LMFDB - Embedded newform 930.2.i.k.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.k.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(1.18614 + 2.05446i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(2.68614 + 4.65253i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.37228 + 4.10891i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.18614 + 2.05446i) q^{21} +(2.50000 - 4.33013i) q^{22} +8.11684 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(-1.18614 - 2.05446i) q^{28} -3.62772 q^{29} +1.00000 q^{30} +(5.55842 + 0.322405i) q^{31} -1.00000 q^{32} +5.00000 q^{33} +(-2.68614 - 4.65253i) q^{34} -2.37228 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.05842 - 8.76144i) q^{37} +(-2.37228 - 4.10891i) q^{38} +2.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.37228 + 5.84096i) q^{41} +(1.18614 - 2.05446i) q^{42} +(-1.68614 - 2.92048i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(0.500000 + 0.866025i) q^{45} -8.11684 q^{46} +12.1168 q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.686141 - 1.18843i) q^{49} +(0.500000 + 0.866025i) q^{50} +(2.68614 - 4.65253i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(0.813859 - 1.40965i) q^{53} -1.00000 q^{54} +(2.50000 + 4.33013i) q^{55} +(1.18614 + 2.05446i) q^{56} +(2.37228 - 4.10891i) q^{57} +3.62772 q^{58} +(5.55842 + 9.62747i) q^{59} -1.00000 q^{60} -2.00000 q^{61} +(-5.55842 - 0.322405i) q^{62} +2.37228 q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} -5.00000 q^{66} +(5.05842 - 8.76144i) q^{67} +(2.68614 + 4.65253i) q^{68} +(-4.05842 - 7.02939i) q^{69} +2.37228 q^{70} +(1.37228 - 2.37686i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(5.05842 + 8.76144i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(2.37228 + 4.10891i) q^{76} +11.8614 q^{77} -2.00000 q^{78} +(1.68614 + 2.92048i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.37228 - 5.84096i) q^{82} +(-1.18614 + 2.05446i) q^{83} +(-1.18614 + 2.05446i) q^{84} +5.37228 q^{85} +(1.68614 + 2.92048i) q^{86} +(1.81386 + 3.14170i) q^{87} +(2.50000 - 4.33013i) q^{88} +(-0.500000 - 0.866025i) q^{90} +4.74456 q^{91} +8.11684 q^{92} +(-2.50000 - 4.97494i) q^{93} -12.1168 q^{94} +4.74456 q^{95} +(0.500000 + 0.866025i) q^{96} +16.3723 q^{97} +(-0.686141 + 1.18843i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} - 10 q^{11} - 2 q^{12} - 4 q^{13} - q^{14} - 4 q^{15} + 4 q^{16} + 5 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} + q^{21} + 10 q^{22} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} + q^{28} - 26 q^{29} + 4 q^{30} + 5 q^{31} - 4 q^{32} + 20 q^{33} - 5 q^{34} + 2 q^{35} - 2 q^{36} - 3 q^{37} + 2 q^{38} + 8 q^{39} - 2 q^{40} - 2 q^{41} - q^{42} - q^{43} - 10 q^{44} + 2 q^{45} + 2 q^{46} + 14 q^{47} - 2 q^{48} - 3 q^{49} + 2 q^{50} + 5 q^{51} - 4 q^{52} + 9 q^{53} - 4 q^{54} + 10 q^{55} - q^{56} - 2 q^{57} + 26 q^{58} + 5 q^{59} - 4 q^{60} - 8 q^{61} - 5 q^{62} - 2 q^{63} + 4 q^{64} + 4 q^{65} - 20 q^{66} + 3 q^{67} + 5 q^{68} + q^{69} - 2 q^{70} - 6 q^{71} + 2 q^{72} - 28 q^{73} + 3 q^{74} - 2 q^{75} - 2 q^{76} - 10 q^{77} - 8 q^{78} + q^{79} + 2 q^{80} - 2 q^{81} + 2 q^{82} + q^{83} + q^{84} + 10 q^{85} + q^{86} + 13 q^{87} + 10 q^{88} - 2 q^{90} - 4 q^{91} - 2 q^{92} - 10 q^{93} - 14 q^{94} - 4 q^{95} + 2 q^{96} + 54 q^{97} + 3 q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 - 10 * q^11 - 2 * q^12 - 4 * q^13 - q^14 - 4 * q^15 + 4 * q^16 + 5 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 + q^21 + 10 * q^22 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 + q^28 - 26 * q^29 + 4 * q^30 + 5 * q^31 - 4 * q^32 + 20 * q^33 - 5 * q^34 + 2 * q^35 - 2 * q^36 - 3 * q^37 + 2 * q^38 + 8 * q^39 - 2 * q^40 - 2 * q^41 - q^42 - q^43 - 10 * q^44 + 2 * q^45 + 2 * q^46 + 14 * q^47 - 2 * q^48 - 3 * q^49 + 2 * q^50 + 5 * q^51 - 4 * q^52 + 9 * q^53 - 4 * q^54 + 10 * q^55 - q^56 - 2 * q^57 + 26 * q^58 + 5 * q^59 - 4 * q^60 - 8 * q^61 - 5 * q^62 - 2 * q^63 + 4 * q^64 + 4 * q^65 - 20 * q^66 + 3 * q^67 + 5 * q^68 + q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 - 28 * q^73 + 3 * q^74 - 2 * q^75 - 2 * q^76 - 10 * q^77 - 8 * q^78 + q^79 + 2 * q^80 - 2 * q^81 + 2 * q^82 + q^83 + q^84 + 10 * q^85 + q^86 + 13 * q^87 + 10 * q^88 - 2 * q^90 - 4 * q^91 - 2 * q^92 - 10 * q^93 - 14 * q^94 - 4 * q^95 + 2 * q^96 + 54 * q^97 + 3 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−1.18614	−	2.05446i	−0.448319	−	0.776511i	0.549958	−	0.835192i	$-0.314644\pi$
$7$	−1.18614	−	2.05446i	−0.448319	−	0.776511i	−0.998277	+	0.0586811i	$0.981310\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	1.18614	+	2.05446i	0.317009	+	0.549076i
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	2.68614	+	4.65253i	0.651485	+	1.12840i	0.982763	+	0.184872i	$0.0591869\pi$
$17$	2.68614	+	4.65253i	0.651485	+	1.12840i	−0.331278	+	0.943533i	$0.607480\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	2.37228	+	4.10891i	0.544239	+	0.942649i	0.998654	+	0.0518593i	$0.0165147\pi$
$19$	2.37228	+	4.10891i	0.544239	+	0.942649i	−0.454416	+	0.890790i	$0.650152\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−1.18614	+	2.05446i	−0.258837	+	0.448319i
$22$	2.50000	−	4.33013i	0.533002	−	0.923186i
$23$	8.11684			1.69248			0.846239	−	0.532803i	$-0.178861\pi$
$23$	8.11684			1.69248			0.846239	+	0.532803i	$0.178861\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	1.00000			0.192450
$28$	−1.18614	−	2.05446i	−0.224160	−	0.388256i
$29$	−3.62772			−0.673650			−0.336825	−	0.941567i	$-0.609353\pi$
$29$	−3.62772			−0.673650			−0.336825	+	0.941567i	$0.609353\pi$
$30$	1.00000			0.182574
$31$	5.55842	+	0.322405i	0.998322	+	0.0579057i
$31$	5.55842	+	0.322405i	0.998322	+	0.0579057i
$32$	−1.00000			−0.176777
$33$	5.00000			0.870388
$34$	−2.68614	−	4.65253i	−0.460669	−	0.797903i
$35$	−2.37228			−0.400989
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−5.05842	−	8.76144i	−0.831599	−	1.44037i	−0.896769	−	0.442498i	$-0.854092\pi$
$37$	−5.05842	−	8.76144i	−0.831599	−	1.44037i	0.0651699	−	0.997874i	$-0.479241\pi$
$38$	−2.37228	−	4.10891i	−0.384835	−	0.666554i
$39$	2.00000			0.320256
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−3.37228	+	5.84096i	−0.526662	+	0.912205i	0.472856	+	0.881140i	$0.343223\pi$
$41$	−3.37228	+	5.84096i	−0.526662	+	0.912205i	−0.999517	+	0.0310651i	$0.990110\pi$
$42$	1.18614	−	2.05446i	0.183025	−	0.317009i
$43$	−1.68614	−	2.92048i	−0.257134	−	0.445369i	0.708339	−	0.705872i	$-0.249445\pi$
$43$	−1.68614	−	2.92048i	−0.257134	−	0.445369i	−0.965473	+	0.260503i	$0.916112\pi$
$44$	−2.50000	+	4.33013i	−0.376889	+	0.652791i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−8.11684			−1.19676
$47$	12.1168			1.76742			0.883712	−	0.468032i	$-0.155037\pi$
$47$	12.1168			1.76742			0.883712	+	0.468032i	$0.155037\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	0.686141	−	1.18843i	0.0980201	−	0.169776i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	2.68614	−	4.65253i	0.376135	−	0.651485i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	0.813859	−	1.40965i	0.111792	−	0.193630i	−0.804701	−	0.593681i	$-0.797674\pi$
$53$	0.813859	−	1.40965i	0.111792	−	0.193630i	0.916493	+	0.400051i	$0.131008\pi$
$54$	−1.00000			−0.136083
$55$	2.50000	+	4.33013i	0.337100	+	0.583874i
$56$	1.18614	+	2.05446i	0.158505	+	0.274538i
$57$	2.37228	−	4.10891i	0.314216	−	0.544239i
$58$	3.62772			0.476343
$59$	5.55842	+	9.62747i	0.723645	+	1.25339i	0.959529	+	0.281609i	$0.0908680\pi$
$59$	5.55842	+	9.62747i	0.723645	+	1.25339i	−0.235884	+	0.971781i	$0.575799\pi$
$60$	−1.00000			−0.129099
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	−5.55842	−	0.322405i	−0.705920	−	0.0409455i
$63$	2.37228			0.298879
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$	−5.00000			−0.615457
$67$	5.05842	−	8.76144i	0.617985	−	1.07038i	−0.371868	−	0.928285i	$-0.621283\pi$
$67$	5.05842	−	8.76144i	0.617985	−	1.07038i	0.989853	−	0.142095i	$-0.0453839\pi$
$68$	2.68614	+	4.65253i	0.325742	+	0.564202i
$69$	−4.05842	−	7.02939i	−0.488577	−	0.846239i
$70$	2.37228			0.283542
$71$	1.37228	−	2.37686i	0.162860	−	0.282082i	−0.773033	−	0.634365i	$-0.781261\pi$
$71$	1.37228	−	2.37686i	0.162860	−	0.282082i	0.935893	+	0.352284i	$0.114595\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	0.0869195	+	0.996215i	$0.472298\pi$
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	−0.906208	+	0.422833i	$0.861036\pi$
$74$	5.05842	+	8.76144i	0.588030	+	1.01850i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	2.37228	+	4.10891i	0.272119	+	0.471325i
$77$	11.8614			1.35173
$78$	−2.00000			−0.226455
$79$	1.68614	+	2.92048i	0.189706	+	0.328580i	0.945152	−	0.326631i	$-0.105913\pi$
$79$	1.68614	+	2.92048i	0.189706	+	0.328580i	−0.755446	+	0.655210i	$0.772580\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.37228	−	5.84096i	0.372406	−	0.645026i
$83$	−1.18614	+	2.05446i	−0.130196	+	0.225506i	−0.923752	−	0.382991i	$-0.874894\pi$
$83$	−1.18614	+	2.05446i	−0.130196	+	0.225506i	0.793556	+	0.608497i	$0.208227\pi$
$84$	−1.18614	+	2.05446i	−0.129419	+	0.224160i
$85$	5.37228			0.582706
$86$	1.68614	+	2.92048i	0.181821	+	0.314924i
$87$	1.81386	+	3.14170i	0.194466	+	0.336825i
$88$	2.50000	−	4.33013i	0.266501	−	0.461593i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	4.74456			0.497365
$92$	8.11684			0.846239
$93$	−2.50000	−	4.97494i	−0.259238	−	0.515877i
$94$	−12.1168			−1.24976
$95$	4.74456			0.486782
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	16.3723			1.66235			0.831177	−	0.556008i	$-0.187668\pi$
$97$	16.3723			1.66235			0.831177	+	0.556008i	$0.187668\pi$
$98$	−0.686141	+	1.18843i	−0.0693107	+	0.120050i
$99$	−2.50000	−	4.33013i	−0.251259	−	0.435194i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−8.48913			−0.844700			−0.422350	−	0.906433i	$-0.638795\pi$
$101$	−8.48913			−0.844700			−0.422350	+	0.906433i	$0.638795\pi$
$102$	−2.68614	+	4.65253i	−0.265968	+	0.460669i
$103$	0.186141	−	0.322405i	0.0183410	−	0.0317675i	−0.856709	−	0.515800i	$-0.827495\pi$
$103$	0.186141	−	0.322405i	0.0183410	−	0.0317675i	0.875050	+	0.484032i	$0.160828\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$	1.18614	+	2.05446i	0.115755	+	0.200494i
$106$	−0.813859	+	1.40965i	−0.0790490	+	0.136917i
$107$	2.81386	+	4.87375i	0.272026	+	0.471163i	0.969381	−	0.245563i	$-0.0789730\pi$
$107$	2.81386	+	4.87375i	0.272026	+	0.471163i	−0.697354	+	0.716726i	$0.745640\pi$
$108$	1.00000			0.0962250
$109$	8.74456			0.837577			0.418789	−	0.908084i	$-0.362455\pi$
$109$	8.74456			0.837577			0.418789	+	0.908084i	$0.362455\pi$
$110$	−2.50000	−	4.33013i	−0.238366	−	0.412861i
$111$	−5.05842	+	8.76144i	−0.480124	+	0.831599i
$112$	−1.18614	−	2.05446i	−0.112080	−	0.194128i
$113$	−8.05842	+	13.9576i	−0.758073	+	1.31302i	0.185760	+	0.982595i	$0.440525\pi$
$113$	−8.05842	+	13.9576i	−0.758073	+	1.31302i	−0.943832	+	0.330425i	$0.892808\pi$
$114$	−2.37228	+	4.10891i	−0.222185	+	0.384835i
$115$	4.05842	−	7.02939i	0.378450	−	0.655494i
$116$	−3.62772			−0.336825
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$	−5.55842	−	9.62747i	−0.511694	−	0.886280i
$119$	6.37228	−	11.0371i	0.584146	−	1.01177i
$120$	1.00000			0.0912871
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	2.00000			0.181071
$123$	6.74456			0.608137
$124$	5.55842	+	0.322405i	0.499161	+	0.0289528i
$125$	−1.00000			−0.0894427
$126$	−2.37228			−0.211340
$127$	1.81386	+	3.14170i	0.160954	+	0.278780i	0.935211	−	0.354091i	$-0.115210\pi$
$127$	1.81386	+	3.14170i	0.160954	+	0.278780i	−0.774257	+	0.632871i	$0.781876\pi$
$128$	−1.00000			−0.0883883
$129$	−1.68614	+	2.92048i	−0.148456	+	0.257134i
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	9.05842	+	15.6896i	0.791438	+	1.37081i	0.925077	+	0.379781i	$0.124001\pi$
$131$	9.05842	+	15.6896i	0.791438	+	1.37081i	−0.133639	+	0.991030i	$0.542666\pi$
$132$	5.00000			0.435194
$133$	5.62772	−	9.74749i	0.487985	−	0.845215i
$134$	−5.05842	+	8.76144i	−0.436981	+	0.756873i
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−2.68614	−	4.65253i	−0.230335	−	0.398951i
$137$	−8.31386	+	14.4000i	−0.710301	+	1.23028i	0.254443	+	0.967088i	$0.418108\pi$
$137$	−8.31386	+	14.4000i	−0.710301	+	1.23028i	−0.964744	+	0.263190i	$0.915226\pi$
$138$	4.05842	+	7.02939i	0.345476	+	0.598382i
$139$	−10.7446			−0.911342			−0.455671	−	0.890148i	$-0.650601\pi$
$139$	−10.7446			−0.911342			−0.455671	+	0.890148i	$0.650601\pi$
$140$	−2.37228			−0.200494
$141$	−6.05842	−	10.4935i	−0.510211	−	0.883712i
$142$	−1.37228	+	2.37686i	−0.115159	+	0.199462i
$143$	−5.00000	−	8.66025i	−0.418121	−	0.724207i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.81386	+	3.14170i	−0.150633	+	0.260904i
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	−1.37228			−0.113184
$148$	−5.05842	−	8.76144i	−0.415800	−	0.720186i
$149$	4.93070	+	8.54023i	0.403939	+	0.699643i	0.994197	−	0.107572i	$-0.0343075\pi$
$149$	4.93070	+	8.54023i	0.403939	+	0.699643i	−0.590258	+	0.807214i	$0.700974\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$	−2.37228	−	4.10891i	−0.192417	−	0.333277i
$153$	−5.37228			−0.434323
$154$	−11.8614			−0.955819
$155$	3.05842	−	4.65253i	0.245658	−	0.373700i
$156$	2.00000			0.160128
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−1.68614	−	2.92048i	−0.134142	−	0.232341i
$159$	−1.62772			−0.129086
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−9.62772	−	16.6757i	−0.758771	−	1.31423i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−13.3723			−1.04740			−0.523699	−	0.851903i	$-0.675448\pi$
$163$	−13.3723			−1.04740			−0.523699	+	0.851903i	$0.675448\pi$
$164$	−3.37228	+	5.84096i	−0.263331	+	0.456103i
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$	1.18614	−	2.05446i	0.0920624	−	0.159457i
$167$	−4.74456	−	8.21782i	−0.367145	−	0.635914i	0.621973	−	0.783039i	$-0.286331\pi$
$167$	−4.74456	−	8.21782i	−0.367145	−	0.635914i	−0.989118	+	0.147125i	$0.952998\pi$
$168$	1.18614	−	2.05446i	0.0915127	−	0.158505i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−5.37228			−0.412035
$171$	−4.74456			−0.362826
$172$	−1.68614	−	2.92048i	−0.128567	−	0.222685i
$173$	−6.93070	+	12.0043i	−0.526932	+	0.912672i	0.472576	+	0.881290i	$0.343324\pi$
$173$	−6.93070	+	12.0043i	−0.526932	+	0.912672i	−0.999507	+	0.0313823i	$0.990009\pi$
$174$	−1.81386	−	3.14170i	−0.137508	−	0.238171i
$175$	−1.18614	+	2.05446i	−0.0896638	+	0.155302i
$176$	−2.50000	+	4.33013i	−0.188445	+	0.326396i
$177$	5.55842	−	9.62747i	0.417797	−	0.723645i
$178$		0			0
$179$	−0.244563	−	0.423595i	−0.0182795	−	0.0316610i	0.856741	−	0.515747i	$-0.172486\pi$
$179$	−0.244563	−	0.423595i	−0.0182795	−	0.0316610i	−0.875020	+	0.484086i	$0.839152\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−11.4891	+	19.8997i	−0.853980	+	1.47914i	0.0236082	+	0.999721i	$0.492485\pi$
$181$	−11.4891	+	19.8997i	−0.853980	+	1.47914i	−0.877588	+	0.479415i	$0.840849\pi$
$182$	−4.74456			−0.351690
$183$	1.00000	+	1.73205i	0.0739221	+	0.128037i
$184$	−8.11684			−0.598382
$185$	−10.1168			−0.743805
$186$	2.50000	+	4.97494i	0.183309	+	0.364780i
$187$	−26.8614			−1.96430
$188$	12.1168			0.883712
$189$	−1.18614	−	2.05446i	−0.0862790	−	0.149440i
$190$	−4.74456			−0.344207
$191$	−4.62772	+	8.01544i	−0.334850	+	0.579977i	−0.983456	−	0.181147i	$-0.942019\pi$
$191$	−4.62772	+	8.01544i	−0.334850	+	0.579977i	0.648606	+	0.761124i	$0.275352\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	6.18614	+	10.7147i	0.445288	+	0.771262i	0.998072	−	0.0620628i	$-0.0197679\pi$
$193$	6.18614	+	10.7147i	0.445288	+	0.771262i	−0.552784	+	0.833325i	$0.686435\pi$
$194$	−16.3723			−1.17546
$195$	1.00000	−	1.73205i	0.0716115	−	0.124035i
$196$	0.686141	−	1.18843i	0.0490100	−	0.0848879i
$197$	8.37228	−	14.5012i	0.596500	−	1.03317i	−0.396833	−	0.917891i	$-0.629891\pi$
$197$	8.37228	−	14.5012i	0.596500	−	1.03317i	0.993333	−	0.115278i	$-0.0367759\pi$
$198$	2.50000	+	4.33013i	0.177667	+	0.307729i
$199$	−2.81386	+	4.87375i	−0.199469	+	0.345491i	−0.948356	−	0.317207i	$-0.897255\pi$
$199$	−2.81386	+	4.87375i	−0.199469	+	0.345491i	0.748887	+	0.662697i	$0.230588\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−10.1168			−0.713587
$202$	8.48913			0.597293
$203$	4.30298	+	7.45299i	0.302010	+	0.523097i
$204$	2.68614	−	4.65253i	0.188067	−	0.325742i
$205$	3.37228	+	5.84096i	0.235530	+	0.407951i
$206$	−0.186141	+	0.322405i	−0.0129690	+	0.0224630i
$207$	−4.05842	+	7.02939i	−0.282080	+	0.488577i
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	−23.7228			−1.64094
$210$	−1.18614	−	2.05446i	−0.0818515	−	0.141771i
$211$	4.37228	+	7.57301i	0.301000	+	0.521348i	0.976363	−	0.216138i	$-0.0693462\pi$
$211$	4.37228	+	7.57301i	0.301000	+	0.521348i	−0.675363	+	0.737486i	$0.736013\pi$
$212$	0.813859	−	1.40965i	0.0558961	−	0.0968149i
$213$	−2.74456			−0.188054
$214$	−2.81386	−	4.87375i	−0.192351	−	0.333163i
$215$	−3.37228			−0.229988
$216$	−1.00000			−0.0680414
$217$	−5.93070	−	11.8020i	−0.402602	−	0.801169i
$218$	−8.74456			−0.592257
$219$	14.0000			0.946032
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$	−10.7446			−0.722757
$222$	5.05842	−	8.76144i	0.339499	−	0.588030i
$223$	−5.81386	−	10.0699i	−0.389325	−	0.674330i	0.603034	−	0.797715i	$-0.293958\pi$
$223$	−5.81386	−	10.0699i	−0.389325	−	0.674330i	−0.992359	+	0.123385i	$0.960625\pi$
$224$	1.18614	+	2.05446i	0.0792524	+	0.137269i
$225$	1.00000			0.0666667
$226$	8.05842	−	13.9576i	0.536038	−	0.928445i
$227$	13.5584	−	23.4839i	0.899904	−	1.55868i	0.0722888	−	0.997384i	$-0.476970\pi$
$227$	13.5584	−	23.4839i	0.899904	−	1.55868i	0.827615	−	0.561296i	$-0.189697\pi$
$228$	2.37228	−	4.10891i	0.157108	−	0.272119i
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$	−4.05842	+	7.02939i	−0.267604	+	0.463504i
$231$	−5.93070	−	10.2723i	−0.390212	−	0.675866i
$232$	3.62772			0.238171
$233$	−16.8614			−1.10463			−0.552314	−	0.833636i	$-0.686255\pi$
$233$	−16.8614			−1.10463			−0.552314	+	0.833636i	$0.686255\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	6.05842	−	10.4935i	0.395208	−	0.684520i
$236$	5.55842	+	9.62747i	0.361822	+	0.626695i
$237$	1.68614	−	2.92048i	0.109527	−	0.189706i
$238$	−6.37228	+	11.0371i	−0.413054	+	0.715430i
$239$	1.74456	−	3.02167i	0.112846	−	0.195456i	−0.804070	−	0.594534i	$-0.797337\pi$
$239$	1.74456	−	3.02167i	0.112846	−	0.195456i	0.916917	+	0.399078i	$0.130670\pi$
$240$	−1.00000			−0.0645497
$241$	−8.55842	−	14.8236i	−0.551296	−	0.954873i	−0.998181	−	0.0602820i	$-0.980800\pi$
$241$	−8.55842	−	14.8236i	−0.551296	−	0.954873i	0.446885	−	0.894591i	$-0.352533\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.00000			−0.128037
$245$	−0.686141	−	1.18843i	−0.0438359	−	0.0759260i
$246$	−6.74456			−0.430018
$247$	−9.48913			−0.603779
$248$	−5.55842	−	0.322405i	−0.352960	−	0.0204727i
$249$	2.37228			0.150337
$250$	1.00000			0.0632456
$251$	−1.68614	−	2.92048i	−0.106428	−	0.184339i	0.807893	−	0.589330i	$-0.200608\pi$
$251$	−1.68614	−	2.92048i	−0.106428	−	0.184339i	−0.914321	+	0.404991i	$0.867275\pi$
$252$	2.37228			0.149440
$253$	−20.2921	+	35.1470i	−1.27575	+	2.20967i
$254$	−1.81386	−	3.14170i	−0.113812	−	0.197128i
$255$	−2.68614	−	4.65253i	−0.168213	−	0.291353i
$256$	1.00000			0.0625000
$257$	12.1753	−	21.0882i	0.759472	−	1.31544i	−0.183648	−	0.982992i	$-0.558791\pi$
$257$	12.1753	−	21.0882i	0.759472	−	1.31544i	0.943120	−	0.332452i	$-0.107876\pi$
$258$	1.68614	−	2.92048i	0.104975	−	0.181821i
$259$	−12.0000	+	20.7846i	−0.745644	+	1.29149i
$260$	1.00000	+	1.73205i	0.0620174	+	0.107417i
$261$	1.81386	−	3.14170i	0.112275	−	0.194466i
$262$	−9.05842	−	15.6896i	−0.559631	−	0.969310i
$263$	−21.6060			−1.33228			−0.666141	−	0.745826i	$-0.732055\pi$
$263$	−21.6060			−1.33228			−0.666141	+	0.745826i	$0.732055\pi$
$264$	−5.00000			−0.307729
$265$	−0.813859	−	1.40965i	−0.0499950	−	0.0865938i
$266$	−5.62772	+	9.74749i	−0.345058	+	0.597657i
$267$		0			0
$268$	5.05842	−	8.76144i	0.308992	−	0.535190i
$269$	12.6861	−	21.9730i	0.773488	−	1.33972i	−0.162153	−	0.986766i	$-0.551844\pi$
$269$	12.6861	−	21.9730i	0.773488	−	1.33972i	0.935641	−	0.352954i	$-0.114823\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	27.1168			1.64723			0.823615	−	0.567149i	$-0.191953\pi$
$271$	27.1168			1.64723			0.823615	+	0.567149i	$0.191953\pi$
$272$	2.68614	+	4.65253i	0.162871	+	0.282101i
$273$	−2.37228	−	4.10891i	−0.143577	−	0.248683i
$274$	8.31386	−	14.4000i	0.502259	−	0.869937i
$275$	5.00000			0.301511
$276$	−4.05842	−	7.02939i	−0.244288	−	0.423120i
$277$	−17.3723			−1.04380			−0.521900	−	0.853007i	$-0.674776\pi$
$277$	−17.3723			−1.04380			−0.521900	+	0.853007i	$0.674776\pi$
$278$	10.7446			0.644416
$279$	−3.05842	+	4.65253i	−0.183103	+	0.278540i
$280$	2.37228			0.141771
$281$	20.2337			1.20704			0.603520	−	0.797348i	$-0.293764\pi$
$281$	20.2337			1.20704			0.603520	+	0.797348i	$0.293764\pi$
$282$	6.05842	+	10.4935i	0.360774	+	0.624879i
$283$	29.6060			1.75989			0.879946	−	0.475074i	$-0.157579\pi$
$283$	29.6060			1.75989			0.879946	+	0.475074i	$0.157579\pi$
$284$	1.37228	−	2.37686i	0.0814299	−	0.141041i
$285$	−2.37228	−	4.10891i	−0.140522	−	0.243391i
$286$	5.00000	+	8.66025i	0.295656	+	0.512092i
$287$	16.0000			0.944450
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−5.93070	+	10.2723i	−0.348865	+	0.604252i
$290$	1.81386	−	3.14170i	0.106513	−	0.184487i
$291$	−8.18614	−	14.1788i	−0.479880	−	0.831177i
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	−16.6753	−	28.8824i	−0.974179	−	1.68733i	−0.682617	−	0.730777i	$-0.739158\pi$
$293$	−16.6753	−	28.8824i	−0.974179	−	1.68733i	−0.291563	−	0.956552i	$-0.594175\pi$
$294$	1.37228			0.0800331
$295$	11.1168			0.647248
$296$	5.05842	+	8.76144i	0.294015	+	0.509249i
$297$	−2.50000	+	4.33013i	−0.145065	+	0.251259i
$298$	−4.93070	−	8.54023i	−0.285628	−	0.494722i
$299$	−8.11684	+	14.0588i	−0.469409	+	0.813041i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−4.00000	+	6.92820i	−0.230556	+	0.399335i
$302$	−5.00000			−0.287718
$303$	4.24456	+	7.35180i	0.243844	+	0.422350i
$304$	2.37228	+	4.10891i	0.136060	+	0.235662i
$305$	−1.00000	+	1.73205i	−0.0572598	+	0.0991769i
$306$	5.37228			0.307113
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	0.542194	−	0.840254i	$-0.317594\pi$
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	−0.998778	+	0.0494267i	$0.984261\pi$
$308$	11.8614			0.675866
$309$	−0.372281			−0.0211783
$310$	−3.05842	+	4.65253i	−0.173707	+	0.264246i
$311$	28.9783			1.64321			0.821603	−	0.570060i	$-0.193080\pi$
$311$	28.9783			1.64321			0.821603	+	0.570060i	$0.193080\pi$
$312$	−2.00000			−0.113228
$313$	15.6753	+	27.1504i	0.886018	+	1.53463i	0.844542	+	0.535489i	$0.179873\pi$
$313$	15.6753	+	27.1504i	0.886018	+	1.53463i	0.0414765	+	0.999139i	$0.486794\pi$
$314$	−14.0000			−0.790066
$315$	1.18614	−	2.05446i	0.0668315	−	0.115755i
$316$	1.68614	+	2.92048i	0.0948528	+	0.164290i
$317$	−3.18614	−	5.51856i	−0.178951	−	0.309953i	0.762570	−	0.646905i	$-0.223937\pi$
$317$	−3.18614	−	5.51856i	−0.178951	−	0.309953i	−0.941522	+	0.336952i	$0.890604\pi$
$318$	1.62772			0.0912779
$319$	9.06930	−	15.7085i	0.507783	−	0.879506i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	2.81386	−	4.87375i	0.157054	−	0.272026i
$322$	9.62772	+	16.6757i	0.536532	+	0.929300i
$323$	−12.7446	+	22.0742i	−0.709126	+	1.22824i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.00000			0.110940
$326$	13.3723			0.740622
$327$	−4.37228	−	7.57301i	−0.241788	−	0.418789i
$328$	3.37228	−	5.84096i	0.186203	−	0.322513i
$329$	−14.3723	−	24.8935i	−0.792370	−	1.37242i
$330$	−2.50000	+	4.33013i	−0.137620	+	0.238366i
$331$	−7.62772	+	13.2116i	−0.419257	+	0.726175i	−0.995865	−	0.0908462i	$-0.971043\pi$
$331$	−7.62772	+	13.2116i	−0.419257	+	0.726175i	0.576608	+	0.817021i	$0.304376\pi$
$332$	−1.18614	+	2.05446i	−0.0650979	+	0.112753i
$333$	10.1168			0.554400
$334$	4.74456	+	8.21782i	0.259611	+	0.449659i
$335$	−5.05842	−	8.76144i	−0.276371	−	0.478689i
$336$	−1.18614	+	2.05446i	−0.0647093	+	0.112080i
$337$	−9.62772			−0.524455			−0.262228	−	0.965006i	$-0.584457\pi$
$337$	−9.62772			−0.524455			−0.262228	+	0.965006i	$0.584457\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	16.1168			0.875347
$340$	5.37228			0.291353
$341$	−15.2921	+	23.2627i	−0.828114	+	1.25974i
$342$	4.74456			0.256557
$343$	−19.8614			−1.07242
$344$	1.68614	+	2.92048i	0.0909106	+	0.157462i
$345$	−8.11684			−0.436996
$346$	6.93070	−	12.0043i	0.372597	−	0.645357i
$347$	5.30298	+	9.18504i	0.284679	+	0.493079i	0.972531	−	0.232772i	$-0.0747796\pi$
$347$	5.30298	+	9.18504i	0.284679	+	0.493079i	−0.687852	+	0.725851i	$0.741446\pi$
$348$	1.81386	+	3.14170i	0.0972331	+	0.168413i
$349$	11.4891			0.614999			0.307499	−	0.951548i	$-0.400508\pi$
$349$	11.4891			0.614999			0.307499	+	0.951548i	$0.400508\pi$
$350$	1.18614	−	2.05446i	0.0634019	−	0.109815i
$351$	−1.00000	+	1.73205i	−0.0533761	+	0.0924500i
$352$	2.50000	−	4.33013i	0.133250	−	0.230797i
$353$	−5.43070	−	9.40625i	−0.289047	−	0.500644i	0.684535	−	0.728980i	$-0.260005\pi$
$353$	−5.43070	−	9.40625i	−0.289047	−	0.500644i	−0.973583	+	0.228335i	$0.926672\pi$
$354$	−5.55842	+	9.62747i	−0.295427	+	0.511694i
$355$	−1.37228	−	2.37686i	−0.0728331	−	0.126151i
$356$		0			0
$357$	−12.7446			−0.674514
$358$	0.244563	+	0.423595i	0.0129255	+	0.0223877i
$359$	−9.62772	+	16.6757i	−0.508132	+	0.880110i	0.491824	+	0.870695i	$0.336330\pi$
$359$	−9.62772	+	16.6757i	−0.508132	+	0.880110i	−0.999956	+	0.00941510i	$0.997003\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	−1.75544	+	3.04051i	−0.0923914	+	0.160027i
$362$	11.4891	−	19.8997i	0.603855	−	1.04591i
$363$	−7.00000	+	12.1244i	−0.367405	+	0.636364i
$364$	4.74456			0.248683
$365$	7.00000	+	12.1244i	0.366397	+	0.634618i
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	−5.25544	+	9.10268i	−0.274332	+	0.475156i	−0.969966	−	0.243239i	$-0.921790\pi$
$367$	−5.25544	+	9.10268i	−0.274332	+	0.475156i	0.695635	+	0.718396i	$0.255123\pi$
$368$	8.11684			0.423120
$369$	−3.37228	−	5.84096i	−0.175554	−	0.304068i
$370$	10.1168			0.525950
$371$	−3.86141			−0.200474
$372$	−2.50000	−	4.97494i	−0.129619	−	0.257938i
$373$	−15.8832			−0.822399			−0.411199	−	0.911545i	$-0.634890\pi$
$373$	−15.8832			−0.822399			−0.411199	+	0.911545i	$0.634890\pi$
$374$	26.8614			1.38897
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−12.1168			−0.624879
$377$	3.62772	−	6.28339i	0.186837	−	0.323611i
$378$	1.18614	+	2.05446i	0.0610085	+	0.105670i
$379$	−3.37228	−	5.84096i	−0.173222	−	0.300030i	0.766322	−	0.642456i	$-0.222085\pi$
$379$	−3.37228	−	5.84096i	−0.173222	−	0.300030i	−0.939545	+	0.342426i	$0.888751\pi$
$380$	4.74456			0.243391
$381$	1.81386	−	3.14170i	0.0929268	−	0.160954i
$382$	4.62772	−	8.01544i	0.236775	−	0.410106i
$383$	−7.68614	+	13.3128i	−0.392743	+	0.680252i	−0.992810	−	0.119698i	$-0.961807\pi$
$383$	−7.68614	+	13.3128i	−0.392743	+	0.680252i	0.600067	+	0.799950i	$0.295141\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	5.93070	−	10.2723i	0.302257	−	0.523524i
$386$	−6.18614	−	10.7147i	−0.314866	−	0.545364i
$387$	3.37228			0.171423
$388$	16.3723			0.831177
$389$	7.31386	+	12.6680i	0.370827	+	0.642292i	0.989693	−	0.143205i	$-0.0457408\pi$
$389$	7.31386	+	12.6680i	0.370827	+	0.642292i	−0.618866	+	0.785497i	$0.712407\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$	21.8030	+	37.7639i	1.10262	+	1.90980i
$392$	−0.686141	+	1.18843i	−0.0346553	+	0.0600248i
$393$	9.05842	−	15.6896i	0.456937	−	0.791438i
$394$	−8.37228	+	14.5012i	−0.421789	+	0.730561i
$395$	3.37228			0.169678
$396$	−2.50000	−	4.33013i	−0.125630	−	0.217597i
$397$	2.43070	+	4.21010i	0.121994	+	0.211299i	0.920554	−	0.390616i	$-0.127738\pi$
$397$	2.43070	+	4.21010i	0.121994	+	0.211299i	−0.798560	+	0.601915i	$0.794405\pi$
$398$	2.81386	−	4.87375i	0.141046	−	0.244299i
$399$	−11.2554			−0.563477
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	4.51087			0.225262			0.112631	−	0.993637i	$-0.464072\pi$
$401$	4.51087			0.225262			0.112631	+	0.993637i	$0.464072\pi$
$402$	10.1168			0.504582
$403$	−6.11684	+	9.30506i	−0.304702	+	0.463518i
$404$	−8.48913			−0.422350
$405$	−1.00000			−0.0496904
$406$	−4.30298	−	7.45299i	−0.213554	−	0.369886i
$407$	50.5842			2.50737
$408$	−2.68614	+	4.65253i	−0.132984	+	0.230335i
$409$	−6.98913	−	12.1055i	−0.345590	−	0.598579i	0.639871	−	0.768483i	$-0.278988\pi$
$409$	−6.98913	−	12.1055i	−0.345590	−	0.598579i	−0.985461	+	0.169903i	$0.945655\pi$
$410$	−3.37228	−	5.84096i	−0.166545	−	0.288465i
$411$	16.6277			0.820185
$412$	0.186141	−	0.322405i	0.00917049	−	0.0158838i
$413$	13.1861	−	22.8391i	0.648848	−	1.12384i
$414$	4.05842	−	7.02939i	0.199461	−	0.345476i
$415$	1.18614	+	2.05446i	0.0582254	+	0.100849i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	5.37228	+	9.30506i	0.263082	+	0.455671i
$418$	23.7228			1.16032
$419$	−12.4891			−0.610134			−0.305067	−	0.952331i	$-0.598679\pi$
$419$	−12.4891			−0.610134			−0.305067	+	0.952331i	$0.598679\pi$
$420$	1.18614	+	2.05446i	0.0578777	+	0.100247i
$421$	−4.25544	+	7.37063i	−0.207397	+	0.359223i	−0.950894	−	0.309517i	$-0.899833\pi$
$421$	−4.25544	+	7.37063i	−0.207397	+	0.359223i	0.743497	+	0.668740i	$0.233166\pi$
$422$	−4.37228	−	7.57301i	−0.212839	−	0.368649i
$423$	−6.05842	+	10.4935i	−0.294571	+	0.510211i
$424$	−0.813859	+	1.40965i	−0.0395245	+	0.0684584i
$425$	2.68614	−	4.65253i	0.130297	−	0.225681i
$426$	2.74456			0.132974
$427$	2.37228	+	4.10891i	0.114803	+	0.198844i
$428$	2.81386	+	4.87375i	0.136013	+	0.235581i
$429$	−5.00000	+	8.66025i	−0.241402	+	0.418121i
$430$	3.37228			0.162626
$431$	−10.6277	−	18.4077i	−0.511919	−	0.886670i	−0.999905	−	0.0138182i	$-0.995601\pi$
$431$	−10.6277	−	18.4077i	−0.511919	−	0.886670i	0.487985	−	0.872852i	$-0.337732\pi$
$432$	1.00000			0.0481125
$433$	6.23369			0.299572			0.149786	−	0.988718i	$-0.452142\pi$
$433$	6.23369			0.299572			0.149786	+	0.988718i	$0.452142\pi$
$434$	5.93070	+	11.8020i	0.284683	+	0.566512i
$435$	3.62772			0.173936
$436$	8.74456			0.418789
$437$	19.2554	+	33.3514i	0.921112	+	1.59541i
$438$	−14.0000			−0.668946
$439$	3.50000	−	6.06218i	0.167046	−	0.289332i	−0.770334	−	0.637641i	$-0.779911\pi$
$439$	3.50000	−	6.06218i	0.167046	−	0.289332i	0.937380	+	0.348309i	$0.113244\pi$
$440$	−2.50000	−	4.33013i	−0.119183	−	0.206431i
$441$	0.686141	+	1.18843i	0.0326734	+	0.0565919i
$442$	10.7446			0.511067
$443$	−8.86141	+	15.3484i	−0.421018	+	0.729225i	−0.996039	−	0.0889137i	$-0.971660\pi$
$443$	−8.86141	+	15.3484i	−0.421018	+	0.729225i	0.575021	+	0.818139i	$0.304994\pi$
$444$	−5.05842	+	8.76144i	−0.240062	+	0.415800i
$445$		0			0
$446$	5.81386	+	10.0699i	0.275294	+	0.476824i
$447$	4.93070	−	8.54023i	0.233214	−	0.403939i
$448$	−1.18614	−	2.05446i	−0.0560399	−	0.0970639i
$449$	13.2554			0.625563			0.312781	−	0.949825i	$-0.398739\pi$
$449$	13.2554			0.625563			0.312781	+	0.949825i	$0.398739\pi$
$450$	−1.00000			−0.0471405
$451$	−16.8614	−	29.2048i	−0.793973	−	1.37520i
$452$	−8.05842	+	13.9576i	−0.379036	+	0.656510i
$453$	−2.50000	−	4.33013i	−0.117460	−	0.203447i
$454$	−13.5584	+	23.4839i	−0.636328	+	1.10215i
$455$	2.37228	−	4.10891i	0.111214	−	0.192629i
$456$	−2.37228	+	4.10891i	−0.111092	+	0.192417i
$457$	15.2554			0.713619			0.356810	−	0.934177i	$-0.383864\pi$
$457$	15.2554			0.713619			0.356810	+	0.934177i	$0.383864\pi$
$458$	8.00000	+	13.8564i	0.373815	+	0.647467i
$459$	2.68614	+	4.65253i	0.125378	+	0.217162i
$460$	4.05842	−	7.02939i	0.189225	−	0.327747i
$461$	−25.0000			−1.16437			−0.582183	−	0.813058i	$-0.697801\pi$
$461$	−25.0000			−1.16437			−0.582183	+	0.813058i	$0.697801\pi$
$462$	5.93070	+	10.2723i	0.275921	+	0.477910i
$463$	24.6060			1.14354			0.571768	−	0.820415i	$-0.306258\pi$
$463$	24.6060			1.14354			0.571768	+	0.820415i	$0.306258\pi$
$464$	−3.62772			−0.168413
$465$	−5.55842	−	0.322405i	−0.257766	−	0.0149512i
$466$	16.8614			0.781090
$467$	−31.1168			−1.43992			−0.719958	−	0.694018i	$-0.755839\pi$
$467$	−31.1168			−1.43992			−0.719958	+	0.694018i	$0.755839\pi$
$468$	−1.00000	−	1.73205i	−0.0462250	−	0.0800641i
$469$	−24.0000			−1.10822
$470$	−6.05842	+	10.4935i	−0.279454	+	0.484029i
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$	−5.55842	−	9.62747i	−0.255847	−	0.443140i
$473$	16.8614			0.775288
$474$	−1.68614	+	2.92048i	−0.0774470	+	0.134142i
$475$	2.37228	−	4.10891i	0.108848	−	0.188530i
$476$	6.37228	−	11.0371i	0.292073	−	0.505885i
$477$	0.813859	+	1.40965i	0.0372641	+	0.0645432i
$478$	−1.74456	+	3.02167i	−0.0797944	+	0.138208i
$479$	−13.0000	−	22.5167i	−0.593985	−	1.02881i	−0.993689	−	0.112168i	$-0.964220\pi$
$479$	−13.0000	−	22.5167i	−0.593985	−	1.02881i	0.399704	−	0.916644i	$-0.369113\pi$
$480$	1.00000			0.0456435
$481$	20.2337			0.922577
$482$	8.55842	+	14.8236i	0.389825	+	0.675197i
$483$	−9.62772	+	16.6757i	−0.438076	+	0.758771i
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	8.18614	−	14.1788i	0.371713	−	0.643827i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	0.813859	−	1.40965i	0.0368795	−	0.0638771i	−0.846997	−	0.531598i	$-0.821592\pi$
$487$	0.813859	−	1.40965i	0.0368795	−	0.0638771i	0.883876	+	0.467721i	$0.154925\pi$
$488$	2.00000			0.0905357
$489$	6.68614	+	11.5807i	0.302358	+	0.523699i
$490$	0.686141	+	1.18843i	0.0309967	+	0.0536878i
$491$	11.5000	−	19.9186i	0.518988	−	0.898913i	−0.480769	−	0.876847i	$-0.659642\pi$
$491$	11.5000	−	19.9186i	0.518988	−	0.898913i	0.999757	−	0.0220657i	$-0.00702431\pi$
$492$	6.74456			0.304068
$493$	−9.74456	−	16.8781i	−0.438873	−	0.760150i
$494$	9.48913			0.426936
$495$	−5.00000			−0.224733
$496$	5.55842	+	0.322405i	0.249581	+	0.0144764i
$497$	−6.51087			−0.292053
$498$	−2.37228			−0.106304
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	0.699903	−	0.714238i	$-0.253227\pi$
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	−0.968500	+	0.249015i	$0.919893\pi$
$500$	−1.00000			−0.0447214
$501$	−4.74456	+	8.21782i	−0.211971	+	0.367145i
$502$	1.68614	+	2.92048i	0.0752561	+	0.130347i
$503$	8.74456	+	15.1460i	0.389901	+	0.675328i	0.992436	−	0.122764i	$-0.0391760\pi$
$503$	8.74456	+	15.1460i	0.389901	+	0.675328i	−0.602535	+	0.798092i	$0.705843\pi$
$504$	−2.37228			−0.105670
$505$	−4.24456	+	7.35180i	−0.188881	+	0.327151i
$506$	20.2921	−	35.1470i	0.902094	−	1.56247i
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	1.81386	+	3.14170i	0.0804770	+	0.139390i
$509$	9.61684	−	16.6569i	0.426259	−	0.738302i	−0.570278	−	0.821452i	$-0.693165\pi$
$509$	9.61684	−	16.6569i	0.426259	−	0.738302i	0.996537	+	0.0831493i	$0.0264978\pi$
$510$	2.68614	+	4.65253i	0.118944	+	0.206018i
$511$	33.2119			1.46921
$512$	−1.00000			−0.0441942
$513$	2.37228	+	4.10891i	0.104739	+	0.181413i
$514$	−12.1753	+	21.0882i	−0.537028	+	0.930160i
$515$	−0.186141	−	0.322405i	−0.00820234	−	0.0142069i
$516$	−1.68614	+	2.92048i	−0.0742282	+	0.128567i
$517$	−30.2921	+	52.4675i	−1.33225	+	2.30752i
$518$	12.0000	−	20.7846i	0.527250	−	0.913223i
$519$	13.8614			0.608448
$520$	−1.00000	−	1.73205i	−0.0438529	−	0.0759555i
$521$	−4.37228	−	7.57301i	−0.191553	−	0.331780i	0.754212	−	0.656631i	$-0.228019\pi$
$521$	−4.37228	−	7.57301i	−0.191553	−	0.331780i	−0.945765	+	0.324851i	$0.894686\pi$
$522$	−1.81386	+	3.14170i	−0.0793905	+	0.137508i
$523$	7.37228			0.322367			0.161184	−	0.986924i	$-0.448469\pi$
$523$	7.37228			0.322367			0.161184	+	0.986924i	$0.448469\pi$
$524$	9.05842	+	15.6896i	0.395719	+	0.685405i
$525$	2.37228			0.103535
$526$	21.6060			0.942065
$527$	13.4307	+	26.7268i	0.585051	+	1.16424i
$528$	5.00000			0.217597
$529$	42.8832			1.86449
$530$	0.813859	+	1.40965i	0.0353518	+	0.0612311i
$531$	−11.1168			−0.482430
$532$	5.62772	−	9.74749i	0.243993	−	0.422607i
$533$	−6.74456	−	11.6819i	−0.292139	−	0.506000i
$534$		0			0
$535$	5.62772			0.243307
$536$	−5.05842	+	8.76144i	−0.218491	+	0.378437i
$537$	−0.244563	+	0.423595i	−0.0105537	+	0.0182795i
$538$	−12.6861	+	21.9730i	−0.546938	+	0.947325i
$539$	3.43070	+	5.94215i	0.147771	+	0.255947i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	13.2337	+	22.9214i	0.568961	+	0.985469i	0.996669	+	0.0815520i	$0.0259877\pi$
$541$	13.2337	+	22.9214i	0.568961	+	0.985469i	−0.427708	+	0.903917i	$0.640679\pi$
$542$	−27.1168			−1.16477
$543$	22.9783			0.986091
$544$	−2.68614	−	4.65253i	−0.115167	−	0.199476i
$545$	4.37228	−	7.57301i	0.187288	−	0.324392i
$546$	2.37228	+	4.10891i	0.101524	+	0.175845i
$547$	17.6861	−	30.6333i	0.756205	−	1.30979i	−0.188568	−	0.982060i	$-0.560385\pi$
$547$	17.6861	−	30.6333i	0.756205	−	1.30979i	0.944773	−	0.327725i	$-0.106282\pi$
$548$	−8.31386	+	14.4000i	−0.355150	+	0.615139i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	−5.00000			−0.213201
$551$	−8.60597	−	14.9060i	−0.366627	−	0.635016i
$552$	4.05842	+	7.02939i	0.172738	+	0.299191i
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$	17.3723			0.738078
$555$	5.05842	+	8.76144i	0.214718	+	0.371903i
$556$	−10.7446			−0.455671
$557$	−22.3723			−0.947944			−0.473972	−	0.880540i	$-0.657180\pi$
$557$	−22.3723			−0.947944			−0.473972	+	0.880540i	$0.657180\pi$
$558$	3.05842	−	4.65253i	0.129473	−	0.196957i
$559$	6.74456			0.285265
$560$	−2.37228			−0.100247
$561$	13.4307	+	23.2627i	0.567045	+	0.982150i
$562$	−20.2337			−0.853507
$563$	18.0475	−	31.2593i	0.760613	−	1.31742i	−0.181921	−	0.983313i	$-0.558232\pi$
$563$	18.0475	−	31.2593i	0.760613	−	1.31742i	0.942535	−	0.334108i	$-0.108435\pi$
$564$	−6.05842	−	10.4935i	−0.255106	−	0.441856i
$565$	8.05842	+	13.9576i	0.339020	+	0.587200i
$566$	−29.6060			−1.24443
$567$	−1.18614	+	2.05446i	−0.0498132	+	0.0862790i
$568$	−1.37228	+	2.37686i	−0.0575796	+	0.0997309i
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	−0.741981	−	0.670421i	$-0.766114\pi$
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	0.951592	+	0.307364i	$0.0994469\pi$
$570$	2.37228	+	4.10891i	0.0993639	+	0.172103i
$571$	−14.7446	+	25.5383i	−0.617041	+	1.06875i	0.372982	+	0.927839i	$0.378335\pi$
$571$	−14.7446	+	25.5383i	−0.617041	+	1.06875i	−0.990023	+	0.140907i	$0.954998\pi$
$572$	−5.00000	−	8.66025i	−0.209061	−	0.362103i
$573$	9.25544			0.386651
$574$	−16.0000			−0.667827
$575$	−4.05842	−	7.02939i	−0.169248	−	0.293146i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−21.8614	−	37.8651i	−0.910102	−	1.57634i	−0.813918	−	0.580980i	$-0.802670\pi$
$577$	−21.8614	−	37.8651i	−0.910102	−	1.57634i	−0.0961843	−	0.995364i	$-0.530664\pi$
$578$	5.93070	−	10.2723i	0.246685	−	0.427270i
$579$	6.18614	−	10.7147i	0.257087	−	0.445288i
$580$	−1.81386	+	3.14170i	−0.0753164	+	0.130452i
$581$	5.62772			0.233477
$582$	8.18614	+	14.1788i	0.339326	+	0.587731i
$583$	4.06930	+	7.04823i	0.168533	+	0.291908i
$584$	7.00000	−	12.1244i	0.289662	−	0.501709i
$585$	−2.00000			−0.0826898
$586$	16.6753	+	28.8824i	0.688849	+	1.19312i
$587$	−33.1168			−1.36688			−0.683439	−	0.730007i	$-0.739517\pi$
$587$	−33.1168			−1.36688			−0.683439	+	0.730007i	$0.739517\pi$
$588$	−1.37228			−0.0565919
$589$	11.8614	+	23.6039i	0.488741	+	0.972582i
$590$	−11.1168			−0.457673
$591$	−16.7446			−0.688779
$592$	−5.05842	−	8.76144i	−0.207900	−	0.360093i
$593$	−37.7228			−1.54909			−0.774545	−	0.632519i	$-0.782021\pi$
$593$	−37.7228			−1.54909			−0.774545	+	0.632519i	$0.782021\pi$
$594$	2.50000	−	4.33013i	0.102576	−	0.177667i
$595$	−6.37228	−	11.0371i	−0.261238	−	0.452478i
$596$	4.93070	+	8.54023i	0.201969	+	0.349821i
$597$	5.62772			0.230327
$598$	8.11684	−	14.0588i	0.331922	−	0.574907i
$599$	−13.3723	+	23.1615i	−0.546377	+	0.946352i	0.452142	+	0.891946i	$0.350660\pi$
$599$	−13.3723	+	23.1615i	−0.546377	+	0.946352i	−0.998519	+	0.0544062i	$0.982673\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	16.1753	+	28.0164i	0.659803	+	1.14281i	0.980666	+	0.195687i	$0.0626936\pi$
$601$	16.1753	+	28.0164i	0.659803	+	1.14281i	−0.320864	+	0.947125i	$0.603973\pi$
$602$	4.00000	−	6.92820i	0.163028	−	0.282372i
$603$	5.05842	+	8.76144i	0.205995	+	0.356794i
$604$	5.00000			0.203447
$605$	−14.0000			−0.569181
$606$	−4.24456	−	7.35180i	−0.172424	−	0.298646i
$607$	−22.2337	+	38.5099i	−0.902438	+	1.56307i	−0.0781171	+	0.996944i	$0.524891\pi$
$607$	−22.2337	+	38.5099i	−0.902438	+	1.56307i	−0.824320	+	0.566124i	$0.808443\pi$
$608$	−2.37228	−	4.10891i	−0.0962087	−	0.166638i
$609$	4.30298	−	7.45299i	0.174366	−	0.302010i
$610$	1.00000	−	1.73205i	0.0404888	−	0.0701287i
$611$	−12.1168	+	20.9870i	−0.490195	+	0.849043i
$612$	−5.37228			−0.217162
$613$	−11.3723	−	19.6974i	−0.459322	−	0.795569i	0.539603	−	0.841920i	$-0.318574\pi$
$613$	−11.3723	−	19.6974i	−0.459322	−	0.795569i	−0.998925	+	0.0463503i	$0.985241\pi$
$614$	8.00000	+	13.8564i	0.322854	+	0.559199i
$615$	3.37228	−	5.84096i	0.135984	−	0.235530i
$616$	−11.8614			−0.477910
$617$	−3.43070	−	5.94215i	−0.138115	−	0.239222i	0.788668	−	0.614819i	$-0.210771\pi$
$617$	−3.43070	−	5.94215i	−0.138115	−	0.239222i	−0.926783	+	0.375597i	$0.877438\pi$
$618$	0.372281			0.0149754
$619$	14.9783			0.602027			0.301013	−	0.953620i	$-0.402675\pi$
$619$	14.9783			0.602027			0.301013	+	0.953620i	$0.402675\pi$
$620$	3.05842	−	4.65253i	0.122829	−	0.186850i
$621$	8.11684			0.325718
$622$	−28.9783			−1.16192
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−15.6753	−	27.1504i	−0.626510	−	1.08515i
$627$	11.8614	+	20.5446i	0.473699	+	0.820471i
$628$	14.0000			0.558661
$629$	27.1753	−	47.0689i	1.08355	−	1.87676i
$630$	−1.18614	+	2.05446i	−0.0472570	+	0.0818515i
$631$	8.98913	−	15.5696i	0.357851	−	0.619817i	−0.629750	−	0.776798i	$-0.716843\pi$
$631$	8.98913	−	15.5696i	0.357851	−	0.619817i	0.987602	+	0.156981i	$0.0501761\pi$
$632$	−1.68614	−	2.92048i	−0.0670711	−	0.116171i
$633$	4.37228	−	7.57301i	0.173783	−	0.301000i
$634$	3.18614	+	5.51856i	0.126538	+	0.219170i
$635$	3.62772			0.143962
$636$	−1.62772			−0.0645432
$637$	1.37228	+	2.37686i	0.0543718	+	0.0941747i
$638$	−9.06930	+	15.7085i	−0.359057	+	0.621905i
$639$	1.37228	+	2.37686i	0.0542866	+	0.0940272i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	6.37228	−	11.0371i	0.251690	−	0.435940i	−0.712301	−	0.701874i	$-0.752347\pi$
$641$	6.37228	−	11.0371i	0.251690	−	0.435940i	0.963991	+	0.265934i	$0.0856803\pi$
$642$	−2.81386	+	4.87375i	−0.111054	+	0.192351i
$643$	24.7446			0.975830			0.487915	−	0.872891i	$-0.337758\pi$
$643$	24.7446			0.975830			0.487915	+	0.872891i	$0.337758\pi$
$644$	−9.62772	−	16.6757i	−0.379385	−	0.657115i
$645$	1.68614	+	2.92048i	0.0663917	+	0.114994i
$646$	12.7446	−	22.0742i	0.501428	−	0.868499i
$647$	4.74456			0.186528			0.0932640	−	0.995641i	$-0.470270\pi$
$647$	4.74456			0.186528			0.0932640	+	0.995641i	$0.470270\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−55.5842			−2.18187
$650$	−2.00000			−0.0784465
$651$	−7.25544	+	11.0371i	−0.284363	+	0.432579i
$652$	−13.3723			−0.523699
$653$	−4.88316			−0.191093			−0.0955463	−	0.995425i	$-0.530460\pi$
$653$	−4.88316			−0.191093			−0.0955463	+	0.995425i	$0.530460\pi$
$654$	4.37228	+	7.57301i	0.170970	+	0.296128i
$655$	18.1168			0.707884
$656$	−3.37228	+	5.84096i	−0.131665	+	0.228051i
$657$	−7.00000	−	12.1244i	−0.273096	−	0.473016i
$658$	14.3723	+	24.8935i	0.560290	+	0.970451i
$659$	39.2337			1.52833			0.764164	−	0.645022i	$-0.223152\pi$
$659$	39.2337			1.52833			0.764164	+	0.645022i	$0.223152\pi$
$660$	2.50000	−	4.33013i	0.0973124	−	0.168550i
$661$	6.48913	−	11.2395i	0.252398	−	0.437166i	−0.711788	−	0.702395i	$-0.752114\pi$
$661$	6.48913	−	11.2395i	0.252398	−	0.437166i	0.964185	+	0.265229i	$0.0854475\pi$
$662$	7.62772	−	13.2116i	0.296460	−	0.513483i
$663$	5.37228	+	9.30506i	0.208642	+	0.361379i
$664$	1.18614	−	2.05446i	0.0460312	−	0.0797284i
$665$	−5.62772	−	9.74749i	−0.218234	−	0.377992i
$666$	−10.1168			−0.392020
$667$	−29.4456			−1.14014
$668$	−4.74456	−	8.21782i	−0.183573	−	0.317957i
$669$	−5.81386	+	10.0699i	−0.224777	+	0.389325i
$670$	5.05842	+	8.76144i	0.195424	+	0.338484i
$671$	5.00000	−	8.66025i	0.193023	−	0.334325i
$672$	1.18614	−	2.05446i	0.0457564	−	0.0792524i
$673$	0.930703	−	1.61203i	0.0358760	−	0.0621390i	−0.847530	−	0.530748i	$-0.821911\pi$
$673$	0.930703	−	1.61203i	0.0358760	−	0.0621390i	0.883406	+	0.468609i	$0.155245\pi$
$674$	9.62772			0.370846
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−1.67527	+	2.90165i	−0.0643857	+	0.111519i	−0.896421	−	0.443203i	$-0.853842\pi$
$677$	−1.67527	+	2.90165i	−0.0643857	+	0.111519i	0.832036	+	0.554722i	$0.187175\pi$
$678$	−16.1168			−0.618964
$679$	−19.4198	−	33.6361i	−0.745265	−	1.29084i
$680$	−5.37228			−0.206018
$681$	−27.1168			−1.03912
$682$	15.2921	−	23.2627i	0.585565	−	0.890773i
$683$	−46.8397			−1.79227			−0.896135	−	0.443782i	$-0.853637\pi$
$683$	−46.8397			−1.79227			−0.896135	+	0.443782i	$0.853637\pi$
$684$	−4.74456			−0.181413
$685$	8.31386	+	14.4000i	0.317656	+	0.550197i
$686$	19.8614			0.758312
$687$	−8.00000	+	13.8564i	−0.305219	+	0.528655i
$688$	−1.68614	−	2.92048i	−0.0642835	−	0.111342i
$689$	1.62772	+	2.81929i	0.0620111	+	0.107406i
$690$	8.11684			0.309003
$691$	17.3723	−	30.0897i	0.660873	−	1.14467i	−0.319514	−	0.947582i	$-0.603520\pi$
$691$	17.3723	−	30.0897i	0.660873	−	1.14467i	0.980387	−	0.197084i	$-0.0631470\pi$
$692$	−6.93070	+	12.0043i	−0.263466	+	0.456336i
$693$	−5.93070	+	10.2723i	−0.225289	+	0.390212i
$694$	−5.30298	−	9.18504i	−0.201299	−	0.348659i
$695$	−5.37228	+	9.30506i	−0.203782	+	0.352961i
$696$	−1.81386	−	3.14170i	−0.0687542	−	0.119086i
$697$	−36.2337			−1.37245
$698$	−11.4891			−0.434870
$699$	8.43070	+	14.6024i	0.318878	+	0.552314i
$700$	−1.18614	+	2.05446i	−0.0448319	+	0.0776511i
$701$	−18.6168	−	32.2453i	−0.703148	−	1.21789i	−0.967356	−	0.253423i	$-0.918444\pi$
$701$	−18.6168	−	32.2453i	−0.703148	−	1.21789i	0.264207	−	0.964466i	$-0.414890\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$	24.0000	−	41.5692i	0.905177	−	1.56781i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	−12.1168			−0.456347
$706$	5.43070	+	9.40625i	0.204387	+	0.354009i
$707$	10.0693	+	17.4405i	0.378695	+	0.655919i
$708$	5.55842	−	9.62747i	0.208898	−	0.361822i
$709$	−3.76631			−0.141447			−0.0707234	−	0.997496i	$-0.522531\pi$
$709$	−3.76631			−0.141447			−0.0707234	+	0.997496i	$0.522531\pi$
$710$	1.37228	+	2.37686i	0.0515008	+	0.0892020i
$711$	−3.37228			−0.126470
$712$		0			0
$713$	45.1168	+	2.61691i	1.68964	+	0.0980041i
$714$	12.7446			0.476953
$715$	−10.0000			−0.373979
$716$	−0.244563	−	0.423595i	−0.00913974	−	0.0158305i
$717$	−3.48913			−0.130304
$718$	9.62772	−	16.6757i	0.359303	−	0.622332i
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	0.998224	−	0.0595683i	$-0.0189724\pi$
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	−0.550700	+	0.834703i	$0.685639\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−0.883156			−0.0328904
$722$	1.75544	−	3.04051i	0.0653306	−	0.113156i
$723$	−8.55842	+	14.8236i	−0.318291	+	0.551296i
$724$	−11.4891	+	19.8997i	−0.426990	+	0.739568i
$725$	1.81386	+	3.14170i	0.0673650	+	0.116680i
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	2.67527	+	4.63370i	0.0992201	+	0.171854i	0.911362	−	0.411606i	$-0.135032\pi$
$727$	2.67527	+	4.63370i	0.0992201	+	0.171854i	−0.812142	+	0.583460i	$0.801699\pi$
$728$	−4.74456			−0.175845
$729$	1.00000			0.0370370
$730$	−7.00000	−	12.1244i	−0.259082	−	0.448743i
$731$	9.05842	−	15.6896i	0.335038	−	0.580303i
$732$	1.00000	+	1.73205i	0.0369611	+	0.0640184i
$733$	0.686141	−	1.18843i	0.0253432	−	0.0438957i	−0.853076	−	0.521787i	$-0.825265\pi$
$733$	0.686141	−	1.18843i	0.0253432	−	0.0438957i	0.878419	+	0.477892i	$0.158599\pi$
$734$	5.25544	−	9.10268i	0.193982	−	0.335986i
$735$	−0.686141	+	1.18843i	−0.0253087	+	0.0438359i
$736$	−8.11684			−0.299191
$737$	25.2921	+	43.8072i	0.931647	+	1.61366i
$738$	3.37228	+	5.84096i	0.124135	+	0.215009i
$739$	18.1168	−	31.3793i	0.666439	−	1.15431i	−0.312454	−	0.949933i	$-0.601151\pi$
$739$	18.1168	−	31.3793i	0.666439	−	1.15431i	0.978893	−	0.204373i	$-0.0655156\pi$
$740$	−10.1168			−0.371903
$741$	4.74456	+	8.21782i	0.174296	+	0.301889i
$742$	3.86141			0.141757
$743$	24.6277			0.903503			0.451752	−	0.892144i	$-0.350799\pi$
$743$	24.6277			0.903503			0.451752	+	0.892144i	$0.350799\pi$
$744$	2.50000	+	4.97494i	0.0916544	+	0.182390i
$745$	9.86141			0.361294
$746$	15.8832			0.581524
$747$	−1.18614	−	2.05446i	−0.0433986	−	0.0751686i
$748$	−26.8614			−0.982150
$749$	6.67527	−	11.5619i	0.243909	−	0.422463i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−13.3614	−	23.1426i	−0.487565	−	0.844487i	0.512333	−	0.858787i	$-0.328781\pi$
$751$	−13.3614	−	23.1426i	−0.487565	−	0.844487i	−0.999898	+	0.0143001i	$0.995448\pi$
$752$	12.1168			0.441856
$753$	−1.68614	+	2.92048i	−0.0614464	+	0.106428i
$754$	−3.62772	+	6.28339i	−0.132114	+	0.228828i
$755$	2.50000	−	4.33013i	0.0909843	−	0.157589i
$756$	−1.18614	−	2.05446i	−0.0431395	−	0.0747198i
$757$	−12.9416	+	22.4155i	−0.470370	+	0.814704i	−0.999426	−	0.0338827i	$-0.989213\pi$
$757$	−12.9416	+	22.4155i	−0.470370	+	0.814704i	0.529056	+	0.848587i	$0.322546\pi$
$758$	3.37228	+	5.84096i	0.122487	+	0.212153i
$759$	40.5842			1.47311
$760$	−4.74456			−0.172103
$761$	−22.2337	−	38.5099i	−0.805971	−	1.39598i	−0.915634	−	0.402013i	$-0.868311\pi$
$761$	−22.2337	−	38.5099i	−0.805971	−	1.39598i	0.109663	−	0.993969i	$-0.465023\pi$
$762$	−1.81386	+	3.14170i	−0.0657092	+	0.113812i
$763$	−10.3723	−	17.9653i	−0.375502	−	0.650388i
$764$	−4.62772	+	8.01544i	−0.167425	+	0.289989i
$765$	−2.68614	+	4.65253i	−0.0971176	+	0.168213i
$766$	7.68614	−	13.3128i	0.277712	−	0.481011i
$767$	−22.2337			−0.802812
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−17.6753	−	30.6145i	−0.637386	−	1.10399i	−0.986004	−	0.166721i	$-0.946682\pi$
$769$	−17.6753	−	30.6145i	−0.637386	−	1.10399i	0.348618	−	0.937265i	$-0.386651\pi$
$770$	−5.93070	+	10.2723i	−0.213728	+	0.370187i
$771$	−24.3505			−0.876963
$772$	6.18614	+	10.7147i	0.222644	+	0.385631i
$773$	−32.9783			−1.18615			−0.593073	−	0.805149i	$-0.702085\pi$
$773$	−32.9783			−1.18615			−0.593073	+	0.805149i	$0.702085\pi$
$774$	−3.37228			−0.121214
$775$	−2.50000	−	4.97494i	−0.0898027	−	0.178705i
$776$	−16.3723			−0.587731
$777$	24.0000			0.860995
$778$	−7.31386	−	12.6680i	−0.262215	−	0.454169i
$779$	−32.0000			−1.14652
$780$	1.00000	−	1.73205i	0.0358057	−	0.0620174i
$781$	6.86141	+	11.8843i	0.245520	+	0.425254i
$782$	−21.8030	−	37.7639i	−0.779673	−	1.35043i
$783$	−3.62772			−0.129644
$784$	0.686141	−	1.18843i	0.0245050	−	0.0424439i
$785$	7.00000	−	12.1244i	0.249841	−	0.432737i
$786$	−9.05842	+	15.6896i	−0.323103	+	0.559631i
$787$	12.0584	+	20.8858i	0.429836	+	0.744498i	0.996858	−	0.0792042i	$-0.0252379\pi$
$787$	12.0584	+	20.8858i	0.429836	+	0.744498i	−0.567022	+	0.823703i	$0.691905\pi$
$788$	8.37228	−	14.5012i	0.298250	−	0.516584i
$789$	10.8030	+	18.7113i	0.384596	+	0.666141i
$790$	−3.37228			−0.119980
$791$	38.2337			1.35943
$792$	2.50000	+	4.33013i	0.0888336	+	0.153864i
$793$	2.00000	−	3.46410i	0.0710221	−	0.123014i
$794$	−2.43070	−	4.21010i	−0.0862624	−	0.149411i
$795$	−0.813859	+	1.40965i	−0.0288646	+	0.0499950i
$796$	−2.81386	+	4.87375i	−0.0997346	+	0.172745i
$797$	−18.3030	+	31.7017i	−0.648325	+	1.12293i	0.335198	+	0.942148i	$0.391197\pi$
$797$	−18.3030	+	31.7017i	−0.648325	+	1.12293i	−0.983523	+	0.180784i	$0.942136\pi$
$798$	11.2554			0.398438
$799$	32.5475	+	56.3740i	1.15145	+	1.99437i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−4.51087			−0.159285
$803$	−35.0000	−	60.6218i	−1.23512	−	2.13930i
$804$	−10.1168			−0.356794
$805$	−19.2554			−0.678665
$806$	6.11684	−	9.30506i	0.215457	−	0.327757i
$807$	−25.3723			−0.893147
$808$	8.48913			0.298646
$809$	17.1168	+	29.6472i	0.601796	+	1.04234i	0.992549	+	0.121846i	$0.0388814\pi$
$809$	17.1168	+	29.6472i	0.601796	+	1.04234i	−0.390753	+	0.920496i	$0.627785\pi$
$810$	1.00000			0.0351364
$811$	0.372281	−	0.644810i	0.0130726	−	0.0226423i	−0.859415	−	0.511278i	$-0.829172\pi$
$811$	0.372281	−	0.644810i	0.0130726	−	0.0226423i	0.872488	+	0.488636i	$0.162505\pi$
$812$	4.30298	+	7.45299i	0.151005	+	0.261549i
$813$	−13.5584	−	23.4839i	−0.475515	−	0.823615i
$814$	−50.5842			−1.77298
$815$	−6.68614	+	11.5807i	−0.234205	+	0.405655i
$816$	2.68614	−	4.65253i	0.0940337	−	0.162871i
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	6.98913	+	12.1055i	0.244369	+	0.423260i
$819$	−2.37228	+	4.10891i	−0.0828942	+	0.143577i
$820$	3.37228	+	5.84096i	0.117765	+	0.203975i
$821$	8.76631			0.305946			0.152973	−	0.988230i	$-0.451115\pi$
$821$	8.76631			0.305946			0.152973	+	0.988230i	$0.451115\pi$
$822$	−16.6277			−0.579958
$823$	−12.4198	−	21.5118i	−0.432928	−	0.749853i	0.564196	−	0.825641i	$-0.309186\pi$
$823$	−12.4198	−	21.5118i	−0.432928	−	0.749853i	−0.997124	+	0.0757876i	$0.975853\pi$
$824$	−0.186141	+	0.322405i	−0.00648452	+	0.0112315i
$825$	−2.50000	−	4.33013i	−0.0870388	−	0.150756i
$826$	−13.1861	+	22.8391i	−0.458805	+	0.794673i
$827$	−0.510875	+	0.884861i	−0.0177649	+	0.0307696i	−0.874771	−	0.484536i	$-0.838988\pi$
$827$	−0.510875	+	0.884861i	−0.0177649	+	0.0307696i	0.857006	+	0.515306i	$0.172322\pi$
$828$	−4.05842	+	7.02939i	−0.141040	+	0.244288i
$829$	50.0000			1.73657			0.868286	−	0.496064i	$-0.165222\pi$
$829$	50.0000			1.73657			0.868286	+	0.496064i	$0.165222\pi$
$830$	−1.18614	−	2.05446i	−0.0411715	−	0.0713112i
$831$	8.68614	+	15.0448i	0.301319	+	0.521900i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	7.37228			0.255434
$834$	−5.37228	−	9.30506i	−0.186027	−	0.322208i
$835$	−9.48913			−0.328385
$836$	−23.7228			−0.820471
$837$	5.55842	+	0.322405i	0.192127	+	0.0111439i
$838$	12.4891			0.431430
$839$	−28.9783			−1.00044			−0.500220	−	0.865898i	$-0.666748\pi$
$839$	−28.9783			−1.00044			−0.500220	+	0.865898i	$0.666748\pi$
$840$	−1.18614	−	2.05446i	−0.0409257	−	0.0708855i
$841$	−15.8397			−0.546195
$842$	4.25544	−	7.37063i	0.146652	−	0.254009i
$843$	−10.1168	−	17.5229i	−0.348443	−	0.603520i
$844$	4.37228	+	7.57301i	0.150500	+	0.260674i
$845$	9.00000			0.309609
$846$	6.05842	−	10.4935i	0.208293	−	0.360774i
$847$	−16.6060	+	28.7624i	−0.570588	+	0.988287i
$848$	0.813859	−	1.40965i	0.0279480	−	0.0484074i
$849$	−14.8030	−	25.6395i	−0.508037	−	0.879946i
$850$	−2.68614	+	4.65253i	−0.0921339	+	0.159581i
$851$	−41.0584	−	71.1153i	−1.40746	−	2.43780i
$852$	−2.74456			−0.0940272
$853$	−12.2337			−0.418873			−0.209437	−	0.977822i	$-0.567163\pi$
$853$	−12.2337			−0.418873			−0.209437	+	0.977822i	$0.567163\pi$
$854$	−2.37228	−	4.10891i	−0.0811778	−	0.140604i
$855$	−2.37228	+	4.10891i	−0.0811303	+	0.140522i
$856$	−2.81386	−	4.87375i	−0.0961757	−	0.166581i
$857$	17.8030	−	30.8357i	0.608138	−	1.05333i	−0.383409	−	0.923579i	$-0.625250\pi$
$857$	17.8030	−	30.8357i	0.608138	−	1.05333i	0.991547	−	0.129748i	$-0.0414168\pi$
$858$	5.00000	−	8.66025i	0.170697	−	0.295656i
$859$	−1.48913	+	2.57924i	−0.0508083	+	0.0880026i	−0.890311	−	0.455353i	$-0.849513\pi$
$859$	−1.48913	+	2.57924i	−0.0508083	+	0.0880026i	0.839503	+	0.543355i	$0.182846\pi$
$860$	−3.37228			−0.114994
$861$	−8.00000	−	13.8564i	−0.272639	−	0.472225i
$862$	10.6277	+	18.4077i	0.361982	+	0.626970i
$863$	13.6861	−	23.7051i	0.465882	−	0.806931i	−0.533359	−	0.845889i	$-0.679071\pi$
$863$	13.6861	−	23.7051i	0.465882	−	0.806931i	0.999241	+	0.0389582i	$0.0124039\pi$
$864$	−1.00000			−0.0340207
$865$	6.93070	+	12.0043i	0.235651	+	0.408159i
$866$	−6.23369			−0.211829
$867$	11.8614			0.402834
$868$	−5.93070	−	11.8020i	−0.201301	−	0.400584i
$869$	−16.8614			−0.571984
$870$	−3.62772			−0.122991
$871$	10.1168	+	17.5229i	0.342796	+	0.593740i
$872$	−8.74456			−0.296128
$873$	−8.18614	+	14.1788i	−0.277059	+	0.479880i
$874$	−19.2554	−	33.3514i	−0.651325	−	1.12813i
$875$	1.18614	+	2.05446i	0.0400989	+	0.0694533i
$876$	14.0000			0.473016
$877$	−0.802985	+	1.39081i	−0.0271149	+	0.0469643i	−0.879264	−	0.476334i	$-0.841965\pi$
$877$	−0.802985	+	1.39081i	−0.0271149	+	0.0469643i	0.852150	+	0.523298i	$0.175299\pi$
$878$	−3.50000	+	6.06218i	−0.118119	+	0.204589i
$879$	−16.6753	+	28.8824i	−0.562443	+	0.974179i
$880$	2.50000	+	4.33013i	0.0842750	+	0.145969i
$881$	−20.2337	+	35.0458i	−0.681690	+	1.18072i	0.292774	+	0.956182i	$0.405421\pi$
$881$	−20.2337	+	35.0458i	−0.681690	+	1.18072i	−0.974465	+	0.224541i	$0.927912\pi$
$882$	−0.686141	−	1.18843i	−0.0231036	−	0.0400165i
$883$	−31.6060			−1.06363			−0.531813	−	0.846862i	$-0.678489\pi$
$883$	−31.6060			−1.06363			−0.531813	+	0.846862i	$0.678489\pi$
$884$	−10.7446			−0.361379
$885$	−5.55842	−	9.62747i	−0.186844	−	0.323624i
$886$	8.86141	−	15.3484i	0.297705	−	0.515640i
$887$	4.43070	+	7.67420i	0.148768	+	0.257675i	0.930773	−	0.365599i	$-0.119136\pi$
$887$	4.43070	+	7.67420i	0.148768	+	0.257675i	−0.782004	+	0.623273i	$0.785802\pi$
$888$	5.05842	−	8.76144i	0.169750	−	0.294015i
$889$	4.30298	−	7.45299i	0.144317	−	0.249965i
$890$		0			0
$891$	5.00000			0.167506
$892$	−5.81386	−	10.0699i	−0.194662	−	0.337165i
$893$	28.7446	+	49.7870i	0.961900	+	1.66606i
$894$	−4.93070	+	8.54023i	−0.164907	+	0.285628i
$895$	−0.489125			−0.0163497
$896$	1.18614	+	2.05446i	0.0396262	+	0.0686346i
$897$	16.2337			0.542027
$898$	−13.2554			−0.442340
$899$	−20.1644	−	1.16959i	−0.672520	−	0.0390082i
$900$	1.00000			0.0333333
$901$	8.74456			0.291324
$902$	16.8614	+	29.2048i	0.561423	+	0.972414i
$903$	8.00000			0.266223
$904$	8.05842	−	13.9576i	0.268019	−	0.464223i
$905$	11.4891	+	19.8997i	0.381911	+	0.661490i
$906$	2.50000	+	4.33013i	0.0830569	+	0.143859i
$907$	−30.2337			−1.00389			−0.501947	−	0.864899i	$-0.667383\pi$
$907$	−30.2337			−1.00389			−0.501947	+	0.864899i	$0.667383\pi$
$908$	13.5584	−	23.4839i	0.449952	−	0.779340i
$909$	4.24456	−	7.35180i	0.140783	−	0.243844i
$910$	−2.37228	+	4.10891i	−0.0786404	+	0.136209i
$911$	17.4891	+	30.2921i	0.579441	+	1.00362i	0.995544	+	0.0943030i	$0.0300623\pi$
$911$	17.4891	+	30.2921i	0.579441	+	1.00362i	−0.416103	+	0.909318i	$0.636604\pi$
$912$	2.37228	−	4.10891i	0.0785541	−	0.136060i
$913$	−5.93070	−	10.2723i	−0.196278	−	0.339963i
$914$	−15.2554			−0.504605
$915$	2.00000			0.0661180
$916$	−8.00000	−	13.8564i	−0.264327	−	0.457829i
$917$	21.4891	−	37.2203i	0.709633	−	1.22912i
$918$	−2.68614	−	4.65253i	−0.0886559	−	0.153556i
$919$	−1.61684	+	2.80046i	−0.0533348	+	0.0923785i	−0.891460	−	0.453099i	$-0.850318\pi$
$919$	−1.61684	+	2.80046i	−0.0533348	+	0.0923785i	0.838125	+	0.545478i	$0.183652\pi$
$920$	−4.05842	+	7.02939i	−0.133802	+	0.231752i
$921$	−8.00000	+	13.8564i	−0.263609	+	0.456584i
$922$	25.0000			0.823331
$923$	2.74456	+	4.75372i	0.0903384	+	0.156471i
$924$	−5.93070	−	10.2723i	−0.195106	−	0.337933i
$925$	−5.05842	+	8.76144i	−0.166320	+	0.288075i
$926$	−24.6060			−0.808602
$927$	0.186141	+	0.322405i	0.00611366	+	0.0105892i
$928$	3.62772			0.119086
$929$	−19.2554			−0.631750			−0.315875	−	0.948801i	$-0.602298\pi$
$929$	−19.2554			−0.631750			−0.315875	+	0.948801i	$0.602298\pi$
$930$	5.55842	+	0.322405i	0.182268	+	0.0105721i
$931$	6.51087			0.213385
$932$	−16.8614			−0.552314
$933$	−14.4891	−	25.0959i	−0.474353	−	0.821603i
$934$	31.1168			1.01817
$935$	−13.4307	+	23.2627i	−0.439231	+	0.760770i
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	−14.2554	−	24.6911i	−0.465705	−	0.806624i	0.533528	−	0.845782i	$-0.320866\pi$
$937$	−14.2554	−	24.6911i	−0.465705	−	0.806624i	−0.999233	+	0.0391578i	$0.987532\pi$
$938$	24.0000			0.783628
$939$	15.6753	−	27.1504i	0.511543	−	0.886018i
$940$	6.05842	−	10.4935i	0.197604	−	0.342260i
$941$	−18.9891	+	32.8901i	−0.619028	+	1.07219i	0.370636	+	0.928778i	$0.379140\pi$
$941$	−18.9891	+	32.8901i	−0.619028	+	1.07219i	−0.989663	+	0.143409i	$0.954193\pi$
$942$	7.00000	+	12.1244i	0.228072	+	0.395033i
$943$	−27.3723	+	47.4102i	−0.891364	+	1.54389i
$944$	5.55842	+	9.62747i	0.180911	+	0.313347i
$945$	−2.37228			−0.0771703
$946$	−16.8614			−0.548212
$947$	10.8614	+	18.8125i	0.352948	+	0.611324i	0.986765	−	0.162159i	$-0.0518458\pi$
$947$	10.8614	+	18.8125i	0.352948	+	0.611324i	−0.633816	+	0.773484i	$0.718512\pi$
$948$	1.68614	−	2.92048i	0.0547633	−	0.0948528i
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$	−2.37228	+	4.10891i	−0.0769670	+	0.133311i
$951$	−3.18614	+	5.51856i	−0.103318	+	0.178951i
$952$	−6.37228	+	11.0371i	−0.206527	+	0.357715i
$953$	−19.4891			−0.631315			−0.315657	−	0.948873i	$-0.602225\pi$
$953$	−19.4891			−0.631315			−0.315657	+	0.948873i	$0.602225\pi$
$954$	−0.813859	−	1.40965i	−0.0263497	−	0.0456390i
$955$	4.62772	+	8.01544i	0.149749	+	0.259374i
$956$	1.74456	−	3.02167i	0.0564232	−	0.0977278i
$957$	−18.1386			−0.586337
$958$	13.0000	+	22.5167i	0.420011	+	0.727480i
$959$	39.4456			1.27377
$960$	−1.00000			−0.0322749
$961$	30.7921	+	3.58413i	0.993294	+	0.115617i
$962$	−20.2337			−0.652360
$963$	−5.62772			−0.181351
$964$	−8.55842	−	14.8236i	−0.275648	−	0.477437i
$965$	12.3723			0.398278
$966$	9.62772	−	16.6757i	0.309767	−	0.536532i
$967$	−26.7446	−	46.3229i	−0.860047	−	1.48965i	−0.871882	−	0.489715i	$-0.837101\pi$
$967$	−26.7446	−	46.3229i	−0.860047	−	1.48965i	0.0118352	−	0.999930i	$-0.496233\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$	25.4891			0.818829
$970$	−8.18614	+	14.1788i	−0.262841	+	0.455254i
$971$	−20.1277	+	34.8622i	−0.645929	+	1.11878i	0.338157	+	0.941090i	$0.390197\pi$
$971$	−20.1277	+	34.8622i	−0.645929	+	1.11878i	−0.984086	+	0.177692i	$0.943137\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	12.7446	+	22.0742i	0.408572	+	0.707667i
$974$	−0.813859	+	1.40965i	−0.0260777	+	0.0451680i
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$	−2.00000			−0.0640184
$977$	34.7446			1.11158			0.555789	−	0.831324i	$-0.312416\pi$
$977$	34.7446			1.11158			0.555789	+	0.831324i	$0.312416\pi$
$978$	−6.68614	−	11.5807i	−0.213799	−	0.370311i
$979$		0			0
$980$	−0.686141	−	1.18843i	−0.0219180	−	0.0379630i
$981$	−4.37228	+	7.57301i	−0.139596	+	0.241788i
$982$	−11.5000	+	19.9186i	−0.366980	+	0.635628i
$983$	−15.2554	+	26.4232i	−0.486573	+	0.842769i	−0.999881	−	0.0154355i	$-0.995087\pi$
$983$	−15.2554	+	26.4232i	−0.486573	+	0.842769i	0.513308	+	0.858204i	$0.328420\pi$
$984$	−6.74456			−0.215009
$985$	−8.37228	−	14.5012i	−0.266763	−	0.462047i
$986$	9.74456	+	16.8781i	0.310330	+	0.537507i
$987$	−14.3723	+	24.8935i	−0.457475	+	0.792370i
$988$	−9.48913			−0.301889
$989$	−13.6861	−	23.7051i	−0.435194	−	0.753778i
$990$	5.00000			0.158910
$991$	−36.4674			−1.15842			−0.579212	−	0.815177i	$-0.696640\pi$
$991$	−36.4674			−1.15842			−0.579212	+	0.815177i	$0.696640\pi$
$992$	−5.55842	−	0.322405i	−0.176480	−	0.0102364i
$993$	15.2554			0.484117
$994$	6.51087			0.206512
$995$	2.81386	+	4.87375i	0.0892053	+	0.154508i
$996$	2.37228			0.0751686
$997$	21.6060	−	37.4226i	0.684268	−	1.18519i	−0.289398	−	0.957209i	$-0.593455\pi$
$997$	21.6060	−	37.4226i	0.684268	−	1.18519i	0.973666	−	0.227978i	$-0.0732114\pi$
$998$	6.00000	+	10.3923i	0.189927	+	0.328963i
$999$	−5.05842	−	8.76144i	−0.160041	−	0.277200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.k.211.1	✓	4
31.5	even	3	inner	930.2.i.k.811.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.k.211.1	✓	4	1.1	even	1	trivial
930.2.i.k.811.1	yes	4	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(1.18614 + 2.05446i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(2.68614 + 4.65253i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.37228 + 4.10891i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.18614 + 2.05446i) q^{21} +(2.50000 - 4.33013i) q^{22} +8.11684 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(-1.18614 - 2.05446i) q^{28} -3.62772 q^{29} +1.00000 q^{30} +(5.55842 + 0.322405i) q^{31} -1.00000 q^{32} +5.00000 q^{33} +(-2.68614 - 4.65253i) q^{34} -2.37228 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.05842 - 8.76144i) q^{37} +(-2.37228 - 4.10891i) q^{38} +2.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.37228 + 5.84096i) q^{41} +(1.18614 - 2.05446i) q^{42} +(-1.68614 - 2.92048i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(0.500000 + 0.866025i) q^{45} -8.11684 q^{46} +12.1168 q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.686141 - 1.18843i) q^{49} +(0.500000 + 0.866025i) q^{50} +(2.68614 - 4.65253i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(0.813859 - 1.40965i) q^{53} -1.00000 q^{54} +(2.50000 + 4.33013i) q^{55} +(1.18614 + 2.05446i) q^{56} +(2.37228 - 4.10891i) q^{57} +3.62772 q^{58} +(5.55842 + 9.62747i) q^{59} -1.00000 q^{60} -2.00000 q^{61} +(-5.55842 - 0.322405i) q^{62} +2.37228 q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} -5.00000 q^{66} +(5.05842 - 8.76144i) q^{67} +(2.68614 + 4.65253i) q^{68} +(-4.05842 - 7.02939i) q^{69} +2.37228 q^{70} +(1.37228 - 2.37686i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(5.05842 + 8.76144i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(2.37228 + 4.10891i) q^{76} +11.8614 q^{77} -2.00000 q^{78} +(1.68614 + 2.92048i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.37228 - 5.84096i) q^{82} +(-1.18614 + 2.05446i) q^{83} +(-1.18614 + 2.05446i) q^{84} +5.37228 q^{85} +(1.68614 + 2.92048i) q^{86} +(1.81386 + 3.14170i) q^{87} +(2.50000 - 4.33013i) q^{88} +(-0.500000 - 0.866025i) q^{90} +4.74456 q^{91} +8.11684 q^{92} +(-2.50000 - 4.97494i) q^{93} -12.1168 q^{94} +4.74456 q^{95} +(0.500000 + 0.866025i) q^{96} +16.3723 q^{97} +(-0.686141 + 1.18843i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} - 10 q^{11} - 2 q^{12} - 4 q^{13} - q^{14} - 4 q^{15} + 4 q^{16} + 5 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} + q^{21} + 10 q^{22} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} + q^{28} - 26 q^{29} + 4 q^{30} + 5 q^{31} - 4 q^{32} + 20 q^{33} - 5 q^{34} + 2 q^{35} - 2 q^{36} - 3 q^{37} + 2 q^{38} + 8 q^{39} - 2 q^{40} - 2 q^{41} - q^{42} - q^{43} - 10 q^{44} + 2 q^{45} + 2 q^{46} + 14 q^{47} - 2 q^{48} - 3 q^{49} + 2 q^{50} + 5 q^{51} - 4 q^{52} + 9 q^{53} - 4 q^{54} + 10 q^{55} - q^{56} - 2 q^{57} + 26 q^{58} + 5 q^{59} - 4 q^{60} - 8 q^{61} - 5 q^{62} - 2 q^{63} + 4 q^{64} + 4 q^{65} - 20 q^{66} + 3 q^{67} + 5 q^{68} + q^{69} - 2 q^{70} - 6 q^{71} + 2 q^{72} - 28 q^{73} + 3 q^{74} - 2 q^{75} - 2 q^{76} - 10 q^{77} - 8 q^{78} + q^{79} + 2 q^{80} - 2 q^{81} + 2 q^{82} + q^{83} + q^{84} + 10 q^{85} + q^{86} + 13 q^{87} + 10 q^{88} - 2 q^{90} - 4 q^{91} - 2 q^{92} - 10 q^{93} - 14 q^{94} - 4 q^{95} + 2 q^{96} + 54 q^{97} + 3 q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 - 10 * q^11 - 2 * q^12 - 4 * q^13 - q^14 - 4 * q^15 + 4 * q^16 + 5 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 + q^21 + 10 * q^22 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 + q^28 - 26 * q^29 + 4 * q^30 + 5 * q^31 - 4 * q^32 + 20 * q^33 - 5 * q^34 + 2 * q^35 - 2 * q^36 - 3 * q^37 + 2 * q^38 + 8 * q^39 - 2 * q^40 - 2 * q^41 - q^42 - q^43 - 10 * q^44 + 2 * q^45 + 2 * q^46 + 14 * q^47 - 2 * q^48 - 3 * q^49 + 2 * q^50 + 5 * q^51 - 4 * q^52 + 9 * q^53 - 4 * q^54 + 10 * q^55 - q^56 - 2 * q^57 + 26 * q^58 + 5 * q^59 - 4 * q^60 - 8 * q^61 - 5 * q^62 - 2 * q^63 + 4 * q^64 + 4 * q^65 - 20 * q^66 + 3 * q^67 + 5 * q^68 + q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 - 28 * q^73 + 3 * q^74 - 2 * q^75 - 2 * q^76 - 10 * q^77 - 8 * q^78 + q^79 + 2 * q^80 - 2 * q^81 + 2 * q^82 + q^83 + q^84 + 10 * q^85 + q^86 + 13 * q^87 + 10 * q^88 - 2 * q^90 - 4 * q^91 - 2 * q^92 - 10 * q^93 - 14 * q^94 - 4 * q^95 + 2 * q^96 + 54 * q^97 + 3 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more