LMFDB - Embedded newform 130.3.k.a.21.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,3,Mod(21,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("130.21");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	130.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.54224343668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 76x^{10} + 1956x^{8} + 19924x^{6} + 77560x^{4} + 85248x^{2} + 2916 $ x^12 + 76x^10 + 1956x^8 + 19924x^6 + 77560x^4 + 85248*x^2 + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.4
Root			$-0.187967i$ of defining polynomial
Character	$\chi$	$=$	130.21
Dual form			130.3.k.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} -0.187967 q^{3} +2.00000i q^{4} +(1.58114 + 1.58114i) q^{5} +(0.187967 + 0.187967i) q^{6} +(-7.64727 + 7.64727i) q^{7} +(2.00000 - 2.00000i) q^{8} -8.96467 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} -0.187967 q^{3} +2.00000i q^{4} +(1.58114 + 1.58114i) q^{5} +(0.187967 + 0.187967i) q^{6} +(-7.64727 + 7.64727i) q^{7} +(2.00000 - 2.00000i) q^{8} -8.96467 q^{9} -3.16228i q^{10} +(1.76217 - 1.76217i) q^{11} -0.375934i q^{12} +(3.66602 + 12.4724i) q^{13} +15.2945 q^{14} +(-0.297202 - 0.297202i) q^{15} -4.00000 q^{16} +26.3908i q^{17} +(8.96467 + 8.96467i) q^{18} +(0.355732 + 0.355732i) q^{19} +(-3.16228 + 3.16228i) q^{20} +(1.43743 - 1.43743i) q^{21} -3.52434 q^{22} -1.62840i q^{23} +(-0.375934 + 0.375934i) q^{24} +5.00000i q^{25} +(8.80636 - 16.1384i) q^{26} +3.37676 q^{27} +(-15.2945 - 15.2945i) q^{28} +21.2188 q^{29} +0.594403i q^{30} +(-20.4455 - 20.4455i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.331229 + 0.331229i) q^{33} +(26.3908 - 26.3908i) q^{34} -24.1828 q^{35} -17.9293i q^{36} +(-4.39433 + 4.39433i) q^{37} -0.711465i q^{38} +(-0.689090 - 2.34439i) q^{39} +6.32456 q^{40} +(-17.0902 - 17.0902i) q^{41} -2.87487 q^{42} -61.5728i q^{43} +(3.52434 + 3.52434i) q^{44} +(-14.1744 - 14.1744i) q^{45} +(-1.62840 + 1.62840i) q^{46} +(-61.9029 + 61.9029i) q^{47} +0.751868 q^{48} -67.9613i q^{49} +(5.00000 - 5.00000i) q^{50} -4.96059i q^{51} +(-24.9448 + 7.33204i) q^{52} +70.4469 q^{53} +(-3.37676 - 3.37676i) q^{54} +5.57247 q^{55} +30.5891i q^{56} +(-0.0668659 - 0.0668659i) q^{57} +(-21.2188 - 21.2188i) q^{58} +(-2.39729 + 2.39729i) q^{59} +(0.594403 - 0.594403i) q^{60} +92.2723 q^{61} +40.8909i q^{62} +(68.5552 - 68.5552i) q^{63} -8.00000i q^{64} +(-13.9241 + 25.5171i) q^{65} +0.662459 q^{66} +(-54.9873 - 54.9873i) q^{67} -52.7815 q^{68} +0.306086i q^{69} +(24.1828 + 24.1828i) q^{70} +(52.9923 + 52.9923i) q^{71} +(-17.9293 + 17.9293i) q^{72} +(-93.9918 + 93.9918i) q^{73} +8.78866 q^{74} -0.939834i q^{75} +(-0.711465 + 0.711465i) q^{76} +26.9515i q^{77} +(-1.65530 + 3.03348i) q^{78} +22.6916 q^{79} +(-6.32456 - 6.32456i) q^{80} +80.0473 q^{81} +34.1805i q^{82} +(84.9136 + 84.9136i) q^{83} +(2.87487 + 2.87487i) q^{84} +(-41.7275 + 41.7275i) q^{85} +(-61.5728 + 61.5728i) q^{86} -3.98843 q^{87} -7.04868i q^{88} +(3.53753 - 3.53753i) q^{89} +28.3488i q^{90} +(-123.415 - 67.3446i) q^{91} +3.25680 q^{92} +(3.84307 + 3.84307i) q^{93} +123.806 q^{94} +1.12492i q^{95} +(-0.751868 - 0.751868i) q^{96} +(38.8105 + 38.8105i) q^{97} +(-67.9613 + 67.9613i) q^{98} +(-15.7973 + 15.7973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 24 q^{8} + 44 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 24 * q^8 + 44 * q^9	$ 12 q - 12 q^{2} + 24 q^{8} + 44 q^{9} + 8 q^{11} - 4 q^{13} + 20 q^{15} - 48 q^{16} - 44 q^{18} + 36 q^{19} + 52 q^{21} - 16 q^{22} + 8 q^{26} + 144 q^{27} - 8 q^{29} - 136 q^{31} + 48 q^{32} - 60 q^{33} - 40 q^{35} - 44 q^{37} - 172 q^{39} + 32 q^{41} - 104 q^{42} + 16 q^{44} - 96 q^{46} - 16 q^{47} + 60 q^{50} - 8 q^{52} + 24 q^{53} - 144 q^{54} - 212 q^{57} + 8 q^{58} + 124 q^{59} - 40 q^{60} + 24 q^{61} - 80 q^{63} - 60 q^{65} + 120 q^{66} + 136 q^{67} + 40 q^{70} + 84 q^{71} + 88 q^{72} + 12 q^{73} + 88 q^{74} - 72 q^{76} + 312 q^{78} - 168 q^{79} + 596 q^{81} + 160 q^{83} + 104 q^{84} + 60 q^{85} + 224 q^{86} - 64 q^{87} - 44 q^{89} - 404 q^{91} + 192 q^{92} + 4 q^{93} + 32 q^{94} - 192 q^{97} + 60 q^{98} - 52 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 24 * q^8 + 44 * q^9 + 8 * q^11 - 4 * q^13 + 20 * q^15 - 48 * q^16 - 44 * q^18 + 36 * q^19 + 52 * q^21 - 16 * q^22 + 8 * q^26 + 144 * q^27 - 8 * q^29 - 136 * q^31 + 48 * q^32 - 60 * q^33 - 40 * q^35 - 44 * q^37 - 172 * q^39 + 32 * q^41 - 104 * q^42 + 16 * q^44 - 96 * q^46 - 16 * q^47 + 60 * q^50 - 8 * q^52 + 24 * q^53 - 144 * q^54 - 212 * q^57 + 8 * q^58 + 124 * q^59 - 40 * q^60 + 24 * q^61 - 80 * q^63 - 60 * q^65 + 120 * q^66 + 136 * q^67 + 40 * q^70 + 84 * q^71 + 88 * q^72 + 12 * q^73 + 88 * q^74 - 72 * q^76 + 312 * q^78 - 168 * q^79 + 596 * q^81 + 160 * q^83 + 104 * q^84 + 60 * q^85 + 224 * q^86 - 64 * q^87 - 44 * q^89 - 404 * q^91 + 192 * q^92 + 4 * q^93 + 32 * q^94 - 192 * q^97 + 60 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−0.187967			−0.0626556			−0.0313278	−	0.999509i	$-0.509974\pi$
$3$	−0.187967			−0.0626556			−0.0313278	+	0.999509i	$0.509974\pi$
$4$			2.00000i			0.500000i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$	0.187967	+	0.187967i	0.0313278	+	0.0313278i
$7$	−7.64727	+	7.64727i	−1.09247	+	1.09247i	−0.0972018	+	0.995265i	$0.530989\pi$
$7$	−7.64727	+	7.64727i	−1.09247	+	1.09247i	−0.995265	+	0.0972018i	$0.969011\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−8.96467			−0.996074
$10$		−	3.16228i		−	0.316228i
$11$	1.76217	−	1.76217i	0.160197	−	0.160197i	−0.622457	−	0.782654i	$-0.713865\pi$
$11$	1.76217	−	1.76217i	0.160197	−	0.160197i	0.782654	+	0.622457i	$0.213865\pi$
$12$		−	0.375934i		−	0.0313278i
$13$	3.66602	+	12.4724i	0.282001	+	0.959414i
$13$	3.66602	+	12.4724i	0.282001	+	0.959414i
$14$	15.2945			1.09247
$15$	−0.297202	−	0.297202i	−0.0198134	−	0.0198134i
$16$	−4.00000			−0.250000
$17$			26.3908i			1.55240i	0.630488	+	0.776199i	$0.282855\pi$
$17$			26.3908i			1.55240i	−0.630488	+	0.776199i	$0.717145\pi$
$18$	8.96467	+	8.96467i	0.498037	+	0.498037i
$19$	0.355732	+	0.355732i	0.0187228	+	0.0187228i	0.716406	−	0.697683i	$-0.245786\pi$
$19$	0.355732	+	0.355732i	0.0187228	+	0.0187228i	−0.697683	+	0.716406i	$0.745786\pi$
$20$	−3.16228	+	3.16228i	−0.158114	+	0.158114i
$21$	1.43743	−	1.43743i	0.0684492	−	0.0684492i
$22$	−3.52434			−0.160197
$23$		−	1.62840i		−	0.0708001i	−0.999373	−	0.0354000i	$-0.988729\pi$
$23$		−	1.62840i		−	0.0708001i	0.999373	−	0.0354000i	$-0.0112705\pi$
$24$	−0.375934	+	0.375934i	−0.0156639	+	0.0156639i
$25$			5.00000i			0.200000i
$26$	8.80636	−	16.1384i	0.338706	−	0.620708i
$27$	3.37676			0.125065
$28$	−15.2945	−	15.2945i	−0.546233	−	0.546233i
$29$	21.2188			0.731683			0.365841	−	0.930677i	$-0.380781\pi$
$29$	21.2188			0.731683			0.365841	+	0.930677i	$0.380781\pi$
$30$			0.594403i			0.0198134i
$31$	−20.4455	−	20.4455i	−0.659531	−	0.659531i	0.295738	−	0.955269i	$-0.404434\pi$
$31$	−20.4455	−	20.4455i	−0.659531	−	0.659531i	−0.955269	+	0.295738i	$0.904434\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−0.331229	+	0.331229i	−0.0100373	+	0.0100373i
$34$	26.3908	−	26.3908i	0.776199	−	0.776199i
$35$	−24.1828			−0.690936
$36$		−	17.9293i		−	0.498037i
$37$	−4.39433	+	4.39433i	−0.118766	+	0.118766i	−0.763992	−	0.645226i	$-0.776763\pi$
$37$	−4.39433	+	4.39433i	−0.118766	+	0.118766i	0.645226	+	0.763992i	$0.276763\pi$
$38$		−	0.711465i		−	0.0187228i
$39$	−0.689090	−	2.34439i	−0.0176690	−	0.0601127i
$40$	6.32456			0.158114
$41$	−17.0902	−	17.0902i	−0.416835	−	0.416835i	0.467276	−	0.884111i	$-0.345235\pi$
$41$	−17.0902	−	17.0902i	−0.416835	−	0.416835i	−0.884111	+	0.467276i	$0.845235\pi$
$42$	−2.87487			−0.0684492
$43$		−	61.5728i		−	1.43193i	−0.698139	−	0.715963i	$-0.745988\pi$
$43$		−	61.5728i		−	1.43193i	0.698139	−	0.715963i	$-0.254012\pi$
$44$	3.52434	+	3.52434i	0.0800986	+	0.0800986i
$45$	−14.1744	−	14.1744i	−0.314986	−	0.314986i
$46$	−1.62840	+	1.62840i	−0.0354000	+	0.0354000i
$47$	−61.9029	+	61.9029i	−1.31708	+	1.31708i	−0.401009	+	0.916074i	$0.631340\pi$
$47$	−61.9029	+	61.9029i	−1.31708	+	1.31708i	−0.916074	+	0.401009i	$0.868660\pi$
$48$	0.751868			0.0156639
$49$		−	67.9613i		−	1.38697i
$50$	5.00000	−	5.00000i	0.100000	−	0.100000i
$51$		−	4.96059i		−	0.0972665i
$52$	−24.9448	+	7.33204i	−0.479707	+	0.141001i
$53$	70.4469			1.32919			0.664594	−	0.747205i	$-0.268605\pi$
$53$	70.4469			1.32919			0.664594	+	0.747205i	$0.268605\pi$
$54$	−3.37676	−	3.37676i	−0.0625326	−	0.0625326i
$55$	5.57247			0.101318
$56$			30.5891i			0.546233i
$57$	−0.0668659	−	0.0668659i	−0.00117309	−	0.00117309i
$58$	−21.2188	−	21.2188i	−0.365841	−	0.365841i
$59$	−2.39729	+	2.39729i	−0.0406320	+	0.0406320i	−0.727131	−	0.686499i	$-0.759147\pi$
$59$	−2.39729	+	2.39729i	−0.0406320	+	0.0406320i	0.686499	+	0.727131i	$0.259147\pi$
$60$	0.594403	−	0.594403i	0.00990672	−	0.00990672i
$61$	92.2723			1.51266			0.756330	−	0.654190i	$-0.226990\pi$
$61$	92.2723			1.51266			0.756330	+	0.654190i	$0.226990\pi$
$62$			40.8909i			0.659531i
$63$	68.5552	−	68.5552i	1.08818	−	1.08818i
$64$		−	8.00000i		−	0.125000i
$65$	−13.9241	+	25.5171i	−0.214217	+	0.392570i
$66$	0.662459			0.0100373
$67$	−54.9873	−	54.9873i	−0.820705	−	0.820705i	0.165504	−	0.986209i	$-0.447075\pi$
$67$	−54.9873	−	54.9873i	−0.820705	−	0.820705i	−0.986209	+	0.165504i	$0.947075\pi$
$68$	−52.7815			−0.776199
$69$			0.306086i			0.00443602i
$70$	24.1828	+	24.1828i	0.345468	+	0.345468i
$71$	52.9923	+	52.9923i	0.746370	+	0.746370i	0.973796	−	0.227425i	$-0.0730307\pi$
$71$	52.9923	+	52.9923i	0.746370	+	0.746370i	−0.227425	+	0.973796i	$0.573031\pi$
$72$	−17.9293	+	17.9293i	−0.249019	+	0.249019i
$73$	−93.9918	+	93.9918i	−1.28756	+	1.28756i	−0.351294	+	0.936265i	$0.614258\pi$
$73$	−93.9918	+	93.9918i	−1.28756	+	1.28756i	−0.936265	+	0.351294i	$0.885742\pi$
$74$	8.78866			0.118766
$75$		−	0.939834i		−	0.0125311i
$76$	−0.711465	+	0.711465i	−0.00936138	+	0.00936138i
$77$			26.9515i			0.350020i
$78$	−1.65530	+	3.03348i	−0.0212219	+	0.0388908i
$79$	22.6916			0.287236			0.143618	−	0.989633i	$-0.454126\pi$
$79$	22.6916			0.287236			0.143618	+	0.989633i	$0.454126\pi$
$80$	−6.32456	−	6.32456i	−0.0790569	−	0.0790569i
$81$	80.0473			0.988238
$82$			34.1805i			0.416835i
$83$	84.9136	+	84.9136i	1.02306	+	1.02306i	0.999728	+	0.0233279i	$0.00742616\pi$
$83$	84.9136	+	84.9136i	1.02306	+	1.02306i	0.0233279	+	0.999728i	$0.492574\pi$
$84$	2.87487	+	2.87487i	0.0342246	+	0.0342246i
$85$	−41.7275	+	41.7275i	−0.490911	+	0.490911i
$86$	−61.5728	+	61.5728i	−0.715963	+	0.715963i
$87$	−3.98843			−0.0458440
$88$		−	7.04868i		−	0.0800986i
$89$	3.53753	−	3.53753i	0.0397475	−	0.0397475i	−0.686954	−	0.726701i	$-0.741052\pi$
$89$	3.53753	−	3.53753i	0.0397475	−	0.0397475i	0.726701	+	0.686954i	$0.241052\pi$
$90$			28.3488i			0.314986i
$91$	−123.415	−	67.3446i	−1.35620	−	0.740051i
$92$	3.25680			0.0354000
$93$	3.84307	+	3.84307i	0.0413233	+	0.0413233i
$94$	123.806			1.31708
$95$			1.12492i			0.0118413i
$96$	−0.751868	−	0.751868i	−0.00783195	−	0.00783195i
$97$	38.8105	+	38.8105i	0.400108	+	0.400108i	0.878271	−	0.478163i	$-0.158697\pi$
$97$	38.8105	+	38.8105i	0.400108	+	0.400108i	−0.478163	+	0.878271i	$0.658697\pi$
$98$	−67.9613	+	67.9613i	−0.693483	+	0.693483i
$99$	−15.7973	+	15.7973i	−0.159568	+	0.159568i
$100$	−10.0000			−0.100000
$101$			92.3028i			0.913889i	0.889495	+	0.456945i	$0.151056\pi$
$101$			92.3028i			0.913889i	−0.889495	+	0.456945i	$0.848944\pi$
$102$	−4.96059	+	4.96059i	−0.0486332	+	0.0486332i
$103$		−	149.203i		−	1.44858i	−0.689498	−	0.724288i	$-0.742169\pi$
$103$		−	149.203i		−	1.44858i	0.689498	−	0.724288i	$-0.257831\pi$
$104$	32.2768	+	17.6127i	0.310354	+	0.169353i
$105$	4.54556			0.0432911
$106$	−70.4469	−	70.4469i	−0.664594	−	0.664594i
$107$	53.2509			0.497672			0.248836	−	0.968546i	$-0.419952\pi$
$107$	53.2509			0.497672			0.248836	+	0.968546i	$0.419952\pi$
$108$			6.75353i			0.0625326i
$109$	37.3176	+	37.3176i	0.342363	+	0.342363i	0.857255	−	0.514892i	$-0.172168\pi$
$109$	37.3176	+	37.3176i	0.342363	+	0.342363i	−0.514892	+	0.857255i	$0.672168\pi$
$110$	−5.57247	−	5.57247i	−0.0506588	−	0.0506588i
$111$	0.825988	−	0.825988i	0.00744134	−	0.00744134i
$112$	30.5891	−	30.5891i	0.273117	−	0.273117i
$113$	151.110			1.33726			0.668629	−	0.743596i	$-0.266881\pi$
$113$	151.110			1.33726			0.668629	+	0.743596i	$0.266881\pi$
$114$			0.133732i			0.00117309i
$115$	2.57473	−	2.57473i	0.0223890	−	0.0223890i
$116$			42.4376i			0.365841i
$117$	−32.8646	−	111.811i	−0.280894	−	0.955648i
$118$	4.79458			0.0406320
$119$	−201.817	−	201.817i	−1.69594	−	1.69594i
$120$	−1.18881			−0.00990672
$121$			114.790i			0.948674i
$122$	−92.2723	−	92.2723i	−0.756330	−	0.756330i
$123$	3.21240	+	3.21240i	0.0261171	+	0.0261171i
$124$	40.8909	−	40.8909i	0.329765	−	0.329765i
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$	−137.110			−1.08818
$127$			68.4199i			0.538740i	0.963037	+	0.269370i	$0.0868154\pi$
$127$			68.4199i			0.538740i	−0.963037	+	0.269370i	$0.913185\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			11.5736i			0.0897182i
$130$	39.4411	−	11.5930i	0.303393	−	0.0891767i
$131$	−99.5106			−0.759623			−0.379811	−	0.925064i	$-0.624011\pi$
$131$	−99.5106			−0.759623			−0.379811	+	0.925064i	$0.624011\pi$
$132$	−0.662459	−	0.662459i	−0.00501863	−	0.00501863i
$133$	−5.44076			−0.0409080
$134$			109.975i			0.820705i
$135$	5.33913	+	5.33913i	0.0395491	+	0.0395491i
$136$	52.7815	+	52.7815i	0.388099	+	0.388099i
$137$	61.7908	−	61.7908i	0.451027	−	0.451027i	−0.444668	−	0.895695i	$-0.646678\pi$
$137$	61.7908	−	61.7908i	0.451027	−	0.451027i	0.895695	+	0.444668i	$0.146678\pi$
$138$	0.306086	−	0.306086i	0.00221801	−	0.00221801i
$139$	−107.381			−0.772527			−0.386263	−	0.922389i	$-0.626234\pi$
$139$	−107.381			−0.772527			−0.386263	+	0.922389i	$0.626234\pi$
$140$		−	48.3656i		−	0.345468i
$141$	11.6357	−	11.6357i	0.0825227	−	0.0825227i
$142$		−	105.985i		−	0.746370i
$143$	28.4386	+	15.5183i	0.198871	+	0.108520i
$144$	35.8587			0.249019
$145$	33.5499	+	33.5499i	0.231378	+	0.231378i
$146$	187.984			1.28756
$147$			12.7745i			0.0869012i
$148$	−8.78866	−	8.78866i	−0.0593828	−	0.0593828i
$149$	−38.2045	−	38.2045i	−0.256406	−	0.256406i	0.567185	−	0.823591i	$-0.308033\pi$
$149$	−38.2045	−	38.2045i	−0.256406	−	0.256406i	−0.823591	+	0.567185i	$0.808033\pi$
$150$	−0.939834	+	0.939834i	−0.00626556	+	0.00626556i
$151$	160.846	−	160.846i	1.06521	−	1.06521i	0.0674880	−	0.997720i	$-0.478502\pi$
$151$	160.846	−	160.846i	1.06521	−	1.06521i	0.997720	−	0.0674880i	$-0.0214984\pi$
$152$	1.42293			0.00936138
$153$		−	236.584i		−	1.54630i
$154$	26.9515	−	26.9515i	0.175010	−	0.175010i
$155$		−	64.6542i		−	0.417124i
$156$	4.68879	−	1.37818i	0.0300563	−	0.00883449i
$157$	63.2532			0.402886			0.201443	−	0.979500i	$-0.435437\pi$
$157$	63.2532			0.402886			0.201443	+	0.979500i	$0.435437\pi$
$158$	−22.6916	−	22.6916i	−0.143618	−	0.143618i
$159$	−13.2417			−0.0832811
$160$			12.6491i			0.0790569i
$161$	12.4528	+	12.4528i	0.0773467	+	0.0773467i
$162$	−80.0473	−	80.0473i	−0.494119	−	0.494119i
$163$	−215.680	+	215.680i	−1.32319	+	1.32319i	−0.412009	+	0.911180i	$0.635173\pi$
$163$	−215.680	+	215.680i	−1.32319	+	1.32319i	−0.911180	+	0.412009i	$0.864827\pi$
$164$	34.1805	−	34.1805i	0.208417	−	0.208417i
$165$	−1.04744			−0.00634812
$166$		−	169.827i		−	1.02306i
$167$	108.083	−	108.083i	0.647204	−	0.647204i	−0.305112	−	0.952316i	$-0.598694\pi$
$167$	108.083	−	108.083i	0.647204	−	0.647204i	0.952316	+	0.305112i	$0.0986940\pi$
$168$		−	5.74973i		−	0.0342246i
$169$	−142.121	+	91.4479i	−0.840950	+	0.541112i
$170$	83.4549			0.490911
$171$	−3.18902	−	3.18902i	−0.0186493	−	0.0186493i
$172$	123.146			0.715963
$173$			192.962i			1.11539i	0.830047	+	0.557694i	$0.188314\pi$
$173$			192.962i			1.11539i	−0.830047	+	0.557694i	$0.811686\pi$
$174$	3.98843	+	3.98843i	0.0229220	+	0.0229220i
$175$	−38.2363	−	38.2363i	−0.218493	−	0.218493i
$176$	−7.04868	+	7.04868i	−0.0400493	+	0.0400493i
$177$	0.450611	−	0.450611i	0.00254583	−	0.00254583i
$178$	−7.07506			−0.0397475
$179$			304.318i			1.70010i	0.526701	+	0.850051i	$0.323429\pi$
$179$			304.318i			1.70010i	−0.526701	+	0.850051i	$0.676571\pi$
$180$	28.3488	−	28.3488i	0.157493	−	0.157493i
$181$		−	14.6359i		−	0.0808616i	−0.999182	−	0.0404308i	$-0.987127\pi$
$181$		−	14.6359i		−	0.0808616i	0.999182	−	0.0404308i	$-0.0128730\pi$
$182$	56.0700	+	190.759i	0.308077	+	1.04813i
$183$	−17.3441			−0.0947767
$184$	−3.25680	−	3.25680i	−0.0177000	−	0.0177000i
$185$	−13.8961			−0.0751140
$186$		−	7.68614i		−	0.0413233i
$187$	46.5050	+	46.5050i	0.248690	+	0.248690i
$188$	−123.806	−	123.806i	−0.658542	−	0.658542i
$189$	−25.8230	+	25.8230i	−0.136630	+	0.136630i
$190$	1.12492	−	1.12492i	0.00592065	−	0.00592065i
$191$	30.9288			0.161931			0.0809654	−	0.996717i	$-0.474200\pi$
$191$	30.9288			0.161931			0.0809654	+	0.996717i	$0.474200\pi$
$192$			1.50374i			0.00783195i
$193$	92.4616	−	92.4616i	0.479076	−	0.479076i	−0.425760	−	0.904836i	$-0.639993\pi$
$193$	92.4616	−	92.4616i	0.479076	−	0.479076i	0.904836	+	0.425760i	$0.139993\pi$
$194$		−	77.6210i		−	0.400108i
$195$	2.61727	−	4.79636i	0.0134219	−	0.0245967i
$196$	135.923			0.693483
$197$	−233.243	−	233.243i	−1.18398	−	1.18398i	−0.978705	−	0.205272i	$-0.934192\pi$
$197$	−233.243	−	233.243i	−1.18398	−	1.18398i	−0.205272	−	0.978705i	$-0.565808\pi$
$198$	31.5945			0.159568
$199$			124.528i			0.625768i	0.949791	+	0.312884i	$0.101295\pi$
$199$			124.528i			0.625768i	−0.949791	+	0.312884i	$0.898705\pi$
$200$	10.0000	+	10.0000i	0.0500000	+	0.0500000i
$201$	10.3358	+	10.3358i	0.0514218	+	0.0514218i
$202$	92.3028	−	92.3028i	0.456945	−	0.456945i
$203$	−162.266	+	162.266i	−0.799339	+	0.799339i
$204$	9.92118			0.0486332
$205$		−	54.0441i		−	0.263630i
$206$	−149.203	+	149.203i	−0.724288	+	0.724288i
$207$			14.5981i			0.0705221i
$208$	−14.6641	−	49.8895i	−0.0705003	−	0.239854i
$209$	1.25372			0.00599866
$210$	−4.54556	−	4.54556i	−0.0216455	−	0.0216455i
$211$	140.279			0.664830			0.332415	−	0.943133i	$-0.392137\pi$
$211$	140.279			0.664830			0.332415	+	0.943133i	$0.392137\pi$
$212$			140.894i			0.664594i
$213$	−9.96080	−	9.96080i	−0.0467643	−	0.0467643i
$214$	−53.2509	−	53.2509i	−0.248836	−	0.248836i
$215$	97.3551	−	97.3551i	0.452815	−	0.452815i
$216$	6.75353	−	6.75353i	0.0312663	−	0.0312663i
$217$	312.704			1.44103
$218$		−	74.6351i		−	0.342363i
$219$	17.6674	−	17.6674i	0.0806728	−	0.0806728i
$220$			11.1449i			0.0506588i
$221$	−329.156	+	96.7490i	−1.48939	+	0.437778i
$222$	−1.65198			−0.00744134
$223$	127.237	+	127.237i	0.570570	+	0.570570i	0.932288	−	0.361718i	$-0.117810\pi$
$223$	127.237	+	127.237i	0.570570	+	0.570570i	−0.361718	+	0.932288i	$0.617810\pi$
$224$	−61.1781			−0.273117
$225$		−	44.8233i		−	0.199215i
$226$	−151.110	−	151.110i	−0.668629	−	0.668629i
$227$	83.4558	+	83.4558i	0.367647	+	0.367647i	0.866618	−	0.498972i	$-0.166289\pi$
$227$	83.4558	+	83.4558i	0.367647	+	0.367647i	−0.498972	+	0.866618i	$0.666289\pi$
$228$	0.133732	−	0.133732i	0.000586543	−	0.000586543i
$229$	−268.902	+	268.902i	−1.17424	+	1.17424i	−0.193055	+	0.981188i	$0.561840\pi$
$229$	−268.902	+	268.902i	−1.17424	+	1.17424i	−0.981188	+	0.193055i	$0.938160\pi$
$230$	−5.14946			−0.0223890
$231$		−	5.06600i		−	0.0219307i
$232$	42.4376	−	42.4376i	0.182921	−	0.182921i
$233$		−	24.5841i		−	0.105511i	−0.998607	−	0.0527555i	$-0.983200\pi$
$233$		−	24.5841i		−	0.105511i	0.998607	−	0.0527555i	$-0.0168004\pi$
$234$	−78.9461	+	144.675i	−0.337377	+	0.618271i
$235$	−195.754			−0.832997
$236$	−4.79458	−	4.79458i	−0.0203160	−	0.0203160i
$237$	−4.26527			−0.0179969
$238$			403.634i			1.69594i
$239$	49.0770	+	49.0770i	0.205343	+	0.205343i	0.802285	−	0.596942i	$-0.203618\pi$
$239$	49.0770	+	49.0770i	0.205343	+	0.205343i	−0.596942	+	0.802285i	$0.703618\pi$
$240$	1.18881	+	1.18881i	0.00495336	+	0.00495336i
$241$	−207.700	+	207.700i	−0.861825	+	0.861825i	−0.991550	−	0.129725i	$-0.958591\pi$
$241$	−207.700	+	207.700i	−0.861825	+	0.861825i	0.129725	+	0.991550i	$0.458591\pi$
$242$	114.790	−	114.790i	0.474337	−	0.474337i
$243$	−45.4371			−0.186984
$244$			184.545i			0.756330i
$245$	107.456	−	107.456i	0.438597	−	0.438597i
$246$		−	6.42480i		−	0.0261171i
$247$	−3.13271	+	5.74095i	−0.0126830	+	0.0232427i
$248$	−81.7818			−0.329765
$249$	−15.9609	−	15.9609i	−0.0641002	−	0.0641002i
$250$	15.8114			0.0632456
$251$		−	196.267i		−	0.781941i	−0.920403	−	0.390971i	$-0.872139\pi$
$251$		−	196.267i		−	0.781941i	0.920403	−	0.390971i	$-0.127861\pi$
$252$	137.110	+	137.110i	0.544089	+	0.544089i
$253$	−2.86952	−	2.86952i	−0.0113420	−	0.0113420i
$254$	68.4199	−	68.4199i	0.269370	−	0.269370i
$255$	7.84338	−	7.84338i	0.0307584	−	0.0307584i
$256$	16.0000			0.0625000
$257$			193.812i			0.754132i	0.926186	+	0.377066i	$0.123067\pi$
$257$			193.812i			0.754132i	−0.926186	+	0.377066i	$0.876933\pi$
$258$	11.5736	−	11.5736i	0.0448591	−	0.0448591i
$259$		−	67.2092i		−	0.259495i
$260$	−51.0341	−	27.8482i	−0.196285	−	0.107108i
$261$	−190.219			−0.728810
$262$	99.5106	+	99.5106i	0.379811	+	0.379811i
$263$	−16.6858			−0.0634441			−0.0317220	−	0.999497i	$-0.510099\pi$
$263$	−16.6858			−0.0634441			−0.0317220	+	0.999497i	$0.510099\pi$
$264$			1.32492i			0.00501863i
$265$	111.386	+	111.386i	0.420326	+	0.420326i
$266$	5.44076	+	5.44076i	0.0204540	+	0.0204540i
$267$	−0.664938	+	0.664938i	−0.00249041	+	0.00249041i
$268$	109.975	−	109.975i	0.410353	−	0.410353i
$269$	342.640			1.27376			0.636878	−	0.770964i	$-0.280225\pi$
$269$	342.640			1.27376			0.636878	+	0.770964i	$0.280225\pi$
$270$		−	10.6783i		−	0.0395491i
$271$	272.106	−	272.106i	1.00408	−	1.00408i	0.00408843	−	0.999992i	$-0.498699\pi$
$271$	272.106	−	272.106i	1.00408	−	1.00408i	0.999992	−	0.00408843i	$-0.00130139\pi$
$272$		−	105.563i		−	0.388099i
$273$	23.1979	+	12.6586i	0.0849739	+	0.0463683i
$274$	−123.582			−0.451027
$275$	8.81084	+	8.81084i	0.0320394	+	0.0320394i
$276$	−0.612171			−0.00221801
$277$		−	233.439i		−	0.842741i	−0.906889	−	0.421371i	$-0.861549\pi$
$277$		−	233.439i		−	0.842741i	0.906889	−	0.421371i	$-0.138451\pi$
$278$	107.381	+	107.381i	0.386263	+	0.386263i
$279$	183.287	+	183.287i	0.656942	+	0.656942i
$280$	−48.3656	+	48.3656i	−0.172734	+	0.172734i
$281$	118.487	−	118.487i	0.421663	−	0.421663i	−0.464113	−	0.885776i	$-0.653627\pi$
$281$	118.487	−	118.487i	0.421663	−	0.421663i	0.885776	+	0.464113i	$0.153627\pi$
$282$	−23.2714			−0.0825227
$283$			128.404i			0.453724i	0.973927	+	0.226862i	$0.0728466\pi$
$283$			128.404i			0.453724i	−0.973927	+	0.226862i	$0.927153\pi$
$284$	−105.985	+	105.985i	−0.373185	+	0.373185i
$285$		−	0.211449i		−	0.000741925i
$286$	−12.9203	−	43.9569i	−0.0451758	−	0.153695i
$287$	261.387			0.910756
$288$	−35.8587	−	35.8587i	−0.124509	−	0.124509i
$289$	−407.472			−1.40994
$290$		−	67.0997i		−	0.231378i
$291$	−7.29509	−	7.29509i	−0.0250690	−	0.0250690i
$292$	−187.984	−	187.984i	−0.643780	−	0.643780i
$293$	328.829	−	328.829i	1.12228	−	1.12228i	0.130884	−	0.991398i	$-0.458218\pi$
$293$	328.829	−	328.829i	1.12228	−	1.12228i	0.991398	−	0.130884i	$-0.0417816\pi$
$294$	12.7745	−	12.7745i	0.0434506	−	0.0434506i
$295$	−7.58090			−0.0256980
$296$			17.5773i			0.0593828i
$297$	5.95043	−	5.95043i	0.0200351	−	0.0200351i
$298$			76.4090i			0.256406i
$299$	20.3100	−	5.96975i	0.0679266	−	0.0199657i
$300$	1.87967			0.00626556
$301$	470.863	+	470.863i	1.56433	+	1.56433i
$302$	−321.693			−1.06521
$303$		−	17.3499i		−	0.0572603i
$304$	−1.42293	−	1.42293i	−0.00468069	−	0.00468069i
$305$	145.895	+	145.895i	0.478345	+	0.478345i
$306$	−236.584	+	236.584i	−0.773152	+	0.773152i
$307$	−156.260	+	156.260i	−0.508990	+	0.508990i	−0.914217	−	0.405226i	$-0.867193\pi$
$307$	−156.260	+	156.260i	−0.508990	+	0.508990i	0.405226	+	0.914217i	$0.367193\pi$
$308$	−53.9031			−0.175010
$309$			28.0453i			0.0907614i
$310$	−64.6542	+	64.6542i	−0.208562	+	0.208562i
$311$		−	392.832i		−	1.26313i	−0.775325	−	0.631563i	$-0.782414\pi$
$311$		−	392.832i		−	1.26313i	0.775325	−	0.631563i	$-0.217586\pi$
$312$	−6.06697	−	3.31061i	−0.0194454	−	0.0106109i
$313$	−504.068			−1.61044			−0.805220	−	0.592976i	$-0.797953\pi$
$313$	−504.068			−1.61044			−0.805220	+	0.592976i	$0.797953\pi$
$314$	−63.2532	−	63.2532i	−0.201443	−	0.201443i
$315$	216.791			0.688224
$316$			45.3832i			0.143618i
$317$	−353.425	−	353.425i	−1.11490	−	1.11490i	−0.992478	−	0.122426i	$-0.960932\pi$
$317$	−353.425	−	353.425i	−1.11490	−	1.11490i	−0.122426	−	0.992478i	$-0.539068\pi$
$318$	13.2417	+	13.2417i	0.0416405	+	0.0416405i
$319$	37.3911	−	37.3911i	0.117213	−	0.117213i
$320$	12.6491	−	12.6491i	0.0395285	−	0.0395285i
$321$	−10.0094			−0.0311819
$322$		−	24.9056i		−	0.0773467i
$323$	−9.38805	+	9.38805i	−0.0290652	+	0.0290652i
$324$			160.095i			0.494119i
$325$	−62.3619	+	18.3301i	−0.191883	+	0.0564003i
$326$	431.359			1.32319
$327$	−7.01447	−	7.01447i	−0.0214510	−	0.0214510i
$328$	−68.3609			−0.208417
$329$		−	946.776i		−	2.87774i
$330$	1.04744	+	1.04744i	0.00317406	+	0.00317406i
$331$	−162.010	−	162.010i	−0.489455	−	0.489455i	0.418679	−	0.908134i	$-0.362493\pi$
$331$	−162.010	−	162.010i	−0.489455	−	0.489455i	−0.908134	+	0.418679i	$0.862493\pi$
$332$	−169.827	+	169.827i	−0.511528	+	0.511528i
$333$	39.3937	−	39.3937i	0.118299	−	0.118299i
$334$	−216.166			−0.647204
$335$		−	173.885i		−	0.519060i
$336$	−5.74973	+	5.74973i	−0.0171123	+	0.0171123i
$337$		−	435.251i		−	1.29155i	−0.763529	−	0.645774i	$-0.776535\pi$
$337$		−	435.251i		−	1.29155i	0.763529	−	0.645774i	$-0.223465\pi$
$338$	233.569	+	50.6727i	0.691031	+	0.149919i
$339$	−28.4037			−0.0837867
$340$	−83.4549	−	83.4549i	−0.245456	−	0.245456i
$341$	−72.0567			−0.211310
$342$			6.37804i			0.0186493i
$343$	145.002	+	145.002i	0.422747	+	0.422747i
$344$	−123.146	−	123.146i	−0.357981	−	0.357981i
$345$	−0.483964	+	0.483964i	−0.00140279	+	0.00140279i
$346$	192.962	−	192.962i	0.557694	−	0.557694i
$347$	297.980			0.858732			0.429366	−	0.903131i	$-0.358737\pi$
$347$	297.980			0.858732			0.429366	+	0.903131i	$0.358737\pi$
$348$		−	7.97686i		−	0.0229220i
$349$	374.694	−	374.694i	1.07362	−	1.07362i	0.0765559	−	0.997065i	$-0.475608\pi$
$349$	374.694	−	374.694i	1.07362	−	1.07362i	0.997065	−	0.0765559i	$-0.0243924\pi$
$350$			76.4727i			0.218493i
$351$	12.3793	+	42.1163i	0.0352686	+	0.119989i
$352$	14.0974			0.0400493
$353$	−218.962	−	218.962i	−0.620289	−	0.620289i	0.325316	−	0.945605i	$-0.394529\pi$
$353$	−218.962	−	218.962i	−0.620289	−	0.620289i	−0.945605	+	0.325316i	$0.894529\pi$
$354$	−0.901222			−0.00254583
$355$			167.576i			0.472046i
$356$	7.07506	+	7.07506i	0.0198738	+	0.0198738i
$357$	37.9349	+	37.9349i	0.106260	+	0.106260i
$358$	304.318	−	304.318i	0.850051	−	0.850051i
$359$	145.885	−	145.885i	0.406366	−	0.406366i	−0.474103	−	0.880469i	$-0.657228\pi$
$359$	145.885	−	145.885i	0.406366	−	0.406366i	0.880469	+	0.474103i	$0.157228\pi$
$360$	−56.6975			−0.157493
$361$		−	360.747i		−	0.999299i
$362$	−14.6359	+	14.6359i	−0.0404308	+	0.0404308i
$363$		−	21.5766i		−	0.0594397i
$364$	134.689	−	246.829i	0.370025	−	0.678102i
$365$	−297.228			−0.814324
$366$	17.3441	+	17.3441i	0.0473883	+	0.0473883i
$367$	−229.252			−0.624665			−0.312333	−	0.949973i	$-0.601110\pi$
$367$	−229.252			−0.624665			−0.312333	+	0.949973i	$0.601110\pi$
$368$			6.51361i			0.0177000i
$369$	153.208	+	153.208i	0.415199	+	0.415199i
$370$	13.8961	+	13.8961i	0.0375570	+	0.0375570i
$371$	−538.726	+	538.726i	−1.45209	+	1.45209i
$372$	−7.68614	+	7.68614i	−0.0206617	+	0.0206617i
$373$	−461.367			−1.23691			−0.618455	−	0.785821i	$-0.712241\pi$
$373$	−461.367			−1.23691			−0.618455	+	0.785821i	$0.712241\pi$
$374$		−	93.0100i		−	0.248690i
$375$	1.48601	−	1.48601i	0.00396269	−	0.00396269i
$376$			247.612i			0.658542i
$377$	77.7885	+	264.649i	0.206335	+	0.701987i
$378$	51.6460			0.136630
$379$	416.393	+	416.393i	1.09866	+	1.09866i	0.994567	+	0.104095i	$0.0331945\pi$
$379$	416.393	+	416.393i	1.09866	+	1.09866i	0.104095	+	0.994567i	$0.466806\pi$
$380$	−2.24985			−0.00592065
$381$		−	12.8607i		−	0.0337551i
$382$	−30.9288	−	30.9288i	−0.0809654	−	0.0809654i
$383$	−50.2312	−	50.2312i	−0.131152	−	0.131152i	0.638484	−	0.769635i	$-0.279562\pi$
$383$	−50.2312	−	50.2312i	−0.131152	−	0.131152i	−0.769635	+	0.638484i	$0.779562\pi$
$384$	1.50374	−	1.50374i	0.00391598	−	0.00391598i
$385$	−42.6141	+	42.6141i	−0.110686	+	0.110686i
$386$	−184.923			−0.479076
$387$			551.980i			1.42630i
$388$	−77.6210	+	77.6210i	−0.200054	+	0.200054i
$389$		−	124.097i		−	0.319016i	−0.987197	−	0.159508i	$-0.949009\pi$
$389$		−	124.097i		−	0.319016i	0.987197	−	0.159508i	$-0.0509907\pi$
$390$	−7.41363	+	2.17909i	−0.0190093	+	0.00558742i
$391$	42.9748			0.109910
$392$	−135.923	−	135.923i	−0.346741	−	0.346741i
$393$	18.7047			0.0475946
$394$			466.487i			1.18398i
$395$	35.8786	+	35.8786i	0.0908319	+	0.0908319i
$396$	−31.5945	−	31.5945i	−0.0797841	−	0.0797841i
$397$	115.669	−	115.669i	0.291358	−	0.291358i	−0.546258	−	0.837617i	$-0.683948\pi$
$397$	115.669	−	115.669i	0.291358	−	0.291358i	0.837617	+	0.546258i	$0.183948\pi$
$398$	124.528	−	124.528i	0.312884	−	0.312884i
$399$	1.02268			0.00256311
$400$		−	20.0000i		−	0.0500000i
$401$	−458.578	+	458.578i	−1.14359	+	1.14359i	−0.155797	+	0.987789i	$0.549795\pi$
$401$	−458.578	+	458.578i	−1.14359	+	1.14359i	−0.987789	+	0.155797i	$0.950205\pi$
$402$		−	20.6716i		−	0.0514218i
$403$	180.050	−	329.957i	0.446775	−	0.818752i
$404$	−184.606			−0.456945
$405$	126.566	+	126.566i	0.312508	+	0.312508i
$406$	324.532			0.799339
$407$			15.4871i			0.0380518i
$408$	−9.92118	−	9.92118i	−0.0243166	−	0.0243166i
$409$	−47.4016	−	47.4016i	−0.115896	−	0.115896i	0.646780	−	0.762676i	$-0.276115\pi$
$409$	−47.4016	−	47.4016i	−0.115896	−	0.115896i	−0.762676	+	0.646780i	$0.776115\pi$
$410$	−54.0441	+	54.0441i	−0.131815	+	0.131815i
$411$	−11.6146	+	11.6146i	−0.0282594	+	0.0282594i
$412$	298.406			0.724288
$413$		−	36.6654i		−	0.0887783i
$414$	14.5981	−	14.5981i	0.0352611	−	0.0352611i
$415$			268.520i			0.647037i
$416$	−35.2255	+	64.5536i	−0.0846766	+	0.155177i
$417$	20.1841			0.0484031
$418$	−1.25372	−	1.25372i	−0.00299933	−	0.00299933i
$419$	566.058			1.35097			0.675487	−	0.737372i	$-0.263934\pi$
$419$	566.058			1.35097			0.675487	+	0.737372i	$0.263934\pi$
$420$			9.09112i			0.0216455i
$421$	−50.5382	−	50.5382i	−0.120043	−	0.120043i	0.644533	−	0.764576i	$-0.277052\pi$
$421$	−50.5382	−	50.5382i	−0.120043	−	0.120043i	−0.764576	+	0.644533i	$0.777052\pi$
$422$	−140.279	−	140.279i	−0.332415	−	0.332415i
$423$	554.939	−	554.939i	1.31191	−	1.31191i
$424$	140.894	−	140.894i	0.332297	−	0.332297i
$425$	−131.954			−0.310480
$426$			19.9216i			0.0467643i
$427$	−705.631	+	705.631i	−1.65253	+	1.65253i
$428$			106.502i			0.248836i
$429$	−5.34551	−	2.91693i	−0.0124604	−	0.00679936i
$430$	−194.710			−0.452815
$431$	333.638	+	333.638i	0.774103	+	0.774103i	0.978821	−	0.204718i	$-0.0656277\pi$
$431$	333.638	+	333.638i	0.774103	+	0.774103i	−0.204718	+	0.978821i	$0.565628\pi$
$432$	−13.5071			−0.0312663
$433$			564.564i			1.30384i	0.758286	+	0.651922i	$0.226037\pi$
$433$			564.564i			1.30384i	−0.758286	+	0.651922i	$0.773963\pi$
$434$	−312.704	−	312.704i	−0.720515	−	0.720515i
$435$	−6.30626	−	6.30626i	−0.0144972	−	0.0144972i
$436$	−74.6351	+	74.6351i	−0.171181	+	0.171181i
$437$	0.579275	−	0.579275i	0.00132557	−	0.00132557i
$438$	−35.3347			−0.0806728
$439$			39.2264i			0.0893541i	0.999001	+	0.0446770i	$0.0142259\pi$
$439$			39.2264i			0.0893541i	−0.999001	+	0.0446770i	$0.985774\pi$
$440$	11.1449	−	11.1449i	0.0253294	−	0.0253294i
$441$			609.251i			1.38152i
$442$	425.905	+	232.407i	0.963585	+	0.525807i
$443$	−288.946			−0.652248			−0.326124	−	0.945327i	$-0.605743\pi$
$443$	−288.946			−0.652248			−0.326124	+	0.945327i	$0.605743\pi$
$444$	1.65198	+	1.65198i	0.00372067	+	0.00372067i
$445$	11.1866			0.0251385
$446$		−	254.474i		−	0.570570i
$447$	7.18118	+	7.18118i	0.0160653	+	0.0160653i
$448$	61.1781	+	61.1781i	0.136558	+	0.136558i
$449$	196.065	−	196.065i	0.436671	−	0.436671i	−0.454219	−	0.890890i	$-0.650082\pi$
$449$	196.065	−	196.065i	0.436671	−	0.436671i	0.890890	+	0.454219i	$0.150082\pi$
$450$	−44.8233	+	44.8233i	−0.0996074	+	0.0996074i
$451$	−60.2318			−0.133552
$452$			302.220i			0.668629i
$453$	−30.2338	+	30.2338i	−0.0667413	+	0.0667413i
$454$		−	166.912i		−	0.367647i
$455$	−88.6545	−	301.617i	−0.194845	−	0.662894i
$456$	−0.267464			−0.000586543
$457$	−263.894	−	263.894i	−0.577448	−	0.577448i	0.356751	−	0.934199i	$-0.383884\pi$
$457$	−263.894	−	263.894i	−0.577448	−	0.577448i	−0.934199	+	0.356751i	$0.883884\pi$
$458$	537.803			1.17424
$459$			89.1153i			0.194151i
$460$	5.14946	+	5.14946i	0.0111945	+	0.0111945i
$461$	379.177	+	379.177i	0.822510	+	0.822510i	0.986467	−	0.163957i	$-0.0524259\pi$
$461$	379.177	+	379.177i	0.822510	+	0.822510i	−0.163957	+	0.986467i	$0.552426\pi$
$462$	−5.06600	+	5.06600i	−0.0109654	+	0.0109654i
$463$	−499.905	+	499.905i	−1.07971	+	1.07971i	−0.0831730	+	0.996535i	$0.526505\pi$
$463$	−499.905	+	499.905i	−1.07971	+	1.07971i	−0.996535	+	0.0831730i	$0.973495\pi$
$464$	−84.8752			−0.182921
$465$			12.1529i			0.0261352i
$466$	−24.5841	+	24.5841i	−0.0527555	+	0.0527555i
$467$			732.570i			1.56867i	0.620335	+	0.784337i	$0.286996\pi$
$467$			732.570i			1.56867i	−0.620335	+	0.784337i	$0.713004\pi$
$468$	223.622	−	65.7293i	0.477824	−	0.140447i
$469$	841.004			1.79319
$470$	195.754	+	195.754i	0.416498	+	0.416498i
$471$	−11.8895			−0.0252431
$472$			9.58916i			0.0203160i
$473$	−108.502	−	108.502i	−0.229390	−	0.229390i
$474$	4.26527	+	4.26527i	0.00899846	+	0.00899846i
$475$	−1.77866	+	1.77866i	−0.00374455	+	0.00374455i
$476$	403.634	−	403.634i	0.847971	−	0.847971i
$477$	−631.533			−1.32397
$478$		−	98.1540i		−	0.205343i
$479$	−403.609	+	403.609i	−0.842607	+	0.842607i	−0.989197	−	0.146590i	$-0.953170\pi$
$479$	−403.609	+	403.609i	−0.842607	+	0.842607i	0.146590	+	0.989197i	$0.453170\pi$
$480$		−	2.37761i		−	0.00495336i
$481$	−70.9174	−	38.6981i	−0.147438	−	0.0804534i
$482$	415.400			0.861825
$483$	−2.34072	−	2.34072i	−0.00484621	−	0.00484621i
$484$	−229.579			−0.474337
$485$			122.730i			0.253051i
$486$	45.4371	+	45.4371i	0.0934920	+	0.0934920i
$487$	−144.597	−	144.597i	−0.296914	−	0.296914i	0.542890	−	0.839804i	$-0.317330\pi$
$487$	−144.597	−	144.597i	−0.296914	−	0.296914i	−0.839804	+	0.542890i	$0.817330\pi$
$488$	184.545	−	184.545i	0.378165	−	0.378165i
$489$	40.5406	−	40.5406i	0.0829052	−	0.0829052i
$490$	−214.913			−0.438597
$491$		−	458.846i		−	0.934513i	−0.884122	−	0.467256i	$-0.845243\pi$
$491$		−	458.846i		−	0.934513i	0.884122	−	0.467256i	$-0.154757\pi$
$492$	−6.42480	+	6.42480i	−0.0130585	+	0.0130585i
$493$			559.980i			1.13586i
$494$	8.87366	−	2.60824i	0.0179629	−	0.00527984i
$495$	−49.9553			−0.100920
$496$	81.7818	+	81.7818i	0.164883	+	0.164883i
$497$	−810.492			−1.63077
$498$			31.9219i			0.0641002i
$499$	−212.583	−	212.583i	−0.426018	−	0.426018i	0.461251	−	0.887270i	$-0.347401\pi$
$499$	−212.583	−	212.583i	−0.426018	−	0.426018i	−0.887270	+	0.461251i	$0.847401\pi$
$500$	−15.8114	−	15.8114i	−0.0316228	−	0.0316228i
$501$	−20.3160	+	20.3160i	−0.0405510	+	0.0405510i
$502$	−196.267	+	196.267i	−0.390971	+	0.390971i
$503$	607.595			1.20794			0.603972	−	0.797006i	$-0.293584\pi$
$503$	607.595			1.20794			0.603972	+	0.797006i	$0.293584\pi$
$504$		−	274.221i		−	0.544089i
$505$	−145.944	+	145.944i	−0.288997	+	0.288997i
$506$			5.73904i			0.0113420i
$507$	26.7140	−	17.1892i	0.0526903	−	0.0339037i
$508$	−136.840			−0.269370
$509$	20.2278	+	20.2278i	0.0397404	+	0.0397404i	0.726698	−	0.686957i	$-0.241054\pi$
$509$	20.2278	+	20.2278i	0.0397404	+	0.0397404i	−0.686957	+	0.726698i	$0.741054\pi$
$510$	−15.6868			−0.0307584
$511$		−	1437.56i		−	2.81323i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	1.20122	+	1.20122i	0.00234157	+	0.00234157i
$514$	193.812	−	193.812i	0.377066	−	0.377066i
$515$	235.911	−	235.911i	0.458080	−	0.458080i
$516$	−23.1473			−0.0448591
$517$			218.167i			0.421986i
$518$	−67.2092	+	67.2092i	−0.129747	+	0.129747i
$519$		−	36.2705i		−	0.0698853i
$520$	23.1859	+	78.8823i	0.0445883	+	0.151697i
$521$	252.102			0.483881			0.241940	−	0.970291i	$-0.422216\pi$
$521$	252.102			0.483881			0.241940	+	0.970291i	$0.422216\pi$
$522$	190.219	+	190.219i	0.364405	+	0.364405i
$523$	−941.789			−1.80074			−0.900372	−	0.435122i	$-0.856705\pi$
$523$	−941.789			−1.80074			−0.900372	+	0.435122i	$0.856705\pi$
$524$		−	199.021i		−	0.379811i
$525$	7.18716	+	7.18716i	0.0136898	+	0.0136898i
$526$	16.6858	+	16.6858i	0.0317220	+	0.0317220i
$527$	539.571	−	539.571i	1.02385	−	1.02385i
$528$	1.32492	−	1.32492i	0.00250931	−	0.00250931i
$529$	526.348			0.994987
$530$		−	222.773i		−	0.420326i
$531$	21.4909	−	21.4909i	0.0404725	−	0.0404725i
$532$		−	10.8815i		−	0.0204540i
$533$	150.503	−	275.809i	0.282369	−	0.517465i
$534$	1.32988			0.00249041
$535$	84.1970	+	84.1970i	0.157378	+	0.157378i
$536$	−219.949			−0.410353
$537$		−	57.2017i		−	0.106521i
$538$	−342.640	−	342.640i	−0.636878	−	0.636878i
$539$	−119.759	−	119.759i	−0.222188	−	0.222188i
$540$	−10.6783	+	10.6783i	−0.0197746	+	0.0197746i
$541$	465.529	−	465.529i	0.860497	−	0.860497i	−0.130898	−	0.991396i	$-0.541786\pi$
$541$	465.529	−	465.529i	0.860497	−	0.860497i	0.991396	+	0.130898i	$0.0417861\pi$
$542$	−544.211			−1.00408
$543$			2.75107i			0.00506643i
$544$	−105.563	+	105.563i	−0.194050	+	0.194050i
$545$			118.008i			0.216529i
$546$	−10.5393	−	35.8564i	−0.0193028	−	0.0656711i
$547$	−477.379			−0.872722			−0.436361	−	0.899772i	$-0.643733\pi$
$547$	−477.379			−0.872722			−0.436361	+	0.899772i	$0.643733\pi$
$548$	123.582	+	123.582i	0.225514	+	0.225514i
$549$	−827.190			−1.50672
$550$		−	17.6217i		−	0.0320394i
$551$	7.54821	+	7.54821i	0.0136991	+	0.0136991i
$552$	0.612171	+	0.612171i	0.00110901	+	0.00110901i
$553$	−173.529	+	173.529i	−0.313795	+	0.313795i
$554$	−233.439	+	233.439i	−0.421371	+	0.421371i
$555$	2.61200			0.00470631
$556$		−	214.762i		−	0.386263i
$557$	402.711	−	402.711i	0.723000	−	0.723000i	−0.246215	−	0.969215i	$-0.579187\pi$
$557$	402.711	−	402.711i	0.723000	−	0.723000i	0.969215	+	0.246215i	$0.0791871\pi$
$558$		−	366.573i		−	0.656942i
$559$	767.959	−	225.727i	1.37381	−	0.403805i
$560$	96.7311			0.172734
$561$	−8.74140	−	8.74140i	−0.0155818	−	0.0155818i
$562$	−236.975			−0.421663
$563$		−	1054.07i		−	1.87223i	−0.351693	−	0.936115i	$-0.614394\pi$
$563$		−	1054.07i		−	1.87223i	0.351693	−	0.936115i	$-0.385606\pi$
$564$	23.2714	+	23.2714i	0.0412613	+	0.0412613i
$565$	238.926	+	238.926i	0.422878	+	0.422878i
$566$	128.404	−	128.404i	0.226862	−	0.226862i
$567$	−612.143	+	612.143i	−1.07962	+	1.07962i
$568$	211.969			0.373185
$569$			94.6489i			0.166343i	0.996535	+	0.0831713i	$0.0265049\pi$
$569$			94.6489i			0.166343i	−0.996535	+	0.0831713i	$0.973495\pi$
$570$	−0.211449	+	0.211449i	−0.000370962	+	0.000370962i
$571$			277.863i			0.486625i	0.969948	+	0.243312i	$0.0782340\pi$
$571$			277.863i			0.486625i	−0.969948	+	0.243312i	$0.921766\pi$
$572$	−31.0366	+	56.8772i	−0.0542598	+	0.0994356i
$573$	−5.81359			−0.0101459
$574$	−261.387	−	261.387i	−0.455378	−	0.455378i
$575$	8.14201			0.0141600
$576$			71.7173i			0.124509i
$577$	−117.434	−	117.434i	−0.203525	−	0.203525i	0.597983	−	0.801509i	$-0.295969\pi$
$577$	−117.434	−	117.434i	−0.203525	−	0.203525i	−0.801509	+	0.597983i	$0.795969\pi$
$578$	407.472	+	407.472i	0.704970	+	0.704970i
$579$	−17.3797	+	17.3797i	−0.0300168	+	0.0300168i
$580$	−67.0997	+	67.0997i	−0.115689	+	0.115689i
$581$	−1298.71			−2.23531
$582$			14.5902i			0.0250690i
$583$	124.139	−	124.139i	0.212932	−	0.212932i
$584$			375.967i			0.643780i
$585$	124.825	−	228.752i	0.213376	−	0.391029i
$586$	−657.657			−1.12228
$587$	172.094	+	172.094i	0.293175	+	0.293175i	0.838333	−	0.545158i	$-0.183530\pi$
$587$	172.094	+	172.094i	0.293175	+	0.293175i	−0.545158	+	0.838333i	$0.683530\pi$
$588$	−25.5490			−0.0434506
$589$		−	14.5462i		−	0.0246965i
$590$	7.58090	+	7.58090i	0.0128490	+	0.0128490i
$591$	43.8421	+	43.8421i	0.0741828	+	0.0741828i
$592$	17.5773	−	17.5773i	0.0296914	−	0.0296914i
$593$	418.270	−	418.270i	0.705345	−	0.705345i	−0.260208	−	0.965553i	$-0.583791\pi$
$593$	418.270	−	418.270i	0.705345	−	0.705345i	0.965553	+	0.260208i	$0.0837910\pi$
$594$	−11.9009			−0.0200351
$595$		−	638.202i		−	1.07261i
$596$	76.4090	−	76.4090i	0.128203	−	0.128203i
$597$		−	23.4071i		−	0.0392079i
$598$	−26.2798	−	14.3403i	−0.0439462	−	0.0239804i
$599$	168.566			0.281412			0.140706	−	0.990051i	$-0.455063\pi$
$599$	168.566			0.281412			0.140706	+	0.990051i	$0.455063\pi$
$600$	−1.87967	−	1.87967i	−0.00313278	−	0.00313278i
$601$	566.888			0.943241			0.471621	−	0.881802i	$-0.343669\pi$
$601$	566.888			0.943241			0.471621	+	0.881802i	$0.343669\pi$
$602$		−	941.727i		−	1.56433i
$603$	492.943	+	492.943i	0.817484	+	0.817484i
$604$	321.693	+	321.693i	0.532604	+	0.532604i
$605$	−181.498	+	181.498i	−0.299997	+	0.299997i
$606$	−17.3499	+	17.3499i	−0.0286301	+	0.0286301i
$607$	1123.79			1.85139			0.925694	−	0.378273i	$-0.123482\pi$
$607$	1123.79			1.85139			0.925694	+	0.378273i	$0.123482\pi$
$608$			2.84586i			0.00468069i
$609$	30.5006	−	30.5006i	0.0500831	−	0.0500831i
$610$		−	291.791i		−	0.478345i
$611$	−999.014	−	545.140i	−1.63505	−	0.892209i
$612$	473.169			0.773152
$613$	233.486	+	233.486i	0.380891	+	0.380891i	0.871423	−	0.490532i	$-0.163198\pi$
$613$	233.486	+	233.486i	0.380891	+	0.380891i	−0.490532	+	0.871423i	$0.663198\pi$
$614$	312.520			0.508990
$615$			10.1585i			0.0165179i
$616$	53.9031	+	53.9031i	0.0875050	+	0.0875050i
$617$	659.727	+	659.727i	1.06925	+	1.06925i	0.997417	+	0.0718332i	$0.0228849\pi$
$617$	659.727	+	659.727i	1.06925	+	1.06925i	0.0718332	+	0.997417i	$0.477115\pi$
$618$	28.0453	−	28.0453i	0.0453807	−	0.0453807i
$619$	25.5045	−	25.5045i	0.0412027	−	0.0412027i	−0.686205	−	0.727408i	$-0.740725\pi$
$619$	25.5045	−	25.5045i	0.0412027	−	0.0412027i	0.727408	+	0.686205i	$0.240725\pi$
$620$	129.308			0.208562
$621$		−	5.49873i		−	0.00885463i
$622$	−392.832	+	392.832i	−0.631563	+	0.631563i
$623$			54.1048i			0.0868457i
$624$	2.75636	+	9.37758i	0.00441724	+	0.0150282i
$625$	−25.0000			−0.0400000
$626$	504.068	+	504.068i	0.805220	+	0.805220i
$627$	−0.235658			−0.000375850
$628$			126.506i			0.201443i
$629$	−115.970	−	115.970i	−0.184372	−	0.184372i
$630$	−216.791	−	216.791i	−0.344112	−	0.344112i
$631$	−184.856	+	184.856i	−0.292957	+	0.292957i	−0.838247	−	0.545290i	$-0.816419\pi$
$631$	−184.856	+	184.856i	−0.292957	+	0.292957i	0.545290	+	0.838247i	$0.316419\pi$
$632$	45.3832	−	45.3832i	0.0718089	−	0.0718089i
$633$	−26.3678			−0.0416553
$634$			706.849i			1.11490i
$635$	−108.181	+	108.181i	−0.170364	+	0.170364i
$636$		−	26.4834i		−	0.0416405i
$637$	847.640	−	249.147i	1.33067	−	0.391126i
$638$	−74.7822			−0.117213
$639$	−475.058	−	475.058i	−0.743440	−	0.743440i
$640$	−25.2982			−0.0395285
$641$		−	303.795i		−	0.473939i	−0.971517	−	0.236970i	$-0.923846\pi$
$641$		−	303.795i		−	0.473939i	0.971517	−	0.236970i	$-0.0761542\pi$
$642$	10.0094	+	10.0094i	0.0155910	+	0.0155910i
$643$	95.1695	+	95.1695i	0.148008	+	0.148008i	0.777228	−	0.629219i	$-0.216625\pi$
$643$	95.1695	+	95.1695i	0.148008	+	0.148008i	−0.629219	+	0.777228i	$0.716625\pi$
$644$	−24.9056	+	24.9056i	−0.0386734	+	0.0386734i
$645$	−18.2995	+	18.2995i	−0.0283714	+	0.0283714i
$646$	18.7761			0.0290652
$647$			1178.14i			1.82093i	0.413586	+	0.910465i	$0.364276\pi$
$647$			1178.14i			1.82093i	−0.413586	+	0.910465i	$0.635724\pi$
$648$	160.095	−	160.095i	0.247060	−	0.247060i
$649$			8.44886i			0.0130183i
$650$	80.6920	+	44.0318i	0.124142	+	0.0677413i
$651$	−58.7779			−0.0902887
$652$	−431.359	−	431.359i	−0.661594	−	0.661594i
$653$	−375.998			−0.575801			−0.287901	−	0.957660i	$-0.592957\pi$
$653$	−375.998			−0.575801			−0.287901	+	0.957660i	$0.592957\pi$
$654$			14.0289i			0.0214510i
$655$	−157.340	−	157.340i	−0.240214	−	0.240214i
$656$	68.3609	+	68.3609i	0.104209	+	0.104209i
$657$	842.606	−	842.606i	1.28250	−	1.28250i
$658$	−946.776	+	946.776i	−1.43887	+	1.43887i
$659$	−173.387			−0.263107			−0.131553	−	0.991309i	$-0.541996\pi$
$659$	−173.387			−0.263107			−0.131553	+	0.991309i	$0.541996\pi$
$660$		−	2.09488i		−	0.00317406i
$661$	288.477	−	288.477i	0.436425	−	0.436425i	−0.454382	−	0.890807i	$-0.650140\pi$
$661$	288.477	−	288.477i	0.436425	−	0.436425i	0.890807	+	0.454382i	$0.150140\pi$
$662$			324.019i			0.489455i
$663$	61.8704	−	18.1856i	0.0933188	−	0.0274293i
$664$	339.655			0.511528
$665$	−8.60260	−	8.60260i	−0.0129362	−	0.0129362i
$666$	−78.7874			−0.118299
$667$		−	34.5527i		−	0.0518032i
$668$	216.166	+	216.166i	0.323602	+	0.323602i
$669$	−23.9163	−	23.9163i	−0.0357494	−	0.0357494i
$670$	−173.885	+	173.885i	−0.259530	+	0.259530i
$671$	162.599	−	162.599i	0.242324	−	0.242324i
$672$	11.4995			0.0171123
$673$		−	356.877i		−	0.530278i	−0.964210	−	0.265139i	$-0.914582\pi$
$673$		−	356.877i		−	0.530278i	0.964210	−	0.265139i	$-0.0854178\pi$
$674$	−435.251	+	435.251i	−0.645774	+	0.645774i
$675$			16.8838i			0.0250131i
$676$	−182.896	−	284.241i	−0.270556	−	0.420475i
$677$	90.7269			0.134013			0.0670066	−	0.997753i	$-0.478655\pi$
$677$	90.7269			0.134013			0.0670066	+	0.997753i	$0.478655\pi$
$678$	28.4037	+	28.4037i	0.0418934	+	0.0418934i
$679$	−593.588			−0.874209
$680$			166.910i			0.245456i
$681$	−15.6869	−	15.6869i	−0.0230351	−	0.0230351i
$682$	72.0567	+	72.0567i	0.105655	+	0.105655i
$683$	−681.207	+	681.207i	−0.997375	+	0.997375i	−0.999997	−	0.00262177i	$-0.999165\pi$
$683$	−681.207	+	681.207i	−0.997375	+	0.997375i	0.00262177	+	0.999997i	$0.499165\pi$
$684$	6.37804	−	6.37804i	0.00932463	−	0.00932463i
$685$	195.400			0.285255
$686$		−	290.005i		−	0.422747i
$687$	50.5446	−	50.5446i	0.0735729	−	0.0735729i
$688$			246.291i			0.357981i
$689$	258.260	+	878.641i	0.374833	+	1.27524i
$690$	0.967928			0.00140279
$691$	171.721	+	171.721i	0.248510	+	0.248510i	0.820359	−	0.571849i	$-0.193774\pi$
$691$	171.721	+	171.721i	0.248510	+	0.248510i	−0.571849	+	0.820359i	$0.693774\pi$
$692$	−385.924			−0.557694
$693$		−	241.612i		−	0.348646i
$694$	−297.980	−	297.980i	−0.429366	−	0.429366i
$695$	−169.785	−	169.785i	−0.244294	−	0.244294i
$696$	−7.97686	+	7.97686i	−0.0114610	+	0.0114610i
$697$	451.024	−	451.024i	0.647094	−	0.647094i
$698$	−749.388			−1.07362
$699$			4.62099i			0.00661086i
$700$	76.4727	−	76.4727i	0.109247	−	0.109247i
$701$			995.235i			1.41974i	0.704335	+	0.709868i	$0.251246\pi$
$701$			995.235i			1.41974i	−0.704335	+	0.709868i	$0.748754\pi$
$702$	29.7370	−	54.4955i	0.0423604	−	0.0776290i
$703$	−3.12641			−0.00444724
$704$	−14.0974	−	14.0974i	−0.0200246	−	0.0200246i
$705$	36.7953			0.0521919
$706$			437.924i			0.620289i
$707$	−705.864	−	705.864i	−0.998393	−	0.998393i
$708$	0.901222	+	0.901222i	0.00127291	+	0.00127291i
$709$	−123.817	+	123.817i	−0.174637	+	0.174637i	−0.789013	−	0.614376i	$-0.789408\pi$
$709$	−123.817	+	123.817i	−0.174637	+	0.174637i	0.614376	+	0.789013i	$0.289408\pi$
$710$	167.576	−	167.576i	0.236023	−	0.236023i
$711$	−203.423			−0.286108
$712$		−	14.1501i		−	0.0198738i
$713$	−33.2934	+	33.2934i	−0.0466948	+	0.0466948i
$714$		−	75.8699i		−	0.106260i
$715$	20.4288	+	69.5019i	0.0285717	+	0.0972055i
$716$	−608.636			−0.850051
$717$	−9.22485	−	9.22485i	−0.0128659	−	0.0128659i
$718$	−291.771			−0.406366
$719$			758.861i			1.05544i	0.849418	+	0.527720i	$0.176953\pi$
$719$			758.861i			1.05544i	−0.849418	+	0.527720i	$0.823047\pi$
$720$	56.6975	+	56.6975i	0.0787466	+	0.0787466i
$721$	1141.00	+	1141.00i	1.58252	+	1.58252i
$722$	−360.747	+	360.747i	−0.499649	+	0.499649i
$723$	39.0407	−	39.0407i	0.0539982	−	0.0539982i
$724$	29.2719			0.0404308
$725$			106.094i			0.146337i
$726$	−21.5766	+	21.5766i	−0.0297199	+	0.0297199i
$727$		−	661.575i		−	0.910006i	−0.890490	−	0.455003i	$-0.849638\pi$
$727$		−	661.575i		−	0.910006i	0.890490	−	0.455003i	$-0.150362\pi$
$728$	−381.518	+	112.140i	−0.524064	+	0.154039i
$729$	−711.885			−0.976523
$730$	297.228	+	297.228i	0.407162	+	0.407162i
$731$	1624.95			2.22292
$732$		−	34.6883i		−	0.0473883i
$733$	272.217	+	272.217i	0.371373	+	0.371373i	0.867977	−	0.496604i	$-0.165420\pi$
$733$	272.217	+	272.217i	0.371373	+	0.371373i	−0.496604	+	0.867977i	$0.665420\pi$
$734$	229.252	+	229.252i	0.312333	+	0.312333i
$735$	−20.1982	+	20.1982i	−0.0274806	+	0.0274806i
$736$	6.51361	−	6.51361i	0.00885001	−	0.00885001i
$737$	−193.794			−0.262949
$738$		−	306.417i		−	0.415199i
$739$	−514.947	+	514.947i	−0.696816	+	0.696816i	−0.963723	−	0.266906i	$-0.913999\pi$
$739$	−514.947	+	514.947i	−0.696816	+	0.696816i	0.266906	+	0.963723i	$0.413999\pi$
$740$		−	27.7922i		−	0.0375570i
$741$	0.588845	−	1.07911i	0.000794663	−	0.00145629i
$742$	1077.45			1.45209
$743$	368.873	+	368.873i	0.496464	+	0.496464i	0.910335	−	0.413871i	$-0.135824\pi$
$743$	368.873	+	368.873i	0.496464	+	0.496464i	−0.413871	+	0.910335i	$0.635824\pi$
$744$	15.3723			0.0206617
$745$		−	120.813i		−	0.162165i
$746$	461.367	+	461.367i	0.618455	+	0.618455i
$747$	−761.223	−	761.223i	−1.01904	−	1.01904i
$748$	−93.0100	+	93.0100i	−0.124345	+	0.124345i
$749$	−407.224	+	407.224i	−0.543690	+	0.543690i
$750$	−2.97202			−0.00396269
$751$		−	1186.78i		−	1.58026i	−0.612939	−	0.790130i	$-0.710013\pi$
$751$		−	1186.78i		−	1.58026i	0.612939	−	0.790130i	$-0.289987\pi$
$752$	247.612	−	247.612i	0.329271	−	0.329271i
$753$			36.8917i			0.0489930i
$754$	186.860	−	342.437i	0.247826	−	0.454161i
$755$	508.641			0.673697
$756$	−51.6460	−	51.6460i	−0.0683148	−	0.0683148i
$757$	−135.304			−0.178737			−0.0893683	−	0.995999i	$-0.528485\pi$
$757$	−135.304			−0.178737			−0.0893683	+	0.995999i	$0.528485\pi$
$758$		−	832.786i		−	1.09866i
$759$	0.539375	+	0.539375i	0.000710638	+	0.000710638i
$760$	2.24985	+	2.24985i	0.00296033	+	0.00296033i
$761$	−636.311	+	636.311i	−0.836152	+	0.836152i	−0.988350	−	0.152198i	$-0.951365\pi$
$761$	−636.311	+	636.311i	−0.836152	+	0.836152i	0.152198	+	0.988350i	$0.451365\pi$
$762$	−12.8607	+	12.8607i	−0.0168775	+	0.0168775i
$763$	−570.755			−0.748040
$764$			61.8576i			0.0809654i
$765$	374.073	−	374.073i	0.488984	−	0.488984i
$766$			100.462i			0.131152i
$767$	−38.6884	−	21.1114i	−0.0504412	−	0.0275247i
$768$	−3.00747			−0.00391598
$769$	562.798	+	562.798i	0.731857	+	0.731857i	0.970987	−	0.239130i	$-0.0768624\pi$
$769$	562.798	+	562.798i	0.731857	+	0.731857i	−0.239130	+	0.970987i	$0.576862\pi$
$770$	85.2283			0.110686
$771$		−	36.4302i		−	0.0472506i
$772$	184.923	+	184.923i	0.239538	+	0.239538i
$773$	−644.968	−	644.968i	−0.834370	−	0.834370i	0.153741	−	0.988111i	$-0.450868\pi$
$773$	−644.968	−	644.968i	−0.834370	−	0.834370i	−0.988111	+	0.153741i	$0.950868\pi$
$774$	551.980	−	551.980i	0.713152	−	0.713152i
$775$	102.227	−	102.227i	0.131906	−	0.131906i
$776$	155.242			0.200054
$777$			12.6331i			0.0162588i
$778$	−124.097	+	124.097i	−0.159508	+	0.159508i
$779$		−	12.1591i		−	0.0156086i
$780$	9.59272	+	5.23453i	0.0122984	+	0.00671094i
$781$	186.763			0.239133
$782$	−42.9748	−	42.9748i	−0.0549549	−	0.0549549i
$783$	71.6508			0.0915081
$784$			271.845i			0.346741i
$785$	100.012	+	100.012i	0.127404	+	0.127404i
$786$	−18.7047	−	18.7047i	−0.0237973	−	0.0237973i
$787$	994.400	−	994.400i	1.26353	−	1.26353i	0.314163	−	0.949369i	$-0.398276\pi$
$787$	994.400	−	994.400i	1.26353	−	1.26353i	0.949369	−	0.314163i	$-0.101724\pi$
$788$	466.487	−	466.487i	0.591989	−	0.591989i
$789$	3.13638			0.00397513
$790$		−	71.7572i		−	0.0908319i
$791$	−1155.58	+	1155.58i	−1.46091	+	1.46091i
$792$			63.1890i			0.0797841i
$793$	338.272	+	1150.86i	0.426572	+	1.45127i
$794$	−231.339			−0.291358
$795$	−20.9369	−	20.9369i	−0.0263358	−	0.0263358i
$796$	−249.056			−0.312884
$797$			977.970i			1.22706i	0.789670	+	0.613532i	$0.210252\pi$
$797$			977.970i			1.22706i	−0.789670	+	0.613532i	$0.789748\pi$
$798$	−1.02268	−	1.02268i	−0.00128156	−	0.00128156i
$799$	−1633.66	−	1633.66i	−2.04464	−	2.04464i
$800$	−20.0000	+	20.0000i	−0.0250000	+	0.0250000i
$801$	−31.7128	+	31.7128i	−0.0395915	+	0.0395915i
$802$	917.156			1.14359
$803$			331.259i			0.412527i
$804$	−20.6716	+	20.6716i	−0.0257109	+	0.0257109i
$805$			39.3793i			0.0489184i
$806$	−510.007	+	149.907i	−0.632763	+	0.185989i
$807$	−64.4051			−0.0798080
$808$	184.606	+	184.606i	0.228472	+	0.228472i
$809$	−918.681			−1.13558			−0.567788	−	0.823175i	$-0.692201\pi$
$809$	−918.681			−1.13558			−0.567788	+	0.823175i	$0.692201\pi$
$810$		−	253.132i		−	0.312508i
$811$	−163.558	−	163.558i	−0.201675	−	0.201675i	0.599042	−	0.800717i	$-0.295548\pi$
$811$	−163.558	−	163.558i	−0.201675	−	0.201675i	−0.800717	+	0.599042i	$0.795548\pi$
$812$	−324.532	−	324.532i	−0.399669	−	0.399669i
$813$	−51.1469	+	51.1469i	−0.0629113	+	0.0629113i
$814$	15.4871	−	15.4871i	0.0190259	−	0.0190259i
$815$	−682.039			−0.836858
$816$			19.8424i			0.0243166i
$817$	21.9034	−	21.9034i	0.0268096	−	0.0268096i
$818$			94.8031i			0.115896i
$819$	1106.37	+	603.722i	1.35088	+	0.737145i
$820$	108.088			0.131815
$821$	507.791	+	507.791i	0.618503	+	0.618503i	0.945147	−	0.326644i	$-0.105918\pi$
$821$	507.791	+	507.791i	0.618503	+	0.618503i	−0.326644	+	0.945147i	$0.605918\pi$
$822$	23.2292			0.0282594
$823$		−	742.190i		−	0.901811i	−0.892572	−	0.450905i	$-0.851101\pi$
$823$		−	742.190i		−	0.901811i	0.892572	−	0.450905i	$-0.148899\pi$
$824$	−298.406	−	298.406i	−0.362144	−	0.362144i
$825$	−1.65615	−	1.65615i	−0.00200745	−	0.00200745i
$826$	−36.6654	+	36.6654i	−0.0443891	+	0.0443891i
$827$	258.499	−	258.499i	0.312575	−	0.312575i	−0.533332	−	0.845906i	$-0.679060\pi$
$827$	258.499	−	258.499i	0.312575	−	0.312575i	0.845906	+	0.533332i	$0.179060\pi$
$828$	−29.1962			−0.0352611
$829$			287.282i			0.346540i	0.984874	+	0.173270i	$0.0554333\pi$
$829$			287.282i			0.346540i	−0.984874	+	0.173270i	$0.944567\pi$
$830$	268.520	−	268.520i	0.323519	−	0.323519i
$831$			43.8789i			0.0528025i
$832$	99.7791	−	29.3281i	0.119927	−	0.0352502i
$833$	1793.55			2.15312
$834$	−20.1841	−	20.1841i	−0.0242016	−	0.0242016i
$835$	341.789			0.409328
$836$			2.50744i			0.00299933i
$837$	−69.0395	−	69.0395i	−0.0824844	−	0.0824844i
$838$	−566.058	−	566.058i	−0.675487	−	0.675487i
$839$	−576.953	+	576.953i	−0.687667	+	0.687667i	−0.961716	−	0.274049i	$-0.911637\pi$
$839$	−576.953	+	576.953i	−0.687667	+	0.687667i	0.274049	+	0.961716i	$0.411637\pi$
$840$	9.09112	−	9.09112i	0.0108228	−	0.0108228i
$841$	−390.763			−0.464641
$842$			101.076i			0.120043i
$843$	−22.2717	+	22.2717i	−0.0264196	+	0.0264196i
$844$			280.558i			0.332415i
$845$	−369.304	−	80.1205i	−0.437047	−	0.0948172i
$846$	−1109.88			−1.31191
$847$	−877.826	−	877.826i	−1.03639	−	1.03639i
$848$	−281.788			−0.332297
$849$		−	24.1357i		−	0.0284283i
$850$	131.954	+	131.954i	0.155240	+	0.155240i
$851$	7.15573	+	7.15573i	0.00840862	+	0.00840862i
$852$	19.9216	−	19.9216i	0.0233821	−	0.0233821i
$853$	30.8511	−	30.8511i	0.0361678	−	0.0361678i	−0.688792	−	0.724959i	$-0.741859\pi$
$853$	30.8511	−	30.8511i	0.0361678	−	0.0361678i	0.724959	+	0.688792i	$0.241859\pi$
$854$	1411.26			1.65253
$855$		−	10.0846i		−	0.0117948i
$856$	106.502	−	106.502i	0.124418	−	0.124418i
$857$		−	1201.42i		−	1.40189i	−0.713214	−	0.700946i	$-0.752761\pi$
$857$		−	1201.42i		−	1.40189i	0.713214	−	0.700946i	$-0.247239\pi$
$858$	2.42859	+	8.26244i	0.00283052	+	0.00962988i
$859$	602.352			0.701225			0.350612	−	0.936521i	$-0.385973\pi$
$859$	602.352			0.701225			0.350612	+	0.936521i	$0.385973\pi$
$860$	194.710	+	194.710i	0.226407	+	0.226407i
$861$	−49.1321			−0.0570640
$862$		−	667.277i		−	0.774103i
$863$	534.595	+	534.595i	0.619462	+	0.619462i	0.945393	−	0.325932i	$-0.105678\pi$
$863$	534.595	+	534.595i	0.619462	+	0.619462i	−0.325932	+	0.945393i	$0.605678\pi$
$864$	13.5071	+	13.5071i	0.0156332	+	0.0156332i
$865$	−305.100	+	305.100i	−0.352717	+	0.352717i
$866$	564.564	−	564.564i	0.651922	−	0.651922i
$867$	76.5913			0.0883406
$868$			625.407i			0.720515i
$869$	39.9865	−	39.9865i	0.0460143	−	0.0460143i
$870$			12.6125i			0.0144972i
$871$	484.238	−	887.406i	0.555956	−	1.01884i
$872$	149.270			0.171181
$873$	−347.923	−	347.923i	−0.398537	−	0.398537i
$874$	−1.15855			−0.00132557
$875$		−	120.914i		−	0.138187i
$876$	35.3347	+	35.3347i	0.0403364	+	0.0403364i
$877$	9.16265	+	9.16265i	0.0104477	+	0.0104477i	0.712311	−	0.701864i	$-0.247648\pi$
$877$	9.16265	+	9.16265i	0.0104477	+	0.0104477i	−0.701864	+	0.712311i	$0.747648\pi$
$878$	39.2264	−	39.2264i	0.0446770	−	0.0446770i
$879$	−61.8089	+	61.8089i	−0.0703173	+	0.0703173i
$880$	−22.2899			−0.0253294
$881$		−	1053.15i		−	1.19540i	−0.801720	−	0.597700i	$-0.796081\pi$
$881$		−	1053.15i		−	1.19540i	0.801720	−	0.597700i	$-0.203919\pi$
$882$	609.251	−	609.251i	0.690761	−	0.690761i
$883$		−	307.257i		−	0.347969i	−0.984748	−	0.173985i	$-0.944336\pi$
$883$		−	307.257i		−	0.347969i	0.984748	−	0.173985i	$-0.0556643\pi$
$884$	−193.498	−	658.311i	−0.218889	−	0.744696i
$885$	1.42496			0.00161012
$886$	288.946	+	288.946i	0.326124	+	0.326124i
$887$	1595.82			1.79912			0.899561	−	0.436796i	$-0.143887\pi$
$887$	1595.82			1.79912			0.899561	+	0.436796i	$0.143887\pi$
$888$		−	3.30395i		−	0.00372067i
$889$	−523.225	−	523.225i	−0.588555	−	0.588555i
$890$	−11.1866	−	11.1866i	−0.0125693	−	0.0125693i
$891$	141.057	−	141.057i	0.158313	−	0.158313i
$892$	−254.474	+	254.474i	−0.285285	+	0.285285i
$893$	−44.0417			−0.0493188
$894$		−	14.3624i		−	0.0160653i
$895$	−481.169	+	481.169i	−0.537619	+	0.537619i
$896$		−	122.356i		−	0.136558i
$897$	−3.81762	+	1.12212i	−0.00425598	+	0.00125096i
$898$	−392.131			−0.436671
$899$	−433.828	−	433.828i	−0.482567	−	0.482567i
$900$	89.6467			0.0996074
$901$			1859.15i			2.06343i
$902$	60.2318	+	60.2318i	0.0667758	+	0.0667758i
$903$	−88.5067	−	88.5067i	−0.0980141	−	0.0980141i
$904$	302.220	−	302.220i	0.334315	−	0.334315i
$905$	23.1415	−	23.1415i	0.0255707	−	0.0255707i
$906$	60.4676			0.0667413
$907$			89.4305i			0.0986003i	0.998784	+	0.0493002i	$0.0156991\pi$
$907$			89.4305i			0.0986003i	−0.998784	+	0.0493002i	$0.984301\pi$
$908$	−166.912	+	166.912i	−0.183823	+	0.183823i
$909$		−	827.464i		−	0.910301i
$910$	−212.962	+	390.271i	−0.234025	+	0.428870i
$911$	−925.761			−1.01620			−0.508101	−	0.861297i	$-0.669653\pi$
$911$	−925.761			−1.01620			−0.508101	+	0.861297i	$0.669653\pi$
$912$	0.267464	+	0.267464i	0.000293271	+	0.000293271i
$913$	299.264			0.327781
$914$			527.788i			0.577448i
$915$	−27.4235	−	27.4235i	−0.0299710	−	0.0299710i
$916$	−537.803	−	537.803i	−0.587122	−	0.587122i
$917$	760.984	−	760.984i	0.829862	−	0.829862i
$918$	89.1153	−	89.1153i	0.0970755	−	0.0970755i
$919$	−731.973			−0.796489			−0.398244	−	0.917279i	$-0.630380\pi$
$919$	−731.973			−0.796489			−0.398244	+	0.917279i	$0.630380\pi$
$920$		−	10.2989i		−	0.0111945i
$921$	29.3717	−	29.3717i	0.0318911	−	0.0318911i
$922$		−	758.355i		−	0.822510i
$923$	−466.669	+	855.211i	−0.505601	+	0.926556i
$924$	10.1320			0.0109654
$925$	−21.9716	−	21.9716i	−0.0237531	−	0.0237531i
$926$	999.810			1.07971
$927$			1337.56i			1.44289i
$928$	84.8752	+	84.8752i	0.0914603	+	0.0914603i
$929$	736.879	+	736.879i	0.793196	+	0.793196i	0.982012	−	0.188817i	$-0.0604652\pi$
$929$	736.879	+	736.879i	0.793196	+	0.793196i	−0.188817	+	0.982012i	$0.560465\pi$
$930$	12.1529	−	12.1529i	0.0130676	−	0.0130676i
$931$	24.1760	−	24.1760i	0.0259678	−	0.0259678i
$932$	49.1682			0.0527555
$933$			73.8394i			0.0791419i
$934$	732.570	−	732.570i	0.784337	−	0.784337i
$935$			147.062i			0.157285i
$936$	−289.351	−	157.892i	−0.309135	−	0.168688i
$937$	−1217.64			−1.29951			−0.649757	−	0.760142i	$-0.725129\pi$
$937$	−1217.64			−1.29951			−0.649757	+	0.760142i	$0.725129\pi$
$938$	−841.004	−	841.004i	−0.896593	−	0.896593i
$939$	94.7481			0.100903
$940$		−	391.508i		−	0.416498i
$941$	−794.782	−	794.782i	−0.844614	−	0.844614i	0.144841	−	0.989455i	$-0.453733\pi$
$941$	−794.782	−	794.782i	−0.844614	−	0.844614i	−0.989455	+	0.144841i	$0.953733\pi$
$942$	11.8895	+	11.8895i	0.0126215	+	0.0126215i
$943$	−27.8298	+	27.8298i	−0.0295119	+	0.0295119i
$944$	9.58916	−	9.58916i	0.0101580	−	0.0101580i
$945$	−81.6595			−0.0864122
$946$			217.003i			0.229390i
$947$	−149.364	+	149.364i	−0.157723	+	0.157723i	−0.781557	−	0.623834i	$-0.785574\pi$
$947$	−149.364	+	149.364i	−0.157723	+	0.157723i	0.623834	+	0.781557i	$0.285574\pi$
$948$		−	8.53054i		−	0.00899846i
$949$	−1516.88	−	827.726i	−1.59840	−	0.872209i
$950$	3.55732			0.00374455
$951$	66.4321	+	66.4321i	0.0698550	+	0.0698550i
$952$	−807.269			−0.847971
$953$			462.887i			0.485715i	0.970062	+	0.242858i	$0.0780848\pi$
$953$			462.887i			0.485715i	−0.970062	+	0.242858i	$0.921915\pi$
$954$	631.533	+	631.533i	0.661985	+	0.661985i
$955$	48.9027	+	48.9027i	0.0512070	+	0.0512070i
$956$	−98.1540	+	98.1540i	−0.102672	+	0.102672i
$957$	−7.02829	+	7.02829i	−0.00734408	+	0.00734408i
$958$	807.218			0.842607
$959$			945.061i			0.985465i
$960$	−2.37761	+	2.37761i	−0.00247668	+	0.00247668i
$961$		−	124.967i		−	0.130038i
$962$	32.2194	+	109.616i	0.0334921	+	0.113945i
$963$	−477.376			−0.495718
$964$	−415.400	−	415.400i	−0.430912	−	0.430912i
$965$	292.389			0.302994
$966$			4.68144i			0.00484621i
$967$	575.890	+	575.890i	0.595543	+	0.595543i	0.939123	−	0.343581i	$-0.111640\pi$
$967$	575.890	+	575.890i	0.595543	+	0.595543i	−0.343581	+	0.939123i	$0.611640\pi$
$968$	229.579	+	229.579i	0.237168	+	0.237168i
$969$	1.76464	−	1.76464i	0.00182110	−	0.00182110i
$970$	122.730	−	122.730i	0.126525	−	0.126525i
$971$	−103.925			−0.107029			−0.0535145	−	0.998567i	$-0.517042\pi$
$971$	−103.925			−0.107029			−0.0535145	+	0.998567i	$0.517042\pi$
$972$		−	90.8742i		−	0.0934920i
$973$	821.172	−	821.172i	0.843959	−	0.843959i
$974$			289.194i			0.296914i
$975$	11.7220	−	3.44545i	0.0120225	−	0.00353379i
$976$	−369.089			−0.378165
$977$	−503.052	−	503.052i	−0.514895	−	0.514895i	0.401128	−	0.916022i	$-0.368618\pi$
$977$	−503.052	−	503.052i	−0.514895	−	0.514895i	−0.916022	+	0.401128i	$0.868618\pi$
$978$	−81.0813			−0.0829052
$979$		−	12.4674i		−	0.0127349i
$980$	214.913	+	214.913i	0.219299	+	0.219299i
$981$	−334.540	−	334.540i	−0.341019	−	0.341019i
$982$	−458.846	+	458.846i	−0.467256	+	0.467256i
$983$	535.042	−	535.042i	0.544295	−	0.544295i	−0.380490	−	0.924785i	$-0.624245\pi$
$983$	535.042	−	535.042i	0.544295	−	0.544295i	0.924785	+	0.380490i	$0.124245\pi$
$984$	12.8496			0.0130585
$985$		−	737.581i		−	0.748813i
$986$	559.980	−	559.980i	0.567931	−	0.567931i
$987$			177.963i			0.180306i
$988$	−11.4819	−	6.26542i	−0.0116214	−	0.00634152i
$989$	−100.265			−0.101380
$990$	49.9553	+	49.9553i	0.0504599	+	0.0504599i
$991$	1066.90			1.07659			0.538295	−	0.842756i	$-0.319068\pi$
$991$	1066.90			1.07659			0.538295	+	0.842756i	$0.319068\pi$
$992$		−	163.564i		−	0.164883i
$993$	30.4524	+	30.4524i	0.0306671	+	0.0306671i
$994$	810.492	+	810.492i	0.815384	+	0.815384i
$995$	−196.896	+	196.896i	−0.197885	+	0.197885i
$996$	31.9219	−	31.9219i	0.0320501	−	0.0320501i
$997$	797.083			0.799481			0.399741	−	0.916628i	$-0.369100\pi$
$997$	797.083			0.799481			0.399741	+	0.916628i	$0.369100\pi$
$998$			425.166i			0.426018i
$999$	−14.8386	+	14.8386i	−0.0148535	+	0.0148535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.3.k.a.21.4	✓	12
3.2	odd	2		1170.3.r.b.541.1		12
5.2	odd	4		650.3.f.m.99.3		12
5.3	odd	4		650.3.f.l.99.4		12
5.4	even	2		650.3.k.k.151.3		12
13.5	odd	4	inner	130.3.k.a.31.4	yes	12
39.5	even	4		1170.3.r.b.811.1		12
65.18	even	4		650.3.f.m.499.4		12
65.44	odd	4		650.3.k.k.551.3		12
65.57	even	4		650.3.f.l.499.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.k.a.21.4	✓	12	1.1	even	1	trivial
130.3.k.a.31.4	yes	12	13.5	odd	4	inner
650.3.f.l.99.4		12	5.3	odd	4
650.3.f.l.499.3		12	65.57	even	4
650.3.f.m.99.3		12	5.2	odd	4
650.3.f.m.499.4		12	65.18	even	4
650.3.k.k.151.3		12	5.4	even	2
650.3.k.k.551.3		12	65.44	odd	4
1170.3.r.b.541.1		12	3.2	odd	2
1170.3.r.b.811.1		12	39.5	even	4

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	130.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} -0.187967 q^{3} +2.00000i q^{4} +(1.58114 + 1.58114i) q^{5} +(0.187967 + 0.187967i) q^{6} +(-7.64727 + 7.64727i) q^{7} +(2.00000 - 2.00000i) q^{8} -8.96467 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} -0.187967 q^{3} +2.00000i q^{4} +(1.58114 + 1.58114i) q^{5} +(0.187967 + 0.187967i) q^{6} +(-7.64727 + 7.64727i) q^{7} +(2.00000 - 2.00000i) q^{8} -8.96467 q^{9} -3.16228i q^{10} +(1.76217 - 1.76217i) q^{11} -0.375934i q^{12} +(3.66602 + 12.4724i) q^{13} +15.2945 q^{14} +(-0.297202 - 0.297202i) q^{15} -4.00000 q^{16} +26.3908i q^{17} +(8.96467 + 8.96467i) q^{18} +(0.355732 + 0.355732i) q^{19} +(-3.16228 + 3.16228i) q^{20} +(1.43743 - 1.43743i) q^{21} -3.52434 q^{22} -1.62840i q^{23} +(-0.375934 + 0.375934i) q^{24} +5.00000i q^{25} +(8.80636 - 16.1384i) q^{26} +3.37676 q^{27} +(-15.2945 - 15.2945i) q^{28} +21.2188 q^{29} +0.594403i q^{30} +(-20.4455 - 20.4455i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.331229 + 0.331229i) q^{33} +(26.3908 - 26.3908i) q^{34} -24.1828 q^{35} -17.9293i q^{36} +(-4.39433 + 4.39433i) q^{37} -0.711465i q^{38} +(-0.689090 - 2.34439i) q^{39} +6.32456 q^{40} +(-17.0902 - 17.0902i) q^{41} -2.87487 q^{42} -61.5728i q^{43} +(3.52434 + 3.52434i) q^{44} +(-14.1744 - 14.1744i) q^{45} +(-1.62840 + 1.62840i) q^{46} +(-61.9029 + 61.9029i) q^{47} +0.751868 q^{48} -67.9613i q^{49} +(5.00000 - 5.00000i) q^{50} -4.96059i q^{51} +(-24.9448 + 7.33204i) q^{52} +70.4469 q^{53} +(-3.37676 - 3.37676i) q^{54} +5.57247 q^{55} +30.5891i q^{56} +(-0.0668659 - 0.0668659i) q^{57} +(-21.2188 - 21.2188i) q^{58} +(-2.39729 + 2.39729i) q^{59} +(0.594403 - 0.594403i) q^{60} +92.2723 q^{61} +40.8909i q^{62} +(68.5552 - 68.5552i) q^{63} -8.00000i q^{64} +(-13.9241 + 25.5171i) q^{65} +0.662459 q^{66} +(-54.9873 - 54.9873i) q^{67} -52.7815 q^{68} +0.306086i q^{69} +(24.1828 + 24.1828i) q^{70} +(52.9923 + 52.9923i) q^{71} +(-17.9293 + 17.9293i) q^{72} +(-93.9918 + 93.9918i) q^{73} +8.78866 q^{74} -0.939834i q^{75} +(-0.711465 + 0.711465i) q^{76} +26.9515i q^{77} +(-1.65530 + 3.03348i) q^{78} +22.6916 q^{79} +(-6.32456 - 6.32456i) q^{80} +80.0473 q^{81} +34.1805i q^{82} +(84.9136 + 84.9136i) q^{83} +(2.87487 + 2.87487i) q^{84} +(-41.7275 + 41.7275i) q^{85} +(-61.5728 + 61.5728i) q^{86} -3.98843 q^{87} -7.04868i q^{88} +(3.53753 - 3.53753i) q^{89} +28.3488i q^{90} +(-123.415 - 67.3446i) q^{91} +3.25680 q^{92} +(3.84307 + 3.84307i) q^{93} +123.806 q^{94} +1.12492i q^{95} +(-0.751868 - 0.751868i) q^{96} +(38.8105 + 38.8105i) q^{97} +(-67.9613 + 67.9613i) q^{98} +(-15.7973 + 15.7973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 24 q^{8} + 44 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 24 * q^8 + 44 * q^9	\( 12 q - 12 q^{2} + 24 q^{8} + 44 q^{9} + 8 q^{11} - 4 q^{13} + 20 q^{15} - 48 q^{16} - 44 q^{18} + 36 q^{19} + 52 q^{21} - 16 q^{22} + 8 q^{26} + 144 q^{27} - 8 q^{29} - 136 q^{31} + 48 q^{32} - 60 q^{33} - 40 q^{35} - 44 q^{37} - 172 q^{39} + 32 q^{41} - 104 q^{42} + 16 q^{44} - 96 q^{46} - 16 q^{47} + 60 q^{50} - 8 q^{52} + 24 q^{53} - 144 q^{54} - 212 q^{57} + 8 q^{58} + 124 q^{59} - 40 q^{60} + 24 q^{61} - 80 q^{63} - 60 q^{65} + 120 q^{66} + 136 q^{67} + 40 q^{70} + 84 q^{71} + 88 q^{72} + 12 q^{73} + 88 q^{74} - 72 q^{76} + 312 q^{78} - 168 q^{79} + 596 q^{81} + 160 q^{83} + 104 q^{84} + 60 q^{85} + 224 q^{86} - 64 q^{87} - 44 q^{89} - 404 q^{91} + 192 q^{92} + 4 q^{93} + 32 q^{94} - 192 q^{97} + 60 q^{98} - 52 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 24 * q^8 + 44 * q^9 + 8 * q^11 - 4 * q^13 + 20 * q^15 - 48 * q^16 - 44 * q^18 + 36 * q^19 + 52 * q^21 - 16 * q^22 + 8 * q^26 + 144 * q^27 - 8 * q^29 - 136 * q^31 + 48 * q^32 - 60 * q^33 - 40 * q^35 - 44 * q^37 - 172 * q^39 + 32 * q^41 - 104 * q^42 + 16 * q^44 - 96 * q^46 - 16 * q^47 + 60 * q^50 - 8 * q^52 + 24 * q^53 - 144 * q^54 - 212 * q^57 + 8 * q^58 + 124 * q^59 - 40 * q^60 + 24 * q^61 - 80 * q^63 - 60 * q^65 + 120 * q^66 + 136 * q^67 + 40 * q^70 + 84 * q^71 + 88 * q^72 + 12 * q^73 + 88 * q^74 - 72 * q^76 + 312 * q^78 - 168 * q^79 + 596 * q^81 + 160 * q^83 + 104 * q^84 + 60 * q^85 + 224 * q^86 - 64 * q^87 - 44 * q^89 - 404 * q^91 + 192 * q^92 + 4 * q^93 + 32 * q^94 - 192 * q^97 + 60 * q^98 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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