LMFDB - Embedded newform 70.3.l.b.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,3,Mod(23,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 4]))

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

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

chi := DirichletCharacter("70.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.2
Root			$0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	70.67
Dual form			70.3.l.b.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(0.423972 + 1.58228i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.12590 + 3.90240i) q^{5} -2.31662 q^{6} +(-2.78771 + 6.42096i) q^{7} +(2.00000 - 2.00000i) q^{8} +(5.47036 - 3.15831i) q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} +(0.423972 + 1.58228i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.12590 + 3.90240i) q^{5} -2.31662 q^{6} +(-2.78771 + 6.42096i) q^{7} +(2.00000 - 2.00000i) q^{8} +(5.47036 - 3.15831i) q^{9} +(-4.18662 - 5.69844i) q^{10} +(-0.341688 + 0.591820i) q^{11} +(0.847944 - 3.16457i) q^{12} +(-11.9499 + 11.9499i) q^{13} +(-7.75082 - 6.15831i) q^{14} +(-7.50000 - 3.29156i) q^{15} +(2.00000 + 3.46410i) q^{16} +(32.4999 - 8.70832i) q^{17} +(2.31205 + 8.62867i) q^{18} +(8.34264 - 4.81662i) q^{19} +(9.31662 - 3.63325i) q^{20} +(-11.3417 - 1.68864i) q^{21} +(-0.683375 - 0.683375i) q^{22} +(23.3702 + 6.26203i) q^{23} +(4.01251 + 2.31662i) q^{24} +(-5.45744 - 24.3971i) q^{25} +(-11.9499 - 20.6978i) q^{26} +(17.7414 + 17.7414i) q^{27} +(11.2494 - 8.33372i) q^{28} -16.5330i q^{29} +(7.24155 - 9.04040i) q^{30} +(-11.9248 + 20.6544i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(-1.08129 - 0.289732i) q^{33} +47.5831i q^{34} +(-16.3430 - 30.9500i) q^{35} -12.6332 q^{36} +(6.79899 - 25.3742i) q^{37} +(3.52601 + 13.1593i) q^{38} +(-23.9745 - 13.8417i) q^{39} +(1.55299 + 14.0566i) q^{40} +0.200503 q^{41} +(6.45807 - 14.8749i) q^{42} +(-41.1161 + 41.1161i) q^{43} +(1.18364 - 0.683375i) q^{44} +(-4.77482 + 31.2201i) q^{45} +(-17.1082 + 29.6322i) q^{46} +(-12.3686 + 46.1601i) q^{47} +(-4.63325 + 4.63325i) q^{48} +(-33.4574 - 35.7995i) q^{49} +(35.3246 + 1.47494i) q^{50} +(27.5581 + 47.7320i) q^{51} +(32.6477 - 8.74792i) q^{52} +(-24.1422 - 90.1000i) q^{53} +(-30.7291 + 17.7414i) q^{54} +(-1.24144 - 3.18338i) q^{55} +(7.26650 + 18.4173i) q^{56} +(11.1583 + 11.1583i) q^{57} +(22.5845 + 6.05150i) q^{58} +(-20.0054 - 11.5501i) q^{59} +(9.69882 + 13.2012i) q^{60} +(6.08312 + 10.5363i) q^{61} +(-23.8496 - 23.8496i) q^{62} +(5.02963 + 43.9294i) q^{63} -8.00000i q^{64} +(-9.27902 - 83.9873i) q^{65} +(0.791562 - 1.37103i) q^{66} +(-1.35519 + 0.363121i) q^{67} +(-64.9998 - 17.4166i) q^{68} +39.6332i q^{69} +(48.2605 - 10.9965i) q^{70} +63.2665 q^{71} +(4.62409 - 17.2573i) q^{72} +(12.1918 + 45.5005i) q^{73} +(32.1732 + 18.5752i) q^{74} +(36.2893 - 18.9789i) q^{75} -19.2665 q^{76} +(-2.84753 - 3.84378i) q^{77} +(27.6834 - 27.6834i) q^{78} +(97.2256 - 56.1332i) q^{79} +(-19.7701 - 3.02365i) q^{80} +(7.87469 - 13.6394i) q^{81} +(-0.0733890 + 0.273892i) q^{82} +(23.1161 - 23.1161i) q^{83} +(17.9557 + 14.2665i) q^{84} +(-67.6082 + 154.049i) q^{85} +(-41.1161 - 71.2152i) q^{86} +(26.1599 - 7.00952i) q^{87} +(0.500265 + 1.86702i) q^{88} +(69.1518 - 39.9248i) q^{89} +(-40.8997 - 17.9499i) q^{90} +(-43.4169 - 110.042i) q^{91} +(-34.2164 - 34.2164i) q^{92} +(-37.7369 - 10.1116i) q^{93} +(-58.5287 - 33.7916i) q^{94} +(-7.28190 + 47.6126i) q^{95} +(-4.63325 - 8.02502i) q^{96} +(-50.6834 - 50.6834i) q^{97} +(61.1493 - 32.6001i) q^{98} +4.31662i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 2 q^{3} - 6 q^{5} + 8 q^{6} - 12 q^{7} + 16 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 2 * q^3 - 6 * q^5 + 8 * q^6 - 12 * q^7 + 16 * q^8	$ 8 q + 4 q^{2} + 2 q^{3} - 6 q^{5} + 8 q^{6} - 12 q^{7} + 16 q^{8} + 18 q^{10} - 16 q^{11} + 4 q^{12} - 16 q^{13} - 60 q^{15} + 16 q^{16} + 62 q^{17} - 12 q^{18} + 48 q^{20} - 104 q^{21} - 32 q^{22} + 22 q^{23} - 6 q^{25} - 16 q^{26} - 4 q^{27} + 12 q^{28} - 50 q^{30} + 24 q^{31} - 16 q^{32} + 30 q^{33} + 70 q^{35} - 48 q^{36} - 134 q^{37} - 12 q^{38} + 12 q^{40} + 320 q^{41} - 100 q^{42} + 16 q^{43} - 58 q^{45} - 44 q^{46} + 102 q^{47} + 16 q^{48} + 4 q^{50} + 48 q^{51} + 16 q^{52} + 98 q^{53} + 136 q^{55} - 48 q^{56} + 76 q^{57} - 40 q^{58} + 40 q^{60} - 84 q^{61} + 48 q^{62} - 76 q^{63} - 210 q^{65} - 60 q^{66} - 130 q^{67} - 124 q^{68} + 146 q^{70} + 400 q^{71} - 24 q^{72} - 246 q^{73} + 40 q^{75} - 48 q^{76} + 86 q^{77} + 248 q^{78} + 24 q^{80} - 136 q^{81} + 160 q^{82} - 160 q^{83} - 448 q^{85} + 16 q^{86} + 196 q^{87} - 32 q^{88} - 168 q^{90} - 480 q^{91} - 88 q^{92} - 210 q^{93} - 80 q^{95} + 16 q^{96} - 432 q^{97} + 176 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 2 * q^3 - 6 * q^5 + 8 * q^6 - 12 * q^7 + 16 * q^8 + 18 * q^10 - 16 * q^11 + 4 * q^12 - 16 * q^13 - 60 * q^15 + 16 * q^16 + 62 * q^17 - 12 * q^18 + 48 * q^20 - 104 * q^21 - 32 * q^22 + 22 * q^23 - 6 * q^25 - 16 * q^26 - 4 * q^27 + 12 * q^28 - 50 * q^30 + 24 * q^31 - 16 * q^32 + 30 * q^33 + 70 * q^35 - 48 * q^36 - 134 * q^37 - 12 * q^38 + 12 * q^40 + 320 * q^41 - 100 * q^42 + 16 * q^43 - 58 * q^45 - 44 * q^46 + 102 * q^47 + 16 * q^48 + 4 * q^50 + 48 * q^51 + 16 * q^52 + 98 * q^53 + 136 * q^55 - 48 * q^56 + 76 * q^57 - 40 * q^58 + 40 * q^60 - 84 * q^61 + 48 * q^62 - 76 * q^63 - 210 * q^65 - 60 * q^66 - 130 * q^67 - 124 * q^68 + 146 * q^70 + 400 * q^71 - 24 * q^72 - 246 * q^73 + 40 * q^75 - 48 * q^76 + 86 * q^77 + 248 * q^78 + 24 * q^80 - 136 * q^81 + 160 * q^82 - 160 * q^83 - 448 * q^85 + 16 * q^86 + 196 * q^87 - 32 * q^88 - 168 * q^90 - 480 * q^91 - 88 * q^92 - 210 * q^93 - 80 * q^95 + 16 * q^96 - 432 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$3$	0.423972	+	1.58228i	0.141324	+	0.527428i	0.999892	+	0.0147277i	$0.00468815\pi$
$3$	0.423972	+	1.58228i	0.141324	+	0.527428i	−0.858568	+	0.512700i	$0.828645\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	−3.12590	+	3.90240i	−0.625181	+	0.780480i
$5$	−3.12590	+	3.90240i	−0.625181	+	0.780480i
$6$	−2.31662			−0.386104
$7$	−2.78771	+	6.42096i	−0.398244	+	0.917280i
$7$	−2.78771	+	6.42096i	−0.398244	+	0.917280i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	5.47036	−	3.15831i	0.607818	−	0.350924i
$10$	−4.18662	−	5.69844i	−0.418662	−	0.569844i
$11$	−0.341688	+	0.591820i	−0.0310625	+	0.0538018i	−0.881139	−	0.472858i	$-0.843222\pi$
$11$	−0.341688	+	0.591820i	−0.0310625	+	0.0538018i	0.850076	+	0.526660i	$0.176556\pi$
$12$	0.847944	−	3.16457i	0.0706620	−	0.263714i
$13$	−11.9499	+	11.9499i	−0.919221	+	0.919221i	−0.996973	−	0.0777517i	$-0.975226\pi$
$13$	−11.9499	+	11.9499i	−0.919221	+	0.919221i	0.0777517	+	0.996973i	$0.475226\pi$
$14$	−7.75082	−	6.15831i	−0.553630	−	0.439879i
$15$	−7.50000	−	3.29156i	−0.500000	−	0.219437i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	32.4999	−	8.70832i	1.91176	−	0.512254i	0.918646	−	0.395082i	$-0.129284\pi$
$17$	32.4999	−	8.70832i	1.91176	−	0.512254i	0.993112	−	0.117172i	$-0.0373829\pi$
$18$	2.31205	+	8.62867i	0.128447	+	0.479371i
$19$	8.34264	−	4.81662i	0.439086	−	0.253507i	−0.264124	−	0.964489i	$-0.585083\pi$
$19$	8.34264	−	4.81662i	0.439086	−	0.253507i	0.703210	+	0.710982i	$0.251749\pi$
$20$	9.31662	−	3.63325i	0.465831	−	0.181662i
$21$	−11.3417	−	1.68864i	−0.540080	−	0.0804115i
$22$	−0.683375	−	0.683375i	−0.0310625	−	0.0310625i
$23$	23.3702	+	6.26203i	1.01610	+	0.272262i	0.728175	−	0.685392i	$-0.240369\pi$
$23$	23.3702	+	6.26203i	1.01610	+	0.272262i	0.287922	+	0.957654i	$0.407036\pi$
$24$	4.01251	+	2.31662i	0.167188	+	0.0965260i
$25$	−5.45744	−	24.3971i	−0.218298	−	0.975882i
$26$	−11.9499	−	20.6978i	−0.459611	−	0.796069i
$27$	17.7414	+	17.7414i	0.657090	+	0.657090i
$28$	11.2494	−	8.33372i	0.401765	−	0.297633i
$29$		−	16.5330i		−	0.570103i	−0.958512	−	0.285052i	$-0.907989\pi$
$29$		−	16.5330i		−	0.570103i	0.958512	−	0.285052i	$-0.0920108\pi$
$30$	7.24155	−	9.04040i	0.241385	−	0.301347i
$31$	−11.9248	+	20.6544i	−0.384671	+	0.666270i	−0.991724	−	0.128392i	$-0.959019\pi$
$31$	−11.9248	+	20.6544i	−0.384671	+	0.666270i	0.607052	+	0.794662i	$0.292352\pi$
$32$	−5.46410	+	1.46410i	−0.170753	+	0.0457532i
$33$	−1.08129	−	0.289732i	−0.0327665	−	0.00877975i
$34$			47.5831i			1.39950i
$35$	−16.3430	−	30.9500i	−0.466944	−	0.884287i
$36$	−12.6332			−0.350924
$37$	6.79899	−	25.3742i	0.183757	−	0.685789i	−0.811137	−	0.584856i	$-0.801151\pi$
$37$	6.79899	−	25.3742i	0.183757	−	0.685789i	0.994893	−	0.100932i	$-0.0321825\pi$
$38$	3.52601	+	13.1593i	0.0927898	+	0.346296i
$39$	−23.9745	−	13.8417i	−0.614731	−	0.354915i
$40$	1.55299	+	14.0566i	0.0388247	+	0.351415i
$41$	0.200503			0.00489031			0.00244515	−	0.999997i	$-0.499222\pi$
$41$	0.200503			0.00489031			0.00244515	+	0.999997i	$0.499222\pi$
$42$	6.45807	−	14.8749i	0.153764	−	0.354165i
$43$	−41.1161	+	41.1161i	−0.956189	+	0.956189i	−0.999080	−	0.0428909i	$-0.986343\pi$
$43$	−41.1161	+	41.1161i	−0.956189	+	0.956189i	0.0428909	+	0.999080i	$0.486343\pi$
$44$	1.18364	−	0.683375i	0.0269009	−	0.0155313i
$45$	−4.77482	+	31.2201i	−0.106107	+	0.693780i
$46$	−17.1082	+	29.6322i	−0.371917	+	0.644179i
$47$	−12.3686	+	46.1601i	−0.263161	+	0.982130i	0.700205	+	0.713942i	$0.253092\pi$
$47$	−12.3686	+	46.1601i	−0.263161	+	0.982130i	−0.963366	+	0.268189i	$0.913575\pi$
$48$	−4.63325	+	4.63325i	−0.0965260	+	0.0965260i
$49$	−33.4574	−	35.7995i	−0.682804	−	0.730602i
$50$	35.3246	+	1.47494i	0.706491	+	0.0294987i
$51$	27.5581	+	47.7320i	0.540354	+	0.935921i
$52$	32.6477	−	8.74792i	0.627840	−	0.168229i
$53$	−24.1422	−	90.1000i	−0.455514	−	1.70000i	−0.686573	−	0.727061i	$-0.740886\pi$
$53$	−24.1422	−	90.1000i	−0.455514	−	1.70000i	0.231059	−	0.972940i	$-0.425781\pi$
$54$	−30.7291	+	17.7414i	−0.569057	+	0.328545i
$55$	−1.24144	−	3.18338i	−0.0225716	−	0.0578795i
$56$	7.26650	+	18.4173i	0.129759	+	0.328881i
$57$	11.1583	+	11.1583i	0.195760	+	0.195760i
$58$	22.5845	+	6.05150i	0.389388	+	0.104336i
$59$	−20.0054	−	11.5501i	−0.339075	−	0.195765i	0.320788	−	0.947151i	$-0.396052\pi$
$59$	−20.0054	−	11.5501i	−0.339075	−	0.195765i	−0.659863	+	0.751386i	$0.729386\pi$
$60$	9.69882	+	13.2012i	0.161647	+	0.220019i
$61$	6.08312	+	10.5363i	0.0997233	+	0.172726i	0.911570	−	0.411145i	$-0.134871\pi$
$61$	6.08312	+	10.5363i	0.0997233	+	0.172726i	−0.811847	+	0.583871i	$0.801538\pi$
$62$	−23.8496	−	23.8496i	−0.384671	−	0.384671i
$63$	5.02963	+	43.9294i	0.0798354	+	0.697292i
$64$		−	8.00000i		−	0.125000i
$65$	−9.27902	−	83.9873i	−0.142754	−	1.29211i
$66$	0.791562	−	1.37103i	0.0119934	−	0.0207731i
$67$	−1.35519	+	0.363121i	−0.0202266	+	0.00541971i	−0.268918	−	0.963163i	$-0.586666\pi$
$67$	−1.35519	+	0.363121i	−0.0202266	+	0.00541971i	0.248692	+	0.968583i	$0.419999\pi$
$68$	−64.9998	−	17.4166i	−0.955879	−	0.256127i
$69$			39.6332i			0.574395i
$70$	48.2605	−	10.9965i	0.689436	−	0.157093i
$71$	63.2665			0.891077			0.445539	−	0.895263i	$-0.353012\pi$
$71$	63.2665			0.891077			0.445539	+	0.895263i	$0.353012\pi$
$72$	4.62409	−	17.2573i	0.0642235	−	0.239685i
$73$	12.1918	+	45.5005i	0.167011	+	0.623295i	0.997775	+	0.0666696i	$0.0212373\pi$
$73$	12.1918	+	45.5005i	0.167011	+	0.623295i	−0.830764	+	0.556625i	$0.812096\pi$
$74$	32.1732	+	18.5752i	0.434773	+	0.251016i
$75$	36.2893	−	18.9789i	0.483857	−	0.253052i
$76$	−19.2665			−0.253507
$77$	−2.84753	−	3.84378i	−0.0369809	−	0.0499193i
$78$	27.6834	−	27.6834i	0.354915	−	0.354915i
$79$	97.2256	−	56.1332i	1.23070	−	0.710547i	0.263528	−	0.964652i	$-0.415114\pi$
$79$	97.2256	−	56.1332i	1.23070	−	0.710547i	0.967177	+	0.254104i	$0.0817807\pi$
$80$	−19.7701	−	3.02365i	−0.247126	−	0.0377956i
$81$	7.87469	−	13.6394i	0.0972183	−	0.168387i
$82$	−0.0733890	+	0.273892i	−0.000894988	+	0.00334014i
$83$	23.1161	−	23.1161i	0.278507	−	0.278507i	−0.554006	−	0.832513i	$-0.686901\pi$
$83$	23.1161	−	23.1161i	0.278507	−	0.278507i	0.832513	+	0.554006i	$0.186901\pi$
$84$	17.9557	+	14.2665i	0.213759	+	0.169839i
$85$	−67.6082	+	154.049i	−0.795390	+	1.81234i
$86$	−41.1161	−	71.2152i	−0.478094	−	0.828084i
$87$	26.1599	−	7.00952i	0.300689	−	0.0805692i
$88$	0.500265	+	1.86702i	0.00568483	+	0.0212161i
$89$	69.1518	−	39.9248i	0.776987	−	0.448593i	−0.0583747	−	0.998295i	$-0.518592\pi$
$89$	69.1518	−	39.9248i	0.776987	−	0.448593i	0.835361	+	0.549701i	$0.185258\pi$
$90$	−40.8997	−	17.9499i	−0.454442	−	0.199443i
$91$	−43.4169	−	110.042i	−0.477109	−	1.20926i
$92$	−34.2164	−	34.2164i	−0.371917	−	0.371917i
$93$	−37.7369	−	10.1116i	−0.405773	−	0.108727i
$94$	−58.5287	−	33.7916i	−0.622646	−	0.359485i
$95$	−7.28190	+	47.6126i	−0.0766516	+	0.501185i
$96$	−4.63325	−	8.02502i	−0.0482630	−	0.0835940i
$97$	−50.6834	−	50.6834i	−0.522509	−	0.522509i	0.395819	−	0.918328i	$-0.370461\pi$
$97$	−50.6834	−	50.6834i	−0.522509	−	0.522509i	−0.918328	+	0.395819i	$0.870461\pi$
$98$	61.1493	−	32.6001i	0.623972	−	0.332654i
$99$			4.31662i			0.0436023i
$100$	−14.9445	+	47.7144i	−0.149445	+	0.477144i
$101$	27.5000	−	47.6314i	0.272277	−	0.471598i	−0.697167	−	0.716908i	$-0.745557\pi$
$101$	27.5000	−	47.6314i	0.272277	−	0.471598i	0.969445	+	0.245310i	$0.0788899\pi$
$102$	−75.2900	+	20.1739i	−0.738137	+	0.197783i
$103$	−0.216259	−	0.0579464i	−0.00209960	−	0.000562586i	0.257769	−	0.966207i	$-0.417013\pi$
$103$	−0.216259	−	0.0579464i	−0.00209960	−	0.000562586i	−0.259869	+	0.965644i	$0.583679\pi$
$104$			47.7995i			0.459611i
$105$	42.0428	−	38.9813i	0.400407	−	0.371250i
$106$	131.916			1.24449
$107$	−34.8304	+	129.989i	−0.325517	+	1.21485i	0.588273	+	0.808662i	$0.299808\pi$
$107$	−34.8304	+	129.989i	−0.325517	+	1.21485i	−0.913791	+	0.406185i	$0.866859\pi$
$108$	−12.9876	−	48.4705i	−0.120256	−	0.448801i
$109$	44.2679	+	25.5581i	0.406127	+	0.234478i	0.689124	−	0.724643i	$-0.257995\pi$
$109$	44.2679	+	25.5581i	0.406127	+	0.234478i	−0.282997	+	0.959121i	$0.591329\pi$
$110$	4.80297	−	0.530637i	0.0436634	−	0.00482398i
$111$	43.0317			0.387673
$112$	−27.8183	+	3.18501i	−0.248377	+	0.0284376i
$113$	63.8496	−	63.8496i	0.565041	−	0.565041i	−0.365694	−	0.930735i	$-0.619168\pi$
$113$	63.8496	−	63.8496i	0.565041	−	0.565041i	0.930735	+	0.365694i	$0.119168\pi$
$114$	−19.3268	+	11.1583i	−0.169533	+	0.0978799i
$115$	−97.4900	+	71.6254i	−0.847739	+	0.622830i
$116$	−16.5330	+	28.6360i	−0.142526	+	0.246862i
$117$	−27.6286	+	103.112i	−0.236142	+	0.881295i
$118$	23.1003	−	23.1003i	0.195765	−	0.195765i
$119$	−34.6844	+	232.957i	−0.291466	+	1.95762i
$120$	−21.5831	+	8.41688i	−0.179859	+	0.0701406i
$121$	60.2665	+	104.385i	0.498070	+	0.862683i
$122$	−16.6194	+	4.45316i	−0.136225	+	0.0365013i
$123$	0.0850074	+	0.317252i	0.000691117	+	0.00257928i
$124$	41.3088	−	23.8496i	0.333135	−	0.192336i
$125$	112.266	+	54.9657i	0.898132	+	0.439726i
$126$	−61.8496	−	9.20866i	−0.490870	−	0.0730846i
$127$	−108.082	−	108.082i	−0.851038	−	0.851038i	0.139223	−	0.990261i	$-0.455540\pi$
$127$	−108.082	−	108.082i	−0.851038	−	0.851038i	−0.990261	+	0.139223i	$0.955540\pi$
$128$	10.9282	+	2.92820i	0.0853766	+	0.0228766i
$129$	−82.4895	−	47.6253i	−0.639453	−	0.369188i
$130$	118.125	+	18.0661i	0.908655	+	0.138970i
$131$	−29.4419	−	50.9949i	−0.224748	−	0.389274i	0.731496	−	0.681846i	$-0.238822\pi$
$131$	−29.4419	−	50.9949i	−0.224748	−	0.389274i	−0.956244	+	0.292571i	$0.905489\pi$
$132$	1.58312	+	1.58312i	0.0119934	+	0.0119934i
$133$	7.67050	+	66.9951i	0.0576730	+	0.503722i
$134$		−	1.98413i		−	0.0148069i
$135$	−124.692	+	13.7761i	−0.923646	+	0.102045i
$136$	47.5831	−	82.4164i	0.349876	−	0.606003i
$137$	−127.278	+	34.1041i	−0.929039	+	0.248935i	−0.691445	−	0.722429i	$-0.743025\pi$
$137$	−127.278	+	34.1041i	−0.929039	+	0.248935i	−0.237594	+	0.971365i	$0.576359\pi$
$138$	−54.1400	−	14.5068i	−0.392319	−	0.105122i
$139$		−	68.2322i		−	0.490879i	−0.969412	−	0.245440i	$-0.921068\pi$
$139$		−	68.2322i		−	0.490879i	0.969412	−	0.245440i	$-0.0789323\pi$
$140$	−2.64308	+	69.9501i	−0.0188792	+	0.499643i
$141$	−78.2824			−0.555194
$142$	−23.1571	+	86.4236i	−0.163078	+	0.608617i
$143$	−2.98905	−	11.1553i	−0.0209025	−	0.0780091i
$144$	21.8814	+	12.6332i	0.151954	+	0.0877309i
$145$	64.5184	+	51.6806i	0.444954	+	0.356418i
$146$	−66.6174			−0.456283
$147$	42.4600	−	68.1171i	0.288844	−	0.463381i
$148$	−37.1504	+	37.1504i	−0.251016	+	0.251016i
$149$	−75.7327	+	43.7243i	−0.508273	+	0.293452i	−0.732124	−	0.681172i	$-0.761471\pi$
$149$	−75.7327	+	43.7243i	−0.508273	+	0.293452i	0.223850	+	0.974624i	$0.428137\pi$
$150$	12.6428	+	56.5188i	0.0842856	+	0.376792i
$151$	117.991	−	204.366i	0.781396	−	1.35342i	−0.149732	−	0.988727i	$-0.547841\pi$
$151$	117.991	−	204.366i	0.781396	−	1.35342i	0.931129	−	0.364691i	$-0.118825\pi$
$152$	7.05203	−	26.3185i	0.0463949	−	0.173148i
$153$	150.282	−	150.282i	0.982238	−	0.982238i
$154$	6.29297	−	2.48287i	0.0408635	−	0.0161225i
$155$	−43.3258	−	111.099i	−0.279521	−	0.716768i
$156$	27.6834	+	47.9490i	0.177458	+	0.307365i
$157$	153.871	−	41.2295i	0.980068	−	0.262609i	0.266995	−	0.963698i	$-0.413969\pi$
$157$	153.871	−	41.2295i	0.980068	−	0.262609i	0.713073	+	0.701089i	$0.247303\pi$
$158$	41.0924	+	153.359i	0.260078	+	0.970626i
$159$	132.328	−	76.3997i	0.832253	−	0.480502i
$160$	11.3668	−	25.8997i	0.0710422	−	0.161873i
$161$	−105.358	+	132.602i	−0.654395	+	0.823618i
$162$	15.7494	+	15.7494i	0.0972183	+	0.0972183i
$163$	−241.134	−	64.6117i	−1.47935	−	0.396391i	−0.573225	−	0.819398i	$-0.694308\pi$
$163$	−241.134	−	64.6117i	−1.47935	−	0.396391i	−0.906126	+	0.423007i	$0.860975\pi$
$164$	−0.347281	−	0.200503i	−0.00211756	−	0.00122258i
$165$	4.51067	−	3.31397i	0.0273374	−	0.0200846i
$166$	23.1161	+	40.0383i	0.139254	+	0.241195i
$167$	−202.799	−	202.799i	−1.21437	−	1.21437i	−0.969575	−	0.244793i	$-0.921280\pi$
$167$	−202.799	−	202.799i	−1.21437	−	1.21437i	−0.244793	−	0.969575i	$-0.578720\pi$
$168$	−26.0607	+	19.3061i	−0.155123	+	0.114917i
$169$		−	116.599i		−	0.689935i
$170$	−185.688	−	148.740i	−1.09228	−	0.874943i
$171$	30.4248	−	52.6973i	0.177923	−	0.308171i
$172$	112.331	−	30.0991i	0.653089	−	0.174995i
$173$	15.1273	+	4.05334i	0.0874409	+	0.0234297i	0.302274	−	0.953221i	$-0.402254\pi$
$173$	15.1273	+	4.05334i	0.0874409	+	0.0234297i	−0.214833	+	0.976651i	$0.568921\pi$
$174$			38.3008i			0.220119i
$175$	171.866	+	32.9698i	0.982093	+	0.188399i
$176$	−2.73350			−0.0155313
$177$	9.79385	−	36.5512i	0.0553325	−	0.206504i
$178$	29.2270	+	109.077i	0.164197	+	0.612790i
$179$	296.960	+	171.450i	1.65899	+	0.957821i	0.973180	+	0.230043i	$0.0738867\pi$
$179$	296.960	+	171.450i	1.65899	+	0.957821i	0.685813	+	0.727777i	$0.259447\pi$
$180$	39.4903	−	49.3000i	0.219391	−	0.273889i
$181$	−88.1320			−0.486917			−0.243459	−	0.969911i	$-0.578282\pi$
$181$	−88.1320			−0.486917			−0.243459	+	0.969911i	$0.578282\pi$
$182$	166.212	−	19.0302i	0.913255	−	0.104562i
$183$	−14.0923	+	14.0923i	−0.0770072	+	0.0770072i
$184$	59.2645	−	34.2164i	0.322090	−	0.185959i
$185$	77.7672	+	105.850i	0.420363	+	0.572160i
$186$	27.6253	−	47.8484i	0.148523	−	0.257250i
$187$	−5.95105	+	22.2096i	−0.0318238	+	0.118768i
$188$	67.5831	−	67.5831i	0.359485	−	0.359485i
$189$	−163.375	+	64.4591i	−0.864418	+	0.341053i
$190$	−62.3747	−	27.3747i	−0.328288	−	0.144077i
$191$	23.5422	+	40.7763i	0.123258	+	0.213488i	0.921050	−	0.389443i	$-0.127333\pi$
$191$	23.5422	+	40.7763i	0.123258	+	0.213488i	−0.797793	+	0.602932i	$0.793999\pi$
$192$	12.6583	−	3.39177i	0.0659285	−	0.0176655i
$193$	−26.4910	−	98.8657i	−0.137259	−	0.512257i	−0.999978	−	0.00657446i	$-0.997907\pi$
$193$	−26.4910	−	98.8657i	−0.137259	−	0.512257i	0.862719	−	0.505683i	$-0.168759\pi$
$194$	87.7862	−	50.6834i	0.452506	−	0.261255i
$195$	128.958	−	50.2903i	0.661322	−	0.257899i
$196$	22.1504	+	95.4639i	0.113012	+	0.487061i
$197$	163.148	+	163.148i	0.828162	+	0.828162i	0.987262	−	0.159101i	$-0.0508594\pi$
$197$	163.148	+	163.148i	0.828162	+	0.828162i	−0.159101	+	0.987262i	$0.550859\pi$
$198$	−5.89662	−	1.57999i	−0.0297809	−	0.00797977i
$199$	−295.082	−	170.365i	−1.48282	−	0.856108i	−0.483013	−	0.875613i	$-0.660458\pi$
$199$	−295.082	−	170.365i	−1.48282	−	0.856108i	−0.999810	+	0.0195053i	$0.993791\pi$
$200$	−59.7090	−	37.8792i	−0.298545	−	0.189396i
$201$	−1.14912	−	1.99034i	−0.00571702	−	0.00990217i
$202$	55.0000	+	55.0000i	0.272277	+	0.272277i
$203$	106.158	+	46.0892i	0.522944	+	0.227040i
$204$		−	110.232i		−	0.540354i
$205$	−0.626752	+	0.782441i	−0.00305733	+	0.00381678i
$206$	0.158312	−	0.274205i	0.000768507	−	0.00133109i
$207$	147.621	−	39.5549i	0.713144	−	0.191086i
$208$	−65.2953	−	17.4958i	−0.313920	−	0.0841146i
$209$			6.58312i			0.0314982i
$210$	37.8607	+	71.6996i	0.180289	+	0.341427i
$211$	113.799			0.539334			0.269667	−	0.962954i	$-0.413086\pi$
$211$	113.799			0.539334			0.269667	+	0.962954i	$0.413086\pi$
$212$	−48.2845	+	180.200i	−0.227757	+	0.850000i
$213$	26.8232	+	100.106i	0.125931	+	0.469979i
$214$	−164.819	−	95.1583i	−0.770182	−	0.444665i
$215$	−31.9265	−	288.977i	−0.148495	−	1.34408i
$216$	70.9657			0.328545
$217$	−99.3780	−	134.147i	−0.457963	−	0.618189i
$218$	−51.1161	+	51.1161i	−0.234478	+	0.234478i
$219$	−66.8258	+	38.5819i	−0.305140	+	0.176173i
$220$	−1.03314	+	6.75520i	−0.00469611	+	0.0307055i
$221$	−284.306	+	492.433i	−1.28645	+	2.22820i
$222$	−15.7507	+	58.7825i	−0.0709491	+	0.264786i
$223$	−158.916	+	158.916i	−0.712626	+	0.712626i	−0.967084	−	0.254458i	$-0.918103\pi$
$223$	−158.916	+	158.916i	−0.712626	+	0.712626i	0.254458	+	0.967084i	$0.418103\pi$
$224$	5.83138	−	39.1662i	0.0260330	−	0.174849i
$225$	−106.908	−	116.224i	−0.475145	−	0.516552i
$226$	63.8496	+	110.591i	0.282520	+	0.489340i
$227$	275.743	−	73.8850i	1.21472	−	0.325485i	0.406111	−	0.913824i	$-0.366885\pi$
$227$	275.743	−	73.8850i	1.21472	−	0.325485i	0.808614	+	0.588339i	$0.200218\pi$
$228$	−8.16845	−	30.4851i	−0.0358265	−	0.133706i
$229$	−271.368	+	156.674i	−1.18501	+	0.684167i	−0.957169	−	0.289531i	$-0.906501\pi$
$229$	−271.368	+	156.674i	−1.18501	+	0.684167i	−0.227843	+	0.973698i	$0.573167\pi$
$230$	−62.1583	−	159.391i	−0.270254	−	0.693002i
$231$	4.87469	−	6.13525i	0.0211025	−	0.0265595i
$232$	−33.0660	−	33.0660i	−0.142526	−	0.142526i
$233$	−48.8705	−	13.0948i	−0.209745	−	0.0562009i	0.152417	−	0.988316i	$-0.451294\pi$
$233$	−48.8705	−	13.0948i	−0.209745	−	0.0562009i	−0.362161	+	0.932115i	$0.617961\pi$
$234$	−130.740	−	75.4829i	−0.558719	−	0.322576i
$235$	−141.472	−	192.559i	−0.602010	−	0.819401i
$236$	23.1003	+	40.0108i	0.0978824	+	0.169537i
$237$	130.040	+	130.040i	0.548691	+	0.548691i
$238$	−305.529	−	132.648i	−1.28374	−	0.557344i
$239$			195.330i			0.817280i	0.912696	+	0.408640i	$0.133997\pi$
$239$			195.330i			0.817280i	−0.912696	+	0.408640i	$0.866003\pi$
$240$	−3.59769	−	32.5639i	−0.0149904	−	0.135683i
$241$	−46.4657	+	80.4810i	−0.192804	+	0.333946i	−0.946178	−	0.323646i	$-0.895091\pi$
$241$	−46.4657	+	80.4810i	−0.192804	+	0.333946i	0.753374	+	0.657592i	$0.228425\pi$
$242$	−164.651	+	44.1181i	−0.680377	+	0.182306i
$243$	243.037	+	65.1216i	1.00015	+	0.267990i
$244$		−	24.3325i		−	0.0997233i
$245$	244.288	−	18.6582i	0.997096	−	0.0761561i
$246$	−0.464489			−0.00188817
$247$	−42.1354	+	157.252i	−0.170589	+	0.636646i
$248$	17.4591	+	65.1584i	0.0703997	+	0.262735i
$249$	46.3769	+	26.7757i	0.186252	+	0.107533i
$250$	−116.177	+	133.240i	−0.464708	+	0.532960i
$251$	−332.665			−1.32536			−0.662679	−	0.748903i	$-0.730581\pi$
$251$	−332.665			−1.32536			−0.662679	+	0.748903i	$0.730581\pi$
$252$	35.2178	−	81.1176i	0.139753	−	0.321895i
$253$	−11.6913	+	11.6913i	−0.0462107	+	0.0462107i
$254$	187.203	−	108.082i	0.737021	−	0.425519i
$255$	−272.413	−	41.6630i	−1.06829	−	0.163384i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	26.4968	−	98.8873i	0.103100	−	0.384776i	−0.895022	−	0.446021i	$-0.852841\pi$
$257$	26.4968	−	98.8873i	0.103100	−	0.384776i	0.998123	+	0.0612455i	$0.0195073\pi$
$258$	95.2506	−	95.2506i	0.369188	−	0.369188i
$259$	143.973	+	114.392i	0.555880	+	0.441667i
$260$	−67.9156	+	154.749i	−0.261214	+	0.595190i
$261$	−52.2164	−	90.4414i	−0.200063	−	0.346519i
$262$	80.4369	−	21.5530i	0.307011	−	0.0822633i
$263$	51.7525	+	193.143i	0.196778	+	0.734384i	0.991800	+	0.127804i	$0.0407927\pi$
$263$	51.7525	+	193.143i	0.196778	+	0.734384i	−0.795022	+	0.606581i	$0.792541\pi$
$264$	−2.74205	+	1.58312i	−0.0103866	+	0.00599668i
$265$	427.073	+	187.431i	1.61160	+	0.707289i
$266$	−94.3246	−	14.0438i	−0.354604	−	0.0527962i
$267$	92.4908	+	92.4908i	0.346408	+	0.346408i
$268$	2.71037	+	0.726242i	0.0101133	+	0.00270986i
$269$	−198.535	−	114.624i	−0.738047	−	0.426112i	0.0833117	−	0.996524i	$-0.473450\pi$
$269$	−198.535	−	114.624i	−0.738047	−	0.426112i	−0.821359	+	0.570412i	$0.806784\pi$
$270$	26.8220	−	175.375i	0.0993406	−	0.649538i
$271$	−28.0911	−	48.6551i	−0.103657	−	0.179539i	0.809532	−	0.587076i	$-0.199721\pi$
$271$	−28.0911	−	48.6551i	−0.103657	−	0.179539i	−0.913189	+	0.407537i	$0.866388\pi$
$272$	95.1662	+	95.1662i	0.349876	+	0.349876i
$273$	155.711	−	115.353i	0.570369	−	0.422537i
$274$		−	186.348i		−	0.680104i
$275$	16.3034	+	5.10635i	0.0592851	+	0.0185685i
$276$	39.6332	−	68.6468i	0.143599	−	0.248720i
$277$	81.9724	−	21.9644i	0.295929	−	0.0792940i	−0.107800	−	0.994173i	$-0.534381\pi$
$277$	81.9724	−	21.9644i	0.295929	−	0.0792940i	0.403729	+	0.914879i	$0.367714\pi$
$278$	93.2070	+	24.9747i	0.335277	+	0.0898372i
$279$			150.649i			0.539961i
$280$	−94.5862	−	29.2140i	−0.337808	−	0.104336i
$281$	136.201			0.484699			0.242350	−	0.970189i	$-0.422082\pi$
$281$	136.201			0.484699			0.242350	+	0.970189i	$0.422082\pi$
$282$	28.6533	−	106.936i	0.101608	−	0.379205i
$283$	81.4189	+	303.860i	0.287699	+	1.07371i	0.946844	+	0.321693i	$0.104252\pi$
$283$	81.4189	+	303.860i	0.287699	+	1.07371i	−0.659145	+	0.752016i	$0.729082\pi$
$284$	−109.581	−	63.2665i	−0.385848	−	0.222769i
$285$	−78.4240	+	8.66437i	−0.275172	+	0.0304013i
$286$	16.3325			0.0571066
$287$	−0.558942	+	1.28742i	−0.00194753	+	0.00448578i
$288$	−25.2665	+	25.2665i	−0.0877309	+	0.0877309i
$289$	730.126	−	421.538i	2.52639	−	1.45861i
$290$	−94.2123	+	69.2173i	−0.324870	+	0.238680i
$291$	58.7072	−	101.684i	0.201743	−	0.349429i
$292$	24.3837	−	91.0010i	0.0835057	−	0.311647i
$293$	−184.699	+	184.699i	−0.630373	+	0.630373i	−0.948162	−	0.317789i	$-0.897060\pi$
$293$	−184.699	+	184.699i	−0.630373	+	0.630373i	0.317789	+	0.948162i	$0.397060\pi$
$294$	77.5082	+	82.9340i	0.263633	+	0.282088i
$295$	107.608	−	41.9645i	0.364774	−	0.142253i
$296$	−37.1504	−	64.3463i	−0.125508	−	0.217386i
$297$	−16.5618	+	4.43771i	−0.0557635	+	0.0149418i
$298$	−32.0084	−	119.457i	−0.107411	−	0.400863i
$299$	−354.102	+	204.441i	−1.18429	+	0.683748i
$300$	−81.8338	−	3.41688i	−0.272779	−	0.0113896i
$301$	−149.385	−	378.625i	−0.496296	−	1.25789i
$302$	235.982	+	235.982i	0.781396	+	0.781396i
$303$	87.0256	+	23.3184i	0.287213	+	0.0769586i
$304$	33.3706	+	19.2665i	0.109772	+	0.0633766i
$305$	−60.1320	−	9.19662i	−0.197154	−	0.0301529i
$306$	150.282	+	260.297i	0.491119	+	0.850643i
$307$	−370.647	−	370.647i	−1.20732	−	1.20732i	−0.971892	−	0.235426i	$-0.924352\pi$
$307$	−370.647	−	370.647i	−1.20732	−	1.20732i	−0.235426	−	0.971892i	$-0.575648\pi$
$308$	1.08828	+	9.50516i	0.00353337	+	0.0308609i
$309$		−	0.366750i		−	0.00118689i
$310$	167.622	−	18.5191i	0.540717	−	0.0597391i
$311$	219.540	−	380.254i	0.705915	−	1.22268i	−0.260445	−	0.965489i	$-0.583869\pi$
$311$	219.540	−	380.254i	0.705915	−	1.22268i	0.966360	−	0.257193i	$-0.0827975\pi$
$312$	−75.6324	+	20.2656i	−0.242411	+	0.0649540i
$313$	−200.972	−	53.8502i	−0.642082	−	0.172045i	−0.0769359	−	0.997036i	$-0.524514\pi$
$313$	−200.972	−	53.8502i	−0.642082	−	0.172045i	−0.565146	+	0.824991i	$0.691180\pi$
$314$			225.282i			0.717460i
$315$	−187.152	−	117.691i	−0.594134	−	0.373624i
$316$	−224.533			−0.710547
$317$	106.760	−	398.433i	0.336781	−	1.25689i	−0.565144	−	0.824993i	$-0.691179\pi$
$317$	106.760	−	398.433i	0.336781	−	1.25689i	0.901925	−	0.431893i	$-0.142154\pi$
$318$	55.9285	+	208.728i	0.175876	+	0.656377i
$319$	9.78456	+	5.64912i	0.0306726	+	0.0177088i
$320$	31.2192	+	25.0072i	0.0975600	+	0.0781476i
$321$	−220.446			−0.686748
$322$	−142.575	−	192.457i	−0.442779	−	0.597692i
$323$	229.190	−	229.190i	0.709567	−	0.709567i
$324$	−27.2787	+	15.7494i	−0.0841936	+	0.0486092i
$325$	356.758	+	226.326i	1.09772	+	0.696388i
$326$	176.523	−	305.746i	0.541480	−	0.937871i
$327$	−21.6718	+	80.8802i	−0.0662746	+	0.247340i
$328$	0.401005	−	0.401005i	0.00122258	−	0.00122258i
$329$	−261.912	−	208.099i	−0.796086	−	0.632520i
$330$	2.87594	+	7.37469i	0.00871498	+	0.0223475i
$331$	186.690	+	323.357i	0.564018	+	0.976908i	0.997140	+	0.0755730i	$0.0240786\pi$
$331$	186.690	+	323.357i	0.564018	+	0.976908i	−0.433122	+	0.901335i	$0.642588\pi$
$332$	−63.1544	+	16.9222i	−0.190224	+	0.0509704i
$333$	−42.9467	−	160.279i	−0.128969	−	0.481319i
$334$	351.259	−	202.799i	1.05167	−	0.607184i
$335$	2.81914	−	6.42356i	0.00841534	−	0.0191748i
$336$	−16.8338	−	42.6660i	−0.0501005	−	0.126982i
$337$	259.016	+	259.016i	0.768593	+	0.768593i	0.977859	−	0.209266i	$-0.0671074\pi$
$337$	259.016	+	259.016i	0.768593	+	0.768593i	−0.209266	+	0.977859i	$0.567107\pi$
$338$	159.277	+	42.6782i	0.471234	+	0.126267i
$339$	128.099	+	73.9578i	0.377872	+	0.218165i
$340$	271.150	−	199.212i	0.797499	−	0.585918i
$341$	−8.14912	−	14.1147i	−0.0238977	−	0.0413921i
$342$	60.8496	+	60.8496i	0.177923	+	0.177923i
$343$	323.136	−	115.030i	0.942089	−	0.335364i
$344$			164.464i			0.478094i
$345$	−154.665	−	123.890i	−0.448304	−	0.359101i
$346$	−11.0739	+	19.1806i	−0.0320056	+	0.0554353i
$347$	−319.953	+	85.7311i	−0.922055	+	0.247064i	−0.688463	−	0.725271i	$-0.741714\pi$
$347$	−319.953	+	85.7311i	−0.922055	+	0.247064i	−0.233591	+	0.972335i	$0.575048\pi$
$348$	−52.3198	−	14.0190i	−0.150344	−	0.0402846i
$349$			383.298i			1.09828i	0.835732	+	0.549138i	$0.185044\pi$
$349$			383.298i			1.09828i	−0.835732	+	0.549138i	$0.814956\pi$
$350$	−107.945	+	222.706i	−0.308414	+	0.636302i
$351$	−424.016			−1.20802
$352$	1.00053	−	3.73403i	0.00284242	−	0.0106080i
$353$	−144.351	−	538.726i	−0.408927	−	1.52614i	−0.796697	−	0.604379i	$-0.793421\pi$
$353$	−144.351	−	538.726i	−0.408927	−	1.52614i	0.387770	−	0.921756i	$-0.373246\pi$
$354$	46.3450	+	26.7573i	0.130918	+	0.0755856i
$355$	−197.765	+	246.891i	−0.557085	+	0.695468i
$356$	−159.699			−0.448593
$357$	−383.309	+	43.8864i	−1.07369	+	0.122931i
$358$	−342.900	+	342.900i	−0.957821	+	0.957821i
$359$	190.670	−	110.083i	0.531113	−	0.306638i	−0.210357	−	0.977625i	$-0.567462\pi$
$359$	190.670	−	110.083i	0.531113	−	0.306638i	0.741470	+	0.670987i	$0.234129\pi$
$360$	52.8906	+	71.9898i	0.146918	+	0.199972i
$361$	−134.100	+	232.268i	−0.371469	+	0.643403i
$362$	32.2585	−	120.391i	0.0891120	−	0.332571i
$363$	−139.615	+	139.615i	−0.384614	+	0.384614i
$364$	−34.8421	+	234.016i	−0.0957202	+	0.642901i
$365$	−215.672	−	94.6529i	−0.590881	−	0.259323i
$366$	−14.0923	−	24.4086i	−0.0385036	−	0.0666902i
$367$	−473.906	+	126.983i	−1.29130	+	0.346002i	−0.838153	−	0.545435i	$-0.816365\pi$
$367$	−473.906	+	126.983i	−1.29130	+	0.346002i	−0.453145	+	0.891437i	$0.649698\pi$
$368$	25.0481	+	93.4809i	0.0680656	+	0.254024i
$369$	1.09682	−	0.633250i	0.00297241	−	0.00171612i
$370$	−173.058	+	67.4883i	−0.467724	+	0.182401i
$371$	645.830	+	96.1563i	1.74078	+	0.259181i
$372$	55.2506	+	55.2506i	0.148523	+	0.148523i
$373$	−42.3394	−	11.3448i	−0.113510	−	0.0304150i	0.201617	−	0.979465i	$-0.435380\pi$
$373$	−42.3394	−	11.3448i	−0.113510	−	0.0304150i	−0.315127	+	0.949049i	$0.602047\pi$
$374$	−28.1607	−	16.2586i	−0.0752959	−	0.0434721i
$375$	−39.3736	+	200.941i	−0.104996	+	0.535844i
$376$	67.5831	+	117.057i	0.179742	+	0.311323i
$377$	197.567	+	197.567i	0.524051	+	0.524051i
$378$	−28.2533	−	246.768i	−0.0747443	−	0.652825i
$379$		−	393.135i		−	1.03729i	−0.854988	−	0.518647i	$-0.826436\pi$
$379$		−	393.135i		−	1.03729i	0.854988	−	0.518647i	$-0.173564\pi$
$380$	60.2252	−	75.1856i	0.158487	−	0.197857i
$381$	125.193	−	216.840i	0.328589	−	0.569134i
$382$	−64.3185	+	17.2341i	−0.168373	+	0.0451154i
$383$	−115.258	−	30.8833i	−0.300935	−	0.0806352i	0.105192	−	0.994452i	$-0.466454\pi$
$383$	−115.258	−	30.8833i	−0.300935	−	0.0806352i	−0.406127	+	0.913817i	$0.633121\pi$
$384$			18.5330i			0.0482630i
$385$	23.9011	+	0.903109i	0.0620807	+	0.00234574i
$386$	144.749			0.374998
$387$	−95.0623	+	354.777i	−0.245639	+	0.916738i
$388$	37.1028	+	138.470i	0.0956258	+	0.356880i
$389$	−369.542	−	213.355i	−0.949979	−	0.548471i	−0.0569045	−	0.998380i	$-0.518123\pi$
$389$	−369.542	−	213.355i	−0.949979	−	0.548471i	−0.893074	+	0.449909i	$0.851456\pi$
$390$	21.4960	+	194.567i	0.0551180	+	0.498890i
$391$	814.061			2.08200
$392$	−138.514	−	4.68424i	−0.353351	−	0.0119496i
$393$	68.2059	−	68.2059i	0.173552	−	0.173552i
$394$	−282.580	+	163.148i	−0.717209	+	0.414081i
$395$	−84.8637	+	554.880i	−0.214845	+	1.40476i
$396$	4.31662	−	7.47661i	0.0109006	−	0.0188803i
$397$	−28.4186	+	106.060i	−0.0715835	+	0.267153i	−0.992437	−	0.122756i	$-0.960827\pi$
$397$	−28.4186	+	106.060i	−0.0715835	+	0.267153i	0.920853	+	0.389909i	$0.127494\pi$
$398$	340.731	−	340.731i	0.856108	−	0.856108i
$399$	−102.753	+	40.5409i	−0.257527	+	0.101606i
$400$	73.5990	−	67.6992i	0.183997	−	0.169248i
$401$	−39.4499	−	68.3292i	−0.0983787	−	0.170397i	0.812635	−	0.582773i	$-0.198032\pi$
$401$	−39.4499	−	68.3292i	−0.0983787	−	0.170397i	−0.911014	+	0.412376i	$0.864699\pi$
$402$	3.13946	−	0.841215i	0.00780959	−	0.00209257i
$403$	−104.317	−	389.317i	−0.258852	−	0.966048i
$404$	−95.2628	+	55.0000i	−0.235799	+	0.136139i
$405$	28.6107	+	73.3655i	0.0706437	+	0.181149i
$406$	−101.815	+	128.144i	−0.250777	+	0.315626i
$407$	12.6938	+	12.6938i	0.0311888	+	0.0311888i
$408$	150.580	+	40.3478i	0.369069	+	0.0988917i
$409$	340.819	+	196.772i	0.833298	+	0.481105i	0.854981	−	0.518660i	$-0.173569\pi$
$409$	340.819	+	196.772i	0.833298	+	0.481105i	−0.0216824	+	0.999765i	$0.506902\pi$
$410$	−0.839427	−	1.14255i	−0.00204738	−	0.00278671i
$411$	−107.925	−	186.931i	−0.262591	−	0.454821i
$412$	0.316625	+	0.316625i	0.000768507	+	0.000768507i
$413$	129.932	−	96.2555i	0.314606	−	0.233064i
$414$			216.132i			0.522058i
$415$	17.9496	+	162.467i	0.0432519	+	0.391487i
$416$	47.7995	−	82.7912i	0.114903	−	0.199017i
$417$	107.963	−	28.9285i	0.258904	−	0.0693730i
$418$	−8.99271	−	2.40959i	−0.0215137	−	0.00576457i
$419$		−	165.330i		−	0.394582i	−0.980345	−	0.197291i	$-0.936786\pi$
$419$		−	165.330i		−	0.394582i	0.980345	−	0.197291i	$-0.0632144\pi$
$420$	−111.802	+	25.4747i	−0.266194	+	0.0606542i
$421$	163.631			0.388672			0.194336	−	0.980935i	$-0.437745\pi$
$421$	163.631			0.388672			0.194336	+	0.980935i	$0.437745\pi$
$422$	−41.6535	+	155.453i	−0.0987050	+	0.368372i
$423$	78.1276	+	291.576i	0.184699	+	0.689306i
$424$	−228.485	−	131.916i	−0.538879	−	0.311122i
$425$	−389.823	−	745.376i	−0.917232	−	1.75383i
$426$	−146.565			−0.344049
$427$	−84.6110	+	9.68741i	−0.198152	+	0.0226871i
$428$	190.317	−	190.317i	0.444665	−	0.444665i
$429$	16.3836	−	9.45907i	0.0381902	−	0.0220491i
$430$	406.435	+	62.1604i	0.945198	+	0.144559i
$431$	−209.872	+	363.509i	−0.486942	+	0.843409i	−0.999887	−	0.0150126i	$-0.995221\pi$
$431$	−209.872	+	363.509i	−0.486942	+	0.843409i	0.512945	+	0.858422i	$0.328555\pi$
$432$	−25.9753	+	96.9410i	−0.0601279	+	0.224400i
$433$	−355.950	+	355.950i	−0.822055	+	0.822055i	−0.986403	−	0.164347i	$-0.947448\pi$
$433$	−355.950	+	355.950i	−0.822055	+	0.822055i	0.164347	+	0.986403i	$0.447448\pi$
$434$	219.623	−	86.6516i	0.506044	−	0.199658i
$435$	−54.4194	+	123.997i	−0.125102	+	0.285052i
$436$	−51.1161	−	88.5357i	−0.117239	−	0.203064i
$437$	225.131	−	60.3237i	0.515174	−	0.138041i
$438$	−28.2439	−	105.408i	−0.0644838	−	0.240657i
$439$	162.609	−	93.8826i	0.370409	−	0.213856i	−0.303228	−	0.952918i	$-0.598064\pi$
$439$	162.609	−	93.8826i	0.370409	−	0.213856i	0.673637	+	0.739062i	$0.264731\pi$
$440$	−8.84962	−	3.88388i	−0.0201128	−	0.00882699i
$441$	−296.090	−	90.1672i	−0.671405	−	0.204461i
$442$	−568.612	−	568.612i	−1.28645	−	1.28645i
$443$	−577.926	−	154.855i	−1.30457	−	0.349560i	−0.461396	−	0.887194i	$-0.652651\pi$
$443$	−577.926	−	154.855i	−1.30457	−	0.349560i	−0.843178	+	0.537635i	$0.819318\pi$
$444$	−74.5332	−	43.0317i	−0.167867	−	0.0969183i
$445$	−60.3594	+	394.659i	−0.135639	+	0.886874i
$446$	−158.916	−	275.250i	−0.356313	−	0.617152i
$447$	−101.293	−	101.293i	−0.226606	−	0.226606i
$448$	51.3677	+	22.3017i	0.114660	+	0.0497805i
$449$		−	93.8630i		−	0.209049i	−0.994522	−	0.104524i	$-0.966668\pi$
$449$		−	93.8630i		−	0.209049i	0.994522	−	0.104524i	$-0.0333321\pi$
$450$	197.896	−	103.498i	0.439770	−	0.229995i
$451$	−0.0685092	+	0.118661i	−0.000151905	+	0.000263107i
$452$	−174.440	+	46.7412i	−0.385930	+	0.103410i
$453$	373.390	+	100.050i	0.824260	+	0.220860i
$454$			403.715i			0.889240i
$455$	565.146	+	174.552i	1.24208	+	0.383631i
$456$	44.6332			0.0978799
$457$	54.8826	−	204.824i	0.120093	−	0.448194i	−0.879524	−	0.475854i	$-0.842139\pi$
$457$	54.8826	−	204.824i	0.120093	−	0.448194i	0.999617	+	0.0276604i	$0.00880571\pi$
$458$	−114.693	−	428.042i	−0.250422	−	0.934589i
$459$	731.093	+	422.096i	1.59279	+	0.919600i
$460$	240.483	−	26.5688i	0.522789	−	0.0577583i
$461$	350.396			0.760078			0.380039	−	0.924970i	$-0.375911\pi$
$461$	350.396			0.760078			0.380039	+	0.924970i	$0.375911\pi$
$462$	6.59665	+	8.90460i	0.0142785	+	0.0192740i
$463$	−327.380	+	327.380i	−0.707084	+	0.707084i	−0.965921	−	0.258837i	$-0.916661\pi$
$463$	−327.380	+	327.380i	−0.707084	+	0.707084i	0.258837	+	0.965921i	$0.416661\pi$
$464$	57.2720	−	33.0660i	0.123431	−	0.0712629i
$465$	157.421	−	115.657i	0.338540	−	0.248724i
$466$	35.7757	−	61.9653i	0.0767719	−	0.132973i
$467$	140.806	−	525.495i	0.301512	−	1.12526i	−0.634395	−	0.773009i	$-0.718751\pi$
$467$	140.806	−	525.495i	0.301512	−	1.12526i	0.935907	−	0.352248i	$-0.114582\pi$
$468$	150.966	−	150.966i	0.322576	−	0.322576i
$469$	1.44628	−	9.71386i	0.00308375	−	0.0207119i
$470$	314.823	−	122.773i	0.669837	−	0.261220i
$471$	130.474	+	225.987i	0.277014	+	0.479803i
$472$	−63.1111	+	16.9106i	−0.133710	+	0.0358275i
$473$	−10.2845	−	38.3822i	−0.0217431	−	0.0811464i
$474$	−225.235	+	130.040i	−0.475180	+	0.274345i
$475$	−163.041	−	177.249i	−0.343244	−	0.373157i
$476$	293.032	−	368.808i	0.615613	−	0.774807i
$477$	−416.631	−	416.631i	−0.873440	−	0.873440i
$478$	−266.826	−	71.4957i	−0.558213	−	0.149573i
$479$	58.5721	+	33.8166i	0.122280	+	0.0705984i	0.559892	−	0.828565i	$-0.310842\pi$
$479$	58.5721	+	33.8166i	0.122280	+	0.0705984i	−0.437612	+	0.899164i	$0.644176\pi$
$480$	45.7999	+	7.00467i	0.0954165	+	0.0145931i
$481$	221.971	+	384.465i	0.461479	+	0.799304i
$482$	−92.9315	−	92.9315i	−0.192804	−	0.192804i
$483$	−254.483	−	110.486i	−0.526881	−	0.228749i
$484$		−	241.066i		−	0.498070i
$485$	356.218	−	39.3554i	0.734470	−	0.0811451i
$486$	−177.916	+	308.159i	−0.366082	+	0.634072i
$487$	720.130	−	192.958i	1.47871	−	0.396218i	0.572799	−	0.819696i	$-0.305857\pi$
$487$	720.130	−	192.958i	1.47871	−	0.396218i	0.905907	+	0.423477i	$0.139191\pi$
$488$	33.2388	+	8.90631i	0.0681123	+	0.0182506i
$489$		−	408.937i		−	0.836271i
$490$	−63.9282	+	340.534i	−0.130466	+	0.694967i
$491$	199.061			0.405419			0.202710	−	0.979239i	$-0.435025\pi$
$491$	199.061			0.405419			0.202710	+	0.979239i	$0.435025\pi$
$492$	0.170015	−	0.634504i	0.000345559	−	0.00128964i
$493$	−143.975	−	537.320i	−0.292038	−	1.08990i
$494$	−199.387	−	115.116i	−0.403617	−	0.233029i
$495$	−16.8452	−	13.4934i	−0.0340307	−	0.0272593i
$496$	−95.3985			−0.192336
$497$	−176.368	+	406.231i	−0.354866	+	0.817367i
$498$	−53.5514	+	53.5514i	−0.107533	+	0.107533i
$499$	−471.810	+	272.400i	−0.945511	+	0.545891i	−0.891684	−	0.452659i	$-0.850476\pi$
$499$	−471.810	+	272.400i	−0.945511	+	0.545891i	−0.0538277	+	0.998550i	$0.517142\pi$
$500$	−139.486	−	207.470i	−0.278971	−	0.414940i
$501$	234.905	−	406.868i	0.468873	−	0.812111i
$502$	121.764	−	454.429i	0.242557	−	0.905237i
$503$	−38.0869	+	38.0869i	−0.0757195	+	0.0757195i	−0.743952	−	0.668233i	$-0.767051\pi$
$503$	−38.0869	+	38.0869i	−0.0757195	+	0.0757195i	0.668233	+	0.743952i	$0.267051\pi$
$504$	97.9180	+	77.7995i	0.194282	+	0.154364i
$505$	99.9144	+	256.207i	0.197850	+	0.507341i
$506$	−11.6913	−	20.2499i	−0.0231054	−	0.0400197i
$507$	184.493	−	49.4347i	0.363891	−	0.0975043i
$508$	79.1214	+	295.285i	0.155751	+	0.581270i
$509$	149.946	−	86.5714i	0.294590	−	0.170081i	−0.345420	−	0.938448i	$-0.612264\pi$
$509$	149.946	−	86.5714i	0.294590	−	0.170081i	0.640010	+	0.768367i	$0.278930\pi$
$510$	156.623	−	356.873i	0.307104	−	0.699752i
$511$	−326.144	−	48.5589i	−0.638247	−	0.0950273i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	233.464	+	62.5566i	0.455096	+	0.121943i
$514$	125.384	+	72.3906i	0.243938	+	0.140838i
$515$	0.902134	−	0.662793i	0.00175172	−	0.00128698i
$516$	95.2506	+	164.979i	0.184594	+	0.319727i
$517$	−23.0923	−	23.0923i	−0.0446660	−	0.0446660i
$518$	−208.960	+	154.800i	−0.403397	+	0.298842i
$519$			25.6541i			0.0494300i
$520$	−186.533	−	149.417i	−0.358717	−	0.287340i
$521$	−121.347	+	210.179i	−0.232912	+	0.403415i	−0.958664	−	0.284541i	$-0.908159\pi$
$521$	−121.347	+	210.179i	−0.232912	+	0.403415i	0.725752	+	0.687957i	$0.241492\pi$
$522$	142.658	−	38.2250i	0.273291	−	0.0732280i
$523$	769.970	+	206.313i	1.47222	+	0.394480i	0.903691	−	0.428185i	$-0.140847\pi$
$523$	769.970	+	206.313i	1.47222	+	0.394480i	0.568527	+	0.822665i	$0.307514\pi$
$524$			117.768i			0.224748i
$525$	20.6987	+	285.919i	0.0394262	+	0.544608i
$526$	−282.781			−0.537607
$527$	−207.690	+	775.110i	−0.394099	+	1.47080i
$528$	−1.15893	−	4.32518i	−0.00219494	−	0.00819162i
$529$	48.8266	+	28.1901i	0.0922998	+	0.0532893i
$530$	−412.356	+	514.787i	−0.778029	+	0.971297i
$531$	−145.916			−0.274794
$532$	53.7094	−	123.709i	0.100957	−	0.232536i
$533$	−2.39598	+	2.39598i	−0.00449527	+	0.00449527i
$534$	−160.199	+	92.4908i	−0.299998	+	0.173204i
$535$	−398.391	−	542.254i	−0.744657	−	1.01356i
$536$	−1.98413	+	3.43661i	−0.00370173	+	0.00641159i
$537$	−145.380	+	542.565i	−0.270726	+	1.01036i
$538$	229.248	−	229.248i	0.426112	−	0.426112i
$539$	32.6188	−	7.56851i	0.0605173	−	0.0140418i
$540$	229.749	+	100.831i	0.425462	+	0.186725i
$541$	−274.812	−	475.988i	−0.507970	−	0.879829i	−0.999957	−	0.00922718i	$-0.997063\pi$
$541$	−274.812	−	475.988i	−0.507970	−	0.879829i	0.491988	−	0.870602i	$-0.336270\pi$
$542$	76.7462	−	20.5641i	0.141598	−	0.0379411i
$543$	−37.3655	−	139.450i	−0.0688130	−	0.256814i
$544$	−164.833	+	95.1662i	−0.303001	+	0.174938i
$545$	−238.115	+	92.8588i	−0.436908	+	0.170383i
$546$	100.581	+	254.927i	0.184214	+	0.466899i
$547$	469.765	+	469.765i	0.858803	+	0.858803i	0.991197	−	0.132394i	$-0.0422665\pi$
$547$	469.765	+	469.765i	0.858803	+	0.858803i	−0.132394	+	0.991197i	$0.542266\pi$
$548$	254.557	+	68.2082i	0.464519	+	0.124468i
$549$	66.5537	+	38.4248i	0.121227	+	0.0699905i
$550$	−12.9429	+	20.4018i	−0.0235325	+	0.0370942i
$551$	−79.6332	−	137.929i	−0.144525	−	0.250325i
$552$	79.2665	+	79.2665i	0.143599	+	0.143599i
$553$	89.3925	+	780.765i	0.161650	+	1.41187i
$554$			120.016i			0.216635i
$555$	−134.513	+	167.927i	−0.242366	+	0.302571i
$556$	−68.2322	+	118.182i	−0.122720	+	0.212557i
$557$	368.629	−	98.7738i	0.661811	−	0.177332i	0.0877479	−	0.996143i	$-0.472033\pi$
$557$	368.629	−	98.7738i	0.661811	−	0.177332i	0.574063	+	0.818811i	$0.305366\pi$
$558$	−205.791	−	55.1414i	−0.368800	−	0.0988197i
$559$		−	982.665i		−	1.75790i
$560$	74.5280	−	118.514i	0.133086	−	0.211632i
$561$	−37.6650			−0.0671390
$562$	−49.8528	+	186.053i	−0.0887061	+	0.331056i
$563$	−47.2076	−	176.181i	−0.0838502	−	0.312933i	0.911244	−	0.411867i	$-0.135123\pi$
$563$	−47.2076	−	176.181i	−0.0838502	−	0.312933i	−0.995094	+	0.0989343i	$0.968457\pi$
$564$	135.589	+	78.2824i	0.240406	+	0.138799i
$565$	49.5789	+	448.755i	0.0877503	+	0.794256i
$566$	−444.881			−0.786009
$567$	65.6254	+	88.5856i	0.115741	+	0.156236i
$568$	126.533	−	126.533i	0.222769	−	0.222769i
$569$	−647.396	+	373.774i	−1.13778	+	0.656897i	−0.945880	−	0.324518i	$-0.894798\pi$
$569$	−647.396	+	373.774i	−1.13778	+	0.656897i	−0.191899	+	0.981415i	$0.561465\pi$
$570$	16.8694	−	110.301i	0.0295955	−	0.193510i
$571$	−92.0727	+	159.475i	−0.161248	+	0.279290i	−0.935317	−	0.353812i	$-0.884885\pi$
$571$	−92.0727	+	159.475i	−0.161248	+	0.279290i	0.774068	+	0.633102i	$0.218219\pi$
$572$	−5.97811	+	22.3106i	−0.0104512	+	0.0390046i
$573$	−54.5384	+	54.5384i	−0.0951805	+	0.0951805i
$574$	−1.55406	−	1.23476i	−0.00270742	−	0.00215114i
$575$	25.2335	−	604.339i	0.0438843	−	1.05102i
$576$	−25.2665	−	43.7629i	−0.0438654	−	0.0759772i
$577$	−957.887	+	256.665i	−1.66012	+	0.444827i	−0.962420	−	0.271567i	$-0.912458\pi$
$577$	−957.887	+	256.665i	−1.66012	+	0.444827i	−0.697696	+	0.716394i	$0.745791\pi$
$578$	308.588	+	1151.66i	0.533888	+	1.99250i
$579$	145.202	−	83.8325i	0.250781	−	0.144788i
$580$	−60.0685	−	154.032i	−0.103566	−	0.265572i
$581$	83.9866	+	212.869i	0.144555	+	0.366383i
$582$	117.414	+	117.414i	0.201743	+	0.201743i
$583$	61.5721	+	16.4982i	0.105613	+	0.0282988i
$584$	115.385	+	66.6174i	0.197577	+	0.114071i
$585$	−316.018	−	430.135i	−0.540201	−	0.735273i
$586$	−184.699	−	319.908i	−0.315186	−	0.545919i
$587$	−103.786	−	103.786i	−0.176808	−	0.176808i	0.613155	−	0.789963i	$-0.289900\pi$
$587$	−103.786	−	103.786i	−0.176808	−	0.176808i	−0.789963	+	0.613155i	$0.789900\pi$
$588$	−141.660	+	75.5222i	−0.240918	+	0.128439i
$589$			229.749i			0.390067i
$590$	17.9372	+	162.356i	0.0304021	+	0.275179i
$591$	−188.976	+	327.316i	−0.319757	+	0.553835i
$592$	101.497	−	27.1960i	0.171447	−	0.0459391i
$593$	−89.9380	−	24.0988i	−0.151666	−	0.0406388i	0.182187	−	0.983264i	$-0.441682\pi$
$593$	−89.9380	−	24.0988i	−0.151666	−	0.0406388i	−0.333853	+	0.942625i	$0.608349\pi$
$594$		−	24.2481i		−	0.0408217i
$595$	−800.669	−	863.552i	−1.34566	−	1.45135i
$596$	174.897			0.293452
$597$	144.460	−	539.133i	0.241977	−	0.903071i
$598$	−149.661	−	558.542i	−0.250269	−	0.934017i
$599$	−469.928	−	271.313i	−0.784520	−	0.452943i	0.0535096	−	0.998567i	$-0.482959\pi$
$599$	−469.928	−	271.313i	−0.784520	−	0.452943i	−0.838030	+	0.545624i	$0.816293\pi$
$600$	34.6208	−	110.536i	0.0577013	−	0.184227i
$601$	422.829			0.703542			0.351771	−	0.936086i	$-0.385580\pi$
$601$	422.829			0.703542			0.351771	+	0.936086i	$0.385580\pi$
$602$	571.890	−	65.4777i	0.949983	−	0.108767i
$603$	−6.26650	+	6.26650i	−0.0103922	+	0.0103922i
$604$	−408.732	+	235.982i	−0.676709	+	0.390698i
$605$	−595.738	−	91.1125i	−0.984691	−	0.150599i
$606$	−63.7072	+	110.344i	−0.105127	+	0.182086i
$607$	−53.2050	+	198.564i	−0.0876524	+	0.327123i	−0.995803	−	0.0915198i	$-0.970828\pi$
$607$	−53.2050	+	198.564i	−0.0876524	+	0.327123i	0.908151	+	0.418643i	$0.137494\pi$
$608$	−38.5330	+	38.5330i	−0.0633766	+	0.0633766i
$609$	−27.9183	+	187.512i	−0.0458428	+	0.307902i
$610$	34.5727	−	78.7757i	0.0566765	−	0.129140i
$611$	−403.805	−	699.411i	−0.660892	−	1.14470i
$612$	−410.579	+	110.014i	−0.670881	+	0.179762i
$613$	65.0019	+	242.590i	0.106039	+	0.395743i	0.998461	−	0.0554588i	$-0.0176621\pi$
$613$	65.0019	+	242.590i	0.106039	+	0.395743i	−0.892422	+	0.451202i	$0.850995\pi$
$614$	641.979	−	370.647i	1.04557	−	0.603659i
$615$	−1.50377	−	0.659966i	−0.00244515	−	0.00107312i
$616$	−13.3826	−	1.99251i	−0.0217250	−	0.00323460i
$617$	206.947	+	206.947i	0.335409	+	0.335409i	0.854636	−	0.519227i	$-0.173780\pi$
$617$	206.947	+	206.947i	0.335409	+	0.335409i	−0.519227	+	0.854636i	$0.673780\pi$
$618$	0.500990	+	0.134240i	0.000810664	+	0.000217217i
$619$	−408.698	−	235.962i	−0.660255	−	0.381199i	0.132119	−	0.991234i	$-0.457822\pi$
$619$	−408.698	−	235.962i	−0.660255	−	0.381199i	−0.792374	+	0.610035i	$0.791155\pi$
$620$	−36.0565	+	235.755i	−0.0581556	+	0.380250i
$621$	303.524	+	525.719i	0.488766	+	0.846568i
$622$	439.079	+	439.079i	0.705915	+	0.705915i
$623$	63.5805	+	555.319i	0.102055	+	0.891363i
$624$		−	110.734i		−	0.177458i
$625$	−565.433	+	266.291i	−0.904692	+	0.426066i
$626$	147.122	−	254.822i	0.235018	−	0.407064i
$627$	−10.4164	+	2.79106i	−0.0166130	+	0.00445145i
$628$	−307.741	−	82.4591i	−0.490034	−	0.131304i
$629$		−	883.865i		−	1.40519i
$630$	229.272	−	212.577i	0.363924	−	0.337423i
$631$	−675.457			−1.07045			−0.535227	−	0.844708i	$-0.679774\pi$
$631$	−675.457			−1.07045			−0.535227	+	0.844708i	$0.679774\pi$
$632$	82.1848	−	306.718i	0.130039	−	0.485313i
$633$	48.2478	+	180.063i	0.0762208	+	0.284460i
$634$	505.192	+	291.673i	0.796833	+	0.460052i
$635$	759.632	−	83.9250i	1.19627	−	0.132165i
$636$	−305.599			−0.480502
$637$	827.611	+	27.9881i	1.29923	+	0.0439373i
$638$	−11.2982	+	11.2982i	−0.0177088	+	0.0177088i
$639$	346.090	−	199.815i	0.541612	−	0.312700i
$640$	−45.5875	+	33.4929i	−0.0712305	+	0.0523327i
$641$	−21.7481	+	37.6688i	−0.0339284	+	0.0587657i	−0.882491	−	0.470329i	$-0.844135\pi$
$641$	−21.7481	+	37.6688i	−0.0339284	+	0.0587657i	0.848563	+	0.529095i	$0.177468\pi$
$642$	80.6889	−	301.135i	0.125684	−	0.469058i
$643$	344.145	−	344.145i	0.535218	−	0.535218i	−0.386902	−	0.922121i	$-0.626455\pi$
$643$	344.145	−	344.145i	0.535218	−	0.535218i	0.922121	+	0.386902i	$0.126455\pi$
$644$	315.087	−	124.317i	0.489266	−	0.193038i
$645$	443.707	−	173.035i	0.687918	−	0.268271i
$646$	229.190	+	396.969i	0.354783	+	0.614503i
$647$	898.982	−	240.882i	1.38946	−	0.372305i	0.514913	−	0.857242i	$-0.327824\pi$
$647$	898.982	−	240.882i	1.38946	−	0.372305i	0.874549	+	0.484937i	$0.161157\pi$
$648$	−11.5293	−	43.0281i	−0.0177922	−	0.0664014i
$649$	13.6712	−	7.89307i	0.0210650	−	0.0121619i
$650$	−439.749	+	404.499i	−0.676537	+	0.622306i
$651$	170.125	−	214.119i	0.261329	−	0.328908i
$652$	353.045	+	353.045i	0.541480	+	0.541480i
$653$	561.631	+	150.489i	0.860078	+	0.230457i	0.661793	−	0.749687i	$-0.269796\pi$
$653$	561.631	+	150.489i	0.860078	+	0.230457i	0.198286	+	0.980144i	$0.436463\pi$
$654$	−102.552	−	59.2084i	−0.156807	−	0.0905328i
$655$	291.035	+	44.5111i	0.444329	+	0.0679559i
$656$	0.401005	+	0.694561i	0.000611288	+	0.00105878i
$657$	210.398	+	210.398i	0.320241	+	0.320241i
$658$	380.135	−	281.609i	0.577713	−	0.427978i
$659$			217.266i			0.329691i	0.986319	+	0.164846i	$0.0527126\pi$
$659$			217.266i			0.329691i	−0.986319	+	0.164846i	$0.947287\pi$
$660$	−11.1267	+	1.22929i	−0.0168586	+	0.00186256i
$661$	−61.8693	+	107.161i	−0.0935995	+	0.162119i	−0.909023	−	0.416745i	$-0.863171\pi$
$661$	−61.8693	+	107.161i	−0.0935995	+	0.162119i	0.815424	+	0.578865i	$0.196504\pi$
$662$	−510.047	+	136.667i	−0.770463	+	0.206445i
$663$	−899.706	−	241.076i	−1.35702	−	0.363613i
$664$		−	92.4645i		−	0.139254i
$665$	−285.419	−	179.487i	−0.429201	−	0.269905i
$666$	234.665			0.352350
$667$	103.530	−	386.380i	0.155218	−	0.579280i
$668$	148.460	+	554.059i	0.222245	+	0.829429i
$669$	−318.825	−	184.074i	−0.476570	−	0.275148i
$670$	7.74286	+	6.20220i	0.0115565	+	0.00925701i
$671$	−8.31411			−0.0123906
$672$	64.4445	−	7.37848i	0.0958995	−	0.0109799i
$673$	−129.111	+	129.111i	−0.191844	+	0.191844i	−0.796493	−	0.604648i	$-0.793314\pi$
$673$	−129.111	+	129.111i	−0.191844	+	0.191844i	0.604648	+	0.796493i	$0.293314\pi$
$674$	−448.629	+	259.016i	−0.665621	+	0.384297i
$675$	336.016	−	529.662i	0.497801	−	0.784684i
$676$	−116.599	+	201.955i	−0.172484	+	0.298751i
$677$	114.123	−	425.912i	0.168571	−	0.629116i	−0.828986	−	0.559269i	$-0.811082\pi$
$677$	114.123	−	425.912i	0.168571	−	0.629116i	0.997558	−	0.0698477i	$-0.0222513\pi$
$678$	−147.916	+	147.916i	−0.218165	+	0.218165i
$679$	466.726	−	184.145i	0.687373	−	0.271201i
$680$	172.881	+	443.314i	0.254237	+	0.651933i
$681$	233.814	+	404.978i	0.343339	+	0.594681i
$682$	22.2638	−	5.96557i	0.0326449	−	0.00874717i
$683$	−12.8921	−	48.1139i	−0.0188757	−	0.0704449i	0.955846	−	0.293869i	$-0.0949431\pi$
$683$	−12.8921	−	48.1139i	−0.0188757	−	0.0704449i	−0.974721	+	0.223424i	$0.928276\pi$
$684$	−105.395	+	60.8496i	−0.154086	+	0.0889614i
$685$	264.772	−	603.297i	0.386528	−	0.880726i
$686$	38.8576	+	483.516i	0.0566437	+	0.704834i
$687$	−362.955	−	362.955i	−0.528319	−	0.528319i
$688$	−224.663	−	60.1982i	−0.326545	−	0.0874974i
$689$	1365.18	+	788.188i	1.98139	+	1.14396i
$690$	225.848	−	165.929i	0.327316	−	0.240477i
$691$	−163.975	−	284.013i	−0.237301	−	0.411017i	0.722638	−	0.691227i	$-0.242929\pi$
$691$	−163.975	−	284.013i	−0.237301	−	0.411017i	−0.959939	+	0.280209i	$0.909596\pi$
$692$	−22.1479	−	22.1479i	−0.0320056	−	0.0320056i
$693$	−27.7169	−	12.0335i	−0.0399955	−	0.0173643i
$694$		−	468.444i		−	0.674991i
$695$	266.269	+	213.287i	0.383122	+	0.306888i
$696$	38.3008	−	66.3389i	0.0550298	−	0.0953144i
$697$	6.51631	−	1.74604i	0.00934908	−	0.00250508i
$698$	−523.595	−	140.297i	−0.750136	−	0.200998i
$699$		−	82.8789i		−	0.118568i
$700$	−264.711	−	228.972i	−0.378159	−	0.327102i
$701$	−85.2715			−0.121643			−0.0608213	−	0.998149i	$-0.519372\pi$
$701$	−85.2715			−0.121643			−0.0608213	+	0.998149i	$0.519372\pi$
$702$	155.201	−	579.216i	0.221083	−	0.825095i
$703$	−65.4964	−	244.436i	−0.0931670	−	0.347704i
$704$	4.73456	+	2.73350i	0.00672523	+	0.00388281i
$705$	244.703	−	305.489i	0.347097	−	0.433318i
$706$	788.749			1.11721
$707$	229.177	+	309.359i	0.324154	+	0.437565i
$708$	−53.5146	+	53.5146i	−0.0755856	+	0.0755856i
$709$	−185.775	+	107.257i	−0.262024	+	0.151280i	−0.625258	−	0.780418i	$-0.715006\pi$
$709$	−185.775	+	107.257i	−0.262024	+	0.151280i	0.363233	+	0.931698i	$0.381673\pi$
$710$	−264.873	−	360.520i	−0.373060	−	0.507775i
$711$	354.573	−	614.138i	0.498696	−	0.863766i
$712$	58.4540	−	218.153i	0.0820983	−	0.306395i
$713$	−408.024	+	408.024i	−0.572263	+	0.572263i
$714$	80.3508	−	539.673i	0.112536	−	0.755844i
$715$	52.8759	+	23.2059i	0.0739524	+	0.0324558i
$716$	−342.900	−	593.920i	−0.478910	−	0.829497i
$717$	−309.068	+	82.8144i	−0.431057	+	0.115501i
$718$	80.5864	+	300.753i	0.112237	+	0.418876i
$719$	−849.937	+	490.711i	−1.18211	+	0.682491i	−0.956502	−	0.291727i	$-0.905770\pi$
$719$	−849.937	+	490.711i	−1.18211	+	0.682491i	−0.225608	+	0.974218i	$0.572437\pi$
$720$	−117.699	+	45.8997i	−0.163471	+	0.0637497i
$721$	0.974937	−	1.22705i	0.00135220	−	0.00170187i
$722$	−268.201	−	268.201i	−0.371469	−	0.371469i
$723$	−147.044	−	39.4003i	−0.203380	−	0.0544956i
$724$	152.649	+	88.1320i	0.210841	+	0.121729i
$725$	−403.356	+	90.2279i	−0.556354	+	0.124452i
$726$	−139.615	−	241.820i	−0.192307	−	0.333085i
$727$	10.5831	+	10.5831i	0.0145573	+	0.0145573i	0.714348	−	0.699791i	$-0.246723\pi$
$727$	10.5831	+	10.5831i	0.0145573	+	0.0145573i	−0.699791	+	0.714348i	$0.746723\pi$
$728$	−306.919	−	133.251i	−0.421591	−	0.183037i
$729$			270.419i			0.370946i
$730$	208.240	−	259.968i	0.285260	−	0.356120i
$731$	−978.217	+	1694.32i	−1.33819	+	2.31781i
$732$	38.5009	−	10.3163i	0.0525969	−	0.0140933i
$733$	1050.80	+	281.561i	1.43356	+	0.384121i	0.890273	−	0.455427i	$-0.150514\pi$
$733$	1050.80	+	281.561i	1.43356	+	0.384121i	0.543285	+	0.839548i	$0.317180\pi$
$734$		−	693.847i		−	0.945296i
$735$	133.094	+	378.623i	0.181080	+	0.515134i
$736$	−136.865			−0.185959
$737$	0.248148	−	0.926100i	0.000336700	−	0.00125658i
$738$	0.463571	+	1.73007i	0.000628145	+	0.00234427i
$739$	−319.303	−	184.350i	−0.432074	−	0.249458i	0.268156	−	0.963376i	$-0.413586\pi$
$739$	−319.303	−	184.350i	−0.432074	−	0.249458i	−0.700230	+	0.713917i	$0.746919\pi$
$740$	−28.8471	−	261.104i	−0.0389825	−	0.352843i
$741$	−266.681			−0.359893
$742$	−367.742	+	847.025i	−0.495609	+	1.14154i
$743$	−45.4536	+	45.4536i	−0.0611758	+	0.0611758i	−0.737033	−	0.675857i	$-0.763774\pi$
$743$	−45.4536	+	45.4536i	−0.0611758	+	0.0611758i	0.675857	+	0.737033i	$0.263774\pi$
$744$	−95.6969	+	55.2506i	−0.128625	+	0.0742616i
$745$	66.1035	−	432.217i	0.0887296	−	0.580158i
$746$	30.9946	−	53.6842i	0.0415477	−	0.0719627i
$747$	53.4455	−	199.461i	0.0715469	−	0.267017i
$748$	32.5171	−	32.5171i	0.0434721	−	0.0434721i
$749$	−737.555	−	586.015i	−0.984719	−	0.782396i
$750$	−260.079	−	127.335i	−0.346772	−	0.169780i
$751$	−392.273	−	679.437i	−0.522334	−	0.904710i	−0.999662	−	0.0259846i	$-0.991728\pi$
$751$	−392.273	−	679.437i	−0.522334	−	0.904710i	0.477328	−	0.878725i	$-0.341605\pi$
$752$	−184.641	+	49.4743i	−0.245533	+	0.0657903i
$753$	−141.041	−	526.371i	−0.187305	−	0.699031i
$754$	−342.197	+	197.567i	−0.453842	+	0.262026i
$755$	428.690	+	1099.28i	0.567801	+	1.45599i
$756$	347.433	+	51.7286i	0.459567	+	0.0684240i
$757$	−535.185	−	535.185i	−0.706981	−	0.706981i	0.258918	−	0.965899i	$-0.416634\pi$
$757$	−535.185	−	535.185i	−0.706981	−	0.706981i	−0.965899	+	0.258918i	$0.916634\pi$
$758$	537.032	+	143.897i	0.708485	+	0.189838i
$759$	−23.4558	−	13.5422i	−0.0309035	−	0.0178421i
$760$	80.6614	+	109.789i	0.106133	+	0.144459i
$761$	44.4816	+	77.0444i	0.0584515	+	0.101241i	0.893770	−	0.448525i	$-0.148050\pi$
$761$	44.4816	+	77.0444i	0.0584515	+	0.101241i	−0.835319	+	0.549766i	$0.814717\pi$
$762$	250.385	+	250.385i	0.328589	+	0.328589i
$763$	−287.513	+	212.994i	−0.376819	+	0.279153i
$764$		−	94.1688i		−	0.123258i
$765$	116.693	+	1056.23i	0.152541	+	1.38069i
$766$	84.3747	−	146.141i	0.110150	−	0.190785i
$767$	377.085	−	101.040i	0.491636	−	0.131733i
$768$	−25.3165	−	6.78355i	−0.0329643	−	0.00883275i
$769$			999.457i			1.29968i	0.760069	+	0.649842i	$0.225165\pi$
$769$			999.457i			1.29968i	−0.760069	+	0.649842i	$0.774835\pi$
$770$	−9.98207	+	32.3189i	−0.0129637	+	0.0419726i
$771$	167.702			0.217512
$772$	−52.9819	+	197.731i	−0.0686295	+	0.256129i
$773$	93.0266	+	347.180i	0.120345	+	0.449133i	0.999631	−	0.0271607i	$-0.00864657\pi$
$773$	93.0266	+	347.180i	0.120345	+	0.449133i	−0.879286	+	0.476294i	$0.841980\pi$
$774$	−449.840	−	259.715i	−0.581188	−	0.335549i
$775$	568.985	+	178.210i	0.734174	+	0.229949i
$776$	−202.734			−0.261255
$777$	−119.960	+	276.305i	−0.154389	+	0.355605i
$778$	426.710	−	426.710i	0.548471	−	0.548471i
$779$	1.67272	−	0.965745i	0.00214727	−	0.00123972i
$780$	−273.652	−	41.8524i	−0.350836	−	0.0536570i
$781$	−21.6174	+	37.4424i	−0.0276791	+	0.0479416i
$782$	−297.967	+	1112.03i	−0.381032	+	1.42203i
$783$	293.319	−	293.319i	0.374609	−	0.374609i
$784$	57.0983	−	187.499i	0.0728295	−	0.239157i
$785$	−320.091	+	729.345i	−0.407759	+	0.929101i
$786$	68.2059	+	118.136i	0.0867760	+	0.150300i
$787$	76.8792	−	20.5997i	0.0976864	−	0.0261750i	−0.209645	−	0.977778i	$-0.567231\pi$
$787$	76.8792	−	20.5997i	0.0976864	−	0.0261750i	0.307331	+	0.951603i	$0.400564\pi$
$788$	−119.433	−	445.728i	−0.151564	−	0.565645i
$789$	−283.666	+	163.774i	−0.359526	+	0.207572i
$790$	−726.919	−	319.026i	−0.920150	−	0.403831i
$791$	231.982	+	587.970i	0.293276	+	0.743325i
$792$	8.63325	+	8.63325i	0.0109006	+	0.0109006i
$793$	−198.600	−	53.2147i	−0.250441	−	0.0671055i
$794$	−134.478	−	77.6412i	−0.169368	−	0.0977849i
$795$	−115.503	+	755.216i	−0.145287	+	0.949957i
$796$	340.731	+	590.163i	0.428054	+	0.741411i
$797$	−320.109	−	320.109i	−0.401642	−	0.401642i	0.477169	−	0.878811i	$-0.341663\pi$
$797$	−320.109	−	320.109i	−0.401642	−	0.401642i	−0.878811	+	0.477169i	$0.841663\pi$
$798$	−17.7697	−	155.202i	−0.0222678	−	0.194489i
$799$			1607.91i			2.01240i
$800$	65.5398	+	125.318i	0.0819247	+	0.156647i
$801$	252.190	−	436.806i	0.314844	−	0.545326i
$802$	107.779	−	28.8793i	0.134388	−	0.0360091i
$803$	−31.0939	−	8.33159i	−0.0387222	−	0.0103756i
$804$			4.59648i			0.00571702i
$805$	−188.130	−	825.650i	−0.233702	−	1.02565i
$806$	570.000			0.707196
$807$	97.1947	−	362.736i	0.120440	−	0.449487i
$808$	−40.2628	−	150.263i	−0.0498302	−	0.185969i
$809$	1001.47	+	578.200i	1.23791	+	0.714709i	0.968667	−	0.248363i	$-0.0798924\pi$
$809$	1001.47	+	578.200i	1.23791	+	0.714709i	0.269245	+	0.963072i	$0.413226\pi$
$810$	−110.691	+	12.2293i	−0.136656	+	0.0150979i
$811$	−143.794			−0.177305			−0.0886526	−	0.996063i	$-0.528256\pi$
$811$	−143.794			−0.177305			−0.0886526	+	0.996063i	$0.528256\pi$
$812$	−137.781	−	185.986i	−0.169681	−	0.229047i
$813$	65.0764	−	65.0764i	0.0800448	−	0.0800448i
$814$	−21.9863	+	12.6938i	−0.0270103	+	0.0155944i
$815$	1005.90	−	739.032i	1.23424	−	0.906788i
$816$	−110.232	+	190.928i	−0.135089	+	0.233980i
$817$	−144.976	+	541.058i	−0.177449	+	0.662250i
$818$	−393.544	+	393.544i	−0.481105	+	0.481105i
$819$	−585.054	−	464.847i	−0.714352	−	0.567579i
$820$	1.86801	−	0.728476i	0.00227806	−	0.000888385i
$821$	254.012	+	439.962i	0.309394	+	0.535885i	0.978230	−	0.207524i	$-0.0665406\pi$
$821$	254.012	+	439.962i	0.309394	+	0.535885i	−0.668836	+	0.743410i	$0.733207\pi$
$822$	294.856	−	79.0064i	0.358706	−	0.0961149i
$823$	−376.812	−	1406.28i	−0.457852	−	1.70873i	−0.679566	−	0.733615i	$-0.737832\pi$
$823$	−376.812	−	1406.28i	−0.457852	−	1.70873i	0.221714	−	0.975112i	$-0.428835\pi$
$824$	−0.548410	+	0.316625i	−0.000665546	+	0.000384253i
$825$	−1.16750	+	27.9616i	−0.00141516	+	0.0338928i
$826$	83.9290	+	212.722i	0.101609	+	0.257533i
$827$	−969.412	−	969.412i	−1.17220	−	1.17220i	−0.981683	−	0.190520i	$-0.938983\pi$
$827$	−969.412	−	969.412i	−1.17220	−	1.17220i	−0.190520	−	0.981683i	$-0.561017\pi$
$828$	−295.242	−	79.1098i	−0.356572	−	0.0955432i
$829$	747.599	+	431.627i	0.901808	+	0.520659i	0.877786	−	0.479052i	$-0.159020\pi$
$829$	747.599	+	431.627i	0.901808	+	0.520659i	0.0240219	+	0.999711i	$0.492353\pi$
$830$	−228.504	−	34.9476i	−0.275306	−	0.0421055i
$831$	69.5079	+	120.391i	0.0836437	+	0.144875i
$832$	95.5990	+	95.5990i	0.114903	+	0.114903i
$833$	−1399.11	−	872.122i	−1.67961	−	1.04697i
$834$			158.069i			0.189531i
$835$	1425.34	−	157.473i	1.70699	−	0.188590i
$836$	6.58312	−	11.4023i	0.00787455	−	0.0136391i
$837$	−578.002	+	154.875i	−0.690563	+	0.185036i
$838$	225.845	+	60.5150i	0.269505	+	0.0722136i
$839$			541.425i			0.645322i	0.946515	+	0.322661i	$0.104577\pi$
$839$			541.425i			0.645322i	−0.946515	+	0.322661i	$0.895423\pi$
$840$	6.12303	−	162.048i	0.00728933	−	0.192914i
$841$	567.660			0.674982
$842$	−59.8930	+	223.524i	−0.0711318	+	0.265468i
$843$	57.7452	+	215.508i	0.0684996	+	0.255644i
$844$	−197.107	−	113.799i	−0.233539	−	0.134834i
$845$	455.016	+	364.477i	0.538480	+	0.431334i
$846$	−426.897			−0.504607
$847$	−838.255	+	95.9748i	−0.989675	+	0.113311i
$848$	263.831	−	263.831i	0.311122	−	0.311122i
$849$	−446.273	+	257.656i	−0.525645	+	0.303482i
$850$	1160.89	−	259.682i	1.36575	−	0.305508i
$851$	317.788	−	550.425i	0.373429	−	0.646797i
$852$	53.6464	−	200.211i	0.0629653	−	0.234990i
$853$	203.211	−	203.211i	0.238231	−	0.238231i	−0.577886	−	0.816117i	$-0.696122\pi$
$853$	203.211	−	203.211i	0.238231	−	0.238231i	0.816117	+	0.577886i	$0.196122\pi$
$854$	17.7365	−	119.127i	0.0207687	−	0.139492i
$855$	110.541	+	283.457i	0.129288	+	0.331528i
$856$	190.317	+	329.638i	0.222333	+	0.385091i
$857$	−1133.64	+	303.758i	−1.32280	+	0.354443i	−0.850026	−	0.526741i	$-0.823414\pi$
$857$	−1133.64	+	303.758i	−1.32280	+	0.354443i	−0.472774	+	0.881184i	$0.656747\pi$
$858$	6.92452	+	25.8426i	0.00807053	+	0.0301196i
$859$	254.787	−	147.102i	0.296609	−	0.171247i	−0.344309	−	0.938856i	$-0.611887\pi$
$859$	254.787	−	147.102i	0.296609	−	0.171247i	0.640919	+	0.767609i	$0.278554\pi$
$860$	−233.678	+	532.449i	−0.271719	+	0.619126i
$861$	−2.27404	−	0.338577i	−0.00264116	−	0.000393237i
$862$	−419.744	−	419.744i	−0.486942	−	0.486942i
$863$	1370.63	+	367.260i	1.58822	+	0.425562i	0.941457	−	0.337132i	$-0.109457\pi$
$863$	1370.63	+	367.260i	1.58822	+	0.425562i	0.646760	+	0.762693i	$0.276123\pi$
$864$	−122.916	−	70.9657i	−0.142264	−	0.0821363i
$865$	−63.1042	+	46.3623i	−0.0729528	+	0.0535980i
$866$	−355.950	−	616.523i	−0.411028	−	0.711921i
$867$	976.546	+	976.546i	1.12635	+	1.12635i
$868$	37.9807	+	331.728i	0.0437565	+	0.382175i
$869$			76.7201i			0.0882855i
$870$	−149.465	−	119.724i	−0.171799	−	0.137614i
$871$	11.8550	−	20.5335i	0.0136108	−	0.0235747i
$872$	139.652	−	37.4196i	0.160151	−	0.0429124i
$873$	−437.330	−	117.182i	−0.500951	−	0.134229i
$874$			329.615i			0.377134i
$875$	−665.899	+	567.630i	−0.761027	+	0.648720i
$876$	154.327			0.176173
$877$	362.410	−	1352.53i	0.413238	−	1.54222i	−0.375101	−	0.926984i	$-0.622392\pi$
$877$	362.410	−	1352.53i	0.413238	−	1.54222i	0.788339	−	0.615241i	$-0.210941\pi$
$878$	68.7268	+	256.492i	0.0782766	+	0.292132i
$879$	−370.554	−	213.939i	−0.421563	−	0.243390i
$880$	8.54466	−	10.6672i	0.00970984	−	0.0121218i
$881$	1069.93			1.21445			0.607223	−	0.794532i	$-0.292284\pi$
$881$	1069.93			1.21445			0.607223	+	0.794532i	$0.292284\pi$
$882$	231.547	−	371.463i	0.262525	−	0.421160i
$883$	1198.71	−	1198.71i	1.35754	−	1.35754i	0.480593	−	0.876944i	$-0.340421\pi$
$883$	1198.71	−	1198.71i	1.35754	−	1.35754i	0.876944	−	0.480593i	$-0.159579\pi$
$884$	984.865	−	568.612i	1.11410	−	0.643227i
$885$	112.023	+	152.475i	0.126579	+	0.172288i
$886$	423.071	−	732.781i	0.477507	−	0.827067i
$887$	−19.9594	+	74.4895i	−0.0225021	+	0.0839791i	−0.976264	−	0.216585i	$-0.930508\pi$
$887$	−19.9594	+	74.4895i	−0.0225021	+	0.0839791i	0.953762	+	0.300564i	$0.0971749\pi$
$888$	86.0635	−	86.0635i	0.0969183	−	0.0969183i
$889$	995.290	−	392.688i	1.11956	−	0.441719i
$890$	−517.021	−	226.908i	−0.580923	−	0.254952i
$891$	5.38137	+	9.32080i	0.00603969	+	0.0104611i
$892$	434.166	−	116.334i	0.486733	−	0.130420i
$893$	119.150	+	444.672i	0.133426	+	0.497953i
$894$	175.444	−	101.293i	0.196246	−	0.113303i
$895$	−1597.33	+	622.920i	−1.78473	+	0.696000i
$896$	−49.2665	+	62.0065i	−0.0549849	+	0.0692037i
$897$	−473.612	−	473.612i	−0.527996	−	0.527996i
$898$	128.219	+	34.3562i	0.142783	+	0.0382586i
$899$	341.479	+	197.153i	0.379843	+	0.219302i
$900$	68.9452	+	308.214i	0.0766058	+	0.342460i
$901$	−1569.24	−	2718.00i	−1.74166	−	3.01665i
$902$	−0.137018	−	0.137018i	−0.000151905	−	0.000151905i
$903$	535.757	−	396.896i	0.593307	−	0.439530i
$904$		−	255.398i		−	0.282520i
$905$	275.492	−	343.926i	0.304411	−	0.380029i
$906$	−273.340	+	473.440i	−0.301700	+	0.522560i
$907$	−973.915	+	260.960i	−1.07378	+	0.287717i	−0.752044	−	0.659113i	$-0.770932\pi$
$907$	−973.915	+	260.960i	−1.07378	+	0.287717i	−0.321732	+	0.946831i	$0.604265\pi$
$908$	−551.485	−	147.770i	−0.607362	−	0.162742i
$909$		−	347.414i		−	0.382194i
$910$	−445.300	+	708.114i	−0.489341	+	0.778147i
$911$	−1241.02			−1.36226			−0.681130	−	0.732162i	$-0.738511\pi$
$911$	−1241.02			−1.36226			−0.681130	+	0.732162i	$0.738511\pi$
$912$	−16.3369	+	60.9702i	−0.0179133	+	0.0668532i
$913$	5.78210	+	21.5791i	0.00633308	+	0.0236354i
$914$	259.707	+	149.942i	0.284143	+	0.164050i
$915$	−10.9426	−	99.0451i	−0.0119591	−	0.108246i
$916$	626.697			0.684167
$917$	409.512	−	46.8865i	0.446578	−	0.0511303i
$918$	−844.193	+	844.193i	−0.919600	+	0.919600i
$919$	−5.83356	+	3.36801i	−0.00634772	+	0.00366486i	−0.503171	−	0.864187i	$-0.667833\pi$
$919$	−5.83356	+	3.36801i	−0.00634772	+	0.00366486i	0.496823	+	0.867852i	$0.334500\pi$
$920$	−51.7292	+	338.231i	−0.0562274	+	0.367642i
$921$	429.325	−	743.612i	0.466150	−	0.807396i
$922$	−128.254	+	478.650i	−0.139104	+	0.519143i
$923$	−756.027	+	756.027i	−0.819097	+	0.819097i
$924$	−14.5785	+	5.75188i	−0.0157776	+	0.00622498i
$925$	−656.160	−	27.3972i	−0.709363	−	0.0296186i
$926$	−327.380	−	567.039i	−0.353542	−	0.612353i
$927$	−1.36603	+	0.366025i	−0.00147360	+	0.000394849i
$928$	24.2060	+	90.3380i	0.0260840	+	0.0973470i
$929$	361.434	−	208.674i	0.389057	−	0.224622i	−0.292694	−	0.956206i	$-0.594552\pi$
$929$	361.434	−	208.674i	0.389057	−	0.224622i	0.681752	+	0.731584i	$0.261218\pi$
$930$	100.370	+	257.375i	0.107924	+	0.276747i
$931$	−451.556	−	137.511i	−0.485022	−	0.147702i
$932$	71.5514	+	71.5514i	0.0767719	+	0.0767719i
$933$	694.748	+	186.157i	0.744639	+	0.199525i
$934$	666.301	+	384.689i	0.713384	+	0.411872i
$935$	−68.0684	−	92.6485i	−0.0728004	−	0.0990893i
$936$	150.966	+	261.480i	0.161288	+	0.279359i
$937$	−46.4937	−	46.4937i	−0.0496198	−	0.0496198i	0.681862	−	0.731481i	$-0.261171\pi$
$937$	−46.4937	−	46.4937i	−0.0496198	−	0.0496198i	−0.731481	+	0.681862i	$0.761171\pi$
$938$	12.7400	+	5.53117i	0.0135821	+	0.00589677i
$939$		−	340.825i		−	0.362966i
$940$	52.4780	+	474.995i	0.0558276	+	0.505314i
$941$	720.442	−	1247.84i	0.765614	−	1.32608i	−0.174308	−	0.984691i	$-0.555769\pi$
$941$	720.442	−	1247.84i	0.765614	−	1.32608i	0.939922	−	0.341390i	$-0.110898\pi$
$942$	−356.461	+	95.5134i	−0.378408	+	0.101394i
$943$	4.68579	+	1.25555i	0.00496902	+	0.00133145i
$944$		−	92.4010i		−	0.0978824i
$945$	259.149	−	839.047i	0.274232	−	0.887881i
$946$	56.1955			0.0594033
$947$	144.671	−	539.920i	0.152768	−	0.570137i	−0.846518	−	0.532359i	$-0.821306\pi$
$947$	144.671	−	539.920i	0.152768	−	0.570137i	0.999286	−	0.0377774i	$-0.0120278\pi$
$948$	−95.1957	−	355.275i	−0.100417	−	0.374763i
$949$	−689.416	−	398.035i	−0.726466	−	0.419425i
$950$	301.804	−	157.840i	0.317689	−	0.166148i
$951$	675.697			0.710512
$952$	396.544	+	535.282i	0.416538	+	0.562271i
$953$	27.0794	−	27.0794i	0.0284149	−	0.0284149i	−0.692757	−	0.721171i	$-0.743604\pi$
$953$	27.0794	−	27.0794i	0.0284149	−	0.0284149i	0.721171	+	0.692757i	$0.243604\pi$
$954$	721.626	−	416.631i	0.756421	−	0.436720i
$955$	−232.716	−	35.5917i	−0.243682	−	0.0372688i
$956$	195.330	−	338.321i	0.204320	−	0.353893i
$957$	−4.79014	+	17.8770i	−0.00500537	+	0.0186803i
$958$	−67.6332	+	67.6332i	−0.0705984	+	0.0705984i
$959$	135.834	−	912.321i	0.141641	−	0.951325i
$960$	−26.3325	+	60.0000i	−0.0274297	+	0.0625000i
$961$	196.098	+	339.651i	0.204056	+	0.353435i
$962$	−606.437	+	162.494i	−0.630391	+	0.168913i
$963$	220.010	+	821.090i	0.228463	+	0.852637i
$964$	160.962	−	92.9315i	0.166973	−	0.0964020i
$965$	468.622	+	205.666i	0.485618	+	0.213126i
$966$	244.074	−	307.190i	0.252665	−	0.318002i
$967$	1012.58	+	1012.58i	1.04713	+	1.04713i	0.998833	+	0.0483007i	$0.0153806\pi$
$967$	1012.58	+	1012.58i	1.04713	+	1.04713i	0.0483007	+	0.998833i	$0.484619\pi$
$968$	329.302	+	88.2363i	0.340188	+	0.0911532i
$969$	459.814	+	265.474i	0.474524	+	0.273967i
$970$	−76.6244	+	501.008i	−0.0789943	+	0.516503i
$971$	676.674	+	1172.03i	0.696884	+	1.20704i	0.969542	+	0.244927i	$0.0787640\pi$
$971$	676.674	+	1172.03i	0.696884	+	1.20704i	−0.272658	+	0.962111i	$0.587903\pi$
$972$	−355.831	−	355.831i	−0.366082	−	0.366082i
$973$	438.116	+	190.212i	0.450274	+	0.195490i
$974$			1054.34i			1.08249i
$975$	−206.857	+	660.448i	−0.212161	+	0.677382i
$976$	−24.3325	+	42.1451i	−0.0249308	+	0.0431815i
$977$	−598.914	+	160.479i	−0.613014	+	0.164256i	−0.551950	−	0.833877i	$-0.686116\pi$
$977$	−598.914	+	160.479i	−0.613014	+	0.164256i	−0.0610638	+	0.998134i	$0.519449\pi$
$978$	558.618	+	149.681i	0.571184	+	0.153048i
$979$			54.5673i			0.0557377i
$980$	−441.778	−	211.971i	−0.450794	−	0.216297i
$981$	322.881			0.329135
$982$	−72.8614	+	271.922i	−0.0741969	+	0.276907i
$983$	−347.318	−	1296.21i	−0.353324	−	1.31862i	−0.882580	−	0.470161i	$-0.844196\pi$
$983$	−347.318	−	1296.21i	−0.353324	−	1.31862i	0.529256	−	0.848462i	$-0.322471\pi$
$984$	0.804519	+	0.464489i	0.000817600	+	0.000472042i
$985$	−1146.65	+	126.683i	−1.16411	+	0.128613i
$986$	786.692			0.797862
$987$	218.228	−	502.648i	0.221103	−	0.509268i
$988$	230.232	−	230.232i	0.233029	−	0.233029i
$989$	−1218.36	+	703.422i	−1.23191	+	0.711246i
$990$	24.5980	−	18.0721i	0.0248465	−	0.0182546i
$991$	−727.843	+	1260.66i	−0.734453	+	1.27211i	0.220510	+	0.975385i	$0.429228\pi$
$991$	−727.843	+	1260.66i	−0.734453	+	1.27211i	−0.954963	+	0.296725i	$0.904105\pi$
$992$	34.9183	−	130.317i	0.0351999	−	0.131368i
$993$	−432.491	+	432.491i	−0.435540	+	0.435540i
$994$	−490.367	−	389.615i	−0.493327	−	0.391967i
$995$	1587.23	−	618.980i	1.59521	−	0.622091i
$996$	−53.5514	−	92.7537i	−0.0537664	−	0.0931262i
$997$	−885.448	+	237.255i	−0.888112	+	0.237969i	−0.673904	−	0.738819i	$-0.735384\pi$
$997$	−885.448	+	237.255i	−0.888112	+	0.237969i	−0.214208	+	0.976788i	$0.568717\pi$
$998$	−199.410	−	744.210i	−0.199810	−	0.745701i
$999$	570.798	−	329.551i	0.571370	−	0.329880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.l.b.67.2	yes	8
5.2	odd	4		350.3.p.b.193.2		8
5.3	odd	4	inner	70.3.l.b.53.1	yes	8
5.4	even	2		350.3.p.b.207.1		8
7.2	even	3	inner	70.3.l.b.37.1	yes	8
7.3	odd	6		490.3.f.k.197.1		4
7.4	even	3		490.3.f.f.197.2		4
35.2	odd	12		350.3.p.b.93.1		8
35.3	even	12		490.3.f.k.393.1		4
35.9	even	6		350.3.p.b.107.2		8
35.18	odd	12		490.3.f.f.393.2		4
35.23	odd	12	inner	70.3.l.b.23.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.b.23.2	✓	8	35.23	odd	12	inner
70.3.l.b.37.1	yes	8	7.2	even	3	inner
70.3.l.b.53.1	yes	8	5.3	odd	4	inner
70.3.l.b.67.2	yes	8	1.1	even	1	trivial
350.3.p.b.93.1		8	35.2	odd	12
350.3.p.b.107.2		8	35.9	even	6
350.3.p.b.193.2		8	5.2	odd	4
350.3.p.b.207.1		8	5.4	even	2
490.3.f.f.197.2		4	7.4	even	3
490.3.f.f.393.2		4	35.18	odd	12
490.3.f.k.197.1		4	7.3	odd	6
490.3.f.k.393.1		4	35.3	even	12

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(0.423972 + 1.58228i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.12590 + 3.90240i) q^{5} -2.31662 q^{6} +(-2.78771 + 6.42096i) q^{7} +(2.00000 - 2.00000i) q^{8} +(5.47036 - 3.15831i) q^{9} +O(q^{10})\)	\(q+(-0.366025 + 1.36603i) q^{2} +(0.423972 + 1.58228i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.12590 + 3.90240i) q^{5} -2.31662 q^{6} +(-2.78771 + 6.42096i) q^{7} +(2.00000 - 2.00000i) q^{8} +(5.47036 - 3.15831i) q^{9} +(-4.18662 - 5.69844i) q^{10} +(-0.341688 + 0.591820i) q^{11} +(0.847944 - 3.16457i) q^{12} +(-11.9499 + 11.9499i) q^{13} +(-7.75082 - 6.15831i) q^{14} +(-7.50000 - 3.29156i) q^{15} +(2.00000 + 3.46410i) q^{16} +(32.4999 - 8.70832i) q^{17} +(2.31205 + 8.62867i) q^{18} +(8.34264 - 4.81662i) q^{19} +(9.31662 - 3.63325i) q^{20} +(-11.3417 - 1.68864i) q^{21} +(-0.683375 - 0.683375i) q^{22} +(23.3702 + 6.26203i) q^{23} +(4.01251 + 2.31662i) q^{24} +(-5.45744 - 24.3971i) q^{25} +(-11.9499 - 20.6978i) q^{26} +(17.7414 + 17.7414i) q^{27} +(11.2494 - 8.33372i) q^{28} -16.5330i q^{29} +(7.24155 - 9.04040i) q^{30} +(-11.9248 + 20.6544i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(-1.08129 - 0.289732i) q^{33} +47.5831i q^{34} +(-16.3430 - 30.9500i) q^{35} -12.6332 q^{36} +(6.79899 - 25.3742i) q^{37} +(3.52601 + 13.1593i) q^{38} +(-23.9745 - 13.8417i) q^{39} +(1.55299 + 14.0566i) q^{40} +0.200503 q^{41} +(6.45807 - 14.8749i) q^{42} +(-41.1161 + 41.1161i) q^{43} +(1.18364 - 0.683375i) q^{44} +(-4.77482 + 31.2201i) q^{45} +(-17.1082 + 29.6322i) q^{46} +(-12.3686 + 46.1601i) q^{47} +(-4.63325 + 4.63325i) q^{48} +(-33.4574 - 35.7995i) q^{49} +(35.3246 + 1.47494i) q^{50} +(27.5581 + 47.7320i) q^{51} +(32.6477 - 8.74792i) q^{52} +(-24.1422 - 90.1000i) q^{53} +(-30.7291 + 17.7414i) q^{54} +(-1.24144 - 3.18338i) q^{55} +(7.26650 + 18.4173i) q^{56} +(11.1583 + 11.1583i) q^{57} +(22.5845 + 6.05150i) q^{58} +(-20.0054 - 11.5501i) q^{59} +(9.69882 + 13.2012i) q^{60} +(6.08312 + 10.5363i) q^{61} +(-23.8496 - 23.8496i) q^{62} +(5.02963 + 43.9294i) q^{63} -8.00000i q^{64} +(-9.27902 - 83.9873i) q^{65} +(0.791562 - 1.37103i) q^{66} +(-1.35519 + 0.363121i) q^{67} +(-64.9998 - 17.4166i) q^{68} +39.6332i q^{69} +(48.2605 - 10.9965i) q^{70} +63.2665 q^{71} +(4.62409 - 17.2573i) q^{72} +(12.1918 + 45.5005i) q^{73} +(32.1732 + 18.5752i) q^{74} +(36.2893 - 18.9789i) q^{75} -19.2665 q^{76} +(-2.84753 - 3.84378i) q^{77} +(27.6834 - 27.6834i) q^{78} +(97.2256 - 56.1332i) q^{79} +(-19.7701 - 3.02365i) q^{80} +(7.87469 - 13.6394i) q^{81} +(-0.0733890 + 0.273892i) q^{82} +(23.1161 - 23.1161i) q^{83} +(17.9557 + 14.2665i) q^{84} +(-67.6082 + 154.049i) q^{85} +(-41.1161 - 71.2152i) q^{86} +(26.1599 - 7.00952i) q^{87} +(0.500265 + 1.86702i) q^{88} +(69.1518 - 39.9248i) q^{89} +(-40.8997 - 17.9499i) q^{90} +(-43.4169 - 110.042i) q^{91} +(-34.2164 - 34.2164i) q^{92} +(-37.7369 - 10.1116i) q^{93} +(-58.5287 - 33.7916i) q^{94} +(-7.28190 + 47.6126i) q^{95} +(-4.63325 - 8.02502i) q^{96} +(-50.6834 - 50.6834i) q^{97} +(61.1493 - 32.6001i) q^{98} +4.31662i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 2 q^{3} - 6 q^{5} + 8 q^{6} - 12 q^{7} + 16 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 2 * q^3 - 6 * q^5 + 8 * q^6 - 12 * q^7 + 16 * q^8	\( 8 q + 4 q^{2} + 2 q^{3} - 6 q^{5} + 8 q^{6} - 12 q^{7} + 16 q^{8} + 18 q^{10} - 16 q^{11} + 4 q^{12} - 16 q^{13} - 60 q^{15} + 16 q^{16} + 62 q^{17} - 12 q^{18} + 48 q^{20} - 104 q^{21} - 32 q^{22} + 22 q^{23} - 6 q^{25} - 16 q^{26} - 4 q^{27} + 12 q^{28} - 50 q^{30} + 24 q^{31} - 16 q^{32} + 30 q^{33} + 70 q^{35} - 48 q^{36} - 134 q^{37} - 12 q^{38} + 12 q^{40} + 320 q^{41} - 100 q^{42} + 16 q^{43} - 58 q^{45} - 44 q^{46} + 102 q^{47} + 16 q^{48} + 4 q^{50} + 48 q^{51} + 16 q^{52} + 98 q^{53} + 136 q^{55} - 48 q^{56} + 76 q^{57} - 40 q^{58} + 40 q^{60} - 84 q^{61} + 48 q^{62} - 76 q^{63} - 210 q^{65} - 60 q^{66} - 130 q^{67} - 124 q^{68} + 146 q^{70} + 400 q^{71} - 24 q^{72} - 246 q^{73} + 40 q^{75} - 48 q^{76} + 86 q^{77} + 248 q^{78} + 24 q^{80} - 136 q^{81} + 160 q^{82} - 160 q^{83} - 448 q^{85} + 16 q^{86} + 196 q^{87} - 32 q^{88} - 168 q^{90} - 480 q^{91} - 88 q^{92} - 210 q^{93} - 80 q^{95} + 16 q^{96} - 432 q^{97} + 176 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 2 * q^3 - 6 * q^5 + 8 * q^6 - 12 * q^7 + 16 * q^8 + 18 * q^10 - 16 * q^11 + 4 * q^12 - 16 * q^13 - 60 * q^15 + 16 * q^16 + 62 * q^17 - 12 * q^18 + 48 * q^20 - 104 * q^21 - 32 * q^22 + 22 * q^23 - 6 * q^25 - 16 * q^26 - 4 * q^27 + 12 * q^28 - 50 * q^30 + 24 * q^31 - 16 * q^32 + 30 * q^33 + 70 * q^35 - 48 * q^36 - 134 * q^37 - 12 * q^38 + 12 * q^40 + 320 * q^41 - 100 * q^42 + 16 * q^43 - 58 * q^45 - 44 * q^46 + 102 * q^47 + 16 * q^48 + 4 * q^50 + 48 * q^51 + 16 * q^52 + 98 * q^53 + 136 * q^55 - 48 * q^56 + 76 * q^57 - 40 * q^58 + 40 * q^60 - 84 * q^61 + 48 * q^62 - 76 * q^63 - 210 * q^65 - 60 * q^66 - 130 * q^67 - 124 * q^68 + 146 * q^70 + 400 * q^71 - 24 * q^72 - 246 * q^73 + 40 * q^75 - 48 * q^76 + 86 * q^77 + 248 * q^78 + 24 * q^80 - 136 * q^81 + 160 * q^82 - 160 * q^83 - 448 * q^85 + 16 * q^86 + 196 * q^87 - 32 * q^88 - 168 * q^90 - 480 * q^91 - 88 * q^92 - 210 * q^93 - 80 * q^95 + 16 * q^96 - 432 * q^97 + 176 * q^98

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