LMFDB - Embedded newform 363.3.h.l.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.1
Root			$1.56693 - 0.738055i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.l.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.40079 + 0.780063i) q^{2} +(1.38791 + 2.65965i) q^{3} +(1.91922 - 1.39439i) q^{4} +(-0.753510 - 0.244830i) q^{5} +(-5.40676 - 5.30259i) q^{6} +(5.45647 - 3.96435i) q^{7} +(2.41516 - 3.32418i) q^{8} +(-5.14743 + 7.38268i) q^{9} +O(q^{10})$	\(q+(-2.40079 + 0.780063i) q^{2} +(1.38791 + 2.65965i) q^{3} +(1.91922 - 1.39439i) q^{4} +(-0.753510 - 0.244830i) q^{5} +(-5.40676 - 5.30259i) q^{6} +(5.45647 - 3.96435i) q^{7} +(2.41516 - 3.32418i) q^{8} +(-5.14743 + 7.38268i) q^{9} +2.00000 q^{10} +(6.37228 + 3.16915i) q^{12} +(-2.93230 - 9.02469i) q^{13} +(-10.0074 + 13.7740i) q^{14} +(-0.394640 - 2.34387i) q^{15} +(-6.13751 + 18.8893i) q^{16} +(-27.8635 - 9.05339i) q^{17} +(6.59893 - 21.7396i) q^{18} +(-21.2235 - 15.4198i) q^{19} +(-1.78754 + 0.580806i) q^{20} +(18.1168 + 9.01011i) q^{21} -26.9205i q^{23} +(12.1932 + 1.80981i) q^{24} +(-19.7176 - 14.3257i) q^{25} +(14.0797 + 19.3790i) q^{26} +(-26.7795 - 3.44386i) q^{27} +(4.94427 - 15.2169i) q^{28} +(15.2490 + 20.9884i) q^{29} +(2.77581 + 5.31929i) q^{30} +(-0.884223 - 2.72136i) q^{31} -33.7013i q^{32} +73.9565 q^{34} +(-5.08209 + 1.65127i) q^{35} +(0.415322 + 21.3465i) q^{36} +(1.93681 - 1.40718i) q^{37} +(62.9815 + 20.4639i) q^{38} +(19.9327 - 20.3243i) q^{39} +(-2.63370 + 1.91350i) q^{40} +(-10.3541 + 14.2512i) q^{41} +(-50.5232 - 7.49908i) q^{42} -12.5109 q^{43} +(5.68614 - 4.30268i) q^{45} +(20.9997 + 64.6305i) q^{46} +(24.4983 - 33.7190i) q^{47} +(-58.7572 + 9.89301i) q^{48} +(-1.08492 + 3.33904i) q^{49} +(58.5127 + 19.0119i) q^{50} +(-14.5931 - 86.6722i) q^{51} +(-18.2117 - 13.2316i) q^{52} +(85.2019 - 27.6838i) q^{53} +(66.9783 - 12.6217i) q^{54} -27.7128i q^{56} +(11.5549 - 77.8482i) q^{57} +(-52.9818 - 38.4935i) q^{58} +(8.67483 + 11.9399i) q^{59} +(-4.02567 - 3.94811i) q^{60} +(19.6058 - 60.3404i) q^{61} +(4.24567 + 5.84366i) q^{62} +(1.18079 + 60.6896i) q^{63} +(1.73906 + 5.35228i) q^{64} +7.51811i q^{65} -63.3288 q^{67} +(-66.1000 + 21.4772i) q^{68} +(71.5991 - 37.3632i) q^{69} +(10.9129 - 7.92871i) q^{70} +(4.32858 + 1.40644i) q^{71} +(12.1095 + 34.9413i) q^{72} +(-43.4979 + 31.6030i) q^{73} +(-3.55219 + 4.88917i) q^{74} +(10.7350 - 72.3245i) q^{75} -62.2337 q^{76} +(-32.0000 + 64.3432i) q^{78} +(-17.2059 - 52.9542i) q^{79} +(9.24935 - 12.7306i) q^{80} +(-28.0079 - 76.0037i) q^{81} +(13.7412 - 42.2910i) q^{82} +(-62.1400 - 20.1905i) q^{83} +(47.3338 - 7.96963i) q^{84} +(18.7789 + 13.6436i) q^{85} +(30.0360 - 9.75927i) q^{86} +(-34.6576 + 69.6868i) q^{87} +14.1341i q^{89} +(-10.2949 + 14.7654i) q^{90} +(-51.7771 - 37.6183i) q^{91} +(-37.5378 - 51.6663i) q^{92} +(6.01063 - 6.12871i) q^{93} +(-32.5123 + 100.062i) q^{94} +(12.2169 + 16.8151i) q^{95} +(89.6334 - 46.7742i) q^{96} +(46.1317 + 141.979i) q^{97} -8.86263i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9}+O(q^{10}) $ 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9	$ 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9} + 32 q^{10} + 56 q^{12} - 8 q^{13} - 13 q^{15} + 22 q^{16} + 38 q^{18} - 36 q^{19} + 152 q^{21} + 24 q^{24} - 86 q^{25} + 20 q^{27} - 64 q^{28} + 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} - 56 q^{39} - 36 q^{40} + 68 q^{42} - 384 q^{43} + 68 q^{45} - 88 q^{46} - 110 q^{48} + 60 q^{49} + 214 q^{51} - 136 q^{52} + 704 q^{54} + 144 q^{57} - 216 q^{58} - 56 q^{60} - 24 q^{61} + 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} + 72 q^{72} - 284 q^{73} + 124 q^{75} - 720 q^{76} - 512 q^{78} - 76 q^{79} - 113 q^{81} - 40 q^{82} + 80 q^{84} - 68 q^{85} + 1008 q^{87} + 14 q^{90} - 256 q^{91} - 25 q^{93} + 260 q^{94} + 272 q^{96} - 218 q^{97}+O(q^{100}) $ 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9 + 32 * q^10 + 56 * q^12 - 8 * q^13 - 13 * q^15 + 22 * q^16 + 38 * q^18 - 36 * q^19 + 152 * q^21 + 24 * q^24 - 86 * q^25 + 20 * q^27 - 64 * q^28 + 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 - 56 * q^39 - 36 * q^40 + 68 * q^42 - 384 * q^43 + 68 * q^45 - 88 * q^46 - 110 * q^48 + 60 * q^49 + 214 * q^51 - 136 * q^52 + 704 * q^54 + 144 * q^57 - 216 * q^58 - 56 * q^60 - 24 * q^61 + 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 + 72 * q^72 - 284 * q^73 + 124 * q^75 - 720 * q^76 - 512 * q^78 - 76 * q^79 - 113 * q^81 - 40 * q^82 + 80 * q^84 - 68 * q^85 + 1008 * q^87 + 14 * q^90 - 256 * q^91 - 25 * q^93 + 260 * q^94 + 272 * q^96 - 218 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−2.40079	+	0.780063i	−1.20039	+	0.390032i	−0.839906	−	0.542732i	$-0.817390\pi$
$2$	−2.40079	+	0.780063i	−1.20039	+	0.390032i	−0.360488	+	0.932764i	$0.617390\pi$
$3$	1.38791	+	2.65965i	0.462636	+	0.886549i
$3$	1.38791	+	2.65965i	0.462636	+	0.886549i
$4$	1.91922	−	1.39439i	0.479804	−	0.348598i
$5$	−0.753510	−	0.244830i	−0.150702	−	0.0489660i	0.232695	−	0.972550i	$-0.425246\pi$
$5$	−0.753510	−	0.244830i	−0.150702	−	0.0489660i	−0.383397	+	0.923584i	$0.625246\pi$
$6$	−5.40676	−	5.30259i	−0.901127	−	0.883765i
$7$	5.45647	−	3.96435i	0.779495	−	0.566336i	−0.125332	−	0.992115i	$-0.540000\pi$
$7$	5.45647	−	3.96435i	0.779495	−	0.566336i	0.904827	+	0.425778i	$0.140000\pi$
$8$	2.41516	−	3.32418i	0.301895	−	0.415522i
$9$	−5.14743	+	7.38268i	−0.571937	+	0.820298i
$10$	2.00000			0.200000
$11$		0			0
$11$		0			0
$12$	6.37228	+	3.16915i	0.531023	+	0.264096i
$13$	−2.93230	−	9.02469i	−0.225562	−	0.694207i	−0.998234	−	0.0594024i	$-0.981080\pi$
$13$	−2.93230	−	9.02469i	−0.225562	−	0.694207i	0.772673	−	0.634805i	$-0.218920\pi$
$14$	−10.0074	+	13.7740i	−0.714812	+	0.983854i
$15$	−0.394640	−	2.34387i	−0.0263093	−	0.156258i
$16$	−6.13751	+	18.8893i	−0.383595	+	1.18058i
$17$	−27.8635	−	9.05339i	−1.63903	−	0.532552i	−0.662707	−	0.748879i	$-0.730592\pi$
$17$	−27.8635	−	9.05339i	−1.63903	−	0.532552i	−0.976321	+	0.216327i	$0.930592\pi$
$18$	6.59893	−	21.7396i	0.366607	−	1.20775i
$19$	−21.2235	−	15.4198i	−1.11703	−	0.811567i	−0.133271	−	0.991080i	$-0.542548\pi$
$19$	−21.2235	−	15.4198i	−1.11703	−	0.811567i	−0.983756	+	0.179513i	$0.942548\pi$
$20$	−1.78754	+	0.580806i	−0.0893769	+	0.0290403i
$21$	18.1168	+	9.01011i	0.862707	+	0.429053i
$22$		0			0
$23$		−	26.9205i		−	1.17046i	−0.810868	−	0.585229i	$-0.801005\pi$
$23$		−	26.9205i		−	1.17046i	0.810868	−	0.585229i	$-0.198995\pi$
$24$	12.1932	+	1.80981i	0.508048	+	0.0754088i
$25$	−19.7176	−	14.3257i	−0.788704	−	0.573027i
$26$	14.0797	+	19.3790i	0.541526	+	0.745346i
$27$	−26.7795	−	3.44386i	−0.991832	−	0.127551i
$28$	4.94427	−	15.2169i	0.176581	−	0.543461i
$29$	15.2490	+	20.9884i	0.525826	+	0.723738i	0.986487	−	0.163838i	$-0.0523875\pi$
$29$	15.2490	+	20.9884i	0.525826	+	0.723738i	−0.460661	+	0.887576i	$0.652388\pi$
$30$	2.77581	+	5.31929i	0.0925271	+	0.177310i
$31$	−0.884223	−	2.72136i	−0.0285233	−	0.0877858i	0.935781	−	0.352581i	$-0.114696\pi$
$31$	−0.884223	−	2.72136i	−0.0285233	−	0.0877858i	−0.964305	+	0.264795i	$0.914696\pi$
$32$		−	33.7013i		−	1.05316i
$33$		0			0
$34$	73.9565			2.17519
$35$	−5.08209	+	1.65127i	−0.145203	+	0.0471792i
$36$	0.415322	+	21.3465i	0.0115367	+	0.592958i
$37$	1.93681	−	1.40718i	0.0523463	−	0.0380318i	−0.561304	−	0.827609i	$-0.689700\pi$
$37$	1.93681	−	1.40718i	0.0523463	−	0.0380318i	0.613651	+	0.789578i	$0.289700\pi$
$38$	62.9815	+	20.4639i	1.65741	+	0.538525i
$39$	19.9327	−	20.3243i	0.511096	−	0.521136i
$40$	−2.63370	+	1.91350i	−0.0658426	+	0.0478375i
$41$	−10.3541	+	14.2512i	−0.252539	+	0.347590i	−0.916399	−	0.400267i	$-0.868917\pi$
$41$	−10.3541	+	14.2512i	−0.252539	+	0.347590i	0.663859	+	0.747857i	$0.268917\pi$
$42$	−50.5232	−	7.49908i	−1.20293	−	0.178550i
$43$	−12.5109			−0.290951			−0.145475	−	0.989362i	$-0.546471\pi$
$43$	−12.5109			−0.290951			−0.145475	+	0.989362i	$0.546471\pi$
$44$		0			0
$45$	5.68614	−	4.30268i	0.126359	−	0.0956150i
$46$	20.9997	+	64.6305i	0.456516	+	1.40501i
$47$	24.4983	−	33.7190i	0.521241	−	0.717426i	−0.464523	−	0.885561i	$-0.653774\pi$
$47$	24.4983	−	33.7190i	0.521241	−	0.717426i	0.985764	+	0.168135i	$0.0537743\pi$
$48$	−58.7572	+	9.89301i	−1.22411	+	0.206104i
$49$	−1.08492	+	3.33904i	−0.0221412	+	0.0681437i
$50$	58.5127	+	19.0119i	1.17025	+	0.380238i
$51$	−14.5931	−	86.6722i	−0.286139	−	1.69946i
$52$	−18.2117	−	13.2316i	−0.350225	−	0.254453i
$53$	85.2019	−	27.6838i	1.60758	−	0.522335i	0.638616	−	0.769526i	$-0.279507\pi$
$53$	85.2019	−	27.6838i	1.60758	−	0.522335i	0.968967	+	0.247191i	$0.0795075\pi$
$54$	66.9783	−	12.6217i	1.24034	−	0.233735i
$55$		0			0
$56$		−	27.7128i		−	0.494872i
$57$	11.5549	−	77.8482i	0.202717	−	1.36576i
$58$	−52.9818	−	38.4935i	−0.913480	−	0.663682i
$59$	8.67483	+	11.9399i	0.147031	+	0.202371i	0.876180	−	0.481984i	$-0.160084\pi$
$59$	8.67483	+	11.9399i	0.147031	+	0.202371i	−0.729149	+	0.684355i	$0.760084\pi$
$60$	−4.02567	−	3.94811i	−0.0670945	−	0.0658018i
$61$	19.6058	−	60.3404i	0.321406	−	0.989186i	−0.651631	−	0.758536i	$-0.725915\pi$
$61$	19.6058	−	60.3404i	0.321406	−	0.989186i	0.973037	−	0.230650i	$-0.0740853\pi$
$62$	4.24567	+	5.84366i	0.0684785	+	0.0942525i
$63$	1.18079	+	60.6896i	0.0187427	+	0.963327i
$64$	1.73906	+	5.35228i	0.0271728	+	0.0836294i
$65$			7.51811i			0.115663i
$66$		0			0
$67$	−63.3288			−0.945206			−0.472603	−	0.881276i	$-0.656685\pi$
$67$	−63.3288			−0.945206			−0.472603	+	0.881276i	$0.656685\pi$
$68$	−66.1000	+	21.4772i	−0.972059	+	0.315841i
$69$	71.5991	−	37.3632i	1.03767	−	0.541495i
$70$	10.9129	−	7.92871i	0.155899	−	0.113267i
$71$	4.32858	+	1.40644i	0.0609660	+	0.0198090i	0.339341	−	0.940663i	$-0.389796\pi$
$71$	4.32858	+	1.40644i	0.0609660	+	0.0198090i	−0.278375	+	0.960472i	$0.589796\pi$
$72$	12.1095	+	34.9413i	0.168188	+	0.485296i
$73$	−43.4979	+	31.6030i	−0.595861	+	0.432918i	−0.844407	−	0.535702i	$-0.820047\pi$
$73$	−43.4979	+	31.6030i	−0.595861	+	0.432918i	0.248546	+	0.968620i	$0.420047\pi$
$74$	−3.55219	+	4.88917i	−0.0480025	+	0.0660698i
$75$	10.7350	−	72.3245i	0.143134	−	0.964327i
$76$	−62.2337			−0.818864
$77$		0			0
$78$	−32.0000	+	64.3432i	−0.410256	+	0.824912i
$79$	−17.2059	−	52.9542i	−0.217796	−	0.670306i	−0.998943	−	0.0459597i	$-0.985365\pi$
$79$	−17.2059	−	52.9542i	−0.217796	−	0.670306i	0.781148	−	0.624346i	$-0.214635\pi$
$80$	9.24935	−	12.7306i	0.115617	−	0.159133i
$81$	−28.0079	−	76.0037i	−0.345777	−	0.938317i
$82$	13.7412	−	42.2910i	0.167575	−	0.515744i
$83$	−62.1400	−	20.1905i	−0.748674	−	0.243259i	−0.0902636	−	0.995918i	$-0.528771\pi$
$83$	−62.1400	−	20.1905i	−0.748674	−	0.243259i	−0.658411	+	0.752659i	$0.728771\pi$
$84$	47.3338	−	7.96963i	0.563497	−	0.0948766i
$85$	18.7789	+	13.6436i	0.220928	+	0.160513i
$86$	30.0360	−	9.75927i	0.349255	−	0.113480i
$87$	−34.6576	+	69.6868i	−0.398363	+	0.800998i
$88$		0			0
$89$			14.1341i			0.158810i	0.996842	+	0.0794052i	$0.0253021\pi$
$89$			14.1341i			0.158810i	−0.996842	+	0.0794052i	$0.974698\pi$
$90$	−10.2949	+	14.7654i	−0.114387	+	0.164060i
$91$	−51.7771	−	37.6183i	−0.568979	−	0.413387i
$92$	−37.5378	−	51.6663i	−0.408019	−	0.561590i
$93$	6.01063	−	6.12871i	0.0646305	−	0.0659001i
$94$	−32.5123	+	100.062i	−0.345875	+	1.06449i
$95$	12.2169	+	16.8151i	0.128599	+	0.177001i
$96$	89.6334	−	46.7742i	0.933681	−	0.487231i
$97$	46.1317	+	141.979i	0.475584	+	1.46370i	0.845168	+	0.534501i	$0.179500\pi$
$97$	46.1317	+	141.979i	0.475584	+	1.46370i	−0.369584	+	0.929198i	$0.620500\pi$
$98$		−	8.86263i		−	0.0904350i
$99$		0			0
$100$	−57.8179			−0.578179
$101$	19.0302	−	6.18329i	0.188418	−	0.0612207i	−0.213288	−	0.976989i	$-0.568417\pi$
$101$	19.0302	−	6.18329i	0.188418	−	0.0612207i	0.401706	+	0.915769i	$0.368417\pi$
$102$	102.645	+	196.698i	1.00632	+	1.92841i
$103$	145.966	−	106.050i	1.41715	−	1.02962i	0.424911	−	0.905235i	$-0.360305\pi$
$103$	145.966	−	106.050i	1.41715	−	1.02962i	0.992234	−	0.124381i	$-0.0396946\pi$
$104$	−37.0817	−	12.0486i	−0.356555	−	0.115852i
$105$	−11.4453	−	11.2248i	−0.109003	−	0.106902i
$106$	−182.957	+	132.926i	−1.72600	+	1.25402i
$107$	37.9288	−	52.2045i	0.354475	−	0.487893i	−0.594124	−	0.804373i	$-0.702501\pi$
$107$	37.9288	−	52.2045i	0.354475	−	0.487893i	0.948599	+	0.316481i	$0.102501\pi$
$108$	−56.1977	+	30.7316i	−0.520349	+	0.284551i
$109$	−110.277			−1.01172			−0.505859	−	0.862616i	$-0.668824\pi$
$109$	−110.277			−1.01172			−0.505859	+	0.862616i	$0.668824\pi$
$110$		0			0
$111$	6.43070	+	3.19820i	0.0579343	+	0.0288126i
$112$	41.3948	+	127.400i	0.369597	+	1.13750i
$113$	−73.6139	+	101.321i	−0.651450	+	0.896645i	−0.999161	−	0.0409573i	$-0.986959\pi$
$113$	−73.6139	+	101.321i	−0.651450	+	0.896645i	0.347710	+	0.937602i	$0.386959\pi$
$114$	32.9857	+	195.911i	0.289348	+	1.71851i
$115$	−6.59096	+	20.2849i	−0.0573127	+	0.176390i
$116$	58.5321	+	19.0182i	0.504587	+	0.163950i
$117$	81.7202	+	24.8057i	0.698464	+	0.212015i
$118$	−30.1403	−	21.8982i	−0.255426	−	0.185578i
$119$	−187.927	+	61.0612i	−1.57922	+	0.513119i
$120$	−8.74456	−	4.34896i	−0.0728714	−	0.0362414i
$121$		0			0
$122$			160.158i			1.31277i
$123$	−52.2737	−	7.75891i	−0.424989	−	0.0630806i
$124$	−5.49166	−	3.98992i	−0.0442876	−	0.0321768i
$125$	22.9924	+	31.6463i	0.183939	+	0.253171i
$126$	−50.1765	−	144.782i	−0.398227	−	1.14906i
$127$	−59.5932	+	183.409i	−0.469238	+	1.44417i	0.384335	+	0.923194i	$0.374431\pi$
$127$	−59.5932	+	183.409i	−0.469238	+	1.44417i	−0.853573	+	0.520973i	$0.825569\pi$
$128$	70.8862	+	97.5664i	0.553798	+	0.762238i
$129$	−17.3639	−	33.2745i	−0.134604	−	0.257942i
$130$	−5.86460	−	18.0494i	−0.0451123	−	0.138841i
$131$			106.098i			0.809905i	0.914338	+	0.404952i	$0.132712\pi$
$131$			106.098i			0.809905i	−0.914338	+	0.404952i	$0.867288\pi$
$132$		0			0
$133$	−176.935			−1.33034
$134$	152.039	−	49.4005i	1.13462	−	0.368660i
$135$	19.3354	+	9.15141i	0.143225	+	0.0677882i
$136$	−97.3898	+	70.7578i	−0.716101	+	0.520278i
$137$	−185.738	−	60.3500i	−1.35575	−	0.440511i	−0.461129	−	0.887333i	$-0.652556\pi$
$137$	−185.738	−	60.3500i	−1.35575	−	0.440511i	−0.894623	+	0.446822i	$0.852556\pi$
$138$	−142.749	+	145.553i	−1.03441	+	1.05473i
$139$	5.61033	−	4.07614i	0.0403621	−	0.0293248i	−0.567421	−	0.823428i	$-0.692059\pi$
$139$	5.61033	−	4.07614i	0.0403621	−	0.0293248i	0.607783	+	0.794103i	$0.292059\pi$
$140$	−7.45111	+	10.2556i	−0.0532222	+	0.0732541i
$141$	123.682	+	18.3580i	0.877178	+	0.130198i
$142$	−11.4891			−0.0809093
$143$		0			0
$144$	−107.861	−	142.543i	−0.749038	−	0.989880i
$145$	−6.35165	−	19.5484i	−0.0438045	−	0.134816i
$146$	79.7768	−	109.803i	0.546416	−	0.752077i
$147$	−10.3864	+	1.74877i	−0.0706560	+	0.0118964i
$148$	1.75500	−	5.40135i	0.0118581	−	0.0364956i
$149$	−64.3841	−	20.9197i	−0.432108	−	0.140400i	0.0848835	−	0.996391i	$-0.472948\pi$
$149$	−64.3841	−	20.9197i	−0.432108	−	0.140400i	−0.516992	+	0.855990i	$0.672948\pi$
$150$	30.6452	+	182.010i	0.204301	+	1.21340i
$151$	22.8415	+	16.5953i	0.151268	+	0.109903i	0.660845	−	0.750522i	$-0.270198\pi$
$151$	22.8415	+	16.5953i	0.151268	+	0.109903i	−0.509577	+	0.860425i	$0.670198\pi$
$152$	−102.516	+	33.3095i	−0.674449	+	0.219142i
$153$	210.264	−	159.105i	1.37427	−	1.03990i
$154$		0			0
$155$			2.26706i			0.0146262i
$156$	9.91515	−	66.8008i	0.0635586	−	0.428210i
$157$	54.8482	+	39.8496i	0.349352	+	0.253819i	0.748597	−	0.663025i	$-0.230728\pi$
$157$	54.8482	+	39.8496i	0.349352	+	0.253819i	−0.399245	+	0.916844i	$0.630728\pi$
$158$	82.6152	+	113.710i	0.522881	+	0.719684i
$159$	191.881	+	188.184i	1.20680	+	1.18355i
$160$	−8.25108	+	25.3942i	−0.0515693	+	0.158714i
$161$	−106.723	−	146.891i	−0.662873	−	0.912366i
$162$	126.529	+	160.621i	0.781042	+	0.991486i
$163$	−20.9728	−	64.5477i	−0.128668	−	0.395998i	0.865884	−	0.500245i	$-0.166757\pi$
$163$	−20.9728	−	64.5477i	−0.128668	−	0.395998i	−0.994551	+	0.104247i	$0.966757\pi$
$164$			41.7888i			0.254810i
$165$		0			0
$166$	164.935			0.993583
$167$	53.4828	−	17.3776i	0.320256	−	0.104058i	−0.144477	−	0.989508i	$-0.546150\pi$
$167$	53.4828	−	17.3776i	0.320256	−	0.104058i	0.464734	+	0.885451i	$0.346150\pi$
$168$	73.7063	−	38.4628i	0.438728	−	0.228945i
$169$	63.8772	−	46.4095i	0.377971	−	0.274612i
$170$	−55.7269	−	18.1068i	−0.327806	−	0.106510i
$171$	223.086	−	77.3141i	1.30459	−	0.452129i
$172$	−24.0111	+	17.4451i	−0.139599	+	0.101425i
$173$	131.979	−	181.653i	0.762883	−	1.05002i	−0.234085	−	0.972216i	$-0.575209\pi$
$173$	131.979	−	181.653i	0.762883	−	1.05002i	0.996969	−	0.0778030i	$-0.0247905\pi$
$174$	28.8454	−	194.338i	0.165778	−	1.11689i
$175$	−164.380			−0.939316
$176$		0			0
$177$	−19.7160	+	39.6434i	−0.111390	+	0.223974i
$178$	−11.0255	−	33.9330i	−0.0619411	−	0.190635i
$179$	−82.5608	+	113.635i	−0.461234	+	0.634833i	−0.974764	−	0.223238i	$-0.928337\pi$
$179$	−82.5608	+	113.635i	−0.461234	+	0.634833i	0.513530	+	0.858071i	$0.328337\pi$
$180$	4.91332	−	16.1865i	0.0272962	−	0.0899248i
$181$	40.4384	−	124.457i	0.223417	−	0.687605i	−0.775032	−	0.631922i	$-0.782266\pi$
$181$	40.4384	−	124.457i	0.223417	−	0.687605i	0.998448	−	0.0556834i	$-0.0177337\pi$
$182$	153.650	+	49.9240i	0.844233	+	0.274308i
$183$	187.695	−	31.6024i	1.02566	−	0.172691i
$184$	−89.4887	−	65.0173i	−0.486351	−	0.353355i
$185$	−1.80393	+	0.586131i	−0.00975095	+	0.00316828i
$186$	−9.64947	+	19.4024i	−0.0518789	+	0.104314i
$187$		0			0
$188$		−	98.8744i		−	0.525928i
$189$	−159.774	+	87.3720i	−0.845365	+	0.462286i
$190$	−42.4470	−	30.8395i	−0.223405	−	0.162313i
$191$	−206.548	−	284.289i	−1.08140	−	1.48842i	−0.857966	−	0.513707i	$-0.828272\pi$
$191$	−206.548	−	284.289i	−1.08140	−	1.48842i	−0.223438	−	0.974718i	$-0.571728\pi$
$192$	−11.8215	+	12.0537i	−0.0615704	+	0.0627799i
$193$	75.8653	−	233.489i	0.393085	−	1.20979i	−0.537359	−	0.843354i	$-0.680578\pi$
$193$	75.8653	−	233.489i	0.393085	−	1.20979i	0.930443	−	0.366436i	$-0.119422\pi$
$194$	−221.505	−	304.875i	−1.14178	−	1.57152i
$195$	−19.9955	+	10.4344i	−0.102541	+	0.0535099i
$196$	2.57374	+	7.92114i	0.0131313	+	0.0404140i
$197$			6.15315i			0.0312343i	0.999878	+	0.0156171i	$0.00497129\pi$
$197$			6.15315i			0.0312343i	−0.999878	+	0.0156171i	$0.995029\pi$
$198$		0			0
$199$	193.272			0.971214			0.485607	−	0.874177i	$-0.338599\pi$
$199$	193.272			0.971214			0.485607	+	0.874177i	$0.338599\pi$
$200$	−95.2422	+	30.9461i	−0.476211	+	0.154730i
$201$	−87.8944	−	168.432i	−0.437286	−	0.837971i
$202$	−40.8642	+	29.6895i	−0.202298	+	0.146978i
$203$	166.411	+	54.0702i	0.819758	+	0.266356i
$204$	−148.862	−	145.994i	−0.729717	−	0.715658i
$205$	11.2910	−	8.20343i	0.0550783	−	0.0400167i
$206$	−267.707	+	368.467i	−1.29955	+	1.78868i
$207$	198.746	+	138.572i	0.960124	+	0.669428i
$208$	188.467			0.906093
$209$		0			0
$210$	36.2337	+	18.0202i	0.172541	+	0.0858106i
$211$	32.9993	+	101.561i	0.156395	+	0.481334i	0.998300	−	0.0582923i	$-0.0185655\pi$
$211$	32.9993	+	101.561i	0.156395	+	0.481334i	−0.841905	+	0.539626i	$0.818566\pi$
$212$	124.919	−	171.936i	0.589239	−	0.811018i
$213$	2.26703	+	13.4645i	0.0106433	+	0.0632137i
$214$	−50.3362	+	154.919i	−0.235216	+	0.723920i
$215$	9.42707	+	3.06304i	0.0438468	+	0.0142467i
$216$	−76.1247	+	80.7023i	−0.352429	+	0.373622i
$217$	−15.6132	−	11.3436i	−0.0719501	−	0.0522748i
$218$	264.752	−	86.0232i	1.21446	−	0.394602i
$219$	−144.424	−	71.8268i	−0.659470	−	0.327976i
$220$		0			0
$221$			278.007i			1.25795i
$222$	−17.9336	−	2.66185i	−0.0807818	−	0.0119903i
$223$	−62.0766	−	45.1013i	−0.278370	−	0.202248i	0.439836	−	0.898078i	$-0.355037\pi$
$223$	−62.0766	−	45.1013i	−0.278370	−	0.202248i	−0.718206	+	0.695830i	$0.755037\pi$
$224$	−133.604	−	183.890i	−0.596445	−	0.820936i
$225$	207.257	−	71.8283i	0.921141	−	0.319237i
$226$	97.6947	−	300.673i	0.432277	−	1.33041i
$227$	−28.3567	−	39.0297i	−0.124920	−	0.171937i	0.741977	−	0.670426i	$-0.233889\pi$
$227$	−28.3567	−	39.0297i	−0.124920	−	0.171937i	−0.866896	+	0.498489i	$0.833889\pi$
$228$	−86.3746	−	165.520i	−0.378836	−	0.725963i
$229$	−4.76374	−	14.6613i	−0.0208023	−	0.0640230i	0.940116	−	0.340853i	$-0.110716\pi$
$229$	−4.76374	−	14.6613i	−0.0208023	−	0.0640230i	−0.960919	+	0.276830i	$0.910716\pi$
$230$		−	53.8411i		−	0.234092i
$231$		0			0
$232$	106.598			0.459474
$233$	−164.728	+	53.5233i	−0.706986	+	0.229714i	−0.640372	−	0.768065i	$-0.721220\pi$
$233$	−164.728	+	53.5233i	−0.706986	+	0.229714i	−0.0666145	+	0.997779i	$0.521220\pi$
$234$	−215.543	+	4.19366i	−0.921124	+	0.0179216i
$235$	−26.7152	+	19.4097i	−0.113682	+	0.0825945i
$236$	33.2977	+	10.8191i	0.141092	+	0.0458436i
$237$	116.959	−	119.257i	0.493499	−	0.503194i
$238$	403.541	−	293.190i	1.69555	−	1.23189i
$239$	−174.218	+	239.790i	−0.728945	+	1.00331i	0.270234	+	0.962795i	$0.412899\pi$
$239$	−174.218	+	239.790i	−0.728945	+	1.00331i	−0.999179	+	0.0405120i	$0.987101\pi$
$240$	46.6962	+	6.93105i	0.194568	+	0.0288794i
$241$	−46.7011			−0.193780			−0.0968902	−	0.995295i	$-0.530890\pi$
$241$	−46.7011			−0.193780			−0.0968902	+	0.995295i	$0.530890\pi$
$242$		0			0
$243$	163.270	−	179.977i	0.671894	−	0.740647i
$244$	−46.5104	−	143.144i	−0.190616	−	0.586657i
$245$	1.63500	−	2.25038i	0.00667345	−	0.00918522i
$246$	131.551	−	22.1493i	0.534758	−	0.0900378i
$247$	−76.9251	+	236.751i	−0.311438	+	0.958506i
$248$	−11.1818	−	3.63320i	−0.0450880	−	0.0146500i
$249$	−32.5449	−	193.293i	−0.130702	−	0.776276i
$250$	−79.8860	−	58.0406i	−0.319544	−	0.232162i
$251$	−197.618	+	64.2100i	−0.787323	+	0.255817i	−0.674964	−	0.737851i	$-0.735841\pi$
$251$	−197.618	+	64.2100i	−0.787323	+	0.255817i	−0.112359	+	0.993668i	$0.535841\pi$
$252$	86.8913	+	114.830i	0.344807	+	0.455674i
$253$		0			0
$254$		−	486.813i		−	1.91659i
$255$	−10.2239	+	68.8812i	−0.0400939	+	0.270122i
$256$	−264.502	−	192.172i	−1.03321	−	0.750673i
$257$	117.403	+	161.592i	0.456821	+	0.628761i	0.973846	−	0.227210i	$-0.0729604\pi$
$257$	117.403	+	161.592i	0.456821	+	0.628761i	−0.517024	+	0.855971i	$0.672960\pi$
$258$	67.6433	+	66.3400i	0.262183	+	0.257132i
$259$	4.98960	−	15.3564i	0.0192649	−	0.0592912i
$260$	10.4832	+	14.4289i	0.0403200	+	0.0554957i
$261$	−233.444	+	4.54193i	−0.894420	+	0.0174020i
$262$	−82.7628	−	254.718i	−0.315888	−	0.972205i
$263$		−	99.7592i		−	0.379313i	−0.981851	−	0.189656i	$-0.939263\pi$
$263$		−	99.7592i		−	0.379313i	0.981851	−	0.189656i	$-0.0607374\pi$
$264$		0			0
$265$	−70.9783			−0.267842
$266$	424.783	−	138.020i	1.59693	−	0.518873i
$267$	−37.5918	+	19.6169i	−0.140793	+	0.0734714i
$268$	−121.542	+	88.3051i	−0.453513	+	0.329497i
$269$	−47.9113	−	15.5673i	−0.178109	−	0.0578711i	0.218605	−	0.975813i	$-0.429849\pi$
$269$	−47.9113	−	15.5673i	−0.178109	−	0.0578711i	−0.396714	+	0.917942i	$0.629849\pi$
$270$	−53.5589	−	6.88773i	−0.198366	−	0.0255101i
$271$	−100.626	+	73.1090i	−0.371313	+	0.269775i	−0.757755	−	0.652539i	$-0.773704\pi$
$271$	−100.626	+	73.1090i	−0.371313	+	0.269775i	0.386442	+	0.922314i	$0.373704\pi$
$272$	342.025	−	470.757i	1.25744	−	1.73072i
$273$	28.1895	−	189.919i	0.103258	−	0.695675i
$274$	492.994			1.79925
$275$		0			0
$276$	85.3151	−	171.545i	0.309113	−	0.621540i
$277$	−90.7653	−	279.347i	−0.327673	−	1.00847i	−0.970220	−	0.242227i	$-0.922122\pi$
$277$	−90.7653	−	279.347i	−0.327673	−	1.00847i	0.642547	−	0.766246i	$-0.277878\pi$
$278$	−10.2896	+	14.1624i	−0.0370128	+	0.0509438i
$279$	24.6424	+	7.48007i	0.0883240	+	0.0268103i
$280$	−6.78493	+	20.8819i	−0.0242319	+	0.0745781i
$281$	−250.771	−	81.4805i	−0.892424	−	0.289966i	−0.173318	−	0.984866i	$-0.555449\pi$
$281$	−250.771	−	81.4805i	−0.892424	−	0.289966i	−0.719107	+	0.694900i	$0.755449\pi$
$282$	−311.255	+	52.4063i	−1.10374	+	0.185838i
$283$	322.626	+	234.402i	1.14002	+	0.828275i	0.987122	−	0.159967i	$-0.0511388\pi$
$283$	322.626	+	234.402i	1.14002	+	0.828275i	0.152900	+	0.988242i	$0.451139\pi$
$284$	10.2686	−	3.33648i	0.0361571	−	0.0117482i
$285$	−27.7663	+	55.8304i	−0.0974257	+	0.195896i
$286$		0			0
$287$			118.809i			0.413967i
$288$	248.806	+	173.475i	0.863908	+	0.602343i
$289$	460.603	+	334.648i	1.59378	+	1.15795i
$290$	30.4979	+	41.9768i	0.105165	+	0.144748i
$291$	−313.587	+	319.747i	−1.07762	+	1.09879i
$292$	−39.4148	+	121.306i	−0.134982	+	0.415432i
$293$	205.042	+	282.216i	0.699803	+	0.963196i	0.999957	+	0.00930526i	$0.00296200\pi$
$293$	205.042	+	282.216i	0.699803	+	0.963196i	−0.300154	+	0.953891i	$0.597038\pi$
$294$	23.5715	−	12.3005i	0.0801750	−	0.0418385i
$295$	−3.61333	−	11.1207i	−0.0122486	−	0.0376972i
$296$		−	9.83686i		−	0.0332326i
$297$		0			0
$298$	170.891			0.573461
$299$	−242.950	+	78.9391i	−0.812540	+	0.264010i
$300$	−80.2459	−	153.775i	−0.267486	−	0.512584i
$301$	−68.2652	+	49.5975i	−0.226795	+	0.164776i
$302$	−67.7831	−	22.0241i	−0.224447	−	0.0729274i
$303$	42.8575	+	42.0318i	0.141444	+	0.138719i
$304$	421.529	−	306.258i	1.38661	−	1.00743i
$305$	−29.5463	+	40.6670i	−0.0968731	+	0.133334i
$306$	−380.686	+	545.997i	−1.24407	+	1.78430i
$307$	398.527			1.29813			0.649067	−	0.760731i	$-0.275160\pi$
$307$	398.527			1.29813			0.649067	+	0.760731i	$0.275160\pi$
$308$		0			0
$309$	484.644	+	241.030i	1.56843	+	0.780031i
$310$	−1.76845	−	5.44272i	−0.00570467	−	0.0175572i
$311$	−258.829	+	356.247i	−0.832247	+	1.14549i	0.155254	+	0.987875i	$0.450380\pi$
$311$	−258.829	+	356.247i	−0.832247	+	1.14549i	−0.987501	+	0.157615i	$0.949620\pi$
$312$	−19.4210	−	115.346i	−0.0622468	−	0.369700i
$313$	163.748	−	503.964i	0.523156	−	1.61011i	−0.244777	−	0.969579i	$-0.578715\pi$
$313$	163.748	−	503.964i	0.523156	−	1.61011i	0.767933	−	0.640530i	$-0.221285\pi$
$314$	−162.764	−	52.8853i	−0.518357	−	0.168425i
$315$	13.9689	−	46.0193i	0.0443457	−	0.146093i
$316$	−106.861	−	77.6388i	−0.338167	−	0.245692i
$317$	−350.394	+	113.850i	−1.10534	+	0.359148i	−0.804157	−	0.594417i	$-0.797383\pi$
$317$	−350.394	+	113.850i	−1.10534	+	0.359148i	−0.301187	+	0.953565i	$0.597383\pi$
$318$	−607.462	−	302.111i	−1.91026	−	0.950035i
$319$		0			0
$320$		−	4.45877i		−	0.0139337i
$321$	191.487	+	28.4222i	0.596533	+	0.0885425i
$322$	370.802	+	269.404i	1.15156	+	0.836657i
$323$	451.759	+	621.793i	1.39864	+	1.92506i
$324$	−159.732	−	106.813i	−0.493001	−	0.329671i
$325$	−71.4669	+	219.952i	−0.219898	+	0.676777i
$326$	100.703	+	138.605i	0.308904	+	0.425170i
$327$	−153.054	−	293.298i	−0.468056	−	0.896936i
$328$	22.3668	+	68.8378i	0.0681914	+	0.209871i
$329$		−	281.107i		−	0.854428i
$330$		0			0
$331$	−115.649			−0.349394			−0.174697	−	0.984622i	$-0.555895\pi$
$331$	−115.649			−0.349394			−0.174697	+	0.984622i	$0.555895\pi$
$332$	−147.413	+	47.8975i	−0.444017	+	0.144270i
$333$	0.419130	+	21.5422i	0.00125865	+	0.0646913i
$334$	−114.845	+	83.4399i	−0.343848	+	0.249820i
$335$	47.7189	+	15.5048i	0.142444	+	0.0462830i
$336$	−281.387	+	286.915i	−0.837462	+	0.853914i
$337$	−43.0977	+	31.3123i	−0.127886	+	0.0929148i	−0.649890	−	0.760029i	$-0.725185\pi$
$337$	−43.0977	+	31.3123i	−0.127886	+	0.0929148i	0.522003	+	0.852943i	$0.325185\pi$
$338$	−117.153	+	161.248i	−0.346607	+	0.477064i
$339$	−371.647	−	55.1630i	−1.09630	−	0.162723i
$340$	55.0652			0.161957
$341$		0			0
$342$	−475.272	+	359.636i	−1.38968	+	1.05157i
$343$	109.442	+	336.829i	0.319074	+	0.982009i
$344$	−30.2157	+	41.5884i	−0.0878364	+	0.120896i
$345$	−63.0982	+	10.6239i	−0.182893	+	0.0307939i
$346$	−175.152	+	539.063i	−0.506220	+	1.55799i
$347$	10.6597	+	3.46354i	0.0307195	+	0.00998137i	0.324336	−	0.945942i	$-0.394859\pi$
$347$	10.6597	+	3.46354i	0.0307195	+	0.00998137i	−0.293617	+	0.955923i	$0.594859\pi$
$348$	30.6554	+	182.070i	0.0880901	+	0.523190i
$349$	−173.143	−	125.796i	−0.496111	−	0.360446i	0.311419	−	0.950273i	$-0.399196\pi$
$349$	−173.143	−	125.796i	−0.496111	−	0.360446i	−0.807530	+	0.589827i	$0.799196\pi$
$350$	394.642	−	128.227i	1.12755	−	0.366363i
$351$	47.4456	+	251.775i	0.135173	+	0.717308i
$352$		0			0
$353$		−	531.528i		−	1.50574i	−0.658167	−	0.752872i	$-0.728668\pi$
$353$		−	531.528i		−	1.50574i	0.658167	−	0.752872i	$-0.271332\pi$
$354$	16.4095	−	110.555i	0.0463546	−	0.312303i
$355$	−2.91729	−	2.11954i	−0.00821772	−	0.00597052i
$356$	19.7085	+	27.1264i	0.0553610	+	0.0761979i
$357$	−423.226	−	415.072i	−1.18551	−	1.16267i
$358$	109.568	−	337.217i	0.306057	−	0.941946i
$359$	102.977	+	141.735i	0.286843	+	0.394806i	0.927986	−	0.372616i	$-0.121539\pi$
$359$	102.977	+	141.735i	0.286843	+	0.394806i	−0.641142	+	0.767422i	$0.721539\pi$
$360$	−0.569939	−	29.2934i	−0.00158316	−	0.0813705i
$361$	101.112	+	311.192i	0.280090	+	0.862027i
$362$			330.338i			0.912537i
$363$		0			0
$364$	−151.826			−0.417104
$365$	40.5134	−	13.1636i	0.110996	−	0.0360647i
$366$	−425.964	+	222.285i	−1.16384	+	0.607335i
$367$	−112.482	+	81.7230i	−0.306490	+	0.222678i	−0.730389	−	0.683031i	$-0.760661\pi$
$367$	−112.482	+	81.7230i	−0.306490	+	0.222678i	0.423899	+	0.905710i	$0.360661\pi$
$368$	508.510	+	165.225i	1.38182	+	0.448981i
$369$	−51.9151	−	149.798i	−0.140691	−	0.405957i
$370$	3.87362	−	2.81435i	0.0104693	−	0.00760636i
$371$	355.153	−	488.826i	0.957285	−	1.31759i
$372$	2.98987	−	20.1435i	0.00803729	−	0.0541492i
$373$	−149.081			−0.399682			−0.199841	−	0.979828i	$-0.564043\pi$
$373$	−149.081			−0.399682			−0.199841	+	0.979828i	$0.564043\pi$
$374$		0			0
$375$	−52.2567	+	105.074i	−0.139351	+	0.280197i
$376$	−52.9208	−	162.874i	−0.140747	−	0.433174i
$377$	144.699	−	199.162i	0.383818	−	0.528280i
$378$	315.428	−	334.395i	0.834465	−	0.884644i
$379$	83.5564	−	257.160i	0.220465	−	0.678522i	−0.778255	−	0.627948i	$-0.783895\pi$
$379$	83.5564	−	257.160i	0.220465	−	0.678522i	0.998720	−	0.0505741i	$-0.0161051\pi$
$380$	46.8937	+	15.2367i	0.123404	+	0.0400965i
$381$	−570.513	+	96.0579i	−1.49741	+	0.252120i
$382$	717.642	+	521.397i	1.87864	+	1.36491i
$383$	600.879	−	195.237i	1.56887	−	0.509758i	0.609714	−	0.792621i	$-0.291284\pi$
$383$	600.879	−	195.237i	1.56887	−	0.509758i	0.959160	+	0.282863i	$0.0912843\pi$
$384$	−161.109	+	323.945i	−0.419554	+	0.843607i
$385$		0			0
$386$			619.738i			1.60554i
$387$	64.3988	−	92.3638i	0.166405	−	0.238666i
$388$	286.511	+	208.162i	0.738430	+	0.536501i
$389$	−270.379	−	372.144i	−0.695061	−	0.956669i	−0.999991	−	0.00429451i	$-0.998633\pi$
$389$	−270.379	−	372.144i	−0.695061	−	0.956669i	0.304930	−	0.952375i	$-0.401367\pi$
$390$	39.8655	−	40.6486i	0.102219	−	0.104227i
$391$	−243.722	+	750.099i	−0.623330	+	1.91841i
$392$	8.47932	+	11.6708i	0.0216309	+	0.0297724i
$393$	−282.182	+	147.253i	−0.718020	+	0.374691i
$394$	−4.79984	−	14.7724i	−0.0121823	−	0.0374934i
$395$			44.1140i			0.111681i
$396$		0			0
$397$	−561.272			−1.41378			−0.706891	−	0.707322i	$-0.749903\pi$
$397$	−561.272			−1.41378			−0.706891	+	0.707322i	$0.749903\pi$
$398$	−464.004	+	150.764i	−1.16584	+	0.378804i
$399$	−245.569	−	470.584i	−0.615461	−	1.17941i
$400$	391.619	−	284.528i	0.979048	−	0.711320i
$401$	−171.043	−	55.5751i	−0.426540	−	0.138591i	0.0878772	−	0.996131i	$-0.471992\pi$
$401$	−171.043	−	55.5751i	−0.426540	−	0.138591i	−0.514417	+	0.857540i	$0.671992\pi$
$402$	342.404	+	335.807i	0.851750	+	0.835340i
$403$	−21.9666	+	15.9597i	−0.0545078	+	0.0396022i
$404$	27.9012	−	38.4027i	0.0690623	−	0.0950561i
$405$	2.49627	+	64.1267i	0.00616364	+	0.158337i
$406$	−441.696			−1.08792
$407$		0			0
$408$	−323.359	−	160.817i	−0.792546	−	0.394159i
$409$	−41.9322	−	129.054i	−0.102524	−	0.315536i	0.886618	−	0.462503i	$-0.153049\pi$
$409$	−41.9322	−	129.054i	−0.102524	−	0.315536i	−0.989141	+	0.146968i	$0.953049\pi$
$410$	−20.7082	+	28.5024i	−0.0505078	+	0.0695181i
$411$	−97.2776	−	577.757i	−0.236685	−	1.40574i
$412$	132.264	−	407.068i	0.321030	−	0.988028i
$413$	94.6678	+	30.7594i	0.229220	+	0.0744781i
$414$	−585.241	−	177.647i	−1.41362	−	0.429098i
$415$	41.8798	+	30.4275i	0.100915	+	0.0733192i
$416$	−304.144	+	98.8222i	−0.731114	+	0.237553i
$417$	18.6277	+	9.26419i	0.0446708	+	0.0222163i
$418$		0			0
$419$		−	50.3361i		−	0.120134i	−0.998194	−	0.0600669i	$-0.980869\pi$
$419$		−	50.3361i		−	0.120134i	0.998194	−	0.0600669i	$-0.0191314\pi$
$420$	−37.6177	−	5.58353i	−0.0895658	−	0.0132941i
$421$	42.6230	+	30.9674i	0.101242	+	0.0735567i	0.637255	−	0.770653i	$-0.280070\pi$
$421$	42.6230	+	30.9674i	0.101242	+	0.0735567i	−0.536012	+	0.844210i	$0.680070\pi$
$422$	−158.449	−	218.086i	−0.375471	−	0.516792i
$423$	122.834	+	354.430i	0.290387	+	0.837895i
$424$	113.750	−	350.087i	0.268279	−	0.825677i
$425$	419.705	+	577.674i	0.987540	+	1.35923i
$426$	−15.9458	−	30.5570i	−0.0374315	−	0.0717301i
$427$	−132.232	−	406.969i	−0.309678	−	0.953090i
$428$		−	153.079i		−	0.357662i
$429$		0			0
$430$	−25.0217			−0.0581901
$431$	472.491	−	153.522i	1.09627	−	0.356199i	0.295603	−	0.955311i	$-0.404480\pi$
$431$	472.491	−	153.522i	1.09627	−	0.356199i	0.800665	+	0.599112i	$0.204480\pi$
$432$	229.412	−	484.709i	0.531045	−	1.12201i
$433$	−417.147	+	303.075i	−0.963388	+	0.699943i	−0.953935	−	0.300013i	$-0.903009\pi$
$433$	−417.147	+	303.075i	−0.963388	+	0.699943i	−0.00945303	+	0.999955i	$0.503009\pi$
$434$	46.3327	+	15.0544i	0.106757	+	0.0346875i
$435$	43.1762	−	44.0245i	0.0992557	−	0.101206i
$436$	−211.646	+	153.770i	−0.485426	+	0.352683i
$437$	−415.108	+	571.348i	−0.949905	+	1.30743i
$438$	402.761	+	59.7812i	0.919545	+	0.136487i
$439$	25.1087			0.0571953			0.0285977	−	0.999591i	$-0.490896\pi$
$439$	25.1087			0.0571953			0.0285977	+	0.999591i	$0.490896\pi$
$440$		0			0
$441$	−19.0665	−	25.1971i	−0.0432347	−	0.0571363i
$442$	−216.863	−	667.435i	−0.490640	−	1.51003i
$443$	511.620	−	704.184i	1.15490	−	1.58958i	0.426397	−	0.904536i	$-0.359783\pi$
$443$	511.620	−	704.184i	1.15490	−	1.58958i	0.728501	−	0.685045i	$-0.240217\pi$
$444$	16.8015	−	2.82888i	0.0378411	−	0.00637135i
$445$	3.46046	−	10.6502i	0.00777632	−	0.0239330i
$446$	184.215	+	59.8550i	0.413037	+	0.134204i
$447$	−33.7202	−	200.273i	−0.0754368	−	0.448039i
$448$	30.7075	+	22.3103i	0.0685434	+	0.0497997i
$449$	547.468	−	177.883i	1.21930	−	0.396176i	0.372476	−	0.928042i	$-0.378509\pi$
$449$	547.468	−	177.883i	1.21930	−	0.396176i	0.846829	+	0.531866i	$0.178509\pi$
$450$	−441.549	+	334.118i	−0.981220	+	0.742484i
$451$		0			0
$452$			297.103i			0.657308i
$453$	−12.4358	+	83.7832i	−0.0274521	+	0.184952i
$454$	98.5241	+	71.5820i	0.217013	+	0.157670i
$455$	29.8045	+	41.0223i	0.0655043	+	0.0901589i
$456$	−230.874	−	226.426i	−0.506304	−	0.496549i
$457$	−7.90846	+	24.3397i	−0.0173052	+	0.0532598i	−0.959336	−	0.282266i	$-0.908914\pi$
$457$	−7.90846	+	24.3397i	−0.0173052	+	0.0532598i	0.942031	+	0.335526i	$0.108914\pi$
$458$	22.8734	+	31.4826i	0.0499420	+	0.0687393i
$459$	714.990	+	338.403i	1.55771	+	0.737261i
$460$	15.6356	+	48.1214i	0.0339904	+	0.104612i
$461$			289.365i			0.627691i	0.949474	+	0.313845i	$0.101617\pi$
$461$			289.365i			0.627691i	−0.949474	+	0.313845i	$0.898383\pi$
$462$		0			0
$463$	−201.052			−0.434237			−0.217118	−	0.976145i	$-0.569666\pi$
$463$	−201.052			−0.434237			−0.217118	+	0.976145i	$0.569666\pi$
$464$	−490.047	+	159.226i	−1.05614	+	0.343160i
$465$	−6.02956	+	3.14646i	−0.0129668	+	0.00676658i
$466$	353.725	−	256.996i	0.759067	−	0.551494i
$467$	104.920	+	34.0906i	0.224668	+	0.0729991i	0.419188	−	0.907899i	$-0.362315\pi$
$467$	104.920	+	34.0906i	0.224668	+	0.0729991i	−0.194520	+	0.980899i	$0.562315\pi$
$468$	191.428	−	66.3425i	0.409034	−	0.141757i
$469$	−345.551	+	251.058i	−0.736783	+	0.535304i
$470$	48.9966	−	67.4381i	0.104248	−	0.143485i
$471$	−29.8615	+	201.184i	−0.0634002	+	0.427143i
$472$	60.6414			0.128477
$473$		0			0
$474$	−187.766	+	377.546i	−0.396131	+	0.796511i
$475$	197.578	+	608.082i	0.415953	+	1.28017i
$476$	−275.529	+	379.233i	−0.578843	+	0.796709i
$477$	−234.190	+	771.518i	−0.490965	+	1.61744i
$478$	231.208	−	711.587i	0.483700	−	1.48867i
$479$	650.078	+	211.223i	1.35716	+	0.440967i	0.895093	−	0.445880i	$-0.147109\pi$
$479$	650.078	+	211.223i	1.35716	+	0.440967i	0.462064	+	0.886847i	$0.347109\pi$
$480$	−78.9914	+	13.2999i	−0.164565	+	0.0277080i
$481$	−18.3786	−	13.3529i	−0.0382092	−	0.0277606i
$482$	112.119	−	36.4298i	0.232613	−	0.0755805i
$483$	242.557	−	487.715i	0.502188	−	1.00976i
$484$		0			0
$485$		−	118.277i		−	0.243870i
$486$	−251.584	+	559.448i	−0.517662	+	1.15113i
$487$	105.254	+	76.4712i	0.216127	+	0.157025i	0.690581	−	0.723255i	$-0.257355\pi$
$487$	105.254	+	76.4712i	0.216127	+	0.157025i	−0.474455	+	0.880280i	$0.657355\pi$
$488$	−153.231	−	210.905i	−0.313998	−	0.432182i
$489$	142.566	−	145.367i	0.291546	−	0.297273i
$490$	−2.16984	+	6.67808i	−0.00442824	+	0.0136287i
$491$	−468.218	−	644.447i	−0.953601	−	1.31252i	−0.949909	−	0.312525i	$-0.898825\pi$
$491$	−468.218	−	644.447i	−0.953601	−	1.31252i	−0.00369120	−	0.999993i	$-0.501175\pi$
$492$	−111.143	+	57.9990i	−0.225901	+	0.117884i
$493$	−234.873	−	722.865i	−0.476416	−	1.46626i
$494$		−	628.395i		−	1.27206i
$495$		0			0
$496$	56.8316			0.114580
$497$	29.1944	−	9.48584i	0.0587413	−	0.0190862i
$498$	228.914	+	438.668i	0.459667	+	0.880859i
$499$	−396.445	+	288.034i	−0.794478	+	0.577222i	−0.909289	−	0.416165i	$-0.863374\pi$
$499$	−396.445	+	288.034i	−0.794478	+	0.577222i	0.114811	+	0.993387i	$0.463374\pi$
$500$	88.2548	+	28.6757i	0.176510	+	0.0573514i
$501$	120.447	+	118.127i	0.240414	+	0.235782i
$502$	424.351	−	308.309i	0.845321	−	0.614162i
$503$	166.509	−	229.179i	0.331031	−	0.455625i	−0.610764	−	0.791813i	$-0.709138\pi$
$503$	166.509	−	229.179i	0.331031	−	0.455625i	0.941795	+	0.336188i	$0.109138\pi$
$504$	204.595	+	142.650i	0.405942	+	0.283035i
$505$	−15.8533			−0.0313927
$506$		0			0
$507$	212.088	+	105.479i	0.418320	+	0.208045i
$508$	141.372	+	435.098i	0.278291	+	0.856492i
$509$	143.214	−	197.117i	0.281363	−	0.387263i	−0.644822	−	0.764333i	$-0.723068\pi$
$509$	143.214	−	197.117i	0.281363	−	0.387263i	0.926185	+	0.377070i	$0.123068\pi$
$510$	−29.1862	−	173.344i	−0.0572278	−	0.339891i
$511$	−112.059	+	344.882i	−0.219293	+	0.674916i
$512$	326.136	+	105.968i	0.636983	+	0.206968i
$513$	515.250	+	486.024i	1.00439	+	0.947416i
$514$	−407.912	−	296.365i	−0.793602	−	0.576586i
$515$	−135.951	+	44.1732i	−0.263983	+	0.0857732i
$516$	−79.7228	−	39.6488i	−0.154502	−	0.0768388i
$517$		0			0
$518$			40.7597i			0.0786867i
$519$	666.308	+	98.8991i	1.28383	+	0.190557i
$520$	24.9915	+	18.1574i	0.0480607	+	0.0349181i
$521$	221.168	+	304.412i	0.424507	+	0.584284i	0.966682	−	0.255982i	$-0.0823988\pi$
$521$	221.168	+	304.412i	0.424507	+	0.584284i	−0.542174	+	0.840266i	$0.682399\pi$
$522$	556.906	−	193.005i	1.06687	−	0.369741i
$523$	−171.765	+	528.637i	−0.328422	+	1.01078i	0.641450	+	0.767165i	$0.278333\pi$
$523$	−171.765	+	528.637i	−0.328422	+	1.01078i	−0.969872	+	0.243614i	$0.921667\pi$
$524$	147.942	+	203.624i	0.282331	+	0.388596i
$525$	−228.145	−	437.194i	−0.434561	−	0.832750i
$526$	77.8185	+	239.501i	0.147944	+	0.455325i
$527$			83.8317i			0.159074i
$528$		0			0
$529$	−195.715			−0.369971
$530$	170.404	−	55.3675i	0.321516	−	0.104467i
$531$	−132.801	+	2.58381i	−0.250097	+	0.00486594i
$532$	−339.576	+	246.716i	−0.638301	+	0.463753i
$533$	158.974	+	51.6538i	0.298263	+	0.0969115i
$534$	74.9475	−	76.4199i	0.140351	−	0.143108i
$535$	−41.3609	+	30.0505i	−0.0773102	+	0.0561691i
$536$	−152.949	+	210.516i	−0.285353	+	0.392754i
$537$	−416.816	−	61.8674i	−0.776194	−	0.115209i
$538$	127.168			0.236373
$539$		0			0
$540$	49.8695	−	9.39764i	0.0923509	−	0.0174030i
$541$	−288.068	−	886.581i	−0.532472	−	1.63878i	−0.749048	−	0.662516i	$-0.769489\pi$
$541$	−288.068	−	886.581i	−0.532472	−	1.63878i	0.216575	−	0.976266i	$-0.430511\pi$
$542$	184.552	−	254.014i	0.340501	−	0.468660i
$543$	387.135	−	65.1823i	0.712956	−	0.120041i
$544$	−305.111	+	939.034i	−0.560865	+	1.72617i
$545$	83.0949	+	26.9992i	0.152468	+	0.0495398i
$546$	80.4722	+	477.946i	0.147385	+	0.875358i
$547$	596.232	+	433.188i	1.09000	+	0.791934i	0.979400	−	0.201931i	$-0.0647215\pi$
$547$	596.232	+	433.188i	1.09000	+	0.791934i	0.110604	+	0.993865i	$0.464722\pi$
$548$	−440.623	+	143.167i	−0.804056	+	0.261254i
$549$	344.554	+	455.341i	0.627604	+	0.829401i
$550$		0			0
$551$		−	680.583i		−	1.23518i
$552$	48.7211	−	328.246i	0.0882629	−	0.594649i
$553$	−303.812	−	220.733i	−0.549389	−	0.399155i
$554$	435.817	+	599.850i	0.786673	+	1.08276i
$555$	−4.06258	−	3.98431i	−0.00731997	−	0.00717893i
$556$	5.08369	−	15.6460i	0.00914334	−	0.0281403i
$557$	−373.631	−	514.259i	−0.670792	−	0.923266i	0.328986	−	0.944335i	$-0.393293\pi$
$557$	−373.631	−	514.259i	−0.670792	−	0.923266i	−0.999778	+	0.0210686i	$0.993293\pi$
$558$	−64.9961	+	1.26458i	−0.116480	+	0.00226627i
$559$	36.6857	+	112.907i	0.0656273	+	0.201980i
$560$		−	106.132i		−	0.189521i
$561$		0			0
$562$	665.609			1.18436
$563$	761.180	−	247.322i	1.35201	−	0.439294i	0.458640	−	0.888622i	$-0.348337\pi$
$563$	761.180	−	247.322i	1.35201	−	0.439294i	0.893367	+	0.449329i	$0.148337\pi$
$564$	262.971	−	137.228i	0.466260	−	0.243313i
$565$	80.2752	−	58.3233i	0.142080	−	0.103227i
$566$	−957.406	−	311.080i	−1.69153	−	0.549611i
$567$	−454.130	−	303.678i	−0.800934	−	0.535587i
$568$	15.1295	−	10.9922i	0.0266364	−	0.0193525i
$569$	30.8852	−	42.5098i	0.0542798	−	0.0747097i	−0.781014	−	0.624513i	$-0.785297\pi$
$569$	30.8852	−	42.5098i	0.0542798	−	0.0747097i	0.835294	+	0.549804i	$0.185297\pi$
$570$	23.1098	−	155.696i	0.0405435	−	0.273152i
$571$	−10.1143			−0.0177133			−0.00885666	−	0.999961i	$-0.502819\pi$
$571$	−10.1143			−0.0177133			−0.00885666	+	0.999961i	$0.502819\pi$
$572$		0			0
$573$	469.439	−	943.912i	0.819265	−	1.64732i
$574$	−92.6782	−	285.234i	−0.161460	−	0.496924i
$575$	−385.655	+	530.808i	−0.670703	+	0.923144i
$576$	−48.4659	−	14.7115i	−0.0841421	−	0.0255409i
$577$	−27.2849	+	83.9744i	−0.0472876	+	0.145536i	−0.971912	−	0.235343i	$-0.924379\pi$
$577$	−27.2849	+	83.9744i	−0.0472876	+	0.145536i	0.924625	+	0.380879i	$0.124379\pi$
$578$	−1366.86	−	444.119i	−2.36480	−	0.768372i
$579$	726.293	−	122.287i	1.25439	−	0.211203i
$580$	−39.4483	−	28.6609i	−0.0680143	−	0.0494153i
$581$	−419.107	+	136.176i	−0.721354	+	0.234382i
$582$	503.432	−	1012.26i	0.865003	−	1.73928i
$583$		0			0
$584$			220.921i			0.378289i
$585$	−55.5038	−	38.6989i	−0.0948783	−	0.0661520i
$586$	−712.410	−	517.596i	−1.21572	−	0.883269i
$587$	−442.139	−	608.552i	−0.753218	−	1.03672i	−0.997748	−	0.0670740i	$-0.978634\pi$
$587$	−442.139	−	608.552i	−0.753218	−	1.03672i	0.244530	−	0.969642i	$-0.421366\pi$
$588$	−17.4953	+	17.8390i	−0.0297540	+	0.0303385i
$589$	−23.1964	+	71.3913i	−0.0393827	+	0.121208i
$590$	17.3497	+	23.8798i	0.0294062	+	0.0404742i
$591$	−16.3652	+	8.54000i	−0.0276907	+	0.0144501i
$592$	14.6934	+	45.2216i	0.0248199	+	0.0763879i
$593$			656.836i			1.10765i	0.832633	+	0.553825i	$0.186832\pi$
$593$			656.836i			1.10765i	−0.832633	+	0.553825i	$0.813168\pi$
$594$		0			0
$595$	156.554			0.263117
$596$	−152.737	+	49.6273i	−0.256271	+	0.0832673i
$597$	268.243	+	514.034i	0.449318	+	0.861029i
$598$	521.693	−	379.032i	0.872396	−	0.633833i
$599$	−384.153	−	124.819i	−0.641323	−	0.208379i	−0.0297389	−	0.999558i	$-0.509468\pi$
$599$	−384.153	−	124.819i	−0.641323	−	0.208379i	−0.611585	+	0.791179i	$0.709468\pi$
$600$	−214.493	−	210.360i	−0.357488	−	0.350600i
$601$	−668.864	+	485.958i	−1.11292	+	0.808582i	−0.983121	−	0.182959i	$-0.941433\pi$
$601$	−668.864	+	485.958i	−1.11292	+	0.808582i	−0.129797	+	0.991541i	$0.541433\pi$
$602$	125.201	−	172.324i	0.207975	−	0.286253i
$603$	325.980	−	467.536i	0.540598	−	0.775350i
$604$	66.9783			0.110891
$605$		0			0
$606$	−135.679	−	67.4778i	−0.223893	−	0.111350i
$607$	357.360	+	1099.84i	0.588731	+	1.81193i	0.583741	+	0.811940i	$0.301588\pi$
$607$	357.360	+	1099.84i	0.588731	+	1.81193i	0.00498960	+	0.999988i	$0.498412\pi$
$608$	−519.666	+	715.259i	−0.854713	+	1.17641i
$609$	87.1553	+	517.638i	0.143112	+	0.849981i
$610$	39.2116	−	120.681i	0.0642812	−	0.197837i
$611$	−376.140	−	122.215i	−0.615615	−	0.200025i
$612$	181.686	−	598.547i	0.296872	−	0.978019i
$613$	−726.699	−	527.978i	−1.18548	−	0.861302i	−0.192701	−	0.981258i	$-0.561725\pi$
$613$	−726.699	−	527.978i	−1.18548	−	0.861302i	−0.992779	+	0.119956i	$0.961725\pi$
$614$	−956.779	+	310.876i	−1.55827	+	0.506313i
$615$	37.4891	+	18.6446i	0.0609579	+	0.0303164i
$616$		0			0
$617$			713.002i			1.15560i	0.816180	+	0.577798i	$0.196088\pi$
$617$			713.002i			1.15560i	−0.816180	+	0.577798i	$0.803912\pi$
$618$	−1351.55	−	200.608i	−2.18697	−	0.324608i
$619$	32.6926	+	23.7525i	0.0528151	+	0.0383724i	0.613880	−	0.789400i	$-0.289608\pi$
$619$	32.6926	+	23.7525i	0.0528151	+	0.0383724i	−0.561064	+	0.827772i	$0.689608\pi$
$620$	3.16116	+	4.35097i	0.00509865	+	0.00701769i
$621$	−92.7107	+	720.917i	−0.149293	+	1.16090i
$622$	343.497	−	1057.18i	0.552247	−	1.69964i
$623$	56.0327	+	77.1224i	0.0899401	+	0.123792i
$624$	261.575	+	501.256i	0.419191	+	0.803296i
$625$	178.709	+	550.010i	0.285935	+	0.880017i
$626$			1337.64i			2.13681i
$627$		0			0
$628$	160.832			0.256101
$629$	−66.7060	+	21.6741i	−0.106051	+	0.0344580i
$630$	2.36158	+	121.379i	0.00374854	+	0.192665i
$631$	605.551	−	439.959i	0.959669	−	0.697240i	0.00659509	−	0.999978i	$-0.497901\pi$
$631$	605.551	−	439.959i	0.959669	−	0.697240i	0.953074	+	0.302738i	$0.0979007\pi$
$632$	−217.584	−	70.6973i	−0.344279	−	0.111863i
$633$	−224.318	+	228.724i	−0.354372	+	0.361334i
$634$	752.412	−	546.659i	1.18677	−	0.862239i
$635$	89.8082	−	123.610i	0.141430	−	0.194662i
$636$	630.664	+	93.6086i	0.991610	+	0.147183i
$637$	33.3151			0.0523000
$638$		0			0
$639$	−32.6644	+	24.7170i	−0.0511180	+	0.0386807i
$640$	−29.5262	−	90.8723i	−0.0461347	−	0.141988i
$641$	−71.8878	+	98.9450i	−0.112149	+	0.154360i	−0.861402	−	0.507924i	$-0.830413\pi$
$641$	−71.8878	+	98.9450i	−0.112149	+	0.154360i	0.749252	+	0.662285i	$0.230413\pi$
$642$	−481.891	+	81.1365i	−0.750609	+	0.126381i
$643$	−194.468	+	598.512i	−0.302439	+	0.930812i	0.678181	+	0.734894i	$0.262768\pi$
$643$	−194.468	+	598.512i	−0.302439	+	0.930812i	−0.980620	+	0.195917i	$0.937232\pi$
$644$	−409.647	−	133.102i	−0.636098	−	0.206681i
$645$	4.93729	+	29.3239i	0.00765471	+	0.0454634i
$646$	−1569.62	−	1140.39i	−2.42975	−	1.76531i
$647$	−176.735	+	57.4246i	−0.273160	+	0.0887552i	−0.442394	−	0.896821i	$-0.645871\pi$
$647$	−176.735	+	57.4246i	−0.273160	+	0.0887552i	0.169234	+	0.985576i	$0.445871\pi$
$648$	−320.293	−	90.4574i	−0.494280	−	0.139595i
$649$		0			0
$650$		−	583.808i		−	0.898166i
$651$	8.50041	−	57.2694i	0.0130575	−	0.0879714i
$652$	−130.256	−	94.6367i	−0.199779	−	0.145148i
$653$	118.977	+	163.758i	0.182201	+	0.250778i	0.890341	−	0.455293i	$-0.150466\pi$
$653$	118.977	+	163.758i	0.182201	+	0.250778i	−0.708140	+	0.706072i	$0.750466\pi$
$654$	596.242	+	584.755i	0.911686	+	0.894120i
$655$	25.9759	−	79.9455i	0.0396578	−	0.122054i
$656$	−205.647	−	283.049i	−0.313487	−	0.431477i
$657$	−9.41303	−	483.805i	−0.0143273	−	0.736385i
$658$	219.281	+	674.878i	0.333254	+	1.02565i
$659$		−	1094.02i		−	1.66012i	−0.557674	−	0.830060i	$-0.688306\pi$
$659$		−	1094.02i		−	1.66012i	0.557674	−	0.830060i	$-0.311694\pi$
$660$		0			0
$661$	1024.53			1.54997			0.774985	−	0.631980i	$-0.217758\pi$
$661$	1024.53			1.54997			0.774985	+	0.631980i	$0.217758\pi$
$662$	277.650	−	90.2139i	0.419411	−	0.136275i
$663$	−739.399	+	385.847i	−1.11523	+	0.581972i
$664$	−217.195	+	157.801i	−0.327100	+	0.237652i
$665$	133.322	+	43.3190i	0.200484	+	0.0651413i
$666$	−17.8105	−	51.3913i	−0.0267425	−	0.0771641i
$667$	565.019	−	410.510i	0.847105	−	0.615458i
$668$	78.4138	−	107.927i	0.117386	−	0.161568i
$669$	33.7969	−	227.698i	0.0505186	−	0.340356i
$670$	−126.658			−0.189041
$671$		0			0
$672$	303.652	−	610.560i	0.451863	−	0.908572i
$673$	−80.1865	−	246.789i	−0.119148	−	0.366700i	0.873642	−	0.486570i	$-0.161752\pi$
$673$	−80.1865	−	246.789i	−0.119148	−	0.366700i	−0.992790	+	0.119870i	$0.961752\pi$
$674$	79.0428	−	108.793i	0.117274	−	0.161414i
$675$	478.691	+	451.538i	0.709172	+	0.668946i
$676$	57.8811	−	178.140i	0.0856229	−	0.263520i
$677$	−110.860	−	36.0206i	−0.163752	−	0.0532062i	0.225994	−	0.974129i	$-0.427437\pi$
$677$	−110.860	−	36.0206i	−0.163752	−	0.0532062i	−0.389746	+	0.920923i	$0.627437\pi$
$678$	935.276	−	157.473i	1.37946	−	0.232262i
$679$	814.570	+	591.820i	1.19966	+	0.871605i
$680$	90.7078	−	29.4727i	0.133394	−	0.0433423i
$681$	64.4486	−	129.588i	0.0946382	−	0.190291i
$682$		0			0
$683$			739.385i			1.08255i	0.840844	+	0.541277i	$0.182059\pi$
$683$			739.385i			1.08255i	−0.840844	+	0.541277i	$0.817941\pi$
$684$	320.344	−	459.451i	0.468338	−	0.671713i
$685$	125.180	+	90.9485i	0.182744	+	0.132772i
$686$	−525.496	−	723.283i	−0.766029	−	1.05435i
$687$	32.3822	−	33.0183i	0.0471356	−	0.0480616i
$688$	76.7856	−	236.322i	0.111607	−	0.343491i
$689$	−499.675	−	687.744i	−0.725218	−	0.998177i
$690$	143.198	−	74.7264i	0.207534	−	0.108299i
$691$	120.215	+	369.984i	0.173973	+	0.535433i	0.999585	−	0.0288049i	$-0.00917015\pi$
$691$	120.215	+	369.984i	0.173973	+	0.535433i	−0.825612	+	0.564238i	$0.809170\pi$
$692$		−	532.662i		−	0.769743i
$693$		0			0
$694$	−28.2934			−0.0407686
$695$	−5.22540	+	1.69784i	−0.00751857	+	0.00244293i
$696$	147.948	+	283.513i	0.212569	+	0.407346i
$697$	417.523	−	303.348i	0.599029	−	0.435220i
$698$	513.807	+	166.946i	0.736114	+	0.239178i
$699$	−370.980	−	363.832i	−0.530729	−	0.520504i
$700$	−315.481	+	229.211i	−0.450688	+	0.327444i
$701$	−684.255	+	941.796i	−0.976112	+	1.34350i	−0.0372140	+	0.999307i	$0.511848\pi$
$701$	−684.255	+	941.796i	−0.976112	+	1.34350i	−0.938898	+	0.344196i	$0.888152\pi$
$702$	−310.307	−	567.448i	−0.442033	−	0.808330i
$703$	−62.8043			−0.0893375
$704$		0			0
$705$	−88.7011	−	44.1140i	−0.125817	−	0.0625730i
$706$	414.625	+	1276.09i	0.587288	+	1.80749i
$707$	79.3250	−	109.181i	0.112199	−	0.154429i
$708$	17.4392	+	103.576i	0.0246317	+	0.146294i
$709$	410.972	−	1264.84i	0.579650	−	1.78398i	−0.0401212	−	0.999195i	$-0.512774\pi$
$709$	410.972	−	1264.84i	0.579650	−	1.78398i	0.619771	−	0.784783i	$-0.287226\pi$
$710$	8.65717	+	2.81288i	0.0121932	+	0.00396181i
$711$	479.510	+	145.553i	0.674416	+	0.204715i
$712$	46.9844	+	34.1361i	0.0659893	+	0.0479440i
$713$	−73.2604	+	23.8038i	−0.102750	+	0.0333854i
$714$	1339.86	+	666.356i	1.87655	+	0.933272i
$715$		0			0
$716$			333.213i			0.465381i
$717$	−879.555	−	130.551i	−1.22672	−	0.182080i
$718$	−357.788	−	259.948i	−0.498312	−	0.362045i
$719$	−492.928	−	678.457i	−0.685574	−	0.943611i	0.314410	−	0.949287i	$-0.398193\pi$
$719$	−492.928	−	678.457i	−0.685574	−	0.943611i	−0.999984	+	0.00567596i	$0.998193\pi$
$720$	46.3759	+	133.815i	0.0644109	+	0.185854i
$721$	376.037	−	1157.32i	0.521549	−	1.60516i
$722$	−485.499	−	668.231i	−0.672436	−	0.925528i
$723$	−64.8167	−	124.208i	−0.0896497	−	0.171796i
$724$	−95.9313	−	295.246i	−0.132502	−	0.407798i
$725$		−	632.292i		−	0.872127i
$726$		0			0
$727$	154.628			0.212693			0.106346	−	0.994329i	$-0.466085\pi$
$727$	154.628			0.212693			0.106346	+	0.994329i	$0.466085\pi$
$728$	−250.100	+	81.2623i	−0.343544	+	0.111624i
$729$	705.280	+	184.450i	0.967462	+	0.253017i
$730$	−86.9957	+	63.2061i	−0.119172	+	0.0865837i
$731$	348.596	+	113.266i	0.476876	+	0.154946i
$732$	316.161	−	322.372i	0.431914	−	0.440399i
$733$	360.030	−	261.577i	0.491173	−	0.356858i	−0.314462	−	0.949270i	$-0.601824\pi$
$733$	360.030	−	261.577i	0.491173	−	0.356858i	0.805635	+	0.592412i	$0.201824\pi$
$734$	206.296	−	283.943i	0.281058	−	0.386843i
$735$	8.25443	+	1.22519i	0.0112305	+	0.00166693i
$736$	−907.255			−1.23268
$737$		0			0
$738$	241.489	+	319.137i	0.327221	+	0.432434i
$739$	−18.9609	−	58.3555i	−0.0256575	−	0.0789655i	0.937408	−	0.348233i	$-0.113218\pi$
$739$	−18.9609	−	58.3555i	−0.0256575	−	0.0789655i	−0.963065	+	0.269268i	$0.913218\pi$
$740$	−2.64483	+	3.64029i	−0.00357409	+	0.00491931i
$741$	−736.439	+	123.995i	−0.993844	+	0.167335i
$742$	−471.331	+	1450.61i	−0.635218	+	1.95500i
$743$	687.852	+	223.497i	0.925776	+	0.300803i	0.732834	−	0.680407i	$-0.238197\pi$
$743$	687.852	+	223.497i	0.925776	+	0.300803i	0.192942	+	0.981210i	$0.438197\pi$
$744$	−5.85632	−	34.7822i	−0.00787140	−	0.0467503i
$745$	43.3923	+	31.5263i	0.0582447	+	0.0423172i
$746$	357.913	−	116.293i	0.479776	−	0.155889i
$747$	468.921	−	354.830i	0.627739	−	0.475007i
$748$		0			0
$749$		−	435.215i		−	0.581062i
$750$	43.4931	−	293.023i	0.0579907	−	0.390698i
$751$	−1040.69	−	756.107i	−1.38574	−	1.00680i	−0.996317	−	0.0857426i	$-0.972674\pi$
$751$	−1040.69	−	756.107i	−1.38574	−	1.00680i	−0.389425	−	0.921058i	$-0.627326\pi$
$752$	486.571	+	669.708i	0.647036	+	0.890569i
$753$	−445.051	−	436.477i	−0.591038	−	0.579650i
$754$	−192.034	+	591.019i	−0.254687	+	0.783845i
$755$	−13.1483	−	18.0970i	−0.0174149	−	0.0239696i
$756$	−184.810	+	390.473i	−0.244458	+	0.516499i
$757$	−84.2743	−	259.370i	−0.111327	−	0.342628i	0.879837	−	0.475276i	$-0.157652\pi$
$757$	−84.2743	−	259.370i	−0.111327	−	0.342628i	−0.991163	+	0.132648i	$0.957652\pi$
$758$			682.566i			0.900483i
$759$		0			0
$760$	85.4021			0.112371
$761$	−453.306	+	147.288i	−0.595671	+	0.193545i	−0.591309	−	0.806445i	$-0.701389\pi$
$761$	−453.306	+	147.288i	−0.595671	+	0.193545i	−0.00436224	+	0.999990i	$0.501389\pi$
$762$	1294.75	−	675.651i	1.69915	−	0.886681i
$763$	−601.724	+	437.178i	−0.788629	+	0.572972i
$764$	−792.821	−	257.603i	−1.03772	−	0.337177i
$765$	−197.389	+	68.4086i	−0.258025	+	0.0894230i
$766$	−1290.29	+	937.447i	−1.68445	+	1.22382i
$767$	82.3165	−	113.299i	0.107323	−	0.147717i
$768$	144.005	−	970.200i	0.187507	−	1.26328i
$769$	22.4401			0.0291808			0.0145904	−	0.999894i	$-0.495356\pi$
$769$	22.4401			0.0291808			0.0145904	+	0.999894i	$0.495356\pi$
$770$		0			0
$771$	−266.832	+	536.525i	−0.346085	+	0.695881i
$772$	−179.974	−	553.903i	−0.233127	−	0.717490i
$773$	721.676	−	993.302i	0.933604	−	1.28500i	−0.0248330	−	0.999692i	$-0.507905\pi$
$773$	721.676	−	993.302i	0.933604	−	1.28500i	0.958437	−	0.285304i	$-0.0920946\pi$
$774$	−82.5584	+	271.981i	−0.106665	+	0.351397i
$775$	−21.5505	+	66.3257i	−0.0278071	+	0.0855816i
$776$	583.378	+	189.551i	0.751776	+	0.244267i
$777$	47.7677	−	8.04270i	0.0614771	−	0.0103510i
$778$	939.418	+	682.527i	1.20748	+	0.877284i
$779$	439.501	−	142.802i	0.564186	−	0.183315i
$780$	−23.8260	+	47.9075i	−0.0305462	+	0.0614199i
$781$		0			0
$782$		−	1990.95i		−	2.54597i
$783$	−336.078	−	614.574i	−0.429218	−	0.784896i
$784$	−56.4135	−	40.9868i	−0.0719560	−	0.0522791i
$785$	−31.5723	−	43.4556i	−0.0402195	−	0.0553574i
$786$	562.592	−	573.644i	0.715765	−	0.729827i
$787$	−269.548	+	829.585i	−0.342501	+	1.05411i	0.620407	+	0.784280i	$0.286968\pi$
$787$	−269.548	+	829.585i	−0.342501	+	1.05411i	−0.962908	+	0.269830i	$0.913032\pi$
$788$	8.57990	+	11.8092i	0.0108882	+	0.0149863i
$789$	265.324	−	138.457i	0.336279	−	0.175484i
$790$	−34.4117	−	105.908i	−0.0435591	−	0.134061i
$791$			844.685i			1.06787i
$792$		0			0
$793$	−602.043			−0.759197
$794$	1347.49	−	437.827i	1.69710	−	0.551420i
$795$	−98.5112	−	188.777i	−0.123913	−	0.237455i
$796$	370.930	−	269.496i	0.465992	−	0.338563i
$797$	53.0365	+	17.2326i	0.0665451	+	0.0216218i	0.342100	−	0.939663i	$-0.388862\pi$
$797$	53.0365	+	17.2326i	0.0665451	+	0.0216218i	−0.275555	+	0.961285i	$0.588862\pi$
$798$	956.644	+	938.212i	1.19880	+	1.17570i
$799$	−987.880	+	717.737i	−1.23640	+	0.898294i
$800$	−482.793	+	664.507i	−0.603491	+	0.830634i
$801$	−104.348	−	72.7544i	−0.130272	−	0.0908295i
$802$	453.989			0.566071
$803$		0			0
$804$	−403.549	−	200.698i	−0.501926	−	0.249625i
$805$	44.4531	+	136.813i	0.0552213	+	0.169954i
$806$	40.2876	−	55.4512i	0.0499847	−	0.0687980i
$807$	−25.0929	−	149.033i	−0.0310940	−	0.184676i
$808$	25.4066	−	78.1935i	0.0314438	−	0.0967741i
$809$	1260.26	+	409.482i	1.55780	+	0.506159i	0.956218	−	0.292655i	$-0.0945389\pi$
$809$	1260.26	+	409.482i	1.55780	+	0.506159i	0.601578	+	0.798814i	$0.294539\pi$
$810$	−56.0159	−	152.007i	−0.0691554	−	0.187663i
$811$	−831.775	−	604.320i	−1.02562	−	0.745154i	−0.0581899	−	0.998306i	$-0.518533\pi$
$811$	−831.775	−	604.320i	−1.02562	−	0.745154i	−0.967427	+	0.253151i	$0.918533\pi$
$812$	394.774	−	128.270i	0.486174	−	0.157968i
$813$	−334.103	−	166.161i	−0.410951	−	0.204380i
$814$		0			0
$815$			53.7721i			0.0659781i
$816$	1726.74	+	256.298i	2.11611	+	0.314091i
$817$	265.525	+	192.915i	0.324999	+	0.236126i
$818$	201.341	+	277.122i	0.246138	+	0.338780i
$819$	544.242	−	188.616i	0.664521	−	0.230301i
$820$	10.2312	−	31.4883i	0.0124770	−	0.0384004i
$821$	524.354	+	721.712i	0.638678	+	0.879064i	0.998544	−	0.0539395i	$-0.0171778\pi$
$821$	524.354	+	721.712i	0.638678	+	0.879064i	−0.359867	+	0.933004i	$0.617178\pi$
$822$	684.230	+	1311.19i	0.832397	+	1.59512i
$823$	−128.335	−	394.975i	−0.155936	−	0.479921i	0.842319	−	0.538980i	$-0.181190\pi$
$823$	−128.335	−	394.975i	−0.155936	−	0.479921i	−0.998255	+	0.0590586i	$0.981190\pi$
$824$		−	741.346i		−	0.899691i
$825$		0			0
$826$	−251.272			−0.304203
$827$	−441.823	+	143.557i	−0.534248	+	0.173588i	−0.563701	−	0.825979i	$-0.690623\pi$
$827$	−441.823	+	143.557i	−0.534248	+	0.173588i	0.0294539	+	0.999566i	$0.490623\pi$
$828$	574.659	−	11.1807i	0.694032	−	0.0135033i
$829$	716.945	−	520.891i	0.864831	−	0.628337i	−0.0643639	−	0.997926i	$-0.520502\pi$
$829$	716.945	−	520.891i	0.864831	−	0.628337i	0.929195	+	0.369590i	$0.120502\pi$
$830$	−124.280	−	40.3810i	−0.149735	−	0.0486518i
$831$	616.990	−	629.111i	0.742467	−	0.757053i
$832$	43.2032	−	31.3890i	0.0519270	−	0.0377271i
$833$	60.4593	−	83.2150i	0.0725802	−	0.0998980i
$834$	−51.9479	−	7.71055i	−0.0622876	−	0.00924526i
$835$	−44.5544			−0.0533585
$836$		0			0
$837$	14.3070	+	75.9217i	0.0170932	+	0.0907069i
$838$	39.2653	+	120.846i	0.0468560	+	0.144208i
$839$	−96.0926	+	132.260i	−0.114532	+	0.157640i	−0.862434	−	0.506169i	$-0.831061\pi$
$839$	−96.0926	+	132.260i	−0.114532	+	0.157640i	0.747902	+	0.663809i	$0.231061\pi$
$840$	−64.9552	+	10.9366i	−0.0773277	+	0.0130197i
$841$	51.9013	−	159.736i	0.0617138	−	0.189935i
$842$	−126.485	−	41.0975i	−0.150220	−	0.0488094i
$843$	−131.338	−	780.050i	−0.155798	−	0.925326i
$844$	204.949	+	148.904i	0.242831	+	0.176427i
$845$	−59.4945	+	19.3309i	−0.0704077	+	0.0228768i
$846$	−571.375	−	755.092i	−0.675384	−	0.892544i
$847$		0			0
$848$			1779.31i			2.09825i
$849$	−175.650	+	1183.40i	−0.206891	+	1.39387i
$850$	−1458.24	−	1059.48i	−1.71558	−	1.24644i
$851$	−37.8819	−	52.1400i	−0.0445146	−	0.0612691i
$852$	23.1257	+	22.6802i	0.0271429	+	0.0266199i
$853$	139.567	−	429.542i	0.163618	−	0.503566i	−0.835313	−	0.549774i	$-0.814714\pi$
$853$	139.567	−	429.542i	0.163618	−	0.503566i	0.998932	+	0.0462082i	$0.0147138\pi$
$854$	634.924	+	873.898i	0.743471	+	1.02330i
$855$	−187.026	+	3.63882i	−0.218744	+	0.00425593i
$856$	−81.9331	−	252.164i	−0.0957163	−	0.294584i
$857$		−	233.720i		−	0.272719i	−0.990659	−	0.136360i	$-0.956460\pi$
$857$		−	233.720i		−	0.272719i	0.990659	−	0.136360i	$-0.0435402\pi$
$858$		0			0
$859$	−694.225			−0.808178			−0.404089	−	0.914720i	$-0.632411\pi$
$859$	−694.225			−0.808178			−0.404089	+	0.914720i	$0.632411\pi$
$860$	22.3637	−	7.26639i	0.0260042	−	0.00844929i
$861$	−315.989	+	164.895i	−0.367002	+	0.191516i
$862$	−1014.59	+	737.146i	−1.17702	+	0.855158i
$863$	1087.43	+	353.326i	1.26005	+	0.409416i	0.861514	−	0.507734i	$-0.169517\pi$
$863$	1087.43	+	353.326i	1.26005	+	0.409416i	0.398541	+	0.917151i	$0.369517\pi$
$864$	−116.063	+	902.502i	−0.134332	+	1.04456i
$865$	−143.922	+	104.565i	−0.166383	+	0.120885i
$866$	765.064	−	1053.02i	0.883446	−	1.21596i
$867$	−250.770	+	1689.50i	−0.289239	+	1.94868i
$868$	−45.7825			−0.0527448
$869$		0			0
$870$	−69.3151	+	139.374i	−0.0796726	+	0.160200i
$871$	185.699	+	571.523i	0.213202	+	0.656169i
$872$	−266.337	+	366.581i	−0.305432	+	0.420391i
$873$	−1285.64	−	390.250i	−1.47267	−	0.447022i
$874$	550.900	−	1695.50i	0.630320	−	1.93993i
$875$	250.915	+	81.5271i	0.286759	+	0.0931738i
$876$	−377.335	+	63.5323i	−0.430748	+	0.0725255i
$877$	−874.028	−	635.019i	−0.996611	−	0.724080i	−0.0352523	−	0.999378i	$-0.511223\pi$
$877$	−874.028	−	635.019i	−0.996611	−	0.724080i	−0.961359	+	0.275298i	$0.911223\pi$
$878$	−60.2808	+	19.5864i	−0.0686569	+	0.0223080i
$879$	−466.016	+	937.030i	−0.530166	+	1.06602i
$880$		0			0
$881$			638.008i			0.724186i	0.932142	+	0.362093i	$0.117938\pi$
$881$			638.008i			0.724186i	−0.932142	+	0.362093i	$0.882062\pi$
$882$	65.4300	+	45.6198i	0.0741837	+	0.0517231i
$883$	786.522	+	571.442i	0.890739	+	0.647160i	0.936071	−	0.351812i	$-0.114434\pi$
$883$	786.522	+	571.442i	0.890739	+	0.647160i	−0.0453316	+	0.998972i	$0.514434\pi$
$884$	387.650	+	533.555i	0.438518	+	0.603569i
$885$	24.5621	−	25.0446i	0.0277538	−	0.0282990i
$886$	−678.982	+	2089.69i	−0.766346	+	2.35857i
$887$	309.160	+	425.523i	0.348546	+	0.479733i	0.946913	−	0.321490i	$-0.104183\pi$
$887$	309.160	+	425.523i	0.348546	+	0.479733i	−0.598367	+	0.801222i	$0.704183\pi$
$888$	26.1626	−	13.6526i	0.0294623	−	0.0153746i
$889$	401.930	+	1237.01i	0.452115	+	1.39147i
$890$			28.2683i			0.0317621i
$891$		0			0
$892$	−182.027			−0.204066
$893$	−1039.88	+	337.877i	−1.16448	+	0.378362i
$894$	237.181	+	454.510i	0.265303	+	0.508401i
$895$	90.0317	−	65.4118i	0.100594	−	0.0730859i
$896$	773.576	+	251.350i	0.863366	+	0.280525i
$897$	−547.141	−	536.600i	−0.609968	−	0.598216i
$898$	−1175.59	+	854.119i	−1.30912	+	0.951135i
$899$	43.6335	−	60.0564i	0.0485356	−	0.0668035i
$900$	297.614	−	426.851i	0.330682	−	0.474279i
$901$	−2624.65			−2.91304
$902$		0			0
$903$	−226.658	−	112.724i	−0.251005	−	0.124833i
$904$	159.019	+	489.412i	0.175907	+	0.541385i
$905$	−60.9415	+	83.8787i	−0.0673386	+	0.0926837i
$906$	−35.5004	−	210.846i	−0.0391837	−	0.232722i
$907$	−177.594	+	546.578i	−0.195804	+	0.602622i	0.804163	+	0.594409i	$0.202614\pi$
$907$	−177.594	+	546.578i	−0.195804	+	0.602622i	−0.999966	+	0.00821243i	$0.997386\pi$
$908$	−108.845	−	35.3660i	−0.119874	−	0.0389493i
$909$	−52.3074	+	172.322i	−0.0575439	+	0.189573i
$910$	−103.554	−	75.2365i	−0.113796	−	0.0826775i
$911$	1216.56	−	395.284i	1.33541	−	0.433901i	0.447651	−	0.894208i	$-0.352261\pi$
$911$	1216.56	−	395.284i	1.33541	−	0.433901i	0.887760	+	0.460307i	$0.152261\pi$
$912$	1399.58	+	696.058i	1.53463	+	0.763222i
$913$		0			0
$914$		−	64.6037i		−	0.0706823i
$915$	−149.167	−	22.1407i	−0.163024	−	0.0241975i
$916$	−29.5862	−	21.4956i	−0.0322994	−	0.0234669i
$917$	420.608	+	578.918i	0.458679	+	0.631317i
$918$	−1980.52	−	254.696i	−2.15742	−	0.277447i
$919$	148.924	−	458.342i	0.162050	−	0.498740i	−0.836756	−	0.547575i	$-0.815551\pi$
$919$	148.924	−	458.342i	0.162050	−	0.498740i	0.998807	+	0.0488354i	$0.0155510\pi$
$920$	51.5124	+	70.9007i	0.0559917	+	0.0770660i
$921$	553.118	+	1059.94i	0.600563	+	1.15086i
$922$	−225.723	−	694.705i	−0.244819	−	0.753476i
$923$		−	43.1883i		−	0.0467912i
$924$		0			0
$925$	−58.3480			−0.0630789
$926$	482.682	−	156.833i	0.521255	−	0.169366i
$927$	31.5873	+	1623.51i	0.0340748	+	1.75136i
$928$	707.335	−	513.909i	0.762215	−	0.553782i
$929$	−1057.82	−	343.707i	−1.13867	−	0.369975i	−0.321803	−	0.946807i	$-0.604289\pi$
$929$	−1057.82	−	343.707i	−1.13867	−	0.369975i	−0.816863	+	0.576832i	$0.804289\pi$
$930$	12.0213	−	12.2574i	0.0129261	−	0.0131800i
$931$	74.5130	−	54.1369i	0.0800355	−	0.0581492i
$932$	−241.516	+	332.418i	−0.259137	+	0.356672i
$933$	−1306.72	−	193.955i	−1.40056	−	0.207883i
$934$	−278.484			−0.298162
$935$		0			0
$936$	279.826	−	211.743i	0.298959	−	0.226221i
$937$	−538.796	−	1658.24i	−0.575023	−	1.76974i	−0.636102	−	0.771605i	$-0.719454\pi$
$937$	−538.796	−	1658.24i	−0.575023	−	1.76974i	0.0610795	−	0.998133i	$-0.480546\pi$
$938$	633.755	−	872.288i	0.675645	−	0.929945i
$939$	1567.63	−	263.944i	1.66947	−	0.281091i
$940$	−24.2074	+	74.5028i	−0.0257526	+	0.0792583i
$941$	−795.268	−	258.398i	−0.845131	−	0.274600i	−0.145726	−	0.989325i	$-0.546552\pi$
$941$	−795.268	−	258.398i	−0.845131	−	0.274600i	−0.699405	+	0.714725i	$0.746552\pi$
$942$	−85.2454	−	506.295i	−0.0904941	−	0.537468i
$943$	383.650	+	278.738i	0.406840	+	0.295586i
$944$	−278.778	+	90.5805i	−0.295316	+	0.0959539i
$945$	141.783	−	26.7181i	0.150034	−	0.0282732i
$946$		0			0
$947$		−	114.725i		−	0.121145i	−0.998164	−	0.0605726i	$-0.980707\pi$
$947$		−	114.725i		−	0.121145i	0.998164	−	0.0605726i	$-0.0192927\pi$
$948$	58.1791	−	391.967i	0.0613703	−	0.413467i
$949$	412.757	+	299.885i	0.434939	+	0.316001i
$950$	−948.684	−	1305.75i	−0.998615	−	1.37448i
$951$	−789.115	−	773.911i	−0.829774	−	0.813787i
$952$	−250.895	+	772.175i	−0.263545	+	0.811108i
$953$	192.241	+	264.597i	0.201722	+	0.277646i	0.897878	−	0.440244i	$-0.145108\pi$
$953$	192.241	+	264.597i	0.201722	+	0.277646i	−0.696157	+	0.717890i	$0.745108\pi$
$954$	−39.5922	−	2034.94i	−0.0415012	−	2.13306i
$955$	86.0335	+	264.784i	0.0900874	+	0.277261i
$956$			703.137i			0.735499i
$957$		0			0
$958$	−1725.47			−1.80111
$959$	−1252.72	+	407.034i	−1.30628	+	0.424436i
$960$	11.8587	−	6.18835i	0.0123529	−	0.00644620i
$961$	770.841	−	560.049i	0.802124	−	0.582777i
$962$	54.5393	+	17.7209i	0.0566937	+	0.0184209i
$963$	190.173	+	548.735i	0.197480	+	0.569818i
$964$	−89.6294	+	65.1196i	−0.0929766	+	0.0675514i
$965$	−114.331	+	157.362i	−0.118477	+	0.163070i
$966$	−201.879	+	1360.11i	−0.208985	+	1.40798i
$967$	−168.674			−0.174430			−0.0872150	−	0.996190i	$-0.527797\pi$
$967$	−168.674			−0.174430			−0.0872150	+	0.996190i	$0.527797\pi$
$968$		0			0
$969$	−1026.75	+	2064.51i	−1.05960	+	2.13056i
$970$	92.2634	+	283.957i	0.0951169	+	0.292740i
$971$	48.0438	−	66.1266i	0.0494787	−	0.0681016i	−0.783561	−	0.621315i	$-0.786599\pi$
$971$	48.0438	−	66.1266i	0.0494787	−	0.0681016i	0.833039	+	0.553214i	$0.186599\pi$
$972$	62.3923	−	573.078i	0.0641896	−	0.589586i
$973$	14.4533	−	44.4827i	0.0148544	−	0.0457170i
$974$	−312.344	−	101.487i	−0.320682	−	0.104196i
$975$	−684.185	+	115.197i	−0.701728	+	0.118151i
$976$	1019.46	+	740.680i	1.04453	+	0.758893i
$977$	−19.3599	+	6.29041i	−0.0198157	+	0.00643850i	−0.318908	−	0.947786i	$-0.603316\pi$
$977$	−19.3599	+	6.29041i	−0.0198157	+	0.00643850i	0.299092	+	0.954224i	$0.403316\pi$
$978$	−228.875	+	460.205i	−0.234024	+	0.470557i
$979$		0			0
$980$		−	6.59879i		−	0.00673346i
$981$	567.644	−	814.141i	0.578638	−	0.829910i
$982$	1626.80	+	1181.94i	1.65662	+	1.20361i
$983$	468.704	+	645.115i	0.476810	+	0.656272i	0.977888	−	0.209130i	$-0.0670631\pi$
$983$	468.704	+	645.115i	0.476810	+	0.656272i	−0.501078	+	0.865402i	$0.667063\pi$
$984$	−152.041	+	155.028i	−0.154513	+	0.157549i
$985$	1.50648	−	4.63646i	0.00152942	−	0.00470706i
$986$	1127.76	+	1552.23i	1.14377	+	1.57427i
$987$	747.644	−	390.150i	0.757492	−	0.395289i
$988$	182.488	+	561.640i	0.184704	+	0.568462i
$989$			336.799i			0.340545i
$990$		0			0
$991$	609.620			0.615156			0.307578	−	0.951523i	$-0.400481\pi$
$991$	609.620			0.615156			0.307578	+	0.951523i	$0.400481\pi$
$992$	−91.7132	+	29.7994i	−0.0924528	+	0.0300397i
$993$	−160.511	−	307.587i	−0.161642	−	0.309755i
$994$	−62.6900	+	45.5470i	−0.0630684	+	0.0458219i
$995$	−145.632	−	47.3187i	−0.146364	−	0.0475565i
$996$	−331.987	−	325.590i	−0.333320	−	0.326898i
$997$	1432.99	−	1041.13i	1.43730	−	1.04426i	0.448708	−	0.893679i	$-0.351884\pi$
$997$	1432.99	−	1041.13i	1.43730	−	1.04426i	0.988597	−	0.150585i	$-0.0481156\pi$
$998$	727.095	−	1000.76i	0.728552	−	1.00277i
$999$	−56.7129	+	31.0133i	−0.0567697	+	0.0310443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.l.269.1		16
3.2	odd	2	inner	363.3.h.l.269.4		16
11.2	odd	10		363.3.h.m.251.1		16
11.3	even	5		363.3.b.h.122.4		4
11.4	even	5	inner	363.3.h.l.245.1		16
11.5	even	5	inner	363.3.h.l.323.4		16
11.6	odd	10		363.3.h.m.323.1		16
11.7	odd	10		363.3.h.m.245.4		16
11.8	odd	10		33.3.b.b.23.1	✓	4
11.9	even	5	inner	363.3.h.l.251.4		16
11.10	odd	2		363.3.h.m.269.4		16
33.2	even	10		363.3.h.m.251.4		16
33.5	odd	10	inner	363.3.h.l.323.1		16
33.8	even	10		33.3.b.b.23.4	yes	4
33.14	odd	10		363.3.b.h.122.1		4
33.17	even	10		363.3.h.m.323.4		16
33.20	odd	10	inner	363.3.h.l.251.1		16
33.26	odd	10	inner	363.3.h.l.245.4		16
33.29	even	10		363.3.h.m.245.1		16
33.32	even	2		363.3.h.m.269.1		16
44.19	even	10		528.3.i.d.353.4		4
132.107	odd	10		528.3.i.d.353.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.b.23.1	✓	4	11.8	odd	10
33.3.b.b.23.4	yes	4	33.8	even	10
363.3.b.h.122.1		4	33.14	odd	10
363.3.b.h.122.4		4	11.3	even	5
363.3.h.l.245.1		16	11.4	even	5	inner
363.3.h.l.245.4		16	33.26	odd	10	inner
363.3.h.l.251.1		16	33.20	odd	10	inner
363.3.h.l.251.4		16	11.9	even	5	inner
363.3.h.l.269.1		16	1.1	even	1	trivial
363.3.h.l.269.4		16	3.2	odd	2	inner
363.3.h.l.323.1		16	33.5	odd	10	inner
363.3.h.l.323.4		16	11.5	even	5	inner
363.3.h.m.245.1		16	33.29	even	10
363.3.h.m.245.4		16	11.7	odd	10
363.3.h.m.251.1		16	11.2	odd	10
363.3.h.m.251.4		16	33.2	even	10
363.3.h.m.269.1		16	33.32	even	2
363.3.h.m.269.4		16	11.10	odd	2
363.3.h.m.323.1		16	11.6	odd	10
363.3.h.m.323.4		16	33.17	even	10
528.3.i.d.353.3		4	132.107	odd	10
528.3.i.d.353.4		4	44.19	even	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.40079 + 0.780063i) q^{2} +(1.38791 + 2.65965i) q^{3} +(1.91922 - 1.39439i) q^{4} +(-0.753510 - 0.244830i) q^{5} +(-5.40676 - 5.30259i) q^{6} +(5.45647 - 3.96435i) q^{7} +(2.41516 - 3.32418i) q^{8} +(-5.14743 + 7.38268i) q^{9} +O(q^{10})\)	\(q+(-2.40079 + 0.780063i) q^{2} +(1.38791 + 2.65965i) q^{3} +(1.91922 - 1.39439i) q^{4} +(-0.753510 - 0.244830i) q^{5} +(-5.40676 - 5.30259i) q^{6} +(5.45647 - 3.96435i) q^{7} +(2.41516 - 3.32418i) q^{8} +(-5.14743 + 7.38268i) q^{9} +2.00000 q^{10} +(6.37228 + 3.16915i) q^{12} +(-2.93230 - 9.02469i) q^{13} +(-10.0074 + 13.7740i) q^{14} +(-0.394640 - 2.34387i) q^{15} +(-6.13751 + 18.8893i) q^{16} +(-27.8635 - 9.05339i) q^{17} +(6.59893 - 21.7396i) q^{18} +(-21.2235 - 15.4198i) q^{19} +(-1.78754 + 0.580806i) q^{20} +(18.1168 + 9.01011i) q^{21} -26.9205i q^{23} +(12.1932 + 1.80981i) q^{24} +(-19.7176 - 14.3257i) q^{25} +(14.0797 + 19.3790i) q^{26} +(-26.7795 - 3.44386i) q^{27} +(4.94427 - 15.2169i) q^{28} +(15.2490 + 20.9884i) q^{29} +(2.77581 + 5.31929i) q^{30} +(-0.884223 - 2.72136i) q^{31} -33.7013i q^{32} +73.9565 q^{34} +(-5.08209 + 1.65127i) q^{35} +(0.415322 + 21.3465i) q^{36} +(1.93681 - 1.40718i) q^{37} +(62.9815 + 20.4639i) q^{38} +(19.9327 - 20.3243i) q^{39} +(-2.63370 + 1.91350i) q^{40} +(-10.3541 + 14.2512i) q^{41} +(-50.5232 - 7.49908i) q^{42} -12.5109 q^{43} +(5.68614 - 4.30268i) q^{45} +(20.9997 + 64.6305i) q^{46} +(24.4983 - 33.7190i) q^{47} +(-58.7572 + 9.89301i) q^{48} +(-1.08492 + 3.33904i) q^{49} +(58.5127 + 19.0119i) q^{50} +(-14.5931 - 86.6722i) q^{51} +(-18.2117 - 13.2316i) q^{52} +(85.2019 - 27.6838i) q^{53} +(66.9783 - 12.6217i) q^{54} -27.7128i q^{56} +(11.5549 - 77.8482i) q^{57} +(-52.9818 - 38.4935i) q^{58} +(8.67483 + 11.9399i) q^{59} +(-4.02567 - 3.94811i) q^{60} +(19.6058 - 60.3404i) q^{61} +(4.24567 + 5.84366i) q^{62} +(1.18079 + 60.6896i) q^{63} +(1.73906 + 5.35228i) q^{64} +7.51811i q^{65} -63.3288 q^{67} +(-66.1000 + 21.4772i) q^{68} +(71.5991 - 37.3632i) q^{69} +(10.9129 - 7.92871i) q^{70} +(4.32858 + 1.40644i) q^{71} +(12.1095 + 34.9413i) q^{72} +(-43.4979 + 31.6030i) q^{73} +(-3.55219 + 4.88917i) q^{74} +(10.7350 - 72.3245i) q^{75} -62.2337 q^{76} +(-32.0000 + 64.3432i) q^{78} +(-17.2059 - 52.9542i) q^{79} +(9.24935 - 12.7306i) q^{80} +(-28.0079 - 76.0037i) q^{81} +(13.7412 - 42.2910i) q^{82} +(-62.1400 - 20.1905i) q^{83} +(47.3338 - 7.96963i) q^{84} +(18.7789 + 13.6436i) q^{85} +(30.0360 - 9.75927i) q^{86} +(-34.6576 + 69.6868i) q^{87} +14.1341i q^{89} +(-10.2949 + 14.7654i) q^{90} +(-51.7771 - 37.6183i) q^{91} +(-37.5378 - 51.6663i) q^{92} +(6.01063 - 6.12871i) q^{93} +(-32.5123 + 100.062i) q^{94} +(12.2169 + 16.8151i) q^{95} +(89.6334 - 46.7742i) q^{96} +(46.1317 + 141.979i) q^{97} -8.86263i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9}+O(q^{10}) \) 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9	\( 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9} + 32 q^{10} + 56 q^{12} - 8 q^{13} - 13 q^{15} + 22 q^{16} + 38 q^{18} - 36 q^{19} + 152 q^{21} + 24 q^{24} - 86 q^{25} + 20 q^{27} - 64 q^{28} + 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} - 56 q^{39} - 36 q^{40} + 68 q^{42} - 384 q^{43} + 68 q^{45} - 88 q^{46} - 110 q^{48} + 60 q^{49} + 214 q^{51} - 136 q^{52} + 704 q^{54} + 144 q^{57} - 216 q^{58} - 56 q^{60} - 24 q^{61} + 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} + 72 q^{72} - 284 q^{73} + 124 q^{75} - 720 q^{76} - 512 q^{78} - 76 q^{79} - 113 q^{81} - 40 q^{82} + 80 q^{84} - 68 q^{85} + 1008 q^{87} + 14 q^{90} - 256 q^{91} - 25 q^{93} + 260 q^{94} + 272 q^{96} - 218 q^{97}+O(q^{100}) \) 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9 + 32 * q^10 + 56 * q^12 - 8 * q^13 - 13 * q^15 + 22 * q^16 + 38 * q^18 - 36 * q^19 + 152 * q^21 + 24 * q^24 - 86 * q^25 + 20 * q^27 - 64 * q^28 + 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 - 56 * q^39 - 36 * q^40 + 68 * q^42 - 384 * q^43 + 68 * q^45 - 88 * q^46 - 110 * q^48 + 60 * q^49 + 214 * q^51 - 136 * q^52 + 704 * q^54 + 144 * q^57 - 216 * q^58 - 56 * q^60 - 24 * q^61 + 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 + 72 * q^72 - 284 * q^73 + 124 * q^75 - 720 * q^76 - 512 * q^78 - 76 * q^79 - 113 * q^81 - 40 * q^82 + 80 * q^84 - 68 * q^85 + 1008 * q^87 + 14 * q^90 - 256 * q^91 - 25 * q^93 + 260 * q^94 + 272 * q^96 - 218 * q^97

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