LMFDB - Embedded newform 950.2.l.g.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1511x^{6} + 4812x^{4} - 7788x^{2} + 5329 $ x^12 - 24x^10 + 264x^8 - 1511x^6 + 4812x^4 - 7788*x^2 + 5329
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.1
Root			$1.97287 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	950.101
Dual form			950.2.l.g.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-2.57374 - 0.936765i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.57374 - 0.936765i) q^{6} +(1.92448 - 3.33331i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.44848 + 2.89362i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.57374 - 0.936765i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.57374 - 0.936765i) q^{6} +(1.92448 - 3.33331i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.44848 + 2.89362i) q^{9} +(-2.86418 - 4.96090i) q^{11} +(-1.36946 + 2.37197i) q^{12} +(5.05999 - 1.84169i) q^{13} +(0.668367 + 3.79050i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-1.05258 + 0.883218i) q^{17} -4.50167 q^{18} +(4.23364 + 1.03746i) q^{19} +(-8.07565 + 6.77628i) q^{21} +(5.38289 + 1.95921i) q^{22} +(-0.274010 + 1.55399i) q^{23} +(-0.475608 - 2.69731i) q^{24} +(-2.69236 + 4.66331i) q^{26} +(-2.05648 - 3.56193i) q^{27} +(-2.94848 - 2.47407i) q^{28} +(5.22668 + 4.38571i) q^{29} +(3.07565 - 5.32718i) q^{31} +(0.939693 - 0.342020i) q^{32} +(2.72445 + 15.4511i) q^{33} +(0.238600 - 1.35317i) q^{34} +(3.44848 - 2.89362i) q^{36} +1.89405 q^{37} +(-3.91002 + 1.92659i) q^{38} -14.7483 q^{39} +(-3.39002 - 1.23387i) q^{41} +(1.83060 - 10.3819i) q^{42} +(-0.568954 - 3.22670i) q^{43} +(-5.38289 + 1.95921i) q^{44} +(-0.788981 - 1.36656i) q^{46} +(-5.55187 - 4.65857i) q^{47} +(2.09813 + 1.76054i) q^{48} +(-3.90728 - 6.76762i) q^{49} +(3.53643 - 1.28716i) q^{51} +(-0.935048 - 5.30292i) q^{52} +(2.04459 - 11.5955i) q^{53} +(3.86492 + 1.40672i) q^{54} +3.84897 q^{56} +(-9.92443 - 6.63607i) q^{57} -6.82295 q^{58} +(-2.00293 + 1.68066i) q^{59} +(-1.05728 + 5.99615i) q^{61} +(1.06816 + 6.05785i) q^{62} +(16.2819 - 5.92612i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.0189 - 10.0850i) q^{66} +(4.81079 + 4.03673i) q^{67} +(0.687022 + 1.18996i) q^{68} +(2.16096 - 3.74288i) q^{69} +(-2.16096 - 12.2554i) q^{71} +(-0.781707 + 4.43328i) q^{72} +(-8.85877 - 3.22433i) q^{73} +(-1.45093 + 1.21747i) q^{74} +(1.75686 - 3.98917i) q^{76} -22.0483 q^{77} +(11.2979 - 9.48004i) q^{78} +(-7.27101 - 2.64643i) q^{79} +(-0.388964 - 2.20593i) q^{81} +(3.39002 - 1.23387i) q^{82} +(-2.24471 + 3.88794i) q^{83} +(5.27101 + 9.12965i) q^{84} +(2.50993 + 2.10608i) q^{86} +(-9.34375 - 16.1838i) q^{87} +(2.86418 - 4.96090i) q^{88} +(0.964940 - 0.351210i) q^{89} +(3.59897 - 20.4108i) q^{91} +(1.48280 + 0.539695i) q^{92} +(-12.9063 + 10.8296i) q^{93} +7.24746 q^{94} -2.73892 q^{96} +(1.01216 - 0.849299i) q^{97} +(7.34329 + 2.67274i) q^{98} +(4.47790 - 25.3954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−2.57374	−	0.936765i	−1.48595	−	0.540842i	−0.533570	−	0.845756i	$-0.679150\pi$
$3$	−2.57374	−	0.936765i	−1.48595	−	0.540842i	−0.952380	+	0.304914i	$0.901372\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	2.57374	−	0.936765i	1.05073	−	0.382433i
$7$	1.92448	−	3.33331i	0.727387	−	1.25987i	−0.230597	−	0.973049i	$-0.574068\pi$
$7$	1.92448	−	3.33331i	0.727387	−	1.25987i	0.957984	−	0.286822i	$-0.0925988\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	3.44848	+	2.89362i	1.14949	+	0.964540i
$10$		0			0
$11$	−2.86418	−	4.96090i	−0.863582	−	1.49577i	−0.868448	−	0.495780i	$-0.834882\pi$
$11$	−2.86418	−	4.96090i	−0.863582	−	1.49577i	0.00486621	−	0.999988i	$-0.498451\pi$
$12$	−1.36946	+	2.37197i	−0.395329	+	0.684730i
$13$	5.05999	−	1.84169i	1.40339	−	0.510792i	0.474206	−	0.880414i	$-0.342735\pi$
$13$	5.05999	−	1.84169i	1.40339	−	0.510792i	0.929182	+	0.369622i	$0.120513\pi$
$14$	0.668367	+	3.79050i	0.178628	+	1.01305i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.05258	+	0.883218i	−0.255288	+	0.214212i	−0.761445	−	0.648229i	$-0.775510\pi$
$17$	−1.05258	+	0.883218i	−0.255288	+	0.214212i	0.506158	+	0.862441i	$0.331065\pi$
$18$	−4.50167			−1.06105
$19$	4.23364	+	1.03746i	0.971263	+	0.238009i
$19$	4.23364	+	1.03746i	0.971263	+	0.238009i
$20$		0			0
$21$	−8.07565	+	6.77628i	−1.76225	+	1.47870i
$22$	5.38289	+	1.95921i	1.14764	+	0.417706i
$23$	−0.274010	+	1.55399i	−0.0571351	+	0.324029i	−0.999957	−	0.00926752i	$-0.997050\pi$
$23$	−0.274010	+	1.55399i	−0.0571351	+	0.324029i	0.942822	+	0.333297i	$0.108161\pi$
$24$	−0.475608	−	2.69731i	−0.0970831	−	0.550586i
$25$		0			0
$26$	−2.69236	+	4.66331i	−0.528016	+	0.914550i
$27$	−2.05648	−	3.56193i	−0.395770	−	0.685494i
$28$	−2.94848	−	2.47407i	−0.557211	−	0.467555i
$29$	5.22668	+	4.38571i	0.970570	+	0.814405i	0.982640	−	0.185522i	$-0.0593976\pi$
$29$	5.22668	+	4.38571i	0.970570	+	0.814405i	−0.0120697	+	0.999927i	$0.503842\pi$
$30$		0			0
$31$	3.07565	−	5.32718i	0.552403	−	0.956791i	−0.445697	−	0.895184i	$-0.647044\pi$
$31$	3.07565	−	5.32718i	0.552403	−	0.956791i	0.998100	−	0.0616068i	$-0.0196225\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	2.72445	+	15.4511i	0.474266	+	2.68970i
$34$	0.238600	−	1.35317i	0.0409196	−	0.232066i
$35$		0			0
$36$	3.44848	−	2.89362i	0.574747	−	0.482270i
$37$	1.89405			0.311381			0.155690	−	0.987806i	$-0.450240\pi$
$37$	1.89405			0.311381			0.155690	+	0.987806i	$0.450240\pi$
$38$	−3.91002	+	1.92659i	−0.634289	+	0.312534i
$39$	−14.7483			−2.36162
$40$		0			0
$41$	−3.39002	−	1.23387i	−0.529433	−	0.192698i	0.0634522	−	0.997985i	$-0.479789\pi$
$41$	−3.39002	−	1.23387i	−0.529433	−	0.192698i	−0.592885	+	0.805287i	$0.702011\pi$
$42$	1.83060	−	10.3819i	0.282468	−	1.60196i
$43$	−0.568954	−	3.22670i	−0.0867647	−	0.492067i	−0.996962	−	0.0778917i	$-0.975181\pi$
$43$	−0.568954	−	3.22670i	−0.0867647	−	0.492067i	0.910197	−	0.414175i	$-0.135930\pi$
$44$	−5.38289	+	1.95921i	−0.811502	+	0.295362i
$45$		0			0
$46$	−0.788981	−	1.36656i	−0.116329	−	0.201488i
$47$	−5.55187	−	4.65857i	−0.809824	−	0.679523i	0.140742	−	0.990046i	$-0.455051\pi$
$47$	−5.55187	−	4.65857i	−0.809824	−	0.679523i	−0.950566	+	0.310523i	$0.899496\pi$
$48$	2.09813	+	1.76054i	0.302839	+	0.254112i
$49$	−3.90728	−	6.76762i	−0.558184	−	0.966802i
$50$		0			0
$51$	3.53643	−	1.28716i	0.495199	−	0.180238i
$52$	−0.935048	−	5.30292i	−0.129668	−	0.735383i
$53$	2.04459	−	11.5955i	0.280847	−	1.59276i	−0.438908	−	0.898532i	$-0.644635\pi$
$53$	2.04459	−	11.5955i	0.280847	−	1.59276i	0.719755	−	0.694229i	$-0.244254\pi$
$54$	3.86492	+	1.40672i	0.525949	+	0.191430i
$55$		0			0
$56$	3.84897			0.514340
$57$	−9.92443	−	6.63607i	−1.31452	−	0.878969i
$58$	−6.82295			−0.895897
$59$	−2.00293	+	1.68066i	−0.260759	+	0.218803i	−0.763789	−	0.645466i	$-0.776663\pi$
$59$	−2.00293	+	1.68066i	−0.260759	+	0.218803i	0.503030	+	0.864269i	$0.332219\pi$
$60$		0			0
$61$	−1.05728	+	5.99615i	−0.135371	+	0.767728i	0.839229	+	0.543778i	$0.183007\pi$
$61$	−1.05728	+	5.99615i	−0.135371	+	0.767728i	−0.974600	+	0.223951i	$0.928105\pi$
$62$	1.06816	+	6.05785i	0.135657	+	0.769348i
$63$	16.2819	−	5.92612i	2.05132	−	0.746621i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−12.0189	−	10.0850i	−1.47942	−	1.24138i
$67$	4.81079	+	4.03673i	0.587732	+	0.493166i	0.887476	−	0.460854i	$-0.152457\pi$
$67$	4.81079	+	4.03673i	0.587732	+	0.493166i	−0.299744	+	0.954020i	$0.596901\pi$
$68$	0.687022	+	1.18996i	0.0833136	+	0.144303i
$69$	2.16096	−	3.74288i	0.260148	−	0.450590i
$70$		0			0
$71$	−2.16096	−	12.2554i	−0.256458	−	1.45445i	−0.792302	−	0.610130i	$-0.791117\pi$
$71$	−2.16096	−	12.2554i	−0.256458	−	1.45445i	0.535843	−	0.844317i	$-0.319994\pi$
$72$	−0.781707	+	4.43328i	−0.0921251	+	0.522467i
$73$	−8.85877	−	3.22433i	−1.03684	−	0.377379i	−0.233159	−	0.972439i	$-0.574906\pi$
$73$	−8.85877	−	3.22433i	−1.03684	−	0.377379i	−0.803682	+	0.595060i	$0.797128\pi$
$74$	−1.45093	+	1.21747i	−0.168667	+	0.141529i
$75$		0			0
$76$	1.75686	−	3.98917i	0.201526	−	0.457589i
$77$	−22.0483			−2.51263
$78$	11.2979	−	9.48004i	1.27923	−	1.07340i
$79$	−7.27101	−	2.64643i	−0.818052	−	0.297747i	−0.101106	−	0.994876i	$-0.532238\pi$
$79$	−7.27101	−	2.64643i	−0.818052	−	0.297747i	−0.716946	+	0.697129i	$0.754460\pi$
$80$		0			0
$81$	−0.388964	−	2.20593i	−0.0432182	−	0.245103i
$82$	3.39002	−	1.23387i	0.374366	−	0.136258i
$83$	−2.24471	+	3.88794i	−0.246388	+	0.426757i	−0.962521	−	0.271207i	$-0.912577\pi$
$83$	−2.24471	+	3.88794i	−0.246388	+	0.426757i	0.716133	+	0.697964i	$0.245911\pi$
$84$	5.27101	+	9.12965i	0.575114	+	0.996127i
$85$		0			0
$86$	2.50993	+	2.10608i	0.270652	+	0.227104i
$87$	−9.34375	−	16.1838i	−1.00176	−	1.73509i
$88$	2.86418	−	4.96090i	0.305322	−	0.528834i
$89$	0.964940	−	0.351210i	0.102283	−	0.0372281i	−0.290372	−	0.956914i	$-0.593779\pi$
$89$	0.964940	−	0.351210i	0.102283	−	0.0372281i	0.392655	+	0.919686i	$0.371557\pi$
$90$		0			0
$91$	3.59897	−	20.4108i	0.377275	−	2.13963i
$92$	1.48280	+	0.539695i	0.154593	+	0.0562671i
$93$	−12.9063	+	10.8296i	−1.33832	+	1.12298i
$94$	7.24746			0.747518
$95$		0			0
$96$	−2.73892			−0.279540
$97$	1.01216	−	0.849299i	0.102769	−	0.0862332i	−0.589956	−	0.807436i	$-0.700855\pi$
$97$	1.01216	−	0.849299i	0.102769	−	0.0862332i	0.692724	+	0.721203i	$0.256410\pi$
$98$	7.34329	+	2.67274i	0.741785	+	0.269988i
$99$	4.47790	−	25.3954i	0.450046	−	2.55234i
$100$		0			0
$101$	13.6667	−	4.97428i	1.35989	−	0.494960i	0.443870	−	0.896091i	$-0.353605\pi$
$101$	13.6667	−	4.97428i	1.35989	−	0.494960i	0.916021	+	0.401131i	$0.131383\pi$
$102$	−1.88170	+	3.25919i	−0.186316	+	0.322708i
$103$	3.79549	+	6.57398i	0.373981	+	0.647754i	0.990174	−	0.139841i	$-0.0446592\pi$
$103$	3.79549	+	6.57398i	0.373981	+	0.647754i	−0.616193	+	0.787595i	$0.711326\pi$
$104$	4.12494	+	3.46124i	0.404484	+	0.339402i
$105$		0			0
$106$	5.88718	+	10.1969i	0.571813	+	0.990409i
$107$	0.682312	−	1.18180i	0.0659616	−	0.114249i	−0.831159	−	0.556035i	$-0.812322\pi$
$107$	0.682312	−	1.18180i	0.0659616	−	0.114249i	0.897120	+	0.441787i	$0.145655\pi$
$108$	−3.86492	+	1.40672i	−0.371902	+	0.135361i
$109$	1.23433	+	7.00026i	0.118228	+	0.670503i	0.985101	+	0.171975i	$0.0550149\pi$
$109$	1.23433	+	7.00026i	0.118228	+	0.670503i	−0.866873	+	0.498528i	$0.833874\pi$
$110$		0			0
$111$	−4.87481	−	1.77428i	−0.462696	−	0.168408i
$112$	−2.94848	+	2.47407i	−0.278605	+	0.233778i
$113$	−11.0635			−1.04077			−0.520385	−	0.853932i	$-0.674212\pi$
$113$	−11.0635			−1.04077			−0.520385	+	0.853932i	$0.674212\pi$
$114$	11.8681	−	1.29577i	1.11155	−	0.121360i
$115$		0			0
$116$	5.22668	−	4.38571i	0.485285	−	0.407203i
$117$	22.7784	+	8.29067i	2.10587	+	0.766472i
$118$	0.454027	−	2.57491i	0.0417965	−	0.237040i
$119$	0.918365	+	5.20830i	0.0841863	+	0.477444i
$120$		0			0
$121$	−10.9070	+	18.8915i	−0.991548	+	1.71741i
$122$	−3.04433	−	5.27293i	−0.275620	−	0.477388i
$123$	7.56920	+	6.35131i	0.682492	+	0.572679i
$124$	−4.71217	−	3.95398i	−0.423166	−	0.355078i
$125$		0			0
$126$	−8.66340	+	15.0055i	−0.771797	+	1.33679i
$127$	0.306386	−	0.111515i	0.0271873	−	0.00989538i	−0.328391	−	0.944542i	$-0.606506\pi$
$127$	0.306386	−	0.111515i	0.0271873	−	0.00989538i	0.355578	+	0.934647i	$0.384284\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−1.55832	+	8.83766i	−0.137202	+	0.778113i
$130$		0			0
$131$	−4.03121	+	3.38258i	−0.352208	+	0.295538i	−0.801676	−	0.597759i	$-0.796058\pi$
$131$	−4.03121	+	3.38258i	−0.352208	+	0.295538i	0.449468	+	0.893296i	$0.351614\pi$
$132$	15.6895			1.36560
$133$	11.6057	−	12.1154i	1.00634	−	1.05054i
$134$	−6.28004			−0.542513
$135$		0			0
$136$	−1.29118	−	0.469950i	−0.110718	−	0.0402979i
$137$	−2.15794	+	12.2383i	−0.184365	+	1.04559i	0.742403	+	0.669953i	$0.233686\pi$
$137$	−2.15794	+	12.2383i	−0.184365	+	1.04559i	−0.926768	+	0.375633i	$0.877425\pi$
$138$	0.750492	+	4.25625i	0.0638861	+	0.362316i
$139$	5.85434	−	2.13081i	0.496559	−	0.180733i	−0.0815867	−	0.996666i	$-0.525999\pi$
$139$	5.85434	−	2.13081i	0.496559	−	0.180733i	0.578146	+	0.815934i	$0.303777\pi$
$140$		0			0
$141$	9.92509	+	17.1908i	0.835844	+	1.44772i
$142$	9.53300	+	7.99914i	0.799992	+	0.671273i
$143$	−23.6291	−	19.8272i	−1.97597	−	1.65803i
$144$	−2.25084	−	3.89856i	−0.187570	−	0.324880i
$145$		0			0
$146$	8.85877	−	3.22433i	0.733157	−	0.266847i
$147$	3.71667	+	21.0783i	0.306546	+	1.73851i
$148$	0.328899	−	1.86528i	0.0270353	−	0.153325i
$149$	−21.4638	−	7.81220i	−1.75839	−	0.640000i	−0.758456	−	0.651725i	$-0.774046\pi$
$149$	−21.4638	−	7.81220i	−1.75839	−	0.640000i	−0.999931	+	0.0117242i	$0.996268\pi$
$150$		0			0
$151$	6.70041			0.545272			0.272636	−	0.962117i	$-0.412105\pi$
$151$	6.70041			0.545272			0.272636	+	0.962117i	$0.412105\pi$
$152$	1.21835	+	4.18517i	0.0988215	+	0.339462i
$153$	−6.18549			−0.500068
$154$	16.8900	−	14.1724i	1.36103	−	1.14204i
$155$		0			0
$156$	−2.56102	+	14.5243i	−0.205046	+	1.16287i
$157$	0.00654942	+	0.0371436i	0.000522700	+	0.00296438i	0.985068	−	0.172166i	$-0.0550765\pi$
$157$	0.00654942	+	0.0371436i	0.000522700	+	0.00296438i	−0.984545	+	0.175130i	$0.943965\pi$
$158$	7.27101	−	2.64643i	0.578450	−	0.210539i
$159$	−16.1245	+	27.9284i	−1.27876	+	2.21487i
$160$		0			0
$161$	4.65259	+	3.90399i	0.366676	+	0.307678i
$162$	1.71591	+	1.43982i	0.134814	+	0.113123i
$163$	5.81624	+	10.0740i	0.455563	+	0.789059i	0.998720	−	0.0505722i	$-0.0161045\pi$
$163$	5.81624	+	10.0740i	0.455563	+	0.789059i	−0.543157	+	0.839631i	$0.682771\pi$
$164$	−1.80379	+	3.12426i	−0.140853	+	0.243964i
$165$		0			0
$166$	−0.779578	−	4.42121i	−0.0605070	−	0.343152i
$167$	−1.85971	+	10.5469i	−0.143909	+	0.816146i	0.824328	+	0.566112i	$0.191553\pi$
$167$	−1.85971	+	10.5469i	−0.143909	+	0.816146i	−0.968237	+	0.250034i	$0.919558\pi$
$168$	−9.90625	−	3.60558i	−0.764284	−	0.278177i
$169$	12.2531	−	10.2816i	0.942546	−	0.790890i
$170$		0			0
$171$	11.5976	+	15.8282i	0.886891	+	1.21041i
$172$	−3.27648			−0.249829
$173$	2.37970	−	1.99680i	0.180925	−	0.151814i	−0.547827	−	0.836591i	$-0.684545\pi$
$173$	2.37970	−	1.99680i	0.180925	−	0.151814i	0.728752	+	0.684777i	$0.240101\pi$
$174$	17.5605	+	6.39150i	1.33126	+	0.484538i
$175$		0			0
$176$	0.994718	+	5.64133i	0.0749797	+	0.425231i
$177$	6.72939	−	2.44930i	0.505812	−	0.184101i
$178$	−0.513434	+	0.889294i	−0.0384835	+	0.0666554i
$179$	10.5528	+	18.2779i	0.788751	+	1.36616i	0.926732	+	0.375723i	$0.122605\pi$
$179$	10.5528	+	18.2779i	0.788751	+	1.36616i	−0.137981	+	0.990435i	$0.544061\pi$
$180$		0			0
$181$	−3.41410	−	2.86477i	−0.253768	−	0.212936i	0.507025	−	0.861931i	$-0.330745\pi$
$181$	−3.41410	−	2.86477i	−0.253768	−	0.212936i	−0.760793	+	0.648995i	$0.775190\pi$
$182$	10.3628	+	17.9489i	0.768144	+	1.33046i
$183$	8.33816	−	14.4421i	0.616374	−	1.06759i
$184$	−1.48280	+	0.539695i	−0.109313	+	0.0397868i
$185$		0			0
$186$	2.92561	−	16.5920i	0.214516	−	1.21658i
$187$	7.39633	+	2.69204i	0.540873	+	0.196862i
$188$	−5.55187	+	4.65857i	−0.404912	+	0.339761i
$189$	−15.8307			−1.15151
$190$		0			0
$191$	−8.06392			−0.583485			−0.291743	−	0.956497i	$-0.594235\pi$
$191$	−8.06392			−0.583485			−0.291743	+	0.956497i	$0.594235\pi$
$192$	2.09813	−	1.76054i	0.151420	−	0.127056i
$193$	0.633380	+	0.230531i	0.0455917	+	0.0165940i	0.364715	−	0.931119i	$-0.381166\pi$
$193$	0.633380	+	0.230531i	0.0455917	+	0.0165940i	−0.319124	+	0.947713i	$0.603389\pi$
$194$	−0.229437	+	1.30120i	−0.0164726	+	0.0934208i
$195$		0			0
$196$	−7.34329	+	2.67274i	−0.524521	+	0.190910i
$197$	3.67816	−	6.37075i	0.262058	−	0.453897i	−0.704731	−	0.709475i	$-0.748932\pi$
$197$	3.67816	−	6.37075i	0.262058	−	0.453897i	0.966789	+	0.255577i	$0.0822656\pi$
$198$	12.8936	+	22.3324i	0.916308	+	1.58709i
$199$	−21.0911	−	17.6976i	−1.49511	−	1.25455i	−0.887926	−	0.459986i	$-0.847854\pi$
$199$	−21.0911	−	17.6976i	−1.49511	−	1.25455i	−0.607185	−	0.794561i	$-0.707701\pi$
$200$		0			0
$201$	−8.60026	−	14.8961i	−0.606616	−	1.05069i
$202$	−7.27192	+	12.5953i	−0.511650	+	0.886204i
$203$	24.6776	−	8.98190i	1.73203	−	0.630406i
$204$	−0.653506	−	3.70622i	−0.0457546	−	0.259487i
$205$		0			0
$206$	−7.13319	−	2.59627i	−0.496993	−	0.180891i
$207$	−5.44158	+	4.56602i	−0.378216	+	0.317361i
$208$	−5.38473			−0.373364
$209$	−6.97916	−	23.9741i	−0.482759	−	1.65832i
$210$		0			0
$211$	−16.3598	+	13.7275i	−1.12625	+	0.945038i	−0.998903	−	0.0468202i	$-0.985091\pi$
$211$	−16.3598	+	13.7275i	−1.12625	+	0.945038i	−0.127349	+	0.991858i	$0.540647\pi$
$212$	−11.0643	−	4.02706i	−0.759897	−	0.276580i
$213$	−5.91868	+	33.5665i	−0.405541	+	2.29994i
$214$	0.236964	+	1.34389i	0.0161986	+	0.0918665i
$215$		0			0
$216$	2.05648	−	3.56193i	0.139926	−	0.242359i
$217$	−11.8381	−	20.5042i	−0.803622	−	1.39191i
$218$	−5.44524	−	4.56910i	−0.368798	−	0.309458i
$219$	19.7797	+	16.5972i	1.33659	+	1.12153i
$220$		0			0
$221$	−3.69942	+	6.40759i	−0.248850	+	0.431021i
$222$	4.87481	−	1.77428i	0.327176	−	0.119082i
$223$	−3.27485	−	18.5726i	−0.219300	−	1.24371i	−0.873286	−	0.487207i	$-0.838016\pi$
$223$	−3.27485	−	18.5726i	−0.219300	−	1.24371i	0.653986	−	0.756506i	$-0.273095\pi$
$224$	0.668367	−	3.79050i	0.0446571	−	0.253263i
$225$		0			0
$226$	8.47516	−	7.11151i	0.563759	−	0.473050i
$227$	5.24641			0.348217			0.174108	−	0.984727i	$-0.444296\pi$
$227$	5.24641			0.348217			0.174108	+	0.984727i	$0.444296\pi$
$228$	−8.25862	+	8.62131i	−0.546940	+	0.570961i
$229$	−3.56871			−0.235827			−0.117913	−	0.993024i	$-0.537621\pi$
$229$	−3.56871			−0.235827			−0.117913	+	0.993024i	$0.537621\pi$
$230$		0			0
$231$	56.7465	+	20.6541i	3.73365	+	1.35894i
$232$	−1.18479	+	6.71929i	−0.0777854	+	0.441143i
$233$	−0.961571	−	5.45334i	−0.0629946	−	0.357260i	−0.999969	−	0.00786247i	$-0.997497\pi$
$233$	−0.961571	−	5.45334i	−0.0629946	−	0.357260i	0.936974	−	0.349398i	$-0.113614\pi$
$234$	−22.7784	+	8.29067i	−1.48907	+	0.541978i
$235$		0			0
$236$	1.30732	+	2.26434i	0.0850991	+	0.147396i
$237$	16.2346	+	13.6225i	1.05455	+	0.884873i
$238$	−4.05134	−	3.39948i	−0.262609	−	0.220355i
$239$	5.69086	+	9.85686i	0.368111	+	0.637587i	0.989270	−	0.146097i	$-0.0466713\pi$
$239$	5.69086	+	9.85686i	0.368111	+	0.637587i	−0.621159	+	0.783684i	$0.713338\pi$
$240$		0			0
$241$	−10.4113	+	3.78939i	−0.670649	+	0.244096i	−0.654827	−	0.755778i	$-0.727259\pi$
$241$	−10.4113	+	3.78939i	−0.670649	+	0.244096i	−0.0158218	+	0.999875i	$0.505036\pi$
$242$	−3.78797	−	21.4826i	−0.243500	−	1.38096i
$243$	−3.20797	+	18.1933i	−0.205791	+	1.16710i
$244$	5.72146	+	2.08244i	0.366279	+	0.133315i
$245$		0			0
$246$	−9.88089			−0.629983
$247$	23.3328	−	2.54750i	1.48463	−	0.162094i
$248$	6.15130			0.390608
$249$	9.41938	−	7.90380i	0.596929	−	0.500883i
$250$		0			0
$251$	0.628522	−	3.56453i	0.0396720	−	0.224991i	−0.958525	−	0.285007i	$-0.908004\pi$
$251$	0.628522	−	3.56453i	0.0396720	−	0.224991i	0.998197	+	0.0600161i	$0.0191152\pi$
$252$	−3.00877	−	17.0636i	−0.189535	−	1.07490i
$253$	8.49400	−	3.09156i	0.534014	−	0.194365i
$254$	−0.163024	+	0.282367i	−0.0102291	+	0.0177173i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	8.30685	+	6.97027i	0.518167	+	0.434794i	0.863992	−	0.503505i	$-0.167957\pi$
$257$	8.30685	+	6.97027i	0.518167	+	0.434794i	−0.345825	+	0.938299i	$0.612401\pi$
$258$	−4.48700	−	7.77171i	−0.279348	−	0.483846i
$259$	3.64508	−	6.31346i	0.226494	−	0.392299i
$260$		0			0
$261$	5.33355	+	30.2481i	0.330138	+	1.87231i
$262$	0.913800	−	5.18242i	0.0564548	−	0.320171i
$263$	9.06203	+	3.29831i	0.558789	+	0.203383i	0.605947	−	0.795505i	$-0.292794\pi$
$263$	9.06203	+	3.29831i	0.558789	+	0.203383i	−0.0471583	+	0.998887i	$0.515017\pi$
$264$	−12.0189	+	10.0850i	−0.739709	+	0.620690i
$265$		0			0
$266$	−1.10286	+	16.7410i	−0.0676206	+	1.02646i
$267$	−2.81251			−0.172123
$268$	4.81079	−	4.03673i	0.293866	−	0.246583i
$269$	7.01729	+	2.55409i	0.427852	+	0.155725i	0.546965	−	0.837155i	$-0.315783\pi$
$269$	7.01729	+	2.55409i	0.427852	+	0.155725i	−0.119113	+	0.992881i	$0.538005\pi$
$270$		0			0
$271$	−5.28922	−	29.9967i	−0.321297	−	1.82217i	−0.534509	−	0.845162i	$-0.679504\pi$
$271$	−5.28922	−	29.9967i	−0.321297	−	1.82217i	0.213212	−	0.977006i	$-0.431607\pi$
$272$	1.29118	−	0.469950i	0.0782892	−	0.0284949i
$273$	−28.3829	+	49.1607i	−1.71781	+	2.97534i
$274$	−6.21353	−	10.7622i	−0.375373	−	0.650166i
$275$		0			0
$276$	−3.31078	−	2.77807i	−0.199285	−	0.167220i
$277$	−4.95727	−	8.58624i	−0.297853	−	0.515897i	0.677791	−	0.735254i	$-0.262937\pi$
$277$	−4.95727	−	8.58624i	−0.297853	−	0.515897i	−0.975645	+	0.219357i	$0.929604\pi$
$278$	−3.11503	+	5.39539i	−0.186827	+	0.323594i
$279$	26.0212	−	9.47093i	1.55785	−	0.567010i
$280$		0			0
$281$	−2.79030	+	15.8246i	−0.166455	+	0.944015i	0.781096	+	0.624411i	$0.214661\pi$
$281$	−2.79030	+	15.8246i	−0.166455	+	0.944015i	−0.947551	+	0.319604i	$0.896450\pi$
$282$	−18.6531	−	6.78916i	−1.11077	−	0.404289i
$283$	7.72748	−	6.48413i	0.459351	−	0.385441i	−0.383541	−	0.923524i	$-0.625296\pi$
$283$	7.72748	−	6.48413i	0.459351	−	0.385441i	0.842892	+	0.538082i	$0.180851\pi$
$284$	−12.4444			−0.738442
$285$		0			0
$286$	30.8456			1.82394
$287$	−10.6369	+	8.92543i	−0.627877	+	0.526851i
$288$	4.23019	+	1.53966i	0.249266	+	0.0907255i
$289$	−2.62417	+	14.8824i	−0.154363	+	0.875436i
$290$		0			0
$291$	−3.40062	+	1.23772i	−0.199348	+	0.0725567i
$292$	−4.71365	+	8.16429i	−0.275846	+	0.477779i
$293$	2.63255	+	4.55971i	0.153795	+	0.266381i	0.932620	−	0.360861i	$-0.117517\pi$
$293$	2.63255	+	4.55971i	0.153795	+	0.266381i	−0.778824	+	0.627242i	$0.784184\pi$
$294$	−16.3960	−	13.7579i	−0.956235	−	0.802376i
$295$		0			0
$296$	0.947027	+	1.64030i	0.0550448	+	0.0953405i
$297$	−11.7803	+	20.4040i	−0.683560	+	1.18396i
$298$	21.4638	−	7.81220i	1.24337	−	0.452549i
$299$	1.47547	+	8.36781i	0.0853287	+	0.483923i
$300$		0			0
$301$	−11.8505	−	4.31324i	−0.683052	−	0.248611i
$302$	−5.13281	+	4.30694i	−0.295360	+	0.247837i
$303$	−39.8344			−2.28843
$304$	−3.62349	−	2.42288i	−0.207821	−	0.138962i
$305$		0			0
$306$	4.73836	−	3.97596i	0.270874	−	0.227290i
$307$	−29.1979	−	10.6272i	−1.66641	−	0.606524i	−0.675061	−	0.737762i	$-0.735883\pi$
$307$	−29.1979	−	10.6272i	−1.66641	−	0.606524i	−0.991351	+	0.131238i	$0.958105\pi$
$308$	−3.82864	+	21.7133i	−0.218157	+	1.23723i
$309$	−3.61033	−	20.4752i	−0.205385	−	1.16479i
$310$		0			0
$311$	8.97919	−	15.5524i	0.509163	−	0.881897i	−0.490780	−	0.871283i	$-0.663288\pi$
$311$	8.97919	−	15.5524i	0.509163	−	0.881897i	0.999944	−	0.0106135i	$-0.00337844\pi$
$312$	−7.37416	−	12.7724i	−0.417480	−	0.723096i
$313$	−11.4377	−	9.59739i	−0.646499	−	0.542477i	0.259508	−	0.965741i	$-0.416440\pi$
$313$	−11.4377	−	9.59739i	−0.646499	−	0.542477i	−0.906006	+	0.423264i	$0.860884\pi$
$314$	−0.0288926	−	0.0242438i	−0.00163050	−	0.00136815i
$315$		0			0
$316$	−3.86882	+	6.70100i	−0.217638	+	0.376961i
$317$	8.48754	−	3.08921i	0.476708	−	0.173507i	−0.0924808	−	0.995714i	$-0.529480\pi$
$317$	8.48754	−	3.08921i	0.476708	−	0.173507i	0.569188	+	0.822207i	$0.307257\pi$
$318$	−5.59998	−	31.7590i	−0.314031	−	1.78096i
$319$	6.78691	−	38.4905i	0.379994	−	2.15505i
$320$		0			0
$321$	−2.86316	+	2.40248i	−0.159806	+	0.134093i
$322$	−6.07353			−0.338465
$323$	−5.37253	+	2.64722i	−0.298936	+	0.147295i
$324$	−2.23996			−0.124442
$325$		0			0
$326$	−10.9310	−	3.97855i	−0.605410	−	0.220351i
$327$	3.38074	−	19.1731i	0.186955	−	1.06028i
$328$	−0.626451	−	3.55278i	−0.0345900	−	0.196170i
$329$	−26.2130	+	9.54073i	−1.44517	+	0.525998i
$330$		0			0
$331$	17.1733	+	29.7451i	0.943931	+	1.63494i	0.757877	+	0.652397i	$0.226237\pi$
$331$	17.1733	+	29.7451i	0.943931	+	1.63494i	0.186054	+	0.982540i	$0.440430\pi$
$332$	3.43909	+	2.88574i	0.188744	+	0.158375i
$333$	6.53161	+	5.48067i	0.357930	+	0.300339i
$334$	−5.35482	−	9.27482i	−0.293003	−	0.507495i
$335$		0			0
$336$	9.90625	−	3.60558i	0.540430	−	0.196701i
$337$	2.01036	+	11.4013i	0.109511	+	0.621068i	0.989322	+	0.145745i	$0.0465578\pi$
$337$	2.01036	+	11.4013i	0.109511	+	0.621068i	−0.879811	+	0.475323i	$0.842331\pi$
$338$	−2.77755	+	15.7523i	−0.151079	+	0.856811i
$339$	28.4747	+	10.3639i	1.54653	+	0.562892i
$340$		0			0
$341$	−35.2368			−1.90818
$342$	−19.0585	−	4.67030i	−1.03056	−	0.252541i
$343$	−3.13526			−0.169288
$344$	2.50993	−	2.10608i	0.135326	−	0.113552i
$345$		0			0
$346$	−0.539433	+	3.05928i	−0.0290001	+	0.164468i
$347$	−0.301806	−	1.71163i	−0.0162018	−	0.0918849i	0.975635	−	0.219402i	$-0.0704105\pi$
$347$	−0.301806	−	1.71163i	−0.0162018	−	0.0918849i	−0.991836	+	0.127517i	$0.959299\pi$
$348$	−17.5605	+	6.39150i	−0.941342	+	0.342620i
$349$	1.15031	−	1.99239i	0.0615744	−	0.106650i	−0.833595	−	0.552376i	$-0.813721\pi$
$349$	1.15031	−	1.99239i	0.0615744	−	0.106650i	0.895169	+	0.445726i	$0.147055\pi$
$350$		0			0
$351$	−16.9657	−	14.2359i	−0.905563	−	0.759858i
$352$	−4.38817	−	3.68212i	−0.233890	−	0.196257i
$353$	14.7355	+	25.5226i	0.784291	+	1.35843i	0.929421	+	0.369020i	$0.120307\pi$
$353$	14.7355	+	25.5226i	0.784291	+	1.35843i	−0.145130	+	0.989413i	$0.546360\pi$
$354$	−3.58064	+	6.20184i	−0.190309	+	0.329624i
$355$		0			0
$356$	−0.178314	−	1.01127i	−0.00945061	−	0.0535971i
$357$	2.51533	−	14.2651i	0.133125	−	0.754990i
$358$	−19.8327	−	7.21852i	−1.04819	−	0.381511i
$359$	10.6986	−	8.97719i	0.564651	−	0.473798i	−0.315215	−	0.949020i	$-0.602077\pi$
$359$	10.6986	−	8.97719i	0.564651	−	0.473798i	0.879866	+	0.475222i	$0.157632\pi$
$360$		0			0
$361$	16.8474	+	8.78444i	0.886703	+	0.462339i
$362$	4.45679			0.234243
$363$	45.7688	−	38.4046i	2.40224	−	2.01572i
$364$	−19.4757	−	7.08859i	−1.02081	−	0.371543i
$365$		0			0
$366$	2.89581	+	16.4230i	0.151367	+	0.858442i
$367$	−27.9058	+	10.1569i	−1.45667	+	0.530185i	−0.944446	−	0.328666i	$-0.893401\pi$
$367$	−27.9058	+	10.1569i	−1.45667	+	0.530185i	−0.512226	+	0.858851i	$0.671179\pi$
$368$	0.788981	−	1.36656i	0.0411285	−	0.0712366i
$369$	−8.12009	−	14.0644i	−0.422715	−	0.732164i
$370$		0			0
$371$	−34.7165	−	29.1306i	−1.80239	−	1.51238i
$372$	8.42396	+	14.5907i	0.436762	+	0.756494i
$373$	5.77175	−	9.99697i	0.298850	−	0.517624i	−0.677023	−	0.735962i	$-0.736730\pi$
$373$	5.77175	−	9.99697i	0.298850	−	0.517624i	0.975873	+	0.218338i	$0.0700636\pi$
$374$	−7.39633	+	2.69204i	−0.382455	+	0.139202i
$375$		0			0
$376$	1.25851	−	7.13735i	0.0649026	−	0.368081i
$377$	34.5240	+	12.5657i	1.77808	+	0.647168i
$378$	12.1270	−	10.1758i	0.623745	−	0.523384i
$379$	8.96195			0.460345			0.230172	−	0.973150i	$-0.426071\pi$
$379$	8.96195			0.460345			0.230172	+	0.973150i	$0.426071\pi$
$380$		0			0
$381$	−0.893021			−0.0457509
$382$	6.17732	−	5.18339i	0.316059	−	0.265205i
$383$	27.2194	+	9.90707i	1.39085	+	0.506227i	0.925449	−	0.378873i	$-0.123688\pi$
$383$	27.2194	+	9.90707i	1.39085	+	0.506227i	0.465400	+	0.885101i	$0.345911\pi$
$384$	−0.475608	+	2.69731i	−0.0242708	+	0.137646i
$385$		0			0
$386$	−0.633380	+	0.230531i	−0.0322382	+	0.0117337i
$387$	7.37481	−	12.7735i	0.374883	−	0.649316i
$388$	−0.660637	−	1.14426i	−0.0335388	−	0.0580909i
$389$	13.7913	+	11.5723i	0.699247	+	0.586738i	0.921559	−	0.388238i	$-0.126916\pi$
$389$	13.7913	+	11.5723i	0.699247	+	0.586738i	−0.222312	+	0.974976i	$0.571360\pi$
$390$		0			0
$391$	−1.08409	−	1.87771i	−0.0548250	−	0.0949597i
$392$	3.90728	−	6.76762i	0.197348	−	0.341816i
$393$	13.5440	−	4.92960i	0.683203	−	0.248665i
$394$	1.27741	+	7.24455i	0.0643550	+	0.364975i
$395$		0			0
$396$	−24.2320	−	8.81974i	−1.21771	−	0.443208i
$397$	14.2345	−	11.9441i	0.714407	−	0.599458i	−0.211425	−	0.977394i	$-0.567810\pi$
$397$	14.2345	−	11.9441i	0.714407	−	0.599458i	0.925832	+	0.377936i	$0.123366\pi$
$398$	27.5325			1.38008
$399$	−41.2195	+	20.3101i	−2.06356	+	1.01678i
$400$		0			0
$401$	21.6450	−	18.1623i	1.08090	−	0.906981i	0.0849030	−	0.996389i	$-0.472942\pi$
$401$	21.6450	−	18.1623i	1.08090	−	0.906981i	0.995995	+	0.0894080i	$0.0284975\pi$
$402$	16.1632	+	5.88293i	0.806148	+	0.293414i
$403$	5.75176	−	32.6199i	0.286516	−	1.62491i
$404$	−2.52551	−	14.3229i	−0.125649	−	0.712590i
$405$		0			0
$406$	−13.1307	+	22.7430i	−0.651664	+	1.12871i
$407$	−5.42491	−	9.39622i	−0.268903	−	0.465753i
$408$	2.88293	+	2.41906i	0.142726	+	0.119761i
$409$	26.3573	+	22.1164i	1.30329	+	1.09359i	0.989567	+	0.144071i	$0.0460192\pi$
$409$	26.3573	+	22.1164i	1.30329	+	1.09359i	0.313718	+	0.949516i	$0.398425\pi$
$410$		0			0
$411$	17.0184	−	29.4767i	0.839454	−	1.45398i
$412$	7.13319	−	2.59627i	0.351427	−	0.127909i
$413$	1.74753	+	9.91076i	0.0859906	+	0.487677i
$414$	1.23351	−	6.99556i	0.0606235	−	0.343813i
$415$		0			0
$416$	4.12494	−	3.46124i	0.202242	−	0.169701i
$417$	−17.0636			−0.835610
$418$	20.7566	+	13.8791i	1.01524	+	0.678850i
$419$	0.950291			0.0464248			0.0232124	−	0.999731i	$-0.492611\pi$
$419$	0.950291			0.0464248			0.0232124	+	0.999731i	$0.492611\pi$
$420$		0			0
$421$	−20.5965	−	7.49650i	−1.00381	−	0.365357i	−0.212757	−	0.977105i	$-0.568244\pi$
$421$	−20.5965	−	7.49650i	−1.00381	−	0.365357i	−0.791052	+	0.611748i	$0.790467\pi$
$422$	3.70846	−	21.0317i	0.180525	−	1.02381i
$423$	−5.66539	−	32.1300i	−0.275461	−	1.56222i
$424$	11.0643	−	4.02706i	0.537328	−	0.195572i
$425$		0			0
$426$	−17.0422	−	29.5179i	−0.825695	−	1.43015i
$427$	17.9523	+	15.0638i	0.868772	+	0.728986i
$428$	−1.04536	−	0.877163i	−0.0505295	−	0.0423993i
$429$	42.2418	+	73.1650i	2.03945	+	3.53244i
$430$		0			0
$431$	23.5122	−	8.55773i	1.13254	−	0.412211i	0.293327	−	0.956012i	$-0.405238\pi$
$431$	23.5122	−	8.55773i	1.13254	−	0.412211i	0.839214	+	0.543801i	$0.183015\pi$
$432$	0.714208	+	4.05048i	0.0343624	+	0.194879i
$433$	6.76319	−	38.3559i	0.325018	−	1.84327i	−0.184531	−	0.982827i	$-0.559077\pi$
$433$	6.76319	−	38.3559i	0.325018	−	1.84327i	0.509549	−	0.860442i	$-0.329812\pi$
$434$	22.2483	+	8.09773i	1.06795	+	0.388704i
$435$		0			0
$436$	7.10825			0.340424
$437$	−2.77226	+	6.29475i	−0.132615	+	0.301119i
$438$	−25.8206			−1.23376
$439$	3.73509	−	3.13411i	0.178266	−	0.149583i	−0.549289	−	0.835633i	$-0.685101\pi$
$439$	3.73509	−	3.13411i	0.178266	−	0.149583i	0.727555	+	0.686050i	$0.240657\pi$
$440$		0			0
$441$	6.10871	−	34.6442i	0.290891	−	1.64972i
$442$	−1.28480	−	7.28644i	−0.0611115	−	0.346581i
$443$	−19.4713	+	7.08698i	−0.925110	+	0.336712i	−0.760269	−	0.649608i	$-0.774933\pi$
$443$	−19.4713	+	7.08698i	−0.925110	+	0.336712i	−0.164840	+	0.986320i	$0.552711\pi$
$444$	−2.59383	+	4.49265i	−0.123098	+	0.213212i
$445$		0			0
$446$	14.4469	+	12.1224i	0.684082	+	0.574013i
$447$	47.9242	+	40.2132i	2.26674	+	1.90202i
$448$	1.92448	+	3.33331i	0.0909234	+	0.157484i
$449$	−8.39412	+	14.5390i	−0.396143	+	0.686140i	−0.993246	−	0.116024i	$-0.962985\pi$
$449$	−8.39412	+	14.5390i	−0.396143	+	0.686140i	0.597103	+	0.802164i	$0.296318\pi$
$450$		0			0
$451$	3.58853	+	20.3516i	0.168978	+	0.958319i
$452$	−1.92116	+	10.8955i	−0.0903639	+	0.512479i
$453$	−17.2451	−	6.27671i	−0.810247	−	0.294906i
$454$	−4.01899	+	3.37233i	−0.188620	+	0.158271i
$455$		0			0
$456$	0.784792	−	11.9128i	0.0367513	−	0.557870i
$457$	−8.48651			−0.396982			−0.198491	−	0.980103i	$-0.563604\pi$
$457$	−8.48651			−0.396982			−0.198491	+	0.980103i	$0.563604\pi$
$458$	2.73379	−	2.29392i	0.127742	−	0.107188i
$459$	5.31057	+	1.93289i	0.247876	+	0.0902195i
$460$		0			0
$461$	−5.74433	−	32.5777i	−0.267540	−	1.51730i	−0.761703	−	0.647926i	$-0.775637\pi$
$461$	−5.74433	−	32.5777i	−0.267540	−	1.51730i	0.494163	−	0.869369i	$-0.335475\pi$
$462$	−56.7465	+	20.6541i	−2.64009	+	0.960913i
$463$	−15.6037	+	27.0264i	−0.725165	+	1.25602i	0.233741	+	0.972299i	$0.424903\pi$
$463$	−15.6037	+	27.0264i	−0.725165	+	1.25602i	−0.958906	+	0.283724i	$0.908430\pi$
$464$	−3.41147	−	5.90885i	−0.158374	−	0.274311i
$465$		0			0
$466$	4.24195	+	3.55942i	0.196504	+	0.164887i
$467$	8.81413	+	15.2665i	0.407869	+	0.706450i	0.994651	−	0.103295i	$-0.0329386\pi$
$467$	8.81413	+	15.2665i	0.407869	+	0.706450i	−0.586782	+	0.809745i	$0.699605\pi$
$468$	12.1201	−	20.9927i	0.560254	−	0.970388i
$469$	22.7140	−	8.26721i	1.04883	−	0.381744i
$470$		0			0
$471$	0.0179383	−	0.101733i	0.000826554	−	0.00468762i
$472$	−2.45695	−	0.894258i	−0.113090	−	0.0411616i
$473$	−14.3777	+	12.0644i	−0.661090	+	0.554720i
$474$	−21.1928			−0.973416
$475$		0			0
$476$	5.28865			0.242405
$477$	40.6036	−	34.0705i	1.85911	−	1.55998i
$478$	−10.6953	−	3.89278i	−0.489192	−	0.178051i
$479$	2.69595	−	15.2895i	0.123181	−	0.698596i	−0.859190	−	0.511656i	$-0.829032\pi$
$479$	2.69595	−	15.2895i	0.123181	−	0.698596i	0.982371	−	0.186939i	$-0.0598568\pi$
$480$		0			0
$481$	9.58389	−	3.48825i	0.436988	−	0.159051i
$482$	5.53972	−	9.59508i	0.252328	−	0.437044i
$483$	−8.31745	−	14.4063i	−0.378457	−	0.655507i
$484$	16.7105	+	14.0218i	0.759570	+	0.637355i
$485$		0			0
$486$	−9.23697	−	15.9989i	−0.418997	−	0.725725i
$487$	12.0831	−	20.9286i	0.547538	−	0.948364i	−0.450904	−	0.892572i	$-0.648898\pi$
$487$	12.0831	−	20.9286i	0.547538	−	0.948364i	0.998442	−	0.0557919i	$-0.0177684\pi$
$488$	−5.72146	+	2.08244i	−0.258998	+	0.0942677i
$489$	−5.53251	−	31.3764i	−0.250189	−	1.41889i
$490$		0			0
$491$	−5.53601	−	2.01494i	−0.249837	−	0.0909331i	0.214066	−	0.976819i	$-0.431329\pi$
$491$	−5.53601	−	2.01494i	−0.249837	−	0.0909331i	−0.463903	+	0.885886i	$0.653551\pi$
$492$	7.56920	−	6.35131i	0.341246	−	0.286339i
$493$	−9.37502			−0.422230
$494$	−16.2365	+	16.9495i	−0.730514	+	0.762596i
$495$		0			0
$496$	−4.71217	+	3.95398i	−0.211583	+	0.177539i
$497$	−45.0097	−	16.3822i	−2.01896	−	0.734841i
$498$	−2.13520	+	12.1093i	−0.0956806	+	0.542632i
$499$	−4.15373	−	23.5570i	−0.185947	−	1.05456i	−0.924733	−	0.380616i	$-0.875712\pi$
$499$	−4.15373	−	23.5570i	−0.185947	−	1.05456i	0.738786	−	0.673940i	$-0.235399\pi$
$500$		0			0
$501$	14.6664	−	25.4030i	0.655247	−	1.13492i
$502$	1.80976	+	3.13459i	0.0807734	+	0.139904i
$503$	−22.1288	−	18.5683i	−0.986675	−	0.827919i	−0.00159206	−	0.999999i	$-0.500507\pi$
$503$	−22.1288	−	18.5683i	−0.986675	−	0.827919i	−0.985083	+	0.172080i	$0.944951\pi$
$504$	13.2731	+	11.1375i	0.591231	+	0.496102i
$505$		0			0
$506$	−4.51957	+	7.82812i	−0.200919	+	0.348002i
$507$	−41.1677	+	14.9838i	−1.82832	+	0.665455i
$508$	−0.0566178	−	0.321096i	−0.00251201	−	0.0142463i
$509$	−3.15957	+	17.9188i	−0.140046	+	0.794238i	0.831167	+	0.556023i	$0.187673\pi$
$509$	−3.15957	+	17.9188i	−0.140046	+	0.794238i	−0.971212	+	0.238215i	$0.923438\pi$
$510$		0			0
$511$	−27.7962	+	23.3238i	−1.22963	+	1.03178i
$512$	−1.00000			−0.0441942
$513$	−5.01104	−	17.2134i	−0.221243	−	0.759991i
$514$	−10.8438			−0.478301
$515$		0			0
$516$	8.43280	+	3.06929i	0.371233	+	0.135118i
$517$	−7.20918	+	40.8853i	−0.317059	+	1.79813i
$518$	1.26592	+	7.17940i	0.0556215	+	0.315445i
$519$	−7.99525	+	2.91003i	−0.350953	+	0.127736i
$520$		0			0
$521$	−7.21014	−	12.4883i	−0.315882	−	0.547124i	0.663743	−	0.747961i	$-0.268967\pi$
$521$	−7.21014	−	12.4883i	−0.315882	−	0.547124i	−0.979625	+	0.200837i	$0.935634\pi$
$522$	−23.5288	−	19.7430i	−1.02983	−	0.864128i
$523$	14.8626	+	12.4712i	0.649895	+	0.545326i	0.907039	−	0.421047i	$-0.138337\pi$
$523$	14.8626	+	12.4712i	0.649895	+	0.545326i	−0.257144	+	0.966373i	$0.582782\pi$
$524$	2.63118	+	4.55734i	0.114944	+	0.199088i
$525$		0			0
$526$	−9.06203	+	3.29831i	−0.395123	+	0.143813i
$527$	1.46770	+	8.32375i	0.0639341	+	0.362588i
$528$	2.72445	−	15.4511i	0.118567	−	0.672424i
$529$	19.2731	+	7.01484i	0.837962	+	0.304993i
$530$		0			0
$531$	−11.7702			−0.510785
$532$	−9.91606	−	13.5332i	−0.429916	−	0.586740i
$533$	−19.4259			−0.841428
$534$	2.15451	−	1.80784i	0.0932346	−	0.0782331i
$535$		0			0
$536$	−1.09052	+	6.18464i	−0.0471032	+	0.267136i
$537$	−10.0380	−	56.9282i	−0.433171	−	2.45663i
$538$	−7.01729	+	2.55409i	−0.302537	+	0.110114i
$539$	−22.3823	+	38.7673i	−0.964075	+	1.66983i
$540$		0			0
$541$	13.0794	+	10.9749i	0.562328	+	0.471849i	0.879090	−	0.476656i	$-0.158151\pi$
$541$	13.0794	+	10.9749i	0.562328	+	0.471849i	−0.316762	+	0.948505i	$0.602596\pi$
$542$	23.3333	+	19.5789i	1.00225	+	0.840988i
$543$	6.10339	+	10.5714i	0.261921	+	0.453661i
$544$	−0.687022	+	1.18996i	−0.0294558	+	0.0510190i
$545$		0			0
$546$	−9.85729	−	55.9035i	−0.421853	−	2.39245i
$547$	4.93480	−	27.9866i	0.210997	−	1.19662i	−0.676723	−	0.736238i	$-0.736601\pi$
$547$	4.93480	−	27.9866i	0.210997	−	1.19662i	0.887720	−	0.460384i	$-0.152288\pi$
$548$	11.6776	+	4.25031i	0.498843	+	0.181564i
$549$	−20.9966	+	17.6182i	−0.896113	+	0.751928i
$550$		0			0
$551$	17.5779	+	23.9900i	0.748843	+	1.02201i
$552$	4.32191			0.183953
$553$	−22.8143	+	19.1435i	−0.970163	+	0.814063i
$554$	9.31661	+	3.39097i	0.395825	+	0.144068i
$555$		0			0
$556$	−1.08184	−	6.13541i	−0.0458802	−	0.260200i
$557$	33.9699	−	12.3640i	1.43935	−	0.523881i	0.499755	−	0.866167i	$-0.333424\pi$
$557$	33.9699	−	12.3640i	1.43935	−	0.523881i	0.939596	+	0.342286i	$0.111201\pi$
$558$	−13.8456	+	23.9812i	−0.586130	+	1.01521i
$559$	−8.82146	−	15.2792i	−0.373108	−	0.646242i
$560$		0			0
$561$	−16.5144	−	13.8572i	−0.697239	−	0.585053i
$562$	−8.03435	−	13.9159i	−0.338908	−	0.587007i
$563$	0.229547	−	0.397587i	0.00967424	−	0.0167563i	−0.861148	−	0.508355i	$-0.830254\pi$
$563$	0.229547	−	0.397587i	0.00967424	−	0.0167563i	0.870822	+	0.491598i	$0.163587\pi$
$564$	18.6531	−	6.78916i	0.785436	−	0.285875i
$565$		0			0
$566$	−1.75168	+	9.93426i	−0.0736285	+	0.417568i
$567$	−8.10158	−	2.94873i	−0.340234	−	0.123835i
$568$	9.53300	−	7.99914i	0.399996	−	0.335636i
$569$	11.7203			0.491339			0.245670	−	0.969354i	$-0.420992\pi$
$569$	11.7203			0.491339			0.245670	+	0.969354i	$0.420992\pi$
$570$		0			0
$571$	2.30956			0.0966521			0.0483260	−	0.998832i	$-0.484611\pi$
$571$	2.30956			0.0966521			0.0483260	+	0.998832i	$0.484611\pi$
$572$	−23.6291	+	19.8272i	−0.987983	+	0.829016i
$573$	20.7545	+	7.55400i	0.867030	+	0.315573i
$574$	2.41119	−	13.6745i	0.100641	−	0.570765i
$575$		0			0
$576$	−4.23019	+	1.53966i	−0.176258	+	0.0641526i
$577$	23.2706	−	40.3059i	0.968768	−	1.67796i	0.269637	−	0.962962i	$-0.413096\pi$
$577$	23.2706	−	40.3059i	0.968768	−	1.67796i	0.699131	−	0.714994i	$-0.253570\pi$
$578$	−7.55600	−	13.0874i	−0.314288	−	0.544363i
$579$	−1.41420	−	1.18666i	−0.0587722	−	0.0493158i
$580$		0			0
$581$	8.63980	+	14.9646i	0.358439	+	0.620835i
$582$	1.80943	−	3.13403i	0.0750034	−	0.129910i
$583$	−63.3801	+	23.0685i	−2.62493	+	0.955398i
$584$	−1.63703	−	9.28408i	−0.0677410	−	0.384178i
$585$		0			0
$586$	−4.94758	−	1.80077i	−0.204383	−	0.0743892i
$587$	−2.23737	+	1.87738i	−0.0923462	+	0.0774876i	−0.687792	−	0.725908i	$-0.741420\pi$
$587$	−2.23737	+	1.87738i	−0.0923462	+	0.0774876i	0.595446	+	0.803395i	$0.296975\pi$
$588$	21.4035			0.882664
$589$	18.5479	−	19.3625i	0.764254	−	0.797818i
$590$		0			0
$591$	−15.4345	+	12.9511i	−0.634891	+	0.532737i
$592$	−1.77983	−	0.647805i	−0.0731505	−	0.0266246i
$593$	2.55975	−	14.5170i	0.105116	−	0.596144i	−0.886058	−	0.463575i	$-0.846566\pi$
$593$	2.55975	−	14.5170i	0.105116	−	0.596144i	0.991174	−	0.132569i	$-0.0423225\pi$
$594$	−4.09124	−	23.2026i	−0.167866	−	0.952013i
$595$		0			0
$596$	−11.4207	+	19.7812i	−0.467809	+	0.810269i
$597$	37.7047	+	65.3064i	1.54315	+	2.67281i
$598$	−6.50900	−	5.46170i	−0.266173	−	0.223346i
$599$	4.45027	+	3.73422i	0.181833	+	0.152576i	0.729161	−	0.684342i	$-0.239911\pi$
$599$	4.45027	+	3.73422i	0.181833	+	0.152576i	−0.547328	+	0.836918i	$0.684355\pi$
$600$		0			0
$601$	3.34531	−	5.79425i	0.136458	−	0.236352i	−0.789695	−	0.613499i	$-0.789761\pi$
$601$	3.34531	−	5.79425i	0.136458	−	0.236352i	0.926153	+	0.377147i	$0.123095\pi$
$602$	11.8505	−	4.31324i	0.482991	−	0.175794i
$603$	4.90916	+	27.8412i	0.199916	+	1.13378i
$604$	1.16351	−	6.59862i	0.0473427	−	0.268494i
$605$		0			0
$606$	30.5149	−	25.6050i	1.23958	−	1.04013i
$607$	−40.7346			−1.65337			−0.826684	−	0.562667i	$-0.809775\pi$
$607$	−40.7346			−1.65337			−0.826684	+	0.562667i	$0.809775\pi$
$608$	4.33315	−	0.473097i	0.175732	−	0.0191866i
$609$	−71.9276			−2.91465
$610$		0			0
$611$	−36.6720	−	13.3475i	−1.48359	−	0.539983i
$612$	−1.07410	+	6.09152i	−0.0434179	+	0.246235i
$613$	−0.989765	−	5.61324i	−0.0399762	−	0.226716i	0.958274	−	0.285852i	$-0.0922766\pi$
$613$	−0.989765	−	5.61324i	−0.0399762	−	0.226716i	−0.998250	+	0.0591357i	$0.981166\pi$
$614$	29.1979	−	10.6272i	1.17833	−	0.428877i
$615$		0			0
$616$	−11.0241	−	19.0944i	−0.444175	−	0.769334i
$617$	−3.88361	−	3.25873i	−0.156348	−	0.131192i	0.561258	−	0.827641i	$-0.310318\pi$
$617$	−3.88361	−	3.25873i	−0.156348	−	0.131192i	−0.717606	+	0.696449i	$0.754762\pi$
$618$	15.9269	+	13.3643i	0.640674	+	0.537589i
$619$	4.89822	+	8.48397i	0.196876	+	0.341000i	0.947514	−	0.319714i	$-0.103587\pi$
$619$	4.89822	+	8.48397i	0.196876	+	0.341000i	−0.750638	+	0.660714i	$0.770254\pi$
$620$		0			0
$621$	6.09870	−	2.21974i	0.244732	−	0.0890753i
$622$	3.11844	+	17.6856i	0.125038	+	0.709126i
$623$	0.686324	−	3.89234i	0.0274970	−	0.155943i
$624$	13.8589	+	5.04423i	0.554800	+	0.201931i
$625$		0			0
$626$	14.9309			0.596759
$627$	−4.49557	+	68.2410i	−0.179536	+	2.72528i
$628$	0.0377166			0.00150506
$629$	−1.99364	+	1.67286i	−0.0794916	+	0.0667014i
$630$		0			0
$631$	−3.95112	+	22.4079i	−0.157292	+	0.892045i	0.799369	+	0.600840i	$0.205167\pi$
$631$	−3.95112	+	22.4079i	−0.157292	+	0.892045i	−0.956661	+	0.291205i	$0.905944\pi$
$632$	−1.34363	−	7.62009i	−0.0534466	−	0.303111i
$633$	54.9652	−	20.0057i	2.18467	−	0.795155i
$634$	−4.51612	+	7.82216i	−0.179358	+	0.310658i
$635$		0			0
$636$	24.7042	+	20.7292i	0.979583	+	0.821968i
$637$	−32.2346	−	27.0481i	−1.27718	−	1.07168i
$638$	19.5421	+	33.8480i	0.773681	+	1.34005i
$639$	28.0104	−	48.5155i	1.10808	−	1.91924i
$640$		0			0
$641$	7.58983	+	43.0441i	0.299780	+	1.70014i	0.647112	+	0.762395i	$0.275977\pi$
$641$	7.58983	+	43.0441i	0.299780	+	1.70014i	−0.347331	+	0.937742i	$0.612912\pi$
$642$	0.649026	−	3.68081i	0.0256150	−	0.145270i
$643$	42.1442	+	15.3392i	1.66201	+	0.604921i	0.990676	−	0.136238i	$-0.0435013\pi$
$643$	42.1442	+	15.3392i	1.66201	+	0.604921i	0.671330	+	0.741159i	$0.265724\pi$
$644$	4.65259	−	3.90399i	0.183338	−	0.153839i
$645$		0			0
$646$	2.41400	−	5.48129i	0.0949776	−	0.215658i
$647$	−3.04207			−0.119596			−0.0597981	−	0.998210i	$-0.519046\pi$
$647$	−3.04207			−0.119596			−0.0597981	+	0.998210i	$0.519046\pi$
$648$	1.71591	−	1.43982i	0.0674071	−	0.0565613i
$649$	14.0743	+	5.12263i	0.552465	+	0.201081i
$650$		0			0
$651$	11.2606	+	63.8620i	0.441337	+	2.50295i
$652$	10.9310	−	3.97855i	0.428090	−	0.155812i
$653$	1.84165	−	3.18983i	0.0720694	−	0.124828i	−0.827739	−	0.561114i	$-0.810373\pi$
$653$	1.84165	−	3.18983i	0.0720694	−	0.124828i	0.899808	+	0.436286i	$0.143706\pi$
$654$	9.73446	+	16.8606i	0.380648	+	0.659301i
$655$		0			0
$656$	2.76357	+	2.31891i	0.107899	+	0.0905383i
$657$	−21.2193	−	36.7530i	−0.827845	−	1.43387i
$658$	13.9476	−	24.1580i	0.543735	−	0.941776i
$659$	−39.2902	+	14.3005i	−1.53053	+	0.557067i	−0.963751	−	0.266803i	$-0.914033\pi$
$659$	−39.2902	+	14.3005i	−1.53053	+	0.557067i	−0.566778	+	0.823870i	$0.691810\pi$
$660$		0			0
$661$	0.336551	−	1.90867i	0.0130903	−	0.0742388i	−0.977563	−	0.210644i	$-0.932444\pi$
$661$	0.336551	−	1.90867i	0.0130903	−	0.0742388i	0.990653	+	0.136405i	$0.0435550\pi$
$662$	−32.2753	−	11.7472i	−1.25441	−	0.456570i
$663$	15.5238	−	13.0260i	0.602893	−	0.505887i
$664$	−4.48941			−0.174223
$665$		0			0
$666$	−8.52641			−0.330392
$667$	−8.24751	+	6.92048i	−0.319345	+	0.267962i
$668$	10.0638	+	3.66291i	0.389379	+	0.141722i
$669$	−8.96955	+	50.8688i	−0.346783	+	1.96670i
$670$		0			0
$671$	32.7746	−	11.9290i	1.26525	−	0.460513i
$672$	−5.27101	+	9.12965i	−0.203334	+	0.352184i
$673$	22.4265	+	38.8439i	0.864479	+	1.49732i	0.867563	+	0.497327i	$0.165685\pi$
$673$	22.4265	+	38.8439i	0.864479	+	1.49732i	−0.00308384	+	0.999995i	$0.500982\pi$
$674$	−8.86863	−	7.44166i	−0.341607	−	0.286642i
$675$		0			0
$676$	−7.99764	−	13.8523i	−0.307602	−	0.532782i
$677$	−15.8298	+	27.4179i	−0.608387	+	1.05376i	0.383119	+	0.923699i	$0.374850\pi$
$677$	−15.8298	+	27.4179i	−0.608387	+	1.05376i	−0.991506	+	0.130058i	$0.958484\pi$
$678$	−28.4747	+	10.3639i	−1.09356	+	0.398025i
$679$	−0.883096	−	5.00829i	−0.0338901	−	0.192200i
$680$		0			0
$681$	−13.5029	−	4.91466i	−0.517433	−	0.188330i
$682$	26.9930	−	22.6498i	1.03362	−	0.867306i
$683$	−46.7025			−1.78702			−0.893511	−	0.449042i	$-0.851765\pi$
$683$	−46.7025			−1.78702			−0.893511	+	0.449042i	$0.851765\pi$
$684$	17.6016	−	8.67288i	0.673015	−	0.331616i
$685$		0			0
$686$	2.40174	−	2.01530i	0.0916990	−	0.0769446i
$687$	9.18494	+	3.34304i	0.350427	+	0.127545i
$688$	−0.568954	+	3.22670i	−0.0216912	+	0.123017i
$689$	−11.0096	−	62.4385i	−0.419432	−	2.37872i
$690$		0			0
$691$	15.2738	−	26.4549i	0.581041	−	1.00639i	−0.414315	−	0.910133i	$-0.635979\pi$
$691$	15.2738	−	26.4549i	0.581041	−	1.00639i	0.995356	−	0.0962590i	$-0.0306877\pi$
$692$	−1.55324	−	2.69028i	−0.0590452	−	0.102269i
$693$	−76.0331	−	63.7993i	−2.88826	−	2.42354i
$694$	1.33141	+	1.11718i	0.0505396	+	0.0424077i
$695$		0			0
$696$	9.34375	−	16.1838i	0.354174	−	0.613447i
$697$	4.65804	−	1.69539i	0.176436	−	0.0642174i
$698$	0.399497	+	2.26566i	0.0151212	+	0.0857564i
$699$	−2.63367	+	14.9363i	−0.0996144	+	0.564941i
$700$		0			0
$701$	21.6536	−	18.1696i	0.817847	−	0.686255i	−0.134620	−	0.990897i	$-0.542981\pi$
$701$	21.6536	−	18.1696i	0.817847	−	0.686255i	0.952467	+	0.304642i	$0.0985370\pi$
$702$	22.1472			0.835891
$703$	8.01874	+	1.96500i	0.302432	+	0.0741115i
$704$	5.72836			0.215896
$705$		0			0
$706$	−27.6937	−	10.0797i	−1.04227	−	0.379354i
$707$	9.72061	−	55.1283i	0.365581	−	2.07331i
$708$	−1.24354	−	7.05248i	−0.0467352	−	0.265048i
$709$	15.9283	−	5.79743i	0.598200	−	0.217727i	−0.0251320	−	0.999684i	$-0.508001\pi$
$709$	15.9283	−	5.79743i	0.598200	−	0.217727i	0.623332	+	0.781957i	$0.285778\pi$
$710$		0			0
$711$	−17.4162	−	30.1657i	−0.653158	−	1.13130i
$712$	0.786626	+	0.660058i	0.0294801	+	0.0247367i
$713$	7.43563	+	6.23924i	0.278467	+	0.233661i
$714$	7.24259	+	12.5445i	0.271047	+	0.469467i
$715$		0			0
$716$	19.8327	−	7.21852i	0.741184	−	0.269769i
$717$	−5.41324	−	30.7000i	−0.202161	−	1.14651i
$718$	−2.42518	+	13.7539i	−0.0905068	+	0.513289i
$719$	−26.7072	−	9.72061i	−0.996009	−	0.362518i	−0.207965	−	0.978136i	$-0.566684\pi$
$719$	−26.7072	−	9.72061i	−0.996009	−	0.362518i	−0.788044	+	0.615619i	$0.788906\pi$
$720$		0			0
$721$	29.2175			1.08812
$722$	−18.5524	+	4.10000i	−0.690447	+	0.152586i
$723$	30.3457			1.12857
$724$	−3.41410	+	2.86477i	−0.126884	+	0.106468i
$725$		0			0
$726$	−10.3749	+	58.8392i	−0.385050	+	2.18373i
$727$	1.72449	+	9.78007i	0.0639578	+	0.362723i	0.999943	+	0.0106831i	$0.00340060\pi$
$727$	1.72449	+	9.78007i	0.0639578	+	0.362723i	−0.935985	+	0.352039i	$0.885488\pi$
$728$	19.4757	−	7.08859i	0.721819	−	0.262721i
$729$	21.9394	−	38.0001i	0.812569	−	1.40741i
$730$		0			0
$731$	3.44875	+	2.89384i	0.127556	+	0.107033i
$732$	−12.7748	−	10.7193i	−0.472170	−	0.396198i
$733$	0.702986	+	1.21761i	0.0259654	+	0.0449734i	0.878716	−	0.477345i	$-0.158401\pi$
$733$	0.702986	+	1.21761i	0.0259654	+	0.0449734i	−0.852751	+	0.522318i	$0.825067\pi$
$734$	14.8484	−	25.7181i	0.548064	−	0.949274i
$735$		0			0
$736$	0.274010	+	1.55399i	0.0101002	+	0.0572808i
$737$	6.24688	−	35.4278i	0.230107	−	1.30500i
$738$	15.2608	+	5.55447i	0.561757	+	0.204463i
$739$	−36.0542	+	30.2530i	−1.32627	+	1.11288i	−0.341342	+	0.939939i	$0.610881\pi$
$739$	−36.0542	+	30.2530i	−1.32627	+	1.11288i	−0.984933	+	0.172937i	$0.944674\pi$
$740$		0			0
$741$	−62.4391	−	15.3008i	−2.29376	−	0.562088i
$742$	45.3191			1.66372
$743$	10.4731	−	8.78794i	0.384219	−	0.322398i	−0.430137	−	0.902764i	$-0.641535\pi$
$743$	10.4731	−	8.78794i	0.384219	−	0.322398i	0.814356	+	0.580365i	$0.197090\pi$
$744$	−15.8319	−	5.76233i	−0.580424	−	0.211257i
$745$		0			0
$746$	2.00451	+	11.3681i	0.0733903	+	0.416217i
$747$	−18.9911	+	6.91218i	−0.694846	+	0.252903i
$748$	3.93550	−	6.81649i	0.143896	−	0.249236i
$749$	−2.62620	−	4.54871i	−0.0959592	−	0.166206i
$750$		0			0
$751$	14.2856	+	11.9871i	0.521290	+	0.437414i	0.865081	−	0.501632i	$-0.167267\pi$
$751$	14.2856	+	11.9871i	0.521290	+	0.437414i	−0.343791	+	0.939046i	$0.611711\pi$
$752$	3.62373	+	6.27648i	0.132144	+	0.228880i
$753$	−4.95678	+	8.58539i	−0.180635	+	0.312869i
$754$	−34.5240	+	12.5657i	−1.25729	+	0.457617i
$755$		0			0
$756$	−2.74897	+	15.5902i	−0.0999789	+	0.567009i
$757$	19.7905	+	7.20316i	0.719299	+	0.261803i	0.675628	−	0.737243i	$-0.263872\pi$
$757$	19.7905	+	7.20316i	0.719299	+	0.261803i	0.0436709	+	0.999046i	$0.486095\pi$
$758$	−6.86525	+	5.76063i	−0.249357	+	0.209236i
$759$	−24.7574			−0.898638
$760$		0			0
$761$	−10.4369			−0.378338			−0.189169	−	0.981945i	$-0.560579\pi$
$761$	−10.4369			−0.378338			−0.189169	+	0.981945i	$0.560579\pi$
$762$	0.684094	−	0.574023i	0.0247821	−	0.0207947i
$763$	25.7095	+	9.35748i	0.930745	+	0.338764i
$764$	−1.40029	+	7.94142i	−0.0506606	+	0.287310i
$765$		0			0
$766$	−27.2194	+	9.90707i	−0.983478	+	0.357957i
$767$	−7.03955	+	12.1929i	−0.254183	+	0.440258i
$768$	−1.36946	−	2.37197i	−0.0494161	−	0.0855912i
$769$	−27.7366	−	23.2738i	−1.00021	−	0.839275i	−0.0131956	−	0.999913i	$-0.504200\pi$
$769$	−27.7366	−	23.2738i	−1.00021	−	0.839275i	−0.987013	+	0.160638i	$0.948645\pi$
$770$		0			0
$771$	−14.8502	−	25.7213i	−0.534816	−	0.926328i
$772$	0.337014	−	0.583726i	0.0121294	−	0.0210088i
$773$	−11.2710	+	4.10232i	−0.405391	+	0.147550i	−0.536664	−	0.843796i	$-0.680316\pi$
$773$	−11.2710	+	4.10232i	−0.405391	+	0.147550i	0.131273	+	0.991346i	$0.458094\pi$
$774$	2.56125	+	14.5255i	0.0920621	+	0.522110i
$775$		0			0
$776$	1.24159	+	0.451903i	0.0445706	+	0.0162224i
$777$	−15.2957	+	12.8346i	−0.548731	+	0.460440i
$778$	−18.0033			−0.645449
$779$	−13.0720	−	8.74076i	−0.468355	−	0.313170i
$780$		0			0
$781$	−54.6084	+	45.8219i	−1.95404	+	1.63964i
$782$	2.03743	+	0.741564i	0.0728584	+	0.0265183i
$783$	4.87301	−	27.6362i	0.174147	−	0.987637i
$784$	1.35699	+	7.69585i	0.0484638	+	0.274852i
$785$		0			0
$786$	−7.20659	+	12.4822i	−0.257051	+	0.445225i
$787$	−10.0197	−	17.3546i	−0.357163	−	0.618624i	0.630323	−	0.776333i	$-0.282922\pi$
$787$	−10.0197	−	17.3546i	−0.357163	−	0.618624i	−0.987486	+	0.157709i	$0.949589\pi$
$788$	−5.63526	−	4.72855i	−0.200748	−	0.168447i
$789$	−20.2336	−	16.9780i	−0.720335	−	0.604433i
$790$		0			0
$791$	−21.2916	+	36.8782i	−0.757043	+	1.31124i
$792$	24.2320	−	8.81974i	0.861048	−	0.313396i
$793$	5.69318	+	32.2876i	0.202171	+	1.14657i
$794$	−3.22669	+	18.2995i	−0.114511	+	0.649424i
$795$		0			0
$796$	−21.0911	+	17.6976i	−0.747555	+	0.627273i
$797$	17.2997			0.612788			0.306394	−	0.951905i	$-0.400878\pi$
$797$	17.2997			0.612788			0.306394	+	0.951905i	$0.400878\pi$
$798$	18.5208	−	42.0538i	0.655631	−	1.48869i
$799$	9.95832			0.352300
$800$		0			0
$801$	4.34385	+	1.58103i	0.153482	+	0.0558630i
$802$	−4.90652	+	27.8262i	−0.173255	+	0.982578i
$803$	9.37751	+	53.1825i	0.330925	+	1.87677i
$804$	−16.1632	+	5.88293i	−0.570032	+	0.207475i
$805$		0			0
$806$	16.5615	+	28.6854i	0.583356	+	1.01040i
$807$	−15.6681	−	13.1471i	−0.551544	−	0.462800i
$808$	11.1412	+	9.34860i	0.391947	+	0.328883i
$809$	13.6286	+	23.6054i	0.479156	+	0.829922i	0.999714	−	0.0239039i	$-0.00760956\pi$
$809$	13.6286	+	23.6054i	0.479156	+	0.829922i	−0.520558	+	0.853826i	$0.674276\pi$
$810$		0			0
$811$	49.4372	−	17.9937i	1.73598	−	0.631843i	0.736949	−	0.675949i	$-0.236266\pi$
$811$	49.4372	−	17.9937i	1.73598	−	0.631843i	0.999027	+	0.0441053i	$0.0140437\pi$
$812$	−4.56023	−	25.8624i	−0.160033	−	0.907591i
$813$	−14.4868	+	82.1585i	−0.508073	+	2.88142i
$814$	10.1955	+	3.71086i	0.357352	+	0.130065i
$815$		0			0
$816$	−3.76339			−0.131745
$817$	0.938820	−	14.2509i	0.0328452	−	0.498577i
$818$	−34.4070			−1.20301
$819$	71.4720	−	59.9722i	2.49744	−	2.09560i
$820$		0			0
$821$	3.56727	−	20.2310i	0.124498	−	0.706066i	−0.857106	−	0.515140i	$-0.827740\pi$
$821$	3.56727	−	20.2310i	0.124498	−	0.706066i	0.981604	−	0.190926i	$-0.0611490\pi$
$822$	5.91041	+	33.5196i	0.206149	+	1.16913i
$823$	−51.0206	+	18.5700i	−1.77847	+	0.647309i	−0.778663	+	0.627442i	$0.784102\pi$
$823$	−51.0206	+	18.5700i	−1.77847	+	0.647309i	−0.999803	+	0.0198664i	$0.993676\pi$
$824$	−3.79549	+	6.57398i	−0.132222	+	0.229016i
$825$		0			0
$826$	−7.70920	−	6.46879i	−0.268238	−	0.225078i
$827$	−9.13189	−	7.66257i	−0.317547	−	0.266454i	0.470056	−	0.882637i	$-0.344234\pi$
$827$	−9.13189	−	7.66257i	−0.317547	−	0.266454i	−0.787603	+	0.616183i	$0.788678\pi$
$828$	3.55174	+	6.15179i	0.123431	+	0.213789i
$829$	7.12734	−	12.3449i	0.247543	−	0.428757i	−0.715301	−	0.698817i	$-0.753710\pi$
$829$	7.12734	−	12.3449i	0.247543	−	0.428757i	0.962843	+	0.270060i	$0.0870435\pi$
$830$		0			0
$831$	4.71543	+	26.7425i	0.163577	+	0.927689i
$832$	−0.935048	+	5.30292i	−0.0324170	+	0.183846i
$833$	10.0900	+	3.67246i	0.349598	+	0.127243i
$834$	13.0715	−	10.9683i	0.452629	−	0.379801i
$835$		0			0
$836$	−24.8218	+	2.71007i	−0.858480	+	0.0937297i
$837$	−25.3001			−0.874498
$838$	−0.727965	+	0.610835i	−0.0251471	+	0.0211010i
$839$	13.7410	+	5.00130i	0.474391	+	0.172664i	0.568140	−	0.822932i	$-0.307663\pi$
$839$	13.7410	+	5.00130i	0.474391	+	0.172664i	−0.0937496	+	0.995596i	$0.529885\pi$
$840$		0			0
$841$	3.04798	+	17.2860i	0.105103	+	0.596068i
$842$	20.5965	−	7.49650i	0.709801	−	0.258346i
$843$	22.0054	−	38.1145i	0.757907	−	1.31273i
$844$	10.6781	+	18.4950i	0.367554	+	0.636623i
$845$		0			0
$846$	24.9927	+	20.9714i	0.859267	+	0.721011i
$847$	41.9808	+	72.7129i	1.44248	+	2.49845i
$848$	−5.88718	+	10.1969i	−0.202166	+	0.350163i
$849$	−25.9626	+	9.44963i	−0.891036	+	0.324310i
$850$		0			0
$851$	−0.518991	+	2.94334i	−0.0177908	+	0.100896i
$852$	32.0288	+	11.6575i	1.09729	+	0.399380i
$853$	29.5837	−	24.8236i	1.01293	−	0.849945i	0.0242034	−	0.999707i	$-0.492295\pi$
$853$	29.5837	−	24.8236i	1.01293	−	0.849945i	0.988722	+	0.149762i	$0.0478506\pi$
$854$	−23.4350			−0.801930
$855$		0			0
$856$	1.36462			0.0466419
$857$	−30.0390	+	25.2057i	−1.02611	+	0.861012i	−0.990383	−	0.138349i	$-0.955820\pi$
$857$	−30.0390	+	25.2057i	−1.02611	+	0.861012i	−0.0357307	+	0.999361i	$0.511376\pi$
$858$	−79.3887	−	28.8951i	−2.71028	−	0.986463i
$859$	−0.982011	+	5.56926i	−0.0335058	+	0.190021i	−0.996967	−	0.0778278i	$-0.975202\pi$
$859$	−0.982011	+	5.56926i	−0.0335058	+	0.190021i	0.963461	+	0.267849i	$0.0863127\pi$
$860$		0			0
$861$	35.7377	−	13.0075i	1.21794	−	0.443293i
$862$	−12.5106	+	21.6689i	−0.426111	+	0.738046i
$863$	−5.13518	−	8.89440i	−0.174804	−	0.302769i	0.765290	−	0.643686i	$-0.222596\pi$
$863$	−5.13518	−	8.89440i	−0.174804	−	0.302769i	−0.940093	+	0.340917i	$0.889262\pi$
$864$	−3.15071	−	2.64376i	−0.107189	−	0.0899426i
$865$		0			0
$866$	19.4738	+	33.7296i	0.661747	+	1.14618i
$867$	20.6953	−	35.8453i	0.702848	−	1.21737i
$868$	−22.2483	+	8.09773i	−0.755158	+	0.274855i
$869$	7.69678	+	43.6506i	0.261095	+	1.48074i
$870$		0			0
$871$	31.7770	+	11.5659i	1.07672	+	0.391894i
$872$	−5.44524	+	4.56910i	−0.184399	+	0.154729i
$873$	5.94795			0.201308
$874$	−1.92252	−	6.60404i	−0.0650301	−	0.223385i
$875$		0			0
$876$	19.7797	−	16.5972i	0.668296	−	0.560767i
$877$	45.8127	+	16.6745i	1.54698	+	0.563056i	0.967708	−	0.252075i	$-0.0811129\pi$
$877$	45.8127	+	16.6745i	1.54698	+	0.563056i	0.579277	+	0.815131i	$0.303335\pi$
$878$	−0.846675	+	4.80173i	−0.0285739	+	0.162051i
$879$	−2.50413	−	14.2016i	−0.0844620	−	0.479008i
$880$		0			0
$881$	21.8207	−	37.7945i	0.735157	−	1.27333i	−0.219497	−	0.975613i	$-0.570442\pi$
$881$	21.8207	−	37.7945i	0.735157	−	1.27333i	0.954654	−	0.297717i	$-0.0962250\pi$
$882$	17.5893	+	30.4656i	0.592263	+	1.02583i
$883$	36.9850	+	31.0341i	1.24464	+	1.04438i	0.997146	+	0.0754921i	$0.0240528\pi$
$883$	36.9850	+	31.0341i	1.24464	+	1.04438i	0.247498	+	0.968888i	$0.420392\pi$
$884$	5.66785	+	4.75589i	0.190630	+	0.159958i
$885$		0			0
$886$	10.3605	−	17.9449i	0.348067	−	0.602869i
$887$	33.1197	−	12.0546i	1.11205	−	0.404753i	0.280305	−	0.959911i	$-0.409564\pi$
$887$	33.1197	−	12.0546i	1.11205	−	0.404753i	0.831745	+	0.555158i	$0.187342\pi$
$888$	−0.900828	−	5.10885i	−0.0302298	−	0.171442i
$889$	0.217920	−	1.23589i	0.00730881	−	0.0414503i
$890$		0			0
$891$	−9.82932	+	8.24778i	−0.329294	+	0.276311i
$892$	−18.8591			−0.631450
$893$	−18.6715	−	25.4826i	−0.624819	−	0.852741i
$894$	−62.5606			−2.09234
$895$		0			0
$896$	−3.61685	−	1.31643i	−0.120830	−	0.0439787i
$897$	4.04119	−	22.9188i	0.134932	−	0.765235i
$898$	−2.91525	−	16.5332i	−0.0972831	−	0.551720i
$899$	39.4389	−	14.3546i	1.31536	−	0.478752i
$900$		0			0
$901$	8.08923	+	14.0110i	0.269491	+	0.466773i
$902$	−15.8307	−	13.2836i	−0.527106	−	0.442294i
$903$	26.4597	+	22.2023i	0.880523	+	0.738846i
$904$	−5.53177	−	9.58131i	−0.183984	−	0.318670i
$905$		0			0
$906$	17.2451	−	6.27671i	0.572931	−	0.208530i
$907$	8.07604	+	45.8015i	0.268160	+	1.52081i	0.759882	+	0.650061i	$0.225257\pi$
$907$	8.07604	+	45.8015i	0.268160	+	1.52081i	−0.491722	+	0.870752i	$0.663632\pi$
$908$	0.911030	−	5.16671i	0.0302336	−	0.171463i
$909$	61.5232	+	22.3926i	2.04060	+	0.742716i
$910$		0			0
$911$	−13.1421			−0.435416			−0.217708	−	0.976014i	$-0.569858\pi$
$911$	−13.1421			−0.435416			−0.217708	+	0.976014i	$0.569858\pi$
$912$	7.05624	+	9.63022i	0.233656	+	0.318889i
$913$	25.7169			0.851106
$914$	6.50105	−	5.45503i	0.215036	−	0.180436i
$915$		0			0
$916$	−0.619700	+	3.51449i	−0.0204755	+	0.116122i
$917$	3.51719	+	19.9470i	0.116148	+	0.658707i
$918$	−5.31057	+	1.93289i	−0.175275	+	0.0637948i
$919$	−14.1951	+	24.5866i	−0.468252	+	0.811037i	−0.999342	−	0.0362788i	$-0.988450\pi$
$919$	−14.1951	+	24.5866i	−0.468252	+	0.811037i	0.531089	+	0.847316i	$0.321783\pi$
$920$		0			0
$921$	65.1927	+	54.7031i	2.14817	+	1.80253i
$922$	25.3410	+	21.2636i	0.834560	+	0.700279i
$923$	−33.5050	−	58.0323i	−1.10283	−	1.91016i
$924$	30.1942	−	52.2979i	0.993316	−	1.72047i
$925$		0			0
$926$	−5.41910	−	30.7333i	−0.178083	−	1.00996i
$927$	−5.93393	+	33.6530i	−0.194896	+	1.10531i
$928$	6.41147	+	2.33359i	0.210467	+	0.0766037i
$929$	6.10973	−	5.12667i	0.200454	−	0.168201i	−0.537035	−	0.843560i	$-0.680456\pi$
$929$	6.10973	−	5.12667i	0.200454	−	0.168201i	0.737489	+	0.675359i	$0.236011\pi$
$930$		0			0
$931$	−9.52091	−	32.7053i	−0.312035	−	1.07187i
$932$	−5.53747			−0.181386
$933$	−37.6791	+	31.6165i	−1.23356	+	1.03508i
$934$	−16.5651	−	6.02922i	−0.542028	−	0.197282i
$935$		0			0
$936$	4.20928	+	23.8720i	0.137585	+	0.780281i
$937$	−32.2761	+	11.7475i	−1.05441	+	0.383775i	−0.810327	−	0.585978i	$-0.800711\pi$
$937$	−32.2761	+	11.7475i	−1.05441	+	0.383775i	−0.244087	+	0.969753i	$0.578488\pi$
$938$	−12.0859	+	20.9333i	−0.394617	+	0.683497i
$939$	20.4473	+	35.4157i	0.667271	+	1.15575i
$940$		0			0
$941$	14.2992	+	11.9984i	0.466140	+	0.391138i	0.845384	−	0.534159i	$-0.179372\pi$
$941$	14.2992	+	11.9984i	0.466140	+	0.391138i	−0.379244	+	0.925297i	$0.623816\pi$
$942$	0.0516513	+	0.0894627i	0.00168289	+	0.00291485i
$943$	2.84632	−	4.92997i	0.0926889	−	0.160542i
$944$	2.45695	−	0.894258i	0.0799670	−	0.0291056i
$945$		0			0
$946$	3.25917	−	18.4837i	0.105965	−	0.600956i
$947$	19.0424	+	6.93088i	0.618796	+	0.225223i	0.632348	−	0.774685i	$-0.282091\pi$
$947$	19.0424	+	6.93088i	0.618796	+	0.225223i	−0.0135513	+	0.999908i	$0.504314\pi$
$948$	16.2346	−	13.6225i	0.527276	−	0.442437i
$949$	−50.7635			−1.64785
$950$		0			0
$951$	−24.7386			−0.802204
$952$	−4.05134	+	3.39948i	−0.131305	+	0.110178i
$953$	2.81385	+	1.02416i	0.0911496	+	0.0331757i	0.387192	−	0.921999i	$-0.373445\pi$
$953$	2.81385	+	1.02416i	0.0911496	+	0.0331757i	−0.296043	+	0.955175i	$0.595667\pi$
$954$	−9.20410	+	52.1990i	−0.297994	+	1.69001i
$955$		0			0
$956$	10.6953	−	3.89278i	0.345911	−	0.125901i
$957$	−53.5243	+	92.7068i	−1.73020	+	2.99679i
$958$	7.76269	+	13.4454i	0.250801	+	0.434400i
$959$	36.6410	+	30.7454i	1.18320	+	0.992822i
$960$		0			0
$961$	−3.41927	−	5.92234i	−0.110299	−	0.191043i
$962$	−5.09948	+	8.83256i	−0.164414	+	0.284773i
$963$	5.77262	−	2.10106i	0.186020	−	0.0677057i
$964$	1.92393	+	10.9111i	0.0619655	+	0.351424i
$965$		0			0
$966$	15.6317	+	5.68947i	0.502942	+	0.183056i
$967$	−29.8805	+	25.0727i	−0.960892	+	0.806284i	−0.981098	−	0.193512i	$-0.938012\pi$
$967$	−29.8805	+	25.0727i	−0.960892	+	0.806284i	0.0202060	+	0.999796i	$0.493568\pi$
$968$	−21.8141			−0.701130
$969$	16.3073	−	1.78045i	0.523867	−	0.0571963i
$970$		0			0
$971$	26.6945	−	22.3993i	0.856667	−	0.718829i	−0.104580	−	0.994516i	$-0.533350\pi$
$971$	26.6945	−	22.3993i	0.856667	−	0.718829i	0.961247	+	0.275688i	$0.0889055\pi$
$972$	17.3598	+	6.31846i	0.556817	+	0.202665i
$973$	4.16397	−	23.6150i	0.133491	−	0.757063i
$974$	4.19642	+	23.7991i	0.134462	+	0.762572i
$975$		0			0
$976$	3.04433	−	5.27293i	0.0974465	−	0.168782i
$977$	26.5190	+	45.9323i	0.848420	+	1.46951i	0.882618	+	0.470091i	$0.155779\pi$
$977$	26.5190	+	45.9323i	0.848420	+	1.46951i	−0.0341985	+	0.999415i	$0.510888\pi$
$978$	24.4065	+	20.4795i	0.780434	+	0.654862i
$979$	−4.50608	−	3.78105i	−0.144015	−	0.120843i
$980$		0			0
$981$	−15.9995	+	27.7120i	−0.510825	+	0.884775i
$982$	5.53601	−	2.01494i	0.176661	−	0.0642994i
$983$	−2.15515	−	12.2225i	−0.0687387	−	0.389836i	−0.999695	−	0.0247053i	$-0.992135\pi$
$983$	−2.15515	−	12.2225i	−0.0687387	−	0.389836i	0.930956	−	0.365131i	$-0.118976\pi$
$984$	−1.71580	+	9.73078i	−0.0546977	+	0.310206i
$985$		0			0
$986$	7.18169	−	6.02615i	0.228711	−	0.191912i
$987$	76.4028			2.43193
$988$	1.54291	−	23.4207i	0.0490864	−	0.745112i
$989$	5.17016			0.164401
$990$		0			0
$991$	48.0653	+	17.4943i	1.52684	+	0.555726i	0.962846	−	0.270050i	$-0.0870403\pi$
$991$	48.0653	+	17.4943i	1.52684	+	0.555726i	0.563998	+	0.825776i	$0.309262\pi$
$992$	1.06816	−	6.05785i	0.0339142	−	0.192337i
$993$	−16.3355	−	92.6435i	−0.518393	−	2.93995i
$994$	45.0097	−	16.3822i	1.42762	−	0.519611i
$995$		0			0
$996$	−6.14806	−	10.6488i	−0.194809	−	0.337419i
$997$	−14.4865	−	12.1556i	−0.458793	−	0.384973i	0.383894	−	0.923377i	$-0.374583\pi$
$997$	−14.4865	−	12.1556i	−0.458793	−	0.384973i	−0.842687	+	0.538405i	$0.819027\pi$
$998$	18.3241	+	15.3757i	0.580039	+	0.486711i
$999$	−3.89509	−	6.74649i	−0.123235	−	0.213449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.g.101.1		12
5.2	odd	4		950.2.u.f.899.1		24
5.3	odd	4		950.2.u.f.899.4		24
5.4	even	2		190.2.k.c.101.2	✓	12
19.16	even	9	inner	950.2.l.g.301.1		12
95.4	even	18		3610.2.a.bf.1.2		6
95.34	odd	18		3610.2.a.bd.1.5		6
95.54	even	18		190.2.k.c.111.2	yes	12
95.73	odd	36		950.2.u.f.149.1		24
95.92	odd	36		950.2.u.f.149.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.101.2	✓	12	5.4	even	2
190.2.k.c.111.2	yes	12	95.54	even	18
950.2.l.g.101.1		12	1.1	even	1	trivial
950.2.l.g.301.1		12	19.16	even	9	inner
950.2.u.f.149.1		24	95.73	odd	36
950.2.u.f.149.4		24	95.92	odd	36
950.2.u.f.899.1		24	5.2	odd	4
950.2.u.f.899.4		24	5.3	odd	4
3610.2.a.bd.1.5		6	95.34	odd	18
3610.2.a.bf.1.2		6	95.4	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.57374 - 0.936765i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.57374 - 0.936765i) q^{6} +(1.92448 - 3.33331i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.44848 + 2.89362i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.57374 - 0.936765i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.57374 - 0.936765i) q^{6} +(1.92448 - 3.33331i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.44848 + 2.89362i) q^{9} +(-2.86418 - 4.96090i) q^{11} +(-1.36946 + 2.37197i) q^{12} +(5.05999 - 1.84169i) q^{13} +(0.668367 + 3.79050i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-1.05258 + 0.883218i) q^{17} -4.50167 q^{18} +(4.23364 + 1.03746i) q^{19} +(-8.07565 + 6.77628i) q^{21} +(5.38289 + 1.95921i) q^{22} +(-0.274010 + 1.55399i) q^{23} +(-0.475608 - 2.69731i) q^{24} +(-2.69236 + 4.66331i) q^{26} +(-2.05648 - 3.56193i) q^{27} +(-2.94848 - 2.47407i) q^{28} +(5.22668 + 4.38571i) q^{29} +(3.07565 - 5.32718i) q^{31} +(0.939693 - 0.342020i) q^{32} +(2.72445 + 15.4511i) q^{33} +(0.238600 - 1.35317i) q^{34} +(3.44848 - 2.89362i) q^{36} +1.89405 q^{37} +(-3.91002 + 1.92659i) q^{38} -14.7483 q^{39} +(-3.39002 - 1.23387i) q^{41} +(1.83060 - 10.3819i) q^{42} +(-0.568954 - 3.22670i) q^{43} +(-5.38289 + 1.95921i) q^{44} +(-0.788981 - 1.36656i) q^{46} +(-5.55187 - 4.65857i) q^{47} +(2.09813 + 1.76054i) q^{48} +(-3.90728 - 6.76762i) q^{49} +(3.53643 - 1.28716i) q^{51} +(-0.935048 - 5.30292i) q^{52} +(2.04459 - 11.5955i) q^{53} +(3.86492 + 1.40672i) q^{54} +3.84897 q^{56} +(-9.92443 - 6.63607i) q^{57} -6.82295 q^{58} +(-2.00293 + 1.68066i) q^{59} +(-1.05728 + 5.99615i) q^{61} +(1.06816 + 6.05785i) q^{62} +(16.2819 - 5.92612i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.0189 - 10.0850i) q^{66} +(4.81079 + 4.03673i) q^{67} +(0.687022 + 1.18996i) q^{68} +(2.16096 - 3.74288i) q^{69} +(-2.16096 - 12.2554i) q^{71} +(-0.781707 + 4.43328i) q^{72} +(-8.85877 - 3.22433i) q^{73} +(-1.45093 + 1.21747i) q^{74} +(1.75686 - 3.98917i) q^{76} -22.0483 q^{77} +(11.2979 - 9.48004i) q^{78} +(-7.27101 - 2.64643i) q^{79} +(-0.388964 - 2.20593i) q^{81} +(3.39002 - 1.23387i) q^{82} +(-2.24471 + 3.88794i) q^{83} +(5.27101 + 9.12965i) q^{84} +(2.50993 + 2.10608i) q^{86} +(-9.34375 - 16.1838i) q^{87} +(2.86418 - 4.96090i) q^{88} +(0.964940 - 0.351210i) q^{89} +(3.59897 - 20.4108i) q^{91} +(1.48280 + 0.539695i) q^{92} +(-12.9063 + 10.8296i) q^{93} +7.24746 q^{94} -2.73892 q^{96} +(1.01216 - 0.849299i) q^{97} +(7.34329 + 2.67274i) q^{98} +(4.47790 - 25.3954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Introduction

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