LMFDB - Embedded newform 350.3.p.b.207.1

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			207.1
Root			$-1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	350.207
Dual form			350.3.p.b.93.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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	$-0.995312\pi$
$3$	−0.423972	−	1.58228i	−0.141324	−	0.527428i	0.858568	−	0.512700i	$-0.171355\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−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
$10$		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	$0.176556\pi$
$12$	−0.847944	+	3.16457i	−0.0706620	+	0.263714i
$13$	11.9499	−	11.9499i	0.919221	−	0.919221i	−0.0777517	−	0.996973i	$-0.524774\pi$
$13$	11.9499	−	11.9499i	0.919221	−	0.919221i	0.996973	+	0.0777517i	$0.0247741\pi$
$14$	−7.75082	−	6.15831i	−0.553630	−	0.439879i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−32.4999	+	8.70832i	−1.91176	+	0.512254i	−0.918646	+	0.395082i	$0.870716\pi$
$17$	−32.4999	+	8.70832i	−1.91176	+	0.512254i	−0.993112	+	0.117172i	$0.962617\pi$
$18$	−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	$0.251749\pi$
$20$		0			0
$21$	−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	−0.287922	−	0.957654i	$-0.592964\pi$
$23$	−23.3702	−	6.26203i	−1.01610	−	0.272262i	−0.728175	+	0.685392i	$0.759631\pi$
$24$	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
$28$	−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	$-0.0920108\pi$
$30$		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	$0.292352\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$	1.08129	+	0.289732i	0.0327665	+	0.00877975i
$34$			47.5831i			1.39950i
$35$		0			0
$36$	−12.6332			−0.350924
$37$	−6.79899	+	25.3742i	−0.183757	+	0.685789i	0.811137	+	0.584856i	$0.198849\pi$
$37$	−6.79899	+	25.3742i	−0.183757	+	0.685789i	−0.994893	+	0.100932i	$0.967817\pi$
$38$	−3.52601	−	13.1593i	−0.0927898	−	0.346296i
$39$	−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	$0.499222\pi$
$42$	−6.45807	+	14.8749i	−0.153764	+	0.354165i
$43$	41.1161	−	41.1161i	0.956189	−	0.956189i	−0.0428909	−	0.999080i	$-0.513657\pi$
$43$	41.1161	−	41.1161i	0.956189	−	0.956189i	0.999080	+	0.0428909i	$0.0136568\pi$
$44$	1.18364	−	0.683375i	0.0269009	−	0.0155313i
$45$		0			0
$46$	−17.1082	+	29.6322i	−0.371917	+	0.644179i
$47$	12.3686	−	46.1601i	0.263161	−	0.982130i	−0.700205	−	0.713942i	$-0.746908\pi$
$47$	12.3686	−	46.1601i	0.263161	−	0.982130i	0.963366	−	0.268189i	$-0.0864251\pi$
$48$	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
$52$	−32.6477	+	8.74792i	−0.627840	+	0.168229i
$53$	24.1422	+	90.1000i	0.455514	+	1.70000i	0.686573	+	0.727061i	$0.259114\pi$
$53$	24.1422	+	90.1000i	0.455514	+	1.70000i	−0.231059	+	0.972940i	$0.574219\pi$
$54$	−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
$58$	−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	$0.729386\pi$
$60$		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
$63$	−5.02963	−	43.9294i	−0.0798354	−	0.697292i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	0.791562	−	1.37103i	0.0119934	−	0.0207731i
$67$	1.35519	−	0.363121i	0.0202266	−	0.00541971i	−0.248692	−	0.968583i	$-0.580001\pi$
$67$	1.35519	−	0.363121i	0.0202266	−	0.00541971i	0.268918	+	0.963163i	$0.413334\pi$
$68$	64.9998	+	17.4166i	0.955879	+	0.256127i
$69$			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	$0.353012\pi$
$72$	−4.62409	+	17.2573i	−0.0642235	+	0.239685i
$73$	−12.1918	−	45.5005i	−0.167011	−	0.623295i	−0.997775	−	0.0666696i	$-0.978763\pi$
$73$	−12.1918	−	45.5005i	−0.167011	−	0.623295i	0.830764	−	0.556625i	$-0.187904\pi$
$74$	32.1732	+	18.5752i	0.434773	+	0.251016i
$75$		0			0
$76$	−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	$0.0817807\pi$
$80$		0			0
$81$	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	−0.832513	−	0.554006i	$-0.813099\pi$
$83$	−23.1161	+	23.1161i	−0.278507	+	0.278507i	0.554006	+	0.832513i	$0.313099\pi$
$84$	17.9557	+	14.2665i	0.213759	+	0.169839i
$85$		0			0
$86$	−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	$0.185258\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	−4.63325	−	8.02502i	−0.0482630	−	0.0835940i
$97$	50.6834	+	50.6834i	0.522509	+	0.522509i	0.918328	−	0.395819i	$-0.129539\pi$
$97$	50.6834	+	50.6834i	0.522509	+	0.522509i	−0.395819	+	0.918328i	$0.629539\pi$
$98$	−61.1493	+	32.6001i	−0.623972	+	0.332654i
$99$			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	$0.0788899\pi$
$102$	75.2900	−	20.1739i	0.738137	−	0.197783i
$103$	0.216259	+	0.0579464i	0.00209960	+	0.000562586i	0.259869	−	0.965644i	$-0.416321\pi$
$103$	0.216259	+	0.0579464i	0.00209960	+	0.000562586i	−0.257769	+	0.966207i	$0.582987\pi$
$104$			47.7995i			0.459611i
$105$		0			0
$106$	131.916			1.24449
$107$	34.8304	−	129.989i	0.325517	−	1.21485i	−0.588273	−	0.808662i	$-0.700192\pi$
$107$	34.8304	−	129.989i	0.325517	−	1.21485i	0.913791	−	0.406185i	$-0.133141\pi$
$108$	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	$0.591329\pi$
$110$		0			0
$111$	43.0317			0.387673
$112$	27.8183	−	3.18501i	0.248377	−	0.0284376i
$113$	−63.8496	+	63.8496i	−0.565041	+	0.565041i	−0.930735	−	0.365694i	$-0.880832\pi$
$113$	−63.8496	+	63.8496i	−0.565041	+	0.565041i	0.365694	+	0.930735i	$0.380832\pi$
$114$	−19.3268	+	11.1583i	−0.169533	+	0.0978799i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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
$125$		0			0
$126$	−61.8496	−	9.20866i	−0.490870	−	0.0730846i
$127$	108.082	+	108.082i	0.851038	+	0.851038i	0.990261	−	0.139223i	$-0.0444604\pi$
$127$	108.082	+	108.082i	0.851038	+	0.851038i	−0.139223	+	0.990261i	$0.544460\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$	−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
$133$	−7.67050	−	66.9951i	−0.0576730	−	0.503722i
$134$		−	1.98413i		−	0.0148069i
$135$		0			0
$136$	47.5831	−	82.4164i	0.349876	−	0.606003i
$137$	127.278	−	34.1041i	0.929039	−	0.248935i	0.237594	−	0.971365i	$-0.423641\pi$
$137$	127.278	−	34.1041i	0.929039	−	0.248935i	0.691445	+	0.722429i	$0.256975\pi$
$138$	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	$-0.0789323\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	$0.428137\pi$
$150$		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	$-0.118825\pi$
$152$	−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
$155$		0			0
$156$	27.6834	+	47.9490i	0.177458	+	0.307365i
$157$	−153.871	+	41.2295i	−0.980068	+	0.262609i	−0.713073	−	0.701089i	$-0.752697\pi$
$157$	−153.871	+	41.2295i	−0.980068	+	0.262609i	−0.266995	+	0.963698i	$0.586031\pi$
$158$	−41.0924	−	153.359i	−0.260078	−	0.970626i
$159$	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
$163$	241.134	+	64.6117i	1.47935	+	0.396391i	0.906126	−	0.423007i	$-0.139025\pi$
$163$	241.134	+	64.6117i	1.47935	+	0.396391i	0.573225	+	0.819398i	$0.305692\pi$
$164$	−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	0.969575	+	0.244793i	$0.0787200\pi$
$167$	202.799	+	202.799i	1.21437	+	1.21437i	0.244793	+	0.969575i	$0.421280\pi$
$168$	26.0607	−	19.3061i	0.155123	−	0.114917i
$169$		−	116.599i		−	0.689935i
$170$		0			0
$171$	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	0.214833	−	0.976651i	$-0.431079\pi$
$173$	−15.1273	−	4.05334i	−0.0874409	−	0.0234297i	−0.302274	+	0.953221i	$0.597746\pi$
$174$			38.3008i			0.220119i
$175$		0			0
$176$	−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	$0.259447\pi$
$180$		0			0
$181$	−88.1320			−0.486917			−0.243459	−	0.969911i	$-0.578282\pi$
$181$	−88.1320			−0.486917			−0.243459	+	0.969911i	$0.578282\pi$
$182$	−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
$185$		0			0
$186$	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
$190$		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	$0.793999\pi$
$192$	−12.6583	+	3.39177i	−0.0659285	+	0.0176655i
$193$	26.4910	+	98.8657i	0.137259	+	0.512257i	0.999978	+	0.00657446i	$0.00209273\pi$
$193$	26.4910	+	98.8657i	0.137259	+	0.512257i	−0.862719	+	0.505683i	$0.831241\pi$
$194$	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	0.159101	−	0.987262i	$-0.449141\pi$
$197$	−163.148	−	163.148i	−0.828162	−	0.828162i	−0.987262	+	0.159101i	$0.949141\pi$
$198$	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	$0.993791\pi$
$200$		0			0
$201$	−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			0
$206$	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
$210$		0			0
$211$	113.799			0.539334			0.269667	−	0.962954i	$-0.413086\pi$
$211$	113.799			0.539334			0.269667	+	0.962954i	$0.413086\pi$
$212$	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
$215$		0			0
$216$	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
$220$		0			0
$221$	−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	−0.254458	−	0.967084i	$-0.581897\pi$
$223$	158.916	−	158.916i	0.712626	−	0.712626i	0.967084	+	0.254458i	$0.0818970\pi$
$224$	5.83138	−	39.1662i	0.0260330	−	0.174849i
$225$		0			0
$226$	63.8496	+	110.591i	0.282520	+	0.489340i
$227$	−275.743	+	73.8850i	−1.21472	+	0.325485i	−0.808614	−	0.588339i	$-0.799782\pi$
$227$	−275.743	+	73.8850i	−1.21472	+	0.325485i	−0.406111	+	0.913824i	$0.633115\pi$
$228$	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	$0.573167\pi$
$230$		0			0
$231$	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	0.362161	−	0.932115i	$-0.382039\pi$
$233$	48.8705	+	13.0948i	0.209745	+	0.0562009i	−0.152417	+	0.988316i	$0.548706\pi$
$234$	−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
$238$	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	$0.866003\pi$
$240$		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	$0.228425\pi$
$242$	164.651	−	44.1181i	0.680377	−	0.182306i
$243$	−243.037	−	65.1216i	−1.00015	−	0.267990i
$244$		−	24.3325i		−	0.0997233i
$245$		0			0
$246$	−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
$250$		0			0
$251$	−332.665			−1.32536			−0.662679	−	0.748903i	$-0.730581\pi$
$251$	−332.665			−1.32536			−0.662679	+	0.748903i	$0.730581\pi$
$252$	−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
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−26.4968	+	98.8873i	−0.103100	+	0.384776i	−0.998123	−	0.0612455i	$-0.980493\pi$
$257$	−26.4968	+	98.8873i	−0.103100	+	0.384776i	0.895022	+	0.446021i	$0.147159\pi$
$258$	−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
$262$	−80.4369	+	21.5530i	−0.307011	+	0.0822633i
$263$	−51.7525	−	193.143i	−0.196778	−	0.734384i	−0.991800	−	0.127804i	$-0.959207\pi$
$263$	−51.7525	−	193.143i	−0.196778	−	0.734384i	0.795022	−	0.606581i	$-0.207459\pi$
$264$	−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
$268$	−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	$0.806784\pi$
$270$		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
$273$	−155.711	+	115.353i	−0.570369	+	0.422537i
$274$		−	186.348i		−	0.680104i
$275$		0			0
$276$	39.6332	−	68.6468i	0.143599	−	0.248720i
$277$	−81.9724	+	21.9644i	−0.295929	+	0.0792940i	−0.403729	−	0.914879i	$-0.632286\pi$
$277$	−81.9724	+	21.9644i	−0.295929	+	0.0792940i	0.107800	+	0.994173i	$0.465619\pi$
$278$	−93.2070	−	24.9747i	−0.335277	−	0.0898372i
$279$			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	$0.422082\pi$
$282$	−28.6533	+	106.936i	−0.101608	+	0.379205i
$283$	−81.4189	−	303.860i	−0.287699	−	1.07371i	−0.946844	−	0.321693i	$-0.895748\pi$
$283$	−81.4189	−	303.860i	−0.287699	−	1.07371i	0.659145	−	0.752016i	$-0.270918\pi$
$284$	−109.581	−	63.2665i	−0.385848	−	0.222769i
$285$		0			0
$286$	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
$290$		0			0
$291$	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	−0.317789	−	0.948162i	$-0.602940\pi$
$293$	184.699	−	184.699i	0.630373	−	0.630373i	0.948162	+	0.317789i	$0.102940\pi$
$294$	77.5082	+	82.9340i	0.263633	+	0.282088i
$295$		0			0
$296$	−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
$300$		0			0
$301$	−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
$305$		0			0
$306$	150.282	+	260.297i	0.491119	+	0.850643i
$307$	370.647	+	370.647i	1.20732	+	1.20732i	0.971892	+	0.235426i	$0.0756484\pi$
$307$	370.647	+	370.647i	1.20732	+	1.20732i	0.235426	+	0.971892i	$0.424352\pi$
$308$	−1.08828	−	9.50516i	−0.00353337	−	0.0308609i
$309$		−	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	$-0.0827975\pi$
$312$	75.6324	−	20.2656i	0.242411	−	0.0649540i
$313$	200.972	+	53.8502i	0.642082	+	0.172045i	0.565146	−	0.824991i	$-0.308820\pi$
$313$	200.972	+	53.8502i	0.642082	+	0.172045i	0.0769359	+	0.997036i	$0.475486\pi$
$314$			225.282i			0.717460i
$315$		0			0
$316$	−224.533			−0.710547
$317$	−106.760	+	398.433i	−0.336781	+	1.25689i	0.565144	+	0.824993i	$0.308821\pi$
$317$	−106.760	+	398.433i	−0.336781	+	1.25689i	−0.901925	+	0.431893i	$0.857846\pi$
$318$	−55.9285	−	208.728i	−0.175876	−	0.656377i
$319$	9.78456	+	5.64912i	0.0306726	+	0.0177088i
$320$		0			0
$321$	−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
$325$		0			0
$326$	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
$330$		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	$0.642588\pi$
$332$	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
$335$		0			0
$336$	−16.8338	−	42.6660i	−0.0501005	−	0.126982i
$337$	−259.016	−	259.016i	−0.768593	−	0.768593i	0.209266	−	0.977859i	$-0.432893\pi$
$337$	−259.016	−	259.016i	−0.768593	−	0.768593i	−0.977859	+	0.209266i	$0.932893\pi$
$338$	−159.277	−	42.6782i	−0.471234	−	0.126267i
$339$	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
$343$	−323.136	+	115.030i	−0.942089	+	0.335364i
$344$			164.464i			0.478094i
$345$		0			0
$346$	−11.0739	+	19.1806i	−0.0320056	+	0.0554353i
$347$	319.953	−	85.7311i	0.922055	−	0.247064i	0.233591	−	0.972335i	$-0.424952\pi$
$347$	319.953	−	85.7311i	0.922055	−	0.247064i	0.688463	+	0.725271i	$0.258286\pi$
$348$	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	$0.814956\pi$
$350$		0			0
$351$	−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	$0.206579\pi$
$353$	144.351	+	538.726i	0.408927	+	1.52614i	−0.387770	+	0.921756i	$0.626754\pi$
$354$	46.3450	+	26.7573i	0.130918	+	0.0755856i
$355$		0			0
$356$	−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	$0.234129\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	−14.0923	−	24.4086i	−0.0385036	−	0.0666902i
$367$	473.906	−	126.983i	1.29130	−	0.346002i	0.453145	−	0.891437i	$-0.350302\pi$
$367$	473.906	−	126.983i	1.29130	−	0.346002i	0.838153	+	0.545435i	$0.183635\pi$
$368$	−25.0481	−	93.4809i	−0.0680656	−	0.254024i
$369$	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
$373$	42.3394	+	11.3448i	0.113510	+	0.0304150i	0.315127	−	0.949049i	$-0.397953\pi$
$373$	42.3394	+	11.3448i	0.113510	+	0.0304150i	−0.201617	+	0.979465i	$0.564620\pi$
$374$	−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
$378$	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	$-0.173564\pi$
$380$		0			0
$381$	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	0.406127	−	0.913817i	$-0.366879\pi$
$383$	115.258	+	30.8833i	0.300935	+	0.0806352i	−0.105192	+	0.994452i	$0.533546\pi$
$384$			18.5330i			0.0482630i
$385$		0			0
$386$	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	$0.851456\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	4.31662	−	7.47661i	0.0109006	−	0.0188803i
$397$	28.4186	−	106.060i	0.0715835	−	0.267153i	−0.920853	−	0.389909i	$-0.872506\pi$
$397$	28.4186	−	106.060i	0.0715835	−	0.267153i	0.992437	+	0.122756i	$0.0391732\pi$
$398$	−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	$0.864699\pi$
$402$	−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
$405$		0			0
$406$	−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			0
$411$	−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
$415$		0			0
$416$	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	$-0.0632144\pi$
$420$		0			0
$421$	163.631			0.388672			0.194336	−	0.980935i	$-0.437745\pi$
$421$	163.631			0.388672			0.194336	+	0.980935i	$0.437745\pi$
$422$	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
$425$		0			0
$426$	−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
$430$		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	$0.328555\pi$
$432$	25.9753	−	96.9410i	0.0601279	−	0.224400i
$433$	355.950	−	355.950i	0.822055	−	0.822055i	−0.164347	−	0.986403i	$-0.552552\pi$
$433$	355.950	−	355.950i	0.822055	−	0.822055i	0.986403	+	0.164347i	$0.0525518\pi$
$434$	219.623	−	86.6516i	0.506044	−	0.199658i
$435$		0			0
$436$	−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	$0.264731\pi$
$440$		0			0
$441$	−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	0.843178	−	0.537635i	$-0.180682\pi$
$443$	577.926	+	154.855i	1.30457	+	0.349560i	0.461396	+	0.887194i	$0.347349\pi$
$444$	−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
$448$	−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	$-0.0333321\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	44.6332			0.0978799
$457$	−54.8826	+	204.824i	−0.120093	+	0.448194i	−0.999617	−	0.0276604i	$-0.991194\pi$
$457$	−54.8826	+	204.824i	−0.120093	+	0.448194i	0.879524	+	0.475854i	$0.157861\pi$
$458$	114.693	+	428.042i	0.250422	+	0.934589i
$459$	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	$0.375911\pi$
$462$	−6.59665	−	8.90460i	−0.0142785	−	0.0192740i
$463$	327.380	−	327.380i	0.707084	−	0.707084i	−0.258837	−	0.965921i	$-0.583339\pi$
$463$	327.380	−	327.380i	0.707084	−	0.707084i	0.965921	+	0.258837i	$0.0833391\pi$
$464$	57.2720	−	33.0660i	0.123431	−	0.0712629i
$465$		0			0
$466$	35.7757	−	61.9653i	0.0767719	−	0.132973i
$467$	−140.806	+	525.495i	−0.301512	+	1.12526i	0.634395	+	0.773009i	$0.281249\pi$
$467$	−140.806	+	525.495i	−0.301512	+	1.12526i	−0.935907	+	0.352248i	$0.885418\pi$
$468$	−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
$472$	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
$475$		0			0
$476$	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	$0.644176\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−177.916	+	308.159i	−0.366082	+	0.634072i
$487$	−720.130	+	192.958i	−1.47871	+	0.396218i	−0.905907	−	0.423477i	$-0.860809\pi$
$487$	−720.130	+	192.958i	−1.47871	+	0.396218i	−0.572799	+	0.819696i	$0.694143\pi$
$488$	−33.2388	−	8.90631i	−0.0681123	−	0.0182506i
$489$		−	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	$0.435025\pi$
$492$	−0.170015	+	0.634504i	−0.000345559	+	0.00128964i
$493$	143.975	+	537.320i	0.292038	+	1.08990i
$494$	−199.387	−	115.116i	−0.403617	−	0.233029i
$495$		0			0
$496$	−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	$0.517142\pi$
$500$		0			0
$501$	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	−0.668233	−	0.743952i	$-0.732949\pi$
$503$	38.0869	−	38.0869i	0.0757195	−	0.0757195i	0.743952	+	0.668233i	$0.232949\pi$
$504$	97.9180	+	77.7995i	0.194282	+	0.154364i
$505$		0			0
$506$	−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	$0.278930\pi$
$510$		0			0
$511$	−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			0
$516$	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
$520$		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	$0.241492\pi$
$522$	−142.658	+	38.2250i	−0.273291	+	0.0732280i
$523$	−769.970	−	206.313i	−1.47222	−	0.394480i	−0.568527	−	0.822665i	$-0.692486\pi$
$523$	−769.970	−	206.313i	−1.47222	−	0.394480i	−0.903691	+	0.428185i	$0.859153\pi$
$524$			117.768i			0.224748i
$525$		0			0
$526$	−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
$530$		0			0
$531$	−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
$535$		0			0
$536$	−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
$540$		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	$-0.336270\pi$
$542$	−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
$545$		0			0
$546$	100.581	+	254.927i	0.184214	+	0.466899i
$547$	−469.765	−	469.765i	−0.858803	−	0.858803i	0.132394	−	0.991197i	$-0.457734\pi$
$547$	−469.765	−	469.765i	−0.858803	−	0.858803i	−0.991197	+	0.132394i	$0.957734\pi$
$548$	−254.557	−	68.2082i	−0.464519	−	0.124468i
$549$	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
$553$	−89.3925	−	780.765i	−0.161650	−	1.41187i
$554$			120.016i			0.216635i
$555$		0			0
$556$	−68.2322	+	118.182i	−0.122720	+	0.212557i
$557$	−368.629	+	98.7738i	−0.661811	+	0.177332i	−0.574063	−	0.818811i	$-0.694634\pi$
$557$	−368.629	+	98.7738i	−0.661811	+	0.177332i	−0.0877479	+	0.996143i	$0.527967\pi$
$558$	205.791	+	55.1414i	0.368800	+	0.0988197i
$559$		−	982.665i		−	1.75790i
$560$		0			0
$561$	−37.6650			−0.0671390
$562$	49.8528	−	186.053i	0.0887061	−	0.331056i
$563$	47.2076	+	176.181i	0.0838502	+	0.312933i	0.995094	−	0.0989343i	$-0.0315434\pi$
$563$	47.2076	+	176.181i	0.0838502	+	0.312933i	−0.911244	+	0.411867i	$0.864877\pi$
$564$	135.589	+	78.2824i	0.240406	+	0.138799i
$565$		0			0
$566$	−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	$0.561465\pi$
$570$		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	$0.218219\pi$
$572$	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
$575$		0			0
$576$	−25.2665	−	43.7629i	−0.0438654	−	0.0759772i
$577$	957.887	−	256.665i	1.66012	−	0.444827i	0.697696	−	0.716394i	$-0.254209\pi$
$577$	957.887	−	256.665i	1.66012	−	0.444827i	0.962420	+	0.271567i	$0.0875419\pi$
$578$	−308.588	−	1151.66i	−0.533888	−	1.99250i
$579$	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
$583$	−61.5721	−	16.4982i	−0.105613	−	0.0282988i
$584$	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	0.789963	−	0.613155i	$-0.210100\pi$
$587$	103.786	+	103.786i	0.176808	+	0.176808i	−0.613155	+	0.789963i	$0.710100\pi$
$588$	141.660	−	75.5222i	0.240918	−	0.128439i
$589$			229.749i			0.390067i
$590$		0			0
$591$	−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	0.333853	−	0.942625i	$-0.391651\pi$
$593$	89.9380	+	24.0988i	0.151666	+	0.0406388i	−0.182187	+	0.983264i	$0.558318\pi$
$594$		−	24.2481i		−	0.0408217i
$595$		0			0
$596$	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	$0.816293\pi$
$600$		0			0
$601$	422.829			0.703542			0.351771	−	0.936086i	$-0.385580\pi$
$601$	422.829			0.703542			0.351771	+	0.936086i	$0.385580\pi$
$602$	−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
$605$		0			0
$606$	−63.7072	+	110.344i	−0.105127	+	0.182086i
$607$	53.2050	−	198.564i	0.0876524	−	0.327123i	−0.908151	−	0.418643i	$-0.862506\pi$
$607$	53.2050	−	198.564i	0.0876524	−	0.327123i	0.995803	+	0.0915198i	$0.0291725\pi$
$608$	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
$612$	410.579	−	110.014i	0.670881	−	0.179762i
$613$	−65.0019	−	242.590i	−0.106039	−	0.395743i	0.892422	−	0.451202i	$-0.149005\pi$
$613$	−65.0019	−	242.590i	−0.106039	−	0.395743i	−0.998461	+	0.0554588i	$0.982338\pi$
$614$	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	0.519227	−	0.854636i	$-0.326220\pi$
$617$	−206.947	−	206.947i	−0.335409	−	0.335409i	−0.854636	+	0.519227i	$0.826220\pi$
$618$	−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	$0.791155\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	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
$630$		0			0
$631$	−675.457			−1.07045			−0.535227	−	0.844708i	$-0.679774\pi$
$631$	−675.457			−1.07045			−0.535227	+	0.844708i	$0.679774\pi$
$632$	−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
$635$		0			0
$636$	−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
$640$		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	$0.177468\pi$
$642$	−80.6889	+	301.135i	−0.125684	+	0.469058i
$643$	−344.145	+	344.145i	−0.535218	+	0.535218i	−0.922121	−	0.386902i	$-0.873545\pi$
$643$	−344.145	+	344.145i	−0.535218	+	0.535218i	0.386902	+	0.922121i	$0.373545\pi$
$644$	315.087	−	124.317i	0.489266	−	0.193038i
$645$		0			0
$646$	229.190	+	396.969i	0.354783	+	0.614503i
$647$	−898.982	+	240.882i	−1.38946	+	0.372305i	−0.874549	−	0.484937i	$-0.838843\pi$
$647$	−898.982	+	240.882i	−1.38946	+	0.372305i	−0.514913	+	0.857242i	$0.672176\pi$
$648$	11.5293	+	43.0281i	0.0177922	+	0.0664014i
$649$	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
$653$	−561.631	−	150.489i	−0.860078	−	0.230457i	−0.198286	−	0.980144i	$-0.563537\pi$
$653$	−561.631	−	150.489i	−0.860078	−	0.230457i	−0.661793	+	0.749687i	$0.730204\pi$
$654$	−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
$658$	−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	$0.947287\pi$
$660$		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	$0.196504\pi$
$662$	510.047	−	136.667i	0.770463	−	0.206445i
$663$	899.706	+	241.076i	1.35702	+	0.363613i
$664$		−	92.4645i		−	0.139254i
$665$		0			0
$666$	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
$670$		0			0
$671$	−8.31411			−0.0123906
$672$	−64.4445	+	7.37848i	−0.0958995	+	0.0109799i
$673$	129.111	−	129.111i	0.191844	−	0.191844i	−0.604648	−	0.796493i	$-0.706686\pi$
$673$	129.111	−	129.111i	0.191844	−	0.191844i	0.796493	+	0.604648i	$0.206686\pi$
$674$	−448.629	+	259.016i	−0.665621	+	0.384297i
$675$		0			0
$676$	−116.599	+	201.955i	−0.172484	+	0.298751i
$677$	−114.123	+	425.912i	−0.168571	+	0.629116i	0.828986	+	0.559269i	$0.188918\pi$
$677$	−114.123	+	425.912i	−0.168571	+	0.629116i	−0.997558	+	0.0698477i	$0.977749\pi$
$678$	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
$682$	−22.2638	+	5.96557i	−0.0326449	+	0.00874717i
$683$	12.8921	+	48.1139i	0.0188757	+	0.0704449i	0.974721	−	0.223424i	$-0.0717236\pi$
$683$	12.8921	+	48.1139i	0.0188757	+	0.0704449i	−0.955846	+	0.293869i	$0.905057\pi$
$684$	−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
$688$	224.663	+	60.1982i	0.326545	+	0.0874974i
$689$	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
$693$	27.7169	+	12.0335i	0.0399955	+	0.0173643i
$694$		−	468.444i		−	0.674991i
$695$		0			0
$696$	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
$700$		0			0
$701$	−85.2715			−0.121643			−0.0608213	−	0.998149i	$-0.519372\pi$
$701$	−85.2715			−0.121643			−0.0608213	+	0.998149i	$0.519372\pi$
$702$	−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
$705$		0			0
$706$	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	$0.381673\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	−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	$0.572437\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−139.615	−	241.820i	−0.192307	−	0.333085i
$727$	−10.5831	−	10.5831i	−0.0145573	−	0.0145573i	0.699791	−	0.714348i	$-0.253277\pi$
$727$	−10.5831	−	10.5831i	−0.0145573	−	0.0145573i	−0.714348	+	0.699791i	$0.753277\pi$
$728$	306.919	+	133.251i	0.421591	+	0.183037i
$729$			270.419i			0.370946i
$730$		0			0
$731$	−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	−0.543285	−	0.839548i	$-0.682820\pi$
$733$	−1050.80	−	281.561i	−1.43356	−	0.384121i	−0.890273	+	0.455427i	$0.849486\pi$
$734$		−	693.847i		−	0.945296i
$735$		0			0
$736$	−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	$0.746919\pi$
$740$		0			0
$741$	−266.681			−0.359893
$742$	367.742	−	847.025i	0.495609	−	1.14154i
$743$	45.4536	−	45.4536i	0.0611758	−	0.0611758i	−0.675857	−	0.737033i	$-0.736226\pi$
$743$	45.4536	−	45.4536i	0.0611758	−	0.0611758i	0.737033	+	0.675857i	$0.236226\pi$
$744$	−95.6969	+	55.2506i	−0.128625	+	0.0742616i
$745$		0			0
$746$	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
$750$		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	$-0.341605\pi$
$752$	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
$755$		0			0
$756$	347.433	+	51.7286i	0.459567	+	0.0684240i
$757$	535.185	+	535.185i	0.706981	+	0.706981i	0.965899	−	0.258918i	$-0.0833660\pi$
$757$	535.185	+	535.185i	0.706981	+	0.706981i	−0.258918	+	0.965899i	$0.583366\pi$
$758$	−537.032	−	143.897i	−0.708485	−	0.189838i
$759$	−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
$763$	287.513	−	212.994i	0.376819	−	0.279153i
$764$		−	94.1688i		−	0.123258i
$765$		0			0
$766$	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	$0.774835\pi$
$770$		0			0
$771$	167.702			0.217512
$772$	52.9819	−	197.731i	0.0686295	−	0.256129i
$773$	−93.0266	−	347.180i	−0.120345	−	0.449133i	0.879286	−	0.476294i	$-0.158020\pi$
$773$	−93.0266	−	347.180i	−0.120345	−	0.449133i	−0.999631	+	0.0271607i	$0.991353\pi$
$774$	−449.840	−	259.715i	−0.581188	−	0.335549i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−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
$785$		0			0
$786$	68.2059	+	118.136i	0.0867760	+	0.150300i
$787$	−76.8792	+	20.5997i	−0.0976864	+	0.0261750i	−0.307331	−	0.951603i	$-0.599436\pi$
$787$	−76.8792	+	20.5997i	−0.0976864	+	0.0261750i	0.209645	+	0.977778i	$0.432769\pi$
$788$	119.433	+	445.728i	0.151564	+	0.565645i
$789$	−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
$793$	198.600	+	53.2147i	0.250441	+	0.0671055i
$794$	−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	0.878811	−	0.477169i	$-0.158337\pi$
$797$	320.109	+	320.109i	0.401642	+	0.401642i	−0.477169	+	0.878811i	$0.658337\pi$
$798$	17.7697	+	155.202i	0.0222678	+	0.194489i
$799$			1607.91i			2.01240i
$800$		0			0
$801$	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
$805$		0			0
$806$	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	$0.413226\pi$
$810$		0			0
$811$	−143.794			−0.177305			−0.0886526	−	0.996063i	$-0.528256\pi$
$811$	−143.794			−0.177305			−0.0886526	+	0.996063i	$0.528256\pi$
$812$	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
$815$		0			0
$816$	−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
$820$		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	$0.733207\pi$
$822$	−294.856	+	79.0064i	−0.358706	+	0.0961149i
$823$	376.812	+	1406.28i	0.457852	+	1.70873i	0.679566	+	0.733615i	$0.262168\pi$
$823$	376.812	+	1406.28i	0.457852	+	1.70873i	−0.221714	+	0.975112i	$0.571165\pi$
$824$	−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	0.981683	+	0.190520i	$0.0610173\pi$
$827$	969.412	+	969.412i	1.17220	+	1.17220i	0.190520	+	0.981683i	$0.438983\pi$
$828$	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	$0.492353\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$	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	$0.895423\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−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
$850$		0			0
$851$	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	−0.816117	−	0.577886i	$-0.803878\pi$
$853$	−203.211	+	203.211i	−0.238231	+	0.238231i	0.577886	+	0.816117i	$0.303878\pi$
$854$	17.7365	−	119.127i	0.0207687	−	0.139492i
$855$		0			0
$856$	190.317	+	329.638i	0.222333	+	0.385091i
$857$	1133.64	−	303.758i	1.32280	−	0.354443i	0.472774	−	0.881184i	$-0.343253\pi$
$857$	1133.64	−	303.758i	1.32280	−	0.354443i	0.850026	+	0.526741i	$0.176586\pi$
$858$	−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	$0.278554\pi$
$860$		0			0
$861$	−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	−0.646760	−	0.762693i	$-0.723877\pi$
$863$	−1370.63	−	367.260i	−1.58822	−	0.425562i	−0.941457	+	0.337132i	$0.890543\pi$
$864$	−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
$868$	−37.9807	−	331.728i	−0.0437565	−	0.382175i
$869$			76.7201i			0.0882855i
$870$		0			0
$871$	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
$875$		0			0
$876$	154.327			0.176173
$877$	−362.410	+	1352.53i	−0.413238	+	1.54222i	0.375101	+	0.926984i	$0.377608\pi$
$877$	−362.410	+	1352.53i	−0.413238	+	1.54222i	−0.788339	+	0.615241i	$0.789059\pi$
$878$	−68.7268	−	256.492i	−0.0782766	−	0.292132i
$879$	−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	$0.292284\pi$
$882$	−231.547	+	371.463i	−0.262525	+	0.421160i
$883$	−1198.71	+	1198.71i	−1.35754	+	1.35754i	−0.480593	+	0.876944i	$0.659579\pi$
$883$	−1198.71	+	1198.71i	−1.35754	+	1.35754i	−0.876944	+	0.480593i	$0.840421\pi$
$884$	984.865	−	568.612i	1.11410	−	0.643227i
$885$		0			0
$886$	423.071	−	732.781i	0.477507	−	0.827067i
$887$	19.9594	−	74.4895i	0.0225021	−	0.0839791i	−0.953762	−	0.300564i	$-0.902825\pi$
$887$	19.9594	−	74.4895i	0.0225021	−	0.0839791i	0.976264	+	0.216585i	$0.0694918\pi$
$888$	−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
$892$	−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
$895$		0			0
$896$	−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
$900$		0			0
$901$	−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
$905$		0			0
$906$	−273.340	+	473.440i	−0.301700	+	0.522560i
$907$	973.915	−	260.960i	1.07378	−	0.287717i	0.321732	−	0.946831i	$-0.395735\pi$
$907$	973.915	−	260.960i	1.07378	−	0.287717i	0.752044	+	0.659113i	$0.229068\pi$
$908$	551.485	+	147.770i	0.607362	+	0.162742i
$909$		−	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	$0.738511\pi$
$912$	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
$915$		0			0
$916$	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	$0.334500\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	−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	$0.261218\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	150.966	+	261.480i	0.161288	+	0.279359i
$937$	46.4937	+	46.4937i	0.0496198	+	0.0496198i	0.731481	−	0.681862i	$-0.238829\pi$
$937$	46.4937	+	46.4937i	0.0496198	+	0.0496198i	−0.681862	+	0.731481i	$0.738829\pi$
$938$	−12.7400	−	5.53117i	−0.0135821	−	0.00589677i
$939$		−	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	$-0.110898\pi$
$942$	356.461	−	95.5134i	0.378408	−	0.101394i
$943$	−4.68579	−	1.25555i	−0.00496902	−	0.00133145i
$944$		−	92.4010i		−	0.0978824i
$945$		0			0
$946$	56.1955			0.0594033
$947$	−144.671	+	539.920i	−0.152768	+	0.570137i	0.846518	+	0.532359i	$0.178694\pi$
$947$	−144.671	+	539.920i	−0.152768	+	0.570137i	−0.999286	+	0.0377774i	$0.987972\pi$
$948$	95.1957	+	355.275i	0.100417	+	0.374763i
$949$	−689.416	−	398.035i	−0.726466	−	0.419425i
$950$		0			0
$951$	675.697			0.710512
$952$	−396.544	−	535.282i	−0.416538	−	0.562271i
$953$	−27.0794	+	27.0794i	−0.0284149	+	0.0284149i	−0.721171	−	0.692757i	$-0.756396\pi$
$953$	−27.0794	+	27.0794i	−0.0284149	+	0.0284149i	0.692757	+	0.721171i	$0.256396\pi$
$954$	721.626	−	416.631i	0.756421	−	0.436720i
$955$		0			0
$956$	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
$960$		0			0
$961$	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
$965$		0			0
$966$	244.074	−	307.190i	0.252665	−	0.318002i
$967$	−1012.58	−	1012.58i	−1.04713	−	1.04713i	−0.998833	−	0.0483007i	$-0.984619\pi$
$967$	−1012.58	−	1012.58i	−1.04713	−	1.04713i	−0.0483007	−	0.998833i	$-0.515381\pi$
$968$	−329.302	−	88.2363i	−0.340188	−	0.0911532i
$969$	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
$973$	−438.116	−	190.212i	−0.450274	−	0.195490i
$974$			1054.34i			1.08249i
$975$		0			0
$976$	−24.3325	+	42.1451i	−0.0249308	+	0.0431815i
$977$	598.914	−	160.479i	0.613014	−	0.164256i	0.0610638	−	0.998134i	$-0.480551\pi$
$977$	598.914	−	160.479i	0.613014	−	0.164256i	0.551950	+	0.833877i	$0.313884\pi$
$978$	−558.618	−	149.681i	−0.571184	−	0.153048i
$979$			54.5673i			0.0557377i
$980$		0			0
$981$	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	$0.155804\pi$
$983$	347.318	+	1296.21i	0.353324	+	1.31862i	−0.529256	+	0.848462i	$0.677529\pi$
$984$	0.804519	+	0.464489i	0.000817600	+	0.000472042i
$985$		0			0
$986$	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
$990$		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	$0.904105\pi$
$992$	−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
$995$		0			0
$996$	−53.5514	−	92.7537i	−0.0537664	−	0.0931262i
$997$	885.448	−	237.255i	0.888112	−	0.237969i	0.214208	−	0.976788i	$-0.431283\pi$
$997$	885.448	−	237.255i	0.888112	−	0.237969i	0.673904	+	0.738819i	$0.264616\pi$
$998$	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	350.3.p.b.207.1		8
5.2	odd	4		70.3.l.b.53.1	yes	8
5.3	odd	4	inner	350.3.p.b.193.2		8
5.4	even	2		70.3.l.b.67.2	yes	8
7.2	even	3	inner	350.3.p.b.107.2		8
35.2	odd	12		70.3.l.b.23.2	✓	8
35.4	even	6		490.3.f.f.197.2		4
35.9	even	6		70.3.l.b.37.1	yes	8
35.17	even	12		490.3.f.k.393.1		4
35.23	odd	12	inner	350.3.p.b.93.1		8
35.24	odd	6		490.3.f.k.197.1		4
35.32	odd	12		490.3.f.f.393.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.b.23.2	✓	8	35.2	odd	12
70.3.l.b.37.1	yes	8	35.9	even	6
70.3.l.b.53.1	yes	8	5.2	odd	4
70.3.l.b.67.2	yes	8	5.4	even	2
350.3.p.b.93.1		8	35.23	odd	12	inner
350.3.p.b.107.2		8	7.2	even	3	inner
350.3.p.b.193.2		8	5.3	odd	4	inner
350.3.p.b.207.1		8	1.1	even	1	trivial
490.3.f.f.197.2		4	35.4	even	6
490.3.f.f.393.2		4	35.32	odd	12
490.3.f.k.197.1		4	35.24	odd	6
490.3.f.k.393.1		4	35.17	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.p (of order \(12\), degree \(4\), minimal)

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