LMFDB - Embedded newform 930.2.bf.a.377.13

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			377.13
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.537394 - 1.64657i) q^{3} -1.00000i q^{4} +(0.858744 + 2.06460i) q^{5} +(1.54430 + 0.784309i) q^{6} +(2.17271 - 0.582177i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.42242 + 1.76972i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.537394 - 1.64657i) q^{3} -1.00000i q^{4} +(0.858744 + 2.06460i) q^{5} +(1.54430 + 0.784309i) q^{6} +(2.17271 - 0.582177i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.42242 + 1.76972i) q^{9} +(-2.06711 - 0.852667i) q^{10} +(-3.70214 + 2.13743i) q^{11} +(-1.64657 + 0.537394i) q^{12} +(-4.67808 - 1.25349i) q^{13} +(-1.12468 + 1.94800i) q^{14} +(2.93803 - 2.52349i) q^{15} -1.00000 q^{16} +(0.808587 + 3.01769i) q^{17} +(0.461528 - 2.96429i) q^{18} +(-1.23394 - 0.712418i) q^{19} +(2.06460 - 0.858744i) q^{20} +(-2.12620 - 3.26468i) q^{21} +(1.10642 - 4.12920i) q^{22} +(-6.67715 - 6.67715i) q^{23} +(0.784309 - 1.54430i) q^{24} +(-3.52512 + 3.54592i) q^{25} +(4.19425 - 2.42155i) q^{26} +(4.21576 + 3.03765i) q^{27} +(-0.582177 - 2.17271i) q^{28} +1.43039 q^{29} +(-0.293126 + 3.86187i) q^{30} +(0.722749 - 5.52066i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.50895 + 4.94721i) q^{33} +(-2.70559 - 1.56207i) q^{34} +(3.06776 + 3.98583i) q^{35} +(1.76972 + 2.42242i) q^{36} +(-1.66823 + 0.447001i) q^{37} +(1.37629 - 0.368775i) q^{38} +(0.450009 + 8.37642i) q^{39} +(-0.852667 + 2.06711i) q^{40} +(-8.16063 + 4.71154i) q^{41} +(3.81192 + 0.805024i) q^{42} +(0.274603 + 1.02483i) q^{43} +(2.13743 + 3.70214i) q^{44} +(-5.73399 - 3.48158i) q^{45} +9.44292 q^{46} +(1.59396 - 1.59396i) q^{47} +(0.537394 + 1.64657i) q^{48} +(-1.68043 + 0.970196i) q^{49} +(-0.0147082 - 4.99998i) q^{50} +(4.53432 - 2.95309i) q^{51} +(-1.25349 + 4.67808i) q^{52} +(1.77636 - 6.62948i) q^{53} +(-5.12894 + 0.833049i) q^{54} +(-7.59212 - 5.80792i) q^{55} +(1.94800 + 1.12468i) q^{56} +(-0.509935 + 2.41463i) q^{57} +(-1.01144 + 1.01144i) q^{58} +(1.64861 - 2.85548i) q^{59} +(-2.52349 - 2.93803i) q^{60} -11.4936 q^{61} +(3.39263 + 4.41475i) q^{62} +(-4.23293 + 5.25536i) q^{63} +1.00000i q^{64} +(-1.42932 - 10.7348i) q^{65} +(-7.39362 + 0.397210i) q^{66} +(-2.03055 + 7.57811i) q^{67} +(3.01769 - 0.808587i) q^{68} +(-7.40617 + 14.5827i) q^{69} +(-4.98765 - 0.649174i) q^{70} +(-5.43224 + 3.13630i) q^{71} +(-2.96429 - 0.461528i) q^{72} +(13.5427 + 3.62877i) q^{73} +(0.863540 - 1.49570i) q^{74} +(7.73300 + 3.89882i) q^{75} +(-0.712418 + 1.23394i) q^{76} +(-6.79932 + 6.79932i) q^{77} +(-6.24123 - 5.60482i) q^{78} +(-14.8161 - 8.55409i) q^{79} +(-0.858744 - 2.06460i) q^{80} +(2.73620 - 8.57398i) q^{81} +(2.43887 - 9.10200i) q^{82} +(-3.23224 + 12.0629i) q^{83} +(-3.26468 + 2.12620i) q^{84} +(-5.53594 + 4.26083i) q^{85} +(-0.918841 - 0.530493i) q^{86} +(-0.768685 - 2.35525i) q^{87} +(-4.12920 - 1.10642i) q^{88} -14.6680 q^{89} +(6.51639 - 1.59269i) q^{90} -10.8939 q^{91} +(-6.67715 + 6.67715i) q^{92} +(-9.47857 + 1.77671i) q^{93} +2.25420i q^{94} +(0.411214 - 3.15938i) q^{95} +(-1.54430 - 0.784309i) q^{96} +(0.220569 + 0.220569i) q^{97} +(0.502210 - 1.87427i) q^{98} +(5.18547 - 11.7295i) 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
$3$	−0.537394	−	1.64657i	−0.310264	−	0.950650i
$3$	−0.537394	−	1.64657i	−0.310264	−	0.950650i
$4$		−	1.00000i		−	0.500000i
$5$	0.858744	+	2.06460i	0.384042	+	0.923316i
$5$	0.858744	+	2.06460i	0.384042	+	0.923316i
$6$	1.54430	+	0.784309i	0.630457	+	0.320193i
$7$	2.17271	−	0.582177i	0.821208	−	0.220042i	0.176334	−	0.984330i	$-0.443576\pi$
$7$	2.17271	−	0.582177i	0.821208	−	0.220042i	0.644875	+	0.764288i	$0.276910\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.42242	+	1.76972i	−0.807472	+	0.589906i
$10$	−2.06711	−	0.852667i	−0.653679	−	0.269637i
$11$	−3.70214	+	2.13743i	−1.11624	+	0.644460i	−0.940438	−	0.339966i	$-0.889584\pi$
$11$	−3.70214	+	2.13743i	−1.11624	+	0.644460i	−0.175799	+	0.984426i	$0.556251\pi$
$12$	−1.64657	+	0.537394i	−0.475325	+	0.155132i
$13$	−4.67808	−	1.25349i	−1.29747	−	0.347655i	−0.456974	−	0.889480i	$-0.651067\pi$
$13$	−4.67808	−	1.25349i	−1.29747	−	0.347655i	−0.840491	+	0.541825i	$0.817733\pi$
$14$	−1.12468	+	1.94800i	−0.300583	+	0.520625i
$15$	2.93803	−	2.52349i	0.758596	−	0.651561i
$16$	−1.00000			−0.250000
$17$	0.808587	+	3.01769i	0.196111	+	0.731897i	0.991976	+	0.126423i	$0.0403497\pi$
$17$	0.808587	+	3.01769i	0.196111	+	0.731897i	−0.795865	+	0.605474i	$0.792984\pi$
$18$	0.461528	−	2.96429i	0.108783	−	0.698689i
$19$	−1.23394	−	0.712418i	−0.283086	−	0.163440i	0.351734	−	0.936100i	$-0.385592\pi$
$19$	−1.23394	−	0.712418i	−0.283086	−	0.163440i	−0.634820	+	0.772660i	$0.718926\pi$
$20$	2.06460	−	0.858744i	0.461658	−	0.192021i
$21$	−2.12620	−	3.26468i	−0.463975	−	0.712411i
$22$	1.10642	−	4.12920i	0.235889	−	0.880348i
$23$	−6.67715	−	6.67715i	−1.39228	−	1.39228i	−0.820186	−	0.572097i	$-0.806130\pi$
$23$	−6.67715	−	6.67715i	−1.39228	−	1.39228i	−0.572097	−	0.820186i	$-0.693870\pi$
$24$	0.784309	−	1.54430i	0.160096	−	0.315229i
$25$	−3.52512	+	3.54592i	−0.705024	+	0.709184i
$26$	4.19425	−	2.42155i	0.822560	−	0.474905i
$27$	4.21576	+	3.03765i	0.811324	+	0.584597i
$28$	−0.582177	−	2.17271i	−0.110021	−	0.410604i
$29$	1.43039			0.265618			0.132809	−	0.991142i	$-0.457600\pi$
$29$	1.43039			0.265618			0.132809	+	0.991142i	$0.457600\pi$
$30$	−0.293126	+	3.86187i	−0.0535172	+	0.705079i
$31$	0.722749	−	5.52066i	0.129810	−	0.991539i
$31$	0.722749	−	5.52066i	0.129810	−	0.991539i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	5.50895	+	4.94721i	0.958984	+	0.861198i
$34$	−2.70559	−	1.56207i	−0.464004	−	0.267893i
$35$	3.06776	+	3.98583i	0.518547	+	0.673729i
$36$	1.76972	+	2.42242i	0.294953	+	0.403736i
$37$	−1.66823	+	0.447001i	−0.274255	+	0.0734865i	−0.393325	−	0.919399i	$-0.628675\pi$
$37$	−1.66823	+	0.447001i	−0.274255	+	0.0734865i	0.119070	+	0.992886i	$0.462009\pi$
$38$	1.37629	−	0.368775i	0.223263	−	0.0598231i
$39$	0.450009	+	8.37642i	0.0720591	+	1.34130i
$40$	−0.852667	+	2.06711i	−0.134818	+	0.326839i
$41$	−8.16063	+	4.71154i	−1.27448	+	0.735819i	−0.975827	−	0.218544i	$-0.929869\pi$
$41$	−8.16063	+	4.71154i	−1.27448	+	0.735819i	−0.298649	+	0.954363i	$0.596536\pi$
$42$	3.81192	+	0.805024i	0.588193	+	0.124218i
$43$	0.274603	+	1.02483i	0.0418766	+	0.156286i	0.983698	−	0.179828i	$-0.0575541\pi$
$43$	0.274603	+	1.02483i	0.0418766	+	0.156286i	−0.941821	+	0.336114i	$0.890887\pi$
$44$	2.13743	+	3.70214i	0.322230	+	0.558119i
$45$	−5.73399	−	3.48158i	−0.854772	−	0.519003i
$46$	9.44292			1.39228
$47$	1.59396	−	1.59396i	0.232503	−	0.232503i	−0.581234	−	0.813737i	$-0.697430\pi$
$47$	1.59396	−	1.59396i	0.232503	−	0.232503i	0.813737	+	0.581234i	$0.197430\pi$
$48$	0.537394	+	1.64657i	0.0775661	+	0.237663i
$49$	−1.68043	+	0.970196i	−0.240061	+	0.138599i
$50$	−0.0147082	−	4.99998i	−0.00208005	−	0.707104i
$51$	4.53432	−	2.95309i	0.634932	−	0.413515i
$52$	−1.25349	+	4.67808i	−0.173827	+	0.648733i
$53$	1.77636	−	6.62948i	0.244002	−	0.910629i	−0.729880	−	0.683575i	$-0.760424\pi$
$53$	1.77636	−	6.62948i	0.244002	−	0.910629i	0.973882	−	0.227054i	$-0.0729092\pi$
$54$	−5.12894	+	0.833049i	−0.697960	+	0.113364i
$55$	−7.59212	−	5.80792i	−1.02372	−	0.783140i
$56$	1.94800	+	1.12468i	0.260313	+	0.150292i
$57$	−0.509935	+	2.41463i	−0.0675426	+	0.319825i
$58$	−1.01144	+	1.01144i	−0.132809	+	0.132809i
$59$	1.64861	−	2.85548i	0.214631	−	0.371752i	−0.738527	−	0.674224i	$-0.764478\pi$
$59$	1.64861	−	2.85548i	0.214631	−	0.371752i	0.953158	+	0.302472i	$0.0978118\pi$
$60$	−2.52349	−	2.93803i	−0.325781	−	0.379298i
$61$	−11.4936			−1.47160			−0.735802	−	0.677196i	$-0.763195\pi$
$61$	−11.4936			−1.47160			−0.735802	+	0.677196i	$0.763195\pi$
$62$	3.39263	+	4.41475i	0.430865	+	0.560674i
$63$	−4.23293	+	5.25536i	−0.533299	+	0.662113i
$64$			1.00000i			0.125000i
$65$	−1.42932	−	10.7348i	−0.177286	−	1.33148i
$66$	−7.39362	+	0.397210i	−0.910091	+	0.0488931i
$67$	−2.03055	+	7.57811i	−0.248071	+	0.925813i	0.723744	+	0.690068i	$0.242420\pi$
$67$	−2.03055	+	7.57811i	−0.248071	+	0.925813i	−0.971815	+	0.235745i	$0.924247\pi$
$68$	3.01769	−	0.808587i	0.365948	−	0.0980556i
$69$	−7.40617	+	14.5827i	−0.891598	+	1.75555i
$70$	−4.98765	−	0.649174i	−0.596138	−	0.0775912i
$71$	−5.43224	+	3.13630i	−0.644688	+	0.372211i	−0.786418	−	0.617695i	$-0.788067\pi$
$71$	−5.43224	+	3.13630i	−0.644688	+	0.372211i	0.141730	+	0.989905i	$0.454733\pi$
$72$	−2.96429	−	0.461528i	−0.349344	−	0.0543916i
$73$	13.5427	+	3.62877i	1.58506	+	0.424715i	0.940487	−	0.339830i	$-0.110369\pi$
$73$	13.5427	+	3.62877i	1.58506	+	0.424715i	0.644571	+	0.764545i	$0.277036\pi$
$74$	0.863540	−	1.49570i	0.100384	−	0.173871i
$75$	7.73300	+	3.89882i	0.892930	+	0.450197i
$76$	−0.712418	+	1.23394i	−0.0817199	+	0.141543i
$77$	−6.79932	+	6.79932i	−0.774855	+	0.774855i
$78$	−6.24123	−	5.60482i	−0.706680	−	0.634621i
$79$	−14.8161	−	8.55409i	−1.66694	−	0.962410i	−0.969272	−	0.245991i	$-0.920886\pi$
$79$	−14.8161	−	8.55409i	−1.66694	−	0.962410i	−0.697671	−	0.716418i	$-0.745780\pi$
$80$	−0.858744	−	2.06460i	−0.0960105	−	0.230829i
$81$	2.73620	−	8.57398i	0.304022	−	0.952665i
$82$	2.43887	−	9.10200i	0.269328	−	1.00515i
$83$	−3.23224	+	12.0629i	−0.354785	+	1.32407i	0.525971	+	0.850503i	$0.323702\pi$
$83$	−3.23224	+	12.0629i	−0.354785	+	1.32407i	−0.880755	+	0.473571i	$0.842965\pi$
$84$	−3.26468	+	2.12620i	−0.356205	+	0.231987i
$85$	−5.53594	+	4.26083i	−0.600457	+	0.462152i
$86$	−0.918841	−	0.530493i	−0.0990811	−	0.0572045i
$87$	−0.768685	−	2.35525i	−0.0824117	−	0.252509i
$88$	−4.12920	−	1.10642i	−0.440174	−	0.117944i
$89$	−14.6680			−1.55480			−0.777400	−	0.629007i	$-0.783462\pi$
$89$	−14.6680			−1.55480			−0.777400	+	0.629007i	$0.783462\pi$
$90$	6.51639	−	1.59269i	0.686888	−	0.167885i
$91$	−10.8939			−1.14199
$92$	−6.67715	+	6.67715i	−0.696141	+	0.696141i
$93$	−9.47857	+	1.77671i	−0.982882	+	0.184236i
$94$			2.25420i			0.232503i
$95$	0.411214	−	3.15938i	0.0421896	−	0.324146i
$96$	−1.54430	−	0.784309i	−0.157614	−	0.0800482i
$97$	0.220569	+	0.220569i	0.0223954	+	0.0223954i	0.718216	−	0.695820i	$-0.244959\pi$
$97$	0.220569	+	0.220569i	0.0223954	+	0.0223954i	−0.695820	+	0.718216i	$0.744959\pi$
$98$	0.502210	−	1.87427i	0.0507309	−	0.189330i
$99$	5.18547	−	11.7295i	0.521160	−	1.17886i
$100$	3.54592	+	3.52512i	0.354592	+	0.352512i
$101$			14.8701i			1.47963i	0.672808	+	0.739817i	$0.265088\pi$
$101$			14.8701i			1.47963i	−0.672808	+	0.739817i	$0.734912\pi$
$102$	−1.11810	+	5.29439i	−0.110709	+	0.524223i
$103$	14.3903	+	3.85586i	1.41791	+	0.379929i	0.884743	−	0.466079i	$-0.154334\pi$
$103$	14.3903	+	3.85586i	1.41791	+	0.379929i	0.533170	+	0.846008i	$0.321000\pi$
$104$	−2.42155	−	4.19425i	−0.237453	−	0.411280i
$105$	4.91438	−	7.19326i	0.479594	−	0.701991i
$106$	3.43167	+	5.94383i	0.333313	+	0.577315i
$107$	2.61675	+	9.76585i	0.252971	+	0.944100i	0.969208	+	0.246243i	$0.0791962\pi$
$107$	2.61675	+	9.76585i	0.252971	+	0.944100i	−0.716237	+	0.697857i	$0.754137\pi$
$108$	3.03765	−	4.21576i	0.292298	−	0.405662i
$109$		−	5.43614i		−	0.520688i	−0.965516	−	0.260344i	$-0.916164\pi$
$109$		−	5.43614i		−	0.520688i	0.965516	−	0.260344i	$-0.0838359\pi$
$110$	9.47526	−	1.26162i	0.903431	−	0.120291i
$111$	1.63252	+	2.50665i	0.154952	+	0.237921i
$112$	−2.17271	+	0.582177i	−0.205302	+	0.0550105i
$113$	1.21628	−	4.53923i	0.114418	−	0.427015i	−0.884825	−	0.465924i	$-0.845722\pi$
$113$	1.21628	−	4.53923i	0.114418	−	0.427015i	0.999243	+	0.0389099i	$0.0123885\pi$
$114$	−1.34682	−	2.06798i	−0.126141	−	0.193684i
$115$	8.05167	−	19.5196i	0.750822	−	1.82021i
$116$		−	1.43039i		−	0.132809i
$117$	13.5506	−	5.24241i	1.25275	−	0.484661i
$118$	0.853385	+	3.18487i	0.0785604	+	0.293192i
$119$	3.51365	+	6.08583i	0.322096	+	0.557887i
$120$	3.86187	+	0.293126i	0.352539	+	0.0267586i
$121$	3.63723	−	6.29986i	0.330657	−	0.572714i
$122$	8.12720	−	8.12720i	0.735802	−	0.735802i
$123$	12.1434	+	10.9051i	1.09493	+	0.983283i
$124$	−5.52066	−	0.722749i	−0.495769	−	0.0649048i
$125$	−10.3481	−	4.23291i	−0.925559	−	0.378603i
$126$	−0.722971	−	6.70923i	−0.0644074	−	0.597706i
$127$	11.2272	−	3.00832i	0.996253	−	0.266945i	0.276378	−	0.961049i	$-0.410866\pi$
$127$	11.2272	−	3.00832i	0.996253	−	0.266945i	0.719875	+	0.694104i	$0.244199\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	1.53990	−	1.00289i	0.135580	−	0.0882999i
$130$	8.60131	+	6.57994i	0.754385	+	0.577099i
$131$	1.74383	+	1.00680i	0.152359	+	0.0879644i	0.574241	−	0.818686i	$-0.305297\pi$
$131$	1.74383	+	1.00680i	0.152359	+	0.0879644i	−0.421882	+	0.906651i	$0.638631\pi$
$132$	4.94721	−	5.50895i	0.430599	−	0.479492i
$133$	−3.09576	−	0.829506i	−0.268436	−	0.0719273i
$134$	−3.92272	−	6.79434i	−0.338871	−	0.586942i
$135$	−2.65127	+	11.3124i	−0.228185	+	0.973618i
$136$	−1.56207	+	2.70559i	−0.133946	+	0.232002i
$137$	7.63802	+	2.04660i	0.652560	+	0.174853i	0.569886	−	0.821724i	$-0.306987\pi$
$137$	7.63802	+	2.04660i	0.652560	+	0.174853i	0.0826739	+	0.996577i	$0.473654\pi$
$138$	−5.07457	−	15.5485i	−0.431976	−	1.32357i
$139$		−	14.1141i		−	1.19715i	−0.801068	−	0.598573i	$-0.795735\pi$
$139$		−	14.1141i		−	1.19715i	0.801068	−	0.598573i	$-0.204265\pi$
$140$	3.98583	−	3.06776i	0.336864	−	0.259273i
$141$	−3.48115	−	1.76799i	−0.293166	−	0.148891i
$142$	1.62347	−	6.05887i	0.136239	−	0.508449i
$143$	19.9981	−	5.35849i	1.67233	−	0.448099i
$144$	2.42242	−	1.76972i	0.201868	−	0.147476i
$145$	1.22834	+	2.95319i	0.102008	+	0.245249i
$146$	−12.1421	+	7.01024i	−1.00489	+	0.580171i
$147$	2.50055	+	2.24557i	0.206242	+	0.185212i
$148$	0.447001	+	1.66823i	0.0367433	+	0.137128i
$149$	−7.07913	+	12.2614i	−0.579945	+	1.00449i	0.415540	+	0.909575i	$0.363593\pi$
$149$	−7.07913	+	12.2614i	−0.579945	+	1.00449i	−0.995485	+	0.0949196i	$0.969741\pi$
$150$	−8.22493	+	2.71117i	−0.671563	+	0.221366i
$151$	22.3947			1.82245			0.911226	−	0.411907i	$-0.135137\pi$
$151$	22.3947			1.82245			0.911226	+	0.411907i	$0.135137\pi$
$152$	−0.368775	−	1.37629i	−0.0299116	−	0.111631i
$153$	−7.29919	−	5.87913i	−0.590105	−	0.475299i
$154$		−	9.61569i		−	0.774855i
$155$	12.0186	−	3.24864i	0.965356	−	0.260937i
$156$	8.37642	−	0.450009i	0.670650	−	0.0360296i
$157$	−7.95160	−	7.95160i	−0.634607	−	0.634607i	0.314613	−	0.949220i	$-0.398125\pi$
$157$	−7.95160	−	7.95160i	−0.634607	−	0.634607i	−0.949220	+	0.314613i	$0.898125\pi$
$158$	16.5252	−	4.42792i	1.31468	−	0.352266i
$159$	−11.8705	+	0.637725i	−0.941395	+	0.0505748i
$160$	2.06711	+	0.852667i	0.163420	+	0.0674092i
$161$	−18.3948	−	10.6203i	−1.44971	−	0.836993i
$162$	4.12794	+	7.99751i	0.324321	+	0.628344i
$163$	−11.6732	+	11.6732i	−0.914313	+	0.914313i	−0.996608	−	0.0822949i	$-0.973775\pi$
$163$	−11.6732	+	11.6732i	−0.914313	+	0.914313i	0.0822949	+	0.996608i	$0.473775\pi$
$164$	4.71154	+	8.16063i	0.367910	+	0.637238i
$165$	−5.48321	+	15.6221i	−0.426868	+	1.21618i
$166$	−6.24421	−	10.8153i	−0.484645	−	0.839429i
$167$	0.0405970	+	0.151510i	0.00314149	+	0.0117242i	0.967479	−	0.252952i	$-0.0814015\pi$
$167$	0.0405970	+	0.151510i	0.00314149	+	0.0117242i	−0.964337	+	0.264676i	$0.914735\pi$
$168$	0.805024	−	3.81192i	0.0621090	−	0.294096i
$169$	9.05485	+	5.22782i	0.696527	+	0.402140i
$170$	0.901641	−	6.92736i	0.0691527	−	0.531304i
$171$	4.24990	−	0.457960i	0.324998	−	0.0350210i
$172$	1.02483	−	0.274603i	0.0781428	−	0.0209383i
$173$	2.10034	−	7.83859i	0.159686	−	0.595957i	−0.838972	−	0.544174i	$-0.816843\pi$
$173$	2.10034	−	7.83859i	0.159686	−	0.595957i	0.998658	−	0.0517825i	$-0.0164903\pi$
$174$	2.20896	+	1.12187i	0.167461	+	0.0850489i
$175$	−5.59472	+	9.75650i	−0.422921	+	0.737522i
$176$	3.70214	−	2.13743i	0.279059	−	0.161115i
$177$	−5.58772	−	1.18005i	−0.419998	−	0.0886977i
$178$	10.3718	−	10.3718i	0.777400	−	0.777400i
$179$	−9.63714	+	16.6920i	−0.720313	+	1.24762i	0.240561	+	0.970634i	$0.422669\pi$
$179$	−9.63714	+	16.6920i	−0.720313	+	1.24762i	−0.960874	+	0.276985i	$0.910665\pi$
$180$	−3.48158	+	5.73399i	−0.259502	+	0.427386i
$181$	3.61457	+	6.26061i	0.268669	+	0.465348i	0.968518	−	0.248943i	$-0.0800830\pi$
$181$	3.61457	+	6.26061i	0.268669	+	0.465348i	−0.699850	+	0.714290i	$0.746750\pi$
$182$	7.70313	−	7.70313i	0.570994	−	0.570994i
$183$	6.17659	+	18.9251i	0.456587	+	1.39898i
$184$		−	9.44292i		−	0.696141i
$185$	−2.35546	−	3.06036i	−0.173177	−	0.225002i
$186$	5.44604	−	7.95868i	0.399323	−	0.583559i
$187$	−9.44360	−	9.44360i	−0.690585	−	0.690585i
$188$	−1.59396	−	1.59396i	−0.116251	−	0.116251i
$189$	10.9281	+	4.14563i	0.794902	+	0.301550i
$190$	1.94325	+	2.52479i	0.140978	+	0.183168i
$191$	17.2428	−	9.95514i	1.24765	−	0.720329i	0.277007	−	0.960868i	$-0.410658\pi$
$191$	17.2428	−	9.95514i	1.24765	−	0.720329i	0.970639	+	0.240539i	$0.0773242\pi$
$192$	1.64657	−	0.537394i	0.118831	−	0.0387830i
$193$	−2.75143	−	10.2685i	−0.198052	−	0.739141i	−0.991456	−	0.130445i	$-0.958359\pi$
$193$	−2.75143	−	10.2685i	−0.198052	−	0.739141i	0.793403	−	0.608696i	$-0.208307\pi$
$194$	−0.311931			−0.0223954
$195$	−16.9075	+	8.12229i	−1.21077	+	0.581649i
$196$	0.970196	+	1.68043i	0.0692997	+	0.120031i
$197$	−8.40137	−	2.25114i	−0.598573	−	0.160387i	−0.0532046	−	0.998584i	$-0.516944\pi$
$197$	−8.40137	−	2.25114i	−0.598573	−	0.160387i	−0.545368	+	0.838197i	$0.683610\pi$
$198$	4.62732	+	11.9607i	0.328849	+	0.850009i
$199$	9.29189	−	5.36468i	0.658685	−	0.380292i	−0.133091	−	0.991104i	$-0.542490\pi$
$199$	9.29189	−	5.36468i	0.658685	−	0.380292i	0.791776	+	0.610812i	$0.209157\pi$
$200$	−4.99998	+	0.0147082i	−0.353552	+	0.00104003i
$201$	13.5691	−	0.728978i	0.957092	−	0.0514182i
$202$	−10.5148	−	10.5148i	−0.739817	−	0.739817i
$203$	3.10784	−	0.832742i	0.218127	−	0.0584470i
$204$	−2.95309	−	4.53432i	−0.206757	−	0.317466i
$205$	−16.7353	−	12.8024i	−1.16885	−	0.894158i
$206$	−12.9019	+	7.44894i	−0.898921	+	0.518992i
$207$	27.9915	+	4.35817i	1.94555	+	0.302914i
$208$	4.67808	+	1.25349i	0.324366	+	0.0869137i
$209$	6.09098			0.421322
$210$	1.61142	+	8.56139i	0.111198	+	0.590792i
$211$	3.39456	−	5.87956i	0.233691	−	0.404765i	−0.725200	−	0.688538i	$-0.758253\pi$
$211$	3.39456	−	5.87956i	0.233691	−	0.404765i	0.958892	+	0.283773i	$0.0915861\pi$
$212$	−6.62948	−	1.77636i	−0.455314	−	0.122001i
$213$	8.08341	+	7.25915i	0.553866	+	0.497389i
$214$	−8.75582	−	5.05518i	−0.598536	−	0.345565i
$215$	−1.88005	+	1.44701i	−0.128219	+	0.0986856i
$216$	0.833049	+	5.12894i	0.0566818	+	0.348980i
$217$	−1.64367	−	12.4156i	−0.111580	−	0.842823i
$218$	3.84393	+	3.84393i	0.260344	+	0.260344i
$219$	−1.30275	−	24.2492i	−0.0880315	−	1.63861i
$220$	−5.80792	+	7.59212i	−0.391570	+	0.511861i
$221$		−	15.1305i		−	1.01779i
$222$	−2.92683	−	0.618106i	−0.196436	−	0.0414846i
$223$	0.102798	+	0.383646i	0.00688384	+	0.0256908i	0.969282	−	0.245951i	$-0.0791001\pi$
$223$	0.102798	+	0.383646i	0.00688384	+	0.0256908i	−0.962398	+	0.271642i	$0.912433\pi$
$224$	1.12468	−	1.94800i	0.0751458	−	0.130156i
$225$	2.26403	−	14.8282i	0.150935	−	0.988544i
$226$	2.34968	+	4.06976i	0.156298	+	0.270716i
$227$	16.6265	+	4.45505i	1.10354	+	0.295692i	0.764205	−	0.644974i	$-0.223132\pi$
$227$	16.6265	+	4.45505i	1.10354	+	0.295692i	0.339334	+	0.940666i	$0.389798\pi$
$228$	2.41463	+	0.509935i	0.159913	+	0.0337713i
$229$	20.8919	+	12.0619i	1.38057	+	0.797075i	0.992227	−	0.124439i	$-0.0397130\pi$
$229$	20.8919	+	12.0619i	1.38057	+	0.797075i	0.388347	+	0.921513i	$0.373046\pi$
$230$	8.10905	+	19.4958i	0.534695	+	1.28552i
$231$	14.8495	+	7.54168i	0.977026	+	0.496206i
$232$	1.01144	+	1.01144i	0.0664044	+	0.0664044i
$233$	4.17746	+	4.17746i	0.273674	+	0.273674i	0.830577	−	0.556903i	$-0.188011\pi$
$233$	4.17746	+	4.17746i	0.273674	+	0.273674i	−0.556903	+	0.830577i	$0.688011\pi$
$234$	−5.87476	+	13.2886i	−0.384045	+	0.868706i
$235$	4.65968	+	1.92208i	0.303964	+	0.125383i
$236$	−2.85548	−	1.64861i	−0.185876	−	0.107316i
$237$	−6.12286	+	28.9927i	−0.397722	+	1.88328i
$238$	−6.78786	−	1.81880i	−0.439992	−	0.117895i
$239$	2.11818	+	3.66879i	0.137014	+	0.237315i	0.926365	−	0.376627i	$-0.122916\pi$
$239$	2.11818	+	3.66879i	0.137014	+	0.237315i	−0.789351	+	0.613942i	$0.789583\pi$
$240$	−2.93803	+	2.52349i	−0.189649	+	0.162890i
$241$	−2.82971	+	4.90119i	−0.182277	+	0.315714i	−0.942656	−	0.333767i	$-0.891680\pi$
$241$	−2.82971	+	4.90119i	−0.182277	+	0.315714i	0.760378	+	0.649480i	$0.225014\pi$
$242$	1.88277	+	7.02658i	0.121029	+	0.451686i
$243$	−15.5881	+	0.102247i	−0.999978	+	0.00655918i
$244$			11.4936i			0.735802i
$245$	−3.44612	−	2.63626i	−0.220165	−	0.168424i
$246$	−16.2978	+	0.875569i	−1.03911	+	0.0558243i
$247$	4.87948	+	4.87948i	0.310474	+	0.310474i
$248$	4.41475	−	3.39263i	0.280337	−	0.215432i
$249$	21.5994	−	1.16039i	1.36881	−	0.0735369i
$250$	10.3103	−	4.32407i	0.652081	−	0.273478i
$251$	−13.0277	−	7.52154i	−0.822300	−	0.474755i	0.0289088	−	0.999582i	$-0.490797\pi$
$251$	−13.0277	−	7.52154i	−0.822300	−	0.474755i	−0.851209	+	0.524827i	$0.824130\pi$
$252$	5.25536	+	4.23293i	0.331057	+	0.266649i
$253$	38.9917	+	10.4478i	2.45139	+	0.656847i
$254$	−5.81163	+	10.0660i	−0.364654	+	0.631599i
$255$	9.99075	+	6.82560i	0.625645	+	0.427435i
$256$	1.00000			0.0625000
$257$	−23.2663	−	6.23419i	−1.45131	−	0.388878i	−0.554832	−	0.831962i	$-0.687218\pi$
$257$	−23.2663	−	6.23419i	−1.45131	−	0.388878i	−0.896480	+	0.443084i	$0.853884\pi$
$258$	−0.379717	+	1.79802i	−0.0236402	+	0.111940i
$259$	−3.36435	+	1.94241i	−0.209051	+	0.120695i
$260$	−10.7348	+	1.42932i	−0.665742	+	0.0886430i
$261$	−3.46501	+	2.53139i	−0.214479	+	0.156689i
$262$	−1.94498	+	0.521157i	−0.120162	+	0.0321972i
$263$	−6.50502	−	6.50502i	−0.401117	−	0.401117i	0.477510	−	0.878627i	$-0.341540\pi$
$263$	−6.50502	−	6.50502i	−0.401117	−	0.401117i	−0.878627	+	0.477510i	$0.841540\pi$
$264$	0.397210	+	7.39362i	0.0244466	+	0.455046i
$265$	15.2126	−	2.02555i	0.934505	−	0.124428i
$266$	2.77558	−	1.60248i	0.170182	−	0.0982545i
$267$	7.88246	+	24.1519i	0.482399	+	1.47807i
$268$	7.57811	+	2.03055i	0.462906	+	0.124035i
$269$	−2.77309	−	4.80314i	−0.169079	−	0.292853i	0.769018	−	0.639228i	$-0.220746\pi$
$269$	−2.77309	−	4.80314i	−0.169079	−	0.292853i	−0.938096	+	0.346375i	$0.887412\pi$
$270$	−6.12436	−	9.87382i	−0.372716	−	0.600901i
$271$	−24.5358			−1.49045			−0.745223	−	0.666815i	$-0.767657\pi$
$271$	−24.5358			−1.49045			−0.745223	+	0.666815i	$0.767657\pi$
$272$	−0.808587	−	3.01769i	−0.0490278	−	0.182974i
$273$	5.85430	+	17.9376i	0.354318	+	1.08563i
$274$	−6.84806	+	3.95373i	−0.413706	+	0.238854i
$275$	5.47132	−	20.6622i	0.329933	−	1.24598i
$276$	14.5827	+	7.40617i	0.877775	+	0.445799i
$277$	−6.44970	−	6.44970i	−0.387525	−	0.387525i	0.486279	−	0.873804i	$-0.338354\pi$
$277$	−6.44970	−	6.44970i	−0.387525	−	0.387525i	−0.873804	+	0.486279i	$0.838354\pi$
$278$	9.98021	+	9.98021i	0.598573	+	0.598573i
$279$	8.01920	+	14.6524i	0.480097	+	0.877215i
$280$	−0.649174	+	4.98765i	−0.0387956	+	0.298069i
$281$		−	6.62366i		−	0.395134i	−0.980289	−	0.197567i	$-0.936696\pi$
$281$		−	6.62366i		−	0.395134i	0.980289	−	0.197567i	$-0.0633041\pi$
$282$	3.71170	−	1.21139i	0.221029	−	0.0721373i
$283$	−5.96508	+	5.96508i	−0.354587	+	0.354587i	−0.861813	−	0.507226i	$-0.830671\pi$
$283$	−5.96508	+	5.96508i	−0.354587	+	0.354587i	0.507226	+	0.861813i	$0.330671\pi$
$284$	3.13630	+	5.43224i	0.186105	+	0.322344i
$285$	−5.42314	+	1.02074i	−0.321239	+	0.0604632i
$286$	−10.3518	+	17.9298i	−0.612115	+	1.06021i
$287$	−14.9877	+	14.9877i	−0.884699	+	0.884699i
$288$	−0.461528	+	2.96429i	−0.0271958	+	0.174672i
$289$	6.26980	−	3.61987i	0.368812	−	0.212934i
$290$	−2.95679	−	1.21965i	−0.173629	−	0.0716203i
$291$	0.244651	−	0.481715i	0.0143417	−	0.0282387i
$292$	3.62877	−	13.5427i	0.212357	−	0.792529i
$293$	20.1284	−	5.39340i	1.17592	−	0.315086i	0.382611	−	0.923910i	$-0.375025\pi$
$293$	20.1284	−	5.39340i	1.17592	−	0.315086i	0.793305	+	0.608824i	$0.208358\pi$
$294$	−3.35602	+	0.180296i	−0.195727	+	0.0105151i
$295$	7.31115	+	0.951594i	0.425672	+	0.0554039i
$296$	−1.49570	−	0.863540i	−0.0869355	−	0.0501922i
$297$	−22.1001	−	2.23492i	−1.28238	−	0.129683i
$298$	−3.66443	−	13.6758i	−0.212275	−	0.792220i
$299$	22.8665	+	39.6060i	1.32240	+	2.29047i
$300$	3.89882	−	7.73300i	0.225098	−	0.446465i
$301$	1.19327	+	2.06680i	0.0687788	+	0.119128i
$302$	−15.8354	+	15.8354i	−0.911226	+	0.911226i
$303$	24.4848	−	7.99112i	1.40662	−	0.459078i
$304$	1.23394	+	0.712418i	0.0707715	+	0.0408600i
$305$	−9.87006	−	23.7296i	−0.565158	−	1.35876i
$306$	9.31848	−	1.00414i	0.532702	−	0.0574027i
$307$	1.74251	−	0.466904i	0.0994502	−	0.0266476i	−0.208751	−	0.977969i	$-0.566940\pi$
$307$	1.74251	−	0.466904i	0.0994502	−	0.0266476i	0.308201	+	0.951321i	$0.400273\pi$
$308$	6.79932	+	6.79932i	0.387427	+	0.387427i
$309$	−1.38427	−	25.7667i	−0.0787486	−	1.46582i
$310$	−6.20128	+	10.7956i	−0.352209	+	0.613147i
$311$		−	14.2413i		−	0.807552i	−0.914858	−	0.403776i	$-0.867698\pi$
$311$		−	14.2413i		−	0.807552i	0.914858	−	0.403776i	$-0.132302\pi$
$312$	−5.60482	+	6.24123i	−0.317310	+	0.353340i
$313$	−2.38901	−	8.91591i	−0.135035	−	0.503957i	−0.999998	−	0.00212107i	$-0.999325\pi$
$313$	−2.38901	−	8.91591i	−0.135035	−	0.503957i	0.864963	−	0.501836i	$-0.167342\pi$
$314$	11.2453			0.634607
$315$	−14.4852	−	4.22628i	−0.816149	−	0.238124i
$316$	−8.55409	+	14.8161i	−0.481205	+	0.833471i
$317$	−1.34481	−	5.01890i	−0.0755321	−	0.281890i	0.917821	−	0.396994i	$-0.129946\pi$
$317$	−1.34481	−	5.01890i	−0.0755321	−	0.281890i	−0.993353	+	0.115104i	$0.963280\pi$
$318$	7.94280	−	8.84468i	0.445410	−	0.495985i
$319$	−5.29552	+	3.05737i	−0.296492	+	0.171180i
$320$	−2.06460	+	0.858744i	−0.115414	+	0.0480052i
$321$	14.6740	−	9.55678i	0.819021	−	0.533408i
$322$	20.5168	−	5.49745i	1.14335	−	0.306361i
$323$	1.15210	−	4.29971i	0.0641047	−	0.239242i
$324$	−8.57398	−	2.73620i	−0.476332	−	0.152011i
$325$	20.9355	−	12.1694i	1.16129	−	0.675037i
$326$		−	16.5084i		−	0.914313i
$327$	−8.95101	+	2.92135i	−0.494992	+	0.161551i
$328$	−9.10200	−	2.43887i	−0.502574	−	0.134664i
$329$	2.53525	−	4.39118i	0.139773	−	0.242093i
$330$	−7.16930	−	14.9237i	−0.394657	−	0.821525i
$331$	16.5850	+	28.7261i	0.911596	+	1.57893i	0.811810	+	0.583921i	$0.198482\pi$
$331$	16.5850	+	28.7261i	0.911596	+	1.57893i	0.0997853	+	0.995009i	$0.468184\pi$
$332$	12.0629	+	3.23224i	0.662037	+	0.177392i
$333$	3.25008	−	4.03512i	0.178104	−	0.221123i
$334$	−0.135840	−	0.0784273i	−0.00743284	−	0.00429135i
$335$	−17.3895	+	2.31539i	−0.950087	+	0.126503i
$336$	2.12620	+	3.26468i	0.115994	+	0.178103i
$337$	0.100486	+	0.100486i	0.00547385	+	0.00547385i	0.709838	−	0.704365i	$-0.248768\pi$
$337$	0.100486	+	0.100486i	0.00547385	+	0.00547385i	−0.704365	+	0.709838i	$0.748768\pi$
$338$	−10.0994	+	2.70612i	−0.549334	+	0.147193i
$339$	−8.12780	+	0.436652i	−0.441441	+	0.0237157i
$340$	4.26083	+	5.53594i	0.231076	+	0.300228i
$341$	9.12430	+	21.9831i	0.494109	+	1.19045i
$342$	−2.68131	+	3.32896i	−0.144989	+	0.180010i
$343$	−14.2200	+	14.2200i	−0.767809	+	0.767809i
$344$	−0.530493	+	0.918841i	−0.0286023	+	0.0495406i
$345$	−36.4674	−	2.76796i	−1.96334	−	0.149022i
$346$	4.05755	+	7.02788i	0.218135	+	0.377821i
$347$	−7.37402	−	27.5202i	−0.395858	−	1.47736i	−0.820314	−	0.571914i	$-0.806201\pi$
$347$	−7.37402	−	27.5202i	−0.395858	−	1.47736i	0.424456	−	0.905449i	$-0.360465\pi$
$348$	−2.35525	+	0.768685i	−0.126255	+	0.0412058i
$349$			27.2492i			1.45862i	0.684184	+	0.729309i	$0.260158\pi$
$349$			27.2492i			1.45862i	−0.684184	+	0.729309i	$0.739842\pi$
$350$	−2.94283	−	10.8550i	−0.157301	−	0.580222i
$351$	−15.9140	−	19.4948i	−0.849427	−	1.04055i
$352$	−1.10642	+	4.12920i	−0.0589722	+	0.220087i
$353$	−7.13401	+	1.91155i	−0.379705	+	0.101742i	−0.443623	−	0.896214i	$-0.646307\pi$
$353$	−7.13401	+	1.91155i	−0.379705	+	0.101742i	0.0639180	+	0.997955i	$0.479640\pi$
$354$	4.78553	−	3.11669i	0.254348	−	0.165650i
$355$	−11.1401	−	8.52210i	−0.591255	−	0.452306i
$356$			14.6680i			0.777400i
$357$	8.13255	−	9.05598i	0.430420	−	0.479293i
$358$	−4.98855	−	18.6175i	−0.263653	−	0.983966i
$359$	0.380333	+	0.658756i	0.0200732	+	0.0347678i	0.875888	−	0.482515i	$-0.160277\pi$
$359$	0.380333	+	0.658756i	0.0200732	+	0.0347678i	−0.855814	+	0.517283i	$0.826943\pi$
$360$	−1.59269	−	6.51639i	−0.0839423	−	0.343444i
$361$	−8.48492	−	14.6963i	−0.446575	−	0.773490i
$362$	−6.98280	−	1.87104i	−0.367008	−	0.0983395i
$363$	−12.3278	−	2.60346i	−0.647042	−	0.136646i
$364$			10.8939i			0.570994i
$365$	4.13780	+	31.0765i	0.216583	+	1.62662i
$366$	−17.7496	−	9.01454i	−0.927784	−	0.471198i
$367$	−0.434814	+	1.62275i	−0.0226971	+	0.0847068i	−0.976345	−	0.216217i	$-0.930628\pi$
$367$	−0.434814	+	1.62275i	−0.0226971	+	0.0847068i	0.953648	+	0.300924i	$0.0972949\pi$
$368$	6.67715	+	6.67715i	0.348071	+	0.348071i
$369$	11.4303	−	25.8553i	0.595040	−	1.34597i
$370$	3.82957	+	0.498443i	0.199090	+	0.0259128i
$371$		−	15.4381i		−	0.801506i
$372$	1.77671	+	9.47857i	0.0921179	+	0.491441i
$373$	0.375372	−	0.375372i	0.0194360	−	0.0194360i	−0.697322	−	0.716758i	$-0.745625\pi$
$373$	0.375372	−	0.375372i	0.0194360	−	0.0194360i	0.716758	+	0.697322i	$0.245625\pi$
$374$	13.3553			0.690585
$375$	−1.40882	+	19.3136i	−0.0727512	+	0.997350i
$376$	2.25420			0.116251
$377$	−6.69150	−	1.79298i	−0.344630	−	0.0923432i
$378$	−10.6587	+	4.79592i	−0.548226	+	0.246676i
$379$	15.5878	+	8.99963i	0.800692	+	0.462280i	0.843713	−	0.536794i	$-0.180365\pi$
$379$	15.5878	+	8.99963i	0.800692	+	0.462280i	−0.0430211	+	0.999074i	$0.513698\pi$
$380$	−3.15938	−	0.411214i	−0.162073	−	0.0210948i
$381$	−10.9869	−	16.8698i	−0.562873	−	0.864265i
$382$	−5.15316	+	19.2319i	−0.263659	+	0.983988i
$383$	3.71464	−	13.8632i	0.189809	−	0.708378i	−0.803740	−	0.594980i	$-0.797160\pi$
$383$	3.71464	−	13.8632i	0.189809	−	0.708378i	0.993550	−	0.113398i	$-0.0361735\pi$
$384$	−0.784309	+	1.54430i	−0.0400241	+	0.0788072i
$385$	−19.8767	−	8.19898i	−1.01301	−	0.417859i
$386$	9.20646	+	5.31535i	0.468597	+	0.270544i
$387$	−2.47887	−	1.99660i	−0.126008	−	0.101493i
$388$	0.220569	−	0.220569i	0.0111977	−	0.0111977i
$389$	−3.96443	+	6.86660i	−0.201005	+	0.348150i	−0.948852	−	0.315720i	$-0.897754\pi$
$389$	−3.96443	+	6.86660i	−0.201005	+	0.348150i	0.747848	+	0.663870i	$0.231087\pi$
$390$	6.21207	−	17.6987i	0.314561	−	0.896210i
$391$	14.7505	−	25.5486i	0.745965	−	1.29205i
$392$	−1.87427	−	0.502210i	−0.0946651	−	0.0253654i
$393$	0.720648	−	3.41239i	0.0363519	−	0.172132i
$394$	7.53246	−	4.34887i	0.379480	−	0.219093i
$395$	4.93749	−	37.9351i	0.248432	−	1.90872i
$396$	−11.7295	−	5.18547i	−0.589429	−	0.260580i
$397$	−10.5910	+	2.83786i	−0.531550	+	0.142428i	−0.514604	−	0.857428i	$-0.672061\pi$
$397$	−10.5910	+	2.83786i	−0.531550	+	0.142428i	−0.0169458	+	0.999856i	$0.505394\pi$
$398$	−2.77696	+	10.3638i	−0.139196	+	0.519488i
$399$	0.297797	+	5.54317i	0.0149085	+	0.277505i
$400$	3.52512	−	3.54592i	0.176256	−	0.177296i
$401$		−	16.2998i		−	0.813974i	−0.913434	−	0.406987i	$-0.866579\pi$
$401$		−	16.2998i		−	0.813974i	0.913434	−	0.406987i	$-0.133421\pi$
$402$	−9.07935	+	10.1103i	−0.452837	+	0.504255i
$403$	−10.3011	+	24.9201i	−0.513137	+	1.24136i
$404$	14.8701			0.739817
$405$	20.0515	−	1.71371i	0.996368	−	0.0851548i
$406$	−1.60873	+	2.78641i	−0.0798401	+	0.138287i
$407$	5.22059	−	5.22059i	0.258775	−	0.258775i
$408$	5.29439	+	1.11810i	0.262112	+	0.0553543i
$409$	−13.3311	−	7.69669i	−0.659178	−	0.380577i	0.132786	−	0.991145i	$-0.457608\pi$
$409$	−13.3311	−	7.69669i	−0.659178	−	0.380577i	−0.791964	+	0.610568i	$0.790941\pi$
$410$	20.8863	−	2.78099i	1.03150	−	0.137344i
$411$	−0.734742	−	13.6764i	−0.0362421	−	0.674607i
$412$	3.85586	−	14.3903i	0.189964	−	0.708957i
$413$	1.91957	−	7.16392i	0.0944557	−	0.352514i
$414$	−22.8747	+	16.7113i	−1.12423	+	0.821316i
$415$	−27.6807	+	3.68566i	−1.35879	+	0.180922i
$416$	−4.19425	+	2.42155i	−0.205640	+	0.118726i
$417$	−23.2400	+	7.58485i	−1.13807	+	0.371432i
$418$	−4.30697	+	4.30697i	−0.210661	+	0.210661i
$419$	2.59048			0.126553			0.0632767	−	0.997996i	$-0.479845\pi$
$419$	2.59048			0.126553			0.0632767	+	0.997996i	$0.479845\pi$
$420$	−7.19326	−	4.91438i	−0.350995	−	0.239797i
$421$	−0.0311916	−	0.0540254i	−0.00152018	−	0.00263304i	0.865264	−	0.501316i	$-0.167151\pi$
$421$	−0.0311916	−	0.0540254i	−0.00152018	−	0.00263304i	−0.866784	+	0.498683i	$0.833817\pi$
$422$	1.75716	+	6.55779i	0.0855370	+	0.319228i
$423$	−1.04037	+	6.68208i	−0.0505847	+	0.324894i
$424$	5.94383	−	3.43167i	0.288658	−	0.166657i
$425$	−13.5508	−	7.77052i	−0.657312	−	0.376926i
$426$	−10.8488	+	0.582835i	−0.525628	+	0.0282385i
$427$	−24.9723	+	6.69130i	−1.20849	+	0.323815i
$428$	9.76585	−	2.61675i	0.472050	−	0.126485i
$429$	−19.5700	−	30.0488i	−0.944849	−	1.45077i
$430$	0.306205	−	2.35259i	0.0147665	−	0.113452i
$431$	−4.62024	−	2.66750i	−0.222549	−	0.128489i	0.384581	−	0.923091i	$-0.374346\pi$
$431$	−4.62024	−	2.66750i	−0.222549	−	0.128489i	−0.607130	+	0.794603i	$0.707679\pi$
$432$	−4.21576	−	3.03765i	−0.202831	−	0.146149i
$433$	25.1472	−	25.1472i	1.20850	−	1.20850i	0.236987	−	0.971513i	$-0.423840\pi$
$433$	25.1472	−	25.1472i	1.20850	−	1.20850i	0.971513	−	0.236987i	$-0.0761598\pi$
$434$	9.94138	+	7.61688i	0.477202	+	0.365622i
$435$	4.20254	−	3.60958i	0.201496	−	0.173066i
$436$	−5.43614			−0.260344
$437$	3.48231	+	12.9962i	0.166581	+	0.621690i
$438$	18.0680	+	16.2256i	0.863320	+	0.775289i
$439$	−21.1025	+	12.1836i	−1.00717	+	0.581489i	−0.910362	−	0.413814i	$-0.864197\pi$
$439$	−21.1025	+	12.1836i	−1.00717	+	0.581489i	−0.0968077	+	0.995303i	$0.530863\pi$
$440$	−1.26162	−	9.47526i	−0.0601455	−	0.451715i
$441$	2.35372	−	5.32410i	0.112082	−	0.253529i
$442$	10.6989	+	10.6989i	0.508895	+	0.508895i
$443$	7.27192	−	27.1392i	0.345499	−	1.28942i	−0.546529	−	0.837440i	$-0.684051\pi$
$443$	7.27192	−	27.1392i	0.345499	−	1.28942i	0.892028	−	0.451980i	$-0.149282\pi$
$444$	2.50665	−	1.63252i	0.118960	−	0.0774759i
$445$	−12.5960	−	30.2834i	−0.597108	−	1.43557i
$446$	−0.343968	−	0.198590i	−0.0162873	−	0.00940350i
$447$	23.9936	+	5.06711i	1.13486	+	0.239666i
$448$	0.582177	+	2.17271i	0.0275053	+	0.102651i
$449$	−8.76805			−0.413790			−0.206895	−	0.978363i	$-0.566336\pi$
$449$	−8.76805			−0.413790			−0.206895	+	0.978363i	$0.566336\pi$
$450$	8.88418	+	12.0860i	0.418804	+	0.569739i
$451$	20.1412	−	34.8856i	0.948412	−	1.64270i
$452$	−4.53923	−	1.21628i	−0.213507	−	0.0572091i
$453$	−12.0347	−	36.8745i	−0.565442	−	1.73251i
$454$	−14.9069	+	8.60650i	−0.699616	+	0.403923i
$455$	−9.35504	−	22.4914i	−0.438571	−	1.05442i
$456$	−2.06798	+	1.34682i	−0.0968420	+	0.0630707i
$457$	21.4662	+	21.4662i	1.00415	+	1.00415i	0.999991	+	0.00415560i	$0.00132277\pi$
$457$	21.4662	+	21.4662i	1.00415	+	1.00415i	0.00415560	+	0.999991i	$0.498677\pi$
$458$	−23.3019	+	6.24371i	−1.08882	+	0.291750i
$459$	−5.75788	+	15.1781i	−0.268755	+	0.708451i
$460$	−19.5196	−	8.05167i	−0.910106	−	0.375411i
$461$			5.84740i			0.272340i	0.990685	+	0.136170i	$0.0434794\pi$
$461$			5.84740i			0.272340i	−0.990685	+	0.136170i	$0.956521\pi$
$462$	−15.8330	+	5.16741i	−0.736616	+	0.240410i
$463$	−4.39374	+	4.39374i	−0.204194	+	0.204194i	−0.801794	−	0.597600i	$-0.796121\pi$
$463$	−4.39374	+	4.39374i	−0.204194	+	0.204194i	0.597600	+	0.801794i	$0.296121\pi$
$464$	−1.43039			−0.0664044
$465$	−11.8078	−	18.0437i	−0.547576	−	0.836756i
$466$	−5.90782			−0.273674
$467$	−11.3196	+	11.3196i	−0.523807	+	0.523807i	−0.918719	−	0.394912i	$-0.870775\pi$
$467$	−11.3196	+	11.3196i	−0.523807	+	0.523807i	0.394912	+	0.918719i	$0.370775\pi$
$468$	−5.24241	−	13.5506i	−0.242330	−	0.626375i
$469$			17.6472i			0.814871i
$470$	−4.65401	+	1.93578i	−0.214673	+	0.0892907i
$471$	−8.81976	+	17.3660i	−0.406393	+	0.800185i
$472$	3.18487	−	0.853385i	0.146596	−	0.0392802i
$473$	−3.20713	−	3.20713i	−0.147464	−	0.147464i
$474$	−16.1715	−	24.8305i	−0.742779	−	1.14050i
$475$	6.87597	−	1.86411i	0.315491	−	0.0855311i
$476$	6.08583	−	3.51365i	0.278943	−	0.161048i
$477$	7.42921	+	19.2030i	0.340160	+	0.879246i
$478$	−4.09201	−	1.09645i	−0.187164	−	0.0501505i
$479$	0.830207	−	1.43796i	0.0379331	−	0.0657021i	−0.846436	−	0.532491i	$-0.821256\pi$
$479$	0.830207	−	1.43796i	0.0379331	−	0.0657021i	0.884369	+	0.466789i	$0.154589\pi$
$480$	0.293126	−	3.86187i	0.0133793	−	0.176270i
$481$	8.36442			0.381385
$482$	−1.46476	−	5.46657i	−0.0667181	−	0.248996i
$483$	−7.60178	+	35.9957i	−0.345893	+	1.63786i
$484$	−6.29986	−	3.63723i	−0.286357	−	0.165328i
$485$	−0.265974	+	0.644798i	−0.0120772	+	0.0292788i
$486$	10.9502	−	11.0948i	0.496710	−	0.503269i
$487$	−2.71733	+	10.1412i	−0.123134	+	0.459543i	−0.999766	−	0.0216183i	$-0.993118\pi$
$487$	−2.71733	+	10.1412i	−0.123134	+	0.459543i	0.876632	+	0.481161i	$0.159785\pi$
$488$	−8.12720	−	8.12720i	−0.367901	−	0.367901i
$489$	25.4938	+	12.9477i	1.15287	+	0.585513i
$490$	4.30089	−	0.572660i	0.194294	−	0.0258701i
$491$	−24.3301	+	14.0470i	−1.09800	+	0.633932i	−0.935696	−	0.352808i	$-0.885227\pi$
$491$	−24.3301	+	14.0470i	−1.09800	+	0.633932i	−0.162307	+	0.986740i	$0.551893\pi$
$492$	10.9051	−	12.1434i	0.491641	−	0.547466i
$493$	1.15660	+	4.31648i	0.0520906	+	0.194405i
$494$	−6.90062			−0.310474
$495$	28.6697	+	0.633285i	1.28861	+	0.0284640i
$496$	−0.722749	+	5.52066i	−0.0324524	+	0.247885i
$497$	−9.97681	+	9.97681i	−0.447521	+	0.447521i
$498$	−14.4526	+	16.0936i	−0.647636	+	0.721173i
$499$	−14.5764	−	8.41570i	−0.652530	−	0.376739i	0.136895	−	0.990586i	$-0.456288\pi$
$499$	−14.5764	−	8.41570i	−0.652530	−	0.376739i	−0.789425	+	0.613847i	$0.789621\pi$
$500$	−4.23291	+	10.3481i	−0.189302	+	0.462780i
$501$	0.227656	−	0.148266i	0.0101709	−	0.00662405i
$502$	14.5305	−	3.89343i	0.648528	−	0.173772i
$503$	−5.62440	+	1.50705i	−0.250779	+	0.0671961i	−0.382019	−	0.924155i	$-0.624771\pi$
$503$	−5.62440	+	1.50705i	−0.250779	+	0.0671961i	0.131239	+	0.991351i	$0.458104\pi$
$504$	−6.70923	+	0.722971i	−0.298853	+	0.0322037i
$505$	−30.7008	+	12.7696i	−1.36617	+	0.568242i
$506$	−34.9590	+	20.1836i	−1.55412	+	0.897270i
$507$	3.74198	−	17.7189i	0.166187	−	0.786923i
$508$	−3.00832	−	11.2272i	−0.133473	−	0.498127i
$509$	−16.5565	−	28.6766i	−0.733852	−	1.27107i	−0.955225	−	0.295880i	$-0.904387\pi$
$509$	−16.5565	−	28.6766i	−0.733852	−	1.27107i	0.221373	−	0.975189i	$-0.428946\pi$
$510$	−11.8910	+	2.23810i	−0.526540	+	0.0991048i
$511$	31.5371			1.39512
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.03794	−	6.75168i	−0.134128	−	0.298094i
$514$	20.8600	−	12.0435i	0.920095	−	0.531217i
$515$	4.39675	+	33.0213i	0.193744	+	1.45509i
$516$	−1.00289	−	1.53990i	−0.0441499	−	0.0677901i
$517$	−2.49408	+	9.30803i	−0.109689	+	0.409367i
$518$	1.00547	−	3.75245i	0.0441776	−	0.164873i
$519$	−14.0355	+	0.754035i	−0.616091	+	0.0330985i
$520$	6.57994	−	8.60131i	0.288550	−	0.377192i
$521$	18.7541	+	10.8277i	0.821630	+	0.474368i	0.850978	−	0.525201i	$-0.176010\pi$
$521$	18.7541	+	10.8277i	0.821630	+	0.474368i	−0.0293481	+	0.999569i	$0.509343\pi$
$522$	0.660166	−	4.24010i	0.0288947	−	0.185584i
$523$	18.7898	−	18.7898i	0.821621	−	0.821621i	−0.164719	−	0.986341i	$-0.552672\pi$
$523$	18.7898	−	18.7898i	0.821621	−	0.821621i	0.986341	+	0.164719i	$0.0526718\pi$
$524$	1.00680	−	1.74383i	0.0439822	−	0.0761794i
$525$	19.0714	+	3.96904i	0.832343	+	0.173223i
$526$	9.19949			0.401117
$527$	17.2440	−	2.28290i	0.751161	−	0.0994447i
$528$	−5.50895	−	4.94721i	−0.239746	−	0.215300i
$529$			66.1688i			2.87690i
$530$	−9.32468	+	12.1892i	−0.405038	+	0.529467i
$531$	1.05977	+	9.83474i	0.0459900	+	0.426791i
$532$	−0.829506	+	3.09576i	−0.0359636	+	0.134218i
$533$	44.0819	−	11.8117i	1.90940	−	0.511622i
$534$	−22.6517	−	11.5042i	−0.980235	−	0.497836i
$535$	−17.9154	+	13.7889i	−0.774551	+	0.596146i
$536$	−6.79434	+	3.92272i	−0.293471	+	0.169436i
$537$	32.6636	+	6.89808i	1.40954	+	0.297674i
$538$	5.35721	+	1.43546i	0.230966	+	0.0618870i
$539$	4.14745	−	7.18360i	0.178643	−	0.309420i
$540$	11.3124	+	2.65127i	0.486809	+	0.114092i
$541$	−8.25022	+	14.2898i	−0.354704	+	0.614366i	−0.987067	−	0.160306i	$-0.948752\pi$
$541$	−8.25022	+	14.2898i	−0.354704	+	0.614366i	0.632363	+	0.774672i	$0.282085\pi$
$542$	17.3495	−	17.3495i	0.745223	−	0.745223i
$543$	8.36612	−	9.31606i	0.359025	−	0.399791i
$544$	2.70559	+	1.56207i	0.116001	+	0.0669732i
$545$	11.2234	−	4.66825i	0.480759	−	0.199966i
$546$	−16.8234	−	8.54416i	−0.719975	−	0.365656i
$547$	−6.95516	+	25.9570i	−0.297381	+	1.10984i	0.641927	+	0.766766i	$0.278135\pi$
$547$	−6.95516	+	25.9570i	−0.297381	+	1.10984i	−0.939308	+	0.343075i	$0.888531\pi$
$548$	2.04660	−	7.63802i	0.0874265	−	0.326280i
$549$	27.8423	−	20.3404i	1.18828	−	0.868108i
$550$	10.7416	+	18.4792i	0.458022	+	0.787955i
$551$	−1.76503	−	1.01904i	−0.0751926	−	0.0434125i
$552$	−15.5485	+	5.07457i	−0.661787	+	0.215988i
$553$	−37.1711	−	9.95998i	−1.58068	−	0.423541i
$554$	9.12125			0.387525
$555$	−3.77331	+	5.52306i	−0.160168	+	0.234441i
$556$	−14.1141			−0.598573
$557$	−3.34007	+	3.34007i	−0.141523	+	0.141523i	−0.774319	−	0.632796i	$-0.781907\pi$
$557$	−3.34007	+	3.34007i	−0.141523	+	0.141523i	0.632796	+	0.774319i	$0.281907\pi$
$558$	−16.0312	−	4.69037i	−0.678656	−	0.198559i
$559$		−	5.13846i		−	0.217334i
$560$	−3.06776	−	3.98583i	−0.129637	−	0.168432i
$561$	−10.4747	+	20.6245i	−0.442241	+	0.870768i
$562$	4.68363	+	4.68363i	0.197567	+	0.197567i
$563$	−2.33239	+	8.70458i	−0.0982984	+	0.366854i	−0.997499	−	0.0706823i	$-0.977482\pi$
$563$	−2.33239	+	8.70458i	−0.0982984	+	0.366854i	0.899201	+	0.437537i	$0.144149\pi$
$564$	−1.76799	+	3.48115i	−0.0744457	+	0.146583i
$565$	10.4161	−	1.38690i	0.438211	−	0.0583473i
$566$		−	8.43589i		−	0.354587i
$567$	0.953403	−	20.2218i	0.0400392	−	0.849234i
$568$	−6.05887	−	1.62347i	−0.254225	−	0.0681193i
$569$	−9.94798	−	17.2304i	−0.417041	−	0.722336i	0.578599	−	0.815612i	$-0.303600\pi$
$569$	−9.94798	−	17.2304i	−0.417041	−	0.722336i	−0.995640	+	0.0932757i	$0.970266\pi$
$570$	3.11297	−	4.55651i	0.130388	−	0.190851i
$571$	−14.5696	−	25.2353i	−0.609719	−	1.05606i	−0.991287	−	0.131723i	$-0.957949\pi$
$571$	−14.5696	−	25.2353i	−0.609719	−	1.05606i	0.381568	−	0.924341i	$-0.375384\pi$
$572$	−5.35849	−	19.9981i	−0.224050	−	0.836164i
$573$	−25.6581	−	23.0417i	−1.07188	−	0.962583i
$574$		−	21.1959i		−	0.884699i
$575$	47.2144	−	0.138888i	1.96898	−	0.00579205i
$576$	−1.76972	−	2.42242i	−0.0737382	−	0.100934i
$577$	1.47847	−	0.396156i	0.0615496	−	0.0164922i	−0.227913	−	0.973682i	$-0.573190\pi$
$577$	1.47847	−	0.396156i	0.0615496	−	0.0164922i	0.289462	+	0.957189i	$0.406523\pi$
$578$	−1.87378	+	6.99306i	−0.0779391	+	0.290873i
$579$	−15.4292	+	10.0486i	−0.641216	+	0.417608i
$580$	2.95319	−	1.22834i	0.122624	−	0.0510041i
$581$			28.0909i			1.16541i
$582$	0.167630	+	0.513618i	0.00694849	+	0.0212902i
$583$	7.59371	+	28.3401i	0.314499	+	1.17373i
$584$	7.01024	+	12.1421i	0.290086	+	0.502443i
$585$	22.4599	+	23.4746i	0.928604	+	0.970554i
$586$	−10.4192	+	18.0467i	−0.430415	+	0.745501i
$587$	−2.58787	+	2.58787i	−0.106813	+	0.106813i	−0.758494	−	0.651681i	$-0.774064\pi$
$587$	−2.58787	+	2.58787i	−0.106813	+	0.106813i	0.651681	+	0.758494i	$0.274064\pi$
$588$	2.24557	−	2.50055i	0.0926059	−	0.103121i
$589$	−4.82484	+	6.29728i	−0.198804	+	0.259475i
$590$	−5.84264	+	4.49689i	−0.240538	+	0.185134i
$591$	0.808172	+	15.0432i	0.0332438	+	0.618796i
$592$	1.66823	−	0.447001i	0.0685639	−	0.0183716i
$593$	15.1385	+	15.1385i	0.621663	+	0.621663i	0.945957	−	0.324293i	$-0.105126\pi$
$593$	15.1385	+	15.1385i	0.621663	+	0.621663i	−0.324293	+	0.945957i	$0.605126\pi$
$594$	17.2075	−	14.0468i	0.706031	−	0.576348i
$595$	−9.54745	+	12.4804i	−0.391407	+	0.511648i
$596$	12.2614	+	7.07913i	0.502247	+	0.289973i
$597$	−13.8267	−	12.4168i	−0.565891	−	0.508188i
$598$	−44.1747	−	11.8366i	−1.80644	−	0.484034i
$599$	18.9866	+	32.8857i	0.775770	+	1.34367i	0.934361	+	0.356329i	$0.115972\pi$
$599$	18.9866	+	32.8857i	0.775770	+	1.34367i	−0.158590	+	0.987344i	$0.550695\pi$
$600$	2.71117	+	8.22493i	0.110683	+	0.335782i
$601$	−18.6012	+	32.2182i	−0.758759	+	1.31421i	0.184724	+	0.982790i	$0.440861\pi$
$601$	−18.6012	+	32.2182i	−0.758759	+	1.31421i	−0.943484	+	0.331419i	$0.892473\pi$
$602$	−2.30522	−	0.617681i	−0.0939536	−	0.0251748i
$603$	−8.49228	−	21.9508i	−0.345832	−	0.893906i
$604$		−	22.3947i		−	0.911226i
$605$	16.1301	+	2.09944i	0.655782	+	0.0853543i
$606$	−11.6628	+	22.9639i	−0.473769	+	0.932847i
$607$	8.83417	−	32.9696i	0.358568	−	1.33819i	−0.517367	−	0.855764i	$-0.673088\pi$
$607$	8.83417	−	32.9696i	0.358568	−	1.33819i	0.875935	−	0.482429i	$-0.160246\pi$
$608$	−1.37629	+	0.368775i	−0.0558157	+	0.0149558i
$609$	−3.04130	−	4.66977i	−0.123240	−	0.189229i
$610$	23.7586	+	9.80021i	0.961957	+	0.396799i
$611$	−9.45466	+	5.45865i	−0.382495	+	0.220833i
$612$	−5.87913	+	7.29919i	−0.237650	+	0.295052i
$613$	0.312573	+	1.16654i	0.0126247	+	0.0471160i	0.971951	−	0.235184i	$-0.0755693\pi$
$613$	0.312573	+	1.16654i	0.0126247	+	0.0471160i	−0.959326	+	0.282300i	$0.908903\pi$
$614$	−0.901989	+	1.56229i	−0.0364013	+	0.0630489i
$615$	−12.0867	+	34.4359i	−0.487381	+	1.38859i
$616$	−9.61569			−0.387427
$617$	−2.31427	−	8.63698i	−0.0931691	−	0.347712i	0.903566	−	0.428448i	$-0.140940\pi$
$617$	−2.31427	−	8.63698i	−0.0931691	−	0.347712i	−0.996735	+	0.0807363i	$0.974273\pi$
$618$	19.1987	+	17.2410i	0.772283	+	0.693535i
$619$		−	13.5641i		−	0.545189i	−0.962129	−	0.272595i	$-0.912118\pi$
$619$		−	13.5641i		−	0.545189i	0.962129	−	0.272595i	$-0.0878818\pi$
$620$	−3.24864	−	12.0186i	−0.130469	−	0.482678i
$621$	−7.86641	−	48.4322i	−0.315668	−	1.94352i
$622$	10.0701	+	10.0701i	0.403776	+	0.403776i
$623$	−31.8692	+	8.53934i	−1.27681	+	0.342121i
$624$	−0.450009	−	8.37642i	−0.0180148	−	0.335325i
$625$	−0.147081	−	24.9996i	−0.00588326	−	0.999983i
$626$	7.99378	+	4.61521i	0.319496	+	0.184461i
$627$	−3.27325	−	10.0292i	−0.130721	−	0.400529i
$628$	−7.95160	+	7.95160i	−0.317303	+	0.317303i
$629$	−2.69782	−	4.67276i	−0.107569	−	0.186315i
$630$	13.2310	−	7.25415i	0.527136	−	0.289012i
$631$	−7.68792	−	13.3159i	−0.306051	−	0.530096i	0.671444	−	0.741056i	$-0.265675\pi$
$631$	−7.68792	−	13.3159i	−0.306051	−	0.530096i	−0.977495	+	0.210960i	$0.932341\pi$
$632$	−4.42792	−	16.5252i	−0.176133	−	0.657338i
$633$	−11.5053	−	2.42977i	−0.457296	−	0.0965745i
$634$	4.49982	+	2.59797i	0.178711	+	0.103179i
$635$	15.8523	+	20.5963i	0.629078	+	0.817338i
$636$	0.637725	+	11.8705i	0.0252874	+	0.470697i
$637$	9.07730	−	2.43226i	0.359656	−	0.0963695i
$638$	1.58261	−	5.90638i	0.0626562	−	0.233836i
$639$	7.60877	−	17.2110i	0.300998	−	0.680855i
$640$	0.852667	−	2.06711i	0.0337046	−	0.0817098i
$641$	−27.7381	+	16.0146i	−1.09559	+	0.632538i	−0.935059	−	0.354493i	$-0.884653\pi$
$641$	−27.7381	+	16.0146i	−1.09559	+	0.632538i	−0.160529	+	0.987031i	$0.551320\pi$
$642$	−3.61840	+	17.1337i	−0.142807	+	0.676214i
$643$	−28.7348	+	28.7348i	−1.13319	+	1.13319i	−0.143546	+	0.989644i	$0.545850\pi$
$643$	−28.7348	+	28.7348i	−1.13319	+	1.13319i	−0.989644	+	0.143546i	$0.954150\pi$
$644$	−10.6203	+	18.3948i	−0.418497	+	0.724857i
$645$	3.39295	+	2.31803i	0.133597	+	0.0912725i
$646$	2.22569	+	3.85501i	0.0875687	+	0.151673i
$647$	28.4699	−	28.4699i	1.11927	−	1.11927i	0.127420	−	0.991849i	$-0.459330\pi$
$647$	28.4699	−	28.4699i	1.11927	−	1.11927i	0.991849	−	0.127420i	$-0.0406695\pi$
$648$	7.99751	−	4.12794i	0.314172	−	0.162161i
$649$			14.0952i			0.553284i
$650$	−6.19860	+	23.4087i	−0.243129	+	0.918166i
$651$	−19.5599	+	9.37847i	−0.766611	+	0.367571i
$652$	11.6732	+	11.6732i	0.457157	+	0.457157i
$653$	6.56683	+	6.56683i	0.256980	+	0.256980i	0.823825	−	0.566845i	$-0.191836\pi$
$653$	6.56683	+	6.56683i	0.256980	+	0.256980i	−0.566845	+	0.823825i	$0.691836\pi$
$654$	4.26362	−	8.39503i	0.166721	−	0.328271i
$655$	−0.581133	+	4.46488i	−0.0227067	+	0.174457i
$656$	8.16063	−	4.71154i	0.318619	−	0.183955i
$657$	−39.2280	+	15.1764i	−1.53043	+	0.592089i
$658$	1.31234	+	4.89772i	0.0511603	+	0.190933i
$659$	−0.507668			−0.0197759			−0.00988796	−	0.999951i	$-0.503147\pi$
$659$	−0.507668			−0.0197759			−0.00988796	+	0.999951i	$0.503147\pi$
$660$	15.6221	+	5.48321i	0.608091	+	0.213434i
$661$	7.15509	+	12.3930i	0.278301	+	0.482031i	0.970963	−	0.239231i	$-0.0768954\pi$
$661$	7.15509	+	12.3930i	0.278301	+	0.482031i	−0.692662	+	0.721263i	$0.743562\pi$
$662$	−32.0398	−	8.58504i	−1.24526	−	0.333667i
$663$	−24.9136	+	8.13105i	−0.967562	+	0.315784i
$664$	−10.8153	+	6.24421i	−0.419715	+	0.242322i
$665$	−0.945868	−	7.10382i	−0.0366792	−	0.275474i
$666$	0.555105	+	5.15142i	0.0215099	+	0.199613i
$667$	−9.55096	−	9.55096i	−0.369815	−	0.369815i
$668$	0.151510	−	0.0405970i	0.00586209	−	0.00157074i
$669$	0.576459	−	0.375433i	0.0222872	−	0.0145151i
$670$	10.6590	−	13.9334i	0.411792	−	0.538295i
$671$	42.5509	−	24.5668i	1.64266	−	0.948390i
$672$	−3.81192	−	0.805024i	−0.147048	−	0.0310545i
$673$	40.5817	+	10.8738i	1.56431	+	0.419155i	0.934024	−	0.357209i	$-0.116272\pi$
$673$	40.5817	+	10.8738i	1.56431	+	0.419155i	0.630284	+	0.776364i	$0.282938\pi$
$674$	−0.142109			−0.00547385
$675$	−25.6323	+	4.24066i	−0.986589	+	0.163223i
$676$	5.22782	−	9.05485i	0.201070	−	0.348264i
$677$	14.0593	+	3.76719i	0.540344	+	0.144785i	0.518661	−	0.854980i	$-0.326431\pi$
$677$	14.0593	+	3.76719i	0.540344	+	0.144785i	0.0216832	+	0.999765i	$0.493097\pi$
$678$	5.43846	−	6.05598i	0.208863	−	0.232579i
$679$	0.607643	+	0.350823i	0.0233192	+	0.0134633i
$680$	−6.92736	−	0.901641i	−0.265652	−	0.0345763i
$681$	−1.59939	−	29.7709i	−0.0612888	−	1.14082i
$682$	−21.9962	−	9.09251i	−0.842279	−	0.348170i
$683$	7.55951	+	7.55951i	0.289257	+	0.289257i	0.836786	−	0.547530i	$-0.184432\pi$
$683$	7.55951	+	7.55951i	0.289257	+	0.289257i	−0.547530	+	0.836786i	$0.684432\pi$
$684$	−0.457960	−	4.24990i	−0.0175105	−	0.162499i
$685$	2.33370	+	17.5269i	0.0891659	+	0.669670i
$686$		−	20.1101i		−	0.767809i
$687$	8.63371	−	40.8820i	0.329396	−	1.55975i
$688$	−0.274603	−	1.02483i	−0.0104692	−	0.0390714i
$689$	−16.6199	+	28.7866i	−0.633169	+	1.09668i
$690$	27.7436	−	23.8291i	1.05618	−	0.907158i
$691$	4.52517	+	7.83782i	0.172145	+	0.298165i	0.939170	−	0.343453i	$-0.111597\pi$
$691$	4.52517	+	7.83782i	0.172145	+	0.298165i	−0.767024	+	0.641618i	$0.778263\pi$
$692$	−7.83859	−	2.10034i	−0.297978	−	0.0798431i
$693$	4.43791	−	28.5037i	0.168582	−	1.08276i
$694$	24.6739	+	14.2455i	0.936610	+	0.540752i
$695$	29.1400	−	12.1204i	1.10534	−	0.459754i
$696$	1.12187	−	2.20896i	0.0425244	−	0.0837303i
$697$	−20.8165	−	20.8165i	−0.788483	−	0.788483i
$698$	−19.2681	−	19.2681i	−0.729309	−	0.729309i
$699$	4.63355	−	9.12343i	0.175257	−	0.345080i
$700$	9.75650	+	5.59472i	0.368761	+	0.211460i
$701$	12.0358	+	6.94886i	0.454585	+	0.262455i	0.709765	−	0.704439i	$-0.248801\pi$
$701$	12.0358	+	6.94886i	0.454585	+	0.262455i	−0.255180	+	0.966894i	$0.582135\pi$
$702$	25.0378	+	2.53199i	0.944991	+	0.0955639i
$703$	2.37695	+	0.636903i	0.0896485	+	0.0240213i
$704$	−2.13743	−	3.70214i	−0.0805575	−	0.139530i
$705$	0.660763	−	8.70542i	0.0248858	−	0.327865i
$706$	3.69284	−	6.39618i	0.138982	−	0.240723i
$707$	8.65705	+	32.3085i	0.325582	+	1.21509i
$708$	−1.18005	+	5.58772i	−0.0443489	+	0.209999i
$709$		−	4.94119i		−	0.185570i	−0.995686	−	0.0927851i	$-0.970423\pi$
$709$		−	4.94119i		−	0.185570i	0.995686	−	0.0927851i	$-0.0295770\pi$
$710$	13.9033	−	1.85121i	0.521781	−	0.0694746i
$711$	51.0291	−	5.49878i	1.91374	−	0.206220i
$712$	−10.3718	−	10.3718i	−0.388700	−	0.388700i
$713$	−41.6882	+	32.0364i	−1.56123	+	1.19977i
$714$	0.652960	+	12.1541i	0.0244364	+	0.454857i
$715$	28.2364	+	36.6865i	1.05598	+	1.37200i
$716$	16.6920	+	9.63714i	0.623810	+	0.360157i
$717$	4.90265	−	5.45933i	0.183093	−	0.203882i
$718$	−0.734746	−	0.196875i	−0.0274205	−	0.00734730i
$719$	−1.11391	+	1.92934i	−0.0415417	+	0.0719523i	−0.886049	−	0.463592i	$-0.846560\pi$
$719$	−1.11391	+	1.92934i	−0.0415417	+	0.0719523i	0.844507	+	0.535545i	$0.179894\pi$
$720$	5.73399	+	3.48158i	0.213693	+	0.129751i
$721$	33.5107			1.24800
$722$	16.3916	+	4.39212i	0.610033	+	0.163458i
$723$	9.59085	+	2.02545i	0.356687	+	0.0753273i
$724$	6.26061	−	3.61457i	0.232674	−	0.134334i
$725$	−5.04231	+	5.07206i	−0.187267	+	0.188372i
$726$	10.5580	−	6.87615i	0.391844	−	0.255198i
$727$	−3.29306	+	0.882373i	−0.122133	+	0.0327254i	−0.319368	−	0.947631i	$-0.603471\pi$
$727$	−3.29306	+	0.882373i	−0.122133	+	0.0327254i	0.197235	+	0.980356i	$0.436804\pi$
$728$	−7.70313	−	7.70313i	−0.285497	−	0.285497i
$729$	8.54532	+	25.6121i	0.316493	+	0.948595i
$730$	−24.9003	−	19.0485i	−0.921600	−	0.705017i
$731$	−2.87059	+	1.65733i	−0.106173	+	0.0612987i
$732$	18.9251	−	6.17659i	0.699491	−	0.228293i
$733$	6.20335	+	1.66218i	0.229126	+	0.0613941i	0.371555	−	0.928411i	$-0.378825\pi$
$733$	6.20335	+	1.66218i	0.229126	+	0.0613941i	−0.142429	+	0.989805i	$0.545491\pi$
$734$	−0.839996	−	1.45492i	−0.0310048	−	0.0537019i
$735$	−2.48887	+	7.09100i	−0.0918034	+	0.261556i
$736$	−9.44292			−0.348071
$737$	−8.68031	−	32.3954i	−0.319743	−	1.19330i
$738$	10.2000	+	26.3649i	0.375467	+	0.970507i
$739$	39.9092	−	23.0416i	1.46808	−	0.847598i	0.468721	−	0.883346i	$-0.344715\pi$
$739$	39.9092	−	23.0416i	1.46808	−	0.847598i	0.999361	+	0.0357486i	$0.0113816\pi$
$740$	−3.06036	+	2.35546i	−0.112501	+	0.0865884i
$741$	5.41222	−	10.6566i	0.198823	−	0.391481i
$742$	10.9164	+	10.9164i	0.400753	+	0.400753i
$743$	−31.2852	−	31.2852i	−1.14774	−	1.14774i	−0.986996	−	0.160746i	$-0.948610\pi$
$743$	−31.2852	−	31.2852i	−1.14774	−	1.14774i	−0.160746	−	0.986996i	$-0.551390\pi$
$744$	−7.95868	−	5.44604i	−0.291779	−	0.199662i
$745$	−31.3940	−	4.08614i	−1.15019	−	0.149705i
$746$			0.530857i			0.0194360i
$747$	−13.5181	−	34.9415i	−0.494600	−	1.27844i
$748$	−9.44360	+	9.44360i	−0.345292	+	0.345292i
$749$	11.3709	+	19.6950i	0.415484	+	0.719639i
$750$	−12.6606	−	14.6530i	−0.462299	−	0.535051i
$751$	−8.35753	+	14.4757i	−0.304971	+	0.528224i	−0.977255	−	0.212069i	$-0.931980\pi$
$751$	−8.35753	+	14.4757i	−0.304971	+	0.528224i	0.672284	+	0.740293i	$0.265313\pi$
$752$	−1.59396	+	1.59396i	−0.0581257	+	0.0581257i
$753$	−5.38378	+	25.4931i	−0.196196	+	0.929020i
$754$	5.99943	−	3.46377i	0.218486	−	0.126143i
$755$	19.2313	+	46.2359i	0.699898	+	1.68270i
$756$	4.14563	−	10.9281i	0.150775	−	0.397451i
$757$	−11.9977	+	44.7759i	−0.436062	+	1.62741i	0.302448	+	0.953166i	$0.402196\pi$
$757$	−11.9977	+	44.7759i	−0.436062	+	1.62741i	−0.738511	+	0.674242i	$0.764471\pi$
$758$	−17.3859	+	4.65855i	−0.631486	+	0.169206i
$759$	−3.75082	−	69.8173i	−0.136146	−	2.53421i
$760$	2.52479	−	1.94325i	0.0915838	−	0.0704890i
$761$	−1.01742	−	0.587406i	−0.0368813	−	0.0212935i	0.481446	−	0.876476i	$-0.340112\pi$
$761$	−1.01742	−	0.587406i	−0.0368813	−	0.0212935i	−0.518327	+	0.855182i	$0.673445\pi$
$762$	19.6976	+	4.15986i	0.713569	+	0.150696i
$763$	−3.16479	−	11.8112i	−0.114573	−	0.427593i
$764$	−9.95514	−	17.2428i	−0.360164	−	0.623823i
$765$	5.86989	−	20.1185i	0.212226	−	0.727388i
$766$	7.17614	+	12.4294i	0.259284	+	0.449094i
$767$	−11.2916	+	11.2916i	−0.407718	+	0.407718i
$768$	−0.537394	−	1.64657i	−0.0193915	−	0.0594156i
$769$	9.52131	+	5.49713i	0.343347	+	0.198232i	0.661751	−	0.749724i	$-0.269814\pi$
$769$	9.52131	+	5.49713i	0.343347	+	0.198232i	−0.318404	+	0.947955i	$0.603147\pi$
$770$	19.8525	−	8.25742i	0.715435	−	0.297577i
$771$	2.23811	+	41.6599i	0.0806035	+	1.50035i
$772$	−10.2685	+	2.75143i	−0.369570	+	0.0990261i
$773$	−7.16829	−	7.16829i	−0.257825	−	0.257825i	0.566344	−	0.824169i	$-0.308357\pi$
$773$	−7.16829	−	7.16829i	−0.257825	−	0.257825i	−0.824169	+	0.566344i	$0.808357\pi$
$774$	3.16464	−	0.341014i	0.113751	−	0.0122575i
$775$	17.0280	+	22.0238i	0.611665	+	0.791117i
$776$			0.311931i			0.0111977i
$777$	5.00630	+	4.49582i	0.179600	+	0.161287i
$778$	−2.05214	−	7.65870i	−0.0735729	−	0.274578i
$779$	13.4263			0.481048
$780$	8.12229	+	16.9075i	0.290824	+	0.605385i
$781$	13.4073	−	23.2221i	0.479750	−	0.830951i
$782$	7.63542	+	28.4958i	0.273042	+	1.01901i
$783$	6.03020	+	4.34504i	0.215502	+	0.155279i
$784$	1.68043	−	0.970196i	0.0600153	−	0.0346498i
$785$	9.58846	−	23.2452i	0.342227	−	0.829658i
$786$	1.90335	+	2.92250i	0.0678901	+	0.104242i
$787$	34.8546	−	9.33927i	1.24243	−	0.332909i	0.423024	−	0.906118i	$-0.360968\pi$
$787$	34.8546	−	9.33927i	1.24243	−	0.332909i	0.819409	+	0.573209i	$0.194302\pi$
$788$	−2.25114	+	8.40137i	−0.0801936	+	0.299286i
$789$	−7.21525	+	14.2068i	−0.256870	+	0.505774i
$790$	23.3328	+	30.3155i	0.830144	+	1.07858i
$791$		−	10.5705i		−	0.375845i
$792$	11.9607	−	4.62732i	0.425004	−	0.164425i
$793$	53.7680	+	14.4071i	1.90936	+	0.511610i
$794$	5.48233	−	9.49568i	0.194561	−	0.336989i
$795$	−11.5104	−	23.9602i	−0.408232	−	0.849782i
$796$	−5.36468	−	9.29189i	−0.190146	−	0.329342i
$797$	−24.0067	−	6.43257i	−0.850360	−	0.227853i	−0.192784	−	0.981241i	$-0.561752\pi$
$797$	−24.0067	−	6.43257i	−0.850360	−	0.227853i	−0.657576	+	0.753388i	$0.728418\pi$
$798$	−4.13019	−	3.70904i	−0.146207	−	0.131298i
$799$	6.09892	+	3.52121i	0.215764	+	0.124572i
$800$	0.0147082	+	4.99998i	0.000520014	+	0.176776i
$801$	35.5319	−	25.9581i	1.25546	−	0.917186i
$802$	11.5257	+	11.5257i	0.406987	+	0.406987i
$803$	−57.8933	+	15.5125i	−2.04301	+	0.547423i
$804$	−0.728978	−	13.5691i	−0.0257091	−	0.478546i
$805$	6.13010	−	47.0980i	0.216058	−	1.65998i
$806$	−10.3372	−	24.9052i	−0.364111	−	0.877248i
$807$	−6.41849	+	7.14728i	−0.225941	+	0.251596i
$808$	−10.5148	+	10.5148i	−0.369909	+	0.369909i
$809$	−13.4207	+	23.2453i	−0.471846	+	0.817262i	−0.999481	−	0.0322095i	$-0.989746\pi$
$809$	−13.4207	+	23.2453i	−0.471846	+	0.817262i	0.527635	+	0.849471i	$0.323079\pi$
$810$	−12.9668	+	15.3903i	−0.455606	+	0.540761i
$811$	7.75592	+	13.4336i	0.272347	+	0.471719i	0.969462	−	0.245240i	$-0.0788668\pi$
$811$	7.75592	+	13.4336i	0.272347	+	0.471719i	−0.697115	+	0.716959i	$0.745533\pi$
$812$	−0.832742	−	3.10784i	−0.0292235	−	0.109064i
$813$	13.1854	+	40.4001i	0.462432	+	1.41689i
$814$			7.38303i			0.258775i
$815$	−34.1246	−	14.0761i	−1.19533	−	0.493065i
$816$	−4.53432	+	2.95309i	−0.158733	+	0.103379i
$817$	0.391265	−	1.46022i	0.0136886	−	0.0510866i
$818$	14.8689	−	3.98410i	0.519877	−	0.139301i
$819$	26.3895	−	19.2791i	0.922123	−	0.673665i
$820$	−12.8024	+	16.7353i	−0.447079	+	0.584423i
$821$			54.9048i			1.91619i	0.286450	+	0.958095i	$0.407525\pi$
$821$			54.9048i			1.91619i	−0.286450	+	0.958095i	$0.592475\pi$
$822$	10.1902	+	9.15113i	0.355425	+	0.319182i
$823$	−1.91464	−	7.14552i	−0.0667400	−	0.249077i	0.924494	−	0.381197i	$-0.124488\pi$
$823$	−1.91464	−	7.14552i	−0.0667400	−	0.249077i	−0.991234	+	0.132120i	$0.957822\pi$
$824$	7.44894	+	12.9019i	0.259496	+	0.449461i
$825$	−36.9621	+	2.09479i	−1.28685	+	0.0729311i
$826$	3.70832	+	6.42300i	0.129029	+	0.223485i
$827$	−46.2632	−	12.3962i	−1.60873	−	0.431058i	−0.661067	−	0.750327i	$-0.729896\pi$
$827$	−46.2632	−	12.3962i	−1.60873	−	0.431058i	−0.947664	+	0.319269i	$0.896563\pi$
$828$	4.35817	−	27.9915i	0.151457	−	0.972773i
$829$			18.5088i			0.642836i	0.946937	+	0.321418i	$0.104160\pi$
$829$			18.5088i			0.642836i	−0.946937	+	0.321418i	$0.895840\pi$
$830$	16.9670	−	22.1793i	0.588934	−	0.769856i
$831$	−7.15388	+	14.0859i	−0.248165	+	0.488636i
$832$	1.25349	−	4.67808i	0.0434568	−	0.162183i
$833$	−4.28652	−	4.28652i	−0.148519	−	0.148519i
$834$	11.0699	−	21.7965i	0.383318	−	0.754750i
$835$	−0.277944	+	0.213925i	−0.00961867	+	0.00740316i
$836$		−	6.09098i		−	0.210661i
$837$	19.8168	−	21.0783i	0.684968	−	0.728573i
$838$	−1.83175	+	1.83175i	−0.0632767	+	0.0632767i
$839$	11.3966			0.393456			0.196728	−	0.980458i	$-0.436968\pi$
$839$	11.3966			0.393456			0.196728	+	0.980458i	$0.436968\pi$
$840$	8.56139	−	1.61142i	0.295396	−	0.0555991i
$841$	−26.9540			−0.929447
$842$	0.0602575	+	0.0161459i	0.00207661	+	0.000556426i
$843$	−10.9063	+	3.55951i	−0.375635	+	0.122596i
$844$	−5.87956	−	3.39456i	−0.202383	−	0.116846i
$845$	−3.01754	+	23.1840i	−0.103807	+	0.797553i
$846$	−3.98929	−	5.46060i	−0.137155	−	0.187739i
$847$	4.23501	−	15.8053i	0.145517	−	0.543076i
$848$	−1.77636	+	6.62948i	−0.0610006	+	0.227657i
$849$	13.0275	+	6.61635i	0.447104	+	0.227072i
$850$	15.0765	−	4.08730i	0.517119	−	0.140193i
$851$	14.1237	+	8.15434i	0.484155	+	0.279527i
$852$	7.25915	−	8.08341i	0.248695	−	0.276933i
$853$	−21.4372	+	21.4372i	−0.733997	+	0.733997i	−0.971409	−	0.237412i	$-0.923701\pi$
$853$	−21.4372	+	21.4372i	−0.733997	+	0.733997i	0.237412	+	0.971409i	$0.423701\pi$
$854$	12.9266	−	22.3895i	0.442339	−	0.766154i
$855$	4.59508	+	8.38106i	0.157148	+	0.286626i
$856$	−5.05518	+	8.75582i	−0.172782	+	0.299268i
$857$	−30.6509	−	8.21289i	−1.04702	−	0.280547i	−0.305998	−	0.952032i	$-0.598990\pi$
$857$	−30.6509	−	8.21289i	−1.04702	−	0.280547i	−0.741018	+	0.671485i	$0.765657\pi$
$858$	35.0858	+	7.40963i	1.19781	+	0.252960i
$859$	−9.09263	+	5.24963i	−0.310237	+	0.179115i	−0.647032	−	0.762463i	$-0.723990\pi$
$859$	−9.09263	+	5.24963i	−0.310237	+	0.179115i	0.336796	+	0.941578i	$0.390657\pi$
$860$	1.44701	+	1.88005i	0.0493428	+	0.0641093i
$861$	32.7328	+	16.6241i	1.11553	+	0.566549i
$862$	5.15320	−	1.38080i	0.175519	−	0.0470301i
$863$	−11.0202	+	41.1279i	−0.375131	+	1.40001i	0.478021	+	0.878348i	$0.341354\pi$
$863$	−11.0202	+	41.1279i	−0.375131	+	1.40001i	−0.853153	+	0.521661i	$0.825313\pi$
$864$	5.12894	−	0.833049i	0.174490	−	0.0283409i
$865$	17.9872	−	2.39498i	0.611582	−	0.0814316i
$866$			35.5636i			1.20850i
$867$	−9.32974	−	8.37840i	−0.316855	−	0.284546i
$868$	−12.4156	+	1.64367i	−0.421412	+	0.0557898i
$869$	73.1351			2.48094
$870$	−0.419285	+	5.52400i	−0.0142151	+	0.187281i
$871$	18.9981	−	32.9057i	0.643727	−	1.11497i
$872$	3.84393	−	3.84393i	0.130172	−	0.130172i
$873$	−0.924654	−	0.143965i	−0.0312948	−	0.00487248i
$874$	−11.6520	−	6.72730i	−0.394136	−	0.227554i
$875$	−24.9477	−	3.17250i	−0.843385	−	0.107250i
$876$	−24.2492	+	1.30275i	−0.819305	+	0.0440158i
$877$	3.03297	−	11.3192i	0.102416	−	0.382222i	−0.895623	−	0.444813i	$-0.853270\pi$
$877$	3.03297	−	11.3192i	0.102416	−	0.382222i	0.998039	+	0.0625919i	$0.0199366\pi$
$878$	6.30667	−	23.5368i	0.212840	−	0.794329i
$879$	−19.6975	−	30.2446i	−0.664381	−	1.02013i
$880$	7.59212	+	5.80792i	0.255930	+	0.195785i
$881$	−19.3489	+	11.1711i	−0.651881	+	0.376364i	−0.789177	−	0.614166i	$-0.789492\pi$
$881$	−19.3489	+	11.1711i	−0.651881	+	0.376364i	0.137295	+	0.990530i	$0.456159\pi$
$882$	2.10037	+	5.42904i	0.0707232	+	0.182805i
$883$	14.8745	−	14.8745i	0.500566	−	0.500566i	−0.411048	−	0.911614i	$-0.634837\pi$
$883$	14.8745	−	14.8745i	0.500566	−	0.500566i	0.911614	+	0.411048i	$0.134837\pi$
$884$	−15.1305			−0.508895
$885$	−2.36210	−	12.5497i	−0.0794010	−	0.421855i
$886$	14.0483	+	24.3323i	0.471961	+	0.817460i
$887$	−10.9231	−	40.7656i	−0.366762	−	1.36877i	−0.865016	−	0.501744i	$-0.832692\pi$
$887$	−10.9231	−	40.7656i	−0.366762	−	1.36877i	0.498254	−	0.867031i	$-0.333975\pi$
$888$	−0.618106	+	2.92683i	−0.0207423	+	0.0982181i
$889$	22.6421	−	13.0724i	0.759392	−	0.438435i
$890$	30.3203	+	12.5069i	1.01634	+	0.419231i
$891$	8.19651	+	37.5905i	0.274593	+	1.25933i
$892$	0.383646	−	0.102798i	0.0128454	−	0.00344192i
$893$	−3.10242	+	0.831290i	−0.103818	+	0.0278181i
$894$	−20.5490	+	13.3831i	−0.687263	+	0.447597i
$895$	−42.7381	−	5.56264i	−1.42858	−	0.185939i
$896$	−1.94800	−	1.12468i	−0.0650781	−	0.0375729i
$897$	52.9259	−	58.9354i	1.76714	−	1.96780i
$898$	6.19995	−	6.19995i	0.206895	−	0.206895i
$899$	1.03382	−	7.89671i	0.0344797	−	0.263370i
$900$	−14.8282	−	2.26403i	−0.494272	−	0.0754676i
$901$	21.4420			0.714338
$902$	10.4258	+	38.9098i	0.347143	+	1.29555i
$903$	2.76189	−	3.07549i	0.0919099	−	0.102346i
$904$	4.06976	−	2.34968i	0.135358	−	0.0781491i
$905$	−9.82165	+	12.8389i	−0.326483	+	0.426779i
$906$	34.5840	+	17.5643i	1.14898	+	0.583536i
$907$	10.6873	+	10.6873i	0.354867	+	0.354867i	0.861917	−	0.507050i	$-0.169264\pi$
$907$	10.6873	+	10.6873i	0.354867	+	0.354867i	−0.507050	+	0.861917i	$0.669264\pi$
$908$	4.45505	−	16.6265i	0.147846	−	0.551769i
$909$	−26.3160	−	36.0217i	−0.872845	−	1.19476i
$910$	22.5189	+	9.28884i	0.746493	+	0.307922i
$911$	44.6598	+	25.7844i	1.47965	+	0.854274i	0.999734	−	0.0230424i	$-0.00733527\pi$
$911$	44.6598	+	25.7844i	1.47965	+	0.854274i	0.479912	+	0.877317i	$0.340669\pi$
$912$	0.509935	−	2.41463i	0.0168856	−	0.0799564i
$913$	−13.8174	−	51.5672i	−0.457289	−	1.70662i
$914$	−30.3578			−1.00415
$915$	−33.7685	+	29.0039i	−1.11635	+	0.958841i
$916$	12.0619	−	20.8919i	0.398537	−	0.690287i
$917$	4.37497	+	1.17227i	0.144474	+	0.0387117i
$918$	−6.66108	−	14.8039i	−0.219848	−	0.488603i
$919$	−44.3810	+	25.6234i	−1.46399	+	0.845237i	−0.999193	−	0.0401783i	$-0.987207\pi$
$919$	−44.3810	+	25.6234i	−1.46399	+	0.845237i	−0.464801	+	0.885415i	$0.653874\pi$
$920$	19.4958	−	8.10905i	0.642758	−	0.267347i
$921$	−1.70520	−	2.61826i	−0.0561884	−	0.0862746i
$922$	−4.13473	−	4.13473i	−0.136170	−	0.136170i
$923$	29.3437	−	7.86263i	0.965861	−	0.258802i
$924$	7.54168	−	14.8495i	0.248103	−	0.488513i
$925$	4.29568	−	7.49114i	0.141241	−	0.246307i
$926$		−	6.21369i		−	0.204194i
$927$	−41.6830	+	16.1262i	−1.36905	+	0.529654i
$928$	1.01144	−	1.01144i	0.0332022	−	0.0332022i
$929$	19.7194			0.646973			0.323487	−	0.946233i	$-0.395145\pi$
$929$	19.7194			0.646973			0.323487	+	0.946233i	$0.395145\pi$
$930$	21.1082	+	4.40941i	0.692166	+	0.144590i
$931$	2.76474			0.0906106
$932$	4.17746	−	4.17746i	0.136837	−	0.136837i
$933$	−23.4494	+	7.65320i	−0.767699	+	0.250555i
$934$		−	16.0083i		−	0.523807i
$935$	11.3876	−	27.6069i	0.372414	−	0.902841i
$936$	13.2886	+	5.87476i	0.434353	+	0.192022i
$937$	−21.4113	+	5.73714i	−0.699476	+	0.187424i	−0.590996	−	0.806675i	$-0.701265\pi$
$937$	−21.4113	+	5.73714i	−0.699476	+	0.187424i	−0.108480	+	0.994099i	$0.534598\pi$
$938$	−12.4784	−	12.4784i	−0.407436	−	0.407436i
$939$	−13.3969	+	8.72503i	−0.437190	+	0.284731i
$940$	1.92208	−	4.65968i	0.0626913	−	0.151982i
$941$	−37.5662	+	21.6888i	−1.22462	+	0.707036i	−0.965900	−	0.258916i	$-0.916635\pi$
$941$	−37.5662	+	21.6888i	−1.22462	+	0.707036i	−0.258722	+	0.965952i	$0.583301\pi$
$942$	−6.04313	−	18.5162i	−0.196896	−	0.603289i
$943$	85.9494	+	23.0301i	2.79890	+	0.749963i
$944$	−1.64861	+	2.85548i	−0.0536578	+	0.0929380i
$945$	0.825376	+	26.1221i	0.0268495	+	0.849753i
$946$	4.53557			0.147464
$947$	−7.30286	−	27.2547i	−0.237311	−	0.885657i	−0.977093	−	0.212811i	$-0.931738\pi$
$947$	−7.30286	−	27.2547i	−0.237311	−	0.885657i	0.739782	−	0.672846i	$-0.234929\pi$
$948$	28.9927	+	6.12286i	0.941641	+	0.198861i
$949$	−58.8054	−	33.9513i	−1.90890	−	1.10211i
$950$	−3.54392	+	6.18017i	−0.114980	+	0.200511i
$951$	−7.54130	+	4.91146i	−0.244543	+	0.159265i
$952$	−1.81880	+	6.78786i	−0.0589477	+	0.219996i
$953$	−4.94739	−	4.94739i	−0.160262	−	0.160262i	0.622421	−	0.782683i	$-0.286149\pi$
$953$	−4.94739	−	4.94739i	−0.160262	−	0.160262i	−0.782683	+	0.622421i	$0.786149\pi$
$954$	−18.8318	−	8.32534i	−0.609703	−	0.269543i
$955$	35.3605	+	27.0505i	1.14424	+	0.875335i
$956$	3.66879	−	2.11818i	0.118657	−	0.0685068i
$957$	7.87997	+	7.07646i	0.254723	+	0.228749i
$958$	0.429747	+	1.60384i	0.0138845	+	0.0518176i
$959$	17.7867			0.574363
$960$	2.52349	+	2.93803i	0.0814452	+	0.0948245i
$961$	−29.9553	−	7.98009i	−0.966299	−	0.257422i
$962$	−5.91454	+	5.91454i	−0.190692	+	0.190692i
$963$	−23.6217	−	19.0260i	−0.761197	−	0.613106i
$964$	4.90119	+	2.82971i	0.157857	+	0.0911387i
$965$	18.8375	−	14.4986i	0.606400	−	0.466726i
$966$	−20.0775	−	30.8281i	−0.645984	−	0.991877i
$967$	−33.2231	+	8.90211i	−1.06838	+	0.286273i	−0.749829	−	0.661632i	$-0.769864\pi$
$967$	−33.2231	+	8.90211i	−1.06838	+	0.286273i	−0.318555	+	0.947904i	$0.603198\pi$
$968$	7.02658	−	1.88277i	0.225843	−	0.0605144i
$969$	−7.69892	+	0.413612i	−0.247325	+	0.0132871i
$970$	−0.267869	−	0.644013i	−0.00860076	−	0.0206780i
$971$	−52.5885	+	30.3620i	−1.68765	+	0.974363i	−0.731332	+	0.682022i	$0.761101\pi$
$971$	−52.5885	+	30.3620i	−1.68765	+	0.974363i	−0.956314	+	0.292341i	$0.905566\pi$
$972$	0.102247	+	15.5881i	0.00327959	+	0.499989i
$973$	−8.21692	−	30.6660i	−0.263422	−	0.983106i
$974$	−5.24948	−	9.09237i	−0.168204	−	0.291338i
$975$	−31.2884	−	27.9322i	−1.00203	−	0.894546i
$976$	11.4936			0.367901
$977$	−31.3536	+	31.3536i	−1.00309	+	1.00309i	−0.00309636	+	0.999995i	$0.500986\pi$
$977$	−31.3536	+	31.3536i	−1.00309	+	1.00309i	−0.999995	+	0.00309636i	$0.999014\pi$
$978$	−27.1822	+	8.87148i	−0.869192	+	0.283679i
$979$	54.3028	−	31.3517i	1.73553	−	1.00201i
$980$	−2.63626	+	3.44612i	−0.0842121	+	0.110082i
$981$	9.62043	+	13.1686i	0.307157	+	0.420441i
$982$	7.27126	−	27.1367i	0.232035	−	0.865967i
$983$	5.31479	−	19.8351i	0.169516	−	0.632641i	−0.827905	−	0.560868i	$-0.810468\pi$
$983$	5.31479	−	19.8351i	0.169516	−	0.632641i	0.997421	−	0.0717730i	$-0.0228657\pi$
$984$	0.875569	+	16.2978i	0.0279121	+	0.519553i
$985$	−2.56693	−	19.2786i	−0.0817891	−	0.614267i
$986$	−3.87005	−	2.23438i	−0.123248	−	0.0711570i
$987$	−8.59282	−	1.81468i	−0.273513	−	0.0577620i
$988$	4.87948	−	4.87948i	0.155237	−	0.155237i
$989$	5.00940	−	8.67654i	0.159290	−	0.275898i
$990$	−20.7203	+	19.8247i	−0.658535	+	0.630071i
$991$	38.7940			1.23233			0.616165	−	0.787617i	$-0.288685\pi$
$991$	38.7940			1.23233			0.616165	+	0.787617i	$0.288685\pi$
$992$	−3.39263	−	4.41475i	−0.107716	−	0.140169i
$993$	38.3870	−	42.7457i	1.21817	−	1.35649i
$994$		−	14.1093i		−	0.447521i
$995$	19.0552	+	14.5771i	0.604092	+	0.462126i
$996$	−1.16039	−	21.5994i	−0.0367685	−	0.684404i
$997$	−6.32579	+	23.6082i	−0.200340	+	0.747678i	0.790480	+	0.612488i	$0.209831\pi$
$997$	−6.32579	+	23.6082i	−0.200340	+	0.747678i	−0.990820	+	0.135190i	$0.956835\pi$
$998$	16.2579	−	4.35629i	0.514634	−	0.137896i
$999$	−8.39070	−	3.18306i	−0.265470	−	0.100707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.13	✓	256
3.2	odd	2	inner	930.2.bf.a.377.46	yes	256
5.3	odd	4	inner	930.2.bf.a.563.62	yes	256
15.8	even	4	inner	930.2.bf.a.563.30	yes	256
31.25	even	3	inner	930.2.bf.a.707.30	yes	256
93.56	odd	6	inner	930.2.bf.a.707.62	yes	256
155.118	odd	12	inner	930.2.bf.a.893.46	yes	256
465.428	even	12	inner	930.2.bf.a.893.13	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.13	✓	256	1.1	even	1	trivial
930.2.bf.a.377.46	yes	256	3.2	odd	2	inner
930.2.bf.a.563.30	yes	256	15.8	even	4	inner
930.2.bf.a.563.62	yes	256	5.3	odd	4	inner
930.2.bf.a.707.30	yes	256	31.25	even	3	inner
930.2.bf.a.707.62	yes	256	93.56	odd	6	inner
930.2.bf.a.893.13	yes	256	465.428	even	12	inner
930.2.bf.a.893.46	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.537394 - 1.64657i) q^{3} -1.00000i q^{4} +(0.858744 + 2.06460i) q^{5} +(1.54430 + 0.784309i) q^{6} +(2.17271 - 0.582177i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.42242 + 1.76972i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.537394 - 1.64657i) q^{3} -1.00000i q^{4} +(0.858744 + 2.06460i) q^{5} +(1.54430 + 0.784309i) q^{6} +(2.17271 - 0.582177i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.42242 + 1.76972i) q^{9} +(-2.06711 - 0.852667i) q^{10} +(-3.70214 + 2.13743i) q^{11} +(-1.64657 + 0.537394i) q^{12} +(-4.67808 - 1.25349i) q^{13} +(-1.12468 + 1.94800i) q^{14} +(2.93803 - 2.52349i) q^{15} -1.00000 q^{16} +(0.808587 + 3.01769i) q^{17} +(0.461528 - 2.96429i) q^{18} +(-1.23394 - 0.712418i) q^{19} +(2.06460 - 0.858744i) q^{20} +(-2.12620 - 3.26468i) q^{21} +(1.10642 - 4.12920i) q^{22} +(-6.67715 - 6.67715i) q^{23} +(0.784309 - 1.54430i) q^{24} +(-3.52512 + 3.54592i) q^{25} +(4.19425 - 2.42155i) q^{26} +(4.21576 + 3.03765i) q^{27} +(-0.582177 - 2.17271i) q^{28} +1.43039 q^{29} +(-0.293126 + 3.86187i) q^{30} +(0.722749 - 5.52066i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.50895 + 4.94721i) q^{33} +(-2.70559 - 1.56207i) q^{34} +(3.06776 + 3.98583i) q^{35} +(1.76972 + 2.42242i) q^{36} +(-1.66823 + 0.447001i) q^{37} +(1.37629 - 0.368775i) q^{38} +(0.450009 + 8.37642i) q^{39} +(-0.852667 + 2.06711i) q^{40} +(-8.16063 + 4.71154i) q^{41} +(3.81192 + 0.805024i) q^{42} +(0.274603 + 1.02483i) q^{43} +(2.13743 + 3.70214i) q^{44} +(-5.73399 - 3.48158i) q^{45} +9.44292 q^{46} +(1.59396 - 1.59396i) q^{47} +(0.537394 + 1.64657i) q^{48} +(-1.68043 + 0.970196i) q^{49} +(-0.0147082 - 4.99998i) q^{50} +(4.53432 - 2.95309i) q^{51} +(-1.25349 + 4.67808i) q^{52} +(1.77636 - 6.62948i) q^{53} +(-5.12894 + 0.833049i) q^{54} +(-7.59212 - 5.80792i) q^{55} +(1.94800 + 1.12468i) q^{56} +(-0.509935 + 2.41463i) q^{57} +(-1.01144 + 1.01144i) q^{58} +(1.64861 - 2.85548i) q^{59} +(-2.52349 - 2.93803i) q^{60} -11.4936 q^{61} +(3.39263 + 4.41475i) q^{62} +(-4.23293 + 5.25536i) q^{63} +1.00000i q^{64} +(-1.42932 - 10.7348i) q^{65} +(-7.39362 + 0.397210i) q^{66} +(-2.03055 + 7.57811i) q^{67} +(3.01769 - 0.808587i) q^{68} +(-7.40617 + 14.5827i) q^{69} +(-4.98765 - 0.649174i) q^{70} +(-5.43224 + 3.13630i) q^{71} +(-2.96429 - 0.461528i) q^{72} +(13.5427 + 3.62877i) q^{73} +(0.863540 - 1.49570i) q^{74} +(7.73300 + 3.89882i) q^{75} +(-0.712418 + 1.23394i) q^{76} +(-6.79932 + 6.79932i) q^{77} +(-6.24123 - 5.60482i) q^{78} +(-14.8161 - 8.55409i) q^{79} +(-0.858744 - 2.06460i) q^{80} +(2.73620 - 8.57398i) q^{81} +(2.43887 - 9.10200i) q^{82} +(-3.23224 + 12.0629i) q^{83} +(-3.26468 + 2.12620i) q^{84} +(-5.53594 + 4.26083i) q^{85} +(-0.918841 - 0.530493i) q^{86} +(-0.768685 - 2.35525i) q^{87} +(-4.12920 - 1.10642i) q^{88} -14.6680 q^{89} +(6.51639 - 1.59269i) q^{90} -10.8939 q^{91} +(-6.67715 + 6.67715i) q^{92} +(-9.47857 + 1.77671i) q^{93} +2.25420i q^{94} +(0.411214 - 3.15938i) q^{95} +(-1.54430 - 0.784309i) q^{96} +(0.220569 + 0.220569i) q^{97} +(0.502210 - 1.87427i) q^{98} +(5.18547 - 11.7295i) 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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