LMFDB - Embedded newform 380.2.bj.a.283.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			283.50
Character	$\chi$	$=$	380.283
Dual form			380.2.bj.a.47.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33545 + 0.465386i) q^{2} +(1.05442 - 0.0922501i) q^{3} +(1.56683 + 1.24300i) q^{4} +(1.20534 - 1.88339i) q^{5} +(1.45106 + 0.367519i) q^{6} +(-0.0324892 + 0.121251i) q^{7} +(1.51394 + 2.38914i) q^{8} +(-1.85112 + 0.326403i) q^{9} +O(q^{10})$	\(q+(1.33545 + 0.465386i) q^{2} +(1.05442 - 0.0922501i) q^{3} +(1.56683 + 1.24300i) q^{4} +(1.20534 - 1.88339i) q^{5} +(1.45106 + 0.367519i) q^{6} +(-0.0324892 + 0.121251i) q^{7} +(1.51394 + 2.38914i) q^{8} +(-1.85112 + 0.326403i) q^{9} +(2.48617 - 1.95421i) q^{10} +(-3.46465 - 2.00031i) q^{11} +(1.76677 + 1.16610i) q^{12} +(5.11107 + 0.447161i) q^{13} +(-0.0998162 + 0.146805i) q^{14} +(1.09720 - 2.09708i) q^{15} +(0.909920 + 3.89513i) q^{16} +(0.810447 + 1.15744i) q^{17} +(-2.62398 - 0.425594i) q^{18} +(-4.32125 + 0.571627i) q^{19} +(4.22961 - 1.45271i) q^{20} +(-0.0230719 + 0.130847i) q^{21} +(-3.69593 - 4.28371i) q^{22} +(-3.92885 + 1.83205i) q^{23} +(1.81674 + 2.37950i) q^{24} +(-2.09429 - 4.54026i) q^{25} +(6.61746 + 2.97578i) q^{26} +(-4.98891 + 1.33678i) q^{27} +(-0.201620 + 0.149596i) q^{28} +(-5.58817 + 0.985345i) q^{29} +(2.44121 - 2.28991i) q^{30} +(5.55113 - 3.20494i) q^{31} +(-0.597592 + 5.62520i) q^{32} +(-3.83773 - 1.78956i) q^{33} +(0.543652 + 1.92287i) q^{34} +(0.189202 + 0.207339i) q^{35} +(-3.30612 - 1.78952i) q^{36} +(2.15454 - 2.15454i) q^{37} +(-6.03683 - 1.24768i) q^{38} +5.43049 q^{39} +(6.32449 + 0.0283902i) q^{40} +(7.14094 + 5.99196i) q^{41} +(-0.0917059 + 0.164002i) q^{42} +(0.422379 - 0.905795i) q^{43} +(-2.94213 - 7.44070i) q^{44} +(-1.61650 + 3.87981i) q^{45} +(-6.09939 + 0.618175i) q^{46} +(-6.65530 + 9.50476i) q^{47} +(1.31877 + 4.02318i) q^{48} +(6.04853 + 3.49212i) q^{49} +(-0.683833 - 7.03792i) q^{50} +(0.961328 + 1.14567i) q^{51} +(7.45237 + 7.05367i) q^{52} +(-4.37973 - 9.39237i) q^{53} +(-7.28454 - 0.536581i) q^{54} +(-7.94346 + 4.11420i) q^{55} +(-0.338873 + 0.105947i) q^{56} +(-4.50370 + 1.00137i) q^{57} +(-7.92126 - 1.28478i) q^{58} +(0.929214 - 5.26983i) q^{59} +(4.32579 - 1.92195i) q^{60} +(-8.86615 - 3.22702i) q^{61} +(8.90477 - 1.69661i) q^{62} +(0.0205647 - 0.235056i) q^{63} +(-3.41594 + 7.23404i) q^{64} +(7.00278 - 9.08714i) q^{65} +(-4.29225 - 4.17589i) q^{66} +(3.28200 - 4.68718i) q^{67} +(-0.168858 + 2.82089i) q^{68} +(-3.97367 + 2.29420i) q^{69} +(0.156177 + 0.364943i) q^{70} +(2.38542 + 6.55389i) q^{71} +(-3.58232 - 3.92843i) q^{72} +(-0.788336 - 9.01072i) q^{73} +(3.87996 - 1.87457i) q^{74} +(-2.62711 - 4.59416i) q^{75} +(-7.48121 - 4.47566i) q^{76} +(0.355104 - 0.355104i) q^{77} +(7.25212 + 2.52727i) q^{78} +(-4.83313 - 4.05548i) q^{79} +(8.43280 + 2.98125i) q^{80} +(0.161856 - 0.0589108i) q^{81} +(6.74776 + 11.3252i) q^{82} +(0.718635 + 0.192558i) q^{83} +(-0.198793 + 0.176337i) q^{84} +(3.15677 - 0.131273i) q^{85} +(0.985610 - 1.01307i) q^{86} +(-5.80140 + 1.55448i) q^{87} +(-0.466259 - 11.3059i) q^{88} +(-3.46730 - 4.13217i) q^{89} +(-3.96436 + 4.42898i) q^{90} +(-0.220273 + 0.605196i) q^{91} +(-8.43309 - 2.01303i) q^{92} +(5.55758 - 3.89146i) q^{93} +(-13.3112 + 9.59580i) q^{94} +(-4.13201 + 8.82760i) q^{95} +(-0.111190 + 5.98647i) q^{96} +(3.98176 + 5.68654i) q^{97} +(6.45230 + 7.47844i) q^{98} +(7.06640 + 2.57196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.33545	+	0.465386i	0.944303	+	0.329078i
$2$	1.33545	+	0.465386i	0.944303	+	0.329078i
$3$	1.05442	−	0.0922501i	0.608772	−	0.0532606i	0.221398	−	0.975183i	$-0.428938\pi$
$3$	1.05442	−	0.0922501i	0.608772	−	0.0532606i	0.387373	+	0.921923i	$0.373382\pi$
$4$	1.56683	+	1.24300i	0.783416	+	0.621498i
$5$	1.20534	−	1.88339i	0.539047	−	0.842276i
$5$	1.20534	−	1.88339i	0.539047	−	0.842276i
$6$	1.45106	+	0.367519i	0.592392	+	0.150039i
$7$	−0.0324892	+	0.121251i	−0.0122798	+	0.0458287i	−0.971794	−	0.235832i	$-0.924219\pi$
$7$	−0.0324892	+	0.121251i	−0.0122798	+	0.0458287i	0.959514	+	0.281661i	$0.0908852\pi$
$8$	1.51394	+	2.38914i	0.535260	+	0.844687i
$9$	−1.85112	+	0.326403i	−0.617041	+	0.108801i
$10$	2.48617	−	1.95421i	0.786198	−	0.617975i
$11$	−3.46465	−	2.00031i	−1.04463	−	0.603117i	−0.123489	−	0.992346i	$-0.539408\pi$
$11$	−3.46465	−	2.00031i	−1.04463	−	0.603117i	−0.921141	+	0.389229i	$0.872742\pi$
$12$	1.76677	+	1.16610i	0.510023	+	0.336625i
$13$	5.11107	+	0.447161i	1.41756	+	0.124020i	0.770023	−	0.638016i	$-0.220245\pi$
$13$	5.11107	+	0.447161i	1.41756	+	0.124020i	0.647534	+	0.762037i	$0.275800\pi$
$14$	−0.0998162	+	0.146805i	−0.0266770	+	0.0392352i
$15$	1.09720	−	2.09708i	0.283296	−	0.541464i
$16$	0.909920	+	3.89513i	0.227480	+	0.973783i
$17$	0.810447	+	1.15744i	0.196562	+	0.280720i	0.905318	−	0.424734i	$-0.139632\pi$
$17$	0.810447	+	1.15744i	0.196562	+	0.280720i	−0.708756	+	0.705454i	$0.750743\pi$
$18$	−2.62398	−	0.425594i	−0.618478	−	0.100314i
$19$	−4.32125	+	0.571627i	−0.991364	+	0.131140i
$19$	−4.32125	+	0.571627i	−0.991364	+	0.131140i
$20$	4.22961	−	1.45271i	0.945770	−	0.324836i
$21$	−0.0230719	+	0.130847i	−0.00503471	+	0.0285532i
$22$	−3.69593	−	4.28371i	−0.787974	−	0.913290i
$23$	−3.92885	+	1.83205i	−0.819223	+	0.382010i	−0.786604	−	0.617458i	$-0.788163\pi$
$23$	−3.92885	+	1.83205i	−0.819223	+	0.382010i	−0.0326190	+	0.999468i	$0.510385\pi$
$24$	1.81674	+	2.37950i	0.370840	+	0.485713i
$25$	−2.09429	−	4.54026i	−0.418858	−	0.908052i
$26$	6.61746	+	2.97578i	1.29779	+	0.583599i
$27$	−4.98891	+	1.33678i	−0.960117	+	0.257263i
$28$	−0.201620	+	0.149596i	−0.0381026	+	0.0282711i
$29$	−5.58817	+	0.985345i	−1.03770	+	0.182974i	−0.666442	−	0.745557i	$-0.732183\pi$
$29$	−5.58817	+	0.985345i	−1.03770	+	0.182974i	−0.371255	+	0.928531i	$0.621072\pi$
$30$	2.44121	−	2.28991i	0.445701	−	0.418079i
$31$	5.55113	−	3.20494i	0.997012	−	0.575625i	0.0896491	−	0.995973i	$-0.471425\pi$
$31$	5.55113	−	3.20494i	0.997012	−	0.575625i	0.907363	+	0.420348i	$0.138092\pi$
$32$	−0.597592	+	5.62520i	−0.105640	+	0.994404i
$33$	−3.83773	−	1.78956i	−0.668063	−	0.311523i
$34$	0.543652	+	1.92287i	0.0932356	+	0.329769i
$35$	0.189202	+	0.207339i	0.0319810	+	0.0350467i
$36$	−3.30612	−	1.78952i	−0.551020	−	0.298254i
$37$	2.15454	−	2.15454i	0.354204	−	0.354204i	−0.507467	−	0.861671i	$-0.669418\pi$
$37$	2.15454	−	2.15454i	0.354204	−	0.354204i	0.861671	+	0.507467i	$0.169418\pi$
$38$	−6.03683	−	1.24768i	−0.979303	−	0.202400i
$39$	5.43049			0.869574
$40$	6.32449	+	0.0283902i	0.999990	+	0.00448889i
$41$	7.14094	+	5.99196i	1.11523	+	0.935787i	0.998354	−	0.0573601i	$-0.0182683\pi$
$41$	7.14094	+	5.99196i	1.11523	+	0.935787i	0.116874	+	0.993147i	$0.462713\pi$
$42$	−0.0917059	+	0.164002i	−0.0141505	+	0.0253061i
$43$	0.422379	−	0.905795i	0.0644122	−	0.138133i	−0.871466	−	0.490456i	$-0.836830\pi$
$43$	0.422379	−	0.905795i	0.0644122	−	0.138133i	0.935878	+	0.352323i	$0.114608\pi$
$44$	−2.94213	−	7.44070i	−0.443543	−	1.12173i
$45$	−1.61650	+	3.87981i	−0.240974	+	0.578368i
$46$	−6.09939	+	0.618175i	−0.899305	+	0.0911449i
$47$	−6.65530	+	9.50476i	−0.970775	+	1.38641i	−0.0489520	+	0.998801i	$0.515588\pi$
$47$	−6.65530	+	9.50476i	−0.970775	+	1.38641i	−0.921823	+	0.387610i	$0.873301\pi$
$48$	1.31877	+	4.02318i	0.190348	+	0.580696i
$49$	6.04853	+	3.49212i	0.864076	+	0.498874i
$50$	−0.683833	−	7.03792i	−0.0967086	−	0.995313i
$51$	0.961328	+	1.14567i	0.134613	+	0.160425i
$52$	7.45237	+	7.05367i	1.03346	+	0.978168i
$53$	−4.37973	−	9.39237i	−0.601602	−	1.29014i	−0.937416	−	0.348212i	$-0.886789\pi$
$53$	−4.37973	−	9.39237i	−0.601602	−	1.29014i	0.335813	−	0.941929i	$-0.390989\pi$
$54$	−7.28454	−	0.536581i	−0.991301	−	0.0730194i
$55$	−7.94346	+	4.11420i	−1.07110	+	0.554758i
$56$	−0.338873	+	0.105947i	−0.0452838	+	0.0141577i
$57$	−4.50370	+	1.00137i	−0.596530	+	0.132635i
$58$	−7.92126	−	1.28478i	−1.04011	−	0.168700i
$59$	0.929214	−	5.26983i	0.120973	−	0.686074i	−0.862645	−	0.505810i	$-0.831194\pi$
$59$	0.929214	−	5.26983i	0.120973	−	0.686074i	0.983618	−	0.180264i	$-0.0576952\pi$
$60$	4.32579	−	1.92195i	0.558457	−	0.248123i
$61$	−8.86615	−	3.22702i	−1.13519	−	0.413177i	−0.295019	−	0.955491i	$-0.595326\pi$
$61$	−8.86615	−	3.22702i	−1.13519	−	0.413177i	−0.840176	+	0.542314i	$0.817548\pi$
$62$	8.90477	−	1.69661i	1.13091	−	0.215470i
$63$	0.0205647	−	0.235056i	0.00259091	−	0.0296143i
$64$	−3.41594	+	7.23404i	−0.426993	+	0.904255i
$65$	7.00278	−	9.08714i	0.868588	−	1.12712i
$66$	−4.29225	−	4.17589i	−0.528339	−	0.514017i
$67$	3.28200	−	4.68718i	0.400960	−	0.572630i	−0.567005	−	0.823714i	$-0.691898\pi$
$67$	3.28200	−	4.68718i	0.400960	−	0.572630i	0.967965	+	0.251084i	$0.0807870\pi$
$68$	−0.168858	+	2.82089i	−0.0204770	+	0.342084i
$69$	−3.97367	+	2.29420i	−0.478374	+	0.276189i
$70$	0.156177	+	0.364943i	0.0186667	+	0.0436190i
$71$	2.38542	+	6.55389i	0.283097	+	0.777803i	0.996989	+	0.0775470i	$0.0247088\pi$
$71$	2.38542	+	6.55389i	0.283097	+	0.777803i	−0.713891	+	0.700256i	$0.753069\pi$
$72$	−3.58232	−	3.92843i	−0.422181	−	0.462970i
$73$	−0.788336	−	9.01072i	−0.0922678	−	1.05463i	−0.891323	−	0.453368i	$-0.850222\pi$
$73$	−0.788336	−	9.01072i	−0.0922678	−	1.05463i	0.799056	−	0.601257i	$-0.205333\pi$
$74$	3.87996	−	1.87457i	0.451036	−	0.217915i
$75$	−2.62711	−	4.59416i	−0.303352	−	0.530488i
$76$	−7.48121	−	4.47566i	−0.858153	−	0.513393i
$77$	0.355104	−	0.355104i	0.0404679	−	0.0404679i
$78$	7.25212	+	2.52727i	0.821141	+	0.286157i
$79$	−4.83313	−	4.05548i	−0.543769	−	0.456277i	0.329055	−	0.944311i	$-0.393270\pi$
$79$	−4.83313	−	4.05548i	−0.543769	−	0.456277i	−0.872825	+	0.488034i	$0.837714\pi$
$80$	8.43280	+	2.98125i	0.942816	+	0.333313i
$81$	0.161856	−	0.0589108i	0.0179840	−	0.00654564i
$82$	6.74776	+	11.3252i	0.745166	+	1.25066i
$83$	0.718635	+	0.192558i	0.0788804	+	0.0211360i	0.298043	−	0.954552i	$-0.403666\pi$
$83$	0.718635	+	0.192558i	0.0788804	+	0.0211360i	−0.219163	+	0.975688i	$0.570333\pi$
$84$	−0.198793	+	0.176337i	−0.0216901	+	0.0192400i
$85$	3.15677	−	0.131273i	0.342400	−	0.0142385i
$86$	0.985610	−	1.01307i	0.106281	−	0.109242i
$87$	−5.80140	+	1.55448i	−0.621975	+	0.166658i
$88$	−0.466259	−	11.3059i	−0.0497034	−	1.20521i
$89$	−3.46730	−	4.13217i	−0.367533	−	0.438009i	0.550305	−	0.834964i	$-0.314511\pi$
$89$	−3.46730	−	4.13217i	−0.367533	−	0.438009i	−0.917838	+	0.396955i	$0.870067\pi$
$90$	−3.96436	+	4.42898i	−0.417880	+	0.466855i
$91$	−0.220273	+	0.605196i	−0.0230909	+	0.0634418i
$92$	−8.43309	−	2.01303i	−0.879210	−	0.209873i
$93$	5.55758	−	3.89146i	0.576294	−	0.403526i
$94$	−13.3112	+	9.59580i	−1.37294	+	0.989731i
$95$	−4.13201	+	8.82760i	−0.423935	+	0.905693i
$96$	−0.111190	+	5.98647i	−0.0113482	+	0.610992i
$97$	3.98176	+	5.68654i	0.404286	+	0.577380i	0.968738	−	0.248085i	$-0.0798014\pi$
$97$	3.98176	+	5.68654i	0.404286	+	0.577380i	−0.564452	+	0.825466i	$0.690912\pi$
$98$	6.45230	+	7.47844i	0.651781	+	0.755437i
$99$	7.06640	+	2.57196i	0.710200	+	0.258492i
$100$	2.36213	−	9.71701i	0.236213	−	0.971701i
$101$	0.317874	−	0.266728i	0.0316296	−	0.0265404i	−0.626836	−	0.779151i	$-0.715650\pi$
$101$	0.317874	−	0.266728i	0.0316296	−	0.0265404i	0.658465	+	0.752611i	$0.271206\pi$
$102$	0.750624	+	1.97736i	0.0743229	+	0.195788i
$103$	−3.20906	−	11.9764i	−0.316198	−	1.18007i	−0.922869	−	0.385114i	$-0.874162\pi$
$103$	−3.20906	−	11.9764i	−0.316198	−	1.18007i	0.606671	−	0.794953i	$-0.292505\pi$
$104$	6.66955	+	12.8880i	0.654004	+	1.26378i
$105$	0.218626	+	0.201170i	0.0213358	+	0.0196321i
$106$	−1.47782	−	14.5813i	−0.143538	−	1.41626i
$107$	0.892261	−	3.32996i	0.0862581	−	0.321920i	−0.909291	−	0.416160i	$-0.863376\pi$
$107$	0.892261	−	3.32996i	0.0862581	−	0.321920i	0.995549	+	0.0942404i	$0.0300422\pi$
$108$	−9.47839	−	4.10670i	−0.912059	−	0.395167i
$109$	6.61359	+	18.1707i	0.633467	+	1.74044i	0.671337	+	0.741152i	$0.265720\pi$
$109$	6.61359	+	18.1707i	0.633467	+	1.74044i	−0.0378702	+	0.999283i	$0.512057\pi$
$110$	−12.5227	+	1.79751i	−1.19400	+	0.171386i
$111$	2.07304	−	2.47055i	0.196764	−	0.234494i
$112$	−0.501852	−	0.0162207i	−0.0474206	−	0.00153271i
$113$	−2.39493	−	2.39493i	−0.225296	−	0.225296i	0.585428	−	0.810724i	$-0.300926\pi$
$113$	−2.39493	−	2.39493i	−0.225296	−	0.225296i	−0.810724	+	0.585428i	$0.800926\pi$
$114$	−6.48047	−	0.758680i	−0.606952	−	0.0710569i
$115$	−1.28516	+	9.60781i	−0.119842	+	0.895933i
$116$	−9.98049	−	5.40220i	−0.926666	−	0.501582i
$117$	−9.60719	+	0.840520i	−0.888185	+	0.0777061i
$118$	3.69342	−	6.60513i	0.340007	−	0.608052i
$119$	−0.166672	+	0.0606635i	−0.0152788	+	0.00556102i
$120$	6.67131	−	0.553500i	0.609005	−	0.0505274i
$121$	2.50251	+	4.33448i	0.227501	+	0.394043i
$122$	−10.3385	−	8.43569i	−0.936000	−	0.763731i
$123$	8.08233	+	5.65931i	0.728759	+	0.510283i
$124$	12.6814	+	1.87842i	1.13882	+	0.168687i
$125$	−11.0754	−	1.52823i	−0.990614	−	0.136689i
$126$	0.136855	−	0.304334i	0.0121920	−	0.0271122i
$127$	13.4403	+	1.17587i	1.19263	+	0.104342i	0.666132	−	0.745834i	$-0.267949\pi$
$127$	13.4403	+	1.17587i	1.19263	+	0.104342i	0.526499	+	0.850176i	$0.323504\pi$
$128$	−7.92843	+	8.07094i	−0.700781	+	0.713377i
$129$	0.361807	−	0.994057i	0.0318553	−	0.0875218i
$130$	13.5809	−	8.87639i	1.19112	−	0.778511i
$131$	21.9564	+	3.87150i	1.91834	+	0.338255i	0.998534	−	0.0541221i	$-0.0172360\pi$
$131$	21.9564	+	3.87150i	1.91834	+	0.338255i	0.919804	+	0.392377i	$0.128347\pi$
$132$	−3.78866	−	7.57423i	−0.329760	−	0.659252i
$133$	0.0710835	−	0.542529i	0.00616372	−	0.0470433i
$134$	6.56428	−	4.73208i	0.567068	−	0.408789i
$135$	−3.49570	+	11.0073i	−0.300862	+	0.947360i
$136$	−1.53831	+	3.68857i	−0.131909	+	0.316292i
$137$	−0.954361	+	0.445026i	−0.0815366	+	0.0380211i	−0.462959	−	0.886380i	$-0.653212\pi$
$137$	−0.954361	+	0.445026i	−0.0815366	+	0.0380211i	0.381422	+	0.924401i	$0.375434\pi$
$138$	−6.37431	+	1.21449i	−0.542617	+	0.103384i
$139$	17.2447	−	14.4700i	1.46268	−	1.22733i	0.540055	−	0.841630i	$-0.318403\pi$
$139$	17.2447	−	14.4700i	1.46268	−	1.22733i	0.922623	−	0.385703i	$-0.126041\pi$
$140$	0.0387261	+	0.560044i	0.00327296	+	0.0473323i
$141$	−6.14069	+	10.6360i	−0.517140	+	0.895712i
$142$	0.135510	+	9.86250i	0.0113717	+	0.827643i
$143$	−16.8136	−	11.7730i	−1.40602	−	0.984508i
$144$	−2.95576	−	6.91337i	−0.246313	−	0.576114i
$145$	−4.87988	+	11.7124i	−0.405252	+	0.972658i
$146$	3.14069	−	12.4002i	0.259925	−	1.02625i
$147$	6.69986	+	3.12420i	0.552595	+	0.257679i
$148$	6.05388	−	0.697714i	0.497625	−	0.0573517i
$149$	5.72753	−	6.82580i	0.469217	−	0.559191i	−0.478589	−	0.878039i	$-0.658851\pi$
$149$	5.72753	−	6.82580i	0.469217	−	0.559191i	0.947806	+	0.318848i	$0.103296\pi$
$150$	−1.37030	−	7.35787i	−0.111884	−	0.600767i
$151$		−	2.73094i		−	0.222241i	−0.993807	−	0.111120i	$-0.964556\pi$
$151$		−	2.73094i		−	0.222241i	0.993807	−	0.111120i	$-0.0354439\pi$
$152$	−7.90784	−	9.45865i	−0.641410	−	0.767198i
$153$	−1.87803	−	1.87803i	−0.151830	−	0.151830i
$154$	0.639483	−	0.308962i	0.0515310	−	0.0248968i
$155$	0.654873	−	14.3180i	0.0526007	−	1.15005i
$156$	8.50866	+	6.75008i	0.681238	+	0.540439i
$157$	−0.894511	+	1.91829i	−0.0713898	+	0.153096i	−0.938764	−	0.344560i	$-0.888028\pi$
$157$	−0.894511	+	1.91829i	−0.0713898	+	0.153096i	0.867374	+	0.497656i	$0.165806\pi$
$158$	−4.56702	−	7.66514i	−0.363332	−	0.609806i
$159$	−5.48454	−	9.49950i	−0.434952	−	0.753359i
$160$	9.87412	+	7.90580i	0.780618	+	0.625009i
$161$	−0.0944938	−	0.535901i	−0.00744715	−	0.0422349i
$162$	0.243566	−	0.00334657i	0.0191364	−	0.000262932i
$163$	0.616279	+	2.29998i	0.0482707	+	0.180149i	0.985852	−	0.167617i	$-0.0536072\pi$
$163$	0.616279	+	2.29998i	0.0482707	+	0.180149i	−0.937582	+	0.347766i	$0.886941\pi$
$164$	3.74066	+	18.2645i	0.292097	+	1.42622i
$165$	−7.99623	+	5.07089i	−0.622506	+	0.394768i
$166$	0.870084	+	0.591593i	0.0675317	+	0.0459165i
$167$	5.67003	+	12.1594i	0.438760	+	0.940924i	0.994015	+	0.109244i	$0.0348430\pi$
$167$	5.67003	+	12.1594i	0.438760	+	0.940924i	−0.555255	+	0.831680i	$0.687379\pi$
$168$	−0.347542	+	0.142974i	−0.0268134	+	0.0110307i
$169$	13.1206	+	2.31352i	1.00928	+	0.177963i
$170$	4.27679	+	1.29381i	0.328015	+	0.0992308i
$171$	7.81260	−	2.46862i	0.597444	−	0.188780i
$172$	1.78770	−	0.894213i	0.136311	−	0.0681831i
$173$	−2.40110	+	1.68127i	−0.182552	+	0.127824i	−0.661281	−	0.750139i	$-0.729987\pi$
$173$	−2.40110	+	1.68127i	−0.182552	+	0.127824i	0.478728	+	0.877963i	$0.341098\pi$
$174$	−8.47089	−	0.623967i	−0.642176	−	0.0473028i
$175$	0.618554	−	0.106426i	0.0467583	−	0.00804503i
$176$	4.63894	−	15.3154i	0.349673	−	1.15444i
$177$	0.493642	−	5.64236i	0.0371044	−	0.424106i
$178$	−2.70734	−	7.13192i	−0.202924	−	0.534560i
$179$	−7.18193	+	12.4395i	−0.536803	+	0.929770i	0.462271	+	0.886739i	$0.347035\pi$
$179$	−7.18193	+	12.4395i	−0.536803	+	0.929770i	−0.999074	+	0.0430312i	$0.986299\pi$
$180$	−7.35537	+	4.06970i	−0.548237	+	0.303338i
$181$	1.93247	+	10.9596i	0.143639	+	0.814619i	0.968450	+	0.249210i	$0.0801708\pi$
$181$	1.93247	+	10.9596i	0.143639	+	0.814619i	−0.824810	+	0.565410i	$0.808718\pi$
$182$	−0.575813	+	0.705695i	−0.0426821	+	0.0523096i
$183$	−9.64637	−	2.58474i	−0.713080	−	0.191069i
$184$	−10.3251	−	6.61294i	−0.761176	−	0.487512i
$185$	−1.46086	−	6.65478i	−0.107405	−	0.489269i
$186$	9.23288	−	2.61041i	0.676988	−	0.191405i
$187$	−0.492672	−	5.63126i	−0.0360277	−	0.411799i
$188$	−22.2421	+	6.61983i	−1.62217	+	0.482801i
$189$		−	0.648343i		−	0.0471600i
$190$	−9.62632	+	9.86580i	−0.698366	+	0.715741i
$191$			15.5746i			1.12694i	0.826137	+	0.563469i	$0.190534\pi$
$191$			15.5746i			1.12694i	−0.826137	+	0.563469i	$0.809466\pi$
$192$	−2.93451	+	7.94286i	−0.211780	+	0.573227i
$193$	2.04527	+	23.3775i	0.147222	+	1.68275i	0.606987	+	0.794712i	$0.292378\pi$
$193$	2.04527	+	23.3775i	0.147222	+	1.68275i	−0.459765	+	0.888040i	$0.652066\pi$
$194$	2.67098	+	9.44712i	0.191765	+	0.678264i
$195$	6.54561	−	10.2277i	0.468741	−	0.732421i
$196$	5.13633	+	12.9899i	0.366881	+	0.927848i
$197$	−2.66468	−	0.713998i	−0.189850	−	0.0508702i	0.162641	−	0.986685i	$-0.447999\pi$
$197$	−2.66468	−	0.713998i	−0.189850	−	0.0508702i	−0.352491	+	0.935815i	$0.614665\pi$
$198$	8.23984	+	6.72332i	0.585580	+	0.477805i
$199$	2.03996	+	11.5692i	0.144609	+	0.820117i	0.967680	+	0.252179i	$0.0811473\pi$
$199$	2.03996	+	11.5692i	0.144609	+	0.820117i	−0.823072	+	0.567937i	$0.807742\pi$
$200$	7.67666	−	11.8772i	0.542822	−	0.839848i
$201$	3.02822	−	5.24504i	0.213594	−	0.369956i
$202$	0.548635	−	0.208266i	0.0386018	−	0.0146536i
$203$	0.0620807	−	0.709586i	0.00435721	−	0.0498031i
$204$	0.0821799	+	2.98999i	0.00575374	+	0.209341i
$205$	19.8925	−	6.22677i	1.38935	−	0.434896i
$206$	1.28811	−	17.4873i	0.0897472	−	1.21839i
$207$	6.67481	−	4.67375i	0.463931	−	0.324848i
$208$	2.90892	+	20.3152i	0.201697	+	1.40860i
$209$	16.1150	+	6.66338i	1.11470	+	0.460916i
$210$	0.198342	+	0.370397i	0.0136869	+	0.0255598i
$211$	12.9059	+	2.27565i	0.888476	+	0.156662i	0.599215	−	0.800588i	$-0.295479\pi$
$211$	12.9059	+	2.27565i	0.888476	+	0.156662i	0.289261	+	0.957250i	$0.406591\pi$
$212$	4.81238	−	20.1602i	0.330515	−	1.38461i
$213$	3.11984	+	6.69052i	0.213768	+	0.458427i
$214$	2.74129	−	4.03174i	0.187390	−	0.275604i
$215$	−1.19685	−	1.88730i	−0.0816245	−	0.128713i
$216$	−10.7467	−	9.89539i	−0.731219	−	0.673296i
$217$	0.208252	+	0.777207i	0.0141371	+	0.0527603i
$218$	0.375701	+	27.3438i	0.0254457	+	1.85196i
$219$	−1.66248	−	9.42839i	−0.112340	−	0.637112i
$220$	−17.5600	−	3.42743i	−1.18389	−	0.231078i
$221$	3.62469	+	6.27815i	0.243823	+	0.422314i
$222$	3.91819	−	2.33452i	0.262972	−	0.156683i
$223$	2.77615	−	5.95348i	0.185905	−	0.398675i	−0.791162	−	0.611607i	$-0.790524\pi$
$223$	2.77615	−	5.95348i	0.185905	−	0.398675i	0.977067	+	0.212932i	$0.0683013\pi$
$224$	−0.662648	−	0.255217i	−0.0442750	−	0.0170524i
$225$	5.35874	+	7.72100i	0.357249	+	0.514734i
$226$	−2.08373	−	4.31287i	−0.138608	−	0.286888i
$227$	−10.6486	−	10.6486i	−0.706775	−	0.706775i	0.259080	−	0.965856i	$-0.416581\pi$
$227$	−10.6486	−	10.6486i	−0.706775	−	0.706775i	−0.965856	+	0.259080i	$0.916581\pi$
$228$	−8.30124	−	4.02910i	−0.549763	−	0.266834i
$229$			7.06767i			0.467045i	0.972351	+	0.233523i	$0.0750253\pi$
$229$			7.06767i			0.467045i	−0.972351	+	0.233523i	$0.924975\pi$
$230$	−6.18760	+	12.2326i	−0.407998	+	0.806595i
$231$	0.341672	−	0.407189i	0.0224804	−	0.0267910i
$232$	−10.8143	−	11.8591i	−0.709994	−	0.778590i
$233$	−0.620243	−	0.289224i	−0.0406335	−	0.0189477i	0.402195	−	0.915554i	$-0.368247\pi$
$233$	−0.620243	−	0.289224i	−0.0406335	−	0.0189477i	−0.442829	+	0.896606i	$0.646025\pi$
$234$	−13.2210	−	3.34858i	−0.864287	−	0.218904i
$235$	9.87919	+	23.9910i	0.644447	+	1.56500i
$236$	8.00631	−	7.10193i	0.521166	−	0.462296i
$237$	−5.47028	−	3.83033i	−0.355333	−	0.248807i
$238$	−0.250813	+	0.00344614i	−0.0162578	+	0.000223380i
$239$	12.7502	−	22.0840i	0.824742	−	1.42850i	−0.0773736	−	0.997002i	$-0.524653\pi$
$239$	12.7502	−	22.0840i	0.824742	−	1.42850i	0.902116	−	0.431494i	$-0.142013\pi$
$240$	9.16677	+	2.36557i	0.591712	+	0.152697i
$241$	−9.38708	+	7.87670i	−0.604675	+	0.507383i	−0.892945	−	0.450167i	$-0.851365\pi$
$241$	−9.38708	+	7.87670i	−0.604675	+	0.507383i	0.288269	+	0.957549i	$0.406920\pi$
$242$	1.32476	+	6.95309i	0.0851589	+	0.446962i
$243$	14.2082	−	6.62540i	0.911457	−	0.425019i
$244$	−9.88059	−	16.0768i	−0.632540	−	1.02921i
$245$	13.8676	−	7.18251i	0.885967	−	0.458874i
$246$	8.15975	+	11.3191i	0.520247	+	0.721680i
$247$	−22.3419	+	0.989334i	−1.42158	+	0.0629498i
$248$	16.0611	+	8.41029i	1.01988	+	0.534054i
$249$	0.775509	+	0.136743i	0.0491459	+	0.00866575i
$250$	−14.0794	−	7.19520i	−0.890458	−	0.455065i
$251$	−0.0918476	+	0.252349i	−0.00579737	+	0.0159281i	−0.942558	−	0.334044i	$-0.891587\pi$
$251$	−0.0918476	+	0.252349i	−0.00579737	+	0.0159281i	0.936760	+	0.349972i	$0.113809\pi$
$252$	0.324395	−	0.342731i	0.0204350	−	0.0215900i
$253$	17.2768	+	1.51152i	1.08618	+	0.0950286i
$254$	17.4015	+	7.82522i	1.09187	+	0.490998i
$255$	3.31646	−	0.429629i	0.207685	−	0.0269044i
$256$	−14.3441	+	7.08851i	−0.896506	+	0.443032i
$257$	−16.4631	−	11.5276i	−1.02694	−	0.719072i	−0.0665660	−	0.997782i	$-0.521204\pi$
$257$	−16.4631	−	11.5276i	−1.02694	−	0.719072i	−0.960375	+	0.278710i	$0.910093\pi$
$258$	0.945794	−	1.15913i	0.0588826	−	0.0721642i
$259$	0.191241	+	0.331239i	0.0118831	+	0.0205822i
$260$	22.2675	−	5.53358i	1.38097	−	0.343178i
$261$	10.0228	−	3.64799i	0.620394	−	0.225805i
$262$	27.5198	+	15.3884i	1.70018	+	0.950698i
$263$	−19.2920	+	1.68783i	−1.18960	+	0.104076i	−0.664714	−	0.747098i	$-0.731446\pi$
$263$	−19.2920	+	1.68783i	−1.18960	+	0.104076i	−0.524883	+	0.851175i	$0.675891\pi$
$264$	−1.53460	−	11.8782i	−0.0944483	−	0.731051i
$265$	−22.9685	−	3.07231i	−1.41095	−	0.188731i
$266$	0.347414	−	0.691437i	0.0213013	−	0.0423948i
$267$	−4.03720	−	4.03720i	−0.247072	−	0.247072i
$268$	10.9685	−	3.26451i	0.670007	−	0.199412i
$269$	12.9359	−	15.4164i	0.788715	−	0.939954i	−0.210577	−	0.977577i	$-0.567534\pi$
$269$	12.9359	−	15.4164i	0.788715	−	0.939954i	0.999292	+	0.0376230i	$0.0119786\pi$
$270$	−9.79097	+	13.0728i	−0.595860	+	0.795588i
$271$	−2.09504	−	5.75607i	−0.127264	−	0.349656i	0.859654	−	0.510877i	$-0.170679\pi$
$271$	−2.09504	−	5.75607i	−0.127264	−	0.349656i	−0.986918	+	0.161221i	$0.948457\pi$
$272$	−3.77093	+	4.20997i	−0.228646	+	0.255267i
$273$	−0.176432	+	0.658454i	−0.0106782	+	0.0398514i
$274$	−1.48161	+	0.150161i	−0.0895071	+	0.00907158i
$275$	−1.82598	+	19.9196i	−0.110111	+	1.20120i
$276$	−9.07775	−	1.34463i	−0.546416	−	0.0809375i
$277$	−0.227982	−	0.850839i	−0.0136981	−	0.0511219i	0.958739	−	0.284289i	$-0.0917576\pi$
$277$	−0.227982	−	0.850839i	−0.0136981	−	0.0511219i	−0.972437	+	0.233167i	$0.925091\pi$
$278$	29.7635	−	11.2985i	1.78510	−	0.677639i
$279$	−9.22972	+	7.74466i	−0.552569	+	0.463660i
$280$	−0.208920	+	0.765930i	−0.0124854	+	0.0457731i
$281$	−9.61078	−	3.49804i	−0.573331	−	0.208676i	0.0390511	−	0.999237i	$-0.487566\pi$
$281$	−9.61078	−	3.49804i	−0.573331	−	0.208676i	−0.612382	+	0.790562i	$0.709789\pi$
$282$	−13.1504	+	11.3460i	−0.783095	+	0.675644i
$283$	11.3973	+	16.2771i	0.677500	+	0.967571i	0.999781	+	0.0209264i	$0.00666158\pi$
$283$	11.3973	+	16.2771i	0.677500	+	0.967571i	−0.322281	+	0.946644i	$0.604450\pi$
$284$	−4.40891	+	13.2339i	−0.261621	+	0.785288i
$285$	−3.54254	+	9.68921i	−0.209842	+	0.573939i
$286$	−16.9746	−	23.5470i	−1.00373	−	1.39236i
$287$	−0.958536	+	0.671174i	−0.0565806	+	0.0396182i
$288$	−0.729866	−	10.6080i	−0.0430078	−	0.625083i
$289$	5.13150	−	14.0987i	0.301853	−	0.829335i
$290$	−11.9676	+	13.3702i	−0.702761	+	0.785125i
$291$	4.72304	+	5.62870i	0.276870	+	0.329960i
$292$	9.96511	−	15.0982i	0.583164	−	0.883554i
$293$	2.62475	−	0.703300i	0.153340	−	0.0410872i	−0.181333	−	0.983422i	$-0.558041\pi$
$293$	2.62475	−	0.703300i	0.153340	−	0.0410872i	0.334672	+	0.942335i	$0.391374\pi$
$294$	7.49334	+	7.29022i	0.437021	+	0.425174i
$295$	−8.80511	−	8.10204i	−0.512653	−	0.471719i
$296$	8.40933	+	1.88563i	0.488782	+	0.109600i
$297$	19.9588	+	5.34794i	1.15813	+	0.310319i
$298$	10.8254	−	6.44997i	0.627101	−	0.373637i
$299$	−20.8999	+	7.60694i	−1.20867	+	0.439921i
$300$	1.59429	−	10.4638i	0.0920464	−	0.604125i
$301$	0.0961061	+	0.0806426i	0.00553946	+	0.00464816i
$302$	1.27094	−	3.64702i	0.0731345	−	0.209863i
$303$	0.310568	−	0.310568i	0.0178417	−	0.0178417i
$304$	−6.15856	−	16.3117i	−0.353218	−	0.935541i
$305$	−16.7645	+	12.8087i	−0.959932	+	0.733425i
$306$	−1.63400	−	3.38202i	−0.0934094	−	0.193337i
$307$	−1.60850	−	18.3853i	−0.0918021	−	1.04930i	−0.892745	−	0.450562i	$-0.851223\pi$
$307$	−1.60850	−	18.3853i	−0.0918021	−	1.04930i	0.800943	−	0.598741i	$-0.204332\pi$
$308$	0.997782	−	0.114995i	0.0568539	−	0.00655245i
$309$	−4.48853	−	12.3321i	−0.255344	−	0.701551i
$310$	7.53794	−	18.8161i	0.428126	−	1.06868i
$311$	−11.1341	+	6.42826i	−0.631355	+	0.364513i	−0.781277	−	0.624185i	$-0.785431\pi$
$311$	−11.1341	+	6.42826i	−0.631355	+	0.364513i	0.149922	+	0.988698i	$0.452098\pi$
$312$	8.22146	+	12.9742i	0.465448	+	0.734518i
$313$	18.0225	−	25.7388i	1.01869	−	1.45484i	0.132695	−	0.991157i	$-0.457637\pi$
$313$	18.0225	−	25.7388i	1.01869	−	1.45484i	0.885999	−	0.463688i	$-0.153474\pi$
$314$	−2.08732	+	2.14547i	−0.117794	+	0.121076i
$315$	−0.417913	−	0.322055i	−0.0235467	−	0.0181457i
$316$	−2.53175	−	12.3618i	−0.142422	−	0.695406i
$317$	1.26794	−	14.4926i	0.0712147	−	0.813988i	−0.873656	−	0.486544i	$-0.838257\pi$
$317$	1.26794	−	14.4926i	0.0712147	−	0.813988i	0.944871	−	0.327444i	$-0.106187\pi$
$318$	−2.90337	−	15.2385i	−0.162813	−	0.854532i
$319$	21.3320	+	7.76422i	1.19436	+	0.434713i
$320$	9.50710	+	15.1531i	0.531463	+	0.847081i
$321$	0.633632	−	3.59350i	0.0353659	−	0.200570i
$322$	0.123210	−	0.759642i	0.00686620	−	0.0423332i
$323$	−4.16377	−	4.53831i	−0.231678	−	0.252518i
$324$	0.326827	+	0.108883i	0.0181571	+	0.00604907i
$325$	−8.67383	−	24.1421i	−0.481138	−	1.33916i
$326$	−0.247374	+	3.35831i	−0.0137008	+	0.186000i
$327$	8.64977	+	18.5495i	0.478333	+	1.02579i
$328$	−3.50462	+	26.1322i	−0.193510	+	1.44291i
$329$	−0.936239	−	1.11577i	−0.0516165	−	0.0615142i
$330$	−13.0385	+	3.05056i	−0.717743	+	0.167928i
$331$	7.01809	+	4.05190i	0.385749	+	0.222712i	0.680317	−	0.732918i	$-0.261842\pi$
$331$	7.01809	+	4.05190i	0.385749	+	0.222712i	−0.294568	+	0.955631i	$0.595176\pi$
$332$	0.886631	+	1.19497i	0.0486602	+	0.0655823i
$333$	−3.28507	+	4.69156i	−0.180021	+	0.257096i
$334$	1.91319	+	18.8770i	0.104685	+	1.03290i
$335$	−4.87183	−	11.8309i	−0.266177	−	0.646393i
$336$	−0.530661	+	0.0291925i	−0.0289499	+	0.00159258i
$337$	−0.714775	+	1.53284i	−0.0389363	+	0.0834992i	−0.924814	−	0.380420i	$-0.875779\pi$
$337$	−0.714775	+	1.53284i	−0.0389363	+	0.0834992i	0.885878	+	0.463919i	$0.153557\pi$
$338$	16.4452	+	9.19574i	0.894501	+	0.500182i
$339$	−2.74620	−	2.30434i	−0.149153	−	0.125154i
$340$	5.10930	+	3.71817i	0.277091	+	0.201646i
$341$	−25.6436			−1.38868
$342$	11.5822	+	0.339162i	0.626292	+	0.0183398i
$343$	−1.24127	+	1.24127i	−0.0670223	+	0.0670223i
$344$	2.80353	−	0.362202i	0.151156	−	0.0195286i
$345$	−0.468779	+	10.2493i	−0.0252382	+	0.551801i
$346$	−3.98897	+	1.12780i	−0.214449	+	0.0606310i
$347$	−3.58058	−	1.66965i	−0.192216	−	0.0896317i	0.324127	−	0.946013i	$-0.394929\pi$
$347$	−3.58058	−	1.66965i	−0.192216	−	0.0896317i	−0.516343	+	0.856382i	$0.672707\pi$
$348$	−11.0220	−	4.77551i	−0.590842	−	0.255994i
$349$	−11.4691	+	6.62170i	−0.613928	+	0.354451i	−0.774501	−	0.632573i	$-0.781999\pi$
$349$	−11.4691	+	6.62170i	−0.613928	+	0.354451i	0.160573	+	0.987024i	$0.448666\pi$
$350$	0.875575	+	0.145741i	0.0468014	+	0.00779017i
$351$	−26.0965	+	4.60151i	−1.39293	+	0.245610i
$352$	13.3226	−	18.2940i	0.710098	−	0.975071i
$353$	−32.0310	+	8.58269i	−1.70484	+	0.456811i	−0.974151	−	0.225899i	$-0.927468\pi$
$353$	−32.0310	+	8.58269i	−1.70484	+	0.456811i	−0.730690	+	0.682709i	$0.760801\pi$
$354$	3.28511	−	7.30533i	0.174602	−	0.388274i
$355$	15.2188	+	3.40703i	0.807728	+	0.180826i
$356$	−0.296405	−	10.7843i	−0.0157094	−	0.571564i
$357$	−0.170146	+	0.0793405i	−0.00900510	+	0.00419915i
$358$	−15.3802	+	13.2699i	−0.812871	+	0.701334i
$359$	0.836764	−	4.74552i	0.0441627	−	0.250459i	−0.954732	−	0.297468i	$-0.903858\pi$
$359$	0.836764	−	4.74552i	0.0441627	−	0.250459i	0.998894	+	0.0470089i	$0.0149689\pi$
$360$	−11.7167	+	2.01178i	−0.617524	+	0.106030i
$361$	18.3465	−	4.94030i	0.965604	−	0.260016i
$362$	−2.51973	+	15.5353i	−0.132434	+	0.816516i
$363$	3.03856	+	4.33952i	0.159483	+	0.227766i
$364$	−1.09739	+	0.674441i	−0.0575188	+	0.0353503i
$365$	−17.9209	−	9.37629i	−0.938022	−	0.490777i
$366$	−11.6793	−	7.94107i	−0.610487	−	0.415086i
$367$	−9.29845	−	0.813509i	−0.485375	−	0.0424648i	−0.158158	−	0.987414i	$-0.550555\pi$
$367$	−9.29845	−	0.813509i	−0.485375	−	0.0424648i	−0.327217	+	0.944949i	$0.606111\pi$
$368$	−10.7110	−	13.6364i	−0.558351	−	0.710845i
$369$	−15.1746	−	8.76104i	−0.789956	−	0.456081i
$370$	1.14614	−	9.56697i	0.0595849	−	0.497363i
$371$	1.28113	−	0.225898i	0.0665130	−	0.0117280i
$372$	13.5449	+	0.810792i	0.702269	+	0.0420376i
$373$	−4.19763	+	15.6658i	−0.217345	+	0.811142i	0.767983	+	0.640470i	$0.221261\pi$
$373$	−4.19763	+	15.6658i	−0.217345	+	0.811142i	−0.985328	+	0.170672i	$0.945406\pi$
$374$	1.96278	−	7.74953i	0.101493	−	0.400719i
$375$	−11.8191	−	0.589690i	−0.610338	−	0.0304515i
$376$	−32.7839	−	1.51075i	−1.69070	−	0.0779108i
$377$	−29.0021	+	2.53736i	−1.49369	+	0.130681i
$378$	0.301730	−	0.865827i	0.0155193	−	0.0445333i
$379$	6.09529			0.313094			0.156547	−	0.987671i	$-0.449964\pi$
$379$	6.09529			0.313094			0.156547	+	0.987671i	$0.449964\pi$
$380$	−17.4468	+	8.69529i	−0.895004	+	0.446059i
$381$	14.2802			0.731597
$382$	−7.24821	+	20.7990i	−0.370850	+	1.06417i
$383$	−19.3301	+	1.69117i	−0.987723	+	0.0864146i	−0.569553	−	0.821954i	$-0.692884\pi$
$383$	−19.3301	+	1.69117i	−0.987723	+	0.0864146i	−0.418170	+	0.908369i	$0.637328\pi$
$384$	−7.61538	+	9.24158i	−0.388621	+	0.471608i
$385$	−0.240775	−	1.09682i	−0.0122710	−	0.0558992i
$386$	−8.14824	+	32.1713i	−0.414735	+	1.63748i
$387$	−0.486222	+	1.81461i	−0.0247161	+	0.0922416i
$388$	−0.829606	+	13.8592i	−0.0421168	+	0.703592i
$389$	16.5952	−	2.92619i	0.841411	−	0.148364i	0.263700	−	0.964605i	$-0.415057\pi$
$389$	16.5952	−	2.92619i	0.841411	−	0.148364i	0.577711	+	0.816241i	$0.303946\pi$
$390$	13.5011	−	10.6123i	0.683657	−	0.537375i
$391$	−5.30462	−	3.06262i	−0.268266	−	0.154884i
$392$	0.813989	+	19.7376i	0.0411126	+	0.996902i
$393$	23.5085	+	2.05673i	1.18585	+	0.103748i
$394$	−3.22625	−	2.19361i	−0.162536	−	0.110512i
$395$	−13.4636	+	4.21440i	−0.677428	+	0.212050i
$396$	7.87492	+	12.8133i	0.395730	+	0.643894i
$397$	−2.64249	−	3.77387i	−0.132623	−	0.189405i	0.747348	−	0.664433i	$-0.231327\pi$
$397$	−2.64249	−	3.77387i	−0.132623	−	0.189405i	−0.879971	+	0.475028i	$0.842438\pi$
$398$	−2.65988	+	16.3994i	−0.133328	+	0.822026i
$399$	0.0249037	−	0.578613i	0.00124674	−	0.0289669i
$400$	15.7793	−	12.2888i	0.788964	−	0.614440i
$401$	−2.45764	+	13.9380i	−0.122729	+	0.696029i	0.859902	+	0.510459i	$0.170524\pi$
$401$	−2.45764	+	13.9380i	−0.122729	+	0.696029i	−0.982631	+	0.185570i	$0.940587\pi$
$402$	6.48500	−	5.59517i	0.323442	−	0.279062i
$403$	29.8053	−	13.8985i	1.48471	−	0.692332i
$404$	0.829596	−	0.0228014i	0.0412740	−	0.00113441i
$405$	0.0841406	−	0.375845i	0.00418098	−	0.0186759i
$406$	0.413137	−	0.918722i	0.0205036	−	0.0455954i
$407$	−11.7745	+	3.15496i	−0.583638	+	0.156385i
$408$	−1.28176	+	4.03122i	−0.0634563	+	0.199575i
$409$	−25.9298	+	4.57212i	−1.28215	+	0.226077i	−0.772891	−	0.634539i	$-0.781190\pi$
$409$	−25.9298	+	4.57212i	−1.28215	+	0.226077i	−0.509255	+	0.860616i	$0.670079\pi$
$410$	29.4632	+	0.942168i	1.45508	+	0.0465304i
$411$	−0.965247	+	0.557286i	−0.0476121	+	0.0274889i
$412$	9.85853	−	22.7538i	0.485695	−	1.12100i
$413$	0.608785	+	0.283881i	0.0299563	+	0.0139689i
$414$	11.0889	−	3.13518i	0.544992	−	0.154086i
$415$	1.22886	−	1.12137i	0.0603225	−	0.0550458i
$416$	−5.56971	+	28.4836i	−0.273077	+	1.39652i
$417$	16.8484	−	16.8484i	0.825069	−	0.825069i
$418$	18.4197	+	16.3983i	0.900938	+	0.802067i
$419$	−30.4640			−1.48827			−0.744133	−	0.668032i	$-0.767137\pi$
$419$	−30.4640			−1.48827			−0.744133	+	0.668032i	$0.767137\pi$
$420$	0.0924978	+	0.586951i	0.00451343	+	0.0286403i
$421$	−22.5625	−	18.9322i	−1.09963	−	0.922697i	−0.102228	−	0.994761i	$-0.532597\pi$
$421$	−22.5625	−	18.9322i	−1.09963	−	0.922697i	−0.997400	+	0.0720639i	$0.977041\pi$
$422$	16.1760	+	9.04522i	0.787436	+	0.440314i
$423$	9.21741	−	19.7668i	0.448166	−	0.961095i
$424$	15.8090	−	24.6833i	0.767751	−	1.19873i
$425$	3.55776	−	6.10365i	0.172577	−	0.296070i
$426$	1.05270	+	10.3868i	0.0510036	+	0.503240i
$427$	0.679334	−	0.970189i	0.0328753	−	0.0469508i
$428$	5.53716	−	4.10841i	0.267649	−	0.198588i
$429$	−18.8147	−	10.8627i	−0.908383	−	0.524455i
$430$	−0.720005	−	3.07738i	−0.0347217	−	0.148405i
$431$	−16.6652	−	19.8609i	−0.802736	−	0.956664i	0.196982	−	0.980407i	$-0.436886\pi$
$431$	−16.6652	−	19.8609i	−0.802736	−	0.956664i	−0.999718	+	0.0237432i	$0.992442\pi$
$432$	−9.74643	−	18.2161i	−0.468925	−	0.876423i
$433$	3.93236	+	8.43298i	0.188977	+	0.405263i	0.977854	−	0.209288i	$-0.0671148\pi$
$433$	3.93236	+	8.43298i	0.188977	+	0.405263i	−0.788877	+	0.614552i	$0.789337\pi$
$434$	−0.0835923	+	1.13484i	−0.00401256	+	0.0544739i
$435$	−4.06500	+	12.8000i	−0.194902	+	0.613711i
$436$	−12.2237	+	36.6910i	−0.585410	+	1.75718i
$437$	15.9303	−	10.1626i	0.762051	−	0.486144i
$438$	2.16769	−	13.3648i	0.103576	−	0.638595i
$439$	−7.09078	+	40.2138i	−0.338425	+	1.91930i	0.0519603	+	0.998649i	$0.483453\pi$
$439$	−7.09078	+	40.2138i	−0.338425	+	1.91930i	−0.390385	+	0.920652i	$0.627658\pi$
$440$	−21.8553	−	12.7493i	−1.04191	−	0.607800i
$441$	−12.3364	−	4.49009i	−0.587449	−	0.213814i
$442$	1.91882	+	10.0710i	0.0912687	+	0.479029i
$443$	0.644898	−	7.37122i	0.0306400	−	0.350217i	−0.965364	−	0.260907i	$-0.915978\pi$
$443$	0.644898	−	7.37122i	0.0306400	−	0.350217i	0.996004	−	0.0893099i	$-0.0284661\pi$
$444$	6.31898	−	1.29416i	0.299886	−	0.0614179i
$445$	−11.9618	+	1.54958i	−0.567042	+	0.0734571i
$446$	6.47807	−	6.65857i	0.306746	−	0.315292i
$447$	5.40956	−	7.72565i	0.255863	−	0.365411i
$448$	−0.766156	−	0.649216i	−0.0361974	−	0.0306726i
$449$	−6.89259	+	3.97944i	−0.325281	+	0.187801i	−0.653744	−	0.756716i	$-0.726803\pi$
$449$	−6.89259	+	3.97944i	−0.325281	+	0.187801i	0.328463	+	0.944517i	$0.393469\pi$
$450$	3.56306	+	12.8049i	0.167964	+	0.603627i
$451$	−12.7550	−	35.0441i	−0.600610	−	1.65016i
$452$	−0.775561	−	6.72934i	−0.0364793	−	0.316521i
$453$	−0.251929	−	2.87957i	−0.0118367	−	0.135294i
$454$	−9.26495	−	19.1764i	−0.434826	−	0.899994i
$455$	0.874313	+	1.14433i	0.0409884	+	0.0536470i
$456$	−9.21077	−	9.24393i	−0.431334	−	0.432887i
$457$	10.4179	−	10.4179i	0.487327	−	0.487327i	−0.420135	−	0.907462i	$-0.638017\pi$
$457$	10.4179	−	10.4179i	0.487327	−	0.487327i	0.907462	+	0.420135i	$0.138017\pi$
$458$	−3.28920	+	9.43850i	−0.153694	+	0.441032i
$459$	−5.59049	−	4.69098i	−0.260942	−	0.218956i
$460$	−13.9561	+	13.4564i	−0.650706	+	0.627406i
$461$	−0.861804	+	0.313671i	−0.0401382	+	0.0146091i	−0.362011	−	0.932174i	$-0.617910\pi$
$461$	−0.861804	+	0.313671i	−0.0401382	+	0.0146091i	0.321873	+	0.946783i	$0.395688\pi$
$462$	0.645784	−	0.384769i	0.0300446	−	0.0179011i
$463$	−37.6306	−	10.0831i	−1.74884	−	0.468601i	−0.764464	−	0.644667i	$-0.776996\pi$
$463$	−37.6306	−	10.0831i	−1.74884	−	0.468601i	−0.984378	+	0.176066i	$0.943663\pi$
$464$	−8.92283	−	20.8701i	−0.414232	−	0.968868i
$465$	−0.630321	−	15.1576i	−0.0292305	−	0.702918i
$466$	−0.693700	−	0.674896i	−0.0321350	−	0.0312640i
$467$	12.1831	−	3.26444i	0.563765	−	0.151060i	0.0343296	−	0.999411i	$-0.489070\pi$
$467$	12.1831	−	3.26444i	0.563765	−	0.151060i	0.529436	+	0.848350i	$0.322404\pi$
$468$	−16.0976	−	10.6247i	−0.744112	−	0.491129i
$469$	0.461697	+	0.550229i	0.0213192	+	0.0254072i
$470$	2.02804	+	36.6363i	0.0935465	+	1.68991i
$471$	−0.766232	+	2.10520i	−0.0353061	+	0.0970027i
$472$	13.9971	−	5.75822i	0.644270	−	0.265043i
$473$	−3.27527	+	2.29337i	−0.150597	+	0.105449i
$474$	−5.52268	−	7.66100i	−0.253665	−	0.351881i
$475$	11.6453	+	18.4225i	0.534322	+	0.845281i
$476$	−0.336551	−	0.112123i	−0.0154258	−	0.00513914i
$477$	11.1731	+	15.9569i	0.511582	+	0.730615i
$478$	27.3048	−	23.5582i	1.24889	−	1.07753i
$479$	−3.95633	−	1.43999i	−0.180769	−	0.0657947i	0.250050	−	0.968233i	$-0.419553\pi$
$479$	−3.95633	−	1.43999i	−0.180769	−	0.0657947i	−0.430819	+	0.902438i	$0.641775\pi$
$480$	11.1408	+	7.42518i	0.508506	+	0.338911i
$481$	11.9754	−	10.0486i	0.546032	−	0.458175i
$482$	−16.2016	+	6.15028i	−0.737965	+	0.280138i
$483$	−0.149073	−	0.556349i	−0.00678307	−	0.0253148i
$484$	−1.46673	+	9.90201i	−0.0666694	+	0.450091i
$485$	15.5093	−	0.644947i	0.704243	−	0.0292855i
$486$	22.0577	−	2.23555i	1.00056	−	0.101407i
$487$	−8.02871	+	29.9636i	−0.363816	+	1.35778i	0.505204	+	0.863000i	$0.331417\pi$
$487$	−8.02871	+	29.9636i	−0.363816	+	1.35778i	−0.869019	+	0.494778i	$0.835249\pi$
$488$	−5.71308	−	26.0680i	−0.258619	−	1.18004i
$489$	0.861993	+	2.36831i	0.0389807	+	0.107098i
$490$	21.8620	−	3.13807i	0.987626	−	0.141764i
$491$	11.5891	−	13.8113i	0.523008	−	0.623297i	−0.438281	−	0.898838i	$-0.644413\pi$
$491$	11.5891	−	13.8113i	0.523008	−	0.623297i	0.961289	+	0.275541i	$0.0888570\pi$
$492$	5.62915	+	18.9135i	0.253782	+	0.852686i
$493$	−5.66939	−	5.66939i	−0.255336	−	0.255336i
$494$	−30.2968	−	9.07639i	−1.36312	−	0.408366i
$495$	13.3614	−	10.2087i	0.600552	−	0.458845i
$496$	17.5348	+	18.7061i	0.787334	+	0.839930i
$497$	−0.872168	+	0.0763048i	−0.0391221	+	0.00342274i
$498$	0.972012	+	0.543524i	0.0435569	+	0.0243559i
$499$	15.8733	−	5.77743i	0.710589	−	0.258633i	0.0386637	−	0.999252i	$-0.487690\pi$
$499$	15.8733	−	5.77743i	0.710589	−	0.258633i	0.671925	+	0.740619i	$0.265468\pi$
$500$	−15.4537	−	16.1612i	−0.691111	−	0.722749i
$501$	7.10032	+	12.2981i	0.317219	+	0.549439i
$502$	−0.240097	+	0.294254i	−0.0107161	+	0.0131332i
$503$	36.2857	+	25.4075i	1.61790	+	1.13287i	0.899194	+	0.437551i	$0.144154\pi$
$503$	36.2857	+	25.4075i	1.61790	+	1.13287i	0.718705	+	0.695315i	$0.244735\pi$
$504$	0.592714	−	0.306730i	0.0264016	−	0.0136628i
$505$	−0.119204	−	0.920178i	−0.00530450	−	0.0409474i
$506$	22.3688	+	10.0589i	0.994412	+	0.447174i
$507$	14.0481	+	1.22905i	0.623898	+	0.0545840i
$508$	19.5970	+	18.5486i	0.869477	+	0.822960i
$509$	1.99162	−	5.47194i	0.0882772	−	0.242540i	−0.887696	−	0.460430i	$-0.847695\pi$
$509$	1.99162	−	5.47194i	0.0882772	−	0.242540i	0.975973	+	0.217890i	$0.0699175\pi$
$510$	4.62890	+	0.969690i	0.204971	+	0.0429386i
$511$	1.11817	+	0.197164i	0.0494651	+	0.00872204i
$512$	−22.4547	+	2.79078i	−0.992365	+	0.123336i
$513$	20.7942	−	8.62835i	0.918088	−	0.380951i
$514$	−16.6208	−	23.0562i	−0.733113	−	1.01697i
$515$	−26.4242	−	8.39176i	−1.16439	−	0.369785i
$516$	1.80250	−	1.10779i	0.0793506	−	0.0487679i
$517$	42.0708	−	19.6179i	1.85027	−	0.862795i
$518$	0.101238	+	0.531353i	0.00444814	+	0.0233463i
$519$	−2.37668	+	1.99427i	−0.104325	+	0.0875387i
$520$	32.3122	+	2.97317i	1.41699	+	0.130382i
$521$	−3.60945	+	6.25176i	−0.158133	+	0.273894i	−0.934195	−	0.356762i	$-0.883881\pi$
$521$	−3.60945	+	6.25176i	−0.158133	+	0.273894i	0.776062	+	0.630656i	$0.217214\pi$
$522$	15.0826	−	0.207233i	0.660147	−	0.00907035i
$523$	−17.2017	−	12.0447i	−0.752176	−	0.526679i	0.133463	−	0.991054i	$-0.457390\pi$
$523$	−17.2017	−	12.0447i	−0.752176	−	0.526679i	−0.885639	+	0.464375i	$0.846279\pi$
$524$	29.5897	+	33.3577i	1.29263	+	1.45724i
$525$	0.642400	−	0.169280i	0.0280366	−	0.00738796i
$526$	−26.5489	−	6.72423i	−1.15759	−	0.293190i
$527$	8.20842	+	3.82765i	0.357564	+	0.166735i
$528$	3.47856	−	16.5768i	0.151385	−	0.721414i
$529$	−2.70464	+	3.22327i	−0.117593	+	0.140142i
$530$	−29.2434	−	14.7921i	−1.27025	−	0.642530i
$531$			10.0584i			0.436498i
$532$	0.785738	−	0.761696i	0.0340661	−	0.0330237i
$533$	33.8185	+	33.8185i	1.46484	+	1.46484i
$534$	−3.51260	−	7.27031i	−0.152005	−	0.314617i
$535$	−5.19613	−	5.69423i	−0.224648	−	0.246183i
$536$	16.1671	+	0.745011i	0.698311	+	0.0321796i
$537$	−6.42526	+	13.7790i	−0.277270	+	0.594608i
$538$	24.4498	−	14.5676i	1.05410	−	0.628053i
$539$	−13.9707	−	24.1979i	−0.601760	−	1.04228i
$540$	−19.1592	+	12.9015i	−0.824482	+	0.555192i
$541$	2.44679	+	13.8764i	0.105196	+	0.596594i	0.991142	+	0.132806i	$0.0423988\pi$
$541$	2.44679	+	13.8764i	0.105196	+	0.596594i	−0.885946	+	0.463788i	$0.846490\pi$
$542$	−0.119014	−	8.66192i	−0.00511208	−	0.372061i
$543$	3.04866	+	11.3778i	0.130831	+	0.488267i
$544$	−6.99514	+	3.86725i	−0.299914	+	0.165807i
$545$	42.1941	+	9.44599i	1.80739	+	0.404622i
$546$	−0.542051	+	0.797220i	−0.0231976	+	0.0341179i
$547$	−4.91550	−	10.5413i	−0.210172	−	0.450715i	0.772757	−	0.634702i	$-0.218877\pi$
$547$	−4.91550	−	10.5413i	−0.210172	−	0.450715i	−0.982929	+	0.183987i	$0.941099\pi$
$548$	−2.04849	−	0.488987i	−0.0875071	−	0.0208885i
$549$	17.4657	+	3.07967i	0.745416	+	0.131437i
$550$	−11.7088	+	25.7518i	−0.499266	+	1.09806i
$551$	23.5846	−	7.45228i	1.00474	−	0.317478i
$552$	−11.4971	−	6.02035i	−0.489348	−	0.256243i
$553$	0.648756	−	0.454264i	0.0275879	−	0.0193173i
$554$	0.0915117	−	1.24235i	0.00388796	−	0.0527823i
$555$	−2.15427	−	6.88219i	−0.0914439	−	0.292133i
$556$	45.0058	−	1.23698i	1.90867	−	0.0524597i
$557$	−1.54186	+	17.6236i	−0.0653308	+	0.746735i	0.890915	+	0.454170i	$0.150064\pi$
$557$	−1.54186	+	17.6236i	−0.0653308	+	0.746735i	−0.956246	+	0.292564i	$0.905491\pi$
$558$	−15.9301	+	6.04718i	−0.674373	+	0.255998i
$559$	2.56385	−	4.44072i	0.108439	−	0.187822i
$560$	−0.635455	+	0.925630i	−0.0268529	+	0.0391150i
$561$	−1.03897	−	5.89229i	−0.0438653	−	0.248773i
$562$	−11.2067	−	9.14417i	−0.472728	−	0.385724i
$563$	33.5834	+	8.99865i	1.41537	+	0.379248i	0.883840	−	0.467790i	$-0.154950\pi$
$563$	33.5834	+	8.99865i	1.41537	+	0.379248i	0.531533	+	0.847038i	$0.321616\pi$
$564$	−22.8419	+	9.03194i	−0.961819	+	0.380313i
$565$	−7.39729	+	1.62386i	−0.311206	+	0.0683164i
$566$	7.64538	+	27.0413i	0.321359	+	1.13663i
$567$	0.00188444	+	0.0215392i	7.91389e−5	+	0.000904562i
$568$	−12.0467	+	15.6213i	−0.505470	+	0.655456i
$569$		−	19.2413i		−	0.806638i	−0.915059	−	0.403319i	$-0.867856\pi$
$569$		−	19.2413i		−	0.806638i	0.915059	−	0.403319i	$-0.132144\pi$
$570$	−9.24009	+	11.2908i	−0.387025	+	0.472918i
$571$			7.21289i			0.301850i	0.988545	+	0.150925i	$0.0482252\pi$
$571$			7.21289i			0.301850i	−0.988545	+	0.150925i	$0.951775\pi$
$572$	−11.7103	−	39.3455i	−0.489631	−	1.64512i
$573$	1.43676	+	16.4222i	0.0600214	+	0.686048i
$574$	−1.59243	+	0.450227i	−0.0664667	+	0.0187921i
$575$	16.5462	+	14.0012i	0.690022	+	0.583889i
$576$	3.96212	−	14.5061i	0.165088	−	0.604420i
$577$	−21.1088	−	5.65610i	−0.878773	−	0.235466i	−0.208895	−	0.977938i	$-0.566987\pi$
$577$	−21.1088	−	5.65610i	−0.878773	−	0.235466i	−0.669877	+	0.742472i	$0.733653\pi$
$578$	13.4142	−	16.4399i	0.557956	−	0.683810i
$579$	4.31316	+	24.4612i	0.179249	+	1.01657i
$580$	−22.2044	+	12.2856i	−0.921986	+	0.510132i
$581$	−0.0466957	+	0.0808794i	−0.00193727	+	0.00335544i
$582$	3.68785	+	9.71487i	0.152866	+	0.402694i
$583$	−3.61346	+	41.3021i	−0.149654	+	1.71056i
$584$	20.3343	−	15.5252i	0.841441	−	0.642436i
$585$	−9.99695	+	19.1072i	−0.413323	+	0.789984i
$586$	3.83252	+	0.282304i	0.158320	+	0.0116619i
$587$	−17.9428	+	12.5637i	−0.740579	+	0.518559i	−0.881918	−	0.471402i	$-0.843748\pi$
$587$	−17.9428	+	12.5637i	−0.740579	+	0.518559i	0.141340	+	0.989961i	$0.454859\pi$
$588$	6.61419	+	13.2230i	0.272764	+	0.545307i
$589$	−22.1558	+	17.0226i	−0.912914	+	0.701402i
$590$	−7.98817	−	14.9176i	−0.328868	−	0.614148i
$591$	−2.87556	−	0.507039i	−0.118285	−	0.0208568i
$592$	10.3527	+	6.43175i	0.425492	+	0.264343i
$593$	−14.3816	−	30.8414i	−0.590580	−	1.26650i	−0.943662	−	0.330911i	$-0.892644\pi$
$593$	−14.3816	−	30.8414i	−0.590580	−	1.26650i	0.353081	−	0.935593i	$-0.385134\pi$
$594$	24.1650	+	16.4304i	0.991503	+	0.674149i
$595$	−0.0866440	+	0.387028i	−0.00355206	+	0.0158666i
$596$	17.4585	−	3.57558i	0.715129	−	0.146462i
$597$	3.21824	+	12.0106i	0.131714	+	0.491562i
$598$	−31.4508	+	0.432131i	−1.28612	+	0.0176711i
$599$	2.22656	+	12.6275i	0.0909748	+	0.515944i	0.995907	+	0.0903873i	$0.0288105\pi$
$599$	2.22656	+	12.6275i	0.0909748	+	0.515944i	−0.904932	+	0.425556i	$0.860078\pi$
$600$	6.99878	−	13.2318i	0.285724	−	0.540187i
$601$	7.52267	+	13.0296i	0.306856	+	0.531490i	0.977673	−	0.210133i	$-0.0673897\pi$
$601$	7.52267	+	13.0296i	0.306856	+	0.531490i	−0.670817	+	0.741623i	$0.734056\pi$
$602$	0.0908145	+	0.152420i	0.00370132	+	0.00621219i
$603$	−4.54548	+	9.74781i	−0.185106	+	0.396961i
$604$	3.39455	−	4.27892i	0.138122	−	0.174107i
$605$	11.1799	+	0.511344i	0.454527	+	0.0207891i
$606$	0.559281	−	0.270213i	0.0227192	−	0.0109766i
$607$	−28.5876	−	28.5876i	−1.16033	−	1.16033i	−0.984402	−	0.175933i	$-0.943706\pi$
$607$	−28.5876	−	28.5876i	−1.16033	−	1.16033i	−0.175933	−	0.984402i	$-0.556294\pi$
$608$	−0.633172	−	24.6495i	−0.0256785	−	0.999670i
$609$		−	0.753931i		−	0.0305508i
$610$	−28.3491	+	9.30339i	−1.14782	+	0.376683i
$611$	−38.2659	+	45.6035i	−1.54807	+	1.84492i
$612$	−0.608171	−	5.27694i	−0.0245839	−	0.213308i
$613$	−29.6957	−	13.8473i	−1.19940	−	0.559289i	−0.282832	−	0.959169i	$-0.591274\pi$
$613$	−29.6957	−	13.8473i	−1.19940	−	0.559289i	−0.916567	+	0.399880i	$0.869052\pi$
$614$	6.40819	−	25.3011i	0.258613	−	1.02107i
$615$	20.4007	−	8.40073i	0.822634	−	0.338750i
$616$	1.38600	+	0.310784i	0.0558435	+	0.0125219i
$617$	34.1717	+	23.9272i	1.37570	+	0.963275i	0.999322	+	0.0368080i	$0.0117190\pi$
$617$	34.1717	+	23.9272i	1.37570	+	0.963275i	0.376377	+	0.926467i	$0.377170\pi$
$618$	−0.254982	−	18.5578i	−0.0102569	−	0.746504i
$619$	22.6746	−	39.2736i	0.911369	−	1.57854i	0.0992377	−	0.995064i	$-0.468360\pi$
$619$	22.6746	−	39.2736i	0.911369	−	1.57854i	0.812132	−	0.583474i	$-0.198307\pi$
$620$	18.8233	−	21.6199i	0.755961	−	0.868274i
$621$	17.1517	−	14.3920i	0.688273	−	0.577530i
$622$	−17.8606	+	3.40295i	−0.716144	+	0.136446i
$623$	0.613681	−	0.286164i	0.0245866	−	0.0114649i
$624$	4.94131	+	21.1525i	0.197811	+	0.846776i
$625$	−16.2279	+	19.0172i	−0.649117	+	0.760689i
$626$	36.0466	−	25.9854i	1.44071	−	1.03858i
$627$	17.6068	+	5.53941i	0.703147	+	0.221223i
$628$	−3.78597	+	1.89376i	−0.151077	+	0.0755691i
$629$	4.23988	+	0.747605i	0.169055	+	0.0298090i
$630$	−0.408221	−	0.624578i	−0.0162639	−	0.0248838i
$631$	1.52629	−	4.19345i	0.0607607	−	0.166939i	−0.905598	−	0.424137i	$-0.860577\pi$
$631$	1.52629	−	4.19345i	0.0607607	−	0.166939i	0.966358	+	0.257199i	$0.0827996\pi$
$632$	2.37200	−	17.6868i	0.0943529	−	0.703542i
$633$	13.8182	+	1.20893i	0.549223	+	0.0480508i
$634$	8.43795	−	18.7641i	0.335114	−	0.745216i
$635$	18.4148	−	23.8959i	0.730768	−	0.948279i
$636$	3.21450	−	21.7014i	0.127463	−	0.860515i
$637$	29.3529	+	20.5532i	1.16301	+	0.814346i
$638$	24.8744	+	20.2963i	0.984787	+	0.803539i
$639$	−6.55492	−	11.3535i	−0.259309	−	0.449136i
$640$	5.64420	+	24.6606i	0.223106	+	0.974794i
$641$	2.80725	−	1.02176i	0.110880	−	0.0403570i	−0.285984	−	0.958234i	$-0.592321\pi$
$641$	2.80725	−	1.02176i	0.110880	−	0.0403570i	0.396864	+	0.917877i	$0.370098\pi$
$642$	2.51855	−	4.50405i	0.0993992	−	0.177760i
$643$	8.00553	−	0.700393i	0.315707	−	0.0276208i	0.0717991	−	0.997419i	$-0.477126\pi$
$643$	8.00553	−	0.700393i	0.315707	−	0.0276208i	0.243908	+	0.969798i	$0.421570\pi$
$644$	0.518067	−	0.957121i	0.0204147	−	0.0377159i
$645$	−1.43609	−	1.87960i	−0.0565460	−	0.0740093i
$646$	−3.44842	−	7.99843i	−0.135676	−	0.314694i
$647$	2.81178	+	2.81178i	0.110542	+	0.110542i	0.760214	−	0.649672i	$-0.225094\pi$
$647$	2.81178	+	2.81178i	0.110542	+	0.110542i	−0.649672	+	0.760214i	$0.725094\pi$
$648$	0.385787	+	0.297508i	0.0151551	+	0.0116872i
$649$	−13.7607	+	16.3994i	−0.540155	+	0.643732i
$650$	−0.348037	−	36.2771i	−0.0136511	−	1.42291i
$651$	0.291283	+	0.800295i	0.0114163	+	0.0313660i
$652$	−1.89327	+	4.36972i	−0.0741461	+	0.171131i
$653$	−2.50781	+	9.35929i	−0.0981384	+	0.366257i	−0.997477	−	0.0709963i	$-0.977382\pi$
$653$	−2.50781	+	9.35929i	−0.0981384	+	0.366257i	0.899338	+	0.437254i	$0.144049\pi$
$654$	2.91862	+	28.7973i	0.114127	+	1.12606i
$655$	33.7566	−	36.6859i	1.31898	−	1.43344i
$656$	−16.8418	+	33.2671i	−0.657561	+	1.29886i
$657$	4.40044	+	16.4227i	0.171677	+	0.640709i
$658$	−0.731034	−	1.92576i	−0.0284987	−	0.0750738i
$659$	1.10385	−	0.926243i	0.0430000	−	0.0360813i	−0.621034	−	0.783783i	$-0.713287\pi$
$659$	1.10385	−	0.926243i	0.0430000	−	0.0360813i	0.664034	+	0.747702i	$0.268843\pi$
$660$	−18.8318	−	1.99406i	−0.733029	−	0.0776186i
$661$	−18.0211	−	6.55916i	−0.700941	−	0.255122i	−0.0331283	−	0.999451i	$-0.510547\pi$
$661$	−18.0211	−	6.55916i	−0.700941	−	0.255122i	−0.667813	+	0.744330i	$0.732769\pi$
$662$	7.48658	+	8.67721i	0.290974	+	0.337249i
$663$	4.40112	+	6.28545i	0.170925	+	0.244107i
$664$	0.627927	+	2.00844i	0.0243683	+	0.0779425i
$665$	−0.936112	−	0.787813i	−0.0363009	−	0.0305501i
$666$	−6.57042	+	4.73650i	−0.254599	+	0.183536i
$667$	20.1499	−	14.1091i	0.780207	−	0.546307i
$668$	−6.23014	+	26.0996i	−0.241051	+	1.00982i
$669$	2.37803	−	6.53359i	0.0919400	−	0.252603i
$670$	−1.00011	−	18.0669i	−0.0386376	−	0.697984i
$671$	24.2630	+	28.9156i	0.936664	+	1.11627i
$672$	−0.722255	−	0.207978i	−0.0278616	−	0.00802291i
$673$	12.6104	−	3.37894i	0.486094	−	0.130249i	−0.00744472	−	0.999972i	$-0.502370\pi$
$673$	12.6104	−	3.37894i	0.486094	−	0.130249i	0.493539	+	0.869724i	$0.335703\pi$
$674$	−1.66791	+	1.71438i	−0.0642454	+	0.0660354i
$675$	16.5175	+	19.8514i	0.635760	+	0.764080i
$676$	17.6821	+	19.9338i	0.680081	+	0.766684i
$677$	−38.7303	−	10.3778i	−1.48853	−	0.398850i	−0.579288	−	0.815123i	$-0.696669\pi$
$677$	−38.7303	−	10.3778i	−1.48853	−	0.398850i	−0.909239	+	0.416273i	$0.863336\pi$
$678$	−2.59500	−	4.35536i	−0.0996603	−	0.167267i
$679$	−0.818864	+	0.298042i	−0.0314251	+	0.0114378i
$680$	5.09281	+	7.34322i	0.195300	+	0.281600i
$681$	−12.2105	−	10.2458i	−0.467908	−	0.392621i
$682$	−34.2456	−	11.9342i	−1.31133	−	0.456983i
$683$	32.6228	−	32.6228i	1.24828	−	1.24828i	0.291799	−	0.956480i	$-0.405746\pi$
$683$	32.6228	−	32.6228i	1.24828	−	1.24828i	0.956480	−	0.291799i	$-0.0942537\pi$
$684$	15.3095	+	5.84311i	0.585374	+	0.223417i
$685$	−0.312179	+	2.33384i	−0.0119277	+	0.0891715i
$686$	−2.23532	+	1.07998i	−0.0853449	+	0.0412338i
$687$	0.651994	+	7.45232i	0.0248751	+	0.284324i
$688$	3.91252	+	0.821022i	0.149164	+	0.0313012i
$689$	−18.1852	−	49.9635i	−0.692802	−	1.90346i
$690$	−5.39589	+	13.4692i	−0.205418	+	0.512762i
$691$	8.11914	−	4.68759i	0.308867	−	0.178324i	−0.337553	−	0.941307i	$-0.609599\pi$
$691$	8.11914	−	4.68759i	0.308867	−	0.178324i	0.646419	+	0.762982i	$0.276266\pi$
$692$	−5.85192	−	0.350295i	−0.222457	−	0.0133162i
$693$	−0.541435	+	0.773249i	−0.0205674	+	0.0293733i
$694$	−4.00464	−	3.89609i	−0.152014	−	0.147893i
$695$	−6.46684	−	49.9199i	−0.245301	−	1.89357i
$696$	−12.4969	−	11.5069i	−0.473692	−	0.436169i
$697$	−1.14797	+	13.1214i	−0.0434825	+	0.497007i
$698$	−18.3980	+	3.50535i	−0.696376	+	0.132679i
$699$	−0.680680	−	0.247747i	−0.0257457	−	0.00937066i
$700$	1.10146	+	0.602109i	0.0416312	+	0.0227576i
$701$	7.42869	−	42.1302i	0.280578	−	1.59124i	−0.440089	−	0.897954i	$-0.645053\pi$
$701$	7.42869	−	42.1302i	0.280578	−	1.59124i	0.720667	−	0.693282i	$-0.243836\pi$
$702$	−36.9919	−	5.99987i	−1.39617	−	0.226450i
$703$	−8.07871	+	10.5419i	−0.304694	+	0.397595i
$704$	26.3054	−	18.2304i	0.991421	−	0.687085i
$705$	12.6300	+	24.3853i	0.475674	+	0.918405i
$706$	−46.7700	−	3.44509i	−1.76021	−	0.129658i
$707$	0.0220136	+	0.0472084i	0.000827908	+	0.00177545i
$708$	7.78688	−	8.22703i	0.292649	−	0.309191i
$709$	26.2453	+	31.2779i	0.985663	+	1.17467i	0.984627	+	0.174668i	$0.0558851\pi$
$709$	26.2453	+	31.2779i	0.985663	+	1.17467i	0.00103533	+	0.999999i	$0.499670\pi$
$710$	18.7382	+	11.6325i	0.703234	+	0.436560i
$711$	10.2704	+	5.92964i	0.385172	+	0.222379i
$712$	4.62301	−	14.5397i	0.173255	−	0.544899i
$713$	−15.9379	+	22.7617i	−0.596880	+	0.852434i
$714$	−0.264145	+	0.0267712i	−0.00988539	+	0.00100189i
$715$	−42.4393	+	17.4760i	−1.58714	+	0.653564i
$716$	−26.7151	+	10.5634i	−0.998390	+	0.394774i
$717$	11.4069	−	24.4621i	0.425997	−	0.913554i
$718$	3.32595	−	5.94797i	0.124124	−	0.221976i
$719$	20.3017	+	17.0352i	0.757126	+	0.635304i	0.937377	−	0.348316i	$-0.113246\pi$
$719$	20.3017	+	17.0352i	0.757126	+	0.635304i	−0.180251	+	0.983621i	$0.557691\pi$
$720$	−16.5833	−	2.76616i	−0.618021	−	0.103089i
$721$	1.55641			0.0579638
$722$	26.7999	+	1.94070i	0.997388	+	0.0722256i
$723$	−9.17133	+	9.17133i	−0.341086	+	0.341086i
$724$	−10.5949	+	19.5739i	−0.393755	+	0.727457i
$725$	16.1770	+	23.3081i	0.600797	+	0.865642i
$726$	2.03828	+	7.20930i	0.0756478	+	0.267562i
$727$	36.4356	+	16.9902i	1.35132	+	0.630132i	0.957334	−	0.288984i	$-0.0933174\pi$
$727$	36.4356	+	16.9902i	1.35132	+	0.630132i	0.393988	+	0.919116i	$0.371095\pi$
$728$	−1.77938	+	0.389971i	−0.0659482	+	0.0144533i
$729$	13.9228	−	8.03832i	0.515658	−	0.297715i
$730$	−19.5688	−	20.8617i	−0.724273	−	0.772125i
$731$	1.39072	−	0.245221i	0.0514376	−	0.00906983i
$732$	−11.9014	−	16.0403i	−0.439889	−	0.592865i
$733$	−30.1857	+	8.08823i	−1.11493	+	0.298745i	−0.768831	−	0.639452i	$-0.779161\pi$
$733$	−30.1857	+	8.08823i	−1.11493	+	0.298745i	−0.346102	+	0.938197i	$0.612495\pi$
$734$	−12.0390	−	5.41377i	−0.444367	−	0.199826i
$735$	13.9597	−	8.85269i	0.514912	−	0.326537i
$736$	−7.95783	−	23.1954i	−0.293329	−	0.854994i
$737$	−20.7468	+	9.67439i	−0.764218	+	0.356361i
$738$	−16.1875	−	18.7619i	−0.595871	−	0.690636i
$739$	−4.21985	+	23.9320i	−0.155230	+	0.880352i	0.803346	+	0.595513i	$0.203051\pi$
$739$	−4.21985	+	23.9320i	−0.155230	+	0.880352i	−0.958575	+	0.284839i	$0.908060\pi$
$740$	5.98294	−	12.2428i	0.219937	−	0.450053i
$741$	−23.4665	+	3.10422i	−0.862064	+	0.114036i
$742$	1.81601	+	0.294546i	0.0666678	+	0.0108131i
$743$	−16.2134	−	23.1551i	−0.594810	−	0.849477i	0.403028	−	0.915187i	$-0.367958\pi$
$743$	−16.2134	−	23.1551i	−0.594810	−	0.849477i	−0.997839	+	0.0657103i	$0.979069\pi$
$744$	17.7111	+	7.38636i	0.649321	+	0.270797i
$745$	−5.95197	−	19.0146i	−0.218063	−	0.696641i
$746$	−12.8963	+	18.9673i	−0.472168	+	0.694441i
$747$	−1.39313	−	0.121883i	−0.0509721	−	0.00445948i
$748$	6.22771	−	9.43563i	0.227707	−	0.345001i
$749$	0.374774	+	0.216376i	0.0136939	+	0.00790619i
$750$	−15.5094	−	6.28797i	−0.566323	−	0.229604i
$751$	−30.0232	+	5.29390i	−1.09556	+	0.193177i	−0.692088	−	0.721813i	$-0.743309\pi$
$751$	−30.0232	+	5.29390i	−1.09556	+	0.193177i	−0.403475	+	0.914991i	$0.632198\pi$
$752$	−43.0781	−	17.2747i	−1.57090	−	0.629944i
$753$	−0.0735670	+	0.274556i	−0.00268093	+	0.0100054i
$754$	−39.9116	−	10.1087i	−1.45350	−	0.368137i
$755$	−5.14341	−	3.29172i	−0.187188	−	0.119798i
$756$	0.805888	−	1.01584i	0.0293099	−	0.0369459i
$757$	1.23126	−	0.107722i	0.0447511	−	0.00391521i	−0.0647582	−	0.997901i	$-0.520628\pi$
$757$	1.23126	−	0.107722i	0.0447511	−	0.00391521i	0.109509	+	0.993986i	$0.465072\pi$
$758$	8.13993	+	2.83666i	0.295655	+	0.103032i
$759$	18.3565			0.666298
$760$	−27.3460	+	3.49257i	−0.991943	+	0.126689i
$761$	27.4694			0.995767			0.497883	−	0.867244i	$-0.334111\pi$
$761$	27.4694			0.995767			0.497883	+	0.867244i	$0.334111\pi$
$762$	19.0704	+	6.64581i	0.690849	+	0.240752i
$763$	−2.41809	+	0.211555i	−0.0875407	+	0.00765882i
$764$	−19.3592	+	24.4028i	−0.700390	+	0.882861i
$765$	−5.80073	+	1.27338i	−0.209726	+	0.0460392i
$766$	−26.6014	−	6.73751i	−0.961147	−	0.243436i
$767$	7.10574	−	26.5190i	0.256574	−	0.957546i
$768$	−14.4708	+	8.79754i	−0.522171	+	0.317454i
$769$	−28.2247	+	4.97677i	−1.01781	+	0.179467i	−0.657570	−	0.753393i	$-0.728416\pi$
$769$	−28.2247	+	4.97677i	−1.01781	+	0.179467i	−0.360238	+	0.932860i	$0.617304\pi$
$770$	0.188903	−	1.57680i	0.00680760	−	0.0568239i
$771$	−18.4225	−	10.6362i	−0.663471	−	0.383055i
$772$	−25.8536	+	39.1709i	−0.930492	+	1.40979i
$773$	−37.0475	−	3.24124i	−1.33251	−	0.116579i	−0.601458	−	0.798905i	$-0.705413\pi$
$773$	−37.0475	−	3.24124i	−1.33251	−	0.116579i	−0.731049	+	0.682325i	$0.760969\pi$
$774$	−1.49382	+	2.19703i	−0.0536941	+	0.0789705i
$775$	−26.1769	−	18.4915i	−0.940303	−	0.664234i
$776$	−7.55775	+	18.1221i	−0.271308	+	0.650544i
$777$	0.232206	+	0.331625i	0.00833035	+	0.0118970i
$778$	23.5238	+	3.81543i	0.843370	+	0.136790i
$779$	−34.2830	−	21.8108i	−1.22832	−	0.781454i
$780$	22.9689	−	7.88892i	0.822417	−	0.282469i
$781$	4.84520	−	27.4785i	0.173375	−	0.983258i
$782$	−5.65873	−	6.55867i	−0.202356	−	0.234537i
$783$	26.5617	−	12.3859i	0.949238	−	0.442637i
$784$	−8.09859	+	26.7374i	−0.289235	+	0.954906i
$785$	2.53468	+	3.99691i	0.0904665	+	0.142656i
$786$	30.4371	+	13.6872i	1.08566	+	0.488205i
$787$	−19.7482	+	5.29152i	−0.703948	+	0.188622i	−0.592998	−	0.805204i	$-0.702056\pi$
$787$	−19.7482	+	5.29152i	−0.703948	+	0.188622i	−0.110950	+	0.993826i	$0.535389\pi$
$788$	−3.28760	−	4.43090i	−0.117116	−	0.157844i
$789$	−20.1862	+	3.55938i	−0.718649	+	0.126717i
$790$	−19.9413	−	0.637678i	−0.709478	−	0.0226876i
$791$	0.368198	−	0.212579i	0.0130916	−	0.00755844i
$792$	4.55338	+	20.7764i	0.161797	+	0.738257i
$793$	−43.8726	−	20.4581i	−1.55796	−	0.726489i
$794$	−1.77260	−	6.26958i	−0.0629072	−	0.222499i
$795$	−24.5020	−	1.12067i	−0.868996	−	0.0397460i
$796$	−11.1842	+	20.6626i	−0.396412	+	0.732366i
$797$	−27.1317	+	27.1317i	−0.961054	+	0.961054i	−0.999270	−	0.0382153i	$-0.987833\pi$
$797$	−27.1317	+	27.1317i	−0.961054	+	0.961054i	0.0382153	+	0.999270i	$0.487833\pi$
$798$	0.302536	−	0.761117i	0.0107097	−	0.0269432i
$799$	−16.3949			−0.580011
$800$	26.7914	−	9.06757i	0.947219	−	0.320587i
$801$	7.76716	+	6.51742i	0.274439	+	0.230282i
$802$	−9.76858	+	17.4696i	−0.344941	+	0.616875i
$803$	−15.2930	+	32.7959i	−0.539677	+	1.15734i
$804$	11.2643	−	4.45402i	0.397260	−	0.157081i
$805$	−1.12321	−	0.467977i	−0.0395878	−	0.0164940i
$806$	46.2716	−	4.68964i	1.62985	−	0.165186i
$807$	12.2177	−	17.4488i	0.430085	−	0.614225i
$808$	1.11849	+	0.355633i	0.0393484	+	0.0125111i
$809$	17.6080	+	10.1660i	0.619063	+	0.357416i	0.776504	−	0.630112i	$-0.216991\pi$
$809$	17.6080	+	10.1660i	0.619063	+	0.357416i	−0.157441	+	0.987528i	$0.550325\pi$
$810$	0.287278	−	0.462763i	0.0100939	−	0.0162598i
$811$	−21.2002	−	25.2655i	−0.744441	−	0.887190i	0.252317	−	0.967645i	$-0.418807\pi$
$811$	−21.2002	−	25.2655i	−0.744441	−	0.887190i	−0.996758	+	0.0804545i	$0.974363\pi$
$812$	0.979282	−	1.03463i	0.0343661	−	0.0363086i
$813$	−2.74005	−	5.87606i	−0.0960979	−	0.206083i
$814$	−17.1924	−	1.26640i	−0.602594	−	0.0443872i
$815$	5.07459	+	1.61158i	0.177755	+	0.0564513i
$816$	−3.58779	+	4.78696i	−0.125598	+	0.167577i
$817$	−1.30743	+	4.15562i	−0.0457412	+	0.145387i
$818$	−36.7556	−	5.96155i	−1.28513	−	0.208441i
$819$	0.210216	−	1.19219i	0.00734553	−	0.0416586i
$820$	38.9080	+	14.9700i	1.35873	+	0.522774i
$821$	−5.38692	−	1.96068i	−0.188005	−	0.0684281i	0.246302	−	0.969193i	$-0.420784\pi$
$821$	−5.38692	−	1.96068i	−0.188005	−	0.0684281i	−0.434307	+	0.900765i	$0.643007\pi$
$822$	−1.54839	+	0.295012i	−0.0540063	+	0.0102897i
$823$	−2.45911	+	28.1078i	−0.0857192	+	0.979775i	0.824558	+	0.565777i	$0.191424\pi$
$823$	−2.45911	+	28.1078i	−0.0857192	+	0.979775i	−0.910278	+	0.413998i	$0.864132\pi$
$824$	23.7548	−	25.7984i	0.827539	−	0.898731i
$825$	−0.0877693	+	21.1722i	−0.00305574	+	0.737120i
$826$	0.680885	+	0.662428i	0.0236910	+	0.0230488i
$827$	20.0197	−	28.5911i	0.696153	−	0.994209i	−0.302997	−	0.952991i	$-0.597987\pi$
$827$	20.0197	−	28.5911i	0.696153	−	0.994209i	0.999150	−	0.0412177i	$-0.0131237\pi$
$828$	16.2678	+	0.973784i	0.565344	+	0.0338413i
$829$	−12.6132	+	7.28223i	−0.438074	+	0.252922i	−0.702780	−	0.711407i	$-0.748058\pi$
$829$	−12.6132	+	7.28223i	−0.438074	+	0.252922i	0.264706	+	0.964329i	$0.414725\pi$
$830$	2.16295	−	0.925631i	0.0750771	−	0.0321291i
$831$	−0.318879	−	0.876113i	−0.0110618	−	0.0303920i
$832$	−20.6939	+	35.4462i	−0.717432	+	1.22888i
$833$	0.860100	+	9.83098i	0.0298007	+	0.340623i
$834$	30.3411	−	14.6591i	1.05063	−	0.507603i
$835$	29.7352	+	3.97744i	1.02903	+	0.137645i
$836$	16.9670	+	30.4713i	0.586816	+	1.05387i
$837$	−23.4098	+	23.4098i	−0.809161	+	0.809161i
$838$	−40.6831	−	14.1775i	−1.40537	−	0.489755i
$839$	38.8688	+	32.6148i	1.34190	+	1.12599i	0.981133	+	0.193334i	$0.0619299\pi$
$839$	38.8688	+	32.6148i	1.34190	+	1.12599i	0.360768	+	0.932655i	$0.382515\pi$
$840$	−0.149633	+	0.826888i	−0.00516283	+	0.0285303i
$841$	3.00563	−	1.09396i	0.103642	−	0.0377227i
$842$	−21.3202	−	35.7831i	−0.734742	−	1.23317i
$843$	−10.4565	−	2.80182i	−0.360142	−	0.0964998i
$844$	17.3927	+	19.6075i	0.598681	+	0.674918i
$845$	20.1721	−	21.9226i	0.693942	−	0.754161i
$846$	21.5085	−	22.1078i	0.739479	−	0.760083i
$847$	−0.606865	+	0.162609i	−0.0208521	+	0.00558732i
$848$	32.5993	−	25.6059i	1.11946	−	0.879311i
$849$	13.5192	+	16.1115i	0.463976	+	0.552945i
$850$	7.59175	−	6.49536i	0.260395	−	0.222789i
$851$	−4.51763	+	12.4121i	−0.154862	+	0.425481i
$852$	−3.42803	+	14.3609i	−0.117442	+	0.491995i
$853$	26.4485	−	18.5194i	0.905579	−	0.634093i	−0.0251976	−	0.999682i	$-0.508021\pi$
$853$	26.4485	−	18.5194i	0.905579	−	0.634093i	0.930776	+	0.365590i	$0.119133\pi$
$854$	1.35873	−	0.979483i	0.0464947	−	0.0335172i
$855$	4.76750	−	17.6897i	0.163045	−	0.604974i
$856$	9.30657	−	2.90965i	0.318092	−	0.0994497i
$857$	−9.76325	−	13.9434i	−0.333506	−	0.476296i	0.617017	−	0.786950i	$-0.288341\pi$
$857$	−9.76325	−	13.9434i	−0.333506	−	0.476296i	−0.950523	+	0.310653i	$0.899452\pi$
$858$	−20.0707	−	23.2626i	−0.685202	−	0.794173i
$859$	2.54401	+	0.925945i	0.0868006	+	0.0315928i	0.385055	−	0.922893i	$-0.374182\pi$
$859$	2.54401	+	0.925945i	0.0868006	+	0.0315928i	−0.298255	+	0.954486i	$0.596405\pi$
$860$	0.470644	−	4.44476i	0.0160488	−	0.151565i
$861$	−0.948787	+	0.796127i	−0.0323346	+	0.0271319i
$862$	−13.0126	−	34.2789i	−0.443209	−	1.16754i
$863$	6.02905	+	22.5007i	0.205231	+	0.765934i	0.989379	+	0.145360i	$0.0464339\pi$
$863$	6.02905	+	22.5007i	0.205231	+	0.765934i	−0.784148	+	0.620574i	$0.786899\pi$
$864$	−4.53830	−	28.8625i	−0.154396	−	0.981922i
$865$	0.272324	+	6.54870i	0.00925929	+	0.222662i
$866$	1.32686	+	13.0919i	0.0450887	+	0.444879i
$867$	4.11017	−	15.3394i	0.139589	−	0.520952i
$868$	−0.639770	+	1.47661i	−0.0217152	+	0.0501194i
$869$	8.63285	+	23.7186i	0.292849	+	0.804597i
$870$	−11.3855	+	15.2019i	−0.386005	+	0.515391i
$871$	18.8705	−	22.4889i	0.639401	−	0.762009i
$872$	−33.3996	+	43.3102i	−1.13105	+	1.46667i
$873$	−9.22683	−	9.22683i	−0.312281	−	0.312281i
$874$	26.0036	−	6.15787i	0.879586	−	0.208293i
$875$	0.545130	−	1.29326i	0.0184288	−	0.0437200i
$876$	9.11463	−	16.8392i	0.307955	−	0.568942i
$877$	−10.8135	+	0.946055i	−0.365144	+	0.0319460i	−0.268252	−	0.963349i	$-0.586446\pi$
$877$	−10.8135	+	0.946055i	−0.365144	+	0.0319460i	−0.0968926	+	0.995295i	$0.530890\pi$
$878$	−28.1843	+	50.4034i	−0.951175	+	1.70103i
$879$	2.70272	−	0.983710i	0.0911605	−	0.0331797i
$880$	−23.2532	−	27.1972i	−0.783867	−	0.916818i
$881$	5.47226	+	9.47823i	0.184365	+	0.319330i	0.943362	−	0.331764i	$-0.107644\pi$
$881$	5.47226	+	9.47823i	0.184365	+	0.319330i	−0.758997	+	0.651094i	$0.774310\pi$
$882$	−14.3850	−	11.7375i	−0.484368	−	0.395221i
$883$	−3.53198	−	2.47312i	−0.118861	−	0.0832270i	0.512635	−	0.858607i	$-0.328670\pi$
$883$	−3.53198	−	2.47312i	−0.118861	−	0.0832270i	−0.631495	+	0.775380i	$0.717558\pi$
$884$	−2.12444	+	14.3423i	−0.0714526	+	0.482383i
$885$	−10.0317	−	7.73070i	−0.337213	−	0.259865i
$886$	4.29169	−	9.54374i	0.144182	−	0.320628i
$887$	12.8782	+	1.12670i	0.432409	+	0.0378309i	0.301283	−	0.953535i	$-0.402585\pi$
$887$	12.8782	+	1.12670i	0.432409	+	0.0378309i	0.131126	+	0.991366i	$0.458141\pi$
$888$	9.04094	+	1.21249i	0.303394	+	0.0406886i
$889$	−0.579239	+	1.59145i	−0.0194271	+	0.0533754i
$890$	−16.6954	−	3.49746i	−0.559632	−	0.117235i
$891$	−0.678614	−	0.119658i	−0.0227344	−	0.00400869i
$892$	11.7499	−	5.87735i	0.393416	−	0.196788i
$893$	23.3261	−	44.8768i	0.780577	−	1.50175i
$894$	10.8196	−	7.79965i	0.361861	−	0.260859i
$895$	14.7716	+	28.5202i	0.493761	+	0.953326i
$896$	−0.721023	−	1.22355i	−0.0240877	−	0.0408760i
$897$	−21.3356	+	9.94895i	−0.712375	+	0.332186i
$898$	−11.0567	+	2.10661i	−0.368965	+	0.0702984i
$899$	−27.8627	+	23.3795i	−0.929272	+	0.779751i
$900$	−1.20093	+	18.7584i	−0.0400312	+	0.625280i
$901$	7.32154	−	12.6813i	0.243916	−	0.422475i
$902$	−0.724580	−	52.7355i	−0.0241259	−	1.75590i
$903$	0.108776	+	0.0761657i	0.00361983	+	0.00253463i
$904$	2.09602	−	9.34760i	0.0697126	−	0.310897i
$905$	22.9704	+	9.57049i	0.763563	+	0.318134i
$906$	1.00367	−	3.96275i	0.0333448	−	0.131654i
$907$	43.9025	+	20.4721i	1.45776	+	0.679764i	0.980050	−	0.198753i	$-0.0636893\pi$
$907$	43.9025	+	20.4721i	1.45776	+	0.679764i	0.477710	+	0.878518i	$0.341467\pi$
$908$	−3.44840	−	29.9208i	−0.114439	−	0.992958i
$909$	−0.501363	+	0.597501i	−0.0166292	+	0.0198179i
$910$	0.635042	+	1.93508i	0.0210514	+	0.0641474i
$911$			0.0962146i			0.00318773i	0.999999	+	0.00159387i	$0.000507343\pi$
$911$			0.0962146i			0.00318773i	−0.999999	+	0.00159387i	$0.999493\pi$
$912$	−7.99849	−	16.6313i	−0.264856	−	0.550718i
$913$	−2.10464	−	2.10464i	−0.0696534	−	0.0696534i
$914$	18.7608	−	9.06415i	0.620552	−	0.299816i
$915$	−16.4953	+	15.0523i	−0.545317	+	0.497615i
$916$	−8.78509	+	11.0739i	−0.290268	+	0.365890i
$917$	−1.18277	+	2.53646i	−0.0390585	+	0.0837613i
$918$	−5.28268	−	8.86628i	−0.174354	−	0.292631i
$919$	7.36825	+	12.7622i	0.243056	+	0.420985i	0.961583	−	0.274513i	$-0.0885168\pi$
$919$	7.36825	+	12.7622i	0.243056	+	0.420985i	−0.718527	+	0.695499i	$0.755183\pi$
$920$	−24.9000	+	11.4753i	−0.820929	+	0.378329i
$921$	−3.39209	−	19.2375i	−0.111773	−	0.633897i
$922$	−1.29687	+	0.0178189i	−0.0427102	+	0.000586833i
$923$	9.26141	+	34.5641i	0.304843	+	1.13769i
$924$	1.04148	−	0.213299i	0.0342620	−	0.00701702i
$925$	−14.2944	−	5.26994i	−0.469996	−	0.173274i
$926$	−45.5611	−	30.9782i	−1.49723	−	1.01801i
$927$	9.84949	+	21.1223i	0.323500	+	0.693748i
$928$	−2.20332	−	32.0234i	−0.0723275	−	1.05122i
$929$	44.0429	+	7.76596i	1.44500	+	0.254793i	0.840500	−	0.541811i	$-0.182261\pi$
$929$	44.0429	+	7.76596i	1.44500	+	0.254793i	0.604502	+	0.796604i	$0.293372\pi$
$930$	6.21239	−	20.5355i	0.203712	−	0.673387i
$931$	−28.1334	−	11.6328i	−0.922036	−	0.381251i
$932$	−0.612312	−	1.22413i	−0.0200569	−	0.0400976i
$933$	−11.1470	+	7.80523i	−0.364937	+	0.255532i
$934$	17.7891	+	1.31035i	0.582076	+	0.0428758i
$935$	−11.1997	−	5.85972i	−0.366269	−	0.191633i
$936$	−16.5529	−	21.6804i	−0.541047	−	0.708645i
$937$	2.75080	−	31.4418i	0.0898648	−	1.02716i	−0.808671	−	0.588261i	$-0.799813\pi$
$937$	2.75080	−	31.4418i	0.0898648	−	1.02716i	0.898536	−	0.438899i	$-0.144632\pi$
$938$	0.360502	+	0.949669i	0.0117708	+	0.0310078i
$939$	16.6290	−	28.8022i	0.542666	−	0.939925i
$940$	−14.3417	+	49.8697i	−0.467775	+	1.62657i
$941$	2.19924	+	12.4725i	0.0716932	+	0.406592i	0.999442	+	0.0333881i	$0.0106297\pi$
$941$	2.19924	+	12.4725i	0.0716932	+	0.406592i	−0.927749	+	0.373204i	$0.878259\pi$
$942$	−2.00299	+	2.45479i	−0.0652611	+	0.0799815i
$943$	−39.0333	−	10.4589i	−1.27110	−	0.340590i
$944$	21.3722	−	1.17572i	0.695606	−	0.0382663i
$945$	−1.22108	−	0.781477i	−0.0397218	−	0.0254215i
$946$	−5.44125	+	1.53840i	−0.176910	+	0.0500178i
$947$	3.96023	+	45.2656i	0.128690	+	1.47093i	0.736276	+	0.676681i	$0.236582\pi$
$947$	3.96023	+	45.2656i	0.128690	+	1.47093i	−0.607586	+	0.794254i	$0.707862\pi$
$948$	−3.80992	−	12.8010i	−0.123740	−	0.415758i
$949$		−	46.4070i		−	1.50643i
$950$	6.97809	+	30.0218i	0.226399	+	0.974035i
$951$		−	15.3984i		−	0.499326i
$952$	−0.397265	−	0.306360i	−0.0128754	−	0.00992919i
$953$	−2.24991	−	25.7166i	−0.0728818	−	0.833042i	−0.941380	−	0.337349i	$-0.890470\pi$
$953$	−2.24991	−	25.7166i	−0.0728818	−	0.833042i	0.868498	−	0.495693i	$-0.165086\pi$
$954$	7.49499	+	26.5094i	0.242659	+	0.858272i
$955$	29.3330	+	18.7728i	0.949193	+	0.607472i
$956$	47.4278	−	18.7535i	1.53392	−	0.606530i
$957$	23.2092	+	6.21889i	0.750248	+	0.201028i
$958$	−4.61331	−	3.76425i	−0.149049	−	0.121617i
$959$	−0.0229536	−	0.130176i	−0.000741209	−	0.00420360i
$960$	11.4224	+	15.1007i	0.368656	+	0.487373i
$961$	5.04334	−	8.73532i	0.162688	−	0.281785i
$962$	20.6690	−	7.84612i	0.666395	−	0.252969i
$963$	−0.564776	+	6.45541i	−0.0181996	+	0.208023i
$964$	−24.4987	+	0.673345i	−0.789049	+	0.0216870i
$965$	46.4942	+	24.3260i	1.49670	+	0.783081i
$966$	0.0598380	−	0.812351i	0.00192525	−	0.0261370i
$967$	−21.6502	+	15.1596i	−0.696223	+	0.487501i	−0.867318	−	0.497754i	$-0.834158\pi$
$967$	−21.6502	+	15.1596i	−0.696223	+	0.487501i	0.171095	+	0.985255i	$0.445269\pi$
$968$	−6.56699	+	12.5410i	−0.211071	+	0.403083i
$969$	−4.80904	−	4.40119i	−0.154489	−	0.141387i
$970$	21.0120	+	6.35654i	0.674656	+	0.204096i
$971$	−15.7956	−	2.78520i	−0.506906	−	0.0893812i	−0.0856542	−	0.996325i	$-0.527298\pi$
$971$	−15.7956	−	2.78520i	−0.506906	−	0.0893812i	−0.421252	+	0.906944i	$0.638409\pi$
$972$	30.4972	+	7.27987i	0.978198	+	0.233502i
$973$	1.19424	+	2.56106i	0.0382857	+	0.0821040i
$974$	−24.6665	+	36.2783i	−0.790367	+	1.16243i
$975$	−11.3730	−	24.6558i	−0.364228	−	0.789618i
$976$	4.50216	−	37.4711i	0.144111	−	1.19942i
$977$	−2.98264	−	11.1314i	−0.0954230	−	0.356124i	0.901660	−	0.432445i	$-0.142349\pi$
$977$	−2.98264	−	11.1314i	−0.0954230	−	0.356124i	−0.997083	+	0.0763216i	$0.975682\pi$
$978$	0.0489676	+	3.56390i	0.00156581	+	0.113961i
$979$	3.74733	+	21.2522i	0.119765	+	0.679223i
$980$	30.6560	+	5.98357i	0.979270	+	0.191138i
$981$	−18.1735	−	31.4775i	−0.580236	−	1.00500i
$982$	21.9042	−	13.0509i	0.698991	−	0.416471i
$983$	−0.0100946	+	0.0216479i	−0.000321966	+	0.000690459i	−0.906469	−	0.422273i	$-0.861232\pi$
$983$	−0.0100946	+	0.0216479i	−0.000321966	+	0.000690459i	0.906147	+	0.422963i	$0.139010\pi$
$984$	−1.28466	+	27.8777i	−0.0409534	+	0.888708i
$985$	−4.55659	+	4.15800i	−0.145185	+	0.132485i
$986$	−4.93271	−	10.2096i	−0.157089	−	0.325141i
$987$	−1.09012	−	1.09012i	−0.0346990	−	0.0346990i
$988$	−36.2357	−	26.2207i	−1.15281	−	0.834193i
$989$			4.33256i			0.137767i
$990$	22.5944	−	7.41488i	0.718099	−	0.235660i
$991$	17.8994	−	21.3317i	0.568594	−	0.677624i	−0.402747	−	0.915311i	$-0.631945\pi$
$991$	17.8994	−	21.3317i	0.568594	−	0.677624i	0.971342	+	0.237687i	$0.0763892\pi$
$992$	14.7111	+	33.1415i	0.467079	+	1.05224i
$993$	7.77383	+	3.62499i	0.246695	+	0.115036i
$994$	−1.20024	−	0.303994i	−0.0380694	−	0.00964211i
$995$	24.2481	+	10.1028i	0.768715	+	0.320281i
$996$	1.04512	+	1.17821i	0.0331159	+	0.0373330i
$997$	18.2354	+	12.7686i	0.577521	+	0.404384i	0.825518	−	0.564376i	$-0.190883\pi$
$997$	18.2354	+	12.7686i	0.577521	+	0.404384i	−0.247997	+	0.968761i	$0.579772\pi$
$998$	23.8867	−	0.328201i	0.756121	−	0.0103890i
$999$	−7.86867	+	13.6289i	−0.248954	+	0.431200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.283.50	yes	672
4.3	odd	2	inner	380.2.bj.a.283.28	yes	672
5.2	odd	4	inner	380.2.bj.a.207.23	yes	672
19.9	even	9	inner	380.2.bj.a.123.1	yes	672
20.7	even	4	inner	380.2.bj.a.207.1	yes	672
76.47	odd	18	inner	380.2.bj.a.123.23	yes	672
95.47	odd	36	inner	380.2.bj.a.47.28	✓	672
380.47	even	36	inner	380.2.bj.a.47.50	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.47.28	✓	672	95.47	odd	36	inner
380.2.bj.a.47.50	yes	672	380.47	even	36	inner
380.2.bj.a.123.1	yes	672	19.9	even	9	inner
380.2.bj.a.123.23	yes	672	76.47	odd	18	inner
380.2.bj.a.207.1	yes	672	20.7	even	4	inner
380.2.bj.a.207.23	yes	672	5.2	odd	4	inner
380.2.bj.a.283.28	yes	672	4.3	odd	2	inner
380.2.bj.a.283.50	yes	672	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33545 + 0.465386i) q^{2} +(1.05442 - 0.0922501i) q^{3} +(1.56683 + 1.24300i) q^{4} +(1.20534 - 1.88339i) q^{5} +(1.45106 + 0.367519i) q^{6} +(-0.0324892 + 0.121251i) q^{7} +(1.51394 + 2.38914i) q^{8} +(-1.85112 + 0.326403i) q^{9} +O(q^{10})\)	\(q+(1.33545 + 0.465386i) q^{2} +(1.05442 - 0.0922501i) q^{3} +(1.56683 + 1.24300i) q^{4} +(1.20534 - 1.88339i) q^{5} +(1.45106 + 0.367519i) q^{6} +(-0.0324892 + 0.121251i) q^{7} +(1.51394 + 2.38914i) q^{8} +(-1.85112 + 0.326403i) q^{9} +(2.48617 - 1.95421i) q^{10} +(-3.46465 - 2.00031i) q^{11} +(1.76677 + 1.16610i) q^{12} +(5.11107 + 0.447161i) q^{13} +(-0.0998162 + 0.146805i) q^{14} +(1.09720 - 2.09708i) q^{15} +(0.909920 + 3.89513i) q^{16} +(0.810447 + 1.15744i) q^{17} +(-2.62398 - 0.425594i) q^{18} +(-4.32125 + 0.571627i) q^{19} +(4.22961 - 1.45271i) q^{20} +(-0.0230719 + 0.130847i) q^{21} +(-3.69593 - 4.28371i) q^{22} +(-3.92885 + 1.83205i) q^{23} +(1.81674 + 2.37950i) q^{24} +(-2.09429 - 4.54026i) q^{25} +(6.61746 + 2.97578i) q^{26} +(-4.98891 + 1.33678i) q^{27} +(-0.201620 + 0.149596i) q^{28} +(-5.58817 + 0.985345i) q^{29} +(2.44121 - 2.28991i) q^{30} +(5.55113 - 3.20494i) q^{31} +(-0.597592 + 5.62520i) q^{32} +(-3.83773 - 1.78956i) q^{33} +(0.543652 + 1.92287i) q^{34} +(0.189202 + 0.207339i) q^{35} +(-3.30612 - 1.78952i) q^{36} +(2.15454 - 2.15454i) q^{37} +(-6.03683 - 1.24768i) q^{38} +5.43049 q^{39} +(6.32449 + 0.0283902i) q^{40} +(7.14094 + 5.99196i) q^{41} +(-0.0917059 + 0.164002i) q^{42} +(0.422379 - 0.905795i) q^{43} +(-2.94213 - 7.44070i) q^{44} +(-1.61650 + 3.87981i) q^{45} +(-6.09939 + 0.618175i) q^{46} +(-6.65530 + 9.50476i) q^{47} +(1.31877 + 4.02318i) q^{48} +(6.04853 + 3.49212i) q^{49} +(-0.683833 - 7.03792i) q^{50} +(0.961328 + 1.14567i) q^{51} +(7.45237 + 7.05367i) q^{52} +(-4.37973 - 9.39237i) q^{53} +(-7.28454 - 0.536581i) q^{54} +(-7.94346 + 4.11420i) q^{55} +(-0.338873 + 0.105947i) q^{56} +(-4.50370 + 1.00137i) q^{57} +(-7.92126 - 1.28478i) q^{58} +(0.929214 - 5.26983i) q^{59} +(4.32579 - 1.92195i) q^{60} +(-8.86615 - 3.22702i) q^{61} +(8.90477 - 1.69661i) q^{62} +(0.0205647 - 0.235056i) q^{63} +(-3.41594 + 7.23404i) q^{64} +(7.00278 - 9.08714i) q^{65} +(-4.29225 - 4.17589i) q^{66} +(3.28200 - 4.68718i) q^{67} +(-0.168858 + 2.82089i) q^{68} +(-3.97367 + 2.29420i) q^{69} +(0.156177 + 0.364943i) q^{70} +(2.38542 + 6.55389i) q^{71} +(-3.58232 - 3.92843i) q^{72} +(-0.788336 - 9.01072i) q^{73} +(3.87996 - 1.87457i) q^{74} +(-2.62711 - 4.59416i) q^{75} +(-7.48121 - 4.47566i) q^{76} +(0.355104 - 0.355104i) q^{77} +(7.25212 + 2.52727i) q^{78} +(-4.83313 - 4.05548i) q^{79} +(8.43280 + 2.98125i) q^{80} +(0.161856 - 0.0589108i) q^{81} +(6.74776 + 11.3252i) q^{82} +(0.718635 + 0.192558i) q^{83} +(-0.198793 + 0.176337i) q^{84} +(3.15677 - 0.131273i) q^{85} +(0.985610 - 1.01307i) q^{86} +(-5.80140 + 1.55448i) q^{87} +(-0.466259 - 11.3059i) q^{88} +(-3.46730 - 4.13217i) q^{89} +(-3.96436 + 4.42898i) q^{90} +(-0.220273 + 0.605196i) q^{91} +(-8.43309 - 2.01303i) q^{92} +(5.55758 - 3.89146i) q^{93} +(-13.3112 + 9.59580i) q^{94} +(-4.13201 + 8.82760i) q^{95} +(-0.111190 + 5.98647i) q^{96} +(3.98176 + 5.68654i) q^{97} +(6.45230 + 7.47844i) q^{98} +(7.06640 + 2.57196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

L-functions

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