LMFDB - Embedded newform 630.2.j.l.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$0.385731i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.l.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.805046 + 1.53359i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73065 - 0.0696054i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.70380 - 2.46922i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.805046 + 1.53359i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73065 - 0.0696054i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.70380 - 2.46922i) q^{9} -1.00000 q^{10} +(1.12056 + 1.94087i) q^{11} +(-0.925606 - 1.46399i) q^{12} +(0.334053 - 0.578596i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.925606 + 1.46399i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.64441 q^{17} +(-1.28651 + 2.71015i) q^{18} -3.40761 q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.73065 + 0.0696054i) q^{21} +(1.12056 - 1.94087i) q^{22} +(-1.62056 + 2.80689i) q^{23} +(-0.805046 + 1.53359i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.668105 q^{26} +(5.15842 - 0.625100i) q^{27} -1.00000 q^{28} +(3.69195 + 6.39465i) q^{29} +(0.805046 - 1.53359i) q^{30} +(-4.40761 + 7.63420i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.87860 + 0.155994i) q^{33} +(-3.32220 - 5.75423i) q^{34} +1.00000 q^{35} +(2.99031 - 0.240925i) q^{36} +3.07571 q^{37} +(1.70380 + 2.95107i) q^{38} +(0.618402 + 0.978097i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.165947 - 0.287429i) q^{41} +(0.925606 + 1.46399i) q^{42} +(1.45461 + 2.51946i) q^{43} -2.24112 q^{44} +(-2.99031 + 0.240925i) q^{45} +3.24112 q^{46} +(3.69411 + 6.39839i) q^{47} +(1.73065 - 0.0696054i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-5.34905 + 10.1898i) q^{51} +(0.334053 + 0.578596i) q^{52} +9.73950 q^{53} +(-3.12056 - 4.15477i) q^{54} +2.24112 q^{55} +(0.500000 + 0.866025i) q^{56} +(2.74328 - 5.22587i) q^{57} +(3.69195 - 6.39465i) q^{58} +(-3.94492 + 6.83281i) q^{59} +(-1.73065 + 0.0696054i) q^{60} +(3.44277 + 5.96304i) q^{61} +8.81521 q^{62} +(1.28651 - 2.71015i) q^{63} +1.00000 q^{64} +(-0.334053 - 0.578596i) q^{65} +(2.07439 + 3.28097i) q^{66} +(1.27682 - 2.21151i) q^{67} +(-3.32220 + 5.75423i) q^{68} +(-3.00000 - 4.74495i) q^{69} +(-0.500000 - 0.866025i) q^{70} +10.3125 q^{71} +(-1.70380 - 2.46922i) q^{72} -2.33621 q^{73} +(-1.53786 - 2.66364i) q^{74} +(1.73065 - 0.0696054i) q^{75} +(1.70380 - 2.95107i) q^{76} +(-1.12056 + 1.94087i) q^{77} +(0.537855 - 1.02460i) q^{78} +(-3.95461 - 6.84959i) q^{79} -1.00000 q^{80} +(-3.19411 + 8.41413i) q^{81} -0.331895 q^{82} +(-3.62272 - 6.27473i) q^{83} +(0.805046 - 1.53359i) q^{84} +(3.32220 - 5.75423i) q^{85} +(1.45461 - 2.51946i) q^{86} +(-12.7790 + 0.513960i) q^{87} +(1.12056 + 1.94087i) q^{88} -7.96124 q^{89} +(1.70380 + 2.46922i) q^{90} +0.668105 q^{91} +(-1.62056 - 2.80689i) q^{92} +(-8.15941 - 12.9053i) q^{93} +(3.69411 - 6.39839i) q^{94} +(-1.70380 + 2.95107i) q^{95} +(-0.925606 - 1.46399i) q^{96} +(-8.05364 - 13.9493i) q^{97} +1.00000 q^{98} +(2.88322 - 6.07377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9} - 8 q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25} - 6 q^{26} + 18 q^{27} - 8 q^{28} - 12 q^{29} + 3 q^{30} - 2 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 8 q^{35} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 4 q^{40} + q^{41} - 3 q^{42} + 5 q^{43} - 4 q^{44} + 12 q^{46} - 11 q^{47} - 4 q^{49} - 4 q^{50} - 21 q^{51} + 3 q^{52} + 44 q^{53} - 18 q^{54} + 4 q^{55} + 4 q^{56} + 9 q^{57} - 12 q^{58} - q^{59} - 4 q^{61} + 4 q^{62} + 3 q^{63} + 8 q^{64} - 3 q^{65} + 27 q^{66} - 21 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 34 q^{71} + 3 q^{72} - 20 q^{73} + 4 q^{74} - 3 q^{76} - 2 q^{77} - 12 q^{78} - 25 q^{79} - 8 q^{80} + 15 q^{81} - 2 q^{82} - 23 q^{83} + 3 q^{84} + 2 q^{85} + 5 q^{86} - 72 q^{87} + 2 q^{88} + 32 q^{89} - 3 q^{90} + 6 q^{91} - 6 q^{92} + 6 q^{93} - 11 q^{94} + 3 q^{95} + 3 q^{96} - 2 q^{97} + 8 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9 - 8 * q^10 + 2 * q^11 + 3 * q^12 + 3 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^22 - 6 * q^23 - 3 * q^24 - 4 * q^25 - 6 * q^26 + 18 * q^27 - 8 * q^28 - 12 * q^29 + 3 * q^30 - 2 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 8 * q^35 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 4 * q^40 + q^41 - 3 * q^42 + 5 * q^43 - 4 * q^44 + 12 * q^46 - 11 * q^47 - 4 * q^49 - 4 * q^50 - 21 * q^51 + 3 * q^52 + 44 * q^53 - 18 * q^54 + 4 * q^55 + 4 * q^56 + 9 * q^57 - 12 * q^58 - q^59 - 4 * q^61 + 4 * q^62 + 3 * q^63 + 8 * q^64 - 3 * q^65 + 27 * q^66 - 21 * q^67 - 2 * q^68 - 24 * q^69 - 4 * q^70 + 34 * q^71 + 3 * q^72 - 20 * q^73 + 4 * q^74 - 3 * q^76 - 2 * q^77 - 12 * q^78 - 25 * q^79 - 8 * q^80 + 15 * q^81 - 2 * q^82 - 23 * q^83 + 3 * q^84 + 2 * q^85 + 5 * q^86 - 72 * q^87 + 2 * q^88 + 32 * q^89 - 3 * q^90 + 6 * q^91 - 6 * q^92 + 6 * q^93 - 11 * q^94 + 3 * q^95 + 3 * q^96 - 2 * q^97 + 8 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.805046	+	1.53359i	−0.464793	+	0.885419i
$3$	−0.805046	+	1.53359i	−0.464793	+	0.885419i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.73065	−	0.0696054i	0.706536	−	0.0284163i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−1.70380	−	2.46922i	−0.567934	−	0.823074i
$10$	−1.00000			−0.316228
$11$	1.12056	+	1.94087i	0.337862	+	0.585193i	0.984030	−	0.178001i	$-0.0569631\pi$
$11$	1.12056	+	1.94087i	0.337862	+	0.585193i	−0.646169	+	0.763195i	$0.723630\pi$
$12$	−0.925606	−	1.46399i	−0.267199	−	0.422616i
$13$	0.334053	−	0.578596i	0.0926495	−	0.160474i	−0.815976	−	0.578086i	$-0.803800\pi$
$13$	0.334053	−	0.578596i	0.0926495	−	0.160474i	0.908625	+	0.417613i	$0.137133\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	0.925606	+	1.46399i	0.238990	+	0.377999i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.64441			1.61151			0.805753	−	0.592252i	$-0.201761\pi$
$17$	6.64441			1.61151			0.805753	+	0.592252i	$0.201761\pi$
$18$	−1.28651	+	2.71015i	−0.303233	+	0.638788i
$19$	−3.40761			−0.781758			−0.390879	−	0.920442i	$-0.627829\pi$
$19$	−3.40761			−0.781758			−0.390879	+	0.920442i	$0.627829\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.73065	+	0.0696054i	−0.377659	+	0.0151891i
$22$	1.12056	−	1.94087i	0.238904	−	0.413794i
$23$	−1.62056	+	2.80689i	−0.337910	+	0.585278i	−0.984039	−	0.177950i	$-0.943053\pi$
$23$	−1.62056	+	2.80689i	−0.337910	+	0.585278i	0.646129	+	0.763228i	$0.276387\pi$
$24$	−0.805046	+	1.53359i	−0.164329	+	0.313043i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.668105			−0.131026
$27$	5.15842	−	0.625100i	0.992738	−	0.120301i
$28$	−1.00000			−0.188982
$29$	3.69195	+	6.39465i	0.685579	+	1.18746i	0.973255	+	0.229729i	$0.0737841\pi$
$29$	3.69195	+	6.39465i	0.685579	+	1.18746i	−0.287676	+	0.957728i	$0.592883\pi$
$30$	0.805046	−	1.53359i	0.146981	−	0.279994i
$31$	−4.40761	+	7.63420i	−0.791629	+	1.37114i	0.133328	+	0.991072i	$0.457434\pi$
$31$	−4.40761	+	7.63420i	−0.791629	+	1.37114i	−0.924958	+	0.380070i	$0.875900\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.87860	+	0.155994i	−0.675177	+	0.0271551i
$34$	−3.32220	−	5.75423i	−0.569753	−	0.986842i
$35$	1.00000			0.169031
$36$	2.99031	−	0.240925i	0.498385	−	0.0401542i
$37$	3.07571			0.505644			0.252822	−	0.967513i	$-0.418641\pi$
$37$	3.07571			0.505644			0.252822	+	0.967513i	$0.418641\pi$
$38$	1.70380	+	2.95107i	0.276393	+	0.478727i
$39$	0.618402	+	0.978097i	0.0990236	+	0.156621i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	0.165947	−	0.287429i	0.0259166	−	0.0448889i	−0.852776	−	0.522277i	$-0.825083\pi$
$41$	0.165947	−	0.287429i	0.0259166	−	0.0448889i	0.878693	+	0.477388i	$0.158416\pi$
$42$	0.925606	+	1.46399i	0.142824	+	0.225898i
$43$	1.45461	+	2.51946i	0.221826	+	0.384215i	0.955363	−	0.295436i	$-0.0954648\pi$
$43$	1.45461	+	2.51946i	0.221826	+	0.384215i	−0.733536	+	0.679650i	$0.762132\pi$
$44$	−2.24112			−0.337862
$45$	−2.99031	+	0.240925i	−0.445769	+	0.0359151i
$46$	3.24112			0.477877
$47$	3.69411	+	6.39839i	0.538842	+	0.933301i	0.998967	+	0.0454471i	$0.0144713\pi$
$47$	3.69411	+	6.39839i	0.538842	+	0.933301i	−0.460125	+	0.887854i	$0.652195\pi$
$48$	1.73065	−	0.0696054i	0.249798	−	0.0100467i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−5.34905	+	10.1898i	−0.749017	+	1.42686i
$52$	0.334053	+	0.578596i	0.0463248	+	0.0802369i
$53$	9.73950			1.33782			0.668912	−	0.743342i	$-0.266760\pi$
$53$	9.73950			1.33782			0.668912	+	0.743342i	$0.266760\pi$
$54$	−3.12056	−	4.15477i	−0.424654	−	0.565392i
$55$	2.24112			0.302193
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	2.74328	−	5.22587i	0.363356	−	0.692184i
$58$	3.69195	−	6.39465i	0.484777	−	0.839659i
$59$	−3.94492	+	6.83281i	−0.513585	+	0.889556i	0.486291	+	0.873797i	$0.338350\pi$
$59$	−3.94492	+	6.83281i	−0.513585	+	0.889556i	−0.999876	+	0.0157586i	$0.994984\pi$
$60$	−1.73065	+	0.0696054i	−0.223426	+	0.00898602i
$61$	3.44277	+	5.96304i	0.440801	+	0.763490i	0.997749	−	0.0670577i	$-0.0213612\pi$
$61$	3.44277	+	5.96304i	0.440801	+	0.763490i	−0.556948	+	0.830547i	$0.688028\pi$
$62$	8.81521			1.11953
$63$	1.28651	−	2.71015i	0.162085	−	0.341446i
$64$	1.00000			0.125000
$65$	−0.334053	−	0.578596i	−0.0414341	−	0.0717660i
$66$	2.07439	+	3.28097i	0.255340	+	0.403859i
$67$	1.27682	−	2.21151i	0.155988	−	0.270179i	−0.777430	−	0.628969i	$-0.783477\pi$
$67$	1.27682	−	2.21151i	0.155988	−	0.270179i	0.933418	+	0.358790i	$0.116811\pi$
$68$	−3.32220	+	5.75423i	−0.402877	+	0.697803i
$69$	−3.00000	−	4.74495i	−0.361158	−	0.571225i
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	10.3125			1.22387			0.611935	−	0.790908i	$-0.290391\pi$
$71$	10.3125			1.22387			0.611935	+	0.790908i	$0.290391\pi$
$72$	−1.70380	−	2.46922i	−0.200795	−	0.291001i
$73$	−2.33621			−0.273433			−0.136716	−	0.990610i	$-0.543655\pi$
$73$	−2.33621			−0.273433			−0.136716	+	0.990610i	$0.543655\pi$
$74$	−1.53786	−	2.66364i	−0.178772	−	0.309642i
$75$	1.73065	−	0.0696054i	0.199838	−	0.00803734i
$76$	1.70380	−	2.95107i	0.195440	−	0.338511i
$77$	−1.12056	+	1.94087i	−0.127700	+	0.221182i
$78$	0.537855	−	1.02460i	0.0609001	−	0.116013i
$79$	−3.95461	−	6.84959i	−0.444929	−	0.770639i	0.553119	−	0.833103i	$-0.313438\pi$
$79$	−3.95461	−	6.84959i	−0.444929	−	0.770639i	−0.998047	+	0.0624634i	$0.980104\pi$
$80$	−1.00000			−0.111803
$81$	−3.19411	+	8.41413i	−0.354901	+	0.934904i
$82$	−0.331895			−0.0366516
$83$	−3.62272	−	6.27473i	−0.397645	−	0.688741i	0.595790	−	0.803140i	$-0.296839\pi$
$83$	−3.62272	−	6.27473i	−0.397645	−	0.688741i	−0.993435	+	0.114399i	$0.963506\pi$
$84$	0.805046	−	1.53359i	0.0878377	−	0.167328i
$85$	3.32220	−	5.75423i	0.360344	−	0.624134i
$86$	1.45461	−	2.51946i	0.156855	−	0.271681i
$87$	−12.7790	+	0.513960i	−1.37005	+	0.0551023i
$88$	1.12056	+	1.94087i	0.119452	+	0.206897i
$89$	−7.96124			−0.843890			−0.421945	−	0.906621i	$-0.638652\pi$
$89$	−7.96124			−0.843890			−0.421945	+	0.906621i	$0.638652\pi$
$90$	1.70380	+	2.46922i	0.179597	+	0.260279i
$91$	0.668105			0.0700365
$92$	−1.62056	−	2.80689i	−0.168955	−	0.292639i
$93$	−8.15941	−	12.9053i	−0.846091	−	1.33822i
$94$	3.69411	−	6.39839i	0.381019	−	0.659944i
$95$	−1.70380	+	2.95107i	−0.174806	+	0.302774i
$96$	−0.925606	−	1.46399i	−0.0944693	−	0.149417i
$97$	−8.05364	−	13.9493i	−0.817723	−	1.41634i	−0.907356	−	0.420363i	$-0.861903\pi$
$97$	−8.05364	−	13.9493i	−0.817723	−	1.41634i	0.0896334	−	0.995975i	$-0.471430\pi$
$98$	1.00000			0.101015
$99$	2.88322	−	6.07377i	0.289774	−	0.610436i
$100$	1.00000			0.100000
$101$	−5.49838	−	9.52347i	−0.547109	−	0.947621i	−0.998471	−	0.0552799i	$-0.982395\pi$
$101$	−5.49838	−	9.52347i	−0.547109	−	0.947621i	0.451362	−	0.892341i	$-0.350938\pi$
$102$	11.4992	−	0.462487i	1.13859	−	0.0457930i
$103$	3.62863	−	6.28497i	0.357540	−	0.619277i	−0.630010	−	0.776587i	$-0.716949\pi$
$103$	3.62863	−	6.28497i	0.357540	−	0.619277i	0.987549	+	0.157311i	$0.0502824\pi$
$104$	0.334053	−	0.578596i	0.0327566	−	0.0567360i
$105$	−0.805046	+	1.53359i	−0.0785644	+	0.149663i
$106$	−4.86975	−	8.43465i	−0.472992	−	0.819246i
$107$	19.5504			1.89001			0.945004	−	0.327059i	$-0.106058\pi$
$107$	19.5504			1.89001			0.945004	+	0.327059i	$0.106058\pi$
$108$	−2.03786	+	4.77987i	−0.196093	+	0.459943i
$109$	−4.81089			−0.460800			−0.230400	−	0.973096i	$-0.574003\pi$
$109$	−4.81089			−0.460800			−0.230400	+	0.973096i	$0.574003\pi$
$110$	−1.12056	−	1.94087i	−0.106841	−	0.185054i
$111$	−2.47609	+	4.71688i	−0.235020	+	0.447707i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−8.06333	+	13.9661i	−0.758534	+	1.31382i	0.185064	+	0.982726i	$0.440751\pi$
$113$	−8.06333	+	13.9661i	−0.758534	+	1.31382i	−0.943598	+	0.331093i	$0.892583\pi$
$114$	−5.89738	+	0.237188i	−0.552340	+	0.0222147i
$115$	1.62056	+	2.80689i	0.151118	+	0.261744i
$116$	−7.38391			−0.685579
$117$	−1.99784	+	0.160964i	−0.184701	+	0.0148811i
$118$	7.88985			0.726319
$119$	3.32220	+	5.75423i	0.304546	+	0.527489i
$120$	0.925606	+	1.46399i	0.0844959	+	0.133643i
$121$	2.98869	−	5.17656i	0.271699	−	0.470597i
$122$	3.44277	−	5.96304i	0.311693	−	0.539869i
$123$	0.307204	+	0.485889i	0.0276996	+	0.0438111i
$124$	−4.40761	−	7.63420i	−0.395815	−	0.685571i
$125$	−1.00000			−0.0894427
$126$	−2.99031	+	0.240925i	−0.266398	+	0.0214633i
$127$	1.24112			0.110132			0.0550658	−	0.998483i	$-0.482463\pi$
$127$	1.24112			0.110132			0.0550658	+	0.998483i	$0.482463\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.03486	+	0.202498i	−0.443294	+	0.0178289i
$130$	−0.334053	+	0.578596i	−0.0292984	+	0.0507462i
$131$	−2.50969	+	4.34691i	−0.219273	+	0.379791i	−0.954586	−	0.297936i	$-0.903702\pi$
$131$	−2.50969	+	4.34691i	−0.219273	+	0.379791i	0.735313	+	0.677727i	$0.237035\pi$
$132$	1.80420	−	3.43696i	0.157036	−	0.299149i
$133$	−1.70380	−	2.95107i	−0.147738	−	0.255890i
$134$	−2.55364			−0.220600
$135$	2.03786	−	4.77987i	0.175391	−	0.411386i
$136$	6.64441			0.569753
$137$	−3.34374	−	5.79153i	−0.285675	−	0.494804i	0.687097	−	0.726565i	$-0.258885\pi$
$137$	−3.34374	−	5.79153i	−0.285675	−	0.494804i	−0.972773	+	0.231761i	$0.925551\pi$
$138$	−2.60925	+	4.97055i	−0.222114	+	0.423122i
$139$	−9.85790	+	17.0744i	−0.836136	+	1.44823i	0.0569655	+	0.998376i	$0.481857\pi$
$139$	−9.85790	+	17.0744i	−0.836136	+	1.44823i	−0.893102	+	0.449855i	$0.851476\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	−12.7864	+	0.514261i	−1.07681	+	0.0433086i
$142$	−5.15626	−	8.93090i	−0.432704	−	0.749464i
$143$	1.49730			0.125211
$144$	−1.28651	+	2.71015i	−0.107209	+	0.225846i
$145$	7.38391			0.613200
$146$	1.16811	+	2.02322i	0.0966731	+	0.167443i
$147$	−0.925606	−	1.46399i	−0.0763427	−	0.120747i
$148$	−1.53786	+	2.66364i	−0.126411	+	0.218950i
$149$	7.43361	−	12.8754i	0.608985	−	1.05479i	−0.382423	−	0.923987i	$-0.624910\pi$
$149$	7.43361	−	12.8754i	0.608985	−	1.05479i	0.991408	−	0.130806i	$-0.0417565\pi$
$150$	−0.925606	−	1.46399i	−0.0755754	−	0.119534i
$151$	−7.35790	−	12.7443i	−0.598778	−	1.03711i	−0.993002	−	0.118099i	$-0.962320\pi$
$151$	−7.35790	−	12.7443i	−0.598778	−	1.03711i	0.394224	−	0.919014i	$-0.371013\pi$
$152$	−3.40761			−0.276393
$153$	−11.3208	−	16.4065i	−0.915229	−	1.32639i
$154$	2.24112			0.180595
$155$	4.40761	+	7.63420i	0.354027	+	0.613193i
$156$	−1.15626	+	0.0465038i	−0.0925747	+	0.00372328i
$157$	−0.978462	+	1.69475i	−0.0780898	+	0.135256i	−0.902426	−	0.430845i	$-0.858215\pi$
$157$	−0.978462	+	1.69475i	−0.0780898	+	0.135256i	0.824336	+	0.566101i	$0.191549\pi$
$158$	−3.95461	+	6.84959i	−0.314612	+	0.544924i
$159$	−7.84074	+	14.9364i	−0.621811	+	1.18453i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−3.24112			−0.255436
$162$	8.88391	−	1.44088i	0.697986	−	0.113207i
$163$	9.64441			0.755408			0.377704	−	0.925926i	$-0.376714\pi$
$163$	9.64441			0.755408			0.377704	+	0.925926i	$0.376714\pi$
$164$	0.165947	+	0.287429i	0.0129583	+	0.0224445i
$165$	−1.80420	+	3.43696i	−0.140457	+	0.267567i
$166$	−3.62272	+	6.27473i	−0.281177	+	0.487014i
$167$	4.32274	−	7.48721i	0.334504	−	0.579378i	−0.648886	−	0.760886i	$-0.724765\pi$
$167$	4.32274	−	7.48721i	0.334504	−	0.579378i	0.983389	+	0.181508i	$0.0580979\pi$
$168$	−1.73065	+	0.0696054i	−0.133523	+	0.00537018i
$169$	6.27682	+	10.8718i	0.482832	+	0.836290i
$170$	−6.64441			−0.509603
$171$	5.80589	+	8.41413i	0.443987	+	0.643445i
$172$	−2.90923			−0.221826
$173$	−4.40761	−	7.63420i	−0.335104	−	0.580417i	0.648401	−	0.761299i	$-0.275438\pi$
$173$	−4.40761	−	7.63420i	−0.335104	−	0.580417i	−0.983505	+	0.180882i	$0.942105\pi$
$174$	6.83459	+	10.8099i	0.518129	+	0.819499i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	1.12056	−	1.94087i	0.0844654	−	0.146298i
$177$	−7.30289	−	11.5506i	−0.548919	−	0.868198i
$178$	3.98062	+	6.89464i	0.298360	+	0.516775i
$179$	15.6964			1.17321			0.586603	−	0.809875i	$-0.300465\pi$
$179$	15.6964			1.17321			0.586603	+	0.809875i	$0.300465\pi$
$180$	1.28651	−	2.71015i	0.0958906	−	0.202002i
$181$	−14.4435			−1.07358			−0.536788	−	0.843717i	$-0.680362\pi$
$181$	−14.4435			−1.07358			−0.536788	+	0.843717i	$0.680362\pi$
$182$	−0.334053	−	0.578596i	−0.0247616	−	0.0428884i
$183$	−11.9165	+	0.479270i	−0.880890	+	0.0354287i
$184$	−1.62056	+	2.80689i	−0.119469	+	0.206927i
$185$	1.53786	−	2.66364i	0.113065	−	0.195835i
$186$	−7.09665	+	13.5189i	−0.520351	+	0.991256i
$187$	7.44546	+	12.8959i	0.544466	+	0.943043i
$188$	−7.38823			−0.538842
$189$	3.12056	+	4.15477i	0.226987	+	0.302215i
$190$	3.40761			0.247214
$191$	−13.2174	−	22.8933i	−0.956379	−	1.65650i	−0.731180	−	0.682185i	$-0.761030\pi$
$191$	−13.2174	−	22.8933i	−0.956379	−	1.65650i	−0.225200	−	0.974313i	$-0.572303\pi$
$192$	−0.805046	+	1.53359i	−0.0580992	+	0.110677i
$193$	−2.98815	+	5.17563i	−0.215092	+	0.372550i	−0.953301	−	0.302022i	$-0.902338\pi$
$193$	−2.98815	+	5.17563i	−0.215092	+	0.372550i	0.738209	+	0.674572i	$0.235672\pi$
$194$	−8.05364	+	13.9493i	−0.578217	+	1.00150i
$195$	1.15626	−	0.0465038i	0.0828013	−	0.00333020i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	8.59347			0.612259			0.306130	−	0.951990i	$-0.400966\pi$
$197$	8.59347			0.612259			0.306130	+	0.951990i	$0.400966\pi$
$198$	−6.70164	+	0.539943i	−0.476265	+	0.0383721i
$199$	−11.8662			−0.841169			−0.420585	−	0.907253i	$-0.638175\pi$
$199$	−11.8662			−0.841169			−0.420585	+	0.907253i	$0.638175\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	2.36366	+	3.73849i	0.166720	+	0.263692i
$202$	−5.49838	+	9.52347i	−0.386865	+	0.670069i
$203$	−3.69195	+	6.39465i	−0.259124	+	0.448817i
$204$	−6.15010	−	9.72732i	−0.430593	−	0.681049i
$205$	−0.165947	−	0.287429i	−0.0115903	−	0.0200749i
$206$	−7.25726			−0.505637
$207$	9.69195	−	0.780868i	0.673637	−	0.0542741i
$208$	−0.668105			−0.0463248
$209$	−3.81843	−	6.61371i	−0.264126	−	0.457480i
$210$	1.73065	−	0.0696054i	0.119426	−	0.00480323i
$211$	12.3428	−	21.3784i	0.849716	−	1.47175i	−0.0317457	−	0.999496i	$-0.510107\pi$
$211$	12.3428	−	21.3784i	0.849716	−	1.47175i	0.881462	−	0.472255i	$-0.156560\pi$
$212$	−4.86975	+	8.43465i	−0.334456	+	0.579294i
$213$	−8.30205	+	15.8152i	−0.568847	+	1.08364i
$214$	−9.77520	−	16.9311i	−0.668219	−	1.15739i
$215$	2.90923			0.198408
$216$	5.15842	−	0.625100i	0.350986	−	0.0425327i
$217$	−8.81521			−0.598415
$218$	2.40545	+	4.16636i	0.162917	+	0.282181i
$219$	1.88076	−	3.58279i	0.127090	−	0.242103i
$220$	−1.12056	+	1.94087i	−0.0755481	+	0.130853i
$221$	2.21958	−	3.84443i	0.149305	−	0.258604i
$222$	5.32298	−	0.214086i	0.357255	−	0.0143685i
$223$	−7.47309	−	12.9438i	−0.500435	−	0.866779i	−1.00000		0.000502387i	$-0.999840\pi$
$223$	−7.47309	−	12.9438i	−0.500435	−	0.866779i	0.499565	−	0.866276i	$-0.333493\pi$
$224$	−1.00000			−0.0668153
$225$	−1.28651	+	2.71015i	−0.0857672	+	0.180676i
$226$	16.1267			1.07273
$227$	6.85199	+	11.8680i	0.454783	+	0.787707i	0.998676	−	0.0514480i	$-0.0163836\pi$
$227$	6.85199	+	11.8680i	0.454783	+	0.787707i	−0.543893	+	0.839155i	$0.683050\pi$
$228$	3.15410	+	4.98869i	0.208885	+	0.330384i
$229$	−2.77898	+	4.81333i	−0.183640	+	0.318074i	−0.943117	−	0.332460i	$-0.892121\pi$
$229$	−2.77898	+	4.81333i	−0.183640	+	0.318074i	0.759477	+	0.650534i	$0.225455\pi$
$230$	1.62056	−	2.80689i	0.106857	−	0.185081i
$231$	−2.07439	−	3.28097i	−0.136485	−	0.215872i
$232$	3.69195	+	6.39465i	0.242389	+	0.419830i
$233$	10.4833			0.686785			0.343392	−	0.939192i	$-0.388424\pi$
$233$	10.4833			0.686785			0.343392	+	0.939192i	$0.388424\pi$
$234$	1.13832	+	1.64970i	0.0744143	+	0.107844i
$235$	7.38823			0.481955
$236$	−3.94492	−	6.83281i	−0.256793	−	0.444778i
$237$	13.6881	−	0.550525i	0.889139	−	0.0357604i
$238$	3.32220	−	5.75423i	0.215347	−	0.372991i
$239$	−7.47900	+	12.9540i	−0.483776	+	0.837925i	−0.999826	−	0.0186333i	$-0.994069\pi$
$239$	−7.47900	+	12.9540i	−0.483776	+	0.837925i	0.516050	+	0.856558i	$0.327402\pi$
$240$	0.805046	−	1.53359i	0.0519655	−	0.0989929i
$241$	7.89306	+	13.6712i	0.508437	+	0.880638i	0.999952	+	0.00976955i	$0.00310979\pi$
$241$	7.89306	+	13.6712i	0.508437	+	0.880638i	−0.491515	+	0.870869i	$0.663557\pi$
$242$	−5.97738			−0.384241
$243$	−10.3324	−	11.6722i	−0.662826	−	0.748774i
$244$	−6.88553			−0.440801
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	0.267190	−	0.508991i	0.0170354	−	0.0324521i
$247$	−1.13832	+	1.97163i	−0.0724295	+	0.125452i
$248$	−4.40761	+	7.63420i	−0.279883	+	0.484772i
$249$	12.5393	−	0.504322i	0.794647	−	0.0319601i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−10.0875			−0.636720			−0.318360	−	0.947970i	$-0.603132\pi$
$251$	−10.0875			−0.636720			−0.318360	+	0.947970i	$0.603132\pi$
$252$	1.70380	+	2.46922i	0.107329	+	0.155546i
$253$	−7.26374			−0.456667
$254$	−0.620560	−	1.07484i	−0.0389374	−	0.0674416i
$255$	6.15010	+	9.72732i	0.385135	+	0.609148i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.64603	−	9.77921i	0.352190	−	0.610010i	−0.634443	−	0.772970i	$-0.718771\pi$
$257$	5.64603	−	9.77921i	0.352190	−	0.610010i	0.986633	+	0.162959i	$0.0521039\pi$
$258$	2.69280	+	4.25906i	0.167646	+	0.265158i
$259$	1.53786	+	2.66364i	0.0955577	+	0.165511i
$260$	0.668105			0.0414341
$261$	9.49946	−	20.0115i	0.588002	−	1.23868i
$262$	5.01938			0.310098
$263$	−4.95245	−	8.57790i	−0.305381	−	0.528936i	0.671965	−	0.740583i	$-0.265451\pi$
$263$	−4.95245	−	8.57790i	−0.305381	−	0.528936i	−0.977346	+	0.211647i	$0.932117\pi$
$264$	−3.87860	+	0.155994i	−0.238711	+	0.00960078i
$265$	4.86975	−	8.43465i	0.299146	−	0.518137i
$266$	−1.70380	+	2.95107i	−0.104467	+	0.180942i
$267$	6.40916	−	12.2093i	0.392234	−	0.747196i
$268$	1.27682	+	2.21151i	0.0779941	+	0.135090i
$269$	6.22174			0.379346			0.189673	−	0.981847i	$-0.439257\pi$
$269$	6.22174			0.379346			0.189673	+	0.981847i	$0.439257\pi$
$270$	−5.15842	+	0.625100i	−0.313931	+	0.0380424i
$271$	30.8242			1.87243			0.936217	−	0.351423i	$-0.114302\pi$
$271$	30.8242			1.87243			0.936217	+	0.351423i	$0.114302\pi$
$272$	−3.32220	−	5.75423i	−0.201438	−	0.348901i
$273$	−0.537855	+	1.02460i	−0.0325525	+	0.0620116i
$274$	−3.34374	+	5.79153i	−0.202003	+	0.349879i
$275$	1.12056	−	1.94087i	0.0675723	−	0.117039i
$276$	5.60925	−	0.225600i	0.337637	−	0.0135795i
$277$	5.49838	+	9.52347i	0.330366	+	0.572210i	0.982584	−	0.185821i	$-0.0594946\pi$
$277$	5.49838	+	9.52347i	0.330366	+	0.572210i	−0.652218	+	0.758032i	$0.726161\pi$
$278$	19.7158			1.18248
$279$	26.3602	−	2.12381i	1.57814	−	0.127149i
$280$	1.00000			0.0597614
$281$	−16.1650	−	27.9987i	−0.964326	−	1.67026i	−0.711416	−	0.702771i	$-0.751946\pi$
$281$	−16.1650	−	27.9987i	−0.964326	−	1.67026i	−0.252910	−	0.967490i	$-0.581388\pi$
$282$	6.83859	+	10.8163i	0.407232	+	0.644099i
$283$	−2.69411	+	4.66634i	−0.160148	+	0.277385i	−0.934922	−	0.354854i	$-0.884531\pi$
$283$	−2.69411	+	4.66634i	−0.160148	+	0.277385i	0.774773	+	0.632239i	$0.217864\pi$
$284$	−5.15626	+	8.93090i	−0.305968	+	0.529951i
$285$	−3.15410	−	4.98869i	−0.186833	−	0.295504i
$286$	−0.748652	−	1.29670i	−0.0442687	−	0.0766757i
$287$	0.331895			0.0195911
$288$	2.99031	−	0.240925i	0.176206	−	0.0141967i
$289$	27.1482			1.59695
$290$	−3.69195	−	6.39465i	−0.216799	−	0.375507i
$291$	27.8761	−	1.12115i	1.63412	−	0.0657232i
$292$	1.16811	−	2.02322i	0.0683582	−	0.118400i
$293$	15.9851	−	27.6870i	0.933859	−	1.61749i	0.157203	−	0.987566i	$-0.449752\pi$
$293$	15.9851	−	27.6870i	0.933859	−	1.61749i	0.776656	−	0.629925i	$-0.216914\pi$
$294$	−0.805046	+	1.53359i	−0.0469512	+	0.0894408i
$295$	3.94492	+	6.83281i	0.229682	+	0.397821i
$296$	3.07571			0.178772
$297$	6.99355	+	9.31134i	0.405807	+	0.540299i
$298$	−14.8672			−0.861235
$299$	1.08270	+	1.87530i	0.0626144	+	0.108451i
$300$	−0.805046	+	1.53359i	−0.0464793	+	0.0885419i
$301$	−1.45461	+	2.51946i	−0.0838425	+	0.145219i
$302$	−7.35790	+	12.7443i	−0.423400	+	0.733350i
$303$	19.0316	−	0.765434i	1.09333	−	0.0439730i
$304$	1.70380	+	2.95107i	0.0977198	+	0.169256i
$305$	6.88553			0.394264
$306$	−8.54808	+	18.0073i	−0.488661	+	1.02941i
$307$	−25.8155			−1.47337			−0.736685	−	0.676236i	$-0.763610\pi$
$307$	−25.8155			−1.47337			−0.736685	+	0.676236i	$0.763610\pi$
$308$	−1.12056	−	1.94087i	−0.0638498	−	0.110591i
$309$	6.71736	+	10.6245i	0.382137	+	0.604408i
$310$	4.40761	−	7.63420i	0.250335	−	0.433593i
$311$	13.8662	−	24.0169i	0.786277	−	1.36187i	−0.141956	−	0.989873i	$-0.545339\pi$
$311$	13.8662	−	24.0169i	0.786277	−	1.36187i	0.928233	−	0.371999i	$-0.121328\pi$
$312$	0.618402	+	0.978097i	0.0350101	+	0.0553738i
$313$	10.9212	+	18.9161i	0.617304	+	1.06920i	0.989976	+	0.141239i	$0.0451086\pi$
$313$	10.9212	+	18.9161i	0.617304	+	1.06920i	−0.372671	+	0.927963i	$0.621558\pi$
$314$	1.95692			0.110436
$315$	−1.70380	−	2.46922i	−0.0959984	−	0.139125i
$316$	7.90923			0.444929
$317$	5.94114	+	10.2904i	0.333688	+	0.577964i	0.983232	−	0.182360i	$-0.0583735\pi$
$317$	5.94114	+	10.2904i	0.333688	+	0.577964i	−0.649544	+	0.760324i	$0.725040\pi$
$318$	16.8557	−	0.677922i	0.945220	−	0.0380160i
$319$	−8.27411	+	14.3312i	−0.463262	+	0.802392i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−15.7390	+	29.9823i	−0.878463	+	1.67345i
$322$	1.62056	+	2.80689i	0.0903103	+	0.156422i
$323$	−22.6415			−1.25981
$324$	−5.68980	−	6.97325i	−0.316100	−	0.387403i
$325$	−0.668105			−0.0370598
$326$	−4.82220	−	8.35230i	−0.267077	−	0.462591i
$327$	3.87299	−	7.37795i	0.214177	−	0.408001i
$328$	0.165947	−	0.287429i	0.00916291	−	0.0158706i
$329$	−3.69411	+	6.39839i	−0.203663	+	0.352755i
$330$	3.87860	−	0.155994i	0.213510	−	0.00858719i
$331$	3.10172	+	5.37233i	0.170486	+	0.295290i	0.938590	−	0.345035i	$-0.112133\pi$
$331$	3.10172	+	5.37233i	0.170486	+	0.295290i	−0.768104	+	0.640325i	$0.778800\pi$
$332$	7.24544			0.397645
$333$	−5.24040	−	7.59461i	−0.287172	−	0.416182i
$334$	−8.64549			−0.473060
$335$	−1.27682	−	2.21151i	−0.0697600	−	0.120828i
$336$	0.925606	+	1.46399i	0.0504959	+	0.0798670i
$337$	0.00753189	−	0.0130456i	0.000410288	−	0.000710640i	−0.865820	−	0.500355i	$-0.833203\pi$
$337$	0.00753189	−	0.0130456i	0.000410288	−	0.000710640i	0.866230	+	0.499645i	$0.166536\pi$
$338$	6.27682	−	10.8718i	0.341414	−	0.591346i
$339$	−14.9269	−	23.6092i	−0.810719	−	1.28227i
$340$	3.32220	+	5.75423i	0.180172	+	0.312067i
$341$	−19.7559			−1.06984
$342$	4.38391	−	9.23511i	0.237055	−	0.499378i
$343$	−1.00000			−0.0539949
$344$	1.45461	+	2.51946i	0.0784275	+	0.135840i
$345$	−5.60925	+	0.225600i	−0.301992	+	0.0121459i
$346$	−4.40761	+	7.63420i	−0.236954	+	0.410417i
$347$	−9.25744	+	16.0344i	−0.496965	+	0.860769i	−0.999994	−	0.00350062i	$-0.998886\pi$
$347$	−9.25744	+	16.0344i	−0.496965	+	0.860769i	0.503029	+	0.864270i	$0.332219\pi$
$348$	5.94439	−	11.3239i	0.318652	−	0.607025i
$349$	11.4395	+	19.8138i	0.612344	+	1.06061i	0.990844	+	0.135009i	$0.0431065\pi$
$349$	11.4395	+	19.8138i	0.612344	+	1.06061i	−0.378501	+	0.925601i	$0.623560\pi$
$350$	−1.00000			−0.0534522
$351$	1.36150	−	3.19346i	0.0726716	−	0.170454i
$352$	−2.24112			−0.119452
$353$	−1.20918	−	2.09436i	−0.0643580	−	0.111471i	0.832051	−	0.554699i	$-0.187167\pi$
$353$	−1.20918	−	2.09436i	−0.0643580	−	0.111471i	−0.896409	+	0.443228i	$0.853833\pi$
$354$	−6.35169	+	12.0998i	−0.337588	+	0.643097i
$355$	5.15626	−	8.93090i	0.273666	−	0.474003i
$356$	3.98062	−	6.89464i	0.210972	−	0.365415i
$357$	−11.4992	+	0.462487i	−0.608600	+	0.0244774i
$358$	−7.84821	−	13.5935i	−0.414791	−	0.718439i
$359$	3.22498			0.170208			0.0851040	−	0.996372i	$-0.472878\pi$
$359$	3.22498			0.170208			0.0851040	+	0.996372i	$0.472878\pi$
$360$	−2.99031	+	0.240925i	−0.157603	+	0.0126979i
$361$	−7.38823			−0.388854
$362$	7.22174	+	12.5084i	0.379566	+	0.657428i
$363$	5.53270	+	8.75080i	0.290391	+	0.459298i
$364$	−0.334053	+	0.578596i	−0.0175091	+	0.0303267i
$365$	−1.16811	+	2.02322i	−0.0611414	+	0.105900i
$366$	6.37329	+	10.0803i	0.333137	+	0.526907i
$367$	3.15194	+	5.45932i	0.164530	+	0.284974i	0.936488	−	0.350699i	$-0.114056\pi$
$367$	3.15194	+	5.45932i	0.164530	+	0.284974i	−0.771958	+	0.635673i	$0.780723\pi$
$368$	3.24112			0.168955
$369$	−0.992468	+	0.0799619i	−0.0516658	+	0.00416265i
$370$	−3.07571			−0.159899
$371$	4.86975	+	8.43465i	0.252825	+	0.437905i
$372$	15.2561	−	0.613587i	0.790990	−	0.0318130i
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	−0.581122	−	0.813816i	$-0.697386\pi$
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	0.995347	+	0.0963587i	$0.0307196\pi$
$374$	7.44546	−	12.8959i	0.384996	−	0.666832i
$375$	0.805046	−	1.53359i	0.0415724	−	0.0791943i
$376$	3.69411	+	6.39839i	0.190509	+	0.329972i
$377$	4.93323			0.254074
$378$	2.03786	−	4.77987i	0.104816	−	0.245850i
$379$	−6.74813			−0.346628			−0.173314	−	0.984867i	$-0.555448\pi$
$379$	−6.74813			−0.346628			−0.173314	+	0.984867i	$0.555448\pi$
$380$	−1.70380	−	2.95107i	−0.0874032	−	0.151387i
$381$	−0.999159	+	1.90337i	−0.0511884	+	0.0975126i
$382$	−13.2174	+	22.8933i	−0.676262	+	1.17132i
$383$	−12.0974	+	20.9533i	−0.618148	+	1.07066i	0.371675	+	0.928363i	$0.378784\pi$
$383$	−12.0974	+	20.9533i	−0.618148	+	1.07066i	−0.989823	+	0.142301i	$0.954550\pi$
$384$	1.73065	−	0.0696054i	0.0883169	−	0.00355204i
$385$	1.12056	+	1.94087i	0.0571090	+	0.0989157i
$386$	5.97630			0.304186
$387$	3.74274	−	7.88443i	0.190254	−	0.400788i
$388$	16.1073			0.817723
$389$	7.76982	+	13.4577i	0.393946	+	0.682334i	0.992966	−	0.118400i	$-0.0377765\pi$
$389$	7.76982	+	13.4577i	0.393946	+	0.682334i	−0.599020	+	0.800734i	$0.704443\pi$
$390$	−0.618402	−	0.978097i	−0.0313140	−	0.0495278i
$391$	−10.7677	+	18.6501i	−0.544544	+	0.943178i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−4.64597	−	7.34830i	−0.234358	−	0.370673i
$394$	−4.29674	−	7.44216i	−0.216466	−	0.374931i
$395$	−7.90923			−0.397956
$396$	3.81843	+	5.53382i	0.191883	+	0.278085i
$397$	10.0089			0.502334			0.251167	−	0.967944i	$-0.419186\pi$
$397$	10.0089			0.502334			0.251167	+	0.967944i	$0.419186\pi$
$398$	5.93308	+	10.2764i	0.297398	+	0.515109i
$399$	5.89738	−	0.237188i	0.295238	−	0.0118742i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−12.6168	+	21.8529i	−0.630052	+	1.09128i	0.357489	+	0.933918i	$0.383633\pi$
$401$	−12.6168	+	21.8529i	−0.630052	+	1.09128i	−0.987541	+	0.157365i	$0.949700\pi$
$402$	2.05579	−	3.91623i	0.102534	−	0.195324i
$403$	2.94474	+	5.10045i	0.146688	+	0.254071i
$404$	10.9968			0.547109
$405$	5.68980	+	6.97325i	0.282728	+	0.346504i
$406$	7.38391			0.366457
$407$	3.44652	+	5.96955i	0.170838	+	0.295899i
$408$	−5.34905	+	10.1898i	−0.264818	+	0.504471i
$409$	−5.64387	+	9.77547i	−0.279072	+	0.483366i	−0.971154	−	0.238452i	$-0.923360\pi$
$409$	−5.64387	+	9.77547i	−0.279072	+	0.483366i	0.692083	+	0.721818i	$0.256693\pi$
$410$	−0.165947	+	0.287429i	−0.00819556	+	0.0141951i
$411$	11.5737	−	0.465485i	0.570889	−	0.0229607i
$412$	3.62863	+	6.28497i	0.178770	+	0.309638i
$413$	−7.88985			−0.388234
$414$	−5.52223	−	8.00304i	−0.271403	−	0.393328i
$415$	−7.24544			−0.355664
$416$	0.334053	+	0.578596i	0.0163783	+	0.0283680i
$417$	−18.2491	−	28.8637i	−0.893661	−	1.41346i
$418$	−3.81843	+	6.61371i	−0.186765	+	0.323487i
$419$	9.65572	−	16.7242i	0.471713	−	0.817031i	−0.527763	−	0.849391i	$-0.676969\pi$
$419$	9.65572	−	16.7242i	0.471713	−	0.817031i	0.999476	+	0.0323609i	$0.0103026\pi$
$420$	−0.925606	−	1.46399i	−0.0451649	−	0.0714352i
$421$	−14.7180	−	25.4923i	−0.717310	−	1.24242i	−0.962062	−	0.272831i	$-0.912040\pi$
$421$	−14.7180	−	25.4923i	−0.717310	−	1.24242i	0.244752	−	0.969586i	$-0.421293\pi$
$422$	−24.6857			−1.20168
$423$	9.50501	−	20.0232i	0.462149	−	0.973560i
$424$	9.73950			0.472992
$425$	−3.32220	−	5.75423i	−0.161151	−	0.279121i
$426$	17.8474	−	0.717807i	0.864708	−	0.0347779i
$427$	−3.44277	+	5.96304i	−0.166607	+	0.288572i
$428$	−9.77520	+	16.9311i	−0.472502	+	0.818397i
$429$	−1.20540	+	2.29625i	−0.0581972	+	0.110864i
$430$	−1.45461	−	2.51946i	−0.0701477	−	0.121499i
$431$	5.28420			0.254531			0.127265	−	0.991869i	$-0.459380\pi$
$431$	5.28420			0.254531			0.127265	+	0.991869i	$0.459380\pi$
$432$	−3.12056	−	4.15477i	−0.150138	−	0.199896i
$433$	−34.1507			−1.64118			−0.820588	−	0.571520i	$-0.806354\pi$
$433$	−34.1507			−1.64118			−0.820588	+	0.571520i	$0.806354\pi$
$434$	4.40761	+	7.63420i	0.211572	+	0.366453i
$435$	−5.94439	+	11.3239i	−0.285011	+	0.542939i
$436$	2.40545	−	4.16636i	0.115200	−	0.199532i
$437$	5.52223	−	9.56478i	0.264164	−	0.457546i
$438$	−4.04317	+	0.162613i	−0.193190	+	0.00776995i
$439$	−3.76767	−	6.52579i	−0.179821	−	0.311459i	0.761998	−	0.647579i	$-0.224218\pi$
$439$	−3.76767	−	6.52579i	−0.179821	−	0.311459i	−0.941819	+	0.336120i	$0.890885\pi$
$440$	2.24112			0.106841
$441$	2.99031	−	0.240925i	0.142396	−	0.0114726i
$442$	−4.43917			−0.211150
$443$	13.2418	+	22.9355i	0.629137	+	1.08970i	0.987725	+	0.156202i	$0.0499251\pi$
$443$	13.2418	+	22.9355i	0.629137	+	1.08970i	−0.358588	+	0.933496i	$0.616742\pi$
$444$	−2.84690	−	4.50280i	−0.135108	−	0.213693i
$445$	−3.98062	+	6.89464i	−0.188700	+	0.326837i
$446$	−7.47309	+	12.9438i	−0.353861	+	0.612905i
$447$	13.7612	+	21.7654i	0.650882	+	1.02947i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−26.0326			−1.22856			−0.614278	−	0.789090i	$-0.710553\pi$
$449$	−26.0326			−1.22856			−0.614278	+	0.789090i	$0.710553\pi$
$450$	2.99031	−	0.240925i	0.140965	−	0.0113573i
$451$	0.743816			0.0350249
$452$	−8.06333	−	13.9661i	−0.379267	−	0.656910i
$453$	25.4679	−	1.02430i	1.19659	−	0.0481258i
$454$	6.85199	−	11.8680i	0.321580	−	0.556993i
$455$	0.334053	−	0.578596i	0.0156606	−	0.0271250i
$456$	2.74328	−	5.22587i	0.128466	−	0.244724i
$457$	−11.6256	−	20.1361i	−0.543821	−	0.941926i	−0.998680	−	0.0513623i	$-0.983644\pi$
$457$	−11.6256	−	20.1361i	−0.543821	−	0.941926i	0.454859	−	0.890563i	$-0.349690\pi$
$458$	5.55795			0.259706
$459$	34.2746	−	4.15342i	1.59980	−	0.193865i
$460$	−3.24112			−0.151118
$461$	−17.3251	−	30.0079i	−0.806908	−	1.39761i	−0.914995	−	0.403465i	$-0.867806\pi$
$461$	−17.3251	−	30.0079i	−0.806908	−	1.39761i	0.108087	−	0.994141i	$-0.465527\pi$
$462$	−1.80420	+	3.43696i	−0.0839392	+	0.159902i
$463$	−1.07464	+	1.86132i	−0.0499425	+	0.0865030i	−0.889916	−	0.456125i	$-0.849237\pi$
$463$	−1.07464	+	1.86132i	−0.0499425	+	0.0865030i	0.839973	+	0.542628i	$0.182570\pi$
$464$	3.69195	−	6.39465i	0.171395	−	0.296864i
$465$	−15.2561	+	0.613587i	−0.707483	+	0.0284544i
$466$	−5.24166	−	9.07882i	−0.242815	−	0.420568i
$467$	30.5041			1.41156			0.705780	−	0.708431i	$-0.250597\pi$
$467$	30.5041			1.41156			0.705780	+	0.708431i	$0.250597\pi$
$468$	0.859522	−	1.81066i	0.0397314	−	0.0836980i
$469$	2.55364			0.117916
$470$	−3.69411	−	6.39839i	−0.170397	−	0.295136i
$471$	−1.81134	−	2.86491i	−0.0834622	−	0.132008i
$472$	−3.94492	+	6.83281i	−0.181580	+	0.314505i
$473$	−3.25996	+	5.64642i	−0.149893	+	0.259623i
$474$	−7.32083	−	11.5790i	−0.336257	−	0.531841i
$475$	1.70380	+	2.95107i	0.0781758	+	0.135405i
$476$	−6.64441			−0.304546
$477$	−16.5942	−	24.0490i	−0.759796	−	1.10113i
$478$	14.9580			0.684163
$479$	−14.9180	−	25.8388i	−0.681621	−	1.18060i	−0.974486	−	0.224449i	$-0.927942\pi$
$479$	−14.9180	−	25.8388i	−0.681621	−	1.18060i	0.292865	−	0.956154i	$-0.405392\pi$
$480$	−1.73065	+	0.0696054i	−0.0789931	+	0.00317704i
$481$	1.02745	−	1.77959i	0.0468477	−	0.0811425i
$482$	7.89306	−	13.6712i	0.359519	−	0.622705i
$483$	2.60925	−	4.97055i	0.118725	−	0.226168i
$484$	2.98869	+	5.17656i	0.135850	+	0.235298i
$485$	−16.1073			−0.731393
$486$	−4.94223	+	14.7843i	−0.224184	+	0.670628i
$487$	−40.0566			−1.81514			−0.907570	−	0.419901i	$-0.862065\pi$
$487$	−40.0566			−1.81514			−0.907570	+	0.419901i	$0.862065\pi$
$488$	3.44277	+	5.96304i	0.155847	+	0.269934i
$489$	−7.76419	+	14.7906i	−0.351109	+	0.668853i
$490$	0.500000	−	0.866025i	0.0225877	−	0.0391230i
$491$	2.87245	−	4.97522i	0.129632	−	0.224529i	−0.793902	−	0.608045i	$-0.791954\pi$
$491$	2.87245	−	4.97522i	0.129632	−	0.224529i	0.923534	+	0.383517i	$0.125287\pi$
$492$	−0.574394	+	0.0231017i	−0.0258957	+	0.00104150i
$493$	24.5309	+	42.4887i	1.10481	+	1.91359i
$494$	2.27664			0.102431
$495$	−3.81843	−	5.53382i	−0.171626	−	0.248727i
$496$	8.81521			0.395815
$497$	5.15626	+	8.93090i	0.231290	+	0.400606i
$498$	−6.70642	−	10.6072i	−0.300522	−	0.475321i
$499$	−14.0061	+	24.2593i	−0.626999	+	1.08599i	0.361152	+	0.932507i	$0.382384\pi$
$499$	−14.0061	+	24.2593i	−0.626999	+	1.08599i	−0.988151	+	0.153487i	$0.950950\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	8.00231	+	12.6569i	0.357517	+	0.565467i
$502$	5.04377	+	8.73606i	0.225114	+	0.389909i
$503$	−21.4230			−0.955203			−0.477602	−	0.878576i	$-0.658494\pi$
$503$	−21.4230			−0.955203			−0.477602	+	0.878576i	$0.658494\pi$
$504$	1.28651	−	2.71015i	0.0573056	−	0.120720i
$505$	−10.9968			−0.489349
$506$	3.63187	+	6.29058i	0.161456	+	0.279651i
$507$	−21.7260	+	0.873801i	−0.964884	+	0.0388069i
$508$	−0.620560	+	1.07484i	−0.0275329	+	0.0476884i
$509$	3.44277	−	5.96304i	0.152598	−	0.264307i	−0.779584	−	0.626298i	$-0.784569\pi$
$509$	3.44277	−	5.96304i	0.152598	−	0.264307i	0.932182	+	0.361991i	$0.117903\pi$
$510$	5.34905	−	10.1898i	0.236860	−	0.451212i
$511$	−1.16811	−	2.02322i	−0.0516739	−	0.0895019i
$512$	1.00000			0.0441942
$513$	−17.5778	+	2.13009i	−0.776081	+	0.0940459i
$514$	−11.2921			−0.498071
$515$	−3.62863	−	6.28497i	−0.159897	−	0.276949i
$516$	2.34206	−	4.46156i	0.103103	−	0.196409i
$517$	−8.27895	+	14.3396i	−0.364108	+	0.630653i
$518$	1.53786	−	2.66364i	0.0675695	−	0.117034i
$519$	15.2561	−	0.613587i	0.669667	−	0.0269335i
$520$	−0.334053	−	0.578596i	−0.0146492	−	0.0253731i
$521$	15.6520			0.685725			0.342863	−	0.939386i	$-0.388603\pi$
$521$	15.6520			0.685725			0.342863	+	0.939386i	$0.388603\pi$
$522$	−22.0802	+	1.77897i	−0.966423	+	0.0778635i
$523$	−19.3656			−0.846799			−0.423399	−	0.905943i	$-0.639163\pi$
$523$	−19.3656			−0.846799			−0.423399	+	0.905943i	$0.639163\pi$
$524$	−2.50969	−	4.34691i	−0.109636	−	0.189896i
$525$	0.925606	+	1.46399i	0.0403968	+	0.0638936i
$526$	−4.95245	+	8.57790i	−0.215937	+	0.374014i
$527$	−29.2859	+	50.7247i	−1.27572	+	2.20960i
$528$	2.07439	+	3.28097i	0.0902764	+	0.142786i
$529$	6.24757	+	10.8211i	0.271633	+	0.470483i
$530$	−9.73950			−0.423057
$531$	23.5931	−	1.90087i	1.02385	−	0.0824905i
$532$	3.40761			0.147738
$533$	−0.110870	−	0.192033i	−0.00480233	−	0.00831787i
$534$	−13.7781	+	0.554146i	−0.596238	+	0.0239802i
$535$	9.77520	−	16.9311i	0.422619	−	0.731997i
$536$	1.27682	−	2.21151i	0.0551501	−	0.0955228i
$537$	−12.6363	+	24.0719i	−0.545298	+	1.03878i
$538$	−3.11087	−	5.38819i	−0.134119	−	0.232301i
$539$	−2.24112			−0.0965319
$540$	3.12056	+	4.15477i	0.134288	+	0.178793i
$541$	38.1474			1.64009			0.820043	−	0.572302i	$-0.193950\pi$
$541$	38.1474			1.64009			0.820043	+	0.572302i	$0.193950\pi$
$542$	−15.4121	−	26.6945i	−0.662005	−	1.14663i
$543$	11.6277	−	22.1504i	0.498991	−	0.950564i
$544$	−3.32220	+	5.75423i	−0.142438	+	0.246710i
$545$	−2.40545	+	4.16636i	−0.103038	+	0.178467i
$546$	1.15626	−	0.0465038i	0.0494833	−	0.00199018i
$547$	−9.58234	−	16.5971i	−0.409711	−	0.709641i	0.585146	−	0.810928i	$-0.301037\pi$
$547$	−9.58234	−	16.5971i	−0.409711	−	0.709641i	−0.994857	+	0.101287i	$0.967704\pi$
$548$	6.68748			0.285675
$549$	8.85829	−	18.6608i	0.378062	−	0.796424i
$550$	−2.24112			−0.0955617
$551$	−12.5807	−	21.7905i	−0.535957	−	0.928305i
$552$	−3.00000	−	4.74495i	−0.127688	−	0.201959i
$553$	3.95461	−	6.84959i	0.168167	−	0.291274i
$554$	5.49838	−	9.52347i	0.233604	−	0.404614i
$555$	2.84690	+	4.50280i	0.120844	+	0.191133i
$556$	−9.85790	−	17.0744i	−0.418068	−	0.724115i
$557$	13.8098			0.585141			0.292570	−	0.956244i	$-0.405489\pi$
$557$	13.8098			0.585141			0.292570	+	0.956244i	$0.405489\pi$
$558$	−15.0194	−	21.7667i	−0.635821	−	0.921458i
$559$	1.94367			0.0822084
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$	−25.7710	+	1.03649i	−1.08805	+	0.0437606i
$562$	−16.1650	+	27.9987i	−0.681881	+	1.18105i
$563$	−12.3584	+	21.4054i	−0.520846	+	0.902132i	0.478860	+	0.877891i	$0.341050\pi$
$563$	−12.3584	+	21.4054i	−0.520846	+	0.902132i	−0.999706	+	0.0242407i	$0.992283\pi$
$564$	5.94786	−	11.3305i	0.250450	−	0.477101i
$565$	8.06333	+	13.9661i	0.339227	+	0.587558i
$566$	5.38823			0.226484
$567$	−8.88391	+	1.44088i	−0.373089	+	0.0605114i
$568$	10.3125			0.432704
$569$	−10.8758	−	18.8375i	−0.455939	−	0.789709i	0.542803	−	0.839860i	$-0.317363\pi$
$569$	−10.8758	−	18.8375i	−0.455939	−	0.789709i	−0.998742	+	0.0501508i	$0.984030\pi$
$570$	−2.74328	+	5.22587i	−0.114903	+	0.218888i
$571$	11.2402	−	19.4686i	0.470388	−	0.814737i	−0.529038	−	0.848598i	$-0.677447\pi$
$571$	11.2402	−	19.4686i	0.470388	−	0.814737i	0.999427	+	0.0338614i	$0.0107805\pi$
$572$	−0.748652	+	1.29670i	−0.0313027	+	0.0542179i
$573$	45.7495	−	1.84001i	1.91121	−	0.0768675i
$574$	−0.165947	−	0.287429i	−0.00692651	−	0.0119971i
$575$	3.24112			0.135164
$576$	−1.70380	−	2.46922i	−0.0709918	−	0.102884i
$577$	−28.2426			−1.17575			−0.587876	−	0.808951i	$-0.700036\pi$
$577$	−28.2426			−1.17575			−0.587876	+	0.808951i	$0.700036\pi$
$578$	−13.5741	−	23.5110i	−0.564608	−	0.977929i
$579$	−5.53170	−	8.74922i	−0.229890	−	0.363605i
$580$	−3.69195	+	6.39465i	−0.153300	+	0.265524i
$581$	3.62272	−	6.27473i	0.150296	−	0.260320i
$582$	−14.9090	−	23.5808i	−0.617997	−	0.977456i
$583$	10.9137	+	18.9031i	0.451999	+	0.782885i
$584$	−2.33621			−0.0966731
$585$	−0.859522	+	1.81066i	−0.0355369	+	0.0748617i
$586$	−31.9702			−1.32068
$587$	17.9607	+	31.1089i	0.741318	+	1.28400i	0.951896	+	0.306423i	$0.0991321\pi$
$587$	17.9607	+	31.1089i	0.741318	+	1.28400i	−0.210578	+	0.977577i	$0.567535\pi$
$588$	1.73065	−	0.0696054i	0.0713709	−	0.00287048i
$589$	15.0194	−	26.0143i	0.618863	−	1.07190i
$590$	3.94492	−	6.83281i	0.162410	−	0.281302i
$591$	−6.91814	+	13.1789i	−0.284574	+	0.542106i
$592$	−1.53786	−	2.66364i	−0.0632055	−	0.109475i
$593$	10.1180			0.415497			0.207749	−	0.978182i	$-0.433386\pi$
$593$	10.1180			0.415497			0.207749	+	0.978182i	$0.433386\pi$
$594$	4.56708	−	10.7123i	0.187390	−	0.439529i
$595$	6.64441			0.272394
$596$	7.43361	+	12.8754i	0.304493	+	0.527397i
$597$	9.55279	−	18.1978i	0.390970	−	0.744787i
$598$	1.08270	−	1.87530i	0.0442751	−	0.0766867i
$599$	9.57964	−	16.5924i	0.391414	−	0.677948i	−0.601223	−	0.799082i	$-0.705320\pi$
$599$	9.57964	−	16.5924i	0.391414	−	0.677948i	0.992636	+	0.121133i	$0.0386529\pi$
$600$	1.73065	−	0.0696054i	0.0706536	−	0.00284163i
$601$	20.3640	+	35.2715i	0.830665	+	1.43875i	0.897512	+	0.440990i	$0.145373\pi$
$601$	20.3640	+	35.2715i	0.830665	+	1.43875i	−0.0668474	+	0.997763i	$0.521294\pi$
$602$	2.90923			0.118571
$603$	−7.63616	+	0.615236i	−0.310969	+	0.0250543i
$604$	14.7158			0.598778
$605$	−2.98869	−	5.17656i	−0.121508	−	0.210457i
$606$	−10.1787	−	16.0991i	−0.413480	−	0.653981i
$607$	14.6250	−	25.3313i	0.593612	−	1.02817i	−0.400130	−	0.916459i	$-0.631035\pi$
$607$	14.6250	−	25.3313i	0.593612	−	1.02817i	0.993741	−	0.111707i	$-0.0356318\pi$
$608$	1.70380	−	2.95107i	0.0690983	−	0.119682i
$609$	−6.83459	−	10.8099i	−0.276952	−	0.438041i
$610$	−3.44277	−	5.96304i	−0.139393	−	0.241437i
$611$	4.93611			0.199694
$612$	19.8688	−	1.60081i	0.803150	−	0.0647088i
$613$	−38.9171			−1.57185			−0.785923	−	0.618324i	$-0.787812\pi$
$613$	−38.9171			−1.57185			−0.785923	+	0.618324i	$0.787812\pi$
$614$	12.9078	+	22.3569i	0.520915	+	0.902251i
$615$	0.574394	−	0.0231017i	0.0231618	−	0.000931549i
$616$	−1.12056	+	1.94087i	−0.0451487	+	0.0781998i
$617$	−7.63256	+	13.2200i	−0.307275	+	0.532217i	−0.977765	−	0.209702i	$-0.932751\pi$
$617$	−7.63256	+	13.2200i	−0.307275	+	0.532217i	0.670490	+	0.741919i	$0.266084\pi$
$618$	5.84243	−	11.1297i	0.235017	−	0.447701i
$619$	−16.2300	−	28.1112i	−0.652338	−	1.12988i	−0.982554	−	0.185978i	$-0.940455\pi$
$619$	−16.2300	−	28.1112i	−0.652338	−	1.12988i	0.330216	−	0.943906i	$-0.392879\pi$
$620$	−8.81521			−0.354027
$621$	−6.60493	+	15.4921i	−0.265047	+	0.621678i
$622$	−27.7323			−1.11196
$623$	−3.98062	−	6.89464i	−0.159480	−	0.276228i
$624$	0.537855	−	1.02460i	0.0215314	−	0.0410168i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.9212	−	18.9161i	0.436500	−	0.756040i
$627$	13.2167	−	0.531566i	0.527825	−	0.0212287i
$628$	−0.978462	−	1.69475i	−0.0390449	−	0.0676278i
$629$	20.4363			0.814848
$630$	−1.28651	+	2.71015i	−0.0512557	+	0.107975i
$631$	14.6046			0.581399			0.290699	−	0.956814i	$-0.406112\pi$
$631$	14.6046			0.581399			0.290699	+	0.956814i	$0.406112\pi$
$632$	−3.95461	−	6.84959i	−0.157306	−	0.272462i
$633$	22.8492	+	36.1395i	0.908174	+	1.43642i
$634$	5.94114	−	10.2904i	0.235953	−	0.408683i
$635$	0.620560	−	1.07484i	0.0246262	−	0.0426538i
$636$	−9.01494	−	14.2585i	−0.357466	−	0.565386i
$637$	0.334053	+	0.578596i	0.0132356	+	0.0229248i
$638$	16.5482			0.655151
$639$	−17.5705	−	25.4639i	−0.695078	−	1.00734i
$640$	−1.00000			−0.0395285
$641$	−16.0206	−	27.7486i	−0.632777	−	1.09600i	−0.986981	−	0.160834i	$-0.948582\pi$
$641$	−16.0206	−	27.7486i	−0.632777	−	1.09600i	0.354205	−	0.935168i	$-0.384752\pi$
$642$	33.8349	−	1.36081i	1.33536	−	0.0537070i
$643$	5.85199	−	10.1359i	0.230780	−	0.399723i	−0.727258	−	0.686364i	$-0.759206\pi$
$643$	5.85199	−	10.1359i	0.230780	−	0.399723i	0.958038	+	0.286642i	$0.0925389\pi$
$644$	1.62056	−	2.80689i	0.0638590	−	0.110607i
$645$	−2.34206	+	4.46156i	−0.0922185	+	0.175674i
$646$	11.3208	+	19.6081i	0.445409	+	0.771472i
$647$	−42.3258			−1.66400			−0.831999	−	0.554777i	$-0.812803\pi$
$647$	−42.3258			−1.66400			−0.831999	+	0.554777i	$0.812803\pi$
$648$	−3.19411	+	8.41413i	−0.125477	+	0.330538i
$649$	−17.6821			−0.694083
$650$	0.334053	+	0.578596i	0.0131026	+	0.0226944i
$651$	7.09665	−	13.5189i	0.278140	−	0.529849i
$652$	−4.82220	+	8.35230i	−0.188852	+	0.327101i
$653$	11.3828	−	19.7156i	0.445445	−	0.771533i	−0.552638	−	0.833421i	$-0.686379\pi$
$653$	11.3828	−	19.7156i	0.445445	−	0.771533i	0.998083	+	0.0618883i	$0.0197122\pi$
$654$	−8.32598	+	0.334864i	−0.325572	+	0.0130942i
$655$	2.50969	+	4.34691i	0.0980617	+	0.169848i
$656$	−0.331895			−0.0129583
$657$	3.98044	+	5.76862i	0.155292	+	0.225055i
$658$	7.38823			0.288023
$659$	15.3622	+	26.6081i	0.598427	+	1.03651i	0.993053	+	0.117664i	$0.0375407\pi$
$659$	15.3622	+	26.6081i	0.598427	+	1.03651i	−0.394626	+	0.918842i	$0.629126\pi$
$660$	−2.07439	−	3.28097i	−0.0807457	−	0.127711i
$661$	17.4833	−	30.2820i	0.680022	−	1.17783i	−0.294951	−	0.955512i	$-0.595303\pi$
$661$	17.4833	−	30.2820i	0.680022	−	1.17783i	0.974974	−	0.222321i	$-0.0713632\pi$
$662$	3.10172	−	5.37233i	0.120552	−	0.208802i
$663$	4.10892	+	6.49887i	0.159577	+	0.252395i
$664$	−3.62272	−	6.27473i	−0.140589	−	0.243507i
$665$	−3.40761			−0.132141
$666$	−3.95692	+	8.33563i	−0.153328	+	0.322999i
$667$	−23.9321			−0.926656
$668$	4.32274	+	7.48721i	0.167252	+	0.289689i
$669$	25.8666	−	1.04034i	1.00006	−	0.0402217i
$670$	−1.27682	+	2.21151i	−0.0493278	+	0.0854382i
$671$	−7.71565	+	13.3639i	−0.297859	+	0.515908i
$672$	0.805046	−	1.53359i	0.0310553	−	0.0591596i
$673$	3.83351	+	6.63984i	0.147771	+	0.255947i	0.930403	−	0.366537i	$-0.119457\pi$
$673$	3.83351	+	6.63984i	0.147771	+	0.255947i	−0.782632	+	0.622484i	$0.786123\pi$
$674$	−0.0150638			−0.000580235
$675$	−3.12056	−	4.15477i	−0.120110	−	0.159917i
$676$	−12.5536			−0.482832
$677$	−5.18371	−	8.97844i	−0.199226	−	0.345070i	0.749052	−	0.662512i	$-0.230509\pi$
$677$	−5.18371	−	8.97844i	−0.199226	−	0.345070i	−0.948278	+	0.317442i	$0.897176\pi$
$678$	−12.9827	+	24.7317i	−0.498597	+	0.949815i
$679$	8.05364	−	13.9493i	0.309070	−	0.535325i
$680$	3.32220	−	5.75423i	0.127401	−	0.220665i
$681$	−23.7168	+	0.953871i	−0.908830	+	0.0365524i
$682$	9.87797	+	17.1092i	0.378247	+	0.655143i
$683$	27.9221			1.06841			0.534205	−	0.845355i	$-0.320611\pi$
$683$	27.9221			1.06841			0.534205	+	0.845355i	$0.320611\pi$
$684$	−10.1898	+	0.820979i	−0.389617	+	0.0313909i
$685$	−6.68748			−0.255516
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−5.14447	−	8.13676i	−0.196274	−	0.310437i
$688$	1.45461	−	2.51946i	0.0554566	−	0.0960536i
$689$	3.25351	−	5.63524i	0.123949	−	0.214685i
$690$	3.00000	+	4.74495i	0.114208	+	0.180637i
$691$	−14.2336	−	24.6533i	−0.541470	−	0.937854i	−0.998820	−	0.0485671i	$-0.984535\pi$
$691$	−14.2336	−	24.6533i	−0.541470	−	0.937854i	0.457350	−	0.889287i	$-0.348799\pi$
$692$	8.81521			0.335104
$693$	6.70164	−	0.539943i	0.254574	−	0.0205107i
$694$	18.5149			0.702815
$695$	9.85790	+	17.0744i	0.373932	+	0.647668i
$696$	−12.7790	+	0.513960i	−0.484386	+	0.0194816i
$697$	1.10262	−	1.90980i	0.0417648	−	0.0723387i
$698$	11.4395	−	19.8138i	0.432992	−	0.749965i
$699$	−8.43955	+	16.0771i	−0.319213	+	0.608092i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	−12.3287			−0.465647			−0.232823	−	0.972519i	$-0.574796\pi$
$701$	−12.3287			−0.465647			−0.232823	+	0.972519i	$0.574796\pi$
$702$	−3.44636	+	0.417633i	−0.130075	+	0.0157625i
$703$	−10.4808			−0.395291
$704$	1.12056	+	1.94087i	0.0422327	+	0.0731492i
$705$	−5.94786	+	11.3305i	−0.224009	+	0.426732i
$706$	−1.20918	+	2.09436i	−0.0455080	+	0.0788221i
$707$	5.49838	−	9.52347i	0.206788	−	0.358167i
$708$	13.6546	−	0.549176i	0.513170	−	0.0206393i
$709$	12.7440	+	22.0732i	0.478610	+	0.828977i	0.999699	−	0.0245256i	$-0.00780751\pi$
$709$	12.7440	+	22.0732i	0.478610	+	0.828977i	−0.521089	+	0.853502i	$0.674474\pi$
$710$	−10.3125			−0.387022
$711$	−10.1753	+	21.4352i	−0.381603	+	0.803882i
$712$	−7.96124			−0.298360
$713$	−14.2856	−	24.7433i	−0.534999	−	0.926646i
$714$	6.15010	+	9.72732i	0.230162	+	0.364036i
$715$	0.748652	−	1.29670i	0.0279980	−	0.0484940i
$716$	−7.84821	+	13.5935i	−0.293301	+	0.508013i
$717$	−13.8452	−	21.8983i	−0.517059	−	0.817807i
$718$	−1.61249	−	2.79292i	−0.0601776	−	0.104231i
$719$	−37.0122			−1.38032			−0.690161	−	0.723656i	$-0.742460\pi$
$719$	−37.0122			−1.38032			−0.690161	+	0.723656i	$0.742460\pi$
$720$	1.70380	+	2.46922i	0.0634970	+	0.0920225i
$721$	7.25726			0.270274
$722$	3.69411	+	6.39839i	0.137481	+	0.238123i
$723$	−27.3203	+	1.09880i	−1.01605	+	0.0408648i
$724$	7.22174	−	12.5084i	0.268394	−	0.464872i
$725$	3.69195	−	6.39465i	0.137116	−	0.237491i
$726$	4.81206	−	9.16686i	0.178592	−	0.340214i
$727$	−21.4418	−	37.1384i	−0.795234	−	1.37739i	−0.922691	−	0.385541i	$-0.874015\pi$
$727$	−21.4418	−	37.1384i	−0.795234	−	1.37739i	0.127457	−	0.991844i	$-0.459319\pi$
$728$	0.668105			0.0247616
$729$	26.2185	−	6.44905i	0.971056	−	0.238854i
$730$	2.33621			0.0864670
$731$	9.66504	+	16.7403i	0.357475	+	0.619164i
$732$	5.54317	−	10.5596i	0.204881	−	0.390294i
$733$	18.4110	−	31.8888i	0.680026	−	1.17784i	−0.294947	−	0.955514i	$-0.595302\pi$
$733$	18.4110	−	31.8888i	0.680026	−	1.17784i	0.974972	−	0.222326i	$-0.0713648\pi$
$734$	3.15194	−	5.45932i	0.116340	−	0.201507i
$735$	−1.73065	+	0.0696054i	−0.0638360	+	0.00256743i
$736$	−1.62056	−	2.80689i	−0.0597346	−	0.103463i
$737$	5.72300			0.210810
$738$	0.565483	+	0.819522i	0.0208157	+	0.0301670i
$739$	−3.65084			−0.134298			−0.0671492	−	0.997743i	$-0.521390\pi$
$739$	−3.65084			−0.134298			−0.0671492	+	0.997743i	$0.521390\pi$
$740$	1.53786	+	2.66364i	0.0565327	+	0.0979175i
$741$	−2.10727	−	3.33297i	−0.0774125	−	0.122440i
$742$	4.86975	−	8.43465i	0.178774	−	0.309646i
$743$	0.909226	−	1.57482i	0.0333563	−	0.0577747i	−0.848865	−	0.528609i	$-0.822714\pi$
$743$	0.909226	−	1.57482i	0.0333563	−	0.0577747i	0.882222	+	0.470834i	$0.156047\pi$
$744$	−8.15941	−	12.9053i	−0.299139	−	0.473133i
$745$	−7.43361	−	12.8754i	−0.272347	−	0.471718i
$746$	−16.0000			−0.585802
$747$	−9.32131	+	19.6362i	−0.341049	+	0.718451i
$748$	−14.8909			−0.544466
$749$	9.77520	+	16.9311i	0.357178	+	0.618650i
$750$	−1.73065	+	0.0696054i	−0.0631945	+	0.00254163i
$751$	−10.4514	+	18.1024i	−0.381377	+	0.660564i	−0.991259	−	0.131928i	$-0.957883\pi$
$751$	−10.4514	+	18.1024i	−0.381377	+	0.660564i	0.609882	+	0.792492i	$0.291217\pi$
$752$	3.69411	−	6.39839i	0.134710	−	0.233325i
$753$	8.12093	−	15.4702i	0.295943	−	0.563764i
$754$	−2.46661	−	4.27230i	−0.0898288	−	0.155588i
$755$	−14.7158			−0.535563
$756$	−5.15842	+	0.625100i	−0.187610	+	0.0227347i
$757$	39.5845			1.43872			0.719361	−	0.694637i	$-0.244435\pi$
$757$	39.5845			1.43872			0.719361	+	0.694637i	$0.244435\pi$
$758$	3.37407	+	5.84405i	0.122552	+	0.212266i
$759$	5.84764	−	11.1396i	0.212256	−	0.404342i
$760$	−1.70380	+	2.95107i	−0.0618034	+	0.107047i
$761$	−22.1234	+	38.3189i	−0.801973	+	1.38906i	0.116343	+	0.993209i	$0.462883\pi$
$761$	−22.1234	+	38.3189i	−0.801973	+	1.38906i	−0.918316	+	0.395849i	$0.870450\pi$
$762$	2.14795	−	0.0863887i	0.0778119	−	0.00312953i
$763$	−2.40545	−	4.16636i	−0.0870830	−	0.150832i
$764$	26.4348			0.956379
$765$	−19.8688	+	1.60081i	−0.718360	+	0.0578773i
$766$	24.1948			0.874194
$767$	2.63562	+	4.56503i	0.0951669	+	0.164834i
$768$	−0.925606	−	1.46399i	−0.0333999	−	0.0528270i
$769$	−11.2341	+	19.4581i	−0.405113	+	0.701676i	−0.994335	−	0.106295i	$-0.966101\pi$
$769$	−11.2341	+	19.4581i	−0.405113	+	0.701676i	0.589222	+	0.807971i	$0.299434\pi$
$770$	1.12056	−	1.94087i	0.0403822	−	0.0699440i
$771$	10.4520	+	16.5314i	0.376419	+	0.595364i
$772$	−2.98815	−	5.17563i	−0.107546	−	0.186275i
$773$	23.6979			0.852353			0.426176	−	0.904640i	$-0.359860\pi$
$773$	23.6979			0.852353			0.426176	+	0.904640i	$0.359860\pi$
$774$	−8.69949	+	0.700907i	−0.312697	+	0.0251936i
$775$	8.81521			0.316652
$776$	−8.05364	−	13.9493i	−0.289109	−	0.500751i
$777$	−5.32298	+	0.214086i	−0.190961	+	0.00768030i
$778$	7.76982	−	13.4577i	0.278562	−	0.482483i
$779$	−0.565483	+	0.979445i	−0.0202605	+	0.0350923i
$780$	−0.537855	+	1.02460i	−0.0192583	+	0.0366866i
$781$	11.5558	+	20.0152i	0.413499	+	0.716201i
$782$	21.5353			0.770102
$783$	23.0419	+	30.6784i	0.823452	+	1.09636i
$784$	1.00000			0.0357143
$785$	0.978462	+	1.69475i	0.0349228	+	0.0604881i
$786$	−4.04083	+	7.69768i	−0.144132	+	0.274567i
$787$	−14.0303	+	24.3012i	−0.500127	+	0.866245i	0.499873	+	0.866099i	$0.333380\pi$
$787$	−14.0303	+	24.3012i	−0.500127	+	0.866245i	−1.00000		0.000146674i	$0.999953\pi$
$788$	−4.29674	+	7.44216i	−0.153065	+	0.265116i
$789$	17.1419	−	0.689435i	0.610270	−	0.0245446i
$790$	3.95461	+	6.84959i	0.140699	+	0.243697i
$791$	−16.1267			−0.573398
$792$	2.88322	−	6.07377i	0.102451	−	0.215822i
$793$	4.60026			0.163360
$794$	−5.00447	−	8.66800i	−0.177602	−	0.307616i
$795$	9.01494	+	14.2585i	0.319727	+	0.505696i
$796$	5.93308	−	10.2764i	0.210292	−	0.364237i
$797$	13.4724	−	23.3348i	0.477216	−	0.826562i	−0.522443	−	0.852674i	$-0.674979\pi$
$797$	13.4724	−	23.3348i	0.477216	−	0.826562i	0.999659	+	0.0261119i	$0.00831263\pi$
$798$	−3.15410	−	4.98869i	−0.111654	−	0.176598i
$799$	24.5452	+	42.5135i	0.868347	+	1.50402i
$800$	1.00000			0.0353553
$801$	13.5644	+	19.6581i	0.479274	+	0.694584i
$802$	25.2336			0.891028
$803$	−2.61786	−	4.53427i	−0.0923824	−	0.160011i
$804$	−4.41945	+	0.177747i	−0.155862	+	0.00626865i
$805$	−1.62056	+	2.80689i	−0.0571172	+	0.0989300i
$806$	2.94474	−	5.10045i	0.103724	−	0.179656i
$807$	−5.00879	+	9.54161i	−0.176318	+	0.335880i
$808$	−5.49838	−	9.52347i	−0.193432	−	0.335035i
$809$	34.0998			1.19888			0.599442	−	0.800418i	$-0.295389\pi$
$809$	34.0998			1.19888			0.599442	+	0.800418i	$0.295389\pi$
$810$	3.19411	−	8.41413i	0.112230	−	0.295643i
$811$	5.07464			0.178195			0.0890973	−	0.996023i	$-0.471602\pi$
$811$	5.07464			0.178195			0.0890973	+	0.996023i	$0.471602\pi$
$812$	−3.69195	−	6.39465i	−0.129562	−	0.224408i
$813$	−24.8149	+	47.2716i	−0.870295	+	1.65789i
$814$	3.44652	−	5.96955i	0.120800	−	0.209232i
$815$	4.82220	−	8.35230i	0.168914	−	0.292568i
$816$	11.4992	−	0.462487i	0.402551	−	0.0161903i
$817$	−4.95675	−	8.58534i	−0.173415	−	0.300363i
$818$	11.2877			0.394667
$819$	−1.13832	−	1.64970i	−0.0397761	−	0.0576452i
$820$	0.331895			0.0115903
$821$	13.8844	+	24.0486i	0.484571	+	0.839301i	0.999843	−	0.0177257i	$-0.00564255\pi$
$821$	13.8844	+	24.0486i	0.484571	+	0.839301i	−0.515272	+	0.857027i	$0.672309\pi$
$822$	−6.18998	−	9.79038i	−0.215900	−	0.341479i
$823$	17.0325	−	29.5011i	0.593715	−	1.02834i	−0.400012	−	0.916510i	$-0.630994\pi$
$823$	17.0325	−	29.5011i	0.593715	−	1.02834i	0.993727	−	0.111835i	$-0.0356727\pi$
$824$	3.62863	−	6.28497i	0.126409	−	0.218947i
$825$	2.07439	+	3.28097i	0.0722211	+	0.114229i
$826$	3.94492	+	6.83281i	0.137261	+	0.237744i
$827$	−15.2426			−0.530035			−0.265018	−	0.964244i	$-0.585378\pi$
$827$	−15.2426			−0.530035			−0.265018	+	0.964244i	$0.585378\pi$
$828$	−4.16973	+	8.78391i	−0.144908	+	0.305262i
$829$	−23.1482			−0.803970			−0.401985	−	0.915646i	$-0.631680\pi$
$829$	−23.1482			−0.803970			−0.401985	+	0.915646i	$0.631680\pi$
$830$	3.62272	+	6.27473i	0.125746	+	0.217799i
$831$	−19.0316	+	0.765434i	−0.660198	+	0.0265526i
$832$	0.334053	−	0.578596i	0.0115812	−	0.0200592i
$833$	−3.32220	+	5.75423i	−0.115108	+	0.199372i
$834$	−15.8721	+	30.2360i	−0.549607	+	1.04699i
$835$	−4.32274	−	7.48721i	−0.149595	−	0.259106i
$836$	7.63685			0.264126
$837$	−17.9641	+	42.1356i	−0.620931	+	1.45642i
$838$	−19.3114			−0.667103
$839$	6.88106	+	11.9183i	0.237561	+	0.411467i	0.960014	−	0.279953i	$-0.0903188\pi$
$839$	6.88106	+	11.9183i	0.237561	+	0.411467i	−0.722453	+	0.691420i	$0.756986\pi$
$840$	−0.805046	+	1.53359i	−0.0277767	+	0.0529139i
$841$	−12.7611	+	22.1028i	−0.440037	+	0.762166i
$842$	−14.7180	+	25.4923i	−0.507214	+	0.878521i
$843$	55.9521	−	2.25035i	1.92709	−	0.0775062i
$844$	12.3428	+	21.3784i	0.424858	+	0.735876i
$845$	12.5536			0.431858
$846$	−22.0931	+	1.78001i	−0.759576	+	0.0611981i
$847$	5.97738			0.205385
$848$	−4.86975	−	8.43465i	−0.167228	−	0.289647i
$849$	−4.98737	−	7.88828i	−0.171166	−	0.270725i
$850$	−3.32220	+	5.75423i	−0.113951	+	0.197368i
$851$	−4.98437	+	8.63319i	−0.170862	+	0.295942i
$852$	−9.54532	−	15.0974i	−0.327017	−	0.517227i
$853$	−9.29314	−	16.0962i	−0.318191	−	0.551123i	0.661920	−	0.749575i	$-0.269742\pi$
$853$	−9.29314	−	16.0962i	−0.318191	−	0.551123i	−0.980111	+	0.198452i	$0.936409\pi$
$854$	6.88553			0.235618
$855$	10.1898	−	0.820979i	0.348484	−	0.0280769i
$856$	19.5504			0.668219
$857$	−5.44924	−	9.43836i	−0.186142	−	0.322408i	0.757818	−	0.652465i	$-0.226265\pi$
$857$	−5.44924	−	9.43836i	−0.186142	−	0.322408i	−0.943961	+	0.330057i	$0.892932\pi$
$858$	2.59131	−	0.104221i	0.0884659	−	0.00355803i
$859$	25.8868	−	44.8372i	0.883246	−	1.52983i	0.0355344	−	0.999368i	$-0.488687\pi$
$859$	25.8868	−	44.8372i	0.883246	−	1.52983i	0.847711	−	0.530458i	$-0.177980\pi$
$860$	−1.45461	+	2.51946i	−0.0496019	+	0.0859130i
$861$	−0.267190	+	0.508991i	−0.00910583	+	0.0173464i
$862$	−2.64210	−	4.57625i	−0.0899902	−	0.155868i
$863$	−12.6746			−0.431447			−0.215724	−	0.976454i	$-0.569211\pi$
$863$	−12.6746			−0.431447			−0.215724	+	0.976454i	$0.569211\pi$
$864$	−2.03786	+	4.77987i	−0.0693292	+	0.162614i
$865$	−8.81521			−0.299726
$866$	17.0753	+	29.5753i	0.580243	+	1.00501i
$867$	−21.8555	+	41.6342i	−0.742253	+	1.41397i
$868$	4.40761	−	7.63420i	0.149604	−	0.259122i
$869$	8.86276	−	15.3508i	0.300649	−	0.520739i
$870$	12.7790	−	0.513960i	0.433248	−	0.0174249i
$871$	−0.853049	−	1.47752i	−0.0289045	−	0.0500640i
$872$	−4.81089			−0.162917
$873$	−20.7221	+	43.6531i	−0.701338	+	1.47743i
$874$	−11.0445			−0.373584
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	2.16241	+	3.42018i	0.0730611	+	0.115557i
$877$	16.1241	−	27.9278i	0.544473	−	0.943055i	−0.454167	−	0.890917i	$-0.650063\pi$
$877$	16.1241	−	27.9278i	0.544473	−	0.943055i	0.998640	−	0.0521383i	$-0.0166037\pi$
$878$	−3.76767	+	6.52579i	−0.127153	+	0.220235i
$879$	29.5918	+	46.8039i	0.998106	+	1.57866i
$880$	−1.12056	−	1.94087i	−0.0377741	−	0.0654266i
$881$	−17.3222			−0.583600			−0.291800	−	0.956479i	$-0.594254\pi$
$881$	−17.3222			−0.583600			−0.291800	+	0.956479i	$0.594254\pi$
$882$	−1.70380	−	2.46922i	−0.0573700	−	0.0831430i
$883$	−1.58915			−0.0534793			−0.0267396	−	0.999642i	$-0.508513\pi$
$883$	−1.58915			−0.0534793			−0.0267396	+	0.999642i	$0.508513\pi$
$884$	2.21958	+	3.84443i	0.0746526	+	0.129302i
$885$	−13.6546	+	0.549176i	−0.458994	+	0.0184604i
$886$	13.2418	−	22.9355i	0.444867	−	0.770533i
$887$	8.69642	−	15.0626i	0.291997	−	0.505754i	−0.682285	−	0.731087i	$-0.739013\pi$
$887$	8.69642	−	15.0626i	0.291997	−	0.505754i	0.974282	+	0.225332i	$0.0723468\pi$
$888$	−2.47609	+	4.71688i	−0.0830921	+	0.158288i
$889$	0.620560	+	1.07484i	0.0208129	+	0.0360490i
$890$	7.96124			0.266861
$891$	−19.9099	+	3.22919i	−0.667007	+	0.108182i
$892$	14.9462			0.500435
$893$	−12.5881	−	21.8032i	−0.421244	−	0.729616i
$894$	11.9688	−	22.8002i	0.400296	−	0.762554i
$895$	7.84821	−	13.5935i	0.262337	−	0.454381i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	−3.74757	+	0.150724i	−0.125128	+	0.00503254i
$898$	13.0163	+	22.5449i	0.434360	+	0.752334i
$899$	−65.0907			−2.17090
$900$	−1.70380	−	2.46922i	−0.0567934	−	0.0823074i
$901$	64.7132			2.15591
$902$	−0.371908	−	0.644164i	−0.0123832	−	0.0214483i
$903$	−2.69280	−	4.25906i	−0.0896107	−	0.141733i
$904$	−8.06333	+	13.9661i	−0.268182	+	0.464505i
$905$	−7.22174	+	12.5084i	−0.240059	+	0.415794i
$906$	−13.6210	−	21.5437i	−0.452529	−	0.715742i
$907$	−18.5190	−	32.0759i	−0.614914	−	1.06506i	−0.990400	−	0.138234i	$-0.955857\pi$
$907$	−18.5190	−	32.0759i	−0.614914	−	1.06506i	0.375486	−	0.926828i	$-0.377476\pi$
$908$	−13.7040			−0.454783
$909$	−14.1474	+	29.8028i	−0.469240	+	0.988498i
$910$	−0.668105			−0.0221475
$911$	8.54772	+	14.8051i	0.283199	+	0.490515i	0.972171	−	0.234273i	$-0.0752711\pi$
$911$	8.54772	+	14.8051i	0.283199	+	0.490515i	−0.688972	+	0.724788i	$0.741938\pi$
$912$	−5.89738	+	0.237188i	−0.195282	+	0.00785407i
$913$	8.11895	−	14.0624i	0.268698	−	0.465398i
$914$	−11.6256	+	20.1361i	−0.384540	+	0.666042i
$915$	−5.54317	+	10.5596i	−0.183251	+	0.349089i
$916$	−2.77898	−	4.81333i	−0.0918199	−	0.159037i
$917$	−5.01938			−0.165755
$918$	−20.7343	−	27.6060i	−0.684333	−	0.911133i
$919$	9.24863			0.305084			0.152542	−	0.988297i	$-0.451254\pi$
$919$	9.24863			0.305084			0.152542	+	0.988297i	$0.451254\pi$
$920$	1.62056	+	2.80689i	0.0534283	+	0.0925405i
$921$	20.7827	−	39.5904i	0.684812	−	1.30455i
$922$	−17.3251	+	30.0079i	−0.570570	+	0.988257i
$923$	3.44492	−	5.96678i	0.113391	−	0.196399i
$924$	3.87860	−	0.155994i	0.127597	−	0.00513183i
$925$	−1.53786	−	2.66364i	−0.0505644	−	0.0875801i
$926$	2.14927			0.0706294
$927$	−21.7015	+	1.74846i	−0.712769	+	0.0574269i
$928$	−7.38391			−0.242389
$929$	7.26050	+	12.5756i	0.238209	+	0.412591i	0.960201	−	0.279312i	$-0.0901063\pi$
$929$	7.26050	+	12.5756i	0.238209	+	0.412591i	−0.721991	+	0.691902i	$0.756773\pi$
$930$	8.15941	+	12.9053i	0.267558	+	0.423183i
$931$	1.70380	−	2.95107i	0.0558399	−	0.0967175i
$932$	−5.24166	+	9.07882i	−0.171696	+	0.297387i
$933$	25.6692	+	40.5997i	0.840371	+	1.32917i
$934$	−15.2520	−	26.4173i	−0.499062	−	0.864401i
$935$	14.8909			0.486985
$936$	−1.99784	+	0.160964i	−0.0653015	+	0.00526126i
$937$	34.5095			1.12738			0.563688	−	0.825988i	$-0.309382\pi$
$937$	34.5095			1.12738			0.563688	+	0.825988i	$0.309382\pi$
$938$	−1.27682	−	2.21151i	−0.0416896	−	0.0722085i
$939$	−37.8017	+	1.52035i	−1.23361	+	0.0496149i
$940$	−3.69411	+	6.39839i	−0.120489	+	0.208693i
$941$	−24.3732	+	42.2156i	−0.794542	+	1.37619i	0.128587	+	0.991698i	$0.458956\pi$
$941$	−24.3732	+	42.2156i	−0.794542	+	1.37619i	−0.923129	+	0.384490i	$0.874377\pi$
$942$	−1.57541	+	3.00112i	−0.0513298	+	0.0977818i
$943$	0.537855	+	0.931593i	0.0175150	+	0.0303368i
$944$	7.88985			0.256793
$945$	5.15842	−	0.625100i	0.167803	−	0.0203345i
$946$	6.51992			0.211981
$947$	28.6214	+	49.5737i	0.930071	+	1.61093i	0.783196	+	0.621775i	$0.213588\pi$
$947$	28.6214	+	49.5737i	0.930071	+	1.61093i	0.146875	+	0.989155i	$0.453079\pi$
$948$	−6.36729	+	12.1295i	−0.206800	+	0.393948i
$949$	−0.780417	+	1.35172i	−0.0253334	+	0.0438788i
$950$	1.70380	−	2.95107i	0.0552787	−	0.0957454i
$951$	−20.5641	+	0.827072i	−0.666837	+	0.0268196i
$952$	3.32220	+	5.75423i	0.107673	+	0.186496i
$953$	−19.1406			−0.620026			−0.310013	−	0.950732i	$-0.600333\pi$
$953$	−19.1406			−0.620026			−0.310013	+	0.950732i	$0.600333\pi$
$954$	−12.5299	+	26.3955i	−0.405672	+	0.854585i
$955$	−26.4348			−0.855412
$956$	−7.47900	−	12.9540i	−0.241888	−	0.418963i
$957$	−15.3171	−	24.2264i	−0.495133	−	0.783127i
$958$	−14.9180	+	25.8388i	−0.481979	+	0.834812i
$959$	3.34374	−	5.79153i	0.107975	−	0.187018i
$960$	0.925606	+	1.46399i	0.0298738	+	0.0472499i
$961$	−23.3540	−	40.4503i	−0.753354	−	1.30485i
$962$	−2.05490			−0.0662526
$963$	−33.3100	−	48.2743i	−1.07340	−	1.55562i
$964$	−15.7861			−0.508437
$965$	2.98815	+	5.17563i	0.0961920	+	0.166609i
$966$	−5.60925	+	0.225600i	−0.180475	+	0.00725855i
$967$	14.0682	−	24.3668i	0.452401	−	0.783582i	−0.546133	−	0.837698i	$-0.683901\pi$
$967$	14.0682	−	24.3668i	0.452401	−	0.783582i	0.998535	+	0.0541162i	$0.0172341\pi$
$968$	2.98869	−	5.17656i	0.0960601	−	0.166381i
$969$	18.2275	−	34.7228i	0.585551	−	1.11546i
$970$	8.05364	+	13.9493i	0.258587	+	0.447885i
$971$	29.1460			0.935341			0.467670	−	0.883903i	$-0.345093\pi$
$971$	29.1460			0.935341			0.467670	+	0.883903i	$0.345093\pi$
$972$	15.2747	−	3.11204i	0.489935	−	0.0998186i
$973$	−19.7158			−0.632060
$974$	20.0283	+	34.6901i	0.641749	+	1.11154i
$975$	0.537855	−	1.02460i	0.0172252	−	0.0328135i
$976$	3.44277	−	5.96304i	0.110200	−	0.190872i
$977$	−5.83030	+	10.0984i	−0.186528	+	0.323076i	−0.944090	−	0.329687i	$-0.893057\pi$
$977$	−5.83030	+	10.0984i	−0.186528	+	0.323076i	0.757562	+	0.652763i	$0.226390\pi$
$978$	16.6911	−	0.671303i	0.533723	−	0.0214659i
$979$	−8.92105	−	15.4517i	−0.285118	−	0.493839i
$980$	−1.00000			−0.0319438
$981$	8.19682	+	11.8792i	0.261704	+	0.379273i
$982$	−5.74489			−0.183327
$983$	14.9708	+	25.9301i	0.477493	+	0.827042i	0.999667	−	0.0257969i	$-0.00821232\pi$
$983$	14.9708	+	25.9301i	0.477493	+	0.827042i	−0.522174	+	0.852839i	$0.674879\pi$
$984$	0.307204	+	0.485889i	0.00979330	+	0.0154896i
$985$	4.29674	−	7.44216i	0.136905	−	0.237127i
$986$	24.5309	−	42.4887i	0.781222	−	1.35312i
$987$	−6.83859	−	10.8163i	−0.217675	−	0.344285i
$988$	−1.13832	−	1.97163i	−0.0362148	−	0.0627258i
$989$	−9.42915			−0.299830
$990$	−2.88322	+	6.07377i	−0.0916347	+	0.193037i
$991$	19.9810			0.634717			0.317358	−	0.948306i	$-0.397204\pi$
$991$	19.9810			0.634717			0.317358	+	0.948306i	$0.397204\pi$
$992$	−4.40761	−	7.63420i	−0.139942	−	0.242386i
$993$	−10.7360	+	0.431793i	−0.340696	+	0.0137025i
$994$	5.15626	−	8.93090i	0.163547	−	0.283271i
$995$	−5.93308	+	10.2764i	−0.188091	+	0.325783i
$996$	−5.83291	+	11.1115i	−0.184823	+	0.352082i
$997$	22.1873	+	38.4295i	0.702679	+	1.21708i	0.967523	+	0.252784i	$0.0813462\pi$
$997$	22.1873	+	38.4295i	0.702679	+	1.21708i	−0.264844	+	0.964291i	$0.585320\pi$
$998$	28.0122			0.886710
$999$	15.8658	−	1.92263i	0.501971	−	0.0608292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.l.211.2	✓	8
3.2	odd	2		1890.2.j.l.631.2		8
9.2	odd	6		1890.2.j.l.1261.2		8
9.4	even	3		5670.2.a.bw.1.2		4
9.5	odd	6		5670.2.a.bv.1.3		4
9.7	even	3	inner	630.2.j.l.421.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.l.211.2	✓	8	1.1	even	1	trivial
630.2.j.l.421.2	yes	8	9.7	even	3	inner
1890.2.j.l.631.2		8	3.2	odd	2
1890.2.j.l.1261.2		8	9.2	odd	6
5670.2.a.bv.1.3		4	9.5	odd	6
5670.2.a.bw.1.2		4	9.4	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.805046 + 1.53359i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73065 - 0.0696054i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.70380 - 2.46922i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.805046 + 1.53359i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.73065 - 0.0696054i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.70380 - 2.46922i) q^{9} -1.00000 q^{10} +(1.12056 + 1.94087i) q^{11} +(-0.925606 - 1.46399i) q^{12} +(0.334053 - 0.578596i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.925606 + 1.46399i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.64441 q^{17} +(-1.28651 + 2.71015i) q^{18} -3.40761 q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.73065 + 0.0696054i) q^{21} +(1.12056 - 1.94087i) q^{22} +(-1.62056 + 2.80689i) q^{23} +(-0.805046 + 1.53359i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.668105 q^{26} +(5.15842 - 0.625100i) q^{27} -1.00000 q^{28} +(3.69195 + 6.39465i) q^{29} +(0.805046 - 1.53359i) q^{30} +(-4.40761 + 7.63420i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.87860 + 0.155994i) q^{33} +(-3.32220 - 5.75423i) q^{34} +1.00000 q^{35} +(2.99031 - 0.240925i) q^{36} +3.07571 q^{37} +(1.70380 + 2.95107i) q^{38} +(0.618402 + 0.978097i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.165947 - 0.287429i) q^{41} +(0.925606 + 1.46399i) q^{42} +(1.45461 + 2.51946i) q^{43} -2.24112 q^{44} +(-2.99031 + 0.240925i) q^{45} +3.24112 q^{46} +(3.69411 + 6.39839i) q^{47} +(1.73065 - 0.0696054i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-5.34905 + 10.1898i) q^{51} +(0.334053 + 0.578596i) q^{52} +9.73950 q^{53} +(-3.12056 - 4.15477i) q^{54} +2.24112 q^{55} +(0.500000 + 0.866025i) q^{56} +(2.74328 - 5.22587i) q^{57} +(3.69195 - 6.39465i) q^{58} +(-3.94492 + 6.83281i) q^{59} +(-1.73065 + 0.0696054i) q^{60} +(3.44277 + 5.96304i) q^{61} +8.81521 q^{62} +(1.28651 - 2.71015i) q^{63} +1.00000 q^{64} +(-0.334053 - 0.578596i) q^{65} +(2.07439 + 3.28097i) q^{66} +(1.27682 - 2.21151i) q^{67} +(-3.32220 + 5.75423i) q^{68} +(-3.00000 - 4.74495i) q^{69} +(-0.500000 - 0.866025i) q^{70} +10.3125 q^{71} +(-1.70380 - 2.46922i) q^{72} -2.33621 q^{73} +(-1.53786 - 2.66364i) q^{74} +(1.73065 - 0.0696054i) q^{75} +(1.70380 - 2.95107i) q^{76} +(-1.12056 + 1.94087i) q^{77} +(0.537855 - 1.02460i) q^{78} +(-3.95461 - 6.84959i) q^{79} -1.00000 q^{80} +(-3.19411 + 8.41413i) q^{81} -0.331895 q^{82} +(-3.62272 - 6.27473i) q^{83} +(0.805046 - 1.53359i) q^{84} +(3.32220 - 5.75423i) q^{85} +(1.45461 - 2.51946i) q^{86} +(-12.7790 + 0.513960i) q^{87} +(1.12056 + 1.94087i) q^{88} -7.96124 q^{89} +(1.70380 + 2.46922i) q^{90} +0.668105 q^{91} +(-1.62056 - 2.80689i) q^{92} +(-8.15941 - 12.9053i) q^{93} +(3.69411 - 6.39839i) q^{94} +(-1.70380 + 2.95107i) q^{95} +(-0.925606 - 1.46399i) q^{96} +(-8.05364 - 13.9493i) q^{97} +1.00000 q^{98} +(2.88322 - 6.07377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9} - 8 q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25} - 6 q^{26} + 18 q^{27} - 8 q^{28} - 12 q^{29} + 3 q^{30} - 2 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 8 q^{35} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 4 q^{40} + q^{41} - 3 q^{42} + 5 q^{43} - 4 q^{44} + 12 q^{46} - 11 q^{47} - 4 q^{49} - 4 q^{50} - 21 q^{51} + 3 q^{52} + 44 q^{53} - 18 q^{54} + 4 q^{55} + 4 q^{56} + 9 q^{57} - 12 q^{58} - q^{59} - 4 q^{61} + 4 q^{62} + 3 q^{63} + 8 q^{64} - 3 q^{65} + 27 q^{66} - 21 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 34 q^{71} + 3 q^{72} - 20 q^{73} + 4 q^{74} - 3 q^{76} - 2 q^{77} - 12 q^{78} - 25 q^{79} - 8 q^{80} + 15 q^{81} - 2 q^{82} - 23 q^{83} + 3 q^{84} + 2 q^{85} + 5 q^{86} - 72 q^{87} + 2 q^{88} + 32 q^{89} - 3 q^{90} + 6 q^{91} - 6 q^{92} + 6 q^{93} - 11 q^{94} + 3 q^{95} + 3 q^{96} - 2 q^{97} + 8 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9 - 8 * q^10 + 2 * q^11 + 3 * q^12 + 3 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^22 - 6 * q^23 - 3 * q^24 - 4 * q^25 - 6 * q^26 + 18 * q^27 - 8 * q^28 - 12 * q^29 + 3 * q^30 - 2 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 8 * q^35 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 4 * q^40 + q^41 - 3 * q^42 + 5 * q^43 - 4 * q^44 + 12 * q^46 - 11 * q^47 - 4 * q^49 - 4 * q^50 - 21 * q^51 + 3 * q^52 + 44 * q^53 - 18 * q^54 + 4 * q^55 + 4 * q^56 + 9 * q^57 - 12 * q^58 - q^59 - 4 * q^61 + 4 * q^62 + 3 * q^63 + 8 * q^64 - 3 * q^65 + 27 * q^66 - 21 * q^67 - 2 * q^68 - 24 * q^69 - 4 * q^70 + 34 * q^71 + 3 * q^72 - 20 * q^73 + 4 * q^74 - 3 * q^76 - 2 * q^77 - 12 * q^78 - 25 * q^79 - 8 * q^80 + 15 * q^81 - 2 * q^82 - 23 * q^83 + 3 * q^84 + 2 * q^85 + 5 * q^86 - 72 * q^87 + 2 * q^88 + 32 * q^89 - 3 * q^90 + 6 * q^91 - 6 * q^92 + 6 * q^93 - 11 * q^94 + 3 * q^95 + 3 * q^96 - 2 * q^97 + 8 * q^98 + 51 * q^99

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