LMFDB - Embedded newform 1050.2.d.g.1049.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(1049,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.1049");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.d (of order $2$, degree $1$, not 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
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} + 4x^{8} - 30x^{6} + 36x^{4} + 729 $ x^12 + 4x^8 - 30x^6 + 36*x^4 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1049.6
Root			$-1.68439 - 0.403509i$ of defining polynomial
Character	$\chi$	$=$	1050.1049
Dual form			1050.2.d.g.1049.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.403509 + 1.68439i) q^{3} +1.00000 q^{4} +(0.403509 - 1.68439i) q^{6} +(1.28088 + 2.31502i) q^{7} -1.00000 q^{8} +(-2.67436 - 1.35934i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.403509 + 1.68439i) q^{3} +1.00000 q^{4} +(0.403509 - 1.68439i) q^{6} +(1.28088 + 2.31502i) q^{7} -1.00000 q^{8} +(-2.67436 - 1.35934i) q^{9} -5.34872i q^{11} +(-0.403509 + 1.68439i) q^{12} +3.95617 q^{13} +(-1.28088 - 2.31502i) q^{14} +1.00000 q^{16} -7.32496i q^{17} +(2.67436 + 1.35934i) q^{18} -0.807019i q^{19} +(-4.41626 + 1.22338i) q^{21} +5.34872i q^{22} -0.281327 q^{23} +(0.403509 - 1.68439i) q^{24} -3.95617 q^{26} +(3.36879 - 3.95617i) q^{27} +(1.28088 + 2.31502i) q^{28} -0.281327i q^{29} -9.07971i q^{31} -1.00000 q^{32} +(9.00935 + 2.15826i) q^{33} +7.32496i q^{34} +(-2.67436 - 1.35934i) q^{36} -6.06739i q^{37} +0.807019i q^{38} +(-1.59635 + 6.66375i) q^{39} +6.15019 q^{41} +(4.41626 - 1.22338i) q^{42} +6.34872i q^{43} -5.34872i q^{44} +0.281327 q^{46} +5.78984i q^{47} +(-0.403509 + 1.68439i) q^{48} +(-3.71867 + 5.93055i) q^{49} +(12.3381 + 2.95569i) q^{51} +3.95617 q^{52} -10.9788 q^{53} +(-3.36879 + 3.95617i) q^{54} +(-1.28088 - 2.31502i) q^{56} +(1.35934 + 0.325639i) q^{57} +0.281327i q^{58} +4.90390 q^{59} -13.2555i q^{61} +9.07971i q^{62} +(-0.278649 - 7.93236i) q^{63} +1.00000 q^{64} +(-9.00935 - 2.15826i) q^{66} +6.71867i q^{67} -7.32496i q^{68} +(0.113518 - 0.473865i) q^{69} +3.36995i q^{71} +(2.67436 + 1.35934i) q^{72} -4.98282 q^{73} +6.06739i q^{74} -0.807019i q^{76} +(12.3824 - 6.85109i) q^{77} +(1.59635 - 6.66375i) q^{78} +3.26010 q^{79} +(5.30441 + 7.27071i) q^{81} -6.15019 q^{82} -1.53511i q^{83} +(-4.41626 + 1.22338i) q^{84} -6.34872i q^{86} +(0.473865 + 0.113518i) q^{87} +5.34872i q^{88} +4.31652 q^{89} +(5.06739 + 9.15863i) q^{91} -0.281327 q^{92} +(15.2938 + 3.66375i) q^{93} -5.78984i q^{94} +(0.403509 - 1.68439i) q^{96} +15.0892 q^{97} +(3.71867 - 5.93055i) q^{98} +(-7.27071 + 14.3044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8	$ 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8} + 12 q^{16} + 14 q^{21} - 20 q^{23} - 12 q^{32} - 12 q^{39} - 14 q^{42} + 20 q^{46} - 28 q^{49} + 28 q^{51} - 20 q^{53} + 8 q^{57} - 30 q^{63} + 12 q^{64} + 44 q^{77} + 12 q^{78} - 56 q^{79} - 16 q^{81} + 14 q^{84} - 20 q^{91} - 20 q^{92} + 48 q^{93} + 28 q^{98} - 48 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8 + 12 * q^16 + 14 * q^21 - 20 * q^23 - 12 * q^32 - 12 * q^39 - 14 * q^42 + 20 * q^46 - 28 * q^49 + 28 * q^51 - 20 * q^53 + 8 * q^57 - 30 * q^63 + 12 * q^64 + 44 * q^77 + 12 * q^78 - 56 * q^79 - 16 * q^81 + 14 * q^84 - 20 * q^91 - 20 * q^92 + 48 * q^93 + 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.403509	+	1.68439i	−0.232966	+	0.972485i
$3$	−0.403509	+	1.68439i	−0.232966	+	0.972485i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	0.403509	−	1.68439i	0.164732	−	0.687651i
$7$	1.28088	+	2.31502i	0.484129	+	0.874997i
$7$	1.28088	+	2.31502i	0.484129	+	0.874997i
$8$	−1.00000			−0.353553
$9$	−2.67436	−	1.35934i	−0.891454	−	0.453112i
$10$		0			0
$11$		−	5.34872i		−	1.61270i	−0.591439	−	0.806350i	$-0.701440\pi$
$11$		−	5.34872i		−	1.61270i	0.591439	−	0.806350i	$-0.298560\pi$
$12$	−0.403509	+	1.68439i	−0.116483	+	0.486242i
$13$	3.95617			1.09724			0.548622	−	0.836070i	$-0.315153\pi$
$13$	3.95617			1.09724			0.548622	+	0.836070i	$0.315153\pi$
$14$	−1.28088	−	2.31502i	−0.342331	−	0.618716i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	7.32496i		−	1.77656i	−0.459300	−	0.888281i	$-0.651900\pi$
$17$		−	7.32496i		−	1.77656i	0.459300	−	0.888281i	$-0.348100\pi$
$18$	2.67436	+	1.35934i	0.630353	+	0.320399i
$19$		−	0.807019i		−	0.185143i	−0.995706	−	0.0925714i	$-0.970491\pi$
$19$		−	0.807019i		−	0.185143i	0.995706	−	0.0925714i	$-0.0295086\pi$
$20$		0			0
$21$	−4.41626	+	1.22338i	−0.963707	+	0.266963i
$22$			5.34872i			1.14035i
$23$	−0.281327			−0.0586607			−0.0293304	−	0.999570i	$-0.509337\pi$
$23$	−0.281327			−0.0586607			−0.0293304	+	0.999570i	$0.509337\pi$
$24$	0.403509	−	1.68439i	0.0823660	−	0.343825i
$25$		0			0
$26$	−3.95617			−0.775869
$27$	3.36879	−	3.95617i	0.648323	−	0.761365i
$28$	1.28088	+	2.31502i	0.242064	+	0.437498i
$29$		−	0.281327i		−	0.0522411i	−0.999659	−	0.0261206i	$-0.991685\pi$
$29$		−	0.281327i		−	0.0522411i	0.999659	−	0.0261206i	$-0.00831538\pi$
$30$		0			0
$31$		−	9.07971i		−	1.63076i	−0.578924	−	0.815382i	$-0.696527\pi$
$31$		−	9.07971i		−	1.63076i	0.578924	−	0.815382i	$-0.303473\pi$
$32$	−1.00000			−0.176777
$33$	9.00935	+	2.15826i	1.56833	+	0.375705i
$34$			7.32496i			1.25622i
$35$		0			0
$36$	−2.67436	−	1.35934i	−0.445727	−	0.226556i
$37$		−	6.06739i		−	0.997473i	−0.866754	−	0.498737i	$-0.833797\pi$
$37$		−	6.06739i		−	0.997473i	0.866754	−	0.498737i	$-0.166203\pi$
$38$			0.807019i			0.130916i
$39$	−1.59635	+	6.66375i	−0.255621	+	1.06705i
$40$		0			0
$41$	6.15019			0.960498			0.480249	−	0.877132i	$-0.340546\pi$
$41$	6.15019			0.960498			0.480249	+	0.877132i	$0.340546\pi$
$42$	4.41626	−	1.22338i	0.681444	−	0.188771i
$43$			6.34872i			0.968171i	0.875021	+	0.484085i	$0.160848\pi$
$43$			6.34872i			0.968171i	−0.875021	+	0.484085i	$0.839152\pi$
$44$		−	5.34872i		−	0.806350i
$45$		0			0
$46$	0.281327			0.0414794
$47$			5.78984i			0.844535i	0.906471	+	0.422268i	$0.138766\pi$
$47$			5.78984i			0.844535i	−0.906471	+	0.422268i	$0.861234\pi$
$48$	−0.403509	+	1.68439i	−0.0582415	+	0.243121i
$49$	−3.71867	+	5.93055i	−0.531239	+	0.847222i
$50$		0			0
$51$	12.3381	+	2.95569i	1.72768	+	0.413879i
$52$	3.95617			0.548622
$53$	−10.9788			−1.50805			−0.754025	−	0.656846i	$-0.771890\pi$
$53$	−10.9788			−1.50805			−0.754025	+	0.656846i	$0.771890\pi$
$54$	−3.36879	+	3.95617i	−0.458434	+	0.538367i
$55$		0			0
$56$	−1.28088	−	2.31502i	−0.171165	−	0.309358i
$57$	1.35934	+	0.325639i	0.180049	+	0.0431320i
$58$			0.281327i			0.0369401i
$59$	4.90390			0.638433			0.319217	−	0.947682i	$-0.396580\pi$
$59$	4.90390			0.638433			0.319217	+	0.947682i	$0.396580\pi$
$60$		0			0
$61$		−	13.2555i		−	1.69719i	−0.529040	−	0.848597i	$-0.677448\pi$
$61$		−	13.2555i		−	1.69719i	0.529040	−	0.848597i	$-0.322552\pi$
$62$			9.07971i			1.15312i
$63$	−0.278649	−	7.93236i	−0.0351064	−	0.999384i
$64$	1.00000			0.125000
$65$		0			0
$66$	−9.00935	−	2.15826i	−1.10897	−	0.265663i
$67$			6.71867i			0.820817i	0.911902	+	0.410408i	$0.134614\pi$
$67$			6.71867i			0.820817i	−0.911902	+	0.410408i	$0.865386\pi$
$68$		−	7.32496i		−	0.888281i
$69$	0.113518	−	0.473865i	0.0136660	−	0.0570467i
$70$		0			0
$71$			3.36995i			0.399940i	0.979802	+	0.199970i	$0.0640844\pi$
$71$			3.36995i			0.399940i	−0.979802	+	0.199970i	$0.935916\pi$
$72$	2.67436	+	1.35934i	0.315176	+	0.160199i
$73$	−4.98282			−0.583195			−0.291598	−	0.956541i	$-0.594187\pi$
$73$	−4.98282			−0.583195			−0.291598	+	0.956541i	$0.594187\pi$
$74$			6.06739i			0.705320i
$75$		0			0
$76$		−	0.807019i		−	0.0925714i
$77$	12.3824	−	6.85109i	1.41111	−	0.780754i
$78$	1.59635	−	6.66375i	0.180751	−	0.754521i
$79$	3.26010			0.366789			0.183395	−	0.983039i	$-0.441291\pi$
$79$	3.26010			0.366789			0.183395	+	0.983039i	$0.441291\pi$
$80$		0			0
$81$	5.30441	+	7.27071i	0.589379	+	0.807857i
$82$	−6.15019			−0.679175
$83$		−	1.53511i		−	0.168501i	−0.996445	−	0.0842503i	$-0.973150\pi$
$83$		−	1.53511i		−	0.168501i	0.996445	−	0.0842503i	$-0.0268495\pi$
$84$	−4.41626	+	1.22338i	−0.481853	+	0.133482i
$85$		0			0
$86$		−	6.34872i		−	0.684600i
$87$	0.473865	+	0.113518i	0.0508037	+	0.0121704i
$88$			5.34872i			0.570176i
$89$	4.31652			0.457550			0.228775	−	0.973479i	$-0.426528\pi$
$89$	4.31652			0.457550			0.228775	+	0.973479i	$0.426528\pi$
$90$		0			0
$91$	5.06739	+	9.15863i	0.531207	+	0.960085i
$92$	−0.281327			−0.0293304
$93$	15.2938	+	3.66375i	1.58589	+	0.379913i
$94$		−	5.78984i		−	0.597177i
$95$		0			0
$96$	0.403509	−	1.68439i	0.0411830	−	0.171913i
$97$	15.0892			1.53207			0.766037	−	0.642796i	$-0.222226\pi$
$97$	15.0892			1.53207			0.766037	+	0.642796i	$0.222226\pi$
$98$	3.71867	−	5.93055i	0.375643	−	0.599076i
$99$	−7.27071	+	14.3044i	−0.730734	+	1.43765i
$100$		0			0
$101$	−5.78984			−0.576111			−0.288055	−	0.957614i	$-0.593009\pi$
$101$	−5.78984			−0.576111			−0.288055	+	0.957614i	$0.593009\pi$
$102$	−12.3381	−	2.95569i	−1.22165	−	0.292657i
$103$	6.95721			0.685514			0.342757	−	0.939424i	$-0.388639\pi$
$103$	6.95721			0.685514			0.342757	+	0.939424i	$0.388639\pi$
$104$	−3.95617			−0.387934
$105$		0			0
$106$	10.9788			1.06635
$107$	10.6088			1.02559			0.512797	−	0.858510i	$-0.328610\pi$
$107$	10.6088			1.02559			0.512797	+	0.858510i	$0.328610\pi$
$108$	3.36879	−	3.95617i	0.324162	−	0.380683i
$109$	18.1348			1.73700			0.868499	−	0.495691i	$-0.165085\pi$
$109$	18.1348			1.73700			0.868499	+	0.495691i	$0.165085\pi$
$110$		0			0
$111$	10.2199	+	2.44825i	0.970028	+	0.232378i
$112$	1.28088	+	2.31502i	0.121032	+	0.218749i
$113$	−8.54142			−0.803510			−0.401755	−	0.915747i	$-0.631600\pi$
$113$	−8.54142			−0.803510			−0.401755	+	0.915747i	$0.631600\pi$
$114$	−1.35934	−	0.325639i	−0.127314	−	0.0304989i
$115$		0			0
$116$		−	0.281327i		−	0.0261206i
$117$	−10.5802	−	5.37777i	−0.978142	−	0.497175i
$118$	−4.90390			−0.451441
$119$	16.9574	−	9.38242i	1.55449	−	0.860085i
$120$		0			0
$121$	−17.6088			−1.60080
$122$			13.2555i			1.20010i
$123$	−2.48166	+	10.3593i	−0.223764	+	0.934070i
$124$		−	9.07971i		−	0.815382i
$125$		0			0
$126$	0.278649	+	7.93236i	0.0248240	+	0.706671i
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	−1.00000			−0.0883883
$129$	−10.6937	−	2.56177i	−0.941532	−	0.225551i
$130$		0			0
$131$	16.5454			1.44558			0.722788	−	0.691070i	$-0.242860\pi$
$131$	16.5454			1.44558			0.722788	+	0.691070i	$0.242860\pi$
$132$	9.00935	+	2.15826i	0.784163	+	0.187852i
$133$	1.86827	−	1.03370i	0.161999	−	0.0896329i
$134$		−	6.71867i		−	0.580405i
$135$		0			0
$136$			7.32496i			0.628110i
$137$	−7.41612			−0.633601			−0.316801	−	0.948492i	$-0.602609\pi$
$137$	−7.41612			−0.633601			−0.316801	+	0.948492i	$0.602609\pi$
$138$	−0.113518	+	0.473865i	−0.00966330	+	0.0403381i
$139$			6.36982i			0.540281i	0.962821	+	0.270141i	$0.0870702\pi$
$139$			6.36982i			0.540281i	−0.962821	+	0.270141i	$0.912930\pi$
$140$		0			0
$141$	−9.75237	−	2.33625i	−0.821298	−	0.196748i
$142$		−	3.36995i		−	0.282800i
$143$		−	21.1604i		−	1.76953i
$144$	−2.67436	−	1.35934i	−0.222863	−	0.113278i
$145$		0			0
$146$	4.98282			0.412381
$147$	−8.48887	−	8.65674i	−0.700150	−	0.713996i
$148$		−	6.06739i		−	0.498737i
$149$		−	7.60882i		−	0.623339i	−0.950191	−	0.311669i	$-0.899112\pi$
$149$		−	7.60882i		−	0.623339i	0.950191	−	0.311669i	$-0.100888\pi$
$150$		0			0
$151$	−4.63005			−0.376788			−0.188394	−	0.982094i	$-0.560328\pi$
$151$	−4.63005			−0.376788			−0.188394	+	0.982094i	$0.560328\pi$
$152$			0.807019i			0.0654578i
$153$	−9.95708	+	19.5896i	−0.804982	+	1.58372i
$154$	−12.3824	+	6.85109i	−0.997804	+	0.552077i
$155$		0			0
$156$	−1.59635	+	6.66375i	−0.127810	+	0.533527i
$157$	−15.3162			−1.22237			−0.611184	−	0.791489i	$-0.709306\pi$
$157$	−15.3162			−1.22237			−0.611184	+	0.791489i	$0.709306\pi$
$158$	−3.26010			−0.259359
$159$	4.43004	−	18.4926i	0.351325	−	1.46656i
$160$		0			0
$161$	−0.360347	−	0.651279i	−0.0283993	−	0.0513280i
$162$	−5.30441	−	7.27071i	−0.416754	−	0.571241i
$163$		−	3.06739i		−	0.240257i	−0.992758	−	0.120128i	$-0.961669\pi$
$163$		−	3.06739i		−	0.240257i	0.992758	−	0.120128i	$-0.0383306\pi$
$164$	6.15019			0.480249
$165$		0			0
$166$			1.53511i			0.119148i
$167$			1.89546i			0.146675i	0.997307	+	0.0733376i	$0.0233651\pi$
$167$			1.89546i			0.146675i	−0.997307	+	0.0733376i	$0.976635\pi$
$168$	4.41626	−	1.22338i	0.340722	−	0.0943857i
$169$	2.65128			0.203945
$170$		0			0
$171$	−1.09701	+	2.15826i	−0.0838904	+	0.165046i
$172$			6.34872i			0.484085i
$173$			8.86007i			0.673619i	0.941573	+	0.336809i	$0.109348\pi$
$173$			8.86007i			0.673619i	−0.941573	+	0.336809i	$0.890652\pi$
$174$	−0.473865	−	0.113518i	−0.0359236	−	0.00860578i
$175$		0			0
$176$		−	5.34872i		−	0.403175i
$177$	−1.97877	+	8.26010i	−0.148733	+	0.620867i
$178$	−4.31652			−0.323537
$179$			11.3487i			0.848243i	0.905605	+	0.424122i	$0.139417\pi$
$179$			11.3487i			0.848243i	−0.905605	+	0.424122i	$0.860583\pi$
$180$		0			0
$181$			8.63303i			0.641688i	0.947132	+	0.320844i	$0.103967\pi$
$181$			8.63303i			0.641688i	−0.947132	+	0.320844i	$0.896033\pi$
$182$	−5.06739	−	9.15863i	−0.375620	−	0.678883i
$183$	22.3275	+	5.34872i	1.65050	+	0.395389i
$184$	0.281327			0.0207397
$185$		0			0
$186$	−15.2938	−	3.66375i	−1.12140	−	0.268639i
$187$	−39.1791			−2.86506
$188$			5.78984i			0.422268i
$189$	13.4737	+	2.73143i	0.980064	+	0.198682i
$190$		0			0
$191$			7.78607i			0.563380i	0.959505	+	0.281690i	$0.0908950\pi$
$191$			7.78607i			0.563380i	−0.959505	+	0.281690i	$0.909105\pi$
$192$	−0.403509	+	1.68439i	−0.0291208	+	0.121561i
$193$		−	25.1715i		−	1.81188i	−0.423404	−	0.905941i	$-0.639165\pi$
$193$		−	25.1715i		−	1.81188i	0.423404	−	0.905941i	$-0.360835\pi$
$194$	−15.0892			−1.08334
$195$		0			0
$196$	−3.71867	+	5.93055i	−0.265619	+	0.423611i
$197$	−2.52597			−0.179968			−0.0899840	−	0.995943i	$-0.528682\pi$
$197$	−2.52597			−0.179968			−0.0899840	+	0.995943i	$0.528682\pi$
$198$	7.27071	−	14.3044i	0.516707	−	1.01657i
$199$		−	0.947731i		−	0.0671828i	−0.999436	−	0.0335914i	$-0.989306\pi$
$199$		−	0.947731i		−	0.0671828i	0.999436	−	0.0335914i	$-0.0106945\pi$
$200$		0			0
$201$	−11.3169	−	2.71105i	−0.798232	−	0.191222i
$202$	5.78984			0.407372
$203$	0.651279	−	0.360347i	0.0457108	−	0.0252914i
$204$	12.3381	+	2.95569i	0.863840	+	0.206940i
$205$		0			0
$206$	−6.95721			−0.484732
$207$	0.752370	+	0.382418i	0.0522933	+	0.0265799i
$208$	3.95617			0.274311
$209$	−4.31652			−0.298580
$210$		0			0
$211$	−12.8901			−0.887394			−0.443697	−	0.896177i	$-0.646333\pi$
$211$	−12.8901			−0.887394			−0.443697	+	0.896177i	$0.646333\pi$
$212$	−10.9788			−0.754025
$213$	−5.67632	−	1.35981i	−0.388935	−	0.0931724i
$214$	−10.6088			−0.725204
$215$		0			0
$216$	−3.36879	+	3.95617i	−0.229217	+	0.269183i
$217$	21.0197	−	11.6300i	1.42691	−	0.789499i
$218$	−18.1348			−1.22824
$219$	2.01062	−	8.39303i	0.135865	−	0.567149i
$220$		0			0
$221$		−	28.9788i		−	1.94932i
$222$	−10.2199	−	2.44825i	−0.685913	−	0.164316i
$223$	−23.7296			−1.58905			−0.794526	−	0.607230i	$-0.792281\pi$
$223$	−23.7296			−1.58905			−0.794526	+	0.607230i	$0.792281\pi$
$224$	−1.28088	−	2.31502i	−0.0855827	−	0.154679i
$225$		0			0
$226$	8.54142			0.568167
$227$		−	10.4667i		−	0.694700i	−0.937736	−	0.347350i	$-0.887082\pi$
$227$		−	10.4667i		−	0.694700i	0.937736	−	0.347350i	$-0.112918\pi$
$228$	1.35934	+	0.325639i	0.0900243	+	0.0215660i
$229$		−	16.4762i		−	1.08878i	−0.838833	−	0.544388i	$-0.816762\pi$
$229$		−	16.4762i		−	1.08878i	0.838833	−	0.544388i	$-0.183238\pi$
$230$		0			0
$231$	6.54351	+	23.6213i	0.430531	+	1.55417i
$232$			0.281327i			0.0184700i
$233$	−27.9575			−1.83156			−0.915780	−	0.401681i	$-0.868426\pi$
$233$	−27.9575			−1.83156			−0.915780	+	0.401681i	$0.868426\pi$
$234$	10.5802	+	5.37777i	0.691651	+	0.351556i
$235$		0			0
$236$	4.90390			0.319217
$237$	−1.31548	+	5.49128i	−0.0854495	+	0.356697i
$238$	−16.9574	+	9.38242i	−1.09919	+	0.608172i
$239$		−	17.2601i		−	1.11646i	−0.829685	−	0.558231i	$-0.811480\pi$
$239$		−	17.2601i		−	1.11646i	0.829685	−	0.558231i	$-0.188520\pi$
$240$		0			0
$241$			19.1935i			1.23636i	0.786037	+	0.618180i	$0.212130\pi$
$241$			19.1935i			1.23636i	−0.786037	+	0.618180i	$0.787870\pi$
$242$	17.6088			1.13194
$243$	−14.3871	+	6.00091i	−0.922934	+	0.384959i
$244$		−	13.2555i		−	0.848597i
$245$		0			0
$246$	2.48166	−	10.3593i	0.158225	−	0.660487i
$247$		−	3.19270i		−	0.203147i
$248$			9.07971i			0.576562i
$249$	2.58574	+	0.619433i	0.163864	+	0.0392550i
$250$		0			0
$251$	21.0271			1.32722			0.663611	−	0.748078i	$-0.269023\pi$
$251$	21.0271			1.32722			0.663611	+	0.748078i	$0.269023\pi$
$252$	−0.278649	−	7.93236i	−0.0175532	−	0.499692i
$253$			1.50474i			0.0946022i
$254$			2.00000i			0.125491i
$255$		0			0
$256$	1.00000			0.0625000
$257$			14.5881i			0.909982i	0.890496	+	0.454991i	$0.150358\pi$
$257$			14.5881i			0.909982i	−0.890496	+	0.454991i	$0.849642\pi$
$258$	10.6937	+	2.56177i	0.665763	+	0.159489i
$259$	14.0462	−	7.77163i	0.872786	−	0.482905i
$260$		0			0
$261$	−0.382418	+	0.752370i	−0.0236711	+	0.0465705i
$262$	−16.5454			−1.02218
$263$	8.91138			0.549499			0.274749	−	0.961516i	$-0.411405\pi$
$263$	8.91138			0.549499			0.274749	+	0.961516i	$0.411405\pi$
$264$	−9.00935	−	2.15826i	−0.554487	−	0.132832i
$265$		0			0
$266$	−1.86827	+	1.03370i	−0.114551	+	0.0633800i
$267$	−1.74175	+	7.27071i	−0.106594	+	0.444960i
$268$			6.71867i			0.410408i
$269$	−22.3352			−1.36180			−0.680901	−	0.732375i	$-0.738412\pi$
$269$	−22.3352			−1.36180			−0.680901	+	0.732375i	$0.738412\pi$
$270$		0			0
$271$		−	7.17684i		−	0.435962i	−0.975953	−	0.217981i	$-0.930053\pi$
$271$		−	7.17684i		−	0.435962i	0.975953	−	0.217981i	$-0.0699471\pi$
$272$		−	7.32496i		−	0.444141i
$273$	−17.4715	+	4.83989i	−1.05742	+	0.292924i
$274$	7.41612			0.448024
$275$		0			0
$276$	0.113518	−	0.473865i	0.00683298	−	0.0285233i
$277$		−	9.32749i		−	0.560435i	−0.959937	−	0.280217i	$-0.909593\pi$
$277$		−	9.32749i		−	0.560435i	0.959937	−	0.280217i	$-0.0904065\pi$
$278$		−	6.36982i		−	0.382037i
$279$	−12.3424	+	24.2824i	−0.738919	+	1.45375i
$280$		0			0
$281$			17.4373i			1.04022i	0.854098	+	0.520112i	$0.174110\pi$
$281$			17.4373i			1.04022i	−0.854098	+	0.520112i	$0.825890\pi$
$282$	9.75237	+	2.33625i	0.580745	+	0.139122i
$283$	16.1776			0.961660			0.480830	−	0.876814i	$-0.340335\pi$
$283$	16.1776			0.961660			0.480830	+	0.876814i	$0.340335\pi$
$284$			3.36995i			0.199970i
$285$		0			0
$286$			21.1604i			1.25124i
$287$	7.87768	+	14.2378i	0.465005	+	0.840433i
$288$	2.67436	+	1.35934i	0.157588	+	0.0800997i
$289$	−36.6550			−2.15618
$290$		0			0
$291$	−6.08862	+	25.4161i	−0.356922	+	1.48992i
$292$	−4.98282			−0.291598
$293$			22.5623i			1.31810i	0.752099	+	0.659050i	$0.229042\pi$
$293$			22.5623i			1.31810i	−0.752099	+	0.659050i	$0.770958\pi$
$294$	8.48887	+	8.65674i	0.495081	+	0.504871i
$295$		0			0
$296$			6.06739i			0.352660i
$297$	−21.1604	−	18.0187i	−1.22785	−	1.04555i
$298$			7.60882i			0.440767i
$299$	−1.11298			−0.0643652
$300$		0			0
$301$	−14.6974	+	8.13197i	−0.847146	+	0.468719i
$302$	4.63005			0.266429
$303$	2.33625	−	9.75237i	0.134214	−	0.560259i
$304$		−	0.807019i		−	0.0462857i
$305$		0			0
$306$	9.95708	−	19.5896i	0.569208	−	1.11986i
$307$	19.4057			1.10754			0.553771	−	0.832669i	$-0.313188\pi$
$307$	19.4057			1.10754			0.553771	+	0.832669i	$0.313188\pi$
$308$	12.3824	−	6.85109i	0.705554	−	0.390377i
$309$	−2.80730	+	11.7187i	−0.159702	+	0.666652i
$310$		0			0
$311$	6.73757			0.382053			0.191026	−	0.981585i	$-0.438818\pi$
$311$	6.73757			0.382053			0.191026	+	0.981585i	$0.438818\pi$
$312$	1.59635	−	6.66375i	0.0903756	−	0.377260i
$313$	21.3875			1.20889			0.604446	−	0.796646i	$-0.293394\pi$
$313$	21.3875			1.20889			0.604446	+	0.796646i	$0.293394\pi$
$314$	15.3162			0.864344
$315$		0			0
$316$	3.26010			0.183395
$317$	−3.47403			−0.195121			−0.0975605	−	0.995230i	$-0.531104\pi$
$317$	−3.47403			−0.195121			−0.0975605	+	0.995230i	$0.531104\pi$
$318$	−4.43004	+	18.4926i	−0.248424	+	1.03701i
$319$	−1.50474			−0.0842493
$320$		0			0
$321$	−4.28076	+	17.8694i	−0.238929	+	0.997374i
$322$	0.360347	+	0.651279i	0.0200814	+	0.0362944i
$323$	−5.91138			−0.328918
$324$	5.30441	+	7.27071i	0.294689	+	0.403928i
$325$		0			0
$326$			3.06739i			0.169887i
$327$	−7.31755	+	30.5461i	−0.404662	+	1.68920i
$328$	−6.15019			−0.339587
$329$	−13.4036	+	7.41612i	−0.738966	+	0.408864i
$330$		0			0
$331$	−8.93261			−0.490980			−0.245490	−	0.969399i	$-0.578949\pi$
$331$	−8.93261			−0.490980			−0.245490	+	0.969399i	$0.578949\pi$
$332$		−	1.53511i		−	0.0842503i
$333$	−8.24763	+	16.2264i	−0.451967	+	0.889201i
$334$		−	1.89546i		−	0.103715i
$335$		0			0
$336$	−4.41626	+	1.22338i	−0.240927	+	0.0667408i
$337$		−	34.2176i		−	1.86395i	−0.362518	−	0.931977i	$-0.618083\pi$
$337$		−	34.2176i		−	1.86395i	0.362518	−	0.931977i	$-0.381917\pi$
$338$	−2.65128			−0.144211
$339$	3.44654	−	14.3871i	0.187191	−	0.781401i
$340$		0			0
$341$	−48.5648			−2.62993
$342$	1.09701	−	2.15826i	0.0593195	−	0.116705i
$343$	−18.4926	−	1.01247i	−0.998505	−	0.0546680i
$344$		−	6.34872i		−	0.342300i
$345$		0			0
$346$		−	8.86007i		−	0.476320i
$347$	11.5260			0.618747			0.309373	−	0.950941i	$-0.399881\pi$
$347$	11.5260			0.618747			0.309373	+	0.950941i	$0.399881\pi$
$348$	0.473865	+	0.113518i	0.0254018	+	0.00608521i
$349$			21.8342i			1.16876i	0.811482	+	0.584378i	$0.198661\pi$
$349$			21.8342i			1.16876i	−0.811482	+	0.584378i	$0.801339\pi$
$350$		0			0
$351$	13.3275	−	15.6513i	0.711369	−	0.835403i
$352$			5.34872i			0.285088i
$353$		−	4.84211i		−	0.257720i	−0.991663	−	0.128860i	$-0.958868\pi$
$353$		−	4.84211i		−	0.257720i	0.991663	−	0.128860i	$-0.0411317\pi$
$354$	1.97877	−	8.26010i	0.105170	−	0.439019i
$355$		0			0
$356$	4.31652			0.228775
$357$	8.96119	+	32.3489i	0.474277	+	1.71209i
$358$		−	11.3487i		−	0.599799i
$359$			30.3063i			1.59950i	0.600331	+	0.799752i	$0.295035\pi$
$359$			30.3063i			1.59950i	−0.600331	+	0.799752i	$0.704965\pi$
$360$		0			0
$361$	18.3487			0.965722
$362$		−	8.63303i		−	0.453742i
$363$	7.10532	−	29.6602i	0.372933	−	1.55676i
$364$	5.06739	+	9.15863i	0.265604	+	0.480043i
$365$		0			0
$366$	−22.3275	−	5.34872i	−1.16708	−	0.279582i
$367$	13.9910			0.730325			0.365162	−	0.930944i	$-0.381013\pi$
$367$	13.9910			0.730325			0.365162	+	0.930944i	$0.381013\pi$
$368$	−0.281327			−0.0146652
$369$	−16.4478	−	8.36018i	−0.856239	−	0.435213i
$370$		0			0
$371$	−14.0625	−	25.4161i	−0.730090	−	1.31954i
$372$	15.2938	+	3.66375i	0.792946	+	0.189956i
$373$			4.24464i			0.219779i	0.993944	+	0.109890i	$0.0350497\pi$
$373$			4.24464i			0.219779i	−0.993944	+	0.109890i	$0.964950\pi$
$374$	39.1791			2.02591
$375$		0			0
$376$		−	5.78984i		−	0.298588i
$377$		−	1.11298i		−	0.0573213i
$378$	−13.4737	−	2.73143i	−0.693010	−	0.140489i
$379$	1.63005			0.0837299			0.0418650	−	0.999123i	$-0.486670\pi$
$379$	1.63005			0.0837299			0.0418650	+	0.999123i	$0.486670\pi$
$380$		0			0
$381$	3.36879	+	0.807019i	0.172588	+	0.0413448i
$382$		−	7.78607i		−	0.398370i
$383$		−	16.9994i		−	0.868631i	−0.900761	−	0.434316i	$-0.856990\pi$
$383$		−	16.9994i		−	0.868631i	0.900761	−	0.434316i	$-0.143010\pi$
$384$	0.403509	−	1.68439i	0.0205915	−	0.0859563i
$385$		0			0
$386$			25.1715i			1.28119i
$387$	8.63005	−	16.9788i	0.438690	−	0.863079i
$388$	15.0892			0.766037
$389$		−	29.4623i		−	1.49380i	−0.664938	−	0.746898i	$-0.731542\pi$
$389$		−	29.4623i		−	1.49380i	0.664938	−	0.746898i	$-0.268458\pi$
$390$		0			0
$391$			2.06071i			0.104214i
$392$	3.71867	−	5.93055i	0.187821	−	0.299538i
$393$	−6.67621	+	27.8689i	−0.336770	+	1.40580i
$394$	2.52597			0.127257
$395$		0			0
$396$	−7.27071	+	14.3044i	−0.365367	+	0.718824i
$397$	−17.8706			−0.896899			−0.448449	−	0.893808i	$-0.648024\pi$
$397$	−17.8706			−0.896899			−0.448449	+	0.893808i	$0.648024\pi$
$398$			0.947731i			0.0475054i
$399$	0.987289	+	3.56400i	0.0494263	+	0.178423i
$400$		0			0
$401$		−	12.6762i		−	0.633020i	−0.948589	−	0.316510i	$-0.897489\pi$
$401$		−	12.6762i		−	0.633020i	0.948589	−	0.316510i	$-0.102511\pi$
$402$	11.3169	+	2.71105i	0.564435	+	0.135215i
$403$		−	35.9209i		−	1.78935i
$404$	−5.78984			−0.288055
$405$		0			0
$406$	−0.651279	+	0.360347i	−0.0323224	+	0.0178837i
$407$	−32.4528			−1.60863
$408$	−12.3381	−	2.95569i	−0.610827	−	0.146328i
$409$		−	5.26425i		−	0.260300i	−0.991494	−	0.130150i	$-0.958454\pi$
$409$		−	5.26425i		−	0.260300i	0.991494	−	0.130150i	$-0.0415459\pi$
$410$		0			0
$411$	2.99247	−	12.4917i	0.147608	−	0.616168i
$412$	6.95721			0.342757
$413$	6.28133	+	11.3526i	0.309084	+	0.558627i
$414$	−0.752370	−	0.382418i	−0.0369770	−	0.0187948i
$415$		0			0
$416$	−3.95617			−0.193967
$417$	−10.7293	−	2.57028i	−0.525416	−	0.125867i
$418$	4.31652			0.211128
$419$	13.1148			0.640700			0.320350	−	0.947299i	$-0.396200\pi$
$419$	13.1148			0.640700			0.320350	+	0.947299i	$0.396200\pi$
$420$		0			0
$421$	3.86521			0.188379			0.0941895	−	0.995554i	$-0.469974\pi$
$421$	3.86521			0.188379			0.0941895	+	0.995554i	$0.469974\pi$
$422$	12.8901			0.627482
$423$	7.87034	−	15.4841i	0.382669	−	0.752864i
$424$	10.9788			0.533176
$425$		0			0
$426$	5.67632	+	1.35981i	0.275019	+	0.0658829i
$427$	30.6868	−	16.9788i	1.48504	−	0.821660i
$428$	10.6088			0.512797
$429$	35.6425	+	8.53844i	1.72084	+	0.412240i
$430$		0			0
$431$			10.2389i			0.493189i	0.969119	+	0.246594i	$0.0793115\pi$
$431$			10.2389i			0.493189i	−0.969119	+	0.246594i	$0.920688\pi$
$432$	3.36879	−	3.95617i	0.162081	−	0.190341i
$433$	22.7030			1.09103			0.545517	−	0.838099i	$-0.316333\pi$
$433$	22.7030			1.09103			0.545517	+	0.838099i	$0.316333\pi$
$434$	−21.0197	+	11.6300i	−1.00898	+	0.558260i
$435$		0			0
$436$	18.1348			0.868499
$437$			0.227036i			0.0108606i
$438$	−2.01062	+	8.39303i	−0.0960709	+	0.401035i
$439$		−	26.4492i		−	1.26235i	−0.775639	−	0.631176i	$-0.782572\pi$
$439$		−	26.4492i		−	1.26235i	0.775639	−	0.631176i	$-0.217428\pi$
$440$		0			0
$441$	18.0067	−	10.8055i	0.857461	−	0.514548i
$442$			28.9788i			1.37838i
$443$	27.8689			1.32409			0.662046	−	0.749463i	$-0.269688\pi$
$443$	27.8689			1.32409			0.662046	+	0.749463i	$0.269688\pi$
$444$	10.2199	+	2.44825i	0.485014	+	0.116189i
$445$		0			0
$446$	23.7296			1.12363
$447$	12.8162	+	3.07023i	0.606187	+	0.145217i
$448$	1.28088	+	2.31502i	0.0605161	+	0.109375i
$449$		−	9.45858i		−	0.446378i	−0.974775	−	0.223189i	$-0.928353\pi$
$449$		−	9.45858i		−	0.446378i	0.974775	−	0.223189i	$-0.0716467\pi$
$450$		0			0
$451$		−	32.8956i		−	1.54900i
$452$	−8.54142			−0.401755
$453$	1.86827	−	7.79882i	0.0877789	−	0.366421i
$454$			10.4667i			0.491227i
$455$		0			0
$456$	−1.35934	−	0.325639i	−0.0636568	−	0.0152495i
$457$			31.8322i			1.48905i	0.667595	+	0.744524i	$0.267324\pi$
$457$			31.8322i			1.48905i	−0.667595	+	0.744524i	$0.732676\pi$
$458$			16.4762i			0.769881i
$459$	−28.9788	−	24.6762i	−1.35261	−	1.15179i
$460$		0			0
$461$	10.6320			0.495179			0.247590	−	0.968865i	$-0.420362\pi$
$461$	10.6320			0.495179			0.247590	+	0.968865i	$0.420362\pi$
$462$	−6.54351	−	23.6213i	−0.304432	−	1.09896i
$463$		−	12.8322i		−	0.596364i	−0.954509	−	0.298182i	$-0.903620\pi$
$463$		−	12.8322i		−	0.596364i	0.954509	−	0.298182i	$-0.0963803\pi$
$464$		−	0.281327i		−	0.0130603i
$465$		0			0
$466$	27.9575			1.29511
$467$			20.8716i			0.965824i	0.875669	+	0.482912i	$0.160421\pi$
$467$			20.8716i			0.965824i	−0.875669	+	0.482912i	$0.839579\pi$
$468$	−10.5802	−	5.37777i	−0.489071	−	0.248587i
$469$	−15.5539	+	8.60584i	−0.718212	+	0.397381i
$470$		0			0
$471$	6.18024	−	25.7985i	0.284770	−	1.18873i
$472$	−4.90390			−0.225720
$473$	33.9575			1.56137
$474$	1.31548	−	5.49128i	0.0604220	−	0.252223i
$475$		0			0
$476$	16.9574	−	9.38242i	0.777243	−	0.430042i
$477$	29.3612	+	14.9238i	1.34436	+	0.683316i
$478$			17.2601i			0.789458i
$479$	−33.6879			−1.53924			−0.769619	−	0.638504i	$-0.779554\pi$
$479$	−33.6879			−1.53924			−0.769619	+	0.638504i	$0.779554\pi$
$480$		0			0
$481$		−	24.0036i		−	1.09447i
$482$		−	19.1935i		−	0.874238i
$483$	1.24241	−	0.344169i	0.0565318	−	0.0156603i
$484$	−17.6088			−0.800401
$485$		0			0
$486$	14.3871	−	6.00091i	0.652613	−	0.272207i
$487$			33.3524i			1.51134i	0.654951	+	0.755671i	$0.272689\pi$
$487$			33.3524i			1.51134i	−0.654951	+	0.755671i	$0.727311\pi$
$488$			13.2555i			0.600049i
$489$	5.16670	+	1.23772i	0.233646	+	0.0559717i
$490$		0			0
$491$			30.0000i			1.35388i	0.736038	+	0.676941i	$0.236695\pi$
$491$			30.0000i			1.35388i	−0.736038	+	0.676941i	$0.763305\pi$
$492$	−2.48166	+	10.3593i	−0.111882	+	0.467035i
$493$	−2.06071			−0.0928096
$494$			3.19270i			0.143646i
$495$		0			0
$496$		−	9.07971i		−	0.407691i
$497$	−7.80152	+	4.31652i	−0.349946	+	0.193622i
$498$	−2.58574	−	0.619433i	−0.115870	−	0.0277574i
$499$	19.1810			0.858657			0.429329	−	0.903148i	$-0.358750\pi$
$499$	19.1810			0.858657			0.429329	+	0.903148i	$0.358750\pi$
$500$		0			0
$501$	−3.19270	−	0.764836i	−0.142639	−	0.0341704i
$502$	−21.0271			−0.938487
$503$		−	36.9851i		−	1.64909i	−0.565800	−	0.824543i	$-0.691432\pi$
$503$		−	36.9851i		−	1.64909i	0.565800	−	0.824543i	$-0.308568\pi$
$504$	0.278649	+	7.93236i	0.0124120	+	0.353335i
$505$		0			0
$506$		−	1.50474i		−	0.0668938i
$507$	−1.06982	+	4.46580i	−0.0475122	+	0.198333i
$508$		−	2.00000i		−	0.0887357i
$509$	36.0374			1.59733			0.798665	−	0.601776i	$-0.205540\pi$
$509$	36.0374			1.59733			0.798665	+	0.601776i	$0.205540\pi$
$510$		0			0
$511$	−6.38242	−	11.5354i	−0.282342	−	0.510294i
$512$	−1.00000			−0.0441942
$513$	−3.19270	−	2.71867i	−0.140961	−	0.120032i
$514$		−	14.5881i		−	0.643455i
$515$		0			0
$516$	−10.6937	−	2.56177i	−0.470766	−	0.112776i
$517$	30.9682			1.36198
$518$	−14.0462	+	7.77163i	−0.617153	+	0.341466i
$519$	−14.9238	−	3.57512i	−0.655084	−	0.156930i
$520$		0			0
$521$	−3.65761			−0.160243			−0.0801214	−	0.996785i	$-0.525531\pi$
$521$	−3.65761			−0.160243			−0.0801214	+	0.996785i	$0.525531\pi$
$522$	0.382418	−	0.752370i	0.0167380	−	0.0329303i
$523$	−2.26321			−0.0989633			−0.0494816	−	0.998775i	$-0.515757\pi$
$523$	−2.26321			−0.0989633			−0.0494816	+	0.998775i	$0.515757\pi$
$524$	16.5454			0.722788
$525$		0			0
$526$	−8.91138			−0.388554
$527$	−66.5084			−2.89715
$528$	9.00935	+	2.15826i	0.392082	+	0.0939261i
$529$	−22.9209			−0.996559
$530$		0			0
$531$	−13.1148	−	6.66605i	−0.569134	−	0.289282i
$532$	1.86827	−	1.03370i	0.0809997	−	0.0448164i
$533$	24.3312			1.05390
$534$	1.74175	−	7.27071i	0.0753731	−	0.314634i
$535$		0			0
$536$		−	6.71867i		−	0.290202i
$537$	−19.1157	−	4.57931i	−0.824904	−	0.197612i
$538$	22.3352			0.962940
$539$	31.7209	+	19.8901i	1.36632	+	0.856729i
$540$		0			0
$541$	15.1502			0.651360			0.325680	−	0.945480i	$-0.394407\pi$
$541$	15.1502			0.651360			0.325680	+	0.945480i	$0.394407\pi$
$542$			7.17684i			0.308272i
$543$	−14.5414	−	3.48351i	−0.624032	−	0.149492i
$544$			7.32496i			0.314055i
$545$		0			0
$546$	17.4715	−	4.83989i	0.747710	−	0.207128i
$547$			2.89014i			0.123574i	0.998089	+	0.0617868i	$0.0196799\pi$
$547$			2.89014i			0.123574i	−0.998089	+	0.0617868i	$0.980320\pi$
$548$	−7.41612			−0.316801
$549$	−18.0187	+	35.4500i	−0.769019	+	1.51297i
$550$		0			0
$551$	−0.227036			−0.00967206
$552$	−0.113518	+	0.473865i	−0.00483165	+	0.0201690i
$553$	4.17580	+	7.54720i	0.177573	+	0.320940i
$554$			9.32749i			0.396287i
$555$		0			0
$556$			6.36982i			0.270141i
$557$	32.4777			1.37613			0.688063	−	0.725651i	$-0.258461\pi$
$557$	32.4777			1.37613			0.688063	+	0.725651i	$0.258461\pi$
$558$	12.3424	−	24.2824i	0.522494	−	1.02796i
$559$			25.1166i			1.06232i
$560$		0			0
$561$	15.8091	−	65.9931i	0.667463	−	2.78623i
$562$		−	17.4373i		−	0.735550i
$563$		−	10.9208i		−	0.460256i	−0.973160	−	0.230128i	$-0.926086\pi$
$563$		−	10.9208i		−	0.460256i	0.973160	−	0.230128i	$-0.0739145\pi$
$564$	−9.75237	−	2.33625i	−0.410649	−	0.0983741i
$565$		0			0
$566$	−16.1776			−0.679996
$567$	−10.0375	+	21.5928i	−0.421537	+	0.906811i
$568$		−	3.36995i		−	0.141400i
$569$		−	4.58388i		−	0.192166i	−0.995373	−	0.0960832i	$-0.969369\pi$
$569$		−	4.58388i		−	0.192166i	0.995373	−	0.0960832i	$-0.0306315\pi$
$570$		0			0
$571$	5.82853			0.243916			0.121958	−	0.992535i	$-0.461083\pi$
$571$	5.82853			0.243916			0.121958	+	0.992535i	$0.461083\pi$
$572$		−	21.1604i		−	0.884763i
$573$	−13.1148	−	3.14175i	−0.547879	−	0.131248i
$574$	−7.87768	−	14.2378i	−0.328808	−	0.594276i
$575$		0			0
$576$	−2.67436	−	1.35934i	−0.111432	−	0.0566390i
$577$	−9.82493			−0.409017			−0.204509	−	0.978865i	$-0.565560\pi$
$577$	−9.82493			−0.409017			−0.204509	+	0.978865i	$0.565560\pi$
$578$	36.6550			1.52465
$579$	42.3987	+	10.1569i	1.76203	+	0.422107i
$580$		0			0
$581$	3.55383	−	1.96630i	0.147438	−	0.0815760i
$582$	6.08862	−	25.4161i	0.252382	−	1.05353i
$583$			58.7224i			2.43203i
$584$	4.98282			0.206191
$585$		0			0
$586$		−	22.5623i		−	0.932038i
$587$		−	27.3106i		−	1.12723i	−0.826037	−	0.563615i	$-0.809410\pi$
$587$		−	27.3106i		−	1.12723i	0.826037	−	0.563615i	$-0.190590\pi$
$588$	−8.48887	−	8.65674i	−0.350075	−	0.356998i
$589$	−7.32749			−0.301924
$590$		0			0
$591$	1.01925	−	4.25473i	0.0419264	−	0.175016i
$592$		−	6.06739i		−	0.249368i
$593$			26.8788i			1.10378i	0.833917	+	0.551889i	$0.186093\pi$
$593$			26.8788i			1.10378i	−0.833917	+	0.551889i	$0.813907\pi$
$594$	21.1604	+	18.0187i	0.868224	+	0.739316i
$595$		0			0
$596$		−	7.60882i		−	0.311669i
$597$	1.59635	+	0.382418i	0.0653343	+	0.0156513i
$598$	1.11298			0.0455130
$599$			6.45858i			0.263890i	0.991257	+	0.131945i	$0.0421223\pi$
$599$			6.45858i			0.263890i	−0.991257	+	0.131945i	$0.957878\pi$
$600$		0			0
$601$		−	1.31548i		−	0.0536595i	−0.999640	−	0.0268298i	$-0.991459\pi$
$601$		−	1.31548i		−	0.0536595i	0.999640	−	0.0268298i	$-0.00854120\pi$
$602$	14.6974	−	8.13197i	0.599023	−	0.331435i
$603$	9.13294	−	17.9682i	0.371922	−	0.731720i
$604$	−4.63005			−0.188394
$605$		0			0
$606$	−2.33625	+	9.75237i	−0.0949039	+	0.396163i
$607$	26.9651			1.09448			0.547240	−	0.836976i	$-0.315679\pi$
$607$	26.9651			1.09448			0.547240	+	0.836976i	$0.315679\pi$
$608$			0.807019i			0.0327289i
$609$	0.344169	+	1.24241i	0.0139464	+	0.0503451i
$610$		0			0
$611$			22.9056i			0.926661i
$612$	−9.95708	+	19.5896i	−0.402491	+	0.791862i
$613$			33.9151i			1.36982i	0.728629	+	0.684909i	$0.240158\pi$
$613$			33.9151i			1.36982i	−0.728629	+	0.684909i	$0.759842\pi$
$614$	−19.4057			−0.783150
$615$		0			0
$616$	−12.3824	+	6.85109i	−0.498902	+	0.276038i
$617$	−13.1253			−0.528405			−0.264203	−	0.964467i	$-0.585109\pi$
$617$	−13.1253			−0.528405			−0.264203	+	0.964467i	$0.585109\pi$
$618$	2.80730	−	11.7187i	0.112926	−	0.471394i
$619$			38.0907i			1.53099i	0.643439	+	0.765497i	$0.277507\pi$
$619$			38.0907i			1.53099i	−0.643439	+	0.765497i	$0.722493\pi$
$620$		0			0
$621$	−0.947731	+	1.11298i	−0.0380311	+	0.0446623i
$622$	−6.73757			−0.270152
$623$	5.52896	+	9.99284i	0.221513	+	0.400355i
$624$	−1.59635	+	6.66375i	−0.0639052	+	0.266763i
$625$		0			0
$626$	−21.3875			−0.854816
$627$	1.74175	−	7.27071i	0.0695590	−	0.290364i
$628$	−15.3162			−0.611184
$629$	−44.4434			−1.77207
$630$		0			0
$631$	−12.0674			−0.480395			−0.240198	−	0.970724i	$-0.577212\pi$
$631$	−12.0674			−0.480395			−0.240198	+	0.970724i	$0.577212\pi$
$632$	−3.26010			−0.129680
$633$	5.20129	−	21.7121i	0.206733	−	0.862977i
$634$	3.47403			0.137971
$635$		0			0
$636$	4.43004	−	18.4926i	0.175662	−	0.733278i
$637$	−14.7117	+	23.4623i	−0.582899	+	0.929609i
$638$	1.50474			0.0595732
$639$	4.58090	−	9.01247i	0.181218	−	0.356528i
$640$		0			0
$641$		−	17.4373i		−	0.688734i	−0.938835	−	0.344367i	$-0.888094\pi$
$641$		−	17.4373i		−	0.688734i	0.938835	−	0.344367i	$-0.111906\pi$
$642$	4.28076	−	17.8694i	0.168948	−	0.705250i
$643$	−6.01688			−0.237283			−0.118641	−	0.992937i	$-0.537854\pi$
$643$	−6.01688			−0.237283			−0.118641	+	0.992937i	$0.537854\pi$
$644$	−0.360347	−	0.651279i	−0.0141997	−	0.0256640i
$645$		0			0
$646$	5.91138			0.232580
$647$			36.7581i			1.44511i	0.691314	+	0.722555i	$0.257032\pi$
$647$			36.7581i			1.44511i	−0.691314	+	0.722555i	$0.742968\pi$
$648$	−5.30441	−	7.27071i	−0.208377	−	0.285621i
$649$		−	26.2296i		−	1.02960i
$650$		0			0
$651$	11.1079	+	40.0983i	0.435354	+	1.57158i
$652$		−	3.06739i		−	0.120128i
$653$	−14.8073			−0.579454			−0.289727	−	0.957109i	$-0.593565\pi$
$653$	−14.8073			−0.579454			−0.289727	+	0.957109i	$0.593565\pi$
$654$	7.31755	−	30.5461i	0.286139	−	1.19445i
$655$		0			0
$656$	6.15019			0.240125
$657$	13.3259	+	6.77333i	0.519892	+	0.264253i
$658$	13.4036	−	7.41612i	0.522528	−	0.289110i
$659$			11.3487i			0.442083i	0.975264	+	0.221042i	$0.0709457\pi$
$659$			11.3487i			0.442083i	−0.975264	+	0.221042i	$0.929054\pi$
$660$		0			0
$661$		−	19.7043i		−	0.766407i	−0.923664	−	0.383203i	$-0.874821\pi$
$661$		−	19.7043i		−	0.766407i	0.923664	−	0.383203i	$-0.125179\pi$
$662$	8.93261			0.347176
$663$	48.8116	+	11.6932i	1.89569	+	0.454126i
$664$			1.53511i			0.0595740i
$665$		0			0
$666$	8.24763	−	16.2264i	0.319589	−	0.628760i
$667$			0.0791449i			0.00306450i
$668$			1.89546i			0.0733376i
$669$	9.57512	−	39.9700i	0.370196	−	1.54533i
$670$		0			0
$671$	−70.9000			−2.73707
$672$	4.41626	−	1.22338i	0.170361	−	0.0471928i
$673$		−	21.7861i		−	0.839791i	−0.907572	−	0.419896i	$-0.862067\pi$
$673$		−	21.7861i		−	0.839791i	0.907572	−	0.419896i	$-0.137933\pi$
$674$			34.2176i			1.31801i
$675$		0			0
$676$	2.65128			0.101972
$677$		−	15.3706i		−	0.590740i	−0.955383	−	0.295370i	$-0.904557\pi$
$677$		−	15.3706i		−	0.590740i	0.955383	−	0.295370i	$-0.0954430\pi$
$678$	−3.44654	+	14.3871i	−0.132364	+	0.552534i
$679$	19.3275	+	34.9318i	0.741721	+	1.34056i
$680$		0			0
$681$	17.6300	+	4.22341i	0.675585	+	0.161842i
$682$	48.5648			1.85964
$683$	22.0462			0.843573			0.421786	−	0.906695i	$-0.361403\pi$
$683$	22.0462			0.843573			0.421786	+	0.906695i	$0.361403\pi$
$684$	−1.09701	+	2.15826i	−0.0419452	+	0.0825231i
$685$		0			0
$686$	18.4926	+	1.01247i	0.706049	+	0.0386561i
$687$	27.7524	+	6.64829i	1.05882	+	0.253648i
$688$			6.34872i			0.242043i
$689$	−43.4339			−1.65470
$690$		0			0
$691$		−	31.7209i		−	1.20672i	−0.797469	−	0.603360i	$-0.793828\pi$
$691$		−	31.7209i		−	1.20672i	0.797469	−	0.603360i	$-0.206172\pi$
$692$			8.86007i			0.336809i
$693$	−42.4280	+	1.49041i	−1.61171	+	0.0566161i
$694$	−11.5260			−0.437520
$695$		0			0
$696$	−0.473865	−	0.113518i	−0.0179618	−	0.00430289i
$697$		−	45.0499i		−	1.70639i
$698$		−	21.8342i		−	0.826435i
$699$	11.2811	−	47.0915i	0.426691	−	1.78116i
$700$		0			0
$701$			49.4316i			1.86700i	0.358571	+	0.933502i	$0.383264\pi$
$701$			49.4316i			1.86700i	−0.358571	+	0.933502i	$0.616736\pi$
$702$	−13.3275	+	15.6513i	−0.503014	+	0.590719i
$703$	−4.89650			−0.184675
$704$		−	5.34872i		−	0.201588i
$705$		0			0
$706$			4.84211i			0.182235i
$707$	−7.41612	−	13.4036i	−0.278912	−	0.504095i
$708$	−1.97877	+	8.26010i	−0.0743667	+	0.310433i
$709$	0.697442			0.0261930			0.0130965	−	0.999914i	$-0.495831\pi$
$709$	0.697442			0.0261930			0.0130965	+	0.999914i	$0.495831\pi$
$710$		0			0
$711$	−8.71867	−	4.43157i	−0.326976	−	0.166197i
$712$	−4.31652			−0.161768
$713$			2.55437i			0.0956618i
$714$	−8.96119	−	32.3489i	−0.335364	−	1.21063i
$715$		0			0
$716$			11.3487i			0.424122i
$717$	29.0728	+	6.96461i	1.08574	+	0.260098i
$718$		−	30.3063i		−	1.13102i
$719$	−32.1430			−1.19873			−0.599366	−	0.800475i	$-0.704581\pi$
$719$	−32.1430			−1.19873			−0.599366	+	0.800475i	$0.704581\pi$
$720$		0			0
$721$	8.91138	+	16.1061i	0.331877	+	0.599823i
$722$	−18.3487			−0.682869
$723$	−32.3293	−	7.74474i	−1.20234	−	0.288030i
$724$			8.63303i			0.320844i
$725$		0			0
$726$	−7.10532	+	29.6602i	−0.263703	+	1.10079i
$727$	−27.3970			−1.01610			−0.508049	−	0.861328i	$-0.669633\pi$
$727$	−27.3970			−1.01610			−0.508049	+	0.861328i	$0.669633\pi$
$728$	−5.06739	−	9.15863i	−0.187810	−	0.339441i
$729$	−4.30256	−	26.6550i	−0.159354	−	0.987222i
$730$		0			0
$731$	46.5041			1.72002
$732$	22.3275	+	5.34872i	0.825248	+	0.197694i
$733$	0.0617893			0.00228224			0.00114112	−	0.999999i	$-0.499637\pi$
$733$	0.0617893			0.00228224			0.00114112	+	0.999999i	$0.499637\pi$
$734$	−13.9910			−0.516417
$735$		0			0
$736$	0.281327			0.0103699
$737$	35.9363			1.32373
$738$	16.4478	+	8.36018i	0.605453	+	0.307742i
$739$	45.0037			1.65549			0.827744	−	0.561106i	$-0.189624\pi$
$739$	45.0037			1.65549			0.827744	+	0.561106i	$0.189624\pi$
$740$		0			0
$741$	5.37777	+	1.28828i	0.197557	+	0.0473263i
$742$	14.0625	+	25.4161i	0.516252	+	0.933055i
$743$	−38.1655			−1.40016			−0.700078	−	0.714066i	$-0.746852\pi$
$743$	−38.1655			−1.40016			−0.700078	+	0.714066i	$0.746852\pi$
$744$	−15.2938	−	3.66375i	−0.560698	−	0.134319i
$745$		0			0
$746$		−	4.24464i		−	0.155407i
$747$	−2.08674	+	4.10545i	−0.0763497	+	0.150211i
$748$	−39.1791			−1.43253
$749$	13.5887	+	24.5597i	0.496519	+	0.897391i
$750$		0			0
$751$	−27.8901			−1.01773			−0.508863	−	0.860848i	$-0.669934\pi$
$751$	−27.8901			−1.01773			−0.508863	+	0.860848i	$0.669934\pi$
$752$			5.78984i			0.211134i
$753$	−8.48464	+	35.4180i	−0.309198	+	1.29070i
$754$			1.11298i			0.0405323i
$755$		0			0
$756$	13.4737	+	2.73143i	0.490032	+	0.0993411i
$757$			38.5876i			1.40249i	0.712921	+	0.701245i	$0.247372\pi$
$757$			38.5876i			1.40249i	−0.712921	+	0.701245i	$0.752628\pi$
$758$	−1.63005			−0.0592060
$759$	−2.53457	−	0.607177i	−0.0919992	−	0.0220391i
$760$		0			0
$761$	−28.9173			−1.04825			−0.524125	−	0.851641i	$-0.675608\pi$
$761$	−28.9173			−1.04825			−0.524125	+	0.851641i	$0.675608\pi$
$762$	−3.36879	−	0.807019i	−0.122038	−	0.0292352i
$763$	23.2286	+	41.9825i	0.840930	+	1.51987i
$764$			7.78607i			0.281690i
$765$		0			0
$766$			16.9994i			0.614215i
$767$	19.4007			0.700517
$768$	−0.403509	+	1.68439i	−0.0145604	+	0.0607803i
$769$		−	30.3191i		−	1.09333i	−0.837350	−	0.546667i	$-0.815896\pi$
$769$		−	30.3191i		−	1.09333i	0.837350	−	0.546667i	$-0.184104\pi$
$770$		0			0
$771$	−24.5721	−	5.88644i	−0.884944	−	0.211995i
$772$		−	25.1715i		−	0.905941i
$773$			23.7370i			0.853761i	0.904308	+	0.426881i	$0.140388\pi$
$773$			23.7370i			0.853761i	−0.904308	+	0.426881i	$0.859612\pi$
$774$	−8.63005	+	16.9788i	−0.310201	+	0.610289i
$775$		0			0
$776$	−15.0892			−0.541670
$777$	7.42272	+	26.7952i	0.266289	+	0.961272i
$778$			29.4623i			1.05627i
$779$		−	4.96332i		−	0.177829i
$780$		0			0
$781$	18.0249			0.644983
$782$		−	2.06071i		−	0.0736908i
$783$	−1.11298	−	0.947731i	−0.0397746	−	0.0338691i
$784$	−3.71867	+	5.93055i	−0.132810	+	0.211806i
$785$		0			0
$786$	6.67621	−	27.8689i	0.238133	−	0.994051i
$787$	−30.7560			−1.09633			−0.548167	−	0.836369i	$-0.684674\pi$
$787$	−30.7560			−1.09633			−0.548167	+	0.836369i	$0.684674\pi$
$788$	−2.52597			−0.0899840
$789$	−3.59582	+	15.0103i	−0.128015	+	0.534379i
$790$		0			0
$791$	−10.9406	−	19.7736i	−0.389002	−	0.703068i
$792$	7.27071	−	14.3044i	0.258353	−	0.508285i
$793$		−	52.4410i		−	1.86224i
$794$	17.8706			0.634203
$795$		0			0
$796$		−	0.947731i		−	0.0335914i
$797$		−	14.1958i		−	0.502842i	−0.967878	−	0.251421i	$-0.919102\pi$
$797$		−	14.1958i		−	0.502842i	0.967878	−	0.251421i	$-0.0808979\pi$
$798$	−0.987289	−	3.56400i	−0.0349497	−	0.126164i
$799$	42.4103			1.50037
$800$		0			0
$801$	−11.5439	−	5.86760i	−0.407884	−	0.207321i
$802$			12.6762i			0.447613i
$803$			26.6517i			0.940519i
$804$	−11.3169	−	2.71105i	−0.399116	−	0.0956112i
$805$		0			0
$806$			35.9209i			1.26526i
$807$	9.01247	−	37.6213i	0.317254	−	1.32433i
$808$	5.78984			0.203686
$809$			39.0404i			1.37259i	0.727325	+	0.686293i	$0.240763\pi$
$809$			39.0404i			1.37259i	−0.727325	+	0.686293i	$0.759237\pi$
$810$		0			0
$811$			42.9328i			1.50758i	0.657118	+	0.753788i	$0.271775\pi$
$811$			42.9328i			1.50758i	−0.657118	+	0.753788i	$0.728225\pi$
$812$	0.651279	−	0.360347i	0.0228554	−	0.0126457i
$813$	12.0886	+	2.89592i	0.423967	+	0.101564i
$814$	32.4528			1.13747
$815$		0			0
$816$	12.3381	+	2.95569i	0.431920	+	0.103470i
$817$	5.12354			0.179250
$818$			5.26425i			0.184060i
$819$	−1.10238	−	31.3818i	−0.0385203	−	1.09657i
$820$		0			0
$821$		−	2.45280i		−	0.0856033i	−0.999084	−	0.0428016i	$-0.986372\pi$
$821$		−	2.45280i		−	0.0856033i	0.999084	−	0.0428016i	$-0.0136283\pi$
$822$	−2.99247	+	12.4917i	−0.104374	+	0.435696i
$823$		−	30.6300i		−	1.06770i	−0.845580	−	0.533848i	$-0.820745\pi$
$823$		−	30.6300i		−	1.06770i	0.845580	−	0.533848i	$-0.179255\pi$
$824$	−6.95721			−0.242366
$825$		0			0
$826$	−6.28133	−	11.3526i	−0.218555	−	0.395009i
$827$	37.8265			1.31535			0.657677	−	0.753300i	$-0.271539\pi$
$827$	37.8265			1.31535			0.657677	+	0.753300i	$0.271539\pi$
$828$	0.752370	+	0.382418i	0.0261467	+	0.0132899i
$829$		−	18.6605i		−	0.648105i	−0.946039	−	0.324052i	$-0.894955\pi$
$829$		−	18.6605i		−	0.648105i	0.946039	−	0.324052i	$-0.105045\pi$
$830$		0			0
$831$	15.7112	+	3.76373i	0.545014	+	0.130562i
$832$	3.95617			0.137156
$833$	43.4410	+	27.2391i	1.50514	+	0.943779i
$834$	10.7293	+	2.57028i	0.371525	+	0.0890016i
$835$		0			0
$836$	−4.31652			−0.149290
$837$	−35.9209	−	30.5876i	−1.24161	−	1.05726i
$838$	−13.1148			−0.453043
$839$	21.1604			0.730540			0.365270	−	0.930902i	$-0.380977\pi$
$839$	21.1604			0.730540			0.365270	+	0.930902i	$0.380977\pi$
$840$		0			0
$841$	28.9209			0.997271
$842$	−3.86521			−0.133204
$843$	−29.3713	−	7.03613i	−1.01160	−	0.242337i
$844$	−12.8901			−0.443697
$845$		0			0
$846$	−7.87034	+	15.4841i	−0.270588	+	0.532355i
$847$	−22.5549	−	40.7648i	−0.774994	−	1.40070i
$848$	−10.9788			−0.377012
$849$	−6.52782	+	27.2495i	−0.224034	+	0.935200i
$850$		0			0
$851$			1.70692i			0.0585125i
$852$	−5.67632	−	1.35981i	−0.194468	−	0.0465862i
$853$	−18.3790			−0.629287			−0.314643	−	0.949210i	$-0.601885\pi$
$853$	−18.3790			−0.629287			−0.314643	+	0.949210i	$0.601885\pi$
$854$	−30.6868	+	16.9788i	−1.05008	+	0.581002i
$855$		0			0
$856$	−10.6088			−0.362602
$857$		−	47.0915i		−	1.60861i	−0.594214	−	0.804307i	$-0.702537\pi$
$857$		−	47.0915i		−	1.60861i	0.594214	−	0.804307i	$-0.297463\pi$
$858$	−35.6425	−	8.53844i	−1.21682	−	0.291497i
$859$			30.5313i			1.04171i	0.853644	+	0.520857i	$0.174388\pi$
$859$			30.5313i			1.04171i	−0.853644	+	0.520857i	$0.825612\pi$
$860$		0			0
$861$	−27.1608	+	7.52401i	−0.925639	+	0.256418i
$862$		−	10.2389i		−	0.348737i
$863$	32.2696			1.09847			0.549235	−	0.835668i	$-0.314919\pi$
$863$	32.2696			1.09847			0.549235	+	0.835668i	$0.314919\pi$
$864$	−3.36879	+	3.95617i	−0.114608	+	0.134592i
$865$		0			0
$866$	−22.7030			−0.771478
$867$	14.7906	−	61.7414i	0.502316	−	2.09685i
$868$	21.0197	−	11.6300i	0.713456	−	0.394750i
$869$		−	17.4373i		−	0.591521i
$870$		0			0
$871$			26.5802i			0.900636i
$872$	−18.1348			−0.614121
$873$	−40.3539	−	20.5113i	−1.36577	−	0.694202i
$874$		−	0.227036i		−	0.00767961i
$875$		0			0
$876$	2.01062	−	8.39303i	0.0679324	−	0.283574i
$877$			9.61460i			0.324662i	0.986736	+	0.162331i	$0.0519012\pi$
$877$			9.61460i			0.324662i	−0.986736	+	0.162331i	$0.948099\pi$
$878$			26.4492i			0.892618i
$879$	−38.0037	−	9.10408i	−1.28183	−	0.307073i
$880$		0			0
$881$	−22.0464			−0.742762			−0.371381	−	0.928481i	$-0.621116\pi$
$881$	−22.0464			−0.742762			−0.371381	+	0.928481i	$0.621116\pi$
$882$	−18.0067	+	10.8055i	−0.606317	+	0.363841i
$883$			31.5876i			1.06301i	0.847056	+	0.531503i	$0.178373\pi$
$883$			31.5876i			1.06301i	−0.847056	+	0.531503i	$0.821627\pi$
$884$		−	28.9788i		−	0.974661i
$885$		0			0
$886$	−27.8689			−0.936274
$887$			17.9472i			0.602607i	0.953528	+	0.301304i	$0.0974218\pi$
$887$			17.9472i			0.602607i	−0.953528	+	0.301304i	$0.902578\pi$
$888$	−10.2199	−	2.44825i	−0.342957	−	0.0821579i
$889$	4.63005	−	2.56177i	0.155287	−	0.0859189i
$890$		0			0
$891$	38.8890	−	28.3718i	1.30283	−	0.950491i
$892$	−23.7296			−0.794526
$893$	4.67251			0.156360
$894$	−12.8162	−	3.07023i	−0.428639	−	0.102684i
$895$		0			0
$896$	−1.28088	−	2.31502i	−0.0427913	−	0.0773395i
$897$	0.449097	−	1.87469i	0.0149949	−	0.0625941i
$898$			9.45858i			0.315637i
$899$	−2.55437			−0.0851929
$900$		0			0
$901$			80.4190i			2.67915i
$902$			32.8956i			1.09531i
$903$	−7.76689	−	28.0376i	−0.258466	−	0.933033i
$904$	8.54142			0.284084
$905$		0			0
$906$	−1.86827	+	7.79882i	−0.0620690	+	0.259098i
$907$			39.9942i			1.32799i	0.747739	+	0.663993i	$0.231140\pi$
$907$			39.9942i			1.32799i	−0.747739	+	0.663993i	$0.768860\pi$
$908$		−	10.4667i		−	0.347350i
$909$	15.4841	+	7.87034i	0.513576	+	0.261043i
$910$		0			0
$911$			15.4740i			0.512677i	0.966587	+	0.256339i	$0.0825163\pi$
$911$			15.4740i			0.512677i	−0.966587	+	0.256339i	$0.917484\pi$
$912$	1.35934	+	0.325639i	0.0450121	+	0.0107830i
$913$	−8.21090			−0.271741
$914$		−	31.8322i		−	1.05292i
$915$		0			0
$916$		−	16.4762i		−	0.544388i
$917$	21.1927	+	38.3029i	0.699845	+	1.26487i
$918$	28.9788	+	24.6762i	0.956442	+	0.814436i
$919$	−25.5721			−0.843547			−0.421773	−	0.906701i	$-0.638592\pi$
$919$	−25.5721			−0.843547			−0.421773	+	0.906701i	$0.638592\pi$
$920$		0			0
$921$	−7.83038	+	32.6868i	−0.258020	+	1.07707i
$922$	−10.6320			−0.350145
$923$			13.3321i			0.438831i
$924$	6.54351	+	23.6213i	0.215266	+	0.777085i
$925$		0			0
$926$			12.8322i			0.421693i
$927$	−18.6061	−	9.45719i	−0.611104	−	0.310615i
$928$			0.281327i			0.00923501i
$929$	27.6092			0.905828			0.452914	−	0.891554i	$-0.350384\pi$
$929$	27.6092			0.905828			0.452914	+	0.891554i	$0.350384\pi$
$930$		0			0
$931$	4.78607	+	3.00104i	0.156857	+	0.0983550i
$932$	−27.9575			−0.915780
$933$	−2.71867	+	11.3487i	−0.0890054	+	0.371540i
$934$		−	20.8716i		−	0.682940i
$935$		0			0
$936$	10.5802	+	5.37777i	0.345825	+	0.175778i
$937$	−36.8988			−1.20543			−0.602716	−	0.797956i	$-0.705915\pi$
$937$	−36.8988			−1.20543			−0.602716	+	0.797956i	$0.705915\pi$
$938$	15.5539	−	8.60584i	0.507852	−	0.280991i
$939$	−8.63005	+	36.0249i	−0.281631	+	1.17563i
$940$		0			0
$941$	45.1245			1.47102			0.735508	−	0.677516i	$-0.236943\pi$
$941$	45.1245			1.47102			0.735508	+	0.677516i	$0.236943\pi$
$942$	−6.18024	+	25.7985i	−0.201363	+	0.840562i
$943$	−1.73021			−0.0563435
$944$	4.90390			0.159608
$945$		0			0
$946$	−33.9575			−1.10405
$947$	−13.3524			−0.433895			−0.216948	−	0.976183i	$-0.569610\pi$
$947$	−13.3524			−0.433895			−0.216948	+	0.976183i	$0.569610\pi$
$948$	−1.31548	+	5.49128i	−0.0427248	+	0.178349i
$949$	−19.7129			−0.639908
$950$		0			0
$951$	1.40180	−	5.85163i	0.0454566	−	0.189752i
$952$	−16.9574	+	9.38242i	−0.549594	+	0.304086i
$953$	−52.2483			−1.69249			−0.846245	−	0.532794i	$-0.821142\pi$
$953$	−52.2483			−1.69249			−0.846245	+	0.532794i	$0.821142\pi$
$954$	−29.3612	−	14.9238i	−0.950604	−	0.483177i
$955$		0			0
$956$		−	17.2601i		−	0.558231i
$957$	0.607177	−	2.53457i	0.0196272	−	0.0819311i
$958$	33.6879			1.08841
$959$	−9.49918	−	17.1685i	−0.306745	−	0.554399i
$960$		0			0
$961$	−51.4410			−1.65939
$962$			24.0036i			0.773908i
$963$	−28.3718	−	14.4210i	−0.914269	−	0.464709i
$964$			19.1935i			0.618180i
$965$		0			0
$966$	−1.24241	+	0.344169i	−0.0399740	+	0.0110735i
$967$			3.46228i			0.111339i	0.998449	+	0.0556697i	$0.0177294\pi$
$967$			3.46228i			0.111339i	−0.998449	+	0.0556697i	$0.982271\pi$
$968$	17.6088			0.565969
$969$	2.38529	−	9.95708i	0.0766267	−	0.319867i
$970$		0			0
$971$	42.3528			1.35917			0.679584	−	0.733598i	$-0.262161\pi$
$971$	42.3528			1.35917			0.679584	+	0.733598i	$0.262161\pi$
$972$	−14.3871	+	6.00091i	−0.461467	+	0.192479i
$973$	−14.7463	+	8.15901i	−0.472745	+	0.261566i
$974$		−	33.3524i		−	1.06868i
$975$		0			0
$976$		−	13.2555i		−	0.424299i
$977$	−16.2483			−0.519831			−0.259915	−	0.965631i	$-0.583695\pi$
$977$	−16.2483			−0.519831			−0.259915	+	0.965631i	$0.583695\pi$
$978$	−5.16670	−	1.23772i	−0.165213	−	0.0395780i
$979$		−	23.0878i		−	0.737891i
$980$		0			0
$981$	−48.4990	−	24.6513i	−1.54845	−	0.787055i
$982$		−	30.0000i		−	0.957338i
$983$			33.9149i			1.08172i	0.841114	+	0.540859i	$0.181901\pi$
$983$			33.9149i			1.08172i	−0.841114	+	0.540859i	$0.818099\pi$
$984$	2.48166	−	10.3593i	0.0791124	−	0.330244i
$985$		0			0
$986$	2.06071			0.0656263
$987$	−7.08317	−	25.5694i	−0.225460	−	0.813884i
$988$		−	3.19270i		−	0.101573i
$989$		−	1.78607i		−	0.0567936i
$990$		0			0
$991$	−41.5971			−1.32137			−0.660687	−	0.750661i	$-0.729735\pi$
$991$	−41.5971			−1.32137			−0.660687	+	0.750661i	$0.729735\pi$
$992$			9.07971i			0.288281i
$993$	3.60439	−	15.0460i	0.114382	−	0.477471i
$994$	7.80152	−	4.31652i	0.247449	−	0.136912i
$995$		0			0
$996$	2.58574	+	0.619433i	0.0819322	+	0.0196275i
$997$	9.45719			0.299512			0.149756	−	0.988723i	$-0.452151\pi$
$997$	9.45719			0.299512			0.149756	+	0.988723i	$0.452151\pi$
$998$	−19.1810			−0.607162
$999$	−24.0036	−	20.4398i	−0.759442	−	0.646685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.d.g.1049.6		12
3.2	odd	2		1050.2.d.h.1049.5		12
5.2	odd	4		1050.2.b.d.251.6	yes	12
5.3	odd	4		1050.2.b.e.251.7	yes	12
5.4	even	2		1050.2.d.h.1049.7		12
7.6	odd	2	inner	1050.2.d.g.1049.7		12
15.2	even	4		1050.2.b.d.251.7	yes	12
15.8	even	4		1050.2.b.e.251.6	yes	12
15.14	odd	2	inner	1050.2.d.g.1049.8		12
21.20	even	2		1050.2.d.h.1049.8		12
35.13	even	4		1050.2.b.e.251.12	yes	12
35.27	even	4		1050.2.b.d.251.1	✓	12
35.34	odd	2		1050.2.d.h.1049.6		12
105.62	odd	4		1050.2.b.d.251.12	yes	12
105.83	odd	4		1050.2.b.e.251.1	yes	12
105.104	even	2	inner	1050.2.d.g.1049.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.b.d.251.1	✓	12	35.27	even	4
1050.2.b.d.251.6	yes	12	5.2	odd	4
1050.2.b.d.251.7	yes	12	15.2	even	4
1050.2.b.d.251.12	yes	12	105.62	odd	4
1050.2.b.e.251.1	yes	12	105.83	odd	4
1050.2.b.e.251.6	yes	12	15.8	even	4
1050.2.b.e.251.7	yes	12	5.3	odd	4
1050.2.b.e.251.12	yes	12	35.13	even	4
1050.2.d.g.1049.5		12	105.104	even	2	inner
1050.2.d.g.1049.6		12	1.1	even	1	trivial
1050.2.d.g.1049.7		12	7.6	odd	2	inner
1050.2.d.g.1049.8		12	15.14	odd	2	inner
1050.2.d.h.1049.5		12	3.2	odd	2
1050.2.d.h.1049.6		12	35.34	odd	2
1050.2.d.h.1049.7		12	5.4	even	2
1050.2.d.h.1049.8		12	21.20	even	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.403509 + 1.68439i) q^{3} +1.00000 q^{4} +(0.403509 - 1.68439i) q^{6} +(1.28088 + 2.31502i) q^{7} -1.00000 q^{8} +(-2.67436 - 1.35934i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.403509 + 1.68439i) q^{3} +1.00000 q^{4} +(0.403509 - 1.68439i) q^{6} +(1.28088 + 2.31502i) q^{7} -1.00000 q^{8} +(-2.67436 - 1.35934i) q^{9} -5.34872i q^{11} +(-0.403509 + 1.68439i) q^{12} +3.95617 q^{13} +(-1.28088 - 2.31502i) q^{14} +1.00000 q^{16} -7.32496i q^{17} +(2.67436 + 1.35934i) q^{18} -0.807019i q^{19} +(-4.41626 + 1.22338i) q^{21} +5.34872i q^{22} -0.281327 q^{23} +(0.403509 - 1.68439i) q^{24} -3.95617 q^{26} +(3.36879 - 3.95617i) q^{27} +(1.28088 + 2.31502i) q^{28} -0.281327i q^{29} -9.07971i q^{31} -1.00000 q^{32} +(9.00935 + 2.15826i) q^{33} +7.32496i q^{34} +(-2.67436 - 1.35934i) q^{36} -6.06739i q^{37} +0.807019i q^{38} +(-1.59635 + 6.66375i) q^{39} +6.15019 q^{41} +(4.41626 - 1.22338i) q^{42} +6.34872i q^{43} -5.34872i q^{44} +0.281327 q^{46} +5.78984i q^{47} +(-0.403509 + 1.68439i) q^{48} +(-3.71867 + 5.93055i) q^{49} +(12.3381 + 2.95569i) q^{51} +3.95617 q^{52} -10.9788 q^{53} +(-3.36879 + 3.95617i) q^{54} +(-1.28088 - 2.31502i) q^{56} +(1.35934 + 0.325639i) q^{57} +0.281327i q^{58} +4.90390 q^{59} -13.2555i q^{61} +9.07971i q^{62} +(-0.278649 - 7.93236i) q^{63} +1.00000 q^{64} +(-9.00935 - 2.15826i) q^{66} +6.71867i q^{67} -7.32496i q^{68} +(0.113518 - 0.473865i) q^{69} +3.36995i q^{71} +(2.67436 + 1.35934i) q^{72} -4.98282 q^{73} +6.06739i q^{74} -0.807019i q^{76} +(12.3824 - 6.85109i) q^{77} +(1.59635 - 6.66375i) q^{78} +3.26010 q^{79} +(5.30441 + 7.27071i) q^{81} -6.15019 q^{82} -1.53511i q^{83} +(-4.41626 + 1.22338i) q^{84} -6.34872i q^{86} +(0.473865 + 0.113518i) q^{87} +5.34872i q^{88} +4.31652 q^{89} +(5.06739 + 9.15863i) q^{91} -0.281327 q^{92} +(15.2938 + 3.66375i) q^{93} -5.78984i q^{94} +(0.403509 - 1.68439i) q^{96} +15.0892 q^{97} +(3.71867 - 5.93055i) q^{98} +(-7.27071 + 14.3044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8	\( 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8} + 12 q^{16} + 14 q^{21} - 20 q^{23} - 12 q^{32} - 12 q^{39} - 14 q^{42} + 20 q^{46} - 28 q^{49} + 28 q^{51} - 20 q^{53} + 8 q^{57} - 30 q^{63} + 12 q^{64} + 44 q^{77} + 12 q^{78} - 56 q^{79} - 16 q^{81} + 14 q^{84} - 20 q^{91} - 20 q^{92} + 48 q^{93} + 28 q^{98} - 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8 + 12 * q^16 + 14 * q^21 - 20 * q^23 - 12 * q^32 - 12 * q^39 - 14 * q^42 + 20 * q^46 - 28 * q^49 + 28 * q^51 - 20 * q^53 + 8 * q^57 - 30 * q^63 + 12 * q^64 + 44 * q^77 + 12 * q^78 - 56 * q^79 - 16 * q^81 + 14 * q^84 - 20 * q^91 - 20 * q^92 + 48 * q^93 + 28 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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