LMFDB - Embedded newform 930.2.j.h.497.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.9
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.33303 - 1.10591i) q^{3} -1.00000i q^{4} +(-0.368595 - 2.20548i) q^{5} +(-0.160600 + 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.553937 - 2.94842i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.33303 - 1.10591i) q^{3} -1.00000i q^{4} +(-0.368595 - 2.20548i) q^{5} +(-0.160600 + 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.553937 - 2.94842i) q^{9} +(1.82015 + 1.29887i) q^{10} -0.0722722i q^{11} +(-1.10591 - 1.33303i) q^{12} +(2.91767 - 2.91767i) q^{13} +4.05393 q^{14} +(-2.93040 - 2.53234i) q^{15} -1.00000 q^{16} +(-4.16969 + 4.16969i) q^{17} +(1.69315 + 2.47654i) q^{18} +3.12636i q^{19} +(-2.20548 + 0.368595i) q^{20} +(-6.99136 - 0.651060i) q^{21} +(0.0511042 + 0.0511042i) q^{22} +(1.55408 + 1.55408i) q^{23} +(1.72459 + 0.160600i) q^{24} +(-4.72828 + 1.62586i) q^{25} +4.12620i q^{26} +(-2.52226 - 4.54293i) q^{27} +(-2.86656 + 2.86656i) q^{28} +3.03469 q^{29} +(3.86274 - 0.281475i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.0799264 - 0.0963410i) q^{33} -5.89683i q^{34} +(-5.26554 + 7.37874i) q^{35} +(-2.94842 - 0.553937i) q^{36} +(-5.90545 - 5.90545i) q^{37} +(-2.21067 - 2.21067i) q^{38} +(0.662667 - 7.11600i) q^{39} +(1.29887 - 1.82015i) q^{40} -1.90694i q^{41} +(5.40401 - 4.48327i) q^{42} +(-0.388846 + 0.388846i) q^{43} -0.0722722 q^{44} +(-6.70685 - 0.134926i) q^{45} -2.19780 q^{46} +(-2.00099 + 2.00099i) q^{47} +(-1.33303 + 1.10591i) q^{48} +9.43435i q^{49} +(2.19374 - 4.49305i) q^{50} +(-0.947029 + 10.1696i) q^{51} +(-2.91767 - 2.91767i) q^{52} +(-6.68933 - 6.68933i) q^{53} +(4.99584 + 1.42883i) q^{54} +(-0.159395 + 0.0266392i) q^{55} -4.05393i q^{56} +(3.45747 + 4.16753i) q^{57} +(-2.14585 + 2.14585i) q^{58} -2.33823 q^{59} +(-2.53234 + 2.93040i) q^{60} +12.8123 q^{61} +(0.707107 - 0.707107i) q^{62} +(-10.0397 + 6.86392i) q^{63} +1.00000i q^{64} +(-7.51029 - 5.35941i) q^{65} +(0.124640 + 0.0116069i) q^{66} +(7.43129 + 7.43129i) q^{67} +(4.16969 + 4.16969i) q^{68} +(3.79031 + 0.352967i) q^{69} +(-1.49426 - 8.94086i) q^{70} +5.69625i q^{71} +(2.47654 - 1.69315i) q^{72} +(6.06642 - 6.06642i) q^{73} +8.35157 q^{74} +(-4.50489 + 7.39635i) q^{75} +3.12636 q^{76} +(-0.207173 + 0.207173i) q^{77} +(4.56320 + 5.50035i) q^{78} -7.62446i q^{79} +(0.368595 + 2.20548i) q^{80} +(-8.38631 - 3.26647i) q^{81} +(1.34841 + 1.34841i) q^{82} +(-0.153300 - 0.153300i) q^{83} +(-0.651060 + 6.99136i) q^{84} +(10.7331 + 7.65924i) q^{85} -0.549911i q^{86} +(4.04533 - 3.35608i) q^{87} +(0.0511042 - 0.0511042i) q^{88} -13.6113 q^{89} +(4.83786 - 4.64705i) q^{90} -16.7273 q^{91} +(1.55408 - 1.55408i) q^{92} +(-1.33303 + 1.10591i) q^{93} -2.82982i q^{94} +(6.89512 - 1.15236i) q^{95} +(0.160600 - 1.72459i) q^{96} +(-2.66031 - 2.66031i) q^{97} +(-6.67109 - 6.67109i) q^{98} +(-0.213089 - 0.0400343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.33303	−	1.10591i	0.769625	−	0.638496i
$3$	1.33303	−	1.10591i	0.769625	−	0.638496i
$4$		−	1.00000i		−	0.500000i
$5$	−0.368595	−	2.20548i	−0.164841	−	0.986320i
$5$	−0.368595	−	2.20548i	−0.164841	−	0.986320i
$6$	−0.160600	+	1.72459i	−0.0655646	+	0.704061i
$7$	−2.86656	−	2.86656i	−1.08346	−	1.08346i	−0.996184	−	0.0872740i	$-0.972184\pi$
$7$	−2.86656	−	2.86656i	−1.08346	−	1.08346i	−0.0872740	−	0.996184i	$-0.527816\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.553937	−	2.94842i	0.184646	−	0.982805i
$10$	1.82015	+	1.29887i	0.575580	+	0.410740i
$11$		−	0.0722722i		−	0.0217909i	−0.999941	−	0.0108954i	$-0.996532\pi$
$11$		−	0.0722722i		−	0.0217909i	0.999941	−	0.0108954i	$-0.00346820\pi$
$12$	−1.10591	−	1.33303i	−0.319248	−	0.384813i
$13$	2.91767	−	2.91767i	0.809215	−	0.809215i	−0.175300	−	0.984515i	$-0.556090\pi$
$13$	2.91767	−	2.91767i	0.809215	−	0.809215i	0.984515	+	0.175300i	$0.0560896\pi$
$14$	4.05393			1.08346
$15$	−2.93040	−	2.53234i	−0.756627	−	0.653847i
$16$	−1.00000			−0.250000
$17$	−4.16969	+	4.16969i	−1.01130	+	1.01130i	−0.0113627	+	0.999935i	$0.503617\pi$
$17$	−4.16969	+	4.16969i	−1.01130	+	1.01130i	−0.999935	+	0.0113627i	$0.996383\pi$
$18$	1.69315	+	2.47654i	0.399080	+	0.583725i
$19$			3.12636i			0.717236i	0.933484	+	0.358618i	$0.116752\pi$
$19$			3.12636i			0.717236i	−0.933484	+	0.358618i	$0.883248\pi$
$20$	−2.20548	+	0.368595i	−0.493160	+	0.0824203i
$21$	−6.99136	−	0.651060i	−1.52564	−	0.142073i
$22$	0.0511042	+	0.0511042i	0.0108954	+	0.0108954i
$23$	1.55408	+	1.55408i	0.324049	+	0.324049i	0.850318	−	0.526269i	$-0.176410\pi$
$23$	1.55408	+	1.55408i	0.324049	+	0.324049i	−0.526269	+	0.850318i	$0.676410\pi$
$24$	1.72459	+	0.160600i	0.352030	+	0.0327823i
$25$	−4.72828	+	1.62586i	−0.945655	+	0.325171i
$26$			4.12620i			0.809215i
$27$	−2.52226	−	4.54293i	−0.485409	−	0.874287i
$28$	−2.86656	+	2.86656i	−0.541729	+	0.541729i
$29$	3.03469			0.563527			0.281764	−	0.959484i	$-0.409081\pi$
$29$	3.03469			0.563527			0.281764	+	0.959484i	$0.409081\pi$
$30$	3.86274	−	0.281475i	0.705237	−	0.0513901i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.0799264	−	0.0963410i	−0.0139134	−	0.0167708i
$34$		−	5.89683i		−	1.01130i
$35$	−5.26554	+	7.37874i	−0.890039	+	1.24723i
$36$	−2.94842	−	0.553937i	−0.491403	−	0.0923228i
$37$	−5.90545	−	5.90545i	−0.970851	−	0.970851i	0.0287364	−	0.999587i	$-0.490852\pi$
$37$	−5.90545	−	5.90545i	−0.970851	−	0.970851i	−0.999587	+	0.0287364i	$0.990852\pi$
$38$	−2.21067	−	2.21067i	−0.358618	−	0.358618i
$39$	0.662667	−	7.11600i	0.106112	−	1.13947i
$40$	1.29887	−	1.82015i	0.205370	−	0.287790i
$41$		−	1.90694i		−	0.297814i	−0.988851	−	0.148907i	$-0.952425\pi$
$41$		−	1.90694i		−	0.297814i	0.988851	−	0.148907i	$-0.0475755\pi$
$42$	5.40401	−	4.48327i	0.833857	−	0.691784i
$43$	−0.388846	+	0.388846i	−0.0592984	+	0.0592984i	−0.736134	−	0.676836i	$-0.763351\pi$
$43$	−0.388846	+	0.388846i	−0.0592984	+	0.0592984i	0.676836	+	0.736134i	$0.263351\pi$
$44$	−0.0722722			−0.0108954
$45$	−6.70685	−	0.134926i	−0.999798	−	0.0201135i
$46$	−2.19780			−0.324049
$47$	−2.00099	+	2.00099i	−0.291874	+	0.291874i	−0.837820	−	0.545946i	$-0.816170\pi$
$47$	−2.00099	+	2.00099i	−0.291874	+	0.291874i	0.545946	+	0.837820i	$0.316170\pi$
$48$	−1.33303	+	1.10591i	−0.192406	+	0.159624i
$49$			9.43435i			1.34776i
$50$	2.19374	−	4.49305i	0.310242	−	0.635413i
$51$	−0.947029	+	10.1696i	−0.132611	+	1.42403i
$52$	−2.91767	−	2.91767i	−0.404607	−	0.404607i
$53$	−6.68933	−	6.68933i	−0.918851	−	0.918851i	0.0780952	−	0.996946i	$-0.475116\pi$
$53$	−6.68933	−	6.68933i	−0.918851	−	0.918851i	−0.996946	+	0.0780952i	$0.975116\pi$
$54$	4.99584	+	1.42883i	0.679848	+	0.194439i
$55$	−0.159395	+	0.0266392i	−0.0214928	+	0.00359203i
$56$		−	4.05393i		−	0.541729i
$57$	3.45747	+	4.16753i	0.457953	+	0.552003i
$58$	−2.14585	+	2.14585i	−0.281764	+	0.281764i
$59$	−2.33823			−0.304411			−0.152206	−	0.988349i	$-0.548638\pi$
$59$	−2.33823			−0.304411			−0.152206	+	0.988349i	$0.548638\pi$
$60$	−2.53234	+	2.93040i	−0.326923	+	0.378314i
$61$	12.8123			1.64045			0.820224	−	0.572043i	$-0.193849\pi$
$61$	12.8123			1.64045			0.820224	+	0.572043i	$0.193849\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	−10.0397	+	6.86392i	−1.26488	+	0.864773i
$64$			1.00000i			0.125000i
$65$	−7.51029	−	5.35941i	−0.931536	−	0.664753i
$66$	0.124640	+	0.0116069i	0.0153421	+	0.00142871i
$67$	7.43129	+	7.43129i	0.907876	+	0.907876i	0.996101	−	0.0882246i	$-0.0281193\pi$
$67$	7.43129	+	7.43129i	0.907876	+	0.907876i	−0.0882246	+	0.996101i	$0.528119\pi$
$68$	4.16969	+	4.16969i	0.505649	+	0.505649i
$69$	3.79031	+	0.352967i	0.456300	+	0.0424922i
$70$	−1.49426	−	8.94086i	−0.178598	−	1.06864i
$71$			5.69625i			0.676020i	0.941142	+	0.338010i	$0.109754\pi$
$71$			5.69625i			0.676020i	−0.941142	+	0.338010i	$0.890246\pi$
$72$	2.47654	−	1.69315i	0.291863	−	0.199540i
$73$	6.06642	−	6.06642i	0.710021	−	0.710021i	−0.256518	−	0.966539i	$-0.582575\pi$
$73$	6.06642	−	6.06642i	0.710021	−	0.710021i	0.966539	+	0.256518i	$0.0825754\pi$
$74$	8.35157			0.970851
$75$	−4.50489	+	7.39635i	−0.520179	+	0.854057i
$76$	3.12636			0.358618
$77$	−0.207173	+	0.207173i	−0.0236095	+	0.0236095i
$78$	4.56320	+	5.50035i	0.516680	+	0.622792i
$79$		−	7.62446i		−	0.857819i	−0.903348	−	0.428909i	$-0.858898\pi$
$79$		−	7.62446i		−	0.857819i	0.903348	−	0.428909i	$-0.141102\pi$
$80$	0.368595	+	2.20548i	0.0412102	+	0.246580i
$81$	−8.38631	−	3.26647i	−0.931812	−	0.362941i
$82$	1.34841	+	1.34841i	0.148907	+	0.148907i
$83$	−0.153300	−	0.153300i	−0.0168269	−	0.0168269i	0.698643	−	0.715470i	$-0.253787\pi$
$83$	−0.153300	−	0.153300i	−0.0168269	−	0.0168269i	−0.715470	+	0.698643i	$0.753787\pi$
$84$	−0.651060	+	6.99136i	−0.0710365	+	0.762820i
$85$	10.7331	+	7.65924i	1.16417	+	0.830761i
$86$		−	0.549911i		−	0.0592984i
$87$	4.04533	−	3.35608i	0.433705	−	0.359810i
$88$	0.0511042	−	0.0511042i	0.00544772	−	0.00544772i
$89$	−13.6113			−1.44280			−0.721398	−	0.692521i	$-0.756500\pi$
$89$	−13.6113			−1.44280			−0.721398	+	0.692521i	$0.756500\pi$
$90$	4.83786	−	4.64705i	0.509956	−	0.489842i
$91$	−16.7273			−1.75350
$92$	1.55408	−	1.55408i	0.162024	−	0.162024i
$93$	−1.33303	+	1.10591i	−0.138229	+	0.114677i
$94$		−	2.82982i		−	0.291874i
$95$	6.89512	−	1.15236i	0.707425	−	0.118230i
$96$	0.160600	−	1.72459i	0.0163911	−	0.176015i
$97$	−2.66031	−	2.66031i	−0.270113	−	0.270113i	0.559033	−	0.829146i	$-0.311173\pi$
$97$	−2.66031	−	2.66031i	−0.270113	−	0.270113i	−0.829146	+	0.559033i	$0.811173\pi$
$98$	−6.67109	−	6.67109i	−0.673882	−	0.673882i
$99$	−0.213089	−	0.0400343i	−0.0214162	−	0.00402360i
$100$	1.62586	+	4.72828i	0.162586	+	0.472828i
$101$		−	13.9690i		−	1.38997i	−0.719026	−	0.694983i	$-0.755412\pi$
$101$		−	13.9690i		−	1.38997i	0.719026	−	0.694983i	$-0.244588\pi$
$102$	−6.52135	−	7.86065i	−0.645710	−	0.778320i
$103$	9.62776	−	9.62776i	0.948652	−	0.948652i	−0.0500930	−	0.998745i	$-0.515952\pi$
$103$	9.62776	−	9.62776i	0.948652	−	0.948652i	0.998745	+	0.0500930i	$0.0159518\pi$
$104$	4.12620			0.404607
$105$	1.14108	+	15.6593i	0.111358	+	1.52819i
$106$	9.46015			0.918851
$107$	13.2804	−	13.2804i	1.28386	−	1.28386i	0.345411	−	0.938451i	$-0.387739\pi$
$107$	13.2804	−	13.2804i	1.28386	−	1.28386i	0.938451	−	0.345411i	$-0.112261\pi$
$108$	−4.54293	+	2.52226i	−0.437144	+	0.242705i
$109$			12.0047i			1.14984i	0.818210	+	0.574920i	$0.194967\pi$
$109$			12.0047i			1.14984i	−0.818210	+	0.574920i	$0.805033\pi$
$110$	0.0938725	−	0.131546i	0.00895039	−	0.0125424i
$111$	−14.4030	−	1.34126i	−1.36708	−	0.127307i
$112$	2.86656	+	2.86656i	0.270865	+	0.270865i
$113$	−14.5548	−	14.5548i	−1.36920	−	1.36920i	−0.861578	−	0.507625i	$-0.830524\pi$
$113$	−14.5548	−	14.5548i	−1.36920	−	1.36920i	−0.507625	−	0.861578i	$-0.669476\pi$
$114$	−5.39169	−	0.502093i	−0.504978	−	0.0470253i
$115$	2.85467	−	4.00032i	0.266199	−	0.373032i
$116$		−	3.03469i		−	0.281764i
$117$	−6.98629	−	10.2187i	−0.645882	−	0.944719i
$118$	1.65338	−	1.65338i	0.152206	−	0.152206i
$119$	23.9053			2.19140
$120$	−0.281475	−	3.86274i	−0.0256951	−	0.352618i
$121$	10.9948			0.999525
$122$	−9.05967	+	9.05967i	−0.820224	+	0.820224i
$123$	−2.10890	−	2.54201i	−0.190153	−	0.229205i
$124$			1.00000i			0.0898027i
$125$	5.32861	+	9.82883i	0.476605	+	0.879117i
$126$	2.24562	−	11.9527i	0.200056	−	1.06483i
$127$	−2.77146	−	2.77146i	−0.245928	−	0.245928i	0.573369	−	0.819297i	$-0.305636\pi$
$127$	−2.77146	−	2.77146i	−0.245928	−	0.245928i	−0.819297	+	0.573369i	$0.805636\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.0883156	+	0.948371i	−0.00777575	+	0.0834994i
$130$	9.10025	−	1.52090i	0.798145	−	0.133391i
$131$		−	15.2844i		−	1.33540i	−0.744429	−	0.667702i	$-0.767278\pi$
$131$		−	15.2844i		−	1.33540i	0.744429	−	0.667702i	$-0.232722\pi$
$132$	−0.0963410	+	0.0799264i	−0.00838541	+	0.00695670i
$133$	8.96191	−	8.96191i	0.777096	−	0.777096i
$134$	−10.5094			−0.907876
$135$	−9.08964	+	7.23729i	−0.782312	+	0.622887i
$136$	−5.89683			−0.505649
$137$	−3.94097	+	3.94097i	−0.336699	+	0.336699i	−0.855124	−	0.518424i	$-0.826519\pi$
$137$	−3.94097	+	3.94097i	−0.336699	+	0.336699i	0.518424	+	0.855124i	$0.326519\pi$
$138$	−2.92974	+	2.43057i	−0.249396	+	0.206904i
$139$			10.9204i			0.926258i	0.886291	+	0.463129i	$0.153273\pi$
$139$			10.9204i			0.926258i	−0.886291	+	0.463129i	$0.846727\pi$
$140$	7.37874	+	5.26554i	0.623617	+	0.445019i
$141$	−0.454469	+	4.88028i	−0.0382732	+	0.410994i
$142$	−4.02786	−	4.02786i	−0.338010	−	0.338010i
$143$	−0.210866	−	0.210866i	−0.0176335	−	0.0176335i
$144$	−0.553937	+	2.94842i	−0.0461614	+	0.245701i
$145$	−1.11857	−	6.69294i	−0.0928922	−	0.555818i
$146$			8.57922i			0.710021i
$147$	10.4335	+	12.5763i	0.860542	+	1.03727i
$148$	−5.90545	+	5.90545i	−0.485425	+	0.485425i
$149$	11.2480			0.921468			0.460734	−	0.887538i	$-0.347586\pi$
$149$	11.2480			0.921468			0.460734	+	0.887538i	$0.347586\pi$
$150$	−2.04457	−	8.41544i	−0.166939	−	0.687118i
$151$	−11.8924			−0.967789			−0.483895	−	0.875126i	$-0.660778\pi$
$151$	−11.8924			−0.967789			−0.483895	+	0.875126i	$0.660778\pi$
$152$	−2.21067	+	2.21067i	−0.179309	+	0.179309i
$153$	9.98423	+	14.6037i	0.807177	+	1.18064i
$154$		−	0.292987i		−	0.0236095i
$155$	0.368595	+	2.20548i	0.0296063	+	0.177148i
$156$	−7.11600	−	0.662667i	−0.569736	−	0.0530558i
$157$	−0.977475	−	0.977475i	−0.0780110	−	0.0780110i	0.667025	−	0.745036i	$-0.267568\pi$
$157$	−0.977475	−	0.977475i	−0.0780110	−	0.0780110i	−0.745036	+	0.667025i	$0.767568\pi$
$158$	5.39131	+	5.39131i	0.428909	+	0.428909i
$159$	−16.3149	−	1.51930i	−1.29385	−	0.120488i
$160$	−1.82015	−	1.29887i	−0.143895	−	0.102685i
$161$		−	8.90974i		−	0.702186i
$162$	8.23976	−	3.62027i	0.647377	−	0.284435i
$163$	12.3528	−	12.3528i	0.967547	−	0.967547i	−0.0319424	−	0.999490i	$-0.510169\pi$
$163$	12.3528	−	12.3528i	0.967547	−	0.967547i	0.999490	+	0.0319424i	$0.0101693\pi$
$164$	−1.90694			−0.148907
$165$	−0.183018	+	0.211787i	−0.0142479	+	0.0164876i
$166$	0.216799			0.0168269
$167$	−7.76866	+	7.76866i	−0.601157	+	0.601157i	−0.940620	−	0.339463i	$-0.889755\pi$
$167$	−7.76866	+	7.76866i	−0.601157	+	0.601157i	0.339463	+	0.940620i	$0.389755\pi$
$168$	−4.48327	−	5.40401i	−0.345892	−	0.416928i
$169$		−	4.02554i		−	0.309657i
$170$	−13.0053	+	2.17354i	−0.997464	+	0.166703i
$171$	9.21781	+	1.73181i	0.704904	+	0.132435i
$172$	0.388846	+	0.388846i	0.0296492	+	0.0296492i
$173$	−13.1245	−	13.1245i	−0.997840	−	0.997840i	0.00215773	−	0.999998i	$-0.499313\pi$
$173$	−13.1245	−	13.1245i	−0.997840	−	0.997840i	−0.999998	+	0.00215773i	$0.999313\pi$
$174$	−0.487370	+	5.23359i	−0.0369474	+	0.396757i
$175$	18.2145	+	8.89327i	1.37689	+	0.672268i
$176$			0.0722722i			0.00544772i
$177$	−3.11692	+	2.58586i	−0.234282	+	0.194365i
$178$	9.62465	−	9.62465i	0.721398	−	0.721398i
$179$	16.8729			1.26114			0.630572	−	0.776131i	$-0.282821\pi$
$179$	16.8729			1.26114			0.630572	+	0.776131i	$0.282821\pi$
$180$	−0.134926	+	6.70685i	−0.0100568	+	0.499899i
$181$	16.8141			1.24978			0.624889	−	0.780713i	$-0.285144\pi$
$181$	16.8141			1.24978			0.624889	+	0.780713i	$0.285144\pi$
$182$	11.8280	−	11.8280i	0.876751	−	0.876751i
$183$	17.0792	−	14.1692i	1.26253	−	1.04742i
$184$			2.19780i			0.162024i
$185$	−10.8476	+	15.2011i	−0.797534	+	1.11761i
$186$	0.160600	−	1.72459i	0.0117757	−	0.126453i
$187$	0.301353	+	0.301353i	0.0220371	+	0.0220371i
$188$	2.00099	+	2.00099i	0.145937	+	0.145937i
$189$	−5.79237	+	20.2528i	−0.421333	+	1.47317i
$190$	−4.06075	+	5.69043i	−0.294598	+	0.412827i
$191$			17.7533i			1.28459i	0.766459	+	0.642293i	$0.222017\pi$
$191$			17.7533i			1.28459i	−0.766459	+	0.642293i	$0.777983\pi$
$192$	1.10591	+	1.33303i	0.0798120	+	0.0962031i
$193$	−4.22668	+	4.22668i	−0.304243	+	0.304243i	−0.842671	−	0.538428i	$-0.819018\pi$
$193$	−4.22668	+	4.22668i	−0.304243	+	0.304243i	0.538428	+	0.842671i	$0.319018\pi$
$194$	3.76224			0.270113
$195$	−15.9385	+	1.16142i	−1.14138	+	0.0831713i
$196$	9.43435			0.673882
$197$	6.01897	−	6.01897i	0.428834	−	0.428834i	−0.459397	−	0.888231i	$-0.651934\pi$
$197$	6.01897	−	6.01897i	0.428834	−	0.428834i	0.888231	+	0.459397i	$0.151934\pi$
$198$	0.178985	−	0.122368i	0.0127199	−	0.00869631i
$199$		−	7.41699i		−	0.525777i	−0.964826	−	0.262888i	$-0.915325\pi$
$199$		−	7.41699i		−	0.525777i	0.964826	−	0.262888i	$-0.0846751\pi$
$200$	−4.49305	−	2.19374i	−0.317707	−	0.155121i
$201$	18.1244	+	1.68781i	1.27840	+	0.119049i
$202$	9.87756	+	9.87756i	0.694983	+	0.694983i
$203$	−8.69912	−	8.69912i	−0.610558	−	0.610558i
$204$	10.1696	+	0.947029i	0.712015	+	0.0663053i
$205$	−4.20571	+	0.702888i	−0.293740	+	0.0490918i
$206$			13.6157i			0.948652i
$207$	5.44294	−	3.72122i	0.378311	−	0.258642i
$208$	−2.91767	+	2.91767i	−0.202304	+	0.202304i
$209$	0.225949			0.0156292
$210$	−11.8797	−	10.2659i	−0.819774	−	0.708416i
$211$	−2.53992			−0.174855			−0.0874275	−	0.996171i	$-0.527865\pi$
$211$	−2.53992			−0.174855			−0.0874275	+	0.996171i	$0.527865\pi$
$212$	−6.68933	+	6.68933i	−0.459425	+	0.459425i
$213$	6.29952	+	7.59327i	0.431636	+	0.520282i
$214$			18.7813i			1.28386i
$215$	1.00092	+	0.714265i	0.0682620	+	0.0487125i
$216$	1.42883	−	4.99584i	0.0972195	−	0.339924i
$217$	2.86656	+	2.86656i	0.194595	+	0.194595i
$218$	−8.48859	−	8.48859i	−0.574920	−	0.574920i
$219$	1.37782	−	14.7956i	0.0931044	−	0.999796i
$220$	0.0266392	+	0.159395i	0.00179601	+	0.0107464i
$221$			24.3315i			1.63671i
$222$	11.1329	−	9.23607i	0.747191	−	0.619884i
$223$	−3.72524	+	3.72524i	−0.249461	+	0.249461i	−0.820749	−	0.571289i	$-0.806444\pi$
$223$	−3.72524	+	3.72524i	−0.249461	+	0.249461i	0.571289	+	0.820749i	$0.306444\pi$
$224$	−4.05393			−0.270865
$225$	2.17453	+	14.8415i	0.144969	+	0.989436i
$226$	20.5836			1.36920
$227$	15.0376	−	15.0376i	0.998082	−	0.998082i	−0.00191666	−	0.999998i	$-0.500610\pi$
$227$	15.0376	−	15.0376i	0.998082	−	0.998082i	0.999998	+	0.00191666i	$0.000610091\pi$
$228$	4.16753	−	3.45747i	0.276002	−	0.228976i
$229$			1.28766i			0.0850909i	0.999095	+	0.0425455i	$0.0135467\pi$
$229$			1.28766i			0.0850909i	−0.999095	+	0.0425455i	$0.986453\pi$
$230$	0.810099	+	4.84721i	0.0534164	+	0.319616i
$231$	−0.0470536	+	0.505281i	−0.00309590	+	0.0332451i
$232$	2.14585	+	2.14585i	0.140882	+	0.140882i
$233$	−18.5176	−	18.5176i	−1.21313	−	1.21313i	−0.969993	−	0.243132i	$-0.921825\pi$
$233$	−18.5176	−	18.5176i	−1.21313	−	1.21313i	−0.243132	−	0.969993i	$-0.578175\pi$
$234$	12.1658	+	2.28566i	0.795300	+	0.149418i
$235$	5.15069	+	3.67558i	0.335994	+	0.239768i
$236$			2.33823i			0.152206i
$237$	−8.43195	−	10.1636i	−0.547714	−	0.660199i
$238$	−16.9036	+	16.9036i	−1.09570	+	1.09570i
$239$	−7.72147			−0.499460			−0.249730	−	0.968315i	$-0.580342\pi$
$239$	−7.72147			−0.499460			−0.249730	+	0.968315i	$0.580342\pi$
$240$	2.93040	+	2.53234i	0.189157	+	0.163462i
$241$	−21.8089			−1.40483			−0.702417	−	0.711766i	$-0.747896\pi$
$241$	−21.8089			−1.40483			−0.702417	+	0.711766i	$0.747896\pi$
$242$	−7.77448	+	7.77448i	−0.499763	+	0.499763i
$243$	−14.7916	+	4.92018i	−0.948883	+	0.315629i
$244$		−	12.8123i		−	0.820224i
$245$	20.8073	−	3.47745i	1.32933	−	0.222166i
$246$	3.28869	+	0.306254i	0.209679	+	0.0195260i
$247$	9.12168	+	9.12168i	0.580398	+	0.580398i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	−0.373890	−	0.0348179i	−0.0236943	−	0.00220650i
$250$	−10.7179	−	3.18214i	−0.677861	−	0.201256i
$251$			25.7679i			1.62646i	0.581944	+	0.813229i	$0.302292\pi$
$251$			25.7679i			1.62646i	−0.581944	+	0.813229i	$0.697708\pi$
$252$	6.86392	+	10.0397i	0.432386	+	0.632442i
$253$	0.112317	−	0.112317i	0.00706131	−	0.00706131i
$254$	3.91944			0.245928
$255$	22.7779	−	1.65981i	1.42641	−	0.103942i
$256$	1.00000			0.0625000
$257$	1.33326	−	1.33326i	0.0831666	−	0.0831666i	−0.664300	−	0.747466i	$-0.731270\pi$
$257$	1.33326	−	1.33326i	0.0831666	−	0.0831666i	0.747466	+	0.664300i	$0.231270\pi$
$258$	−0.608151	−	0.733048i	−0.0378618	−	0.0456376i
$259$			33.8567i			2.10375i
$260$	−5.35941	+	7.51029i	−0.332377	+	0.465768i
$261$	1.68103	−	8.94752i	0.104053	−	0.553838i
$262$	10.8077	+	10.8077i	0.667702	+	0.667702i
$263$	16.4679	+	16.4679i	1.01546	+	1.01546i	0.999879	+	0.0155767i	$0.00495842\pi$
$263$	16.4679	+	16.4679i	1.01546	+	1.01546i	0.0155767	+	0.999879i	$0.495042\pi$
$264$	0.0116069	−	0.124640i	0.000714355	−	0.00767106i
$265$	−12.2875	+	17.2188i	−0.754817	+	1.05775i
$266$			12.6740i			0.777096i
$267$	−18.1443	+	15.0529i	−1.11041	+	0.921220i
$268$	7.43129	−	7.43129i	0.453938	−	0.453938i
$269$	30.4001			1.85353			0.926764	−	0.375643i	$-0.122578\pi$
$269$	30.4001			1.85353			0.926764	+	0.375643i	$0.122578\pi$
$270$	1.30981	−	11.5449i	0.0797124	−	0.702599i
$271$	12.4459			0.756036			0.378018	−	0.925798i	$-0.376606\pi$
$271$	12.4459			0.756036			0.378018	+	0.925798i	$0.376606\pi$
$272$	4.16969	−	4.16969i	0.252825	−	0.252825i
$273$	−22.2980	+	18.4989i	−1.34954	+	1.11960i
$274$		−	5.57337i		−	0.336699i
$275$	0.117504	+	0.341723i	0.00708577	+	0.0206067i
$276$	0.352967	−	3.79031i	0.0212461	−	0.228150i
$277$	−1.07651	−	1.07651i	−0.0646812	−	0.0646812i	0.674026	−	0.738707i	$-0.264563\pi$
$277$	−1.07651	−	1.07651i	−0.0646812	−	0.0646812i	−0.738707	+	0.674026i	$0.764563\pi$
$278$	−7.72190	−	7.72190i	−0.463129	−	0.463129i
$279$	−0.553937	+	2.94842i	−0.0331633	+	0.176517i
$280$	−8.94086	+	1.49426i	−0.534318	+	0.0892990i
$281$			28.3035i			1.68844i	0.535993	+	0.844222i	$0.319937\pi$
$281$			28.3035i			1.68844i	−0.535993	+	0.844222i	$0.680063\pi$
$282$	−3.12952	−	3.77224i	−0.186360	−	0.224634i
$283$	−9.27422	+	9.27422i	−0.551295	+	0.551295i	−0.926814	−	0.375520i	$-0.877464\pi$
$283$	−9.27422	+	9.27422i	−0.551295	+	0.551295i	0.375520	+	0.926814i	$0.377464\pi$
$284$	5.69625			0.338010
$285$	7.91700	−	9.16150i	0.468963	−	0.542680i
$286$	0.298210			0.0176335
$287$	−5.46636	+	5.46636i	−0.322669	+	0.322669i
$288$	−1.69315	−	2.47654i	−0.0997699	−	0.145931i
$289$		−	17.7726i		−	1.04545i
$290$	5.52357	+	3.94167i	0.324355	+	0.231463i
$291$	−6.48832	−	0.604215i	−0.380352	−	0.0354197i
$292$	−6.06642	−	6.06642i	−0.355011	−	0.355011i
$293$	8.37669	+	8.37669i	0.489371	+	0.489371i	0.908108	−	0.418736i	$-0.137527\pi$
$293$	8.37669	+	8.37669i	0.489371	+	0.489371i	−0.418736	+	0.908108i	$0.637527\pi$
$294$	−16.2704	−	1.51515i	−0.948907	−	0.0883655i
$295$	0.861858	+	5.15691i	0.0501793	+	0.300247i
$296$		−	8.35157i		−	0.485425i
$297$	−0.328328	+	0.182289i	−0.0190515	+	0.0105775i
$298$	−7.95351	+	7.95351i	−0.460734	+	0.460734i
$299$	9.06858			0.524450
$300$	7.39635	+	4.50489i	0.427029	+	0.260090i
$301$	2.22930			0.128495
$302$	8.40919	−	8.40919i	0.483895	−	0.483895i
$303$	−15.4484	−	18.6211i	−0.887488	−	1.06975i
$304$		−	3.12636i		−	0.179309i
$305$	−4.72255	−	28.2573i	−0.270412	−	1.61801i
$306$	−17.3863	−	3.26647i	−0.993909	−	0.186732i
$307$	−10.4197	−	10.4197i	−0.594684	−	0.594684i	0.344209	−	0.938893i	$-0.388147\pi$
$307$	−10.4197	−	10.4197i	−0.594684	−	0.594684i	−0.938893	+	0.344209i	$0.888147\pi$
$308$	0.207173	+	0.207173i	0.0118048	+	0.0118048i
$309$	2.18668	−	23.4815i	0.124396	−	1.33582i
$310$	−1.82015	−	1.29887i	−0.103377	−	0.0737710i
$311$		−	1.14021i		−	0.0646554i	−0.999477	−	0.0323277i	$-0.989708\pi$
$311$		−	1.14021i		−	0.0646554i	0.999477	−	0.0323277i	$-0.0102920\pi$
$312$	5.50035	−	4.56320i	0.311396	−	0.258340i
$313$	9.62782	−	9.62782i	0.544197	−	0.544197i	−0.380560	−	0.924756i	$-0.624269\pi$
$313$	9.62782	−	9.62782i	0.544197	−	0.544197i	0.924756	+	0.380560i	$0.124269\pi$
$314$	1.38236			0.0780110
$315$	18.8388	+	19.6124i	1.06145	+	1.10503i
$316$	−7.62446			−0.428909
$317$	20.6739	−	20.6739i	1.16116	−	1.16116i	0.176938	−	0.984222i	$-0.443381\pi$
$317$	20.6739	−	20.6739i	1.16116	−	1.16116i	0.984222	−	0.176938i	$-0.0566193\pi$
$318$	12.6107	−	10.4620i	0.707171	−	0.586683i
$319$		−	0.219324i		−	0.0122798i
$320$	2.20548	−	0.368595i	0.123290	−	0.0206051i
$321$	3.01627	−	32.3900i	0.168352	−	1.80783i
$322$	6.30014	+	6.30014i	0.351093	+	0.351093i
$323$	−13.0360	−	13.0360i	−0.725340	−	0.725340i
$324$	−3.26647	+	8.38631i	−0.181471	+	0.465906i
$325$	−9.05182	+	18.5392i	−0.502105	+	1.02837i
$326$			17.4695i			0.967547i
$327$	13.2761	+	16.0026i	0.734168	+	0.884945i
$328$	1.34841	−	1.34841i	0.0744535	−	0.0744535i
$329$	11.4719			0.632466
$330$	−0.0203429	−	0.279169i	−0.00111984	−	0.0153677i
$331$	4.84875			0.266512			0.133256	−	0.991082i	$-0.457457\pi$
$331$	4.84875			0.266512			0.133256	+	0.991082i	$0.457457\pi$
$332$	−0.153300	+	0.153300i	−0.00841345	+	0.00841345i
$333$	−20.6830	+	14.1405i	−1.13342	+	0.774894i
$334$		−	10.9865i		−	0.601157i
$335$	13.6504	−	19.1287i	0.745802	−	1.04511i
$336$	6.99136	+	0.651060i	0.381410	+	0.0355182i
$337$	−1.86250	−	1.86250i	−0.101457	−	0.101457i	0.654556	−	0.756013i	$-0.272855\pi$
$337$	−1.86250	−	1.86250i	−0.101457	−	0.101457i	−0.756013	+	0.654556i	$0.772855\pi$
$338$	2.84649	+	2.84649i	0.154829	+	0.154829i
$339$	−35.4983	−	3.30573i	−1.92800	−	0.179542i
$340$	7.65924	−	10.7331i	0.415380	−	0.582083i
$341$			0.0722722i			0.00391376i
$342$	−7.74255	+	5.29340i	−0.418669	+	0.286235i
$343$	6.97821	−	6.97821i	0.376788	−	0.376788i
$344$	−0.549911			−0.0296492
$345$	−0.618628	−	8.48955i	−0.0333058	−	0.457062i
$346$	18.5609			0.997840
$347$	−16.5685	+	16.5685i	−0.889444	+	0.889444i	−0.994470	−	0.105026i	$-0.966508\pi$
$347$	−16.5685	+	16.5685i	−0.889444	+	0.889444i	0.105026	+	0.994470i	$0.466508\pi$
$348$	−3.35608	−	4.04533i	−0.179905	−	0.216852i
$349$		−	30.9903i		−	1.65888i	−0.558599	−	0.829438i	$-0.688661\pi$
$349$		−	30.9903i		−	1.65888i	0.558599	−	0.829438i	$-0.311339\pi$
$350$	−19.1681	+	6.59111i	−1.02458	+	0.352310i
$351$	−20.6139	−	5.89563i	−1.10029	−	0.314686i
$352$	−0.0511042	−	0.0511042i	−0.00272386	−	0.00272386i
$353$	−6.53675	−	6.53675i	−0.347916	−	0.347916i	0.511417	−	0.859333i	$-0.329121\pi$
$353$	−6.53675	−	6.53675i	−0.347916	−	0.347916i	−0.859333	+	0.511417i	$0.829121\pi$
$354$	0.375518	−	4.03248i	0.0199586	−	0.214324i
$355$	12.5630	−	2.09961i	0.666772	−	0.111436i
$356$			13.6113i			0.721398i
$357$	31.8665	−	26.4371i	1.68656	−	1.39920i
$358$	−11.9310	+	11.9310i	−0.630572	+	0.630572i
$359$	19.5683			1.03278			0.516388	−	0.856355i	$-0.327276\pi$
$359$	19.5683			1.03278			0.516388	+	0.856355i	$0.327276\pi$
$360$	−4.64705	−	4.83786i	−0.244921	−	0.254978i
$361$	9.22587			0.485572
$362$	−11.8893	+	11.8893i	−0.624889	+	0.624889i
$363$	14.6564	−	12.1592i	0.769260	−	0.638193i
$364$			16.7273i			0.876751i
$365$	−15.6154	−	11.1433i	−0.817348	−	0.583268i
$366$	−2.05765	+	22.0960i	−0.107555	+	1.15497i
$367$	22.2509	+	22.2509i	1.16149	+	1.16149i	0.984150	+	0.177336i	$0.0567479\pi$
$367$	22.2509	+	22.2509i	1.16149	+	1.16149i	0.177336	+	0.984150i	$0.443252\pi$
$368$	−1.55408	−	1.55408i	−0.0810121	−	0.0810121i
$369$	−5.62245	−	1.05632i	−0.292693	−	0.0549900i
$370$	−3.07835	−	18.4192i	−0.160036	−	0.957570i
$371$			38.3508i			1.99107i
$372$	1.10591	+	1.33303i	0.0573386	+	0.0691144i
$373$	14.3722	−	14.3722i	0.744164	−	0.744164i	−0.229213	−	0.973376i	$-0.573615\pi$
$373$	14.3722	−	14.3722i	0.744164	−	0.744164i	0.973376	+	0.229213i	$0.0736152\pi$
$374$	−0.426177			−0.0220371
$375$	17.9730	+	7.20917i	0.928120	+	0.372280i
$376$	−2.82982			−0.145937
$377$	8.85420	−	8.85420i	0.456015	−	0.456015i
$378$	−10.2251	−	18.4167i	−0.525921	−	0.947254i
$379$			27.6521i			1.42039i	0.704005	+	0.710195i	$0.251393\pi$
$379$			27.6521i			1.42039i	−0.704005	+	0.710195i	$0.748607\pi$
$380$	−1.15236	−	6.89512i	−0.0591149	−	0.353712i
$381$	−6.75943	−	0.629461i	−0.346296	−	0.0322483i
$382$	−12.5535	−	12.5535i	−0.642293	−	0.642293i
$383$	8.40290	+	8.40290i	0.429368	+	0.429368i	0.888413	−	0.459045i	$-0.151808\pi$
$383$	8.40290	+	8.40290i	0.429368	+	0.429368i	−0.459045	+	0.888413i	$0.651808\pi$
$384$	−1.72459	−	0.160600i	−0.0880076	−	0.00819557i
$385$	0.533278	+	0.380552i	0.0271784	+	0.0193947i
$386$		−	5.97743i		−	0.304243i
$387$	0.931083	+	1.36188i	0.0473296	+	0.0692280i
$388$	−2.66031	+	2.66031i	−0.135057	+	0.135057i
$389$	−18.8733			−0.956913			−0.478457	−	0.878111i	$-0.658804\pi$
$389$	−18.8733			−0.956913			−0.478457	+	0.878111i	$0.658804\pi$
$390$	10.4489	−	12.0914i	0.529102	−	0.612274i
$391$	−12.9601			−0.655419
$392$	−6.67109	+	6.67109i	−0.336941	+	0.336941i
$393$	−16.9031	−	20.3746i	−0.852650	−	1.02776i
$394$			8.51211i			0.428834i
$395$	−16.8156	+	2.81034i	−0.846084	+	0.141403i
$396$	−0.0400343	+	0.213089i	−0.00201180	+	0.0107081i
$397$	−11.7617	−	11.7617i	−0.590303	−	0.590303i	0.347410	−	0.937713i	$-0.387061\pi$
$397$	−11.7617	−	11.7617i	−0.590303	−	0.590303i	−0.937713	+	0.347410i	$0.887061\pi$
$398$	5.24461	+	5.24461i	0.262888	+	0.262888i
$399$	2.03545	−	21.8575i	0.101900	−	1.09424i
$400$	4.72828	−	1.62586i	0.236414	−	0.0812928i
$401$		−	12.7272i		−	0.635567i	−0.948163	−	0.317783i	$-0.897062\pi$
$401$		−	12.7272i		−	0.635567i	0.948163	−	0.317783i	$-0.102938\pi$
$402$	−14.0094	+	11.6225i	−0.698724	+	0.579675i
$403$	−2.91767	+	2.91767i	−0.145339	+	0.145339i
$404$	−13.9690			−0.694983
$405$	−4.11299	+	19.6998i	−0.204376	+	0.978892i
$406$	12.3024			0.610558
$407$	−0.426800	+	0.426800i	−0.0211557	+	0.0211557i
$408$	−7.86065	+	6.52135i	−0.389160	+	0.322855i
$409$		−	18.7099i		−	0.925144i	−0.886582	−	0.462572i	$-0.846927\pi$
$409$		−	18.7099i		−	0.925144i	0.886582	−	0.462572i	$-0.153073\pi$
$410$	2.47687	−	3.47091i	0.122324	−	0.171416i
$411$	−0.895081	+	9.61177i	−0.0441511	+	0.474114i
$412$	−9.62776	−	9.62776i	−0.474326	−	0.474326i
$413$	6.70267	+	6.70267i	0.329817	+	0.329817i
$414$	−1.21745	+	6.48004i	−0.0598342	+	0.318477i
$415$	−0.281595	+	0.394606i	−0.0138229	+	0.0193705i
$416$		−	4.12620i		−	0.202304i
$417$	12.0770	+	14.5572i	0.591412	+	0.712871i
$418$	−0.159770	+	0.159770i	−0.00781461	+	0.00781461i
$419$	4.40881			0.215384			0.107692	−	0.994184i	$-0.465654\pi$
$419$	4.40881			0.215384			0.107692	+	0.994184i	$0.465654\pi$
$420$	15.6593	−	1.14108i	0.764095	−	0.0556791i
$421$	−22.3290			−1.08825			−0.544124	−	0.839005i	$-0.683138\pi$
$421$	−22.3290			−1.08825			−0.544124	+	0.839005i	$0.683138\pi$
$422$	1.79599	−	1.79599i	0.0874275	−	0.0874275i
$423$	4.79132	+	7.00816i	0.232962	+	0.340748i
$424$		−	9.46015i		−	0.459425i
$425$	12.9361	−	26.4948i	0.627494	−	1.28518i
$426$	−9.82369	−	0.914816i	−0.475959	−	0.0443230i
$427$	−36.7273	−	36.7273i	−1.77736	−	1.77736i
$428$	−13.2804	−	13.2804i	−0.641931	−	0.641931i
$429$	−0.514289	−	0.0478924i	−0.0248301	−	0.00231227i
$430$	−1.21282	+	0.202694i	−0.0584873	+	0.00977479i
$431$			12.2320i			0.589194i	0.955622	+	0.294597i	$0.0951853\pi$
$431$			12.2320i			0.589194i	−0.955622	+	0.294597i	$0.904815\pi$
$432$	2.52226	+	4.54293i	0.121352	+	0.218572i
$433$	−5.46824	+	5.46824i	−0.262787	+	0.262787i	−0.826185	−	0.563399i	$-0.809494\pi$
$433$	−5.46824	+	5.46824i	−0.262787	+	0.262787i	0.563399	+	0.826185i	$0.309494\pi$
$434$	−4.05393			−0.194595
$435$	−8.89286	−	7.68485i	−0.426380	−	0.368460i
$436$	12.0047			0.574920
$437$	−4.85862	+	4.85862i	−0.232419	+	0.232419i
$438$	9.48782	+	11.4364i	0.453346	+	0.546450i
$439$		−	33.1668i		−	1.58296i	−0.611192	−	0.791482i	$-0.709310\pi$
$439$		−	33.1668i		−	1.58296i	0.611192	−	0.791482i	$-0.290690\pi$
$440$	−0.131546	−	0.0938725i	−0.00627121	−	0.00447519i
$441$	27.8164	+	5.22603i	1.32459	+	0.248859i
$442$	−17.2050	−	17.2050i	−0.818357	−	0.818357i
$443$	−12.0207	−	12.0207i	−0.571122	−	0.571122i	0.361320	−	0.932442i	$-0.382326\pi$
$443$	−12.0207	−	12.0207i	−0.571122	−	0.571122i	−0.932442	+	0.361320i	$0.882326\pi$
$444$	−1.34126	+	14.4030i	−0.0636534	+	0.683538i
$445$	5.01706	+	30.0195i	0.237831	+	1.42306i
$446$		−	5.26828i		−	0.249461i
$447$	14.9939	−	12.4392i	0.709185	−	0.588354i
$448$	2.86656	−	2.86656i	0.135432	−	0.135432i
$449$	2.93274			0.138404			0.0692022	−	0.997603i	$-0.477955\pi$
$449$	2.93274			0.138404			0.0692022	+	0.997603i	$0.477955\pi$
$450$	−12.0322	−	8.95693i	−0.567203	−	0.422234i
$451$	−0.137819			−0.00648963
$452$	−14.5548	+	14.5548i	−0.684602	+	0.684602i
$453$	−15.8529	+	13.1519i	−0.744835	+	0.617930i
$454$			21.2664i			0.998082i
$455$	6.16561	+	36.8918i	0.289048	+	1.72951i
$456$	−0.502093	+	5.39169i	−0.0235126	+	0.252489i
$457$	−3.36381	−	3.36381i	−0.157352	−	0.157352i	0.624040	−	0.781392i	$-0.285490\pi$
$457$	−3.36381	−	3.36381i	−0.157352	−	0.157352i	−0.781392	+	0.624040i	$0.785490\pi$
$458$	−0.910513	−	0.910513i	−0.0425455	−	0.0425455i
$459$	29.4596	+	8.42556i	1.37506	+	0.393271i
$460$	−4.00032	−	2.85467i	−0.186516	−	0.133100i
$461$		−	29.5785i		−	1.37761i	−0.724947	−	0.688804i	$-0.758136\pi$
$461$		−	29.5785i		−	1.37761i	0.724947	−	0.688804i	$-0.241864\pi$
$462$	−0.324016	−	0.390560i	−0.0150746	−	0.0181705i
$463$	3.99421	−	3.99421i	0.185627	−	0.185627i	−0.608176	−	0.793803i	$-0.708098\pi$
$463$	3.99421	−	3.99421i	0.185627	−	0.185627i	0.793803	+	0.608176i	$0.208098\pi$
$464$	−3.03469			−0.140882
$465$	2.93040	+	2.53234i	0.135894	+	0.117434i
$466$	26.1878			1.21313
$467$	−10.7098	+	10.7098i	−0.495590	+	0.495590i	−0.910062	−	0.414472i	$-0.863966\pi$
$467$	−10.7098	+	10.7098i	−0.495590	+	0.495590i	0.414472	+	0.910062i	$0.363966\pi$
$468$	−10.2187	+	6.98629i	−0.472359	+	0.322941i
$469$		−	42.6045i		−	1.96729i
$470$	−6.24111	+	1.04306i	−0.287881	+	0.0481127i
$471$	−2.38400	−	0.222006i	−0.109849	−	0.0102295i
$472$	−1.65338	−	1.65338i	−0.0761028	−	0.0761028i
$473$	0.0281028	+	0.0281028i	0.00129217	+	0.00129217i
$474$	13.1491	+	1.22449i	0.603956	+	0.0562425i
$475$	−5.08301	−	14.7823i	−0.233225	−	0.678258i
$476$		−	23.9053i		−	1.09570i
$477$	−23.4284	+	16.0175i	−1.07271	+	0.733389i
$478$	5.45990	−	5.45990i	0.249730	−	0.249730i
$479$	34.0257			1.55468			0.777338	−	0.629084i	$-0.216570\pi$
$479$	34.0257			1.55468			0.777338	+	0.629084i	$0.216570\pi$
$480$	−3.86274	+	0.281475i	−0.176309	+	0.0128475i
$481$	−34.4603			−1.57125
$482$	15.4212	−	15.4212i	0.702417	−	0.702417i
$483$	−9.85335	−	11.8770i	−0.448343	−	0.540420i
$484$		−	10.9948i		−	0.499763i
$485$	−4.88668	+	6.84783i	−0.221892	+	0.310944i
$486$	6.98016	−	13.9383i	0.316627	−	0.632256i
$487$	−18.7416	−	18.7416i	−0.849261	−	0.849261i	0.140780	−	0.990041i	$-0.455039\pi$
$487$	−18.7416	−	18.7416i	−0.849261	−	0.849261i	−0.990041	+	0.140780i	$0.955039\pi$
$488$	9.05967	+	9.05967i	0.410112	+	0.410112i
$489$	2.80560	−	30.1277i	0.126874	−	1.36242i
$490$	−12.2540	+	17.1719i	−0.553580	+	0.775747i
$491$		−	35.1520i		−	1.58639i	−0.608970	−	0.793193i	$-0.708417\pi$
$491$		−	35.1520i		−	1.58639i	0.608970	−	0.793193i	$-0.291583\pi$
$492$	−2.54201	+	2.10890i	−0.114603	+	0.0950765i
$493$	−12.6537	+	12.6537i	−0.569894	+	0.569894i
$494$	−12.9000			−0.580398
$495$	−0.00975138	+	0.484719i	−0.000438292	+	0.0217865i
$496$	1.00000			0.0449013
$497$	16.3286	−	16.3286i	0.732440	−	0.732440i
$498$	0.289000	−	0.239760i	0.0129504	−	0.0107439i
$499$			24.5578i			1.09936i	0.835376	+	0.549679i	$0.185250\pi$
$499$			24.5578i			1.09936i	−0.835376	+	0.549679i	$0.814750\pi$
$500$	9.82883	−	5.32861i	0.439559	−	0.238303i
$501$	−1.76444	+	18.9473i	−0.0788292	+	0.846502i
$502$	−18.2207	−	18.2207i	−0.813229	−	0.813229i
$503$	9.22718	+	9.22718i	0.411420	+	0.411420i	0.882233	−	0.470813i	$-0.156039\pi$
$503$	9.22718	+	9.22718i	0.411420	+	0.411420i	−0.470813	+	0.882233i	$0.656039\pi$
$504$	−11.9527	−	2.24562i	−0.532414	−	0.100028i
$505$	−30.8083	+	5.14890i	−1.37095	+	0.229123i
$506$			0.158840i			0.00706131i
$507$	−4.45188	−	5.36617i	−0.197715	−	0.238320i
$508$	−2.77146	+	2.77146i	−0.122964	+	0.122964i
$509$	−14.7415			−0.653406			−0.326703	−	0.945127i	$-0.605938\pi$
$509$	−14.7415			−0.653406			−0.326703	+	0.945127i	$0.605938\pi$
$510$	−14.9328	+	17.2801i	−0.661234	+	0.765176i
$511$	−34.7795			−1.53856
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	14.2028	−	7.88550i	0.627071	−	0.348153i
$514$			1.88552i			0.0831666i
$515$	−24.7826	−	17.6851i	−1.09205	−	0.779298i
$516$	0.948371	+	0.0883156i	0.0417497	+	0.00388788i
$517$	0.144616	+	0.144616i	0.00636019	+	0.00636019i
$518$	−23.9403	−	23.9403i	−1.05188	−	1.05188i
$519$	−32.0099	−	2.98087i	−1.40508	−	0.130846i
$520$	−1.52090	−	9.10025i	−0.0666957	−	0.399072i
$521$			16.5929i			0.726948i	0.931604	+	0.363474i	$0.118409\pi$
$521$			16.5929i			0.726948i	−0.931604	+	0.363474i	$0.881591\pi$
$522$	5.13819	+	7.51552i	0.224892	+	0.328945i
$523$	−0.437151	+	0.437151i	−0.0191153	+	0.0191153i	−0.716600	−	0.697485i	$-0.754303\pi$
$523$	−0.437151	+	0.437151i	−0.0191153	+	0.0191153i	0.697485	+	0.716600i	$0.254303\pi$
$524$	−15.2844			−0.667702
$525$	34.1156	−	8.28856i	1.48893	−	0.361743i
$526$	−23.2892			−1.01546
$527$	4.16969	−	4.16969i	0.181635	−	0.181635i
$528$	0.0799264	+	0.0963410i	0.00347835	+	0.00419271i
$529$		−	18.1697i		−	0.789985i
$530$	−3.48696	−	20.8642i	−0.151464	−	0.906281i
$531$	−1.29523	+	6.89406i	−0.0562082	+	0.299177i
$532$	−8.96191	−	8.96191i	−0.388548	−	0.388548i
$533$	−5.56381	−	5.56381i	−0.240995	−	0.240995i
$534$	2.18597	−	23.4739i	0.0945963	−	1.01582i
$535$	−34.1847	−	24.3945i	−1.47793	−	1.05467i
$536$			10.5094i			0.453938i
$537$	22.4921	−	18.6599i	0.970607	−	0.805235i
$538$	−21.4961	+	21.4961i	−0.926764	+	0.926764i
$539$	0.681841			0.0293690
$540$	7.23729	+	9.08964i	0.311443	+	0.391156i
$541$	16.9164			0.727292			0.363646	−	0.931537i	$-0.381532\pi$
$541$	16.9164			0.727292			0.363646	+	0.931537i	$0.381532\pi$
$542$	−8.80059	+	8.80059i	−0.378018	+	0.378018i
$543$	22.4136	−	18.5948i	0.961861	−	0.797979i
$544$			5.89683i			0.252825i
$545$	26.4761	−	4.42486i	1.13411	−	0.189540i
$546$	2.68640	−	28.8478i	0.114968	−	1.23457i
$547$	−2.12387	−	2.12387i	−0.0908099	−	0.0908099i	0.660243	−	0.751052i	$-0.270453\pi$
$547$	−2.12387	−	2.12387i	−0.0908099	−	0.0908099i	−0.751052	+	0.660243i	$0.770453\pi$
$548$	3.94097	+	3.94097i	0.168350	+	0.168350i
$549$	7.09721	−	37.7760i	0.302901	−	1.61224i
$550$	−0.324723	−	0.158547i	−0.0138462	−	0.00676045i
$551$			9.48753i			0.404182i
$552$	2.43057	+	2.92974i	0.103452	+	0.124698i
$553$	−21.8560	+	21.8560i	−0.929411	+	0.929411i
$554$	1.52242			0.0646812
$555$	2.35076	+	32.2600i	0.0997843	+	1.36936i
$556$	10.9204			0.463129
$557$	13.9923	−	13.9923i	0.592873	−	0.592873i	−0.345534	−	0.938406i	$-0.612302\pi$
$557$	13.9923	−	13.9923i	0.592873	−	0.592873i	0.938406	+	0.345534i	$0.112302\pi$
$558$	−1.69315	−	2.47654i	−0.0716768	−	0.104840i
$559$			2.26904i			0.0959704i
$560$	5.26554	−	7.37874i	0.222510	−	0.311809i
$561$	0.734980	+	0.0684439i	0.0310309	+	0.00288970i
$562$	−20.0136	−	20.0136i	−0.844222	−	0.844222i
$563$	13.4923	+	13.4923i	0.568632	+	0.568632i	0.931745	−	0.363113i	$-0.118286\pi$
$563$	13.4923	+	13.4923i	0.568632	+	0.568632i	−0.363113	+	0.931745i	$0.618286\pi$
$564$	4.88028	+	0.454469i	0.205497	+	0.0191366i
$565$	−26.7355	+	37.4652i	−1.12477	+	1.57617i
$566$		−	13.1157i		−	0.551295i
$567$	14.6763	+	33.4034i	0.616348	+	1.40281i
$568$	−4.02786	+	4.02786i	−0.169005	+	0.169005i
$569$	−7.22021			−0.302687			−0.151343	−	0.988481i	$-0.548360\pi$
$569$	−7.22021			−0.302687			−0.151343	+	0.988481i	$0.548360\pi$
$570$	0.879994	+	12.0763i	0.0368589	+	0.505822i
$571$	34.6113			1.44844			0.724220	−	0.689569i	$-0.242200\pi$
$571$	34.6113			1.44844			0.724220	+	0.689569i	$0.242200\pi$
$572$	−0.210866	+	0.210866i	−0.00881676	+	0.00881676i
$573$	19.6335	+	23.6657i	0.820203	+	0.988650i
$574$		−	7.73060i		−	0.322669i
$575$	−9.87484	−	4.82141i	−0.411809	−	0.201067i
$576$	2.94842	+	0.553937i	0.122851	+	0.0230807i
$577$	21.1679	+	21.1679i	0.881230	+	0.881230i	0.993660	−	0.112429i	$-0.0358632\pi$
$577$	21.1679	+	21.1679i	0.881230	+	0.881230i	−0.112429	+	0.993660i	$0.535863\pi$
$578$	12.5671	+	12.5671i	0.522724	+	0.522724i
$579$	−0.959973	+	10.3086i	−0.0398951	+	0.428411i
$580$	−6.69294	+	1.11857i	−0.277909	+	0.0464461i
$581$			0.878889i			0.0364625i
$582$	5.01518	−	4.16069i	0.207886	−	0.172466i
$583$	−0.483453	+	0.483453i	−0.0200226	+	0.0200226i
$584$	8.57922			0.355011
$585$	−19.9620	+	19.1747i	−0.825327	+	0.792775i
$586$	−11.8464			−0.489371
$587$	−2.92963	+	2.92963i	−0.120919	+	0.120919i	−0.764977	−	0.644058i	$-0.777250\pi$
$587$	−2.92963	+	2.92963i	−0.120919	+	0.120919i	0.644058	+	0.764977i	$0.277250\pi$
$588$	12.5763	−	10.4335i	0.518637	−	0.430271i
$589$		−	3.12636i		−	0.128819i
$590$	−4.25591	−	3.03706i	−0.175213	−	0.125034i
$591$	1.36704	−	14.6799i	0.0562326	−	0.603850i
$592$	5.90545	+	5.90545i	0.242713	+	0.242713i
$593$	0.395154	+	0.395154i	0.0162270	+	0.0162270i	0.715174	−	0.698947i	$-0.246348\pi$
$593$	0.395154	+	0.395154i	0.0162270	+	0.0162270i	−0.698947	+	0.715174i	$0.746348\pi$
$594$	0.103265	−	0.361061i	0.00423700	−	0.0148145i
$595$	−8.81139	−	52.7227i	−0.361232	−	2.16142i
$596$		−	11.2480i		−	0.460734i
$597$	−8.20251	−	9.88707i	−0.335706	−	0.404651i
$598$	−6.41246	+	6.41246i	−0.262225	+	0.262225i
$599$	−14.1461			−0.577993			−0.288997	−	0.957330i	$-0.593322\pi$
$599$	−14.1461			−0.577993			−0.288997	+	0.957330i	$0.593322\pi$
$600$	−8.41544	+	2.04457i	−0.343559	+	0.0834694i
$601$	23.2224			0.947262			0.473631	−	0.880723i	$-0.342943\pi$
$601$	23.2224			0.947262			0.473631	+	0.880723i	$0.342943\pi$
$602$	−1.57635	+	1.57635i	−0.0642474	+	0.0642474i
$603$	26.0270	−	17.7941i	1.05990	−	0.724630i
$604$			11.8924i			0.483895i
$605$	−4.05262	−	24.2487i	−0.164762	−	0.985852i
$606$	24.0908	+	2.24341i	0.978620	+	0.0911325i
$607$	34.6439	+	34.6439i	1.40615	+	1.40615i	0.778459	+	0.627695i	$0.216001\pi$
$607$	34.6439	+	34.6439i	1.40615	+	1.40615i	0.627695	+	0.778459i	$0.283999\pi$
$608$	2.21067	+	2.21067i	0.0896546	+	0.0896546i
$609$	−21.2166	−	1.97576i	−0.859740	−	0.0800620i
$610$	23.3203	+	16.6416i	0.944209	+	0.673797i
$611$			11.6764i			0.472377i
$612$	14.6037	−	9.98423i	0.590320	−	0.403589i
$613$	−9.06737	+	9.06737i	−0.366228	+	0.366228i	−0.866099	−	0.499872i	$-0.833380\pi$
$613$	−9.06737	+	9.06737i	−0.366228	+	0.366228i	0.499872	+	0.866099i	$0.333380\pi$
$614$	14.7357			0.594684
$615$	−4.82901	+	5.58810i	−0.194725	+	0.225334i
$616$	−0.292987			−0.0118048
$617$	0.624644	−	0.624644i	0.0251472	−	0.0251472i	−0.694421	−	0.719569i	$-0.744340\pi$
$617$	0.624644	−	0.624644i	0.0251472	−	0.0251472i	0.719569	+	0.694421i	$0.244340\pi$
$618$	15.0577	+	18.1501i	0.605710	+	0.730106i
$619$			26.1921i			1.05275i	0.850253	+	0.526374i	$0.176449\pi$
$619$			26.1921i			1.05275i	−0.850253	+	0.526374i	$0.823551\pi$
$620$	2.20548	−	0.368595i	0.0885742	−	0.0148031i
$621$	3.14028	−	10.9799i	0.126015	−	0.440608i
$622$	0.806250	+	0.806250i	0.0323277	+	0.0323277i
$623$	39.0177	+	39.0177i	1.56321	+	1.56321i
$624$	−0.662667	+	7.11600i	−0.0265279	+	0.284868i
$625$	19.7132	−	15.3750i	0.788527	−	0.615000i
$626$			13.6158i			0.544197i
$627$	0.301197	−	0.249879i	0.0120286	−	0.00997920i
$628$	−0.977475	+	0.977475i	−0.0390055	+	0.0390055i
$629$	49.2478			1.96364
$630$	−27.1891	−	0.546979i	−1.08324	−	0.0217922i
$631$	−44.9178			−1.78815			−0.894075	−	0.447917i	$-0.852166\pi$
$631$	−44.9178			−1.78815			−0.894075	+	0.447917i	$0.852166\pi$
$632$	5.39131	−	5.39131i	0.214455	−	0.214455i
$633$	−3.38578	+	2.80891i	−0.134573	+	0.111644i
$634$			29.2373i			1.16116i
$635$	−5.09086	+	7.13395i	−0.202024	+	0.283102i
$636$	−1.51930	+	16.3149i	−0.0602440	+	0.646927i
$637$	27.5263	+	27.5263i	1.09063	+	1.09063i
$638$	0.155085	+	0.155085i	0.00613988	+	0.00613988i
$639$	16.7949	+	3.15536i	0.664396	+	0.124824i
$640$	−1.29887	+	1.82015i	−0.0513425	+	0.0719476i
$641$		−	38.6006i		−	1.52463i	−0.647204	−	0.762317i	$-0.724062\pi$
$641$		−	38.6006i		−	1.52463i	0.647204	−	0.762317i	$-0.275938\pi$
$642$	20.7704	+	25.0360i	0.819741	+	0.988093i
$643$	1.94839	−	1.94839i	0.0768371	−	0.0768371i	−0.667644	−	0.744481i	$-0.732697\pi$
$643$	1.94839	−	1.94839i	0.0768371	−	0.0768371i	0.744481	+	0.667644i	$0.232697\pi$
$644$	−8.90974			−0.351093
$645$	2.12416	−	0.154786i	0.0836389	−	0.00609471i
$646$	18.4356			0.725340
$647$	11.6947	−	11.6947i	0.459767	−	0.459767i	−0.438812	−	0.898579i	$-0.644601\pi$
$647$	11.6947	−	11.6947i	0.459767	−	0.459767i	0.898579	+	0.438812i	$0.144601\pi$
$648$	−3.62027	−	8.23976i	−0.142218	−	0.323688i
$649$			0.168989i			0.00663339i
$650$	−6.70861	−	19.5098i	−0.263133	−	0.765238i
$651$	6.99136	+	0.651060i	0.274013	+	0.0255171i
$652$	−12.3528	−	12.3528i	−0.483774	−	0.483774i
$653$	12.5022	+	12.5022i	0.489247	+	0.489247i	0.908069	−	0.418821i	$-0.137557\pi$
$653$	12.5022	+	12.5022i	0.489247	+	0.489247i	−0.418821	+	0.908069i	$0.637557\pi$
$654$	−20.7031	−	1.92795i	−0.809556	−	0.0753887i
$655$	−33.7094	+	5.63375i	−1.31714	+	0.220129i
$656$			1.90694i			0.0744535i
$657$	−14.5259	−	21.2468i	−0.566710	−	0.828915i
$658$	−8.11186	+	8.11186i	−0.316233	+	0.316233i
$659$	−2.94693			−0.114796			−0.0573981	−	0.998351i	$-0.518280\pi$
$659$	−2.94693			−0.114796			−0.0573981	+	0.998351i	$0.518280\pi$
$660$	0.211787	+	0.183018i	0.00824379	+	0.00712395i
$661$	−8.85216			−0.344309			−0.172154	−	0.985070i	$-0.555073\pi$
$661$	−8.85216			−0.344309			−0.172154	+	0.985070i	$0.555073\pi$
$662$	−3.42859	+	3.42859i	−0.133256	+	0.133256i
$663$	26.9084	+	32.4346i	1.04504	+	1.25966i
$664$		−	0.216799i		−	0.00841345i
$665$	−23.0686	−	16.4620i	−0.894562	−	0.638368i
$666$	4.62625	−	24.6239i	0.179263	−	0.954157i
$667$	4.71615	+	4.71615i	0.182610	+	0.182610i
$668$	7.76866	+	7.76866i	0.300578	+	0.300578i
$669$	−0.846085	+	9.08563i	−0.0327115	+	0.351271i
$670$	3.87372	+	23.1783i	0.149655	+	0.895457i
$671$		−	0.925974i		−	0.0357468i
$672$	−5.40401	+	4.48327i	−0.208464	+	0.172946i
$673$	10.7486	−	10.7486i	0.414327	−	0.414327i	−0.468916	−	0.883243i	$-0.655355\pi$
$673$	10.7486	−	10.7486i	0.414327	−	0.414327i	0.883243	+	0.468916i	$0.155355\pi$
$674$	2.63397			0.101457
$675$	19.3121	+	17.3794i	0.743323	+	0.668933i
$676$	−4.02554			−0.154829
$677$	−17.0622	+	17.0622i	−0.655753	+	0.655753i	−0.954372	−	0.298619i	$-0.903474\pi$
$677$	−17.0622	+	17.0622i	−0.655753	+	0.655753i	0.298619	+	0.954372i	$0.403474\pi$
$678$	27.4386	−	22.7636i	1.05377	−	0.874231i
$679$			15.2519i			0.585313i
$680$	2.17354	+	13.0053i	0.0833515	+	0.498732i
$681$	3.41538	−	36.6758i	0.130878	−	1.40542i
$682$	−0.0511042	−	0.0511042i	−0.00195688	−	0.00195688i
$683$	−6.31969	−	6.31969i	−0.241816	−	0.241816i	0.575785	−	0.817601i	$-0.304697\pi$
$683$	−6.31969	−	6.31969i	−0.241816	−	0.241816i	−0.817601	+	0.575785i	$0.804697\pi$
$684$	1.73181	−	9.21781i	0.0662173	−	0.352452i
$685$	10.1443	+	7.23910i	0.387595	+	0.276592i
$686$			9.86867i			0.376788i
$687$	1.42403	+	1.71649i	0.0543302	+	0.0654881i
$688$	0.388846	−	0.388846i	0.0148246	−	0.0148246i
$689$	−39.0345			−1.48710
$690$	6.44045	+	5.56558i	0.245184	+	0.211878i
$691$	1.88357			0.0716545			0.0358272	−	0.999358i	$-0.488593\pi$
$691$	1.88357			0.0716545			0.0358272	+	0.999358i	$0.488593\pi$
$692$	−13.1245	+	13.1245i	−0.498920	+	0.498920i
$693$	0.496071	+	0.725592i	0.0188442	+	0.0275630i
$694$		−	23.4314i		−	0.889444i
$695$	24.0848	−	4.02521i	0.913587	−	0.152685i
$696$	5.23359	+	0.487370i	0.198379	+	0.0184737i
$697$	7.95134	+	7.95134i	0.301179	+	0.301179i
$698$	21.9135	+	21.9135i	0.829438	+	0.829438i
$699$	−45.1631	−	4.20575i	−1.70823	−	0.159076i
$700$	8.89327	−	18.2145i	0.336134	−	0.688444i
$701$			25.8155i			0.975039i	0.873112	+	0.487520i	$0.162098\pi$
$701$			25.8155i			0.975039i	−0.873112	+	0.487520i	$0.837902\pi$
$702$	18.7450	−	10.4074i	0.707486	−	0.392800i
$703$	18.4626	−	18.4626i	0.696329	−	0.696329i
$704$	0.0722722			0.00272386
$705$	10.9309	−	0.796526i	0.411681	−	0.0299989i
$706$	9.24436			0.347916
$707$	−40.0430	+	40.0430i	−1.50597	+	1.50597i
$708$	2.58586	+	3.11692i	0.0971826	+	0.117141i
$709$		−	1.46369i		−	0.0549702i	−0.999622	−	0.0274851i	$-0.991250\pi$
$709$		−	1.46369i		−	0.0549702i	0.999622	−	0.0274851i	$-0.00874988\pi$
$710$	−7.39870	+	10.3680i	−0.277668	+	0.389104i
$711$	−22.4801	−	4.22347i	−0.843069	−	0.158393i
$712$	−9.62465	−	9.62465i	−0.360699	−	0.360699i
$713$	−1.55408	−	1.55408i	−0.0582008	−	0.0582008i
$714$	−3.83919	+	41.2269i	−0.143678	+	1.54288i
$715$	−0.387337	+	0.542785i	−0.0144856	+	0.0202990i
$716$		−	16.8729i		−	0.630572i
$717$	−10.2929	+	8.53923i	−0.384397	+	0.318903i
$718$	−13.8369	+	13.8369i	−0.516388	+	0.516388i
$719$	−2.98907			−0.111474			−0.0557368	−	0.998445i	$-0.517751\pi$
$719$	−2.98907			−0.111474			−0.0557368	+	0.998445i	$0.517751\pi$
$720$	6.70685	+	0.134926i	0.249949	+	0.00502838i
$721$	−55.1971			−2.05565
$722$	−6.52367	+	6.52367i	−0.242786	+	0.242786i
$723$	−29.0719	+	24.1186i	−1.08119	+	0.896980i
$724$		−	16.8141i		−	0.624889i
$725$	−14.3488	+	4.93397i	−0.532902	+	0.183243i
$726$	−1.76576	+	18.9615i	−0.0655334	+	0.703726i
$727$	21.9220	+	21.9220i	0.813043	+	0.813043i	0.985089	−	0.172046i	$-0.0550379\pi$
$727$	21.9220	+	21.9220i	0.813043	+	0.813043i	−0.172046	+	0.985089i	$0.555038\pi$
$728$	−11.8280	−	11.8280i	−0.438375	−	0.438375i
$729$	−14.2764	+	22.9169i	−0.528756	+	0.848774i
$730$	18.9213	−	3.16226i	0.700308	−	0.117040i
$731$		−	3.24273i		−	0.119937i
$732$	−14.1692	−	17.0792i	−0.523710	−	0.631265i
$733$	−17.9804	+	17.9804i	−0.664122	+	0.664122i	−0.956349	−	0.292227i	$-0.905604\pi$
$733$	−17.9804	+	17.9804i	−0.664122	+	0.664122i	0.292227	+	0.956349i	$0.405604\pi$
$734$	−31.4675			−1.16149
$735$	23.8910	−	27.6464i	0.881231	−	1.01975i
$736$	2.19780			0.0810121
$737$	0.537076	−	0.537076i	0.0197834	−	0.0197834i
$738$	4.72261	−	3.22874i	0.173842	−	0.118851i
$739$		−	22.6850i		−	0.834481i	−0.908796	−	0.417241i	$-0.862997\pi$
$739$		−	22.6850i		−	0.834481i	0.908796	−	0.417241i	$-0.137003\pi$
$740$	15.2011	+	10.8476i	0.558803	+	0.398767i
$741$	22.2472	+	2.07174i	0.817271	+	0.0761071i
$742$	−27.1181	−	27.1181i	−0.995537	−	0.995537i
$743$	0.287185	+	0.287185i	0.0105358	+	0.0105358i	0.712355	−	0.701819i	$-0.247629\pi$
$743$	0.287185	+	0.287185i	0.0105358	+	0.0105358i	−0.701819	+	0.712355i	$0.747629\pi$
$744$	−1.72459	−	0.160600i	−0.0632265	−	0.00588787i
$745$	−4.14594	−	24.8071i	−0.151895	−	0.908863i
$746$			20.3253i			0.744164i
$747$	−0.536912	+	0.367074i	−0.0196446	+	0.0134305i
$748$	0.301353	−	0.301353i	0.0110185	−	0.0110185i
$749$	−76.1380			−2.78202
$750$	−17.8065	+	7.61116i	−0.650200	+	0.277920i
$751$	1.98580			0.0724630			0.0362315	−	0.999343i	$-0.488465\pi$
$751$	1.98580			0.0724630			0.0362315	+	0.999343i	$0.488465\pi$
$752$	2.00099	−	2.00099i	0.0729685	−	0.0729685i
$753$	28.4970	+	34.3494i	1.03849	+	1.25176i
$754$			12.5217i			0.456015i
$755$	4.38348	+	26.2284i	0.159531	+	0.954550i
$756$	20.2528	+	5.79237i	0.736587	+	0.210666i
$757$	33.4398	+	33.4398i	1.21539	+	1.21539i	0.969228	+	0.246163i	$0.0791699\pi$
$757$	33.4398	+	33.4398i	1.21539	+	1.21539i	0.246163	+	0.969228i	$0.420830\pi$
$758$	−19.5530	−	19.5530i	−0.710195	−	0.710195i
$759$	0.0255097	−	0.273934i	0.000925943	−	0.00994318i
$760$	5.69043	+	4.06075i	0.206414	+	0.147299i
$761$		−	39.8343i		−	1.44399i	−0.691897	−	0.721996i	$-0.743225\pi$
$761$		−	39.8343i		−	1.44399i	0.691897	−	0.721996i	$-0.256775\pi$
$762$	5.22473	−	4.33454i	0.189272	−	0.157024i
$763$	34.4121	−	34.4121i	1.24580	−	1.24580i
$764$	17.7533			0.642293
$765$	28.5281	−	27.4029i	1.03143	−	0.990753i
$766$	−11.8835			−0.429368
$767$	−6.82216	+	6.82216i	−0.246334	+	0.246334i
$768$	1.33303	−	1.10591i	0.0481016	−	0.0399060i
$769$			1.26340i			0.0455593i	0.999741	+	0.0227797i	$0.00725162\pi$
$769$			1.26340i			0.0455593i	−0.999741	+	0.0227797i	$0.992748\pi$
$770$	−0.646176	+	0.107993i	−0.0232866	+	0.00389181i
$771$	0.302814	−	3.25174i	0.0109056	−	0.117109i
$772$	4.22668	+	4.22668i	0.152122	+	0.152122i
$773$	14.8407	+	14.8407i	0.533782	+	0.533782i	0.921696	−	0.387914i	$-0.126804\pi$
$773$	14.8407	+	14.8407i	0.533782	+	0.533782i	−0.387914	+	0.921696i	$0.626804\pi$
$774$	−1.62137	−	0.304616i	−0.0582788	−	0.0109492i
$775$	4.72828	−	1.62586i	0.169845	−	0.0584025i
$776$		−	3.76224i		−	0.135057i
$777$	37.4424	+	45.1320i	1.34324	+	1.61910i
$778$	13.3454	−	13.3454i	0.478457	−	0.478457i
$779$	5.96178			0.213603
$780$	1.16142	+	15.9385i	0.0415857	+	0.570688i
$781$	0.411681			0.0147311
$782$	9.16416	−	9.16416i	0.327710	−	0.327710i
$783$	−7.65427	−	13.7864i	−0.273541	−	0.492685i
$784$		−	9.43435i		−	0.336941i
$785$	−1.79551	+	2.51609i	−0.0640844	+	0.0898032i
$786$	26.3593	+	2.45467i	0.940205	+	0.0875552i
$787$	36.6649	+	36.6649i	1.30696	+	1.30696i	0.923596	+	0.383367i	$0.125236\pi$
$787$	36.6649	+	36.6649i	1.30696	+	1.30696i	0.383367	+	0.923596i	$0.374764\pi$
$788$	−6.01897	−	6.01897i	−0.214417	−	0.214417i
$789$	40.1642	+	3.74023i	1.42988	+	0.133156i
$790$	9.90321	−	13.8776i	0.352340	−	0.493744i
$791$			83.4446i			2.96695i
$792$	−0.122368	−	0.178985i	−0.00434815	−	0.00635995i
$793$	37.3820	−	37.3820i	1.32747	−	1.32747i
$794$	16.6336			0.590303
$795$	2.66280	+	36.5421i	0.0944397	+	1.29601i
$796$	−7.41699			−0.262888
$797$	−8.54415	+	8.54415i	−0.302649	+	0.302649i	−0.842049	−	0.539400i	$-0.818651\pi$
$797$	−8.54415	+	8.54415i	−0.302649	+	0.302649i	0.539400	+	0.842049i	$0.318651\pi$
$798$	14.0163	+	16.8949i	0.496173	+	0.598072i
$799$		−	16.6870i		−	0.590343i
$800$	−2.19374	+	4.49305i	−0.0775605	+	0.158853i
$801$	−7.53981	+	40.1318i	−0.266406	+	1.41799i
$802$	8.99950	+	8.99950i	0.317783	+	0.317783i
$803$	−0.438434	−	0.438434i	−0.0154720	−	0.0154720i
$804$	1.68781	−	18.1244i	0.0595245	−	0.639200i
$805$	−19.6503	+	3.28409i	−0.692580	+	0.115749i
$806$		−	4.12620i		−	0.145339i
$807$	40.5243	−	33.6197i	1.42652	−	1.18347i
$808$	9.87756	−	9.87756i	0.347491	−	0.347491i
$809$	22.9717			0.807641			0.403820	−	0.914838i	$-0.367682\pi$
$809$	22.9717			0.807641			0.403820	+	0.914838i	$0.367682\pi$
$810$	−11.0216	−	16.8382i	−0.387258	−	0.591634i
$811$	−36.5655			−1.28399			−0.641994	−	0.766710i	$-0.721892\pi$
$811$	−36.5655			−1.28399			−0.641994	+	0.766710i	$0.721892\pi$
$812$	−8.69912	+	8.69912i	−0.305279	+	0.305279i
$813$	16.5908	−	13.7640i	0.581864	−	0.482726i
$814$		−	0.603587i		−	0.0211557i
$815$	−31.7971	−	22.6907i	−1.11380	−	0.794820i
$816$	0.947029	−	10.1696i	0.0331527	−	0.356008i
$817$	−1.21567	−	1.21567i	−0.0425310	−	0.0425310i
$818$	13.2299	+	13.2299i	0.462572	+	0.462572i
$819$	−9.26589	+	49.3191i	−0.323776	+	1.72335i
$820$	0.702888	+	4.20571i	0.0245459	+	0.146870i
$821$		−	37.4440i		−	1.30680i	−0.757011	−	0.653402i	$-0.773341\pi$
$821$		−	37.4440i		−	1.30680i	0.757011	−	0.653402i	$-0.226659\pi$
$822$	−6.16363	−	7.42946i	−0.214981	−	0.259132i
$823$	−3.41342	+	3.41342i	−0.118984	+	0.118984i	−0.764092	−	0.645108i	$-0.776813\pi$
$823$	−3.41342	+	3.41342i	−0.118984	+	0.118984i	0.645108	+	0.764092i	$0.276813\pi$
$824$	13.6157			0.474326
$825$	0.534551	+	0.325578i	0.0186107	+	0.0113352i
$826$	−9.47900			−0.329817
$827$	−25.9363	+	25.9363i	−0.901894	+	0.901894i	−0.995600	−	0.0937057i	$-0.970129\pi$
$827$	−25.9363	+	25.9363i	−0.901894	+	0.901894i	0.0937057	+	0.995600i	$0.470129\pi$
$828$	−3.72122	−	5.44294i	−0.129321	−	0.189155i
$829$			21.0807i			0.732164i	0.930583	+	0.366082i	$0.119301\pi$
$829$			21.0807i			0.732164i	−0.930583	+	0.366082i	$0.880699\pi$
$830$	−0.0799111	−	0.478146i	−0.00277376	−	0.0165967i
$831$	−2.62554	−	0.244499i	−0.0910790	−	0.00848159i
$832$	2.91767	+	2.91767i	0.101152	+	0.101152i
$833$	−39.3383	−	39.3383i	−1.36299	−	1.36299i
$834$	−18.8332	−	1.75382i	−0.652142	−	0.0607297i
$835$	19.9971	+	14.2701i	0.692028	+	0.493838i
$836$		−	0.225949i		−	0.00781461i
$837$	2.52226	+	4.54293i	0.0871821	+	0.157027i
$838$	−3.11750	+	3.11750i	−0.107692	+	0.107692i
$839$	−18.2647			−0.630569			−0.315285	−	0.948997i	$-0.602100\pi$
$839$	−18.2647			−0.630569			−0.315285	+	0.948997i	$0.602100\pi$
$840$	−10.2659	+	11.8797i	−0.354208	+	0.409887i
$841$	−19.7907			−0.682437
$842$	15.7890	−	15.7890i	0.544124	−	0.544124i
$843$	31.3010	+	37.7294i	1.07807	+	1.29947i
$844$			2.53992i			0.0874275i
$845$	−8.87825	+	1.48379i	−0.305421	+	0.0510441i
$846$	−8.34349	−	1.56754i	−0.286855	−	0.0538933i
$847$	−31.5172	−	31.5172i	−1.08294	−	1.08294i
$848$	6.68933	+	6.68933i	0.229713	+	0.229713i
$849$	−2.10638	+	22.6192i	−0.0722908	+	0.776290i
$850$	9.58740	+	27.8818i	0.328845	+	0.956339i
$851$		−	18.3551i		−	0.629205i
$852$	7.59327	−	6.29952i	0.260141	−	0.215818i
$853$	−22.0588	+	22.0588i	−0.755279	+	0.755279i	−0.975459	−	0.220180i	$-0.929335\pi$
$853$	−22.0588	+	22.0588i	−0.755279	+	0.755279i	0.220180	+	0.975459i	$0.429335\pi$
$854$	51.9402			1.77736
$855$	0.421826	−	20.9680i	0.0144262	−	0.717091i
$856$	18.7813			0.641931
$857$	29.4683	−	29.4683i	1.00662	−	1.00662i	0.00663960	−	0.999978i	$-0.497887\pi$
$857$	29.4683	−	29.4683i	1.00662	−	1.00662i	0.999978	−	0.00663960i	$-0.00211346\pi$
$858$	0.397523	−	0.329793i	0.0135712	−	0.0112589i
$859$			53.9577i			1.84101i	0.390729	+	0.920506i	$0.372223\pi$
$859$			53.9577i			1.84101i	−0.390729	+	0.920506i	$0.627777\pi$
$860$	0.714265	−	1.00092i	0.0243562	−	0.0341310i
$861$	−1.24153	+	13.3321i	−0.0423113	+	0.454357i
$862$	−8.64931	−	8.64931i	−0.294597	−	0.294597i
$863$	−13.6856	−	13.6856i	−0.465864	−	0.465864i	0.434708	−	0.900572i	$-0.356852\pi$
$863$	−13.6856	−	13.6856i	−0.465864	−	0.465864i	−0.900572	+	0.434708i	$0.856852\pi$
$864$	−4.99584	−	1.42883i	−0.169962	−	0.0486097i
$865$	−24.1083	+	33.7835i	−0.819705	+	1.14867i
$866$		−	7.73325i		−	0.262787i
$867$	−19.6549	−	23.6914i	−0.667514	−	0.804603i
$868$	2.86656	−	2.86656i	0.0972974	−	0.0972974i
$869$	−0.551037			−0.0186926
$870$	11.7222	−	0.854190i	0.397420	−	0.0289597i
$871$	43.3640			1.46933
$872$	−8.48859	+	8.48859i	−0.287460	+	0.287460i
$873$	−9.31733	+	6.37005i	−0.315344	+	0.215593i
$874$		−	6.87113i		−	0.232419i
$875$	12.9002	−	43.4497i	0.436105	−	1.46887i
$876$	−14.7956	−	1.37782i	−0.499898	−	0.0465522i
$877$	−36.5887	−	36.5887i	−1.23551	−	1.23551i	−0.961816	−	0.273696i	$-0.911754\pi$
$877$	−36.5887	−	36.5887i	−1.23551	−	1.23551i	−0.273696	−	0.961816i	$-0.588246\pi$
$878$	23.4525	+	23.4525i	0.791482	+	0.791482i
$879$	20.4302	+	1.90253i	0.689094	+	0.0641708i
$880$	0.159395	−	0.0266392i	0.00537320	−	0.000898006i
$881$			1.05931i			0.0356889i	0.999841	+	0.0178445i	$0.00568037\pi$
$881$			1.05931i			0.0356889i	−0.999841	+	0.0178445i	$0.994320\pi$
$882$	−23.3645	+	15.9738i	−0.786724	+	0.537865i
$883$	−10.1350	+	10.1350i	−0.341069	+	0.341069i	−0.856769	−	0.515700i	$-0.827532\pi$
$883$	−10.1350	+	10.1350i	−0.341069	+	0.341069i	0.515700	+	0.856769i	$0.327532\pi$
$884$	24.3315			0.818357
$885$	6.85195	+	5.92118i	0.230326	+	0.199038i
$886$	16.9999			0.571122
$887$	10.5215	−	10.5215i	0.353278	−	0.353278i	−0.508050	−	0.861328i	$-0.669633\pi$
$887$	10.5215	−	10.5215i	0.353278	−	0.353278i	0.861328	+	0.508050i	$0.169633\pi$
$888$	−9.23607	−	11.1329i	−0.309942	−	0.373596i
$889$			15.8891i			0.532905i
$890$	−24.7746	−	17.6794i	−0.830445	−	0.592614i
$891$	−0.236075	+	0.606097i	−0.00790882	+	0.0203050i
$892$	3.72524	+	3.72524i	0.124730	+	0.124730i
$893$	−6.25581	−	6.25581i	−0.209343	−	0.209343i
$894$	−1.80642	+	19.3981i	−0.0604157	+	0.648770i
$895$	−6.21928	−	37.2129i	−0.207888	−	1.24389i
$896$			4.05393i			0.135432i
$897$	12.0887	−	10.0290i	0.403630	−	0.334859i
$898$	−2.07376	+	2.07376i	−0.0692022	+	0.0692022i
$899$	−3.03469			−0.101212
$900$	14.8415	−	2.17453i	0.494718	−	0.0724845i
$901$	55.7849			1.85846
$902$	0.0974526	−	0.0974526i	0.00324482	−	0.00324482i
$903$	2.97173	−	2.46540i	0.0988928	−	0.0820434i
$904$		−	20.5836i		−	0.684602i
$905$	−6.19757	−	37.0830i	−0.206014	−	1.23268i
$906$	1.90992	−	20.5095i	0.0634527	−	0.681382i
$907$	−20.3221	−	20.3221i	−0.674786	−	0.674786i	0.284030	−	0.958815i	$-0.408329\pi$
$907$	−20.3221	−	20.3221i	−0.674786	−	0.674786i	−0.958815	+	0.284030i	$0.908329\pi$
$908$	−15.0376	−	15.0376i	−0.499041	−	0.499041i
$909$	−41.1864	−	7.73794i	−1.36607	−	0.256651i
$910$	−30.4462	−	21.7267i	−1.00928	−	0.720233i
$911$		−	38.8464i		−	1.28704i	−0.765429	−	0.643520i	$-0.777473\pi$
$911$		−	38.8464i		−	1.28704i	0.765429	−	0.643520i	$-0.222527\pi$
$912$	−3.45747	−	4.16753i	−0.114488	−	0.138001i
$913$	−0.0110794	+	0.0110794i	−0.000366673	+	0.000366673i
$914$	4.75714			0.157352
$915$	−37.5452	−	32.4451i	−1.24121	−	1.07260i
$916$	1.28766			0.0425455
$917$	−43.8137	+	43.8137i	−1.44685	+	1.44685i
$918$	−26.7889	+	14.8733i	−0.884165	+	0.490893i
$919$			0.402327i			0.0132715i	0.999978	+	0.00663577i	$0.00211225\pi$
$919$			0.402327i			0.0132715i	−0.999978	+	0.00663577i	$0.997888\pi$
$920$	4.84721	−	0.810099i	0.159808	−	0.0267082i
$921$	−25.4130	−	2.36655i	−0.837387	−	0.0779804i
$922$	20.9152	+	20.9152i	0.688804	+	0.688804i
$923$	16.6197	+	16.6197i	0.547046	+	0.547046i
$924$	0.505281	+	0.0470536i	0.0166225	+	0.00154795i
$925$	37.5240	+	18.3212i	1.23378	+	0.602397i
$926$			5.64867i			0.185627i
$927$	−23.0535	−	33.7198i	−0.757175	−	1.10750i
$928$	2.14585	−	2.14585i	0.0704409	−	0.0704409i
$929$	29.8543			0.979489			0.489745	−	0.871866i	$-0.337090\pi$
$929$	29.8543			0.979489			0.489745	+	0.871866i	$0.337090\pi$
$930$	−3.86274	+	0.281475i	−0.126664	+	0.00922994i
$931$	−29.4952			−0.966665
$932$	−18.5176	+	18.5176i	−0.606563	+	0.606563i
$933$	−1.26097	−	1.51993i	−0.0412822	−	0.0497604i
$934$		−	15.1459i		−	0.495590i
$935$	0.553550	−	0.775704i	0.0181030	−	0.0253682i
$936$	2.28566	−	12.1658i	0.0747090	−	0.397650i
$937$	22.7912	+	22.7912i	0.744558	+	0.744558i	0.973451	−	0.228894i	$-0.0735109\pi$
$937$	22.7912	+	22.7912i	0.744558	+	0.744558i	−0.228894	+	0.973451i	$0.573511\pi$
$938$	30.1259	+	30.1259i	0.983646	+	0.983646i
$939$	2.18669	−	23.4817i	0.0713600	−	0.766295i
$940$	3.67558	−	5.15069i	0.119884	−	0.167997i
$941$		−	27.9112i		−	0.909880i	−0.890522	−	0.454940i	$-0.849661\pi$
$941$		−	27.9112i		−	0.909880i	0.890522	−	0.454940i	$-0.150339\pi$
$942$	1.84272	−	1.52876i	0.0600392	−	0.0498097i
$943$	2.96354	−	2.96354i	0.0965062	−	0.0965062i
$944$	2.33823			0.0761028
$945$	46.8022	+	5.30987i	1.52247	+	0.172730i
$946$	−0.0397433			−0.00129217
$947$	−42.8165	+	42.8165i	−1.39135	+	1.39135i	−0.569043	+	0.822308i	$0.692686\pi$
$947$	−42.8165	+	42.8165i	−1.39135	+	1.39135i	−0.822308	+	0.569043i	$0.807314\pi$
$948$	−10.1636	+	8.43195i	−0.330099	+	0.273857i
$949$		−	35.3996i		−	1.14912i
$950$	14.0469	+	6.85843i	0.455741	+	0.222517i
$951$	4.69550	−	50.4223i	0.152262	−	1.63505i
$952$	16.9036	+	16.9036i	0.547850	+	0.547850i
$953$	37.2483	+	37.2483i	1.20659	+	1.20659i	0.972124	+	0.234467i	$0.0753343\pi$
$953$	37.2483	+	37.2483i	1.20659	+	1.20659i	0.234467	+	0.972124i	$0.424666\pi$
$954$	5.24033	−	27.8924i	0.169662	−	0.903051i
$955$	39.1546	−	6.54379i	1.26701	−	0.211752i
$956$			7.72147i			0.249730i
$957$	−0.242552	−	0.292365i	−0.00784058	−	0.00945082i
$958$	−24.0598	+	24.0598i	−0.777338	+	0.777338i
$959$	22.5940			0.729600
$960$	2.53234	−	2.93040i	0.0817308	−	0.0945784i
$961$	1.00000			0.0322581
$962$	24.3671	−	24.3671i	0.785627	−	0.785627i
$963$	−31.7996	−	46.5126i	−1.02473	−	1.49885i
$964$			21.8089i			0.702417i
$965$	10.8798	+	7.76392i	0.350233	+	0.249930i
$966$	15.3656	+	1.43090i	0.494382	+	0.0460385i
$967$	27.2787	+	27.2787i	0.877225	+	0.877225i	0.993247	−	0.116022i	$-0.0370142\pi$
$967$	27.2787	+	27.2787i	0.877225	+	0.877225i	−0.116022	+	0.993247i	$0.537014\pi$
$968$	7.77448	+	7.77448i	0.249881	+	0.249881i
$969$	−31.7939	−	2.96076i	−1.02137	−	0.0951132i
$970$	−1.38674	−	8.29755i	−0.0445256	−	0.266418i
$971$		−	39.9374i		−	1.28165i	−0.767686	−	0.640826i	$-0.778592\pi$
$971$		−	39.9374i		−	1.28165i	0.767686	−	0.640826i	$-0.221408\pi$
$972$	4.92018	+	14.7916i	0.157815	+	0.474441i
$973$	31.3040	−	31.3040i	1.00356	−	1.00356i
$974$	26.5046			0.849261
$975$	8.43633	+	34.7238i	0.270179	+	1.11205i
$976$	−12.8123			−0.410112
$977$	−36.0641	+	36.0641i	−1.15379	+	1.15379i	−0.168007	+	0.985786i	$0.553733\pi$
$977$	−36.0641	+	36.0641i	−1.15379	+	1.15379i	−0.985786	+	0.168007i	$0.946267\pi$
$978$	19.3197	+	23.2874i	0.617775	+	0.744649i
$979$			0.983720i			0.0314398i
$980$	−3.47745	−	20.8073i	−0.111083	−	0.664663i
$981$	35.3948	+	6.64983i	1.13007	+	0.212313i
$982$	24.8562	+	24.8562i	0.793193	+	0.793193i
$983$	−18.5071	−	18.5071i	−0.590286	−	0.590286i	0.347423	−	0.937709i	$-0.387057\pi$
$983$	−18.5071	−	18.5071i	−0.590286	−	0.590286i	−0.937709	+	0.347423i	$0.887057\pi$
$984$	0.306254	−	3.28869i	0.00976302	−	0.104840i
$985$	−15.4933	−	11.0562i	−0.493657	−	0.352278i
$986$		−	17.8950i		−	0.569894i
$987$	15.2924	−	12.6869i	0.486762	−	0.403827i
$988$	9.12168	−	9.12168i	0.290199	−	0.290199i
$989$	−1.20860			−0.0384311
$990$	−0.335853	−	0.349643i	−0.0106741	−	0.0111124i
$991$	−16.0869			−0.511019			−0.255509	−	0.966807i	$-0.582243\pi$
$991$	−16.0869			−0.511019			−0.255509	+	0.966807i	$0.582243\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	6.46353	−	5.36227i	0.205114	−	0.170167i
$994$			23.0922i			0.732440i
$995$	−16.3580	+	2.73386i	−0.518584	+	0.0866693i
$996$	−0.0348179	+	0.373890i	−0.00110325	+	0.0118472i
$997$	−9.40355	−	9.40355i	−0.297814	−	0.297814i	0.542343	−	0.840157i	$-0.317537\pi$
$997$	−9.40355	−	9.40355i	−0.297814	−	0.297814i	−0.840157	+	0.542343i	$0.817537\pi$
$998$	−17.3650	−	17.3650i	−0.549679	−	0.549679i
$999$	−11.9330	+	41.7231i	−0.377542	+	1.32006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.497.9	✓	40
3.2	odd	2	inner	930.2.j.h.497.17	yes	40
5.3	odd	4	inner	930.2.j.h.683.17	yes	40
15.8	even	4	inner	930.2.j.h.683.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.9	✓	40	1.1	even	1	trivial
930.2.j.h.497.17	yes	40	3.2	odd	2	inner
930.2.j.h.683.9	yes	40	15.8	even	4	inner
930.2.j.h.683.17	yes	40	5.3	odd	4	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.33303 - 1.10591i) q^{3} -1.00000i q^{4} +(-0.368595 - 2.20548i) q^{5} +(-0.160600 + 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.553937 - 2.94842i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.33303 - 1.10591i) q^{3} -1.00000i q^{4} +(-0.368595 - 2.20548i) q^{5} +(-0.160600 + 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.553937 - 2.94842i) q^{9} +(1.82015 + 1.29887i) q^{10} -0.0722722i q^{11} +(-1.10591 - 1.33303i) q^{12} +(2.91767 - 2.91767i) q^{13} +4.05393 q^{14} +(-2.93040 - 2.53234i) q^{15} -1.00000 q^{16} +(-4.16969 + 4.16969i) q^{17} +(1.69315 + 2.47654i) q^{18} +3.12636i q^{19} +(-2.20548 + 0.368595i) q^{20} +(-6.99136 - 0.651060i) q^{21} +(0.0511042 + 0.0511042i) q^{22} +(1.55408 + 1.55408i) q^{23} +(1.72459 + 0.160600i) q^{24} +(-4.72828 + 1.62586i) q^{25} +4.12620i q^{26} +(-2.52226 - 4.54293i) q^{27} +(-2.86656 + 2.86656i) q^{28} +3.03469 q^{29} +(3.86274 - 0.281475i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.0799264 - 0.0963410i) q^{33} -5.89683i q^{34} +(-5.26554 + 7.37874i) q^{35} +(-2.94842 - 0.553937i) q^{36} +(-5.90545 - 5.90545i) q^{37} +(-2.21067 - 2.21067i) q^{38} +(0.662667 - 7.11600i) q^{39} +(1.29887 - 1.82015i) q^{40} -1.90694i q^{41} +(5.40401 - 4.48327i) q^{42} +(-0.388846 + 0.388846i) q^{43} -0.0722722 q^{44} +(-6.70685 - 0.134926i) q^{45} -2.19780 q^{46} +(-2.00099 + 2.00099i) q^{47} +(-1.33303 + 1.10591i) q^{48} +9.43435i q^{49} +(2.19374 - 4.49305i) q^{50} +(-0.947029 + 10.1696i) q^{51} +(-2.91767 - 2.91767i) q^{52} +(-6.68933 - 6.68933i) q^{53} +(4.99584 + 1.42883i) q^{54} +(-0.159395 + 0.0266392i) q^{55} -4.05393i q^{56} +(3.45747 + 4.16753i) q^{57} +(-2.14585 + 2.14585i) q^{58} -2.33823 q^{59} +(-2.53234 + 2.93040i) q^{60} +12.8123 q^{61} +(0.707107 - 0.707107i) q^{62} +(-10.0397 + 6.86392i) q^{63} +1.00000i q^{64} +(-7.51029 - 5.35941i) q^{65} +(0.124640 + 0.0116069i) q^{66} +(7.43129 + 7.43129i) q^{67} +(4.16969 + 4.16969i) q^{68} +(3.79031 + 0.352967i) q^{69} +(-1.49426 - 8.94086i) q^{70} +5.69625i q^{71} +(2.47654 - 1.69315i) q^{72} +(6.06642 - 6.06642i) q^{73} +8.35157 q^{74} +(-4.50489 + 7.39635i) q^{75} +3.12636 q^{76} +(-0.207173 + 0.207173i) q^{77} +(4.56320 + 5.50035i) q^{78} -7.62446i q^{79} +(0.368595 + 2.20548i) q^{80} +(-8.38631 - 3.26647i) q^{81} +(1.34841 + 1.34841i) q^{82} +(-0.153300 - 0.153300i) q^{83} +(-0.651060 + 6.99136i) q^{84} +(10.7331 + 7.65924i) q^{85} -0.549911i q^{86} +(4.04533 - 3.35608i) q^{87} +(0.0511042 - 0.0511042i) q^{88} -13.6113 q^{89} +(4.83786 - 4.64705i) q^{90} -16.7273 q^{91} +(1.55408 - 1.55408i) q^{92} +(-1.33303 + 1.10591i) q^{93} -2.82982i q^{94} +(6.89512 - 1.15236i) q^{95} +(0.160600 - 1.72459i) q^{96} +(-2.66031 - 2.66031i) q^{97} +(-6.67109 - 6.67109i) q^{98} +(-0.213089 - 0.0400343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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