LMFDB - Embedded newform 690.2.i.f.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
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			47.4
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.144577 - 1.72601i) q^{3} -1.00000i q^{4} +(1.25275 + 1.85219i) q^{5} +(1.32270 + 1.11824i) q^{6} +(-2.31531 - 2.31531i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.95819 + 0.499082i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.144577 - 1.72601i) q^{3} -1.00000i q^{4} +(1.25275 + 1.85219i) q^{5} +(1.32270 + 1.11824i) q^{6} +(-2.31531 - 2.31531i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.95819 + 0.499082i) q^{9} +(-2.19553 - 0.423868i) q^{10} -0.0826422i q^{11} +(-1.72601 + 0.144577i) q^{12} +(-2.92164 + 2.92164i) q^{13} +3.27434 q^{14} +(3.01578 - 2.43004i) q^{15} -1.00000 q^{16} +(-5.30247 + 5.30247i) q^{17} +(1.73886 - 2.44466i) q^{18} -6.47652i q^{19} +(1.85219 - 1.25275i) q^{20} +(-3.66150 + 4.33098i) q^{21} +(0.0584368 + 0.0584368i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(1.11824 - 1.32270i) q^{24} +(-1.86123 + 4.64067i) q^{25} -4.13182i q^{26} +(1.28911 + 5.03371i) q^{27} +(-2.31531 + 2.31531i) q^{28} +1.98555 q^{29} +(-0.414176 + 3.85077i) q^{30} -4.16017 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.142641 + 0.0119482i) q^{33} -7.49883i q^{34} +(1.38789 - 7.18891i) q^{35} +(0.499082 + 2.95819i) q^{36} +(4.80467 + 4.80467i) q^{37} +(4.57959 + 4.57959i) q^{38} +(5.46517 + 4.62037i) q^{39} +(-0.423868 + 2.19553i) q^{40} -0.882958i q^{41} +(-0.473395 - 5.65154i) q^{42} +(-1.69981 + 1.69981i) q^{43} -0.0826422 q^{44} +(-4.63028 - 4.85392i) q^{45} +1.00000 q^{46} +(-7.63231 + 7.63231i) q^{47} +(0.144577 + 1.72601i) q^{48} +3.72133i q^{49} +(-1.96536 - 4.59754i) q^{50} +(9.91872 + 8.38549i) q^{51} +(2.92164 + 2.92164i) q^{52} +(-7.26221 - 7.26221i) q^{53} +(-4.47090 - 2.64783i) q^{54} +(0.153069 - 0.103530i) q^{55} -3.27434i q^{56} +(-11.1785 + 0.936357i) q^{57} +(-1.40400 + 1.40400i) q^{58} -10.0777 q^{59} +(-2.43004 - 3.01578i) q^{60} -0.876183 q^{61} +(2.94168 - 2.94168i) q^{62} +(8.00467 + 5.69361i) q^{63} +1.00000i q^{64} +(-9.07153 - 1.75135i) q^{65} +(0.0924137 - 0.109311i) q^{66} +(0.768241 + 0.768241i) q^{67} +(5.30247 + 5.30247i) q^{68} +(-1.11824 + 1.32270i) q^{69} +(4.10194 + 6.06471i) q^{70} +1.70346i q^{71} +(-2.44466 - 1.73886i) q^{72} +(-0.265720 + 0.265720i) q^{73} -6.79483 q^{74} +(8.27892 + 2.54156i) q^{75} -6.47652 q^{76} +(-0.191342 + 0.191342i) q^{77} +(-7.13155 + 0.597367i) q^{78} +16.8063i q^{79} +(-1.25275 - 1.85219i) q^{80} +(8.50183 - 2.95276i) q^{81} +(0.624346 + 0.624346i) q^{82} +(-8.84618 - 8.84618i) q^{83} +(4.33098 + 3.66150i) q^{84} +(-16.4639 - 3.17852i) q^{85} -2.40390i q^{86} +(-0.287065 - 3.42708i) q^{87} +(0.0584368 - 0.0584368i) q^{88} +5.65142 q^{89} +(6.70634 + 0.158137i) q^{90} +13.5290 q^{91} +(-0.707107 + 0.707107i) q^{92} +(0.601465 + 7.18048i) q^{93} -10.7937i q^{94} +(11.9958 - 8.11347i) q^{95} +(-1.32270 - 1.11824i) q^{96} +(-7.30890 - 7.30890i) q^{97} +(-2.63138 - 2.63138i) q^{98} +(0.0412452 + 0.244472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.144577	−	1.72601i	−0.0834716	−	0.996510i
$3$	−0.144577	−	1.72601i	−0.0834716	−	0.996510i
$4$		−	1.00000i		−	0.500000i
$5$	1.25275	+	1.85219i	0.560247	+	0.828325i
$5$	1.25275	+	1.85219i	0.560247	+	0.828325i
$6$	1.32270	+	1.11824i	0.539991	+	0.456519i
$7$	−2.31531	−	2.31531i	−0.875106	−	0.875106i	0.117918	−	0.993023i	$-0.462378\pi$
$7$	−2.31531	−	2.31531i	−0.875106	−	0.875106i	−0.993023	+	0.117918i	$0.962378\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.95819	+	0.499082i	−0.986065	+	0.166361i
$10$	−2.19553	−	0.423868i	−0.694286	−	0.134039i
$11$		−	0.0826422i		−	0.0249176i	−0.999922	−	0.0124588i	$-0.996034\pi$
$11$		−	0.0826422i		−	0.0249176i	0.999922	−	0.0124588i	$-0.00396585\pi$
$12$	−1.72601	+	0.144577i	−0.498255	+	0.0417358i
$13$	−2.92164	+	2.92164i	−0.810317	+	0.810317i	−0.984681	−	0.174364i	$-0.944213\pi$
$13$	−2.92164	+	2.92164i	−0.810317	+	0.810317i	0.174364	+	0.984681i	$0.444213\pi$
$14$	3.27434			0.875106
$15$	3.01578	−	2.43004i	0.778670	−	0.627434i
$16$	−1.00000			−0.250000
$17$	−5.30247	+	5.30247i	−1.28604	+	1.28604i	−0.348866	+	0.937172i	$0.613433\pi$
$17$	−5.30247	+	5.30247i	−1.28604	+	1.28604i	−0.937172	+	0.348866i	$0.886567\pi$
$18$	1.73886	−	2.44466i	0.409852	−	0.576213i
$19$		−	6.47652i		−	1.48582i	−0.669393	−	0.742908i	$-0.733446\pi$
$19$		−	6.47652i		−	1.48582i	0.669393	−	0.742908i	$-0.266554\pi$
$20$	1.85219	−	1.25275i	0.414163	−	0.280124i
$21$	−3.66150	+	4.33098i	−0.799005	+	0.945098i
$22$	0.0584368	+	0.0584368i	0.0124588	+	0.0124588i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	1.11824	−	1.32270i	0.228260	−	0.269995i
$25$	−1.86123	+	4.64067i	−0.372246	+	0.928134i
$26$		−	4.13182i		−	0.810317i
$27$	1.28911	+	5.03371i	0.248088	+	0.968737i
$28$	−2.31531	+	2.31531i	−0.437553	+	0.437553i
$29$	1.98555			0.368708			0.184354	−	0.982860i	$-0.440981\pi$
$29$	1.98555			0.368708			0.184354	+	0.982860i	$0.440981\pi$
$30$	−0.414176	+	3.85077i	−0.0756179	+	0.703052i
$31$	−4.16017			−0.747188			−0.373594	−	0.927592i	$-0.621875\pi$
$31$	−4.16017			−0.747188			−0.373594	+	0.927592i	$0.621875\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.142641	+	0.0119482i	−0.0248306	+	0.00207991i
$34$		−	7.49883i		−	1.28604i
$35$	1.38789	−	7.18891i	0.234596	−	1.21515i
$36$	0.499082	+	2.95819i	0.0831803	+	0.493032i
$37$	4.80467	+	4.80467i	0.789883	+	0.789883i	0.981475	−	0.191591i	$-0.0613649\pi$
$37$	4.80467	+	4.80467i	0.789883	+	0.789883i	−0.191591	+	0.981475i	$0.561365\pi$
$38$	4.57959	+	4.57959i	0.742908	+	0.742908i
$39$	5.46517	+	4.62037i	0.875128	+	0.739851i
$40$	−0.423868	+	2.19553i	−0.0670194	+	0.347143i
$41$		−	0.882958i		−	0.137895i	−0.997620	−	0.0689474i	$-0.978036\pi$
$41$		−	0.882958i		−	0.137895i	0.997620	−	0.0689474i	$-0.0219641\pi$
$42$	−0.473395	−	5.65154i	−0.0730465	−	0.872052i
$43$	−1.69981	+	1.69981i	−0.259219	+	0.259219i	−0.824736	−	0.565518i	$-0.808676\pi$
$43$	−1.69981	+	1.69981i	−0.259219	+	0.259219i	0.565518	+	0.824736i	$0.308676\pi$
$44$	−0.0826422			−0.0124588
$45$	−4.63028	−	4.85392i	−0.690241	−	0.723579i
$46$	1.00000			0.147442
$47$	−7.63231	+	7.63231i	−1.11329	+	1.11329i	−0.120584	+	0.992703i	$0.538477\pi$
$47$	−7.63231	+	7.63231i	−1.11329	+	1.11329i	−0.992703	+	0.120584i	$0.961523\pi$
$48$	0.144577	+	1.72601i	0.0208679	+	0.249128i
$49$			3.72133i			0.531619i
$50$	−1.96536	−	4.59754i	−0.277944	−	0.650190i
$51$	9.91872	+	8.38549i	1.38890	+	1.17420i
$52$	2.92164	+	2.92164i	0.405159	+	0.405159i
$53$	−7.26221	−	7.26221i	−0.997541	−	0.997541i	0.00245571	−	0.999997i	$-0.499218\pi$
$53$	−7.26221	−	7.26221i	−0.997541	−	0.997541i	−0.999997	+	0.00245571i	$0.999218\pi$
$54$	−4.47090	−	2.64783i	−0.608413	−	0.360324i
$55$	0.153069	−	0.103530i	0.0206398	−	0.0139600i
$56$		−	3.27434i		−	0.437553i
$57$	−11.1785	+	0.936357i	−1.48063	+	0.124023i
$58$	−1.40400	+	1.40400i	−0.184354	+	0.184354i
$59$	−10.0777			−1.31201			−0.656003	−	0.754759i	$-0.727754\pi$
$59$	−10.0777			−1.31201			−0.656003	+	0.754759i	$0.727754\pi$
$60$	−2.43004	−	3.01578i	−0.313717	−	0.389335i
$61$	−0.876183			−0.112184			−0.0560919	−	0.998426i	$-0.517864\pi$
$61$	−0.876183			−0.112184			−0.0560919	+	0.998426i	$0.517864\pi$
$62$	2.94168	−	2.94168i	0.373594	−	0.373594i
$63$	8.00467	+	5.69361i	1.00849	+	0.717328i
$64$			1.00000i			0.125000i
$65$	−9.07153	−	1.75135i	−1.12518	−	0.217228i
$66$	0.0924137	−	0.109311i	0.0113753	−	0.0134553i
$67$	0.768241	+	0.768241i	0.0938556	+	0.0938556i	0.752476	−	0.658620i	$-0.228860\pi$
$67$	0.768241	+	0.768241i	0.0938556	+	0.0938556i	−0.658620	+	0.752476i	$0.728860\pi$
$68$	5.30247	+	5.30247i	0.643019	+	0.643019i
$69$	−1.11824	+	1.32270i	−0.134620	+	0.159235i
$70$	4.10194	+	6.06471i	0.490276	+	0.724872i
$71$			1.70346i			0.202163i	0.994878	+	0.101082i	$0.0322303\pi$
$71$			1.70346i			0.202163i	−0.994878	+	0.101082i	$0.967770\pi$
$72$	−2.44466	−	1.73886i	−0.288106	−	0.204926i
$73$	−0.265720	+	0.265720i	−0.0311002	+	0.0311002i	−0.722486	−	0.691386i	$-0.757001\pi$
$73$	−0.265720	+	0.265720i	−0.0311002	+	0.0311002i	0.691386	+	0.722486i	$0.257001\pi$
$74$	−6.79483			−0.789883
$75$	8.27892	+	2.54156i	0.955967	+	0.293474i
$76$	−6.47652			−0.742908
$77$	−0.191342	+	0.191342i	−0.0218055	+	0.0218055i
$78$	−7.13155	+	0.597367i	−0.807490	+	0.0676385i
$79$			16.8063i			1.89085i	0.325834	+	0.945427i	$0.394355\pi$
$79$			16.8063i			1.89085i	−0.325834	+	0.945427i	$0.605645\pi$
$80$	−1.25275	−	1.85219i	−0.140062	−	0.207081i
$81$	8.50183	−	2.95276i	0.944648	−	0.328085i
$82$	0.624346	+	0.624346i	0.0689474	+	0.0689474i
$83$	−8.84618	−	8.84618i	−0.970994	−	0.970994i	0.0285970	−	0.999591i	$-0.490896\pi$
$83$	−8.84618	−	8.84618i	−0.970994	−	0.970994i	−0.999591	+	0.0285970i	$0.990896\pi$
$84$	4.33098	+	3.66150i	0.472549	+	0.399503i
$85$	−16.4639	−	3.17852i	−1.78576	−	0.344758i
$86$		−	2.40390i		−	0.259219i
$87$	−0.287065	−	3.42708i	−0.0307766	−	0.367421i
$88$	0.0584368	−	0.0584368i	0.00622939	−	0.00622939i
$89$	5.65142			0.599049			0.299525	−	0.954089i	$-0.403172\pi$
$89$	5.65142			0.599049			0.299525	+	0.954089i	$0.403172\pi$
$90$	6.70634	+	0.158137i	0.706910	+	0.0166691i
$91$	13.5290			1.41823
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	0.601465	+	7.18048i	0.0623690	+	0.744581i
$94$		−	10.7937i		−	1.11329i
$95$	11.9958	−	8.11347i	1.23074	−	0.832425i
$96$	−1.32270	−	1.11824i	−0.134998	−	0.114130i
$97$	−7.30890	−	7.30890i	−0.742107	−	0.742107i	0.230876	−	0.972983i	$-0.425841\pi$
$97$	−7.30890	−	7.30890i	−0.742107	−	0.742107i	−0.972983	+	0.230876i	$0.925841\pi$
$98$	−2.63138	−	2.63138i	−0.265810	−	0.265810i
$99$	0.0412452	+	0.244472i	0.00414530	+	0.0245703i
$100$	4.64067	+	1.86123i	0.464067	+	0.186123i
$101$		−	2.99650i		−	0.298163i	−0.988825	−	0.149082i	$-0.952368\pi$
$101$		−	2.99650i		−	0.298163i	0.988825	−	0.149082i	$-0.0476317\pi$
$102$	−12.9430	+	1.08416i	−1.28155	+	0.107348i
$103$	7.92493	−	7.92493i	0.780866	−	0.780866i	−0.199111	−	0.979977i	$-0.563805\pi$
$103$	7.92493	−	7.92493i	0.780866	−	0.780866i	0.979977	+	0.199111i	$0.0638053\pi$
$104$	−4.13182			−0.405159
$105$	−12.6088	−	1.35616i	−1.23049	−	0.132347i
$106$	10.2703			0.997541
$107$	−5.54562	+	5.54562i	−0.536115	+	0.536115i	−0.922386	−	0.386270i	$-0.873763\pi$
$107$	−5.54562	+	5.54562i	−0.536115	+	0.536115i	0.386270	+	0.922386i	$0.373763\pi$
$108$	5.03371	−	1.28911i	0.484369	−	0.124044i
$109$		−	14.3159i		−	1.37121i	−0.727974	−	0.685605i	$-0.759538\pi$
$109$		−	14.3159i		−	1.37121i	0.727974	−	0.685605i	$-0.240462\pi$
$110$	−0.0350294	+	0.181443i	−0.00333992	+	0.0172999i
$111$	7.59825	−	8.98754i	0.721194	−	0.853060i
$112$	2.31531	+	2.31531i	0.218776	+	0.218776i
$113$	1.54977	+	1.54977i	0.145791	+	0.145791i	0.776235	−	0.630444i	$-0.217127\pi$
$113$	1.54977	+	1.54977i	0.145791	+	0.145791i	−0.630444	+	0.776235i	$0.717127\pi$
$114$	7.24230	−	8.56651i	0.678304	−	0.802327i
$115$	0.423868	−	2.19553i	0.0395259	−	0.204734i
$116$		−	1.98555i		−	0.184354i
$117$	7.18465	−	10.1009i	0.664221	−	0.933831i
$118$	7.12601	−	7.12601i	0.656003	−	0.656003i
$119$	24.5538			2.25084
$120$	3.85077	+	0.414176i	0.351526	+	0.0378090i
$121$	10.9932			0.999379
$122$	0.619555	−	0.619555i	0.0560919	−	0.0560919i
$123$	−1.52399	+	0.127655i	−0.137414	+	0.0115103i
$124$			4.16017i			0.373594i
$125$	−10.9271	+	2.36626i	−0.977347	+	0.211645i
$126$	−9.68615	+	1.63417i	−0.862911	+	0.145583i
$127$	−2.65907	−	2.65907i	−0.235954	−	0.235954i	0.579218	−	0.815172i	$-0.303358\pi$
$127$	−2.65907	−	2.65907i	−0.235954	−	0.235954i	−0.815172	+	0.579218i	$0.803358\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.17964	+	2.68813i	0.279952	+	0.236677i
$130$	7.65293	−	5.17615i	0.671206	−	0.453978i
$131$		−	12.0048i		−	1.04887i	−0.851452	−	0.524433i	$-0.824277\pi$
$131$		−	12.0048i		−	1.04887i	0.851452	−	0.524433i	$-0.175723\pi$
$132$	0.0119482	+	0.142641i	0.00103995	+	0.0124153i
$133$	−14.9952	+	14.9952i	−1.30025	+	1.30025i
$134$	−1.08646			−0.0938556
$135$	−7.70846	+	8.69365i	−0.663439	+	0.748231i
$136$	−7.49883			−0.643019
$137$	4.13246	−	4.13246i	0.353060	−	0.353060i	−0.508187	−	0.861247i	$-0.669684\pi$
$137$	4.13246	−	4.13246i	0.353060	−	0.353060i	0.861247	+	0.508187i	$0.169684\pi$
$138$	−0.144577	−	1.72601i	−0.0123072	−	0.146927i
$139$			0.433456i			0.0367652i	0.999831	+	0.0183826i	$0.00585170\pi$
$139$			0.433456i			0.0367652i	−0.999831	+	0.0183826i	$0.994148\pi$
$140$	−7.18891	−	1.38789i	−0.607574	−	0.117298i
$141$	14.2769	+	12.0700i	1.20233	+	1.01647i
$142$	−1.20453	−	1.20453i	−0.101082	−	0.101082i
$143$	0.241451	+	0.241451i	0.0201911	+	0.0201911i
$144$	2.95819	−	0.499082i	0.246516	−	0.0415902i
$145$	2.48740	+	3.67762i	0.206568	+	0.305410i
$146$		−	0.375785i		−	0.0311002i
$147$	6.42305	−	0.538020i	0.529764	−	0.0443751i
$148$	4.80467	−	4.80467i	0.394942	−	0.394942i
$149$	20.0239			1.64042			0.820212	−	0.572059i	$-0.193855\pi$
$149$	20.0239			1.64042			0.820212	+	0.572059i	$0.193855\pi$
$150$	−7.65123	+	4.05693i	−0.624720	+	0.331247i
$151$	−17.1989			−1.39963			−0.699814	−	0.714325i	$-0.746734\pi$
$151$	−17.1989			−1.39963			−0.699814	+	0.714325i	$0.746734\pi$
$152$	4.57959	−	4.57959i	0.371454	−	0.371454i
$153$	13.0394	−	18.3321i	1.05417	−	1.48206i
$154$		−	0.270599i		−	0.0218055i
$155$	−5.21166	−	7.70543i	−0.418610	−	0.618915i
$156$	4.62037	−	5.46517i	0.369926	−	0.437564i
$157$	16.4821	+	16.4821i	1.31542	+	1.31542i	0.917362	+	0.398054i	$0.130314\pi$
$157$	16.4821	+	16.4821i	1.31542	+	1.31542i	0.398054	+	0.917362i	$0.369686\pi$
$158$	−11.8838	−	11.8838i	−0.945427	−	0.945427i
$159$	−11.4847	+	13.5846i	−0.910794	+	1.07733i
$160$	2.19553	+	0.423868i	0.173572	+	0.0335097i
$161$			3.27434i			0.258055i
$162$	−3.92379	+	8.09962i	−0.308282	+	0.636367i
$163$	7.21629	−	7.21629i	0.565224	−	0.565224i	−0.365563	−	0.930787i	$-0.619124\pi$
$163$	7.21629	−	7.21629i	0.565224	−	0.565224i	0.930787	+	0.365563i	$0.119124\pi$
$164$	−0.882958			−0.0689474
$165$	−0.200824	−	0.249230i	−0.0156341	−	0.0194025i
$166$	12.5104			0.970994
$167$	11.3314	−	11.3314i	0.876846	−	0.876846i	−0.116361	−	0.993207i	$-0.537123\pi$
$167$	11.3314	−	11.3314i	0.876846	−	0.876846i	0.993207	+	0.116361i	$0.0371228\pi$
$168$	−5.65154	+	0.473395i	−0.436026	+	0.0365232i
$169$		−	4.07197i		−	0.313229i
$170$	13.8893	−	9.39417i	1.06526	−	0.720500i
$171$	3.23232	+	19.1588i	0.247181	+	1.46511i
$172$	1.69981	+	1.69981i	0.129609	+	0.129609i
$173$	−6.03766	−	6.03766i	−0.459035	−	0.459035i	0.439304	−	0.898339i	$-0.355225\pi$
$173$	−6.03766	−	6.03766i	−0.459035	−	0.459035i	−0.898339	+	0.439304i	$0.855225\pi$
$174$	2.62629	+	2.22032i	0.199099	+	0.168322i
$175$	15.0539	−	6.43528i	1.13797	−	0.486461i
$176$			0.0826422i			0.00622939i
$177$	1.45700	+	17.3942i	0.109515	+	1.30743i
$178$	−3.99616	+	3.99616i	−0.299525	+	0.299525i
$179$	10.2241			0.764188			0.382094	−	0.924123i	$-0.375203\pi$
$179$	10.2241			0.764188			0.382094	+	0.924123i	$0.375203\pi$
$180$	−4.85392	+	4.63028i	−0.361790	+	0.345121i
$181$	−7.86650			−0.584712			−0.292356	−	0.956310i	$-0.594439\pi$
$181$	−7.86650			−0.584712			−0.292356	+	0.956310i	$0.594439\pi$
$182$	−9.56646	+	9.56646i	−0.709113	+	0.709113i
$183$	0.126676	+	1.51230i	0.00936416	+	0.111792i
$184$		−	1.00000i		−	0.0737210i
$185$	−2.88011	+	14.9182i	−0.211750	+	1.09681i
$186$	−5.50266	−	4.65206i	−0.403475	−	0.341106i
$187$	0.438208	+	0.438208i	0.0320449	+	0.0320449i
$188$	7.63231	+	7.63231i	0.556644	+	0.556644i
$189$	8.66992	−	14.6393i	0.630644	−	1.06485i
$190$	−2.74519	+	14.2194i	−0.199157	+	1.03158i
$191$			23.2816i			1.68460i	0.539009	+	0.842300i	$0.318799\pi$
$191$			23.2816i			1.68460i	−0.539009	+	0.842300i	$0.681201\pi$
$192$	1.72601	−	0.144577i	0.124564	−	0.0104340i
$193$	−13.3531	+	13.3531i	−0.961176	+	0.961176i	−0.999274	−	0.0380984i	$-0.987870\pi$
$193$	−13.3531	+	13.3531i	−0.961176	+	0.961176i	0.0380984	+	0.999274i	$0.487870\pi$
$194$	10.3363			0.742107
$195$	−1.71130	+	15.9107i	−0.122549	+	1.13939i
$196$	3.72133			0.265810
$197$	3.92746	−	3.92746i	0.279820	−	0.279820i	−0.553217	−	0.833037i	$-0.686600\pi$
$197$	3.92746	−	3.92746i	0.279820	−	0.279820i	0.833037	+	0.553217i	$0.186600\pi$
$198$	−0.202032	−	0.143703i	−0.0143578	−	0.0102125i
$199$		−	14.6406i		−	1.03784i	−0.854822	−	0.518921i	$-0.826334\pi$
$199$		−	14.6406i		−	1.03784i	0.854822	−	0.518921i	$-0.173666\pi$
$200$	−4.59754	+	1.96536i	−0.325095	+	0.138972i
$201$	1.21492	−	1.43706i	0.0856937	−	0.101362i
$202$	2.11885	+	2.11885i	0.149082	+	0.149082i
$203$	−4.59717	−	4.59717i	−0.322658	−	0.322658i
$204$	8.38549	−	9.91872i	0.587102	−	0.694449i
$205$	1.63541	−	1.10613i	0.114222	−	0.0772553i
$206$			11.2075i			0.780866i
$207$	2.44466	+	1.73886i	0.169916	+	0.120859i
$208$	2.92164	−	2.92164i	0.202579	−	0.202579i
$209$	−0.535234			−0.0370229
$210$	9.87469	−	7.95679i	0.681418	−	0.549071i
$211$	1.39261			0.0958715			0.0479357	−	0.998850i	$-0.484736\pi$
$211$	1.39261			0.0958715			0.0479357	+	0.998850i	$0.484736\pi$
$212$	−7.26221	+	7.26221i	−0.498771	+	0.498771i
$213$	2.94018	−	0.246281i	0.201458	−	0.0168749i
$214$		−	7.84269i		−	0.536115i
$215$	−5.27782	−	1.01894i	−0.359944	−	0.0694908i
$216$	−2.64783	+	4.47090i	−0.180162	+	0.304206i
$217$	9.63209	+	9.63209i	0.653869	+	0.653869i
$218$	10.1228	+	10.1228i	0.685605	+	0.685605i
$219$	0.497052	+	0.420218i	0.0335876	+	0.0283957i
$220$	−0.103530	−	0.153069i	−0.00698000	−	0.0103199i
$221$		−	30.9839i		−	2.08420i
$222$	0.982377	+	11.7279i	0.0659328	+	0.787127i
$223$	16.9943	−	16.9943i	1.13802	−	1.13802i	0.149216	−	0.988805i	$-0.452325\pi$
$223$	16.9943	−	16.9943i	1.13802	−	1.13802i	0.988805	−	0.149216i	$-0.0476749\pi$
$224$	−3.27434			−0.218776
$225$	3.18980	−	14.6569i	0.212653	−	0.977128i
$226$	−2.19171			−0.145791
$227$	−6.77558	+	6.77558i	−0.449711	+	0.449711i	−0.895258	−	0.445547i	$-0.853009\pi$
$227$	−6.77558	+	6.77558i	−0.449711	+	0.449711i	0.445547	+	0.895258i	$0.353009\pi$
$228$	0.936357	+	11.1785i	0.0620117	+	0.740316i
$229$			11.6200i			0.767870i	0.923360	+	0.383935i	$0.125431\pi$
$229$			11.6200i			0.767870i	−0.923360	+	0.383935i	$0.874569\pi$
$230$	1.25275	+	1.85219i	0.0826040	+	0.122130i
$231$	0.357922	+	0.302594i	0.0235495	+	0.0199093i
$232$	1.40400	+	1.40400i	0.0921770	+	0.0921770i
$233$	−12.9668	−	12.9668i	−0.849484	−	0.849484i	0.140585	−	0.990069i	$-0.455102\pi$
$233$	−12.9668	−	12.9668i	−0.849484	−	0.849484i	−0.990069	+	0.140585i	$0.955102\pi$
$234$	2.06212	+	12.2227i	0.134805	+	0.799026i
$235$	−23.6979	−	4.57512i	−1.54588	−	0.298448i
$236$			10.0777i			0.656003i
$237$	29.0077	−	2.42980i	1.88426	−	0.157833i
$238$	−17.3621	+	17.3621i	−1.12542	+	1.12542i
$239$	−6.05401			−0.391602			−0.195801	−	0.980644i	$-0.562731\pi$
$239$	−6.05401			−0.391602			−0.195801	+	0.980644i	$0.562731\pi$
$240$	−3.01578	+	2.43004i	−0.194667	+	0.156858i
$241$	−17.7288			−1.14201			−0.571007	−	0.820945i	$-0.693447\pi$
$241$	−17.7288			−1.14201			−0.571007	+	0.820945i	$0.693447\pi$
$242$	−7.77335	+	7.77335i	−0.499690	+	0.499690i
$243$	−6.32566	−	14.2473i	−0.405791	−	0.913966i
$244$			0.876183i			0.0560919i
$245$	−6.89263	+	4.66191i	−0.440354	+	0.297838i
$246$	0.987358	−	1.16789i	0.0629517	−	0.0744620i
$247$	18.9221	+	18.9221i	1.20398	+	1.20398i
$248$	−2.94168	−	2.94168i	−0.186797	−	0.186797i
$249$	−13.9896	+	16.5475i	−0.886555	+	1.04866i
$250$	6.05341	−	9.39980i	0.382851	−	0.594496i
$251$			22.3292i			1.40941i	0.709501	+	0.704705i	$0.248921\pi$
$251$			22.3292i			1.40941i	−0.709501	+	0.704705i	$0.751079\pi$
$252$	5.69361	−	8.00467i	0.358664	−	0.504247i
$253$	−0.0584368	+	0.0584368i	−0.00367389	+	0.00367389i
$254$	3.76049			0.235954
$255$	−3.10584	+	28.8763i	−0.194495	+	1.80830i
$256$	1.00000			0.0625000
$257$	3.75966	−	3.75966i	0.234521	−	0.234521i	−0.580056	−	0.814577i	$-0.696969\pi$
$257$	3.75966	−	3.75966i	0.234521	−	0.234521i	0.814577	+	0.580056i	$0.196969\pi$
$258$	−4.14914	+	0.347548i	−0.258314	+	0.0216374i
$259$		−	22.2486i		−	1.38246i
$260$	−1.75135	+	9.07153i	−0.108614	+	0.562592i
$261$	−5.87365	+	0.990953i	−0.363570	+	0.0613385i
$262$	8.48869	+	8.48869i	0.524433	+	0.524433i
$263$	−9.73597	−	9.73597i	−0.600346	−	0.600346i	0.340058	−	0.940404i	$-0.389553\pi$
$263$	−9.73597	−	9.73597i	−0.600346	−	0.600346i	−0.940404	+	0.340058i	$0.889553\pi$
$264$	−0.109311	−	0.0924137i	−0.00672763	−	0.00568767i
$265$	4.35326	−	22.5487i	0.267419	−	1.38516i
$266$		−	21.2064i		−	1.30025i
$267$	−0.817066	−	9.75439i	−0.0500036	−	0.596959i
$268$	0.768241	−	0.768241i	0.0469278	−	0.0469278i
$269$	−1.99991			−0.121937			−0.0609684	−	0.998140i	$-0.519419\pi$
$269$	−1.99991			−0.121937			−0.0609684	+	0.998140i	$0.519419\pi$
$270$	−0.696637	−	11.5980i	−0.0423960	−	0.705835i
$271$	−7.75320			−0.470973			−0.235487	−	0.971878i	$-0.575668\pi$
$271$	−7.75320			−0.470973			−0.235487	+	0.971878i	$0.575668\pi$
$272$	5.30247	−	5.30247i	0.321510	−	0.321510i
$273$	−1.95599	−	23.3512i	−0.118382	−	1.41328i
$274$			5.84419i			0.353060i
$275$	0.383515	+	0.153816i	0.0231268	+	0.00927545i
$276$	1.32270	+	1.11824i	0.0796173	+	0.0673101i
$277$	−8.36272	−	8.36272i	−0.502467	−	0.502467i	0.409737	−	0.912204i	$-0.365621\pi$
$277$	−8.36272	−	8.36272i	−0.502467	−	0.502467i	−0.912204	+	0.409737i	$0.865621\pi$
$278$	−0.306500	−	0.306500i	−0.0183826	−	0.0183826i
$279$	12.3066	−	2.07627i	0.736776	−	0.124303i
$280$	6.06471	−	4.10194i	0.362436	−	0.245138i
$281$		−	10.4388i		−	0.622729i	−0.950291	−	0.311365i	$-0.899214\pi$
$281$		−	10.4388i		−	0.622729i	0.950291	−	0.311365i	$-0.100786\pi$
$282$	−18.6300	+	1.56052i	−1.10940	+	0.0929279i
$283$	9.18213	−	9.18213i	0.545821	−	0.545821i	−0.379408	−	0.925229i	$-0.623872\pi$
$283$	9.18213	−	9.18213i	0.545821	−	0.545821i	0.925229	+	0.379408i	$0.123872\pi$
$284$	1.70346			0.101082
$285$	−15.7382	−	19.5317i	−0.932252	−	1.15696i
$286$	−0.341463			−0.0201911
$287$	−2.04432	+	2.04432i	−0.120673	+	0.120673i
$288$	−1.73886	+	2.44466i	−0.102463	+	0.144053i
$289$		−	39.2325i		−	2.30779i
$290$	−4.35933	−	0.841612i	−0.255989	−	0.0494212i
$291$	−11.5585	+	13.6719i	−0.677572	+	0.801462i
$292$	0.265720	+	0.265720i	0.0155501	+	0.0155501i
$293$	12.9233	+	12.9233i	0.754988	+	0.754988i	0.975406	−	0.220418i	$-0.0707421\pi$
$293$	12.9233	+	12.9233i	0.754988	+	0.754988i	−0.220418	+	0.975406i	$0.570742\pi$
$294$	−4.16134	+	4.92222i	−0.242694	+	0.287070i
$295$	−12.6249	−	18.6658i	−0.735048	−	1.08677i
$296$			6.79483i			0.394942i
$297$	0.415997	−	0.106534i	0.0241386	−	0.00618176i
$298$	−14.1591	+	14.1591i	−0.820212	+	0.820212i
$299$	4.13182			0.238950
$300$	2.54156	−	8.27892i	0.146737	−	0.477984i
$301$	7.87119			0.453688
$302$	12.1615	−	12.1615i	0.699814	−	0.699814i
$303$	−5.17198	+	0.433226i	−0.297123	+	0.0248882i
$304$			6.47652i			0.371454i
$305$	−1.09764	−	1.62286i	−0.0628507	−	0.0929246i
$306$	3.74253	+	22.1830i	0.213946	+	1.26812i
$307$	−9.27023	−	9.27023i	−0.529080	−	0.529080i	0.391218	−	0.920298i	$-0.372054\pi$
$307$	−9.27023	−	9.27023i	−0.529080	−	0.529080i	−0.920298	+	0.391218i	$0.872054\pi$
$308$	0.191342	+	0.191342i	0.0109027	+	0.0109027i
$309$	−14.8242	−	12.5327i	−0.843321	−	0.712961i
$310$	9.13376	+	1.76336i	0.518763	+	0.100152i
$311$		−	34.1062i		−	1.93399i	−0.254804	−	0.966993i	$-0.582011\pi$
$311$		−	34.1062i		−	1.93399i	0.254804	−	0.966993i	$-0.417989\pi$
$312$	0.597367	+	7.13155i	0.0338193	+	0.403745i
$313$	−21.0097	+	21.0097i	−1.18754	+	1.18754i	−0.209795	+	0.977745i	$0.567280\pi$
$313$	−21.0097	+	21.0097i	−1.18754	+	1.18754i	−0.977745	+	0.209795i	$0.932720\pi$
$314$	−23.3092			−1.31542
$315$	−0.517796	+	21.9589i	−0.0291745	+	1.23724i
$316$	16.8063			0.945427
$317$	1.88900	−	1.88900i	0.106097	−	0.106097i	−0.652066	−	0.758163i	$-0.726097\pi$
$317$	1.88900	−	1.88900i	0.106097	−	0.106097i	0.758163	+	0.652066i	$0.226097\pi$
$318$	−1.48485	−	17.7266i	−0.0832664	−	0.994060i
$319$		−	0.164090i		−	0.00918730i
$320$	−1.85219	+	1.25275i	−0.103541	+	0.0700309i
$321$	10.3735	+	8.77000i	0.578995	+	0.489494i
$322$	−2.31531	−	2.31531i	−0.129027	−	0.129027i
$323$	34.3416	+	34.3416i	1.91082	+	1.91082i
$324$	−2.95276	−	8.50183i	−0.164042	−	0.472324i
$325$	−8.12054	−	18.9962i	−0.450446	−	1.05372i
$326$			10.2054i			0.565224i
$327$	−24.7092	+	2.06974i	−1.36642	+	0.114457i
$328$	0.624346	−	0.624346i	0.0344737	−	0.0344737i
$329$	35.3424			1.94849
$330$	0.318236	+	0.0342284i	0.0175183	+	0.00188421i
$331$	−18.4120			−1.01202			−0.506008	−	0.862529i	$-0.668879\pi$
$331$	−18.4120			−1.01202			−0.506008	+	0.862529i	$0.668879\pi$
$332$	−8.84618	+	8.84618i	−0.485497	+	0.485497i
$333$	−16.6111	−	11.8152i	−0.910282	−	0.647471i
$334$			16.0250i			0.876846i
$335$	−0.460514	+	2.38534i	−0.0251606	+	0.130325i
$336$	3.66150	−	4.33098i	0.199751	−	0.236274i
$337$	−4.80586	−	4.80586i	−0.261792	−	0.261792i	0.563990	−	0.825782i	$-0.309266\pi$
$337$	−4.80586	−	4.80586i	−0.261792	−	0.261792i	−0.825782	+	0.563990i	$0.809266\pi$
$338$	2.87932	+	2.87932i	0.156614	+	0.156614i
$339$	2.45086	−	2.89898i	0.133112	−	0.157451i
$340$	−3.17852	+	16.4639i	−0.172379	+	0.892879i
$341$			0.343805i			0.0186181i
$342$	−15.8329	−	11.2617i	−0.856146	−	0.608965i
$343$	−7.59113	+	7.59113i	−0.409883	+	0.409883i
$344$	−2.40390			−0.129609
$345$	−3.85077	−	0.414176i	−0.207319	−	0.0222985i
$346$	8.53854			0.459035
$347$	−17.1222	+	17.1222i	−0.919167	+	0.919167i	−0.996969	−	0.0778017i	$-0.975210\pi$
$347$	−17.1222	+	17.1222i	−0.919167	+	0.919167i	0.0778017	+	0.996969i	$0.475210\pi$
$348$	−3.42708	+	0.287065i	−0.183711	+	0.0153883i
$349$			2.01226i			0.107714i	0.998549	+	0.0538569i	$0.0171515\pi$
$349$			2.01226i			0.107714i	−0.998549	+	0.0538569i	$0.982849\pi$
$350$	−6.09430	+	15.1952i	−0.325754	+	0.812215i
$351$	−18.4730	−	10.9404i	−0.986015	−	0.583954i
$352$	−0.0584368	−	0.0584368i	−0.00311469	−	0.00311469i
$353$	−23.0099	−	23.0099i	−1.22469	−	1.22469i	−0.965945	−	0.258749i	$-0.916690\pi$
$353$	−23.0099	−	23.0099i	−1.22469	−	1.22469i	−0.258749	−	0.965945i	$-0.583310\pi$
$354$	−13.3298	−	11.2693i	−0.708471	−	0.598956i
$355$	−3.15513	+	2.13401i	−0.167457	+	0.113261i
$356$		−	5.65142i		−	0.299525i
$357$	−3.54991	−	42.3799i	−0.187881	−	2.24298i
$358$	−7.22956	+	7.22956i	−0.382094	+	0.382094i
$359$	19.5535			1.03199			0.515996	−	0.856591i	$-0.327422\pi$
$359$	19.5535			1.03199			0.515996	+	0.856591i	$0.327422\pi$
$360$	0.158137	−	6.70634i	0.00833457	−	0.353455i
$361$	−22.9454			−1.20765
$362$	5.56245	−	5.56245i	0.292356	−	0.292356i
$363$	−1.58936	−	18.9743i	−0.0834198	−	0.995891i
$364$		−	13.5290i		−	0.709113i
$365$	−0.825046	−	0.159283i	−0.0431849	−	0.00833727i
$366$	−1.15893	−	0.979782i	−0.0605782	−	0.0512140i
$367$	6.00838	+	6.00838i	0.313635	+	0.313635i	0.846316	−	0.532681i	$-0.178815\pi$
$367$	6.00838	+	6.00838i	0.313635	+	0.313635i	−0.532681	+	0.846316i	$0.678815\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	0.440668	+	2.61196i	0.0229403	+	0.135973i
$370$	−8.51224	−	12.5853i	−0.442530	−	0.654280i
$371$			33.6286i			1.74591i
$372$	7.18048	−	0.601465i	0.372290	−	0.0311845i
$373$	−18.4696	+	18.4696i	−0.956318	+	0.956318i	−0.999085	−	0.0427675i	$-0.986383\pi$
$373$	−18.4696	+	18.4696i	−0.956318	+	0.956318i	0.0427675	+	0.999085i	$0.486383\pi$
$374$	−0.619720			−0.0320449
$375$	5.66398	+	18.5181i	0.292487	+	0.956270i
$376$	−10.7937			−0.556644
$377$	−5.80107	+	5.80107i	−0.298770	+	0.298770i
$378$	4.22098	+	16.4821i	0.217104	+	0.847747i
$379$		−	2.21381i		−	0.113716i	−0.998382	−	0.0568579i	$-0.981892\pi$
$379$		−	2.21381i		−	0.113716i	0.998382	−	0.0568579i	$-0.0181082\pi$
$380$	−8.11347	−	11.9958i	−0.416212	−	0.615370i
$381$	−4.20513	+	4.97401i	−0.215435	+	0.254826i
$382$	−16.4626	−	16.4626i	−0.842300	−	0.842300i
$383$	24.0015	+	24.0015i	1.22642	+	1.22642i	0.965308	+	0.261112i	$0.0840893\pi$
$383$	24.0015	+	24.0015i	1.22642	+	1.22642i	0.261112	+	0.965308i	$0.415911\pi$
$384$	−1.11824	+	1.32270i	−0.0570649	+	0.0674989i
$385$	−0.594107	−	0.114698i	−0.0302785	−	0.00584557i
$386$		−	18.8841i		−	0.961176i
$387$	4.18003	−	5.87672i	0.212483	−	0.298730i
$388$	−7.30890	+	7.30890i	−0.371053	+	0.371053i
$389$	8.89237			0.450861			0.225431	−	0.974259i	$-0.427621\pi$
$389$	8.89237			0.450861			0.225431	+	0.974259i	$0.427621\pi$
$390$	−10.0405	−	12.4607i	−0.508421	−	0.630970i
$391$	7.49883			0.379232
$392$	−2.63138	+	2.63138i	−0.132905	+	0.132905i
$393$	−20.7204	+	1.73562i	−1.04521	+	0.0875505i
$394$			5.55427i			0.279820i
$395$	−31.1284	+	21.0541i	−1.56624	+	1.05935i
$396$	0.244472	−	0.0412452i	0.0122852	−	0.00207265i
$397$	21.4168	+	21.4168i	1.07488	+	1.07488i	0.996960	+	0.0779195i	$0.0248277\pi$
$397$	21.4168	+	21.4168i	1.07488	+	1.07488i	0.0779195	+	0.996960i	$0.475172\pi$
$398$	10.3524	+	10.3524i	0.518921	+	0.518921i
$399$	28.0497	+	23.7138i	1.40424	+	1.18717i
$400$	1.86123	−	4.64067i	0.0930614	−	0.232034i
$401$			32.8935i			1.64262i	0.570480	+	0.821312i	$0.306757\pi$
$401$			32.8935i			1.64262i	−0.570480	+	0.821312i	$0.693243\pi$
$402$	0.157077	+	1.87523i	0.00783428	+	0.0935280i
$403$	12.1545	−	12.1545i	0.605460	−	0.605460i
$404$	−2.99650			−0.149082
$405$	16.1198	+	12.0479i	0.800998	+	0.598667i
$406$	6.50138			0.322658
$407$	0.397069	−	0.397069i	0.0196820	−	0.0196820i
$408$	1.08416	+	12.9430i	0.0536739	+	0.640775i
$409$			29.4036i			1.45392i	0.686682	+	0.726958i	$0.259066\pi$
$409$			29.4036i			1.45392i	−0.686682	+	0.726958i	$0.740934\pi$
$410$	−0.374258	+	1.93856i	−0.0184833	+	0.0957385i
$411$	−7.73012	−	6.53520i	−0.381299	−	0.322358i
$412$	−7.92493	−	7.92493i	−0.390433	−	0.390433i
$413$	23.3330	+	23.3330i	1.14814	+	1.14814i
$414$	−2.95819	+	0.499082i	−0.145387	+	0.0245285i
$415$	5.30275	−	27.4669i	0.260302	−	1.34830i
$416$			4.13182i			0.202579i
$417$	0.748148	−	0.0626678i	0.0366369	−	0.00306885i
$418$	0.378468	−	0.378468i	0.0185115	−	0.0185115i
$419$	4.84269			0.236581			0.118290	−	0.992979i	$-0.462259\pi$
$419$	4.84269			0.236581			0.118290	+	0.992979i	$0.462259\pi$
$420$	−1.35616	+	12.6088i	−0.0661736	+	0.615245i
$421$	19.4455			0.947714			0.473857	−	0.880602i	$-0.342861\pi$
$421$	19.4455			0.947714			0.473857	+	0.880602i	$0.342861\pi$
$422$	−0.984727	+	0.984727i	−0.0479357	+	0.0479357i
$423$	18.7687	−	26.3870i	0.912567	−	1.28298i
$424$		−	10.2703i		−	0.498771i
$425$	−14.7379	−	34.4762i	−0.714895	−	1.67234i
$426$	−1.90487	+	2.25317i	−0.0922913	+	0.109166i
$427$	2.02864	+	2.02864i	0.0981726	+	0.0981726i
$428$	5.54562	+	5.54562i	0.268058	+	0.268058i
$429$	0.381837	−	0.451654i	0.0184353	−	0.0218061i
$430$	4.45248	−	3.01148i	0.214717	−	0.145227i
$431$			23.4150i			1.12786i	0.825822	+	0.563932i	$0.190712\pi$
$431$			23.4150i			1.12786i	−0.825822	+	0.563932i	$0.809288\pi$
$432$	−1.28911	−	5.03371i	−0.0620221	−	0.242184i
$433$	−18.6129	+	18.6129i	−0.894478	+	0.894478i	−0.994941	−	0.100463i	$-0.967968\pi$
$433$	−18.6129	+	18.6129i	−0.894478	+	0.894478i	0.100463	+	0.994941i	$0.467968\pi$
$434$	−13.6218			−0.653869
$435$	5.98798	−	4.82497i	0.287102	−	0.231340i
$436$	−14.3159			−0.685605
$437$	−4.57959	+	4.57959i	−0.219072	+	0.219072i
$438$	−0.648607	+	0.0543299i	−0.0309917	+	0.00259598i
$439$			2.74419i			0.130973i	0.997853	+	0.0654864i	$0.0208599\pi$
$439$			2.74419i			0.130973i	−0.997853	+	0.0654864i	$0.979140\pi$
$440$	0.181443	+	0.0350294i	0.00864996	+	0.00166996i
$441$	−1.85725	−	11.0084i	−0.0884405	−	0.524211i
$442$	21.9089	+	21.9089i	1.04210	+	1.04210i
$443$	−5.24175	−	5.24175i	−0.249043	−	0.249043i	0.571535	−	0.820578i	$-0.306348\pi$
$443$	−5.24175	−	5.24175i	−0.249043	−	0.249043i	−0.820578	+	0.571535i	$0.806348\pi$
$444$	−8.98754	−	7.59825i	−0.426530	−	0.360597i
$445$	7.07983	+	10.4675i	0.335616	+	0.496208i
$446$			24.0335i			1.13802i
$447$	−2.89500	−	34.5614i	−0.136929	−	1.63470i
$448$	2.31531	−	2.31531i	0.109388	−	0.109388i
$449$	−4.17586			−0.197071			−0.0985356	−	0.995134i	$-0.531416\pi$
$449$	−4.17586			−0.197071			−0.0985356	+	0.995134i	$0.531416\pi$
$450$	8.10848	+	12.6195i	0.382237	+	0.594890i
$451$	−0.0729696			−0.00343600
$452$	1.54977	−	1.54977i	0.0728953	−	0.0728953i
$453$	2.48657	+	29.6854i	0.116829	+	1.39474i
$454$		−	9.58212i		−	0.449711i
$455$	16.9485	+	25.0583i	0.794558	+	1.17475i
$456$	−8.56651	−	7.24230i	−0.401164	−	0.339152i
$457$	3.72841	+	3.72841i	0.174408	+	0.174408i	0.788913	−	0.614505i	$-0.210644\pi$
$457$	3.72841	+	3.72841i	0.174408	+	0.174408i	−0.614505	+	0.788913i	$0.710644\pi$
$458$	−8.21656	−	8.21656i	−0.383935	−	0.383935i
$459$	−33.5266	−	19.8557i	−1.56489	−	0.926783i
$460$	−2.19553	−	0.423868i	−0.102367	−	0.0197630i
$461$			11.3512i			0.528680i	0.964430	+	0.264340i	$0.0851541\pi$
$461$			11.3512i			0.528680i	−0.964430	+	0.264340i	$0.914846\pi$
$462$	−0.467056	+	0.0391224i	−0.0217294	+	0.00182014i
$463$	15.3561	−	15.3561i	0.713657	−	0.713657i	−0.253641	−	0.967298i	$-0.581628\pi$
$463$	15.3561	−	15.3561i	0.713657	−	0.713657i	0.967298	+	0.253641i	$0.0816282\pi$
$464$	−1.98555			−0.0921770
$465$	−12.5461	+	10.1094i	−0.581813	+	0.468811i
$466$	18.3378			0.849484
$467$	5.99931	−	5.99931i	0.277615	−	0.277615i	−0.554541	−	0.832156i	$-0.687106\pi$
$467$	5.99931	−	5.99931i	0.277615	−	0.277615i	0.832156	+	0.554541i	$0.187106\pi$
$468$	−10.1009	−	7.18465i	−0.466915	−	0.332110i
$469$		−	3.55743i		−	0.164267i
$470$	19.9920	−	13.5219i	0.922164	−	0.623717i
$471$	26.0653	−	30.8312i	1.20103	−	1.42063i
$472$	−7.12601	−	7.12601i	−0.328001	−	0.328001i
$473$	0.140476	+	0.140476i	0.00645910	+	0.00645910i
$474$	−18.7934	+	22.2297i	−0.863211	+	1.02104i
$475$	30.0554	+	12.0543i	1.37904	+	0.553088i
$476$		−	24.5538i		−	1.12542i
$477$	25.1075	+	17.8586i	1.14959	+	0.817689i
$478$	4.28083	−	4.28083i	0.195801	−	0.195801i
$479$	−31.7615			−1.45122			−0.725611	−	0.688105i	$-0.758443\pi$
$479$	−31.7615			−1.45122			−0.725611	+	0.688105i	$0.758443\pi$
$480$	0.414176	−	3.85077i	0.0189045	−	0.175763i
$481$	−28.0751			−1.28011
$482$	12.5362	−	12.5362i	0.571007	−	0.571007i
$483$	5.65154	−	0.473395i	0.257154	−	0.0215402i
$484$		−	10.9932i		−	0.499690i
$485$	4.38125	−	22.6937i	0.198942	−	1.03047i
$486$	14.5473	+	5.60146i	0.659878	+	0.254087i
$487$	8.53395	+	8.53395i	0.386710	+	0.386710i	0.873512	−	0.486802i	$-0.161837\pi$
$487$	8.53395	+	8.53395i	0.386710	+	0.386710i	−0.486802	+	0.873512i	$0.661837\pi$
$488$	−0.619555	−	0.619555i	−0.0280459	−	0.0280459i
$489$	−13.4987	−	11.4121i	−0.610431	−	0.516071i
$490$	1.57736	−	8.17029i	0.0712577	−	0.369096i
$491$			15.5734i			0.702820i	0.936222	+	0.351410i	$0.114298\pi$
$491$			15.5734i			0.702820i	−0.936222	+	0.351410i	$0.885702\pi$
$492$	0.127655	+	1.52399i	0.00575515	+	0.0687068i
$493$	−10.5283	+	10.5283i	−0.474173	+	0.474173i
$494$	−26.7599			−1.20398
$495$	−0.401138	+	0.382656i	−0.0180298	+	0.0171991i
$496$	4.16017			0.186797
$497$	3.94403	−	3.94403i	0.176914	−	0.176914i
$498$	−1.80871	−	21.5930i	−0.0810504	−	0.967605i
$499$			29.9183i			1.33933i	0.742664	+	0.669664i	$0.233562\pi$
$499$			29.9183i			1.33933i	−0.742664	+	0.669664i	$0.766438\pi$
$500$	2.36626	+	10.9271i	0.105822	+	0.488673i
$501$	−21.1962	−	17.9197i	−0.946978	−	0.800595i
$502$	−15.7892	−	15.7892i	−0.704705	−	0.704705i
$503$	−3.60669	−	3.60669i	−0.160814	−	0.160814i	0.622113	−	0.782927i	$-0.286274\pi$
$503$	−3.60669	−	3.60669i	−0.160814	−	0.160814i	−0.782927	+	0.622113i	$0.786274\pi$
$504$	1.63417	+	9.68615i	0.0727915	+	0.431455i
$505$	5.55010	−	3.75387i	0.246976	−	0.167045i
$506$		−	0.0826422i		−	0.00367389i
$507$	−7.02825	+	0.588714i	−0.312136	+	0.0261457i
$508$	−2.65907	+	2.65907i	−0.117977	+	0.117977i
$509$	−28.7783			−1.27558			−0.637789	−	0.770211i	$-0.720151\pi$
$509$	−28.7783			−1.27558			−0.637789	+	0.770211i	$0.720151\pi$
$510$	−18.2225	−	22.6148i	−0.806904	−	1.00140i
$511$	1.23045			0.0544319
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	32.6009	−	8.34892i	1.43937	−	0.368614i
$514$			5.31696i			0.234521i
$515$	24.6065	+	4.75052i	1.08429	+	0.209333i
$516$	2.68813	−	3.17964i	0.118338	−	0.139976i
$517$	0.630751	+	0.630751i	0.0277404	+	0.0277404i
$518$	15.7322	+	15.7322i	0.691231	+	0.691231i
$519$	−9.54813	+	11.2939i	−0.419116	+	0.495749i
$520$	−5.17615	−	7.65293i	−0.226989	−	0.335603i
$521$			10.8265i			0.474319i	0.971471	+	0.237159i	$0.0762164\pi$
$521$			10.8265i			0.474319i	−0.971471	+	0.237159i	$0.923784\pi$
$522$	3.45259	−	4.85401i	0.151116	−	0.212454i
$523$	0.723443	−	0.723443i	0.0316339	−	0.0316339i	−0.691113	−	0.722747i	$-0.742879\pi$
$523$	0.723443	−	0.723443i	0.0316339	−	0.0316339i	0.722747	+	0.691113i	$0.242879\pi$
$524$	−12.0048			−0.524433
$525$	−13.2838	−	25.0528i	−0.579752	−	1.09339i
$526$	13.7687			0.600346
$527$	22.0592	−	22.0592i	0.960913	−	0.960913i
$528$	0.142641	−	0.0119482i	0.00620765	−	0.000519977i
$529$			1.00000i			0.0434783i
$530$	12.8662	+	19.0226i	0.558870	+	0.826289i
$531$	29.8118	−	5.02960i	1.29372	−	0.218266i
$532$	14.9952	+	14.9952i	0.650123	+	0.650123i
$533$	2.57969	+	2.57969i	0.111739	+	0.111739i
$534$	7.47515	+	6.31964i	0.323481	+	0.273478i
$535$	−17.2188	−	3.32427i	−0.744435	−	0.143721i
$536$			1.08646i			0.0469278i
$537$	−1.47818	−	17.6469i	−0.0637880	−	0.761521i
$538$	1.41415	−	1.41415i	0.0609684	−	0.0609684i
$539$	0.307539			0.0132467
$540$	8.69365	+	7.70846i	0.374115	+	0.331719i
$541$	−1.29260			−0.0555732			−0.0277866	−	0.999614i	$-0.508846\pi$
$541$	−1.29260			−0.0555732			−0.0277866	+	0.999614i	$0.508846\pi$
$542$	5.48234	−	5.48234i	0.235487	−	0.235487i
$543$	1.13732	+	13.5776i	0.0488069	+	0.582672i
$544$			7.49883i			0.321510i
$545$	26.5157	−	17.9342i	1.13581	−	0.768217i
$546$	17.8949	+	15.1287i	0.765829	+	0.647448i
$547$	2.94655	+	2.94655i	0.125985	+	0.125985i	0.767288	−	0.641303i	$-0.221606\pi$
$547$	2.94655	+	2.94655i	0.125985	+	0.125985i	−0.641303	+	0.767288i	$0.721606\pi$
$548$	−4.13246	−	4.13246i	−0.176530	−	0.176530i
$549$	2.59192	−	0.437287i	0.110620	−	0.0186630i
$550$	−0.379950	+	0.162422i	−0.0162011	+	0.00692570i
$551$		−	12.8595i		−	0.547832i
$552$	−1.72601	+	0.144577i	−0.0734637	+	0.00615361i
$553$	38.9118	−	38.9118i	1.65470	−	1.65470i
$554$	11.8267			0.502467
$555$	26.1654	+	2.81426i	1.11066	+	0.119459i
$556$	0.433456			0.0183826
$557$	1.34754	−	1.34754i	0.0570969	−	0.0570969i	−0.677982	−	0.735079i	$-0.737145\pi$
$557$	1.34754	−	1.34754i	0.0570969	−	0.0570969i	0.735079	+	0.677982i	$0.237145\pi$
$558$	−7.23393	+	10.1702i	−0.306237	+	0.430540i
$559$		−	9.93248i		−	0.420099i
$560$	−1.38789	+	7.18891i	−0.0586491	+	0.303787i
$561$	0.692995	−	0.819705i	0.0292583	−	0.0346080i
$562$	7.38138	+	7.38138i	0.311365	+	0.311365i
$563$	6.51282	+	6.51282i	0.274483	+	0.274483i	0.830902	−	0.556419i	$-0.187825\pi$
$563$	6.51282	+	6.51282i	0.274483	+	0.274483i	−0.556419	+	0.830902i	$0.687825\pi$
$564$	12.0700	−	14.2769i	0.508237	−	0.601165i
$565$	−0.928997	+	4.81196i	−0.0390832	+	0.202441i
$566$			12.9855i			0.545821i
$567$	−26.5210	−	12.8478i	−1.11378	−	0.539558i
$568$	−1.20453	+	1.20453i	−0.0505408	+	0.0505408i
$569$	−11.6625			−0.488917			−0.244458	−	0.969660i	$-0.578610\pi$
$569$	−11.6625			−0.488917			−0.244458	+	0.969660i	$0.578610\pi$
$570$	24.9396	+	2.68242i	1.04461	+	0.112354i
$571$	−30.0173			−1.25619			−0.628093	−	0.778138i	$-0.716164\pi$
$571$	−30.0173			−1.25619			−0.628093	+	0.778138i	$0.716164\pi$
$572$	0.241451	−	0.241451i	0.0100956	−	0.0100956i
$573$	40.1842	−	3.36599i	1.67872	−	0.140616i
$574$		−	2.89111i		−	0.120673i
$575$	4.59754	−	1.96536i	0.191731	−	0.0819613i
$576$	−0.499082	−	2.95819i	−0.0207951	−	0.123258i
$577$	30.9222	+	30.9222i	1.28731	+	1.28731i	0.936415	+	0.350894i	$0.114122\pi$
$577$	30.9222	+	30.9222i	1.28731	+	1.28731i	0.350894	+	0.936415i	$0.385878\pi$
$578$	27.7415	+	27.7415i	1.15390	+	1.15390i
$579$	24.9780	+	21.1169i	1.03805	+	0.877590i
$580$	3.67762	−	2.48740i	0.152705	−	0.103284i
$581$			40.9633i			1.69944i
$582$	−1.49440	−	17.8406i	−0.0619448	−	0.739517i
$583$	−0.600165	+	0.600165i	−0.0248563	+	0.0248563i
$584$	−0.375785			−0.0155501
$585$	27.7094	+	0.653396i	1.14564	+	0.0270146i
$586$	−18.2763			−0.754988
$587$	−22.4198	+	22.4198i	−0.925363	+	0.925363i	−0.997402	−	0.0720385i	$-0.977050\pi$
$587$	−22.4198	+	22.4198i	−0.925363	+	0.925363i	0.0720385	+	0.997402i	$0.477050\pi$
$588$	−0.538020	−	6.42305i	−0.0221876	−	0.264882i
$589$			26.9434i			1.11018i
$590$	22.1259	+	4.27162i	0.910907	+	0.175860i
$591$	−7.34664	−	6.21100i	−0.302201	−	0.255486i
$592$	−4.80467	−	4.80467i	−0.197471	−	0.197471i
$593$	−1.81620	−	1.81620i	−0.0745825	−	0.0745825i	0.668831	−	0.743414i	$-0.266795\pi$
$593$	−1.81620	−	1.81620i	−0.0745825	−	0.0745825i	−0.743414	+	0.668831i	$0.766795\pi$
$594$	−0.218823	+	0.369485i	−0.00897840	+	0.0151602i
$595$	30.7598	+	45.4783i	1.26103	+	1.86443i
$596$		−	20.0239i		−	0.820212i
$597$	−25.2697	+	2.11669i	−1.03422	+	0.0866304i
$598$	−2.92164	+	2.92164i	−0.119475	+	0.119475i
$599$	8.91093			0.364091			0.182045	−	0.983290i	$-0.441728\pi$
$599$	8.91093			0.364091			0.182045	+	0.983290i	$0.441728\pi$
$600$	4.05693	+	7.65123i	0.165623	+	0.312360i
$601$	−45.6488			−1.86205			−0.931027	−	0.364951i	$-0.881086\pi$
$601$	−45.6488			−1.86205			−0.931027	+	0.364951i	$0.881086\pi$
$602$	−5.56577	+	5.56577i	−0.226844	+	0.226844i
$603$	−2.65602	−	1.88919i	−0.108162	−	0.0769338i
$604$			17.1989i			0.699814i
$605$	13.7717	+	20.3615i	0.559900	+	0.827811i
$606$	3.35081	−	3.96348i	0.136117	−	0.161005i
$607$	−14.6214	−	14.6214i	−0.593463	−	0.593463i	0.345102	−	0.938565i	$-0.387844\pi$
$607$	−14.6214	−	14.6214i	−0.593463	−	0.593463i	−0.938565	+	0.345102i	$0.887844\pi$
$608$	−4.57959	−	4.57959i	−0.185727	−	0.185727i
$609$	−7.27010	+	8.59939i	−0.294599	+	0.348465i
$610$	1.92368	+	0.371386i	0.0778877	+	0.0150370i
$611$		−	44.5978i		−	1.80423i
$612$	−18.3321	−	13.0394i	−0.741032	−	0.527086i
$613$	25.3682	−	25.3682i	1.02461	−	1.02461i	0.0249223	−	0.999689i	$-0.492066\pi$
$613$	25.3682	−	25.3682i	1.02461	−	1.02461i	0.999689	−	0.0249223i	$-0.00793383\pi$
$614$	13.1101			0.529080
$615$	−2.14562	−	2.66280i	−0.0865199	−	0.107375i
$616$	−0.270599			−0.0109027
$617$	15.8956	−	15.8956i	0.639931	−	0.639931i	−0.310607	−	0.950538i	$-0.600532\pi$
$617$	15.8956	−	15.8956i	0.639931	−	0.639931i	0.950538	+	0.310607i	$0.100532\pi$
$618$	19.3443	−	1.62035i	0.778141	−	0.0651802i
$619$			40.8815i			1.64317i	0.570088	+	0.821584i	$0.306909\pi$
$619$			40.8815i			1.64317i	−0.570088	+	0.821584i	$0.693091\pi$
$620$	−7.70543	+	5.21166i	−0.309458	+	0.209305i
$621$	2.64783	−	4.47090i	0.106254	−	0.179411i
$622$	24.1167	+	24.1167i	0.966993	+	0.966993i
$623$	−13.0848	−	13.0848i	−0.524231	−	0.524231i
$624$	−5.46517	−	4.62037i	−0.218782	−	0.184963i
$625$	−18.0717	−	17.2747i	−0.722867	−	0.690988i
$626$		−	29.7123i		−	1.18754i
$627$	0.0773826	+	0.923817i	0.00309036	+	0.0368937i
$628$	16.4821	−	16.4821i	0.657708	−	0.657708i
$629$	−50.9533			−2.03164
$630$	−15.1611	−	15.8934i	−0.604034	−	0.633208i
$631$	−0.512624			−0.0204072			−0.0102036	−	0.999948i	$-0.503248\pi$
$631$	−0.512624			−0.0204072			−0.0102036	+	0.999948i	$0.503248\pi$
$632$	−11.8838	+	11.8838i	−0.472714	+	0.472714i
$633$	−0.201340	−	2.40366i	−0.00800255	−	0.0955369i
$634$			2.67145i			0.106097i
$635$	1.59395	−	8.25625i	0.0632540	−	0.327639i
$636$	13.5846	+	11.4847i	0.538663	+	0.455397i
$637$	−10.8724	−	10.8724i	−0.430780	−	0.430780i
$638$	0.116029	+	0.116029i	0.00459365	+	0.00459365i
$639$	−0.850164	−	5.03916i	−0.0336320	−	0.199346i
$640$	0.423868	−	2.19553i	0.0167549	−	0.0867858i
$641$		−	41.0820i		−	1.62264i	−0.584600	−	0.811322i	$-0.698749\pi$
$641$		−	41.0820i		−	1.62264i	0.584600	−	0.811322i	$-0.301251\pi$
$642$	−13.5365	+	1.13387i	−0.534244	+	0.0447504i
$643$	−11.1338	+	11.1338i	−0.439076	+	0.439076i	−0.891701	−	0.452625i	$-0.850488\pi$
$643$	−11.1338	+	11.1338i	−0.439076	+	0.439076i	0.452625	+	0.891701i	$0.350488\pi$
$644$	3.27434			0.129027
$645$	−0.995637	+	9.25686i	−0.0392032	+	0.364489i
$646$	−48.5664			−1.91082
$647$	−19.7653	+	19.7653i	−0.777052	+	0.777052i	−0.979329	−	0.202276i	$-0.935166\pi$
$647$	−19.7653	+	19.7653i	−0.777052	+	0.777052i	0.202276	+	0.979329i	$0.435166\pi$
$648$	8.09962	+	3.92379i	0.318183	+	0.154141i
$649$			0.832843i			0.0326920i
$650$	19.1744	+	7.69027i	0.752083	+	0.301637i
$651$	15.2325	−	18.0176i	0.597007	−	0.706166i
$652$	−7.21629	−	7.21629i	−0.282612	−	0.282612i
$653$	1.85033	+	1.85033i	0.0724089	+	0.0724089i	0.742384	−	0.669975i	$-0.233695\pi$
$653$	1.85033	+	1.85033i	0.0724089	+	0.0724089i	−0.669975	+	0.742384i	$0.733695\pi$
$654$	16.0085	−	18.9356i	0.625984	−	0.740441i
$655$	22.2352	−	15.0391i	0.868802	−	0.587624i
$656$			0.882958i			0.0344737i
$657$	0.653436	−	0.918668i	0.0254930	−	0.0358406i
$658$	−24.9908	+	24.9908i	−0.974244	+	0.974244i
$659$	−28.7705			−1.12074			−0.560370	−	0.828243i	$-0.689341\pi$
$659$	−28.7705			−1.12074			−0.560370	+	0.828243i	$0.689341\pi$
$660$	−0.249230	+	0.200824i	−0.00970127	+	0.00781706i
$661$	−10.2697			−0.399445			−0.199722	−	0.979853i	$-0.564004\pi$
$661$	−10.2697			−0.399445			−0.199722	+	0.979853i	$0.564004\pi$
$662$	13.0193	−	13.0193i	0.506008	−	0.506008i
$663$	−53.4783	+	4.47956i	−2.07693	+	0.173972i
$664$		−	12.5104i		−	0.485497i
$665$	−46.5591	−	8.98871i	−1.80549	−	0.348567i
$666$	20.1004	−	3.39118i	0.778876	−	0.131405i
$667$	−1.40400	−	1.40400i	−0.0543630	−	0.0543630i
$668$	−11.3314	−	11.3314i	−0.438423	−	0.438423i
$669$	−31.7892	−	26.8752i	−1.22904	−	1.03906i
$670$	−1.36106	−	2.01233i	−0.0525823	−	0.0777429i
$671$			0.0724097i			0.00279535i
$672$	0.473395	+	5.65154i	0.0182616	+	0.218013i
$673$	6.49107	−	6.49107i	0.250212	−	0.250212i	−0.570845	−	0.821058i	$-0.693384\pi$
$673$	6.49107	−	6.49107i	0.250212	−	0.250212i	0.821058	+	0.570845i	$0.193384\pi$
$674$	6.79651			0.261792
$675$	−25.7591	−	3.38656i	−0.991468	−	0.130349i
$676$	−4.07197			−0.156614
$677$	11.6214	−	11.6214i	0.446646	−	0.446646i	−0.447592	−	0.894238i	$-0.647718\pi$
$677$	11.6214	−	11.6214i	0.446646	−	0.446646i	0.894238	+	0.447592i	$0.147718\pi$
$678$	0.316871	+	3.78291i	0.0121694	+	0.145282i
$679$			33.8448i			1.29884i
$680$	−9.39417	−	13.8893i	−0.360250	−	0.532629i
$681$	12.6743	+	10.7151i	0.485680	+	0.410604i
$682$	−0.243107	−	0.243107i	−0.00930906	−	0.00930906i
$683$	−13.1189	−	13.1189i	−0.501983	−	0.501983i	0.410071	−	0.912054i	$-0.365504\pi$
$683$	−13.1189	−	13.1189i	−0.501983	−	0.501983i	−0.912054	+	0.410071i	$0.865504\pi$
$684$	19.1588	−	3.23232i	0.732556	−	0.123591i
$685$	12.8311	+	2.47716i	0.490250	+	0.0946476i
$686$		−	10.7355i		−	0.409883i
$687$	20.0561	−	1.67998i	0.765190	−	0.0640953i
$688$	1.69981	−	1.69981i	0.0648047	−	0.0648047i
$689$	42.4351			1.61665
$690$	3.01578	−	2.43004i	0.114809	−	0.0925101i
$691$	26.0545			0.991159			0.495580	−	0.868563i	$-0.334956\pi$
$691$	26.0545			0.991159			0.495580	+	0.868563i	$0.334956\pi$
$692$	−6.03766	+	6.03766i	−0.229517	+	0.229517i
$693$	0.470533	−	0.661524i	0.0178741	−	0.0251292i
$694$		−	24.2144i		−	0.919167i
$695$	−0.802843	+	0.543012i	−0.0304536	+	0.0205976i
$696$	2.22032	−	2.62629i	0.0841611	−	0.0995494i
$697$	4.68186	+	4.68186i	0.177338	+	0.177338i
$698$	−1.42288	−	1.42288i	−0.0538569	−	0.0538569i
$699$	−20.5061	+	24.2555i	−0.775611	+	0.917427i
$700$	−6.43528	−	15.0539i	−0.243231	−	0.568985i
$701$			39.5869i			1.49518i	0.664162	+	0.747588i	$0.268788\pi$
$701$			39.5869i			1.49518i	−0.664162	+	0.747588i	$0.731212\pi$
$702$	20.7984	−	5.32636i	0.784985	−	0.201030i
$703$	31.1176	−	31.1176i	1.17362	−	1.17362i
$704$	0.0826422			0.00311469
$705$	−4.47050	+	41.5642i	−0.168369	+	1.56540i
$706$	32.5409			1.22469
$707$	−6.93784	+	6.93784i	−0.260924	+	0.260924i
$708$	17.3942	−	1.45700i	0.653713	−	0.0547576i
$709$			0.0916175i			0.00344077i	0.999999	+	0.00172038i	$0.000547616\pi$
$709$			0.0916175i			0.00344077i	−0.999999	+	0.00172038i	$0.999452\pi$
$710$	0.722041	−	3.73998i	0.0270977	−	0.140359i
$711$	−8.38771	−	49.7162i	−0.314564	−	1.86450i
$712$	3.99616	+	3.99616i	0.149762	+	0.149762i
$713$	2.94168	+	2.94168i	0.110167	+	0.110167i
$714$	32.4773	+	27.4570i	1.21543	+	1.02755i
$715$	−0.144735	+	0.749691i	−0.00541279	+	0.0280369i
$716$		−	10.2241i		−	0.382094i
$717$	0.875272	+	10.4493i	0.0326876	+	0.390235i
$718$	−13.8264	+	13.8264i	−0.515996	+	0.515996i
$719$	9.47790			0.353466			0.176733	−	0.984259i	$-0.443447\pi$
$719$	9.47790			0.353466			0.176733	+	0.984259i	$0.443447\pi$
$720$	4.63028	+	4.85392i	0.172560	+	0.180895i
$721$	−36.6974			−1.36668
$722$	16.2248	−	16.2248i	0.603825	−	0.603825i
$723$	2.56318	+	30.6001i	0.0953258	+	1.13803i
$724$			7.86650i			0.292356i
$725$	−3.69556	+	9.21430i	−0.137250	+	0.342210i
$726$	14.5407	+	12.2930i	0.539656	+	0.456236i
$727$	−16.4918	−	16.4918i	−0.611648	−	0.611648i	0.331727	−	0.943375i	$-0.392369\pi$
$727$	−16.4918	−	16.4918i	−0.611648	−	0.611648i	−0.943375	+	0.331727i	$0.892369\pi$
$728$	9.56646	+	9.56646i	0.354557	+	0.354557i
$729$	−23.6764	+	12.9780i	−0.876904	+	0.480665i
$730$	0.696026	−	0.470765i	0.0257611	−	0.0174238i
$731$		−	18.0264i		−	0.666731i
$732$	1.51230	−	0.126676i	0.0558961	−	0.00468208i
$733$	14.5823	−	14.5823i	0.538610	−	0.538610i	−0.384510	−	0.923121i	$-0.625630\pi$
$733$	14.5823	−	14.5823i	0.538610	−	0.538610i	0.923121	+	0.384510i	$0.125630\pi$
$734$	−8.49714			−0.313635
$735$	9.04300	+	11.2227i	0.333556	+	0.413956i
$736$	−1.00000			−0.0368605
$737$	0.0634891	−	0.0634891i	0.00233865	−	0.00233865i
$738$	−2.15854	−	1.53534i	−0.0794568	−	0.0565165i
$739$			8.04723i			0.296022i	0.988986	+	0.148011i	$0.0472871\pi$
$739$			8.04723i			0.296022i	−0.988986	+	0.148011i	$0.952713\pi$
$740$	14.9182	+	2.88011i	0.548405	+	0.105875i
$741$	29.9239	−	35.3953i	1.09928	−	1.30028i
$742$	−23.7790	−	23.7790i	−0.872954	−	0.872954i
$743$	−3.40804	−	3.40804i	−0.125029	−	0.125029i	0.641823	−	0.766852i	$-0.278178\pi$
$743$	−3.40804	−	3.40804i	−0.125029	−	0.125029i	−0.766852	+	0.641823i	$0.778178\pi$
$744$	−4.65206	+	5.50266i	−0.170553	+	0.201737i
$745$	25.0850	+	37.0882i	0.919044	+	1.35881i
$746$		−	26.1199i		−	0.956318i
$747$	30.5837	+	21.7537i	1.11900	+	0.795928i
$748$	0.438208	−	0.438208i	0.0160225	−	0.0160225i
$749$	25.6797			0.938315
$750$	−17.0993	−	9.08922i	−0.624378	−	0.331891i
$751$	40.5910			1.48119			0.740594	−	0.671953i	$-0.234544\pi$
$751$	40.5910			1.48119			0.740594	+	0.671953i	$0.234544\pi$
$752$	7.63231	−	7.63231i	0.278322	−	0.278322i
$753$	38.5404	−	3.22830i	1.40449	−	0.117646i
$754$		−	8.20395i		−	0.298770i
$755$	−21.5460	−	31.8557i	−0.784138	−	1.15935i
$756$	−14.6393	−	8.66992i	−0.532426	−	0.315322i
$757$	34.6920	+	34.6920i	1.26090	+	1.26090i	0.950657	+	0.310243i	$0.100411\pi$
$757$	34.6920	+	34.6920i	1.26090	+	1.26090i	0.310243	+	0.950657i	$0.399589\pi$
$758$	1.56540	+	1.56540i	0.0568579	+	0.0568579i
$759$	0.109311	+	0.0924137i	0.00396774	+	0.00335441i
$760$	14.2194	+	2.74519i	0.515791	+	0.0995786i
$761$		−	50.5466i		−	1.83231i	−0.400823	−	0.916156i	$-0.631276\pi$
$761$		−	50.5466i		−	1.83231i	0.400823	−	0.916156i	$-0.368724\pi$
$762$	−0.543680	−	6.49063i	−0.0196955	−	0.235131i
$763$	−33.1457	+	33.1457i	−1.19995	+	1.19995i
$764$	23.2816			0.842300
$765$	50.2897	+	1.18585i	1.81823	+	0.0428743i
$766$	−33.9433			−1.22642
$767$	29.4434	−	29.4434i	1.06314	−	1.06314i
$768$	−0.144577	−	1.72601i	−0.00521698	−	0.0622819i
$769$		−	52.5084i		−	1.89350i	−0.321969	−	0.946750i	$-0.604345\pi$
$769$		−	52.5084i		−	1.89350i	0.321969	−	0.946750i	$-0.395655\pi$
$770$	0.501201	−	0.338993i	0.0180620	−	0.0122165i
$771$	−7.03275	−	5.94563i	−0.253278	−	0.214127i
$772$	13.3531	+	13.3531i	0.480588	+	0.480588i
$773$	−20.1139	−	20.1139i	−0.723445	−	0.723445i	0.245860	−	0.969305i	$-0.420930\pi$
$773$	−20.1139	−	20.1139i	−0.723445	−	0.723445i	−0.969305	+	0.245860i	$0.920930\pi$
$774$	1.19974	+	7.11119i	0.0431238	+	0.255607i
$775$	7.74302	−	19.3060i	0.278138	−	0.693491i
$776$		−	10.3363i		−	0.371053i
$777$	−38.4013	+	3.21664i	−1.37764	+	0.115396i
$778$	−6.28786	+	6.28786i	−0.225431	+	0.225431i
$779$	−5.71850			−0.204886
$780$	15.9107	+	1.71130i	0.569695	+	0.0612745i
$781$	0.140777			0.00503741
$782$	−5.30247	+	5.30247i	−0.189616	+	0.189616i
$783$	2.55959	+	9.99469i	0.0914722	+	0.357181i
$784$		−	3.72133i		−	0.132905i
$785$	−9.88004	+	51.1760i	−0.352634	+	1.82655i
$786$	13.4243	−	15.8788i	0.478827	−	0.566378i
$787$	−7.69708	−	7.69708i	−0.274371	−	0.274371i	0.556486	−	0.830857i	$-0.312149\pi$
$787$	−7.69708	−	7.69708i	−0.274371	−	0.274371i	−0.830857	+	0.556486i	$0.812149\pi$
$788$	−3.92746	−	3.92746i	−0.139910	−	0.139910i
$789$	−15.3968	+	18.2120i	−0.548139	+	0.648363i
$790$	7.12365	−	36.8986i	0.253448	−	1.31279i
$791$		−	7.17642i		−	0.255164i
$792$	−0.143703	+	0.202032i	−0.00510626	+	0.00717891i
$793$	2.55989	−	2.55989i	0.0909045	−	0.0909045i
$794$	−30.2880			−1.07488
$795$	−39.5487	−	4.25372i	−1.40265	−	0.150864i
$796$	−14.6406			−0.518921
$797$	1.30291	−	1.30291i	0.0461515	−	0.0461515i	−0.683654	−	0.729806i	$-0.739610\pi$
$797$	1.30291	−	1.30291i	0.0461515	−	0.0461515i	0.729806	+	0.683654i	$0.239610\pi$
$798$	−36.6023	+	3.06596i	−1.29571	+	0.108534i
$799$		−	80.9403i		−	2.86346i
$800$	1.96536	+	4.59754i	0.0694861	+	0.162547i
$801$	−16.7180	+	2.82052i	−0.590702	+	0.0996582i
$802$	−23.2592	−	23.2592i	−0.821312	−	0.821312i
$803$	0.0219597	+	0.0219597i	0.000774941	+	0.000774941i
$804$	−1.43706	−	1.21492i	−0.0506811	−	0.0428469i
$805$	−6.06471	+	4.10194i	−0.213753	+	0.144574i
$806$			17.1891i			0.605460i
$807$	0.289141	+	3.45186i	0.0101783	+	0.121511i
$808$	2.11885	−	2.11885i	0.0745408	−	0.0745408i
$809$	8.03171			0.282380			0.141190	−	0.989983i	$-0.454907\pi$
$809$	8.03171			0.282380			0.141190	+	0.989983i	$0.454907\pi$
$810$	−19.9176	+	2.87921i	−0.699833	+	0.101165i
$811$	24.6723			0.866363			0.433181	−	0.901307i	$-0.357391\pi$
$811$	24.6723			0.866363			0.433181	+	0.901307i	$0.357391\pi$
$812$	−4.59717	+	4.59717i	−0.161329	+	0.161329i
$813$	1.12093	+	13.3821i	0.0393129	+	0.469329i
$814$			0.561540i			0.0196820i
$815$	22.4062	+	4.32573i	0.784854	+	0.151524i
$816$	−9.91872	−	8.38549i	−0.347225	−	0.293551i
$817$	11.0089	+	11.0089i	0.385152	+	0.385152i
$818$	−20.7915	−	20.7915i	−0.726958	−	0.726958i
$819$	−40.0215	+	6.75209i	−1.39846	+	0.235937i
$820$	−1.10613	−	1.63541i	−0.0386276	−	0.0571109i
$821$			27.9798i			0.976501i	0.872704	+	0.488250i	$0.162365\pi$
$821$			27.9798i			0.976501i	−0.872704	+	0.488250i	$0.837635\pi$
$822$	10.0871	−	0.844935i	0.351828	−	0.0294705i
$823$	−6.77408	+	6.77408i	−0.236130	+	0.236130i	−0.815245	−	0.579116i	$-0.803398\pi$
$823$	−6.77408	+	6.77408i	−0.236130	+	0.236130i	0.579116	+	0.815245i	$0.303398\pi$
$824$	11.2075			0.390433
$825$	0.210040	−	0.684188i	0.00731264	−	0.0238204i
$826$	−32.9979			−1.14814
$827$	1.39537	−	1.39537i	0.0485217	−	0.0485217i	−0.682430	−	0.730951i	$-0.739077\pi$
$827$	1.39537	−	1.39537i	0.0485217	−	0.0485217i	0.730951	+	0.682430i	$0.239077\pi$
$828$	1.73886	−	2.44466i	0.0604294	−	0.0849579i
$829$			32.2465i			1.11997i	0.828504	+	0.559984i	$0.189193\pi$
$829$			32.2465i			1.11997i	−0.828504	+	0.559984i	$0.810807\pi$
$830$	15.6724	+	23.1716i	0.543997	+	0.804299i
$831$	−13.2251	+	15.6432i	−0.458772	+	0.542655i
$832$	−2.92164	−	2.92164i	−0.101290	−	0.101290i
$833$	−19.7323	−	19.7323i	−0.683683	−	0.683683i
$834$	−0.484707	+	0.573333i	−0.0167840	+	0.0198529i
$835$	35.1832	+	6.79247i	1.21757	+	0.235063i
$836$			0.535234i			0.0185115i
$837$	−5.36290	−	20.9411i	−0.185369	−	0.723829i
$838$	−3.42430	+	3.42430i	−0.118290	+	0.118290i
$839$	8.38491			0.289479			0.144740	−	0.989470i	$-0.453766\pi$
$839$	8.38491			0.289479			0.144740	+	0.989470i	$0.453766\pi$
$840$	−7.95679	−	9.87469i	−0.274535	−	0.340709i
$841$	−25.0576			−0.864055
$842$	−13.7500	+	13.7500i	−0.473857	+	0.473857i
$843$	−18.0175	+	1.50922i	−0.620556	+	0.0519802i
$844$		−	1.39261i		−	0.0479357i
$845$	7.54208	−	5.10117i	0.259455	−	0.175486i
$846$	5.38695	+	31.9299i	0.185207	+	1.09777i
$847$	−25.4526	−	25.4526i	−0.874562	−	0.874562i
$848$	7.26221	+	7.26221i	0.249385	+	0.249385i
$849$	−17.1759	−	14.5209i	−0.589477	−	0.498356i
$850$	34.7996	+	13.9570i	1.19362	+	0.478722i
$851$		−	6.79483i		−	0.232924i
$852$	−0.246281	−	2.94018i	−0.00843744	−	0.100729i
$853$	−2.47888	+	2.47888i	−0.0848752	+	0.0848752i	−0.748270	−	0.663395i	$-0.769115\pi$
$853$	−2.47888	+	2.47888i	−0.0848752	+	0.0848752i	0.663395	+	0.748270i	$0.269115\pi$
$854$	−2.86893			−0.0981726
$855$	−31.4365	+	29.9881i	−1.07511	+	1.02557i
$856$	−7.84269			−0.268058
$857$	−13.4091	+	13.4091i	−0.458047	+	0.458047i	−0.898014	−	0.439967i	$-0.854990\pi$
$857$	−13.4091	+	13.4091i	−0.458047	+	0.458047i	0.439967	+	0.898014i	$0.354990\pi$
$858$	0.0493677	+	0.589367i	0.00168539	+	0.0201207i
$859$			40.6567i			1.38719i	0.720366	+	0.693594i	$0.243974\pi$
$859$			40.6567i			1.38719i	−0.720366	+	0.693594i	$0.756026\pi$
$860$	−1.01894	+	5.27782i	−0.0347454	+	0.179972i
$861$	3.82408	+	3.23295i	0.130324	+	0.110179i
$862$	−16.5569	−	16.5569i	−0.563932	−	0.563932i
$863$	−14.4645	−	14.4645i	−0.492376	−	0.492376i	0.416678	−	0.909054i	$-0.363194\pi$
$863$	−14.4645	−	14.4645i	−0.492376	−	0.492376i	−0.909054	+	0.416678i	$0.863194\pi$
$864$	4.47090	+	2.64783i	0.152103	+	0.0900811i
$865$	3.61921	−	18.7466i	0.123057	−	0.637403i
$866$		−	26.3226i		−	0.894478i
$867$	−67.7155	+	5.67212i	−2.29974	+	0.192635i
$868$	9.63209	−	9.63209i	0.326934	−	0.326934i
$869$	1.38891			0.0471155
$870$	−0.822369	+	7.64591i	−0.0278809	+	0.259221i
$871$	−4.48905			−0.152106
$872$	10.1228	−	10.1228i	0.342802	−	0.342802i
$873$	25.2689	+	17.9734i	0.855223	+	0.608308i
$874$		−	6.47652i		−	0.219072i
$875$	30.7782	+	19.8209i	1.04049	+	0.670070i
$876$	0.420218	−	0.497052i	0.0141978	−	0.0167938i
$877$	28.2774	+	28.2774i	0.954860	+	0.954860i	0.999024	−	0.0441640i	$-0.0140624\pi$
$877$	28.2774	+	28.2774i	0.954860	+	0.954860i	−0.0441640	+	0.999024i	$0.514062\pi$
$878$	−1.94043	−	1.94043i	−0.0654864	−	0.0654864i
$879$	20.4373	−	24.1741i	0.689333	−	0.815373i
$880$	−0.153069	+	0.103530i	−0.00515996	+	0.00349000i
$881$			16.0524i			0.540818i	0.962746	+	0.270409i	$0.0871589\pi$
$881$			16.0524i			0.540818i	−0.962746	+	0.270409i	$0.912841\pi$
$882$	9.09741	+	6.47086i	0.306326	+	0.217885i
$883$	−39.6316	+	39.6316i	−1.33371	+	1.33371i	−0.431687	+	0.902024i	$0.642081\pi$
$883$	−39.6316	+	39.6316i	−1.33371	+	1.33371i	−0.902024	+	0.431687i	$0.857919\pi$
$884$	−30.9839			−1.04210
$885$	−30.3921	+	24.4892i	−1.02162	+	0.823197i
$886$	7.41295			0.249043
$887$	25.8440	−	25.8440i	0.867756	−	0.867756i	−0.124467	−	0.992224i	$-0.539722\pi$
$887$	25.8440	−	25.8440i	0.867756	−	0.867756i	0.992224	+	0.124467i	$0.0397222\pi$
$888$	11.7279	−	0.982377i	0.393563	−	0.0329664i
$889$			12.3131i			0.412969i
$890$	−12.4078	−	2.39546i	−0.415912	−	0.0802959i
$891$	−0.244023	−	0.702610i	−0.00817507	−	0.0235383i
$892$	−16.9943	−	16.9943i	−0.569010	−	0.569010i
$893$	49.4309	+	49.4309i	1.65414	+	1.65414i
$894$	26.4857	+	22.3915i	0.885814	+	0.748885i
$895$	12.8083	+	18.9371i	0.428134	+	0.632996i
$896$			3.27434i			0.109388i
$897$	−0.597367	−	7.13155i	−0.0199455	−	0.238116i
$898$	2.95278	−	2.95278i	0.0985356	−	0.0985356i
$899$	−8.26023			−0.275494
$900$	−14.6569	−	3.18980i	−0.488564	−	0.106327i
$901$	77.0154			2.56575
$902$	0.0515973	−	0.0515973i	0.00171800	−	0.00171800i
$903$	−1.13799	−	13.5857i	−0.0378700	−	0.452104i
$904$			2.19171i			0.0728953i
$905$	−9.85477	−	14.5703i	−0.327583	−	0.484332i
$906$	−22.7490	−	19.2325i	−0.755786	−	0.638957i
$907$	26.9227	+	26.9227i	0.893953	+	0.893953i	0.994893	−	0.100939i	$-0.0321848\pi$
$907$	26.9227	+	26.9227i	0.893953	+	0.893953i	−0.100939	+	0.994893i	$0.532185\pi$
$908$	6.77558	+	6.77558i	0.224856	+	0.224856i
$909$	1.49550	+	8.86424i	0.0496026	+	0.294008i
$910$	−29.7033	−	5.73452i	−0.984655	−	0.190098i
$911$			3.29887i			0.109296i	0.998506	+	0.0546482i	$0.0174037\pi$
$911$			3.29887i			0.109296i	−0.998506	+	0.0546482i	$0.982596\pi$
$912$	11.1785	−	0.936357i	0.370158	−	0.0310059i
$913$	−0.731067	+	0.731067i	−0.0241948	+	0.0241948i
$914$	−5.27277			−0.174408
$915$	−2.64237	+	2.12916i	−0.0873541	+	0.0703879i
$916$	11.6200			0.383935
$917$	−27.7949	+	27.7949i	−0.917868	+	0.917868i
$918$	37.7469	−	9.66678i	1.24583	−	0.319051i
$919$			26.6450i			0.878936i	0.898258	+	0.439468i	$0.144833\pi$
$919$			26.6450i			0.878936i	−0.898258	+	0.439468i	$0.855167\pi$
$920$	1.85219	−	1.25275i	0.0610649	−	0.0413020i
$921$	−14.6602	+	17.3407i	−0.483070	+	0.571396i
$922$	−8.02653	−	8.02653i	−0.264340	−	0.264340i
$923$	−4.97689	−	4.97689i	−0.163816	−	0.163816i
$924$	0.302594	−	0.357922i	0.00995463	−	0.0117748i
$925$	−31.2395	+	13.3543i	−1.02715	+	0.439087i
$926$			21.7168i			0.713657i
$927$	−19.4883	+	27.3987i	−0.640080	+	0.899890i
$928$	1.40400	−	1.40400i	0.0460885	−	0.0460885i
$929$	−7.77474			−0.255081			−0.127541	−	0.991833i	$-0.540708\pi$
$929$	−7.77474			−0.255081			−0.127541	+	0.991833i	$0.540708\pi$
$930$	1.72304	−	16.0199i	0.0565008	−	0.525312i
$931$	24.1013			0.789889
$932$	−12.9668	+	12.9668i	−0.424742	+	0.424742i
$933$	−58.8675	+	4.93098i	−1.92724	+	0.161433i
$934$			8.48431i			0.277615i
$935$	−0.262679	+	1.36061i	−0.00859054	+	0.0444967i
$936$	12.2227	−	2.06212i	0.399513	−	0.0674025i
$937$	8.36629	+	8.36629i	0.273315	+	0.273315i	0.830433	−	0.557118i	$-0.188093\pi$
$937$	8.36629	+	8.36629i	0.273315	+	0.273315i	−0.557118	+	0.830433i	$0.688093\pi$
$938$	2.51549	+	2.51549i	0.0821335	+	0.0821335i
$939$	39.3005	+	33.2254i	1.28252	+	1.08427i
$940$	−4.57512	+	23.6979i	−0.149224	+	0.772940i
$941$		−	35.8516i		−	1.16873i	−0.811491	−	0.584364i	$-0.801344\pi$
$941$		−	35.8516i		−	1.16873i	0.811491	−	0.584364i	$-0.198656\pi$
$942$	3.36998	+	40.2319i	0.109800	+	1.31083i
$943$	−0.624346	+	0.624346i	−0.0203315	+	0.0203315i
$944$	10.0777			0.328001
$945$	37.9760	−	2.28103i	1.23536	−	0.0742019i
$946$	−0.198663			−0.00645910
$947$	3.74296	−	3.74296i	0.121630	−	0.121630i	−0.643672	−	0.765302i	$-0.722590\pi$
$947$	3.74296	−	3.74296i	0.121630	−	0.121630i	0.765302	+	0.643672i	$0.222590\pi$
$948$	−2.42980	−	29.0077i	−0.0789163	−	0.942128i
$949$		−	1.55268i		−	0.0504020i
$950$	−29.7761	+	12.7287i	−0.966063	+	0.412974i
$951$	−3.53353	−	2.98732i	−0.114583	−	0.0968705i
$952$	17.3621	+	17.3621i	0.562710	+	0.562710i
$953$	15.5762	+	15.5762i	0.504563	+	0.504563i	0.912852	−	0.408290i	$-0.133875\pi$
$953$	15.5762	+	15.5762i	0.504563	+	0.504563i	−0.408290	+	0.912852i	$0.633875\pi$
$954$	−30.3816	+	5.12573i	−0.983641	+	0.165952i
$955$	−43.1220	+	29.1661i	−1.39540	+	0.943793i
$956$			6.05401i			0.195801i
$957$	−0.283221	+	0.0237237i	−0.00915524	+	0.000766879i
$958$	22.4588	−	22.4588i	0.725611	−	0.725611i
$959$	−19.1359			−0.617930
$960$	2.43004	+	3.01578i	0.0784292	+	0.0973337i
$961$	−13.6930			−0.441709
$962$	19.8521	−	19.8521i	0.640056	−	0.640056i
$963$	13.6373	−	19.1727i	0.439456	−	0.617833i
$964$			17.7288i			0.571007i
$965$	−41.4605	−	8.00437i	−1.33466	−	0.257670i
$966$	−3.66150	+	4.33098i	−0.117807	+	0.139347i
$967$	−34.8919	−	34.8919i	−1.12205	−	1.12205i	−0.991433	−	0.130614i	$-0.958305\pi$
$967$	−34.8919	−	34.8919i	−1.12205	−	1.12205i	−0.130614	−	0.991433i	$-0.541695\pi$
$968$	7.77335	+	7.77335i	0.249845	+	0.249845i
$969$	54.3088	−	64.2388i	1.74465	−	2.06365i
$970$	12.9489	+	19.1449i	0.415763	+	0.614706i
$971$			9.46212i			0.303654i	0.988407	+	0.151827i	$0.0485156\pi$
$971$			9.46212i			0.303654i	−0.988407	+	0.151827i	$0.951484\pi$
$972$	−14.2473	+	6.32566i	−0.456983	+	0.202896i
$973$	1.00359	−	1.00359i	0.0321735	−	0.0321735i
$974$	−12.0688			−0.386710
$975$	−31.6135	+	16.7625i	−1.01244	+	0.536830i
$976$	0.876183			0.0280459
$977$	39.3682	−	39.3682i	1.25950	−	1.25950i	0.308170	−	0.951331i	$-0.400283\pi$
$977$	39.3682	−	39.3682i	1.25950	−	1.25950i	0.951331	−	0.308170i	$-0.0997166\pi$
$978$	17.6145	−	1.47546i	0.563251	−	0.0471801i
$979$		−	0.467046i		−	0.0149268i
$980$	4.66191	+	6.89263i	0.148919	+	0.220177i
$981$	7.14478	+	42.3491i	0.228115	+	1.35210i
$982$	−11.0121	−	11.0121i	−0.351410	−	0.351410i
$983$	5.98476	+	5.98476i	0.190884	+	0.190884i	0.796078	−	0.605194i	$-0.206904\pi$
$983$	5.98476	+	5.98476i	0.190884	+	0.190884i	−0.605194	+	0.796078i	$0.706904\pi$
$984$	−1.16789	−	0.987358i	−0.0372310	−	0.0314758i
$985$	12.1945	+	2.35428i	0.388551	+	0.0750135i
$986$		−	14.8893i		−	0.474173i
$987$	−5.10970	−	61.0012i	−0.162643	−	1.94169i
$988$	18.9221	−	18.9221i	0.601991	−	0.601991i
$989$	2.40390			0.0764395
$990$	0.0130688	−	0.554227i	0.000415354	−	0.0176145i
$991$	15.7047			0.498876			0.249438	−	0.968391i	$-0.419754\pi$
$991$	15.7047			0.498876			0.249438	+	0.968391i	$0.419754\pi$
$992$	−2.94168	+	2.94168i	−0.0933986	+	0.0933986i
$993$	2.66195	+	31.7792i	0.0844746	+	1.00848i
$994$			5.57770i			0.176914i
$995$	27.1171	−	18.3410i	0.859671	−	0.581449i
$996$	16.5475	+	13.9896i	0.524328	+	0.443277i
$997$	−36.2178	−	36.2178i	−1.14703	−	1.14703i	−0.987134	−	0.159894i	$-0.948885\pi$
$997$	−36.2178	−	36.2178i	−1.14703	−	1.14703i	−0.159894	−	0.987134i	$-0.551115\pi$
$998$	−21.1555	−	21.1555i	−0.669664	−	0.669664i
$999$	−17.9916	+	30.3790i	−0.569228	+	0.961150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.47.4	✓	32
3.2	odd	2	inner	690.2.i.f.47.15	yes	32
5.3	odd	4	inner	690.2.i.f.323.15	yes	32
15.8	even	4	inner	690.2.i.f.323.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.4	✓	32	1.1	even	1	trivial
690.2.i.f.47.15	yes	32	3.2	odd	2	inner
690.2.i.f.323.4	yes	32	15.8	even	4	inner
690.2.i.f.323.15	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.144577 - 1.72601i) q^{3} -1.00000i q^{4} +(1.25275 + 1.85219i) q^{5} +(1.32270 + 1.11824i) q^{6} +(-2.31531 - 2.31531i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.95819 + 0.499082i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.144577 - 1.72601i) q^{3} -1.00000i q^{4} +(1.25275 + 1.85219i) q^{5} +(1.32270 + 1.11824i) q^{6} +(-2.31531 - 2.31531i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.95819 + 0.499082i) q^{9} +(-2.19553 - 0.423868i) q^{10} -0.0826422i q^{11} +(-1.72601 + 0.144577i) q^{12} +(-2.92164 + 2.92164i) q^{13} +3.27434 q^{14} +(3.01578 - 2.43004i) q^{15} -1.00000 q^{16} +(-5.30247 + 5.30247i) q^{17} +(1.73886 - 2.44466i) q^{18} -6.47652i q^{19} +(1.85219 - 1.25275i) q^{20} +(-3.66150 + 4.33098i) q^{21} +(0.0584368 + 0.0584368i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(1.11824 - 1.32270i) q^{24} +(-1.86123 + 4.64067i) q^{25} -4.13182i q^{26} +(1.28911 + 5.03371i) q^{27} +(-2.31531 + 2.31531i) q^{28} +1.98555 q^{29} +(-0.414176 + 3.85077i) q^{30} -4.16017 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.142641 + 0.0119482i) q^{33} -7.49883i q^{34} +(1.38789 - 7.18891i) q^{35} +(0.499082 + 2.95819i) q^{36} +(4.80467 + 4.80467i) q^{37} +(4.57959 + 4.57959i) q^{38} +(5.46517 + 4.62037i) q^{39} +(-0.423868 + 2.19553i) q^{40} -0.882958i q^{41} +(-0.473395 - 5.65154i) q^{42} +(-1.69981 + 1.69981i) q^{43} -0.0826422 q^{44} +(-4.63028 - 4.85392i) q^{45} +1.00000 q^{46} +(-7.63231 + 7.63231i) q^{47} +(0.144577 + 1.72601i) q^{48} +3.72133i q^{49} +(-1.96536 - 4.59754i) q^{50} +(9.91872 + 8.38549i) q^{51} +(2.92164 + 2.92164i) q^{52} +(-7.26221 - 7.26221i) q^{53} +(-4.47090 - 2.64783i) q^{54} +(0.153069 - 0.103530i) q^{55} -3.27434i q^{56} +(-11.1785 + 0.936357i) q^{57} +(-1.40400 + 1.40400i) q^{58} -10.0777 q^{59} +(-2.43004 - 3.01578i) q^{60} -0.876183 q^{61} +(2.94168 - 2.94168i) q^{62} +(8.00467 + 5.69361i) q^{63} +1.00000i q^{64} +(-9.07153 - 1.75135i) q^{65} +(0.0924137 - 0.109311i) q^{66} +(0.768241 + 0.768241i) q^{67} +(5.30247 + 5.30247i) q^{68} +(-1.11824 + 1.32270i) q^{69} +(4.10194 + 6.06471i) q^{70} +1.70346i q^{71} +(-2.44466 - 1.73886i) q^{72} +(-0.265720 + 0.265720i) q^{73} -6.79483 q^{74} +(8.27892 + 2.54156i) q^{75} -6.47652 q^{76} +(-0.191342 + 0.191342i) q^{77} +(-7.13155 + 0.597367i) q^{78} +16.8063i q^{79} +(-1.25275 - 1.85219i) q^{80} +(8.50183 - 2.95276i) q^{81} +(0.624346 + 0.624346i) q^{82} +(-8.84618 - 8.84618i) q^{83} +(4.33098 + 3.66150i) q^{84} +(-16.4639 - 3.17852i) q^{85} -2.40390i q^{86} +(-0.287065 - 3.42708i) q^{87} +(0.0584368 - 0.0584368i) q^{88} +5.65142 q^{89} +(6.70634 + 0.158137i) q^{90} +13.5290 q^{91} +(-0.707107 + 0.707107i) q^{92} +(0.601465 + 7.18048i) q^{93} -10.7937i q^{94} +(11.9958 - 8.11347i) q^{95} +(-1.32270 - 1.11824i) q^{96} +(-7.30890 - 7.30890i) q^{97} +(-2.63138 - 2.63138i) q^{98} +(0.0412452 + 0.244472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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