LMFDB - Embedded newform 731.2.f.d.259.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.6
Character	$\chi$	$=$	731.259
Dual form			731.2.f.d.302.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17355i q^{2} +(-2.09748 + 2.09748i) q^{3} -2.72432 q^{4} +(0.426175 - 0.426175i) q^{5} +(4.55898 + 4.55898i) q^{6} +(2.68508 + 2.68508i) q^{7} +1.57435i q^{8} -5.79886i q^{9} +O(q^{10})$	\(q-2.17355i q^{2} +(-2.09748 + 2.09748i) q^{3} -2.72432 q^{4} +(0.426175 - 0.426175i) q^{5} +(4.55898 + 4.55898i) q^{6} +(2.68508 + 2.68508i) q^{7} +1.57435i q^{8} -5.79886i q^{9} +(-0.926312 - 0.926312i) q^{10} +(1.10028 + 1.10028i) q^{11} +(5.71422 - 5.71422i) q^{12} -3.90048 q^{13} +(5.83615 - 5.83615i) q^{14} +1.78779i q^{15} -2.02671 q^{16} +(-3.83378 + 1.51727i) q^{17} -12.6041 q^{18} -1.17848i q^{19} +(-1.16104 + 1.16104i) q^{20} -11.2638 q^{21} +(2.39151 - 2.39151i) q^{22} +(1.74487 + 1.74487i) q^{23} +(-3.30218 - 3.30218i) q^{24} +4.63675i q^{25} +8.47790i q^{26} +(5.87055 + 5.87055i) q^{27} +(-7.31502 - 7.31502i) q^{28} +(3.18488 - 3.18488i) q^{29} +3.88584 q^{30} +(-1.42132 + 1.42132i) q^{31} +7.55386i q^{32} -4.61563 q^{33} +(3.29786 + 8.33292i) q^{34} +2.28862 q^{35} +15.7980i q^{36} +(-7.17690 + 7.17690i) q^{37} -2.56149 q^{38} +(8.18119 - 8.18119i) q^{39} +(0.670949 + 0.670949i) q^{40} +(7.34665 + 7.34665i) q^{41} +24.4824i q^{42} -1.00000i q^{43} +(-2.99752 - 2.99752i) q^{44} +(-2.47133 - 2.47133i) q^{45} +(3.79256 - 3.79256i) q^{46} -7.67828 q^{47} +(4.25098 - 4.25098i) q^{48} +7.41928i q^{49} +10.0782 q^{50} +(4.85885 - 11.2237i) q^{51} +10.6262 q^{52} +2.03384i q^{53} +(12.7599 - 12.7599i) q^{54} +0.937822 q^{55} +(-4.22726 + 4.22726i) q^{56} +(2.47184 + 2.47184i) q^{57} +(-6.92249 - 6.92249i) q^{58} +7.69785i q^{59} -4.87051i q^{60} +(-5.52500 - 5.52500i) q^{61} +(3.08932 + 3.08932i) q^{62} +(15.5704 - 15.5704i) q^{63} +12.3653 q^{64} +(-1.66229 + 1.66229i) q^{65} +10.0323i q^{66} +6.98986 q^{67} +(10.4445 - 4.13353i) q^{68} -7.31966 q^{69} -4.97444i q^{70} +(-10.0536 + 10.0536i) q^{71} +9.12945 q^{72} +(-8.55053 + 8.55053i) q^{73} +(15.5993 + 15.5993i) q^{74} +(-9.72550 - 9.72550i) q^{75} +3.21056i q^{76} +5.90867i q^{77} +(-17.7822 - 17.7822i) q^{78} +(6.29260 + 6.29260i) q^{79} +(-0.863732 + 0.863732i) q^{80} -7.23018 q^{81} +(15.9683 - 15.9683i) q^{82} +0.0828265i q^{83} +30.6862 q^{84} +(-0.987241 + 2.28048i) q^{85} -2.17355 q^{86} +13.3604i q^{87} +(-1.73223 + 1.73223i) q^{88} -0.223076 q^{89} +(-5.37155 + 5.37155i) q^{90} +(-10.4731 - 10.4731i) q^{91} +(-4.75359 - 4.75359i) q^{92} -5.96240i q^{93} +16.6891i q^{94} +(-0.502239 - 0.502239i) q^{95} +(-15.8441 - 15.8441i) q^{96} +(-6.81542 + 6.81542i) q^{97} +16.1262 q^{98} +(6.38036 - 6.38036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		−	2.17355i		−	1.53693i	−0.639890	−	0.768466i	$-0.721020\pi$
$2$		−	2.17355i		−	1.53693i	0.639890	−	0.768466i	$-0.278980\pi$
$3$	−2.09748	+	2.09748i	−1.21098	+	1.21098i	−0.240277	+	0.970704i	$0.577238\pi$
$3$	−2.09748	+	2.09748i	−1.21098	+	1.21098i	−0.970704	+	0.240277i	$0.922762\pi$
$4$	−2.72432			−1.36216
$5$	0.426175	−	0.426175i	0.190591	−	0.190591i	−0.605360	−	0.795951i	$-0.706971\pi$
$5$	0.426175	−	0.426175i	0.190591	−	0.190591i	0.795951	+	0.605360i	$0.206971\pi$
$6$	4.55898	+	4.55898i	1.86120	+	1.86120i
$7$	2.68508	+	2.68508i	1.01486	+	1.01486i	0.999888	+	0.0149761i	$0.00476723\pi$
$7$	2.68508	+	2.68508i	1.01486	+	1.01486i	0.0149761	+	0.999888i	$0.495233\pi$
$8$			1.57435i			0.556618i
$9$		−	5.79886i		−	1.93295i
$10$	−0.926312	−	0.926312i	−0.292926	−	0.292926i
$11$	1.10028	+	1.10028i	0.331747	+	0.331747i	0.853249	−	0.521503i	$-0.174628\pi$
$11$	1.10028	+	1.10028i	0.331747	+	0.331747i	−0.521503	+	0.853249i	$0.674628\pi$
$12$	5.71422	−	5.71422i	1.64955	−	1.64955i
$13$	−3.90048			−1.08180			−0.540900	−	0.841087i	$-0.681916\pi$
$13$	−3.90048			−1.08180			−0.540900	+	0.841087i	$0.681916\pi$
$14$	5.83615	−	5.83615i	1.55978	−	1.55978i
$15$			1.78779i			0.461604i
$16$	−2.02671			−0.506677
$17$	−3.83378	+	1.51727i	−0.929829	+	0.367991i
$17$	−3.83378	+	1.51727i	−0.929829	+	0.367991i
$18$	−12.6041			−2.97082
$19$		−	1.17848i		−	0.270362i	−0.990821	−	0.135181i	$-0.956838\pi$
$19$		−	1.17848i		−	0.270362i	0.990821	−	0.135181i	$-0.0431616\pi$
$20$	−1.16104	+	1.16104i	−0.259616	+	0.259616i
$21$	−11.2638			−2.45796
$22$	2.39151	−	2.39151i	0.509872	−	0.509872i
$23$	1.74487	+	1.74487i	0.363830	+	0.363830i	0.865221	−	0.501391i	$-0.167178\pi$
$23$	1.74487	+	1.74487i	0.363830	+	0.363830i	−0.501391	+	0.865221i	$0.667178\pi$
$24$	−3.30218	−	3.30218i	−0.674054	−	0.674054i
$25$			4.63675i			0.927350i
$26$			8.47790i			1.66265i
$27$	5.87055	+	5.87055i	1.12979	+	1.12979i
$28$	−7.31502	−	7.31502i	−1.38241	−	1.38241i
$29$	3.18488	−	3.18488i	0.591417	−	0.591417i	−0.346597	−	0.938014i	$-0.612663\pi$
$29$	3.18488	−	3.18488i	0.591417	−	0.591417i	0.938014	+	0.346597i	$0.112663\pi$
$30$	3.88584			0.709455
$31$	−1.42132	+	1.42132i	−0.255277	+	0.255277i	−0.823130	−	0.567853i	$-0.807774\pi$
$31$	−1.42132	+	1.42132i	−0.255277	+	0.255277i	0.567853	+	0.823130i	$0.307774\pi$
$32$			7.55386i			1.33535i
$33$	−4.61563			−0.803478
$34$	3.29786	+	8.33292i	0.565578	+	1.42908i
$35$	2.28862			0.386848
$36$			15.7980i			2.63299i
$37$	−7.17690	+	7.17690i	−1.17987	+	1.17987i	−0.200099	+	0.979776i	$0.564126\pi$
$37$	−7.17690	+	7.17690i	−1.17987	+	1.17987i	−0.979776	+	0.200099i	$0.935874\pi$
$38$	−2.56149			−0.415528
$39$	8.18119	−	8.18119i	1.31004	−	1.31004i
$40$	0.670949	+	0.670949i	0.106086	+	0.106086i
$41$	7.34665	+	7.34665i	1.14735	+	1.14735i	0.987071	+	0.160283i	$0.0512407\pi$
$41$	7.34665	+	7.34665i	1.14735	+	1.14735i	0.160283	+	0.987071i	$0.448759\pi$
$42$			24.4824i			3.77772i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−2.99752	−	2.99752i	−0.451892	−	0.451892i
$45$	−2.47133	−	2.47133i	−0.368403	−	0.368403i
$46$	3.79256	−	3.79256i	0.559183	−	0.559183i
$47$	−7.67828			−1.11999			−0.559996	−	0.828495i	$-0.689197\pi$
$47$	−7.67828			−1.11999			−0.559996	+	0.828495i	$0.689197\pi$
$48$	4.25098	−	4.25098i	0.613577	−	0.613577i
$49$			7.41928i			1.05990i
$50$	10.0782			1.42527
$51$	4.85885	−	11.2237i	0.680375	−	1.57164i
$52$	10.6262			1.47359
$53$			2.03384i			0.279369i	0.990196	+	0.139684i	$0.0446088\pi$
$53$			2.03384i			0.279369i	−0.990196	+	0.139684i	$0.955391\pi$
$54$	12.7599	−	12.7599i	1.73641	−	1.73641i
$55$	0.937822			0.126456
$56$	−4.22726	+	4.22726i	−0.564892	+	0.564892i
$57$	2.47184	+	2.47184i	0.327404	+	0.327404i
$58$	−6.92249	−	6.92249i	−0.908967	−	0.908967i
$59$			7.69785i			1.00217i	0.865397	+	0.501087i	$0.167066\pi$
$59$			7.69785i			1.00217i	−0.865397	+	0.501087i	$0.832934\pi$
$60$		−	4.87051i		−	0.628780i
$61$	−5.52500	−	5.52500i	−0.707404	−	0.707404i	0.258585	−	0.965989i	$-0.416744\pi$
$61$	−5.52500	−	5.52500i	−0.707404	−	0.707404i	−0.965989	+	0.258585i	$0.916744\pi$
$62$	3.08932	+	3.08932i	0.392344	+	0.392344i
$63$	15.5704	−	15.5704i	1.96168	−	1.96168i
$64$	12.3653			1.54566
$65$	−1.66229	+	1.66229i	−0.206181	+	0.206181i
$66$			10.0323i			1.23489i
$67$	6.98986			0.853947			0.426973	−	0.904264i	$-0.359580\pi$
$67$	6.98986			0.853947			0.426973	+	0.904264i	$0.359580\pi$
$68$	10.4445	−	4.13353i	1.26658	−	0.501264i
$69$	−7.31966			−0.881184
$70$		−	4.97444i		−	0.594559i
$71$	−10.0536	+	10.0536i	−1.19315	+	1.19315i	−0.216967	+	0.976179i	$0.569616\pi$
$71$	−10.0536	+	10.0536i	−1.19315	+	1.19315i	−0.976179	+	0.216967i	$0.930384\pi$
$72$	9.12945			1.07592
$73$	−8.55053	+	8.55053i	−1.00076	+	1.00076i	−0.000764496		1.00000i	$0.500243\pi$
$73$	−8.55053	+	8.55053i	−1.00076	+	1.00076i	−1.00000		0.000764496i	$0.999757\pi$
$74$	15.5993	+	15.5993i	1.81339	+	1.81339i
$75$	−9.72550	−	9.72550i	−1.12300	−	1.12300i
$76$			3.21056i			0.368277i
$77$			5.90867i			0.673355i
$78$	−17.7822	−	17.7822i	−2.01344	−	2.01344i
$79$	6.29260	+	6.29260i	0.707973	+	0.707973i	0.966109	−	0.258136i	$-0.0831081\pi$
$79$	6.29260	+	6.29260i	0.707973	+	0.707973i	−0.258136	+	0.966109i	$0.583108\pi$
$80$	−0.863732	+	0.863732i	−0.0965681	+	0.0965681i
$81$	−7.23018			−0.803353
$82$	15.9683	−	15.9683i	1.76341	−	1.76341i
$83$			0.0828265i			0.00909139i	0.999990	+	0.00454569i	$0.00144694\pi$
$83$			0.0828265i			0.00909139i	−0.999990	+	0.00454569i	$0.998553\pi$
$84$	30.6862			3.34814
$85$	−0.987241	+	2.28048i	−0.107081	+	0.247353i
$86$	−2.17355			−0.234380
$87$			13.3604i			1.43239i
$88$	−1.73223	+	1.73223i	−0.184656	+	0.184656i
$89$	−0.223076			−0.0236460			−0.0118230	−	0.999930i	$-0.503763\pi$
$89$	−0.223076			−0.0236460			−0.0118230	+	0.999930i	$0.503763\pi$
$90$	−5.37155	+	5.37155i	−0.566211	+	0.566211i
$91$	−10.4731	−	10.4731i	−1.09788	−	1.09788i
$92$	−4.75359	−	4.75359i	−0.495596	−	0.495596i
$93$		−	5.96240i		−	0.618272i
$94$			16.6891i			1.72135i
$95$	−0.502239	−	0.502239i	−0.0515286	−	0.0515286i
$96$	−15.8441	−	15.8441i	−1.61708	−	1.61708i
$97$	−6.81542	+	6.81542i	−0.692001	+	0.692001i	−0.962672	−	0.270671i	$-0.912754\pi$
$97$	−6.81542	+	6.81542i	−0.692001	+	0.692001i	0.270671	+	0.962672i	$0.412754\pi$
$98$	16.1262			1.62899
$99$	6.38036	−	6.38036i	0.641250	−	0.641250i
$100$		−	12.6320i		−	1.26320i
$101$	−2.10702			−0.209657			−0.104828	−	0.994490i	$-0.533429\pi$
$101$	−2.10702			−0.209657			−0.104828	+	0.994490i	$0.533429\pi$
$102$	−24.3953	−	10.5610i	−2.41550	−	1.04569i
$103$	−12.0073			−1.18311			−0.591556	−	0.806264i	$-0.701486\pi$
$103$	−12.0073			−1.18311			−0.591556	+	0.806264i	$0.701486\pi$
$104$		−	6.14074i		−	0.602149i
$105$	−4.80035	+	4.80035i	−0.468466	+	0.468466i
$106$	4.42065			0.429371
$107$	9.67820	−	9.67820i	0.935627	−	0.935627i	−0.0624226	−	0.998050i	$-0.519883\pi$
$107$	9.67820	−	9.67820i	0.935627	−	0.935627i	0.998050	+	0.0624226i	$0.0198827\pi$
$108$	−15.9933	−	15.9933i	−1.53895	−	1.53895i
$109$	−11.9181	−	11.9181i	−1.14155	−	1.14155i	−0.988166	−	0.153385i	$-0.950982\pi$
$109$	−11.9181	−	11.9181i	−1.14155	−	1.14155i	−0.153385	−	0.988166i	$-0.549018\pi$
$110$		−	2.03840i		−	0.194354i
$111$		−	30.1068i		−	2.85761i
$112$	−5.44187	−	5.44187i	−0.514208	−	0.514208i
$113$	8.52574	+	8.52574i	0.802034	+	0.802034i	0.983413	−	0.181379i	$-0.0580561\pi$
$113$	8.52574	+	8.52574i	0.802034	+	0.802034i	−0.181379	+	0.983413i	$0.558056\pi$
$114$	5.37268	−	5.37268i	0.503197	−	0.503197i
$115$	1.48724			0.138686
$116$	−8.67663	+	8.67663i	−0.805605	+	0.805605i
$117$			22.6183i			2.09107i
$118$	16.7317			1.54027
$119$	−14.3680	−	6.22003i	−1.31711	−	0.570189i
$120$	−2.81461			−0.256937
$121$		−	8.57877i		−	0.779888i
$122$	−12.0089	+	12.0089i	−1.08723	+	1.08723i
$123$	−30.8189			−2.77885
$124$	3.87215	−	3.87215i	0.347729	−	0.347729i
$125$	4.10694	+	4.10694i	0.367336	+	0.367336i
$126$	−33.8430	−	33.8430i	−3.01498	−	3.01498i
$127$		−	14.4775i		−	1.28467i	−0.766424	−	0.642335i	$-0.777966\pi$
$127$		−	14.4775i		−	1.28467i	0.766424	−	0.642335i	$-0.222034\pi$
$128$		−	11.7689i		−	1.04023i
$129$	2.09748	+	2.09748i	0.184673	+	0.184673i
$130$	3.61306	+	3.61306i	0.316887	+	0.316887i
$131$	9.33408	−	9.33408i	0.815522	−	0.815522i	−0.169934	−	0.985456i	$-0.554355\pi$
$131$	9.33408	−	9.33408i	0.815522	−	0.815522i	0.985456	+	0.169934i	$0.0543553\pi$
$132$	12.5745			1.09447
$133$	3.16431	−	3.16431i	0.274381	−	0.274381i
$134$		−	15.1928i		−	1.31246i
$135$	5.00376			0.430655
$136$	−2.38871	−	6.03573i	−0.204831	−	0.517560i
$137$	7.03981			0.601451			0.300726	−	0.953711i	$-0.402771\pi$
$137$	7.03981			0.601451			0.300726	+	0.953711i	$0.402771\pi$
$138$			15.9097i			1.35432i
$139$	1.99986	−	1.99986i	0.169626	−	0.169626i	−0.617189	−	0.786815i	$-0.711729\pi$
$139$	1.99986	−	1.99986i	0.169626	−	0.169626i	0.786815	+	0.617189i	$0.211729\pi$
$140$	−6.23495			−0.526949
$141$	16.1051	−	16.1051i	1.35629	−	1.35629i
$142$	21.8521	+	21.8521i	1.83378	+	1.83378i
$143$	−4.29162	−	4.29162i	−0.358883	−	0.358883i
$144$			11.7526i			0.979383i
$145$		−	2.71463i		−	0.225437i
$146$	18.5850	+	18.5850i	1.53811	+	1.53811i
$147$	−15.5618	−	15.5618i	−1.28352	−	1.28352i
$148$	19.5522	−	19.5522i	1.60718	−	1.60718i
$149$	3.11097			0.254860			0.127430	−	0.991848i	$-0.459327\pi$
$149$	3.11097			0.254860			0.127430	+	0.991848i	$0.459327\pi$
$150$	−21.1389	+	21.1389i	−1.72598	+	1.72598i
$151$			8.92117i			0.725995i	0.931790	+	0.362997i	$0.118247\pi$
$151$			8.92117i			0.725995i	−0.931790	+	0.362997i	$0.881753\pi$
$152$	1.85535			0.150488
$153$	8.79841	+	22.2316i	0.711310	+	1.79732i
$154$	12.8428			1.03490
$155$			1.21146i			0.0973071i
$156$	−22.2882	+	22.2882i	−1.78448	+	1.78448i
$157$	10.6783			0.852219			0.426110	−	0.904672i	$-0.359884\pi$
$157$	10.6783			0.852219			0.426110	+	0.904672i	$0.359884\pi$
$158$	13.6773	−	13.6773i	1.08811	−	1.08811i
$159$	−4.26593	−	4.26593i	−0.338311	−	0.338311i
$160$	3.21926	+	3.21926i	0.254505	+	0.254505i
$161$			9.37022i			0.738477i
$162$			15.7152i			1.23470i
$163$	8.73509	+	8.73509i	0.684185	+	0.684185i	0.960940	−	0.276756i	$-0.0892592\pi$
$163$	8.73509	+	8.73509i	0.684185	+	0.684185i	−0.276756	+	0.960940i	$0.589259\pi$
$164$	−20.0147	−	20.0147i	−1.56288	−	1.56288i
$165$	−1.96706	+	1.96706i	−0.153136	+	0.153136i
$166$	0.180028			0.0139728
$167$	−11.4704	+	11.4704i	−0.887604	+	0.887604i	−0.994293	−	0.106688i	$-0.965975\pi$
$167$	−11.4704	+	11.4704i	−0.887604	+	0.887604i	0.106688	+	0.994293i	$0.465975\pi$
$168$		−	17.7332i		−	1.36815i
$169$	2.21376			0.170290
$170$	4.95674	+	2.14582i	0.380165	+	0.164577i
$171$	−6.83385			−0.522597
$172$			2.72432i			0.207728i
$173$	10.6324	−	10.6324i	0.808367	−	0.808367i	−0.176020	−	0.984387i	$-0.556322\pi$
$173$	10.6324	−	10.6324i	0.808367	−	0.808367i	0.984387	+	0.176020i	$0.0563223\pi$
$174$	29.0396			2.20149
$175$	−12.4500	+	12.4500i	−0.941134	+	0.941134i
$176$	−2.22994	−	2.22994i	−0.168088	−	0.168088i
$177$	−16.1461	−	16.1461i	−1.21361	−	1.21361i
$178$			0.484868i			0.0363424i
$179$		−	11.5017i		−	0.859679i	−0.902905	−	0.429840i	$-0.858570\pi$
$179$		−	11.5017i		−	0.859679i	0.902905	−	0.429840i	$-0.141430\pi$
$180$	6.73269	+	6.73269i	0.501825	+	0.501825i
$181$	6.41868	+	6.41868i	0.477096	+	0.477096i	0.904202	−	0.427105i	$-0.140467\pi$
$181$	6.41868	+	6.41868i	0.477096	+	0.477096i	−0.427105	+	0.904202i	$0.640467\pi$
$182$	−22.7638	+	22.7638i	−1.68737	+	1.68737i
$183$	23.1772			1.71331
$184$	−2.74704	+	2.74704i	−0.202515	+	0.202515i
$185$			6.11722i			0.449747i
$186$	−12.9596			−0.950243
$187$	−5.88765	−	2.54881i	−0.430547	−	0.186388i
$188$	20.9181			1.52561
$189$			31.5258i			2.29316i
$190$	−1.09164	+	1.09164i	−0.0791960	+	0.0791960i
$191$	3.96963			0.287233			0.143616	−	0.989633i	$-0.454127\pi$
$191$	3.96963			0.287233			0.143616	+	0.989633i	$0.454127\pi$
$192$	−25.9360	+	25.9360i	−1.87177	+	1.87177i
$193$	−17.2648	−	17.2648i	−1.24275	−	1.24275i	−0.958856	−	0.283891i	$-0.908374\pi$
$193$	−17.2648	−	17.2648i	−1.24275	−	1.24275i	−0.283891	−	0.958856i	$-0.591626\pi$
$194$	14.8137	+	14.8137i	1.06356	+	1.06356i
$195$		−	6.97323i		−	0.499363i
$196$		−	20.2125i		−	1.44375i
$197$	7.76423	+	7.76423i	0.553178	+	0.553178i	0.927357	−	0.374178i	$-0.122075\pi$
$197$	7.76423	+	7.76423i	0.553178	+	0.553178i	−0.374178	+	0.927357i	$0.622075\pi$
$198$	−13.8680	−	13.8680i	−0.985558	−	0.985558i
$199$	11.1449	−	11.1449i	0.790039	−	0.790039i	−0.191461	−	0.981500i	$-0.561323\pi$
$199$	11.1449	−	11.1449i	0.790039	−	0.790039i	0.981500	+	0.191461i	$0.0613226\pi$
$200$	−7.29988			−0.516180
$201$	−14.6611	+	14.6611i	−1.03411	+	1.03411i
$202$			4.57972i			0.322228i
$203$	17.1033			1.20041
$204$	−13.2371	+	30.5771i	−0.926781	+	2.14082i
$205$	6.26191			0.437351
$206$			26.0984i			1.81836i
$207$	10.1182	−	10.1182i	0.703267	−	0.703267i
$208$	7.90514			0.548123
$209$	1.29666	−	1.29666i	0.0896917	−	0.0896917i
$210$	10.4338	+	10.4338i	0.720000	+	0.720000i
$211$	0.995753	+	0.995753i	0.0685505	+	0.0685505i	0.740551	−	0.672000i	$-0.234565\pi$
$211$	0.995753	+	0.995753i	0.0685505	+	0.0685505i	−0.672000	+	0.740551i	$0.734565\pi$
$212$		−	5.54083i		−	0.380546i
$213$		−	42.1746i		−	2.88976i
$214$	−21.0361	−	21.0361i	−1.43800	−	1.43800i
$215$	−0.426175	−	0.426175i	−0.0290649	−	0.0290649i
$216$	−9.24233	+	9.24233i	−0.628861	+	0.628861i
$217$	−7.63273			−0.518143
$218$	−25.9047	+	25.9047i	−1.75449	+	1.75449i
$219$		−	35.8692i		−	2.42381i
$220$	−2.55493			−0.172253
$221$	14.9536	−	5.91807i	1.00589	−	0.398093i
$222$	−65.4387			−4.39196
$223$		−	24.3046i		−	1.62756i	−0.581174	−	0.813779i	$-0.697407\pi$
$223$		−	24.3046i		−	1.62756i	0.581174	−	0.813779i	$-0.302593\pi$
$224$	−20.2827	+	20.2827i	−1.35520	+	1.35520i
$225$	26.8879			1.79252
$226$	18.5311	−	18.5311i	1.23267	−	1.23267i
$227$	−6.99473	−	6.99473i	−0.464256	−	0.464256i	0.435791	−	0.900048i	$-0.356469\pi$
$227$	−6.99473	−	6.99473i	−0.464256	−	0.464256i	−0.900048	+	0.435791i	$0.856469\pi$
$228$	−6.73410	−	6.73410i	−0.445977	−	0.445977i
$229$			12.4329i			0.821588i	0.911728	+	0.410794i	$0.134748\pi$
$229$			12.4329i			0.821588i	−0.911728	+	0.410794i	$0.865252\pi$
$230$		−	3.23259i		−	0.213150i
$231$	−12.3933	−	12.3933i	−0.815421	−	0.815421i
$232$	5.01412	+	5.01412i	0.329193	+	0.329193i
$233$	−3.07181	+	3.07181i	−0.201241	+	0.201241i	−0.800532	−	0.599291i	$-0.795449\pi$
$233$	−3.07181	+	3.07181i	−0.201241	+	0.201241i	0.599291	+	0.800532i	$0.295449\pi$
$234$	49.1621			3.21383
$235$	−3.27229	+	3.27229i	−0.213461	+	0.213461i
$236$		−	20.9714i		−	1.36512i
$237$	−26.3972			−1.71468
$238$	−13.5195	+	31.2296i	−0.876342	+	2.02431i
$239$	18.7769			1.21458			0.607288	−	0.794482i	$-0.292257\pi$
$239$	18.7769			1.21458			0.607288	+	0.794482i	$0.292257\pi$
$240$		−	3.62332i		−	0.233884i
$241$	−6.80550	+	6.80550i	−0.438381	+	0.438381i	−0.891467	−	0.453086i	$-0.850323\pi$
$241$	−6.80550	+	6.80550i	−0.438381	+	0.438381i	0.453086	+	0.891467i	$0.350323\pi$
$242$	−18.6464			−1.19864
$243$	−2.44649	+	2.44649i	−0.156943	+	0.156943i
$244$	15.0519	+	15.0519i	0.963599	+	0.963599i
$245$	3.16191	+	3.16191i	0.202007	+	0.202007i
$246$			66.9865i			4.27090i
$247$			4.59665i			0.292478i
$248$	−2.23767	−	2.23767i	−0.142092	−	0.142092i
$249$	−0.173727	−	0.173727i	−0.0110095	−	0.0110095i
$250$	8.92664	−	8.92664i	0.564570	−	0.564570i
$251$	9.07963			0.573101			0.286551	−	0.958065i	$-0.407491\pi$
$251$	9.07963			0.573101			0.286551	+	0.958065i	$0.407491\pi$
$252$	−42.4188	+	42.4188i	−2.67213	+	2.67213i
$253$			3.83969i			0.241399i
$254$	−31.4676			−1.97445
$255$	−2.71255	−	6.85399i	−0.169866	−	0.429213i
$256$	−0.849629			−0.0531018
$257$			24.1812i			1.50838i	0.656653	+	0.754192i	$0.271971\pi$
$257$			24.1812i			1.50838i	−0.656653	+	0.754192i	$0.728029\pi$
$258$	4.55898	−	4.55898i	0.283830	−	0.283830i
$259$	−38.5410			−2.39482
$260$	4.52861	−	4.52861i	0.280852	−	0.280852i
$261$	−18.4686	−	18.4686i	−1.14318	−	1.14318i
$262$	−20.2881	−	20.2881i	−1.25340	−	1.25340i
$263$			16.8545i			1.03929i	0.854382	+	0.519645i	$0.173936\pi$
$263$			16.8545i			1.03929i	−0.854382	+	0.519645i	$0.826064\pi$
$264$		−	7.26663i		−	0.447230i
$265$	0.866769	+	0.866769i	0.0532452	+	0.0532452i
$266$	−6.87780	−	6.87780i	−0.421705	−	0.421705i
$267$	0.467898	−	0.467898i	0.0286349	−	0.0286349i
$268$	−19.0426			−1.16321
$269$	2.82699	−	2.82699i	0.172365	−	0.172365i	−0.615653	−	0.788017i	$-0.711108\pi$
$269$	2.82699	−	2.82699i	0.172365	−	0.172365i	0.788017	+	0.615653i	$0.211108\pi$
$270$		−	10.8759i		−	0.661888i
$271$	−16.3132			−0.990956			−0.495478	−	0.868620i	$-0.665007\pi$
$271$	−16.3132			−0.990956			−0.495478	+	0.868620i	$0.665007\pi$
$272$	7.76996	−	3.07506i	0.471123	−	0.186453i
$273$	43.9343			2.65902
$274$		−	15.3014i		−	0.924390i
$275$	−5.10172	+	5.10172i	−0.307645	+	0.307645i
$276$	19.9411			1.20031
$277$	10.7009	−	10.7009i	0.642957	−	0.642957i	−0.308324	−	0.951281i	$-0.599768\pi$
$277$	10.7009	−	10.7009i	0.642957	−	0.642957i	0.951281	+	0.308324i	$0.0997682\pi$
$278$	−4.34680	−	4.34680i	−0.260704	−	0.260704i
$279$	8.24206	+	8.24206i	0.493439	+	0.493439i
$280$			3.60310i			0.215327i
$281$		−	21.9765i		−	1.31101i	−0.755192	−	0.655504i	$-0.772456\pi$
$281$		−	21.9765i		−	1.31101i	0.755192	−	0.655504i	$-0.227544\pi$
$282$	−35.0052	−	35.0052i	−2.08453	−	2.08453i
$283$	6.29438	+	6.29438i	0.374162	+	0.374162i	0.868991	−	0.494829i	$-0.164769\pi$
$283$	6.29438	+	6.29438i	0.374162	+	0.374162i	−0.494829	+	0.868991i	$0.664769\pi$
$284$	27.3893	−	27.3893i	1.62526	−	1.62526i
$285$	2.10687			0.124800
$286$	−9.32805	+	9.32805i	−0.551579	+	0.551579i
$287$			39.4527i			2.32882i
$288$	43.8038			2.58116
$289$	12.3958	−	11.6337i	0.729165	−	0.684338i
$290$	−5.90038			−0.346482
$291$		−	28.5904i		−	1.67600i
$292$	23.2944	−	23.2944i	1.36320	−	1.36320i
$293$	−12.3353			−0.720634			−0.360317	−	0.932830i	$-0.617331\pi$
$293$	−12.3353			−0.720634			−0.360317	+	0.932830i	$0.617331\pi$
$294$	−33.8244	+	33.8244i	−1.97268	+	1.97268i
$295$	3.28063	+	3.28063i	0.191005	+	0.191005i
$296$	−11.2990	−	11.2990i	−0.656739	−	0.656739i
$297$			12.9185i			0.749607i
$298$		−	6.76184i		−	0.391703i
$299$	−6.80583	−	6.80583i	−0.393591	−	0.393591i
$300$	26.4954	+	26.4954i	1.52971	+	1.52971i
$301$	2.68508	−	2.68508i	0.154765	−	0.154765i
$302$	19.3906			1.11580
$303$	4.41944	−	4.41944i	0.253890	−	0.253890i
$304$			2.38844i			0.136986i
$305$	−4.70923			−0.269650
$306$	48.3214	−	19.1238i	2.76235	−	1.09323i
$307$	5.26148			0.300289			0.150144	−	0.988664i	$-0.452026\pi$
$307$	5.26148			0.300289			0.150144	+	0.988664i	$0.452026\pi$
$308$		−	16.0971i		−	0.917219i
$309$	25.1850	−	25.1850i	1.43273	−	1.43273i
$310$	2.63318			0.149555
$311$	1.88700	−	1.88700i	0.107002	−	0.107002i	−0.651579	−	0.758581i	$-0.725893\pi$
$311$	1.88700	−	1.88700i	0.107002	−	0.107002i	0.758581	+	0.651579i	$0.225893\pi$
$312$	12.8801	+	12.8801i	0.729191	+	0.729191i
$313$	−2.12030	−	2.12030i	−0.119846	−	0.119846i	0.644640	−	0.764486i	$-0.277007\pi$
$313$	−2.12030	−	2.12030i	−0.119846	−	0.119846i	−0.764486	+	0.644640i	$0.777007\pi$
$314$		−	23.2098i		−	1.30980i
$315$		−	13.2714i		−	0.747759i
$316$	−17.1431	−	17.1431i	−0.964374	−	0.964374i
$317$	17.7897	+	17.7897i	0.999169	+	0.999169i	1.00000		0.000830855i	$-0.000264469\pi$
$317$	17.7897	+	17.7897i	0.999169	+	0.999169i	−0.000830855		1.00000i	$0.500264\pi$
$318$	−9.27223	+	9.27223i	−0.519961	+	0.519961i
$319$	7.00850			0.392401
$320$	5.26977	−	5.26977i	0.294589	−	0.294589i
$321$			40.5997i			2.26605i
$322$	20.3666			1.13499
$323$	1.78807	+	4.51804i	0.0994909	+	0.251391i
$324$	19.6973			1.09430
$325$		−	18.0856i		−	1.00321i
$326$	18.9862	−	18.9862i	1.05155	−	1.05155i
$327$	49.9962			2.76480
$328$	−11.5662	+	11.5662i	−0.638638	+	0.638638i
$329$	−20.6168	−	20.6168i	−1.13664	−	1.13664i
$330$	4.27551	+	4.27551i	0.235359	+	0.235359i
$331$			16.7271i			0.919406i	0.888073	+	0.459703i	$0.152044\pi$
$331$			16.7271i			0.919406i	−0.888073	+	0.459703i	$0.847956\pi$
$332$		−	0.225646i		−	0.0123839i
$333$	41.6178	+	41.6178i	2.28064	+	2.28064i
$334$	24.9314	+	24.9314i	1.36419	+	1.36419i
$335$	2.97890	−	2.97890i	0.162755	−	0.162755i
$336$	22.8284			1.24539
$337$	5.49122	−	5.49122i	0.299126	−	0.299126i	−0.541546	−	0.840671i	$-0.682161\pi$
$337$	5.49122	−	5.49122i	0.299126	−	0.299126i	0.840671	+	0.541546i	$0.182161\pi$
$338$		−	4.81173i		−	0.261724i
$339$	−35.7652			−1.94250
$340$	2.68956	−	6.21277i	0.145862	−	0.336935i
$341$	−3.12771			−0.169375
$342$			14.8537i			0.803197i
$343$	−1.12581	+	1.12581i	−0.0607881	+	0.0607881i
$344$	1.57435			0.0848835
$345$	−3.11945	+	3.11945i	−0.167946	+	0.167946i
$346$	−23.1101	−	23.1101i	−1.24241	−	1.24241i
$347$	−18.8034	−	18.8034i	−1.00942	−	1.00942i	−0.999955	−	0.00946647i	$-0.996987\pi$
$347$	−18.8034	−	18.8034i	−1.00942	−	1.00942i	−0.00946647	−	0.999955i	$-0.503013\pi$
$348$		−	36.3982i		−	1.95115i
$349$			2.72729i			0.145988i	0.997332	+	0.0729942i	$0.0232555\pi$
$349$			2.72729i			0.145988i	−0.997332	+	0.0729942i	$0.976745\pi$
$350$	27.0608	+	27.0608i	1.44646	+	1.44646i
$351$	−22.8980	−	22.8980i	−1.22220	−	1.22220i
$352$	−8.31135	+	8.31135i	−0.442997	+	0.442997i
$353$	−17.2654			−0.918943			−0.459471	−	0.888193i	$-0.651961\pi$
$353$	−17.2654			−0.918943			−0.459471	+	0.888193i	$0.651961\pi$
$354$	−35.0944	+	35.0944i	−1.86524	+	1.86524i
$355$			8.56920i			0.454806i
$356$	0.607732			0.0322097
$357$	43.1830	−	17.0902i	2.28549	−	0.904509i
$358$	−24.9996			−1.32127
$359$		−	3.67001i		−	0.193695i	−0.995299	−	0.0968477i	$-0.969124\pi$
$359$		−	3.67001i		−	0.193695i	0.995299	−	0.0968477i	$-0.0308760\pi$
$360$	3.89074	−	3.89074i	0.205060	−	0.205060i
$361$	17.6112			0.926904
$362$	13.9513	−	13.9513i	0.733265	−	0.733265i
$363$	17.9938	+	17.9938i	0.944431	+	0.944431i
$364$	28.5321	+	28.5321i	1.49549	+	1.49549i
$365$			7.28804i			0.381473i
$366$		−	50.3768i		−	2.63324i
$367$	9.46743	+	9.46743i	0.494196	+	0.494196i	0.909625	−	0.415430i	$-0.136369\pi$
$367$	9.46743	+	9.46743i	0.494196	+	0.494196i	−0.415430	+	0.909625i	$0.636369\pi$
$368$	−3.53634	−	3.53634i	−0.184345	−	0.184345i
$369$	42.6022	−	42.6022i	2.21778	−	2.21778i
$370$	13.2961			0.691231
$371$	−5.46101	+	5.46101i	−0.283521	+	0.283521i
$372$			16.2435i			0.842187i
$373$	−8.75774			−0.453459			−0.226729	−	0.973958i	$-0.572803\pi$
$373$	−8.75774			−0.453459			−0.226729	+	0.973958i	$0.572803\pi$
$374$	−5.53998	+	12.7971i	−0.286465	+	0.661722i
$375$	−17.2285			−0.889673
$376$		−	12.0883i		−	0.623408i
$377$	−12.4226	+	12.4226i	−0.639794	+	0.639794i
$378$	68.5229			3.52444
$379$	24.2922	−	24.2922i	1.24781	−	1.24781i	0.291123	−	0.956686i	$-0.405971\pi$
$379$	24.2922	−	24.2922i	1.24781	−	1.24781i	0.956686	−	0.291123i	$-0.0940289\pi$
$380$	1.36826	+	1.36826i	0.0701903	+	0.0701903i
$381$	30.3663	+	30.3663i	1.55571	+	1.55571i
$382$		−	8.62820i		−	0.441457i
$383$			27.7185i			1.41635i	0.706036	+	0.708175i	$0.250481\pi$
$383$			27.7185i			1.41635i	−0.706036	+	0.708175i	$0.749519\pi$
$384$	24.6850	+	24.6850i	1.25970	+	1.25970i
$385$	2.51812	+	2.51812i	0.128335	+	0.128335i
$386$	−37.5259	+	37.5259i	−1.91002	+	1.91002i
$387$	−5.79886			−0.294772
$388$	18.5674	−	18.5674i	0.942617	−	0.942617i
$389$		−	15.3867i		−	0.780138i	−0.920786	−	0.390069i	$-0.872451\pi$
$389$		−	15.3867i		−	0.780138i	0.920786	−	0.390069i	$-0.127549\pi$
$390$	−15.1567			−0.767488
$391$	−9.33688	−	4.04202i	−0.472187	−	0.204414i
$392$	−11.6806			−0.589958
$393$			39.1561i			1.97516i
$394$	16.8759	−	16.8759i	0.850198	−	0.850198i
$395$	5.36349			0.269867
$396$	−17.3822	+	17.3822i	−0.873487	+	0.873487i
$397$	24.9378	+	24.9378i	1.25159	+	1.25159i	0.955006	+	0.296588i	$0.0958487\pi$
$397$	24.9378	+	24.9378i	1.25159	+	1.25159i	0.296588	+	0.955006i	$0.404151\pi$
$398$	−24.2239	−	24.2239i	−1.21424	−	1.21424i
$399$			13.2742i			0.664540i
$400$		−	9.39734i		−	0.469867i
$401$	−25.3794	−	25.3794i	−1.26738	−	1.26738i	−0.947434	−	0.319950i	$-0.896334\pi$
$401$	−25.3794	−	25.3794i	−1.26738	−	1.26738i	−0.319950	−	0.947434i	$-0.603666\pi$
$402$	31.8666	+	31.8666i	1.58936	+	1.58936i
$403$	5.54385	−	5.54385i	0.276159	−	0.276159i
$404$	5.74021			0.285586
$405$	−3.08132	+	3.08132i	−0.153112	+	0.153112i
$406$		−	37.1748i		−	1.84496i
$407$	−15.7932			−0.782839
$408$	17.6701	+	7.64955i	0.874801	+	0.378709i
$409$	−2.91945			−0.144358			−0.0721788	−	0.997392i	$-0.522995\pi$
$409$	−2.91945			−0.144358			−0.0721788	+	0.997392i	$0.522995\pi$
$410$		−	13.6106i		−	0.672179i
$411$	−14.7659	+	14.7659i	−0.728346	+	0.728346i
$412$	32.7117			1.61159
$413$	−20.6693	+	20.6693i	−1.01707	+	1.01707i
$414$	−21.9925	−	21.9925i	−1.08087	−	1.08087i
$415$	0.0352985	+	0.0352985i	0.00173274	+	0.00173274i
$416$		−	29.4637i		−	1.44458i
$417$			8.38934i			0.410828i
$418$	−2.81835	−	2.81835i	−0.137850	−	0.137850i
$419$	−20.1165	−	20.1165i	−0.982753	−	0.982753i	0.0171004	−	0.999854i	$-0.494557\pi$
$419$	−20.1165	−	20.1165i	−0.982753	−	0.982753i	−0.999854	+	0.0171004i	$0.994557\pi$
$420$	13.0777	−	13.0777i	0.638126	−	0.638126i
$421$	−28.2665			−1.37762			−0.688812	−	0.724940i	$-0.741868\pi$
$421$	−28.2665			−1.37762			−0.688812	+	0.724940i	$0.741868\pi$
$422$	2.16432	−	2.16432i	0.105357	−	0.105357i
$423$			44.5253i			2.16489i
$424$	−3.20198			−0.155502
$425$	−7.03519	−	17.7763i	−0.341257	−	0.862277i
$426$	−91.6686			−4.44136
$427$		−	29.6701i		−	1.43584i
$428$	−26.3666	+	26.3666i	−1.27448	+	1.27448i
$429$	18.0032			0.869202
$430$	−0.926312	+	0.926312i	−0.0446707	+	0.0446707i
$431$	−3.33972	−	3.33972i	−0.160868	−	0.160868i	0.622083	−	0.782951i	$-0.286287\pi$
$431$	−3.33972	−	3.33972i	−0.160868	−	0.160868i	−0.782951	+	0.622083i	$0.786287\pi$
$432$	−11.8979	−	11.8979i	−0.572438	−	0.572438i
$433$			33.6337i			1.61633i	0.588954	+	0.808166i	$0.299540\pi$
$433$			33.6337i			1.61633i	−0.588954	+	0.808166i	$0.700460\pi$
$434$			16.5901i			0.796352i
$435$	5.69388	+	5.69388i	0.273001	+	0.273001i
$436$	32.4689	+	32.4689i	1.55498	+	1.55498i
$437$	2.05630	−	2.05630i	0.0983660	−	0.0983660i
$438$	−77.9635			−3.72524
$439$	12.9170	−	12.9170i	0.616494	−	0.616494i	−0.328136	−	0.944630i	$-0.606421\pi$
$439$	12.9170	−	12.9170i	0.616494	−	0.616494i	0.944630	+	0.328136i	$0.106421\pi$
$440$			1.47646i			0.0703876i
$441$	43.0234			2.04873
$442$	−12.8632	−	32.5024i	−0.611842	−	1.54598i
$443$	24.7086			1.17394			0.586970	−	0.809609i	$-0.300321\pi$
$443$	24.7086			1.17394			0.586970	+	0.809609i	$0.300321\pi$
$444$			82.0207i			3.89253i
$445$	−0.0950694	+	0.0950694i	−0.00450672	+	0.00450672i
$446$	−52.8273			−2.50145
$447$	−6.52519	+	6.52519i	−0.308631	+	0.308631i
$448$	33.2018	+	33.2018i	1.56864	+	1.56864i
$449$	25.3280	+	25.3280i	1.19530	+	1.19530i	0.975558	+	0.219743i	$0.0705217\pi$
$449$	25.3280	+	25.3280i	1.19530	+	1.19530i	0.219743	+	0.975558i	$0.429478\pi$
$450$		−	58.4421i		−	2.75499i
$451$			16.1667i			0.761262i
$452$	−23.2269	−	23.2269i	−1.09250	−	1.09250i
$453$	−18.7120	−	18.7120i	−0.879166	−	0.879166i
$454$	−15.2034	+	15.2034i	−0.713530	+	0.713530i
$455$	−8.92674			−0.418492
$456$	−3.89155	+	3.89155i	−0.182239	+	0.182239i
$457$			0.835945i			0.0391038i	0.999809	+	0.0195519i	$0.00622397\pi$
$457$			0.835945i			0.0391038i	−0.999809	+	0.0195519i	$0.993776\pi$
$458$	27.0235			1.26273
$459$	−31.4136	−	13.5992i	−1.46626	−	0.634758i
$460$	−4.05172			−0.188912
$461$		−	17.5523i		−	0.817493i	−0.912648	−	0.408747i	$-0.865966\pi$
$461$		−	17.5523i		−	0.817493i	0.912648	−	0.408747i	$-0.134034\pi$
$462$	−26.9375	+	26.9375i	−1.25325	+	1.25325i
$463$	36.7673			1.70872			0.854360	−	0.519681i	$-0.173949\pi$
$463$	36.7673			1.70872			0.854360	+	0.519681i	$0.173949\pi$
$464$	−6.45482	+	6.45482i	−0.299657	+	0.299657i
$465$	−2.54102	−	2.54102i	−0.117837	−	0.117837i
$466$	6.67674	+	6.67674i	0.309294	+	0.309294i
$467$		−	3.70372i		−	0.171388i	−0.996322	−	0.0856939i	$-0.972689\pi$
$467$		−	3.70372i		−	0.171388i	0.996322	−	0.0856939i	$-0.0273107\pi$
$468$		−	61.6197i		−	2.84837i
$469$	18.7683	+	18.7683i	0.866640	+	0.866640i
$470$	7.11249	+	7.11249i	0.328075	+	0.328075i
$471$	−22.3975	+	22.3975i	−1.03202	+	1.03202i
$472$	−12.1191			−0.557828
$473$	1.10028	−	1.10028i	0.0505909	−	0.0505909i
$474$			57.3757i			2.63535i
$475$	5.46432			0.250720
$476$	39.1430	+	16.9454i	1.79412	+	0.776690i
$477$	11.7939			0.540007
$478$		−	40.8125i		−	1.86672i
$479$	9.37662	−	9.37662i	0.428429	−	0.428429i	−0.459664	−	0.888093i	$-0.652030\pi$
$479$	9.37662	−	9.37662i	0.428429	−	0.428429i	0.888093	+	0.459664i	$0.152030\pi$
$480$	−13.5047			−0.616402
$481$	27.9934	−	27.9934i	1.27639	−	1.27639i
$482$	14.7921	+	14.7921i	0.673762	+	0.673762i
$483$	−19.6539	−	19.6539i	−0.894282	−	0.894282i
$484$			23.3714i			1.06233i
$485$			5.80911i			0.263778i
$486$	5.31758	+	5.31758i	0.241210	+	0.241210i
$487$	−17.8406	−	17.8406i	−0.808435	−	0.808435i	0.175962	−	0.984397i	$-0.443696\pi$
$487$	−17.8406	−	17.8406i	−0.808435	−	0.808435i	−0.984397	+	0.175962i	$0.943696\pi$
$488$	8.69831	−	8.69831i	0.393754	−	0.393754i
$489$	−36.6434			−1.65707
$490$	6.87257	−	6.87257i	0.310471	−	0.310471i
$491$		−	8.06742i		−	0.364078i	−0.983291	−	0.182039i	$-0.941730\pi$
$491$		−	8.06742i		−	0.364078i	0.983291	−	0.182039i	$-0.0582696\pi$
$492$	83.9607			3.78524
$493$	−7.37782	+	17.0424i	−0.332280	+	0.767553i
$494$	9.99104			0.449518
$495$		−	5.43829i		−	0.244433i
$496$	2.88061	−	2.88061i	0.129343	−	0.129343i
$497$	−53.9895			−2.42176
$498$	−0.377604	+	0.377604i	−0.0169209	+	0.0169209i
$499$	−15.8259	−	15.8259i	−0.708465	−	0.708465i	0.257747	−	0.966212i	$-0.417020\pi$
$499$	−15.8259	−	15.8259i	−0.708465	−	0.708465i	−0.966212	+	0.257747i	$0.917020\pi$
$500$	−11.1886	−	11.1886i	−0.500371	−	0.500371i
$501$		−	48.1178i		−	2.14974i
$502$		−	19.7350i		−	0.880818i
$503$	25.3579	+	25.3579i	1.13065	+	1.13065i	0.990069	+	0.140584i	$0.0448979\pi$
$503$	25.3579	+	25.3579i	1.13065	+	1.13065i	0.140584	+	0.990069i	$0.455102\pi$
$504$	24.5133	+	24.5133i	1.09191	+	1.09191i
$505$	−0.897959	+	0.897959i	−0.0399587	+	0.0399587i
$506$	8.34575			0.371014
$507$	−4.64333	+	4.64333i	−0.206217	+	0.206217i
$508$			39.4414i			1.74993i
$509$	−15.8393			−0.702063			−0.351032	−	0.936364i	$-0.614169\pi$
$509$	−15.8393			−0.702063			−0.351032	+	0.936364i	$0.614169\pi$
$510$	−14.8975	+	5.89586i	−0.659672	+	0.261073i
$511$	−45.9177			−2.03128
$512$		−	21.6910i		−	0.958616i
$513$	6.91834	−	6.91834i	0.305452	−	0.305452i
$514$	52.5592			2.31829
$515$	−5.11720	+	5.11720i	−0.225491	+	0.225491i
$516$	−5.71422	−	5.71422i	−0.251554	−	0.251554i
$517$	−8.44825	−	8.44825i	−0.371554	−	0.371554i
$518$			83.7709i			3.68068i
$519$			44.6025i			1.95783i
$520$	−2.61703	−	2.61703i	−0.114764	−	0.114764i
$521$	12.4755	+	12.4755i	0.546563	+	0.546563i	0.925445	−	0.378882i	$-0.123691\pi$
$521$	12.4755	+	12.4755i	0.546563	+	0.546563i	−0.378882	+	0.925445i	$0.623691\pi$
$522$	−40.1425	+	40.1425i	−1.75699	+	1.75699i
$523$	−17.4479			−0.762945			−0.381473	−	0.924380i	$-0.624583\pi$
$523$	−17.4479			−0.762945			−0.381473	+	0.924380i	$0.624583\pi$
$524$	−25.4290	+	25.4290i	−1.11087	+	1.11087i
$525$		−	52.2274i		−	2.27939i
$526$	36.6340			1.59732
$527$	3.29252	−	7.60558i	0.143424	−	0.331304i
$528$	9.35454			0.407104
$529$		−	16.9109i		−	0.735255i
$530$	1.88397	−	1.88397i	0.0818343	−	0.0818343i
$531$	44.6387			1.93716
$532$	−8.62061	+	8.62061i	−0.373751	+	0.373751i
$533$	−28.6555	−	28.6555i	−1.24121	−	1.24121i
$534$	−1.01700	−	1.01700i	−0.0440099	−	0.0440099i
$535$		−	8.24921i		−	0.356644i
$536$			11.0045i			0.475322i
$537$	24.1247	+	24.1247i	1.04106	+	1.04106i
$538$	−6.14461	−	6.14461i	−0.264913	−	0.264913i
$539$	−8.16328	+	8.16328i	−0.351617	+	0.351617i
$540$	−13.6319			−0.586622
$541$	−32.3911	+	32.3911i	−1.39260	+	1.39260i	−0.573163	+	0.819442i	$0.694284\pi$
$541$	−32.3911	+	32.3911i	−1.39260	+	1.39260i	−0.819442	+	0.573163i	$0.805716\pi$
$542$			35.4576i			1.52303i
$543$	−26.9261			−1.15551
$544$	−11.4612	−	28.9599i	−0.491396	−	1.24164i
$545$	−10.1584			−0.435139
$546$		−	95.4934i		−	4.08674i
$547$	3.06124	−	3.06124i	0.130889	−	0.130889i	−0.638627	−	0.769516i	$-0.720497\pi$
$547$	3.06124	−	3.06124i	0.130889	−	0.130889i	0.769516	+	0.638627i	$0.220497\pi$
$548$	−19.1787			−0.819274
$549$	−32.0387	+	32.0387i	−1.36738	+	1.36738i
$550$	11.0888	+	11.0888i	0.472830	+	0.472830i
$551$	−3.75332	−	3.75332i	−0.159897	−	0.159897i
$552$		−	11.5237i		−	0.490483i
$553$			33.7923i			1.43699i
$554$	−23.2590	−	23.2590i	−0.988182	−	0.988182i
$555$	−12.8308	−	12.8308i	−0.544635	−	0.544635i
$556$	−5.44827	+	5.44827i	−0.231058	+	0.231058i
$557$	−26.0816			−1.10511			−0.552556	−	0.833476i	$-0.686348\pi$
$557$	−26.0816			−1.10511			−0.552556	+	0.833476i	$0.686348\pi$
$558$	17.9145	−	17.9145i	0.758382	−	0.758382i
$559$			3.90048i			0.164973i
$560$	−4.63837			−0.196007
$561$	17.6953	−	7.00314i	0.747097	−	0.295673i
$562$	−47.7670			−2.01493
$563$		−	19.1047i		−	0.805165i	−0.915384	−	0.402583i	$-0.868113\pi$
$563$		−	19.1047i		−	0.805165i	0.915384	−	0.402583i	$-0.131887\pi$
$564$	−43.8754	+	43.8754i	−1.84749	+	1.84749i
$565$	7.26691			0.305721
$566$	13.6812	−	13.6812i	0.575062	−	0.575062i
$567$	−19.4136	−	19.4136i	−0.815294	−	0.815294i
$568$	−15.8280	−	15.8280i	−0.664127	−	0.664127i
$569$			19.4252i			0.814345i	0.913351	+	0.407173i	$0.133485\pi$
$569$			19.4252i			0.814345i	−0.913351	+	0.407173i	$0.866515\pi$
$570$		−	4.57940i		−	0.191810i
$571$	18.1749	+	18.1749i	0.760595	+	0.760595i	0.976430	−	0.215835i	$-0.0692474\pi$
$571$	18.1749	+	18.1749i	0.760595	+	0.760595i	−0.215835	+	0.976430i	$0.569247\pi$
$572$	11.6918	+	11.6918i	0.488857	+	0.488857i
$573$	−8.32624	+	8.32624i	−0.347833	+	0.347833i
$574$	85.7524			3.57923
$575$	−8.09052	+	8.09052i	−0.337398	+	0.337398i
$576$		−	71.7045i		−	2.98769i
$577$	25.2796			1.05240			0.526201	−	0.850360i	$-0.323616\pi$
$577$	25.2796			1.05240			0.526201	+	0.850360i	$0.323616\pi$
$578$	−25.2865	−	26.9429i	−1.05178	−	1.12068i
$579$	72.4252			3.00989
$580$			7.39552i			0.307082i
$581$	−0.222395	+	0.222395i	−0.00922652	+	0.00922652i
$582$	−62.1427			−2.57590
$583$	−2.23779	+	2.23779i	−0.0926797	+	0.0926797i
$584$	−13.4616	−	13.4616i	−0.557043	−	0.557043i
$585$	9.63936	+	9.63936i	0.398539	+	0.398539i
$586$			26.8113i			1.10757i
$587$			24.4078i			1.00742i	0.863874	+	0.503709i	$0.168031\pi$
$587$			24.4078i			1.00742i	−0.863874	+	0.503709i	$0.831969\pi$
$588$	42.3954	+	42.3954i	1.74836	+	1.74836i
$589$	1.67500	+	1.67500i	0.0690173	+	0.0690173i
$590$	7.13061	−	7.13061i	0.293563	−	0.293563i
$591$	−32.5706			−1.33978
$592$	14.5455	−	14.5455i	0.597816	−	0.597816i
$593$			37.1255i			1.52456i	0.647247	+	0.762281i	$0.275920\pi$
$593$			37.1255i			1.52456i	−0.647247	+	0.762281i	$0.724080\pi$
$594$	28.0790			1.15209
$595$	−8.77409	+	3.47245i	−0.359703	+	0.142357i
$596$	−8.47528			−0.347161
$597$			46.7523i			1.91345i
$598$	−14.7928	+	14.7928i	−0.604924	+	0.604924i
$599$	2.13504			0.0872353			0.0436176	−	0.999048i	$-0.486112\pi$
$599$	2.13504			0.0872353			0.0436176	+	0.999048i	$0.486112\pi$
$600$	15.3114	−	15.3114i	0.625084	−	0.625084i
$601$	−29.2377	−	29.2377i	−1.19263	−	1.19263i	−0.976326	−	0.216306i	$-0.930599\pi$
$601$	−29.2377	−	29.2377i	−1.19263	−	1.19263i	−0.216306	−	0.976326i	$-0.569401\pi$
$602$	−5.83615	−	5.83615i	−0.237864	−	0.237864i
$603$		−	40.5332i		−	1.65064i
$604$		−	24.3042i		−	0.988922i
$605$	−3.65605	−	3.65605i	−0.148640	−	0.148640i
$606$	−9.60588	−	9.60588i	−0.390212	−	0.390212i
$607$	−16.2859	+	16.2859i	−0.661022	+	0.661022i	−0.955621	−	0.294599i	$-0.904814\pi$
$607$	−16.2859	+	16.2859i	−0.661022	+	0.661022i	0.294599	+	0.955621i	$0.404814\pi$
$608$	8.90209			0.361027
$609$	−35.8738	+	35.8738i	−1.45368	+	1.45368i
$610$			10.2358i			0.414433i
$611$	29.9490			1.21161
$612$	−23.9697	−	60.5660i	−0.968919	−	2.44823i
$613$	−46.3992			−1.87405			−0.937023	−	0.349267i	$-0.886431\pi$
$613$	−46.3992			−1.87405			−0.937023	+	0.349267i	$0.886431\pi$
$614$		−	11.4361i		−	0.461524i
$615$	−13.1342	+	13.1342i	−0.529624	+	0.529624i
$616$	−9.30233			−0.374802
$617$	−4.17567	+	4.17567i	−0.168106	+	0.168106i	−0.786146	−	0.618040i	$-0.787927\pi$
$617$	−4.17567	+	4.17567i	−0.168106	+	0.168106i	0.618040	+	0.786146i	$0.287927\pi$
$618$	−54.7410	−	54.7410i	−2.20200	−	2.20200i
$619$	32.5920	+	32.5920i	1.30998	+	1.30998i	0.921423	+	0.388561i	$0.127028\pi$
$619$	32.5920	+	32.5920i	1.30998	+	1.30998i	0.388561	+	0.921423i	$0.372972\pi$
$620$		−	3.30042i		−	0.132548i
$621$			20.4867i			0.822103i
$622$	−4.10149	−	4.10149i	−0.164455	−	0.164455i
$623$	−0.598977	−	0.598977i	−0.0239975	−	0.0239975i
$624$	−16.5809	+	16.5809i	−0.663767	+	0.663767i
$625$	−19.6832			−0.787328
$626$	−4.60857	+	4.60857i	−0.184196	+	0.184196i
$627$			5.43943i			0.217230i
$628$	−29.0911			−1.16086
$629$	16.6254	−	38.4039i	0.662898	−	1.53127i
$630$	−28.8461			−1.14925
$631$			18.0013i			0.716618i	0.933603	+	0.358309i	$0.116647\pi$
$631$			18.0013i			0.716618i	−0.933603	+	0.358309i	$0.883353\pi$
$632$	−9.90678	+	9.90678i	−0.394071	+	0.394071i
$633$	−4.17715			−0.166027
$634$	38.6668	−	38.6668i	1.53566	−	1.53566i
$635$	−6.16994	−	6.16994i	−0.244847	−	0.244847i
$636$	11.6218	+	11.6218i	0.460834	+	0.460834i
$637$		−	28.9388i		−	1.14660i
$638$		−	15.2333i		−	0.603094i
$639$	58.2995	+	58.2995i	2.30629	+	2.30629i
$640$	−5.01559	−	5.01559i	−0.198258	−	0.198258i
$641$	−23.7153	+	23.7153i	−0.936700	+	0.936700i	−0.998112	−	0.0614126i	$-0.980439\pi$
$641$	−23.7153	+	23.7153i	−0.936700	+	0.936700i	0.0614126	+	0.998112i	$0.480439\pi$
$642$	88.2455			3.48277
$643$	−5.47205	+	5.47205i	−0.215797	+	0.215797i	−0.806724	−	0.590928i	$-0.798762\pi$
$643$	−5.47205	+	5.47205i	−0.215797	+	0.215797i	0.590928	+	0.806724i	$0.298762\pi$
$644$		−	25.5275i		−	1.00592i
$645$	1.78779			0.0703940
$646$	9.82020	−	3.88646i	0.386370	−	0.152911i
$647$	38.6008			1.51755			0.758776	−	0.651351i	$-0.225798\pi$
$647$	38.6008			1.51755			0.758776	+	0.651351i	$0.225798\pi$
$648$		−	11.3829i		−	0.447161i
$649$	−8.46978	+	8.46978i	−0.332468	+	0.332468i
$650$	−39.3099			−1.54186
$651$	16.0095	−	16.0095i	0.627462	−	0.627462i
$652$	−23.7972	−	23.7972i	−0.931970	−	0.931970i
$653$	29.1812	+	29.1812i	1.14195	+	1.14195i	0.988094	+	0.153854i	$0.0491684\pi$
$653$	29.1812	+	29.1812i	1.14195	+	1.14195i	0.153854	+	0.988094i	$0.450832\pi$
$654$		−	108.669i		−	4.24931i
$655$		−	7.95589i		−	0.310862i
$656$	−14.8895	−	14.8895i	−0.581338	−	0.581338i
$657$	49.5833	+	49.5833i	1.93443	+	1.93443i
$658$	−44.8116	+	44.8116i	−1.74694	+	1.74694i
$659$	27.2181			1.06026			0.530132	−	0.847915i	$-0.322142\pi$
$659$	27.2181			1.06026			0.530132	+	0.847915i	$0.322142\pi$
$660$	5.35892	−	5.35892i	0.208596	−	0.208596i
$661$			16.5298i			0.642936i	0.946920	+	0.321468i	$0.104176\pi$
$661$			16.5298i			0.642936i	−0.946920	+	0.321468i	$0.895824\pi$
$662$	36.3573			1.41307
$663$	−18.9519	+	43.7780i	−0.736030	+	1.70020i
$664$	−0.130398			−0.00506043
$665$		−	2.69710i		−	0.104589i
$666$	90.4584	−	90.4584i	3.50519	−	3.50519i
$667$	11.1144			0.430351
$668$	31.2490	−	31.2490i	1.20906	−	1.20906i
$669$	50.9785	+	50.9785i	1.97094	+	1.97094i
$670$	−6.47479	−	6.47479i	−0.250143	−	0.250143i
$671$		−	12.1581i		−	0.469358i
$672$		−	85.0852i		−	3.28223i
$673$	5.28595	+	5.28595i	0.203758	+	0.203758i	0.801608	−	0.597850i	$-0.203978\pi$
$673$	5.28595	+	5.28595i	0.203758	+	0.203758i	−0.597850	+	0.801608i	$0.703978\pi$
$674$	−11.9354	−	11.9354i	−0.459736	−	0.459736i
$675$	−27.2203	+	27.2203i	−1.04771	+	1.04771i
$676$	−6.03101			−0.231962
$677$	11.2912	−	11.2912i	0.433956	−	0.433956i	−0.456016	−	0.889972i	$-0.650724\pi$
$677$	11.2912	−	11.2912i	0.433956	−	0.433956i	0.889972	+	0.456016i	$0.150724\pi$
$678$			77.7374i			2.98549i
$679$	−36.5998			−1.40457
$680$	−3.59028	−	1.55427i	−0.137681	−	0.0596034i
$681$	29.3426			1.12441
$682$			6.79823i			0.260318i
$683$	15.7167	−	15.7167i	0.601382	−	0.601382i	−0.339297	−	0.940679i	$-0.610189\pi$
$683$	15.7167	−	15.7167i	0.601382	−	0.601382i	0.940679	+	0.339297i	$0.110189\pi$
$684$	18.6176			0.711862
$685$	3.00019	−	3.00019i	0.114631	−	0.114631i
$686$	2.44701	+	2.44701i	0.0934272	+	0.0934272i
$687$	−26.0777	−	26.0777i	−0.994928	−	0.994928i
$688$			2.02671i			0.0772676i
$689$		−	7.93294i		−	0.302221i
$690$	6.78029	+	6.78029i	0.258121	+	0.258121i
$691$	−8.68498	−	8.68498i	−0.330392	−	0.330392i	0.522343	−	0.852735i	$-0.325058\pi$
$691$	−8.68498	−	8.68498i	−0.330392	−	0.330392i	−0.852735	+	0.522343i	$0.825058\pi$
$692$	−28.9661	+	28.9661i	−1.10113	+	1.10113i
$693$	34.2635			1.30156
$694$	−40.8702	+	40.8702i	−1.55141	+	1.55141i
$695$		−	1.70458i		−	0.0646584i
$696$	−21.0341			−0.797294
$697$	−39.3123	−	17.0186i	−1.48906	−	0.644627i
$698$	5.92790			0.224374
$699$		−	12.8861i		−	0.487398i
$700$	33.9179	−	33.9179i	1.28198	−	1.28198i
$701$	−10.3212			−0.389826			−0.194913	−	0.980821i	$-0.562442\pi$
$701$	−10.3212			−0.389826			−0.194913	+	0.980821i	$0.562442\pi$
$702$	−49.7699	+	49.7699i	−1.87845	+	1.87845i
$703$	8.45784	+	8.45784i	0.318993	+	0.318993i
$704$	13.6053	+	13.6053i	0.512768	+	0.512768i
$705$		−	13.7271i		−	0.516994i
$706$			37.5271i			1.41235i
$707$	−5.65752	−	5.65752i	−0.212773	−	0.212773i
$708$	43.9872	+	43.9872i	1.65314	+	1.65314i
$709$	−27.3331	+	27.3331i	−1.02652	+	1.02652i	−0.0268775	+	0.999639i	$0.508556\pi$
$709$	−27.3331	+	27.3331i	−1.02652	+	1.02652i	−0.999639	+	0.0268775i	$0.991444\pi$
$710$	18.6256			0.699006
$711$	36.4899	−	36.4899i	1.36848	−	1.36848i
$712$		−	0.351201i		−	0.0131618i
$713$	−4.96005			−0.185755
$714$	−37.1464	−	93.8604i	−1.39017	−	3.51264i
$715$	−3.65796			−0.136800
$716$			31.3344i			1.17102i
$717$	−39.3842	+	39.3842i	−1.47083	+	1.47083i
$718$	−7.97694			−0.297697
$719$	13.3458	−	13.3458i	0.497714	−	0.497714i	−0.413011	−	0.910726i	$-0.635523\pi$
$719$	13.3458	−	13.3458i	0.497714	−	0.497714i	0.910726	+	0.413011i	$0.135523\pi$
$720$	5.00866	+	5.00866i	0.186662	+	0.186662i
$721$	−32.2405	−	32.2405i	−1.20070	−	1.20070i
$722$		−	38.2788i		−	1.42459i
$723$		−	28.5488i		−	1.06174i
$724$	−17.4866	−	17.4866i	−0.649883	−	0.649883i
$725$	14.7675	+	14.7675i	0.548450	+	0.548450i
$726$	39.1105	−	39.1105i	1.45153	−	1.45153i
$727$	40.6838			1.50888			0.754439	−	0.656370i	$-0.227909\pi$
$727$	40.6838			1.50888			0.754439	+	0.656370i	$0.227909\pi$
$728$	16.4884	−	16.4884i	0.611099	−	0.611099i
$729$		−	31.9535i		−	1.18346i
$730$	15.8409			0.586299
$731$	1.51727	+	3.83378i	0.0561181	+	0.141798i
$732$	−63.1421			−2.33380
$733$			19.7797i			0.730581i	0.930894	+	0.365291i	$0.119030\pi$
$733$			19.7797i			0.730581i	−0.930894	+	0.365291i	$0.880970\pi$
$734$	20.5779	−	20.5779i	0.759546	−	0.759546i
$735$	−13.2641			−0.489254
$736$	−13.1805	+	13.1805i	−0.485840	+	0.485840i
$737$	7.69079	+	7.69079i	0.283294	+	0.283294i
$738$	−92.5980	−	92.5980i	−3.40858	−	3.40858i
$739$			20.1038i			0.739529i	0.929126	+	0.369764i	$0.120562\pi$
$739$			20.1038i			0.739529i	−0.929126	+	0.369764i	$0.879438\pi$
$740$		−	16.6653i		−	0.612628i
$741$	−9.64138	−	9.64138i	−0.354185	−	0.354185i
$742$	11.8698	+	11.8698i	0.435753	+	0.435753i
$743$	−31.8750	+	31.8750i	−1.16938	+	1.16938i	−0.187026	+	0.982355i	$0.559885\pi$
$743$	−31.8750	+	31.8750i	−1.16938	+	1.16938i	−0.982355	+	0.187026i	$0.940115\pi$
$744$	9.38693			0.344141
$745$	1.32581	−	1.32581i	0.0485741	−	0.0485741i
$746$			19.0354i			0.696935i
$747$	0.480299			0.0175732
$748$	16.0399	+	6.94380i	0.586475	+	0.253890i
$749$	51.9735			1.89907
$750$			37.4469i			1.36737i
$751$	−13.5159	+	13.5159i	−0.493200	+	0.493200i	−0.909313	−	0.416113i	$-0.863392\pi$
$751$	−13.5159	+	13.5159i	−0.493200	+	0.493200i	0.416113	+	0.909313i	$0.363392\pi$
$752$	15.5616			0.567475
$753$	−19.0444	+	19.0444i	−0.694015	+	0.694015i
$754$	27.0011	+	27.0011i	0.983320	+	0.983320i
$755$	3.80198	+	3.80198i	0.138368	+	0.138368i
$756$		−	85.8864i		−	3.12366i
$757$		−	14.5893i		−	0.530258i	−0.964213	−	0.265129i	$-0.914585\pi$
$757$		−	14.5893i		−	0.530258i	0.964213	−	0.265129i	$-0.0854145\pi$
$758$	−52.8004	−	52.8004i	−1.91780	−	1.91780i
$759$	−8.05367	−	8.05367i	−0.292330	−	0.292330i
$760$	0.790701	−	0.790701i	0.0286818	−	0.0286818i
$761$	23.2086			0.841310			0.420655	−	0.907221i	$-0.361800\pi$
$761$	23.2086			0.841310			0.420655	+	0.907221i	$0.361800\pi$
$762$	66.0027	−	66.0027i	2.39103	−	2.39103i
$763$		−	64.0023i		−	2.31704i
$764$	−10.8146			−0.391257
$765$	13.2242	+	5.72487i	0.478122	+	0.206983i
$766$	60.2476			2.17684
$767$		−	30.0253i		−	1.08415i
$768$	1.78208	−	1.78208i	0.0643053	−	0.0643053i
$769$	−13.3796			−0.482480			−0.241240	−	0.970465i	$-0.577554\pi$
$769$	−13.3796			−0.482480			−0.241240	+	0.970465i	$0.577554\pi$
$770$	5.47327	−	5.47327i	0.197243	−	0.197243i
$771$	−50.7197	−	50.7197i	−1.82663	−	1.82663i
$772$	47.0349	+	47.0349i	1.69282	+	1.69282i
$773$			4.30058i			0.154681i	0.997005	+	0.0773406i	$0.0246429\pi$
$773$			4.30058i			0.154681i	−0.997005	+	0.0773406i	$0.975357\pi$
$774$			12.6041i			0.453045i
$775$	−6.59032	−	6.59032i	−0.236731	−	0.236731i
$776$	−10.7299	−	10.7299i	−0.385180	−	0.385180i
$777$	80.8391	−	80.8391i	2.90009	−	2.90009i
$778$	−33.4438			−1.19902
$779$	8.65789	−	8.65789i	0.310201	−	0.310201i
$780$			18.9973i			0.680214i
$781$	−22.1236			−0.791644
$782$	−8.78554	+	20.2942i	−0.314170	+	0.725719i
$783$	37.3940			1.33635
$784$		−	15.0367i		−	0.537026i
$785$	4.55081	−	4.55081i	0.162425	−	0.162425i
$786$	85.1078			3.03569
$787$	−8.39595	+	8.39595i	−0.299283	+	0.299283i	−0.840733	−	0.541450i	$-0.817876\pi$
$787$	−8.39595	+	8.39595i	−0.299283	+	0.299283i	0.541450	+	0.840733i	$0.317876\pi$
$788$	−21.1523	−	21.1523i	−0.753518	−	0.753518i
$789$	−35.3519	−	35.3519i	−1.25856	−	1.25856i
$790$		−	11.6578i		−	0.414767i
$791$			45.7846i			1.62791i
$792$	10.0449	+	10.0449i	0.356931	+	0.356931i
$793$	21.5502	+	21.5502i	0.765269	+	0.765269i
$794$	54.2036	−	54.2036i	1.92361	−	1.92361i
$795$	−3.63607			−0.128958
$796$	−30.3622	+	30.3622i	−1.07616	+	1.07616i
$797$		−	39.8625i		−	1.41200i	−0.708211	−	0.706000i	$-0.750498\pi$
$797$		−	39.8625i		−	1.41200i	0.708211	−	0.706000i	$-0.249502\pi$
$798$	28.8521			1.02135
$799$	29.4369	−	11.6500i	1.04140	−	0.412148i
$800$	−35.0254			−1.23833
$801$			1.29359i			0.0457067i
$802$	−55.1633	+	55.1633i	−1.94788	+	1.94788i
$803$	−18.8159			−0.664000
$804$	39.9416	−	39.9416i	1.40863	−	1.40863i
$805$	3.99335	+	3.99335i	0.140747	+	0.140747i
$806$	−12.0498	−	12.0498i	−0.424437	−	0.424437i
$807$			11.8591i			0.417461i
$808$		−	3.31720i		−	0.116699i
$809$	−18.0109	−	18.0109i	−0.633230	−	0.633230i	0.315647	−	0.948877i	$-0.397778\pi$
$809$	−18.0109	−	18.0109i	−0.633230	−	0.633230i	−0.948877	+	0.315647i	$0.897778\pi$
$810$	6.69740	+	6.69740i	0.235323	+	0.235323i
$811$	−18.4468	+	18.4468i	−0.647756	+	0.647756i	−0.952450	−	0.304694i	$-0.901446\pi$
$811$	−18.4468	+	18.4468i	−0.647756	+	0.647756i	0.304694	+	0.952450i	$0.401446\pi$
$812$	−46.5949			−1.63516
$813$	34.2166	−	34.2166i	1.20003	−	1.20003i
$814$			34.3273i			1.20317i
$815$	7.44534			0.260799
$816$	−9.84748	+	22.7472i	−0.344731	+	0.796313i
$817$	−1.17848			−0.0412298
$818$			6.34558i			0.221868i
$819$	−60.7320	+	60.7320i	−2.12215	+	2.12215i
$820$	−17.0595			−0.595743
$821$	33.6273	−	33.6273i	1.17360	−	1.17360i	0.192256	−	0.981345i	$-0.438420\pi$
$821$	33.6273	−	33.6273i	1.17360	−	1.17360i	0.981345	−	0.192256i	$-0.0615804\pi$
$822$	32.0944	+	32.0944i	1.11942	+	1.11942i
$823$	−32.9195	−	32.9195i	−1.14750	−	1.14750i	−0.987043	−	0.160459i	$-0.948703\pi$
$823$	−32.9195	−	32.9195i	−1.14750	−	1.14750i	−0.160459	−	0.987043i	$-0.551297\pi$
$824$		−	18.9037i		−	0.658542i
$825$		−	21.4015i		−	0.745105i
$826$	44.9258	+	44.9258i	1.56317	+	1.56317i
$827$	34.4014	+	34.4014i	1.19625	+	1.19625i	0.975280	+	0.220975i	$0.0709238\pi$
$827$	34.4014	+	34.4014i	1.19625	+	1.19625i	0.220975	+	0.975280i	$0.429076\pi$
$828$	−27.5654	+	27.5654i	−0.957963	+	0.957963i
$829$	−30.6059			−1.06299			−0.531494	−	0.847062i	$-0.678369\pi$
$829$	−30.6059			−1.06299			−0.531494	+	0.847062i	$0.678369\pi$
$830$	0.0767231	−	0.0767231i	0.00266310	−	0.00266310i
$831$			44.8900i			1.55722i
$832$	−48.2306			−1.67209
$833$	−11.2570	−	28.4439i	−0.390033	−	0.985524i
$834$	18.2347			0.631415
$835$			9.77676i			0.338339i
$836$	−3.53252	+	3.53252i	−0.122175	+	0.122175i
$837$	−16.6879			−0.576819
$838$	−43.7241	+	43.7241i	−1.51043	+	1.51043i
$839$	−12.8831	−	12.8831i	−0.444773	−	0.444773i	0.448839	−	0.893612i	$-0.351837\pi$
$839$	−12.8831	−	12.8831i	−0.444773	−	0.444773i	−0.893612	+	0.448839i	$0.851837\pi$
$840$	−7.55744	−	7.55744i	−0.260756	−	0.260756i
$841$			8.71313i			0.300453i
$842$			61.4387i			2.11732i
$843$	46.0953	+	46.0953i	1.58761	+	1.58761i
$844$	−2.71275	−	2.71275i	−0.0933768	−	0.0933768i
$845$	0.943450	−	0.943450i	0.0324557	−	0.0324557i
$846$	96.7779			3.32729
$847$	23.0347	−	23.0347i	0.791481	−	0.791481i
$848$		−	4.12199i		−	0.141550i
$849$	−26.4047			−0.906207
$850$	−38.6377	+	15.2913i	−1.32526	+	0.524489i
$851$	−25.0455			−0.858548
$852$			114.897i			3.93631i
$853$	1.89172	−	1.89172i	0.0647712	−	0.0647712i	−0.673979	−	0.738750i	$-0.735416\pi$
$853$	1.89172	−	1.89172i	0.0647712	−	0.0647712i	0.738750	+	0.673979i	$0.235416\pi$
$854$	−64.4895			−2.20679
$855$	−2.91241	+	2.91241i	−0.0996024	+	0.0996024i
$856$	15.2369	+	15.2369i	0.520787	+	0.520787i
$857$	−9.40670	−	9.40670i	−0.321327	−	0.321327i	0.527949	−	0.849276i	$-0.322961\pi$
$857$	−9.40670	−	9.40670i	−0.321327	−	0.321327i	−0.849276	+	0.527949i	$0.822961\pi$
$858$		−	39.1308i		−	1.33590i
$859$		−	21.0053i		−	0.716692i	−0.933589	−	0.358346i	$-0.883341\pi$
$859$		−	21.0053i		−	0.716692i	0.933589	−	0.358346i	$-0.116659\pi$
$860$	1.16104	+	1.16104i	0.0395910	+	0.0395910i
$861$	−82.7512	−	82.7512i	−2.82015	−	2.82015i
$862$	−7.25904	+	7.25904i	−0.247244	+	0.247244i
$863$	23.5766			0.802557			0.401279	−	0.915956i	$-0.368566\pi$
$863$	23.5766			0.802557			0.401279	+	0.915956i	$0.368566\pi$
$864$	−44.3453	+	44.3453i	−1.50866	+	1.50866i
$865$		−	9.06252i		−	0.308135i
$866$	73.1046			2.48419
$867$	−1.59840	+	50.4015i	−0.0542844	+	1.71173i
$868$	20.7940			0.705795
$869$			13.8472i			0.469735i
$870$	12.3759	−	12.3759i	0.419583	−	0.419583i
$871$	−27.2638			−0.923799
$872$	18.7634	−	18.7634i	0.635408	−	0.635408i
$873$	39.5216	+	39.5216i	1.33760	+	1.33760i
$874$	−4.46946	−	4.46946i	−0.151182	−	0.151182i
$875$			22.0549i			0.745591i
$876$			97.7192i			3.30163i
$877$	1.88829	+	1.88829i	0.0637629	+	0.0637629i	0.738269	−	0.674506i	$-0.235643\pi$
$877$	1.88829	+	1.88829i	0.0637629	+	0.0637629i	−0.674506	+	0.738269i	$0.735643\pi$
$878$	−28.0757	−	28.0757i	−0.947509	−	0.947509i
$879$	25.8730	−	25.8730i	0.872674	−	0.872674i
$880$	−1.90069			−0.0640723
$881$	20.5091	−	20.5091i	0.690970	−	0.690970i	−0.271475	−	0.962445i	$-0.587512\pi$
$881$	20.5091	−	20.5091i	0.690970	−	0.690970i	0.962445	+	0.271475i	$0.0875115\pi$
$882$		−	93.5135i		−	3.14876i
$883$	14.8260			0.498935			0.249468	−	0.968383i	$-0.419744\pi$
$883$	14.8260			0.498935			0.249468	+	0.968383i	$0.419744\pi$
$884$	−40.7385	+	16.1227i	−1.37018	+	0.542267i
$885$	−13.7621			−0.462608
$886$		−	53.7053i		−	1.80427i
$887$	35.4664	−	35.4664i	1.19085	−	1.19085i	0.214016	−	0.976830i	$-0.431345\pi$
$887$	35.4664	−	35.4664i	1.19085	−	1.19085i	0.976830	−	0.214016i	$-0.0686546\pi$
$888$	47.3988			1.59060
$889$	38.8732	−	38.8732i	1.30377	−	1.30377i
$890$	0.206638	+	0.206638i	0.00692653	+	0.00692653i
$891$	−7.95521	−	7.95521i	−0.266510	−	0.266510i
$892$			66.2137i			2.21700i
$893$			9.04871i			0.302804i
$894$	14.1828	+	14.1828i	0.474345	+	0.474345i
$895$	−4.90174	−	4.90174i	−0.163847	−	0.163847i
$896$	31.6003	−	31.6003i	1.05569	−	1.05569i
$897$	28.5502			0.953264
$898$	55.0516	−	55.0516i	1.83710	−	1.83710i
$899$			9.05348i			0.301951i
$900$	−73.2512			−2.44171
$901$	−3.08587	−	7.79729i	−0.102805	−	0.259765i
$902$	35.1392			1.17001
$903$			11.2638i			0.374836i
$904$	−13.4225	+	13.4225i	−0.446427	+	0.446427i
$905$	5.47095			0.181861
$906$	−40.6715	+	40.6715i	−1.35122	+	1.35122i
$907$	−12.1479	−	12.1479i	−0.403365	−	0.403365i	0.476052	−	0.879417i	$-0.342067\pi$
$907$	−12.1479	−	12.1479i	−0.403365	−	0.403365i	−0.879417	+	0.476052i	$0.842067\pi$
$908$	19.0559	+	19.0559i	0.632392	+	0.632392i
$909$			12.2183i			0.405256i
$910$			19.4027i			0.643194i
$911$	5.41152	+	5.41152i	0.179292	+	0.179292i	0.791047	−	0.611755i	$-0.209536\pi$
$911$	5.41152	+	5.41152i	0.179292	+	0.179292i	−0.611755	+	0.791047i	$0.709536\pi$
$912$	−5.00971	−	5.00971i	−0.165888	−	0.165888i
$913$	−0.0911322	+	0.0911322i	−0.00301604	+	0.00301604i
$914$	1.81697			0.0601000
$915$	9.87752	−	9.87752i	0.326541	−	0.326541i
$916$		−	33.8712i		−	1.11914i
$917$	50.1254			1.65529
$918$	−29.5586	+	68.2791i	−0.975580	+	2.25355i
$919$	33.5661			1.10724			0.553622	−	0.832768i	$-0.313245\pi$
$919$	33.5661			1.10724			0.553622	+	0.832768i	$0.313245\pi$
$920$			2.34144i			0.0771949i
$921$	−11.0359	+	11.0359i	−0.363644	+	0.363644i
$922$	−38.1509			−1.25643
$923$	39.2140	−	39.2140i	1.29074	−	1.29074i
$924$	33.7634	+	33.7634i	1.11073	+	1.11073i
$925$	−33.2775	−	33.2775i	−1.09416	−	1.09416i
$926$		−	79.9156i		−	2.62619i
$927$			69.6285i			2.28690i
$928$	24.0581	+	24.0581i	0.789746	+	0.789746i
$929$	−1.40786	−	1.40786i	−0.0461904	−	0.0461904i	0.683634	−	0.729825i	$-0.260398\pi$
$929$	−1.40786	−	1.40786i	−0.0461904	−	0.0461904i	−0.729825	+	0.683634i	$0.760398\pi$
$930$	−5.52304	+	5.52304i	−0.181108	+	0.181108i
$931$	8.74349			0.286556
$932$	8.36861	−	8.36861i	0.274123	−	0.274123i
$933$			7.91590i			0.259155i
$934$	−8.05022			−0.263411
$935$	−3.59541	+	1.42293i	−0.117582	+	0.0465346i
$936$	−35.6093			−1.16393
$937$			19.7796i			0.646171i	0.946370	+	0.323085i	$0.104720\pi$
$937$			19.7796i			0.646171i	−0.946370	+	0.323085i	$0.895280\pi$
$938$	40.7939	−	40.7939i	1.33197	−	1.33197i
$939$	8.89457			0.290263
$940$	8.91477	−	8.91477i	0.290768	−	0.290768i
$941$	30.7206	+	30.7206i	1.00146	+	1.00146i	0.999999	+	0.00146547i	$0.000466474\pi$
$941$	30.7206	+	30.7206i	1.00146	+	1.00146i	0.00146547	+	0.999999i	$0.499534\pi$
$942$	48.6821	+	48.6821i	1.58615	+	1.58615i
$943$			25.6379i			0.834885i
$944$		−	15.6013i		−	0.507779i
$945$	13.4355	+	13.4355i	0.437056	+	0.437056i
$946$	−2.39151	−	2.39151i	−0.0777548	−	0.0777548i
$947$	15.5204	−	15.5204i	0.504345	−	0.504345i	−0.408440	−	0.912785i	$-0.633927\pi$
$947$	15.5204	−	15.5204i	0.504345	−	0.504345i	0.912785	+	0.408440i	$0.133927\pi$
$948$	71.9146			2.33568
$949$	33.3512	−	33.3512i	1.08263	−	1.08263i
$950$		−	11.8770i		−	0.385340i
$951$	−74.6271			−2.41995
$952$	9.79253	−	22.6203i	0.317378	−	0.733128i
$953$	−18.6510			−0.604165			−0.302082	−	0.953282i	$-0.597682\pi$
$953$	−18.6510			−0.604165			−0.302082	+	0.953282i	$0.597682\pi$
$954$		−	25.6347i		−	0.829954i
$955$	1.69176	−	1.69176i	0.0547440	−	0.0547440i
$956$	−51.1543			−1.65445
$957$	−14.7002	+	14.7002i	−0.475190	+	0.475190i
$958$	−20.3806	−	20.3806i	−0.658466	−	0.658466i
$959$	18.9024	+	18.9024i	0.610391	+	0.610391i
$960$			22.1065i			0.713484i
$961$			26.9597i			0.869667i
$962$	−60.8450	−	60.8450i	−1.96172	−	1.96172i
$963$	−56.1225	−	56.1225i	−1.80852	−	1.80852i
$964$	18.5404	−	18.5404i	0.597145	−	0.597145i
$965$	−14.7156			−0.473713
$966$	−42.7187	+	42.7187i	−1.37445	+	1.37445i
$967$		−	12.9987i		−	0.418010i	−0.977915	−	0.209005i	$-0.932978\pi$
$967$		−	12.9987i		−	0.418010i	0.977915	−	0.209005i	$-0.0670225\pi$
$968$	13.5060			0.434100
$969$	−13.2270	−	5.72607i	−0.424911	−	0.183948i
$970$	12.6264			0.405409
$971$			7.39333i			0.237263i	0.992938	+	0.118632i	$0.0378507\pi$
$971$			7.39333i			0.237263i	−0.992938	+	0.118632i	$0.962149\pi$
$972$	6.66504	−	6.66504i	0.213781	−	0.213781i
$973$	10.7396			0.344295
$974$	−38.7774	+	38.7774i	−1.24251	+	1.24251i
$975$	37.9341	+	37.9341i	1.21486	+	1.21486i
$976$	11.1976	+	11.1976i	0.358426	+	0.358426i
$977$		−	45.4111i		−	1.45283i	−0.687256	−	0.726415i	$-0.741185\pi$
$977$		−	45.4111i		−	1.45283i	0.687256	−	0.726415i	$-0.258815\pi$
$978$			79.6462i			2.54681i
$979$	−0.245446	−	0.245446i	−0.00784449	−	0.00784449i
$980$	−8.61407	−	8.61407i	−0.275166	−	0.275166i
$981$	−69.1117	+	69.1117i	−2.20657	+	2.20657i
$982$	−17.5349			−0.559563
$983$	−30.4405	+	30.4405i	−0.970902	+	0.970902i	−0.999588	−	0.0286865i	$-0.990868\pi$
$983$	−30.4405	+	30.4405i	−0.970902	+	0.970902i	0.0286865	+	0.999588i	$0.490868\pi$
$984$		−	48.5199i		−	1.54676i
$985$	6.61783			0.210862
$986$	37.0426	+	16.0361i	1.17968	+	0.510692i
$987$	86.4867			2.75290
$988$		−	12.5227i		−	0.398402i
$989$	1.74487	−	1.74487i	0.0554836	−	0.0554836i
$990$	−11.8204			−0.375677
$991$	3.14157	−	3.14157i	0.0997952	−	0.0997952i	−0.655446	−	0.755242i	$-0.727519\pi$
$991$	3.14157	−	3.14157i	0.0997952	−	0.0997952i	0.755242	+	0.655446i	$0.227519\pi$
$992$	−10.7365	−	10.7365i	−0.340884	−	0.340884i
$993$	−35.0848	−	35.0848i	−1.11338	−	1.11338i
$994$			117.349i			3.72208i
$995$		−	9.49932i		−	0.301149i
$996$	0.473288	+	0.473288i	0.0149967	+	0.0149967i
$997$	−25.8703	−	25.8703i	−0.819322	−	0.819322i	0.166688	−	0.986010i	$-0.446693\pi$
$997$	−25.8703	−	25.8703i	−0.819322	−	0.819322i	−0.986010	+	0.166688i	$0.946693\pi$
$998$	−34.3984	+	34.3984i	−1.08886	+	1.08886i
$999$	−84.2647			−2.66602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.d.259.6	✓	68
17.13	even	4	inner	731.2.f.d.302.29	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.d.259.6	✓	68	1.1	even	1	trivial
731.2.f.d.302.29	yes	68	17.13	even	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.17355i q^{2} +(-2.09748 + 2.09748i) q^{3} -2.72432 q^{4} +(0.426175 - 0.426175i) q^{5} +(4.55898 + 4.55898i) q^{6} +(2.68508 + 2.68508i) q^{7} +1.57435i q^{8} -5.79886i q^{9} +O(q^{10})\)	\(q-2.17355i q^{2} +(-2.09748 + 2.09748i) q^{3} -2.72432 q^{4} +(0.426175 - 0.426175i) q^{5} +(4.55898 + 4.55898i) q^{6} +(2.68508 + 2.68508i) q^{7} +1.57435i q^{8} -5.79886i q^{9} +(-0.926312 - 0.926312i) q^{10} +(1.10028 + 1.10028i) q^{11} +(5.71422 - 5.71422i) q^{12} -3.90048 q^{13} +(5.83615 - 5.83615i) q^{14} +1.78779i q^{15} -2.02671 q^{16} +(-3.83378 + 1.51727i) q^{17} -12.6041 q^{18} -1.17848i q^{19} +(-1.16104 + 1.16104i) q^{20} -11.2638 q^{21} +(2.39151 - 2.39151i) q^{22} +(1.74487 + 1.74487i) q^{23} +(-3.30218 - 3.30218i) q^{24} +4.63675i q^{25} +8.47790i q^{26} +(5.87055 + 5.87055i) q^{27} +(-7.31502 - 7.31502i) q^{28} +(3.18488 - 3.18488i) q^{29} +3.88584 q^{30} +(-1.42132 + 1.42132i) q^{31} +7.55386i q^{32} -4.61563 q^{33} +(3.29786 + 8.33292i) q^{34} +2.28862 q^{35} +15.7980i q^{36} +(-7.17690 + 7.17690i) q^{37} -2.56149 q^{38} +(8.18119 - 8.18119i) q^{39} +(0.670949 + 0.670949i) q^{40} +(7.34665 + 7.34665i) q^{41} +24.4824i q^{42} -1.00000i q^{43} +(-2.99752 - 2.99752i) q^{44} +(-2.47133 - 2.47133i) q^{45} +(3.79256 - 3.79256i) q^{46} -7.67828 q^{47} +(4.25098 - 4.25098i) q^{48} +7.41928i q^{49} +10.0782 q^{50} +(4.85885 - 11.2237i) q^{51} +10.6262 q^{52} +2.03384i q^{53} +(12.7599 - 12.7599i) q^{54} +0.937822 q^{55} +(-4.22726 + 4.22726i) q^{56} +(2.47184 + 2.47184i) q^{57} +(-6.92249 - 6.92249i) q^{58} +7.69785i q^{59} -4.87051i q^{60} +(-5.52500 - 5.52500i) q^{61} +(3.08932 + 3.08932i) q^{62} +(15.5704 - 15.5704i) q^{63} +12.3653 q^{64} +(-1.66229 + 1.66229i) q^{65} +10.0323i q^{66} +6.98986 q^{67} +(10.4445 - 4.13353i) q^{68} -7.31966 q^{69} -4.97444i q^{70} +(-10.0536 + 10.0536i) q^{71} +9.12945 q^{72} +(-8.55053 + 8.55053i) q^{73} +(15.5993 + 15.5993i) q^{74} +(-9.72550 - 9.72550i) q^{75} +3.21056i q^{76} +5.90867i q^{77} +(-17.7822 - 17.7822i) q^{78} +(6.29260 + 6.29260i) q^{79} +(-0.863732 + 0.863732i) q^{80} -7.23018 q^{81} +(15.9683 - 15.9683i) q^{82} +0.0828265i q^{83} +30.6862 q^{84} +(-0.987241 + 2.28048i) q^{85} -2.17355 q^{86} +13.3604i q^{87} +(-1.73223 + 1.73223i) q^{88} -0.223076 q^{89} +(-5.37155 + 5.37155i) q^{90} +(-10.4731 - 10.4731i) q^{91} +(-4.75359 - 4.75359i) q^{92} -5.96240i q^{93} +16.6891i q^{94} +(-0.502239 - 0.502239i) q^{95} +(-15.8441 - 15.8441i) q^{96} +(-6.81542 + 6.81542i) q^{97} +16.1262 q^{98} +(6.38036 - 6.38036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Introduction

L-functions

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