LMFDB - Embedded newform 630.2.i.g.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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, 2]))

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

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

chi := DirichletCharacter("630.121");

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.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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
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			121.4
Root			$-1.67391 - 0.444996i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.g.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.451577 - 1.67215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.451577 - 1.67215i) q^{6} +(1.85185 - 1.88962i) q^{7} +1.00000 q^{8} +(-2.59216 - 1.51021i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.451577 - 1.67215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.451577 - 1.67215i) q^{6} +(1.85185 - 1.88962i) q^{7} +1.00000 q^{8} +(-2.59216 - 1.51021i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.39342 + 2.41348i) q^{11} +(0.451577 - 1.67215i) q^{12} +(0.900271 - 1.55932i) q^{13} +(1.85185 - 1.88962i) q^{14} +(-1.67391 + 0.444996i) q^{15} +1.00000 q^{16} +(-0.292288 - 0.506258i) q^{17} +(-2.59216 - 1.51021i) q^{18} +(2.54440 - 4.40702i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.32347 - 3.94987i) q^{21} +(-1.39342 + 2.41348i) q^{22} +(1.60798 + 2.78511i) q^{23} +(0.451577 - 1.67215i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.900271 - 1.55932i) q^{26} +(-3.69585 + 3.65249i) q^{27} +(1.85185 - 1.88962i) q^{28} +(0.226360 + 0.392067i) q^{29} +(-1.67391 + 0.444996i) q^{30} -7.90880 q^{31} +1.00000 q^{32} +(3.40646 + 3.41988i) q^{33} +(-0.292288 - 0.506258i) q^{34} +(-2.56238 - 0.658939i) q^{35} +(-2.59216 - 1.51021i) q^{36} +(1.10468 - 1.91336i) q^{37} +(2.54440 - 4.40702i) q^{38} +(-2.20086 - 2.20954i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.43287 + 4.21385i) q^{41} +(-2.32347 - 3.94987i) q^{42} +(2.41093 + 4.17585i) q^{43} +(-1.39342 + 2.41348i) q^{44} +(-0.0118004 + 2.99998i) q^{45} +(1.60798 + 2.78511i) q^{46} +10.7631 q^{47} +(0.451577 - 1.67215i) q^{48} +(-0.141315 - 6.99857i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.978530 + 0.260135i) q^{51} +(0.900271 - 1.55932i) q^{52} +(2.04440 + 3.54100i) q^{53} +(-3.69585 + 3.65249i) q^{54} +2.78685 q^{55} +(1.85185 - 1.88962i) q^{56} +(-6.22020 - 6.24472i) q^{57} +(0.226360 + 0.392067i) q^{58} +7.99759 q^{59} +(-1.67391 + 0.444996i) q^{60} +15.1555 q^{61} -7.90880 q^{62} +(-7.65400 + 2.10151i) q^{63} +1.00000 q^{64} -1.80054 q^{65} +(3.40646 + 3.41988i) q^{66} -13.9329 q^{67} +(-0.292288 - 0.506258i) q^{68} +(5.38324 - 1.43109i) q^{69} +(-2.56238 - 0.658939i) q^{70} -5.78685 q^{71} +(-2.59216 - 1.51021i) q^{72} +(3.03944 + 5.26447i) q^{73} +(1.10468 - 1.91336i) q^{74} +(1.22233 + 1.22715i) q^{75} +(2.54440 - 4.40702i) q^{76} +(1.98015 + 7.10244i) q^{77} +(-2.20086 - 2.20954i) q^{78} -0.652178 q^{79} +(-0.500000 - 0.866025i) q^{80} +(4.43854 + 7.82939i) q^{81} +(-2.43287 + 4.21385i) q^{82} +(1.43293 + 2.48191i) q^{83} +(-2.32347 - 3.94987i) q^{84} +(-0.292288 + 0.506258i) q^{85} +(2.41093 + 4.17585i) q^{86} +(0.757813 - 0.201459i) q^{87} +(-1.39342 + 2.41348i) q^{88} +(1.58384 - 2.74329i) q^{89} +(-0.0118004 + 2.99998i) q^{90} +(-1.27935 - 4.58878i) q^{91} +(1.60798 + 2.78511i) q^{92} +(-3.57143 + 13.2247i) q^{93} +10.7631 q^{94} -5.08879 q^{95} +(0.451577 - 1.67215i) q^{96} +(5.00019 + 8.66058i) q^{97} +(-0.141315 - 6.99857i) q^{98} +(7.25683 - 4.15176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.451577	−	1.67215i	0.260718	−	0.965415i
$3$	0.451577	−	1.67215i	0.260718	−	0.965415i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.451577	−	1.67215i	0.184356	−	0.682651i
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$8$	1.00000			0.353553
$9$	−2.59216	−	1.51021i	−0.864052	−	0.503403i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.39342	+	2.41348i	−0.420133	+	0.727691i	−0.995952	−	0.0898856i	$-0.971350\pi$
$11$	−1.39342	+	2.41348i	−0.420133	+	0.727691i	0.575819	+	0.817577i	$0.304683\pi$
$12$	0.451577	−	1.67215i	0.130359	−	0.482707i
$13$	0.900271	−	1.55932i	0.249690	−	0.432476i	−0.713750	−	0.700401i	$-0.753005\pi$
$13$	0.900271	−	1.55932i	0.249690	−	0.432476i	0.963440	+	0.267925i	$0.0863379\pi$
$14$	1.85185	−	1.88962i	0.494927	−	0.505022i
$15$	−1.67391	+	0.444996i	−0.432202	+	0.114898i
$16$	1.00000			0.250000
$17$	−0.292288	−	0.506258i	−0.0708904	−	0.122786i	0.828401	−	0.560135i	$-0.189251\pi$
$17$	−0.292288	−	0.506258i	−0.0708904	−	0.122786i	−0.899292	+	0.437349i	$0.855917\pi$
$18$	−2.59216	−	1.51021i	−0.610977	−	0.355959i
$19$	2.54440	−	4.40702i	0.583725	−	1.01104i	−0.411309	−	0.911496i	$-0.634928\pi$
$19$	2.54440	−	4.40702i	0.583725	−	1.01104i	0.995033	−	0.0995444i	$-0.0317385\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−2.32347	−	3.94987i	−0.507022	−	0.861933i
$22$	−1.39342	+	2.41348i	−0.297079	+	0.514556i
$23$	1.60798	+	2.78511i	0.335288	+	0.580735i	0.983540	−	0.180690i	$-0.0578332\pi$
$23$	1.60798	+	2.78511i	0.335288	+	0.580735i	−0.648252	+	0.761425i	$0.724500\pi$
$24$	0.451577	−	1.67215i	0.0921778	−	0.341326i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.900271	−	1.55932i	0.176558	−	0.305807i
$27$	−3.69585	+	3.65249i	−0.711267	+	0.702922i
$28$	1.85185	−	1.88962i	0.349966	−	0.357104i
$29$	0.226360	+	0.392067i	0.0420340	+	0.0728050i	0.886277	−	0.463156i	$-0.153283\pi$
$29$	0.226360	+	0.392067i	0.0420340	+	0.0728050i	−0.844243	+	0.535961i	$0.819950\pi$
$30$	−1.67391	+	0.444996i	−0.305613	+	0.0812449i
$31$	−7.90880			−1.42046			−0.710231	−	0.703969i	$-0.751410\pi$
$31$	−7.90880			−1.42046			−0.710231	+	0.703969i	$0.751410\pi$
$32$	1.00000			0.176777
$33$	3.40646	+	3.41988i	0.592988	+	0.595325i
$34$	−0.292288	−	0.506258i	−0.0501271	−	0.0868226i
$35$	−2.56238	−	0.658939i	−0.433122	−	0.111381i
$36$	−2.59216	−	1.51021i	−0.432026	−	0.251701i
$37$	1.10468	−	1.91336i	0.181608	−	0.314555i	−0.760820	−	0.648963i	$-0.775203\pi$
$37$	1.10468	−	1.91336i	0.181608	−	0.314555i	0.942428	+	0.334408i	$0.108536\pi$
$38$	2.54440	−	4.40702i	0.412756	−	0.714914i
$39$	−2.20086	−	2.20954i	−0.352420	−	0.353809i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−2.43287	+	4.21385i	−0.379950	+	0.658093i	−0.991055	−	0.133457i	$-0.957392\pi$
$41$	−2.43287	+	4.21385i	−0.379950	+	0.658093i	0.611105	+	0.791550i	$0.290725\pi$
$42$	−2.32347	−	3.94987i	−0.358519	−	0.609479i
$43$	2.41093	+	4.17585i	0.367663	+	0.636811i	0.989200	−	0.146574i	$-0.0468246\pi$
$43$	2.41093	+	4.17585i	0.367663	+	0.636811i	−0.621537	+	0.783385i	$0.713491\pi$
$44$	−1.39342	+	2.41348i	−0.210066	+	0.363846i
$45$	−0.0118004	+	2.99998i	−0.00175911	+	0.447210i
$46$	1.60798	+	2.78511i	0.237084	+	0.410642i
$47$	10.7631			1.56996			0.784981	−	0.619519i	$-0.212672\pi$
$47$	10.7631			1.56996			0.784981	+	0.619519i	$0.212672\pi$
$48$	0.451577	−	1.67215i	0.0651796	−	0.241354i
$49$	−0.141315	−	6.99857i	−0.0201879	−	0.999796i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−0.978530	+	0.260135i	−0.137022	+	0.0364261i
$52$	0.900271	−	1.55932i	0.124845	−	0.216238i
$53$	2.04440	+	3.54100i	0.280819	+	0.486394i	0.971587	−	0.236684i	$-0.0760605\pi$
$53$	2.04440	+	3.54100i	0.280819	+	0.486394i	−0.690767	+	0.723077i	$0.742727\pi$
$54$	−3.69585	+	3.65249i	−0.502941	+	0.497041i
$55$	2.78685			0.375778
$56$	1.85185	−	1.88962i	0.247464	−	0.252511i
$57$	−6.22020	−	6.24472i	−0.823886	−	0.827133i
$58$	0.226360	+	0.392067i	0.0297225	+	0.0514809i
$59$	7.99759			1.04120			0.520599	−	0.853801i	$-0.325709\pi$
$59$	7.99759			1.04120			0.520599	+	0.853801i	$0.325709\pi$
$60$	−1.67391	+	0.444996i	−0.216101	+	0.0574488i
$61$	15.1555			1.94046			0.970230	−	0.242187i	$-0.0778648\pi$
$61$	15.1555			1.94046			0.970230	+	0.242187i	$0.0778648\pi$
$62$	−7.90880			−1.00442
$63$	−7.65400	+	2.10151i	−0.964313	+	0.264765i
$64$	1.00000			0.125000
$65$	−1.80054			−0.223330
$66$	3.40646	+	3.41988i	0.419306	+	0.420958i
$67$	−13.9329			−1.70218			−0.851089	−	0.525022i	$-0.824057\pi$
$67$	−13.9329			−1.70218			−0.851089	+	0.525022i	$0.824057\pi$
$68$	−0.292288	−	0.506258i	−0.0354452	−	0.0613929i
$69$	5.38324	−	1.43109i	0.648066	−	0.172283i
$70$	−2.56238	−	0.658939i	−0.306263	−	0.0787582i
$71$	−5.78685			−0.686772			−0.343386	−	0.939194i	$-0.611574\pi$
$71$	−5.78685			−0.686772			−0.343386	+	0.939194i	$0.611574\pi$
$72$	−2.59216	−	1.51021i	−0.305489	−	0.177980i
$73$	3.03944	+	5.26447i	0.355740	+	0.616160i	0.987244	−	0.159213i	$-0.0508955\pi$
$73$	3.03944	+	5.26447i	0.355740	+	0.616160i	−0.631504	+	0.775372i	$0.717562\pi$
$74$	1.10468	−	1.91336i	0.128417	−	0.222424i
$75$	1.22233	+	1.22715i	0.141143	+	0.141699i
$76$	2.54440	−	4.40702i	0.291862	−	0.505520i
$77$	1.98015	+	7.10244i	0.225659	+	0.809398i
$78$	−2.20086	−	2.20954i	−0.249199	−	0.250181i
$79$	−0.652178			−0.0733757			−0.0366879	−	0.999327i	$-0.511681\pi$
$79$	−0.652178			−0.0733757			−0.0366879	+	0.999327i	$0.511681\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	4.43854	+	7.82939i	0.493172	+	0.869932i
$82$	−2.43287	+	4.21385i	−0.268665	+	0.465342i
$83$	1.43293	+	2.48191i	0.157284	+	0.272425i	0.933888	−	0.357564i	$-0.116393\pi$
$83$	1.43293	+	2.48191i	0.157284	+	0.272425i	−0.776604	+	0.629989i	$0.783059\pi$
$84$	−2.32347	−	3.94987i	−0.253511	−	0.430966i
$85$	−0.292288	+	0.506258i	−0.0317031	+	0.0549114i
$86$	2.41093	+	4.17585i	0.259977	+	0.450294i
$87$	0.757813	−	0.201459i	0.0812461	−	0.0215987i
$88$	−1.39342	+	2.41348i	−0.148539	+	0.257278i
$89$	1.58384	−	2.74329i	0.167887	−	0.290788i	−0.769790	−	0.638297i	$-0.779639\pi$
$89$	1.58384	−	2.74329i	0.167887	−	0.290788i	0.937677	+	0.347509i	$0.112972\pi$
$90$	−0.0118004	+	2.99998i	−0.00124388	+	0.316225i
$91$	−1.27935	−	4.58878i	−0.134112	−	0.481035i
$92$	1.60798	+	2.78511i	0.167644	+	0.290368i
$93$	−3.57143	+	13.2247i	−0.370340	+	1.37134i
$94$	10.7631			1.11013
$95$	−5.08879			−0.522099
$96$	0.451577	−	1.67215i	0.0460889	−	0.170663i
$97$	5.00019	+	8.66058i	0.507692	+	0.879349i	0.999960	+	0.00890523i	$0.00283466\pi$
$97$	5.00019	+	8.66058i	0.507692	+	0.879349i	−0.492268	+	0.870444i	$0.663832\pi$
$98$	−0.141315	−	6.99857i	−0.0142750	−	0.706963i
$99$	7.25683	−	4.15176i	0.729338	−	0.417267i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−8.09492	+	14.0208i	−0.805474	+	1.39512i	0.110496	+	0.993877i	$0.464756\pi$
$101$	−8.09492	+	14.0208i	−0.805474	+	1.39512i	−0.915970	+	0.401246i	$0.868577\pi$
$102$	−0.978530	+	0.260135i	−0.0968889	+	0.0257572i
$103$	−2.70080	−	4.67793i	−0.266118	−	0.460930i	0.701738	−	0.712435i	$-0.252408\pi$
$103$	−2.70080	−	4.67793i	−0.266118	−	0.460930i	−0.967856	+	0.251505i	$0.919074\pi$
$104$	0.900271	−	1.55932i	0.0882788	−	0.152903i
$105$	−2.25896	+	3.98712i	−0.220452	+	0.389103i
$106$	2.04440	+	3.54100i	0.198569	+	0.343932i
$107$	−4.42199	+	7.65912i	−0.427490	+	0.740435i	−0.996649	−	0.0817927i	$-0.973935\pi$
$107$	−4.42199	+	7.65912i	−0.427490	+	0.740435i	0.569159	+	0.822227i	$0.307269\pi$
$108$	−3.69585	+	3.65249i	−0.355633	+	0.351461i
$109$	3.15594	+	5.46624i	0.302284	+	0.523571i	0.976653	−	0.214823i	$-0.0689176\pi$
$109$	3.15594	+	5.46624i	0.302284	+	0.523571i	−0.674369	+	0.738395i	$0.735584\pi$
$110$	2.78685			0.265715
$111$	−2.70058	−	2.71122i	−0.256328	−	0.257338i
$112$	1.85185	−	1.88962i	0.174983	−	0.178552i
$113$	7.44112	−	12.8884i	0.700002	−	1.21244i	−0.268463	−	0.963290i	$-0.586516\pi$
$113$	7.44112	−	12.8884i	0.700002	−	1.21244i	0.968465	−	0.249149i	$-0.0801508\pi$
$114$	−6.22020	−	6.24472i	−0.582575	−	0.584871i
$115$	1.60798	−	2.78511i	0.149945	−	0.259713i
$116$	0.226360	+	0.392067i	0.0210170	+	0.0364025i
$117$	−4.68853	+	2.68239i	−0.433455	+	0.247987i
$118$	7.99759			0.736238
$119$	−1.49791	−	0.385200i	−0.137313	−	0.0353113i
$120$	−1.67391	+	0.444996i	−0.152806	+	0.0406224i
$121$	1.61674	+	2.80028i	0.146977	+	0.254571i
$122$	15.1555			1.37211
$123$	5.94755	+	5.97099i	0.536273	+	0.538386i
$124$	−7.90880			−0.710231
$125$	1.00000			0.0894427
$126$	−7.65400	+	2.10151i	−0.681872	+	0.187217i
$127$	10.2360			0.908294			0.454147	−	0.890927i	$-0.349944\pi$
$127$	10.2360			0.908294			0.454147	+	0.890927i	$0.349944\pi$
$128$	1.00000			0.0883883
$129$	8.07136	−	2.14571i	0.710644	−	0.188919i
$130$	−1.80054			−0.157918
$131$	−2.24198	−	3.88323i	−0.195883	−	0.339279i	0.751307	−	0.659953i	$-0.229424\pi$
$131$	−2.24198	−	3.88323i	−0.195883	−	0.339279i	−0.947190	+	0.320674i	$0.896091\pi$
$132$	3.40646	+	3.41988i	0.296494	+	0.297662i
$133$	−3.61576	−	12.9691i	−0.313526	−	1.12456i
$134$	−13.9329			−1.20362
$135$	5.01108	+	1.37445i	0.431285	+	0.118294i
$136$	−0.292288	−	0.506258i	−0.0250635	−	0.0434113i
$137$	−9.26338	+	16.0447i	−0.791424	+	1.37079i	0.133661	+	0.991027i	$0.457327\pi$
$137$	−9.26338	+	16.0447i	−0.791424	+	1.37079i	−0.925085	+	0.379760i	$0.876007\pi$
$138$	5.38324	−	1.43109i	0.458252	−	0.121823i
$139$	8.90825	−	15.4295i	0.755588	−	1.30872i	−0.189494	−	0.981882i	$-0.560685\pi$
$139$	8.90825	−	15.4295i	0.755588	−	1.30872i	0.945082	−	0.326834i	$-0.105982\pi$
$140$	−2.56238	−	0.658939i	−0.216561	−	0.0556905i
$141$	4.86038	−	17.9975i	0.409318	−	1.51567i
$142$	−5.78685			−0.485621
$143$	2.50892	+	4.34557i	0.209806	+	0.363395i
$144$	−2.59216	−	1.51021i	−0.216013	−	0.125851i
$145$	0.226360	−	0.392067i	0.0187982	−	0.0325594i
$146$	3.03944	+	5.26447i	0.251546	+	0.435691i
$147$	−11.7665	−	2.92410i	−0.970482	−	0.241175i
$148$	1.10468	−	1.91336i	0.0908042	−	0.157278i
$149$	5.35400	+	9.27339i	0.438616	+	0.759706i	0.997583	−	0.0694843i	$-0.0221354\pi$
$149$	5.35400	+	9.27339i	0.438616	+	0.759706i	−0.558967	+	0.829190i	$0.688802\pi$
$150$	1.22233	+	1.22715i	0.0998031	+	0.100196i
$151$	3.20293	−	5.54764i	0.260651	−	0.451461i	−0.705764	−	0.708447i	$-0.749396\pi$
$151$	3.20293	−	5.54764i	0.260651	−	0.451461i	0.966415	+	0.256986i	$0.0827295\pi$
$152$	2.54440	−	4.40702i	0.206378	−	0.357457i
$153$	−0.00689826	+	1.75372i	−0.000557691	+	0.141780i
$154$	1.98015	+	7.10244i	0.159565	+	0.572331i
$155$	3.95440	+	6.84922i	0.317625	+	0.550143i
$156$	−2.20086	−	2.20954i	−0.176210	−	0.176905i
$157$	−8.54730			−0.682149			−0.341075	−	0.940036i	$-0.610791\pi$
$157$	−8.54730			−0.682149			−0.341075	+	0.940036i	$0.610791\pi$
$158$	−0.652178			−0.0518845
$159$	6.84428	−	1.81950i	0.542786	−	0.144296i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	8.24053	+	2.11912i	0.649445	+	0.167010i
$162$	4.43854	+	7.82939i	0.348725	+	0.615135i
$163$	−2.89129	+	5.00787i	−0.226463	+	0.392246i	−0.956758	−	0.290887i	$-0.906050\pi$
$163$	−2.89129	+	5.00787i	−0.226463	+	0.392246i	0.730294	+	0.683133i	$0.239383\pi$
$164$	−2.43287	+	4.21385i	−0.189975	+	0.329046i
$165$	1.25848	−	4.66002i	0.0979723	−	0.362782i
$166$	1.43293	+	2.48191i	0.111217	+	0.192633i
$167$	−9.13796	+	15.8274i	−0.707116	+	1.22476i	0.258806	+	0.965929i	$0.416671\pi$
$167$	−9.13796	+	15.8274i	−0.707116	+	1.22476i	−0.965922	+	0.258832i	$0.916662\pi$
$168$	−2.32347	−	3.94987i	−0.179259	−	0.304739i
$169$	4.87902	+	8.45072i	0.375310	+	0.650055i
$170$	−0.292288	+	0.506258i	−0.0224175	+	0.0388283i
$171$	−13.2510	+	7.58113i	−1.01333	+	0.579743i
$172$	2.41093	+	4.17585i	0.183832	+	0.318406i
$173$	7.94364			0.603944			0.301972	−	0.953317i	$-0.402355\pi$
$173$	7.94364			0.603944			0.301972	+	0.953317i	$0.402355\pi$
$174$	0.757813	−	0.201459i	0.0574497	−	0.0152726i
$175$	0.710533	+	2.54856i	0.0537113	+	0.192653i
$176$	−1.39342	+	2.41348i	−0.105033	+	0.181923i
$177$	3.61153	−	13.3732i	0.271459	−	1.00519i
$178$	1.58384	−	2.74329i	0.118714	−	0.205618i
$179$	−1.31236	−	2.27307i	−0.0980903	−	0.169897i	0.812804	−	0.582537i	$-0.197940\pi$
$179$	−1.31236	−	2.27307i	−0.0980903	−	0.169897i	−0.910894	+	0.412640i	$0.864607\pi$
$180$	−0.0118004	+	2.99998i	−0.000879553	+	0.223605i
$181$	−6.70153			−0.498121			−0.249061	−	0.968488i	$-0.580122\pi$
$181$	−6.70153			−0.498121			−0.249061	+	0.968488i	$0.580122\pi$
$182$	−1.27935	−	4.58878i	−0.0948314	−	0.340143i
$183$	6.84387	−	25.3422i	0.505913	−	1.87335i
$184$	1.60798	+	2.78511i	0.118542	+	0.205321i
$185$	−2.20936			−0.162436
$186$	−3.57143	+	13.2247i	−0.261870	+	0.969680i
$187$	1.62913			0.119133
$188$	10.7631			0.784981
$189$	0.0576631	+	13.7476i	0.00419437	+	0.999991i
$190$	−5.08879			−0.369180
$191$	−23.8590			−1.72638			−0.863189	−	0.504881i	$-0.831536\pi$
$191$	−23.8590			−1.72638			−0.863189	+	0.504881i	$0.831536\pi$
$192$	0.451577	−	1.67215i	0.0325898	−	0.120677i
$193$	−18.3945			−1.32407			−0.662034	−	0.749474i	$-0.730307\pi$
$193$	−18.3945			−1.32407			−0.662034	+	0.749474i	$0.730307\pi$
$194$	5.00019	+	8.66058i	0.358993	+	0.621794i
$195$	−0.813084	+	3.01077i	−0.0582262	+	0.215606i
$196$	−0.141315	−	6.99857i	−0.0100939	−	0.499898i
$197$	−22.1862			−1.58070			−0.790351	−	0.612654i	$-0.790102\pi$
$197$	−22.1862			−1.58070			−0.790351	+	0.612654i	$0.790102\pi$
$198$	7.25683	−	4.15176i	0.515720	−	0.295052i
$199$	−8.85412	−	15.3358i	−0.627652	−	1.08713i	−0.988022	−	0.154316i	$-0.950683\pi$
$199$	−8.85412	−	15.3358i	−0.627652	−	1.08713i	0.360369	−	0.932810i	$-0.382651\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−6.29179	+	23.2979i	−0.443789	+	1.64331i
$202$	−8.09492	+	14.0208i	−0.569556	+	0.986500i
$203$	1.16004	+	0.298315i	0.0814190	+	0.0209376i
$204$	−0.978530	+	0.260135i	−0.0685108	+	0.0182131i
$205$	4.86573			0.339838
$206$	−2.70080	−	4.67793i	−0.188174	−	0.325927i
$207$	0.0379498	−	9.64782i	0.00263769	−	0.670570i
$208$	0.900271	−	1.55932i	0.0624226	−	0.108119i
$209$	7.09084	+	12.2817i	0.490484	+	0.849543i
$210$	−2.25896	+	3.98712i	−0.155883	+	0.275137i
$211$	5.62457	−	9.74204i	0.387211	−	0.670670i	−0.604862	−	0.796330i	$-0.706772\pi$
$211$	5.62457	−	9.74204i	0.387211	−	0.670670i	0.992073	+	0.125661i	$0.0401051\pi$
$212$	2.04440	+	3.54100i	0.140410	+	0.243197i
$213$	−2.61321	+	9.67646i	−0.179054	+	0.663020i
$214$	−4.42199	+	7.65912i	−0.302281	+	0.523566i
$215$	2.41093	−	4.17585i	0.164424	−	0.284791i
$216$	−3.69585	+	3.65249i	−0.251471	+	0.248521i
$217$	−14.6459	+	14.9446i	−0.994228	+	1.01451i
$218$	3.15594	+	5.46624i	0.213747	+	0.370221i
$219$	10.1755	−	2.70508i	0.687598	−	0.182793i
$220$	2.78685			0.187889
$221$	−1.05256			−0.0708025
$222$	−2.70058	−	2.71122i	−0.181251	−	0.181965i
$223$	−10.4941	−	18.1763i	−0.702737	−	1.21718i	−0.967502	−	0.252863i	$-0.918628\pi$
$223$	−10.4941	−	18.1763i	−0.702737	−	1.21718i	0.264766	−	0.964313i	$-0.414705\pi$
$224$	1.85185	−	1.88962i	0.123732	−	0.126255i
$225$	2.60396	−	1.48977i	0.173597	−	0.0993179i
$226$	7.44112	−	12.8884i	0.494976	−	0.857324i
$227$	8.03831	−	13.9228i	0.533522	−	0.924086i	−0.465712	−	0.884936i	$-0.654202\pi$
$227$	8.03831	−	13.9228i	0.533522	−	0.924086i	0.999233	−	0.0391500i	$-0.0124650\pi$
$228$	−6.22020	−	6.24472i	−0.411943	−	0.413567i
$229$	6.82422	+	11.8199i	0.450957	+	0.781081i	0.998446	−	0.0557324i	$-0.0177494\pi$
$229$	6.82422	+	11.8199i	0.450957	+	0.781081i	−0.547489	+	0.836813i	$0.684416\pi$
$230$	1.60798	−	2.78511i	0.106027	−	0.183645i
$231$	12.7705	−	0.103799i	0.840238	−	0.00682950i
$232$	0.226360	+	0.392067i	0.0148613	+	0.0257405i
$233$	−2.31738	+	4.01383i	−0.151817	+	0.262955i	−0.931895	−	0.362727i	$-0.881846\pi$
$233$	−2.31738	+	4.01383i	−0.151817	+	0.262955i	0.780079	+	0.625682i	$0.215179\pi$
$234$	−4.68853	+	2.68239i	−0.306499	+	0.175353i
$235$	−5.38156	−	9.32114i	−0.351054	−	0.608044i
$236$	7.99759			0.520599
$237$	−0.294509	+	1.09054i	−0.0191304	+	0.0708380i
$238$	−1.49791	−	0.385200i	−0.0970950	−	0.0249688i
$239$	12.1347	−	21.0179i	0.784928	−	1.35954i	−0.144114	−	0.989561i	$-0.546033\pi$
$239$	12.1347	−	21.0179i	0.784928	−	1.35954i	0.929042	−	0.369974i	$-0.120634\pi$
$240$	−1.67391	+	0.444996i	−0.108050	+	0.0287244i
$241$	14.3357	−	24.8302i	0.923446	−	1.59946i	0.129405	−	0.991592i	$-0.458693\pi$
$241$	14.3357	−	24.8302i	0.923446	−	1.59946i	0.794041	−	0.607864i	$-0.207974\pi$
$242$	1.61674	+	2.80028i	0.103928	+	0.180009i
$243$	15.0962	−	3.88633i	0.968424	−	0.249308i
$244$	15.1555			0.970230
$245$	−5.99028	+	3.62167i	−0.382705	+	0.231380i
$246$	5.94755	+	5.97099i	0.379202	+	0.380697i
$247$	−4.58129	−	7.93503i	−0.291501	−	0.504894i
$248$	−7.90880			−0.502209
$249$	4.79719	−	1.27530i	0.304010	−	0.0808186i
$250$	1.00000			0.0632456
$251$	−29.7152			−1.87561			−0.937805	−	0.347163i	$-0.887145\pi$
$251$	−29.7152			−1.87561			−0.937805	+	0.347163i	$0.887145\pi$
$252$	−7.65400	+	2.10151i	−0.482156	+	0.132383i
$253$	−8.96240			−0.563461
$254$	10.2360			0.642261
$255$	0.714548	+	0.717364i	0.0447467	+	0.0449231i
$256$	1.00000			0.0625000
$257$	−6.09269	−	10.5528i	−0.380051	−	0.658268i	0.611018	−	0.791617i	$-0.290760\pi$
$257$	−6.09269	−	10.5528i	−0.380051	−	0.658268i	−0.991069	+	0.133349i	$0.957427\pi$
$258$	8.07136	−	2.14571i	0.502501	−	0.133586i
$259$	−1.56983	−	5.63069i	−0.0975442	−	0.349874i
$260$	−1.80054			−0.111665
$261$	0.00534230	−	1.35815i	0.000330680	−	0.0840674i
$262$	−2.24198	−	3.88323i	−0.138510	−	0.239907i
$263$	−3.88707	+	6.73260i	−0.239687	+	0.415150i	−0.960624	−	0.277850i	$-0.910378\pi$
$263$	−3.88707	+	6.73260i	−0.239687	+	0.415150i	0.720937	+	0.693000i	$0.243712\pi$
$264$	3.40646	+	3.41988i	0.209653	+	0.210479i
$265$	2.04440	−	3.54100i	0.125586	−	0.217522i
$266$	−3.61576	−	12.9691i	−0.221696	−	0.795185i
$267$	−3.87196	−	3.88722i	−0.236960	−	0.237894i
$268$	−13.9329			−0.851089
$269$	0.415139	+	0.719041i	0.0253114	+	0.0438407i	0.878404	−	0.477919i	$-0.158609\pi$
$269$	0.415139	+	0.719041i	0.0253114	+	0.0438407i	−0.853092	+	0.521760i	$0.825276\pi$
$270$	5.01108	+	1.37445i	0.304964	+	0.0836466i
$271$	−1.24892	+	2.16319i	−0.0758664	+	0.131405i	−0.901463	−	0.432857i	$-0.857506\pi$
$271$	−1.24892	+	2.16319i	−0.0758664	+	0.131405i	0.825596	+	0.564261i	$0.190839\pi$
$272$	−0.292288	−	0.506258i	−0.0177226	−	0.0306964i
$273$	−8.25085	+	0.0670633i	−0.499364	+	0.00405886i
$274$	−9.26338	+	16.0447i	−0.559622	+	0.969293i
$275$	−1.39342	−	2.41348i	−0.0840266	−	0.145538i
$276$	5.38324	−	1.43109i	0.324033	−	0.0861417i
$277$	−9.47491	+	16.4110i	−0.569292	+	0.986043i	0.427344	+	0.904089i	$0.359449\pi$
$277$	−9.47491	+	16.4110i	−0.569292	+	0.986043i	−0.996636	+	0.0819535i	$0.973884\pi$
$278$	8.90825	−	15.4295i	0.534281	−	0.925402i
$279$	20.5008	+	11.9439i	1.22735	+	0.715064i
$280$	−2.56238	−	0.658939i	−0.153132	−	0.0393791i
$281$	−9.87626	−	17.1062i	−0.589168	−	1.02047i	−0.994342	−	0.106229i	$-0.966122\pi$
$281$	−9.87626	−	17.1062i	−0.589168	−	1.02047i	0.405174	−	0.914240i	$-0.367211\pi$
$282$	4.86038	−	17.9975i	0.289431	−	1.07174i
$283$	6.28414			0.373553			0.186777	−	0.982402i	$-0.440196\pi$
$283$	6.28414			0.373553			0.186777	+	0.982402i	$0.440196\pi$
$284$	−5.78685			−0.343386
$285$	−2.29798	+	8.50921i	−0.136121	+	0.504042i
$286$	2.50892	+	4.34557i	0.148355	+	0.256959i
$287$	3.45727	+	12.4006i	0.204076	+	0.731984i
$288$	−2.59216	−	1.51021i	−0.152744	−	0.0889899i
$289$	8.32913	−	14.4265i	0.489949	−	0.848617i
$290$	0.226360	−	0.392067i	0.0132923	−	0.0230230i
$291$	16.7397	−	4.45013i	0.981301	−	0.260871i
$292$	3.03944	+	5.26447i	0.177870	+	0.308080i
$293$	1.91839	−	3.32275i	0.112073	−	0.194117i	−0.804533	−	0.593908i	$-0.797584\pi$
$293$	1.91839	−	3.32275i	0.112073	−	0.194117i	0.916606	+	0.399792i	$0.130917\pi$
$294$	−11.7665	−	2.92410i	−0.686234	−	0.170537i
$295$	−3.99880	−	6.92612i	−0.232819	−	0.403254i
$296$	1.10468	−	1.91336i	0.0642083	−	0.111212i
$297$	−3.66533	−	14.0093i	−0.212684	−	0.812903i
$298$	5.35400	+	9.27339i	0.310149	+	0.537193i
$299$	5.79048			0.334872
$300$	1.22233	+	1.22715i	0.0705715	+	0.0708496i
$301$	12.3554	+	3.17731i	0.712156	+	0.183137i
$302$	3.20293	−	5.54764i	0.184308	−	0.319231i
$303$	19.7894	+	19.8674i	1.13687	+	1.14135i
$304$	2.54440	−	4.40702i	0.145931	−	0.252760i
$305$	−7.57773	−	13.1250i	−0.433900	−	0.751537i
$306$	−0.00689826	+	1.75372i	−0.000394347	+	0.100253i
$307$	−3.47207			−0.198162			−0.0990808	−	0.995079i	$-0.531590\pi$
$307$	−3.47207			−0.198162			−0.0990808	+	0.995079i	$0.531590\pi$
$308$	1.98015	+	7.10244i	0.112829	+	0.404699i
$309$	−9.04180	+	2.40369i	−0.514370	+	0.136741i
$310$	3.95440	+	6.84922i	0.224595	+	0.389010i
$311$	−16.0291			−0.908924			−0.454462	−	0.890766i	$-0.650169\pi$
$311$	−16.0291			−0.908924			−0.454462	+	0.890766i	$0.650169\pi$
$312$	−2.20086	−	2.20954i	−0.124599	−	0.125090i
$313$	−29.5659			−1.67117			−0.835583	−	0.549364i	$-0.814870\pi$
$313$	−29.5659			−1.67117			−0.835583	+	0.549364i	$0.814870\pi$
$314$	−8.54730			−0.482352
$315$	5.64696	+	5.57780i	0.318170	+	0.314273i
$316$	−0.652178			−0.0366879
$317$	5.36618			0.301395			0.150697	−	0.988580i	$-0.451848\pi$
$317$	5.36618			0.301395			0.150697	+	0.988580i	$0.451848\pi$
$318$	6.84428	−	1.81950i	0.383808	−	0.102032i
$319$	−1.26166			−0.0706395
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	10.8103	+	10.8529i	0.603372	+	0.605750i
$322$	8.24053	+	2.11912i	0.459227	+	0.118094i
$323$	−2.97479			−0.165522
$324$	4.43854	+	7.82939i	0.246586	+	0.434966i
$325$	0.900271	+	1.55932i	0.0499381	+	0.0864952i
$326$	−2.89129	+	5.00787i	−0.160134	+	0.277360i
$327$	10.5655	−	2.80876i	0.584274	−	0.155325i
$328$	−2.43287	+	4.21385i	−0.134333	+	0.232671i
$329$	19.9317	−	20.3382i	1.09887	−	1.12128i
$330$	1.25848	−	4.66002i	0.0692768	−	0.256526i
$331$	31.9627			1.75683			0.878415	−	0.477899i	$-0.158601\pi$
$331$	31.9627			1.75683			0.878415	+	0.477899i	$0.158601\pi$
$332$	1.43293	+	2.48191i	0.0786422	+	0.136212i
$333$	−5.75308	+	3.29144i	−0.315267	+	0.180370i
$334$	−9.13796	+	15.8274i	−0.500007	+	0.866037i
$335$	6.96646	+	12.0663i	0.380618	+	0.659251i
$336$	−2.32347	−	3.94987i	−0.126756	−	0.215483i
$337$	10.9734	−	19.0065i	0.597759	−	1.03535i	−0.395392	−	0.918513i	$-0.629391\pi$
$337$	10.9734	−	19.0065i	0.597759	−	1.03535i	0.993151	−	0.116837i	$-0.0372754\pi$
$338$	4.87902	+	8.45072i	0.265384	+	0.459658i
$339$	−18.1911	−	18.2628i	−0.988003	−	0.991897i
$340$	−0.292288	+	0.506258i	−0.0158516	+	0.0274557i
$341$	11.0203	−	19.0877i	0.596783	−	1.03366i
$342$	−13.2510	+	7.58113i	−0.716532	+	0.409940i
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$	2.41093	+	4.17585i	0.129989	+	0.225147i
$345$	−3.93098	−	3.94648i	−0.211637	−	0.212471i
$346$	7.94364			0.427053
$347$	17.0794			0.916871			0.458435	−	0.888728i	$-0.348410\pi$
$347$	17.0794			0.916871			0.458435	+	0.888728i	$0.348410\pi$
$348$	0.757813	−	0.201459i	0.0406231	−	0.0107993i
$349$	11.6655	+	20.2053i	0.624442	+	1.08157i	0.988648	+	0.150247i	$0.0480069\pi$
$349$	11.6655	+	20.2053i	0.624442	+	1.08157i	−0.364206	+	0.931318i	$0.618660\pi$
$350$	0.710533	+	2.54856i	0.0379796	+	0.136226i
$351$	2.36812	+	9.05123i	0.126401	+	0.483119i
$352$	−1.39342	+	2.41348i	−0.0742697	+	0.128639i
$353$	3.45541	−	5.98494i	0.183913	−	0.318546i	−0.759297	−	0.650744i	$-0.774457\pi$
$353$	3.45541	−	5.98494i	0.183913	−	0.318546i	0.943210	+	0.332198i	$0.107790\pi$
$354$	3.61153	−	13.3732i	0.191951	−	0.710775i
$355$	2.89342	+	5.01156i	0.153567	+	0.265986i
$356$	1.58384	−	2.74329i	0.0839434	−	0.145394i
$357$	−1.32053	+	2.33078i	−0.0698900	+	0.123358i
$358$	−1.31236	−	2.27307i	−0.0693603	−	0.120136i
$359$	0.648078	−	1.12250i	0.0342043	−	0.0592435i	−0.848417	−	0.529329i	$-0.822444\pi$
$359$	0.648078	−	1.12250i	0.0342043	−	0.0592435i	0.882621	+	0.470086i	$0.155777\pi$
$360$	−0.0118004	+	2.99998i	−0.000621938	+	0.158113i
$361$	−3.44791	−	5.97195i	−0.181469	−	0.314313i
$362$	−6.70153			−0.352225
$363$	5.41257	−	1.43889i	0.284086	−	0.0755222i
$364$	−1.27935	−	4.58878i	−0.0670559	−	0.240518i
$365$	3.03944	−	5.26447i	0.159092	−	0.275555i
$366$	6.84387	−	25.3422i	0.357735	−	1.32466i
$367$	−8.09878	+	14.0275i	−0.422753	+	0.732229i	−0.996208	−	0.0870080i	$-0.972269\pi$
$367$	−8.09878	+	14.0275i	−0.422753	+	0.732229i	0.573455	+	0.819237i	$0.305603\pi$
$368$	1.60798	+	2.78511i	0.0838219	+	0.145184i
$369$	12.6702	−	7.24882i	0.659582	−	0.377358i
$370$	−2.20936			−0.114859
$371$	10.4770	+	2.69426i	0.543941	+	0.139879i
$372$	−3.57143	+	13.2247i	−0.185170	+	0.685668i
$373$	15.2409	+	26.3980i	0.789142	+	1.36683i	0.926493	+	0.376312i	$0.122808\pi$
$373$	15.2409	+	26.3980i	0.789142	+	1.36683i	−0.137351	+	0.990522i	$0.543859\pi$
$374$	1.62913			0.0842401
$375$	0.451577	−	1.67215i	0.0233194	−	0.0863493i
$376$	10.7631			0.555066
$377$	0.815142			0.0419819
$378$	0.0576631	+	13.7476i	0.00296587	+	0.707101i
$379$	−19.7281			−1.01337			−0.506683	−	0.862132i	$-0.669129\pi$
$379$	−19.7281			−1.01337			−0.506683	+	0.862132i	$0.669129\pi$
$380$	−5.08879			−0.261050
$381$	4.62232	−	17.1160i	0.236809	−	0.876881i
$382$	−23.8590			−1.22073
$383$	−15.0364	−	26.0438i	−0.768325	−	1.33078i	−0.938470	−	0.345359i	$-0.887757\pi$
$383$	−15.0364	−	26.0438i	−0.768325	−	1.33078i	0.170145	−	0.985419i	$-0.445576\pi$
$384$	0.451577	−	1.67215i	0.0230445	−	0.0853314i
$385$	5.16082	−	5.26608i	0.263020	−	0.268384i
$386$	−18.3945			−0.936258
$387$	0.0569000	−	14.4655i	0.00289239	−	0.735321i
$388$	5.00019	+	8.66058i	0.253846	+	0.439674i
$389$	3.26051	−	5.64736i	0.165314	−	0.286333i	−0.771453	−	0.636287i	$-0.780470\pi$
$389$	3.26051	−	5.64736i	0.165314	−	0.286333i	0.936767	+	0.349954i	$0.113803\pi$
$390$	−0.813084	+	3.01077i	−0.0411721	+	0.152456i
$391$	0.939990	−	1.62811i	0.0475373	−	0.0823370i
$392$	−0.141315	−	6.99857i	−0.00713749	−	0.353481i
$393$	−7.50576	+	1.99535i	−0.378615	+	0.100652i
$394$	−22.1862			−1.11773
$395$	0.326089	+	0.564803i	0.0164073	+	0.0284183i
$396$	7.25683	−	4.15176i	0.364669	−	0.208634i
$397$	−11.4013	+	19.7477i	−0.572217	+	0.991108i	0.424121	+	0.905605i	$0.360583\pi$
$397$	−11.4013	+	19.7477i	−0.572217	+	0.991108i	−0.996338	+	0.0855029i	$0.972750\pi$
$398$	−8.85412	−	15.3358i	−0.443817	−	0.768714i
$399$	−23.3190	+	0.189538i	−1.16741	+	0.00948878i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−10.5979	−	18.3561i	−0.529234	−	0.916661i	−0.999419	−	0.0340926i	$-0.989146\pi$
$401$	−10.5979	−	18.3561i	−0.529234	−	0.916661i	0.470184	−	0.882568i	$-0.344187\pi$
$402$	−6.29179	+	23.2979i	−0.313806	+	1.16199i
$403$	−7.12006	+	12.3323i	−0.354676	+	0.614316i
$404$	−8.09492	+	14.0208i	−0.402737	+	0.697561i
$405$	4.56118	−	7.75859i	0.226647	−	0.385527i
$406$	1.16004	+	0.298315i	0.0575719	+	0.0148051i
$407$	3.07858	+	5.33225i	0.152599	+	0.264310i
$408$	−0.978530	+	0.260135i	−0.0484444	+	0.0128786i
$409$	−27.2707			−1.34845			−0.674224	−	0.738527i	$-0.735522\pi$
$409$	−27.2707			−1.34845			−0.674224	+	0.738527i	$0.735522\pi$
$410$	4.86573			0.240301
$411$	22.6459	+	22.7351i	1.11704	+	1.12144i
$412$	−2.70080	−	4.67793i	−0.133059	−	0.230465i
$413$	14.8103	−	15.1124i	0.728768	−	0.743632i
$414$	0.0379498	−	9.64782i	0.00186513	−	0.474165i
$415$	1.43293	−	2.48191i	0.0703397	−	0.121832i
$416$	0.900271	−	1.55932i	0.0441394	−	0.0764517i
$417$	−21.7777	−	21.8635i	−1.06646	−	1.07066i
$418$	7.09084	+	12.2817i	0.346824	+	0.600717i
$419$	12.7856	−	22.1452i	0.624615	−	1.08187i	−0.364000	−	0.931399i	$-0.618589\pi$
$419$	12.7856	−	22.1452i	0.624615	−	1.08187i	0.988615	−	0.150467i	$-0.0480776\pi$
$420$	−2.25896	+	3.98712i	−0.110226	+	0.194551i
$421$	9.08024	+	15.7274i	0.442544	+	0.766509i	0.997878	−	0.0651191i	$-0.0207427\pi$
$421$	9.08024	+	15.7274i	0.442544	+	0.766509i	−0.555334	+	0.831628i	$0.687409\pi$
$422$	5.62457	−	9.74204i	0.273800	−	0.474235i
$423$	−27.8997	−	16.2546i	−1.35653	−	0.790323i
$424$	2.04440	+	3.54100i	0.0992847	+	0.171966i
$425$	0.584577			0.0283561
$426$	−2.61321	+	9.67646i	−0.126610	+	0.468826i
$427$	28.0656	−	28.6381i	1.35819	−	1.38589i
$428$	−4.42199	+	7.65912i	−0.213745	+	0.370217i
$429$	8.39941	−	2.23292i	0.405527	−	0.107806i
$430$	2.41093	−	4.17585i	0.116265	−	0.201377i
$431$	−7.59234	−	13.1503i	−0.365710	−	0.633429i	0.623180	−	0.782079i	$-0.285841\pi$
$431$	−7.59234	−	13.1503i	−0.365710	−	0.633429i	−0.988890	+	0.148650i	$0.952507\pi$
$432$	−3.69585	+	3.65249i	−0.177817	+	0.175731i
$433$	1.12571			0.0540982			0.0270491	−	0.999634i	$-0.491389\pi$
$433$	1.12571			0.0540982			0.0270491	+	0.999634i	$0.491389\pi$
$434$	−14.6459	+	14.9446i	−0.703025	+	0.717364i
$435$	−0.553375	−	0.555556i	−0.0265323	−	0.0266369i
$436$	3.15594	+	5.46624i	0.151142	+	0.261786i
$437$	16.3654			0.782862
$438$	10.1755	−	2.70508i	0.486205	−	0.129254i
$439$	−31.8681			−1.52098			−0.760491	−	0.649348i	$-0.775042\pi$
$439$	−31.8681			−1.52098			−0.760491	+	0.649348i	$0.775042\pi$
$440$	2.78685			0.132858
$441$	−10.2030	+	18.3548i	−0.485857	+	0.874039i
$442$	−1.05256			−0.0500650
$443$	−18.5538			−0.881520			−0.440760	−	0.897625i	$-0.645291\pi$
$443$	−18.5538			−0.881520			−0.440760	+	0.897625i	$0.645291\pi$
$444$	−2.70058	−	2.71122i	−0.128164	−	0.128669i
$445$	−3.16768			−0.150162
$446$	−10.4941	−	18.1763i	−0.496910	−	0.860673i
$447$	17.9242	−	4.76502i	0.847787	−	0.225378i
$448$	1.85185	−	1.88962i	0.0874916	−	0.0892761i
$449$	−11.7410			−0.554094			−0.277047	−	0.960856i	$-0.589356\pi$
$449$	−11.7410			−0.554094			−0.277047	+	0.960856i	$0.589356\pi$
$450$	2.60396	−	1.48977i	0.122752	−	0.0702284i
$451$	−6.78003	−	11.7433i	−0.319259	−	0.552973i
$452$	7.44112	−	12.8884i	0.350001	−	0.606219i
$453$	−7.83010	−	7.86096i	−0.367890	−	0.369340i
$454$	8.03831	−	13.9228i	0.377257	−	0.653428i
$455$	−3.33433	+	3.40234i	−0.156316	+	0.159504i
$456$	−6.22020	−	6.24472i	−0.291288	−	0.292436i
$457$	5.59537			0.261741			0.130870	−	0.991400i	$-0.458223\pi$
$457$	5.59537			0.261741			0.130870	+	0.991400i	$0.458223\pi$
$458$	6.82422	+	11.8199i	0.318875	+	0.552308i
$459$	2.92936	+	0.803474i	0.136731	+	0.0375029i
$460$	1.60798	−	2.78511i	0.0749726	−	0.129856i
$461$	2.78195	+	4.81847i	0.129568	+	0.224419i	0.923509	−	0.383576i	$-0.125308\pi$
$461$	2.78195	+	4.81847i	0.129568	+	0.224419i	−0.793941	+	0.607995i	$0.791974\pi$
$462$	12.7705	−	0.103799i	0.594138	−	0.00482919i
$463$	−7.03397	+	12.1832i	−0.326896	+	0.566201i	−0.981894	−	0.189430i	$-0.939336\pi$
$463$	−7.03397	+	12.1832i	−0.326896	+	0.566201i	0.654998	+	0.755631i	$0.272669\pi$
$464$	0.226360	+	0.392067i	0.0105085	+	0.0182013i
$465$	13.2386	−	3.51939i	0.613927	−	0.163208i
$466$	−2.31738	+	4.01383i	−0.107351	+	0.185937i
$467$	4.64000	−	8.03672i	0.214714	−	0.371895i	−0.738470	−	0.674286i	$-0.764451\pi$
$467$	4.64000	−	8.03672i	0.214714	−	0.371895i	0.953184	+	0.302391i	$0.0977848\pi$
$468$	−4.68853	+	2.68239i	−0.216728	+	0.123994i
$469$	−25.8017	+	26.3279i	−1.19141	+	1.21571i
$470$	−5.38156	−	9.32114i	−0.248233	−	0.429952i
$471$	−3.85977	+	14.2924i	−0.177849	+	0.658557i
$472$	7.99759			0.368119
$473$	−13.4378			−0.617870
$474$	−0.294509	+	1.09054i	−0.0135272	+	0.0500901i
$475$	2.54440	+	4.40702i	0.116745	+	0.202208i
$476$	−1.49791	−	0.385200i	−0.0686566	−	0.0176556i
$477$	0.0482495	−	12.2663i	0.00220919	−	0.561635i
$478$	12.1347	−	21.0179i	0.555028	−	0.961337i
$479$	−4.74662	+	8.22138i	−0.216878	+	0.375644i	−0.953852	−	0.300277i	$-0.902921\pi$
$479$	−4.74662	+	8.22138i	−0.216878	+	0.375644i	0.736974	+	0.675922i	$0.236254\pi$
$480$	−1.67391	+	0.444996i	−0.0764032	+	0.0203112i
$481$	−1.98903	−	3.44509i	−0.0906917	−	0.157083i
$482$	14.3357	−	24.8302i	0.652975	−	1.13099i
$483$	7.26472	−	12.8224i	0.330556	−	0.583441i
$484$	1.61674	+	2.80028i	0.0734884	+	0.127286i
$485$	5.00019	−	8.66058i	0.227047	−	0.393257i
$486$	15.0962	−	3.88633i	0.684779	−	0.176287i
$487$	18.3576	+	31.7962i	0.831860	+	1.44082i	0.896561	+	0.442919i	$0.146057\pi$
$487$	18.3576	+	31.7962i	0.831860	+	1.44082i	−0.0647013	+	0.997905i	$0.520609\pi$
$488$	15.1555			0.686056
$489$	7.06825	+	7.09611i	0.319637	+	0.320897i
$490$	−5.99028	+	3.62167i	−0.270613	+	0.163610i
$491$	−0.627842	+	1.08745i	−0.0283341	+	0.0490761i	−0.879845	−	0.475261i	$-0.842354\pi$
$491$	−0.627842	+	1.08745i	−0.0283341	+	0.0490761i	0.851511	+	0.524337i	$0.175687\pi$
$492$	5.94755	+	5.97099i	0.268136	+	0.269193i
$493$	0.132325	−	0.229193i	0.00595961	−	0.0103224i
$494$	−4.58129	−	7.93503i	−0.206122	−	0.357014i
$495$	−7.22394	−	4.20872i	−0.324692	−	0.189168i
$496$	−7.90880			−0.355116
$497$	−10.7164	+	10.9349i	−0.480695	+	0.490499i
$498$	4.79719	−	1.27530i	0.214967	−	0.0571474i
$499$	−3.99415	−	6.91807i	−0.178803	−	0.309695i	0.762668	−	0.646790i	$-0.223889\pi$
$499$	−3.99415	−	6.91807i	−0.178803	−	0.309695i	−0.941471	+	0.337095i	$0.890556\pi$
$500$	1.00000			0.0447214
$501$	22.3393	+	22.4273i	0.998045	+	1.00198i
$502$	−29.7152			−1.32626
$503$	−43.8954			−1.95720			−0.978599	−	0.205775i	$-0.934029\pi$
$503$	−43.8954			−1.95720			−0.978599	+	0.205775i	$0.934029\pi$
$504$	−7.65400	+	2.10151i	−0.340936	+	0.0936087i
$505$	16.1898			0.720438
$506$	−8.96240			−0.398427
$507$	16.3341	−	4.34230i	0.725423	−	0.192848i
$508$	10.2360			0.454147
$509$	−6.75366	−	11.6977i	−0.299351	−	0.518491i	0.676637	−	0.736317i	$-0.263437\pi$
$509$	−6.75366	−	11.6977i	−0.299351	−	0.518491i	−0.975988	+	0.217826i	$0.930103\pi$
$510$	0.714548	+	0.717364i	0.0316407	+	0.0317654i
$511$	15.5764	+	4.00561i	0.689061	+	0.177198i
$512$	1.00000			0.0441942
$513$	6.69291	+	25.5811i	0.295499	+	1.12943i
$514$	−6.09269	−	10.5528i	−0.268737	−	0.465466i
$515$	−2.70080	+	4.67793i	−0.119012	+	0.206134i
$516$	8.07136	−	2.14571i	0.355322	−	0.0944596i
$517$	−14.9976	+	25.9766i	−0.659593	+	1.14245i
$518$	−1.56983	−	5.63069i	−0.0689742	−	0.247398i
$519$	3.58717	−	13.2829i	0.157459	−	0.583056i
$520$	−1.80054			−0.0789590
$521$	17.3609	+	30.0700i	0.760597	+	1.31739i	0.942543	+	0.334084i	$0.108427\pi$
$521$	17.3609	+	30.0700i	0.760597	+	1.31739i	−0.181947	+	0.983308i	$0.558240\pi$
$522$	0.00534230	−	1.35815i	0.000233826	−	0.0594446i
$523$	2.27883	−	3.94704i	0.0996461	−	0.172592i	−0.811892	−	0.583808i	$-0.801562\pi$
$523$	2.27883	−	3.94704i	0.0996461	−	0.172592i	0.911538	+	0.411215i	$0.134896\pi$
$524$	−2.24198	−	3.88323i	−0.0979414	−	0.169640i
$525$	4.58242	−	0.0372462i	0.199993	−	0.00162556i
$526$	−3.88707	+	6.73260i	−0.169484	+	0.293556i
$527$	2.31165	+	4.00390i	0.100697	+	0.174412i
$528$	3.40646	+	3.41988i	0.148247	+	0.148831i
$529$	6.32878	−	10.9618i	0.275165	−	0.476599i
$530$	2.04440	−	3.54100i	0.0888029	−	0.153811i
$531$	−20.7310	−	12.0780i	−0.899649	−	0.524142i
$532$	−3.61576	−	12.9691i	−0.156763	−	0.562281i
$533$	4.38048	+	7.58721i	0.189740	+	0.328639i
$534$	−3.87196	−	3.88722i	−0.167556	−	0.168217i
$535$	8.84399			0.382359
$536$	−13.9329			−0.601811
$537$	−4.39354	+	1.16799i	−0.189595	+	0.0504025i
$538$	0.415139	+	0.719041i	0.0178979	+	0.0310001i
$539$	17.0878	+	9.41091i	0.736025	+	0.405357i
$540$	5.01108	+	1.37445i	0.215642	+	0.0591471i
$541$	−13.8405	+	23.9724i	−0.595048	+	1.03065i	0.398492	+	0.917172i	$0.369534\pi$
$541$	−13.8405	+	23.9724i	−0.595048	+	1.03065i	−0.993540	+	0.113482i	$0.963800\pi$
$542$	−1.24892	+	2.16319i	−0.0536457	+	0.0929170i
$543$	−3.02626	+	11.2060i	−0.129869	+	0.480894i
$544$	−0.292288	−	0.506258i	−0.0125318	−	0.0217057i
$545$	3.15594	−	5.46624i	0.135186	−	0.234148i
$546$	−8.25085	+	0.0670633i	−0.353104	+	0.00287005i
$547$	17.4333	+	30.1953i	0.745393	+	1.29106i	0.950011	+	0.312217i	$0.101072\pi$
$547$	17.4333	+	30.1953i	0.745393	+	1.29106i	−0.204617	+	0.978842i	$0.565595\pi$
$548$	−9.26338	+	16.0447i	−0.395712	+	0.685394i
$549$	−39.2853	−	22.8879i	−1.67666	−	0.976832i
$550$	−1.39342	−	2.41348i	−0.0594158	−	0.102911i
$551$	2.30380			0.0981451
$552$	5.38324	−	1.43109i	0.229126	−	0.0609114i
$553$	−1.20773	+	1.23237i	−0.0513581	+	0.0524056i
$554$	−9.47491	+	16.4110i	−0.402550	+	0.697237i
$555$	−0.997698	+	3.69438i	−0.0423499	+	0.156818i
$556$	8.90825	−	15.4295i	0.377794	−	0.654358i
$557$	13.5004	+	23.3834i	0.572031	+	0.990787i	0.996357	+	0.0852772i	$0.0271776\pi$
$557$	13.5004	+	23.3834i	0.572031	+	0.990787i	−0.424326	+	0.905509i	$0.639489\pi$
$558$	20.5008	+	11.9439i	0.867870	+	0.505627i
$559$	8.68196			0.367208
$560$	−2.56238	−	0.658939i	−0.108280	−	0.0278452i
$561$	0.735676	−	2.72414i	0.0310603	−	0.115013i
$562$	−9.87626	−	17.1062i	−0.416605	−	0.721581i
$563$	36.7305			1.54801			0.774003	−	0.633182i	$-0.218251\pi$
$563$	36.7305			1.54801			0.774003	+	0.633182i	$0.218251\pi$
$564$	4.86038	−	17.9975i	0.204659	−	0.757833i
$565$	−14.8822			−0.626101
$566$	6.28414			0.264142
$567$	23.0141	+	6.11169i	0.966500	+	0.256667i
$568$	−5.78685			−0.242811
$569$	11.7830			0.493968			0.246984	−	0.969020i	$-0.420561\pi$
$569$	11.7830			0.493968			0.246984	+	0.969020i	$0.420561\pi$
$570$	−2.29798	+	8.50921i	−0.0962519	+	0.356412i
$571$	−7.23717			−0.302866			−0.151433	−	0.988468i	$-0.548389\pi$
$571$	−7.23717			−0.302866			−0.151433	+	0.988468i	$0.548389\pi$
$572$	2.50892	+	4.34557i	0.104903	+	0.181697i
$573$	−10.7742	+	39.8958i	−0.450098	+	1.66667i
$574$	3.45727	+	12.4006i	0.144304	+	0.517591i
$575$	−3.21597			−0.134115
$576$	−2.59216	−	1.51021i	−0.108006	−	0.0629253i
$577$	14.0488	+	24.3333i	0.584860	+	1.01301i	0.994893	+	0.100937i	$0.0321840\pi$
$577$	14.0488	+	24.3333i	0.584860	+	1.01301i	−0.410033	+	0.912071i	$0.634483\pi$
$578$	8.32913	−	14.4265i	0.346446	−	0.600063i
$579$	−8.30656	+	30.7584i	−0.345209	+	1.27828i
$580$	0.226360	−	0.392067i	0.00939909	−	0.0162797i
$581$	7.34342	+	1.88842i	0.304656	+	0.0783450i
$582$	16.7397	−	4.45013i	0.693885	−	0.184464i
$583$	−11.3948			−0.471926
$584$	3.03944	+	5.26447i	0.125773	+	0.217845i
$585$	4.66729	+	2.71919i	0.192969	+	0.112425i
$586$	1.91839	−	3.32275i	0.0792479	−	0.137261i
$587$	−16.9445	−	29.3488i	−0.699376	−	1.21135i	−0.968683	−	0.248300i	$-0.920128\pi$
$587$	−16.9445	−	29.3488i	−0.699376	−	1.21135i	0.269308	−	0.963054i	$-0.413205\pi$
$588$	−11.7665	−	2.92410i	−0.485241	−	0.120588i
$589$	−20.1231	+	34.8543i	−0.829159	+	1.43614i
$590$	−3.99880	−	6.92612i	−0.164628	−	0.285144i
$591$	−10.0188	+	37.0986i	−0.412118	+	1.52603i
$592$	1.10468	−	1.91336i	0.0454021	−	0.0786388i
$593$	15.1112	−	26.1734i	0.620543	−	1.07481i	−0.368841	−	0.929492i	$-0.620245\pi$
$593$	15.1112	−	26.1734i	0.620543	−	1.07481i	0.989385	−	0.145320i	$-0.0464212\pi$
$594$	−3.66533	−	14.0093i	−0.150390	−	0.574809i
$595$	0.415361	+	1.48983i	0.0170282	+	0.0610770i
$596$	5.35400	+	9.27339i	0.219308	+	0.379853i
$597$	−29.6420	+	7.88011i	−1.21317	+	0.322511i
$598$	5.79048			0.236790
$599$	−10.6379			−0.434654			−0.217327	−	0.976099i	$-0.569734\pi$
$599$	−10.6379			−0.434654			−0.217327	+	0.976099i	$0.569734\pi$
$600$	1.22233	+	1.22715i	0.0499016	+	0.0500982i
$601$	−12.3311	−	21.3581i	−0.502996	−	0.871215i	−0.999994	−	0.00346297i	$-0.998898\pi$
$601$	−12.3311	−	21.3581i	−0.502996	−	0.871215i	0.496998	−	0.867752i	$-0.334436\pi$
$602$	12.3554	+	3.17731i	0.503570	+	0.129497i
$603$	36.1163	+	21.0416i	1.47077	+	0.856881i
$604$	3.20293	−	5.54764i	0.130325	−	0.225730i
$605$	1.61674	−	2.80028i	0.0657300	−	0.113848i
$606$	19.7894	+	19.8674i	0.803889	+	0.807057i
$607$	−11.0399	−	19.1217i	−0.448096	−	0.776124i	0.550167	−	0.835055i	$-0.314564\pi$
$607$	−11.0399	−	19.1217i	−0.448096	−	0.776124i	−0.998262	+	0.0589307i	$0.981231\pi$
$608$	2.54440	−	4.40702i	0.103189	−	0.178728i
$609$	1.02267	−	1.80505i	0.0414409	−	0.0731443i
$610$	−7.57773	−	13.1250i	−0.306814	−	0.531417i
$611$	9.68973	−	16.7831i	0.392004	−	0.678972i
$612$	−0.00689826	+	1.75372i	−0.000278846	+	0.0708898i
$613$	7.43019	+	12.8695i	0.300103	+	0.519793i	0.976159	−	0.217057i	$-0.0696458\pi$
$613$	7.43019	+	12.8695i	0.300103	+	0.519793i	−0.676056	+	0.736850i	$0.736312\pi$
$614$	−3.47207			−0.140121
$615$	2.19726	−	8.13623i	0.0886019	−	0.328084i
$616$	1.98015	+	7.10244i	0.0797824	+	0.286165i
$617$	8.99342	−	15.5771i	0.362062	−	0.627109i	−0.626238	−	0.779632i	$-0.715406\pi$
$617$	8.99342	−	15.5771i	0.362062	−	0.627109i	0.988300	+	0.152523i	$0.0487397\pi$
$618$	−9.04180	+	2.40369i	−0.363715	+	0.0966908i
$619$	−15.6924	+	27.1801i	−0.630732	+	1.09246i	0.356671	+	0.934230i	$0.383912\pi$
$619$	−15.6924	+	27.1801i	−0.630732	+	1.09246i	−0.987402	+	0.158229i	$0.949422\pi$
$620$	3.95440	+	6.84922i	0.158812	+	0.275071i
$621$	−16.1154	−	4.42019i	−0.646691	−	0.177376i
$622$	−16.0291			−0.642707
$623$	−2.25074	−	8.07301i	−0.0901741	−	0.323439i
$624$	−2.20086	−	2.20954i	−0.0881051	−	0.0884523i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−29.5659			−1.18169
$627$	23.7389	−	6.31080i	0.948039	−	0.252029i
$628$	−8.54730			−0.341075
$629$	−1.29154			−0.0514972
$630$	5.64696	+	5.57780i	0.224980	+	0.222225i
$631$	0.938145			0.0373470			0.0186735	−	0.999826i	$-0.494056\pi$
$631$	0.938145			0.0373470			0.0186735	+	0.999826i	$0.494056\pi$
$632$	−0.652178			−0.0259422
$633$	−13.7502	−	13.8044i	−0.546521	−	0.548675i
$634$	5.36618			0.213118
$635$	−5.11798	−	8.86460i	−0.203101	−	0.351781i
$636$	6.84428	−	1.81950i	0.271393	−	0.0721478i
$637$	−11.0402	−	6.08026i	−0.437429	−	0.240909i
$638$	−1.26166			−0.0499496
$639$	15.0004	+	8.73934i	0.593407	+	0.345723i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−4.52630	+	7.83978i	−0.178778	+	0.309653i	−0.941462	−	0.337118i	$-0.890548\pi$
$641$	−4.52630	+	7.83978i	−0.178778	+	0.309653i	0.762684	+	0.646771i	$0.223881\pi$
$642$	10.8103	+	10.8529i	0.426649	+	0.428330i
$643$	0.665474	−	1.15263i	0.0262437	−	0.0454555i	−0.852605	−	0.522556i	$-0.824979\pi$
$643$	0.665474	−	1.15263i	0.0262437	−	0.0454555i	0.878849	+	0.477100i	$0.158312\pi$
$644$	8.24053	+	2.11912i	0.324722	+	0.0835052i
$645$	−5.89392	−	5.91715i	−0.232073	−	0.232987i
$646$	−2.97479			−0.117042
$647$	13.7896	+	23.8842i	0.542124	+	0.938986i	0.998782	+	0.0493439i	$0.0157130\pi$
$647$	13.7896	+	23.8842i	0.542124	+	0.938986i	−0.456658	+	0.889642i	$0.650954\pi$
$648$	4.43854	+	7.82939i	0.174362	+	0.307567i
$649$	−11.1440	+	19.3020i	−0.437441	+	0.757671i
$650$	0.900271	+	1.55932i	0.0353115	+	0.0611614i
$651$	18.3758	+	31.2387i	0.720206	+	1.22434i
$652$	−2.89129	+	5.00787i	−0.113232	+	0.196123i
$653$	17.0806	+	29.5844i	0.668414	+	1.15773i	0.978348	+	0.206969i	$0.0663598\pi$
$653$	17.0806	+	29.5844i	0.668414	+	1.15773i	−0.309934	+	0.950758i	$0.600307\pi$
$654$	10.5655	−	2.80876i	0.413144	−	0.109831i
$655$	−2.24198	+	3.88323i	−0.0876015	+	0.151730i
$656$	−2.43287	+	4.21385i	−0.0949875	+	0.164523i
$657$	0.0717335	−	18.2365i	0.00279859	−	0.711475i
$658$	19.9317	−	20.3382i	0.777017	−	0.792865i
$659$	−1.70021	−	2.94485i	−0.0662308	−	0.114715i	0.831008	−	0.556260i	$-0.187764\pi$
$659$	−1.70021	−	2.94485i	−0.0662308	−	0.114715i	−0.897239	+	0.441545i	$0.854431\pi$
$660$	1.25848	−	4.66002i	0.0489861	−	0.181391i
$661$	23.7489			0.923724			0.461862	−	0.886952i	$-0.347182\pi$
$661$	23.7489			0.923724			0.461862	+	0.886952i	$0.347182\pi$
$662$	31.9627			1.24227
$663$	−0.475310	+	1.76003i	−0.0184595	+	0.0683538i
$664$	1.43293	+	2.48191i	0.0556084	+	0.0963166i
$665$	−9.42367	+	9.61588i	−0.365434	+	0.372888i
$666$	−5.75308	+	3.29144i	−0.222927	+	0.127541i
$667$	−0.727966	+	1.26087i	−0.0281870	+	0.0488212i
$668$	−9.13796	+	15.8274i	−0.353558	+	0.612381i
$669$	−35.1324	+	9.33967i	−1.35830	+	0.361092i
$670$	6.96646	+	12.0663i	0.269138	+	0.466161i
$671$	−21.1180	+	36.5774i	−0.815251	+	1.41206i
$672$	−2.32347	−	3.94987i	−0.0896297	−	0.152370i
$673$	21.5103	+	37.2570i	0.829162	+	1.43615i	0.898696	+	0.438571i	$0.144515\pi$
$673$	21.5103	+	37.2570i	0.829162	+	1.43615i	−0.0695344	+	0.997580i	$0.522151\pi$
$674$	10.9734	−	19.0065i	0.422680	−	0.732103i
$675$	−1.31523	−	5.02695i	−0.0506231	−	0.193487i
$676$	4.87902	+	8.45072i	0.187655	+	0.325028i
$677$	39.9911			1.53698			0.768491	−	0.639860i	$-0.221008\pi$
$677$	39.9911			1.53698			0.768491	+	0.639860i	$0.221008\pi$
$678$	−18.1911	−	18.2628i	−0.698624	−	0.701377i
$679$	25.6248	+	6.58964i	0.983389	+	0.252887i
$680$	−0.292288	+	0.506258i	−0.0112088	+	0.0194141i
$681$	−19.6510	−	19.7285i	−0.753028	−	0.755996i
$682$	11.0203	−	19.0877i	0.421989	−	0.730907i
$683$	10.1241	+	17.5354i	0.387387	+	0.670975i	0.992097	−	0.125471i	$-0.0400442\pi$
$683$	10.1241	+	17.5354i	0.387387	+	0.670975i	−0.604710	+	0.796446i	$0.706711\pi$
$684$	−13.2510	+	7.58113i	−0.506664	+	0.289872i
$685$	18.5268			0.707871
$686$	−13.4863	−	12.6933i	−0.514910	−	0.484631i
$687$	22.8463	−	6.07351i	0.871640	−	0.231719i
$688$	2.41093	+	4.17585i	0.0919158	+	0.159203i
$689$	7.36204			0.280472
$690$	−3.93098	−	3.94648i	−0.149650	−	0.150240i
$691$	−29.1281			−1.10809			−0.554043	−	0.832488i	$-0.686916\pi$
$691$	−29.1281			−1.10809			−0.554043	+	0.832488i	$0.686916\pi$
$692$	7.94364			0.301972
$693$	5.59330	−	21.4011i	0.212472	−	0.812959i
$694$	17.0794			0.648326
$695$	−17.8165			−0.675818
$696$	0.757813	−	0.201459i	0.0287248	−	0.00763628i
$697$	2.84440			0.107739
$698$	11.6655	+	20.2053i	0.441547	+	0.764782i
$699$	5.66523	+	5.68756i	0.214279	+	0.215123i
$700$	0.710533	+	2.54856i	0.0268556	+	0.0963264i
$701$	10.0769			0.380600			0.190300	−	0.981726i	$-0.439054\pi$
$701$	10.0769			0.380600			0.190300	+	0.981726i	$0.439054\pi$
$702$	2.36812	+	9.05123i	0.0893789	+	0.341617i
$703$	−5.62149	−	9.73671i	−0.212019	−	0.367227i
$704$	−1.39342	+	2.41348i	−0.0525166	+	0.0909614i
$705$	−18.0165	+	4.78955i	−0.678541	+	0.180385i
$706$	3.45541	−	5.98494i	0.130046	−	0.225246i
$707$	11.5034	+	41.2607i	0.432630	+	1.55177i
$708$	3.61153	−	13.3732i	0.135730	−	0.502594i
$709$	33.4563			1.25648			0.628240	−	0.778020i	$-0.283776\pi$
$709$	33.4563			1.25648			0.628240	+	0.778020i	$0.283776\pi$
$710$	2.89342	+	5.01156i	0.108588	+	0.188080i
$711$	1.69055	+	0.984924i	0.0634005	+	0.0369375i
$712$	1.58384	−	2.74329i	0.0593569	−	0.102809i
$713$	−12.7172	−	22.0269i	−0.476263	−	0.824912i
$714$	−1.32053	+	2.33078i	−0.0494197	+	0.0872272i
$715$	2.50892	−	4.34557i	0.0938282	−	0.162515i
$716$	−1.31236	−	2.27307i	−0.0490452	−	0.0849487i
$717$	−29.6653	−	29.7822i	−1.10787	−	1.11224i
$718$	0.648078	−	1.12250i	0.0241861	−	0.0418915i
$719$	−15.9426	+	27.6133i	−0.594558	+	1.02980i	0.399052	+	0.916928i	$0.369339\pi$
$719$	−15.9426	+	27.6133i	−0.594558	+	1.02980i	−0.993609	+	0.112875i	$0.963994\pi$
$720$	−0.0118004	+	2.99998i	−0.000439776	+	0.111803i
$721$	−13.8410	−	3.55932i	−0.515465	−	0.132556i
$722$	−3.44791	−	5.97195i	−0.128318	−	0.222253i
$723$	−35.0461	−	35.1843i	−1.30338	−	1.30852i
$724$	−6.70153			−0.249061
$725$	−0.452720			−0.0168136
$726$	5.41257	−	1.43889i	0.200879	−	0.0534023i
$727$	−9.67508	−	16.7577i	−0.358829	−	0.621510i	0.628937	−	0.777457i	$-0.283491\pi$
$727$	−9.67508	−	16.7577i	−0.358829	−	0.621510i	−0.987765	+	0.155947i	$0.950157\pi$
$728$	−1.27935	−	4.58878i	−0.0474157	−	0.170072i
$729$	0.318605	−	26.9981i	0.0118002	−	0.999930i
$730$	3.03944	−	5.26447i	0.112495	−	0.194847i
$731$	1.40937	−	2.44111i	0.0521276	−	0.0902876i
$732$	6.84387	−	25.3422i	0.252957	−	0.936674i
$733$	8.08284	+	13.9999i	0.298547	+	0.517098i	0.975804	−	0.218649i	$-0.0701648\pi$
$733$	8.08284	+	13.9999i	0.298547	+	0.517098i	−0.677257	+	0.735747i	$0.736831\pi$
$734$	−8.09878	+	14.0275i	−0.298931	+	0.517764i
$735$	3.35089	+	11.6521i	0.123599	+	0.429794i
$736$	1.60798	+	2.78511i	0.0592710	+	0.102660i
$737$	19.4145	−	33.6268i	0.715141	−	1.23866i
$738$	12.6702	−	7.24882i	0.466395	−	0.266833i
$739$	−7.26443	−	12.5824i	−0.267227	−	0.462850i	0.700918	−	0.713242i	$-0.252774\pi$
$739$	−7.26443	−	12.5824i	−0.267227	−	0.462850i	−0.968145	+	0.250392i	$0.919441\pi$
$740$	−2.20936			−0.0812178
$741$	−15.3374	+	4.07732i	−0.563432	+	0.149784i
$742$	10.4770	+	2.69426i	0.384625	+	0.0989095i
$743$	−25.3577	+	43.9208i	−0.930283	+	1.61130i	−0.147445	+	0.989070i	$0.547105\pi$
$743$	−25.3577	+	43.9208i	−0.930283	+	1.61130i	−0.782837	+	0.622226i	$0.786228\pi$
$744$	−3.57143	+	13.2247i	−0.130935	+	0.484840i
$745$	5.35400	−	9.27339i	0.196155	−	0.339751i
$746$	15.2409	+	26.3980i	0.558008	+	0.966498i
$747$	0.0338184	−	8.59751i	0.00123735	−	0.314566i
$748$	1.62913			0.0595667
$749$	6.28395	+	22.5394i	0.229610	+	0.823572i
$750$	0.451577	−	1.67215i	0.0164893	−	0.0610582i
$751$	−4.85361	−	8.40669i	−0.177111	−	0.306765i	0.763779	−	0.645478i	$-0.223342\pi$
$751$	−4.85361	−	8.40669i	−0.177111	−	0.306765i	−0.940890	+	0.338713i	$0.890008\pi$
$752$	10.7631			0.392491
$753$	−13.4187	+	49.6883i	−0.489006	+	1.81074i
$754$	0.815142			0.0296857
$755$	−6.40586			−0.233133
$756$	0.0576631	+	13.7476i	0.00209719	+	0.499996i
$757$	14.3875			0.522922			0.261461	−	0.965214i	$-0.415796\pi$
$757$	14.3875			0.522922			0.261461	+	0.965214i	$0.415796\pi$
$758$	−19.7281			−0.716559
$759$	−4.04722	+	14.9865i	−0.146905	+	0.543974i
$760$	−5.08879			−0.184590
$761$	−9.38256	−	16.2511i	−0.340118	−	0.589101i	0.644337	−	0.764742i	$-0.277134\pi$
$761$	−9.38256	−	16.2511i	−0.340118	−	0.589101i	−0.984454	+	0.175641i	$0.943800\pi$
$762$	4.62232	−	17.1160i	0.167449	−	0.620048i
$763$	16.1734	+	4.15914i	0.585518	+	0.150571i
$764$	−23.8590			−0.863189
$765$	1.52221	−	0.870885i	0.0550357	−	0.0314869i
$766$	−15.0364	−	26.0438i	−0.543288	−	0.941003i
$767$	7.20000	−	12.4708i	0.259977	−	0.450293i
$768$	0.451577	−	1.67215i	0.0162949	−	0.0603384i
$769$	−13.3435	+	23.1117i	−0.481181	+	0.833429i	−0.999767	−	0.0215960i	$-0.993125\pi$
$769$	−13.3435	+	23.1117i	−0.481181	+	0.833429i	0.518586	+	0.855025i	$0.326459\pi$
$770$	5.16082	−	5.26608i	0.185983	−	0.189776i
$771$	−20.3972	+	5.42245i	−0.734588	+	0.195285i
$772$	−18.3945			−0.662034
$773$	7.30713	+	12.6563i	0.262819	+	0.455216i	0.966990	−	0.254814i	$-0.0820144\pi$
$773$	7.30713	+	12.6563i	0.262819	+	0.455216i	−0.704171	+	0.710031i	$0.748681\pi$
$774$	0.0569000	−	14.4655i	0.00204523	−	0.519950i
$775$	3.95440	−	6.84922i	0.142046	−	0.246031i
$776$	5.00019	+	8.66058i	0.179496	+	0.310897i
$777$	−10.1242	+	0.0822903i	−0.363205	+	0.00295215i
$778$	3.26051	−	5.64736i	0.116895	−	0.202468i
$779$	12.3804	+	21.4434i	0.443572	+	0.768290i
$780$	−0.813084	+	3.01077i	−0.0291131	+	0.107803i
$781$	8.06352	−	13.9664i	0.288536	−	0.499758i
$782$	0.939990	−	1.62811i	0.0336140	−	0.0582211i
$783$	−2.26861	−	0.622243i	−0.0810737	−	0.0222371i
$784$	−0.141315	−	6.99857i	−0.00504697	−	0.249949i
$785$	4.27365	+	7.40218i	0.152533	+	0.264195i
$786$	−7.50576	+	1.99535i	−0.267721	+	0.0711717i
$787$	28.9526			1.03205			0.516024	−	0.856574i	$-0.327412\pi$
$787$	28.9526			1.03205			0.516024	+	0.856574i	$0.327412\pi$
$788$	−22.1862			−0.790351
$789$	9.50260	+	9.54005i	0.338301	+	0.339635i
$790$	0.326089	+	0.564803i	0.0116017	+	0.0200948i
$791$	−10.5743	−	37.9282i	−0.375980	−	1.34857i
$792$	7.25683	−	4.15176i	0.257860	−	0.147526i
$793$	13.6440	−	23.6322i	0.484514	−	0.839202i
$794$	−11.4013	+	19.7477i	−0.404618	+	0.700819i
$795$	−4.99787	−	5.01757i	−0.177256	−	0.177955i
$796$	−8.85412	−	15.3358i	−0.313826	−	0.543563i
$797$	−18.4017	+	31.8727i	−0.651823	+	1.12899i	0.330857	+	0.943681i	$0.392662\pi$
$797$	−18.4017	+	31.8727i	−0.651823	+	1.12899i	−0.982680	+	0.185310i	$0.940671\pi$
$798$	−23.3190	+	0.189538i	−0.825484	+	0.00670958i
$799$	−3.14594	−	5.44892i	−0.111295	−	0.192769i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−8.24850	+	4.71911i	−0.291447	+	0.166742i
$802$	−10.5979	−	18.3561i	−0.374225	−	0.648177i
$803$	−16.9409			−0.597832
$804$	−6.29179	+	23.2979i	−0.221894	+	0.821654i
$805$	−2.28505	−	8.19607i	−0.0805374	−	0.288874i
$806$	−7.12006	+	12.3323i	−0.250793	+	0.434387i
$807$	1.38981	−	0.369470i	0.0489236	−	0.0130060i
$808$	−8.09492	+	14.0208i	−0.284778	+	0.493250i
$809$	−26.1763	−	45.3387i	−0.920310	−	1.59402i	−0.798935	−	0.601417i	$-0.794603\pi$
$809$	−26.1763	−	45.3387i	−0.920310	−	1.59402i	−0.121375	−	0.992607i	$-0.538730\pi$
$810$	4.56118	−	7.75859i	0.160263	−	0.272609i
$811$	−39.0074			−1.36973			−0.684867	−	0.728668i	$-0.740140\pi$
$811$	−39.0074			−1.36973			−0.684867	+	0.728668i	$0.740140\pi$
$812$	1.16004	+	0.298315i	0.0407095	+	0.0104688i
$813$	3.05319	+	3.06523i	0.107080	+	0.107502i
$814$	3.07858	+	5.33225i	0.107904	+	0.186895i
$815$	5.78258			0.202555
$816$	−0.978530	+	0.260135i	−0.0342554	+	0.00910653i
$817$	24.5374			0.858456
$818$	−27.2707			−0.953497
$819$	−3.61376	+	13.8269i	−0.126275	+	0.483152i
$820$	4.86573			0.169919
$821$	−26.1555			−0.912834			−0.456417	−	0.889766i	$-0.650867\pi$
$821$	−26.1555			−0.912834			−0.456417	+	0.889766i	$0.650867\pi$
$822$	22.6459	+	22.7351i	0.789866	+	0.792979i
$823$	39.2791			1.36918			0.684591	−	0.728927i	$-0.259981\pi$
$823$	39.2791			1.36918			0.684591	+	0.728927i	$0.259981\pi$
$824$	−2.70080	−	4.67793i	−0.0940869	−	0.162963i
$825$	−4.66493	+	1.24014i	−0.162412	+	0.0431760i
$826$	14.8103	−	15.1124i	0.515317	−	0.525827i
$827$	−36.5075			−1.26949			−0.634745	−	0.772722i	$-0.718895\pi$
$827$	−36.5075			−1.26949			−0.634745	+	0.772722i	$0.718895\pi$
$828$	0.0379498	−	9.64782i	0.00131885	−	0.335285i
$829$	−3.49566	−	6.05466i	−0.121409	−	0.210287i	0.798914	−	0.601445i	$-0.205408\pi$
$829$	−3.49566	−	6.05466i	−0.121409	−	0.210287i	−0.920324	+	0.391158i	$0.872075\pi$
$830$	1.43293	−	2.48191i	0.0497377	−	0.0861482i
$831$	23.1630	+	23.2543i	0.803515	+	0.806682i
$832$	0.900271	−	1.55932i	0.0312113	−	0.0540595i
$833$	−3.50178	+	2.11714i	−0.121330	+	0.0733547i
$834$	−21.7777	−	21.8635i	−0.754100	−	0.757072i
$835$	18.2759			0.632464
$836$	7.09084	+	12.2817i	0.245242	+	0.424771i
$837$	29.2297	−	28.8868i	1.01033	−	0.998475i
$838$	12.7856	−	22.1452i	0.441670	−	0.764994i
$839$	−5.28978	−	9.16218i	−0.182624	−	0.316313i	0.760150	−	0.649748i	$-0.225126\pi$
$839$	−5.28978	−	9.16218i	−0.182624	−	0.316313i	−0.942773	+	0.333435i	$0.891792\pi$
$840$	−2.25896	+	3.98712i	−0.0779414	+	0.137569i
$841$	14.3975	−	24.9372i	0.496466	−	0.859905i
$842$	9.08024	+	15.7274i	0.312926	+	0.542003i
$843$	−33.0640	+	8.78980i	−1.13878	+	0.302737i
$844$	5.62457	−	9.74204i	0.193606	−	0.335335i
$845$	4.87902	−	8.45072i	0.167844	−	0.290714i
$846$	−27.8997	−	16.2546i	−0.959211	−	0.558843i
$847$	8.28543	+	2.13067i	0.284691	+	0.0732107i
$848$	2.04440	+	3.54100i	0.0702049	+	0.121598i
$849$	2.83777	−	10.5080i	0.0973921	−	0.360634i
$850$	0.584577			0.0200508
$851$	7.10523			0.243564
$852$	−2.61321	+	9.67646i	−0.0895270	+	0.331510i
$853$	−19.9884	−	34.6209i	−0.684390	−	1.18540i	−0.973628	−	0.228141i	$-0.926735\pi$
$853$	−19.9884	−	34.6209i	−0.684390	−	1.18540i	0.289238	−	0.957257i	$-0.406598\pi$
$854$	28.0656	−	28.6381i	0.960386	−	0.979974i
$855$	13.1909	+	7.68513i	0.451121	+	0.262826i
$856$	−4.42199	+	7.65912i	−0.151141	+	0.261783i
$857$	3.40882	−	5.90425i	0.116443	−	0.201685i	−0.801913	−	0.597441i	$-0.796184\pi$
$857$	3.40882	−	5.90425i	0.116443	−	0.201685i	0.918356	+	0.395756i	$0.129517\pi$
$858$	8.39941	−	2.23292i	0.286751	−	0.0762306i
$859$	−25.7653	−	44.6268i	−0.879101	−	1.52265i	−0.852329	−	0.523006i	$-0.824811\pi$
$859$	−25.7653	−	44.6268i	−0.879101	−	1.52265i	−0.0267717	−	0.999642i	$-0.508523\pi$
$860$	2.41093	−	4.17585i	0.0822120	−	0.142395i
$861$	22.2969	−	0.181230i	0.759875	−	0.00617630i
$862$	−7.59234	−	13.1503i	−0.258596	−	0.447902i
$863$	−4.81166	+	8.33404i	−0.163791	+	0.283694i	−0.936225	−	0.351400i	$-0.885706\pi$
$863$	−4.81166	+	8.33404i	−0.163791	+	0.283694i	0.772434	+	0.635095i	$0.219039\pi$
$864$	−3.69585	+	3.65249i	−0.125735	+	0.124260i
$865$	−3.97182	−	6.87940i	−0.135046	−	0.233906i
$866$	1.12571			0.0382532
$867$	−20.3620	−	20.4422i	−0.691529	−	0.694254i
$868$	−14.6459	+	14.9446i	−0.497114	+	0.507253i
$869$	0.908760	−	1.57402i	0.0308276	−	0.0533949i
$870$	−0.553375	−	0.555556i	−0.0187612	−	0.0188351i
$871$	−12.5434	+	21.7258i	−0.425017	+	0.736151i
$872$	3.15594	+	5.46624i	0.106874	+	0.185110i
$873$	0.118009	−	30.0009i	0.00399399	−	1.01538i
$874$	16.3654			0.553567
$875$	1.85185	−	1.88962i	0.0626039	−	0.0638808i
$876$	10.1755	−	2.70508i	0.343799	−	0.0913963i
$877$	−9.19794	−	15.9313i	−0.310592	−	0.537962i	0.667898	−	0.744252i	$-0.267194\pi$
$877$	−9.19794	−	15.9313i	−0.310592	−	0.537962i	−0.978491	+	0.206291i	$0.933861\pi$
$878$	−31.8681			−1.07550
$879$	−4.68982	−	4.70831i	−0.158184	−	0.158807i
$880$	2.78685			0.0939446
$881$	43.3923			1.46192			0.730962	−	0.682419i	$-0.239072\pi$
$881$	43.3923			1.46192			0.730962	+	0.682419i	$0.239072\pi$
$882$	−10.2030	+	18.3548i	−0.343553	+	0.618039i
$883$	43.8094			1.47430			0.737152	−	0.675727i	$-0.236170\pi$
$883$	43.8094			1.47430			0.737152	+	0.675727i	$0.236170\pi$
$884$	−1.05256			−0.0354013
$885$	−13.3873	+	3.55890i	−0.450008	+	0.119631i
$886$	−18.5538			−0.623328
$887$	−18.5569	−	32.1414i	−0.623079	−	1.07920i	−0.988909	−	0.148523i	$-0.952548\pi$
$887$	−18.5569	−	32.1414i	−0.623079	−	1.07920i	0.365830	−	0.930682i	$-0.380785\pi$
$888$	−2.70058	−	2.71122i	−0.0906255	−	0.0909827i
$889$	18.9554	−	19.3420i	0.635745	−	0.648711i
$890$	−3.16768			−0.106181
$891$	−25.0808	−	0.197314i	−0.840240	−	0.00661028i
$892$	−10.4941	−	18.1763i	−0.351368	−	0.608588i
$893$	27.3856	−	47.4333i	0.916426	−	1.58730i
$894$	17.9242	−	4.76502i	0.599476	−	0.159366i
$895$	−1.31236	+	2.27307i	−0.0438673	+	0.0759804i
$896$	1.85185	−	1.88962i	0.0618659	−	0.0631277i
$897$	2.61485	−	9.68254i	0.0873073	−	0.323291i
$898$	−11.7410			−0.391804
$899$	−1.79024	−	3.10078i	−0.0597077	−	0.103417i
$900$	2.60396	−	1.48977i	0.0867985	−	0.0496590i
$901$	1.19511	−	2.06999i	0.0398148	−	0.0689612i
$902$	−6.78003	−	11.7433i	−0.225750	−	0.391011i
$903$	10.8924	−	19.2253i	0.362475	−	0.639779i
$904$	7.44112	−	12.8884i	0.247488	−	0.428662i
$905$	3.35077	+	5.80370i	0.111383	+	0.192921i
$906$	−7.83010	−	7.86096i	−0.260138	−	0.261163i
$907$	−10.2036	+	17.6731i	−0.338804	+	0.586825i	−0.984208	−	0.177016i	$-0.943356\pi$
$907$	−10.2036	+	17.6731i	−0.338804	+	0.586825i	0.645404	+	0.763841i	$0.276689\pi$
$908$	8.03831	−	13.9228i	0.266761	−	0.462043i
$909$	42.1576	−	24.1191i	1.39828	−	0.799980i
$910$	−3.33433	+	3.40234i	−0.110532	+	0.112786i
$911$	21.8699	+	37.8799i	0.724584	+	1.25502i	0.959145	+	0.282915i	$0.0913013\pi$
$911$	21.8699	+	37.8799i	0.724584	+	1.25502i	−0.234561	+	0.972101i	$0.575365\pi$
$912$	−6.22020	−	6.24472i	−0.205972	−	0.206783i
$913$	−7.98670			−0.264321
$914$	5.59537			0.185078
$915$	−25.3689	+	6.74413i	−0.838670	+	0.222954i
$916$	6.82422	+	11.8199i	0.225479	+	0.390540i
$917$	−11.4896	−	2.95466i	−0.379421	−	0.0975713i
$918$	2.92936	+	0.803474i	0.0966833	+	0.0265186i
$919$	−6.82483	+	11.8210i	−0.225131	+	0.389937i	−0.956359	−	0.292196i	$-0.905614\pi$
$919$	−6.82483	+	11.8210i	−0.225131	+	0.389937i	0.731228	+	0.682133i	$0.238948\pi$
$920$	1.60798	−	2.78511i	0.0530136	−	0.0918223i
$921$	−1.56791	+	5.80582i	−0.0516644	+	0.191308i
$922$	2.78195	+	4.81847i	0.0916185	+	0.158688i
$923$	−5.20973	+	9.02352i	−0.171480	+	0.297013i
$924$	12.7705	−	0.103799i	0.420119	−	0.00341475i
$925$	1.10468	+	1.91336i	0.0363217	+	0.0629110i
$926$	−7.03397	+	12.1832i	−0.231151	+	0.400364i
$927$	−0.0637413	+	16.2047i	−0.00209354	+	0.532232i
$928$	0.226360	+	0.392067i	0.00743063	+	0.0128702i
$929$	13.2845			0.435849			0.217924	−	0.975966i	$-0.430071\pi$
$929$	13.2845			0.435849			0.217924	+	0.975966i	$0.430071\pi$
$930$	13.2386	−	3.51939i	0.434112	−	0.115405i
$931$	−31.2024	−	17.1844i	−1.02262	−	0.563195i
$932$	−2.31738	+	4.01383i	−0.0759085	+	0.131477i
$933$	−7.23836	+	26.8029i	−0.236973	+	0.877489i
$934$	4.64000	−	8.03672i	0.151826	−	0.262970i
$935$	−0.814563	−	1.41086i	−0.0266391	−	0.0461402i
$936$	−4.68853	+	2.68239i	−0.153250	+	0.0876767i
$937$	39.7166			1.29748			0.648742	−	0.761008i	$-0.275295\pi$
$937$	39.7166			1.29748			0.648742	+	0.761008i	$0.275295\pi$
$938$	−25.8017	+	26.3279i	−0.842454	+	0.859637i
$939$	−13.3513	+	49.4386i	−0.435703	+	1.61337i
$940$	−5.38156	−	9.32114i	−0.175527	−	0.304022i
$941$	−27.4633			−0.895277			−0.447639	−	0.894215i	$-0.647735\pi$
$941$	−27.4633			−0.895277			−0.447639	+	0.894215i	$0.647735\pi$
$942$	−3.85977	+	14.2924i	−0.125758	+	0.465670i
$943$	−15.6480			−0.509570
$944$	7.99759			0.260299
$945$	11.8769	−	6.92374i	0.386357	−	0.225229i
$946$	−13.4378			−0.436900
$947$	20.1032			0.653266			0.326633	−	0.945151i	$-0.394086\pi$
$947$	20.1032			0.653266			0.326633	+	0.945151i	$0.394086\pi$
$948$	−0.294509	+	1.09054i	−0.00956520	+	0.0354190i
$949$	10.9453			0.355299
$950$	2.54440	+	4.40702i	0.0825511	+	0.142983i
$951$	2.42325	−	8.97305i	0.0785791	−	0.290971i
$952$	−1.49791	−	0.385200i	−0.0485475	−	0.0124844i
$953$	7.30264			0.236556			0.118278	−	0.992981i	$-0.462263\pi$
$953$	7.30264			0.236556			0.118278	+	0.992981i	$0.462263\pi$
$954$	0.0482495	−	12.2663i	0.00156214	−	0.397136i
$955$	11.9295	+	20.6625i	0.386030	+	0.668623i
$956$	12.1347	−	21.0179i	0.392464	−	0.679768i
$957$	−0.569738	+	2.10968i	−0.0184170	+	0.0681964i
$958$	−4.74662	+	8.22138i	−0.153356	+	0.265621i
$959$	13.1639	+	47.2165i	0.425084	+	1.52470i
$960$	−1.67391	+	0.444996i	−0.0540252	+	0.0143622i
$961$	31.5491			1.01771
$962$	−1.98903	−	3.44509i	−0.0641287	−	0.111074i
$963$	23.0294	−	13.1755i	0.742110	−	0.424574i
$964$	14.3357	−	24.8302i	0.461723	−	0.799728i
$965$	9.19727	+	15.9301i	0.296071	+	0.512809i
$966$	7.26472	−	12.8224i	0.233739	−	0.412555i
$967$	21.8317	−	37.8135i	0.702059	−	1.21600i	−0.265684	−	0.964060i	$-0.585598\pi$
$967$	21.8317	−	37.8135i	0.702059	−	1.21600i	0.967743	−	0.251941i	$-0.0810689\pi$
$968$	1.61674	+	2.80028i	0.0519641	+	0.0900045i
$969$	−1.34335	+	4.97429i	−0.0431546	+	0.159797i
$970$	5.00019	−	8.66058i	0.160546	−	0.278075i
$971$	−0.713412	+	1.23567i	−0.0228945	+	0.0396544i	−0.877246	−	0.480042i	$-0.840622\pi$
$971$	−0.713412	+	1.23567i	−0.0228945	+	0.0396544i	0.854351	+	0.519696i	$0.173955\pi$
$972$	15.0962	−	3.88633i	0.484212	−	0.124654i
$973$	−12.6592	−	45.4063i	−0.405836	−	1.45566i
$974$	18.3576	+	31.7962i	0.588214	+	1.01882i
$975$	3.01395	−	0.801235i	0.0965236	−	0.0256601i
$976$	15.1555			0.485115
$977$	−32.9580			−1.05442			−0.527209	−	0.849735i	$-0.676762\pi$
$977$	−32.9580			−1.05442			−0.527209	+	0.849735i	$0.676762\pi$
$978$	7.06825	+	7.09611i	0.226018	+	0.226908i
$979$	4.41392	+	7.64513i	0.141069	+	0.244340i
$980$	−5.99028	+	3.62167i	−0.191353	+	0.115690i
$981$	0.0744829	−	18.9355i	0.00237806	−	0.604563i
$982$	−0.627842	+	1.08745i	−0.0200352	+	0.0347021i
$983$	14.6901	−	25.4440i	0.468542	−	0.811539i	−0.530811	−	0.847490i	$-0.678113\pi$
$983$	14.6901	−	25.4440i	0.468542	−	0.811539i	0.999354	+	0.0359513i	$0.0114461\pi$
$984$	5.94755	+	5.97099i	0.189601	+	0.190348i
$985$	11.0931	+	19.2138i	0.353456	+	0.612203i
$986$	0.132325	−	0.229193i	0.00421408	−	0.00729900i
$987$	−25.0078	−	42.5130i	−0.796006	−	1.35320i
$988$	−4.58129	−	7.93503i	−0.145750	−	0.252447i
$989$	−7.75346	+	13.4294i	−0.246546	+	0.427030i
$990$	−7.22394	−	4.20872i	−0.229592	−	0.133762i
$991$	−12.9004	−	22.3441i	−0.409794	−	0.709785i	0.585072	−	0.810981i	$-0.301066\pi$
$991$	−12.9004	−	22.3441i	−0.409794	−	0.709785i	−0.994866	+	0.101197i	$0.967733\pi$
$992$	−7.90880			−0.251105
$993$	14.4336	−	53.4464i	0.458038	−	1.69607i
$994$	−10.7164	+	10.9349i	−0.339902	+	0.346835i
$995$	−8.85412	+	15.3358i	−0.280695	+	0.486177i
$996$	4.79719	−	1.27530i	0.152005	−	0.0404093i
$997$	7.44930	−	12.9026i	0.235922	−	0.408628i	−0.723618	−	0.690200i	$-0.757522\pi$
$997$	7.44930	−	12.9026i	0.235922	−	0.408628i	0.959540	+	0.281572i	$0.0908558\pi$
$998$	−3.99415	−	6.91807i	−0.126433	−	0.218988i
$999$	2.90581	+	11.1063i	0.0919358	+	0.351389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.g.121.4	✓	12
3.2	odd	2		1890.2.i.g.1171.6		12
7.4	even	3		630.2.l.g.571.1	yes	12
9.2	odd	6		1890.2.l.g.1801.1		12
9.7	even	3		630.2.l.g.331.1	yes	12
21.11	odd	6		1890.2.l.g.361.1		12
63.11	odd	6		1890.2.i.g.991.6		12
63.25	even	3	inner	630.2.i.g.151.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.4	✓	12	1.1	even	1	trivial
630.2.i.g.151.4	yes	12	63.25	even	3	inner
630.2.l.g.331.1	yes	12	9.7	even	3
630.2.l.g.571.1	yes	12	7.4	even	3
1890.2.i.g.991.6		12	63.11	odd	6
1890.2.i.g.1171.6		12	3.2	odd	2
1890.2.l.g.361.1		12	21.11	odd	6
1890.2.l.g.1801.1		12	9.2	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.451577 - 1.67215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.451577 - 1.67215i) q^{6} +(1.85185 - 1.88962i) q^{7} +1.00000 q^{8} +(-2.59216 - 1.51021i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.451577 - 1.67215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.451577 - 1.67215i) q^{6} +(1.85185 - 1.88962i) q^{7} +1.00000 q^{8} +(-2.59216 - 1.51021i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.39342 + 2.41348i) q^{11} +(0.451577 - 1.67215i) q^{12} +(0.900271 - 1.55932i) q^{13} +(1.85185 - 1.88962i) q^{14} +(-1.67391 + 0.444996i) q^{15} +1.00000 q^{16} +(-0.292288 - 0.506258i) q^{17} +(-2.59216 - 1.51021i) q^{18} +(2.54440 - 4.40702i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.32347 - 3.94987i) q^{21} +(-1.39342 + 2.41348i) q^{22} +(1.60798 + 2.78511i) q^{23} +(0.451577 - 1.67215i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.900271 - 1.55932i) q^{26} +(-3.69585 + 3.65249i) q^{27} +(1.85185 - 1.88962i) q^{28} +(0.226360 + 0.392067i) q^{29} +(-1.67391 + 0.444996i) q^{30} -7.90880 q^{31} +1.00000 q^{32} +(3.40646 + 3.41988i) q^{33} +(-0.292288 - 0.506258i) q^{34} +(-2.56238 - 0.658939i) q^{35} +(-2.59216 - 1.51021i) q^{36} +(1.10468 - 1.91336i) q^{37} +(2.54440 - 4.40702i) q^{38} +(-2.20086 - 2.20954i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.43287 + 4.21385i) q^{41} +(-2.32347 - 3.94987i) q^{42} +(2.41093 + 4.17585i) q^{43} +(-1.39342 + 2.41348i) q^{44} +(-0.0118004 + 2.99998i) q^{45} +(1.60798 + 2.78511i) q^{46} +10.7631 q^{47} +(0.451577 - 1.67215i) q^{48} +(-0.141315 - 6.99857i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.978530 + 0.260135i) q^{51} +(0.900271 - 1.55932i) q^{52} +(2.04440 + 3.54100i) q^{53} +(-3.69585 + 3.65249i) q^{54} +2.78685 q^{55} +(1.85185 - 1.88962i) q^{56} +(-6.22020 - 6.24472i) q^{57} +(0.226360 + 0.392067i) q^{58} +7.99759 q^{59} +(-1.67391 + 0.444996i) q^{60} +15.1555 q^{61} -7.90880 q^{62} +(-7.65400 + 2.10151i) q^{63} +1.00000 q^{64} -1.80054 q^{65} +(3.40646 + 3.41988i) q^{66} -13.9329 q^{67} +(-0.292288 - 0.506258i) q^{68} +(5.38324 - 1.43109i) q^{69} +(-2.56238 - 0.658939i) q^{70} -5.78685 q^{71} +(-2.59216 - 1.51021i) q^{72} +(3.03944 + 5.26447i) q^{73} +(1.10468 - 1.91336i) q^{74} +(1.22233 + 1.22715i) q^{75} +(2.54440 - 4.40702i) q^{76} +(1.98015 + 7.10244i) q^{77} +(-2.20086 - 2.20954i) q^{78} -0.652178 q^{79} +(-0.500000 - 0.866025i) q^{80} +(4.43854 + 7.82939i) q^{81} +(-2.43287 + 4.21385i) q^{82} +(1.43293 + 2.48191i) q^{83} +(-2.32347 - 3.94987i) q^{84} +(-0.292288 + 0.506258i) q^{85} +(2.41093 + 4.17585i) q^{86} +(0.757813 - 0.201459i) q^{87} +(-1.39342 + 2.41348i) q^{88} +(1.58384 - 2.74329i) q^{89} +(-0.0118004 + 2.99998i) q^{90} +(-1.27935 - 4.58878i) q^{91} +(1.60798 + 2.78511i) q^{92} +(-3.57143 + 13.2247i) q^{93} +10.7631 q^{94} -5.08879 q^{95} +(0.451577 - 1.67215i) q^{96} +(5.00019 + 8.66058i) q^{97} +(-0.141315 - 6.99857i) q^{98} +(7.25683 - 4.15176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more