LMFDB - Embedded newform 350.3.p.e.93.4

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 8 x^{13} - 722 x^{12} + 1354 x^{11} - 1232 x^{10} + 9306 x^{9} + \cdots + 52200625 $ x^16 - 2x^15 + 2x^14 - 8x^13 - 722x^12 + 1354x^11 - 1232x^10 + 9306x^9 + 505731x^8 - 1157418x^7 + 1256080x^6 - 9824090x^5 + 5294974x^4 + 30978760x^3 + 12152450x^2 + 35619250*x + 52200625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
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			93.4
Root			$4.90868 - 1.31528i$ of defining polynomial
Character	$\chi$	$=$	350.93
Dual form			350.3.p.e.207.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(1.31528 - 4.90868i) q^{3} +(-1.73205 + 1.00000i) q^{4} -7.18681 q^{6} +(0.145113 - 6.99850i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-14.5710 - 8.41254i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(1.31528 - 4.90868i) q^{3} +(-1.73205 + 1.00000i) q^{4} -7.18681 q^{6} +(0.145113 - 6.99850i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-14.5710 - 8.41254i) q^{9} +(0.474367 + 0.821627i) q^{11} +(2.63055 + 9.81736i) q^{12} +(-0.862338 - 0.862338i) q^{13} +(-9.61324 + 2.36340i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-29.3872 - 7.87429i) q^{17} +(-6.15841 + 22.9835i) q^{18} +(20.9123 + 12.0737i) q^{19} +(-34.1625 - 9.91727i) q^{21} +(0.948733 - 0.948733i) q^{22} +(5.47452 - 1.46689i) q^{23} +(12.4479 - 7.18681i) q^{24} +(-0.862338 + 1.49361i) q^{26} +(-28.1187 + 28.1187i) q^{27} +(6.74715 + 12.2669i) q^{28} +7.33636i q^{29} +(-23.5316 - 40.7579i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(4.65703 - 1.24785i) q^{33} +43.0259i q^{34} +33.6502 q^{36} +(2.13074 + 7.95202i) q^{37} +(8.83857 - 32.9860i) q^{38} +(-5.36716 + 3.09873i) q^{39} +53.3601 q^{41} +(-1.04290 + 50.2968i) q^{42} +(33.0776 + 33.0776i) q^{43} +(-1.64325 - 0.948733i) q^{44} +(-4.00763 - 6.94142i) q^{46} +(7.87429 + 29.3872i) q^{47} +(-14.3736 - 14.3736i) q^{48} +(-48.9579 - 2.03114i) q^{49} +(-77.3047 + 133.896i) q^{51} +(2.35595 + 0.631275i) q^{52} +(-3.48276 + 12.9978i) q^{53} +(48.7030 + 28.1187i) q^{54} +(14.2872 - 13.7068i) q^{56} +(86.7715 - 86.7715i) q^{57} +(10.0217 - 2.68529i) q^{58} +(43.5119 - 25.1216i) q^{59} +(22.7478 - 39.4004i) q^{61} +(-47.0632 + 47.0632i) q^{62} +(-60.9896 + 100.754i) q^{63} +8.00000i q^{64} +(-3.40918 - 5.90487i) q^{66} +(-65.9999 - 17.6846i) q^{67} +(58.7745 - 15.7486i) q^{68} -28.8020i q^{69} -11.9203 q^{71} +(-12.3168 - 45.9670i) q^{72} +(14.2554 - 53.2017i) q^{73} +(10.0828 - 5.82128i) q^{74} -48.2949 q^{76} +(5.81899 - 3.20062i) q^{77} +(6.19746 + 6.19746i) q^{78} +(-61.4002 - 35.4495i) q^{79} +(25.3289 + 43.8709i) q^{81} +(-19.5312 - 72.8913i) q^{82} +(-85.7452 - 85.7452i) q^{83} +(69.0885 - 16.9853i) q^{84} +(33.0776 - 57.2921i) q^{86} +(36.0118 + 9.64934i) q^{87} +(-0.694521 + 2.59199i) q^{88} +(-135.750 - 78.3752i) q^{89} +(-6.16021 + 5.90994i) q^{91} +(-8.01526 + 8.01526i) q^{92} +(-231.018 + 61.9011i) q^{93} +(37.2615 - 21.5130i) q^{94} +(-14.3736 + 24.8958i) q^{96} +(87.1790 - 87.1790i) q^{97} +(15.1452 + 67.6212i) q^{98} -15.9625i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	1.31528	−	4.90868i	0.438426	−	1.63623i	−0.294308	−	0.955711i	$-0.595089\pi$
$3$	1.31528	−	4.90868i	0.438426	−	1.63623i	0.732733	−	0.680516i	$-0.238244\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−7.18681			−1.19780
$7$	0.145113	−	6.99850i	0.0207304	−	0.999785i
$7$	0.145113	−	6.99850i	0.0207304	−	0.999785i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−14.5710	−	8.41254i	−1.61899	−	0.934727i
$10$		0			0
$11$	0.474367	+	0.821627i	0.0431242	+	0.0746934i	0.886782	−	0.462188i	$-0.152936\pi$
$11$	0.474367	+	0.821627i	0.0431242	+	0.0746934i	−0.843658	+	0.536882i	$0.819602\pi$
$12$	2.63055	+	9.81736i	0.219213	+	0.818113i
$13$	−0.862338	−	0.862338i	−0.0663337	−	0.0663337i	0.673162	−	0.739495i	$-0.264936\pi$
$13$	−0.862338	−	0.862338i	−0.0663337	−	0.0663337i	−0.739495	+	0.673162i	$0.764936\pi$
$14$	−9.61324	+	2.36340i	−0.686660	+	0.168814i
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−29.3872	−	7.87429i	−1.72866	−	0.463193i	−0.748787	−	0.662810i	$-0.769364\pi$
$17$	−29.3872	−	7.87429i	−1.72866	−	0.463193i	−0.979874	+	0.199617i	$0.936030\pi$
$18$	−6.15841	+	22.9835i	−0.342134	+	1.27686i
$19$	20.9123	+	12.0737i	1.10065	+	0.635459i	0.936391	−	0.350959i	$-0.114144\pi$
$19$	20.9123	+	12.0737i	1.10065	+	0.635459i	0.164256	+	0.986418i	$0.447478\pi$
$20$		0			0
$21$	−34.1625	−	9.91727i	−1.62679	−	0.472251i
$22$	0.948733	−	0.948733i	0.0431242	−	0.0431242i
$23$	5.47452	−	1.46689i	0.238023	−	0.0637780i	−0.137836	−	0.990455i	$-0.544015\pi$
$23$	5.47452	−	1.46689i	0.238023	−	0.0637780i	0.375858	+	0.926677i	$0.377348\pi$
$24$	12.4479	−	7.18681i	0.518663	−	0.299450i
$25$		0			0
$26$	−0.862338	+	1.49361i	−0.0331669	+	0.0574467i
$27$	−28.1187	+	28.1187i	−1.04143	+	1.04143i
$28$	6.74715	+	12.2669i	0.240970	+	0.438102i
$29$			7.33636i			0.252978i	0.991968	+	0.126489i	$0.0403708\pi$
$29$			7.33636i			0.252978i	−0.991968	+	0.126489i	$0.959629\pi$
$30$		0			0
$31$	−23.5316	−	40.7579i	−0.759083	−	1.31477i	−0.943319	−	0.331889i	$-0.892314\pi$
$31$	−23.5316	−	40.7579i	−0.759083	−	1.31477i	0.184235	−	0.982882i	$-0.441019\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	4.65703	−	1.24785i	0.141122	−	0.0378135i
$34$			43.0259i			1.26547i
$35$		0			0
$36$	33.6502			0.934727
$37$	2.13074	+	7.95202i	0.0575875	+	0.214919i	0.988723	−	0.149753i	$-0.0478477\pi$
$37$	2.13074	+	7.95202i	0.0575875	+	0.214919i	−0.931136	+	0.364672i	$0.881181\pi$
$38$	8.83857	−	32.9860i	0.232594	−	0.868053i
$39$	−5.36716	+	3.09873i	−0.137619	+	0.0794546i
$40$		0			0
$41$	53.3601			1.30147			0.650733	−	0.759306i	$-0.274462\pi$
$41$	53.3601			1.30147			0.650733	+	0.759306i	$0.274462\pi$
$42$	−1.04290	+	50.2968i	−0.0248308	+	1.19754i
$43$	33.0776	+	33.0776i	0.769247	+	0.769247i	0.977974	−	0.208727i	$-0.0669319\pi$
$43$	33.0776	+	33.0776i	0.769247	+	0.769247i	−0.208727	+	0.977974i	$0.566932\pi$
$44$	−1.64325	−	0.948733i	−0.0373467	−	0.0215621i
$45$		0			0
$46$	−4.00763	−	6.94142i	−0.0871224	−	0.150900i
$47$	7.87429	+	29.3872i	0.167538	+	0.625260i	0.997703	+	0.0677424i	$0.0215796\pi$
$47$	7.87429	+	29.3872i	0.167538	+	0.625260i	−0.830165	+	0.557518i	$0.811754\pi$
$48$	−14.3736	−	14.3736i	−0.299450	−	0.299450i
$49$	−48.9579	−	2.03114i	−0.999141	−	0.0414518i
$50$		0			0
$51$	−77.3047	+	133.896i	−1.51578	+	2.62541i
$52$	2.35595	+	0.631275i	0.0453068	+	0.0121399i
$53$	−3.48276	+	12.9978i	−0.0657125	+	0.245242i	−0.990967	−	0.134104i	$-0.957184\pi$
$53$	−3.48276	+	12.9978i	−0.0657125	+	0.245242i	0.925255	+	0.379346i	$0.123851\pi$
$54$	48.7030	+	28.1187i	0.901907	+	0.520717i
$55$		0			0
$56$	14.2872	−	13.7068i	0.255129	−	0.244764i
$57$	86.7715	−	86.7715i	1.52231	−	1.52231i
$58$	10.0217	−	2.68529i	0.172787	−	0.0462982i
$59$	43.5119	−	25.1216i	0.737490	−	0.425790i	−0.0836659	−	0.996494i	$-0.526663\pi$
$59$	43.5119	−	25.1216i	0.737490	−	0.425790i	0.821156	+	0.570704i	$0.193330\pi$
$60$		0			0
$61$	22.7478	−	39.4004i	0.372915	−	0.645909i	−0.617097	−	0.786887i	$-0.711691\pi$
$61$	22.7478	−	39.4004i	0.372915	−	0.645909i	0.990013	+	0.140978i	$0.0450248\pi$
$62$	−47.0632	+	47.0632i	−0.759083	+	0.759083i
$63$	−60.9896	+	100.754i	−0.968089	+	1.59927i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−3.40918	−	5.90487i	−0.0516542	−	0.0894678i
$67$	−65.9999	−	17.6846i	−0.985073	−	0.263949i	−0.269893	−	0.962890i	$-0.586988\pi$
$67$	−65.9999	−	17.6846i	−0.985073	−	0.263949i	−0.715180	+	0.698941i	$0.753655\pi$
$68$	58.7745	−	15.7486i	0.864331	−	0.231597i
$69$		−	28.8020i		−	0.417421i
$70$		0			0
$71$	−11.9203			−0.167892			−0.0839460	−	0.996470i	$-0.526752\pi$
$71$	−11.9203			−0.167892			−0.0839460	+	0.996470i	$0.526752\pi$
$72$	−12.3168	−	45.9670i	−0.171067	−	0.638430i
$73$	14.2554	−	53.2017i	0.195279	−	0.728791i	−0.796916	−	0.604091i	$-0.793536\pi$
$73$	14.2554	−	53.2017i	0.195279	−	0.728791i	0.992194	−	0.124700i	$-0.0397969\pi$
$74$	10.0828	−	5.82128i	0.136253	−	0.0786660i
$75$		0			0
$76$	−48.2949			−0.635459
$77$	5.81899	−	3.20062i	0.0755713	−	0.0415665i
$78$	6.19746	+	6.19746i	0.0794546	+	0.0794546i
$79$	−61.4002	−	35.4495i	−0.777218	−	0.448727i	0.0582252	−	0.998303i	$-0.481456\pi$
$79$	−61.4002	−	35.4495i	−0.777218	−	0.448727i	−0.835444	+	0.549576i	$0.814789\pi$
$80$		0			0
$81$	25.3289	+	43.8709i	0.312702	+	0.541616i
$82$	−19.5312	−	72.8913i	−0.238185	−	0.888918i
$83$	−85.7452	−	85.7452i	−1.03307	−	1.03307i	−0.999434	−	0.0336406i	$-0.989290\pi$
$83$	−85.7452	−	85.7452i	−1.03307	−	1.03307i	−0.0336406	−	0.999434i	$-0.510710\pi$
$84$	69.0885	−	16.9853i	0.822482	−	0.202206i
$85$		0			0
$86$	33.0776	−	57.2921i	0.384624	−	0.666188i
$87$	36.0118	+	9.64934i	0.413929	+	0.110912i
$88$	−0.694521	+	2.59199i	−0.00789228	+	0.0294544i
$89$	−135.750	−	78.3752i	−1.52528	−	0.880621i	−0.999551	−	0.0299681i	$-0.990459\pi$
$89$	−135.750	−	78.3752i	−1.52528	−	0.880621i	−0.525729	−	0.850652i	$-0.676207\pi$
$90$		0			0
$91$	−6.16021	+	5.90994i	−0.0676946	+	0.0649443i
$92$	−8.01526	+	8.01526i	−0.0871224	+	0.0871224i
$93$	−231.018	+	61.9011i	−2.48406	+	0.665603i
$94$	37.2615	−	21.5130i	0.396399	−	0.228861i
$95$		0			0
$96$	−14.3736	+	24.8958i	−0.149725	+	0.259332i
$97$	87.1790	−	87.1790i	0.898753	−	0.898753i	−0.0965731	−	0.995326i	$-0.530788\pi$
$97$	87.1790	−	87.1790i	0.898753	−	0.898753i	0.995326	+	0.0965731i	$0.0307882\pi$
$98$	15.1452	+	67.6212i	0.154543	+	0.690012i
$99$		−	15.9625i		−	0.161238i
$100$		0			0
$101$	25.2261	+	43.6929i	0.249763	+	0.432603i	0.963460	−	0.267852i	$-0.0863138\pi$
$101$	25.2261	+	43.6929i	0.249763	+	0.432603i	−0.713697	+	0.700455i	$0.752980\pi$
$102$	211.200	+	56.5910i	2.07059	+	0.554813i
$103$	139.636	−	37.4152i	1.35569	−	0.363255i	0.493455	−	0.869771i	$-0.335734\pi$
$103$	139.636	−	37.4152i	1.35569	−	0.363255i	0.862230	+	0.506517i	$0.169067\pi$
$104$		−	3.44935i		−	0.0331669i
$105$		0			0
$106$	19.0302			0.179530
$107$	1.79591	+	6.70244i	0.0167842	+	0.0626397i	0.973810	−	0.227363i	$-0.0730104\pi$
$107$	1.79591	+	6.70244i	0.0167842	+	0.0626397i	−0.957026	+	0.290003i	$0.906344\pi$
$108$	20.5843	−	76.8217i	0.190595	−	0.711312i
$109$	42.3291	−	24.4387i	0.388340	−	0.224208i	−0.293100	−	0.956082i	$-0.594687\pi$
$109$	42.3291	−	24.4387i	0.388340	−	0.224208i	0.681441	+	0.731873i	$0.261354\pi$
$110$		0			0
$111$	41.8364			0.376905
$112$	−23.9533	−	14.4997i	−0.213869	−	0.129461i
$113$	8.29274	+	8.29274i	0.0733871	+	0.0733871i	0.742848	−	0.669461i	$-0.233475\pi$
$113$	8.29274	+	8.29274i	0.0733871	+	0.0733871i	−0.669461	+	0.742848i	$0.733475\pi$
$114$	−150.293	−	86.7715i	−1.31836	−	0.761153i
$115$		0			0
$116$	−7.33636	−	12.7069i	−0.0632445	−	0.109543i
$117$	5.31063	+	19.8196i	0.0453900	+	0.169398i
$118$	−50.2432	−	50.2432i	−0.425790	−	0.425790i
$119$	−59.3726	+	204.524i	−0.498930	+	1.71869i
$120$		0			0
$121$	60.0500	−	104.010i	0.496281	−	0.859583i
$122$	−62.1483	−	16.6526i	−0.509412	−	0.136497i
$123$	70.1834	−	261.928i	0.570596	−	2.12949i
$124$	81.5158	+	47.0632i	0.657385	+	0.379542i
$125$		0			0
$126$	159.956	+	46.4348i	1.26949	+	0.368530i
$127$	80.3440	−	80.3440i	0.632630	−	0.632630i	−0.316097	−	0.948727i	$-0.602373\pi$
$127$	80.3440	−	80.3440i	0.632630	−	0.632630i	0.948727	+	0.316097i	$0.102373\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$	205.874	−	118.861i	1.59592	−	0.921405i
$130$		0			0
$131$	−12.5429	+	21.7250i	−0.0957475	+	0.165840i	−0.909920	−	0.414783i	$-0.863857\pi$
$131$	−12.5429	+	21.7250i	−0.0957475	+	0.165840i	0.814173	+	0.580623i	$0.197191\pi$
$132$	−6.81836	+	6.81836i	−0.0516542	+	0.0516542i
$133$	87.5325	−	144.603i	0.658139	−	1.08724i
$134$			96.6305i			0.721123i
$135$		0			0
$136$	−43.0259	−	74.5231i	−0.316367	−	0.547964i
$137$	−66.0647	−	17.7020i	−0.482224	−	0.129212i	0.00951399	−	0.999955i	$-0.496972\pi$
$137$	−66.0647	−	17.7020i	−0.482224	−	0.129212i	−0.491738	+	0.870743i	$0.663638\pi$
$138$	−39.3443	+	10.5423i	−0.285104	+	0.0763933i
$139$			67.3054i			0.484212i	0.970250	+	0.242106i	$0.0778381\pi$
$139$			67.3054i			0.484212i	−0.970250	+	0.242106i	$0.922162\pi$
$140$		0			0
$141$	154.609			1.09652
$142$	4.36314	+	16.2835i	0.0307264	+	0.114672i
$143$	0.299456	−	1.11758i	0.00209410	−	0.00781528i
$144$	−58.2838	+	33.6502i	−0.404749	+	0.233682i
$145$		0			0
$146$	−77.8927			−0.533512
$147$	−74.3634	+	237.647i	−0.505873	+	1.61665i
$148$	−11.6426	−	11.6426i	−0.0786660	−	0.0786660i
$149$	51.9776	+	30.0093i	0.348843	+	0.201404i	0.664175	−	0.747577i	$-0.268783\pi$
$149$	51.9776	+	30.0093i	0.348843	+	0.201404i	−0.315333	+	0.948981i	$0.602116\pi$
$150$		0			0
$151$	−23.9018	−	41.3992i	−0.158290	−	0.274167i	0.775962	−	0.630780i	$-0.217265\pi$
$151$	−23.9018	−	41.3992i	−0.158290	−	0.274167i	−0.934252	+	0.356613i	$0.883932\pi$
$152$	17.6771	+	65.9720i	0.116297	+	0.434026i
$153$	361.957	+	361.957i	2.36573	+	2.36573i
$154$	−6.50203	−	6.77738i	−0.0422210	−	0.0440089i
$155$		0			0
$156$	6.19746	−	10.7343i	0.0397273	−	0.0688097i
$157$	101.024	+	27.0694i	0.643466	+	0.172416i	0.565773	−	0.824561i	$-0.308578\pi$
$157$	101.024	+	27.0694i	0.643466	+	0.172416i	0.0776933	+	0.996977i	$0.475245\pi$
$158$	−25.9508	+	96.8497i	−0.164246	+	0.612973i
$159$	59.2214	+	34.1915i	0.372462	+	0.215041i
$160$		0			0
$161$	−9.47163	−	38.5263i	−0.0588300	−	0.239294i
$162$	50.6578	−	50.6578i	0.312702	−	0.312702i
$163$	−39.7089	+	10.6400i	−0.243613	+	0.0652759i	−0.378559	−	0.925577i	$-0.623580\pi$
$163$	−39.7089	+	10.6400i	−0.243613	+	0.0652759i	0.134946	+	0.990853i	$0.456914\pi$
$164$	−92.4225	+	53.3601i	−0.563552	+	0.325367i
$165$		0			0
$166$	−85.7452	+	148.515i	−0.516537	+	0.894669i
$167$	−26.4354	+	26.4354i	−0.158296	+	0.158296i	−0.781811	−	0.623515i	$-0.785704\pi$
$167$	−26.4354	+	26.4354i	−0.158296	+	0.158296i	0.623515	+	0.781811i	$0.285704\pi$
$168$	−48.4905	−	88.1596i	−0.288634	−	0.524759i
$169$		−	167.513i		−	0.991200i
$170$		0			0
$171$	−203.141	−	351.851i	−1.18796	−	2.05761i
$172$	−90.3698	−	24.2145i	−0.525406	−	0.140782i
$173$	−242.480	+	64.9724i	−1.40162	+	0.375563i	−0.878926	−	0.476958i	$-0.841739\pi$
$173$	−242.480	+	64.9724i	−1.40162	+	0.375563i	−0.522693	+	0.852521i	$0.675073\pi$
$174$		−	52.7250i		−	0.303017i
$175$		0			0
$176$	3.79493			0.0215621
$177$	−66.0838	−	246.628i	−0.373355	−	1.39338i
$178$	−57.3746	+	214.125i	−0.322329	+	1.20295i
$179$	46.8192	−	27.0311i	0.261560	−	0.151012i	−0.363486	−	0.931600i	$-0.618414\pi$
$179$	46.8192	−	27.0311i	0.261560	−	0.151012i	0.625046	+	0.780588i	$0.285080\pi$
$180$		0			0
$181$	201.453			1.11300			0.556501	−	0.830847i	$-0.312143\pi$
$181$	201.453			1.11300			0.556501	+	0.830847i	$0.312143\pi$
$182$	10.3279	+	6.25181i	0.0567468	+	0.0343506i
$183$	−163.484	−	163.484i	−0.893357	−	0.893357i
$184$	13.8828	+	8.01526i	0.0754502	+	0.0435612i
$185$		0			0
$186$	169.117	+	292.919i	0.909231	+	1.57483i
$187$	−7.47060	−	27.8807i	−0.0399497	−	0.149094i
$188$	−43.0259	−	43.0259i	−0.228861	−	0.228861i
$189$	192.708	+	200.869i	1.01962	+	1.06280i
$190$		0			0
$191$	−87.8707	+	152.197i	−0.460056	+	0.796841i	−0.998963	−	0.0455246i	$-0.985504\pi$
$191$	−87.8707	+	152.197i	−0.460056	+	0.796841i	0.538907	+	0.842365i	$0.318837\pi$
$192$	39.2694	+	10.5222i	0.204528	+	0.0548032i
$193$	13.5073	−	50.4101i	0.0699862	−	0.261192i	−0.922064	−	0.387039i	$-0.873498\pi$
$193$	13.5073	−	50.4101i	0.0699862	−	0.261192i	0.992050	+	0.125846i	$0.0401647\pi$
$194$	−150.998	−	87.1790i	−0.778343	−	0.449376i
$195$		0			0
$196$	86.8287	−	45.4398i	0.443003	−	0.231836i
$197$	62.8178	−	62.8178i	0.318872	−	0.318872i	−0.529462	−	0.848334i	$-0.677606\pi$
$197$	62.8178	−	62.8178i	0.318872	−	0.318872i	0.848334	+	0.529462i	$0.177606\pi$
$198$	−21.8052	+	5.84269i	−0.110127	+	0.0295085i
$199$	22.4632	−	12.9692i	0.112881	−	0.0651717i	−0.442497	−	0.896770i	$-0.645907\pi$
$199$	22.4632	−	12.9692i	0.112881	−	0.0651717i	0.555377	+	0.831598i	$0.312574\pi$
$200$		0			0
$201$	−173.616	+	300.712i	−0.863762	+	1.49608i
$202$	50.4522	−	50.4522i	0.249763	−	0.249763i
$203$	51.3435	+	1.06460i	0.252924	+	0.00524432i
$204$		−	309.219i		−	1.51578i
$205$		0			0
$206$	−102.220	−	177.051i	−0.496215	−	0.859470i
$207$	−92.1093	−	24.6806i	−0.444973	−	0.119230i
$208$	−4.71190	+	1.26255i	−0.0226534	+	0.00606996i
$209$			22.9095i			0.109615i
$210$		0			0
$211$	−223.675			−1.06007			−0.530036	−	0.847975i	$-0.677822\pi$
$211$	−223.675			−1.06007			−0.530036	+	0.847975i	$0.677822\pi$
$212$	−6.96552	−	25.9957i	−0.0328562	−	0.122621i
$213$	−15.6785	+	58.5131i	−0.0736081	+	0.274709i
$214$	8.49836	−	4.90653i	0.0397119	−	0.0229277i
$215$		0			0
$216$	−112.475			−0.520717
$217$	−288.659	+	158.771i	−1.33022	+	0.731664i
$218$	−48.8774	−	48.8774i	−0.224208	−	0.224208i
$219$	−242.400	−	139.950i	−1.10685	−	0.639041i
$220$		0			0
$221$	18.5514	+	32.1320i	0.0839432	+	0.145394i
$222$	−15.3132	−	57.1496i	−0.0689784	−	0.257431i
$223$	131.856	+	131.856i	0.591282	+	0.591282i	0.937978	−	0.346696i	$-0.112696\pi$
$223$	131.856	+	131.856i	0.591282	+	0.591282i	−0.346696	+	0.937978i	$0.612696\pi$
$224$	−11.0394	+	38.0280i	−0.0492831	+	0.169768i
$225$		0			0
$226$	8.29274	−	14.3634i	0.0366935	−	0.0635551i
$227$	366.184	+	98.1186i	1.61314	+	0.432241i	0.948977	−	0.315344i	$-0.102120\pi$
$227$	366.184	+	98.1186i	1.61314	+	0.432241i	0.664166	+	0.747585i	$0.268787\pi$
$228$	−63.5211	+	237.064i	−0.278601	+	1.03975i
$229$	39.8456	+	23.0049i	0.173998	+	0.100458i	0.584470	−	0.811415i	$-0.301303\pi$
$229$	39.8456	+	23.0049i	0.173998	+	0.100458i	−0.410471	+	0.911873i	$0.634636\pi$
$230$		0			0
$231$	−8.05726	−	32.7733i	−0.0348799	−	0.141876i
$232$	−14.6727	+	14.6727i	−0.0632445	+	0.0632445i
$233$	100.854	−	27.0237i	0.432849	−	0.115981i	−0.0358143	−	0.999358i	$-0.511402\pi$
$233$	100.854	−	27.0237i	0.432849	−	0.115981i	0.468663	+	0.883377i	$0.344736\pi$
$234$	25.1302	−	14.5089i	0.107394	−	0.0620039i
$235$		0			0
$236$	−50.2432	+	87.0238i	−0.212895	+	0.368745i
$237$	−254.768	+	254.768i	−1.07497	+	1.07497i
$238$	301.117	+	6.24360i	1.26520	+	0.0262336i
$239$			4.00351i			0.0167511i	0.999965	+	0.00837554i	$0.00266605\pi$
$239$			4.00351i			0.0167511i	−0.999965	+	0.00837554i	$0.997334\pi$
$240$		0			0
$241$	148.899	+	257.901i	0.617839	+	1.07013i	0.989879	+	0.141912i	$0.0453249\pi$
$241$	148.899	+	257.901i	0.617839	+	1.07013i	−0.372041	+	0.928216i	$0.621342\pi$
$242$	−164.060	−	43.9596i	−0.677932	−	0.181651i
$243$	−97.0348	+	26.0004i	−0.399320	+	0.106998i
$244$			90.9914i			0.372915i
$245$		0			0
$246$	−383.489			−1.55890
$247$	−7.62184	−	28.4451i	−0.0308577	−	0.115162i
$248$	34.4526	−	128.579i	0.138922	−	0.518463i
$249$	−533.674	+	308.117i	−2.14327	+	1.23742i
$250$		0			0
$251$	300.624			1.19770			0.598852	−	0.800860i	$-0.295624\pi$
$251$	300.624			1.19770			0.598852	+	0.800860i	$0.295624\pi$
$252$	4.88306	−	235.501i	0.0193772	−	0.934526i
$253$	3.80217	+	3.80217i	0.0150283	+	0.0150283i
$254$	−139.160	−	80.3440i	−0.547873	−	0.316315i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	85.5296	+	319.201i	0.332800	+	1.24203i	0.906235	+	0.422775i	$0.138944\pi$
$257$	85.5296	+	319.201i	0.332800	+	1.24203i	−0.573435	+	0.819251i	$0.694389\pi$
$258$	−237.723	−	237.723i	−0.921405	−	0.921405i
$259$	55.9614	−	13.7580i	0.216067	−	0.0531198i
$260$		0			0
$261$	61.7175	−	106.898i	0.236465	−	0.409570i
$262$	34.2679	+	9.18206i	0.130794	+	0.0350460i
$263$	−97.9751	+	365.648i	−0.372529	+	1.39030i	0.484393	+	0.874851i	$0.339041\pi$
$263$	−97.9751	+	365.648i	−0.372529	+	1.39030i	−0.856922	+	0.515446i	$0.827626\pi$
$264$	11.8097	+	6.81836i	0.0447339	+	0.0258271i
$265$		0			0
$266$	−229.570	−	66.6434i	−0.863044	−	0.250539i
$267$	−563.268	+	563.268i	−2.10962	+	2.10962i
$268$	132.000	−	35.3692i	0.492536	−	0.131975i
$269$	125.485	−	72.4489i	0.466488	−	0.269327i	−0.248280	−	0.968688i	$-0.579865\pi$
$269$	125.485	−	72.4489i	0.466488	−	0.269327i	0.714768	+	0.699361i	$0.246532\pi$
$270$		0			0
$271$	165.311	−	286.326i	0.610002	−	1.05655i	−0.381237	−	0.924477i	$-0.624502\pi$
$271$	165.311	−	286.326i	0.610002	−	1.05655i	0.991239	−	0.132078i	$-0.0421648\pi$
$272$	−86.0518	+	86.0518i	−0.316367	+	0.316367i
$273$	20.9076	+	38.0117i	0.0765846	+	0.139237i
$274$			96.7254i			0.353012i
$275$		0			0
$276$	28.8020	+	49.8866i	0.104355	+	0.180749i
$277$	75.9189	+	20.3424i	0.274075	+	0.0734383i	0.393239	−	0.919436i	$-0.371355\pi$
$277$	75.9189	+	20.3424i	0.274075	+	0.0734383i	−0.119163	+	0.992875i	$0.538021\pi$
$278$	91.9409	−	24.6355i	0.330723	−	0.0886169i
$279$			791.842i			2.83814i
$280$		0			0
$281$	−342.866			−1.22016			−0.610081	−	0.792339i	$-0.708863\pi$
$281$	−342.866			−1.22016			−0.610081	+	0.792339i	$0.708863\pi$
$282$	−56.5910	−	211.200i	−0.200677	−	0.748938i
$283$	24.0385	−	89.7129i	0.0849417	−	0.317007i	−0.910361	−	0.413814i	$-0.864196\pi$
$283$	24.0385	−	89.7129i	0.0849417	−	0.317007i	0.995303	+	0.0968072i	$0.0308630\pi$
$284$	20.6466	−	11.9203i	0.0726994	−	0.0419730i
$285$		0			0
$286$	−1.63626			−0.00572118
$287$	7.74323	−	373.441i	0.0269799	−	1.30119i
$288$	67.3004	+	67.3004i	0.233682	+	0.233682i
$289$	551.324	+	318.307i	1.90770	+	1.10141i
$290$		0			0
$291$	−313.269	−	542.598i	−1.07653	−	1.86460i
$292$	28.5107	+	106.403i	0.0976394	+	0.364395i
$293$	345.276	+	345.276i	1.17842	+	1.17842i	0.980147	+	0.198270i	$0.0635323\pi$
$293$	345.276	+	345.276i	1.17842	+	1.17842i	0.198270	+	0.980147i	$0.436468\pi$
$294$	351.851	+	14.5974i	1.19677	+	0.0496510i
$295$		0			0
$296$	−11.6426	+	20.1655i	−0.0393330	+	0.0681267i
$297$	−36.4416	−	9.76451i	−0.122699	−	0.0328771i
$298$	21.9683	−	81.9868i	0.0737191	−	0.275124i
$299$	−5.98585	−	3.45593i	−0.0200196	−	0.0115583i
$300$		0			0
$301$	236.294	−	226.694i	0.785029	−	0.753135i
$302$	−47.8037	+	47.8037i	−0.158290	+	0.158290i
$303$	247.654	−	66.3586i	0.817339	−	0.219005i
$304$	83.6492	−	48.2949i	0.275162	−	0.158865i
$305$		0			0
$306$	361.957	−	626.929i	1.18287	−	2.04879i
$307$	344.100	−	344.100i	1.12085	−	1.12085i	0.129233	−	0.991614i	$-0.458748\pi$
$307$	344.100	−	344.100i	1.12085	−	1.12085i	0.991614	−	0.129233i	$-0.0412517\pi$
$308$	−6.87816	+	11.3626i	−0.0223317	+	0.0368917i
$309$		−	734.638i		−	2.37747i
$310$		0			0
$311$	165.159	+	286.064i	0.531059	+	0.919821i	0.999343	+	0.0362433i	$0.0115391\pi$
$311$	165.159	+	286.064i	0.531059	+	0.919821i	−0.468284	+	0.883578i	$0.655128\pi$
$312$	−16.9318	−	4.53685i	−0.0542685	−	0.0145412i
$313$	82.7090	−	22.1618i	0.264246	−	0.0708045i	−0.124263	−	0.992249i	$-0.539657\pi$
$313$	82.7090	−	22.1618i	0.264246	−	0.0708045i	0.388509	+	0.921445i	$0.372990\pi$
$314$		−	147.910i		−	0.471050i
$315$		0			0
$316$	141.798			0.448727
$317$	45.6055	+	170.202i	0.143866	+	0.536915i	0.999803	+	0.0198354i	$0.00631421\pi$
$317$	45.6055	+	170.202i	0.143866	+	0.536915i	−0.855937	+	0.517080i	$0.827019\pi$
$318$	25.0299	−	93.4129i	0.0787104	−	0.293751i
$319$	−6.02775	+	3.48012i	−0.0188958	+	0.0109095i
$320$		0			0
$321$	35.2623			0.109851
$322$	−49.1610	+	27.0401i	−0.152674	+	0.0839754i
$323$	−519.483	−	519.483i	−1.60831	−	1.60831i
$324$	−87.7419	−	50.6578i	−0.270808	−	0.156351i
$325$		0			0
$326$	29.0689	+	50.3489i	0.0891685	+	0.154444i
$327$	−64.2873	−	239.924i	−0.196597	−	0.733711i
$328$	106.720	+	106.720i	0.325367	+	0.325367i
$329$	206.809	−	50.8437i	0.628599	−	0.154540i
$330$		0			0
$331$	−160.736	+	278.404i	−0.485608	+	0.841098i	−0.999863	−	0.0165391i	$-0.994735\pi$
$331$	−160.736	+	278.404i	−0.485608	+	0.841098i	0.514255	+	0.857637i	$0.328069\pi$
$332$	234.260	+	62.7698i	0.705603	+	0.189066i
$333$	35.8498	−	133.793i	0.107657	−	0.401782i
$334$	45.7874	+	26.4354i	0.137088	+	0.0791479i
$335$		0			0
$336$	−102.679	+	98.5079i	−0.305594	+	0.293178i
$337$	77.9872	−	77.9872i	0.231416	−	0.231416i	−0.581868	−	0.813284i	$-0.697678\pi$
$337$	77.9872	−	77.9872i	0.231416	−	0.231416i	0.813284	+	0.581868i	$0.197678\pi$
$338$	−228.827	+	61.3139i	−0.677002	+	0.181402i
$339$	51.6137	−	29.7992i	0.152253	−	0.0879031i
$340$		0			0
$341$	22.3252	−	38.6684i	0.0654698	−	0.113397i
$342$	−406.283	+	406.283i	−1.18796	+	1.18796i
$343$	−21.3193	+	342.337i	−0.0621555	+	0.998066i
$344$			132.311i			0.384624i
$345$		0			0
$346$	177.508	+	307.453i	0.513028	+	0.888591i
$347$	−325.624	−	87.2508i	−0.938398	−	0.251443i	−0.242966	−	0.970035i	$-0.578120\pi$
$347$	−325.624	−	87.2508i	−0.938398	−	0.251443i	−0.695432	+	0.718592i	$0.744787\pi$
$348$	−72.0237	+	19.2987i	−0.206965	+	0.0554560i
$349$			287.505i			0.823797i	0.911230	+	0.411899i	$0.135134\pi$
$349$			287.505i			0.823797i	−0.911230	+	0.411899i	$0.864866\pi$
$350$		0			0
$351$	48.4957			0.138164
$352$	−1.38904	−	5.18397i	−0.00394614	−	0.0147272i
$353$	−42.9263	+	160.203i	−0.121604	+	0.453834i	−0.999696	−	0.0246589i	$-0.992150\pi$
$353$	−42.9263	+	160.203i	−0.121604	+	0.453834i	0.878092	+	0.478493i	$0.158817\pi$
$354$	−312.712	+	180.544i	−0.883366	+	0.510012i
$355$		0			0
$356$	313.501			0.880621
$357$	925.851	+	560.447i	2.59342	+	1.56988i
$358$	−54.0621	−	54.0621i	−0.151012	−	0.151012i
$359$	−324.332	−	187.253i	−0.903432	−	0.521597i	−0.0251201	−	0.999684i	$-0.507997\pi$
$359$	−324.332	−	187.253i	−0.903432	−	0.521597i	−0.878312	+	0.478088i	$0.841330\pi$
$360$		0			0
$361$	111.049	+	192.343i	0.307616	+	0.532806i
$362$	−73.7371	−	275.191i	−0.203694	−	0.760195i
$363$	−431.567	−	431.567i	−1.18889	−	1.18889i
$364$	4.75986	−	16.3965i	0.0130765	−	0.0450454i
$365$		0			0
$366$	−163.484	+	283.163i	−0.446678	+	0.773670i
$367$	31.5361	+	8.45008i	0.0859295	+	0.0230247i	0.301528	−	0.953457i	$-0.402503\pi$
$367$	31.5361	+	8.45008i	0.0859295	+	0.0230247i	−0.215598	+	0.976482i	$0.569170\pi$
$368$	5.86758	−	21.8981i	0.0159445	−	0.0595057i
$369$	−777.508	−	448.895i	−2.10707	−	1.21652i
$370$		0			0
$371$	90.4599	+	26.2602i	0.243827	+	0.0707823i
$372$	338.234	−	338.234i	0.909231	−	0.909231i
$373$	711.719	−	190.704i	1.90809	−	0.511272i	0.913580	−	0.406658i	$-0.133306\pi$
$373$	711.719	−	190.704i	1.90809	−	0.511272i	0.994513	−	0.104614i	$-0.0333606\pi$
$374$	−35.3512	+	20.4101i	−0.0945221	+	0.0545723i
$375$		0			0
$376$	−43.0259	+	74.5231i	−0.114431	+	0.198200i
$377$	6.32643	−	6.32643i	0.0167810	−	0.0167810i
$378$	203.856	−	336.767i	0.539301	−	0.890919i
$379$			287.166i			0.757693i	0.925460	+	0.378846i	$0.123679\pi$
$379$			287.166i			0.757693i	−0.925460	+	0.378846i	$0.876321\pi$
$380$		0			0
$381$	−288.708	−	500.057i	−0.757764	−	1.31249i
$382$	240.067	+	64.3258i	0.628448	+	0.168392i
$383$	−441.247	+	118.232i	−1.15208	+	0.308699i	−0.783799	−	0.621014i	$-0.786721\pi$
$383$	−441.247	+	118.232i	−1.15208	+	0.308699i	−0.368283	+	0.929714i	$0.620054\pi$
$384$		−	57.4944i		−	0.149725i
$385$		0			0
$386$	−73.8055			−0.191206
$387$	−203.706	−	760.240i	−0.526371	−	1.96444i
$388$	−63.8195	+	238.178i	−0.164483	+	0.613860i
$389$	470.416	−	271.595i	1.20930	−	0.698187i	0.246690	−	0.969094i	$-0.420657\pi$
$389$	470.416	−	271.595i	1.20930	−	0.698187i	0.962605	+	0.270907i	$0.0873237\pi$
$390$		0			0
$391$	−172.432			−0.441002
$392$	−93.8535	−	101.978i	−0.239422	−	0.260148i
$393$	90.1435	+	90.1435i	0.229373	+	0.229373i
$394$	−108.804	−	62.8178i	−0.276151	−	0.159436i
$395$		0			0
$396$	15.9625	+	27.6479i	0.0403094	+	0.0698179i
$397$	−165.368	−	617.160i	−0.416543	−	1.55456i	−0.781725	−	0.623623i	$-0.785660\pi$
$397$	−165.368	−	617.160i	−0.416543	−	1.55456i	0.365182	−	0.930936i	$-0.381007\pi$
$398$	−25.9383	−	25.9383i	−0.0651717	−	0.0651717i
$399$	−594.678	−	619.861i	−1.49042	−	1.55354i
$400$		0			0
$401$	−223.636	+	387.349i	−0.557696	+	0.965958i	0.439992	+	0.898002i	$0.354981\pi$
$401$	−223.636	+	387.349i	−0.557696	+	0.965958i	−0.997688	+	0.0679566i	$0.978352\pi$
$402$	474.328	+	127.096i	1.17992	+	0.316159i
$403$	−14.8549	+	55.4393i	−0.0368608	+	0.137566i
$404$	−87.3858	−	50.4522i	−0.216302	−	0.124882i
$405$		0			0
$406$	−17.3388	−	70.5262i	−0.0427063	−	0.173710i
$407$	−5.52284	+	5.52284i	−0.0135696	+	0.0135696i
$408$	−422.401	+	113.182i	−1.03530	+	0.277407i
$409$	−19.9762	+	11.5333i	−0.0488417	+	0.0281988i	−0.524222	−	0.851582i	$-0.675644\pi$
$409$	−19.9762	+	11.5333i	−0.0488417	+	0.0281988i	0.475380	+	0.879780i	$0.342310\pi$
$410$		0			0
$411$	−173.787	+	301.007i	−0.422839	+	0.732378i
$412$	−204.441	+	204.441i	−0.496215	+	0.496215i
$413$	−169.499	−	308.163i	−0.410410	−	0.746158i
$414$			134.857i			0.325743i
$415$		0			0
$416$	3.44935	+	5.97446i	0.00829172	+	0.0143617i
$417$	330.381	+	88.5253i	0.792280	+	0.212291i
$418$	31.2949	−	8.38545i	0.0748682	−	0.0200609i
$419$		−	502.792i		−	1.19998i	−0.800007	−	0.599990i	$-0.795171\pi$
$419$		−	502.792i		−	1.19998i	0.800007	−	0.599990i	$-0.204829\pi$
$420$		0			0
$421$	48.4897			0.115177			0.0575887	−	0.998340i	$-0.481659\pi$
$421$	48.4897			0.115177			0.0575887	+	0.998340i	$0.481659\pi$
$422$	81.8708	+	305.546i	0.194007	+	0.724043i
$423$	132.486	−	494.443i	0.313205	−	1.16890i
$424$	−32.9612	+	19.0302i	−0.0777387	+	0.0448824i
$425$		0			0
$426$	85.6691			0.201101
$427$	−272.443	−	164.918i	−0.638039	−	0.386225i
$428$	−9.81306	−	9.81306i	−0.0229277	−	0.0229277i
$429$	−5.09200	−	2.93987i	−0.0118695	−	0.00685284i
$430$		0			0
$431$	185.726	+	321.686i	0.430918	+	0.746372i	0.996953	−	0.0780097i	$-0.0248565\pi$
$431$	185.726	+	321.686i	0.430918	+	0.746372i	−0.566035	+	0.824381i	$0.691523\pi$
$432$	41.1686	+	153.643i	0.0952977	+	0.355656i
$433$	−449.707	−	449.707i	−1.03858	−	1.03858i	−0.999225	−	0.0393595i	$-0.987468\pi$
$433$	−449.707	−	449.707i	−1.03858	−	1.03858i	−0.0393595	−	0.999225i	$-0.512532\pi$
$434$	322.542	+	336.201i	0.743184	+	0.774656i
$435$		0			0
$436$	−48.8774	+	84.6582i	−0.112104	+	0.194170i
$437$	132.196	+	35.4217i	0.302507	+	0.0810566i
$438$	−102.450	+	382.350i	−0.233905	+	0.872946i
$439$	508.790	+	293.750i	1.15897	+	0.669134i	0.951058	−	0.309012i	$-0.0999984\pi$
$439$	508.790	+	293.750i	1.15897	+	0.669134i	0.207917	+	0.978147i	$0.433332\pi$
$440$		0			0
$441$	696.276	+	441.456i	1.57886	+	1.00103i
$442$	37.1029	−	37.1029i	0.0839432	−	0.0839432i
$443$	4.58686	−	1.22904i	0.0103541	−	0.00277437i	−0.253638	−	0.967299i	$-0.581627\pi$
$443$	4.58686	−	1.22904i	0.0103541	−	0.00277437i	0.263992	+	0.964525i	$0.414961\pi$
$444$	−72.4628	+	41.8364i	−0.163205	+	0.0942262i
$445$		0			0
$446$	131.856	−	228.381i	0.295641	−	0.512065i
$447$	215.671	−	215.671i	0.482485	−	0.482485i
$448$	55.9880	+	1.16090i	0.124973	+	0.00259130i
$449$			40.6375i			0.0905067i	0.998976	+	0.0452533i	$0.0144095\pi$
$449$			40.6375i			0.0905067i	−0.998976	+	0.0452533i	$0.985590\pi$
$450$		0			0
$451$	25.3123	+	43.8421i	0.0561248	+	0.0972109i
$452$	−22.6562	−	6.07071i	−0.0501243	−	0.0134308i
$453$	−234.653	+	62.8750i	−0.517997	+	0.138797i
$454$		−	536.130i		−	1.18090i
$455$		0			0
$456$	347.086			0.761153
$457$	−85.0810	−	317.526i	−0.186173	−	0.694806i	−0.994376	−	0.105903i	$-0.966227\pi$
$457$	−85.0810	−	317.526i	−0.186173	−	0.694806i	0.808204	−	0.588903i	$-0.200440\pi$
$458$	16.8407	−	62.8505i	0.0367702	−	0.137228i
$459$	1047.75	−	604.916i	2.28267	−	1.31790i
$460$		0			0
$461$	64.7559			0.140468			0.0702341	−	0.997531i	$-0.477625\pi$
$461$	64.7559			0.140468			0.0702341	+	0.997531i	$0.477625\pi$
$462$	−41.8199	+	23.0023i	−0.0905194	+	0.0497884i
$463$	604.400	+	604.400i	1.30540	+	1.30540i	0.924698	+	0.380701i	$0.124317\pi$
$463$	604.400	+	604.400i	1.30540	+	1.30540i	0.380701	+	0.924698i	$0.375683\pi$
$464$	25.4139	+	14.6727i	0.0547713	+	0.0316222i
$465$		0			0
$466$	−73.8301	−	127.877i	−0.158434	−	0.274415i
$467$	92.4995	+	345.213i	0.198072	+	0.739214i	0.991450	+	0.130485i	$0.0416535\pi$
$467$	92.4995	+	345.213i	0.198072	+	0.739214i	−0.793379	+	0.608729i	$0.791680\pi$
$468$	−29.0178	−	29.0178i	−0.0620039	−	0.0620039i
$469$	−133.343	+	459.334i	−0.284314	+	0.979389i
$470$		0			0
$471$	265.750	−	460.292i	0.564224	−	0.977265i
$472$	137.267	+	36.7806i	0.290820	+	0.0779250i
$473$	−11.4866	+	42.8684i	−0.0242845	+	0.0906309i
$474$	441.272	+	254.768i	0.930953	+	0.537486i
$475$		0			0
$476$	−101.687	−	413.618i	−0.213629	−	0.868946i
$477$	160.092	−	160.092i	0.335623	−	0.335623i
$478$	5.46889	−	1.46539i	0.0114412	−	0.00306566i
$479$	508.668	−	293.679i	1.06194	−	0.613109i	0.135969	−	0.990713i	$-0.456585\pi$
$479$	508.668	−	293.679i	1.06194	−	0.613109i	0.925967	+	0.377604i	$0.123252\pi$
$480$		0			0
$481$	5.01992	−	8.69475i	0.0104364	−	0.0180764i
$482$	297.798	−	297.798i	0.617839	−	0.617839i
$483$	−201.571	−	4.17954i	−0.417331	−	0.00865329i
$484$			240.200i			0.496281i
$485$		0			0
$486$	71.0344	+	123.035i	0.146161	+	0.253159i
$487$	549.440	+	147.222i	1.12821	+	0.302304i	0.774202	−	0.632938i	$-0.218151\pi$
$487$	549.440	+	147.222i	1.12821	+	0.302304i	0.354010	+	0.935242i	$0.384818\pi$
$488$	124.297	−	33.3052i	0.254706	−	0.0682483i
$489$			208.913i			0.427224i
$490$		0			0
$491$	485.037			0.987856			0.493928	−	0.869503i	$-0.335561\pi$
$491$	485.037			0.987856			0.493928	+	0.869503i	$0.335561\pi$
$492$	140.367	+	523.856i	0.285298	+	1.06475i
$493$	57.7686	−	215.595i	0.117178	−	0.437313i
$494$	−36.0669	+	20.8233i	−0.0730100	+	0.0421523i
$495$		0			0
$496$	−188.253			−0.379542
$497$	−1.72979	+	83.4244i	−0.00348046	+	0.167856i
$498$	616.234	+	616.234i	1.23742	+	1.23742i
$499$	−500.231	−	288.808i	−1.00247	−	0.578774i	−0.0934891	−	0.995620i	$-0.529802\pi$
$499$	−500.231	−	288.808i	−1.00247	−	0.578774i	−0.908977	+	0.416846i	$0.863135\pi$
$500$		0			0
$501$	94.9930	+	164.533i	0.189607	+	0.328409i
$502$	−110.036	−	410.660i	−0.219195	−	0.818047i
$503$	417.802	+	417.802i	0.830620	+	0.830620i	0.987602	−	0.156981i	$-0.0501763\pi$
$503$	417.802	+	417.802i	0.830620	+	0.830620i	−0.156981	+	0.987602i	$0.550176\pi$
$504$	−323.487	+	79.5288i	−0.641840	+	0.157795i
$505$		0			0
$506$	3.80217	−	6.58555i	0.00751417	−	0.0130149i
$507$	−822.266	−	220.326i	−1.62183	−	0.434567i
$508$	−58.8159	+	219.504i	−0.115779	+	0.432094i
$509$	−136.905	−	79.0420i	−0.268968	−	0.155289i	0.359451	−	0.933164i	$-0.382964\pi$
$509$	−136.905	−	79.0420i	−0.268968	−	0.155289i	−0.628419	+	0.777875i	$0.716297\pi$
$510$		0			0
$511$	−370.263	−	107.486i	−0.724586	−	0.210345i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−927.523	+	248.529i	−1.80804	+	0.484462i
$514$	404.730	−	233.671i	0.787413	−	0.454613i
$515$		0			0
$516$	−237.723	+	411.748i	−0.460703	+	0.797960i
$517$	−20.4101	+	20.4101i	−0.0394779	+	0.0394779i
$518$	−39.2771	−	71.4089i	−0.0758245	−	0.137855i
$519$			1275.71i			2.45802i
$520$		0			0
$521$	58.2493	+	100.891i	0.111803	+	0.193648i	0.916497	−	0.400041i	$-0.131004\pi$
$521$	58.2493	+	100.891i	0.111803	+	0.193648i	−0.804694	+	0.593689i	$0.797671\pi$
$522$	−168.615	−	45.1803i	−0.323018	−	0.0865523i
$523$	−244.396	+	65.4858i	−0.467297	+	0.125212i	−0.484782	−	0.874635i	$-0.661101\pi$
$523$	−244.396	+	65.4858i	−0.467297	+	0.125212i	0.0174845	+	0.999847i	$0.494434\pi$
$524$		−	50.1717i		−	0.0957475i
$525$		0			0
$526$	535.346			1.01777
$527$	370.589	+	1383.06i	0.703205	+	2.62440i
$528$	4.99139	−	18.6281i	0.00945338	−	0.0352805i
$529$	−430.309	+	248.439i	−0.813438	+	0.469639i
$530$		0			0
$531$	−845.347			−1.59199
$532$	−7.00819	+	337.991i	−0.0131733	+	0.635322i
$533$	−46.0145	−	46.0145i	−0.0863311	−	0.0863311i
$534$	975.608	+	563.268i	1.82698	+	1.05481i
$535$		0			0
$536$	−96.6305	−	167.369i	−0.180281	−	0.312256i
$537$	−71.1067	−	265.374i	−0.132415	−	0.494178i
$538$	−144.898	−	144.898i	−0.269327	−	0.269327i
$539$	−21.5551	−	41.1886i	−0.0399910	−	0.0764167i
$540$		0			0
$541$	420.568	−	728.445i	0.777390	−	1.34648i	−0.156052	−	0.987749i	$-0.549877\pi$
$541$	420.568	−	728.445i	0.777390	−	1.34648i	0.933442	−	0.358730i	$-0.116790\pi$
$542$	−451.637	−	121.016i	−0.833279	−	0.223276i
$543$	264.967	−	988.871i	0.487969	−	1.82112i
$544$	149.046	+	86.0518i	0.273982	+	0.158183i
$545$		0			0
$546$	44.2722	−	42.4736i	0.0810846	−	0.0777904i
$547$	−228.297	+	228.297i	−0.417362	+	0.417362i	−0.884294	−	0.466931i	$-0.845360\pi$
$547$	−228.297	+	228.297i	−0.417362	+	0.417362i	0.466931	+	0.884294i	$0.345360\pi$
$548$	132.129	−	35.4040i	0.241112	−	0.0646058i
$549$	−662.916	+	382.734i	−1.20750	+	0.697148i
$550$		0			0
$551$	−88.5771	+	153.420i	−0.160757	+	0.278439i
$552$	57.6041	−	57.6041i	0.104355	−	0.104355i
$553$	−257.003	+	424.565i	−0.464743	+	0.767749i
$554$		−	111.153i		−	0.200637i
$555$		0			0
$556$	−67.3054	−	116.576i	−0.121053	−	0.209670i
$557$	−925.810	−	248.070i	−1.66214	−	0.445368i	−0.699162	−	0.714963i	$-0.746443\pi$
$557$	−925.810	−	248.070i	−1.66214	−	0.445368i	−0.962974	+	0.269595i	$0.913110\pi$
$558$	1081.68	−	289.834i	1.93849	−	0.519416i
$559$		−	57.0482i		−	0.102054i
$560$		0			0
$561$	−146.683			−0.261467
$562$	125.497	+	468.363i	0.223305	+	0.833386i
$563$	240.016	−	895.754i	0.426317	−	1.59104i	−0.334713	−	0.942320i	$-0.608639\pi$
$563$	240.016	−	895.754i	0.426317	−	1.59104i	0.761030	−	0.648717i	$-0.224694\pi$
$564$	−267.791	+	154.609i	−0.474807	+	0.274130i
$565$		0			0
$566$	−131.349			−0.232065
$567$	310.706	−	170.898i	0.547982	−	0.301407i
$568$	−23.8407	−	23.8407i	−0.0419730	−	0.0419730i
$569$	−391.524	−	226.046i	−0.688091	−	0.397270i	0.114805	−	0.993388i	$-0.463376\pi$
$569$	−391.524	−	226.046i	−0.688091	−	0.397270i	−0.802897	+	0.596118i	$0.796709\pi$
$570$		0			0
$571$	−195.371	−	338.393i	−0.342157	−	0.592633i	0.642676	−	0.766138i	$-0.277824\pi$
$571$	−195.371	−	338.393i	−0.342157	−	0.592633i	−0.984833	+	0.173505i	$0.944491\pi$
$572$	0.598912	+	2.23517i	0.00104705	+	0.00390764i
$573$	631.510	+	631.510i	1.10211	+	1.10211i
$574$	−512.964	+	126.111i	−0.893665	+	0.219706i
$575$		0			0
$576$	67.3004	−	116.568i	0.116841	−	0.202374i
$577$	−438.134	−	117.398i	−0.759330	−	0.203462i	−0.141677	−	0.989913i	$-0.545250\pi$
$577$	−438.134	−	117.398i	−0.759330	−	0.203462i	−0.617653	+	0.786451i	$0.711916\pi$
$578$	233.017	−	869.631i	0.403144	−	1.50455i
$579$	−229.681	−	132.606i	−0.396686	−	0.229027i
$580$		0			0
$581$	−612.530	+	587.645i	−1.05427	+	1.01144i
$582$	−626.539	+	626.539i	−1.07653	+	1.07653i
$583$	−12.3315	+	3.30421i	−0.0211518	+	0.00566760i
$584$	134.914	−	77.8927i	0.231017	−	0.133378i
$585$		0			0
$586$	345.276	−	598.036i	0.589209	−	1.02054i
$587$	132.759	−	132.759i	0.226165	−	0.226165i	−0.584924	−	0.811088i	$-0.698876\pi$
$587$	132.759	−	132.759i	0.226165	−	0.226165i	0.811088	+	0.584924i	$0.198876\pi$
$588$	−108.846	−	485.980i	−0.185112	−	0.826497i
$589$		−	1136.45i		−	1.92946i
$590$		0			0
$591$	−225.730	−	390.975i	−0.381946	−	0.661549i
$592$	31.8081	+	8.52295i	0.0537299	+	0.0143969i
$593$	132.343	−	35.4612i	0.223176	−	0.0597997i	−0.145498	−	0.989358i	$-0.546479\pi$
$593$	132.343	−	35.4612i	0.223176	−	0.0597997i	0.368674	+	0.929559i	$0.379812\pi$
$594$			53.3543i			0.0898220i
$595$		0			0
$596$	−120.037			−0.201404
$597$	−34.1161	−	127.323i	−0.0571458	−	0.213271i
$598$	−2.52992	+	9.44178i	−0.00423063	+	0.0157889i
$599$	−533.617	+	308.084i	−0.890847	+	0.514331i	−0.874220	−	0.485531i	$-0.838626\pi$
$599$	−533.617	+	308.084i	−0.890847	+	0.514331i	−0.0166277	+	0.999862i	$0.505293\pi$
$600$		0			0
$601$	−660.812			−1.09952			−0.549760	−	0.835322i	$-0.685281\pi$
$601$	−660.812			−1.09952			−0.549760	+	0.835322i	$0.685281\pi$
$602$	−396.159	−	239.808i	−0.658071	−	0.398351i
$603$	812.909	+	812.909i	1.34811	+	1.34811i
$604$	82.7984	+	47.8037i	0.137083	+	0.0791451i
$605$		0			0
$606$	−181.295	−	314.012i	−0.299167	−	0.518172i
$607$	100.052	+	373.398i	0.164830	+	0.615153i	0.998062	+	0.0622299i	$0.0198212\pi$
$607$	100.052	+	373.398i	0.164830	+	0.615153i	−0.833232	+	0.552924i	$0.813512\pi$
$608$	−96.5897	−	96.5897i	−0.158865	−	0.158865i
$609$	72.7567	−	250.628i	0.119469	−	0.411541i
$610$		0			0
$611$	18.5514	−	32.1320i	0.0303624	−	0.0525893i
$612$	−988.886	−	264.971i	−1.61583	−	0.432959i
$613$	13.3884	−	49.9662i	0.0218408	−	0.0815109i	−0.954145	−	0.299344i	$-0.903232\pi$
$613$	13.3884	−	49.9662i	0.0218408	−	0.0815109i	0.975986	+	0.217833i	$0.0698988\pi$
$614$	−595.999	−	344.100i	−0.970683	−	0.560424i
$615$		0			0
$616$	18.0392	+	5.23673i	0.0292845	+	0.00850119i
$617$	616.887	−	616.887i	0.999816	−	0.999816i	−0.000183933	−	1.00000i	$-0.500059\pi$
$617$	616.887	−	616.887i	0.999816	−	0.999816i	1.00000		0.000183933i	$5.85476e-5\pi$
$618$	−1003.53	+	268.896i	−1.62384	+	0.435107i
$619$	−449.823	+	259.705i	−0.726693	+	0.419556i	−0.817211	−	0.576339i	$-0.804481\pi$
$619$	−449.823	+	259.705i	−0.726693	+	0.419556i	0.0905183	+	0.995895i	$0.471148\pi$
$620$		0			0
$621$	−112.689	+	195.184i	−0.181464	+	0.314305i
$622$	330.319	−	330.319i	0.531059	−	0.531059i
$623$	−568.208	+	938.672i	−0.912051	+	1.50670i
$624$			24.7898i			0.0397273i
$625$		0			0
$626$	−60.5472	−	104.871i	−0.0967208	−	0.167525i
$627$	112.455	+	30.1323i	0.179354	+	0.0480579i
$628$	−202.048	+	54.1387i	−0.321733	+	0.0862081i
$629$		−	250.466i		−	0.398197i
$630$		0			0
$631$	−427.140			−0.676925			−0.338463	−	0.940980i	$-0.609907\pi$
$631$	−427.140			−0.676925			−0.338463	+	0.940980i	$0.609907\pi$
$632$	−51.9016	−	193.699i	−0.0821228	−	0.306486i
$633$	−294.195	+	1097.95i	−0.464763	+	1.73452i
$634$	215.808	−	124.597i	0.340390	−	0.196525i
$635$		0			0
$636$	−136.766			−0.215041
$637$	40.4667	+	43.9698i	0.0635271	+	0.0690264i
$638$	6.96025	+	6.96025i	0.0109095	+	0.0109095i
$639$	173.691	+	100.280i	0.271816	+	0.156933i
$640$		0			0
$641$	−135.063	−	233.937i	−0.210707	−	0.364956i	0.741229	−	0.671252i	$-0.234243\pi$
$641$	−135.063	−	233.937i	−0.210707	−	0.364956i	−0.951936	+	0.306297i	$0.900910\pi$
$642$	−12.9069	−	48.1692i	−0.0201042	−	0.0750298i
$643$	−192.668	−	192.668i	−0.299639	−	0.299639i	0.541234	−	0.840872i	$-0.317957\pi$
$643$	−192.668	−	192.668i	−0.299639	−	0.299639i	−0.840872	+	0.541234i	$0.817957\pi$
$644$	54.9316	+	57.2579i	0.0852976	+	0.0889097i
$645$		0			0
$646$	−519.483	+	899.770i	−0.804153	+	1.39283i
$647$	237.128	+	63.5381i	0.366503	+	0.0982042i	0.437370	−	0.899282i	$-0.355910\pi$
$647$	237.128	+	63.5381i	0.366503	+	0.0982042i	−0.0708670	+	0.997486i	$0.522577\pi$
$648$	−37.0841	+	138.400i	−0.0572285	+	0.213580i
$649$	41.2812	+	23.8337i	0.0636074	+	0.0367237i
$650$		0			0
$651$	399.691	+	1625.76i	0.613964	+	2.49733i
$652$	58.1379	−	58.1379i	0.0891685	−	0.0891685i
$653$	−440.504	+	118.033i	−0.674585	+	0.180755i	−0.579819	−	0.814745i	$-0.696877\pi$
$653$	−440.504	+	118.033i	−0.674585	+	0.180755i	−0.0947659	+	0.995500i	$0.530210\pi$
$654$	−304.211	+	175.636i	−0.465154	+	0.268557i
$655$		0			0
$656$	106.720	−	184.845i	0.162683	−	0.281776i
$657$	−655.276	+	655.276i	−0.997376	+	0.997376i
$658$	−145.151	−	263.896i	−0.220595	−	0.401058i
$659$			973.026i			1.47652i	0.674517	+	0.738259i	$0.264352\pi$
$659$			973.026i			1.47652i	−0.674517	+	0.738259i	$0.735648\pi$
$660$		0			0
$661$	152.550	+	264.224i	0.230787	+	0.399734i	0.958040	−	0.286635i	$-0.0925367\pi$
$661$	152.550	+	264.224i	0.230787	+	0.399734i	−0.727253	+	0.686369i	$0.759203\pi$
$662$	439.140	+	117.667i	0.663353	+	0.177745i
$663$	182.126	−	48.8006i	0.274700	−	0.0736057i
$664$		−	342.981i		−	0.516537i
$665$		0			0
$666$	−195.887			−0.294125
$667$	10.7617	+	40.1631i	0.0161344	+	0.0602145i
$668$	19.3520	−	72.2228i	0.0289701	−	0.108118i
$669$	820.666	−	473.811i	1.22670	−	0.708238i
$670$		0			0
$671$	43.1633			0.0643268
$672$	172.148	+	104.206i	0.256172	+	0.155069i
$673$	−567.081	−	567.081i	−0.842616	−	0.842616i	0.146582	−	0.989198i	$-0.453173\pi$
$673$	−567.081	−	567.081i	−0.842616	−	0.842616i	−0.989198	+	0.146582i	$0.953173\pi$
$674$	−135.078	−	77.9872i	−0.200412	−	0.115708i
$675$		0			0
$676$	167.513	+	290.141i	0.247800	+	0.429202i
$677$	−103.404	−	385.908i	−0.152738	−	0.570027i	−0.999288	−	0.0377179i	$-0.987991\pi$
$677$	−103.404	−	385.908i	−0.152738	−	0.570027i	0.846550	−	0.532309i	$-0.178676\pi$
$678$	−59.5983	−	59.5983i	−0.0879031	−	0.0879031i
$679$	−597.471	−	622.773i	−0.879928	−	0.917191i
$680$		0			0
$681$	963.266	−	1668.42i	1.41449	−	2.44996i
$682$	−60.9936	−	16.3432i	−0.0894334	−	0.0239636i
$683$	−246.473	+	919.851i	−0.360869	+	1.34678i	0.512067	+	0.858945i	$0.328880\pi$
$683$	−246.473	+	919.851i	−0.360869	+	1.34678i	−0.872936	+	0.487835i	$0.837787\pi$
$684$	703.702	+	406.283i	1.02880	+	0.593980i
$685$		0			0
$686$	475.444	−	96.1812i	0.693067	−	0.140206i
$687$	165.332	−	165.332i	0.240657	−	0.240657i
$688$	180.740	−	48.4290i	0.262703	−	0.0703910i
$689$	14.2119	−	8.20522i	0.0206268	−	0.0119089i
$690$		0			0
$691$	235.417	−	407.754i	0.340690	−	0.590093i	−0.643871	−	0.765134i	$-0.722673\pi$
$691$	235.417	−	407.754i	0.340690	−	0.590093i	0.984561	+	0.175042i	$0.0560060\pi$
$692$	355.016	−	355.016i	0.513028	−	0.513028i
$693$	−111.714	−	2.31636i	−0.161203	−	0.00334251i
$694$			476.747i			0.686955i
$695$		0			0
$696$	52.7250	+	91.3224i	0.0757543	+	0.131210i
$697$	−1568.11	−	420.173i	−2.24980	−	0.602831i
$698$	392.740	−	105.234i	0.562664	−	0.150765i
$699$		−	530.602i		−	0.759088i
$700$		0			0
$701$	−1335.50			−1.90514			−0.952569	−	0.304322i	$-0.901570\pi$
$701$	−1335.50			−1.90514			−0.952569	+	0.304322i	$0.901570\pi$
$702$	−17.7506	−	66.2463i	−0.0252858	−	0.0943679i
$703$	−51.4518	+	192.021i	−0.0731890	+	0.273145i
$704$	−6.57302	+	3.79493i	−0.00933667	+	0.00539053i
$705$		0			0
$706$	234.554			0.332229
$707$	309.445	−	170.204i	0.437688	−	0.240742i
$708$	361.088	+	361.088i	0.510012	+	0.510012i
$709$	1150.06	+	663.986i	1.62208	+	0.936510i	0.986362	+	0.164592i	$0.0526307\pi$
$709$	1150.06	+	663.986i	1.62208	+	0.936510i	0.635722	+	0.771918i	$0.280703\pi$
$710$		0			0
$711$	596.440	+	1033.06i	0.838875	+	1.45297i
$712$	−114.749	−	428.250i	−0.161165	−	0.601475i
$713$	−188.612	−	188.612i	−0.264532	−	0.264532i
$714$	426.700	−	1469.87i	0.597618	−	2.05865i
$715$		0			0
$716$	−54.0621	+	93.6384i	−0.0755058	+	0.130780i
$717$	19.6519	+	5.26572i	0.0274086	+	0.00734410i
$718$	−137.079	+	511.585i	−0.190918	+	0.712515i
$719$	244.147	+	140.958i	0.339564	+	0.196048i	0.660079	−	0.751196i	$-0.270523\pi$
$719$	244.147	+	140.958i	0.339564	+	0.196048i	−0.320515	+	0.947243i	$0.603856\pi$
$720$		0			0
$721$	−241.588	−	982.668i	−0.335073	−	1.36292i
$722$	222.098	−	222.098i	0.307616	−	0.307616i
$723$	1461.80	−	391.687i	2.02185	−	0.541753i
$724$	−348.928	+	201.453i	−0.481944	+	0.278251i
$725$		0			0
$726$	−431.567	+	747.497i	−0.594445	+	1.02961i
$727$	−830.098	+	830.098i	−1.14181	+	1.14181i	−0.153694	+	0.988118i	$0.549117\pi$
$727$	−830.098	+	830.098i	−1.14181	+	1.14181i	−0.988118	+	0.153694i	$0.950883\pi$
$728$	−24.1403	−	0.500544i	−0.0331597	−	0.000687561i
$729$			966.430i			1.32569i
$730$		0			0
$731$	−711.598	−	1232.52i	−0.973458	−	1.68608i
$732$	446.647	+	119.679i	0.610174	+	0.163496i
$733$	1152.36	−	308.773i	1.57211	−	0.421245i	0.635637	−	0.771988i	$-0.280737\pi$
$733$	1152.36	−	308.773i	1.57211	−	0.421245i	0.936472	+	0.350743i	$0.114071\pi$
$734$		−	46.1721i		−	0.0629048i
$735$		0			0
$736$	−32.0610			−0.0435612
$737$	−16.7780	−	62.6163i	−0.0227652	−	0.0849610i
$738$	−328.614	+	1226.40i	−0.445276	+	1.66179i
$739$	−491.205	+	283.597i	−0.664688	+	0.383758i	−0.794061	−	0.607838i	$-0.792037\pi$
$739$	−491.205	+	283.597i	−0.664688	+	0.383758i	0.129373	+	0.991596i	$0.458704\pi$
$740$		0			0
$741$	−149.653			−0.201960
$742$	2.76151	−	133.182i	0.00372172	−	0.179491i
$743$	121.240	+	121.240i	0.163176	+	0.163176i	0.783972	−	0.620796i	$-0.213190\pi$
$743$	121.240	+	121.240i	0.163176	+	0.163176i	−0.620796	+	0.783972i	$0.713190\pi$
$744$	−585.838	−	338.234i	−0.787417	−	0.454615i
$745$		0			0
$746$	−521.014	−	902.423i	−0.698411	−	1.20968i
$747$	528.054	+	1970.72i	0.706900	+	2.63819i
$748$	40.8201	+	40.8201i	0.0545723	+	0.0545723i
$749$	47.1676	−	11.5961i	0.0629741	−	0.0154821i
$750$		0			0
$751$	−499.516	+	865.187i	−0.665135	+	1.15205i	0.314114	+	0.949385i	$0.398293\pi$
$751$	−499.516	+	865.187i	−0.665135	+	1.15205i	−0.979249	+	0.202662i	$0.935041\pi$
$752$	117.549	+	31.4972i	0.156315	+	0.0418845i
$753$	395.404	−	1475.67i	0.525104	−	1.95972i
$754$	−10.9577	−	6.32643i	−0.0145327	−	0.00839048i
$755$		0			0
$756$	−534.649	−	155.207i	−0.707208	−	0.205300i
$757$	−290.904	+	290.904i	−0.384285	+	0.384285i	−0.872643	−	0.488358i	$-0.837596\pi$
$757$	−290.904	+	290.904i	−0.384285	+	0.384285i	0.488358	+	0.872643i	$0.337596\pi$
$758$	392.275	−	105.110i	0.517514	−	0.138667i
$759$	23.6645	−	13.6627i	0.0311786	−	0.0180010i
$760$		0			0
$761$	185.178	−	320.737i	0.243335	−	0.421468i	−0.718327	−	0.695705i	$-0.755092\pi$
$761$	185.178	−	320.737i	0.243335	−	0.421468i	0.961662	+	0.274237i	$0.0884253\pi$
$762$	−577.416	+	577.416i	−0.757764	+	0.757764i
$763$	−164.892	−	299.786i	−0.216110	−	0.392905i
$764$		−	351.483i		−	0.460056i
$765$		0			0
$766$	323.016	+	559.479i	0.421691	+	0.730391i
$767$	−59.1853	−	15.8587i	−0.0771647	−	0.0206762i
$768$	−78.5389	+	21.0444i	−0.102264	+	0.0274016i
$769$			615.359i			0.800207i	0.916470	+	0.400103i	$0.131026\pi$
$769$			615.359i			0.800207i	−0.916470	+	0.400103i	$0.868974\pi$
$770$		0			0
$771$	1679.35			2.17814
$772$	27.0147	+	100.820i	0.0349931	+	0.130596i
$773$	218.298	−	814.698i	0.282403	−	1.05394i	−0.668313	−	0.743880i	$-0.732983\pi$
$773$	218.298	−	814.698i	0.282403	−	1.05394i	0.950716	−	0.310063i	$-0.100350\pi$
$774$	−963.945	+	556.534i	−1.24541	+	0.719036i
$775$		0			0
$776$	348.716			0.449376
$777$	6.07099	−	292.792i	0.00781337	−	0.376824i
$778$	−543.189	−	543.189i	−0.698187	−	0.698187i
$779$	1115.88	+	644.255i	1.43246	+	0.827029i
$780$		0			0
$781$	−5.65461	−	9.79407i	−0.00724021	−	0.0125404i
$782$	63.1144	+	235.546i	0.0807090	+	0.301210i
$783$	−206.289	−	206.289i	−0.263460	−	0.263460i
$784$	−104.952	+	165.533i	−0.133867	+	0.211139i
$785$		0			0
$786$	90.1435	−	156.133i	0.114686	−	0.198643i
$787$	440.137	+	117.934i	0.559259	+	0.149853i	0.527366	−	0.849638i	$-0.323180\pi$
$787$	440.137	+	117.934i	0.559259	+	0.149853i	0.0318931	+	0.999491i	$0.489846\pi$
$788$	−45.9858	+	171.622i	−0.0583577	+	0.217794i
$789$	1665.99	+	961.857i	2.11151	+	1.21908i
$790$		0			0
$791$	59.2401	−	56.8333i	0.0748927	−	0.0718500i
$792$	31.9250	−	31.9250i	0.0403094	−	0.0403094i
$793$	−53.5928	+	14.3602i	−0.0675824	+	0.0181086i
$794$	−782.528	+	451.793i	−0.985551	+	0.569008i
$795$		0			0
$796$	−25.9383	+	44.9265i	−0.0325858	+	0.0564403i
$797$	1040.82	−	1040.82i	1.30592	−	1.30592i	0.381592	−	0.924331i	$-0.375376\pi$
$797$	1040.82	−	1040.82i	1.30592	−	1.30592i	0.924331	−	0.381592i	$-0.124624\pi$
$798$	−629.079	+	1039.23i	−0.788319	+	1.30229i
$799$		−	925.614i		−	1.15847i
$800$		0			0
$801$	1318.67	+	2284.00i	1.64628	+	2.85144i
$802$	610.985	+	163.713i	0.761827	+	0.204131i
$803$	50.4742	−	13.5245i	0.0628571	−	0.0168425i
$804$		−	694.465i		−	0.863762i
$805$		0			0
$806$	81.1687			0.100706
$807$	−190.581	−	711.257i	−0.236160	−	0.881360i
$808$	−36.9336	+	137.838i	−0.0457099	+	0.170592i
$809$	192.279	−	111.012i	0.237674	−	0.137221i	−0.376433	−	0.926444i	$-0.622850\pi$
$809$	192.279	−	111.012i	0.237674	−	0.137221i	0.614107	+	0.789222i	$0.289516\pi$
$810$		0			0
$811$	1418.65			1.74926			0.874632	−	0.484788i	$-0.161103\pi$
$811$	1418.65			1.74926			0.874632	+	0.484788i	$0.161103\pi$
$812$	−89.9941	+	49.4996i	−0.110830	+	0.0609600i
$813$	−1188.06	−	1188.06i	−1.46132	−	1.46132i
$814$	9.56585	+	5.52284i	0.0117517	+	0.00678482i
$815$		0			0
$816$	309.219	+	535.583i	0.378945	+	0.656351i
$817$	292.359	+	1091.10i	0.357845	+	1.33549i
$818$	23.0666	+	23.0666i	0.0281988	+	0.0281988i
$819$	139.478	−	34.2904i	0.170302	−	0.0418686i
$820$		0			0
$821$	192.277	−	333.033i	0.234198	−	0.405643i	−0.724841	−	0.688916i	$-0.758087\pi$
$821$	192.277	−	333.033i	0.234198	−	0.405643i	0.959039	+	0.283273i	$0.0914202\pi$
$822$	474.794	+	127.221i	0.577608	+	0.154770i
$823$	−17.2796	+	64.4885i	−0.0209959	+	0.0783578i	−0.975629	−	0.219427i	$-0.929581\pi$
$823$	−17.2796	+	64.4885i	−0.0209959	+	0.0783578i	0.954633	+	0.297785i	$0.0962478\pi$
$824$	354.102	+	204.441i	0.429735	+	0.248108i
$825$		0			0
$826$	−358.918	+	344.336i	−0.434525	+	0.416872i
$827$	−595.969	+	595.969i	−0.720639	+	0.720639i	−0.968735	−	0.248096i	$-0.920195\pi$
$827$	−595.969	+	595.969i	−0.720639	+	0.720639i	0.248096	+	0.968735i	$0.420195\pi$
$828$	184.219	−	49.3612i	0.222486	−	0.0596150i
$829$	−609.282	+	351.769i	−0.734960	+	0.424329i	−0.820234	−	0.572028i	$-0.806157\pi$
$829$	−609.282	+	351.769i	−0.734960	+	0.424329i	0.0852739	+	0.996358i	$0.472823\pi$
$830$		0			0
$831$	199.709	−	345.905i	0.240323	−	0.416252i
$832$	6.89871	−	6.89871i	0.00829172	−	0.00829172i
$833$	1422.74	+	445.198i	1.70798	+	0.534451i
$834$		−	483.711i		−	0.579989i
$835$		0			0
$836$	−22.9095	−	39.6804i	−0.0274037	−	0.0474645i
$837$	1807.74	+	484.381i	2.15978	+	0.578711i
$838$	−686.826	+	184.035i	−0.819602	+	0.219612i
$839$		−	3.00042i		−	0.00357618i	−0.999998	−	0.00178809i	$-0.999431\pi$
$839$		−	3.00042i		−	0.00357618i	0.999998	−	0.00178809i	$-0.000569167\pi$
$840$		0			0
$841$	787.178			0.936002
$842$	−17.7485	−	66.2382i	−0.0210789	−	0.0786677i
$843$	−450.963	+	1683.02i	−0.534950	+	1.99646i
$844$	387.417	−	223.675i	0.459025	−	0.265018i
$845$		0			0
$846$	−723.915			−0.855691
$847$	−719.197	−	435.352i	−0.849110	−	0.513993i
$848$	38.0603	+	38.0603i	0.0448824	+	0.0448824i
$849$	−408.755	−	235.995i	−0.481454	−	0.277968i
$850$		0			0
$851$	23.3295	+	40.4079i	0.0274143	+	0.0474829i
$852$	−31.3571	−	117.026i	−0.0368041	−	0.137355i
$853$	−657.357	−	657.357i	−0.770641	−	0.770641i	0.207577	−	0.978219i	$-0.433442\pi$
$853$	−657.357	−	657.357i	−0.770641	−	0.770641i	−0.978219	+	0.207577i	$0.933442\pi$
$854$	−125.561	+	432.528i	−0.147027	+	0.506473i
$855$		0			0
$856$	−9.81306	+	16.9967i	−0.0114639	+	0.0198560i
$857$	−1022.44	−	273.963i	−1.19305	−	0.319677i	−0.392960	−	0.919556i	$-0.628549\pi$
$857$	−1022.44	−	273.963i	−1.19305	−	0.319677i	−0.800091	+	0.599879i	$0.795216\pi$
$858$	−2.15213	+	8.03187i	−0.00250831	+	0.00936115i
$859$	−747.383	−	431.502i	−0.870062	−	0.502331i	−0.00269328	−	0.999996i	$-0.500857\pi$
$859$	−747.383	−	431.502i	−0.870062	−	0.502331i	−0.867369	+	0.497666i	$0.834191\pi$
$860$		0			0
$861$	−1822.92	−	529.187i	−2.11721	−	0.614619i
$862$	371.451	−	371.451i	0.430918	−	0.430918i
$863$	1176.48	−	315.238i	1.36325	−	0.365282i	0.498241	−	0.867039i	$-0.333980\pi$
$863$	1176.48	−	315.238i	1.36325	−	0.365282i	0.865009	+	0.501757i	$0.167313\pi$
$864$	194.812	−	112.475i	0.225477	−	0.130179i
$865$		0			0
$866$	−449.707	+	778.916i	−0.519292	+	0.899441i
$867$	2287.61	−	2287.61i	2.63854	−	2.63854i
$868$	341.200	−	563.658i	0.393088	−	0.649376i
$869$		−	67.2641i		−	0.0774041i
$870$		0			0
$871$	41.6641	+	72.1644i	0.0478348	+	0.0828523i
$872$	133.536	+	35.7808i	0.153137	+	0.0410330i
$873$	−2003.68	+	536.884i	−2.29516	+	0.614988i
$874$		−	193.548i		−	0.221451i
$875$		0			0
$876$	559.800			0.639041
$877$	350.753	+	1309.03i	0.399946	+	1.49262i	0.813190	+	0.581999i	$0.197729\pi$
$877$	350.753	+	1309.03i	0.399946	+	1.49262i	−0.413244	+	0.910620i	$0.635604\pi$
$878$	215.040	−	802.540i	0.244920	−	0.914055i
$879$	2148.98	−	1240.72i	2.44481	−	1.41151i
$880$		0			0
$881$	906.106			1.02850			0.514248	−	0.857641i	$-0.328071\pi$
$881$	906.106			1.02850			0.514248	+	0.857641i	$0.328071\pi$
$882$	348.185	−	1112.71i	0.394768	−	1.26158i
$883$	479.615	+	479.615i	0.543166	+	0.543166i	0.924455	−	0.381290i	$-0.124520\pi$
$883$	479.615	+	479.615i	0.543166	+	0.543166i	−0.381290	+	0.924455i	$0.624520\pi$
$884$	−64.2641	−	37.1029i	−0.0726969	−	0.0419716i
$885$		0			0
$886$	−3.35781	−	5.81590i	−0.00378986	−	0.00656422i
$887$	−99.6947	−	372.066i	−0.112395	−	0.419465i	0.886683	−	0.462377i	$-0.153003\pi$
$887$	−99.6947	−	372.066i	−0.112395	−	0.419465i	−0.999079	+	0.0429116i	$0.986337\pi$
$888$	83.6729	+	83.6729i	0.0942262	+	0.0942262i
$889$	−550.628	−	573.946i	−0.619379	−	0.645608i
$890$		0			0
$891$	−24.0304	+	41.6218i	−0.0269701	+	0.0467136i
$892$	−360.237	−	96.5252i	−0.403853	−	0.108212i
$893$	−190.144	+	709.626i	−0.212927	+	0.794654i
$894$	−373.553	−	215.671i	−0.417844	−	0.241242i
$895$		0			0
$896$	−18.9072	−	76.9059i	−0.0211018	−	0.0858325i
$897$	−24.8371	+	24.8371i	−0.0276891	+	0.0276891i
$898$	55.5119	−	14.8744i	0.0618172	−	0.0165639i
$899$	299.015	−	172.636i	0.332608	−	0.192031i
$900$		0			0
$901$	204.697	−	354.546i	0.227189	−	0.393503i
$902$	50.6245	−	50.6245i	0.0561248	−	0.0561248i
$903$	−801.975	−	1458.05i	−0.888123	−	1.61468i
$904$			33.1710i			0.0366935i
$905$		0			0
$906$	171.778	+	297.528i	0.189600	+	0.328397i
$907$	790.213	+	211.737i	0.871238	+	0.233448i	0.666623	−	0.745395i	$-0.267739\pi$
$907$	790.213	+	211.737i	0.871238	+	0.233448i	0.204615	+	0.978842i	$0.434406\pi$
$908$	−732.367	+	196.237i	−0.806572	+	0.216120i
$909$		−	848.863i		−	0.933843i
$910$		0			0
$911$	719.634			0.789939			0.394969	−	0.918694i	$-0.370755\pi$
$911$	719.634			0.789939			0.394969	+	0.918694i	$0.370755\pi$
$912$	−127.042	−	474.128i	−0.139301	−	0.519877i
$913$	29.7759	−	111.125i	0.0326133	−	0.121714i
$914$	−402.607	+	232.446i	−0.440490	+	0.254317i
$915$		0			0
$916$	−92.0195			−0.100458
$917$	150.222	+	90.9341i	0.163819	+	0.0991648i
$918$	−1209.83	−	1209.83i	−1.31790	−	1.31790i
$919$	395.313	+	228.234i	0.430156	+	0.248351i	0.699413	−	0.714718i	$-0.253445\pi$
$919$	395.313	+	228.234i	0.430156	+	0.248351i	−0.269257	+	0.963068i	$0.586778\pi$
$920$		0			0
$921$	−1236.49	−	2141.66i	−1.34255	−	2.32537i
$922$	−23.7023	−	88.4582i	−0.0257075	−	0.0959416i
$923$	10.2794	+	10.2794i	0.0111369	+	0.0111369i
$924$	46.7288	+	48.7077i	0.0505723	+	0.0527140i
$925$		0			0
$926$	604.400	−	1046.85i	0.652700	−	1.13051i
$927$	−2349.38	−	629.515i	−2.53439	−	0.679088i
$928$	10.7412	−	40.0866i	0.0115745	−	0.0431968i
$929$	−260.770	−	150.556i	−0.280700	−	0.162062i	0.353040	−	0.935608i	$-0.385148\pi$
$929$	−260.770	−	150.556i	−0.280700	−	0.162062i	−0.633740	+	0.773546i	$0.718481\pi$
$930$		0			0
$931$	−999.298	−	633.579i	−1.07336	−	0.680536i
$932$	−147.660	+	147.660i	−0.158434	+	0.158434i
$933$	1621.43	−	434.461i	1.73787	−	0.465660i
$934$	437.712	−	252.713i	0.468643	−	0.270571i
$935$		0			0
$936$	−29.0178	+	50.2604i	−0.0310020	+	0.0536970i
$937$	−201.407	+	201.407i	−0.214949	+	0.214949i	−0.806366	−	0.591417i	$-0.798569\pi$
$937$	−201.407	+	201.407i	−0.214949	+	0.214949i	0.591417	+	0.806366i	$0.298569\pi$
$938$	676.268	+	14.0223i	0.720968	+	0.0149491i
$939$		−	435.141i		−	0.463409i
$940$		0			0
$941$	235.272	+	407.502i	0.250023	+	0.433052i	0.963532	−	0.267594i	$-0.0862285\pi$
$941$	235.272	+	407.502i	0.250023	+	0.433052i	−0.713509	+	0.700646i	$0.752895\pi$
$942$	−726.041	−	194.542i	−0.770745	−	0.206520i
$943$	292.121	−	78.2737i	0.309779	−	0.0830050i
$944$		−	200.973i		−	0.212895i
$945$		0			0
$946$	62.7637			0.0663464
$947$	−73.4049	−	273.951i	−0.0775131	−	0.289283i	0.916278	−	0.400542i	$-0.131178\pi$
$947$	−73.4049	−	273.951i	−0.0775131	−	0.289283i	−0.993791	+	0.111259i	$0.964512\pi$
$948$	186.503	−	696.040i	0.196733	−	0.734219i
$949$	−58.1708	+	33.5849i	−0.0612970	+	0.0353898i
$950$		0			0
$951$	895.451			0.941589
$952$	−527.793	+	290.302i	−0.554404	+	0.304940i
$953$	−627.876	−	627.876i	−0.658842	−	0.658842i	0.296264	−	0.955106i	$-0.404259\pi$
$953$	−627.876	−	627.876i	−0.658842	−	0.658842i	−0.955106	+	0.296264i	$0.904259\pi$
$954$	−277.288	−	160.092i	−0.290658	−	0.167811i
$955$		0			0
$956$	−4.00351	−	6.93428i	−0.00418777	−	0.00725343i
$957$	9.15465	+	34.1656i	0.00956599	+	0.0357008i
$958$	−587.359	−	587.359i	−0.613109	−	0.613109i
$959$	−133.474	+	459.785i	−0.139180	+	0.479442i
$960$		0			0
$961$	−626.971	+	1085.94i	−0.652415	+	1.13002i
$962$	−13.7147	−	3.67483i	−0.0142564	−	0.00381999i
$963$	30.2164	−	112.769i	0.0313774	−	0.117102i
$964$	−515.802	−	297.798i	−0.535064	−	0.308919i
$965$		0			0
$966$	68.0708	+	276.881i	0.0704666	+	0.286626i
$967$	929.872	−	929.872i	0.961604	−	0.961604i	−0.0376852	−	0.999290i	$-0.511998\pi$
$967$	929.872	−	929.872i	0.961604	−	0.961604i	0.999290	+	0.0376852i	$0.0119984\pi$
$968$	328.119	−	87.9192i	0.338966	−	0.0908257i
$969$	−3233.24	+	1866.71i	−3.33667	+	1.92643i
$970$		0			0
$971$	−628.982	+	1089.43i	−0.647767	+	1.12196i	0.335888	+	0.941902i	$0.390964\pi$
$971$	−628.982	+	1089.43i	−0.647767	+	1.12196i	−0.983655	+	0.180063i	$0.942370\pi$
$972$	142.069	−	142.069i	0.146161	−	0.146161i
$973$	471.037	+	9.76686i	0.484108	+	0.0100379i
$974$		−	804.435i		−	0.825909i
$975$		0			0
$976$	−90.9914	−	157.602i	−0.0932289	−	0.161477i
$977$	182.799	+	48.9808i	0.187102	+	0.0501339i	0.351153	−	0.936318i	$-0.385790\pi$
$977$	182.799	+	48.9808i	0.187102	+	0.0501339i	−0.164051	+	0.986452i	$0.552456\pi$
$978$	285.380	−	76.4674i	0.291800	−	0.0781875i
$979$		−	148.714i		−	0.151904i
$980$		0			0
$981$	−822.367			−0.838295
$982$	−177.536	−	662.573i	−0.180790	−	0.674718i
$983$	−363.301	+	1355.86i	−0.369583	+	1.37930i	0.491516	+	0.870868i	$0.336443\pi$
$983$	−363.301	+	1355.86i	−0.369583	+	1.37930i	−0.861100	+	0.508436i	$0.830224\pi$
$984$	664.222	−	383.489i	0.675023	−	0.389725i
$985$		0			0
$986$	−315.654			−0.320135
$987$	22.4358	−	1082.03i	0.0227313	−	1.09629i
$988$	41.6465	+	41.6465i	0.0421523	+	0.0421523i
$989$	229.606	+	132.563i	0.232159	+	0.134037i
$990$		0			0
$991$	258.071	+	446.992i	0.260414	+	0.451051i	0.966352	−	0.257223i	$-0.0828075\pi$
$991$	258.071	+	446.992i	0.260414	+	0.451051i	−0.705938	+	0.708274i	$0.749474\pi$
$992$	68.9052	+	257.158i	0.0694609	+	0.259232i
$993$	1155.18	+	1155.18i	1.16332	+	1.16332i
$994$	114.593	−	28.1725i	0.115285	−	0.0283426i
$995$		0			0
$996$	616.234	−	1067.35i	0.618709	−	1.07164i
$997$	1276.18	+	341.950i	1.28002	+	0.342979i	0.833860	−	0.551976i	$-0.186126\pi$
$997$	1276.18	+	341.950i	1.28002	+	0.342979i	0.446155	+	0.894955i	$0.352793\pi$
$998$	−211.422	+	789.039i	−0.211846	+	0.790620i
$999$	−283.514	−	163.687i	−0.283798	−	0.163851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.p.e.93.4		16
5.2	odd	4	inner	350.3.p.e.107.1		16
5.3	odd	4		70.3.l.c.37.4	yes	16
5.4	even	2		70.3.l.c.23.1	✓	16
7.4	even	3	inner	350.3.p.e.193.1		16
35.4	even	6		70.3.l.c.53.4	yes	16
35.9	even	6		490.3.f.o.393.1		8
35.18	odd	12		70.3.l.c.67.1	yes	16
35.19	odd	6		490.3.f.p.393.4		8
35.23	odd	12		490.3.f.o.197.1		8
35.32	odd	12	inner	350.3.p.e.207.4		16
35.33	even	12		490.3.f.p.197.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.1	✓	16	5.4	even	2
70.3.l.c.37.4	yes	16	5.3	odd	4
70.3.l.c.53.4	yes	16	35.4	even	6
70.3.l.c.67.1	yes	16	35.18	odd	12
350.3.p.e.93.4		16	1.1	even	1	trivial
350.3.p.e.107.1		16	5.2	odd	4	inner
350.3.p.e.193.1		16	7.4	even	3	inner
350.3.p.e.207.4		16	35.32	odd	12	inner
490.3.f.o.197.1		8	35.23	odd	12
490.3.f.o.393.1		8	35.9	even	6
490.3.f.p.197.4		8	35.33	even	12
490.3.f.p.393.4		8	35.19	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)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(1.31528 - 4.90868i) q^{3} +(-1.73205 + 1.00000i) q^{4} -7.18681 q^{6} +(0.145113 - 6.99850i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-14.5710 - 8.41254i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(1.31528 - 4.90868i) q^{3} +(-1.73205 + 1.00000i) q^{4} -7.18681 q^{6} +(0.145113 - 6.99850i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-14.5710 - 8.41254i) q^{9} +(0.474367 + 0.821627i) q^{11} +(2.63055 + 9.81736i) q^{12} +(-0.862338 - 0.862338i) q^{13} +(-9.61324 + 2.36340i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-29.3872 - 7.87429i) q^{17} +(-6.15841 + 22.9835i) q^{18} +(20.9123 + 12.0737i) q^{19} +(-34.1625 - 9.91727i) q^{21} +(0.948733 - 0.948733i) q^{22} +(5.47452 - 1.46689i) q^{23} +(12.4479 - 7.18681i) q^{24} +(-0.862338 + 1.49361i) q^{26} +(-28.1187 + 28.1187i) q^{27} +(6.74715 + 12.2669i) q^{28} +7.33636i q^{29} +(-23.5316 - 40.7579i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(4.65703 - 1.24785i) q^{33} +43.0259i q^{34} +33.6502 q^{36} +(2.13074 + 7.95202i) q^{37} +(8.83857 - 32.9860i) q^{38} +(-5.36716 + 3.09873i) q^{39} +53.3601 q^{41} +(-1.04290 + 50.2968i) q^{42} +(33.0776 + 33.0776i) q^{43} +(-1.64325 - 0.948733i) q^{44} +(-4.00763 - 6.94142i) q^{46} +(7.87429 + 29.3872i) q^{47} +(-14.3736 - 14.3736i) q^{48} +(-48.9579 - 2.03114i) q^{49} +(-77.3047 + 133.896i) q^{51} +(2.35595 + 0.631275i) q^{52} +(-3.48276 + 12.9978i) q^{53} +(48.7030 + 28.1187i) q^{54} +(14.2872 - 13.7068i) q^{56} +(86.7715 - 86.7715i) q^{57} +(10.0217 - 2.68529i) q^{58} +(43.5119 - 25.1216i) q^{59} +(22.7478 - 39.4004i) q^{61} +(-47.0632 + 47.0632i) q^{62} +(-60.9896 + 100.754i) q^{63} +8.00000i q^{64} +(-3.40918 - 5.90487i) q^{66} +(-65.9999 - 17.6846i) q^{67} +(58.7745 - 15.7486i) q^{68} -28.8020i q^{69} -11.9203 q^{71} +(-12.3168 - 45.9670i) q^{72} +(14.2554 - 53.2017i) q^{73} +(10.0828 - 5.82128i) q^{74} -48.2949 q^{76} +(5.81899 - 3.20062i) q^{77} +(6.19746 + 6.19746i) q^{78} +(-61.4002 - 35.4495i) q^{79} +(25.3289 + 43.8709i) q^{81} +(-19.5312 - 72.8913i) q^{82} +(-85.7452 - 85.7452i) q^{83} +(69.0885 - 16.9853i) q^{84} +(33.0776 - 57.2921i) q^{86} +(36.0118 + 9.64934i) q^{87} +(-0.694521 + 2.59199i) q^{88} +(-135.750 - 78.3752i) q^{89} +(-6.16021 + 5.90994i) q^{91} +(-8.01526 + 8.01526i) q^{92} +(-231.018 + 61.9011i) q^{93} +(37.2615 - 21.5130i) q^{94} +(-14.3736 + 24.8958i) q^{96} +(87.1790 - 87.1790i) q^{97} +(15.1452 + 67.6212i) q^{98} -15.9625i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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