LMFDB - Embedded newform 630.2.i.f.121.5

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:	12.0.91830304992969.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 4x^{9} - 7x^{8} + x^{7} + 7x^{6} + 2x^{5} - 28x^{4} + 32x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 4x^9 - 7x^8 + x^7 + 7x^6 + 2x^5 - 28x^4 + 32x^3 + 16x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.5
Root			$-1.41396 - 0.0268737i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.f.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.35166 - 1.08306i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.35166 + 1.08306i) q^{6} +(2.32383 + 1.26483i) q^{7} -1.00000 q^{8} +(0.653981 - 2.92785i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.35166 - 1.08306i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.35166 + 1.08306i) q^{6} +(2.32383 + 1.26483i) q^{7} -1.00000 q^{8} +(0.653981 - 2.92785i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.975553 + 1.68971i) q^{11} +(1.35166 - 1.08306i) q^{12} +(2.18226 - 3.77979i) q^{13} +(-2.32383 - 1.26483i) q^{14} +(-1.61378 - 0.629046i) q^{15} +1.00000 q^{16} +(2.22435 + 3.85269i) q^{17} +(-0.653981 + 2.92785i) q^{18} +(2.18226 - 3.77979i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(4.51092 - 0.807211i) q^{21} +(0.975553 - 1.68971i) q^{22} +(-0.957909 - 1.65915i) q^{23} +(-1.35166 + 1.08306i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.18226 + 3.77979i) q^{26} +(-2.28706 - 4.66576i) q^{27} +(2.32383 + 1.26483i) q^{28} +(0.725310 + 1.25627i) q^{29} +(1.61378 + 0.629046i) q^{30} +2.78372 q^{31} -1.00000 q^{32} +(0.511429 + 3.34049i) q^{33} +(-2.22435 - 3.85269i) q^{34} +(-0.0665372 - 2.64491i) q^{35} +(0.653981 - 2.92785i) q^{36} +(-1.44648 + 2.50538i) q^{37} +(-2.18226 + 3.77979i) q^{38} +(-1.14404 - 7.47251i) q^{39} +(0.500000 + 0.866025i) q^{40} +(4.07219 - 7.05324i) q^{41} +(-4.51092 + 0.807211i) q^{42} +(-1.39891 - 2.42298i) q^{43} +(-0.975553 + 1.68971i) q^{44} +(-2.86258 + 0.897561i) q^{45} +(0.957909 + 1.65915i) q^{46} -6.79782 q^{47} +(1.35166 - 1.08306i) q^{48} +(3.80039 + 5.87852i) q^{49} +(0.500000 - 0.866025i) q^{50} +(7.17925 + 2.79844i) q^{51} +(2.18226 - 3.77979i) q^{52} +(-3.07762 - 5.33060i) q^{53} +(2.28706 + 4.66576i) q^{54} +1.95111 q^{55} +(-2.32383 - 1.26483i) q^{56} +(-1.14404 - 7.47251i) q^{57} +(-0.725310 - 1.25627i) q^{58} -8.10635 q^{59} +(-1.61378 - 0.629046i) q^{60} +0.523345 q^{61} -2.78372 q^{62} +(5.22299 - 5.97665i) q^{63} +1.00000 q^{64} -4.36452 q^{65} +(-0.511429 - 3.34049i) q^{66} -11.0791 q^{67} +(2.22435 + 3.85269i) q^{68} +(-3.09172 - 1.20514i) q^{69} +(0.0665372 + 2.64491i) q^{70} +16.3384 q^{71} +(-0.653981 + 2.92785i) q^{72} +(7.69829 + 13.3338i) q^{73} +(1.44648 - 2.50538i) q^{74} +(0.262123 + 1.71210i) q^{75} +(2.18226 - 3.77979i) q^{76} +(-4.40422 + 2.69268i) q^{77} +(1.14404 + 7.47251i) q^{78} +7.55094 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-8.14462 - 3.82952i) q^{81} +(-4.07219 + 7.05324i) q^{82} +(1.48957 + 2.58002i) q^{83} +(4.51092 - 0.807211i) q^{84} +(2.22435 - 3.85269i) q^{85} +(1.39891 + 2.42298i) q^{86} +(2.34099 + 0.912507i) q^{87} +(0.975553 - 1.68971i) q^{88} +(4.62826 - 8.01637i) q^{89} +(2.86258 - 0.897561i) q^{90} +(9.85201 - 6.02339i) q^{91} +(-0.957909 - 1.65915i) q^{92} +(3.76264 - 3.01492i) q^{93} +6.79782 q^{94} -4.36452 q^{95} +(-1.35166 + 1.08306i) q^{96} +(-6.19076 - 10.7227i) q^{97} +(-3.80039 - 5.87852i) q^{98} +(4.30922 + 3.96131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * 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
$3$	1.35166	−	1.08306i	0.780382	−	0.625302i
$3$	1.35166	−	1.08306i	0.780382	−	0.625302i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.35166	+	1.08306i	−0.551814	+	0.442156i
$7$	2.32383	+	1.26483i	0.878326	+	0.478062i
$7$	2.32383	+	1.26483i	0.878326	+	0.478062i
$8$	−1.00000			−0.353553
$9$	0.653981	−	2.92785i	0.217994	−	0.975950i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.975553	+	1.68971i	−0.294140	+	0.509466i	−0.974785	−	0.223148i	$-0.928367\pi$
$11$	−0.975553	+	1.68971i	−0.294140	+	0.509466i	0.680644	+	0.732614i	$0.261700\pi$
$12$	1.35166	−	1.08306i	0.390191	−	0.312651i
$13$	2.18226	−	3.77979i	0.605250	−	1.04832i	−0.386761	−	0.922180i	$-0.626406\pi$
$13$	2.18226	−	3.77979i	0.605250	−	1.04832i	0.992012	−	0.126145i	$-0.0402604\pi$
$14$	−2.32383	−	1.26483i	−0.621070	−	0.338041i
$15$	−1.61378	−	0.629046i	−0.416677	−	0.162419i
$16$	1.00000			0.250000
$17$	2.22435	+	3.85269i	0.539485	+	0.934415i	0.998932	+	0.0462097i	$0.0147142\pi$
$17$	2.22435	+	3.85269i	0.539485	+	0.934415i	−0.459447	+	0.888205i	$0.651952\pi$
$18$	−0.653981	+	2.92785i	−0.154145	+	0.690101i
$19$	2.18226	−	3.77979i	0.500645	−	0.867143i	−0.499355	−	0.866398i	$-0.666430\pi$
$19$	2.18226	−	3.77979i	0.500645	−	0.867143i	1.00000		0.000745051i	$-0.000237157\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	4.51092	−	0.807211i	0.984364	−	0.176148i
$22$	0.975553	−	1.68971i	0.207989	−	0.360247i
$23$	−0.957909	−	1.65915i	−0.199738	−	0.345956i	0.748705	−	0.662903i	$-0.230676\pi$
$23$	−0.957909	−	1.65915i	−0.199738	−	0.345956i	−0.948443	+	0.316947i	$0.897342\pi$
$24$	−1.35166	+	1.08306i	−0.275907	+	0.221078i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.18226	+	3.77979i	−0.427977	+	0.741277i
$27$	−2.28706	−	4.66576i	−0.440146	−	0.897926i
$28$	2.32383	+	1.26483i	0.439163	+	0.239031i
$29$	0.725310	+	1.25627i	0.134687	+	0.233284i	0.925478	−	0.378802i	$-0.123664\pi$
$29$	0.725310	+	1.25627i	0.134687	+	0.233284i	−0.790791	+	0.612086i	$0.790331\pi$
$30$	1.61378	+	0.629046i	0.294635	+	0.114848i
$31$	2.78372			0.499970			0.249985	−	0.968250i	$-0.419574\pi$
$31$	2.78372			0.499970			0.249985	+	0.968250i	$0.419574\pi$
$32$	−1.00000			−0.176777
$33$	0.511429	+	3.34049i	0.0890284	+	0.581505i
$34$	−2.22435	−	3.85269i	−0.381473	−	0.660731i
$35$	−0.0665372	−	2.64491i	−0.0112468	−	0.447072i
$36$	0.653981	−	2.92785i	0.108997	−	0.487975i
$37$	−1.44648	+	2.50538i	−0.237800	+	0.411881i	−0.960083	−	0.279716i	$-0.909760\pi$
$37$	−1.44648	+	2.50538i	−0.237800	+	0.411881i	0.722283	+	0.691598i	$0.243093\pi$
$38$	−2.18226	+	3.77979i	−0.354010	+	0.613163i
$39$	−1.14404	−	7.47251i	−0.183193	−	1.19656i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	4.07219	−	7.05324i	0.635969	−	1.10153i	−0.350340	−	0.936623i	$-0.613934\pi$
$41$	4.07219	−	7.05324i	0.635969	−	1.10153i	0.986309	−	0.164908i	$-0.0527328\pi$
$42$	−4.51092	+	0.807211i	−0.696050	+	0.124555i
$43$	−1.39891	−	2.42298i	−0.213332	−	0.369501i	0.739423	−	0.673241i	$-0.235098\pi$
$43$	−1.39891	−	2.42298i	−0.213332	−	0.369501i	−0.952755	+	0.303739i	$0.901765\pi$
$44$	−0.975553	+	1.68971i	−0.147070	+	0.254733i
$45$	−2.86258	+	0.897561i	−0.426729	+	0.133801i
$46$	0.957909	+	1.65915i	0.141236	+	0.244628i
$47$	−6.79782			−0.991564			−0.495782	−	0.868447i	$-0.665118\pi$
$47$	−6.79782			−0.991564			−0.495782	+	0.868447i	$0.665118\pi$
$48$	1.35166	−	1.08306i	0.195096	−	0.156326i
$49$	3.80039	+	5.87852i	0.542913	+	0.839789i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	7.17925	+	2.79844i	1.00530	+	0.391860i
$52$	2.18226	−	3.77979i	0.302625	−	0.524162i
$53$	−3.07762	−	5.33060i	−0.422744	−	0.732214i	0.573463	−	0.819232i	$-0.305600\pi$
$53$	−3.07762	−	5.33060i	−0.422744	−	0.732214i	−0.996207	+	0.0870173i	$0.972266\pi$
$54$	2.28706	+	4.66576i	0.311230	+	0.634930i
$55$	1.95111			0.263087
$56$	−2.32383	−	1.26483i	−0.310535	−	0.169021i
$57$	−1.14404	−	7.47251i	−0.151532	−	0.989758i
$58$	−0.725310	−	1.25627i	−0.0952379	−	0.164957i
$59$	−8.10635			−1.05536			−0.527679	−	0.849444i	$-0.676938\pi$
$59$	−8.10635			−1.05536			−0.527679	+	0.849444i	$0.676938\pi$
$60$	−1.61378	−	0.629046i	−0.208339	−	0.0812095i
$61$	0.523345			0.0670074			0.0335037	−	0.999439i	$-0.489333\pi$
$61$	0.523345			0.0670074			0.0335037	+	0.999439i	$0.489333\pi$
$62$	−2.78372			−0.353532
$63$	5.22299	−	5.97665i	0.658035	−	0.752988i
$64$	1.00000			0.125000
$65$	−4.36452			−0.541352
$66$	−0.511429	−	3.34049i	−0.0629526	−	0.411186i
$67$	−11.0791			−1.35353			−0.676766	−	0.736198i	$-0.736619\pi$
$67$	−11.0791			−1.35353			−0.676766	+	0.736198i	$0.736619\pi$
$68$	2.22435	+	3.85269i	0.269742	+	0.467207i
$69$	−3.09172	−	1.20514i	−0.372199	−	0.145082i
$70$	0.0665372	+	2.64491i	0.00795272	+	0.316128i
$71$	16.3384			1.93902			0.969508	−	0.245059i	$-0.0788073\pi$
$71$	16.3384			1.93902			0.969508	+	0.245059i	$0.0788073\pi$
$72$	−0.653981	+	2.92785i	−0.0770724	+	0.345051i
$73$	7.69829	+	13.3338i	0.901017	+	1.56061i	0.826176	+	0.563412i	$0.190512\pi$
$73$	7.69829	+	13.3338i	0.901017	+	1.56061i	0.0748413	+	0.997195i	$0.476155\pi$
$74$	1.44648	−	2.50538i	0.168150	−	0.291244i
$75$	0.262123	+	1.71210i	0.0302673	+	0.197696i
$76$	2.18226	−	3.77979i	0.250323	−	0.433571i
$77$	−4.40422	+	2.69268i	−0.501908	+	0.306860i
$78$	1.14404	+	7.47251i	0.129537	+	0.846095i
$79$	7.55094			0.849547			0.424773	−	0.905300i	$-0.360354\pi$
$79$	7.55094			0.849547			0.424773	+	0.905300i	$0.360354\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−8.14462	−	3.82952i	−0.904958	−	0.425502i
$82$	−4.07219	+	7.05324i	−0.449698	+	0.778900i
$83$	1.48957	+	2.58002i	0.163502	+	0.283194i	0.936122	−	0.351675i	$-0.114388\pi$
$83$	1.48957	+	2.58002i	0.163502	+	0.283194i	−0.772620	+	0.634868i	$0.781054\pi$
$84$	4.51092	−	0.807211i	0.492182	−	0.0880739i
$85$	2.22435	−	3.85269i	0.241265	−	0.417883i
$86$	1.39891	+	2.42298i	0.150848	+	0.261277i
$87$	2.34099	+	0.912507i	0.250980	+	0.0978310i
$88$	0.975553	−	1.68971i	0.103994	−	0.180123i
$89$	4.62826	−	8.01637i	0.490594	−	0.849734i	−0.509347	−	0.860561i	$-0.670113\pi$
$89$	4.62826	−	8.01637i	0.490594	−	0.849734i	0.999941	+	0.0108272i	$0.00344647\pi$
$90$	2.86258	−	0.897561i	0.301743	−	0.0946113i
$91$	9.85201	−	6.02339i	1.03277	−	0.631423i
$92$	−0.957909	−	1.65915i	−0.0998689	−	0.172978i
$93$	3.76264	−	3.01492i	0.390168	−	0.312633i
$94$	6.79782			0.701142
$95$	−4.36452			−0.447791
$96$	−1.35166	+	1.08306i	−0.137953	+	0.110539i
$97$	−6.19076	−	10.7227i	−0.628576	−	1.08873i	−0.987838	−	0.155489i	$-0.950305\pi$
$97$	−6.19076	−	10.7227i	−0.628576	−	1.08873i	0.359261	−	0.933237i	$-0.383029\pi$
$98$	−3.80039	−	5.87852i	−0.383897	−	0.593821i
$99$	4.30922	+	3.96131i	0.433093	+	0.398127i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−2.88844	+	5.00292i	−0.287410	+	0.497809i	−0.973191	−	0.229999i	$-0.926128\pi$
$101$	−2.88844	+	5.00292i	−0.287410	+	0.497809i	0.685780	+	0.727808i	$0.259461\pi$
$102$	−7.17925	−	2.79844i	−0.710852	−	0.277087i
$103$	6.70201	+	11.6082i	0.660368	+	1.14379i	0.980519	+	0.196425i	$0.0629332\pi$
$103$	6.70201	+	11.6082i	0.660368	+	1.14379i	−0.320150	+	0.947367i	$0.603733\pi$
$104$	−2.18226	+	3.77979i	−0.213988	+	0.370639i
$105$	−2.95453	−	3.50297i	−0.288332	−	0.341855i
$106$	3.07762	+	5.33060i	0.298925	+	0.517754i
$107$	0.143309	−	0.248218i	0.0138542	−	0.0239961i	−0.859015	−	0.511950i	$-0.828923\pi$
$107$	0.143309	−	0.248218i	0.0138542	−	0.0239961i	0.872869	+	0.487954i	$0.162257\pi$
$108$	−2.28706	−	4.66576i	−0.220073	−	0.448963i
$109$	−5.85760	−	10.1457i	−0.561056	−	0.971778i	−0.997405	−	0.0720001i	$-0.977062\pi$
$109$	−5.85760	−	10.1457i	−0.561056	−	0.971778i	0.436348	−	0.899778i	$-0.356272\pi$
$110$	−1.95111			−0.186031
$111$	0.758310	+	4.95304i	0.0719756	+	0.470122i
$112$	2.32383	+	1.26483i	0.219581	+	0.119516i
$113$	−4.14879	+	7.18591i	−0.390285	+	0.675994i	−0.992487	−	0.122350i	$-0.960957\pi$
$113$	−4.14879	+	7.18591i	−0.390285	+	0.675994i	0.602202	+	0.798344i	$0.294290\pi$
$114$	1.14404	+	7.47251i	0.107149	+	0.699864i
$115$	−0.957909	+	1.65915i	−0.0893255	+	0.154716i
$116$	0.725310	+	1.25627i	0.0673434	+	0.116642i
$117$	−9.63950	−	8.86124i	−0.891172	−	0.819222i
$118$	8.10635			0.746250
$119$	0.296004	+	11.7664i	0.0271347	+	1.07863i
$120$	1.61378	+	0.629046i	0.147318	+	0.0574238i
$121$	3.59659	+	6.22948i	0.326963	+	0.566316i
$122$	−0.523345			−0.0473814
$123$	−2.13483	−	13.9440i	−0.192491	−	1.25729i
$124$	2.78372			0.249985
$125$	1.00000			0.0894427
$126$	−5.22299	+	5.97665i	−0.465301	+	0.532443i
$127$	−17.0531			−1.51322			−0.756609	−	0.653868i	$-0.773145\pi$
$127$	−17.0531			−1.51322			−0.756609	+	0.653868i	$0.773145\pi$
$128$	−1.00000			−0.0883883
$129$	−4.51508	−	1.75996i	−0.397530	−	0.154956i
$130$	4.36452			0.382794
$131$	6.05853	+	10.4937i	0.529337	+	0.916838i	0.999415	+	0.0342129i	$0.0108924\pi$
$131$	6.05853	+	10.4937i	0.529337	+	0.916838i	−0.470078	+	0.882625i	$0.655774\pi$
$132$	0.511429	+	3.34049i	0.0445142	+	0.290753i
$133$	9.85201	−	6.02339i	0.854278	−	0.522294i
$134$	11.0791			0.957091
$135$	−2.89714	+	4.31354i	−0.249346	+	0.371250i
$136$	−2.22435	−	3.85269i	−0.190737	−	0.330366i
$137$	−6.96001	+	12.0551i	−0.594634	+	1.02994i	0.398964	+	0.916966i	$0.369370\pi$
$137$	−6.96001	+	12.0551i	−0.594634	+	1.02994i	−0.993598	+	0.112970i	$0.963964\pi$
$138$	3.09172	+	1.20514i	0.263185	+	0.102588i
$139$	−11.1729	+	19.3521i	−0.947676	+	1.64142i	−0.197373	+	0.980328i	$0.563241\pi$
$139$	−11.1729	+	19.3521i	−0.947676	+	1.64142i	−0.750303	+	0.661094i	$0.770092\pi$
$140$	−0.0665372	−	2.64491i	−0.00562342	−	0.223536i
$141$	−9.18835	+	7.36242i	−0.773799	+	0.620027i
$142$	−16.3384			−1.37109
$143$	4.25783	+	7.37477i	0.356057	+	0.616709i
$144$	0.653981	−	2.92785i	0.0544984	−	0.243988i
$145$	0.725310	−	1.25627i	0.0602338	−	0.104328i
$146$	−7.69829	−	13.3338i	−0.637115	−	1.10352i
$147$	11.5036	+	3.82975i	0.948802	+	0.315872i
$148$	−1.44648	+	2.50538i	−0.118900	+	0.205941i
$149$	3.72142	+	6.44569i	0.304870	+	0.528051i	0.977232	−	0.212171i	$-0.0680535\pi$
$149$	3.72142	+	6.44569i	0.304870	+	0.528051i	−0.672362	+	0.740222i	$0.734720\pi$
$150$	−0.262123	−	1.71210i	−0.0214022	−	0.139793i
$151$	−3.31670	+	5.74470i	−0.269909	+	0.467497i	−0.968838	−	0.247694i	$-0.920327\pi$
$151$	−3.31670	+	5.74470i	−0.269909	+	0.467497i	0.698929	+	0.715191i	$0.253660\pi$
$152$	−2.18226	+	3.77979i	−0.177005	+	0.306581i
$153$	12.7348	−	3.99298i	1.02955	−	0.322814i
$154$	4.40422	−	2.69268i	0.354902	−	0.216983i
$155$	−1.39186	−	2.41077i	−0.111797	−	0.193638i
$156$	−1.14404	−	7.47251i	−0.0915965	−	0.598279i
$157$	10.0020			0.798243			0.399122	−	0.916898i	$-0.369315\pi$
$157$	10.0020			0.798243			0.399122	+	0.916898i	$0.369315\pi$
$158$	−7.55094			−0.600720
$159$	−9.93325	−	3.87193i	−0.787758	−	0.307064i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−0.127473	−	5.06718i	−0.0100463	−	0.399349i
$162$	8.14462	+	3.82952i	0.639902	+	0.300875i
$163$	−9.74187	+	16.8734i	−0.763043	+	1.32163i	0.178233	+	0.983988i	$0.442962\pi$
$163$	−9.74187	+	16.8734i	−0.763043	+	1.32163i	−0.941275	+	0.337640i	$0.890371\pi$
$164$	4.07219	−	7.05324i	0.317985	−	0.550765i
$165$	2.63724	−	2.11316i	0.205309	−	0.164509i
$166$	−1.48957	−	2.58002i	−0.115613	−	0.200248i
$167$	−11.3506	+	19.6598i	−0.878334	+	1.52132i	−0.0251665	+	0.999683i	$0.508012\pi$
$167$	−11.3506	+	19.6598i	−0.878334	+	1.52132i	−0.853168	+	0.521636i	$0.825322\pi$
$168$	−4.51092	+	0.807211i	−0.348025	+	0.0622777i
$169$	−3.02453	−	5.23864i	−0.232656	−	0.402972i
$170$	−2.22435	+	3.85269i	−0.170600	+	0.295488i
$171$	−9.63950	−	8.86124i	−0.737151	−	0.677636i
$172$	−1.39891	−	2.42298i	−0.106666	−	0.184751i
$173$	−9.96320			−0.757488			−0.378744	−	0.925501i	$-0.623644\pi$
$173$	−9.96320			−0.757488			−0.378744	+	0.925501i	$0.623644\pi$
$174$	−2.34099	−	0.912507i	−0.177470	−	0.0691770i
$175$	−2.25729	+	1.38008i	−0.170635	+	0.104324i
$176$	−0.975553	+	1.68971i	−0.0735351	+	0.127367i
$177$	−10.9571	+	8.77963i	−0.823583	+	0.659918i
$178$	−4.62826	+	8.01637i	−0.346902	+	0.600853i
$179$	2.42336	+	4.19738i	0.181130	+	0.313727i	0.942266	−	0.334866i	$-0.108691\pi$
$179$	2.42336	+	4.19738i	0.181130	+	0.313727i	−0.761136	+	0.648593i	$0.775358\pi$
$180$	−2.86258	+	0.897561i	−0.213364	+	0.0669003i
$181$	1.87609			0.139449			0.0697243	−	0.997566i	$-0.477788\pi$
$181$	1.87609			0.139449			0.0697243	+	0.997566i	$0.477788\pi$
$182$	−9.85201	+	6.02339i	−0.730280	+	0.446483i
$183$	0.707385	−	0.566812i	0.0522914	−	0.0418999i
$184$	0.957909	+	1.65915i	0.0706180	+	0.122314i
$185$	2.89296			0.212695
$186$	−3.76264	+	3.01492i	−0.275890	+	0.221065i
$187$	−8.67990			−0.634737
$188$	−6.79782			−0.495782
$189$	0.586664	−	13.7352i	0.0426735	−	0.999089i
$190$	4.36452			0.316636
$191$	−2.49331			−0.180410			−0.0902050	−	0.995923i	$-0.528752\pi$
$191$	−2.49331			−0.180410			−0.0902050	+	0.995923i	$0.528752\pi$
$192$	1.35166	−	1.08306i	0.0975478	−	0.0781628i
$193$	−19.1600			−1.37917			−0.689584	−	0.724206i	$-0.742206\pi$
$193$	−19.1600			−1.37917			−0.689584	+	0.724206i	$0.742206\pi$
$194$	6.19076	+	10.7227i	0.444470	+	0.769845i
$195$	−5.89936	+	4.72702i	−0.422462	+	0.338509i
$196$	3.80039	+	5.87852i	0.271456	+	0.419895i
$197$	12.6440			0.900851			0.450425	−	0.892814i	$-0.351272\pi$
$197$	12.6440			0.900851			0.450425	+	0.892814i	$0.351272\pi$
$198$	−4.30922	−	3.96131i	−0.306243	−	0.281518i
$199$	10.0418	+	17.3929i	0.711842	+	1.23295i	0.964165	+	0.265303i	$0.0854721\pi$
$199$	10.0418	+	17.3929i	0.711842	+	1.23295i	−0.252323	+	0.967643i	$0.581195\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−14.9752	+	11.9993i	−1.05627	+	0.846367i
$202$	2.88844	−	5.00292i	0.203230	−	0.352004i
$203$	0.0965203	+	3.83677i	0.00677440	+	0.269288i
$204$	7.17925	+	2.79844i	0.502648	+	0.195930i
$205$	−8.14438			−0.568828
$206$	−6.70201	−	11.6082i	−0.466951	−	0.808783i
$207$	−5.48419	+	1.71956i	−0.381178	+	0.119518i
$208$	2.18226	−	3.77979i	0.151313	−	0.262081i
$209$	4.25783	+	7.37477i	0.294520	+	0.510123i
$210$	2.95453	+	3.50297i	0.203882	+	0.241728i
$211$	−0.986346	+	1.70840i	−0.0679029	+	0.117611i	−0.897978	−	0.440040i	$-0.854964\pi$
$211$	−0.986346	+	1.70840i	−0.0679029	+	0.117611i	0.830075	+	0.557652i	$0.188297\pi$
$212$	−3.07762	−	5.33060i	−0.211372	−	0.366107i
$213$	22.0841	−	17.6954i	1.51317	−	1.21247i
$214$	−0.143309	+	0.248218i	−0.00979637	+	0.0169678i
$215$	−1.39891	+	2.42298i	−0.0954048	+	0.165246i
$216$	2.28706	+	4.66576i	0.155615	+	0.317465i
$217$	6.46889	+	3.52094i	0.439137	+	0.239017i
$218$	5.85760	+	10.1457i	0.396727	+	0.687151i
$219$	24.8468	+	9.68516i	1.67899	+	0.654463i
$220$	1.95111			0.131544
$221$	19.4165			1.30609
$222$	−0.758310	−	4.95304i	−0.0508945	−	0.332426i
$223$	−4.76467	−	8.25264i	−0.319066	−	0.552638i	0.661228	−	0.750185i	$-0.270036\pi$
$223$	−4.76467	−	8.25264i	−0.319066	−	0.552638i	−0.980293	+	0.197547i	$0.936702\pi$
$224$	−2.32383	−	1.26483i	−0.155268	−	0.0845103i
$225$	2.20860	+	2.03029i	0.147240	+	0.135353i
$226$	4.14879	−	7.18591i	0.275973	−	0.478000i
$227$	2.67450	−	4.63237i	0.177513	−	0.307461i	−0.763515	−	0.645790i	$-0.776528\pi$
$227$	2.67450	−	4.63237i	0.177513	−	0.307461i	0.941028	+	0.338329i	$0.109862\pi$
$228$	−1.14404	−	7.47251i	−0.0757659	−	0.494879i
$229$	2.93966	+	5.09164i	0.194258	+	0.336465i	0.946657	−	0.322243i	$-0.104437\pi$
$229$	2.93966	+	5.09164i	0.194258	+	0.336465i	−0.752399	+	0.658708i	$0.771103\pi$
$230$	0.957909	−	1.65915i	0.0631627	−	0.109401i
$231$	−3.03669	+	8.40962i	−0.199800	+	0.553312i
$232$	−0.725310	−	1.25627i	−0.0476190	−	0.0824785i
$233$	9.70278	−	16.8057i	0.635650	−	1.10098i	−0.350727	−	0.936478i	$-0.614065\pi$
$233$	9.70278	−	16.8057i	0.635650	−	1.10098i	0.986377	−	0.164500i	$-0.0526012\pi$
$234$	9.63950	+	8.86124i	0.630154	+	0.579278i
$235$	3.39891	+	5.88708i	0.221720	+	0.384031i
$236$	−8.10635			−0.527679
$237$	10.2063	−	8.17809i	0.662972	−	0.531224i
$238$	−0.296004	−	11.7664i	−0.0191871	−	0.762705i
$239$	7.54422	−	13.0670i	0.487995	−	0.845232i	−0.511910	−	0.859039i	$-0.671062\pi$
$239$	7.54422	−	13.0670i	0.487995	−	0.845232i	0.999905	+	0.0138075i	$0.00439520\pi$
$240$	−1.61378	−	0.629046i	−0.104169	−	0.0406047i
$241$	−2.07805	+	3.59929i	−0.133859	+	0.231850i	−0.925161	−	0.379575i	$-0.876070\pi$
$241$	−2.07805	+	3.59929i	−0.133859	+	0.231850i	0.791302	+	0.611425i	$0.209404\pi$
$242$	−3.59659	−	6.22948i	−0.231198	−	0.400446i
$243$	−15.1564	+	3.64486i	−0.972280	+	0.233818i
$244$	0.523345			0.0335037
$245$	3.19076	−	6.23049i	0.203850	−	0.398052i
$246$	2.13483	+	13.9440i	0.136112	+	0.889037i
$247$	−9.52453	−	16.4970i	−0.606031	−	1.04968i
$248$	−2.78372			−0.176766
$249$	4.80770	+	1.87402i	0.304676	+	0.118761i
$250$	−1.00000			−0.0632456
$251$	−17.8669			−1.12775			−0.563875	−	0.825860i	$-0.690690\pi$
$251$	−17.8669			−1.12775			−0.563875	+	0.825860i	$0.690690\pi$
$252$	5.22299	−	5.97665i	0.329017	−	0.376494i
$253$	3.73797			0.235004
$254$	17.0531			1.07001
$255$	−1.16611	−	7.61663i	−0.0730244	−	0.476972i
$256$	1.00000			0.0625000
$257$	11.1361	+	19.2882i	0.694649	+	1.20317i	0.970299	+	0.241909i	$0.0777736\pi$
$257$	11.1361	+	19.2882i	0.694649	+	1.20317i	−0.275650	+	0.961258i	$0.588893\pi$
$258$	4.51508	+	1.75996i	0.281096	+	0.109570i
$259$	−6.53026	+	3.99252i	−0.405771	+	0.248083i
$260$	−4.36452			−0.270676
$261$	4.15252	−	1.30202i	0.257035	−	0.0805931i
$262$	−6.05853	−	10.4937i	−0.374297	−	0.648302i
$263$	8.14728	−	14.1115i	0.502383	−	0.870153i	−0.497613	−	0.867399i	$-0.665790\pi$
$263$	8.14728	−	14.1115i	0.502383	−	0.870153i	0.999996	−	0.00275381i	$-0.000876566\pi$
$264$	−0.511429	−	3.34049i	−0.0314763	−	0.205593i
$265$	−3.07762	+	5.33060i	−0.189057	+	0.327456i
$266$	−9.85201	+	6.02339i	−0.604066	+	0.369318i
$267$	−2.42634	−	15.8481i	−0.148490	−	0.969887i
$268$	−11.0791			−0.676766
$269$	−3.84635	−	6.66207i	−0.234516	−	0.406194i	0.724616	−	0.689153i	$-0.242017\pi$
$269$	−3.84635	−	6.66207i	−0.234516	−	0.406194i	−0.959132	+	0.282959i	$0.908684\pi$
$270$	2.89714	−	4.31354i	0.176314	−	0.262513i
$271$	3.32919	−	5.76633i	0.202234	−	0.350279i	−0.747014	−	0.664808i	$-0.768513\pi$
$271$	3.32919	−	5.76633i	0.202234	−	0.350279i	0.949248	+	0.314529i	$0.101847\pi$
$272$	2.22435	+	3.85269i	0.134871	+	0.233604i
$273$	6.79292	−	18.8119i	0.411127	−	1.13855i
$274$	6.96001	−	12.0551i	0.420470	−	0.728275i
$275$	−0.975553	−	1.68971i	−0.0588281	−	0.101893i
$276$	−3.09172	−	1.20514i	−0.186100	−	0.0725408i
$277$	13.1846	−	22.8363i	0.792184	−	1.37210i	−0.132428	−	0.991193i	$-0.542277\pi$
$277$	13.1846	−	22.8363i	0.792184	−	1.37210i	0.924612	−	0.380910i	$-0.124389\pi$
$278$	11.1729	−	19.3521i	0.670108	−	1.16066i
$279$	1.82050	−	8.15031i	0.108990	−	0.487946i
$280$	0.0665372	+	2.64491i	0.00397636	+	0.158064i
$281$	−15.3086	−	26.5153i	−0.913235	−	1.58177i	−0.809466	−	0.587167i	$-0.800243\pi$
$281$	−15.3086	−	26.5153i	−0.913235	−	1.58177i	−0.103769	−	0.994601i	$-0.533090\pi$
$282$	9.18835	−	7.36242i	0.547159	−	0.438426i
$283$	−28.7863			−1.71117			−0.855585	−	0.517662i	$-0.826802\pi$
$283$	−28.7863			−1.71117			−0.855585	+	0.517662i	$0.826802\pi$
$284$	16.3384			0.969508
$285$	−5.89936	+	4.72702i	−0.349448	+	0.280005i
$286$	−4.25783	−	7.37477i	−0.251770	−	0.436079i
$287$	18.3843	−	11.2399i	1.08519	−	0.663470i
$288$	−0.653981	+	2.92785i	−0.0385362	+	0.172525i
$289$	−1.39548	+	2.41705i	−0.0820873	+	0.142179i
$290$	−0.725310	+	1.25627i	−0.0425917	+	0.0737710i
$291$	−19.9811	−	7.78854i	−1.17131	−	0.456572i
$292$	7.69829	+	13.3338i	0.450509	+	0.780304i
$293$	−0.549142	+	0.951142i	−0.0320812	+	0.0555663i	−0.881620	−	0.471959i	$-0.843547\pi$
$293$	−0.549142	+	0.951142i	−0.0320812	+	0.0555663i	0.849539	+	0.527526i	$0.176880\pi$
$294$	−11.5036	−	3.82975i	−0.670904	−	0.223355i
$295$	4.05318	+	7.02031i	0.235985	+	0.408738i
$296$	1.44648	−	2.50538i	0.0840749	−	0.145622i
$297$	10.1149	+	0.687229i	0.586928	+	0.0398771i
$298$	−3.72142	−	6.44569i	−0.215576	−	0.373389i
$299$	−8.36163			−0.483566
$300$	0.262123	+	1.71210i	0.0151337	+	0.0988482i
$301$	−0.186159	−	7.39999i	−0.0107300	−	0.426528i
$302$	3.31670	−	5.74470i	0.190855	−	0.330570i
$303$	1.51425	+	9.89060i	0.0869914	+	0.568200i
$304$	2.18226	−	3.77979i	0.125161	−	0.216786i
$305$	−0.261672	−	0.453230i	−0.0149833	−	0.0259519i
$306$	−12.7348	+	3.99298i	−0.727999	+	0.228264i
$307$	−24.2439			−1.38367			−0.691837	−	0.722054i	$-0.743198\pi$
$307$	−24.2439			−1.38367			−0.691837	+	0.722054i	$0.743198\pi$
$308$	−4.40422	+	2.69268i	−0.250954	+	0.153430i
$309$	21.6312	+	8.43174i	1.23056	+	0.479665i
$310$	1.39186	+	2.41077i	0.0790522	+	0.136922i
$311$	32.9797			1.87010			0.935052	−	0.354510i	$-0.115352\pi$
$311$	32.9797			1.87010			0.935052	+	0.354510i	$0.115352\pi$
$312$	1.14404	+	7.47251i	0.0647685	+	0.423047i
$313$	22.7978			1.28861			0.644303	−	0.764770i	$-0.277148\pi$
$313$	22.7978			1.28861			0.644303	+	0.764770i	$0.277148\pi$
$314$	−10.0020			−0.564443
$315$	−7.78743	−	1.53491i	−0.438772	−	0.0864825i
$316$	7.55094			0.424773
$317$	16.1846			0.909016			0.454508	−	0.890743i	$-0.349815\pi$
$317$	16.1846			0.909016			0.454508	+	0.890743i	$0.349815\pi$
$318$	9.93325	+	3.87193i	0.557029	+	0.217127i
$319$	−2.83032			−0.158467
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−0.0751289	−	0.490718i	−0.00419328	−	0.0273892i
$322$	0.127473	+	5.06718i	0.00710381	+	0.282383i
$323$	19.4165			1.08036
$324$	−8.14462	−	3.82952i	−0.452479	−	0.212751i
$325$	2.18226	+	3.77979i	0.121050	+	0.209665i
$326$	9.74187	−	16.8734i	0.539553	−	0.934532i
$327$	−18.9058	−	7.36940i	−1.04549	−	0.407529i
$328$	−4.07219	+	7.05324i	−0.224849	+	0.389450i
$329$	−15.7970	−	8.59812i	−0.870916	−	0.474029i
$330$	−2.63724	+	2.11316i	−0.145175	+	0.116325i
$331$	26.0659			1.43271			0.716355	−	0.697736i	$-0.245809\pi$
$331$	26.0659			1.43271			0.716355	+	0.697736i	$0.245809\pi$
$332$	1.48957	+	2.58002i	0.0817510	+	0.141597i
$333$	6.38940	+	5.87355i	0.350137	+	0.321868i
$334$	11.3506	−	19.6598i	0.621076	−	1.07574i
$335$	5.53957	+	9.59481i	0.302659	+	0.524220i
$336$	4.51092	−	0.807211i	0.246091	−	0.0440369i
$337$	−4.71953	+	8.17447i	−0.257089	+	0.445292i	−0.965461	−	0.260548i	$-0.916097\pi$
$337$	−4.71953	+	8.17447i	−0.257089	+	0.445292i	0.708372	+	0.705840i	$0.249430\pi$
$338$	3.02453	+	5.23864i	0.164513	+	0.284944i
$339$	2.17498	+	14.2063i	0.118129	+	0.771580i
$340$	2.22435	−	3.85269i	0.120632	−	0.208941i
$341$	−2.71566	+	4.70367i	−0.147061	+	0.254718i
$342$	9.63950	+	8.86124i	0.521244	+	0.479161i
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$	1.39891	+	2.42298i	0.0754242	+	0.130638i
$345$	0.502180	+	3.28008i	0.0270364	+	0.176593i
$346$	9.96320			0.535625
$347$	25.3732			1.36210			0.681052	−	0.732235i	$-0.261523\pi$
$347$	25.3732			1.36210			0.681052	+	0.732235i	$0.261523\pi$
$348$	2.34099	+	0.912507i	0.125490	+	0.0489155i
$349$	−8.02651	−	13.9023i	−0.429649	−	0.744174i	0.567193	−	0.823585i	$-0.308029\pi$
$349$	−8.02651	−	13.9023i	−0.429649	−	0.744174i	−0.996842	+	0.0794110i	$0.974696\pi$
$350$	2.25729	−	1.38008i	0.120657	−	0.0737684i
$351$	−22.6266	−	1.53730i	−1.20772	−	0.0820548i
$352$	0.975553	−	1.68971i	0.0519972	−	0.0900617i
$353$	−11.8383	+	20.5045i	−0.630088	+	1.09135i	0.357445	+	0.933934i	$0.383648\pi$
$353$	−11.8383	+	20.5045i	−0.630088	+	1.09135i	−0.987533	+	0.157411i	$0.949685\pi$
$354$	10.9571	−	8.77963i	0.582361	−	0.466632i
$355$	−8.16922	−	14.1495i	−0.433577	−	0.750978i
$356$	4.62826	−	8.01637i	0.245297	−	0.424867i
$357$	13.1438	+	15.5837i	0.695644	+	0.824775i
$358$	−2.42336	−	4.19738i	−0.128078	−	0.221838i
$359$	−5.38333	+	9.32419i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$359$	−5.38333	+	9.32419i	−0.284121	+	0.492112i	0.688275	+	0.725450i	$0.258368\pi$
$360$	2.86258	−	0.897561i	0.150871	−	0.0473056i
$361$	−0.0245294	−	0.0424862i	−0.00129102	−	0.00223612i
$362$	−1.87609			−0.0986051
$363$	11.6082	+	4.52484i	0.609275	+	0.237493i
$364$	9.85201	−	6.02339i	0.516386	−	0.315711i
$365$	7.69829	−	13.3338i	0.402947	−	0.697925i
$366$	−0.707385	+	0.566812i	−0.0369756	+	0.0296277i
$367$	−10.4353	+	18.0745i	−0.544720	+	0.943483i	0.453904	+	0.891051i	$0.350031\pi$
$367$	−10.4353	+	18.0745i	−0.544720	+	0.943483i	−0.998624	+	0.0524329i	$0.983302\pi$
$368$	−0.957909	−	1.65915i	−0.0499345	−	0.0864890i
$369$	−17.9877	−	16.5354i	−0.936402	−	0.860801i
$370$	−2.89296			−0.150398
$371$	−0.409553	−	16.2801i	−0.0212629	−	0.845221i
$372$	3.76264	−	3.01492i	0.195084	−	0.156316i
$373$	−1.51656	−	2.62677i	−0.0785247	−	0.136009i	0.824089	−	0.566460i	$-0.191688\pi$
$373$	−1.51656	−	2.62677i	−0.0785247	−	0.136009i	−0.902614	+	0.430452i	$0.858354\pi$
$374$	8.67990			0.448827
$375$	1.35166	−	1.08306i	0.0697995	−	0.0559288i
$376$	6.79782			0.350571
$377$	6.33127			0.326077
$378$	−0.586664	+	13.7352i	−0.0301747	+	0.706463i
$379$	−24.2090			−1.24353			−0.621766	−	0.783203i	$-0.713585\pi$
$379$	−24.2090			−1.24353			−0.621766	+	0.783203i	$0.713585\pi$
$380$	−4.36452			−0.223895
$381$	−23.0500	+	18.4695i	−1.18089	+	0.946219i
$382$	2.49331			0.127569
$383$	14.8738	+	25.7623i	0.760018	+	1.31639i	0.942841	+	0.333244i	$0.108143\pi$
$383$	14.8738	+	25.7623i	0.760018	+	1.31639i	−0.182823	+	0.983146i	$0.558523\pi$
$384$	−1.35166	+	1.08306i	−0.0689767	+	0.0552695i
$385$	4.53404	+	2.46783i	0.231076	+	0.125772i
$386$	19.1600			0.975218
$387$	−8.00899	+	2.51121i	−0.407120	+	0.127652i
$388$	−6.19076	−	10.7227i	−0.314288	−	0.544363i
$389$	0.628857	−	1.08921i	0.0318843	−	0.0552252i	−0.849643	−	0.527358i	$-0.823183\pi$
$389$	0.628857	−	1.08921i	0.0318843	−	0.0552252i	0.881527	+	0.472133i	$0.156516\pi$
$390$	5.89936	−	4.72702i	0.298726	−	0.239362i
$391$	4.26146	−	7.38106i	0.215511	−	0.373276i
$392$	−3.80039	−	5.87852i	−0.191949	−	0.296910i
$393$	19.5543	+	7.62219i	0.986386	+	0.384489i
$394$	−12.6440			−0.636998
$395$	−3.77547	−	6.53930i	−0.189964	−	0.329028i
$396$	4.30922	+	3.96131i	0.216546	+	0.199063i
$397$	14.3741	−	24.8967i	0.721416	−	1.24953i	−0.239016	−	0.971016i	$-0.576825\pi$
$397$	14.3741	−	24.8967i	0.721416	−	1.24953i	0.960432	−	0.278514i	$-0.0898418\pi$
$398$	−10.0418	−	17.3929i	−0.503348	−	0.871825i
$399$	6.79292	−	18.8119i	0.340072	−	0.941771i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−12.8554	−	22.2662i	−0.641967	−	1.11192i	−0.984993	−	0.172594i	$-0.944785\pi$
$401$	−12.8554	−	22.2662i	−0.641967	−	1.11192i	0.343026	−	0.939326i	$-0.388548\pi$
$402$	14.9752	−	11.9993i	0.746897	−	0.598472i
$403$	6.07480	−	10.5219i	0.302607	−	0.524131i
$404$	−2.88844	+	5.00292i	−0.143705	+	0.248905i
$405$	0.755851	+	8.96820i	0.0375585	+	0.445634i
$406$	−0.0965203	−	3.83677i	−0.00479022	−	0.190416i
$407$	−2.82224	−	4.88826i	−0.139893	−	0.242302i
$408$	−7.17925	−	2.79844i	−0.355426	−	0.138543i
$409$	−18.9989			−0.939436			−0.469718	−	0.882816i	$-0.655644\pi$
$409$	−18.9989			−0.939436			−0.469718	+	0.882816i	$0.655644\pi$
$410$	8.14438			0.402222
$411$	3.64875	+	23.8325i	0.179980	+	1.17557i
$412$	6.70201	+	11.6082i	0.330184	+	0.571896i
$413$	−18.8378	−	10.2532i	−0.926948	−	0.504527i
$414$	5.48419	−	1.71956i	0.269533	−	0.0845120i
$415$	1.48957	−	2.58002i	0.0731203	−	0.126648i
$416$	−2.18226	+	3.77979i	−0.106994	+	0.185319i
$417$	5.85736	+	38.2584i	0.286836	+	1.87352i
$418$	−4.25783	−	7.37477i	−0.208257	−	0.360712i
$419$	−13.7359	+	23.7914i	−0.671045	+	1.16228i	0.306563	+	0.951850i	$0.400821\pi$
$419$	−13.7359	+	23.7914i	−0.671045	+	1.16228i	−0.977608	+	0.210433i	$0.932512\pi$
$420$	−2.95453	−	3.50297i	−0.144166	−	0.170927i
$421$	−4.13097	−	7.15504i	−0.201331	−	0.348715i	0.747627	−	0.664119i	$-0.231193\pi$
$421$	−4.13097	−	7.15504i	−0.201331	−	0.348715i	−0.948958	+	0.315404i	$0.897860\pi$
$422$	0.986346	−	1.70840i	0.0480146	−	0.0831637i
$423$	−4.44564	+	19.9030i	−0.216155	+	0.967717i
$424$	3.07762	+	5.33060i	0.149463	+	0.258877i
$425$	−4.44870			−0.215794
$426$	−22.0841	+	17.6954i	−1.06998	+	0.857347i
$427$	1.21617	+	0.661944i	0.0588544	+	0.0320337i
$428$	0.143309	−	0.248218i	0.00692708	−	0.0119981i
$429$	13.7424	+	5.35673i	0.663491	+	0.258626i
$430$	1.39891	−	2.42298i	0.0674614	−	0.116847i
$431$	−9.94534	−	17.2258i	−0.479050	−	0.829739i	0.520661	−	0.853763i	$-0.325686\pi$
$431$	−9.94534	−	17.2258i	−0.479050	−	0.829739i	−0.999711	+	0.0240240i	$0.992352\pi$
$432$	−2.28706	−	4.66576i	−0.110036	−	0.224482i
$433$	10.8766			0.522694			0.261347	−	0.965245i	$-0.415833\pi$
$433$	10.8766			0.522694			0.261347	+	0.965245i	$0.415833\pi$
$434$	−6.46889	−	3.52094i	−0.310517	−	0.169011i
$435$	−0.380241	−	2.48361i	−0.0182311	−	0.119080i
$436$	−5.85760	−	10.1457i	−0.280528	−	0.485889i
$437$	−8.36163			−0.399991
$438$	−24.8468	−	9.68516i	−1.18723	−	0.462775i
$439$	−3.64494			−0.173964			−0.0869818	−	0.996210i	$-0.527722\pi$
$439$	−3.64494			−0.173964			−0.0869818	+	0.996210i	$0.527722\pi$
$440$	−1.95111			−0.0930154
$441$	19.6968	−	7.28253i	0.937944	−	0.346787i
$442$	−19.4165			−0.923547
$443$	−19.0366			−0.904458			−0.452229	−	0.891902i	$-0.649371\pi$
$443$	−19.0366			−0.904458			−0.452229	+	0.891902i	$0.649371\pi$
$444$	0.758310	+	4.95304i	0.0359878	+	0.235061i
$445$	−9.25651			−0.438801
$446$	4.76467	+	8.25264i	0.225613	+	0.390774i
$447$	12.0111	+	4.68189i	0.568107	+	0.221446i
$448$	2.32383	+	1.26483i	0.109791	+	0.0597578i
$449$	5.22159			0.246422			0.123211	−	0.992380i	$-0.460681\pi$
$449$	5.22159			0.246422			0.123211	+	0.992380i	$0.460681\pi$
$450$	−2.20860	−	2.03029i	−0.104115	−	0.0957088i
$451$	7.94528	+	13.7616i	0.374128	+	0.648009i
$452$	−4.14879	+	7.18591i	−0.195143	+	0.337997i
$453$	1.73877	+	11.3571i	0.0816944	+	0.533601i
$454$	−2.67450	+	4.63237i	−0.125521	+	0.217408i
$455$	−10.1424	−	5.52040i	−0.475484	−	0.258800i
$456$	1.14404	+	7.47251i	0.0535746	+	0.349932i
$457$	−22.6223			−1.05823			−0.529113	−	0.848551i	$-0.677475\pi$
$457$	−22.6223			−1.05823			−0.529113	+	0.848551i	$0.677475\pi$
$458$	−2.93966	−	5.09164i	−0.137361	−	0.237917i
$459$	12.8885	−	19.1896i	0.601584	−	0.895696i
$460$	−0.957909	+	1.65915i	−0.0446628	+	0.0773582i
$461$	−12.0085	−	20.7994i	−0.559293	−	0.968724i	−0.997556	−	0.0698768i	$-0.977739\pi$
$461$	−12.0085	−	20.7994i	−0.559293	−	0.968724i	0.438263	−	0.898847i	$-0.355594\pi$
$462$	3.03669	−	8.40962i	0.141280	−	0.391251i
$463$	3.05932	−	5.29890i	0.142179	−	0.246261i	−0.786138	−	0.618051i	$-0.787923\pi$
$463$	3.05932	−	5.29890i	0.142179	−	0.246261i	0.928317	+	0.371790i	$0.121256\pi$
$464$	0.725310	+	1.25627i	0.0336717	+	0.0583211i
$465$	−4.49232	−	1.75109i	−0.208326	−	0.0812046i
$466$	−9.70278	+	16.8057i	−0.449472	+	0.778509i
$467$	−9.30663	+	16.1196i	−0.430660	+	0.745924i	−0.996930	−	0.0782949i	$-0.975052\pi$
$467$	−9.30663	+	16.1196i	−0.430660	+	0.745924i	0.566271	+	0.824219i	$0.308386\pi$
$468$	−9.63950	−	8.86124i	−0.445586	−	0.409611i
$469$	−25.7460	−	14.0133i	−1.18884	−	0.647073i
$470$	−3.39891	−	5.88708i	−0.156780	−	0.271551i
$471$	13.5193	−	10.8327i	0.622935	−	0.499144i
$472$	8.10635			0.373125
$473$	5.45884			0.250998
$474$	−10.2063	+	8.17809i	−0.468792	+	0.375632i
$475$	2.18226	+	3.77979i	0.100129	+	0.173429i
$476$	0.296004	+	11.7664i	0.0135673	+	0.539314i
$477$	−17.6199	+	5.52471i	−0.806760	+	0.252959i
$478$	−7.54422	+	13.0670i	−0.345064	+	0.597669i
$479$	−5.16999	+	8.95469i	−0.236223	+	0.409150i	−0.959627	−	0.281274i	$-0.909243\pi$
$479$	−5.16999	+	8.95469i	−0.236223	+	0.409150i	0.723404	+	0.690424i	$0.242576\pi$
$480$	1.61378	+	0.629046i	0.0736589	+	0.0287119i
$481$	6.31319	+	10.9348i	0.287857	+	0.498583i
$482$	2.07805	−	3.59929i	0.0946526	−	0.163943i
$483$	−5.66034	−	6.71105i	−0.257554	−	0.305363i
$484$	3.59659	+	6.22948i	0.163481	+	0.283158i
$485$	−6.19076	+	10.7227i	−0.281108	+	0.486893i
$486$	15.1564	−	3.64486i	0.687506	−	0.165334i
$487$	−12.7645	−	22.1088i	−0.578415	−	1.00184i	−0.995661	−	0.0930512i	$-0.970338\pi$
$487$	−12.7645	−	22.1088i	−0.578415	−	1.00184i	0.417246	−	0.908794i	$-0.362995\pi$
$488$	−0.523345			−0.0236907
$489$	5.10713	+	33.3582i	0.230953	+	1.50851i
$490$	−3.19076	+	6.23049i	−0.144144	+	0.281465i
$491$	15.6620	−	27.1274i	0.706817	−	1.22424i	−0.259215	−	0.965820i	$-0.583464\pi$
$491$	15.6620	−	27.1274i	0.706817	−	1.22424i	0.966032	−	0.258423i	$-0.0832028\pi$
$492$	−2.13483	−	13.9440i	−0.0962454	−	0.628644i
$493$	−3.22669	+	5.58879i	−0.145323	+	0.251707i
$494$	9.52453	+	16.4970i	0.428529	+	0.742234i
$495$	1.27599	−	5.71255i	0.0573513	−	0.256760i
$496$	2.78372			0.124993
$497$	37.9678	+	20.6654i	1.70309	+	0.926971i
$498$	−4.80770	−	1.87402i	−0.215438	−	0.0839769i
$499$	−6.88782	−	11.9301i	−0.308341	−	0.534063i	0.669658	−	0.742669i	$-0.266441\pi$
$499$	−6.88782	−	11.9301i	−0.308341	−	0.534063i	−0.978000	+	0.208607i	$0.933107\pi$
$500$	1.00000			0.0447214
$501$	5.95049	+	38.8667i	0.265848	+	1.73644i
$502$	17.8669			0.797439
$503$	35.1229			1.56605			0.783027	−	0.621987i	$-0.213674\pi$
$503$	35.1229			1.56605			0.783027	+	0.621987i	$0.213674\pi$
$504$	−5.22299	+	5.97665i	−0.232650	+	0.266221i
$505$	5.77688			0.257068
$506$	−3.73797			−0.166173
$507$	−9.76188	−	3.80514i	−0.433540	−	0.168992i
$508$	−17.0531			−0.756609
$509$	−14.2484	−	24.6790i	−0.631551	−	1.09388i	−0.987235	−	0.159272i	$-0.949085\pi$
$509$	−14.2484	−	24.6790i	−0.631551	−	1.09388i	0.355684	−	0.934606i	$-0.384248\pi$
$510$	1.16611	+	7.61663i	0.0516361	+	0.337270i
$511$	1.02445	+	40.7227i	0.0453188	+	1.80146i
$512$	−1.00000			−0.0441942
$513$	−22.6266	−	1.53730i	−0.998987	−	0.0678733i
$514$	−11.1361	−	19.2882i	−0.491191	−	0.850768i
$515$	6.70201	−	11.6082i	0.295326	−	0.511519i
$516$	−4.51508	−	1.75996i	−0.198765	−	0.0774778i
$517$	6.63164	−	11.4863i	0.291659	−	0.505168i
$518$	6.53026	−	3.99252i	0.286923	−	0.175421i
$519$	−13.4669	+	10.7907i	−0.591131	+	0.473659i
$520$	4.36452			0.191397
$521$	−10.6203	−	18.3949i	−0.465284	−	0.805896i	0.533930	−	0.845529i	$-0.320714\pi$
$521$	−10.6203	−	18.3949i	−0.465284	−	0.805896i	−0.999214	+	0.0396329i	$0.987381\pi$
$522$	−4.15252	+	1.30202i	−0.181751	+	0.0569879i
$523$	0.532595	−	0.922481i	0.0232887	−	0.0403373i	−0.854146	−	0.520033i	$-0.825920\pi$
$523$	0.532595	−	0.922481i	0.0232887	−	0.0403373i	0.877435	+	0.479696i	$0.159253\pi$
$524$	6.05853	+	10.4937i	0.264668	+	0.458419i
$525$	−1.55640	+	4.31018i	−0.0679267	+	0.188112i
$526$	−8.14728	+	14.1115i	−0.355238	+	0.615291i
$527$	6.19196	+	10.7248i	0.269726	+	0.467180i
$528$	0.511429	+	3.34049i	0.0222571	+	0.145376i
$529$	9.66482	−	16.7400i	0.420210	−	0.727824i
$530$	3.07762	−	5.33060i	0.133683	−	0.231547i
$531$	−5.30140	+	23.7342i	−0.230061	+	1.02998i
$532$	9.85201	−	6.02339i	0.427139	−	0.261147i
$533$	−17.7732	−	30.7840i	−0.769841	−	1.33340i
$534$	2.42634	+	15.8481i	0.104998	+	0.685814i
$535$	−0.286617			−0.0123915
$536$	11.0791			0.478546
$537$	7.82155	+	3.04880i	0.337525	+	0.131566i
$538$	3.84635	+	6.66207i	0.165828	+	0.287222i
$539$	−13.6405	+	0.686732i	−0.587537	+	0.0295797i
$540$	−2.89714	+	4.31354i	−0.124673	+	0.185625i
$541$	16.7916	−	29.0840i	0.721929	−	1.25042i	−0.238296	−	0.971193i	$-0.576589\pi$
$541$	16.7916	−	29.0840i	0.721929	−	1.25042i	0.960226	−	0.279226i	$-0.0900777\pi$
$542$	−3.32919	+	5.76633i	−0.143001	+	0.247685i
$543$	2.53584	−	2.03191i	0.108823	−	0.0871976i
$544$	−2.22435	−	3.85269i	−0.0953683	−	0.165183i
$545$	−5.85760	+	10.1457i	−0.250912	+	0.434592i
$546$	−6.79292	+	18.8119i	−0.290710	+	0.805074i
$547$	4.60195	+	7.97081i	0.196765	+	0.340807i	0.947478	−	0.319822i	$-0.103623\pi$
$547$	4.60195	+	7.97081i	0.196765	+	0.340807i	−0.750713	+	0.660629i	$0.770290\pi$
$548$	−6.96001	+	12.0551i	−0.297317	+	0.514968i
$549$	0.342257	−	1.53228i	0.0146072	−	0.0653959i
$550$	0.975553	+	1.68971i	0.0415977	+	0.0720494i
$551$	6.33127			0.269721
$552$	3.09172	+	1.20514i	0.131592	+	0.0512941i
$553$	17.5471	+	9.55069i	0.746179	+	0.406137i
$554$	−13.1846	+	22.8363i	−0.560158	+	0.970223i
$555$	3.91030	−	3.13324i	0.165983	−	0.132998i
$556$	−11.1729	+	19.3521i	−0.473838	+	0.820711i
$557$	−6.56454	−	11.3701i	−0.278148	−	0.481767i	0.692776	−	0.721153i	$-0.256387\pi$
$557$	−6.56454	−	11.3701i	−0.278148	−	0.481767i	−0.970925	+	0.239386i	$0.923054\pi$
$558$	−1.82050	+	8.15031i	−0.0770678	+	0.345030i
$559$	−12.2111			−0.516476
$560$	−0.0665372	−	2.64491i	−0.00281171	−	0.111768i
$561$	−11.7323	+	9.40081i	−0.495338	+	0.396903i
$562$	15.3086	+	26.5153i	0.645754	+	1.11848i
$563$	−15.1443			−0.638258			−0.319129	−	0.947711i	$-0.603390\pi$
$563$	−15.1443			−0.638258			−0.319129	+	0.947711i	$0.603390\pi$
$564$	−9.18835	+	7.36242i	−0.386900	+	0.310014i
$565$	8.29758			0.349082
$566$	28.7863			1.20998
$567$	−14.0830	−	19.2007i	−0.591431	−	0.806355i
$568$	−16.3384			−0.685546
$569$	6.68629			0.280304			0.140152	−	0.990130i	$-0.455241\pi$
$569$	6.68629			0.280304			0.140152	+	0.990130i	$0.455241\pi$
$570$	5.89936	−	4.72702i	0.247097	−	0.197993i
$571$	−35.4931			−1.48534			−0.742669	−	0.669658i	$-0.766441\pi$
$571$	−35.4931			−1.48534			−0.742669	+	0.669658i	$0.766441\pi$
$572$	4.25783	+	7.37477i	0.178029	+	0.308355i
$573$	−3.37012	+	2.70040i	−0.140789	+	0.112811i
$574$	−18.3843	+	11.2399i	−0.767344	+	0.469144i
$575$	1.91582			0.0798952
$576$	0.653981	−	2.92785i	0.0272492	−	0.121994i
$577$	−9.11156	−	15.7817i	−0.379319	−	0.657000i	0.611644	−	0.791133i	$-0.290508\pi$
$577$	−9.11156	−	15.7817i	−0.379319	−	0.657000i	−0.990963	+	0.134133i	$0.957175\pi$
$578$	1.39548	−	2.41705i	0.0580445	−	0.100536i
$579$	−25.8979	+	20.7514i	−1.07628	+	0.862397i
$580$	0.725310	−	1.25627i	0.0301169	−	0.0521640i
$581$	0.198224	+	7.87959i	0.00822373	+	0.326900i
$582$	19.9811	+	7.78854i	0.828243	+	0.322845i
$583$	12.0095			0.497385
$584$	−7.69829	−	13.3338i	−0.318558	−	0.551758i
$585$	−2.85431	+	12.7787i	−0.118011	+	0.528333i
$586$	0.549142	−	0.951142i	0.0226849	−	0.0392913i
$587$	8.24544	+	14.2815i	0.340326	+	0.589461i	0.984493	−	0.175423i	$-0.0561294\pi$
$587$	8.24544	+	14.2815i	0.340326	+	0.589461i	−0.644167	+	0.764884i	$0.722796\pi$
$588$	11.5036	+	3.82975i	0.474401	+	0.157936i
$589$	6.07480	−	10.5219i	0.250308	−	0.433546i
$590$	−4.05318	−	7.02031i	−0.166867	−	0.289022i
$591$	17.0905	−	13.6942i	0.703008	−	0.563304i
$592$	−1.44648	+	2.50538i	−0.0594500	+	0.102970i
$593$	−5.75349	+	9.96534i	−0.236268	+	0.409227i	−0.959640	−	0.281230i	$-0.909258\pi$
$593$	−5.75349	+	9.96534i	−0.236268	+	0.409227i	0.723373	+	0.690458i	$0.242591\pi$
$594$	−10.1149	−	0.687229i	−0.415021	−	0.0281974i
$595$	10.0420	−	6.13957i	0.411683	−	0.251698i
$596$	3.72142	+	6.44569i	0.152435	+	0.264026i
$597$	32.4105	+	12.6335i	1.32647	+	0.517053i
$598$	8.36163			0.341933
$599$	30.2105			1.23437			0.617184	−	0.786819i	$-0.288274\pi$
$599$	30.2105			1.23437			0.617184	+	0.786819i	$0.288274\pi$
$600$	−0.262123	−	1.71210i	−0.0107011	−	0.0698963i
$601$	−6.52349	−	11.2990i	−0.266099	−	0.460896i	0.701752	−	0.712421i	$-0.252401\pi$
$601$	−6.52349	−	11.2990i	−0.266099	−	0.460896i	−0.967851	+	0.251525i	$0.919068\pi$
$602$	0.186159	+	7.39999i	0.00758728	+	0.301601i
$603$	−7.24554	+	32.4380i	−0.295061	+	1.32098i
$604$	−3.31670	+	5.74470i	−0.134955	+	0.233748i
$605$	3.59659	−	6.22948i	0.146222	−	0.253264i
$606$	−1.51425	−	9.89060i	−0.0615122	−	0.401778i
$607$	−18.2681	−	31.6412i	−0.741478	−	1.28428i	−0.951822	−	0.306650i	$-0.900792\pi$
$607$	−18.2681	−	31.6412i	−0.741478	−	1.28428i	0.210345	−	0.977627i	$-0.432541\pi$
$608$	−2.18226	+	3.77979i	−0.0885024	+	0.153291i
$609$	4.28590	+	5.08148i	0.173673	+	0.205912i
$610$	0.261672	+	0.453230i	0.0105948	+	0.0183507i
$611$	−14.8346	+	25.6943i	−0.600144	+	1.03948i
$612$	12.7348	−	3.99298i	0.514773	−	0.161407i
$613$	5.27920	+	9.14385i	0.213225	+	0.369317i	0.952722	−	0.303843i	$-0.0982699\pi$
$613$	5.27920	+	9.14385i	0.213225	+	0.369317i	−0.739497	+	0.673160i	$0.764937\pi$
$614$	24.2439			0.978405
$615$	−11.0084	+	8.82081i	−0.443903	+	0.355690i
$616$	4.40422	−	2.69268i	0.177451	−	0.108491i
$617$	−6.87172	+	11.9022i	−0.276645	+	0.479163i	−0.970549	−	0.240905i	$-0.922556\pi$
$617$	−6.87172	+	11.9022i	−0.276645	+	0.479163i	0.693904	+	0.720068i	$0.255889\pi$
$618$	−21.6312	−	8.43174i	−0.870134	−	0.339174i
$619$	−18.5457	+	32.1221i	−0.745415	+	1.29110i	0.204586	+	0.978849i	$0.434415\pi$
$619$	−18.5457	+	32.1221i	−0.745415	+	1.29110i	−0.950001	+	0.312247i	$0.898918\pi$
$620$	−1.39186	−	2.41077i	−0.0558984	−	0.0968188i
$621$	−5.55039	+	8.26395i	−0.222729	+	0.331621i
$622$	−32.9797			−1.32236
$623$	20.8947	−	12.7747i	0.837127	−	0.511809i
$624$	−1.14404	−	7.47251i	−0.0457983	−	0.299140i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−22.7978			−0.911182
$627$	13.7424	+	5.35673i	0.548820	+	0.213927i
$628$	10.0020			0.399122
$629$	−12.8699			−0.513157
$630$	7.78743	+	1.53491i	0.310259	+	0.0611524i
$631$	−5.65943			−0.225298			−0.112649	−	0.993635i	$-0.535934\pi$
$631$	−5.65943			−0.225298			−0.112649	+	0.993635i	$0.535934\pi$
$632$	−7.55094			−0.300360
$633$	0.517088	+	3.37745i	0.0205524	+	0.134242i
$634$	−16.1846			−0.642771
$635$	8.52655	+	14.7684i	0.338366	+	0.586067i
$636$	−9.93325	−	3.87193i	−0.393879	−	0.153532i
$637$	30.5130	−	1.53618i	1.20897	−	0.0608658i
$638$	2.83032			0.112053
$639$	10.6850	−	47.8365i	0.422693	−	1.89238i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−19.9524	+	34.5585i	−0.788071	+	1.36498i	0.139076	+	0.990282i	$0.455587\pi$
$641$	−19.9524	+	34.5585i	−0.788071	+	1.36498i	−0.927147	+	0.374698i	$0.877747\pi$
$642$	0.0751289	+	0.490718i	0.00296510	+	0.0193671i
$643$	5.44186	−	9.42557i	0.214606	−	0.371708i	−0.738545	−	0.674205i	$-0.764487\pi$
$643$	5.44186	−	9.42557i	0.214606	−	0.371708i	0.953151	+	0.302496i	$0.0978200\pi$
$644$	−0.127473	−	5.06718i	−0.00502315	−	0.199675i
$645$	0.733372	+	4.79015i	0.0288765	+	0.188612i
$646$	−19.4165			−0.763931
$647$	−18.1896	−	31.5053i	−0.715108	−	1.23860i	−0.962918	−	0.269794i	$-0.913044\pi$
$647$	−18.1896	−	31.5053i	−0.715108	−	1.23860i	0.247810	−	0.968809i	$-0.420289\pi$
$648$	8.14462	+	3.82952i	0.319951	+	0.150438i
$649$	7.90818	−	13.6974i	0.310423	−	0.537669i
$650$	−2.18226	−	3.77979i	−0.0855953	−	0.148255i
$651$	12.5571	−	2.24705i	0.492153	−	0.0880686i
$652$	−9.74187	+	16.8734i	−0.381521	+	0.660814i
$653$	−12.1389	−	21.0252i	−0.475033	−	0.822781i	0.524558	−	0.851375i	$-0.324230\pi$
$653$	−12.1389	−	21.0252i	−0.475033	−	0.822781i	−0.999591	+	0.0285935i	$0.990897\pi$
$654$	18.9058	+	7.36940i	0.739276	+	0.288166i
$655$	6.05853	−	10.4937i	0.236726	−	0.410022i
$656$	4.07219	−	7.05324i	0.158992	−	0.275383i
$657$	44.0740	−	13.8194i	1.71949	−	0.539146i
$658$	15.7970	+	8.59812i	0.615831	+	0.335189i
$659$	−11.6790	−	20.2285i	−0.454948	−	0.787992i	0.543738	−	0.839255i	$-0.317009\pi$
$659$	−11.6790	−	20.2285i	−0.454948	−	0.787992i	−0.998685	+	0.0512629i	$0.983675\pi$
$660$	2.63724	−	2.11316i	0.102654	−	0.0822545i
$661$	38.7731			1.50810			0.754049	−	0.656819i	$-0.228098\pi$
$661$	38.7731			1.50810			0.754049	+	0.656819i	$0.228098\pi$
$662$	−26.0659			−1.01308
$663$	26.2445	−	21.0291i	1.01925	−	0.816703i
$664$	−1.48957	−	2.58002i	−0.0578067	−	0.100124i
$665$	−10.1424	−	5.52040i	−0.393306	−	0.214072i
$666$	−6.38940	−	5.87355i	−0.247584	−	0.227595i
$667$	1.38956	−	2.40679i	0.0538041	−	0.0931914i
$668$	−11.3506	+	19.6598i	−0.439167	+	0.760660i
$669$	−15.3783	−	5.99439i	−0.594559	−	0.231756i
$670$	−5.53957	−	9.59481i	−0.214012	−	0.370680i
$671$	−0.510551	+	0.884300i	−0.0197096	+	0.0341380i
$672$	−4.51092	+	0.807211i	−0.174013	+	0.0311388i
$673$	−1.74075	−	3.01507i	−0.0671011	−	0.116222i	0.830523	−	0.556984i	$-0.188042\pi$
$673$	−1.74075	−	3.01507i	−0.0671011	−	0.116222i	−0.897624	+	0.440762i	$0.854708\pi$
$674$	4.71953	−	8.17447i	0.181790	−	0.314869i
$675$	5.18420	+	0.352225i	0.199540	+	0.0135572i
$676$	−3.02453	−	5.23864i	−0.116328	−	0.201486i
$677$	42.6713			1.63999			0.819996	−	0.572369i	$-0.193976\pi$
$677$	42.6713			1.63999			0.819996	+	0.572369i	$0.193976\pi$
$678$	−2.17498	−	14.2063i	−0.0835297	−	0.545589i
$679$	−0.823832	−	32.7480i	−0.0316158	−	1.25675i
$680$	−2.22435	+	3.85269i	−0.0853000	+	0.147744i
$681$	−1.40209	−	9.15803i	−0.0537284	−	0.350937i
$682$	2.71566	−	4.70367i	0.103988	−	0.180113i
$683$	18.2150	+	31.5493i	0.696977	+	1.20720i	0.969510	+	0.245053i	$0.0788054\pi$
$683$	18.2150	+	31.5493i	0.696977	+	1.20720i	−0.272533	+	0.962147i	$0.587861\pi$
$684$	−9.63950	−	8.86124i	−0.368575	−	0.338818i
$685$	13.9200			0.531857
$686$	−1.39610	−	18.4676i	−0.0533035	−	0.705095i
$687$	9.48796	+	3.69836i	0.361988	+	0.141101i
$688$	−1.39891	−	2.42298i	−0.0533329	−	0.0923753i
$689$	−26.8647			−1.02346
$690$	−0.502180	−	3.28008i	−0.0191176	−	0.124870i
$691$	42.1047			1.60174			0.800870	−	0.598838i	$-0.204371\pi$
$691$	42.1047			1.60174			0.800870	+	0.598838i	$0.204371\pi$
$692$	−9.96320			−0.378744
$693$	5.00350	+	14.6559i	0.190067	+	0.556730i
$694$	−25.3732			−0.963153
$695$	22.3459			0.847627
$696$	−2.34099	−	0.912507i	−0.0887350	−	0.0345885i
$697$	36.2319			1.37238
$698$	8.02651	+	13.9023i	0.303808	+	0.526210i
$699$	−5.08664	−	33.2243i	−0.192394	−	1.25666i
$700$	−2.25729	+	1.38008i	−0.0853177	+	0.0521621i
$701$	−11.5020			−0.434425			−0.217212	−	0.976124i	$-0.569696\pi$
$701$	−11.5020			−0.434425			−0.217212	+	0.976124i	$0.569696\pi$
$702$	22.6266	+	1.53730i	0.853985	+	0.0580215i
$703$	6.31319	+	10.9348i	0.238107	+	0.412413i
$704$	−0.975553	+	1.68971i	−0.0367676	+	0.0636833i
$705$	10.9702	+	4.27614i	0.413162	+	0.161049i
$706$	11.8383	−	20.5045i	0.445540	−	0.771698i
$707$	−13.0401	+	7.97255i	−0.490424	+	0.299839i
$708$	−10.9571	+	8.77963i	−0.411791	+	0.329959i
$709$	21.5931			0.810945			0.405473	−	0.914107i	$-0.367107\pi$
$709$	21.5931			0.810945			0.405473	+	0.914107i	$0.367107\pi$
$710$	8.16922	+	14.1495i	0.306585	+	0.531022i
$711$	4.93817	−	22.1080i	0.185196	−	0.829116i
$712$	−4.62826	+	8.01637i	−0.173451	+	0.300426i
$713$	−2.66655	−	4.61860i	−0.0998630	−	0.172968i
$714$	−13.1438	−	15.5837i	−0.491895	−	0.583204i
$715$	4.25783	−	7.37477i	0.159234	−	0.275801i
$716$	2.42336	+	4.19738i	0.0905651	+	0.156863i
$717$	−3.95502	−	25.8329i	−0.147703	−	0.964748i
$718$	5.38333	−	9.32419i	0.200904	−	0.347976i
$719$	−9.97207	+	17.2721i	−0.371895	+	0.644142i	−0.989857	−	0.142066i	$-0.954625\pi$
$719$	−9.97207	+	17.2721i	−0.371895	+	0.644142i	0.617962	+	0.786208i	$0.287959\pi$
$720$	−2.86258	+	0.897561i	−0.106682	+	0.0334501i
$721$	0.891866	+	35.4525i	0.0332148	+	1.32032i
$722$	0.0245294	+	0.0424862i	0.000912890	+	0.00158117i
$723$	1.08941	+	7.11566i	0.0405155	+	0.264634i
$724$	1.87609			0.0697243
$725$	−1.45062			−0.0538747
$726$	−11.6082	−	4.52484i	−0.430822	−	0.167933i
$727$	4.04784	+	7.01107i	0.150126	+	0.260026i	0.931274	−	0.364320i	$-0.118699\pi$
$727$	4.04784	+	7.01107i	0.150126	+	0.260026i	−0.781148	+	0.624346i	$0.785365\pi$
$728$	−9.85201	+	6.02339i	−0.365140	+	0.223242i
$729$	−16.5387	+	21.3418i	−0.612544	+	0.790437i
$730$	−7.69829	+	13.3338i	−0.284927	+	0.493507i
$731$	6.22334	−	10.7791i	0.230178	−	0.398681i
$732$	0.707385	−	0.566812i	0.0261457	−	0.0209500i
$733$	12.0305	+	20.8374i	0.444357	+	0.769648i	0.998007	−	0.0631009i	$-0.0200990\pi$
$733$	12.0305	+	20.8374i	0.444357	+	0.769648i	−0.553651	+	0.832749i	$0.686766\pi$
$734$	10.4353	−	18.0745i	0.385176	−	0.667144i
$735$	−2.43515	−	11.8773i	−0.0898218	−	0.438101i
$736$	0.957909	+	1.65915i	0.0353090	+	0.0611570i
$737$	10.8083	−	18.7205i	0.398128	−	0.689579i
$738$	17.9877	+	16.5354i	0.662136	+	0.608678i
$739$	21.2530	+	36.8113i	0.781805	+	1.35413i	0.930889	+	0.365302i	$0.119034\pi$
$739$	21.2530	+	36.8113i	0.781805	+	1.35413i	−0.149083	+	0.988825i	$0.547632\pi$
$740$	2.89296			0.106347
$741$	−30.7411	−	11.9827i	−1.12930	−	0.440197i
$742$	0.409553	+	16.2801i	0.0150352	+	0.597661i
$743$	−1.81072	+	3.13626i	−0.0664289	+	0.115058i	−0.897327	−	0.441366i	$-0.854494\pi$
$743$	−1.81072	+	3.13626i	−0.0664289	+	0.115058i	0.830898	+	0.556425i	$0.187827\pi$
$744$	−3.76264	+	3.01492i	−0.137945	+	0.110532i
$745$	3.72142	−	6.44569i	0.136342	−	0.236152i
$746$	1.51656	+	2.62677i	0.0555254	+	0.0961727i
$747$	8.52806	−	2.67397i	0.312025	−	0.0978354i
$748$	−8.67990			−0.317368
$749$	0.646979	−	0.395555i	0.0236401	−	0.0144533i
$750$	−1.35166	+	1.08306i	−0.0493557	+	0.0395476i
$751$	8.43848	+	14.6159i	0.307925	+	0.533341i	0.977908	−	0.209035i	$-0.0670322\pi$
$751$	8.43848	+	14.6159i	0.307925	+	0.533341i	−0.669984	+	0.742376i	$0.733699\pi$
$752$	−6.79782			−0.247891
$753$	−24.1500	+	19.3509i	−0.880076	+	0.705185i
$754$	−6.33127			−0.230571
$755$	6.63341			0.241414
$756$	0.586664	−	13.7352i	0.0213368	−	0.499545i
$757$	−30.2150			−1.09818			−0.549092	−	0.835762i	$-0.685026\pi$
$757$	−30.2150			−1.09818			−0.549092	+	0.835762i	$0.685026\pi$
$758$	24.2090			0.879310
$759$	5.05247	−	4.04843i	0.183393	−	0.146949i
$760$	4.36452			0.158318
$761$	−15.8907	−	27.5235i	−0.576037	−	0.997725i	−0.995928	−	0.0901506i	$-0.971265\pi$
$761$	−15.8907	−	27.5235i	−0.576037	−	0.997725i	0.419891	−	0.907574i	$-0.362068\pi$
$762$	23.0500	−	18.4695i	0.835014	−	0.669078i
$763$	−0.779497	−	30.9857i	−0.0282197	−	1.12176i
$764$	−2.49331			−0.0902050
$765$	−9.82542	−	9.03216i	−0.355239	−	0.326558i
$766$	−14.8738	−	25.7623i	−0.537414	−	0.930828i
$767$	−17.6902	+	30.6403i	−0.638756	+	1.10636i
$768$	1.35166	−	1.08306i	0.0487739	−	0.0390814i
$769$	−22.8027	+	39.4954i	−0.822286	+	1.42424i	0.0816900	+	0.996658i	$0.473968\pi$
$769$	−22.8027	+	39.4954i	−0.822286	+	1.42424i	−0.903976	+	0.427583i	$0.859365\pi$
$770$	−4.53404	−	2.46783i	−0.163396	−	0.0889343i
$771$	35.9424	+	14.0102i	1.29444	+	0.504565i
$772$	−19.1600			−0.689584
$773$	−24.0935	−	41.7312i	−0.866585	−	1.50097i	−0.865465	−	0.500969i	$-0.832977\pi$
$773$	−24.0935	−	41.7312i	−0.866585	−	1.50097i	−0.00111947	−	0.999999i	$-0.500356\pi$
$774$	8.00899	−	2.51121i	0.287877	−	0.0902637i
$775$	−1.39186	+	2.41077i	−0.0499970	+	0.0865974i
$776$	6.19076	+	10.7227i	0.222235	+	0.384923i
$777$	−4.50259	+	12.4692i	−0.161530	+	0.447329i
$778$	−0.628857	+	1.08921i	−0.0225456	+	0.0390501i
$779$	−17.7732	−	30.7840i	−0.636790	−	1.10295i
$780$	−5.89936	+	4.72702i	−0.211231	+	0.169255i
$781$	−15.9390	+	27.6072i	−0.570343	+	0.987863i
$782$	−4.26146	+	7.38106i	−0.152389	+	0.263946i
$783$	4.20265	−	6.25731i	0.150190	−	0.223618i
$784$	3.80039	+	5.87852i	0.135728	+	0.209947i
$785$	−5.00098	−	8.66195i	−0.178493	−	0.309158i
$786$	−19.5543	−	7.62219i	−0.697480	−	0.271875i
$787$	−0.551762			−0.0196682			−0.00983410	−	0.999952i	$-0.503130\pi$
$787$	−0.551762			−0.0196682			−0.00983410	+	0.999952i	$0.503130\pi$
$788$	12.6440			0.450425
$789$	−4.27118	−	27.8980i	−0.152058	−	0.993193i
$790$	3.77547	+	6.53930i	0.134325	+	0.232658i
$791$	−18.7301	+	11.4513i	−0.665965	+	0.407162i
$792$	−4.30922	−	3.96131i	−0.153121	−	0.140759i
$793$	1.14208	−	1.97813i	0.0405563	−	0.0702455i
$794$	−14.3741	+	24.8967i	−0.510118	+	0.883551i
$795$	1.61343	+	10.5384i	0.0572225	+	0.373759i
$796$	10.0418	+	17.3929i	0.355921	+	0.616473i
$797$	−7.30285	+	12.6489i	−0.258680	+	0.448047i	−0.965889	−	0.258958i	$-0.916621\pi$
$797$	−7.30285	+	12.6489i	−0.258680	+	0.448047i	0.707209	+	0.707005i	$0.249954\pi$
$798$	−6.79292	+	18.8119i	−0.240467	+	0.665933i
$799$	−15.1207	−	26.1899i	−0.534933	−	0.926532i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−20.4440	−	18.7934i	−0.722352	−	0.664032i
$802$	12.8554	+	22.2662i	0.453939	+	0.786246i
$803$	−30.0404			−1.06010
$804$	−14.9752	+	11.9993i	−0.528136	+	0.423183i
$805$	−4.32457	+	2.64398i	−0.152421	+	0.0931882i
$806$	−6.07480	+	10.5219i	−0.213976	+	0.370617i
$807$	−12.4144	−	4.83906i	−0.437006	−	0.170343i
$808$	2.88844	−	5.00292i	0.101615	−	0.176002i
$809$	27.2636	+	47.2219i	0.958537	+	1.66023i	0.726059	+	0.687632i	$0.241350\pi$
$809$	27.2636	+	47.2219i	0.958537	+	1.66023i	0.232477	+	0.972602i	$0.425317\pi$
$810$	−0.755851	−	8.96820i	−0.0265579	−	0.315111i
$811$	21.0842			0.740367			0.370184	−	0.928959i	$-0.379295\pi$
$811$	21.0842			0.740367			0.370184	+	0.928959i	$0.379295\pi$
$812$	0.0965203	+	3.83677i	0.00338720	+	0.134644i
$813$	−1.74531	−	11.3998i	−0.0612108	−	0.399809i
$814$	2.82224	+	4.88826i	0.0989194	+	0.171333i
$815$	19.4837			0.682486
$816$	7.17925	+	2.79844i	0.251324	+	0.0979650i
$817$	−12.2111			−0.427214
$818$	18.9989			0.664282
$819$	−11.1926	−	32.7844i	−0.391100	−	1.14558i
$820$	−8.14438			−0.284414
$821$	−17.9837			−0.627635			−0.313817	−	0.949483i	$-0.601608\pi$
$821$	−17.9837			−0.627635			−0.313817	+	0.949483i	$0.601608\pi$
$822$	−3.64875	−	23.8325i	−0.127265	−	0.831254i
$823$	−31.5369			−1.09931			−0.549654	−	0.835393i	$-0.685240\pi$
$823$	−31.5369			−1.09931			−0.549654	+	0.835393i	$0.685240\pi$
$824$	−6.70201	−	11.6082i	−0.233476	−	0.404391i
$825$	−3.14867	−	1.22734i	−0.109623	−	0.0427303i
$826$	18.8378	+	10.2532i	0.655451	+	0.356754i
$827$	33.9625			1.18099			0.590496	−	0.807041i	$-0.298932\pi$
$827$	33.9625			1.18099			0.590496	+	0.807041i	$0.298932\pi$
$828$	−5.48419	+	1.71956i	−0.190589	+	0.0597590i
$829$	18.2714	+	31.6470i	0.634593	+	1.09915i	0.986601	+	0.163150i	$0.0521654\pi$
$829$	18.2714	+	31.6470i	0.634593	+	1.09915i	−0.352009	+	0.935997i	$0.614501\pi$
$830$	−1.48957	+	2.58002i	−0.0517039	+	0.0895537i
$831$	−6.91195	−	45.1466i	−0.239773	−	1.56612i
$832$	2.18226	−	3.77979i	0.0756563	−	0.131041i
$833$	−14.1947	+	27.7176i	−0.491818	+	0.960359i
$834$	−5.85736	−	38.2584i	−0.202824	−	1.32478i
$835$	22.7012			0.785606
$836$	4.25783	+	7.37477i	0.147260	+	0.255062i
$837$	−6.36654	−	12.9882i	−0.220060	−	0.448936i
$838$	13.7359	−	23.7914i	0.474500	−	0.821859i
$839$	−9.57790	−	16.5894i	−0.330666	−	0.572730i	0.651977	−	0.758239i	$-0.273940\pi$
$839$	−9.57790	−	16.5894i	−0.330666	−	0.572730i	−0.982643	+	0.185509i	$0.940607\pi$
$840$	2.95453	+	3.50297i	0.101941	+	0.120864i
$841$	13.4478	−	23.2924i	0.463719	−	0.803185i
$842$	4.13097	+	7.15504i	0.142362	+	0.246579i
$843$	−49.4096	−	19.2596i	−1.70176	−	0.663337i
$844$	−0.986346	+	1.70840i	−0.0339514	+	0.0588056i
$845$	−3.02453	+	5.23864i	−0.104047	+	0.180215i
$846$	4.44564	−	19.9030i	0.152844	−	0.684279i
$847$	0.478614	+	19.0254i	0.0164454	+	0.653719i
$848$	−3.07762	−	5.33060i	−0.105686	−	0.183054i
$849$	−38.9094	+	31.1772i	−1.33537	+	1.07000i
$850$	4.44870			0.152589
$851$	5.54239			0.189991
$852$	22.0841	−	17.6954i	0.756587	−	0.606236i
$853$	−26.7657	−	46.3595i	−0.916439	−	1.58732i	−0.804781	−	0.593571i	$-0.797717\pi$
$853$	−26.7657	−	46.3595i	−0.916439	−	1.58732i	−0.111657	−	0.993747i	$-0.535616\pi$
$854$	−1.21617	−	0.661944i	−0.0416163	−	0.0226513i
$855$	−2.85431	+	12.7787i	−0.0976155	+	0.437021i
$856$	−0.143309	+	0.248218i	−0.00489819	+	0.00848391i
$857$	15.3692	−	26.6203i	0.525002	−	0.909331i	−0.474574	−	0.880216i	$-0.657398\pi$
$857$	15.3692	−	26.6203i	0.525002	−	0.909331i	0.999576	−	0.0291151i	$-0.00926895\pi$
$858$	−13.7424	−	5.35673i	−0.469159	−	0.182876i
$859$	1.38692	+	2.40222i	0.0473211	+	0.0819625i	0.888716	−	0.458459i	$-0.151598\pi$
$859$	1.38692	+	2.40222i	0.0473211	+	0.0819625i	−0.841395	+	0.540421i	$0.818265\pi$
$860$	−1.39891	+	2.42298i	−0.0477024	+	0.0826230i
$861$	12.6759	−	35.1037i	0.431993	−	1.19633i
$862$	9.94534	+	17.2258i	0.338740	+	0.586714i
$863$	5.72509	−	9.91615i	0.194884	−	0.337550i	−0.751978	−	0.659188i	$-0.770900\pi$
$863$	5.72509	−	9.91615i	0.194884	−	0.337550i	0.946863	+	0.321638i	$0.104233\pi$
$864$	2.28706	+	4.66576i	0.0778075	+	0.158732i
$865$	4.98160	+	8.62839i	0.169380	+	0.293374i
$866$	−10.8766			−0.369600
$867$	0.731576	+	4.77842i	0.0248456	+	0.162284i
$868$	6.46889	+	3.52094i	0.219568	+	0.119508i
$869$	−7.36634	+	12.7589i	−0.249886	+	0.432815i
$870$	0.380241	+	2.48361i	0.0128914	+	0.0842023i
$871$	−24.1776	+	41.8768i	−0.819225	+	1.41894i
$872$	5.85760	+	10.1457i	0.198363	+	0.343575i
$873$	−35.4431	+	11.1132i	−1.19957	+	0.376124i
$874$	8.36163			0.282836
$875$	2.32383	+	1.26483i	0.0785599	+	0.0427592i
$876$	24.8468	+	9.68516i	0.839495	+	0.327231i
$877$	−4.51334	−	7.81733i	−0.152405	−	0.263972i	0.779706	−	0.626145i	$-0.215368\pi$
$877$	−4.51334	−	7.81733i	−0.152405	−	0.263972i	−0.932111	+	0.362173i	$0.882035\pi$
$878$	3.64494			0.123011
$879$	0.287885	+	1.88037i	0.00971013	+	0.0634235i
$880$	1.95111			0.0657718
$881$	49.8752			1.68034			0.840169	−	0.542325i	$-0.182456\pi$
$881$	49.8752			1.68034			0.840169	+	0.542325i	$0.182456\pi$
$882$	−19.6968	+	7.28253i	−0.663226	+	0.245215i
$883$	35.4377			1.19257			0.596286	−	0.802772i	$-0.296642\pi$
$883$	35.4377			1.19257			0.596286	+	0.802772i	$0.296642\pi$
$884$	19.4165			0.653047
$885$	13.0819	+	5.09927i	0.439744	+	0.171410i
$886$	19.0366			0.639549
$887$	20.1250	+	34.8575i	0.675730	+	1.17040i	0.976255	+	0.216625i	$0.0695050\pi$
$887$	20.1250	+	34.8575i	0.675730	+	1.17040i	−0.300524	+	0.953774i	$0.597162\pi$
$888$	−0.758310	−	4.95304i	−0.0254472	−	0.166213i
$889$	−39.6285	−	21.5693i	−1.32910	−	0.723413i
$890$	9.25651			0.310279
$891$	14.4163	−	10.0261i	0.482963	−	0.335888i
$892$	−4.76467	−	8.25264i	−0.159533	−	0.276319i
$893$	−14.8346	+	25.6943i	−0.496422	+	0.859827i
$894$	−12.0111	−	4.68189i	−0.401713	−	0.156586i
$895$	2.42336	−	4.19738i	0.0810039	−	0.140303i
$896$	−2.32383	−	1.26483i	−0.0776338	−	0.0422551i
$897$	−11.3021	+	9.05612i	−0.377366	+	0.302375i
$898$	−5.22159			−0.174247
$899$	2.01906	+	3.49711i	0.0673394	+	0.116635i
$900$	2.20860	+	2.03029i	0.0736201	+	0.0676763i
$901$	13.6914	−	23.7143i	0.456128	−	0.790037i
$902$	−7.94528	−	13.7616i	−0.264549	−	0.458212i
$903$	−8.26623	−	9.80067i	−0.275083	−	0.326146i
$904$	4.14879	−	7.18591i	0.137987	−	0.239000i
$905$	−0.938045	−	1.62474i	−0.0311817	−	0.0540082i
$906$	−1.73877	−	11.3571i	−0.0577666	−	0.377313i
$907$	23.2449	−	40.2614i	0.771835	−	1.33686i	−0.164721	−	0.986340i	$-0.552672\pi$
$907$	23.2449	−	40.2614i	0.771835	−	1.33686i	0.936556	−	0.350518i	$-0.113994\pi$
$908$	2.67450	−	4.63237i	0.0887564	−	0.153731i
$909$	12.7588	+	11.7287i	0.423184	+	0.389017i
$910$	10.1424	+	5.52040i	0.336218	+	0.182999i
$911$	3.12575	+	5.41395i	0.103561	+	0.179372i	0.913149	−	0.407626i	$-0.133643\pi$
$911$	3.12575	+	5.41395i	0.103561	+	0.179372i	−0.809589	+	0.586998i	$0.800310\pi$
$912$	−1.14404	−	7.47251i	−0.0378830	−	0.247439i
$913$	−5.81263			−0.192370
$914$	22.6223			0.748279
$915$	−0.844566	−	0.329208i	−0.0279205	−	0.0108833i
$916$	2.93966	+	5.09164i	0.0971292	+	0.168233i
$917$	0.806236	+	32.0486i	0.0266243	+	1.05834i
$918$	−12.8885	+	19.1896i	−0.425384	+	0.633353i
$919$	−25.6342	+	44.3997i	−0.845594	+	1.46461i	0.0395113	+	0.999219i	$0.487420\pi$
$919$	−25.6342	+	44.3997i	−0.845594	+	1.46461i	−0.885105	+	0.465392i	$0.845913\pi$
$920$	0.957909	−	1.65915i	0.0315813	−	0.0547005i
$921$	−32.7696	+	26.2575i	−1.07979	+	0.865215i
$922$	12.0085	+	20.7994i	0.395480	+	0.684991i
$923$	35.6548	−	61.7558i	1.17359	−	2.03272i
$924$	−3.03669	+	8.40962i	−0.0998999	+	0.276656i
$925$	−1.44648	−	2.50538i	−0.0475600	−	0.0823763i
$926$	−3.05932	+	5.29890i	−0.100535	+	0.174133i
$927$	38.3701	−	12.0309i	1.26024	−	0.395147i
$928$	−0.725310	−	1.25627i	−0.0238095	−	0.0412392i
$929$	−20.4326			−0.670372			−0.335186	−	0.942152i	$-0.608799\pi$
$929$	−20.4326			−0.670372			−0.335186	+	0.942152i	$0.608799\pi$
$930$	4.49232	+	1.75109i	0.147309	+	0.0574203i
$931$	30.5130	−	1.53618i	1.00002	−	0.0503464i
$932$	9.70278	−	16.8057i	0.317825	−	0.550489i
$933$	44.5774	−	35.7188i	1.45940	−	1.16938i
$934$	9.30663	−	16.1196i	0.304522	−	0.527448i
$935$	4.33995	+	7.51701i	0.141931	+	0.245833i
$936$	9.63950	+	8.86124i	0.315077	+	0.289639i
$937$	33.9435			1.10889			0.554444	−	0.832221i	$-0.312931\pi$
$937$	33.9435			1.10889			0.554444	+	0.832221i	$0.312931\pi$
$938$	25.7460	+	14.0133i	0.840638	+	0.457549i
$939$	30.8149	−	24.6913i	1.00561	−	0.805769i
$940$	3.39891	+	5.88708i	0.110860	+	0.192016i
$941$	−16.3649			−0.533480			−0.266740	−	0.963769i	$-0.585946\pi$
$941$	−16.3649			−0.533480			−0.266740	+	0.963769i	$0.585946\pi$
$942$	−13.5193	+	10.8327i	−0.440482	+	0.352948i
$943$	−15.6032			−0.508109
$944$	−8.10635			−0.263839
$945$	−12.1884	+	6.35954i	−0.396488	+	0.206876i
$946$	−5.45884			−0.177482
$947$	−2.36977			−0.0770071			−0.0385035	−	0.999258i	$-0.512259\pi$
$947$	−2.36977			−0.0770071			−0.0385035	+	0.999258i	$0.512259\pi$
$948$	10.2063	−	8.17809i	0.331486	−	0.265612i
$949$	67.1988			2.18136
$950$	−2.18226	−	3.77979i	−0.0708019	−	0.122633i
$951$	21.8761	−	17.5288i	0.709380	−	0.568410i
$952$	−0.296004	−	11.7664i	−0.00959356	−	0.381353i
$953$	−33.1840			−1.07494			−0.537468	−	0.843284i	$-0.680619\pi$
$953$	−33.1840			−1.07494			−0.537468	+	0.843284i	$0.680619\pi$
$954$	17.6199	−	5.52471i	0.570466	−	0.178869i
$955$	1.24666	+	2.15927i	0.0403409	+	0.0698725i
$956$	7.54422	−	13.0670i	0.243997	−	0.422616i
$957$	−3.82563	+	3.06539i	−0.123665	+	0.0990900i
$958$	5.16999	−	8.95469i	0.167035	−	0.289313i
$959$	−31.4216	+	19.2107i	−1.01466	+	0.620347i
$960$	−1.61378	−	0.629046i	−0.0520847	−	0.0203024i
$961$	−23.2509			−0.750030
$962$	−6.31319	−	10.9348i	−0.203546	−	0.352551i
$963$	−0.633024	−	0.581916i	−0.0203989	−	0.0187520i
$964$	−2.07805	+	3.59929i	−0.0669295	+	0.115925i
$965$	9.58000	+	16.5930i	0.308391	+	0.534149i
$966$	5.66034	+	6.71105i	0.182118	+	0.215924i
$967$	7.34084	−	12.7147i	0.236066	−	0.408878i	−0.723516	−	0.690307i	$-0.757475\pi$
$967$	7.34084	−	12.7147i	0.236066	−	0.408878i	0.959582	+	0.281430i	$0.0908086\pi$
$968$	−3.59659	−	6.22948i	−0.115599	−	0.200223i
$969$	26.2445	−	21.0291i	0.843095	−	0.675553i
$970$	6.19076	−	10.7227i	0.198773	−	0.344285i
$971$	6.44485	−	11.1628i	0.206825	−	0.358232i	−0.743888	−	0.668305i	$-0.767020\pi$
$971$	6.44485	−	11.1628i	0.206825	−	0.358232i	0.950713	+	0.310073i	$0.100354\pi$
$972$	−15.1564	+	3.64486i	−0.486140	+	0.116909i
$973$	−50.4412	+	30.8391i	−1.61707	+	0.988656i
$974$	12.7645	+	22.1088i	0.409001	+	0.708411i
$975$	7.04340	+	2.74548i	0.225569	+	0.0879259i
$976$	0.523345			0.0167519
$977$	−54.7139			−1.75045			−0.875226	−	0.483713i	$-0.839288\pi$
$977$	−54.7139			−1.75045			−0.875226	+	0.483713i	$0.839288\pi$
$978$	−5.10713	−	33.3582i	−0.163308	−	1.06668i
$979$	9.03022	+	15.6408i	0.288607	+	0.499882i
$980$	3.19076	−	6.23049i	0.101925	−	0.199026i
$981$	−33.5357	+	10.5151i	−1.07071	+	0.335722i
$982$	−15.6620	+	27.1274i	−0.499795	+	0.865670i
$983$	8.41994	−	14.5838i	0.268555	−	0.465150i	−0.699934	−	0.714207i	$-0.746787\pi$
$983$	8.41994	−	14.5838i	0.268555	−	0.465150i	0.968489	+	0.249057i	$0.0801207\pi$
$984$	2.13483	+	13.9440i	0.0680558	+	0.444519i
$985$	−6.32202	−	10.9501i	−0.201436	−	0.348898i
$986$	3.22669	−	5.58879i	0.102759	−	0.177983i
$987$	−30.6644	+	5.48727i	−0.976059	+	0.174662i
$988$	−9.52453	−	16.4970i	−0.303016	−	0.524838i
$989$	−2.68006	+	4.64200i	−0.0852209	+	0.147607i
$990$	−1.27599	+	5.71255i	−0.0405535	+	0.181557i
$991$	−3.71053	−	6.42682i	−0.117869	−	0.204155i	0.801054	−	0.598592i	$-0.204273\pi$
$991$	−3.71053	−	6.42682i	−0.117869	−	0.204155i	−0.918923	+	0.394437i	$0.870940\pi$
$992$	−2.78372			−0.0883831
$993$	35.2323	−	28.2308i	1.11806	−	0.895877i
$994$	−37.9678	−	20.6654i	−1.20427	−	0.655467i
$995$	10.0418	−	17.3929i	0.318345	−	0.551390i
$996$	4.80770	+	1.87402i	0.152338	+	0.0593806i
$997$	−8.84289	+	15.3163i	−0.280057	+	0.485073i	−0.971399	−	0.237455i	$-0.923687\pi$
$997$	−8.84289	+	15.3163i	−0.280057	+	0.485073i	0.691341	+	0.722528i	$0.257020\pi$
$998$	6.88782	+	11.9301i	0.218030	+	0.377639i
$999$	14.9977	+	1.01897i	0.474506	+	0.0322389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.f.121.5	✓	12
3.2	odd	2		1890.2.i.h.1171.5		12
7.4	even	3		630.2.l.h.571.1	yes	12
9.2	odd	6		1890.2.l.f.1801.4		12
9.7	even	3		630.2.l.h.331.1	yes	12
21.11	odd	6		1890.2.l.f.361.4		12
63.11	odd	6		1890.2.i.h.991.5		12
63.25	even	3	inner	630.2.i.f.151.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.f.121.5	✓	12	1.1	even	1	trivial
630.2.i.f.151.5	yes	12	63.25	even	3	inner
630.2.l.h.331.1	yes	12	9.7	even	3
630.2.l.h.571.1	yes	12	7.4	even	3
1890.2.i.h.991.5		12	63.11	odd	6
1890.2.i.h.1171.5		12	3.2	odd	2
1890.2.l.f.361.4		12	21.11	odd	6
1890.2.l.f.1801.4		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.35166 - 1.08306i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.35166 + 1.08306i) q^{6} +(2.32383 + 1.26483i) q^{7} -1.00000 q^{8} +(0.653981 - 2.92785i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.35166 - 1.08306i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.35166 + 1.08306i) q^{6} +(2.32383 + 1.26483i) q^{7} -1.00000 q^{8} +(0.653981 - 2.92785i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.975553 + 1.68971i) q^{11} +(1.35166 - 1.08306i) q^{12} +(2.18226 - 3.77979i) q^{13} +(-2.32383 - 1.26483i) q^{14} +(-1.61378 - 0.629046i) q^{15} +1.00000 q^{16} +(2.22435 + 3.85269i) q^{17} +(-0.653981 + 2.92785i) q^{18} +(2.18226 - 3.77979i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(4.51092 - 0.807211i) q^{21} +(0.975553 - 1.68971i) q^{22} +(-0.957909 - 1.65915i) q^{23} +(-1.35166 + 1.08306i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.18226 + 3.77979i) q^{26} +(-2.28706 - 4.66576i) q^{27} +(2.32383 + 1.26483i) q^{28} +(0.725310 + 1.25627i) q^{29} +(1.61378 + 0.629046i) q^{30} +2.78372 q^{31} -1.00000 q^{32} +(0.511429 + 3.34049i) q^{33} +(-2.22435 - 3.85269i) q^{34} +(-0.0665372 - 2.64491i) q^{35} +(0.653981 - 2.92785i) q^{36} +(-1.44648 + 2.50538i) q^{37} +(-2.18226 + 3.77979i) q^{38} +(-1.14404 - 7.47251i) q^{39} +(0.500000 + 0.866025i) q^{40} +(4.07219 - 7.05324i) q^{41} +(-4.51092 + 0.807211i) q^{42} +(-1.39891 - 2.42298i) q^{43} +(-0.975553 + 1.68971i) q^{44} +(-2.86258 + 0.897561i) q^{45} +(0.957909 + 1.65915i) q^{46} -6.79782 q^{47} +(1.35166 - 1.08306i) q^{48} +(3.80039 + 5.87852i) q^{49} +(0.500000 - 0.866025i) q^{50} +(7.17925 + 2.79844i) q^{51} +(2.18226 - 3.77979i) q^{52} +(-3.07762 - 5.33060i) q^{53} +(2.28706 + 4.66576i) q^{54} +1.95111 q^{55} +(-2.32383 - 1.26483i) q^{56} +(-1.14404 - 7.47251i) q^{57} +(-0.725310 - 1.25627i) q^{58} -8.10635 q^{59} +(-1.61378 - 0.629046i) q^{60} +0.523345 q^{61} -2.78372 q^{62} +(5.22299 - 5.97665i) q^{63} +1.00000 q^{64} -4.36452 q^{65} +(-0.511429 - 3.34049i) q^{66} -11.0791 q^{67} +(2.22435 + 3.85269i) q^{68} +(-3.09172 - 1.20514i) q^{69} +(0.0665372 + 2.64491i) q^{70} +16.3384 q^{71} +(-0.653981 + 2.92785i) q^{72} +(7.69829 + 13.3338i) q^{73} +(1.44648 - 2.50538i) q^{74} +(0.262123 + 1.71210i) q^{75} +(2.18226 - 3.77979i) q^{76} +(-4.40422 + 2.69268i) q^{77} +(1.14404 + 7.47251i) q^{78} +7.55094 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-8.14462 - 3.82952i) q^{81} +(-4.07219 + 7.05324i) q^{82} +(1.48957 + 2.58002i) q^{83} +(4.51092 - 0.807211i) q^{84} +(2.22435 - 3.85269i) q^{85} +(1.39891 + 2.42298i) q^{86} +(2.34099 + 0.912507i) q^{87} +(0.975553 - 1.68971i) q^{88} +(4.62826 - 8.01637i) q^{89} +(2.86258 - 0.897561i) q^{90} +(9.85201 - 6.02339i) q^{91} +(-0.957909 - 1.65915i) q^{92} +(3.76264 - 3.01492i) q^{93} +6.79782 q^{94} -4.36452 q^{95} +(-1.35166 + 1.08306i) q^{96} +(-6.19076 - 10.7227i) q^{97} +(-3.80039 - 5.87852i) q^{98} +(4.30922 + 3.96131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * q^99

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