LMFDB - Embedded newform 483.2.i.f.415.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + \cdots + 4 $ x^12 - x^11 + 8x^10 - 3x^9 + 42x^8 - 15x^7 + 101x^6 + 6x^5 + 150x^4 - 28x^3 + 40x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.5
Root			$0.916322 + 1.58712i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.f.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.916322 - 1.58712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.679293 - 1.17657i) q^{4} +(0.471745 - 0.817086i) q^{5} +1.83264 q^{6} +(-1.16166 - 2.37709i) q^{7} +1.17548 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.916322 - 1.58712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.679293 - 1.17657i) q^{4} +(0.471745 - 0.817086i) q^{5} +1.83264 q^{6} +(-1.16166 - 2.37709i) q^{7} +1.17548 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.864540 - 1.49743i) q^{10} +(-1.04340 - 1.80722i) q^{11} +(0.679293 - 1.17657i) q^{12} +3.64405 q^{13} +(-4.83717 - 0.334494i) q^{14} +0.943490 q^{15} +(2.43571 - 4.21877i) q^{16} +(-0.149720 - 0.259323i) q^{17} +(0.916322 + 1.58712i) q^{18} +(0.289732 - 0.501830i) q^{19} -1.28181 q^{20} +(1.47779 - 2.19457i) q^{21} -3.82436 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.587742 + 1.01800i) q^{24} +(2.05491 + 3.55921i) q^{25} +(3.33912 - 5.78353i) q^{26} -1.00000 q^{27} +(-2.00771 + 2.98151i) q^{28} -5.89363 q^{29} +(0.864540 - 1.49743i) q^{30} +(3.01194 + 5.21683i) q^{31} +(-3.28830 - 5.69551i) q^{32} +(1.04340 - 1.80722i) q^{33} -0.548767 q^{34} +(-2.49029 - 0.172206i) q^{35} +1.35859 q^{36} +(0.618718 - 1.07165i) q^{37} +(-0.530975 - 0.919676i) q^{38} +(1.82202 + 3.15584i) q^{39} +(0.554529 - 0.960472i) q^{40} +8.42024 q^{41} +(-2.12890 - 4.35636i) q^{42} -9.08583 q^{43} +(-1.41755 + 2.45527i) q^{44} +(0.471745 + 0.817086i) q^{45} +(-0.916322 - 1.58712i) q^{46} +(-2.53123 + 4.38422i) q^{47} +4.87142 q^{48} +(-4.30111 + 5.52273i) q^{49} +7.53185 q^{50} +(0.149720 - 0.259323i) q^{51} +(-2.47538 - 4.28748i) q^{52} +(-1.16288 - 2.01417i) q^{53} +(-0.916322 + 1.58712i) q^{54} -1.96887 q^{55} +(-1.36551 - 2.79423i) q^{56} +0.579464 q^{57} +(-5.40047 + 9.35388i) q^{58} +(-1.04007 - 1.80146i) q^{59} +(-0.640906 - 1.11008i) q^{60} +(-6.22701 + 10.7855i) q^{61} +11.0396 q^{62} +(2.63945 + 0.182520i) q^{63} -2.30974 q^{64} +(1.71906 - 2.97750i) q^{65} +(-1.91218 - 3.31200i) q^{66} +(2.06882 + 3.58330i) q^{67} +(-0.203407 + 0.352312i) q^{68} +1.00000 q^{69} +(-2.55522 + 3.79459i) q^{70} -11.6439 q^{71} +(-0.587742 + 1.01800i) q^{72} +(5.78499 + 10.0199i) q^{73} +(-1.13389 - 1.96395i) q^{74} +(-2.05491 + 3.55921i) q^{75} -0.787251 q^{76} +(-3.08386 + 4.57963i) q^{77} +6.67825 q^{78} +(-8.57920 + 14.8596i) q^{79} +(-2.29807 - 3.98037i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.71565 - 13.3639i) q^{82} +10.9740 q^{83} +(-3.58592 - 0.247969i) q^{84} -0.282519 q^{85} +(-8.32554 + 14.4203i) q^{86} +(-2.94682 - 5.10403i) q^{87} +(-1.22650 - 2.12436i) q^{88} +(-1.33781 + 2.31715i) q^{89} +1.72908 q^{90} +(-4.23314 - 8.66223i) q^{91} -1.35859 q^{92} +(-3.01194 + 5.21683i) q^{93} +(4.63885 + 8.03472i) q^{94} +(-0.273359 - 0.473472i) q^{95} +(3.28830 - 5.69551i) q^{96} +0.589843 q^{97} +(4.82401 + 11.8870i) q^{98} +2.08680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.916322	−	1.58712i	0.647938	−	1.12226i	−0.335677	−	0.941977i	$-0.608965\pi$
$2$	0.916322	−	1.58712i	0.647938	−	1.12226i	0.983615	−	0.180284i	$-0.0577016\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.679293	−	1.17657i	−0.339646	−	0.588285i
$5$	0.471745	−	0.817086i	0.210971	−	0.365412i	−0.741048	−	0.671452i	$-0.765671\pi$
$5$	0.471745	−	0.817086i	0.210971	−	0.365412i	0.952019	+	0.306040i	$0.0990042\pi$
$6$	1.83264			0.748174
$7$	−1.16166	−	2.37709i	−0.439065	−	0.898455i
$7$	−1.16166	−	2.37709i	−0.439065	−	0.898455i
$8$	1.17548			0.415597
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.864540	−	1.49743i	−0.273392	−	0.473528i
$11$	−1.04340	−	1.80722i	−0.314597	−	0.544898i	0.664755	−	0.747062i	$-0.268536\pi$
$11$	−1.04340	−	1.80722i	−0.314597	−	0.544898i	−0.979352	+	0.202164i	$0.935203\pi$
$12$	0.679293	−	1.17657i	0.196095	−	0.339646i
$13$	3.64405			1.01068			0.505339	−	0.862921i	$-0.331368\pi$
$13$	3.64405			1.01068			0.505339	+	0.862921i	$0.331368\pi$
$14$	−4.83717	−	0.334494i	−1.29279	−	0.0893973i
$15$	0.943490			0.243608
$16$	2.43571	−	4.21877i	0.608927	−	1.05469i
$17$	−0.149720	−	0.259323i	−0.0363124	−	0.0628950i	0.847298	−	0.531118i	$-0.178228\pi$
$17$	−0.149720	−	0.259323i	−0.0363124	−	0.0628950i	−0.883610	+	0.468223i	$0.844894\pi$
$18$	0.916322	+	1.58712i	0.215979	+	0.374087i
$19$	0.289732	−	0.501830i	0.0664690	−	0.115128i	−0.830876	−	0.556458i	$-0.812160\pi$
$19$	0.289732	−	0.501830i	0.0664690	−	0.115128i	0.897345	+	0.441330i	$0.145493\pi$
$20$	−1.28181			−0.286622
$21$	1.47779	−	2.19457i	0.322480	−	0.478894i
$22$	−3.82436			−0.815357
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	0.587742	+	1.01800i	0.119972	+	0.207798i
$25$	2.05491	+	3.55921i	0.410983	+	0.711843i
$26$	3.33912	−	5.78353i	0.654856	−	1.13424i
$27$	−1.00000			−0.192450
$28$	−2.00771	+	2.98151i	−0.379421	+	0.563452i
$29$	−5.89363			−1.09442			−0.547210	−	0.836995i	$-0.684310\pi$
$29$	−5.89363			−1.09442			−0.547210	+	0.836995i	$0.684310\pi$
$30$	0.864540	−	1.49743i	0.157843	−	0.273392i
$31$	3.01194	+	5.21683i	0.540960	+	0.936970i	0.998849	+	0.0479608i	$0.0152723\pi$
$31$	3.01194	+	5.21683i	0.540960	+	0.936970i	−0.457889	+	0.889009i	$0.651394\pi$
$32$	−3.28830	−	5.69551i	−0.581295	−	1.00683i
$33$	1.04340	−	1.80722i	0.181633	−	0.314597i
$34$	−0.548767			−0.0941128
$35$	−2.49029	−	0.172206i	−0.420936	−	0.0291081i
$36$	1.35859			0.226431
$37$	0.618718	−	1.07165i	0.101717	−	0.176178i	−0.810675	−	0.585496i	$-0.800900\pi$
$37$	0.618718	−	1.07165i	0.101717	−	0.176178i	0.912392	+	0.409318i	$0.134233\pi$
$38$	−0.530975	−	0.919676i	−0.0861356	−	0.149191i
$39$	1.82202	+	3.15584i	0.291757	+	0.505339i
$40$	0.554529	−	0.960472i	0.0876787	−	0.151864i
$41$	8.42024			1.31502			0.657510	−	0.753446i	$-0.271610\pi$
$41$	8.42024			1.31502			0.657510	+	0.753446i	$0.271610\pi$
$42$	−2.12890	−	4.35636i	−0.328497	−	0.672201i
$43$	−9.08583			−1.38558			−0.692788	−	0.721142i	$-0.743618\pi$
$43$	−9.08583			−1.38558			−0.692788	+	0.721142i	$0.743618\pi$
$44$	−1.41755	+	2.45527i	−0.213703	+	0.370145i
$45$	0.471745	+	0.817086i	0.0703236	+	0.121804i
$46$	−0.916322	−	1.58712i	−0.135104	−	0.234008i
$47$	−2.53123	+	4.38422i	−0.369218	+	0.639505i	−0.989444	−	0.144919i	$-0.953708\pi$
$47$	−2.53123	+	4.38422i	−0.369218	+	0.639505i	0.620225	+	0.784424i	$0.287041\pi$
$48$	4.87142			0.703128
$49$	−4.30111	+	5.52273i	−0.614444	+	0.788961i
$50$	7.53185			1.06516
$51$	0.149720	−	0.259323i	0.0209650	−	0.0363124i
$52$	−2.47538	−	4.28748i	−0.343273	−	0.594566i
$53$	−1.16288	−	2.01417i	−0.159734	−	0.276668i	0.775039	−	0.631914i	$-0.217730\pi$
$53$	−1.16288	−	2.01417i	−0.159734	−	0.276668i	−0.934773	+	0.355246i	$0.884397\pi$
$54$	−0.916322	+	1.58712i	−0.124696	+	0.215979i
$55$	−1.96887			−0.265483
$56$	−1.36551	−	2.79423i	−0.182474	−	0.373395i
$57$	0.579464			0.0767518
$58$	−5.40047	+	9.35388i	−0.709116	+	1.22822i
$59$	−1.04007	−	1.80146i	−0.135406	−	0.234530i	0.790346	−	0.612660i	$-0.209901\pi$
$59$	−1.04007	−	1.80146i	−0.135406	−	0.234530i	−0.925753	+	0.378130i	$0.876567\pi$
$60$	−0.640906	−	1.11008i	−0.0827406	−	0.143311i
$61$	−6.22701	+	10.7855i	−0.797287	+	1.38094i	0.124089	+	0.992271i	$0.460399\pi$
$61$	−6.22701	+	10.7855i	−0.797287	+	1.38094i	−0.921376	+	0.388671i	$0.872934\pi$
$62$	11.0396			1.40203
$63$	2.63945	+	0.182520i	0.332539	+	0.0229954i
$64$	−2.30974			−0.288718
$65$	1.71906	−	2.97750i	0.213223	−	0.369314i
$66$	−1.91218	−	3.31200i	−0.235373	−	0.407679i
$67$	2.06882	+	3.58330i	0.252746	+	0.437769i	0.964281	−	0.264882i	$-0.0853329\pi$
$67$	2.06882	+	3.58330i	0.252746	+	0.437769i	−0.711535	+	0.702651i	$0.752000\pi$
$68$	−0.203407	+	0.352312i	−0.0246668	+	0.0427241i
$69$	1.00000			0.120386
$70$	−2.55522	+	3.79459i	−0.305407	+	0.453540i
$71$	−11.6439			−1.38188			−0.690938	−	0.722914i	$-0.742802\pi$
$71$	−11.6439			−1.38188			−0.690938	+	0.722914i	$0.742802\pi$
$72$	−0.587742	+	1.01800i	−0.0692661	+	0.119972i
$73$	5.78499	+	10.0199i	0.677082	+	1.17274i	0.975856	+	0.218416i	$0.0700891\pi$
$73$	5.78499	+	10.0199i	0.677082	+	1.17274i	−0.298774	+	0.954324i	$0.596578\pi$
$74$	−1.13389	−	1.96395i	−0.131812	−	0.228305i
$75$	−2.05491	+	3.55921i	−0.237281	+	0.410983i
$76$	−0.787251			−0.0903039
$77$	−3.08386	+	4.57963i	−0.351438	+	0.521897i
$78$	6.67825			0.756163
$79$	−8.57920	+	14.8596i	−0.965235	+	1.67184i	−0.256254	+	0.966609i	$0.582488\pi$
$79$	−8.57920	+	14.8596i	−0.965235	+	1.67184i	−0.708981	+	0.705227i	$0.750845\pi$
$80$	−2.29807	−	3.98037i	−0.256932	−	0.445018i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.71565	−	13.3639i	0.852051	−	1.47580i
$83$	10.9740			1.20455			0.602274	−	0.798289i	$-0.294261\pi$
$83$	10.9740			1.20455			0.602274	+	0.798289i	$0.294261\pi$
$84$	−3.58592	−	0.247969i	−0.391256	−	0.0270556i
$85$	−0.282519			−0.0306434
$86$	−8.32554	+	14.4203i	−0.897766	+	1.55498i
$87$	−2.94682	−	5.10403i	−0.315932	−	0.547210i
$88$	−1.22650	−	2.12436i	−0.130745	−	0.226458i
$89$	−1.33781	+	2.31715i	−0.141807	+	0.245617i	−0.928177	−	0.372139i	$-0.878625\pi$
$89$	−1.33781	+	2.31715i	−0.141807	+	0.245617i	0.786370	+	0.617756i	$0.211958\pi$
$90$	1.72908			0.182261
$91$	−4.23314	−	8.66223i	−0.443753	−	0.908048i
$92$	−1.35859			−0.141642
$93$	−3.01194	+	5.21683i	−0.312323	+	0.540960i
$94$	4.63885	+	8.03472i	0.478461	+	0.828718i
$95$	−0.273359	−	0.473472i	−0.0280460	−	0.0485772i
$96$	3.28830	−	5.69551i	0.335611	−	0.581295i
$97$	0.589843			0.0598895			0.0299447	−	0.999552i	$-0.490467\pi$
$97$	0.589843			0.0598895			0.0299447	+	0.999552i	$0.490467\pi$
$98$	4.82401	+	11.8870i	0.487299	+	1.20076i
$99$	2.08680			0.209731
$100$	2.79178	−	4.83550i	0.279178	−	0.483550i
$101$	−3.11417	−	5.39390i	−0.309872	−	0.536713i	0.668462	−	0.743746i	$-0.266953\pi$
$101$	−3.11417	−	5.39390i	−0.309872	−	0.536713i	−0.978334	+	0.207033i	$0.933619\pi$
$102$	−0.274384	−	0.475246i	−0.0271680	−	0.0470564i
$103$	9.32274	−	16.1475i	0.918597	−	1.59106i	0.117049	−	0.993126i	$-0.462656\pi$
$103$	9.32274	−	16.1475i	0.918597	−	1.59106i	0.801548	−	0.597931i	$-0.204010\pi$
$104$	4.28352			0.420034
$105$	−1.09601	−	2.24276i	−0.106960	−	0.218871i
$106$	−4.26230			−0.413992
$107$	0.324442	−	0.561949i	0.0313650	−	0.0543257i	−0.849917	−	0.526917i	$-0.823348\pi$
$107$	0.324442	−	0.561949i	0.0313650	−	0.0543257i	0.881282	+	0.472591i	$0.156681\pi$
$108$	0.679293	+	1.17657i	0.0653650	+	0.113215i
$109$	6.82667	+	11.8241i	0.653876	+	1.13255i	0.982174	+	0.187973i	$0.0601916\pi$
$109$	6.82667	+	11.8241i	0.653876	+	1.13255i	−0.328298	+	0.944574i	$0.606475\pi$
$110$	−1.80412	+	3.12483i	−0.172016	+	0.297941i
$111$	1.23744			0.117452
$112$	−12.8579	−	0.889131i	−1.21495	−	0.0840150i
$113$	0.547279			0.0514836			0.0257418	−	0.999669i	$-0.491805\pi$
$113$	0.547279			0.0514836			0.0257418	+	0.999669i	$0.491805\pi$
$114$	0.530975	−	0.919676i	0.0497304	−	0.0861356i
$115$	−0.471745	−	0.817086i	−0.0439904	−	0.0761937i
$116$	4.00350	+	6.93427i	0.371716	+	0.643831i
$117$	−1.82202	+	3.15584i	−0.168446	+	0.291757i
$118$	−3.81217			−0.350939
$119$	−0.442510	+	0.657142i	−0.0405648	+	0.0602401i
$120$	1.10906			0.101243
$121$	3.32263	−	5.75497i	0.302057	−	0.523179i
$122$	11.4119	+	19.7660i	1.03319	+	1.78953i
$123$	4.21012	+	7.29214i	0.379614	+	0.657510i
$124$	4.09197	−	7.08751i	0.367470	−	0.636477i
$125$	8.59503			0.768763
$126$	2.70827	−	4.02186i	0.241271	−	0.358296i
$127$	−1.01278			−0.0898693			−0.0449347	−	0.998990i	$-0.514308\pi$
$127$	−1.01278			−0.0898693			−0.0449347	+	0.998990i	$0.514308\pi$
$128$	4.46013	−	7.72518i	0.394224	−	0.682816i
$129$	−4.54291	−	7.86856i	−0.399981	−	0.692788i
$130$	−3.15043	−	5.45670i	−0.276311	−	0.478584i
$131$	7.51553	−	13.0173i	0.656635	−	1.13733i	−0.324846	−	0.945767i	$-0.605313\pi$
$131$	7.51553	−	13.0173i	0.656635	−	1.13733i	0.981481	−	0.191558i	$-0.0613541\pi$
$132$	−2.83510			−0.246764
$133$	−1.52946	−	0.105764i	−0.132621	−	0.00917087i
$134$	7.58281			0.655055
$135$	−0.471745	+	0.817086i	−0.0406013	+	0.0703236i
$136$	−0.175994	−	0.304830i	−0.0150913	−	0.0261389i
$137$	−4.63934	−	8.03557i	−0.396365	−	0.686525i	0.596909	−	0.802309i	$-0.296395\pi$
$137$	−4.63934	−	8.03557i	−0.396365	−	0.686525i	−0.993274	+	0.115784i	$0.963062\pi$
$138$	0.916322	−	1.58712i	0.0780025	−	0.135104i
$139$	6.58750			0.558744			0.279372	−	0.960183i	$-0.409874\pi$
$139$	6.58750			0.558744			0.279372	+	0.960183i	$0.409874\pi$
$140$	1.48903	+	3.04698i	0.125846	+	0.257517i
$141$	−5.06246			−0.426336
$142$	−10.6696	+	18.4802i	−0.895370	+	1.55083i
$143$	−3.80220	−	6.58561i	−0.317956	−	0.550716i
$144$	2.43571	+	4.21877i	0.202976	+	0.351564i
$145$	−2.78029	+	4.81560i	−0.230890	+	0.399914i
$146$	21.2037			1.75483
$147$	−6.93337	−	0.963504i	−0.571855	−	0.0794685i
$148$	−1.68116			−0.138191
$149$	2.94451	−	5.10005i	0.241224	−	0.417812i	−0.719839	−	0.694141i	$-0.755784\pi$
$149$	2.94451	−	5.10005i	0.241224	−	0.417812i	0.961063	+	0.276329i	$0.0891178\pi$
$150$	3.76593	+	6.52278i	0.307487	+	0.532582i
$151$	−6.57693	−	11.3916i	−0.535223	−	0.927033i	−0.999153	−	0.0411608i	$-0.986894\pi$
$151$	−6.57693	−	11.3916i	−0.535223	−	0.927033i	0.463930	−	0.885872i	$-0.346439\pi$
$152$	0.340575	−	0.589894i	0.0276243	−	0.0478467i
$153$	0.299440			0.0242083
$154$	4.44260	+	9.09085i	0.357995	+	0.732562i
$155$	5.68346			0.456507
$156$	2.47538	−	4.28748i	0.198189	−	0.343273i
$157$	4.21279	+	7.29677i	0.336217	+	0.582345i	0.983718	−	0.179720i	$-0.0575190\pi$
$157$	4.21279	+	7.29677i	0.336217	+	0.582345i	−0.647501	+	0.762065i	$0.724186\pi$
$158$	15.7226	+	27.2324i	1.25082	+	2.16649i
$159$	1.16288	−	2.01417i	0.0922227	−	0.159734i
$160$	−6.20496			−0.490545
$161$	−2.63945	−	0.182520i	−0.208018	−	0.0143846i
$162$	−1.83264			−0.143986
$163$	−2.07868	+	3.60038i	−0.162815	+	0.282004i	−0.935877	−	0.352326i	$-0.885391\pi$
$163$	−2.07868	+	3.60038i	−0.162815	+	0.282004i	0.773062	+	0.634330i	$0.218724\pi$
$164$	−5.71981	−	9.90699i	−0.446642	−	0.773606i
$165$	−0.984437	−	1.70510i	−0.0766383	−	0.132741i
$166$	10.0557	−	17.4170i	0.780473	−	1.35182i
$167$	−3.04445			−0.235587			−0.117793	−	0.993038i	$-0.537582\pi$
$167$	−3.04445			−0.235587			−0.117793	+	0.993038i	$0.537582\pi$
$168$	1.73712	−	2.57968i	0.134022	−	0.199027i
$169$	0.279097			0.0214690
$170$	−0.258878	+	0.448390i	−0.0198550	+	0.0343899i
$171$	0.289732	+	0.501830i	0.0221563	+	0.0383759i
$172$	6.17194	+	10.6901i	0.470606	+	0.815113i
$173$	−8.02715	+	13.9034i	−0.610293	+	1.05706i	0.380898	+	0.924617i	$0.375615\pi$
$173$	−8.02715	+	13.9034i	−0.610293	+	1.05706i	−0.991191	+	0.132441i	$0.957719\pi$
$174$	−10.8009			−0.818816
$175$	6.07347	−	9.01930i	0.459111	−	0.681795i
$176$	−10.1657			−0.766267
$177$	1.04007	−	1.80146i	0.0781768	−	0.135406i
$178$	2.45172	+	4.24651i	0.183764	+	0.318289i
$179$	2.67255	+	4.62898i	0.199755	+	0.345987i	0.948449	−	0.316930i	$-0.102652\pi$
$179$	2.67255	+	4.62898i	0.199755	+	0.345987i	−0.748694	+	0.662916i	$0.769319\pi$
$180$	0.640906	−	1.11008i	0.0477703	−	0.0827406i
$181$	−11.6201			−0.863716			−0.431858	−	0.901942i	$-0.642142\pi$
$181$	−11.6201			−0.863716			−0.431858	+	0.901942i	$0.642142\pi$
$182$	−17.6269	−	1.21891i	−1.30659	−	0.0903519i
$183$	−12.4540			−0.920628
$184$	0.587742	−	1.01800i	0.0433289	−	0.0750479i
$185$	−0.583754	−	1.01109i	−0.0429184	−	0.0743369i
$186$	5.51981	+	9.56059i	0.404732	+	0.701017i
$187$	−0.312436	+	0.541155i	−0.0228476	+	0.0395732i
$188$	6.87779			0.501614
$189$	1.16166	+	2.37709i	0.0844981	+	0.172908i
$190$	−1.00194			−0.0726883
$191$	8.53757	−	14.7875i	0.617757	−	1.06999i	−0.372137	−	0.928178i	$-0.621375\pi$
$191$	8.53757	−	14.7875i	0.617757	−	1.06999i	0.989894	−	0.141809i	$-0.0452918\pi$
$192$	−1.15487	−	2.00030i	−0.0833457	−	0.144359i
$193$	2.32526	+	4.02747i	0.167376	+	0.289903i	0.937496	−	0.347995i	$-0.113137\pi$
$193$	2.32526	+	4.02747i	0.167376	+	0.289903i	−0.770121	+	0.637898i	$0.779804\pi$
$194$	0.540486	−	0.936149i	0.0388046	−	0.0672116i
$195$	3.43812			0.246209
$196$	9.41958	+	1.30900i	0.672827	+	0.0935002i
$197$	0.254912			0.0181618			0.00908088	−	0.999959i	$-0.497109\pi$
$197$	0.254912			0.0181618			0.00908088	+	0.999959i	$0.497109\pi$
$198$	1.91218	−	3.31200i	0.135893	−	0.235373i
$199$	−2.73799	−	4.74233i	−0.194091	−	0.336175i	0.752511	−	0.658579i	$-0.228842\pi$
$199$	−2.73799	−	4.74233i	−0.194091	−	0.336175i	−0.946602	+	0.322404i	$0.895509\pi$
$200$	2.41552	+	4.18380i	0.170803	+	0.295840i
$201$	−2.06882	+	3.58330i	−0.145923	+	0.252746i
$202$	−11.4143			−0.803110
$203$	6.84638	+	14.0097i	0.480522	+	0.983287i
$204$	−0.406815			−0.0284827
$205$	3.97220	−	6.88006i	0.277431	−	0.480524i
$206$	−17.0853	−	29.5926i	−1.19039	−	2.06181i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	8.87584	−	15.3734i	0.615429	−	1.06595i
$209$	−1.20923			−0.0836438
$210$	−4.56382	−	0.315592i	−0.314933	−	0.0217779i
$211$	−3.18599			−0.219332			−0.109666	−	0.993968i	$-0.534978\pi$
$211$	−3.18599			−0.219332			−0.109666	+	0.993968i	$0.534978\pi$
$212$	−1.57988	+	2.73643i	−0.108506	+	0.187939i
$213$	−5.82195	−	10.0839i	−0.398913	−	0.690938i
$214$	−0.594586	−	1.02985i	−0.0406451	−	0.0703993i
$215$	−4.28619	+	7.42390i	−0.292316	+	0.506306i
$216$	−1.17548			−0.0799816
$217$	8.90203	−	13.2198i	0.604309	−	0.897419i
$218$	25.0217			1.69468
$219$	−5.78499	+	10.0199i	−0.390914	+	0.677082i
$220$	1.33744	+	2.31652i	0.0901703	+	0.156180i
$221$	−0.545587	−	0.944985i	−0.0367002	−	0.0635665i
$222$	1.13389	−	1.96395i	0.0761017	−	0.131812i
$223$	−22.7674			−1.52462			−0.762309	−	0.647213i	$-0.775934\pi$
$223$	−22.7674			−1.52462			−0.762309	+	0.647213i	$0.775934\pi$
$224$	−9.71885	+	14.4328i	−0.649368	+	0.964333i
$225$	−4.10983			−0.273988
$226$	0.501484	−	0.868595i	0.0333582	−	0.0577781i
$227$	−5.22604	−	9.05176i	−0.346864	−	0.600787i	0.638826	−	0.769351i	$-0.279420\pi$
$227$	−5.22604	−	9.05176i	−0.346864	−	0.600787i	−0.985691	+	0.168564i	$0.946087\pi$
$228$	−0.393625	−	0.681779i	−0.0260685	−	0.0451519i
$229$	5.38392	−	9.32522i	0.355779	−	0.616228i	−0.631472	−	0.775399i	$-0.717549\pi$
$229$	5.38392	−	9.32522i	0.355779	−	0.616228i	0.987251	+	0.159171i	$0.0508822\pi$
$230$	−1.72908			−0.114012
$231$	−5.50800	−	0.380883i	−0.362400	−	0.0250602i
$232$	−6.92787			−0.454837
$233$	−5.87538	+	10.1765i	−0.384909	+	0.666682i	−0.991757	−	0.128136i	$-0.959100\pi$
$233$	−5.87538	+	10.1765i	−0.384909	+	0.666682i	0.606848	+	0.794818i	$0.292434\pi$
$234$	3.33912	+	5.78353i	0.218285	+	0.378081i
$235$	2.38819	+	4.13647i	0.155788	+	0.269833i
$236$	−1.41303	+	2.44744i	−0.0919804	+	0.159315i
$237$	−17.1584			−1.11456
$238$	0.637479	+	1.30447i	0.0413216	+	0.0845561i
$239$	−12.5491			−0.811734			−0.405867	−	0.913932i	$-0.633030\pi$
$239$	−12.5491			−0.811734			−0.405867	+	0.913932i	$0.633030\pi$
$240$	2.29807	−	3.98037i	0.148339	−	0.256932i
$241$	5.31523	+	9.20624i	0.342384	+	0.593026i	0.984875	−	0.173267i	$-0.0554324\pi$
$241$	5.31523	+	9.20624i	0.342384	+	0.593026i	−0.642491	+	0.766293i	$0.722099\pi$
$242$	−6.08920	−	10.5468i	−0.391429	−	0.677974i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	16.9199			1.08318
$245$	2.48352	+	6.11969i	0.158666	+	0.390973i
$246$	15.4313			0.983864
$247$	1.05580	−	1.82869i	0.0671788	−	0.116357i
$248$	3.54049	+	6.13230i	0.224821	+	0.389402i
$249$	5.48698	+	9.50373i	0.347723	+	0.602274i
$250$	7.87581	−	13.6413i	0.498110	−	0.862752i
$251$	−17.4415			−1.10090			−0.550450	−	0.834868i	$-0.685544\pi$
$251$	−17.4415			−1.10090			−0.550450	+	0.834868i	$0.685544\pi$
$252$	−1.57821	−	3.22948i	−0.0994179	−	0.203438i
$253$	−2.08680			−0.131196
$254$	−0.928029	+	1.60739i	−0.0582297	+	0.100857i
$255$	−0.141259	−	0.244668i	−0.00884600	−	0.0153217i
$256$	−10.4836	−	18.1581i	−0.655224	−	1.13488i
$257$	−9.36304	+	16.2173i	−0.584050	+	1.01160i	0.410943	+	0.911661i	$0.365200\pi$
$257$	−9.36304	+	16.2173i	−0.584050	+	1.01160i	−0.994993	+	0.0999435i	$0.968134\pi$
$258$	−16.6511			−1.03665
$259$	−3.26615	−	0.225857i	−0.202948	−	0.0140341i
$260$	−4.67098			−0.289682
$261$	2.94682	−	5.10403i	0.182403	−	0.315932i
$262$	−13.7733	−	23.8560i	−0.850917	−	1.47383i
$263$	−14.9543	−	25.9016i	−0.922121	−	1.59716i	−0.796128	−	0.605129i	$-0.793122\pi$
$263$	−14.9543	−	25.9016i	−0.922121	−	1.59716i	−0.125993	−	0.992031i	$-0.540212\pi$
$264$	1.22650	−	2.12436i	0.0754859	−	0.130745i
$265$	−2.19434			−0.134797
$266$	−1.56934	+	2.33052i	−0.0962225	+	0.142894i
$267$	−2.67561			−0.163745
$268$	2.81067	−	4.86821i	0.171689	−	0.297374i
$269$	−11.3230	−	19.6121i	−0.690378	−	1.19577i	−0.971714	−	0.236161i	$-0.924111\pi$
$269$	−11.3230	−	19.6121i	−0.690378	−	1.19577i	0.281336	−	0.959609i	$-0.409222\pi$
$270$	0.864540	+	1.49743i	0.0526143	+	0.0911306i
$271$	6.36818	−	11.0300i	0.386839	−	0.670026i	−0.605183	−	0.796086i	$-0.706900\pi$
$271$	6.36818	−	11.0300i	0.386839	−	0.670026i	0.992023	+	0.126061i	$0.0402334\pi$
$272$	−1.45870			−0.0884465
$273$	5.38514	−	7.99712i	0.325924	−	0.484008i
$274$	−17.0045			−1.02728
$275$	4.28820	−	7.42737i	0.258588	−	0.447887i
$276$	−0.679293	−	1.17657i	−0.0408886	−	0.0708212i
$277$	14.5063	+	25.1257i	0.871601	+	1.50966i	0.860340	+	0.509720i	$0.170251\pi$
$277$	14.5063	+	25.1257i	0.871601	+	1.50966i	0.0112606	+	0.999937i	$0.496416\pi$
$278$	6.03627	−	10.4551i	0.362031	−	0.627057i
$279$	−6.02387			−0.360640
$280$	−2.92730	−	0.202425i	−0.174940	−	0.0120972i
$281$	−12.4466			−0.742504			−0.371252	−	0.928532i	$-0.621071\pi$
$281$	−12.4466			−0.742504			−0.371252	+	0.928532i	$0.621071\pi$
$282$	−4.63885	+	8.03472i	−0.276239	+	0.478461i
$283$	−4.68198	−	8.10943i	−0.278315	−	0.482056i	0.692651	−	0.721273i	$-0.256443\pi$
$283$	−4.68198	−	8.10943i	−0.278315	−	0.482056i	−0.970966	+	0.239217i	$0.923109\pi$
$284$	7.90962	+	13.6999i	0.469349	+	0.812937i
$285$	0.273359	−	0.473472i	0.0161924	−	0.0280460i
$286$	−13.9362			−0.824063
$287$	−9.78143	−	20.0157i	−0.577379	−	1.18149i
$288$	6.57660			0.387530
$289$	8.45517	−	14.6448i	0.497363	−	0.861458i
$290$	5.09528	+	8.82529i	0.299205	+	0.518239i
$291$	0.294921	+	0.510819i	0.0172886	+	0.0299447i
$292$	7.85941	−	13.6129i	0.459937	−	0.796634i
$293$	5.69521			0.332717			0.166359	−	0.986065i	$-0.446799\pi$
$293$	5.69521			0.332717			0.166359	+	0.986065i	$0.446799\pi$
$294$	−7.88240	+	10.1212i	−0.459711	+	0.590280i
$295$	−1.96260			−0.114267
$296$	0.727293	−	1.25971i	0.0422731	−	0.0732191i
$297$	1.04340	+	1.80722i	0.0605442	+	0.104866i
$298$	−5.39625	−	9.34657i	−0.312596	−	0.541433i
$299$	1.82202	−	3.15584i	0.105370	−	0.182507i
$300$	5.58355			0.322367
$301$	10.5546	+	21.5978i	0.608358	+	1.24488i
$302$	−24.1063			−1.38716
$303$	3.11417	−	5.39390i	0.178904	−	0.309872i
$304$	−1.41140	−	2.44462i	−0.0809496	−	0.140209i
$305$	5.87512	+	10.1760i	0.336409	+	0.582677i
$306$	0.274384	−	0.475246i	0.0156855	−	0.0271680i
$307$	17.0596			0.973642			0.486821	−	0.873502i	$-0.338156\pi$
$307$	17.0596			0.973642			0.486821	+	0.873502i	$0.338156\pi$
$308$	7.48309	+	0.517462i	0.426389	+	0.0294851i
$309$	18.6455			1.06070
$310$	5.20788	−	9.02032i	0.295788	−	0.512320i
$311$	8.26214	+	14.3104i	0.468503	+	0.811471i	0.999352	−	0.0359958i	$-0.0114603\pi$
$311$	8.26214	+	14.3104i	0.468503	+	0.811471i	−0.530849	+	0.847466i	$0.678127\pi$
$312$	2.14176	+	3.70964i	0.121253	+	0.210017i
$313$	0.746938	−	1.29374i	0.0422195	−	0.0731262i	−0.844143	−	0.536117i	$-0.819890\pi$
$313$	0.746938	−	1.29374i	0.0422195	−	0.0731262i	0.886363	+	0.462991i	$0.153224\pi$
$314$	15.4411			0.871391
$315$	1.39428	−	2.07055i	0.0785588	−	0.116662i
$316$	23.3112			1.31135
$317$	9.11172	−	15.7820i	0.511765	−	0.886403i	−0.488142	−	0.872764i	$-0.662325\pi$
$317$	9.11172	−	15.7820i	0.511765	−	0.886403i	0.999907	−	0.0136387i	$-0.00434146\pi$
$318$	−2.13115	−	3.69126i	−0.119509	−	0.206996i
$319$	6.14942	+	10.6511i	0.344301	+	0.596347i
$320$	−1.08961	+	1.88726i	−0.0609111	+	0.105501i
$321$	0.648883			0.0362171
$322$	−2.70827	+	4.02186i	−0.150926	+	0.224130i
$323$	−0.173515			−0.00965461
$324$	−0.679293	+	1.17657i	−0.0377385	+	0.0653650i
$325$	7.48821	+	12.9700i	0.415371	+	0.719444i
$326$	3.80948	+	6.59822i	0.210988	+	0.365442i
$327$	−6.82667	+	11.8241i	−0.377516	+	0.653876i
$328$	9.89786			0.546518
$329$	13.3621	+	0.924001i	0.736677	+	0.0509418i
$330$	−3.60825			−0.198627
$331$	11.4774	−	19.8795i	0.630857	−	1.09268i	−0.356520	−	0.934288i	$-0.616037\pi$
$331$	11.4774	−	19.8795i	0.630857	−	1.09268i	0.987377	−	0.158388i	$-0.0506298\pi$
$332$	−7.45453	−	12.9116i	−0.409121	−	0.708618i
$333$	0.618718	+	1.07165i	0.0339055	+	0.0587261i
$334$	−2.78970	+	4.83189i	−0.152645	+	0.264390i
$335$	3.90381			0.213288
$336$	−5.65892	−	11.5798i	−0.308719	−	0.631729i
$337$	22.2266			1.21076			0.605381	−	0.795936i	$-0.293021\pi$
$337$	22.2266			1.21076			0.605381	+	0.795936i	$0.293021\pi$
$338$	0.255743	−	0.442960i	0.0139106	−	0.0240938i
$339$	0.273639	+	0.473957i	0.0148620	+	0.0257418i
$340$	0.191913	+	0.332403i	0.0104079	+	0.0180271i
$341$	6.28531	−	10.8865i	0.340369	−	0.589536i
$342$	1.06195			0.0574237
$343$	18.1244	+	3.80860i	0.978627	+	0.205645i
$344$	−10.6802			−0.575840
$345$	0.471745	−	0.817086i	0.0253979	−	0.0439904i
$346$	14.7109	+	25.4800i	0.790863	+	1.36982i
$347$	2.70421	+	4.68383i	0.145170	+	0.251441i	0.929436	−	0.368983i	$-0.120294\pi$
$347$	2.70421	+	4.68383i	0.145170	+	0.251441i	−0.784267	+	0.620424i	$0.786961\pi$
$348$	−4.00350	+	6.93427i	−0.214610	+	0.371716i
$349$	10.3938			0.556369			0.278184	−	0.960528i	$-0.410267\pi$
$349$	10.3938			0.556369			0.278184	+	0.960528i	$0.410267\pi$
$350$	−8.74943	−	17.9039i	−0.467677	−	0.957003i
$351$	−3.64405			−0.194505
$352$	−6.86203	+	11.8854i	−0.365747	+	0.633493i
$353$	6.53453	+	11.3181i	0.347798	+	0.602404i	0.985858	−	0.167583i	$-0.0535962\pi$
$353$	6.53453	+	11.3181i	0.347798	+	0.602404i	−0.638060	+	0.769987i	$0.720263\pi$
$354$	−1.90609	−	3.30144i	−0.101307	−	0.175469i
$355$	−5.49295	+	9.51407i	−0.291535	+	0.504954i
$356$	3.63505			0.192657
$357$	−0.790356	−	0.0546538i	−0.0418301	−	0.00289258i
$358$	9.79565			0.517716
$359$	9.61160	−	16.6478i	0.507281	−	0.878636i	−0.492684	−	0.870209i	$-0.663984\pi$
$359$	9.61160	−	16.6478i	0.507281	−	0.878636i	0.999964	−	0.00842778i	$-0.00268268\pi$
$360$	0.554529	+	0.960472i	0.0292262	+	0.0506213i
$361$	9.33211	+	16.1637i	0.491164	+	0.850721i
$362$	−10.6478	+	18.4425i	−0.559634	+	0.969315i
$363$	6.64526			0.348786
$364$	−7.31618	+	10.8648i	−0.383472	+	0.569469i
$365$	10.9162			0.571378
$366$	−11.4119	+	19.7660i	−0.596510	+	1.03319i
$367$	0.887548	+	1.53728i	0.0463296	+	0.0802452i	0.888260	−	0.459340i	$-0.151914\pi$
$367$	0.887548	+	1.53728i	0.0463296	+	0.0802452i	−0.841931	+	0.539586i	$0.818581\pi$
$368$	−2.43571	−	4.21877i	−0.126970	−	0.219919i
$369$	−4.21012	+	7.29214i	−0.219170	+	0.379614i
$370$	−2.13963			−0.111234
$371$	−3.43700	+	5.10406i	−0.178440	+	0.264989i
$372$	8.18395			0.424318
$373$	3.72011	−	6.44341i	0.192620	−	0.333627i	−0.753498	−	0.657450i	$-0.771635\pi$
$373$	3.72011	−	6.44341i	0.192620	−	0.333627i	0.946118	+	0.323823i	$0.104968\pi$
$374$	0.572584	+	0.991744i	0.0296076	+	0.0512819i
$375$	4.29751	+	7.44351i	0.221923	+	0.384381i
$376$	−2.97542	+	5.15359i	−0.153446	+	0.265776i
$377$	−21.4767			−1.10611
$378$	4.83717	+	0.334494i	0.248797	+	0.0172045i
$379$	−4.31050			−0.221415			−0.110708	−	0.993853i	$-0.535312\pi$
$379$	−4.31050			−0.221415			−0.110708	+	0.993853i	$0.535312\pi$
$380$	−0.371382	+	0.643252i	−0.0190515	+	0.0329981i
$381$	−0.506388	−	0.877090i	−0.0259430	−	0.0449347i
$382$	−15.6463	−	27.1002i	−0.800536	−	1.38657i
$383$	−17.3457	+	30.0437i	−0.886326	+	1.53516i	−0.0421400	+	0.999112i	$0.513418\pi$
$383$	−17.3457	+	30.0437i	−0.886326	+	1.53516i	−0.844186	+	0.536050i	$0.819916\pi$
$384$	8.92027			0.455211
$385$	2.28716	+	4.68019i	0.116564	+	0.238525i
$386$	8.52275			0.433796
$387$	4.54291	−	7.86856i	0.230929	−	0.399981i
$388$	−0.400676	−	0.693991i	−0.0203412	−	0.0352321i
$389$	−16.5719	−	28.7034i	−0.840230	−	1.45532i	−0.889700	−	0.456546i	$-0.849086\pi$
$389$	−16.5719	−	28.7034i	−0.840230	−	1.45532i	0.0494696	−	0.998776i	$-0.484247\pi$
$390$	3.15043	−	5.45670i	0.159528	−	0.276311i
$391$	−0.299440			−0.0151433
$392$	−5.05588	+	6.49188i	−0.255361	+	0.327889i
$393$	15.0311			0.758217
$394$	0.233582	−	0.404576i	0.0117677	−	0.0203822i
$395$	8.09439	+	14.0199i	0.407273	+	0.705417i
$396$	−1.41755	−	2.45527i	−0.0712345	−	0.123382i
$397$	14.2282	−	24.6439i	0.714092	−	1.23684i	−0.249217	−	0.968448i	$-0.580173\pi$
$397$	14.2282	−	24.6439i	0.714092	−	1.23684i	0.963309	−	0.268396i	$-0.0864935\pi$
$398$	−10.0355			−0.503035
$399$	−0.673138	−	1.37744i	−0.0336991	−	0.0689581i
$400$	20.0207			1.00103
$401$	18.9406	−	32.8060i	0.945846	−	1.63825i	0.191798	−	0.981434i	$-0.438568\pi$
$401$	18.9406	−	32.8060i	0.945846	−	1.63825i	0.754048	−	0.656819i	$-0.228099\pi$
$402$	3.79141	+	6.56691i	0.189098	+	0.327528i
$403$	10.9756	+	19.0104i	0.546736	+	0.946974i
$404$	−4.23087	+	7.32808i	−0.210494	+	0.364586i
$405$	−0.943490			−0.0468824
$406$	28.5085	+	1.97139i	1.41485	+	0.0978382i
$407$	−2.58228			−0.127999
$408$	0.175994	−	0.304830i	0.00871298	−	0.0150913i
$409$	−0.478573	−	0.828913i	−0.0236639	−	0.0409871i	0.853951	−	0.520354i	$-0.174200\pi$
$409$	−0.478573	−	0.828913i	−0.0236639	−	0.0409871i	−0.877615	+	0.479366i	$0.840866\pi$
$410$	−7.27964	−	12.6087i	−0.359516	−	0.622699i
$411$	4.63934	−	8.03557i	0.228842	−	0.396365i
$412$	−25.3315			−1.24799
$413$	−3.07402	+	4.56503i	−0.151263	+	0.224630i
$414$	1.83264			0.0900696
$415$	5.17691	−	8.96667i	0.254124	−	0.440157i
$416$	−11.9827	−	20.7547i	−0.587502	−	1.01758i
$417$	3.29375	+	5.70494i	0.161296	+	0.279372i
$418$	−1.10804	+	1.91918i	−0.0541960	+	0.0938702i
$419$	−40.7600			−1.99126			−0.995628	−	0.0934066i	$-0.970224\pi$
$419$	−40.7600			−1.99126			−0.995628	+	0.0934066i	$0.970224\pi$
$420$	−1.89425	+	2.81302i	−0.0924299	+	0.137261i
$421$	−26.0184			−1.26806			−0.634031	−	0.773308i	$-0.718601\pi$
$421$	−26.0184			−1.26806			−0.634031	+	0.773308i	$0.718601\pi$
$422$	−2.91939	+	5.05653i	−0.142114	+	0.246148i
$423$	−2.53123	−	4.38422i	−0.123073	−	0.213168i
$424$	−1.36695	−	2.36763i	−0.0663850	−	0.114982i
$425$	0.615323	−	1.06577i	0.0298476	−	0.0516975i
$426$	−21.3391			−1.03388
$427$	32.8718	+	2.27311i	1.59078	+	0.110003i
$428$	−0.881564			−0.0426120
$429$	3.80220	−	6.58561i	0.183572	−	0.317956i
$430$	7.85506	+	13.6054i	0.378805	+	0.656109i
$431$	15.7221	+	27.2314i	0.757305	+	1.31169i	0.944220	+	0.329315i	$0.106818\pi$
$431$	15.7221	+	27.2314i	0.757305	+	1.31169i	−0.186914	+	0.982376i	$0.559849\pi$
$432$	−2.43571	+	4.21877i	−0.117188	+	0.202976i
$433$	3.61281			0.173621			0.0868103	−	0.996225i	$-0.472333\pi$
$433$	3.61281			0.173621			0.0868103	+	0.996225i	$0.472333\pi$
$434$	−12.8243	−	26.2422i	−0.615584	−	1.25966i
$435$	−5.56058			−0.266609
$436$	9.27461	−	16.0641i	0.444173	−	0.769331i
$437$	−0.289732	−	0.501830i	−0.0138598	−	0.0240058i
$438$	10.6018	+	18.3629i	0.506575	+	0.877414i
$439$	−9.02553	+	15.6327i	−0.430765	+	0.746107i	−0.996939	−	0.0781784i	$-0.975090\pi$
$439$	−9.02553	+	15.6327i	−0.430765	+	0.746107i	0.566174	+	0.824286i	$0.308423\pi$
$440$	−2.31438			−0.110334
$441$	−2.63227	−	6.48623i	−0.125346	−	0.308868i
$442$	−1.99973			−0.0951177
$443$	17.6650	−	30.5967i	0.839291	−	1.45369i	−0.0511975	−	0.998689i	$-0.516304\pi$
$443$	17.6650	−	30.5967i	0.839291	−	1.45369i	0.890488	−	0.455006i	$-0.150363\pi$
$444$	−0.840581	−	1.45593i	−0.0398922	−	0.0690953i
$445$	1.26221	+	2.18620i	0.0598343	+	0.103636i
$446$	−20.8623	+	36.1345i	−0.987857	+	1.71102i
$447$	5.88903			0.278541
$448$	2.68313	+	5.49047i	0.126766	+	0.259400i
$449$	5.95593			0.281078			0.140539	−	0.990075i	$-0.455116\pi$
$449$	5.95593			0.281078			0.140539	+	0.990075i	$0.455116\pi$
$450$	−3.76593	+	6.52278i	−0.177527	+	0.307487i
$451$	−8.78568	−	15.2172i	−0.413701	−	0.716552i
$452$	−0.371762	−	0.643911i	−0.0174862	−	0.0302870i
$453$	6.57693	−	11.3916i	0.309011	−	0.535223i
$454$	−19.1549			−0.898986
$455$	−9.07475	−	0.627526i	−0.425431	−	0.0294189i
$456$	0.681151			0.0318978
$457$	−15.9837	+	27.6846i	−0.747685	+	1.29503i	0.201244	+	0.979541i	$0.435502\pi$
$457$	−15.9837	+	27.6846i	−0.747685	+	1.29503i	−0.948930	+	0.315488i	$0.897832\pi$
$458$	−9.86681	−	17.0898i	−0.461046	−	0.798554i
$459$	0.149720	+	0.259323i	0.00698833	+	0.0121041i
$460$	−0.640906	+	1.11008i	−0.0298824	+	0.0517578i
$461$	7.10536			0.330930			0.165465	−	0.986216i	$-0.447088\pi$
$461$	7.10536			0.330930			0.165465	+	0.986216i	$0.447088\pi$
$462$	−5.65161	+	8.39283i	−0.262937	+	0.390470i
$463$	−42.0816			−1.95570			−0.977848	−	0.209314i	$-0.932877\pi$
$463$	−42.0816			−1.95570			−0.977848	+	0.209314i	$0.932877\pi$
$464$	−14.3552	+	24.8639i	−0.666422	+	1.15428i
$465$	2.84173	+	4.92202i	0.131782	+	0.228253i
$466$	10.7675	+	18.6498i	0.498794	+	0.863936i
$467$	−13.2253	+	22.9069i	−0.611995	+	1.06001i	0.378908	+	0.925434i	$0.376300\pi$
$467$	−13.2253	+	22.9069i	−0.611995	+	1.06001i	−0.990904	+	0.134573i	$0.957034\pi$
$468$	4.95075			0.228849
$469$	6.11456	−	9.08032i	0.282344	−	0.419290i
$470$	8.75341			0.403765
$471$	−4.21279	+	7.29677i	−0.194115	+	0.336217i
$472$	−1.22259	−	2.11759i	−0.0562743	−	0.0974700i
$473$	9.48015	+	16.4201i	0.435898	+	0.754997i
$474$	−15.7226	+	27.2324i	−0.722164	+	1.25082i
$475$	2.38150			0.109271
$476$	1.07377	+	0.0742518i	0.0492160	+	0.00340333i
$477$	2.32577			0.106490
$478$	−11.4990	+	19.9169i	−0.525953	+	0.910977i
$479$	12.6414	+	21.8956i	0.577601	+	1.00043i	0.995754	+	0.0920572i	$0.0293443\pi$
$479$	12.6414	+	21.8956i	0.577601	+	1.00043i	−0.418153	+	0.908377i	$0.637322\pi$
$480$	−3.10248	−	5.37365i	−0.141608	−	0.245272i
$481$	2.25464	−	3.90515i	0.102803	−	0.178059i
$482$	19.4818			0.887373
$483$	−1.16166	−	2.37709i	−0.0528572	−	0.108161i
$484$	−9.02816			−0.410371
$485$	0.278255	−	0.481952i	0.0126349	−	0.0218843i
$486$	−0.916322	−	1.58712i	−0.0415652	−	0.0719931i
$487$	−9.98826	−	17.3002i	−0.452611	−	0.783945i	0.545936	−	0.837827i	$-0.316174\pi$
$487$	−9.98826	−	17.3002i	−0.452611	−	0.783945i	−0.998547	+	0.0538814i	$0.982841\pi$
$488$	−7.31976	+	12.6782i	−0.331350	+	0.573915i
$489$	−4.15736			−0.188002
$490$	11.9884	+	1.66598i	0.541579	+	0.0752611i
$491$	−41.0091			−1.85072			−0.925358	−	0.379095i	$-0.876235\pi$
$491$	−41.0091			−1.85072			−0.925358	+	0.379095i	$0.876235\pi$
$492$	5.71981	−	9.90699i	0.257869	−	0.446642i
$493$	0.882395	+	1.52835i	0.0397411	+	0.0688335i
$494$	−1.93490	−	3.35135i	−0.0870553	−	0.150784i
$495$	0.984437	−	1.70510i	0.0442472	−	0.0766383i
$496$	29.3448			1.31762
$497$	13.5262	+	27.6786i	0.606734	+	1.24155i
$498$	20.1114			0.901212
$499$	−7.02344	+	12.1650i	−0.314412	+	0.544578i	−0.979312	−	0.202354i	$-0.935141\pi$
$499$	−7.02344	+	12.1650i	−0.314412	+	0.544578i	0.664900	+	0.746932i	$0.268474\pi$
$500$	−5.83854	−	10.1126i	−0.261107	−	0.452251i
$501$	−1.52222	−	2.63657i	−0.0680080	−	0.117793i
$502$	−15.9821	+	27.6817i	−0.713314	+	1.23550i
$503$	12.8463			0.572787			0.286393	−	0.958112i	$-0.407544\pi$
$503$	12.8463			0.572787			0.286393	+	0.958112i	$0.407544\pi$
$504$	3.10263	+	0.214549i	0.138202	+	0.00955679i
$505$	−5.87638			−0.261495
$506$	−1.91218	+	3.31200i	−0.0850068	+	0.147236i
$507$	0.139549	+	0.241705i	0.00619757	+	0.0107345i
$508$	0.687971	+	1.19160i	0.0305238	+	0.0528687i
$509$	13.3906	−	23.1932i	0.593528	−	1.02802i	−0.400224	−	0.916417i	$-0.631068\pi$
$509$	13.3906	−	23.1932i	0.593528	−	1.02802i	0.993753	−	0.111604i	$-0.0355989\pi$
$510$	−0.517756			−0.0229266
$511$	17.0980	−	25.3911i	0.756372	−	1.12324i
$512$	−20.5848			−0.909730
$513$	−0.289732	+	0.501830i	−0.0127920	+	0.0221563i
$514$	17.1591	+	29.7205i	0.756856	+	1.31091i
$515$	−8.79591	−	15.2350i	−0.387594	−	0.671333i
$516$	−6.17194	+	10.6901i	−0.271704	+	0.470606i
$517$	10.5644			0.464620
$518$	−3.35130	+	4.97680i	−0.147248	+	0.218668i
$519$	−16.0543			−0.704705
$520$	2.02073	−	3.50001i	0.0886149	−	0.153485i
$521$	13.4152	+	23.2359i	0.587732	+	1.01798i	0.994529	+	0.104463i	$0.0333123\pi$
$521$	13.4152	+	23.2359i	0.587732	+	1.01798i	−0.406797	+	0.913519i	$0.633354\pi$
$522$	−5.40047	−	9.35388i	−0.236372	−	0.409408i
$523$	8.04730	−	13.9383i	0.351884	−	0.609481i	−0.634696	−	0.772762i	$-0.718875\pi$
$523$	8.04730	−	13.9383i	0.351884	−	0.609481i	0.986580	+	0.163282i	$0.0522079\pi$
$524$	−20.4210			−0.892095
$525$	10.8477	+	0.750125i	0.473431	+	0.0327382i
$526$	−54.8118			−2.38991
$527$	0.901895	−	1.56213i	0.0392871	−	0.0680473i
$528$	−5.08284	−	8.80373i	−0.221202	−	0.383133i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−2.01072	+	3.48267i	−0.0873401	+	0.151277i
$531$	2.08015			0.0902708
$532$	0.914516	+	1.87137i	0.0396493	+	0.0811340i
$533$	30.6838			1.32906
$534$	−2.45172	+	4.24651i	−0.106096	+	0.183764i
$535$	−0.306107	−	0.530193i	−0.0132342	−	0.0229223i
$536$	2.43186	+	4.21211i	0.105040	+	0.181935i
$537$	−2.67255	+	4.62898i	−0.115329	+	0.199755i
$538$	−41.5022			−1.78929
$539$	14.4686	+	2.01064i	0.623205	+	0.0866044i
$540$	1.28181			0.0551604
$541$	0.338479	−	0.586263i	0.0145524	−	0.0252054i	−0.858658	−	0.512550i	$-0.828701\pi$
$541$	0.338479	−	0.586263i	0.0145524	−	0.0252054i	0.873210	+	0.487344i	$0.162034\pi$
$542$	−11.6706	−	20.2141i	−0.501296	−	0.868270i
$543$	−5.81006	−	10.0633i	−0.249333	−	0.431858i
$544$	−0.984649	+	1.70546i	−0.0422165	+	0.0731211i
$545$	12.8818			0.551795
$546$	−7.75783	−	15.8748i	−0.332005	−	0.679378i
$547$	−8.38777			−0.358635			−0.179318	−	0.983791i	$-0.557389\pi$
$547$	−8.38777			−0.358635			−0.179318	+	0.983791i	$0.557389\pi$
$548$	−6.30293	+	10.9170i	−0.269248	+	0.466351i
$549$	−6.22701	−	10.7855i	−0.265762	−	0.460314i
$550$	−7.85874	−	13.6117i	−0.335098	−	0.580406i
$551$	−1.70757	+	2.95760i	−0.0727450	+	0.125998i
$552$	1.17548			0.0500320
$553$	45.2887	+	3.13175i	1.92587	+	0.133176i
$554$	53.1699			2.25897
$555$	0.583754	−	1.01109i	0.0247790	−	0.0429184i
$556$	−4.47484	−	7.75065i	−0.189775	−	0.328701i
$557$	1.24944	+	2.16409i	0.0529404	+	0.0916955i	0.891281	−	0.453451i	$-0.149807\pi$
$557$	1.24944	+	2.16409i	0.0529404	+	0.0916955i	−0.838341	+	0.545147i	$0.816474\pi$
$558$	−5.51981	+	9.56059i	−0.233672	+	0.404732i
$559$	−33.1092			−1.40037
$560$	−6.79212	+	10.0865i	−0.287019	+	0.426234i
$561$	−0.624872			−0.0263821
$562$	−11.4051	+	19.7543i	−0.481097	+	0.833284i
$563$	20.2290	+	35.0377i	0.852551	+	1.47666i	0.878899	+	0.477008i	$0.158279\pi$
$563$	20.2290	+	35.0377i	0.852551	+	1.47666i	−0.0263482	+	0.999653i	$0.508388\pi$
$564$	3.43889	+	5.95634i	0.144804	+	0.250807i
$565$	0.258176	−	0.447174i	0.0108615	−	0.0188127i
$566$	−17.1608			−0.721323
$567$	−1.47779	+	2.19457i	−0.0620614	+	0.0921632i
$568$	−13.6872			−0.574303
$569$	6.24012	−	10.8082i	0.261599	−	0.453104i	−0.705068	−	0.709140i	$-0.749083\pi$
$569$	6.24012	−	10.8082i	0.261599	−	0.453104i	0.966667	+	0.256037i	$0.0824167\pi$
$570$	−0.500970	−	0.867705i	−0.0209833	−	0.0363442i
$571$	15.4964	+	26.8405i	0.648502	+	1.12324i	0.983481	+	0.181013i	$0.0579377\pi$
$571$	15.4964	+	26.8405i	0.648502	+	1.12324i	−0.334978	+	0.942226i	$0.608729\pi$
$572$	−5.16562	+	8.94711i	−0.215985	+	0.374098i
$573$	17.0751			0.713324
$574$	−40.7301	−	2.81652i	−1.70004	−	0.117559i
$575$	4.10983			0.171392
$576$	1.15487	−	2.00030i	0.0481197	−	0.0833457i
$577$	−5.26512	−	9.11945i	−0.219190	−	0.379648i	0.735371	−	0.677665i	$-0.237008\pi$
$577$	−5.26512	−	9.11945i	−0.219190	−	0.379648i	−0.954560	+	0.298017i	$0.903675\pi$
$578$	−15.4953	−	26.8387i	−0.644520	−	1.11634i
$579$	−2.32526	+	4.02747i	−0.0966345	+	0.167376i
$580$	7.55452			0.313684
$581$	−12.7480	−	26.0861i	−0.528875	−	1.08223i
$582$	1.08097			0.0448077
$583$	−2.42671	+	4.20318i	−0.100504	+	0.174078i
$584$	6.80017	+	11.7782i	0.281393	+	0.487387i
$585$	1.71906	+	2.97750i	0.0710744	+	0.123105i
$586$	5.21864	−	9.03895i	0.215580	−	0.373396i
$587$	7.06244			0.291498			0.145749	−	0.989322i	$-0.453441\pi$
$587$	7.06244			0.291498			0.145749	+	0.989322i	$0.453441\pi$
$588$	3.57616	+	8.81210i	0.147478	+	0.363405i
$589$	3.49062			0.143828
$590$	−1.79837	+	3.11487i	−0.0740378	+	0.128237i
$591$	0.127456	+	0.220761i	0.00524285	+	0.00908088i
$592$	−3.01403	−	5.22046i	−0.123876	−	0.214559i
$593$	−19.9462	+	34.5479i	−0.819094	+	1.41871i	0.0872571	+	0.996186i	$0.472190\pi$
$593$	−19.9462	+	34.5479i	−0.819094	+	1.41871i	−0.906351	+	0.422526i	$0.861144\pi$
$594$	3.82436			0.156916
$595$	0.328190	+	0.671572i	0.0134545	+	0.0275318i
$596$	−8.00075			−0.327723
$597$	2.73799	−	4.74233i	0.112058	−	0.194091i
$598$	−3.33912	−	5.78353i	−0.136547	−	0.236506i
$599$	−5.93228	−	10.2750i	−0.242386	−	0.419826i	0.719007	−	0.695003i	$-0.244597\pi$
$599$	−5.93228	−	10.2750i	−0.242386	−	0.419826i	−0.961394	+	0.275177i	$0.911264\pi$
$600$	−2.41552	+	4.18380i	−0.0986132	+	0.170803i
$601$	15.0105			0.612290			0.306145	−	0.951985i	$-0.400961\pi$
$601$	15.0105			0.612290			0.306145	+	0.951985i	$0.400961\pi$
$602$	43.9497	+	3.03916i	1.79126	+	0.123867i
$603$	−4.13763			−0.168498
$604$	−8.93532	+	15.4764i	−0.363573	+	0.629727i
$605$	−3.13487	−	5.42975i	−0.127451	−	0.220751i
$606$	−5.70717	−	9.88511i	−0.231838	−	0.401555i
$607$	2.09995	−	3.63722i	0.0852343	−	0.147630i	−0.820257	−	0.571996i	$-0.806169\pi$
$607$	2.09995	−	3.63722i	0.0852343	−	0.147630i	0.905491	+	0.424365i	$0.139503\pi$
$608$	−3.81090			−0.154553
$609$	−8.70955	+	12.9340i	−0.352929	+	0.524111i
$610$	21.5340			0.871887
$611$	−9.22393	+	15.9763i	−0.373160	+	0.646333i
$612$	−0.203407	−	0.352312i	−0.00822226	−	0.0142414i
$613$	−15.4932	−	26.8351i	−0.625766	−	1.08386i	−0.988392	−	0.151924i	$-0.951453\pi$
$613$	−15.4932	−	26.8351i	−0.625766	−	1.08386i	0.362626	−	0.931935i	$-0.381880\pi$
$614$	15.6321	−	27.0755i	0.630859	−	1.09268i
$615$	7.94441			0.320349
$616$	−3.62502	+	5.38328i	−0.146056	+	0.216899i
$617$	1.93041			0.0777153			0.0388577	−	0.999245i	$-0.487628\pi$
$617$	1.93041			0.0777153			0.0388577	+	0.999245i	$0.487628\pi$
$618$	17.0853	−	29.5926i	0.687270	−	1.19039i
$619$	−16.6422	−	28.8251i	−0.668907	−	1.15858i	−0.978210	−	0.207617i	$-0.933429\pi$
$619$	−16.6422	−	28.8251i	−0.668907	−	1.15858i	0.309304	−	0.950963i	$-0.399904\pi$
$620$	−3.86073	−	6.68699i	−0.155051	−	0.268556i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	30.2831			1.21424
$623$	7.06214	+	0.488353i	0.282939	+	0.0195654i
$624$	17.7517			0.710636
$625$	−6.21991	+	10.7732i	−0.248796	+	0.430928i
$626$	−1.36887	−	2.37096i	−0.0547112	−	0.0947625i
$627$	−0.604613	−	1.04722i	−0.0241459	−	0.0418219i
$628$	5.72343	−	9.91328i	0.228390	−	0.395583i
$629$	−0.370538			−0.0147743
$630$	−2.00860	−	4.11018i	−0.0800245	−	0.163753i
$631$	4.49815			0.179068			0.0895342	−	0.995984i	$-0.471462\pi$
$631$	4.49815			0.179068			0.0895342	+	0.995984i	$0.471462\pi$
$632$	−10.0847	+	17.4672i	−0.401149	+	0.694810i
$633$	−1.59299	−	2.75914i	−0.0633158	−	0.109666i
$634$	−16.6985	−	28.9227i	−0.663184	−	1.14867i
$635$	−0.477772	+	0.827525i	−0.0189598	+	0.0328393i
$636$	−3.15975			−0.125292
$637$	−15.6734	+	20.1251i	−0.621004	+	0.797385i
$638$	22.5394			0.892343
$639$	5.82195	−	10.0839i	0.230313	−	0.398913i
$640$	−4.20809	−	7.28863i	−0.166339	−	0.288108i
$641$	13.4105	+	23.2276i	0.529681	+	0.917435i	0.999401	+	0.0346188i	$0.0110217\pi$
$641$	13.4105	+	23.2276i	0.529681	+	0.917435i	−0.469720	+	0.882816i	$0.655645\pi$
$642$	0.594586	−	1.02985i	0.0234664	−	0.0406451i
$643$	−21.1912			−0.835701			−0.417850	−	0.908516i	$-0.637216\pi$
$643$	−21.1912			−0.835701			−0.417850	+	0.908516i	$0.637216\pi$
$644$	1.57821	+	3.22948i	0.0621902	+	0.127259i
$645$	−8.57238			−0.337537
$646$	−0.158995	+	0.275388i	−0.00625559	+	0.0108350i
$647$	−1.64119	−	2.84262i	−0.0645218	−	0.111755i	0.831960	−	0.554836i	$-0.187219\pi$
$647$	−1.64119	−	2.84262i	−0.0645218	−	0.111755i	−0.896482	+	0.443081i	$0.853886\pi$
$648$	−0.587742	−	1.01800i	−0.0230887	−	0.0399908i
$649$	−2.17043	+	3.75929i	−0.0851967	+	0.147565i
$650$	27.4464			1.07654
$651$	15.8997	+	1.09948i	0.623159	+	0.0430919i
$652$	5.64813			0.221198
$653$	−16.3956	+	28.3981i	−0.641610	+	1.11130i	0.343463	+	0.939166i	$0.388400\pi$
$653$	−16.3956	+	28.3981i	−0.641610	+	1.11130i	−0.985073	+	0.172135i	$0.944933\pi$
$654$	12.5109	+	21.6694i	0.489213	+	0.847342i
$655$	−7.09082	−	12.2817i	−0.277061	−	0.479884i
$656$	20.5092	−	35.5230i	0.800751	−	1.38694i
$657$	−11.5700			−0.451388
$658$	13.7105	−	20.3605i	0.534491	−	0.793737i
$659$	11.1625			0.434828			0.217414	−	0.976079i	$-0.430238\pi$
$659$	11.1625			0.434828			0.217414	+	0.976079i	$0.430238\pi$
$660$	−1.33744	+	2.31652i	−0.0520599	+	0.0901703i
$661$	−4.19731	−	7.26995i	−0.163256	−	0.282768i	0.772778	−	0.634676i	$-0.218866\pi$
$661$	−4.19731	−	7.26995i	−0.163256	−	0.282768i	−0.936035	+	0.351908i	$0.885533\pi$
$662$	−21.0341	−	36.4321i	−0.817512	−	1.41597i
$663$	0.545587	−	0.944985i	0.0211888	−	0.0367002i
$664$	12.8997			0.500606
$665$	−0.807935	+	1.19981i	−0.0313304	+	0.0465266i
$666$	2.26778			0.0878747
$667$	−2.94682	+	5.10403i	−0.114101	+	0.197629i
$668$	2.06807	+	3.58201i	0.0800161	+	0.138592i
$669$	−11.3837	−	19.7172i	−0.440119	−	0.762309i
$670$	3.57715	−	6.19581i	0.138197	−	0.239365i
$671$	25.9891			1.00330
$672$	−17.3586	−	1.20036i	−0.669623	−	0.0463050i
$673$	30.3183			1.16869			0.584343	−	0.811507i	$-0.301352\pi$
$673$	30.3183			1.16869			0.584343	+	0.811507i	$0.301352\pi$
$674$	20.3668	−	35.2763i	0.784498	−	1.35879i
$675$	−2.05491	−	3.55921i	−0.0790937	−	0.136994i
$676$	−0.189589	−	0.328377i	−0.00729187	−	0.0126299i
$677$	5.15063	−	8.92116i	0.197955	−	0.342868i	−0.749910	−	0.661540i	$-0.769903\pi$
$677$	5.15063	−	8.92116i	0.197955	−	0.342868i	0.947865	+	0.318672i	$0.103237\pi$
$678$	1.00297			0.0385187
$679$	−0.685195	−	1.40211i	−0.0262954	−	0.0538080i
$680$	−0.332096			−0.0127353
$681$	5.22604	−	9.05176i	0.200262	−	0.346864i
$682$	−11.5187	−	19.9510i	−0.441075	−	0.763965i
$683$	24.0871	+	41.7200i	0.921666	+	1.59637i	0.796837	+	0.604194i	$0.206505\pi$
$683$	24.0871	+	41.7200i	0.921666	+	1.59637i	0.124829	+	0.992178i	$0.460162\pi$
$684$	0.393625	−	0.681779i	0.0150506	−	0.0260685i
$685$	−8.75433			−0.334486
$686$	22.6525	−	25.2757i	0.864876	−	0.965029i
$687$	10.7678			0.410819
$688$	−22.1304	+	38.3310i	−0.843714	+	1.46136i
$689$	−4.23760	−	7.33975i	−0.161440	−	0.279622i
$690$	−0.864540	−	1.49743i	−0.0329125	−	0.0570061i
$691$	18.3597	−	31.8000i	0.698437	−	1.20973i	−0.270571	−	0.962700i	$-0.587212\pi$
$691$	18.3597	−	31.8000i	0.698437	−	1.20973i	0.969008	−	0.247029i	$-0.0794543\pi$
$692$	21.8111			0.829135
$693$	−2.42415	−	4.96051i	−0.0920857	−	0.188434i
$694$	9.91171			0.376243
$695$	3.10762	−	5.38255i	0.117879	−	0.204172i
$696$	−3.46394	−	5.99971i	−0.131300	−	0.227419i
$697$	−1.26068	−	2.18356i	−0.0477516	−	0.0827082i
$698$	9.52410	−	16.4962i	0.360492	−	0.624391i
$699$	−11.7508			−0.444455
$700$	−14.7375	−	1.01911i	−0.557025	−	0.0385187i
$701$	35.3581			1.33546			0.667728	−	0.744406i	$-0.267267\pi$
$701$	35.3581			1.33546			0.667728	+	0.744406i	$0.267267\pi$
$702$	−3.33912	+	5.78353i	−0.126027	+	0.218285i
$703$	−0.358524	−	0.620983i	−0.0135220	−	0.0234208i
$704$	2.40999	+	4.17422i	0.0908299	+	0.157322i
$705$	−2.38819	+	4.13647i	−0.0899445	+	0.155788i
$706$	23.9509			0.901405
$707$	−9.20419	+	13.6685i	−0.346159	+	0.514058i
$708$	−2.82606			−0.106210
$709$	5.49808	−	9.52295i	0.206485	−	0.357642i	−0.744120	−	0.668046i	$-0.767131\pi$
$709$	5.49808	−	9.52295i	0.206485	−	0.357642i	0.950605	+	0.310404i	$0.100464\pi$
$710$	10.0666	+	17.4359i	0.377794	+	0.654358i
$711$	−8.57920	−	14.8596i	−0.321745	−	0.557279i
$712$	−1.57257	+	2.72377i	−0.0589346	+	0.102078i
$713$	6.02387			0.225596
$714$	−0.810963	+	1.20431i	−0.0303495	+	0.0450701i
$715$	−7.17468			−0.268318
$716$	3.63088	−	6.28887i	0.135692	−	0.235026i
$717$	−6.27455	−	10.8678i	−0.234327	−	0.405867i
$718$	−17.6146	−	30.5095i	−0.657373	−	1.13860i
$719$	18.2877	−	31.6752i	0.682016	−	1.18129i	−0.292348	−	0.956312i	$-0.594437\pi$
$719$	18.2877	−	31.6752i	0.682016	−	1.18129i	0.974365	−	0.224975i	$-0.0722300\pi$
$720$	4.59613			0.171288
$721$	−49.2138	−	3.40317i	−1.83282	−	0.126741i
$722$	34.2049			1.27297
$723$	−5.31523	+	9.20624i	−0.197675	+	0.342384i
$724$	7.89346	+	13.6719i	0.293358	+	0.508111i
$725$	−12.1109	−	20.9767i	−0.449788	−	0.779055i
$726$	6.08920	−	10.5468i	0.225991	−	0.391429i
$727$	−12.9513			−0.480337			−0.240169	−	0.970731i	$-0.577203\pi$
$727$	−12.9513			−0.480337			−0.240169	+	0.970731i	$0.577203\pi$
$728$	−4.97599	−	10.1823i	−0.184422	−	0.377382i
$729$	1.00000			0.0370370
$730$	10.0027	−	17.3252i	0.370217	−	0.641235i
$731$	1.36033	+	2.35616i	0.0503136	+	0.0871457i
$732$	8.45993	+	14.6530i	0.312688	+	0.541592i
$733$	−3.13178	+	5.42440i	−0.115675	+	0.200355i	−0.918049	−	0.396466i	$-0.870236\pi$
$733$	−3.13178	+	5.42440i	−0.115675	+	0.200355i	0.802374	+	0.596821i	$0.203570\pi$
$734$	3.25312			0.120075
$735$	−4.05805	+	5.21063i	−0.149683	+	0.192197i
$736$	−6.57660			−0.242417
$737$	4.31721	−	7.47763i	0.159026	−	0.275442i
$738$	7.71565	+	13.3639i	0.284017	+	0.491932i
$739$	−16.2107	−	28.0778i	−0.596322	−	1.03286i	−0.993359	−	0.115057i	$-0.963295\pi$
$739$	−16.2107	−	28.0778i	−0.596322	−	1.03286i	0.397037	−	0.917803i	$-0.370039\pi$
$740$	−0.793079	+	1.37365i	−0.0291542	+	0.0504965i
$741$	2.11159			0.0775714
$742$	4.95134	+	10.1319i	0.181769	+	0.371953i
$743$	−4.32354			−0.158615			−0.0793076	−	0.996850i	$-0.525271\pi$
$743$	−4.32354			−0.158615			−0.0793076	+	0.996850i	$0.525271\pi$
$744$	−3.54049	+	6.13230i	−0.129801	+	0.224821i
$745$	−2.77812	−	4.81184i	−0.101782	−	0.176292i
$746$	−6.81763	−	11.8085i	−0.249611	−	0.432339i
$747$	−5.48698	+	9.50373i	−0.200758	+	0.347723i
$748$	0.848942			0.0310404
$749$	−1.71269	−	0.118434i	−0.0625805	−	0.00432749i
$750$	15.7516			0.575168
$751$	6.02158	−	10.4297i	0.219730	−	0.380584i	−0.734995	−	0.678072i	$-0.762816\pi$
$751$	6.02158	−	10.4297i	0.219730	−	0.380584i	0.954726	+	0.297488i	$0.0961489\pi$
$752$	12.3307	+	21.3574i	0.449654	+	0.778823i
$753$	−8.72076	−	15.1048i	−0.317802	−	0.550450i
$754$	−19.6796	+	34.0860i	−0.716687	+	1.24134i
$755$	−12.4105			−0.451665
$756$	2.00771	−	2.98151i	0.0730195	−	0.108436i
$757$	17.8806			0.649880			0.324940	−	0.945735i	$-0.394656\pi$
$757$	17.8806			0.649880			0.324940	+	0.945735i	$0.394656\pi$
$758$	−3.94980	+	6.84126i	−0.143463	+	0.248486i
$759$	−1.04340	−	1.80722i	−0.0378730	−	0.0655980i
$760$	−0.321329	−	0.556559i	−0.0116558	−	0.0201885i
$761$	−13.1480	+	22.7730i	−0.476615	+	0.825522i	−0.999641	−	0.0267950i	$-0.991470\pi$
$761$	−13.1480	+	22.7730i	−0.476615	+	0.825522i	0.523026	+	0.852317i	$0.324803\pi$
$762$	−1.85606			−0.0672379
$763$	20.1768	−	29.9632i	0.730448	−	1.08474i
$764$	−23.1980			−0.839276
$765$	0.141259	−	0.244668i	0.00510724	−	0.00884600i
$766$	31.7886	+	55.0594i	1.14857	+	1.98938i
$767$	−3.79008	−	6.56462i	−0.136852	−	0.237035i
$768$	10.4836	−	18.1581i	0.378294	−	0.655224i
$769$	−32.2632			−1.16344			−0.581720	−	0.813389i	$-0.697620\pi$
$769$	−32.2632			−1.16344			−0.581720	+	0.813389i	$0.697620\pi$
$770$	9.52378	+	0.658577i	0.343213	+	0.0237335i
$771$	−18.7261			−0.674403
$772$	3.15906	−	5.47166i	0.113697	−	0.196929i
$773$	5.28783	+	9.15878i	0.190190	+	0.329419i	0.945313	−	0.326164i	$-0.105756\pi$
$773$	5.28783	+	9.15878i	0.190190	+	0.329419i	−0.755123	+	0.655583i	$0.772423\pi$
$774$	−8.32554	−	14.4203i	−0.299255	−	0.518326i
$775$	−12.3785	+	21.4403i	−0.444650	+	0.770157i
$776$	0.693351			0.0248899
$777$	−1.43748	−	2.94149i	−0.0515692	−	0.105526i
$778$	−60.7409			−2.17767
$779$	2.43961	−	4.22553i	0.0874081	−	0.151395i
$780$	−2.33549	−	4.04519i	−0.0836240	−	0.144841i
$781$	12.1492	+	21.0431i	0.434734	+	0.752982i
$782$	−0.274384	+	0.475246i	−0.00981194	+	0.0169948i
$783$	5.89363			0.210621
$784$	12.8229	+	31.5971i	0.457960	+	1.12847i
$785$	7.94945			0.283728
$786$	13.7733	−	23.8560i	0.491277	−	0.850917i
$787$	13.7617	+	23.8360i	0.490552	+	0.849660i	0.999941	−	0.0108760i	$-0.00346200\pi$
$787$	13.7617	+	23.8360i	0.490552	+	0.849660i	−0.509389	+	0.860536i	$0.670129\pi$
$788$	−0.173160	−	0.299922i	−0.00616857	−	0.0106843i
$789$	14.9543	−	25.9016i	0.532387	−	0.922121i
$790$	29.6683			1.05555
$791$	−0.635750	−	1.30093i	−0.0226047	−	0.0462557i
$792$	2.45300			0.0871636
$793$	−22.6915	+	39.3029i	−0.805800	+	1.39569i
$794$	−26.0752	−	45.1636i	−0.925374	−	1.60280i
$795$	−1.09717	−	1.90035i	−0.0389126	−	0.0673985i
$796$	−3.71979	+	6.44286i	−0.131844	+	0.228361i
$797$	−43.4629			−1.53953			−0.769767	−	0.638324i	$-0.779628\pi$
$797$	−43.4629			−1.53953			−0.769767	+	0.638324i	$0.779628\pi$
$798$	−2.80296	−	0.193827i	−0.0992239	−	0.00686141i
$799$	1.51590			0.0536288
$800$	13.5144	−	23.4075i	0.477805	−	0.827582i
$801$	−1.33781	−	2.31715i	−0.0472691	−	0.0818724i
$802$	−34.7113	−	60.1217i	−1.22570	−	2.12297i
$803$	12.0721	−	20.9095i	0.426016	−	0.737881i
$804$	5.62133			0.198249
$805$	−1.39428	+	2.07055i	−0.0491419	+	0.0729774i
$806$	40.2289			1.41700
$807$	11.3230	−	19.6121i	0.398590	−	0.690378i
$808$	−3.66066	−	6.34045i	−0.128782	−	0.223056i
$809$	−21.4072	−	37.0784i	−0.752639	−	1.30361i	−0.946540	−	0.322587i	$-0.895447\pi$
$809$	−21.4072	−	37.0784i	−0.752639	−	1.30361i	0.193901	−	0.981021i	$-0.437886\pi$
$810$	−0.864540	+	1.49743i	−0.0303769	+	0.0526143i
$811$	45.2610			1.58933			0.794664	−	0.607049i	$-0.207647\pi$
$811$	45.2610			1.58933			0.794664	+	0.607049i	$0.207647\pi$
$812$	11.8327	−	17.5719i	0.415245	−	0.616653i
$813$	12.7364			0.446684
$814$	−2.36620	+	4.09838i	−0.0829353	+	0.143648i
$815$	1.96121	+	3.39692i	0.0686983	+	0.118989i
$816$	−0.729349	−	1.26327i	−0.0255323	−	0.0442233i
$817$	−2.63245	+	4.55954i	−0.0920979	+	0.159518i
$818$	−1.75411			−0.0613310
$819$	9.61828	+	0.665112i	0.336090	+	0.0232409i
$820$	−10.7932			−0.376913
$821$	18.1607	−	31.4552i	0.633812	−	1.09779i	−0.352954	−	0.935641i	$-0.614823\pi$
$821$	18.1607	−	31.4552i	0.633812	−	1.09779i	0.986766	−	0.162153i	$-0.0518439\pi$
$822$	−8.50225	−	14.7263i	−0.296550	−	0.513640i
$823$	−26.0501	−	45.1200i	−0.908048	−	1.57279i	−0.816772	−	0.576960i	$-0.804239\pi$
$823$	−26.0501	−	45.1200i	−0.908048	−	1.57279i	−0.0912763	−	0.995826i	$-0.529095\pi$
$824$	10.9587	−	18.9811i	0.381766	−	0.661238i
$825$	8.57639			0.298592
$826$	4.42844	+	9.06187i	0.154085	+	0.315303i
$827$	−21.6989			−0.754545			−0.377273	−	0.926102i	$-0.623138\pi$
$827$	−21.6989			−0.754545			−0.377273	+	0.926102i	$0.623138\pi$
$828$	0.679293	−	1.17657i	0.0236071	−	0.0408886i
$829$	6.78776	+	11.7567i	0.235749	+	0.408329i	0.959490	−	0.281743i	$-0.0909125\pi$
$829$	6.78776	+	11.7567i	0.235749	+	0.408329i	−0.723741	+	0.690071i	$0.757579\pi$
$830$	−9.48743	−	16.4327i	−0.329314	−	0.570388i
$831$	−14.5063	+	25.1257i	−0.503219	+	0.871601i
$832$	−8.41682			−0.291801
$833$	2.07613	+	0.288512i	0.0719336	+	0.00999634i
$834$	12.0725			0.418038
$835$	−1.43620	+	2.48758i	−0.0497018	+	0.0860861i
$836$	0.821418	+	1.42274i	0.0284093	+	0.0492064i
$837$	−3.01194	−	5.21683i	−0.104108	−	0.180320i
$838$	−37.3493	+	64.6909i	−1.29021	+	2.23471i
$839$	−40.6915			−1.40483			−0.702413	−	0.711770i	$-0.747894\pi$
$839$	−40.6915			−1.40483			−0.702413	+	0.711770i	$0.747894\pi$
$840$	−1.28834	−	2.63633i	−0.0444521	−	0.0909620i
$841$	5.73489			0.197755
$842$	−23.8413	+	41.2943i	−0.821625	+	1.42310i
$843$	−6.22332	−	10.7791i	−0.214343	−	0.371252i
$844$	2.16422	+	3.74853i	0.0744954	+	0.129030i
$845$	0.131663	−	0.228046i	0.00452933	−	0.00784503i
$846$	−9.27770			−0.318974
$847$	−17.5398	−	1.21289i	−0.602676	−	0.0416755i
$848$	−11.3298			−0.389066
$849$	4.68198	−	8.10943i	0.160685	−	0.278315i
$850$	−1.12767	−	1.95318i	−0.0386787	−	0.0669935i
$851$	−0.618718	−	1.07165i	−0.0212094	−	0.0367357i
$852$	−7.90962	+	13.6999i	−0.270979	+	0.469349i
$853$	−53.5882			−1.83482			−0.917412	−	0.397938i	$-0.869726\pi$
$853$	−53.5882			−1.83482			−0.917412	+	0.397938i	$0.869726\pi$
$854$	33.7288	−	50.0884i	1.15418	−	1.71399i
$855$	0.546718			0.0186974
$856$	0.381376	−	0.660563i	0.0130352	−	0.0225776i
$857$	7.59264	+	13.1508i	0.259360	+	0.449224i	0.966071	−	0.258278i	$-0.0831552\pi$
$857$	7.59264	+	13.1508i	0.259360	+	0.449224i	−0.706711	+	0.707502i	$0.749822\pi$
$858$	−6.96808	−	12.0691i	−0.237886	−	0.412031i
$859$	18.9692	−	32.8557i	0.647222	−	1.12102i	−0.336562	−	0.941661i	$-0.609264\pi$
$859$	18.9692	−	32.8557i	0.647222	−	1.12102i	0.983784	−	0.179360i	$-0.0574025\pi$
$860$	11.6463			0.397136
$861$	12.4434	−	18.4788i	0.424068	−	0.629756i
$862$	57.6259			1.96275
$863$	−17.4820	+	30.2797i	−0.595094	+	1.03073i	0.398440	+	0.917195i	$0.369552\pi$
$863$	−17.4820	+	30.2797i	−0.595094	+	1.03073i	−0.993534	+	0.113539i	$0.963781\pi$
$864$	3.28830	+	5.69551i	0.111870	+	0.193765i
$865$	7.57353	+	13.1177i	0.257508	+	0.446016i
$866$	3.31050	−	5.73395i	0.112495	−	0.194848i
$867$	16.9103			0.574305
$868$	−21.6011	−	1.49373i	−0.733189	−	0.0507006i
$869$	35.8062			1.21464
$870$	−5.09528	+	8.82529i	−0.172746	+	0.299205i
$871$	7.53887	+	13.0577i	0.255445	+	0.442444i
$872$	8.02464	+	13.8991i	0.271749	+	0.470683i
$873$	−0.294921	+	0.510819i	−0.00998158	+	0.0172886i
$874$	−1.06195			−0.0359210
$875$	−9.98447	−	20.4311i	−0.337537	−	0.690699i
$876$	15.7188			0.531089
$877$	−19.5214	+	33.8120i	−0.659191	+	1.14175i	0.321635	+	0.946864i	$0.395768\pi$
$877$	−19.5214	+	33.8120i	−0.659191	+	1.14175i	−0.980826	+	0.194888i	$0.937566\pi$
$878$	16.5406	+	28.6491i	0.558218	+	0.966862i
$879$	2.84760	+	4.93219i	0.0960473	+	0.166359i
$880$	−4.79560	+	8.30623i	−0.161660	+	0.280003i
$881$	21.5235			0.725145			0.362572	−	0.931956i	$-0.381899\pi$
$881$	21.5235			0.725145			0.362572	+	0.931956i	$0.381899\pi$
$882$	−12.7064	−	1.76576i	−0.427847	−	0.0594562i
$883$	−17.0630			−0.574217			−0.287109	−	0.957898i	$-0.592694\pi$
$883$	−17.0630			−0.574217			−0.287109	+	0.957898i	$0.592694\pi$
$884$	−0.741227	+	1.28384i	−0.0249302	+	0.0431803i
$885$	−0.981299	−	1.69966i	−0.0329860	−	0.0571335i
$886$	−32.3737	−	56.0729i	−1.08762	−	1.88381i
$887$	−21.5732	+	37.3659i	−0.724357	+	1.25462i	0.234882	+	0.972024i	$0.424530\pi$
$887$	−21.5732	+	37.3659i	−0.724357	+	1.25462i	−0.959238	+	0.282599i	$0.908804\pi$
$888$	1.45459			0.0488127
$889$	1.17650	+	2.40746i	0.0394585	+	0.0807436i
$890$	4.62635			0.155076
$891$	−1.04340	+	1.80722i	−0.0349552	+	0.0605442i
$892$	15.4657	+	26.7874i	0.517831	+	0.896910i
$893$	1.46676	+	2.54050i	0.0490831	+	0.0850145i
$894$	5.39625	−	9.34657i	0.180478	−	0.312596i
$895$	5.04304			0.168570
$896$	−23.5446	−	1.62813i	−0.786569	−	0.0543919i
$897$	3.64405			0.121671
$898$	5.45755	−	9.45276i	0.182121	−	0.315443i
$899$	−17.7512	−	30.7461i	−0.592037	−	1.02544i
$900$	2.79178	+	4.83550i	0.0930592	+	0.161183i
$901$	−0.348214	+	0.603124i	−0.0116007	+	0.0200930i
$902$	−32.2020			−1.07221
$903$	−13.4270	+	19.9395i	−0.446821	+	0.663544i
$904$	0.643318			0.0213964
$905$	−5.48173	+	9.49463i	−0.182219	+	0.315612i
$906$	−12.0532	−	20.8767i	−0.400440	−	0.693582i
$907$	4.74298	+	8.21508i	0.157488	+	0.272777i	0.933962	−	0.357372i	$-0.116327\pi$
$907$	4.74298	+	8.21508i	0.157488	+	0.272777i	−0.776474	+	0.630149i	$0.782994\pi$
$908$	−7.10002	+	12.2976i	−0.235622	+	0.408110i
$909$	6.22834			0.206581
$910$	−9.31135	+	13.8277i	−0.308668	+	0.458383i
$911$	17.7773			0.588988			0.294494	−	0.955653i	$-0.404849\pi$
$911$	17.7773			0.588988			0.294494	+	0.955653i	$0.404849\pi$
$912$	1.41140	−	2.44462i	0.0467363	−	0.0809496i
$913$	−11.4502	−	19.8324i	−0.378947	−	0.656356i
$914$	29.2924	+	50.7360i	0.968907	+	1.67820i
$915$	−5.87512	+	10.1760i	−0.194226	+	0.336409i
$916$	−14.6290			−0.483357
$917$	−39.6737	−	2.74347i	−1.31014	−	0.0905973i
$918$	0.548767			0.0181120
$919$	−1.75335	+	3.03689i	−0.0578376	+	0.100178i	−0.893494	−	0.449074i	$-0.851754\pi$
$919$	−1.75335	+	3.03689i	−0.0578376	+	0.100178i	0.835657	+	0.549252i	$0.185087\pi$
$920$	−0.554529	−	0.960472i	−0.0182823	−	0.0316658i
$921$	8.52979	+	14.7740i	0.281066	+	0.486821i
$922$	6.51080	−	11.2770i	0.214422	−	0.371389i
$923$	−42.4309			−1.39663
$924$	3.29341	+	6.73928i	0.108345	+	0.221706i
$925$	5.08565			0.167215
$926$	−38.5603	+	66.7884i	−1.26717	+	2.19480i
$927$	9.32274	+	16.1475i	0.306199	+	0.530352i
$928$	19.3800	+	33.5672i	0.636181	+	1.10190i
$929$	−7.62220	+	13.2020i	−0.250076	+	0.433145i	−0.963547	−	0.267541i	$-0.913789\pi$
$929$	−7.62220	+	13.2020i	−0.250076	+	0.433145i	0.713470	+	0.700686i	$0.247122\pi$
$930$	10.4158			0.341546
$931$	1.52530	+	3.75853i	0.0499898	+	0.123181i
$932$	15.9644			0.522932
$933$	−8.26214	+	14.3104i	−0.270490	+	0.468503i
$934$	24.2373	+	41.9803i	0.793070	+	1.37364i
$935$	0.294780	+	0.510574i	0.00964033	+	0.0166975i
$936$	−2.14176	+	3.70964i	−0.0700057	+	0.121253i
$937$	−16.0219			−0.523414			−0.261707	−	0.965147i	$-0.584285\pi$
$937$	−16.0219			−0.523414			−0.261707	+	0.965147i	$0.584285\pi$
$938$	−8.80863	−	18.0250i	−0.287612	−	0.588538i
$939$	1.49388			0.0487508
$940$	3.24456	−	5.61975i	0.105826	−	0.183296i
$941$	4.14969	+	7.18748i	0.135276	+	0.234305i	0.925703	−	0.378251i	$-0.123475\pi$
$941$	4.14969	+	7.18748i	0.135276	+	0.234305i	−0.790427	+	0.612556i	$0.790141\pi$
$942$	7.72055	+	13.3724i	0.251549	+	0.435696i
$943$	4.21012	−	7.29214i	0.137100	−	0.237465i
$944$	−10.1333			−0.329810
$945$	2.49029	+	0.172206i	0.0810092	+	0.00560185i
$946$	34.7475			1.12974
$947$	−24.1605	+	41.8472i	−0.785111	+	1.35985i	0.143822	+	0.989604i	$0.454061\pi$
$947$	−24.1605	+	41.8472i	−0.785111	+	1.35985i	−0.928933	+	0.370249i	$0.879273\pi$
$948$	11.6556	+	20.1881i	0.378556	+	0.655677i
$949$	21.0808	+	36.5130i	0.684312	+	1.18526i
$950$	2.18222	−	3.77971i	0.0708005	−	0.122630i
$951$	18.2234			0.590935
$952$	−0.520163	+	0.772460i	−0.0168586	+	0.0250356i
$953$	12.0181			0.389303			0.194652	−	0.980872i	$-0.437642\pi$
$953$	12.0181			0.389303			0.194652	+	0.980872i	$0.437642\pi$
$954$	2.13115	−	3.69126i	0.0689986	−	0.119509i
$955$	−8.05511	−	13.9519i	−0.260657	−	0.451472i
$956$	8.52452	+	14.7649i	0.275703	+	0.477531i
$957$	−6.14942	+	10.6511i	−0.198782	+	0.344301i
$958$	46.3344			1.49700
$959$	−13.7119	+	20.3627i	−0.442782	+	0.657545i
$960$	−2.17922			−0.0703340
$961$	−2.64353	+	4.57873i	−0.0852752	+	0.147701i
$962$	−4.13195	−	7.15675i	−0.133219	−	0.230743i
$963$	0.324442	+	0.561949i	0.0104550	+	0.0181086i
$964$	7.22119	−	12.5075i	0.232579	−	0.402838i
$965$	4.38772			0.141246
$966$	−4.83717	−	0.334494i	−0.155633	−	0.0107622i
$967$	20.9914			0.675036			0.337518	−	0.941319i	$-0.390413\pi$
$967$	20.9914			0.675036			0.337518	+	0.941319i	$0.390413\pi$
$968$	3.90570	−	6.76488i	0.125534	−	0.217431i
$969$	−0.0867573	−	0.150268i	−0.00278705	−	0.00482731i
$970$	−0.509943	−	0.883247i	−0.0163733	−	0.0283594i
$971$	2.64763	−	4.58583i	0.0849665	−	0.147166i	−0.820410	−	0.571775i	$-0.806255\pi$
$971$	2.64763	−	4.58583i	0.0849665	−	0.147166i	0.905377	+	0.424609i	$0.139588\pi$
$972$	−1.35859			−0.0435767
$973$	−7.65241	−	15.6591i	−0.245325	−	0.502007i
$974$	−36.6098			−1.17305
$975$	−7.48821	+	12.9700i	−0.239815	+	0.415371i
$976$	30.3344	+	52.5407i	0.970980	+	1.68179i
$977$	13.3384	+	23.1028i	0.426733	+	0.739124i	0.996581	−	0.0826270i	$-0.0263310\pi$
$977$	13.3384	+	23.1028i	0.426733	+	0.739124i	−0.569847	+	0.821751i	$0.692998\pi$
$978$	−3.80948	+	6.59822i	−0.121814	+	0.210988i
$979$	5.58347			0.178448
$980$	5.51321	−	7.07909i	0.176113	−	0.226133i
$981$	−13.6533			−0.435917
$982$	−37.5776	+	65.0862i	−1.19915	+	2.07699i
$983$	−3.31971	−	5.74990i	−0.105882	−	0.183393i	0.808216	−	0.588886i	$-0.200433\pi$
$983$	−3.31971	−	5.74990i	−0.105882	−	0.183393i	−0.914098	+	0.405493i	$0.867100\pi$
$984$	4.94893	+	8.57180i	0.157766	+	0.273259i
$985$	0.120254	−	0.208285i	0.00383160	−	0.00663652i
$986$	3.23423			0.102999
$987$	5.88085	+	12.0339i	0.187189	+	0.383044i
$988$	−2.86878			−0.0912681
$989$	−4.54291	+	7.86856i	−0.144456	+	0.250206i
$990$	−1.80412	−	3.12483i	−0.0573388	−	0.0993137i
$991$	−15.1721	−	26.2789i	−0.481958	−	0.834777i	0.517827	−	0.855485i	$-0.326741\pi$
$991$	−15.1721	−	26.2789i	−0.481958	−	0.834777i	−0.999786	+	0.0207088i	$0.993408\pi$
$992$	19.8083	−	34.3090i	0.628915	−	1.08931i
$993$	22.9549			0.728451
$994$	56.3235	+	3.89482i	1.78647	+	0.123536i
$995$	−5.16652			−0.163790
$996$	7.45453	−	12.9116i	0.236206	−	0.409121i
$997$	−23.4924	−	40.6900i	−0.744011	−	1.28867i	−0.950655	−	0.310249i	$-0.899588\pi$
$997$	−23.4924	−	40.6900i	−0.744011	−	1.28867i	0.206644	−	0.978416i	$-0.433746\pi$
$998$	12.8715	+	22.2940i	0.407439	+	0.705705i
$999$	−0.618718	+	1.07165i	−0.0195754	+	0.0339055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.f.415.5	yes	12
7.2	even	3		3381.2.a.bc.1.2		6
7.4	even	3	inner	483.2.i.f.277.5	✓	12
7.5	odd	6		3381.2.a.bd.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.5	✓	12	7.4	even	3	inner
483.2.i.f.415.5	yes	12	1.1	even	1	trivial
3381.2.a.bc.1.2		6	7.2	even	3
3381.2.a.bd.1.2		6	7.5	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.916322 - 1.58712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.679293 - 1.17657i) q^{4} +(0.471745 - 0.817086i) q^{5} +1.83264 q^{6} +(-1.16166 - 2.37709i) q^{7} +1.17548 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.916322 - 1.58712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.679293 - 1.17657i) q^{4} +(0.471745 - 0.817086i) q^{5} +1.83264 q^{6} +(-1.16166 - 2.37709i) q^{7} +1.17548 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.864540 - 1.49743i) q^{10} +(-1.04340 - 1.80722i) q^{11} +(0.679293 - 1.17657i) q^{12} +3.64405 q^{13} +(-4.83717 - 0.334494i) q^{14} +0.943490 q^{15} +(2.43571 - 4.21877i) q^{16} +(-0.149720 - 0.259323i) q^{17} +(0.916322 + 1.58712i) q^{18} +(0.289732 - 0.501830i) q^{19} -1.28181 q^{20} +(1.47779 - 2.19457i) q^{21} -3.82436 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.587742 + 1.01800i) q^{24} +(2.05491 + 3.55921i) q^{25} +(3.33912 - 5.78353i) q^{26} -1.00000 q^{27} +(-2.00771 + 2.98151i) q^{28} -5.89363 q^{29} +(0.864540 - 1.49743i) q^{30} +(3.01194 + 5.21683i) q^{31} +(-3.28830 - 5.69551i) q^{32} +(1.04340 - 1.80722i) q^{33} -0.548767 q^{34} +(-2.49029 - 0.172206i) q^{35} +1.35859 q^{36} +(0.618718 - 1.07165i) q^{37} +(-0.530975 - 0.919676i) q^{38} +(1.82202 + 3.15584i) q^{39} +(0.554529 - 0.960472i) q^{40} +8.42024 q^{41} +(-2.12890 - 4.35636i) q^{42} -9.08583 q^{43} +(-1.41755 + 2.45527i) q^{44} +(0.471745 + 0.817086i) q^{45} +(-0.916322 - 1.58712i) q^{46} +(-2.53123 + 4.38422i) q^{47} +4.87142 q^{48} +(-4.30111 + 5.52273i) q^{49} +7.53185 q^{50} +(0.149720 - 0.259323i) q^{51} +(-2.47538 - 4.28748i) q^{52} +(-1.16288 - 2.01417i) q^{53} +(-0.916322 + 1.58712i) q^{54} -1.96887 q^{55} +(-1.36551 - 2.79423i) q^{56} +0.579464 q^{57} +(-5.40047 + 9.35388i) q^{58} +(-1.04007 - 1.80146i) q^{59} +(-0.640906 - 1.11008i) q^{60} +(-6.22701 + 10.7855i) q^{61} +11.0396 q^{62} +(2.63945 + 0.182520i) q^{63} -2.30974 q^{64} +(1.71906 - 2.97750i) q^{65} +(-1.91218 - 3.31200i) q^{66} +(2.06882 + 3.58330i) q^{67} +(-0.203407 + 0.352312i) q^{68} +1.00000 q^{69} +(-2.55522 + 3.79459i) q^{70} -11.6439 q^{71} +(-0.587742 + 1.01800i) q^{72} +(5.78499 + 10.0199i) q^{73} +(-1.13389 - 1.96395i) q^{74} +(-2.05491 + 3.55921i) q^{75} -0.787251 q^{76} +(-3.08386 + 4.57963i) q^{77} +6.67825 q^{78} +(-8.57920 + 14.8596i) q^{79} +(-2.29807 - 3.98037i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.71565 - 13.3639i) q^{82} +10.9740 q^{83} +(-3.58592 - 0.247969i) q^{84} -0.282519 q^{85} +(-8.32554 + 14.4203i) q^{86} +(-2.94682 - 5.10403i) q^{87} +(-1.22650 - 2.12436i) q^{88} +(-1.33781 + 2.31715i) q^{89} +1.72908 q^{90} +(-4.23314 - 8.66223i) q^{91} -1.35859 q^{92} +(-3.01194 + 5.21683i) q^{93} +(4.63885 + 8.03472i) q^{94} +(-0.273359 - 0.473472i) q^{95} +(3.28830 - 5.69551i) q^{96} +0.589843 q^{97} +(4.82401 + 11.8870i) q^{98} +2.08680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

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