LMFDB - Embedded newform 429.2.bd.a.175.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			175.1
Character	$\chi$	$=$	429.175
Dual form			429.2.bd.a.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55489 + 0.684581i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(4.32676 - 2.49806i) q^{4} +(-2.81573 + 2.81573i) q^{5} +(0.684581 - 2.55489i) q^{6} +(-2.71459 - 0.727372i) q^{7} +(-5.60366 + 5.60366i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.55489 + 0.684581i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(4.32676 - 2.49806i) q^{4} +(-2.81573 + 2.81573i) q^{5} +(0.684581 - 2.55489i) q^{6} +(-2.71459 - 0.727372i) q^{7} +(-5.60366 + 5.60366i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(5.26630 - 9.12149i) q^{10} +(0.108880 - 3.31484i) q^{11} +4.99612i q^{12} +(-1.12646 + 3.42507i) q^{13} +7.43342 q^{14} +(-1.03063 - 3.84637i) q^{15} +(5.48447 - 9.49938i) q^{16} +(0.408347 + 0.707277i) q^{17} +(1.87031 + 1.87031i) q^{18} +(-0.0308856 + 0.115266i) q^{19} +(-5.14915 + 19.2169i) q^{20} +(1.98722 - 1.98722i) q^{21} +(1.99110 + 8.54358i) q^{22} +(-5.97852 - 3.45170i) q^{23} +(-2.05108 - 7.65475i) q^{24} -10.8567i q^{25} +(0.533254 - 9.52182i) q^{26} +1.00000 q^{27} +(-13.5624 + 3.63403i) q^{28} +(4.48350 + 2.58855i) q^{29} +(5.26630 + 9.12149i) q^{30} +(-4.79316 + 4.79316i) q^{31} +(-3.40696 + 12.7149i) q^{32} +(2.81629 + 1.75171i) q^{33} +(-1.52747 - 1.52747i) q^{34} +(9.69165 - 5.59547i) q^{35} +(-4.32676 - 2.49806i) q^{36} +(8.78532 - 2.35402i) q^{37} -0.315637i q^{38} +(-2.40296 - 2.68808i) q^{39} -31.5569i q^{40} +(7.35389 - 1.97047i) q^{41} +(-3.71671 + 6.43753i) q^{42} +(1.75279 + 3.03593i) q^{43} +(-7.80956 - 14.6145i) q^{44} +(3.84637 + 1.03063i) q^{45} +(17.6374 + 4.72594i) q^{46} +(1.67231 + 1.67231i) q^{47} +(5.48447 + 9.49938i) q^{48} +(0.777740 + 0.449028i) q^{49} +(7.43231 + 27.7377i) q^{50} -0.816693 q^{51} +(3.68208 + 17.6334i) q^{52} +6.49016 q^{53} +(-2.55489 + 0.684581i) q^{54} +(9.02713 + 9.64028i) q^{55} +(19.2876 - 11.1357i) q^{56} +(-0.0843809 - 0.0843809i) q^{57} +(-13.2269 - 3.54414i) q^{58} +(2.54445 - 9.49602i) q^{59} +(-14.0677 - 14.0677i) q^{60} +(1.23600 - 0.713606i) q^{61} +(8.96468 - 15.5273i) q^{62} +(0.727372 + 2.71459i) q^{63} -12.8797i q^{64} +(-6.47226 - 12.8159i) q^{65} +(-8.39451 - 2.54745i) q^{66} +(-1.73257 - 6.46604i) q^{67} +(3.53364 + 2.04015i) q^{68} +(5.97852 - 3.45170i) q^{69} +(-20.9305 + 20.9305i) q^{70} +(2.79924 + 0.750055i) q^{71} +(7.65475 + 2.05108i) q^{72} +(0.797494 - 0.797494i) q^{73} +(-20.8340 + 12.0285i) q^{74} +(9.40220 + 5.42836i) q^{75} +(0.154308 + 0.575885i) q^{76} +(-2.70668 + 8.91922i) q^{77} +(7.97951 + 5.22272i) q^{78} -7.81765i q^{79} +(11.3049 + 42.1905i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-17.4394 + 10.0687i) q^{82} +(-10.4366 - 10.4366i) q^{83} +(3.63403 - 13.5624i) q^{84} +(-3.14130 - 0.841709i) q^{85} +(-6.55654 - 6.55654i) q^{86} +(-4.48350 + 2.58855i) q^{87} +(17.9651 + 19.1854i) q^{88} +(-9.16067 + 2.45459i) q^{89} -10.5326 q^{90} +(5.54918 - 8.47829i) q^{91} -34.4902 q^{92} +(-1.75442 - 6.54757i) q^{93} +(-5.41740 - 3.12774i) q^{94} +(-0.237594 - 0.411525i) q^{95} +(-9.30798 - 9.30798i) q^{96} +(4.41716 + 1.18358i) q^{97} +(-2.29444 - 0.614792i) q^{98} +(-2.92517 + 1.56313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.55489	+	0.684581i	−1.80658	+	0.484072i	−0.994974	−	0.100133i	$-0.968073\pi$
$2$	−2.55489	+	0.684581i	−1.80658	+	0.484072i	−0.811606	+	0.584205i	$0.801406\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	4.32676	−	2.49806i	2.16338	−	1.24903i
$5$	−2.81573	+	2.81573i	−1.25923	+	1.25923i	−0.307776	+	0.951459i	$0.599585\pi$
$5$	−2.81573	+	2.81573i	−1.25923	+	1.25923i	−0.951459	+	0.307776i	$0.900415\pi$
$6$	0.684581	−	2.55489i	0.279479	−	1.04303i
$7$	−2.71459	−	0.727372i	−1.02602	−	0.274921i	−0.293710	−	0.955895i	$-0.594890\pi$
$7$	−2.71459	−	0.727372i	−1.02602	−	0.274921i	−0.732308	+	0.680974i	$0.761557\pi$
$8$	−5.60366	+	5.60366i	−1.98119	+	1.98119i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	5.26630	−	9.12149i	1.66535	−	2.88447i
$11$	0.108880	−	3.31484i	0.0328284	−	0.999461i
$11$	0.108880	−	3.31484i	0.0328284	−	0.999461i
$12$			4.99612i			1.44225i
$13$	−1.12646	+	3.42507i	−0.312425	+	0.949943i
$13$	−1.12646	+	3.42507i	−0.312425	+	0.949943i
$14$	7.43342			1.98666
$15$	−1.03063	−	3.84637i	−0.266108	−	0.993127i
$16$	5.48447	−	9.49938i	1.37112	−	2.37484i
$17$	0.408347	+	0.707277i	0.0990386	+	0.171540i	0.911287	−	0.411772i	$-0.135090\pi$
$17$	0.408347	+	0.707277i	0.0990386	+	0.171540i	−0.812248	+	0.583312i	$0.801757\pi$
$18$	1.87031	+	1.87031i	0.440836	+	0.440836i
$19$	−0.0308856	+	0.115266i	−0.00708563	+	0.0264439i	−0.969378	−	0.245573i	$-0.921024\pi$
$19$	−0.0308856	+	0.115266i	−0.00708563	+	0.0264439i	0.962293	+	0.272017i	$0.0876906\pi$
$20$	−5.14915	+	19.2169i	−1.15138	+	4.29703i
$21$	1.98722	−	1.98722i	0.433646	−	0.433646i
$22$	1.99110	+	8.54358i	0.424504	+	1.82150i
$23$	−5.97852	−	3.45170i	−1.24661	−	0.719730i	−0.276177	−	0.961107i	$-0.589068\pi$
$23$	−5.97852	−	3.45170i	−1.24661	−	0.719730i	−0.970431	+	0.241377i	$0.922401\pi$
$24$	−2.05108	−	7.65475i	−0.418676	−	1.56252i
$25$		−	10.8567i		−	2.17135i
$26$	0.533254	−	9.52182i	0.104580	−	1.86738i
$27$	1.00000			0.192450
$28$	−13.5624	+	3.63403i	−2.56305	+	0.686768i
$29$	4.48350	+	2.58855i	0.832565	+	0.480681i	0.854730	−	0.519073i	$-0.173723\pi$
$29$	4.48350	+	2.58855i	0.832565	+	0.480681i	−0.0221654	+	0.999754i	$0.507056\pi$
$30$	5.26630	+	9.12149i	0.961490	+	1.66535i
$31$	−4.79316	+	4.79316i	−0.860876	+	0.860876i	−0.991440	−	0.130564i	$-0.958321\pi$
$31$	−4.79316	+	4.79316i	−0.860876	+	0.860876i	0.130564	+	0.991440i	$0.458321\pi$
$32$	−3.40696	+	12.7149i	−0.602271	+	2.24771i
$33$	2.81629	+	1.75171i	0.490254	+	0.304934i
$34$	−1.52747	−	1.52747i	−0.261959	−	0.261959i
$35$	9.69165	−	5.59547i	1.63819	−	0.945808i
$36$	−4.32676	−	2.49806i	−0.721127	−	0.416343i
$37$	8.78532	−	2.35402i	1.44430	−	0.386998i	0.550261	−	0.834992i	$-0.314528\pi$
$37$	8.78532	−	2.35402i	1.44430	−	0.386998i	0.894037	+	0.447994i	$0.147861\pi$
$38$		−	0.315637i		−	0.0512031i
$39$	−2.40296	−	2.68808i	−0.384782	−	0.430437i
$40$		−	31.5569i		−	4.98958i
$41$	7.35389	−	1.97047i	1.14849	−	0.307736i	0.366127	−	0.930565i	$-0.380683\pi$
$41$	7.35389	−	1.97047i	1.14849	−	0.307736i	0.782358	+	0.622829i	$0.214017\pi$
$42$	−3.71671	+	6.43753i	−0.573501	+	0.993332i
$43$	1.75279	+	3.03593i	0.267299	+	0.462975i	0.968163	−	0.250319i	$-0.0805357\pi$
$43$	1.75279	+	3.03593i	0.267299	+	0.462975i	−0.700865	+	0.713294i	$0.747202\pi$
$44$	−7.80956	−	14.6145i	−1.17734	−	2.20322i
$45$	3.84637	+	1.03063i	0.573382	+	0.153637i
$46$	17.6374	+	4.72594i	2.60050	+	0.696802i
$47$	1.67231	+	1.67231i	0.243932	+	0.243932i	0.818474	−	0.574543i	$-0.194820\pi$
$47$	1.67231	+	1.67231i	0.243932	+	0.243932i	−0.574543	+	0.818474i	$0.694820\pi$
$48$	5.48447	+	9.49938i	0.791615	+	1.37112i
$49$	0.777740	+	0.449028i	0.111106	+	0.0641469i
$50$	7.43231	+	27.7377i	1.05109	+	3.92271i
$51$	−0.816693			−0.114360
$52$	3.68208	+	17.6334i	0.510612	+	2.44532i
$53$	6.49016			0.891491			0.445746	−	0.895160i	$-0.352939\pi$
$53$	6.49016			0.891491			0.445746	+	0.895160i	$0.352939\pi$
$54$	−2.55489	+	0.684581i	−0.347677	+	0.0931596i
$55$	9.02713	+	9.64028i	1.21722	+	1.29989i
$56$	19.2876	−	11.1357i	2.57741	−	1.48807i
$57$	−0.0843809	−	0.0843809i	−0.0111765	−	0.0111765i
$58$	−13.2269	−	3.54414i	−1.73678	−	0.465369i
$59$	2.54445	−	9.49602i	0.331259	−	1.23628i	−0.576609	−	0.817020i	$-0.695624\pi$
$59$	2.54445	−	9.49602i	0.331259	−	1.23628i	0.907868	−	0.419256i	$-0.137709\pi$
$60$	−14.0677	−	14.0677i	−1.81614	−	1.81614i
$61$	1.23600	−	0.713606i	0.158254	−	0.0913679i	−0.418782	−	0.908087i	$-0.637543\pi$
$61$	1.23600	−	0.713606i	0.158254	−	0.0913679i	0.577036	+	0.816719i	$0.304209\pi$
$62$	8.96468	−	15.5273i	1.13852	−	1.97197i
$63$	0.727372	+	2.71459i	0.0916402	+	0.342006i
$64$		−	12.8797i		−	1.60997i
$65$	−6.47226	−	12.8159i	−0.802785	−	1.58962i
$66$	−8.39451	−	2.54745i	−1.03329	−	0.313569i
$67$	−1.73257	−	6.46604i	−0.211667	−	0.789953i	−0.987313	−	0.158785i	$-0.949242\pi$
$67$	−1.73257	−	6.46604i	−0.211667	−	0.789953i	0.775646	−	0.631168i	$-0.217424\pi$
$68$	3.53364	+	2.04015i	0.428517	+	0.247404i
$69$	5.97852	−	3.45170i	0.719730	−	0.415536i
$70$	−20.9305	+	20.9305i	−2.50168	+	2.50168i
$71$	2.79924	+	0.750055i	0.332209	+	0.0890152i	0.421068	−	0.907029i	$-0.361655\pi$
$71$	2.79924	+	0.750055i	0.332209	+	0.0890152i	−0.0888589	+	0.996044i	$0.528322\pi$
$72$	7.65475	+	2.05108i	0.902121	+	0.241722i
$73$	0.797494	−	0.797494i	0.0933396	−	0.0933396i	−0.658895	−	0.752235i	$-0.728976\pi$
$73$	0.797494	−	0.797494i	0.0933396	−	0.0933396i	0.752235	+	0.658895i	$0.228976\pi$
$74$	−20.8340	+	12.0285i	−2.42191	+	1.39829i
$75$	9.40220	+	5.42836i	1.08567	+	0.626813i
$76$	0.154308	+	0.575885i	0.0177003	+	0.0660585i
$77$	−2.70668	+	8.91922i	−0.308455	+	1.01644i
$78$	7.97951	+	5.22272i	0.903502	+	0.591357i
$79$		−	7.81765i		−	0.879554i	−0.898107	−	0.439777i	$-0.855057\pi$
$79$		−	7.81765i		−	0.879554i	0.898107	−	0.439777i	$-0.144943\pi$
$80$	11.3049	+	42.1905i	1.26393	+	4.71705i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−17.4394	+	10.0687i	−1.92586	+	1.11190i
$83$	−10.4366	−	10.4366i	−1.14557	−	1.14557i	−0.987414	−	0.158156i	$-0.949445\pi$
$83$	−10.4366	−	10.4366i	−1.14557	−	1.14557i	−0.158156	−	0.987414i	$-0.550555\pi$
$84$	3.63403	−	13.5624i	0.396505	−	1.47978i
$85$	−3.14130	−	0.841709i	−0.340722	−	0.0912962i
$86$	−6.55654	−	6.55654i	−0.707009	−	0.707009i
$87$	−4.48350	+	2.58855i	−0.480681	+	0.277522i
$88$	17.9651	+	19.1854i	1.91509	+	2.04517i
$89$	−9.16067	+	2.45459i	−0.971029	+	0.260186i	−0.709262	−	0.704945i	$-0.750972\pi$
$89$	−9.16067	+	2.45459i	−0.971029	+	0.260186i	−0.261767	+	0.965131i	$0.584305\pi$
$90$	−10.5326			−1.11023
$91$	5.54918	−	8.47829i	0.581712	−	0.888766i
$92$	−34.4902			−3.59585
$93$	−1.75442	−	6.54757i	−0.181925	−	0.678952i
$94$	−5.41740	−	3.12774i	−0.558762	−	0.322602i
$95$	−0.237594	−	0.411525i	−0.0243767	−	0.0422216i
$96$	−9.30798	−	9.30798i	−0.949992	−	0.949992i
$97$	4.41716	+	1.18358i	0.448495	+	0.120174i	0.475995	−	0.879448i	$-0.342088\pi$
$97$	4.41716	+	1.18358i	0.448495	+	0.120174i	−0.0275001	+	0.999622i	$0.508755\pi$
$98$	−2.29444	−	0.614792i	−0.231773	−	0.0621034i
$99$	−2.92517	+	1.56313i	−0.293991	+	0.157100i
$100$	−27.1207	−	46.9745i	−2.71207	−	4.69745i
$101$	−6.30737	+	10.9247i	−0.627607	+	1.08705i	0.360424	+	0.932789i	$0.382632\pi$
$101$	−6.30737	+	10.9247i	−0.627607	+	1.08705i	−0.988031	+	0.154258i	$0.950701\pi$
$102$	2.08656	−	0.559093i	0.206600	−	0.0553584i
$103$			2.12584i			0.209465i	0.994500	+	0.104733i	$0.0333987\pi$
$103$			2.12584i			0.209465i	−0.994500	+	0.104733i	$0.966601\pi$
$104$	−12.8806	−	25.5052i	−1.26305	−	2.50099i
$105$			11.1909i			1.09212i
$106$	−16.5816	+	4.44304i	−1.61055	+	0.431546i
$107$	−4.65789	−	2.68924i	−0.450296	−	0.259978i	0.257659	−	0.966236i	$-0.417049\pi$
$107$	−4.65789	−	2.68924i	−0.450296	−	0.259978i	−0.707955	+	0.706258i	$0.750382\pi$
$108$	4.32676	−	2.49806i	0.416343	−	0.240376i
$109$	0.373883	+	0.373883i	0.0358115	+	0.0358115i	0.724786	−	0.688974i	$-0.241939\pi$
$109$	0.373883	+	0.373883i	0.0358115	+	0.0358115i	−0.688974	+	0.724786i	$0.741939\pi$
$110$	−29.6629	−	18.4501i	−2.82824	−	1.75914i
$111$	−2.35402	+	8.78532i	−0.223434	+	0.833866i
$112$	−21.7977	+	21.7977i	−2.05968	+	2.05968i
$113$	−4.55532	−	7.89004i	−0.428528	−	0.742232i	0.568215	−	0.822880i	$-0.307634\pi$
$113$	−4.55532	−	7.89004i	−0.428528	−	0.742232i	−0.996743	+	0.0806480i	$0.974301\pi$
$114$	0.273350	+	0.157818i	0.0256015	+	0.0147810i
$115$	26.5530	−	7.11486i	2.47608	−	0.663464i
$116$	25.8654			2.40154
$117$	3.52943	−	0.736988i	0.326296	−	0.0681346i
$118$			26.0032i			2.39379i
$119$	−0.594040	−	2.21699i	−0.0544555	−	0.203231i
$120$	27.3290	+	15.7784i	2.49479	+	1.44037i
$121$	−10.9763	−	0.721836i	−0.997845	−	0.0656214i
$122$	−2.66933	+	2.66933i	−0.241670	+	0.241670i
$123$	−1.97047	+	7.35389i	−0.177671	+	0.663078i
$124$	−8.76527	+	32.7124i	−0.787144	+	2.93766i
$125$	16.4910	+	16.4910i	1.47500	+	1.47500i
$126$	−3.71671	−	6.43753i	−0.331111	−	0.573501i
$127$	7.31704	−	12.6735i	0.649282	−	1.12459i	−0.334012	−	0.942569i	$-0.608403\pi$
$127$	7.31704	−	12.6735i	0.649282	−	1.12459i	0.983295	−	0.182021i	$-0.0582639\pi$
$128$	2.00331	+	7.47645i	0.177069	+	0.660831i
$129$	−3.50559			−0.308650
$130$	25.3094	+	28.3124i	2.21978	+	2.48316i
$131$			2.60548i			0.227642i	0.993501	+	0.113821i	$0.0363090\pi$
$131$			2.60548i			0.227642i	−0.993501	+	0.113821i	$0.963691\pi$
$132$	16.5613	+	0.543975i	1.44148	+	0.0473469i
$133$	0.167683	−	0.290436i	0.0145400	−	0.0251840i
$134$	8.85306	+	15.3339i	0.764788	+	1.32465i
$135$	−2.81573	+	2.81573i	−0.242340	+	0.242340i
$136$	−6.25158	−	1.67511i	−0.536069	−	0.143639i
$137$	−1.82717	+	6.81910i	−0.156106	+	0.582595i	0.842902	+	0.538067i	$0.180845\pi$
$137$	−1.82717	+	6.81910i	−0.156106	+	0.582595i	−0.999008	+	0.0445282i	$0.985822\pi$
$138$	−12.9115	+	12.9115i	−1.09910	+	1.09910i
$139$	−1.13614	+	0.655949i	−0.0963659	+	0.0556369i	−0.547408	−	0.836866i	$-0.684386\pi$
$139$	−1.13614	+	0.655949i	−0.0963659	+	0.0556369i	0.451043	+	0.892502i	$0.351052\pi$
$140$	27.9556	−	48.4206i	2.36268	−	4.09229i
$141$	−2.28442	+	0.612108i	−0.192383	+	0.0515488i
$142$	−7.66524			−0.643252
$143$	11.2309	+	4.10696i	0.939174	+	0.343441i
$144$	−10.9689			−0.914078
$145$	−19.9130	+	5.33567i	−1.65369	+	0.443104i
$146$	−1.49156	+	2.58346i	−0.123442	+	0.213809i
$147$	−0.777740	+	0.449028i	−0.0641469	+	0.0370352i
$148$	32.1315	−	32.1315i	2.64120	−	2.64120i
$149$	5.48577	−	20.4732i	0.449412	−	1.67723i	−0.254607	−	0.967045i	$-0.581946\pi$
$149$	5.48577	−	20.4732i	0.449412	−	1.67723i	0.704018	−	0.710182i	$-0.251387\pi$
$150$	−27.7377	−	7.43231i	−2.26478	−	0.606845i
$151$	−3.06814	+	3.06814i	−0.249682	+	0.249682i	−0.820840	−	0.571158i	$-0.806494\pi$
$151$	−3.06814	+	3.06814i	−0.249682	+	0.249682i	0.571158	+	0.820840i	$0.306494\pi$
$152$	−0.472842	−	0.818987i	−0.0383526	−	0.0664286i
$153$	0.408347	−	0.707277i	0.0330129	−	0.0571800i
$154$	0.809347	−	24.6406i	0.0652191	−	1.98559i
$155$		−	26.9925i		−	2.16809i
$156$	−17.1120	−	5.62794i	−1.37006	−	0.450596i
$157$	−19.9044			−1.58855			−0.794273	−	0.607561i	$-0.792148\pi$
$157$	−19.9044			−1.58855			−0.794273	+	0.607561i	$0.792148\pi$
$158$	5.35181	+	19.9732i	0.425767	+	1.58899i
$159$	−3.24508	+	5.62064i	−0.257351	+	0.445746i
$160$	−26.2088	−	45.3950i	−2.07199	−	3.58879i
$161$	13.7186	+	13.7186i	1.08117	+	1.08117i
$162$	0.684581	−	2.55489i	0.0537857	−	0.200731i
$163$	2.48382	−	9.26976i	0.194548	−	0.726063i	−0.797835	−	0.602875i	$-0.794022\pi$
$163$	2.48382	−	9.26976i	0.194548	−	0.726063i	0.992383	−	0.123188i	$-0.0393118\pi$
$164$	26.8962	−	26.8962i	2.10024	−	2.10024i
$165$	−12.8623	+	2.99758i	−1.00133	+	0.233361i
$166$	33.8092	+	19.5198i	2.62410	+	1.51503i
$167$	0.311080	+	1.16097i	0.0240721	+	0.0898384i	0.976917	−	0.213620i	$-0.0685254\pi$
$167$	0.311080	+	1.16097i	0.0240721	+	0.0898384i	−0.952845	+	0.303458i	$0.901859\pi$
$168$			22.2714i			1.71827i
$169$	−10.4622	−	7.71642i	−0.804782	−	0.593571i
$170$	8.60190			0.659735
$171$	0.115266	−	0.0308856i	0.00881465	−	0.00236188i
$172$	15.1678	+	8.75716i	1.15654	+	0.667727i
$173$	−8.81361	−	15.2656i	−0.670086	−	1.16062i	−0.977879	−	0.209170i	$-0.932924\pi$
$173$	−8.81361	−	15.2656i	−0.670086	−	1.16062i	0.307793	−	0.951453i	$-0.400409\pi$
$174$	9.68277	−	9.68277i	0.734049	−	0.734049i
$175$	−7.89687	+	29.4715i	−0.596948	+	2.22784i
$176$	−30.8918	−	19.2144i	−2.32855	−	1.44834i
$177$	6.95157	+	6.95157i	0.522512	+	0.522512i
$178$	21.7241	−	12.5424i	1.62829	−	0.940095i
$179$	−6.88752	−	3.97651i	−0.514797	−	0.297218i	0.220006	−	0.975499i	$-0.429392\pi$
$179$	−6.88752	−	3.97651i	−0.514797	−	0.297218i	−0.734803	+	0.678280i	$0.762726\pi$
$180$	19.2169	−	5.14915i	1.43234	−	0.383795i
$181$			5.97345i			0.444003i	0.975046	+	0.222002i	$0.0712591\pi$
$181$			5.97345i			0.444003i	−0.975046	+	0.222002i	$0.928741\pi$
$182$	−8.37347	+	25.4600i	−0.620683	+	1.88722i
$183$			1.42721i			0.105503i
$184$	52.8438	−	14.1595i	3.89570	−	1.04385i
$185$	−18.1088	+	31.3654i	−1.33139	+	2.30603i
$186$	8.96468	+	15.5273i	0.657323	+	1.13852i
$187$	2.38897	−	1.27659i	0.174699	−	0.0933539i
$188$	11.4132	+	3.05816i	0.832394	+	0.223039i
$189$	−2.71459	−	0.727372i	−0.197457	−	0.0529085i
$190$	0.888750	+	0.888750i	0.0644767	+	0.0644767i
$191$	4.61065	+	7.98588i	0.333615	+	0.577838i	0.983218	−	0.182436i	$-0.0583982\pi$
$191$	4.61065	+	7.98588i	0.333615	+	0.577838i	−0.649603	+	0.760274i	$0.725065\pi$
$192$	11.1542	+	6.43987i	0.804984	+	0.464758i
$193$	−2.59810	−	9.69626i	−0.187016	−	0.697952i	−0.994190	−	0.107639i	$-0.965671\pi$
$193$	−2.59810	−	9.69626i	−0.187016	−	0.697952i	0.807174	−	0.590313i	$-0.200996\pi$
$194$	−12.0956			−0.868415
$195$	14.3350	+	0.802809i	1.02655	+	0.0574904i
$196$	4.48679			0.320485
$197$	13.0682	−	3.50161i	0.931071	−	0.249480i	0.238760	−	0.971079i	$-0.423259\pi$
$197$	13.0682	−	3.50161i	0.931071	−	0.249480i	0.692311	+	0.721599i	$0.256593\pi$
$198$	6.40341	−	5.99613i	0.455071	−	0.426127i
$199$	5.01054	−	2.89284i	0.355188	−	0.205068i	−0.311780	−	0.950154i	$-0.600925\pi$
$199$	5.01054	−	2.89284i	0.355188	−	0.205068i	0.666968	+	0.745087i	$0.267592\pi$
$200$	60.8374	+	60.8374i	4.30186	+	4.30186i
$201$	6.46604	+	1.73257i	0.456080	+	0.122206i
$202$	8.63581	−	32.2293i	0.607613	−	2.26764i
$203$	−10.2880	−	10.2880i	−0.722077	−	0.722077i
$204$	−3.53364	+	2.04015i	−0.247404	+	0.142839i
$205$	−15.1583	+	26.2549i	−1.05870	+	1.83372i
$206$	−1.45531	−	5.43129i	−0.101396	−	0.378416i
$207$			6.90341i			0.479820i
$208$	26.3580	+	29.4854i	1.82760	+	2.04444i
$209$	0.378727	+	0.114931i	0.0261971	+	0.00794993i
$210$	−7.66111	−	28.5916i	−0.528667	−	1.97301i
$211$	−10.8534	−	6.26619i	−0.747177	−	0.431383i	0.0774962	−	0.996993i	$-0.475307\pi$
$211$	−10.8534	−	6.26619i	−0.747177	−	0.431383i	−0.824673	+	0.565610i	$0.808641\pi$
$212$	28.0814	−	16.2128i	1.92864	−	1.11350i
$213$	−2.04919	+	2.04919i	−0.140408	+	0.140408i
$214$	13.7414	+	3.68200i	0.939343	+	0.251696i
$215$	−13.4838	−	3.61297i	−0.919586	−	0.246402i
$216$	−5.60366	+	5.60366i	−0.381281	+	0.381281i
$217$	16.4978	−	9.52504i	1.11995	−	0.646602i
$218$	−1.21118	−	0.699278i	−0.0820318	−	0.0473611i
$219$	0.291903	+	1.08940i	0.0197250	+	0.0736146i
$220$	63.1402	+	19.1609i	4.25691	+	1.29183i
$221$	−2.88246	+	0.601893i	−0.193895	+	0.0404877i
$222$		−	24.0570i		−	1.61460i
$223$	−0.423718	−	1.58134i	−0.0283743	−	0.105894i	0.950286	−	0.311377i	$-0.100790\pi$
$223$	−0.423718	−	1.58134i	−0.0283743	−	0.105894i	−0.978661	+	0.205483i	$0.934124\pi$
$224$	18.4970	−	32.0377i	1.23588	−	2.14061i
$225$	−9.40220	+	5.42836i	−0.626813	+	0.361891i
$226$	17.0397	+	17.0397i	1.13346	+	1.13346i
$227$	−0.708986	+	2.64597i	−0.0470571	+	0.175619i	−0.985455	−	0.169938i	$-0.945643\pi$
$227$	−0.708986	+	2.64597i	−0.0470571	+	0.175619i	0.938398	+	0.345557i	$0.112310\pi$
$228$	−0.575885	−	0.154308i	−0.0381389	−	0.0102193i
$229$	−6.94408	−	6.94408i	−0.458877	−	0.458877i	0.439409	−	0.898287i	$-0.355188\pi$
$229$	−6.94408	−	6.94408i	−0.458877	−	0.458877i	−0.898287	+	0.439409i	$0.855188\pi$
$230$	−62.9694	+	36.3554i	−4.15208	+	2.39720i
$231$	−6.37093	−	6.80367i	−0.419176	−	0.447648i
$232$	−39.6294	+	10.6187i	−2.60180	+	0.697149i
$233$	7.03002			0.460552			0.230276	−	0.973125i	$-0.426037\pi$
$233$	7.03002			0.460552			0.230276	+	0.973125i	$0.426037\pi$
$234$	−8.51277	+	4.29910i	−0.556497	+	0.281041i
$235$	−9.41756			−0.614334
$236$	−12.7124	−	47.4432i	−0.827505	−	3.08829i
$237$	6.77028	+	3.90882i	0.439777	+	0.253905i
$238$	3.03541	+	5.25749i	0.196757	+	0.340792i
$239$	−4.57865	−	4.57865i	−0.296168	−	0.296168i	0.543343	−	0.839511i	$-0.317158\pi$
$239$	−4.57865	−	4.57865i	−0.296168	−	0.296168i	−0.839511	+	0.543343i	$0.817158\pi$
$240$	−42.1905	−	11.3049i	−2.72339	−	0.729730i
$241$	4.40873	+	1.18132i	0.283991	+	0.0760952i	0.398003	−	0.917384i	$-0.369703\pi$
$241$	4.40873	+	1.18132i	0.283991	+	0.0760952i	−0.114012	+	0.993479i	$0.536370\pi$
$242$	28.5374	−	5.66995i	1.83445	−	0.364478i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.56526	−	6.17521i	0.228242	−	0.395327i
$245$	−3.45425	+	0.925565i	−0.220684	+	0.0591322i
$246$		−	20.1373i		−	1.28391i
$247$	−0.360004	−	0.235628i	−0.0229065	−	0.0149927i
$248$		−	53.7185i		−	3.41113i
$249$	14.2567	−	3.82008i	0.903483	−	0.242088i
$250$	−53.4221	−	30.8433i	−3.37871	−	1.95070i
$251$	20.7729	−	11.9932i	1.31117	−	0.757006i	0.328883	−	0.944371i	$-0.393328\pi$
$251$	20.7729	−	11.9932i	1.31117	−	0.757006i	0.982291	+	0.187364i	$0.0599945\pi$
$252$	9.92836	+	9.92836i	0.625428	+	0.625428i
$253$	−12.0928	+	19.4420i	−0.760266	+	1.22231i
$254$	−10.0182	+	37.3885i	−0.628598	+	2.34596i
$255$	2.29959	−	2.29959i	0.144006	−	0.144006i
$256$	2.64327	+	4.57829i	0.165205	+	0.286143i
$257$	23.3640	+	13.4892i	1.45741	+	0.841435i	0.998883	−	0.0472459i	$-0.0150444\pi$
$257$	23.3640	+	13.4892i	1.45741	+	0.841435i	0.458525	+	0.888681i	$0.348378\pi$
$258$	8.95639	−	2.39986i	0.557601	−	0.149409i
$259$	−25.5608			−1.58827
$260$	−60.0188	−	39.2833i	−3.72221	−	2.43625i
$261$		−	5.17710i		−	0.320454i
$262$	−1.78366	−	6.65671i	−0.110195	−	0.411253i
$263$	7.74890	+	4.47383i	0.477818	+	0.275868i	0.719507	−	0.694486i	$-0.244368\pi$
$263$	7.74890	+	4.47383i	0.477818	+	0.275868i	−0.241689	+	0.970354i	$0.577701\pi$
$264$	−25.5976	+	5.96556i	−1.57542	+	0.367155i
$265$	−18.2746	+	18.2746i	−1.12260	+	1.12260i
$266$	−0.229585	+	0.856824i	−0.0140768	+	0.0525352i
$267$	2.45459	−	9.16067i	0.150219	−	0.560624i
$268$	−23.6490	−	23.6490i	−1.44459	−	1.44459i
$269$	−2.66175	−	4.61028i	−0.162290	−	0.281094i	0.773400	−	0.633919i	$-0.218555\pi$
$269$	−2.66175	−	4.61028i	−0.162290	−	0.281094i	−0.935689	+	0.352825i	$0.885221\pi$
$270$	5.26630	−	9.12149i	0.320497	−	0.555116i
$271$	−1.81101	−	6.75877i	−0.110011	−	0.410566i	0.888855	−	0.458189i	$-0.151502\pi$
$271$	−1.81101	−	6.75877i	−0.110011	−	0.410566i	−0.998865	+	0.0476236i	$0.984835\pi$
$272$	8.95826			0.543174
$273$	4.56782	+	9.04487i	0.276457	+	0.547421i
$274$		−	18.6729i		−	1.12807i
$275$	−35.9883	−	1.18208i	−2.17018	−	0.0712818i
$276$	17.2451	−	29.8694i	1.03803	−	1.79793i
$277$	−14.7494	−	25.5466i	−0.886203	−	1.53495i	−0.844329	−	0.535825i	$-0.820001\pi$
$277$	−14.7494	−	25.5466i	−0.886203	−	1.53495i	−0.0418738	−	0.999123i	$-0.513333\pi$
$278$	2.45366	−	2.45366i	0.147160	−	0.147160i
$279$	6.54757	+	1.75442i	0.391993	+	0.105034i
$280$	−22.9536	+	85.6639i	−1.37174	+	5.11940i
$281$	−12.7578	+	12.7578i	−0.761069	+	0.761069i	−0.976516	−	0.215447i	$-0.930879\pi$
$281$	−12.7578	+	12.7578i	−0.761069	+	0.761069i	0.215447	+	0.976516i	$0.430879\pi$
$282$	5.41740	−	3.12774i	0.322602	−	0.186254i
$283$	−7.55896	+	13.0925i	−0.449334	+	0.778269i	−0.998343	−	0.0575475i	$-0.981672\pi$
$283$	−7.55896	+	13.0925i	−0.449334	+	0.778269i	0.549009	+	0.835816i	$0.315005\pi$
$284$	13.9853	−	3.74736i	0.829878	−	0.222365i
$285$	0.475189			0.0281477
$286$	−31.5052	−	2.80438i	−1.86294	−	0.165827i
$287$	−21.3961			−1.26297
$288$	12.7149	−	3.40696i	0.749235	−	0.200757i
$289$	8.16651	−	14.1448i	0.480383	−	0.832047i
$290$	47.2229	−	27.2641i	2.77302	−	1.60100i
$291$	−3.23359	+	3.23359i	−0.189556	+	0.189556i
$292$	1.45838	−	5.44275i	0.0853453	−	0.318513i
$293$	24.4514	+	6.55174i	1.42847	+	0.382757i	0.888479	−	0.458916i	$-0.151762\pi$
$293$	24.4514	+	6.55174i	1.42847	+	0.382757i	0.539988	+	0.841673i	$0.318429\pi$
$294$	1.67964	−	1.67964i	0.0979588	−	0.0979588i
$295$	19.5738	+	33.9028i	1.13963	+	1.97390i
$296$	−36.0388	+	62.4211i	−2.09472	+	3.62815i
$297$	0.108880	−	3.31484i	0.00631783	−	0.192346i
$298$			56.0621i			3.24759i
$299$	18.5569	−	16.5886i	1.07317	−	0.959345i
$300$	54.2415			3.13163
$301$	−2.54987	−	9.51623i	−0.146972	−	0.548506i
$302$	5.73837	−	9.93915i	0.330206	−	0.571934i
$303$	−6.30737	−	10.9247i	−0.362349	−	0.627607i
$304$	0.925569	+	0.925569i	0.0530850	+	0.0530850i
$305$	−1.47093	+	5.48958i	−0.0842251	+	0.314332i
$306$	−0.559093	+	2.08656i	−0.0319612	+	0.119281i
$307$	1.98011	−	1.98011i	0.113011	−	0.113011i	−0.648340	−	0.761351i	$-0.724536\pi$
$307$	1.98011	−	1.98011i	0.113011	−	0.113011i	0.761351	+	0.648340i	$0.224536\pi$
$308$	10.5696	+	45.3528i	0.602257	+	2.58422i
$309$	−1.84103	−	1.06292i	−0.104733	−	0.0604674i
$310$	18.4786	+	68.9629i	1.04951	+	3.91683i
$311$		−	26.2148i		−	1.48651i	−0.669010	−	0.743253i	$-0.733282\pi$
$311$		−	26.2148i		−	1.48651i	0.669010	−	0.743253i	$-0.266718\pi$
$312$	28.5285	+	1.59769i	1.61511	+	0.0904514i
$313$	−12.2846			−0.694366			−0.347183	−	0.937797i	$-0.612862\pi$
$313$	−12.2846			−0.694366			−0.347183	+	0.937797i	$0.612862\pi$
$314$	50.8536	−	13.6262i	2.86984	−	0.768970i
$315$	−9.69165	−	5.59547i	−0.546062	−	0.315269i
$316$	−19.5289	−	33.8251i	−1.09859	−	1.90281i
$317$	−12.9242	+	12.9242i	−0.725898	+	0.725898i	−0.969800	−	0.243902i	$-0.921573\pi$
$317$	−12.9242	+	12.9242i	−0.725898	+	0.725898i	0.243902	+	0.969800i	$0.421573\pi$
$318$	4.44304	−	16.5816i	0.249153	−	0.929852i
$319$	9.06878	−	14.5802i	0.507754	−	0.816336i
$320$	36.2660	+	36.2660i	2.02733	+	2.02733i
$321$	4.65789	−	2.68924i	0.259978	−	0.150099i
$322$	−44.4409	−	25.6580i	−2.47659	−	1.42986i
$323$	−0.0941374	+	0.0252240i	−0.00523794	+	0.00140350i
$324$			4.99612i			0.277562i
$325$	37.1850	+	12.2297i	2.06265	+	0.678382i
$326$			25.3836i			1.40587i
$327$	−0.510734	+	0.136851i	−0.0282437	+	0.00756787i
$328$	−30.1669	+	52.2506i	−1.66569	+	2.88506i
$329$	−3.32324	−	5.75602i	−0.183216	−	0.317340i
$330$	30.8097	−	16.4638i	1.69602	−	0.906301i
$331$	30.7350	+	8.23542i	1.68935	+	0.452660i	0.970222	−	0.242218i	$-0.0778751\pi$
$331$	30.7350	+	8.23542i	1.68935	+	0.452660i	0.719127	+	0.694878i	$0.244542\pi$
$332$	−71.2282	−	19.0855i	−3.90916	−	1.04746i
$333$	−6.43130	−	6.43130i	−0.352433	−	0.352433i
$334$	−1.58955	−	2.75319i	−0.0869764	−	0.150648i
$335$	23.0851	+	13.3282i	1.26128	+	0.728198i
$336$	−7.97849	−	29.7761i	−0.435263	−	1.62442i
$337$	2.98266			0.162476			0.0812378	−	0.996695i	$-0.474113\pi$
$337$	2.98266			0.162476			0.0812378	+	0.996695i	$0.474113\pi$
$338$	32.0122	+	12.5524i	1.74123	+	0.682761i
$339$	9.11063			0.494822
$340$	−15.6943	+	4.20528i	−0.851143	+	0.228063i
$341$	15.3667	+	16.4104i	0.832151	+	0.888673i
$342$	−0.273350	+	0.157818i	−0.0147810	+	0.00853384i
$343$	12.1259	+	12.1259i	0.654736	+	0.654736i
$344$	−26.8344	−	7.19025i	−1.44681	−	0.387672i
$345$	−7.11486	+	26.5530i	−0.383051	+	1.42957i
$346$	32.9683	+	32.9683i	1.77239	+	1.77239i
$347$	26.6384	−	15.3797i	1.43002	−	0.825624i	0.432900	−	0.901442i	$-0.357490\pi$
$347$	26.6384	−	15.3797i	1.43002	−	0.825624i	0.997122	+	0.0758182i	$0.0241569\pi$
$348$	−12.9327	+	22.4001i	−0.693265	+	1.20077i
$349$	−1.55056	−	5.78675i	−0.0829993	−	0.309758i	0.911928	−	0.410349i	$-0.134593\pi$
$349$	−1.55056	−	5.78675i	−0.0829993	−	0.309758i	−0.994928	+	0.100591i	$0.967927\pi$
$350$		−	80.7026i		−	4.31374i
$351$	−1.12646	+	3.42507i	−0.0601261	+	0.182817i
$352$	41.7770	+	12.6779i	2.22672	+	0.675735i
$353$	−1.89070	−	7.05621i	−0.100632	−	0.375564i	0.897181	−	0.441663i	$-0.145611\pi$
$353$	−1.89070	−	7.05621i	−0.100632	−	0.375564i	−0.997813	+	0.0660991i	$0.978945\pi$
$354$	−22.5194	−	13.0016i	−1.19689	−	0.691027i
$355$	−9.99389	+	5.76997i	−0.530420	+	0.306238i
$356$	−33.5043	+	33.5043i	−1.77573	+	1.77573i
$357$	2.21699	+	0.594040i	0.117335	+	0.0314399i
$358$	20.3191	+	5.44449i	1.07390	+	0.287750i
$359$	−14.8368	+	14.8368i	−0.783056	+	0.783056i	−0.980345	−	0.197289i	$-0.936786\pi$
$359$	−14.8368	+	14.8368i	−0.783056	+	0.783056i	0.197289	+	0.980345i	$0.436786\pi$
$360$	−27.3290	+	15.7784i	−1.44037	+	0.831596i
$361$	16.4422	+	9.49288i	0.865376	+	0.499625i
$362$	−4.08931	−	15.2615i	−0.214929	−	0.802128i
$363$	6.11327	−	9.14483i	0.320864	−	0.479979i
$364$	2.83073	−	50.5457i	0.148370	−	2.64931i
$365$			4.49106i			0.235073i
$366$	−0.977042	−	3.64637i	−0.0510708	−	0.190599i
$367$	−8.32480	+	14.4190i	−0.434551	+	0.752664i	−0.997259	−	0.0739916i	$-0.976426\pi$
$367$	−8.32480	+	14.4190i	−0.434551	+	0.752664i	0.562708	+	0.826656i	$0.309760\pi$
$368$	−65.5781	+	37.8615i	−3.41849	+	1.97367i
$369$	−5.38342	−	5.38342i	−0.280250	−	0.280250i
$370$	24.7939	−	92.5322i	1.28898	−	4.81052i
$371$	−17.6181	−	4.72075i	−0.914686	−	0.245089i
$372$	−23.9472	−	23.9472i	−1.24160	−	1.24160i
$373$	−4.96701	+	2.86770i	−0.257182	+	0.148484i	−0.623048	−	0.782183i	$-0.714106\pi$
$373$	−4.96701	+	2.86770i	−0.257182	+	0.148484i	0.365866	+	0.930667i	$0.380773\pi$
$374$	−5.22962	+	4.89700i	−0.270417	+	0.253218i
$375$	−22.5271	+	6.03612i	−1.16330	+	0.311704i
$376$	−18.7421			−0.966551
$377$	−13.9164	+	12.4404i	−0.716733	+	0.640712i
$378$	7.43342			0.382334
$379$	−2.04056	−	7.61548i	−0.104817	−	0.391181i	0.893508	−	0.449048i	$-0.148237\pi$
$379$	−2.04056	−	7.61548i	−0.104817	−	0.391181i	−0.998324	+	0.0578671i	$0.981570\pi$
$380$	−2.05603	−	1.18705i	−0.105472	−	0.0608943i
$381$	7.31704	+	12.6735i	0.374863	+	0.649282i
$382$	−17.2467	−	17.2467i	−0.882417	−	0.882417i
$383$	1.84092	+	0.493274i	0.0940667	+	0.0252051i	0.305545	−	0.952178i	$-0.401161\pi$
$383$	1.84092	+	0.493274i	0.0940667	+	0.0252051i	−0.211479	+	0.977383i	$0.567828\pi$
$384$	−7.47645	−	2.00331i	−0.381531	−	0.102231i
$385$	−17.4929	−	32.7355i	−0.891519	−	1.66835i
$386$	13.2757	+	22.9943i	0.675718	+	1.17038i
$387$	1.75279	−	3.03593i	0.0890995	−	0.154325i
$388$	22.0687	−	5.91328i	1.12037	−	0.300201i
$389$			36.9359i			1.87273i	0.351033	+	0.936363i	$0.385831\pi$
$389$			36.9359i			1.87273i	−0.351033	+	0.936363i	$0.614169\pi$
$390$	−37.1740	+	7.76239i	−1.88238	+	0.393064i
$391$		−	5.63797i		−	0.285124i
$392$	−6.87440	+	1.84199i	−0.347209	+	0.0930345i
$393$	−2.25641	−	1.30274i	−0.113821	−	0.0657145i
$394$	−30.9907	+	17.8925i	−1.56129	+	0.901410i
$395$	22.0124	+	22.0124i	1.10757	+	1.10757i
$396$	−8.75175	+	14.0705i	−0.439792	+	0.707071i
$397$	5.93625	−	22.1544i	0.297932	−	1.11190i	−0.640929	−	0.767600i	$-0.721451\pi$
$397$	5.93625	−	22.1544i	0.297932	−	1.11190i	0.938861	−	0.344297i	$-0.111883\pi$
$398$	−10.8210	+	10.8210i	−0.542408	+	0.542408i
$399$	0.167683	+	0.290436i	0.00839466	+	0.0145400i
$400$	−103.132	−	59.5434i	−5.15661	−	2.97717i
$401$	−15.4961	+	4.15216i	−0.773837	+	0.207349i	−0.624066	−	0.781372i	$-0.714520\pi$
$401$	−15.4961	+	4.15216i	−0.773837	+	0.207349i	−0.149771	+	0.988721i	$0.547854\pi$
$402$	−17.7061			−0.883101
$403$	−11.0176	−	21.8162i	−0.548824	−	1.08674i
$404$			63.0247i			3.13560i
$405$	−1.03063	−	3.84637i	−0.0512124	−	0.191127i
$406$	33.3277	+	19.2418i	1.65403	+	0.954953i
$407$	−6.84665	−	29.3782i	−0.339376	−	1.45622i
$408$	4.57647	−	4.57647i	0.226569	−	0.226569i
$409$	1.09152	−	4.07362i	0.0539723	−	0.201427i	−0.933675	−	0.358122i	$-0.883417\pi$
$409$	1.09152	−	4.07362i	0.0539723	−	0.201427i	0.987647	+	0.156695i	$0.0500839\pi$
$410$	20.7542	−	77.4556i	1.02497	−	3.82526i
$411$	−4.99193	−	4.99193i	−0.246234	−	0.246234i
$412$	5.31047	+	9.19801i	0.261628	+	0.453153i
$413$	−13.8143	+	23.9270i	−0.679756	+	1.17737i
$414$	−4.72594	−	17.6374i	−0.232267	−	0.866833i
$415$	58.7736			2.88508
$416$	−39.7117	−	25.9920i	−1.94703	−	1.27436i
$417$		−	1.31190i		−	0.0642439i
$418$	−1.04628	−	0.0343664i	−0.0511755	−	0.00168092i
$419$	7.42652	−	12.8631i	0.362809	−	0.628404i	−0.625613	−	0.780134i	$-0.715151\pi$
$419$	7.42652	−	12.8631i	0.362809	−	0.628404i	0.988422	+	0.151730i	$0.0484844\pi$
$420$	27.9556	+	48.4206i	1.36410	+	2.36268i
$421$	−2.06083	+	2.06083i	−0.100439	+	0.100439i	−0.755541	−	0.655102i	$-0.772626\pi$
$421$	−2.06083	+	2.06083i	−0.100439	+	0.100439i	0.655102	+	0.755541i	$0.272626\pi$
$422$	32.0189	+	8.57943i	1.55865	+	0.417640i
$423$	0.612108	−	2.28442i	0.0297617	−	0.111072i
$424$	−36.3686	+	36.3686i	−1.76622	+	1.76622i
$425$	7.67872	−	4.43331i	0.372472	−	0.215047i
$426$	3.83262	−	6.63829i	0.185691	−	0.321626i
$427$	−3.87429	+	1.03811i	−0.187490	+	0.0502378i
$428$	−26.8715			−1.29888
$429$	−9.17218	+	7.67276i	−0.442837	+	0.370444i
$430$	36.9229			1.78058
$431$	−24.3563	+	6.52624i	−1.17320	+	0.314358i	−0.792226	−	0.610228i	$-0.791078\pi$
$431$	−24.3563	+	6.52624i	−1.17320	+	0.314358i	−0.380974	+	0.924586i	$0.624411\pi$
$432$	5.48447	−	9.49938i	0.263872	−	0.457039i
$433$	−25.6512	+	14.8097i	−1.23272	+	0.711710i	−0.967596	−	0.252505i	$-0.918746\pi$
$433$	−25.6512	+	14.8097i	−1.23272	+	0.711710i	−0.265122	+	0.964215i	$0.585412\pi$
$434$	−35.6295	+	35.6295i	−1.71027	+	1.71027i
$435$	5.33567	−	19.9130i	0.255826	−	0.954756i
$436$	2.55169	+	0.683723i	0.122204	+	0.0327444i
$437$	0.582516	−	0.582516i	0.0278655	−	0.0278655i
$438$	−1.49156	−	2.58346i	−0.0712695	−	0.123442i
$439$	18.4653	−	31.9828i	0.881298	−	1.52645i	0.0314000	−	0.999507i	$-0.490003\pi$
$439$	18.4653	−	31.9828i	0.881298	−	1.52645i	0.849898	−	0.526947i	$-0.176663\pi$
$440$	−104.606	−	3.43590i	−4.98689	−	0.163800i
$441$		−	0.898057i		−	0.0427646i
$442$	6.95232	−	3.51105i	0.330688	−	0.167003i
$443$	−0.417773			−0.0198490			−0.00992450	−	0.999951i	$-0.503159\pi$
$443$	−0.417773			−0.0198490			−0.00992450	+	0.999951i	$0.503159\pi$
$444$	11.7610	+	43.8925i	0.558150	+	2.08304i
$445$	18.8825	−	32.7055i	0.895118	−	1.55039i
$446$	2.16511	+	3.75007i	0.102521	+	0.177571i
$447$	14.9874	+	14.9874i	0.708879	+	0.708879i
$448$	−9.36836	+	34.9632i	−0.442613	+	1.65186i
$449$	8.42495	−	31.4423i	0.397598	−	1.48386i	−0.419712	−	0.907657i	$-0.637869\pi$
$449$	8.42495	−	31.4423i	0.397598	−	1.48386i	0.817310	−	0.576198i	$-0.195464\pi$
$450$	20.3054	−	20.3054i	0.957208	−	0.957208i
$451$	−5.73110	−	24.5915i	−0.269867	−	1.15797i
$452$	−39.4195	−	22.7589i	−1.85414	−	1.07049i
$453$	−1.12302	−	4.19116i	−0.0527640	−	0.196918i
$454$		−	7.24553i		−	0.340050i
$455$	8.24759	+	39.4976i	0.386653	+	1.85168i
$456$	0.945684			0.0442857
$457$	−1.72426	+	0.462015i	−0.0806576	+	0.0216121i	−0.298922	−	0.954277i	$-0.596627\pi$
$457$	−1.72426	+	0.462015i	−0.0806576	+	0.0216121i	0.218265	+	0.975890i	$0.429960\pi$
$458$	22.4951	+	12.9876i	1.05113	+	0.606869i
$459$	0.408347	+	0.707277i	0.0190600	+	0.0330129i
$460$	97.1153	−	97.1153i	4.52802	−	4.52802i
$461$	−2.66091	+	9.93064i	−0.123931	+	0.462516i	−0.999799	−	0.0200338i	$-0.993623\pi$
$461$	−2.66091	+	9.93064i	−0.123931	+	0.462516i	0.875869	+	0.482550i	$0.160289\pi$
$462$	20.9347	+	13.0212i	0.973970	+	0.605801i
$463$	−6.68283	−	6.68283i	−0.310577	−	0.310577i	0.534556	−	0.845133i	$-0.320479\pi$
$463$	−6.68283	−	6.68283i	−0.310577	−	0.310577i	−0.845133	+	0.534556i	$0.820479\pi$
$464$	49.1792	−	28.3936i	2.28309	−	1.31814i
$465$	23.3762	+	13.4963i	1.08405	+	0.625874i
$466$	−17.9609	+	4.81262i	−0.832024	+	0.222940i
$467$		−	10.5945i		−	0.490257i	−0.969491	−	0.245128i	$-0.921170\pi$
$467$		−	10.5945i		−	0.490257i	0.969491	−	0.245128i	$-0.0788301\pi$
$468$	13.4300	−	12.0055i	0.620800	−	0.554954i
$469$			18.8129i			0.868697i
$470$	24.0608	−	6.44708i	1.10984	−	0.297382i
$471$	9.95222	−	17.2377i	0.458574	−	0.794273i
$472$	38.9543	+	67.4707i	1.79301	+	3.10559i
$473$	10.2545	−	5.47968i	0.471500	−	0.251956i
$474$	−19.9732	−	5.35181i	−0.917401	−	0.245817i
$475$	1.25142	+	0.335316i	0.0574189	+	0.0153854i
$476$	−8.10843	−	8.10843i	−0.371649	−	0.371649i
$477$	−3.24508	−	5.62064i	−0.148582	−	0.257351i
$478$	14.8324	+	8.56349i	0.678418	+	0.391685i
$479$	9.52439	+	35.5455i	0.435181	+	1.62412i	0.740634	+	0.671909i	$0.234525\pi$
$479$	9.52439	+	35.5455i	0.435181	+	1.62412i	−0.305453	+	0.952207i	$0.598808\pi$
$480$	52.4176			2.39253
$481$	−1.83366	+	32.7420i	−0.0836078	+	1.49291i
$482$	−12.0725			−0.549888
$483$	−18.7399	+	5.02134i	−0.852695	+	0.228479i
$484$	−49.2950	+	24.2962i	−2.24068	+	1.10437i
$485$	−15.7702	+	9.10493i	−0.716088	+	0.413434i
$486$	1.87031	+	1.87031i	0.0848390	+	0.0848390i
$487$	−29.5821	−	7.92650i	−1.34049	−	0.359184i	−0.483876	−	0.875136i	$-0.660772\pi$
$487$	−29.5821	−	7.92650i	−1.34049	−	0.359184i	−0.856617	+	0.515952i	$0.827438\pi$
$488$	−2.92733	+	10.9249i	−0.132514	+	0.494549i
$489$	6.78593	+	6.78593i	0.306870	+	0.306870i
$490$	8.19162	−	4.72943i	0.370060	−	0.213654i
$491$	−2.56394	+	4.44087i	−0.115709	+	0.200414i	−0.918063	−	0.396435i	$-0.870247\pi$
$491$	−2.56394	+	4.44087i	−0.115709	+	0.200414i	0.802354	+	0.596848i	$0.203581\pi$
$492$	9.84470	+	36.7409i	0.443833	+	1.65641i
$493$			4.22810i			0.190424i
$494$	1.08108	+	0.355553i	0.0486400	+	0.0159971i
$495$	3.83516	−	12.6379i	0.172378	−	0.568030i
$496$	19.2441	+	71.8199i	0.864085	+	3.22481i
$497$	−7.05323	−	4.07218i	−0.316380	−	0.182662i
$498$	−33.8092	+	19.5198i	−1.51503	+	0.874701i
$499$	11.2190	−	11.2190i	0.502233	−	0.502233i	−0.409898	−	0.912131i	$-0.634436\pi$
$499$	11.2190	−	11.2190i	0.502233	−	0.502233i	0.912131	+	0.409898i	$0.134436\pi$
$500$	112.548	+	30.1572i	5.03330	+	1.34867i
$501$	−1.16097	−	0.311080i	−0.0518682	−	0.0138980i
$502$	−44.8621	+	44.8621i	−2.00229	+	2.00229i
$503$	29.1541	−	16.8321i	1.29992	−	0.750507i	0.319527	−	0.947577i	$-0.396476\pi$
$503$	29.1541	−	16.8321i	1.29992	−	0.750507i	0.980389	+	0.197070i	$0.0631425\pi$
$504$	−19.2876	−	11.1357i	−0.859137	−	0.496023i
$505$	−13.0011	−	48.5209i	−0.578543	−	2.15915i
$506$	17.5861	−	57.9507i	0.781796	−	2.57622i
$507$	11.9137	−	5.20229i	0.529106	−	0.231042i
$508$		−	73.1135i		−	3.24389i
$509$	1.48978	+	5.55994i	0.0660334	+	0.246440i	0.991051	−	0.133484i	$-0.0426166\pi$
$509$	1.48978	+	5.55994i	0.0660334	+	0.246440i	−0.925017	+	0.379925i	$0.875950\pi$
$510$	−4.30095	+	7.44946i	−0.190449	+	0.329868i
$511$	−2.74494	+	1.58479i	−0.121429	+	0.0701071i
$512$	−20.8338	−	20.8338i	−0.920731	−	0.920731i
$513$	−0.0308856	+	0.115266i	−0.00136363	+	0.00508914i
$514$	−68.9270	−	18.4689i	−3.04024	−	0.814630i
$515$	−5.98580	−	5.98580i	−0.263766	−	0.263766i
$516$	−15.1678	+	8.75716i	−0.667727	+	0.385513i
$517$	5.72552	−	5.36136i	0.251808	−	0.235792i
$518$	65.3050	−	17.4984i	2.86934	−	0.768836i
$519$	17.6272			0.773749
$520$	108.084	+	35.5476i	4.73981	+	1.55887i
$521$	−27.9723			−1.22549			−0.612744	−	0.790281i	$-0.709934\pi$
$521$	−27.9723			−1.22549			−0.612744	+	0.790281i	$0.709934\pi$
$522$	3.54414	+	13.2269i	0.155123	+	0.578926i
$523$	−37.0468	−	21.3890i	−1.61994	−	0.935275i	−0.986933	−	0.161133i	$-0.948485\pi$
$523$	−37.0468	−	21.3890i	−1.61994	−	0.935275i	−0.633012	−	0.774142i	$-0.718181\pi$
$524$	6.50863	+	11.2733i	0.284331	+	0.492476i
$525$	−21.5747	−	21.5747i	−0.941596	−	0.941596i
$526$	−22.8603	−	6.12540i	−0.996756	−	0.267080i
$527$	−5.34736	−	1.43282i	−0.232935	−	0.0624146i
$528$	32.0860	−	17.1458i	1.39637	−	0.746177i
$529$	12.3285	+	21.3536i	0.536022	+	0.928417i
$530$	34.1791	−	59.1999i	1.48464	−	2.57148i
$531$	−9.49602	+	2.54445i	−0.412092	+	0.110420i
$532$		−	1.67553i		−	0.0726434i
$533$	−1.53490	+	27.4072i	−0.0664838	+	1.18714i
$534$			25.0849i			1.08553i
$535$	20.6876	−	5.54322i	0.894402	−	0.239654i
$536$	45.9423	+	26.5248i	1.98440	+	1.14570i
$537$	6.88752	−	3.97651i	0.297218	−	0.171599i
$538$	9.95659	+	9.95659i	0.429259	+	0.429259i
$539$	1.57314	−	2.52919i	0.0677598	−	0.108940i
$540$	−5.14915	+	19.2169i	−0.221584	+	0.826963i
$541$	25.6913	−	25.6913i	1.10455	−	1.10455i	0.110700	−	0.993854i	$-0.464691\pi$
$541$	25.6913	−	25.6913i	1.10455	−	1.10455i	0.993854	−	0.110700i	$-0.0353092\pi$
$542$	9.25384	+	16.0281i	0.397487	+	0.688467i
$543$	−5.17316	−	2.98673i	−0.222002	−	0.128173i
$544$	−10.3842	+	2.78244i	−0.445219	+	0.119296i
$545$	−2.10551			−0.0901903
$546$	−17.8622	−	19.9816i	−0.764433	−	0.855134i
$547$			22.3775i			0.956795i	0.878143	+	0.478397i	$0.158782\pi$
$547$			22.3775i			0.956795i	−0.878143	+	0.478397i	$0.841218\pi$
$548$	9.12876	+	34.0690i	0.389961	+	1.45536i
$549$	−1.23600	−	0.713606i	−0.0527513	−	0.0304560i
$550$	92.7553	−	21.6168i	3.95510	−	0.921744i
$551$	−0.436848	+	0.436848i	−0.0186104	+	0.0186104i
$552$	−14.1595	+	52.8438i	−0.602667	+	2.24918i
$553$	−5.68634	+	21.2217i	−0.241808	+	0.902438i
$554$	55.1717	+	55.1717i	2.34402	+	2.34402i
$555$	−18.1088	−	31.3654i	−0.768677	−	1.33139i
$556$	−3.27720	+	5.67627i	−0.138984	+	0.240728i
$557$	−6.32965	−	23.6226i	−0.268196	−	1.00092i	−0.960265	−	0.279090i	$-0.909967\pi$
$557$	−6.32965	−	23.6226i	−0.268196	−	1.00092i	0.692069	−	0.721831i	$-0.256699\pi$
$558$	−17.9294			−0.759011
$559$	−12.3727	+	2.58358i	−0.523310	+	0.109274i
$560$		−	122.753i		−	5.18725i
$561$	−0.0889212	+	2.70721i	−0.00375426	+	0.114298i
$562$	23.8611	−	41.3287i	1.00652	−	1.74334i
$563$	13.5906	+	23.5397i	0.572777	+	0.992079i	0.996279	+	0.0861839i	$0.0274673\pi$
$563$	13.5906	+	23.5397i	0.572777	+	0.992079i	−0.423502	+	0.905895i	$0.639199\pi$
$564$	−8.35506	+	8.35506i	−0.351811	+	0.351811i
$565$	35.0428	+	9.38970i	1.47426	+	0.395027i
$566$	10.3494	−	38.6247i	0.435020	−	1.62352i
$567$	1.98722	−	1.98722i	0.0834552	−	0.0834552i
$568$	−19.8891	+	11.4830i	−0.834527	+	0.481815i
$569$	−12.5965	+	21.8178i	−0.528074	+	0.914652i	0.471390	+	0.881925i	$0.343752\pi$
$569$	−12.5965	+	21.8178i	−0.528074	+	0.914652i	−0.999464	+	0.0327267i	$0.989581\pi$
$570$	−1.21405	+	0.325305i	−0.0508512	+	0.0136255i
$571$	18.9700			0.793869			0.396935	−	0.917847i	$-0.370074\pi$
$571$	18.9700			0.793869			0.396935	+	0.917847i	$0.370074\pi$
$572$	58.8528	−	10.2856i	2.46076	−	0.430061i
$573$	−9.22130			−0.385225
$574$	54.6646	−	14.6473i	2.28166	−	0.611368i
$575$	−37.4742	+	64.9072i	−1.56278	+	2.70682i
$576$	−11.1542	+	6.43987i	−0.464758	+	0.268328i
$577$	12.9085	−	12.9085i	0.537388	−	0.537388i	−0.385373	−	0.922761i	$-0.625927\pi$
$577$	12.9085	−	12.9085i	0.537388	−	0.537388i	0.922761	+	0.385373i	$0.125927\pi$
$578$	−11.1813	+	41.7291i	−0.465079	+	1.73570i
$579$	9.69626	+	2.59810i	0.402963	+	0.107974i
$580$	−72.8300	+	72.8300i	−3.02410	+	3.02410i
$581$	20.7399	+	35.9225i	0.860435	+	1.49032i
$582$	6.04781	−	10.4751i	0.250690	−	0.434208i
$583$	0.706645	−	21.5138i	0.0292663	−	0.891011i
$584$			8.93778i			0.369848i
$585$	−7.86277	+	12.0131i	−0.325085	+	0.496680i
$586$	−66.9559			−2.76592
$587$	−1.47525	−	5.50569i	−0.0608899	−	0.227244i	0.928775	−	0.370644i	$-0.120863\pi$
$587$	−1.47525	−	5.50569i	−0.0608899	−	0.227244i	−0.989665	+	0.143400i	$0.954196\pi$
$588$	−2.24340	+	3.88568i	−0.0925161	+	0.160243i
$589$	−0.404451	−	0.700529i	−0.0166651	−	0.0288648i
$590$	−73.2180	−	73.2180i	−3.01434	−	3.01434i
$591$	−3.50161	+	13.0682i	−0.144037	+	0.537554i
$592$	25.8211	−	96.3657i	1.06124	−	3.96060i
$593$	5.58158	−	5.58158i	0.229208	−	0.229208i	−0.583154	−	0.812362i	$-0.698182\pi$
$593$	5.58158	−	5.58158i	0.229208	−	0.229208i	0.812362	+	0.583154i	$0.198182\pi$
$594$	1.99110	+	8.54358i	0.0816958	+	0.350547i
$595$	7.91510	+	4.56979i	0.324488	+	0.187343i
$596$	−27.4075	−	102.286i	−1.12266	−	4.18981i
$597$			5.78567i			0.236792i
$598$	−36.0546	+	55.0858i	−1.47438	+	2.25263i
$599$	−40.8241			−1.66803			−0.834013	−	0.551744i	$-0.813962\pi$
$599$	−40.8241			−1.66803			−0.834013	+	0.551744i	$0.813962\pi$
$600$	−83.1055	+	22.2680i	−3.39277	+	0.909089i
$601$	35.1175	+	20.2751i	1.43247	+	0.827038i	0.997309	−	0.0733134i	$-0.0233573\pi$
$601$	35.1175	+	20.2751i	1.43247	+	0.827038i	0.435163	+	0.900352i	$0.356691\pi$
$602$	13.0293	+	22.5673i	0.531033	+	0.919776i
$603$	−4.73347	+	4.73347i	−0.192762	+	0.192762i
$604$	−5.61073	+	20.9395i	−0.228297	+	0.852017i
$605$	32.9388	−	28.8738i	1.33915	−	1.17389i
$606$	23.5935	+	23.5935i	0.958419	+	0.958419i
$607$	−38.3464	+	22.1393i	−1.55643	+	0.898608i	−0.558841	+	0.829275i	$0.688754\pi$
$607$	−38.3464	+	22.1393i	−1.55643	+	0.898608i	−0.997594	+	0.0693326i	$0.977913\pi$
$608$	−1.36038	−	0.785416i	−0.0551707	−	0.0318528i
$609$	14.0537	−	3.76567i	0.569484	−	0.152593i
$610$		−	15.0322i		−	0.608638i
$611$	−7.61157	+	3.84398i	−0.307931	+	0.155511i
$612$		−	4.08029i		−	0.164936i
$613$	3.51736	−	0.942473i	0.142065	−	0.0380661i	−0.187086	−	0.982344i	$-0.559904\pi$
$613$	3.51736	−	0.942473i	0.142065	−	0.0380661i	0.329151	+	0.944277i	$0.393238\pi$
$614$	−3.70342	+	6.41451i	−0.149458	+	0.258869i
$615$	−15.1583	−	26.2549i	−0.611242	−	1.05870i
$616$	−34.8130	−	65.1476i	−1.40265	−	2.62487i
$617$	4.57034	+	1.22462i	0.183995	+	0.0493013i	0.349640	−	0.936884i	$-0.386304\pi$
$617$	4.57034	+	1.22462i	0.183995	+	0.0493013i	−0.165645	+	0.986185i	$0.552971\pi$
$618$	5.43129	+	1.45531i	0.218478	+	0.0585411i
$619$	−24.8361	−	24.8361i	−0.998247	−	0.998247i	0.00175185	−	0.999998i	$-0.499442\pi$
$619$	−24.8361	−	24.8361i	−0.998247	−	0.998247i	−0.999998	+	0.00175185i	$0.999442\pi$
$620$	−67.4289	−	116.790i	−2.70801	−	4.69041i
$621$	−5.97852	−	3.45170i	−0.239910	−	0.138512i
$622$	17.9462	+	66.9760i	0.719576	+	2.68549i
$623$	26.6528			1.06782
$624$	−38.7141	+	8.08398i	−1.54980	+	0.323618i
$625$	−38.5849			−1.54340
$626$	31.3858	−	8.40979i	1.25443	−	0.336123i
$627$	−0.288896	+	0.270522i	−0.0115374	+	0.0108036i
$628$	−86.1218	+	49.7224i	−3.43663	+	1.98414i
$629$	5.25240	+	5.25240i	0.209427	+	0.209427i
$630$	28.5916	+	7.66111i	1.13912	+	0.305226i
$631$	−3.89769	+	14.5464i	−0.155164	+	0.579082i	0.843927	+	0.536458i	$0.180238\pi$
$631$	−3.89769	+	14.5464i	−0.155164	+	0.579082i	−0.999091	+	0.0426233i	$0.986428\pi$
$632$	43.8075	+	43.8075i	1.74257	+	1.74257i
$633$	10.8534	−	6.26619i	0.431383	−	0.249059i
$634$	24.1723	−	41.8677i	0.960007	−	1.66278i
$635$	15.0823	+	56.2880i	0.598524	+	2.23372i
$636$			32.4256i			1.28576i
$637$	−2.41405	+	2.15800i	−0.0956480	+	0.0855030i
$638$	−13.1884	+	43.4592i	−0.522133	+	1.72057i
$639$	−0.750055	−	2.79924i	−0.0296717	−	0.110736i
$640$	−26.6925	−	15.4109i	−1.05511	−	0.609170i
$641$	26.5994	−	15.3572i	1.05061	−	0.606572i	0.127793	−	0.991801i	$-0.459211\pi$
$641$	26.5994	−	15.3572i	1.05061	−	0.606572i	0.922821	+	0.385229i	$0.125877\pi$
$642$	−10.0594	+	10.0594i	−0.397013	+	0.397013i
$643$	41.7648	+	11.1909i	1.64704	+	0.441324i	0.958783	−	0.284139i	$-0.0917077\pi$
$643$	41.7648	+	11.1909i	1.64704	+	0.441324i	0.688261	+	0.725463i	$0.258374\pi$
$644$	93.6267	+	25.0872i	3.68941	+	0.988574i
$645$	9.87081	−	9.87081i	0.388663	−	0.388663i
$646$	0.223243	−	0.128889i	0.00878337	−	0.00507108i
$647$	−13.0005	−	7.50583i	−0.511102	−	0.295085i	0.222185	−	0.975005i	$-0.428681\pi$
$647$	−13.0005	−	7.50583i	−0.511102	−	0.295085i	−0.733286	+	0.679920i	$0.762015\pi$
$648$	−2.05108	−	7.65475i	−0.0805742	−	0.300707i
$649$	−31.2007	−	9.46836i	−1.22474	−	0.371666i
$650$	−103.376	−	5.78939i	−4.05473	−	0.227079i
$651$			19.0501i			0.746631i
$652$	−12.4095	−	46.3128i	−0.485992	−	1.81375i
$653$	17.4015	−	30.1403i	0.680974	−	1.17948i	−0.293710	−	0.955895i	$-0.594890\pi$
$653$	17.4015	−	30.1403i	0.680974	−	1.17948i	0.974684	−	0.223587i	$-0.0717767\pi$
$654$	1.21118	−	0.699278i	0.0473611	−	0.0273439i
$655$	−7.33633	−	7.33633i	−0.286654	−	0.286654i
$656$	21.6140	−	80.6644i	0.843884	−	3.14942i
$657$	−1.08940	−	0.291903i	−0.0425014	−	0.0113882i
$658$	12.4310	+	12.4310i	0.484610	+	0.484610i
$659$	−7.44895	+	4.30065i	−0.290170	+	0.167530i	−0.638018	−	0.770021i	$-0.720246\pi$
$659$	−7.44895	+	4.30065i	−0.290170	+	0.167530i	0.347849	+	0.937551i	$0.386912\pi$
$660$	−48.1639	+	45.1006i	−1.87478	+	1.75554i
$661$	27.7831	−	7.44445i	1.08064	−	0.289556i	0.325780	−	0.945446i	$-0.394373\pi$
$661$	27.7831	−	7.44445i	1.08064	−	0.289556i	0.754856	+	0.655890i	$0.227707\pi$
$662$	−84.1624			−3.27106
$663$	0.919975	−	2.79723i	0.0357289	−	0.108635i
$664$	116.967			4.53919
$665$	0.345639	+	1.28994i	0.0134033	+	0.0500218i
$666$	20.8340	+	12.0285i	0.807302	+	0.466096i
$667$	−17.8698	−	30.9514i	−0.691921	−	1.19844i
$668$	4.24614	+	4.24614i	0.164288	+	0.164288i
$669$	1.58134	+	0.423718i	0.0611380	+	0.0163819i
$670$	−68.1042	−	18.2485i	−2.63109	−	0.705000i
$671$	−2.23091	−	4.17484i	−0.0861234	−	0.161168i
$672$	18.4970	+	32.0377i	0.713536	+	1.23588i
$673$	−8.09402	+	14.0193i	−0.312002	+	0.540403i	−0.978796	−	0.204839i	$-0.934333\pi$
$673$	−8.09402	+	14.0193i	−0.312002	+	0.540403i	0.666794	+	0.745242i	$0.267666\pi$
$674$	−7.62036	+	2.04187i	−0.293525	+	0.0786499i
$675$		−	10.8567i		−	0.417876i
$676$	−64.5434	−	7.25203i	−2.48244	−	0.278924i
$677$		−	18.9384i		−	0.727864i	−0.931426	−	0.363932i	$-0.881434\pi$
$677$		−	18.9384i		−	0.727864i	0.931426	−	0.363932i	$-0.118566\pi$
$678$	−23.2767	+	6.23696i	−0.893935	+	0.239529i
$679$	−11.1299	−	6.42584i	−0.427126	−	0.246601i
$680$	22.3194	−	12.8861i	0.855912	−	0.494161i
$681$	−1.93699	−	1.93699i	−0.0742255	−	0.0742255i
$682$	−50.4944	−	31.4071i	−1.93353	−	1.20264i
$683$	4.15988	−	15.5249i	0.159174	−	0.594044i	−0.839538	−	0.543301i	$-0.817174\pi$
$683$	4.15988	−	15.5249i	0.159174	−	0.594044i	0.998712	−	0.0507431i	$-0.0161590\pi$
$684$	0.421577	−	0.421577i	0.0161194	−	0.0161194i
$685$	−14.0559	−	24.3456i	−0.537050	−	0.930198i
$686$	−39.2814	−	22.6792i	−1.49977	−	0.865894i
$687$	9.48578	−	2.54171i	0.361905	−	0.0969722i
$688$	38.4526			1.46599
$689$	−7.31092	+	22.2292i	−0.278524	+	0.846866i
$690$		−	72.7107i		−	2.76805i
$691$	6.07422	+	22.6693i	0.231074	+	0.862381i	0.979879	+	0.199591i	$0.0639613\pi$
$691$	6.07422	+	22.6693i	0.231074	+	0.862381i	−0.748805	+	0.662790i	$0.769372\pi$
$692$	−76.2688	−	44.0338i	−2.89930	−	1.67391i
$693$	9.07761	−	2.11556i	0.344830	−	0.0803633i
$694$	−57.5295	+	57.5295i	−2.18379	+	2.18379i
$695$	1.35208	−	5.04604i	0.0512874	−	0.191407i
$696$	10.6187	−	39.6294i	0.402499	−	1.50215i
$697$	4.39661	+	4.39661i	0.166533	+	0.166533i
$698$	7.92300	+	13.7230i	0.299890	+	0.519425i
$699$	−3.51501	+	6.08818i	−0.132950	+	0.230276i
$700$	39.4537	+	147.243i	1.49121	+	5.56527i
$701$	−34.3067			−1.29575			−0.647874	−	0.761748i	$-0.724342\pi$
$701$	−34.3067			−1.29575			−0.647874	+	0.761748i	$0.724342\pi$
$702$	0.533254	−	9.52182i	0.0201264	−	0.359378i
$703$			1.08536i			0.0409351i
$704$	−42.6943	−	1.40234i	−1.60910	−	0.0528527i
$705$	4.70878	−	8.15585i	0.177343	−	0.307167i
$706$	9.66109	+	16.7335i	0.363600	+	0.629773i
$707$	25.0682	−	25.0682i	0.942787	−	0.942787i
$708$	47.4432	+	12.7124i	1.78303	+	0.477760i
$709$	−7.95217	+	29.6779i	−0.298650	+	1.11458i	0.639625	+	0.768687i	$0.279090\pi$
$709$	−7.95217	+	29.6779i	−0.298650	+	1.11458i	−0.938275	+	0.345890i	$0.887577\pi$
$710$	21.5833	−	21.5833i	0.810006	−	0.810006i
$711$	−6.77028	+	3.90882i	−0.253905	+	0.146592i
$712$	37.5786	−	65.0880i	1.40832	−	2.43928i
$713$	45.2005	−	12.1114i	1.69277	−	0.453577i
$714$	−6.07082			−0.227195
$715$	−43.1873	+	20.0591i	−1.61511	+	0.750168i
$716$	−39.7342			−1.48494
$717$	6.25455	−	1.67590i	0.233580	−	0.0625877i
$718$	27.7494	−	48.0634i	1.03560	−	1.79371i
$719$	1.95795	−	1.13042i	0.0730192	−	0.0421577i	−0.463046	−	0.886334i	$-0.653243\pi$
$719$	1.95795	−	1.13042i	0.0730192	−	0.0421577i	0.536065	+	0.844177i	$0.319910\pi$
$720$	30.8856	−	30.8856i	1.15104	−	1.15104i
$721$	1.54628	−	5.77078i	0.0575863	−	0.214915i
$722$	−48.5065	−	12.9973i	−1.80523	−	0.483709i
$723$	−3.22741	+	3.22741i	−0.120029	+	0.120029i
$724$	14.9220	+	25.8457i	0.554573	+	0.960549i
$725$	28.1032	−	48.6761i	1.04373	−	1.80779i
$726$	−9.35837	+	27.5491i	−0.347322	+	1.02244i
$727$		−	9.68370i		−	0.359148i	−0.983744	−	0.179574i	$-0.942528\pi$
$727$		−	9.68370i		−	0.359148i	0.983744	−	0.179574i	$-0.0574720\pi$
$728$	16.4137	+	78.6052i	0.608334	+	2.91330i
$729$	1.00000			0.0370370
$730$	−3.07450	−	11.4742i	−0.113792	−	0.424678i
$731$	−1.43150	+	2.47942i	−0.0529458	+	0.0917048i
$732$	3.56526	+	6.17521i	0.131776	+	0.228242i
$733$	−16.3544	−	16.3544i	−0.604062	−	0.604062i	0.337326	−	0.941388i	$-0.390478\pi$
$733$	−16.3544	−	16.3544i	−0.604062	−	0.604062i	−0.941388	+	0.337326i	$0.890478\pi$
$734$	11.3980	−	42.5379i	0.420708	−	1.57010i
$735$	0.925565	−	3.45425i	0.0341400	−	0.127412i
$736$	64.2568	−	64.2568i	2.36854	−	2.36854i
$737$	−21.6225	+	5.03917i	−0.796476	+	0.185620i
$738$	17.4394	+	10.0687i	0.641955	+	0.370633i
$739$	4.99479	+	18.6408i	0.183736	+	0.685713i	0.994898	+	0.100891i	$0.0321692\pi$
$739$	4.99479	+	18.6408i	0.183736	+	0.685713i	−0.811161	+	0.584823i	$0.801164\pi$
$740$			180.948i			6.65177i
$741$	0.384062	−	0.193958i	0.0141089	−	0.00712524i
$742$	48.2440			1.77109
$743$	−31.9767	+	8.56813i	−1.17311	+	0.314334i	−0.792191	−	0.610273i	$-0.791060\pi$
$743$	−31.9767	+	8.56813i	−1.17311	+	0.314334i	−0.380921	+	0.924608i	$0.624393\pi$
$744$	46.5216	+	26.8592i	1.70556	+	0.984707i
$745$	42.2005	+	73.0935i	1.54611	+	2.67794i
$746$	10.7270	−	10.7270i	0.392743	−	0.392743i
$747$	−3.82008	+	14.2567i	−0.139769	+	0.521626i
$748$	7.14750	−	11.4913i	0.261338	−	0.420164i
$749$	10.6882	+	10.6882i	0.390538	+	0.390538i
$750$	53.4221	−	30.8433i	1.95070	−	1.12624i
$751$	7.86414	+	4.54036i	0.286966	+	0.165680i	0.636573	−	0.771216i	$-0.280351\pi$
$751$	7.86414	+	4.54036i	0.286966	+	0.165680i	−0.349607	+	0.936897i	$0.613685\pi$
$752$	25.0576	−	6.71418i	0.913758	−	0.244841i
$753$			23.9865i			0.874116i
$754$	27.0385	−	41.3107i	0.984686	−	1.50445i
$755$		−	17.2781i		−	0.628816i
$756$	−13.5624	+	3.63403i	−0.493260	+	0.132168i
$757$	−6.58463	+	11.4049i	−0.239323	+	0.414519i	−0.960520	−	0.278211i	$-0.910259\pi$
$757$	−6.58463	+	11.4049i	−0.239323	+	0.414519i	0.721198	+	0.692729i	$0.243592\pi$
$758$	10.4268	+	18.0598i	0.378719	+	0.655961i
$759$	−10.7909	−	20.1937i	−0.391685	−	0.732983i
$760$	3.63745	+	0.974651i	0.131944	+	0.0353543i
$761$	6.18424	+	1.65706i	0.224178	+	0.0600684i	0.369160	−	0.929366i	$-0.379646\pi$
$761$	6.18424	+	1.65706i	0.224178	+	0.0600684i	−0.144981	+	0.989434i	$0.546312\pi$
$762$	−27.3703	−	27.3703i	−0.991520	−	0.991520i
$763$	−0.742987	−	1.28689i	−0.0268979	−	0.0465886i
$764$	39.8984	+	23.0353i	1.44347	+	0.833389i
$765$	0.841709	+	3.14130i	0.0304321	+	0.113574i
$766$	−5.04104			−0.182140
$767$	29.6583	+	19.4118i	1.07090	+	0.700920i
$768$	−5.28655			−0.190762
$769$	−50.2605	+	13.4673i	−1.81244	+	0.485642i	−0.995804	−	0.0915101i	$-0.970831\pi$
$769$	−50.2605	+	13.4673i	−1.81244	+	0.485642i	−0.816637	+	0.577152i	$0.804164\pi$
$770$	67.1024	+	71.6602i	2.41820	+	2.58246i
$771$	−23.3640	+	13.4892i	−0.841435	+	0.485803i
$772$	−35.4632	−	35.4632i	−1.27635	−	1.27635i
$773$	5.45135	+	1.46068i	0.196071	+	0.0525372i	0.355518	−	0.934669i	$-0.384304\pi$
$773$	5.45135	+	1.46068i	0.196071	+	0.0525372i	−0.159447	+	0.987207i	$0.550971\pi$
$774$	−2.39986	+	8.95639i	−0.0862611	+	0.321931i
$775$	52.0380	+	52.0380i	1.86926	+	1.86926i
$776$	−31.3847	+	18.1199i	−1.12664	+	0.650468i
$777$	12.7804	−	22.1363i	0.458494	−	0.794135i
$778$	−25.2856	−	94.3673i	−0.906534	−	3.38323i
$779$			0.908517i			0.0325510i
$780$	64.0297	−	32.3362i	2.29263	−	1.15782i
$781$	2.79109	−	9.19737i	0.0998731	−	0.329108i
$782$	3.85964	+	14.4044i	0.138021	+	0.515100i
$783$	4.48350	+	2.58855i	0.160227	+	0.0925072i
$784$	8.53098	−	4.92536i	0.304678	−	0.175906i
$785$	56.0456	−	56.0456i	2.00035	−	2.00035i
$786$	6.65671	+	1.78366i	0.237437	+	0.0636210i
$787$	−30.5294	−	8.18033i	−1.08826	−	0.291597i	−0.330282	−	0.943882i	$-0.607144\pi$
$787$	−30.5294	−	8.18033i	−1.08826	−	0.291597i	−0.757974	+	0.652285i	$0.773810\pi$
$788$	47.7958	−	47.7958i	1.70265	−	1.70265i
$789$	−7.74890	+	4.47383i	−0.275868	+	0.159273i
$790$	−71.3086	−	41.1700i	−2.53705	−	1.46476i
$791$	6.62681	+	24.7316i	0.235622	+	0.879355i
$792$	7.63245	−	25.1509i	0.271207	−	0.893699i
$793$	1.05184	+	5.03724i	0.0373519	+	0.178878i
$794$			60.6659i			2.15295i
$795$	−6.68895	−	24.9635i	−0.237233	−	0.885364i
$796$	14.4529	−	25.0332i	0.512271	−	0.887280i
$797$	22.3770	−	12.9194i	0.792635	−	0.457628i	−0.0482544	−	0.998835i	$-0.515366\pi$
$797$	22.3770	−	12.9194i	0.792635	−	0.457628i	0.840889	+	0.541207i	$0.182033\pi$
$798$	−0.627239	−	0.627239i	−0.0222040	−	0.0222040i
$799$	−0.499905	+	1.86567i	−0.0176854	+	0.0660026i
$800$	138.043	+	36.9884i	4.88055	+	1.30774i
$801$	6.70607	+	6.70607i	0.236948	+	0.236948i
$802$	36.7483	−	21.2166i	1.29763	−	0.749185i
$803$	−2.55673	−	2.73039i	−0.0902251	−	0.0963535i
$804$	32.3051	−	8.65613i	1.13931	−	0.305278i
$805$	−77.2557			−2.72290
$806$	43.0836	+	48.1956i	1.51756	+	1.69762i
$807$	5.32350			0.187396
$808$	−25.8739	−	96.5626i	−0.910240	−	3.39706i
$809$	−19.2427	−	11.1098i	−0.676537	−	0.390599i	0.122012	−	0.992529i	$-0.461065\pi$
$809$	−19.2427	−	11.1098i	−0.676537	−	0.390599i	−0.798549	+	0.601930i	$0.794399\pi$
$810$	5.26630	+	9.12149i	0.185039	+	0.320497i
$811$	7.56357	+	7.56357i	0.265593	+	0.265593i	0.827322	−	0.561729i	$-0.189864\pi$
$811$	7.56357	+	7.56357i	0.265593	+	0.265593i	−0.561729	+	0.827322i	$0.689864\pi$
$812$	−70.2138	−	18.8137i	−2.46402	−	0.660233i
$813$	6.75877	+	1.81101i	0.237040	+	0.0635147i
$814$	37.6042	+	70.3710i	1.31803	+	2.46650i
$815$	19.1074	+	33.0950i	0.669303	+	1.15927i
$816$	−4.47913	+	7.75808i	−0.156801	+	0.271587i
$817$	−0.404077	+	0.108272i	−0.0141369	+	0.00378796i
$818$			11.1549i			0.390021i
$819$	−10.1170	−	0.566586i	−0.353517	−	0.0197981i
$820$			151.465i			5.28939i
$821$	−30.1771	+	8.08592i	−1.05319	+	0.282200i	−0.743568	−	0.668660i	$-0.766868\pi$
$821$	−30.1771	+	8.08592i	−1.05319	+	0.282200i	−0.309619	+	0.950861i	$0.600201\pi$
$822$	16.1712	+	9.33645i	0.564035	+	0.325646i
$823$	8.89044	−	5.13290i	0.309901	−	0.178922i	−0.336981	−	0.941511i	$-0.609406\pi$
$823$	8.89044	−	5.13290i	0.309901	−	0.178922i	0.646882	+	0.762590i	$0.276073\pi$
$824$	−11.9125	−	11.9125i	−0.414991	−	0.414991i
$825$	19.0178	−	30.5757i	0.662116	−	1.06451i
$826$	18.9140	−	70.5879i	0.658101	−	2.45607i
$827$	−18.0640	+	18.0640i	−0.628145	+	0.628145i	−0.947601	−	0.319456i	$-0.896500\pi$
$827$	−18.0640	+	18.0640i	−0.628145	+	0.628145i	0.319456	+	0.947601i	$0.396500\pi$
$828$	17.2451	+	29.8694i	0.599309	+	1.03803i
$829$	4.87244	+	2.81311i	0.169227	+	0.0977032i	0.582221	−	0.813030i	$-0.302184\pi$
$829$	4.87244	+	2.81311i	0.169227	+	0.0977032i	−0.412994	+	0.910734i	$0.635517\pi$
$830$	−150.160	+	40.2353i	−5.21214	+	1.39659i
$831$	29.4987			1.02330
$832$	44.1140	+	14.5086i	1.52938	+	0.502994i
$833$			0.733437i			0.0254121i
$834$	0.898100	+	3.35176i	0.0310987	+	0.116062i
$835$	−4.14490	−	2.39306i	−0.143440	−	0.0828152i
$836$	1.92576	−	0.448803i	0.0666040	−	0.0155222i
$837$	−4.79316	+	4.79316i	−0.165676	+	0.165676i
$838$	−10.1681	+	37.9479i	−0.351251	+	1.31089i
$839$	8.69471	−	32.4491i	0.300175	−	1.12027i	−0.636846	−	0.770991i	$-0.719761\pi$
$839$	8.69471	−	32.4491i	0.300175	−	1.12027i	0.937020	−	0.349275i	$-0.113572\pi$
$840$	−62.7103	−	62.7103i	−2.16371	−	2.16371i
$841$	−1.09883	−	1.90323i	−0.0378908	−	0.0656288i
$842$	3.85440	−	6.67601i	0.132831	−	0.230071i
$843$	−4.66969	−	17.4275i	−0.160833	−	0.600236i
$844$	−62.6133			−2.15524
$845$	51.1861	−	7.73128i	1.76085	−	0.265964i
$846$			6.25548i			0.215068i
$847$	29.2711	+	9.94333i	1.00577	+	0.341657i
$848$	35.5951	−	61.6525i	1.22234	−	2.11715i
$849$	−7.55896	−	13.0925i	−0.259423	−	0.449334i
$850$	−16.5833	+	16.5833i	−0.568803	+	0.568803i
$851$	−60.6486	−	16.2508i	−2.07901	−	0.557069i
$852$	−3.74736	+	13.9853i	−0.128383	+	0.479130i
$853$	4.96994	−	4.96994i	0.170168	−	0.170168i	−0.616885	−	0.787053i	$-0.711606\pi$
$853$	4.96994	−	4.96994i	0.170168	−	0.170168i	0.787053	+	0.616885i	$0.211606\pi$
$854$	9.18772	−	5.30453i	0.314397	−	0.181517i
$855$	−0.237594	+	0.411525i	−0.00812555	+	0.0140739i
$856$	41.1708	−	11.0317i	1.40719	−	0.377056i
$857$	−25.7785			−0.880575			−0.440288	−	0.897857i	$-0.645124\pi$
$857$	−25.7785			−0.880575			−0.440288	+	0.897857i	$0.645124\pi$
$858$	18.1813	−	25.8821i	0.620699	−	0.883602i
$859$	−4.61287			−0.157389			−0.0786945	−	0.996899i	$-0.525075\pi$
$859$	−4.61287			−0.157389			−0.0786945	+	0.996899i	$0.525075\pi$
$860$	−67.3665	+	18.0508i	−2.29718	+	0.615527i
$861$	10.6980	−	18.5295i	0.364588	−	0.631485i
$862$	57.7598	−	33.3476i	1.96731	−	1.13583i
$863$	−28.3858	+	28.3858i	−0.966263	+	0.966263i	−0.999449	−	0.0331863i	$-0.989435\pi$
$863$	−28.3858	+	28.3858i	−0.966263	+	0.966263i	0.0331863	+	0.999449i	$0.489435\pi$
$864$	−3.40696	+	12.7149i	−0.115907	+	0.432571i
$865$	67.8007	+	18.1671i	2.30529	+	0.617701i
$866$	55.3975	−	55.3975i	1.88249	−	1.88249i
$867$	8.16651	+	14.1448i	0.277349	+	0.480383i
$868$	47.5882	−	82.4251i	1.61525	−	2.79769i
$869$	−25.9142	−	0.851182i	−0.879080	−	0.0288744i
$870$			54.5283i			1.84868i
$871$	24.0983	+	1.34959i	0.816540	+	0.0457290i
$872$	−4.19023			−0.141899
$873$	−1.18358	−	4.41716i	−0.0400580	−	0.149498i
$874$	−1.08948	+	1.88704i	−0.0368524	+	0.0638302i
$875$	−32.7712	−	56.7613i	−1.10787	−	1.91888i
$876$	3.98437	+	3.98437i	0.134619	+	0.134619i
$877$	12.9472	−	48.3197i	0.437197	−	1.63164i	−0.298557	−	0.954392i	$-0.596505\pi$
$877$	12.9472	−	48.3197i	0.437197	−	1.63164i	0.735754	−	0.677249i	$-0.236828\pi$
$878$	−25.2819	+	94.3534i	−0.853223	+	3.18427i
$879$	−17.8997	+	17.8997i	−0.603741	+	0.603741i
$880$	141.086	−	32.8803i	4.75600	−	1.10839i
$881$	−16.2242	−	9.36702i	−0.546606	−	0.315583i	0.201146	−	0.979561i	$-0.435533\pi$
$881$	−16.2242	−	9.36702i	−0.546606	−	0.315583i	−0.747752	+	0.663978i	$0.768867\pi$
$882$	0.614792	+	2.29444i	0.0207011	+	0.0772577i
$883$			16.0993i			0.541785i	0.962610	+	0.270892i	$0.0873187\pi$
$883$			16.0993i			0.541785i	−0.962610	+	0.270892i	$0.912681\pi$
$884$	−10.9682	+	9.80480i	−0.368899	+	0.329771i
$885$	−39.1476			−1.31593
$886$	1.06736	−	0.285999i	0.0358588	−	0.00960834i
$887$	−45.6294	−	26.3441i	−1.53208	−	0.884549i	−0.999266	−	0.0383202i	$-0.987799\pi$
$887$	−45.6294	−	26.3441i	−1.53208	−	0.884549i	−0.532819	−	0.846229i	$-0.678867\pi$
$888$	−36.0388	−	62.4211i	−1.20938	−	2.09472i
$889$	−29.0811	+	29.0811i	−0.975348	+	0.975348i
$890$	−25.8532	+	96.4856i	−0.866602	+	3.23420i
$891$	2.81629	+	1.75171i	0.0943494	+	0.0586845i
$892$	−5.78360	−	5.78360i	−0.193649	−	0.193649i
$893$	−0.244412	+	0.141111i	−0.00817892	+	0.00472210i
$894$	−48.5512	−	28.0311i	−1.62380	−	0.937499i
$895$	30.5902	−	8.19663i	1.02252	−	0.273983i
$896$		−	21.7526i		−	0.726705i
$897$	5.08773	+	24.3651i	0.169874	+	0.813526i
$898$			86.0993i			2.87317i
$899$	−33.8974	+	9.08279i	−1.13054	+	0.302928i
$900$	−27.1207	+	46.9745i	−0.904024	+	1.56582i
$901$	2.65023	+	4.59034i	0.0882921	+	0.152926i
$902$	31.4772	+	58.9052i	1.04808	+	1.96133i
$903$	9.51623	+	2.54987i	0.316680	+	0.0848542i
$904$	69.7396	+	18.6867i	2.31950	+	0.621509i
$905$	−16.8197	−	16.8197i	−0.559105	−	0.559105i
$906$	5.73837	+	9.93915i	0.190645	+	0.330206i
$907$	8.30573	+	4.79532i	0.275787	+	0.159226i	0.631515	−	0.775364i	$-0.282434\pi$
$907$	8.30573	+	4.79532i	0.275787	+	0.159226i	−0.355727	+	0.934590i	$0.615767\pi$
$908$	3.54218	+	13.2196i	0.117551	+	0.438707i
$909$	12.6147			0.418405
$910$	−48.1110	−	95.2660i	−1.59486	−	3.15804i
$911$	44.6508			1.47935			0.739674	−	0.672965i	$-0.234980\pi$
$911$	44.6508			1.47935			0.739674	+	0.672965i	$0.234980\pi$
$912$	−1.26435	+	0.338782i	−0.0418668	+	0.0112182i
$913$	−35.7321	+	33.4594i	−1.18256	+	1.10735i
$914$	4.08902	−	2.36079i	0.135253	−	0.0780881i
$915$	−4.01865	−	4.01865i	−0.132852	−	0.132852i
$916$	−47.3921	−	12.6987i	−1.56588	−	0.419576i
$917$	1.89515	−	7.07280i	0.0625834	−	0.233564i
$918$	−1.52747	−	1.52747i	−0.0504140	−	0.0504140i
$919$	−25.5954	+	14.7775i	−0.844313	+	0.487464i	−0.858728	−	0.512432i	$-0.828745\pi$
$919$	−25.5954	+	14.7775i	−0.844313	+	0.487464i	0.0144151	+	0.999896i	$0.495411\pi$
$920$	−108.925	+	188.663i	−3.59115	+	6.22005i
$921$	0.724771	+	2.70488i	0.0238820	+	0.0891289i
$922$		−	27.1933i		−	0.895564i
$923$	−5.72223	+	8.74269i	−0.188350	+	0.287769i
$924$	−44.5615	−	13.5229i	−1.46596	−	0.444871i
$925$	−25.5569	−	95.3798i	−0.840307	−	3.13607i
$926$	21.6488	+	12.4990i	0.711425	+	0.410741i
$927$	1.84103	−	1.06292i	0.0604674	−	0.0349109i
$928$	−48.1883	+	48.1883i	−1.58186	+	1.58186i
$929$	−27.3114	−	7.31806i	−0.896057	−	0.240098i	−0.218735	−	0.975784i	$-0.570193\pi$
$929$	−27.3114	−	7.31806i	−0.896057	−	0.240098i	−0.677322	+	0.735686i	$0.736860\pi$
$930$	−68.9629	−	18.4786i	−2.26138	−	0.605936i
$931$	−0.0757788	+	0.0757788i	−0.00248355	+	0.00248355i
$932$	30.4172	−	17.5614i	0.996350	−	0.575243i
$933$	22.7027	+	13.1074i	0.743253	+	0.429117i
$934$	7.25282	+	27.0679i	0.237320	+	0.885688i
$935$	−3.13215	+	10.3213i	−0.102432	+	0.337541i
$936$	−15.6479	+	23.9075i	−0.511467	+	0.781443i
$937$		−	36.1973i		−	1.18251i	−0.806484	−	0.591256i	$-0.798632\pi$
$937$		−	36.1973i		−	1.18251i	0.806484	−	0.591256i	$-0.201368\pi$
$938$	−12.8789	−	48.0648i	−0.420512	−	1.56937i
$939$	6.14229	−	10.6388i	0.200446	−	0.347183i
$940$	−40.7476	+	23.5256i	−1.32904	+	0.767321i
$941$	−6.15479	−	6.15479i	−0.200640	−	0.200640i	0.599634	−	0.800274i	$-0.295313\pi$
$941$	−6.15479	−	6.15479i	−0.200640	−	0.200640i	−0.800274	+	0.599634i	$0.795313\pi$
$942$	−13.6262	+	50.8536i	−0.443965	+	1.65690i
$943$	−50.7669	−	13.6030i	−1.65320	−	0.442973i
$944$	−76.2513	−	76.2513i	−2.48177	−	2.48177i
$945$	9.69165	−	5.59547i	0.315269	−	0.182021i
$946$	−22.4477	+	21.0200i	−0.729838	+	0.683418i
$947$	2.23221	−	0.598119i	0.0725370	−	0.0194362i	−0.222368	−	0.974963i	$-0.571379\pi$
$947$	2.23221	−	0.598119i	0.0725370	−	0.0194362i	0.294905	+	0.955527i	$0.404712\pi$
$948$	39.0579			1.26854
$949$	1.83312	+	3.62982i	0.0595057	+	0.117829i
$950$	−3.42678			−0.111180
$951$	−4.73060	−	17.6549i	−0.153400	−	0.572498i
$952$	15.7520	+	9.09444i	0.510527	+	0.294753i
$953$	14.7741	+	25.5894i	0.478579	+	0.828923i	0.999698	−	0.0245609i	$-0.00781876\pi$
$953$	14.7741	+	25.5894i	0.478579	+	0.828923i	−0.521120	+	0.853484i	$0.674485\pi$
$954$	12.1386	+	12.1386i	0.393002	+	0.393002i
$955$	−35.4685	−	9.50375i	−1.14773	−	0.307534i
$956$	−31.2485	−	8.37300i	−1.01065	−	0.270802i
$957$	8.09246	+	15.1439i	0.261592	+	0.489533i
$958$	−48.6676	−	84.2947i	−1.57238	−	2.72344i
$959$	9.92004	−	17.1820i	0.320335	−	0.554836i
$960$	−49.5402	+	13.2743i	−1.59890	+	0.428425i
$961$		−	14.9487i		−	0.482215i
$962$	−17.7298	−	84.9076i	−0.571630	−	2.73753i
$963$			5.37847i			0.173319i
$964$	22.0265	−	5.90199i	0.709426	−	0.190090i
$965$	34.6177	+	19.9865i	1.11438	+	0.643389i
$966$	44.4409	−	25.6580i	1.42986	−	0.825531i
$967$	18.3692	+	18.3692i	0.590713	+	0.590713i	0.937824	−	0.347111i	$-0.112837\pi$
$967$	18.3692	+	18.3692i	0.590713	+	0.590713i	−0.347111	+	0.937824i	$0.612837\pi$
$968$	65.5524	−	57.4625i	2.10693	−	1.84692i
$969$	0.0252240	−	0.0941374i	0.000810313	−	0.00302413i
$970$	34.0581	−	34.0581i	1.09354	−	1.09354i
$971$	−9.61751	−	16.6580i	−0.308641	−	0.534581i	0.669425	−	0.742880i	$-0.266541\pi$
$971$	−9.61751	−	16.6580i	−0.308641	−	0.534581i	−0.978065	+	0.208299i	$0.933207\pi$
$972$	−4.32676	−	2.49806i	−0.138781	−	0.0801252i
$973$	3.56126	−	0.954237i	0.114169	−	0.0305914i
$974$	81.0054			2.59558
$975$	−29.1837	+	26.0883i	−0.934628	+	0.835495i
$976$		−	15.6550i		−	0.501104i
$977$	8.16188	+	30.4606i	0.261122	+	0.974520i	0.964582	+	0.263785i	$0.0849708\pi$
$977$	8.16188	+	30.4606i	0.261122	+	0.974520i	−0.703460	+	0.710735i	$0.748362\pi$
$978$	−21.9828	−	12.6918i	−0.702933	−	0.405839i
$979$	7.13917	+	30.6334i	0.228169	+	0.979047i
$980$	−12.6336	+	12.6336i	−0.403566	+	0.403566i
$981$	0.136851	−	0.510734i	0.00436931	−	0.0163065i
$982$	3.51045	−	13.1012i	0.112023	−	0.418075i
$983$	−32.9232	−	32.9232i	−1.05009	−	1.05009i	−0.998678	−	0.0514099i	$-0.983629\pi$
$983$	−32.9232	−	32.9232i	−1.05009	−	1.05009i	−0.0514099	−	0.998678i	$-0.516371\pi$
$984$	−30.1669	−	52.2506i	−0.961686	−	1.66569i
$985$	−26.9370	+	46.6562i	−0.858283	+	1.48659i
$986$	−2.89448	−	10.8023i	−0.0921789	−	0.344016i
$987$	6.64648			0.211560
$988$	−2.14627	−	0.120198i	−0.0682818	−	0.00382401i
$989$		−	24.2005i		−	0.769531i
$990$	−1.14678	+	34.9138i	−0.0364472	+	1.10963i
$991$	−4.22928	+	7.32533i	−0.134348	+	0.232697i	−0.925348	−	0.379119i	$-0.876227\pi$
$991$	−4.22928	+	7.32533i	−0.134348	+	0.232697i	0.791000	+	0.611816i	$0.209561\pi$
$992$	−44.6146	−	77.2748i	−1.41652	−	2.45348i
$993$	−22.4996	+	22.4996i	−0.714003	+	0.714003i
$994$	20.8080	+	5.57547i	0.659988	+	0.176843i
$995$	−5.96289	+	22.2538i	−0.189036	+	0.705493i
$996$	52.1427	−	52.1427i	1.65220	−	1.65220i
$997$	2.16322	−	1.24894i	0.0685099	−	0.0395542i	−0.465354	−	0.885125i	$-0.654073\pi$
$997$	2.16322	−	1.24894i	0.0685099	−	0.0395542i	0.533864	+	0.845571i	$0.320740\pi$
$998$	−20.9831	+	36.3437i	−0.664207	+	1.15044i
$999$	8.78532	−	2.35402i	0.277955	−	0.0744779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.a.175.1	yes	56
11.10	odd	2	inner	429.2.bd.a.175.14	yes	56
13.11	odd	12	inner	429.2.bd.a.76.14	yes	56
143.76	even	12	inner	429.2.bd.a.76.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.1	✓	56	143.76	even	12	inner
429.2.bd.a.76.14	yes	56	13.11	odd	12	inner
429.2.bd.a.175.1	yes	56	1.1	even	1	trivial
429.2.bd.a.175.14	yes	56	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55489 + 0.684581i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(4.32676 - 2.49806i) q^{4} +(-2.81573 + 2.81573i) q^{5} +(0.684581 - 2.55489i) q^{6} +(-2.71459 - 0.727372i) q^{7} +(-5.60366 + 5.60366i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.55489 + 0.684581i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(4.32676 - 2.49806i) q^{4} +(-2.81573 + 2.81573i) q^{5} +(0.684581 - 2.55489i) q^{6} +(-2.71459 - 0.727372i) q^{7} +(-5.60366 + 5.60366i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(5.26630 - 9.12149i) q^{10} +(0.108880 - 3.31484i) q^{11} +4.99612i q^{12} +(-1.12646 + 3.42507i) q^{13} +7.43342 q^{14} +(-1.03063 - 3.84637i) q^{15} +(5.48447 - 9.49938i) q^{16} +(0.408347 + 0.707277i) q^{17} +(1.87031 + 1.87031i) q^{18} +(-0.0308856 + 0.115266i) q^{19} +(-5.14915 + 19.2169i) q^{20} +(1.98722 - 1.98722i) q^{21} +(1.99110 + 8.54358i) q^{22} +(-5.97852 - 3.45170i) q^{23} +(-2.05108 - 7.65475i) q^{24} -10.8567i q^{25} +(0.533254 - 9.52182i) q^{26} +1.00000 q^{27} +(-13.5624 + 3.63403i) q^{28} +(4.48350 + 2.58855i) q^{29} +(5.26630 + 9.12149i) q^{30} +(-4.79316 + 4.79316i) q^{31} +(-3.40696 + 12.7149i) q^{32} +(2.81629 + 1.75171i) q^{33} +(-1.52747 - 1.52747i) q^{34} +(9.69165 - 5.59547i) q^{35} +(-4.32676 - 2.49806i) q^{36} +(8.78532 - 2.35402i) q^{37} -0.315637i q^{38} +(-2.40296 - 2.68808i) q^{39} -31.5569i q^{40} +(7.35389 - 1.97047i) q^{41} +(-3.71671 + 6.43753i) q^{42} +(1.75279 + 3.03593i) q^{43} +(-7.80956 - 14.6145i) q^{44} +(3.84637 + 1.03063i) q^{45} +(17.6374 + 4.72594i) q^{46} +(1.67231 + 1.67231i) q^{47} +(5.48447 + 9.49938i) q^{48} +(0.777740 + 0.449028i) q^{49} +(7.43231 + 27.7377i) q^{50} -0.816693 q^{51} +(3.68208 + 17.6334i) q^{52} +6.49016 q^{53} +(-2.55489 + 0.684581i) q^{54} +(9.02713 + 9.64028i) q^{55} +(19.2876 - 11.1357i) q^{56} +(-0.0843809 - 0.0843809i) q^{57} +(-13.2269 - 3.54414i) q^{58} +(2.54445 - 9.49602i) q^{59} +(-14.0677 - 14.0677i) q^{60} +(1.23600 - 0.713606i) q^{61} +(8.96468 - 15.5273i) q^{62} +(0.727372 + 2.71459i) q^{63} -12.8797i q^{64} +(-6.47226 - 12.8159i) q^{65} +(-8.39451 - 2.54745i) q^{66} +(-1.73257 - 6.46604i) q^{67} +(3.53364 + 2.04015i) q^{68} +(5.97852 - 3.45170i) q^{69} +(-20.9305 + 20.9305i) q^{70} +(2.79924 + 0.750055i) q^{71} +(7.65475 + 2.05108i) q^{72} +(0.797494 - 0.797494i) q^{73} +(-20.8340 + 12.0285i) q^{74} +(9.40220 + 5.42836i) q^{75} +(0.154308 + 0.575885i) q^{76} +(-2.70668 + 8.91922i) q^{77} +(7.97951 + 5.22272i) q^{78} -7.81765i q^{79} +(11.3049 + 42.1905i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-17.4394 + 10.0687i) q^{82} +(-10.4366 - 10.4366i) q^{83} +(3.63403 - 13.5624i) q^{84} +(-3.14130 - 0.841709i) q^{85} +(-6.55654 - 6.55654i) q^{86} +(-4.48350 + 2.58855i) q^{87} +(17.9651 + 19.1854i) q^{88} +(-9.16067 + 2.45459i) q^{89} -10.5326 q^{90} +(5.54918 - 8.47829i) q^{91} -34.4902 q^{92} +(-1.75442 - 6.54757i) q^{93} +(-5.41740 - 3.12774i) q^{94} +(-0.237594 - 0.411525i) q^{95} +(-9.30798 - 9.30798i) q^{96} +(4.41716 + 1.18358i) q^{97} +(-2.29444 - 0.614792i) q^{98} +(-2.92517 + 1.56313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more