LMFDB - Embedded newform 350.3.p.b.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,3,Mod(93,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, 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("350.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.p (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:	$9.53680925261$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.2
Root			$-0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	350.193
Dual form			350.3.p.b.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(1.58228 - 0.423972i) q^{3} +(1.73205 + 1.00000i) q^{4} -2.31662 q^{6} +(-6.42096 - 2.78771i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-5.47036 + 3.15831i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.58228 - 0.423972i) q^{3} +(1.73205 + 1.00000i) q^{4} -2.31662 q^{6} +(-6.42096 - 2.78771i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-5.47036 + 3.15831i) q^{9} +(-0.341688 + 0.591820i) q^{11} +(3.16457 + 0.847944i) q^{12} +(11.9499 + 11.9499i) q^{13} +(7.75082 + 6.15831i) q^{14} +(2.00000 + 3.46410i) q^{16} +(8.70832 + 32.4999i) q^{17} +(8.62867 - 2.31205i) q^{18} +(-8.34264 + 4.81662i) q^{19} +(-11.3417 - 1.68864i) q^{21} +(0.683375 - 0.683375i) q^{22} +(6.26203 - 23.3702i) q^{23} +(-4.01251 - 2.31662i) q^{24} +(-11.9499 - 20.6978i) q^{26} +(-17.7414 + 17.7414i) q^{27} +(-8.33372 - 11.2494i) q^{28} +16.5330i q^{29} +(-11.9248 + 20.6544i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-0.289732 + 1.08129i) q^{33} -47.5831i q^{34} -12.6332 q^{36} +(25.3742 + 6.79899i) q^{37} +(13.1593 - 3.52601i) q^{38} +(23.9745 + 13.8417i) q^{39} +0.200503 q^{41} +(14.8749 + 6.45807i) q^{42} +(41.1161 + 41.1161i) q^{43} +(-1.18364 + 0.683375i) q^{44} +(-17.1082 + 29.6322i) q^{46} +(-46.1601 - 12.3686i) q^{47} +(4.63325 + 4.63325i) q^{48} +(33.4574 + 35.7995i) q^{49} +(27.5581 + 47.7320i) q^{51} +(8.74792 + 32.6477i) q^{52} +(-90.1000 + 24.1422i) q^{53} +(30.7291 - 17.7414i) q^{54} +(7.26650 + 18.4173i) q^{56} +(-11.1583 + 11.1583i) q^{57} +(6.05150 - 22.5845i) q^{58} +(20.0054 + 11.5501i) q^{59} +(6.08312 + 10.5363i) q^{61} +(23.8496 - 23.8496i) q^{62} +(43.9294 - 5.02963i) q^{63} +8.00000i q^{64} +(0.791562 - 1.37103i) q^{66} +(-0.363121 - 1.35519i) q^{67} +(-17.4166 + 64.9998i) q^{68} -39.6332i q^{69} +63.2665 q^{71} +(17.2573 + 4.62409i) q^{72} +(45.5005 - 12.1918i) q^{73} +(-32.1732 - 18.5752i) q^{74} -19.2665 q^{76} +(3.84378 - 2.84753i) q^{77} +(-27.6834 - 27.6834i) q^{78} +(-97.2256 + 56.1332i) q^{79} +(7.87469 - 13.6394i) q^{81} +(-0.273892 - 0.0733890i) q^{82} +(-23.1161 - 23.1161i) q^{83} +(-17.9557 - 14.2665i) q^{84} +(-41.1161 - 71.2152i) q^{86} +(7.00952 + 26.1599i) q^{87} +(1.86702 - 0.500265i) q^{88} +(-69.1518 + 39.9248i) q^{89} +(-43.4169 - 110.042i) q^{91} +(34.2164 - 34.2164i) q^{92} +(-10.1116 + 37.7369i) q^{93} +(58.5287 + 33.7916i) q^{94} +(-4.63325 - 8.02502i) q^{96} +(50.6834 - 50.6834i) q^{97} +(-32.6001 - 61.1493i) q^{98} -4.31662i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 2 q^{3} + 8 q^{6} + 12 q^{7} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 2 * q^3 + 8 * q^6 + 12 * q^7 - 16 * q^8	$ 8 q - 4 q^{2} - 2 q^{3} + 8 q^{6} + 12 q^{7} - 16 q^{8} - 16 q^{11} - 4 q^{12} + 16 q^{13} + 16 q^{16} - 62 q^{17} + 12 q^{18} - 104 q^{21} + 32 q^{22} - 22 q^{23} - 16 q^{26} + 4 q^{27} - 12 q^{28} + 24 q^{31} + 16 q^{32} - 30 q^{33} - 48 q^{36} + 134 q^{37} + 12 q^{38} + 320 q^{41} + 100 q^{42} - 16 q^{43} - 44 q^{46} - 102 q^{47} - 16 q^{48} + 48 q^{51} - 16 q^{52} - 98 q^{53} - 48 q^{56} - 76 q^{57} + 40 q^{58} - 84 q^{61} - 48 q^{62} + 76 q^{63} - 60 q^{66} + 130 q^{67} + 124 q^{68} + 400 q^{71} + 24 q^{72} + 246 q^{73} - 48 q^{76} - 86 q^{77} - 248 q^{78} - 136 q^{81} - 160 q^{82} + 160 q^{83} + 16 q^{86} - 196 q^{87} + 32 q^{88} - 480 q^{91} + 88 q^{92} + 210 q^{93} + 16 q^{96} + 432 q^{97} - 176 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 2 * q^3 + 8 * q^6 + 12 * q^7 - 16 * q^8 - 16 * q^11 - 4 * q^12 + 16 * q^13 + 16 * q^16 - 62 * q^17 + 12 * q^18 - 104 * q^21 + 32 * q^22 - 22 * q^23 - 16 * q^26 + 4 * q^27 - 12 * q^28 + 24 * q^31 + 16 * q^32 - 30 * q^33 - 48 * q^36 + 134 * q^37 + 12 * q^38 + 320 * q^41 + 100 * q^42 - 16 * q^43 - 44 * q^46 - 102 * q^47 - 16 * q^48 + 48 * q^51 - 16 * q^52 - 98 * q^53 - 48 * q^56 - 76 * q^57 + 40 * q^58 - 84 * q^61 - 48 * q^62 + 76 * q^63 - 60 * q^66 + 130 * q^67 + 124 * q^68 + 400 * q^71 + 24 * q^72 + 246 * q^73 - 48 * q^76 - 86 * q^77 - 248 * q^78 - 136 * q^81 - 160 * q^82 + 160 * q^83 + 16 * q^86 - 196 * q^87 + 32 * q^88 - 480 * q^91 + 88 * q^92 + 210 * q^93 + 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$	1.58228	−	0.423972i	0.527428	−	0.141324i	0.0147277	−	0.999892i	$-0.495312\pi$
$3$	1.58228	−	0.423972i	0.527428	−	0.141324i	0.512700	+	0.858568i	$0.328645\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−2.31662			−0.386104
$7$	−6.42096	−	2.78771i	−0.917280	−	0.398244i
$7$	−6.42096	−	2.78771i	−0.917280	−	0.398244i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	−5.47036	+	3.15831i	−0.607818	+	0.350924i
$10$		0			0
$11$	−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	$0.176556\pi$
$12$	3.16457	+	0.847944i	0.263714	+	0.0706620i
$13$	11.9499	+	11.9499i	0.919221	+	0.919221i	0.996973	−	0.0777517i	$-0.0247741\pi$
$13$	11.9499	+	11.9499i	0.919221	+	0.919221i	−0.0777517	+	0.996973i	$0.524774\pi$
$14$	7.75082	+	6.15831i	0.553630	+	0.439879i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	8.70832	+	32.4999i	0.512254	+	1.91176i	0.395082	+	0.918646i	$0.370716\pi$
$17$	8.70832	+	32.4999i	0.512254	+	1.91176i	0.117172	+	0.993112i	$0.462617\pi$
$18$	8.62867	−	2.31205i	0.479371	−	0.128447i
$19$	−8.34264	+	4.81662i	−0.439086	+	0.253507i	−0.703210	−	0.710982i	$-0.748251\pi$
$19$	−8.34264	+	4.81662i	−0.439086	+	0.253507i	0.264124	+	0.964489i	$0.414917\pi$
$20$		0			0
$21$	−11.3417	−	1.68864i	−0.540080	−	0.0804115i
$22$	0.683375	−	0.683375i	0.0310625	−	0.0310625i
$23$	6.26203	−	23.3702i	0.272262	−	1.01610i	−0.685392	−	0.728175i	$-0.740369\pi$
$23$	6.26203	−	23.3702i	0.272262	−	1.01610i	0.957654	−	0.287922i	$-0.0929643\pi$
$24$	−4.01251	−	2.31662i	−0.167188	−	0.0965260i
$25$		0			0
$26$	−11.9499	−	20.6978i	−0.459611	−	0.796069i
$27$	−17.7414	+	17.7414i	−0.657090	+	0.657090i
$28$	−8.33372	−	11.2494i	−0.297633	−	0.401765i
$29$			16.5330i			0.570103i	0.958512	+	0.285052i	$0.0920108\pi$
$29$			16.5330i			0.570103i	−0.958512	+	0.285052i	$0.907989\pi$
$30$		0			0
$31$	−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	$0.292352\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$	−0.289732	+	1.08129i	−0.00877975	+	0.0327665i
$34$		−	47.5831i		−	1.39950i
$35$		0			0
$36$	−12.6332			−0.350924
$37$	25.3742	+	6.79899i	0.685789	+	0.183757i	0.584856	−	0.811137i	$-0.301151\pi$
$37$	25.3742	+	6.79899i	0.685789	+	0.183757i	0.100932	+	0.994893i	$0.467817\pi$
$38$	13.1593	−	3.52601i	0.346296	−	0.0927898i
$39$	23.9745	+	13.8417i	0.614731	+	0.354915i
$40$		0			0
$41$	0.200503			0.00489031			0.00244515	−	0.999997i	$-0.499222\pi$
$41$	0.200503			0.00489031			0.00244515	+	0.999997i	$0.499222\pi$
$42$	14.8749	+	6.45807i	0.354165	+	0.153764i
$43$	41.1161	+	41.1161i	0.956189	+	0.956189i	0.999080	−	0.0428909i	$-0.0136568\pi$
$43$	41.1161	+	41.1161i	0.956189	+	0.956189i	−0.0428909	+	0.999080i	$0.513657\pi$
$44$	−1.18364	+	0.683375i	−0.0269009	+	0.0155313i
$45$		0			0
$46$	−17.1082	+	29.6322i	−0.371917	+	0.644179i
$47$	−46.1601	−	12.3686i	−0.982130	−	0.263161i	−0.268189	−	0.963366i	$-0.586425\pi$
$47$	−46.1601	−	12.3686i	−0.982130	−	0.263161i	−0.713942	+	0.700205i	$0.753092\pi$
$48$	4.63325	+	4.63325i	0.0965260	+	0.0965260i
$49$	33.4574	+	35.7995i	0.682804	+	0.730602i
$50$		0			0
$51$	27.5581	+	47.7320i	0.540354	+	0.935921i
$52$	8.74792	+	32.6477i	0.168229	+	0.627840i
$53$	−90.1000	+	24.1422i	−1.70000	+	0.455514i	−0.972940	−	0.231059i	$-0.925781\pi$
$53$	−90.1000	+	24.1422i	−1.70000	+	0.455514i	−0.727061	+	0.686573i	$0.759114\pi$
$54$	30.7291	−	17.7414i	0.569057	−	0.328545i
$55$		0			0
$56$	7.26650	+	18.4173i	0.129759	+	0.328881i
$57$	−11.1583	+	11.1583i	−0.195760	+	0.195760i
$58$	6.05150	−	22.5845i	0.104336	−	0.389388i
$59$	20.0054	+	11.5501i	0.339075	+	0.195765i	0.659863	−	0.751386i	$-0.270614\pi$
$59$	20.0054	+	11.5501i	0.339075	+	0.195765i	−0.320788	+	0.947151i	$0.603948\pi$
$60$		0			0
$61$	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
$63$	43.9294	−	5.02963i	0.697292	−	0.0798354i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	0.791562	−	1.37103i	0.0119934	−	0.0207731i
$67$	−0.363121	−	1.35519i	−0.00541971	−	0.0202266i	0.963163	−	0.268918i	$-0.0866661\pi$
$67$	−0.363121	−	1.35519i	−0.00541971	−	0.0202266i	−0.968583	+	0.248692i	$0.919999\pi$
$68$	−17.4166	+	64.9998i	−0.256127	+	0.955879i
$69$		−	39.6332i		−	0.574395i
$70$		0			0
$71$	63.2665			0.891077			0.445539	−	0.895263i	$-0.353012\pi$
$71$	63.2665			0.891077			0.445539	+	0.895263i	$0.353012\pi$
$72$	17.2573	+	4.62409i	0.239685	+	0.0642235i
$73$	45.5005	−	12.1918i	0.623295	−	0.167011i	0.0666696	−	0.997775i	$-0.478763\pi$
$73$	45.5005	−	12.1918i	0.623295	−	0.167011i	0.556625	+	0.830764i	$0.312096\pi$
$74$	−32.1732	−	18.5752i	−0.434773	−	0.251016i
$75$		0			0
$76$	−19.2665			−0.253507
$77$	3.84378	−	2.84753i	0.0499193	−	0.0369809i
$78$	−27.6834	−	27.6834i	−0.354915	−	0.354915i
$79$	−97.2256	+	56.1332i	−1.23070	+	0.710547i	−0.967177	−	0.254104i	$-0.918219\pi$
$79$	−97.2256	+	56.1332i	−1.23070	+	0.710547i	−0.263528	+	0.964652i	$0.584886\pi$
$80$		0			0
$81$	7.87469	−	13.6394i	0.0972183	−	0.168387i
$82$	−0.273892	−	0.0733890i	−0.00334014	−	0.000894988i
$83$	−23.1161	−	23.1161i	−0.278507	−	0.278507i	0.554006	−	0.832513i	$-0.313099\pi$
$83$	−23.1161	−	23.1161i	−0.278507	−	0.278507i	−0.832513	+	0.554006i	$0.813099\pi$
$84$	−17.9557	−	14.2665i	−0.213759	−	0.169839i
$85$		0			0
$86$	−41.1161	−	71.2152i	−0.478094	−	0.828084i
$87$	7.00952	+	26.1599i	0.0805692	+	0.300689i
$88$	1.86702	−	0.500265i	0.0212161	−	0.00568483i
$89$	−69.1518	+	39.9248i	−0.776987	+	0.448593i	−0.835361	−	0.549701i	$-0.814742\pi$
$89$	−69.1518	+	39.9248i	−0.776987	+	0.448593i	0.0583747	+	0.998295i	$0.481408\pi$
$90$		0			0
$91$	−43.4169	−	110.042i	−0.477109	−	1.20926i
$92$	34.2164	−	34.2164i	0.371917	−	0.371917i
$93$	−10.1116	+	37.7369i	−0.108727	+	0.405773i
$94$	58.5287	+	33.7916i	0.622646	+	0.359485i
$95$		0			0
$96$	−4.63325	−	8.02502i	−0.0482630	−	0.0835940i
$97$	50.6834	−	50.6834i	0.522509	−	0.522509i	−0.395819	−	0.918328i	$-0.629539\pi$
$97$	50.6834	−	50.6834i	0.522509	−	0.522509i	0.918328	+	0.395819i	$0.129539\pi$
$98$	−32.6001	−	61.1493i	−0.332654	−	0.623972i
$99$		−	4.31662i		−	0.0436023i
$100$		0			0
$101$	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	$0.0788899\pi$
$102$	−20.1739	−	75.2900i	−0.197783	−	0.738137i
$103$	−0.0579464	+	0.216259i	−0.000562586	+	0.00209960i	−0.966207	−	0.257769i	$-0.917013\pi$
$103$	−0.0579464	+	0.216259i	−0.000562586	+	0.00209960i	0.965644	+	0.259869i	$0.0836793\pi$
$104$		−	47.7995i		−	0.459611i
$105$		0			0
$106$	131.916			1.24449
$107$	−129.989	−	34.8304i	−1.21485	−	0.325517i	−0.406185	−	0.913791i	$-0.633141\pi$
$107$	−129.989	−	34.8304i	−1.21485	−	0.325517i	−0.808662	+	0.588273i	$0.799808\pi$
$108$	−48.4705	+	12.9876i	−0.448801	+	0.120256i
$109$	−44.2679	−	25.5581i	−0.406127	−	0.234478i	0.282997	−	0.959121i	$-0.408671\pi$
$109$	−44.2679	−	25.5581i	−0.406127	−	0.234478i	−0.689124	+	0.724643i	$0.742005\pi$
$110$		0			0
$111$	43.0317			0.387673
$112$	−3.18501	−	27.8183i	−0.0284376	−	0.248377i
$113$	−63.8496	−	63.8496i	−0.565041	−	0.565041i	0.365694	−	0.930735i	$-0.380832\pi$
$113$	−63.8496	−	63.8496i	−0.565041	−	0.565041i	−0.930735	+	0.365694i	$0.880832\pi$
$114$	19.3268	−	11.1583i	0.169533	−	0.0978799i
$115$		0			0
$116$	−16.5330	+	28.6360i	−0.142526	+	0.246862i
$117$	−103.112	−	27.6286i	−0.881295	−	0.236142i
$118$	−23.1003	−	23.1003i	−0.195765	−	0.195765i
$119$	34.6844	−	232.957i	0.291466	−	1.95762i
$120$		0			0
$121$	60.2665	+	104.385i	0.498070	+	0.862683i
$122$	−4.45316	−	16.6194i	−0.0365013	−	0.136225i
$123$	0.317252	−	0.0850074i	0.00257928	−	0.000691117i
$124$	−41.3088	+	23.8496i	−0.333135	+	0.192336i
$125$		0			0
$126$	−61.8496	−	9.20866i	−0.490870	−	0.0730846i
$127$	108.082	−	108.082i	0.851038	−	0.851038i	−0.139223	−	0.990261i	$-0.544460\pi$
$127$	108.082	−	108.082i	0.851038	−	0.851038i	0.990261	+	0.139223i	$0.0444604\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$	82.4895	+	47.6253i	0.639453	+	0.369188i
$130$		0			0
$131$	−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
$133$	66.9951	−	7.67050i	0.503722	−	0.0576730i
$134$			1.98413i			0.0148069i
$135$		0			0
$136$	47.5831	−	82.4164i	0.349876	−	0.606003i
$137$	−34.1041	−	127.278i	−0.248935	−	0.929039i	−0.971365	−	0.237594i	$-0.923641\pi$
$137$	−34.1041	−	127.278i	−0.248935	−	0.929039i	0.722429	−	0.691445i	$-0.243025\pi$
$138$	−14.5068	+	54.1400i	−0.105122	+	0.392319i
$139$			68.2322i			0.490879i	0.969412	+	0.245440i	$0.0789323\pi$
$139$			68.2322i			0.490879i	−0.969412	+	0.245440i	$0.921068\pi$
$140$		0			0
$141$	−78.2824			−0.555194
$142$	−86.4236	−	23.1571i	−0.608617	−	0.163078i
$143$	−11.1553	+	2.98905i	−0.0780091	+	0.0209025i
$144$	−21.8814	−	12.6332i	−0.151954	−	0.0877309i
$145$		0			0
$146$	−66.6174			−0.456283
$147$	68.1171	+	42.4600i	0.463381	+	0.288844i
$148$	37.1504	+	37.1504i	0.251016	+	0.251016i
$149$	75.7327	−	43.7243i	0.508273	−	0.293452i	−0.223850	−	0.974624i	$-0.571863\pi$
$149$	75.7327	−	43.7243i	0.508273	−	0.293452i	0.732124	+	0.681172i	$0.238529\pi$
$150$		0			0
$151$	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	$-0.118825\pi$
$152$	26.3185	+	7.05203i	0.173148	+	0.0463949i
$153$	−150.282	−	150.282i	−0.982238	−	0.982238i
$154$	−6.29297	+	2.48287i	−0.0408635	+	0.0161225i
$155$		0			0
$156$	27.6834	+	47.9490i	0.177458	+	0.307365i
$157$	41.2295	+	153.871i	0.262609	+	0.980068i	0.963698	+	0.266995i	$0.0860307\pi$
$157$	41.2295	+	153.871i	0.262609	+	0.980068i	−0.701089	+	0.713073i	$0.747303\pi$
$158$	153.359	−	41.0924i	0.970626	−	0.260078i
$159$	−132.328	+	76.3997i	−0.832253	+	0.480502i
$160$		0			0
$161$	−105.358	+	132.602i	−0.654395	+	0.823618i
$162$	−15.7494	+	15.7494i	−0.0972183	+	0.0972183i
$163$	−64.6117	+	241.134i	−0.396391	+	1.47935i	0.423007	+	0.906126i	$0.360975\pi$
$163$	−64.6117	+	241.134i	−0.396391	+	1.47935i	−0.819398	+	0.573225i	$0.805692\pi$
$164$	0.347281	+	0.200503i	0.00211756	+	0.00122258i
$165$		0			0
$166$	23.1161	+	40.0383i	0.139254	+	0.241195i
$167$	202.799	−	202.799i	1.21437	−	1.21437i	0.244793	−	0.969575i	$-0.421280\pi$
$167$	202.799	−	202.799i	1.21437	−	1.21437i	0.969575	−	0.244793i	$-0.0787200\pi$
$168$	19.3061	+	26.0607i	0.114917	+	0.155123i
$169$			116.599i			0.689935i
$170$		0			0
$171$	30.4248	−	52.6973i	0.177923	−	0.308171i
$172$	30.0991	+	112.331i	0.174995	+	0.653089i
$173$	4.05334	−	15.1273i	0.0234297	−	0.0874409i	−0.953221	−	0.302274i	$-0.902254\pi$
$173$	4.05334	−	15.1273i	0.0234297	−	0.0874409i	0.976651	+	0.214833i	$0.0689208\pi$
$174$		−	38.3008i		−	0.220119i
$175$		0			0
$176$	−2.73350			−0.0155313
$177$	36.5512	+	9.79385i	0.206504	+	0.0553325i
$178$	109.077	−	29.2270i	0.612790	−	0.164197i
$179$	−296.960	−	171.450i	−1.65899	−	0.957821i	−0.973180	−	0.230043i	$-0.926113\pi$
$179$	−296.960	−	171.450i	−1.65899	−	0.957821i	−0.685813	−	0.727777i	$-0.740553\pi$
$180$		0			0
$181$	−88.1320			−0.486917			−0.243459	−	0.969911i	$-0.578282\pi$
$181$	−88.1320			−0.486917			−0.243459	+	0.969911i	$0.578282\pi$
$182$	19.0302	+	166.212i	0.104562	+	0.913255i
$183$	14.0923	+	14.0923i	0.0770072	+	0.0770072i
$184$	−59.2645	+	34.2164i	−0.322090	+	0.185959i
$185$		0			0
$186$	27.6253	−	47.8484i	0.148523	−	0.257250i
$187$	−22.2096	−	5.95105i	−0.118768	−	0.0318238i
$188$	−67.5831	−	67.5831i	−0.359485	−	0.359485i
$189$	163.375	−	64.4591i	0.864418	−	0.341053i
$190$		0			0
$191$	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	$0.793999\pi$
$192$	3.39177	+	12.6583i	0.0176655	+	0.0659285i
$193$	−98.8657	+	26.4910i	−0.512257	+	0.137259i	−0.505683	−	0.862719i	$-0.668759\pi$
$193$	−98.8657	+	26.4910i	−0.512257	+	0.137259i	−0.00657446	+	0.999978i	$0.502093\pi$
$194$	−87.7862	+	50.6834i	−0.452506	+	0.261255i
$195$		0			0
$196$	22.1504	+	95.4639i	0.113012	+	0.487061i
$197$	−163.148	+	163.148i	−0.828162	+	0.828162i	−0.987262	−	0.159101i	$-0.949141\pi$
$197$	−163.148	+	163.148i	−0.828162	+	0.828162i	0.159101	+	0.987262i	$0.449141\pi$
$198$	−1.57999	+	5.89662i	−0.00797977	+	0.0297809i
$199$	295.082	+	170.365i	1.48282	+	0.856108i	0.999810	−	0.0195053i	$-0.00620911\pi$
$199$	295.082	+	170.365i	1.48282	+	0.856108i	0.483013	+	0.875613i	$0.339542\pi$
$200$		0			0
$201$	−1.14912	−	1.99034i	−0.00571702	−	0.00990217i
$202$	−55.0000	+	55.0000i	−0.272277	+	0.272277i
$203$	46.0892	−	106.158i	0.227040	−	0.522944i
$204$			110.232i			0.540354i
$205$		0			0
$206$	0.158312	−	0.274205i	0.000768507	−	0.00133109i
$207$	39.5549	+	147.621i	0.191086	+	0.713144i
$208$	−17.4958	+	65.2953i	−0.0841146	+	0.313920i
$209$		−	6.58312i		−	0.0314982i
$210$		0			0
$211$	113.799			0.539334			0.269667	−	0.962954i	$-0.413086\pi$
$211$	113.799			0.539334			0.269667	+	0.962954i	$0.413086\pi$
$212$	−180.200	−	48.2845i	−0.850000	−	0.227757i
$213$	100.106	−	26.8232i	0.469979	−	0.125931i
$214$	164.819	+	95.1583i	0.770182	+	0.444665i
$215$		0			0
$216$	70.9657			0.328545
$217$	134.147	−	99.3780i	0.618189	−	0.457963i
$218$	51.1161	+	51.1161i	0.234478	+	0.234478i
$219$	66.8258	−	38.5819i	0.305140	−	0.176173i
$220$		0			0
$221$	−284.306	+	492.433i	−1.28645	+	2.22820i
$222$	−58.7825	−	15.7507i	−0.264786	−	0.0709491i
$223$	158.916	+	158.916i	0.712626	+	0.712626i	0.967084	−	0.254458i	$-0.0818970\pi$
$223$	158.916	+	158.916i	0.712626	+	0.712626i	−0.254458	+	0.967084i	$0.581897\pi$
$224$	−5.83138	+	39.1662i	−0.0260330	+	0.174849i
$225$		0			0
$226$	63.8496	+	110.591i	0.282520	+	0.489340i
$227$	73.8850	+	275.743i	0.325485	+	1.21472i	0.913824	+	0.406111i	$0.133115\pi$
$227$	73.8850	+	275.743i	0.325485	+	1.21472i	−0.588339	+	0.808614i	$0.700218\pi$
$228$	−30.4851	+	8.16845i	−0.133706	+	0.0358265i
$229$	271.368	−	156.674i	1.18501	−	0.684167i	0.227843	−	0.973698i	$-0.426833\pi$
$229$	271.368	−	156.674i	1.18501	−	0.684167i	0.957169	+	0.289531i	$0.0934994\pi$
$230$		0			0
$231$	4.87469	−	6.13525i	0.0211025	−	0.0265595i
$232$	33.0660	−	33.0660i	0.142526	−	0.142526i
$233$	−13.0948	+	48.8705i	−0.0562009	+	0.209745i	−0.988316	−	0.152417i	$-0.951294\pi$
$233$	−13.0948	+	48.8705i	−0.0562009	+	0.209745i	0.932115	+	0.362161i	$0.117961\pi$
$234$	130.740	+	75.4829i	0.558719	+	0.322576i
$235$		0			0
$236$	23.1003	+	40.0108i	0.0978824	+	0.169537i
$237$	−130.040	+	130.040i	−0.548691	+	0.548691i
$238$	−132.648	+	305.529i	−0.557344	+	1.28374i
$239$		−	195.330i		−	0.817280i	−0.912696	−	0.408640i	$-0.866003\pi$
$239$		−	195.330i		−	0.817280i	0.912696	−	0.408640i	$-0.133997\pi$
$240$		0			0
$241$	−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	$0.228425\pi$
$242$	−44.1181	−	164.651i	−0.182306	−	0.680377i
$243$	65.1216	−	243.037i	0.267990	−	1.00015i
$244$			24.3325i			0.0997233i
$245$		0			0
$246$	−0.464489			−0.00188817
$247$	−157.252	−	42.1354i	−0.636646	−	0.170589i
$248$	65.1584	−	17.4591i	0.262735	−	0.0703997i
$249$	−46.3769	−	26.7757i	−0.186252	−	0.107533i
$250$		0			0
$251$	−332.665			−1.32536			−0.662679	−	0.748903i	$-0.730581\pi$
$251$	−332.665			−1.32536			−0.662679	+	0.748903i	$0.730581\pi$
$252$	81.1176	+	35.2178i	0.321895	+	0.139753i
$253$	11.6913	+	11.6913i	0.0462107	+	0.0462107i
$254$	−187.203	+	108.082i	−0.737021	+	0.425519i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	98.8873	+	26.4968i	0.384776	+	0.103100i	0.446021	−	0.895022i	$-0.352841\pi$
$257$	98.8873	+	26.4968i	0.384776	+	0.103100i	−0.0612455	+	0.998123i	$0.519507\pi$
$258$	−95.2506	−	95.2506i	−0.369188	−	0.369188i
$259$	−143.973	−	114.392i	−0.555880	−	0.441667i
$260$		0			0
$261$	−52.2164	−	90.4414i	−0.200063	−	0.346519i
$262$	21.5530	+	80.4369i	0.0822633	+	0.307011i
$263$	193.143	−	51.7525i	0.734384	−	0.196778i	0.127804	−	0.991800i	$-0.459207\pi$
$263$	193.143	−	51.7525i	0.734384	−	0.196778i	0.606581	+	0.795022i	$0.292541\pi$
$264$	2.74205	−	1.58312i	0.0103866	−	0.00599668i
$265$		0			0
$266$	−94.3246	−	14.0438i	−0.354604	−	0.0527962i
$267$	−92.4908	+	92.4908i	−0.346408	+	0.346408i
$268$	0.726242	−	2.71037i	0.00270986	−	0.0101133i
$269$	198.535	+	114.624i	0.738047	+	0.426112i	0.821359	−	0.570412i	$-0.193216\pi$
$269$	198.535	+	114.624i	0.738047	+	0.426112i	−0.0833117	+	0.996524i	$0.526550\pi$
$270$		0			0
$271$	−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
$273$	−115.353	−	155.711i	−0.422537	−	0.570369i
$274$			186.348i			0.680104i
$275$		0			0
$276$	39.6332	−	68.6468i	0.143599	−	0.248720i
$277$	21.9644	+	81.9724i	0.0792940	+	0.295929i	0.994173	−	0.107800i	$-0.0343806\pi$
$277$	21.9644	+	81.9724i	0.0792940	+	0.295929i	−0.914879	+	0.403729i	$0.867714\pi$
$278$	24.9747	−	93.2070i	0.0898372	−	0.335277i
$279$		−	150.649i		−	0.539961i
$280$		0			0
$281$	136.201			0.484699			0.242350	−	0.970189i	$-0.422082\pi$
$281$	136.201			0.484699			0.242350	+	0.970189i	$0.422082\pi$
$282$	106.936	+	28.6533i	0.379205	+	0.101608i
$283$	303.860	−	81.4189i	1.07371	−	0.287699i	0.321693	−	0.946844i	$-0.395748\pi$
$283$	303.860	−	81.4189i	1.07371	−	0.287699i	0.752016	+	0.659145i	$0.229082\pi$
$284$	109.581	+	63.2665i	0.385848	+	0.222769i
$285$		0			0
$286$	16.3325			0.0571066
$287$	−1.28742	−	0.558942i	−0.00448578	−	0.00194753i
$288$	25.2665	+	25.2665i	0.0877309	+	0.0877309i
$289$	−730.126	+	421.538i	−2.52639	+	1.45861i
$290$		0			0
$291$	58.7072	−	101.684i	0.201743	−	0.349429i
$292$	91.0010	+	24.3837i	0.311647	+	0.0835057i
$293$	184.699	+	184.699i	0.630373	+	0.630373i	0.948162	−	0.317789i	$-0.102940\pi$
$293$	184.699	+	184.699i	0.630373	+	0.630373i	−0.317789	+	0.948162i	$0.602940\pi$
$294$	−77.5082	−	82.9340i	−0.263633	−	0.282088i
$295$		0			0
$296$	−37.1504	−	64.3463i	−0.125508	−	0.217386i
$297$	−4.43771	−	16.5618i	−0.0149418	−	0.0557635i
$298$	−119.457	+	32.0084i	−0.400863	+	0.107411i
$299$	354.102	−	204.441i	1.18429	−	0.683748i
$300$		0			0
$301$	−149.385	−	378.625i	−0.496296	−	1.25789i
$302$	−235.982	+	235.982i	−0.781396	+	0.781396i
$303$	23.3184	−	87.0256i	0.0769586	−	0.287213i
$304$	−33.3706	−	19.2665i	−0.109772	−	0.0633766i
$305$		0			0
$306$	150.282	+	260.297i	0.491119	+	0.850643i
$307$	370.647	−	370.647i	1.20732	−	1.20732i	0.235426	−	0.971892i	$-0.424352\pi$
$307$	370.647	−	370.647i	1.20732	−	1.20732i	0.971892	−	0.235426i	$-0.0756484\pi$
$308$	9.50516	−	1.08828i	0.0308609	−	0.00353337i
$309$			0.366750i			0.00118689i
$310$		0			0
$311$	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	$-0.0827975\pi$
$312$	−20.2656	−	75.6324i	−0.0649540	−	0.242411i
$313$	−53.8502	+	200.972i	−0.172045	+	0.642082i	0.824991	+	0.565146i	$0.191180\pi$
$313$	−53.8502	+	200.972i	−0.172045	+	0.642082i	−0.997036	+	0.0769359i	$0.975486\pi$
$314$		−	225.282i		−	0.717460i
$315$		0			0
$316$	−224.533			−0.710547
$317$	398.433	+	106.760i	1.25689	+	0.336781i	0.824993	−	0.565144i	$-0.191179\pi$
$317$	398.433	+	106.760i	1.25689	+	0.336781i	0.431893	+	0.901925i	$0.357846\pi$
$318$	208.728	−	55.9285i	0.656377	−	0.175876i
$319$	−9.78456	−	5.64912i	−0.0306726	−	0.0177088i
$320$		0			0
$321$	−220.446			−0.686748
$322$	192.457	−	142.575i	0.597692	−	0.442779i
$323$	−229.190	−	229.190i	−0.709567	−	0.709567i
$324$	27.2787	−	15.7494i	0.0841936	−	0.0486092i
$325$		0			0
$326$	176.523	−	305.746i	0.541480	−	0.937871i
$327$	−80.8802	−	21.6718i	−0.247340	−	0.0662746i
$328$	−0.401005	−	0.401005i	−0.00122258	−	0.00122258i
$329$	261.912	+	208.099i	0.796086	+	0.632520i
$330$		0			0
$331$	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	$0.642588\pi$
$332$	−16.9222	−	63.1544i	−0.0509704	−	0.190224i
$333$	−160.279	+	42.9467i	−0.481319	+	0.128969i
$334$	−351.259	+	202.799i	−1.05167	+	0.607184i
$335$		0			0
$336$	−16.8338	−	42.6660i	−0.0501005	−	0.126982i
$337$	−259.016	+	259.016i	−0.768593	+	0.768593i	−0.977859	−	0.209266i	$-0.932893\pi$
$337$	−259.016	+	259.016i	−0.768593	+	0.768593i	0.209266	+	0.977859i	$0.432893\pi$
$338$	42.6782	−	159.277i	0.126267	−	0.471234i
$339$	−128.099	−	73.9578i	−0.377872	−	0.218165i
$340$		0			0
$341$	−8.14912	−	14.1147i	−0.0238977	−	0.0413921i
$342$	−60.8496	+	60.8496i	−0.177923	+	0.177923i
$343$	−115.030	−	323.136i	−0.335364	−	0.942089i
$344$		−	164.464i		−	0.478094i
$345$		0			0
$346$	−11.0739	+	19.1806i	−0.0320056	+	0.0554353i
$347$	−85.7311	−	319.953i	−0.247064	−	0.922055i	−0.972335	−	0.233591i	$-0.924952\pi$
$347$	−85.7311	−	319.953i	−0.247064	−	0.922055i	0.725271	−	0.688463i	$-0.241714\pi$
$348$	−14.0190	+	52.3198i	−0.0402846	+	0.150344i
$349$		−	383.298i		−	1.09828i	−0.835732	−	0.549138i	$-0.814956\pi$
$349$		−	383.298i		−	1.09828i	0.835732	−	0.549138i	$-0.185044\pi$
$350$		0			0
$351$	−424.016			−1.20802
$352$	3.73403	+	1.00053i	0.0106080	+	0.00284242i
$353$	−538.726	+	144.351i	−1.52614	+	0.408927i	−0.921756	−	0.387770i	$-0.873246\pi$
$353$	−538.726	+	144.351i	−1.52614	+	0.408927i	−0.604379	+	0.796697i	$0.706579\pi$
$354$	−46.3450	−	26.7573i	−0.130918	−	0.0755856i
$355$		0			0
$356$	−159.699			−0.448593
$357$	−43.8864	−	383.309i	−0.122931	−	1.07369i
$358$	342.900	+	342.900i	0.957821	+	0.957821i
$359$	−190.670	+	110.083i	−0.531113	+	0.306638i	−0.741470	−	0.670987i	$-0.765871\pi$
$359$	−190.670	+	110.083i	−0.531113	+	0.306638i	0.210357	+	0.977625i	$0.432538\pi$
$360$		0			0
$361$	−134.100	+	232.268i	−0.371469	+	0.643403i
$362$	120.391	+	32.2585i	0.332571	+	0.0891120i
$363$	139.615	+	139.615i	0.384614	+	0.384614i
$364$	34.8421	−	234.016i	0.0957202	−	0.642901i
$365$		0			0
$366$	−14.0923	−	24.4086i	−0.0385036	−	0.0666902i
$367$	−126.983	−	473.906i	−0.346002	−	1.29130i	−0.891437	−	0.453145i	$-0.850302\pi$
$367$	−126.983	−	473.906i	−0.346002	−	1.29130i	0.545435	−	0.838153i	$-0.316365\pi$
$368$	93.4809	−	25.0481i	0.254024	−	0.0680656i
$369$	−1.09682	+	0.633250i	−0.00297241	+	0.00171612i
$370$		0			0
$371$	645.830	+	96.1563i	1.74078	+	0.259181i
$372$	−55.2506	+	55.2506i	−0.148523	+	0.148523i
$373$	−11.3448	+	42.3394i	−0.0304150	+	0.113510i	−0.979465	−	0.201617i	$-0.935380\pi$
$373$	−11.3448	+	42.3394i	−0.0304150	+	0.113510i	0.949049	+	0.315127i	$0.102047\pi$
$374$	28.1607	+	16.2586i	0.0752959	+	0.0434721i
$375$		0			0
$376$	67.5831	+	117.057i	0.179742	+	0.311323i
$377$	−197.567	+	197.567i	−0.524051	+	0.524051i
$378$	−246.768	+	28.2533i	−0.652825	+	0.0747443i
$379$			393.135i			1.03729i	0.854988	+	0.518647i	$0.173564\pi$
$379$			393.135i			1.03729i	−0.854988	+	0.518647i	$0.826436\pi$
$380$		0			0
$381$	125.193	−	216.840i	0.328589	−	0.569134i
$382$	−17.2341	−	64.3185i	−0.0451154	−	0.168373i
$383$	−30.8833	+	115.258i	−0.0806352	+	0.300935i	−0.994452	−	0.105192i	$-0.966454\pi$
$383$	−30.8833	+	115.258i	−0.0806352	+	0.300935i	0.913817	+	0.406127i	$0.133121\pi$
$384$		−	18.5330i		−	0.0482630i
$385$		0			0
$386$	144.749			0.374998
$387$	−354.777	−	95.0623i	−0.916738	−	0.245639i
$388$	138.470	−	37.1028i	0.356880	−	0.0956258i
$389$	369.542	+	213.355i	0.949979	+	0.548471i	0.893074	−	0.449909i	$-0.148544\pi$
$389$	369.542	+	213.355i	0.949979	+	0.548471i	0.0569045	+	0.998380i	$0.481877\pi$
$390$		0			0
$391$	814.061			2.08200
$392$	4.68424	−	138.514i	0.0119496	−	0.353351i
$393$	−68.2059	−	68.2059i	−0.173552	−	0.173552i
$394$	282.580	−	163.148i	0.717209	−	0.414081i
$395$		0			0
$396$	4.31662	−	7.47661i	0.0109006	−	0.0188803i
$397$	−106.060	−	28.4186i	−0.267153	−	0.0715835i	0.122756	−	0.992437i	$-0.460827\pi$
$397$	−106.060	−	28.4186i	−0.267153	−	0.0715835i	−0.389909	+	0.920853i	$0.627494\pi$
$398$	−340.731	−	340.731i	−0.856108	−	0.856108i
$399$	102.753	−	40.5409i	0.257527	−	0.101606i
$400$		0			0
$401$	−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	$0.864699\pi$
$402$	0.841215	+	3.13946i	0.00209257	+	0.00780959i
$403$	−389.317	+	104.317i	−0.966048	+	0.258852i
$404$	95.2628	−	55.0000i	0.235799	−	0.136139i
$405$		0			0
$406$	−101.815	+	128.144i	−0.250777	+	0.315626i
$407$	−12.6938	+	12.6938i	−0.0311888	+	0.0311888i
$408$	40.3478	−	150.580i	0.0988917	−	0.369069i
$409$	−340.819	−	196.772i	−0.833298	−	0.481105i	0.0216824	−	0.999765i	$-0.493098\pi$
$409$	−340.819	−	196.772i	−0.833298	−	0.481105i	−0.854981	+	0.518660i	$0.826431\pi$
$410$		0			0
$411$	−107.925	−	186.931i	−0.262591	−	0.454821i
$412$	−0.316625	+	0.316625i	−0.000768507	+	0.000768507i
$413$	−96.2555	−	129.932i	−0.233064	−	0.314606i
$414$		−	216.132i		−	0.522058i
$415$		0			0
$416$	47.7995	−	82.7912i	0.114903	−	0.199017i
$417$	28.9285	+	107.963i	0.0693730	+	0.258904i
$418$	−2.40959	+	8.99271i	−0.00576457	+	0.0215137i
$419$			165.330i			0.394582i	0.980345	+	0.197291i	$0.0632144\pi$
$419$			165.330i			0.394582i	−0.980345	+	0.197291i	$0.936786\pi$
$420$		0			0
$421$	163.631			0.388672			0.194336	−	0.980935i	$-0.437745\pi$
$421$	163.631			0.388672			0.194336	+	0.980935i	$0.437745\pi$
$422$	−155.453	−	41.6535i	−0.368372	−	0.0987050i
$423$	291.576	−	78.1276i	0.689306	−	0.184699i
$424$	228.485	+	131.916i	0.538879	+	0.311122i
$425$		0			0
$426$	−146.565			−0.344049
$427$	−9.68741	−	84.6110i	−0.0226871	−	0.198152i
$428$	−190.317	−	190.317i	−0.444665	−	0.444665i
$429$	−16.3836	+	9.45907i	−0.0381902	+	0.0220491i
$430$		0			0
$431$	−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	$0.328555\pi$
$432$	−96.9410	−	25.9753i	−0.224400	−	0.0601279i
$433$	355.950	+	355.950i	0.822055	+	0.822055i	0.986403	−	0.164347i	$-0.0525518\pi$
$433$	355.950	+	355.950i	0.822055	+	0.822055i	−0.164347	+	0.986403i	$0.552552\pi$
$434$	−219.623	+	86.6516i	−0.506044	+	0.199658i
$435$		0			0
$436$	−51.1161	−	88.5357i	−0.117239	−	0.203064i
$437$	60.3237	+	225.131i	0.138041	+	0.515174i
$438$	−105.408	+	28.2439i	−0.240657	+	0.0644838i
$439$	−162.609	+	93.8826i	−0.370409	+	0.213856i	−0.673637	−	0.739062i	$-0.735269\pi$
$439$	−162.609	+	93.8826i	−0.370409	+	0.213856i	0.303228	+	0.952918i	$0.401936\pi$
$440$		0			0
$441$	−296.090	−	90.1672i	−0.671405	−	0.204461i
$442$	568.612	−	568.612i	1.28645	−	1.28645i
$443$	−154.855	+	577.926i	−0.349560	+	1.30457i	0.537635	+	0.843178i	$0.319318\pi$
$443$	−154.855	+	577.926i	−0.349560	+	1.30457i	−0.887194	+	0.461396i	$0.847349\pi$
$444$	74.5332	+	43.0317i	0.167867	+	0.0969183i
$445$		0			0
$446$	−158.916	−	275.250i	−0.356313	−	0.617152i
$447$	101.293	−	101.293i	0.226606	−	0.226606i
$448$	22.3017	−	51.3677i	0.0497805	−	0.114660i
$449$			93.8630i			0.209049i	0.994522	+	0.104524i	$0.0333321\pi$
$449$			93.8630i			0.209049i	−0.994522	+	0.104524i	$0.966668\pi$
$450$		0			0
$451$	−0.0685092	+	0.118661i	−0.000151905	+	0.000263107i
$452$	−46.7412	−	174.440i	−0.103410	−	0.385930i
$453$	100.050	−	373.390i	0.220860	−	0.824260i
$454$		−	403.715i		−	0.889240i
$455$		0			0
$456$	44.6332			0.0978799
$457$	204.824	+	54.8826i	0.448194	+	0.120093i	0.475854	−	0.879524i	$-0.342139\pi$
$457$	204.824	+	54.8826i	0.448194	+	0.120093i	−0.0276604	+	0.999617i	$0.508806\pi$
$458$	−428.042	+	114.693i	−0.934589	+	0.250422i
$459$	−731.093	−	422.096i	−1.59279	−	0.919600i
$460$		0			0
$461$	350.396			0.760078			0.380039	−	0.924970i	$-0.375911\pi$
$461$	350.396			0.760078			0.380039	+	0.924970i	$0.375911\pi$
$462$	−8.90460	+	6.59665i	−0.0192740	+	0.0142785i
$463$	327.380	+	327.380i	0.707084	+	0.707084i	0.965921	−	0.258837i	$-0.0833391\pi$
$463$	327.380	+	327.380i	0.707084	+	0.707084i	−0.258837	+	0.965921i	$0.583339\pi$
$464$	−57.2720	+	33.0660i	−0.123431	+	0.0712629i
$465$		0			0
$466$	35.7757	−	61.9653i	0.0767719	−	0.132973i
$467$	525.495	+	140.806i	1.12526	+	0.301512i	0.773009	−	0.634395i	$-0.218751\pi$
$467$	525.495	+	140.806i	1.12526	+	0.301512i	0.352248	+	0.935907i	$0.385418\pi$
$468$	−150.966	−	150.966i	−0.322576	−	0.322576i
$469$	−1.44628	+	9.71386i	−0.00308375	+	0.0207119i
$470$		0			0
$471$	130.474	+	225.987i	0.277014	+	0.479803i
$472$	−16.9106	−	63.1111i	−0.0358275	−	0.133710i
$473$	−38.3822	+	10.2845i	−0.0811464	+	0.0217431i
$474$	225.235	−	130.040i	0.475180	−	0.274345i
$475$		0			0
$476$	293.032	−	368.808i	0.615613	−	0.774807i
$477$	416.631	−	416.631i	0.873440	−	0.873440i
$478$	−71.4957	+	266.826i	−0.149573	+	0.558213i
$479$	−58.5721	−	33.8166i	−0.122280	−	0.0705984i	0.437612	−	0.899164i	$-0.355824\pi$
$479$	−58.5721	−	33.8166i	−0.122280	−	0.0705984i	−0.559892	+	0.828565i	$0.689158\pi$
$480$		0			0
$481$	221.971	+	384.465i	0.461479	+	0.799304i
$482$	92.9315	−	92.9315i	0.192804	−	0.192804i
$483$	−110.486	+	254.483i	−0.228749	+	0.526881i
$484$			241.066i			0.498070i
$485$		0			0
$486$	−177.916	+	308.159i	−0.366082	+	0.634072i
$487$	192.958	+	720.130i	0.396218	+	1.47871i	0.819696	+	0.572799i	$0.194143\pi$
$487$	192.958	+	720.130i	0.396218	+	1.47871i	−0.423477	+	0.905907i	$0.639191\pi$
$488$	8.90631	−	33.2388i	0.0182506	−	0.0681123i
$489$			408.937i			0.836271i
$490$		0			0
$491$	199.061			0.405419			0.202710	−	0.979239i	$-0.435025\pi$
$491$	199.061			0.405419			0.202710	+	0.979239i	$0.435025\pi$
$492$	0.634504	+	0.170015i	0.00128964	+	0.000345559i
$493$	−537.320	+	143.975i	−1.08990	+	0.292038i
$494$	199.387	+	115.116i	0.403617	+	0.233029i
$495$		0			0
$496$	−95.3985			−0.192336
$497$	−406.231	−	176.368i	−0.817367	−	0.354866i
$498$	53.5514	+	53.5514i	0.107533	+	0.107533i
$499$	471.810	−	272.400i	0.945511	−	0.545891i	0.0538277	−	0.998550i	$-0.482858\pi$
$499$	471.810	−	272.400i	0.945511	−	0.545891i	0.891684	+	0.452659i	$0.149524\pi$
$500$		0			0
$501$	234.905	−	406.868i	0.468873	−	0.812111i
$502$	454.429	+	121.764i	0.905237	+	0.242557i
$503$	38.0869	+	38.0869i	0.0757195	+	0.0757195i	0.743952	−	0.668233i	$-0.232949\pi$
$503$	38.0869	+	38.0869i	0.0757195	+	0.0757195i	−0.668233	+	0.743952i	$0.732949\pi$
$504$	−97.9180	−	77.7995i	−0.194282	−	0.154364i
$505$		0			0
$506$	−11.6913	−	20.2499i	−0.0231054	−	0.0400197i
$507$	49.4347	+	184.493i	0.0975043	+	0.363891i
$508$	295.285	−	79.1214i	0.581270	−	0.155751i
$509$	−149.946	+	86.5714i	−0.294590	+	0.170081i	−0.640010	−	0.768367i	$-0.721070\pi$
$509$	−149.946	+	86.5714i	−0.294590	+	0.170081i	0.345420	+	0.938448i	$0.387736\pi$
$510$		0			0
$511$	−326.144	−	48.5589i	−0.638247	−	0.0950273i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	62.5566	−	233.464i	0.121943	−	0.455096i
$514$	−125.384	−	72.3906i	−0.243938	−	0.140838i
$515$		0			0
$516$	95.2506	+	164.979i	0.184594	+	0.319727i
$517$	23.0923	−	23.0923i	0.0446660	−	0.0446660i
$518$	154.800	+	208.960i	0.298842	+	0.403397i
$519$		−	25.6541i		−	0.0494300i
$520$		0			0
$521$	−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	$0.241492\pi$
$522$	38.2250	+	142.658i	0.0732280	+	0.273291i
$523$	206.313	−	769.970i	0.394480	−	1.47222i	−0.428185	−	0.903691i	$-0.640847\pi$
$523$	206.313	−	769.970i	0.394480	−	1.47222i	0.822665	−	0.568527i	$-0.192486\pi$
$524$		−	117.768i		−	0.224748i
$525$		0			0
$526$	−282.781			−0.537607
$527$	−775.110	−	207.690i	−1.47080	−	0.394099i
$528$	−4.32518	+	1.15893i	−0.00819162	+	0.00219494i
$529$	−48.8266	−	28.1901i	−0.0922998	−	0.0532893i
$530$		0			0
$531$	−145.916			−0.274794
$532$	123.709	+	53.7094i	0.232536	+	0.100957i
$533$	2.39598	+	2.39598i	0.00449527	+	0.00449527i
$534$	160.199	−	92.4908i	0.299998	−	0.173204i
$535$		0			0
$536$	−1.98413	+	3.43661i	−0.00370173	+	0.00641159i
$537$	−542.565	−	145.380i	−1.01036	−	0.270726i
$538$	−229.248	−	229.248i	−0.426112	−	0.426112i
$539$	−32.6188	+	7.56851i	−0.0605173	+	0.0140418i
$540$		0			0
$541$	−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	$-0.336270\pi$
$542$	20.5641	+	76.7462i	0.0379411	+	0.141598i
$543$	−139.450	+	37.3655i	−0.256814	+	0.0688130i
$544$	164.833	−	95.1662i	0.303001	−	0.174938i
$545$		0			0
$546$	100.581	+	254.927i	0.184214	+	0.466899i
$547$	−469.765	+	469.765i	−0.858803	+	0.858803i	−0.991197	−	0.132394i	$-0.957734\pi$
$547$	−469.765	+	469.765i	−0.858803	+	0.858803i	0.132394	+	0.991197i	$0.457734\pi$
$548$	68.2082	−	254.557i	0.124468	−	0.464519i
$549$	−66.5537	−	38.4248i	−0.121227	−	0.0699905i
$550$		0			0
$551$	−79.6332	−	137.929i	−0.144525	−	0.250325i
$552$	−79.2665	+	79.2665i	−0.143599	+	0.143599i
$553$	780.765	−	89.3925i	1.41187	−	0.161650i
$554$		−	120.016i		−	0.216635i
$555$		0			0
$556$	−68.2322	+	118.182i	−0.122720	+	0.212557i
$557$	98.7738	+	368.629i	0.177332	+	0.661811i	0.996143	+	0.0877479i	$0.0279670\pi$
$557$	98.7738	+	368.629i	0.177332	+	0.661811i	−0.818811	+	0.574063i	$0.805366\pi$
$558$	−55.1414	+	205.791i	−0.0988197	+	0.368800i
$559$			982.665i			1.75790i
$560$		0			0
$561$	−37.6650			−0.0671390
$562$	−186.053	−	49.8528i	−0.331056	−	0.0887061i
$563$	−176.181	+	47.2076i	−0.312933	+	0.0838502i	−0.411867	−	0.911244i	$-0.635123\pi$
$563$	−176.181	+	47.2076i	−0.312933	+	0.0838502i	0.0989343	+	0.995094i	$0.468457\pi$
$564$	−135.589	−	78.2824i	−0.240406	−	0.138799i
$565$		0			0
$566$	−444.881			−0.786009
$567$	−88.5856	+	65.6254i	−0.156236	+	0.115741i
$568$	−126.533	−	126.533i	−0.222769	−	0.222769i
$569$	647.396	−	373.774i	1.13778	−	0.656897i	0.191899	−	0.981415i	$-0.438535\pi$
$569$	647.396	−	373.774i	1.13778	−	0.656897i	0.945880	+	0.324518i	$0.105202\pi$
$570$		0			0
$571$	−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	$0.218219\pi$
$572$	−22.3106	−	5.97811i	−0.0390046	−	0.0104512i
$573$	54.5384	+	54.5384i	0.0951805	+	0.0951805i
$574$	1.55406	+	1.23476i	0.00270742	+	0.00215114i
$575$		0			0
$576$	−25.2665	−	43.7629i	−0.0438654	−	0.0759772i
$577$	−256.665	−	957.887i	−0.444827	−	1.66012i	−0.716394	−	0.697696i	$-0.754209\pi$
$577$	−256.665	−	957.887i	−0.444827	−	1.66012i	0.271567	−	0.962420i	$-0.412458\pi$
$578$	1151.66	−	308.588i	1.99250	−	0.533888i
$579$	−145.202	+	83.8325i	−0.250781	+	0.144788i
$580$		0			0
$581$	83.9866	+	212.869i	0.144555	+	0.366383i
$582$	−117.414	+	117.414i	−0.201743	+	0.201743i
$583$	16.4982	−	61.5721i	0.0282988	−	0.105613i
$584$	−115.385	−	66.6174i	−0.197577	−	0.114071i
$585$		0			0
$586$	−184.699	−	319.908i	−0.315186	−	0.545919i
$587$	103.786	−	103.786i	0.176808	−	0.176808i	−0.613155	−	0.789963i	$-0.710100\pi$
$587$	103.786	−	103.786i	0.176808	−	0.176808i	0.789963	+	0.613155i	$0.210100\pi$
$588$	75.5222	+	141.660i	0.128439	+	0.240918i
$589$		−	229.749i		−	0.390067i
$590$		0			0
$591$	−188.976	+	327.316i	−0.319757	+	0.553835i
$592$	27.1960	+	101.497i	0.0459391	+	0.171447i
$593$	−24.0988	+	89.9380i	−0.0406388	+	0.151666i	−0.983264	−	0.182187i	$-0.941682\pi$
$593$	−24.0988	+	89.9380i	−0.0406388	+	0.151666i	0.942625	+	0.333853i	$0.108349\pi$
$594$			24.2481i			0.0408217i
$595$		0			0
$596$	174.897			0.293452
$597$	539.133	+	144.460i	0.903071	+	0.241977i
$598$	−558.542	+	149.661i	−0.934017	+	0.250269i
$599$	469.928	+	271.313i	0.784520	+	0.452943i	0.838030	−	0.545624i	$-0.183707\pi$
$599$	469.928	+	271.313i	0.784520	+	0.452943i	−0.0535096	+	0.998567i	$0.517041\pi$
$600$		0			0
$601$	422.829			0.703542			0.351771	−	0.936086i	$-0.385580\pi$
$601$	422.829			0.703542			0.351771	+	0.936086i	$0.385580\pi$
$602$	65.4777	+	571.890i	0.108767	+	0.949983i
$603$	6.26650	+	6.26650i	0.0103922	+	0.0103922i
$604$	408.732	−	235.982i	0.676709	−	0.390698i
$605$		0			0
$606$	−63.7072	+	110.344i	−0.105127	+	0.182086i
$607$	−198.564	−	53.2050i	−0.327123	−	0.0876524i	0.0915198	−	0.995803i	$-0.470828\pi$
$607$	−198.564	−	53.2050i	−0.327123	−	0.0876524i	−0.418643	+	0.908151i	$0.637494\pi$
$608$	38.5330	+	38.5330i	0.0633766	+	0.0633766i
$609$	27.9183	−	187.512i	0.0458428	−	0.307902i
$610$		0			0
$611$	−403.805	−	699.411i	−0.660892	−	1.14470i
$612$	−110.014	−	410.579i	−0.179762	−	0.670881i
$613$	242.590	−	65.0019i	0.395743	−	0.106039i	−0.0554588	−	0.998461i	$-0.517662\pi$
$613$	242.590	−	65.0019i	0.395743	−	0.106039i	0.451202	+	0.892422i	$0.350995\pi$
$614$	−641.979	+	370.647i	−1.04557	+	0.603659i
$615$		0			0
$616$	−13.3826	−	1.99251i	−0.0217250	−	0.00323460i
$617$	−206.947	+	206.947i	−0.335409	+	0.335409i	−0.854636	−	0.519227i	$-0.826220\pi$
$617$	−206.947	+	206.947i	−0.335409	+	0.335409i	0.519227	+	0.854636i	$0.326220\pi$
$618$	0.134240	−	0.500990i	0.000217217	−	0.000810664i
$619$	408.698	+	235.962i	0.660255	+	0.381199i	0.792374	−	0.610035i	$-0.208845\pi$
$619$	408.698	+	235.962i	0.660255	+	0.381199i	−0.132119	+	0.991234i	$0.542178\pi$
$620$		0			0
$621$	303.524	+	525.719i	0.488766	+	0.846568i
$622$	−439.079	+	439.079i	−0.705915	+	0.705915i
$623$	555.319	−	63.5805i	0.891363	−	0.102055i
$624$			110.734i			0.177458i
$625$		0			0
$626$	147.122	−	254.822i	0.235018	−	0.407064i
$627$	−2.79106	−	10.4164i	−0.00445145	−	0.0166130i
$628$	−82.4591	+	307.741i	−0.131304	+	0.490034i
$629$			883.865i			1.40519i
$630$		0			0
$631$	−675.457			−1.07045			−0.535227	−	0.844708i	$-0.679774\pi$
$631$	−675.457			−1.07045			−0.535227	+	0.844708i	$0.679774\pi$
$632$	306.718	+	82.1848i	0.485313	+	0.130039i
$633$	180.063	−	48.2478i	0.284460	−	0.0762208i
$634$	−505.192	−	291.673i	−0.796833	−	0.460052i
$635$		0			0
$636$	−305.599			−0.480502
$637$	−27.9881	+	827.611i	−0.0439373	+	1.29923i
$638$	11.2982	+	11.2982i	0.0177088	+	0.0177088i
$639$	−346.090	+	199.815i	−0.541612	+	0.312700i
$640$		0			0
$641$	−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	$0.177468\pi$
$642$	301.135	+	80.6889i	0.469058	+	0.125684i
$643$	−344.145	−	344.145i	−0.535218	−	0.535218i	0.386902	−	0.922121i	$-0.373545\pi$
$643$	−344.145	−	344.145i	−0.535218	−	0.535218i	−0.922121	+	0.386902i	$0.873545\pi$
$644$	−315.087	+	124.317i	−0.489266	+	0.193038i
$645$		0			0
$646$	229.190	+	396.969i	0.354783	+	0.614503i
$647$	240.882	+	898.982i	0.372305	+	1.38946i	0.857242	+	0.514913i	$0.172176\pi$
$647$	240.882	+	898.982i	0.372305	+	1.38946i	−0.484937	+	0.874549i	$0.661157\pi$
$648$	−43.0281	+	11.5293i	−0.0664014	+	0.0177922i
$649$	−13.6712	+	7.89307i	−0.0210650	+	0.0121619i
$650$		0			0
$651$	170.125	−	214.119i	0.261329	−	0.328908i
$652$	−353.045	+	353.045i	−0.541480	+	0.541480i
$653$	150.489	−	561.631i	0.230457	−	0.860078i	−0.749687	−	0.661793i	$-0.769796\pi$
$653$	150.489	−	561.631i	0.230457	−	0.860078i	0.980144	−	0.198286i	$-0.0635374\pi$
$654$	102.552	+	59.2084i	0.156807	+	0.0905328i
$655$		0			0
$656$	0.401005	+	0.694561i	0.000611288	+	0.00105878i
$657$	−210.398	+	210.398i	−0.320241	+	0.320241i
$658$	−281.609	−	380.135i	−0.427978	−	0.577713i
$659$		−	217.266i		−	0.329691i	−0.986319	−	0.164846i	$-0.947287\pi$
$659$		−	217.266i		−	0.329691i	0.986319	−	0.164846i	$-0.0527126\pi$
$660$		0			0
$661$	−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	$0.196504\pi$
$662$	−136.667	−	510.047i	−0.206445	−	0.770463i
$663$	−241.076	+	899.706i	−0.363613	+	1.35702i
$664$			92.4645i			0.139254i
$665$		0			0
$666$	234.665			0.352350
$667$	386.380	+	103.530i	0.579280	+	0.155218i
$668$	554.059	−	148.460i	0.829429	−	0.222245i
$669$	318.825	+	184.074i	0.476570	+	0.275148i
$670$		0			0
$671$	−8.31411			−0.0123906
$672$	7.37848	+	64.4445i	0.0109799	+	0.0958995i
$673$	129.111	+	129.111i	0.191844	+	0.191844i	0.796493	−	0.604648i	$-0.206686\pi$
$673$	129.111	+	129.111i	0.191844	+	0.191844i	−0.604648	+	0.796493i	$0.706686\pi$
$674$	448.629	−	259.016i	0.665621	−	0.384297i
$675$		0			0
$676$	−116.599	+	201.955i	−0.172484	+	0.298751i
$677$	425.912	+	114.123i	0.629116	+	0.168571i	0.559269	−	0.828986i	$-0.311082\pi$
$677$	425.912	+	114.123i	0.629116	+	0.168571i	0.0698477	+	0.997558i	$0.477749\pi$
$678$	147.916	+	147.916i	0.218165	+	0.218165i
$679$	−466.726	+	184.145i	−0.687373	+	0.271201i
$680$		0			0
$681$	233.814	+	404.978i	0.343339	+	0.594681i
$682$	5.96557	+	22.2638i	0.00874717	+	0.0326449i
$683$	−48.1139	+	12.8921i	−0.0704449	+	0.0188757i	−0.293869	−	0.955846i	$-0.594943\pi$
$683$	−48.1139	+	12.8921i	−0.0704449	+	0.0188757i	0.223424	+	0.974721i	$0.428276\pi$
$684$	105.395	−	60.8496i	0.154086	−	0.0889614i
$685$		0			0
$686$	38.8576	+	483.516i	0.0566437	+	0.704834i
$687$	362.955	−	362.955i	0.528319	−	0.528319i
$688$	−60.1982	+	224.663i	−0.0874974	+	0.326545i
$689$	−1365.18	−	788.188i	−1.98139	−	1.14396i
$690$		0			0
$691$	−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
$693$	−12.0335	+	27.7169i	−0.0173643	+	0.0399955i
$694$			468.444i			0.674991i
$695$		0			0
$696$	38.3008	−	66.3389i	0.0550298	−	0.0953144i
$697$	1.74604	+	6.51631i	0.00250508	+	0.00934908i
$698$	−140.297	+	523.595i	−0.200998	+	0.750136i
$699$			82.8789i			0.118568i
$700$		0			0
$701$	−85.2715			−0.121643			−0.0608213	−	0.998149i	$-0.519372\pi$
$701$	−85.2715			−0.121643			−0.0608213	+	0.998149i	$0.519372\pi$
$702$	579.216	+	155.201i	0.825095	+	0.221083i
$703$	−244.436	+	65.4964i	−0.347704	+	0.0931670i
$704$	−4.73456	−	2.73350i	−0.00672523	−	0.00388281i
$705$		0			0
$706$	788.749			1.11721
$707$	−309.359	+	229.177i	−0.437565	+	0.324154i
$708$	53.5146	+	53.5146i	0.0755856	+	0.0755856i
$709$	185.775	−	107.257i	0.262024	−	0.151280i	−0.363233	−	0.931698i	$-0.618327\pi$
$709$	185.775	−	107.257i	0.262024	−	0.151280i	0.625258	+	0.780418i	$0.284994\pi$
$710$		0			0
$711$	354.573	−	614.138i	0.498696	−	0.863766i
$712$	218.153	+	58.4540i	0.306395	+	0.0820983i
$713$	408.024	+	408.024i	0.572263	+	0.572263i
$714$	−80.3508	+	539.673i	−0.112536	+	0.755844i
$715$		0			0
$716$	−342.900	−	593.920i	−0.478910	−	0.829497i
$717$	−82.8144	−	309.068i	−0.115501	−	0.431057i
$718$	300.753	−	80.5864i	0.418876	−	0.112237i
$719$	849.937	−	490.711i	1.18211	−	0.682491i	0.225608	−	0.974218i	$-0.427563\pi$
$719$	849.937	−	490.711i	1.18211	−	0.682491i	0.956502	+	0.291727i	$0.0942298\pi$
$720$		0			0
$721$	0.974937	−	1.22705i	0.00135220	−	0.00170187i
$722$	268.201	−	268.201i	0.371469	−	0.371469i
$723$	−39.4003	+	147.044i	−0.0544956	+	0.203380i
$724$	−152.649	−	88.1320i	−0.210841	−	0.121729i
$725$		0			0
$726$	−139.615	−	241.820i	−0.192307	−	0.333085i
$727$	−10.5831	+	10.5831i	−0.0145573	+	0.0145573i	−0.714348	−	0.699791i	$-0.753277\pi$
$727$	−10.5831	+	10.5831i	−0.0145573	+	0.0145573i	0.699791	+	0.714348i	$0.253277\pi$
$728$	−133.251	+	306.919i	−0.183037	+	0.421591i
$729$		−	270.419i		−	0.370946i
$730$		0			0
$731$	−978.217	+	1694.32i	−1.33819	+	2.31781i
$732$	10.3163	+	38.5009i	0.0140933	+	0.0525969i
$733$	281.561	−	1050.80i	0.384121	−	1.43356i	−0.455427	−	0.890273i	$-0.650514\pi$
$733$	281.561	−	1050.80i	0.384121	−	1.43356i	0.839548	−	0.543285i	$-0.182820\pi$
$734$			693.847i			0.945296i
$735$		0			0
$736$	−136.865			−0.185959
$737$	0.926100	+	0.248148i	0.00125658	+	0.000336700i
$738$	1.73007	−	0.463571i	0.00234427	−	0.000628145i
$739$	319.303	+	184.350i	0.432074	+	0.249458i	0.700230	−	0.713917i	$-0.253081\pi$
$739$	319.303	+	184.350i	0.432074	+	0.249458i	−0.268156	+	0.963376i	$0.586414\pi$
$740$		0			0
$741$	−266.681			−0.359893
$742$	−847.025	−	367.742i	−1.14154	−	0.495609i
$743$	45.4536	+	45.4536i	0.0611758	+	0.0611758i	0.737033	−	0.675857i	$-0.236226\pi$
$743$	45.4536	+	45.4536i	0.0611758	+	0.0611758i	−0.675857	+	0.737033i	$0.736226\pi$
$744$	95.6969	−	55.2506i	0.128625	−	0.0742616i
$745$		0			0
$746$	30.9946	−	53.6842i	0.0415477	−	0.0719627i
$747$	199.461	+	53.4455i	0.267017	+	0.0715469i
$748$	−32.5171	−	32.5171i	−0.0434721	−	0.0434721i
$749$	737.555	+	586.015i	0.984719	+	0.782396i
$750$		0			0
$751$	−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	$-0.341605\pi$
$752$	−49.4743	−	184.641i	−0.0657903	−	0.245533i
$753$	−526.371	+	141.041i	−0.699031	+	0.187305i
$754$	342.197	−	197.567i	0.453842	−	0.262026i
$755$		0			0
$756$	347.433	+	51.7286i	0.459567	+	0.0684240i
$757$	535.185	−	535.185i	0.706981	−	0.706981i	−0.258918	−	0.965899i	$-0.583366\pi$
$757$	535.185	−	535.185i	0.706981	−	0.706981i	0.965899	+	0.258918i	$0.0833660\pi$
$758$	143.897	−	537.032i	0.189838	−	0.708485i
$759$	23.4558	+	13.5422i	0.0309035	+	0.0178421i
$760$		0			0
$761$	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
$763$	212.994	+	287.513i	0.279153	+	0.376819i
$764$			94.1688i			0.123258i
$765$		0			0
$766$	84.3747	−	146.141i	0.110150	−	0.190785i
$767$	101.040	+	377.085i	0.131733	+	0.491636i
$768$	−6.78355	+	25.3165i	−0.00883275	+	0.0329643i
$769$		−	999.457i		−	1.29968i	−0.760069	−	0.649842i	$-0.774835\pi$
$769$		−	999.457i		−	1.29968i	0.760069	−	0.649842i	$-0.225165\pi$
$770$		0			0
$771$	167.702			0.217512
$772$	−197.731	−	52.9819i	−0.256129	−	0.0686295i
$773$	347.180	−	93.0266i	0.449133	−	0.120345i	−0.0271607	−	0.999631i	$-0.508647\pi$
$773$	347.180	−	93.0266i	0.449133	−	0.120345i	0.476294	+	0.879286i	$0.341980\pi$
$774$	449.840	+	259.715i	0.581188	+	0.335549i
$775$		0			0
$776$	−202.734			−0.261255
$777$	−276.305	−	119.960i	−0.355605	−	0.154389i
$778$	−426.710	−	426.710i	−0.548471	−	0.548471i
$779$	−1.67272	+	0.965745i	−0.00214727	+	0.00123972i
$780$		0			0
$781$	−21.6174	+	37.4424i	−0.0276791	+	0.0479416i
$782$	−1112.03	−	297.967i	−1.42203	−	0.381032i
$783$	−293.319	−	293.319i	−0.374609	−	0.374609i
$784$	−57.0983	+	187.499i	−0.0728295	+	0.239157i
$785$		0			0
$786$	68.2059	+	118.136i	0.0867760	+	0.150300i
$787$	20.5997	+	76.8792i	0.0261750	+	0.0976864i	0.977778	−	0.209645i	$-0.0672307\pi$
$787$	20.5997	+	76.8792i	0.0261750	+	0.0976864i	−0.951603	+	0.307331i	$0.900564\pi$
$788$	−445.728	+	119.433i	−0.565645	+	0.151564i
$789$	283.666	−	163.774i	0.359526	−	0.207572i
$790$		0			0
$791$	231.982	+	587.970i	0.293276	+	0.743325i
$792$	−8.63325	+	8.63325i	−0.0109006	+	0.0109006i
$793$	−53.2147	+	198.600i	−0.0671055	+	0.250441i
$794$	134.478	+	77.6412i	0.169368	+	0.0977849i
$795$		0			0
$796$	340.731	+	590.163i	0.428054	+	0.741411i
$797$	320.109	−	320.109i	0.401642	−	0.401642i	−0.477169	−	0.878811i	$-0.658337\pi$
$797$	320.109	−	320.109i	0.401642	−	0.401642i	0.878811	+	0.477169i	$0.158337\pi$
$798$	−155.202	+	17.7697i	−0.194489	+	0.0222678i
$799$		−	1607.91i		−	2.01240i
$800$		0			0
$801$	252.190	−	436.806i	0.314844	−	0.545326i
$802$	28.8793	+	107.779i	0.0360091	+	0.134388i
$803$	−8.33159	+	31.0939i	−0.0103756	+	0.0387222i
$804$		−	4.59648i		−	0.00571702i
$805$		0			0
$806$	570.000			0.707196
$807$	362.736	+	97.1947i	0.449487	+	0.120440i
$808$	−150.263	+	40.2628i	−0.185969	+	0.0498302i
$809$	−1001.47	−	578.200i	−1.23791	−	0.714709i	−0.269245	−	0.963072i	$-0.586774\pi$
$809$	−1001.47	−	578.200i	−1.23791	−	0.714709i	−0.968667	+	0.248363i	$0.920108\pi$
$810$		0			0
$811$	−143.794			−0.177305			−0.0886526	−	0.996063i	$-0.528256\pi$
$811$	−143.794			−0.177305			−0.0886526	+	0.996063i	$0.528256\pi$
$812$	185.986	−	137.781i	0.229047	−	0.169681i
$813$	−65.0764	−	65.0764i	−0.0800448	−	0.0800448i
$814$	21.9863	−	12.6938i	0.0270103	−	0.0155944i
$815$		0			0
$816$	−110.232	+	190.928i	−0.135089	+	0.233980i
$817$	−541.058	−	144.976i	−0.662250	−	0.177449i
$818$	393.544	+	393.544i	0.481105	+	0.481105i
$819$	585.054	+	464.847i	0.714352	+	0.567579i
$820$		0			0
$821$	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	$0.733207\pi$
$822$	79.0064	+	294.856i	0.0961149	+	0.358706i
$823$	−1406.28	+	376.812i	−1.70873	+	0.457852i	−0.975112	−	0.221714i	$-0.928835\pi$
$823$	−1406.28	+	376.812i	−1.70873	+	0.457852i	−0.733615	+	0.679566i	$0.762168\pi$
$824$	0.548410	−	0.316625i	0.000665546	−	0.000384253i
$825$		0			0
$826$	83.9290	+	212.722i	0.101609	+	0.257533i
$827$	969.412	−	969.412i	1.17220	−	1.17220i	0.190520	−	0.981683i	$-0.438983\pi$
$827$	969.412	−	969.412i	1.17220	−	1.17220i	0.981683	−	0.190520i	$-0.0610173\pi$
$828$	−79.1098	+	295.242i	−0.0955432	+	0.356572i
$829$	−747.599	−	431.627i	−0.901808	−	0.520659i	−0.0240219	−	0.999711i	$-0.507647\pi$
$829$	−747.599	−	431.627i	−0.901808	−	0.520659i	−0.877786	+	0.479052i	$0.840980\pi$
$830$		0			0
$831$	69.5079	+	120.391i	0.0836437	+	0.144875i
$832$	−95.5990	+	95.5990i	−0.114903	+	0.114903i
$833$	−872.122	+	1399.11i	−1.04697	+	1.67961i
$834$		−	158.069i		−	0.189531i
$835$		0			0
$836$	6.58312	−	11.4023i	0.00787455	−	0.0136391i
$837$	−154.875	−	578.002i	−0.185036	−	0.690563i
$838$	60.5150	−	225.845i	0.0722136	−	0.269505i
$839$		−	541.425i		−	0.645322i	−0.946515	−	0.322661i	$-0.895423\pi$
$839$		−	541.425i		−	0.645322i	0.946515	−	0.322661i	$-0.104577\pi$
$840$		0			0
$841$	567.660			0.674982
$842$	−223.524	−	59.8930i	−0.265468	−	0.0711318i
$843$	215.508	−	57.7452i	0.255644	−	0.0684996i
$844$	197.107	+	113.799i	0.233539	+	0.134834i
$845$		0			0
$846$	−426.897			−0.504607
$847$	−95.9748	−	838.255i	−0.113311	−	0.989675i
$848$	−263.831	−	263.831i	−0.311122	−	0.311122i
$849$	446.273	−	257.656i	0.525645	−	0.303482i
$850$		0			0
$851$	317.788	−	550.425i	0.373429	−	0.646797i
$852$	200.211	+	53.6464i	0.234990	+	0.0629653i
$853$	−203.211	−	203.211i	−0.238231	−	0.238231i	0.577886	−	0.816117i	$-0.303878\pi$
$853$	−203.211	−	203.211i	−0.238231	−	0.238231i	−0.816117	+	0.577886i	$0.803878\pi$
$854$	−17.7365	+	119.127i	−0.0207687	+	0.139492i
$855$		0			0
$856$	190.317	+	329.638i	0.222333	+	0.385091i
$857$	−303.758	−	1133.64i	−0.354443	−	1.32280i	−0.881184	−	0.472774i	$-0.843253\pi$
$857$	−303.758	−	1133.64i	−0.354443	−	1.32280i	0.526741	−	0.850026i	$-0.323414\pi$
$858$	25.8426	−	6.92452i	0.0301196	−	0.00807053i
$859$	−254.787	+	147.102i	−0.296609	+	0.171247i	−0.640919	−	0.767609i	$-0.721446\pi$
$859$	−254.787	+	147.102i	−0.296609	+	0.171247i	0.344309	+	0.938856i	$0.388113\pi$
$860$		0			0
$861$	−2.27404	−	0.338577i	−0.00264116	−	0.000393237i
$862$	419.744	−	419.744i	0.486942	−	0.486942i
$863$	367.260	−	1370.63i	0.425562	−	1.58822i	−0.337132	−	0.941457i	$-0.609457\pi$
$863$	367.260	−	1370.63i	0.425562	−	1.58822i	0.762693	−	0.646760i	$-0.223877\pi$
$864$	122.916	+	70.9657i	0.142264	+	0.0821363i
$865$		0			0
$866$	−355.950	−	616.523i	−0.411028	−	0.711921i
$867$	−976.546	+	976.546i	−1.12635	+	1.12635i
$868$	331.728	−	37.9807i	0.382175	−	0.0437565i
$869$		−	76.7201i		−	0.0882855i
$870$		0			0
$871$	11.8550	−	20.5335i	0.0136108	−	0.0235747i
$872$	37.4196	+	139.652i	0.0429124	+	0.160151i
$873$	−117.182	+	437.330i	−0.134229	+	0.500951i
$874$		−	329.615i		−	0.377134i
$875$		0			0
$876$	154.327			0.176173
$877$	1352.53	+	362.410i	1.54222	+	0.413238i	0.926984	−	0.375101i	$-0.122392\pi$
$877$	1352.53	+	362.410i	1.54222	+	0.413238i	0.615241	+	0.788339i	$0.289059\pi$
$878$	256.492	−	68.7268i	0.292132	−	0.0782766i
$879$	370.554	+	213.939i	0.421563	+	0.243390i
$880$		0			0
$881$	1069.93			1.21445			0.607223	−	0.794532i	$-0.292284\pi$
$881$	1069.93			1.21445			0.607223	+	0.794532i	$0.292284\pi$
$882$	371.463	+	231.547i	0.421160	+	0.262525i
$883$	−1198.71	−	1198.71i	−1.35754	−	1.35754i	−0.876944	−	0.480593i	$-0.840421\pi$
$883$	−1198.71	−	1198.71i	−1.35754	−	1.35754i	−0.480593	−	0.876944i	$-0.659579\pi$
$884$	−984.865	+	568.612i	−1.11410	+	0.643227i
$885$		0			0
$886$	423.071	−	732.781i	0.477507	−	0.827067i
$887$	−74.4895	−	19.9594i	−0.0839791	−	0.0225021i	0.216585	−	0.976264i	$-0.430508\pi$
$887$	−74.4895	−	19.9594i	−0.0839791	−	0.0225021i	−0.300564	+	0.953762i	$0.597175\pi$
$888$	−86.0635	−	86.0635i	−0.0969183	−	0.0969183i
$889$	−995.290	+	392.688i	−1.11956	+	0.441719i
$890$		0			0
$891$	5.38137	+	9.32080i	0.00603969	+	0.0104611i
$892$	116.334	+	434.166i	0.130420	+	0.486733i
$893$	444.672	−	119.150i	0.497953	−	0.133426i
$894$	−175.444	+	101.293i	−0.196246	+	0.113303i
$895$		0			0
$896$	−49.2665	+	62.0065i	−0.0549849	+	0.0692037i
$897$	473.612	−	473.612i	0.527996	−	0.527996i
$898$	34.3562	−	128.219i	0.0382586	−	0.142783i
$899$	−341.479	−	197.153i	−0.379843	−	0.219302i
$900$		0			0
$901$	−1569.24	−	2718.00i	−1.74166	−	3.01665i
$902$	0.137018	−	0.137018i	0.000151905	−	0.000151905i
$903$	−396.896	−	535.757i	−0.439530	−	0.593307i
$904$			255.398i			0.282520i
$905$		0			0
$906$	−273.340	+	473.440i	−0.301700	+	0.522560i
$907$	−260.960	−	973.915i	−0.287717	−	1.07378i	−0.946831	−	0.321732i	$-0.895735\pi$
$907$	−260.960	−	973.915i	−0.287717	−	1.07378i	0.659113	−	0.752044i	$-0.270932\pi$
$908$	−147.770	+	551.485i	−0.162742	+	0.607362i
$909$			347.414i			0.382194i
$910$		0			0
$911$	−1241.02			−1.36226			−0.681130	−	0.732162i	$-0.738511\pi$
$911$	−1241.02			−1.36226			−0.681130	+	0.732162i	$0.738511\pi$
$912$	−60.9702	−	16.3369i	−0.0668532	−	0.0179133i
$913$	21.5791	−	5.78210i	0.0236354	−	0.00633308i
$914$	−259.707	−	149.942i	−0.284143	−	0.164050i
$915$		0			0
$916$	626.697			0.684167
$917$	46.8865	+	409.512i	0.0511303	+	0.446578i
$918$	844.193	+	844.193i	0.919600	+	0.919600i
$919$	5.83356	−	3.36801i	0.00634772	−	0.00366486i	−0.496823	−	0.867852i	$-0.665500\pi$
$919$	5.83356	−	3.36801i	0.00634772	−	0.00366486i	0.503171	+	0.864187i	$0.332167\pi$
$920$		0			0
$921$	429.325	−	743.612i	0.466150	−	0.807396i
$922$	−478.650	−	128.254i	−0.519143	−	0.139104i
$923$	756.027	+	756.027i	0.819097	+	0.819097i
$924$	14.5785	−	5.75188i	0.0157776	−	0.00622498i
$925$		0			0
$926$	−327.380	−	567.039i	−0.353542	−	0.612353i
$927$	−0.366025	−	1.36603i	−0.000394849	−	0.00147360i
$928$	90.3380	−	24.2060i	0.0973470	−	0.0260840i
$929$	−361.434	+	208.674i	−0.389057	+	0.224622i	−0.681752	−	0.731584i	$-0.738782\pi$
$929$	−361.434	+	208.674i	−0.389057	+	0.224622i	0.292694	+	0.956206i	$0.405448\pi$
$930$		0			0
$931$	−451.556	−	137.511i	−0.485022	−	0.147702i
$932$	−71.5514	+	71.5514i	−0.0767719	+	0.0767719i
$933$	186.157	−	694.748i	0.199525	−	0.744639i
$934$	−666.301	−	384.689i	−0.713384	−	0.411872i
$935$		0			0
$936$	150.966	+	261.480i	0.161288	+	0.279359i
$937$	46.4937	−	46.4937i	0.0496198	−	0.0496198i	−0.681862	−	0.731481i	$-0.738829\pi$
$937$	46.4937	−	46.4937i	0.0496198	−	0.0496198i	0.731481	+	0.681862i	$0.238829\pi$
$938$	5.53117	−	12.7400i	0.00589677	−	0.0135821i
$939$			340.825i			0.362966i
$940$		0			0
$941$	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	$-0.110898\pi$
$942$	−95.5134	−	356.461i	−0.101394	−	0.378408i
$943$	1.25555	−	4.68579i	0.00133145	−	0.00496902i
$944$			92.4010i			0.0978824i
$945$		0			0
$946$	56.1955			0.0594033
$947$	539.920	+	144.671i	0.570137	+	0.152768i	0.532359	−	0.846518i	$-0.321306\pi$
$947$	539.920	+	144.671i	0.570137	+	0.152768i	0.0377774	+	0.999286i	$0.487972\pi$
$948$	−355.275	+	95.1957i	−0.374763	+	0.100417i
$949$	689.416	+	398.035i	0.726466	+	0.419425i
$950$		0			0
$951$	675.697			0.710512
$952$	−535.282	+	396.544i	−0.562271	+	0.416538i
$953$	−27.0794	−	27.0794i	−0.0284149	−	0.0284149i	0.692757	−	0.721171i	$-0.256396\pi$
$953$	−27.0794	−	27.0794i	−0.0284149	−	0.0284149i	−0.721171	+	0.692757i	$0.756396\pi$
$954$	−721.626	+	416.631i	−0.756421	+	0.436720i
$955$		0			0
$956$	195.330	−	338.321i	0.204320	−	0.353893i
$957$	−17.8770	−	4.79014i	−0.0186803	−	0.00500537i
$958$	67.6332	+	67.6332i	0.0705984	+	0.0705984i
$959$	−135.834	+	912.321i	−0.141641	+	0.951325i
$960$		0			0
$961$	196.098	+	339.651i	0.204056	+	0.353435i
$962$	−162.494	−	606.437i	−0.168913	−	0.630391i
$963$	821.090	−	220.010i	0.852637	−	0.228463i
$964$	−160.962	+	92.9315i	−0.166973	+	0.0964020i
$965$		0			0
$966$	244.074	−	307.190i	0.252665	−	0.318002i
$967$	−1012.58	+	1012.58i	−1.04713	+	1.04713i	−0.0483007	+	0.998833i	$0.515381\pi$
$967$	−1012.58	+	1012.58i	−1.04713	+	1.04713i	−0.998833	+	0.0483007i	$0.984619\pi$
$968$	88.2363	−	329.302i	0.0911532	−	0.340188i
$969$	−459.814	−	265.474i	−0.474524	−	0.273967i
$970$		0			0
$971$	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
$973$	190.212	−	438.116i	0.195490	−	0.450274i
$974$		−	1054.34i		−	1.08249i
$975$		0			0
$976$	−24.3325	+	42.1451i	−0.0249308	+	0.0431815i
$977$	−160.479	−	598.914i	−0.164256	−	0.613014i	−0.998134	−	0.0610638i	$-0.980551\pi$
$977$	−160.479	−	598.914i	−0.164256	−	0.613014i	0.833877	−	0.551950i	$-0.186116\pi$
$978$	149.681	−	558.618i	0.153048	−	0.571184i
$979$		−	54.5673i		−	0.0557377i
$980$		0			0
$981$	322.881			0.329135
$982$	−271.922	−	72.8614i	−0.276907	−	0.0741969i
$983$	−1296.21	+	347.318i	−1.31862	+	0.353324i	−0.848462	−	0.529256i	$-0.822471\pi$
$983$	−1296.21	+	347.318i	−1.31862	+	0.353324i	−0.470161	+	0.882580i	$0.655804\pi$
$984$	−0.804519	−	0.464489i	−0.000817600	−	0.000472042i
$985$		0			0
$986$	786.692			0.797862
$987$	502.648	+	218.228i	0.509268	+	0.221103i
$988$	−230.232	−	230.232i	−0.233029	−	0.233029i
$989$	1218.36	−	703.422i	1.23191	−	0.711246i
$990$		0			0
$991$	−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	$0.904105\pi$
$992$	130.317	+	34.9183i	0.131368	+	0.0351999i
$993$	432.491	+	432.491i	0.435540	+	0.435540i
$994$	490.367	+	389.615i	0.493327	+	0.391967i
$995$		0			0
$996$	−53.5514	−	92.7537i	−0.0537664	−	0.0931262i
$997$	−237.255	−	885.448i	−0.237969	−	0.888112i	−0.976788	−	0.214208i	$-0.931283\pi$
$997$	−237.255	−	885.448i	−0.237969	−	0.888112i	0.738819	−	0.673904i	$-0.235384\pi$
$998$	−744.210	+	199.410i	−0.745701	+	0.199810i
$999$	−570.798	+	329.551i	−0.571370	+	0.329880i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.b.23.2	✓	8	35.9	even	6
70.3.l.b.37.1	yes	8	35.23	odd	12
70.3.l.b.53.1	yes	8	5.4	even	2
70.3.l.b.67.2	yes	8	5.3	odd	4
350.3.p.b.93.1		8	7.2	even	3	inner
350.3.p.b.107.2		8	35.2	odd	12	inner
350.3.p.b.193.2		8	1.1	even	1	trivial
350.3.p.b.207.1		8	5.2	odd	4	inner
490.3.f.f.197.2		4	35.18	odd	12
490.3.f.f.393.2		4	35.4	even	6
490.3.f.k.197.1		4	35.3	even	12
490.3.f.k.393.1		4	35.24	odd	6

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.p (of order \(12\), degree \(4\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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