LMFDB - Embedded newform 861.2.i.g.247.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.i (of order $3$, degree $2$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.1
Character	$\chi$	$=$	861.247
Dual form			861.2.i.g.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34508 + 2.32975i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.61848 - 4.53533i) q^{4} +(-1.70362 + 2.95075i) q^{5} -2.69016 q^{6} +(2.44234 - 1.01735i) q^{7} +8.70791 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.34508 + 2.32975i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.61848 - 4.53533i) q^{4} +(-1.70362 + 2.95075i) q^{5} -2.69016 q^{6} +(2.44234 - 1.01735i) q^{7} +8.70791 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.58300 - 7.93800i) q^{10} +(3.08104 + 5.33652i) q^{11} +(2.61848 - 4.53533i) q^{12} +3.11534 q^{13} +(-0.914976 + 7.05843i) q^{14} -3.40724 q^{15} +(-6.47588 + 11.2166i) q^{16} +(-1.35880 - 2.35350i) q^{17} +(-1.34508 - 2.32975i) q^{18} +(-3.57894 + 6.19891i) q^{19} +17.8435 q^{20} +(2.10222 + 1.60645i) q^{21} -16.5770 q^{22} +(-1.77663 + 3.07721i) q^{23} +(4.35396 + 7.54127i) q^{24} +(-3.30464 - 5.72380i) q^{25} +(-4.19038 + 7.25796i) q^{26} -1.00000 q^{27} +(-11.0092 - 8.41291i) q^{28} -1.79174 q^{29} +(4.58300 - 7.93800i) q^{30} +(3.45495 + 5.98414i) q^{31} +(-8.71323 - 15.0918i) q^{32} +(-3.08104 + 5.33652i) q^{33} +7.31075 q^{34} +(-1.15887 + 8.93991i) q^{35} +5.23695 q^{36} +(4.38300 - 7.59159i) q^{37} +(-9.62792 - 16.6761i) q^{38} +(1.55767 + 2.69797i) q^{39} +(-14.8350 + 25.6949i) q^{40} +1.00000 q^{41} +(-6.57027 + 2.73682i) q^{42} +3.02053 q^{43} +(16.1353 - 27.9471i) q^{44} +(-1.70362 - 2.95075i) q^{45} +(-4.77942 - 8.27819i) q^{46} +(2.49811 - 4.32685i) q^{47} -12.9518 q^{48} +(4.93001 - 4.96941i) q^{49} +17.7800 q^{50} +(1.35880 - 2.35350i) q^{51} +(-8.15745 - 14.1291i) q^{52} +(1.29006 + 2.23445i) q^{53} +(1.34508 - 2.32975i) q^{54} -20.9957 q^{55} +(21.2677 - 8.85897i) q^{56} -7.15789 q^{57} +(2.41003 - 4.17430i) q^{58} +(-4.81967 - 8.34791i) q^{59} +(8.92177 + 15.4530i) q^{60} +(-2.26103 + 3.91622i) q^{61} -18.5887 q^{62} +(-0.340120 + 2.62380i) q^{63} +20.9764 q^{64} +(-5.30736 + 9.19261i) q^{65} +(-8.28848 - 14.3561i) q^{66} +(0.869242 + 1.50557i) q^{67} +(-7.11595 + 12.3252i) q^{68} -3.55326 q^{69} +(-19.2689 - 14.7248i) q^{70} -14.2790 q^{71} +(-4.35396 + 7.54127i) q^{72} +(-0.492440 - 0.852932i) q^{73} +(11.7910 + 20.4226i) q^{74} +(3.30464 - 5.72380i) q^{75} +37.4855 q^{76} +(12.9540 + 9.89908i) q^{77} -8.38076 q^{78} +(4.34274 - 7.52185i) q^{79} +(-22.0649 - 38.2175i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.34508 + 2.32975i) q^{82} +1.55919 q^{83} +(1.78119 - 13.7407i) q^{84} +9.25948 q^{85} +(-4.06285 + 7.03707i) q^{86} +(-0.895871 - 1.55169i) q^{87} +(26.8294 + 46.4699i) q^{88} +(-2.23931 + 3.87860i) q^{89} +9.16601 q^{90} +(7.60871 - 3.16938i) q^{91} +18.6083 q^{92} +(-3.45495 + 5.98414i) q^{93} +(6.72031 + 11.6399i) q^{94} +(-12.1943 - 21.1212i) q^{95} +(8.71323 - 15.0918i) q^{96} -4.47579 q^{97} +(4.94620 + 18.1699i) q^{98} -6.16208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9} - 3 q^{10} + 16 q^{11} + 14 q^{12} + 42 q^{13} - 14 q^{14} - 20 q^{15} - 22 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} + 80 q^{20} + 2 q^{22} + 7 q^{23} - 6 q^{24} - 22 q^{25} - 2 q^{26} - 28 q^{27} - 59 q^{28} - 32 q^{29} + 3 q^{30} - 8 q^{31} + 19 q^{32} - 16 q^{33} + 66 q^{34} - 8 q^{35} + 28 q^{36} - q^{37} - 32 q^{38} + 21 q^{39} + 13 q^{40} + 28 q^{41} - 10 q^{42} + 28 q^{43} + 36 q^{44} - 10 q^{45} + 12 q^{46} - 12 q^{47} - 44 q^{48} + 8 q^{49} - 2 q^{50} + 12 q^{51} - 60 q^{52} + 20 q^{53} - 2 q^{54} - 22 q^{55} + q^{56} - 4 q^{57} - 21 q^{58} - 25 q^{59} + 40 q^{60} - 26 q^{61} - 66 q^{62} + 84 q^{64} + 8 q^{65} + q^{66} + 22 q^{67} - 15 q^{68} + 14 q^{69} - 120 q^{70} - 72 q^{71} + 6 q^{72} - 31 q^{73} + 65 q^{74} + 22 q^{75} - 4 q^{76} - 18 q^{77} - 4 q^{78} - 12 q^{79} - 112 q^{80} - 14 q^{81} + 2 q^{82} + 40 q^{83} - 37 q^{84} + 80 q^{85} + 9 q^{86} - 16 q^{87} + 54 q^{88} - 39 q^{89} + 6 q^{90} - 17 q^{91} + 126 q^{92} + 8 q^{93} - 14 q^{94} + 55 q^{95} - 19 q^{96} + 36 q^{97} - 19 q^{98} - 32 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9 - 3 * q^10 + 16 * q^11 + 14 * q^12 + 42 * q^13 - 14 * q^14 - 20 * q^15 - 22 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 + 80 * q^20 + 2 * q^22 + 7 * q^23 - 6 * q^24 - 22 * q^25 - 2 * q^26 - 28 * q^27 - 59 * q^28 - 32 * q^29 + 3 * q^30 - 8 * q^31 + 19 * q^32 - 16 * q^33 + 66 * q^34 - 8 * q^35 + 28 * q^36 - q^37 - 32 * q^38 + 21 * q^39 + 13 * q^40 + 28 * q^41 - 10 * q^42 + 28 * q^43 + 36 * q^44 - 10 * q^45 + 12 * q^46 - 12 * q^47 - 44 * q^48 + 8 * q^49 - 2 * q^50 + 12 * q^51 - 60 * q^52 + 20 * q^53 - 2 * q^54 - 22 * q^55 + q^56 - 4 * q^57 - 21 * q^58 - 25 * q^59 + 40 * q^60 - 26 * q^61 - 66 * q^62 + 84 * q^64 + 8 * q^65 + q^66 + 22 * q^67 - 15 * q^68 + 14 * q^69 - 120 * q^70 - 72 * q^71 + 6 * q^72 - 31 * q^73 + 65 * q^74 + 22 * q^75 - 4 * q^76 - 18 * q^77 - 4 * q^78 - 12 * q^79 - 112 * q^80 - 14 * q^81 + 2 * q^82 + 40 * q^83 - 37 * q^84 + 80 * q^85 + 9 * q^86 - 16 * q^87 + 54 * q^88 - 39 * q^89 + 6 * q^90 - 17 * q^91 + 126 * q^92 + 8 * q^93 - 14 * q^94 + 55 * q^95 - 19 * q^96 + 36 * q^97 - 19 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.34508	+	2.32975i	−0.951115	+	1.64738i	−0.208096	+	0.978108i	$0.566727\pi$
$2$	−1.34508	+	2.32975i	−0.951115	+	1.64738i	−0.743019	+	0.669270i	$0.766607\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.61848	−	4.53533i	−1.30924	−	2.26767i
$5$	−1.70362	+	2.95075i	−0.761882	+	1.31962i	0.179998	+	0.983667i	$0.442391\pi$
$5$	−1.70362	+	2.95075i	−0.761882	+	1.31962i	−0.941880	+	0.335951i	$0.890942\pi$
$6$	−2.69016			−1.09825
$7$	2.44234	−	1.01735i	0.923116	−	0.384521i
$7$	2.44234	−	1.01735i	0.923116	−	0.384521i
$8$	8.70791			3.07871
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.58300	−	7.93800i	−1.44927	−	2.51022i
$11$	3.08104	+	5.33652i	0.928968	+	1.60902i	0.785051	+	0.619431i	$0.212637\pi$
$11$	3.08104	+	5.33652i	0.928968	+	1.60902i	0.143917	+	0.989590i	$0.454030\pi$
$12$	2.61848	−	4.53533i	0.755889	−	1.30924i
$13$	3.11534			0.864041			0.432020	−	0.901864i	$-0.357801\pi$
$13$	3.11534			0.864041			0.432020	+	0.901864i	$0.357801\pi$
$14$	−0.914976	+	7.05843i	−0.244538	+	1.88645i
$15$	−3.40724			−0.879745
$16$	−6.47588	+	11.2166i	−1.61897	+	2.80414i
$17$	−1.35880	−	2.35350i	−0.329556	−	0.570809i	0.652867	−	0.757472i	$-0.273566\pi$
$17$	−1.35880	−	2.35350i	−0.329556	−	0.570809i	−0.982424	+	0.186664i	$0.940233\pi$
$18$	−1.34508	−	2.32975i	−0.317038	−	0.549126i
$19$	−3.57894	+	6.19891i	−0.821066	+	1.42213i	0.0838233	+	0.996481i	$0.473287\pi$
$19$	−3.57894	+	6.19891i	−0.821066	+	1.42213i	−0.904889	+	0.425647i	$0.860046\pi$
$20$	17.8435			3.98994
$21$	2.10222	+	1.60645i	0.458741	+	0.350556i
$22$	−16.5770			−3.53422
$23$	−1.77663	+	3.07721i	−0.370453	+	0.641644i	−0.989635	−	0.143604i	$-0.954131\pi$
$23$	−1.77663	+	3.07721i	−0.370453	+	0.641644i	0.619182	+	0.785247i	$0.287464\pi$
$24$	4.35396	+	7.54127i	0.888748	+	1.53936i
$25$	−3.30464	−	5.72380i	−0.660927	−	1.14476i
$26$	−4.19038	+	7.25796i	−0.821802	+	1.42340i
$27$	−1.00000			−0.192450
$28$	−11.0092	−	8.41291i	−2.08054	−	1.58989i
$29$	−1.79174			−0.332718			−0.166359	−	0.986065i	$-0.553201\pi$
$29$	−1.79174			−0.332718			−0.166359	+	0.986065i	$0.553201\pi$
$30$	4.58300	−	7.93800i	0.836738	−	1.44927i
$31$	3.45495	+	5.98414i	0.620527	+	1.07478i	0.989388	+	0.145299i	$0.0464144\pi$
$31$	3.45495	+	5.98414i	0.620527	+	1.07478i	−0.368861	+	0.929484i	$0.620252\pi$
$32$	−8.71323	−	15.0918i	−1.54030	−	2.66787i
$33$	−3.08104	+	5.33652i	−0.536340	+	0.928968i
$34$	7.31075			1.25378
$35$	−1.15887	+	8.93991i	−0.195885	+	1.51112i
$36$	5.23695			0.872825
$37$	4.38300	−	7.59159i	0.720562	−	1.24805i	−0.240213	−	0.970720i	$-0.577217\pi$
$37$	4.38300	−	7.59159i	0.720562	−	1.24805i	0.960775	−	0.277329i	$-0.0894492\pi$
$38$	−9.62792	−	16.6761i	−1.56186	−	2.70521i
$39$	1.55767	+	2.69797i	0.249427	+	0.432020i
$40$	−14.8350	+	25.6949i	−2.34561	+	4.06272i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−6.57027	+	2.73682i	−1.01381	+	0.422301i
$43$	3.02053			0.460626			0.230313	−	0.973117i	$-0.426025\pi$
$43$	3.02053			0.460626			0.230313	+	0.973117i	$0.426025\pi$
$44$	16.1353	−	27.9471i	2.43248	−	4.21318i
$45$	−1.70362	−	2.95075i	−0.253961	−	0.439873i
$46$	−4.77942	−	8.27819i	−0.704687	−	1.22055i
$47$	2.49811	−	4.32685i	0.364387	−	0.631136i	−0.624291	−	0.781192i	$-0.714612\pi$
$47$	2.49811	−	4.32685i	0.364387	−	0.631136i	0.988678	+	0.150056i	$0.0479453\pi$
$48$	−12.9518			−1.86943
$49$	4.93001	−	4.96941i	0.704287	−	0.709915i
$50$	17.7800			2.51447
$51$	1.35880	−	2.35350i	0.190270	−	0.329556i
$52$	−8.15745	−	14.1291i	−1.13123	−	1.95936i
$53$	1.29006	+	2.23445i	0.177203	+	0.306925i	0.940922	−	0.338625i	$-0.109962\pi$
$53$	1.29006	+	2.23445i	0.177203	+	0.306925i	−0.763718	+	0.645550i	$0.776628\pi$
$54$	1.34508	−	2.32975i	0.183042	−	0.317038i
$55$	−20.9957			−2.83106
$56$	21.2677	−	8.85897i	2.84201	−	1.18383i
$57$	−7.15789			−0.948085
$58$	2.41003	−	4.17430i	0.316453	−	0.548113i
$59$	−4.81967	−	8.34791i	−0.627468	−	1.08681i	−0.988058	−	0.154082i	$-0.950758\pi$
$59$	−4.81967	−	8.34791i	−0.627468	−	1.08681i	0.360590	−	0.932724i	$-0.382575\pi$
$60$	8.92177	+	15.4530i	1.15180	+	1.99497i
$61$	−2.26103	+	3.91622i	−0.289496	+	0.501421i	−0.973689	−	0.227879i	$-0.926821\pi$
$61$	−2.26103	+	3.91622i	−0.289496	+	0.501421i	0.684194	+	0.729300i	$0.260154\pi$
$62$	−18.5887			−2.36077
$63$	−0.340120	+	2.62380i	−0.0428511	+	0.330568i
$64$	20.9764			2.62205
$65$	−5.30736	+	9.19261i	−0.658297	+	1.14020i
$66$	−8.28848	−	14.3561i	−1.02024	−	1.76711i
$67$	0.869242	+	1.50557i	0.106195	+	0.183935i	0.914226	−	0.405205i	$-0.132800\pi$
$67$	0.869242	+	1.50557i	0.106195	+	0.183935i	−0.808031	+	0.589140i	$0.799467\pi$
$68$	−7.11595	+	12.3252i	−0.862936	+	1.49465i
$69$	−3.55326			−0.427762
$70$	−19.2689	−	14.7248i	−2.30308	−	1.75994i
$71$	−14.2790			−1.69460			−0.847301	−	0.531113i	$-0.821774\pi$
$71$	−14.2790			−1.69460			−0.847301	+	0.531113i	$0.821774\pi$
$72$	−4.35396	+	7.54127i	−0.513119	+	0.888748i
$73$	−0.492440	−	0.852932i	−0.0576358	−	0.0998281i	0.835768	−	0.549083i	$-0.185023\pi$
$73$	−0.492440	−	0.852932i	−0.0576358	−	0.0998281i	−0.893404	+	0.449255i	$0.851690\pi$
$74$	11.7910	+	20.4226i	1.37067	+	2.37408i
$75$	3.30464	−	5.72380i	0.381586	−	0.660927i
$76$	37.4855			4.29988
$77$	12.9540	+	9.89908i	1.47625	+	1.12811i
$78$	−8.38076			−0.948935
$79$	4.34274	−	7.52185i	0.488597	−	0.846274i	−0.511317	−	0.859392i	$-0.670842\pi$
$79$	4.34274	−	7.52185i	0.488597	−	0.846274i	0.999914	+	0.0131177i	$0.00417560\pi$
$80$	−22.0649	−	38.2175i	−2.46693	−	4.27284i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.34508	+	2.32975i	−0.148539	+	0.257277i
$83$	1.55919			0.171144			0.0855719	−	0.996332i	$-0.472728\pi$
$83$	1.55919			0.171144			0.0855719	+	0.996332i	$0.472728\pi$
$84$	1.78119	−	13.7407i	0.194344	−	1.49923i
$85$	9.25948			1.00433
$86$	−4.06285	+	7.03707i	−0.438109	+	0.758826i
$87$	−0.895871	−	1.55169i	−0.0960474	−	0.166359i
$88$	26.8294	+	46.4699i	2.86003	+	4.95371i
$89$	−2.23931	+	3.87860i	−0.237367	+	0.411131i	−0.959958	−	0.280145i	$-0.909618\pi$
$89$	−2.23931	+	3.87860i	−0.237367	+	0.411131i	0.722591	+	0.691276i	$0.242951\pi$
$90$	9.16601			0.966182
$91$	7.60871	−	3.16938i	0.797610	−	0.332242i
$92$	18.6083			1.94005
$93$	−3.45495	+	5.98414i	−0.358261	+	0.620527i
$94$	6.72031	+	11.6399i	0.693147	+	1.20057i
$95$	−12.1943	−	21.1212i	−1.25111	−	2.16699i
$96$	8.71323	−	15.0918i	0.889291	−	1.54030i
$97$	−4.47579			−0.454448			−0.227224	−	0.973843i	$-0.572965\pi$
$97$	−4.47579			−0.454448			−0.227224	+	0.973843i	$0.572965\pi$
$98$	4.94620	+	18.1699i	0.499641	+	1.83544i
$99$	−6.16208			−0.619312
$100$	−17.3062	+	29.9752i	−1.73062	+	2.99752i
$101$	−1.75631	−	3.04202i	−0.174760	−	0.302692i	0.765319	−	0.643652i	$-0.222581\pi$
$101$	−1.75631	−	3.04202i	−0.174760	−	0.302692i	−0.940078	+	0.340959i	$0.889248\pi$
$102$	3.65538	+	6.33130i	0.361936	+	0.626892i
$103$	−5.77054	+	9.99487i	−0.568588	+	0.984823i	0.428118	+	0.903723i	$0.359177\pi$
$103$	−5.77054	+	9.99487i	−0.568588	+	0.984823i	−0.996706	+	0.0811005i	$0.974157\pi$
$104$	27.1281			2.66013
$105$	−8.32162	+	3.46634i	−0.812107	+	0.338280i
$106$	−6.94093			−0.674162
$107$	2.69974	−	4.67609i	0.260994	−	0.452054i	−0.705513	−	0.708697i	$-0.749283\pi$
$107$	2.69974	−	4.67609i	0.260994	−	0.452054i	0.966506	+	0.256643i	$0.0826165\pi$
$108$	2.61848	+	4.53533i	0.251963	+	0.436413i
$109$	−9.34945	−	16.1937i	−0.895514	−	1.55108i	−0.833167	−	0.553022i	$-0.813475\pi$
$109$	−9.34945	−	16.1937i	−0.895514	−	1.55108i	−0.0623478	−	0.998054i	$-0.519859\pi$
$110$	28.2408	−	48.9146i	2.69266	−	4.66382i
$111$	8.76601			0.832033
$112$	−4.40515	+	33.9828i	−0.416248	+	3.21107i
$113$	9.53967			0.897417			0.448709	−	0.893678i	$-0.351884\pi$
$113$	9.53967			0.897417			0.448709	+	0.893678i	$0.351884\pi$
$114$	9.62792	−	16.6761i	0.901738	−	1.56186i
$115$	−6.05340	−	10.4848i	−0.564483	−	0.977713i
$116$	4.69163	+	8.12614i	0.435607	+	0.754494i
$117$	−1.55767	+	2.69797i	−0.144007	+	0.249427i
$118$	25.9314			2.38717
$119$	−5.71297	−	4.36568i	−0.523707	−	0.400201i
$120$	−29.6699			−2.70848
$121$	−13.4856	+	23.3578i	−1.22596	+	2.12343i
$122$	−6.08254	−	10.5353i	−0.550687	−	0.953818i
$123$	0.500000	+	0.866025i	0.0450835	+	0.0780869i
$124$	18.0934	−	31.3387i	1.62483	−	2.81430i
$125$	5.48317			0.490429
$126$	−5.65529	−	4.32161i	−0.503814	−	0.385000i
$127$	14.8639			1.31896			0.659478	−	0.751724i	$-0.270777\pi$
$127$	14.8639			1.31896			0.659478	+	0.751724i	$0.270777\pi$
$128$	−10.7885	+	18.6862i	−0.953577	+	1.65164i
$129$	1.51026	+	2.61586i	0.132971	+	0.230313i
$130$	−14.2776	−	24.7296i	−1.25223	−	2.16893i
$131$	3.07563	−	5.32714i	0.268719	−	0.465435i	−0.699812	−	0.714327i	$-0.746733\pi$
$131$	3.07563	−	5.32714i	0.268719	−	0.465435i	0.968531	+	0.248892i	$0.0800664\pi$
$132$	32.2705			2.80879
$133$	−2.43454	+	18.7809i	−0.211101	+	1.62851i
$134$	−4.67680			−0.404014
$135$	1.70362	−	2.95075i	0.146624	−	0.253961i
$136$	−11.8323	−	20.4941i	−1.01461	−	1.75736i
$137$	−0.570421	−	0.987999i	−0.0487344	−	0.0844104i	0.840629	−	0.541611i	$-0.182185\pi$
$137$	−0.570421	−	0.987999i	−0.0487344	−	0.0844104i	−0.889364	+	0.457201i	$0.848852\pi$
$138$	4.77942	−	8.27819i	0.406851	−	0.704687i
$139$	−6.86085			−0.581929			−0.290965	−	0.956734i	$-0.593976\pi$
$139$	−6.86085			−0.581929			−0.290965	+	0.956734i	$0.593976\pi$
$140$	43.5799	−	18.1531i	3.68318	−	1.53421i
$141$	4.99622			0.420758
$142$	19.2064	−	33.2664i	1.61176	−	2.79165i
$143$	9.59849	+	16.6251i	0.802666	+	1.39026i
$144$	−6.47588	−	11.2166i	−0.539657	−	0.934713i
$145$	3.05244	−	5.28699i	0.253492	−	0.439061i
$146$	2.64948			0.219273
$147$	6.76864	+	1.78481i	0.558268	+	0.147209i
$148$	−45.9072			−3.77355
$149$	9.09682	−	15.7562i	0.745241	−	1.29079i	−0.204842	−	0.978795i	$-0.565668\pi$
$149$	9.09682	−	15.7562i	0.745241	−	1.29079i	0.950082	−	0.311999i	$-0.100999\pi$
$150$	8.88999	+	15.3979i	0.725865	+	1.25723i
$151$	3.98346	+	6.89955i	0.324169	+	0.561478i	0.981344	−	0.192261i	$-0.0615820\pi$
$151$	3.98346	+	6.89955i	0.324169	+	0.561478i	−0.657175	+	0.753738i	$0.728249\pi$
$152$	−31.1651	+	53.9796i	−2.52783	+	4.37832i
$153$	2.71759			0.219704
$154$	−40.4865	+	16.8645i	−3.26250	+	1.35898i
$155$	−23.5436			−1.89107
$156$	8.15745	−	14.1291i	0.653119	−	1.13123i
$157$	7.66976	+	13.2844i	0.612113	+	1.06021i	0.990884	+	0.134721i	$0.0430137\pi$
$157$	7.66976	+	13.2844i	0.612113	+	1.06021i	−0.378770	+	0.925491i	$0.623653\pi$
$158$	11.6827	+	20.2350i	0.929423	+	1.60981i
$159$	−1.29006	+	2.23445i	−0.102308	+	0.177203i
$160$	59.3761			4.69409
$161$	−1.20853	+	9.32304i	−0.0952458	+	0.734759i
$162$	2.69016			0.211359
$163$	−5.03059	+	8.71325i	−0.394027	+	0.682474i	−0.992976	−	0.118312i	$-0.962252\pi$
$163$	−5.03059	+	8.71325i	−0.394027	+	0.682474i	0.598950	+	0.800787i	$0.295585\pi$
$164$	−2.61848	−	4.53533i	−0.204469	−	0.354150i
$165$	−10.4978	−	18.1828i	−0.817255	−	1.41553i
$166$	−2.09724	+	3.63252i	−0.162777	+	0.281939i
$167$	−25.0532			−1.93868			−0.969338	−	0.245732i	$-0.920972\pi$
$167$	−25.0532			−1.93868			−0.969338	+	0.245732i	$0.920972\pi$
$168$	18.3059	+	13.9888i	1.41233	+	1.07926i
$169$	−3.29464			−0.253434
$170$	−12.4547	+	21.5722i	−0.955235	+	1.65452i
$171$	−3.57894	−	6.19891i	−0.273689	−	0.474043i
$172$	−7.90918	−	13.6991i	−0.603070	−	1.04455i
$173$	1.88278	−	3.26107i	0.143145	−	0.247935i	−0.785534	−	0.618818i	$-0.787612\pi$
$173$	1.88278	−	3.26107i	0.143145	−	0.247935i	0.928679	+	0.370883i	$0.120945\pi$
$174$	4.82007			0.365408
$175$	−13.8941	−	10.6175i	−1.05030	−	0.802605i
$176$	−79.8098			−6.01589
$177$	4.81967	−	8.34791i	0.362269	−	0.627468i
$178$	−6.02411	−	10.4341i	−0.451526	−	0.782066i
$179$	8.51567	+	14.7496i	0.636491	+	1.10243i	0.986197	+	0.165575i	$0.0529481\pi$
$179$	8.51567	+	14.7496i	0.636491	+	1.10243i	−0.349706	+	0.936859i	$0.613719\pi$
$180$	−8.92177	+	15.4530i	−0.664990	+	1.15180i
$181$	8.03112			0.596948			0.298474	−	0.954418i	$-0.403522\pi$
$181$	8.03112			0.596948			0.298474	+	0.954418i	$0.403522\pi$
$182$	−2.85046	+	21.9894i	−0.211290	+	1.62997i
$183$	−4.52207			−0.334281
$184$	−15.4707	+	26.7961i	−1.14052	+	1.97544i
$185$	14.9339	+	25.8663i	1.09797	+	1.90173i
$186$	−9.29435	−	16.0983i	−0.681495	−	1.18038i
$187$	8.37301	−	14.5025i	0.612295	−	1.06053i
$188$	−26.1650			−1.90828
$189$	−2.44234	+	1.01735i	−0.177654	+	0.0740011i
$190$	65.6093			4.75980
$191$	−0.0126823	+	0.0219664i	−0.000917660	+	0.00158943i	−0.866484	−	0.499205i	$-0.833625\pi$
$191$	−0.0126823	+	0.0219664i	−0.000917660	+	0.00158943i	0.865566	+	0.500795i	$0.166959\pi$
$192$	10.4882	+	18.1661i	0.756922	+	1.31103i
$193$	3.23915	+	5.61038i	0.233159	+	0.403844i	0.958736	−	0.284297i	$-0.0917603\pi$
$193$	3.23915	+	5.61038i	0.233159	+	0.403844i	−0.725577	+	0.688141i	$0.758427\pi$
$194$	6.02029	−	10.4275i	0.432232	−	0.748647i
$195$	−10.6147			−0.760135
$196$	−35.4470	−	9.34697i	−2.53193	−	0.667641i
$197$	5.96735			0.425156			0.212578	−	0.977144i	$-0.431814\pi$
$197$	5.96735			0.425156			0.212578	+	0.977144i	$0.431814\pi$
$198$	8.28848	−	14.3561i	0.589037	−	1.02024i
$199$	−0.350132	−	0.606446i	−0.0248202	−	0.0429898i	0.853349	−	0.521341i	$-0.174568\pi$
$199$	−0.350132	−	0.606446i	−0.0248202	−	0.0429898i	−0.878169	+	0.478351i	$0.841235\pi$
$200$	−28.7765	−	49.8423i	−2.03480	−	3.52438i
$201$	−0.869242	+	1.50557i	−0.0613116	+	0.106195i
$202$	9.44951			0.664865
$203$	−4.37603	+	1.82282i	−0.307137	+	0.127937i
$204$	−14.2319			−0.996432
$205$	−1.70362	+	2.95075i	−0.118986	+	0.206090i
$206$	−15.5237	−	26.8878i	−1.08158	−	1.87336i
$207$	−1.77663	−	3.07721i	−0.123484	−	0.213881i
$208$	−20.1746	+	34.9434i	−1.39886	+	2.42289i
$209$	−44.1075			−3.05098
$210$	3.11754	−	24.0498i	0.215131	−	1.65959i
$211$	5.72349			0.394021			0.197010	−	0.980401i	$-0.436877\pi$
$211$	5.72349			0.394021			0.197010	+	0.980401i	$0.436877\pi$
$212$	6.75598	−	11.7017i	0.464002	−	0.803676i
$213$	−7.13949	−	12.3660i	−0.489190	−	0.847301i
$214$	7.26273	+	12.5794i	0.496470	+	0.859911i
$215$	−5.14583	+	8.91284i	−0.350943	+	0.607851i
$216$	−8.70791			−0.592499
$217$	14.5261	+	11.1004i	0.986095	+	0.753545i
$218$	50.3030			3.40695
$219$	0.492440	−	0.852932i	0.0332760	−	0.0576358i
$220$	54.9767	+	95.2224i	3.70653	+	6.41989i
$221$	−4.23312	−	7.33197i	−0.284750	−	0.493202i
$222$	−11.7910	+	20.4226i	−0.791359	+	1.37067i
$223$	−5.28384			−0.353832			−0.176916	−	0.984226i	$-0.556612\pi$
$223$	−5.28384			−0.353832			−0.176916	+	0.984226i	$0.556612\pi$
$224$	−36.6342	−	27.9948i	−2.44773	−	1.87048i
$225$	6.60927			0.440618
$226$	−12.8316	+	22.2250i	−0.853546	+	1.47839i
$227$	5.79879	+	10.0438i	0.384879	+	0.666630i	0.991752	−	0.128169i	$-0.0409099\pi$
$227$	5.79879	+	10.0438i	0.384879	+	0.666630i	−0.606873	+	0.794798i	$0.707577\pi$
$228$	18.7428	+	32.4634i	1.24127	+	2.14994i
$229$	6.61391	−	11.4556i	0.437060	−	0.757009i	−0.560402	−	0.828221i	$-0.689353\pi$
$229$	6.61391	−	11.4556i	0.437060	−	0.757009i	0.997461	+	0.0712116i	$0.0226866\pi$
$230$	32.5692			2.14755
$231$	−2.09584	+	16.1681i	−0.137896	+	1.06378i
$232$	−15.6023			−1.02434
$233$	−5.44098	+	9.42406i	−0.356451	+	0.617391i	−0.987365	−	0.158462i	$-0.949347\pi$
$233$	−5.44098	+	9.42406i	−0.356451	+	0.617391i	0.630914	+	0.775852i	$0.282680\pi$
$234$	−4.19038	−	7.25796i	−0.273934	−	0.474467i
$235$	8.51165	+	14.7426i	0.555239	+	0.961702i
$236$	−25.2404	+	43.7176i	−1.64301	+	2.84578i
$237$	8.68549			0.564183
$238$	17.8553	−	7.43757i	1.15739	−	0.482106i
$239$	19.8211			1.28212			0.641061	−	0.767490i	$-0.278494\pi$
$239$	19.8211			1.28212			0.641061	+	0.767490i	$0.278494\pi$
$240$	22.0649	−	38.2175i	1.42428	−	2.46693i
$241$	−5.31548	−	9.20668i	−0.342400	−	0.593055i	0.642478	−	0.766304i	$-0.277907\pi$
$241$	−5.31548	−	9.20668i	−0.342400	−	0.593055i	−0.984878	+	0.173250i	$0.944573\pi$
$242$	−36.2784	−	62.8361i	−2.33207	−	4.03926i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	23.6818			1.51607
$245$	6.26464	+	23.0132i	0.400233	+	1.47026i
$246$	−2.69016			−0.171518
$247$	−11.1496	+	19.3117i	−0.709434	+	1.22878i
$248$	30.0854	+	52.1094i	1.91042	+	3.30895i
$249$	0.779597	+	1.35030i	0.0494049	+	0.0855719i
$250$	−7.37529	+	12.7744i	−0.466455	+	0.807923i
$251$	7.22243			0.455876			0.227938	−	0.973676i	$-0.426802\pi$
$251$	7.22243			0.455876			0.227938	+	0.973676i	$0.426802\pi$
$252$	12.7904	−	5.32780i	0.805719	−	0.335620i
$253$	−21.8955			−1.37656
$254$	−19.9931	+	34.6291i	−1.25448	+	2.17282i
$255$	4.62974	+	8.01895i	0.289926	+	0.502166i
$256$	−8.04633	−	13.9366i	−0.502895	−	0.871040i
$257$	−11.0196	+	19.0866i	−0.687387	+	1.19059i	0.285294	+	0.958440i	$0.407909\pi$
$257$	−11.0196	+	19.0866i	−0.687387	+	1.19059i	−0.972680	+	0.232149i	$0.925424\pi$
$258$	−8.12570			−0.505884
$259$	2.98149	−	23.0002i	0.185261	−	1.42917i
$260$	55.5887			3.44747
$261$	0.895871	−	1.55169i	0.0554530	−	0.0960474i
$262$	8.27393	+	14.3309i	0.511165	+	0.885363i
$263$	4.63964	+	8.03609i	0.286092	+	0.495527i	0.972874	−	0.231338i	$-0.0743102\pi$
$263$	4.63964	+	8.03609i	0.286092	+	0.495527i	−0.686781	+	0.726864i	$0.740977\pi$
$264$	−26.8294	+	46.4699i	−1.65124	+	2.86003i
$265$	−8.79108			−0.540032
$266$	−40.4800	−	30.9336i	−2.48199	−	1.89666i
$267$	−4.47862			−0.274087
$268$	4.55218	−	7.88461i	0.278069	−	0.481629i
$269$	11.2962	+	19.5656i	0.688743	+	1.19294i	0.972245	+	0.233966i	$0.0751705\pi$
$269$	11.2962	+	19.5656i	0.688743	+	1.19294i	−0.283502	+	0.958972i	$0.591496\pi$
$270$	4.58300	+	7.93800i	0.278913	+	0.483091i
$271$	−3.12923	+	5.41999i	−0.190087	+	0.329241i	−0.945279	−	0.326263i	$-0.894210\pi$
$271$	−3.12923	+	5.41999i	−0.190087	+	0.329241i	0.755192	+	0.655504i	$0.227544\pi$
$272$	35.1976			2.13417
$273$	6.54912	+	5.00465i	0.396371	+	0.302895i
$274$	3.06905			0.185408
$275$	20.3634	−	35.2705i	1.22796	−	2.12689i
$276$	9.30413	+	16.1152i	0.560043	+	0.970023i
$277$	−10.4535	−	18.1060i	−0.628092	−	1.08789i	−0.987934	−	0.154874i	$-0.950503\pi$
$277$	−10.4535	−	18.1060i	−0.628092	−	1.08789i	0.359842	−	0.933013i	$-0.382830\pi$
$278$	9.22838	−	15.9840i	0.553482	−	0.958658i
$279$	−6.90989			−0.413684
$280$	−10.0913	+	77.8479i	−0.603072	+	4.65230i
$281$	−4.42179			−0.263782			−0.131891	−	0.991264i	$-0.542105\pi$
$281$	−4.42179			−0.263782			−0.131891	+	0.991264i	$0.542105\pi$
$282$	−6.72031	+	11.6399i	−0.400189	+	0.693147i
$283$	10.1466	+	17.5744i	0.603150	+	1.04469i	0.992341	+	0.123530i	$0.0394214\pi$
$283$	10.1466	+	17.5744i	0.603150	+	1.04469i	−0.389191	+	0.921157i	$0.627245\pi$
$284$	37.3892	+	64.7599i	2.21864	+	3.84279i
$285$	12.1943	−	21.1212i	0.722329	−	1.25111i
$286$	−51.6429			−3.05371
$287$	2.44234	−	1.01735i	0.144167	−	0.0600521i
$288$	17.4265			1.02686
$289$	4.80735	−	8.32657i	0.282785	−	0.489798i
$290$	8.21156	+	14.2228i	0.482199	+	0.835194i
$291$	−2.23790	−	3.87615i	−0.131188	−	0.227224i
$292$	−2.57889	+	4.46676i	−0.150918	+	0.261397i
$293$	17.7507			1.03701			0.518503	−	0.855076i	$-0.326490\pi$
$293$	17.7507			1.03701			0.518503	+	0.855076i	$0.326490\pi$
$294$	−13.2625	+	13.3685i	−0.773485	+	0.779666i
$295$	32.8435			1.91222
$296$	38.1668	−	66.1069i	2.21840	−	3.84238i
$297$	−3.08104	−	5.33652i	−0.178780	−	0.309656i
$298$	24.4719	+	42.3866i	1.41762	+	2.45539i
$299$	−5.53481	+	9.58658i	−0.320086	+	0.554406i
$300$	−34.6124			−1.99835
$301$	7.37715	−	3.07293i	0.425212	−	0.177121i
$302$	−21.4323			−1.23329
$303$	1.75631	−	3.04202i	0.100897	−	0.174760i
$304$	−46.3536	−	80.2868i	−2.65856	−	4.60477i
$305$	−7.70388	−	13.3435i	−0.441123	−	0.764047i
$306$	−3.65538	+	6.33130i	−0.208964	+	0.361936i
$307$	−0.0193606			−0.00110497			−0.000552483	−	1.00000i	$-0.500176\pi$
$307$	−0.0193606			−0.00110497			−0.000552483		1.00000i	$0.500176\pi$
$308$	10.9758	−	84.6713i	0.625406	−	4.82460i
$309$	−11.5411			−0.656549
$310$	31.6681	−	54.8507i	1.79863	−	3.11531i
$311$	−5.53492	−	9.58676i	−0.313857	−	0.543615i	0.665337	−	0.746543i	$-0.268288\pi$
$311$	−5.53492	−	9.58676i	−0.313857	−	0.543615i	−0.979194	+	0.202927i	$0.934954\pi$
$312$	13.5641	+	23.4937i	0.767914	+	1.33007i
$313$	1.06256	−	1.84041i	0.0600596	−	0.104026i	−0.834432	−	0.551111i	$-0.814204\pi$
$313$	1.06256	−	1.84041i	0.0600596	−	0.104026i	0.894492	+	0.447084i	$0.147538\pi$
$314$	−41.2657			−2.32876
$315$	−7.16275	−	5.47356i	−0.403575	−	0.308400i
$316$	−45.4855			−2.55876
$317$	10.2827	−	17.8102i	0.577535	−	1.00032i	−0.418226	−	0.908343i	$-0.637348\pi$
$317$	10.2827	−	17.8102i	0.577535	−	1.00032i	0.995761	−	0.0919767i	$-0.0293185\pi$
$318$	−3.47046	−	6.01102i	−0.194614	−	0.337081i
$319$	−5.52043	−	9.56166i	−0.309085	−	0.535350i
$320$	−35.7358	+	61.8963i	−1.99769	+	3.46011i
$321$	5.39948			0.301370
$322$	−20.0947	−	15.3558i	−1.11984	−	0.855746i
$323$	19.4522			1.08235
$324$	−2.61848	+	4.53533i	−0.145471	+	0.251963i
$325$	−10.2951	−	17.8316i	−0.571068	−	0.989118i
$326$	−13.5331	−	23.4400i	−0.749529	−	1.29822i
$327$	9.34945	−	16.1937i	0.517026	−	0.895514i
$328$	8.70791			0.480814
$329$	1.69931	−	13.1091i	0.0936861	−	0.722727i
$330$	56.4817			3.10921
$331$	13.8228	−	23.9418i	0.759769	−	1.31596i	−0.183199	−	0.983076i	$-0.558645\pi$
$331$	13.8228	−	23.9418i	0.759769	−	1.31596i	0.942968	−	0.332882i	$-0.108021\pi$
$332$	−4.08271	−	7.07146i	−0.224068	−	0.388097i
$333$	4.38300	+	7.59159i	0.240187	+	0.416016i
$334$	33.6986	−	58.3676i	1.84390	−	3.19373i
$335$	−5.92343			−0.323632
$336$	−31.6326	+	13.1764i	−1.72570	+	0.718834i
$337$	−9.41963			−0.513120			−0.256560	−	0.966528i	$-0.582589\pi$
$337$	−9.41963			−0.513120			−0.256560	+	0.966528i	$0.582589\pi$
$338$	4.43155	−	7.67568i	0.241045	−	0.417502i
$339$	4.76984	+	8.26160i	0.259062	+	0.448709i
$340$	−24.2457	−	41.9948i	−1.31491	−	2.27749i
$341$	−21.2896	+	36.8748i	−1.15290	+	1.99688i
$342$	19.2558			1.04124
$343$	6.98513	−	17.1525i	0.377162	−	0.926147i
$344$	26.3025			1.41814
$345$	6.05340	−	10.4848i	0.325904	−	0.564483i
$346$	5.06498	+	8.77281i	0.272295	+	0.471629i
$347$	0.469652	+	0.813462i	0.0252123	+	0.0436689i	0.878356	−	0.478007i	$-0.158641\pi$
$347$	0.469652	+	0.813462i	0.0252123	+	0.0436689i	−0.853144	+	0.521676i	$0.825307\pi$
$348$	−4.69163	+	8.12614i	−0.251498	+	0.435607i
$349$	3.17758			0.170092			0.0850461	−	0.996377i	$-0.472896\pi$
$349$	3.17758			0.170092			0.0850461	+	0.996377i	$0.472896\pi$
$350$	43.4247	−	18.0884i	2.32115	−	0.966866i
$351$	−3.11534			−0.166285
$352$	53.6916	−	92.9966i	2.86177	−	4.95674i
$353$	−9.71988	−	16.8353i	−0.517337	−	0.896054i	−0.999797	−	0.0201362i	$-0.993590\pi$
$353$	−9.71988	−	16.8353i	−0.517337	−	0.896054i	0.482460	−	0.875918i	$-0.339743\pi$
$354$	12.9657	+	22.4572i	0.689118	+	1.19359i
$355$	24.3259	−	42.1337i	1.29109	−	2.23623i
$356$	23.4543			1.24308
$357$	0.924307	−	7.13041i	0.0489195	−	0.377382i
$358$	−45.8170			−2.42150
$359$	14.3400	−	24.8377i	0.756839	−	1.31088i	−0.187616	−	0.982242i	$-0.560076\pi$
$359$	14.3400	−	24.8377i	0.756839	−	1.31088i	0.944455	−	0.328641i	$-0.106590\pi$
$360$	−14.8350	−	25.6949i	−0.781871	−	1.35424i
$361$	−16.1177	−	27.9166i	−0.848298	−	1.46930i
$362$	−10.8025	+	18.7105i	−0.567766	+	0.983400i
$363$	−26.9712			−1.41562
$364$	−34.2974	−	26.2091i	−1.79767	−	1.37373i
$365$	3.35572			0.175647
$366$	6.08254	−	10.5353i	0.317939	−	0.550687i
$367$	17.8450	+	30.9085i	0.931503	+	1.61341i	0.780755	+	0.624837i	$0.214835\pi$
$367$	17.8450	+	30.9085i	0.931503	+	1.61341i	0.150748	+	0.988572i	$0.451832\pi$
$368$	−23.0105	−	39.8554i	−1.19951	−	2.07760i
$369$	−0.500000	+	0.866025i	−0.0260290	+	0.0450835i
$370$	−80.3493			−4.17716
$371$	5.42397	+	4.14483i	0.281598	+	0.215189i
$372$	36.1868			1.87620
$373$	−3.30144	+	5.71827i	−0.170942	+	0.296081i	−0.938750	−	0.344600i	$-0.888014\pi$
$373$	−3.30144	+	5.71827i	−0.170942	+	0.296081i	0.767807	+	0.640681i	$0.221348\pi$
$374$	22.5247	+	39.0140i	1.16473	+	2.01736i
$375$	2.74158	+	4.74856i	0.141575	+	0.245215i
$376$	21.7533	−	37.6779i	1.12184	−	1.94309i
$377$	−5.58189			−0.287482
$378$	0.914976	−	7.05843i	0.0470613	−	0.363047i
$379$	6.60966			0.339515			0.169758	−	0.985486i	$-0.445702\pi$
$379$	6.60966			0.339515			0.169758	+	0.985486i	$0.445702\pi$
$380$	−63.8610	+	110.611i	−3.27600	+	5.67420i
$381$	7.43194	+	12.8725i	0.380750	+	0.659478i
$382$	−0.0341174	−	0.0590931i	−0.00174560	−	0.00302347i
$383$	−13.9891	+	24.2298i	−0.714809	+	1.23809i	0.248224	+	0.968703i	$0.420153\pi$
$383$	−13.9891	+	24.2298i	−0.714809	+	1.23809i	−0.963033	+	0.269383i	$0.913180\pi$
$384$	−21.5770			−1.10110
$385$	−51.2785	+	21.3599i	−2.61339	+	1.08860i
$386$	−17.4277			−0.887045
$387$	−1.51026	+	2.61586i	−0.0767711	+	0.132971i
$388$	11.7197	+	20.2992i	0.594980	+	1.03054i
$389$	11.9854	+	20.7592i	0.607681	+	1.05254i	0.991622	+	0.129177i	$0.0412336\pi$
$389$	11.9854	+	20.7592i	0.607681	+	1.05254i	−0.383940	+	0.923358i	$0.625433\pi$
$390$	14.2776	−	24.7296i	0.722976	−	1.25223i
$391$	9.65631			0.488341
$392$	42.9301	−	43.2732i	2.16830	−	2.18562i
$393$	6.15126			0.310290
$394$	−8.02656	+	13.9024i	−0.404372	+	0.700393i
$395$	14.7968	+	25.6287i	0.744506	+	1.28952i
$396$	16.1353	+	27.9471i	0.810827	+	1.40439i
$397$	−3.13579	+	5.43135i	−0.157381	+	0.272592i	−0.933923	−	0.357473i	$-0.883638\pi$
$397$	−3.13579	+	5.43135i	−0.157381	+	0.272592i	0.776542	+	0.630065i	$0.216972\pi$
$398$	1.88382			0.0944274
$399$	−17.4820	+	7.28205i	−0.875193	+	0.364559i
$400$	85.6017			4.28009
$401$	−1.14519	+	1.98353i	−0.0571882	+	0.0990529i	−0.893202	−	0.449655i	$-0.851547\pi$
$401$	−1.14519	+	1.98353i	−0.0571882	+	0.0990529i	0.836014	+	0.548708i	$0.184880\pi$
$402$	−2.33840	−	4.05023i	−0.116629	−	0.202007i
$403$	10.7633	+	18.6427i	0.536160	+	0.928657i
$404$	−9.19772	+	15.9309i	−0.457604	+	0.792593i
$405$	3.40724			0.169307
$406$	1.63940	−	12.6469i	0.0813621	−	0.627654i
$407$	54.0168			2.67752
$408$	11.8323	−	20.4941i	0.585785	−	1.01461i
$409$	−3.27472	−	5.67197i	−0.161924	−	0.280461i	0.773635	−	0.633632i	$-0.218437\pi$
$409$	−3.27472	−	5.67197i	−0.161924	−	0.280461i	−0.935559	+	0.353171i	$0.885103\pi$
$410$	−4.58300	−	7.93800i	−0.226338	−	0.392030i
$411$	0.570421	−	0.987999i	0.0281368	−	0.0487344i
$412$	60.4401			2.97767
$413$	−20.2640	−	15.4851i	−0.997125	−	0.761974i
$414$	9.55884			0.469791
$415$	−2.65627	+	4.60080i	−0.130391	+	0.225844i
$416$	−27.1447	−	47.0160i	−1.33088	−	2.30515i
$417$	−3.43042	−	5.94167i	−0.167989	−	0.290965i
$418$	59.3280	−	102.759i	2.90183	−	5.02612i
$419$	29.0673			1.42003			0.710016	−	0.704185i	$-0.248688\pi$
$419$	29.0673			1.42003			0.710016	+	0.704185i	$0.248688\pi$
$420$	37.5110	+	28.6648i	1.83035	+	1.39870i
$421$	30.5913			1.49093			0.745463	−	0.666547i	$-0.232228\pi$
$421$	30.5913			1.49093			0.745463	+	0.666547i	$0.232228\pi$
$422$	−7.69854	+	13.3343i	−0.374759	+	0.649102i
$423$	2.49811	+	4.32685i	0.121462	+	0.210379i
$424$	11.2337	+	19.4574i	0.545558	+	0.944934i
$425$	−8.98065	+	15.5549i	−0.435626	+	0.754526i
$426$	38.4127			1.86110
$427$	−1.53804	+	11.8650i	−0.0744312	+	0.574187i
$428$	−28.2768			−1.36681
$429$	−9.59849	+	16.6251i	−0.463420	+	0.802666i
$430$	−13.8431	−	23.9770i	−0.667574	−	1.15627i
$431$	1.30917	+	2.26756i	0.0630607	+	0.109224i	0.895832	−	0.444393i	$-0.146580\pi$
$431$	1.30917	+	2.26756i	0.0630607	+	0.109224i	−0.832771	+	0.553617i	$0.813247\pi$
$432$	6.47588	−	11.2166i	0.311571	−	0.539657i
$433$	−32.7329			−1.57304			−0.786520	−	0.617564i	$-0.788120\pi$
$433$	−32.7329			−1.57304			−0.786520	+	0.617564i	$0.788120\pi$
$434$	−45.3999	+	18.9112i	−2.17926	+	0.907765i
$435$	6.10489			0.292707
$436$	−48.9626	+	84.8057i	−2.34488	+	4.06146i
$437$	−12.7169	−	22.0264i	−0.608333	−	1.05366i
$438$	1.32474	+	2.29452i	0.0632986	+	0.109636i
$439$	−13.4937	+	23.3718i	−0.644019	+	1.11547i	0.340508	+	0.940242i	$0.389401\pi$
$439$	−13.4937	+	23.3718i	−0.644019	+	1.11547i	−0.984527	+	0.175232i	$0.943932\pi$
$440$	−182.828			−8.71601
$441$	1.83863	+	6.75422i	0.0875537	+	0.321629i
$442$	22.7755			1.08332
$443$	17.6025	−	30.4885i	0.836322	−	1.44855i	−0.0566278	−	0.998395i	$-0.518035\pi$
$443$	17.6025	−	30.4885i	0.836322	−	1.44855i	0.892950	−	0.450157i	$-0.148632\pi$
$444$	−22.9536	−	39.7568i	−1.08933	−	1.88677i
$445$	−7.62987	−	13.2153i	−0.361691	−	0.626466i
$446$	7.10718	−	12.3100i	0.336535	−	0.582895i
$447$	18.1936			0.860530
$448$	51.2315	−	21.3403i	2.42046	−	1.00823i
$449$	−5.93471			−0.280076			−0.140038	−	0.990146i	$-0.544723\pi$
$449$	−5.93471			−0.280076			−0.140038	+	0.990146i	$0.544723\pi$
$450$	−8.88999	+	15.3979i	−0.419078	+	0.725865i
$451$	3.08104	+	5.33652i	0.145080	+	0.251287i
$452$	−24.9794	−	43.2656i	−1.17493	−	2.03504i
$453$	−3.98346	+	6.89955i	−0.187159	+	0.324169i
$454$	−31.1993			−1.46426
$455$	−3.61027	+	27.8509i	−0.169252	+	1.30567i
$456$	−62.3303			−2.91888
$457$	16.2920	−	28.2186i	0.762109	−	1.32001i	−0.179652	−	0.983730i	$-0.557497\pi$
$457$	16.2920	−	28.2186i	0.762109	−	1.32001i	0.941761	−	0.336282i	$-0.109169\pi$
$458$	17.7925	+	30.8175i	0.831387	+	1.44001i
$459$	1.35880	+	2.35350i	0.0634232	+	0.109852i
$460$	−31.7014	+	54.9084i	−1.47808	+	2.56012i
$461$	33.2676			1.54943			0.774714	−	0.632311i	$-0.217894\pi$
$461$	33.2676			1.54943			0.774714	+	0.632311i	$0.217894\pi$
$462$	−34.8484	−	26.6301i	−1.62129	−	1.23894i
$463$	8.98217			0.417437			0.208718	−	0.977976i	$-0.433071\pi$
$463$	8.98217			0.417437			0.208718	+	0.977976i	$0.433071\pi$
$464$	11.6031	−	20.0972i	0.538661	−	0.932988i
$465$	−11.7718	−	20.3894i	−0.545905	−	0.945536i
$466$	−14.6371	−	25.3522i	−0.678051	−	1.17442i
$467$	−0.809905	+	1.40280i	−0.0374780	+	0.0649137i	−0.884156	−	0.467192i	$-0.845266\pi$
$467$	−0.809905	+	1.40280i	−0.0374780	+	0.0649137i	0.846678	+	0.532106i	$0.178599\pi$
$468$	16.3149			0.754157
$469$	3.65467	+	2.79279i	0.168757	+	0.128959i
$470$	−45.7954			−2.11238
$471$	−7.66976	+	13.2844i	−0.353404	+	0.612113i
$472$	−41.9693	−	72.6929i	−1.93179	−	3.34596i
$473$	9.30637	+	16.1191i	0.427907	+	0.741157i
$474$	−11.6827	+	20.2350i	−0.536603	+	0.929423i
$475$	47.3084			2.17066
$476$	−4.84055	+	37.3416i	−0.221866	+	1.71155i
$477$	−2.58012			−0.118135
$478$	−26.6610	+	46.1782i	−1.21945	+	2.11214i
$479$	16.3187	+	28.2648i	0.745620	+	1.29145i	0.949905	+	0.312540i	$0.101180\pi$
$479$	16.3187	+	28.2648i	0.745620	+	1.29145i	−0.204285	+	0.978912i	$0.565487\pi$
$480$	29.6881	+	51.4212i	1.35507	+	2.34705i
$481$	13.6546	−	23.6504i	0.622594	−	1.07837i
$482$	28.5990			1.30265
$483$	−8.67826	+	3.61490i	−0.394874	+	0.164484i
$484$	141.247			6.42032
$485$	7.62504	−	13.2070i	0.346235	−	0.599697i
$486$	1.34508	+	2.32975i	0.0610140	+	0.105679i
$487$	17.8276	+	30.8783i	0.807844	+	1.39923i	0.914354	+	0.404916i	$0.132699\pi$
$487$	17.8276	+	30.8783i	0.807844	+	1.39923i	−0.106509	+	0.994312i	$0.533967\pi$
$488$	−19.6889	+	34.1021i	−0.891274	+	1.54373i
$489$	−10.0612			−0.454983
$490$	−62.0414	−	16.3596i	−2.80274	−	0.739051i
$491$	−30.7265			−1.38667			−0.693335	−	0.720616i	$-0.743859\pi$
$491$	−30.7265			−1.38667			−0.693335	+	0.720616i	$0.743859\pi$
$492$	2.61848	−	4.53533i	0.118050	−	0.204469i
$493$	2.43461	+	4.21687i	0.109649	+	0.189918i
$494$	−29.9943	−	51.9516i	−1.34951	−	2.33741i
$495$	10.4978	−	18.1828i	0.471843	−	0.817255i
$496$	−89.4953			−4.01846
$497$	−34.8741	+	14.5267i	−1.56432	+	0.651610i
$498$	−4.19448			−0.187959
$499$	9.63341	−	16.6856i	0.431251	−	0.746948i	−0.565731	−	0.824590i	$-0.691406\pi$
$499$	9.63341	−	16.6856i	0.431251	−	0.746948i	0.996981	+	0.0776422i	$0.0247392\pi$
$500$	−14.3575	−	24.8680i	−0.642089	−	1.11213i
$501$	−12.5266	−	21.6967i	−0.559647	−	0.969338i
$502$	−9.71474	+	16.8264i	−0.433590	+	0.751000i
$503$	29.6789			1.32332			0.661659	−	0.749804i	$-0.269852\pi$
$503$	29.6789			1.32332			0.661659	+	0.749804i	$0.269852\pi$
$504$	−2.96173	+	22.8478i	−0.131926	+	1.01772i
$505$	11.9683			0.532584
$506$	29.4512	−	51.0109i	1.30926	−	2.26771i
$507$	−1.64732	−	2.85324i	−0.0731601	−	0.126717i
$508$	−38.9207	−	67.4127i	−1.72683	−	2.99095i
$509$	−9.31318	+	16.1309i	−0.412799	+	0.714989i	−0.995195	−	0.0979163i	$-0.968782\pi$
$509$	−9.31318	+	16.1309i	−0.412799	+	0.714989i	0.582395	+	0.812906i	$0.302116\pi$
$510$	−24.9095			−1.10301
$511$	−2.07043	−	1.58216i	−0.0915905	−	0.0699908i
$512$	0.137808			0.00609032
$513$	3.57894	−	6.19891i	0.158014	−	0.273689i
$514$	−29.6446	−	51.3459i	−1.30757	−	2.26477i
$515$	−19.6616	−	34.0549i	−0.866393	−	1.50064i
$516$	7.90918	−	13.6991i	0.348182	−	0.603070i
$517$	30.7871			1.35402
$518$	49.5744	+	37.8833i	2.17817	+	1.66450i
$519$	3.76556			0.165290
$520$	−46.2160	+	80.0485i	−2.02671	+	3.51036i
$521$	4.60265	+	7.97203i	0.201646	+	0.349261i	0.949059	−	0.315099i	$-0.102038\pi$
$521$	4.60265	+	7.97203i	0.201646	+	0.349261i	−0.747413	+	0.664360i	$0.768704\pi$
$522$	2.41003	+	4.17430i	0.105484	+	0.182704i
$523$	10.4910	−	18.1710i	0.458740	−	0.794561i	−0.540155	−	0.841566i	$-0.681634\pi$
$523$	10.4910	−	18.1710i	0.458740	−	0.794561i	0.998895	+	0.0470050i	$0.0149677\pi$
$524$	−32.2138			−1.40727
$525$	2.24794	−	17.3414i	0.0981083	−	0.756840i
$526$	−24.9627			−1.08843
$527$	9.38913	−	16.2625i	0.408997	−	0.708404i
$528$	−39.9049	−	69.1173i	−1.73664	−	3.00794i
$529$	5.18717	+	8.98444i	0.225529	+	0.390628i
$530$	11.8247	−	20.4810i	0.513632	−	0.889637i
$531$	9.63934			0.418312
$532$	91.5522	−	38.1358i	3.96929	−	1.65340i
$533$	3.11534			0.134940
$534$	6.02411	−	10.4341i	0.260689	−	0.451526i
$535$	9.19866	+	15.9325i	0.397693	+	0.688824i
$536$	7.56929	+	13.1104i	0.326943	+	0.566283i
$537$	−8.51567	+	14.7496i	−0.367478	+	0.636491i
$538$	−60.7773			−2.62029
$539$	41.7089	+	10.9981i	1.79653	+	0.473724i
$540$	−17.8435			−0.767864
$541$	−4.84560	+	8.39282i	−0.208328	+	0.360835i	−0.951188	−	0.308612i	$-0.900136\pi$
$541$	−4.84560	+	8.39282i	−0.208328	+	0.360835i	0.742860	+	0.669447i	$0.233469\pi$
$542$	−8.41813	−	14.5806i	−0.361590	−	0.626292i
$543$	4.01556	+	6.95515i	0.172324	+	0.298474i
$544$	−23.6790	+	41.0133i	−1.01523	+	1.75843i
$545$	63.7116			2.72910
$546$	−20.4686	+	8.52615i	−0.875977	+	0.364885i
$547$	−13.5021			−0.577306			−0.288653	−	0.957434i	$-0.593207\pi$
$547$	−13.5021			−0.577306			−0.288653	+	0.957434i	$0.593207\pi$
$548$	−2.98727	+	5.17410i	−0.127610	+	0.221027i
$549$	−2.26103	−	3.91622i	−0.0964985	−	0.167140i
$550$	54.7808	+	94.8832i	2.33586	+	4.04583i
$551$	6.41254	−	11.1068i	0.273183	−	0.473168i
$552$	−30.9415			−1.31696
$553$	2.95410	−	22.7890i	0.125621	−	0.969085i
$554$	56.2433			2.38955
$555$	−14.9339	+	25.8663i	−0.633910	+	1.09797i
$556$	17.9650	+	31.1162i	0.761884	+	1.31962i
$557$	12.8295	+	22.2213i	0.543602	+	0.941546i	0.998693	+	0.0511011i	$0.0162731\pi$
$557$	12.8295	+	22.2213i	0.543602	+	0.941546i	−0.455092	+	0.890444i	$0.650394\pi$
$558$	9.29435	−	16.0983i	0.393461	−	0.681495i
$559$	9.40998			0.398000
$560$	−92.7703	−	70.8923i	−3.92026	−	2.99575i
$561$	16.7460			0.707017
$562$	5.94766	−	10.3016i	0.250887	−	0.434549i
$563$	7.82464	+	13.5527i	0.329769	+	0.571177i	0.982466	−	0.186442i	$-0.0596958\pi$
$563$	7.82464	+	13.5527i	0.329769	+	0.571177i	−0.652697	+	0.757619i	$0.726362\pi$
$564$	−13.0825	−	22.6595i	−0.550872	−	0.954138i
$565$	−16.2520	+	28.1492i	−0.683726	+	1.18425i
$566$	−54.5917			−2.29466
$567$	−2.10222	−	1.60645i	−0.0882848	−	0.0674646i
$568$	−124.340			−5.21719
$569$	−10.0897	+	17.4759i	−0.422984	+	0.732630i	−0.996230	−	0.0867538i	$-0.972351\pi$
$569$	−10.0897	+	17.4759i	−0.422984	+	0.732630i	0.573246	+	0.819383i	$0.305684\pi$
$570$	32.8046	+	56.8193i	1.37403	+	2.37990i
$571$	−18.1842	−	31.4960i	−0.760986	−	1.31807i	−0.942343	−	0.334649i	$-0.891382\pi$
$571$	−18.1842	−	31.4960i	−0.760986	−	1.31807i	0.181357	−	0.983417i	$-0.441951\pi$
$572$	50.2669	−	87.0647i	2.10176	−	3.64036i
$573$	−0.0253646			−0.00105962
$574$	−0.914976	+	7.05843i	−0.0381904	+	0.294613i
$575$	23.4845			0.979370
$576$	−10.4882	+	18.1661i	−0.437009	+	0.756922i
$577$	5.81734	+	10.0759i	0.242179	+	0.419466i	0.961335	−	0.275383i	$-0.0888045\pi$
$577$	5.81734	+	10.0759i	0.242179	+	0.419466i	−0.719156	+	0.694849i	$0.755471\pi$
$578$	12.9325	+	22.3998i	0.537922	+	0.931708i
$579$	−3.23915	+	5.61038i	−0.134615	+	0.233159i
$580$	−31.9710			−1.32752
$581$	3.80807	−	1.58624i	0.157986	−	0.0658084i
$582$	12.0406			0.499098
$583$	−7.94945	+	13.7688i	−0.329232	+	0.570247i
$584$	−4.28813	−	7.42726i	−0.177444	−	0.307342i
$585$	−5.30736	−	9.19261i	−0.219432	−	0.380068i
$586$	−23.8761	+	41.3545i	−0.986311	+	1.70834i
$587$	−16.6760			−0.688291			−0.344146	−	0.938916i	$-0.611831\pi$
$587$	−16.6760			−0.688291			−0.344146	+	0.938916i	$0.611831\pi$
$588$	−9.62880	−	35.3715i	−0.397085	−	1.45870i
$589$	−49.4602			−2.03797
$590$	−44.1771	+	76.5171i	−1.81874	+	3.15016i
$591$	2.98368	+	5.16788i	0.122732	+	0.212578i
$592$	56.7676	+	98.3244i	2.33314	+	4.04111i
$593$	1.41121	−	2.44429i	0.0579516	−	0.100375i	−0.835594	−	0.549347i	$-0.814876\pi$
$593$	1.41121	−	2.44429i	0.0579516	−	0.100375i	0.893546	+	0.448972i	$0.148210\pi$
$594$	16.5770			0.680161
$595$	22.6148	−	9.42011i	0.927115	−	0.386187i
$596$	−95.2792			−3.90279
$597$	0.350132	−	0.606446i	0.0143299	−	0.0248202i
$598$	−14.8895	−	25.7894i	−0.608878	−	1.05461i
$599$	−4.19318	−	7.26280i	−0.171329	−	0.296750i	0.767556	−	0.640982i	$-0.221473\pi$
$599$	−4.19318	−	7.26280i	−0.171329	−	0.296750i	−0.938885	+	0.344232i	$0.888139\pi$
$600$	28.7765	−	49.8423i	1.17479	−	2.03480i
$601$	27.8657			1.13667			0.568333	−	0.822799i	$-0.307589\pi$
$601$	27.8657			1.13667			0.568333	+	0.822799i	$0.307589\pi$
$602$	−2.76371	+	21.3202i	−0.112640	+	0.868947i
$603$	−1.73848			−0.0707966
$604$	20.8612	−	36.1326i	0.848829	−	1.47022i
$605$	−45.9487	−	79.5855i	−1.86808	−	3.23561i
$606$	4.72476	+	8.18352i	0.191930	+	0.332433i
$607$	−14.4488	+	25.0261i	−0.586459	+	1.01578i	0.408233	+	0.912878i	$0.366145\pi$
$607$	−14.4488	+	25.0261i	−0.586459	+	1.01578i	−0.994692	+	0.102899i	$0.967188\pi$
$608$	124.737			5.05874
$609$	−3.76663	−	2.87835i	−0.152631	−	0.116636i
$610$	41.4493			1.67823
$611$	7.78247	−	13.4796i	0.314845	−	0.545327i
$612$	−7.11595	−	12.3252i	−0.287645	−	0.498216i
$613$	−7.45007	−	12.9039i	−0.300905	−	0.521183i	0.675436	−	0.737419i	$-0.263955\pi$
$613$	−7.45007	−	12.9039i	−0.300905	−	0.521183i	−0.976341	+	0.216235i	$0.930622\pi$
$614$	0.0260415	−	0.0451052i	0.00105095	−	0.00182030i
$615$	−3.40724			−0.137393
$616$	112.803	+	86.2004i	4.54494	+	3.47311i
$617$	−31.5116			−1.26861			−0.634305	−	0.773083i	$-0.718714\pi$
$617$	−31.5116			−1.26861			−0.634305	+	0.773083i	$0.718714\pi$
$618$	15.5237	−	26.8878i	0.624453	−	1.08158i
$619$	2.73351	+	4.73457i	0.109869	+	0.190299i	0.915717	−	0.401824i	$-0.131624\pi$
$619$	2.73351	+	4.73457i	0.109869	+	0.190299i	−0.805848	+	0.592122i	$0.798290\pi$
$620$	61.6485	+	106.778i	2.47586	+	4.28832i
$621$	1.77663	−	3.07721i	0.0712937	−	0.123484i
$622$	29.7796			1.19405
$623$	−1.52327	+	11.7510i	−0.0610285	+	0.470794i
$624$	−40.3492			−1.61526
$625$	7.18195	−	12.4395i	0.287278	−	0.497580i
$626$	2.85846	+	4.95100i	0.114247	+	0.197882i
$627$	−22.0537	−	38.1982i	−0.880741	−	1.52549i
$628$	40.1662	−	69.5698i	1.60280	−	2.77614i
$629$	−23.8224			−0.949863
$630$	22.3865	−	9.32501i	0.891899	−	0.371517i
$631$	16.3281			0.650011			0.325005	−	0.945712i	$-0.394634\pi$
$631$	16.3281			0.650011			0.325005	+	0.945712i	$0.394634\pi$
$632$	37.8162	−	65.4996i	1.50425	−	2.60544i
$633$	2.86174	+	4.95668i	0.113744	+	0.197010i
$634$	27.6621	+	47.9122i	1.09860	+	1.90284i
$635$	−25.3224	+	43.8597i	−1.00489	+	1.74052i
$636$	13.5120			0.535784
$637$	15.3587	−	15.4814i	0.608533	−	0.613395i
$638$	29.7016			1.17590
$639$	7.13949	−	12.3660i	0.282434	−	0.489190i
$640$	−36.7590	−	63.6684i	−1.45303	−	2.51671i
$641$	−9.35229	−	16.1986i	−0.369393	−	0.639808i	0.620077	−	0.784541i	$-0.287101\pi$
$641$	−9.35229	−	16.1986i	−0.369393	−	0.639808i	−0.989471	+	0.144733i	$0.953768\pi$
$642$	−7.26273	+	12.5794i	−0.286637	+	0.496470i
$643$	−10.5311			−0.415307			−0.207654	−	0.978202i	$-0.566583\pi$
$643$	−10.5311			−0.415307			−0.207654	+	0.978202i	$0.566583\pi$
$644$	45.4476	−	18.9311i	1.79089	−	0.745988i
$645$	−10.2917			−0.405234
$646$	−26.1648	+	45.3187i	−1.02944	+	1.78304i
$647$	−5.62146	−	9.73665i	−0.221002	−	0.382787i	0.734110	−	0.679030i	$-0.237600\pi$
$647$	−5.62146	−	9.73665i	−0.221002	−	0.382787i	−0.955113	+	0.296243i	$0.904266\pi$
$648$	−4.35396	−	7.54127i	−0.171040	−	0.296249i
$649$	29.6992	−	51.4405i	1.16580	−	2.01922i
$650$	55.3907			2.17260
$651$	−2.35019	+	18.1302i	−0.0921112	+	0.710577i
$652$	52.6900			2.06350
$653$	−4.79125	+	8.29869i	−0.187496	+	0.324753i	−0.944415	−	0.328756i	$-0.893371\pi$
$653$	−4.79125	+	8.29869i	−0.187496	+	0.324753i	0.756919	+	0.653509i	$0.226704\pi$
$654$	25.1515	+	43.5637i	0.983501	+	1.70347i
$655$	10.4794	+	18.1508i	0.409464	+	0.709212i
$656$	−6.47588	+	11.2166i	−0.252841	+	0.437933i
$657$	0.984881			0.0384239
$658$	28.2551	+	21.5917i	1.10150	+	0.841732i
$659$	−7.57775			−0.295187			−0.147594	−	0.989048i	$-0.547153\pi$
$659$	−7.57775			−0.295187			−0.147594	+	0.989048i	$0.547153\pi$
$660$	−54.9767	+	95.2224i	−2.13996	+	3.70653i
$661$	−8.34875	−	14.4605i	−0.324729	−	0.562447i	0.656729	−	0.754127i	$-0.271940\pi$
$661$	−8.34875	−	14.4605i	−0.324729	−	0.562447i	−0.981457	+	0.191680i	$0.938606\pi$
$662$	37.1855	+	64.4071i	1.44525	+	2.50325i
$663$	4.23312	−	7.33197i	0.164401	−	0.284750i
$664$	13.5773			0.526902
$665$	−51.2702	−	39.1791i	−1.98817	−	1.51930i
$666$	−23.5820			−0.913782
$667$	3.18326	−	5.51357i	0.123256	−	0.213486i
$668$	65.6012	+	113.625i	2.53819	+	4.39627i
$669$	−2.64192	−	4.57594i	−0.102143	−	0.176916i
$670$	7.96748	−	13.8001i	0.307811	−	0.533144i
$671$	−27.8653			−1.07573
$672$	5.92709	−	45.7235i	0.228642	−	1.76382i
$673$	30.0090			1.15676			0.578380	−	0.815767i	$-0.303685\pi$
$673$	30.0090			1.15676			0.578380	+	0.815767i	$0.303685\pi$
$674$	12.6702	−	21.9453i	0.488036	−	0.845303i
$675$	3.30464	+	5.72380i	0.127195	+	0.220309i
$676$	8.62694	+	14.9423i	0.331805	+	0.574704i
$677$	18.8383	−	32.6289i	0.724014	−	1.25403i	−0.235364	−	0.971907i	$-0.575628\pi$
$677$	18.8383	−	32.6289i	0.724014	−	1.25403i	0.959379	−	0.282122i	$-0.0910383\pi$
$678$	−25.6632			−0.985591
$679$	−10.9314	+	4.55343i	−0.419508	+	0.174745i
$680$	80.6308			3.09205
$681$	−5.79879	+	10.0438i	−0.222210	+	0.384879i
$682$	−57.2725	−	99.1989i	−2.19308	−	3.79852i
$683$	−10.7768	−	18.6660i	−0.412363	−	0.714234i	0.582784	−	0.812627i	$-0.301963\pi$
$683$	−10.7768	−	18.6660i	−0.412363	−	0.714234i	−0.995148	+	0.0983926i	$0.968630\pi$
$684$	−18.7428	+	32.4634i	−0.716647	+	1.24127i
$685$	3.88712			0.148519
$686$	30.5654	+	39.3450i	1.16699	+	1.50220i
$687$	13.2278			0.504673
$688$	−19.5606	+	33.8799i	−0.745741	+	1.29166i
$689$	4.01898	+	6.96107i	0.153111	+	0.265196i
$690$	16.2846	+	28.2058i	0.619945	+	1.07378i
$691$	15.8957	−	27.5321i	0.604701	−	1.04737i	−0.387398	−	0.921913i	$-0.626626\pi$
$691$	15.8957	−	27.5321i	0.604701	−	1.04737i	0.992099	−	0.125460i	$-0.0400406\pi$
$692$	−19.7201			−0.749645
$693$	−15.0499	+	6.26897i	−0.571697	+	0.238139i
$694$	−2.52688			−0.0959190
$695$	11.6883	−	20.2447i	0.443361	−	0.767924i
$696$	−7.80116	−	13.5120i	−0.295702	−	0.512172i
$697$	−1.35880	−	2.35350i	−0.0514681	−	0.0891453i
$698$	−4.27410	+	7.40296i	−0.161777	+	0.280206i
$699$	−10.8820			−0.411594
$700$	−11.7724	+	90.8160i	−0.444954	+	3.43252i
$701$	−27.0893			−1.02315			−0.511574	−	0.859239i	$-0.670937\pi$
$701$	−27.0893			−1.02315			−0.511574	+	0.859239i	$0.670937\pi$
$702$	4.19038	−	7.25796i	0.158156	−	0.273934i
$703$	31.3731	+	54.3397i	1.18326	+	2.04946i
$704$	64.6292	+	111.941i	2.43581	+	4.21894i
$705$	−8.51165	+	14.7426i	−0.320567	+	0.555239i
$706$	52.2960			1.96819
$707$	−7.38429	−	5.64286i	−0.277715	−	0.212222i
$708$	−50.4808			−1.89718
$709$	−16.2024	+	28.0633i	−0.608493	+	1.05394i	0.382997	+	0.923750i	$0.374892\pi$
$709$	−16.2024	+	28.0633i	−0.608493	+	1.05394i	−0.991489	+	0.130190i	$0.958441\pi$
$710$	65.4406	+	113.346i	2.45594	+	4.25382i
$711$	4.34274	+	7.52185i	0.162866	+	0.282091i
$712$	−19.4997	+	33.7745i	−0.730784	+	1.26575i
$713$	−24.5526			−0.919504
$714$	15.3688	+	11.7444i	0.575162	+	0.439522i
$715$	−65.4087			−2.44615
$716$	44.5962	−	77.2428i	1.66664	−	2.88670i
$717$	9.91056	+	17.1656i	0.370117	+	0.641061i
$718$	38.5770	+	66.8173i	1.43968	+	2.49360i
$719$	18.7440	−	32.4655i	0.699032	−	1.21076i	−0.269770	−	0.962925i	$-0.586948\pi$
$719$	18.7440	−	32.4655i	0.699032	−	1.21076i	0.968802	−	0.247835i	$-0.0797191\pi$
$720$	44.1297			1.64462
$721$	−3.92535	+	30.2815i	−0.146188	+	1.12774i
$722$	86.7182			3.22732
$723$	5.31548	−	9.20668i	0.197685	−	0.342400i
$724$	−21.0293	−	36.4238i	−0.781547	−	1.35368i
$725$	5.92105	+	10.2556i	0.219902	+	0.380882i
$726$	36.2784	−	62.8361i	1.34642	−	2.33207i
$727$	−45.2143			−1.67690			−0.838452	−	0.544975i	$-0.816539\pi$
$727$	−45.2143			−1.67690			−0.838452	+	0.544975i	$0.816539\pi$
$728$	66.2560	−	27.5987i	2.45561	−	1.02288i
$729$	1.00000			0.0370370
$730$	−4.51371	+	7.81798i	−0.167060	+	0.289356i
$731$	−4.10428	−	7.10883i	−0.151802	−	0.262929i
$732$	11.8409	+	20.5091i	0.437653	+	0.758037i
$733$	−15.8411	+	27.4376i	−0.585106	+	1.01343i	0.409757	+	0.912195i	$0.365614\pi$
$733$	−15.8411	+	27.4376i	−0.585106	+	1.01343i	−0.994862	+	0.101238i	$0.967720\pi$
$734$	−96.0119			−3.54386
$735$	−16.7977	+	16.9319i	−0.619593	+	0.624544i
$736$	61.9208			2.28243
$737$	−5.35634	+	9.27745i	−0.197303	+	0.341739i
$738$	−1.34508	−	2.32975i	−0.0495130	−	0.0857591i
$739$	−5.72150	−	9.90992i	−0.210469	−	0.364542i	0.741393	−	0.671072i	$-0.234166\pi$
$739$	−5.72150	−	9.90992i	−0.210469	−	0.364542i	−0.951861	+	0.306529i	$0.900832\pi$
$740$	78.2083	−	135.461i	2.87500	−	4.97964i
$741$	−22.2993			−0.819184
$742$	−16.9521	+	7.06133i	−0.622330	+	0.259230i
$743$	6.82660			0.250444			0.125222	−	0.992129i	$-0.460036\pi$
$743$	6.82660			0.250444			0.125222	+	0.992129i	$0.460036\pi$
$744$	−30.0854	+	52.1094i	−1.10298	+	1.91042i
$745$	30.9950	+	53.6850i	1.13557	+	1.96687i
$746$	−8.88140	−	15.3830i	−0.325171	−	0.563213i
$747$	−0.779597	+	1.35030i	−0.0285240	+	0.0494049i
$748$	−87.6981			−3.20656
$749$	1.83647	−	14.1671i	0.0671031	−	0.517656i
$750$	−14.7506			−0.538615
$751$	−14.9560	+	25.9046i	−0.545754	+	0.945274i	0.452805	+	0.891610i	$0.350423\pi$
$751$	−14.9560	+	25.9046i	−0.545754	+	0.945274i	−0.998559	+	0.0536640i	$0.982910\pi$
$752$	32.3549	+	56.0404i	1.17986	+	2.04358i
$753$	3.61121	+	6.25480i	0.131600	+	0.227938i
$754$	7.50808	−	13.0044i	0.273428	−	0.473592i
$755$	−27.1452			−0.987914
$756$	11.0092	+	8.41291i	0.400401	+	0.305975i
$757$	38.1911			1.38808			0.694039	−	0.719938i	$-0.255830\pi$
$757$	38.1911			1.38808			0.694039	+	0.719938i	$0.255830\pi$
$758$	−8.89051	+	15.3988i	−0.322918	+	0.559310i
$759$	−10.9477	−	18.9620i	−0.397378	−	0.688278i
$760$	−106.187	−	183.921i	−3.85181	−	6.67153i
$761$	−4.07726	+	7.06202i	−0.147801	+	0.255998i	−0.930414	−	0.366510i	$-0.880553\pi$
$761$	−4.07726	+	7.06202i	−0.147801	+	0.255998i	0.782614	+	0.622508i	$0.213886\pi$
$762$	−39.9862			−1.44855
$763$	−39.3091	−	30.0389i	−1.42309	−	1.08748i
$764$	0.132833			0.00480574
$765$	−4.62974	+	8.01895i	−0.167389	+	0.289926i
$766$	−37.6329	−	65.1821i	−1.35973	−	2.35512i
$767$	−15.0149	−	26.0066i	−0.542157	−	0.939044i
$768$	8.04633	−	13.9366i	0.290347	−	0.502895i
$769$	−5.15883			−0.186032			−0.0930160	−	0.995665i	$-0.529651\pi$
$769$	−5.15883			−0.186032			−0.0930160	+	0.995665i	$0.529651\pi$
$770$	19.2105	−	148.197i	0.692300	−	5.34063i
$771$	−22.0393			−0.793726
$772$	16.9633	−	29.3813i	0.610522	−	1.05746i
$773$	−1.14570	−	1.98441i	−0.0412079	−	0.0713741i	0.844686	−	0.535262i	$-0.179787\pi$
$773$	−1.14570	−	1.98441i	−0.0412079	−	0.0713741i	−0.885894	+	0.463888i	$0.846454\pi$
$774$	−4.06285	−	7.03707i	−0.146036	−	0.252942i
$775$	22.8347	−	39.5508i	0.820246	−	1.42071i
$776$	−38.9748			−1.39911
$777$	21.4095	−	8.91807i	0.768063	−	0.319934i
$778$	−64.4850			−2.31190
$779$	−3.57894	+	6.19891i	−0.128229	+	0.222099i
$780$	27.7944	+	48.1413i	0.995198	+	1.72373i
$781$	−43.9941	−	76.2000i	−1.57423	−	2.72665i
$782$	−12.9885	+	22.4968i	−0.464468	+	0.804482i
$783$	1.79174			0.0640316
$784$	23.8135	+	87.4790i	0.850481	+	3.12425i
$785$	−52.2654			−1.86543
$786$	−8.27393	+	14.3309i	−0.295121	+	0.511165i
$787$	−2.61784	−	4.53424i	−0.0933161	−	0.161628i	0.815588	−	0.578632i	$-0.196413\pi$
$787$	−2.61784	−	4.53424i	−0.0933161	−	0.161628i	−0.908905	+	0.417004i	$0.863080\pi$
$788$	−15.6254	−	27.0639i	−0.556631	−	0.964113i
$789$	−4.63964	+	8.03609i	−0.165176	+	0.286092i
$790$	−79.6112			−2.83244
$791$	23.2991	−	9.70516i	0.828420	−	0.345076i
$792$	−53.6589			−1.90668
$793$	−7.04389	+	12.2004i	−0.250136	+	0.433248i
$794$	−8.43578	−	14.6112i	−0.299375	−	0.518532i
$795$	−4.39554	−	7.61330i	−0.155894	−	0.270016i
$796$	−1.83362	+	3.17593i	−0.0649911	+	0.112568i
$797$	−36.8582			−1.30558			−0.652792	−	0.757537i	$-0.726402\pi$
$797$	−36.8582			−1.30558			−0.652792	+	0.757537i	$0.726402\pi$
$798$	6.54929	−	50.5235i	0.231842	−	1.78851i
$799$	−13.5777			−0.480344
$800$	−57.5881	+	99.7456i	−2.03605	+	3.52654i
$801$	−2.23931	−	3.87860i	−0.0791222	−	0.137044i
$802$	−3.08075	−	5.33602i	−0.108785	−	0.188421i
$803$	3.03446	−	5.25583i	0.107084	−	0.185474i
$804$	9.10436			0.321086
$805$	−25.4511	−	19.4490i	−0.897034	−	0.685487i
$806$	−57.9102			−2.03980
$807$	−11.2962	+	19.5656i	−0.397646	+	0.688743i
$808$	−15.2938	−	26.4897i	−0.538034	−	0.931903i
$809$	−15.2247	−	26.3700i	−0.535272	−	0.927119i	−0.999150	−	0.0412196i	$-0.986876\pi$
$809$	−15.2247	−	26.3700i	−0.535272	−	0.927119i	0.463878	−	0.885899i	$-0.346458\pi$
$810$	−4.58300	+	7.93800i	−0.161030	+	0.278913i
$811$	25.5091			0.895747			0.447874	−	0.894097i	$-0.352181\pi$
$811$	25.5091			0.895747			0.447874	+	0.894097i	$0.352181\pi$
$812$	19.7256	+	15.0738i	0.692235	+	0.528985i
$813$	−6.25846			−0.219494
$814$	−72.6569	+	125.846i	−2.54662	+	4.41088i
$815$	−17.1404	−	29.6881i	−0.600403	−	1.03993i
$816$	17.5988	+	30.4820i	0.616081	+	1.06708i
$817$	−10.8103	+	18.7240i	−0.378205	+	0.655070i
$818$	17.6190			0.616034
$819$	−1.05959	+	8.17403i	−0.0370250	+	0.285624i
$820$	17.8435			0.623124
$821$	−0.154991	+	0.268452i	−0.00540921	+	0.00936903i	−0.868717	−	0.495308i	$-0.835055\pi$
$821$	−0.154991	+	0.268452i	−0.00540921	+	0.00936903i	0.863308	+	0.504677i	$0.168388\pi$
$822$	1.53452	+	2.65787i	0.0535227	+	0.0927040i
$823$	13.3242	+	23.0782i	0.464452	+	0.804455i	0.999177	−	0.0405718i	$-0.0129179\pi$
$823$	13.3242	+	23.0782i	0.464452	+	0.804455i	−0.534725	+	0.845026i	$0.679585\pi$
$824$	−50.2494	+	87.0344i	−1.75052	+	3.03199i
$825$	40.7268			1.41793
$826$	63.3331	−	26.3812i	2.20364	−	0.917919i
$827$	−29.5685			−1.02820			−0.514099	−	0.857731i	$-0.671874\pi$
$827$	−29.5685			−1.02820			−0.514099	+	0.857731i	$0.671874\pi$
$828$	−9.30413	+	16.1152i	−0.323341	+	0.560043i
$829$	7.89526	+	13.6750i	0.274214	+	0.474952i	0.969936	−	0.243358i	$-0.0782491\pi$
$829$	7.89526	+	13.6750i	0.274214	+	0.474952i	−0.695723	+	0.718310i	$0.744916\pi$
$830$	−7.14579	−	12.3769i	−0.248034	−	0.429608i
$831$	10.4535	−	18.1060i	0.362629	−	0.628092i
$832$	65.3488			2.26556
$833$	−18.3944	−	4.85039i	−0.637328	−	0.168056i
$834$	18.4568			0.639105
$835$	42.6811	−	73.9259i	1.47704	−	2.55831i
$836$	115.494	+	200.042i	3.99446	+	6.91860i
$837$	−3.45495	−	5.98414i	−0.119420	−	0.206842i
$838$	−39.0979	+	67.7195i	−1.35061	+	2.33933i
$839$	38.4714			1.32818			0.664091	−	0.747652i	$-0.268819\pi$
$839$	38.4714			1.32818			0.664091	+	0.747652i	$0.268819\pi$
$840$	−72.4640	+	30.1846i	−2.50024	+	1.04147i
$841$	−25.7897			−0.889299
$842$	−41.1477	+	71.2699i	−1.41804	+	2.45612i
$843$	−2.21090	−	3.82938i	−0.0761473	−	0.131891i
$844$	−14.9868	−	25.9579i	−0.515867	−	0.893508i
$845$	5.61281	−	9.72168i	0.193087	−	0.334436i
$846$	−13.4406			−0.462098
$847$	−9.17344	+	70.7670i	−0.315203	+	2.43158i
$848$	−33.4171			−1.14755
$849$	−10.1466	+	17.5744i	−0.348229	+	0.603150i
$850$	−24.1594	−	41.8453i	−0.828660	−	1.43528i
$851$	15.5740	+	26.9749i	0.533869	+	0.924687i
$852$	−37.3892	+	64.7599i	−1.28093	+	2.21864i
$853$	53.8643			1.84428			0.922140	−	0.386857i	$-0.126439\pi$
$853$	53.8643			1.84428			0.922140	+	0.386857i	$0.126439\pi$
$854$	−25.5736	−	19.5426i	−0.875111	−	0.668734i
$855$	24.3886			0.834073
$856$	23.5091	−	40.7190i	0.803525	−	1.39175i
$857$	6.75155	+	11.6940i	0.230628	+	0.399460i	0.957993	−	0.286791i	$-0.0925885\pi$
$857$	6.75155	+	11.6940i	0.230628	+	0.399460i	−0.727365	+	0.686251i	$0.759255\pi$
$858$	−25.8215	−	44.7241i	−0.881530	−	1.52686i
$859$	−8.76881	+	15.1880i	−0.299188	+	0.518209i	−0.975950	−	0.217993i	$-0.930049\pi$
$859$	−8.76881	+	15.1880i	−0.299188	+	0.518209i	0.676762	+	0.736201i	$0.263382\pi$
$860$	53.8969			1.83787
$861$	2.10222	+	1.60645i	0.0716433	+	0.0547477i
$862$	−7.04377			−0.239912
$863$	6.15382	−	10.6587i	0.209479	−	0.362828i	−0.742072	−	0.670320i	$-0.766157\pi$
$863$	6.15382	−	10.6587i	0.209479	−	0.362828i	0.951550	+	0.307493i	$0.0994900\pi$
$864$	8.71323	+	15.0918i	0.296430	+	0.513432i
$865$	6.41509	+	11.1113i	0.218120	+	0.377794i
$866$	44.0283	−	76.2592i	1.49614	−	2.59139i
$867$	9.61469			0.326532
$868$	12.3078	−	94.9468i	0.417755	−	3.22270i
$869$	53.5207			1.81556
$870$	−8.21156	+	14.2228i	−0.278398	+	0.482199i
$871$	2.70799	+	4.69037i	0.0917567	+	0.158927i
$872$	−81.4142	−	141.013i	−2.75703	−	4.77532i
$873$	2.23790	−	3.87615i	0.0757413	−	0.131188i
$874$	68.4211			2.31438
$875$	13.3917	−	5.57828i	0.452723	−	0.188580i
$876$	−5.15777			−0.174265
$877$	−10.5522	+	18.2769i	−0.356322	+	0.617167i	−0.987343	−	0.158598i	$-0.949303\pi$
$877$	−10.5522	+	18.2769i	−0.356322	+	0.617167i	0.631021	+	0.775765i	$0.282636\pi$
$878$	−36.3002	−	62.8738i	−1.22507	−	2.12189i
$879$	8.87533	+	15.3725i	0.299358	+	0.518503i
$880$	135.965	−	235.499i	4.58340	−	7.93867i
$881$	−13.4813			−0.454198			−0.227099	−	0.973872i	$-0.572924\pi$
$881$	−13.4813			−0.454198			−0.227099	+	0.973872i	$0.572924\pi$
$882$	−18.2087	−	4.80142i	−0.613119	−	0.161672i
$883$	−27.9922			−0.942012			−0.471006	−	0.882130i	$-0.656109\pi$
$883$	−27.9922			−0.942012			−0.471006	+	0.882130i	$0.656109\pi$
$884$	−22.1686	+	38.3972i	−0.745611	+	1.29144i
$885$	16.4218	+	28.4433i	0.552012	+	0.956112i
$886$	47.3536	+	82.0189i	1.59088	+	2.75548i
$887$	−5.24358	+	9.08215i	−0.176062	+	0.304949i	−0.940528	−	0.339715i	$-0.889669\pi$
$887$	−5.24358	+	9.08215i	−0.176062	+	0.304949i	0.764466	+	0.644664i	$0.223003\pi$
$888$	76.3337			2.56159
$889$	36.3026	−	15.1217i	1.21755	−	0.507166i
$890$	41.0511			1.37604
$891$	3.08104	−	5.33652i	0.103219	−	0.178780i
$892$	13.8356	+	23.9640i	0.463250	+	0.802373i
$893$	17.8812	+	30.9711i	0.598371	+	1.03641i
$894$	−24.4719	+	42.3866i	−0.818462	+	1.41762i
$895$	−58.0298			−1.93972
$896$	−7.33876	+	56.6137i	−0.245171	+	1.89133i
$897$	−11.0696			−0.369604
$898$	7.98266	−	13.8264i	0.266385	−	0.461392i
$899$	−6.19037	−	10.7220i	−0.206460	−	0.357600i
$900$	−17.3062	−	29.9752i	−0.576874	−	0.999175i
$901$	3.50585	−	6.07232i	0.116797	−	0.202298i
$902$	−16.5770			−0.551953
$903$	6.34981	+	4.85233i	0.211308	+	0.161476i
$904$	83.0707			2.76289
$905$	−13.6820	+	23.6979i	−0.454804	+	0.787743i
$906$	−10.7161	−	18.5609i	−0.356020	−	0.616644i
$907$	11.7385	+	20.3317i	0.389770	+	0.675102i	0.992418	−	0.122905i	$-0.0392210\pi$
$907$	11.7385	+	20.3317i	0.389770	+	0.675102i	−0.602648	+	0.798007i	$0.705888\pi$
$908$	30.3680	−	52.5989i	1.00780	−	1.74555i
$909$	3.51262			0.116506
$910$	−60.0293	−	45.8726i	−1.98995	−	1.52066i
$911$	−9.86885			−0.326970			−0.163485	−	0.986546i	$-0.552273\pi$
$911$	−9.86885			−0.326970			−0.163485	+	0.986546i	$0.552273\pi$
$912$	46.3536	−	80.2868i	1.53492	−	2.65856i
$913$	4.80394	+	8.32066i	0.158987	+	0.275374i
$914$	43.8282	+	75.9126i	1.44971	+	2.51097i
$915$	7.70388	−	13.3435i	0.254682	−	0.441123i
$916$	−69.2735			−2.28886
$917$	2.09216	−	16.1397i	0.0690893	−	0.532978i
$918$	−7.31075			−0.241291
$919$	29.6935	−	51.4306i	0.979497	−	1.69654i	0.315279	−	0.948999i	$-0.397902\pi$
$919$	29.6935	−	51.4306i	0.979497	−	1.69654i	0.664218	−	0.747539i	$-0.268765\pi$
$920$	−52.7125	−	91.3008i	−1.73788	−	3.01010i
$921$	−0.00968029	−	0.0167668i	−0.000318976	−	0.000552483i
$922$	−44.7476	+	77.5051i	−1.47368	+	2.55250i
$923$	−44.4839			−1.46421
$924$	78.8154	−	32.8303i	2.59284	−	1.08004i
$925$	−57.9369			−1.90495
$926$	−12.0817	+	20.9262i	−0.397030	+	0.687677i
$927$	−5.77054	−	9.99487i	−0.189529	−	0.328274i
$928$	15.6119	+	27.0405i	0.512484	+	0.887649i
$929$	25.5819	−	44.3091i	0.839314	−	1.45373i	−0.0511546	−	0.998691i	$-0.516290\pi$
$929$	25.5819	−	44.3091i	0.839314	−	1.45373i	0.890469	−	0.455044i	$-0.150377\pi$
$930$	63.3361			2.07687
$931$	13.1607	+	48.3459i	0.431324	+	1.58447i
$932$	56.9883			1.86671
$933$	5.53492	−	9.58676i	0.181205	−	0.313857i
$934$	−2.17877	−	3.77375i	−0.0712917	−	0.123481i
$935$	28.5288	+	49.4134i	0.932993	+	1.61599i
$936$	−13.5641	+	23.4937i	−0.443355	+	0.767914i
$937$	−8.46933			−0.276681			−0.138341	−	0.990385i	$-0.544177\pi$
$937$	−8.46933			−0.276681			−0.138341	+	0.990385i	$0.544177\pi$
$938$	−11.4223	+	4.75793i	−0.372952	+	0.155352i
$939$	2.12513			0.0693508
$940$	44.5751	−	77.2064i	1.45388	−	2.51819i
$941$	18.7064	+	32.4005i	0.609812	+	1.05622i	0.991271	+	0.131839i	$0.0420882\pi$
$941$	18.7064	+	32.4005i	0.609812	+	1.05622i	−0.381460	+	0.924386i	$0.624578\pi$
$942$	−20.6329	−	35.7372i	−0.672255	−	1.16438i
$943$	−1.77663	+	3.07721i	−0.0578551	+	0.100208i
$944$	124.846			4.06341
$945$	1.15887	−	8.93991i	0.0376980	−	0.290815i
$946$	−50.0712			−1.62796
$947$	12.2532	−	21.2232i	0.398176	−	0.689661i	−0.595325	−	0.803485i	$-0.702977\pi$
$947$	12.2532	−	21.2232i	0.398176	−	0.689661i	0.993501	+	0.113824i	$0.0363101\pi$
$948$	−22.7427	−	39.3916i	−0.738650	−	1.27938i
$949$	−1.53412	−	2.65717i	−0.0497996	−	0.0862555i
$950$	−63.6336	+	110.217i	−2.06455	+	3.57590i
$951$	20.5654			0.666880
$952$	−49.7480	−	38.0160i	−1.61234	−	1.23210i
$953$	38.4568			1.24574			0.622869	−	0.782326i	$-0.285967\pi$
$953$	38.4568			1.24574			0.622869	+	0.782326i	$0.285967\pi$
$954$	3.47046	−	6.01102i	0.112360	−	0.194614i
$955$	−0.0432117	−	0.0748448i	−0.00139830	−	0.00242192i
$956$	−51.9012	−	89.8954i	−1.67860	−	2.90743i
$957$	5.52043	−	9.56166i	0.178450	−	0.309085i
$958$	−87.7997			−2.83668
$959$	−2.39830	−	1.83271i	−0.0774451	−	0.0591812i
$960$	−71.4717			−2.30674
$961$	−8.37330	+	14.5030i	−0.270106	+	0.467838i
$962$	36.7329	+	63.6233i	1.18432	+	2.05130i
$963$	2.69974	+	4.67609i	0.0869979	+	0.150685i
$964$	−27.8369	+	48.2150i	−0.896567	+	1.55290i
$965$	−22.0731			−0.710559
$966$	3.25115	−	25.0805i	0.104604	−	0.806951i
$967$	39.5442			1.27166			0.635828	−	0.771831i	$-0.280659\pi$
$967$	39.5442			1.27166			0.635828	+	0.771831i	$0.280659\pi$
$968$	−117.432	+	203.397i	−3.77439	+	6.53744i
$969$	9.72611	+	16.8461i	0.312448	+	0.541175i
$970$	20.5126	+	35.5288i	0.658619	+	1.14076i
$971$	−9.64166	+	16.6999i	−0.309416	+	0.535924i	−0.978235	−	0.207502i	$-0.933467\pi$
$971$	−9.64166	+	16.6999i	−0.309416	+	0.535924i	0.668819	+	0.743425i	$0.266800\pi$
$972$	−5.23695			−0.167975
$973$	−16.7565	+	6.97986i	−0.537188	+	0.223764i
$974$	−95.9180			−3.07341
$975$	10.2951	−	17.8316i	0.329706	−	0.571068i
$976$	−29.2844	−	50.7220i	−0.937370	−	1.62357i
$977$	−28.3272	−	49.0641i	−0.906266	−	1.56970i	−0.819208	−	0.573496i	$-0.805587\pi$
$977$	−28.3272	−	49.0641i	−0.906266	−	1.56970i	−0.0870584	−	0.996203i	$-0.527747\pi$
$978$	13.5331	−	23.4400i	0.432741	−	0.749529i
$979$	−27.5976			−0.882024
$980$	87.9688	−	88.6718i	2.81006	−	2.83252i
$981$	18.6989			0.597010
$982$	41.3296	−	71.5850i	1.31888	−	2.28437i
$983$	−12.5950	−	21.8151i	−0.401717	−	0.695795i	0.592216	−	0.805779i	$-0.298253\pi$
$983$	−12.5950	−	21.8151i	−0.401717	−	0.695795i	−0.993933	+	0.109985i	$0.964920\pi$
$984$	4.35396	+	7.54127i	0.138799	+	0.240407i
$985$	−10.1661	+	17.6082i	−0.323919	+	0.561044i
$986$	−13.0990			−0.417156
$987$	12.2024	−	5.08289i	0.388408	−	0.161790i
$988$	116.780			3.71527
$989$	−5.36637	+	9.29482i	−0.170640	+	0.295558i
$990$	28.2408	+	48.9146i	0.897553	+	1.55461i
$991$	15.7962	+	27.3598i	0.501783	+	0.869113i	0.999998	+	0.00205970i	$0.000655622\pi$
$991$	15.7962	+	27.3598i	0.501783	+	0.869113i	−0.498215	+	0.867053i	$0.666011\pi$
$992$	60.2075	−	104.282i	1.91159	−	3.31097i
$993$	27.6456			0.877305
$994$	13.0649	−	100.787i	0.414394	−	3.19678i
$995$	2.38597			0.0756402
$996$	4.08271	−	7.07146i	0.129366	−	0.224068i
$997$	−24.5113	−	42.4548i	−0.776280	−	1.34456i	−0.934072	−	0.357084i	$-0.883771\pi$
$997$	−24.5113	−	42.4548i	−0.776280	−	1.34456i	0.157792	−	0.987472i	$-0.449562\pi$
$998$	25.9154	+	44.8868i	0.820337	+	1.42087i
$999$	−4.38300	+	7.59159i	−0.138672	+	0.240187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.g.247.1	✓	28
7.2	even	3		6027.2.a.bj.1.14		14
7.4	even	3	inner	861.2.i.g.739.1	yes	28
7.5	odd	6		6027.2.a.bk.1.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.1	✓	28	1.1	even	1	trivial
861.2.i.g.739.1	yes	28	7.4	even	3	inner
6027.2.a.bj.1.14		14	7.2	even	3
6027.2.a.bk.1.14		14	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34508 + 2.32975i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.61848 - 4.53533i) q^{4} +(-1.70362 + 2.95075i) q^{5} -2.69016 q^{6} +(2.44234 - 1.01735i) q^{7} +8.70791 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.34508 + 2.32975i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.61848 - 4.53533i) q^{4} +(-1.70362 + 2.95075i) q^{5} -2.69016 q^{6} +(2.44234 - 1.01735i) q^{7} +8.70791 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.58300 - 7.93800i) q^{10} +(3.08104 + 5.33652i) q^{11} +(2.61848 - 4.53533i) q^{12} +3.11534 q^{13} +(-0.914976 + 7.05843i) q^{14} -3.40724 q^{15} +(-6.47588 + 11.2166i) q^{16} +(-1.35880 - 2.35350i) q^{17} +(-1.34508 - 2.32975i) q^{18} +(-3.57894 + 6.19891i) q^{19} +17.8435 q^{20} +(2.10222 + 1.60645i) q^{21} -16.5770 q^{22} +(-1.77663 + 3.07721i) q^{23} +(4.35396 + 7.54127i) q^{24} +(-3.30464 - 5.72380i) q^{25} +(-4.19038 + 7.25796i) q^{26} -1.00000 q^{27} +(-11.0092 - 8.41291i) q^{28} -1.79174 q^{29} +(4.58300 - 7.93800i) q^{30} +(3.45495 + 5.98414i) q^{31} +(-8.71323 - 15.0918i) q^{32} +(-3.08104 + 5.33652i) q^{33} +7.31075 q^{34} +(-1.15887 + 8.93991i) q^{35} +5.23695 q^{36} +(4.38300 - 7.59159i) q^{37} +(-9.62792 - 16.6761i) q^{38} +(1.55767 + 2.69797i) q^{39} +(-14.8350 + 25.6949i) q^{40} +1.00000 q^{41} +(-6.57027 + 2.73682i) q^{42} +3.02053 q^{43} +(16.1353 - 27.9471i) q^{44} +(-1.70362 - 2.95075i) q^{45} +(-4.77942 - 8.27819i) q^{46} +(2.49811 - 4.32685i) q^{47} -12.9518 q^{48} +(4.93001 - 4.96941i) q^{49} +17.7800 q^{50} +(1.35880 - 2.35350i) q^{51} +(-8.15745 - 14.1291i) q^{52} +(1.29006 + 2.23445i) q^{53} +(1.34508 - 2.32975i) q^{54} -20.9957 q^{55} +(21.2677 - 8.85897i) q^{56} -7.15789 q^{57} +(2.41003 - 4.17430i) q^{58} +(-4.81967 - 8.34791i) q^{59} +(8.92177 + 15.4530i) q^{60} +(-2.26103 + 3.91622i) q^{61} -18.5887 q^{62} +(-0.340120 + 2.62380i) q^{63} +20.9764 q^{64} +(-5.30736 + 9.19261i) q^{65} +(-8.28848 - 14.3561i) q^{66} +(0.869242 + 1.50557i) q^{67} +(-7.11595 + 12.3252i) q^{68} -3.55326 q^{69} +(-19.2689 - 14.7248i) q^{70} -14.2790 q^{71} +(-4.35396 + 7.54127i) q^{72} +(-0.492440 - 0.852932i) q^{73} +(11.7910 + 20.4226i) q^{74} +(3.30464 - 5.72380i) q^{75} +37.4855 q^{76} +(12.9540 + 9.89908i) q^{77} -8.38076 q^{78} +(4.34274 - 7.52185i) q^{79} +(-22.0649 - 38.2175i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.34508 + 2.32975i) q^{82} +1.55919 q^{83} +(1.78119 - 13.7407i) q^{84} +9.25948 q^{85} +(-4.06285 + 7.03707i) q^{86} +(-0.895871 - 1.55169i) q^{87} +(26.8294 + 46.4699i) q^{88} +(-2.23931 + 3.87860i) q^{89} +9.16601 q^{90} +(7.60871 - 3.16938i) q^{91} +18.6083 q^{92} +(-3.45495 + 5.98414i) q^{93} +(6.72031 + 11.6399i) q^{94} +(-12.1943 - 21.1212i) q^{95} +(8.71323 - 15.0918i) q^{96} -4.47579 q^{97} +(4.94620 + 18.1699i) q^{98} -6.16208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9} - 3 q^{10} + 16 q^{11} + 14 q^{12} + 42 q^{13} - 14 q^{14} - 20 q^{15} - 22 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} + 80 q^{20} + 2 q^{22} + 7 q^{23} - 6 q^{24} - 22 q^{25} - 2 q^{26} - 28 q^{27} - 59 q^{28} - 32 q^{29} + 3 q^{30} - 8 q^{31} + 19 q^{32} - 16 q^{33} + 66 q^{34} - 8 q^{35} + 28 q^{36} - q^{37} - 32 q^{38} + 21 q^{39} + 13 q^{40} + 28 q^{41} - 10 q^{42} + 28 q^{43} + 36 q^{44} - 10 q^{45} + 12 q^{46} - 12 q^{47} - 44 q^{48} + 8 q^{49} - 2 q^{50} + 12 q^{51} - 60 q^{52} + 20 q^{53} - 2 q^{54} - 22 q^{55} + q^{56} - 4 q^{57} - 21 q^{58} - 25 q^{59} + 40 q^{60} - 26 q^{61} - 66 q^{62} + 84 q^{64} + 8 q^{65} + q^{66} + 22 q^{67} - 15 q^{68} + 14 q^{69} - 120 q^{70} - 72 q^{71} + 6 q^{72} - 31 q^{73} + 65 q^{74} + 22 q^{75} - 4 q^{76} - 18 q^{77} - 4 q^{78} - 12 q^{79} - 112 q^{80} - 14 q^{81} + 2 q^{82} + 40 q^{83} - 37 q^{84} + 80 q^{85} + 9 q^{86} - 16 q^{87} + 54 q^{88} - 39 q^{89} + 6 q^{90} - 17 q^{91} + 126 q^{92} + 8 q^{93} - 14 q^{94} + 55 q^{95} - 19 q^{96} + 36 q^{97} - 19 q^{98} - 32 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9 - 3 * q^10 + 16 * q^11 + 14 * q^12 + 42 * q^13 - 14 * q^14 - 20 * q^15 - 22 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 + 80 * q^20 + 2 * q^22 + 7 * q^23 - 6 * q^24 - 22 * q^25 - 2 * q^26 - 28 * q^27 - 59 * q^28 - 32 * q^29 + 3 * q^30 - 8 * q^31 + 19 * q^32 - 16 * q^33 + 66 * q^34 - 8 * q^35 + 28 * q^36 - q^37 - 32 * q^38 + 21 * q^39 + 13 * q^40 + 28 * q^41 - 10 * q^42 + 28 * q^43 + 36 * q^44 - 10 * q^45 + 12 * q^46 - 12 * q^47 - 44 * q^48 + 8 * q^49 - 2 * q^50 + 12 * q^51 - 60 * q^52 + 20 * q^53 - 2 * q^54 - 22 * q^55 + q^56 - 4 * q^57 - 21 * q^58 - 25 * q^59 + 40 * q^60 - 26 * q^61 - 66 * q^62 + 84 * q^64 + 8 * q^65 + q^66 + 22 * q^67 - 15 * q^68 + 14 * q^69 - 120 * q^70 - 72 * q^71 + 6 * q^72 - 31 * q^73 + 65 * q^74 + 22 * q^75 - 4 * q^76 - 18 * q^77 - 4 * q^78 - 12 * q^79 - 112 * q^80 - 14 * q^81 + 2 * q^82 + 40 * q^83 - 37 * q^84 + 80 * q^85 + 9 * q^86 - 16 * q^87 + 54 * q^88 - 39 * q^89 + 6 * q^90 - 17 * q^91 + 126 * q^92 + 8 * q^93 - 14 * q^94 + 55 * q^95 - 19 * q^96 + 36 * q^97 - 19 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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