LMFDB - Embedded newform 350.3.p.e.107.1

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			107.1
Root			$-1.31528 - 4.90868i$ of defining polynomial
Character	$\chi$	$=$	350.107
Dual form			350.3.p.e.193.1

$q$-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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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	−0.680516	−	0.732733i	$-0.738244\pi$
$3$	−4.90868	−	1.31528i	−1.63623	−	0.438426i	−0.955711	+	0.294308i	$0.904911\pi$
$4$	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	0.886782	−	0.462188i	$-0.152936\pi$
$11$	0.474367	+	0.821627i	0.0431242	+	0.0746934i	−0.843658	+	0.536882i	$0.819602\pi$
$12$	−9.81736	+	2.63055i	−0.818113	+	0.219213i
$13$	−0.862338	+	0.862338i	−0.0663337	+	0.0663337i	−0.739495	−	0.673162i	$-0.764936\pi$
$13$	−0.862338	+	0.862338i	−0.0663337	+	0.0663337i	0.673162	+	0.739495i	$0.264936\pi$
$14$	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	−0.199617	−	0.979874i	$-0.563970\pi$
$17$	7.87429	−	29.3872i	0.463193	−	1.72866i	0.662810	−	0.748787i	$-0.269364\pi$
$18$	22.9835	+	6.15841i	1.27686	+	0.342134i
$19$	−20.9123	−	12.0737i	−1.10065	−	0.635459i	−0.164256	−	0.986418i	$-0.552522\pi$
$19$	−20.9123	−	12.0737i	−1.10065	−	0.635459i	−0.936391	+	0.350959i	$0.885856\pi$
$20$		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	0.926677	−	0.375858i	$-0.122652\pi$
$23$	−1.46689	−	5.47452i	−0.0637780	−	0.238023i	−0.990455	+	0.137836i	$0.955985\pi$
$24$	−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	$-0.959629\pi$
$29$		−	7.33636i		−	0.252978i	0.991968	−	0.126489i	$-0.0403708\pi$
$30$		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	$-0.441019\pi$
$32$	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	−0.364672	−	0.931136i	$-0.618819\pi$
$37$	−7.95202	+	2.13074i	−0.214919	+	0.0575875i	0.149753	+	0.988723i	$0.452152\pi$
$38$	−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	−0.208727	−	0.977974i	$-0.566932\pi$
$43$	33.0776	−	33.0776i	0.769247	−	0.769247i	0.977974	+	0.208727i	$0.0669319\pi$
$44$	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	−0.557518	−	0.830165i	$-0.688246\pi$
$47$	−29.3872	+	7.87429i	−0.625260	+	0.167538i	−0.0677424	+	0.997703i	$0.521580\pi$
$48$	−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	0.379346	−	0.925255i	$-0.376149\pi$
$53$	12.9978	+	3.48276i	0.245242	+	0.0657125i	−0.134104	+	0.990967i	$0.542816\pi$
$54$	−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	−0.821156	−	0.570704i	$-0.806670\pi$
$59$	−43.5119	+	25.1216i	−0.737490	+	0.425790i	0.0836659	+	0.996494i	$0.473337\pi$
$60$		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
$63$	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	−0.698941	−	0.715180i	$-0.746345\pi$
$67$	17.6846	−	65.9999i	0.263949	−	0.985073i	0.962890	−	0.269893i	$-0.0869884\pi$
$68$	−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	−0.124700	−	0.992194i	$-0.539797\pi$
$73$	−53.2017	−	14.2554i	−0.728791	−	0.195279i	−0.604091	+	0.796916i	$0.706464\pi$
$74$	−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	0.835444	−	0.549576i	$-0.185211\pi$
$79$	61.4002	+	35.4495i	0.777218	+	0.448727i	−0.0582252	+	0.998303i	$0.518544\pi$
$80$		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	−0.0336406	+	0.999434i	$0.510710\pi$
$83$	−85.7452	+	85.7452i	−1.03307	+	1.03307i	−0.999434	+	0.0336406i	$0.989290\pi$
$84$	−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	0.999551	+	0.0299681i	$0.00954058\pi$
$89$	135.750	+	78.3752i	1.52528	+	0.880621i	0.525729	+	0.850652i	$0.323793\pi$
$90$		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	0.995326	−	0.0965731i	$-0.0307882\pi$
$97$	87.1790	+	87.1790i	0.898753	+	0.898753i	−0.0965731	+	0.995326i	$0.530788\pi$
$98$	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	0.963460	−	0.267852i	$-0.0863138\pi$
$101$	25.2261	+	43.6929i	0.249763	+	0.432603i	−0.713697	+	0.700455i	$0.752980\pi$
$102$	−56.5910	+	211.200i	−0.554813	+	2.07059i
$103$	−37.4152	−	139.636i	−0.363255	−	1.35569i	−0.869771	−	0.493455i	$-0.835734\pi$
$103$	−37.4152	−	139.636i	−0.363255	−	1.35569i	0.506517	−	0.862230i	$-0.330933\pi$
$104$			3.44935i			0.0331669i
$105$		0			0
$106$	19.0302			0.179530
$107$	−6.70244	+	1.79591i	−0.0626397	+	0.0167842i	−0.290003	−	0.957026i	$-0.593656\pi$
$107$	−6.70244	+	1.79591i	−0.0626397	+	0.0167842i	0.227363	+	0.973810i	$0.426990\pi$
$108$	−76.8217	−	20.5843i	−0.711312	−	0.190595i
$109$	−42.3291	+	24.4387i	−0.388340	+	0.224208i	−0.681441	−	0.731873i	$-0.738646\pi$
$109$	−42.3291	+	24.4387i	−0.388340	+	0.224208i	0.293100	+	0.956082i	$0.405313\pi$
$110$		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	−0.669461	−	0.742848i	$-0.733475\pi$
$113$	8.29274	−	8.29274i	0.0733871	−	0.0733871i	0.742848	+	0.669461i	$0.233475\pi$
$114$	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	0.948727	−	0.316097i	$-0.102373\pi$
$127$	80.3440	+	80.3440i	0.632630	+	0.632630i	−0.316097	+	0.948727i	$0.602373\pi$
$128$	−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	−0.909920	−	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
$133$	−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	−0.870743	−	0.491738i	$-0.836362\pi$
$137$	17.7020	−	66.0647i	0.129212	−	0.482224i	0.999955	+	0.00951399i	$0.00302844\pi$
$138$	10.5423	+	39.3443i	0.0763933	+	0.285104i
$139$		−	67.3054i		−	0.484212i	−0.970250	−	0.242106i	$-0.922162\pi$
$139$		−	67.3054i		−	0.484212i	0.970250	−	0.242106i	$-0.0778381\pi$
$140$		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	0.315333	−	0.948981i	$-0.397884\pi$
$149$	−51.9776	−	30.0093i	−0.348843	−	0.201404i	−0.664175	+	0.747577i	$0.731217\pi$
$150$		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	$0.883932\pi$
$152$	−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	0.824561	+	0.565773i	$0.191422\pi$
$157$	−27.0694	+	101.024i	−0.172416	+	0.643466i	−0.996977	+	0.0776933i	$0.975245\pi$
$158$	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	0.990853	−	0.134946i	$-0.0430863\pi$
$163$	10.6400	+	39.7089i	0.0652759	+	0.243613i	−0.925577	+	0.378559i	$0.876420\pi$
$164$	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	0.623515	−	0.781811i	$-0.285704\pi$
$167$	−26.4354	−	26.4354i	−0.158296	−	0.158296i	−0.781811	+	0.623515i	$0.785704\pi$
$168$	−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	0.852521	+	0.522693i	$0.175073\pi$
$173$	64.9724	+	242.480i	0.375563	+	1.40162i	−0.476958	+	0.878926i	$0.658261\pi$
$174$			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	−0.625046	−	0.780588i	$-0.714920\pi$
$179$	−46.8192	+	27.0311i	−0.261560	+	0.151012i	0.363486	+	0.931600i	$0.381586\pi$
$180$		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	−0.998963	−	0.0455246i	$-0.985504\pi$
$191$	−87.8707	+	152.197i	−0.460056	+	0.796841i	0.538907	+	0.842365i	$0.318837\pi$
$192$	−10.5222	+	39.2694i	−0.0548032	+	0.204528i
$193$	−50.4101	−	13.5073i	−0.261192	−	0.0699862i	0.125846	−	0.992050i	$-0.459835\pi$
$193$	−50.4101	−	13.5073i	−0.261192	−	0.0699862i	−0.387039	+	0.922064i	$0.626502\pi$
$194$	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	0.848334	−	0.529462i	$-0.177606\pi$
$197$	62.8178	+	62.8178i	0.318872	+	0.318872i	−0.529462	+	0.848334i	$0.677606\pi$
$198$	5.84269	+	21.8052i	0.0295085	+	0.110127i
$199$	−22.4632	+	12.9692i	−0.112881	+	0.0651717i	−0.555377	−	0.831598i	$-0.687426\pi$
$199$	−22.4632	+	12.9692i	−0.112881	+	0.0651717i	0.442497	+	0.896770i	$0.354093\pi$
$200$		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	−0.346696	−	0.937978i	$-0.612696\pi$
$223$	131.856	−	131.856i	0.591282	−	0.591282i	0.937978	+	0.346696i	$0.112696\pi$
$224$	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	0.315344	+	0.948977i	$0.397880\pi$
$227$	−98.1186	+	366.184i	−0.432241	+	1.61314i	−0.747585	+	0.664166i	$0.768787\pi$
$228$	237.064	+	63.5211i	1.03975	+	0.278601i
$229$	−39.8456	−	23.0049i	−0.173998	−	0.100458i	0.410471	−	0.911873i	$-0.365364\pi$
$229$	−39.8456	−	23.0049i	−0.173998	−	0.100458i	−0.584470	+	0.811415i	$0.698697\pi$
$230$		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	0.883377	−	0.468663i	$-0.155264\pi$
$233$	−27.0237	−	100.854i	−0.115981	−	0.432849i	−0.999358	+	0.0358143i	$0.988598\pi$
$234$	−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	$-0.997334\pi$
$239$		−	4.00351i		−	0.0167511i	0.999965	−	0.00837554i	$-0.00266605\pi$
$240$		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	$0.621342\pi$
$242$	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	−0.819251	−	0.573435i	$-0.805611\pi$
$257$	−319.201	+	85.5296i	−1.24203	+	0.332800i	−0.422775	+	0.906235i	$0.638944\pi$
$258$	−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	0.874851	−	0.484393i	$-0.160959\pi$
$263$	365.648	+	97.9751i	1.39030	+	0.372529i	0.515446	+	0.856922i	$0.327626\pi$
$264$	−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	−0.714768	−	0.699361i	$-0.753468\pi$
$269$	−125.485	+	72.4489i	−0.466488	+	0.269327i	0.248280	+	0.968688i	$0.420135\pi$
$270$		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
$273$	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	−0.992875	−	0.119163i	$-0.961979\pi$
$277$	−20.3424	+	75.9189i	−0.0734383	+	0.274075i	0.919436	+	0.393239i	$0.128645\pi$
$278$	−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	0.0968072	−	0.995303i	$-0.469137\pi$
$283$	−89.7129	−	24.0385i	−0.317007	−	0.0849417i	−0.413814	+	0.910361i	$0.635804\pi$
$284$	−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	0.198270	−	0.980147i	$-0.436468\pi$
$293$	345.276	−	345.276i	1.17842	−	1.17842i	0.980147	−	0.198270i	$-0.0635323\pi$
$294$	−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	0.991614	+	0.129233i	$0.0412517\pi$
$307$	344.100	+	344.100i	1.12085	+	1.12085i	0.129233	+	0.991614i	$0.458748\pi$
$308$	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	0.999343	+	0.0362433i	$0.0115391\pi$
$311$	165.159	+	286.064i	0.531059	+	0.919821i	−0.468284	+	0.883578i	$0.655128\pi$
$312$	4.53685	−	16.9318i	0.0145412	−	0.0542685i
$313$	−22.1618	−	82.7090i	−0.0708045	−	0.264246i	0.921445	−	0.388509i	$-0.127010\pi$
$313$	−22.1618	−	82.7090i	−0.0708045	−	0.264246i	−0.992249	+	0.124263i	$0.960343\pi$
$314$			147.910i			0.471050i
$315$		0			0
$316$	141.798			0.448727
$317$	−170.202	+	45.6055i	−0.536915	+	0.143866i	−0.517080	−	0.855937i	$-0.672981\pi$
$317$	−170.202	+	45.6055i	−0.536915	+	0.143866i	−0.0198354	+	0.999803i	$0.506314\pi$
$318$	−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	−0.999863	−	0.0165391i	$-0.994735\pi$
$331$	−160.736	+	278.404i	−0.485608	+	0.841098i	0.514255	+	0.857637i	$0.328069\pi$
$332$	−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	0.813284	−	0.581868i	$-0.197678\pi$
$337$	77.9872	+	77.9872i	0.231416	+	0.231416i	−0.581868	+	0.813284i	$0.697678\pi$
$338$	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	−0.718592	−	0.695432i	$-0.755213\pi$
$347$	87.2508	−	325.624i	0.251443	−	0.938398i	0.970035	−	0.242966i	$-0.0781204\pi$
$348$	19.2987	+	72.0237i	0.0554560	+	0.206965i
$349$		−	287.505i		−	0.823797i	−0.911230	−	0.411899i	$-0.864866\pi$
$349$		−	287.505i		−	0.823797i	0.911230	−	0.411899i	$-0.135134\pi$
$350$		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	0.478493	−	0.878092i	$-0.341183\pi$
$353$	160.203	+	42.9263i	0.453834	+	0.121604i	−0.0246589	+	0.999696i	$0.507850\pi$
$354$	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	0.878312	−	0.478088i	$-0.158670\pi$
$359$	324.332	+	187.253i	0.903432	+	0.521597i	0.0251201	+	0.999684i	$0.492003\pi$
$360$		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	−0.976482	−	0.215598i	$-0.930830\pi$
$367$	−8.45008	+	31.5361i	−0.0230247	+	0.0859295i	0.953457	+	0.301528i	$0.0974966\pi$
$368$	−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	−0.406658	−	0.913580i	$-0.633306\pi$
$373$	−190.704	−	711.719i	−0.511272	−	1.90809i	−0.104614	−	0.994513i	$-0.533361\pi$
$374$	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	$-0.876321\pi$
$379$		−	287.166i		−	0.757693i	0.925460	−	0.378846i	$-0.123679\pi$
$380$		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	0.929714	+	0.368283i	$0.120054\pi$
$383$	118.232	+	441.247i	0.308699	+	1.15208i	−0.621014	+	0.783799i	$0.713279\pi$
$384$			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	−0.962605	−	0.270907i	$-0.912676\pi$
$389$	−470.416	+	271.595i	−1.20930	+	0.698187i	−0.246690	+	0.969094i	$0.579343\pi$
$390$		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	0.623623	−	0.781725i	$-0.285660\pi$
$397$	617.160	−	165.368i	1.55456	−	0.416543i	0.930936	+	0.365182i	$0.118993\pi$
$398$	−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	$0.978352\pi$
$402$	−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	−0.475380	−	0.879780i	$-0.657690\pi$
$409$	19.9762	−	11.5333i	0.0488417	−	0.0281988i	0.524222	+	0.851582i	$0.324356\pi$
$410$		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	$0.204829\pi$
$419$			502.792i			1.19998i	−0.800007	+	0.599990i	$0.795171\pi$
$420$		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	0.996953	−	0.0780097i	$-0.0248565\pi$
$431$	185.726	+	321.686i	0.430918	+	0.746372i	−0.566035	+	0.824381i	$0.691523\pi$
$432$	−153.643	+	41.1686i	−0.355656	+	0.0952977i
$433$	−449.707	+	449.707i	−1.03858	+	1.03858i	−0.0393595	+	0.999225i	$0.512532\pi$
$433$	−449.707	+	449.707i	−1.03858	+	1.03858i	−0.999225	+	0.0393595i	$0.987468\pi$
$434$	−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	−0.207917	−	0.978147i	$-0.566668\pi$
$439$	−508.790	−	293.750i	−1.15897	−	0.669134i	−0.951058	+	0.309012i	$0.900002\pi$
$440$		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	0.964525	−	0.263992i	$-0.0850394\pi$
$443$	−1.22904	−	4.58686i	−0.00277437	−	0.0103541i	−0.967299	+	0.253638i	$0.918373\pi$
$444$	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	$-0.985590\pi$
$449$		−	40.6375i		−	0.0905067i	0.998976	−	0.0452533i	$-0.0144095\pi$
$450$		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	0.105903	−	0.994376i	$-0.466227\pi$
$457$	317.526	−	85.0810i	0.694806	−	0.186173i	0.588903	+	0.808204i	$0.299560\pi$
$458$	−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	0.380701	−	0.924698i	$-0.375683\pi$
$463$	604.400	−	604.400i	1.30540	−	1.30540i	0.924698	−	0.380701i	$-0.124317\pi$
$464$	−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	−0.608729	−	0.793379i	$-0.708320\pi$
$467$	−345.213	+	92.4995i	−0.739214	+	0.198072i	−0.130485	+	0.991450i	$0.541653\pi$
$468$	−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	−0.925967	−	0.377604i	$-0.876748\pi$
$479$	−508.668	+	293.679i	−1.06194	+	0.613109i	−0.135969	+	0.990713i	$0.543415\pi$
$480$		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	0.632938	+	0.774202i	$0.281849\pi$
$487$	−147.222	+	549.440i	−0.302304	+	1.12821i	−0.935242	+	0.354010i	$0.884818\pi$
$488$	−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	0.908977	−	0.416846i	$-0.136865\pi$
$499$	500.231	+	288.808i	1.00247	+	0.578774i	0.0934891	+	0.995620i	$0.470198\pi$
$500$		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	−0.156981	−	0.987602i	$-0.550176\pi$
$503$	417.802	−	417.802i	0.830620	−	0.830620i	0.987602	+	0.156981i	$0.0501763\pi$
$504$	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	0.628419	−	0.777875i	$-0.283703\pi$
$509$	136.905	+	79.0420i	0.268968	+	0.155289i	−0.359451	+	0.933164i	$0.617036\pi$
$510$		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	0.916497	−	0.400041i	$-0.131004\pi$
$521$	58.2493	+	100.891i	0.111803	+	0.193648i	−0.804694	+	0.593689i	$0.797671\pi$
$522$	45.1803	−	168.615i	0.0865523	−	0.323018i
$523$	65.4858	+	244.396i	0.125212	+	0.467297i	0.999847	−	0.0174845i	$-0.00556577\pi$
$523$	65.4858	+	244.396i	0.125212	+	0.467297i	−0.874635	+	0.484782i	$0.838899\pi$
$524$			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	−0.156052	−	0.987749i	$-0.549877\pi$
$541$	420.568	−	728.445i	0.777390	−	1.34648i	0.933442	−	0.358730i	$-0.116790\pi$
$542$	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	0.466931	−	0.884294i	$-0.345360\pi$
$547$	−228.297	−	228.297i	−0.417362	−	0.417362i	−0.884294	+	0.466931i	$0.845360\pi$
$548$	−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	−0.269595	−	0.962974i	$-0.586890\pi$
$557$	248.070	−	925.810i	0.445368	−	1.66214i	0.714963	−	0.699162i	$-0.246443\pi$
$558$	−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	−0.648717	−	0.761030i	$-0.724694\pi$
$563$	−895.754	−	240.016i	−1.59104	−	0.426317i	−0.942320	+	0.334713i	$0.891361\pi$
$564$	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	0.802897	−	0.596118i	$-0.203291\pi$
$569$	391.524	+	226.046i	0.688091	+	0.397270i	−0.114805	+	0.993388i	$0.536624\pi$
$570$		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	$0.944491\pi$
$572$	−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	−0.786451	−	0.617653i	$-0.788084\pi$
$577$	117.398	−	438.134i	0.203462	−	0.759330i	0.989913	−	0.141677i	$-0.0452496\pi$
$578$	−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	0.811088	−	0.584924i	$-0.198876\pi$
$587$	132.759	+	132.759i	0.226165	+	0.226165i	−0.584924	+	0.811088i	$0.698876\pi$
$588$	−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	0.929559	−	0.368674i	$-0.120188\pi$
$593$	−35.4612	−	132.343i	−0.0597997	−	0.223176i	−0.989358	+	0.145498i	$0.953521\pi$
$594$		−	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	0.0166277	−	0.999862i	$-0.494707\pi$
$599$	533.617	−	308.084i	0.890847	−	0.514331i	0.874220	+	0.485531i	$0.161374\pi$
$600$		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	−0.552924	−	0.833232i	$-0.686488\pi$
$607$	−373.398	+	100.052i	−0.615153	+	0.164830i	−0.0622299	+	0.998062i	$0.519821\pi$
$608$	−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	0.217833	−	0.975986i	$-0.430101\pi$
$613$	−49.9662	−	13.3884i	−0.0815109	−	0.0218408i	−0.299344	+	0.954145i	$0.596768\pi$
$614$	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	1.00000		0.000183933i	$-5.85476e-5\pi$
$617$	616.887	+	616.887i	0.999816	+	0.999816i	−0.000183933		1.00000i	$0.500059\pi$
$618$	268.896	+	1003.53i	0.435107	+	1.62384i
$619$	449.823	−	259.705i	0.726693	−	0.419556i	−0.0905183	−	0.995895i	$-0.528852\pi$
$619$	449.823	−	259.705i	0.726693	−	0.419556i	0.817211	+	0.576339i	$0.195519\pi$
$620$		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	0.741229	−	0.671252i	$-0.234243\pi$
$641$	−135.063	−	233.937i	−0.210707	−	0.364956i	−0.951936	+	0.306297i	$0.900910\pi$
$642$	48.1692	−	12.9069i	0.0750298	−	0.0201042i
$643$	−192.668	+	192.668i	−0.299639	+	0.299639i	−0.840872	−	0.541234i	$-0.817957\pi$
$643$	−192.668	+	192.668i	−0.299639	+	0.299639i	0.541234	+	0.840872i	$0.317957\pi$
$644$	−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	−0.997486	−	0.0708670i	$-0.977423\pi$
$647$	−63.5381	+	237.128i	−0.0982042	+	0.366503i	0.899282	+	0.437370i	$0.144090\pi$
$648$	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	0.995500	+	0.0947659i	$0.0302103\pi$
$653$	118.033	+	440.504i	0.180755	+	0.674585i	−0.814745	+	0.579819i	$0.803123\pi$
$654$	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	$-0.735648\pi$
$659$		−	973.026i		−	1.47652i	0.674517	−	0.738259i	$-0.264352\pi$
$660$		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	$0.759203\pi$
$662$	−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	−0.989198	−	0.146582i	$-0.953173\pi$
$673$	−567.081	+	567.081i	−0.842616	+	0.842616i	0.146582	+	0.989198i	$0.453173\pi$
$674$	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	0.0377179	−	0.999288i	$-0.487991\pi$
$677$	385.908	−	103.404i	0.570027	−	0.152738i	0.532309	+	0.846550i	$0.321324\pi$
$678$	−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	0.858945	−	0.512067i	$-0.171120\pi$
$683$	919.851	+	246.473i	1.34678	+	0.360869i	0.487835	+	0.872936i	$0.337787\pi$
$684$	−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	−0.643871	−	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
$693$	−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	−0.986362	−	0.164592i	$-0.947369\pi$
$709$	−1150.06	−	663.986i	−1.62208	−	0.936510i	−0.635722	−	0.771918i	$-0.719297\pi$
$710$		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	0.320515	−	0.947243i	$-0.396144\pi$
$719$	−244.147	−	140.958i	−0.339564	−	0.196048i	−0.660079	+	0.751196i	$0.729477\pi$
$720$		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	−0.988118	−	0.153694i	$-0.950883\pi$
$727$	−830.098	−	830.098i	−1.14181	−	1.14181i	−0.153694	−	0.988118i	$-0.549117\pi$
$728$	−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	−0.771988	−	0.635637i	$-0.780737\pi$
$733$	−308.773	−	1152.36i	−0.421245	−	1.57211i	0.350743	−	0.936472i	$-0.385929\pi$
$734$			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	−0.129373	−	0.991596i	$-0.541296\pi$
$739$	491.205	−	283.597i	0.664688	−	0.383758i	0.794061	+	0.607838i	$0.207963\pi$
$740$		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	−0.620796	−	0.783972i	$-0.713190\pi$
$743$	121.240	−	121.240i	0.163176	−	0.163176i	0.783972	+	0.620796i	$0.213190\pi$
$744$	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	0.314114	+	0.949385i	$0.398293\pi$
$751$	−499.516	+	865.187i	−0.665135	+	1.15205i	−0.979249	+	0.202662i	$0.935041\pi$
$752$	−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	0.488358	−	0.872643i	$-0.337596\pi$
$757$	−290.904	−	290.904i	−0.384285	−	0.384285i	−0.872643	+	0.488358i	$0.837596\pi$
$758$	−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	−0.718327	−	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
$763$	−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	$-0.868974\pi$
$769$		−	615.359i		−	0.800207i	0.916470	−	0.400103i	$-0.131026\pi$
$770$		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	−0.310063	−	0.950716i	$-0.600350\pi$
$773$	−814.698	−	218.298i	−1.05394	−	0.282403i	−0.743880	+	0.668313i	$0.767017\pi$
$774$	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	0.849638	+	0.527366i	$0.176820\pi$
$787$	−117.934	+	440.137i	−0.149853	+	0.559259i	−0.999491	+	0.0318931i	$0.989846\pi$
$788$	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	0.924331	+	0.381592i	$0.124624\pi$
$797$	1040.82	+	1040.82i	1.30592	+	1.30592i	0.381592	+	0.924331i	$0.375376\pi$
$798$	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	−0.614107	−	0.789222i	$-0.710484\pi$
$809$	−192.279	+	111.012i	−0.237674	+	0.137221i	0.376433	+	0.926444i	$0.377150\pi$
$810$		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	−0.724841	−	0.688916i	$-0.758087\pi$
$821$	192.277	−	333.033i	0.234198	−	0.405643i	0.959039	+	0.283273i	$0.0914202\pi$
$822$	−127.221	+	474.794i	−0.154770	+	0.577608i
$823$	64.4885	+	17.2796i	0.0783578	+	0.0209959i	0.297785	−	0.954633i	$-0.403752\pi$
$823$	64.4885	+	17.2796i	0.0783578	+	0.0209959i	−0.219427	+	0.975629i	$0.570419\pi$
$824$	−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	0.248096	−	0.968735i	$-0.420195\pi$
$827$	−595.969	−	595.969i	−0.720639	−	0.720639i	−0.968735	+	0.248096i	$0.920195\pi$
$828$	−49.3612	−	184.219i	−0.0596150	−	0.222486i
$829$	609.282	−	351.769i	0.734960	−	0.424329i	−0.0852739	−	0.996358i	$-0.527177\pi$
$829$	609.282	−	351.769i	0.734960	−	0.424329i	0.820234	+	0.572028i	$0.193843\pi$
$830$		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	$0.000569167\pi$
$839$			3.00042i			0.00357618i	−0.999998	+	0.00178809i	$0.999431\pi$
$840$		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	−0.978219	−	0.207577i	$-0.933442\pi$
$853$	−657.357	+	657.357i	−0.770641	+	0.770641i	0.207577	+	0.978219i	$0.433442\pi$
$854$	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	−0.599879	−	0.800091i	$-0.704784\pi$
$857$	273.963	−	1022.44i	0.319677	−	1.19305i	0.919556	−	0.392960i	$-0.128549\pi$
$858$	8.03187	+	2.15213i	0.00936115	+	0.00250831i
$859$	747.383	+	431.502i	0.870062	+	0.502331i	0.867369	−	0.497666i	$-0.165809\pi$
$859$	747.383	+	431.502i	0.870062	+	0.502331i	0.00269328	+	0.999996i	$0.499143\pi$
$860$		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	−0.867039	−	0.498241i	$-0.833980\pi$
$863$	−315.238	−	1176.48i	−0.365282	−	1.36325i	0.501757	−	0.865009i	$-0.332687\pi$
$864$	−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	−0.910620	−	0.413244i	$-0.864396\pi$
$877$	−1309.03	+	350.753i	−1.49262	+	0.399946i	−0.581999	+	0.813190i	$0.697729\pi$
$878$	−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	−0.381290	−	0.924455i	$-0.624520\pi$
$883$	479.615	−	479.615i	0.543166	−	0.543166i	0.924455	+	0.381290i	$0.124520\pi$
$884$	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	−0.0429116	−	0.999079i	$-0.513663\pi$
$887$	372.066	−	99.6947i	0.419465	−	0.112395i	0.462377	+	0.886683i	$0.346997\pi$
$888$	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	0.745395	+	0.666623i	$0.232261\pi$
$907$	−211.737	+	790.213i	−0.233448	+	0.871238i	−0.978842	+	0.204615i	$0.934406\pi$
$908$	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	0.269257	−	0.963068i	$-0.413222\pi$
$919$	−395.313	−	228.234i	−0.430156	−	0.248351i	−0.699413	+	0.714718i	$0.746555\pi$
$920$		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	0.633740	−	0.773546i	$-0.281519\pi$
$929$	260.770	+	150.556i	0.280700	+	0.162062i	−0.353040	+	0.935608i	$0.614852\pi$
$930$		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	0.591417	−	0.806366i	$-0.298569\pi$
$937$	−201.407	−	201.407i	−0.214949	−	0.214949i	−0.806366	+	0.591417i	$0.798569\pi$
$938$	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	0.963532	−	0.267594i	$-0.0862285\pi$
$941$	235.272	+	407.502i	0.250023	+	0.433052i	−0.713509	+	0.700646i	$0.752895\pi$
$942$	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	−0.111259	−	0.993791i	$-0.535488\pi$
$947$	273.951	−	73.4049i	0.289283	−	0.0775131i	0.400542	+	0.916278i	$0.368822\pi$
$948$	−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	−0.955106	−	0.296264i	$-0.904259\pi$
$953$	−627.876	+	627.876i	−0.658842	+	0.658842i	0.296264	+	0.955106i	$0.404259\pi$
$954$	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	0.999290	−	0.0376852i	$-0.0119984\pi$
$967$	929.872	+	929.872i	0.961604	+	0.961604i	−0.0376852	+	0.999290i	$0.511998\pi$
$968$	−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	0.335888	+	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
$973$	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	−0.986452	−	0.164051i	$-0.947544\pi$
$977$	−48.9808	+	182.799i	−0.0501339	+	0.187102i	0.936318	+	0.351153i	$0.114210\pi$
$978$	−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	0.870868	−	0.491516i	$-0.163557\pi$
$983$	1355.86	+	363.301i	1.37930	+	0.369583i	0.508436	+	0.861100i	$0.330224\pi$
$984$	−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	0.966352	−	0.257223i	$-0.0828075\pi$
$991$	258.071	+	446.992i	0.260414	+	0.451051i	−0.705938	+	0.708274i	$0.749474\pi$
$992$	−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	0.551976	+	0.833860i	$0.313874\pi$
$997$	−341.950	+	1276.18i	−0.342979	+	1.28002i	−0.894955	+	0.446155i	$0.852793\pi$
$998$	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.107.1		16
5.2	odd	4		70.3.l.c.23.1	✓	16
5.3	odd	4	inner	350.3.p.e.93.4		16
5.4	even	2		70.3.l.c.37.4	yes	16
7.4	even	3	inner	350.3.p.e.207.4		16
35.2	odd	12		490.3.f.o.393.1		8
35.4	even	6		70.3.l.c.67.1	yes	16
35.9	even	6		490.3.f.o.197.1		8
35.12	even	12		490.3.f.p.393.4		8
35.18	odd	12	inner	350.3.p.e.193.1		16
35.19	odd	6		490.3.f.p.197.4		8
35.32	odd	12		70.3.l.c.53.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.1	✓	16	5.2	odd	4
70.3.l.c.37.4	yes	16	5.4	even	2
70.3.l.c.53.4	yes	16	35.32	odd	12
70.3.l.c.67.1	yes	16	35.4	even	6
350.3.p.e.93.4		16	5.3	odd	4	inner
350.3.p.e.107.1		16	1.1	even	1	trivial
350.3.p.e.193.1		16	35.18	odd	12	inner
350.3.p.e.207.4		16	7.4	even	3	inner
490.3.f.o.197.1		8	35.9	even	6
490.3.f.o.393.1		8	35.2	odd	12
490.3.f.p.197.4		8	35.19	odd	6
490.3.f.p.393.4		8	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(-4.90868 - 1.31528i) q^{3} +(1.73205 - 1.00000i) q^{4} -7.18681 q^{6} +(6.99850 + 0.145113i) q^{7} +(2.00000 - 2.00000i) q^{8} +(14.5710 + 8.41254i) q^{9} +O(q^{10})\)	\(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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