	2.55113i	−0.178533	+	0.149807i
$291$	−11.8494	+	3.66414i	−0.694622	+	0.214796i
$292$	0.995731	−	5.64707i	0.0582707	−	0.330470i
$293$	2.56953	−	0.935233i	0.150114	−	0.0546369i	−0.265871	−	0.964009i	$-0.585659\pi$
$293$	2.56953	−	0.935233i	0.150114	−	0.0546369i	0.415984	+	0.909372i	$0.363437\pi$
$294$	10.6669	−	5.76351i	0.622104	−	0.336135i
$295$	−0.736557	−	4.17722i	−0.0428840	−	0.243207i
$296$	−2.25391	−	3.90388i	−0.131006	−	0.226909i
$297$	19.7520	−	12.1273i	1.14613	−	0.703699i
$298$	0.856396	−	1.48332i	0.0496097	−	0.0859265i
$299$	−3.11725	+	2.61568i	−0.180275	+	0.151269i
$300$	5.82557	−	4.41913i	0.336339	−	0.255138i
$301$	20.4267	+	20.0032i	1.17738	+	1.15297i
$302$	−0.0584423	−	0.0490389i	−0.00336298	−	0.00282187i
$303$	0.603001	−	0.186464i	0.0346415	−	0.0107121i
$304$	−0.634118	+	0.532088i	−0.0363692	+	0.0305174i
$305$	11.7322			0.671782
$306$	−0.341023	−	0.752966i	−0.0194950	−	0.0430442i
$307$	−0.543824	+	0.941930i	−0.0310377	+	0.0537588i	−0.881127	−	0.472880i	$-0.843215\pi$
$307$	−0.543824	+	0.941930i	−0.0310377	+	0.0537588i	0.850089	+	0.526639i	$0.176548\pi$
$308$	−1.15165	−	11.7453i	−0.0656215	−	0.669249i
$309$	7.64592	−	11.8564i	0.434961	−	0.674489i
$310$	2.44817	−	0.891061i	0.139047	−	0.0506089i
$311$	22.0778	+	18.5255i	1.25192	+	1.05048i	0.996495	+	0.0836544i	$0.0266592\pi$
$311$	22.0778	+	18.5255i	1.25192	+	1.05048i	0.255423	+	0.966829i	$0.417785\pi$
$312$	−10.0885	−	0.496405i	−0.571148	−	0.0281034i
$313$	20.2517	+	7.37101i	1.14469	+	0.416634i	0.843606	−	0.536962i	$-0.180428\pi$
$313$	20.2517	+	7.37101i	1.14469	+	0.416634i	0.301087	+	0.953597i	$0.402651\pi$
$314$	11.5511	−	20.0071i	0.651866	−	1.12907i
$315$	−4.49812	−	5.36709i	−0.253441	−	0.302401i
$316$	−6.78040	−	11.7440i	−0.381427	−	0.660652i
$317$	0.447121	+	2.53575i	0.0251128	+	0.142422i	0.994786	−	0.101983i	$-0.0325186\pi$
$317$	0.447121	+	2.53575i	0.0251128	+	0.142422i	−0.969673	+	0.244405i	$0.921408\pi$
$318$	1.53622	−	6.75243i	0.0861468	−	0.378657i
$319$	−18.8557	+	6.86291i	−1.05572	+	0.384249i
$320$	−0.675855	−	0.567110i	−0.0377814	−	0.0317024i
$321$	−2.89798	−	22.9947i	−0.161749	−	1.28344i
$322$	−0.180160	−	1.83738i	−0.0100399	−	0.102393i
$323$	0.228080			0.0126907
$324$	8.82652	+	1.75857i	0.490362	+	0.0976984i
$325$	−12.3094	+	21.3206i	−0.682804	+	1.18265i
$326$	17.8110	+	6.48268i	0.986460	+	0.359042i
$327$	6.86077	−	5.20440i	0.379401	−	0.287804i
$328$	2.63653	−	0.959619i	0.145578	−	0.0529861i
$329$	−16.9776	+	4.74025i	−0.936003	+	0.261339i
$330$	−6.51211	+	2.01372i	−0.358480	+	0.110852i
$331$	3.81701	+	21.6473i	0.209802	+	1.18984i	0.889703	+	0.456540i	$0.150912\pi$
$331$	3.81701	+	21.6473i	0.209802	+	1.18984i	−0.679901	+	0.733304i	$0.737977\pi$
$332$	−9.35150			−0.513230
$333$	−9.45613	−	9.66774i	−0.518193	−	0.529789i
$334$	−12.5328			−0.685763
$335$	−3.18387	+	2.67158i	−0.173953	+	0.145964i
$336$	2.77170	−	3.64934i	0.151208	−	0.199088i
$337$	−1.49240	+	8.46384i	−0.0812963	+	0.461054i	0.916798	+	0.399351i	$0.130764\pi$
$337$	−1.49240	+	8.46384i	−0.0812963	+	0.461054i	−0.998095	+	0.0617036i	$0.980347\pi$
$338$	19.7410	−	7.18514i	1.07377	−	0.390820i
$339$	0.979513	+	1.90732i	0.0531999	+	0.103591i
$340$	0.0422124	+	0.239398i	0.00228929	+	0.0129832i
$341$	13.1719			0.713297
$342$	−1.44681	+	2.01836i	−0.0782345	+	0.109140i
$343$	−5.35303	−	17.7298i	−0.289037	−	0.957318i
$344$	10.1543	+	3.69585i	0.547481	+	0.199267i
$345$	−1.01873	+	0.315018i	−0.0548463	+	0.0169600i
$346$	−8.12881	+	2.95865i	−0.437008	+	0.159058i
$347$	4.16032	−	23.5944i	0.223338	−	1.26661i	−0.642499	−	0.766286i	$-0.722102\pi$
$347$	4.16032	−	23.5944i	0.223338	−	1.26661i	0.865837	−	0.500326i	$-0.166786\pi$
$348$	−7.18188	−	3.02149i	−0.384989	−	0.161969i
$349$	1.60274	+	9.08960i	0.0857928	+	0.486555i	0.997183	+	0.0750112i	$0.0238993\pi$
$349$	1.60274	+	9.08960i	0.0857928	+	0.486555i	−0.911390	+	0.411544i	$0.864990\pi$
$350$	−4.82612	−	10.0728i	−0.257967	−	0.538416i
$351$	−29.6885	+	6.06669i	−1.58466	+	0.323816i
$352$	−2.23029	−	3.86298i	−0.118875	−	0.205897i
$353$	−12.6250	−	4.59512i	−0.671961	−	0.244574i	−0.0165688	−	0.999863i	$-0.505274\pi$
$353$	−12.6250	−	4.59512i	−0.671961	−	0.244574i	−0.655392	+	0.755289i	$0.727496\pi$
$354$	6.63433	−	5.03263i	0.352611	−	0.267481i
$355$	6.10074	+	5.11913i	0.323793	+	0.271695i
$356$	−13.3291	−	11.1845i	−0.706443	−	0.592776i
$357$	−1.23135	+	0.279373i	−0.0651697	+	0.0147860i
$358$	−10.4762	−	3.81303i	−0.553685	−	0.201525i
$359$	2.66059	−	4.60827i	0.140420	−	0.243215i	−0.787235	−	0.616654i	$-0.788488\pi$
$359$	2.66059	−	4.60827i	0.140420	−	0.243215i	0.927655	+	0.373438i	$0.121821\pi$
$360$	−2.38629	−	1.14506i	−0.125769	−	0.0603499i
$361$	9.15739	+	15.8611i	0.481968	+	0.834793i
$362$	−12.7327	−	4.63434i	−0.669218	−	0.243576i
$363$	−15.3911	−	0.757320i	−0.807822	−	0.0397490i
$364$	−3.83702	+	14.9443i	−0.201115	+	0.783296i
$365$	−0.878499	+	4.98222i	−0.0459828	+	0.260781i
$366$	10.5220	+	20.4885i	0.549993	+	1.07095i
$367$	−0.759874	−	4.30946i	−0.0396651	−	0.224952i	0.958531	−	0.284988i	$-0.0919896\pi$
$367$	−0.759874	−	4.30946i	−0.0396651	−	0.224952i	−0.998196	+	0.0600359i	$0.980878\pi$
$368$	−0.348897	−	0.604307i	−0.0181875	−	0.0315017i
$369$	6.94798	−	4.75133i	0.361697	−	0.247345i
$370$	1.98855	+	3.44426i	0.103380	+	0.179059i
$371$	−9.63328	−	4.36983i	−0.500135	−	0.226870i
$372$	3.75175	+	3.47622i	0.194519	+	0.180234i
$373$	2.15942	−	12.2467i	0.111811	−	0.634109i	−0.876470	−	0.481457i	$-0.840108\pi$
$373$	2.15942	−	12.2467i	0.111811	−	0.634109i	0.988280	−	0.152652i	$-0.0487812\pi$
$374$	−0.213418	+	1.21036i	−0.0110356	+	0.0625860i
$375$	−11.2271	+	8.51657i	−0.579764	+	0.439794i
$376$	−5.10365	+	4.28247i	−0.263201	+	0.220852i
$377$	26.2334			1.35109
$378$	5.33870	−	12.6688i	0.274593	−	0.651612i
$379$	26.4250			1.35736			0.678681	−	0.734434i	$-0.262552\pi$
$379$	26.4250			1.35736			0.678681	+	0.734434i	$0.262552\pi$
$380$	0.559461	−	0.469444i	0.0286997	−	0.0240819i
$381$	1.13014	+	8.96735i	0.0578989	+	0.459411i
$382$	3.96123	−	22.4653i	0.202674	−	1.14942i
$383$	2.50848	−	14.2263i	0.128177	−	0.726930i	−0.851192	−	0.524854i	$-0.824120\pi$
$383$	2.50848	−	14.2263i	0.128177	−	0.726930i	0.979370	−	0.202076i	$-0.0647690\pi$
$384$	0.384234	−	1.68889i	0.0196078	−	0.0861860i
$385$	1.01606	+	10.3624i	0.0517834	+	0.528119i
$386$	−11.8926	−	20.5985i	−0.605316	−	1.04844i
$387$	32.2612	+	3.18254i	1.63993	+	0.161778i
$388$	3.58042	+	6.20148i	0.181768	+	0.314832i
$389$	2.72286	+	15.4421i	0.138054	+	0.782946i	0.972684	+	0.232134i	$0.0745708\pi$
$389$	2.72286	+	15.4421i	0.138054	+	0.782946i	−0.834629	+	0.550812i	$0.814318\pi$
$390$	8.90072	+	0.437961i	0.450706	+	0.0221770i
$391$	−0.0333863	+	0.189343i	−0.00168842	+	0.00957548i
$392$	−4.61084	−	5.26689i	−0.232883	−	0.266018i
$393$	16.1436	+	31.4350i	0.814337	+	1.58568i
$394$	−0.0624246	−	0.0227207i	−0.00314491	−	0.00114465i
$395$	5.98212	+	10.3613i	0.300993	+	0.521335i
$396$	−9.35705	−	9.56644i	−0.470210	−	0.480732i
$397$	0.888262	−	1.53851i	0.0445806	−	0.0772159i	−0.842874	−	0.538111i	$-0.819138\pi$
$397$	0.888262	−	1.53851i	0.0445806	−	0.0772159i	0.887455	+	0.460895i	$0.152472\pi$
$398$	3.51200	+	1.27826i	0.176041	+	0.0640736i
$399$	2.57656	+	2.78407i	0.128989	+	0.139378i
$400$	−3.23394	−	2.71360i	−0.161697	−	0.135680i
$401$	22.7166	+	19.0615i	1.13441	+	0.951884i	0.999242	−	0.0389384i	$-0.0123976\pi$
$401$	22.7166	+	19.0615i	1.13441	+	0.951884i	0.135170	+	0.990822i	$0.456842\pi$
$402$	−7.52098	−	3.16415i	−0.375112	−	0.157814i
$403$	−16.1820	−	5.88977i	−0.806083	−	0.293390i
$404$	−0.182204	−	0.315586i	−0.00906498	−	0.0157010i
$405$	−7.78734	−	1.55153i	−0.386956	−	0.0770960i
$406$	−6.72413	+	9.82038i	−0.333713	+	0.487377i
$407$	3.49163	+	19.8020i	0.173074	+	0.981549i
$408$	−0.380216	+	0.288422i	−0.0188235	+	0.0142790i
$409$	1.18322	−	6.71039i	0.0585066	−	0.331807i	−0.941480	−	0.337070i	$-0.890564\pi$
$409$	1.18322	−	6.71039i	0.0585066	−	0.331807i	0.999986	+	0.00526273i	$0.00167519\pi$
$410$	−2.32612	+	0.846640i	−0.114879	+	0.0418126i
$411$	−23.7566	−	22.0119i	−1.17183	−	1.08577i
$412$	−7.65402	−	2.78584i	−0.377087	−	0.137248i
$413$	−5.49613	−	11.4713i	−0.270447	−	0.564464i
$414$	−1.46378	−	1.49653i	−0.0719407	−	0.0735505i
$415$	8.25051			0.405002
$416$	1.01265	+	5.74304i	0.0496494	+	0.281576i
$417$	27.5394	+	1.35508i	1.34861	+	0.0663587i
$418$	3.46971	−	1.26287i	0.169709	−	0.0617691i
$419$	4.70505	−	26.6837i	0.229857	−	1.30358i	−0.623323	−	0.781964i	$-0.714218\pi$
$419$	4.70505	−	26.6837i	0.229857	−	1.30358i	0.853180	−	0.521617i	$-0.174671\pi$
$420$	−2.44537	+	3.21969i	−0.119322	+	0.157105i
$421$	−21.5456	+	18.0789i	−1.05007	+	0.881113i	−0.993101	−	0.117263i	$-0.962588\pi$
$421$	−21.5456	+	18.0789i	−1.05007	+	0.881113i	−0.0569682	+	0.998376i	$0.518143\pi$
$422$	19.7089			0.959412
$423$	−11.6445	+	16.2446i	−0.566177	+	0.789838i
$424$	−3.99813			−0.194167
$425$	0.201985	+	1.14551i	0.00979769	+	0.0555655i
$426$	−3.46836	+	15.2451i	−0.168043	+	0.738629i
$427$	33.8865	−	9.46135i	1.63988	−	0.457867i
$428$	−12.5740	+	4.57657i	−0.607788	+	0.221217i
$429$	41.5293	+	17.4718i	2.00505	+	0.843546i
$430$	−8.95876	−	3.26072i	−0.432030	−	0.157246i
$431$	−20.4365	+	35.3970i	−0.984390	+	1.70501i	−0.339772	+	0.940508i	$0.610350\pi$
$431$	−20.4365	+	35.3970i	−0.984390	+	1.70501i	−0.644618	+	0.764505i	$0.722983\pi$
$432$	−0.140468	−	5.19425i	−0.00675829	−	0.249909i
$433$	18.9809			0.912166			0.456083	−	0.889937i	$-0.349252\pi$
$433$	18.9809			0.912166			0.456083	+	0.889937i	$0.349252\pi$
$434$	6.35256	−	4.54801i	0.304933	−	0.218311i
$435$	6.33633	+	2.66576i	0.303804	+	0.127813i
$436$	−3.80861	−	3.19580i	−0.182399	−	0.153051i
$437$	0.542787	−	0.197558i	0.0259650	−	0.00945050i
$438$	−9.48860	+	2.93413i	−0.453383	+	0.140198i
$439$	−2.19738	−	12.4620i	−0.104875	−	0.594778i	−0.991270	−	0.131848i	$-0.957909\pi$
$439$	−2.19738	−	12.4620i	−0.104875	−	0.594778i	0.886395	−	0.462931i	$-0.153202\pi$
$440$	1.96771	+	3.40817i	0.0938069	+	0.162478i
$441$	−17.3204	−	11.8745i	−0.824780	−	0.565453i
$442$	0.803397	−	1.39152i	0.0382137	−	0.0661881i
$443$	−38.2455	−	13.9202i	−1.81710	−	0.661370i	−0.995872	−	0.0907685i	$-0.971068\pi$
$443$	−38.2455	−	13.9202i	−1.81710	−	0.661370i	−0.821227	−	0.570601i	$-0.806710\pi$
$444$	−4.23148	+	6.56169i	−0.200817	+	0.311404i
$445$	11.7599	+	9.86769i	0.557470	+	0.467773i
$446$	−14.0745	+	5.12270i	−0.666446	+	0.242567i
$447$	−2.96306	−	0.145798i	−0.140148	−	0.00689599i
$448$	−2.40944	−	1.09297i	−0.113836	−	0.0516379i
$449$	−4.21584	+	7.30204i	−0.198958	+	0.344605i	−0.948191	−	0.317702i	$-0.897089\pi$
$449$	−4.21584	+	7.30204i	−0.198958	+	0.344605i	0.749233	+	0.662306i	$0.230422\pi$
$450$	−11.4183	−	5.47905i	−0.538264	−	0.258285i
$451$	−12.5152			−0.589319
$452$	0.948298	−	0.795717i	0.0446042	−	0.0374274i
$453$	−0.0293136	+	0.128848i	−0.00137727	+	0.00605378i
$454$	−11.8759	−	9.96504i	−0.557362	−	0.467683i
$455$	3.38528	−	13.1849i	0.158704	−	0.618116i
$456$	1.32157	+	0.555996i	0.0618881	+	0.0260369i
$457$	−4.30174	+	3.60958i	−0.201227	+	0.168849i	−0.737833	−	0.674984i	$-0.764151\pi$
$457$	−4.30174	+	3.60958i	−0.201227	+	0.168849i	0.536606	+	0.843833i	$0.319706\pi$
$458$	6.53157	−	11.3130i	0.305200	−	0.528623i
$459$	−0.890294	+	1.12122i	−0.0415554	+	0.0523342i
$460$	0.307820	+	0.533160i	0.0143522	+	0.0248587i
$461$	−4.56772	−	25.9048i	−0.212740	−	1.20651i	−0.884786	−	0.465998i	$-0.845695\pi$
$461$	−4.56772	−	25.9048i	−0.212740	−	1.20651i	0.672046	−	0.740510i	$-0.265416\pi$
$462$	−17.1852	+	11.0680i	−0.799530	+	0.514929i
$463$	12.3467	−	4.49381i	0.573798	−	0.208845i	−0.0387907	−	0.999247i	$-0.512351\pi$
$463$	12.3467	−	4.49381i	0.573798	−	0.208845i	0.612588	+	0.790402i	$0.290128\pi$
$464$	−0.781152	+	4.43013i	−0.0362641	+	0.205664i
$465$	−3.31004	−	3.06695i	−0.153499	−	0.142227i
$466$	22.1276	−	18.5673i	1.02504	−	0.860112i
$467$	−13.4232	+	23.2497i	−0.621151	+	1.07587i	0.368120	+	0.929778i	$0.380001\pi$
$467$	−13.4232	+	23.2497i	−0.621151	+	1.07587i	−0.989272	+	0.146087i	$0.953332\pi$
$468$	7.21778	+	15.9366i	0.333642	+	0.736670i
$469$	−7.04162	+	10.2841i	−0.325152	+	0.474874i
$470$	4.50278	−	3.77828i	0.207698	−	0.174279i
$471$	−39.9658	−	1.96652i	−1.84153	−	0.0906126i
$472$	−3.68291	−	3.09033i	−0.169519	−	0.142244i
$473$	−36.9240	−	30.9829i	−1.69777	−	1.42459i
$474$	−12.7295	+	19.7395i	−0.584685	+	0.906663i
$475$	2.67700	−	2.24627i	0.122829	−	0.103066i
$476$	0.314986	+	0.657423i	0.0144373	+	0.0301329i
$477$	−11.6193	+	2.97600i	−0.532013	+	0.136262i
$478$	10.7247	−	18.5758i	0.490537	−	0.849635i
$479$	−23.0360	+	19.3295i	−1.05254	+	0.883188i	−0.993359	−	0.115059i	$-0.963294\pi$
$479$	−23.0360	+	19.3295i	−1.05254	+	0.883188i	−0.0591837	+	0.998247i	$0.518850\pi$
$480$	−0.338996	+	1.49005i	−0.0154730	+	0.0680114i
$481$	4.56485	−	25.8886i	0.208139	−	1.18042i
$482$	22.2770	−	8.10815i	1.01469	−	0.369316i
$483$	−2.68839	+	1.73143i	−0.122326	+	0.0787826i
$484$	1.54491	+	8.76163i	0.0702233	+	0.398256i
$485$	−3.15889	−	5.47135i	−0.143438	−	0.248441i
$486$	−4.27456	−	14.9909i	−0.193898	−	0.680003i
$487$	6.71776	−	11.6355i	0.304411	−	0.527255i	−0.672719	−	0.739898i	$-0.734874\pi$
$487$	6.71776	−	11.6355i	0.304411	−	0.527255i	0.977130	+	0.212643i	$0.0682071\pi$
$488$	10.1867	−	8.54764i	0.461129	−	0.386933i
$489$	−4.10497	−	32.5718i	−0.185633	−	1.47295i
$490$	4.06799	+	4.64680i	0.183773	+	0.209921i
$491$	21.1654	+	17.7599i	0.955183	+	0.801493i	0.980163	−	0.198194i	$-0.0635078\pi$
$491$	21.1654	+	17.7599i	0.955183	+	0.801493i	−0.0249800	+	0.999688i	$0.507952\pi$
$492$	−3.56472	−	3.30293i	−0.160710	−	0.148907i
$493$	0.949487	−	0.796715i	0.0427628	−	0.0358822i
$494$	−4.82732			−0.217192
$495$	8.25541	+	8.44014i	0.371053	+	0.379356i
$496$	1.47648	−	2.55733i	0.0662957	−	0.114828i
$497$	21.7493	+	9.86588i	0.975590	+	0.442545i
$498$	7.39947	+	14.4083i	0.331578	+	0.645652i
$499$	−9.17050	+	3.33779i	−0.410528	+	0.149420i	−0.539025	−	0.842290i	$-0.681207\pi$
$499$	−9.17050	+	3.33779i	−0.410528	+	0.149420i	0.128497	+	0.991710i	$0.458985\pi$
$500$	6.23247	+	5.22966i	0.278724	+	0.233878i
$501$	9.91669	+	19.3099i	0.443045	+	0.862701i
$502$	−7.52628	−	2.73934i	−0.335914	−	0.122263i
$503$	−5.74261	+	9.94650i	−0.256051	+	0.443493i	−0.965180	−	0.261585i	$-0.915755\pi$
$503$	−5.74261	+	9.94650i	−0.256051	+	0.443493i	0.709130	+	0.705078i	$0.249088\pi$
$504$	−7.81585	−	1.38291i	−0.348146	−	0.0615996i
$505$	0.160752	+	0.278431i	0.00715338	+	0.0123900i
$506$	0.540492	+	3.06528i	0.0240278	+	0.136268i
$507$	−26.6908	−	24.7306i	−1.18538	−	1.09833i
$508$	4.90356	−	1.78475i	0.217560	−	0.0791854i
$509$	−31.6802	−	26.5828i	−1.40420	−	1.17826i	−0.959199	−	0.282732i	$-0.908759\pi$
$509$	−31.6802	−	26.5828i	−1.40420	−	1.17826i	−0.445000	−	0.895531i	$-0.646796\pi$
$510$	0.335452	−	0.254465i	0.0148541	−	0.0112679i
$511$	1.48048	+	15.0988i	0.0654924	+	0.667932i
$512$	−1.00000			−0.0441942
$513$	4.25458	+	0.632126i	0.187844	+	0.0279091i
$514$	9.38413	−	16.2538i	0.413916	−	0.716924i
$515$	6.75289	+	2.45785i	0.297568	+	0.108306i
$516$	−2.34029	−	18.5696i	−0.103026	−	0.817479i
$517$	27.9257	−	10.1641i	1.22817	−	0.447018i
$518$	8.52122	+	8.34456i	0.374401	+	0.366639i
$519$	10.9905	+	10.1834i	0.482431	+	0.447002i
$520$	−0.893429	−	5.06689i	−0.0391794	−	0.222198i
$521$	2.84046			0.124443			0.0622215	−	0.998062i	$-0.480181\pi$
$521$	2.84046			0.124443			0.0622215	+	0.998062i	$0.480181\pi$
$522$	1.02738	+	13.4563i	0.0449673	+	0.588964i
$523$	−3.04989			−0.133362			−0.0666812	−	0.997774i	$-0.521241\pi$
$523$	−3.04989			−0.133362			−0.0666812	+	0.997774i	$0.521241\pi$
$524$	15.6291	−	13.1144i	0.682762	−	0.572906i
$525$	−11.7010	+	15.4061i	−0.510674	+	0.672377i
$526$	−4.22513	+	23.9619i	−0.184224	+	1.04479i
$527$	−0.764561	+	0.278277i	−0.0333048	+	0.0121220i
$528$	−4.18714	+	6.49294i	−0.182222	+	0.282569i
$529$	−3.90936	−	22.1711i	−0.169972	−	0.963959i
$530$	3.52742			0.153221
$531$	−13.0035	−	6.23971i	−0.564304	−	0.270780i
$532$	1.23734	−	1.80709i	0.0536453	−	0.0783472i
$533$	15.3753	+	5.59615i	0.665978	+	0.242396i
$534$	−6.68565	+	29.3867i	−0.289316	+	1.27169i
$535$	11.0936	−	4.03775i	0.479619	−	0.174567i
$536$	−0.818035	+	4.63931i	−0.0353337	+	0.200387i
$537$	2.41449	+	19.1583i	0.104193	+	0.826742i
$538$	1.47469	+	8.36338i	0.0635784	+	0.360571i
$539$	11.2915	+	29.1109i	0.486359	+	1.25390i
$540$	0.123931	+	4.58271i	0.00533312	+	0.197209i
$541$	−9.49589	−	16.4474i	−0.408260	−	0.707128i	0.586435	−	0.809997i	$-0.300531\pi$
$541$	−9.49589	−	16.4474i	−0.408260	−	0.707128i	−0.994695	+	0.102869i	$0.967198\pi$
$542$	0.950724	+	0.346035i	0.0408371	+	0.0148635i
$543$	2.93456	+	23.2849i	0.125934	+	0.999252i
$544$	0.211069	+	0.177108i	0.00904950	+	0.00759343i
$545$	3.36021	+	2.81955i	0.143935	+	0.120776i
$546$	26.0615	−	5.91296i	1.11533	−	0.253051i
$547$	8.71723	+	3.17281i	0.372722	+	0.135660i	0.521588	−	0.853198i	$-0.325340\pi$
$547$	8.71723	+	3.17281i	0.372722	+	0.135660i	−0.148866	+	0.988857i	$0.547562\pi$
$548$	−9.34925	+	16.1934i	−0.399380	+	0.691747i
$549$	23.2420	−	32.4235i	0.991945	−	1.38380i
$550$	9.41541	+	16.3080i	0.401475	+	0.695374i
$551$	−3.49919	−	1.27360i	−0.149070	−	0.0542572i
$552$	−0.655018	+	1.01573i	−0.0278794	+	0.0432322i
$553$	25.6343	+	25.1028i	1.09008	+	1.06748i
$554$	−3.65923	+	20.7525i	−0.155466	+	0.881690i
$555$	3.73329	−	5.78916i	0.158469	−	0.245736i
$556$	−2.76433	−	15.6773i	−0.117234	−	0.664865i
$557$	−13.7041	−	23.7362i	−0.580661	−	1.00573i	−0.995401	−	0.0957943i	$-0.969461\pi$
$557$	−13.7041	−	23.7362i	−0.580661	−	1.00573i	0.414740	−	0.909940i	$-0.363872\pi$
$558$	2.38738	−	8.53110i	0.101066	−	0.361150i
$559$	31.5082	+	54.5737i	1.33265	+	2.30822i
$560$	2.12577	+	0.964288i	0.0898302	+	0.0407486i
$561$	2.03372	−	0.628883i	0.0858639	−	0.0265514i
$562$	3.20650	−	18.1850i	0.135258	−	0.767087i
$563$	2.72875	−	15.4755i	0.115003	−	0.652215i	−0.871746	−	0.489959i	$-0.837012\pi$
$563$	2.72875	−	15.4755i	0.115003	−	0.652215i	0.986749	−	0.162256i	$-0.0518771\pi$
$564$	10.6365	+	4.47489i	0.447879	+	0.188427i
$565$	−0.836651	+	0.702034i	−0.0351982	+	0.0295348i
$566$	14.3598			0.603589
$567$	−23.7437	+	1.79872i	−0.997143	+	0.0755390i
$568$	9.02669			0.378752
$569$	−0.359574	+	0.301719i	−0.0150741	+	0.0126487i	−0.650294	−	0.759683i	$-0.725354\pi$
$569$	−0.359574	+	0.301719i	−0.0150741	+	0.0126487i	0.635219	+	0.772332i	$0.280910\pi$
$570$	−1.16597	−	0.490537i	−0.0488373	−	0.0205463i
$571$	1.66162	−	9.42349i	0.0695364	−	0.394361i	−0.930098	−	0.367312i	$-0.880278\pi$
$571$	1.66162	−	9.42349i	0.0695364	−	0.394361i	0.999634	−	0.0270484i	$-0.00861084\pi$
$572$	4.51702	−	25.6173i	0.188866	−	1.07111i
$573$	−37.7477	+	11.6726i	−1.57693	+	0.487631i
$574$	−6.03587	+	4.32128i	−0.251933	+	0.180367i
$575$	1.47291	+	2.55115i	0.0614244	+	0.106390i
$576$	−2.90619	+	0.744348i	−0.121091	+	0.0310145i
$577$	6.83284	+	11.8348i	0.284455	+	0.492690i	0.972477	−	0.233000i	$-0.0748541\pi$
$577$	6.83284	+	11.8348i	0.284455	+	0.492690i	−0.688022	+	0.725690i	$0.741521\pi$
$578$	2.93884	+	16.6670i	0.122239	+	0.693254i
$579$	−22.3271	+	34.6223i	−0.927881	+	1.43885i
$580$	0.689184	−	3.90855i	0.0286168	−	0.162294i
$581$	23.8303	−	6.65359i	0.988648	−	0.276037i
$582$	6.72187	−	10.4235i	0.278630	−	0.432069i
$583$	16.7585	+	6.09959i	0.694065	+	0.252619i
$584$	2.86709	+	4.96595i	0.118641	+	0.205492i
$585$	−6.36800	−	14.0603i	−0.263284	−	0.581323i
$586$	−1.36722	+	2.36809i	−0.0564793	+	0.0978250i
$587$	−18.3159	−	6.66645i	−0.755979	−	0.275154i	−0.0648598	−	0.997894i	$-0.520660\pi$
$587$	−18.3159	−	6.66645i	−0.755979	−	0.275154i	−0.691120	+	0.722740i	$0.742882\pi$
$588$	−4.46658	+	11.2716i	−0.184198	+	0.464834i
$589$	1.87252	+	1.57123i	0.0771558	+	0.0647414i
$590$	3.24930	+	2.72649i	0.133772	+	0.112248i
$591$	0.0143872	+	0.114159i	0.000591812	+	0.00469586i
$592$	4.23596	+	1.54176i	0.174097	+	0.0633661i
$593$	−0.0251136	−	0.0434980i	−0.00103129	−	0.00178625i	0.865509	−	0.500893i	$-0.166995\pi$
$593$	−0.0251136	−	0.0434980i	−0.00103129	−	0.00178625i	−0.866541	+	0.499107i	$0.833662\pi$
$594$	−7.33562	+	21.9864i	−0.300984	+	0.902113i
$595$	−0.277901	−	0.580022i	−0.0113928	−	0.0237786i
$596$	0.297423	+	1.68677i	0.0121829	+	0.0690928i
$597$	−0.809424	−	6.42255i	−0.0331275	−	0.262858i
$598$	0.706623	−	4.00746i	0.0288960	−	0.163877i
$599$	2.82578	−	1.02850i	0.115458	−	0.0420233i	−0.283645	−	0.958929i	$-0.591544\pi$
$599$	2.82578	−	1.02850i	0.115458	−	0.0420233i	0.399103	+	0.916906i	$0.369322\pi$
$600$	−1.62208	+	7.12985i	−0.0662213	+	0.291075i
$601$	14.2762	+	5.19610i	0.582337	+	0.211953i	0.616356	−	0.787468i	$-0.288608\pi$
$601$	14.2762	+	5.19610i	0.582337	+	0.211953i	−0.0340188	+	0.999421i	$0.510831\pi$
$602$	−28.5056	−	2.19334i	−1.16180	−	0.0893938i
$603$	1.07589	+	14.0916i	0.0438137	+	0.573855i
$604$	0.0762910			0.00310424
$605$	−1.36302	−	7.73009i	−0.0554148	−	0.314273i
$606$	−0.342069	+	0.530441i	−0.0138956	+	0.0215477i
$607$	−5.53740	+	2.01545i	−0.224756	+	0.0818045i	−0.451944	−	0.892046i	$-0.649269\pi$
$607$	−5.53740	+	2.01545i	−0.224756	+	0.0818045i	0.227188	+	0.973851i	$0.427047\pi$
$608$	0.143743	−	0.815207i	0.00582955	−	0.0330610i
$609$	20.4513	+	2.58972i	0.828728	+	0.104941i
$610$	−8.98736	+	7.54129i	−0.363887	+	0.305338i
$611$	−38.8523			−1.57180
$612$	0.745236	+	0.357600i	0.0301244	+	0.0144551i
$613$	−17.4177			−0.703495			−0.351748	−	0.936095i	$-0.614412\pi$
$613$	−17.4177			−0.703495			−0.351748	+	0.936095i	$0.614412\pi$
$614$	−0.188868	−	1.07112i	−0.00762209	−	0.0432270i
$615$	3.14503	+	2.91406i	0.126820	+	0.117506i
$616$	8.43193	+	8.25713i	0.339732	+	0.332689i
$617$	1.34658	−	0.490114i	0.0542112	−	0.0197312i	−0.314772	−	0.949167i	$-0.601928\pi$
$617$	1.34658	−	0.490114i	0.0542112	−	0.0197312i	0.368983	+	0.929436i	$0.379706\pi$
$618$	1.76405	+	13.9973i	0.0709605	+	0.563052i
$619$	21.3944	+	7.78692i	0.859913	+	0.312983i	0.734075	−	0.679068i	$-0.237616\pi$
$619$	21.3944	+	7.78692i	0.859913	+	0.312983i	0.125838	+	0.992051i	$0.459838\pi$
$620$	−1.30264	+	2.25625i	−0.0523154	+	0.0906130i
$621$	−1.14755	+	3.43946i	−0.0460497	+	0.138021i
$622$	−28.8205			−1.15560
$623$	41.9242	+	19.0176i	1.67966	+	0.761924i
$624$	8.04731	−	6.10448i	0.322150	−	0.244375i
$625$	10.6710	+	8.95403i	0.426840	+	0.358161i
$626$	−20.2517	+	7.37101i	−0.809420	+	0.294605i
$627$	−4.69122	−	4.34670i	−0.187349	−	0.173590i
$628$	4.01165	+	22.7512i	0.160082	+	0.907873i
$629$	−0.621021	−	1.07564i	−0.0247617	−	0.0428886i
$630$	6.89566	+	1.22009i	0.274730	+	0.0486097i
$631$	5.98954	−	10.3742i	0.238440	−	0.412990i	−0.721827	−	0.692073i	$-0.756697\pi$
$631$	5.98954	−	10.3742i	0.238440	−	0.412990i	0.960267	+	0.279084i	$0.0900308\pi$
$632$	12.7430	+	4.63807i	0.506889	+	0.184492i
$633$	−15.5948	−	30.3664i	−0.619839	−	1.20696i
$634$	−1.97246	−	1.65509i	−0.0783365	−	0.0657321i
$635$	−4.32624	+	1.57462i	−0.171682	+	0.0624870i
$636$	3.16356	+	6.16012i	0.125443	+	0.244265i
$637$	−0.855034	−	40.8125i	−0.0338777	−	1.61705i
$638$	10.0329	−	17.3775i	0.397207	−	0.687982i
$639$	26.2333	−	6.71900i	1.03777	−	0.265800i
$640$	0.882266			0.0348746
$641$	−1.67451	+	1.40508i	−0.0661390	+	0.0554972i	−0.675258	−	0.737582i	$-0.735968\pi$
$641$	−1.67451	+	1.40508i	−0.0661390	+	0.0554972i	0.609119	+	0.793079i	$0.291523\pi$
$642$	17.0007	+	15.7521i	0.670962	+	0.621687i
$643$	−23.2444	−	19.5044i	−0.916671	−	0.769178i	0.0567052	−	0.998391i	$-0.481940\pi$
$643$	−23.2444	−	19.5044i	−0.916671	−	0.769178i	−0.973376	+	0.229213i	$0.926385\pi$
$644$	1.31905	+	1.29171i	0.0519780	+	0.0509005i
$645$	2.06476	+	16.3833i	0.0812998	+	0.645091i
$646$	−0.174719	+	0.146607i	−0.00687423	+	0.00576817i
$647$	−12.9853	+	22.4913i	−0.510507	+	0.884223i	0.489419	+	0.872049i	$0.337209\pi$
$647$	−12.9853	+	22.4913i	−0.510507	+	0.884223i	−0.999926	+	0.0121748i	$0.996125\pi$
$648$	−7.89189	+	4.32643i	−0.310023	+	0.169958i
$649$	10.7226	+	18.5720i	0.420897	+	0.729015i
$650$	−4.27502	−	24.2448i	−0.167680	−	0.950961i
$651$	−12.0339	−	6.18905i	−0.471644	−	0.242568i
$652$	−17.8110	+	6.48268i	−0.697533	+	0.253881i
$653$	2.54992	−	14.4613i	0.0997861	−	0.565915i	−0.893389	−	0.449284i	$-0.851679\pi$
$653$	2.54992	−	14.4613i	0.0997861	−	0.565915i	0.993175	−	0.116631i	$-0.0372096\pi$
$654$	−1.91033	+	8.39682i	−0.0746997	+	0.328342i
$655$	−13.7891	+	11.5704i	−0.538783	+	0.452093i
$656$	−1.40287	+	2.42984i	−0.0547729	+	0.0948694i
$657$	12.0287	+	12.2979i	0.469285	+	0.479786i
$658$	9.95859	−	14.5442i	0.388226	−	0.566992i
$659$	26.4156	−	22.1653i	1.02901	−	0.863438i	0.0382730	−	0.999267i	$-0.487814\pi$
$659$	26.4156	−	22.1653i	1.02901	−	0.863438i	0.990732	+	0.135829i	$0.0433699\pi$
$660$	3.69417	−	5.72850i	0.143795	−	0.222982i
$661$	−26.9569	−	22.6195i	−1.04850	−	0.879796i	−0.0555650	−	0.998455i	$-0.517696\pi$
$661$	−26.9569	−	22.6195i	−1.04850	−	0.879796i	−0.992935	+	0.118659i	$0.962140\pi$
$662$	−16.8386	−	14.1293i	−0.654452	−	0.549150i
$663$	−2.77969	−	0.136775i	−0.107954	−	0.00531190i
$664$	7.16367	−	6.01103i	0.278004	−	0.233273i
$665$	−1.09166	+	1.59433i	−0.0423327	+	0.0618256i
$666$	13.4581	+	1.32763i	0.521492	+	0.0514447i
$667$	1.56950	−	2.71846i	0.0607714	−	0.105259i
$668$	9.60067	−	8.05592i	0.371461	−	0.311693i
$669$	19.0294	+	17.6319i	0.735718	+	0.681687i
$670$	0.721724	−	4.09310i	0.0278826	−	0.158130i
$671$	−55.7386	+	20.2872i	−2.15176	+	0.783178i
$672$	0.222509	+	4.57717i	0.00858348	+	0.176568i
$673$	−1.28861	−	7.30805i	−0.0496721	−	0.281705i	0.949847	−	0.312715i	$-0.101239\pi$
$673$	−1.28861	−	7.30805i	−0.0496721	−	0.281705i	−0.999519	+	0.0310105i	$0.990127\pi$
$674$	−4.29720	−	7.44297i	−0.165522	−	0.286693i
$675$	0.593003	+	21.9281i	0.0228247	+	0.844013i
$676$	−10.5040	+	18.1934i	−0.403999	+	0.699747i
$677$	19.5464	−	16.4014i	0.751230	−	0.630357i	−0.184598	−	0.982814i	$-0.559098\pi$
$677$	19.5464	−	16.4014i	0.751230	−	0.630357i	0.935828	+	0.352457i	$0.114654\pi$
$678$	−1.97635	−	0.831470i	−0.0759013	−	0.0319324i
$679$	−13.5363	−	13.2557i	−0.519475	−	0.508706i
$680$	−0.186219	−	0.156256i	−0.00714117	−	0.00599215i
$681$	−5.95672	+	26.1827i	−0.228262	+	1.00332i
$682$	−10.0902	+	8.46672i	−0.386376	+	0.324208i
$683$	−22.1958			−0.849298			−0.424649	−	0.905358i	$-0.639603\pi$
$683$	−22.1958			−0.849298			−0.424649	+	0.905358i	$0.639603\pi$
$684$	−0.189053	−	2.47614i	−0.00722862	−	0.0946776i
$685$	8.24853	−	14.2869i	0.315160	−	0.545873i
$686$	15.4971	+	10.1409i	0.591684	+	0.387183i
$687$	−22.5987	−	1.11197i	−0.862194	−	0.0424244i
$688$	−10.1543	+	3.69585i	−0.387128	+	0.140903i
$689$	−17.8608	−	14.9870i	−0.680443	−	0.570960i
$690$	0.577900	−	0.896142i	0.0220003	−	0.0341155i
$691$	−18.0204	−	6.55891i	−0.685530	−	0.249513i	−0.0243100	−	0.999704i	$-0.507739\pi$
$691$	−18.0204	−	6.55891i	−0.685530	−	0.249513i	−0.661220	+	0.750192i	$0.729961\pi$
$692$	4.32525	−	7.49155i	0.164421	−	0.284786i
$693$	30.6510	+	17.7205i	1.16433	+	0.673146i
$694$	11.9792	+	20.7485i	0.454723	+	0.787604i
$695$	2.43887	+	13.8315i	0.0925118	+	0.524660i
$696$	7.44381	−	2.30183i	0.282157	−	0.0872506i
$697$	0.726446	−	0.264405i	0.0275161	−	0.0100150i
$698$	−7.07046	−	5.93282i	−0.267621	−	0.224560i
$699$	−46.1162	−	19.4015i	−1.74427	−	0.733833i
$700$	10.1717	+	4.61408i	0.384455	+	0.174396i
$701$	9.73401			0.367648			0.183824	−	0.982959i	$-0.441152\pi$
$701$	9.73401			0.367648			0.183824	+	0.982959i	$0.441152\pi$
$702$	18.8432	−	23.7308i	0.711189	−	0.895661i
$703$	−1.86575	+	3.23157i	−0.0703679	+	0.121881i
$704$	4.19158	+	1.52561i	0.157976	+	0.0574986i
$705$	−9.38425	−	3.94805i	−0.353431	−	0.148692i
$706$	12.6250	−	4.59512i	0.475148	−	0.172940i
$707$	0.688847	+	0.674567i	0.0259068	+	0.0253697i
$708$	−1.84728	+	8.11969i	−0.0694249	+	0.305156i
$709$	2.52360	+	14.3121i	0.0947758	+	0.537500i	0.994816	+	0.101693i	$0.0324260\pi$
$709$	2.52360	+	14.3121i	0.0947758	+	0.537500i	−0.900040	+	0.435807i	$0.856463\pi$
$710$	−7.96395			−0.298882
$711$	40.4859	+	3.99390i	1.51834	+	0.149783i
$712$	17.4000			0.652091
$713$	−1.57847	+	1.32450i	−0.0591143	+	0.0496028i
$714$	0.763688	−	1.00551i	0.0285803	−	0.0376301i
$715$	−3.98521	+	22.6013i	−0.149039	+	0.845240i
$716$	10.4762	−	3.81303i	0.391515	−	0.142500i
$717$	−37.1066	−	1.82584i	−1.38577	−	0.0681871i
$718$	0.924012	+	5.24033i	0.0344838	+	0.195567i
$719$	−24.1039			−0.898926			−0.449463	−	0.893299i	$-0.648385\pi$
$719$	−24.1039			−0.898926			−0.449463	+	0.893299i	$0.648385\pi$
$720$	2.56403	−	0.656713i	0.0955559	−	0.0244742i
$721$	21.4868	+	1.65328i	0.800209	+	0.0615714i
$722$	−17.2103	−	6.26402i	−0.640500	−	0.233123i
$723$	−30.1195	−	27.9075i	−1.12016	−	1.03789i
$724$	12.7327	−	4.63434i	0.473209	−	0.172234i
$725$	3.29771	−	18.7023i	0.122474	−	0.694585i
$726$	12.2770	−	9.31306i	0.455644	−	0.345640i
$727$	0.656915	+	3.72555i	0.0243636	+	0.138173i	0.994563	−	0.104134i	$-0.0332070\pi$
$727$	0.656915	+	3.72555i	0.0243636	+	0.138173i	−0.970200	+	0.242307i	$0.922096\pi$
$728$	−6.66670	−	13.9144i	−0.247084	−	0.515702i
$729$	−19.7150	+	18.4478i	−0.730184	+	0.683250i
$730$	−2.52954	−	4.38129i	−0.0936224	−	0.162159i
$731$	2.79781	+	1.01832i	0.103481	+	0.0376640i
$732$	−21.2301	−	8.93170i	−0.784686	−	0.330125i
$733$	−22.1318	−	18.5708i	−0.817458	−	0.685928i	0.134918	−	0.990857i	$-0.456923\pi$
$733$	−22.1318	−	18.5708i	−0.817458	−	0.685928i	−0.952375	+	0.304929i	$0.901367\pi$
$734$	3.35216	+	2.81280i	0.123731	+	0.103822i
$735$	3.94071	−	9.94458i	0.145355	−	0.366811i
$736$	0.655712	+	0.238660i	0.0241699	+	0.00879711i
$737$	10.5066	−	18.1980i	0.387016	−	0.670332i
$738$	−2.26836	+	8.10581i	−0.0834995	+	0.298379i
$739$	12.5477	+	21.7333i	0.461576	+	0.799472i	0.999040	−	0.0438143i	$-0.0139510\pi$
$739$	12.5477	+	21.7333i	0.461576	+	0.799472i	−0.537464	+	0.843287i	$0.680618\pi$
$740$	−3.73725	−	1.36025i	−0.137384	−	0.0500036i
$741$	3.81967	+	7.43769i	0.140319	+	0.273231i
$742$	10.1884	−	2.84467i	0.374028	−	0.104431i
$743$	−2.23097	+	12.6525i	−0.0818463	+	0.464174i	0.916146	+	0.400844i	$0.131283\pi$
$743$	−2.23097	+	12.6525i	−0.0818463	+	0.464174i	−0.997993	+	0.0633296i	$0.979828\pi$
$744$	−5.10848	−	0.251364i	−0.187286	−	0.00921543i
$745$	−0.262406	−	1.48818i	−0.00961382	−	0.0545227i
$746$	6.21780	+	10.7695i	0.227650	+	0.394301i
$747$	16.3447	−	22.8015i	0.598021	−	0.834262i
$748$	−0.614514	−	1.06437i	−0.0224689	−	0.0389172i
$749$	28.7860	−	20.6088i	1.05182	−	0.753029i
$750$	3.12609	−	13.7407i	0.114149	−	0.501739i
$751$	7.24822	−	41.1067i	0.264491	−	1.50001i	−0.505988	−	0.862540i	$-0.668872\pi$
$751$	7.24822	−	41.1067i	0.264491	−	1.50001i	0.770480	−	0.637465i	$-0.220017\pi$
$752$	1.15690	−	6.56113i	0.0421879	−	0.239260i
$753$	1.73461	+	13.7636i	0.0632127	+	0.501575i
$754$	−20.0960	+	16.8625i	−0.731853	+	0.614097i
$755$	−0.0673090			−0.00244963
$756$	4.05366	+	13.1365i	0.147430	+	0.477770i
$757$	−33.0272			−1.20039			−0.600197	−	0.799852i	$-0.704911\pi$
$757$	−33.0272			−1.20039			−0.600197	+	0.799852i	$0.704911\pi$
$758$	−20.2427	+	16.9857i	−0.735249	+	0.616947i
$759$	4.29516	−	3.25820i	0.155904	−	0.118265i
$760$	−0.126820	+	0.719229i	−0.00460023	+	0.0260892i
$761$	−7.16345	+	40.6260i	−0.259675	+	1.47269i	0.524106	+	0.851653i	$0.324399\pi$
$761$	−7.16345	+	40.6260i	−0.259675	+	1.47269i	−0.783781	+	0.621037i	$0.786712\pi$
$762$	−6.62984	−	6.14295i	−0.240174	−	0.222536i
$763$	11.9792	+	5.43400i	0.433678	+	0.196724i
$764$	11.4059	+	19.7556i	0.412652	+	0.714734i
$765$	−0.657497	−	0.315499i	−0.0237718	−	0.0114069i
$766$	7.22289	+	12.5104i	0.260974	+	0.452019i
$767$	−4.86852	−	27.6108i	−0.175792	−	0.996967i
$768$	0.791260	+	1.54075i	0.0285522	+	0.0555970i
$769$	−0.00824195	+	0.0467424i	−0.000297212	+	0.00168557i	−0.984956	−	0.172805i	$-0.944717\pi$
$769$	−0.00824195	+	0.0467424i	−0.000297212	+	0.00168557i	0.984659	+	0.174491i	$0.0558280\pi$
$770$	−7.43920	−	7.28498i	−0.268090	−	0.262533i
$771$	−32.4683	−	1.59761i	−1.16932	−	0.0575364i
$772$	22.3507	+	8.13500i	0.804420	+	0.292785i
$773$	−13.2049	−	22.8716i	−0.474949	−	0.822635i	0.524640	−	0.851324i	$-0.324200\pi$
$773$	−13.2049	−	22.8716i	−0.474949	−	0.822635i	−0.999588	+	0.0286891i	$0.990867\pi$
$774$	−26.7592	+	18.2992i	−0.961841	+	0.657749i
$775$	−6.23310	+	10.7960i	−0.223900	+	0.387805i
$776$	−6.72900	−	2.44915i	−0.241557	−	0.0879195i
$777$	6.11438	−	19.7318i	0.219352	−	0.707874i
$778$	−12.0118	−	10.0791i	−0.430645	−	0.361354i
$779$	−1.77917	−	1.49290i	−0.0637454	−	0.0534887i
$780$	−7.09987	+	5.38578i	−0.254216	+	0.192842i
$781$	−37.8361	−	13.7712i	−1.35388	−	0.492773i
$782$	−0.0961319	−	0.166505i	−0.00343767	−	0.00595422i
$783$	19.9198	−	12.2303i	0.711875	−	0.437077i
$784$	6.91760	+	1.07088i	0.247057	+	0.0382456i
$785$	−3.53935	−	20.0726i	−0.126325	−	0.716423i
$786$	−32.5727	−	13.7037i	−1.16183	−	0.488794i
$787$	5.74400	−	32.5759i	0.204752	−	1.16120i	−0.693079	−	0.720862i	$-0.743746\pi$
$787$	5.74400	−	32.5759i	0.204752	−	1.16120i	0.897830	−	0.440342i	$-0.145143\pi$
$788$	0.0624246	−	0.0227207i	0.00222378	−	0.000809392i
$789$	40.2625	−	12.4502i	1.43338	−	0.443240i
$790$	−11.2427	−	4.09201i	−0.399997	−	0.145587i
$791$	−1.85038	+	2.70243i	−0.0657921	+	0.0960873i
$792$	13.3171	+	1.31372i	0.473203	+	0.0466810i
$793$	77.5477			2.75380
$794$	0.308490	+	1.74953i	0.0109479	+	0.0620887i
$795$	−2.79111	−	5.43486i	−0.0989903	−	0.192755i
$796$	−3.51200	+	1.27826i	−0.124480	+	0.0453069i
$797$	−8.70231	+	49.3532i	−0.308251	+	1.74818i	0.299539	+	0.954084i	$0.403167\pi$
$797$	−8.70231	+	49.3532i	−0.308251	+	1.74818i	−0.607791	+	0.794097i	$0.707944\pi$
$798$	−3.76332	−	0.476545i	−0.133220	−	0.0168695i
$799$	−1.40621	+	1.17995i	−0.0497482	+	0.0417437i
$800$	4.22161			0.149256
$801$	50.5676	−	12.9516i	1.78672	−	0.457623i
$802$	−29.6544			−1.04713
$803$	−4.44154	−	25.1892i	−0.156738	−	0.888908i
$804$	7.79528	−	2.41051i	0.274918	−	0.0850122i
$805$	−1.16376	−	1.13963i	−0.0410170	−	0.0401667i
$806$	16.1820	−	5.88977i	0.569987	−	0.207458i
$807$	11.7190	−	8.88974i	0.412529	−	0.312934i
$808$	0.342431	+	0.124635i	0.0120467	+	0.00438464i
$809$	2.43501	−	4.21755i	0.0856102	−	0.148281i	−0.820041	−	0.572305i	$-0.806049\pi$
$809$	2.43501	−	4.21755i	0.0856102	−	0.148281i	0.905651	+	0.424024i	$0.139383\pi$
$810$	6.96275	−	3.81707i	0.244646	−	0.134118i
$811$	15.2009			0.533777			0.266889	−	0.963727i	$-0.414004\pi$
$811$	15.2009			0.533777			0.266889	+	0.963727i	$0.414004\pi$
$812$	−1.16144	−	11.8450i	−0.0407584	−	0.415679i
$813$	−0.219117	−	1.73863i	−0.00768476	−	0.0609764i
$814$	−15.4032	−	12.9248i	−0.539883	−	0.453016i
$815$	15.7140	−	5.71945i	0.550439	−	0.200343i
$816$	0.105868	−	0.465342i	0.00370613	−	0.0162902i
$817$	−1.55328	−	8.80908i	−0.0543423	−	0.308191i
$818$	3.40695	+	5.90102i	0.119121	+	0.206324i
$819$	−29.7319	−	35.4756i	−1.03892	−	1.23962i
$820$	1.23770	−	2.14377i	0.0432225	−	0.0748636i
$821$	46.7439	+	17.0134i	1.63137	+	0.593771i	0.985500	−	0.169674i	$-0.0542715\pi$
$821$	46.7439	+	17.0134i	1.63137	+	0.593771i	0.645873	+	0.763445i	$0.276494\pi$
$822$	32.3476	+	1.59167i	1.12825	+	0.0555158i
$823$	27.4371	+	23.0224i	0.956396	+	0.802511i	0.980363	−	0.197202i	$-0.0631853\pi$
$823$	27.4371	+	23.0224i	0.956396	+	0.802511i	−0.0239674	+	0.999713i	$0.507630\pi$
$824$	7.65402	−	2.78584i	0.266641	−	0.0970492i
$825$	17.6764	−	27.4106i	0.615415	−	0.954316i
$826$	11.5839	+	5.25465i	0.403054	+	0.182833i
$827$	1.19083	−	2.06257i	0.0414091	−	0.0717227i	−0.844578	−	0.535433i	$-0.820149\pi$
$827$	1.19083	−	2.06257i	0.0414091	−	0.0717227i	0.885987	+	0.463710i	$0.153482\pi$
$828$	2.08327	+	0.205513i	0.0723986	+	0.00714206i
$829$	20.3791			0.707794			0.353897	−	0.935284i	$-0.384856\pi$
$829$	20.3791			0.707794			0.353897	+	0.935284i	$0.384856\pi$
$830$	−6.32026	+	5.30333i	−0.219379	+	0.184081i
$831$	34.8698	−	10.7827i	1.20962	−	0.374048i
$832$	−4.46729	−	3.74850i	−0.154875	−	0.129956i
$833$	−1.27043	−	1.45119i	−0.0440178	−	0.0502808i
$834$	−21.9675	+	16.6640i	−0.760671	+	0.577026i
$835$	−8.47034	+	7.10746i	−0.293128	+	0.245964i
$836$	−1.84620	+	3.19771i	−0.0638520	+	0.110595i
$837$	−15.0333	+	3.07198i	−0.519628	+	0.106183i
$838$	13.5476	+	23.4652i	0.467996	+	0.810592i
$839$	−4.98838	−	28.2905i	−0.172218	−	0.976696i	−0.941306	−	0.337554i	$-0.890401\pi$
$839$	−4.98838	−	28.2905i	−0.172218	−	0.976696i	0.769088	−	0.639142i	$-0.220711\pi$
$840$	−0.196312	−	4.03828i	−0.00677342	−	0.139334i
$841$	8.23522	−	2.99738i	0.283973	−	0.103358i
$842$	4.88399	−	27.6985i	0.168314	−	0.954554i
$843$	−30.5557	+	9.44864i	−1.05239	+	0.325428i
$844$	−15.0979	+	12.6686i	−0.519690	+	0.436072i
$845$	9.26730	−	16.0514i	0.318805	−	0.552186i
$846$	−1.52158	−	19.9290i	−0.0523129	−	0.685174i
$847$	−10.1708	−	21.2280i	−0.349472	−	0.729401i
$848$	3.06275	−	2.56995i	0.105175	−	0.0882525i
$849$	−11.3624	−	22.1249i	−0.389956	−	0.759325i
$850$	−0.891050	−	0.747679i	−0.0305628	−	0.0256452i
$851$	−2.40961	−	2.02191i	−0.0826005	−	0.0693101i
$852$	−7.14247	−	13.9079i	−0.244697	−	0.476476i
$853$	−0.279865	+	0.234835i	−0.00958241	+	0.00804060i	−0.647566	−	0.762009i	$-0.724213\pi$
$853$	−0.279865	+	0.234835i	−0.00958241	+	0.00804060i	0.637984	+	0.770050i	$0.279769\pi$
$854$	−19.8769	+	29.0296i	−0.680175	+	0.993374i
$855$	0.166795	+	2.18462i	0.00570427	+	0.0747123i
$856$	6.69049	−	11.5883i	0.228676	−	0.396079i
$857$	−31.2010	+	26.1807i	−1.06580	+	0.894317i	−0.994666	−	0.103150i	$-0.967108\pi$
$857$	−31.2010	+	26.1807i	−1.06580	+	0.894317i	−0.0711391	+	0.997466i	$0.522663\pi$
$858$	−43.0440	+	13.3104i	−1.46950	+	0.454408i
$859$	−0.849958	+	4.82035i	−0.0290002	+	0.164468i	−0.995868	−	0.0908076i	$-0.971055\pi$
$859$	−0.849958	+	4.82035i	−0.0290002	+	0.164468i	0.966868	+	0.255276i	$0.0821663\pi$
$860$	8.95876	−	3.26072i	0.305491	−	0.111190i
$861$	11.4340	+	5.88051i	0.389668	+	0.200407i
$862$	−7.09751	−	40.2520i	−0.241742	−	1.37099i
$863$	−0.198547	−	0.343894i	−0.00675862	−	0.0117063i	0.862626	−	0.505842i	$-0.168818\pi$
$863$	−0.198547	−	0.343894i	−0.00675862	−	0.0117063i	−0.869385	+	0.494135i	$0.835485\pi$
$864$	3.44641	+	3.88874i	0.117249	+	0.132298i
$865$	−3.81602	+	6.60954i	−0.129749	+	0.224731i
$866$	−14.5403	+	12.2007i	−0.494098	+	0.414597i
$867$	23.3542	−	17.7159i	0.793151	−	0.601664i
$868$	−1.94295	+	7.56732i	−0.0659479	+	0.256852i
$869$	−46.3373	−	38.8816i	−1.57189	−	1.31897i
$870$	−6.56742	+	2.03083i	−0.222657	+	0.0688514i
$871$	−21.0448	+	17.6587i	−0.713077	+	0.598343i
$872$	4.97179			0.168366
$873$	−21.3788	−	2.10900i	−0.723562	−	0.0713787i
$874$	−0.288811	+	0.500235i	−0.00976918	+	0.0169207i
$875$	−19.6030	−	8.89229i	−0.662703	−	0.300614i
$876$	5.38266	−	8.34683i	0.181863	−	0.282013i
$877$	−44.2848	+	16.1183i	−1.49539	+	0.544278i	−0.954863	−	0.297048i	$-0.903998\pi$
$877$	−44.2848	+	16.1183i	−1.49539	+	0.544278i	−0.540529	+	0.841326i	$0.681776\pi$
$878$	9.69371	+	8.13399i	0.327147	+	0.274509i
$879$	4.73046	+	0.232763i	0.159555	+	0.00785091i
$880$	−3.69809	−	1.34599i	−0.124662	−	0.0453734i
$881$	8.78796	−	15.2212i	0.296074	−	0.512815i	−0.679160	−	0.733990i	$-0.737656\pi$
$881$	8.78796	−	15.2212i	0.296074	−	0.512815i	0.975234	+	0.221175i	$0.0709892\pi$
$882$	20.9010	−	2.03693i	0.703773	−	0.0685869i
$883$	−8.84432	−	15.3188i	−0.297635	−	0.515519i	0.677959	−	0.735099i	$-0.262865\pi$
$883$	−8.84432	−	15.3188i	−0.297635	−	0.515519i	−0.975594	+	0.219580i	$0.929531\pi$
$884$	0.279017	+	1.58238i	0.00938436	+	0.0532213i
$885$	1.62979	−	7.16372i	0.0547848	−	0.240806i
$886$	38.2455	−	13.9202i	1.28488	−	0.467659i
$887$	2.57553	+	2.16113i	0.0864779	+	0.0725636i	0.685002	−	0.728541i	$-0.259801\pi$
$887$	2.57553	+	2.16113i	0.0864779	+	0.0725636i	−0.598524	+	0.801105i	$0.704246\pi$
$888$	−0.976278	−	7.74649i	−0.0327617	−	0.259955i
$889$	−11.2258	+	8.03693i	−0.376502	+	0.269550i
$890$	−15.3514			−0.514580
$891$	39.6799	−	6.09463i	1.32933	−	0.204178i
$892$	7.48888	−	12.9711i	0.250746	−	0.434305i
$893$	5.18238	+	1.88623i	0.173422	+	0.0631203i
$894$	2.36355	−	1.79293i	0.0790489	−	0.0599645i
$895$	−9.24281	+	3.36411i	−0.308953	+	0.112450i
$896$	2.54829	−	0.711499i	0.0851323	−	0.0237695i
$897$	−6.73361	+	2.08221i	−0.224829	+	0.0695231i
$898$	−1.46414	−	8.30358i	−0.0488591	−	0.277094i
$899$	13.2838			0.443039
$900$	12.2688	−	3.14234i	0.408960	−	0.104745i
$901$	−1.10161			−0.0366999
$902$	9.58722	−	8.04464i	0.319220	−	0.267857i
$903$	19.1760	+	45.6554i	0.638136	+	1.51932i
$904$	−0.214962	+	1.21911i	−0.00714952	+	0.0405469i
$905$	−11.2337	+	4.08872i	−0.373420	+	0.135914i
$906$	−0.0603661	−	0.117545i	−0.00200553	−	0.00390518i
$907$	0.186410	+	1.05718i	0.00618964	+	0.0351032i	0.987746	−	0.156069i	$-0.0498822\pi$
$907$	0.186410	+	1.05718i	0.00618964	+	0.0351032i	−0.981557	+	0.191172i	$0.938771\pi$
$908$	15.5029			0.514480
$909$	1.08794	+	0.107325i	0.0360848	+	0.00355973i
$910$	5.88180	+	12.2762i	0.194980	+	0.406952i
$911$	−0.225681	−	0.0821413i	−0.00747716	−	0.00272146i	0.338279	−	0.941046i	$-0.390155\pi$
$911$	−0.225681	−	0.0821413i	−0.00747716	−	0.00272146i	−0.345756	+	0.938324i	$0.612378\pi$
$912$	−1.36977	+	0.423569i	−0.0453575	+	0.0140258i
$913$	−39.1975	+	14.2667i	−1.29725	+	0.472160i
$914$	0.975124	−	5.53020i	0.0322542	−	0.182923i
$915$	18.7306	+	7.88014i	0.619214	+	0.260509i
$916$	2.26839	+	12.8647i	0.0749498	+	0.425061i
$917$	−30.4967	+	44.5394i	−1.00709	+	1.47082i
$918$	−0.0387034	−	1.43118i	−0.00127740	−	0.0472359i
$919$	−14.5162	−	25.1428i	−0.478845	−	0.829384i	0.520861	−	0.853642i	$-0.325611\pi$
$919$	−14.5162	−	25.1428i	−0.478845	−	0.829384i	−0.999706	+	0.0242578i	$0.992278\pi$
$920$	−0.578512	−	0.210561i	−0.0190730	−	0.00694200i
$921$	−1.50089	+	1.13854i	−0.0494560	+	0.0375160i
$922$	20.1504	+	16.9082i	0.663617	+	0.556841i
$923$	40.3249	+	33.8366i	1.32731	+	1.11374i
$924$	6.05031	−	19.5250i	0.199041	−	0.642326i
$925$	−17.8826	−	6.50872i	−0.587975	−	0.214005i
$926$	−6.56952	+	11.3787i	−0.215888	+	0.373929i
$927$	20.1704	−	13.7934i	0.662484	−	0.453036i
$928$	−2.24924	−	3.89579i	−0.0738348	−	0.127886i
$929$	39.4327	+	14.3523i	1.29375	+	0.470885i	0.894955	−	0.446157i	$-0.147208\pi$
$929$	39.4327	+	14.3523i	1.29375	+	0.470885i	0.398791	+	0.917042i	$0.369430\pi$
$930$	4.50704	+	0.221769i	0.147792	+	0.00727211i
$931$	−1.86734	+	5.48534i	−0.0611997	+	0.179775i
$932$	−5.01592	+	28.4467i	−0.164302	+	0.931802i
$933$	22.8045	+	44.4052i	0.746587	+	1.45376i
$934$	−4.66183	−	26.4385i	−0.152540	−	0.865095i
$935$	0.542165	+	0.939057i	0.0177307	+	0.0307104i
$936$	−15.7730	−	7.56864i	−0.515556	−	0.247389i
$937$	5.18146	+	8.97455i	0.169271	+	0.293186i	0.938164	−	0.346192i	$-0.112525\pi$
$937$	5.18146	+	8.97455i	0.169271	+	0.293186i	−0.768893	+	0.639378i	$0.779192\pi$
$938$	−1.21627	−	12.4043i	−0.0397128	−	0.405015i
$939$	27.3812	+	25.3704i	0.893553	+	0.827931i
$940$	−1.02070	+	5.78866i	−0.0332915	+	0.188805i
$941$	6.15385	−	34.9002i	0.200610	−	1.13772i	−0.703590	−	0.710606i	$-0.748421\pi$
$941$	6.15385	−	34.9002i	0.200610	−	1.13772i	0.904200	−	0.427109i	$-0.140468\pi$
$942$	31.8797	−	24.1831i	1.03870	−	0.787928i
$943$	1.49978	−	1.25847i	0.0488397	−	0.0409814i
$944$	4.80769			0.156477
$945$	−3.57641	−	11.5899i	−0.116341	−	0.377019i
$946$	48.2008			1.56714
$947$	21.5657	−	18.0958i	0.700790	−	0.588033i	−0.221208	−	0.975227i	$-0.571000\pi$
$947$	21.5657	−	18.0958i	0.700790	−	0.588033i	0.921998	+	0.387194i	$0.126556\pi$
$948$	−2.93692	−	23.3037i	−0.0953868	−	0.756868i
$949$	−5.80674	+	32.9316i	−0.188495	+	1.06901i
$950$	−0.606826	+	3.44148i	−0.0196880	+	0.111656i
$951$	−0.989351	+	4.34868i	−0.0320819	+	0.141016i
$952$	−0.663876	−	0.301146i	−0.0215163	−	0.00976021i
$953$	−2.74690	−	4.75777i	−0.0889808	−	0.154119i	0.818100	−	0.575076i	$-0.195028\pi$
$953$	−2.74690	−	4.75777i	−0.0889808	−	0.154119i	−0.907081	+	0.420957i	$0.861694\pi$
$954$	6.98799	−	9.74852i	0.226245	−	0.315620i
$955$	−10.0631	−	17.4297i	−0.325633	−	0.564013i
$956$	3.72466	+	21.1236i	0.120464	+	0.683185i
$957$	−34.7130	−	1.70806i	−1.12211	−	0.0552137i
$958$	5.22184	−	29.6145i	0.168710	−	0.956802i
$959$	12.3030	−	47.9174i	0.397285	−	1.54733i
$960$	−0.698102	−	1.35935i	−0.0225312	−	0.0438728i
$961$	20.9364	+	7.62024i	0.675369	+	0.245814i
$962$	13.1440	+	22.7660i	0.423778	+	0.734006i
$963$	10.8181	−	38.6578i	0.348610	−	1.24573i
$964$	−11.8533	+	20.5306i	−0.381770	+	0.661245i
$965$	−19.7193	−	7.17723i	−0.634786	−	0.231043i
$966$	0.946484	−	3.05441i	0.0304526	−	0.0982740i
$967$	−2.85297	−	2.39393i	−0.0917455	−	0.0769836i	0.595761	−	0.803162i	$-0.296850\pi$
$967$	−2.85297	−	2.39393i	−0.0917455	−	0.0769836i	−0.687507	+	0.726178i	$0.741295\pi$
$968$	−6.81534	−	5.71875i	−0.219053	−	0.183808i
$969$	0.364132	+	0.153194i	0.0116976	+	0.00492131i
$970$	5.93676	+	2.16081i	0.190618	+	0.0693793i
$971$	1.86108	+	3.22348i	0.0597248	+	0.103446i	0.894342	−	0.447384i	$-0.147644\pi$
$971$	1.86108	+	3.22348i	0.0597248	+	0.103446i	−0.834617	+	0.550831i	$0.814311\pi$
$972$	12.9105	+	8.73609i	0.414104	+	0.280210i
$973$	18.1987	+	37.9834i	0.583423	+	1.21769i
$974$	2.33305	+	13.2314i	0.0747558	+	0.423961i
$975$	−33.9726	+	25.7707i	−1.08799	+	0.825324i
$976$	−2.30913	+	13.0957i	−0.0739135	+	0.419184i
$977$	44.7054	−	16.2714i	1.43025	−	0.520569i	0.493248	−	0.869889i	$-0.335810\pi$
$977$	44.7054	−	16.2714i	1.43025	−	0.520569i	0.937004	+	0.349320i	$0.113587\pi$
$978$	24.0813	+	22.3128i	0.770036	+	0.713485i
$979$	−72.9333	−	26.5455i	−2.33096	−	0.848399i
$980$	−6.10317	−	0.944799i	−0.194958	−	0.0301805i
$981$	14.4490	−	3.70074i	0.461320	−	0.118155i
$982$	−27.6295			−0.881693
$983$	3.69968	+	20.9819i	0.118002	+	0.669220i	0.985220	+	0.171293i	$0.0547944\pi$
$983$	3.69968	+	20.9819i	0.118002	+	0.669220i	−0.867219	+	0.497928i	$0.834095\pi$
$984$	4.85381	+	0.238832i	0.154734	+	0.00761370i
$985$	−0.0550751	+	0.0200457i	−0.00175484	+	0.000638709i
$986$	−0.215231	+	1.22064i	−0.00685436	+	0.0388730i
$987$	−30.2888	−	3.83543i	−0.964104	−	0.122083i
$988$	3.69795	−	3.10294i	0.117647	−	0.0987178i
$989$	7.54032			0.239768
$990$	−11.7492	−	1.15905i	−0.373415	−	0.0368371i
$991$	−52.9314			−1.68142			−0.840710	−	0.541485i	$-0.817862\pi$
$991$	−52.9314			−1.68142			−0.840710	+	0.541485i	$0.817862\pi$
$992$	0.512775	+	2.90809i	0.0162806	+	0.0923319i
$993$	−8.44594	+	37.1240i	−0.268024	+	1.17810i
$994$	−23.0026	+	6.42249i	−0.729599	+	0.203709i
$995$	3.09852	−	1.12777i	0.0982297	−	0.0357527i
$996$	−14.9298	−	6.28112i	−0.473069	−	0.199025i
$997$	45.7605	+	16.6554i	1.44925	+	0.527483i	0.942381	−	0.334541i	$-0.108581\pi$
$997$	45.7605	+	16.6554i	1.44925	+	0.527483i	0.506867	+	0.862024i	$0.330803\pi$
$998$	4.87952	−	8.45157i	0.154458	−	0.267530i
$999$	−8.60333	−	21.7861i	−0.272197	−	0.689281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.67.11	✓	72
7.2	even	3		378.2.w.b.121.2	yes	72
27.25	even	9		378.2.w.b.25.2	yes	72
189.79	even	9	inner	378.2.v.a.79.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.11	✓	72	1.1	even	1	trivial
378.2.v.a.79.11	yes	72	189.79	even	9	inner
378.2.w.b.25.2	yes	72	27.25	even	9
378.2.w.b.121.2	yes	72	7.2	even	3

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.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.59651 + 0.671670i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.153204 + 0.868862i) q^{5} +(-1.65474 + 0.511691i) q^{6} +(0.258184 + 2.63312i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.09772 + 2.14466i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.59651 + 0.671670i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.153204 + 0.868862i) q^{5} +(-1.65474 + 0.511691i) q^{6} +(0.258184 + 2.63312i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.09772 + 2.14466i) q^{9} +(-0.441133 - 0.764065i) q^{10} +(-0.774572 - 4.39282i) q^{11} +(0.938697 - 1.45563i) q^{12} +(-1.01265 + 5.74304i) q^{13} +(-1.89032 - 1.85113i) q^{14} +(-0.828181 + 1.28425i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.137765 + 0.238617i) q^{17} +(-2.98551 - 0.294518i) q^{18} +(0.413891 - 0.716881i) q^{19} +(0.829059 + 0.301753i) q^{20} +(-1.35639 + 4.37724i) q^{21} +(3.41700 + 2.86721i) q^{22} +(0.534541 + 0.448533i) q^{23} +(0.216574 + 1.71846i) q^{24} +(3.96701 + 1.44387i) q^{25} +(-2.91582 - 5.05034i) q^{26} +(1.90854 + 4.83296i) q^{27} +(2.63795 + 0.202975i) q^{28} +(-0.781152 - 4.43013i) q^{29} +(-0.191076 - 1.51614i) q^{30} +(-0.512775 + 2.90809i) q^{31} +(0.939693 - 0.342020i) q^{32} +(1.71391 - 7.53345i) q^{33} +(-0.258914 - 0.0942371i) q^{34} +(-2.32738 - 0.179078i) q^{35} +(2.47634 - 1.69343i) q^{36} -4.50782 q^{37} +(0.143743 + 0.815207i) q^{38} +(-5.47414 + 8.48868i) q^{39} +(-0.829059 + 0.301753i) q^{40} +(0.487212 - 2.76311i) q^{41} +(-1.77457 - 4.22503i) q^{42} +(8.27783 - 6.94593i) q^{43} -4.46058 q^{44} +(-2.18479 + 1.49406i) q^{45} -0.697794 q^{46} +(1.15690 + 6.56113i) q^{47} +(-1.27051 - 1.17720i) q^{48} +(-6.86668 + 1.35966i) q^{49} +(-3.96701 + 1.44387i) q^{50} +(0.0596729 + 0.473488i) q^{51} +(5.47994 + 1.99454i) q^{52} +(-1.99907 + 3.46249i) q^{53} +(-4.56859 - 2.47548i) q^{54} +3.93542 q^{55} +(-2.15126 + 1.54016i) q^{56} +(1.14229 - 0.866513i) q^{57} +(3.44603 + 2.89156i) q^{58} +(-4.51775 + 1.64433i) q^{59} +(1.12093 + 1.03861i) q^{60} +(-2.30913 - 13.0957i) q^{61} +(-1.47648 - 2.55733i) q^{62} +(-5.10556 + 6.07727i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.83477 - 1.75971i) q^{65} +(3.52948 + 6.87264i) q^{66} +(3.60874 + 3.02809i) q^{67} +(0.258914 - 0.0942371i) q^{68} +(0.552137 + 1.07513i) q^{69} +(1.89798 - 1.35883i) q^{70} +(4.51335 - 7.81735i) q^{71} +(-0.808471 + 2.88901i) q^{72} +5.73418 q^{73} +(3.45319 - 2.89757i) q^{74} +(5.36359 + 4.96969i) q^{75} +(-0.634118 - 0.532088i) q^{76} +(11.3668 - 3.17370i) q^{77} +(-1.26298 - 10.0214i) q^{78} +(10.3882 - 8.71672i) q^{79} +(0.441133 - 0.764065i) q^{80} +(-0.199145 + 8.99780i) q^{81} +(1.40287 + 2.42984i) q^{82} +(-1.62387 - 9.20943i) q^{83} +(4.07520 + 2.09589i) q^{84} +(-0.228431 + 0.0831422i) q^{85} +(-1.87643 + 10.6418i) q^{86} +(1.72846 - 7.59745i) q^{87} +(3.41700 - 2.86721i) q^{88} +(8.69998 - 15.0688i) q^{89} +(0.713287 - 2.54887i) q^{90} +(-15.3836 - 1.18368i) q^{91} +(0.534541 - 0.448533i) q^{92} +(-2.77193 + 4.29839i) q^{93} +(-5.10365 - 4.28247i) q^{94} +(0.559461 + 0.469444i) q^{95} +(1.72996 + 0.0851228i) q^{96} +(-5.48553 + 4.60290i) q^{97} +(4.38621 - 5.45538i) q^{98} +(7.79627 - 10.8761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

L-functions

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