LMFDB - Embedded newform 630.2.t.b.311.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.7
Character	$\chi$	$=$	630.311
Dual form			630.2.t.b.551.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.70388 - 0.311090i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.63115 - 0.582530i) q^{6} +(2.53870 - 0.744985i) q^{7} -1.00000i q^{8} +(2.80645 - 1.06012i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.70388 - 0.311090i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.63115 - 0.582530i) q^{6} +(2.53870 - 0.744985i) q^{7} -1.00000i q^{8} +(2.80645 - 1.06012i) q^{9} +(0.866025 + 0.500000i) q^{10} +0.441750i q^{11} +(1.12135 + 1.32006i) q^{12} +(3.17590 + 1.83361i) q^{13} +(-2.57107 - 0.624174i) q^{14} +(-1.70388 + 0.311090i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.136107 - 0.235743i) q^{17} +(-2.96052 - 0.485129i) q^{18} +(-3.25564 + 1.87965i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(4.09389 - 2.05913i) q^{21} +(0.220875 - 0.382566i) q^{22} -2.59564i q^{23} +(-0.311090 - 1.70388i) q^{24} +1.00000 q^{25} +(-1.83361 - 3.17590i) q^{26} +(4.45207 - 2.67939i) q^{27} +(1.91453 + 1.82609i) q^{28} +(-2.38822 + 1.37884i) q^{29} +(1.63115 + 0.582530i) q^{30} +(7.57702 - 4.37459i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.137424 + 0.752691i) q^{33} +(-0.235743 + 0.136107i) q^{34} +(-2.53870 + 0.744985i) q^{35} +(2.32132 + 1.90039i) q^{36} +(0.0597017 + 0.103406i) q^{37} +3.75929 q^{38} +(5.98178 + 2.13626i) q^{39} +1.00000i q^{40} +(3.93435 - 6.81449i) q^{41} +(-4.57498 - 0.263686i) q^{42} +(0.849825 + 1.47194i) q^{43} +(-0.382566 + 0.220875i) q^{44} +(-2.80645 + 1.06012i) q^{45} +(-1.29782 + 2.24789i) q^{46} +(-3.94756 + 6.83738i) q^{47} +(-0.582530 + 1.63115i) q^{48} +(5.89000 - 3.78259i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(0.158572 - 0.444021i) q^{51} +3.66721i q^{52} +(0.0822585 + 0.0474920i) q^{53} +(-5.19530 + 0.0943837i) q^{54} -0.441750i q^{55} +(-0.744985 - 2.53870i) q^{56} +(-4.96250 + 4.21550i) q^{57} +2.75767 q^{58} +(1.60532 + 2.78050i) q^{59} +(-1.12135 - 1.32006i) q^{60} +(-11.2595 - 6.50065i) q^{61} -8.74919 q^{62} +(6.33495 - 4.78210i) q^{63} -1.00000 q^{64} +(-3.17590 - 1.83361i) q^{65} +(0.257333 - 0.720561i) q^{66} +(0.268733 + 0.465460i) q^{67} +0.272213 q^{68} +(-0.807478 - 4.42267i) q^{69} +(2.57107 + 0.624174i) q^{70} +3.75218i q^{71} +(-1.06012 - 2.80645i) q^{72} +(9.64229 + 5.56698i) q^{73} -0.119403i q^{74} +(1.70388 - 0.311090i) q^{75} +(-3.25564 - 1.87965i) q^{76} +(0.329097 + 1.12147i) q^{77} +(-4.11225 - 4.84095i) q^{78} +(-1.51395 + 2.62224i) q^{79} +(0.500000 - 0.866025i) q^{80} +(6.75228 - 5.95036i) q^{81} +(-6.81449 + 3.93435i) q^{82} +(-4.29210 - 7.43413i) q^{83} +(3.83021 + 2.51585i) q^{84} +(-0.136107 + 0.235743i) q^{85} -1.69965i q^{86} +(-3.64030 + 3.09233i) q^{87} +0.441750 q^{88} +(-6.35119 - 11.0006i) q^{89} +(2.96052 + 0.485129i) q^{90} +(9.42867 + 2.28898i) q^{91} +(2.24789 - 1.29782i) q^{92} +(11.5495 - 9.81094i) q^{93} +(6.83738 - 3.94756i) q^{94} +(3.25564 - 1.87965i) q^{95} +(1.32006 - 1.12135i) q^{96} +(-12.9284 + 7.46424i) q^{97} +(-6.99218 + 0.330818i) q^{98} +(0.468309 + 1.23975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.70388	−	0.311090i	0.983738	−	0.179608i
$3$	1.70388	−	0.311090i	0.983738	−	0.179608i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.63115	−	0.582530i	−0.665915	−	0.237817i
$7$	2.53870	−	0.744985i	0.959538	−	0.281578i
$7$	2.53870	−	0.744985i	0.959538	−	0.281578i
$8$		−	1.00000i		−	0.353553i
$9$	2.80645	−	1.06012i	0.935482	−	0.353375i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			0.441750i			0.133193i	0.997780	+	0.0665963i	$0.0212140\pi$
$11$			0.441750i			0.133193i	−0.997780	+	0.0665963i	$0.978786\pi$
$12$	1.12135	+	1.32006i	0.323707	+	0.381069i
$13$	3.17590	+	1.83361i	0.880836	+	0.508551i	0.870934	−	0.491400i	$-0.163515\pi$
$13$	3.17590	+	1.83361i	0.880836	+	0.508551i	0.00990217	+	0.999951i	$0.496848\pi$
$14$	−2.57107	−	0.624174i	−0.687148	−	0.166818i
$15$	−1.70388	+	0.311090i	−0.439941	+	0.0803231i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.136107	−	0.235743i	0.0330107	−	0.0571762i	−0.849048	−	0.528316i	$-0.822824\pi$
$17$	0.136107	−	0.235743i	0.0330107	−	0.0571762i	0.882059	+	0.471139i	$0.156157\pi$
$18$	−2.96052	−	0.485129i	−0.697800	−	0.114346i
$19$	−3.25564	+	1.87965i	−0.746896	+	0.431221i	−0.824571	−	0.565758i	$-0.808584\pi$
$19$	−3.25564	+	1.87965i	−0.746896	+	0.431221i	0.0776753	+	0.996979i	$0.475250\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	4.09389	−	2.05913i	0.893361	−	0.449340i
$22$	0.220875	−	0.382566i	0.0470907	−	0.0815634i
$23$		−	2.59564i		−	0.541228i	−0.962688	−	0.270614i	$-0.912773\pi$
$23$		−	2.59564i		−	0.541228i	0.962688	−	0.270614i	$-0.0872267\pi$
$24$	−0.311090	−	1.70388i	−0.0635010	−	0.347804i
$25$	1.00000			0.200000
$26$	−1.83361	−	3.17590i	−0.359600	−	0.622845i
$27$	4.45207	−	2.67939i	0.856800	−	0.515648i
$28$	1.91453	+	1.82609i	0.361811	+	0.345098i
$29$	−2.38822	+	1.37884i	−0.443481	+	0.256044i	−0.705073	−	0.709135i	$-0.749086\pi$
$29$	−2.38822	+	1.37884i	−0.443481	+	0.256044i	0.261592	+	0.965178i	$0.415752\pi$
$30$	1.63115	+	0.582530i	0.297806	+	0.106355i
$31$	7.57702	−	4.37459i	1.36087	−	0.785700i	0.371133	−	0.928580i	$-0.378970\pi$
$31$	7.57702	−	4.37459i	1.36087	−	0.785700i	0.989740	+	0.142880i	$0.0456362\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.137424	+	0.752691i	0.0239224	+	0.131027i
$34$	−0.235743	+	0.136107i	−0.0404297	+	0.0233421i
$35$	−2.53870	+	0.744985i	−0.429119	+	0.125925i
$36$	2.32132	+	1.90039i	0.386886	+	0.316732i
$37$	0.0597017	+	0.103406i	0.00981490	+	0.0169999i	0.870891	−	0.491476i	$-0.163542\pi$
$37$	0.0597017	+	0.103406i	0.00981490	+	0.0169999i	−0.861076	+	0.508476i	$0.830209\pi$
$38$	3.75929			0.609838
$39$	5.98178	+	2.13626i	0.957852	+	0.342076i
$40$			1.00000i			0.158114i
$41$	3.93435	−	6.81449i	0.614442	−	1.06424i	−0.376041	−	0.926603i	$-0.622715\pi$
$41$	3.93435	−	6.81449i	0.614442	−	1.06424i	0.990482	−	0.137641i	$-0.0439520\pi$
$42$	−4.57498	−	0.263686i	−0.705935	−	0.0406876i
$43$	0.849825	+	1.47194i	0.129597	+	0.224469i	0.923521	−	0.383549i	$-0.125298\pi$
$43$	0.849825	+	1.47194i	0.129597	+	0.224469i	−0.793923	+	0.608018i	$0.791965\pi$
$44$	−0.382566	+	0.220875i	−0.0576741	+	0.0332981i
$45$	−2.80645	+	1.06012i	−0.418360	+	0.158034i
$46$	−1.29782	+	2.24789i	−0.191353	+	0.331433i
$47$	−3.94756	+	6.83738i	−0.575811	+	0.997334i	0.420142	+	0.907458i	$0.361980\pi$
$47$	−3.94756	+	6.83738i	−0.575811	+	0.997334i	−0.995953	+	0.0898756i	$0.971353\pi$
$48$	−0.582530	+	1.63115i	−0.0840810	+	0.235437i
$49$	5.89000	−	3.78259i	0.841428	−	0.540369i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	0.158572	−	0.444021i	0.0222046	−	0.0621754i
$52$			3.66721i			0.508551i
$53$	0.0822585	+	0.0474920i	0.0112991	+	0.00652352i	0.505639	−	0.862745i	$-0.331257\pi$
$53$	0.0822585	+	0.0474920i	0.0112991	+	0.00652352i	−0.494340	+	0.869269i	$0.664590\pi$
$54$	−5.19530	+	0.0943837i	−0.706990	+	0.0128440i
$55$		−	0.441750i		−	0.0595655i
$56$	−0.744985	−	2.53870i	−0.0995528	−	0.339248i
$57$	−4.96250	+	4.21550i	−0.657299	+	0.558357i
$58$	2.75767			0.362100
$59$	1.60532	+	2.78050i	0.208995	+	0.361990i	0.951398	−	0.307963i	$-0.0996473\pi$
$59$	1.60532	+	2.78050i	0.208995	+	0.361990i	−0.742403	+	0.669954i	$0.766314\pi$
$60$	−1.12135	−	1.32006i	−0.144766	−	0.170419i
$61$	−11.2595	−	6.50065i	−1.44163	−	0.832323i	−0.443667	−	0.896192i	$-0.646323\pi$
$61$	−11.2595	−	6.50065i	−1.44163	−	0.832323i	−0.997958	+	0.0638687i	$0.979656\pi$
$62$	−8.74919			−1.11115
$63$	6.33495	−	4.78210i	0.798128	−	0.602487i
$64$	−1.00000			−0.125000
$65$	−3.17590	−	1.83361i	−0.393922	−	0.227431i
$66$	0.257333	−	0.720561i	0.0316755	−	0.0886949i
$67$	0.268733	+	0.465460i	0.0328310	+	0.0568650i	0.881974	−	0.471298i	$-0.156214\pi$
$67$	0.268733	+	0.465460i	0.0328310	+	0.0568650i	−0.849143	+	0.528163i	$0.822881\pi$
$68$	0.272213			0.0330107
$69$	−0.807478	−	4.42267i	−0.0972089	−	0.532427i
$70$	2.57107	+	0.624174i	0.307302	+	0.0746031i
$71$			3.75218i			0.445302i	0.974898	+	0.222651i	$0.0714711\pi$
$71$			3.75218i			0.445302i	−0.974898	+	0.222651i	$0.928529\pi$
$72$	−1.06012	−	2.80645i	−0.124937	−	0.330743i
$73$	9.64229	+	5.56698i	1.12854	+	0.651565i	0.943568	−	0.331178i	$-0.107446\pi$
$73$	9.64229	+	5.56698i	1.12854	+	0.651565i	0.184976	+	0.982743i	$0.440779\pi$
$74$		−	0.119403i		−	0.0138804i
$75$	1.70388	−	0.311090i	0.196748	−	0.0359216i
$76$	−3.25564	−	1.87965i	−0.373448	−	0.215610i
$77$	0.329097	+	1.12147i	0.0375041	+	0.127803i
$78$	−4.11225	−	4.84095i	−0.465620	−	0.548130i
$79$	−1.51395	+	2.62224i	−0.170333	+	0.295026i	−0.938536	−	0.345181i	$-0.887818\pi$
$79$	−1.51395	+	2.62224i	−0.170333	+	0.295026i	0.768203	+	0.640206i	$0.221151\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	6.75228	−	5.95036i	0.750253	−	0.661151i
$82$	−6.81449	+	3.93435i	−0.752534	+	0.434476i
$83$	−4.29210	−	7.43413i	−0.471119	−	0.816002i	0.528335	−	0.849036i	$-0.322816\pi$
$83$	−4.29210	−	7.43413i	−0.471119	−	0.816002i	−0.999454	+	0.0330340i	$0.989483\pi$
$84$	3.83021	+	2.51585i	0.417910	+	0.274502i
$85$	−0.136107	+	0.235743i	−0.0147628	+	0.0255700i
$86$		−	1.69965i		−	0.183278i
$87$	−3.64030	+	3.09233i	−0.390281	+	0.331533i
$88$	0.441750			0.0470907
$89$	−6.35119	−	11.0006i	−0.673225	−	1.16606i	−0.976984	−	0.213311i	$-0.931575\pi$
$89$	−6.35119	−	11.0006i	−0.673225	−	1.16606i	0.303760	−	0.952749i	$-0.401758\pi$
$90$	2.96052	+	0.485129i	0.312066	+	0.0511371i
$91$	9.42867	+	2.28898i	0.988393	+	0.239950i
$92$	2.24789	−	1.29782i	0.234359	−	0.135307i
$93$	11.5495	−	9.81094i	1.19762	−	1.01735i
$94$	6.83738	−	3.94756i	0.705222	−	0.407160i
$95$	3.25564	−	1.87965i	0.334022	−	0.192848i
$96$	1.32006	−	1.12135i	0.134728	−	0.114448i
$97$	−12.9284	+	7.46424i	−1.31268	+	0.757879i	−0.982540	−	0.186052i	$-0.940431\pi$
$97$	−12.9284	+	7.46424i	−1.31268	+	0.757879i	−0.330144	+	0.943930i	$0.607097\pi$
$98$	−6.99218	+	0.330818i	−0.706317	+	0.0334176i
$99$	0.468309	+	1.23975i	0.0470669	+	0.124599i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	4.57755			0.455483			0.227742	−	0.973722i	$-0.426866\pi$
$101$	4.57755			0.455483			0.227742	+	0.973722i	$0.426866\pi$
$102$	−0.359338	+	0.305247i	−0.0355798	+	0.0302240i
$103$			4.60214i			0.453462i	0.973957	+	0.226731i	$0.0728039\pi$
$103$			4.60214i			0.453462i	−0.973957	+	0.226731i	$0.927196\pi$
$104$	1.83361	−	3.17590i	0.179800	−	0.311423i
$105$	−4.09389	+	2.05913i	−0.399523	+	0.200951i
$106$	−0.0474920	−	0.0822585i	−0.00461283	−	0.00798965i
$107$	−14.0223	+	8.09579i	−1.35559	+	0.782650i	−0.989026	−	0.147743i	$-0.952799\pi$
$107$	−14.0223	+	8.09579i	−1.35559	+	0.782650i	−0.366563	+	0.930393i	$0.619466\pi$
$108$	4.54645	+	2.51591i	0.437482	+	0.242093i
$109$	−1.37107	+	2.37476i	−0.131325	+	0.227461i	−0.924187	−	0.381939i	$-0.875256\pi$
$109$	−1.37107	+	2.37476i	−0.131325	+	0.227461i	0.792863	+	0.609400i	$0.208590\pi$
$110$	−0.220875	+	0.382566i	−0.0210596	+	0.0364763i
$111$	0.133894	+	0.157620i	0.0127086	+	0.0149606i
$112$	−0.624174	+	2.57107i	−0.0589789	+	0.242943i
$113$	−2.85536	−	1.64854i	−0.268610	−	0.155082i	0.359646	−	0.933089i	$-0.382898\pi$
$113$	−2.85536	−	1.64854i	−0.268610	−	0.155082i	−0.628256	+	0.778007i	$0.716231\pi$
$114$	6.40540	−	1.16948i	0.599921	−	0.109532i
$115$			2.59564i			0.242045i
$116$	−2.38822	−	1.37884i	−0.221740	−	0.128022i
$117$	10.8568	+	1.77907i	1.00372	+	0.164475i
$118$		−	3.21065i		−	0.295564i
$119$	0.169908	−	0.699879i	0.0155755	−	0.0641578i
$120$	0.311090	+	1.70388i	0.0283985	+	0.155543i
$121$	10.8049			0.982260
$122$	6.50065	+	11.2595i	0.588541	+	1.01938i
$123$	4.58375	−	12.8350i	0.413303	−	1.15730i
$124$	7.57702	+	4.37459i	0.680436	+	0.392850i
$125$	−1.00000			−0.0894427
$126$	−7.87727	+	0.973942i	−0.701763	+	0.0867657i
$127$	−21.1104			−1.87325			−0.936623	−	0.350339i	$-0.886066\pi$
$127$	−21.1104			−1.87325			−0.936623	+	0.350339i	$0.886066\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.90591	+	2.24364i	0.167806	+	0.197542i
$130$	1.83361	+	3.17590i	0.160818	+	0.278545i
$131$	5.08532			0.444307			0.222153	−	0.975012i	$-0.428691\pi$
$131$	5.08532			0.444307			0.222153	+	0.975012i	$0.428691\pi$
$132$	−0.583137	+	0.495358i	−0.0507556	+	0.0431154i
$133$	−6.86479	+	7.19726i	−0.595253	+	0.624082i
$134$		−	0.537467i		−	0.0464301i
$135$	−4.45207	+	2.67939i	−0.383173	+	0.230605i
$136$	−0.235743	−	0.136107i	−0.0202148	−	0.0116710i
$137$			13.6419i			1.16551i	0.812649	+	0.582753i	$0.198024\pi$
$137$			13.6419i			1.16551i	−0.812649	+	0.582753i	$0.801976\pi$
$138$	−1.51204	+	4.23388i	−0.128713	+	0.360412i
$139$	−8.22684	−	4.74977i	−0.697791	−	0.402870i	0.108733	−	0.994071i	$-0.465321\pi$
$139$	−8.22684	−	4.74977i	−0.697791	−	0.402870i	−0.806524	+	0.591201i	$0.798654\pi$
$140$	−1.91453	−	1.82609i	−0.161807	−	0.154332i
$141$	−4.59915	+	12.8782i	−0.387318	+	1.08454i
$142$	1.87609	−	3.24949i	0.157438	−	0.272691i
$143$	−0.809995	+	1.40295i	−0.0677352	+	0.117321i
$144$	−0.485129	+	2.96052i	−0.0404274	+	0.246710i
$145$	2.38822	−	1.37884i	0.198331	−	0.114506i
$146$	−5.56698	−	9.64229i	−0.460726	−	0.798001i
$147$	8.85915	−	8.27741i	0.730690	−	0.682709i
$148$	−0.0597017	+	0.103406i	−0.00490745	+	0.00849995i
$149$			14.3445i			1.17515i	0.809170	+	0.587574i	$0.199917\pi$
$149$			14.3445i			1.17515i	−0.809170	+	0.587574i	$0.800083\pi$
$150$	−1.63115	−	0.582530i	−0.133183	−	0.0475634i
$151$	0.679789			0.0553204			0.0276602	−	0.999617i	$-0.491194\pi$
$151$	0.679789			0.0553204			0.0276602	+	0.999617i	$0.491194\pi$
$152$	1.87965	+	3.25564i	0.152459	+	0.264068i
$153$	0.132058	−	0.805891i	0.0106763	−	0.0651524i
$154$	0.275729	−	1.13577i	0.0222189	−	0.0915229i
$155$	−7.57702	+	4.37459i	−0.608601	+	0.351376i
$156$	1.14083	+	6.24851i	0.0913398	+	0.500281i
$157$	−20.6832	+	11.9414i	−1.65070	+	0.953030i	−0.673911	+	0.738812i	$0.735387\pi$
$157$	−20.6832	+	11.9414i	−1.65070	+	0.953030i	−0.976786	+	0.214218i	$0.931280\pi$
$158$	2.62224	−	1.51395i	0.208615	−	0.120444i
$159$	0.154933	+	0.0553310i	0.0122870	+	0.00438804i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−1.93371	−	6.58955i	−0.152398	−	0.519329i
$162$	−8.82282	+	1.77702i	−0.693186	+	0.139616i
$163$	−7.98983	−	13.8388i	−0.625812	−	1.08394i	−0.988383	−	0.151982i	$-0.951434\pi$
$163$	−7.98983	−	13.8388i	−0.625812	−	1.08394i	0.362571	−	0.931956i	$-0.381899\pi$
$164$	7.86869			0.614442
$165$	−0.137424	−	0.752691i	−0.0106984	−	0.0585969i
$166$			8.58419i			0.666263i
$167$	2.36183	−	4.09080i	0.182764	−	0.316556i	−0.760057	−	0.649856i	$-0.774829\pi$
$167$	2.36183	−	4.09080i	0.182764	−	0.316556i	0.942821	+	0.333300i	$0.108162\pi$
$168$	−2.05913	−	4.09389i	−0.158866	−	0.315851i
$169$	0.224227	+	0.388373i	0.0172483	+	0.0298749i
$170$	0.235743	−	0.136107i	0.0180807	−	0.0104389i
$171$	−7.14413	+	8.72651i	−0.546325	+	0.667333i
$172$	−0.849825	+	1.47194i	−0.0647985	+	0.112234i
$173$	−10.1399	+	17.5629i	−0.770925	+	1.33528i	0.166132	+	0.986104i	$0.446872\pi$
$173$	−10.1399	+	17.5629i	−0.770925	+	1.33528i	−0.937057	+	0.349177i	$0.886461\pi$
$174$	4.69876	−	0.857885i	0.356212	−	0.0650361i
$175$	2.53870	−	0.744985i	0.191908	−	0.0563156i
$176$	−0.382566	−	0.220875i	−0.0288370	−	0.0166491i
$177$	3.60027	+	4.23825i	0.270613	+	0.318567i
$178$			12.7024i			0.952084i
$179$	−13.2165	−	7.63053i	−0.987846	−	0.570333i	−0.0832159	−	0.996532i	$-0.526519\pi$
$179$	−13.2165	−	7.63053i	−0.987846	−	0.570333i	−0.904630	+	0.426199i	$0.859852\pi$
$180$	−2.32132	−	1.90039i	−0.173021	−	0.141647i
$181$			24.7207i			1.83748i	0.394866	+	0.918739i	$0.370791\pi$
$181$			24.7207i			1.83748i	−0.394866	+	0.918739i	$0.629209\pi$
$182$	−7.02097	−	6.69665i	−0.520429	−	0.496389i
$183$	−21.2071	−	7.57365i	−1.56767	−	0.559860i
$184$	−2.59564			−0.191353
$185$	−0.0597017	−	0.103406i	−0.00438936	−	0.00760259i
$186$	−14.9076	+	2.72179i	−1.09308	+	0.199571i
$187$	0.104140	+	0.0601250i	0.00761544	+	0.00439678i
$188$	−7.89512			−0.575811
$189$	9.30636	−	10.1189i	0.676938	−	0.736040i
$190$	−3.75929			−0.272728
$191$	−4.76721	−	2.75235i	−0.344943	−	0.199153i	0.317513	−	0.948254i	$-0.397152\pi$
$191$	−4.76721	−	2.75235i	−0.344943	−	0.199153i	−0.662456	+	0.749101i	$0.730486\pi$
$192$	−1.70388	+	0.311090i	−0.122967	+	0.0224510i
$193$	7.52344	+	13.0310i	0.541549	+	0.937991i	0.998815	+	0.0486607i	$0.0154953\pi$
$193$	7.52344	+	13.0310i	0.541549	+	0.937991i	−0.457266	+	0.889330i	$0.651171\pi$
$194$	14.9285			1.07180
$195$	−5.98178	−	2.13626i	−0.428364	−	0.152981i
$196$	6.22081	+	3.20959i	0.444344	+	0.229257i
$197$			19.6584i			1.40061i	0.713846	+	0.700303i	$0.246952\pi$
$197$			19.6584i			1.40061i	−0.713846	+	0.700303i	$0.753048\pi$
$198$	0.214306	−	1.30781i	0.0152300	−	0.0929418i
$199$	−9.23999	−	5.33471i	−0.655005	−	0.378168i	0.135366	−	0.990796i	$-0.456779\pi$
$199$	−9.23999	−	5.33471i	−0.655005	−	0.378168i	−0.790371	+	0.612628i	$0.790112\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	0.602691	+	0.709490i	0.0425105	+	0.0500435i
$202$	−3.96428	−	2.28878i	−0.278926	−	0.161038i
$203$	−5.03575	+	5.27964i	−0.353440	+	0.370558i
$204$	0.463820	−	0.0846828i	0.0324739	−	0.00592898i
$205$	−3.93435	+	6.81449i	−0.274787	+	0.475944i
$206$	2.30107	−	3.98557i	0.160323	−	0.277688i
$207$	−2.75170	−	7.28452i	−0.191256	−	0.506309i
$208$	−3.17590	+	1.83361i	−0.220209	+	0.127138i
$209$	−0.830333	−	1.43818i	−0.0574354	−	0.0994810i
$210$	4.57498	+	0.263686i	0.315704	+	0.0181961i
$211$	−0.581500	+	1.00719i	−0.0400321	+	0.0693376i	−0.885347	−	0.464930i	$-0.846079\pi$
$211$	−0.581500	+	1.00719i	−0.0400321	+	0.0693376i	0.845315	+	0.534268i	$0.179413\pi$
$212$			0.0949840i			0.00652352i
$213$	1.16727	+	6.39329i	0.0799799	+	0.438061i
$214$	16.1916			1.10683
$215$	−0.849825	−	1.47194i	−0.0579575	−	0.100385i
$216$	−2.67939	−	4.45207i	−0.182309	−	0.302925i
$217$	15.9768	−	16.7505i	1.08457	−	1.13710i
$218$	2.37476	−	1.37107i	0.160839	−	0.0928605i
$219$	18.1612	+	6.48587i	1.22722	+	0.438274i
$220$	0.382566	−	0.220875i	0.0257926	−	0.0148914i
$221$	0.864522	−	0.499132i	0.0581540	−	0.0335752i
$222$	−0.0371452	−	0.203450i	−0.00249302	−	0.0136546i
$223$	−2.45476	+	1.41726i	−0.164383	+	0.0949066i	−0.579935	−	0.814663i	$-0.696922\pi$
$223$	−2.45476	+	1.41726i	−0.164383	+	0.0949066i	0.415552	+	0.909570i	$0.363589\pi$
$224$	1.82609	−	1.91453i	0.122011	−	0.127920i
$225$	2.80645	−	1.06012i	0.187096	−	0.0706749i
$226$	1.64854	+	2.85536i	0.109660	+	0.189936i
$227$	11.2496			0.746662			0.373331	−	0.927698i	$-0.378216\pi$
$227$	11.2496			0.746662			0.373331	+	0.927698i	$0.378216\pi$
$228$	−6.13198	−	2.18990i	−0.406100	−	0.145030i
$229$		−	16.1969i		−	1.07032i	−0.844751	−	0.535160i	$-0.820251\pi$
$229$		−	16.1969i		−	1.07032i	0.844751	−	0.535160i	$-0.179749\pi$
$230$	1.29782	−	2.24789i	0.0855757	−	0.148221i
$231$	0.909621	+	1.80848i	0.0598487	+	0.118989i
$232$	1.37884	+	2.38822i	0.0905251	+	0.156794i
$233$	3.21321	−	1.85515i	0.210504	−	0.121535i	−0.391042	−	0.920373i	$-0.627885\pi$
$233$	3.21321	−	1.85515i	0.210504	−	0.121535i	0.601546	+	0.798838i	$0.294552\pi$
$234$	−8.51276	−	6.96914i	−0.556497	−	0.455587i
$235$	3.94756	−	6.83738i	0.257511	−	0.446021i
$236$	−1.60532	+	2.78050i	−0.104498	+	0.180995i
$237$	−1.76385	+	4.93898i	−0.114574	+	0.320821i
$238$	−0.497085	+	0.521159i	−0.0322212	+	0.0337817i
$239$	7.04916	+	4.06984i	0.455972	+	0.263256i	0.710349	−	0.703849i	$-0.248537\pi$
$239$	7.04916	+	4.06984i	0.455972	+	0.263256i	−0.254377	+	0.967105i	$0.581870\pi$
$240$	0.582530	−	1.63115i	0.0376022	−	0.105290i
$241$		−	28.4731i		−	1.83412i	−0.398754	−	0.917058i	$-0.630557\pi$
$241$		−	28.4731i		−	1.83412i	0.398754	−	0.917058i	$-0.369443\pi$
$242$	−9.35728	−	5.40243i	−0.601509	−	0.347281i
$243$	9.65400	−	12.2393i	0.619304	−	0.785151i
$244$		−	13.0013i		−	0.832323i
$245$	−5.89000	+	3.78259i	−0.376298	+	0.241661i
$246$	−10.3872	+	8.82359i	−0.662261	+	0.562572i
$247$	−13.7861			−0.877191
$248$	−4.37459	−	7.57702i	−0.277787	−	0.481141i
$249$	−9.62592	−	11.3317i	−0.610018	−	0.718115i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	4.61055			0.291015			0.145508	−	0.989357i	$-0.453518\pi$
$251$	4.61055			0.291015			0.145508	+	0.989357i	$0.453518\pi$
$252$	7.30889	+	3.09518i	0.460417	+	0.194978i
$253$	1.14662			0.0720876
$254$	18.2821	+	10.5552i	1.14712	+	0.662292i
$255$	−0.158572	+	0.444021i	−0.00993019	+	0.0278057i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	27.2946			1.70259			0.851297	−	0.524685i	$-0.175817\pi$
$257$	27.2946			1.70259			0.851297	+	0.524685i	$0.175817\pi$
$258$	−0.528744	−	2.89601i	−0.0329182	−	0.180297i
$259$	0.228601	+	0.218041i	0.0142046	+	0.0135484i
$260$		−	3.66721i		−	0.227431i
$261$	−5.24066	+	6.40144i	−0.324389	+	0.396239i
$262$	−4.40402	−	2.54266i	−0.272081	−	0.157086i
$263$			29.9074i			1.84417i	0.386985	+	0.922086i	$0.373516\pi$
$263$			29.9074i			1.84417i	−0.386985	+	0.922086i	$0.626484\pi$
$264$	0.752691	−	0.137424i	0.0463249	−	0.00845786i
$265$	−0.0822585	−	0.0474920i	−0.00505310	−	0.00291741i
$266$	9.54372	−	2.80062i	0.585163	−	0.171717i
$267$	−14.2439	−	16.7679i	−0.871711	−	1.02618i
$268$	−0.268733	+	0.465460i	−0.0164155	+	0.0284325i
$269$	6.84004	−	11.8473i	0.417044	−	0.722342i	−0.578596	−	0.815614i	$-0.696399\pi$
$269$	6.84004	−	11.8473i	0.417044	−	0.722342i	0.995641	+	0.0932721i	$0.0297326\pi$
$270$	5.19530	−	0.0943837i	0.316176	−	0.00574401i
$271$	−2.74454	+	1.58456i	−0.166719	+	0.0962551i	−0.581038	−	0.813877i	$-0.697353\pi$
$271$	−2.74454	+	1.58456i	−0.166719	+	0.0962551i	0.414319	+	0.910132i	$0.364020\pi$
$272$	0.136107	+	0.235743i	0.00825267	+	0.0142940i
$273$	16.7774	+	0.966992i	1.01542	+	0.0585250i
$274$	6.82095	−	11.8142i	0.412068	−	0.713724i
$275$			0.441750i			0.0266385i
$276$	3.42641	−	2.91063i	0.206245	−	0.175199i
$277$	1.51760			0.0911837			0.0455919	−	0.998960i	$-0.485483\pi$
$277$	1.51760			0.0911837			0.0455919	+	0.998960i	$0.485483\pi$
$278$	4.74977	+	8.22684i	0.284872	+	0.493413i
$279$	16.6269	−	20.3096i	0.995425	−	1.21591i
$280$	0.744985	+	2.53870i	0.0445214	+	0.151716i
$281$	3.08954	−	1.78375i	0.184307	−	0.106409i	−0.405008	−	0.914313i	$-0.632731\pi$
$281$	3.08954	−	1.78375i	0.184307	−	0.106409i	0.589315	+	0.807904i	$0.299398\pi$
$282$	10.4221	−	8.85323i	0.620624	−	0.527202i
$283$	11.4290	−	6.59851i	0.679381	−	0.392241i	−0.120241	−	0.992745i	$-0.538367\pi$
$283$	11.4290	−	6.59851i	0.679381	−	0.392241i	0.799622	+	0.600504i	$0.205033\pi$
$284$	−3.24949	+	1.87609i	−0.192822	+	0.111326i
$285$	4.96250	−	4.21550i	0.293953	−	0.249705i
$286$	1.40295	−	0.809995i	0.0829583	−	0.0478960i
$287$	4.91143	−	20.2310i	0.289913	−	1.19420i
$288$	1.90039	−	2.32132i	0.111982	−	0.136785i
$289$	8.46295	+	14.6583i	0.497821	+	0.862251i
$290$	−2.75767			−0.161936
$291$	−19.7065	+	16.7401i	−1.15522	+	0.981323i
$292$			11.1340i			0.651565i
$293$	11.0248	−	19.0955i	0.644074	−	1.11557i	−0.340440	−	0.940266i	$-0.610576\pi$
$293$	11.0248	−	19.0955i	0.644074	−	1.11557i	0.984515	−	0.175303i	$-0.0560905\pi$
$294$	−11.8110	+	2.73887i	−0.688829	+	0.159734i
$295$	−1.60532	−	2.78050i	−0.0934655	−	0.161887i
$296$	0.103406	−	0.0597017i	0.00601037	−	0.00347009i
$297$	1.18362	+	1.96670i	0.0686805	+	0.114119i
$298$	7.17226	−	12.4227i	0.415478	−	0.719629i
$299$	4.75938	−	8.24349i	0.275242	−	0.476733i
$300$	1.12135	+	1.32006i	0.0647414	+	0.0762138i
$301$	3.25402	+	3.10371i	0.187559	+	0.178895i
$302$	−0.588715	−	0.339894i	−0.0338767	−	0.0195587i
$303$	7.79962	−	1.42403i	0.448077	−	0.0818085i
$304$		−	3.75929i		−	0.215610i
$305$	11.2595	+	6.50065i	0.644715	+	0.372226i
$306$	−0.517311	+	0.631893i	−0.0295727	+	0.0361229i
$307$		−	29.2097i		−	1.66709i	−0.552453	−	0.833544i	$-0.686308\pi$
$307$		−	29.2097i		−	1.66709i	0.552453	−	0.833544i	$-0.313692\pi$
$308$	−0.806673	+	0.845741i	−0.0459645	+	0.0481906i
$309$	1.43168	+	7.84152i	0.0814455	+	0.446088i
$310$	8.74919			0.496920
$311$	−12.3964	−	21.4711i	−0.702933	−	1.21752i	−0.967432	−	0.253130i	$-0.918540\pi$
$311$	−12.3964	−	21.4711i	−0.702933	−	1.21752i	0.264499	−	0.964386i	$-0.414793\pi$
$312$	2.13626	−	5.98178i	0.120942	−	0.338652i
$313$	−29.3510	−	16.9458i	−1.65902	−	0.957835i	−0.973169	−	0.230092i	$-0.926097\pi$
$313$	−29.3510	−	16.9458i	−1.65902	−	0.957835i	−0.685850	−	0.727743i	$-0.740569\pi$
$314$	23.8829			1.34779
$315$	−6.33495	+	4.78210i	−0.356934	+	0.269441i
$316$	−3.02791			−0.170333
$317$	29.5986	+	17.0887i	1.66242	+	0.959799i	0.971554	+	0.236818i	$0.0761045\pi$
$317$	29.5986	+	17.0887i	1.66242	+	0.959799i	0.690867	+	0.722981i	$0.257229\pi$
$318$	−0.106511	−	0.125385i	−0.00597282	−	0.00703123i
$319$	−0.609101	−	1.05499i	−0.0341031	−	0.0590683i
$320$	1.00000			0.0559017
$321$	−21.3739	+	18.1565i	−1.19297	+	1.01340i
$322$	−1.62013	+	6.67357i	−0.0902864	+	0.371904i
$323$			1.02333i			0.0569395i
$324$	8.52930	+	2.87246i	0.473850	+	0.159581i
$325$	3.17590	+	1.83361i	0.176167	+	0.101710i
$326$			15.9797i			0.885032i
$327$	−1.59738	+	4.47285i	−0.0883353	+	0.247349i
$328$	−6.81449	−	3.93435i	−0.376267	−	0.217238i
$329$	−4.92793	+	20.2989i	−0.271686	+	1.11912i
$330$	−0.257333	+	0.720561i	−0.0141657	+	0.0396656i
$331$	9.09408	−	15.7514i	0.499856	−	0.865776i	−0.500144	−	0.865942i	$-0.666720\pi$
$331$	9.09408	−	15.7514i	0.499856	−	0.865776i	1.00000		0.000166208i	$5.29056e-5\pi$
$332$	4.29210	−	7.43413i	0.235559	−	0.408001i
$333$	0.277173	+	0.226913i	0.0151890	+	0.0124348i
$334$	−4.09080	+	2.36183i	−0.223839	+	0.129233i
$335$	−0.268733	−	0.465460i	−0.0146825	−	0.0254308i
$336$	−0.263686	+	4.57498i	−0.0143852	+	0.249586i
$337$	1.19477	−	2.06941i	0.0650834	−	0.112728i	−0.831648	−	0.555304i	$-0.812602\pi$
$337$	1.19477	−	2.06941i	0.0650834	−	0.112728i	0.896731	+	0.442576i	$0.145935\pi$
$338$		−	0.448455i		−	0.0243927i
$339$	−5.37806	−	1.92065i	−0.292096	−	0.104316i
$340$	−0.272213			−0.0147628
$341$	1.93248	+	3.34715i	0.104649	+	0.181258i
$342$	10.5503	−	3.98532i	0.570492	−	0.215501i
$343$	12.1350	−	13.9908i	0.655226	−	0.755433i
$344$	1.47194	−	0.849825i	0.0793616	−	0.0458195i
$345$	0.807478	+	4.42267i	0.0434731	+	0.238109i
$346$	17.5629	−	10.1399i	0.944186	−	0.545126i
$347$	−21.2317	+	12.2581i	−1.13978	+	0.658052i	−0.946376	−	0.323068i	$-0.895286\pi$
$347$	−21.2317	+	12.2581i	−1.13978	+	0.658052i	−0.193403	+	0.981119i	$0.561953\pi$
$348$	−4.49819	−	1.60643i	−0.241128	−	0.0861136i
$349$	−17.2041	+	9.93277i	−0.920912	+	0.531689i	−0.883926	−	0.467627i	$-0.845109\pi$
$349$	−17.2041	+	9.93277i	−0.920912	+	0.531689i	−0.0369861	+	0.999316i	$0.511776\pi$
$350$	−2.57107	−	0.624174i	−0.137430	−	0.0333635i
$351$	19.0523	−	0.346125i	1.01693	−	0.0184748i
$352$	0.220875	+	0.382566i	0.0117727	+	0.0203909i
$353$	32.1481			1.71107			0.855535	−	0.517744i	$-0.173228\pi$
$353$	32.1481			1.71107			0.855535	+	0.517744i	$0.173228\pi$
$354$	−0.998801	−	5.47057i	−0.0530857	−	0.290758i
$355$		−	3.75218i		−	0.199145i
$356$	6.35119	−	11.0006i	0.336612	−	0.583030i
$357$	0.0717787	−	1.24537i	0.00379893	−	0.0659120i
$358$	7.63053	+	13.2165i	0.403286	+	0.698512i
$359$	−24.4812	+	14.1342i	−1.29207	+	0.745976i	−0.979021	−	0.203761i	$-0.934683\pi$
$359$	−24.4812	+	14.1342i	−1.29207	+	0.745976i	−0.313048	+	0.949737i	$0.601350\pi$
$360$	1.06012	+	2.80645i	0.0558734	+	0.147913i
$361$	−2.43386	+	4.21556i	−0.128098	+	0.221872i
$362$	12.3604	−	21.4088i	0.649646	−	1.12522i
$363$	18.4102	−	3.36129i	0.966286	−	0.176422i
$364$	2.73202	+	9.30995i	0.143197	+	0.487974i
$365$	−9.64229	−	5.56698i	−0.504700	−	0.291389i
$366$	14.5791	+	17.1625i	0.762060	+	0.897100i
$367$		−	33.6602i		−	1.75705i	−0.477699	−	0.878524i	$-0.658529\pi$
$367$		−	33.6602i		−	1.75705i	0.477699	−	0.878524i	$-0.341471\pi$
$368$	2.24789	+	1.29782i	0.117179	+	0.0676535i
$369$	3.81733	−	23.2954i	0.198722	−	1.21271i
$370$			0.119403i			0.00620749i
$371$	0.244210	+	0.0592865i	0.0126788	+	0.00307800i
$372$	14.2713	+	5.09667i	0.739930	+	0.264250i
$373$	−11.9740			−0.619991			−0.309996	−	0.950738i	$-0.600328\pi$
$373$	−11.9740			−0.619991			−0.309996	+	0.950738i	$0.600328\pi$
$374$	−0.0601250	−	0.104140i	−0.00310899	−	0.00538493i
$375$	−1.70388	+	0.311090i	−0.0879882	+	0.0160646i
$376$	6.83738	+	3.94756i	0.352611	+	0.203580i
$377$	−10.1130			−0.520845
$378$	−13.1190	+	4.11003i	−0.674768	+	0.211397i
$379$	−10.9629			−0.563126			−0.281563	−	0.959543i	$-0.590853\pi$
$379$	−10.9629			−0.563126			−0.281563	+	0.959543i	$0.590853\pi$
$380$	3.25564	+	1.87965i	0.167011	+	0.0964238i
$381$	−35.9697	+	6.56724i	−1.84278	+	0.336450i
$382$	2.75235	+	4.76721i	0.140822	+	0.243912i
$383$	−20.1252			−1.02835			−0.514174	−	0.857686i	$-0.671901\pi$
$383$	−20.1252			−1.02835			−0.514174	+	0.857686i	$0.671901\pi$
$384$	1.63115	+	0.582530i	0.0832394	+	0.0297271i
$385$	−0.329097	−	1.12147i	−0.0167723	−	0.0571554i
$386$		−	15.0469i		−	0.765866i
$387$	3.94542	+	3.23000i	0.200557	+	0.164190i
$388$	−12.9284	−	7.46424i	−0.656342	−	0.378939i
$389$			27.3409i			1.38624i	0.720823	+	0.693119i	$0.243764\pi$
$389$			27.3409i			1.38624i	−0.720823	+	0.693119i	$0.756236\pi$
$390$	4.11225	+	4.84095i	0.208232	+	0.245131i
$391$	−0.611905	−	0.353283i	−0.0309454	−	0.0178663i
$392$	−3.78259	−	5.89000i	−0.191049	−	0.297490i
$393$	8.66480	−	1.58199i	0.437082	−	0.0798011i
$394$	9.82922	−	17.0247i	0.495189	−	0.857692i
$395$	1.51395	−	2.62224i	0.0761753	−	0.131939i
$396$	−0.839497	+	1.02544i	−0.0421863	+	0.0515304i
$397$	13.5525	−	7.82456i	0.680182	−	0.392703i	−0.119742	−	0.992805i	$-0.538207\pi$
$397$	13.5525	−	7.82456i	0.680182	−	0.392703i	0.799924	+	0.600102i	$0.204873\pi$
$398$	5.33471	+	9.23999i	0.267405	+	0.463159i
$399$	−9.45782	+	14.3989i	−0.473483	+	0.720846i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	39.1525i		−	1.95518i	−0.210509	−	0.977592i	$-0.567512\pi$
$401$		−	39.1525i		−	1.95518i	0.210509	−	0.977592i	$-0.432488\pi$
$402$	−0.167201	−	0.915781i	−0.00833921	−	0.0456750i
$403$	32.0851			1.59827
$404$	2.28878	+	3.96428i	0.113871	+	0.197230i
$405$	−6.75228	+	5.95036i	−0.335523	+	0.295676i
$406$	7.00091	−	2.05443i	0.347449	−	0.101959i
$407$	−0.0456797	+	0.0263732i	−0.00226426	+	0.00130727i
$408$	−0.444021	−	0.158572i	−0.0219823	−	0.00785050i
$409$	−22.7149	+	13.1145i	−1.12318	+	0.648468i	−0.942211	−	0.335021i	$-0.891257\pi$
$409$	−22.7149	+	13.1145i	−1.12318	+	0.648468i	−0.180969	+	0.983489i	$0.557923\pi$
$410$	6.81449	−	3.93435i	0.336544	−	0.194303i
$411$	4.24386	+	23.2442i	0.209334	+	1.14655i
$412$	−3.98557	+	2.30107i	−0.196355	+	0.113366i
$413$	6.14687	+	5.86292i	0.302467	+	0.288495i
$414$	−1.25922	+	7.68443i	−0.0618873	+	0.377669i
$415$	4.29210	+	7.43413i	0.210691	+	0.364927i
$416$	3.66721			0.179800
$417$	−15.4952	−	5.53377i	−0.758803	−	0.270990i
$418$			1.66067i			0.0812259i
$419$	18.3795	−	31.8342i	0.897897	−	1.55520i	0.0677203	−	0.997704i	$-0.478427\pi$
$419$	18.3795	−	31.8342i	0.897897	−	1.55520i	0.830177	−	0.557500i	$-0.188239\pi$
$420$	−3.83021	−	2.51585i	−0.186895	−	0.122761i
$421$	6.54747	+	11.3406i	0.319104	+	0.552705i	0.980301	−	0.197507i	$-0.0632847\pi$
$421$	6.54747	+	11.3406i	0.319104	+	0.552705i	−0.661197	+	0.750212i	$0.729951\pi$
$422$	1.00719	−	0.581500i	0.0490291	−	0.0283070i
$423$	−3.83015	+	23.3736i	−0.186228	+	1.13646i
$424$	0.0474920	−	0.0822585i	0.00230641	−	0.00399483i
$425$	0.136107	−	0.235743i	0.00660214	−	0.0114352i
$426$	2.18576	−	6.12039i	0.105900	−	0.296534i
$427$	−33.4273	−	8.11508i	−1.61766	−	0.392716i
$428$	−14.0223	−	8.09579i	−0.677795	−	0.391325i
$429$	−0.943694	+	2.64245i	−0.0455620	+	0.127579i
$430$			1.69965i			0.0819644i
$431$	17.9103	+	10.3405i	0.862710	+	0.498086i	0.864919	−	0.501911i	$-0.167370\pi$
$431$	17.9103	+	10.3405i	0.862710	+	0.498086i	−0.00220853	+	0.999998i	$0.500703\pi$
$432$	0.0943837	+	5.19530i	0.00454104	+	0.249959i
$433$			5.36529i			0.257839i	0.991655	+	0.128920i	$0.0411509\pi$
$433$			5.36529i			0.257839i	−0.991655	+	0.128920i	$0.958849\pi$
$434$	−22.2116	+	6.51801i	−1.06619	+	0.312875i
$435$	3.64030	−	3.09233i	0.174539	−	0.148266i
$436$	−2.74214			−0.131325
$437$	4.87888	+	8.45048i	0.233389	+	0.404241i
$438$	−12.4851	−	14.6975i	−0.596562	−	0.702274i
$439$	−9.07559	−	5.23979i	−0.433154	−	0.250082i	0.267535	−	0.963548i	$-0.413791\pi$
$439$	−9.07559	−	5.23979i	−0.433154	−	0.250082i	−0.700689	+	0.713466i	$0.747124\pi$
$440$	−0.441750			−0.0210596
$441$	12.5199	−	16.8597i	0.596188	−	0.802845i
$442$	−0.998264			−0.0474826
$443$	−6.73544	−	3.88871i	−0.320010	−	0.184758i	0.331387	−	0.943495i	$-0.392484\pi$
$443$	−6.73544	−	3.88871i	−0.320010	−	0.184758i	−0.651397	+	0.758737i	$0.725817\pi$
$444$	−0.0695561	+	0.194765i	−0.00330099	+	0.00924315i
$445$	6.35119	+	11.0006i	0.301075	+	0.521478i
$446$	2.83452			0.134218
$447$	4.46244	+	24.4414i	0.211066	+	1.15604i
$448$	−2.53870	+	0.744985i	−0.119942	+	0.0351972i
$449$		−	3.73404i		−	0.176220i	−0.996111	−	0.0881102i	$-0.971917\pi$
$449$		−	3.73404i		−	0.176220i	0.996111	−	0.0881102i	$-0.0280828\pi$
$450$	−2.96052	−	0.485129i	−0.139560	−	0.0228692i
$451$	3.01030	+	1.73800i	0.141749	+	0.0818390i
$452$		−	3.29709i		−	0.155082i
$453$	1.15828	−	0.211476i	0.0544208	−	0.00993600i
$454$	−9.74244	−	5.62480i	−0.457235	−	0.263985i
$455$	−9.42867	−	2.28898i	−0.442023	−	0.107309i
$456$	4.21550	+	4.96250i	0.197409	+	0.232390i
$457$	−1.45393	+	2.51828i	−0.0680121	+	0.117800i	−0.898026	−	0.439942i	$-0.854999\pi$
$457$	−1.45393	+	2.51828i	−0.0680121	+	0.117800i	0.830014	+	0.557742i	$0.188332\pi$
$458$	−8.09843	+	14.0269i	−0.378415	+	0.655434i
$459$	−0.0256925	−	1.41423i	−0.00119922	−	0.0660105i
$460$	−2.24789	+	1.29782i	−0.104808	+	0.0605111i
$461$	−4.88443	−	8.46009i	−0.227491	−	0.394026i	0.729573	−	0.683903i	$-0.239719\pi$
$461$	−4.88443	−	8.46009i	−0.227491	−	0.394026i	−0.957064	+	0.289877i	$0.906385\pi$
$462$	0.116483	−	2.02100i	0.00541929	−	0.0940253i
$463$	1.43617	−	2.48752i	0.0667446	−	0.115605i	−0.830722	−	0.556688i	$-0.812072\pi$
$463$	1.43617	−	2.48752i	0.0667446	−	0.115605i	0.897467	+	0.441083i	$0.145405\pi$
$464$		−	2.75767i		−	0.128022i
$465$	−11.5495	+	9.81094i	−0.535594	+	0.454971i
$466$	−3.71029			−0.171876
$467$	1.92955	+	3.34208i	0.0892890	+	0.154653i	0.907211	−	0.420676i	$-0.138207\pi$
$467$	1.92955	+	3.34208i	0.0892890	+	0.154653i	−0.817922	+	0.575329i	$0.804874\pi$
$468$	3.88770	+	10.2918i	0.179709	+	0.475740i
$469$	1.02899	+	0.981461i	0.0475145	+	0.0453196i
$470$	−6.83738	+	3.94756i	−0.315385	+	0.182087i
$471$	−31.5269	+	26.7812i	−1.45268	+	1.23401i
$472$	2.78050	−	1.60532i	0.127983	−	0.0738910i
$473$	−0.650229	+	0.375410i	−0.0298975	+	0.0172614i
$474$	3.99703	−	3.39536i	0.183589	−	0.155954i
$475$	−3.25564	+	1.87965i	−0.149379	+	0.0862441i
$476$	0.691067	−	0.202795i	0.0316750	−	0.00929508i
$477$	0.281201	+	0.0460795i	0.0128753	+	0.00210983i
$478$	−4.06984	−	7.04916i	−0.186150	−	0.322421i
$479$	−16.3287			−0.746079			−0.373039	−	0.927815i	$-0.621684\pi$
$479$	−16.3287			−0.746079			−0.373039	+	0.927815i	$0.621684\pi$
$480$	−1.32006	+	1.12135i	−0.0602523	+	0.0511826i
$481$			0.437878i			0.0199655i
$482$	−14.2366	+	24.6585i	−0.648458	+	1.12316i
$483$	−5.34477	−	10.6263i	−0.243195	−	0.483512i
$484$	5.40243	+	9.35728i	0.245565	+	0.425331i
$485$	12.9284	−	7.46424i	0.587050	−	0.338934i
$486$	−14.4803	+	5.77254i	−0.656838	+	0.261848i
$487$	7.05835	−	12.2254i	0.319844	−	0.553987i	−0.660611	−	0.750728i	$-0.729703\pi$
$487$	7.05835	−	12.2254i	0.319844	−	0.553987i	0.980455	+	0.196742i	$0.0630360\pi$
$488$	−6.50065	+	11.2595i	−0.294271	+	0.509692i
$489$	−17.9189	−	21.0942i	−0.810319	−	0.953911i
$490$	6.99218	−	0.330818i	0.315874	−	0.0149448i
$491$	−9.00388	−	5.19839i	−0.406339	−	0.234600i	0.282876	−	0.959156i	$-0.408711\pi$
$491$	−9.00388	−	5.19839i	−0.406339	−	0.234600i	−0.689216	+	0.724556i	$0.742045\pi$
$492$	13.4073	−	2.44787i	0.604450	−	0.110359i
$493$			0.750675i			0.0338087i
$494$	11.9391	+	6.89307i	0.537167	+	0.310134i
$495$	−0.468309	−	1.23975i	−0.0210489	−	0.0557225i
$496$			8.74919i			0.392850i
$497$	2.79532	+	9.52567i	0.125387	+	0.427285i
$498$	2.67046	+	14.6265i	0.119666	+	0.655428i
$499$	−15.8790			−0.710840			−0.355420	−	0.934707i	$-0.615662\pi$
$499$	−15.8790			−0.710840			−0.355420	+	0.934707i	$0.615662\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	2.75167	−	7.70500i	0.122936	−	0.344234i
$502$	−3.99285	−	2.30527i	−0.178210	−	0.102889i
$503$	−0.0186342			−0.000830858			−0.000415429	−	1.00000i	$-0.500132\pi$
$503$	−0.0186342			−0.000830858			−0.000415429		1.00000i	$0.500132\pi$
$504$	−4.78210	−	6.33495i	−0.213011	−	0.282181i
$505$	−4.57755			−0.203698
$506$	−0.993004	−	0.573311i	−0.0441444	−	0.0254868i
$507$	0.502877	+	0.591989i	0.0223335	+	0.0262911i
$508$	−10.5552	−	18.2821i	−0.468311	−	0.811139i
$509$	32.9617			1.46100			0.730502	−	0.682911i	$-0.239286\pi$
$509$	32.9617			1.46100			0.730502	+	0.682911i	$0.239286\pi$
$510$	0.359338	−	0.305247i	0.0159118	−	0.0135166i
$511$	28.6262	+	6.94953i	1.26635	+	0.307429i
$512$			1.00000i			0.0441942i
$513$	−9.45804	+	17.0914i	−0.417583	+	0.754605i
$514$	−23.6379	−	13.6473i	−1.04262	−	0.601958i
$515$		−	4.60214i		−	0.202795i
$516$	−0.990097	+	2.77239i	−0.0435866	+	0.122048i
$517$	−3.02041	−	1.74383i	−0.132837	−	0.0766937i
$518$	−0.0889537	−	0.303129i	−0.00390840	−	0.0133187i
$519$	−11.8136	+	33.0795i	−0.518561	+	1.45203i
$520$	−1.83361	+	3.17590i	−0.0804090	+	0.139272i
$521$	3.94706	−	6.83651i	0.172924	−	0.299513i	−0.766517	−	0.642224i	$-0.778012\pi$
$521$	3.94706	−	6.83651i	0.172924	−	0.299513i	0.939441	+	0.342711i	$0.111345\pi$
$522$	7.73926	−	2.92348i	0.338738	−	0.127957i
$523$	2.84277	−	1.64127i	0.124306	−	0.0717679i	−0.436558	−	0.899676i	$-0.643803\pi$
$523$	2.84277	−	1.64127i	0.124306	−	0.0717679i	0.560864	+	0.827908i	$0.310469\pi$
$524$	2.54266	+	4.40402i	0.111077	+	0.192390i
$525$	4.09389	−	2.05913i	0.178672	−	0.0898679i
$526$	14.9537	−	25.9006i	0.652013	−	1.12932i
$527$		−	2.38164i		−	0.103746i
$528$	−0.720561	−	0.257333i	−0.0313584	−	0.0111990i
$529$	16.2627			0.707072
$530$	0.0474920	+	0.0822585i	0.00206292	+	0.00357308i
$531$	7.45293	+	6.10149i	0.323430	+	0.264782i
$532$	−9.66541	−	2.34645i	−0.419049	−	0.101732i
$533$	24.9902	−	14.4281i	1.08244	−	0.624950i
$534$	3.95159	+	21.6434i	0.171002	+	0.936601i
$535$	14.0223	−	8.09579i	0.606238	−	0.350012i
$536$	0.465460	−	0.268733i	0.0201048	−	0.0116075i
$537$	−24.8931	−	8.89003i	−1.07422	−	0.383633i
$538$	−11.8473	+	6.84004i	−0.510773	+	0.294895i
$539$	1.67096	+	2.60190i	0.0719732	+	0.112072i
$540$	−4.54645	−	2.51591i	−0.195648	−	0.108267i
$541$	7.89978	+	13.6828i	0.339638	+	0.588270i	0.984365	−	0.176143i	$-0.0563621\pi$
$541$	7.89978	+	13.6828i	0.339638	+	0.588270i	−0.644727	+	0.764413i	$0.723029\pi$
$542$	3.16912			0.136125
$543$	7.69038	+	42.1213i	0.330026	+	1.80760i
$544$		−	0.272213i		−	0.0116710i
$545$	1.37107	−	2.37476i	0.0587302	−	0.101724i
$546$	−14.0462	−	9.22616i	−0.601122	−	0.394843i
$547$	−8.85022	−	15.3290i	−0.378408	−	0.655422i	0.612423	−	0.790531i	$-0.290195\pi$
$547$	−8.85022	−	15.3290i	−0.378408	−	0.655422i	−0.990831	+	0.135108i	$0.956862\pi$
$548$	−11.8142	+	6.82095i	−0.504679	+	0.291376i
$549$	−38.4905	−	6.30731i	−1.64274	−	0.269189i
$550$	0.220875	−	0.382566i	0.00941814	−	0.0163127i
$551$	5.18345	−	8.97800i	0.220823	−	0.382476i
$552$	−4.42267	+	0.807478i	−0.188241	+	0.0343685i
$553$	−1.88994	+	7.78496i	−0.0803685	+	0.331050i
$554$	−1.31428	−	0.758800i	−0.0558384	−	0.0322383i
$555$	−0.133894	−	0.157620i	−0.00568346	−	0.00669059i
$556$		−	9.49953i		−	0.402870i
$557$	27.5064	+	15.8808i	1.16548	+	0.672892i	0.952612	−	0.304188i	$-0.0983852\pi$
$557$	27.5064	+	15.8808i	1.16548	+	0.672892i	0.212871	+	0.977080i	$0.431719\pi$
$558$	−24.5541	+	9.27522i	−1.03946	+	0.392651i
$559$			6.23298i			0.263627i
$560$	0.624174	−	2.57107i	0.0263762	−	0.108648i
$561$	0.196146	+	0.0700493i	0.00828130	+	0.00295748i
$562$	−3.56750			−0.150486
$563$	21.3085	+	36.9074i	0.898046	+	1.55546i	0.829989	+	0.557780i	$0.188347\pi$
$563$	21.3085	+	36.9074i	0.898046	+	1.55546i	0.0680571	+	0.997681i	$0.478320\pi$
$564$	−13.4524	+	2.45610i	−0.566447	+	0.103420i
$565$	2.85536	+	1.64854i	0.120126	+	0.0693548i
$566$	−13.1970			−0.554712
$567$	12.7091	−	20.1365i	0.533731	−	0.845654i
$568$	3.75218			0.157438
$569$	−14.8343	−	8.56459i	−0.621886	−	0.359046i	0.155717	−	0.987802i	$-0.450231\pi$
$569$	−14.8343	−	8.56459i	−0.621886	−	0.359046i	−0.777603	+	0.628756i	$0.783565\pi$
$570$	−6.40540	+	1.16948i	−0.268293	+	0.0489841i
$571$	−7.40719	−	12.8296i	−0.309981	−	0.536904i	0.668377	−	0.743823i	$-0.266989\pi$
$571$	−7.40719	−	12.8296i	−0.309981	−	0.536904i	−0.978358	+	0.206920i	$0.933656\pi$
$572$	−1.61999			−0.0677352
$573$	−8.97900	−	3.20665i	−0.375103	−	0.133960i
$574$	−14.3689	+	15.0648i	−0.599747	+	0.628793i
$575$		−	2.59564i		−	0.108246i
$576$	−2.80645	+	1.06012i	−0.116935	+	0.0441718i
$577$	29.2079	+	16.8632i	1.21594	+	0.702025i	0.964048	−	0.265730i	$-0.0856129\pi$
$577$	29.2079	+	16.8632i	1.21594	+	0.702025i	0.251895	+	0.967755i	$0.418946\pi$
$578$		−	16.9259i		−	0.704025i
$579$	16.8729	+	19.8628i	0.701213	+	0.825471i
$580$	2.38822	+	1.37884i	0.0991653	+	0.0572531i
$581$	−16.4347	−	15.6755i	−0.681825	−	0.650328i
$582$	25.4364	−	4.64410i	1.05437	−	0.192504i
$583$	−0.0209796	+	0.0363377i	−0.000868885	+	0.00150495i
$584$	5.56698	−	9.64229i	0.230363	−	0.399001i
$585$	−10.8568	−	1.77907i	−0.448875	−	0.0735555i
$586$	−19.0955	+	11.0248i	−0.788826	+	0.455429i
$587$	5.76762	+	9.98982i	0.238055	+	0.412324i	0.960156	−	0.279464i	$-0.0901567\pi$
$587$	5.76762	+	9.98982i	0.238055	+	0.412324i	−0.722101	+	0.691788i	$0.756823\pi$
$588$	11.5980	+	3.53354i	0.478294	+	0.145721i
$589$	−16.4454	+	28.4842i	−0.677620	+	1.17367i
$590$			3.21065i			0.132180i
$591$	6.11555	+	33.4957i	0.251560	+	1.37783i
$592$	−0.119403			−0.00490745
$593$	−11.7771	−	20.3985i	−0.483627	−	0.837666i	0.516197	−	0.856470i	$-0.327347\pi$
$593$	−11.7771	−	20.3985i	−0.483627	−	0.837666i	−0.999823	+	0.0188043i	$0.994014\pi$
$594$	−0.0416940	−	2.29502i	−0.00171072	−	0.0941658i
$595$	−0.169908	+	0.699879i	−0.00696557	+	0.0286922i
$596$	−12.4227	+	7.17226i	−0.508854	+	0.293787i
$597$	−17.4035	−	6.21526i	−0.712276	−	0.254374i
$598$	−8.24349	+	4.75938i	−0.337101	+	0.194626i
$599$	−31.9172	+	18.4274i	−1.30410	+	0.752923i	−0.981105	−	0.193477i	$-0.938023\pi$
$599$	−31.9172	+	18.4274i	−1.30410	+	0.752923i	−0.322996	+	0.946400i	$0.604690\pi$
$600$	−0.311090	−	1.70388i	−0.0127002	−	0.0695608i
$601$	−3.58818	+	2.07164i	−0.146365	+	0.0845039i	−0.571394	−	0.820676i	$-0.693597\pi$
$601$	−3.58818	+	2.07164i	−0.146365	+	0.0845039i	0.425029	+	0.905180i	$0.360264\pi$
$602$	−1.26621	−	4.31490i	−0.0516070	−	0.175862i
$603$	1.24763	+	1.02140i	0.0508075	+	0.0415945i
$604$	0.339894	+	0.588715i	0.0138301	+	0.0239545i
$605$	−10.8049			−0.439280
$606$	−7.46669	−	2.66656i	−0.303313	−	0.108322i
$607$		−	19.7232i		−	0.800540i	−0.916397	−	0.400270i	$-0.868916\pi$
$607$		−	19.7232i		−	0.800540i	0.916397	−	0.400270i	$-0.131084\pi$
$608$	−1.87965	+	3.25564i	−0.0762297	+	0.132034i
$609$	−6.93789	+	10.5625i	−0.281138	+	0.428013i
$610$	−6.50065	−	11.2595i	−0.263204	−	0.455882i
$611$	−25.0741	+	14.4766i	−1.01439	+	0.585659i
$612$	0.763951	−	0.288580i	0.0308809	−	0.0116651i
$613$	3.80772	−	6.59516i	0.153792	−	0.266376i	−0.778826	−	0.627240i	$-0.784185\pi$
$613$	3.80772	−	6.59516i	0.153792	−	0.266376i	0.932619	+	0.360864i	$0.117518\pi$
$614$	−14.6049	+	25.2964i	−0.589405	+	1.02088i
$615$	−4.58375	+	12.8350i	−0.184835	+	0.517559i
$616$	1.12147	−	0.329097i	0.0451853	−	0.0132597i
$617$	32.0531	+	18.5058i	1.29041	+	0.745017i	0.978726	−	0.205170i	$-0.0657747\pi$
$617$	32.0531	+	18.5058i	1.29041	+	0.745017i	0.311681	+	0.950187i	$0.399108\pi$
$618$	2.68089	−	7.50679i	0.107841	−	0.301967i
$619$		−	21.0131i		−	0.844587i	−0.906459	−	0.422294i	$-0.861225\pi$
$619$		−	21.0131i		−	0.844587i	0.906459	−	0.422294i	$-0.138775\pi$
$620$	−7.57702	−	4.37459i	−0.304300	−	0.175688i
$621$	−6.95472	−	11.5560i	−0.279083	−	0.463725i
$622$			24.7927i			0.994097i
$623$	−24.3190	−	23.1956i	−0.974322	−	0.929314i
$624$	−4.84095	+	4.11225i	−0.193793	+	0.164622i
$625$	1.00000			0.0400000
$626$	16.9458	+	29.3510i	0.677292	+	1.17310i
$627$	−1.86220	−	2.19218i	−0.0743689	−	0.0875474i
$628$	−20.6832	−	11.9414i	−0.825349	−	0.476515i
$629$	0.0325032			0.00129599
$630$	7.87727	−	0.973942i	0.313838	−	0.0388028i
$631$	24.9229			0.992166			0.496083	−	0.868275i	$-0.334771\pi$
$631$	24.9229			0.992166			0.496083	+	0.868275i	$0.334771\pi$
$632$	2.62224	+	1.51395i	0.104307	+	0.0602218i
$633$	−0.677482	+	1.89703i	−0.0269275	+	0.0754001i
$634$	−17.0887	−	29.5986i	−0.678681	−	1.17551i
$635$	21.1104			0.837741
$636$	0.0295486	+	0.161842i	0.00117168	+	0.00641744i
$637$	25.6418	−	1.21318i	1.01597	−	0.0480679i
$638$			1.21820i			0.0482291i
$639$	3.97778	+	10.5303i	0.157359	+	0.416572i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			6.42378i			0.253724i	0.991920	+	0.126862i	$0.0404905\pi$
$641$			6.42378i			0.253724i	−0.991920	+	0.126862i	$0.959509\pi$
$642$	27.5886	−	5.03704i	1.08883	−	0.198796i
$643$	34.0574	+	19.6630i	1.34309	+	0.775434i	0.987260	−	0.159116i	$-0.0508642\pi$
$643$	34.0574	+	19.6630i	1.34309	+	0.775434i	0.355832	+	0.934550i	$0.384198\pi$
$644$	4.73986	−	4.96942i	0.186777	−	0.195822i
$645$	−1.90591	−	2.24364i	−0.0750451	−	0.0883433i
$646$	0.511664	−	0.886229i	0.0201312	−	0.0348682i
$647$	13.4151	−	23.2356i	0.527401	−	0.913486i	−0.472089	−	0.881551i	$-0.656500\pi$
$647$	13.4151	−	23.2356i	0.527401	−	0.913486i	0.999490	−	0.0319349i	$-0.0101669\pi$
$648$	−5.95036	−	6.75228i	−0.233752	−	0.265254i
$649$	−1.22829	+	0.709151i	−0.0482144	+	0.0278366i
$650$	−1.83361	−	3.17590i	−0.0719200	−	0.124569i
$651$	22.0116	−	33.5112i	0.862704	−	1.31341i
$652$	7.98983	−	13.8388i	0.312906	−	0.541969i
$653$		−	40.2139i		−	1.57369i	−0.617149	−	0.786846i	$-0.711712\pi$
$653$		−	40.2139i		−	1.57369i	0.617149	−	0.786846i	$-0.288288\pi$
$654$	3.61979	−	3.07491i	0.141545	−	0.120238i
$655$	−5.08532			−0.198700
$656$	3.93435	+	6.81449i	0.153610	+	0.266061i
$657$	32.9622	+	5.40140i	1.28598	+	0.210729i
$658$	14.4172	−	15.1154i	0.562040	−	0.589260i
$659$	18.2869	−	10.5580i	0.712357	−	0.411280i	−0.0995760	−	0.995030i	$-0.531749\pi$
$659$	18.2869	−	10.5580i	0.712357	−	0.411280i	0.811933	+	0.583750i	$0.198415\pi$
$660$	0.583137	−	0.495358i	0.0226986	−	0.0192818i
$661$	22.9592	−	13.2555i	0.893010	−	0.515580i	0.0180841	−	0.999836i	$-0.494243\pi$
$661$	22.9592	−	13.2555i	0.893010	−	0.515580i	0.874926	+	0.484257i	$0.160910\pi$
$662$	−15.7514	+	9.09408i	−0.612196	+	0.353452i
$663$	1.31777	−	1.11941i	0.0511779	−	0.0434742i
$664$	−7.43413	+	4.29210i	−0.288500	+	0.166566i
$665$	6.86479	−	7.19726i	0.266205	−	0.279098i
$666$	−0.126582	−	0.335099i	−0.00490497	−	0.0129848i
$667$	3.57896	+	6.19895i	0.138578	+	0.240024i
$668$	4.72365			0.182764
$669$	−3.74174	+	3.17850i	−0.144664	+	0.122888i
$670$			0.537467i			0.0207642i
$671$	2.87166	−	4.97386i	0.110859	−	0.192014i
$672$	2.51585	−	3.83021i	0.0970510	−	0.147754i
$673$	17.0764	+	29.5771i	0.658245	+	1.14011i	0.981070	+	0.193655i	$0.0620344\pi$
$673$	17.0764	+	29.5771i	0.658245	+	1.14011i	−0.322824	+	0.946459i	$0.604632\pi$
$674$	−2.06941	+	1.19477i	−0.0797105	+	0.0460209i
$675$	4.45207	−	2.67939i	0.171360	−	0.103130i
$676$	−0.224227	+	0.388373i	−0.00862413	+	0.0149374i
$677$	−3.73419	+	6.46780i	−0.143516	+	0.248578i	−0.928818	−	0.370535i	$-0.879174\pi$
$677$	−3.73419	+	6.46780i	−0.143516	+	0.248578i	0.785302	+	0.619113i	$0.212508\pi$
$678$	3.69721	+	4.35236i	0.141990	+	0.167152i
$679$	−27.2607	+	28.5810i	−1.04617	+	1.09684i
$680$	0.235743	+	0.136107i	0.00904035	+	0.00521945i
$681$	19.1680	−	3.49964i	0.734520	−	0.134107i
$682$		−	3.86495i		−	0.147997i
$683$	−20.4287	−	11.7945i	−0.781681	−	0.451304i	0.0553445	−	0.998467i	$-0.482374\pi$
$683$	−20.4287	−	11.7945i	−0.781681	−	0.451304i	−0.837026	+	0.547163i	$0.815708\pi$
$684$	−11.1294	−	1.82374i	−0.425545	−	0.0697325i
$685$		−	13.6419i		−	0.521230i
$686$	−17.5046	+	6.04891i	−0.668328	+	0.230949i
$687$	−5.03869	−	27.5976i	−0.192238	−	1.05291i
$688$	−1.69965			−0.0647985
$689$	0.174163	+	0.301660i	0.00663509	+	0.0114923i
$690$	1.51204	−	4.23388i	0.0575623	−	0.161181i
$691$	14.1003	+	8.14082i	0.536401	+	0.309692i	0.743619	−	0.668603i	$-0.233108\pi$
$691$	14.1003	+	8.14082i	0.536401	+	0.309692i	−0.207218	+	0.978295i	$0.566441\pi$
$692$	−20.2799			−0.770925
$693$	2.11249	+	2.79846i	0.0802468	+	0.106305i
$694$	24.5163			0.930626
$695$	8.22684	+	4.74977i	0.312062	+	0.180169i
$696$	3.09233	+	3.64030i	0.117214	+	0.137985i
$697$	−1.07098	−	1.85499i	−0.0405663	−	0.0702629i
$698$	19.8655			0.751921
$699$	4.89781	−	4.16055i	0.185252	−	0.157366i
$700$	1.91453	+	1.82609i	0.0723623	+	0.0690196i
$701$		−	4.22872i		−	0.159717i	−0.996806	−	0.0798583i	$-0.974553\pi$
$701$		−	4.22872i		−	0.159717i	0.996806	−	0.0798583i	$-0.0254468\pi$
$702$	−16.6728	−	9.22638i	−0.629274	−	0.348227i
$703$	−0.388735	−	0.224436i	−0.0146614	−	0.00846477i
$704$		−	0.441750i		−	0.0166491i
$705$	4.59915	−	12.8782i	0.173214	−	0.485019i
$706$	−27.8411	−	16.0741i	−1.04781	−	0.604955i
$707$	11.6210	−	3.41021i	0.437054	−	0.128254i
$708$	−1.87030	+	5.23705i	−0.0702901	+	0.196821i
$709$	2.89202	−	5.00912i	0.108612	−	0.188121i	−0.806596	−	0.591103i	$-0.798693\pi$
$709$	2.89202	−	5.00912i	0.108612	−	0.188121i	0.915208	+	0.402981i	$0.132026\pi$
$710$	−1.87609	+	3.24949i	−0.0704085	+	0.121951i
$711$	−1.46892	+	8.96416i	−0.0550890	+	0.336182i
$712$	−11.0006	+	6.35119i	−0.412264	+	0.238021i
$713$	−11.3549	−	19.6672i	−0.425243	−	0.736543i
$714$	−0.684847	+	1.04263i	−0.0256298	+	0.0390196i
$715$	0.809995	−	1.40295i	0.0302921	−	0.0524675i
$716$		−	15.2611i		−	0.570333i
$717$	13.2770	+	4.74160i	0.495840	+	0.177078i
$718$	28.2685			1.05497
$719$	−7.58926	−	13.1450i	−0.283032	−	0.490225i	0.689098	−	0.724668i	$-0.258007\pi$
$719$	−7.58926	−	13.1450i	−0.283032	−	0.490225i	−0.972130	+	0.234443i	$0.924673\pi$
$720$	0.485129	−	2.96052i	0.0180797	−	0.110332i
$721$	3.42852	+	11.6835i	0.127685	+	0.435115i
$722$	4.21556	−	2.43386i	0.156887	−	0.0905787i
$723$	−8.85771	−	48.5149i	−0.329422	−	1.80429i
$724$	−21.4088	+	12.3604i	−0.795651	+	0.459369i
$725$	−2.38822	+	1.37884i	−0.0886961	+	0.0512087i
$726$	−17.6244	−	6.29416i	−0.654102	−	0.233598i
$727$	23.3867	−	13.5023i	0.867364	−	0.500773i	0.000892806	−	1.00000i	$-0.499716\pi$
$727$	23.3867	−	13.5023i	0.867364	−	0.500773i	0.866471	+	0.499227i	$0.166382\pi$
$728$	2.28898	−	9.42867i	0.0848353	−	0.349450i
$729$	12.6418	−	23.8576i	0.468214	−	0.883615i
$730$	5.56698	+	9.64229i	0.206043	+	0.356877i
$731$	0.462667			0.0171123
$732$	−4.04458	−	22.1527i	−0.149492	−	0.818788i
$733$			18.1508i			0.670416i	0.942144	+	0.335208i	$0.108807\pi$
$733$			18.1508i			0.670416i	−0.942144	+	0.335208i	$0.891193\pi$
$734$	−16.8301	+	29.1506i	−0.621210	+	1.07597i
$735$	−8.85915	+	8.27741i	−0.326775	+	0.305317i
$736$	−1.29782	−	2.24789i	−0.0478383	−	0.0828583i
$737$	−0.205617	+	0.118713i	−0.00757399	+	0.00437285i
$738$	−14.9536	+	18.2657i	−0.550449	+	0.672371i
$739$	2.83491	−	4.91021i	0.104284	−	0.180625i	−0.809162	−	0.587586i	$-0.800078\pi$
$739$	2.83491	−	4.91021i	0.104284	−	0.180625i	0.913445	+	0.406961i	$0.133412\pi$
$740$	0.0597017	−	0.103406i	0.00219468	−	0.00380129i
$741$	−23.4900	+	4.28873i	−0.862926	+	0.157550i
$742$	−0.181849	−	0.173449i	−0.00667590	−	0.00636751i
$743$	14.9685	+	8.64209i	0.549142	+	0.317047i	0.748776	−	0.662823i	$-0.230642\pi$
$743$	14.9685	+	8.64209i	0.549142	+	0.317047i	−0.199634	+	0.979871i	$0.563975\pi$
$744$	−9.81094	−	11.5495i	−0.359686	−	0.423424i
$745$		−	14.3445i		−	0.525543i
$746$	10.3698	+	5.98701i	0.379665	+	0.219200i
$747$	−19.9266	−	16.3133i	−0.729077	−	0.596874i
$748$			0.120250i			0.00439678i
$749$	−29.5672	+	30.9992i	−1.08036	+	1.13269i
$750$	1.63115	+	0.582530i	0.0595613	+	0.0212710i
$751$	−38.8281			−1.41686			−0.708429	−	0.705782i	$-0.750596\pi$
$751$	−38.8281			−1.41686			−0.708429	+	0.705782i	$0.750596\pi$
$752$	−3.94756	−	6.83738i	−0.143953	−	0.249334i
$753$	7.85584	−	1.43430i	0.286283	−	0.0522687i
$754$	8.75810	+	5.05649i	0.318951	+	0.184146i
$755$	−0.679789			−0.0247401
$756$	13.4164	+	3.00010i	0.487949	+	0.109113i
$757$	−33.5417			−1.21910			−0.609548	−	0.792749i	$-0.708649\pi$
$757$	−33.5417			−1.21910			−0.609548	+	0.792749i	$0.708649\pi$
$758$	9.49414	+	5.48144i	0.344843	+	0.199095i
$759$	1.95371	−	0.356703i	0.0709153	−	0.0129475i
$760$	−1.87965	−	3.25564i	−0.0681820	−	0.118095i
$761$	−26.6928			−0.967612			−0.483806	−	0.875175i	$-0.660746\pi$
$761$	−26.6928			−0.967612			−0.483806	+	0.875175i	$0.660746\pi$
$762$	34.4343	+	12.2975i	1.24742	+	0.445490i
$763$	−1.71157	+	7.05023i	−0.0619631	+	0.255236i
$764$		−	5.50470i		−	0.199153i
$765$	−0.132058	+	0.805891i	−0.00477458	+	0.0291370i
$766$	17.4289	+	10.0626i	0.629732	+	0.363576i
$767$			11.7741i			0.425139i
$768$	−1.12135	−	1.32006i	−0.0404634	−	0.0476336i
$769$	36.2335	+	20.9194i	1.30661	+	0.754373i	0.981529	−	0.191313i	$-0.0612744\pi$
$769$	36.2335	+	20.9194i	1.30661	+	0.754373i	0.325083	+	0.945685i	$0.394608\pi$
$770$	−0.275729	+	1.13577i	−0.00993658	+	0.0409303i
$771$	46.5069	−	8.49110i	1.67491	−	0.305799i
$772$	−7.52344	+	13.0310i	−0.270775	+	0.468995i
$773$	0.0374243	−	0.0648208i	0.00134606	−	0.00233144i	−0.865352	−	0.501165i	$-0.832905\pi$
$773$	0.0374243	−	0.0648208i	0.00134606	−	0.00233144i	0.866698	+	0.498834i	$0.166238\pi$
$774$	−1.80184	−	4.76997i	−0.0647657	−	0.171453i
$775$	7.57702	−	4.37459i	0.272175	−	0.157140i
$776$	7.46424	+	12.9284i	0.267951	+	0.464104i
$777$	0.457340	+	0.300401i	0.0164070	+	0.0107768i
$778$	13.6704	−	23.6779i	0.490109	−	0.848894i
$779$			29.5807i			1.05984i
$780$	−1.14083	−	6.24851i	−0.0408484	−	0.223733i
$781$	−1.65753			−0.0593110
$782$	0.353283	+	0.611905i	0.0126334	+	0.0218817i
$783$	−6.93806	+	12.5376i	−0.247946	+	0.448058i
$784$	0.330818	+	6.99218i	0.0118149	+	0.249721i
$785$	20.6832	−	11.9414i	0.738214	−	0.426208i
$786$	−8.29494	−	2.96235i	−0.295871	−	0.105664i
$787$	−28.9107	+	16.6916i	−1.03055	+	0.594991i	−0.917143	−	0.398557i	$-0.869511\pi$
$787$	−28.9107	+	16.6916i	−1.03055	+	0.594991i	−0.113411	+	0.993548i	$0.536178\pi$
$788$	−17.0247	+	9.82922i	−0.606480	+	0.350151i
$789$	9.30391	+	50.9588i	0.331228	+	1.81418i
$790$	−2.62224	+	1.51395i	−0.0932953	+	0.0538640i
$791$	−8.47705	−	2.05796i	−0.301409	−	0.0731726i
$792$	1.23975	−	0.468309i	0.0440525	−	0.0166406i
$793$	−23.8393	−	41.2908i	−0.846557	−	1.46628i
$794$	−15.6491			−0.555366
$795$	−0.154933	−	0.0553310i	−0.00549492	−	0.00196239i
$796$		−	10.6694i		−	0.378168i
$797$	−15.3572	+	26.5995i	−0.543980	+	0.942201i	0.454690	+	0.890650i	$0.349750\pi$
$797$	−15.3572	+	26.5995i	−0.543980	+	0.942201i	−0.998670	+	0.0515514i	$0.983583\pi$
$798$	15.3902	−	7.74088i	0.544805	−	0.274024i
$799$	1.07458	+	1.86122i	0.0380158	+	0.0658454i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−29.4863	−	24.1395i	−1.04185	−	0.852927i
$802$	−19.5763	+	33.9071i	−0.691262	+	1.19730i
$803$	−2.45921	+	4.25948i	−0.0867837	+	0.150314i
$804$	−0.313091	+	0.876690i	−0.0110419	+	0.0309185i
$805$	1.93371	+	6.58955i	0.0681544	+	0.232251i
$806$	−27.7865	−	16.0426i	−0.978739	−	0.565075i
$807$	7.96906	−	22.3143i	0.280524	−	0.785500i
$808$		−	4.57755i		−	0.161038i
$809$	−8.63831	−	4.98733i	−0.303707	−	0.175345i	0.340400	−	0.940281i	$-0.389437\pi$
$809$	−8.63831	−	4.98733i	−0.303707	−	0.175345i	−0.644107	+	0.764936i	$0.722771\pi$
$810$	8.82282	−	1.77702i	0.310002	−	0.0624383i
$811$			56.5329i			1.98514i	0.121685	+	0.992569i	$0.461170\pi$
$811$			56.5329i			1.98514i	−0.121685	+	0.992569i	$0.538830\pi$
$812$	−7.09018	−	1.72127i	−0.248816	−	0.0604047i
$813$	−4.18343	+	3.55370i	−0.146719	+	0.124634i
$814$	0.0527464			0.00184876
$815$	7.98983	+	13.8388i	0.279872	+	0.484752i
$816$	0.305247	+	0.359338i	0.0106858	+	0.0125794i
$817$	−5.53345	−	3.19474i	−0.193591	−	0.111770i
$818$	26.2289			0.917072
$819$	28.8876	−	3.57165i	1.00942	−	0.124804i
$820$	−7.86869			−0.274787
$821$	−35.7881	−	20.6622i	−1.24901	−	0.721117i	−0.278099	−	0.960552i	$-0.589704\pi$
$821$	−35.7881	−	20.6622i	−1.24901	−	0.721117i	−0.970912	+	0.239435i	$0.923038\pi$
$822$	7.94682	−	22.2520i	0.277177	−	0.776128i
$823$	13.5798	+	23.5209i	0.473363	+	0.819888i	0.999535	−	0.0304896i	$-0.00970664\pi$
$823$	13.5798	+	23.5209i	0.473363	+	0.819888i	−0.526172	+	0.850378i	$0.676373\pi$
$824$	4.60214			0.160323
$825$	0.137424	+	0.752691i	0.00478449	+	0.0262053i
$826$	−2.39188	−	8.15087i	−0.0832242	−	0.283605i
$827$			5.74951i			0.199930i	0.994991	+	0.0999650i	$0.0318731\pi$
$827$			5.74951i			0.199930i	−0.994991	+	0.0999650i	$0.968127\pi$
$828$	4.93273	−	6.02530i	0.171424	−	0.209394i
$829$	−26.3765	−	15.2285i	−0.916093	−	0.528907i	−0.0337068	−	0.999432i	$-0.510731\pi$
$829$	−26.3765	−	15.2285i	−0.916093	−	0.528907i	−0.882387	+	0.470525i	$0.844065\pi$
$830$		−	8.58419i		−	0.297962i
$831$	2.58581	−	0.472110i	0.0897009	−	0.0163773i
$832$	−3.17590	−	1.83361i	−0.110105	−	0.0635689i
$833$	−0.0900529	−	1.90336i	−0.00312015	−	0.0659476i
$834$	10.6523	+	12.5400i	0.368861	+	0.434224i
$835$	−2.36183	+	4.09080i	−0.0817344	+	0.141568i
$836$	0.830333	−	1.43818i	0.0287177	−	0.0497405i
$837$	22.0122	−	39.7777i	0.760851	−	1.37492i
$838$	−31.8342	+	18.3795i	−1.09970	+	0.634909i
$839$	−15.5311	−	26.9006i	−0.536193	−	0.928713i	−0.999105	−	0.0423086i	$-0.986529\pi$
$839$	−15.5311	−	26.9006i	−0.536193	−	0.928713i	0.462912	−	0.886404i	$-0.346805\pi$
$840$	2.05913	+	4.09389i	0.0710468	+	0.141253i
$841$	−10.6976	+	18.5288i	−0.368883	+	0.638925i
$842$		−	13.0949i		−	0.451282i
$843$	4.70932	−	4.00043i	0.162197	−	0.137782i
$844$	−1.16300			−0.0400321
$845$	−0.224227	−	0.388373i	−0.00771366	−	0.0133605i
$846$	15.0038	−	18.3271i	0.515842	−	0.630098i
$847$	27.4303	−	8.04945i	0.942516	−	0.276583i
$848$	−0.0822585	+	0.0474920i	−0.00282477	+	0.00163088i
$849$	17.4209	−	14.7985i	0.597884	−	0.507885i
$850$	−0.235743	+	0.136107i	−0.00808593	+	0.00466842i
$851$	0.268406	−	0.154964i	0.00920083	−	0.00531210i
$852$	−4.95312	+	4.20753i	−0.169691	+	0.144148i
$853$	−44.5942	+	25.7465i	−1.52688	+	0.881542i	−0.527385	+	0.849626i	$0.676827\pi$
$853$	−44.5942	+	25.7465i	−1.52688	+	0.881542i	−0.999491	+	0.0319155i	$0.989839\pi$
$854$	24.8913	+	23.7415i	0.851764	+	0.812417i
$855$	7.14413	−	8.72651i	0.244324	−	0.298440i
$856$	8.09579	+	14.0223i	0.276708	+	0.479273i
$857$	17.8647			0.610247			0.305123	−	0.952313i	$-0.401302\pi$
$857$	17.8647			0.610247			0.305123	+	0.952313i	$0.401302\pi$
$858$	2.13849	−	1.81658i	0.0730068	−	0.0620171i
$859$		−	1.26629i		−	0.0432054i	−0.999767	−	0.0216027i	$-0.993123\pi$
$859$		−	1.26629i		−	0.0432054i	0.999767	−	0.0216027i	$-0.00687689\pi$
$860$	0.849825	−	1.47194i	0.0289788	−	0.0501927i
$861$	2.07486	−	35.9991i	0.0707111	−	1.22685i
$862$	−10.3405	−	17.9103i	−0.352200	−	0.610028i
$863$	−35.3845	+	20.4293i	−1.20450	+	0.695420i	−0.961553	−	0.274619i	$-0.911448\pi$
$863$	−35.3845	+	20.4293i	−1.20450	+	0.695420i	−0.242949	+	0.970039i	$0.578115\pi$
$864$	2.51591	−	4.54645i	0.0855930	−	0.154673i
$865$	10.1399	−	17.5629i	0.344768	−	0.597156i
$866$	2.68264	−	4.64647i	0.0911599	−	0.157894i
$867$	18.9799	+	22.3432i	0.644592	+	0.758816i
$868$	22.4948	+	5.46102i	0.763523	+	0.185359i
$869$	−1.15838	−	0.668788i	−0.0392952	−	0.0226871i
$870$	−4.69876	+	0.857885i	−0.159303	+	0.0290850i
$871$			1.97101i			0.0667850i
$872$	2.37476	+	1.37107i	0.0804196	+	0.0464303i
$873$	−28.3699	+	34.6537i	−0.960177	+	1.17285i
$874$		−	9.75777i		−	0.330061i
$875$	−2.53870	+	0.744985i	−0.0858237	+	0.0251851i
$876$	3.46366	+	18.9710i	0.117026	+	0.640970i
$877$	20.0847			0.678213			0.339107	−	0.940748i	$-0.389875\pi$
$877$	20.0847			0.678213			0.339107	+	0.940748i	$0.389875\pi$
$878$	5.23979	+	9.07559i	0.176834	+	0.306286i
$879$	12.8445	−	35.9662i	0.433235	−	1.21311i
$880$	0.382566	+	0.220875i	0.0128963	+	0.00744569i
$881$	26.6064			0.896393			0.448196	−	0.893935i	$-0.352067\pi$
$881$	26.6064			0.896393			0.448196	+	0.893935i	$0.352067\pi$
$882$	−19.2725	+	8.34100i	−0.648938	+	0.280856i
$883$	−27.6319			−0.929887			−0.464943	−	0.885340i	$-0.653925\pi$
$883$	−27.6319			−0.929887			−0.464943	+	0.885340i	$0.653925\pi$
$884$	0.864522	+	0.499132i	0.0290770	+	0.0167876i
$885$	−3.60027	−	4.23825i	−0.121022	−	0.142467i
$886$	3.88871	+	6.73544i	0.130644	+	0.226282i
$887$	8.98710			0.301757			0.150879	−	0.988552i	$-0.451790\pi$
$887$	8.98710			0.301757			0.150879	+	0.988552i	$0.451790\pi$
$888$	0.157620	−	0.133894i	0.00528938	−	0.00449317i
$889$	−53.5930	+	15.7269i	−1.79745	+	0.527464i
$890$		−	12.7024i		−	0.425785i
$891$	2.62857	+	2.98282i	0.0880604	+	0.0999281i
$892$	−2.45476	−	1.41726i	−0.0821915	−	0.0474533i
$893$		−	29.6801i		−	0.993206i
$894$	8.35612	−	23.3981i	0.279470	−	0.782550i
$895$	13.2165	+	7.63053i	0.441778	+	0.255061i
$896$	2.57107	+	0.624174i	0.0858935	+	0.0208522i
$897$	5.54497	−	15.5266i	0.185141	−	0.518417i
$898$	−1.86702	+	3.23378i	−0.0623033	+	0.107912i
$899$	−12.0637	+	20.8949i	−0.402347	+	0.696885i
$900$	2.32132	+	1.90039i	0.0773772	+	0.0633464i
$901$	0.0223918	−	0.0129279i	0.000745981	−	0.000430692i
$902$	−1.73800	−	3.01030i	−0.0578689	−	0.100232i
$903$	6.51001	+	4.27606i	0.216640	+	0.142298i
$904$	−1.64854	+	2.85536i	−0.0548298	+	0.0949680i
$905$		−	24.7207i		−	0.821745i
$906$	−1.10884	−	0.395998i	−0.0368387	−	0.0131561i
$907$	30.2147			1.00326			0.501631	−	0.865081i	$-0.332733\pi$
$907$	30.2147			1.00326			0.501631	+	0.865081i	$0.332733\pi$
$908$	5.62480	+	9.74244i	0.186666	+	0.323314i
$909$	12.8467	−	4.85277i	0.426097	−	0.160956i
$910$	7.02097	+	6.69665i	0.232743	+	0.221992i
$911$	25.4482	−	14.6925i	0.843135	−	0.486784i	−0.0151935	−	0.999885i	$-0.504836\pi$
$911$	25.4482	−	14.6925i	0.843135	−	0.486784i	0.858329	+	0.513100i	$0.171503\pi$
$912$	−1.16948	−	6.40540i	−0.0387253	−	0.212104i
$913$	3.28402	−	1.89603i	0.108685	−	0.0627495i
$914$	2.51828	−	1.45393i	0.0832974	−	0.0480918i
$915$	21.2071	+	7.57365i	0.701085	+	0.250377i
$916$	14.0269	−	8.09843i	0.463462	−	0.267580i
$917$	12.9101	−	3.78849i	0.426329	−	0.125107i
$918$	−0.684863	+	1.23760i	−0.0226039	+	0.0408470i
$919$	15.7829	+	27.3368i	0.520630	+	0.901758i	0.999712	+	0.0239876i	$0.00763621\pi$
$919$	15.7829	+	27.3368i	0.520630	+	0.901758i	−0.479082	+	0.877770i	$0.659030\pi$
$920$	2.59564			0.0855757
$921$	−9.08687	−	49.7700i	−0.299422	−	1.63998i
$922$			9.76887i			0.321721i
$923$	−6.88003	+	11.9166i	−0.226459	+	0.392238i
$924$	−1.11138	+	1.69199i	−0.0365616	+	0.0556625i
$925$	0.0597017	+	0.103406i	0.00196298	+	0.00339998i
$926$	−2.48752	+	1.43617i	−0.0817451	+	0.0471956i
$927$	4.87884	+	12.9157i	0.160242	+	0.424206i
$928$	−1.37884	+	2.38822i	−0.0452625	+	0.0783970i
$929$	25.4122	−	44.0152i	0.833747	−	1.44409i	−0.0613000	−	0.998119i	$-0.519525\pi$
$929$	25.4122	−	44.0152i	0.833747	−	1.44409i	0.895047	−	0.445972i	$-0.147142\pi$
$930$	14.9076	−	2.72179i	0.488840	−	0.0892509i
$931$	−12.0658	+	23.3859i	−0.395441	+	0.766441i
$932$	3.21321	+	1.85515i	0.105252	+	0.0607673i
$933$	−27.8014	−	32.7279i	−0.910178	−	1.07146i
$934$		−	3.85910i		−	0.126274i
$935$	−0.104140	−	0.0601250i	−0.00340573	−	0.00196630i
$936$	1.77907	−	10.8568i	0.0581508	−	0.354867i
$937$			19.6915i			0.643294i	0.946860	+	0.321647i	$0.104236\pi$
$937$			19.6915i			0.643294i	−0.946860	+	0.321647i	$0.895764\pi$
$938$	−0.400405	−	1.36447i	−0.0130737	−	0.0445514i
$939$	−55.2825	−	19.7429i	−1.80407	−	0.644286i
$940$	7.89512			0.257511
$941$	13.5916	+	23.5413i	0.443072	+	0.767424i	0.997916	−	0.0645309i	$-0.0205551\pi$
$941$	13.5916	+	23.5413i	0.443072	+	0.767424i	−0.554843	+	0.831955i	$0.687222\pi$
$942$	40.6937	−	7.42973i	1.32587	−	0.242074i
$943$	−17.6879	−	10.2121i	−0.575999	−	0.332553i
$944$	−3.21065			−0.104498
$945$	−9.30636	+	10.1189i	−0.302736	+	0.329167i
$946$	0.750819			0.0244112
$947$	−6.80067	−	3.92637i	−0.220992	−	0.127590i	0.385418	−	0.922742i	$-0.374057\pi$
$947$	−6.80067	−	3.92637i	−0.220992	−	0.127590i	−0.606409	+	0.795153i	$0.707391\pi$
$948$	−5.15920	+	0.941952i	−0.167563	+	0.0305932i
$949$	20.4153	+	35.3603i	0.662709	+	1.14784i
$950$	3.75929			0.121968
$951$	55.7487	+	19.9094i	1.80778	+	0.645607i
$952$	−0.699879	−	0.169908i	−0.0226832	−	0.00550676i
$953$			14.7756i			0.478628i	0.970942	+	0.239314i	$0.0769225\pi$
$953$			14.7756i			0.478628i	−0.970942	+	0.239314i	$0.923078\pi$
$954$	−0.220488	−	0.180507i	−0.00713856	−	0.00584412i
$955$	4.76721	+	2.75235i	0.154263	+	0.0890639i
$956$			8.13967i			0.263256i
$957$	−1.36604	−	1.60810i	−0.0441577	−	0.0519826i
$958$	14.1411	+	8.16437i	0.456878	+	0.263779i
$959$	10.1630	+	34.6327i	0.328181	+	1.11835i
$960$	1.70388	−	0.311090i	0.0549926	−	0.0100404i
$961$	22.7741	−	39.4460i	0.734649	−	1.27245i
$962$	0.218939	−	0.379213i	0.00705887	−	0.0122263i
$963$	−30.7703	+	37.5858i	−0.991561	+	1.21119i
$964$	24.6585	−	14.2366i	0.794195	−	0.458529i
$965$	−7.52344	−	13.0310i	−0.242188	−	0.419482i
$966$	−0.684433	+	11.8750i	−0.0220213	+	0.382072i
$967$	11.9085	−	20.6261i	0.382950	−	0.663290i	−0.608532	−	0.793529i	$-0.708241\pi$
$967$	11.9085	−	20.6261i	0.382950	−	0.663290i	0.991483	+	0.130240i	$0.0415747\pi$
$968$		−	10.8049i		−	0.347281i
$969$	0.318348	+	1.74363i	0.0102268	+	0.0560136i
$970$	−14.9285			−0.479324
$971$	−14.5985	−	25.2854i	−0.468489	−	0.811446i	0.530863	−	0.847458i	$-0.321868\pi$
$971$	−14.5985	−	25.2854i	−0.468489	−	0.811446i	−0.999351	+	0.0360115i	$0.988535\pi$
$972$	15.4265	+	2.24096i	0.494806	+	0.0718789i
$973$	−24.4240	−	5.92936i	−0.782997	−	0.190087i
$974$	−12.2254	+	7.05835i	−0.391728	+	0.226164i
$975$	5.98178	+	2.13626i	0.191570	+	0.0684152i
$976$	11.2595	−	6.50065i	0.360406	−	0.208081i
$977$	−26.9080	+	15.5354i	−0.860864	+	0.497020i	−0.864302	−	0.502974i	$-0.832239\pi$
$977$	−26.9080	+	15.5354i	−0.860864	+	0.497020i	0.00343741	+	0.999994i	$0.498906\pi$
$978$	4.97112	+	27.2275i	0.158959	+	0.870640i
$979$	4.85950	−	2.80564i	0.155310	−	0.0896685i
$980$	−6.22081	−	3.20959i	−0.198717	−	0.102527i
$981$	−1.33029	+	8.11814i	−0.0424729	+	0.259192i
$982$	5.19839	+	9.00388i	0.165887	+	0.287325i
$983$	30.3387			0.967654			0.483827	−	0.875164i	$-0.339246\pi$
$983$	30.3387			0.967654			0.483827	+	0.875164i	$0.339246\pi$
$984$	−12.8350	−	4.58375i	−0.409166	−	0.146125i
$985$		−	19.6584i		−	0.626370i
$986$	0.375337	−	0.650104i	0.0119532	−	0.0207035i
$987$	−2.08183	+	36.1201i	−0.0662655	+	1.14971i
$988$	−6.89307	−	11.9391i	−0.219298	−	0.379835i
$989$	3.82062	−	2.20584i	0.121489	−	0.0701416i
$990$	−0.214306	+	1.30781i	−0.00681108	+	0.0415648i
$991$	14.0266	−	24.2947i	0.445568	−	0.771747i	−0.552523	−	0.833497i	$-0.686335\pi$
$991$	14.0266	−	24.2947i	0.445568	−	0.771747i	0.998092	+	0.0617506i	$0.0196683\pi$
$992$	4.37459	−	7.57702i	0.138893	−	0.240571i
$993$	10.5952	−	29.6677i	0.336227	−	0.941475i
$994$	2.34202	−	9.64713i	0.0742843	−	0.305989i
$995$	9.23999	+	5.33471i	0.292927	+	0.169122i
$996$	5.00055	−	14.0021i	0.158449	−	0.443674i
$997$			30.1817i			0.955863i	0.878397	+	0.477931i	$0.158613\pi$
$997$			30.1817i			0.955863i	−0.878397	+	0.477931i	$0.841387\pi$
$998$	13.7516	+	7.93948i	0.435299	+	0.251320i
$999$	0.542862	+	0.300408i	0.0171754	+	0.00950449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.311.7	✓	28
3.2	odd	2		1890.2.t.b.1151.10		28
7.5	odd	6		630.2.bk.b.131.11	yes	28
9.2	odd	6		630.2.bk.b.101.4	yes	28
9.7	even	3		1890.2.bk.b.521.8		28
21.5	even	6		1890.2.bk.b.341.8		28
63.47	even	6	inner	630.2.t.b.551.7	yes	28
63.61	odd	6		1890.2.t.b.1601.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.7	✓	28	1.1	even	1	trivial
630.2.t.b.551.7	yes	28	63.47	even	6	inner
630.2.bk.b.101.4	yes	28	9.2	odd	6
630.2.bk.b.131.11	yes	28	7.5	odd	6
1890.2.t.b.1151.10		28	3.2	odd	2
1890.2.t.b.1601.10		28	63.61	odd	6
1890.2.bk.b.341.8		28	21.5	even	6
1890.2.bk.b.521.8		28	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.70388 - 0.311090i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.63115 - 0.582530i) q^{6} +(2.53870 - 0.744985i) q^{7} -1.00000i q^{8} +(2.80645 - 1.06012i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.70388 - 0.311090i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.63115 - 0.582530i) q^{6} +(2.53870 - 0.744985i) q^{7} -1.00000i q^{8} +(2.80645 - 1.06012i) q^{9} +(0.866025 + 0.500000i) q^{10} +0.441750i q^{11} +(1.12135 + 1.32006i) q^{12} +(3.17590 + 1.83361i) q^{13} +(-2.57107 - 0.624174i) q^{14} +(-1.70388 + 0.311090i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.136107 - 0.235743i) q^{17} +(-2.96052 - 0.485129i) q^{18} +(-3.25564 + 1.87965i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(4.09389 - 2.05913i) q^{21} +(0.220875 - 0.382566i) q^{22} -2.59564i q^{23} +(-0.311090 - 1.70388i) q^{24} +1.00000 q^{25} +(-1.83361 - 3.17590i) q^{26} +(4.45207 - 2.67939i) q^{27} +(1.91453 + 1.82609i) q^{28} +(-2.38822 + 1.37884i) q^{29} +(1.63115 + 0.582530i) q^{30} +(7.57702 - 4.37459i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.137424 + 0.752691i) q^{33} +(-0.235743 + 0.136107i) q^{34} +(-2.53870 + 0.744985i) q^{35} +(2.32132 + 1.90039i) q^{36} +(0.0597017 + 0.103406i) q^{37} +3.75929 q^{38} +(5.98178 + 2.13626i) q^{39} +1.00000i q^{40} +(3.93435 - 6.81449i) q^{41} +(-4.57498 - 0.263686i) q^{42} +(0.849825 + 1.47194i) q^{43} +(-0.382566 + 0.220875i) q^{44} +(-2.80645 + 1.06012i) q^{45} +(-1.29782 + 2.24789i) q^{46} +(-3.94756 + 6.83738i) q^{47} +(-0.582530 + 1.63115i) q^{48} +(5.89000 - 3.78259i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(0.158572 - 0.444021i) q^{51} +3.66721i q^{52} +(0.0822585 + 0.0474920i) q^{53} +(-5.19530 + 0.0943837i) q^{54} -0.441750i q^{55} +(-0.744985 - 2.53870i) q^{56} +(-4.96250 + 4.21550i) q^{57} +2.75767 q^{58} +(1.60532 + 2.78050i) q^{59} +(-1.12135 - 1.32006i) q^{60} +(-11.2595 - 6.50065i) q^{61} -8.74919 q^{62} +(6.33495 - 4.78210i) q^{63} -1.00000 q^{64} +(-3.17590 - 1.83361i) q^{65} +(0.257333 - 0.720561i) q^{66} +(0.268733 + 0.465460i) q^{67} +0.272213 q^{68} +(-0.807478 - 4.42267i) q^{69} +(2.57107 + 0.624174i) q^{70} +3.75218i q^{71} +(-1.06012 - 2.80645i) q^{72} +(9.64229 + 5.56698i) q^{73} -0.119403i q^{74} +(1.70388 - 0.311090i) q^{75} +(-3.25564 - 1.87965i) q^{76} +(0.329097 + 1.12147i) q^{77} +(-4.11225 - 4.84095i) q^{78} +(-1.51395 + 2.62224i) q^{79} +(0.500000 - 0.866025i) q^{80} +(6.75228 - 5.95036i) q^{81} +(-6.81449 + 3.93435i) q^{82} +(-4.29210 - 7.43413i) q^{83} +(3.83021 + 2.51585i) q^{84} +(-0.136107 + 0.235743i) q^{85} -1.69965i q^{86} +(-3.64030 + 3.09233i) q^{87} +0.441750 q^{88} +(-6.35119 - 11.0006i) q^{89} +(2.96052 + 0.485129i) q^{90} +(9.42867 + 2.28898i) q^{91} +(2.24789 - 1.29782i) q^{92} +(11.5495 - 9.81094i) q^{93} +(6.83738 - 3.94756i) q^{94} +(3.25564 - 1.87965i) q^{95} +(1.32006 - 1.12135i) q^{96} +(-12.9284 + 7.46424i) q^{97} +(-6.99218 + 0.330818i) q^{98} +(0.468309 + 1.23975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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