LMFDB - Embedded newform 930.2.bf.a.377.8

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			377.8
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.34147 + 1.09565i) q^{3} -1.00000i q^{4} +(2.02568 + 0.946905i) q^{5} +(0.173818 - 1.72331i) q^{6} +(2.29933 - 0.616104i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.599084 - 2.93957i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.34147 + 1.09565i) q^{3} -1.00000i q^{4} +(2.02568 + 0.946905i) q^{5} +(0.173818 - 1.72331i) q^{6} +(2.29933 - 0.616104i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.599084 - 2.93957i) q^{9} +(-2.10193 + 0.762808i) q^{10} +(-3.89412 + 2.24827i) q^{11} +(1.09565 + 1.34147i) q^{12} +(-4.30320 - 1.15304i) q^{13} +(-1.19022 + 2.06152i) q^{14} +(-3.75487 + 0.949198i) q^{15} -1.00000 q^{16} +(0.151407 + 0.565058i) q^{17} +(1.65498 + 2.50221i) q^{18} +(1.61169 + 0.930509i) q^{19} +(0.946905 - 2.02568i) q^{20} +(-2.40945 + 3.34575i) q^{21} +(1.16379 - 4.34333i) q^{22} +(6.26316 + 6.26316i) q^{23} +(-1.72331 - 0.173818i) q^{24} +(3.20674 + 3.83625i) q^{25} +(3.85815 - 2.22750i) q^{26} +(2.41710 + 4.59974i) q^{27} +(-0.616104 - 2.29933i) 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} +(-2.93957 - 0.599084i) q^{36} +(5.24532 - 1.40548i) q^{37} +(-1.79760 + 0.481667i) q^{38} +(7.03595 - 3.16805i) q^{39} +(0.762808 + 2.10193i) q^{40} +(-6.84503 + 3.95198i) q^{41} +(-0.662070 - 4.06954i) q^{42} +(0.505920 + 1.88812i) q^{43} +(2.24827 + 3.89412i) q^{44} +(3.99705 - 5.38736i) q^{45} -8.85745 q^{46} +(5.31159 - 5.31159i) q^{47} +(1.34147 - 1.09565i) q^{48} +(-1.15484 + 0.666749i) q^{49} +(-4.98015 - 0.445127i) q^{50} +(-0.822215 - 0.592119i) q^{51} +(-1.15304 + 4.30320i) q^{52} +(-3.27477 + 12.2216i) q^{53} +(-4.96166 - 1.54336i) q^{54} +(-10.0171 + 0.866914i) q^{55} +(2.06152 + 1.19022i) q^{56} +(-3.18155 + 0.517603i) q^{57} +(3.14658 - 3.14658i) q^{58} +(-2.50677 + 4.34185i) q^{59} +(0.949198 + 3.75487i) q^{60} -7.10958 q^{61} +(-3.24674 - 4.52313i) q^{62} +(-0.433591 - 7.12815i) q^{63} +1.00000i q^{64} +(-7.62508 - 6.41041i) q^{65} +(3.19759 + 7.10156i) q^{66} +(-2.15419 + 8.03955i) q^{67} +(0.565058 - 0.151407i) q^{68} +(-15.2641 - 1.53959i) q^{69} +(-4.36307 + 3.04896i) q^{70} +(-2.05257 + 1.18505i) q^{71} +(2.50221 - 1.65498i) q^{72} +(-8.56816 - 2.29583i) q^{73} +(-2.71518 + 4.70283i) q^{74} +(-8.50495 - 1.63273i) 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} +(-2.02568 - 0.946905i) q^{80} +(-8.28220 - 3.52210i) q^{81} +(2.04570 - 7.63464i) q^{82} +(3.79711 - 14.1710i) q^{83} +(3.34575 + 2.40945i) q^{84} +(-0.228354 + 1.28799i) q^{85} +(-1.69284 - 0.977362i) q^{86} +(5.96946 - 4.87559i) q^{87} +(-4.34333 - 1.16379i) q^{88} +5.51996 q^{89} +(0.983096 + 6.63578i) q^{90} -10.6049 q^{91} +(6.26316 - 6.26316i) q^{92} +(-4.80892 - 8.35908i) q^{93} +7.51173i q^{94} +(2.38366 + 3.41103i) q^{95} +(-0.173818 + 1.72331i) q^{96} +(12.1061 + 12.1061i) q^{97} +(0.345135 - 1.28806i) q^{98} +(4.27606 + 12.7940i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.34147	+	1.09565i	−0.774498	+	0.632576i
$3$	−1.34147	+	1.09565i	−0.774498	+	0.632576i
$4$		−	1.00000i		−	0.500000i
$5$	2.02568	+	0.946905i	0.905911	+	0.423469i
$5$	2.02568	+	0.946905i	0.905911	+	0.423469i
$6$	0.173818	−	1.72331i	0.0709610	−	0.703537i
$7$	2.29933	−	0.616104i	0.869065	−	0.232865i	0.203382	−	0.979100i	$-0.434807\pi$
$7$	2.29933	−	0.616104i	0.869065	−	0.232865i	0.665683	+	0.746234i	$0.268140\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.599084	−	2.93957i	0.199695	−	0.979858i
$10$	−2.10193	+	0.762808i	−0.664690	+	0.241221i
$11$	−3.89412	+	2.24827i	−1.17412	+	0.677880i	−0.954647	−	0.297739i	$-0.903768\pi$
$11$	−3.89412	+	2.24827i	−1.17412	+	0.677880i	−0.219474	+	0.975618i	$0.570434\pi$
$12$	1.09565	+	1.34147i	0.316288	+	0.387249i
$13$	−4.30320	−	1.15304i	−1.19349	−	0.319796i	−0.393228	−	0.919441i	$-0.628642\pi$
$13$	−4.30320	−	1.15304i	−1.19349	−	0.319796i	−0.800266	+	0.599645i	$0.795308\pi$
$14$	−1.19022	+	2.06152i	−0.318100	+	0.550965i
$15$	−3.75487	+	0.949198i	−0.969502	+	0.245082i
$16$	−1.00000			−0.250000
$17$	0.151407	+	0.565058i	0.0367215	+	0.137047i	0.981853	−	0.189644i	$-0.0607333\pi$
$17$	0.151407	+	0.565058i	0.0367215	+	0.137047i	−0.945131	+	0.326690i	$0.894067\pi$
$18$	1.65498	+	2.50221i	0.390082	+	0.589776i
$19$	1.61169	+	0.930509i	0.369747	+	0.213473i	0.673348	−	0.739326i	$-0.264856\pi$
$19$	1.61169	+	0.930509i	0.369747	+	0.213473i	−0.303601	+	0.952799i	$0.598189\pi$
$20$	0.946905	−	2.02568i	0.211734	−	0.452955i
$21$	−2.40945	+	3.34575i	−0.525784	+	0.730104i
$22$	1.16379	−	4.34333i	0.248121	−	0.926001i
$23$	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	$0.375354\pi$
$24$	−1.72331	−	0.173818i	−0.351769	−	0.0354805i
$25$	3.20674	+	3.83625i	0.641349	+	0.767250i
$26$	3.85815	−	2.22750i	0.756645	−	0.436849i
$27$	2.41710	+	4.59974i	0.465172	+	0.885220i
$28$	−0.616104	−	2.29933i	−0.116433	−	0.434532i
$29$	−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
$36$	−2.93957	−	0.599084i	−0.489929	−	0.0998473i
$37$	5.24532	−	1.40548i	0.862326	−	0.231060i	0.199560	−	0.979886i	$-0.436049\pi$
$37$	5.24532	−	1.40548i	0.862326	−	0.231060i	0.662766	+	0.748826i	$0.269382\pi$
$38$	−1.79760	+	0.481667i	−0.291610	+	0.0781366i
$39$	7.03595	−	3.16805i	1.12665	−	0.507294i
$40$	0.762808	+	2.10193i	0.120611	+	0.332345i
$41$	−6.84503	+	3.95198i	−1.06901	+	0.617195i	−0.927912	−	0.372800i	$-0.878398\pi$
$41$	−6.84503	+	3.95198i	−1.06901	+	0.617195i	−0.141102	+	0.989995i	$0.545065\pi$
$42$	−0.662070	−	4.06954i	−0.102160	−	0.627944i
$43$	0.505920	+	1.88812i	0.0771520	+	0.287935i	0.993713	−	0.111960i	$-0.0357130\pi$
$43$	0.505920	+	1.88812i	0.0771520	+	0.287935i	−0.916561	+	0.399896i	$0.869046\pi$
$44$	2.24827	+	3.89412i	0.338940	+	0.587061i
$45$	3.99705	−	5.38736i	0.595845	−	0.803100i
$46$	−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	$0.0654468\pi$
$48$	1.34147	−	1.09565i	0.193625	−	0.158144i
$49$	−1.15484	+	0.666749i	−0.164978	+	0.0952499i
$50$	−4.98015	−	0.445127i	−0.704299	−	0.0629505i
$51$	−0.822215	−	0.592119i	−0.115133	−	0.0829132i
$52$	−1.15304	+	4.30320i	−0.159898	+	0.596747i
$53$	−3.27477	+	12.2216i	−0.449824	+	1.67877i	0.253050	+	0.967453i	$0.418566\pi$
$53$	−3.27477	+	12.2216i	−0.449824	+	1.67877i	−0.702874	+	0.711314i	$0.748100\pi$
$54$	−4.96166	−	1.54336i	−0.675196	−	0.210024i
$55$	−10.0171	+	0.866914i	−1.35071	+	0.116895i
$56$	2.06152	+	1.19022i	0.275483	+	0.159050i
$57$	−3.18155	+	0.517603i	−0.421406	+	0.0685582i
$58$	3.14658	−	3.14658i	0.413166	−	0.413166i
$59$	−2.50677	+	4.34185i	−0.326354	+	0.565261i	−0.981785	−	0.189993i	$-0.939153\pi$
$59$	−2.50677	+	4.34185i	−0.326354	+	0.565261i	0.655432	+	0.755254i	$0.272487\pi$
$60$	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	$0.650412\pi$
$62$	−3.24674	−	4.52313i	−0.412336	−	0.574438i
$63$	−0.433591	−	7.12815i	−0.0546273	−	0.898062i
$64$			1.00000i			0.125000i
$65$	−7.62508	−	6.41041i	−0.945775	−	0.795113i
$66$	3.19759	+	7.10156i	0.393597	+	0.874141i
$67$	−2.15419	+	8.03955i	−0.263176	+	0.982187i	0.700181	+	0.713965i	$0.253103\pi$
$67$	−2.15419	+	8.03955i	−0.263176	+	0.982187i	−0.963357	+	0.268222i	$0.913564\pi$
$68$	0.565058	−	0.151407i	0.0685233	−	0.0183608i
$69$	−15.2641	−	1.53959i	−1.83758	−	0.185344i
$70$	−4.36307	+	3.04896i	−0.521487	+	0.364420i
$71$	−2.05257	+	1.18505i	−0.243595	+	0.140640i	−0.616828	−	0.787098i	$-0.711583\pi$
$71$	−2.05257	+	1.18505i	−0.243595	+	0.140640i	0.373233	+	0.927738i	$0.378249\pi$
$72$	2.50221	−	1.65498i	0.294888	−	0.195041i
$73$	−8.56816	−	2.29583i	−1.00283	−	0.268707i	−0.280198	−	0.959942i	$-0.590400\pi$
$73$	−8.56816	−	2.29583i	−1.00283	−	0.268707i	−0.722630	+	0.691236i	$0.757067\pi$
$74$	−2.71518	+	4.70283i	−0.315633	+	0.546693i
$75$	−8.50495	−	1.63273i	−0.982067	−	0.188531i
$76$	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	$-0.249987\pi$
$79$	3.98508	+	2.30079i	0.448357	+	0.258859i	−0.258779	+	0.965937i	$0.583320\pi$
$80$	−2.02568	−	0.946905i	−0.226478	−	0.105867i
$81$	−8.28220	−	3.52210i	−0.920244	−	0.391345i
$82$	2.04570	−	7.63464i	0.225909	−	0.843105i
$83$	3.79711	−	14.1710i	0.416787	−	1.55547i	−0.364443	−	0.931226i	$-0.618741\pi$
$83$	3.79711	−	14.1710i	0.416787	−	1.55547i	0.781230	−	0.624243i	$-0.214593\pi$
$84$	3.34575	+	2.40945i	0.365052	+	0.262892i
$85$	−0.228354	+	1.28799i	−0.0247685	+	0.139702i
$86$	−1.69284	−	0.977362i	−0.182544	−	0.105392i
$87$	5.96946	−	4.87559i	0.639993	−	0.522718i
$88$	−4.34333	−	1.16379i	−0.463000	−	0.124061i
$89$	5.51996			0.585115			0.292558	−	0.956248i	$-0.405494\pi$
$89$	5.51996			0.585115			0.292558	+	0.956248i	$0.405494\pi$
$90$	0.983096	+	6.63578i	0.103627	+	0.699472i
$91$	−10.6049			−1.11169
$92$	6.26316	−	6.26316i	0.652980	−	0.652980i
$93$	−4.80892	−	8.35908i	−0.498662	−	0.866797i
$94$			7.51173i			0.774776i
$95$	2.38366	+	3.41103i	0.244558	+	0.349964i
$96$	−0.173818	+	1.72331i	−0.0177402	+	0.175884i
$97$	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	$0.414657\pi$
$98$	0.345135	−	1.28806i	0.0348639	−	0.130114i
$99$	4.27606	+	12.7940i	0.429760	+	1.28584i
$100$	3.83625	−	3.20674i	0.383625	−	0.320674i
$101$		−	17.9346i		−	1.78456i	−0.451485	−	0.892278i	$-0.649106\pi$
$101$		−	17.9346i		−	1.78456i	0.451485	−	0.892278i	$-0.350894\pi$
$102$	1.00009	−	0.162703i	0.0990232	−	0.0161100i
$103$	2.38602	+	0.639332i	0.235101	+	0.0629952i	0.374446	−	0.927249i	$-0.377833\pi$
$103$	2.38602	+	0.639332i	0.235101	+	0.0629952i	−0.139345	+	0.990244i	$0.544500\pi$
$104$	−2.22750	−	3.85815i	−0.218424	−	0.378322i
$105$	−8.04887	+	4.49591i	−0.785489	+	0.438756i
$106$	−6.32637	−	10.9576i	−0.614471	−	1.06430i
$107$	−0.529256	−	1.97521i	−0.0511651	−	0.190951i	0.935613	−	0.353027i	$-0.114848\pi$
$107$	−0.529256	−	1.97521i	−0.0511651	−	0.190951i	−0.986778	+	0.162076i	$0.948181\pi$
$108$	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	$0.829680\pi$
$110$	6.47018	−	7.69618i	0.616908	−	0.733802i
$111$	−5.49653	+	7.63247i	−0.521707	+	0.724442i
$112$	−2.29933	+	0.616104i	−0.217266	+	0.0582163i
$113$	3.41995	−	12.7634i	0.321722	−	1.20068i	−0.595845	−	0.803100i	$-0.703183\pi$
$113$	3.41995	−	12.7634i	0.321722	−	1.20068i	0.917567	−	0.397582i	$-0.130151\pi$
$114$	1.88369	−	2.61569i	0.176424	−	0.244982i
$115$	6.75654	+	18.6178i	0.630050	+	1.73612i
$116$			4.44994i			0.413166i
$117$	−5.96743	+	11.9588i	−0.551689	+	1.10559i
$118$	−1.29760	−	4.84271i	−0.119454	−	0.445807i
$119$	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
$127$	5.85153	−	1.56791i	0.519240	−	0.139130i	0.0103248	−	0.999947i	$-0.496713\pi$
$127$	5.85153	−	1.56791i	0.519240	−	0.139130i	0.508915	+	0.860817i	$0.330047\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−2.74740	−	1.97854i	−0.241895	−	0.174201i
$130$	9.92459	−	0.858905i	0.870444	−	0.0753309i
$131$	1.48650	+	0.858234i	0.129876	+	0.0749842i	0.563531	−	0.826095i	$-0.309443\pi$
$131$	1.48650	+	0.858234i	0.129876	+	0.0749842i	−0.433654	+	0.901079i	$0.642776\pi$
$132$	−7.28260	−	2.76052i	−0.633869	−	0.240272i
$133$	4.27909	+	1.14658i	0.371044	+	0.0994210i
$134$	−4.16158	−	7.20806i	−0.359505	−	0.622682i
$135$	0.540758	+	11.6064i	0.0465411	+	0.998916i
$136$	−0.292495	+	0.506617i	−0.0250813	+	0.0434420i
$137$	−8.34763	−	2.23674i	−0.713186	−	0.191098i	−0.116057	−	0.993243i	$-0.537025\pi$
$137$	−8.34763	−	2.23674i	−0.713186	−	0.191098i	−0.597129	+	0.802145i	$0.703692\pi$
$138$	11.8820	−	9.70470i	1.01146	−	0.826119i
$139$			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
$141$	−1.30567	+	12.9450i	−0.109958	+	1.09017i
$142$	0.613427	−	2.28934i	0.0514777	−	0.192117i
$143$	19.3495	−	5.18469i	1.61809	−	0.433566i
$144$	−0.599084	+	2.93957i	−0.0499237	+	0.244965i
$145$	−9.01414	−	4.21367i	−0.748584	−	0.349926i
$146$	7.68200	−	4.43521i	0.635767	−	0.367060i
$147$	0.818662	−	2.15973i	0.0675221	−	0.178132i
$148$	−1.40548	−	5.24532i	−0.115530	−	0.431163i
$149$	3.09353	−	5.35816i	0.253432	−	0.438957i	−0.711036	−	0.703155i	$-0.751774\pi$
$149$	3.09353	−	5.35816i	0.253432	−	0.438957i	0.964469	+	0.264198i	$0.0851072\pi$
$150$	7.16842	−	4.85939i	0.585299	−	0.396768i
$151$	−8.77775			−0.714323			−0.357162	−	0.934043i	$-0.616255\pi$
$151$	−8.77775			−0.714323			−0.357162	+	0.934043i	$0.616255\pi$
$152$	0.481667	+	1.79760i	0.0390683	+	0.145805i
$153$	1.75173	−	0.106554i	0.141619	−	0.00861441i
$154$		−	10.7038i		−	0.862534i
$155$	−7.03068	+	10.2747i	−0.564718	+	0.825284i
$156$	−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	$0.894291\pi$
$158$	−4.44478	+	1.19098i	−0.353608	+	0.0947490i
$159$	−8.99765	−	19.9829i	−0.713560	−	1.58475i
$160$	2.10193	−	0.762808i	0.166172	−	0.0603053i
$161$	18.2598	+	10.5423i	1.43908	+	0.830851i
$162$	8.34690	−	3.36589i	0.655794	−	0.264450i
$163$	−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
$165$	12.4879	−	12.1383i	0.972178	−	0.944962i
$166$	7.33545	+	12.7054i	0.569341	+	0.986128i
$167$	0.605183	+	2.25858i	0.0468305	+	0.174774i	0.985380	−	0.170371i	$-0.0544965\pi$
$167$	0.605183	+	2.25858i	0.0468305	+	0.174774i	−0.938550	+	0.345145i	$0.887830\pi$
$168$	−4.06954	+	0.662070i	−0.313972	+	0.0510798i
$169$	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
$172$	1.88812	−	0.505920i	0.143968	−	0.0385760i
$173$	−1.83021	+	6.83042i	−0.139148	+	0.519307i	0.860798	+	0.508946i	$0.169965\pi$
$173$	−1.83021	+	6.83042i	−0.139148	+	0.519307i	−0.999946	+	0.0103612i	$0.996702\pi$
$174$	−0.773480	+	7.66861i	−0.0586374	+	0.581356i
$175$	9.73689	+	6.84511i	0.736039	+	0.517442i
$176$	3.89412	−	2.24827i	0.293530	−	0.169470i
$177$	−1.39441	−	8.57102i	−0.104810	−	0.644237i
$178$	−3.90320	+	3.90320i	−0.292558	+	0.292558i
$179$	−4.01402	+	6.95249i	−0.300022	+	0.519654i	−0.976141	−	0.217139i	$-0.930327\pi$
$179$	−4.01402	+	6.95249i	−0.300022	+	0.519654i	0.676119	+	0.736793i	$0.263661\pi$
$180$	−5.38736	−	3.99705i	−0.401550	−	0.297922i
$181$	10.8428	+	18.7804i	0.805943	+	1.39593i	0.915653	+	0.401970i	$0.131674\pi$
$181$	10.8428	+	18.7804i	0.805943	+	1.39593i	−0.109710	+	0.993964i	$0.534992\pi$
$182$	7.49878	−	7.49878i	0.555846	−	0.555846i
$183$	9.53729	−	7.78964i	0.705017	−	0.575827i
$184$			8.85745i			0.652980i
$185$	11.9562	+	2.11977i	0.879037	+	0.155849i
$186$	9.31119	+	2.51034i	0.682729	+	0.184067i
$187$	−1.86000	−	1.86000i	−0.136017	−	0.136017i
$188$	−5.31159	−	5.31159i	−0.387388	−	0.387388i
$189$	8.39163	+	9.08713i	0.610402	+	0.660992i
$190$	−4.09746	−	0.726458i	−0.297261	−	0.0527028i
$191$	12.0391	−	6.95079i	0.871120	−	0.502941i	0.00339985	−	0.999994i	$-0.498918\pi$
$191$	12.0391	−	6.95079i	0.871120	−	0.502941i	0.867720	+	0.497053i	$0.165584\pi$
$192$	−1.09565	−	1.34147i	−0.0790720	−	0.0968123i
$193$	−5.97588	−	22.3023i	−0.430154	−	1.60536i	−0.752405	−	0.658701i	$-0.771106\pi$
$193$	−5.97588	−	22.3023i	−0.430154	−	1.60536i	0.322251	−	0.946654i	$-0.395560\pi$
$194$	−17.1206			−1.22918
$195$	17.2524	+	0.244918i	1.23547	+	0.0175389i
$196$	0.666749	+	1.15484i	0.0476250	+	0.0824889i
$197$	−18.1100	−	4.85255i	−1.29028	−	0.345730i	−0.452515	−	0.891757i	$-0.649473\pi$
$197$	−18.1100	−	4.85255i	−1.29028	−	0.345730i	−0.837768	+	0.546027i	$0.816140\pi$
$198$	−12.0703	−	6.02307i	−0.857801	−	0.428041i
$199$	−2.19235	+	1.26575i	−0.155412	+	0.0897269i	−0.575689	−	0.817669i	$-0.695266\pi$
$199$	−2.19235	+	1.26575i	−0.155412	+	0.0897269i	0.420277	+	0.907396i	$0.361933\pi$
$200$	−0.445127	+	4.98015i	−0.0314752	+	0.352150i
$201$	−5.91878	−	13.1451i	−0.417479	−	0.927181i
$202$	12.6817	+	12.6817i	0.892278	+	0.892278i
$203$	−10.2319	+	2.74162i	−0.718137	+	0.192424i
$204$	−0.592119	+	0.822215i	−0.0414566	+	0.0575666i
$205$	−17.6080	+	1.52385i	−1.22979	+	0.106430i
$206$	−2.13924	+	1.23509i	−0.149048	+	0.0860531i
$207$	22.1632	−	14.6589i	1.54045	−	1.01886i
$208$	4.30320	+	1.15304i	0.298373	+	0.0799489i
$209$	−8.36814			−0.578837
$210$	2.51233	−	8.87050i	0.173367	−	0.612123i
$211$	3.49428	−	6.05227i	0.240556	−	0.416656i	−0.720317	−	0.693645i	$-0.756004\pi$
$211$	3.49428	−	6.05227i	0.240556	−	0.416656i	0.960873	+	0.276990i	$0.0893368\pi$
$212$	12.2216	+	3.27477i	0.839384	+	0.224912i
$213$	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
$217$	1.30970	+	13.1889i	0.0889081	+	0.895319i
$218$	−7.52869	−	7.52869i	−0.509907	−	0.509907i
$219$	14.0094	−	6.30795i	0.946665	−	0.426252i
$220$	0.866914	+	10.0171i	0.0584473	+	0.675355i
$221$		−	2.60614i		−	0.175308i
$222$	−1.51034	−	9.28360i	−0.101368	−	0.623075i
$223$	5.84733	+	21.8225i	0.391566	+	1.46134i	0.827551	+	0.561390i	$0.189733\pi$
$223$	5.84733	+	21.8225i	0.391566	+	1.46134i	−0.435985	+	0.899954i	$0.643600\pi$
$224$	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
$227$	18.5870	+	4.98038i	1.23366	+	0.330559i	0.816005	−	0.578045i	$-0.196184\pi$
$227$	18.5870	+	4.98038i	1.23366	+	0.330559i	0.417659	+	0.908604i	$0.362851\pi$
$228$	0.517603	+	3.18155i	0.0342791	+	0.210703i
$229$	4.32734	+	2.49839i	0.285959	+	0.165098i	0.636118	−	0.771592i	$-0.280539\pi$
$229$	4.32734	+	2.49839i	0.285959	+	0.165098i	−0.350159	+	0.936690i	$0.613873\pi$
$230$	−17.9423	−	8.38716i	−1.18308	−	0.553033i
$231$	1.86051	−	18.4459i	0.122412	−	1.21365i
$232$	−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	$0.617834\pi$
$234$	−4.23655	−	12.6758i	−0.276952	−	0.828641i
$235$	15.7892	−	5.73001i	1.02997	−	0.373784i
$236$	4.34185	+	2.50677i	0.282631	+	0.163177i
$237$	−7.86674	+	1.27983i	−0.511000	+	0.0831341i
$238$	−1.34509	−	0.360415i	−0.0871890	−	0.0233622i
$239$	5.95318	+	10.3112i	0.385079	+	0.666977i	0.991780	−	0.127953i	$-0.0408408\pi$
$239$	5.95318	+	10.3112i	0.385079	+	0.666977i	−0.606701	+	0.794930i	$0.707507\pi$
$240$	3.75487	−	0.949198i	0.242376	−	0.0612705i
$241$	14.1772	−	24.5556i	0.913231	−	1.58176i	0.103761	−	0.994602i	$-0.466912\pi$
$241$	14.1772	−	24.5556i	0.913231	−	1.58176i	0.809470	−	0.587161i	$-0.199754\pi$
$242$	2.38603	+	8.90478i	0.153380	+	0.572421i
$243$	14.9693	−	4.34963i	0.960283	−	0.279029i
$244$			7.10958i			0.455144i
$245$	−2.97069	+	0.257093i	−0.189790	+	0.0164250i
$246$	5.62068	+	12.4830i	0.358362	+	0.795888i
$247$	−5.86251	−	5.86251i	−0.373022	−	0.373022i
$248$	−4.52313	+	3.24674i	−0.287219	+	0.206168i
$249$	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	$-0.551147\pi$
$251$	−17.3458	−	10.0146i	−1.09486	−	0.632116i	−0.934865	+	0.355002i	$0.884480\pi$
$252$	−7.12815	+	0.433591i	−0.449031	+	0.0273136i
$253$	−38.4708	−	10.3082i	−2.41864	−	0.648073i
$254$	−3.02898	+	5.24634i	−0.190055	+	0.329185i
$255$	−1.10486	−	1.97800i	−0.0691893	−	0.123867i
$256$	1.00000			0.0625000
$257$	27.9169	+	7.48030i	1.74141	+	0.466608i	0.982759	−	0.184893i	$-0.0591937\pi$
$257$	27.9169	+	7.48030i	1.74141	+	0.466608i	0.758648	+	0.651501i	$0.225860\pi$
$258$	3.34174	−	0.543666i	0.208048	−	0.0338472i
$259$	11.1948	−	6.46333i	0.695612	−	0.401612i
$260$	−6.41041	+	7.62508i	−0.397557	+	0.472888i
$261$	−2.66589	+	13.0809i	−0.165014	+	0.809689i
$262$	−1.65798	+	0.444254i	−0.102430	+	0.0274461i
$263$	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
$265$	−18.2063	+	21.6562i	−1.11841	+	1.33033i
$266$	−3.83653	+	2.21502i	−0.235233	+	0.135812i
$267$	−7.40487	+	6.04797i	−0.453171	+	0.370130i
$268$	8.03955	+	2.15419i	0.491093	+	0.131588i
$269$	−8.25970	−	14.3062i	−0.503603	−	0.872266i	−0.999991	−	0.00416518i	$-0.998674\pi$
$269$	−8.25970	−	14.3062i	−0.503603	−	0.872266i	0.496389	−	0.868100i	$-0.334659\pi$
$270$	−8.58931	−	7.82456i	−0.522729	−	0.476188i
$271$	2.15831			0.131108			0.0655540	−	0.997849i	$-0.479119\pi$
$271$	2.15831			0.131108			0.0655540	+	0.997849i	$0.479119\pi$
$272$	−0.151407	−	0.565058i	−0.00918038	−	0.0342617i
$273$	14.2261	−	11.6193i	0.861004	−	0.703230i
$274$	7.48428	−	4.32105i	0.452142	−	0.261044i
$275$	−21.1124	−	7.72918i	−1.27312	−	0.466087i
$276$	−1.53959	+	15.2641i	−0.0926722	+	0.918792i
$277$	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
$279$	15.6097	+	5.94454i	0.934528	+	0.355891i
$280$	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	$-0.353624\pi$
$282$	−8.23026	−	10.0768i	−0.490105	−	0.600062i
$283$	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
$285$	−6.93491	−	1.96412i	−0.410789	−	0.116345i
$286$	−10.0161	+	17.3483i	−0.592262	+	1.02583i
$287$	−13.3042	+	13.3042i	−0.785319	+	0.785319i
$288$	−1.65498	−	2.50221i	−0.0975204	−	0.147444i
$289$	14.4261	−	8.32889i	0.848592	−	0.489935i
$290$	9.35347	−	3.39445i	0.549255	−	0.199329i
$291$	−29.5040	−	2.97586i	−1.72955	−	0.174448i
$292$	−2.29583	+	8.56816i	−0.134353	+	0.501414i
$293$	12.9804	−	3.47808i	0.758322	−	0.203192i	0.141116	−	0.989993i	$-0.454931\pi$
$293$	12.9804	−	3.47808i	0.758322	−	0.203192i	0.617207	+	0.786801i	$0.288264\pi$
$294$	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
$297$	−19.7540	−	12.4776i	−1.14624	−	0.724026i
$298$	1.60133	+	5.97625i	0.0927626	+	0.346195i
$299$	−19.7300	−	34.1733i	−1.14101	−	1.97630i
$300$	−1.63273	+	8.50495i	−0.0942657	+	0.491034i
$301$	2.32655	+	4.02971i	0.134100	+	0.232268i
$302$	6.20681	−	6.20681i	0.357162	−	0.357162i
$303$	19.6501	+	24.0587i	1.12887	+	1.38214i
$304$	−1.61169	−	0.930509i	−0.0924366	−	0.0533683i
$305$	−14.4017	−	6.73210i	−0.824641	−	0.385479i
$306$	−1.16332	+	1.31401i	−0.0665025	+	0.0751169i
$307$	19.6277	−	5.25923i	1.12021	−	0.300160i	0.349243	−	0.937032i	$-0.386439\pi$
$307$	19.6277	−	5.25923i	1.12021	−	0.300160i	0.770969	+	0.636872i	$0.219772\pi$
$308$	7.56870	+	7.56870i	0.431267	+	0.431267i
$309$	−3.90126	+	1.75661i	−0.221935	+	0.0999298i
$310$	−2.29387	−	12.2368i	−0.130283	−	0.695001i
$311$			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
$313$	−2.80568	−	10.4709i	−0.158587	−	0.591853i	−0.998771	−	0.0495531i	$-0.984220\pi$
$313$	−2.80568	−	10.4709i	−0.158587	−	0.591853i	0.840185	−	0.542300i	$-0.182446\pi$
$314$	10.9747			0.619338
$315$	5.87136	−	14.8499i	0.330814	−	0.836697i
$316$	2.30079	−	3.98508i	0.129430	−	0.224178i
$317$	7.02249	+	26.2083i	0.394422	+	1.47200i	0.822762	+	0.568386i	$0.192432\pi$
$317$	7.02249	+	26.2083i	0.394422	+	1.47200i	−0.428340	+	0.903618i	$0.640901\pi$
$318$	20.4924	+	7.76777i	1.14916	+	0.435595i
$319$	17.3286	−	10.0047i	0.970215	−	0.560154i
$320$	−0.946905	+	2.02568i	−0.0529336	+	0.113239i
$321$	2.87413	+	2.06980i	0.160418	+	0.115525i
$322$	−20.3662	+	5.45711i	−1.13496	+	0.304113i
$323$	−0.281771	+	1.05158i	−0.0156781	+	0.0585116i
$324$	−3.52210	+	8.28220i	−0.195672	+	0.460122i
$325$	−9.37592	−	20.2057i	−0.520082	−	1.12081i
$326$		−	4.59087i		−	0.254265i
$327$	−11.6656	−	14.2829i	−0.645110	−	0.789844i
$328$	−7.63464	−	2.04570i	−0.421552	−	0.112955i
$329$	8.94062	−	15.4856i	0.492912	−	0.853749i
$330$	−0.247201	+	17.4133i	−0.0136080	+	0.958570i
$331$	2.73839	+	4.74303i	0.150516	+	0.260701i	0.931417	−	0.363953i	$-0.118573\pi$
$331$	2.73839	+	4.74303i	0.150516	+	0.260701i	−0.780902	+	0.624654i	$0.785240\pi$
$332$	−14.1710	−	3.79711i	−0.777734	−	0.208393i
$333$	−0.989124	−	16.2610i	−0.0542037	−	0.891099i
$334$	−2.02498	−	1.16912i	−0.110802	−	0.0639717i
$335$	−11.9764	+	14.2457i	−0.654340	+	0.778327i
$336$	2.40945	−	3.34575i	0.131446	−	0.182526i
$337$	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	$0.743364\pi$
$338$	−6.61374	+	1.77215i	−0.359740	+	0.0963921i
$339$	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
$347$	2.03903	+	7.60976i	0.109461	+	0.408513i	0.998813	−	0.0487094i	$-0.0155108\pi$
$347$	2.03903	+	7.60976i	0.109461	+	0.408513i	−0.889352	+	0.457223i	$0.848844\pi$
$348$	−4.87559	−	5.96946i	−0.261359	−	0.319997i
$349$		−	16.2739i		−	0.871121i	−0.900160	−	0.435560i	$-0.856550\pi$
$349$		−	16.2739i		−	0.871121i	0.900160	−	0.435560i	$-0.143450\pi$
$350$	−11.7252	+	2.04479i	−0.626741	+	0.109299i
$351$	−5.09760	−	22.5806i	−0.272090	−	1.20526i
$352$	−1.16379	+	4.34333i	−0.0620303	+	0.231500i
$353$	16.4514	−	4.40814i	0.875620	−	0.234622i	0.207104	−	0.978319i	$-0.433596\pi$
$353$	16.4514	−	4.40814i	0.875620	−	0.234622i	0.668516	+	0.743697i	$0.266930\pi$
$354$	7.04662	+	5.07463i	0.374524	+	0.269713i
$355$	−5.27997	+	0.456945i	−0.280232	+	0.0242521i
$356$		−	5.51996i		−	0.292558i
$357$	−2.25535	−	0.854906i	−0.119366	−	0.0452464i
$358$	−2.07781	−	7.75450i	−0.109816	−	0.409838i
$359$	15.3124	+	26.5219i	0.808158	+	1.39977i	0.914138	+	0.405403i	$0.132869\pi$
$359$	15.3124	+	26.5219i	0.808158	+	1.39977i	−0.105980	+	0.994368i	$0.533798\pi$
$360$	6.63578	−	0.983096i	0.349736	−	0.0518137i
$361$	−7.76831	−	13.4551i	−0.408858	−	0.708163i
$362$	−20.9468	−	5.61267i	−1.10094	−	0.294995i
$363$	2.56405	+	15.7604i	0.134578	+	0.827207i
$364$			10.6049i			0.555846i
$365$	−15.1824	−	12.7638i	−0.794683	−	0.668090i
$366$	−1.23577	+	12.2520i	−0.0645950	+	0.640422i
$367$	5.37372	−	20.0550i	0.280506	−	1.04686i	−0.671556	−	0.740954i	$-0.734374\pi$
$367$	5.37372	−	20.0550i	0.280506	−	1.04686i	0.952061	−	0.305907i	$-0.0989598\pi$
$368$	−6.26316	−	6.26316i	−0.326490	−	0.326490i
$369$	7.51639	+	22.4890i	0.391288	+	1.17073i
$370$	−9.95321	+	6.95540i	−0.517443	+	0.361594i
$371$			30.1191i			1.56371i
$372$	−8.35908	+	4.80892i	−0.433398	+	0.249331i
$373$	−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
$375$	−15.6823	−	11.3608i	−0.809828	−	0.586667i
$376$	7.51173			0.387388
$377$	19.1490	+	5.13095i	0.986223	+	0.264258i
$378$	−12.3594	−	0.491792i	−0.635697	−	0.0252950i
$379$	−21.0770	−	12.1688i	−1.08265	−	0.625070i	−0.151042	−	0.988527i	$-0.548263\pi$
$379$	−21.0770	−	12.1688i	−1.08265	−	0.625070i	−0.931611	+	0.363458i	$0.881596\pi$
$380$	3.41103	−	2.38366i	0.174982	−	0.122279i
$381$	−6.13177	+	8.51457i	−0.314140	+	0.436215i
$382$	−3.59799	+	13.4279i	−0.184089	+	0.687031i
$383$	−7.77005	+	28.9982i	−0.397031	+	1.48174i	0.421263	+	0.906939i	$0.361587\pi$
$383$	−7.77005	+	28.9982i	−0.397031	+	1.48174i	−0.818293	+	0.574801i	$0.805080\pi$
$384$	1.72331	+	0.173818i	0.0879421	+	0.00887012i
$385$	−22.4986	+	8.16491i	−1.14663	+	0.416122i
$386$	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	−0.378787	−	0.925484i	$-0.623659\pi$
$389$	12.0725	−	20.9102i	0.612099	−	1.06019i	0.990886	−	0.134703i	$-0.0430080\pi$
$390$	−12.3725	+	12.0261i	−0.626505	+	0.608966i
$391$	−2.59076	+	4.48733i	−0.131021	+	0.226934i
$392$	−1.28806	−	0.345135i	−0.0650569	−	0.0174319i
$393$	−2.93443	+	0.477400i	−0.148022	+	0.0240816i
$394$	16.2370	−	9.37442i	0.818006	−	0.472276i
$395$	5.89387	+	8.43415i	0.296553	+	0.424368i
$396$	12.7940	−	4.27606i	0.642921	−	0.214880i
$397$	10.4099	−	2.78932i	0.522457	−	0.139992i	0.0120540	−	0.999927i	$-0.496163\pi$
$397$	10.4099	−	2.78932i	0.522457	−	0.139992i	0.510403	+	0.859935i	$0.329496\pi$
$398$	0.655203	−	2.44525i	0.0328423	−	0.122569i
$399$	−6.99653	+	3.15030i	−0.350265	+	0.157712i
$400$	−3.20674	−	3.83625i	−0.160337	−	0.191812i
$401$			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
$403$	10.2188	−	22.6017i	0.509034	−	1.12587i
$404$	−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
$408$	−0.162703	−	1.00009i	−0.00805500	−	0.0495116i
$409$	9.85182	+	5.68795i	0.487141	+	0.281251i	0.723388	−	0.690442i	$-0.242584\pi$
$409$	9.85182	+	5.68795i	0.487141	+	0.281251i	−0.236247	+	0.971693i	$0.575917\pi$
$410$	11.3732	−	13.5282i	0.561682	−	0.668112i
$411$	13.6488	−	6.14559i	0.673245	−	0.303140i
$412$	0.639332	−	2.38602i	0.0314976	−	0.117551i
$413$	−3.08886	+	11.5278i	−0.151993	+	0.567245i
$414$	−5.30636	+	26.0371i	−0.260793	+	1.27966i
$415$	21.1103	−	25.1104i	1.03626	−	1.23262i
$416$	−3.85815	+	2.22750i	−0.189161	+	0.109212i
$417$	−4.29743	−	5.26158i	−0.210446	−	0.257661i
$418$	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	$0.586946\pi$
$420$	4.49591	+	8.04887i	0.219378	+	0.392745i
$421$	−4.76629	−	8.25546i	−0.232295	−	0.402347i	0.726188	−	0.687496i	$-0.241290\pi$
$421$	−4.76629	−	8.25546i	−0.232295	−	0.402347i	−0.958483	+	0.285149i	$0.907957\pi$
$422$	1.80877	+	6.75043i	0.0880497	+	0.328606i
$423$	−12.4317	−	18.7959i	−0.604452	−	0.913889i
$424$	−10.9576	+	6.32637i	−0.532148	+	0.307236i
$425$	−1.68218	+	2.39283i	−0.0815977	+	0.116069i
$426$	1.68543	+	3.74319i	0.0816595	+	0.181358i
$427$	−16.3473	+	4.38024i	−0.791100	+	0.211975i
$428$	−1.97521	+	0.529256i	−0.0954753	+	0.0255825i
$429$	−20.2762	+	28.1555i	−0.978944	+	1.35936i
$430$	−2.50368	−	3.58278i	−0.120738	−	0.172777i
$431$	−5.52809	−	3.19165i	−0.266279	−	0.153736i	0.360917	−	0.932598i	$-0.382464\pi$
$431$	−5.52809	−	3.19165i	−0.266279	−	0.153736i	−0.627195	+	0.778862i	$0.715797\pi$
$432$	−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
$437$	4.26634	+	15.9222i	0.204087	+	0.761662i
$438$	−5.44572	+	14.3665i	−0.260207	+	0.686459i
$439$	17.7540	−	10.2503i	0.847352	−	0.489219i	−0.0124042	−	0.999923i	$-0.503948\pi$
$439$	17.7540	−	10.2503i	0.847352	−	0.489219i	0.859757	+	0.510704i	$0.170615\pi$
$440$	−7.69618	−	6.47018i	−0.366901	−	0.308454i
$441$	1.26811	+	3.79419i	0.0603862	+	0.180676i
$442$	1.84282	+	1.84282i	0.0876538	+	0.0876538i
$443$	1.90076	−	7.09374i	0.0903080	−	0.337034i	−0.905958	−	0.423367i	$-0.860848\pi$
$443$	1.90076	−	7.09374i	0.0903080	−	0.337034i	0.996266	+	0.0863328i	$0.0275148\pi$
$444$	7.63247	+	5.49653i	0.362221	+	0.260854i
$445$	11.1817	+	5.22688i	0.530062	+	0.247778i
$446$	−19.5655	−	11.2962i	−0.926455	−	0.534889i
$447$	1.72081	+	10.5773i	0.0813913	+	0.500287i
$448$	0.616104	+	2.29933i	0.0291082	+	0.108633i
$449$	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
$452$	−12.7634	−	3.41995i	−0.600341	−	0.160861i
$453$	11.7751	−	9.61738i	0.553242	−	0.451864i
$454$	−16.6647	+	9.62135i	−0.782112	+	0.451552i
$455$	−21.4821	−	10.0418i	−1.00709	−	0.470767i
$456$	−2.61569	−	1.88369i	−0.122491	−	0.0882120i
$457$	−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	$0.974677\pi$
$458$	−4.82652	+	1.29326i	−0.225529	+	0.0604302i
$459$	−2.23315	+	2.06223i	−0.104235	+	0.0962569i
$460$	18.6178	−	6.75654i	0.868058	−	0.315025i
$461$		−	27.5480i		−	1.28304i	−0.767108	−	0.641519i	$-0.778305\pi$
$461$		−	27.5480i		−	1.28304i	0.767108	−	0.641519i	$-0.221695\pi$
$462$	11.7276	+	14.3588i	0.545618	+	0.668031i
$463$	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
$465$	−1.82607	−	21.4864i	−0.0846821	−	0.996408i
$466$	−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	$-0.134737\pi$
$468$	11.9588	+	5.96743i	0.552796	+	0.275844i
$469$			19.8128i			0.914869i
$470$	−7.11289	+	15.2163i	−0.328093	+	0.701878i
$471$	18.9128	+	1.90760i	0.871455	+	0.0878977i
$472$	−4.84271	+	1.29760i	−0.222904	+	0.0597269i
$473$	−6.21511	−	6.21511i	−0.285771	−	0.285771i
$474$	4.65765	−	6.46760i	0.213933	−	0.297067i
$475$	1.59861	+	9.16674i	0.0733492	+	0.420599i
$476$	1.20597	−	0.696268i	0.0552756	−	0.0319134i
$477$	33.9645	+	16.9482i	1.55513	+	0.776005i
$478$	−11.5007	−	3.08159i	−0.526028	−	0.140949i
$479$	4.99248	−	8.64723i	0.228112	−	0.395102i	−0.729136	−	0.684368i	$-0.760078\pi$
$479$	4.99248	−	8.64723i	0.228112	−	0.395102i	0.957249	+	0.289266i	$0.0934113\pi$
$480$	−1.98391	+	3.32628i	−0.0905526	+	0.151823i
$481$	−24.1923			−1.10307
$482$	7.33864	+	27.3882i	0.334266	+	1.24750i
$483$	−36.0458	+	5.86426i	−1.64014	+	0.266833i
$484$	−7.98381	−	4.60945i	−0.362900	−	0.209521i
$485$	13.0597	+	35.9863i	0.593010	+	1.63405i
$486$	−7.50926	+	13.6606i	−0.340627	+	0.619656i
$487$	2.76753	−	10.3285i	0.125409	−	0.468031i	−0.874445	−	0.485124i	$-0.838774\pi$
$487$	2.76753	−	10.3285i	0.125409	−	0.468031i	0.999854	+	0.0170929i	$0.00544109\pi$
$488$	−5.02723	−	5.02723i	−0.227572	−	0.227572i
$489$	0.797976	−	7.91147i	0.0360857	−	0.357769i
$490$	1.91880	−	2.28239i	0.0866827	−	0.103108i
$491$	−15.4158	+	8.90031i	−0.695705	+	0.401665i	−0.805746	−	0.592262i	$-0.798235\pi$
$491$	−15.4158	+	8.90031i	−0.695705	+	0.401665i	0.110041	+	0.993927i	$0.464902\pi$
$492$	−12.8012	−	4.85240i	−0.577125	−	0.218763i
$493$	−0.673751	−	2.51447i	−0.0303442	−	0.113246i
$494$	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	$-0.431146\pi$
$499$	−11.7031	−	6.75678i	−0.523902	−	0.302475i	−0.738530	+	0.674221i	$0.764480\pi$
$500$	10.8075	−	2.86327i	0.483325	−	0.128049i
$501$	−3.28645	−	2.36674i	−0.146828	−	0.105738i
$502$	19.3467	−	5.18394i	0.863487	−	0.231371i
$503$	−26.4737	+	7.09362i	−1.18041	+	0.316289i	−0.795087	−	0.606495i	$-0.792575\pi$
$503$	−26.4737	+	7.09362i	−1.18041	+	0.316289i	−0.385318	+	0.922784i	$0.625908\pi$
$504$	4.73377	−	5.34696i	0.210859	−	0.238172i
$505$	16.9823	−	36.3297i	0.755704	−	1.61665i
$506$	34.4920	−	19.9140i	1.53336	−	0.885284i
$507$	−11.7055	+	1.90436i	−0.519861	+	0.0845758i
$508$	−1.56791	−	5.85153i	−0.0695649	−	0.259620i
$509$	−1.45238	−	2.51559i	−0.0643755	−	0.111502i	0.832041	−	0.554714i	$-0.187172\pi$
$509$	−1.45238	−	2.51559i	−0.0643755	−	0.111502i	−0.896417	+	0.443212i	$0.853839\pi$
$510$	2.17991	+	0.617401i	0.0965282	+	0.0273390i
$511$	−21.1155			−0.934094
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.384480	+	9.66248i	−0.0169752	+	0.426609i
$514$	−25.0296	+	14.4508i	−1.10401	+	0.637399i
$515$	4.22792	+	3.55441i	0.186304	+	0.156626i
$516$	−1.97854	+	2.74740i	−0.0871004	+	0.120948i
$517$	−8.74208	+	32.6259i	−0.384476	+	1.43489i
$518$	−3.34566	+	12.4862i	−0.147000	+	0.548612i
$519$	−5.02861	−	11.1681i	−0.220732	−	0.490224i
$520$	−0.858905	−	9.92459i	−0.0376655	−	0.435222i
$521$	24.8819	+	14.3656i	1.09010	+	0.629367i	0.933602	−	0.358312i	$-0.116647\pi$
$521$	24.8819	+	14.3656i	1.09010	+	0.629367i	0.156494	+	0.987679i	$0.449981\pi$
$522$	−7.36454	−	11.1347i	−0.322337	−	0.487352i
$523$	−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
$527$	−3.24115	+	0.321857i	−0.141187	+	0.0140203i
$528$	−2.76052	+	7.28260i	−0.120136	+	0.316934i
$529$			55.4545i			2.41106i
$530$	−2.43939	−	28.1870i	−0.105960	−	1.22437i
$531$	11.2614	+	9.96997i	0.488705	+	0.432660i
$532$	1.14658	−	4.27909i	0.0497105	−	0.185522i
$533$	34.0123	−	9.11358i	1.47324	−	0.394753i
$534$	0.959470	−	9.51259i	0.0415203	−	0.411650i
$535$	0.798233	−	4.50229i	0.0345106	−	0.194651i
$536$	−7.20806	+	4.16158i	−0.311341	+	0.179753i
$537$	−2.23283	−	13.7245i	−0.0963539	−	0.592258i
$538$	15.9565	+	4.27554i	0.687934	+	0.184331i
$539$	2.99807	−	5.19281i	0.129136	−	0.223670i
$540$	11.6064	−	0.540758i	0.499458	−	0.0232705i
$541$	−15.6275	+	27.0676i	−0.671879	+	1.16373i	0.305492	+	0.952195i	$0.401179\pi$
$541$	−15.6275	+	27.0676i	−0.671879	+	1.16373i	−0.977371	+	0.211534i	$0.932154\pi$
$542$	−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
$545$	−10.0819	+	21.5677i	−0.431859	+	0.923861i
$546$	−1.84332	+	18.2755i	−0.0788868	+	0.782117i
$547$	4.14641	−	15.4746i	0.177288	−	0.661647i	−0.818863	−	0.573989i	$-0.805395\pi$
$547$	4.14641	−	15.4746i	0.177288	−	0.661647i	0.996151	−	0.0876580i	$-0.0279383\pi$
$548$	−2.23674	+	8.34763i	−0.0955488	+	0.356593i
$549$	−4.25924	+	20.8992i	−0.181780	+	0.891954i
$550$	20.3941	−	9.46335i	0.869606	−	0.403518i
$551$	−7.17191	−	4.14071i	−0.305534	−	0.176400i
$552$	−9.70470	−	11.8820i	−0.413060	−	0.505732i
$553$	10.5805	+	2.83505i	0.449931	+	0.120559i
$554$	−13.5199			−0.574404
$555$	−18.3614	+	10.2562i	−0.779399	+	0.435353i
$556$	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	$0.313540\pi$
$558$	−15.2411	+	6.83429i	−0.645209	+	0.289319i
$559$		−	8.70830i		−	0.368322i
$560$	−5.24109	−	0.929219i	−0.221477	−	0.0392667i
$561$	4.53305	+	0.457218i	0.191386	+	0.0193037i
$562$	21.2439	+	21.2439i	0.896118	+	0.896118i
$563$	−9.25567	+	34.5426i	−0.390080	+	1.45580i	0.439921	+	0.898036i	$0.355006\pi$
$563$	−9.25567	+	34.5426i	−0.390080	+	1.45580i	−0.830001	+	0.557762i	$0.811660\pi$
$564$	12.9450	+	1.30567i	0.545083	+	0.0549788i
$565$	19.0135	−	22.6162i	0.799902	−	0.951471i
$566$			6.37167i			0.267821i
$567$	−21.2135	−	2.99579i	−0.890883	−	0.125811i
$568$	−2.28934	−	0.613427i	−0.0960586	−	0.0257388i
$569$	−15.1076	−	26.1671i	−0.633342	−	1.09698i	−0.986864	−	0.161555i	$-0.948349\pi$
$569$	−15.1076	−	26.1671i	−0.633342	−	1.09698i	0.353521	−	0.935426i	$-0.384984\pi$
$570$	6.29257	−	3.51488i	0.263567	−	0.147222i
$571$	21.6398	+	37.4812i	0.905598	+	1.56854i	0.820113	+	0.572201i	$0.193910\pi$
$571$	21.6398	+	37.4812i	0.905598	+	1.56854i	0.0854844	+	0.996340i	$0.472756\pi$
$572$	−5.18469	−	19.3495i	−0.216783	−	0.809045i
$573$	−8.53446	+	22.5150i	−0.356532	+	0.940577i
$574$		−	18.8149i		−	0.785319i
$575$	−3.94269	+	44.1114i	−0.164422	+	1.83957i
$576$	2.93957	+	0.599084i	0.122482	+	0.0249618i
$577$	−37.2427	+	9.97914i	−1.55043	+	0.415437i	−0.929619	−	0.368521i	$-0.879864\pi$
$577$	−37.2427	+	9.97914i	−1.55043	+	0.415437i	−0.620813	+	0.783958i	$0.713197\pi$
$578$	−4.31135	+	16.0902i	−0.179329	+	0.669263i
$579$	32.4521	+	23.3704i	1.34866	+	0.971240i
$580$	−4.21367	+	9.01414i	−0.174963	+	0.374292i
$581$		−	34.9232i		−	1.44886i
$582$	22.9667	−	18.7582i	0.952001	−	0.777553i
$583$	−14.7251	−	54.9550i	−0.609853	−	2.27600i
$584$	−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
$592$	−5.24532	+	1.40548i	−0.215581	+	0.0577649i
$593$	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	$0.615953\pi$
$594$	22.7912	−	5.14514i	0.935134	−	0.211108i
$595$	0.268475	+	3.10221i	0.0110064	+	0.127178i
$596$	−5.35816	−	3.09353i	−0.219479	−	0.126716i
$597$	1.55414	−	4.10003i	0.0636069	−	0.167803i
$598$	38.1154	+	10.2130i	1.55865	+	0.417640i
$599$	−12.3674	−	21.4210i	−0.505320	−	0.875240i	−0.999981	−	0.00615370i	$-0.998041\pi$
$599$	−12.3674	−	21.4210i	−0.505320	−	0.875240i	0.494661	−	0.869086i	$-0.335292\pi$
$600$	−4.85939	−	7.16842i	−0.198384	−	0.292650i
$601$	9.33337	−	16.1659i	0.380716	−	0.659419i	−0.610449	−	0.792056i	$-0.709011\pi$
$601$	9.33337	−	16.1659i	0.380716	−	0.659419i	0.991165	+	0.132636i	$0.0423442\pi$
$602$	−4.49455	−	1.20431i	−0.183184	−	0.0490841i
$603$	22.3423	+	11.1488i	0.909849	+	0.454013i
$604$			8.77775i			0.357162i
$605$	16.8972	−	11.8079i	0.686968	−	0.480060i
$606$	−30.9068	−	3.11735i	−1.25550	−	0.126634i
$607$	−1.99677	+	7.45205i	−0.0810465	+	0.302469i	−0.994536	−	0.104392i	$-0.966710\pi$
$607$	−1.99677	+	7.45205i	−0.0810465	+	0.302469i	0.913490	+	0.406862i	$0.133377\pi$
$608$	1.79760	−	0.481667i	0.0729025	−	0.0195342i
$609$	10.7219	−	14.8884i	0.434473	−	0.603308i
$610$	14.9439	−	5.42325i	0.605060	−	0.219581i
$611$	−28.9813	+	16.7324i	−1.17246	+	0.676920i
$612$	−0.106554	−	1.75173i	−0.00430721	−	0.0708097i
$613$	2.08992	+	7.79968i	0.0844110	+	0.315026i	0.995202	−	0.0978415i	$-0.0311938\pi$
$613$	2.08992	+	7.79968i	0.0844110	+	0.315026i	−0.910791	+	0.412868i	$0.864527\pi$
$614$	−10.1600	+	17.5977i	−0.410026	+	0.710186i
$615$	21.9510	−	21.3364i	0.885148	−	0.860368i
$616$	−10.7038			−0.431267
$617$	3.33332	+	12.4401i	0.134194	+	0.500820i	1.00000		0.000439697i	$0.000139960\pi$
$617$	3.33332	+	12.4401i	0.134194	+	0.500820i	−0.865805	+	0.500381i	$0.833193\pi$
$618$	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	$-0.150379\pi$
$620$	10.2747	+	7.03068i	0.412642	+	0.282359i
$621$	−13.6702	+	43.9476i	−0.548567	+	1.76356i
$622$	−9.85592	−	9.85592i	−0.395186	−	0.395186i
$623$	12.6922	−	3.40087i	0.508503	−	0.136253i
$624$	−7.03595	+	3.16805i	−0.281663	+	0.126824i
$625$	−4.43360	+	24.6037i	−0.177344	+	0.984149i
$626$	9.38800	+	5.42016i	0.375220	+	0.216633i
$627$	11.2256	−	9.16859i	0.448308	−	0.366158i
$628$	−7.76029	+	7.76029i	−0.309669	+	0.309669i
$629$	1.58835	+	2.75111i	0.0633319	+	0.109694i
$630$	6.34879	+	14.6521i	0.252942	+	0.583756i
$631$	0.489585	+	0.847986i	0.0194901	+	0.0337578i	0.875606	−	0.483026i	$-0.160462\pi$
$631$	0.489585	+	0.847986i	0.0194901	+	0.0337578i	−0.856116	+	0.516784i	$0.827129\pi$
$632$	1.19098	+	4.44478i	0.0473745	+	0.176804i
$633$	1.94372	+	11.9475i	0.0772561	+	0.474869i
$634$	−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
$637$	5.73832	−	1.53758i	0.227360	−	0.0609210i
$638$	−5.17880	+	19.3275i	−0.205031	+	0.765185i
$639$	2.25388	+	6.74362i	0.0891623	+	0.266773i
$640$	−0.762808	−	2.10193i	−0.0301526	−	0.0830862i
$641$	−33.8851	+	19.5636i	−1.33838	+	0.772715i	−0.986567	−	0.163354i	$-0.947769\pi$
$641$	−33.8851	+	19.5636i	−1.33838	+	0.772715i	−0.351815	+	0.936070i	$0.614435\pi$
$642$	−3.49589	+	0.568743i	−0.137972	+	0.0224465i
$643$	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
$645$	−3.69186	−	6.60941i	−0.145367	−	0.260245i
$646$	−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	$-0.113100\pi$
$648$	−3.36589	−	8.34690i	−0.132225	−	0.327897i
$649$		−	22.5436i		−	0.884914i
$650$	20.9173	+	7.65778i	0.820445	+	0.300363i
$651$	−16.2074	−	16.2575i	−0.635216	−	0.637181i
$652$	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	$0.883350\pi$
$654$	18.3484	+	1.85067i	0.717477	+	0.0723670i
$655$	2.19851	+	3.14608i	0.0859030	+	0.122928i
$656$	6.84503	−	3.95198i	0.267253	−	0.154299i
$657$	−11.8818	+	23.8113i	−0.463554	+	0.928969i
$658$	4.62800	+	17.2719i	0.180418	+	0.673330i
$659$	−18.8583			−0.734614			−0.367307	−	0.930100i	$-0.619720\pi$
$659$	−18.8583			−0.734614			−0.367307	+	0.930100i	$0.619720\pi$
$660$	−12.1383	−	12.4879i	−0.472481	−	0.486089i
$661$	−3.82620	−	6.62717i	−0.148822	−	0.257767i	0.781970	−	0.623315i	$-0.214215\pi$
$661$	−3.82620	−	6.62717i	−0.148822	−	0.257767i	−0.930792	+	0.365549i	$0.880881\pi$
$662$	−5.29017	−	1.41750i	−0.205608	−	0.0550925i
$663$	2.85542	+	3.49605i	0.110895	+	0.135775i
$664$	12.7054	−	7.33545i	0.493064	−	0.284671i
$665$	7.58236	+	6.37449i	0.294031	+	0.247192i
$666$	12.1977	+	10.7989i	0.472651	+	0.418447i
$667$	−27.8707	−	27.8707i	−1.07916	−	1.07916i
$668$	2.25858	−	0.605183i	0.0873869	−	0.0234153i
$669$	−31.7540	−	22.8676i	−1.22768	−	0.884113i
$670$	−1.60467	−	18.5418i	−0.0619937	−	0.716333i
$671$	27.6856	−	15.9843i	1.06879	−	0.617066i
$672$	0.662070	+	4.06954i	0.0255399	+	0.156986i
$673$	16.6203	+	4.45338i	0.640664	+	0.171665i	0.564504	−	0.825430i	$-0.309067\pi$
$673$	16.6203	+	4.45338i	0.640664	+	0.171665i	0.0761597	+	0.997096i	$0.475734\pi$
$674$	−0.765358			−0.0294805
$675$	−9.89471	+	24.0228i	−0.380848	+	0.924638i
$676$	3.42352	−	5.92972i	0.131674	−	0.228066i
$677$	38.8265	+	10.4035i	1.49222	+	0.399840i	0.910487	−	0.413539i	$-0.135707\pi$
$677$	38.8265	+	10.4035i	1.49222	+	0.399840i	0.581735	+	0.813378i	$0.302374\pi$
$678$	−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
$682$	22.8124	+	10.3141i	0.873532	+	0.394946i
$683$	−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
$685$	−14.7916	−	12.4353i	−0.565159	−	0.475129i
$686$		−	19.8374i		−	0.757396i
$687$	−8.54237	+	1.38975i	−0.325912	+	0.0530223i
$688$	−0.505920	−	1.88812i	−0.0192880	−	0.0719838i
$689$	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	0.997238	−	0.0742686i	$-0.0236622\pi$
$691$	11.4164	+	19.7738i	0.434301	+	0.752231i	−0.562938	+	0.826499i	$0.690329\pi$
$692$	6.83042	+	1.83021i	0.259654	+	0.0695740i
$693$	17.7145	+	26.7830i	0.672917	+	1.01740i
$694$	−6.82273	−	3.93910i	−0.258987	−	0.149526i
$695$	−3.71400	+	7.94522i	−0.140880	+	0.301379i
$696$	7.66861	+	0.773480i	0.290678	+	0.0293187i
$697$	−3.26948	−	3.26948i	−0.123840	−	0.123840i
$698$	11.5074	+	11.5074i	0.435560	+	0.435560i
$699$	−21.2221	−	2.14053i	−0.802693	−	0.0809621i
$700$	6.84511	−	9.73689i	0.258721	−	0.368020i
$701$	32.1511	+	18.5624i	1.21433	+	0.701094i	0.963700	−	0.266989i	$-0.0860287\pi$
$701$	32.1511	+	18.5624i	1.21433	+	0.701094i	0.250631	+	0.968083i	$0.419362\pi$
$702$	19.5715	+	12.3624i	0.738677	+	0.466587i
$703$	9.76164	+	2.61562i	0.368167	+	0.0986501i
$704$	−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
$707$	−11.0496	−	41.2375i	−0.415561	−	1.55090i
$708$	−8.57102	+	1.39441i	−0.322119	+	0.0524052i
$709$		−	47.2641i		−	1.77504i	−0.460767	−	0.887521i	$-0.652426\pi$
$709$		−	47.2641i		−	1.77504i	0.460767	−	0.887521i	$-0.347574\pi$
$710$	3.41039	−	4.05661i	0.127990	−	0.152242i
$711$	9.15074	−	10.3361i	0.343180	−	0.387633i
$712$	3.90320	+	3.90320i	0.146279	+	0.146279i
$713$	−40.0634	+	28.7578i	−1.50039	+	1.07699i
$714$	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
$718$	−29.5813	−	7.92629i	−1.10396	−	0.295806i
$719$	−2.91043	+	5.04102i	−0.108541	+	0.187998i	−0.915179	−	0.403047i	$-0.867951\pi$
$719$	−2.91043	+	5.04102i	−0.108541	+	0.187998i	0.806638	+	0.591045i	$0.201284\pi$
$720$	−3.99705	+	5.38736i	−0.148961	+	0.200775i
$721$	5.88014			0.218988
$722$	15.0072	+	4.02117i	0.558511	+	0.149653i
$723$	7.88617	+	48.4738i	0.293290	+	1.80276i
$724$	18.7804	−	10.8428i	0.697967	−	0.402971i
$725$	−14.2698	−	17.0711i	−0.529967	−	0.634004i
$726$	−12.9573	−	9.33124i	−0.480892	−	0.346315i
$727$	−15.4255	+	4.13326i	−0.572101	+	0.153294i	−0.533260	−	0.845951i	$-0.679033\pi$
$727$	−15.4255	+	4.13326i	−0.572101	+	0.153294i	−0.0388410	+	0.999245i	$0.512367\pi$
$728$	−7.49878	−	7.49878i	−0.277923	−	0.277923i
$729$	−15.3152	+	22.2361i	−0.567230	+	0.823559i
$730$	19.7610	−	1.71018i	0.731387	−	0.0632964i
$731$	−0.990296	+	0.571747i	−0.0366274	+	0.0211468i
$732$	−7.78964	−	9.53729i	−0.287914	−	0.352509i
$733$	4.56442	+	1.22303i	0.168591	+	0.0451738i	0.342127	−	0.939654i	$-0.388853\pi$
$733$	4.56442	+	1.22303i	0.168591	+	0.0451738i	−0.173536	+	0.984827i	$0.555519\pi$
$734$	10.3812	+	17.9808i	0.383178	+	0.663684i
$735$	3.70341	−	3.59973i	0.136602	−	0.132778i
$736$	8.85745			0.326490
$737$	−9.68641	−	36.1502i	−0.356804	−	1.33161i
$738$	−21.2170	−	10.5873i	−0.781010	−	0.389723i
$739$	17.8083	−	10.2817i	0.655090	−	0.378217i	−0.135313	−	0.990803i	$-0.543204\pi$
$739$	17.8083	−	10.2817i	0.655090	−	0.378217i	0.790404	+	0.612586i	$0.209871\pi$
$740$	2.11977	−	11.9562i	0.0779243	−	0.439518i
$741$	14.2877	+	1.44110i	0.524870	+	0.0529400i
$742$	−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	$0.843616\pi$
$744$	2.51034	−	9.31119i	0.0920336	−	0.341365i
$745$	11.3402	−	7.92462i	0.415472	−	0.290336i
$746$		−	20.3276i		−	0.744246i
$747$	−39.3819	−	19.6515i	−1.44091	−	0.719011i
$748$	−1.86000	+	1.86000i	−0.0680083	+	0.0680083i
$749$	−2.43387	−	4.21558i	−0.0889316	−	0.154034i
$750$	19.1223	−	3.05575i	0.698248	−	0.111580i
$751$	7.06771	−	12.2416i	0.257905	−	0.446704i	−0.707776	−	0.706437i	$-0.750301\pi$
$751$	7.06771	−	12.2416i	0.257905	−	0.446704i	0.965680	+	0.259733i	$0.0836347\pi$
$752$	−5.31159	+	5.31159i	−0.193694	+	0.193694i
$753$	34.2414	−	5.57071i	1.24783	−	0.203008i
$754$	−17.1685	+	9.91224i	−0.625240	+	0.360983i
$755$	−17.7809	−	8.31169i	−0.647113	−	0.302494i
$756$	9.08713	−	8.39163i	0.330496	−	0.305201i
$757$	3.90831	−	14.5860i	0.142050	−	0.530138i	−0.857819	−	0.513952i	$-0.828181\pi$
$757$	3.90831	−	14.5860i	0.142050	−	0.530138i	0.999869	−	0.0161860i	$-0.00515239\pi$
$758$	23.5083	−	6.29904i	0.853861	−	0.228791i
$759$	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	$-0.307446\pi$
$761$	3.88153	+	2.24100i	0.140705	+	0.0812363i	−0.427995	+	0.903781i	$0.640780\pi$
$762$	−1.68489	−	10.3565i	−0.0610373	−	0.375177i
$763$	6.55976	+	24.4814i	0.237479	+	0.886285i
$764$	−6.95079	−	12.0391i	−0.251471	−	0.435560i
$765$	3.64935	+	1.44288i	0.131942	+	0.0521675i
$766$	−15.0106	−	25.9991i	−0.542354	−	0.939385i
$767$	15.7935	−	15.7935i	0.570269	−	0.570269i
$768$	−1.34147	+	1.09565i	−0.0484061	+	0.0395360i
$769$	−15.4794	−	8.93705i	−0.558202	−	0.322278i	0.194221	−	0.980958i	$-0.437782\pi$
$769$	−15.4794	−	8.93705i	−0.558202	−	0.322278i	−0.752424	+	0.658679i	$0.771115\pi$
$770$	10.1354	−	21.6824i	0.365256	−	0.781378i
$771$	−45.6455	+	20.5526i	−1.64388	+	0.740185i
$772$	−22.3023	+	5.97588i	−0.802678	+	0.215077i
$773$	−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
$775$	−23.9711	+	14.1559i	−0.861066	+	0.508493i
$776$			17.1206i			0.614592i
$777$	−7.93593	+	20.9360i	−0.284700	+	0.751075i
$778$	6.24918	+	23.3222i	0.224044	+	0.836143i
$779$	−14.7094			−0.527019
$780$	0.244918	−	17.2524i	0.00876946	−	0.617735i
$781$	5.32863	−	9.22946i	0.190673	−	0.330256i
$782$	−1.34108	−	5.00497i	−0.0479569	−	0.178977i
$783$	−10.7560	−	20.4686i	−0.384387	−	0.731487i
$784$	1.15484	−	0.666749i	0.0412444	−	0.0238125i
$785$	−8.37159	−	23.0681i	−0.298795	−	0.823336i
$786$	1.73738	−	2.41253i	0.0619703	−	0.0860520i
$787$	19.7155	−	5.28276i	0.702783	−	0.188310i	0.110306	−	0.993898i	$-0.464817\pi$
$787$	19.7155	−	5.28276i	0.702783	−	0.188310i	0.592477	+	0.805588i	$0.298150\pi$
$788$	−4.85255	+	18.1100i	−0.172865	+	0.645141i
$789$	−19.6409	−	1.98104i	−0.699235	−	0.0705270i
$790$	−10.1314	−	1.79625i	−0.360460	−	0.0639078i
$791$		−	31.4544i		−	1.11839i
$792$	−6.02307	+	12.0703i	−0.214020	+	0.428900i
$793$	30.5940	+	8.19763i	1.08642	+	0.291106i
$794$	−5.38855	+	9.33324i	−0.191232	+	0.331224i
$795$	0.695596	−	48.9989i	0.0246702	−	1.73781i
$796$	1.26575	+	2.19235i	0.0448635	+	0.0777058i
$797$	37.5314	+	10.0565i	1.32943	+	0.356219i	0.852502	−	0.522724i	$-0.175084\pi$
$797$	37.5314	+	10.0565i	1.32943	+	0.356219i	0.476927	+	0.878943i	$0.341751\pi$
$798$	2.71969	−	7.17489i	0.0962760	−	0.253988i
$799$	3.80557	+	2.19715i	0.134631	+	0.0777294i
$800$	4.98015	+	0.445127i	0.176075	+	0.0157376i
$801$	3.30692	−	16.2263i	0.116844	−	0.573330i
$802$	−18.0191	−	18.0191i	−0.636277	−	0.636277i
$803$	38.5271	−	10.3233i	1.35959	−	0.364302i
$804$	−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	−0.935028	−	0.354573i	$-0.884626\pi$
$809$	−4.56351	+	7.90423i	−0.160445	+	0.277898i	0.774584	+	0.632471i	$0.217959\pi$
$810$	20.0953	+	1.08550i	0.706077	+	0.0381407i
$811$	14.9920	+	25.9669i	0.526440	+	0.911822i	0.999525	+	0.0308049i	$0.00980704\pi$
$811$	14.9920	+	25.9669i	0.526440	+	0.911822i	−0.473085	+	0.881017i	$0.656860\pi$
$812$	2.74162	+	10.2319i	0.0962121	+	0.359068i
$813$	−2.89531	+	2.36476i	−0.101543	+	0.0829358i
$814$		−	24.4178i		−	0.855845i
$815$	−9.64970	+	3.50195i	−0.338014	+	0.122668i
$816$	0.822215	+	0.592119i	0.0287833	+	0.0207283i
$817$	−0.941525	+	3.51382i	−0.0329398	+	0.122933i
$818$	−10.9883	+	2.94430i	−0.384196	+	0.102945i
$819$	−6.35321	+	31.1738i	−0.221999	+	1.08930i
$820$	1.52385	+	17.6080i	0.0532151	+	0.614897i
$821$			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
$823$	8.55848	+	31.9407i	0.298330	+	1.11338i	0.938537	+	0.345179i	$0.112182\pi$
$823$	8.55848	+	31.9407i	0.298330	+	1.11338i	−0.640207	+	0.768202i	$0.721151\pi$
$824$	1.23509	+	2.13924i	0.0430265	+	0.0745241i
$825$	36.7901	−	12.7634i	1.28087	−	0.444364i
$826$	−5.96722	−	10.3355i	−0.207626	−	0.359619i
$827$	47.8938	+	12.8331i	1.66543	+	0.446251i	0.963873	−	0.266361i	$-0.0858215\pi$
$827$	47.8938	+	12.8331i	1.66543	+	0.446251i	0.701558	+	0.712612i	$0.252488\pi$
$828$	−14.6589	−	22.1632i	−0.509431	−	0.770225i
$829$		−	36.6571i		−	1.27316i	−0.771213	−	0.636578i	$-0.780350\pi$
$829$		−	36.6571i		−	1.27316i	0.771213	−	0.636578i	$-0.219650\pi$
$830$	2.82848	+	32.6830i	0.0981781	+	1.13444i
$831$	−23.2989	−	2.35000i	−0.808228	−	0.0815204i
$832$	1.15304	−	4.30320i	0.0399745	−	0.149187i
$833$	−0.551603	−	0.551603i	−0.0191119	−	0.0191119i
$834$	6.75924	+	0.681758i	0.234053	+	0.0236074i
$835$	−0.912749	+	5.14820i	−0.0315870	+	0.178161i
$836$			8.36814i			0.289418i
$837$	−27.4531	+	9.12839i	−0.948918	+	0.315523i
$838$	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	$0.609219\pi$
$840$	−8.87050	−	2.51233i	−0.306061	−	0.0866835i
$841$	−9.19805			−0.317174
$842$	9.20777	+	2.46721i	0.317321	+	0.0850258i
$843$	32.9171	+	40.3022i	1.13373	+	1.38808i
$844$	−6.05227	−	3.49428i	−0.208328	−	0.120278i
$845$	8.76995	+	12.5498i	0.301695	+	0.431727i
$846$	22.0813	+	4.50016i	0.759170	+	0.154719i
$847$	5.67980	−	21.1973i	0.195160	−	0.728348i
$848$	3.27477	−	12.2216i	0.112456	−	0.419692i
$849$	−1.10751	+	10.9803i	−0.0380097	+	0.376845i
$850$	−0.502505	−	2.88147i	−0.0172358	−	0.0988334i
$851$	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
$855$	11.4550	−	4.96345i	0.391752	−	0.169746i
$856$	1.02244	−	1.77092i	0.0349464	−	0.0605289i
$857$	0.608207	+	0.162969i	0.0207760	+	0.00556690i	0.269192	−	0.963087i	$-0.413243\pi$
$857$	0.608207	+	0.162969i	0.0207760	+	0.00556690i	−0.248416	+	0.968653i	$0.579910\pi$
$858$	−5.57152	−	34.2464i	−0.190208	−	1.16915i
$859$	−44.1181	+	25.4716i	−1.50529	+	0.869080i	−0.505309	+	0.862938i	$0.668621\pi$
$859$	−44.1181	+	25.4716i	−1.50529	+	0.869080i	−0.999981	+	0.00614122i	$0.998045\pi$
$860$	4.30378	+	0.763037i	0.146758	+	0.0260194i
$861$	3.27037	−	32.4239i	0.111454	−	1.10500i
$862$	6.16579	−	1.65212i	0.210008	−	0.0562714i
$863$	11.5764	−	43.2036i	0.394064	−	1.47067i	−0.429303	−	0.903160i	$-0.641241\pi$
$863$	11.5764	−	43.2036i	0.394064	−	1.47067i	0.823368	−	0.567508i	$-0.192093\pi$
$864$	4.96166	+	1.54336i	0.168799	+	0.0525061i
$865$	−10.1752	+	12.1032i	−0.345966	+	0.411521i
$866$			6.71325i			0.228126i
$867$	−10.2265	+	26.9789i	−0.347312	+	0.916253i
$868$	13.1889	−	1.30970i	0.447659	−	0.0444541i
$869$	−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
$873$	42.8392	−	28.3341i	1.44989	−	0.958965i
$874$	−14.2755	−	8.24194i	−0.482874	−	0.278788i
$875$	13.2421	+	23.0859i	0.447666	+	0.780446i
$876$	−6.30795	−	14.0094i	−0.213126	−	0.473333i
$877$	−7.67496	+	28.6433i	−0.259165	+	0.967217i	0.706561	+	0.707652i	$0.250246\pi$
$877$	−7.67496	+	28.6433i	−0.259165	+	0.967217i	−0.965726	+	0.259564i	$0.916421\pi$
$878$	−5.30594	+	19.8020i	−0.179067	+	0.668286i
$879$	−13.6020	+	18.8878i	−0.458785	+	0.637068i
$880$	10.0171	−	0.866914i	0.337678	−	0.0292237i
$881$	−2.80434	+	1.61908i	−0.0944805	+	0.0545483i	−0.546496	−	0.837462i	$-0.684039\pi$
$881$	−2.80434	+	1.61908i	−0.0944805	+	0.0545483i	0.452015	+	0.892010i	$0.350705\pi$
$882$	−3.57959	−	1.78621i	−0.120531	−	0.0601447i
$883$	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
$885$	5.29131	−	18.6825i	0.177865	−	0.628005i
$886$	3.67199	+	6.36008i	0.123363	+	0.213671i
$887$	−1.18976	−	4.44026i	−0.0399484	−	0.149089i	0.943071	−	0.332592i	$-0.107923\pi$
$887$	−1.18976	−	4.44026i	−0.0399484	−	0.149089i	−0.983019	+	0.183502i	$0.941256\pi$
$888$	−9.28360	+	1.51034i	−0.311537	+	0.0506838i
$889$	12.4886	−	7.21030i	0.418855	−	0.241826i
$890$	−11.6026	+	4.21067i	−0.388920	+	0.141142i
$891$	40.1705	−	4.90513i	1.34576	−	0.164328i
$892$	21.8225	−	5.84733i	0.730672	−	0.195783i
$893$	13.5031	−	3.61815i	0.451865	−	0.121077i
$894$	−8.69604	−	6.26246i	−0.290839	−	0.209448i
$895$	−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
$902$	9.19856	+	34.3295i	0.306278	+	1.14305i
$903$	−7.53616	−	2.85663i	−0.250788	−	0.0950628i
$904$	11.4434	−	6.60683i	0.380601	−	0.219740i
$905$	4.18091	+	48.3101i	0.138978	+	1.60588i
$906$	−1.52573	+	15.1268i	−0.0506891	+	0.502553i
$907$	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	$0.463512\pi$
$908$	4.98038	−	18.5870i	0.165280	−	0.616832i
$909$	−52.7200	−	10.7443i	−1.74861	−	0.356367i
$910$	22.2907	−	8.08948i	0.738931	−	0.268164i
$911$	−13.6326	−	7.87076i	−0.451667	−	0.260770i	0.256867	−	0.966447i	$-0.417310\pi$
$911$	−13.6326	−	7.87076i	−0.451667	−	0.260770i	−0.708534	+	0.705677i	$0.750643\pi$
$912$	3.18155	−	0.517603i	0.105352	−	0.0171396i
$913$	17.0739	+	63.7205i	0.565062	+	2.10884i
$914$	27.7342			0.917365
$915$	26.6955	−	6.74840i	0.882527	−	0.223095i
$916$	2.49839	−	4.32734i	0.0825492	−	0.142979i
$917$	3.94672	+	1.05752i	0.130332	+	0.0349224i
$918$	0.120857	−	3.03730i	0.00398888	−	0.100246i
$919$	3.48863	−	2.01416i	0.115079	−	0.0664410i	−0.441356	−	0.897332i	$-0.645502\pi$
$919$	3.48863	−	2.01416i	0.115079	−	0.0664410i	0.556435	+	0.830891i	$0.312169\pi$
$920$	−8.38716	+	17.9423i	−0.276517	+	0.591542i
$921$	−20.5677	+	28.5603i	−0.677728	+	0.941093i
$922$	19.4794	+	19.4794i	0.641519	+	0.641519i
$923$	10.1990	−	2.73282i	0.335705	−	0.0899519i
$924$	−18.4459	−	1.86051i	−0.606824	−	0.0612062i
$925$	22.2122	+	15.6153i	0.730332	+	0.513430i
$926$			20.9458i			0.688321i
$927$	3.30879	−	6.63086i	0.108675	−	0.217786i
$928$	−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	$0.309563\pi$
$930$	16.4844	+	13.9020i	0.540545	+	0.455863i
$931$	−2.48166			−0.0813333
$932$	8.70784	−	8.70784i	0.285235	−	0.285235i
$933$	−15.2716	−	18.6979i	−0.499971	−	0.612142i
$934$			40.4176i			1.32250i
$935$	−2.00652	−	5.52900i	−0.0656202	−	0.180818i
$936$	−12.6758	+	4.23655i	−0.414320	+	0.138476i
$937$	−2.38876	+	0.640066i	−0.0780374	+	0.0209101i	−0.297626	−	0.954682i	$-0.596195\pi$
$937$	−2.38876	+	0.640066i	−0.0780374	+	0.0209101i	0.219589	+	0.975592i	$0.429528\pi$
$938$	−14.0097	−	14.0097i	−0.457434	−	0.457434i
$939$	15.2363	+	10.9724i	0.497217	+	0.358071i
$940$	−5.73001	−	15.7892i	−0.186892	−	0.514985i
$941$	12.5617	−	7.25247i	0.409498	−	0.236424i	−0.281076	−	0.959686i	$-0.590691\pi$
$941$	12.5617	−	7.25247i	0.409498	−	0.236424i	0.690574	+	0.723262i	$0.257358\pi$
$942$	−14.7222	+	12.0245i	−0.479676	+	0.391779i
$943$	−67.6234	−	18.1196i	−2.20212	−	0.590057i
$944$	2.50677	−	4.34185i	0.0815884	−	0.141315i
$945$	8.39410	+	26.3537i	0.273060	+	0.857285i
$946$	8.78950			0.285771
$947$	−0.405658	−	1.51394i	−0.0131821	−	0.0491963i	0.959022	−	0.283333i	$-0.0914403\pi$
$947$	−0.405658	−	1.51394i	−0.0131821	−	0.0491963i	−0.972204	+	0.234137i	$0.924774\pi$
$948$	1.27983	+	7.86674i	0.0415671	+	0.255500i
$949$	34.2233	+	19.7589i	1.11094	+	0.641400i
$950$	−7.61225	−	5.35148i	−0.246974	−	0.173625i
$951$	−38.1357	−	27.4634i	−1.23663	−	0.890562i
$952$	−0.360415	+	1.34509i	−0.0116811	+	0.0435945i
$953$	−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	$0.905401\pi$
$954$	−36.0007	+	12.0323i	−1.16557	+	0.389561i
$955$	30.9691	−	2.68016i	1.00214	−	0.0867280i
$956$	10.3112	−	5.95318i	0.333488	−	0.192540i
$957$	−12.2841	+	32.4071i	−0.397090	+	1.04757i
$958$	2.58430	+	9.64473i	0.0834949	+	0.311607i
$959$	−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
$966$	21.3416	−	29.6349i	0.686653	−	0.953486i
$967$	−22.4522	+	6.01606i	−0.722016	+	0.193464i	−0.601071	−	0.799196i	$-0.705259\pi$
$967$	−22.4522	+	6.01606i	−0.722016	+	0.193464i	−0.120945	+	0.992659i	$0.538592\pi$
$968$	8.90478	−	2.38603i	0.286211	−	0.0766899i
$969$	−0.774183	−	1.71939i	−0.0248704	−	0.0552347i
$970$	−34.6807	−	16.2115i	−1.11353	−	0.520521i
$971$	1.41143	−	0.814890i	0.0452950	−	0.0261511i	−0.477182	−	0.878805i	$-0.658342\pi$
$971$	1.41143	−	0.814890i	0.0452950	−	0.0261511i	0.522476	+	0.852654i	$0.325008\pi$
$972$	−4.34963	−	14.9693i	−0.139514	−	0.480141i
$973$	2.41651	+	9.01855i	0.0774698	+	0.289121i
$974$	5.34645	+	9.26032i	0.171311	+	0.296720i
$975$	34.7159	+	16.8325i	1.11180	+	0.539072i
$976$	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	$0.286575\pi$
$978$	5.03000	+	6.15851i	0.160842	+	0.196927i
$979$	−21.4954	+	12.4104i	−0.686996	+	0.396638i
$980$	0.257093	+	2.97069i	0.00821252	+	0.0948952i
$981$	31.2982	+	6.37855i	0.999274	+	0.203652i
$982$	4.60714	−	17.1941i	0.147020	−	0.548685i
$983$	3.48367	−	13.0012i	0.111112	−	0.414675i	−0.887855	−	0.460124i	$-0.847805\pi$
$983$	3.48367	−	13.0012i	0.111112	−	0.414675i	0.998967	+	0.0454488i	$0.0144718\pi$
$984$	12.4830	−	5.62068i	0.397944	−	0.179181i
$985$	−32.0901	−	26.9781i	−1.02248	−	0.859595i
$986$	2.25441	+	1.30159i	0.0717952	+	0.0414510i
$987$	4.97329	+	30.5693i	0.158302	+	0.973031i
$988$	−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	$0.516273\pi$
$992$	3.24674	+	4.52313i	0.103084	+	0.143610i
$993$	−8.87019	−	3.36231i	−0.281487	−	0.106700i
$994$		−	5.64189i		−	0.178950i
$995$	−5.63955	+	0.488064i	−0.178786	+	0.0154727i
$996$	23.1703	−	10.4328i	0.734178	−	0.330576i
$997$	−0.624260	+	2.32977i	−0.0197705	+	0.0737846i	−0.975106	−	0.221738i	$-0.928827\pi$
$997$	−0.624260	+	2.32977i	−0.0197705	+	0.0737846i	0.955336	+	0.295522i	$0.0954937\pi$
$998$	13.0531	−	3.49757i	0.413189	−	0.110714i
$999$	19.1433	+	20.7299i	0.605668	+	0.655866i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.8	✓	256	1.1	even	1	trivial
930.2.bf.a.377.63	yes	256	3.2	odd	2	inner
930.2.bf.a.563.13	yes	256	15.8	even	4	inner
930.2.bf.a.563.40	yes	256	5.3	odd	4	inner
930.2.bf.a.707.13	yes	256	31.25	even	3	inner
930.2.bf.a.707.40	yes	256	93.56	odd	6	inner
930.2.bf.a.893.8	yes	256	465.428	even	12	inner
930.2.bf.a.893.63	yes	256	155.118	odd	12	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.34147 + 1.09565i) q^{3} -1.00000i q^{4} +(2.02568 + 0.946905i) q^{5} +(0.173818 - 1.72331i) q^{6} +(2.29933 - 0.616104i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.599084 - 2.93957i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.34147 + 1.09565i) q^{3} -1.00000i q^{4} +(2.02568 + 0.946905i) q^{5} +(0.173818 - 1.72331i) q^{6} +(2.29933 - 0.616104i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.599084 - 2.93957i) q^{9} +(-2.10193 + 0.762808i) q^{10} +(-3.89412 + 2.24827i) q^{11} +(1.09565 + 1.34147i) q^{12} +(-4.30320 - 1.15304i) q^{13} +(-1.19022 + 2.06152i) q^{14} +(-3.75487 + 0.949198i) q^{15} -1.00000 q^{16} +(0.151407 + 0.565058i) q^{17} +(1.65498 + 2.50221i) q^{18} +(1.61169 + 0.930509i) q^{19} +(0.946905 - 2.02568i) q^{20} +(-2.40945 + 3.34575i) q^{21} +(1.16379 - 4.34333i) q^{22} +(6.26316 + 6.26316i) q^{23} +(-1.72331 - 0.173818i) q^{24} +(3.20674 + 3.83625i) q^{25} +(3.85815 - 2.22750i) q^{26} +(2.41710 + 4.59974i) q^{27} +(-0.616104 - 2.29933i) 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} +(-2.93957 - 0.599084i) q^{36} +(5.24532 - 1.40548i) q^{37} +(-1.79760 + 0.481667i) q^{38} +(7.03595 - 3.16805i) q^{39} +(0.762808 + 2.10193i) q^{40} +(-6.84503 + 3.95198i) q^{41} +(-0.662070 - 4.06954i) q^{42} +(0.505920 + 1.88812i) q^{43} +(2.24827 + 3.89412i) q^{44} +(3.99705 - 5.38736i) q^{45} -8.85745 q^{46} +(5.31159 - 5.31159i) q^{47} +(1.34147 - 1.09565i) q^{48} +(-1.15484 + 0.666749i) q^{49} +(-4.98015 - 0.445127i) q^{50} +(-0.822215 - 0.592119i) q^{51} +(-1.15304 + 4.30320i) q^{52} +(-3.27477 + 12.2216i) q^{53} +(-4.96166 - 1.54336i) q^{54} +(-10.0171 + 0.866914i) q^{55} +(2.06152 + 1.19022i) q^{56} +(-3.18155 + 0.517603i) q^{57} +(3.14658 - 3.14658i) q^{58} +(-2.50677 + 4.34185i) q^{59} +(0.949198 + 3.75487i) q^{60} -7.10958 q^{61} +(-3.24674 - 4.52313i) q^{62} +(-0.433591 - 7.12815i) q^{63} +1.00000i q^{64} +(-7.62508 - 6.41041i) q^{65} +(3.19759 + 7.10156i) q^{66} +(-2.15419 + 8.03955i) q^{67} +(0.565058 - 0.151407i) q^{68} +(-15.2641 - 1.53959i) q^{69} +(-4.36307 + 3.04896i) q^{70} +(-2.05257 + 1.18505i) q^{71} +(2.50221 - 1.65498i) q^{72} +(-8.56816 - 2.29583i) q^{73} +(-2.71518 + 4.70283i) q^{74} +(-8.50495 - 1.63273i) 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} +(-2.02568 - 0.946905i) q^{80} +(-8.28220 - 3.52210i) q^{81} +(2.04570 - 7.63464i) q^{82} +(3.79711 - 14.1710i) q^{83} +(3.34575 + 2.40945i) q^{84} +(-0.228354 + 1.28799i) q^{85} +(-1.69284 - 0.977362i) q^{86} +(5.96946 - 4.87559i) q^{87} +(-4.34333 - 1.16379i) q^{88} +5.51996 q^{89} +(0.983096 + 6.63578i) q^{90} -10.6049 q^{91} +(6.26316 - 6.26316i) q^{92} +(-4.80892 - 8.35908i) q^{93} +7.51173i q^{94} +(2.38366 + 3.41103i) q^{95} +(-0.173818 + 1.72331i) q^{96} +(12.1061 + 12.1061i) q^{97} +(0.345135 - 1.28806i) q^{98} +(4.27606 + 12.7940i) 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

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