LMFDB - Embedded newform 930.2.k.a.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.1
Character	$\chi$	$=$	930.433
Dual form			930.2.k.a.247.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23600 - 0.0168647i) q^{5} +1.00000i q^{6} +(-2.83917 + 2.83917i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23600 - 0.0168647i) q^{5} +1.00000i q^{6} +(-2.83917 + 2.83917i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.59302 - 1.56917i) q^{10} +1.81284i q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.73747 - 3.73747i) q^{13} -4.01520i q^{14} +(-1.59302 + 1.56917i) q^{15} -1.00000 q^{16} +(-0.414677 - 0.414677i) q^{17} +(0.707107 + 0.707107i) q^{18} -5.16282i q^{19} +(-0.0168647 + 2.23600i) q^{20} +4.01520i q^{21} +(-1.28187 - 1.28187i) q^{22} +(1.45623 - 1.45623i) q^{23} +1.00000 q^{24} +(4.99943 + 0.0754191i) q^{25} +5.28558i q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.83917 + 2.83917i) q^{28} -1.79508 q^{29} +(0.0168647 - 2.23600i) q^{30} +(0.282430 - 5.56060i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.28187 + 1.28187i) q^{33} +0.586441 q^{34} +(6.39629 - 6.30052i) q^{35} -1.00000 q^{36} +(7.51505 + 7.51505i) q^{37} +(3.65066 + 3.65066i) q^{38} -5.28558i q^{39} +(-1.56917 - 1.59302i) q^{40} +8.55556 q^{41} +(-2.83917 - 2.83917i) q^{42} +(1.19646 - 1.19646i) q^{43} +1.81284 q^{44} +(-0.0168647 + 2.23600i) q^{45} +2.05941i q^{46} +(5.64339 - 5.64339i) q^{47} +(-0.707107 + 0.707107i) q^{48} -9.12181i q^{49} +(-3.58846 + 3.48180i) q^{50} -0.586441 q^{51} +(-3.73747 - 3.73747i) q^{52} +(-10.0735 + 10.0735i) q^{53} +1.00000 q^{54} +(0.0305730 - 4.05352i) q^{55} -4.01520 q^{56} +(-3.65066 - 3.65066i) q^{57} +(1.26931 - 1.26931i) q^{58} -11.6359i q^{59} +(1.56917 + 1.59302i) q^{60} -14.9734i q^{61} +(3.73223 + 4.13164i) q^{62} +(2.83917 + 2.83917i) q^{63} +1.00000i q^{64} +(-8.42004 + 8.29397i) q^{65} -1.81284 q^{66} +(8.55487 - 8.55487i) q^{67} +(-0.414677 + 0.414677i) q^{68} -2.05941i q^{69} +(-0.0677151 + 8.97800i) q^{70} -8.79233 q^{71} +(0.707107 - 0.707107i) q^{72} +(8.90002 - 8.90002i) q^{73} -10.6279 q^{74} +(3.58846 - 3.48180i) q^{75} -5.16282 q^{76} +(-5.14697 - 5.14697i) q^{77} +(3.73747 + 3.73747i) q^{78} -1.10953 q^{79} +(2.23600 + 0.0168647i) q^{80} -1.00000 q^{81} +(-6.04969 + 6.04969i) q^{82} +(-4.92882 + 4.92882i) q^{83} +4.01520 q^{84} +(0.920225 + 0.934212i) q^{85} +1.69205i q^{86} +(-1.26931 + 1.26931i) q^{87} +(-1.28187 + 1.28187i) q^{88} +2.43433 q^{89} +(-1.56917 - 1.59302i) q^{90} +21.2227i q^{91} +(-1.45623 - 1.45623i) q^{92} +(-3.73223 - 4.13164i) q^{93} +7.98096i q^{94} +(-0.0870693 + 11.5441i) q^{95} -1.00000i q^{96} +(2.65820 - 2.65820i) q^{97} +(6.45009 + 6.45009i) q^{98} +1.81284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−2.23600	−	0.0168647i	−0.999972	−	0.00754212i
$5$	−2.23600	−	0.0168647i	−0.999972	−	0.00754212i
$6$			1.00000i			0.408248i
$7$	−2.83917	+	2.83917i	−1.07311	+	1.07311i	−0.0759987	+	0.997108i	$0.524214\pi$
$7$	−2.83917	+	2.83917i	−1.07311	+	1.07311i	−0.997108	+	0.0759987i	$0.975786\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	1.59302	−	1.56917i	0.503757	−	0.496215i
$11$			1.81284i			0.546592i	0.961930	+	0.273296i	$0.0881139\pi$
$11$			1.81284i			0.546592i	−0.961930	+	0.273296i	$0.911886\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	3.73747	−	3.73747i	1.03659	−	1.03659i	0.0372835	−	0.999305i	$-0.488130\pi$
$13$	3.73747	−	3.73747i	1.03659	−	1.03659i	0.999305	−	0.0372835i	$-0.0118705\pi$
$14$		−	4.01520i		−	1.07311i
$15$	−1.59302	+	1.56917i	−0.411316	+	0.405158i
$16$	−1.00000			−0.250000
$17$	−0.414677	−	0.414677i	−0.100574	−	0.100574i	0.655029	−	0.755603i	$-0.272656\pi$
$17$	−0.414677	−	0.414677i	−0.100574	−	0.100574i	−0.755603	+	0.655029i	$0.772656\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$		−	5.16282i		−	1.18443i	−0.805780	−	0.592216i	$-0.798253\pi$
$19$		−	5.16282i		−	1.18443i	0.805780	−	0.592216i	$-0.201747\pi$
$20$	−0.0168647	+	2.23600i	−0.00377106	+	0.499986i
$21$			4.01520i			0.876188i
$22$	−1.28187	−	1.28187i	−0.273296	−	0.273296i
$23$	1.45623	−	1.45623i	0.303644	−	0.303644i	−0.538794	−	0.842438i	$-0.681120\pi$
$23$	1.45623	−	1.45623i	0.303644	−	0.303644i	0.842438	+	0.538794i	$0.181120\pi$
$24$	1.00000			0.204124
$25$	4.99943	+	0.0754191i	0.999886	+	0.0150838i
$26$			5.28558i			1.03659i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.83917	+	2.83917i	0.536553	+	0.536553i
$29$	−1.79508			−0.333337			−0.166669	−	0.986013i	$-0.553301\pi$
$29$	−1.79508			−0.333337			−0.166669	+	0.986013i	$0.553301\pi$
$30$	0.0168647	−	2.23600i	0.00307906	−	0.408237i
$31$	0.282430	−	5.56060i	0.0507259	−	0.998713i
$31$	0.282430	−	5.56060i	0.0507259	−	0.998713i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.28187	+	1.28187i	0.223145	+	0.223145i
$34$	0.586441			0.100574
$35$	6.39629	−	6.30052i	1.08117	−	1.06498i
$36$	−1.00000			−0.166667
$37$	7.51505	+	7.51505i	1.23547	+	1.23547i	0.961834	+	0.273633i	$0.0882252\pi$
$37$	7.51505	+	7.51505i	1.23547	+	1.23547i	0.273633	+	0.961834i	$0.411775\pi$
$38$	3.65066	+	3.65066i	0.592216	+	0.592216i
$39$		−	5.28558i		−	0.846371i
$40$	−1.56917	−	1.59302i	−0.248107	−	0.251878i
$41$	8.55556			1.33615			0.668077	−	0.744092i	$-0.267118\pi$
$41$	8.55556			1.33615			0.668077	+	0.744092i	$0.267118\pi$
$42$	−2.83917	−	2.83917i	−0.438094	−	0.438094i
$43$	1.19646	−	1.19646i	0.182458	−	0.182458i	−0.609968	−	0.792426i	$-0.708818\pi$
$43$	1.19646	−	1.19646i	0.182458	−	0.182458i	0.792426	+	0.609968i	$0.208818\pi$
$44$	1.81284			0.273296
$45$	−0.0168647	+	2.23600i	−0.00251404	+	0.333324i
$46$			2.05941i			0.303644i
$47$	5.64339	−	5.64339i	0.823174	−	0.823174i	−0.163388	−	0.986562i	$-0.552242\pi$
$47$	5.64339	−	5.64339i	0.823174	−	0.823174i	0.986562	+	0.163388i	$0.0522423\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	9.12181i		−	1.30312i
$50$	−3.58846	+	3.48180i	−0.507485	+	0.492401i
$51$	−0.586441			−0.0821182
$52$	−3.73747	−	3.73747i	−0.518294	−	0.518294i
$53$	−10.0735	+	10.0735i	−1.38370	+	1.38370i	−0.545753	+	0.837946i	$0.683756\pi$
$53$	−10.0735	+	10.0735i	−1.38370	+	1.38370i	−0.837946	+	0.545753i	$0.816244\pi$
$54$	1.00000			0.136083
$55$	0.0305730	−	4.05352i	0.00412246	−	0.546577i
$56$	−4.01520			−0.536553
$57$	−3.65066	−	3.65066i	−0.483542	−	0.483542i
$58$	1.26931	−	1.26931i	0.166669	−	0.166669i
$59$		−	11.6359i		−	1.51487i	−0.652913	−	0.757433i	$-0.726453\pi$
$59$		−	11.6359i		−	1.51487i	0.652913	−	0.757433i	$-0.273547\pi$
$60$	1.56917	+	1.59302i	0.202579	+	0.205658i
$61$		−	14.9734i		−	1.91715i	−0.284845	−	0.958574i	$-0.591942\pi$
$61$		−	14.9734i		−	1.91715i	0.284845	−	0.958574i	$-0.408058\pi$
$62$	3.73223	+	4.13164i	0.473993	+	0.524719i
$63$	2.83917	+	2.83917i	0.357702	+	0.357702i
$64$			1.00000i			0.125000i
$65$	−8.42004	+	8.29397i	−1.04438	+	1.02874i
$66$	−1.81284			−0.223145
$67$	8.55487	−	8.55487i	1.04514	−	1.04514i	0.0462116	−	0.998932i	$-0.485285\pi$
$67$	8.55487	−	8.55487i	1.04514	−	1.04514i	0.998932	−	0.0462116i	$-0.0147148\pi$
$68$	−0.414677	+	0.414677i	−0.0502869	+	0.0502869i
$69$		−	2.05941i		−	0.247924i
$70$	−0.0677151	+	8.97800i	−0.00809350	+	1.07308i
$71$	−8.79233			−1.04346			−0.521729	−	0.853112i	$-0.674713\pi$
$71$	−8.79233			−1.04346			−0.521729	+	0.853112i	$0.674713\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	8.90002	−	8.90002i	1.04167	−	1.04167i	0.0425747	−	0.999093i	$-0.486444\pi$
$73$	8.90002	−	8.90002i	1.04167	−	1.04167i	0.999093	−	0.0425747i	$-0.0135560\pi$
$74$	−10.6279			−1.23547
$75$	3.58846	−	3.48180i	0.414360	−	0.402044i
$76$	−5.16282			−0.592216
$77$	−5.14697	−	5.14697i	−0.586552	−	0.586552i
$78$	3.73747	+	3.73747i	0.423185	+	0.423185i
$79$	−1.10953			−0.124832			−0.0624159	−	0.998050i	$-0.519881\pi$
$79$	−1.10953			−0.124832			−0.0624159	+	0.998050i	$0.519881\pi$
$80$	2.23600	+	0.0168647i	0.249993	+	0.00188553i
$81$	−1.00000			−0.111111
$82$	−6.04969	+	6.04969i	−0.668077	+	0.668077i
$83$	−4.92882	+	4.92882i	−0.541008	+	0.541008i	−0.923825	−	0.382816i	$-0.874954\pi$
$83$	−4.92882	+	4.92882i	−0.541008	+	0.541008i	0.382816	+	0.923825i	$0.374954\pi$
$84$	4.01520			0.438094
$85$	0.920225	+	0.934212i	0.0998125	+	0.101330i
$86$			1.69205i			0.182458i
$87$	−1.26931	+	1.26931i	−0.136084	+	0.136084i
$88$	−1.28187	+	1.28187i	−0.136648	+	0.136648i
$89$	2.43433			0.258039			0.129019	−	0.991642i	$-0.458817\pi$
$89$	2.43433			0.258039			0.129019	+	0.991642i	$0.458817\pi$
$90$	−1.56917	−	1.59302i	−0.165405	−	0.167919i
$91$			21.2227i			2.22474i
$92$	−1.45623	−	1.45623i	−0.151822	−	0.151822i
$93$	−3.73223	−	4.13164i	−0.387014	−	0.428431i
$94$			7.98096i			0.823174i
$95$	−0.0870693	+	11.5441i	−0.00893312	+	1.18440i
$96$		−	1.00000i		−	0.102062i
$97$	2.65820	−	2.65820i	0.269900	−	0.269900i	−0.559160	−	0.829060i	$-0.688876\pi$
$97$	2.65820	−	2.65820i	0.269900	−	0.269900i	0.829060	+	0.559160i	$0.188876\pi$
$98$	6.45009	+	6.45009i	0.651558	+	0.651558i
$99$	1.81284			0.182197
$100$	0.0754191	−	4.99943i	0.00754191	−	0.499943i
$101$	4.23820			0.421717			0.210859	−	0.977517i	$-0.432374\pi$
$101$	4.23820			0.421717			0.210859	+	0.977517i	$0.432374\pi$
$102$	0.414677	−	0.414677i	0.0410591	−	0.0410591i
$103$	−7.89307	−	7.89307i	−0.777727	−	0.777727i	0.201717	−	0.979444i	$-0.435348\pi$
$103$	−7.89307	−	7.89307i	−0.777727	−	0.777727i	−0.979444	+	0.201717i	$0.935348\pi$
$104$	5.28558			0.518294
$105$	0.0677151	−	8.97800i	0.00660832	−	0.876163i
$106$		−	14.2461i		−	1.38370i
$107$	−3.14386	+	3.14386i	−0.303928	+	0.303928i	−0.842549	−	0.538620i	$-0.818946\pi$
$107$	−3.14386	+	3.14386i	−0.303928	+	0.303928i	0.538620	+	0.842549i	$0.318946\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$			2.89765i			0.277544i	0.990324	+	0.138772i	$0.0443156\pi$
$109$			2.89765i			0.277544i	−0.990324	+	0.138772i	$0.955684\pi$
$110$	2.84465	+	2.88789i	0.271227	+	0.275349i
$111$	10.6279			1.00875
$112$	2.83917	−	2.83917i	0.268277	−	0.268277i
$113$	9.16924	+	9.16924i	0.862570	+	0.862570i	0.991636	−	0.129066i	$-0.0411979\pi$
$113$	9.16924	+	9.16924i	0.862570	+	0.862570i	−0.129066	+	0.991636i	$0.541198\pi$
$114$	5.16282			0.483542
$115$	−3.28069	+	3.23157i	−0.305926	+	0.301345i
$116$			1.79508i			0.166669i
$117$	−3.73747	−	3.73747i	−0.345529	−	0.345529i
$118$	8.22783	+	8.22783i	0.757433	+	0.757433i
$119$	2.35468			0.215853
$120$	−2.23600	−	0.0168647i	−0.204118	−	0.00153953i
$121$	7.71361			0.701237
$122$	10.5878	+	10.5878i	0.958574	+	0.958574i
$123$	6.04969	−	6.04969i	0.545482	−	0.545482i
$124$	−5.56060	−	0.282430i	−0.499356	−	0.0253629i
$125$	−11.1775	−	0.252951i	−0.999744	−	0.0226246i
$126$	−4.01520			−0.357702
$127$	9.32720	+	9.32720i	0.827655	+	0.827655i	0.987192	−	0.159537i	$-0.0510001\pi$
$127$	9.32720	+	9.32720i	0.827655	+	0.827655i	−0.159537	+	0.987192i	$0.551000\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		−	1.69205i		−	0.148976i
$130$	0.0891398	−	11.8186i	0.00781807	−	1.03656i
$131$	−7.47150			−0.652788			−0.326394	−	0.945234i	$-0.605834\pi$
$131$	−7.47150			−0.652788			−0.326394	+	0.945234i	$0.605834\pi$
$132$	1.28187	−	1.28187i	0.111573	−	0.111573i
$133$	14.6581	+	14.6581i	1.27102	+	1.27102i
$134$			12.0984i			1.04514i
$135$	1.56917	+	1.59302i	0.135053	+	0.137105i
$136$		−	0.586441i		−	0.0502869i
$137$	−0.215572	−	0.215572i	−0.0184176	−	0.0184176i	0.697838	−	0.716256i	$-0.254146\pi$
$137$	−0.215572	−	0.215572i	−0.0184176	−	0.0184176i	−0.716256	+	0.697838i	$0.754146\pi$
$138$	1.45623	+	1.45623i	0.123962	+	0.123962i
$139$	−19.6874			−1.66986			−0.834932	−	0.550353i	$-0.814493\pi$
$139$	−19.6874			−1.66986			−0.834932	+	0.550353i	$0.814493\pi$
$140$	−6.30052	−	6.39629i	−0.532491	−	0.540585i
$141$		−	7.98096i		−	0.672118i
$142$	6.21711	−	6.21711i	0.521729	−	0.521729i
$143$	6.77544	+	6.77544i	0.566591	+	0.566591i
$144$			1.00000i			0.0833333i
$145$	4.01380	+	0.0302734i	0.333328	+	0.00251407i
$146$			12.5865i			1.04167i
$147$	−6.45009	−	6.45009i	−0.531995	−	0.531995i
$148$	7.51505	−	7.51505i	0.617733	−	0.617733i
$149$		−	12.2318i		−	1.00207i	−0.865427	−	0.501034i	$-0.832953\pi$
$149$		−	12.2318i		−	1.00207i	0.865427	−	0.501034i	$-0.167047\pi$
$150$	−0.0754191	+	4.99943i	−0.00615794	+	0.408202i
$151$			4.95980i			0.403622i	0.979424	+	0.201811i	$0.0646827\pi$
$151$			4.95980i			0.403622i	−0.979424	+	0.201811i	$0.935317\pi$
$152$	3.65066	−	3.65066i	0.296108	−	0.296108i
$153$	−0.414677	+	0.414677i	−0.0335246	+	0.0335246i
$154$	7.27891			0.586552
$155$	−0.725292	+	12.4288i	−0.0582568	+	0.998302i
$156$	−5.28558			−0.423185
$157$	−8.57571	+	8.57571i	−0.684416	+	0.684416i	−0.960992	−	0.276576i	$-0.910800\pi$
$157$	−8.57571	+	8.57571i	−0.684416	+	0.684416i	0.276576	+	0.960992i	$0.410800\pi$
$158$	0.784556	−	0.784556i	0.0624159	−	0.0624159i
$159$			14.2461i			1.12979i
$160$	−1.59302	+	1.56917i	−0.125939	+	0.124054i
$161$			8.26895i			0.651685i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−2.48033	−	2.48033i	−0.194274	−	0.194274i	0.603266	−	0.797540i	$-0.293866\pi$
$163$	−2.48033	−	2.48033i	−0.194274	−	0.194274i	−0.797540	+	0.603266i	$0.793866\pi$
$164$		−	8.55556i		−	0.668077i
$165$	−2.84465	−	2.88789i	−0.221456	−	0.224822i
$166$		−	6.97041i		−	0.541008i
$167$	10.9137	+	10.9137i	0.844524	+	0.844524i	0.989443	−	0.144920i	$-0.0462923\pi$
$167$	10.9137	+	10.9137i	0.844524	+	0.844524i	−0.144920	+	0.989443i	$0.546292\pi$
$168$	−2.83917	+	2.83917i	−0.219047	+	0.219047i
$169$		−	14.9374i		−	1.14903i
$170$	−1.31129	−	0.00989016i	−0.100571	−	0.000758540i
$171$	−5.16282			−0.394810
$172$	−1.19646	−	1.19646i	−0.0912291	−	0.0912291i
$173$	−1.04967	−	1.04967i	−0.0798047	−	0.0798047i	0.666078	−	0.745882i	$-0.267972\pi$
$173$	−1.04967	−	1.04967i	−0.0798047	−	0.0798047i	−0.745882	+	0.666078i	$0.767972\pi$
$174$		−	1.79508i		−	0.136084i
$175$	−14.4084	+	13.9801i	−1.08917	+	1.05680i
$176$		−	1.81284i		−	0.136648i
$177$	−8.22783	−	8.22783i	−0.618441	−	0.618441i
$178$	−1.72133	+	1.72133i	−0.129019	+	0.129019i
$179$	18.3644			1.37262			0.686311	−	0.727308i	$-0.259229\pi$
$179$	18.3644			1.37262			0.686311	+	0.727308i	$0.259229\pi$
$180$	2.23600	+	0.0168647i	0.166662	+	0.00125702i
$181$			13.7840i			1.02455i	0.858821	+	0.512277i	$0.171198\pi$
$181$			13.7840i			1.02455i	−0.858821	+	0.512277i	$0.828802\pi$
$182$	−15.0067	−	15.0067i	−1.11237	−	1.11237i
$183$	−10.5878	−	10.5878i	−0.782672	−	0.782672i
$184$	2.05941			0.151822
$185$	−16.6769	−	16.9304i	−1.22611	−	1.24475i
$186$	5.56060	+	0.282430i	0.407723	+	0.0207087i
$187$	0.751743	−	0.751743i	0.0549729	−	0.0549729i
$188$	−5.64339	−	5.64339i	−0.411587	−	0.411587i
$189$	4.01520			0.292063
$190$	−8.10133	−	8.22446i	−0.587732	−	0.596665i
$191$	−19.5990			−1.41813			−0.709067	−	0.705141i	$-0.750884\pi$
$191$	−19.5990			−1.41813			−0.709067	+	0.705141i	$0.750884\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	4.73249	+	4.73249i	0.340652	+	0.340652i	0.856613	−	0.515960i	$-0.172565\pi$
$193$	4.73249	+	4.73249i	0.340652	+	0.340652i	−0.515960	+	0.856613i	$0.672565\pi$
$194$			3.75927i			0.269900i
$195$	−0.0891398	+	11.8186i	−0.00638343	+	0.846347i
$196$	−9.12181			−0.651558
$197$	1.58776	+	1.58776i	0.113123	+	0.113123i	0.761403	−	0.648279i	$-0.224511\pi$
$197$	1.58776	+	1.58776i	0.113123	+	0.113123i	−0.648279	+	0.761403i	$0.724511\pi$
$198$	−1.28187	+	1.28187i	−0.0910987	+	0.0910987i
$199$	17.3755			1.23172			0.615860	−	0.787856i	$-0.288809\pi$
$199$	17.3755			1.23172			0.615860	+	0.787856i	$0.288809\pi$
$200$	3.48180	+	3.58846i	0.246201	+	0.253743i
$201$		−	12.0984i		−	0.853356i
$202$	−2.99686	+	2.99686i	−0.210859	+	0.210859i
$203$	5.09653	−	5.09653i	0.357706	−	0.357706i
$204$			0.586441i			0.0410591i
$205$	−19.1303	−	0.144287i	−1.33612	−	0.0100774i
$206$	11.1625			0.777727
$207$	−1.45623	−	1.45623i	−0.101215	−	0.101215i
$208$	−3.73747	+	3.73747i	−0.259147	+	0.259147i
$209$	9.35936			0.647401
$210$	6.30052	+	6.39629i	0.434777	+	0.441386i
$211$	−23.2793			−1.60261			−0.801305	−	0.598256i	$-0.795861\pi$
$211$	−23.2793			−1.60261			−0.801305	+	0.598256i	$0.795861\pi$
$212$	10.0735	+	10.0735i	0.691849	+	0.691849i
$213$	−6.21711	+	6.21711i	−0.425990	+	0.425990i
$214$		−	4.44609i		−	0.303928i
$215$	−2.69546	+	2.65511i	−0.183829	+	0.181077i
$216$		−	1.00000i		−	0.0680414i
$217$	14.9856	+	16.5894i	1.01729	+	1.12616i
$218$	−2.04895	−	2.04895i	−0.138772	−	0.138772i
$219$		−	12.5865i		−	0.850518i
$220$	−4.05352	−	0.0305730i	−0.273288	−	0.00206123i
$221$	−3.09968			−0.208507
$222$	−7.51505	+	7.51505i	−0.504377	+	0.504377i
$223$	−5.52774	+	5.52774i	−0.370165	+	0.370165i	−0.867537	−	0.497372i	$-0.834298\pi$
$223$	−5.52774	+	5.52774i	−0.370165	+	0.370165i	0.497372	+	0.867537i	$0.334298\pi$
$224$			4.01520i			0.268277i
$225$	0.0754191	−	4.99943i	0.00502794	−	0.333295i
$226$	−12.9673			−0.862570
$227$	1.59847	−	1.59847i	0.106094	−	0.106094i	−0.652067	−	0.758161i	$-0.726098\pi$
$227$	1.59847	−	1.59847i	0.106094	−	0.106094i	0.758161	+	0.652067i	$0.226098\pi$
$228$	−3.65066	+	3.65066i	−0.241771	+	0.241771i
$229$	−5.86981			−0.387888			−0.193944	−	0.981013i	$-0.562128\pi$
$229$	−5.86981			−0.387888			−0.193944	+	0.981013i	$0.562128\pi$
$230$	0.0347314	−	4.60486i	0.00229012	−	0.303635i
$231$	−7.27891			−0.478917
$232$	−1.26931	−	1.26931i	−0.0833343	−	0.0833343i
$233$	−13.4027	−	13.4027i	−0.878037	−	0.878037i	0.115294	−	0.993331i	$-0.463219\pi$
$233$	−13.4027	−	13.4027i	−0.878037	−	0.878037i	−0.993331	+	0.115294i	$0.963219\pi$
$234$	5.28558			0.345529
$235$	−12.7138	+	12.5235i	−0.829359	+	0.816942i
$236$	−11.6359			−0.757433
$237$	−0.784556	+	0.784556i	−0.0509624	+	0.0509624i
$238$	−1.66501	+	1.66501i	−0.107926	+	0.107926i
$239$	10.9303			0.707025			0.353512	−	0.935430i	$-0.384987\pi$
$239$	10.9303			0.707025			0.353512	+	0.935430i	$0.384987\pi$
$240$	1.59302	−	1.56917i	0.102829	−	0.101289i
$241$			6.76866i			0.436008i	0.975948	+	0.218004i	$0.0699545\pi$
$241$			6.76866i			0.436008i	−0.975948	+	0.218004i	$0.930045\pi$
$242$	−5.45434	+	5.45434i	−0.350619	+	0.350619i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−14.9734			−0.958574
$245$	−0.153837	+	20.3964i	−0.00982826	+	1.30308i
$246$			8.55556i			0.545482i
$247$	−19.2959	−	19.2959i	−1.22777	−	1.22777i
$248$	4.13164	−	3.73223i	0.262360	−	0.236997i
$249$			6.97041i			0.441732i
$250$	8.08253	−	7.72481i	0.511184	−	0.488560i
$251$		−	28.2567i		−	1.78355i	−0.452483	−	0.891773i	$-0.649462\pi$
$251$		−	28.2567i		−	1.78355i	0.452483	−	0.891773i	$-0.350538\pi$
$252$	2.83917	−	2.83917i	0.178851	−	0.178851i
$253$	2.63991	+	2.63991i	0.165969	+	0.165969i
$254$	−13.1907			−0.827655
$255$	1.31129	+	0.00989016i	0.0821159	+	0.000619346i
$256$	1.00000			0.0625000
$257$	8.77504	−	8.77504i	0.547372	−	0.547372i	−0.378308	−	0.925680i	$-0.623494\pi$
$257$	8.77504	−	8.77504i	0.547372	−	0.547372i	0.925680	+	0.378308i	$0.123494\pi$
$258$	1.19646	+	1.19646i	0.0744882	+	0.0744882i
$259$	−42.6731			−2.65158
$260$	8.29397	+	8.42004i	0.514370	+	0.522188i
$261$			1.79508i			0.111112i
$262$	5.28315	−	5.28315i	0.326394	−	0.326394i
$263$	1.31711	−	1.31711i	0.0812163	−	0.0812163i	−0.665332	−	0.746548i	$-0.731710\pi$
$263$	1.31711	−	1.31711i	0.0812163	−	0.0812163i	0.746548	+	0.665332i	$0.231710\pi$
$264$			1.81284i			0.111573i
$265$	22.6942	−	22.3545i	1.39410	−	1.37322i
$266$	−20.7297			−1.27102
$267$	1.72133	−	1.72133i	0.105344	−	0.105344i
$268$	−8.55487	−	8.55487i	−0.522572	−	0.522572i
$269$	−19.5940			−1.19467			−0.597334	−	0.801993i	$-0.703773\pi$
$269$	−19.5940			−1.19467			−0.597334	+	0.801993i	$0.703773\pi$
$270$	−2.23600	−	0.0168647i	−0.136079	−	0.00102635i
$271$		−	11.4482i		−	0.695426i	−0.937601	−	0.347713i	$-0.886958\pi$
$271$		−	11.4482i		−	0.695426i	0.937601	−	0.347713i	$-0.113042\pi$
$272$	0.414677	+	0.414677i	0.0251435	+	0.0251435i
$273$	15.0067	+	15.0067i	0.908246	+	0.908246i
$274$	0.304865			0.0184176
$275$	−0.136723	+	9.06317i	−0.00824469	+	0.546530i
$276$	−2.05941			−0.123962
$277$	5.53299	+	5.53299i	0.332445	+	0.332445i	0.853514	−	0.521069i	$-0.174467\pi$
$277$	5.53299	+	5.53299i	0.332445	+	0.332445i	−0.521069	+	0.853514i	$0.674467\pi$
$278$	13.9211	−	13.9211i	0.834932	−	0.834932i
$279$	−5.56060	−	0.282430i	−0.332904	−	0.0169086i
$280$	8.97800	+	0.0677151i	0.536538	+	0.00404675i
$281$	17.4877			1.04323			0.521616	−	0.853181i	$-0.325329\pi$
$281$	17.4877			1.04323			0.521616	+	0.853181i	$0.325329\pi$
$282$	5.64339	+	5.64339i	0.336059	+	0.336059i
$283$	10.8760	+	10.8760i	0.646510	+	0.646510i	0.952148	−	0.305637i	$-0.0988696\pi$
$283$	10.8760	+	10.8760i	0.646510	+	0.646510i	−0.305637	+	0.952148i	$0.598870\pi$
$284$			8.79233i			0.521729i
$285$	8.10133	+	8.22446i	0.479881	+	0.487175i
$286$	−9.58192			−0.566591
$287$	−24.2907	+	24.2907i	−1.43384	+	1.43384i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	16.6561i		−	0.979770i
$290$	−2.85959	+	2.81678i	−0.167921	+	0.165407i
$291$		−	3.75927i		−	0.220372i
$292$	−8.90002	−	8.90002i	−0.520834	−	0.520834i
$293$	3.96890	+	3.96890i	0.231866	+	0.231866i	0.813471	−	0.581605i	$-0.197575\pi$
$293$	3.96890	+	3.96890i	0.231866	+	0.231866i	−0.581605	+	0.813471i	$0.697575\pi$
$294$	9.12181			0.531995
$295$	−0.196236	+	26.0179i	−0.0114253	+	1.51482i
$296$			10.6279i			0.617733i
$297$	1.28187	−	1.28187i	0.0743818	−	0.0743818i
$298$	8.64919	+	8.64919i	0.501034	+	0.501034i
$299$		−	10.8852i		−	0.629508i
$300$	−3.48180	−	3.58846i	−0.201022	−	0.207180i
$301$			6.79390i			0.391594i
$302$	−3.50710	−	3.50710i	−0.201811	−	0.201811i
$303$	2.99686	−	2.99686i	0.172165	−	0.172165i
$304$			5.16282i			0.296108i
$305$	−0.252522	+	33.4806i	−0.0144594	+	1.91709i
$306$		−	0.586441i		−	0.0335246i
$307$	6.27483	−	6.27483i	0.358123	−	0.358123i	−0.504997	−	0.863121i	$-0.668507\pi$
$307$	6.27483	−	6.27483i	0.358123	−	0.358123i	0.863121	+	0.504997i	$0.168507\pi$
$308$	−5.14697	+	5.14697i	−0.293276	+	0.293276i
$309$	−11.1625			−0.635012
$310$	−8.27560	−	9.30132i	−0.470022	−	0.528279i
$311$	−4.48228			−0.254167			−0.127083	−	0.991892i	$-0.540562\pi$
$311$	−4.48228			−0.254167			−0.127083	+	0.991892i	$0.540562\pi$
$312$	3.73747	−	3.73747i	0.211593	−	0.211593i
$313$	−12.6723	+	12.6723i	−0.716279	+	0.716279i	−0.967841	−	0.251562i	$-0.919056\pi$
$313$	−12.6723	+	12.6723i	−0.716279	+	0.716279i	0.251562	+	0.967841i	$0.419056\pi$
$314$		−	12.1279i		−	0.684416i
$315$	−6.30052	−	6.39629i	−0.354994	−	0.360390i
$316$			1.10953i			0.0624159i
$317$	16.2672	−	16.2672i	0.913657	−	0.913657i	−0.0829008	−	0.996558i	$-0.526418\pi$
$317$	16.2672	−	16.2672i	0.913657	−	0.913657i	0.996558	+	0.0829008i	$0.0264185\pi$
$318$	−10.0735	−	10.0735i	−0.564893	−	0.564893i
$319$		−	3.25419i		−	0.182199i
$320$	0.0168647	−	2.23600i	0.000942765	−	0.124996i
$321$			4.44609i			0.248156i
$322$	−5.84703	−	5.84703i	−0.325842	−	0.325842i
$323$	−2.14090	+	2.14090i	−0.119123	+	0.119123i
$324$			1.00000i			0.0555556i
$325$	18.9671	−	18.4034i	1.05211	−	1.02083i
$326$	3.50771			0.194274
$327$	2.04895	+	2.04895i	0.113307	+	0.113307i
$328$	6.04969	+	6.04969i	0.334038	+	0.334038i
$329$			32.0451i			1.76671i
$330$	4.05352	+	0.0305730i	0.223139	+	0.00168299i
$331$			8.08274i			0.444267i	0.975016	+	0.222134i	$0.0713021\pi$
$331$			8.08274i			0.444267i	−0.975016	+	0.222134i	$0.928698\pi$
$332$	4.92882	+	4.92882i	0.270504	+	0.270504i
$333$	7.51505	−	7.51505i	0.411822	−	0.411822i
$334$	−15.4342			−0.844524
$335$	−19.2730	+	18.9844i	−1.05300	+	1.03723i
$336$		−	4.01520i		−	0.219047i
$337$	7.23881	+	7.23881i	0.394323	+	0.394323i	0.876225	−	0.481902i	$-0.160054\pi$
$337$	7.23881	+	7.23881i	0.394323	+	0.394323i	−0.481902	+	0.876225i	$0.660054\pi$
$338$	10.5623	+	10.5623i	0.574515	+	0.574515i
$339$	12.9673			0.704285
$340$	0.934212	−	0.920225i	0.0506648	−	0.0499062i
$341$	10.0805	+	0.512000i	0.545888	+	0.0277264i
$342$	3.65066	−	3.65066i	0.197405	−	0.197405i
$343$	6.02419	+	6.02419i	0.325275	+	0.325275i
$344$	1.69205			0.0912291
$345$	−0.0347314	+	4.60486i	−0.00186988	+	0.247917i
$346$	1.48445			0.0798047
$347$	9.36929	+	9.36929i	0.502970	+	0.502970i	0.912360	−	0.409390i	$-0.134258\pi$
$347$	9.36929	+	9.36929i	0.502970	+	0.502970i	−0.409390	+	0.912360i	$0.634258\pi$
$348$	1.26931	+	1.26931i	0.0680422	+	0.0680422i
$349$			3.98693i			0.213416i	0.994290	+	0.106708i	$0.0340309\pi$
$349$			3.98693i			0.213416i	−0.994290	+	0.106708i	$0.965969\pi$
$350$	0.302822	−	20.0737i	0.0161865	−	1.07298i
$351$	−5.28558			−0.282124
$352$	1.28187	+	1.28187i	0.0683240	+	0.0683240i
$353$	21.1352	−	21.1352i	1.12491	−	1.12491i	0.133919	−	0.990992i	$-0.457244\pi$
$353$	21.1352	−	21.1352i	1.12491	−	1.12491i	0.990992	−	0.133919i	$-0.0427560\pi$
$354$	11.6359			0.618441
$355$	19.6597	+	0.148280i	1.04343	+	0.00786988i
$356$		−	2.43433i		−	0.129019i
$357$	1.66501	−	1.66501i	0.0881216	−	0.0881216i
$358$	−12.9856	+	12.9856i	−0.686311	+	0.686311i
$359$		−	31.7569i		−	1.67607i	−0.545619	−	0.838033i	$-0.683705\pi$
$359$		−	31.7569i		−	1.67607i	0.545619	−	0.838033i	$-0.316295\pi$
$360$	−1.59302	+	1.56917i	−0.0839595	+	0.0827025i
$361$	−7.65467			−0.402877
$362$	−9.74673	−	9.74673i	−0.512277	−	0.512277i
$363$	5.45434	−	5.45434i	0.286279	−	0.286279i
$364$	21.2227			1.11237
$365$	−20.0506	+	19.7504i	−1.04949	+	1.03378i
$366$	14.9734			0.782672
$367$	−6.96777	−	6.96777i	−0.363714	−	0.363714i	0.501464	−	0.865178i	$-0.332795\pi$
$367$	−6.96777	−	6.96777i	−0.363714	−	0.363714i	−0.865178	+	0.501464i	$0.832795\pi$
$368$	−1.45623	+	1.45623i	−0.0759110	+	0.0759110i
$369$		−	8.55556i		−	0.445385i
$370$	23.7640	+	0.179236i	1.23543	+	0.00931804i
$371$		−	57.2007i		−	2.96971i
$372$	−4.13164	+	3.73223i	−0.214216	+	0.193507i
$373$	2.87777	+	2.87777i	0.149005	+	0.149005i	0.777674	−	0.628668i	$-0.216400\pi$
$373$	2.87777	+	2.87777i	0.149005	+	0.149005i	−0.628668	+	0.777674i	$0.716400\pi$
$374$			1.06312i			0.0549729i
$375$	−8.08253	+	7.72481i	−0.417380	+	0.398907i
$376$	7.98096			0.411587
$377$	−6.70905	+	6.70905i	−0.345533	+	0.345533i
$378$	−2.83917	+	2.83917i	−0.146031	+	0.146031i
$379$		−	23.6210i		−	1.21333i	−0.794958	−	0.606664i	$-0.792507\pi$
$379$		−	23.6210i		−	1.21333i	0.794958	−	0.606664i	$-0.207493\pi$
$380$	11.5441	+	0.0870693i	0.592199	+	0.00446656i
$381$	13.1907			0.675778
$382$	13.8586	−	13.8586i	0.709067	−	0.709067i
$383$	−26.4171	+	26.4171i	−1.34985	+	1.34985i	−0.464035	+	0.885817i	$0.653599\pi$
$383$	−26.4171	+	26.4171i	−1.34985	+	1.34985i	−0.885817	+	0.464035i	$0.846401\pi$
$384$	−1.00000			−0.0510310
$385$	11.4218	+	11.5954i	0.582111	+	0.590959i
$386$	−6.69276			−0.340652
$387$	−1.19646	−	1.19646i	−0.0608194	−	0.0608194i
$388$	−2.65820	−	2.65820i	−0.134950	−	0.134950i
$389$	−5.92403			−0.300360			−0.150180	−	0.988659i	$-0.547985\pi$
$389$	−5.92403			−0.300360			−0.150180	+	0.988659i	$0.547985\pi$
$390$	−8.29397	−	8.42004i	−0.419982	−	0.426365i
$391$	−1.20773			−0.0610773
$392$	6.45009	−	6.45009i	0.325779	−	0.325779i
$393$	−5.28315	+	5.28315i	−0.266500	+	0.266500i
$394$	−2.24543			−0.113123
$395$	2.48091	+	0.0187119i	0.124828	+	0.000941497i
$396$		−	1.81284i		−	0.0910987i
$397$	15.6861	−	15.6861i	0.787262	−	0.787262i	−0.193783	−	0.981044i	$-0.562076\pi$
$397$	15.6861	−	15.6861i	0.787262	−	0.787262i	0.981044	+	0.193783i	$0.0620757\pi$
$398$	−12.2864	+	12.2864i	−0.615860	+	0.615860i
$399$	20.7297			1.03778
$400$	−4.99943	−	0.0754191i	−0.249972	−	0.00377095i
$401$		−	2.84987i		−	0.142316i	−0.997465	−	0.0711578i	$-0.977331\pi$
$401$		−	2.84987i		−	0.142316i	0.997465	−	0.0711578i	$-0.0226694\pi$
$402$	8.55487	+	8.55487i	0.426678	+	0.426678i
$403$	−19.7270	−	21.8381i	−0.982672	−	1.08784i
$404$		−	4.23820i		−	0.210859i
$405$	2.23600	+	0.0168647i	0.111108	+	0.000838013i
$406$			7.20758i			0.357706i
$407$	−13.6236	+	13.6236i	−0.675296	+	0.675296i
$408$	−0.414677	−	0.414677i	−0.0205296	−	0.0205296i
$409$	−1.33013			−0.0657707			−0.0328854	−	0.999459i	$-0.510470\pi$
$409$	−1.33013			−0.0657707			−0.0328854	+	0.999459i	$0.510470\pi$
$410$	13.6292	−	13.4251i	0.673096	−	0.663019i
$411$	−0.304865			−0.0150379
$412$	−7.89307	+	7.89307i	−0.388864	+	0.388864i
$413$	33.0364	+	33.0364i	1.62561	+	1.62561i
$414$	2.05941			0.101215
$415$	11.1040	−	10.9377i	0.545073	−	0.536913i
$416$		−	5.28558i		−	0.259147i
$417$	−13.9211	+	13.9211i	−0.681719	+	0.681719i
$418$	−6.61807	+	6.61807i	−0.323700	+	0.323700i
$419$		−	30.2573i		−	1.47817i	−0.673615	−	0.739083i	$-0.735259\pi$
$419$		−	30.2573i		−	1.47817i	0.673615	−	0.739083i	$-0.264741\pi$
$420$	−8.97800	−	0.0677151i	−0.438081	−	0.00330416i
$421$	20.4624			0.997276			0.498638	−	0.866810i	$-0.333834\pi$
$421$	20.4624			0.997276			0.498638	+	0.866810i	$0.333834\pi$
$422$	16.4609	−	16.4609i	0.801305	−	0.801305i
$423$	−5.64339	−	5.64339i	−0.274391	−	0.274391i
$424$	−14.2461			−0.691849
$425$	−2.04187	−	2.10442i	−0.0990454	−	0.102079i
$426$		−	8.79233i		−	0.425990i
$427$	42.5121	+	42.5121i	2.05730	+	2.05730i
$428$	3.14386	+	3.14386i	0.151964	+	0.151964i
$429$	9.58192			0.462620
$430$	0.0285359	−	3.78343i	0.00137612	−	0.182453i
$431$	20.4577			0.985413			0.492706	−	0.870196i	$-0.336008\pi$
$431$	20.4577			0.985413			0.492706	+	0.870196i	$0.336008\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	20.4839	−	20.4839i	0.984393	−	0.984393i	−0.0154872	−	0.999880i	$-0.504930\pi$
$433$	20.4839	−	20.4839i	0.984393	−	0.984393i	0.999880	+	0.0154872i	$0.00492991\pi$
$434$	−22.3269	−	1.13401i	−1.07173	−	0.0544343i
$435$	2.85959	−	2.81678i	0.137107	−	0.135054i
$436$	2.89765			0.138772
$437$	−7.51823	−	7.51823i	−0.359646	−	0.359646i
$438$	8.90002	+	8.90002i	0.425259	+	0.425259i
$439$			17.6096i			0.840460i	0.907418	+	0.420230i	$0.138051\pi$
$439$			17.6096i			0.840460i	−0.907418	+	0.420230i	$0.861949\pi$
$440$	2.88789	−	2.84465i	0.137675	−	0.135614i
$441$	−9.12181			−0.434372
$442$	2.19181	−	2.19181i	0.104254	−	0.104254i
$443$	−20.5622	−	20.5622i	−0.976942	−	0.976942i	0.0227982	−	0.999740i	$-0.492742\pi$
$443$	−20.5622	−	20.5622i	−0.976942	−	0.976942i	−0.999740	+	0.0227982i	$0.992742\pi$
$444$		−	10.6279i		−	0.504377i
$445$	−5.44318	−	0.0410543i	−0.258032	−	0.00194616i
$446$		−	7.81741i		−	0.370165i
$447$	−8.64919	−	8.64919i	−0.409093	−	0.409093i
$448$	−2.83917	−	2.83917i	−0.134138	−	0.134138i
$449$	−21.0915			−0.995370			−0.497685	−	0.867358i	$-0.665816\pi$
$449$	−21.0915			−0.995370			−0.497685	+	0.867358i	$0.665816\pi$
$450$	3.48180	+	3.58846i	0.164134	+	0.169162i
$451$			15.5099i			0.730331i
$452$	9.16924	−	9.16924i	0.431285	−	0.431285i
$453$	3.50710	+	3.50710i	0.164778	+	0.164778i
$454$			2.26058i			0.106094i
$455$	0.357914	−	47.4540i	0.0167793	−	2.22468i
$456$		−	5.16282i		−	0.241771i
$457$	−28.2999	−	28.2999i	−1.32382	−	1.32382i	−0.910661	−	0.413155i	$-0.864427\pi$
$457$	−28.2999	−	28.2999i	−1.32382	−	1.32382i	−0.413155	−	0.910661i	$-0.635573\pi$
$458$	4.15058	−	4.15058i	0.193944	−	0.193944i
$459$			0.586441i			0.0273727i
$460$	3.23157	+	3.28069i	0.150673	+	0.152963i
$461$		−	4.46650i		−	0.208026i	−0.994576	−	0.104013i	$-0.966832\pi$
$461$		−	4.46650i		−	0.208026i	0.994576	−	0.104013i	$-0.0331683\pi$
$462$	5.14697	−	5.14697i	0.239459	−	0.239459i
$463$	−15.0939	+	15.0939i	−0.701474	+	0.701474i	−0.964727	−	0.263253i	$-0.915205\pi$
$463$	−15.0939	+	15.0939i	−0.701474	+	0.701474i	0.263253	+	0.964727i	$0.415205\pi$
$464$	1.79508			0.0833343
$465$	8.27560	+	9.30132i	0.383772	+	0.431338i
$466$	18.9542			0.878037
$467$	13.9515	−	13.9515i	0.645601	−	0.645601i	−0.306326	−	0.951927i	$-0.599100\pi$
$467$	13.9515	−	13.9515i	0.645601	−	0.645601i	0.951927	+	0.306326i	$0.0990998\pi$
$468$	−3.73747	+	3.73747i	−0.172765	+	0.172765i
$469$			48.5775i			2.24310i
$470$	0.134597	−	17.8455i	0.00620847	−	0.823150i
$471$			12.1279i			0.558824i
$472$	8.22783	−	8.22783i	0.378717	−	0.378717i
$473$	2.16899	+	2.16899i	0.0997302	+	0.0997302i
$474$		−	1.10953i		−	0.0509624i
$475$	0.389375	−	25.8111i	0.0178657	−	1.18430i
$476$		−	2.35468i		−	0.107926i
$477$	10.0735	+	10.0735i	0.461233	+	0.461233i
$478$	−7.72891	+	7.72891i	−0.353512	+	0.353512i
$479$			25.0115i			1.14280i	0.820671	+	0.571402i	$0.193600\pi$
$479$			25.0115i			1.14280i	−0.820671	+	0.571402i	$0.806400\pi$
$480$	−0.0168647	+	2.23600i	−0.000769765	+	0.102059i
$481$	56.1746			2.56134
$482$	−4.78616	−	4.78616i	−0.218004	−	0.218004i
$483$	5.84703	+	5.84703i	0.266049	+	0.266049i
$484$		−	7.71361i		−	0.350619i
$485$	−5.98859	+	5.89893i	−0.271928	+	0.267856i
$486$		−	1.00000i		−	0.0453609i
$487$	−16.4821	−	16.4821i	−0.746877	−	0.746877i	0.227014	−	0.973891i	$-0.427104\pi$
$487$	−16.4821	−	16.4821i	−0.746877	−	0.746877i	−0.973891	+	0.227014i	$0.927104\pi$
$488$	10.5878	−	10.5878i	0.479287	−	0.479287i
$489$	−3.50771			−0.158624
$490$	−14.3137	−	14.5312i	−0.646625	−	0.656453i
$491$		−	5.29985i		−	0.239179i	−0.992823	−	0.119590i	$-0.961842\pi$
$491$		−	5.29985i		−	0.239179i	0.992823	−	0.119590i	$-0.0381578\pi$
$492$	−6.04969	−	6.04969i	−0.272741	−	0.272741i
$493$	0.744376	+	0.744376i	0.0335250	+	0.0335250i
$494$	27.2885			1.22777
$495$	−4.05352	−	0.0305730i	−0.182192	−	0.00137415i
$496$	−0.282430	+	5.56060i	−0.0126815	+	0.249678i
$497$	24.9629	−	24.9629i	1.11974	−	1.11974i
$498$	−4.92882	−	4.92882i	−0.220866	−	0.220866i
$499$	15.7106			0.703303			0.351652	−	0.936131i	$-0.385620\pi$
$499$	15.7106			0.703303			0.351652	+	0.936131i	$0.385620\pi$
$500$	−0.252951	+	11.1775i	−0.0113123	+	0.499872i
$501$	15.4342			0.689551
$502$	19.9805	+	19.9805i	0.891773	+	0.891773i
$503$	11.2912	+	11.2912i	0.503450	+	0.503450i	0.912508	−	0.409058i	$-0.134143\pi$
$503$	11.2912	+	11.2912i	0.503450	+	0.503450i	−0.409058	+	0.912508i	$0.634143\pi$
$504$			4.01520i			0.178851i
$505$	−9.47664	−	0.0714760i	−0.421705	−	0.00318064i
$506$	−3.73339			−0.165969
$507$	−10.5623	−	10.5623i	−0.469090	−	0.469090i
$508$	9.32720	−	9.32720i	0.413828	−	0.413828i
$509$	20.6363			0.914687			0.457343	−	0.889290i	$-0.348801\pi$
$509$	20.6363			0.914687			0.457343	+	0.889290i	$0.348801\pi$
$510$	−0.934212	+	0.920225i	−0.0413676	+	0.0407483i
$511$			50.5374i			2.23564i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.65066	+	3.65066i	−0.161181	+	0.161181i
$514$			12.4098i			0.547372i
$515$	17.5158	+	17.7821i	0.771839	+	0.783571i
$516$	−1.69205			−0.0744882
$517$	10.2306	+	10.2306i	0.449940	+	0.449940i
$518$	30.1744	−	30.1744i	1.32579	−	1.32579i
$519$	−1.48445			−0.0651603
$520$	−11.8186	−	0.0891398i	−0.518279	−	0.00390904i
$521$	23.9987			1.05140			0.525700	−	0.850670i	$-0.323803\pi$
$521$	23.9987			1.05140			0.525700	+	0.850670i	$0.323803\pi$
$522$	−1.26931	−	1.26931i	−0.0555562	−	0.0555562i
$523$	−10.7635	+	10.7635i	−0.470653	+	0.470653i	−0.902126	−	0.431473i	$-0.857994\pi$
$523$	−10.7635	+	10.7635i	−0.470653	+	0.470653i	0.431473	+	0.902126i	$0.357994\pi$
$524$			7.47150i			0.326394i
$525$	−0.302822	+	20.0737i	−0.0132163	+	0.876088i
$526$			1.86267i			0.0812163i
$527$	−2.42297	+	2.18873i	−0.105546	+	0.0953427i
$528$	−1.28187	−	1.28187i	−0.0557863	−	0.0557863i
$529$			18.7588i			0.815601i
$530$	−0.240255	+	31.8542i	−0.0104360	+	1.38366i
$531$	−11.6359			−0.504955
$532$	14.6581	−	14.6581i	0.635511	−	0.635511i
$533$	31.9762	−	31.9762i	1.38504	−	1.38504i
$534$			2.43433i			0.105344i
$535$	7.08270	−	6.97666i	0.306212	−	0.301627i
$536$	12.0984			0.522572
$537$	12.9856	−	12.9856i	0.560371	−	0.560371i
$538$	13.8550	−	13.8550i	0.597334	−	0.597334i
$539$	16.5364			0.712273
$540$	1.59302	−	1.56917i	0.0685526	−	0.0675263i
$541$	14.6540			0.630026			0.315013	−	0.949087i	$-0.397991\pi$
$541$	14.6540			0.630026			0.315013	+	0.949087i	$0.397991\pi$
$542$	8.09507	+	8.09507i	0.347713	+	0.347713i
$543$	9.74673	+	9.74673i	0.418272	+	0.418272i
$544$	−0.586441			−0.0251435
$545$	0.0488680	−	6.47915i	0.00209327	−	0.277536i
$546$	−21.2227			−0.908246
$547$	1.41116	−	1.41116i	0.0603370	−	0.0603370i	−0.676294	−	0.736631i	$-0.736415\pi$
$547$	1.41116	−	1.41116i	0.0603370	−	0.0603370i	0.736631	+	0.676294i	$0.236415\pi$
$548$	−0.215572	+	0.215572i	−0.00920879	+	0.00920879i
$549$	−14.9734			−0.639049
$550$	−6.31195	−	6.50531i	−0.269143	−	0.277387i
$551$			9.26765i			0.394815i
$552$	1.45623	−	1.45623i	0.0619811	−	0.0619811i
$553$	3.15015	−	3.15015i	0.133958	−	0.133958i
$554$	−7.82482			−0.332445
$555$	−23.7640	−	0.179236i	−1.00873	−	0.00760815i
$556$			19.6874i			0.834932i
$557$	1.16052	+	1.16052i	0.0491728	+	0.0491728i	0.731266	−	0.682093i	$-0.238930\pi$
$557$	1.16052	+	1.16052i	0.0491728	+	0.0491728i	−0.682093	+	0.731266i	$0.738930\pi$
$558$	4.13164	−	3.73223i	0.174906	−	0.157998i
$559$		−	8.94346i		−	0.378268i
$560$	−6.39629	+	6.30052i	−0.270292	+	0.266246i
$561$		−	1.06312i		−	0.0448852i
$562$	−12.3657	+	12.3657i	−0.521616	+	0.521616i
$563$	−14.8766	−	14.8766i	−0.626975	−	0.626975i	0.320331	−	0.947306i	$-0.396206\pi$
$563$	−14.8766	−	14.8766i	−0.626975	−	0.626975i	−0.947306	+	0.320331i	$0.896206\pi$
$564$	−7.98096			−0.336059
$565$	−20.3478	−	20.6571i	−0.856040	−	0.869051i
$566$	−15.3810			−0.646510
$567$	2.83917	−	2.83917i	0.119234	−	0.119234i
$568$	−6.21711	−	6.21711i	−0.260864	−	0.260864i
$569$	12.8516			0.538766			0.269383	−	0.963033i	$-0.413180\pi$
$569$	12.8516			0.538766			0.269383	+	0.963033i	$0.413180\pi$
$570$	−11.5441	−	0.0870693i	−0.483528	−	0.00364693i
$571$			14.2956i			0.598251i	0.954214	+	0.299126i	$0.0966949\pi$
$571$			14.2956i			0.598251i	−0.954214	+	0.299126i	$0.903305\pi$
$572$	6.77544	−	6.77544i	0.283295	−	0.283295i
$573$	−13.8586	+	13.8586i	−0.578951	+	0.578951i
$574$		−	34.3522i		−	1.43384i
$575$	7.39013	−	7.17047i	0.308190	−	0.299029i
$576$	1.00000			0.0416667
$577$	−15.4127	+	15.4127i	−0.641641	+	0.641641i	−0.950959	−	0.309318i	$-0.899899\pi$
$577$	−15.4127	+	15.4127i	−0.641641	+	0.641641i	0.309318	+	0.950959i	$0.399899\pi$
$578$	11.7776	+	11.7776i	0.489885	+	0.489885i
$579$	6.69276			0.278141
$580$	0.0302734	−	4.01380i	0.00125703	−	0.166664i
$581$		−	27.9876i		−	1.16112i
$582$	2.65820	+	2.65820i	0.110186	+	0.110186i
$583$	−18.2616	−	18.2616i	−0.756319	−	0.756319i
$584$	12.5865			0.520834
$585$	8.29397	+	8.42004i	0.342914	+	0.348126i
$586$	−5.61287			−0.231866
$587$	5.01818	+	5.01818i	0.207123	+	0.207123i	0.803043	−	0.595921i	$-0.203213\pi$
$587$	5.01818	+	5.01818i	0.207123	+	0.207123i	−0.595921	+	0.803043i	$0.703213\pi$
$588$	−6.45009	+	6.45009i	−0.265997	+	0.265997i
$589$	−28.7083	−	1.45813i	−1.18291	−	0.0600813i
$590$	−18.2587	−	18.5362i	−0.751699	−	0.763124i
$591$	2.24543			0.0923646
$592$	−7.51505	−	7.51505i	−0.308867	−	0.308867i
$593$	−21.6830	−	21.6830i	−0.890414	−	0.890414i	0.104148	−	0.994562i	$-0.466788\pi$
$593$	−21.6830	−	21.6830i	−0.890414	−	0.890414i	−0.994562	+	0.104148i	$0.966788\pi$
$594$			1.81284i			0.0743818i
$595$	−5.26507	−	0.0397109i	−0.215847	−	0.00162799i
$596$	−12.2318			−0.501034
$597$	12.2864	−	12.2864i	0.502847	−	0.502847i
$598$	7.69700	+	7.69700i	0.314754	+	0.314754i
$599$			7.03123i			0.287288i	0.989629	+	0.143644i	$0.0458821\pi$
$599$			7.03123i			0.287288i	−0.989629	+	0.143644i	$0.954118\pi$
$600$	4.99943	+	0.0754191i	0.204101	+	0.00307897i
$601$			45.4765i			1.85503i	0.373790	+	0.927514i	$0.378058\pi$
$601$			45.4765i			1.85503i	−0.373790	+	0.927514i	$0.621942\pi$
$602$	−4.80402	−	4.80402i	−0.195797	−	0.195797i
$603$	−8.55487	−	8.55487i	−0.348381	−	0.348381i
$604$	4.95980			0.201811
$605$	−17.2477	−	0.130088i	−0.701217	−	0.00528882i
$606$			4.23820i			0.172165i
$607$	−27.8097	+	27.8097i	−1.12876	+	1.12876i	−0.138380	+	0.990379i	$0.544189\pi$
$607$	−27.8097	+	27.8097i	−1.12876	+	1.12876i	−0.990379	+	0.138380i	$0.955811\pi$
$608$	−3.65066	−	3.65066i	−0.148054	−	0.148054i
$609$		−	7.20758i		−	0.292066i
$610$	−23.4958	−	23.8529i	−0.951317	−	0.965776i
$611$		−	42.1841i		−	1.70658i
$612$	0.414677	+	0.414677i	0.0167623	+	0.0167623i
$613$	−15.0503	+	15.0503i	−0.607876	+	0.607876i	−0.942391	−	0.334514i	$-0.891428\pi$
$613$	−15.0503	+	15.0503i	−0.607876	+	0.607876i	0.334514	+	0.942391i	$0.391428\pi$
$614$			8.87395i			0.358123i
$615$	−13.6292	+	13.4251i	−0.549581	+	0.541353i
$616$		−	7.27891i		−	0.293276i
$617$	−14.3220	+	14.3220i	−0.576582	+	0.576582i	−0.933960	−	0.357378i	$-0.883671\pi$
$617$	−14.3220	+	14.3220i	−0.576582	+	0.576582i	0.357378	+	0.933960i	$0.383671\pi$
$618$	7.89307	−	7.89307i	0.317506	−	0.317506i
$619$	−38.4334			−1.54477			−0.772384	−	0.635156i	$-0.780936\pi$
$619$	−38.4334			−1.54477			−0.772384	+	0.635156i	$0.780936\pi$
$620$	12.4288	+	0.725292i	0.499151	+	0.0291284i
$621$	−2.05941			−0.0826414
$622$	3.16945	−	3.16945i	0.127083	−	0.127083i
$623$	−6.91150	+	6.91150i	−0.276903	+	0.276903i
$624$			5.28558i			0.211593i
$625$	24.9886	+	0.754105i	0.999545	+	0.0301642i
$626$		−	17.9213i		−	0.716279i
$627$	6.61807	−	6.61807i	0.264300	−	0.264300i
$628$	8.57571	+	8.57571i	0.342208	+	0.342208i
$629$		−	6.23263i		−	0.248511i
$630$	8.97800	+	0.0677151i	0.357692	+	0.00269783i
$631$			29.2550i			1.16462i	0.812965	+	0.582312i	$0.197852\pi$
$631$			29.2550i			1.16462i	−0.812965	+	0.582312i	$0.802148\pi$
$632$	−0.784556	−	0.784556i	−0.0312080	−	0.0312080i
$633$	−16.4609	+	16.4609i	−0.654263	+	0.654263i
$634$			23.0053i			0.913657i
$635$	−20.6984	−	21.0130i	−0.821389	−	0.833874i
$636$	14.2461			0.564893
$637$	−34.0925	−	34.0925i	−1.35079	−	1.35079i
$638$	2.30106	+	2.30106i	0.0910997	+	0.0910997i
$639$			8.79233i			0.347819i
$640$	1.56917	+	1.59302i	0.0620268	+	0.0629696i
$641$		−	29.1397i		−	1.15095i	−0.817820	−	0.575474i	$-0.804818\pi$
$641$		−	29.1397i		−	1.15095i	0.817820	−	0.575474i	$-0.195182\pi$
$642$	−3.14386	−	3.14386i	−0.124078	−	0.124078i
$643$	−1.87409	+	1.87409i	−0.0739070	+	0.0739070i	−0.743094	−	0.669187i	$-0.766642\pi$
$643$	−1.87409	+	1.87409i	−0.0739070	+	0.0739070i	0.669187	+	0.743094i	$0.266642\pi$
$644$	8.26895			0.325842
$645$	−0.0285359	+	3.78343i	−0.00112360	+	0.148972i
$646$		−	3.02769i		−	0.119123i
$647$	−3.40045	−	3.40045i	−0.133686	−	0.133686i	0.637098	−	0.770783i	$-0.280135\pi$
$647$	−3.40045	−	3.40045i	−0.133686	−	0.133686i	−0.770783	+	0.637098i	$0.780135\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	21.0940			0.828014
$650$	−0.398634	+	26.4249i	−0.0156357	+	1.03647i
$651$	22.3269	+	1.13401i	0.875060	+	0.0444454i
$652$	−2.48033	+	2.48033i	−0.0971371	+	0.0971371i
$653$	−24.4242	−	24.4242i	−0.955793	−	0.955793i	0.0432702	−	0.999063i	$-0.486222\pi$
$653$	−24.4242	−	24.4242i	−0.955793	−	0.955793i	−0.999063	+	0.0432702i	$0.986222\pi$
$654$	−2.89765			−0.113307
$655$	16.7063	+	0.126005i	0.652770	+	0.00492341i
$656$	−8.55556			−0.334038
$657$	−8.90002	−	8.90002i	−0.347223	−	0.347223i
$658$	−22.6593	−	22.6593i	−0.883353	−	0.883353i
$659$			19.7438i			0.769109i	0.923102	+	0.384554i	$0.125645\pi$
$659$			19.7438i			0.769109i	−0.923102	+	0.384554i	$0.874355\pi$
$660$	−2.88789	+	2.84465i	−0.112411	+	0.110728i
$661$	−44.7293			−1.73977			−0.869884	−	0.493256i	$-0.835806\pi$
$661$	−44.7293			−1.73977			−0.869884	+	0.493256i	$0.835806\pi$
$662$	−5.71536	−	5.71536i	−0.222134	−	0.222134i
$663$	−2.19181	+	2.19181i	−0.0851228	+	0.0851228i
$664$	−6.97041			−0.270504
$665$	−32.5284	−	33.0228i	−1.26140	−	1.28057i
$666$			10.6279i			0.411822i
$667$	−2.61404	+	2.61404i	−0.101216	+	0.101216i
$668$	10.9137	−	10.9137i	0.422262	−	0.422262i
$669$			7.81741i			0.302238i
$670$	0.204036	−	27.0521i	0.00788260	−	1.04511i
$671$	27.1444			1.04790
$672$	2.83917	+	2.83917i	0.109523	+	0.109523i
$673$	23.5284	−	23.5284i	0.906953	−	0.906953i	−0.0890720	−	0.996025i	$-0.528390\pi$
$673$	23.5284	−	23.5284i	0.906953	−	0.906953i	0.996025	+	0.0890720i	$0.0283901\pi$
$674$	−10.2372			−0.394323
$675$	−3.48180	−	3.58846i	−0.134015	−	0.138120i
$676$	−14.9374			−0.574515
$677$	9.30147	+	9.30147i	0.357485	+	0.357485i	0.862885	−	0.505400i	$-0.168655\pi$
$677$	9.30147	+	9.30147i	0.357485	+	0.357485i	−0.505400	+	0.862885i	$0.668655\pi$
$678$	−9.16924	+	9.16924i	−0.352143	+	0.352143i
$679$			15.0942i			0.579262i
$680$	−0.00989016	+	1.31129i	−0.000379270	+	0.0502855i
$681$		−	2.26058i		−	0.0866256i
$682$	−7.49001	+	6.76593i	−0.286807	+	0.259081i
$683$	−11.2854	−	11.2854i	−0.431825	−	0.431825i	0.457424	−	0.889249i	$-0.348772\pi$
$683$	−11.2854	−	11.2854i	−0.431825	−	0.431825i	−0.889249	+	0.457424i	$0.848772\pi$
$684$			5.16282i			0.197405i
$685$	0.478385	+	0.485656i	0.0182781	+	0.0185560i
$686$	−8.51949			−0.325275
$687$	−4.15058	+	4.15058i	−0.158355	+	0.158355i
$688$	−1.19646	+	1.19646i	−0.0456145	+	0.0456145i
$689$			75.2987i			2.86865i
$690$	−3.23157	−	3.28069i	−0.123024	−	0.124894i
$691$	17.7194			0.674077			0.337038	−	0.941491i	$-0.390575\pi$
$691$	17.7194			0.674077			0.337038	+	0.941491i	$0.390575\pi$
$692$	−1.04967	+	1.04967i	−0.0399024	+	0.0399024i
$693$	−5.14697	+	5.14697i	−0.195517	+	0.195517i
$694$	−13.2502			−0.502970
$695$	44.0211	+	0.332022i	1.66982	+	0.0125943i
$696$	−1.79508			−0.0680422
$697$	−3.54779	−	3.54779i	−0.134382	−	0.134382i
$698$	−2.81919	−	2.81919i	−0.106708	−	0.106708i
$699$	−18.9542			−0.716914
$700$	13.9801	+	14.4084i	0.528399	+	0.544586i
$701$	39.6615			1.49799			0.748997	−	0.662573i	$-0.230536\pi$
$701$	39.6615			1.49799			0.748997	+	0.662573i	$0.230536\pi$
$702$	3.73747	−	3.73747i	0.141062	−	0.141062i
$703$	38.7988	−	38.7988i	1.46333	−	1.46333i
$704$	−1.81284			−0.0683240
$705$	−0.134597	+	17.8455i	−0.00506920	+	0.672099i
$706$			29.8896i			1.12491i
$707$	−12.0330	+	12.0330i	−0.452547	+	0.452547i
$708$	−8.22783	+	8.22783i	−0.309221	+	0.309221i
$709$	33.6757			1.26472			0.632358	−	0.774676i	$-0.282087\pi$
$709$	33.6757			1.26472			0.632358	+	0.774676i	$0.282087\pi$
$710$	−14.0063	+	13.7966i	−0.525649	+	0.517779i
$711$			1.10953i			0.0416106i
$712$	1.72133	+	1.72133i	0.0645097	+	0.0645097i
$713$	−7.68620	−	8.50877i	−0.287851	−	0.318656i
$714$			2.35468i			0.0881216i
$715$	−15.0357	−	15.2642i	−0.562302	−	0.570848i
$716$		−	18.3644i		−	0.686311i
$717$	7.72891	−	7.72891i	0.288642	−	0.288642i
$718$	22.4555	+	22.4555i	0.838033	+	0.838033i
$719$	−13.3655			−0.498448			−0.249224	−	0.968446i	$-0.580176\pi$
$719$	−13.3655			−0.498448			−0.249224	+	0.968446i	$0.580176\pi$
$720$	0.0168647	−	2.23600i	0.000628510	−	0.0833310i
$721$	44.8196			1.66917
$722$	5.41267	−	5.41267i	0.201439	−	0.201439i
$723$	4.78616	+	4.78616i	0.177999	+	0.177999i
$724$	13.7840			0.512277
$725$	−8.97436	−	0.135383i	−0.333299	−	0.00502800i
$726$			7.71361i			0.286279i
$727$	14.8577	−	14.8577i	0.551041	−	0.551041i	−0.375700	−	0.926741i	$-0.622598\pi$
$727$	14.8577	−	14.8577i	0.551041	−	0.551041i	0.926741	+	0.375700i	$0.122598\pi$
$728$	−15.0067	+	15.0067i	−0.556185	+	0.556185i
$729$			1.00000i			0.0370370i
$730$	0.212268	−	28.1435i	0.00785639	−	1.04164i
$731$	−0.992287			−0.0367010
$732$	−10.5878	+	10.5878i	−0.391336	+	0.391336i
$733$	−10.6557	−	10.6557i	−0.393576	−	0.393576i	0.482384	−	0.875960i	$-0.339771\pi$
$733$	−10.6557	−	10.6557i	−0.393576	−	0.393576i	−0.875960	+	0.482384i	$0.839771\pi$
$734$	9.85391			0.363714
$735$	14.3137	+	14.5312i	0.527967	+	0.535992i
$736$		−	2.05941i		−	0.0759110i
$737$	15.5086	+	15.5086i	0.571267	+	0.571267i
$738$	6.04969	+	6.04969i	0.222692	+	0.222692i
$739$	10.0706			0.370454			0.185227	−	0.982696i	$-0.440698\pi$
$739$	10.0706			0.370454			0.185227	+	0.982696i	$0.440698\pi$
$740$	−16.9304	+	16.6769i	−0.622375	+	0.613057i
$741$	−27.2885			−1.00247
$742$	40.4470	+	40.4470i	1.48486	+	1.48486i
$743$	−33.5732	+	33.5732i	−1.23168	+	1.23168i	−0.268365	+	0.963317i	$0.586483\pi$
$743$	−33.5732	+	33.5732i	−1.23168	+	1.23168i	−0.963317	+	0.268365i	$0.913517\pi$
$744$	0.282430	−	5.56060i	0.0103544	−	0.203861i
$745$	−0.206286	+	27.3504i	−0.00755772	+	1.00204i
$746$	−4.06978			−0.149005
$747$	4.92882	+	4.92882i	0.180336	+	0.180336i
$748$	−0.751743	−	0.751743i	−0.0274864	−	0.0274864i
$749$		−	17.8519i		−	0.652295i
$750$	0.252951	−	11.1775i	0.00923647	−	0.408144i
$751$	11.0374			0.402762			0.201381	−	0.979513i	$-0.435457\pi$
$751$	11.0374			0.402762			0.201381	+	0.979513i	$0.435457\pi$
$752$	−5.64339	+	5.64339i	−0.205793	+	0.205793i
$753$	−19.9805	−	19.9805i	−0.728130	−	0.728130i
$754$		−	9.48802i		−	0.345533i
$755$	0.0836454	−	11.0901i	0.00304417	−	0.403611i
$756$		−	4.01520i		−	0.146031i
$757$	22.8491	+	22.8491i	0.830466	+	0.830466i	0.987580	−	0.157114i	$-0.0502190\pi$
$757$	22.8491	+	22.8491i	0.830466	+	0.830466i	−0.157114	+	0.987580i	$0.550219\pi$
$758$	16.7025	+	16.7025i	0.606664	+	0.606664i
$759$	3.73339			0.135513
$760$	−8.22446	+	8.10133i	−0.298333	+	0.293866i
$761$			12.3772i			0.448673i	0.974512	+	0.224336i	$0.0720214\pi$
$761$			12.3772i			0.448673i	−0.974512	+	0.224336i	$0.927979\pi$
$762$	−9.32720	+	9.32720i	−0.337889	+	0.337889i
$763$	−8.22693	−	8.22693i	−0.297835	−	0.297835i
$764$			19.5990i			0.709067i
$765$	0.934212	−	0.920225i	0.0337765	−	0.0332708i
$766$		−	37.3595i		−	1.34985i
$767$	−43.4889	−	43.4889i	−1.57029	−	1.57029i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$			23.5731i			0.850069i	0.905177	+	0.425034i	$0.139738\pi$
$769$			23.5731i			0.850069i	−0.905177	+	0.425034i	$0.860262\pi$
$770$	−16.2757	−	0.122757i	−0.586535	−	0.00442384i
$771$		−	12.4098i		−	0.446927i
$772$	4.73249	−	4.73249i	0.170326	−	0.170326i
$773$	−24.1943	+	24.1943i	−0.870209	+	0.870209i	−0.992495	−	0.122286i	$-0.960978\pi$
$773$	−24.1943	+	24.1943i	−0.870209	+	0.870209i	0.122286	+	0.992495i	$0.460978\pi$
$774$	1.69205			0.0608194
$775$	1.83136	−	27.7785i	0.0657845	−	0.997834i
$776$	3.75927			0.134950
$777$	−30.1744	+	30.1744i	−1.08250	+	1.08250i
$778$	4.18892	−	4.18892i	0.150180	−	0.150180i
$779$		−	44.1708i		−	1.58258i
$780$	11.8186	+	0.0891398i	0.423173	+	0.00319172i
$781$		−	15.9391i		−	0.570345i
$782$	0.853991	−	0.853991i	0.0305387	−	0.0305387i
$783$	1.26931	+	1.26931i	0.0453614	+	0.0453614i
$784$			9.12181i			0.325779i
$785$	19.3200	−	19.0307i	0.689559	−	0.679235i
$786$		−	7.47150i		−	0.266500i
$787$	33.4928	+	33.4928i	1.19389	+	1.19389i	0.975966	+	0.217925i	$0.0699287\pi$
$787$	33.4928	+	33.4928i	1.19389	+	1.19389i	0.217925	+	0.975966i	$0.430071\pi$
$788$	1.58776	−	1.58776i	0.0565615	−	0.0565615i
$789$		−	1.86267i		−	0.0663128i
$790$	−1.76750	+	1.74104i	−0.0628849	+	0.0619434i
$791$	−52.0662			−1.85126
$792$	1.28187	+	1.28187i	0.0455493	+	0.0455493i
$793$	−55.9627	−	55.9627i	−1.98729	−	1.98729i
$794$			22.1835i			0.787262i
$795$	0.240255	−	31.8542i	0.00852098	−	1.12975i
$796$		−	17.3755i		−	0.615860i
$797$	−29.3974	−	29.3974i	−1.04131	−	1.04131i	−0.999109	−	0.0422003i	$-0.986563\pi$
$797$	−29.3974	−	29.3974i	−1.04131	−	1.04131i	−0.0422003	−	0.999109i	$-0.513437\pi$
$798$	−14.6581	+	14.6581i	−0.518892	+	0.518892i
$799$	−4.68037			−0.165579
$800$	3.58846	−	3.48180i	0.126871	−	0.123100i
$801$		−	2.43433i		−	0.0860130i
$802$	2.01516	+	2.01516i	0.0711578	+	0.0711578i
$803$	16.1343	+	16.1343i	0.569367	+	0.569367i
$804$	−12.0984			−0.426678
$805$	0.139453	−	18.4894i	0.00491509	−	0.651666i
$806$	29.3910	+	1.49281i	1.03525	+	0.0525818i
$807$	−13.8550	+	13.8550i	−0.487721	+	0.487721i
$808$	2.99686	+	2.99686i	0.105429	+	0.105429i
$809$	54.1334			1.90323			0.951615	−	0.307292i	$-0.0994227\pi$
$809$	54.1334			1.90323			0.951615	+	0.307292i	$0.0994227\pi$
$810$	−1.59302	+	1.56917i	−0.0559730	+	0.0551350i
$811$	−2.90824			−0.102122			−0.0510611	−	0.998696i	$-0.516260\pi$
$811$	−2.90824			−0.102122			−0.0510611	+	0.998696i	$0.516260\pi$
$812$	−5.09653	−	5.09653i	−0.178853	−	0.178853i
$813$	−8.09507	−	8.09507i	−0.283906	−	0.283906i
$814$		−	19.2667i		−	0.675296i
$815$	5.50419	+	5.58785i	0.192803	+	0.195734i
$816$	0.586441			0.0205296
$817$	−6.17709	−	6.17709i	−0.216109	−	0.216109i
$818$	0.940544	−	0.940544i	0.0328854	−	0.0328854i
$819$	21.2227			0.741580
$820$	−0.144287	+	19.1303i	−0.00503872	+	0.668058i
$821$			41.3350i			1.44260i	0.692623	+	0.721300i	$0.256455\pi$
$821$			41.3350i			1.44260i	−0.692623	+	0.721300i	$0.743545\pi$
$822$	0.215572	−	0.215572i	0.00751895	−	0.00751895i
$823$	−9.57203	+	9.57203i	−0.333660	+	0.333660i	−0.853975	−	0.520315i	$-0.825815\pi$
$823$	−9.57203	+	9.57203i	−0.333660	+	0.333660i	0.520315	+	0.853975i	$0.325815\pi$
$824$		−	11.1625i		−	0.388864i
$825$	6.31195	+	6.50531i	0.219754	+	0.226486i
$826$	−46.7205			−1.62561
$827$	7.03974	+	7.03974i	0.244796	+	0.244796i	0.818831	−	0.574035i	$-0.194623\pi$
$827$	7.03974	+	7.03974i	0.244796	+	0.244796i	−0.574035	+	0.818831i	$0.694623\pi$
$828$	−1.45623	+	1.45623i	−0.0506073	+	0.0506073i
$829$	−32.1278			−1.11584			−0.557922	−	0.829894i	$-0.688401\pi$
$829$	−32.1278			−1.11584			−0.557922	+	0.829894i	$0.688401\pi$
$830$	−0.117554	+	15.5859i	−0.00408035	+	0.540993i
$831$	7.82482			0.271440
$832$	3.73747	+	3.73747i	0.129574	+	0.129574i
$833$	−3.78260	+	3.78260i	−0.131059	+	0.131059i
$834$		−	19.6874i		−	0.681719i
$835$	−24.2189	−	24.5870i	−0.838130	−	0.850869i
$836$		−	9.35936i		−	0.323700i
$837$	−4.13164	+	3.73223i	−0.142810	+	0.129005i
$838$	21.3951	+	21.3951i	0.739083	+	0.739083i
$839$		−	17.0844i		−	0.589819i	−0.955525	−	0.294910i	$-0.904710\pi$
$839$		−	17.0844i		−	0.589819i	0.955525	−	0.294910i	$-0.0952896\pi$
$840$	6.39629	−	6.30052i	0.220693	−	0.217389i
$841$	−25.7777			−0.888886
$842$	−14.4691	+	14.4691i	−0.498638	+	0.498638i
$843$	12.3657	−	12.3657i	0.425897	−	0.425897i
$844$			23.2793i			0.801305i
$845$	−0.251915	+	33.4001i	−0.00866613	+	1.14900i
$846$	7.98096			0.274391
$847$	−21.9003	+	21.9003i	−0.752502	+	0.752502i
$848$	10.0735	−	10.0735i	0.345925	−	0.345925i
$849$	15.3810			0.527874
$850$	2.93187	+	0.0442289i	0.100562	+	0.00151704i
$851$	21.8872			0.750284
$852$	6.21711	+	6.21711i	0.212995	+	0.212995i
$853$	4.39603	+	4.39603i	0.150517	+	0.150517i	0.778349	−	0.627832i	$-0.216057\pi$
$853$	4.39603	+	4.39603i	0.150517	+	0.150517i	−0.627832	+	0.778349i	$0.716057\pi$
$854$	−60.1211			−2.05730
$855$	11.5441	+	0.0870693i	0.394799	+	0.00297771i
$856$	−4.44609			−0.151964
$857$	−31.8651	+	31.8651i	−1.08849	+	1.08849i	−0.0928080	+	0.995684i	$0.529584\pi$
$857$	−31.8651	+	31.8651i	−1.08849	+	1.08849i	−0.995684	+	0.0928080i	$0.970416\pi$
$858$	−6.77544	+	6.77544i	−0.231310	+	0.231310i
$859$	16.8374			0.574486			0.287243	−	0.957858i	$-0.407261\pi$
$859$	16.8374			0.574486			0.287243	+	0.957858i	$0.407261\pi$
$860$	2.65511	+	2.69546i	0.0905384	+	0.0919146i
$861$			34.3522i			1.17072i
$862$	−14.4658	+	14.4658i	−0.492706	+	0.492706i
$863$	7.09777	−	7.09777i	0.241611	−	0.241611i	−0.575905	−	0.817516i	$-0.695350\pi$
$863$	7.09777	−	7.09777i	0.241611	−	0.241611i	0.817516	+	0.575905i	$0.195350\pi$
$864$	−1.00000			−0.0340207
$865$	2.32936	+	2.36476i	0.0792006	+	0.0804044i
$866$			28.9686i			0.984393i
$867$	−11.7776	−	11.7776i	−0.399989	−	0.399989i
$868$	16.5894	−	14.9856i	0.563080	−	0.508645i
$869$		−	2.01140i		−	0.0682321i
$870$	−0.0302734	+	4.01380i	−0.00102636	+	0.136080i
$871$		−	63.9471i		−	2.16677i
$872$	−2.04895	+	2.04895i	−0.0693861	+	0.0693861i
$873$	−2.65820	−	2.65820i	−0.0899666	−	0.0899666i
$874$	10.6324			0.359646
$875$	32.4530	−	31.0166i	1.09711	−	1.04855i
$876$	−12.5865			−0.425259
$877$	20.5935	−	20.5935i	0.695394	−	0.695394i	−0.268020	−	0.963413i	$-0.586369\pi$
$877$	20.5935	−	20.5935i	0.695394	−	0.695394i	0.963413	+	0.268020i	$0.0863693\pi$
$878$	−12.4519	−	12.4519i	−0.420230	−	0.420230i
$879$	5.61287			0.189318
$880$	−0.0305730	+	4.05352i	−0.00103062	+	0.136644i
$881$			41.0877i			1.38428i	0.721764	+	0.692140i	$0.243332\pi$
$881$			41.0877i			1.38428i	−0.721764	+	0.692140i	$0.756668\pi$
$882$	6.45009	−	6.45009i	0.217186	−	0.217186i
$883$	8.04851	−	8.04851i	0.270854	−	0.270854i	−0.558590	−	0.829444i	$-0.688657\pi$
$883$	8.04851	−	8.04851i	0.270854	−	0.270854i	0.829444	+	0.558590i	$0.188657\pi$
$884$			3.09968i			0.104254i
$885$	18.2587	+	18.5362i	0.613760	+	0.623088i
$886$	29.0794			0.976942
$887$	−11.8546	+	11.8546i	−0.398040	+	0.398040i	−0.877541	−	0.479502i	$-0.840818\pi$
$887$	−11.8546	+	11.8546i	−0.398040	+	0.398040i	0.479502	+	0.877541i	$0.340818\pi$
$888$	7.51505	+	7.51505i	0.252189	+	0.252189i
$889$	−52.9631			−1.77632
$890$	3.87794	−	3.81988i	0.129989	−	0.128043i
$891$		−	1.81284i		−	0.0607325i
$892$	5.52774	+	5.52774i	0.185082	+	0.185082i
$893$	−29.1358	−	29.1358i	−0.974992	−	0.974992i
$894$	12.2318			0.409093
$895$	−41.0630	−	0.309711i	−1.37258	−	0.0103525i
$896$	4.01520			0.134138
$897$	−7.69700	−	7.69700i	−0.256995	−	0.256995i
$898$	14.9140	−	14.9140i	0.497685	−	0.497685i
$899$	−0.506983	+	9.98169i	−0.0169088	+	0.332908i
$900$	−4.99943	−	0.0754191i	−0.166648	−	0.00251397i
$901$	8.35447			0.278328
$902$	−10.9671	−	10.9671i	−0.365165	−	0.365165i
$903$	4.80402	+	4.80402i	0.159868	+	0.159868i
$904$			12.9673i			0.431285i
$905$	0.232462	−	30.8210i	0.00772731	−	1.02452i
$906$	−4.95980			−0.164778
$907$	−35.1388	+	35.1388i	−1.16676	+	1.16676i	−0.183800	+	0.982964i	$0.558840\pi$
$907$	−35.1388	+	35.1388i	−1.16676	+	1.16676i	−0.982964	+	0.183800i	$0.941160\pi$
$908$	−1.59847	−	1.59847i	−0.0530471	−	0.0530471i
$909$		−	4.23820i		−	0.140572i
$910$	33.3019	+	33.8081i	1.10395	+	1.12073i
$911$			52.9255i			1.75350i	0.480948	+	0.876749i	$0.340293\pi$
$911$			52.9255i			1.75350i	−0.480948	+	0.876749i	$0.659707\pi$
$912$	3.65066	+	3.65066i	0.120886	+	0.120886i
$913$	−8.93517	−	8.93517i	−0.295711	−	0.295711i
$914$	40.0222			1.32382
$915$	23.4958	+	23.8529i	0.776747	+	0.788553i
$916$			5.86981i			0.193944i
$917$	21.2129	−	21.2129i	0.700511	−	0.700511i
$918$	−0.414677	−	0.414677i	−0.0136864	−	0.0136864i
$919$			8.92081i			0.294270i	0.989116	+	0.147135i	$0.0470052\pi$
$919$			8.92081i			0.294270i	−0.989116	+	0.147135i	$0.952995\pi$
$920$	−4.60486	−	0.0347314i	−0.151818	−	0.00114506i
$921$		−	8.87395i		−	0.292407i
$922$	3.15829	+	3.15829i	0.104013	+	0.104013i
$923$	−32.8611	+	32.8611i	−1.08164	+	1.08164i
$924$			7.27891i			0.239459i
$925$	37.0042	+	38.1378i	1.21669	+	1.25396i
$926$		−	21.3460i		−	0.701474i
$927$	−7.89307	+	7.89307i	−0.259242	+	0.259242i
$928$	−1.26931	+	1.26931i	−0.0416671	+	0.0416671i
$929$	28.0418			0.920022			0.460011	−	0.887913i	$-0.347845\pi$
$929$	28.0418			0.920022			0.460011	+	0.887913i	$0.347845\pi$
$930$	−12.4288	−	0.725292i	−0.407555	−	0.0237833i
$931$	−47.0942			−1.54345
$932$	−13.4027	+	13.4027i	−0.439019	+	0.439019i
$933$	−3.16945	+	3.16945i	−0.103763	+	0.103763i
$934$			19.7305i			0.645601i
$935$	−1.69358	+	1.66822i	−0.0553859	+	0.0545567i
$936$		−	5.28558i		−	0.172765i
$937$	−14.4424	+	14.4424i	−0.471811	+	0.471811i	−0.902500	−	0.430689i	$-0.858271\pi$
$937$	−14.4424	+	14.4424i	−0.471811	+	0.471811i	0.430689	+	0.902500i	$0.358271\pi$
$938$	−34.3495	−	34.3495i	−1.12155	−	1.12155i
$939$			17.9213i			0.584839i
$940$	12.5235	+	12.7138i	0.408471	+	0.414679i
$941$		−	13.3280i		−	0.434480i	−0.976118	−	0.217240i	$-0.930295\pi$
$941$		−	13.3280i		−	0.434480i	0.976118	−	0.217240i	$-0.0697054\pi$
$942$	−8.57571	−	8.57571i	−0.279412	−	0.279412i
$943$	12.4588	−	12.4588i	0.405715	−	0.405715i
$944$			11.6359i			0.378717i
$945$	−8.97800	−	0.0677151i	−0.292054	−	0.00220277i
$946$	−3.06741			−0.0997302
$947$	−14.5858	−	14.5858i	−0.473975	−	0.473975i	0.429223	−	0.903198i	$-0.358787\pi$
$947$	−14.5858	−	14.5858i	−0.473975	−	0.473975i	−0.903198	+	0.429223i	$0.858787\pi$
$948$	0.784556	+	0.784556i	0.0254812	+	0.0254812i
$949$		−	66.5271i		−	2.15956i
$950$	17.9759	+	18.5266i	0.583215	+	0.601081i
$951$		−	23.0053i		−	0.745998i
$952$	1.66501	+	1.66501i	0.0539632	+	0.0539632i
$953$	−13.8772	+	13.8772i	−0.449526	+	0.449526i	−0.895197	−	0.445671i	$-0.852965\pi$
$953$	−13.8772	+	13.8772i	−0.449526	+	0.449526i	0.445671	+	0.895197i	$0.352965\pi$
$954$	−14.2461			−0.461233
$955$	43.8235	+	0.330531i	1.41809	+	0.0106957i
$956$		−	10.9303i		−	0.353512i
$957$	−2.30106	−	2.30106i	−0.0743826	−	0.0743826i
$958$	−17.6858	−	17.6858i	−0.571402	−	0.571402i
$959$	1.22409			0.0395281
$960$	−1.56917	−	1.59302i	−0.0506447	−	0.0514145i
$961$	−30.8405	−	3.14095i	−0.994854	−	0.101321i
$962$	−39.7214	+	39.7214i	−1.28067	+	1.28067i
$963$	3.14386	+	3.14386i	0.101309	+	0.101309i
$964$	6.76866			0.218004
$965$	−10.5021	−	10.6617i	−0.338073	−	0.343212i
$966$	−8.26895			−0.266049
$967$	22.8235	+	22.8235i	0.733953	+	0.733953i	0.971400	−	0.237448i	$-0.0763108\pi$
$967$	22.8235	+	22.8235i	0.733953	+	0.733953i	−0.237448	+	0.971400i	$0.576311\pi$
$968$	5.45434	+	5.45434i	0.175309	+	0.175309i
$969$			3.02769i			0.0972634i
$970$	0.0633989	−	8.40574i	0.00203562	−	0.269892i
$971$	−31.9071			−1.02395			−0.511973	−	0.859001i	$-0.671085\pi$
$971$	−31.9071			−1.02395			−0.511973	+	0.859001i	$0.671085\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	55.8960	−	55.8960i	1.79194	−	1.79194i
$974$	23.3093			0.746877
$975$	0.398634	−	26.4249i	0.0127665	−	0.846274i
$976$			14.9734i			0.479287i
$977$	−15.4638	+	15.4638i	−0.494731	+	0.494731i	−0.909793	−	0.415062i	$-0.863760\pi$
$977$	−15.4638	+	15.4638i	−0.494731	+	0.494731i	0.415062	+	0.909793i	$0.363760\pi$
$978$	2.48033	−	2.48033i	0.0793121	−	0.0793121i
$979$			4.41306i			0.141042i
$980$	20.3964	+	0.153837i	0.651539	+	0.00491413i
$981$	2.89765			0.0925148
$982$	3.74756	+	3.74756i	0.119590	+	0.119590i
$983$	28.3652	−	28.3652i	0.904708	−	0.904708i	−0.0911306	−	0.995839i	$-0.529048\pi$
$983$	28.3652	−	28.3652i	0.904708	−	0.904708i	0.995839	+	0.0911306i	$0.0290481\pi$
$984$	8.55556			0.272741
$985$	−3.52346	−	3.57701i	−0.112267	−	0.113973i
$986$	−1.05271			−0.0335250
$987$	22.6593	+	22.6593i	0.721255	+	0.721255i
$988$	−19.2959	+	19.2959i	−0.613884	+	0.613884i
$989$		−	3.48463i		−	0.110805i
$990$	2.88789	−	2.84465i	0.0917832	−	0.0904090i
$991$			4.08527i			0.129773i	0.997893	+	0.0648864i	$0.0206685\pi$
$991$			4.08527i			0.129773i	−0.997893	+	0.0648864i	$0.979332\pi$
$992$	−3.73223	−	4.13164i	−0.118498	−	0.131180i
$993$	5.71536	+	5.71536i	0.181371	+	0.181371i
$994$			35.3029i			1.11974i
$995$	−38.8518	−	0.293033i	−1.23168	−	0.00928977i
$996$	6.97041			0.220866
$997$	26.8718	−	26.8718i	0.851038	−	0.851038i	−0.139223	−	0.990261i	$-0.544460\pi$
$997$	26.8718	−	26.8718i	0.851038	−	0.851038i	0.990261	+	0.139223i	$0.0444605\pi$
$998$	−11.1091	+	11.1091i	−0.351652	+	0.351652i
$999$		−	10.6279i		−	0.336252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.a.433.1	yes	32
5.2	odd	4		930.2.k.b.247.1	yes	32
31.30	odd	2		930.2.k.b.433.1	yes	32
155.92	even	4	inner	930.2.k.a.247.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.1	✓	32	155.92	even	4	inner
930.2.k.a.433.1	yes	32	1.1	even	1	trivial
930.2.k.b.247.1	yes	32	5.2	odd	4
930.2.k.b.433.1	yes	32	31.30	odd	2

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23600 - 0.0168647i) q^{5} +1.00000i q^{6} +(-2.83917 + 2.83917i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23600 - 0.0168647i) q^{5} +1.00000i q^{6} +(-2.83917 + 2.83917i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.59302 - 1.56917i) q^{10} +1.81284i q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.73747 - 3.73747i) q^{13} -4.01520i q^{14} +(-1.59302 + 1.56917i) q^{15} -1.00000 q^{16} +(-0.414677 - 0.414677i) q^{17} +(0.707107 + 0.707107i) q^{18} -5.16282i q^{19} +(-0.0168647 + 2.23600i) q^{20} +4.01520i q^{21} +(-1.28187 - 1.28187i) q^{22} +(1.45623 - 1.45623i) q^{23} +1.00000 q^{24} +(4.99943 + 0.0754191i) q^{25} +5.28558i q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.83917 + 2.83917i) q^{28} -1.79508 q^{29} +(0.0168647 - 2.23600i) q^{30} +(0.282430 - 5.56060i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.28187 + 1.28187i) q^{33} +0.586441 q^{34} +(6.39629 - 6.30052i) q^{35} -1.00000 q^{36} +(7.51505 + 7.51505i) q^{37} +(3.65066 + 3.65066i) q^{38} -5.28558i q^{39} +(-1.56917 - 1.59302i) q^{40} +8.55556 q^{41} +(-2.83917 - 2.83917i) q^{42} +(1.19646 - 1.19646i) q^{43} +1.81284 q^{44} +(-0.0168647 + 2.23600i) q^{45} +2.05941i q^{46} +(5.64339 - 5.64339i) q^{47} +(-0.707107 + 0.707107i) q^{48} -9.12181i q^{49} +(-3.58846 + 3.48180i) q^{50} -0.586441 q^{51} +(-3.73747 - 3.73747i) q^{52} +(-10.0735 + 10.0735i) q^{53} +1.00000 q^{54} +(0.0305730 - 4.05352i) q^{55} -4.01520 q^{56} +(-3.65066 - 3.65066i) q^{57} +(1.26931 - 1.26931i) q^{58} -11.6359i q^{59} +(1.56917 + 1.59302i) q^{60} -14.9734i q^{61} +(3.73223 + 4.13164i) q^{62} +(2.83917 + 2.83917i) q^{63} +1.00000i q^{64} +(-8.42004 + 8.29397i) q^{65} -1.81284 q^{66} +(8.55487 - 8.55487i) q^{67} +(-0.414677 + 0.414677i) q^{68} -2.05941i q^{69} +(-0.0677151 + 8.97800i) q^{70} -8.79233 q^{71} +(0.707107 - 0.707107i) q^{72} +(8.90002 - 8.90002i) q^{73} -10.6279 q^{74} +(3.58846 - 3.48180i) q^{75} -5.16282 q^{76} +(-5.14697 - 5.14697i) q^{77} +(3.73747 + 3.73747i) q^{78} -1.10953 q^{79} +(2.23600 + 0.0168647i) q^{80} -1.00000 q^{81} +(-6.04969 + 6.04969i) q^{82} +(-4.92882 + 4.92882i) q^{83} +4.01520 q^{84} +(0.920225 + 0.934212i) q^{85} +1.69205i q^{86} +(-1.26931 + 1.26931i) q^{87} +(-1.28187 + 1.28187i) q^{88} +2.43433 q^{89} +(-1.56917 - 1.59302i) q^{90} +21.2227i q^{91} +(-1.45623 - 1.45623i) q^{92} +(-3.73223 - 4.13164i) q^{93} +7.98096i q^{94} +(-0.0870693 + 11.5441i) q^{95} -1.00000i q^{96} +(2.65820 - 2.65820i) q^{97} +(6.45009 + 6.45009i) q^{98} +1.81284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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