LMFDB - Embedded newform 756.2.e.b.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(323,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.6
Character	$\chi$	$=$	756.323
Dual form			756.2.e.b.323.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21808 + 0.718530i) q^{2} +(0.967429 - 1.75045i) q^{4} -1.77738i q^{5} +1.00000i q^{7} +(0.0793484 + 2.82731i) q^{8} +O(q^{10})$	\(q+(-1.21808 + 0.718530i) q^{2} +(0.967429 - 1.75045i) q^{4} -1.77738i q^{5} +1.00000i q^{7} +(0.0793484 + 2.82731i) q^{8} +(1.27710 + 2.16499i) q^{10} -5.69996 q^{11} -0.512468 q^{13} +(-0.718530 - 1.21808i) q^{14} +(-2.12816 - 3.38688i) q^{16} +1.25544i q^{17} +2.17781i q^{19} +(-3.11122 - 1.71949i) q^{20} +(6.94299 - 4.09559i) q^{22} -4.44103 q^{23} +1.84092 q^{25} +(0.624227 - 0.368224i) q^{26} +(1.75045 + 0.967429i) q^{28} +4.23700i q^{29} +6.10220i q^{31} +(5.02584 + 2.59633i) q^{32} +(-0.902069 - 1.52922i) q^{34} +1.77738 q^{35} -2.77042 q^{37} +(-1.56482 - 2.65274i) q^{38} +(5.02521 - 0.141032i) q^{40} +9.84121i q^{41} +3.69524i q^{43} +(-5.51430 + 9.97750i) q^{44} +(5.40952 - 3.19101i) q^{46} -3.24194 q^{47} -1.00000 q^{49} +(-2.24238 + 1.32275i) q^{50} +(-0.495777 + 0.897051i) q^{52} -2.68179i q^{53} +10.1310i q^{55} +(-2.82731 + 0.0793484i) q^{56} +(-3.04441 - 5.16100i) q^{58} +6.33178 q^{59} -12.2880 q^{61} +(-4.38461 - 7.43295i) q^{62} +(-7.98741 + 0.448686i) q^{64} +0.910852i q^{65} -9.83939i q^{67} +(2.19758 + 1.21455i) q^{68} +(-2.16499 + 1.27710i) q^{70} +8.69040 q^{71} -15.9201 q^{73} +(3.37459 - 1.99063i) q^{74} +(3.81215 + 2.10688i) q^{76} -5.69996i q^{77} +14.4957i q^{79} +(-6.01977 + 3.78256i) q^{80} +(-7.07120 - 11.9874i) q^{82} -10.1621 q^{83} +2.23139 q^{85} +(-2.65514 - 4.50109i) q^{86} +(-0.452282 - 16.1156i) q^{88} -17.1585i q^{89} -0.512468i q^{91} +(-4.29638 + 7.77381i) q^{92} +(3.94893 - 2.32943i) q^{94} +3.87080 q^{95} +2.72350 q^{97} +(1.21808 - 0.718530i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4}+O(q^{10}) $ 24 * q + 4 * q^4	$ 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.21808	+	0.718530i	−0.861311	+	0.508078i
$2$	−1.21808	+	0.718530i	−0.861311	+	0.508078i
$3$		0			0
$3$		0			0
$4$	0.967429	−	1.75045i	0.483714	−	0.875226i
$5$		−	1.77738i		−	0.794869i	−0.917631	−	0.397434i	$-0.869901\pi$
$5$		−	1.77738i		−	0.794869i	0.917631	−	0.397434i	$-0.130099\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.0793484	+	2.82731i	0.0280539	+	0.999606i
$9$		0			0
$10$	1.27710	+	2.16499i	0.403855	+	0.684630i
$11$	−5.69996			−1.71860			−0.859301	−	0.511470i	$-0.829101\pi$
$11$	−5.69996			−1.71860			−0.859301	+	0.511470i	$0.829101\pi$
$12$		0			0
$13$	−0.512468			−0.142133			−0.0710666	−	0.997472i	$-0.522640\pi$
$13$	−0.512468			−0.142133			−0.0710666	+	0.997472i	$0.522640\pi$
$14$	−0.718530	−	1.21808i	−0.192035	−	0.325545i
$15$		0			0
$16$	−2.12816	−	3.38688i	−0.532041	−	0.846719i
$17$			1.25544i			0.304488i	0.988343	+	0.152244i	$0.0486500\pi$
$17$			1.25544i			0.304488i	−0.988343	+	0.152244i	$0.951350\pi$
$18$		0			0
$19$			2.17781i			0.499624i	0.968294	+	0.249812i	$0.0803688\pi$
$19$			2.17781i			0.499624i	−0.968294	+	0.249812i	$0.919631\pi$
$20$	−3.11122	−	1.71949i	−0.695690	−	0.384490i
$21$		0			0
$22$	6.94299	−	4.09559i	1.48025	−	0.873183i
$23$	−4.44103			−0.926018			−0.463009	−	0.886353i	$-0.653230\pi$
$23$	−4.44103			−0.926018			−0.463009	+	0.886353i	$0.653230\pi$
$24$		0			0
$25$	1.84092			0.368183
$26$	0.624227	−	0.368224i	0.122421	−	0.0722147i
$27$		0			0
$28$	1.75045	+	0.967429i	0.330804	+	0.182827i
$29$			4.23700i			0.786791i	0.919369	+	0.393396i	$0.128700\pi$
$29$			4.23700i			0.786791i	−0.919369	+	0.393396i	$0.871300\pi$
$30$		0			0
$31$			6.10220i			1.09599i	0.836483	+	0.547994i	$0.184608\pi$
$31$			6.10220i			1.09599i	−0.836483	+	0.547994i	$0.815392\pi$
$32$	5.02584	+	2.59633i	0.888451	+	0.458971i
$33$		0			0
$34$	−0.902069	−	1.52922i	−0.154704	−	0.262259i
$35$	1.77738			0.300432
$36$		0			0
$37$	−2.77042			−0.455454			−0.227727	−	0.973725i	$-0.573129\pi$
$37$	−2.77042			−0.455454			−0.227727	+	0.973725i	$0.573129\pi$
$38$	−1.56482	−	2.65274i	−0.253848	−	0.430332i
$39$		0			0
$40$	5.02521	−	0.141032i	0.794556	−	0.0222992i
$41$			9.84121i			1.53694i	0.639887	+	0.768469i	$0.278981\pi$
$41$			9.84121i			1.53694i	−0.639887	+	0.768469i	$0.721019\pi$
$42$		0			0
$43$			3.69524i			0.563518i	0.959485	+	0.281759i	$0.0909179\pi$
$43$			3.69524i			0.563518i	−0.959485	+	0.281759i	$0.909082\pi$
$44$	−5.51430	+	9.97750i	−0.831313	+	1.50416i
$45$		0			0
$46$	5.40952	−	3.19101i	0.797590	−	0.470489i
$47$	−3.24194			−0.472885			−0.236442	−	0.971645i	$-0.575981\pi$
$47$	−3.24194			−0.472885			−0.236442	+	0.971645i	$0.575981\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−2.24238	+	1.32275i	−0.317120	+	0.187066i
$51$		0			0
$52$	−0.495777	+	0.897051i	−0.0687519	+	0.124399i
$53$		−	2.68179i		−	0.368372i	−0.982891	−	0.184186i	$-0.941035\pi$
$53$		−	2.68179i		−	0.368372i	0.982891	−	0.184186i	$-0.0589648\pi$
$54$		0			0
$55$			10.1310i			1.36606i
$56$	−2.82731	+	0.0793484i	−0.377816	+	0.0106034i
$57$		0			0
$58$	−3.04441	−	5.16100i	−0.399751	−	0.677672i
$59$	6.33178			0.824327			0.412164	−	0.911110i	$-0.364773\pi$
$59$	6.33178			0.824327			0.412164	+	0.911110i	$0.364773\pi$
$60$		0			0
$61$	−12.2880			−1.57332			−0.786660	−	0.617386i	$-0.788192\pi$
$61$	−12.2880			−1.57332			−0.786660	+	0.617386i	$0.788192\pi$
$62$	−4.38461	−	7.43295i	−0.556846	−	0.943986i
$63$		0			0
$64$	−7.98741	+	0.448686i	−0.998426	+	0.0560857i
$65$			0.910852i			0.112977i
$66$		0			0
$67$		−	9.83939i		−	1.20207i	−0.799222	−	0.601037i	$-0.794755\pi$
$67$		−	9.83939i		−	1.20207i	0.799222	−	0.601037i	$-0.205245\pi$
$68$	2.19758	+	1.21455i	0.266496	+	0.147285i
$69$		0			0
$70$	−2.16499	+	1.27710i	−0.258766	+	0.152643i
$71$	8.69040			1.03136			0.515680	−	0.856781i	$-0.327539\pi$
$71$	8.69040			1.03136			0.515680	+	0.856781i	$0.327539\pi$
$72$		0			0
$73$	−15.9201			−1.86331			−0.931656	−	0.363342i	$-0.881636\pi$
$73$	−15.9201			−1.86331			−0.931656	+	0.363342i	$0.881636\pi$
$74$	3.37459	−	1.99063i	0.392288	−	0.231406i
$75$		0			0
$76$	3.81215	+	2.10688i	0.437284	+	0.241675i
$77$		−	5.69996i		−	0.649571i
$78$		0			0
$79$			14.4957i			1.63090i	0.578830	+	0.815449i	$0.303510\pi$
$79$			14.4957i			1.63090i	−0.578830	+	0.815449i	$0.696490\pi$
$80$	−6.01977	+	3.78256i	−0.673030	+	0.422903i
$81$		0			0
$82$	−7.07120	−	11.9874i	−0.780884	−	1.32378i
$83$	−10.1621			−1.11543			−0.557717	−	0.830032i	$-0.688322\pi$
$83$	−10.1621			−1.11543			−0.557717	+	0.830032i	$0.688322\pi$
$84$		0			0
$85$	2.23139			0.242028
$86$	−2.65514	−	4.50109i	−0.286311	−	0.485365i
$87$		0			0
$88$	−0.452282	−	16.1156i	−0.0482135	−	1.71793i
$89$		−	17.1585i		−	1.81880i	−0.415926	−	0.909398i	$-0.636543\pi$
$89$		−	17.1585i		−	1.81880i	0.415926	−	0.909398i	$-0.363457\pi$
$90$		0			0
$91$		−	0.512468i		−	0.0537213i
$92$	−4.29638	+	7.77381i	−0.447928	+	0.810475i
$93$		0			0
$94$	3.94893	−	2.32943i	0.407301	−	0.240262i
$95$	3.87080			0.397136
$96$		0			0
$97$	2.72350			0.276530			0.138265	−	0.990395i	$-0.455847\pi$
$97$	2.72350			0.276530			0.138265	+	0.990395i	$0.455847\pi$
$98$	1.21808	−	0.718530i	0.123044	−	0.0725825i
$99$		0			0
$100$	1.78096	−	3.22244i	0.178096	−	0.322244i
$101$			6.46990i			0.643780i	0.946777	+	0.321890i	$0.104318\pi$
$101$			6.46990i			0.643780i	−0.946777	+	0.321890i	$0.895682\pi$
$102$		0			0
$103$		−	12.6888i		−	1.25026i	−0.780521	−	0.625130i	$-0.785046\pi$
$103$		−	12.6888i		−	1.25026i	0.780521	−	0.625130i	$-0.214954\pi$
$104$	−0.0406635	−	1.44891i	−0.00398739	−	0.142077i
$105$		0			0
$106$	1.92694	+	3.26663i	0.187161	+	0.317283i
$107$	−1.63494			−0.158056			−0.0790280	−	0.996872i	$-0.525182\pi$
$107$	−1.63494			−0.158056			−0.0790280	+	0.996872i	$0.525182\pi$
$108$		0			0
$109$	−17.4500			−1.67141			−0.835704	−	0.549180i	$-0.814940\pi$
$109$	−17.4500			−1.67141			−0.835704	+	0.549180i	$0.814940\pi$
$110$	−7.27943	−	12.3403i	−0.694066	−	1.17661i
$111$		0			0
$112$	3.38688	−	2.12816i	0.320030	−	0.201092i
$113$			13.8177i			1.29986i	0.759994	+	0.649930i	$0.225202\pi$
$113$			13.8177i			1.29986i	−0.759994	+	0.649930i	$0.774798\pi$
$114$		0			0
$115$			7.89340i			0.736063i
$116$	7.41667	+	4.09900i	0.688620	+	0.380582i
$117$		0			0
$118$	−7.71260	+	4.54957i	−0.710002	+	0.418822i
$119$	−1.25544			−0.115086
$120$		0			0
$121$	21.4895			1.95359
$122$	14.9678	−	8.82932i	1.35512	−	0.799369i
$123$		0			0
$124$	10.6816	+	5.90344i	0.959236	+	0.530145i
$125$		−	12.1589i		−	1.08753i
$126$		0			0
$127$			15.9500i			1.41534i	0.706545	+	0.707668i	$0.250253\pi$
$127$			15.9500i			1.41534i	−0.706545	+	0.707668i	$0.749747\pi$
$128$	9.40689	−	6.28573i	0.831460	−	0.555585i
$129$		0			0
$130$	−0.654474	−	1.10949i	−0.0574012	−	0.0973086i
$131$	−2.04595			−0.178756			−0.0893778	−	0.995998i	$-0.528488\pi$
$131$	−2.04595			−0.178756			−0.0893778	+	0.995998i	$0.528488\pi$
$132$		0			0
$133$	−2.17781			−0.188840
$134$	7.06990	+	11.9851i	0.610746	+	1.03536i
$135$		0			0
$136$	−3.54951	+	0.0996168i	−0.304368	+	0.00854207i
$137$			15.7620i			1.34664i	0.739353	+	0.673318i	$0.235132\pi$
$137$			15.7620i			1.34664i	−0.739353	+	0.673318i	$0.764868\pi$
$138$		0			0
$139$			20.0296i			1.69889i	0.527675	+	0.849446i	$0.323064\pi$
$139$			20.0296i			1.69889i	−0.527675	+	0.849446i	$0.676936\pi$
$140$	1.71949	−	3.11122i	0.145323	−	0.262946i
$141$		0			0
$142$	−10.5856	+	6.24431i	−0.888322	+	0.524011i
$143$	2.92105			0.244270
$144$		0			0
$145$	7.53077			0.625396
$146$	19.3920	−	11.4391i	1.60489	−	0.946707i
$147$		0			0
$148$	−2.68018	+	4.84948i	−0.220310	+	0.398625i
$149$		−	15.6040i		−	1.27833i	−0.769071	−	0.639163i	$-0.779281\pi$
$149$		−	15.6040i		−	1.27833i	0.769071	−	0.639163i	$-0.220719\pi$
$150$		0			0
$151$		−	13.1152i		−	1.06730i	−0.845706	−	0.533649i	$-0.820820\pi$
$151$		−	13.1152i		−	1.06730i	0.845706	−	0.533649i	$-0.179180\pi$
$152$	−6.15736	+	0.172806i	−0.499428	+	0.0140164i
$153$		0			0
$154$	4.09559	+	6.94299i	0.330032	+	0.559482i
$155$	10.8459			0.871166
$156$		0			0
$157$	−0.0800390			−0.00638781			−0.00319391	−	0.999995i	$-0.501017\pi$
$157$	−0.0800390			−0.00638781			−0.00319391	+	0.999995i	$0.501017\pi$
$158$	−10.4156	−	17.6569i	−0.828622	−	1.40471i
$159$		0			0
$160$	4.61467	−	8.93283i	0.364821	−	0.706203i
$161$		−	4.44103i		−	0.350002i
$162$		0			0
$163$		−	6.89783i		−	0.540279i	−0.962821	−	0.270140i	$-0.912930\pi$
$163$		−	6.89783i		−	0.540279i	0.962821	−	0.270140i	$-0.0870699\pi$
$164$	17.2266	+	9.52067i	1.34517	+	0.743439i
$165$		0			0
$166$	12.3782	−	7.30176i	0.960735	−	0.566726i
$167$	−5.11590			−0.395880			−0.197940	−	0.980214i	$-0.563425\pi$
$167$	−5.11590			−0.395880			−0.197940	+	0.980214i	$0.563425\pi$
$168$		0			0
$169$	−12.7374			−0.979798
$170$	−2.71801	+	1.60332i	−0.208462	+	0.122969i
$171$		0			0
$172$	6.46833	+	3.57488i	0.493206	+	0.272582i
$173$		−	5.75630i		−	0.437643i	−0.975765	−	0.218822i	$-0.929779\pi$
$173$		−	5.75630i		−	0.437643i	0.975765	−	0.218822i	$-0.0702213\pi$
$174$		0			0
$175$			1.84092i			0.139160i
$176$	12.1304	+	19.3050i	0.914366	+	1.45517i
$177$		0			0
$178$	12.3289	+	20.9004i	0.924090	+	1.56655i
$179$	18.5140			1.38380			0.691900	−	0.721993i	$-0.256774\pi$
$179$	18.5140			1.38380			0.691900	+	0.721993i	$0.256774\pi$
$180$		0			0
$181$	14.7269			1.09464			0.547322	−	0.836922i	$-0.315647\pi$
$181$	14.7269			1.09464			0.547322	+	0.836922i	$0.315647\pi$
$182$	0.368224	+	0.624227i	0.0272946	+	0.0462708i
$183$		0			0
$184$	−0.352388	−	12.5562i	−0.0259784	−	0.925654i
$185$			4.92409i			0.362026i
$186$		0			0
$187$		−	7.15593i		−	0.523294i
$188$	−3.13634	+	5.67485i	−0.228741	+	0.413881i
$189$		0			0
$190$	−4.71494	+	2.78129i	−0.342058	+	0.201776i
$191$	18.9511			1.37125			0.685625	−	0.727955i	$-0.259529\pi$
$191$	18.9511			1.37125			0.685625	+	0.727955i	$0.259529\pi$
$192$		0			0
$193$	10.4127			0.749525			0.374763	−	0.927121i	$-0.377724\pi$
$193$	10.4127			0.749525			0.374763	+	0.927121i	$0.377724\pi$
$194$	−3.31744	+	1.95692i	−0.238178	+	0.140499i
$195$		0			0
$196$	−0.967429	+	1.75045i	−0.0691021	+	0.125032i
$197$		−	8.83709i		−	0.629617i	−0.949155	−	0.314808i	$-0.898060\pi$
$197$		−	8.83709i		−	0.629617i	0.949155	−	0.314808i	$-0.101940\pi$
$198$		0			0
$199$		−	24.8494i		−	1.76153i	−0.473556	−	0.880764i	$-0.657030\pi$
$199$		−	24.8494i		−	1.76153i	0.473556	−	0.880764i	$-0.342970\pi$
$200$	0.146074	+	5.20485i	0.0103290	+	0.368038i
$201$		0			0
$202$	−4.64882	−	7.88085i	−0.327090	−	0.554495i
$203$	−4.23700			−0.297379
$204$		0			0
$205$	17.4916			1.22166
$206$	9.11725	+	15.4559i	0.635229	+	1.07686i
$207$		0			0
$208$	1.09062	+	1.73567i	0.0756206	+	0.120347i
$209$		−	12.4134i		−	0.858655i
$210$		0			0
$211$		−	3.03213i		−	0.208740i	−0.994539	−	0.104370i	$-0.966717\pi$
$211$		−	3.03213i		−	0.208740i	0.994539	−	0.104370i	$-0.0332827\pi$
$212$	−4.69434	−	2.59444i	−0.322408	−	0.178187i
$213$		0			0
$214$	1.99149	−	1.17476i	0.136135	−	0.0803047i
$215$	6.56784			0.447923
$216$		0			0
$217$	−6.10220			−0.414244
$218$	21.2555	−	12.5384i	1.43960	−	0.849205i
$219$		0			0
$220$	17.7338	+	9.80102i	1.19561	+	0.660785i
$221$		−	0.643371i		−	0.0432779i
$222$		0			0
$223$		−	16.9042i		−	1.13199i	−0.824409	−	0.565995i	$-0.808492\pi$
$223$		−	16.9042i		−	1.13199i	0.824409	−	0.565995i	$-0.191508\pi$
$224$	−2.59633	+	5.02584i	−0.173475	+	0.335803i
$225$		0			0
$226$	−9.92843	−	16.8310i	−0.660430	−	1.11958i
$227$	−10.7083			−0.710732			−0.355366	−	0.934727i	$-0.615644\pi$
$227$	−10.7083			−0.710732			−0.355366	+	0.934727i	$0.615644\pi$
$228$		0			0
$229$	−7.41416			−0.489941			−0.244971	−	0.969531i	$-0.578778\pi$
$229$	−7.41416			−0.489941			−0.244971	+	0.969531i	$0.578778\pi$
$230$	−5.67165	−	9.61478i	−0.373977	−	0.633980i
$231$		0			0
$232$	−11.9793	+	0.336199i	−0.786482	+	0.0220726i
$233$		−	12.6093i		−	0.826065i	−0.910716	−	0.413032i	$-0.864470\pi$
$233$		−	12.6093i		−	0.826065i	0.910716	−	0.413032i	$-0.135530\pi$
$234$		0			0
$235$			5.76215i			0.375882i
$236$	6.12554	−	11.0835i	0.398739	−	0.721472i
$237$		0			0
$238$	1.52922	−	0.902069i	0.0991246	−	0.0584724i
$239$	0.412605			0.0266892			0.0133446	−	0.999911i	$-0.495752\pi$
$239$	0.412605			0.0266892			0.0133446	+	0.999911i	$0.495752\pi$
$240$		0			0
$241$	5.14927			0.331694			0.165847	−	0.986152i	$-0.446964\pi$
$241$	5.14927			0.331694			0.165847	+	0.986152i	$0.446964\pi$
$242$	−26.1759	+	15.4409i	−1.68265	+	0.992577i
$243$		0			0
$244$	−11.8878	+	21.5096i	−0.761038	+	1.37701i
$245$			1.77738i			0.113553i
$246$		0			0
$247$		−	1.11606i		−	0.0710132i
$248$	−17.2528	+	0.484200i	−1.09556	+	0.0307467i
$249$		0			0
$250$	8.73655	+	14.8105i	0.552548	+	0.936699i
$251$	4.59516			0.290044			0.145022	−	0.989428i	$-0.453675\pi$
$251$	4.59516			0.290044			0.145022	+	0.989428i	$0.453675\pi$
$252$		0			0
$253$	25.3137			1.59146
$254$	−11.4606	−	19.4284i	−0.719101	−	1.21905i
$255$		0			0
$256$	−6.94185	+	14.4156i	−0.433865	+	0.900978i
$257$			27.1639i			1.69443i	0.531246	+	0.847217i	$0.321724\pi$
$257$			27.1639i			1.69443i	−0.531246	+	0.847217i	$0.678276\pi$
$258$		0			0
$259$		−	2.77042i		−	0.172145i
$260$	1.59440	+	0.881184i	0.0988806	+	0.0546487i
$261$		0			0
$262$	2.49213	−	1.47008i	0.153964	−	0.0908217i
$263$	0.767669			0.0473365			0.0236683	−	0.999720i	$-0.492465\pi$
$263$	0.767669			0.0473365			0.0236683	+	0.999720i	$0.492465\pi$
$264$		0			0
$265$	−4.76656			−0.292807
$266$	2.65274	−	1.56482i	0.162650	−	0.0959455i
$267$		0			0
$268$	−17.2234	−	9.51891i	−1.05209	−	0.581460i
$269$		−	0.439484i		−	0.0267958i	−0.999910	−	0.0133979i	$-0.995735\pi$
$269$		−	0.439484i		−	0.0267958i	0.999910	−	0.0133979i	$-0.00426481\pi$
$270$		0			0
$271$		−	4.55136i		−	0.276476i	−0.990399	−	0.138238i	$-0.955856\pi$
$271$		−	4.55136i		−	0.276476i	0.990399	−	0.138238i	$-0.0441438\pi$
$272$	4.25201	−	2.67177i	0.257816	−	0.162000i
$273$		0			0
$274$	−11.3255	−	19.1993i	−0.684196	−	1.15987i
$275$	−10.4931			−0.632761
$276$		0			0
$277$	−16.8178			−1.01048			−0.505241	−	0.862978i	$-0.668597\pi$
$277$	−16.8178			−1.01048			−0.505241	+	0.862978i	$0.668597\pi$
$278$	−14.3919	−	24.3977i	−0.863169	−	1.46328i
$279$		0			0
$280$	0.141032	+	5.02521i	0.00842829	+	0.300314i
$281$			26.2121i			1.56369i	0.623476	+	0.781843i	$0.285720\pi$
$281$			26.2121i			1.56369i	−0.623476	+	0.781843i	$0.714280\pi$
$282$		0			0
$283$			3.35005i			0.199140i	0.995031	+	0.0995700i	$0.0317467\pi$
$283$			3.35005i			0.199140i	−0.995031	+	0.0995700i	$0.968253\pi$
$284$	8.40734	−	15.2121i	0.498884	−	0.902673i
$285$		0			0
$286$	−3.55807	+	2.09886i	−0.210393	+	0.124108i
$287$	−9.84121			−0.580908
$288$		0			0
$289$	15.4239			0.907287
$290$	−9.17306	+	5.41108i	−0.538661	+	0.317750i
$291$		0			0
$292$	−15.4016	+	27.8674i	−0.901311	+	1.63082i
$293$		−	19.1757i		−	1.12025i	−0.828407	−	0.560127i	$-0.810752\pi$
$293$		−	19.1757i		−	1.12025i	0.828407	−	0.560127i	$-0.189248\pi$
$294$		0			0
$295$		−	11.2540i		−	0.655232i
$296$	−0.219828	−	7.83284i	−0.0127773	−	0.455275i
$297$		0			0
$298$	11.2119	+	19.0068i	0.649489	+	1.10104i
$299$	2.27589			0.131618
$300$		0			0
$301$	−3.69524			−0.212990
$302$	9.42365	+	15.9753i	0.542270	+	0.919275i
$303$		0			0
$304$	7.37597	−	4.63474i	0.423041	−	0.265820i
$305$			21.8405i			1.25058i
$306$		0			0
$307$			1.19494i			0.0681987i	0.999418	+	0.0340993i	$0.0108563\pi$
$307$			1.19494i			0.0681987i	−0.999418	+	0.0340993i	$0.989144\pi$
$308$	−9.97750	−	5.51430i	−0.568521	−	0.314207i
$309$		0			0
$310$	−13.2112	+	7.79313i	−0.750345	+	0.442620i
$311$	−10.3434			−0.586520			−0.293260	−	0.956033i	$-0.594740\pi$
$311$	−10.3434			−0.586520			−0.293260	+	0.956033i	$0.594740\pi$
$312$		0			0
$313$	−6.63988			−0.375308			−0.187654	−	0.982235i	$-0.560088\pi$
$313$	−6.63988			−0.375308			−0.187654	+	0.982235i	$0.560088\pi$
$314$	0.0974938	−	0.0575105i	0.00550189	−	0.00324550i
$315$		0			0
$316$	25.3741	+	14.0236i	1.42740	+	0.788888i
$317$			4.43176i			0.248913i	0.992225	+	0.124456i	$0.0397187\pi$
$317$			4.43176i			0.248913i	−0.992225	+	0.124456i	$0.960281\pi$
$318$		0			0
$319$		−	24.1507i		−	1.35218i
$320$	0.797485	+	14.1967i	0.0445808	+	0.793618i
$321$		0			0
$322$	3.19101	+	5.40952i	0.177828	+	0.301461i
$323$	−2.73410			−0.152130
$324$		0			0
$325$	−0.943412			−0.0523311
$326$	4.95630	+	8.40209i	0.274504	+	0.465349i
$327$		0			0
$328$	−27.8242	+	0.780884i	−1.53633	+	0.0431171i
$329$		−	3.24194i		−	0.178734i
$330$		0			0
$331$			13.6448i			0.749987i	0.927027	+	0.374994i	$0.122355\pi$
$331$			13.6448i			0.749987i	−0.927027	+	0.374994i	$0.877645\pi$
$332$	−9.83109	+	17.7882i	−0.539551	+	0.976256i
$333$		0			0
$334$	6.23156	−	3.67593i	0.340976	−	0.201138i
$335$	−17.4883			−0.955491
$336$		0			0
$337$	−0.561461			−0.0305847			−0.0152924	−	0.999883i	$-0.504868\pi$
$337$	−0.561461			−0.0305847			−0.0152924	+	0.999883i	$0.504868\pi$
$338$	15.5151	−	9.15219i	0.843911	−	0.497813i
$339$		0			0
$340$	2.15871	−	3.90594i	0.117072	−	0.211829i
$341$		−	34.7823i		−	1.88357i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−10.4476	+	0.293211i	−0.563296	+	0.0158089i
$345$		0			0
$346$	4.13608	+	7.01163i	0.222357	+	0.376947i
$347$	0.719348			0.0386166			0.0193083	−	0.999814i	$-0.493854\pi$
$347$	0.719348			0.0386166			0.0193083	+	0.999814i	$0.493854\pi$
$348$		0			0
$349$	23.0049			1.23142			0.615712	−	0.787971i	$-0.288869\pi$
$349$	23.0049			1.23142			0.615712	+	0.787971i	$0.288869\pi$
$350$	−1.32275	−	2.24238i	−0.0707042	−	0.119860i
$351$		0			0
$352$	−28.6471	−	14.7990i	−1.52689	−	0.788788i
$353$			25.9014i			1.37859i	0.724479	+	0.689297i	$0.242080\pi$
$353$			25.9014i			1.37859i	−0.724479	+	0.689297i	$0.757920\pi$
$354$		0			0
$355$		−	15.4461i		−	0.819796i
$356$	−30.0351	−	16.5996i	−1.59186	−	0.879778i
$357$		0			0
$358$	−22.5515	+	13.3029i	−1.19188	+	0.703078i
$359$	−5.22039			−0.275522			−0.137761	−	0.990466i	$-0.543991\pi$
$359$	−5.22039			−0.275522			−0.137761	+	0.990466i	$0.543991\pi$
$360$		0			0
$361$	14.2571			0.750376
$362$	−17.9386	+	10.5817i	−0.942830	+	0.556164i
$363$		0			0
$364$	−0.897051	−	0.495777i	−0.0470183	−	0.0259858i
$365$			28.2962i			1.48109i
$366$		0			0
$367$		−	16.0189i		−	0.836179i	−0.908406	−	0.418090i	$-0.862700\pi$
$367$		−	16.0189i		−	0.836179i	0.908406	−	0.418090i	$-0.137300\pi$
$368$	9.45123	+	15.0412i	0.492679	+	0.784077i
$369$		0			0
$370$	−3.53811	−	5.99793i	−0.183937	−	0.311817i
$371$	2.68179			0.139231
$372$		0			0
$373$	17.4776			0.904957			0.452478	−	0.891775i	$-0.350540\pi$
$373$	17.4776			0.904957			0.452478	+	0.891775i	$0.350540\pi$
$374$	5.14175	+	8.71649i	0.265874	+	0.450719i
$375$		0			0
$376$	−0.257242	−	9.16597i	−0.0132663	−	0.472699i
$377$		−	2.17133i		−	0.111829i
$378$		0			0
$379$		−	12.7835i		−	0.656643i	−0.944566	−	0.328322i	$-0.893517\pi$
$379$		−	12.7835i		−	0.656643i	0.944566	−	0.328322i	$-0.106483\pi$
$380$	3.74472	−	6.77565i	0.192100	−	0.347583i
$381$		0			0
$382$	−23.0839	+	13.6169i	−1.18107	+	0.696702i
$383$	−28.4854			−1.45553			−0.727767	−	0.685824i	$-0.759442\pi$
$383$	−28.4854			−1.45553			−0.727767	+	0.685824i	$0.759442\pi$
$384$		0			0
$385$	−10.1310			−0.516323
$386$	−12.6835	+	7.48187i	−0.645575	+	0.380817i
$387$		0			0
$388$	2.63480	−	4.76736i	0.133762	−	0.242026i
$389$		−	12.5332i		−	0.635460i	−0.948181	−	0.317730i	$-0.897079\pi$
$389$		−	12.5332i		−	0.635460i	0.948181	−	0.317730i	$-0.102921\pi$
$390$		0			0
$391$		−	5.57543i		−	0.281962i
$392$	−0.0793484	−	2.82731i	−0.00400770	−	0.142801i
$393$		0			0
$394$	6.34972	+	10.7643i	0.319894	+	0.542296i
$395$	25.7644			1.29635
$396$		0			0
$397$	−39.2467			−1.96974			−0.984868	−	0.173305i	$-0.944555\pi$
$397$	−39.2467			−1.96974			−0.984868	+	0.173305i	$0.944555\pi$
$398$	17.8550	+	30.2685i	0.894992	+	1.51722i
$399$		0			0
$400$	−3.91777	−	6.23495i	−0.195889	−	0.311748i
$401$		−	0.962805i		−	0.0480802i	−0.999711	−	0.0240401i	$-0.992347\pi$
$401$		−	0.962805i		−	0.0480802i	0.999711	−	0.0240401i	$-0.00765294\pi$
$402$		0			0
$403$		−	3.12718i		−	0.155776i
$404$	11.3253	+	6.25917i	0.563453	+	0.311405i
$405$		0			0
$406$	5.16100	−	3.04441i	0.256136	−	0.151092i
$407$	15.7913			0.782744
$408$		0			0
$409$	−37.8153			−1.86985			−0.934923	−	0.354850i	$-0.884532\pi$
$409$	−37.8153			−1.86985			−0.934923	+	0.354850i	$0.884532\pi$
$410$	−21.3061	+	12.5682i	−1.05223	+	0.620700i
$411$		0			0
$412$	−22.2111	−	12.2755i	−1.09426	−	0.604769i
$413$			6.33178i			0.311566i
$414$		0			0
$415$			18.0619i			0.886623i
$416$	−2.57558	−	1.33054i	−0.126278	−	0.0652349i
$417$		0			0
$418$	8.91943	+	15.1205i	0.436263	+	0.739569i
$419$	17.8548			0.872266			0.436133	−	0.899882i	$-0.356348\pi$
$419$	17.8548			0.872266			0.436133	+	0.899882i	$0.356348\pi$
$420$		0			0
$421$	20.9005			1.01863			0.509313	−	0.860581i	$-0.329900\pi$
$421$	20.9005			1.01863			0.509313	+	0.860581i	$0.329900\pi$
$422$	2.17868	+	3.69337i	0.106056	+	0.179791i
$423$		0			0
$424$	7.58225	−	0.212795i	0.368227	−	0.0103343i
$425$			2.31115i			0.112107i
$426$		0			0
$427$		−	12.2880i		−	0.594659i
$428$	−1.58169	+	2.86189i	−0.0764540	+	0.138335i
$429$		0			0
$430$	−8.00015	+	4.71919i	−0.385801	+	0.227580i
$431$	−29.1829			−1.40569			−0.702844	−	0.711344i	$-0.748087\pi$
$431$	−29.1829			−1.40569			−0.702844	+	0.711344i	$0.748087\pi$
$432$		0			0
$433$	5.33084			0.256184			0.128092	−	0.991762i	$-0.459115\pi$
$433$	5.33084			0.256184			0.128092	+	0.991762i	$0.459115\pi$
$434$	7.43295	−	4.38461i	0.356793	−	0.210468i
$435$		0			0
$436$	−16.8816	+	30.5454i	−0.808484	+	1.46286i
$437$		−	9.67172i		−	0.462661i
$438$		0			0
$439$			13.7677i			0.657098i	0.944487	+	0.328549i	$0.106560\pi$
$439$			13.7677i			0.657098i	−0.944487	+	0.328549i	$0.893440\pi$
$440$	−28.6435	+	0.803878i	−1.36553	+	0.0383234i
$441$		0			0
$442$	0.462282	+	0.783677i	0.0219885	+	0.0372757i
$443$	−22.4956			−1.06880			−0.534400	−	0.845232i	$-0.679462\pi$
$443$	−22.4956			−1.06880			−0.534400	+	0.845232i	$0.679462\pi$
$444$		0			0
$445$	−30.4972			−1.44571
$446$	12.1462	+	20.5907i	0.575139	+	0.974996i
$447$		0			0
$448$	−0.448686	−	7.98741i	−0.0211984	−	0.377370i
$449$			10.1291i			0.478023i	0.971017	+	0.239012i	$0.0768234\pi$
$449$			10.1291i			0.478023i	−0.971017	+	0.239012i	$0.923177\pi$
$450$		0			0
$451$		−	56.0945i		−	2.64139i
$452$	24.1872	+	13.3676i	1.13767	+	0.628761i
$453$		0			0
$454$	13.0435	−	7.69421i	0.612162	−	0.361107i
$455$	−0.910852			−0.0427014
$456$		0			0
$457$	36.5924			1.71172			0.855861	−	0.517206i	$-0.173028\pi$
$457$	36.5924			1.71172			0.855861	+	0.517206i	$0.173028\pi$
$458$	9.03102	−	5.32729i	0.421992	−	0.248928i
$459$		0			0
$460$	13.8170	+	7.63630i	0.644222	+	0.356044i
$461$		−	21.8574i		−	1.01800i	−0.860767	−	0.508999i	$-0.830016\pi$
$461$		−	21.8574i		−	1.01800i	0.860767	−	0.508999i	$-0.169984\pi$
$462$		0			0
$463$			8.86782i			0.412122i	0.978539	+	0.206061i	$0.0660646\pi$
$463$			8.86782i			0.412122i	−0.978539	+	0.206061i	$0.933935\pi$
$464$	14.3502	−	9.01703i	0.666191	−	0.418605i
$465$		0			0
$466$	9.06018	+	15.3592i	0.419705	+	0.711499i
$467$	−31.4552			−1.45557			−0.727786	−	0.685805i	$-0.759450\pi$
$467$	−31.4552			−1.45557			−0.727786	+	0.685805i	$0.759450\pi$
$468$		0			0
$469$	9.83939			0.454341
$470$	−4.14028	−	7.01875i	−0.190977	−	0.323751i
$471$		0			0
$472$	0.502416	+	17.9019i	0.0231256	+	0.824003i
$473$		−	21.0627i		−	0.968464i
$474$		0			0
$475$			4.00917i			0.183953i
$476$	−1.21455	+	2.19758i	−0.0556686	+	0.100726i
$477$		0			0
$478$	−0.502585	+	0.296469i	−0.0229877	+	0.0135602i
$479$	0.0498152			0.00227612			0.00113806	−	0.999999i	$-0.499638\pi$
$479$	0.0498152			0.00227612			0.00113806	+	0.999999i	$0.499638\pi$
$480$		0			0
$481$	1.41975			0.0647351
$482$	−6.27221	+	3.69991i	−0.285692	+	0.168526i
$483$		0			0
$484$	20.7896	−	37.6164i	0.944981	−	1.70984i
$485$		−	4.84071i		−	0.219805i
$486$		0			0
$487$			36.0443i			1.63332i	0.577116	+	0.816662i	$0.304178\pi$
$487$			36.0443i			1.63332i	−0.577116	+	0.816662i	$0.695822\pi$
$488$	−0.975035	−	34.7421i	−0.0441378	−	1.57270i
$489$		0			0
$490$	−1.27710	−	2.16499i	−0.0576936	−	0.0978042i
$491$	−6.76025			−0.305086			−0.152543	−	0.988297i	$-0.548746\pi$
$491$	−6.76025			−0.305086			−0.152543	+	0.988297i	$0.548746\pi$
$492$		0			0
$493$	−5.31929			−0.239569
$494$	0.801922	+	1.35945i	0.0360802	+	0.0611644i
$495$		0			0
$496$	20.6674	−	12.9865i	0.927993	−	0.583110i
$497$			8.69040i			0.389818i
$498$		0			0
$499$			37.2138i			1.66592i	0.553333	+	0.832960i	$0.313356\pi$
$499$			37.2138i			1.66592i	−0.553333	+	0.832960i	$0.686644\pi$
$500$	−21.2836	−	11.7629i	−0.951831	−	0.526052i
$501$		0			0
$502$	−5.59726	+	3.30176i	−0.249818	+	0.147365i
$503$	30.2697			1.34966			0.674830	−	0.737973i	$-0.264217\pi$
$503$	30.2697			1.34966			0.674830	+	0.737973i	$0.264217\pi$
$504$		0			0
$505$	11.4995			0.511720
$506$	−30.8340	+	18.1886i	−1.37074	+	0.808584i
$507$		0			0
$508$	27.9198	+	15.4305i	1.23874	+	0.684619i
$509$			9.18307i			0.407032i	0.979072	+	0.203516i	$0.0652369\pi$
$509$			9.18307i			0.407032i	−0.979072	+	0.203516i	$0.934763\pi$
$510$		0			0
$511$		−	15.9201i		−	0.704266i
$512$	−1.90236	−	22.5473i	−0.0840733	−	0.996460i
$513$		0			0
$514$	−19.5180	−	33.0877i	−0.860904	−	1.45944i
$515$	−22.5528			−0.993793
$516$		0			0
$517$	18.4789			0.812701
$518$	1.99063	+	3.37459i	0.0874632	+	0.148271i
$519$		0			0
$520$	−2.57526	+	0.0722746i	−0.112933	+	0.00316945i
$521$			18.8522i			0.825930i	0.910747	+	0.412965i	$0.135507\pi$
$521$			18.8522i			0.825930i	−0.910747	+	0.412965i	$0.864493\pi$
$522$		0			0
$523$		−	40.4459i		−	1.76858i	−0.466941	−	0.884288i	$-0.654644\pi$
$523$		−	40.4459i		−	1.76858i	0.466941	−	0.884288i	$-0.345356\pi$
$524$	−1.97931	+	3.58134i	−0.0864666	+	0.156452i
$525$		0			0
$526$	−0.935081	+	0.551593i	−0.0407715	+	0.0240506i
$527$	−7.66092			−0.333715
$528$		0			0
$529$	−3.27727			−0.142490
$530$	5.80604	−	3.42491i	0.252198	−	0.148769i
$531$		0			0
$532$	−2.10688	+	3.81215i	−0.0913447	+	0.165278i
$533$		−	5.04331i		−	0.218450i
$534$		0			0
$535$			2.90592i			0.125634i
$536$	27.8190	−	0.780740i	1.20160	−	0.0337228i
$537$		0			0
$538$	0.315782	+	0.535326i	0.0136143	+	0.0230795i
$539$	5.69996			0.245515
$540$		0			0
$541$	31.1154			1.33775			0.668877	−	0.743373i	$-0.266775\pi$
$541$	31.1154			1.33775			0.668877	+	0.743373i	$0.266775\pi$
$542$	3.27029	+	5.54392i	0.140471	+	0.238132i
$543$		0			0
$544$	−3.25953	+	6.30962i	−0.139751	+	0.270523i
$545$			31.0153i			1.32855i
$546$		0			0
$547$		−	16.9309i		−	0.723913i	−0.932195	−	0.361957i	$-0.882109\pi$
$547$		−	16.9309i		−	0.723913i	0.932195	−	0.361957i	$-0.117891\pi$
$548$	27.5906	+	15.2486i	1.17861	+	0.651388i
$549$		0			0
$550$	12.7815	−	7.53964i	0.545004	−	0.321491i
$551$	−9.22739			−0.393100
$552$		0			0
$553$	−14.4957			−0.616421
$554$	20.4854	−	12.0841i	0.870340	−	0.513404i
$555$		0			0
$556$	35.0609	+	19.3773i	1.48691	+	0.821779i
$557$		−	13.3461i		−	0.565491i	−0.959195	−	0.282746i	$-0.908755\pi$
$557$		−	13.3461i		−	0.565491i	0.959195	−	0.282746i	$-0.0912452\pi$
$558$		0			0
$559$		−	1.89369i		−	0.0800946i
$560$	−3.78256	−	6.01977i	−0.159842	−	0.254382i
$561$		0			0
$562$	−18.8342	−	31.9284i	−0.794473	−	1.34682i
$563$	28.5226			1.20209			0.601043	−	0.799217i	$-0.294752\pi$
$563$	28.5226			1.20209			0.601043	+	0.799217i	$0.294752\pi$
$564$		0			0
$565$	24.5593			1.03322
$566$	−2.40711	−	4.08063i	−0.101179	−	0.171522i
$567$		0			0
$568$	0.689569	+	24.5705i	0.0289337	+	1.03095i
$569$			40.1079i			1.68141i	0.541493	+	0.840705i	$0.317859\pi$
$569$			40.1079i			1.68141i	−0.541493	+	0.840705i	$0.682141\pi$
$570$		0			0
$571$			16.3731i			0.685192i	0.939483	+	0.342596i	$0.111306\pi$
$571$			16.3731i			0.685192i	−0.939483	+	0.342596i	$0.888694\pi$
$572$	2.82591	−	5.11315i	0.118157	−	0.213792i
$573$		0			0
$574$	11.9874	−	7.07120i	0.500343	−	0.295146i
$575$	−8.17556			−0.340945
$576$		0			0
$577$	−28.9429			−1.20491			−0.602454	−	0.798153i	$-0.705810\pi$
$577$	−28.9429			−1.20491			−0.602454	+	0.798153i	$0.705810\pi$
$578$	−18.7875	+	11.0825i	−0.781457	+	0.460972i
$579$		0			0
$580$	7.28548	−	13.1822i	0.302513	−	0.547363i
$581$		−	10.1621i		−	0.421594i
$582$		0			0
$583$			15.2861i			0.633084i
$584$	−1.26324	−	45.0112i	−0.0522731	−	1.86258i
$585$		0			0
$586$	13.7783	+	23.3574i	0.569176	+	0.964887i
$587$	−36.4188			−1.50317			−0.751583	−	0.659639i	$-0.770709\pi$
$587$	−36.4188			−1.50317			−0.751583	+	0.659639i	$0.770709\pi$
$588$		0			0
$589$	−13.2894			−0.547582
$590$	8.08632	+	13.7082i	0.332909	+	0.564359i
$591$		0			0
$592$	5.89590	+	9.38306i	0.242320	+	0.385641i
$593$			14.1539i			0.581231i	0.956840	+	0.290616i	$0.0938601\pi$
$593$			14.1539i			0.581231i	−0.956840	+	0.290616i	$0.906140\pi$
$594$		0			0
$595$			2.23139i			0.0914780i
$596$	−27.3140	−	15.0957i	−1.11882	−	0.618345i
$597$		0			0
$598$	−2.77221	+	1.63529i	−0.113364	+	0.0668721i
$599$	19.9325			0.814422			0.407211	−	0.913334i	$-0.366501\pi$
$599$	19.9325			0.814422			0.407211	+	0.913334i	$0.366501\pi$
$600$		0			0
$601$	4.68704			0.191188			0.0955941	−	0.995420i	$-0.469525\pi$
$601$	4.68704			0.191188			0.0955941	+	0.995420i	$0.469525\pi$
$602$	4.50109	−	2.65514i	0.183451	−	0.108215i
$603$		0			0
$604$	−22.9575	−	12.6880i	−0.934126	−	0.516267i
$605$		−	38.1951i		−	1.55285i
$606$		0			0
$607$			36.7658i			1.49228i	0.665791	+	0.746138i	$0.268094\pi$
$607$			36.7658i			1.49228i	−0.665791	+	0.746138i	$0.731906\pi$
$608$	−5.65432	+	10.9453i	−0.229313	+	0.443892i
$609$		0			0
$610$	−15.6931	−	26.6034i	−0.635393	−	1.07714i
$611$	1.66139			0.0672126
$612$		0			0
$613$	26.9250			1.08749			0.543745	−	0.839250i	$-0.317006\pi$
$613$	26.9250			1.08749			0.543745	+	0.839250i	$0.317006\pi$
$614$	−0.858599	−	1.45553i	−0.0346502	−	0.0587403i
$615$		0			0
$616$	16.1156	−	0.452282i	0.649315	−	0.0182230i
$617$		−	15.8268i		−	0.637164i	−0.947895	−	0.318582i	$-0.896793\pi$
$617$		−	15.8268i		−	0.637164i	0.947895	−	0.318582i	$-0.103207\pi$
$618$		0			0
$619$			36.4424i			1.46474i	0.680906	+	0.732371i	$0.261586\pi$
$619$			36.4424i			1.46474i	−0.680906	+	0.732371i	$0.738414\pi$
$620$	10.4927	−	18.9853i	0.421396	−	0.762467i
$621$		0			0
$622$	12.5991	−	7.43204i	0.505177	−	0.297998i
$623$	17.1585			0.687441
$624$		0			0
$625$	−12.4064			−0.496258
$626$	8.08789	−	4.77095i	0.323257	−	0.190686i
$627$		0			0
$628$	−0.0774321	+	0.140104i	−0.00308988	+	0.00559078i
$629$		−	3.47808i		−	0.138680i
$630$		0			0
$631$			27.4997i			1.09475i	0.836888	+	0.547373i	$0.184372\pi$
$631$			27.4997i			1.09475i	−0.836888	+	0.547373i	$0.815628\pi$
$632$	−40.9840	+	1.15021i	−1.63026	+	0.0457530i
$633$		0			0
$634$	−3.18436	−	5.39824i	−0.126467	−	0.214391i
$635$	28.3493			1.12501
$636$		0			0
$637$	0.512468			0.0203047
$638$	17.3530	+	29.4175i	0.687013	+	1.16465i
$639$		0			0
$640$	−11.1721	−	16.7196i	−0.441617	−	0.660902i
$641$		−	27.1974i		−	1.07423i	−0.843508	−	0.537117i	$-0.819513\pi$
$641$		−	27.1974i		−	1.07423i	0.843508	−	0.537117i	$-0.180487\pi$
$642$		0			0
$643$			1.24175i			0.0489699i	0.999700	+	0.0244850i	$0.00779458\pi$
$643$			1.24175i			0.0489699i	−0.999700	+	0.0244850i	$0.992205\pi$
$644$	−7.77381	−	4.29638i	−0.306331	−	0.169301i
$645$		0			0
$646$	3.33035	−	1.96454i	0.131031	−	0.0772936i
$647$	−11.7442			−0.461711			−0.230855	−	0.972988i	$-0.574152\pi$
$647$	−11.7442			−0.461711			−0.230855	+	0.972988i	$0.574152\pi$
$648$		0			0
$649$	−36.0909			−1.41669
$650$	1.14915	−	0.677870i	0.0450733	−	0.0265882i
$651$		0			0
$652$	−12.0743	−	6.67316i	−0.472867	−	0.261341i
$653$		−	24.6481i		−	0.964553i	−0.876019	−	0.482277i	$-0.839810\pi$
$653$		−	24.6481i		−	0.964553i	0.876019	−	0.482277i	$-0.160190\pi$
$654$		0			0
$655$			3.63643i			0.142087i
$656$	33.3309	−	20.9437i	1.30135	−	0.817714i
$657$		0			0
$658$	2.32943	+	3.94893i	0.0908106	+	0.153945i
$659$	13.2043			0.514368			0.257184	−	0.966362i	$-0.417205\pi$
$659$	13.2043			0.514368			0.257184	+	0.966362i	$0.417205\pi$
$660$		0			0
$661$	1.88602			0.0733578			0.0366789	−	0.999327i	$-0.488322\pi$
$661$	1.88602			0.0733578			0.0366789	+	0.999327i	$0.488322\pi$
$662$	−9.80421	−	16.6205i	−0.381052	−	0.645972i
$663$		0			0
$664$	−0.806344	−	28.7314i	−0.0312922	−	1.11499i
$665$			3.87080i			0.150103i
$666$		0			0
$667$		−	18.8166i		−	0.728583i
$668$	−4.94927	+	8.95513i	−0.191493	+	0.346485i
$669$		0			0
$670$	21.3022	−	12.5659i	0.822975	−	0.485463i
$671$	70.0412			2.70391
$672$		0			0
$673$	3.20501			0.123544			0.0617720	−	0.998090i	$-0.480325\pi$
$673$	3.20501			0.123544			0.0617720	+	0.998090i	$0.480325\pi$
$674$	0.683904	−	0.403427i	0.0263430	−	0.0155394i
$675$		0			0
$676$	−12.3225	+	22.2962i	−0.473943	+	0.857545i
$677$		−	17.5333i		−	0.673859i	−0.941530	−	0.336929i	$-0.890612\pi$
$677$		−	17.5333i		−	0.673859i	0.941530	−	0.336929i	$-0.109388\pi$
$678$		0			0
$679$			2.72350i			0.104519i
$680$	0.177057	+	6.30884i	0.00678983	+	0.241933i
$681$		0			0
$682$	24.9921	+	42.3675i	0.956997	+	1.62234i
$683$	37.7296			1.44368			0.721842	−	0.692058i	$-0.243296\pi$
$683$	37.7296			1.44368			0.721842	+	0.692058i	$0.243296\pi$
$684$		0			0
$685$	28.0150			1.07040
$686$	0.718530	+	1.21808i	0.0274336	+	0.0465064i
$687$		0			0
$688$	12.5153	−	7.86406i	0.477141	−	0.299815i
$689$			1.37433i			0.0523578i
$690$		0			0
$691$			25.3506i			0.964383i	0.876066	+	0.482191i	$0.160159\pi$
$691$			25.3506i			0.964383i	−0.876066	+	0.482191i	$0.839841\pi$
$692$	−10.0761	−	5.56881i	−0.383037	−	0.211694i
$693$		0			0
$694$	−0.876223	+	0.516874i	−0.0332610	+	0.0196203i
$695$	35.6003			1.35040
$696$		0			0
$697$	−12.3550			−0.467979
$698$	−28.0218	+	16.5297i	−1.06064	+	0.625659i
$699$		0			0
$700$	3.22244	+	1.78096i	0.121797	+	0.0673138i
$701$		−	1.21339i		−	0.0458290i	−0.999737	−	0.0229145i	$-0.992705\pi$
$701$		−	1.21339i		−	0.0458290i	0.999737	−	0.0229145i	$-0.00729455\pi$
$702$		0			0
$703$		−	6.03345i		−	0.227556i
$704$	45.5279	−	2.55749i	1.71590	−	0.0963890i
$705$		0			0
$706$	−18.6110	−	31.5500i	−0.700433	−	1.18740i
$707$	−6.46990			−0.243326
$708$		0			0
$709$	−8.22386			−0.308854			−0.154427	−	0.988004i	$-0.549353\pi$
$709$	−8.22386			−0.308854			−0.154427	+	0.988004i	$0.549353\pi$
$710$	11.0985	+	18.8146i	0.416520	+	0.706100i
$711$		0			0
$712$	48.5125	−	1.36150i	1.81808	−	0.0510243i
$713$		−	27.1000i		−	1.01490i
$714$		0			0
$715$		−	5.19182i		−	0.194163i
$716$	17.9110	−	32.4078i	0.669364	−	1.21114i
$717$		0			0
$718$	6.35884	−	3.75101i	0.237310	−	0.139986i
$719$	35.6595			1.32987			0.664937	−	0.746900i	$-0.268459\pi$
$719$	35.6595			1.32987			0.664937	+	0.746900i	$0.268459\pi$
$720$		0			0
$721$	12.6888			0.472554
$722$	−17.3663	+	10.2442i	−0.646307	+	0.381249i
$723$		0			0
$724$	14.2473	−	25.7788i	0.529495	−	0.958061i
$725$			7.79997i			0.289683i
$726$		0			0
$727$		−	15.9790i		−	0.592629i	−0.955090	−	0.296315i	$-0.904242\pi$
$727$		−	15.9790i		−	0.592629i	0.955090	−	0.296315i	$-0.0957577\pi$
$728$	1.44891	−	0.0406635i	0.0537001	−	0.00150709i
$729$		0			0
$730$	−20.3316	−	34.4669i	−0.752508	−	1.27568i
$731$	−4.63913			−0.171585
$732$		0			0
$733$	−12.6771			−0.468238			−0.234119	−	0.972208i	$-0.575221\pi$
$733$	−12.6771			−0.468238			−0.234119	+	0.972208i	$0.575221\pi$
$734$	11.5101	+	19.5123i	0.424844	+	0.720211i
$735$		0			0
$736$	−22.3199	−	11.5304i	−0.822722	−	0.425015i
$737$			56.0841i			2.06589i
$738$		0			0
$739$			38.5265i			1.41722i	0.705599	+	0.708611i	$0.250678\pi$
$739$			38.5265i			1.41722i	−0.705599	+	0.708611i	$0.749322\pi$
$740$	8.61938	+	4.76371i	0.316855	+	0.175117i
$741$		0			0
$742$	−3.26663	+	1.92694i	−0.119922	+	0.0707404i
$743$	−15.3776			−0.564150			−0.282075	−	0.959392i	$-0.591023\pi$
$743$	−15.3776			−0.564150			−0.282075	+	0.959392i	$0.591023\pi$
$744$		0			0
$745$	−27.7342			−1.01610
$746$	−21.2891	+	12.5582i	−0.779449	+	0.459788i
$747$		0			0
$748$	−12.5261	−	6.92286i	−0.458000	−	0.253125i
$749$		−	1.63494i		−	0.0597396i
$750$		0			0
$751$			18.2436i			0.665717i	0.942977	+	0.332858i	$0.108013\pi$
$751$			18.2436i			0.665717i	−0.942977	+	0.332858i	$0.891987\pi$
$752$	6.89937	+	10.9800i	0.251594	+	0.400401i
$753$		0			0
$754$	1.56017	+	2.64485i	0.0568179	+	0.0963197i
$755$	−23.3107			−0.848362
$756$		0			0
$757$	−28.1105			−1.02169			−0.510847	−	0.859672i	$-0.670668\pi$
$757$	−28.1105			−1.02169			−0.510847	+	0.859672i	$0.670668\pi$
$758$	9.18531	+	15.5713i	0.333626	+	0.565574i
$759$		0			0
$760$	0.307142	+	10.9440i	0.0111412	+	0.396979i
$761$		−	24.4068i		−	0.884745i	−0.896831	−	0.442373i	$-0.854137\pi$
$761$		−	24.4068i		−	0.884745i	0.896831	−	0.442373i	$-0.145863\pi$
$762$		0			0
$763$		−	17.4500i		−	0.631733i
$764$	18.3338	−	33.1729i	0.663294	−	1.20015i
$765$		0			0
$766$	34.6974	−	20.4676i	1.25367	−	0.739524i
$767$	−3.24484			−0.117164
$768$		0			0
$769$	−19.3164			−0.696566			−0.348283	−	0.937389i	$-0.613235\pi$
$769$	−19.3164			−0.696566			−0.348283	+	0.937389i	$0.613235\pi$
$770$	12.3403	−	7.27943i	0.444715	−	0.262332i
$771$		0			0
$772$	10.0736	−	18.2270i	0.362556	−	0.656004i
$773$		−	18.2525i		−	0.656496i	−0.944592	−	0.328248i	$-0.893542\pi$
$773$		−	18.2525i		−	0.656496i	0.944592	−	0.328248i	$-0.106458\pi$
$774$		0			0
$775$			11.2336i			0.403524i
$776$	0.216106	+	7.70020i	0.00775774	+	0.276421i
$777$		0			0
$778$	9.00550	+	15.2664i	0.322863	+	0.547329i
$779$	−21.4323			−0.767892
$780$		0			0
$781$	−49.5349			−1.77250
$782$	4.00611	+	6.79131i	0.143258	+	0.242857i
$783$		0			0
$784$	2.12816	+	3.38688i	0.0760058	+	0.120960i
$785$			0.142260i			0.00507747i
$786$		0			0
$787$			1.55435i			0.0554067i	0.999616	+	0.0277034i	$0.00881938\pi$
$787$			1.55435i			0.0554067i	−0.999616	+	0.0277034i	$0.991181\pi$
$788$	−15.4689	−	8.54926i	−0.551057	−	0.304555i
$789$		0			0
$790$	−31.3831	+	18.5125i	−1.11656	+	0.658646i
$791$	−13.8177			−0.491301
$792$		0			0
$793$	6.29723			0.223621
$794$	47.8056	−	28.2000i	1.69656	−	1.00078i
$795$		0			0
$796$	−43.4977	−	24.0400i	−1.54173	−	0.852076i
$797$			50.2238i			1.77902i	0.456917	+	0.889509i	$0.348954\pi$
$797$			50.2238i			1.77902i	−0.456917	+	0.889509i	$0.651046\pi$
$798$		0			0
$799$		−	4.07004i		−	0.143988i
$800$	9.25215	+	4.77963i	0.327113	+	0.168985i
$801$		0			0
$802$	0.691805	+	1.17277i	0.0244285	+	0.0414120i
$803$	90.7442			3.20229
$804$		0			0
$805$	−7.89340			−0.278206
$806$	2.24698	+	3.80915i	0.0791464	+	0.134172i
$807$		0			0
$808$	−18.2925	+	0.513376i	−0.643526	+	0.0180605i
$809$			34.7159i			1.22055i	0.792191	+	0.610273i	$0.208940\pi$
$809$			34.7159i			1.22055i	−0.792191	+	0.610273i	$0.791060\pi$
$810$		0			0
$811$			14.9516i			0.525022i	0.964929	+	0.262511i	$0.0845505\pi$
$811$			14.9516i			0.525022i	−0.964929	+	0.262511i	$0.915449\pi$
$812$	−4.09900	+	7.41667i	−0.143847	+	0.260274i
$813$		0			0
$814$	−19.2350	+	11.3465i	−0.674186	+	0.397695i
$815$	−12.2601			−0.429451
$816$		0			0
$817$	−8.04753			−0.281547
$818$	46.0620	−	27.1714i	1.61052	−	0.950027i
$819$		0			0
$820$	16.9219	−	30.6182i	0.590937	−	1.06923i
$821$			10.6443i			0.371489i	0.982598	+	0.185745i	$0.0594697\pi$
$821$			10.6443i			0.371489i	−0.982598	+	0.185745i	$0.940530\pi$
$822$		0			0
$823$		−	13.2066i		−	0.460353i	−0.973149	−	0.230177i	$-0.926070\pi$
$823$		−	13.2066i		−	0.460353i	0.973149	−	0.230177i	$-0.0739304\pi$
$824$	35.8751	−	1.00683i	1.24977	−	0.0350747i
$825$		0			0
$826$	−4.54957	−	7.71260i	−0.158300	−	0.268356i
$827$	−27.7296			−0.964251			−0.482126	−	0.876102i	$-0.660135\pi$
$827$	−27.7296			−0.964251			−0.482126	+	0.876102i	$0.660135\pi$
$828$		0			0
$829$	−40.7817			−1.41641			−0.708203	−	0.706009i	$-0.750494\pi$
$829$	−40.7817			−1.41641			−0.708203	+	0.706009i	$0.750494\pi$
$830$	−12.9780	−	22.0008i	−0.450473	−	0.763659i
$831$		0			0
$832$	4.09329	−	0.229937i	0.141909	−	0.00797164i
$833$		−	1.25544i		−	0.0434983i
$834$		0			0
$835$			9.09290i			0.314673i
$836$	−21.7291	−	12.0091i	−0.751517	−	0.415344i
$837$		0			0
$838$	−21.7486	+	12.8292i	−0.751293	+	0.443179i
$839$	−50.3696			−1.73895			−0.869475	−	0.493976i	$-0.835543\pi$
$839$	−50.3696			−1.73895			−0.869475	+	0.493976i	$0.835543\pi$
$840$		0			0
$841$	11.0478			0.380959
$842$	−25.4584	+	15.0176i	−0.877354	+	0.517541i
$843$		0			0
$844$	−5.30760	−	2.93337i	−0.182695	−	0.100971i
$845$			22.6392i			0.778811i
$846$		0			0
$847$			21.4895i			0.738389i
$848$	−9.08288	+	5.70728i	−0.311907	+	0.195989i
$849$		0			0
$850$	−1.66063	−	2.81517i	−0.0569593	−	0.0965594i
$851$	12.3035			0.421759
$852$		0			0
$853$	−48.7107			−1.66782			−0.833912	−	0.551898i	$-0.813904\pi$
$853$	−48.7107			−1.66782			−0.833912	+	0.551898i	$0.813904\pi$
$854$	8.82932	+	14.9678i	0.302133	+	0.512187i
$855$		0			0
$856$	−0.129730	−	4.62250i	−0.00443409	−	0.157994i
$857$		−	41.6837i		−	1.42389i	−0.702236	−	0.711944i	$-0.747815\pi$
$857$		−	41.6837i		−	1.42389i	0.702236	−	0.711944i	$-0.252185\pi$
$858$		0			0
$859$			22.1704i			0.756443i	0.925715	+	0.378221i	$0.123464\pi$
$859$			22.1704i			0.756443i	−0.925715	+	0.378221i	$0.876536\pi$
$860$	6.35392	−	11.4967i	0.216667	−	0.392034i
$861$		0			0
$862$	35.5470	−	20.9688i	1.21074	−	0.714199i
$863$	−12.7864			−0.435255			−0.217627	−	0.976032i	$-0.569832\pi$
$863$	−12.7864			−0.435255			−0.217627	+	0.976032i	$0.569832\pi$
$864$		0			0
$865$	−10.2311			−0.347869
$866$	−6.49338	+	3.83037i	−0.220654	+	0.130161i
$867$		0			0
$868$	−5.90344	+	10.6816i	−0.200376	+	0.362557i
$869$		−	82.6251i		−	2.80286i
$870$		0			0
$871$			5.04238i			0.170854i
$872$	−1.38463	−	49.3367i	−0.0468895	−	1.67075i
$873$		0			0
$874$	6.94942	+	11.7809i	0.235068	+	0.398495i
$875$	12.1589			0.411046
$876$		0			0
$877$	18.2391			0.615889			0.307944	−	0.951404i	$-0.400359\pi$
$877$	18.2391			0.615889			0.307944	+	0.951404i	$0.400359\pi$
$878$	−9.89252	−	16.7702i	−0.333857	−	0.565966i
$879$		0			0
$880$	34.3124	−	21.5604i	1.15667	−	0.726801i
$881$			37.9811i			1.27962i	0.768535	+	0.639808i	$0.220986\pi$
$881$			37.9811i			1.27962i	−0.768535	+	0.639808i	$0.779014\pi$
$882$		0			0
$883$			39.5614i			1.33135i	0.746243	+	0.665674i	$0.231856\pi$
$883$			39.5614i			1.33135i	−0.746243	+	0.665674i	$0.768144\pi$
$884$	−1.12619	−	0.622416i	−0.0378779	−	0.0209341i
$885$		0			0
$886$	27.4014	−	16.1638i	0.920570	−	0.543033i
$887$	−34.9835			−1.17463			−0.587315	−	0.809358i	$-0.699815\pi$
$887$	−34.9835			−1.17463			−0.587315	+	0.809358i	$0.699815\pi$
$888$		0			0
$889$	−15.9500			−0.534947
$890$	37.1480	−	21.9131i	1.24520	−	0.734530i
$891$		0			0
$892$	−29.5900	−	16.3536i	−0.990747	−	0.547560i
$893$		−	7.06032i		−	0.236265i
$894$		0			0
$895$		−	32.9064i		−	1.09994i
$896$	6.28573	+	9.40689i	0.209991	+	0.314262i
$897$		0			0
$898$	−7.27809	−	12.3381i	−0.242873	−	0.411727i
$899$	−25.8550			−0.862313
$900$		0			0
$901$	3.36681			0.112165
$902$	40.3056	+	68.3275i	1.34203	+	2.27506i
$903$		0			0
$904$	−39.0670	+	1.09641i	−1.29935	+	0.0364661i
$905$		−	26.1754i		−	0.870099i
$906$		0			0
$907$		−	3.02234i		−	0.100355i	−0.998740	−	0.0501776i	$-0.984021\pi$
$907$		−	3.02234i		−	0.100355i	0.998740	−	0.0501776i	$-0.0159787\pi$
$908$	−10.3595	+	18.7443i	−0.343791	+	0.622051i
$909$		0			0
$910$	1.10949	−	0.654474i	0.0367792	−	0.0216956i
$911$	6.88097			0.227977			0.113988	−	0.993482i	$-0.463637\pi$
$911$	6.88097			0.227977			0.113988	+	0.993482i	$0.463637\pi$
$912$		0			0
$913$	57.9234			1.91699
$914$	−44.5724	+	26.2928i	−1.47433	+	0.869687i
$915$		0			0
$916$	−7.17267	+	12.9781i	−0.236992	+	0.428809i
$917$		−	2.04595i		−	0.0675633i
$918$		0			0
$919$			46.4569i			1.53247i	0.642560	+	0.766236i	$0.277872\pi$
$919$			46.4569i			1.53247i	−0.642560	+	0.766236i	$0.722128\pi$
$920$	−22.3171	+	0.626328i	−0.735774	+	0.0206494i
$921$		0			0
$922$	15.7052	+	26.6240i	0.517222	+	0.876814i
$923$	−4.45355			−0.146591
$924$		0			0
$925$	−5.10011			−0.167691
$926$	−6.37180	−	10.8017i	−0.209390	−	0.354966i
$927$		0			0
$928$	−11.0007	+	21.2945i	−0.361114	+	0.699026i
$929$			36.2391i			1.18896i	0.804109	+	0.594482i	$0.202643\pi$
$929$			36.2391i			1.18896i	−0.804109	+	0.594482i	$0.797357\pi$
$930$		0			0
$931$		−	2.17781i		−	0.0713749i
$932$	−22.0720	−	12.1986i	−0.722993	−	0.399579i
$933$		0			0
$934$	38.3148	−	22.6015i	1.25370	−	0.739543i
$935$	−12.7188			−0.415950
$936$		0			0
$937$	8.14696			0.266150			0.133075	−	0.991106i	$-0.457515\pi$
$937$	8.14696			0.266150			0.133075	+	0.991106i	$0.457515\pi$
$938$	−11.9851	+	7.06990i	−0.391329	+	0.230840i
$939$		0			0
$940$	10.0864	+	5.57447i	0.328981	+	0.181819i
$941$		−	6.15493i		−	0.200645i	−0.994955	−	0.100322i	$-0.968013\pi$
$941$		−	6.15493i		−	0.200645i	0.994955	−	0.100322i	$-0.0319874\pi$
$942$		0			0
$943$		−	43.7051i		−	1.42323i
$944$	−13.4750	−	21.4449i	−0.438576	−	0.697973i
$945$		0			0
$946$	15.1342	+	25.6560i	0.492055	+	0.834149i
$947$	14.4270			0.468813			0.234406	−	0.972139i	$-0.424685\pi$
$947$	14.4270			0.468813			0.234406	+	0.972139i	$0.424685\pi$
$948$		0			0
$949$	8.15857			0.264838
$950$	−2.88071	−	4.88348i	−0.0934625	−	0.158441i
$951$		0			0
$952$	−0.0996168	−	3.54951i	−0.00322860	−	0.115040i
$953$		−	28.3909i		−	0.919671i	−0.888004	−	0.459835i	$-0.847908\pi$
$953$		−	28.3909i		−	0.919671i	0.888004	−	0.459835i	$-0.152092\pi$
$954$		0			0
$955$		−	33.6833i		−	1.08996i
$956$	0.399166	−	0.722245i	0.0129099	−	0.0233591i
$957$		0			0
$958$	−0.0606788	+	0.0357937i	−0.00196044	+	0.00115644i
$959$	−15.7620			−0.508981
$960$		0			0
$961$	−6.23683			−0.201188
$962$	−1.72937	+	1.02013i	−0.0557571	+	0.0328905i
$963$		0			0
$964$	4.98155	−	9.01355i	0.160445	−	0.290307i
$965$		−	18.5074i		−	0.595775i
$966$		0			0
$967$		−	7.70383i		−	0.247739i	−0.992299	−	0.123869i	$-0.960470\pi$
$967$		−	7.70383i		−	0.247739i	0.992299	−	0.123869i	$-0.0395304\pi$
$968$	1.70516	+	60.7576i	0.0548059	+	1.95282i
$969$		0			0
$970$	3.47819	+	5.89636i	0.111678	+	0.189321i
$971$	−44.1871			−1.41803			−0.709016	−	0.705192i	$-0.750861\pi$
$971$	−44.1871			−1.41803			−0.709016	+	0.705192i	$0.750861\pi$
$972$		0			0
$973$	−20.0296			−0.642121
$974$	−25.8989	−	43.9048i	−0.829855	−	1.40680i
$975$		0			0
$976$	26.1509	+	41.6180i	0.837071	+	1.33216i
$977$			18.6157i			0.595570i	0.954633	+	0.297785i	$0.0962479\pi$
$977$			18.6157i			0.595570i	−0.954633	+	0.297785i	$0.903752\pi$
$978$		0			0
$979$			97.8027i			3.12579i
$980$	3.11122	+	1.71949i	0.0993843	+	0.0549271i
$981$		0			0
$982$	8.23451	−	4.85744i	0.262774	−	0.155007i
$983$	10.0037			0.319069			0.159535	−	0.987192i	$-0.449001\pi$
$983$	10.0037			0.319069			0.159535	+	0.987192i	$0.449001\pi$
$984$		0			0
$985$	−15.7069			−0.500463
$986$	6.47931	−	3.82207i	0.206343	−	0.121719i
$987$		0			0
$988$	−1.95361	−	1.07971i	−0.0621526	−	0.0343501i
$989$		−	16.4106i		−	0.521828i
$990$		0			0
$991$		−	16.7166i		−	0.531020i	−0.964108	−	0.265510i	$-0.914460\pi$
$991$		−	16.7166i		−	0.531020i	0.964108	−	0.265510i	$-0.0855403\pi$
$992$	−15.8433	+	30.6687i	−0.503026	+	0.973731i
$993$		0			0
$994$	−6.24431	−	10.5856i	−0.198058	−	0.335754i
$995$	−44.1668			−1.40018
$996$		0			0
$997$	26.3797			0.835453			0.417727	−	0.908573i	$-0.362827\pi$
$997$	26.3797			0.835453			0.417727	+	0.908573i	$0.362827\pi$
$998$	−26.7393	−	45.3294i	−0.846417	−	1.43488i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.b.323.6	yes	24
3.2	odd	2	inner	756.2.e.b.323.19	yes	24
4.3	odd	2	inner	756.2.e.b.323.20	yes	24
12.11	even	2	inner	756.2.e.b.323.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.b.323.5	✓	24	12.11	even	2	inner
756.2.e.b.323.6	yes	24	1.1	even	1	trivial
756.2.e.b.323.19	yes	24	3.2	odd	2	inner
756.2.e.b.323.20	yes	24	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21808 + 0.718530i) q^{2} +(0.967429 - 1.75045i) q^{4} -1.77738i q^{5} +1.00000i q^{7} +(0.0793484 + 2.82731i) q^{8} +O(q^{10})\)	\(q+(-1.21808 + 0.718530i) q^{2} +(0.967429 - 1.75045i) q^{4} -1.77738i q^{5} +1.00000i q^{7} +(0.0793484 + 2.82731i) q^{8} +(1.27710 + 2.16499i) q^{10} -5.69996 q^{11} -0.512468 q^{13} +(-0.718530 - 1.21808i) q^{14} +(-2.12816 - 3.38688i) q^{16} +1.25544i q^{17} +2.17781i q^{19} +(-3.11122 - 1.71949i) q^{20} +(6.94299 - 4.09559i) q^{22} -4.44103 q^{23} +1.84092 q^{25} +(0.624227 - 0.368224i) q^{26} +(1.75045 + 0.967429i) q^{28} +4.23700i q^{29} +6.10220i q^{31} +(5.02584 + 2.59633i) q^{32} +(-0.902069 - 1.52922i) q^{34} +1.77738 q^{35} -2.77042 q^{37} +(-1.56482 - 2.65274i) q^{38} +(5.02521 - 0.141032i) q^{40} +9.84121i q^{41} +3.69524i q^{43} +(-5.51430 + 9.97750i) q^{44} +(5.40952 - 3.19101i) q^{46} -3.24194 q^{47} -1.00000 q^{49} +(-2.24238 + 1.32275i) q^{50} +(-0.495777 + 0.897051i) q^{52} -2.68179i q^{53} +10.1310i q^{55} +(-2.82731 + 0.0793484i) q^{56} +(-3.04441 - 5.16100i) q^{58} +6.33178 q^{59} -12.2880 q^{61} +(-4.38461 - 7.43295i) q^{62} +(-7.98741 + 0.448686i) q^{64} +0.910852i q^{65} -9.83939i q^{67} +(2.19758 + 1.21455i) q^{68} +(-2.16499 + 1.27710i) q^{70} +8.69040 q^{71} -15.9201 q^{73} +(3.37459 - 1.99063i) q^{74} +(3.81215 + 2.10688i) q^{76} -5.69996i q^{77} +14.4957i q^{79} +(-6.01977 + 3.78256i) q^{80} +(-7.07120 - 11.9874i) q^{82} -10.1621 q^{83} +2.23139 q^{85} +(-2.65514 - 4.50109i) q^{86} +(-0.452282 - 16.1156i) q^{88} -17.1585i q^{89} -0.512468i q^{91} +(-4.29638 + 7.77381i) q^{92} +(3.94893 - 2.32943i) q^{94} +3.87080 q^{95} +2.72350 q^{97} +(1.21808 - 0.718530i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4}+O(q^{10}) \) 24 * q + 4 * q^4	\( 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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