LMFDB - Embedded newform 930.2.bf.a.707.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (of order $12$, degree $4$, 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:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			707.13
Character	$\chi$	$=$	930.707
Dual form			930.2.bf.a.563.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.278129 - 1.70957i) q^{3} -1.00000i q^{4} +(-0.192796 - 2.22774i) q^{5} +(1.40552 + 1.01218i) q^{6} +(-0.616104 + 2.29933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.84529 + 0.950965i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.278129 - 1.70957i) q^{3} -1.00000i q^{4} +(-0.192796 - 2.22774i) q^{5} +(1.40552 + 1.01218i) q^{6} +(-0.616104 + 2.29933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.84529 + 0.950965i) q^{9} +(1.71158 + 1.43892i) q^{10} +(3.89412 + 2.24827i) q^{11} +(-1.70957 + 0.278129i) q^{12} +(1.15304 + 4.30320i) q^{13} +(-1.19022 - 2.06152i) q^{14} +(-3.75487 + 0.949198i) q^{15} -1.00000 q^{16} +(-0.565058 - 0.151407i) q^{17} +(1.33949 - 2.68436i) q^{18} +(-1.61169 + 0.930509i) q^{19} +(-2.22774 + 0.192796i) q^{20} +(4.10223 + 0.413764i) q^{21} +(-4.34333 + 1.16379i) q^{22} +(6.26316 + 6.26316i) q^{23} +(1.01218 - 1.40552i) q^{24} +(-4.92566 + 0.858997i) q^{25} +(-3.85815 - 2.22750i) q^{26} +(2.41710 + 4.59974i) q^{27} +(2.29933 + 0.616104i) q^{28} -4.44994 q^{29} +(1.98391 - 3.32628i) q^{30} +(-0.902546 - 5.49413i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.76052 - 7.28260i) q^{33} +(0.506617 - 0.292495i) q^{34} +(5.24109 + 0.929219i) q^{35} +(0.950965 + 2.84529i) q^{36} +(-1.40548 + 5.24532i) q^{37} +(0.481667 - 1.79760i) q^{38} +(7.03595 - 3.16805i) q^{39} +(1.43892 - 1.71158i) q^{40} +(6.84503 + 3.95198i) q^{41} +(-3.19329 + 2.60814i) q^{42} +(-1.88812 - 0.505920i) q^{43} +(2.24827 - 3.89412i) q^{44} +(2.66706 + 6.15522i) q^{45} -8.85745 q^{46} +(5.31159 - 5.31159i) q^{47} +(0.278129 + 1.70957i) q^{48} +(1.15484 + 0.666749i) q^{49} +(2.87556 - 4.09037i) q^{50} +(-0.101682 + 1.00812i) q^{51} +(4.30320 - 1.15304i) q^{52} +(12.2216 - 3.27477i) q^{53} +(-4.96166 - 1.54336i) q^{54} +(4.25780 - 9.10855i) q^{55} +(-2.06152 + 1.19022i) q^{56} +(2.03903 + 2.49650i) q^{57} +(3.14658 - 3.14658i) q^{58} +(-2.50677 - 4.34185i) q^{59} +(0.949198 + 3.75487i) q^{60} -7.10958 q^{61} +(4.52313 + 3.24674i) q^{62} +(-0.433591 - 7.12815i) q^{63} +1.00000i q^{64} +(9.36412 - 3.39831i) q^{65} +(3.19759 + 7.10156i) q^{66} +(8.03955 - 2.15419i) q^{67} +(-0.151407 + 0.565058i) q^{68} +(8.96538 - 12.4493i) q^{69} +(-4.36307 + 3.04896i) q^{70} +(2.05257 + 1.18505i) q^{71} +(-2.68436 - 1.33949i) q^{72} +(2.29583 + 8.56816i) q^{73} +(-2.71518 - 4.70283i) q^{74} +(2.83849 + 8.18187i) q^{75} +(0.930509 + 1.61169i) q^{76} +(-7.56870 + 7.56870i) q^{77} +(-2.73502 + 7.21532i) q^{78} +(-3.98508 + 2.30079i) q^{79} +(0.192796 + 2.22774i) q^{80} +(7.19133 - 5.41154i) q^{81} +(-7.63464 + 2.04570i) q^{82} +(-14.1710 + 3.79711i) q^{83} +(0.413764 - 4.10223i) q^{84} +(-0.228354 + 1.28799i) q^{85} +(1.69284 - 0.977362i) q^{86} +(1.23766 + 7.60750i) q^{87} +(1.16379 + 4.34333i) q^{88} +5.51996 q^{89} +(-6.23830 - 2.46650i) q^{90} -10.6049 q^{91} +(6.26316 - 6.26316i) q^{92} +(-9.14159 + 3.07105i) q^{93} +7.51173i q^{94} +(2.38366 + 3.41103i) q^{95} +(-1.40552 - 1.01218i) q^{96} +(12.1061 + 12.1061i) q^{97} +(-1.28806 + 0.345135i) q^{98} +(-13.2179 - 2.69381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.278129	−	1.70957i	−0.160578	−	0.987023i
$3$	−0.278129	−	1.70957i	−0.160578	−	0.987023i
$4$		−	1.00000i		−	0.500000i
$5$	−0.192796	−	2.22774i	−0.0862208	−	0.996276i
$5$	−0.192796	−	2.22774i	−0.0862208	−	0.996276i
$6$	1.40552	+	1.01218i	0.573801	+	0.413223i
$7$	−0.616104	+	2.29933i	−0.232865	+	0.869065i	0.746234	+	0.665683i	$0.231860\pi$
$7$	−0.616104	+	2.29933i	−0.232865	+	0.869065i	−0.979100	+	0.203382i	$0.934807\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.84529	+	0.950965i	−0.948429	+	0.316988i
$10$	1.71158	+	1.43892i	0.541248	+	0.455028i
$11$	3.89412	+	2.24827i	1.17412	+	0.677880i	0.954647	−	0.297739i	$-0.0962324\pi$
$11$	3.89412	+	2.24827i	1.17412	+	0.677880i	0.219474	+	0.975618i	$0.429566\pi$
$12$	−1.70957	+	0.278129i	−0.493512	+	0.0802890i
$13$	1.15304	+	4.30320i	0.319796	+	1.19349i	0.919441	+	0.393228i	$0.128642\pi$
$13$	1.15304	+	4.30320i	0.319796	+	1.19349i	−0.599645	+	0.800266i	$0.704692\pi$
$14$	−1.19022	−	2.06152i	−0.318100	−	0.550965i
$15$	−3.75487	+	0.949198i	−0.969502	+	0.245082i
$16$	−1.00000			−0.250000
$17$	−0.565058	−	0.151407i	−0.137047	−	0.0367215i	0.189644	−	0.981853i	$-0.439267\pi$
$17$	−0.565058	−	0.151407i	−0.137047	−	0.0367215i	−0.326690	+	0.945131i	$0.605933\pi$
$18$	1.33949	−	2.68436i	0.315720	−	0.632709i
$19$	−1.61169	+	0.930509i	−0.369747	+	0.213473i	−0.673348	−	0.739326i	$-0.735144\pi$
$19$	−1.61169	+	0.930509i	−0.369747	+	0.213473i	0.303601	+	0.952799i	$0.401811\pi$
$20$	−2.22774	+	0.192796i	−0.498138	+	0.0431104i
$21$	4.10223	+	0.413764i	0.895180	+	0.0902907i
$22$	−4.34333	+	1.16379i	−0.926001	+	0.248121i
$23$	6.26316	+	6.26316i	1.30596	+	1.30596i	0.924305	+	0.381656i	$0.124646\pi$
$23$	6.26316	+	6.26316i	1.30596	+	1.30596i	0.381656	+	0.924305i	$0.375354\pi$
$24$	1.01218	−	1.40552i	0.206611	−	0.286900i
$25$	−4.92566	+	0.858997i	−0.985132	+	0.171799i
$26$	−3.85815	−	2.22750i	−0.756645	−	0.436849i
$27$	2.41710	+	4.59974i	0.465172	+	0.885220i
$28$	2.29933	+	0.616104i	0.434532	+	0.116433i
$29$	−4.44994			−0.826333			−0.413166	−	0.910656i	$-0.635577\pi$
$29$	−4.44994			−0.826333			−0.413166	+	0.910656i	$0.635577\pi$
$30$	1.98391	−	3.32628i	0.362210	−	0.607292i
$31$	−0.902546	−	5.49413i	−0.162102	−	0.986774i
$31$	−0.902546	−	5.49413i	−0.162102	−	0.986774i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.76052	−	7.28260i	0.480545	−	1.26774i
$34$	0.506617	−	0.292495i	0.0868841	−	0.0501625i
$35$	5.24109	+	0.929219i	0.885906	+	0.157067i
$36$	0.950965	+	2.84529i	0.158494	+	0.474215i
$37$	−1.40548	+	5.24532i	−0.231060	+	0.862326i	0.748826	+	0.662766i	$0.230618\pi$
$37$	−1.40548	+	5.24532i	−0.231060	+	0.862326i	−0.979886	+	0.199560i	$0.936049\pi$
$38$	0.481667	−	1.79760i	0.0781366	−	0.291610i
$39$	7.03595	−	3.16805i	1.12665	−	0.507294i
$40$	1.43892	−	1.71158i	0.227514	−	0.270624i
$41$	6.84503	+	3.95198i	1.06901	+	0.617195i	0.927912	−	0.372800i	$-0.121602\pi$
$41$	6.84503	+	3.95198i	1.06901	+	0.617195i	0.141102	+	0.989995i	$0.454935\pi$
$42$	−3.19329	+	2.60814i	−0.492735	+	0.402445i
$43$	−1.88812	−	0.505920i	−0.287935	−	0.0771520i	0.111960	−	0.993713i	$-0.464287\pi$
$43$	−1.88812	−	0.505920i	−0.287935	−	0.0771520i	−0.399896	+	0.916561i	$0.630954\pi$
$44$	2.24827	−	3.89412i	0.338940	−	0.587061i
$45$	2.66706	+	6.15522i	0.397582	+	0.917567i
$46$	−8.85745			−1.30596
$47$	5.31159	−	5.31159i	0.774776	−	0.774776i	−0.204162	−	0.978937i	$-0.565447\pi$
$47$	5.31159	−	5.31159i	0.774776	−	0.774776i	0.978937	+	0.204162i	$0.0654468\pi$
$48$	0.278129	+	1.70957i	0.0401445	+	0.246756i
$49$	1.15484	+	0.666749i	0.164978	+	0.0952499i
$50$	2.87556	−	4.09037i	0.406666	−	0.578466i
$51$	−0.101682	+	1.00812i	−0.0142383	+	0.141165i
$52$	4.30320	−	1.15304i	0.596747	−	0.159898i
$53$	12.2216	−	3.27477i	1.67877	−	0.449824i	0.711314	−	0.702874i	$-0.248100\pi$
$53$	12.2216	−	3.27477i	1.67877	−	0.449824i	0.967453	+	0.253050i	$0.0814338\pi$
$54$	−4.96166	−	1.54336i	−0.675196	−	0.210024i
$55$	4.25780	−	9.10855i	0.574121	−	1.22820i
$56$	−2.06152	+	1.19022i	−0.275483	+	0.159050i
$57$	2.03903	+	2.49650i	0.270076	+	0.330669i
$58$	3.14658	−	3.14658i	0.413166	−	0.413166i
$59$	−2.50677	−	4.34185i	−0.326354	−	0.565261i	0.655432	−	0.755254i	$-0.272487\pi$
$59$	−2.50677	−	4.34185i	−0.326354	−	0.565261i	−0.981785	+	0.189993i	$0.939153\pi$
$60$	0.949198	+	3.75487i	0.122541	+	0.484751i
$61$	−7.10958			−0.910289			−0.455144	−	0.890418i	$-0.650412\pi$
$61$	−7.10958			−0.910289			−0.455144	+	0.890418i	$0.650412\pi$
$62$	4.52313	+	3.24674i	0.574438	+	0.412336i
$63$	−0.433591	−	7.12815i	−0.0546273	−	0.898062i
$64$			1.00000i			0.125000i
$65$	9.36412	−	3.39831i	1.16148	−	0.421509i
$66$	3.19759	+	7.10156i	0.393597	+	0.874141i
$67$	8.03955	−	2.15419i	0.982187	−	0.263176i	0.268222	−	0.963357i	$-0.413564\pi$
$67$	8.03955	−	2.15419i	0.982187	−	0.263176i	0.713965	+	0.700181i	$0.246897\pi$
$68$	−0.151407	+	0.565058i	−0.0183608	+	0.0685233i
$69$	8.96538	−	12.4493i	1.07930	−	1.49872i
$70$	−4.36307	+	3.04896i	−0.521487	+	0.364420i
$71$	2.05257	+	1.18505i	0.243595	+	0.140640i	0.616828	−	0.787098i	$-0.288417\pi$
$71$	2.05257	+	1.18505i	0.243595	+	0.140640i	−0.373233	+	0.927738i	$0.621751\pi$
$72$	−2.68436	−	1.33949i	−0.316354	−	0.157860i
$73$	2.29583	+	8.56816i	0.268707	+	1.00283i	0.959942	+	0.280198i	$0.0904000\pi$
$73$	2.29583	+	8.56816i	0.268707	+	1.00283i	−0.691236	+	0.722630i	$0.742933\pi$
$74$	−2.71518	−	4.70283i	−0.315633	−	0.546693i
$75$	2.83849	+	8.18187i	0.327761	+	0.944761i
$76$	0.930509	+	1.61169i	0.106737	+	0.184873i
$77$	−7.56870	+	7.56870i	−0.862534	+	0.862534i
$78$	−2.73502	+	7.21532i	−0.309680	+	0.816974i
$79$	−3.98508	+	2.30079i	−0.448357	+	0.258859i	−0.707136	−	0.707078i	$-0.750013\pi$
$79$	−3.98508	+	2.30079i	−0.448357	+	0.258859i	0.258779	+	0.965937i	$0.416680\pi$
$80$	0.192796	+	2.22774i	0.0215552	+	0.249069i
$81$	7.19133	−	5.41154i	0.799037	−	0.601282i
$82$	−7.63464	+	2.04570i	−0.843105	+	0.225909i
$83$	−14.1710	+	3.79711i	−1.55547	+	0.416787i	−0.931226	−	0.364443i	$-0.881259\pi$
$83$	−14.1710	+	3.79711i	−1.55547	+	0.416787i	−0.624243	+	0.781230i	$0.714593\pi$
$84$	0.413764	−	4.10223i	0.0451453	−	0.447590i
$85$	−0.228354	+	1.28799i	−0.0247685	+	0.139702i
$86$	1.69284	−	0.977362i	0.182544	−	0.105392i
$87$	1.23766	+	7.60750i	0.132691	+	0.815610i
$88$	1.16379	+	4.34333i	0.124061	+	0.463000i
$89$	5.51996			0.585115			0.292558	−	0.956248i	$-0.405494\pi$
$89$	5.51996			0.585115			0.292558	+	0.956248i	$0.405494\pi$
$90$	−6.23830	−	2.46650i	−0.657574	−	0.259992i
$91$	−10.6049			−1.11169
$92$	6.26316	−	6.26316i	0.652980	−	0.652980i
$93$	−9.14159	+	3.07105i	−0.947939	+	0.318453i
$94$			7.51173i			0.774776i
$95$	2.38366	+	3.41103i	0.244558	+	0.349964i
$96$	−1.40552	−	1.01218i	−0.143450	−	0.103306i
$97$	12.1061	+	12.1061i	1.22918	+	1.22918i	0.964273	+	0.264912i	$0.0853428\pi$
$97$	12.1061	+	12.1061i	1.22918	+	1.22918i	0.264912	+	0.964273i	$0.414657\pi$
$98$	−1.28806	+	0.345135i	−0.130114	+	0.0348639i
$99$	−13.2179	−	2.69381i	−1.32845	−	0.270738i
$100$	0.858997	+	4.92566i	0.0858997	+	0.492566i
$101$		−	17.9346i		−	1.78456i	−0.451485	−	0.892278i	$-0.649106\pi$
$101$		−	17.9346i		−	1.78456i	0.451485	−	0.892278i	$-0.350894\pi$
$102$	−0.640948	−	0.784748i	−0.0634633	−	0.0777016i
$103$	−0.639332	−	2.38602i	−0.0629952	−	0.235101i	0.927249	−	0.374446i	$-0.122167\pi$
$103$	−0.639332	−	2.38602i	−0.0629952	−	0.235101i	−0.990244	+	0.139345i	$0.955500\pi$
$104$	−2.22750	+	3.85815i	−0.218424	+	0.378322i
$105$	0.130867	−	9.21848i	0.0127713	−	0.899632i
$106$	−6.32637	+	10.9576i	−0.614471	+	1.06430i
$107$	1.97521	+	0.529256i	0.190951	+	0.0511651i	0.353027	−	0.935613i	$-0.385152\pi$
$107$	1.97521	+	0.529256i	0.190951	+	0.0511651i	−0.162076	+	0.986778i	$0.551819\pi$
$108$	4.59974	−	2.41710i	0.442610	−	0.232586i
$109$			10.6472i			1.01981i	0.860229	+	0.509907i	$0.170320\pi$
$109$			10.6472i			1.01981i	−0.860229	+	0.509907i	$0.829680\pi$
$110$	3.43000	+	9.45144i	0.327038	+	0.901159i
$111$	9.35818	+	0.943895i	0.888239	+	0.0895905i
$112$	0.616104	−	2.29933i	0.0582163	−	0.217266i
$113$	−12.7634	+	3.41995i	−1.20068	+	0.321722i	−0.803100	−	0.595845i	$-0.796817\pi$
$113$	−12.7634	+	3.41995i	−1.20068	+	0.321722i	−0.397582	+	0.917567i	$0.630151\pi$
$114$	−3.20710	−	0.323478i	−0.300373	−	0.0302965i
$115$	12.7452	−	15.1602i	1.18850	−	1.41370i
$116$			4.44994i			0.413166i
$117$	−7.37293	−	11.1473i	−0.681627	−	1.03057i
$118$	4.84271	+	1.29760i	0.445807	+	0.119454i
$119$	0.696268	−	1.20597i	0.0638268	−	0.110551i
$120$	−3.32628	−	1.98391i	−0.303646	−	0.181105i
$121$	4.60945	+	7.98381i	0.419041	+	0.725801i
$122$	5.02723	−	5.02723i	0.455144	−	0.455144i
$123$	4.85240	−	12.8012i	0.437526	−	1.15425i
$124$	−5.49413	+	0.902546i	−0.493387	+	0.0810511i
$125$	2.86327	+	10.8075i	0.256098	+	0.966651i
$126$	5.34696	+	4.73377i	0.476345	+	0.421718i
$127$	−1.56791	+	5.85153i	−0.139130	+	0.519240i	0.860817	+	0.508915i	$0.169953\pi$
$127$	−1.56791	+	5.85153i	−0.139130	+	0.519240i	−0.999947	+	0.0103248i	$0.996713\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.339766	+	3.36859i	−0.0299148	+	0.296588i
$130$	−4.21846	+	9.02440i	−0.369984	+	0.791492i
$131$	−1.48650	+	0.858234i	−0.129876	+	0.0749842i	−0.563531	−	0.826095i	$-0.690557\pi$
$131$	−1.48650	+	0.858234i	−0.129876	+	0.0749842i	0.433654	+	0.901079i	$0.357224\pi$
$132$	−7.28260	−	2.76052i	−0.633869	−	0.240272i
$133$	−1.14658	−	4.27909i	−0.0994210	−	0.371044i
$134$	−4.16158	+	7.20806i	−0.359505	+	0.622682i
$135$	9.78102	−	6.27149i	0.841816	−	0.539764i
$136$	−0.292495	−	0.506617i	−0.0250813	−	0.0434420i
$137$	2.23674	+	8.34763i	0.191098	+	0.713186i	0.993243	+	0.116057i	$0.0370254\pi$
$137$	2.23674	+	8.34763i	0.191098	+	0.713186i	−0.802145	+	0.597129i	$0.796308\pi$
$138$	2.46352	+	15.1425i	0.209708	+	1.28901i
$139$			3.92225i			0.332681i	0.986068	+	0.166340i	$0.0531951\pi$
$139$			3.92225i			0.332681i	−0.986068	+	0.166340i	$0.946805\pi$
$140$	0.929219	−	5.24109i	0.0785333	−	0.442953i
$141$	−10.5579	−	7.60326i	−0.889133	−	0.640310i
$142$	−2.28934	+	0.613427i	−0.192117	+	0.0514777i
$143$	−5.18469	+	19.3495i	−0.433566	+	1.61809i
$144$	2.84529	−	0.950965i	0.237107	−	0.0792471i
$145$	0.857928	+	9.91331i	0.0712471	+	0.823256i
$146$	−7.68200	−	4.43521i	−0.635767	−	0.367060i
$147$	0.818662	−	2.15973i	0.0675221	−	0.178132i
$148$	5.24532	+	1.40548i	0.431163	+	0.115530i
$149$	3.09353	+	5.35816i	0.253432	+	0.438957i	0.964469	−	0.264198i	$-0.0851072\pi$
$149$	3.09353	+	5.35816i	0.253432	+	0.438957i	−0.711036	+	0.703155i	$0.751774\pi$
$150$	−7.79257	−	3.77834i	−0.636261	−	0.308500i
$151$	−8.77775			−0.714323			−0.357162	−	0.934043i	$-0.616255\pi$
$151$	−8.77775			−0.714323			−0.357162	+	0.934043i	$0.616255\pi$
$152$	−1.79760	−	0.481667i	−0.145805	−	0.0390683i
$153$	1.75173	−	0.106554i	0.141619	−	0.00861441i
$154$		−	10.7038i		−	0.862534i
$155$	−12.0655	+	3.06988i	−0.969123	+	0.246579i
$156$	−3.16805	−	7.03595i	−0.253647	−	0.563327i
$157$	−7.76029	−	7.76029i	−0.619338	−	0.619338i	0.326023	−	0.945362i	$-0.394291\pi$
$157$	−7.76029	−	7.76029i	−0.619338	−	0.619338i	−0.945362	+	0.326023i	$0.894291\pi$
$158$	1.19098	−	4.44478i	0.0947490	−	0.353608i
$159$	−8.99765	−	19.9829i	−0.713560	−	1.58475i
$160$	−1.71158	−	1.43892i	−0.135312	−	0.113757i
$161$	−18.2598	+	10.5423i	−1.43908	+	0.830851i
$162$	−1.25850	+	8.91158i	−0.0988772	+	0.700159i
$163$	−3.24623	+	3.24623i	−0.254265	+	0.254265i	−0.822716	−	0.568452i	$-0.807543\pi$
$163$	−3.24623	+	3.24623i	−0.254265	+	0.254265i	0.568452	+	0.822716i	$0.307543\pi$
$164$	3.95198	−	6.84503i	0.308598	−	0.534507i
$165$	−16.7560	−	4.74567i	−1.30445	−	0.369450i
$166$	7.33545	−	12.7054i	0.569341	−	0.986128i
$167$	−2.25858	−	0.605183i	−0.174774	−	0.0468305i	0.170371	−	0.985380i	$-0.445503\pi$
$167$	−2.25858	−	0.605183i	−0.174774	−	0.0468305i	−0.345145	+	0.938550i	$0.612170\pi$
$168$	2.60814	+	3.19329i	0.201222	+	0.246368i
$169$	−5.92972	+	3.42352i	−0.456132	+	0.263348i
$170$	−0.749277	−	1.07222i	−0.0574670	−	0.0822355i
$171$	3.70084	−	4.18022i	0.283010	−	0.319670i
$172$	−0.505920	+	1.88812i	−0.0385760	+	0.143968i
$173$	6.83042	−	1.83021i	0.519307	−	0.139148i	0.0103612	−	0.999946i	$-0.496702\pi$
$173$	6.83042	−	1.83021i	0.519307	−	0.139148i	0.508946	+	0.860798i	$0.330035\pi$
$174$	−6.25447	−	4.50416i	−0.474150	−	0.341459i
$175$	1.05960	−	11.8549i	0.0800982	−	0.896150i
$176$	−3.89412	−	2.24827i	−0.293530	−	0.169470i
$177$	−6.72551	+	5.49311i	−0.505521	+	0.412887i
$178$	−3.90320	+	3.90320i	−0.292558	+	0.292558i
$179$	−4.01402	−	6.95249i	−0.300022	−	0.519654i	0.676119	−	0.736793i	$-0.263661\pi$
$179$	−4.01402	−	6.95249i	−0.300022	−	0.519654i	−0.976141	+	0.217139i	$0.930327\pi$
$180$	6.15522	−	2.66706i	0.458783	−	0.198791i
$181$	10.8428	−	18.7804i	0.805943	−	1.39593i	−0.109710	−	0.993964i	$-0.534992\pi$
$181$	10.8428	−	18.7804i	0.805943	−	1.39593i	0.915653	−	0.401970i	$-0.131674\pi$
$182$	7.49878	−	7.49878i	0.555846	−	0.555846i
$183$	1.97738	+	12.1544i	0.146172	+	0.898476i
$184$			8.85745i			0.652980i
$185$	11.9562	+	2.11977i	0.879037	+	0.155849i
$186$	4.29252	−	8.63564i	0.314743	−	0.633196i
$187$	−1.86000	−	1.86000i	−0.136017	−	0.136017i
$188$	−5.31159	−	5.31159i	−0.387388	−	0.387388i
$189$	−12.0655	+	2.72380i	−0.877636	+	0.198127i
$190$	−4.09746	−	0.726458i	−0.297261	−	0.0527028i
$191$	−12.0391	−	6.95079i	−0.871120	−	0.502941i	−0.00339985	−	0.999994i	$-0.501082\pi$
$191$	−12.0391	−	6.95079i	−0.871120	−	0.502941i	−0.867720	+	0.497053i	$0.834416\pi$
$192$	1.70957	−	0.278129i	0.123378	−	0.0200723i
$193$	22.3023	+	5.97588i	1.60536	+	0.430154i	0.946654	−	0.322251i	$-0.104440\pi$
$193$	22.3023	+	5.97588i	1.60536	+	0.430154i	0.658701	+	0.752405i	$0.271106\pi$
$194$	−17.1206			−1.22918
$195$	−8.41410	−	15.0635i	−0.602546	−	1.07872i
$196$	0.666749	−	1.15484i	0.0476250	−	0.0824889i
$197$	4.85255	+	18.1100i	0.345730	+	1.29028i	0.891757	+	0.452515i	$0.149473\pi$
$197$	4.85255	+	18.1100i	0.345730	+	1.29028i	−0.546027	+	0.837768i	$0.683860\pi$
$198$	11.2513	−	7.44168i	0.799595	−	0.528857i
$199$	2.19235	+	1.26575i	0.155412	+	0.0897269i	0.575689	−	0.817669i	$-0.304734\pi$
$199$	2.19235	+	1.26575i	0.155412	+	0.0897269i	−0.420277	+	0.907396i	$0.638067\pi$
$200$	−4.09037	−	2.87556i	−0.289233	−	0.203333i
$201$	−5.91878	−	13.1451i	−0.417479	−	0.927181i
$202$	12.6817	+	12.6817i	0.892278	+	0.892278i
$203$	2.74162	−	10.2319i	0.192424	−	0.718137i
$204$	1.00812	+	0.101682i	0.0705824	+	0.00711916i
$205$	7.48430	−	16.0109i	0.522726	−	1.11825i
$206$	2.13924	+	1.23509i	0.149048	+	0.0860531i
$207$	−23.7766	−	11.8645i	−1.65259	−	0.824637i
$208$	−1.15304	−	4.30320i	−0.0799489	−	0.298373i
$209$	−8.36814			−0.578837
$210$	6.42591	+	6.61099i	0.443430	+	0.456201i
$211$	3.49428	+	6.05227i	0.240556	+	0.416656i	0.960873	−	0.276990i	$-0.0893368\pi$
$211$	3.49428	+	6.05227i	0.240556	+	0.416656i	−0.720317	+	0.693645i	$0.756004\pi$
$212$	−3.27477	−	12.2216i	−0.224912	−	0.839384i
$213$	1.45505	−	3.83861i	0.0996986	−	0.263017i
$214$	−1.77092	+	1.02244i	−0.121058	+	0.0698928i
$215$	−0.763037	+	4.30378i	−0.0520387	+	0.293515i
$216$	−1.54336	+	4.96166i	−0.105012	+	0.337598i
$217$	13.1889	+	1.30970i	0.895319	+	0.0889081i
$218$	−7.52869	−	7.52869i	−0.509907	−	0.509907i
$219$	14.0094	−	6.30795i	0.946665	−	0.426252i
$220$	−9.10855	−	4.25780i	−0.614098	−	0.287061i
$221$		−	2.60614i		−	0.175308i
$222$	−7.28466	+	5.94980i	−0.488915	+	0.399324i
$223$	−21.8225	−	5.84733i	−1.46134	−	0.391566i	−0.561390	−	0.827551i	$-0.689733\pi$
$223$	−21.8225	−	5.84733i	−1.46134	−	0.391566i	−0.899954	+	0.435985i	$0.856400\pi$
$224$	1.19022	+	2.06152i	0.0795250	+	0.137741i
$225$	13.1980	−	7.12823i	0.879870	−	0.475215i
$226$	6.60683	−	11.4434i	0.439480	−	0.761202i
$227$	−4.98038	−	18.5870i	−0.330559	−	1.23366i	−0.908604	−	0.417659i	$-0.862851\pi$
$227$	−4.98038	−	18.5870i	−0.330559	−	1.23366i	0.578045	−	0.816005i	$-0.303816\pi$
$228$	2.49650	−	2.03903i	0.165335	−	0.135038i
$229$	−4.32734	+	2.49839i	−0.285959	+	0.165098i	−0.636118	−	0.771592i	$-0.719461\pi$
$229$	−4.32734	+	2.49839i	−0.285959	+	0.165098i	0.350159	+	0.936690i	$0.386127\pi$
$230$	1.70768	+	19.7321i	0.112601	+	1.30110i
$231$	15.0443	+	10.8342i	0.989844	+	0.712837i
$232$	−3.14658	−	3.14658i	−0.206583	−	0.206583i
$233$	8.70784	+	8.70784i	0.570470	+	0.570470i	0.932260	−	0.361790i	$-0.117834\pi$
$233$	8.70784	+	8.70784i	0.570470	+	0.570470i	−0.361790	+	0.932260i	$0.617834\pi$
$234$	13.0958	+	2.66892i	0.856100	+	0.174473i
$235$	−12.8569	−	10.8088i	−0.838692	−	0.705089i
$236$	−4.34185	+	2.50677i	−0.282631	+	0.163177i
$237$	5.04174	+	6.17288i	0.327496	+	0.400972i
$238$	0.360415	+	1.34509i	0.0233622	+	0.0871890i
$239$	5.95318	−	10.3112i	0.385079	−	0.666977i	−0.606701	−	0.794930i	$-0.707507\pi$
$239$	5.95318	−	10.3112i	0.385079	−	0.666977i	0.991780	+	0.127953i	$0.0408408\pi$
$240$	3.75487	−	0.949198i	0.242376	−	0.0612705i
$241$	14.1772	+	24.5556i	0.913231	+	1.58176i	0.809470	+	0.587161i	$0.199754\pi$
$241$	14.1772	+	24.5556i	0.913231	+	1.58176i	0.103761	+	0.994602i	$0.466912\pi$
$242$	−8.90478	−	2.38603i	−0.572421	−	0.153380i
$243$	−11.2515	−	10.7890i	−0.721787	−	0.692115i
$244$			7.10958i			0.455144i
$245$	1.26270	−	2.70124i	0.0806707	−	0.172576i
$246$	5.62068	+	12.4830i	0.358362	+	0.795888i
$247$	−5.86251	−	5.86251i	−0.373022	−	0.373022i
$248$	3.24674	−	4.52313i	0.206168	−	0.287219i
$249$	10.4328	+	23.1703i	0.661152	+	1.46836i
$250$	−9.66668	−	5.61741i	−0.611375	−	0.355276i
$251$	17.3458	−	10.0146i	1.09486	−	0.632116i	0.159992	−	0.987118i	$-0.448853\pi$
$251$	17.3458	−	10.0146i	1.09486	−	0.632116i	0.934865	+	0.355002i	$0.115520\pi$
$252$	−7.12815	+	0.433591i	−0.449031	+	0.0273136i
$253$	10.3082	+	38.4708i	0.648073	+	2.41864i
$254$	−3.02898	−	5.24634i	−0.190055	−	0.329185i
$255$	2.26543	+	0.0321604i	0.141867	+	0.00201396i
$256$	1.00000			0.0625000
$257$	−7.48030	−	27.9169i	−0.466608	−	1.74141i	−0.651501	−	0.758648i	$-0.725860\pi$
$257$	−7.48030	−	27.9169i	−0.466608	−	1.74141i	0.184893	−	0.982759i	$-0.440806\pi$
$258$	−2.14170	−	2.62220i	−0.133336	−	0.163251i
$259$	−11.1948	−	6.46333i	−0.695612	−	0.401612i
$260$	−3.39831	−	9.36412i	−0.210754	−	0.580738i
$261$	12.6614	−	4.23174i	0.783718	−	0.261938i
$262$	0.444254	−	1.65798i	0.0274461	−	0.102430i
$263$	8.05905	+	8.05905i	0.496942	+	0.496942i	0.910485	−	0.413542i	$-0.135709\pi$
$263$	8.05905	+	8.05905i	0.496942	+	0.496942i	−0.413542	+	0.910485i	$0.635709\pi$
$264$	7.10156	−	3.19759i	0.437071	−	0.196798i
$265$	−9.65161	−	26.5952i	−0.592894	−	1.63373i
$266$	3.83653	+	2.21502i	0.235233	+	0.135812i
$267$	−1.53526	−	9.43679i	−0.0939566	−	0.577522i
$268$	−2.15419	−	8.03955i	−0.131588	−	0.491093i
$269$	−8.25970	+	14.3062i	−0.503603	+	0.872266i	0.496389	+	0.868100i	$0.334659\pi$
$269$	−8.25970	+	14.3062i	−0.503603	+	0.872266i	−0.999991	+	0.00416518i	$0.998674\pi$
$270$	−2.48161	+	11.3508i	−0.151026	+	0.690790i
$271$	2.15831			0.131108			0.0655540	−	0.997849i	$-0.479119\pi$
$271$	2.15831			0.131108			0.0655540	+	0.997849i	$0.479119\pi$
$272$	0.565058	+	0.151407i	0.0342617	+	0.00918038i
$273$	2.94953	+	18.1298i	0.178513	+	1.09727i
$274$	−7.48428	−	4.32105i	−0.452142	−	0.261044i
$275$	−21.1124	−	7.72918i	−1.27312	−	0.466087i
$276$	−12.4493	−	8.96538i	−0.749361	−	0.539652i
$277$	9.55998	+	9.55998i	0.574404	+	0.574404i	0.933356	−	0.358952i	$-0.116866\pi$
$277$	9.55998	+	9.55998i	0.574404	+	0.574404i	−0.358952	+	0.933356i	$0.616866\pi$
$278$	−2.77345	−	2.77345i	−0.166340	−	0.166340i
$279$	7.79273	+	14.7741i	0.466538	+	0.884501i
$280$	3.04896	+	4.36307i	0.182210	+	0.260743i
$281$		−	30.0433i		−	1.79224i	−0.443816	−	0.896118i	$-0.646376\pi$
$281$		−	30.0433i		−	1.79224i	0.443816	−	0.896118i	$-0.353624\pi$
$282$	12.8419	−	2.08923i	0.764722	−	0.124412i
$283$	4.50545	−	4.50545i	0.267821	−	0.267821i	−0.560400	−	0.828222i	$-0.689353\pi$
$283$	4.50545	−	4.50545i	0.267821	−	0.267821i	0.828222	+	0.560400i	$0.189353\pi$
$284$	1.18505	−	2.05257i	0.0703198	−	0.121797i
$285$	5.16844	−	5.02375i	0.306152	−	0.297581i
$286$	−10.0161	−	17.3483i	−0.592262	−	1.02583i
$287$	−13.3042	+	13.3042i	−0.785319	+	0.785319i
$288$	−1.33949	+	2.68436i	−0.0789301	+	0.158177i
$289$	−14.4261	−	8.32889i	−0.848592	−	0.489935i
$290$	−7.61642	−	6.40312i	−0.447251	−	0.376004i
$291$	17.3292	−	24.0633i	1.01585	−	1.41061i
$292$	8.56816	−	2.29583i	0.501414	−	0.134353i
$293$	−3.47808	+	12.9804i	−0.203192	+	0.758322i	0.786801	+	0.617207i	$0.211736\pi$
$293$	−3.47808	+	12.9804i	−0.203192	+	0.758322i	−0.989993	+	0.141116i	$0.954931\pi$
$294$	0.948281	+	2.10604i	0.0553049	+	0.122827i
$295$	−9.18923	+	6.42152i	−0.535018	+	0.373876i
$296$	−4.70283	+	2.71518i	−0.273346	+	0.157817i
$297$	−0.928972	+	23.3463i	−0.0539044	+	1.35469i
$298$	−5.97625	−	1.60133i	−0.346195	−	0.0927626i
$299$	−19.7300	+	34.1733i	−1.14101	+	1.97630i
$300$	8.18187	−	2.83849i	0.472380	−	0.163880i
$301$	2.32655	−	4.02971i	0.134100	−	0.232268i
$302$	6.20681	−	6.20681i	0.357162	−	0.357162i
$303$	−30.6605	+	4.98813i	−1.76140	+	0.286561i
$304$	1.61169	−	0.930509i	0.0924366	−	0.0533683i
$305$	1.37070	+	15.8383i	0.0784858	+	0.906899i
$306$	−1.16332	+	1.31401i	−0.0665025	+	0.0751169i
$307$	−5.25923	+	19.6277i	−0.300160	+	1.12021i	0.636872	+	0.770969i	$0.280228\pi$
$307$	−5.25923	+	19.6277i	−0.300160	+	1.12021i	−0.937032	+	0.349243i	$0.886439\pi$
$308$	7.56870	+	7.56870i	0.431267	+	0.431267i
$309$	−3.90126	+	1.75661i	−0.221935	+	0.0999298i
$310$	6.36085	−	10.7023i	0.361272	−	0.607851i
$311$			13.9384i			0.790373i	0.918601	+	0.395186i	$0.129320\pi$
$311$			13.9384i			0.790373i	−0.918601	+	0.395186i	$0.870680\pi$
$312$	7.21532	+	2.73502i	0.408487	+	0.154840i
$313$	10.4709	+	2.80568i	0.591853	+	0.158587i	0.542300	−	0.840185i	$-0.317554\pi$
$313$	10.4709	+	2.80568i	0.591853	+	0.158587i	0.0495531	+	0.998771i	$0.484220\pi$
$314$	10.9747			0.619338
$315$	−15.7961	+	2.34020i	−0.890008	+	0.131855i
$316$	2.30079	+	3.98508i	0.129430	+	0.224178i
$317$	−26.2083	−	7.02249i	−1.47200	−	0.394422i	−0.568386	−	0.822762i	$-0.692432\pi$
$317$	−26.2083	−	7.02249i	−1.47200	−	0.394422i	−0.903618	+	0.428340i	$0.859099\pi$
$318$	20.4924	+	7.76777i	1.14916	+	0.435595i
$319$	−17.3286	−	10.0047i	−0.970215	−	0.560154i
$320$	2.22774	−	0.192796i	0.124535	−	0.0107776i
$321$	0.355438	−	3.52397i	0.0198386	−	0.196689i
$322$	5.45711	−	20.3662i	0.304113	−	1.13496i
$323$	1.05158	−	0.281771i	0.0585116	−	0.0156781i
$324$	−5.41154	−	7.19133i	−0.300641	−	0.399518i
$325$	−9.37592	−	20.2057i	−0.520082	−	1.12081i
$326$		−	4.59087i		−	0.254265i
$327$	18.2021	−	2.96129i	1.00658	−	0.163760i
$328$	2.04570	+	7.63464i	0.112955	+	0.421552i
$329$	8.94062	+	15.4856i	0.492912	+	0.853749i
$330$	15.2039	−	8.49256i	0.836950	−	0.467500i
$331$	2.73839	−	4.74303i	0.150516	−	0.260701i	−0.780902	−	0.624654i	$-0.785240\pi$
$331$	2.73839	−	4.74303i	0.150516	−	0.260701i	0.931417	+	0.363953i	$0.118573\pi$
$332$	3.79711	+	14.1710i	0.208393	+	0.777734i
$333$	−0.989124	−	16.2610i	−0.0542037	−	0.891099i
$334$	2.02498	−	1.16912i	0.110802	−	0.0639717i
$335$	−6.34897	−	17.4947i	−0.346881	−	0.955838i
$336$	−4.10223	−	0.413764i	−0.223795	−	0.0225727i
$337$	0.541190	+	0.541190i	0.0294805	+	0.0294805i	0.721693	−	0.692213i	$-0.243364\pi$
$337$	0.541190	+	0.541190i	0.0294805	+	0.0294805i	−0.692213	+	0.721693i	$0.743364\pi$
$338$	1.77215	−	6.61374i	0.0963921	−	0.359740i
$339$	9.39654	+	20.8688i	0.510350	+	1.13344i
$340$	1.28799	+	0.228354i	0.0698512	+	0.0123843i
$341$	8.83766	−	23.4240i	0.478586	−	1.26848i
$342$	0.338979	+	5.57275i	0.0183299	+	0.301340i
$343$	−14.0272	+	14.0272i	−0.757396	+	0.757396i
$344$	−0.977362	−	1.69284i	−0.0526958	−	0.0912718i
$345$	−29.4623	−	17.5724i	−1.58620	−	0.946064i
$346$	−3.53569	+	6.12399i	−0.190080	+	0.329228i
$347$	−7.60976	−	2.03903i	−0.408513	−	0.109461i	0.0487094	−	0.998813i	$-0.484489\pi$
$347$	−7.60976	−	2.03903i	−0.408513	−	0.109461i	−0.457223	+	0.889352i	$0.651156\pi$
$348$	7.60750	−	1.23766i	0.407805	−	0.0663454i
$349$		−	16.2739i		−	0.871121i	−0.900160	−	0.435560i	$-0.856550\pi$
$349$		−	16.2739i		−	0.871121i	0.900160	−	0.435560i	$-0.143450\pi$
$350$	7.63346	+	9.13196i	0.408026	+	0.488124i
$351$	−17.0066	+	15.7050i	−0.907745	+	0.838269i
$352$	4.34333	−	1.16379i	0.231500	−	0.0620303i
$353$	−4.40814	+	16.4514i	−0.234622	+	0.875620i	0.743697	+	0.668516i	$0.233070\pi$
$353$	−4.40814	+	16.4514i	−0.234622	+	0.875620i	−0.978319	+	0.207104i	$0.933596\pi$
$354$	0.871444	−	8.63987i	0.0463167	−	0.459204i
$355$	2.24426	−	4.80106i	0.119113	−	0.254814i
$356$		−	5.51996i		−	0.292558i
$357$	−2.25535	−	0.854906i	−0.119366	−	0.0452464i
$358$	7.75450	+	2.07781i	0.409838	+	0.109816i
$359$	15.3124	−	26.5219i	0.808158	−	1.39977i	−0.105980	−	0.994368i	$-0.533798\pi$
$359$	15.3124	−	26.5219i	0.808158	−	1.39977i	0.914138	−	0.405403i	$-0.132869\pi$
$360$	−2.46650	+	6.23830i	−0.129996	+	0.328787i
$361$	−7.76831	+	13.4551i	−0.408858	+	0.708163i
$362$	5.61267	+	20.9468i	0.294995	+	1.10094i
$363$	12.3669	−	10.1007i	0.649093	−	0.530151i
$364$			10.6049i			0.555846i
$365$	18.6450	−	6.76642i	0.975925	−	0.354171i
$366$	−9.99265	−	7.19621i	−0.522324	−	0.376152i
$367$	−20.0550	+	5.37372i	−1.04686	+	0.280506i	−0.740954	−	0.671556i	$-0.765626\pi$
$367$	−20.0550	+	5.37372i	−1.04686	+	0.280506i	−0.305907	+	0.952061i	$0.598960\pi$
$368$	−6.26316	−	6.26316i	−0.326490	−	0.326490i
$369$	−23.2343	−	4.73514i	−1.20953	−	0.246501i
$370$	−9.95321	+	6.95540i	−0.517443	+	0.361594i
$371$			30.1191i			1.56371i
$372$	3.07105	+	9.14159i	0.159226	+	0.473969i
$373$	−14.3738	+	14.3738i	−0.744246	+	0.744246i	−0.973392	−	0.229146i	$-0.926407\pi$
$373$	−14.3738	+	14.3738i	−0.744246	+	0.744246i	0.229146	+	0.973392i	$0.426407\pi$
$374$	2.63044			0.136017
$375$	17.6798	−	7.90085i	0.912983	−	0.407998i
$376$	7.51173			0.387388
$377$	−5.13095	−	19.1490i	−0.264258	−	0.986223i
$378$	6.60558	−	10.4576i	0.339754	−	0.537882i
$379$	21.0770	−	12.1688i	1.08265	−	0.625070i	0.151042	−	0.988527i	$-0.451737\pi$
$379$	21.0770	−	12.1688i	1.08265	−	0.625070i	0.931611	+	0.363458i	$0.118404\pi$
$380$	3.41103	−	2.38366i	0.174982	−	0.122279i
$381$	10.4397	+	1.05298i	0.534843	+	0.0539459i
$382$	13.4279	−	3.59799i	0.687031	−	0.184089i
$383$	28.9982	−	7.77005i	1.48174	−	0.397031i	0.574801	−	0.818293i	$-0.305080\pi$
$383$	28.9982	−	7.77005i	1.48174	−	0.397031i	0.906939	+	0.421263i	$0.138413\pi$
$384$	−1.01218	+	1.40552i	−0.0516528	+	0.0717251i
$385$	18.3203	+	15.4019i	0.933690	+	0.784953i
$386$	−19.9957	+	11.5445i	−1.01775	+	0.587601i
$387$	5.85335	−	0.356047i	0.297543	−	0.0180989i
$388$	12.1061	−	12.1061i	0.614592	−	0.614592i
$389$	12.0725	+	20.9102i	0.612099	+	1.06019i	0.990886	+	0.134703i	$0.0430080\pi$
$389$	12.0725	+	20.9102i	0.612099	+	1.06019i	−0.378787	+	0.925484i	$0.623659\pi$
$390$	16.6012	+	4.70183i	0.840632	+	0.238086i
$391$	−2.59076	−	4.48733i	−0.131021	−	0.226934i
$392$	0.345135	+	1.28806i	0.0174319	+	0.0650569i
$393$	1.88065	+	2.30259i	0.0948665	+	0.116150i
$394$	−16.2370	−	9.37442i	−0.818006	−	0.472276i
$395$	5.89387	+	8.43415i	0.296553	+	0.424368i
$396$	−2.69381	+	13.2179i	−0.135369	+	0.664226i
$397$	−2.78932	+	10.4099i	−0.139992	+	0.522457i	0.859935	+	0.510403i	$0.170504\pi$
$397$	−2.78932	+	10.4099i	−0.139992	+	0.522457i	−0.999927	+	0.0120540i	$0.996163\pi$
$398$	−2.44525	+	0.655203i	−0.122569	+	0.0328423i
$399$	−6.99653	+	3.15030i	−0.350265	+	0.157712i
$400$	4.92566	−	0.858997i	0.246283	−	0.0429498i
$401$			25.4829i			1.27255i	0.771461	+	0.636277i	$0.219527\pi$
$401$			25.4829i			1.27255i	−0.771461	+	0.636277i	$0.780473\pi$
$402$	13.4802	+	5.10975i	0.672330	+	0.254851i
$403$	22.6017	−	10.2188i	1.12587	−	0.509034i
$404$	−17.9346			−0.892278
$405$	−13.4420	−	14.9771i	−0.667937	−	0.744218i
$406$	5.29641	+	9.17365i	0.262856	+	0.455281i
$407$	−17.2660	+	17.2660i	−0.855845	+	0.855845i
$408$	−0.784748	+	0.640948i	−0.0388508	+	0.0317316i
$409$	−9.85182	+	5.68795i	−0.487141	+	0.281251i	−0.723388	−	0.690442i	$-0.757416\pi$
$409$	−9.85182	+	5.68795i	−0.487141	+	0.281251i	0.236247	+	0.971693i	$0.424083\pi$
$410$	6.02920	+	16.6136i	0.297761	+	0.820487i
$411$	13.6488	−	6.14559i	0.673245	−	0.303140i
$412$	−2.38602	+	0.639332i	−0.117551	+	0.0314976i
$413$	11.5278	−	3.08886i	0.567245	−	0.151993i
$414$	25.2020	−	8.42313i	1.23861	−	0.413974i
$415$	11.1911	+	30.8372i	0.549348	+	1.51374i
$416$	3.85815	+	2.22750i	0.189161	+	0.109212i
$417$	6.70538	−	1.09089i	0.328364	−	0.0534212i
$418$	5.91717	−	5.91717i	0.289418	−	0.289418i
$419$	−11.0439			−0.539529			−0.269765	−	0.962926i	$-0.586946\pi$
$419$	−11.0439			−0.539529			−0.269765	+	0.962926i	$0.586946\pi$
$420$	−9.21848	−	0.130867i	−0.449816	−	0.00638565i
$421$	−4.76629	+	8.25546i	−0.232295	+	0.402347i	−0.958483	−	0.285149i	$-0.907957\pi$
$421$	−4.76629	+	8.25546i	−0.232295	+	0.402347i	0.726188	+	0.687496i	$0.241290\pi$
$422$	−6.75043	−	1.80877i	−0.328606	−	0.0880497i
$423$	−10.0619	+	20.1642i	−0.489225	+	0.980415i
$424$	10.9576	+	6.32637i	0.532148	+	0.307236i
$425$	2.91334	+	0.260395i	0.141318	+	0.0126310i
$426$	1.68543	+	3.74319i	0.0816595	+	0.181358i
$427$	4.38024	−	16.3473i	0.211975	−	0.791100i
$428$	0.529256	−	1.97521i	0.0255825	−	0.0954753i
$429$	34.5215	+	3.48194i	1.66671	+	0.168110i
$430$	−2.50368	−	3.58278i	−0.120738	−	0.172777i
$431$	5.52809	−	3.19165i	0.266279	−	0.153736i	−0.360917	−	0.932598i	$-0.617536\pi$
$431$	5.52809	−	3.19165i	0.266279	−	0.153736i	0.627195	+	0.778862i	$0.284203\pi$
$432$	−2.41710	−	4.59974i	−0.116293	−	0.221305i
$433$	4.74699	−	4.74699i	0.228126	−	0.228126i	−0.583784	−	0.811909i	$-0.698428\pi$
$433$	4.74699	−	4.74699i	0.228126	−	0.228126i	0.811909	+	0.583784i	$0.198428\pi$
$434$	−10.2520	+	8.39984i	−0.492113	+	0.403205i
$435$	16.7089	−	4.22387i	0.801132	−	0.202519i
$436$	10.6472			0.509907
$437$	−15.9222	−	4.26634i	−0.761662	−	0.204087i
$438$	−5.44572	+	14.3665i	−0.260207	+	0.686459i
$439$	−17.7540	−	10.2503i	−0.847352	−	0.489219i	0.0124042	−	0.999923i	$-0.496052\pi$
$439$	−17.7540	−	10.2503i	−0.847352	−	0.489219i	−0.859757	+	0.510704i	$0.829385\pi$
$440$	9.45144	−	3.43000i	0.450580	−	0.163519i
$441$	−3.91992	−	0.798878i	−0.186663	−	0.0380418i
$442$	1.84282	+	1.84282i	0.0876538	+	0.0876538i
$443$	−7.09374	+	1.90076i	−0.337034	+	0.0903080i	−0.423367	−	0.905958i	$-0.639152\pi$
$443$	−7.09374	+	1.90076i	−0.337034	+	0.0903080i	0.0863328	+	0.996266i	$0.472485\pi$
$444$	0.943895	−	9.35818i	0.0447953	−	0.444119i
$445$	−1.06422	−	12.2971i	−0.0504491	−	0.582936i
$446$	19.5655	−	11.2962i	0.926455	−	0.534889i
$447$	8.29977	−	6.77889i	0.392566	−	0.320630i
$448$	−2.29933	−	0.616104i	−0.108633	−	0.0291082i
$449$	22.1228			1.04404			0.522019	−	0.852934i	$-0.325179\pi$
$449$	22.1228			1.04404			0.522019	+	0.852934i	$0.325179\pi$
$450$	−4.29201	+	14.3728i	−0.202327	+	0.677542i
$451$	17.7702	+	30.7790i	0.836768	+	1.44933i
$452$	3.41995	+	12.7634i	0.160861	+	0.600341i
$453$	2.44135	+	15.0062i	0.114705	+	0.705054i
$454$	16.6647	+	9.62135i	0.782112	+	0.451552i
$455$	2.04457	+	23.6249i	0.0958510	+	1.10755i
$456$	−0.323478	+	3.20710i	−0.0151483	+	0.150186i
$457$	−19.6110	−	19.6110i	−0.917365	−	0.917365i	0.0794721	−	0.996837i	$-0.474677\pi$
$457$	−19.6110	−	19.6110i	−0.917365	−	0.917365i	−0.996837	+	0.0794721i	$0.974677\pi$
$458$	1.29326	−	4.82652i	0.0604302	−	0.225529i
$459$	−0.669371	−	2.96508i	−0.0312436	−	0.138398i
$460$	−15.1602	−	12.7452i	−0.706849	−	0.594248i
$461$		−	27.5480i		−	1.28304i	−0.767108	−	0.641519i	$-0.778305\pi$
$461$		−	27.5480i		−	1.28304i	0.767108	−	0.641519i	$-0.221695\pi$
$462$	−18.2989	+	2.97703i	−0.851341	+	0.138504i
$463$	14.8109	−	14.8109i	0.688321	−	0.688321i	−0.273540	−	0.961861i	$-0.588195\pi$
$463$	14.8109	−	14.8109i	0.688321	−	0.688321i	0.961861	+	0.273540i	$0.0881946\pi$
$464$	4.44994			0.206583
$465$	8.60395	+	19.7730i	0.398999	+	0.916951i
$466$	−12.3147			−0.570470
$467$	28.5795	−	28.5795i	1.32250	−	1.32250i	0.410760	−	0.911743i	$-0.365263\pi$
$467$	28.5795	−	28.5795i	1.32250	−	1.32250i	0.911743	−	0.410760i	$-0.134737\pi$
$468$	−11.1473	+	7.37293i	−0.515286	+	0.340814i
$469$			19.8128i			0.914869i
$470$	16.7342	−	1.44823i	0.771890	−	0.0668018i
$471$	−11.1084	+	15.4252i	−0.511849	+	0.710754i
$472$	1.29760	−	4.84271i	0.0597269	−	0.222904i
$473$	−6.21511	−	6.21511i	−0.285771	−	0.285771i
$474$	−7.92993	−	0.799838i	−0.364234	−	0.0367378i
$475$	7.13932	−	5.96780i	0.327575	−	0.273822i
$476$	−1.20597	−	0.696268i	−0.0552756	−	0.0319134i
$477$	−31.6598	+	20.9400i	−1.44960	+	0.958776i
$478$	3.08159	+	11.5007i	0.140949	+	0.526028i
$479$	4.99248	+	8.64723i	0.228112	+	0.395102i	0.957249	−	0.289266i	$-0.0934113\pi$
$479$	4.99248	+	8.64723i	0.228112	+	0.395102i	−0.729136	+	0.684368i	$0.760078\pi$
$480$	−1.98391	+	3.32628i	−0.0905526	+	0.151823i
$481$	−24.1923			−1.10307
$482$	−27.3882	−	7.33864i	−1.24750	−	0.334266i
$483$	23.1015	+	28.2844i	1.05115	+	1.28699i
$484$	7.98381	−	4.60945i	0.362900	−	0.209521i
$485$	24.6352	−	29.3032i	1.11863	−	1.33059i
$486$	15.5850	−	0.327069i	0.706951	−	0.0148361i
$487$	−10.3285	+	2.76753i	−0.468031	+	0.125409i	−0.485124	−	0.874445i	$-0.661226\pi$
$487$	−10.3285	+	2.76753i	−0.468031	+	0.125409i	0.0170929	+	0.999854i	$0.494559\pi$
$488$	−5.02723	−	5.02723i	−0.227572	−	0.227572i
$489$	6.45255	+	4.64680i	0.291794	+	0.210136i
$490$	1.01720	+	2.80293i	0.0459526	+	0.126623i
$491$	15.4158	+	8.90031i	0.695705	+	0.401665i	0.805746	−	0.592262i	$-0.201765\pi$
$491$	15.4158	+	8.90031i	0.695705	+	0.401665i	−0.110041	+	0.993927i	$0.535098\pi$
$492$	−12.8012	−	4.85240i	−0.577125	−	0.218763i
$493$	2.51447	+	0.673751i	0.113246	+	0.0303442i
$494$	8.29084			0.373022
$495$	−3.45275	+	29.9655i	−0.155190	+	1.34685i
$496$	0.902546	+	5.49413i	0.0405255	+	0.246693i
$497$	−3.98942	+	3.98942i	−0.178950	+	0.178950i
$498$	−23.7610	−	9.00676i	−1.06475	−	0.403602i
$499$	11.7031	−	6.75678i	0.523902	−	0.302475i	−0.214627	−	0.976696i	$-0.568854\pi$
$499$	11.7031	−	6.75678i	0.523902	−	0.302475i	0.738530	+	0.674221i	$0.235520\pi$
$500$	10.8075	−	2.86327i	0.483325	−	0.128049i
$501$	−0.406430	+	4.02952i	−0.0181580	+	0.180026i
$502$	−5.18394	+	19.3467i	−0.231371	+	0.863487i
$503$	7.09362	−	26.4737i	0.316289	−	1.18041i	−0.606495	−	0.795087i	$-0.707425\pi$
$503$	7.09362	−	26.4737i	0.316289	−	1.18041i	0.922784	−	0.385318i	$-0.125908\pi$
$504$	4.73377	−	5.34696i	0.210859	−	0.238172i
$505$	−39.9536	+	3.45771i	−1.77791	+	0.153866i
$506$	−34.4920	−	19.9140i	−1.53336	−	0.885284i
$507$	7.50200	+	9.18511i	0.333175	+	0.407925i
$508$	5.85153	+	1.56791i	0.259620	+	0.0695649i
$509$	−1.45238	+	2.51559i	−0.0643755	+	0.111502i	−0.896417	−	0.443212i	$-0.853839\pi$
$509$	−1.45238	+	2.51559i	−0.0643755	+	0.111502i	0.832041	+	0.554714i	$0.187172\pi$
$510$	−1.62464	+	1.57916i	−0.0719404	+	0.0699264i
$511$	−21.1155			−0.934094
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−8.17571	−	5.16421i	−0.360967	−	0.228005i
$514$	25.0296	+	14.4508i	1.10401	+	0.637399i
$515$	−5.19217	+	1.88428i	−0.228794	+	0.0830312i
$516$	3.36859	+	0.339766i	0.148294	+	0.0149574i
$517$	32.6259	−	8.74208i	1.43489	−	0.384476i
$518$	12.4862	−	3.34566i	0.548612	−	0.147000i
$519$	−5.02861	−	11.1681i	−0.220732	−	0.490224i
$520$	9.02440	+	4.21846i	0.395746	+	0.184992i
$521$	−24.8819	+	14.3656i	−1.09010	+	0.629367i	−0.933602	−	0.358312i	$-0.883353\pi$
$521$	−24.8819	+	14.3656i	−1.09010	+	0.629367i	−0.156494	+	0.987679i	$0.550019\pi$
$522$	−5.96064	+	11.9452i	−0.260890	+	0.522828i
$523$	−20.8336	+	20.8336i	−0.910991	+	0.910991i	−0.996350	−	0.0853591i	$-0.972796\pi$
$523$	−20.8336	+	20.8336i	−0.910991	+	0.910991i	0.0853591	+	0.996350i	$0.472796\pi$
$524$	0.858234	+	1.48650i	0.0374921	+	0.0649382i
$525$	−20.5616	+	1.48574i	−0.897383	+	0.0648432i
$526$	−11.3972			−0.496942
$527$	−0.321857	+	3.24115i	−0.0140203	+	0.141187i
$528$	−2.76052	+	7.28260i	−0.120136	+	0.316934i
$529$			55.4545i			2.41106i
$530$	25.6304	+	11.9809i	1.11331	+	0.520419i
$531$	11.2614	+	9.96997i	0.488705	+	0.432660i
$532$	−4.27909	+	1.14658i	−0.185522	+	0.0497105i
$533$	−9.11358	+	34.0123i	−0.394753	+	1.47324i
$534$	7.75841	+	5.58722i	0.335739	+	0.241783i
$535$	0.798233	−	4.50229i	0.0345106	−	0.194651i
$536$	7.20806	+	4.16158i	0.311341	+	0.179753i
$537$	−10.7694	+	8.79596i	−0.464733	+	0.379574i
$538$	−4.27554	−	15.9565i	−0.184331	−	0.687934i
$539$	2.99807	+	5.19281i	0.129136	+	0.223670i
$540$	−6.27149	−	9.78102i	−0.269882	−	0.420908i
$541$	−15.6275	−	27.0676i	−0.671879	−	1.16373i	−0.977371	−	0.211534i	$-0.932154\pi$
$541$	−15.6275	−	27.0676i	−0.671879	−	1.16373i	0.305492	−	0.952195i	$-0.401179\pi$
$542$	−1.52616	+	1.52616i	−0.0655540	+	0.0655540i
$543$	−35.1221	−	13.3133i	−1.50724	−	0.571328i
$544$	−0.506617	+	0.292495i	−0.0217210	+	0.0125406i
$545$	23.7191	−	2.05273i	1.01602	−	0.0879292i
$546$	−14.9053	−	10.7341i	−0.637890	−	0.459377i
$547$	−15.4746	+	4.14641i	−0.661647	+	0.177288i	−0.573989	−	0.818863i	$-0.694605\pi$
$547$	−15.4746	+	4.14641i	−0.661647	+	0.177288i	−0.0876580	+	0.996151i	$0.527938\pi$
$548$	8.34763	−	2.23674i	0.356593	−	0.0955488i
$549$	20.2288	−	6.76097i	0.863345	−	0.288551i
$550$	20.3941	−	9.46335i	0.869606	−	0.403518i
$551$	7.17191	−	4.14071i	0.305534	−	0.176400i
$552$	15.1425	−	2.46352i	0.644506	−	0.104854i
$553$	−2.83505	−	10.5805i	−0.120559	−	0.449931i
$554$	−13.5199			−0.574404
$555$	0.298539	−	21.0296i	0.0126723	−	0.892656i
$556$	3.92225			0.166340
$557$	−6.61834	+	6.61834i	−0.280428	+	0.280428i	−0.833280	−	0.552852i	$-0.813540\pi$
$557$	−6.61834	+	6.61834i	−0.280428	+	0.280428i	0.552852	+	0.833280i	$0.313540\pi$
$558$	−15.9571	−	4.93656i	−0.675520	−	0.208981i
$559$		−	8.70830i		−	0.368322i
$560$	−5.24109	−	0.929219i	−0.221477	−	0.0392667i
$561$	−2.66249	+	3.69713i	−0.112410	+	0.156093i
$562$	21.2439	+	21.2439i	0.896118	+	0.896118i
$563$	34.5426	−	9.25567i	1.45580	−	0.390080i	0.557762	−	0.830001i	$-0.311660\pi$
$563$	34.5426	−	9.25567i	1.45580	−	0.390080i	0.898036	+	0.439921i	$0.144994\pi$
$564$	−7.60326	+	10.5579i	−0.320155	+	0.444567i
$565$	10.0795	+	27.7742i	0.424047	+	1.16847i
$566$			6.37167i			0.267821i
$567$	8.01231	+	19.8693i	0.336485	+	0.834433i
$568$	0.613427	+	2.28934i	0.0257388	+	0.0960586i
$569$	−15.1076	+	26.1671i	−0.633342	+	1.09698i	0.353521	+	0.935426i	$0.384984\pi$
$569$	−15.1076	+	26.1671i	−0.633342	+	1.09698i	−0.986864	+	0.161555i	$0.948349\pi$
$570$	−0.102311	+	7.20696i	−0.00428534	+	0.301866i
$571$	21.6398	−	37.4812i	0.905598	−	1.56854i	0.0854844	−	0.996340i	$-0.472756\pi$
$571$	21.6398	−	37.4812i	0.905598	−	1.56854i	0.820113	−	0.572201i	$-0.193910\pi$
$572$	19.3495	+	5.18469i	0.809045	+	0.216783i
$573$	−8.53446	+	22.5150i	−0.356532	+	0.940577i
$574$		−	18.8149i		−	0.785319i
$575$	−36.2303	−	25.4702i	−1.51091	−	1.06218i
$576$	−0.950965	−	2.84529i	−0.0396236	−	0.118554i
$577$	9.97914	−	37.2427i	0.415437	−	1.55043i	−0.368521	−	0.929619i	$-0.620136\pi$
$577$	9.97914	−	37.2427i	0.415437	−	1.55043i	0.783958	−	0.620813i	$-0.213197\pi$
$578$	16.0902	−	4.31135i	0.669263	−	0.179329i
$579$	4.01329	−	39.7895i	0.166787	−	1.65360i
$580$	9.91331	−	0.857928i	0.411628	−	0.0356235i
$581$		−	34.9232i		−	1.44886i
$582$	4.76173	+	29.2689i	0.197380	+	1.21323i
$583$	54.9550	+	14.7251i	2.27600	+	0.609853i
$584$	−4.43521	+	7.68200i	−0.183530	+	0.317883i
$585$	−23.4119	+	18.5741i	−0.967965	+	0.767946i
$586$	−6.71914	−	11.6379i	−0.277565	−	0.480757i
$587$	−12.0093	+	12.0093i	−0.495677	+	0.495677i	−0.910089	−	0.414412i	$-0.863987\pi$
$587$	−12.0093	+	12.0093i	−0.495677	+	0.495677i	0.414412	+	0.910089i	$0.363987\pi$
$588$	−2.15973	−	0.818662i	−0.0890659	−	0.0337610i
$589$	6.56695	+	8.01499i	0.270587	+	0.330252i
$590$	1.95706	−	11.0385i	0.0805710	−	0.454447i
$591$	29.6107	−	13.3327i	1.21802	−	0.548435i
$592$	1.40548	−	5.24532i	0.0577649	−	0.215581i
$593$	14.0779	+	14.0779i	0.578108	+	0.578108i	0.934382	−	0.356273i	$-0.115953\pi$
$593$	14.0779	+	14.0779i	0.578108	+	0.578108i	−0.356273	+	0.934382i	$0.615953\pi$
$594$	−15.8514	−	17.1652i	−0.650391	−	0.704296i
$595$	−2.82083	−	1.31860i	−0.115643	−	0.0540573i
$596$	5.35816	−	3.09353i	0.219479	−	0.126716i
$597$	1.55414	−	4.10003i	0.0636069	−	0.167803i
$598$	−10.2130	−	38.1154i	−0.417640	−	1.55865i
$599$	−12.3674	+	21.4210i	−0.505320	+	0.875240i	0.494661	+	0.869086i	$0.335292\pi$
$599$	−12.3674	+	21.4210i	−0.505320	+	0.875240i	−0.999981	+	0.00615370i	$0.998041\pi$
$600$	−3.77834	+	7.79257i	−0.154250	+	0.318130i
$601$	9.33337	+	16.1659i	0.380716	+	0.659419i	0.991165	−	0.132636i	$-0.0423442\pi$
$601$	9.33337	+	16.1659i	0.380716	+	0.659419i	−0.610449	+	0.792056i	$0.709011\pi$
$602$	1.20431	+	4.49455i	0.0490841	+	0.183184i
$603$	−20.8263	+	13.7746i	−0.848111	+	0.560946i
$604$			8.77775i			0.357162i
$605$	16.8972	−	11.8079i	0.686968	−	0.480060i
$606$	18.1531	−	25.2074i	0.737419	−	1.02398i
$607$	7.45205	−	1.99677i	0.302469	−	0.0810465i	−0.104392	−	0.994536i	$-0.533290\pi$
$607$	7.45205	−	1.99677i	0.302469	−	0.0810465i	0.406862	+	0.913490i	$0.366623\pi$
$608$	−0.481667	+	1.79760i	−0.0195342	+	0.0729025i
$609$	−18.2547	−	1.84122i	−0.739717	−	0.0746101i
$610$	−12.1686	−	10.2301i	−0.492692	−	0.414207i
$611$	28.9813	+	16.7324i	1.17246	+	0.676920i
$612$	−0.106554	−	1.75173i	−0.00430721	−	0.0708097i
$613$	−7.79968	−	2.08992i	−0.315026	−	0.0844110i	0.0978415	−	0.995202i	$-0.468806\pi$
$613$	−7.79968	−	2.08992i	−0.315026	−	0.0844110i	−0.412868	+	0.910791i	$0.635473\pi$
$614$	−10.1600	−	17.5977i	−0.410026	−	0.710186i
$615$	−29.4534	−	8.34187i	−1.18767	−	0.336376i
$616$	−10.7038			−0.431267
$617$	−12.4401	−	3.33332i	−0.500820	−	0.134194i	−0.000439697	−	1.00000i	$-0.500140\pi$
$617$	−12.4401	−	3.33332i	−0.500820	−	0.134194i	−0.500381	+	0.865805i	$0.666807\pi$
$618$	1.51650	−	4.00071i	0.0610025	−	0.160932i
$619$		−	22.6431i		−	0.910103i	−0.890465	−	0.455051i	$-0.849621\pi$
$619$		−	22.6431i		−	0.910103i	0.890465	−	0.455051i	$-0.150379\pi$
$620$	3.06988	+	12.0655i	0.123289	+	0.484561i
$621$	−13.6702	+	43.9476i	−0.548567	+	1.76356i
$622$	−9.85592	−	9.85592i	−0.395186	−	0.395186i
$623$	−3.40087	+	12.6922i	−0.136253	+	0.508503i
$624$	−7.03595	+	3.16805i	−0.281663	+	0.126824i
$625$	23.5242	−	8.46225i	0.940970	−	0.338490i
$626$	−9.38800	+	5.42016i	−0.375220	+	0.216633i
$627$	2.32743	+	14.3060i	0.0929484	+	0.571325i
$628$	−7.76029	+	7.76029i	−0.309669	+	0.309669i
$629$	1.58835	−	2.75111i	0.0633319	−	0.109694i
$630$	9.51474	−	12.8243i	0.379076	−	0.510932i
$631$	0.489585	−	0.847986i	0.0194901	−	0.0337578i	−0.856116	−	0.516784i	$-0.827129\pi$
$631$	0.489585	−	0.847986i	0.0194901	−	0.0337578i	0.875606	+	0.483026i	$0.160462\pi$
$632$	−4.44478	−	1.19098i	−0.176804	−	0.0473745i
$633$	9.37495	−	7.65705i	0.372621	−	0.304340i
$634$	23.4977	−	13.5664i	0.933213	−	0.538791i
$635$	13.3380	+	2.36476i	0.529302	+	0.0938425i
$636$	−19.9829	+	8.99765i	−0.792375	+	0.356780i
$637$	−1.53758	+	5.73832i	−0.0609210	+	0.227360i
$638$	19.3275	−	5.17880i	0.765185	−	0.205031i
$639$	−6.96709	−	1.41989i	−0.275614	−	0.0561700i
$640$	−1.43892	+	1.71158i	−0.0568785	+	0.0676561i
$641$	33.8851	+	19.5636i	1.33838	+	0.772715i	0.986567	−	0.163354i	$-0.0522314\pi$
$641$	33.8851	+	19.5636i	1.33838	+	0.772715i	0.351815	+	0.936070i	$0.385565\pi$
$642$	2.24049	+	2.74315i	0.0884250	+	0.108264i
$643$	14.3870	−	14.3870i	0.567367	−	0.567367i	−0.364023	−	0.931390i	$-0.618597\pi$
$643$	14.3870	−	14.3870i	0.567367	−	0.567367i	0.931390	+	0.364023i	$0.118597\pi$
$644$	10.5423	+	18.2598i	0.415426	+	0.719538i
$645$	7.56985	+	0.107463i	0.298062	+	0.00423134i
$646$	−0.544339	+	0.942823i	−0.0214167	+	0.0370949i
$647$	32.6963	−	32.6963i	1.28542	−	1.28542i	0.347886	−	0.937537i	$-0.386900\pi$
$647$	32.6963	−	32.6963i	1.28542	−	1.28542i	0.937537	−	0.347886i	$-0.113100\pi$
$648$	8.91158	+	1.25850i	0.350080	+	0.0494386i
$649$		−	22.5436i		−	0.884914i
$650$	20.9173	+	7.65778i	0.820445	+	0.300363i
$651$	−1.42918	−	22.9116i	−0.0560141	−	0.897977i
$652$	3.24623	+	3.24623i	0.127132	+	0.127132i
$653$	−14.7006	−	14.7006i	−0.575279	−	0.575279i	0.358320	−	0.933599i	$-0.383350\pi$
$653$	−14.7006	−	14.7006i	−0.575279	−	0.575279i	−0.933599	+	0.358320i	$0.883350\pi$
$654$	−10.7769	+	14.9648i	−0.421410	+	0.585170i
$655$	2.19851	+	3.14608i	0.0859030	+	0.122928i
$656$	−6.84503	−	3.95198i	−0.267253	−	0.154299i
$657$	−14.6803	−	22.1956i	−0.572734	−	0.865934i
$658$	−17.2719	−	4.62800i	−0.673330	−	0.180418i
$659$	−18.8583			−0.734614			−0.367307	−	0.930100i	$-0.619720\pi$
$659$	−18.8583			−0.734614			−0.367307	+	0.930100i	$0.619720\pi$
$660$	−4.74567	+	16.7560i	−0.184725	+	0.652225i
$661$	−3.82620	+	6.62717i	−0.148822	+	0.257767i	−0.930792	−	0.365549i	$-0.880881\pi$
$661$	−3.82620	+	6.62717i	−0.148822	+	0.257767i	0.781970	+	0.623315i	$0.214215\pi$
$662$	1.41750	+	5.29017i	0.0550925	+	0.205608i
$663$	−4.45538	+	0.724842i	−0.173033	+	0.0281505i
$664$	−12.7054	−	7.33545i	−0.493064	−	0.284671i
$665$	−9.31165	+	3.37927i	−0.361090	+	0.131043i
$666$	12.1977	+	10.7989i	0.472651	+	0.418447i
$667$	−27.8707	−	27.8707i	−1.07916	−	1.07916i
$668$	−0.605183	+	2.25858i	−0.0234153	+	0.0873869i
$669$	−3.92696	+	38.9335i	−0.151825	+	1.50526i
$670$	16.8600	+	7.88123i	0.651360	+	0.304479i
$671$	−27.6856	−	15.9843i	−1.06879	−	0.617066i
$672$	3.19329	−	2.60814i	0.123184	−	0.100611i
$673$	−4.45338	−	16.6203i	−0.171665	−	0.640664i	−0.997096	−	0.0761597i	$-0.975734\pi$
$673$	−4.45338	−	16.6203i	−0.171665	−	0.640664i	0.825430	−	0.564504i	$-0.190933\pi$
$674$	−0.765358			−0.0294805
$675$	−15.8570	−	20.5805i	−0.610336	−	0.792143i
$676$	3.42352	+	5.92972i	0.131674	+	0.228066i
$677$	−10.4035	−	38.8265i	−0.399840	−	1.49222i	−0.813378	−	0.581735i	$-0.802374\pi$
$677$	−10.4035	−	38.8265i	−0.399840	−	1.49222i	0.413539	−	0.910487i	$-0.364293\pi$
$678$	−21.4008	−	8.11214i	−0.821895	−	0.311545i
$679$	−35.2944	+	20.3772i	−1.35448	+	0.782007i
$680$	−1.07222	+	0.749277i	−0.0411177	+	0.0287335i
$681$	−30.3907	+	13.6839i	−1.16457	+	0.524369i
$682$	10.3141	+	22.8124i	0.394946	+	0.873532i
$683$	−29.2884	−	29.2884i	−1.12069	−	1.12069i	−0.991638	−	0.129051i	$-0.958807\pi$
$683$	−29.2884	−	29.2884i	−1.12069	−	1.12069i	−0.129051	−	0.991638i	$-0.541193\pi$
$684$	−4.18022	−	3.70084i	−0.159835	−	0.141505i
$685$	18.1651	−	6.59226i	0.694053	−	0.251877i
$686$		−	19.8374i		−	0.757396i
$687$	5.47475	+	6.70303i	0.208875	+	0.255737i
$688$	1.88812	+	0.505920i	0.0719838	+	0.0192880i
$689$	28.1840	+	48.8161i	1.07372	+	1.85975i
$690$	33.2586	−	8.40748i	1.26613	−	0.320067i
$691$	11.4164	−	19.7738i	0.434301	−	0.752231i	−0.562938	−	0.826499i	$-0.690329\pi$
$691$	11.4164	−	19.7738i	0.434301	−	0.752231i	0.997238	+	0.0742686i	$0.0236622\pi$
$692$	−1.83021	−	6.83042i	−0.0695740	−	0.259654i
$693$	14.3376	−	28.7327i	0.544639	−	1.09147i
$694$	6.82273	−	3.93910i	0.258987	−	0.149526i
$695$	8.73776	−	0.756192i	0.331442	−	0.0286840i
$696$	−4.50416	+	6.25447i	−0.170730	+	0.237075i
$697$	−3.26948	−	3.26948i	−0.123840	−	0.123840i
$698$	11.5074	+	11.5074i	0.435560	+	0.435560i
$699$	12.4648	−	17.3086i	0.471462	−	0.654672i
$700$	−11.8549	−	1.05960i	−0.448075	−	0.0400491i
$701$	−32.1511	+	18.5624i	−1.21433	+	0.701094i	−0.963700	−	0.266989i	$-0.913971\pi$
$701$	−32.1511	+	18.5624i	−1.21433	+	0.701094i	−0.250631	+	0.968083i	$0.580638\pi$
$702$	0.920390	−	23.1306i	0.0347379	−	0.873007i
$703$	−2.61562	−	9.76164i	−0.0986501	−	0.368167i
$704$	−2.24827	+	3.89412i	−0.0847349	+	0.146765i
$705$	−14.9026	+	24.9861i	−0.561263	+	0.941030i
$706$	−8.51587	−	14.7499i	−0.320499	−	0.555121i
$707$	41.2375	+	11.0496i	1.55090	+	0.415561i
$708$	5.49311	+	6.72551i	0.206444	+	0.252760i
$709$		−	47.2641i		−	1.77504i	−0.460767	−	0.887521i	$-0.652426\pi$
$709$		−	47.2641i		−	1.77504i	0.460767	−	0.887521i	$-0.347574\pi$
$710$	1.80793	+	4.98179i	0.0678505	+	0.186963i
$711$	9.15074	−	10.3361i	0.343180	−	0.387633i
$712$	3.90320	+	3.90320i	0.146279	+	0.146279i
$713$	28.7578	−	40.0634i	1.07699	−	1.50039i
$714$	2.19928	−	0.990264i	0.0823061	−	0.0370597i
$715$	44.1053	+	7.81965i	1.64945	+	0.292438i
$716$	−6.95249	+	4.01402i	−0.259827	+	0.150011i
$717$	−19.2835	−	7.30955i	−0.720157	−	0.272980i
$718$	7.92629	+	29.5813i	0.295806	+	1.10396i
$719$	−2.91043	−	5.04102i	−0.108541	−	0.187998i	0.806638	−	0.591045i	$-0.201284\pi$
$719$	−2.91043	−	5.04102i	−0.108541	−	0.187998i	−0.915179	+	0.403047i	$0.867951\pi$
$720$	−2.66706	−	6.15522i	−0.0993956	−	0.229392i
$721$	5.88014			0.218988
$722$	−4.02117	−	15.0072i	−0.149653	−	0.558511i
$723$	38.0365	−	31.0665i	1.41459	−	1.15538i
$724$	−18.7804	−	10.8428i	−0.697967	−	0.402971i
$725$	21.9189	−	3.82248i	0.814047	−	0.141963i
$726$	−1.60241	+	15.8870i	−0.0594711	+	0.589622i
$727$	4.13326	−	15.4255i	0.153294	−	0.572101i	−0.845951	−	0.533260i	$-0.820967\pi$
$727$	4.13326	−	15.4255i	0.153294	−	0.572101i	0.999245	−	0.0388410i	$-0.0123666\pi$
$728$	−7.49878	−	7.49878i	−0.277923	−	0.277923i
$729$	−15.3152	+	22.2361i	−0.567230	+	0.823559i
$730$	−8.39943	+	17.9686i	−0.310877	+	0.665048i
$731$	0.990296	+	0.571747i	0.0366274	+	0.0211468i
$732$	12.1544	−	1.97738i	0.449238	−	0.0730862i
$733$	−1.22303	−	4.56442i	−0.0451738	−	0.168591i	0.939654	−	0.342127i	$-0.111147\pi$
$733$	−1.22303	−	4.56442i	−0.0451738	−	0.168591i	−0.984827	+	0.173536i	$0.944481\pi$
$734$	10.3812	−	17.9808i	0.383178	−	0.663684i
$735$	−4.96916	−	1.40738i	−0.183290	−	0.0519120i
$736$	8.85745			0.326490
$737$	36.1502	+	9.68641i	1.33161	+	0.356804i
$738$	19.7774	−	13.0809i	0.728015	−	0.481513i
$739$	−17.8083	−	10.2817i	−0.655090	−	0.378217i	0.135313	−	0.990803i	$-0.456796\pi$
$739$	−17.8083	−	10.2817i	−0.655090	−	0.378217i	−0.790404	+	0.612586i	$0.790129\pi$
$740$	2.11977	−	11.9562i	0.0779243	−	0.439518i
$741$	−8.39185	+	11.6529i	−0.308282	+	0.428081i
$742$	−21.2974	−	21.2974i	−0.781853	−	0.781853i
$743$	−11.1746	−	11.1746i	−0.409956	−	0.409956i	0.471767	−	0.881723i	$-0.343616\pi$
$743$	−11.1746	−	11.1746i	−0.409956	−	0.409956i	−0.881723	+	0.471767i	$0.843616\pi$
$744$	−8.63564	−	4.29252i	−0.316598	−	0.157371i
$745$	11.3402	−	7.92462i	0.415472	−	0.290336i
$746$		−	20.3276i		−	0.744246i
$747$	36.7096	−	24.2800i	1.34314	−	0.888358i
$748$	−1.86000	+	1.86000i	−0.0680083	+	0.0680083i
$749$	−2.43387	+	4.21558i	−0.0889316	+	0.154034i
$750$	−6.91479	+	18.0883i	−0.252492	+	0.660490i
$751$	7.06771	+	12.2416i	0.257905	+	0.446704i	0.965680	−	0.259733i	$-0.0836347\pi$
$751$	7.06771	+	12.2416i	0.257905	+	0.446704i	−0.707776	+	0.706437i	$0.750301\pi$
$752$	−5.31159	+	5.31159i	−0.193694	+	0.193694i
$753$	−21.9451	−	26.8686i	−0.799723	−	0.979145i
$754$	17.1685	+	9.91224i	0.625240	+	0.360983i
$755$	1.69231	+	19.5546i	0.0615895	+	0.711663i
$756$	2.72380	+	12.0655i	0.0990637	+	0.438818i
$757$	−14.5860	+	3.90831i	−0.530138	+	0.142050i	−0.513952	−	0.857819i	$-0.671819\pi$
$757$	−14.5860	+	3.90831i	−0.530138	+	0.142050i	−0.0161860	+	0.999869i	$0.505152\pi$
$758$	−6.29904	+	23.5083i	−0.228791	+	0.853861i
$759$	62.9017	−	28.3225i	2.28319	−	1.02804i
$760$	−0.726458	+	4.09746i	−0.0263514	+	0.148631i
$761$	−3.88153	+	2.24100i	−0.140705	+	0.0812363i	−0.568700	−	0.822545i	$-0.692554\pi$
$761$	−3.88153	+	2.24100i	−0.140705	+	0.0812363i	0.427995	+	0.903781i	$0.359220\pi$
$762$	−8.12656	+	6.63742i	−0.294394	+	0.240448i
$763$	−24.4814	−	6.55976i	−0.886285	−	0.237479i
$764$	−6.95079	+	12.0391i	−0.251471	+	0.435560i
$765$	−0.575102	−	3.88187i	−0.0207929	−	0.140349i
$766$	−15.0106	+	25.9991i	−0.542354	+	0.939385i
$767$	15.7935	−	15.7935i	0.570269	−	0.570269i
$768$	−0.278129	−	1.70957i	−0.0100361	−	0.0616889i
$769$	15.4794	−	8.93705i	0.558202	−	0.322278i	−0.194221	−	0.980958i	$-0.562218\pi$
$769$	15.4794	−	8.93705i	0.558202	−	0.322278i	0.752424	+	0.658679i	$0.228885\pi$
$770$	−23.8452	+	2.06364i	−0.859321	+	0.0743683i
$771$	−45.6455	+	20.5526i	−1.64388	+	0.740185i
$772$	5.97588	−	22.3023i	0.215077	−	0.802678i
$773$	−27.4632	−	27.4632i	−0.987783	−	0.987783i	0.0121433	−	0.999926i	$-0.496135\pi$
$773$	−27.4632	−	27.4632i	−0.987783	−	0.987783i	−0.999926	+	0.0121433i	$0.996135\pi$
$774$	−3.88718	+	4.39071i	−0.139722	+	0.157821i
$775$	9.16507	+	26.2869i	0.329219	+	0.944254i
$776$			17.1206i			0.614592i
$777$	−7.93593	+	20.9360i	−0.284700	+	0.751075i
$778$	−23.3222	−	6.24918i	−0.836143	−	0.224044i
$779$	−14.7094			−0.527019
$780$	−15.0635	+	8.41410i	−0.539359	+	0.301273i
$781$	5.32863	+	9.22946i	0.190673	+	0.330256i
$782$	5.00497	+	1.34108i	0.178977	+	0.0479569i
$783$	−10.7560	−	20.4686i	−0.384387	−	0.731487i
$784$	−1.15484	−	0.666749i	−0.0412444	−	0.0238125i
$785$	−15.7918	+	18.7841i	−0.563632	+	0.670432i
$786$	−2.95800	−	0.298353i	−0.105508	−	0.0106419i
$787$	−5.28276	+	19.7155i	−0.188310	+	0.702783i	0.805588	+	0.592477i	$0.201850\pi$
$787$	−5.28276	+	19.7155i	−0.188310	+	0.702783i	−0.993898	+	0.110306i	$0.964817\pi$
$788$	18.1100	−	4.85255i	0.645141	−	0.172865i
$789$	11.5361	−	16.0190i	0.410696	−	0.570292i
$790$	−10.1314	−	1.79625i	−0.360460	−	0.0639078i
$791$		−	31.4544i		−	1.11839i
$792$	−7.44168	−	11.2513i	−0.264428	−	0.399797i
$793$	−8.19763	−	30.5940i	−0.291106	−	1.08642i
$794$	−5.38855	−	9.33324i	−0.191232	−	0.331224i
$795$	−42.7821	+	23.8971i	−1.51732	+	0.847541i
$796$	1.26575	−	2.19235i	0.0448635	−	0.0777058i
$797$	−10.0565	−	37.5314i	−0.356219	−	1.32943i	−0.878943	−	0.476927i	$-0.841751\pi$
$797$	−10.0565	−	37.5314i	−0.356219	−	1.32943i	0.522724	−	0.852502i	$-0.324916\pi$
$798$	2.71969	−	7.17489i	0.0962760	−	0.253988i
$799$	−3.80557	+	2.19715i	−0.134631	+	0.0777294i
$800$	−2.87556	+	4.09037i	−0.101667	+	0.144616i
$801$	−15.7059	+	5.24929i	−0.554940	+	0.185475i
$802$	−18.0191	−	18.0191i	−0.636277	−	0.636277i
$803$	−10.3233	+	38.5271i	−0.364302	+	1.35959i
$804$	−13.1451	+	5.91878i	−0.463590	+	0.208739i
$805$	27.0060	+	38.6457i	0.951836	+	1.36208i
$806$	−8.75602	+	23.2076i	−0.308417	+	0.817451i
$807$	26.7548	+	10.1416i	0.941814	+	0.357001i
$808$	12.6817	−	12.6817i	0.446139	−	0.446139i
$809$	−4.56351	−	7.90423i	−0.160445	−	0.277898i	0.774584	−	0.632471i	$-0.217959\pi$
$809$	−4.56351	−	7.90423i	−0.160445	−	0.277898i	−0.935028	+	0.354573i	$0.884626\pi$
$810$	20.0953	+	1.08550i	0.706077	+	0.0381407i
$811$	14.9920	−	25.9669i	0.526440	−	0.911822i	−0.473085	−	0.881017i	$-0.656860\pi$
$811$	14.9920	−	25.9669i	0.526440	−	0.911822i	0.999525	−	0.0308049i	$-0.00980704\pi$
$812$	−10.2319	−	2.74162i	−0.359068	−	0.0962121i
$813$	−0.600289	−	3.68979i	−0.0210531	−	0.129407i
$814$		−	24.4178i		−	0.855845i
$815$	7.85762	+	6.60591i	0.275241	+	0.231395i
$816$	0.101682	−	1.00812i	0.00355958	−	0.0352912i
$817$	3.51382	−	0.941525i	0.122933	−	0.0329398i
$818$	2.94430	−	10.9883i	0.102945	−	0.384196i
$819$	30.1739	−	10.0849i	1.05436	−	0.352394i
$820$	−16.0109	−	7.48430i	−0.559124	−	0.261363i
$821$			31.1994i			1.08887i	0.838804	+	0.544434i	$0.183255\pi$
$821$			31.1994i			1.08887i	−0.838804	+	0.544434i	$0.816745\pi$
$822$	−5.30556	+	13.9967i	−0.185053	+	0.488192i
$823$	−31.9407	−	8.55848i	−1.11338	−	0.298330i	−0.345179	−	0.938537i	$-0.612182\pi$
$823$	−31.9407	−	8.55848i	−1.11338	−	0.298330i	−0.768202	+	0.640207i	$0.778849\pi$
$824$	1.23509	−	2.13924i	0.0430265	−	0.0745241i
$825$	−7.34165	+	38.2429i	−0.255603	+	1.33145i
$826$	−5.96722	+	10.3355i	−0.207626	+	0.359619i
$827$	−12.8331	−	47.8938i	−0.446251	−	1.66543i	−0.712612	−	0.701558i	$-0.752488\pi$
$827$	−12.8331	−	47.8938i	−0.446251	−	1.66543i	0.266361	−	0.963873i	$-0.414179\pi$
$828$	−11.8645	+	23.7766i	−0.412318	+	0.826293i
$829$		−	36.6571i		−	1.27316i	−0.771213	−	0.636578i	$-0.780350\pi$
$829$		−	36.6571i		−	1.27316i	0.771213	−	0.636578i	$-0.219650\pi$
$830$	−29.7185	−	13.8919i	−1.03154	−	0.482196i
$831$	13.6846	−	19.0024i	0.474713	−	0.659186i
$832$	−4.30320	+	1.15304i	−0.149187	+	0.0399745i
$833$	−0.551603	−	0.551603i	−0.0191119	−	0.0191119i
$834$	−3.97004	+	5.51280i	−0.137471	+	0.190893i
$835$	−0.912749	+	5.14820i	−0.0315870	+	0.178161i
$836$			8.36814i			0.289418i
$837$	23.0900	−	17.4313i	0.798107	−	0.602516i
$838$	7.80921	−	7.80921i	0.269765	−	0.269765i
$839$	−19.4896			−0.672855			−0.336428	−	0.941709i	$-0.609219\pi$
$839$	−19.4896			−0.672855			−0.336428	+	0.941709i	$0.609219\pi$
$840$	6.61099	−	6.42591i	0.228101	−	0.221715i
$841$	−9.19805			−0.317174
$842$	−2.46721	−	9.20777i	−0.0850258	−	0.317321i
$843$	−51.3613	+	8.35593i	−1.76898	+	0.287794i
$844$	6.05227	−	3.49428i	0.208328	−	0.120278i
$845$	8.76995	+	12.5498i	0.301695	+	0.431727i
$846$	−7.14339	−	21.3730i	−0.245595	−	0.734820i
$847$	−21.1973	+	5.67980i	−0.728348	+	0.195160i
$848$	−12.2216	+	3.27477i	−0.419692	+	0.112456i
$849$	−8.95550	−	6.44931i	−0.307352	−	0.221340i
$850$	−2.24417	+	1.87591i	−0.0769744	+	0.0643434i
$851$	−41.6551	+	24.0496i	−1.42792	+	0.824409i
$852$	−3.83861	−	1.45505i	−0.131509	−	0.0498493i
$853$	36.0216	−	36.0216i	1.23336	−	1.23336i	0.270689	−	0.962667i	$-0.412749\pi$
$853$	36.0216	−	36.0216i	1.23336	−	1.23336i	0.962667	−	0.270689i	$-0.0872515\pi$
$854$	8.46197	+	14.6566i	0.289563	+	0.501537i
$855$	−10.0260	−	7.43857i	−0.342881	−	0.254394i
$856$	1.02244	+	1.77092i	0.0349464	+	0.0605289i
$857$	−0.162969	−	0.608207i	−0.00556690	−	0.0207760i	0.963087	−	0.269192i	$-0.0867566\pi$
$857$	−0.162969	−	0.608207i	−0.00556690	−	0.0207760i	−0.968653	+	0.248416i	$0.920090\pi$
$858$	−26.8725	+	21.9483i	−0.917411	+	0.749302i
$859$	44.1181	+	25.4716i	1.50529	+	0.869080i	0.999981	+	0.00614122i	$0.00195482\pi$
$859$	44.1181	+	25.4716i	1.50529	+	0.869080i	0.505309	+	0.862938i	$0.331379\pi$
$860$	4.30378	+	0.763037i	0.146758	+	0.0260194i
$861$	26.4447	+	19.0442i	0.901233	+	0.649023i
$862$	−1.65212	+	6.16579i	−0.0562714	+	0.210008i
$863$	−43.2036	+	11.5764i	−1.47067	+	0.394064i	−0.903160	−	0.429303i	$-0.858759\pi$
$863$	−43.2036	+	11.5764i	−1.47067	+	0.394064i	−0.567508	+	0.823368i	$0.692093\pi$
$864$	4.96166	+	1.54336i	0.168799	+	0.0525061i
$865$	−5.39410	−	14.8636i	−0.183405	−	0.505376i
$866$			6.71325i			0.228126i
$867$	−10.2265	+	26.9789i	−0.347312	+	0.916253i
$868$	1.30970	−	13.1889i	0.0444541	−	0.447659i
$869$	−20.6912			−0.701901
$870$	−8.82826	+	14.8017i	−0.299306	+	0.501825i
$871$	18.5398	+	32.1119i	0.628198	+	1.08807i
$872$	−7.52869	+	7.52869i	−0.254954	+	0.254954i
$873$	−45.9577	−	22.9328i	−1.55543	−	0.776157i
$874$	14.2755	−	8.24194i	0.482874	−	0.278788i
$875$	−26.6140	−	0.0749318i	−0.899719	−	0.00253316i
$876$	−6.30795	−	14.0094i	−0.213126	−	0.473333i
$877$	28.6433	−	7.67496i	0.967217	−	0.259165i	0.259564	−	0.965726i	$-0.416421\pi$
$877$	28.6433	−	7.67496i	0.967217	−	0.259165i	0.707652	+	0.706561i	$0.249754\pi$
$878$	19.8020	−	5.30594i	0.668286	−	0.179067i
$879$	23.1583	+	2.33582i	0.781110	+	0.0787852i
$880$	−4.25780	+	9.10855i	−0.143530	+	0.307049i
$881$	2.80434	+	1.61908i	0.0944805	+	0.0545483i	0.546496	−	0.837462i	$-0.315961\pi$
$881$	2.80434	+	1.61908i	0.0944805	+	0.0545483i	−0.452015	+	0.892010i	$0.649295\pi$
$882$	3.33669	−	2.20691i	0.112352	−	0.0743105i
$883$	8.88594	−	8.88594i	0.299036	−	0.299036i	−0.541600	−	0.840636i	$-0.682181\pi$
$883$	8.88594	−	8.88594i	0.299036	−	0.299036i	0.840636	+	0.541600i	$0.182181\pi$
$884$	−2.60614			−0.0876538
$885$	13.5339	+	13.9237i	0.454936	+	0.468039i
$886$	3.67199	−	6.36008i	0.123363	−	0.213671i
$887$	4.44026	+	1.18976i	0.149089	+	0.0399484i	0.332592	−	0.943071i	$-0.392077\pi$
$887$	4.44026	+	1.18976i	0.149089	+	0.0399484i	−0.183502	+	0.983019i	$0.558744\pi$
$888$	5.94980	+	7.28466i	0.199662	+	0.244457i
$889$	−12.4886	−	7.21030i	−0.418855	−	0.241826i
$890$	9.44785	+	7.94281i	0.316693	+	0.266244i
$891$	40.1705	−	4.90513i	1.34576	−	0.164328i
$892$	−5.84733	+	21.8225i	−0.195783	+	0.730672i
$893$	−3.61815	+	13.5031i	−0.121077	+	0.451865i
$894$	−1.07542	+	10.6622i	−0.0359676	+	0.356598i
$895$	−14.7145	+	10.2826i	−0.491850	+	0.343710i
$896$	2.06152	−	1.19022i	0.0688706	−	0.0397625i
$897$	63.9093	+	24.2253i	2.13387	+	0.808858i
$898$	−15.6432	+	15.6432i	−0.522019	+	0.522019i
$899$	4.01628	+	24.4485i	0.133950	+	0.815404i
$900$	−7.12823	−	13.1980i	−0.237608	−	0.439935i
$901$	−7.40174			−0.246588
$902$	−34.3295	−	9.19856i	−1.14305	−	0.306278i
$903$	−7.53616	−	2.85663i	−0.250788	−	0.0950628i
$904$	−11.4434	−	6.60683i	−0.380601	−	0.219740i
$905$	−43.9282	−	20.5343i	−1.46022	−	0.682583i
$906$	−12.3373	−	8.88470i	−0.409879	−	0.295175i
$907$	33.3635	+	33.3635i	1.10782	+	1.10782i	0.993437	+	0.114381i	$0.0364884\pi$
$907$	33.3635	+	33.3635i	1.10782	+	1.10782i	0.114381	+	0.993437i	$0.463512\pi$
$908$	−18.5870	+	4.98038i	−0.616832	+	0.165280i
$909$	17.0552	+	51.0290i	0.565684	+	1.69253i
$910$	−18.1511	−	15.2596i	−0.601702	−	0.505851i
$911$	13.6326	−	7.87076i	0.451667	−	0.260770i	−0.256867	−	0.966447i	$-0.582690\pi$
$911$	13.6326	−	7.87076i	0.451667	−	0.260770i	0.708534	+	0.705677i	$0.249357\pi$
$912$	−2.03903	−	2.49650i	−0.0675191	−	0.0826673i
$913$	−63.7205	−	17.0739i	−2.10884	−	0.565062i
$914$	27.7342			0.917365
$915$	26.6955	−	6.74840i	0.882527	−	0.223095i
$916$	2.49839	+	4.32734i	0.0825492	+	0.142979i
$917$	−1.05752	−	3.94672i	−0.0349224	−	0.130332i
$918$	2.56995	+	1.62331i	0.0848209	+	0.0535774i
$919$	−3.48863	−	2.01416i	−0.115079	−	0.0664410i	0.441356	−	0.897332i	$-0.354498\pi$
$919$	−3.48863	−	2.01416i	−0.115079	−	0.0664410i	−0.556435	+	0.830891i	$0.687831\pi$
$920$	19.7321	−	1.70768i	0.650548	−	0.0563005i
$921$	35.0178	+	3.53200i	1.15387	+	0.116383i
$922$	19.4794	+	19.4794i	0.641519	+	0.641519i
$923$	−2.73282	+	10.1990i	−0.0899519	+	0.335705i
$924$	10.8342	−	15.0443i	0.356418	−	0.494922i
$925$	2.41720	−	27.0440i	0.0794771	−	0.889201i
$926$			20.9458i			0.688321i
$927$	4.08810	+	6.18093i	0.134271	+	0.203008i
$928$	−3.14658	+	3.14658i	−0.103292	+	0.103292i
$929$	34.3332			1.12644			0.563218	−	0.826308i	$-0.309563\pi$
$929$	34.3332			1.12644			0.563218	+	0.826308i	$0.309563\pi$
$930$	−20.0655	−	7.89772i	−0.657975	−	0.258976i
$931$	−2.48166			−0.0813333
$932$	8.70784	−	8.70784i	0.285235	−	0.285235i
$933$	23.8287	−	3.87667i	0.780116	−	0.126917i
$934$			40.4176i			1.32250i
$935$	−3.78500	+	4.50220i	−0.123783	+	0.147238i
$936$	2.66892	−	13.0958i	0.0872364	−	0.428050i
$937$	0.640066	−	2.38876i	0.0209101	−	0.0780374i	−0.954682	−	0.297626i	$-0.903805\pi$
$937$	0.640066	−	2.38876i	0.0209101	−	0.0780374i	0.975592	+	0.219589i	$0.0704717\pi$
$938$	−14.0097	−	14.0097i	−0.457434	−	0.457434i
$939$	1.88424	−	18.6812i	0.0614900	−	0.609638i
$940$	−10.8088	+	12.8569i	−0.352544	+	0.419346i
$941$	−12.5617	−	7.25247i	−0.409498	−	0.236424i	0.281076	−	0.959686i	$-0.409309\pi$
$941$	−12.5617	−	7.25247i	−0.409498	−	0.236424i	−0.690574	+	0.723262i	$0.742642\pi$
$942$	−3.05239	−	18.7621i	−0.0994521	−	0.611301i
$943$	18.1196	+	67.6234i	0.590057	+	2.20212i
$944$	2.50677	+	4.34185i	0.0815884	+	0.141315i
$945$	8.39410	+	26.3537i	0.273060	+	0.857285i
$946$	8.78950			0.285771
$947$	1.51394	+	0.405658i	0.0491963	+	0.0131821i	0.283333	−	0.959022i	$-0.408560\pi$
$947$	1.51394	+	0.405658i	0.0491963	+	0.0131821i	−0.234137	+	0.972204i	$0.575226\pi$
$948$	6.17288	−	5.04174i	0.200486	−	0.163748i
$949$	−34.2233	+	19.7589i	−1.11094	+	0.641400i
$950$	−0.828389	+	9.26814i	−0.0268765	+	0.300698i
$951$	−4.71617	+	46.7581i	−0.152932	+	1.51624i
$952$	1.34509	−	0.360415i	0.0435945	−	0.0116811i
$953$	−20.4773	−	20.4773i	−0.663326	−	0.663326i	0.292837	−	0.956162i	$-0.405401\pi$
$953$	−20.4773	−	20.4773i	−0.663326	−	0.663326i	−0.956162	+	0.292837i	$0.905401\pi$
$954$	7.58005	−	37.1937i	0.245413	−	1.20419i
$955$	−13.1635	+	28.1601i	−0.425960	+	0.911240i
$956$	−10.3112	−	5.95318i	−0.333488	−	0.192540i
$957$	−12.2841	+	32.4071i	−0.397090	+	1.04757i
$958$	−9.64473	−	2.58430i	−0.311607	−	0.0834949i
$959$	−20.5720			−0.664305
$960$	−0.949198	−	3.75487i	−0.0306352	−	0.121188i
$961$	−29.3708	+	9.91741i	−0.947446	+	0.319916i
$962$	17.1065	−	17.1065i	0.551536	−	0.551536i
$963$	−6.12334	+	0.372470i	−0.197322	+	0.0120027i
$964$	24.5556	−	14.1772i	0.790882	−	0.456616i
$965$	9.01294	−	50.8359i	0.290137	−	1.63647i
$966$	−36.3353	−	3.66489i	−1.16907	−	0.117916i
$967$	6.01606	−	22.4522i	0.193464	−	0.722016i	−0.799196	−	0.601071i	$-0.794741\pi$
$967$	6.01606	−	22.4522i	0.193464	−	0.722016i	0.992659	−	0.120945i	$-0.0385924\pi$
$968$	−2.38603	+	8.90478i	−0.0766899	+	0.286211i
$969$	−0.774183	−	1.71939i	−0.0248704	−	0.0552347i
$970$	3.30077	+	38.1402i	0.105981	+	1.22461i
$971$	−1.41143	−	0.814890i	−0.0452950	−	0.0261511i	0.477182	−	0.878805i	$-0.341658\pi$
$971$	−1.41143	−	0.814890i	−0.0452950	−	0.0261511i	−0.522476	+	0.852654i	$0.674992\pi$
$972$	−10.7890	+	11.2515i	−0.346057	+	0.360894i
$973$	−9.01855	−	2.41651i	−0.289121	−	0.0774698i
$974$	5.34645	−	9.26032i	0.171311	−	0.296720i
$975$	−31.9353	+	21.6486i	−1.02275	+	0.693310i
$976$	7.10958			0.227572
$977$	−5.06802	+	5.06802i	−0.162140	+	0.162140i	−0.783514	−	0.621374i	$-0.786575\pi$
$977$	−5.06802	+	5.06802i	−0.162140	+	0.162140i	0.621374	+	0.783514i	$0.286575\pi$
$978$	−7.84843	+	1.27685i	−0.250965	+	0.0408293i
$979$	21.4954	+	12.4104i	0.686996	+	0.396638i
$980$	−2.70124	−	1.26270i	−0.0862879	−	0.0403354i
$981$	−10.1251	−	30.2943i	−0.323269	−	0.967222i
$982$	−17.1941	+	4.60714i	−0.548685	+	0.147020i
$983$	−13.0012	+	3.48367i	−0.414675	+	0.111112i	−0.460124	−	0.887855i	$-0.652195\pi$
$983$	−13.0012	+	3.48367i	−0.414675	+	0.111112i	0.0454488	+	0.998967i	$0.485528\pi$
$984$	12.4830	−	5.62068i	0.397944	−	0.179181i
$985$	39.4088	−	14.3018i	1.25567	−	0.455692i
$986$	−2.25441	+	1.30159i	−0.0717952	+	0.0414510i
$987$	23.9871	−	19.5916i	0.763519	−	0.623609i
$988$	−5.86251	+	5.86251i	−0.186511	+	0.186511i
$989$	−8.65693	−	14.9942i	−0.275274	−	0.476789i
$990$	−18.7473	−	23.6302i	−0.595829	−	0.751019i
$991$	−3.21736			−0.102203			−0.0511015	−	0.998693i	$-0.516273\pi$
$991$	−3.21736			−0.102203			−0.0511015	+	0.998693i	$0.516273\pi$
$992$	−4.52313	−	3.24674i	−0.143610	−	0.103084i
$993$	−8.87019	−	3.36231i	−0.281487	−	0.106700i
$994$		−	5.64189i		−	0.178950i
$995$	2.39710	−	5.12802i	0.0759931	−	0.162569i
$996$	23.1703	−	10.4328i	0.734178	−	0.330576i
$997$	2.32977	−	0.624260i	0.0737846	−	0.0197705i	−0.221738	−	0.975106i	$-0.571173\pi$
$997$	2.32977	−	0.624260i	0.0737846	−	0.0197705i	0.295522	+	0.955336i	$0.404506\pi$
$998$	−3.49757	+	13.0531i	−0.110714	+	0.413189i
$999$	−27.5243	+	6.21365i	−0.870831	+	0.196591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.707.13	yes	256
3.2	odd	2	inner	930.2.bf.a.707.40	yes	256
5.3	odd	4	inner	930.2.bf.a.893.63	yes	256
15.8	even	4	inner	930.2.bf.a.893.8	yes	256
31.5	even	3	inner	930.2.bf.a.377.8	✓	256
93.5	odd	6	inner	930.2.bf.a.377.63	yes	256
155.98	odd	12	inner	930.2.bf.a.563.40	yes	256
465.98	even	12	inner	930.2.bf.a.563.13	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.8	✓	256	31.5	even	3	inner
930.2.bf.a.377.63	yes	256	93.5	odd	6	inner
930.2.bf.a.563.13	yes	256	465.98	even	12	inner
930.2.bf.a.563.40	yes	256	155.98	odd	12	inner
930.2.bf.a.707.13	yes	256	1.1	even	1	trivial
930.2.bf.a.707.40	yes	256	3.2	odd	2	inner
930.2.bf.a.893.8	yes	256	15.8	even	4	inner
930.2.bf.a.893.63	yes	256	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.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.278129 - 1.70957i) q^{3} -1.00000i q^{4} +(-0.192796 - 2.22774i) q^{5} +(1.40552 + 1.01218i) q^{6} +(-0.616104 + 2.29933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.84529 + 0.950965i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.278129 - 1.70957i) q^{3} -1.00000i q^{4} +(-0.192796 - 2.22774i) q^{5} +(1.40552 + 1.01218i) q^{6} +(-0.616104 + 2.29933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.84529 + 0.950965i) q^{9} +(1.71158 + 1.43892i) q^{10} +(3.89412 + 2.24827i) q^{11} +(-1.70957 + 0.278129i) q^{12} +(1.15304 + 4.30320i) q^{13} +(-1.19022 - 2.06152i) q^{14} +(-3.75487 + 0.949198i) q^{15} -1.00000 q^{16} +(-0.565058 - 0.151407i) q^{17} +(1.33949 - 2.68436i) q^{18} +(-1.61169 + 0.930509i) q^{19} +(-2.22774 + 0.192796i) q^{20} +(4.10223 + 0.413764i) q^{21} +(-4.34333 + 1.16379i) q^{22} +(6.26316 + 6.26316i) q^{23} +(1.01218 - 1.40552i) q^{24} +(-4.92566 + 0.858997i) q^{25} +(-3.85815 - 2.22750i) q^{26} +(2.41710 + 4.59974i) q^{27} +(2.29933 + 0.616104i) q^{28} -4.44994 q^{29} +(1.98391 - 3.32628i) q^{30} +(-0.902546 - 5.49413i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.76052 - 7.28260i) q^{33} +(0.506617 - 0.292495i) q^{34} +(5.24109 + 0.929219i) q^{35} +(0.950965 + 2.84529i) q^{36} +(-1.40548 + 5.24532i) q^{37} +(0.481667 - 1.79760i) q^{38} +(7.03595 - 3.16805i) q^{39} +(1.43892 - 1.71158i) q^{40} +(6.84503 + 3.95198i) q^{41} +(-3.19329 + 2.60814i) q^{42} +(-1.88812 - 0.505920i) q^{43} +(2.24827 - 3.89412i) q^{44} +(2.66706 + 6.15522i) q^{45} -8.85745 q^{46} +(5.31159 - 5.31159i) q^{47} +(0.278129 + 1.70957i) q^{48} +(1.15484 + 0.666749i) q^{49} +(2.87556 - 4.09037i) q^{50} +(-0.101682 + 1.00812i) q^{51} +(4.30320 - 1.15304i) q^{52} +(12.2216 - 3.27477i) q^{53} +(-4.96166 - 1.54336i) q^{54} +(4.25780 - 9.10855i) q^{55} +(-2.06152 + 1.19022i) q^{56} +(2.03903 + 2.49650i) q^{57} +(3.14658 - 3.14658i) q^{58} +(-2.50677 - 4.34185i) q^{59} +(0.949198 + 3.75487i) q^{60} -7.10958 q^{61} +(4.52313 + 3.24674i) q^{62} +(-0.433591 - 7.12815i) q^{63} +1.00000i q^{64} +(9.36412 - 3.39831i) q^{65} +(3.19759 + 7.10156i) q^{66} +(8.03955 - 2.15419i) q^{67} +(-0.151407 + 0.565058i) q^{68} +(8.96538 - 12.4493i) q^{69} +(-4.36307 + 3.04896i) q^{70} +(2.05257 + 1.18505i) q^{71} +(-2.68436 - 1.33949i) q^{72} +(2.29583 + 8.56816i) q^{73} +(-2.71518 - 4.70283i) q^{74} +(2.83849 + 8.18187i) q^{75} +(0.930509 + 1.61169i) q^{76} +(-7.56870 + 7.56870i) q^{77} +(-2.73502 + 7.21532i) q^{78} +(-3.98508 + 2.30079i) q^{79} +(0.192796 + 2.22774i) q^{80} +(7.19133 - 5.41154i) q^{81} +(-7.63464 + 2.04570i) q^{82} +(-14.1710 + 3.79711i) q^{83} +(0.413764 - 4.10223i) q^{84} +(-0.228354 + 1.28799i) q^{85} +(1.69284 - 0.977362i) q^{86} +(1.23766 + 7.60750i) q^{87} +(1.16379 + 4.34333i) q^{88} +5.51996 q^{89} +(-6.23830 - 2.46650i) q^{90} -10.6049 q^{91} +(6.26316 - 6.26316i) q^{92} +(-9.14159 + 3.07105i) q^{93} +7.51173i q^{94} +(2.38366 + 3.41103i) q^{95} +(-1.40552 - 1.01218i) q^{96} +(12.1061 + 12.1061i) q^{97} +(-1.28806 + 0.345135i) q^{98} +(-13.2179 - 2.69381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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