LMFDB - Embedded newform 350.3.p.e.193.1

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:	$16$
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			193.1
Root			$-1.31528 + 4.90868i$ of defining polynomial
Character	$\chi$	$=$	350.193
Dual form			350.3.p.e.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(-4.90868 + 1.31528i) q^{3} +(1.73205 + 1.00000i) q^{4} -7.18681 q^{6} +(6.99850 - 0.145113i) q^{7} +(2.00000 + 2.00000i) q^{8} +(14.5710 - 8.41254i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(-4.90868 + 1.31528i) q^{3} +(1.73205 + 1.00000i) q^{4} -7.18681 q^{6} +(6.99850 - 0.145113i) q^{7} +(2.00000 + 2.00000i) q^{8} +(14.5710 - 8.41254i) q^{9} +(0.474367 - 0.821627i) q^{11} +(-9.81736 - 2.63055i) q^{12} +(-0.862338 - 0.862338i) q^{13} +(9.61324 + 2.36340i) q^{14} +(2.00000 + 3.46410i) q^{16} +(7.87429 + 29.3872i) q^{17} +(22.9835 - 6.15841i) q^{18} +(-20.9123 + 12.0737i) q^{19} +(-34.1625 + 9.91727i) q^{21} +(0.948733 - 0.948733i) q^{22} +(-1.46689 + 5.47452i) q^{23} +(-12.4479 - 7.18681i) q^{24} +(-0.862338 - 1.49361i) q^{26} +(-28.1187 + 28.1187i) q^{27} +(12.2669 + 6.74715i) q^{28} +7.33636i q^{29} +(-23.5316 + 40.7579i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-1.24785 + 4.65703i) q^{33} +43.0259i q^{34} +33.6502 q^{36} +(-7.95202 - 2.13074i) q^{37} +(-32.9860 + 8.83857i) q^{38} +(5.36716 + 3.09873i) q^{39} +53.3601 q^{41} +(-50.2968 + 1.04290i) q^{42} +(33.0776 + 33.0776i) q^{43} +(1.64325 - 0.948733i) q^{44} +(-4.00763 + 6.94142i) q^{46} +(-29.3872 - 7.87429i) q^{47} +(-14.3736 - 14.3736i) q^{48} +(48.9579 - 2.03114i) q^{49} +(-77.3047 - 133.896i) q^{51} +(-0.631275 - 2.35595i) q^{52} +(12.9978 - 3.48276i) q^{53} +(-48.7030 + 28.1187i) q^{54} +(14.2872 + 13.7068i) q^{56} +(86.7715 - 86.7715i) q^{57} +(-2.68529 + 10.0217i) q^{58} +(-43.5119 - 25.1216i) q^{59} +(22.7478 + 39.4004i) q^{61} +(-47.0632 + 47.0632i) q^{62} +(100.754 - 60.9896i) q^{63} +8.00000i q^{64} +(-3.40918 + 5.90487i) q^{66} +(17.6846 + 65.9999i) q^{67} +(-15.7486 + 58.7745i) q^{68} -28.8020i q^{69} -11.9203 q^{71} +(45.9670 + 12.3168i) q^{72} +(-53.2017 + 14.2554i) q^{73} +(-10.0828 - 5.82128i) q^{74} -48.2949 q^{76} +(3.20062 - 5.81899i) q^{77} +(6.19746 + 6.19746i) q^{78} +(61.4002 - 35.4495i) q^{79} +(25.3289 - 43.8709i) q^{81} +(72.8913 + 19.5312i) q^{82} +(-85.7452 - 85.7452i) q^{83} +(-69.0885 - 16.9853i) q^{84} +(33.0776 + 57.2921i) q^{86} +(-9.64934 - 36.0118i) q^{87} +(2.59199 - 0.694521i) q^{88} +(135.750 - 78.3752i) q^{89} +(-6.16021 - 5.90994i) q^{91} +(-8.01526 + 8.01526i) q^{92} +(61.9011 - 231.018i) q^{93} +(-37.2615 - 21.5130i) q^{94} +(-14.3736 - 24.8958i) q^{96} +(87.1790 - 87.1790i) q^{97} +(67.6212 + 15.1452i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	−4.90868	+	1.31528i	−1.63623	+	0.438426i	−0.955711	−	0.294308i	$-0.904911\pi$
$3$	−4.90868	+	1.31528i	−1.63623	+	0.438426i	−0.680516	+	0.732733i	$0.738244\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−7.18681			−1.19780
$7$	6.99850	−	0.145113i	0.999785	−	0.0207304i
$7$	6.99850	−	0.145113i	0.999785	−	0.0207304i
$8$	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	−0.843658	−	0.536882i	$-0.819602\pi$
$11$	0.474367	−	0.821627i	0.0431242	−	0.0746934i	0.886782	+	0.462188i	$0.152936\pi$
$12$	−9.81736	−	2.63055i	−0.818113	−	0.219213i
$13$	−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
$17$	7.87429	+	29.3872i	0.463193	+	1.72866i	0.662810	+	0.748787i	$0.269364\pi$
$17$	7.87429	+	29.3872i	0.463193	+	1.72866i	−0.199617	+	0.979874i	$0.563970\pi$
$18$	22.9835	−	6.15841i	1.27686	−	0.342134i
$19$	−20.9123	+	12.0737i	−1.10065	+	0.635459i	−0.936391	−	0.350959i	$-0.885856\pi$
$19$	−20.9123	+	12.0737i	−1.10065	+	0.635459i	−0.164256	+	0.986418i	$0.552522\pi$
$20$		0			0
$21$	−34.1625	+	9.91727i	−1.62679	+	0.472251i
$22$	0.948733	−	0.948733i	0.0431242	−	0.0431242i
$23$	−1.46689	+	5.47452i	−0.0637780	+	0.238023i	−0.990455	−	0.137836i	$-0.955985\pi$
$23$	−1.46689	+	5.47452i	−0.0637780	+	0.238023i	0.926677	+	0.375858i	$0.122652\pi$
$24$	−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
$28$	12.2669	+	6.74715i	0.438102	+	0.240970i
$29$			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	0.184235	+	0.982882i	$0.441019\pi$
$31$	−23.5316	+	40.7579i	−0.759083	+	1.31477i	−0.943319	+	0.331889i	$0.892314\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−1.24785	+	4.65703i	−0.0378135	+	0.141122i
$34$			43.0259i			1.26547i
$35$		0			0
$36$	33.6502			0.934727
$37$	−7.95202	−	2.13074i	−0.214919	−	0.0575875i	0.149753	−	0.988723i	$-0.452152\pi$
$37$	−7.95202	−	2.13074i	−0.214919	−	0.0575875i	−0.364672	+	0.931136i	$0.618819\pi$
$38$	−32.9860	+	8.83857i	−0.868053	+	0.232594i
$39$	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	$0.274462\pi$
$42$	−50.2968	+	1.04290i	−1.19754	+	0.0248308i
$43$	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
$47$	−29.3872	−	7.87429i	−0.625260	−	0.167538i	−0.0677424	−	0.997703i	$-0.521580\pi$
$47$	−29.3872	−	7.87429i	−0.625260	−	0.167538i	−0.557518	+	0.830165i	$0.688246\pi$
$48$	−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
$52$	−0.631275	−	2.35595i	−0.0121399	−	0.0453068i
$53$	12.9978	−	3.48276i	0.245242	−	0.0657125i	−0.134104	−	0.990967i	$-0.542816\pi$
$53$	12.9978	−	3.48276i	0.245242	−	0.0657125i	0.379346	+	0.925255i	$0.376149\pi$
$54$	−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
$58$	−2.68529	+	10.0217i	−0.0462982	+	0.172787i
$59$	−43.5119	−	25.1216i	−0.737490	−	0.425790i	0.0836659	−	0.996494i	$-0.473337\pi$
$59$	−43.5119	−	25.1216i	−0.737490	−	0.425790i	−0.821156	+	0.570704i	$0.806670\pi$
$60$		0			0
$61$	22.7478	+	39.4004i	0.372915	+	0.645909i	0.990013	−	0.140978i	$-0.0450248\pi$
$61$	22.7478	+	39.4004i	0.372915	+	0.645909i	−0.617097	+	0.786887i	$0.711691\pi$
$62$	−47.0632	+	47.0632i	−0.759083	+	0.759083i
$63$	100.754	−	60.9896i	1.59927	−	0.968089i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−3.40918	+	5.90487i	−0.0516542	+	0.0894678i
$67$	17.6846	+	65.9999i	0.263949	+	0.985073i	0.962890	+	0.269893i	$0.0869884\pi$
$67$	17.6846	+	65.9999i	0.263949	+	0.985073i	−0.698941	+	0.715180i	$0.746345\pi$
$68$	−15.7486	+	58.7745i	−0.231597	+	0.864331i
$69$		−	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	$0.526752\pi$
$72$	45.9670	+	12.3168i	0.638430	+	0.171067i
$73$	−53.2017	+	14.2554i	−0.728791	+	0.195279i	−0.604091	−	0.796916i	$-0.706464\pi$
$73$	−53.2017	+	14.2554i	−0.728791	+	0.195279i	−0.124700	+	0.992194i	$0.539797\pi$
$74$	−10.0828	−	5.82128i	−0.136253	−	0.0786660i
$75$		0			0
$76$	−48.2949			−0.635459
$77$	3.20062	−	5.81899i	0.0415665	−	0.0755713i
$78$	6.19746	+	6.19746i	0.0794546	+	0.0794546i
$79$	61.4002	−	35.4495i	0.777218	−	0.448727i	−0.0582252	−	0.998303i	$-0.518544\pi$
$79$	61.4002	−	35.4495i	0.777218	−	0.448727i	0.835444	+	0.549576i	$0.185211\pi$
$80$		0			0
$81$	25.3289	−	43.8709i	0.312702	−	0.541616i
$82$	72.8913	+	19.5312i	0.888918	+	0.238185i
$83$	−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
$87$	−9.64934	−	36.0118i	−0.110912	−	0.413929i
$88$	2.59199	−	0.694521i	0.0294544	−	0.00789228i
$89$	135.750	−	78.3752i	1.52528	−	0.880621i	0.525729	−	0.850652i	$-0.323793\pi$
$89$	135.750	−	78.3752i	1.52528	−	0.880621i	0.999551	−	0.0299681i	$-0.00954058\pi$
$90$		0			0
$91$	−6.16021	−	5.90994i	−0.0676946	−	0.0649443i
$92$	−8.01526	+	8.01526i	−0.0871224	+	0.0871224i
$93$	61.9011	−	231.018i	0.665603	−	2.48406i
$94$	−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	$0.0307882\pi$
$98$	67.6212	+	15.1452i	0.690012	+	0.154543i
$99$		−	15.9625i		−	0.161238i
$100$		0			0
$101$	25.2261	−	43.6929i	0.249763	−	0.432603i	−0.713697	−	0.700455i	$-0.752980\pi$
$101$	25.2261	−	43.6929i	0.249763	−	0.432603i	0.963460	+	0.267852i	$0.0863138\pi$
$102$	−56.5910	−	211.200i	−0.554813	−	2.07059i
$103$	−37.4152	+	139.636i	−0.363255	+	1.35569i	0.506517	+	0.862230i	$0.330933\pi$
$103$	−37.4152	+	139.636i	−0.363255	+	1.35569i	−0.869771	+	0.493455i	$0.835734\pi$
$104$		−	3.44935i		−	0.0331669i
$105$		0			0
$106$	19.0302			0.179530
$107$	−6.70244	−	1.79591i	−0.0626397	−	0.0167842i	0.227363	−	0.973810i	$-0.426990\pi$
$107$	−6.70244	−	1.79591i	−0.0626397	−	0.0167842i	−0.290003	+	0.957026i	$0.593656\pi$
$108$	−76.8217	+	20.5843i	−0.711312	+	0.190595i
$109$	−42.3291	−	24.4387i	−0.388340	−	0.224208i	0.293100	−	0.956082i	$-0.405313\pi$
$109$	−42.3291	−	24.4387i	−0.388340	−	0.224208i	−0.681441	+	0.731873i	$0.738646\pi$
$110$		0			0
$111$	41.8364			0.376905
$112$	14.4997	+	23.9533i	0.129461	+	0.213869i
$113$	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
$117$	−19.8196	−	5.31063i	−0.169398	−	0.0453900i
$118$	−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
$122$	16.6526	+	62.1483i	0.136497	+	0.509412i
$123$	−261.928	+	70.1834i	−2.12949	+	0.570596i
$124$	−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	$0.102373\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	−205.874	−	118.861i	−1.59592	−	0.921405i
$130$		0			0
$131$	−12.5429	−	21.7250i	−0.0957475	−	0.165840i	0.814173	−	0.580623i	$-0.197191\pi$
$131$	−12.5429	−	21.7250i	−0.0957475	−	0.165840i	−0.909920	+	0.414783i	$0.863857\pi$
$132$	−6.81836	+	6.81836i	−0.0516542	+	0.0516542i
$133$	−144.603	+	87.5325i	−1.08724	+	0.658139i
$134$			96.6305i			0.721123i
$135$		0			0
$136$	−43.0259	+	74.5231i	−0.316367	+	0.547964i
$137$	17.7020	+	66.0647i	0.129212	+	0.482224i	0.999955	−	0.00951399i	$-0.00302844\pi$
$137$	17.7020	+	66.0647i	0.129212	+	0.482224i	−0.870743	+	0.491738i	$0.836362\pi$
$138$	10.5423	−	39.3443i	0.0763933	−	0.285104i
$139$			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
$142$	−16.2835	−	4.36314i	−0.114672	−	0.0307264i
$143$	−1.11758	+	0.299456i	−0.00781528	+	0.00209410i
$144$	58.2838	+	33.6502i	0.404749	+	0.233682i
$145$		0			0
$146$	−77.8927			−0.533512
$147$	−237.647	+	74.3634i	−1.61665	+	0.505873i
$148$	−11.6426	−	11.6426i	−0.0786660	−	0.0786660i
$149$	−51.9776	+	30.0093i	−0.348843	+	0.201404i	−0.664175	−	0.747577i	$-0.731217\pi$
$149$	−51.9776	+	30.0093i	−0.348843	+	0.201404i	0.315333	+	0.948981i	$0.397884\pi$
$150$		0			0
$151$	−23.9018	+	41.3992i	−0.158290	+	0.274167i	−0.934252	−	0.356613i	$-0.883932\pi$
$151$	−23.9018	+	41.3992i	−0.158290	+	0.274167i	0.775962	+	0.630780i	$0.217265\pi$
$152$	−65.9720	−	17.6771i	−0.434026	−	0.116297i
$153$	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
$157$	−27.0694	−	101.024i	−0.172416	−	0.643466i	−0.996977	−	0.0776933i	$-0.975245\pi$
$157$	−27.0694	−	101.024i	−0.172416	−	0.643466i	0.824561	−	0.565773i	$-0.191422\pi$
$158$	96.8497	−	25.9508i	0.612973	−	0.164246i
$159$	−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
$163$	10.6400	−	39.7089i	0.0652759	−	0.243613i	−0.925577	−	0.378559i	$-0.876420\pi$
$163$	10.6400	−	39.7089i	0.0652759	−	0.243613i	0.990853	+	0.134946i	$0.0430863\pi$
$164$	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	$0.285704\pi$
$168$	−88.1596	−	48.4905i	−0.524759	−	0.288634i
$169$		−	167.513i		−	0.991200i
$170$		0			0
$171$	−203.141	+	351.851i	−1.18796	+	2.05761i
$172$	24.2145	+	90.3698i	0.140782	+	0.525406i
$173$	64.9724	−	242.480i	0.375563	−	1.40162i	−0.476958	−	0.878926i	$-0.658261\pi$
$173$	64.9724	−	242.480i	0.375563	−	1.40162i	0.852521	−	0.522693i	$-0.175073\pi$
$174$		−	52.7250i		−	0.303017i
$175$		0			0
$176$	3.79493			0.0215621
$177$	246.628	+	66.0838i	1.39338	+	0.373355i
$178$	214.125	−	57.3746i	1.20295	−	0.322329i
$179$	−46.8192	−	27.0311i	−0.261560	−	0.151012i	0.363486	−	0.931600i	$-0.381586\pi$
$179$	−46.8192	−	27.0311i	−0.261560	−	0.151012i	−0.625046	+	0.780588i	$0.714920\pi$
$180$		0			0
$181$	201.453			1.11300			0.556501	−	0.830847i	$-0.312143\pi$
$181$	201.453			1.11300			0.556501	+	0.830847i	$0.312143\pi$
$182$	−6.25181	−	10.3279i	−0.0343506	−	0.0567468i
$183$	−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
$187$	27.8807	+	7.47060i	0.149094	+	0.0399497i
$188$	−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	0.538907	−	0.842365i	$-0.318837\pi$
$191$	−87.8707	−	152.197i	−0.460056	−	0.796841i	−0.998963	+	0.0455246i	$0.985504\pi$
$192$	−10.5222	−	39.2694i	−0.0548032	−	0.204528i
$193$	−50.4101	+	13.5073i	−0.261192	+	0.0699862i	−0.387039	−	0.922064i	$-0.626502\pi$
$193$	−50.4101	+	13.5073i	−0.261192	+	0.0699862i	0.125846	+	0.992050i	$0.459835\pi$
$194$	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	$0.177606\pi$
$198$	5.84269	−	21.8052i	0.0295085	−	0.110127i
$199$	−22.4632	−	12.9692i	−0.112881	−	0.0651717i	0.442497	−	0.896770i	$-0.354093\pi$
$199$	−22.4632	−	12.9692i	−0.112881	−	0.0651717i	−0.555377	+	0.831598i	$0.687426\pi$
$200$		0			0
$201$	−173.616	−	300.712i	−0.863762	−	1.49608i
$202$	50.4522	−	50.4522i	0.249763	−	0.249763i
$203$	1.06460	+	51.3435i	0.00524432	+	0.252924i
$204$		−	309.219i		−	1.51578i
$205$		0			0
$206$	−102.220	+	177.051i	−0.496215	+	0.859470i
$207$	24.6806	+	92.1093i	0.119230	+	0.444973i
$208$	1.26255	−	4.71190i	0.00606996	−	0.0226534i
$209$			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	$0.677822\pi$
$212$	25.9957	+	6.96552i	0.122621	+	0.0328562i
$213$	58.5131	−	15.6785i	0.274709	−	0.0736081i
$214$	−8.49836	−	4.90653i	−0.0397119	−	0.0229277i
$215$		0			0
$216$	−112.475			−0.520717
$217$	−158.771	+	288.659i	−0.731664	+	1.33022i
$218$	−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
$222$	57.1496	+	15.3132i	0.257431	+	0.0689784i
$223$	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
$227$	−98.1186	−	366.184i	−0.432241	−	1.61314i	−0.747585	−	0.664166i	$-0.768787\pi$
$227$	−98.1186	−	366.184i	−0.432241	−	1.61314i	0.315344	−	0.948977i	$-0.397880\pi$
$228$	237.064	−	63.5211i	1.03975	−	0.278601i
$229$	−39.8456	+	23.0049i	−0.173998	+	0.100458i	−0.584470	−	0.811415i	$-0.698697\pi$
$229$	−39.8456	+	23.0049i	−0.173998	+	0.100458i	0.410471	+	0.911873i	$0.365364\pi$
$230$		0			0
$231$	−8.05726	+	32.7733i	−0.0348799	+	0.141876i
$232$	−14.6727	+	14.6727i	−0.0632445	+	0.0632445i
$233$	−27.0237	+	100.854i	−0.115981	+	0.432849i	−0.999358	−	0.0358143i	$-0.988598\pi$
$233$	−27.0237	+	100.854i	−0.115981	+	0.432849i	0.883377	+	0.468663i	$0.155264\pi$
$234$	−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
$238$	6.24360	+	301.117i	0.0262336	+	1.26520i
$239$			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	−0.372041	−	0.928216i	$-0.621342\pi$
$241$	148.899	−	257.901i	0.617839	−	1.07013i	0.989879	−	0.141912i	$-0.0453249\pi$
$242$	43.9596	+	164.060i	0.181651	+	0.677932i
$243$	26.0004	−	97.0348i	0.106998	−	0.399320i
$244$			90.9914i			0.372915i
$245$		0			0
$246$	−383.489			−1.55890
$247$	28.4451	+	7.62184i	0.115162	+	0.0308577i
$248$	−128.579	+	34.4526i	−0.518463	+	0.138922i
$249$	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	$0.295624\pi$
$252$	235.501	−	4.88306i	0.934526	−	0.0193772i
$253$	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
$257$	−319.201	−	85.5296i	−1.24203	−	0.332800i	−0.422775	−	0.906235i	$-0.638944\pi$
$257$	−319.201	−	85.5296i	−1.24203	−	0.332800i	−0.819251	+	0.573435i	$0.805611\pi$
$258$	−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
$262$	−9.18206	−	34.2679i	−0.0350460	−	0.130794i
$263$	365.648	−	97.9751i	1.39030	−	0.372529i	0.515446	−	0.856922i	$-0.327626\pi$
$263$	365.648	−	97.9751i	1.39030	−	0.372529i	0.874851	+	0.484393i	$0.160959\pi$
$264$	−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
$268$	−35.3692	+	132.000i	−0.131975	+	0.492536i
$269$	−125.485	−	72.4489i	−0.466488	−	0.269327i	0.248280	−	0.968688i	$-0.420135\pi$
$269$	−125.485	−	72.4489i	−0.466488	−	0.269327i	−0.714768	+	0.699361i	$0.753468\pi$
$270$		0			0
$271$	165.311	+	286.326i	0.610002	+	1.05655i	0.991239	+	0.132078i	$0.0421648\pi$
$271$	165.311	+	286.326i	0.610002	+	1.05655i	−0.381237	+	0.924477i	$0.624502\pi$
$272$	−86.0518	+	86.0518i	−0.316367	+	0.316367i
$273$	38.0117	+	20.9076i	0.139237	+	0.0765846i
$274$			96.7254i			0.353012i
$275$		0			0
$276$	28.8020	−	49.8866i	0.104355	−	0.180749i
$277$	−20.3424	−	75.9189i	−0.0734383	−	0.274075i	0.919436	−	0.393239i	$-0.128645\pi$
$277$	−20.3424	−	75.9189i	−0.0734383	−	0.274075i	−0.992875	+	0.119163i	$0.961979\pi$
$278$	−24.6355	+	91.9409i	−0.0886169	+	0.330723i
$279$			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	$0.708863\pi$
$282$	211.200	+	56.5910i	0.748938	+	0.200677i
$283$	−89.7129	+	24.0385i	−0.317007	+	0.0849417i	−0.413814	−	0.910361i	$-0.635804\pi$
$283$	−89.7129	+	24.0385i	−0.317007	+	0.0849417i	0.0968072	+	0.995303i	$0.469137\pi$
$284$	−20.6466	−	11.9203i	−0.0726994	−	0.0419730i
$285$		0			0
$286$	−1.63626			−0.00572118
$287$	373.441	−	7.74323i	1.30119	−	0.0269799i
$288$	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
$292$	−106.403	−	28.5107i	−0.364395	−	0.0976394i
$293$	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
$297$	9.76451	+	36.4416i	0.0328771	+	0.122699i
$298$	−81.9868	+	21.9683i	−0.275124	+	0.0737191i
$299$	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
$303$	−66.3586	+	247.654i	−0.219005	+	0.817339i
$304$	−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	$-0.0412517\pi$
$308$	11.3626	−	6.87816i	0.0368917	−	0.0223317i
$309$		−	734.638i		−	2.37747i
$310$		0			0
$311$	165.159	−	286.064i	0.531059	−	0.919821i	−0.468284	−	0.883578i	$-0.655128\pi$
$311$	165.159	−	286.064i	0.531059	−	0.919821i	0.999343	−	0.0362433i	$-0.0115391\pi$
$312$	4.53685	+	16.9318i	0.0145412	+	0.0542685i
$313$	−22.1618	+	82.7090i	−0.0708045	+	0.264246i	−0.992249	−	0.124263i	$-0.960343\pi$
$313$	−22.1618	+	82.7090i	−0.0708045	+	0.264246i	0.921445	+	0.388509i	$0.127010\pi$
$314$		−	147.910i		−	0.471050i
$315$		0			0
$316$	141.798			0.448727
$317$	−170.202	−	45.6055i	−0.536915	−	0.143866i	−0.0198354	−	0.999803i	$-0.506314\pi$
$317$	−170.202	−	45.6055i	−0.536915	−	0.143866i	−0.517080	+	0.855937i	$0.672981\pi$
$318$	−93.4129	+	25.0299i	−0.293751	+	0.0787104i
$319$	6.02775	+	3.48012i	0.0188958	+	0.0109095i
$320$		0			0
$321$	35.2623			0.109851
$322$	−27.0401	+	49.1610i	−0.0839754	+	0.152674i
$323$	−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
$327$	239.924	+	64.2873i	0.733711	+	0.196597i
$328$	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	0.514255	−	0.857637i	$-0.328069\pi$
$331$	−160.736	−	278.404i	−0.485608	−	0.841098i	−0.999863	+	0.0165391i	$0.994735\pi$
$332$	−62.7698	−	234.260i	−0.189066	−	0.705603i
$333$	−133.793	+	35.8498i	−0.401782	+	0.107657i
$334$	−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	$0.197678\pi$
$338$	61.3139	−	228.827i	0.181402	−	0.677002i
$339$	−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
$343$	342.337	−	21.3193i	0.998066	−	0.0621555i
$344$			132.311i			0.384624i
$345$		0			0
$346$	177.508	−	307.453i	0.513028	−	0.888591i
$347$	87.2508	+	325.624i	0.251443	+	0.938398i	0.970035	+	0.242966i	$0.0781204\pi$
$347$	87.2508	+	325.624i	0.251443	+	0.938398i	−0.718592	+	0.695432i	$0.755213\pi$
$348$	19.2987	−	72.0237i	0.0554560	−	0.206965i
$349$			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
$352$	5.18397	+	1.38904i	0.0147272	+	0.00394614i
$353$	160.203	−	42.9263i	0.453834	−	0.121604i	−0.0246589	−	0.999696i	$-0.507850\pi$
$353$	160.203	−	42.9263i	0.453834	−	0.121604i	0.478493	+	0.878092i	$0.341183\pi$
$354$	312.712	+	180.544i	0.883366	+	0.510012i
$355$		0			0
$356$	313.501			0.880621
$357$	−560.447	−	925.851i	−1.56988	−	2.59342i
$358$	−54.0621	−	54.0621i	−0.151012	−	0.151012i
$359$	324.332	−	187.253i	0.903432	−	0.521597i	0.0251201	−	0.999684i	$-0.492003\pi$
$359$	324.332	−	187.253i	0.903432	−	0.521597i	0.878312	+	0.478088i	$0.158670\pi$
$360$		0			0
$361$	111.049	−	192.343i	0.307616	−	0.532806i
$362$	275.191	+	73.7371i	0.760195	+	0.203694i
$363$	−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
$367$	−8.45008	−	31.5361i	−0.0230247	−	0.0859295i	0.953457	−	0.301528i	$-0.0974966\pi$
$367$	−8.45008	−	31.5361i	−0.0230247	−	0.0859295i	−0.976482	+	0.215598i	$0.930830\pi$
$368$	−21.8981	+	5.86758i	−0.0595057	+	0.0159445i
$369$	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
$373$	−190.704	+	711.719i	−0.511272	+	1.90809i	−0.104614	+	0.994513i	$0.533361\pi$
$373$	−190.704	+	711.719i	−0.511272	+	1.90809i	−0.406658	+	0.913580i	$0.633306\pi$
$374$	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
$378$	−336.767	+	203.856i	−0.890919	+	0.539301i
$379$			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
$382$	−64.3258	−	240.067i	−0.168392	−	0.628448i
$383$	118.232	−	441.247i	0.308699	−	1.15208i	−0.621014	−	0.783799i	$-0.713279\pi$
$383$	118.232	−	441.247i	0.308699	−	1.15208i	0.929714	−	0.368283i	$-0.120054\pi$
$384$		−	57.4944i		−	0.149725i
$385$		0			0
$386$	−73.8055			−0.191206
$387$	760.240	+	203.706i	1.96444	+	0.526371i
$388$	238.178	−	63.8195i	0.613860	−	0.164483i
$389$	−470.416	−	271.595i	−1.20930	−	0.698187i	−0.246690	−	0.969094i	$-0.579343\pi$
$389$	−470.416	−	271.595i	−1.20930	−	0.698187i	−0.962605	+	0.270907i	$0.912676\pi$
$390$		0			0
$391$	−172.432			−0.441002
$392$	101.978	+	93.8535i	0.260148	+	0.239422i
$393$	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
$397$	617.160	+	165.368i	1.55456	+	0.416543i	0.930936	−	0.365182i	$-0.118993\pi$
$397$	617.160	+	165.368i	1.55456	+	0.416543i	0.623623	+	0.781725i	$0.285660\pi$
$398$	−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	−0.997688	−	0.0679566i	$-0.978352\pi$
$401$	−223.636	−	387.349i	−0.557696	−	0.965958i	0.439992	−	0.898002i	$-0.354981\pi$
$402$	−127.096	−	474.328i	−0.316159	−	1.17992i
$403$	55.4393	−	14.8549i	0.137566	−	0.0368608i
$404$	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
$408$	113.182	−	422.401i	0.277407	−	1.03530i
$409$	19.9762	+	11.5333i	0.0488417	+	0.0281988i	0.524222	−	0.851582i	$-0.324356\pi$
$409$	19.9762	+	11.5333i	0.0488417	+	0.0281988i	−0.475380	+	0.879780i	$0.657690\pi$
$410$		0			0
$411$	−173.787	−	301.007i	−0.422839	−	0.732378i
$412$	−204.441	+	204.441i	−0.496215	+	0.496215i
$413$	−308.163	−	169.499i	−0.746158	−	0.410410i
$414$			134.857i			0.325743i
$415$		0			0
$416$	3.44935	−	5.97446i	0.00829172	−	0.0143617i
$417$	−88.5253	−	330.381i	−0.212291	−	0.792280i
$418$	−8.38545	+	31.2949i	−0.0200609	+	0.0748682i
$419$		−	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	$0.481659\pi$
$422$	−305.546	−	81.8708i	−0.724043	−	0.194007i
$423$	−494.443	+	132.486i	−1.16890	+	0.313205i
$424$	32.9612	+	19.0302i	0.0777387	+	0.0448824i
$425$		0			0
$426$	85.6691			0.201101
$427$	164.918	+	272.443i	0.386225	+	0.638039i
$428$	−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	−0.566035	−	0.824381i	$-0.691523\pi$
$431$	185.726	−	321.686i	0.430918	−	0.746372i	0.996953	+	0.0780097i	$0.0248565\pi$
$432$	−153.643	−	41.1686i	−0.355656	−	0.0952977i
$433$	−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
$437$	−35.4217	−	132.196i	−0.0810566	−	0.302507i
$438$	382.350	−	102.450i	0.872946	−	0.233905i
$439$	−508.790	+	293.750i	−1.15897	+	0.669134i	−0.951058	−	0.309012i	$-0.900002\pi$
$439$	−508.790	+	293.750i	−1.15897	+	0.669134i	−0.207917	+	0.978147i	$0.566668\pi$
$440$		0			0
$441$	696.276	−	441.456i	1.57886	−	1.00103i
$442$	37.1029	−	37.1029i	0.0839432	−	0.0839432i
$443$	−1.22904	+	4.58686i	−0.00277437	+	0.0103541i	−0.967299	−	0.253638i	$-0.918373\pi$
$443$	−1.22904	+	4.58686i	−0.00277437	+	0.0103541i	0.964525	+	0.263992i	$0.0850394\pi$
$444$	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
$448$	1.16090	+	55.9880i	0.00259130	+	0.124973i
$449$			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
$452$	6.07071	+	22.6562i	0.0134308	+	0.0501243i
$453$	62.8750	−	234.653i	0.138797	−	0.517997i
$454$		−	536.130i		−	1.18090i
$455$		0			0
$456$	347.086			0.761153
$457$	317.526	+	85.0810i	0.694806	+	0.186173i	0.588903	−	0.808204i	$-0.299560\pi$
$457$	317.526	+	85.0810i	0.694806	+	0.186173i	0.105903	+	0.994376i	$0.466227\pi$
$458$	−62.8505	+	16.8407i	−0.137228	+	0.0367702i
$459$	−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	$0.477625\pi$
$462$	−23.0023	+	41.8199i	−0.0497884	+	0.0905194i
$463$	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
$467$	−345.213	−	92.4995i	−0.739214	−	0.198072i	−0.130485	−	0.991450i	$-0.541653\pi$
$467$	−345.213	−	92.4995i	−0.739214	−	0.198072i	−0.608729	+	0.793379i	$0.708320\pi$
$468$	−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
$472$	−36.7806	−	137.267i	−0.0779250	−	0.290820i
$473$	42.8684	−	11.4866i	0.0906309	−	0.0242845i
$474$	−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
$478$	−1.46539	+	5.46889i	−0.00306566	+	0.0114412i
$479$	−508.668	−	293.679i	−1.06194	−	0.613109i	−0.135969	−	0.990713i	$-0.543415\pi$
$479$	−508.668	−	293.679i	−1.06194	−	0.613109i	−0.925967	+	0.377604i	$0.876748\pi$
$480$		0			0
$481$	5.01992	+	8.69475i	0.0104364	+	0.0180764i
$482$	297.798	−	297.798i	0.617839	−	0.617839i
$483$	−4.17954	−	201.571i	−0.00865329	−	0.417331i
$484$			240.200i			0.496281i
$485$		0			0
$486$	71.0344	−	123.035i	0.146161	−	0.253159i
$487$	−147.222	−	549.440i	−0.302304	−	1.12821i	−0.935242	−	0.354010i	$-0.884818\pi$
$487$	−147.222	−	549.440i	−0.302304	−	1.12821i	0.632938	−	0.774202i	$-0.281849\pi$
$488$	−33.3052	+	124.297i	−0.0682483	+	0.254706i
$489$			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	$0.335561\pi$
$492$	−523.856	−	140.367i	−1.06475	−	0.285298i
$493$	−215.595	+	57.7686i	−0.437313	+	0.117178i
$494$	36.0669	+	20.8233i	0.0730100	+	0.0421523i
$495$		0			0
$496$	−188.253			−0.379542
$497$	−83.4244	+	1.72979i	−0.167856	+	0.00348046i
$498$	616.234	+	616.234i	1.23742	+	1.23742i
$499$	500.231	−	288.808i	1.00247	−	0.578774i	0.0934891	−	0.995620i	$-0.470198\pi$
$499$	500.231	−	288.808i	1.00247	−	0.578774i	0.908977	+	0.416846i	$0.136865\pi$
$500$		0			0
$501$	94.9930	−	164.533i	0.189607	−	0.328409i
$502$	410.660	+	110.036i	0.818047	+	0.219195i
$503$	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
$507$	220.326	+	822.266i	0.434567	+	1.62183i
$508$	219.504	−	58.8159i	0.432094	−	0.115779i
$509$	136.905	−	79.0420i	0.268968	−	0.155289i	−0.359451	−	0.933164i	$-0.617036\pi$
$509$	136.905	−	79.0420i	0.268968	−	0.155289i	0.628419	+	0.777875i	$0.283703\pi$
$510$		0			0
$511$	−370.263	+	107.486i	−0.724586	+	0.210345i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	248.529	−	927.523i	0.484462	−	1.80804i
$514$	−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
$518$	−71.4089	−	39.2771i	−0.137855	−	0.0758245i
$519$			1275.71i			2.45802i
$520$		0			0
$521$	58.2493	−	100.891i	0.111803	−	0.193648i	−0.804694	−	0.593689i	$-0.797671\pi$
$521$	58.2493	−	100.891i	0.111803	−	0.193648i	0.916497	+	0.400041i	$0.131004\pi$
$522$	45.1803	+	168.615i	0.0865523	+	0.323018i
$523$	65.4858	−	244.396i	0.125212	−	0.467297i	−0.874635	−	0.484782i	$-0.838899\pi$
$523$	65.4858	−	244.396i	0.125212	−	0.467297i	0.999847	+	0.0174845i	$0.00556577\pi$
$524$		−	50.1717i		−	0.0957475i
$525$		0			0
$526$	535.346			1.01777
$527$	−1383.06	−	370.589i	−2.62440	−	0.703205i
$528$	−18.6281	+	4.99139i	−0.0352805	+	0.00945338i
$529$	430.309	+	248.439i	0.813438	+	0.469639i
$530$		0			0
$531$	−845.347			−1.59199
$532$	−337.991	+	7.00819i	−0.635322	+	0.0131733i
$533$	−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
$537$	265.374	+	71.1067i	0.494178	+	0.132415i
$538$	−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	0.933442	+	0.358730i	$0.116790\pi$
$541$	420.568	+	728.445i	0.777390	+	1.34648i	−0.156052	+	0.987749i	$0.549877\pi$
$542$	121.016	+	451.637i	0.223276	+	0.833279i
$543$	−988.871	+	264.967i	−1.82112	+	0.487969i
$544$	−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	$0.345360\pi$
$548$	−35.4040	+	132.129i	−0.0646058	+	0.241112i
$549$	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
$553$	424.565	−	257.003i	0.767749	−	0.464743i
$554$		−	111.153i		−	0.200637i
$555$		0			0
$556$	−67.3054	+	116.576i	−0.121053	+	0.209670i
$557$	248.070	+	925.810i	0.445368	+	1.66214i	0.714963	+	0.699162i	$0.246443\pi$
$557$	248.070	+	925.810i	0.445368	+	1.66214i	−0.269595	+	0.962974i	$0.586890\pi$
$558$	−289.834	+	1081.68i	−0.519416	+	1.93849i
$559$		−	57.0482i		−	0.102054i
$560$		0			0
$561$	−146.683			−0.261467
$562$	−468.363	−	125.497i	−0.833386	−	0.223305i
$563$	−895.754	+	240.016i	−1.59104	+	0.426317i	−0.942320	−	0.334713i	$-0.891361\pi$
$563$	−895.754	+	240.016i	−1.59104	+	0.426317i	−0.648717	+	0.761030i	$0.724694\pi$
$564$	267.791	+	154.609i	0.474807	+	0.274130i
$565$		0			0
$566$	−131.349			−0.232065
$567$	170.898	−	310.706i	0.301407	−	0.547982i
$568$	−23.8407	−	23.8407i	−0.0419730	−	0.0419730i
$569$	391.524	−	226.046i	0.688091	−	0.397270i	−0.114805	−	0.993388i	$-0.536624\pi$
$569$	391.524	−	226.046i	0.688091	−	0.397270i	0.802897	+	0.596118i	$0.203291\pi$
$570$		0			0
$571$	−195.371	+	338.393i	−0.342157	+	0.592633i	−0.984833	−	0.173505i	$-0.944491\pi$
$571$	−195.371	+	338.393i	−0.342157	+	0.592633i	0.642676	+	0.766138i	$0.277824\pi$
$572$	−2.23517	−	0.598912i	−0.00390764	−	0.00104705i
$573$	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
$577$	117.398	+	438.134i	0.203462	+	0.759330i	0.989913	+	0.141677i	$0.0452496\pi$
$577$	117.398	+	438.134i	0.203462	+	0.759330i	−0.786451	+	0.617653i	$0.788084\pi$
$578$	−869.631	+	233.017i	−1.50455	+	0.403144i
$579$	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
$583$	3.30421	−	12.3315i	0.00566760	−	0.0211518i
$584$	−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	$0.198876\pi$
$588$	−485.980	−	108.846i	−0.826497	−	0.185112i
$589$		−	1136.45i		−	1.92946i
$590$		0			0
$591$	−225.730	+	390.975i	−0.381946	+	0.661549i
$592$	−8.52295	−	31.8081i	−0.0143969	−	0.0537299i
$593$	−35.4612	+	132.343i	−0.0597997	+	0.223176i	−0.989358	−	0.145498i	$-0.953521\pi$
$593$	−35.4612	+	132.343i	−0.0597997	+	0.223176i	0.929559	+	0.368674i	$0.120188\pi$
$594$			53.3543i			0.0898220i
$595$		0			0
$596$	−120.037			−0.201404
$597$	127.323	+	34.1161i	0.213271	+	0.0571458i
$598$	9.44178	−	2.52992i	0.0157889	−	0.00423063i
$599$	533.617	+	308.084i	0.890847	+	0.514331i	0.874220	−	0.485531i	$-0.161374\pi$
$599$	533.617	+	308.084i	0.890847	+	0.514331i	0.0166277	+	0.999862i	$0.494707\pi$
$600$		0			0
$601$	−660.812			−1.09952			−0.549760	−	0.835322i	$-0.685281\pi$
$601$	−660.812			−1.09952			−0.549760	+	0.835322i	$0.685281\pi$
$602$	239.808	+	396.159i	0.398351	+	0.658071i
$603$	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
$607$	−373.398	−	100.052i	−0.615153	−	0.164830i	−0.0622299	−	0.998062i	$-0.519821\pi$
$607$	−373.398	−	100.052i	−0.615153	−	0.164830i	−0.552924	+	0.833232i	$0.686488\pi$
$608$	−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
$612$	264.971	+	988.886i	0.432959	+	1.61583i
$613$	−49.9662	+	13.3884i	−0.0815109	+	0.0218408i	−0.299344	−	0.954145i	$-0.596768\pi$
$613$	−49.9662	+	13.3884i	−0.0815109	+	0.0218408i	0.217833	+	0.975986i	$0.430101\pi$
$614$	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	$5.85476e-5\pi$
$618$	268.896	−	1003.53i	0.435107	−	1.62384i
$619$	449.823	+	259.705i	0.726693	+	0.419556i	0.817211	−	0.576339i	$-0.195519\pi$
$619$	449.823	+	259.705i	0.726693	+	0.419556i	−0.0905183	+	0.995895i	$0.528852\pi$
$620$		0			0
$621$	−112.689	−	195.184i	−0.181464	−	0.314305i
$622$	330.319	−	330.319i	0.531059	−	0.531059i
$623$	938.672	−	568.208i	1.50670	−	0.912051i
$624$			24.7898i			0.0397273i
$625$		0			0
$626$	−60.5472	+	104.871i	−0.0967208	+	0.167525i
$627$	−30.1323	−	112.455i	−0.0480579	−	0.179354i
$628$	54.1387	−	202.048i	0.0862081	−	0.321733i
$629$		−	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	$0.609907\pi$
$632$	193.699	+	51.9016i	0.306486	+	0.0821228i
$633$	1097.95	−	294.195i	1.73452	−	0.464763i
$634$	−215.808	−	124.597i	−0.340390	−	0.196525i
$635$		0			0
$636$	−136.766			−0.215041
$637$	−43.9698	−	40.4667i	−0.0690264	−	0.0635271i
$638$	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	−0.951936	−	0.306297i	$-0.900910\pi$
$641$	−135.063	+	233.937i	−0.210707	+	0.364956i	0.741229	+	0.671252i	$0.234243\pi$
$642$	48.1692	+	12.9069i	0.0750298	+	0.0201042i
$643$	−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
$647$	−63.5381	−	237.128i	−0.0982042	−	0.366503i	0.899282	−	0.437370i	$-0.144090\pi$
$647$	−63.5381	−	237.128i	−0.0982042	−	0.366503i	−0.997486	+	0.0708670i	$0.977423\pi$
$648$	138.400	−	37.0841i	0.213580	−	0.0572285i
$649$	−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
$653$	118.033	−	440.504i	0.180755	−	0.674585i	−0.814745	−	0.579819i	$-0.803123\pi$
$653$	118.033	−	440.504i	0.180755	−	0.674585i	0.995500	−	0.0947659i	$-0.0302103\pi$
$654$	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
$658$	−263.896	−	145.151i	−0.401058	−	0.220595i
$659$			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	−0.727253	−	0.686369i	$-0.759203\pi$
$661$	152.550	−	264.224i	0.230787	−	0.399734i	0.958040	+	0.286635i	$0.0925367\pi$
$662$	−117.667	−	439.140i	−0.177745	−	0.663353i
$663$	−48.8006	+	182.126i	−0.0736057	+	0.274700i
$664$		−	342.981i		−	0.516537i
$665$		0			0
$666$	−195.887			−0.294125
$667$	−40.1631	−	10.7617i	−0.0602145	−	0.0161344i
$668$	−72.2228	+	19.3520i	−0.108118	+	0.0289701i
$669$	−820.666	−	473.811i	−1.22670	−	0.708238i
$670$		0			0
$671$	43.1633			0.0643268
$672$	−104.206	−	172.148i	−0.155069	−	0.256172i
$673$	−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
$677$	385.908	+	103.404i	0.570027	+	0.152738i	0.532309	−	0.846550i	$-0.321324\pi$
$677$	385.908	+	103.404i	0.570027	+	0.152738i	0.0377179	+	0.999288i	$0.487991\pi$
$678$	−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
$682$	16.3432	+	60.9936i	0.0239636	+	0.0894334i
$683$	919.851	−	246.473i	1.34678	−	0.360869i	0.487835	−	0.872936i	$-0.337787\pi$
$683$	919.851	−	246.473i	1.34678	−	0.360869i	0.858945	+	0.512067i	$0.171120\pi$
$684$	−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
$688$	−48.4290	+	180.740i	−0.0703910	+	0.262703i
$689$	−14.2119	−	8.20522i	−0.0206268	−	0.0119089i
$690$		0			0
$691$	235.417	+	407.754i	0.340690	+	0.590093i	0.984561	−	0.175042i	$-0.0560060\pi$
$691$	235.417	+	407.754i	0.340690	+	0.590093i	−0.643871	+	0.765134i	$0.722673\pi$
$692$	355.016	−	355.016i	0.513028	−	0.513028i
$693$	−2.31636	−	111.714i	−0.00334251	−	0.161203i
$694$			476.747i			0.686955i
$695$		0			0
$696$	52.7250	−	91.3224i	0.0757543	−	0.131210i
$697$	420.173	+	1568.11i	0.602831	+	2.24980i
$698$	−105.234	+	392.740i	−0.150765	+	0.562664i
$699$		−	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	$0.901570\pi$
$702$	66.2463	+	17.7506i	0.0943679	+	0.0252858i
$703$	192.021	−	51.4518i	0.273145	−	0.0731890i
$704$	6.57302	+	3.79493i	0.00933667	+	0.00539053i
$705$		0			0
$706$	234.554			0.332229
$707$	170.204	−	309.445i	0.240742	−	0.437688i
$708$	361.088	+	361.088i	0.510012	+	0.510012i
$709$	−1150.06	+	663.986i	−1.62208	+	0.936510i	−0.635722	+	0.771918i	$0.719297\pi$
$709$	−1150.06	+	663.986i	−1.62208	+	0.936510i	−0.986362	+	0.164592i	$0.947369\pi$
$710$		0			0
$711$	596.440	−	1033.06i	0.838875	−	1.45297i
$712$	428.250	+	114.749i	0.601475	+	0.161165i
$713$	−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
$717$	−5.26572	−	19.6519i	−0.00734410	−	0.0274086i
$718$	511.585	−	137.079i	0.712515	−	0.190918i
$719$	−244.147	+	140.958i	−0.339564	+	0.196048i	−0.660079	−	0.751196i	$-0.729477\pi$
$719$	−244.147	+	140.958i	−0.339564	+	0.196048i	0.320515	+	0.947243i	$0.396144\pi$
$720$		0			0
$721$	−241.588	+	982.668i	−0.335073	+	1.36292i
$722$	222.098	−	222.098i	0.307616	−	0.307616i
$723$	−391.687	+	1461.80i	−0.541753	+	2.02185i
$724$	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	$0.950883\pi$
$728$	−0.500544	−	24.1403i	−0.000687561	−	0.0331597i
$729$			966.430i			1.32569i
$730$		0			0
$731$	−711.598	+	1232.52i	−0.973458	+	1.68608i
$732$	−119.679	−	446.647i	−0.163496	−	0.610174i
$733$	−308.773	+	1152.36i	−0.421245	+	1.57211i	0.350743	+	0.936472i	$0.385929\pi$
$733$	−308.773	+	1152.36i	−0.421245	+	1.57211i	−0.771988	+	0.635637i	$0.780737\pi$
$734$		−	46.1721i		−	0.0629048i
$735$		0			0
$736$	−32.0610			−0.0435612
$737$	62.6163	+	16.7780i	0.0849610	+	0.0227652i
$738$	1226.40	−	328.614i	1.66179	−	0.445276i
$739$	491.205	+	283.597i	0.664688	+	0.383758i	0.794061	−	0.607838i	$-0.207963\pi$
$739$	491.205	+	283.597i	0.664688	+	0.383758i	−0.129373	+	0.991596i	$0.541296\pi$
$740$		0			0
$741$	−149.653			−0.201960
$742$	133.182	−	2.76151i	0.179491	−	0.00372172i
$743$	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
$747$	−1970.72	−	528.054i	−2.63819	−	0.706900i
$748$	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	−0.979249	−	0.202662i	$-0.935041\pi$
$751$	−499.516	−	865.187i	−0.665135	−	1.15205i	0.314114	−	0.949385i	$-0.398293\pi$
$752$	−31.4972	−	117.549i	−0.0418845	−	0.156315i
$753$	−1475.67	+	395.404i	−1.95972	+	0.525104i
$754$	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	$0.337596\pi$
$758$	−105.110	+	392.275i	−0.138667	+	0.517514i
$759$	−23.6645	−	13.6627i	−0.0311786	−	0.0180010i
$760$		0			0
$761$	185.178	+	320.737i	0.243335	+	0.421468i	0.961662	−	0.274237i	$-0.0884253\pi$
$761$	185.178	+	320.737i	0.243335	+	0.421468i	−0.718327	+	0.695705i	$0.755092\pi$
$762$	−577.416	+	577.416i	−0.757764	+	0.757764i
$763$	−299.786	−	164.892i	−0.392905	−	0.216110i
$764$		−	351.483i		−	0.460056i
$765$		0			0
$766$	323.016	−	559.479i	0.421691	−	0.730391i
$767$	15.8587	+	59.1853i	0.0206762	+	0.0771647i
$768$	21.0444	−	78.5389i	0.0274016	−	0.102264i
$769$			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
$772$	−100.820	−	27.0147i	−0.130596	−	0.0349931i
$773$	−814.698	+	218.298i	−1.05394	+	0.282403i	−0.743880	−	0.668313i	$-0.767017\pi$
$773$	−814.698	+	218.298i	−1.05394	+	0.282403i	−0.310063	+	0.950716i	$0.600350\pi$
$774$	963.945	+	556.534i	1.24541	+	0.719036i
$775$		0			0
$776$	348.716			0.449376
$777$	292.792	−	6.07099i	0.376824	−	0.00781337i
$778$	−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
$782$	−235.546	−	63.1144i	−0.301210	−	0.0807090i
$783$	−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
$787$	−117.934	−	440.137i	−0.149853	−	0.559259i	−0.999491	−	0.0318931i	$-0.989846\pi$
$787$	−117.934	−	440.137i	−0.149853	−	0.559259i	0.849638	−	0.527366i	$-0.176820\pi$
$788$	171.622	−	45.9858i	0.217794	−	0.0583577i
$789$	−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
$793$	14.3602	−	53.5928i	0.0181086	−	0.0675824i
$794$	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	$-0.124624\pi$
$798$	1039.23	−	629.079i	1.30229	−	0.788319i
$799$		−	925.614i		−	1.15847i
$800$		0			0
$801$	1318.67	−	2284.00i	1.64628	−	2.85144i
$802$	−163.713	−	610.985i	−0.204131	−	0.761827i
$803$	−13.5245	+	50.4742i	−0.0168425	+	0.0628571i
$804$		−	694.465i		−	0.863762i
$805$		0			0
$806$	81.1687			0.100706
$807$	711.257	+	190.581i	0.881360	+	0.236160i
$808$	137.838	−	36.9336i	0.170592	−	0.0457099i
$809$	−192.279	−	111.012i	−0.237674	−	0.137221i	0.376433	−	0.926444i	$-0.377150\pi$
$809$	−192.279	−	111.012i	−0.237674	−	0.137221i	−0.614107	+	0.789222i	$0.710484\pi$
$810$		0			0
$811$	1418.65			1.74926			0.874632	−	0.484788i	$-0.161103\pi$
$811$	1418.65			1.74926			0.874632	+	0.484788i	$0.161103\pi$
$812$	−49.4996	+	89.9941i	−0.0609600	+	0.110830i
$813$	−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
$817$	−1091.10	−	292.359i	−1.33549	−	0.357845i
$818$	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	0.959039	−	0.283273i	$-0.0914202\pi$
$821$	192.277	+	333.033i	0.234198	+	0.405643i	−0.724841	+	0.688916i	$0.758087\pi$
$822$	−127.221	−	474.794i	−0.154770	−	0.577608i
$823$	64.4885	−	17.2796i	0.0783578	−	0.0209959i	−0.219427	−	0.975629i	$-0.570419\pi$
$823$	64.4885	−	17.2796i	0.0783578	−	0.0209959i	0.297785	+	0.954633i	$0.403752\pi$
$824$	−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	$0.420195\pi$
$828$	−49.3612	+	184.219i	−0.0596150	+	0.222486i
$829$	609.282	+	351.769i	0.734960	+	0.424329i	0.820234	−	0.572028i	$-0.193843\pi$
$829$	609.282	+	351.769i	0.734960	+	0.424329i	−0.0852739	+	0.996358i	$0.527177\pi$
$830$		0			0
$831$	199.709	+	345.905i	0.240323	+	0.416252i
$832$	6.89871	−	6.89871i	0.00829172	−	0.00829172i
$833$	445.198	+	1422.74i	0.534451	+	1.70798i
$834$		−	483.711i		−	0.579989i
$835$		0			0
$836$	−22.9095	+	39.6804i	−0.0274037	+	0.0474645i
$837$	−484.381	−	1807.74i	−0.578711	−	2.15978i
$838$	184.035	−	686.826i	0.219612	−	0.819602i
$839$		−	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
$842$	66.2382	+	17.7485i	0.0786677	+	0.0210789i
$843$	1683.02	−	450.963i	1.99646	−	0.534950i
$844$	−387.417	−	223.675i	−0.459025	−	0.265018i
$845$		0			0
$846$	−723.915			−0.855691
$847$	435.352	+	719.197i	0.513993	+	0.849110i
$848$	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
$852$	117.026	+	31.3571i	0.137355	+	0.0368041i
$853$	−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
$857$	273.963	+	1022.44i	0.319677	+	1.19305i	0.919556	+	0.392960i	$0.128549\pi$
$857$	273.963	+	1022.44i	0.319677	+	1.19305i	−0.599879	+	0.800091i	$0.704784\pi$
$858$	8.03187	−	2.15213i	0.00936115	−	0.00250831i
$859$	747.383	−	431.502i	0.870062	−	0.502331i	0.00269328	−	0.999996i	$-0.499143\pi$
$859$	747.383	−	431.502i	0.870062	−	0.502331i	0.867369	+	0.497666i	$0.165809\pi$
$860$		0			0
$861$	−1822.92	+	529.187i	−2.11721	+	0.614619i
$862$	371.451	−	371.451i	0.430918	−	0.430918i
$863$	−315.238	+	1176.48i	−0.365282	+	1.36325i	0.501757	+	0.865009i	$0.332687\pi$
$863$	−315.238	+	1176.48i	−0.365282	+	1.36325i	−0.867039	+	0.498241i	$0.833980\pi$
$864$	−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
$868$	−563.658	+	341.200i	−0.649376	+	0.393088i
$869$		−	67.2641i		−	0.0774041i
$870$		0			0
$871$	41.6641	−	72.1644i	0.0478348	−	0.0828523i
$872$	−35.7808	−	133.536i	−0.0410330	−	0.153137i
$873$	536.884	−	2003.68i	0.614988	−	2.29516i
$874$		−	193.548i		−	0.221451i
$875$		0			0
$876$	559.800			0.639041
$877$	−1309.03	−	350.753i	−1.49262	−	0.399946i	−0.581999	−	0.813190i	$-0.697729\pi$
$877$	−1309.03	−	350.753i	−1.49262	−	0.399946i	−0.910620	+	0.413244i	$0.864396\pi$
$878$	−802.540	+	215.040i	−0.914055	+	0.244920i
$879$	−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	$0.328071\pi$
$882$	1112.71	−	348.185i	1.26158	−	0.394768i
$883$	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
$887$	372.066	+	99.6947i	0.419465	+	0.112395i	0.462377	−	0.886683i	$-0.346997\pi$
$887$	372.066	+	99.6947i	0.419465	+	0.112395i	−0.0429116	+	0.999079i	$0.513663\pi$
$888$	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
$892$	96.5252	+	360.237i	0.108212	+	0.403853i
$893$	709.626	−	190.144i	0.794654	−	0.212927i
$894$	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
$898$	−14.8744	+	55.5119i	−0.0165639	+	0.0618172i
$899$	−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
$903$	−1458.05	−	801.975i	−1.61468	−	0.888123i
$904$			33.1710i			0.0366935i
$905$		0			0
$906$	171.778	−	297.528i	0.189600	−	0.328397i
$907$	−211.737	−	790.213i	−0.233448	−	0.871238i	−0.978842	−	0.204615i	$-0.934406\pi$
$907$	−211.737	−	790.213i	−0.233448	−	0.871238i	0.745395	−	0.666623i	$-0.232261\pi$
$908$	196.237	−	732.367i	0.216120	−	0.806572i
$909$		−	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	$0.370755\pi$
$912$	474.128	+	127.042i	0.519877	+	0.139301i
$913$	−111.125	+	29.7759i	−0.121714	+	0.0326133i
$914$	402.607	+	232.446i	0.440490	+	0.254317i
$915$		0			0
$916$	−92.0195			−0.100458
$917$	−90.9341	−	150.222i	−0.0991648	−	0.163819i
$918$	−1209.83	−	1209.83i	−1.31790	−	1.31790i
$919$	−395.313	+	228.234i	−0.430156	+	0.248351i	−0.699413	−	0.714718i	$-0.746555\pi$
$919$	−395.313	+	228.234i	−0.430156	+	0.248351i	0.269257	+	0.963068i	$0.413222\pi$
$920$		0			0
$921$	−1236.49	+	2141.66i	−1.34255	+	2.32537i
$922$	88.4582	+	23.7023i	0.0959416	+	0.0257075i
$923$	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
$927$	629.515	+	2349.38i	0.679088	+	2.53439i
$928$	−40.0866	+	10.7412i	−0.0431968	+	0.0115745i
$929$	260.770	−	150.556i	0.280700	−	0.162062i	−0.353040	−	0.935608i	$-0.614852\pi$
$929$	260.770	−	150.556i	0.280700	−	0.162062i	0.633740	+	0.773546i	$0.281519\pi$
$930$		0			0
$931$	−999.298	+	633.579i	−1.07336	+	0.680536i
$932$	−147.660	+	147.660i	−0.158434	+	0.158434i
$933$	−434.461	+	1621.43i	−0.465660	+	1.73787i
$934$	−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	$0.298569\pi$
$938$	14.0223	+	676.268i	0.0149491	+	0.720968i
$939$		−	435.141i		−	0.463409i
$940$		0			0
$941$	235.272	−	407.502i	0.250023	−	0.433052i	−0.713509	−	0.700646i	$-0.752895\pi$
$941$	235.272	−	407.502i	0.250023	−	0.433052i	0.963532	+	0.267594i	$0.0862285\pi$
$942$	194.542	+	726.041i	0.206520	+	0.770745i
$943$	−78.2737	+	292.121i	−0.0830050	+	0.309779i
$944$		−	200.973i		−	0.212895i
$945$		0			0
$946$	62.7637			0.0663464
$947$	273.951	+	73.4049i	0.289283	+	0.0775131i	0.400542	−	0.916278i	$-0.368822\pi$
$947$	273.951	+	73.4049i	0.289283	+	0.0775131i	−0.111259	+	0.993791i	$0.535488\pi$
$948$	−696.040	+	186.503i	−0.734219	+	0.196733i
$949$	58.1708	+	33.5849i	0.0612970	+	0.0353898i
$950$		0			0
$951$	895.451			0.941589
$952$	−290.302	+	527.793i	−0.304940	+	0.554404i
$953$	−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
$957$	−34.1656	−	9.15465i	−0.0357008	−	0.00956599i
$958$	−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
$962$	3.67483	+	13.7147i	0.00381999	+	0.0142564i
$963$	−112.769	+	30.2164i	−0.117102	+	0.0313774i
$964$	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	$0.0119984\pi$
$968$	−87.9192	+	328.119i	−0.0908257	+	0.338966i
$969$	3233.24	+	1866.71i	3.33667	+	1.92643i
$970$		0			0
$971$	−628.982	−	1089.43i	−0.647767	−	1.12196i	−0.983655	−	0.180063i	$-0.942370\pi$
$971$	−628.982	−	1089.43i	−0.647767	−	1.12196i	0.335888	−	0.941902i	$-0.390964\pi$
$972$	142.069	−	142.069i	0.146161	−	0.146161i
$973$	9.76686	+	471.037i	0.0100379	+	0.484108i
$974$		−	804.435i		−	0.825909i
$975$		0			0
$976$	−90.9914	+	157.602i	−0.0932289	+	0.161477i
$977$	−48.9808	−	182.799i	−0.0501339	−	0.187102i	0.936318	−	0.351153i	$-0.114210\pi$
$977$	−48.9808	−	182.799i	−0.0501339	−	0.187102i	−0.986452	+	0.164051i	$0.947544\pi$
$978$	−76.4674	+	285.380i	−0.0781875	+	0.291800i
$979$		−	148.714i		−	0.151904i
$980$		0			0
$981$	−822.367			−0.838295
$982$	662.573	+	177.536i	0.674718	+	0.180790i
$983$	1355.86	−	363.301i	1.37930	−	0.369583i	0.508436	−	0.861100i	$-0.330224\pi$
$983$	1355.86	−	363.301i	1.37930	−	0.369583i	0.870868	+	0.491516i	$0.163557\pi$
$984$	−664.222	−	383.489i	−0.675023	−	0.389725i
$985$		0			0
$986$	−315.654			−0.320135
$987$	1082.03	−	22.4358i	1.09629	−	0.0227313i
$988$	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	−0.705938	−	0.708274i	$-0.749474\pi$
$991$	258.071	−	446.992i	0.260414	−	0.451051i	0.966352	+	0.257223i	$0.0828075\pi$
$992$	−257.158	−	68.9052i	−0.259232	−	0.0694609i
$993$	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
$997$	−341.950	−	1276.18i	−0.342979	−	1.28002i	−0.894955	−	0.446155i	$-0.852793\pi$
$997$	−341.950	−	1276.18i	−0.342979	−	1.28002i	0.551976	−	0.833860i	$-0.313874\pi$
$998$	789.039	−	211.422i	0.790620	−	0.211846i
$999$	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.193.1		16
5.2	odd	4	inner	350.3.p.e.207.4		16
5.3	odd	4		70.3.l.c.67.1	yes	16
5.4	even	2		70.3.l.c.53.4	yes	16
7.2	even	3	inner	350.3.p.e.93.4		16
35.2	odd	12	inner	350.3.p.e.107.1		16
35.3	even	12		490.3.f.p.197.4		8
35.4	even	6		490.3.f.o.393.1		8
35.9	even	6		70.3.l.c.23.1	✓	16
35.18	odd	12		490.3.f.o.197.1		8
35.23	odd	12		70.3.l.c.37.4	yes	16
35.24	odd	6		490.3.f.p.393.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.1	✓	16	35.9	even	6
70.3.l.c.37.4	yes	16	35.23	odd	12
70.3.l.c.53.4	yes	16	5.4	even	2
70.3.l.c.67.1	yes	16	5.3	odd	4
350.3.p.e.93.4		16	7.2	even	3	inner
350.3.p.e.107.1		16	35.2	odd	12	inner
350.3.p.e.193.1		16	1.1	even	1	trivial
350.3.p.e.207.4		16	5.2	odd	4	inner
490.3.f.o.197.1		8	35.18	odd	12
490.3.f.o.393.1		8	35.4	even	6
490.3.f.p.197.4		8	35.3	even	12
490.3.f.p.393.4		8	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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