LMFDB - Embedded newform 520.2.by.c.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(61,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("520.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.by (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.2
Character	$\chi$	$=$	520.61
Dual form			520.2.by.c.341.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40811 + 0.131283i) q^{2} +(-1.26478 - 0.730219i) q^{3} +(1.96553 - 0.369722i) q^{4} -1.00000i q^{5} +(1.87680 + 0.862182i) q^{6} +(1.29319 + 2.23987i) q^{7} +(-2.71914 + 0.778649i) q^{8} +(-0.433561 - 0.750950i) q^{9} +O(q^{10})$	\(q+(-1.40811 + 0.131283i) q^{2} +(-1.26478 - 0.730219i) q^{3} +(1.96553 - 0.369722i) q^{4} -1.00000i q^{5} +(1.87680 + 0.862182i) q^{6} +(1.29319 + 2.23987i) q^{7} +(-2.71914 + 0.778649i) q^{8} +(-0.433561 - 0.750950i) q^{9} +(0.131283 + 1.40811i) q^{10} +(-5.64276 - 3.25785i) q^{11} +(-2.75593 - 0.967651i) q^{12} +(2.78890 + 2.28517i) q^{13} +(-2.11501 - 2.98420i) q^{14} +(-0.730219 + 1.26478i) q^{15} +(3.72661 - 1.45340i) q^{16} +(-0.646488 - 1.11975i) q^{17} +(0.709088 + 1.00050i) q^{18} +(1.24120 - 0.716607i) q^{19} +(-0.369722 - 1.96553i) q^{20} -3.77725i q^{21} +(8.37332 + 3.84660i) q^{22} +(-0.0547143 + 0.0947679i) q^{23} +(4.00768 + 1.00075i) q^{24} -1.00000 q^{25} +(-4.22708 - 2.85163i) q^{26} +5.64769i q^{27} +(3.36993 + 3.92441i) q^{28} +(-0.764027 - 0.441111i) q^{29} +(0.862182 - 1.87680i) q^{30} -8.69745 q^{31} +(-5.05666 + 2.53578i) q^{32} +(4.75789 + 8.24090i) q^{33} +(1.05733 + 1.49186i) q^{34} +(2.23987 - 1.29319i) q^{35} +(-1.12982 - 1.31572i) q^{36} +(-8.04677 - 4.64580i) q^{37} +(-1.65366 + 1.17201i) q^{38} +(-1.85866 - 4.92674i) q^{39} +(0.778649 + 2.71914i) q^{40} +(-1.97333 + 3.41791i) q^{41} +(0.495890 + 5.31877i) q^{42} +(-9.38995 + 5.42129i) q^{43} +(-12.2955 - 4.31715i) q^{44} +(-0.750950 + 0.433561i) q^{45} +(0.0646021 - 0.140626i) q^{46} -0.158218 q^{47} +(-5.77463 - 0.883017i) q^{48} +(0.155319 - 0.269021i) q^{49} +(1.40811 - 0.131283i) q^{50} +1.88831i q^{51} +(6.32655 + 3.46046i) q^{52} +0.718497i q^{53} +(-0.741448 - 7.95255i) q^{54} +(-3.25785 + 5.64276i) q^{55} +(-5.26043 - 5.08357i) q^{56} -2.09312 q^{57} +(1.13374 + 0.520828i) q^{58} +(-5.04877 + 2.91491i) q^{59} +(-0.967651 + 2.75593i) q^{60} +(-0.0201595 + 0.0116391i) q^{61} +(12.2469 - 1.14183i) q^{62} +(1.12135 - 1.94224i) q^{63} +(6.78741 - 4.23451i) q^{64} +(2.28517 - 2.78890i) q^{65} +(-7.78151 - 10.9794i) q^{66} +(-9.32858 - 5.38586i) q^{67} +(-1.68469 - 1.96188i) q^{68} +(0.138403 - 0.0799067i) q^{69} +(-2.98420 + 2.11501i) q^{70} +(0.759086 + 1.31478i) q^{71} +(1.76364 + 1.70434i) q^{72} +1.16182 q^{73} +(11.9406 + 5.48538i) q^{74} +(1.26478 + 0.730219i) q^{75} +(2.17467 - 1.86741i) q^{76} -16.8521i q^{77} +(3.26399 + 6.69337i) q^{78} -5.45068 q^{79} +(-1.45340 - 3.72661i) q^{80} +(2.82336 - 4.89021i) q^{81} +(2.32995 - 5.07185i) q^{82} +16.1231i q^{83} +(-1.39653 - 7.42429i) q^{84} +(-1.11975 + 0.646488i) q^{85} +(12.5103 - 8.86650i) q^{86} +(0.644215 + 1.11581i) q^{87} +(17.8802 + 4.46481i) q^{88} +(2.35050 - 4.07118i) q^{89} +(1.00050 - 0.709088i) q^{90} +(-1.51192 + 9.20195i) q^{91} +(-0.0725047 + 0.206498i) q^{92} +(11.0003 + 6.35104i) q^{93} +(0.222788 - 0.0207714i) q^{94} +(-0.716607 - 1.24120i) q^{95} +(8.24722 + 0.485270i) q^{96} +(-0.372104 - 0.644503i) q^{97} +(-0.183388 + 0.399201i) q^{98} +5.64991i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

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 $

$2$	−1.40811	+	0.131283i	−0.995682	+	0.0928314i
$2$	−1.40811	+	0.131283i	−0.995682	+	0.0928314i
$3$	−1.26478	−	0.730219i	−0.730219	−	0.421592i	0.0882835	−	0.996095i	$-0.471862\pi$
$3$	−1.26478	−	0.730219i	−0.730219	−	0.421592i	−0.818502	+	0.574503i	$0.805195\pi$
$4$	1.96553	−	0.369722i	0.982765	−	0.184861i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.87680	+	0.862182i	0.766202	+	0.351984i
$7$	1.29319	+	2.23987i	0.488780	+	0.846592i	0.999917	−	0.0129078i	$-0.00410879\pi$
$7$	1.29319	+	2.23987i	0.488780	+	0.846592i	−0.511137	+	0.859499i	$0.670775\pi$
$8$	−2.71914	+	0.778649i	−0.961360	+	0.275294i
$9$	−0.433561	−	0.750950i	−0.144520	−	0.250317i
$10$	0.131283	+	1.40811i	0.0415154	+	0.445282i
$11$	−5.64276	−	3.25785i	−1.70136	−	0.982279i	−0.944391	−	0.328826i	$-0.893347\pi$
$11$	−5.64276	−	3.25785i	−1.70136	−	0.982279i	−0.756967	−	0.653453i	$-0.773320\pi$
$12$	−2.75593	−	0.967651i	−0.795569	−	0.279337i
$13$	2.78890	+	2.28517i	0.773502	+	0.633793i
$13$	2.78890	+	2.28517i	0.773502	+	0.633793i
$14$	−2.11501	−	2.98420i	−0.565260	−	0.797562i
$15$	−0.730219	+	1.26478i	−0.188542	+	0.326564i
$16$	3.72661	−	1.45340i	0.931653	−	0.363350i
$17$	−0.646488	−	1.11975i	−0.156796	−	0.271579i	0.776915	−	0.629605i	$-0.216783\pi$
$17$	−0.646488	−	1.11975i	−0.156796	−	0.271579i	−0.933712	+	0.358026i	$0.883450\pi$
$18$	0.709088	+	1.00050i	0.167134	+	0.235820i
$19$	1.24120	−	0.716607i	0.284751	−	0.164401i	−0.350822	−	0.936442i	$-0.614098\pi$
$19$	1.24120	−	0.716607i	0.284751	−	0.164401i	0.635572	+	0.772042i	$0.280764\pi$
$20$	−0.369722	−	1.96553i	−0.0826724	−	0.439506i
$21$		−	3.77725i		−	0.824263i
$22$	8.37332	+	3.84660i	1.78520	+	0.820098i
$23$	−0.0547143	+	0.0947679i	−0.0114087	+	0.0197605i	−0.871673	−	0.490087i	$-0.836965\pi$
$23$	−0.0547143	+	0.0947679i	−0.0114087	+	0.0197605i	0.860265	+	0.509848i	$0.170298\pi$
$24$	4.00768	+	1.00075i	0.818065	+	0.204277i
$25$	−1.00000			−0.200000
$26$	−4.22708	−	2.85163i	−0.828998	−	0.559251i
$27$			5.64769i			1.08690i
$28$	3.36993	+	3.92441i	0.636857	+	0.741644i
$29$	−0.764027	−	0.441111i	−0.141876	−	0.0819123i	0.427382	−	0.904071i	$-0.359436\pi$
$29$	−0.764027	−	0.441111i	−0.141876	−	0.0819123i	−0.569258	+	0.822159i	$0.692769\pi$
$30$	0.862182	−	1.87680i	0.157412	−	0.342656i
$31$	−8.69745			−1.56211			−0.781054	−	0.624463i	$-0.785318\pi$
$31$	−8.69745			−1.56211			−0.781054	+	0.624463i	$0.785318\pi$
$32$	−5.05666	+	2.53578i	−0.893900	+	0.448267i
$33$	4.75789	+	8.24090i	0.828242	+	1.43456i
$34$	1.05733	+	1.49186i	0.181330	+	0.255851i
$35$	2.23987	−	1.29319i	0.378607	−	0.218589i
$36$	−1.12982	−	1.31572i	−0.188303	−	0.219286i
$37$	−8.04677	−	4.64580i	−1.32288	−	0.763765i	−0.338693	−	0.940897i	$-0.609985\pi$
$37$	−8.04677	−	4.64580i	−1.32288	−	0.763765i	−0.984187	+	0.177131i	$0.943318\pi$
$38$	−1.65366	+	1.17201i	−0.268259	+	0.190125i
$39$	−1.85866	−	4.92674i	−0.297624	−	0.788910i
$40$	0.778649	+	2.71914i	0.123115	+	0.429933i
$41$	−1.97333	+	3.41791i	−0.308183	+	0.533788i	−0.977965	−	0.208769i	$-0.933054\pi$
$41$	−1.97333	+	3.41791i	−0.308183	+	0.533788i	0.669782	+	0.742558i	$0.266388\pi$
$42$	0.495890	+	5.31877i	0.0765174	+	0.820703i
$43$	−9.38995	+	5.42129i	−1.43195	+	0.826739i	−0.997270	−	0.0738443i	$-0.976473\pi$
$43$	−9.38995	+	5.42129i	−1.43195	+	0.826739i	−0.434684	+	0.900583i	$0.643140\pi$
$44$	−12.2955	−	4.31715i	−1.85362	−	0.650835i
$45$	−0.750950	+	0.433561i	−0.111945	+	0.0646315i
$46$	0.0646021	−	0.140626i	0.00952505	−	0.0207342i
$47$	−0.158218			−0.0230784			−0.0115392	−	0.999933i	$-0.503673\pi$
$47$	−0.158218			−0.0230784			−0.0115392	+	0.999933i	$0.503673\pi$
$48$	−5.77463	−	0.883017i	−0.833496	−	0.127453i
$49$	0.155319	−	0.269021i	0.0221885	−	0.0384315i
$50$	1.40811	−	0.131283i	0.199136	−	0.0185663i
$51$			1.88831i			0.264416i
$52$	6.32655	+	3.46046i	0.877334	+	0.479879i
$53$			0.718497i			0.0986931i	0.998782	+	0.0493466i	$0.0157139\pi$
$53$			0.718497i			0.0986931i	−0.998782	+	0.0493466i	$0.984286\pi$
$54$	−0.741448	−	7.95255i	−0.100898	−	1.08221i
$55$	−3.25785	+	5.64276i	−0.439289	+	0.760870i
$56$	−5.26043	−	5.08357i	−0.702955	−	0.679321i
$57$	−2.09312			−0.277240
$58$	1.13374	+	0.520828i	0.148868	+	0.0683880i
$59$	−5.04877	+	2.91491i	−0.657294	+	0.379489i	−0.791245	−	0.611499i	$-0.790567\pi$
$59$	−5.04877	+	2.91491i	−0.657294	+	0.379489i	0.133951	+	0.990988i	$0.457233\pi$
$60$	−0.967651	+	2.75593i	−0.124923	+	0.355789i
$61$	−0.0201595	+	0.0116391i	−0.00258116	+	0.00149023i	−0.501290	−	0.865279i	$-0.667141\pi$
$61$	−0.0201595	+	0.0116391i	−0.00258116	+	0.00149023i	0.498709	+	0.866770i	$0.333808\pi$
$62$	12.2469	−	1.14183i	1.55536	−	0.145013i
$63$	1.12135	−	1.94224i	0.141277	−	0.244700i
$64$	6.78741	−	4.23451i	0.848426	−	0.529314i
$65$	2.28517	−	2.78890i	0.283441	−	0.345921i
$66$	−7.78151	−	10.9794i	−0.957837	−	1.35148i
$67$	−9.32858	−	5.38586i	−1.13967	−	0.657987i	−0.193319	−	0.981136i	$-0.561925\pi$
$67$	−9.32858	−	5.38586i	−1.13967	−	0.657987i	−0.946348	+	0.323148i	$0.895259\pi$
$68$	−1.68469	−	1.96188i	−0.204298	−	0.237913i
$69$	0.138403	−	0.0799067i	0.0166617	−	0.00961964i
$70$	−2.98420	+	2.11501i	−0.356680	+	0.252792i
$71$	0.759086	+	1.31478i	0.0900869	+	0.156035i	0.907548	−	0.419949i	$-0.137952\pi$
$71$	0.759086	+	1.31478i	0.0900869	+	0.156035i	−0.817461	+	0.575985i	$0.804619\pi$
$72$	1.76364	+	1.70434i	0.207847	+	0.200859i
$73$	1.16182			0.135981			0.0679905	−	0.997686i	$-0.478341\pi$
$73$	1.16182			0.135981			0.0679905	+	0.997686i	$0.478341\pi$
$74$	11.9406	+	5.48538i	1.38807	+	0.637663i
$75$	1.26478	+	0.730219i	0.146044	+	0.0843184i
$76$	2.17467	−	1.86741i	0.249452	−	0.214207i
$77$		−	16.8521i		−	1.92047i
$78$	3.26399	+	6.69337i	0.369574	+	0.757875i
$79$	−5.45068			−0.613250			−0.306625	−	0.951830i	$-0.599200\pi$
$79$	−5.45068			−0.613250			−0.306625	+	0.951830i	$0.599200\pi$
$80$	−1.45340	−	3.72661i	−0.162495	−	0.416648i
$81$	2.82336	−	4.89021i	0.313707	−	0.543357i
$82$	2.32995	−	5.07185i	0.257300	−	0.560092i
$83$			16.1231i			1.76974i	0.465836	+	0.884871i	$0.345754\pi$
$83$			16.1231i			1.76974i	−0.465836	+	0.884871i	$0.654246\pi$
$84$	−1.39653	−	7.42429i	−0.152374	−	0.810056i
$85$	−1.11975	+	0.646488i	−0.121454	+	0.0701215i
$86$	12.5103	−	8.86650i	1.34902	−	0.956099i
$87$	0.644215	+	1.11581i	0.0690671	+	0.119628i
$88$	17.8802	+	4.46481i	1.90603	+	0.475950i
$89$	2.35050	−	4.07118i	0.249152	−	0.431544i	−0.714139	−	0.700004i	$-0.753181\pi$
$89$	2.35050	−	4.07118i	0.249152	−	0.431544i	0.963291	+	0.268460i	$0.0865147\pi$
$90$	1.00050	−	0.709088i	0.105462	−	0.0747444i
$91$	−1.51192	+	9.20195i	−0.158492	+	0.964626i
$92$	−0.0725047	+	0.206498i	−0.00755914	+	0.0215289i
$93$	11.0003	+	6.35104i	1.14068	+	0.658572i
$94$	0.222788	−	0.0207714i	0.0229788	−	0.00214240i
$95$	−0.716607	−	1.24120i	−0.0735223	−	0.127344i
$96$	8.24722	+	0.485270i	0.841728	+	0.0495277i
$97$	−0.372104	−	0.644503i	−0.0377814	−	0.0654394i	0.846516	−	0.532363i	$-0.178696\pi$
$97$	−0.372104	−	0.644503i	−0.0377814	−	0.0654394i	−0.884298	+	0.466923i	$0.845362\pi$
$98$	−0.183388	+	0.399201i	−0.0185250	+	0.0403254i
$99$			5.64991i			0.567838i
$100$	−1.96553	+	0.369722i	−0.196553	+	0.0369722i
$101$	10.4160	+	6.01370i	1.03643	+	0.598385i	0.918821	−	0.394674i	$-0.129143\pi$
$101$	10.4160	+	6.01370i	1.03643	+	0.598385i	0.117613	+	0.993060i	$0.462476\pi$
$102$	−0.247904	−	2.65894i	−0.0245461	−	0.263275i
$103$	−4.16951			−0.410834			−0.205417	−	0.978675i	$-0.565855\pi$
$103$	−4.16951			−0.410834			−0.205417	+	0.978675i	$0.565855\pi$
$104$	−9.36276	−	4.04213i	−0.918094	−	0.396363i
$105$	−3.77725			−0.368621
$106$	−0.0943267	−	1.01172i	−0.00916182	−	0.0982670i
$107$	−5.68516	−	3.28233i	−0.549605	−	0.317315i	0.199358	−	0.979927i	$-0.436114\pi$
$107$	−5.68516	−	3.28233i	−0.549605	−	0.317315i	−0.748963	+	0.662612i	$0.769448\pi$
$108$	2.08808	+	11.1007i	0.200925	+	1.06817i
$109$		−	10.2404i		−	0.980849i	−0.871484	−	0.490425i	$-0.836842\pi$
$109$		−	10.2404i		−	0.980849i	0.871484	−	0.490425i	$-0.163158\pi$
$110$	3.84660	−	8.37332i	0.366759	−	0.798364i
$111$	6.78490	+	11.7518i	0.643995	+	1.11543i
$112$	8.07464	+	6.46761i	0.762982	+	0.611131i
$113$	−0.674343	−	1.16800i	−0.0634369	−	0.109876i	0.832563	−	0.553931i	$-0.186873\pi$
$113$	−0.674343	−	1.16800i	−0.0634369	−	0.109876i	−0.896000	+	0.444055i	$0.853539\pi$
$114$	2.94733	−	0.274792i	0.276043	−	0.0257366i
$115$	0.0947679	+	0.0547143i	0.00883715	+	0.00510213i
$116$	−1.66481	−	0.584540i	−0.154573	−	0.0542731i
$117$	0.506893	−	3.08509i	0.0468622	−	0.285217i
$118$	6.72653	−	4.76732i	0.619227	−	0.438868i
$119$	1.67206	−	2.89610i	0.153278	−	0.265485i
$120$	1.00075	−	4.00768i	0.0913553	−	0.365850i
$121$	15.7272	+	27.2403i	1.42974	+	2.47639i
$122$	0.0268587	−	0.0190357i	0.00243167	−	0.00172341i
$123$	4.99165	−	2.88193i	0.450082	−	0.259855i
$124$	−17.0951	+	3.21564i	−1.53519	+	0.288773i
$125$			1.00000i			0.0894427i
$126$	−1.32400	+	2.88210i	−0.117952	+	0.256758i
$127$	7.84112	−	13.5812i	0.695787	−	1.20514i	−0.274127	−	0.961693i	$-0.588389\pi$
$127$	7.84112	−	13.5812i	0.695787	−	1.20514i	0.969915	−	0.243445i	$-0.0782776\pi$
$128$	−9.00148	+	6.85371i	−0.795626	+	0.605788i
$129$	15.8349			1.39419
$130$	−2.85163	+	4.22708i	−0.250105	+	0.370739i
$131$		−	16.0987i		−	1.40655i	−0.710919	−	0.703274i	$-0.751721\pi$
$131$		−	16.0987i		−	1.40655i	0.710919	−	0.703274i	$-0.248279\pi$
$132$	12.3986	+	14.4386i	1.07916	+	1.25672i
$133$	3.21021	+	1.85342i	0.278361	+	0.160712i
$134$	13.8427	+	6.35918i	1.19583	+	0.549349i
$135$	5.64769			0.486076
$136$	2.62978	+	2.54137i	0.225502	+	0.217920i
$137$	−9.15888	−	15.8636i	−0.782496	−	1.35532i	−0.930484	−	0.366333i	$-0.880613\pi$
$137$	−9.15888	−	15.8636i	−0.782496	−	1.35532i	0.147988	−	0.988989i	$-0.452720\pi$
$138$	−0.184395	+	0.130687i	−0.0156968	+	0.0111248i
$139$	16.7206	−	9.65363i	1.41822	−	0.818810i	0.422079	−	0.906559i	$-0.361301\pi$
$139$	16.7206	−	9.65363i	1.41822	−	0.818810i	0.996143	+	0.0877487i	$0.0279672\pi$
$140$	3.92441	−	3.36993i	0.331673	−	0.284811i
$141$	0.200110	+	0.115534i	0.0168523	+	0.00972969i
$142$	−1.24148	−	1.75169i	−0.104183	−	0.146998i
$143$	−8.29236	−	21.9805i	−0.693442	−	1.83810i
$144$	−2.70715	−	2.16836i	−0.225595	−	0.180697i
$145$	−0.441111	+	0.764027i	−0.0366323	+	0.0634490i
$146$	−1.63597	+	0.152528i	−0.135394	+	0.0126233i
$147$	−0.392888	+	0.226834i	−0.0324049	+	0.0187090i
$148$	−17.5338	−	6.15640i	−1.44127	−	0.506053i
$149$	−7.91859	+	4.57180i	−0.648716	+	0.374536i	−0.787964	−	0.615721i	$-0.788865\pi$
$149$	−7.91859	+	4.57180i	−0.648716	+	0.374536i	0.139248	+	0.990258i	$0.455531\pi$
$150$	−1.87680	−	0.862182i	−0.153240	−	0.0703969i
$151$	12.5324			1.01987			0.509936	−	0.860212i	$-0.329669\pi$
$151$	12.5324			1.01987			0.509936	+	0.860212i	$0.329669\pi$
$152$	−2.81700	+	2.91501i	−0.228489	+	0.236439i
$153$	−0.560585	+	0.970961i	−0.0453206	+	0.0784976i
$154$	2.21240	+	23.7295i	0.178280	+	1.91218i
$155$			8.69745i			0.698596i
$156$	−5.47477	−	8.99647i	−0.438333	−	0.720294i
$157$		−	6.47168i		−	0.516496i	−0.966079	−	0.258248i	$-0.916855\pi$
$157$		−	6.47168i		−	0.516496i	0.966079	−	0.258248i	$-0.0831452\pi$
$158$	7.67514	−	0.715584i	0.610602	−	0.0569288i
$159$	0.524660	−	0.908737i	0.0416082	−	0.0720676i
$160$	2.53578	+	5.05666i	0.200471	+	0.399764i
$161$	−0.283024			−0.0223054
$162$	−3.33360	+	7.25660i	−0.261912	+	0.570132i
$163$	5.38381	−	3.10835i	0.421693	−	0.243464i	−0.274108	−	0.961699i	$-0.588383\pi$
$163$	5.38381	−	3.10835i	0.421693	−	0.243464i	0.695801	+	0.718234i	$0.255049\pi$
$164$	−2.61497	+	7.44759i	−0.204195	+	0.581559i
$165$	8.24090	−	4.75789i	0.641553	−	0.370401i
$166$	−2.11670	−	22.7031i	−0.164288	−	1.76210i
$167$	8.98486	−	15.5622i	0.695270	−	1.20424i	−0.274820	−	0.961496i	$-0.588618\pi$
$167$	8.98486	−	15.5622i	0.695270	−	1.20424i	0.970090	−	0.242747i	$-0.0780484\pi$
$168$	2.94115	+	10.2708i	0.226915	+	0.792413i
$169$	2.55595	+	12.7463i	0.196612	+	0.980481i
$170$	1.49186	−	1.05733i	0.114420	−	0.0810934i
$171$	−1.07627	−	0.621386i	−0.0823046	−	0.0475186i
$172$	−16.4518	+	14.1274i	−1.25444	+	1.07720i
$173$	−12.7252	+	7.34688i	−0.967477	+	0.558573i	−0.898466	−	0.439043i	$-0.855318\pi$
$173$	−12.7252	+	7.34688i	−0.967477	+	0.558573i	−0.0690106	+	0.997616i	$0.521984\pi$
$174$	−1.05361	−	1.48661i	−0.0798741	−	0.112700i
$175$	−1.29319	−	2.23987i	−0.0977560	−	0.169318i
$176$	−25.7633	−	3.93956i	−1.94199	−	0.296955i
$177$	8.51409			0.639958
$178$	−2.77527	+	6.04124i	−0.208016	+	0.452810i
$179$	15.2694	+	8.81579i	1.14129	+	0.658923i	0.946749	−	0.321972i	$-0.104346\pi$
$179$	15.2694	+	8.81579i	1.14129	+	0.658923i	0.194539	+	0.980895i	$0.437679\pi$
$180$	−1.31572	+	1.12982i	−0.0980678	+	0.0842118i
$181$		−	19.2558i		−	1.43127i	−0.698475	−	0.715635i	$-0.746137\pi$
$181$		−	19.2558i		−	1.43127i	0.698475	−	0.715635i	$-0.253863\pi$
$182$	0.920877	−	13.1558i	0.0682599	−	0.975174i
$183$	0.0339963			0.00251308
$184$	0.0749846	−	0.300290i	0.00552794	−	0.0221377i
$185$	−4.64580	+	8.04677i	−0.341566	+	0.591610i
$186$	−16.3234	−	7.49879i	−1.19689	−	0.549838i
$187$			8.42465i			0.616071i
$188$	−0.310982	+	0.0584966i	−0.0226807	+	0.00426630i
$189$	−12.6501	+	7.30354i	−0.920159	+	0.531254i
$190$	1.17201	+	1.65366i	0.0850264	+	0.119969i
$191$	−9.34869	−	16.1924i	−0.676448	−	1.17164i	−0.976044	−	0.217575i	$-0.930185\pi$
$191$	−9.34869	−	16.1924i	−0.676448	−	1.17164i	0.299596	−	0.954066i	$-0.403148\pi$
$192$	−11.6767	+	0.399410i	−0.842691	+	0.0288250i
$193$	−3.47030	+	6.01074i	−0.249798	+	0.432662i	−0.963470	−	0.267818i	$-0.913697\pi$
$193$	−3.47030	+	6.01074i	−0.249798	+	0.432662i	0.713672	+	0.700480i	$0.247031\pi$
$194$	0.608575	+	0.858678i	0.0436931	+	0.0616495i
$195$	−4.92674	+	1.85866i	−0.352811	+	0.133101i
$196$	0.205822	−	0.586193i	0.0147015	−	0.0418709i
$197$	23.1308	+	13.3546i	1.64800	+	0.951474i	0.977865	+	0.209237i	$0.0670980\pi$
$197$	23.1308	+	13.3546i	1.64800	+	0.951474i	0.670137	+	0.742238i	$0.266235\pi$
$198$	−0.741740	−	7.95568i	−0.0527132	−	0.565386i
$199$	−4.55395	−	7.88767i	−0.322821	−	0.559142i	0.658248	−	0.752801i	$-0.271298\pi$
$199$	−4.55395	−	7.88767i	−0.322821	−	0.559142i	−0.981069	+	0.193659i	$0.937964\pi$
$200$	2.71914	−	0.778649i	0.192272	−	0.0550588i
$201$	7.86571	+	13.6238i	0.554804	+	0.960950i
$202$	−15.4564	−	7.10048i	−1.08751	−	0.499588i
$203$		−	2.28176i		−	0.160148i
$204$	0.698150	+	3.71153i	0.0488803	+	0.259859i
$205$	3.41791	+	1.97333i	0.238717	+	0.137824i
$206$	5.87112	−	0.547387i	0.409060	−	0.0381383i
$207$	0.0948879			0.00659517
$208$	13.7144	+	4.46257i	0.950924	+	0.309424i
$209$	−9.33839			−0.645950
$210$	5.31877	−	0.495890i	0.367030	−	0.0342196i
$211$	6.64036	+	3.83381i	0.457141	+	0.263931i	0.710842	−	0.703352i	$-0.248314\pi$
$211$	6.64036	+	3.83381i	0.457141	+	0.263931i	−0.253700	+	0.967283i	$0.581648\pi$
$212$	0.265644	+	1.41223i	0.0182445	+	0.0969921i
$213$		−	2.21720i		−	0.151920i
$214$	8.43623	+	3.87550i	0.576688	+	0.264924i
$215$	5.42129	+	9.38995i	0.369729	+	0.640389i
$216$	−4.39757	−	15.3568i	−0.299217	−	1.04490i
$217$	−11.2475	−	19.4812i	−0.763527	−	1.32247i
$218$	1.34439	+	14.4195i	0.0910536	+	0.976614i
$219$	−1.46944	−	0.848384i	−0.0992959	−	0.0573285i
$220$	−4.31715	+	12.2955i	−0.291062	+	0.828964i
$221$	0.755833	−	4.60021i	0.0508428	−	0.309444i
$222$	−11.0967	−	15.6570i	−0.744761	−	1.05083i
$223$	−10.8061	+	18.7168i	−0.723631	+	1.25337i	0.235903	+	0.971777i	$0.424195\pi$
$223$	−10.8061	+	18.7168i	−0.723631	+	1.25337i	−0.959535	+	0.281590i	$0.909138\pi$
$224$	−12.2190	−	8.04701i	−0.816419	−	0.537664i
$225$	0.433561	+	0.750950i	0.0289041	+	0.0500634i
$226$	1.10289	+	1.55613i	0.0733629	+	0.103513i
$227$	−15.0034	+	8.66222i	−0.995811	+	0.574932i	−0.907006	−	0.421117i	$-0.861638\pi$
$227$	−15.0034	+	8.66222i	−0.995811	+	0.574932i	−0.0888049	+	0.996049i	$0.528305\pi$
$228$	−4.11409	+	0.773872i	−0.272462	+	0.0512509i
$229$			11.5667i			0.764346i	0.924091	+	0.382173i	$0.124824\pi$
$229$			11.5667i			0.764346i	−0.924091	+	0.382173i	$0.875176\pi$
$230$	−0.140626	−	0.0646021i	−0.00927263	−	0.00425973i
$231$	−12.3057	+	21.3141i	−0.809656	+	1.40237i
$232$	2.42097	+	0.604533i	0.158944	+	0.0396895i
$233$	3.13608			0.205452			0.102726	−	0.994710i	$-0.467244\pi$
$233$	3.13608			0.205452			0.102726	+	0.994710i	$0.467244\pi$
$234$	−0.308738	+	4.41068i	−0.0201828	+	0.288335i
$235$			0.158218i			0.0103210i
$236$	−8.84580	+	7.59598i	−0.575813	+	0.494456i
$237$	6.89389	+	3.98019i	0.447806	+	0.258541i
$238$	−1.97424	+	4.29753i	−0.127971	+	0.278568i
$239$	−18.2643			−1.18142			−0.590710	−	0.806884i	$-0.701152\pi$
$239$	−18.2643			−1.18142			−0.590710	+	0.806884i	$0.701152\pi$
$240$	−0.883017	+	5.77463i	−0.0569985	+	0.372751i
$241$	−7.18424	−	12.4435i	−0.462778	−	0.801555i	0.536320	−	0.844014i	$-0.319814\pi$
$241$	−7.18424	−	12.4435i	−0.462778	−	0.801555i	−0.999098	+	0.0424599i	$0.986481\pi$
$242$	−25.7218	−	36.2925i	−1.65346	−	2.33297i
$243$	7.53128	−	4.34819i	0.483132	−	0.278936i
$244$	−0.0353208	+	0.0303304i	−0.00226119	+	0.00194170i
$245$	−0.269021	−	0.155319i	−0.0171871	−	0.00992298i
$246$	−6.65042	+	4.71338i	−0.424016	+	0.300514i
$247$	5.09915	+	0.837811i	0.324451	+	0.0533086i
$248$	23.6496	−	6.77227i	1.50175	−	0.430039i
$249$	11.7734	−	20.3921i	0.746109	−	1.29230i
$250$	−0.131283	−	1.40811i	−0.00830309	−	0.0890565i
$251$	13.4916	−	7.78938i	0.851582	−	0.491661i	−0.00960199	−	0.999954i	$-0.503056\pi$
$251$	13.4916	−	7.78938i	0.851582	−	0.491661i	0.861184	+	0.508293i	$0.169723\pi$
$252$	1.48597	−	4.23213i	0.0936070	−	0.266599i
$253$	0.617479	−	0.356502i	0.0388206	−	0.0224131i
$254$	−9.25815	+	20.1532i	−0.580908	+	1.26453i
$255$	1.88831			0.118251
$256$	11.7753	−	10.8325i	0.735954	−	0.677032i
$257$	−11.5051	+	19.9274i	−0.717669	+	1.24304i	0.244252	+	0.969712i	$0.421458\pi$
$257$	−11.5051	+	19.9274i	−0.717669	+	1.24304i	−0.961921	+	0.273328i	$0.911876\pi$
$258$	−22.2972	+	2.07886i	−1.38817	+	0.129424i
$259$		−	24.0316i		−	1.49325i
$260$	3.46046	−	6.32655i	0.214609	−	0.392356i
$261$			0.764995i			0.0473520i
$262$	2.11349	+	22.6686i	0.130572	+	1.40047i
$263$	2.76189	−	4.78374i	0.170306	−	0.294978i	−0.768221	−	0.640185i	$-0.778858\pi$
$263$	2.76189	−	4.78374i	0.170306	−	0.294978i	0.938527	+	0.345207i	$0.112191\pi$
$264$	−19.3541	−	18.7034i	−1.19116	−	1.15112i
$265$	0.718497			0.0441369
$266$	−4.76364	−	2.18836i	−0.292078	−	0.134177i
$267$	−5.94571	+	3.43276i	−0.363871	+	0.210081i
$268$	−20.3269	−	7.13708i	−1.24166	−	0.435967i
$269$	−11.7100	+	6.76077i	−0.713971	+	0.412211i	−0.812530	−	0.582920i	$-0.801910\pi$
$269$	−11.7100	+	6.76077i	−0.713971	+	0.412211i	0.0985587	+	0.995131i	$0.468577\pi$
$270$	−7.95255	+	0.741448i	−0.483977	+	0.0451231i
$271$	−4.70750	+	8.15362i	−0.285960	+	0.495297i	−0.972842	−	0.231472i	$-0.925646\pi$
$271$	−4.70750	+	8.15362i	−0.285960	+	0.495297i	0.686882	+	0.726769i	$0.258979\pi$
$272$	−4.03665	−	3.23327i	−0.244758	−	0.196046i
$273$	8.63167	−	10.5344i	0.522412	−	0.637569i
$274$	14.9793	+	21.1353i	0.904933	+	1.27683i
$275$	5.64276	+	3.25785i	0.340271	+	0.196456i
$276$	0.242491	−	0.208229i	0.0145962	−	0.0125339i
$277$	15.7554	−	9.09640i	0.946652	−	0.546550i	0.0546124	−	0.998508i	$-0.482608\pi$
$277$	15.7554	−	9.09640i	0.946652	−	0.546550i	0.892039	+	0.451958i	$0.149274\pi$
$278$	−22.2770	+	15.7885i	−1.33609	+	0.946930i
$279$	3.77088	+	6.53136i	0.225757	+	0.391022i
$280$	−5.08357	+	5.26043i	−0.303802	+	0.314371i
$281$	−32.0610			−1.91260			−0.956300	−	0.292389i	$-0.905550\pi$
$281$	−32.0610			−1.91260			−0.956300	+	0.292389i	$0.905550\pi$
$282$	−0.296944	−	0.136413i	−0.0176828	−	0.00812325i
$283$	11.8649	+	6.85017i	0.705292	+	0.407201i	0.809315	−	0.587374i	$-0.199838\pi$
$283$	11.8649	+	6.85017i	0.705292	+	0.407201i	−0.104023	+	0.994575i	$0.533172\pi$
$284$	1.97811	+	2.30358i	0.117379	+	0.136692i
$285$			2.09312i			0.123986i
$286$	14.5622	+	29.8623i	0.861081	+	1.76579i
$287$	−10.2076			−0.602534
$288$	4.09662	+	2.69788i	0.241396	+	0.158974i
$289$	7.66411	−	13.2746i	0.450830	−	0.780860i
$290$	0.520828	−	1.13374i	0.0305841	−	0.0665757i
$291$			1.08687i			0.0637134i
$292$	2.28360	−	0.429551i	0.133637	−	0.0251376i
$293$	21.9551	−	12.6758i	1.28263	−	0.740527i	0.305301	−	0.952256i	$-0.401243\pi$
$293$	21.9551	−	12.6758i	1.28263	−	0.740527i	0.977328	+	0.211729i	$0.0679095\pi$
$294$	0.523449	−	0.370986i	0.0305281	−	0.0216364i
$295$	2.91491	+	5.04877i	0.169713	+	0.293951i
$296$	25.4977	+	6.36696i	1.48202	+	0.370072i
$297$	18.3993	−	31.8686i	1.06764	−	1.84920i
$298$	10.5500	−	7.47716i	0.611146	−	0.433140i
$299$	−0.369154	+	0.139267i	−0.0213487	+	0.00805400i
$300$	2.75593	+	0.967651i	0.159114	+	0.0558673i
$301$	−24.2860	−	14.0215i	−1.39982	−	0.808187i
$302$	−17.6469	+	1.64530i	−1.01547	+	0.0946761i
$303$	−8.78263	−	15.2120i	−0.504549	−	0.873904i
$304$	3.58395	−	4.47447i	0.205554	−	0.256629i
$305$	0.0116391	+	0.0201595i	0.000666452	+	0.00115433i
$306$	0.661892	−	1.44081i	0.0378379	−	0.0823658i
$307$			4.55656i			0.260057i	0.991510	+	0.130028i	$0.0415069\pi$
$307$			4.55656i			0.260057i	−0.991510	+	0.130028i	$0.958493\pi$
$308$	−6.23059	−	33.1233i	−0.355021	−	1.88737i
$309$	5.27350	+	3.04465i	0.299999	+	0.173204i
$310$	−1.14183	−	12.2469i	−0.0648516	−	0.695580i
$311$	19.6323			1.11324			0.556622	−	0.830766i	$-0.312097\pi$
$311$	19.6323			1.11324			0.556622	+	0.830766i	$0.312097\pi$
$312$	8.89015	+	11.9492i	0.503306	+	0.676493i
$313$	−22.6549			−1.28053			−0.640265	−	0.768154i	$-0.721176\pi$
$313$	−22.6549			−1.28053			−0.640265	+	0.768154i	$0.721176\pi$
$314$	0.849624	+	9.11281i	0.0479470	+	0.514266i
$315$	−1.94224	−	1.12135i	−0.109433	−	0.0631812i
$316$	−10.7135	+	2.01524i	−0.602680	+	0.113366i
$317$		−	1.26977i		−	0.0713175i	−0.999364	−	0.0356587i	$-0.988647\pi$
$317$		−	1.26977i		−	0.0713175i	0.999364	−	0.0356587i	$-0.0113529\pi$
$318$	−0.619475	+	1.34848i	−0.0347384	+	0.0756189i
$319$	2.87415	+	4.97817i	0.160922	+	0.278724i
$320$	−4.23451	−	6.78741i	−0.236716	−	0.379428i
$321$	4.79363	+	8.30282i	0.267555	+	0.463418i
$322$	0.398528	−	0.0371563i	0.0222091	−	0.00207064i
$323$	−1.60484	−	0.926556i	−0.0892958	−	0.0515549i
$324$	3.74139	−	10.6557i	0.207855	−	0.591984i
$325$	−2.78890	−	2.28517i	−0.154700	−	0.126759i
$326$	−7.17291	+	5.08369i	−0.397271	+	0.281559i
$327$	−7.47771	+	12.9518i	−0.413518	+	0.716234i
$328$	2.70441	−	10.8303i	0.149326	−	0.598004i
$329$	−0.204606	−	0.354388i	−0.0112803	−	0.0195380i
$330$	−10.9794	+	7.78151i	−0.604398	+	0.428358i
$331$	3.63293	−	2.09747i	0.199684	−	0.115288i	−0.396824	−	0.917895i	$-0.629888\pi$
$331$	3.63293	−	2.09747i	0.199684	−	0.115288i	0.596508	+	0.802607i	$0.296554\pi$
$332$	5.96107	+	31.6905i	0.327156	+	1.73924i
$333$			8.05696i			0.441519i
$334$	−10.6086	+	23.0929i	−0.580476	+	1.26359i
$335$	−5.38586	+	9.32858i	−0.294261	+	0.509675i
$336$	−5.48985	−	14.0763i	−0.299496	−	0.767927i
$337$	−13.0294			−0.709755			−0.354877	−	0.934913i	$-0.615477\pi$
$337$	−13.0294			−0.709755			−0.354877	+	0.934913i	$0.615477\pi$
$338$	−5.27242	−	17.6125i	−0.286782	−	0.957996i
$339$			1.96967i			0.106978i
$340$	−1.96188	+	1.68469i	−0.106398	+	0.0913650i
$341$	49.0777	+	28.3350i	2.65771	+	1.53443i
$342$	1.59708	+	0.733681i	0.0863604	+	0.0396729i
$343$	18.9081			1.02094
$344$	21.3113	−	22.0527i	1.14903	−	1.18900i
$345$	−0.0799067	−	0.138403i	−0.00430203	−	0.00745134i
$346$	16.9539	−	12.0158i	0.911446	−	0.645973i
$347$	4.31466	−	2.49107i	0.231623	−	0.133728i	−0.379698	−	0.925111i	$-0.623972\pi$
$347$	4.31466	−	2.49107i	0.231623	−	0.133728i	0.611321	+	0.791383i	$0.290639\pi$
$348$	1.67877	+	1.95498i	0.0899913	+	0.104798i
$349$	−22.3448	−	12.9008i	−1.19609	−	0.690562i	−0.236408	−	0.971654i	$-0.575970\pi$
$349$	−22.3448	−	12.9008i	−1.19609	−	0.690562i	−0.959681	+	0.281092i	$0.909304\pi$
$350$	2.11501	+	2.98420i	0.113052	+	0.159512i
$351$	−12.9060	+	15.7509i	−0.688869	+	0.840719i
$352$	36.7947	+	2.16502i	1.96117	+	0.115396i
$353$	4.29278	−	7.43531i	0.228481	−	0.395742i	−0.728877	−	0.684645i	$-0.759957\pi$
$353$	4.29278	−	7.43531i	0.228481	−	0.395742i	0.957358	+	0.288903i	$0.0932906\pi$
$354$	−11.9887	+	1.11776i	−0.637194	+	0.0594082i
$355$	1.31478	−	0.759086i	0.0697810	−	0.0402881i
$356$	3.11477	−	8.87106i	0.165082	−	0.470165i
$357$	−4.22957	+	2.44195i	−0.223853	+	0.129241i
$358$	−22.6583	−	10.4090i	−1.19753	−	0.550130i
$359$	−16.1795			−0.853921			−0.426960	−	0.904270i	$-0.640416\pi$
$359$	−16.1795			−0.853921			−0.426960	+	0.904270i	$0.640416\pi$
$360$	1.70434	−	1.76364i	0.0898268	−	0.0929520i
$361$	−8.47295	+	14.6756i	−0.445945	+	0.772399i
$362$	2.52796	+	27.1142i	0.132867	+	1.42509i
$363$		−	45.9372i		−	2.41108i
$364$	0.430447	+	18.6457i	0.0225615	+	0.977299i
$365$		−	1.16182i		−	0.0608125i
$366$	−0.0478704	+	0.00446315i	−0.00250223	+	0.000233293i
$367$	9.20853	−	15.9496i	0.480682	−	0.832565i	−0.519073	−	0.854730i	$-0.673723\pi$
$367$	9.20853	−	15.9496i	0.480682	−	0.832565i	0.999754	+	0.0221652i	$0.00705599\pi$
$368$	−0.0661632	+	0.432685i	−0.00344900	+	0.0225552i
$369$	3.42224			0.178155
$370$	5.48538	−	11.9406i	0.285171	−	0.620764i
$371$	−1.60934	+	0.929153i	−0.0835528	+	0.0482392i
$372$	23.9696	+	8.41610i	1.24277	+	0.436354i
$373$	−2.89710	+	1.67264i	−0.150006	+	0.0866060i	−0.573124	−	0.819468i	$-0.694269\pi$
$373$	−2.89710	+	1.67264i	−0.150006	+	0.0866060i	0.423118	+	0.906074i	$0.360935\pi$
$374$	−1.10602	−	11.8628i	−0.0571908	−	0.613411i
$375$	0.730219	−	1.26478i	0.0377083	−	0.0653127i
$376$	0.430216	−	0.123196i	0.0221867	−	0.00635336i
$377$	−1.12278	−	2.97615i	−0.0578262	−	0.153280i
$378$	16.8539	−	11.9449i	0.866869	−	0.614380i
$379$	6.59316	+	3.80657i	0.338668	+	0.195530i	0.659683	−	0.751544i	$-0.270691\pi$
$379$	6.59316	+	3.80657i	0.338668	+	0.195530i	−0.321015	+	0.947074i	$0.604024\pi$
$380$	−1.86741	−	2.17467i	−0.0957961	−	0.111558i
$381$	−19.8345	+	11.4515i	−1.01615	+	0.586677i
$382$	15.2897	+	21.5733i	0.782292	+	1.10379i
$383$	1.46609	+	2.53935i	0.0749140	+	0.129755i	0.901049	−	0.433718i	$-0.142798\pi$
$383$	1.46609	+	2.53935i	0.0749140	+	0.129755i	−0.826135	+	0.563472i	$0.809465\pi$
$384$	16.3896	−	2.09536i	0.836376	−	0.106929i
$385$	−16.8521			−0.858862
$386$	4.09745	−	8.91936i	0.208554	−	0.453983i
$387$	8.14224	+	4.70092i	0.413893	+	0.238961i
$388$	−0.969669	−	1.12921i	−0.0492275	−	0.0573272i
$389$			9.79848i			0.496803i	0.968657	+	0.248401i	$0.0799052\pi$
$389$			9.79848i			0.496803i	−0.968657	+	0.248401i	$0.920095\pi$
$390$	6.69337	−	3.26399i	0.338932	−	0.165279i
$391$	0.141488			0.00715538
$392$	−0.212861	+	0.852444i	−0.0107511	+	0.0430549i
$393$	−11.7556	+	20.3612i	−0.592989	+	1.02709i
$394$	−34.3239	−	15.7680i	−1.72921	−	0.794379i
$395$			5.45068i			0.274254i
$396$	2.08890	+	11.1051i	0.104971	+	0.558051i
$397$	−27.7473	+	16.0199i	−1.39260	+	0.804016i	−0.993602	−	0.112937i	$-0.963974\pi$
$397$	−27.7473	+	16.0199i	−1.39260	+	0.804016i	−0.398995	+	0.916953i	$0.630641\pi$
$398$	7.44796	+	10.5088i	0.373333	+	0.526759i
$399$	−2.70680	−	4.68831i	−0.135509	−	0.234709i
$400$	−3.72661	+	1.45340i	−0.186331	+	0.0726699i
$401$	−3.13401	+	5.42827i	−0.156505	+	0.271075i	−0.933606	−	0.358301i	$-0.883356\pi$
$401$	−3.13401	+	5.42827i	−0.156505	+	0.271075i	0.777101	+	0.629376i	$0.216689\pi$
$402$	−12.8643	−	18.1511i	−0.641615	−	0.905297i
$403$	−24.2563	−	19.8752i	−1.20829	−	0.990054i
$404$	22.6964	+	7.96906i	1.12919	+	0.396476i
$405$	−4.89021	−	2.82336i	−0.242997	−	0.140294i
$406$	0.299558	+	3.21297i	0.0148668	+	0.159457i
$407$	30.2707	+	52.4303i	1.50046	+	2.59888i
$408$	−1.47033	−	5.13458i	−0.0727923	−	0.254199i
$409$	8.51090	+	14.7413i	0.420837	+	0.728911i	0.996022	−	0.0891127i	$-0.0284031\pi$
$409$	8.51090	+	14.7413i	0.420837	+	0.728911i	−0.575185	+	0.818024i	$0.695070\pi$
$410$	−5.07185	−	2.32995i	−0.250481	−	0.115068i
$411$			26.7519i			1.31958i
$412$	−8.19529	+	1.54156i	−0.403753	+	0.0759472i
$413$	−13.0580	−	7.53906i	−0.642544	−	0.370973i
$414$	−0.133612	+	0.0124572i	−0.00656669	+	0.000612238i
$415$	16.1231			0.791453
$416$	−19.8972	−	4.48330i	−0.975542	−	0.219812i
$417$	−28.1971			−1.38082
$418$	13.1495	−	1.22598i	0.643161	−	0.0599644i
$419$	−28.9698	−	16.7257i	−1.41527	−	0.817106i	−0.419391	−	0.907806i	$-0.637756\pi$
$419$	−28.9698	−	16.7257i	−1.41527	−	0.817106i	−0.995878	+	0.0906996i	$0.971090\pi$
$420$	−7.42429	+	1.39653i	−0.362268	+	0.0681437i
$421$			26.3486i			1.28415i	0.766640	+	0.642077i	$0.221927\pi$
$421$			26.3486i			1.28415i	−0.766640	+	0.642077i	$0.778073\pi$
$422$	−9.85365	−	4.52665i	−0.479668	−	0.220354i
$423$	0.0685972	+	0.118814i	0.00333531	+	0.00577692i
$424$	−0.559457	−	1.95369i	−0.0271696	−	0.0948796i
$425$	0.646488	+	1.11975i	0.0313593	+	0.0543159i
$426$	0.291081	+	3.12205i	0.0141029	+	0.151264i
$427$	−0.0521401	−	0.0301031i	−0.00252324	−	0.00145679i
$428$	−12.3879	−	4.34958i	−0.598791	−	0.210245i
$429$	−5.56262	+	33.8557i	−0.268566	+	1.63457i
$430$	−8.86650	−	12.5103i	−0.427580	−	0.603301i
$431$	13.8867	−	24.0525i	0.668900	−	1.15857i	−0.309311	−	0.950961i	$-0.600099\pi$
$431$	13.8867	−	24.0525i	0.668900	−	1.15857i	0.978212	−	0.207609i	$-0.0665681\pi$
$432$	8.20835	+	21.0467i	0.394924	+	1.01261i
$433$	−2.84345	−	4.92500i	−0.136647	−	0.236680i	0.789578	−	0.613650i	$-0.210299\pi$
$433$	−2.84345	−	4.92500i	−0.136647	−	0.236680i	−0.926226	+	0.376970i	$0.876966\pi$
$434$	18.3952	+	25.9550i	0.882997	+	1.24588i
$435$	1.11581	−	0.644215i	0.0534992	−	0.0308878i
$436$	−3.78609	−	20.1277i	−0.181321	−	0.963944i
$437$			0.156834i			0.00750241i
$438$	2.18051	+	1.00170i	0.104189	+	0.0478632i
$439$	7.71290	−	13.3591i	0.368116	−	0.637596i	−0.621155	−	0.783688i	$-0.713336\pi$
$439$	7.71290	−	13.3591i	0.368116	−	0.637596i	0.989271	+	0.146092i	$0.0466694\pi$
$440$	4.46481	−	17.8802i	0.212851	−	0.852404i
$441$	−0.269362			−0.0128267
$442$	−0.460362	+	6.57682i	−0.0218972	+	0.312827i
$443$			14.2242i			0.675811i	0.941180	+	0.337906i	$0.109718\pi$
$443$			14.2242i			0.675811i	−0.941180	+	0.337906i	$0.890282\pi$
$444$	17.6808	+	20.5900i	0.839095	+	0.977157i
$445$	−4.07118	−	2.35050i	−0.192993	−	0.111424i
$446$	12.7590	−	27.7739i	0.604155	−	1.31513i
$447$	13.3537			0.631606
$448$	18.2622	+	9.72690i	0.862806	+	0.459553i
$449$	5.40824	+	9.36735i	0.255231	+	0.442073i	0.964958	−	0.262404i	$-0.0845152\pi$
$449$	5.40824	+	9.36735i	0.255231	+	0.442073i	−0.709727	+	0.704476i	$0.751182\pi$
$450$	−0.709088	−	1.00050i	−0.0334267	−	0.0471640i
$451$	22.2701	−	12.8577i	1.04866	−	0.605443i
$452$	−1.75728	−	2.04641i	−0.0826553	−	0.0962552i
$453$	−15.8507	−	9.15139i	−0.744729	−	0.429970i
$454$	19.9892	−	14.1670i	0.938139	−	0.664892i
$455$	9.20195	+	1.51192i	0.431394	+	0.0708797i
$456$	5.69147	−	1.62981i	0.266528	−	0.0763226i
$457$	20.5457	−	35.5862i	0.961087	−	1.66465i	0.241307	−	0.970449i	$-0.422424\pi$
$457$	20.5457	−	35.5862i	0.961087	−	1.66465i	0.719780	−	0.694202i	$-0.244243\pi$
$458$	−1.51851	−	16.2871i	−0.0709553	−	0.761046i
$459$	6.32400	−	3.65117i	0.295179	−	0.170422i
$460$	0.206498	+	0.0725047i	0.00962802	+	0.00338055i
$461$	29.9669	−	17.3014i	1.39570	−	0.805807i	0.401760	−	0.915745i	$-0.368398\pi$
$461$	29.9669	−	17.3014i	1.39570	−	0.805807i	0.993938	+	0.109938i	$0.0350651\pi$
$462$	14.5296	−	31.6281i	0.675976	−	1.47147i
$463$	10.7326			0.498787			0.249393	−	0.968402i	$-0.419769\pi$
$463$	10.7326			0.498787			0.249393	+	0.968402i	$0.419769\pi$
$464$	−3.48834	−	0.533414i	−0.161942	−	0.0247631i
$465$	6.35104	−	11.0003i	0.294523	−	0.510128i
$466$	−4.41594	+	0.411716i	−0.204565	+	0.0190724i
$467$			2.65779i			0.122988i	0.998107	+	0.0614940i	$0.0195865\pi$
$467$			2.65779i			0.122988i	−0.998107	+	0.0614940i	$0.980414\pi$
$468$	−0.144314	−	6.25125i	−0.00667090	−	0.288964i
$469$		−	27.8598i		−	1.28644i
$470$	−0.0207714	−	0.222788i	−0.000958112	−	0.0102764i
$471$	−4.72574	+	8.18522i	−0.217751	+	0.377155i
$472$	11.4586	−	11.8573i	0.527425	−	0.545775i
$473$	70.6470			3.24835
$474$	−10.2299	−	4.69948i	−0.469873	−	0.215854i
$475$	−1.24120	+	0.716607i	−0.0569501	+	0.0328802i
$476$	2.21574	−	6.31057i	0.101558	−	0.289244i
$477$	0.539555	−	0.311512i	0.0247045	−	0.0142632i
$478$	25.7181	−	2.39780i	1.17632	−	0.109673i
$479$	9.48519	−	16.4288i	0.433389	−	0.750652i	−0.563773	−	0.825930i	$-0.690651\pi$
$479$	9.48519	−	16.4288i	0.433389	−	0.750652i	0.997163	+	0.0752772i	$0.0239842\pi$
$480$	0.485270	−	8.24722i	0.0221494	−	0.376432i
$481$	−11.8252	−	31.3450i	−0.539182	−	1.42921i
$482$	11.7498	+	16.5786i	0.535189	+	0.755133i
$483$	0.357962	+	0.206669i	0.0162878	+	0.00940377i
$484$	40.9836	+	47.7269i	1.86289	+	2.16940i
$485$	−0.644503	+	0.372104i	−0.0292654	+	0.0168964i
$486$	−10.0340	+	7.11145i	−0.455152	+	0.322582i
$487$	13.0850	+	22.6638i	0.592936	+	1.02700i	0.993835	+	0.110873i	$0.0353646\pi$
$487$	13.0850	+	22.6638i	0.592936	+	1.02700i	−0.400899	+	0.916122i	$0.631302\pi$
$488$	0.0457536	−	0.0473454i	0.00207117	−	0.00214323i
$489$	−9.07909			−0.410571
$490$	0.399201	+	0.183388i	0.0180341	+	0.00828463i
$491$	−15.9776	−	9.22466i	−0.721058	−	0.416303i	0.0940840	−	0.995564i	$-0.470008\pi$
$491$	−15.9776	−	9.22466i	−0.721058	−	0.416303i	−0.815142	+	0.579261i	$0.803341\pi$
$492$	8.74572	−	7.51004i	0.394287	−	0.338579i
$493$			1.14069i			0.0513742i
$494$	−7.29014	−	0.510293i	−0.327999	−	0.0229592i
$495$	5.64991			0.253945
$496$	−32.4120	+	12.6409i	−1.45534	+	0.567592i
$497$	−1.96328	+	3.40051i	−0.0880654	+	0.152534i
$498$	−13.9011	+	30.2600i	−0.622922	+	1.35598i
$499$		−	27.5195i		−	1.23194i	−0.787769	−	0.615970i	$-0.788764\pi$
$499$		−	27.5195i		−	1.23194i	0.787769	−	0.615970i	$-0.211236\pi$
$500$	0.369722	+	1.96553i	0.0165345	+	0.0879011i
$501$	−22.7277	+	13.1218i	−1.01540	+	0.586240i
$502$	−17.9750	+	12.7395i	−0.802264	+	0.568592i
$503$	−7.07512	−	12.2545i	−0.315464	−	0.546400i	0.664072	−	0.747669i	$-0.268827\pi$
$503$	−7.07512	−	12.2545i	−0.315464	−	0.546400i	−0.979536	+	0.201269i	$0.935493\pi$
$504$	−1.53679	+	6.15437i	−0.0684541	+	0.274137i
$505$	6.01370	−	10.4160i	0.267606	−	0.463507i
$506$	−0.822674	+	0.583057i	−0.0365723	+	0.0259201i
$507$	6.07485	−	17.9876i	0.269794	−	0.798856i
$508$	10.3907	−	29.5933i	0.461012	−	1.31299i
$509$	24.0381	+	13.8784i	1.06547	+	0.615150i	0.926941	−	0.375208i	$-0.122429\pi$
$509$	24.0381	+	13.8784i	1.06547	+	0.615150i	0.138531	+	0.990358i	$0.455762\pi$
$510$	−2.65894	+	0.247904i	−0.117740	+	0.0109774i
$511$	1.50246	+	2.60233i	0.0664648	+	0.115120i
$512$	−15.1587	+	16.7992i	−0.669926	+	0.742428i
$513$	4.04717	+	7.00991i	0.178687	+	0.309495i
$514$	13.5843	−	29.5704i	0.599177	−	1.30429i
$515$			4.16951i			0.183731i
$516$	31.1240	−	5.85451i	1.37016	−	0.257731i
$517$	0.892786	+	0.515450i	0.0392647	+	0.0226695i
$518$	3.15495	+	33.8391i	0.138621	+	1.48680i
$519$	21.4593			0.941959
$520$	−4.04213	+	9.36276i	−0.177259	+	0.410584i
$521$	7.62264			0.333954			0.166977	−	0.985961i	$-0.446599\pi$
$521$	7.62264			0.333954			0.166977	+	0.985961i	$0.446599\pi$
$522$	−0.100431	−	1.07720i	−0.00439575	−	0.0471476i
$523$	−28.8246	−	16.6419i	−1.26041	−	0.727700i	−0.287259	−	0.957853i	$-0.592744\pi$
$523$	−28.8246	−	16.6419i	−1.26041	−	0.727700i	−0.973154	+	0.230153i	$0.926077\pi$
$524$	−5.95203	−	31.6424i	−0.260016	−	1.38231i
$525$			3.77725i			0.164853i
$526$	−3.26102	+	7.09861i	−0.142187	+	0.309514i
$527$	5.62280	+	9.73898i	0.244933	+	0.424237i
$528$	29.7081	+	23.7955i	1.29288	+	1.03557i
$529$	11.4940	+	19.9082i	0.499740	+	0.865575i
$530$	−1.01172	+	0.0943267i	−0.0439463	+	0.00409729i
$531$	4.37790	+	2.52758i	0.189985	+	0.109688i
$532$	6.99502	+	2.45606i	0.303272	+	0.106484i
$533$	−13.3140	+	5.02281i	−0.576692	+	0.217562i
$534$	7.92153	−	5.61426i	0.342798	−	0.242953i
$535$	−3.28233	+	5.68516i	−0.141907	+	0.245791i
$536$	29.5594	+	7.38119i	1.27677	+	0.318819i
$537$	−12.8749	−	22.3000i	−0.555593	−	0.962316i
$538$	15.6013	−	11.0572i	0.672622	−	0.476710i
$539$	−1.75286	+	1.01201i	−0.0755010	+	0.0435905i
$540$	11.1007	−	2.08808i	0.477698	−	0.0898565i
$541$		−	10.0400i		−	0.431655i	−0.976432	−	0.215827i	$-0.930755\pi$
$541$		−	10.0400i		−	0.431655i	0.976432	−	0.215827i	$-0.0692448\pi$
$542$	5.55822	−	12.0992i	0.238746	−	0.519704i
$543$	−14.0609	+	24.3542i	−0.603412	+	1.04514i
$544$	6.10852	+	4.02284i	0.261900	+	0.172478i
$545$	−10.2404			−0.438649
$546$	−10.7713	+	15.9667i	−0.460970	+	0.683312i
$547$			43.7284i			1.86969i	0.355056	+	0.934845i	$0.384462\pi$
$547$			43.7284i			1.86969i	−0.355056	+	0.934845i	$0.615538\pi$
$548$	−23.8672	−	27.7942i	−1.01956	−	1.18731i
$549$	0.0174808	+	0.0100925i	0.000746060	+	0.000430738i
$550$	−8.37332	−	3.84660i	−0.357039	−	0.164020i
$551$	−1.26441			−0.0538658
$552$	−0.314116	+	0.325044i	−0.0133697	+	0.0138348i
$553$	−7.04877	−	12.2088i	−0.299744	−	0.519172i
$554$	−20.9911	+	14.8771i	−0.891827	+	0.632068i
$555$	11.7518	−	6.78490i	0.498836	−	0.288003i
$556$	29.2956	−	25.1565i	1.24241	−	1.06687i
$557$	−26.4446	−	15.2678i	−1.12049	−	0.646918i	−0.178967	−	0.983855i	$-0.557276\pi$
$557$	−26.4446	−	15.2678i	−1.12049	−	0.646918i	−0.941527	+	0.336937i	$0.890609\pi$
$558$	−6.16726	−	8.70179i	−0.261081	−	0.368376i
$559$	−38.5762	−	6.33823i	−1.63160	−	0.268078i
$560$	6.46761	−	8.07464i	0.273306	−	0.341216i
$561$	6.15184	−	10.6553i	0.259731	−	0.449867i
$562$	45.1453	−	4.20908i	1.90434	−	0.177549i
$563$	10.5500	−	6.09104i	0.444629	−	0.256707i	−0.260930	−	0.965358i	$-0.584029\pi$
$563$	10.5500	−	6.09104i	0.444629	−	0.256707i	0.705559	+	0.708651i	$0.250696\pi$
$564$	0.436038	+	0.153100i	0.0183605	+	0.00644666i
$565$	−1.16800	+	0.674343i	−0.0491380	+	0.0283698i
$566$	−17.6063	−	8.08812i	−0.740048	−	0.339969i
$567$	14.6046			0.613335
$568$	−3.08781	−	2.98399i	−0.129562	−	0.125206i
$569$	−19.7520	+	34.2114i	−0.828046	+	1.43422i	0.0715223	+	0.997439i	$0.477214\pi$
$569$	−19.7520	+	34.2114i	−0.828046	+	1.43422i	−0.899569	+	0.436779i	$0.856119\pi$
$570$	−0.274792	−	2.94733i	−0.0115098	−	0.123450i
$571$			5.22063i			0.218477i	0.994016	+	0.109238i	$0.0348412\pi$
$571$			5.22063i			0.218477i	−0.994016	+	0.109238i	$0.965159\pi$
$572$	−24.4256	−	40.1375i	−1.02128	−	1.67823i
$573$			27.3064i			1.14074i
$574$	14.3734	−	1.34009i	0.599932	−	0.0559341i
$575$	0.0547143	−	0.0947679i	0.00228174	−	0.00395209i
$576$	−6.12266	−	3.26109i	−0.255111	−	0.135879i
$577$	−32.7240			−1.36232			−0.681160	−	0.732135i	$-0.738524\pi$
$577$	−32.7240			−1.36232			−0.681160	+	0.732135i	$0.738524\pi$
$578$	−9.04914	+	19.6983i	−0.376395	+	0.819339i
$579$	8.77831	−	5.06816i	0.364814	−	0.210625i
$580$	−0.584540	+	1.66481i	−0.0242717	+	0.0691273i
$581$	−36.1137	+	20.8503i	−1.49825	+	0.865015i
$582$	−0.142688	−	1.53043i	−0.00591460	−	0.0634383i
$583$	2.34076	−	4.05431i	0.0969442	−	0.167912i
$584$	−3.15915	+	0.904652i	−0.130727	+	0.0374348i
$585$	−3.08509	−	0.506893i	−0.127553	−	0.0209574i
$586$	−29.2510	+	20.7312i	−1.20835	+	0.856397i
$587$	−7.98692	−	4.61125i	−0.329656	−	0.190327i	0.326033	−	0.945359i	$-0.394288\pi$
$587$	−7.98692	−	4.61125i	−0.329656	−	0.190327i	−0.655688	+	0.755032i	$0.727621\pi$
$588$	−0.688367	+	0.591108i	−0.0283878	+	0.0243769i
$589$	−10.7953	+	6.23265i	−0.444811	+	0.256812i
$590$	−4.76732	−	6.72653i	−0.196268	−	0.276927i
$591$	−19.5035	−	33.7811i	−0.802268	−	1.38957i
$592$	−36.7394	−	5.61794i	−1.50998	−	0.230896i
$593$	−3.48277			−0.143020			−0.0715101	−	0.997440i	$-0.522782\pi$
$593$	−3.48277			−0.143020			−0.0715101	+	0.997440i	$0.522782\pi$
$594$	−21.7244	+	47.2899i	−0.891364	+	1.94033i
$595$	−2.89610	−	1.67206i	−0.118729	−	0.0685480i
$596$	−13.8739	+	11.9137i	−0.568298	+	0.488004i
$597$			13.3015i			0.544394i
$598$	0.501525	−	0.244566i	0.0205089	−	0.0100011i
$599$	−12.1571			−0.496726			−0.248363	−	0.968667i	$-0.579893\pi$
$599$	−12.1571			−0.496726			−0.248363	+	0.968667i	$0.579893\pi$
$600$	−4.00768	−	1.00075i	−0.163613	−	0.0408553i
$601$	−8.95416	+	15.5091i	−0.365248	+	0.632628i	−0.988816	−	0.149141i	$-0.952349\pi$
$601$	−8.95416	+	15.5091i	−0.365248	+	0.632628i	0.623568	+	0.781769i	$0.285682\pi$
$602$	36.0380	+	16.5554i	1.46880	+	0.674749i
$603$			9.34040i			0.380371i
$604$	24.6328	−	4.63350i	1.00229	−	0.188535i
$605$	27.2403	−	15.7272i	1.10748	−	0.639401i
$606$	14.3640	+	20.2671i	0.583496	+	0.823293i
$607$	−10.7731	−	18.6596i	−0.437267	−	0.757369i	0.560210	−	0.828350i	$-0.310720\pi$
$607$	−10.7731	−	18.6596i	−0.437267	−	0.757369i	−0.997478	+	0.0709813i	$0.977387\pi$
$608$	−4.45916	+	6.77105i	−0.180843	+	0.274602i
$609$	−1.66619	+	2.88592i	−0.0675173	+	0.116943i
$610$	−0.0190357	−	0.0268587i	−0.000770732	−	0.00108748i
$611$	−0.441254	−	0.361555i	−0.0178512	−	0.0146270i
$612$	−0.742860	+	2.11571i	−0.0300283	+	0.0855226i
$613$	−33.4895	−	19.3352i	−1.35263	−	0.780940i	−0.364010	−	0.931395i	$-0.618593\pi$
$613$	−33.4895	−	19.3352i	−1.35263	−	0.780940i	−0.988617	+	0.150455i	$0.951926\pi$
$614$	−0.598201	−	6.41613i	−0.0241414	−	0.258934i
$615$	−2.88193	−	4.99165i	−0.116211	−	0.201283i
$616$	13.1219	+	45.8231i	0.528695	+	1.84627i
$617$	−7.19754	−	12.4665i	−0.289762	−	0.501883i	0.683991	−	0.729491i	$-0.260243\pi$
$617$	−7.19754	−	12.4665i	−0.289762	−	0.501883i	−0.973753	+	0.227608i	$0.926910\pi$
$618$	−7.82536	−	3.59488i	−0.314782	−	0.144607i
$619$		−	34.6284i		−	1.39183i	−0.718122	−	0.695917i	$-0.754998\pi$
$619$		−	34.6284i		−	1.39183i	0.718122	−	0.695917i	$-0.245002\pi$
$620$	3.21564	+	17.0951i	0.129143	+	0.686556i
$621$	−0.535220	−	0.309009i	−0.0214776	−	0.0124001i
$622$	−27.6444	+	2.57739i	−1.10844	+	0.103344i
$623$	12.1586			0.487123
$624$	−14.0870	−	15.6587i	−0.563932	−	0.626849i
$625$	1.00000			0.0400000
$626$	31.9005	−	2.97421i	1.27500	−	0.118873i
$627$	11.8110	+	6.81907i	0.471685	+	0.272327i
$628$	−2.39272	−	12.7203i	−0.0954800	−	0.507594i
$629$			12.0138i			0.479023i
$630$	2.88210	+	1.32400i	0.114826	+	0.0527495i
$631$	19.7851	+	34.2688i	0.787633	+	1.36422i	0.927413	+	0.374038i	$0.122027\pi$
$631$	19.7851	+	34.2688i	0.787633	+	1.36422i	−0.139780	+	0.990183i	$0.544640\pi$
$632$	14.8212	−	4.24417i	0.589554	−	0.168824i
$633$	−5.59905	−	9.69783i	−0.222542	−	0.385454i
$634$	0.166700	+	1.78797i	0.00662050	+	0.0710095i
$635$	−13.5812	−	7.84112i	−0.538954	−	0.311165i
$636$	0.695254	−	1.98013i	0.0275686	−	0.0785172i
$637$	1.04793	−	0.395341i	0.0415205	−	0.0156640i
$638$	−4.70066	−	6.63247i	−0.186101	−	0.262582i
$639$	0.658221	−	1.14007i	0.0260388	−	0.0451005i
$640$	6.85371	+	9.00148i	0.270917	+	0.355815i
$641$	13.6367	+	23.6194i	0.538617	+	0.932912i	0.998979	+	0.0451804i	$0.0143863\pi$
$641$	13.6367	+	23.6194i	0.538617	+	0.932912i	−0.460362	+	0.887731i	$0.652280\pi$
$642$	−7.83997	−	11.0619i	−0.309419	−	0.436580i
$643$	25.6108	−	14.7864i	1.00999	−	0.583118i	0.0988014	−	0.995107i	$-0.468499\pi$
$643$	25.6108	−	14.7864i	1.00999	−	0.583118i	0.911189	+	0.411989i	$0.135166\pi$
$644$	−0.556291	+	0.104640i	−0.0219210	+	0.00412340i
$645$		−	15.8349i		−	0.623499i
$646$	2.38143	+	1.09400i	0.0936961	+	0.0430429i
$647$	3.34060	−	5.78610i	0.131333	−	0.227475i	−0.792858	−	0.609407i	$-0.791408\pi$
$647$	3.34060	−	5.78610i	0.131333	−	0.227475i	0.924191	+	0.381932i	$0.124741\pi$
$648$	−3.86936	+	15.4956i	−0.152003	+	0.608723i
$649$	37.9854			1.49106
$650$	4.22708	+	2.85163i	0.165800	+	0.111850i
$651$			32.8524i			1.28759i
$652$	9.43282	−	8.10006i	0.369418	−	0.317223i
$653$	−25.9030	−	14.9551i	−1.01366	−	0.585238i	−0.101401	−	0.994846i	$-0.532332\pi$
$653$	−25.9030	−	14.9551i	−1.01366	−	0.585238i	−0.912262	+	0.409607i	$0.865666\pi$
$654$	8.82906	−	19.2192i	0.345243	−	0.751529i
$655$	−16.0987			−0.629027
$656$	−2.38625	+	15.6053i	−0.0931676	+	0.609284i
$657$	−0.503721	−	0.872471i	−0.0196520	−	0.0340383i
$658$	0.334632	+	0.472154i	0.0130453	+	0.0184065i
$659$	−33.3170	+	19.2356i	−1.29785	+	0.749311i	−0.980032	−	0.198842i	$-0.936282\pi$
$659$	−33.3170	+	19.2356i	−1.29785	+	0.749311i	−0.317814	+	0.948153i	$0.602949\pi$
$660$	14.4386	−	12.3986i	0.562023	−	0.482615i
$661$	−25.0011	−	14.4344i	−0.972432	−	0.561434i	−0.0724549	−	0.997372i	$-0.523083\pi$
$661$	−25.0011	−	14.4344i	−0.972432	−	0.561434i	−0.899977	+	0.435938i	$0.856417\pi$
$662$	−4.84019	+	3.43041i	−0.188119	+	0.133327i
$663$	−4.31512	+	5.26632i	−0.167585	+	0.204527i
$664$	−12.5543	−	43.8410i	−0.487200	−	1.70136i
$665$	1.85342	−	3.21021i	0.0718724	−	0.124487i
$666$	−1.05775	−	11.3451i	−0.0409868	−	0.439612i
$667$	0.0836064	−	0.0482702i	0.00323725	−	0.00186903i
$668$	11.9063	−	33.9099i	0.460669	−	1.31202i
$669$	27.3346	−	15.7817i	1.05682	−	0.610154i
$670$	6.35918	−	13.8427i	0.245676	−	0.534791i
$671$	0.151674			0.00585530
$672$	9.57828	+	19.1002i	0.369490	+	0.736808i
$673$	−14.9622	+	25.9152i	−0.576749	+	0.998959i	0.419100	+	0.907940i	$0.362346\pi$
$673$	−14.9622	+	25.9152i	−0.576749	+	0.998959i	−0.995849	+	0.0910190i	$0.970988\pi$
$674$	18.3467	−	1.71054i	0.706690	−	0.0658875i
$675$		−	5.64769i		−	0.217380i
$676$	9.73637	+	24.1082i	0.374476	+	0.927237i
$677$			0.615332i			0.0236491i	0.999930	+	0.0118246i	$0.00376397\pi$
$677$			0.615332i			0.0236491i	−0.999930	+	0.0118246i	$0.996236\pi$
$678$	−0.258585	−	2.77351i	−0.00993091	−	0.106516i
$679$	0.962403	−	1.66693i	0.0369336	−	0.0639709i
$680$	2.54137	−	2.62978i	0.0974570	−	0.100848i
$681$	25.3013			0.969546
$682$	−72.8265	−	33.4556i	−2.78867	−	1.28108i
$683$	2.96593	−	1.71238i	0.113488	−	0.0655224i	−0.442181	−	0.896926i	$-0.645795\pi$
$683$	2.96593	−	1.71238i	0.113488	−	0.0655224i	0.555670	+	0.831403i	$0.312462\pi$
$684$	−2.34518	−	0.823431i	−0.0896704	−	0.0314847i
$685$	−15.8636	+	9.15888i	−0.606119	+	0.349943i
$686$	−26.6246	+	2.48232i	−1.01653	+	0.0947753i
$687$	8.44619	−	14.6292i	0.322242	−	0.558140i
$688$	−27.1134	+	33.8504i	−1.03369	+	1.29053i
$689$	−1.64189	+	2.00382i	−0.0625511	+	0.0763394i
$690$	0.130687	+	0.184395i	0.00497518	+	0.00701980i
$691$	−18.4325	−	10.6420i	−0.701205	−	0.404841i	0.106591	−	0.994303i	$-0.466006\pi$
$691$	−18.4325	−	10.6420i	−0.701205	−	0.404841i	−0.807796	+	0.589462i	$0.799340\pi$
$692$	−22.2954	+	19.1453i	−0.847544	+	0.727794i
$693$	−12.6551	+	7.30641i	−0.480727	+	0.277548i
$694$	−5.74847	+	4.07414i	−0.218209	+	0.154652i
$695$	−9.65363	−	16.7206i	−0.366183	−	0.634248i
$696$	−2.62054	−	2.53243i	−0.0993312	−	0.0959916i
$697$	5.10295			0.193288
$698$	33.1575	+	15.2322i	1.25503	+	0.576546i
$699$	−3.96644	−	2.29003i	−0.150025	−	0.0866168i
$700$	−3.36993	−	3.92441i	−0.127371	−	0.148329i
$701$			20.9801i			0.792406i	0.918163	+	0.396203i	$0.129672\pi$
$701$			20.9801i			0.792406i	−0.918163	+	0.396203i	$0.870328\pi$
$702$	16.1051	−	23.8732i	0.607850	−	0.901037i
$703$	−13.3169			−0.502255
$704$	−52.0952	+	1.78196i	−1.96341	+	0.0671601i
$705$	0.115534	−	0.200110i	0.00435125	−	0.00753658i
$706$	−5.06856	+	11.0333i	−0.190758	+	0.415243i
$707$			31.1074i			1.16991i
$708$	16.7347	−	3.14784i	0.628928	−	0.118303i
$709$	−6.46080	+	3.73014i	−0.242640	+	0.140089i	−0.616390	−	0.787441i	$-0.711405\pi$
$709$	−6.46080	+	3.73014i	−0.242640	+	0.140089i	0.373749	+	0.927530i	$0.378072\pi$
$710$	−1.75169	+	1.24148i	−0.0657397	+	0.0465920i
$711$	2.36321	+	4.09319i	0.0886271	+	0.153507i
$712$	−3.22130	+	12.9003i	−0.120723	+	0.483460i
$713$	0.475875	−	0.824239i	0.0178216	−	0.0308680i
$714$	5.63510	−	3.99379i	0.210888	−	0.149464i
$715$	−21.9805	+	8.29236i	−0.822025	+	0.310117i
$716$	33.2718	+	11.6823i	1.24343	+	0.436587i
$717$	23.1002	+	13.3369i	0.862695	+	0.498077i
$718$	22.7824	−	2.12410i	0.850233	−	0.0792706i
$719$	−20.3159	−	35.1882i	−0.757655	−	1.31230i	−0.944043	−	0.329821i	$-0.893012\pi$
$719$	−20.3159	−	35.1882i	−0.757655	−	1.31230i	0.186388	−	0.982476i	$-0.440322\pi$
$720$	−2.16836	+	2.70715i	−0.0808101	+	0.100889i
$721$	−5.39197	−	9.33916i	−0.200807	−	0.347809i
$722$	10.0042	−	21.7771i	0.372316	−	0.810461i
$723$			20.9843i			0.780414i
$724$	−7.11928	−	37.8478i	−0.264586	−	1.40660i
$725$	0.764027	+	0.441111i	0.0283753	+	0.0163825i
$726$	6.03078	+	64.6844i	0.223823	+	2.40066i
$727$	14.9258			0.553566			0.276783	−	0.960932i	$-0.410732\pi$
$727$	14.9258			0.553566			0.276783	+	0.960932i	$0.410732\pi$
$728$	−3.05398	−	26.1986i	−0.113188	−	0.970985i
$729$	−29.6407			−1.09780
$730$	0.152528	+	1.63597i	0.00564531	+	0.0605499i
$731$	12.1410	+	7.00960i	0.449050	+	0.259259i
$732$	0.0668207	−	0.0125692i	0.00246977	−	0.000464570i
$733$			16.9429i			0.625801i	0.949786	+	0.312901i	$0.101301\pi$
$733$			16.9429i			0.625801i	−0.949786	+	0.312901i	$0.898699\pi$
$734$	−10.8727	+	23.6677i	−0.401318	+	0.873592i
$735$	0.226834	+	0.392888i	0.00836690	+	0.0144919i
$736$	0.0363606	−	0.617952i	0.00134027	−	0.0227780i
$737$	35.0927	+	60.7823i	1.29265	+	2.23894i
$738$	−4.81888	+	0.449284i	−0.177386	+	0.0165384i
$739$	36.1511	+	20.8719i	1.32984	+	0.767784i	0.985275	−	0.170978i	$-0.0546928\pi$
$739$	36.1511	+	20.8719i	1.32984	+	0.767784i	0.344566	+	0.938762i	$0.388026\pi$
$740$	−6.15640	+	17.5338i	−0.226314	+	0.644556i
$741$	−5.83750	−	4.78314i	−0.214446	−	0.175713i
$742$	2.14414	−	1.51963i	0.0787139	−	0.0557872i
$743$	0.856416	−	1.48336i	0.0314189	−	0.0544190i	−0.849888	−	0.526963i	$-0.823331\pi$
$743$	0.856416	−	1.48336i	0.0314189	−	0.0544190i	0.881307	+	0.472544i	$0.156664\pi$
$744$	−34.8566	−	8.70396i	−1.27791	−	0.319102i
$745$	4.57180	+	7.91859i	0.167498	+	0.290115i
$746$	3.85983	−	2.73560i	0.141318	−	0.100157i
$747$	12.1077	−	6.99036i	0.442996	−	0.255764i
$748$	3.11478	+	16.5589i	0.113888	+	0.605453i
$749$		−	16.9787i		−	0.620388i
$750$	−0.862182	+	1.87680i	−0.0314824	+	0.0685312i
$751$	−14.4280	+	24.9900i	−0.526485	+	0.911899i	0.473039	+	0.881042i	$0.343157\pi$
$751$	−14.4280	+	24.9900i	−0.526485	+	0.911899i	−0.999524	+	0.0308573i	$0.990176\pi$
$752$	−0.589616	+	0.229954i	−0.0215011	+	0.00838555i
$753$	−22.7518			−0.829122
$754$	1.97171	+	4.04334i	0.0718056	+	0.147250i
$755$		−	12.5324i		−	0.456101i
$756$	−22.1639	+	19.0323i	−0.806092	+	0.692199i
$757$	−18.6517	−	10.7686i	−0.677907	−	0.391390i	0.121159	−	0.992633i	$-0.461339\pi$
$757$	−18.6517	−	10.7686i	−0.677907	−	0.391390i	−0.799066	+	0.601243i	$0.794672\pi$
$758$	−9.78362	−	4.49448i	−0.355357	−	0.163247i
$759$	−1.04130			−0.0377967
$760$	2.91501	+	2.81700i	0.105739	+	0.102184i
$761$	1.59579	+	2.76400i	0.0578475	+	0.100195i	0.893499	−	0.449065i	$-0.148243\pi$
$761$	1.59579	+	2.76400i	0.0578475	+	0.100195i	−0.835651	+	0.549260i	$0.814910\pi$
$762$	26.4257	−	18.7288i	0.957304	−	0.678474i
$763$	22.9371	−	13.2427i	0.830379	−	0.479419i
$764$	−24.3618	−	28.3702i	−0.881380	−	1.02640i
$765$	0.970961	+	0.560585i	0.0351052	+	0.0202680i
$766$	−2.39779	−	3.38320i	−0.0866358	−	0.122240i
$767$	−20.7416	−	3.40793i	−0.748936	−	0.123053i
$768$	−22.8032	+	5.10217i	−0.822838	+	0.184109i
$769$	−2.79952	+	4.84892i	−0.100953	+	0.174856i	−0.912078	−	0.410017i	$-0.865523\pi$
$769$	−2.79952	+	4.84892i	−0.100953	+	0.174856i	0.811124	+	0.584874i	$0.198856\pi$
$770$	23.7295	−	2.21240i	0.855153	−	0.0797293i
$771$	29.1028	−	16.8025i	1.04811	−	0.605127i
$772$	−4.59868	+	13.0973i	−0.165510	+	0.471383i
$773$	6.32487	−	3.65167i	0.227490	−	0.131341i	−0.381924	−	0.924194i	$-0.624738\pi$
$773$	6.32487	−	3.65167i	0.227490	−	0.131341i	0.609414	+	0.792853i	$0.291405\pi$
$774$	−12.0823	−	5.55046i	−0.434289	−	0.199507i
$775$	8.69745			0.312422
$776$	1.51364	+	1.46275i	0.0543367	+	0.0525098i
$777$	−17.5483	+	30.3946i	−0.629543	+	1.09040i
$778$	−1.28638	−	13.7973i	−0.0461189	−	0.494657i
$779$			5.65641i			0.202662i
$780$	−8.99647	+	5.47477i	−0.322125	+	0.196028i
$781$		−	9.89196i		−	0.353962i
$782$	−0.199231	+	0.0185751i	−0.00712448	+	0.000664244i
$783$	2.49126	−	4.31499i	0.0890304	−	0.154205i
$784$	0.187820	−	1.22828i	0.00670785	−	0.0438670i
$785$	−6.47168			−0.230984
$786$	13.8800	−	30.2141i	0.495083	−	1.07770i
$787$	−7.27684	+	4.20128i	−0.259391	+	0.149760i	−0.624057	−	0.781379i	$-0.714517\pi$
$787$	−7.27684	+	4.20128i	−0.259391	+	0.149760i	0.364666	+	0.931139i	$0.381183\pi$
$788$	50.4018	+	17.6968i	1.79549	+	0.630424i
$789$	−6.98635	+	4.03357i	−0.248721	+	0.143599i
$790$	−0.715584	−	7.67514i	−0.0254593	−	0.273069i
$791$	1.74411	−	3.02088i	0.0620133	−	0.107410i
$792$	−4.39930	−	15.3629i	−0.156322	−	0.545897i
$793$	−0.0828202	−	0.0136077i	−0.00294103	−	0.000483223i
$794$	36.9680	−	26.2005i	1.31195	−	0.929821i
$795$	−0.908737	−	0.524660i	−0.0322296	−	0.0186078i
$796$	−11.8672	−	13.8197i	−0.420620	−	0.489828i
$797$	42.2239	−	24.3780i	1.49565	−	0.863512i	0.495660	−	0.868517i	$-0.334926\pi$
$797$	42.2239	−	24.3780i	1.49565	−	0.863512i	0.999987	+	0.00500415i	$0.00159288\pi$
$798$	4.42696	+	6.24629i	0.156713	+	0.221116i
$799$	0.102286	+	0.177165i	0.00361862	+	0.00626763i
$800$	5.05666	−	2.53578i	0.178780	−	0.0896535i
$801$	−4.07634			−0.144030
$802$	3.70038	−	8.05503i	0.130665	−	0.284433i
$803$	−6.55589	−	3.78504i	−0.231352	−	0.133571i
$804$	20.4973	+	23.8699i	0.722884	+	0.841826i
$805$			0.283024i			0.00997527i
$806$	36.7648	+	24.8020i	1.29499	+	0.873611i
$807$	19.7474			0.695140
$808$	−33.0052	−	8.24163i	−1.16112	−	0.289940i
$809$	−13.1332	+	22.7475i	−0.461740	+	0.799758i	−0.999048	−	0.0436287i	$-0.986108\pi$
$809$	−13.1332	+	22.7475i	−0.461740	+	0.799758i	0.537307	+	0.843386i	$0.319441\pi$
$810$	7.25660	+	3.33360i	0.254971	+	0.117131i
$811$		−	45.7082i		−	1.60503i	−0.596630	−	0.802516i	$-0.703494\pi$
$811$		−	45.7082i		−	1.60503i	0.596630	−	0.802516i	$-0.296506\pi$
$812$	−0.843618	−	4.48487i	−0.0296052	−	0.157388i
$813$	11.9079	−	6.87500i	0.417627	−	0.241117i
$814$	−49.5076	−	69.8535i	−1.73524	−	2.44836i
$815$	−3.10835	−	5.38381i	−0.108881	−	0.188587i
$816$	2.74447	+	7.03700i	0.0960757	+	0.246344i
$817$	−7.76986	+	13.4578i	−0.271833	+	0.470829i
$818$	−13.9195	−	19.6400i	−0.486685	−	0.686696i
$819$	7.56571	−	2.85423i	0.264367	−	0.0997350i
$820$	7.44759	+	2.61497i	0.260081	+	0.0913186i
$821$	29.3468	+	16.9434i	1.02421	+	0.591328i	0.915321	−	0.402725i	$-0.131937\pi$
$821$	29.3468	+	16.9434i	1.02421	+	0.591328i	0.108890	+	0.994054i	$0.465270\pi$
$822$	−3.51208	−	37.6696i	−0.122498	−	1.31388i
$823$	10.9064	+	18.8905i	0.380175	+	0.658482i	0.991087	−	0.133216i	$-0.0425304\pi$
$823$	10.9064	+	18.8905i	0.380175	+	0.658482i	−0.610912	+	0.791698i	$0.709197\pi$
$824$	11.3375	−	3.24659i	0.394959	−	0.113100i
$825$	−4.75789	−	8.24090i	−0.165648	−	0.286911i
$826$	19.3769	+	8.90150i	0.674208	+	0.309723i
$827$		−	17.8065i		−	0.619192i	−0.950868	−	0.309596i	$-0.899806\pi$
$827$		−	17.8065i		−	0.619192i	0.950868	−	0.309596i	$-0.100194\pi$
$828$	0.186505	−	0.0350822i	0.00648150	−	0.00121919i
$829$	28.0343	+	16.1856i	0.973672	+	0.562150i	0.900354	−	0.435159i	$-0.143308\pi$
$829$	28.0343	+	16.1856i	0.973672	+	0.562150i	0.0733185	+	0.997309i	$0.476641\pi$
$830$	−22.7031	+	2.11670i	−0.788035	+	0.0734717i
$831$	−26.5694			−0.921683
$832$	28.6060	+	3.70079i	0.991735	+	0.128302i
$833$	−0.401648			−0.0139163
$834$	39.7045	−	3.70180i	1.37485	−	0.128183i
$835$	−15.5622	−	8.98486i	−0.538554	−	0.310934i
$836$	−18.3549	+	3.45261i	−0.634817	+	0.119411i
$837$		−	49.1205i		−	1.69785i
$838$	42.9884	+	19.7484i	1.48501	+	0.682196i
$839$	18.5118	+	32.0634i	0.639098	+	1.10695i	0.985631	+	0.168913i	$0.0540255\pi$
$839$	18.5118	+	32.0634i	0.639098	+	1.10695i	−0.346533	+	0.938038i	$0.612641\pi$
$840$	10.2708	−	2.94115i	0.354378	−	0.101479i
$841$	−14.1108	−	24.4407i	−0.486581	−	0.842783i
$842$	−3.45914	−	37.1017i	−0.119210	−	1.27861i
$843$	40.5500	+	23.4115i	1.39662	+	0.806336i
$844$	14.4693	+	5.08039i	0.498053	+	0.174874i
$845$	12.7463	−	2.55595i	0.438485	−	0.0879274i
$846$	−0.112190	−	0.158297i	−0.00385719	−	0.00544236i
$847$	−40.6765	+	70.4537i	−1.39766	+	2.42082i
$848$	1.04426	+	2.67756i	0.0358601	+	0.0919477i
$849$	−10.0043	−	17.3279i	−0.343345	−	0.594691i
$850$	−1.05733	−	1.49186i	−0.0362661	−	0.0511702i
$851$	0.880546	−	0.508383i	0.0301847	−	0.0174272i
$852$	−0.819746	−	4.35796i	−0.0280840	−	0.149301i
$853$			1.04508i			0.0357828i	0.999840	+	0.0178914i	$0.00569531\pi$
$853$			1.04508i			0.0357828i	−0.999840	+	0.0178914i	$0.994305\pi$
$854$	0.0773709	+	0.0355433i	0.00264758	+	0.00121626i
$855$	−0.621386	+	1.07627i	−0.0212510	+	0.0368077i
$856$	18.0145	+	4.49835i	0.615723	+	0.153751i
$857$	−44.7824			−1.52974			−0.764868	−	0.644187i	$-0.777196\pi$
$857$	−44.7824			−1.52974			−0.764868	+	0.644187i	$0.777196\pi$
$858$	3.38808	−	48.4027i	0.115667	−	1.65244i
$859$			15.0255i			0.512664i	0.966589	+	0.256332i	$0.0825141\pi$
$859$			15.0255i			0.512664i	−0.966589	+	0.256332i	$0.917486\pi$
$860$	14.1274	+	16.4518i	0.481739	+	0.561003i
$861$	12.9103	+	7.45376i	0.439982	+	0.254024i
$862$	−16.3963	+	35.6916i	−0.558460	+	1.21566i
$863$	−33.5123			−1.14077			−0.570386	−	0.821377i	$-0.693206\pi$
$863$	−33.5123			−1.14077			−0.570386	+	0.821377i	$0.693206\pi$
$864$	−14.3213	−	28.5584i	−0.487221	−	0.971578i
$865$	7.34688	+	12.7252i	0.249801	+	0.432669i
$866$	4.65045	+	6.56163i	0.158029	+	0.222973i
$867$	−19.3868	+	11.1929i	−0.658409	+	0.380132i
$868$	−29.3098	−	34.1324i	−0.994840	−	1.15853i
$869$	30.7569	+	17.7575i	1.04336	+	0.602382i
$870$	−1.48661	+	1.05361i	−0.0504008	+	0.0357208i
$871$	−13.7089	−	36.3381i	−0.464507	−	1.23127i
$872$	7.97365	+	27.8450i	0.270022	+	0.942949i
$873$	−0.322660	+	0.558863i	−0.0109204	+	0.0189147i
$874$	−0.0205897	−	0.220840i	−0.000696459	−	0.00747001i
$875$	−2.23987	+	1.29319i	−0.0757215	+	0.0437178i
$876$	−3.20190	−	1.12424i	−0.108182	−	0.0379845i
$877$	29.7703	−	17.1879i	1.00527	−	0.580395i	0.0954689	−	0.995432i	$-0.469565\pi$
$877$	29.7703	−	17.1879i	1.00527	−	0.580395i	0.909804	+	0.415038i	$0.136232\pi$
$878$	−9.10675	+	19.8237i	−0.307338	+	0.669016i
$879$	−37.0243			−1.24880
$880$	−3.93956	+	25.7633i	−0.132802	+	0.868482i
$881$	19.5395	−	33.8434i	0.658302	−	1.14021i	−0.322753	−	0.946483i	$-0.604608\pi$
$881$	19.5395	−	33.8434i	0.658302	−	1.14021i	0.981055	−	0.193729i	$-0.0620583\pi$
$882$	0.379290	−	0.0353627i	0.0127714	−	0.00119072i
$883$			12.6153i			0.424539i	0.977211	+	0.212270i	$0.0680855\pi$
$883$			12.6153i			0.424539i	−0.977211	+	0.212270i	$0.931915\pi$
$884$	−0.215188	−	9.32130i	−0.00723755	−	0.313509i
$885$		−	8.51409i		−	0.286198i
$886$	−1.86740	−	20.0292i	−0.0627365	−	0.672893i
$887$	15.2192	−	26.3604i	0.511010	−	0.885095i	−0.488909	−	0.872335i	$-0.662605\pi$
$887$	15.2192	−	26.3604i	0.511010	−	0.885095i	0.999919	−	0.0127600i	$-0.00406175\pi$
$888$	−27.5996	−	26.6717i	−0.926182	−	0.895043i
$889$	40.5602			1.36035
$890$	6.04124	+	2.77527i	0.202503	+	0.0930274i
$891$	−31.8632	+	18.3962i	−1.06746	+	0.616296i
$892$	−14.3198	+	40.7836i	−0.479461	+	1.36554i
$893$	−0.196380	+	0.113380i	−0.00657160	+	0.00379412i
$894$	−18.8034	+	1.75311i	−0.628879	+	0.0586329i
$895$	8.81579	−	15.2694i	0.294679	−	0.510400i
$896$	−26.9921	−	11.2990i	−0.901741	−	0.377473i
$897$	0.568592	+	0.0934219i	0.0189847	+	0.00311927i
$898$	−8.84516	−	12.4802i	−0.295167	−	0.416470i
$899$	6.64509	+	3.83655i	0.221626	+	0.127956i
$900$	1.12982	+	1.31572i	0.0376607	+	0.0438573i
$901$	0.804537	−	0.464500i	0.0268030	−	0.0154747i
$902$	−29.6707	+	21.0286i	−0.987926	+	0.700177i
$903$	20.4775	+	35.4681i	0.681450	+	1.18031i
$904$	2.74309	+	2.65087i	0.0912339	+	0.0881665i
$905$	−19.2558			−0.640083
$906$	23.5209	+	10.8052i	0.781428	+	0.358979i
$907$	−15.1303	−	8.73545i	−0.502392	−	0.290056i	0.227309	−	0.973823i	$-0.427007\pi$
$907$	−15.1303	−	8.73545i	−0.502392	−	0.290056i	−0.729701	+	0.683767i	$0.760341\pi$
$908$	−26.2870	+	22.5729i	−0.872365	+	0.749109i
$909$		−	10.4292i		−	0.345916i
$910$	−13.1558	−	0.920877i	−0.436111	−	0.0305268i
$911$	35.5800			1.17882			0.589410	−	0.807834i	$-0.299360\pi$
$911$	35.5800			1.17882			0.589410	+	0.807834i	$0.299360\pi$
$912$	−7.80024	+	3.04214i	−0.258292	+	0.100735i
$913$	52.5267	−	90.9790i	1.73838	−	3.01096i
$914$	−24.2586	+	52.8064i	−0.802405	+	1.74668i
$915$		−	0.0339963i		−	0.00112388i
$916$	4.27645	+	22.7346i	0.141298	+	0.751173i
$917$	36.0589	−	20.8186i	1.19077	−	0.687492i
$918$	−8.42554	+	5.97147i	−0.278084	+	0.197088i
$919$	4.49025	+	7.77734i	0.148120	+	0.256551i	0.930532	−	0.366209i	$-0.119345\pi$
$919$	4.49025	+	7.77734i	0.148120	+	0.256551i	−0.782413	+	0.622760i	$0.786011\pi$
$920$	−0.300290	−	0.0749846i	−0.00990027	−	0.00247217i
$921$	3.32729	−	5.76303i	0.109638	−	0.189898i
$922$	−39.9252	+	28.2964i	−1.31487	+	0.931892i
$923$	−0.887475	+	5.40142i	−0.0292116	+	0.177790i
$924$	−16.3069	+	46.4432i	−0.536459	+	1.52787i
$925$	8.04677	+	4.64580i	0.264576	+	0.152753i
$926$	−15.1127	+	1.40901i	−0.496633	+	0.0463031i
$927$	1.80774	+	3.13110i	0.0593739	+	0.102839i
$928$	4.98199	+	0.293143i	0.163542	+	0.00962288i
$929$	−7.35996	−	12.7478i	−0.241473	−	0.418243i	0.719661	−	0.694325i	$-0.244297\pi$
$929$	−7.35996	−	12.7478i	−0.241473	−	0.418243i	−0.961134	+	0.276082i	$0.910964\pi$
$930$	−7.49879	+	16.3234i	−0.245895	+	0.535266i
$931$		−	0.445211i		−	0.0145912i
$932$	6.16407	−	1.15948i	0.201911	−	0.0379800i
$933$	−24.8304	−	14.3359i	−0.812912	−	0.469335i
$934$	−0.348924	−	3.74246i	−0.0114171	−	0.122457i
$935$	8.42465			0.275516
$936$	1.02389	+	8.78348i	0.0334670	+	0.287097i
$937$	−49.0465			−1.60228			−0.801139	−	0.598478i	$-0.795772\pi$
$937$	−49.0465			−1.60228			−0.801139	+	0.598478i	$0.795772\pi$
$938$	3.65752	+	39.2295i	0.119422	+	1.28089i
$939$	28.6534	+	16.5430i	0.935067	+	0.539861i
$940$	0.0584966	+	0.310982i	0.00190795	+	0.0101431i
$941$		−	8.88800i		−	0.289741i	−0.989451	−	0.144870i	$-0.953723\pi$
$941$		−	8.88800i		−	0.289741i	0.989451	−	0.144870i	$-0.0462765\pi$
$942$	5.57976	−	12.1461i	0.181799	−	0.395741i
$943$	−0.215939	−	0.374017i	−0.00703194	−	0.0121797i
$944$	−14.5783	+	18.2006i	−0.474483	+	0.592380i
$945$	7.30354	+	12.6501i	0.237584	+	0.411508i
$946$	−99.4785	+	9.27478i	−3.23433	+	0.301549i
$947$	−28.3390	−	16.3615i	−0.920895	−	0.531679i	−0.0369742	−	0.999316i	$-0.511772\pi$
$947$	−28.3390	−	16.3615i	−0.920895	−	0.531679i	−0.883920	+	0.467637i	$0.845105\pi$
$948$	15.0217	+	5.27436i	0.487882	+	0.171303i
$949$	3.24021	+	2.65497i	0.105182	+	0.0861839i
$950$	1.65366	−	1.17201i	0.0536519	−	0.0380249i
$951$	−0.927211	+	1.60598i	−0.0300669	+	0.0520773i
$952$	−2.29153	+	9.17685i	−0.0742688	+	0.297423i
$953$	21.7442	+	37.6621i	0.704364	+	1.21999i	0.966921	+	0.255078i	$0.0821011\pi$
$953$	21.7442	+	37.6621i	0.704364	+	1.21999i	−0.262556	+	0.964917i	$0.584566\pi$
$954$	−0.718855	+	0.509478i	−0.0232738	+	0.0164949i
$955$	−16.1924	+	9.34869i	−0.523974	+	0.302517i
$956$	−35.8990	+	6.75271i	−1.16106	+	0.218398i
$957$		−	8.39503i		−	0.271373i
$958$	−11.1993	+	24.3788i	−0.361834	+	0.787643i
$959$	23.6883	−	41.0294i	0.764936	−	1.32491i
$960$	0.399410	+	11.6767i	0.0128909	+	0.376863i
$961$	44.6457			1.44018
$962$	20.7662	+	42.5846i	0.669529	+	1.37298i
$963$			5.69236i			0.183434i
$964$	−18.7215	−	21.8018i	−0.602978	−	0.702190i
$965$	6.01074	+	3.47030i	0.193493	+	0.111713i
$966$	−0.531180	−	0.244018i	−0.0170904	−	0.00785115i
$967$	−42.6141			−1.37038			−0.685189	−	0.728365i	$-0.740280\pi$
$967$	−42.6141			−1.37038			−0.685189	+	0.728365i	$0.740280\pi$
$968$	−63.9750	−	61.8241i	−2.05623	−	1.98710i
$969$	1.35318	+	2.34377i	0.0434703	+	0.0752928i
$970$	0.858678	−	0.608575i	0.0275705	−	0.0195402i
$971$	−21.4375	+	12.3770i	−0.687963	+	0.397195i	−0.802848	−	0.596183i	$-0.796683\pi$
$971$	−21.4375	+	12.3770i	−0.687963	+	0.397195i	0.114886	+	0.993379i	$0.463350\pi$
$972$	13.1953	−	11.3310i	0.423241	−	0.363441i
$973$	43.2458	+	24.9680i	1.38640	+	0.800436i
$974$	−21.4004	−	30.1952i	−0.685713	−	0.967517i
$975$	1.85866	+	4.92674i	0.0595247	+	0.157782i
$976$	−0.0582103	+	0.0726741i	−0.00186327	+	0.00232624i
$977$	7.55599	−	13.0874i	0.241738	−	0.418702i	−0.719472	−	0.694522i	$-0.755616\pi$
$977$	7.55599	−	13.0874i	0.241738	−	0.418702i	0.961209	+	0.275820i	$0.0889493\pi$
$978$	12.7843	−	1.19193i	0.408798	−	0.0381138i
$979$	−26.5266	+	15.3151i	−0.847794	+	0.489474i
$980$	−0.586193	−	0.205822i	−0.0187253	−	0.00657473i
$981$	−7.69001	+	4.43983i	−0.245523	+	0.141753i
$982$	23.7092	+	10.8917i	0.756590	+	0.347569i
$983$	31.5256			1.00551			0.502755	−	0.864429i	$-0.332320\pi$
$983$	31.5256			1.00551			0.502755	+	0.864429i	$0.332320\pi$
$984$	−11.3290	+	11.7231i	−0.361154	+	0.373719i
$985$	13.3546	−	23.1308i	0.425512	−	0.737009i
$986$	−0.149754	−	1.60622i	−0.00476914	−	0.0511524i
$987$			0.597628i			0.0190227i
$988$	10.3323	−	0.238527i	0.328714	−	0.00758856i
$989$		−	1.18649i		−	0.0377281i
$990$	−7.95568	+	0.741740i	−0.252848	+	0.0235740i
$991$	8.12006	−	14.0644i	0.257942	−	0.446769i	−0.707748	−	0.706465i	$-0.750289\pi$
$991$	8.12006	−	14.0644i	0.257942	−	0.446769i	0.965691	+	0.259696i	$0.0836222\pi$
$992$	43.9801	−	22.0549i	1.39637	−	0.700242i
$993$	−6.12645			−0.194417
$994$	2.31808	−	5.04603i	0.0735252	−	0.160050i
$995$	−7.88767	+	4.55395i	−0.250056	+	0.144370i
$996$	15.6016	−	44.4342i	0.494354	−	1.40795i
$997$	−27.7816	+	16.0397i	−0.879852	+	0.507983i	−0.870610	−	0.491975i	$-0.836275\pi$
$997$	−27.7816	+	16.0397i	−0.879852	+	0.507983i	−0.00924226	+	0.999957i	$0.502942\pi$
$998$	3.61285	+	38.7504i	0.114363	+	1.22662i
$999$	26.2381	−	45.4457i	0.830135	−	1.43784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.by.c.61.2	✓	104
8.5	even	2	inner	520.2.by.c.61.33	yes	104
13.3	even	3	inner	520.2.by.c.341.33	yes	104
104.29	even	6	inner	520.2.by.c.341.2	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.by.c.61.2	✓	104	1.1	even	1	trivial
520.2.by.c.61.33	yes	104	8.5	even	2	inner
520.2.by.c.341.2	yes	104	104.29	even	6	inner
520.2.by.c.341.33	yes	104	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40811 + 0.131283i) q^{2} +(-1.26478 - 0.730219i) q^{3} +(1.96553 - 0.369722i) q^{4} -1.00000i q^{5} +(1.87680 + 0.862182i) q^{6} +(1.29319 + 2.23987i) q^{7} +(-2.71914 + 0.778649i) q^{8} +(-0.433561 - 0.750950i) q^{9} +O(q^{10})\)	\(q+(-1.40811 + 0.131283i) q^{2} +(-1.26478 - 0.730219i) q^{3} +(1.96553 - 0.369722i) q^{4} -1.00000i q^{5} +(1.87680 + 0.862182i) q^{6} +(1.29319 + 2.23987i) q^{7} +(-2.71914 + 0.778649i) q^{8} +(-0.433561 - 0.750950i) q^{9} +(0.131283 + 1.40811i) q^{10} +(-5.64276 - 3.25785i) q^{11} +(-2.75593 - 0.967651i) q^{12} +(2.78890 + 2.28517i) q^{13} +(-2.11501 - 2.98420i) q^{14} +(-0.730219 + 1.26478i) q^{15} +(3.72661 - 1.45340i) q^{16} +(-0.646488 - 1.11975i) q^{17} +(0.709088 + 1.00050i) q^{18} +(1.24120 - 0.716607i) q^{19} +(-0.369722 - 1.96553i) q^{20} -3.77725i q^{21} +(8.37332 + 3.84660i) q^{22} +(-0.0547143 + 0.0947679i) q^{23} +(4.00768 + 1.00075i) q^{24} -1.00000 q^{25} +(-4.22708 - 2.85163i) q^{26} +5.64769i q^{27} +(3.36993 + 3.92441i) q^{28} +(-0.764027 - 0.441111i) q^{29} +(0.862182 - 1.87680i) q^{30} -8.69745 q^{31} +(-5.05666 + 2.53578i) q^{32} +(4.75789 + 8.24090i) q^{33} +(1.05733 + 1.49186i) q^{34} +(2.23987 - 1.29319i) q^{35} +(-1.12982 - 1.31572i) q^{36} +(-8.04677 - 4.64580i) q^{37} +(-1.65366 + 1.17201i) q^{38} +(-1.85866 - 4.92674i) q^{39} +(0.778649 + 2.71914i) q^{40} +(-1.97333 + 3.41791i) q^{41} +(0.495890 + 5.31877i) q^{42} +(-9.38995 + 5.42129i) q^{43} +(-12.2955 - 4.31715i) q^{44} +(-0.750950 + 0.433561i) q^{45} +(0.0646021 - 0.140626i) q^{46} -0.158218 q^{47} +(-5.77463 - 0.883017i) q^{48} +(0.155319 - 0.269021i) q^{49} +(1.40811 - 0.131283i) q^{50} +1.88831i q^{51} +(6.32655 + 3.46046i) q^{52} +0.718497i q^{53} +(-0.741448 - 7.95255i) q^{54} +(-3.25785 + 5.64276i) q^{55} +(-5.26043 - 5.08357i) q^{56} -2.09312 q^{57} +(1.13374 + 0.520828i) q^{58} +(-5.04877 + 2.91491i) q^{59} +(-0.967651 + 2.75593i) q^{60} +(-0.0201595 + 0.0116391i) q^{61} +(12.2469 - 1.14183i) q^{62} +(1.12135 - 1.94224i) q^{63} +(6.78741 - 4.23451i) q^{64} +(2.28517 - 2.78890i) q^{65} +(-7.78151 - 10.9794i) q^{66} +(-9.32858 - 5.38586i) q^{67} +(-1.68469 - 1.96188i) q^{68} +(0.138403 - 0.0799067i) q^{69} +(-2.98420 + 2.11501i) q^{70} +(0.759086 + 1.31478i) q^{71} +(1.76364 + 1.70434i) q^{72} +1.16182 q^{73} +(11.9406 + 5.48538i) q^{74} +(1.26478 + 0.730219i) q^{75} +(2.17467 - 1.86741i) q^{76} -16.8521i q^{77} +(3.26399 + 6.69337i) q^{78} -5.45068 q^{79} +(-1.45340 - 3.72661i) q^{80} +(2.82336 - 4.89021i) q^{81} +(2.32995 - 5.07185i) q^{82} +16.1231i q^{83} +(-1.39653 - 7.42429i) q^{84} +(-1.11975 + 0.646488i) q^{85} +(12.5103 - 8.86650i) q^{86} +(0.644215 + 1.11581i) q^{87} +(17.8802 + 4.46481i) q^{88} +(2.35050 - 4.07118i) q^{89} +(1.00050 - 0.709088i) q^{90} +(-1.51192 + 9.20195i) q^{91} +(-0.0725047 + 0.206498i) q^{92} +(11.0003 + 6.35104i) q^{93} +(0.222788 - 0.0207714i) q^{94} +(-0.716607 - 1.24120i) q^{95} +(8.24722 + 0.485270i) q^{96} +(-0.372104 - 0.644503i) q^{97} +(-0.183388 + 0.399201i) q^{98} +5.64991i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

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