LMFDB - Embedded newform 806.2.g.g.497.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [806,2,Mod(373,806)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(806, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("806.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 806 = 2 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	806.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.43594240292$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 29 x^{18} - 54 x^{17} + 432 x^{16} - 677 x^{15} + 4182 x^{14} - 4871 x^{13} + \cdots + 59049 $ x^20 - 3x^19 + 29x^18 - 54x^17 + 432x^16 - 677x^15 + 4182x^14 - 4871x^13 + 27278x^12 - 27611x^11 + 125006x^10 - 99235x^9 + 376204x^8 - 307824x^7 + 737259x^6 - 492573x^5 + 858681x^4 - 599670x^3 + 564660x^2 - 189540*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			497.5
Root			$0.428084 - 0.741463i$ of defining polynomial
Character	$\chi$	$=$	806.497
Dual form			806.2.g.g.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.428084 - 0.741463i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.23921 q^{5} +(-0.428084 + 0.741463i) q^{6} +(2.58272 - 4.47340i) q^{7} +1.00000 q^{8} +(1.13349 - 1.96326i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.428084 - 0.741463i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.23921 q^{5} +(-0.428084 + 0.741463i) q^{6} +(2.58272 - 4.47340i) q^{7} +1.00000 q^{8} +(1.13349 - 1.96326i) q^{9} +(1.11960 + 1.93921i) q^{10} +(0.668757 + 1.15832i) q^{11} +0.856168 q^{12} +(-2.61363 + 2.48374i) q^{13} -5.16544 q^{14} +(0.958569 + 1.66029i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.94108 - 3.36205i) q^{17} -2.26698 q^{18} +(2.92964 - 5.07428i) q^{19} +(1.11960 - 1.93921i) q^{20} -4.42248 q^{21} +(0.668757 - 1.15832i) q^{22} +(2.81158 + 4.86979i) q^{23} +(-0.428084 - 0.741463i) q^{24} +0.0140566 q^{25} +(3.45779 + 1.02160i) q^{26} -4.50942 q^{27} +(2.58272 + 4.47340i) q^{28} +(-1.53948 - 2.66646i) q^{29} +(0.958569 - 1.66029i) q^{30} -1.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.572568 - 0.991718i) q^{33} -3.88216 q^{34} +(-5.78325 + 10.0169i) q^{35} +(1.13349 + 1.96326i) q^{36} +(-4.17590 - 7.23287i) q^{37} -5.85927 q^{38} +(2.96045 + 0.874662i) q^{39} -2.23921 q^{40} +(2.04713 + 3.54573i) q^{41} +(2.21124 + 3.82998i) q^{42} +(-1.25568 + 2.17490i) q^{43} -1.33751 q^{44} +(-2.53812 + 4.39615i) q^{45} +(2.81158 - 4.86979i) q^{46} -8.26408 q^{47} +(-0.428084 + 0.741463i) q^{48} +(-9.84089 - 17.0449i) q^{49} +(-0.00702829 - 0.0121733i) q^{50} -3.32378 q^{51} +(-0.844164 - 3.50534i) q^{52} -7.95742 q^{53} +(2.25471 + 3.90527i) q^{54} +(-1.49749 - 2.59372i) q^{55} +(2.58272 - 4.47340i) q^{56} -5.01652 q^{57} +(-1.53948 + 2.66646i) q^{58} +(-2.34063 + 4.05410i) q^{59} -1.91714 q^{60} +(-4.74655 + 8.22127i) q^{61} +(0.500000 + 0.866025i) q^{62} +(-5.85497 - 10.1411i) q^{63} +1.00000 q^{64} +(5.85246 - 5.56160i) q^{65} -1.14514 q^{66} +(-0.113765 - 0.197046i) q^{67} +(1.94108 + 3.36205i) q^{68} +(2.40718 - 4.16936i) q^{69} +11.5665 q^{70} +(2.02092 - 3.50033i) q^{71} +(1.13349 - 1.96326i) q^{72} +6.22699 q^{73} +(-4.17590 + 7.23287i) q^{74} +(-0.00601739 - 0.0104224i) q^{75} +(2.92964 + 5.07428i) q^{76} +6.90885 q^{77} +(-0.722746 - 3.00116i) q^{78} -2.15511 q^{79} +(1.11960 + 1.93921i) q^{80} +(-1.47006 - 2.54621i) q^{81} +(2.04713 - 3.54573i) q^{82} +0.874607 q^{83} +(2.21124 - 3.82998i) q^{84} +(-4.34648 + 7.52833i) q^{85} +2.51136 q^{86} +(-1.31805 + 2.28294i) q^{87} +(0.668757 + 1.15832i) q^{88} +(5.33405 + 9.23885i) q^{89} +5.07623 q^{90} +(4.36048 + 18.1066i) q^{91} -5.62315 q^{92} +(0.428084 + 0.741463i) q^{93} +(4.13204 + 7.15690i) q^{94} +(-6.56007 + 11.3624i) q^{95} +0.856168 q^{96} +(8.84783 - 15.3249i) q^{97} +(-9.84089 + 17.0449i) q^{98} +3.03211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{2} - 3 q^{3} - 10 q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 20 q^{8} - 19 q^{9}+O(q^{10}) $ 20 * q - 10 * q^2 - 3 * q^3 - 10 * q^4 + 6 * q^5 - 3 * q^6 - q^7 + 20 * q^8 - 19 * q^9	\( 20 q - 10 q^{2} - 3 q^{3} - 10 q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 20 q^{8} - 19 q^{9} - 3 q^{10} - 5 q^{11} + 6 q^{12} + 8 q^{13} + 2 q^{14} - 6 q^{15} - 10 q^{16} - 4 q^{17} + 38 q^{18} + 10 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} - 4 q^{23} - 3 q^{24} + 46 q^{25} - q^{26} + 36 q^{27} - q^{28} - 9 q^{29} - 6 q^{30} - 20 q^{31} - 10 q^{32} + 9 q^{33} + 8 q^{34} - 42 q^{35} - 19 q^{36} - 14 q^{37} - 20 q^{38} + 10 q^{39} + 6 q^{40} - 6 q^{41} - 2 q^{42} - 5 q^{43} + 10 q^{44} + 18 q^{45} - 4 q^{46} - 8 q^{47} - 3 q^{48} - 23 q^{49} - 23 q^{50} - 18 q^{51} - 7 q^{52} + 68 q^{53} - 18 q^{54} + 12 q^{55} - q^{56} + 46 q^{57} - 9 q^{58} - 10 q^{59} + 12 q^{60} - 30 q^{61} + 10 q^{62} - 35 q^{63} + 20 q^{64} - 6 q^{65} - 18 q^{66} + 4 q^{67} - 4 q^{68} + 21 q^{69} + 84 q^{70} - 3 q^{71} - 19 q^{72} - 12 q^{73} - 14 q^{74} + 5 q^{75} + 10 q^{76} - 62 q^{77} - 14 q^{78} + 22 q^{79} - 3 q^{80} - 10 q^{81} - 6 q^{82} + 94 q^{83} - 2 q^{84} - 25 q^{85} + 10 q^{86} - 34 q^{87} - 5 q^{88} + 4 q^{89} - 36 q^{90} + 40 q^{91} + 8 q^{92} + 3 q^{93} + 4 q^{94} - q^{95} + 6 q^{96} + 50 q^{97} - 23 q^{98} + 54 q^{99}+O(q^{100}) \) 20 * q - 10 * q^2 - 3 * q^3 - 10 * q^4 + 6 * q^5 - 3 * q^6 - q^7 + 20 * q^8 - 19 * q^9 - 3 * q^10 - 5 * q^11 + 6 * q^12 + 8 * q^13 + 2 * q^14 - 6 * q^15 - 10 * q^16 - 4 * q^17 + 38 * q^18 + 10 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 - 4 * q^23 - 3 * q^24 + 46 * q^25 - q^26 + 36 * q^27 - q^28 - 9 * q^29 - 6 * q^30 - 20 * q^31 - 10 * q^32 + 9 * q^33 + 8 * q^34 - 42 * q^35 - 19 * q^36 - 14 * q^37 - 20 * q^38 + 10 * q^39 + 6 * q^40 - 6 * q^41 - 2 * q^42 - 5 * q^43 + 10 * q^44 + 18 * q^45 - 4 * q^46 - 8 * q^47 - 3 * q^48 - 23 * q^49 - 23 * q^50 - 18 * q^51 - 7 * q^52 + 68 * q^53 - 18 * q^54 + 12 * q^55 - q^56 + 46 * q^57 - 9 * q^58 - 10 * q^59 + 12 * q^60 - 30 * q^61 + 10 * q^62 - 35 * q^63 + 20 * q^64 - 6 * q^65 - 18 * q^66 + 4 * q^67 - 4 * q^68 + 21 * q^69 + 84 * q^70 - 3 * q^71 - 19 * q^72 - 12 * q^73 - 14 * q^74 + 5 * q^75 + 10 * q^76 - 62 * q^77 - 14 * q^78 + 22 * q^79 - 3 * q^80 - 10 * q^81 - 6 * q^82 + 94 * q^83 - 2 * q^84 - 25 * q^85 + 10 * q^86 - 34 * q^87 - 5 * q^88 + 4 * q^89 - 36 * q^90 + 40 * q^91 + 8 * q^92 + 3 * q^93 + 4 * q^94 - q^95 + 6 * q^96 + 50 * q^97 - 23 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/806\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.428084	−	0.741463i	−0.247154	−	0.428084i	0.715581	−	0.698530i	$-0.246162\pi$
$3$	−0.428084	−	0.741463i	−0.247154	−	0.428084i	−0.962735	+	0.270446i	$0.912829\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.23921			−1.00140			−0.500702	−	0.865620i	$-0.666925\pi$
$5$	−2.23921			−1.00140			−0.500702	+	0.865620i	$0.666925\pi$
$6$	−0.428084	+	0.741463i	−0.174765	+	0.302701i
$7$	2.58272	−	4.47340i	0.976176	−	1.69079i	0.300180	−	0.953883i	$-0.402953\pi$
$7$	2.58272	−	4.47340i	0.976176	−	1.69079i	0.675997	−	0.736905i	$-0.263713\pi$
$8$	1.00000			0.353553
$9$	1.13349	−	1.96326i	0.377829	−	0.654420i
$10$	1.11960	+	1.93921i	0.354050	+	0.613233i
$11$	0.668757	+	1.15832i	0.201638	+	0.349247i	0.949056	−	0.315107i	$-0.102040\pi$
$11$	0.668757	+	1.15832i	0.201638	+	0.349247i	−0.747418	+	0.664354i	$0.768707\pi$
$12$	0.856168			0.247154
$13$	−2.61363	+	2.48374i	−0.724890	+	0.688864i
$13$	−2.61363	+	2.48374i	−0.724890	+	0.688864i
$14$	−5.16544			−1.38052
$15$	0.958569	+	1.66029i	0.247502	+	0.428685i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.94108	−	3.36205i	0.470781	−	0.815417i	−0.528661	−	0.848833i	$-0.677306\pi$
$17$	1.94108	−	3.36205i	0.470781	−	0.815417i	0.999442	+	0.0334168i	$0.0106389\pi$
$18$	−2.26698			−0.534331
$19$	2.92964	−	5.07428i	0.672105	−	1.16412i	−0.305201	−	0.952288i	$-0.598724\pi$
$19$	2.92964	−	5.07428i	0.672105	−	1.16412i	0.977306	−	0.211832i	$-0.0679429\pi$
$20$	1.11960	−	1.93921i	0.250351	−	0.433621i
$21$	−4.42248			−0.965065
$22$	0.668757	−	1.15832i	0.142580	−	0.246955i
$23$	2.81158	+	4.86979i	0.586254	+	1.01542i	0.994718	+	0.102648i	$0.0327314\pi$
$23$	2.81158	+	4.86979i	0.586254	+	1.01542i	−0.408464	+	0.912775i	$0.633935\pi$
$24$	−0.428084	−	0.741463i	−0.0873823	−	0.151351i
$25$	0.0140566			0.00281131
$26$	3.45779	+	1.02160i	0.678129	+	0.200353i
$27$	−4.50942			−0.867838
$28$	2.58272	+	4.47340i	0.488088	+	0.845394i
$29$	−1.53948	−	2.66646i	−0.285874	−	0.495149i	0.686946	−	0.726708i	$-0.258951\pi$
$29$	−1.53948	−	2.66646i	−0.285874	−	0.495149i	−0.972821	+	0.231559i	$0.925617\pi$
$30$	0.958569	−	1.66029i	0.175010	−	0.303126i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.572568	−	0.991718i	0.0996714	−	0.172636i
$34$	−3.88216			−0.665785
$35$	−5.78325	+	10.0169i	−0.977548	+	1.69316i
$36$	1.13349	+	1.96326i	0.188915	+	0.327210i
$37$	−4.17590	−	7.23287i	−0.686514	−	1.18908i	−0.972958	−	0.230980i	$-0.925807\pi$
$37$	−4.17590	−	7.23287i	−0.686514	−	1.18908i	0.286445	−	0.958097i	$-0.407527\pi$
$38$	−5.85927			−0.950500
$39$	2.96045	+	0.874662i	0.474052	+	0.140058i
$40$	−2.23921			−0.354050
$41$	2.04713	+	3.54573i	0.319707	+	0.553749i	0.980427	−	0.196883i	$-0.0630821\pi$
$41$	2.04713	+	3.54573i	0.319707	+	0.553749i	−0.660720	+	0.750633i	$0.729749\pi$
$42$	2.21124	+	3.82998i	0.341202	+	0.590979i
$43$	−1.25568	+	2.17490i	−0.191490	+	0.331670i	−0.945744	−	0.324912i	$-0.894665\pi$
$43$	−1.25568	+	2.17490i	−0.191490	+	0.331670i	0.754255	+	0.656582i	$0.227998\pi$
$44$	−1.33751			−0.201638
$45$	−2.53812	+	4.39615i	−0.378360	+	0.655339i
$46$	2.81158	−	4.86979i	0.414544	−	0.718012i
$47$	−8.26408			−1.20544			−0.602720	−	0.797953i	$-0.705916\pi$
$47$	−8.26408			−1.20544			−0.602720	+	0.797953i	$0.705916\pi$
$48$	−0.428084	+	0.741463i	−0.0617886	+	0.107021i
$49$	−9.84089	−	17.0449i	−1.40584	−	2.43499i
$50$	−0.00702829	−	0.0121733i	−0.000993950	−	0.00172157i
$51$	−3.32378			−0.465422
$52$	−0.844164	−	3.50534i	−0.117064	−	0.486103i
$53$	−7.95742			−1.09304			−0.546518	−	0.837448i	$-0.684047\pi$
$53$	−7.95742			−1.09304			−0.546518	+	0.837448i	$0.684047\pi$
$54$	2.25471	+	3.90527i	0.306827	+	0.531440i
$55$	−1.49749	−	2.59372i	−0.201921	−	0.349738i
$56$	2.58272	−	4.47340i	0.345131	−	0.597784i
$57$	−5.01652			−0.664455
$58$	−1.53948	+	2.66646i	−0.202144	+	0.350123i
$59$	−2.34063	+	4.05410i	−0.304725	+	0.527799i	−0.977200	−	0.212321i	$-0.931898\pi$
$59$	−2.34063	+	4.05410i	−0.304725	+	0.527799i	0.672475	+	0.740120i	$0.265231\pi$
$60$	−1.91714			−0.247502
$61$	−4.74655	+	8.22127i	−0.607734	+	1.05263i	0.383879	+	0.923383i	$0.374588\pi$
$61$	−4.74655	+	8.22127i	−0.607734	+	1.05263i	−0.991613	+	0.129242i	$0.958745\pi$
$62$	0.500000	+	0.866025i	0.0635001	+	0.109985i
$63$	−5.85497	−	10.1411i	−0.737656	−	1.27766i
$64$	1.00000			0.125000
$65$	5.85246	−	5.56160i	0.725909	−	0.689832i
$66$	−1.14514			−0.140957
$67$	−0.113765	−	0.197046i	−0.0138985	−	0.0240730i	0.858992	−	0.511988i	$-0.171091\pi$
$67$	−0.113765	−	0.197046i	−0.0138985	−	0.0240730i	−0.872891	+	0.487915i	$0.837758\pi$
$68$	1.94108	+	3.36205i	0.235390	+	0.407708i
$69$	2.40718	−	4.16936i	0.289791	−	0.501932i
$70$	11.5665			1.38246
$71$	2.02092	−	3.50033i	0.239839	−	0.415413i	−0.720829	−	0.693113i	$-0.756239\pi$
$71$	2.02092	−	3.50033i	0.239839	−	0.415413i	0.960668	+	0.277700i	$0.0895722\pi$
$72$	1.13349	−	1.96326i	0.133583	−	0.231372i
$73$	6.22699			0.728815			0.364407	−	0.931240i	$-0.381272\pi$
$73$	6.22699			0.728815			0.364407	+	0.931240i	$0.381272\pi$
$74$	−4.17590	+	7.23287i	−0.485439	+	0.840804i
$75$	−0.00601739	−	0.0104224i	−0.000694829	−	0.00120348i
$76$	2.92964	+	5.07428i	0.336052	+	0.582060i
$77$	6.90885			0.787337
$78$	−0.722746	−	3.00116i	−0.0818348	−	0.339814i
$79$	−2.15511			−0.242468			−0.121234	−	0.992624i	$-0.538685\pi$
$79$	−2.15511			−0.242468			−0.121234	+	0.992624i	$0.538685\pi$
$80$	1.11960	+	1.93921i	0.125176	+	0.216810i
$81$	−1.47006	−	2.54621i	−0.163340	−	0.282912i
$82$	2.04713	−	3.54573i	0.226067	−	0.391560i
$83$	0.874607			0.0960006			0.0480003	−	0.998847i	$-0.484715\pi$
$83$	0.874607			0.0960006			0.0480003	+	0.998847i	$0.484715\pi$
$84$	2.21124	−	3.82998i	0.241266	−	0.417885i
$85$	−4.34648	+	7.52833i	−0.471442	+	0.816562i
$86$	2.51136			0.270807
$87$	−1.31805	+	2.28294i	−0.141310	+	0.244757i
$88$	0.668757	+	1.15832i	0.0712898	+	0.123477i
$89$	5.33405	+	9.23885i	0.565408	+	0.979316i	0.997012	+	0.0772525i	$0.0246148\pi$
$89$	5.33405	+	9.23885i	0.565408	+	0.979316i	−0.431603	+	0.902064i	$0.642052\pi$
$90$	5.07623			0.535082
$91$	4.36048	+	18.1066i	0.457102	+	1.89809i
$92$	−5.62315			−0.586254
$93$	0.428084	+	0.741463i	0.0443902	+	0.0768861i
$94$	4.13204	+	7.15690i	0.426187	+	0.738178i
$95$	−6.56007	+	11.3624i	−0.673049	+	1.16575i
$96$	0.856168			0.0873823
$97$	8.84783	−	15.3249i	0.898361	−	1.55601i	0.0687712	−	0.997632i	$-0.478092\pi$
$97$	8.84783	−	15.3249i	0.898361	−	1.55601i	0.829589	−	0.558374i	$-0.188575\pi$
$98$	−9.84089	+	17.0449i	−0.994080	+	1.72180i
$99$	3.03211			0.304739
$100$	−0.00702829	+	0.0121733i	−0.000702829	+	0.00121733i
$101$	8.12205	+	14.0678i	0.808174	+	1.39980i	0.914127	+	0.405428i	$0.132878\pi$
$101$	8.12205	+	14.0678i	0.808174	+	1.39980i	−0.105953	+	0.994371i	$0.533789\pi$
$102$	1.66189	+	2.87848i	0.164552	+	0.285012i
$103$	19.8337			1.95427			0.977135	−	0.212618i	$-0.0681989\pi$
$103$	19.8337			1.95427			0.977135	+	0.212618i	$0.0681989\pi$
$104$	−2.61363	+	2.48374i	−0.256287	+	0.243550i
$105$	9.90287			0.966421
$106$	3.97871	+	6.89133i	0.386446	+	0.669345i
$107$	−9.55023	−	16.5415i	−0.923255	−	1.59912i	−0.794344	−	0.607469i	$-0.792185\pi$
$107$	−9.55023	−	16.5415i	−0.923255	−	1.59912i	−0.128912	−	0.991656i	$-0.541148\pi$
$108$	2.25471	−	3.90527i	0.216959	−	0.375785i
$109$	−3.08347			−0.295343			−0.147672	−	0.989036i	$-0.547178\pi$
$109$	−3.08347			−0.295343			−0.147672	+	0.989036i	$0.547178\pi$
$110$	−1.49749	+	2.59372i	−0.142780	+	0.247302i
$111$	−3.57527	+	6.19255i	−0.339350	+	0.587771i
$112$	−5.16544			−0.488088
$113$	−4.59802	+	7.96400i	−0.432545	+	0.749190i	−0.997092	−	0.0762111i	$-0.975718\pi$
$113$	−4.59802	+	7.96400i	−0.432545	+	0.749190i	0.564547	+	0.825401i	$0.309051\pi$
$114$	2.50826	+	4.34444i	0.234920	+	0.406894i
$115$	−6.29571	−	10.9045i	−0.587078	−	1.01685i
$116$	3.07896			0.285874
$117$	1.91370	+	7.94652i	0.176922	+	0.734656i
$118$	4.68127			0.430946
$119$	−10.0265	−	17.3665i	−0.919131	−	1.59198i
$120$	0.958569	+	1.66029i	0.0875050	+	0.151563i
$121$	4.60553	−	7.97701i	0.418684	−	0.725183i
$122$	9.49310			0.859465
$123$	1.75268	−	3.03574i	0.158034	−	0.273723i
$124$	0.500000	−	0.866025i	0.0449013	−	0.0777714i
$125$	11.1646			0.998589
$126$	−5.85497	+	10.1411i	−0.521602	+	0.903441i
$127$	−8.07489	−	13.9861i	−0.716531	−	1.24107i	−0.962366	−	0.271756i	$-0.912396\pi$
$127$	−8.07489	−	13.9861i	−0.716531	−	1.24107i	0.245835	−	0.969312i	$-0.420938\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.15015			0.189310
$130$	−7.74272	−	2.28758i	−0.679081	−	0.200634i
$131$	4.03203			0.352280			0.176140	−	0.984365i	$-0.443639\pi$
$131$	4.03203			0.352280			0.176140	+	0.984365i	$0.443639\pi$
$132$	0.572568	+	0.991718i	0.0498357	+	0.0863179i
$133$	−15.1329	−	26.2109i	−1.31219	−	2.27277i
$134$	−0.113765	+	0.197046i	−0.00982776	+	0.0170222i
$135$	10.0975			0.869057
$136$	1.94108	−	3.36205i	0.166446	−	0.288293i
$137$	2.53454	−	4.38995i	0.216540	−	0.375058i	−0.737208	−	0.675666i	$-0.763856\pi$
$137$	2.53454	−	4.38995i	0.216540	−	0.375058i	0.953748	+	0.300608i	$0.0971895\pi$
$138$	−4.81436			−0.409826
$139$	−7.81288	+	13.5323i	−0.662680	+	1.14780i	0.317229	+	0.948349i	$0.397248\pi$
$139$	−7.81288	+	13.5323i	−0.662680	+	1.14780i	−0.979909	+	0.199446i	$0.936086\pi$
$140$	−5.78325	−	10.0169i	−0.488774	−	0.846581i
$141$	3.53772	+	6.12751i	0.297930	+	0.516029i
$142$	−4.04183			−0.339183
$143$	−4.62485	−	1.36641i	−0.386749	−	0.114265i
$144$	−2.26698			−0.188915
$145$	3.44722	+	5.97076i	0.286276	+	0.495845i
$146$	−3.11350	−	5.39274i	−0.257675	−	0.446306i
$147$	−8.42545	+	14.5933i	−0.694920	+	1.20364i
$148$	8.35180			0.686514
$149$	5.92336	−	10.2596i	0.485260	−	0.840495i	−0.514596	−	0.857433i	$-0.672058\pi$
$149$	5.92336	−	10.2596i	0.485260	−	0.840495i	0.999857	+	0.0169373i	$0.00539156\pi$
$150$	−0.00601739	+	0.0104224i	−0.000491318	+	0.000850988i
$151$	−1.86097			−0.151444			−0.0757218	−	0.997129i	$-0.524126\pi$
$151$	−1.86097			−0.151444			−0.0757218	+	0.997129i	$0.524126\pi$
$152$	2.92964	−	5.07428i	0.237625	−	0.411578i
$153$	−4.40038	−	7.62168i	−0.355750	−	0.616177i
$154$	−3.45443	−	5.98324i	−0.278366	−	0.482143i
$155$	2.23921			0.179858
$156$	−2.23771	+	2.12649i	−0.179160	+	0.170256i
$157$	−8.72284			−0.696158			−0.348079	−	0.937465i	$-0.613166\pi$
$157$	−8.72284			−0.696158			−0.348079	+	0.937465i	$0.613166\pi$
$158$	1.07755	+	1.86638i	0.0857255	+	0.148481i
$159$	3.40644	+	5.90013i	0.270148	+	0.467911i
$160$	1.11960	−	1.93921i	0.0885125	−	0.153308i
$161$	29.0461			2.28915
$162$	−1.47006	+	2.54621i	−0.115499	+	0.200049i
$163$	9.62956	−	16.6789i	0.754246	−	1.30639i	−0.191503	−	0.981492i	$-0.561336\pi$
$163$	9.62956	−	16.6789i	0.754246	−	1.30639i	0.945749	−	0.324900i	$-0.105331\pi$
$164$	−4.09425			−0.319707
$165$	−1.28210	+	2.22066i	−0.0998114	+	0.172878i
$166$	−0.437304	−	0.757432i	−0.0339413	−	0.0587881i
$167$	7.60275	+	13.1683i	0.588318	+	1.01900i	0.994453	+	0.105184i	$0.0335431\pi$
$167$	7.60275	+	13.1683i	0.588318	+	1.01900i	−0.406135	+	0.913813i	$0.633124\pi$
$168$	−4.42248			−0.341202
$169$	0.662114	−	12.9831i	0.0509319	−	0.998702i
$170$	8.69297			0.666720
$171$	−6.64142	−	11.5033i	−0.507882	−	0.879677i
$172$	−1.25568	−	2.17490i	−0.0957448	−	0.165835i
$173$	8.02075	−	13.8924i	0.609807	−	1.05622i	−0.381465	−	0.924383i	$-0.624580\pi$
$173$	8.02075	−	13.8924i	0.609807	−	1.05622i	0.991272	−	0.131833i	$-0.0420862\pi$
$174$	2.63611			0.199843
$175$	0.0363042	−	0.0628807i	0.00274434	−	0.00475334i
$176$	0.668757	−	1.15832i	0.0504095	−	0.0873118i
$177$	4.00795			0.301256
$178$	5.33405	−	9.23885i	0.399804	−	0.692481i
$179$	4.87992	+	8.45227i	0.364742	+	0.631752i	0.988735	−	0.149678i	$-0.0478237\pi$
$179$	4.87992	+	8.45227i	0.364742	+	0.631752i	−0.623992	+	0.781430i	$0.714490\pi$
$180$	−2.53812	−	4.39615i	−0.189180	−	0.327670i
$181$	−11.4749			−0.852922			−0.426461	−	0.904506i	$-0.640240\pi$
$181$	−11.4749			−0.852922			−0.426461	+	0.904506i	$0.640240\pi$
$182$	13.5005	−	12.8296i	1.00073	−	0.950992i
$183$	8.12769			0.600816
$184$	2.81158	+	4.86979i	0.207272	+	0.359006i
$185$	9.35071	+	16.1959i	0.687478	+	1.19075i
$186$	0.428084	−	0.741463i	0.0313886	−	0.0543667i
$187$	5.19244			0.379709
$188$	4.13204	−	7.15690i	0.301360	−	0.521971i
$189$	−11.6466	+	20.1724i	−0.847163	+	1.46733i
$190$	13.1201			0.951835
$191$	−5.63889	+	9.76685i	−0.408016	+	0.706704i	−0.994667	−	0.103135i	$-0.967113\pi$
$191$	−5.63889	+	9.76685i	−0.408016	+	0.706704i	0.586651	+	0.809840i	$0.300446\pi$
$192$	−0.428084	−	0.741463i	−0.0308943	−	0.0535105i
$193$	3.90210	+	6.75863i	0.280879	+	0.486497i	0.971602	−	0.236623i	$-0.0760407\pi$
$193$	3.90210	+	6.75863i	0.280879	+	0.486497i	−0.690722	+	0.723120i	$0.742707\pi$
$194$	−17.6957			−1.27047
$195$	−6.62907	−	1.95855i	−0.474717	−	0.140255i
$196$	19.6818			1.40584
$197$	7.28389	+	12.6161i	0.518956	+	0.898858i	0.999757	+	0.0220285i	$0.00701245\pi$
$197$	7.28389	+	12.6161i	0.518956	+	0.898858i	−0.480801	+	0.876829i	$0.659654\pi$
$198$	−1.51606	−	2.62589i	−0.107741	−	0.186614i
$199$	−2.93846	+	5.08957i	−0.208302	+	0.360790i	−0.951180	−	0.308637i	$-0.900127\pi$
$199$	−2.93846	+	5.08957i	−0.208302	+	0.360790i	0.742878	+	0.669427i	$0.233460\pi$
$200$	0.0140566			0.000993950
$201$	−0.0974015	+	0.168704i	−0.00687017	+	0.0118995i
$202$	8.12205	−	14.0678i	0.571466	−	0.989808i
$203$	−15.9042			−1.11626
$204$	1.66189	−	2.87848i	0.116356	−	0.201534i
$205$	−4.58394	−	7.93962i	−0.320156	−	0.554527i
$206$	−9.91684	−	17.1765i	−0.690939	−	1.19674i
$207$	12.7476			0.886016
$208$	3.45779	+	1.02160i	0.239755	+	0.0708353i
$209$	7.83686			0.542087
$210$	−4.95143	−	8.57613i	−0.341681	−	0.591809i
$211$	−7.59056	−	13.1472i	−0.522556	−	0.905094i	−0.999656	−	0.0262443i	$-0.991645\pi$
$211$	−7.59056	−	13.1472i	−0.522556	−	0.905094i	0.477100	−	0.878849i	$-0.341688\pi$
$212$	3.97871	−	6.89133i	0.273259	−	0.473298i
$213$	−3.46049			−0.237109
$214$	−9.55023	+	16.5415i	−0.652840	+	1.13075i
$215$	2.81173	−	4.87006i	0.191759	−	0.332136i
$216$	−4.50942			−0.306827
$217$	−2.58272	+	4.47340i	−0.175326	+	0.303674i
$218$	1.54174	+	2.67036i	0.104420	+	0.180860i
$219$	−2.66568	−	4.61709i	−0.180130	−	0.311994i
$220$	2.99497			0.201921
$221$	3.27718	+	13.6083i	0.220447	+	0.915392i
$222$	7.15054			0.479913
$223$	−3.87973	−	6.71989i	−0.259806	−	0.449997i	0.706384	−	0.707829i	$-0.250325\pi$
$223$	−3.87973	−	6.71989i	−0.259806	−	0.449997i	−0.966190	+	0.257832i	$0.916992\pi$
$224$	2.58272	+	4.47340i	0.172565	+	0.298892i
$225$	0.0159330	−	0.0275967i	0.00106220	−	0.00183978i
$226$	9.19604			0.611711
$227$	8.17756	−	14.1639i	0.542764	−	0.940094i	−0.455980	−	0.889990i	$-0.650711\pi$
$227$	8.17756	−	14.1639i	0.542764	−	0.940094i	0.998744	−	0.0501042i	$-0.0159554\pi$
$228$	2.50826	−	4.34444i	0.166114	−	0.287717i
$229$	25.6445			1.69464			0.847319	−	0.531084i	$-0.178215\pi$
$229$	25.6445			1.69464			0.847319	+	0.531084i	$0.178215\pi$
$230$	−6.29571	+	10.9045i	−0.415127	+	0.719020i
$231$	−2.95757	−	5.12266i	−0.194594	−	0.337046i
$232$	−1.53948	−	2.66646i	−0.101072	−	0.175062i
$233$	9.00846			0.590164			0.295082	−	0.955472i	$-0.404653\pi$
$233$	9.00846			0.590164			0.295082	+	0.955472i	$0.404653\pi$
$234$	5.92504	−	5.63057i	0.387332	−	0.368082i
$235$	18.5050			1.20713
$236$	−2.34063	−	4.05410i	−0.152362	−	0.263899i
$237$	0.922567	+	1.59793i	0.0599271	+	0.103797i
$238$	−10.0265	+	17.3665i	−0.649923	+	1.12570i
$239$	1.63086			0.105491			0.0527457	−	0.998608i	$-0.483203\pi$
$239$	1.63086			0.105491			0.0527457	+	0.998608i	$0.483203\pi$
$240$	0.958569	−	1.66029i	0.0618754	−	0.107171i
$241$	2.56662	−	4.44552i	0.165331	−	0.286361i	−0.771442	−	0.636300i	$-0.780464\pi$
$241$	2.56662	−	4.44552i	0.165331	−	0.286361i	0.936773	+	0.349939i	$0.113798\pi$
$242$	−9.21106			−0.592109
$243$	−8.02274	+	13.8958i	−0.514659	+	0.891415i
$244$	−4.74655	−	8.22127i	−0.303867	−	0.526313i
$245$	22.0358	+	38.1671i	1.40782	+	2.43841i
$246$	−3.50537			−0.223494
$247$	4.94619	+	20.5387i	0.314718	+	1.30685i
$248$	−1.00000			−0.0635001
$249$	−0.374405	−	0.648489i	−0.0237270	−	0.0410963i
$250$	−5.58228	−	9.66880i	−0.353055	−	0.611509i
$251$	−5.36580	+	9.29385i	−0.338687	+	0.586622i	−0.984186	−	0.177138i	$-0.943316\pi$
$251$	−5.36580	+	9.29385i	−0.338687	+	0.586622i	0.645499	+	0.763761i	$0.276649\pi$
$252$	11.7099			0.737656
$253$	−3.76052	+	6.51342i	−0.236422	+	0.409495i
$254$	−8.07489	+	13.9861i	−0.506664	+	0.877568i
$255$	7.44264			0.466076
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.98819	+	5.17570i	0.186398	+	0.322851i	0.944047	−	0.329812i	$-0.106985\pi$
$257$	2.98819	+	5.17570i	0.186398	+	0.322851i	−0.757649	+	0.652663i	$0.773652\pi$
$258$	−1.07507	−	1.86208i	−0.0669312	−	0.115928i
$259$	−43.1407			−2.68063
$260$	1.89026	+	7.84918i	0.117229	+	0.486786i
$261$	−6.97994			−0.432047
$262$	−2.01602	−	3.49184i	−0.124550	−	0.215727i
$263$	−7.35679	−	12.7423i	−0.453639	−	0.785726i	0.544970	−	0.838456i	$-0.316541\pi$
$263$	−7.35679	−	12.7423i	−0.453639	−	0.785726i	−0.998609	+	0.0527296i	$0.983208\pi$
$264$	0.572568	−	0.991718i	0.0352391	−	0.0610360i
$265$	17.8183			1.09457
$266$	−15.1329	+	26.2109i	−0.927856	+	1.60709i
$267$	4.56684	−	7.91001i	0.279486	−	0.484085i
$268$	0.227529			0.0138985
$269$	13.7746	−	23.8582i	0.839849	−	1.45466i	−0.0501710	−	0.998741i	$-0.515977\pi$
$269$	13.7746	−	23.8582i	0.839849	−	1.45466i	0.890020	−	0.455921i	$-0.150690\pi$
$270$	−5.04876	−	8.74471i	−0.307258	−	0.532186i
$271$	10.9197	+	18.9134i	0.663323	+	1.14891i	0.979737	+	0.200287i	$0.0641876\pi$
$271$	10.9197	+	18.9134i	0.663323	+	1.14891i	−0.316415	+	0.948621i	$0.602479\pi$
$272$	−3.88216			−0.235390
$273$	11.5587	−	10.9843i	0.699566	−	0.664799i
$274$	−5.06907			−0.306234
$275$	0.00940043	+	0.0162820i	0.000566867	+	0.000981843i
$276$	2.40718	+	4.16936i	0.144895	+	0.250966i
$277$	9.61112	−	16.6470i	0.577476	−	1.00022i	−0.418291	−	0.908313i	$-0.637371\pi$
$277$	9.61112	−	16.6470i	0.577476	−	1.00022i	0.995768	−	0.0919055i	$-0.0292958\pi$
$278$	15.6258			0.937171
$279$	−1.13349	+	1.96326i	−0.0678602	+	0.117537i
$280$	−5.78325	+	10.0169i	−0.345615	+	0.598623i
$281$	−3.19020			−0.190311			−0.0951557	−	0.995462i	$-0.530335\pi$
$281$	−3.19020			−0.190311			−0.0951557	+	0.995462i	$0.530335\pi$
$282$	3.53772	−	6.12751i	0.210668	−	0.364888i
$283$	−3.24165	−	5.61470i	−0.192696	−	0.333759i	0.753447	−	0.657509i	$-0.228390\pi$
$283$	−3.24165	−	5.61470i	−0.192696	−	0.333759i	−0.946143	+	0.323750i	$0.895056\pi$
$284$	2.02092	+	3.50033i	0.119919	+	0.207706i
$285$	11.2330			0.665388
$286$	1.12908	+	4.68844i	0.0667640	+	0.277233i
$287$	21.1486			1.24836
$288$	1.13349	+	1.96326i	0.0667914	+	0.115686i
$289$	0.964420	+	1.67043i	0.0567306	+	0.0982603i
$290$	3.44722	−	5.97076i	0.202428	−	0.350615i
$291$	−15.1504			−0.888135
$292$	−3.11350	+	5.39274i	−0.182204	+	0.315586i
$293$	−6.81757	+	11.8084i	−0.398287	+	0.689852i	−0.993515	−	0.113704i	$-0.963728\pi$
$293$	−6.81757	+	11.8084i	−0.398287	+	0.689852i	0.595228	+	0.803557i	$0.297062\pi$
$294$	16.8509			0.982765
$295$	5.24117	−	9.07797i	0.305153	−	0.528540i
$296$	−4.17590	−	7.23287i	−0.242719	−	0.420402i
$297$	−3.01570	−	5.22335i	−0.174989	−	0.303090i
$298$	−11.8467			−0.686262
$299$	−19.4437	−	5.74462i	−1.12446	−	0.332220i
$300$	0.0120348			0.000694829
$301$	6.48615	+	11.2343i	0.373855	+	0.647536i
$302$	0.930485	+	1.61165i	0.0535434	+	0.0927399i
$303$	6.95384	−	12.0444i	0.399488	−	0.691933i
$304$	−5.85927			−0.336052
$305$	10.6285	−	18.4091i	0.608587	−	1.05410i
$306$	−4.40038	+	7.62168i	−0.251553	+	0.435703i
$307$	−22.6756			−1.29416			−0.647081	−	0.762421i	$-0.724011\pi$
$307$	−22.6756			−1.29416			−0.647081	+	0.762421i	$0.724011\pi$
$308$	−3.45443	+	5.98324i	−0.196834	+	0.340927i
$309$	−8.49048	−	14.7059i	−0.483007	−	0.836592i
$310$	−1.11960	−	1.93921i	−0.0635893	−	0.110140i
$311$	−21.1779			−1.20089			−0.600445	−	0.799666i	$-0.705010\pi$
$311$	−21.1779			−1.20089			−0.600445	+	0.799666i	$0.705010\pi$
$312$	2.96045	+	0.874662i	0.167603	+	0.0495180i
$313$	12.0246			0.679670			0.339835	−	0.940485i	$-0.389629\pi$
$313$	12.0246			0.679670			0.339835	+	0.940485i	$0.389629\pi$
$314$	4.36142	+	7.55420i	0.246129	+	0.426308i
$315$	13.1105	+	22.7080i	0.738693	+	1.27945i
$316$	1.07755	−	1.86638i	0.0606171	−	0.104992i
$317$	21.5633			1.21112			0.605559	−	0.795801i	$-0.292950\pi$
$317$	21.5633			1.21112			0.605559	+	0.795801i	$0.292950\pi$
$318$	3.40644	−	5.90013i	0.191024	−	0.330863i
$319$	2.05908	−	3.56643i	0.115286	−	0.199682i
$320$	−2.23921			−0.125176
$321$	−8.17660	+	14.1623i	−0.456373	+	0.790461i
$322$	−14.5230	−	25.1546i	−0.809337	−	1.40181i
$323$	−11.3733	−	19.6992i	−0.632828	−	1.09609i
$324$	2.94011			0.163340
$325$	−0.0367387	+	0.0349128i	−0.00203789	+	0.00193661i
$326$	−19.2591			−1.06666
$327$	1.31998	+	2.28628i	0.0729953	+	0.126432i
$328$	2.04713	+	3.54573i	0.113034	+	0.195780i
$329$	−21.3438	+	36.9685i	−1.17672	+	2.03814i
$330$	2.56420			0.141155
$331$	6.48618	−	11.2344i	0.356512	−	0.617498i	−0.630863	−	0.775894i	$-0.717299\pi$
$331$	6.48618	−	11.2344i	0.356512	−	0.617498i	0.987376	+	0.158396i	$0.0506324\pi$
$332$	−0.437304	+	0.757432i	−0.0240002	+	0.0415695i
$333$	−18.9333			−1.03754
$334$	7.60275	−	13.1683i	0.416004	−	0.720540i
$335$	0.254743	+	0.441227i	0.0139181	+	0.0241068i
$336$	2.21124	+	3.82998i	0.120633	+	0.208943i
$337$	−7.69034			−0.418919			−0.209460	−	0.977817i	$-0.567171\pi$
$337$	−7.69034			−0.418919			−0.209460	+	0.977817i	$0.567171\pi$
$338$	−11.5748	+	5.91816i	−0.629585	+	0.321905i
$339$	7.87335			0.427622
$340$	−4.34648	−	7.52833i	−0.235721	−	0.408281i
$341$	−0.668757	−	1.15832i	−0.0362152	−	0.0627266i
$342$	−6.64142	+	11.5033i	−0.359127	+	0.622026i
$343$	−65.5070			−3.53704
$344$	−1.25568	+	2.17490i	−0.0677018	+	0.117263i
$345$	−5.39018	+	9.33607i	−0.290198	+	0.502637i
$346$	−16.0415			−0.862397
$347$	2.23932	−	3.87862i	0.120213	−	0.208215i	−0.799638	−	0.600482i	$-0.794976\pi$
$347$	2.23932	−	3.87862i	0.120213	−	0.208215i	0.919852	+	0.392266i	$0.128309\pi$
$348$	−1.31805	−	2.28294i	−0.0706551	−	0.122378i
$349$	8.42180	+	14.5870i	0.450809	+	0.780824i	0.998436	−	0.0558984i	$-0.0178023\pi$
$349$	8.42180	+	14.5870i	0.450809	+	0.780824i	−0.547628	+	0.836722i	$0.684469\pi$
$350$	−0.0726084			−0.00388108
$351$	11.7859	−	11.2002i	0.629087	−	0.597822i
$352$	−1.33751			−0.0712898
$353$	−10.6087	−	18.3748i	−0.564645	−	0.977993i	−0.997083	−	0.0763297i	$-0.975680\pi$
$353$	−10.6087	−	18.3748i	−0.564645	−	0.977993i	0.432438	−	0.901664i	$-0.357653\pi$
$354$	−2.00398	−	3.47099i	−0.106510	−	0.184481i
$355$	−4.52525	+	7.83797i	−0.240175	+	0.415996i
$356$	−10.6681			−0.565408
$357$	−8.58439	+	14.8686i	−0.454334	+	0.786930i
$358$	4.87992	−	8.45227i	0.257912	−	0.446716i
$359$	22.1511			1.16909			0.584546	−	0.811361i	$-0.301273\pi$
$359$	22.1511			1.16909			0.584546	+	0.811361i	$0.301273\pi$
$360$	−2.53812	+	4.39615i	−0.133771	+	0.231697i
$361$	−7.66555	−	13.2771i	−0.403450	−	0.698796i
$362$	5.73745	+	9.93755i	0.301553	+	0.522306i
$363$	−7.88621			−0.413919
$364$	−17.8610	−	5.27702i	−0.936172	−	0.276591i
$365$	−13.9435			−0.729838
$366$	−4.06385	−	7.03879i	−0.212421	−	0.367923i
$367$	−8.34502	−	14.4540i	−0.435607	−	0.754493i	0.561738	−	0.827315i	$-0.310133\pi$
$367$	−8.34502	−	14.4540i	−0.435607	−	0.754493i	−0.997345	+	0.0728223i	$0.976799\pi$
$368$	2.81158	−	4.86979i	0.146564	−	0.253856i
$369$	9.28157			0.483179
$370$	9.35071	−	16.1959i	0.486120	−	0.841985i
$371$	−20.5518	+	35.5967i	−1.06700	+	1.84809i
$372$	−0.856168			−0.0443902
$373$	1.95077	−	3.37884i	0.101007	−	0.174950i	−0.811093	−	0.584918i	$-0.801127\pi$
$373$	1.95077	−	3.37884i	0.101007	−	0.174950i	0.912100	+	0.409968i	$0.134460\pi$
$374$	−2.59622	−	4.49679i	−0.134247	−	0.232523i
$375$	−4.77937	−	8.27812i	−0.246806	−	0.427480i
$376$	−8.26408			−0.426187
$377$	10.6464	+	3.14547i	0.548318	+	0.162000i
$378$	23.2931			1.19807
$379$	0.323130	+	0.559678i	0.0165981	+	0.0287487i	0.874205	−	0.485557i	$-0.161383\pi$
$379$	0.323130	+	0.559678i	0.0165981	+	0.0287487i	−0.857607	+	0.514305i	$0.828050\pi$
$380$	−6.56007	−	11.3624i	−0.336524	−	0.582877i
$381$	−6.91346	+	11.9745i	−0.354187	+	0.613471i
$382$	11.2778			0.577022
$383$	−9.70193	+	16.8042i	−0.495746	+	0.858656i	−0.999988	−	0.00490568i	$-0.998438\pi$
$383$	−9.70193	+	16.8042i	−0.495746	+	0.858656i	0.504242	+	0.863562i	$0.331772\pi$
$384$	−0.428084	+	0.741463i	−0.0218456	+	0.0378376i
$385$	−15.4704			−0.788443
$386$	3.90210	−	6.75863i	0.198612	−	0.344005i
$387$	2.84660	+	4.93046i	0.144701	+	0.250629i
$388$	8.84783	+	15.3249i	0.449180	+	0.778003i
$389$	−5.41344			−0.274473			−0.137236	−	0.990538i	$-0.543822\pi$
$389$	−5.41344			−0.274473			−0.137236	+	0.990538i	$0.543822\pi$
$390$	1.61838	+	6.72022i	0.0819498	+	0.340291i
$391$	21.8300			1.10399
$392$	−9.84089	−	17.0449i	−0.497040	−	0.860898i
$393$	−1.72605	−	2.98960i	−0.0870676	−	0.150806i
$394$	7.28389	−	12.6161i	0.366957	−	0.635589i
$395$	4.82573			0.242809
$396$	−1.51606	+	2.62589i	−0.0761847	+	0.131956i
$397$	−4.45858	+	7.72249i	−0.223770	+	0.387581i	−0.955950	−	0.293531i	$-0.905170\pi$
$397$	−4.45858	+	7.72249i	−0.223770	+	0.387581i	0.732180	+	0.681111i	$0.238503\pi$
$398$	5.87693			0.294584
$399$	−12.9563	+	22.4409i	−0.648625	+	1.12345i
$400$	−0.00702829	−	0.0121733i	−0.000351414	−	0.000608667i
$401$	−17.8791	−	30.9675i	−0.892838	−	1.54644i	−0.836457	−	0.548032i	$-0.815377\pi$
$401$	−17.8791	−	30.9675i	−0.892838	−	1.54644i	−0.0563808	−	0.998409i	$-0.517956\pi$
$402$	0.194803			0.00971589
$403$	2.61363	−	2.48374i	0.130194	−	0.123724i
$404$	−16.2441			−0.808174
$405$	3.29176	+	5.70150i	0.163569	+	0.283310i
$406$	7.95210	+	13.7734i	0.394656	+	0.683564i
$407$	5.58533	−	9.67407i	0.276854	−	0.479526i
$408$	−3.32378			−0.164552
$409$	−4.72878	+	8.19049i	−0.233823	+	0.404994i	−0.958930	−	0.283643i	$-0.908457\pi$
$409$	−4.72878	+	8.19049i	−0.233823	+	0.404994i	0.725107	+	0.688636i	$0.241790\pi$
$410$	−4.58394	+	7.93962i	−0.226385	+	0.392110i
$411$	−4.33998			−0.214075
$412$	−9.91684	+	17.1765i	−0.488568	+	0.846224i
$413$	12.0904	+	20.9412i	0.594930	+	1.03045i
$414$	−6.37378	−	11.0397i	−0.313254	−	0.542572i
$415$	−1.95843			−0.0961355
$416$	−0.844164	−	3.50534i	−0.0413885	−	0.171863i
$417$	13.3783			0.655137
$418$	−3.91843	−	6.78692i	−0.191657	−	0.331959i
$419$	8.21786	+	14.2337i	0.401469	+	0.695364i	0.993903	−	0.110254i	$-0.0351666\pi$
$419$	8.21786	+	14.2337i	0.401469	+	0.695364i	−0.592435	+	0.805618i	$0.701833\pi$
$420$	−4.95143	+	8.57613i	−0.241605	+	0.418472i
$421$	24.5505			1.19652			0.598259	−	0.801303i	$-0.295859\pi$
$421$	24.5505			1.19652			0.598259	+	0.801303i	$0.295859\pi$
$422$	−7.59056	+	13.1472i	−0.369503	+	0.639998i
$423$	−9.36723	+	16.2245i	−0.455450	+	0.788863i
$424$	−7.95742			−0.386446
$425$	0.0272849	−	0.0472589i	0.00132351	−	0.00229239i
$426$	1.73024	+	2.99687i	0.0838306	+	0.145199i
$427$	24.5180	+	42.4665i	1.18651	+	2.05510i
$428$	19.1005			0.923255
$429$	0.966683	+	4.01409i	0.0466719	+	0.193802i
$430$	−5.62346			−0.271188
$431$	−15.9697	−	27.6603i	−0.769232	−	1.33235i	−0.937980	−	0.346689i	$-0.887306\pi$
$431$	−15.9697	−	27.6603i	−0.769232	−	1.33235i	0.168748	−	0.985659i	$-0.446028\pi$
$432$	2.25471	+	3.90527i	0.108480	+	0.187892i
$433$	17.5182	−	30.3424i	0.841869	−	1.45816i	−0.0464430	−	0.998921i	$-0.514789\pi$
$433$	17.5182	−	30.3424i	0.841869	−	1.45816i	0.888312	−	0.459240i	$-0.151878\pi$
$434$	5.16544			0.247949
$435$	2.95140	−	5.11197i	0.141509	−	0.245100i
$436$	1.54174	−	2.67036i	0.0738358	−	0.127887i
$437$	32.9476			1.57610
$438$	−2.66568	+	4.61709i	−0.127371	+	0.220613i
$439$	12.9422	+	22.4166i	0.617698	+	1.06988i	0.989905	+	0.141734i	$0.0452679\pi$
$439$	12.9422	+	22.4166i	0.617698	+	1.06988i	−0.372207	+	0.928150i	$0.621399\pi$
$440$	−1.49749	−	2.59372i	−0.0713899	−	0.123651i
$441$	−44.6181			−2.12467
$442$	10.1465	−	9.64226i	0.482621	−	0.458635i
$443$	15.3964			0.731503			0.365752	−	0.930712i	$-0.380812\pi$
$443$	15.3964			0.731503			0.365752	+	0.930712i	$0.380812\pi$
$444$	−3.57527	−	6.19255i	−0.169675	−	0.293886i
$445$	−11.9441	−	20.6877i	−0.566203	−	0.980692i
$446$	−3.87973	+	6.71989i	−0.183710	+	0.318196i
$447$	−10.1428			−0.479737
$448$	2.58272	−	4.47340i	0.122022	−	0.211348i
$449$	13.4296	−	23.2608i	0.633783	−	1.09774i	−0.352988	−	0.935628i	$-0.614834\pi$
$449$	13.4296	−	23.2608i	0.633783	−	1.09774i	0.986772	−	0.162117i	$-0.0518322\pi$
$450$	−0.0318659			−0.00150217
$451$	−2.73806	+	4.74246i	−0.128930	+	0.223314i
$452$	−4.59802	−	7.96400i	−0.216273	−	0.374595i
$453$	0.796652	+	1.37984i	0.0374300	+	0.0648306i
$454$	−16.3551			−0.767584
$455$	−9.76402	−	40.5445i	−0.457744	−	1.90075i
$456$	−5.01652			−0.234920
$457$	9.08214	+	15.7307i	0.424845	+	0.735852i	0.996406	−	0.0847070i	$-0.0269954\pi$
$457$	9.08214	+	15.7307i	0.424845	+	0.735852i	−0.571561	+	0.820559i	$0.693662\pi$
$458$	−12.8223	−	22.2088i	−0.599145	−	1.03775i
$459$	−8.75314	+	15.1609i	−0.408561	+	0.707649i
$460$	12.5914			0.587078
$461$	−5.05949	+	8.76329i	−0.235644	+	0.408147i	−0.959460	−	0.281846i	$-0.909053\pi$
$461$	−5.05949	+	8.76329i	−0.235644	+	0.408147i	0.723816	+	0.689993i	$0.242387\pi$
$462$	−2.95757	+	5.12266i	−0.137599	+	0.238328i
$463$	28.8558			1.34104			0.670521	−	0.741890i	$-0.266071\pi$
$463$	28.8558			1.34104			0.670521	+	0.741890i	$0.266071\pi$
$464$	−1.53948	+	2.66646i	−0.0714686	+	0.123787i
$465$	−0.958569	−	1.66029i	−0.0444526	−	0.0769941i
$466$	−4.50423	−	7.80156i	−0.208654	−	0.361400i
$467$	−5.19829			−0.240548			−0.120274	−	0.992741i	$-0.538377\pi$
$467$	−5.19829			−0.240548			−0.120274	+	0.992741i	$0.538377\pi$
$468$	−7.83874	−	2.31595i	−0.362346	−	0.107055i
$469$	−1.17529			−0.0542698
$470$	−9.25250	−	16.0258i	−0.426786	−	0.739215i
$471$	3.73411	+	6.46766i	0.172059	+	0.298014i
$472$	−2.34063	+	4.05410i	−0.107736	+	0.186605i
$473$	−3.35898			−0.154446
$474$	0.922567	−	1.59793i	0.0423749	−	0.0733955i
$475$	0.0411807	−	0.0713270i	0.00188950	−	0.00327271i
$476$	20.0531			0.919131
$477$	−9.01964	+	15.6225i	−0.412981	+	0.715304i
$478$	−0.815428	−	1.41236i	−0.0372968	−	0.0646000i
$479$	−10.7316	−	18.5877i	−0.490339	−	0.849291i	0.509600	−	0.860412i	$-0.329794\pi$
$479$	−10.7316	−	18.5877i	−0.490339	−	0.849291i	−0.999938	+	0.0111202i	$0.996460\pi$
$480$	−1.91714			−0.0875050
$481$	28.8788	+	8.53221i	1.31676	+	0.389035i
$482$	−5.13324			−0.233813
$483$	−12.4342	−	21.5366i	−0.565774	−	0.979949i
$484$	4.60553	+	7.97701i	0.209342	+	0.362591i
$485$	−19.8121	+	34.3156i	−0.899623	+	1.55819i
$486$	16.0455			0.727838
$487$	−10.1636	+	17.6039i	−0.460557	+	0.797707i	−0.998989	−	0.0449615i	$-0.985683\pi$
$487$	−10.1636	+	17.6039i	−0.460557	+	0.797707i	0.538432	+	0.842669i	$0.319017\pi$
$488$	−4.74655	+	8.22127i	−0.214866	+	0.372159i
$489$	−16.4890			−0.745660
$490$	22.0358	−	38.1671i	0.995476	−	1.72422i
$491$	16.7800	+	29.0638i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$491$	16.7800	+	29.0638i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$492$	1.75268	+	3.03574i	0.0790171	+	0.136862i
$493$	−11.9530			−0.538337
$494$	15.3140	−	14.5529i	0.689008	−	0.654765i
$495$	−6.78954			−0.305167
$496$	0.500000	+	0.866025i	0.0224507	+	0.0388857i
$497$	−10.4389	−	18.0807i	−0.468250	−	0.811032i
$498$	−0.374405	+	0.648489i	−0.0167775	+	0.0290595i
$499$	39.6186			1.77357			0.886787	−	0.462178i	$-0.152932\pi$
$499$	39.6186			1.77357			0.886787	+	0.462178i	$0.152932\pi$
$500$	−5.58228	+	9.66880i	−0.249647	+	0.432402i
$501$	6.50923	−	11.2743i	0.290811	−	0.503699i
$502$	10.7316			0.478975
$503$	−10.7091	+	18.5488i	−0.477497	+	0.827049i	−0.999667	−	0.0257924i	$-0.991789\pi$
$503$	−10.7091	+	18.5488i	−0.477497	+	0.827049i	0.522171	+	0.852841i	$0.325122\pi$
$504$	−5.85497	−	10.1411i	−0.260801	−	0.451720i
$505$	−18.1870	−	31.5008i	−0.809310	−	1.40177i
$506$	7.52105			0.334351
$507$	−9.90995	+	5.06694i	−0.440116	+	0.225030i
$508$	16.1498			0.716531
$509$	13.5844	+	23.5289i	0.602119	+	1.04290i	0.992500	+	0.122248i	$0.0390102\pi$
$509$	13.5844	+	23.5289i	0.602119	+	1.04290i	−0.390380	+	0.920654i	$0.627656\pi$
$510$	−3.72132	−	6.44551i	−0.164783	−	0.285412i
$511$	16.0826	−	27.8559i	0.711452	−	1.23227i
$512$	1.00000			0.0441942
$513$	−13.2110	+	22.8820i	−0.583278	+	1.01027i
$514$	2.98819	−	5.17570i	0.131803	−	0.228290i
$515$	−44.4118			−1.95702
$516$	−1.07507	+	1.86208i	−0.0473275	+	0.0819736i
$517$	−5.52666	−	9.57245i	−0.243062	−	0.420996i
$518$	21.5704	+	37.3610i	0.947747	+	1.64155i
$519$	−13.7342			−0.602865
$520$	5.85246	−	5.56160i	0.256647	−	0.243892i
$521$	−37.3311			−1.63551			−0.817753	−	0.575570i	$-0.804780\pi$
$521$	−37.3311			−1.63551			−0.817753	+	0.575570i	$0.804780\pi$
$522$	3.48997	+	6.04480i	0.152752	+	0.264574i
$523$	−8.26926	−	14.3228i	−0.361590	−	0.626292i	0.626633	−	0.779314i	$-0.284433\pi$
$523$	−8.26926	−	14.3228i	−0.361590	−	0.626292i	−0.988223	+	0.153023i	$0.951099\pi$
$524$	−2.01602	+	3.49184i	−0.0880701	+	0.152542i
$525$	−0.0621650			−0.00271310
$526$	−7.35679	+	12.7423i	−0.320771	+	0.555592i
$527$	−1.94108	+	3.36205i	−0.0845548	+	0.146453i
$528$	−1.14514			−0.0498357
$529$	−4.30993	+	7.46501i	−0.187388	+	0.324566i
$530$	−8.90916	−	15.4311i	−0.386989	−	0.670285i
$531$	5.30616	+	9.19055i	0.230268	+	0.398836i
$532$	30.2657			1.31219
$533$	−14.1571	−	4.18269i	−0.613211	−	0.181173i
$534$	−9.13369			−0.395253
$535$	21.3849	+	37.0398i	0.924552	+	1.60137i
$536$	−0.113765	−	0.197046i	−0.00491388	−	0.00851109i
$537$	4.17803	−	7.23656i	0.180295	−	0.312281i
$538$	−27.5491			−1.18773
$539$	13.1623	−	22.7978i	0.566942	−	0.981972i
$540$	−5.04876	+	8.74471i	−0.217264	+	0.376313i
$541$	7.39543			0.317954			0.158977	−	0.987282i	$-0.449180\pi$
$541$	7.39543			0.317954			0.158977	+	0.987282i	$0.449180\pi$
$542$	10.9197	−	18.9134i	0.469040	−	0.812401i
$543$	4.91222	+	8.50821i	0.210803	+	0.365122i
$544$	1.94108	+	3.36205i	0.0832231	+	0.144147i
$545$	6.90454			0.295758
$546$	−15.2920	−	4.51802i	−0.654439	−	0.193353i
$547$	21.9051			0.936594			0.468297	−	0.883571i	$-0.344868\pi$
$547$	21.9051			0.936594			0.468297	+	0.883571i	$0.344868\pi$
$548$	2.53454	+	4.38995i	0.108270	+	0.187529i
$549$	10.7603	+	18.6374i	0.459239	+	0.795426i
$550$	0.00940043	−	0.0162820i	0.000400836	−	0.000694268i
$551$	−18.0405			−0.768551
$552$	2.40718	−	4.16936i	0.102456	−	0.177460i
$553$	−5.56604	+	9.64066i	−0.236692	+	0.409963i
$554$	−19.2222			−0.816675
$555$	8.00578	−	13.8664i	0.339826	−	0.588597i
$556$	−7.81288	−	13.5323i	−0.331340	−	0.573898i
$557$	−18.3115	−	31.7165i	−0.775884	−	1.34387i	−0.934296	−	0.356497i	$-0.883971\pi$
$557$	−18.3115	−	31.7165i	−0.775884	−	1.34387i	0.158413	−	0.987373i	$-0.449362\pi$
$558$	2.26698			0.0959688
$559$	−2.12000	−	8.80317i	−0.0896665	−	0.372334i
$560$	11.5665			0.488774
$561$	−2.22280	−	3.85001i	−0.0938468	−	0.162547i
$562$	1.59510	+	2.76279i	0.0672852	+	0.116541i
$563$	3.41115	−	5.90828i	0.143763	−	0.249004i	−0.785148	−	0.619308i	$-0.787413\pi$
$563$	3.41115	−	5.90828i	0.143763	−	0.249004i	0.928911	+	0.370304i	$0.120746\pi$
$564$	−7.07544			−0.297930
$565$	10.2959	−	17.8331i	0.433153	−	0.750243i
$566$	−3.24165	+	5.61470i	−0.136257	+	0.236003i
$567$	−15.1870			−0.637793
$568$	2.02092	−	3.50033i	0.0847957	−	0.146871i
$569$	−13.6997	−	23.7285i	−0.574319	−	0.994750i	−0.996115	−	0.0880593i	$-0.971933\pi$
$569$	−13.6997	−	23.7285i	−0.574319	−	0.994750i	0.421796	−	0.906691i	$-0.361400\pi$
$570$	−5.61652	−	9.72810i	−0.235250	−	0.407465i
$571$	−14.7062			−0.615437			−0.307718	−	0.951477i	$-0.599566\pi$
$571$	−14.7062			−0.615437			−0.307718	+	0.951477i	$0.599566\pi$
$572$	3.49577	−	3.32203i	0.146165	−	0.138901i
$573$	9.65568			0.403372
$574$	−10.5743	−	18.3152i	−0.441363	−	0.764463i
$575$	0.0395211	+	0.0684526i	0.00164815	+	0.00285467i
$576$	1.13349	−	1.96326i	0.0472287	−	0.0818025i
$577$	39.2201			1.63276			0.816378	−	0.577518i	$-0.195979\pi$
$577$	39.2201			1.63276			0.816378	+	0.577518i	$0.195979\pi$
$578$	0.964420	−	1.67043i	0.0401146	−	0.0694805i
$579$	3.34085	−	5.78652i	0.138841	−	0.240480i
$580$	−6.89444			−0.286276
$581$	2.25887	−	3.91247i	0.0937135	−	0.162317i
$582$	7.57522	+	13.1207i	0.314003	+	0.543869i
$583$	−5.32158	−	9.21725i	−0.220397	−	0.381739i
$584$	6.22699			0.257675
$585$	−4.28517	−	17.7939i	−0.177170	−	0.735688i
$586$	13.6351			0.563262
$587$	0.466800	+	0.808521i	0.0192669	+	0.0333712i	0.875498	−	0.483222i	$-0.160533\pi$
$587$	0.466800	+	0.808521i	0.0192669	+	0.0333712i	−0.856231	+	0.516593i	$0.827200\pi$
$588$	−8.42545	−	14.5933i	−0.347460	−	0.601818i
$589$	−2.92964	+	5.07428i	−0.120714	+	0.209082i
$590$	−10.4823			−0.431551
$591$	6.23624	−	10.8015i	0.256524	−	0.444313i
$592$	−4.17590	+	7.23287i	−0.171628	+	0.297269i
$593$	−4.68653			−0.192453			−0.0962264	−	0.995359i	$-0.530677\pi$
$593$	−4.68653			−0.192453			−0.0962264	+	0.995359i	$0.530677\pi$
$594$	−3.01570	+	5.22335i	−0.123736	+	0.214317i
$595$	22.4515	+	38.8871i	0.920422	+	1.59422i
$596$	5.92336	+	10.2596i	0.242630	+	0.420248i
$597$	5.03164			0.205931
$598$	4.74686	+	19.7110i	0.194114	+	0.806045i
$599$	−17.2762			−0.705884			−0.352942	−	0.935645i	$-0.614819\pi$
$599$	−17.2762			−0.705884			−0.352942	+	0.935645i	$0.614819\pi$
$600$	−0.00601739	−	0.0104224i	−0.000245659	−	0.000425494i
$601$	−2.26694	−	3.92646i	−0.0924705	−	0.160164i	0.816080	−	0.577939i	$-0.196143\pi$
$601$	−2.26694	−	3.92646i	−0.0924705	−	0.160164i	−0.908550	+	0.417776i	$0.862810\pi$
$602$	6.48615	−	11.2343i	0.264356	−	0.457877i
$603$	−0.515803			−0.0210051
$604$	0.930485	−	1.61165i	0.0378609	−	0.0655770i
$605$	−10.3127	+	17.8622i	−0.419272	+	0.726201i
$606$	−13.9077			−0.564961
$607$	−8.59519	+	14.8873i	−0.348868	+	0.604257i	−0.986049	−	0.166457i	$-0.946767\pi$
$607$	−8.59519	+	14.8873i	−0.348868	+	0.604257i	0.637181	+	0.770714i	$0.280101\pi$
$608$	2.92964	+	5.07428i	0.118812	+	0.205789i
$609$	6.80833	+	11.7924i	0.275888	+	0.477851i
$610$	−21.2570			−0.860673
$611$	21.5992	−	20.5258i	0.873811	−	0.830384i
$612$	8.80076			0.355750
$613$	7.46799	+	12.9349i	0.301629	+	0.522437i	0.976505	−	0.215494i	$-0.0691362\pi$
$613$	7.46799	+	12.9349i	0.301629	+	0.522437i	−0.674876	+	0.737931i	$0.735803\pi$
$614$	11.3378	+	19.6376i	0.457556	+	0.792509i
$615$	−3.92462	+	6.79765i	−0.158256	+	0.274108i
$616$	6.90885			0.278366
$617$	0.204443	−	0.354105i	0.00823055	−	0.0142557i	−0.861881	−	0.507111i	$-0.830713\pi$
$617$	0.204443	−	0.354105i	0.00823055	−	0.0142557i	0.870111	+	0.492855i	$0.164047\pi$
$618$	−8.49048	+	14.7059i	−0.341537	+	0.591560i
$619$	12.3998			0.498391			0.249196	−	0.968453i	$-0.419834\pi$
$619$	12.3998			0.498391			0.249196	+	0.968453i	$0.419834\pi$
$620$	−1.11960	+	1.93921i	−0.0449644	+	0.0778806i
$621$	−12.6786	−	21.9599i	−0.508773	−	0.881221i
$622$	10.5890	+	18.3406i	0.424579	+	0.735392i
$623$	55.1055			2.20775
$624$	−0.722746	−	3.00116i	−0.0289330	−	0.120142i
$625$	−25.0701			−1.00280
$626$	−6.01230	−	10.4136i	−0.240300	−	0.416211i
$627$	−3.35484	−	5.81074i	−0.133979	−	0.232059i
$628$	4.36142	−	7.55420i	0.174040	−	0.301445i
$629$	−32.4230			−1.29279
$630$	13.1105	−	22.7080i	0.522335	−	0.904710i
$631$	−7.86788	+	13.6276i	−0.313215	+	0.542505i	−0.979057	−	0.203589i	$-0.934739\pi$
$631$	−7.86788	+	13.6276i	−0.313215	+	0.542505i	0.665841	+	0.746093i	$0.268073\pi$
$632$	−2.15511			−0.0857255
$633$	−6.49880	+	11.2562i	−0.258304	+	0.447396i
$634$	−10.7817	−	18.6744i	−0.428195	−	0.741655i
$635$	18.0814	+	31.3179i	0.717537	+	1.24281i
$636$	−6.81288			−0.270148
$637$	68.0555	+	20.1069i	2.69646	+	0.796666i
$638$	−4.11816			−0.163039
$639$	−4.58137	−	7.93516i	−0.181236	−	0.313910i
$640$	1.11960	+	1.93921i	0.0442563	+	0.0766541i
$641$	22.9656	−	39.7776i	0.907086	−	1.57112i	0.0889943	−	0.996032i	$-0.471635\pi$
$641$	22.9656	−	39.7776i	0.907086	−	1.57112i	0.818092	−	0.575087i	$-0.195032\pi$
$642$	16.3532			0.645409
$643$	14.4382	−	25.0078i	0.569389	−	0.986210i	−0.427238	−	0.904139i	$-0.640513\pi$
$643$	14.4382	−	25.0078i	0.569389	−	0.986210i	0.996626	−	0.0820710i	$-0.0261534\pi$
$644$	−14.5230	+	25.1546i	−0.572288	+	0.991231i
$645$	−4.81463			−0.189576
$646$	−11.3733	+	19.6992i	−0.447477	+	0.775053i
$647$	−4.04502	−	7.00619i	−0.159026	−	0.275442i	0.775491	−	0.631358i	$-0.217502\pi$
$647$	−4.04502	−	7.00619i	−0.159026	−	0.275442i	−0.934518	+	0.355916i	$0.884169\pi$
$648$	−1.47006	−	2.54621i	−0.0577493	−	0.100025i
$649$	−6.26127			−0.245776
$650$	0.0486047	+	0.0143602i	0.00190643	+	0.000563254i
$651$	4.42248			0.173331
$652$	9.62956	+	16.6789i	0.377123	+	0.653196i
$653$	−0.198487	−	0.343790i	−0.00776741	−	0.0134535i	0.862116	−	0.506712i	$-0.169139\pi$
$653$	−0.198487	−	0.343790i	−0.00776741	−	0.0134535i	−0.869883	+	0.493258i	$0.835806\pi$
$654$	1.31998	−	2.28628i	0.0516155	−	0.0894006i
$655$	−9.02856			−0.352775
$656$	2.04713	−	3.54573i	0.0799268	−	0.138437i
$657$	7.05823	−	12.2252i	0.275368	−	0.476951i
$658$	42.6876			1.66414
$659$	2.16765	−	3.75448i	0.0844396	−	0.146254i	−0.820713	−	0.571341i	$-0.806423\pi$
$659$	2.16765	−	3.75448i	0.0844396	−	0.146254i	0.905152	+	0.425087i	$0.139757\pi$
$660$	−1.28210	−	2.22066i	−0.0499057	−	0.0864392i
$661$	−17.7105	−	30.6754i	−0.688857	−	1.19313i	−0.972208	−	0.234119i	$-0.924780\pi$
$661$	−17.7105	−	30.6754i	−0.688857	−	1.19313i	0.283351	−	0.959016i	$-0.408554\pi$
$662$	−12.9724			−0.504185
$663$	8.68713	−	8.25539i	0.337380	−	0.320613i
$664$	0.874607			0.0339413
$665$	33.8856	+	58.6917i	1.31403	+	2.27597i
$666$	9.46667	+	16.3968i	0.366826	+	0.635361i
$667$	8.65674	−	14.9939i	0.335190	−	0.580567i
$668$	−15.2055			−0.588318
$669$	−3.32170	+	5.75335i	−0.128424	+	0.222437i
$670$	0.254743	−	0.441227i	0.00984156	−	0.0170461i
$671$	−12.6972			−0.490169
$672$	2.21124	−	3.82998i	0.0853005	−	0.147745i
$673$	21.4656	+	37.1795i	0.827437	+	1.43316i	0.900042	+	0.435803i	$0.143536\pi$
$673$	21.4656	+	37.1795i	0.827437	+	1.43316i	−0.0726047	+	0.997361i	$0.523131\pi$
$674$	3.84517	+	6.66003i	0.148110	+	0.256535i
$675$	−0.0633869			−0.00243976
$676$	10.9127	+	7.06497i	0.419718	+	0.271730i
$677$	−37.9858			−1.45991			−0.729957	−	0.683493i	$-0.760460\pi$
$677$	−37.9858			−1.45991			−0.729957	+	0.683493i	$0.760460\pi$
$678$	−3.93668	−	6.81852i	−0.151187	−	0.261864i
$679$	−45.7029	−	79.1598i	−1.75392	−	3.03787i
$680$	−4.34648	+	7.52833i	−0.166680	+	0.288698i
$681$	−14.0027			−0.536586
$682$	−0.668757	+	1.15832i	−0.0256080	+	0.0443544i
$683$	−5.25859	+	9.10815i	−0.201215	+	0.348514i	−0.948920	−	0.315517i	$-0.897822\pi$
$683$	−5.25859	+	9.10815i	−0.201215	+	0.348514i	0.747705	+	0.664031i	$0.231156\pi$
$684$	13.2828			0.507882
$685$	−5.67536	+	9.83001i	−0.216844	+	0.375585i
$686$	32.7535	+	56.7307i	1.25053	+	2.16599i
$687$	−10.9780	−	19.0145i	−0.418837	−	0.725448i
$688$	2.51136			0.0957448
$689$	20.7977	−	19.7641i	0.792331	−	0.752953i
$690$	10.7804			0.410401
$691$	8.87193	+	15.3666i	0.337504	+	0.584574i	0.983963	−	0.178375i	$-0.0570839\pi$
$691$	8.87193	+	15.3666i	0.337504	+	0.584574i	−0.646458	+	0.762949i	$0.723751\pi$
$692$	8.02075	+	13.8924i	0.304903	+	0.528108i
$693$	7.83110	−	13.5639i	0.297479	−	0.515249i
$694$	−4.47865			−0.170007
$695$	17.4947	−	30.3017i	0.663611	−	1.14941i
$696$	−1.31805	+	2.28294i	−0.0499607	+	0.0865345i
$697$	15.8945			0.602049
$698$	8.42180	−	14.5870i	0.318770	−	0.552126i
$699$	−3.85638	−	6.67944i	−0.145862	−	0.252640i
$700$	0.0363042	+	0.0628807i	0.00137217	+	0.00237667i
$701$	−7.67471			−0.289870			−0.144935	−	0.989441i	$-0.546297\pi$
$701$	−7.67471			−0.289870			−0.144935	+	0.989441i	$0.546297\pi$
$702$	−15.5926	−	4.60683i	−0.588506	−	0.173873i
$703$	−48.9355			−1.84564
$704$	0.668757	+	1.15832i	0.0252047	+	0.0436559i
$705$	−7.92169	−	13.7208i	−0.298348	−	0.516754i
$706$	−10.6087	+	18.3748i	−0.399264	+	0.691546i
$707$	83.9080			3.15568
$708$	−2.00398	+	3.47099i	−0.0753140	+	0.130448i
$709$	0.132296	−	0.229144i	0.00496850	−	0.00860569i	−0.863530	−	0.504297i	$-0.831752\pi$
$709$	0.132296	−	0.229144i	0.00496850	−	0.00860569i	0.868499	+	0.495691i	$0.165085\pi$
$710$	9.05050			0.339659
$711$	−2.44279	+	4.23103i	−0.0916117	+	0.158676i
$712$	5.33405	+	9.23885i	0.199902	+	0.346241i
$713$	−2.81158	−	4.86979i	−0.105294	−	0.182375i
$714$	17.1688			0.642526
$715$	10.3560	+	3.05967i	0.387292	+	0.114425i
$716$	−9.75984			−0.364742
$717$	−0.698144	−	1.20922i	−0.0260726	−	0.0451592i
$718$	−11.0756	−	19.1834i	−0.413337	−	0.715920i
$719$	−24.5516	+	42.5247i	−0.915621	+	1.58590i	−0.109632	+	0.993972i	$0.534967\pi$
$719$	−24.5516	+	42.5247i	−0.915621	+	1.58590i	−0.805989	+	0.591930i	$0.798366\pi$
$720$	5.07623			0.189180
$721$	51.2249	−	88.7241i	1.90771	−	3.30426i
$722$	−7.66555	+	13.2771i	−0.285282	+	0.494123i
$723$	−4.39492			−0.163449
$724$	5.73745	−	9.93755i	0.213231	−	0.369326i
$725$	−0.0216398	−	0.0374813i	−0.000803683	−	0.00139202i
$726$	3.94310	+	6.82966i	0.146342	+	0.253472i
$727$	−12.4654			−0.462314			−0.231157	−	0.972916i	$-0.574251\pi$
$727$	−12.4654			−0.462314			−0.231157	+	0.972916i	$0.574251\pi$
$728$	4.36048	+	18.1066i	0.161610	+	0.671076i
$729$	4.91729			0.182122
$730$	6.97177	+	12.0755i	0.258037	+	0.446933i
$731$	4.87475	+	8.44332i	0.180299	+	0.312288i
$732$	−4.06385	+	7.03879i	−0.150204	+	0.260161i
$733$	7.89125			0.291470			0.145735	−	0.989324i	$-0.453445\pi$
$733$	7.89125			0.291470			0.145735	+	0.989324i	$0.453445\pi$
$734$	−8.34502	+	14.4540i	−0.308020	+	0.533507i
$735$	18.8663	−	32.6775i	0.695896	−	1.20533i
$736$	−5.62315			−0.207272
$737$	0.152162	−	0.263552i	0.00560495	−	0.00970805i
$738$	−4.64079	−	8.03808i	−0.170830	−	0.295886i
$739$	10.8323	+	18.7621i	0.398472	+	0.690174i	0.993538	−	0.113503i	$-0.0362072\pi$
$739$	10.8323	+	18.7621i	0.398472	+	0.690174i	−0.595065	+	0.803677i	$0.702874\pi$
$740$	−18.7014			−0.687478
$741$	13.1113	−	12.4597i	0.481657	−	0.457719i
$742$	41.1036			1.50896
$743$	−8.70490	−	15.0773i	−0.319352	−	0.553134i	0.661001	−	0.750385i	$-0.270132\pi$
$743$	−8.70490	−	15.0773i	−0.319352	−	0.553134i	−0.980353	+	0.197251i	$0.936799\pi$
$744$	0.428084	+	0.741463i	0.0156943	+	0.0271834i
$745$	−13.2636	+	22.9733i	−0.485942	+	0.841676i
$746$	−3.90155			−0.142846
$747$	0.991357	−	1.71708i	0.0362719	−	0.0628247i
$748$	−2.59622	+	4.49679i	−0.0949273	+	0.164419i
$749$	−98.6622			−3.60504
$750$	−4.77937	+	8.27812i	−0.174518	+	0.302274i
$751$	8.30945	+	14.3924i	0.303216	+	0.525186i	0.976863	−	0.213868i	$-0.0686063\pi$
$751$	8.30945	+	14.3924i	0.303216	+	0.525186i	−0.673647	+	0.739054i	$0.735273\pi$
$752$	4.13204	+	7.15690i	0.150680	+	0.260985i
$753$	9.18806			0.334831
$754$	−2.59915	−	10.7928i	−0.0946554	−	0.393051i
$755$	4.16710			0.151656
$756$	−11.6466	−	20.1724i	−0.423581	−	0.733664i
$757$	0.684985	+	1.18643i	0.0248962	+	0.0431215i	0.878205	−	0.478284i	$-0.158741\pi$
$757$	0.684985	+	1.18643i	0.0248962	+	0.0431215i	−0.853309	+	0.521406i	$0.825408\pi$
$758$	0.323130	−	0.559678i	0.0117366	−	0.0203284i
$759$	6.43928			0.233731
$760$	−6.56007	+	11.3624i	−0.237959	+	0.412157i
$761$	6.46617	−	11.1997i	0.234398	−	0.405990i	−0.724699	−	0.689065i	$-0.758021\pi$
$761$	6.46617	−	11.1997i	0.234398	−	0.405990i	0.959098	+	0.283075i	$0.0913547\pi$
$762$	13.8269			0.500897
$763$	−7.96374	+	13.7936i	−0.288307	+	0.499362i
$764$	−5.63889	−	9.76685i	−0.204008	−	0.353352i
$765$	9.85337	+	17.0665i	0.356249	+	0.617042i
$766$	19.4039			0.701090
$767$	−3.95176	−	16.4094i	−0.142690	−	0.592510i
$768$	0.856168			0.0308943
$769$	13.7514	+	23.8182i	0.495890	+	0.858906i	0.999989	−	0.00473969i	$-0.00150870\pi$
$769$	13.7514	+	23.8182i	0.495890	+	0.858906i	−0.504099	+	0.863646i	$0.668175\pi$
$770$	7.73518	+	13.3977i	0.278757	+	0.482820i
$771$	2.55839	−	4.43127i	0.0921383	−	0.159588i
$772$	−7.80419			−0.280879
$773$	21.6712	−	37.5356i	0.779458	−	1.35006i	−0.152796	−	0.988258i	$-0.548828\pi$
$773$	21.6712	−	37.5356i	0.779458	−	1.35006i	0.932254	−	0.361803i	$-0.117839\pi$
$774$	2.84660	−	4.93046i	0.102319	−	0.177222i
$775$	−0.0140566			−0.000504927
$776$	8.84783	−	15.3249i	0.317618	−	0.550131i
$777$	18.4679	+	31.9873i	0.662531	+	1.14754i
$778$	2.70672	+	4.68818i	0.0970407	+	0.168079i
$779$	23.9893			0.859507
$780$	5.01069	−	4.76167i	0.179411	−	0.170495i
$781$	5.40601			0.193442
$782$	−10.9150	−	18.9053i	−0.390319	−	0.676053i
$783$	6.94216	+	12.0242i	0.248093	+	0.429709i
$784$	−9.84089	+	17.0449i	−0.351460	+	0.608747i
$785$	19.5323			0.697136
$786$	−1.72605	+	2.98960i	−0.0615661	+	0.106636i
$787$	14.8247	−	25.6771i	0.528442	−	0.915289i	−0.471008	−	0.882129i	$-0.656110\pi$
$787$	14.8247	−	25.6771i	0.528442	−	0.915289i	0.999450	−	0.0331599i	$-0.0105571\pi$
$788$	−14.5678			−0.518956
$789$	−6.29865	+	10.9096i	−0.224238	+	0.388391i
$790$	−2.41287	−	4.17921i	−0.0858460	−	0.148690i
$791$	23.7508	+	41.1376i	0.844481	+	1.46268i
$792$	3.03211			0.107741
$793$	−8.01373	−	33.2765i	−0.284576	−	1.18168i
$794$	8.91717			0.316458
$795$	−7.62774	−	13.2116i	−0.270528	−	0.468568i
$796$	−2.93846	−	5.08957i	−0.104151	−	0.180395i
$797$	10.8200	−	18.7408i	0.383265	−	0.663835i	−0.608262	−	0.793737i	$-0.708133\pi$
$797$	10.8200	−	18.7408i	0.383265	−	0.663835i	0.991527	+	0.129902i	$0.0414662\pi$
$798$	25.9125			0.917294
$799$	−16.0412	+	27.7842i	−0.567498	+	0.982935i
$800$	−0.00702829	+	0.0121733i	−0.000248487	+	0.000430393i
$801$	24.1843			0.854512
$802$	−17.8791	+	30.9675i	−0.631332	+	1.09350i
$803$	4.16435	+	7.21286i	0.146957	+	0.254536i
$804$	−0.0974015	−	0.168704i	−0.00343509	−	0.00594975i
$805$	−65.0402			−2.29237
$806$	−3.45779	−	1.02160i	−0.121796	−	0.0359844i
$807$	−23.5867			−0.830290
$808$	8.12205	+	14.0678i	0.285733	+	0.494904i
$809$	9.05973	+	15.6919i	0.318523	+	0.551698i	0.980180	−	0.198108i	$-0.0634798\pi$
$809$	9.05973	+	15.6919i	0.318523	+	0.551698i	−0.661657	+	0.749807i	$0.730146\pi$
$810$	3.29176	−	5.70150i	0.115661	−	0.200330i
$811$	25.8167			0.906547			0.453273	−	0.891371i	$-0.350256\pi$
$811$	25.8167			0.906547			0.453273	+	0.891371i	$0.350256\pi$
$812$	7.95210	−	13.7734i	0.279064	−	0.483353i
$813$	9.34907	−	16.1931i	0.327886	−	0.567915i
$814$	−11.1707			−0.391531
$815$	−21.5626	+	37.3475i	−0.755305	+	1.30823i
$816$	1.66189	+	2.87848i	0.0581778	+	0.100767i
$817$	7.35738	+	12.7434i	0.257402	+	0.445834i
$818$	9.45757			0.330676
$819$	40.4905	+	11.9629i	1.41485	+	0.418017i
$820$	9.16789			0.320156
$821$	8.79456	+	15.2326i	0.306932	+	0.531622i	0.977690	−	0.210055i	$-0.0673642\pi$
$821$	8.79456	+	15.2326i	0.306932	+	0.531622i	−0.670757	+	0.741677i	$0.734031\pi$
$822$	2.16999	+	3.75853i	0.0756871	+	0.131094i
$823$	9.82986	−	17.0258i	0.342647	−	0.593483i	−0.642276	−	0.766473i	$-0.722010\pi$
$823$	9.82986	−	17.0258i	0.342647	−	0.593483i	0.984923	+	0.172991i	$0.0553431\pi$
$824$	19.8337			0.690939
$825$	0.00804835	−	0.0139402i	0.000280208	−	0.000485334i
$826$	12.0904	−	20.9412i	0.420679	−	0.728638i
$827$	45.5442			1.58373			0.791863	−	0.610698i	$-0.209111\pi$
$827$	45.5442			1.58373			0.791863	+	0.610698i	$0.209111\pi$
$828$	−6.37378	+	11.0397i	−0.221504	+	0.383656i
$829$	−7.61683	−	13.1927i	−0.264544	−	0.458203i	0.702900	−	0.711288i	$-0.251888\pi$
$829$	−7.61683	−	13.1927i	−0.264544	−	0.458203i	−0.967444	+	0.253085i	$0.918555\pi$
$830$	0.979214	+	1.69605i	0.0339890	+	0.0588707i
$831$	−16.4575			−0.570903
$832$	−2.61363	+	2.48374i	−0.0906113	+	0.0861080i
$833$	−76.4078			−2.64737
$834$	−6.68914	−	11.5859i	−0.231626	−	0.401188i
$835$	−17.0241	−	29.4867i	−0.589145	−	1.02043i
$836$	−3.91843	+	6.78692i	−0.135522	+	0.234731i
$837$	4.50942			0.155868
$838$	8.21786	−	14.2337i	0.283881	−	0.491697i
$839$	10.9826	−	19.0224i	0.379161	−	0.656726i	−0.611779	−	0.791028i	$-0.709546\pi$
$839$	10.9826	−	19.0224i	0.379161	−	0.656726i	0.990940	+	0.134302i	$0.0428794\pi$
$840$	9.90287			0.341681
$841$	9.75999	−	16.9048i	0.336552	−	0.582924i
$842$	−12.2753	−	21.2614i	−0.423033	−	0.732715i
$843$	1.36567	+	2.36542i	0.0470363	+	0.0814692i
$844$	15.1811			0.522556
$845$	−1.48261	+	29.0719i	−0.0510034	+	1.00010i
$846$	18.7345			0.644104
$847$	−23.7896	−	41.2048i	−0.817420	−	1.41581i
$848$	3.97871	+	6.89133i	0.136629	+	0.236649i
$849$	−2.77539	+	4.80712i	−0.0952513	+	0.164980i
$850$	−0.0545699			−0.00187173
$851$	23.4817	−	40.6715i	0.804943	−	1.39420i
$852$	1.73024	−	2.99687i	0.0592772	−	0.102671i
$853$	19.1576			0.655945			0.327973	−	0.944687i	$-0.393635\pi$
$853$	19.1576			0.655945			0.327973	+	0.944687i	$0.393635\pi$
$854$	24.5180	−	42.4665i	0.838990	−	1.45317i
$855$	14.8715	+	25.7582i	0.508595	+	0.880913i
$856$	−9.55023	−	16.5415i	−0.326420	−	0.565376i
$857$	41.4235			1.41500			0.707500	−	0.706714i	$-0.249823\pi$
$857$	41.4235			1.41500			0.707500	+	0.706714i	$0.249823\pi$
$858$	2.99296	−	2.84422i	0.102178	−	0.0971000i
$859$	−3.03415			−0.103524			−0.0517619	−	0.998659i	$-0.516484\pi$
$859$	−3.03415			−0.103524			−0.0517619	+	0.998659i	$0.516484\pi$
$860$	2.81173	+	4.87006i	0.0958793	+	0.166068i
$861$	−9.05338	−	15.6809i	−0.308538	−	0.534404i
$862$	−15.9697	+	27.6603i	−0.543929	+	0.942113i
$863$	5.41327			0.184270			0.0921348	−	0.995747i	$-0.470631\pi$
$863$	5.41327			0.184270			0.0921348	+	0.995747i	$0.470631\pi$
$864$	2.25471	−	3.90527i	0.0767067	−	0.132860i
$865$	−17.9601	+	31.1079i	−0.610663	+	1.05770i
$866$	−35.0363			−1.19058
$867$	0.825706	−	1.43016i	0.0280424	−	0.0485709i
$868$	−2.58272	−	4.47340i	−0.0876632	−	0.151837i
$869$	−1.44124	−	2.49631i	−0.0488908	−	0.0846814i
$870$	−5.90280			−0.200124
$871$	0.786748	+	0.232444i	0.0266580	+	0.00787606i
$872$	−3.08347			−0.104420
$873$	−20.0578	−	34.7412i	−0.678854	−	1.17581i
$874$	−16.4738	−	28.5335i	−0.557235	−	0.965159i
$875$	28.8350	−	49.9436i	0.974800	−	1.68840i
$876$	5.33135			0.180130
$877$	0.803859	−	1.39232i	0.0271444	−	0.0470155i	−0.852134	−	0.523323i	$-0.824692\pi$
$877$	0.803859	−	1.39232i	0.0271444	−	0.0470155i	0.879278	+	0.476308i	$0.158025\pi$
$878$	12.9422	−	22.4166i	0.436778	−	0.756522i
$879$	11.6740			0.393753
$880$	−1.49749	+	2.59372i	−0.0504803	+	0.0874344i
$881$	9.21615	+	15.9628i	0.310500	+	0.537802i	0.978471	−	0.206386i	$-0.0661702\pi$
$881$	9.21615	+	15.9628i	0.310500	+	0.537802i	−0.667971	+	0.744188i	$0.732837\pi$
$882$	22.3091	+	38.6404i	0.751185	+	1.30109i
$883$	−31.8746			−1.07267			−0.536334	−	0.844006i	$-0.680191\pi$
$883$	−31.8746			−1.07267			−0.536334	+	0.844006i	$0.680191\pi$
$884$	−13.4237	−	3.96602i	−0.451488	−	0.133392i
$885$	−8.97464			−0.301679
$886$	−7.69818	−	13.3336i	−0.258626	−	0.447953i
$887$	4.41385	+	7.64502i	0.148203	+	0.256695i	0.930563	−	0.366131i	$-0.119318\pi$
$887$	4.41385	+	7.64502i	0.148203	+	0.256695i	−0.782361	+	0.622826i	$0.785985\pi$
$888$	−3.57527	+	6.19255i	−0.119978	+	0.207808i
$889$	−83.4208			−2.79784
$890$	−11.9441	+	20.6877i	−0.400366	+	0.693454i
$891$	1.96622	−	3.40559i	0.0658709	−	0.114092i
$892$	7.75945			0.259806
$893$	−24.2107	+	41.9342i	−0.810182	+	1.40328i
$894$	5.07139	+	8.78390i	0.169613	+	0.293778i
$895$	−10.9272	−	18.9264i	−0.365255	−	0.632640i
$896$	−5.16544			−0.172565
$897$	4.06411	+	16.8760i	0.135697	+	0.563472i
$898$	−26.8592			−0.896305
$899$	1.53948	+	2.66646i	0.0513446	+	0.0889314i
$900$	0.0159330	+	0.0275967i	0.000531099	+	0.000919890i
$901$	−15.4460	+	26.7532i	−0.514580	+	0.891279i
$902$	5.47612			0.182335
$903$	5.55323	−	9.61848i	0.184800	−	0.320083i
$904$	−4.59802	+	7.96400i	−0.152928	+	0.264879i
$905$	25.6947			0.854120
$906$	0.796652	−	1.37984i	0.0264670	−	0.0458422i
$907$	16.1373	+	27.9506i	0.535831	+	0.928086i	0.999123	+	0.0418801i	$0.0133347\pi$
$907$	16.1373	+	27.9506i	0.535831	+	0.928086i	−0.463292	+	0.886206i	$0.653332\pi$
$908$	8.17756	+	14.1639i	0.271382	+	0.470047i
$909$	36.8250			1.22141
$910$	−30.2305	+	28.7281i	−1.00213	+	0.952328i
$911$	26.1068			0.864956			0.432478	−	0.901644i	$-0.357639\pi$
$911$	26.1068			0.864956			0.432478	+	0.901644i	$0.357639\pi$
$912$	2.50826	+	4.34444i	0.0830568	+	0.143859i
$913$	0.584900	+	1.01308i	0.0193574	+	0.0335279i
$914$	9.08214	−	15.7307i	0.300410	−	0.520326i
$915$	−18.1996			−0.601660
$916$	−12.8223	+	22.2088i	−0.423660	+	0.733800i
$917$	10.4136	−	18.0369i	0.343888	−	0.595631i
$918$	17.5063			0.577793
$919$	0.365019	−	0.632231i	0.0120409	−	0.0208554i	−0.859942	−	0.510391i	$-0.829501\pi$
$919$	0.365019	−	0.632231i	0.0120409	−	0.0208554i	0.871983	+	0.489536i	$0.162834\pi$
$920$	−6.29571	−	10.9045i	−0.207563	−	0.359510i
$921$	9.70704	+	16.8131i	0.319858	+	0.554010i
$922$	10.1190			0.333251
$923$	3.41197	+	14.1680i	0.112306	+	0.466345i
$924$	5.91514			0.194594
$925$	−0.0586989	−	0.101669i	−0.00193001	−	0.00334287i
$926$	−14.4279	−	24.9899i	−0.474130	−	0.821217i
$927$	22.4812	−	38.9387i	0.738381	−	1.27891i
$928$	3.07896			0.101072
$929$	−18.2154	+	31.5499i	−0.597627	+	1.03512i	0.395543	+	0.918447i	$0.370556\pi$
$929$	−18.2154	+	31.5499i	−0.597627	+	1.03512i	−0.993170	+	0.116673i	$0.962777\pi$
$930$	−0.958569	+	1.66029i	−0.0314327	+	0.0544431i
$931$	−115.321			−3.77949
$932$	−4.50423	+	7.80156i	−0.147541	+	0.255548i
$933$	9.06593	+	15.7027i	0.296805	+	0.514082i
$934$	2.59915	+	4.50186i	0.0850467	+	0.147305i
$935$	−11.6270			−0.380242
$936$	1.91370	+	7.94652i	0.0625512	+	0.259740i
$937$	25.4421			0.831158			0.415579	−	0.909557i	$-0.363579\pi$
$937$	25.4421			0.831158			0.415579	+	0.909557i	$0.363579\pi$
$938$	0.587644	+	1.01783i	0.0191873	+	0.0332333i
$939$	−5.14754	−	8.91580i	−0.167984	−	0.290956i
$940$	−9.25250	+	16.0258i	−0.301783	+	0.522704i
$941$	−41.4465			−1.35112			−0.675558	−	0.737307i	$-0.736097\pi$
$941$	−41.4465			−1.35112			−0.675558	+	0.737307i	$0.736097\pi$
$942$	3.73411	−	6.46766i	0.121664	−	0.210728i
$943$	−11.5113	+	19.9382i	−0.374860	+	0.649276i
$944$	4.68127			0.152362
$945$	26.0791	−	45.1703i	0.848353	−	1.46939i
$946$	1.67949	+	2.90896i	0.0546050	+	0.0945786i
$947$	−0.794856	−	1.37673i	−0.0258293	−	0.0447377i	0.852822	−	0.522202i	$-0.174889\pi$
$947$	−0.794856	−	1.37673i	−0.0258293	−	0.0447377i	−0.878651	+	0.477464i	$0.841556\pi$
$948$	−1.84513			−0.0599271
$949$	−16.2751	+	15.4662i	−0.528311	+	0.502054i
$950$	−0.0823613			−0.00267215
$951$	−9.23091	−	15.9884i	−0.299333	−	0.518460i
$952$	−10.0265	−	17.3665i	−0.324962	−	0.562850i
$953$	0.328991	−	0.569830i	0.0106571	−	0.0184586i	−0.860648	−	0.509201i	$-0.829941\pi$
$953$	0.328991	−	0.569830i	0.0106571	−	0.0184586i	0.871305	+	0.490742i	$0.163274\pi$
$954$	18.0393			0.584043
$955$	12.6267	−	21.8700i	0.408589	−	0.707697i
$956$	−0.815428	+	1.41236i	−0.0263728	+	0.0456791i
$957$	−3.52583			−0.113974
$958$	−10.7316	+	18.5877i	−0.346722	+	0.600540i
$959$	−13.0920	−	22.6760i	−0.422763	−	0.732247i
$960$	0.958569	+	1.66029i	0.0309377	+	0.0535857i
$961$	1.00000			0.0322581
$962$	−7.05029	−	29.2759i	−0.227310	−	0.943892i
$963$	−43.3003			−1.39533
$964$	2.56662	+	4.44552i	0.0826653	+	0.143180i
$965$	−8.73761	−	15.1340i	−0.281274	−	0.487180i
$966$	−12.4342	+	21.5366i	−0.400062	+	0.692928i
$967$	−1.02716			−0.0330311			−0.0165156	−	0.999864i	$-0.505257\pi$
$967$	−1.02716			−0.0330311			−0.0165156	+	0.999864i	$0.505257\pi$
$968$	4.60553	−	7.97701i	0.148027	−	0.256391i
$969$	−9.73747	+	16.8658i	−0.312813	+	0.541807i
$970$	39.6243			1.27226
$971$	5.05037	−	8.74751i	0.162074	−	0.280721i	−0.773538	−	0.633750i	$-0.781515\pi$
$971$	5.05037	−	8.74751i	0.162074	−	0.280721i	0.935612	+	0.353029i	$0.114848\pi$
$972$	−8.02274	−	13.8958i	−0.257329	−	0.445708i
$973$	40.3570	+	69.9003i	1.29378	+	2.24090i
$974$	20.3272			0.651325
$975$	0.0416138	+	0.0122948i	0.00133271	+	0.000393747i
$976$	9.49310			0.303867
$977$	−11.4605	−	19.8502i	−0.366655	−	0.635065i	0.622385	−	0.782711i	$-0.286164\pi$
$977$	−11.4605	−	19.8502i	−0.366655	−	0.635065i	−0.989040	+	0.147646i	$0.952830\pi$
$978$	8.24452	+	14.2799i	0.263631	+	0.456622i
$979$	−7.13437	+	12.3571i	−0.228015	+	0.394934i
$980$	−44.0716			−1.40782
$981$	−3.49508	+	6.05365i	−0.111589	+	0.193278i
$982$	16.7800	−	29.0638i	0.535472	−	0.927464i
$983$	−16.2937			−0.519690			−0.259845	−	0.965650i	$-0.583671\pi$
$983$	−16.2937			−0.519690			−0.259845	+	0.965650i	$0.583671\pi$
$984$	1.75268	−	3.03574i	0.0558735	−	0.0967758i
$985$	−16.3102	−	28.2500i	−0.519685	−	0.900121i
$986$	5.97651	+	10.3516i	0.190331	+	0.329663i
$987$	36.5477			1.16333
$988$	−20.2602	−	5.98584i	−0.644561	−	0.190435i
$989$	−14.1218			−0.449046
$990$	3.39477	+	5.87991i	0.107893	+	0.186876i
$991$	26.4668	+	45.8419i	0.840747	+	1.45622i	0.889264	+	0.457394i	$0.151217\pi$
$991$	26.4668	+	45.8419i	0.840747	+	1.45622i	−0.0485169	+	0.998822i	$0.515449\pi$
$992$	0.500000	−	0.866025i	0.0158750	−	0.0274963i
$993$	−11.1065			−0.352454
$994$	−10.4389	+	18.0807i	−0.331102	+	0.573486i
$995$	6.57984	−	11.3966i	0.208595	−	0.361297i
$996$	0.748811			0.0237270
$997$	−16.7497	+	29.0114i	−0.530470	+	0.918800i	0.468898	+	0.883252i	$0.344651\pi$
$997$	−16.7497	+	29.0114i	−0.530470	+	0.918800i	−0.999368	+	0.0355481i	$0.988682\pi$
$998$	−19.8093	−	34.3108i	−0.627053	−	1.08609i
$999$	18.8309	+	32.6160i	0.595782	+	1.03193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	806.2.g.g.497.5	yes	20
13.9	even	3	inner	806.2.g.g.373.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
806.2.g.g.373.5	✓	20	13.9	even	3	inner
806.2.g.g.497.5	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 806 = 2 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	806.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.428084 - 0.741463i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.23921 q^{5} +(-0.428084 + 0.741463i) q^{6} +(2.58272 - 4.47340i) q^{7} +1.00000 q^{8} +(1.13349 - 1.96326i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.428084 - 0.741463i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.23921 q^{5} +(-0.428084 + 0.741463i) q^{6} +(2.58272 - 4.47340i) q^{7} +1.00000 q^{8} +(1.13349 - 1.96326i) q^{9} +(1.11960 + 1.93921i) q^{10} +(0.668757 + 1.15832i) q^{11} +0.856168 q^{12} +(-2.61363 + 2.48374i) q^{13} -5.16544 q^{14} +(0.958569 + 1.66029i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.94108 - 3.36205i) q^{17} -2.26698 q^{18} +(2.92964 - 5.07428i) q^{19} +(1.11960 - 1.93921i) q^{20} -4.42248 q^{21} +(0.668757 - 1.15832i) q^{22} +(2.81158 + 4.86979i) q^{23} +(-0.428084 - 0.741463i) q^{24} +0.0140566 q^{25} +(3.45779 + 1.02160i) q^{26} -4.50942 q^{27} +(2.58272 + 4.47340i) q^{28} +(-1.53948 - 2.66646i) q^{29} +(0.958569 - 1.66029i) q^{30} -1.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.572568 - 0.991718i) q^{33} -3.88216 q^{34} +(-5.78325 + 10.0169i) q^{35} +(1.13349 + 1.96326i) q^{36} +(-4.17590 - 7.23287i) q^{37} -5.85927 q^{38} +(2.96045 + 0.874662i) q^{39} -2.23921 q^{40} +(2.04713 + 3.54573i) q^{41} +(2.21124 + 3.82998i) q^{42} +(-1.25568 + 2.17490i) q^{43} -1.33751 q^{44} +(-2.53812 + 4.39615i) q^{45} +(2.81158 - 4.86979i) q^{46} -8.26408 q^{47} +(-0.428084 + 0.741463i) q^{48} +(-9.84089 - 17.0449i) q^{49} +(-0.00702829 - 0.0121733i) q^{50} -3.32378 q^{51} +(-0.844164 - 3.50534i) q^{52} -7.95742 q^{53} +(2.25471 + 3.90527i) q^{54} +(-1.49749 - 2.59372i) q^{55} +(2.58272 - 4.47340i) q^{56} -5.01652 q^{57} +(-1.53948 + 2.66646i) q^{58} +(-2.34063 + 4.05410i) q^{59} -1.91714 q^{60} +(-4.74655 + 8.22127i) q^{61} +(0.500000 + 0.866025i) q^{62} +(-5.85497 - 10.1411i) q^{63} +1.00000 q^{64} +(5.85246 - 5.56160i) q^{65} -1.14514 q^{66} +(-0.113765 - 0.197046i) q^{67} +(1.94108 + 3.36205i) q^{68} +(2.40718 - 4.16936i) q^{69} +11.5665 q^{70} +(2.02092 - 3.50033i) q^{71} +(1.13349 - 1.96326i) q^{72} +6.22699 q^{73} +(-4.17590 + 7.23287i) q^{74} +(-0.00601739 - 0.0104224i) q^{75} +(2.92964 + 5.07428i) q^{76} +6.90885 q^{77} +(-0.722746 - 3.00116i) q^{78} -2.15511 q^{79} +(1.11960 + 1.93921i) q^{80} +(-1.47006 - 2.54621i) q^{81} +(2.04713 - 3.54573i) q^{82} +0.874607 q^{83} +(2.21124 - 3.82998i) q^{84} +(-4.34648 + 7.52833i) q^{85} +2.51136 q^{86} +(-1.31805 + 2.28294i) q^{87} +(0.668757 + 1.15832i) q^{88} +(5.33405 + 9.23885i) q^{89} +5.07623 q^{90} +(4.36048 + 18.1066i) q^{91} -5.62315 q^{92} +(0.428084 + 0.741463i) q^{93} +(4.13204 + 7.15690i) q^{94} +(-6.56007 + 11.3624i) q^{95} +0.856168 q^{96} +(8.84783 - 15.3249i) q^{97} +(-9.84089 + 17.0449i) q^{98} +3.03211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{2} - 3 q^{3} - 10 q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 20 q^{8} - 19 q^{9}+O(q^{10}) \) 20 * q - 10 * q^2 - 3 * q^3 - 10 * q^4 + 6 * q^5 - 3 * q^6 - q^7 + 20 * q^8 - 19 * q^9	\( 20 q - 10 q^{2} - 3 q^{3} - 10 q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 20 q^{8} - 19 q^{9} - 3 q^{10} - 5 q^{11} + 6 q^{12} + 8 q^{13} + 2 q^{14} - 6 q^{15} - 10 q^{16} - 4 q^{17} + 38 q^{18} + 10 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} - 4 q^{23} - 3 q^{24} + 46 q^{25} - q^{26} + 36 q^{27} - q^{28} - 9 q^{29} - 6 q^{30} - 20 q^{31} - 10 q^{32} + 9 q^{33} + 8 q^{34} - 42 q^{35} - 19 q^{36} - 14 q^{37} - 20 q^{38} + 10 q^{39} + 6 q^{40} - 6 q^{41} - 2 q^{42} - 5 q^{43} + 10 q^{44} + 18 q^{45} - 4 q^{46} - 8 q^{47} - 3 q^{48} - 23 q^{49} - 23 q^{50} - 18 q^{51} - 7 q^{52} + 68 q^{53} - 18 q^{54} + 12 q^{55} - q^{56} + 46 q^{57} - 9 q^{58} - 10 q^{59} + 12 q^{60} - 30 q^{61} + 10 q^{62} - 35 q^{63} + 20 q^{64} - 6 q^{65} - 18 q^{66} + 4 q^{67} - 4 q^{68} + 21 q^{69} + 84 q^{70} - 3 q^{71} - 19 q^{72} - 12 q^{73} - 14 q^{74} + 5 q^{75} + 10 q^{76} - 62 q^{77} - 14 q^{78} + 22 q^{79} - 3 q^{80} - 10 q^{81} - 6 q^{82} + 94 q^{83} - 2 q^{84} - 25 q^{85} + 10 q^{86} - 34 q^{87} - 5 q^{88} + 4 q^{89} - 36 q^{90} + 40 q^{91} + 8 q^{92} + 3 q^{93} + 4 q^{94} - q^{95} + 6 q^{96} + 50 q^{97} - 23 q^{98} + 54 q^{99}+O(q^{100}) \) 20 * q - 10 * q^2 - 3 * q^3 - 10 * q^4 + 6 * q^5 - 3 * q^6 - q^7 + 20 * q^8 - 19 * q^9 - 3 * q^10 - 5 * q^11 + 6 * q^12 + 8 * q^13 + 2 * q^14 - 6 * q^15 - 10 * q^16 - 4 * q^17 + 38 * q^18 + 10 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 - 4 * q^23 - 3 * q^24 + 46 * q^25 - q^26 + 36 * q^27 - q^28 - 9 * q^29 - 6 * q^30 - 20 * q^31 - 10 * q^32 + 9 * q^33 + 8 * q^34 - 42 * q^35 - 19 * q^36 - 14 * q^37 - 20 * q^38 + 10 * q^39 + 6 * q^40 - 6 * q^41 - 2 * q^42 - 5 * q^43 + 10 * q^44 + 18 * q^45 - 4 * q^46 - 8 * q^47 - 3 * q^48 - 23 * q^49 - 23 * q^50 - 18 * q^51 - 7 * q^52 + 68 * q^53 - 18 * q^54 + 12 * q^55 - q^56 + 46 * q^57 - 9 * q^58 - 10 * q^59 + 12 * q^60 - 30 * q^61 + 10 * q^62 - 35 * q^63 + 20 * q^64 - 6 * q^65 - 18 * q^66 + 4 * q^67 - 4 * q^68 + 21 * q^69 + 84 * q^70 - 3 * q^71 - 19 * q^72 - 12 * q^73 - 14 * q^74 + 5 * q^75 + 10 * q^76 - 62 * q^77 - 14 * q^78 + 22 * q^79 - 3 * q^80 - 10 * q^81 - 6 * q^82 + 94 * q^83 - 2 * q^84 - 25 * q^85 + 10 * q^86 - 34 * q^87 - 5 * q^88 + 4 * q^89 - 36 * q^90 + 40 * q^91 + 8 * q^92 + 3 * q^93 + 4 * q^94 - q^95 + 6 * q^96 + 50 * q^97 - 23 * q^98 + 54 * q^99

Introduction

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