LMFDB - Embedded newform 520.2.by.c.61.16

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			61.16
Character	$\chi$	$=$	520.61
Dual form			520.2.by.c.341.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.893979 - 1.09581i) q^{2} +(-0.566349 - 0.326982i) q^{3} +(-0.401602 + 1.95926i) q^{4} +1.00000i q^{5} +(0.147994 + 0.912926i) q^{6} +(0.582724 + 1.00931i) q^{7} +(2.50601 - 1.31146i) q^{8} +(-1.28617 - 2.22770i) q^{9} +O(q^{10})$	\(q+(-0.893979 - 1.09581i) q^{2} +(-0.566349 - 0.326982i) q^{3} +(-0.401602 + 1.95926i) q^{4} +1.00000i q^{5} +(0.147994 + 0.912926i) q^{6} +(0.582724 + 1.00931i) q^{7} +(2.50601 - 1.31146i) q^{8} +(-1.28617 - 2.22770i) q^{9} +(1.09581 - 0.893979i) q^{10} +(-0.0715430 - 0.0413054i) q^{11} +(0.868090 - 0.978310i) q^{12} +(-3.17138 + 1.71533i) q^{13} +(0.585067 - 1.54086i) q^{14} +(0.326982 - 0.566349i) q^{15} +(-3.67743 - 1.57369i) q^{16} +(1.84116 + 3.18898i) q^{17} +(-1.29134 + 3.40092i) q^{18} +(-0.984822 + 0.568587i) q^{19} +(-1.95926 - 0.401602i) q^{20} -0.762160i q^{21} +(0.0186951 + 0.115324i) q^{22} +(-4.08484 + 7.07515i) q^{23} +(-1.84810 - 0.0766728i) q^{24} -1.00000 q^{25} +(4.71482 + 1.94176i) q^{26} +3.64410i q^{27} +(-2.21152 + 0.736371i) q^{28} +(3.65309 + 2.10911i) q^{29} +(-0.912926 + 0.147994i) q^{30} -7.17175 q^{31} +(1.56308 + 5.43661i) q^{32} +(0.0270122 + 0.0467865i) q^{33} +(1.84856 - 4.86844i) q^{34} +(-1.00931 + 0.582724i) q^{35} +(4.88119 - 1.62529i) q^{36} +(8.01115 + 4.62524i) q^{37} +(1.50347 + 0.570873i) q^{38} +(2.35699 + 0.0655083i) q^{39} +(1.31146 + 2.50601i) q^{40} +(-1.49627 + 2.59161i) q^{41} +(-0.835183 + 0.681355i) q^{42} +(-4.80126 + 2.77201i) q^{43} +(0.109660 - 0.123583i) q^{44} +(2.22770 - 1.28617i) q^{45} +(11.4048 - 1.84883i) q^{46} -0.293254 q^{47} +(1.56814 + 2.09371i) q^{48} +(2.82087 - 4.88588i) q^{49} +(0.893979 + 1.09581i) q^{50} -2.40810i q^{51} +(-2.08715 - 6.90245i) q^{52} +4.81827i q^{53} +(3.99324 - 3.25775i) q^{54} +(0.0413054 - 0.0715430i) q^{55} +(2.78398 + 1.76511i) q^{56} +0.743670 q^{57} +(-0.954600 - 5.88860i) q^{58} +(-5.26086 + 3.03736i) q^{59} +(0.978310 + 0.868090i) q^{60} +(9.69723 - 5.59870i) q^{61} +(6.41140 + 7.85888i) q^{62} +(1.49896 - 2.59627i) q^{63} +(4.56013 - 6.57307i) q^{64} +(-1.71533 - 3.17138i) q^{65} +(0.0271208 - 0.0714264i) q^{66} +(-1.42901 - 0.825039i) q^{67} +(-6.98747 + 2.32662i) q^{68} +(4.62689 - 2.67134i) q^{69} +(1.54086 + 0.585067i) q^{70} +(6.55471 + 11.3531i) q^{71} +(-6.14469 - 3.89588i) q^{72} -10.8117 q^{73} +(-2.09342 - 12.9136i) q^{74} +(0.566349 + 0.326982i) q^{75} +(-0.718506 - 2.15787i) q^{76} -0.0962785i q^{77} +(-2.03531 - 2.64138i) q^{78} -10.0329 q^{79} +(1.57369 - 3.67743i) q^{80} +(-2.66694 + 4.61928i) q^{81} +(4.17754 - 0.677221i) q^{82} +6.23077i q^{83} +(1.49327 + 0.306085i) q^{84} +(-3.18898 + 1.84116i) q^{85} +(7.32983 + 2.78315i) q^{86} +(-1.37928 - 2.38899i) q^{87} +(-0.233458 - 0.00968555i) q^{88} +(2.69577 - 4.66920i) q^{89} +(-3.40092 - 1.29134i) q^{90} +(-3.57933 - 2.20133i) q^{91} +(-12.2216 - 10.8447i) q^{92} +(4.06171 + 2.34503i) q^{93} +(0.262163 + 0.321351i) q^{94} +(-0.568587 - 0.984822i) q^{95} +(0.892421 - 3.59012i) q^{96} +(0.603364 + 1.04506i) q^{97} +(-7.87580 + 1.27674i) q^{98} +0.212502i 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 $

$2$	−0.893979	−	1.09581i	−0.632139	−	0.774855i
$2$	−0.893979	−	1.09581i	−0.632139	−	0.774855i
$3$	−0.566349	−	0.326982i	−0.326982	−	0.188783i	0.327519	−	0.944845i	$-0.393788\pi$
$3$	−0.566349	−	0.326982i	−0.326982	−	0.188783i	−0.654500	+	0.756062i	$0.727121\pi$
$4$	−0.401602	+	1.95926i	−0.200801	+	0.979632i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.147994	+	0.912926i	0.0604184	+	0.372700i
$7$	0.582724	+	1.00931i	0.220249	+	0.381482i	0.954883	−	0.296981i	$-0.0959797\pi$
$7$	0.582724	+	1.00931i	0.220249	+	0.381482i	−0.734635	+	0.678463i	$0.762646\pi$
$8$	2.50601	−	1.31146i	0.886007	−	0.463672i
$9$	−1.28617	−	2.22770i	−0.428722	−	0.742568i
$10$	1.09581	−	0.893979i	0.346526	−	0.282701i
$11$	−0.0715430	−	0.0413054i	−0.0215710	−	0.0124540i	0.489176	−	0.872185i	$-0.337298\pi$
$11$	−0.0715430	−	0.0413054i	−0.0215710	−	0.0124540i	−0.510747	+	0.859731i	$0.670631\pi$
$12$	0.868090	−	0.978310i	0.250596	−	0.282414i
$13$	−3.17138	+	1.71533i	−0.879582	+	0.475747i
$13$	−3.17138	+	1.71533i	−0.879582	+	0.475747i
$14$	0.585067	−	1.54086i	0.156366	−	0.411811i
$15$	0.326982	−	0.566349i	0.0844263	−	0.146231i
$16$	−3.67743	−	1.57369i	−0.919358	−	0.393422i
$17$	1.84116	+	3.18898i	0.446547	+	0.773441i	0.998159	−	0.0606595i	$-0.0193204\pi$
$17$	1.84116	+	3.18898i	0.446547	+	0.773441i	−0.551612	+	0.834101i	$0.685987\pi$
$18$	−1.29134	+	3.40092i	−0.304371	+	0.801604i
$19$	−0.984822	+	0.568587i	−0.225934	+	0.130443i	−0.608695	−	0.793405i	$-0.708307\pi$
$19$	−0.984822	+	0.568587i	−0.225934	+	0.130443i	0.382761	+	0.923847i	$0.374973\pi$
$20$	−1.95926	−	0.401602i	−0.438105	−	0.0898009i
$21$		−	0.762160i		−	0.166317i
$22$	0.0186951	+	0.115324i	0.00398581	+	0.0245871i
$23$	−4.08484	+	7.07515i	−0.851748	+	1.47527i	0.0278813	+	0.999611i	$0.491124\pi$
$23$	−4.08484	+	7.07515i	−0.851748	+	1.47527i	−0.879629	+	0.475660i	$0.842209\pi$
$24$	−1.84810	−	0.0766728i	−0.377241	−	0.0156508i
$25$	−1.00000			−0.200000
$26$	4.71482	+	1.94176i	0.924653	+	0.380811i
$27$			3.64410i			0.701307i
$28$	−2.21152	+	0.736371i	−0.417939	+	0.139161i
$29$	3.65309	+	2.10911i	0.678362	+	0.391653i	0.799238	−	0.601015i	$-0.205237\pi$
$29$	3.65309	+	2.10911i	0.678362	+	0.391653i	−0.120876	+	0.992668i	$0.538570\pi$
$30$	−0.912926	+	0.147994i	−0.166677	+	0.0270199i
$31$	−7.17175			−1.28808			−0.644042	−	0.764990i	$-0.722744\pi$
$31$	−7.17175			−1.28808			−0.644042	+	0.764990i	$0.722744\pi$
$32$	1.56308	+	5.43661i	0.276317	+	0.961067i
$33$	0.0270122	+	0.0467865i	0.00470222	+	0.00814448i
$34$	1.84856	−	4.86844i	0.317026	−	0.834931i
$35$	−1.00931	+	0.582724i	−0.170604	+	0.0984983i
$36$	4.88119	−	1.62529i	0.813532	−	0.270881i
$37$	8.01115	+	4.62524i	1.31702	+	0.760385i	0.983249	−	0.182268i	$-0.0583438\pi$
$37$	8.01115	+	4.62524i	1.31702	+	0.760385i	0.333776	+	0.942652i	$0.391677\pi$
$38$	1.50347	+	0.570873i	0.243896	+	0.0926078i
$39$	2.35699	+	0.0655083i	0.377420	+	0.0104897i
$40$	1.31146	+	2.50601i	0.207360	+	0.396234i
$41$	−1.49627	+	2.59161i	−0.233678	+	0.404741i	−0.958888	−	0.283786i	$-0.908409\pi$
$41$	−1.49627	+	2.59161i	−0.233678	+	0.404741i	0.725210	+	0.688528i	$0.241743\pi$
$42$	−0.835183	+	0.681355i	−0.128872	+	0.105135i
$43$	−4.80126	+	2.77201i	−0.732185	+	0.422727i	−0.819221	−	0.573478i	$-0.805594\pi$
$43$	−4.80126	+	2.77201i	−0.732185	+	0.422727i	0.0870357	+	0.996205i	$0.472261\pi$
$44$	0.109660	−	0.123583i	0.0165319	−	0.0186309i
$45$	2.22770	−	1.28617i	0.332087	−	0.191730i
$46$	11.4048	−	1.84883i	1.68154	−	0.272595i
$47$	−0.293254			−0.0427755			−0.0213878	−	0.999771i	$-0.506808\pi$
$47$	−0.293254			−0.0427755			−0.0213878	+	0.999771i	$0.506808\pi$
$48$	1.56814	+	2.09371i	0.226342	+	0.302201i
$49$	2.82087	−	4.88588i	0.402981	−	0.697983i
$50$	0.893979	+	1.09581i	0.126428	+	0.154971i
$51$		−	2.40810i		−	0.337201i
$52$	−2.08715	−	6.90245i	−0.289436	−	0.957197i
$53$			4.81827i			0.661841i	0.943659	+	0.330920i	$0.107359\pi$
$53$			4.81827i			0.661841i	−0.943659	+	0.330920i	$0.892641\pi$
$54$	3.99324	−	3.25775i	0.543412	−	0.443324i
$55$	0.0413054	−	0.0715430i	0.00556961	−	0.00964685i
$56$	2.78398	+	1.76511i	0.372025	+	0.235873i
$57$	0.743670			0.0985015
$58$	−0.954600	−	5.88860i	−0.125345	−	0.773211i
$59$	−5.26086	+	3.03736i	−0.684906	+	0.395430i	−0.801701	−	0.597726i	$-0.796071\pi$
$59$	−5.26086	+	3.03736i	−0.684906	+	0.395430i	0.116795	+	0.993156i	$0.462738\pi$
$60$	0.978310	+	0.868090i	0.126299	+	0.112070i
$61$	9.69723	−	5.59870i	1.24160	−	0.716840i	0.272183	−	0.962246i	$-0.412254\pi$
$61$	9.69723	−	5.59870i	1.24160	−	0.716840i	0.969420	+	0.245406i	$0.0789212\pi$
$62$	6.41140	+	7.85888i	0.814249	+	0.998079i
$63$	1.49896	−	2.59627i	0.188851	−	0.327100i
$64$	4.56013	−	6.57307i	0.570017	−	0.821633i
$65$	−1.71533	−	3.17138i	−0.212760	−	0.393361i
$66$	0.0271208	−	0.0714264i	0.00333834	−	0.00879198i
$67$	−1.42901	−	0.825039i	−0.174581	−	0.100795i	0.410163	−	0.912012i	$-0.365472\pi$
$67$	−1.42901	−	0.825039i	−0.174581	−	0.100795i	−0.584744	+	0.811218i	$0.698805\pi$
$68$	−6.98747	+	2.32662i	−0.847355	+	0.282144i
$69$	4.62689	−	2.67134i	0.557012	−	0.321591i
$70$	1.54086	+	0.585067i	0.184167	+	0.0699288i
$71$	6.55471	+	11.3531i	0.777900	+	1.34736i	0.933150	+	0.359488i	$0.117049\pi$
$71$	6.55471	+	11.3531i	0.777900	+	1.34736i	−0.155249	+	0.987875i	$0.549618\pi$
$72$	−6.14469	−	3.89588i	−0.724159	−	0.459134i
$73$	−10.8117			−1.26541			−0.632706	−	0.774392i	$-0.718056\pi$
$73$	−10.8117			−1.26541			−0.632706	+	0.774392i	$0.718056\pi$
$74$	−2.09342	−	12.9136i	−0.243355	−	1.50117i
$75$	0.566349	+	0.326982i	0.0653963	+	0.0377566i
$76$	−0.718506	−	2.15787i	−0.0824183	−	0.247525i
$77$		−	0.0962785i		−	0.0109720i
$78$	−2.03531	−	2.64138i	−0.230454	−	0.299077i
$79$	−10.0329			−1.12879			−0.564393	−	0.825506i	$-0.690890\pi$
$79$	−10.0329			−1.12879			−0.564393	+	0.825506i	$0.690890\pi$
$80$	1.57369	−	3.67743i	0.175944	−	0.411149i
$81$	−2.66694	+	4.61928i	−0.296327	+	0.513254i
$82$	4.17754	−	0.677221i	0.461333	−	0.0747865i
$83$			6.23077i			0.683916i	0.939715	+	0.341958i	$0.111090\pi$
$83$			6.23077i			0.683916i	−0.939715	+	0.341958i	$0.888910\pi$
$84$	1.49327	+	0.306085i	0.162929	+	0.0333966i
$85$	−3.18898	+	1.84116i	−0.345893	+	0.199702i
$86$	7.32983	+	2.78315i	0.790395	+	0.300115i
$87$	−1.37928	−	2.38899i	−0.147875	−	0.256126i
$88$	−0.233458	−	0.00968555i	−0.0248867	−	0.00103248i
$89$	2.69577	−	4.66920i	0.285751	−	0.494935i	−0.687040	−	0.726619i	$-0.741090\pi$
$89$	2.69577	−	4.66920i	0.285751	−	0.494935i	0.972791	+	0.231685i	$0.0744238\pi$
$90$	−3.40092	−	1.29134i	−0.358488	−	0.136119i
$91$	−3.57933	−	2.20133i	−0.375216	−	0.230762i
$92$	−12.2216	−	10.8447i	−1.27419	−	1.13064i
$93$	4.06171	+	2.34503i	0.421180	+	0.243168i
$94$	0.262163	+	0.321351i	0.0270401	+	0.0331448i
$95$	−0.568587	−	0.984822i	−0.0583358	−	0.101041i
$96$	0.892421	−	3.59012i	0.0910824	−	0.366415i
$97$	0.603364	+	1.04506i	0.0612623	+	0.106109i	0.895030	−	0.446006i	$-0.147154\pi$
$97$	0.603364	+	1.04506i	0.0612623	+	0.106109i	−0.833768	+	0.552116i	$0.813821\pi$
$98$	−7.87580	+	1.27674i	−0.795576	+	0.128971i
$99$			0.212502i			0.0213573i
$100$	0.401602	−	1.95926i	0.0401602	−	0.195926i
$101$	−0.297663	−	0.171856i	−0.0296186	−	0.0171003i	0.485118	−	0.874449i	$-0.338777\pi$
$101$	−0.297663	−	0.171856i	−0.0296186	−	0.0171003i	−0.514736	+	0.857349i	$0.672110\pi$
$102$	−2.63882	+	2.15279i	−0.261282	+	0.213158i
$103$	2.38124			0.234631			0.117315	−	0.993095i	$-0.462571\pi$
$103$	2.38124			0.234631			0.117315	+	0.993095i	$0.462571\pi$
$104$	−5.69791	+	8.45777i	−0.558726	+	0.829353i
$105$	0.762160			0.0743792
$106$	5.27992	−	4.30744i	0.512831	−	0.418375i
$107$	−5.55175	−	3.20531i	−0.536708	−	0.309869i	0.207036	−	0.978333i	$-0.433618\pi$
$107$	−5.55175	−	3.20531i	−0.536708	−	0.309869i	−0.743744	+	0.668465i	$0.766952\pi$
$108$	−7.13975	−	1.46348i	−0.687023	−	0.140823i
$109$			11.5974i			1.11083i	0.831573	+	0.555415i	$0.187441\pi$
$109$			11.5974i			1.11083i	−0.831573	+	0.555415i	$0.812559\pi$
$110$	−0.115324	+	0.0186951i	−0.0109957	+	0.00178251i
$111$	−3.02474	−	5.23900i	−0.287095	−	0.497264i
$112$	−0.554593	−	4.62869i	−0.0524041	−	0.437370i
$113$	−3.68461	−	6.38193i	−0.346619	−	0.600362i	0.639027	−	0.769184i	$-0.279337\pi$
$113$	−3.68461	−	6.38193i	−0.346619	−	0.600362i	−0.985647	+	0.168822i	$0.946004\pi$
$114$	−0.664826	−	0.814921i	−0.0622666	−	0.0763244i
$115$	−7.07515	−	4.08484i	−0.659761	−	0.380913i
$116$	−5.59940	+	6.31035i	−0.519891	+	0.585901i
$117$	7.90017	+	4.85870i	0.730371	+	0.449187i
$118$	8.03147	+	3.04957i	0.739357	+	0.280736i
$119$	−2.14577	+	3.71659i	−0.196703	+	0.340699i
$120$	0.0766728	−	1.84810i	0.00699924	−	0.168707i
$121$	−5.49659	−	9.52037i	−0.499690	−	0.865488i
$122$	−14.8042	−	5.62121i	−1.34031	−	0.508920i
$123$	1.69482	−	0.978503i	0.152816	−	0.0882286i
$124$	2.88019	−	14.0514i	0.258649	−	1.26185i
$125$		−	1.00000i		−	0.0894427i
$126$	−4.18506	+	0.678440i	−0.372835	+	0.0604402i
$127$	7.35241	−	12.7347i	0.652421	−	1.13003i	−0.330113	−	0.943941i	$-0.607087\pi$
$127$	7.35241	−	12.7347i	0.652421	−	1.13003i	0.982534	−	0.186084i	$-0.0595798\pi$
$128$	−11.2795	+	0.879143i	−0.996976	+	0.0777060i
$129$	3.62558			0.319215
$130$	−1.94176	+	4.71482i	−0.170304	+	0.413517i
$131$		−	20.1982i		−	1.76473i	−0.470568	−	0.882364i	$-0.655951\pi$
$131$		−	20.1982i		−	1.76473i	0.470568	−	0.882364i	$-0.344049\pi$
$132$	−0.102515	+	0.0341345i	−0.00892280	+	0.00297102i
$133$	−1.14776	−	0.662659i	−0.0995233	−	0.0574598i
$134$	0.373418	+	2.30349i	0.0322584	+	0.198991i
$135$	−3.64410			−0.313634
$136$	8.79618	+	5.57699i	0.754266	+	0.478223i
$137$	8.68742	+	15.0470i	0.742216	+	1.28556i	0.951484	+	0.307698i	$0.0995585\pi$
$137$	8.68742	+	15.0470i	0.742216	+	1.28556i	−0.209268	+	0.977858i	$0.567108\pi$
$138$	−7.06362	−	2.68207i	−0.601295	−	0.228313i
$139$	10.6633	−	6.15645i	0.904449	−	0.522184i	0.0258077	−	0.999667i	$-0.491784\pi$
$139$	10.6633	−	6.15645i	0.904449	−	0.522184i	0.878641	+	0.477483i	$0.158451\pi$
$140$	−0.736371	−	2.21152i	−0.0622347	−	0.186908i
$141$	0.166084	+	0.0958888i	0.0139868	+	0.00807529i
$142$	6.58106	−	17.3321i	0.552270	−	1.45448i
$143$	0.297742	+	0.00827521i	0.0248985	+	0.000692008i
$144$	1.22408	+	10.2163i	0.102006	+	0.851355i
$145$	−2.10911	+	3.65309i	−0.175152	+	0.303373i
$146$	9.66543	+	11.8476i	0.799917	+	0.980511i
$147$	−3.19519	+	1.84474i	−0.263535	+	0.152152i
$148$	−12.2794	+	13.8385i	−1.00936	+	1.13751i
$149$	−5.52280	+	3.18859i	−0.452446	+	0.261220i	−0.708862	−	0.705347i	$-0.750791\pi$
$149$	−5.52280	+	3.18859i	−0.452446	+	0.261220i	0.256417	+	0.966566i	$0.417458\pi$
$150$	−0.147994	−	0.912926i	−0.0120837	−	0.0745401i
$151$	−8.80854			−0.716829			−0.358415	−	0.933563i	$-0.616683\pi$
$151$	−8.80854			−0.716829			−0.358415	+	0.933563i	$0.616683\pi$
$152$	−1.72229	+	2.71644i	−0.139696	+	0.220332i
$153$	4.73607	−	8.20312i	0.382889	−	0.663183i
$154$	−0.105503	+	0.0860710i	−0.00850167	+	0.00693580i
$155$		−	7.17175i		−	0.576049i
$156$	−1.07492	+	4.59165i	−0.0860623	+	0.367626i
$157$		−	18.8315i		−	1.50292i	−0.659779	−	0.751460i	$-0.729350\pi$
$157$		−	18.8315i		−	1.50292i	0.659779	−	0.751460i	$-0.270650\pi$
$158$	8.96918	+	10.9941i	0.713549	+	0.874645i
$159$	1.57549	−	2.72882i	0.124944	−	0.216410i
$160$	−5.43661	+	1.56308i	−0.429802	+	0.123573i
$161$	−9.52134			−0.750387
$162$	7.44605	−	1.20708i	0.585017	−	0.0948370i
$163$	−17.1137	+	9.88059i	−1.34045	+	0.773908i	−0.986873	−	0.161499i	$-0.948367\pi$
$163$	−17.1137	+	9.88059i	−1.34045	+	0.773908i	−0.353574	+	0.935406i	$0.615034\pi$
$164$	−4.47674	−	3.97238i	−0.349575	−	0.310190i
$165$	−0.0467865	+	0.0270122i	−0.00364232	+	0.00210290i
$166$	6.82774	−	5.57018i	0.529936	−	0.432330i
$167$	4.50432	−	7.80171i	0.348555	−	0.603714i	−0.637438	−	0.770501i	$-0.720006\pi$
$167$	4.50432	−	7.80171i	0.348555	−	0.603714i	0.985993	+	0.166787i	$0.0533393\pi$
$168$	−0.999544	−	1.90998i	−0.0771165	−	0.147358i
$169$	7.11529	−	10.8799i	0.547330	−	0.836917i
$170$	4.86844	+	1.84856i	0.373393	+	0.141778i
$171$	2.53329	+	1.46259i	0.193725	+	0.111847i
$172$	−3.50290	−	10.5202i	−0.267094	−	0.802156i
$173$	0.211505	−	0.122113i	0.0160804	−	0.00928404i	−0.491938	−	0.870630i	$-0.663711\pi$
$173$	0.211505	−	0.122113i	0.0160804	−	0.00928404i	0.508019	+	0.861346i	$0.330378\pi$
$174$	−1.38483	+	3.64714i	−0.104984	+	0.276489i
$175$	−0.582724	−	1.00931i	−0.0440498	−	0.0762965i
$176$	0.198093	+	0.264484i	0.0149318	+	0.0199362i
$177$	3.97264			0.298602
$178$	−7.52652	+	1.22012i	−0.564137	+	0.0914521i
$179$	−7.57467	−	4.37324i	−0.566157	−	0.326871i	0.189456	−	0.981889i	$-0.439328\pi$
$179$	−7.57467	−	4.37324i	−0.566157	−	0.326871i	−0.755613	+	0.655018i	$0.772661\pi$
$180$	1.62529	+	4.88119i	0.121142	+	0.363822i
$181$		−	20.3752i		−	1.51447i	−0.653140	−	0.757237i	$-0.726549\pi$
$181$		−	20.3752i		−	1.51447i	0.653140	−	0.757237i	$-0.273451\pi$
$182$	0.787605	+	5.89022i	0.0583812	+	0.436612i
$183$	−7.32269			−0.541309
$184$	−0.957840	+	23.0875i	−0.0706129	+	1.70203i
$185$	−4.62524	+	8.01115i	−0.340054	+	0.588991i
$186$	−1.06138	−	6.54728i	−0.0778240	−	0.480070i
$187$		−	0.304199i		−	0.0222452i
$188$	0.117771	−	0.574563i	0.00858936	−	0.0419043i
$189$	−3.67802	+	2.12350i	−0.267536	+	0.154462i
$190$	−0.570873	+	1.50347i	−0.0414155	+	0.109073i
$191$	8.77284	+	15.1950i	0.634780	+	1.09947i	0.986562	+	0.163390i	$0.0522427\pi$
$191$	8.77284	+	15.1950i	0.634780	+	1.09947i	−0.351781	+	0.936082i	$0.614424\pi$
$192$	−4.73190	+	2.23157i	−0.341495	+	0.161050i
$193$	5.99959	−	10.3916i	0.431860	−	0.748003i	−0.565174	−	0.824972i	$-0.691191\pi$
$193$	5.99959	−	10.3916i	0.431860	−	0.748003i	0.997033	+	0.0769690i	$0.0245243\pi$
$194$	0.605789	−	1.59543i	0.0434931	−	0.114545i
$195$	−0.0655083	+	2.35699i	−0.00469115	+	0.168787i
$196$	8.43987	+	7.48900i	0.602848	+	0.534929i
$197$	18.9738	+	10.9545i	1.35183	+	0.780478i	0.988505	−	0.151185i	$-0.0483090\pi$
$197$	18.9738	+	10.9545i	1.35183	+	0.780478i	0.363323	+	0.931663i	$0.381642\pi$
$198$	0.232862	−	0.189973i	0.0165488	−	0.0135008i
$199$	13.0953	+	22.6817i	0.928302	+	1.60787i	0.786162	+	0.618020i	$0.212065\pi$
$199$	13.0953	+	22.6817i	0.928302	+	1.60787i	0.142140	+	0.989847i	$0.454602\pi$
$200$	−2.50601	+	1.31146i	−0.177201	+	0.0927344i
$201$	0.539545	+	0.934519i	0.0380566	+	0.0659159i
$202$	0.0777832	+	0.479818i	0.00547280	+	0.0337599i
$203$			4.91612i			0.345044i
$204$	4.71810	+	0.967097i	0.330333	+	0.0677103i
$205$	−2.59161	−	1.49627i	−0.181006	−	0.104504i
$206$	−2.12878	−	2.60939i	−0.148319	−	0.181805i
$207$	21.0151			1.46065
$208$	14.3619	−	1.31725i	0.995820	−	0.0913345i
$209$	0.0939428			0.00649816
$210$	−0.681355	−	0.835183i	−0.0470180	−	0.0576331i
$211$	−5.08017	−	2.93304i	−0.349734	−	0.201919i	0.314834	−	0.949147i	$-0.398051\pi$
$211$	−5.08017	−	2.93304i	−0.349734	−	0.201919i	−0.664568	+	0.747228i	$0.731384\pi$
$212$	−9.44027	−	1.93503i	−0.648360	−	0.132898i
$213$		−	8.57307i		−	0.587417i
$214$	1.45074	+	8.94915i	0.0991709	+	0.611751i
$215$	−2.77201	−	4.80126i	−0.189049	−	0.327443i
$216$	4.77910	+	9.13214i	0.325177	+	0.621363i
$217$	−4.17915	−	7.23850i	−0.283699	−	0.491382i
$218$	12.7086	−	10.3678i	0.860733	−	0.702199i
$219$	6.12319	+	3.53522i	0.413767	+	0.238888i
$220$	0.123583	+	0.109660i	0.00833198	+	0.00739327i
$221$	−11.3092	−	6.95527i	−0.760737	−	0.467862i
$222$	−3.03690	+	7.99809i	−0.203823	+	0.536797i
$223$	7.79650	−	13.5039i	0.522092	−	0.904290i	−0.477578	−	0.878590i	$-0.658485\pi$
$223$	7.79650	−	13.5039i	0.522092	−	0.904290i	0.999670	−	0.0257004i	$-0.00818159\pi$
$224$	−4.57637	+	4.74568i	−0.305771	+	0.317084i
$225$	1.28617	+	2.22770i	0.0857444	+	0.148514i
$226$	−3.69942	+	9.74295i	−0.246082	+	0.648092i
$227$	8.95469	−	5.16999i	0.594343	−	0.343144i	−0.172470	−	0.985015i	$-0.555175\pi$
$227$	8.95469	−	5.16999i	0.594343	−	0.343144i	0.766813	+	0.641871i	$0.221841\pi$
$228$	−0.298659	+	1.45705i	−0.0197792	+	0.0964952i
$229$			3.79374i			0.250697i	0.992113	+	0.125349i	$0.0400049\pi$
$229$			3.79374i			0.250697i	−0.992113	+	0.125349i	$0.959995\pi$
$230$	1.84883	+	11.4048i	0.121908	+	0.752009i
$231$	−0.0314813	+	0.0545272i	−0.00207132	+	0.00358763i
$232$	11.9207	+	0.494559i	0.782632	+	0.0324694i
$233$	20.7857			1.36172			0.680858	−	0.732415i	$-0.261607\pi$
$233$	20.7857			1.36172			0.680858	+	0.732415i	$0.261607\pi$
$234$	−1.73837	−	13.0007i	−0.113641	−	0.849880i
$235$		−	0.293254i		−	0.0191298i
$236$	−3.83822	−	11.5272i	−0.249847	−	0.750358i
$237$	5.68210	+	3.28056i	0.369092	+	0.213095i
$238$	5.99096	−	0.971193i	0.388336	−	0.0629531i
$239$	1.14851			0.0742908			0.0371454	−	0.999310i	$-0.488174\pi$
$239$	1.14851			0.0742908			0.0371454	+	0.999310i	$0.488174\pi$
$240$	−2.09371	+	1.56814i	−0.135148	+	0.101223i
$241$	1.42659	+	2.47092i	0.0918947	+	0.159166i	0.908308	−	0.418301i	$-0.137374\pi$
$241$	1.42659	+	2.47092i	0.0918947	+	0.159166i	−0.816414	+	0.577467i	$0.804041\pi$
$242$	−5.51869	+	14.5342i	−0.354755	+	0.934296i
$243$	12.4885	−	7.21023i	0.801137	−	0.462537i
$244$	7.07491	+	21.2479i	0.452924	+	1.36026i
$245$	4.88588	+	2.82087i	0.312148	+	0.180218i
$246$	−2.58739	−	0.982437i	−0.164966	−	0.0626379i
$247$	2.14793	−	3.49250i	0.136669	−	0.222222i
$248$	−17.9725	+	9.40548i	−1.14125	+	0.597249i
$249$	2.03735	−	3.52879i	0.129112	−	0.223628i
$250$	−1.09581	+	0.893979i	−0.0693051	+	0.0565402i
$251$	0.294868	−	0.170242i	0.0186119	−	0.0107456i	−0.490665	−	0.871348i	$-0.663246\pi$
$251$	0.294868	−	0.170242i	0.0186119	−	0.0107456i	0.509277	+	0.860603i	$0.329913\pi$
$252$	4.48480	+	3.97953i	0.282516	+	0.250687i
$253$	0.584483	−	0.337452i	0.0367461	−	0.0212154i
$254$	−20.5278	+	3.32775i	−1.28803	+	0.208802i
$255$	2.40810			0.150801
$256$	11.0470	+	11.5743i	0.690438	+	0.723391i
$257$	−7.84230	+	13.5833i	−0.489189	+	0.847301i	−0.999923	−	0.0124383i	$-0.996041\pi$
$257$	−7.84230	+	13.5833i	−0.489189	+	0.847301i	0.510733	+	0.859739i	$0.329374\pi$
$258$	−3.24120	−	3.97295i	−0.201788	−	0.247345i
$259$			10.7810i			0.669896i
$260$	6.90245	−	2.08715i	0.428072	−	0.129440i
$261$		−	10.8507i		−	0.671640i
$262$	−22.1334	+	18.0568i	−1.36741	+	1.11555i
$263$	−7.30153	+	12.6466i	−0.450231	+	0.779824i	−0.998400	−	0.0565442i	$-0.981992\pi$
$263$	−7.30153	+	12.6466i	−0.450231	+	0.779824i	0.548169	+	0.836368i	$0.315325\pi$
$264$	0.129051	+	0.0818217i	0.00794256	+	0.00503578i
$265$	−4.81827			−0.295984
$266$	0.299924	+	1.85013i	0.0183895	+	0.113439i
$267$	−3.05349	+	1.76293i	−0.186870	+	0.107890i
$268$	2.19036	−	2.46847i	0.133798	−	0.150786i
$269$	4.51592	−	2.60727i	0.275341	−	0.158968i	−0.355972	−	0.934497i	$-0.615850\pi$
$269$	4.51592	−	2.60727i	0.275341	−	0.158968i	0.631312	+	0.775529i	$0.282517\pi$
$270$	3.25775	+	3.99324i	0.198260	+	0.243021i
$271$	0.0463259	−	0.0802389i	0.00281410	−	0.00487416i	−0.864615	−	0.502435i	$-0.832438\pi$
$271$	0.0463259	−	0.0802389i	0.00281410	−	0.00487416i	0.867429	+	0.497561i	$0.165771\pi$
$272$	−1.75228	−	14.6247i	−0.106247	−	0.886751i
$273$	1.30736	+	2.41710i	0.0791247	+	0.146289i
$274$	8.72234	−	22.9715i	0.526936	−	1.38776i
$275$	0.0715430	+	0.0413054i	0.00431420	+	0.00249081i
$276$	3.37569	+	10.1381i	0.203192	+	0.610242i
$277$	−25.3143	+	14.6152i	−1.52099	+	0.878145i	−0.521298	+	0.853375i	$0.674552\pi$
$277$	−25.3143	+	14.6152i	−1.52099	+	0.878145i	−0.999693	+	0.0247703i	$0.992115\pi$
$278$	−16.2791	−	6.18120i	−0.976354	−	0.370724i
$279$	9.22407	+	15.9766i	0.552230	+	0.956491i
$280$	−1.76511	+	2.78398i	−0.105486	+	0.166375i
$281$	11.1926			0.667697			0.333849	−	0.942627i	$-0.391653\pi$
$281$	11.1926			0.667697			0.333849	+	0.942627i	$0.391653\pi$
$282$	−0.0433999	−	0.267719i	−0.00258443	−	0.0159425i
$283$	8.64970	+	4.99391i	0.514171	+	0.296857i	0.734547	−	0.678558i	$-0.237395\pi$
$283$	8.64970	+	4.99391i	0.514171	+	0.296857i	−0.220375	+	0.975415i	$0.570728\pi$
$284$	−24.8761	+	8.28298i	−1.47612	+	0.491505i
$285$			0.743670i			0.0440512i
$286$	−0.257107	−	0.333667i	−0.0152031	−	0.0197301i
$287$	−3.48764			−0.205869
$288$	10.1008	−	10.4745i	0.595194	−	0.617215i
$289$	1.72027	−	2.97959i	0.101192	−	0.175270i
$290$	5.88860	−	0.954600i	0.345791	−	0.0560560i
$291$		−	0.789155i		−	0.0462611i
$292$	4.34199	−	21.1830i	0.254096	−	1.23964i
$293$	−13.4166	+	7.74610i	−0.783808	+	0.452532i	−0.837778	−	0.546011i	$-0.816146\pi$
$293$	−13.4166	+	7.74610i	−0.783808	+	0.452532i	0.0539701	+	0.998543i	$0.482812\pi$
$294$	4.87792	+	1.85216i	0.284486	+	0.108020i
$295$	−3.03736	−	5.26086i	−0.176842	−	0.306299i
$296$	26.1418	+	1.08456i	1.51946	+	0.0630386i
$297$	0.150521	−	0.260710i	0.00873411	−	0.0151279i
$298$	8.43136	+	3.20141i	0.488416	+	0.185453i
$299$	0.818367	−	29.4448i	0.0473274	−	1.70284i
$300$	−0.868090	+	0.978310i	−0.0501192	+	0.0564828i
$301$	−5.59562	−	3.23063i	−0.322526	−	0.186211i
$302$	7.87466	+	9.65249i	0.453135	+	0.555439i
$303$	0.112387	+	0.194661i	0.00645648	+	0.0111830i
$304$	4.51639	−	0.541139i	0.259033	−	0.0310364i
$305$	5.59870	+	9.69723i	0.320581	+	0.555262i
$306$	−13.2230	+	2.14358i	−0.755909	+	0.122540i
$307$			20.1693i			1.15112i	0.817758	+	0.575562i	$0.195217\pi$
$307$			20.1693i			1.15112i	−0.817758	+	0.575562i	$0.804783\pi$
$308$	0.188635	+	0.0386656i	0.0107485	+	0.00220318i
$309$	−1.34861	−	0.778623i	−0.0767200	−	0.0442943i
$310$	−7.85888	+	6.41140i	−0.446355	+	0.364143i
$311$	−3.39128			−0.192302			−0.0961510	−	0.995367i	$-0.530653\pi$
$311$	−3.39128			−0.192302			−0.0961510	+	0.995367i	$0.530653\pi$
$312$	5.99254	−	2.92694i	0.339261	−	0.165705i
$313$	2.38856			0.135009			0.0675046	−	0.997719i	$-0.478496\pi$
$313$	2.38856			0.135009			0.0675046	+	0.997719i	$0.478496\pi$
$314$	−20.6358	+	16.8350i	−1.16454	+	0.950054i
$315$	2.59627	+	1.49896i	0.146283	+	0.0844568i
$316$	4.02922	−	19.6570i	0.226661	−	1.10579i
$317$			17.6455i			0.991072i	0.868587	+	0.495536i	$0.165028\pi$
$317$			17.6455i			0.991072i	−0.868587	+	0.495536i	$0.834972\pi$
$318$	−4.39873	+	0.713077i	−0.246668	+	0.0399873i
$319$	−0.174235	−	0.301785i	−0.00975531	−	0.0168967i
$320$	6.57307	+	4.56013i	0.367446	+	0.254919i
$321$	2.09615	+	3.63064i	0.116996	+	0.202643i
$322$	8.51188	+	10.4336i	0.474349	+	0.581441i
$323$	−3.62643	−	2.09372i	−0.201780	−	0.116498i
$324$	−7.97935	−	7.08036i	−0.443297	−	0.393353i
$325$	3.17138	−	1.71533i	0.175916	−	0.0951493i
$326$	26.1265	+	9.92031i	1.44701	+	0.549435i
$327$	3.79214	−	6.56818i	0.209706	−	0.363221i
$328$	−0.350854	+	8.45688i	−0.0193727	+	0.466953i
$329$	−0.170886	−	0.295984i	−0.00942127	−	0.0163181i
$330$	0.0714264	+	0.0271208i	0.00393189	+	0.00149295i
$331$	4.79626	−	2.76912i	0.263626	−	0.152205i	−0.362361	−	0.932038i	$-0.618029\pi$
$331$	4.79626	−	2.76912i	0.263626	−	0.152205i	0.625988	+	0.779833i	$0.284696\pi$
$332$	−12.2077	−	2.50229i	−0.669986	−	0.137331i
$333$		−	23.7953i		−	1.30397i
$334$	−12.5760	+	2.03869i	−0.688126	+	0.111552i
$335$	0.825039	−	1.42901i	0.0450767	−	0.0780751i
$336$	−1.19940	+	2.80279i	−0.0654327	+	0.152905i
$337$	27.2142			1.48245			0.741226	−	0.671255i	$-0.234244\pi$
$337$	27.2142			1.48245			0.741226	+	0.671255i	$0.234244\pi$
$338$	−18.2833	+	1.92941i	−0.994478	+	0.104946i
$339$			4.81920i			0.261743i
$340$	−2.32662	−	6.98747i	−0.126178	−	0.378949i
$341$	0.513089	+	0.296232i	0.0277853	+	0.0160419i
$342$	−0.661981	−	4.08353i	−0.0357958	−	0.220812i
$343$	14.7333			0.795522
$344$	−8.39660	+	13.2433i	−0.452715	+	0.714033i
$345$	2.67134	+	4.62689i	0.143820	+	0.249103i
$346$	−0.322893	−	0.122603i	−0.0173589	−	0.00659120i
$347$	−17.1234	+	9.88620i	−0.919233	+	0.530719i	−0.883390	−	0.468638i	$-0.844745\pi$
$347$	−17.1234	+	9.88620i	−0.919233	+	0.530719i	−0.0358425	+	0.999357i	$0.511411\pi$
$348$	5.23458	−	1.74296i	0.280603	−	0.0934323i
$349$	−22.4492	−	12.9610i	−1.20168	−	0.693788i	−0.240748	−	0.970588i	$-0.577393\pi$
$349$	−22.4492	−	12.9610i	−1.20168	−	0.693788i	−0.960928	+	0.276800i	$0.910726\pi$
$350$	−0.585067	+	1.54086i	−0.0312731	+	0.0823622i
$351$	−6.25083	−	11.5568i	−0.333645	−	0.616858i
$352$	0.112734	−	0.453515i	0.00600872	−	0.0241724i
$353$	−2.71865	+	4.70884i	−0.144699	+	0.250626i	−0.929261	−	0.369425i	$-0.879555\pi$
$353$	−2.71865	+	4.70884i	−0.144699	+	0.250626i	0.784561	+	0.620051i	$0.212888\pi$
$354$	−3.55146	−	4.35326i	−0.188758	−	0.231373i
$355$	−11.3531	+	6.55471i	−0.602559	+	0.347888i
$356$	8.06558	+	7.15688i	0.427475	+	0.379314i
$357$	2.43051	−	1.40326i	0.128636	−	0.0742683i
$358$	1.97936	+	12.2100i	0.104612	+	0.645318i
$359$	−8.57988			−0.452829			−0.226414	−	0.974031i	$-0.572700\pi$
$359$	−8.57988			−0.452829			−0.226414	+	0.974031i	$0.572700\pi$
$360$	3.89588	−	6.14469i	0.205331	−	0.323854i
$361$	−8.85342	+	15.3346i	−0.465969	+	0.807083i
$362$	−22.3273	+	18.2150i	−1.17350	+	0.957358i
$363$			7.18913i			0.377332i
$364$	5.75046	−	6.12880i	0.301406	−	0.321236i
$365$		−	10.8117i		−	0.565910i
$366$	6.54633	+	8.02428i	0.342182	+	0.419436i
$367$	18.0985	−	31.3476i	0.944735	−	1.63633i	0.188455	−	0.982082i	$-0.439652\pi$
$367$	18.0985	−	31.3476i	0.944735	−	1.63633i	0.756280	−	0.654248i	$-0.227015\pi$
$368$	26.1558	−	19.5901i	1.36347	−	1.02121i
$369$	7.69779			0.400731
$370$	12.9136	−	2.09342i	0.671345	−	0.108832i
$371$	−4.86312	+	2.80772i	−0.252481	+	0.145770i
$372$	−6.22573	+	7.01620i	−0.322789	+	0.363773i
$373$	−10.7736	+	6.22013i	−0.557835	+	0.322066i	−0.752276	−	0.658848i	$-0.771044\pi$
$373$	−10.7736	+	6.22013i	−0.557835	+	0.322066i	0.194441	+	0.980914i	$0.437711\pi$
$374$	−0.333344	+	0.271948i	−0.0172368	+	0.0140621i
$375$	−0.326982	+	0.566349i	−0.0168853	+	0.0292461i
$376$	−0.734897	+	0.384592i	−0.0378994	+	0.0198338i
$377$	−15.2032	−	0.422545i	−0.783003	−	0.0217622i
$378$	5.61503	+	2.13204i	0.288806	+	0.109660i
$379$	24.9450	+	14.4020i	1.28134	+	0.739782i	0.977093	−	0.212812i	$-0.0682621\pi$
$379$	24.9450	+	14.4020i	1.28134	+	0.739782i	0.304246	+	0.952593i	$0.401595\pi$
$380$	2.15787	−	0.718506i	0.110696	−	0.0368586i
$381$	−8.32805	+	4.80820i	−0.426659	+	0.246332i
$382$	8.80811	−	23.1974i	0.450662	−	1.18688i
$383$	−2.51310	−	4.35281i	−0.128413	−	0.222418i	0.794649	−	0.607070i	$-0.207655\pi$
$383$	−2.51310	−	4.35281i	−0.128413	−	0.222418i	−0.923062	+	0.384651i	$0.874322\pi$
$384$	6.67559	+	3.19029i	0.340662	+	0.162804i
$385$	0.0962785			0.00490681
$386$	−16.7507	+	2.71546i	−0.852589	+	0.138213i
$387$	12.3504	+	7.13053i	0.627808	+	0.362465i
$388$	−2.28985	+	0.762452i	−0.116250	+	0.0387077i
$389$		−	6.19871i		−	0.314287i	−0.987576	−	0.157144i	$-0.949771\pi$
$389$		−	6.19871i		−	0.314287i	0.987576	−	0.157144i	$-0.0502286\pi$
$390$	2.64138	−	2.03531i	0.133751	−	0.103062i
$391$	−30.0834			−1.52138
$392$	0.661455	−	15.9435i	0.0334085	−	0.805269i
$393$	−6.60445	+	11.4392i	−0.333150	+	0.577033i
$394$	−4.95810	−	30.5848i	−0.249785	−	1.54084i
$395$		−	10.0329i		−	0.504808i
$396$	−0.416348	−	0.0853412i	−0.0209223	−	0.00428856i
$397$	−15.7617	+	9.10005i	−0.791059	+	0.456718i	−0.840335	−	0.542067i	$-0.817642\pi$
$397$	−15.7617	+	9.10005i	−0.791059	+	0.456718i	0.0492760	+	0.998785i	$0.484309\pi$
$398$	13.1480	−	34.6270i	0.659048	−	1.73569i
$399$	0.433354	+	0.750592i	0.0216949	+	0.0375766i
$400$	3.67743	+	1.57369i	0.183872	+	0.0786844i
$401$	11.5905	−	20.0753i	0.578802	−	1.00251i	−0.416815	−	0.908991i	$-0.636854\pi$
$401$	11.5905	−	20.0753i	0.578802	−	1.00251i	0.995617	−	0.0935229i	$-0.0298128\pi$
$402$	0.541714	−	1.42668i	0.0270182	−	0.0711563i
$403$	22.7443	−	12.3019i	1.13298	−	0.612802i
$404$	0.456253	−	0.514183i	0.0226994	−	0.0255815i
$405$	−4.61928	−	2.66694i	−0.229534	−	0.132522i
$406$	5.38714	−	4.39491i	0.267359	−	0.218116i
$407$	−0.382094	−	0.661807i	−0.0189397	−	0.0328045i
$408$	−3.15813	−	6.03471i	−0.156351	−	0.298763i
$409$	−2.29895	−	3.98189i	−0.113676	−	0.196892i	0.803574	−	0.595205i	$-0.202929\pi$
$409$	−2.29895	−	3.98189i	−0.113676	−	0.196892i	−0.917250	+	0.398313i	$0.869596\pi$
$410$	0.677221	+	4.17754i	0.0334455	+	0.206314i
$411$		−	11.3625i		−	0.560471i
$412$	−0.956311	+	4.66548i	−0.0471141	+	0.229852i
$413$	−6.13126	−	3.53988i	−0.301700	−	0.174186i
$414$	−18.7871	−	23.0286i	−0.923335	−	1.13179i
$415$	−6.23077			−0.305856
$416$	−14.2827	−	14.5604i	−0.700268	−	0.713880i
$417$	−8.05219			−0.394317
$418$	−0.0839829	−	0.102943i	−0.00410774	−	0.00503513i
$419$	21.9054	+	12.6471i	1.07015	+	0.617851i	0.928222	−	0.372026i	$-0.121337\pi$
$419$	21.9054	+	12.6471i	1.07015	+	0.617851i	0.141927	+	0.989877i	$0.454670\pi$
$420$	−0.306085	+	1.49327i	−0.0149354	+	0.0728643i
$421$			20.3807i			0.993293i	0.867953	+	0.496646i	$0.165435\pi$
$421$			20.3807i			0.993293i	−0.867953	+	0.496646i	$0.834565\pi$
$422$	1.32751	+	8.18898i	0.0646224	+	0.398633i
$423$	0.377174	+	0.653284i	0.0183388	+	0.0317638i
$424$	6.31898	+	12.0746i	0.306877	+	0.586396i
$425$	−1.84116	−	3.18898i	−0.0893093	−	0.154688i
$426$	−9.39446	+	7.66415i	−0.455163	+	0.371329i
$427$	11.3016	+	6.52499i	0.546924	+	0.315767i
$428$	8.50964	−	9.59010i	0.411329	−	0.463555i
$429$	−0.165920	−	0.102043i	−0.00801070	−	0.00492668i
$430$	−2.78315	+	7.32983i	−0.134216	+	0.353476i
$431$	13.4254	−	23.2535i	0.646679	−	1.12008i	−0.337232	−	0.941421i	$-0.609491\pi$
$431$	13.4254	−	23.2535i	0.646679	−	1.12008i	0.983911	−	0.178659i	$-0.0571759\pi$
$432$	5.73468	−	13.4009i	0.275910	−	0.644753i
$433$	−5.49788	−	9.52261i	−0.264211	−	0.457627i	0.703145	−	0.711046i	$-0.251778\pi$
$433$	−5.49788	−	9.52261i	−0.264211	−	0.457627i	−0.967357	+	0.253419i	$0.918445\pi$
$434$	−4.19595	+	11.0506i	−0.201412	+	0.530447i
$435$	2.38899	−	1.37928i	0.114543	−	0.0661315i
$436$	−22.7224	−	4.65754i	−1.08821	−	0.223056i
$437$		−	9.29035i		−	0.444418i
$438$	−1.60007	−	9.87027i	−0.0764542	−	0.471620i
$439$	−18.9942	+	32.8990i	−0.906545	+	1.57018i	−0.0877144	+	0.996146i	$0.527956\pi$
$439$	−18.9942	+	32.8990i	−0.906545	+	1.57018i	−0.818830	+	0.574036i	$0.805377\pi$
$440$	0.00968555	−	0.233458i	0.000461741	−	0.0111297i
$441$	−14.5124			−0.691067
$442$	2.48850	+	18.6106i	0.118366	+	0.885215i
$443$		−	29.6288i		−	1.40771i	−0.710345	−	0.703854i	$-0.751461\pi$
$443$		−	29.6288i		−	1.40771i	0.710345	−	0.703854i	$-0.248539\pi$
$444$	11.4793	−	3.82227i	0.544784	−	0.181397i
$445$	4.66920	+	2.69577i	0.221341	+	0.127792i
$446$	−21.7677	+	3.52875i	−1.03073	+	0.167091i
$447$	4.17044			0.197255
$448$	9.29154	+	0.772294i	0.438984	+	0.0364874i
$449$	−1.09381	−	1.89453i	−0.0516200	−	0.0894085i	0.839061	−	0.544038i	$-0.183105\pi$
$449$	−1.09381	−	1.89453i	−0.0516200	−	0.0894085i	−0.890681	+	0.454629i	$0.849772\pi$
$450$	1.29134	−	3.40092i	0.0608742	−	0.160321i
$451$	0.214095	−	0.123608i	0.0100813	−	0.00582046i
$452$	13.9836	−	4.65613i	0.657735	−	0.219006i
$453$	4.98871	+	2.88023i	0.234390	+	0.135325i
$454$	−13.6706	−	5.19078i	−0.641595	−	0.243615i
$455$	2.20133	−	3.57933i	0.103200	−	0.167802i
$456$	1.86364	−	0.975295i	0.0872730	−	0.0456724i
$457$	−20.6705	+	35.8024i	−0.966926	+	1.67476i	−0.262577	+	0.964911i	$0.584572\pi$
$457$	−20.6705	+	35.8024i	−0.966926	+	1.67476i	−0.704349	+	0.709854i	$0.748761\pi$
$458$	4.15722	−	3.39152i	0.194254	−	0.158476i
$459$	−11.6210	+	6.70937i	−0.542420	+	0.313166i
$460$	10.8447	−	12.2216i	0.505636	−	0.569836i
$461$	−6.22350	+	3.59314i	−0.289857	+	0.167349i	−0.637878	−	0.770138i	$-0.720187\pi$
$461$	−6.22350	+	3.59314i	−0.289857	+	0.167349i	0.348020	+	0.937487i	$0.386854\pi$
$462$	0.0878951	−	0.0142487i	0.00408925	−	0.000662908i
$463$	−18.2926			−0.850127			−0.425064	−	0.905163i	$-0.639748\pi$
$463$	−18.2926			−0.850127			−0.425064	+	0.905163i	$0.639748\pi$
$464$	−10.1149	−	13.5049i	−0.469573	−	0.626951i
$465$	−2.34503	+	4.06171i	−0.108748	+	0.188357i
$466$	−18.5820	−	22.7772i	−0.860794	−	1.05513i
$467$		−	20.6598i		−	0.956022i	−0.878354	−	0.478011i	$-0.841358\pi$
$467$		−	20.6598i		−	0.956022i	0.878354	−	0.478011i	$-0.158642\pi$
$468$	−12.6922	+	13.5273i	−0.586697	+	0.625297i
$469$		−	1.92308i		−	0.0887996i
$470$	−0.321351	+	0.262163i	−0.0148228	+	0.0120927i
$471$	−6.15756	+	10.6652i	−0.283725	+	0.491427i
$472$	−9.20037	+	14.5111i	−0.423481	+	0.667926i
$473$	0.457995			0.0210586
$474$	−1.48481	−	9.15926i	−0.0681994	−	0.420699i
$475$	0.984822	−	0.568587i	0.0451867	−	0.0260886i
$476$	−6.42004	−	5.69673i	−0.294262	−	0.261109i
$477$	10.7337	−	6.19710i	0.491462	−	0.283746i
$478$	−1.02674	−	1.25855i	−0.0469621	−	0.0575646i
$479$	−7.87988	+	13.6484i	−0.360041	+	0.623609i	−0.987967	−	0.154664i	$-0.950571\pi$
$479$	−7.87988	+	13.6484i	−0.360041	+	0.623609i	0.627926	+	0.778273i	$0.283904\pi$
$480$	3.59012	+	0.892421i	0.163866	+	0.0407333i
$481$	−33.3402	−	0.926631i	−1.52018	−	0.0422508i
$482$	1.43232	−	3.77223i	0.0652406	−	0.171820i
$483$	5.39240	+	3.11330i	0.245363	+	0.141660i
$484$	20.8604	−	6.94587i	0.948198	−	0.315721i
$485$	−1.04506	+	0.603364i	−0.0474536	+	0.0273973i
$486$	−19.0655	−	7.23922i	−0.864829	−	0.328378i
$487$	−18.9928	−	32.8965i	−0.860645	−	1.49068i	−0.871307	−	0.490739i	$-0.836727\pi$
$487$	−18.9928	−	32.8965i	−0.860645	−	1.49068i	0.0106614	−	0.999943i	$-0.496606\pi$
$488$	16.9588	−	26.7479i	0.767690	−	1.21082i
$489$	12.9231			0.584402
$490$	−1.27674	−	7.87580i	−0.0576774	−	0.355792i
$491$	16.7431	+	9.66663i	0.755605	+	0.436249i	0.827716	−	0.561148i	$-0.189640\pi$
$491$	16.7431	+	9.66663i	0.755605	+	0.436249i	−0.0721104	+	0.997397i	$0.522973\pi$
$492$	1.23650	+	3.71356i	0.0557459	+	0.167420i
$493$			15.5329i			0.699564i
$494$	−5.74732	+	0.768498i	−0.258584	+	0.0345764i
$495$	−0.212502			−0.00955126
$496$	26.3736	+	11.2861i	1.18421	+	0.506761i
$497$	−7.63917	+	13.2314i	−0.342664	+	0.593511i
$498$	−5.68823	+	0.922118i	−0.254896	+	0.0413211i
$499$			24.4145i			1.09294i	0.837478	+	0.546471i	$0.184029\pi$
$499$			24.4145i			1.09294i	−0.837478	+	0.546471i	$0.815971\pi$
$500$	1.95926	+	0.401602i	0.0876210	+	0.0179602i
$501$	−5.10203	+	2.94566i	−0.227942	+	0.131602i
$502$	−0.450158	−	0.170926i	−0.0200916	−	0.00762881i
$503$	18.2545	+	31.6178i	0.813930	+	1.40977i	0.910094	+	0.414402i	$0.136009\pi$
$503$	18.2545	+	31.6178i	0.813930	+	1.40977i	−0.0961645	+	0.995365i	$0.530657\pi$
$504$	0.351486	−	8.47211i	0.0156564	−	0.377378i
$505$	0.171856	−	0.297663i	0.00764748	−	0.0132458i
$506$	−0.892299	−	0.338808i	−0.0396675	−	0.0150619i
$507$	−7.58727	+	3.83526i	−0.336963	+	0.170330i
$508$	21.9980	+	19.5196i	0.976003	+	0.866042i
$509$	0.867801	+	0.501025i	0.0384646	+	0.0222075i	0.519109	−	0.854708i	$-0.326264\pi$
$509$	0.867801	+	0.501025i	0.0384646	+	0.0222075i	−0.480644	+	0.876916i	$0.659597\pi$
$510$	−2.15279	−	2.63882i	−0.0953272	−	0.116849i
$511$	−6.30023	−	10.9123i	−0.278706	−	0.482733i
$512$	2.80739	−	22.4526i	0.124070	−	0.992273i
$513$	−2.07199	−	3.58879i	−0.0914805	−	0.158449i
$514$	21.8955	−	3.54948i	0.965771	−	0.156561i
$515$			2.38124i			0.104930i
$516$	−1.45604	+	7.10348i	−0.0640986	+	0.312713i
$517$	0.0209803	+	0.0121130i	0.000922712	+	0.000532728i
$518$	11.8139	−	9.63795i	0.519072	−	0.423467i
$519$	−0.159714			−0.00701067
$520$	−8.45777	−	5.69791i	−0.370898	−	0.249870i
$521$	−1.80054			−0.0788830			−0.0394415	−	0.999222i	$-0.512558\pi$
$521$	−1.80054			−0.0788830			−0.0394415	+	0.999222i	$0.512558\pi$
$522$	−11.8903	+	9.70028i	−0.520424	+	0.424570i
$523$	22.8933	+	13.2174i	1.00105	+	0.577958i	0.908560	−	0.417755i	$-0.137183\pi$
$523$	22.8933	+	13.2174i	1.00105	+	0.577958i	0.0924930	+	0.995713i	$0.470516\pi$
$524$	39.5737	+	8.11164i	1.72878	+	0.354359i
$525$			0.762160i			0.0332634i
$526$	20.3857	−	3.30472i	0.888859	−	0.144093i
$527$	−13.2043	−	22.8706i	−0.575190	−	0.996258i
$528$	−0.0257082	−	0.214563i	−0.00111880	−	0.00933765i
$529$	−21.8718	−	37.8831i	−0.950950	−	1.64709i
$530$	4.30744	+	5.27992i	0.187103	+	0.229345i
$531$	13.5327	+	7.81310i	0.587268	+	0.339059i
$532$	1.75926	−	1.98264i	0.0762738	−	0.0859582i
$533$	0.299766	−	10.7856i	0.0129843	−	0.467175i
$534$	4.66159	+	1.77002i	0.201727	+	0.0765962i
$535$	3.20531	−	5.55175i	0.138578	−	0.240023i
$536$	−4.66311	−	0.193461i	−0.201416	−	0.00835622i
$537$	2.85994	+	4.95355i	0.123415	+	0.213762i
$538$	−6.89421	−	2.61775i	−0.297231	−	0.112859i
$539$	−0.403626	+	0.233034i	−0.0173854	+	0.0100375i
$540$	1.46348	−	7.13975i	0.0629780	−	0.307246i
$541$		−	0.802158i		−	0.0344875i	−0.999851	−	0.0172437i	$-0.994511\pi$
$541$		−	0.802158i		−	0.0344875i	0.999851	−	0.0172437i	$-0.00548912\pi$
$542$	−0.129341	+	0.0209674i	−0.00555567	+	0.000900629i
$543$	−6.66230	+	11.5394i	−0.285907	+	0.495205i
$544$	−14.4594	+	14.9943i	−0.619940	+	0.642876i
$545$	−11.5974			−0.496779
$546$	1.47993	−	3.59345i	0.0633353	−	0.153785i
$547$		−	2.81096i		−	0.120188i	−0.998193	−	0.0600940i	$-0.980860\pi$
$547$		−	2.81096i		−	0.120188i	0.998193	−	0.0600940i	$-0.0191400\pi$
$548$	−32.9700	+	10.9780i	−1.40841	+	0.468958i
$549$	−24.9445	−	14.4017i	−1.06461	−	0.614650i
$550$	−0.0186951	−	0.115324i	−0.000797162	−	0.00491742i
$551$	−4.79686			−0.204353
$552$	8.09165	−	12.7624i	0.344404	−	0.543203i
$553$	−5.84639	−	10.1262i	−0.248614	−	0.430612i
$554$	38.6460	+	14.6740i	1.64191	+	0.623439i
$555$	5.23900	−	3.02474i	0.222383	−	0.128393i
$556$	7.77972	+	23.3646i	0.329934	+	0.990882i
$557$	18.8962	+	10.9097i	0.800658	+	0.462260i	0.843701	−	0.536813i	$-0.180372\pi$
$557$	18.8962	+	10.9097i	0.800658	+	0.462260i	−0.0430431	+	0.999073i	$0.513705\pi$
$558$	9.26115	−	24.3905i	0.392056	−	1.03253i
$559$	10.4717	−	17.0268i	0.442906	−	0.720158i
$560$	4.62869	−	0.554593i	0.195598	−	0.0234358i
$561$	−0.0994674	+	0.172283i	−0.00419952	+	0.00727378i
$562$	−10.0060	−	12.2650i	−0.422077	−	0.517369i
$563$	25.5308	−	14.7402i	1.07600	−	0.621226i	0.146182	−	0.989258i	$-0.453302\pi$
$563$	25.5308	−	14.7402i	1.07600	−	0.621226i	0.929813	+	0.368032i	$0.119968\pi$
$564$	−0.254571	+	0.286894i	−0.0107194	+	0.0120804i
$565$	6.38193	−	3.68461i	0.268490	−	0.155013i
$566$	−2.26028	−	13.9429i	−0.0950065	−	0.586063i
$567$	−6.21637			−0.261063
$568$	31.3153	+	19.8546i	1.31396	+	0.833082i
$569$	−0.0900980	+	0.156054i	−0.00377710	+	0.00654213i	−0.867908	−	0.496725i	$-0.834536\pi$
$569$	−0.0900980	+	0.156054i	−0.00377710	+	0.00654213i	0.864131	+	0.503268i	$0.167869\pi$
$570$	0.814921	−	0.664826i	0.0341333	−	0.0278465i
$571$			40.4271i			1.69182i	0.533325	+	0.845910i	$0.320942\pi$
$571$			40.4271i			1.69182i	−0.533325	+	0.845910i	$0.679058\pi$
$572$	−0.135787	+	0.580032i	−0.00567754	+	0.0242524i
$573$		−	11.4742i		−	0.479343i
$574$	3.11788	+	3.82179i	0.130138	+	0.159519i
$575$	4.08484	−	7.07515i	0.170350	−	0.295054i
$576$	−20.5079	−	1.70458i	−0.854497	−	0.0710240i
$577$	−14.1658			−0.589729			−0.294864	−	0.955539i	$-0.595274\pi$
$577$	−14.1658			−0.589729			−0.294864	+	0.955539i	$0.595274\pi$
$578$	−4.80295	+	0.778606i	−0.199777	+	0.0323857i
$579$	−6.79572	+	3.92351i	−0.282420	+	0.163055i
$580$	−6.31035	−	5.59940i	−0.262023	−	0.232502i
$581$	−6.28876	+	3.63082i	−0.260902	+	0.150632i
$582$	−0.864765	+	0.705489i	−0.0358456	+	0.0292434i
$583$	0.199021	−	0.344714i	0.00824259	−	0.0142766i
$584$	−27.0942	+	14.1791i	−1.12116	+	0.586736i
$585$	−4.85870	+	7.90017i	−0.200883	+	0.326632i
$586$	20.4824	+	7.77724i	0.846122	+	0.321275i
$587$	−5.28494	−	3.05126i	−0.218133	−	0.125939i	0.386952	−	0.922100i	$-0.373528\pi$
$587$	−5.28494	−	3.05126i	−0.218133	−	0.125939i	−0.605085	+	0.796161i	$0.706861\pi$
$588$	−2.33114	−	7.00107i	−0.0961348	−	0.288719i
$589$	7.06290	−	4.07777i	0.291022	−	0.168021i
$590$	−3.04957	+	8.03147i	−0.125549	+	0.330650i
$591$	−7.16386	−	12.4082i	−0.294682	−	0.510404i
$592$	−22.1818	−	29.6160i	−0.911665	−	1.21721i
$593$	8.08371			0.331958			0.165979	−	0.986129i	$-0.446922\pi$
$593$	8.08371			0.331958			0.165979	+	0.986129i	$0.446922\pi$
$594$	−0.420251	+	0.0681268i	−0.0172431	+	0.00279528i
$595$	−3.71659	−	2.14577i	−0.152365	−	0.0879682i
$596$	−4.02933	−	12.1012i	−0.165048	−	0.495683i
$597$		−	17.1277i		−	0.700990i
$598$	−32.9976	+	25.4263i	−1.34937	+	1.03976i
$599$	−13.9755			−0.571024			−0.285512	−	0.958375i	$-0.592164\pi$
$599$	−13.9755			−0.571024			−0.285512	+	0.958375i	$0.592164\pi$
$600$	1.84810	+	0.0766728i	0.0754483	+	0.00313015i
$601$	14.6374	−	25.3528i	0.597073	−	1.03416i	−0.396178	−	0.918174i	$-0.629664\pi$
$601$	14.6374	−	25.3528i	0.597073	−	1.03416i	0.993251	−	0.115987i	$-0.0370030\pi$
$602$	1.46221	+	9.01986i	0.0595951	+	0.367622i
$603$			4.24455i			0.172851i
$604$	3.53753	−	17.2583i	0.143940	−	0.702229i
$605$	9.52037	−	5.49659i	0.387058	−	0.223468i
$606$	0.112839	−	0.297178i	0.00458378	−	0.0120720i
$607$	−3.23743	−	5.60739i	−0.131403	−	0.227597i	0.792815	−	0.609463i	$-0.208615\pi$
$607$	−3.23743	−	5.60739i	−0.131403	−	0.227597i	−0.924218	+	0.381866i	$0.875282\pi$
$608$	−4.63055	−	4.46534i	−0.187793	−	0.181094i
$609$	1.60748	−	2.78424i	0.0651385	−	0.112823i
$610$	5.62121	−	14.8042i	0.227596	−	0.599406i
$611$	0.930021	−	0.503028i	0.0376246	−	0.0203503i
$612$	14.1701	+	12.5736i	0.572791	+	0.508258i
$613$	19.0542	+	11.0009i	0.769591	+	0.444323i	0.832729	−	0.553681i	$-0.186777\pi$
$613$	19.0542	+	11.0009i	0.769591	+	0.444323i	−0.0631379	+	0.998005i	$0.520111\pi$
$614$	22.1018	−	18.0310i	0.891954	−	0.727670i
$615$	0.978503	+	1.69482i	0.0394570	+	0.0683416i
$616$	−0.126266	−	0.241274i	−0.00508739	−	0.00972123i
$617$	10.9879	+	19.0315i	0.442354	+	0.766180i	0.997864	−	0.0653302i	$-0.0208101\pi$
$617$	10.9879	+	19.0315i	0.442354	+	0.766180i	−0.555509	+	0.831510i	$0.687477\pi$
$618$	0.352410	+	2.17390i	0.0141760	+	0.0874470i
$619$			4.09706i			0.164675i	0.996605	+	0.0823373i	$0.0262385\pi$
$619$			4.09706i			0.164675i	−0.996605	+	0.0823373i	$0.973762\pi$
$620$	14.0514	+	2.88019i	0.564316	+	0.115671i
$621$	−25.7826	−	14.8856i	−1.03462	−	0.597337i
$622$	3.03174	+	3.71620i	0.121562	+	0.149006i
$623$	6.28355			0.251745
$624$	−8.56457	−	3.95006i	−0.342857	−	0.158129i
$625$	1.00000			0.0400000
$626$	−2.13532	−	2.61741i	−0.0853446	−	0.104613i
$627$	−0.0532044	−	0.0307176i	−0.00212478	−	0.00122674i
$628$	36.8959	+	7.56277i	1.47231	+	0.301787i
$629$			34.0632i			1.35819i
$630$	−0.678440	−	4.18506i	−0.0270297	−	0.166737i
$631$	15.7480	+	27.2764i	0.626919	+	1.08586i	0.988166	+	0.153386i	$0.0490178\pi$
$631$	15.7480	+	27.2764i	0.626919	+	1.08586i	−0.361247	+	0.932470i	$0.617649\pi$
$632$	−25.1424	+	13.1577i	−1.00011	+	0.523386i
$633$	1.91810	+	3.32225i	0.0762376	+	0.132047i
$634$	19.3362	−	15.7747i	0.767937	−	0.626495i
$635$	12.7347	+	7.35241i	0.505363	+	0.291771i
$636$	4.71377	+	4.18269i	0.186913	+	0.165855i
$637$	−0.565139	+	20.3337i	−0.0223916	+	0.805650i
$638$	−0.174936	+	0.460718i	−0.00692578	+	0.0182400i
$639$	16.8609	−	29.2039i	0.667006	−	1.15529i
$640$	−0.879143	−	11.2795i	−0.0347512	−	0.445861i
$641$	10.5284	+	18.2357i	0.415845	+	0.720265i	0.995517	−	0.0945852i	$-0.0301525\pi$
$641$	10.5284	+	18.2357i	0.415845	+	0.720265i	−0.579672	+	0.814850i	$0.696819\pi$
$642$	2.10458	−	5.54271i	0.0830611	−	0.218753i
$643$	8.80010	−	5.08074i	0.347042	−	0.200365i	−0.316340	−	0.948646i	$-0.602454\pi$
$643$	8.80010	−	5.08074i	0.347042	−	0.200365i	0.663382	+	0.748281i	$0.269121\pi$
$644$	3.82379	−	18.6548i	0.150678	−	0.735103i
$645$			3.62558i			0.142757i
$646$	0.947632	+	5.84562i	0.0372841	+	0.229993i
$647$	−18.2319	+	31.5787i	−0.716772	+	1.24148i	0.245501	+	0.969396i	$0.421048\pi$
$647$	−18.2319	+	31.5787i	−0.716772	+	1.24148i	−0.962272	+	0.272089i	$0.912286\pi$
$648$	−0.625363	+	15.0735i	−0.0245666	+	0.592145i
$649$	0.501837			0.0196988
$650$	−4.71482	−	1.94176i	−0.184931	−	0.0761622i
$651$			5.46602i			0.214230i
$652$	−12.4858	−	37.4983i	−0.488982	−	1.46855i
$653$	18.6189	+	10.7496i	0.728614	+	0.420666i	0.817915	−	0.575339i	$-0.195130\pi$
$653$	18.6189	+	10.7496i	0.728614	+	0.420666i	−0.0893009	+	0.996005i	$0.528463\pi$
$654$	−10.5876	+	1.71635i	−0.414007	+	0.0671146i
$655$	20.1982			0.789210
$656$	9.58080	−	7.17581i	0.374067	−	0.280168i
$657$	13.9056	+	24.0853i	0.542510	+	0.939655i
$658$	−0.171573	+	0.451862i	−0.00668862	+	0.0176154i
$659$	38.4829	−	22.2181i	1.49908	−	0.865495i	0.499083	−	0.866554i	$-0.333670\pi$
$659$	38.4829	−	22.2181i	1.49908	−	0.865495i	0.999999	+	0.00105893i	$0.000337067\pi$
$660$	−0.0341345	−	0.102515i	−0.00132868	−	0.00399040i
$661$	6.53620	+	3.77368i	0.254229	+	0.146779i	0.621699	−	0.783256i	$-0.286443\pi$
$661$	6.53620	+	3.77368i	0.254229	+	0.146779i	−0.367470	+	0.930035i	$0.619776\pi$
$662$	−7.32219	−	2.78025i	−0.284585	−	0.108058i
$663$	4.13068	+	7.63700i	0.160422	+	0.296596i
$664$	8.17142	+	15.6143i	0.317113	+	0.605954i
$665$	0.662659	−	1.14776i	0.0256968	−	0.0445082i
$666$	−26.0751	+	21.2725i	−1.01039	+	0.824293i
$667$	−29.8446	+	17.2308i	−1.15559	+	0.667179i
$668$	13.4767	+	11.9583i	0.521428	+	0.462682i
$669$	−8.83107	+	5.09862i	−0.341429	+	0.197124i
$670$	−2.30349	+	0.373418i	−0.0889916	+	0.0144264i
$671$	−0.925025			−0.0357102
$672$	4.14357	−	1.19132i	0.159842	−	0.0459562i
$673$	−17.1425	+	29.6916i	−0.660793	+	1.14453i	0.319615	+	0.947548i	$0.396447\pi$
$673$	−17.1425	+	29.6916i	−0.660793	+	1.14453i	−0.980408	+	0.196979i	$0.936887\pi$
$674$	−24.3289	−	29.8216i	−0.937116	−	1.14869i
$675$		−	3.64410i		−	0.140261i
$676$	18.4591	+	18.3101i	0.709966	+	0.704236i
$677$		−	1.92673i		−	0.0740504i	−0.999314	−	0.0370252i	$-0.988212\pi$
$677$		−	1.92673i		−	0.0740504i	0.999314	−	0.0370252i	$-0.0117882\pi$
$678$	5.28093	−	4.30827i	0.202813	−	0.165458i
$679$	−0.703189	+	1.21796i	−0.0269859	+	0.0467410i
$680$	−5.57699	+	8.79618i	−0.213868	+	0.337318i
$681$	−6.76197			−0.259119
$682$	−0.134077	−	0.827073i	−0.00513406	−	0.0316703i
$683$	−23.7471	+	13.7104i	−0.908658	+	0.524614i	−0.879999	−	0.474975i	$-0.842457\pi$
$683$	−23.7471	+	13.7104i	−0.908658	+	0.524614i	−0.0286590	+	0.999589i	$0.509124\pi$
$684$	−3.88298	+	4.37600i	−0.148470	+	0.167321i
$685$	−15.0470	+	8.68742i	−0.574918	+	0.331929i
$686$	−13.1712	−	16.1449i	−0.502881	−	0.616415i
$687$	1.24048	−	2.14858i	0.0473274	−	0.0819734i
$688$	22.0186	−	2.63819i	0.839451	−	0.100580i
$689$	−8.26492	−	15.2806i	−0.314869	−	0.582143i
$690$	2.68207	−	7.06362i	0.102105	−	0.268907i
$691$	−19.1219	−	11.0401i	−0.727433	−	0.419984i	0.0900493	−	0.995937i	$-0.471298\pi$
$691$	−19.1219	−	11.0401i	−0.727433	−	0.419984i	−0.817482	+	0.575954i	$0.804631\pi$
$692$	0.154310	+	0.463435i	0.00586598	+	0.0176172i
$693$	−0.214480	+	0.123830i	−0.00814742	+	0.00470392i
$694$	26.1414	+	9.92595i	0.992313	+	0.376784i
$695$	6.15645	+	10.6633i	0.233528	+	0.404482i
$696$	−6.58956	−	4.17794i	−0.249777	−	0.158364i
$697$	−11.0195			−0.417392
$698$	5.86625	+	36.1869i	0.222041	+	1.36970i
$699$	−11.7720	−	6.79654i	−0.445256	−	0.257069i
$700$	2.21152	−	0.736371i	0.0835877	−	0.0278322i
$701$			27.8129i			1.05048i	0.850955	+	0.525239i	$0.176024\pi$
$701$			27.8129i			1.05048i	−0.850955	+	0.525239i	$0.823976\pi$
$702$	−7.07598	+	17.1813i	−0.267066	+	0.648466i
$703$	−10.5194			−0.396747
$704$	−0.597748	+	0.281899i	−0.0225285	+	0.0106245i
$705$	−0.0958888	+	0.166084i	−0.00361138	+	0.00625509i
$706$	7.59042	−	1.23048i	0.285669	−	0.0463098i
$707$		−	0.400578i		−	0.0150653i
$708$	−1.59542	+	7.78345i	−0.0599595	+	0.292520i
$709$	−10.9037	+	6.29527i	−0.409498	+	0.236424i	−0.690574	−	0.723262i	$-0.742642\pi$
$709$	−10.9037	+	6.29527i	−0.409498	+	0.236424i	0.281076	+	0.959686i	$0.409309\pi$
$710$	17.3321	+	6.58106i	0.650464	+	0.246983i
$711$	12.9039	+	22.3503i	0.483935	+	0.838201i
$712$	0.632121	−	15.2364i	0.0236897	−	0.571010i
$713$	29.2955	−	50.7412i	1.09712	−	1.90027i
$714$	−3.71053	−	1.40890i	−0.138863	−	0.0527267i
$715$	−0.00827521	+	0.297742i	−0.000309475	+	0.0111349i
$716$	11.6103	−	13.0845i	0.433898	−	0.488990i
$717$	−0.650456	−	0.375541i	−0.0242917	−	0.0140248i
$718$	7.67023	+	9.40192i	0.286251	+	0.350877i
$719$	4.16371	+	7.21176i	0.155280	+	0.268953i	0.933161	−	0.359459i	$-0.117039\pi$
$719$	4.16371	+	7.21176i	0.155280	+	0.268953i	−0.777881	+	0.628412i	$0.783705\pi$
$720$	−10.2163	+	1.22408i	−0.380737	+	0.0456186i
$721$	1.38761	+	2.40341i	0.0516772	+	0.0895075i
$722$	24.7186	−	4.00712i	0.919929	−	0.149130i
$723$		−	1.86587i		−	0.0693926i
$724$	39.9203	+	8.18270i	1.48363	+	0.304108i
$725$	−3.65309	−	2.10911i	−0.135672	−	0.0783305i
$726$	7.87793	−	6.42694i	0.292377	−	0.238526i
$727$	11.1177			0.412334			0.206167	−	0.978517i	$-0.433901\pi$
$727$	11.1177			0.412334			0.206167	+	0.978517i	$0.433901\pi$
$728$	−11.8568	−	0.822395i	−0.439442	−	0.0304800i
$729$	6.57121			0.243378
$730$	−11.8476	+	9.66543i	−0.438498	+	0.357734i
$731$	−17.6798	−	10.2074i	−0.653910	−	0.377535i
$732$	2.94080	−	14.3471i	0.108695	−	0.530283i
$733$		−	24.2938i		−	0.897311i	−0.893705	−	0.448656i	$-0.851903\pi$
$733$		−	24.2938i		−	0.897311i	0.893705	−	0.448656i	$-0.148097\pi$
$734$	−50.5307	+	8.19152i	−1.86512	+	0.302355i
$735$	−1.84474	−	3.19519i	−0.0680443	−	0.117856i
$736$	−44.8498	−	11.1486i	−1.65319	−	0.410944i
$737$	0.0681570	+	0.118051i	0.00251060	+	0.00434848i
$738$	−6.88166	−	8.43532i	−0.253318	−	0.310508i
$739$	−0.371502	−	0.214487i	−0.0136659	−	0.00789003i	0.493151	−	0.869943i	$-0.335845\pi$
$739$	−0.371502	−	0.214487i	−0.0136659	−	0.00789003i	−0.506817	+	0.862053i	$0.669178\pi$
$740$	−13.8385	−	12.2794i	−0.508712	−	0.451398i
$741$	−2.35846	+	1.27564i	−0.0866402	+	0.0468618i
$742$	7.42426	+	2.81901i	0.272553	+	0.103489i
$743$	−5.55404	+	9.61988i	−0.203758	+	0.352919i	−0.949736	−	0.313051i	$-0.898649\pi$
$743$	−5.55404	+	9.61988i	−0.203758	+	0.352919i	0.745978	+	0.665970i	$0.231982\pi$
$744$	13.2541	+	0.549878i	0.485919	+	0.0201595i
$745$	−3.18859	−	5.52280i	−0.116821	−	0.202340i
$746$	16.4474	+	6.24514i	0.602184	+	0.228651i
$747$	13.8803	−	8.01380i	0.507854	−	0.293210i
$748$	0.596006	+	0.122167i	0.0217921	+	0.00446686i
$749$		−	7.47124i		−	0.272993i
$750$	0.912926	−	0.147994i	0.0333353	−	0.00540398i
$751$	−8.92905	+	15.4656i	−0.325826	+	0.564347i	−0.981679	−	0.190542i	$-0.938976\pi$
$751$	−8.92905	+	15.4656i	−0.325826	+	0.564347i	0.655853	+	0.754888i	$0.272309\pi$
$752$	1.07842	+	0.461491i	0.0393260	+	0.0168288i
$753$	−0.222664			−0.00811432
$754$	13.1283	+	17.0375i	0.478104	+	0.620470i
$755$		−	8.80854i		−	0.320576i
$756$	−2.68341	−	8.05901i	−0.0975946	−	0.293103i
$757$	−26.2548	−	15.1582i	−0.954245	−	0.550934i	−0.0598483	−	0.998207i	$-0.519062\pi$
$757$	−26.2548	−	15.1582i	−0.954245	−	0.550934i	−0.894397	+	0.447274i	$0.852395\pi$
$758$	−6.51845	−	40.2101i	−0.236761	−	1.46050i
$759$	−0.441362			−0.0160204
$760$	−2.71644	−	1.72229i	−0.0985356	−	0.0624740i
$761$	22.9196	+	39.6978i	0.830833	+	1.43905i	0.897378	+	0.441262i	$0.145469\pi$
$761$	22.9196	+	39.6978i	0.830833	+	1.43905i	−0.0665454	+	0.997783i	$0.521198\pi$
$762$	12.7140	+	4.82753i	0.460579	+	0.174883i
$763$	−11.7054	+	6.75809i	−0.423762	+	0.244659i
$764$	−33.2942	+	11.0860i	−1.20454	+	0.401076i
$765$	8.20312	+	4.73607i	0.296584	+	0.171233i
$766$	−2.52320	+	6.64520i	−0.0911669	+	0.240101i
$767$	11.4741	−	18.6567i	0.414306	−	0.673655i
$768$	−2.47189	−	10.1672i	−0.0891968	−	0.366879i
$769$	−18.3698	+	31.8175i	−0.662433	+	1.14737i	0.317542	+	0.948244i	$0.397143\pi$
$769$	−18.3698	+	31.8175i	−0.662433	+	1.14737i	−0.979975	+	0.199123i	$0.936191\pi$
$770$	−0.0860710	−	0.105503i	−0.00310178	−	0.00380206i
$771$	8.88296	−	5.12858i	0.319912	−	0.184701i
$772$	17.9504	+	15.9281i	0.646050	+	0.573263i
$773$	−20.4967	+	11.8338i	−0.737215	+	0.425631i	−0.821056	−	0.570848i	$-0.806615\pi$
$773$	−20.4967	+	11.8338i	−0.737215	+	0.425631i	0.0838408	+	0.996479i	$0.473281\pi$
$774$	−3.22733	−	19.9083i	−0.116004	−	0.715589i
$775$	7.17175			0.257617
$776$	2.88259	+	1.82763i	0.103479	+	0.0656081i
$777$	3.52517	−	6.10578i	0.126465	−	0.219044i
$778$	−6.79262	+	5.54152i	−0.243527	+	0.198673i
$779$		−	3.40303i		−	0.121926i
$780$	−4.59165	−	1.07492i	−0.164408	−	0.0384882i
$781$		−	1.08298i		−	0.0387520i
$782$	26.8939	+	32.9657i	0.961724	+	1.17885i
$783$	−7.68582	+	13.3122i	−0.274669	+	0.475740i
$784$	−18.0624	+	13.5283i	−0.645086	+	0.483155i
$785$	18.8315			0.672126
$786$	18.4395	−	2.98922i	0.657715	−	0.106622i
$787$	−14.0553	+	8.11481i	−0.501016	+	0.289262i	−0.729133	−	0.684372i	$-0.760076\pi$
$787$	−14.0553	+	8.11481i	−0.501016	+	0.289262i	0.228117	+	0.973634i	$0.426743\pi$
$788$	−29.0827	+	32.7753i	−1.03603	+	1.16757i
$789$	8.27042	−	4.77493i	0.294435	−	0.169992i
$790$	−10.9941	+	8.96918i	−0.391153	+	0.319109i
$791$	4.29422	−	7.43781i	0.152685	−	0.264458i
$792$	0.278689	+	0.532532i	0.00990277	+	0.0189227i
$793$	−21.1500	+	34.3895i	−0.751058	+	1.22121i
$794$	24.0626	+	9.13663i	0.853950	+	0.324247i
$795$	2.72882	+	1.57549i	0.0967814	+	0.0558768i
$796$	−49.6986	+	16.5482i	−1.76152	+	0.586534i
$797$	−9.62130	+	5.55486i	−0.340804	+	0.196763i	−0.660628	−	0.750714i	$-0.729710\pi$
$797$	−9.62130	+	5.55486i	−0.340804	+	0.196763i	0.319823	+	0.947477i	$0.396376\pi$
$798$	0.435096	−	1.14589i	0.0154022	−	0.0405640i
$799$	−0.539928	−	0.935182i	−0.0191013	−	0.0330844i
$800$	−1.56308	−	5.43661i	−0.0552634	−	0.192213i
$801$	−13.8688			−0.490030
$802$	−32.3604	+	5.24594i	−1.14269	+	0.185241i
$803$	0.773501	+	0.446581i	0.0272962	+	0.0157595i
$804$	−2.04765	+	0.681807i	−0.0722151	+	0.0240455i
$805$		−	9.52134i		−	0.335583i
$806$	−33.8135	−	13.9258i	−1.19103	−	0.490517i
$807$	−3.41012			−0.120042
$808$	−0.971328	−	0.0402979i	−0.0341712	−	0.00141767i
$809$	16.6182	−	28.7836i	0.584266	−	1.01198i	−0.410701	−	0.911770i	$-0.634716\pi$
$809$	16.6182	−	28.7836i	0.584266	−	1.01198i	0.994967	−	0.100208i	$-0.0319508\pi$
$810$	1.20708	+	7.44605i	0.0424124	+	0.261628i
$811$		−	4.44663i		−	0.156142i	−0.996948	−	0.0780711i	$-0.975124\pi$
$811$		−	4.44663i		−	0.156142i	0.996948	−	0.0780711i	$-0.0248761\pi$
$812$	−9.63199	−	1.97432i	−0.338016	−	0.0692852i
$813$	−0.0524733	+	0.0302955i	−0.00184032	+	0.00106251i
$814$	−0.383630	+	1.01034i	−0.0134462	+	0.0354126i
$815$	−9.88059	−	17.1137i	−0.346102	−	0.599466i
$816$	−3.78960	+	8.85562i	−0.132662	+	0.310009i
$817$	3.15226	−	5.45987i	0.110284	−	0.191017i
$818$	−2.30819	+	6.07894i	−0.0807039	+	0.212545i
$819$	−0.300305	+	10.8050i	−0.0104935	+	0.377557i
$820$	3.97238	−	4.47674i	0.138721	−	0.156335i
$821$	39.0532	+	22.5473i	1.36296	+	0.786908i	0.990017	−	0.140945i	$-0.0450140\pi$
$821$	39.0532	+	22.5473i	1.36296	+	0.786908i	0.372947	+	0.927853i	$0.378347\pi$
$822$	−12.4511	+	10.1578i	−0.434284	+	0.354295i
$823$	13.4740	+	23.3377i	0.469675	+	0.813501i	0.999399	−	0.0346691i	$-0.0110377\pi$
$823$	13.4740	+	23.3377i	0.469675	+	0.813501i	−0.529724	+	0.848170i	$0.677704\pi$
$824$	5.96741	−	3.12291i	0.207885	−	0.108792i
$825$	−0.0270122	−	0.0467865i	−0.000940444	−	0.00162890i
$826$	1.60218	+	9.88328i	0.0557469	+	0.343883i
$827$		−	43.4884i		−	1.51224i	−0.654433	−	0.756120i	$-0.727093\pi$
$827$		−	43.4884i		−	1.51224i	0.654433	−	0.756120i	$-0.272907\pi$
$828$	−8.43971	+	41.1742i	−0.293300	+	1.43090i
$829$	−14.9402	−	8.62576i	−0.518896	−	0.299585i	0.217587	−	0.976041i	$-0.430182\pi$
$829$	−14.9402	−	8.62576i	−0.518896	−	0.299585i	−0.736483	+	0.676456i	$0.763515\pi$
$830$	5.57018	+	6.82774i	0.193344	+	0.236994i
$831$	19.1157			0.663115
$832$	−3.18694	+	28.6678i	−0.110487	+	0.993878i
$833$	20.7746			0.719799
$834$	7.19849	+	8.82367i	0.249263	+	0.305539i
$835$	7.80171	+	4.50432i	0.269989	+	0.155878i
$836$	−0.0377276	+	0.184059i	−0.00130484	+	0.00636580i
$837$		−	26.1346i		−	0.903343i
$838$	−5.72416	−	35.3104i	−0.197738	−	1.21978i
$839$	−8.06553	−	13.9699i	−0.278453	−	0.482295i	0.692547	−	0.721372i	$-0.256488\pi$
$839$	−8.06553	−	13.9699i	−0.278453	−	0.482295i	−0.971000	+	0.239078i	$0.923155\pi$
$840$	1.90998	−	0.999544i	0.0659005	−	0.0344876i
$841$	−5.60328	−	9.70517i	−0.193217	−	0.334661i
$842$	22.3333	−	18.2199i	0.769658	−	0.627899i
$843$	−6.33894	−	3.65979i	−0.218325	−	0.126050i
$844$	7.78680	−	8.77549i	0.268033	−	0.302065i
$845$	10.8799	+	7.11529i	0.374281	+	0.244774i
$846$	0.378690	−	0.997334i	0.0130196	−	0.0342890i
$847$	6.40599	−	11.0955i	0.220112	−	0.381246i
$848$	7.58246	−	17.7189i	0.260383	−	0.608469i
$849$	−3.26583	−	5.65658i	−0.112083	−	0.194133i
$850$	−1.84856	+	4.86844i	−0.0634051	+	0.166986i
$851$	−65.4485	+	37.7867i	−2.24355	+	1.29531i
$852$	16.7969	+	3.44296i	0.575453	+	0.117954i
$853$		−	24.7296i		−	0.846724i	−0.905961	−	0.423362i	$-0.860850\pi$
$853$		−	24.7296i		−	0.846724i	0.905961	−	0.423362i	$-0.139150\pi$
$854$	−2.95326	−	18.2176i	−0.101058	−	0.623395i
$855$	−1.46259	+	2.53329i	−0.0500197	+	0.0866366i
$856$	−18.1164	−	0.751602i	−0.619205	−	0.0256892i
$857$	−31.1919			−1.06549			−0.532747	−	0.846275i	$-0.678840\pi$
$857$	−31.1919			−1.06549			−0.532747	+	0.846275i	$0.678840\pi$
$858$	0.0365095	+	0.273041i	0.00124641	+	0.00932147i
$859$			18.5067i			0.631442i	0.948852	+	0.315721i	$0.102246\pi$
$859$			18.5067i			0.631442i	−0.948852	+	0.315721i	$0.897754\pi$
$860$	10.5202	−	3.50290i	0.358735	−	0.119448i
$861$	1.97522	+	1.14039i	0.0673154	+	0.0388645i
$862$	−37.4834	+	6.07643i	−1.27669	+	0.206964i
$863$	31.9459			1.08745			0.543725	−	0.839263i	$-0.317013\pi$
$863$	31.9459			1.08745			0.543725	+	0.839263i	$0.317013\pi$
$864$	−19.8116	+	5.69604i	−0.674003	+	0.193783i
$865$	0.122113	+	0.211505i	0.00415195	+	0.00719139i
$866$	−5.51998	+	14.5376i	−0.187577	+	0.494009i
$867$	−1.94854	+	1.12499i	−0.0661760	+	0.0382068i
$868$	15.8605	−	5.28107i	0.538340	−	0.179251i
$869$	0.717781	+	0.414411i	0.0243491	+	0.0140579i
$870$	−3.64714	−	1.38483i	−0.123650	−	0.0469501i
$871$	5.94714	+	0.165290i	0.201511	+	0.00560065i
$872$	15.2096	+	29.0632i	0.515061	+	0.984204i
$873$	1.55205	−	2.68823i	0.0525290	−	0.0909829i
$874$	−10.1805	+	8.30538i	−0.344359	+	0.280934i
$875$	1.00931	−	0.582724i	0.0341208	−	0.0196997i
$876$	−9.38552	+	10.5772i	−0.317107	+	0.357370i
$877$	15.1007	−	8.71837i	0.509913	−	0.294398i	−0.222885	−	0.974845i	$-0.571547\pi$
$877$	15.1007	−	8.71837i	0.509913	−	0.294398i	0.732798	+	0.680446i	$0.238214\pi$
$878$	53.0315	−	8.59692i	1.78973	−	0.290132i
$879$	10.1313			0.341721
$880$	−0.264484	+	0.198093i	−0.00891575	+	0.00667770i
$881$	25.6843	−	44.4865i	0.865326	−	1.49879i	−0.00139639	−	0.999999i	$-0.500444\pi$
$881$	25.6843	−	44.4865i	0.865326	−	1.49879i	0.866723	−	0.498790i	$-0.166222\pi$
$882$	12.9738	+	15.9028i	0.436850	+	0.535477i
$883$		−	21.1389i		−	0.711382i	−0.934604	−	0.355691i	$-0.884246\pi$
$883$		−	21.1389i		−	0.711382i	0.934604	−	0.355691i	$-0.115754\pi$
$884$	18.1690	−	19.3644i	0.611090	−	0.651295i
$885$			3.97264i			0.133539i
$886$	−32.4676	+	26.4876i	−1.09077	+	0.889867i
$887$	−1.13424	+	1.96456i	−0.0380840	+	0.0659634i	−0.884439	−	0.466656i	$-0.845459\pi$
$887$	−1.13424	+	1.96456i	−0.0380840	+	0.0659634i	0.846355	+	0.532619i	$0.178792\pi$
$888$	−14.4508	−	9.16213i	−0.484936	−	0.307461i
$889$	17.1377			0.574780
$890$	−1.22012	−	7.52652i	−0.0408986	−	0.252290i
$891$	0.381602	−	0.220318i	0.0127842	−	0.00738094i
$892$	23.3267	+	20.6986i	0.781035	+	0.693040i
$893$	0.288803	−	0.166741i	0.00966443	−	0.00557976i
$894$	−3.72829	−	4.57002i	−0.124693	−	0.152844i
$895$	4.37324	−	7.57467i	0.146181	−	0.253193i
$896$	−7.46016	−	10.8722i	−0.249226	−	0.363214i
$897$	−10.0914	+	16.4085i	−0.336942	+	0.547862i
$898$	−1.09821	+	2.89228i	−0.0366476	+	0.0965166i
$899$	−26.1991	−	15.1260i	−0.873788	−	0.504482i
$900$	−4.88119	+	1.62529i	−0.162706	+	0.0541763i
$901$	−15.3654	+	8.87121i	−0.511895	+	0.295543i
$902$	−0.326847	−	0.124105i	−0.0108828	−	0.00413223i
$903$	2.11271	+	3.65933i	0.0703068	+	0.121775i
$904$	−17.6033	−	11.1609i	−0.585478	−	0.371207i
$905$	20.3752			0.677293
$906$	−1.30361	−	8.04155i	−0.0433096	−	0.267162i
$907$	−51.3414	−	29.6420i	−1.70476	−	0.984246i	−0.940784	−	0.339008i	$-0.889909\pi$
$907$	−51.3414	−	29.6420i	−1.70476	−	0.984246i	−0.763981	−	0.645238i	$-0.776758\pi$
$908$	6.53316	+	19.6209i	0.216811	+	0.651142i
$909$			0.884140i			0.0293251i
$910$	−5.89022	+	0.787605i	−0.195259	+	0.0261089i
$911$	−5.15838			−0.170905			−0.0854525	−	0.996342i	$-0.527234\pi$
$911$	−5.15838			−0.170905			−0.0854525	+	0.996342i	$0.527234\pi$
$912$	−2.73480	−	1.17030i	−0.0905581	−	0.0387526i
$913$	0.257364	−	0.445768i	0.00851751	−	0.0147528i
$914$	57.7116	−	9.35562i	1.90893	−	0.309457i
$915$		−	7.32269i		−	0.242081i
$916$	−7.43294	−	1.52357i	−0.245591	−	0.0503402i
$917$	20.3862	−	11.7700i	0.673213	−	0.388679i
$918$	17.7411	+	6.73634i	0.585543	+	0.222332i
$919$	14.9184	+	25.8394i	0.492112	+	0.852364i	0.999959	−	0.00908401i	$-0.00289157\pi$
$919$	14.9184	+	25.8394i	0.492112	+	0.852364i	−0.507846	+	0.861448i	$0.669558\pi$
$920$	−23.0875	−	0.957840i	−0.761172	−	0.0315791i
$921$	6.59500	−	11.4229i	0.217313	−	0.376396i
$922$	9.50108	+	3.60758i	0.312901	+	0.118809i
$923$	−40.2617	−	24.7615i	−1.32523	−	0.815033i
$924$	−0.0941903	−	0.0835784i	−0.00309863	−	0.00274953i
$925$	−8.01115	−	4.62524i	−0.263405	−	0.152077i
$926$	16.3532	+	20.0452i	0.537398	+	0.658725i
$927$	−3.06267	−	5.30471i	−0.100591	−	0.174229i
$928$	−5.75634	+	23.1572i	−0.188961	+	0.760171i
$929$	−8.46268	−	14.6578i	−0.277652	−	0.480907i	0.693149	−	0.720794i	$-0.256223\pi$
$929$	−8.46268	−	14.6578i	−0.277652	−	0.480907i	−0.970801	+	0.239888i	$0.922889\pi$
$930$	6.54728	−	1.06138i	0.214694	−	0.0348040i
$931$			6.41563i			0.210264i
$932$	−8.34757	+	40.7247i	−0.273434	+	1.33398i
$933$	1.92065	+	1.10889i	0.0628792	+	0.0363033i
$934$	−22.6392	+	18.4695i	−0.740779	+	0.604339i
$935$	0.304199			0.00994837
$936$	26.1699	+	1.81516i	0.855389	+	0.0593303i
$937$	44.0639			1.43951			0.719753	−	0.694231i	$-0.244255\pi$
$937$	44.0639			1.43951			0.719753	+	0.694231i	$0.244255\pi$
$938$	−2.10733	+	1.71919i	−0.0688068	+	0.0561337i
$939$	−1.35276	−	0.781015i	−0.0441456	−	0.0254874i
$940$	0.574563	+	0.117771i	0.0187402	+	0.00384128i
$941$			42.5939i			1.38852i	0.719724	+	0.694261i	$0.244269\pi$
$941$			42.5939i			1.38852i	−0.719724	+	0.694261i	$0.755731\pi$
$942$	17.1918	−	2.78696i	0.560139	−	0.0908040i
$943$	−12.2240	−	21.1726i	−0.398069	−	0.689475i
$944$	24.1263	−	2.89073i	0.785244	−	0.0940853i
$945$	−2.12350	−	3.67802i	−0.0690776	−	0.119646i
$946$	−0.409438	−	0.501876i	−0.0133120	−	0.0163174i
$947$	29.9660	+	17.3009i	0.973764	+	0.562203i	0.900382	−	0.435101i	$-0.143287\pi$
$947$	29.9660	+	17.3009i	0.973764	+	0.562203i	0.0733820	+	0.997304i	$0.476621\pi$
$948$	−8.70943	+	9.81526i	−0.282869	+	0.318785i
$949$	34.2880	−	18.5456i	1.11303	−	0.602016i
$950$	−1.50347	−	0.570873i	−0.0487791	−	0.0185216i
$951$	5.76977	−	9.99353i	0.187098	−	0.324062i
$952$	−0.503155	+	12.1279i	−0.0163074	+	0.393068i
$953$	0.595121	+	1.03078i	0.0192779	+	0.0333903i	0.875503	−	0.483212i	$-0.160530\pi$
$953$	0.595121	+	1.03078i	0.0192779	+	0.0333903i	−0.856226	+	0.516602i	$0.827197\pi$
$954$	−16.3865	−	6.22201i	−0.530534	−	0.201445i
$955$	−15.1950	+	8.77284i	−0.491699	+	0.283882i
$956$	−0.461243	+	2.25023i	−0.0149177	+	0.0727777i
$957$			0.227887i			0.00736654i
$958$	22.0005	−	3.56649i	0.710803	−	0.115228i
$959$	−10.1247	+	17.5365i	−0.326945	+	0.566285i
$960$	−2.23157	−	4.73190i	−0.0720235	−	0.152721i
$961$	20.4340			0.659163
$962$	28.7900	+	37.3629i	0.928228	+	1.20463i
$963$			16.4902i			0.531390i
$964$	−5.41411	+	1.80274i	−0.174377	+	0.0580622i
$965$	10.3916	+	5.99959i	0.334517	+	0.193133i
$966$	−1.40910	−	8.69227i	−0.0453371	−	0.279669i
$967$	21.2867			0.684534			0.342267	−	0.939603i	$-0.388805\pi$
$967$	21.2867			0.684534			0.342267	+	0.939603i	$0.388805\pi$
$968$	−26.2601	−	16.6495i	−0.844031	−	0.535136i
$969$	1.36921	+	2.37155i	0.0439855	+	0.0761851i
$970$	1.59543	+	0.605789i	0.0512262	+	0.0194507i
$971$	49.0174	−	28.3002i	1.57304	−	0.908196i	0.577249	−	0.816568i	$-0.304126\pi$
$971$	49.0174	−	28.3002i	1.57304	−	0.908196i	0.995793	−	0.0916278i	$-0.0292070\pi$
$972$	9.11135	+	27.3639i	0.292247	+	0.877697i
$973$	12.4275	+	7.17503i	0.398408	+	0.230021i
$974$	−19.0691	+	50.2213i	−0.611015	+	1.60919i
$975$	−2.35699	−	0.0655083i	−0.0754840	−	0.00209794i
$976$	−44.4715	+	5.32842i	−1.42350	+	0.170559i
$977$	12.2854	−	21.2790i	0.393045	−	0.680774i	−0.599804	−	0.800147i	$-0.704755\pi$
$977$	12.2854	−	21.2790i	0.393045	−	0.680774i	0.992850	+	0.119373i	$0.0380883\pi$
$978$	−11.5530	−	14.1613i	−0.369423	−	0.452827i
$979$	−0.385726	+	0.222699i	−0.0123279	+	0.00711750i
$980$	−7.48900	+	8.43987i	−0.239227	+	0.269602i
$981$	25.8356	−	14.9162i	0.824868	−	0.476238i
$982$	−4.37519	−	26.9890i	−0.139618	−	0.861254i
$983$	−52.8365			−1.68522			−0.842612	−	0.538522i	$-0.818983\pi$
$983$	−52.8365			−1.68522			−0.842612	+	0.538522i	$0.818983\pi$
$984$	2.96395	−	4.67482i	0.0944873	−	0.149028i
$985$	−10.9545	+	18.9738i	−0.349041	+	0.604556i
$986$	17.0211	−	13.8860i	0.542061	−	0.442222i
$987$			0.223507i			0.00711430i
$988$	5.98011	+	5.61095i	0.190253	+	0.178508i
$989$		−	45.2929i		−	1.44023i
$990$	0.189973	+	0.232862i	0.00603772	+	0.00740085i
$991$	23.8242	−	41.2648i	0.756801	−	1.31082i	−0.187673	−	0.982232i	$-0.560094\pi$
$991$	23.8242	−	41.2648i	0.756801	−	1.31082i	0.944474	−	0.328586i	$-0.106572\pi$
$992$	−11.2101	−	38.9900i	−0.355920	−	1.23794i
$993$	−3.62181			−0.114935
$994$	21.3284	−	3.45754i	0.676496	−	0.109667i
$995$	−22.6817	+	13.0953i	−0.719060	+	0.415149i
$996$	6.09563	+	5.40887i	0.193147	+	0.171387i
$997$	23.0475	−	13.3065i	0.729922	−	0.421421i	−0.0884715	−	0.996079i	$-0.528198\pi$
$997$	23.0475	−	13.3065i	0.729922	−	0.421421i	0.818394	+	0.574658i	$0.194865\pi$
$998$	26.7536	−	21.8260i	0.846872	−	0.690891i
$999$	−16.8548	+	29.1934i	−0.533263	+	0.923639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.by.c.61.16	✓	104
8.5	even	2	inner	520.2.by.c.61.49	yes	104
13.3	even	3	inner	520.2.by.c.341.49	yes	104
104.29	even	6	inner	520.2.by.c.341.16	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.by.c.61.16	✓	104	1.1	even	1	trivial
520.2.by.c.61.49	yes	104	8.5	even	2	inner
520.2.by.c.341.16	yes	104	104.29	even	6	inner
520.2.by.c.341.49	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)

\(f(q)\)	\(=\)	\(q+(-0.893979 - 1.09581i) q^{2} +(-0.566349 - 0.326982i) q^{3} +(-0.401602 + 1.95926i) q^{4} +1.00000i q^{5} +(0.147994 + 0.912926i) q^{6} +(0.582724 + 1.00931i) q^{7} +(2.50601 - 1.31146i) q^{8} +(-1.28617 - 2.22770i) q^{9} +O(q^{10})\)	\(q+(-0.893979 - 1.09581i) q^{2} +(-0.566349 - 0.326982i) q^{3} +(-0.401602 + 1.95926i) q^{4} +1.00000i q^{5} +(0.147994 + 0.912926i) q^{6} +(0.582724 + 1.00931i) q^{7} +(2.50601 - 1.31146i) q^{8} +(-1.28617 - 2.22770i) q^{9} +(1.09581 - 0.893979i) q^{10} +(-0.0715430 - 0.0413054i) q^{11} +(0.868090 - 0.978310i) q^{12} +(-3.17138 + 1.71533i) q^{13} +(0.585067 - 1.54086i) q^{14} +(0.326982 - 0.566349i) q^{15} +(-3.67743 - 1.57369i) q^{16} +(1.84116 + 3.18898i) q^{17} +(-1.29134 + 3.40092i) q^{18} +(-0.984822 + 0.568587i) q^{19} +(-1.95926 - 0.401602i) q^{20} -0.762160i q^{21} +(0.0186951 + 0.115324i) q^{22} +(-4.08484 + 7.07515i) q^{23} +(-1.84810 - 0.0766728i) q^{24} -1.00000 q^{25} +(4.71482 + 1.94176i) q^{26} +3.64410i q^{27} +(-2.21152 + 0.736371i) q^{28} +(3.65309 + 2.10911i) q^{29} +(-0.912926 + 0.147994i) q^{30} -7.17175 q^{31} +(1.56308 + 5.43661i) q^{32} +(0.0270122 + 0.0467865i) q^{33} +(1.84856 - 4.86844i) q^{34} +(-1.00931 + 0.582724i) q^{35} +(4.88119 - 1.62529i) q^{36} +(8.01115 + 4.62524i) q^{37} +(1.50347 + 0.570873i) q^{38} +(2.35699 + 0.0655083i) q^{39} +(1.31146 + 2.50601i) q^{40} +(-1.49627 + 2.59161i) q^{41} +(-0.835183 + 0.681355i) q^{42} +(-4.80126 + 2.77201i) q^{43} +(0.109660 - 0.123583i) q^{44} +(2.22770 - 1.28617i) q^{45} +(11.4048 - 1.84883i) q^{46} -0.293254 q^{47} +(1.56814 + 2.09371i) q^{48} +(2.82087 - 4.88588i) q^{49} +(0.893979 + 1.09581i) q^{50} -2.40810i q^{51} +(-2.08715 - 6.90245i) q^{52} +4.81827i q^{53} +(3.99324 - 3.25775i) q^{54} +(0.0413054 - 0.0715430i) q^{55} +(2.78398 + 1.76511i) q^{56} +0.743670 q^{57} +(-0.954600 - 5.88860i) q^{58} +(-5.26086 + 3.03736i) q^{59} +(0.978310 + 0.868090i) q^{60} +(9.69723 - 5.59870i) q^{61} +(6.41140 + 7.85888i) q^{62} +(1.49896 - 2.59627i) q^{63} +(4.56013 - 6.57307i) q^{64} +(-1.71533 - 3.17138i) q^{65} +(0.0271208 - 0.0714264i) q^{66} +(-1.42901 - 0.825039i) q^{67} +(-6.98747 + 2.32662i) q^{68} +(4.62689 - 2.67134i) q^{69} +(1.54086 + 0.585067i) q^{70} +(6.55471 + 11.3531i) q^{71} +(-6.14469 - 3.89588i) q^{72} -10.8117 q^{73} +(-2.09342 - 12.9136i) q^{74} +(0.566349 + 0.326982i) q^{75} +(-0.718506 - 2.15787i) q^{76} -0.0962785i q^{77} +(-2.03531 - 2.64138i) q^{78} -10.0329 q^{79} +(1.57369 - 3.67743i) q^{80} +(-2.66694 + 4.61928i) q^{81} +(4.17754 - 0.677221i) q^{82} +6.23077i q^{83} +(1.49327 + 0.306085i) q^{84} +(-3.18898 + 1.84116i) q^{85} +(7.32983 + 2.78315i) q^{86} +(-1.37928 - 2.38899i) q^{87} +(-0.233458 - 0.00968555i) q^{88} +(2.69577 - 4.66920i) q^{89} +(-3.40092 - 1.29134i) q^{90} +(-3.57933 - 2.20133i) q^{91} +(-12.2216 - 10.8447i) q^{92} +(4.06171 + 2.34503i) q^{93} +(0.262163 + 0.321351i) q^{94} +(-0.568587 - 0.984822i) q^{95} +(0.892421 - 3.59012i) q^{96} +(0.603364 + 1.04506i) q^{97} +(-7.87580 + 1.27674i) q^{98} +0.212502i 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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