LMFDB - Embedded newform 650.3.f.l.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,3,Mod(99,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("650.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	650.f (of order $4$, degree $2$, not 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:	$17.7112171834$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.4
Root			$-0.187967i$ of defining polynomial
Character	$\chi$	$=$	650.99
Dual form			650.3.f.l.499.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -0.187967i q^{3} -2.00000i q^{4} +(0.187967 + 0.187967i) q^{6} +(7.64727 + 7.64727i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.96467 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -0.187967i q^{3} -2.00000i q^{4} +(0.187967 + 0.187967i) q^{6} +(7.64727 + 7.64727i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.96467 q^{9} +(1.76217 - 1.76217i) q^{11} -0.375934 q^{12} +(-12.4724 + 3.66602i) q^{13} -15.2945 q^{14} -4.00000 q^{16} +26.3908 q^{17} +(-8.96467 + 8.96467i) q^{18} +(-0.355732 - 0.355732i) q^{19} +(1.43743 - 1.43743i) q^{21} +3.52434i q^{22} +1.62840 q^{23} +(0.375934 - 0.375934i) q^{24} +(8.80636 - 16.1384i) q^{26} -3.37676i q^{27} +(15.2945 - 15.2945i) q^{28} -21.2188 q^{29} +(-20.4455 - 20.4455i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.331229 - 0.331229i) q^{33} +(-26.3908 + 26.3908i) q^{34} -17.9293i q^{36} +(4.39433 + 4.39433i) q^{37} +0.711465 q^{38} +(0.689090 + 2.34439i) q^{39} +(-17.0902 - 17.0902i) q^{41} +2.87487i q^{42} +61.5728 q^{43} +(-3.52434 - 3.52434i) q^{44} +(-1.62840 + 1.62840i) q^{46} +(61.9029 + 61.9029i) q^{47} +0.751868i q^{48} +67.9613i q^{49} -4.96059i q^{51} +(7.33204 + 24.9448i) q^{52} +70.4469i q^{53} +(3.37676 + 3.37676i) q^{54} +30.5891i q^{56} +(-0.0668659 + 0.0668659i) q^{57} +(21.2188 - 21.2188i) q^{58} +(2.39729 - 2.39729i) q^{59} +92.2723 q^{61} +40.8909 q^{62} +(68.5552 + 68.5552i) q^{63} +8.00000i q^{64} +0.662459 q^{66} +(-54.9873 + 54.9873i) q^{67} -52.7815i q^{68} -0.306086i q^{69} +(52.9923 + 52.9923i) q^{71} +(17.9293 + 17.9293i) q^{72} +(-93.9918 - 93.9918i) q^{73} -8.78866 q^{74} +(-0.711465 + 0.711465i) q^{76} +26.9515 q^{77} +(-3.03348 - 1.65530i) q^{78} -22.6916 q^{79} +80.0473 q^{81} +34.1805 q^{82} +(-84.9136 + 84.9136i) q^{83} +(-2.87487 - 2.87487i) q^{84} +(-61.5728 + 61.5728i) q^{86} +3.98843i q^{87} +7.04868 q^{88} +(-3.53753 + 3.53753i) q^{89} +(-123.415 - 67.3446i) q^{91} -3.25680i q^{92} +(-3.84307 + 3.84307i) q^{93} -123.806 q^{94} +(-0.751868 - 0.751868i) q^{96} +(38.8105 - 38.8105i) q^{97} +(-67.9613 - 67.9613i) q^{98} +(15.7973 - 15.7973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 48 q^{16} + 44 q^{18} - 36 q^{19} + 52 q^{21} + 96 q^{23} + 8 q^{26} + 8 q^{29} - 136 q^{31} + 48 q^{32} - 60 q^{33} + 44 q^{37} + 72 q^{38} + 172 q^{39} + 32 q^{41} - 224 q^{43} - 16 q^{44} - 96 q^{46} + 16 q^{47} - 8 q^{52} + 144 q^{54} - 212 q^{57} - 8 q^{58} - 124 q^{59} + 24 q^{61} + 272 q^{62} - 80 q^{63} + 120 q^{66} + 136 q^{67} + 84 q^{71} - 88 q^{72} + 12 q^{73} - 88 q^{74} - 72 q^{76} - 48 q^{77} - 32 q^{78} + 168 q^{79} + 596 q^{81} - 64 q^{82} - 160 q^{83} - 104 q^{84} + 224 q^{86} + 32 q^{88} + 44 q^{89} - 404 q^{91} - 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 - 48 * q^16 + 44 * q^18 - 36 * q^19 + 52 * q^21 + 96 * q^23 + 8 * q^26 + 8 * q^29 - 136 * q^31 + 48 * q^32 - 60 * q^33 + 44 * q^37 + 72 * q^38 + 172 * q^39 + 32 * q^41 - 224 * q^43 - 16 * q^44 - 96 * q^46 + 16 * q^47 - 8 * q^52 + 144 * q^54 - 212 * q^57 - 8 * q^58 - 124 * q^59 + 24 * q^61 + 272 * q^62 - 80 * q^63 + 120 * q^66 + 136 * q^67 + 84 * q^71 - 88 * q^72 + 12 * q^73 - 88 * q^74 - 72 * q^76 - 48 * q^77 - 32 * q^78 + 168 * q^79 + 596 * q^81 - 64 * q^82 - 160 * q^83 - 104 * q^84 + 224 * q^86 + 32 * q^88 + 44 * q^89 - 404 * q^91 - 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 $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$		−	0.187967i		−	0.0626556i	−0.999509	−	0.0313278i	$-0.990026\pi$
$3$		−	0.187967i		−	0.0626556i	0.999509	−	0.0313278i	$-0.00997358\pi$
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	0.187967	+	0.187967i	0.0313278	+	0.0313278i
$7$	7.64727	+	7.64727i	1.09247	+	1.09247i	0.995265	+	0.0972018i	$0.0309892\pi$
$7$	7.64727	+	7.64727i	1.09247	+	1.09247i	0.0972018	+	0.995265i	$0.469011\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	8.96467			0.996074
$10$		0			0
$11$	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	$0.213865\pi$
$12$	−0.375934			−0.0313278
$13$	−12.4724	+	3.66602i	−0.959414	+	0.282001i
$13$	−12.4724	+	3.66602i	−0.959414	+	0.282001i
$14$	−15.2945			−1.09247
$15$		0			0
$16$	−4.00000			−0.250000
$17$	26.3908			1.55240			0.776199	−	0.630488i	$-0.217145\pi$
$17$	26.3908			1.55240			0.776199	+	0.630488i	$0.217145\pi$
$18$	−8.96467	+	8.96467i	−0.498037	+	0.498037i
$19$	−0.355732	−	0.355732i	−0.0187228	−	0.0187228i	0.697683	−	0.716406i	$-0.254214\pi$
$19$	−0.355732	−	0.355732i	−0.0187228	−	0.0187228i	−0.716406	+	0.697683i	$0.754214\pi$
$20$		0			0
$21$	1.43743	−	1.43743i	0.0684492	−	0.0684492i
$22$			3.52434i			0.160197i
$23$	1.62840			0.0708001			0.0354000	−	0.999373i	$-0.488729\pi$
$23$	1.62840			0.0708001			0.0354000	+	0.999373i	$0.488729\pi$
$24$	0.375934	−	0.375934i	0.0156639	−	0.0156639i
$25$		0			0
$26$	8.80636	−	16.1384i	0.338706	−	0.620708i
$27$		−	3.37676i		−	0.125065i
$28$	15.2945	−	15.2945i	0.546233	−	0.546233i
$29$	−21.2188			−0.731683			−0.365841	−	0.930677i	$-0.619219\pi$
$29$	−21.2188			−0.731683			−0.365841	+	0.930677i	$0.619219\pi$
$30$		0			0
$31$	−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
$35$		0			0
$36$		−	17.9293i		−	0.498037i
$37$	4.39433	+	4.39433i	0.118766	+	0.118766i	0.763992	−	0.645226i	$-0.223237\pi$
$37$	4.39433	+	4.39433i	0.118766	+	0.118766i	−0.645226	+	0.763992i	$0.723237\pi$
$38$	0.711465			0.0187228
$39$	0.689090	+	2.34439i	0.0176690	+	0.0601127i
$40$		0			0
$41$	−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	$0.845235\pi$
$42$			2.87487i			0.0684492i
$43$	61.5728			1.43193			0.715963	−	0.698139i	$-0.245988\pi$
$43$	61.5728			1.43193			0.715963	+	0.698139i	$0.245988\pi$
$44$	−3.52434	−	3.52434i	−0.0800986	−	0.0800986i
$45$		0			0
$46$	−1.62840	+	1.62840i	−0.0354000	+	0.0354000i
$47$	61.9029	+	61.9029i	1.31708	+	1.31708i	0.916074	+	0.401009i	$0.131340\pi$
$47$	61.9029	+	61.9029i	1.31708	+	1.31708i	0.401009	+	0.916074i	$0.368660\pi$
$48$			0.751868i			0.0156639i
$49$			67.9613i			1.38697i
$50$		0			0
$51$		−	4.96059i		−	0.0972665i
$52$	7.33204	+	24.9448i	0.141001	+	0.479707i
$53$			70.4469i			1.32919i	0.747205	+	0.664594i	$0.231395\pi$
$53$			70.4469i			1.32919i	−0.747205	+	0.664594i	$0.768605\pi$
$54$	3.37676	+	3.37676i	0.0625326	+	0.0625326i
$55$		0			0
$56$			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	−0.686499	−	0.727131i	$-0.740853\pi$
$59$	2.39729	−	2.39729i	0.0406320	−	0.0406320i	0.727131	+	0.686499i	$0.240853\pi$
$60$		0			0
$61$	92.2723			1.51266			0.756330	−	0.654190i	$-0.226990\pi$
$61$	92.2723			1.51266			0.756330	+	0.654190i	$0.226990\pi$
$62$	40.8909			0.659531
$63$	68.5552	+	68.5552i	1.08818	+	1.08818i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	0.662459			0.0100373
$67$	−54.9873	+	54.9873i	−0.820705	+	0.820705i	−0.986209	−	0.165504i	$-0.947075\pi$
$67$	−54.9873	+	54.9873i	−0.820705	+	0.820705i	0.165504	+	0.986209i	$0.447075\pi$
$68$		−	52.7815i		−	0.776199i
$69$		−	0.306086i		−	0.00443602i
$70$		0			0
$71$	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	−0.936265	−	0.351294i	$-0.885742\pi$
$73$	−93.9918	−	93.9918i	−1.28756	−	1.28756i	−0.351294	−	0.936265i	$-0.614258\pi$
$74$	−8.78866			−0.118766
$75$		0			0
$76$	−0.711465	+	0.711465i	−0.00936138	+	0.00936138i
$77$	26.9515			0.350020
$78$	−3.03348	−	1.65530i	−0.0388908	−	0.0212219i
$79$	−22.6916			−0.287236			−0.143618	−	0.989633i	$-0.545874\pi$
$79$	−22.6916			−0.287236			−0.143618	+	0.989633i	$0.545874\pi$
$80$		0			0
$81$	80.0473			0.988238
$82$	34.1805			0.416835
$83$	−84.9136	+	84.9136i	−1.02306	+	1.02306i	−0.0233279	+	0.999728i	$0.507426\pi$
$83$	−84.9136	+	84.9136i	−1.02306	+	1.02306i	−0.999728	+	0.0233279i	$0.992574\pi$
$84$	−2.87487	−	2.87487i	−0.0342246	−	0.0342246i
$85$		0			0
$86$	−61.5728	+	61.5728i	−0.715963	+	0.715963i
$87$			3.98843i			0.0458440i
$88$	7.04868			0.0800986
$89$	−3.53753	+	3.53753i	−0.0397475	+	0.0397475i	−0.726701	−	0.686954i	$-0.758948\pi$
$89$	−3.53753	+	3.53753i	−0.0397475	+	0.0397475i	0.686954	+	0.726701i	$0.258948\pi$
$90$		0			0
$91$	−123.415	−	67.3446i	−1.35620	−	0.740051i
$92$		−	3.25680i		−	0.0354000i
$93$	−3.84307	+	3.84307i	−0.0413233	+	0.0413233i
$94$	−123.806			−1.31708
$95$		0			0
$96$	−0.751868	−	0.751868i	−0.00783195	−	0.00783195i
$97$	38.8105	−	38.8105i	0.400108	−	0.400108i	−0.478163	−	0.878271i	$-0.658697\pi$
$97$	38.8105	−	38.8105i	0.400108	−	0.400108i	0.878271	+	0.478163i	$0.158697\pi$
$98$	−67.9613	−	67.9613i	−0.693483	−	0.693483i
$99$	15.7973	−	15.7973i	0.159568	−	0.159568i
$100$		0			0
$101$			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
$103$	149.203			1.44858			0.724288	−	0.689498i	$-0.242169\pi$
$103$	149.203			1.44858			0.724288	+	0.689498i	$0.242169\pi$
$104$	−32.2768	−	17.6127i	−0.310354	−	0.169353i
$105$		0			0
$106$	−70.4469	−	70.4469i	−0.664594	−	0.664594i
$107$		−	53.2509i		−	0.497672i	−0.968546	−	0.248836i	$-0.919952\pi$
$107$		−	53.2509i		−	0.497672i	0.968546	−	0.248836i	$-0.0800480\pi$
$108$	−6.75353			−0.0625326
$109$	−37.3176	−	37.3176i	−0.342363	−	0.342363i	0.514892	−	0.857255i	$-0.327832\pi$
$109$	−37.3176	−	37.3176i	−0.342363	−	0.342363i	−0.857255	+	0.514892i	$0.827832\pi$
$110$		0			0
$111$	0.825988	−	0.825988i	0.00744134	−	0.00744134i
$112$	−30.5891	−	30.5891i	−0.273117	−	0.273117i
$113$			151.110i			1.33726i	0.743596	+	0.668629i	$0.233119\pi$
$113$			151.110i			1.33726i	−0.743596	+	0.668629i	$0.766881\pi$
$114$		−	0.133732i		−	0.00117309i
$115$		0			0
$116$			42.4376i			0.365841i
$117$	−111.811	+	32.8646i	−0.955648	+	0.280894i
$118$			4.79458i			0.0406320i
$119$	201.817	+	201.817i	1.69594	+	1.69594i
$120$		0			0
$121$			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
$125$		0			0
$126$	−137.110			−1.08818
$127$	68.4199			0.538740			0.269370	−	0.963037i	$-0.413185\pi$
$127$	68.4199			0.538740			0.269370	+	0.963037i	$0.413185\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	11.5736i		−	0.0897182i
$130$		0			0
$131$	−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
$133$		−	5.44076i		−	0.0409080i
$134$		−	109.975i		−	0.820705i
$135$		0			0
$136$	52.7815	+	52.7815i	0.388099	+	0.388099i
$137$	−61.7908	−	61.7908i	−0.451027	−	0.451027i	0.444668	−	0.895695i	$-0.353322\pi$
$137$	−61.7908	−	61.7908i	−0.451027	−	0.451027i	−0.895695	+	0.444668i	$0.853322\pi$
$138$	0.306086	+	0.306086i	0.00221801	+	0.00221801i
$139$	107.381			0.772527			0.386263	−	0.922389i	$-0.373766\pi$
$139$	107.381			0.772527			0.386263	+	0.922389i	$0.373766\pi$
$140$		0			0
$141$	11.6357	−	11.6357i	0.0825227	−	0.0825227i
$142$	−105.985			−0.746370
$143$	−15.5183	+	28.4386i	−0.108520	+	0.198871i
$144$	−35.8587			−0.249019
$145$		0			0
$146$	187.984			1.28756
$147$	12.7745			0.0869012
$148$	8.78866	−	8.78866i	0.0593828	−	0.0593828i
$149$	38.2045	+	38.2045i	0.256406	+	0.256406i	0.823591	−	0.567185i	$-0.191967\pi$
$149$	38.2045	+	38.2045i	0.256406	+	0.256406i	−0.567185	+	0.823591i	$0.691967\pi$
$150$		0			0
$151$	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	$-0.0214984\pi$
$152$		−	1.42293i		−	0.00936138i
$153$	236.584			1.54630
$154$	−26.9515	+	26.9515i	−0.175010	+	0.175010i
$155$		0			0
$156$	4.68879	−	1.37818i	0.0300563	−	0.00883449i
$157$		−	63.2532i		−	0.402886i	−0.979500	−	0.201443i	$-0.935437\pi$
$157$		−	63.2532i		−	0.402886i	0.979500	−	0.201443i	$-0.0645631\pi$
$158$	22.6916	−	22.6916i	0.143618	−	0.143618i
$159$	13.2417			0.0832811
$160$		0			0
$161$	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	−0.911180	−	0.412009i	$-0.864827\pi$
$163$	−215.680	−	215.680i	−1.32319	−	1.32319i	−0.412009	−	0.911180i	$-0.635173\pi$
$164$	−34.1805	+	34.1805i	−0.208417	+	0.208417i
$165$		0			0
$166$		−	169.827i		−	1.02306i
$167$	−108.083	−	108.083i	−0.647204	−	0.647204i	0.305112	−	0.952316i	$-0.401306\pi$
$167$	−108.083	−	108.083i	−0.647204	−	0.647204i	−0.952316	+	0.305112i	$0.901306\pi$
$168$	5.74973			0.0342246
$169$	142.121	−	91.4479i	0.840950	−	0.541112i
$170$		0			0
$171$	−3.18902	−	3.18902i	−0.0186493	−	0.0186493i
$172$		−	123.146i		−	0.715963i
$173$	−192.962			−1.11539			−0.557694	−	0.830047i	$-0.688314\pi$
$173$	−192.962			−1.11539			−0.557694	+	0.830047i	$0.688314\pi$
$174$	−3.98843	−	3.98843i	−0.0229220	−	0.0229220i
$175$		0			0
$176$	−7.04868	+	7.04868i	−0.0400493	+	0.0400493i
$177$	−0.450611	−	0.450611i	−0.00254583	−	0.00254583i
$178$		−	7.07506i		−	0.0397475i
$179$		−	304.318i		−	1.70010i	−0.526701	−	0.850051i	$-0.676571\pi$
$179$		−	304.318i		−	1.70010i	0.526701	−	0.850051i	$-0.323429\pi$
$180$		0			0
$181$		−	14.6359i		−	0.0808616i	−0.999182	−	0.0404308i	$-0.987127\pi$
$181$		−	14.6359i		−	0.0808616i	0.999182	−	0.0404308i	$-0.0128730\pi$
$182$	190.759	−	56.0700i	1.04813	−	0.308077i
$183$		−	17.3441i		−	0.0947767i
$184$	3.25680	+	3.25680i	0.0177000	+	0.0177000i
$185$		0			0
$186$		−	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
$190$		0			0
$191$	30.9288			0.161931			0.0809654	−	0.996717i	$-0.474200\pi$
$191$	30.9288			0.161931			0.0809654	+	0.996717i	$0.474200\pi$
$192$	1.50374			0.00783195
$193$	92.4616	+	92.4616i	0.479076	+	0.479076i	0.904836	−	0.425760i	$-0.139993\pi$
$193$	92.4616	+	92.4616i	0.479076	+	0.479076i	−0.425760	+	0.904836i	$0.639993\pi$
$194$			77.6210i			0.400108i
$195$		0			0
$196$	135.923			0.693483
$197$	−233.243	+	233.243i	−1.18398	+	1.18398i	−0.205272	+	0.978705i	$0.565808\pi$
$197$	−233.243	+	233.243i	−1.18398	+	1.18398i	−0.978705	+	0.205272i	$0.934192\pi$
$198$			31.5945i			0.159568i
$199$		−	124.528i		−	0.625768i	−0.949791	−	0.312884i	$-0.898705\pi$
$199$		−	124.528i		−	0.625768i	0.949791	−	0.312884i	$-0.101295\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	−149.203	+	149.203i	−0.724288	+	0.724288i
$207$	14.5981			0.0705221
$208$	49.8895	−	14.6641i	0.239854	−	0.0705003i
$209$	−1.25372			−0.00599866
$210$		0			0
$211$	140.279			0.664830			0.332415	−	0.943133i	$-0.392137\pi$
$211$	140.279			0.664830			0.332415	+	0.943133i	$0.392137\pi$
$212$	140.894			0.664594
$213$	9.96080	−	9.96080i	0.0467643	−	0.0467643i
$214$	53.2509	+	53.2509i	0.248836	+	0.248836i
$215$		0			0
$216$	6.75353	−	6.75353i	0.0312663	−	0.0312663i
$217$		−	312.704i		−	1.44103i
$218$	74.6351			0.342363
$219$	−17.6674	+	17.6674i	−0.0806728	+	0.0806728i
$220$		0			0
$221$	−329.156	+	96.7490i	−1.48939	+	0.437778i
$222$			1.65198i			0.00744134i
$223$	−127.237	+	127.237i	−0.570570	+	0.570570i	−0.932288	−	0.361718i	$-0.882190\pi$
$223$	−127.237	+	127.237i	−0.570570	+	0.570570i	0.361718	+	0.932288i	$0.382190\pi$
$224$	61.1781			0.273117
$225$		0			0
$226$	−151.110	−	151.110i	−0.668629	−	0.668629i
$227$	83.4558	−	83.4558i	0.367647	−	0.367647i	−0.498972	−	0.866618i	$-0.666289\pi$
$227$	83.4558	−	83.4558i	0.367647	−	0.367647i	0.866618	+	0.498972i	$0.166289\pi$
$228$	0.133732	+	0.133732i	0.000586543	+	0.000586543i
$229$	268.902	−	268.902i	1.17424	−	1.17424i	0.193055	−	0.981188i	$-0.438160\pi$
$229$	268.902	−	268.902i	1.17424	−	1.17424i	0.981188	−	0.193055i	$-0.0618397\pi$
$230$		0			0
$231$		−	5.06600i		−	0.0219307i
$232$	−42.4376	−	42.4376i	−0.182921	−	0.182921i
$233$	24.5841			0.105511			0.0527555	−	0.998607i	$-0.483200\pi$
$233$	24.5841			0.105511			0.0527555	+	0.998607i	$0.483200\pi$
$234$	78.9461	−	144.675i	0.337377	−	0.618271i
$235$		0			0
$236$	−4.79458	−	4.79458i	−0.0203160	−	0.0203160i
$237$			4.26527i			0.0179969i
$238$	−403.634			−1.69594
$239$	−49.0770	−	49.0770i	−0.205343	−	0.205343i	0.596942	−	0.802285i	$-0.296382\pi$
$239$	−49.0770	−	49.0770i	−0.205343	−	0.205343i	−0.802285	+	0.596942i	$0.796382\pi$
$240$		0			0
$241$	−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
$243$		−	45.4371i		−	0.186984i
$244$		−	184.545i		−	0.756330i
$245$		0			0
$246$		−	6.42480i		−	0.0261171i
$247$	5.74095	+	3.13271i	0.0232427	+	0.0126830i
$248$		−	81.7818i		−	0.329765i
$249$	15.9609	+	15.9609i	0.0641002	+	0.0641002i
$250$		0			0
$251$		−	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
$255$		0			0
$256$	16.0000			0.0625000
$257$	193.812			0.754132			0.377066	−	0.926186i	$-0.376933\pi$
$257$	193.812			0.754132			0.377066	+	0.926186i	$0.376933\pi$
$258$	11.5736	+	11.5736i	0.0448591	+	0.0448591i
$259$			67.2092i			0.259495i
$260$		0			0
$261$	−190.219			−0.728810
$262$	99.5106	−	99.5106i	0.379811	−	0.379811i
$263$		−	16.6858i		−	0.0634441i	−0.999497	−	0.0317220i	$-0.989901\pi$
$263$		−	16.6858i		−	0.0634441i	0.999497	−	0.0317220i	$-0.0100991\pi$
$264$		−	1.32492i		−	0.00501863i
$265$		0			0
$266$	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	$-0.719775\pi$
$269$	−342.640			−1.27376			−0.636878	+	0.770964i	$0.719775\pi$
$270$		0			0
$271$	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	$-0.00130139\pi$
$272$	−105.563			−0.388099
$273$	−12.6586	+	23.1979i	−0.0463683	+	0.0849739i
$274$	123.582			0.451027
$275$		0			0
$276$	−0.612171			−0.00221801
$277$	−233.439			−0.842741			−0.421371	−	0.906889i	$-0.638451\pi$
$277$	−233.439			−0.842741			−0.421371	+	0.906889i	$0.638451\pi$
$278$	−107.381	+	107.381i	−0.386263	+	0.386263i
$279$	−183.287	−	183.287i	−0.656942	−	0.656942i
$280$		0			0
$281$	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	$0.153627\pi$
$282$			23.2714i			0.0825227i
$283$	−128.404			−0.453724			−0.226862	−	0.973927i	$-0.572847\pi$
$283$	−128.404			−0.453724			−0.226862	+	0.973927i	$0.572847\pi$
$284$	105.985	−	105.985i	0.373185	−	0.373185i
$285$		0			0
$286$	−12.9203	−	43.9569i	−0.0451758	−	0.153695i
$287$		−	261.387i		−	0.910756i
$288$	35.8587	−	35.8587i	0.124509	−	0.124509i
$289$	407.472			1.40994
$290$		0			0
$291$	−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	0.991398	+	0.130884i	$0.0417816\pi$
$293$	328.829	+	328.829i	1.12228	+	1.12228i	0.130884	+	0.991398i	$0.458218\pi$
$294$	−12.7745	+	12.7745i	−0.0434506	+	0.0434506i
$295$		0			0
$296$			17.5773i			0.0593828i
$297$	−5.95043	−	5.95043i	−0.0200351	−	0.0200351i
$298$	−76.4090			−0.256406
$299$	−20.3100	+	5.96975i	−0.0679266	+	0.0199657i
$300$		0			0
$301$	470.863	+	470.863i	1.56433	+	1.56433i
$302$			321.693i			1.06521i
$303$	17.3499			0.0572603
$304$	1.42293	+	1.42293i	0.00468069	+	0.00468069i
$305$		0			0
$306$	−236.584	+	236.584i	−0.773152	+	0.773152i
$307$	156.260	+	156.260i	0.508990	+	0.508990i	0.914217	−	0.405226i	$-0.132807\pi$
$307$	156.260	+	156.260i	0.508990	+	0.508990i	−0.405226	+	0.914217i	$0.632807\pi$
$308$		−	53.9031i		−	0.175010i
$309$		−	28.0453i		−	0.0907614i
$310$		0			0
$311$		−	392.832i		−	1.26313i	−0.775325	−	0.631563i	$-0.782414\pi$
$311$		−	392.832i		−	1.26313i	0.775325	−	0.631563i	$-0.217586\pi$
$312$	−3.31061	+	6.06697i	−0.0106109	+	0.0194454i
$313$		−	504.068i		−	1.61044i	−0.592976	−	0.805220i	$-0.702047\pi$
$313$		−	504.068i		−	1.61044i	0.592976	−	0.805220i	$-0.297953\pi$
$314$	63.2532	+	63.2532i	0.201443	+	0.201443i
$315$		0			0
$316$			45.3832i			0.143618i
$317$	−353.425	+	353.425i	−1.11490	+	1.11490i	−0.122426	+	0.992478i	$0.539068\pi$
$317$	−353.425	+	353.425i	−1.11490	+	1.11490i	−0.992478	+	0.122426i	$0.960932\pi$
$318$	−13.2417	+	13.2417i	−0.0416405	+	0.0416405i
$319$	−37.3911	+	37.3911i	−0.117213	+	0.117213i
$320$		0			0
$321$	−10.0094			−0.0311819
$322$	−24.9056			−0.0773467
$323$	−9.38805	−	9.38805i	−0.0290652	−	0.0290652i
$324$		−	160.095i		−	0.494119i
$325$		0			0
$326$	431.359			1.32319
$327$	−7.01447	+	7.01447i	−0.0214510	+	0.0214510i
$328$		−	68.3609i		−	0.208417i
$329$			946.776i			2.87774i
$330$		0			0
$331$	−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
$335$		0			0
$336$	−5.74973	+	5.74973i	−0.0171123	+	0.0171123i
$337$	−435.251			−1.29155			−0.645774	−	0.763529i	$-0.723465\pi$
$337$	−435.251			−1.29155			−0.645774	+	0.763529i	$0.723465\pi$
$338$	−50.6727	+	233.569i	−0.149919	+	0.691031i
$339$	28.4037			0.0837867
$340$		0			0
$341$	−72.0567			−0.211310
$342$	6.37804			0.0186493
$343$	−145.002	+	145.002i	−0.422747	+	0.422747i
$344$	123.146	+	123.146i	0.357981	+	0.357981i
$345$		0			0
$346$	192.962	−	192.962i	0.557694	−	0.557694i
$347$		−	297.980i		−	0.858732i	−0.903131	−	0.429366i	$-0.858737\pi$
$347$		−	297.980i		−	0.858732i	0.903131	−	0.429366i	$-0.141263\pi$
$348$	7.97686			0.0229220
$349$	−374.694	+	374.694i	−1.07362	+	1.07362i	−0.0765559	+	0.997065i	$0.524392\pi$
$349$	−374.694	+	374.694i	−1.07362	+	1.07362i	−0.997065	+	0.0765559i	$0.975608\pi$
$350$		0			0
$351$	12.3793	+	42.1163i	0.0352686	+	0.119989i
$352$		−	14.0974i		−	0.0400493i
$353$	218.962	−	218.962i	0.620289	−	0.620289i	−0.325316	−	0.945605i	$-0.605471\pi$
$353$	218.962	−	218.962i	0.620289	−	0.620289i	0.945605	+	0.325316i	$0.105471\pi$
$354$	0.901222			0.00254583
$355$		0			0
$356$	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	−0.880469	−	0.474103i	$-0.842772\pi$
$359$	−145.885	+	145.885i	−0.406366	+	0.406366i	0.474103	+	0.880469i	$0.342772\pi$
$360$		0			0
$361$		−	360.747i		−	0.999299i
$362$	14.6359	+	14.6359i	0.0404308	+	0.0404308i
$363$	21.5766			0.0594397
$364$	−134.689	+	246.829i	−0.370025	+	0.678102i
$365$		0			0
$366$	17.3441	+	17.3441i	0.0473883	+	0.0473883i
$367$			229.252i			0.624665i	0.949973	+	0.312333i	$0.101110\pi$
$367$			229.252i			0.624665i	−0.949973	+	0.312333i	$0.898890\pi$
$368$	−6.51361			−0.0177000
$369$	−153.208	−	153.208i	−0.415199	−	0.415199i
$370$		0			0
$371$	−538.726	+	538.726i	−1.45209	+	1.45209i
$372$	7.68614	+	7.68614i	0.0206617	+	0.0206617i
$373$		−	461.367i		−	1.23691i	−0.785821	−	0.618455i	$-0.787759\pi$
$373$		−	461.367i		−	1.23691i	0.785821	−	0.618455i	$-0.212241\pi$
$374$			93.0100i			0.248690i
$375$		0			0
$376$			247.612i			0.658542i
$377$	264.649	−	77.7885i	0.701987	−	0.206335i
$378$			51.6460i			0.136630i
$379$	−416.393	−	416.393i	−1.09866	−	1.09866i	−0.994567	−	0.104095i	$-0.966806\pi$
$379$	−416.393	−	416.393i	−1.09866	−	1.09866i	−0.104095	−	0.994567i	$-0.533194\pi$
$380$		0			0
$381$		−	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	$-0.720438\pi$
$383$	50.2312	−	50.2312i	0.131152	−	0.131152i	0.769635	+	0.638484i	$0.220438\pi$
$384$	−1.50374	+	1.50374i	−0.00391598	+	0.00391598i
$385$		0			0
$386$	−184.923			−0.479076
$387$	551.980			1.42630
$388$	−77.6210	−	77.6210i	−0.200054	−	0.200054i
$389$			124.097i			0.319016i	0.987197	+	0.159508i	$0.0509907\pi$
$389$			124.097i			0.319016i	−0.987197	+	0.159508i	$0.949009\pi$
$390$		0			0
$391$	42.9748			0.109910
$392$	−135.923	+	135.923i	−0.346741	+	0.346741i
$393$			18.7047i			0.0475946i
$394$		−	466.487i		−	1.18398i
$395$		0			0
$396$	−31.5945	−	31.5945i	−0.0797841	−	0.0797841i
$397$	−115.669	−	115.669i	−0.291358	−	0.291358i	0.546258	−	0.837617i	$-0.316052\pi$
$397$	−115.669	−	115.669i	−0.291358	−	0.291358i	−0.837617	+	0.546258i	$0.816052\pi$
$398$	124.528	+	124.528i	0.312884	+	0.312884i
$399$	−1.02268			−0.00256311
$400$		0			0
$401$	−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	$0.950205\pi$
$402$	−20.6716			−0.0514218
$403$	329.957	+	180.050i	0.818752	+	0.446775i
$404$	184.606			0.456945
$405$		0			0
$406$	324.532			0.799339
$407$	15.4871			0.0380518
$408$	9.92118	−	9.92118i	0.0243166	−	0.0243166i
$409$	47.4016	+	47.4016i	0.115896	+	0.115896i	0.762676	−	0.646780i	$-0.223885\pi$
$409$	47.4016	+	47.4016i	0.115896	+	0.115896i	−0.646780	+	0.762676i	$0.723885\pi$
$410$		0			0
$411$	−11.6146	+	11.6146i	−0.0282594	+	0.0282594i
$412$		−	298.406i		−	0.724288i
$413$	36.6654			0.0887783
$414$	−14.5981	+	14.5981i	−0.0352611	+	0.0352611i
$415$		0			0
$416$	−35.2255	+	64.5536i	−0.0846766	+	0.155177i
$417$		−	20.1841i		−	0.0484031i
$418$	1.25372	−	1.25372i	0.00299933	−	0.00299933i
$419$	−566.058			−1.35097			−0.675487	−	0.737372i	$-0.736066\pi$
$419$	−566.058			−1.35097			−0.675487	+	0.737372i	$0.736066\pi$
$420$		0			0
$421$	−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
$425$		0			0
$426$			19.9216i			0.0467643i
$427$	705.631	+	705.631i	1.65253	+	1.65253i
$428$	−106.502			−0.248836
$429$	5.34551	+	2.91693i	0.0124604	+	0.00679936i
$430$		0			0
$431$	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	$0.565628\pi$
$432$			13.5071i			0.0312663i
$433$	−564.564			−1.30384			−0.651922	−	0.758286i	$-0.726037\pi$
$433$	−564.564			−1.30384			−0.651922	+	0.758286i	$0.726037\pi$
$434$	312.704	+	312.704i	0.720515	+	0.720515i
$435$		0			0
$436$	−74.6351	+	74.6351i	−0.171181	+	0.171181i
$437$	−0.579275	−	0.579275i	−0.00132557	−	0.00132557i
$438$		−	35.3347i		−	0.0806728i
$439$		−	39.2264i		−	0.0893541i	−0.999001	−	0.0446770i	$-0.985774\pi$
$439$		−	39.2264i		−	0.0893541i	0.999001	−	0.0446770i	$-0.0142259\pi$
$440$		0			0
$441$			609.251i			1.38152i
$442$	232.407	−	425.905i	0.525807	−	0.963585i
$443$		−	288.946i		−	0.652248i	−0.945327	−	0.326124i	$-0.894257\pi$
$443$		−	288.946i		−	0.652248i	0.945327	−	0.326124i	$-0.105743\pi$
$444$	−1.65198	−	1.65198i	−0.00372067	−	0.00372067i
$445$		0			0
$446$		−	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	−0.890890	−	0.454219i	$-0.849918\pi$
$449$	−196.065	+	196.065i	−0.436671	+	0.436671i	0.454219	+	0.890890i	$0.349918\pi$
$450$		0			0
$451$	−60.2318			−0.133552
$452$	302.220			0.668629
$453$	−30.2338	−	30.2338i	−0.0667413	−	0.0667413i
$454$			166.912i			0.367647i
$455$		0			0
$456$	−0.267464			−0.000586543
$457$	−263.894	+	263.894i	−0.577448	+	0.577448i	−0.934199	−	0.356751i	$-0.883884\pi$
$457$	−263.894	+	263.894i	−0.577448	+	0.577448i	0.356751	+	0.934199i	$0.383884\pi$
$458$			537.803i			1.17424i
$459$		−	89.1153i		−	0.194151i
$460$		0			0
$461$	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	−0.996535	−	0.0831730i	$-0.973495\pi$
$463$	−499.905	−	499.905i	−1.07971	−	1.07971i	−0.0831730	−	0.996535i	$-0.526505\pi$
$464$	84.8752			0.182921
$465$		0			0
$466$	−24.5841	+	24.5841i	−0.0527555	+	0.0527555i
$467$	732.570			1.56867			0.784337	−	0.620335i	$-0.213004\pi$
$467$	732.570			1.56867			0.784337	+	0.620335i	$0.213004\pi$
$468$	65.7293	+	223.622i	0.140447	+	0.477824i
$469$	−841.004			−1.79319
$470$		0			0
$471$	−11.8895			−0.0252431
$472$	9.58916			0.0203160
$473$	108.502	−	108.502i	0.229390	−	0.229390i
$474$	−4.26527	−	4.26527i	−0.00899846	−	0.00899846i
$475$		0			0
$476$	403.634	−	403.634i	0.847971	−	0.847971i
$477$			631.533i			1.32397i
$478$	98.1540			0.205343
$479$	403.609	−	403.609i	0.842607	−	0.842607i	−0.146590	−	0.989197i	$-0.546830\pi$
$479$	403.609	−	403.609i	0.842607	−	0.842607i	0.989197	+	0.146590i	$0.0468298\pi$
$480$		0			0
$481$	−70.9174	−	38.6981i	−0.147438	−	0.0804534i
$482$		−	415.400i		−	0.861825i
$483$	2.34072	−	2.34072i	0.00484621	−	0.00484621i
$484$	229.579			0.474337
$485$		0			0
$486$	45.4371	+	45.4371i	0.0934920	+	0.0934920i
$487$	−144.597	+	144.597i	−0.296914	+	0.296914i	−0.839804	−	0.542890i	$-0.817330\pi$
$487$	−144.597	+	144.597i	−0.296914	+	0.296914i	0.542890	+	0.839804i	$0.317330\pi$
$488$	184.545	+	184.545i	0.378165	+	0.378165i
$489$	−40.5406	+	40.5406i	−0.0829052	+	0.0829052i
$490$		0			0
$491$		−	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
$493$	−559.980			−1.13586
$494$	−8.87366	+	2.60824i	−0.0179629	+	0.00527984i
$495$		0			0
$496$	81.7818	+	81.7818i	0.164883	+	0.164883i
$497$			810.492i			1.63077i
$498$	−31.9219			−0.0641002
$499$	212.583	+	212.583i	0.426018	+	0.426018i	0.887270	−	0.461251i	$-0.152599\pi$
$499$	212.583	+	212.583i	0.426018	+	0.426018i	−0.461251	+	0.887270i	$0.652599\pi$
$500$		0			0
$501$	−20.3160	+	20.3160i	−0.0405510	+	0.0405510i
$502$	196.267	+	196.267i	0.390971	+	0.390971i
$503$			607.595i			1.20794i	0.797006	+	0.603972i	$0.206416\pi$
$503$			607.595i			1.20794i	−0.797006	+	0.603972i	$0.793584\pi$
$504$			274.221i			0.544089i
$505$		0			0
$506$			5.73904i			0.0113420i
$507$	−17.1892	−	26.7140i	−0.0339037	−	0.0526903i
$508$		−	136.840i		−	0.269370i
$509$	−20.2278	−	20.2278i	−0.0397404	−	0.0397404i	0.686957	−	0.726698i	$-0.258946\pi$
$509$	−20.2278	−	20.2278i	−0.0397404	−	0.0397404i	−0.726698	+	0.686957i	$0.758946\pi$
$510$		0			0
$511$		−	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
$515$		0			0
$516$	−23.1473			−0.0448591
$517$	218.167			0.421986
$518$	−67.2092	−	67.2092i	−0.129747	−	0.129747i
$519$			36.2705i			0.0698853i
$520$		0			0
$521$	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
$523$		−	941.789i		−	1.80074i	−0.435122	−	0.900372i	$-0.643295\pi$
$523$		−	941.789i		−	1.80074i	0.435122	−	0.900372i	$-0.356705\pi$
$524$			199.021i			0.379811i
$525$		0			0
$526$	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
$530$		0			0
$531$	21.4909	−	21.4909i	0.0404725	−	0.0404725i
$532$	−10.8815			−0.0204540
$533$	275.809	+	150.503i	0.517465	+	0.282369i
$534$	−1.32988			−0.00249041
$535$		0			0
$536$	−219.949			−0.410353
$537$	−57.2017			−0.106521
$538$	342.640	−	342.640i	0.636878	−	0.636878i
$539$	119.759	+	119.759i	0.222188	+	0.222188i
$540$		0			0
$541$	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	$0.0417861\pi$
$542$			544.211i			1.00408i
$543$	−2.75107			−0.00506643
$544$	105.563	−	105.563i	0.194050	−	0.194050i
$545$		0			0
$546$	−10.5393	−	35.8564i	−0.0193028	−	0.0656711i
$547$			477.379i			0.872722i	0.899772	+	0.436361i	$0.143733\pi$
$547$			477.379i			0.872722i	−0.899772	+	0.436361i	$0.856267\pi$
$548$	−123.582	+	123.582i	−0.225514	+	0.225514i
$549$	827.190			1.50672
$550$		0			0
$551$	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
$555$		0			0
$556$		−	214.762i		−	0.386263i
$557$	−402.711	−	402.711i	−0.723000	−	0.723000i	0.246215	−	0.969215i	$-0.420813\pi$
$557$	−402.711	−	402.711i	−0.723000	−	0.723000i	−0.969215	+	0.246215i	$0.920813\pi$
$558$	366.573			0.656942
$559$	−767.959	+	225.727i	−1.37381	+	0.403805i
$560$		0			0
$561$	−8.74140	−	8.74140i	−0.0155818	−	0.0155818i
$562$			236.975i			0.421663i
$563$	1054.07			1.87223			0.936115	−	0.351693i	$-0.114394\pi$
$563$	1054.07			1.87223			0.936115	+	0.351693i	$0.114394\pi$
$564$	−23.2714	−	23.2714i	−0.0412613	−	0.0412613i
$565$		0			0
$566$	128.404	−	128.404i	0.226862	−	0.226862i
$567$	612.143	+	612.143i	1.07962	+	1.07962i
$568$			211.969i			0.373185i
$569$		−	94.6489i		−	0.166343i	−0.996535	−	0.0831713i	$-0.973495\pi$
$569$		−	94.6489i		−	0.166343i	0.996535	−	0.0831713i	$-0.0265049\pi$
$570$		0			0
$571$			277.863i			0.486625i	0.969948	+	0.243312i	$0.0782340\pi$
$571$			277.863i			0.486625i	−0.969948	+	0.243312i	$0.921766\pi$
$572$	56.8772	+	31.0366i	0.0994356	+	0.0542598i
$573$		−	5.81359i		−	0.0101459i
$574$	261.387	+	261.387i	0.455378	+	0.455378i
$575$		0			0
$576$			71.7173i			0.124509i
$577$	−117.434	+	117.434i	−0.203525	+	0.203525i	−0.801509	−	0.597983i	$-0.795969\pi$
$577$	−117.434	+	117.434i	−0.203525	+	0.203525i	0.597983	+	0.801509i	$0.295969\pi$
$578$	−407.472	+	407.472i	−0.704970	+	0.704970i
$579$	17.3797	−	17.3797i	0.0300168	−	0.0300168i
$580$		0			0
$581$	−1298.71			−2.23531
$582$	14.5902			0.0250690
$583$	124.139	+	124.139i	0.212932	+	0.212932i
$584$		−	375.967i		−	0.643780i
$585$		0			0
$586$	−657.657			−1.12228
$587$	172.094	−	172.094i	0.293175	−	0.293175i	−0.545158	−	0.838333i	$-0.683530\pi$
$587$	172.094	−	172.094i	0.293175	−	0.293175i	0.838333	+	0.545158i	$0.183530\pi$
$588$		−	25.5490i		−	0.0434506i
$589$			14.5462i			0.0246965i
$590$		0			0
$591$	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	0.965553	−	0.260208i	$-0.0837910\pi$
$593$	418.270	+	418.270i	0.705345	+	0.705345i	−0.260208	+	0.965553i	$0.583791\pi$
$594$	11.9009			0.0200351
$595$		0			0
$596$	76.4090	−	76.4090i	0.128203	−	0.128203i
$597$	−23.4071			−0.0392079
$598$	14.3403	−	26.2798i	0.0239804	−	0.0439462i
$599$	−168.566			−0.281412			−0.140706	−	0.990051i	$-0.544937\pi$
$599$	−168.566			−0.281412			−0.140706	+	0.990051i	$0.544937\pi$
$600$		0			0
$601$	566.888			0.943241			0.471621	−	0.881802i	$-0.343669\pi$
$601$	566.888			0.943241			0.471621	+	0.881802i	$0.343669\pi$
$602$	−941.727			−1.56433
$603$	−492.943	+	492.943i	−0.817484	+	0.817484i
$604$	−321.693	−	321.693i	−0.532604	−	0.532604i
$605$		0			0
$606$	−17.3499	+	17.3499i	−0.0286301	+	0.0286301i
$607$		−	1123.79i		−	1.85139i	−0.378273	−	0.925694i	$-0.623482\pi$
$607$		−	1123.79i		−	1.85139i	0.378273	−	0.925694i	$-0.376518\pi$
$608$	−2.84586			−0.00468069
$609$	−30.5006	+	30.5006i	−0.0500831	+	0.0500831i
$610$		0			0
$611$	−999.014	−	545.140i	−1.63505	−	0.892209i
$612$		−	473.169i		−	0.773152i
$613$	−233.486	+	233.486i	−0.380891	+	0.380891i	−0.871423	−	0.490532i	$-0.836802\pi$
$613$	−233.486	+	233.486i	−0.380891	+	0.380891i	0.490532	+	0.871423i	$0.336802\pi$
$614$	−312.520			−0.508990
$615$		0			0
$616$	53.9031	+	53.9031i	0.0875050	+	0.0875050i
$617$	659.727	−	659.727i	1.06925	−	1.06925i	0.0718332	−	0.997417i	$-0.477115\pi$
$617$	659.727	−	659.727i	1.06925	−	1.06925i	0.997417	−	0.0718332i	$-0.0228849\pi$
$618$	28.0453	+	28.0453i	0.0453807	+	0.0453807i
$619$	−25.5045	+	25.5045i	−0.0412027	+	0.0412027i	−0.727408	−	0.686205i	$-0.759275\pi$
$619$	−25.5045	+	25.5045i	−0.0412027	+	0.0412027i	0.686205	+	0.727408i	$0.259275\pi$
$620$		0			0
$621$		−	5.49873i		−	0.00885463i
$622$	392.832	+	392.832i	0.631563	+	0.631563i
$623$	−54.1048			−0.0868457
$624$	−2.75636	−	9.37758i	−0.00441724	−	0.0150282i
$625$		0			0
$626$	504.068	+	504.068i	0.805220	+	0.805220i
$627$			0.235658i			0.000375850i
$628$	−126.506			−0.201443
$629$	115.970	+	115.970i	0.184372	+	0.184372i
$630$		0			0
$631$	−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
$633$		−	26.3678i		−	0.0416553i
$634$		−	706.849i		−	1.11490i
$635$		0			0
$636$		−	26.4834i		−	0.0416405i
$637$	−249.147	−	847.640i	−0.391126	−	1.33067i
$638$		−	74.7822i		−	0.117213i
$639$	475.058	+	475.058i	0.743440	+	0.743440i
$640$		0			0
$641$		−	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	$-0.783375\pi$
$643$	−95.1695	+	95.1695i	−0.148008	+	0.148008i	0.629219	+	0.777228i	$0.283375\pi$
$644$	24.9056	−	24.9056i	0.0386734	−	0.0386734i
$645$		0			0
$646$	18.7761			0.0290652
$647$	1178.14			1.82093			0.910465	−	0.413586i	$-0.135724\pi$
$647$	1178.14			1.82093			0.910465	+	0.413586i	$0.135724\pi$
$648$	160.095	+	160.095i	0.247060	+	0.247060i
$649$		−	8.44886i		−	0.0130183i
$650$		0			0
$651$	−58.7779			−0.0902887
$652$	−431.359	+	431.359i	−0.661594	+	0.661594i
$653$		−	375.998i		−	0.575801i	−0.957660	−	0.287901i	$-0.907043\pi$
$653$		−	375.998i		−	0.575801i	0.957660	−	0.287901i	$-0.0929573\pi$
$654$		−	14.0289i		−	0.0214510i
$655$		0			0
$656$	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	$-0.458004\pi$
$659$	173.387			0.263107			0.131553	+	0.991309i	$0.458004\pi$
$660$		0			0
$661$	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	$0.150140\pi$
$662$	324.019			0.489455
$663$	18.1856	+	61.8704i	0.0274293	+	0.0933188i
$664$	−339.655			−0.511528
$665$		0			0
$666$	−78.7874			−0.118299
$667$	−34.5527			−0.0518032
$668$	−216.166	+	216.166i	−0.323602	+	0.323602i
$669$	23.9163	+	23.9163i	0.0357494	+	0.0357494i
$670$		0			0
$671$	162.599	−	162.599i	0.242324	−	0.242324i
$672$		−	11.4995i		−	0.0171123i
$673$	356.877			0.530278			0.265139	−	0.964210i	$-0.414582\pi$
$673$	356.877			0.530278			0.265139	+	0.964210i	$0.414582\pi$
$674$	435.251	−	435.251i	0.645774	−	0.645774i
$675$		0			0
$676$	−182.896	−	284.241i	−0.270556	−	0.420475i
$677$		−	90.7269i		−	0.134013i	−0.997753	−	0.0670066i	$-0.978655\pi$
$677$		−	90.7269i		−	0.134013i	0.997753	−	0.0670066i	$-0.0213449\pi$
$678$	−28.4037	+	28.4037i	−0.0418934	+	0.0418934i
$679$	593.588			0.874209
$680$		0			0
$681$	−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	0.00262177	−	0.999997i	$-0.499165\pi$
$683$	−681.207	−	681.207i	−0.997375	−	0.997375i	−0.999997	+	0.00262177i	$0.999165\pi$
$684$	−6.37804	+	6.37804i	−0.00932463	+	0.00932463i
$685$		0			0
$686$		−	290.005i		−	0.422747i
$687$	−50.5446	−	50.5446i	−0.0735729	−	0.0735729i
$688$	−246.291			−0.357981
$689$	−258.260	−	878.641i	−0.374833	−	1.27524i
$690$		0			0
$691$	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	$0.693774\pi$
$692$			385.924i			0.557694i
$693$	241.612			0.348646
$694$	297.980	+	297.980i	0.429366	+	0.429366i
$695$		0			0
$696$	−7.97686	+	7.97686i	−0.0114610	+	0.0114610i
$697$	−451.024	−	451.024i	−0.647094	−	0.647094i
$698$		−	749.388i		−	1.07362i
$699$		−	4.62099i		−	0.00661086i
$700$		0			0
$701$			995.235i			1.41974i	0.704335	+	0.709868i	$0.251246\pi$
$701$			995.235i			1.41974i	−0.704335	+	0.709868i	$0.748754\pi$
$702$	−54.4955	−	29.7370i	−0.0776290	−	0.0423604i
$703$		−	3.12641i		−	0.00444724i
$704$	14.0974	+	14.0974i	0.0200246	+	0.0200246i
$705$		0			0
$706$			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	−0.614376	−	0.789013i	$-0.710592\pi$
$709$	123.817	−	123.817i	0.174637	−	0.174637i	0.789013	+	0.614376i	$0.210592\pi$
$710$		0			0
$711$	−203.423			−0.286108
$712$	−14.1501			−0.0198738
$713$	−33.2934	−	33.2934i	−0.0466948	−	0.0466948i
$714$			75.8699i			0.106260i
$715$		0			0
$716$	−608.636			−0.850051
$717$	−9.22485	+	9.22485i	−0.0128659	+	0.0128659i
$718$		−	291.771i		−	0.406366i
$719$		−	758.861i		−	1.05544i	−0.849418	−	0.527720i	$-0.823047\pi$
$719$		−	758.861i		−	1.05544i	0.849418	−	0.527720i	$-0.176953\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−21.5766	+	21.5766i	−0.0297199	+	0.0297199i
$727$	−661.575			−0.910006			−0.455003	−	0.890490i	$-0.650362\pi$
$727$	−661.575			−0.910006			−0.455003	+	0.890490i	$0.650362\pi$
$728$	−112.140	−	381.518i	−0.154039	−	0.524064i
$729$	711.885			0.976523
$730$		0			0
$731$	1624.95			2.22292
$732$	−34.6883			−0.0473883
$733$	−272.217	+	272.217i	−0.371373	+	0.371373i	−0.867977	−	0.496604i	$-0.834580\pi$
$733$	−272.217	+	272.217i	−0.371373	+	0.371373i	0.496604	+	0.867977i	$0.334580\pi$
$734$	−229.252	−	229.252i	−0.312333	−	0.312333i
$735$		0			0
$736$	6.51361	−	6.51361i	0.00885001	−	0.00885001i
$737$			193.794i			0.262949i
$738$	306.417			0.415199
$739$	514.947	−	514.947i	0.696816	−	0.696816i	−0.266906	−	0.963723i	$-0.586001\pi$
$739$	514.947	−	514.947i	0.696816	−	0.696816i	0.963723	+	0.266906i	$0.0860014\pi$
$740$		0			0
$741$	0.588845	−	1.07911i	0.000794663	−	0.00145629i
$742$		−	1077.45i		−	1.45209i
$743$	−368.873	+	368.873i	−0.496464	+	0.496464i	−0.910335	−	0.413871i	$-0.864176\pi$
$743$	−368.873	+	368.873i	−0.496464	+	0.496464i	0.413871	+	0.910335i	$0.364176\pi$
$744$	−15.3723			−0.0206617
$745$		0			0
$746$	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
$750$		0			0
$751$		−	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
$753$	−36.8917			−0.0489930
$754$	−186.860	+	342.437i	−0.247826	+	0.454161i
$755$		0			0
$756$	−51.6460	−	51.6460i	−0.0683148	−	0.0683148i
$757$			135.304i			0.178737i	0.995999	+	0.0893683i	$0.0284848\pi$
$757$			135.304i			0.178737i	−0.995999	+	0.0893683i	$0.971515\pi$
$758$	832.786			1.09866
$759$	−0.539375	−	0.539375i	−0.000710638	−	0.000710638i
$760$		0			0
$761$	−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
$763$		−	570.755i		−	0.748040i
$764$		−	61.8576i		−	0.0809654i
$765$		0			0
$766$			100.462i			0.131152i
$767$	−21.1114	+	38.6884i	−0.0275247	+	0.0504412i
$768$		−	3.00747i		−	0.00391598i
$769$	−562.798	−	562.798i	−0.731857	−	0.731857i	0.239130	−	0.970987i	$-0.423138\pi$
$769$	−562.798	−	562.798i	−0.731857	−	0.731857i	−0.970987	+	0.239130i	$0.923138\pi$
$770$		0			0
$771$		−	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	$-0.549132\pi$
$773$	644.968	−	644.968i	0.834370	−	0.834370i	0.988111	+	0.153741i	$0.0491322\pi$
$774$	−551.980	+	551.980i	−0.713152	+	0.713152i
$775$		0			0
$776$	155.242			0.200054
$777$	12.6331			0.0162588
$778$	−124.097	−	124.097i	−0.159508	−	0.159508i
$779$			12.1591i			0.0156086i
$780$		0			0
$781$	186.763			0.239133
$782$	−42.9748	+	42.9748i	−0.0549549	+	0.0549549i
$783$			71.6508i			0.0915081i
$784$		−	271.845i		−	0.346741i
$785$		0			0
$786$	−18.7047	−	18.7047i	−0.0237973	−	0.0237973i
$787$	−994.400	−	994.400i	−1.26353	−	1.26353i	−0.949369	−	0.314163i	$-0.898276\pi$
$787$	−994.400	−	994.400i	−1.26353	−	1.26353i	−0.314163	−	0.949369i	$-0.601724\pi$
$788$	466.487	+	466.487i	0.591989	+	0.591989i
$789$	−3.13638			−0.00397513
$790$		0			0
$791$	−1155.58	+	1155.58i	−1.46091	+	1.46091i
$792$	63.1890			0.0797841
$793$	−1150.86	+	338.272i	−1.45127	+	0.426572i
$794$	231.339			0.291358
$795$		0			0
$796$	−249.056			−0.312884
$797$	977.970			1.22706			0.613532	−	0.789670i	$-0.289748\pi$
$797$	977.970			1.22706			0.613532	+	0.789670i	$0.289748\pi$
$798$	1.02268	−	1.02268i	0.00128156	−	0.00128156i
$799$	1633.66	+	1633.66i	2.04464	+	2.04464i
$800$		0			0
$801$	−31.7128	+	31.7128i	−0.0395915	+	0.0395915i
$802$		−	917.156i		−	1.14359i
$803$	−331.259			−0.412527
$804$	20.6716	−	20.6716i	0.0257109	−	0.0257109i
$805$		0			0
$806$	−510.007	+	149.907i	−0.632763	+	0.185989i
$807$			64.4051i			0.0798080i
$808$	−184.606	+	184.606i	−0.228472	+	0.228472i
$809$	918.681			1.13558			0.567788	−	0.823175i	$-0.307799\pi$
$809$	918.681			1.13558			0.567788	+	0.823175i	$0.307799\pi$
$810$		0			0
$811$	−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
$815$		0			0
$816$			19.8424i			0.0243166i
$817$	−21.9034	−	21.9034i	−0.0268096	−	0.0268096i
$818$	−94.8031			−0.115896
$819$	−1106.37	−	603.722i	−1.35088	−	0.737145i
$820$		0			0
$821$	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	$0.605918\pi$
$822$		−	23.2292i		−	0.0282594i
$823$	742.190			0.901811			0.450905	−	0.892572i	$-0.351101\pi$
$823$	742.190			0.901811			0.450905	+	0.892572i	$0.351101\pi$
$824$	298.406	+	298.406i	0.362144	+	0.362144i
$825$		0			0
$826$	−36.6654	+	36.6654i	−0.0443891	+	0.0443891i
$827$	−258.499	−	258.499i	−0.312575	−	0.312575i	0.533332	−	0.845906i	$-0.320940\pi$
$827$	−258.499	−	258.499i	−0.312575	−	0.312575i	−0.845906	+	0.533332i	$0.820940\pi$
$828$		−	29.1962i		−	0.0352611i
$829$		−	287.282i		−	0.346540i	−0.984874	−	0.173270i	$-0.944567\pi$
$829$		−	287.282i		−	0.346540i	0.984874	−	0.173270i	$-0.0554333\pi$
$830$		0			0
$831$			43.8789i			0.0528025i
$832$	−29.3281	−	99.7791i	−0.0352502	−	0.119927i
$833$			1793.55i			2.15312i
$834$	20.1841	+	20.1841i	0.0242016	+	0.0242016i
$835$		0			0
$836$			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	−0.274049	−	0.961716i	$-0.588363\pi$
$839$	576.953	−	576.953i	0.687667	−	0.687667i	0.961716	+	0.274049i	$0.0883630\pi$
$840$		0			0
$841$	−390.763			−0.464641
$842$	101.076			0.120043
$843$	−22.2717	−	22.2717i	−0.0264196	−	0.0264196i
$844$		−	280.558i		−	0.332415i
$845$		0			0
$846$	−1109.88			−1.31191
$847$	−877.826	+	877.826i	−1.03639	+	1.03639i
$848$		−	281.788i		−	0.332297i
$849$			24.1357i			0.0284283i
$850$		0			0
$851$	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	0.724959	−	0.688792i	$-0.241859\pi$
$853$	30.8511	+	30.8511i	0.0361678	+	0.0361678i	−0.688792	+	0.724959i	$0.741859\pi$
$854$	−1411.26			−1.65253
$855$		0			0
$856$	106.502	−	106.502i	0.124418	−	0.124418i
$857$	−1201.42			−1.40189			−0.700946	−	0.713214i	$-0.747239\pi$
$857$	−1201.42			−1.40189			−0.700946	+	0.713214i	$0.747239\pi$
$858$	−8.26244	+	2.42859i	−0.00962988	+	0.00283052i
$859$	−602.352			−0.701225			−0.350612	−	0.936521i	$-0.614027\pi$
$859$	−602.352			−0.701225			−0.350612	+	0.936521i	$0.614027\pi$
$860$		0			0
$861$	−49.1321			−0.0570640
$862$	−667.277			−0.774103
$863$	−534.595	+	534.595i	−0.619462	+	0.619462i	−0.945393	−	0.325932i	$-0.894322\pi$
$863$	−534.595	+	534.595i	−0.619462	+	0.619462i	0.325932	+	0.945393i	$0.394322\pi$
$864$	−13.5071	−	13.5071i	−0.0156332	−	0.0156332i
$865$		0			0
$866$	564.564	−	564.564i	0.651922	−	0.651922i
$867$		−	76.5913i		−	0.0883406i
$868$	−625.407			−0.720515
$869$	−39.9865	+	39.9865i	−0.0460143	+	0.0460143i
$870$		0			0
$871$	484.238	−	887.406i	0.555956	−	1.01884i
$872$		−	149.270i		−	0.171181i
$873$	347.923	−	347.923i	0.398537	−	0.398537i
$874$	1.15855			0.00132557
$875$		0			0
$876$	35.3347	+	35.3347i	0.0403364	+	0.0403364i
$877$	9.16265	−	9.16265i	0.0104477	−	0.0104477i	−0.701864	−	0.712311i	$-0.747648\pi$
$877$	9.16265	−	9.16265i	0.0104477	−	0.0104477i	0.712311	+	0.701864i	$0.247648\pi$
$878$	39.2264	+	39.2264i	0.0446770	+	0.0446770i
$879$	61.8089	−	61.8089i	0.0703173	−	0.0703173i
$880$		0			0
$881$		−	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
$883$	307.257			0.347969			0.173985	−	0.984748i	$-0.444336\pi$
$883$	307.257			0.347969			0.173985	+	0.984748i	$0.444336\pi$
$884$	193.498	+	658.311i	0.218889	+	0.744696i
$885$		0			0
$886$	288.946	+	288.946i	0.326124	+	0.326124i
$887$		−	1595.82i		−	1.79912i	−0.436796	−	0.899561i	$-0.643887\pi$
$887$		−	1595.82i		−	1.79912i	0.436796	−	0.899561i	$-0.356113\pi$
$888$	3.30395			0.00372067
$889$	523.225	+	523.225i	0.588555	+	0.588555i
$890$		0			0
$891$	141.057	−	141.057i	0.158313	−	0.158313i
$892$	254.474	+	254.474i	0.285285	+	0.285285i
$893$		−	44.0417i		−	0.0493188i
$894$			14.3624i			0.0160653i
$895$		0			0
$896$		−	122.356i		−	0.136558i
$897$	1.12212	+	3.81762i	0.00125096	+	0.00425598i
$898$		−	392.131i		−	0.436671i
$899$	433.828	+	433.828i	0.482567	+	0.482567i
$900$		0			0
$901$			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
$905$		0			0
$906$	60.4676			0.0667413
$907$	89.4305			0.0986003			0.0493002	−	0.998784i	$-0.484301\pi$
$907$	89.4305			0.0986003			0.0493002	+	0.998784i	$0.484301\pi$
$908$	−166.912	−	166.912i	−0.183823	−	0.183823i
$909$			827.464i			0.910301i
$910$		0			0
$911$	−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
$913$			299.264i			0.327781i
$914$		−	527.788i		−	0.577448i
$915$		0			0
$916$	−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	$-0.369620\pi$
$919$	731.973			0.796489			0.398244	+	0.917279i	$0.369620\pi$
$920$		0			0
$921$	29.3717	−	29.3717i	0.0318911	−	0.0318911i
$922$	−758.355			−0.822510
$923$	−855.211	−	466.669i	−0.926556	−	0.505601i
$924$	−10.1320			−0.0109654
$925$		0			0
$926$	999.810			1.07971
$927$	1337.56			1.44289
$928$	−84.8752	+	84.8752i	−0.0914603	+	0.0914603i
$929$	−736.879	−	736.879i	−0.793196	−	0.793196i	0.188817	−	0.982012i	$-0.439535\pi$
$929$	−736.879	−	736.879i	−0.793196	−	0.793196i	−0.982012	+	0.188817i	$0.939535\pi$
$930$		0			0
$931$	24.1760	−	24.1760i	0.0259678	−	0.0259678i
$932$		−	49.1682i		−	0.0527555i
$933$	−73.8394			−0.0791419
$934$	−732.570	+	732.570i	−0.784337	+	0.784337i
$935$		0			0
$936$	−289.351	−	157.892i	−0.309135	−	0.168688i
$937$			1217.64i			1.29951i	0.760142	+	0.649757i	$0.225129\pi$
$937$			1217.64i			1.29951i	−0.760142	+	0.649757i	$0.774871\pi$
$938$	841.004	−	841.004i	0.896593	−	0.896593i
$939$	−94.7481			−0.100903
$940$		0			0
$941$	−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
$945$		0			0
$946$			217.003i			0.229390i
$947$	149.364	+	149.364i	0.157723	+	0.157723i	0.781557	−	0.623834i	$-0.214426\pi$
$947$	149.364	+	149.364i	0.157723	+	0.157723i	−0.623834	+	0.781557i	$0.714426\pi$
$948$	8.53054			0.00899846
$949$	1516.88	+	827.726i	1.59840	+	0.872209i
$950$		0			0
$951$	66.4321	+	66.4321i	0.0698550	+	0.0698550i
$952$			807.269i			0.847971i
$953$	−462.887			−0.485715			−0.242858	−	0.970062i	$-0.578085\pi$
$953$	−462.887			−0.485715			−0.242858	+	0.970062i	$0.578085\pi$
$954$	−631.533	−	631.533i	−0.661985	−	0.661985i
$955$		0			0
$956$	−98.1540	+	98.1540i	−0.102672	+	0.102672i
$957$	7.02829	+	7.02829i	0.00734408	+	0.00734408i
$958$			807.218i			0.842607i
$959$		−	945.061i		−	0.985465i
$960$		0			0
$961$		−	124.967i		−	0.130038i
$962$	109.616	−	32.2194i	0.113945	−	0.0334921i
$963$		−	477.376i		−	0.495718i
$964$	415.400	+	415.400i	0.430912	+	0.430912i
$965$		0			0
$966$			4.68144i			0.00484621i
$967$	575.890	−	575.890i	0.595543	−	0.595543i	−0.343581	−	0.939123i	$-0.611640\pi$
$967$	575.890	−	575.890i	0.595543	−	0.595543i	0.939123	+	0.343581i	$0.111640\pi$
$968$	−229.579	+	229.579i	−0.237168	+	0.237168i
$969$	−1.76464	+	1.76464i	−0.00182110	+	0.00182110i
$970$		0			0
$971$	−103.925			−0.107029			−0.0535145	−	0.998567i	$-0.517042\pi$
$971$	−103.925			−0.107029			−0.0535145	+	0.998567i	$0.517042\pi$
$972$	−90.8742			−0.0934920
$973$	821.172	+	821.172i	0.843959	+	0.843959i
$974$		−	289.194i		−	0.296914i
$975$		0			0
$976$	−369.089			−0.378165
$977$	−503.052	+	503.052i	−0.514895	+	0.514895i	−0.916022	−	0.401128i	$-0.868618\pi$
$977$	−503.052	+	503.052i	−0.514895	+	0.514895i	0.401128	+	0.916022i	$0.368618\pi$
$978$		−	81.0813i		−	0.0829052i
$979$			12.4674i			0.0127349i
$980$		0			0
$981$	−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	0.924785	−	0.380490i	$-0.124245\pi$
$983$	535.042	+	535.042i	0.544295	+	0.544295i	−0.380490	+	0.924785i	$0.624245\pi$
$984$	−12.8496			−0.0130585
$985$		0			0
$986$	559.980	−	559.980i	0.567931	−	0.567931i
$987$	177.963			0.180306
$988$	6.26542	−	11.4819i	0.00634152	−	0.0116214i
$989$	100.265			0.101380
$990$		0			0
$991$	1066.90			1.07659			0.538295	−	0.842756i	$-0.319068\pi$
$991$	1066.90			1.07659			0.538295	+	0.842756i	$0.319068\pi$
$992$	−163.564			−0.164883
$993$	−30.4524	+	30.4524i	−0.0306671	+	0.0306671i
$994$	−810.492	−	810.492i	−0.815384	−	0.815384i
$995$		0			0
$996$	31.9219	−	31.9219i	0.0320501	−	0.0320501i
$997$		−	797.083i		−	0.799481i	−0.916628	−	0.399741i	$-0.869100\pi$
$997$		−	797.083i		−	0.799481i	0.916628	−	0.399741i	$-0.130900\pi$
$998$	−425.166			−0.426018
$999$	14.8386	−	14.8386i	0.0148535	−	0.0148535i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.k.a.21.4	✓	12	5.2	odd	4
130.3.k.a.31.4	yes	12	65.57	even	4
650.3.f.l.99.4		12	1.1	even	1	trivial
650.3.f.l.499.3		12	65.44	odd	4	inner
650.3.f.m.99.3		12	5.4	even	2
650.3.f.m.499.4		12	13.5	odd	4
650.3.k.k.151.3		12	5.3	odd	4
650.3.k.k.551.3		12	65.18	even	4
1170.3.r.b.541.1		12	15.2	even	4
1170.3.r.b.811.1		12	195.122	odd	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	650.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -0.187967i q^{3} -2.00000i q^{4} +(0.187967 + 0.187967i) q^{6} +(7.64727 + 7.64727i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.96467 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -0.187967i q^{3} -2.00000i q^{4} +(0.187967 + 0.187967i) q^{6} +(7.64727 + 7.64727i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.96467 q^{9} +(1.76217 - 1.76217i) q^{11} -0.375934 q^{12} +(-12.4724 + 3.66602i) q^{13} -15.2945 q^{14} -4.00000 q^{16} +26.3908 q^{17} +(-8.96467 + 8.96467i) q^{18} +(-0.355732 - 0.355732i) q^{19} +(1.43743 - 1.43743i) q^{21} +3.52434i q^{22} +1.62840 q^{23} +(0.375934 - 0.375934i) q^{24} +(8.80636 - 16.1384i) q^{26} -3.37676i q^{27} +(15.2945 - 15.2945i) q^{28} -21.2188 q^{29} +(-20.4455 - 20.4455i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.331229 - 0.331229i) q^{33} +(-26.3908 + 26.3908i) q^{34} -17.9293i q^{36} +(4.39433 + 4.39433i) q^{37} +0.711465 q^{38} +(0.689090 + 2.34439i) q^{39} +(-17.0902 - 17.0902i) q^{41} +2.87487i q^{42} +61.5728 q^{43} +(-3.52434 - 3.52434i) q^{44} +(-1.62840 + 1.62840i) q^{46} +(61.9029 + 61.9029i) q^{47} +0.751868i q^{48} +67.9613i q^{49} -4.96059i q^{51} +(7.33204 + 24.9448i) q^{52} +70.4469i q^{53} +(3.37676 + 3.37676i) q^{54} +30.5891i q^{56} +(-0.0668659 + 0.0668659i) q^{57} +(21.2188 - 21.2188i) q^{58} +(2.39729 - 2.39729i) q^{59} +92.2723 q^{61} +40.8909 q^{62} +(68.5552 + 68.5552i) q^{63} +8.00000i q^{64} +0.662459 q^{66} +(-54.9873 + 54.9873i) q^{67} -52.7815i q^{68} -0.306086i q^{69} +(52.9923 + 52.9923i) q^{71} +(17.9293 + 17.9293i) q^{72} +(-93.9918 - 93.9918i) q^{73} -8.78866 q^{74} +(-0.711465 + 0.711465i) q^{76} +26.9515 q^{77} +(-3.03348 - 1.65530i) q^{78} -22.6916 q^{79} +80.0473 q^{81} +34.1805 q^{82} +(-84.9136 + 84.9136i) q^{83} +(-2.87487 - 2.87487i) q^{84} +(-61.5728 + 61.5728i) q^{86} +3.98843i q^{87} +7.04868 q^{88} +(-3.53753 + 3.53753i) q^{89} +(-123.415 - 67.3446i) q^{91} -3.25680i q^{92} +(-3.84307 + 3.84307i) q^{93} -123.806 q^{94} +(-0.751868 - 0.751868i) q^{96} +(38.8105 - 38.8105i) q^{97} +(-67.9613 - 67.9613i) q^{98} +(15.7973 - 15.7973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 24 q^{8} - 44 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 24 * q^8 - 44 * q^9	\( 12 q - 12 q^{2} + 24 q^{8} - 44 q^{9} + 8 q^{11} - 4 q^{13} - 48 q^{16} + 44 q^{18} - 36 q^{19} + 52 q^{21} + 96 q^{23} + 8 q^{26} + 8 q^{29} - 136 q^{31} + 48 q^{32} - 60 q^{33} + 44 q^{37} + 72 q^{38} + 172 q^{39} + 32 q^{41} - 224 q^{43} - 16 q^{44} - 96 q^{46} + 16 q^{47} - 8 q^{52} + 144 q^{54} - 212 q^{57} - 8 q^{58} - 124 q^{59} + 24 q^{61} + 272 q^{62} - 80 q^{63} + 120 q^{66} + 136 q^{67} + 84 q^{71} - 88 q^{72} + 12 q^{73} - 88 q^{74} - 72 q^{76} - 48 q^{77} - 32 q^{78} + 168 q^{79} + 596 q^{81} - 64 q^{82} - 160 q^{83} - 104 q^{84} + 224 q^{86} + 32 q^{88} + 44 q^{89} - 404 q^{91} - 4 q^{93} - 32 q^{94} - 192 q^{97} + 60 q^{98} + 52 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 24 * q^8 - 44 * q^9 + 8 * q^11 - 4 * q^13 - 48 * q^16 + 44 * q^18 - 36 * q^19 + 52 * q^21 + 96 * q^23 + 8 * q^26 + 8 * q^29 - 136 * q^31 + 48 * q^32 - 60 * q^33 + 44 * q^37 + 72 * q^38 + 172 * q^39 + 32 * q^41 - 224 * q^43 - 16 * q^44 - 96 * q^46 + 16 * q^47 - 8 * q^52 + 144 * q^54 - 212 * q^57 - 8 * q^58 - 124 * q^59 + 24 * q^61 + 272 * q^62 - 80 * q^63 + 120 * q^66 + 136 * q^67 + 84 * q^71 - 88 * q^72 + 12 * q^73 - 88 * q^74 - 72 * q^76 - 48 * q^77 - 32 * q^78 + 168 * q^79 + 596 * q^81 - 64 * q^82 - 160 * q^83 - 104 * q^84 + 224 * q^86 + 32 * q^88 + 44 * q^89 - 404 * q^91 - 4 * q^93 - 32 * q^94 - 192 * q^97 + 60 * q^98 + 52 * q^99

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