LMFDB - Embedded newform 250.3.f.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,3,Mod(7,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

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

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

chi := DirichletCharacter("250.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	250.f (of order $20$, degree $8$, 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:	$6.81200660901$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.1
Root			$-2.26402i$ of defining polynomial
Character	$\chi$	$=$	250.7
Dual form			250.3.f.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26007 - 0.642040i) q^{2} +(-4.49348 + 0.711697i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-5.20517 + 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(0.442463 - 2.79360i) q^{8} +(11.1253 - 3.61484i) q^{9} +O(q^{10})$	\(q+(1.26007 - 0.642040i) q^{2} +(-4.49348 + 0.711697i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-5.20517 + 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(0.442463 - 2.79360i) q^{8} +(11.1253 - 3.61484i) q^{9} +(3.53728 - 10.8866i) q^{11} +(-4.13085 + 8.10725i) q^{12} +(-19.7315 - 10.0537i) q^{13} +(6.82270 + 2.21683i) q^{14} +(-1.23607 - 3.80423i) q^{16} +(-19.6167 - 3.10698i) q^{17} +(11.6979 - 11.6979i) q^{18} +(-15.8404 - 21.8024i) q^{19} +(-18.6705 - 13.5649i) q^{21} +(-2.53241 - 15.9890i) q^{22} +(0.242965 + 0.476846i) q^{23} +12.8679i q^{24} -31.3180 q^{26} +(-10.9361 + 5.57222i) q^{27} +(10.0204 - 1.58707i) q^{28} +(3.67470 - 5.05779i) q^{29} +(5.42369 - 3.94054i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-8.14670 + 51.4362i) q^{33} +(-26.7133 + 8.67968i) q^{34} +(7.22967 - 22.2506i) q^{36} +(2.67310 - 5.24626i) q^{37} +(-33.9580 - 17.3025i) q^{38} +(95.8181 + 31.1332i) q^{39} +(7.33457 + 22.5735i) q^{41} +(-32.2354 - 5.10558i) q^{42} +(44.7386 - 44.7386i) q^{43} +(-13.4566 - 18.5214i) q^{44} +(0.612308 + 0.444868i) q^{46} +(-4.31877 - 27.2676i) q^{47} +(8.26170 + 16.2145i) q^{48} -23.2682i q^{49} +90.3585 q^{51} +(-39.4630 + 20.1074i) q^{52} +(-86.0658 + 13.6315i) q^{53} +(-10.2027 + 14.0428i) q^{54} +(11.6075 - 8.43332i) q^{56} +(86.6950 + 86.6950i) q^{57} +(1.38309 - 8.73248i) q^{58} +(-20.7422 + 6.73954i) q^{59} +(-21.3293 + 65.6449i) q^{61} +(4.30427 - 8.44760i) q^{62} +(52.8715 + 26.9394i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(22.7587 + 70.0439i) q^{66} +(91.1840 + 14.4421i) q^{67} +(-28.0880 + 28.0880i) q^{68} +(-1.43113 - 1.96978i) q^{69} +(12.7283 + 9.24768i) q^{71} +(-5.17587 - 32.6792i) q^{72} +(30.7991 + 60.4466i) q^{73} -8.32691i q^{74} -53.8984 q^{76} +(51.7371 - 26.3614i) q^{77} +(140.727 - 22.2889i) q^{78} +(-71.8966 + 98.9571i) q^{79} +(-39.9985 + 29.0606i) q^{81} +(23.7352 + 23.7352i) q^{82} +(9.64518 - 60.8973i) q^{83} +(-43.8969 + 14.2630i) q^{84} +(27.6500 - 85.0979i) q^{86} +(-12.9126 + 25.3423i) q^{87} +(-28.8478 - 14.6987i) q^{88} +(-75.7710 - 24.6195i) q^{89} +(-34.7133 - 106.837i) q^{91} +(1.05718 + 0.167440i) q^{92} +(-21.5668 + 21.5668i) q^{93} +(-22.9488 - 31.5864i) q^{94} +(20.8207 + 15.1271i) q^{96} +(-21.2725 - 134.309i) q^{97} +(-14.9391 - 29.3197i) q^{98} -133.904i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9} + 32 q^{11} - 16 q^{12} - 8 q^{13} + 30 q^{14} + 16 q^{16} + 8 q^{17} - 16 q^{18} - 30 q^{19} - 68 q^{21} - 8 q^{22} + 42 q^{23} - 56 q^{26} - 40 q^{27} + 4 q^{28} - 100 q^{29} + 132 q^{31} - 64 q^{32} + 134 q^{33} - 100 q^{34} + 48 q^{36} - 82 q^{37} + 20 q^{38} + 320 q^{39} - 88 q^{41} - 128 q^{42} - 78 q^{43} - 40 q^{44} - 26 q^{46} + 168 q^{47} + 32 q^{48} - 168 q^{51} - 16 q^{52} - 518 q^{53} - 80 q^{54} + 48 q^{56} + 280 q^{57} + 80 q^{58} + 350 q^{59} + 372 q^{61} - 158 q^{62} + 142 q^{63} - 202 q^{66} + 158 q^{67} - 196 q^{68} + 30 q^{69} + 122 q^{71} + 68 q^{72} + 352 q^{73} + 40 q^{76} + 96 q^{77} + 158 q^{78} - 760 q^{79} - 144 q^{81} + 352 q^{82} + 32 q^{83} + 20 q^{84} + 264 q^{86} - 440 q^{87} - 244 q^{88} - 550 q^{89} - 798 q^{91} - 436 q^{92} + 54 q^{93} - 190 q^{94} - 16 q^{96} + 618 q^{97} + 336 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9 + 32 * q^11 - 16 * q^12 - 8 * q^13 + 30 * q^14 + 16 * q^16 + 8 * q^17 - 16 * q^18 - 30 * q^19 - 68 * q^21 - 8 * q^22 + 42 * q^23 - 56 * q^26 - 40 * q^27 + 4 * q^28 - 100 * q^29 + 132 * q^31 - 64 * q^32 + 134 * q^33 - 100 * q^34 + 48 * q^36 - 82 * q^37 + 20 * q^38 + 320 * q^39 - 88 * q^41 - 128 * q^42 - 78 * q^43 - 40 * q^44 - 26 * q^46 + 168 * q^47 + 32 * q^48 - 168 * q^51 - 16 * q^52 - 518 * q^53 - 80 * q^54 + 48 * q^56 + 280 * q^57 + 80 * q^58 + 350 * q^59 + 372 * q^61 - 158 * q^62 + 142 * q^63 - 202 * q^66 + 158 * q^67 - 196 * q^68 + 30 * q^69 + 122 * q^71 + 68 * q^72 + 352 * q^73 + 40 * q^76 + 96 * q^77 + 158 * q^78 - 760 * q^79 - 144 * q^81 + 352 * q^82 + 32 * q^83 + 20 * q^84 + 264 * q^86 - 440 * q^87 - 244 * q^88 - 550 * q^89 - 798 * q^91 - 436 * q^92 + 54 * q^93 - 190 * q^94 - 16 * q^96 + 618 * q^97 + 336 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	1.26007	−	0.642040i	0.630037	−	0.321020i
$2$	1.26007	−	0.642040i	0.630037	−	0.321020i
$3$	−4.49348	+	0.711697i	−1.49783	+	0.237232i	−0.850903	−	0.525323i	$-0.823945\pi$
$3$	−4.49348	+	0.711697i	−1.49783	+	0.237232i	−0.646923	+	0.762555i	$0.723945\pi$
$4$	1.17557	−	1.61803i	0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−5.20517	+	3.78178i	−0.867529	+	0.630297i
$7$	3.58690	+	3.58690i	0.512415	+	0.512415i	0.915266	−	0.402851i	$-0.131981\pi$
$7$	3.58690	+	3.58690i	0.512415	+	0.512415i	−0.402851	+	0.915266i	$0.631981\pi$
$8$	0.442463	−	2.79360i	0.0553079	−	0.349201i
$9$	11.1253	−	3.61484i	1.23615	−	0.401648i
$10$		0			0
$11$	3.53728	−	10.8866i	0.321571	−	0.989692i	−0.651394	−	0.758739i	$-0.725816\pi$
$11$	3.53728	−	10.8866i	0.321571	−	0.989692i	0.972965	−	0.230953i	$-0.0741844\pi$
$12$	−4.13085	+	8.10725i	−0.344238	+	0.675604i
$13$	−19.7315	−	10.0537i	−1.51781	−	0.773361i	−0.521025	−	0.853541i	$-0.674450\pi$
$13$	−19.7315	−	10.0537i	−1.51781	−	0.773361i	−0.996780	+	0.0801805i	$0.974450\pi$
$14$	6.82270	+	2.21683i	0.487336	+	0.158345i
$15$		0			0
$16$	−1.23607	−	3.80423i	−0.0772542	−	0.237764i
$17$	−19.6167	−	3.10698i	−1.15392	−	0.182764i	−0.449994	−	0.893032i	$-0.648574\pi$
$17$	−19.6167	−	3.10698i	−1.15392	−	0.182764i	−0.703931	+	0.710268i	$0.748574\pi$
$18$	11.6979	−	11.6979i	0.649881	−	0.649881i
$19$	−15.8404	−	21.8024i	−0.833703	−	1.14749i	−0.987222	−	0.159348i	$-0.949061\pi$
$19$	−15.8404	−	21.8024i	−0.833703	−	1.14749i	0.153520	−	0.988146i	$-0.450939\pi$
$20$		0			0
$21$	−18.6705	−	13.5649i	−0.889070	−	0.645947i
$22$	−2.53241	−	15.9890i	−0.115110	−	0.726773i
$23$	0.242965	+	0.476846i	0.0105637	+	0.0207324i	0.896228	−	0.443594i	$-0.146297\pi$
$23$	0.242965	+	0.476846i	0.0105637	+	0.0207324i	−0.885664	+	0.464326i	$0.846297\pi$
$24$			12.8679i			0.536162i
$25$		0			0
$26$	−31.3180			−1.20454
$27$	−10.9361	+	5.57222i	−0.405041	+	0.206378i
$28$	10.0204	−	1.58707i	0.357871	−	0.0566812i
$29$	3.67470	−	5.05779i	0.126714	−	0.174406i	−0.740947	−	0.671564i	$-0.765623\pi$
$29$	3.67470	−	5.05779i	0.126714	−	0.174406i	0.867660	+	0.497157i	$0.165623\pi$
$30$		0			0
$31$	5.42369	−	3.94054i	0.174958	−	0.127114i	−0.496860	−	0.867831i	$-0.665514\pi$
$31$	5.42369	−	3.94054i	0.174958	−	0.127114i	0.671818	+	0.740716i	$0.265514\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−8.14670	+	51.4362i	−0.246870	+	1.55867i
$34$	−26.7133	+	8.67968i	−0.785686	+	0.255285i
$35$		0			0
$36$	7.22967	−	22.2506i	0.200824	−	0.618073i
$37$	2.67310	−	5.24626i	0.0722460	−	0.141791i	−0.852059	−	0.523446i	$-0.824646\pi$
$37$	2.67310	−	5.24626i	0.0722460	−	0.141791i	0.924305	+	0.381656i	$0.124646\pi$
$38$	−33.9580	−	17.3025i	−0.893632	−	0.455328i
$39$	95.8181	+	31.1332i	2.45688	+	0.798287i
$40$		0			0
$41$	7.33457	+	22.5735i	0.178892	+	0.550573i	0.999790	−	0.0205022i	$-0.00652650\pi$
$41$	7.33457	+	22.5735i	0.178892	+	0.550573i	−0.820898	+	0.571075i	$0.806526\pi$
$42$	−32.2354	−	5.10558i	−0.767508	−	0.121561i
$43$	44.7386	−	44.7386i	1.04043	−	1.04043i	0.0412854	−	0.999147i	$-0.486855\pi$
$43$	44.7386	−	44.7386i	1.04043	−	1.04043i	0.999147	−	0.0412854i	$-0.0131453\pi$
$44$	−13.4566	−	18.5214i	−0.305832	−	0.420941i
$45$		0			0
$46$	0.612308	+	0.444868i	0.0133110	+	0.00967104i
$47$	−4.31877	−	27.2676i	−0.0918886	−	0.580162i	−0.990074	−	0.140545i	$-0.955114\pi$
$47$	−4.31877	−	27.2676i	−0.0918886	−	0.580162i	0.898186	−	0.439616i	$-0.144886\pi$
$48$	8.26170	+	16.2145i	0.172119	+	0.337802i
$49$		−	23.2682i		−	0.474862i
$50$		0			0
$51$	90.3585			1.77174
$52$	−39.4630	+	20.1074i	−0.758903	+	0.386680i
$53$	−86.0658	+	13.6315i	−1.62388	+	0.257198i	−0.901015	−	0.433788i	$-0.857177\pi$
$53$	−86.0658	+	13.6315i	−1.62388	+	0.257198i	−0.722868	+	0.690986i	$0.757177\pi$
$54$	−10.2027	+	14.0428i	−0.188939	+	0.260052i
$55$		0			0
$56$	11.6075	−	8.43332i	0.207276	−	0.150595i
$57$	86.6950	+	86.6950i	1.52096	+	1.52096i
$58$	1.38309	−	8.73248i	0.0238464	−	0.150560i
$59$	−20.7422	+	6.73954i	−0.351562	+	0.114229i	−0.479474	−	0.877556i	$-0.659173\pi$
$59$	−20.7422	+	6.73954i	−0.351562	+	0.114229i	0.127912	+	0.991786i	$0.459173\pi$
$60$		0			0
$61$	−21.3293	+	65.6449i	−0.349661	+	1.07615i	0.609380	+	0.792878i	$0.291418\pi$
$61$	−21.3293	+	65.6449i	−0.349661	+	1.07615i	−0.959041	+	0.283267i	$0.908582\pi$
$62$	4.30427	−	8.44760i	0.0694237	−	0.136252i
$63$	52.8715	+	26.9394i	0.839231	+	0.427609i
$64$	−7.60845	−	2.47214i	−0.118882	−	0.0386271i
$65$		0			0
$66$	22.7587	+	70.0439i	0.344828	+	1.06127i
$67$	91.1840	+	14.4421i	1.36096	+	0.215554i	0.793861	−	0.608099i	$-0.208068\pi$
$67$	91.1840	+	14.4421i	1.36096	+	0.215554i	0.567094	+	0.823653i	$0.308068\pi$
$68$	−28.0880	+	28.0880i	−0.413060	+	0.413060i
$69$	−1.43113	−	1.96978i	−0.0207410	−	0.0285475i
$70$		0			0
$71$	12.7283	+	9.24768i	0.179272	+	0.130249i	0.673803	−	0.738911i	$-0.264660\pi$
$71$	12.7283	+	9.24768i	0.179272	+	0.130249i	−0.494530	+	0.869161i	$0.664660\pi$
$72$	−5.17587	−	32.6792i	−0.0718871	−	0.453878i
$73$	30.7991	+	60.4466i	0.421905	+	0.828036i	0.999928	+	0.0120152i	$0.00382464\pi$
$73$	30.7991	+	60.4466i	0.421905	+	0.828036i	−0.578022	+	0.816021i	$0.696175\pi$
$74$		−	8.32691i		−	0.112526i
$75$		0			0
$76$	−53.8984			−0.709190
$77$	51.7371	−	26.3614i	0.671911	−	0.342356i
$78$	140.727	−	22.2889i	1.80419	−	0.285755i
$79$	−71.8966	+	98.9571i	−0.910083	+	1.25262i	0.0570551	+	0.998371i	$0.481829\pi$
$79$	−71.8966	+	98.9571i	−0.910083	+	1.25262i	−0.967138	+	0.254251i	$0.918171\pi$
$80$		0			0
$81$	−39.9985	+	29.0606i	−0.493809	+	0.358773i
$82$	23.7352	+	23.7352i	0.289453	+	0.289453i
$83$	9.64518	−	60.8973i	0.116207	−	0.733702i	−0.858929	−	0.512095i	$-0.828870\pi$
$83$	9.64518	−	60.8973i	0.116207	−	0.733702i	0.975136	−	0.221607i	$-0.0711304\pi$
$84$	−43.8969	+	14.2630i	−0.522582	+	0.169797i
$85$		0			0
$86$	27.6500	−	85.0979i	0.321511	−	0.989510i
$87$	−12.9126	+	25.3423i	−0.148420	+	0.291291i
$88$	−28.8478	−	14.6987i	−0.327816	−	0.167030i
$89$	−75.7710	−	24.6195i	−0.851359	−	0.276623i	−0.149344	−	0.988785i	$-0.547716\pi$
$89$	−75.7710	−	24.6195i	−0.851359	−	0.276623i	−0.702015	+	0.712162i	$0.747716\pi$
$90$		0			0
$91$	−34.7133	−	106.837i	−0.381465	−	1.17403i
$92$	1.05718	+	0.167440i	0.0114910	+	0.00182000i
$93$	−21.5668	+	21.5668i	−0.231901	+	0.231901i
$94$	−22.9488	−	31.5864i	−0.244137	−	0.336025i
$95$		0			0
$96$	20.8207	+	15.1271i	0.216882	+	0.157574i
$97$	−21.2725	−	134.309i	−0.219304	−	1.38463i	−0.814087	−	0.580743i	$-0.802762\pi$
$97$	−21.2725	−	134.309i	−0.219304	−	1.38463i	0.594783	−	0.803886i	$-0.297238\pi$
$98$	−14.9391	−	29.3197i	−0.152440	−	0.299180i
$99$		−	133.904i		−	1.35256i
$100$		0			0
$101$	60.2160			0.596198			0.298099	−	0.954535i	$-0.403648\pi$
$101$	60.2160			0.596198			0.298099	+	0.954535i	$0.403648\pi$
$102$	113.858	−	58.0138i	1.11626	−	0.568762i
$103$	70.9888	−	11.2435i	0.689211	−	0.109160i	0.198002	−	0.980202i	$-0.436555\pi$
$103$	70.9888	−	11.2435i	0.689211	−	0.109160i	0.491210	+	0.871041i	$0.336555\pi$
$104$	−36.8165	+	50.6735i	−0.354005	+	0.487246i
$105$		0			0
$106$	−99.6973	+	72.4343i	−0.940540	+	0.683342i
$107$	−9.22591	−	9.22591i	−0.0862234	−	0.0862234i	0.662680	−	0.748903i	$-0.269419\pi$
$107$	−9.22591	−	9.22591i	−0.0862234	−	0.0862234i	−0.748903	+	0.662680i	$0.769419\pi$
$108$	−3.84011	+	24.2455i	−0.0355566	+	0.224495i
$109$	−4.89779	+	1.59139i	−0.0449339	+	0.0145999i	−0.331398	−	0.943491i	$-0.607520\pi$
$109$	−4.89779	+	1.59139i	−0.0449339	+	0.0145999i	0.286464	+	0.958091i	$0.407520\pi$
$110$		0			0
$111$	−8.27778	+	25.4764i	−0.0745746	+	0.229517i
$112$	9.21174	−	18.0791i	0.0822477	−	0.161420i
$113$	94.1774	+	47.9858i	0.833428	+	0.424653i	0.817993	−	0.575228i	$-0.195087\pi$
$113$	94.1774	+	47.9858i	0.833428	+	0.424653i	0.0154352	+	0.999881i	$0.495087\pi$
$114$	164.904	+	53.5804i	1.44652	+	0.470004i
$115$		0			0
$116$	−3.86380	−	11.8916i	−0.0333087	−	0.102514i
$117$	−255.861	−	40.5245i	−2.18685	−	0.346363i
$118$	−21.8096	+	21.8096i	−0.184827	+	0.184827i
$119$	−59.2189	−	81.5078i	−0.497638	−	0.684939i
$120$		0			0
$121$	−8.11501	−	5.89590i	−0.0670662	−	0.0487265i
$122$	15.2701	+	96.4116i	0.125165	+	0.790259i
$123$	−49.0232	−	96.2135i	−0.398563	−	0.782223i
$124$		−	13.4081i		−	0.108130i
$125$		0			0
$126$	83.9182			0.666017
$127$	54.6898	−	27.8658i	0.430628	−	0.219416i	−0.225221	−	0.974308i	$-0.572311\pi$
$127$	54.6898	−	27.8658i	0.430628	−	0.219416i	0.655850	+	0.754892i	$0.272311\pi$
$128$	−11.1744	+	1.76985i	−0.0873001	+	0.0138270i
$129$	−169.192	+	232.872i	−1.31156	+	1.80521i
$130$		0			0
$131$	58.9504	−	42.8300i	0.450003	−	0.326947i	−0.339594	−	0.940572i	$-0.610290\pi$
$131$	58.9504	−	42.8300i	0.450003	−	0.326947i	0.789597	+	0.613626i	$0.210290\pi$
$132$	73.6486	+	73.6486i	0.557944	+	0.557944i
$133$	21.3852	−	135.021i	0.160791	−	1.01519i
$134$	124.171	−	40.3456i	0.926649	−	0.301087i
$135$		0			0
$136$	−17.3594	+	53.4266i	−0.127642	+	0.392843i
$137$	−71.7926	+	140.901i	−0.524033	+	1.02847i	0.465619	+	0.884985i	$0.345832\pi$
$137$	−71.7926	+	140.901i	−0.524033	+	1.02847i	−0.989652	+	0.143488i	$0.954168\pi$
$138$	−3.06800	−	1.56323i	−0.0222319	−	0.0113277i
$139$	112.170	+	36.4463i	0.806981	+	0.262204i	0.683318	−	0.730120i	$-0.260536\pi$
$139$	112.170	+	36.4463i	0.806981	+	0.262204i	0.123662	+	0.992324i	$0.460536\pi$
$140$		0			0
$141$	38.8126	+	119.453i	0.275266	+	0.847183i
$142$	21.9760	+	3.48066i	0.154761	+	0.0245117i
$143$	−179.246	+	179.246i	−1.25347	+	1.25347i
$144$	−27.5033	−	37.8551i	−0.190995	−	0.262882i
$145$		0			0
$146$	77.6183	+	56.3930i	0.531632	+	0.386253i
$147$	16.5599	+	104.555i	0.112653	+	0.711260i
$148$	−5.34620	−	10.4925i	−0.0361230	−	0.0708954i
$149$		−	127.548i		−	0.856024i	−0.903773	−	0.428012i	$-0.859214\pi$
$149$		−	127.548i		−	0.856024i	0.903773	−	0.428012i	$-0.140786\pi$
$150$		0			0
$151$	−89.8058			−0.594741			−0.297370	−	0.954762i	$-0.596110\pi$
$151$	−89.8058			−0.594741			−0.297370	+	0.954762i	$0.596110\pi$
$152$	−67.9160	+	34.6049i	−0.446816	+	0.227664i
$153$	−229.474	+	36.3450i	−1.49983	+	0.237549i
$154$	48.2675	−	66.4346i	0.313426	−	0.431393i
$155$		0			0
$156$	163.016	−	118.438i	1.04497	−	0.759216i
$157$	−58.6460	−	58.6460i	−0.373541	−	0.373541i	0.495224	−	0.868765i	$-0.335086\pi$
$157$	−58.6460	−	58.6460i	−0.373541	−	0.373541i	−0.868765	+	0.495224i	$0.835086\pi$
$158$	−27.0606	+	170.854i	−0.171269	+	1.08135i
$159$	377.033	−	122.506i	2.37128	−	0.770475i
$160$		0			0
$161$	−0.838909	+	2.58190i	−0.00521061	+	0.0160366i
$162$	−31.7430	+	62.2991i	−0.195944	+	0.384563i
$163$	169.873	+	86.5547i	1.04217	+	0.531011i	0.889342	−	0.457243i	$-0.151163\pi$
$163$	169.873	+	86.5547i	1.04217	+	0.531011i	0.152825	+	0.988253i	$0.451163\pi$
$164$	45.1470	+	14.6691i	0.275286	+	0.0894460i
$165$		0			0
$166$	−26.9448	−	82.9276i	−0.162318	−	0.499564i
$167$	−132.520	−	20.9891i	−0.793532	−	0.125683i	−0.253509	−	0.967333i	$-0.581585\pi$
$167$	−132.520	−	20.9891i	−0.793532	−	0.125683i	−0.540024	+	0.841650i	$0.681585\pi$
$168$	−46.1559	+	46.1559i	−0.274738	+	0.274738i
$169$	188.919	+	260.024i	1.11786	+	1.53861i
$170$		0			0
$171$	−255.041	−	185.298i	−1.49147	−	1.08362i
$172$	−19.7952	−	124.982i	−0.115088	−	0.726639i
$173$	−56.6075	−	111.098i	−0.327211	−	0.642187i	0.667533	−	0.744580i	$-0.267350\pi$
$173$	−56.6075	−	111.098i	−0.327211	−	0.642187i	−0.994744	+	0.102393i	$0.967350\pi$
$174$			40.2236i			0.231170i
$175$		0			0
$176$	−45.7875			−0.260156
$177$	88.4080	−	45.0461i	0.499480	−	0.254498i
$178$	−111.284	+	17.6256i	−0.625189	+	0.0990203i
$179$	−103.351	+	142.251i	−0.577381	+	0.794697i	−0.993405	−	0.114656i	$-0.963423\pi$
$179$	−103.351	+	142.251i	−0.577381	+	0.794697i	0.416024	+	0.909354i	$0.363423\pi$
$180$		0			0
$181$	4.01656	−	2.91820i	0.0221909	−	0.0161227i	−0.576635	−	0.817002i	$-0.695634\pi$
$181$	4.01656	−	2.91820i	0.0221909	−	0.0161227i	0.598825	+	0.800880i	$0.295634\pi$
$182$	−112.335	−	112.335i	−0.617223	−	0.617223i
$183$	49.1235	−	310.154i	0.268435	−	1.69483i
$184$	1.43962	−	0.467762i	0.00782404	−	0.00254218i
$185$		0			0
$186$	−13.3290	+	41.0224i	−0.0716613	+	0.220551i
$187$	−103.214	+	202.569i	−0.551948	+	1.08326i
$188$	−49.1969	−	25.0671i	−0.261686	−	0.133336i
$189$	−59.2138	−	19.2397i	−0.313300	−	0.101797i
$190$		0			0
$191$	−57.5605	−	177.153i	−0.301364	−	0.927503i	−0.981009	−	0.193962i	$-0.937866\pi$
$191$	−57.5605	−	177.153i	−0.301364	−	0.927503i	0.679645	−	0.733541i	$-0.262134\pi$
$192$	35.9478	+	5.69358i	0.187228	+	0.0296540i
$193$	149.932	−	149.932i	0.776850	−	0.776850i	−0.202444	−	0.979294i	$-0.564888\pi$
$193$	149.932	−	149.932i	0.776850	−	0.776850i	0.979294	+	0.202444i	$0.0648883\pi$
$194$	−113.037	−	155.581i	−0.582663	−	0.801966i
$195$		0			0
$196$	−37.6488	−	27.3534i	−0.192086	−	0.139558i
$197$	−47.1692	−	297.815i	−0.239437	−	1.51175i	−0.755472	−	0.655181i	$-0.772592\pi$
$197$	−47.1692	−	297.815i	−0.239437	−	1.51175i	0.516034	−	0.856568i	$-0.327408\pi$
$198$	−85.9715	−	168.729i	−0.434200	−	0.852165i
$199$		−	137.629i		−	0.691604i	−0.938307	−	0.345802i	$-0.887607\pi$
$199$		−	137.629i		−	0.691604i	0.938307	−	0.345802i	$-0.112393\pi$
$200$		0			0
$201$	−420.012			−2.08961
$202$	75.8765	−	38.6610i	0.375626	−	0.191391i
$203$	31.3226	−	4.96101i	0.154298	−	0.0244385i
$204$	106.223	−	146.203i	0.520700	−	0.716682i
$205$		0			0
$206$	82.2323	−	59.7453i	0.399186	−	0.290026i
$207$	4.42679	+	4.42679i	0.0213854	+	0.0213854i
$208$	−13.8571	+	87.4900i	−0.0666205	+	0.420625i
$209$	−293.386	+	95.3268i	−1.40376	+	0.456109i
$210$		0			0
$211$	34.9377	−	107.527i	0.165582	−	0.509608i	−0.833497	−	0.552524i	$-0.813665\pi$
$211$	34.9377	−	107.527i	0.165582	−	0.509608i	0.999079	+	0.0429161i	$0.0136648\pi$
$212$	−79.1202	+	155.282i	−0.373208	+	0.732463i
$213$	−63.7761	−	32.4955i	−0.299418	−	0.152561i
$214$	−17.5487	−	5.70192i	−0.0820034	−	0.0266445i
$215$		0			0
$216$	10.7278	+	33.0166i	0.0496655	+	0.152855i
$217$	33.5886	+	5.31992i	0.154786	+	0.0245157i
$218$	−5.14985	+	5.14985i	−0.0236231	+	0.0236231i
$219$	−181.415	−	249.696i	−0.828378	−	1.14016i
$220$		0			0
$221$	355.830	+	258.526i	1.61009	+	1.16980i
$222$	5.92624	+	37.4168i	0.0266948	+	0.168544i
$223$	108.822	+	213.575i	0.487992	+	0.957738i	0.995379	+	0.0960197i	$0.0306112\pi$
$223$	108.822	+	213.575i	0.487992	+	0.957738i	−0.507388	+	0.861718i	$0.669389\pi$
$224$		−	28.6952i		−	0.128104i
$225$		0			0
$226$	149.479			0.661413
$227$	−109.878	+	55.9856i	−0.484044	+	0.246633i	−0.678944	−	0.734190i	$-0.737562\pi$
$227$	−109.878	+	55.9856i	−0.484044	+	0.246633i	0.194900	+	0.980823i	$0.437562\pi$
$228$	242.191	−	38.3594i	1.06224	−	0.168243i
$229$	150.862	−	207.644i	0.658787	−	0.906742i	−0.340654	−	0.940189i	$-0.610648\pi$
$229$	150.862	−	207.644i	0.658787	−	0.906742i	0.999440	+	0.0334469i	$0.0106485\pi$
$230$		0			0
$231$	−213.718	+	155.275i	−0.925187	+	0.672188i
$232$	−12.5035	−	12.5035i	−0.0538945	−	0.0538945i
$233$	1.62731	−	10.2744i	0.00698416	−	0.0440962i	−0.983950	−	0.178444i	$-0.942894\pi$
$233$	1.62731	−	10.2744i	0.00698416	−	0.0440962i	0.990934	+	0.134347i	$0.0428938\pi$
$234$	−348.423	+	113.209i	−1.48899	+	0.483801i
$235$		0			0
$236$	−13.4791	+	41.4843i	−0.0571147	+	0.175781i
$237$	252.638	−	495.830i	1.06598	−	2.09211i
$238$	−126.951	−	64.6849i	−0.533409	−	0.271785i
$239$	−69.6575	−	22.6331i	−0.291454	−	0.0946992i	0.159641	−	0.987175i	$-0.448966\pi$
$239$	−69.6575	−	22.6331i	−0.291454	−	0.0946992i	−0.451095	+	0.892476i	$0.648966\pi$
$240$		0			0
$241$	−20.2934	−	62.4568i	−0.0842052	−	0.259157i	0.900085	−	0.435714i	$-0.143504\pi$
$241$	−20.2934	−	62.4568i	−0.0842052	−	0.259157i	−0.984290	+	0.176557i	$0.943504\pi$
$242$	−14.0109	−	2.21911i	−0.0578964	−	0.00916988i
$243$	237.160	−	237.160i	0.975969	−	0.975969i
$244$	81.1415	+	111.682i	0.332547	+	0.457712i
$245$		0			0
$246$	−123.546	−	89.7612i	−0.502218	−	0.364883i
$247$	93.3593	+	589.447i	0.377973	+	2.38643i
$248$	−8.60854	−	16.8952i	−0.0347118	−	0.0681258i
$249$			280.505i			1.12653i
$250$		0			0
$251$	−47.1625			−0.187898			−0.0939492	−	0.995577i	$-0.529949\pi$
$251$	−47.1625			−0.187898			−0.0939492	+	0.995577i	$0.529949\pi$
$252$	105.743	−	53.8788i	0.419615	−	0.213805i
$253$	6.05068	−	0.958333i	0.0239157	−	0.00378788i
$254$	51.0222	−	70.2260i	0.200875	−	0.276480i
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−85.1375	−	85.1375i	−0.331274	−	0.331274i	0.521796	−	0.853070i	$-0.325262\pi$
$257$	−85.1375	−	85.1375i	−0.331274	−	0.331274i	−0.853070	+	0.521796i	$0.825262\pi$
$258$	−63.6807	+	402.064i	−0.246824	+	1.55839i
$259$	28.4060	−	9.22967i	0.109676	−	0.0356358i
$260$		0			0
$261$	22.5991	−	69.5529i	0.0865866	−	0.266486i
$262$	46.7833	−	91.8175i	0.178562	−	0.350448i
$263$	−308.908	−	157.397i	−1.17456	−	0.598467i	−0.245860	−	0.969305i	$-0.579070\pi$
$263$	−308.908	−	157.397i	−1.17456	−	0.598467i	−0.928697	+	0.370839i	$0.879070\pi$
$264$	140.088	+	45.5173i	0.530636	+	0.172414i
$265$		0			0
$266$	−59.7418	−	183.866i	−0.224593	−	0.691227i
$267$	357.997	+	56.7011i	1.34081	+	0.212364i
$268$	130.561	−	130.561i	0.487168	−	0.487168i
$269$	114.651	+	157.804i	0.426212	+	0.586631i	0.967079	−	0.254478i	$-0.0819035\pi$
$269$	114.651	+	157.804i	0.426212	+	0.586631i	−0.540866	+	0.841109i	$0.681903\pi$
$270$		0			0
$271$	295.640	+	214.795i	1.09092	+	0.792602i	0.979555	−	0.201177i	$-0.0644768\pi$
$271$	295.640	+	214.795i	1.09092	+	0.792602i	0.111368	+	0.993779i	$0.464477\pi$
$272$	12.4279	+	78.4669i	0.0456909	+	0.288481i
$273$	232.019	+	455.362i	0.849885	+	1.66799i
$274$			223.639i			0.816201i
$275$		0			0
$276$	−4.86956			−0.0176433
$277$	90.3980	−	46.0601i	0.326346	−	0.166282i	−0.283139	−	0.959079i	$-0.591376\pi$
$277$	90.3980	−	46.0601i	0.326346	−	0.166282i	0.609486	+	0.792797i	$0.291376\pi$
$278$	164.743	−	26.0927i	0.592600	−	0.0938586i
$279$	46.0959	−	63.4456i	0.165218	−	0.227404i
$280$		0			0
$281$	324.001	−	235.401i	1.15303	−	0.837725i	0.164149	−	0.986436i	$-0.447512\pi$
$281$	324.001	−	235.401i	1.15303	−	0.837725i	0.988881	+	0.148710i	$0.0475121\pi$
$282$	125.600	+	125.600i	0.445390	+	0.445390i
$283$	−39.0193	+	246.358i	−0.137877	+	0.870523i	0.817670	+	0.575687i	$0.195265\pi$
$283$	−39.0193	+	246.358i	−0.137877	+	0.870523i	−0.955548	+	0.294837i	$0.904735\pi$
$284$	29.9261	−	9.72359i	0.105374	−	0.0342380i
$285$		0			0
$286$	−110.780	+	340.947i	−0.387344	+	1.19212i
$287$	−54.6606	+	107.277i	−0.190455	+	0.373789i
$288$	−58.9606	−	30.0419i	−0.204724	−	0.104312i
$289$	100.307	+	32.5918i	0.347084	+	0.112774i
$290$		0			0
$291$	191.175	+	588.375i	0.656957	+	2.02191i
$292$	134.011	+	21.2253i	0.458943	+	0.0726894i
$293$	−353.989	+	353.989i	−1.20815	+	1.20815i	−0.236529	+	0.971624i	$0.576010\pi$
$293$	−353.989	+	353.989i	−1.20815	+	1.20815i	−0.971624	+	0.236529i	$0.923990\pi$
$294$	87.9953	+	121.115i	0.299304	+	0.411956i
$295$		0			0
$296$	−13.4732	−	9.78887i	−0.0455176	−	0.0330705i
$297$	21.9786	+	138.768i	0.0740021	+	0.467231i
$298$	−81.8906	−	160.719i	−0.274801	−	0.539326i
$299$		−	11.8516i		−	0.0396374i
$300$		0			0
$301$	320.946			1.06627
$302$	−113.162	+	57.6589i	−0.374708	+	0.190923i
$303$	−270.579	+	42.8555i	−0.893000	+	0.141437i
$304$	−63.3614	+	87.2095i	−0.208426	+	0.286873i
$305$		0			0
$306$	−265.819	+	193.129i	−0.868688	+	0.631139i
$307$	−235.076	−	235.076i	−0.765718	−	0.765718i	0.211631	−	0.977350i	$-0.432122\pi$
$307$	−235.076	−	235.076i	−0.765718	−	0.765718i	−0.977350	+	0.211631i	$0.932122\pi$
$308$	18.1670	−	114.702i	0.0589839	−	0.372409i
$309$	−310.985	+	101.045i	−1.00642	+	0.327006i
$310$		0			0
$311$	73.4853	−	226.164i	0.236287	−	0.727217i	−0.760661	−	0.649149i	$-0.775125\pi$
$311$	73.4853	−	226.164i	0.236287	−	0.727217i	0.996948	−	0.0780676i	$-0.0248750\pi$
$312$	129.370	−	253.903i	0.414647	−	0.813791i
$313$	33.6349	+	17.1378i	0.107460	+	0.0547535i	0.506894	−	0.862008i	$-0.330793\pi$
$313$	33.6349	+	17.1378i	0.107460	+	0.0547535i	−0.399434	+	0.916762i	$0.630793\pi$
$314$	−111.551	−	36.2452i	−0.355259	−	0.115431i
$315$		0			0
$316$	75.5965	+	232.662i	0.239230	+	0.736273i
$317$	191.456	+	30.3237i	0.603963	+	0.0956583i	0.450925	−	0.892562i	$-0.351094\pi$
$317$	191.456	+	30.3237i	0.603963	+	0.0956583i	0.153038	+	0.988220i	$0.451094\pi$
$318$	396.436	−	396.436i	1.24665	−	1.24665i
$319$	−42.0638	−	57.8958i	−0.131861	−	0.181492i
$320$		0			0
$321$	48.0225	+	34.8904i	0.149603	+	0.108693i
$322$	0.600592	+	3.79199i	0.00186519	+	0.0117764i
$323$	242.996	+	476.907i	0.752310	+	1.47649i
$324$			98.8817i			0.305191i
$325$		0			0
$326$	269.624			0.827068
$327$	20.8755	−	10.6366i	0.0638396	−	0.0325279i
$328$	66.3067	−	10.5019i	0.202155	−	0.0320181i
$329$	82.3153	−	113.297i	0.250199	−	0.344369i
$330$		0			0
$331$	206.636	−	150.130i	0.624279	−	0.453566i	−0.230134	−	0.973159i	$-0.573917\pi$
$331$	206.636	−	150.130i	0.624279	−	0.453566i	0.854414	+	0.519593i	$0.173917\pi$
$332$	−87.1953	−	87.1953i	−0.262636	−	0.262636i
$333$	10.7748	−	68.0291i	0.0323566	−	0.204292i
$334$	−180.461	+	58.6352i	−0.540301	+	0.175555i
$335$		0			0
$336$	−28.5259	+	87.7938i	−0.0848986	+	0.261291i
$337$	−166.116	+	326.020i	−0.492925	+	0.967419i	0.501814	+	0.864975i	$0.332666\pi$
$337$	−166.116	+	326.020i	−0.492925	+	0.967419i	−0.994739	+	0.102444i	$0.967334\pi$
$338$	404.997	+	206.356i	1.19822	+	0.610522i
$339$	−457.335	−	148.597i	−1.34907	−	0.438340i
$340$		0			0
$341$	−23.7141	−	72.9845i	−0.0695428	−	0.214031i
$342$	−440.339	−	69.7429i	−1.28754	−	0.203927i
$343$	259.219	−	259.219i	0.755741	−	0.755741i
$344$	−105.187	−	144.777i	−0.305776	−	0.420864i
$345$		0			0
$346$	−142.659	−	103.648i	−0.412310	−	0.299560i
$347$	−71.6649	−	452.474i	−0.206527	−	1.30396i	−0.845187	−	0.534471i	$-0.820511\pi$
$347$	−71.6649	−	452.474i	−0.206527	−	1.30396i	0.638660	−	0.769489i	$-0.279489\pi$
$348$	25.8251	+	50.6846i	0.0742101	+	0.145646i
$349$			98.1992i			0.281373i	0.990054	+	0.140686i	$0.0449310\pi$
$349$			98.1992i			0.281373i	−0.990054	+	0.140686i	$0.955069\pi$
$350$		0			0
$351$	271.807			0.774378
$352$	−57.6956	+	29.3974i	−0.163908	+	0.0835152i
$353$	139.455	−	22.0875i	0.395058	−	0.0625710i	0.0442546	−	0.999020i	$-0.485909\pi$
$353$	139.455	−	22.0875i	0.395058	−	0.0625710i	0.350803	+	0.936449i	$0.385909\pi$
$354$	82.4792	−	113.523i	0.232992	−	0.320686i
$355$		0			0
$356$	−128.909	+	93.6581i	−0.362105	+	0.263085i
$357$	324.108	+	324.108i	0.907864	+	0.907864i
$358$	−38.8996	+	245.602i	−0.108658	+	0.686039i
$359$	419.653	−	136.354i	1.16895	−	0.379815i	0.340699	−	0.940172i	$-0.389336\pi$
$359$	419.653	−	136.354i	1.16895	−	0.379815i	0.828251	+	0.560358i	$0.189336\pi$
$360$		0			0
$361$	−112.872	+	347.383i	−0.312664	+	0.962281i
$362$	3.18756	−	6.25594i	0.00880541	−	0.0172816i
$363$	40.6607	+	20.7177i	0.112013	+	0.0570735i
$364$	−213.673	−	69.4266i	−0.587014	−	0.190732i
$365$		0			0
$366$	−137.232	−	422.356i	−0.374950	−	1.15398i
$367$	340.331	+	53.9032i	0.927333	+	0.146875i	0.601792	−	0.798653i	$-0.294454\pi$
$367$	340.331	+	53.9032i	0.927333	+	0.146875i	0.325541	+	0.945528i	$0.394454\pi$
$368$	1.51371	−	1.51371i	0.00411334	−	0.00411334i
$369$	163.199	+	224.624i	0.442274	+	0.608737i
$370$		0			0
$371$	−357.605	−	259.815i	−0.963894	−	0.700310i
$372$	9.54251	+	60.2490i	0.0256519	+	0.161960i
$373$	−161.454	−	316.871i	−0.432852	−	0.849520i	−0.999670	−	0.0256771i	$-0.991826\pi$
$373$	−161.454	−	316.871i	−0.432852	−	0.849520i	0.566818	−	0.823843i	$-0.308174\pi$
$374$			321.520i			0.859679i
$375$		0			0
$376$	−78.0858			−0.207675
$377$	−123.357	+	62.8533i	−0.327206	+	0.166720i
$378$	−86.9663	+	13.7741i	−0.230070	+	0.0364395i
$379$	155.812	−	214.457i	0.411115	−	0.565851i	−0.552375	−	0.833596i	$-0.686278\pi$
$379$	155.812	−	214.457i	0.411115	−	0.565851i	0.963490	+	0.267745i	$0.0862784\pi$
$380$		0			0
$381$	−225.915	+	164.137i	−0.592954	+	0.430806i
$382$	−186.270	−	186.270i	−0.487617	−	0.487617i
$383$	60.2315	−	380.286i	0.157262	−	0.992915i	−0.775218	−	0.631694i	$-0.782360\pi$
$383$	60.2315	−	380.286i	0.157262	−	0.992915i	0.932480	−	0.361221i	$-0.117640\pi$
$384$	48.9524	−	15.9056i	0.127480	−	0.0414208i
$385$		0			0
$386$	92.6631	−	285.188i	0.240060	−	0.738828i
$387$	336.009	−	659.454i	0.868239	−	1.70402i
$388$	−242.324	−	123.470i	−0.624546	−	0.318222i
$389$	−607.465	−	197.377i	−1.56161	−	0.507397i	−0.604370	−	0.796704i	$-0.706575\pi$
$389$	−607.465	−	197.377i	−1.56161	−	0.507397i	−0.957236	+	0.289307i	$0.906575\pi$
$390$		0			0
$391$	−3.28463	−	10.1090i	−0.00840059	−	0.0258543i
$392$	−65.0022	−	10.2953i	−0.165822	−	0.0262636i
$393$	−234.411	+	234.411i	−0.596464	+	0.596464i
$394$	−250.645	−	344.984i	−0.636156	−	0.875593i
$395$		0			0
$396$	−216.661	−	157.413i	−0.547123	−	0.397508i
$397$	−3.12348	−	19.7208i	−0.00786770	−	0.0496747i	0.983442	−	0.181222i	$-0.0580054\pi$
$397$	−3.12348	−	19.7208i	−0.00786770	−	0.0496747i	−0.991310	+	0.131548i	$0.958005\pi$
$398$	−88.3634	−	173.423i	−0.222019	−	0.435736i
$399$			621.933i			1.55873i
$400$		0			0
$401$	−546.371			−1.36252			−0.681261	−	0.732041i	$-0.738568\pi$
$401$	−546.371			−1.36252			−0.681261	+	0.732041i	$0.738568\pi$
$402$	−529.246	+	269.664i	−1.31653	+	0.670806i
$403$	−146.634	+	23.2246i	−0.363857	+	0.0576293i
$404$	70.7881	−	97.4315i	0.175218	−	0.241167i
$405$		0			0
$406$	36.2836	−	26.3616i	0.0893685	−	0.0649300i
$407$	−47.6585	−	47.6585i	−0.117097	−	0.117097i
$408$	39.9804	−	252.426i	0.0979911	−	0.618691i
$409$	396.232	−	128.743i	0.968782	−	0.314776i	0.218458	−	0.975846i	$-0.429897\pi$
$409$	396.232	−	128.743i	0.968782	−	0.314776i	0.750324	+	0.661070i	$0.229897\pi$
$410$		0			0
$411$	222.320	−	684.229i	0.540924	−	1.66479i
$412$	65.2599	−	128.080i	0.158398	−	0.310873i
$413$	−98.5743	−	50.2261i	−0.238679	−	0.121613i
$414$	8.42025	+	2.73591i	0.0203388	+	0.00660847i
$415$		0			0
$416$	38.7111	+	119.141i	0.0930556	+	0.286396i
$417$	−529.974	−	83.9396i	−1.27092	−	0.201294i
$418$	−308.484	+	308.484i	−0.738000	+	0.738000i
$419$	245.790	+	338.302i	0.586612	+	0.807402i	0.994401	−	0.105674i	$-0.0337000\pi$
$419$	245.790	+	338.302i	0.586612	+	0.807402i	−0.407789	+	0.913076i	$0.633700\pi$
$420$		0			0
$421$	−240.021	−	174.386i	−0.570122	−	0.414218i	0.265028	−	0.964241i	$-0.414619\pi$
$421$	−240.021	−	174.386i	−0.570122	−	0.414218i	−0.835149	+	0.550023i	$0.814619\pi$
$422$	−25.0126	−	157.924i	−0.0592717	−	0.374227i
$423$	−146.616	−	287.749i	−0.346609	−	0.680258i
$424$			246.465i			0.581286i
$425$		0			0
$426$	−101.226			−0.237620
$427$	−311.968	+	158.956i	−0.730605	+	0.372262i
$428$	−25.7735	+	4.08213i	−0.0602185	+	0.00953768i
$429$	677.870	−	933.008i	1.58012	−	2.17484i
$430$		0			0
$431$	−319.131	+	231.862i	−0.740442	+	0.537963i	−0.892850	−	0.450355i	$-0.851297\pi$
$431$	−319.131	+	231.862i	−0.740442	+	0.537963i	0.152408	+	0.988318i	$0.451297\pi$
$432$	34.7157	+	34.7157i	0.0803605	+	0.0803605i
$433$	−17.7920	+	112.334i	−0.0410901	+	0.259432i	−0.999678	−	0.0253633i	$-0.991926\pi$
$433$	−17.7920	+	112.334i	−0.0410901	+	0.259432i	0.958588	+	0.284796i	$0.0919258\pi$
$434$	45.7397	−	14.8617i	0.105391	−	0.0342436i
$435$		0			0
$436$	−3.18278	+	9.79559i	−0.00729995	+	0.0224669i
$437$	6.54773	−	12.8506i	0.0149834	−	0.0294065i
$438$	−388.911	−	198.160i	−0.887924	−	0.452420i
$439$	541.776	+	176.034i	1.23411	+	0.400988i	0.852203	−	0.523211i	$-0.175266\pi$
$439$	541.776	+	176.034i	1.23411	+	0.400988i	0.381911	+	0.924199i	$0.375266\pi$
$440$		0			0
$441$	−84.1108	−	258.867i	−0.190728	−	0.586999i
$442$	614.356	+	97.3044i	1.38995	+	0.220146i
$443$	−277.860	+	277.860i	−0.627222	+	0.627222i	−0.947368	−	0.320146i	$-0.896268\pi$
$443$	−277.860	+	277.860i	−0.627222	+	0.627222i	0.320146	+	0.947368i	$0.396268\pi$
$444$	31.4905	+	43.3430i	0.0709246	+	0.0976194i
$445$		0			0
$446$	274.248	+	199.253i	0.614905	+	0.446755i
$447$	90.7752	+	573.132i	0.203077	+	1.28217i
$448$	−18.4235	−	36.1581i	−0.0411238	−	0.0807101i
$449$		−	733.358i		−	1.63331i	−0.577124	−	0.816657i	$-0.695825\pi$
$449$		−	733.358i		−	1.63331i	0.577124	−	0.816657i	$-0.304175\pi$
$450$		0			0
$451$	271.693			0.602424
$452$	188.355	−	95.9716i	0.416714	−	0.212327i
$453$	403.540	−	63.9145i	0.890818	−	0.141092i
$454$	−102.509	+	141.092i	−0.225792	+	0.310775i
$455$		0			0
$456$	280.551	−	203.832i	0.615243	−	0.447000i
$457$	637.278	+	637.278i	1.39448	+	1.39448i	0.814948	+	0.579535i	$0.196766\pi$
$457$	637.278	+	637.278i	1.39448	+	1.39448i	0.579535	+	0.814948i	$0.303234\pi$
$458$	56.7818	−	358.506i	0.123978	−	0.782764i
$459$	231.843	−	75.3304i	0.505105	−	0.164119i
$460$		0			0
$461$	−199.771	+	614.831i	−0.433342	+	1.33369i	0.461434	+	0.887175i	$0.347335\pi$
$461$	−199.771	+	614.831i	−0.433342	+	1.33369i	−0.894776	+	0.446515i	$0.852665\pi$
$462$	−169.608	+	332.874i	−0.367116	+	0.720507i
$463$	300.113	+	152.915i	0.648192	+	0.330271i	0.746988	−	0.664837i	$-0.231499\pi$
$463$	300.113	+	152.915i	0.648192	+	0.330271i	−0.0987958	+	0.995108i	$0.531499\pi$
$464$	−23.7831	−	7.72761i	−0.0512568	−	0.0166543i
$465$		0			0
$466$	−4.54606	−	13.9913i	−0.00975549	−	0.0300243i
$467$	556.933	+	88.2096i	1.19258	+	0.188886i	0.720997	−	0.692938i	$-0.243684\pi$
$467$	556.933	+	88.2096i	1.19258	+	0.188886i	0.471579	+	0.881824i	$0.343684\pi$
$468$	−366.353	+	366.353i	−0.782806	+	0.782806i
$469$	275.266	+	378.871i	0.586921	+	0.807827i
$470$		0			0
$471$	305.263	+	221.786i	0.648116	+	0.470884i
$472$	9.64996	+	60.9274i	0.0204448	+	0.129084i
$473$	−328.799	−	645.305i	−0.695136	−	1.36428i
$474$		−	786.986i		−	1.66031i
$475$		0			0
$476$	−201.498			−0.423316
$477$	−908.234	+	462.768i	−1.90405	+	0.970164i
$478$	−102.305	+	16.2035i	−0.214027	+	0.0338986i
$479$	−478.041	+	657.967i	−0.997998	+	1.37363i	−0.0714519	+	0.997444i	$0.522763\pi$
$479$	−478.041	+	657.967i	−0.997998	+	1.37363i	−0.926546	+	0.376182i	$0.877237\pi$
$480$		0			0
$481$	−105.489	+	76.6419i	−0.219311	+	0.159339i
$482$	−65.6710	−	65.6710i	−0.136247	−	0.136247i
$483$	1.93209	−	12.1987i	0.00400019	−	0.0252562i
$484$	−19.0795	+	6.19932i	−0.0394205	+	0.0128085i
$485$		0			0
$486$	146.573	−	451.106i	0.301591	−	0.928202i
$487$	54.4449	−	106.854i	0.111796	−	0.219413i	−0.828329	−	0.560243i	$-0.810708\pi$
$487$	54.4449	−	106.854i	0.111796	−	0.219413i	0.940125	+	0.340830i	$0.110708\pi$
$488$	173.948	+	88.6311i	0.356452	+	0.181621i
$489$	−824.922	−	268.033i	−1.68696	−	0.548126i
$490$		0			0
$491$	−47.2164	−	145.317i	−0.0961637	−	0.295962i	0.891391	−	0.453234i	$-0.149730\pi$
$491$	−47.2164	−	145.317i	−0.0961637	−	0.295962i	−0.987555	+	0.157273i	$0.949730\pi$
$492$	−213.307	−	33.7845i	−0.433551	−	0.0686677i
$493$	−87.8000	+	87.8000i	−0.178093	+	0.178093i
$494$	496.088	+	682.806i	1.00423	+	1.38220i
$495$		0			0
$496$	−21.6948	−	15.7622i	−0.0437395	−	0.0317786i
$497$	12.4848	+	78.8259i	0.0251203	+	0.158603i
$498$	180.095	+	353.457i	0.361637	+	0.709753i
$499$		−	424.984i		−	0.851671i	−0.904801	−	0.425836i	$-0.859980\pi$
$499$		−	424.984i		−	0.851671i	0.904801	−	0.425836i	$-0.140020\pi$
$500$		0			0
$501$	610.413			1.21839
$502$	−59.4282	+	30.2802i	−0.118383	+	0.0603191i
$503$	−593.435	+	93.9909i	−1.17979	+	0.186861i	−0.715365	−	0.698751i	$-0.753740\pi$
$503$	−593.435	+	93.9909i	−1.17979	+	0.186861i	−0.464427	+	0.885611i	$0.653740\pi$
$504$	98.6518	−	135.782i	0.195738	−	0.269410i
$505$		0			0
$506$	7.00901	−	5.09234i	0.0138518	−	0.0100639i
$507$	−1033.96	−	1033.96i	−2.03937	−	2.03937i
$508$	19.2038	−	121.248i	0.0378028	−	0.238678i
$509$	103.142	−	33.5130i	0.202637	−	0.0658408i	−0.205940	−	0.978565i	$-0.566025\pi$
$509$	103.142	−	33.5130i	0.202637	−	0.0658408i	0.408577	+	0.912724i	$0.366025\pi$
$510$		0			0
$511$	−106.343	+	327.290i	−0.208107	+	0.640489i
$512$	−10.2726	+	20.1612i	−0.0200637	+	0.0393773i
$513$	294.719	+	150.167i	0.574501	+	0.292723i
$514$	−161.941	−	52.6179i	−0.315061	−	0.102369i
$515$		0			0
$516$	177.899	+	547.516i	0.344765	+	1.06108i
$517$	−312.129	−	49.4363i	−0.603730	−	0.0956215i
$518$	29.8678	−	29.8678i	0.0576599	−	0.0576599i
$519$	333.433	+	458.931i	0.642452	+	0.884260i
$520$		0			0
$521$	−161.044	−	117.005i	−0.309105	−	0.224578i	0.422407	−	0.906406i	$-0.361185\pi$
$521$	−161.044	−	117.005i	−0.309105	−	0.224578i	−0.731512	+	0.681828i	$0.761185\pi$
$522$	−16.1792	−	102.151i	−0.0309946	−	0.195692i
$523$	−288.049	−	565.327i	−0.550762	−	1.08093i	−0.983752	−	0.179533i	$-0.942541\pi$
$523$	−288.049	−	565.327i	−0.550762	−	1.08093i	0.432990	−	0.901399i	$-0.357459\pi$
$524$		−	145.734i		−	0.278117i
$525$		0			0
$526$	−490.302			−0.932134
$527$	−118.638	+	60.4492i	−0.225120	+	0.114704i
$528$	205.745	−	32.5868i	0.389668	−	0.0617174i
$529$	310.770	−	427.738i	0.587467	−	0.808579i
$530$		0			0
$531$	−206.401	+	149.959i	−0.388702	+	0.282409i
$532$	−193.329	−	193.329i	−0.363400	−	0.363400i
$533$	82.2249	−	519.148i	0.154268	−	0.974011i
$534$	487.507	−	158.401i	0.912934	−	0.296630i
$535$		0			0
$536$	80.6912	−	248.342i	0.150543	−	0.463325i
$537$	363.167	−	712.756i	0.676289	−	1.32729i
$538$	245.785	+	125.234i	0.456850	+	0.232777i
$539$	−253.312	−	82.3061i	−0.469967	−	0.152702i
$540$		0			0
$541$	−287.608	−	885.166i	−0.531622	−	1.63617i	−0.750836	−	0.660489i	$-0.770349\pi$
$541$	−287.608	−	885.166i	−0.531622	−	1.63617i	0.219214	−	0.975677i	$-0.429651\pi$
$542$	510.435	+	80.8450i	0.941762	+	0.149161i
$543$	−15.9714	+	15.9714i	−0.0294133	+	0.0294133i
$544$	66.0390	+	90.8948i	0.121395	+	0.167086i
$545$		0			0
$546$	584.721	+	424.825i	1.07092	+	0.778067i
$547$	−106.845	−	674.591i	−0.195328	−	1.23326i	−0.869220	−	0.494425i	$-0.835379\pi$
$547$	−106.845	−	674.591i	−0.195328	−	1.23326i	0.673892	−	0.738830i	$-0.264621\pi$
$548$	143.585	+	281.802i	0.262017	+	0.514237i
$549$			807.422i			1.47071i
$550$		0			0
$551$	−168.480			−0.305772
$552$	−6.13601	+	3.12645i	−0.0111160	+	0.00566386i
$553$	−612.836	+	97.0637i	−1.10820	+	0.175522i
$554$	84.3357	−	116.078i	0.152231	−	0.209527i
$555$		0			0
$556$	190.836	−	138.650i	0.343229	−	0.249371i
$557$	18.5591	+	18.5591i	0.0333198	+	0.0333198i	0.723570	−	0.690251i	$-0.242500\pi$
$557$	18.5591	+	18.5591i	0.0333198	+	0.0333198i	−0.690251	+	0.723570i	$0.742500\pi$
$558$	17.3497	−	109.542i	0.0310926	−	0.196311i
$559$	−1332.55	+	432.971i	−2.38380	+	0.774545i
$560$		0			0
$561$	319.623	−	983.699i	0.569738	−	1.75347i
$562$	257.129	−	504.644i	0.457525	−	0.897943i
$563$	841.019	+	428.520i	1.49382	+	0.761138i	0.994446	−	0.105251i	$-0.0335646\pi$
$563$	841.019	+	428.520i	1.49382	+	0.761138i	0.499371	+	0.866388i	$0.333565\pi$
$564$	238.906	+	77.6251i	0.423591	+	0.137633i
$565$		0			0
$566$	109.004	+	335.481i	0.192587	+	0.592723i
$567$	−247.709	−	39.2332i	−0.436876	−	0.0691943i
$568$	31.4662	−	31.4662i	0.0553982	−	0.0553982i
$569$	−212.998	−	293.167i	−0.374337	−	0.515231i	0.579736	−	0.814804i	$-0.303156\pi$
$569$	−212.998	−	293.167i	−0.374337	−	0.515231i	−0.954073	+	0.299573i	$0.903156\pi$
$570$		0			0
$571$	−908.751	−	660.246i	−1.59151	−	1.15630i	−0.901750	−	0.432258i	$-0.857717\pi$
$571$	−908.751	−	660.246i	−1.59151	−	1.15630i	−0.689758	−	0.724040i	$-0.742283\pi$
$572$	79.3099	+	500.743i	0.138654	+	0.875425i
$573$	384.726	+	755.067i	0.671424	+	1.31774i
$574$			170.272i			0.296640i
$575$		0			0
$576$	−93.5828			−0.162470
$577$	−83.8317	+	42.7144i	−0.145289	+	0.0740284i	−0.525124	−	0.851026i	$-0.675981\pi$
$577$	−83.8317	+	42.7144i	−0.145289	+	0.0740284i	0.379835	+	0.925054i	$0.375981\pi$
$578$	147.320	−	23.3331i	0.254878	−	0.0403688i
$579$	−567.010	+	780.423i	−0.979292	+	1.34788i
$580$		0			0
$581$	253.029	−	183.836i	0.435506	−	0.316414i
$582$	618.654	+	618.654i	1.06298	+	1.06298i
$583$	−156.038	+	985.183i	−0.267646	+	1.68985i
$584$	182.491	−	59.2951i	0.312485	−	0.101533i
$585$		0			0
$586$	−218.777	+	673.327i	−0.373340	+	1.14902i
$587$	−178.229	+	349.794i	−0.303627	+	0.595901i	−0.991526	−	0.129905i	$-0.958533\pi$
$587$	−178.229	+	349.794i	−0.303627	+	0.595901i	0.687900	+	0.725806i	$0.258533\pi$
$588$	188.641	+	96.1176i	0.320819	+	0.163465i
$589$	−171.826	−	55.8298i	−0.291726	−	0.0947875i
$590$		0			0
$591$	423.907	+	1304.65i	0.717271	+	2.20753i
$592$	−23.2621	−	3.68435i	−0.0392941	−	0.00622357i
$593$	730.554	−	730.554i	1.23196	−	1.23196i	0.268754	−	0.963209i	$-0.413388\pi$
$593$	730.554	−	730.554i	1.23196	−	1.23196i	0.963209	−	0.268754i	$-0.0866120\pi$
$594$	116.789	+	160.746i	0.196614	+	0.270616i
$595$		0			0
$596$	−206.376	−	149.941i	−0.346269	−	0.251579i
$597$	97.9503	+	618.434i	0.164071	+	1.03590i
$598$	−7.60918	−	14.9339i	−0.0127244	−	0.0249730i
$599$			287.501i			0.479968i	0.970777	+	0.239984i	$0.0771422\pi$
$599$			287.501i			0.479968i	−0.970777	+	0.239984i	$0.922858\pi$
$600$		0			0
$601$	481.352			0.800919			0.400459	−	0.916314i	$-0.368851\pi$
$601$	481.352			0.800919			0.400459	+	0.916314i	$0.368851\pi$
$602$	404.416	−	206.060i	0.671787	−	0.342293i
$603$	1066.66	−	168.942i	1.76892	−	0.280169i
$604$	−105.573	+	145.309i	−0.174790	+	0.240578i
$605$		0			0
$606$	−313.435	+	227.724i	−0.517219	+	0.375781i
$607$	−431.854	−	431.854i	−0.711456	−	0.711456i	0.255383	−	0.966840i	$-0.417798\pi$
$607$	−431.854	−	431.854i	−0.711456	−	0.711456i	−0.966840	+	0.255383i	$0.917798\pi$
$608$	−23.8481	+	150.571i	−0.0392238	+	0.247650i
$609$	−137.217	+	44.5844i	−0.225315	+	0.0732092i
$610$		0			0
$611$	−188.924	+	581.450i	−0.309205	+	0.951636i
$612$	−210.955	+	414.022i	−0.344698	+	0.676507i
$613$	267.994	+	136.550i	0.437185	+	0.222757i	0.658709	−	0.752398i	$-0.271103\pi$
$613$	267.994	+	136.550i	0.437185	+	0.222757i	−0.221524	+	0.975155i	$0.571103\pi$
$614$	−447.140	−	145.285i	−0.728242	−	0.236620i
$615$		0			0
$616$	−50.7515	−	156.197i	−0.0823888	−	0.253567i
$617$	41.3822	+	6.55430i	0.0670700	+	0.0106228i	0.189879	−	0.981807i	$-0.439190\pi$
$617$	41.3822	+	6.55430i	0.0670700	+	0.0106228i	−0.122809	+	0.992430i	$0.539190\pi$
$618$	−326.988	+	326.988i	−0.529108	+	0.529108i
$619$	−491.415	−	676.375i	−0.793885	−	1.09269i	−0.993613	−	0.112838i	$-0.964006\pi$
$619$	−491.415	−	676.375i	−0.793885	−	1.09269i	0.199728	−	0.979851i	$-0.435994\pi$
$620$		0			0
$621$	−5.31418	−	3.86098i	−0.00855746	−	0.00621736i
$622$	−52.6097	−	332.164i	−0.0845814	−	0.534026i
$623$	−183.476	−	360.091i	−0.294503	−	0.577995i
$624$		−	402.997i		−	0.645828i
$625$		0			0
$626$	53.3856			0.0852805
$627$	1250.48	−	637.151i	1.99438	−	1.01619i
$628$	−163.834	+	25.9487i	−0.260882	+	0.0413196i
$629$	−68.7376	+	94.6091i	−0.109281	+	0.150412i
$630$		0			0
$631$	559.824	−	406.736i	0.887201	−	0.644589i	−0.0479460	−	0.998850i	$-0.515268\pi$
$631$	559.824	−	406.736i	0.887201	−	0.644589i	0.935147	+	0.354261i	$0.115268\pi$
$632$	244.635	+	244.635i	0.387081	+	0.387081i
$633$	−80.4651	+	508.036i	−0.127117	+	0.802585i
$634$	260.718	−	84.7124i	0.411227	−	0.133616i
$635$		0			0
$636$	245.011	−	754.066i	0.385237	−	1.18564i
$637$	−233.932	+	459.116i	−0.367239	+	0.720748i
$638$	−90.1748	−	45.9464i	−0.141340	−	0.0720162i
$639$	175.036	+	56.8726i	0.273921	+	0.0890025i
$640$		0			0
$641$	353.774	+	1088.81i	0.551910	+	1.69860i	0.703967	+	0.710233i	$0.251410\pi$
$641$	353.774	+	1088.81i	0.551910	+	1.69860i	−0.152057	+	0.988372i	$0.548590\pi$
$642$	82.9128	+	13.1321i	0.129148	+	0.0204550i
$643$	160.690	−	160.690i	0.249906	−	0.249906i	−0.571026	−	0.820932i	$-0.693454\pi$
$643$	160.690	−	160.690i	0.249906	−	0.249906i	0.820932	+	0.571026i	$0.193454\pi$
$644$	3.19140	+	4.39258i	0.00495559	+	0.00682078i
$645$		0			0
$646$	612.386	+	444.925i	0.947966	+	0.688738i
$647$	31.2660	+	197.406i	0.0483246	+	0.305110i	0.999998	−	0.00200241i	$-0.000637388\pi$
$647$	31.2660	+	197.406i	0.0483246	+	0.305110i	−0.951673	+	0.307112i	$0.900637\pi$
$648$	63.4860	+	124.598i	0.0979722	+	0.192281i
$649$			249.652i			0.384671i
$650$		0			0
$651$	−154.716			−0.237659
$652$	339.746	−	173.109i	0.521083	−	0.265505i
$653$	778.694	−	123.333i	1.19249	−	0.188871i	0.471529	−	0.881850i	$-0.343702\pi$
$653$	778.694	−	123.333i	1.19249	−	0.188871i	0.720958	+	0.692979i	$0.243702\pi$
$654$	19.4756	−	26.8058i	0.0297792	−	0.0409875i
$655$		0			0
$656$	76.8086	−	55.8047i	0.117086	−	0.0850682i
$657$	561.155	+	561.155i	0.854117	+	0.854117i
$658$	30.9820	−	195.613i	0.0470851	−	0.297284i
$659$	−119.459	+	38.8147i	−0.181274	+	0.0588994i	−0.398247	−	0.917278i	$-0.630381\pi$
$659$	−119.459	+	38.8147i	−0.181274	+	0.0588994i	0.216974	+	0.976177i	$0.430381\pi$
$660$		0			0
$661$	−358.442	+	1103.17i	−0.542272	+	1.66894i	0.185118	+	0.982716i	$0.440733\pi$
$661$	−358.442	+	1103.17i	−0.542272	+	1.66894i	−0.727390	+	0.686224i	$0.759267\pi$
$662$	163.988	−	321.844i	0.247715	−	0.486169i
$663$	−1782.91	−	908.437i	−2.68915	−	1.37019i
$664$	−165.855	−	53.8897i	−0.249782	−	0.0811591i
$665$		0			0
$666$	−30.1004	−	92.6395i	−0.0451958	−	0.139098i
$667$	3.30461	+	0.523399i	0.00495444	+	0.000784706i
$668$	−189.748	+	189.748i	−0.284053	+	0.284053i
$669$	−640.991	−	882.248i	−0.958133	−	1.31876i
$670$		0			0
$671$	639.203	+	464.408i	0.952612	+	0.692113i
$672$	20.4223	+	128.941i	0.0303903	+	0.191877i
$673$	−107.355	−	210.697i	−0.159517	−	0.313071i	0.797390	−	0.603465i	$-0.206214\pi$
$673$	−107.355	−	210.697i	−0.159517	−	0.313071i	−0.956907	+	0.290394i	$0.906214\pi$
$674$			517.462i			0.767748i
$675$		0			0
$676$	642.816			0.950911
$677$	686.535	−	349.807i	1.01408	−	0.516701i	0.133729	−	0.991018i	$-0.457305\pi$
$677$	686.535	−	349.807i	1.01408	−	0.516701i	0.880354	+	0.474317i	$0.157305\pi$
$678$	−671.682	+	106.384i	−0.990681	+	0.156908i
$679$	405.451	−	558.056i	0.597130	−	0.821879i
$680$		0			0
$681$	453.890	−	329.770i	0.666504	−	0.484244i
$682$	−76.7404	−	76.7404i	−0.112523	−	0.112523i
$683$	−70.1140	+	442.682i	−0.102656	+	0.648144i	0.881681	+	0.471846i	$0.156412\pi$
$683$	−70.1140	+	442.682i	−0.102656	+	0.648144i	−0.984337	+	0.176298i	$0.943588\pi$
$684$	−599.638	+	194.834i	−0.876663	+	0.284845i
$685$		0			0
$686$	160.206	−	493.064i	0.233537	−	0.718753i
$687$	−530.116	+	1040.41i	−0.771639	+	1.51443i
$688$	−225.496	−	114.896i	−0.327755	−	0.167000i
$689$	1835.25	+	596.309i	2.66365	+	0.865471i
$690$		0			0
$691$	−316.495	−	974.071i	−0.458024	−	1.40965i	−0.867547	−	0.497355i	$-0.834305\pi$
$691$	−316.495	−	974.071i	−0.458024	−	1.40965i	0.409523	−	0.912300i	$-0.365695\pi$
$692$	−246.307	−	39.0112i	−0.355935	−	0.0563746i
$693$	480.300	−	480.300i	0.693074	−	0.693074i
$694$	−380.809	−	524.139i	−0.548717	−	0.755244i
$695$		0			0
$696$	65.0831	+	47.2856i	0.0935102	+	0.0679391i
$697$	−73.7448	−	465.606i	−0.105803	−	0.668015i
$698$	63.0477	+	123.738i	0.0903263	+	0.177275i
$699$			47.3260i			0.0677054i
$700$		0			0
$701$	−1352.58			−1.92951			−0.964753	−	0.263156i	$-0.915237\pi$
$701$	−1352.58			−1.92951			−0.964753	+	0.263156i	$0.915237\pi$
$702$	342.496	−	174.511i	0.487887	−	0.248591i
$703$	−156.724	+	24.8226i	−0.222936	+	0.0353095i
$704$	−53.8264	+	74.0857i	−0.0764579	+	0.105235i
$705$		0			0
$706$	161.543	−	117.368i	0.228814	−	0.166243i
$707$	215.989	+	215.989i	0.305501	+	0.305501i
$708$	31.0437	−	196.002i	0.0438470	−	0.276839i
$709$	131.683	−	42.7865i	0.185731	−	0.0603477i	−0.214675	−	0.976686i	$-0.568869\pi$
$709$	131.683	−	42.7865i	0.185731	−	0.0603477i	0.400406	+	0.916338i	$0.368869\pi$
$710$		0			0
$711$	−442.159	+	1360.82i	−0.621883	+	1.91396i
$712$	−102.303	+	200.781i	−0.143684	+	0.281996i
$713$	3.19680	+	1.62885i	0.00448359	+	0.00228451i
$714$	616.489	+	200.309i	0.863430	+	0.280545i
$715$		0			0
$716$	108.670	+	334.452i	0.151774	+	0.467111i
$717$	329.112	+	52.1263i	0.459013	+	0.0727005i
$718$	441.249	−	441.249i	0.614553	−	0.614553i
$719$	−165.133	−	227.286i	−0.229670	−	0.316114i	0.678592	−	0.734515i	$-0.262590\pi$
$719$	−165.133	−	227.286i	−0.229670	−	0.316114i	−0.908262	+	0.418402i	$0.862590\pi$
$720$		0			0
$721$	294.959	+	214.301i	0.409098	+	0.297227i
$722$	80.8072	+	510.197i	0.111921	+	0.706644i
$723$	135.638	+	266.205i	0.187605	+	0.368196i
$724$		−	9.92948i		−	0.0137147i
$725$		0			0
$726$	64.5371			0.0888940
$727$	164.629	−	83.8826i	0.226449	−	0.115382i	−0.337085	−	0.941474i	$-0.609441\pi$
$727$	164.629	−	83.8826i	0.226449	−	0.115382i	0.563535	+	0.826092i	$0.309441\pi$
$728$	−313.818	+	49.7040i	−0.431069	+	0.0682747i
$729$	−635.343	+	874.475i	−0.871527	+	1.19955i
$730$		0			0
$731$	−1016.63	+	738.623i	−1.39073	+	1.01043i
$732$	−444.091	−	444.091i	−0.606682	−	0.606682i
$733$	14.4800	−	91.4234i	0.0197545	−	0.124725i	−0.975840	−	0.218485i	$-0.929889\pi$
$733$	14.4800	−	91.4234i	0.0197545	−	0.124725i	0.995595	+	0.0937599i	$0.0298886\pi$
$734$	463.450	−	150.584i	0.631404	−	0.205155i
$735$		0			0
$736$	0.935524	−	2.87925i	0.00127109	−	0.00391202i
$737$	479.769	−	941.600i	0.650975	−	1.27761i
$738$	349.860	+	178.263i	0.474065	+	0.241548i
$739$	−146.136	−	47.4824i	−0.197748	−	0.0642523i	0.208468	−	0.978029i	$-0.433152\pi$
$739$	−146.136	−	47.4824i	−0.197748	−	0.0642523i	−0.406217	+	0.913777i	$0.633152\pi$
$740$		0			0
$741$	−839.015	−	2582.22i	−1.13227	−	3.48478i
$742$	−617.420	−	97.7897i	−0.832102	−	0.131792i
$743$	−379.385	+	379.385i	−0.510613	+	0.510613i	−0.914714	−	0.404101i	$-0.867584\pi$
$743$	−379.385	+	379.385i	−0.510613	+	0.510613i	0.404101	+	0.914714i	$0.367584\pi$
$744$	50.7065	+	69.7916i	0.0681539	+	0.0938058i
$745$		0			0
$746$	−406.887	−	295.621i	−0.545425	−	0.396275i
$747$	−112.828	−	712.368i	−0.151041	−	0.953638i
$748$	206.429	+	405.139i	0.275974	+	0.541630i
$749$		−	66.1849i		−	0.0883644i
$750$		0			0
$751$	1091.70			1.45366			0.726829	−	0.686819i	$-0.240993\pi$
$751$	1091.70			1.45366			0.726829	+	0.686819i	$0.240993\pi$
$752$	−98.3939	+	50.1342i	−0.130843	+	0.0666678i
$753$	211.924	−	33.5654i	0.281439	−	0.0445756i
$754$	−115.084	+	158.400i	−0.152631	+	0.210079i
$755$		0			0
$756$	−100.740	+	73.1922i	−0.133255	+	0.0968151i
$757$	167.215	+	167.215i	0.220892	+	0.220892i	0.808874	−	0.587982i	$-0.200077\pi$
$757$	167.215	+	167.215i	0.220892	+	0.220892i	−0.587982	+	0.808874i	$0.700077\pi$
$758$	58.6450	−	370.270i	0.0773681	−	0.488483i
$759$	−26.5065	+	8.61250i	−0.0349230	+	0.0113472i
$760$		0			0
$761$	274.175	−	843.824i	0.360283	−	1.10884i	−0.592600	−	0.805497i	$-0.701899\pi$
$761$	274.175	−	843.824i	0.360283	−	1.10884i	0.952883	−	0.303339i	$-0.0981015\pi$
$762$	−179.287	+	351.871i	−0.235285	+	0.461774i
$763$	−23.2761	−	11.8598i	−0.0305060	−	0.0155436i
$764$	−354.306	−	115.121i	−0.463751	−	0.150682i
$765$		0			0
$766$	−168.263	−	517.860i	−0.219664	−	0.676057i
$767$	477.031	+	75.5543i	0.621944	+	0.0985062i
$768$	51.4716	−	51.4716i	0.0670203	−	0.0670203i
$769$	−259.529	−	357.212i	−0.337489	−	0.464514i	0.606217	−	0.795300i	$-0.292686\pi$
$769$	−259.529	−	357.212i	−0.337489	−	0.464514i	−0.943706	+	0.330785i	$0.892686\pi$
$770$		0			0
$771$	443.156	+	321.971i	0.574780	+	0.417602i
$772$	−66.3395	−	418.851i	−0.0859320	−	0.542553i
$773$	343.883	+	674.908i	0.444868	+	0.873102i	0.999168	+	0.0407854i	$0.0129860\pi$
$773$	343.883	+	674.908i	0.444868	+	0.873102i	−0.554300	+	0.832317i	$0.687014\pi$
$774$		−	1046.69i		−	1.35231i
$775$		0			0
$776$	−384.618			−0.495642
$777$	−121.073	+	61.6898i	−0.155821	+	0.0793948i
$778$	−892.174	+	141.307i	−1.14675	+	0.181628i
$779$	375.974	−	517.483i	0.482636	−	0.664292i
$780$		0			0
$781$	145.700	−	105.857i	0.186555	−	0.135540i
$782$	−10.6293	−	10.6293i	−0.0135924	−	0.0135924i
$783$	−12.0037	+	75.7886i	−0.0153304	+	0.0967926i
$784$	−88.5176	+	28.7611i	−0.112905	+	0.0366851i
$785$		0			0
$786$	−144.874	+	445.875i	−0.184318	+	0.567271i
$787$	−503.295	+	987.772i	−0.639511	+	1.25511i	0.312753	+	0.949834i	$0.398749\pi$
$787$	−503.295	+	987.772i	−0.639511	+	1.25511i	−0.952264	+	0.305276i	$0.901251\pi$
$788$	−537.325	−	273.781i	−0.681884	−	0.347437i
$789$	1500.09	+	487.409i	1.90126	+	0.617756i
$790$		0			0
$791$	165.685	+	509.926i	0.209463	+	0.644660i
$792$	−374.074	−	59.2475i	−0.472316	−	0.0748075i
$793$	1080.83	−	1080.83i	1.36297	−	1.36297i
$794$	−16.5974	−	22.8443i	−0.0209035	−	0.0287712i
$795$		0			0
$796$	−222.689	−	161.793i	−0.279760	−	0.203257i
$797$	46.2648	+	292.105i	0.0580487	+	0.366505i	0.999564	+	0.0295343i	$0.00940244\pi$
$797$	46.2648	+	292.105i	0.0580487	+	0.366505i	−0.941515	+	0.336971i	$0.890598\pi$
$798$	399.306	+	783.682i	0.500383	+	0.982057i
$799$			548.320i			0.686257i
$800$		0			0
$801$	−931.972			−1.16351
$802$	−688.468	+	350.792i	−0.858439	+	0.437396i
$803$	767.004	−	121.482i	0.955173	−	0.151285i
$804$	−493.753	+	679.593i	−0.614121	+	0.845265i
$805$		0			0
$806$	−169.859	+	123.410i	−0.210743	+	0.153114i
$807$	−627.491	−	627.491i	−0.777560	−	0.777560i
$808$	26.6434	−	168.220i	0.0329745	−	0.208193i
$809$	173.388	−	56.3370i	0.214323	−	0.0696378i	−0.199887	−	0.979819i	$-0.564058\pi$
$809$	173.388	−	56.3370i	0.214323	−	0.0696378i	0.414211	+	0.910181i	$0.364058\pi$
$810$		0			0
$811$	368.062	−	1132.78i	0.453837	−	1.39677i	−0.418659	−	0.908144i	$-0.637500\pi$
$811$	368.062	−	1132.78i	0.453837	−	1.39677i	0.872495	−	0.488622i	$-0.162500\pi$
$812$	28.7948	−	56.5130i	0.0354616	−	0.0695973i
$813$	−1481.32	−	754.771i	−1.82204	−	0.928377i
$814$	−90.6519	−	29.4546i	−0.111366	−	0.0361850i
$815$		0			0
$816$	−111.689	−	343.744i	−0.136874	−	0.421255i
$817$	−1684.08	−	266.733i	−2.06130	−	0.326478i
$818$	416.623	−	416.623i	0.509319	−	0.509319i
$819$	−772.393	−	1063.11i	−0.943093	−	1.29806i
$820$		0			0
$821$	388.310	+	282.124i	0.472972	+	0.343634i	0.798598	−	0.601864i	$-0.205575\pi$
$821$	388.310	+	282.124i	0.472972	+	0.343634i	−0.325626	+	0.945499i	$0.605575\pi$
$822$	−159.163	−	1004.92i	−0.193629	−	1.22253i
$823$	79.7683	+	156.554i	0.0969238	+	0.190224i	0.934377	−	0.356285i	$-0.115957\pi$
$823$	79.7683	+	156.554i	0.0969238	+	0.190224i	−0.837454	+	0.546508i	$0.815957\pi$
$824$		−	203.289i		−	0.246710i
$825$		0			0
$826$	−156.458			−0.189416
$827$	143.662	−	73.1995i	0.173715	−	0.0885121i	−0.364971	−	0.931019i	$-0.618921\pi$
$827$	143.662	−	73.1995i	0.173715	−	0.0885121i	0.538686	+	0.842507i	$0.318921\pi$
$828$	12.3667	−	1.95869i	0.0149356	−	0.00236557i
$829$	−920.375	+	1266.79i	−1.11022	+	1.52809i	−0.289136	+	0.957288i	$0.593368\pi$
$829$	−920.375	+	1266.79i	−1.11022	+	1.52809i	−0.821087	+	0.570803i	$0.806632\pi$
$830$		0			0
$831$	−373.420	+	271.306i	−0.449363	+	0.326481i
$832$	125.272	+	125.272i	0.150567	+	0.150567i
$833$	−72.2940	+	456.446i	−0.0867875	+	0.547955i
$834$	−721.698	+	234.494i	−0.865346	+	0.281168i
$835$		0			0
$836$	−190.654	+	586.772i	−0.228055	+	0.701880i
$837$	−37.3565	+	73.3162i	−0.0446314	+	0.0875940i
$838$	526.917	+	268.478i	0.628779	+	0.320379i
$839$	1047.63	+	340.396i	1.24867	+	0.405717i	0.857443	−	0.514579i	$-0.172052\pi$
$839$	1047.63	+	340.396i	1.24867	+	0.405717i	0.391224	+	0.920295i	$0.372052\pi$
$840$		0			0
$841$	247.805	+	762.667i	0.294656	+	0.906857i
$842$	−414.407	−	65.6356i	−0.492170	−	0.0779520i
$843$	−1288.36	+	1288.36i	−1.52830	+	1.52830i
$844$	−132.911	−	182.936i	−0.157477	−	0.216749i
$845$		0			0
$846$	−369.493	−	268.452i	−0.436753	−	0.317319i
$847$	−7.95974	−	50.2558i	−0.00939757	−	0.0593339i
$848$	158.240	+	310.564i	0.186604	+	0.366231i
$849$		−	1134.77i		−	1.33660i
$850$		0			0
$851$	3.15113			0.00370285
$852$	−127.552	+	64.9911i	−0.149709	+	0.0762806i
$853$	438.442	−	69.4424i	0.514000	−	0.0814096i	0.105954	−	0.994371i	$-0.466210\pi$
$853$	438.442	−	69.4424i	0.514000	−	0.0814096i	0.408046	+	0.912961i	$0.366210\pi$
$854$	−291.047	+	400.592i	−0.340804	+	0.469077i
$855$		0			0
$856$	−29.8557	+	21.6914i	−0.0348781	+	0.0253404i
$857$	155.970	+	155.970i	0.181996	+	0.181996i	0.792225	−	0.610229i	$-0.208923\pi$
$857$	155.970	+	155.970i	0.181996	+	0.181996i	−0.610229	+	0.792225i	$0.708923\pi$
$858$	255.138	−	1610.88i	0.297364	−	1.87748i
$859$	−391.117	+	127.082i	−0.455316	+	0.147941i	−0.527691	−	0.849436i	$-0.676942\pi$
$859$	−391.117	+	127.082i	−0.455316	+	0.147941i	0.0723749	+	0.997377i	$0.476942\pi$
$860$		0			0
$861$	169.267	−	520.950i	0.196593	−	0.605053i
$862$	−253.263	+	497.057i	−0.293809	+	0.576633i
$863$	−275.247	−	140.246i	−0.318943	−	0.162509i	0.287189	−	0.957874i	$-0.407279\pi$
$863$	−275.247	−	140.246i	−0.318943	−	0.162509i	−0.606131	+	0.795365i	$0.707279\pi$
$864$	66.0333	+	21.4555i	0.0764274	+	0.0248328i
$865$		0			0
$866$	49.7038	+	152.973i	0.0573947	+	0.176643i
$867$	−473.924	−	75.0621i	−0.546625	−	0.0865769i
$868$	48.0936	−	48.0936i	0.0554074	−	0.0554074i
$869$	822.990	+	1132.75i	0.947054	+	1.30351i
$870$		0			0
$871$	−1654.00	−	1201.70i	−1.89897	−	1.37968i
$872$	2.27862	+	14.3866i	0.00261309	+	0.0164984i
$873$	−722.168	−	1417.33i	−0.827225	−	1.62352i
$874$		−	20.3966i		−	0.0233371i
$875$		0			0
$876$	−617.282			−0.704660
$877$	−315.106	+	160.555i	−0.359300	+	0.183073i	−0.624317	−	0.781171i	$-0.714623\pi$
$877$	−315.106	+	160.555i	−0.359300	+	0.183073i	0.265016	+	0.964244i	$0.414623\pi$
$878$	795.699	−	126.026i	0.906263	−	0.143538i
$879$	1338.71	−	1842.57i	1.52299	−	2.09622i
$880$		0			0
$881$	1399.81	−	1017.02i	1.58889	−	1.15440i	0.683387	−	0.730056i	$-0.260506\pi$
$881$	1399.81	−	1017.02i	1.58889	−	1.15440i	0.905503	−	0.424340i	$-0.139494\pi$
$882$	−272.188	−	272.188i	−0.308604	−	0.308604i
$883$	−199.959	+	1262.49i	−0.226454	+	1.42978i	0.568288	+	0.822830i	$0.307606\pi$
$883$	−199.959	+	1262.49i	−0.226454	+	1.42978i	−0.794742	+	0.606947i	$0.792394\pi$
$884$	836.607	−	271.830i	0.946388	−	0.307500i
$885$		0			0
$886$	−171.727	+	528.520i	−0.193822	+	0.596524i
$887$	−760.633	+	1492.83i	−0.857534	+	1.68301i	−0.135909	+	0.990721i	$0.543395\pi$
$887$	−760.633	+	1492.83i	−0.857534	+	1.68301i	−0.721625	+	0.692284i	$0.756605\pi$
$888$	67.5083	+	34.3972i	0.0760229	+	0.0387356i
$889$	296.119	+	96.2150i	0.333092	+	0.108228i
$890$		0			0
$891$	174.886	+	538.244i	0.196281	+	0.604090i
$892$	473.500	+	74.9951i	0.530830	+	0.0840752i
$893$	−526.088	+	526.088i	−0.589124	+	0.589124i
$894$	482.357	+	663.907i	0.539549	+	0.742626i
$895$		0			0
$896$	−46.4299	−	33.7333i	−0.0518191	−	0.0376487i
$897$	8.43473	+	53.2548i	0.00940327	+	0.0593699i
$898$	−470.845	−	924.085i	−0.524326	−	1.02905i
$899$		−	41.9122i		−	0.0466209i
$900$		0			0
$901$	1730.68			1.92085
$902$	342.354	−	174.438i	0.379549	−	0.193390i
$903$	−1442.16	+	228.416i	−1.59708	+	0.252953i
$904$	175.723	−	241.862i	0.194384	−	0.267547i
$905$		0			0
$906$	467.455	−	339.626i	0.515955	−	0.374863i
$907$	324.628	+	324.628i	0.357914	+	0.357914i	0.863044	−	0.505129i	$-0.168555\pi$
$907$	324.628	+	324.628i	0.357914	+	0.357914i	−0.505129	+	0.863044i	$0.668555\pi$
$908$	−38.5827	+	243.601i	−0.0424919	+	0.268283i
$909$	669.922	−	217.671i	0.736988	−	0.239462i
$910$		0			0
$911$	184.738	−	568.566i	0.202786	−	0.624112i	−0.797011	−	0.603965i	$-0.793587\pi$
$911$	184.738	−	568.566i	0.202786	−	0.624112i	0.999797	−	0.0201467i	$-0.00641332\pi$
$912$	222.646	−	436.968i	0.244130	−	0.479132i
$913$	−628.848	−	320.414i	−0.688771	−	0.350946i
$914$	1212.18	+	393.860i	1.32623	+	0.430919i
$915$		0			0
$916$	−158.626	−	488.200i	−0.173172	−	0.532970i
$917$	365.077	+	57.8225i	0.398121	+	0.0630561i
$918$	243.774	−	243.774i	0.265549	−	0.265549i
$919$	432.747	+	595.625i	0.470889	+	0.648123i	0.976722	−	0.214508i	$-0.0688149\pi$
$919$	432.747	+	595.625i	0.470889	+	0.648123i	−0.505833	+	0.862631i	$0.668815\pi$
$920$		0			0
$921$	1223.61	+	889.004i	1.32857	+	0.965260i
$922$	143.020	+	902.993i	0.155119	+	0.979385i
$923$	−158.176	−	310.437i	−0.171371	−	0.336335i
$924$			528.341i			0.571797i
$925$		0			0
$926$	476.342			0.514408
$927$	749.130	−	381.701i	0.808122	−	0.411759i
$928$	−34.9299	+	5.53236i	−0.0376400	+	0.00596159i
$929$	469.300	−	645.936i	0.505167	−	0.695303i	−0.477928	−	0.878399i	$-0.658612\pi$
$929$	469.300	−	645.936i	0.505167	−	0.695303i	0.983095	+	0.183096i	$0.0586120\pi$
$930$		0			0
$931$	−507.303	+	368.577i	−0.544901	+	0.395894i
$932$	−14.7114	−	14.7114i	−0.0157847	−	0.0157847i
$933$	−169.244	+	1068.56i	−0.181398	+	1.14530i
$934$	758.411	−	246.423i	0.812003	−	0.263836i
$935$		0			0
$936$	−226.419	+	696.845i	−0.241900	+	0.744493i
$937$	641.022	−	1258.08i	0.684122	−	1.34266i	−0.243776	−	0.969831i	$-0.578386\pi$
$937$	641.022	−	1258.08i	0.684122	−	1.34266i	0.927898	−	0.372833i	$-0.121614\pi$
$938$	590.105	+	300.674i	0.629110	+	0.320548i
$939$	−163.335	−	53.0706i	−0.173945	−	0.0565182i
$940$		0			0
$941$	−135.437	−	416.831i	−0.143928	−	0.442966i	0.852943	−	0.522004i	$-0.174815\pi$
$941$	−135.437	−	416.831i	−0.143928	−	0.442966i	−0.996872	+	0.0790378i	$0.974815\pi$
$942$	527.049	+	83.4764i	0.559500	+	0.0886161i
$943$	−8.98204	+	8.98204i	−0.00952496	+	0.00952496i
$944$	51.2775	+	70.5774i	0.0543194	+	0.0747642i
$945$		0			0
$946$	−828.622	−	602.029i	−0.875922	−	0.636395i
$947$	−149.155	−	941.730i	−0.157503	−	0.994435i	−0.932158	−	0.362051i	$-0.882077\pi$
$947$	−149.155	−	941.730i	−0.157503	−	0.994435i	0.774655	−	0.632384i	$-0.217923\pi$
$948$	−505.276	−	991.661i	−0.532992	−	1.04606i
$949$		−	1502.35i		−	1.58308i
$950$		0			0
$951$	−881.886			−0.927325
$952$	−253.903	+	129.370i	−0.266705	+	0.135893i
$953$	47.5024	−	7.52363i	0.0498451	−	0.00789468i	−0.131462	−	0.991321i	$-0.541967\pi$
$953$	47.5024	−	7.52363i	0.0498451	−	0.00789468i	0.181307	+	0.983427i	$0.441967\pi$
$954$	−847.326	+	1166.24i	−0.888182	+	1.22248i
$955$		0			0
$956$	−118.508	+	86.1014i	−0.123963	+	0.0900642i
$957$	230.217	+	230.217i	0.240561	+	0.240561i
$958$	−179.926	+	1136.01i	−0.187814	+	1.18581i
$959$	−762.911	+	247.885i	−0.795528	+	0.258483i
$960$		0			0
$961$	−283.077	+	871.221i	−0.294565	+	0.906577i
$962$	−83.7162	+	164.302i	−0.0870230	+	0.170792i
$963$	−135.991	−	69.2910i	−0.141216	−	0.0719533i
$964$	−124.914	−	40.5869i	−0.129578	−	0.0421026i
$965$		0			0
$966$	−5.39750	−	16.6118i	−0.00558747	−	0.0171965i
$967$	−993.084	−	157.289i	−1.02697	−	0.162657i	−0.379856	−	0.925046i	$-0.624026\pi$
$967$	−993.084	−	157.289i	−1.02697	−	0.162657i	−0.647119	+	0.762389i	$0.724026\pi$
$968$	−20.0614	+	20.0614i	−0.0207246	+	0.0207246i
$969$	−1431.31	−	1970.03i	−1.47710	−	2.03306i
$970$		0			0
$971$	722.828	+	525.165i	0.744416	+	0.540850i	0.894091	−	0.447885i	$-0.147823\pi$
$971$	722.828	+	525.165i	0.744416	+	0.540850i	−0.149675	+	0.988735i	$0.547823\pi$
$972$	−104.935	−	662.533i	−0.107958	−	0.681618i
$973$	271.615	+	533.074i	0.279152	+	0.547866i
$974$		−	169.600i		−	0.174127i
$975$		0			0
$976$	276.092			0.282882
$977$	−626.489	+	319.212i	−0.641237	+	0.326727i	−0.744198	−	0.667959i	$-0.767168\pi$
$977$	−626.489	+	319.212i	−0.641237	+	0.326727i	0.102961	+	0.994685i	$0.467168\pi$
$978$	−1211.55	+	191.891i	−1.23880	+	0.196207i
$979$	−536.046	+	737.804i	−0.547544	+	0.753630i
$980$		0			0
$981$	−48.7369	+	35.4094i	−0.0496809	+	0.0360953i
$982$	−152.795	−	152.795i	−0.155596	−	0.155596i
$983$	236.985	−	1496.27i	0.241084	−	1.52214i	−0.508981	−	0.860777i	$-0.669978\pi$
$983$	236.985	−	1496.27i	0.241084	−	1.52214i	0.750065	−	0.661364i	$-0.230022\pi$
$984$	−290.473	+	94.3805i	−0.295197	+	0.0959152i
$985$		0			0
$986$	−54.2634	+	167.005i	−0.0550338	+	0.169377i
$987$	−289.249	+	567.683i	−0.293058	+	0.575160i
$988$	1063.50	+	541.878i	1.07641	+	0.548460i
$989$	32.2034	+	10.4635i	0.0325615	+	0.0105799i
$990$		0			0
$991$	349.037	+	1074.23i	0.352207	+	1.08398i	0.957611	+	0.288063i	$0.0930114\pi$
$991$	349.037	+	1074.23i	0.352207	+	1.08398i	−0.605404	+	0.795918i	$0.706989\pi$
$992$	−37.4570	−	5.93260i	−0.0377590	−	0.00598044i
$993$	−821.669	+	821.669i	−0.827461	+	0.827461i
$994$	66.3411	+	91.3107i	0.0667416	+	0.0918619i
$995$		0			0
$996$	453.867	+	329.753i	0.455689	+	0.331078i
$997$	215.165	+	1358.50i	0.215813	+	1.36259i	0.823006	+	0.568033i	$0.192295\pi$
$997$	215.165	+	1358.50i	0.215813	+	1.36259i	−0.607194	+	0.794554i	$0.707705\pi$
$998$	−272.857	−	535.511i	−0.273403	−	0.536584i
$999$			72.2687i			0.0723410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.a.7.1		16
5.2	odd	4		250.3.f.b.243.2		16
5.3	odd	4		50.3.f.a.3.1	✓	16
5.4	even	2		250.3.f.c.7.2		16
20.3	even	4		400.3.bg.a.353.2		16
25.6	even	5		50.3.f.a.17.1	yes	16
25.8	odd	20	inner	250.3.f.a.143.1		16
25.17	odd	20		250.3.f.c.143.2		16
25.19	even	10		250.3.f.b.107.2		16
100.31	odd	10		400.3.bg.a.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.3.1	✓	16	5.3	odd	4
50.3.f.a.17.1	yes	16	25.6	even	5
250.3.f.a.7.1		16	1.1	even	1	trivial
250.3.f.a.143.1		16	25.8	odd	20	inner
250.3.f.b.107.2		16	25.19	even	10
250.3.f.b.243.2		16	5.2	odd	4
250.3.f.c.7.2		16	5.4	even	2
250.3.f.c.143.2		16	25.17	odd	20
400.3.bg.a.17.2		16	100.31	odd	10
400.3.bg.a.353.2		16	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	250.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26007 - 0.642040i) q^{2} +(-4.49348 + 0.711697i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-5.20517 + 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(0.442463 - 2.79360i) q^{8} +(11.1253 - 3.61484i) q^{9} +O(q^{10})\)	\(q+(1.26007 - 0.642040i) q^{2} +(-4.49348 + 0.711697i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-5.20517 + 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(0.442463 - 2.79360i) q^{8} +(11.1253 - 3.61484i) q^{9} +(3.53728 - 10.8866i) q^{11} +(-4.13085 + 8.10725i) q^{12} +(-19.7315 - 10.0537i) q^{13} +(6.82270 + 2.21683i) q^{14} +(-1.23607 - 3.80423i) q^{16} +(-19.6167 - 3.10698i) q^{17} +(11.6979 - 11.6979i) q^{18} +(-15.8404 - 21.8024i) q^{19} +(-18.6705 - 13.5649i) q^{21} +(-2.53241 - 15.9890i) q^{22} +(0.242965 + 0.476846i) q^{23} +12.8679i q^{24} -31.3180 q^{26} +(-10.9361 + 5.57222i) q^{27} +(10.0204 - 1.58707i) q^{28} +(3.67470 - 5.05779i) q^{29} +(5.42369 - 3.94054i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-8.14670 + 51.4362i) q^{33} +(-26.7133 + 8.67968i) q^{34} +(7.22967 - 22.2506i) q^{36} +(2.67310 - 5.24626i) q^{37} +(-33.9580 - 17.3025i) q^{38} +(95.8181 + 31.1332i) q^{39} +(7.33457 + 22.5735i) q^{41} +(-32.2354 - 5.10558i) q^{42} +(44.7386 - 44.7386i) q^{43} +(-13.4566 - 18.5214i) q^{44} +(0.612308 + 0.444868i) q^{46} +(-4.31877 - 27.2676i) q^{47} +(8.26170 + 16.2145i) q^{48} -23.2682i q^{49} +90.3585 q^{51} +(-39.4630 + 20.1074i) q^{52} +(-86.0658 + 13.6315i) q^{53} +(-10.2027 + 14.0428i) q^{54} +(11.6075 - 8.43332i) q^{56} +(86.6950 + 86.6950i) q^{57} +(1.38309 - 8.73248i) q^{58} +(-20.7422 + 6.73954i) q^{59} +(-21.3293 + 65.6449i) q^{61} +(4.30427 - 8.44760i) q^{62} +(52.8715 + 26.9394i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(22.7587 + 70.0439i) q^{66} +(91.1840 + 14.4421i) q^{67} +(-28.0880 + 28.0880i) q^{68} +(-1.43113 - 1.96978i) q^{69} +(12.7283 + 9.24768i) q^{71} +(-5.17587 - 32.6792i) q^{72} +(30.7991 + 60.4466i) q^{73} -8.32691i q^{74} -53.8984 q^{76} +(51.7371 - 26.3614i) q^{77} +(140.727 - 22.2889i) q^{78} +(-71.8966 + 98.9571i) q^{79} +(-39.9985 + 29.0606i) q^{81} +(23.7352 + 23.7352i) q^{82} +(9.64518 - 60.8973i) q^{83} +(-43.8969 + 14.2630i) q^{84} +(27.6500 - 85.0979i) q^{86} +(-12.9126 + 25.3423i) q^{87} +(-28.8478 - 14.6987i) q^{88} +(-75.7710 - 24.6195i) q^{89} +(-34.7133 - 106.837i) q^{91} +(1.05718 + 0.167440i) q^{92} +(-21.5668 + 21.5668i) q^{93} +(-22.9488 - 31.5864i) q^{94} +(20.8207 + 15.1271i) q^{96} +(-21.2725 - 134.309i) q^{97} +(-14.9391 - 29.3197i) q^{98} -133.904i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9} + 32 q^{11} - 16 q^{12} - 8 q^{13} + 30 q^{14} + 16 q^{16} + 8 q^{17} - 16 q^{18} - 30 q^{19} - 68 q^{21} - 8 q^{22} + 42 q^{23} - 56 q^{26} - 40 q^{27} + 4 q^{28} - 100 q^{29} + 132 q^{31} - 64 q^{32} + 134 q^{33} - 100 q^{34} + 48 q^{36} - 82 q^{37} + 20 q^{38} + 320 q^{39} - 88 q^{41} - 128 q^{42} - 78 q^{43} - 40 q^{44} - 26 q^{46} + 168 q^{47} + 32 q^{48} - 168 q^{51} - 16 q^{52} - 518 q^{53} - 80 q^{54} + 48 q^{56} + 280 q^{57} + 80 q^{58} + 350 q^{59} + 372 q^{61} - 158 q^{62} + 142 q^{63} - 202 q^{66} + 158 q^{67} - 196 q^{68} + 30 q^{69} + 122 q^{71} + 68 q^{72} + 352 q^{73} + 40 q^{76} + 96 q^{77} + 158 q^{78} - 760 q^{79} - 144 q^{81} + 352 q^{82} + 32 q^{83} + 20 q^{84} + 264 q^{86} - 440 q^{87} - 244 q^{88} - 550 q^{89} - 798 q^{91} - 436 q^{92} + 54 q^{93} - 190 q^{94} - 16 q^{96} + 618 q^{97} + 336 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9 + 32 * q^11 - 16 * q^12 - 8 * q^13 + 30 * q^14 + 16 * q^16 + 8 * q^17 - 16 * q^18 - 30 * q^19 - 68 * q^21 - 8 * q^22 + 42 * q^23 - 56 * q^26 - 40 * q^27 + 4 * q^28 - 100 * q^29 + 132 * q^31 - 64 * q^32 + 134 * q^33 - 100 * q^34 + 48 * q^36 - 82 * q^37 + 20 * q^38 + 320 * q^39 - 88 * q^41 - 128 * q^42 - 78 * q^43 - 40 * q^44 - 26 * q^46 + 168 * q^47 + 32 * q^48 - 168 * q^51 - 16 * q^52 - 518 * q^53 - 80 * q^54 + 48 * q^56 + 280 * q^57 + 80 * q^58 + 350 * q^59 + 372 * q^61 - 158 * q^62 + 142 * q^63 - 202 * q^66 + 158 * q^67 - 196 * q^68 + 30 * q^69 + 122 * q^71 + 68 * q^72 + 352 * q^73 + 40 * q^76 + 96 * q^77 + 158 * q^78 - 760 * q^79 - 144 * q^81 + 352 * q^82 + 32 * q^83 + 20 * q^84 + 264 * q^86 - 440 * q^87 - 244 * q^88 - 550 * q^89 - 798 * q^91 - 436 * q^92 + 54 * q^93 - 190 * q^94 - 16 * q^96 + 618 * q^97 + 336 * q^98

Introduction

L-functions

Modular forms

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