LMFDB - Embedded newform 1260.2.c.e.811.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(811,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1260.811");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.c (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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.7
Root			$0.309204 - 1.38000i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.e.811.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} -1.00000i q^{5} +(2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +O(q^{10})$	\(q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} -1.00000i q^{5} +(2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +(-1.38000 + 0.309204i) q^{10} -0.987080i q^{11} +4.69157i q^{13} +(-0.709355 - 3.67380i) q^{14} +(2.54341 - 3.08724i) q^{16} -3.93531i q^{17} -0.223896 q^{19} +(0.853401 + 1.80879i) q^{20} +(-1.36217 + 0.305209i) q^{22} +5.88128i q^{23} -1.00000 q^{25} +(6.47436 - 1.45065i) q^{26} +(-4.85050 + 2.11486i) q^{28} +10.2502 q^{29} +2.77439 q^{31} +(-5.04682 - 2.55532i) q^{32} +(-5.43072 + 1.21681i) q^{34} +(0.0785232 - 2.64459i) q^{35} +8.26915 q^{37} +(0.0692296 + 0.308976i) q^{38} +(2.23224 - 1.73698i) q^{40} +7.34910i q^{41} -4.32318i q^{43} +(0.842376 + 1.78542i) q^{44} +(8.11616 - 1.81852i) q^{46} -2.40779 q^{47} +(6.98767 + 0.415323i) q^{49} +(0.309204 + 1.38000i) q^{50} +(-4.00380 - 8.48605i) q^{52} +8.35002 q^{53} -0.987080 q^{55} +(4.41830 + 6.03976i) q^{56} +(-3.16941 - 14.1453i) q^{58} -13.9829 q^{59} +4.93374i q^{61} +(-0.857851 - 3.82865i) q^{62} +(-1.96583 + 7.75471i) q^{64} +4.69157 q^{65} -7.84723i q^{67} +(3.35840 + 7.11814i) q^{68} +(-3.67380 + 0.709355i) q^{70} -8.49881i q^{71} -14.4665i q^{73} +(-2.55685 - 11.4114i) q^{74} +(0.404980 - 0.191073i) q^{76} +(0.0775087 - 2.61042i) q^{77} -11.5183i q^{79} +(-3.08724 - 2.54341i) q^{80} +(10.1417 - 2.27237i) q^{82} +1.67114 q^{83} -3.93531 q^{85} +(-5.96597 + 1.33674i) q^{86} +(2.20340 - 1.71453i) q^{88} -0.493375i q^{89} +(-0.368398 + 12.4073i) q^{91} +(-5.01910 - 10.6380i) q^{92} +(0.744498 + 3.32274i) q^{94} +0.223896i q^{95} -4.31036i q^{97} +(-1.58747 - 9.77138i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	−0.309204	−	1.38000i	−0.218640	−	0.975806i
$2$	−0.309204	−	1.38000i	−0.218640	−	0.975806i
$3$		0			0
$3$		0			0
$4$	−1.80879	+	0.853401i	−0.904393	+	0.426701i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	2.64459	+	0.0785232i	0.999559	+	0.0296790i
$7$	2.64459	+	0.0785232i	0.999559	+	0.0296790i
$8$	1.73698	+	2.23224i	0.614114	+	0.789218i
$9$		0			0
$10$	−1.38000	+	0.309204i	−0.436394	+	0.0977789i
$11$		−	0.987080i		−	0.297616i	−0.988866	−	0.148808i	$-0.952456\pi$
$11$		−	0.987080i		−	0.297616i	0.988866	−	0.148808i	$-0.0475436\pi$
$12$		0			0
$13$			4.69157i			1.30121i	0.759417	+	0.650604i	$0.225484\pi$
$13$			4.69157i			1.30121i	−0.759417	+	0.650604i	$0.774516\pi$
$14$	−0.709355	−	3.67380i	−0.189583	−	0.981865i
$15$		0			0
$16$	2.54341	−	3.08724i	0.635853	−	0.771810i
$17$		−	3.93531i		−	0.954453i	−0.878780	−	0.477227i	$-0.841642\pi$
$17$		−	3.93531i		−	0.954453i	0.878780	−	0.477227i	$-0.158358\pi$
$18$		0			0
$19$	−0.223896			−0.0513653			−0.0256826	−	0.999670i	$-0.508176\pi$
$19$	−0.223896			−0.0513653			−0.0256826	+	0.999670i	$0.508176\pi$
$20$	0.853401	+	1.80879i	0.190826	+	0.404457i
$21$		0			0
$22$	−1.36217	+	0.305209i	−0.290415	+	0.0650708i
$23$			5.88128i			1.22633i	0.789954	+	0.613166i	$0.210104\pi$
$23$			5.88128i			1.22633i	−0.789954	+	0.613166i	$0.789896\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	6.47436	−	1.45065i	1.26973	−	0.284497i
$27$		0			0
$28$	−4.85050	+	2.11486i	−0.916659	+	0.399671i
$29$	10.2502			1.90342			0.951710	−	0.307000i	$-0.0993252\pi$
$29$	10.2502			1.90342			0.951710	+	0.307000i	$0.0993252\pi$
$30$		0			0
$31$	2.77439			0.498295			0.249147	−	0.968466i	$-0.419850\pi$
$31$	2.77439			0.498295			0.249147	+	0.968466i	$0.419850\pi$
$32$	−5.04682	−	2.55532i	−0.892160	−	0.451720i
$33$		0			0
$34$	−5.43072	+	1.21681i	−0.931361	+	0.208682i
$35$	0.0785232	−	2.64459i	0.0132728	−	0.447017i
$36$		0			0
$37$	8.26915			1.35944			0.679720	−	0.733472i	$-0.262101\pi$
$37$	8.26915			1.35944			0.679720	+	0.733472i	$0.262101\pi$
$38$	0.0692296	+	0.308976i	0.0112305	+	0.0501225i
$39$		0			0
$40$	2.23224	−	1.73698i	0.352949	−	0.274640i
$41$			7.34910i			1.14774i	0.818948	+	0.573868i	$0.194558\pi$
$41$			7.34910i			1.14774i	−0.818948	+	0.573868i	$0.805442\pi$
$42$		0			0
$43$		−	4.32318i		−	0.659278i	−0.944107	−	0.329639i	$-0.893073\pi$
$43$		−	4.32318i		−	0.659278i	0.944107	−	0.329639i	$-0.106927\pi$
$44$	0.842376	+	1.78542i	0.126993	+	0.269162i
$45$		0			0
$46$	8.11616	−	1.81852i	1.19666	−	0.268126i
$47$	−2.40779			−0.351212			−0.175606	−	0.984461i	$-0.556188\pi$
$47$	−2.40779			−0.351212			−0.175606	+	0.984461i	$0.556188\pi$
$48$		0			0
$49$	6.98767	+	0.415323i	0.998238	+	0.0593318i
$50$	0.309204	+	1.38000i	0.0437280	+	0.195161i
$51$		0			0
$52$	−4.00380	−	8.48605i	−0.555227	−	1.17680i
$53$	8.35002			1.14696			0.573482	−	0.819218i	$-0.305592\pi$
$53$	8.35002			1.14696			0.573482	+	0.819218i	$0.305592\pi$
$54$		0			0
$55$	−0.987080			−0.133098
$56$	4.41830	+	6.03976i	0.590420	+	0.807096i
$57$		0			0
$58$	−3.16941	−	14.1453i	−0.416164	−	1.85737i
$59$	−13.9829			−1.82042			−0.910210	−	0.414147i	$-0.864080\pi$
$59$	−13.9829			−1.82042			−0.910210	+	0.414147i	$0.864080\pi$
$60$		0			0
$61$			4.93374i			0.631700i	0.948809	+	0.315850i	$0.102290\pi$
$61$			4.93374i			0.631700i	−0.948809	+	0.315850i	$0.897710\pi$
$62$	−0.857851	−	3.82865i	−0.108947	−	0.486239i
$63$		0			0
$64$	−1.96583	+	7.75471i	−0.245729	+	0.969339i
$65$	4.69157			0.581918
$66$		0			0
$67$		−	7.84723i		−	0.958692i	−0.877626	−	0.479346i	$-0.840874\pi$
$67$		−	7.84723i		−	0.958692i	0.877626	−	0.479346i	$-0.159126\pi$
$68$	3.35840	+	7.11814i	0.407266	+	0.863201i
$69$		0			0
$70$	−3.67380	+	0.709355i	−0.439103	+	0.0847841i
$71$		−	8.49881i		−	1.00862i	−0.863522	−	0.504311i	$-0.831746\pi$
$71$		−	8.49881i		−	1.00862i	0.863522	−	0.504311i	$-0.168254\pi$
$72$		0			0
$73$		−	14.4665i		−	1.69318i	−0.532244	−	0.846591i	$-0.678651\pi$
$73$		−	14.4665i		−	1.69318i	0.532244	−	0.846591i	$-0.321349\pi$
$74$	−2.55685	−	11.4114i	−0.297228	−	1.32655i
$75$		0			0
$76$	0.404980	−	0.191073i	0.0464544	−	0.0219176i
$77$	0.0775087	−	2.61042i	0.00883294	−	0.297485i
$78$		0			0
$79$		−	11.5183i		−	1.29591i	−0.761678	−	0.647956i	$-0.775624\pi$
$79$		−	11.5183i		−	1.29591i	0.761678	−	0.647956i	$-0.224376\pi$
$80$	−3.08724	−	2.54341i	−0.345164	−	0.284362i
$81$		0			0
$82$	10.1417	−	2.27237i	1.11997	−	0.250941i
$83$	1.67114			0.183431			0.0917156	−	0.995785i	$-0.470765\pi$
$83$	1.67114			0.183431			0.0917156	+	0.995785i	$0.470765\pi$
$84$		0			0
$85$	−3.93531			−0.426845
$86$	−5.96597	+	1.33674i	−0.643327	+	0.144145i
$87$		0			0
$88$	2.20340	−	1.71453i	0.234884	−	0.182770i
$89$		−	0.493375i		−	0.0522977i	−0.999658	−	0.0261488i	$-0.991676\pi$
$89$		−	0.493375i		−	0.0522977i	0.999658	−	0.0261488i	$-0.00832438\pi$
$90$		0			0
$91$	−0.368398	+	12.4073i	−0.0386186	+	1.30064i
$92$	−5.01910	−	10.6380i	−0.523277	−	1.10909i
$93$		0			0
$94$	0.744498	+	3.32274i	0.0767891	+	0.342715i
$95$			0.223896i			0.0229713i
$96$		0			0
$97$		−	4.31036i		−	0.437650i	−0.975764	−	0.218825i	$-0.929778\pi$
$97$		−	4.31036i		−	0.437650i	0.975764	−	0.218825i	$-0.0702224\pi$
$98$	−1.58747	−	9.77138i	−0.160359	−	0.987059i
$99$		0			0
$100$	1.80879	−	0.853401i	0.180879	−	0.0853401i
$101$		−	6.03671i		−	0.600675i	−0.953833	−	0.300338i	$-0.902901\pi$
$101$		−	6.03671i		−	0.600675i	0.953833	−	0.300338i	$-0.0970994\pi$
$102$		0			0
$103$	7.83090			0.771602			0.385801	−	0.922582i	$-0.373925\pi$
$103$	7.83090			0.771602			0.385801	+	0.922582i	$0.373925\pi$
$104$	−10.4727	+	8.14915i	−1.02694	+	0.799090i
$105$		0			0
$106$	−2.58186	−	11.5230i	−0.250772	−	1.11921i
$107$			13.9860i			1.35208i	0.736866	+	0.676039i	$0.236305\pi$
$107$			13.9860i			1.35208i	−0.736866	+	0.676039i	$0.763695\pi$
$108$		0			0
$109$	4.06579			0.389432			0.194716	−	0.980860i	$-0.437621\pi$
$109$	4.06579			0.389432			0.194716	+	0.980860i	$0.437621\pi$
$110$	0.305209	+	1.36217i	0.0291005	+	0.129878i
$111$		0			0
$112$	6.96869	−	7.96476i	0.658479	−	0.752599i
$113$	8.66412			0.815052			0.407526	−	0.913194i	$-0.366392\pi$
$113$	8.66412			0.815052			0.407526	+	0.913194i	$0.366392\pi$
$114$		0			0
$115$	5.88128			0.548433
$116$	−18.5405	+	8.74756i	−1.72144	+	0.812190i
$117$		0			0
$118$	4.32357	+	19.2964i	0.398017	+	1.77638i
$119$	0.309013	−	10.4073i	0.0283272	−	0.954033i
$120$		0			0
$121$	10.0257			0.911425
$122$	6.80855	−	1.52553i	0.616417	−	0.138115i
$123$		0			0
$124$	−5.01827	+	2.36767i	−0.450654	+	0.212623i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	5.18615i		−	0.460197i	−0.973167	−	0.230098i	$-0.926095\pi$
$127$		−	5.18615i		−	0.460197i	0.973167	−	0.230098i	$-0.0739048\pi$
$128$	11.3093	+	0.315057i	0.999612	+	0.0278473i
$129$		0			0
$130$	−1.45065	−	6.47436i	−0.127231	−	0.567839i
$131$	11.3617			0.992679			0.496340	−	0.868128i	$-0.334677\pi$
$131$	11.3617			0.992679			0.496340	+	0.868128i	$0.334677\pi$
$132$		0			0
$133$	−0.592112	−	0.0175810i	−0.0513427	−	0.00152447i
$134$	−10.8292	+	2.42640i	−0.935497	+	0.209609i
$135$		0			0
$136$	8.78458	−	6.83554i	0.753272	−	0.586143i
$137$	5.85931			0.500595			0.250297	−	0.968169i	$-0.419472\pi$
$137$	5.85931			0.500595			0.250297	+	0.968169i	$0.419472\pi$
$138$		0			0
$139$	−18.1460			−1.53912			−0.769562	−	0.638572i	$-0.779525\pi$
$139$	−18.1460			−1.53912			−0.769562	+	0.638572i	$0.779525\pi$
$140$	2.11486	+	4.85050i	0.178738	+	0.409942i
$141$		0			0
$142$	−11.7283	+	2.62786i	−0.984220	+	0.220525i
$143$	4.63096			0.387260
$144$		0			0
$145$		−	10.2502i		−	0.851235i
$146$	−19.9638	+	4.47311i	−1.65222	+	0.370198i
$147$		0			0
$148$	−14.9571	+	7.05690i	−1.22947	+	0.580074i
$149$	−15.4737			−1.26766			−0.633829	−	0.773473i	$-0.718518\pi$
$149$	−15.4737			−1.26766			−0.633829	+	0.773473i	$0.718518\pi$
$150$		0			0
$151$			11.5322i			0.938474i	0.883072	+	0.469237i	$0.155471\pi$
$151$			11.5322i			0.938474i	−0.883072	+	0.469237i	$0.844529\pi$
$152$	−0.388902	−	0.499791i	−0.0315441	−	0.0405384i
$153$		0			0
$154$	−3.62634	+	0.700190i	−0.292219	+	0.0564229i
$155$		−	2.77439i		−	0.222844i
$156$		0			0
$157$		−	0.806743i		−	0.0643851i	−0.999482	−	0.0321926i	$-0.989751\pi$
$157$		−	0.806743i		−	0.0643851i	0.999482	−	0.0321926i	$-0.0102490\pi$
$158$	−15.8952	+	3.56151i	−1.26456	+	0.283338i
$159$		0			0
$160$	−2.55532	+	5.04682i	−0.202015	+	0.398986i
$161$	−0.461817	+	15.5536i	−0.0363963	+	1.22579i
$162$		0			0
$163$			6.48272i			0.507766i	0.967235	+	0.253883i	$0.0817077\pi$
$163$			6.48272i			0.507766i	−0.967235	+	0.253883i	$0.918292\pi$
$164$	−6.27173	−	13.2929i	−0.489740	−	1.03800i
$165$		0			0
$166$	−0.516722	−	2.30616i	−0.0401054	−	0.178993i
$167$	7.65678			0.592499			0.296250	−	0.955111i	$-0.404264\pi$
$167$	7.65678			0.592499			0.296250	+	0.955111i	$0.404264\pi$
$168$		0			0
$169$	−9.01087			−0.693144
$170$	1.21681	+	5.43072i	0.0933254	+	0.416517i
$171$		0			0
$172$	3.68941	+	7.81970i	0.281315	+	0.596247i
$173$			7.12007i			0.541329i	0.962674	+	0.270665i	$0.0872434\pi$
$173$			7.12007i			0.541329i	−0.962674	+	0.270665i	$0.912757\pi$
$174$		0			0
$175$	−2.64459	−	0.0785232i	−0.199912	−	0.00593580i
$176$	−3.04735	−	2.51055i	−0.229703	−	0.189240i
$177$		0			0
$178$	−0.680856	+	0.152554i	−0.0510323	+	0.0114344i
$179$			20.8439i			1.55794i	0.627059	+	0.778972i	$0.284258\pi$
$179$			20.8439i			1.55794i	−0.627059	+	0.778972i	$0.715742\pi$
$180$		0			0
$181$			24.4428i			1.81682i	0.418079	+	0.908411i	$0.362703\pi$
$181$			24.4428i			1.81682i	−0.418079	+	0.908411i	$0.637297\pi$
$182$	17.2359	−	3.32799i	1.27761	−	0.246687i
$183$		0			0
$184$	−13.1285	+	10.2156i	−0.967843	+	0.753107i
$185$		−	8.26915i		−	0.607960i
$186$		0			0
$187$	−3.88447			−0.284061
$188$	4.35517	−	2.05481i	0.317634	−	0.149862i
$189$		0			0
$190$	0.308976	−	0.0692296i	0.0224155	−	0.00502244i
$191$		−	19.3047i		−	1.39684i	−0.715689	−	0.698419i	$-0.753887\pi$
$191$		−	19.3047i		−	1.39684i	0.715689	−	0.698419i	$-0.246113\pi$
$192$		0			0
$193$	−15.2505			−1.09776			−0.548879	−	0.835902i	$-0.684945\pi$
$193$	−15.2505			−1.09776			−0.548879	+	0.835902i	$0.684945\pi$
$194$	−5.94828	+	1.33278i	−0.427062	+	0.0956880i
$195$		0			0
$196$	−12.9936	+	5.21206i	−0.928117	+	0.372290i
$197$	−3.00729			−0.214260			−0.107130	−	0.994245i	$-0.534166\pi$
$197$	−3.00729			−0.214260			−0.107130	+	0.994245i	$0.534166\pi$
$198$		0			0
$199$	−22.1587			−1.57079			−0.785395	−	0.618995i	$-0.787540\pi$
$199$	−22.1587			−1.57079			−0.785395	+	0.618995i	$0.787540\pi$
$200$	−1.73698	−	2.23224i	−0.122823	−	0.157844i
$201$		0			0
$202$	−8.33065	+	1.86658i	−0.586142	+	0.131332i
$203$	27.1076	+	0.804881i	1.90258	+	0.0564916i
$204$		0			0
$205$	7.34910			0.513283
$206$	−2.42135	−	10.8066i	−0.168703	−	0.752933i
$207$		0			0
$208$	14.4840	+	11.9326i	1.00429	+	0.827377i
$209$			0.221003i			0.0152871i
$210$		0			0
$211$			12.6769i			0.872714i	0.899774	+	0.436357i	$0.143731\pi$
$211$			12.6769i			0.872714i	−0.899774	+	0.436357i	$0.856269\pi$
$212$	−15.1034	+	7.12592i	−1.03731	+	0.489410i
$213$		0			0
$214$	19.3006	−	4.32453i	1.31936	−	0.295618i
$215$	−4.32318			−0.294838
$216$		0			0
$217$	7.33710	+	0.217854i	0.498075	+	0.0147889i
$218$	−1.25716	−	5.61078i	−0.0851455	−	0.380010i
$219$		0			0
$220$	1.78542	−	0.842376i	0.120373	−	0.0567930i
$221$	18.4628			1.24194
$222$		0			0
$223$	−6.45632			−0.432347			−0.216173	−	0.976355i	$-0.569358\pi$
$223$	−6.45632			−0.432347			−0.216173	+	0.976355i	$0.569358\pi$
$224$	−13.1461	−	7.15404i	−0.878360	−	0.478000i
$225$		0			0
$226$	−2.67898	−	11.9565i	−0.178203	−	0.795332i
$227$	14.0882			0.935066			0.467533	−	0.883976i	$-0.345143\pi$
$227$	14.0882			0.935066			0.467533	+	0.883976i	$0.345143\pi$
$228$		0			0
$229$			9.74932i			0.644253i	0.946697	+	0.322126i	$0.104398\pi$
$229$			9.74932i			0.644253i	−0.946697	+	0.322126i	$0.895602\pi$
$230$	−1.81852	−	8.11616i	−0.119909	−	0.535164i
$231$		0			0
$232$	17.8044	+	22.8810i	1.16892	+	1.50221i
$233$	−1.64231			−0.107591			−0.0537955	−	0.998552i	$-0.517132\pi$
$233$	−1.64231			−0.107591			−0.0537955	+	0.998552i	$0.517132\pi$
$234$		0			0
$235$			2.40779i			0.157067i
$236$	25.2921	−	11.9330i	1.64637	−	0.776774i
$237$		0			0
$238$	−14.4576	+	2.79153i	−0.937144	+	0.180948i
$239$			9.77724i			0.632437i	0.948686	+	0.316219i	$0.102413\pi$
$239$			9.77724i			0.632437i	−0.948686	+	0.316219i	$0.897587\pi$
$240$		0			0
$241$			6.84106i			0.440671i	0.975424	+	0.220336i	$0.0707152\pi$
$241$			6.84106i			0.440671i	−0.975424	+	0.220336i	$0.929285\pi$
$242$	−3.09998	−	13.8354i	−0.199274	−	0.889373i
$243$		0			0
$244$	−4.21046	−	8.92408i	−0.269547	−	0.571305i
$245$	0.415323	−	6.98767i	0.0265340	−	0.446426i
$246$		0			0
$247$		−	1.05043i		−	0.0668370i
$248$	4.81904	+	6.19311i	0.306009	+	0.393263i
$249$		0			0
$250$	1.38000	−	0.309204i	0.0872787	−	0.0195558i
$251$	2.34972			0.148313			0.0741564	−	0.997247i	$-0.476374\pi$
$251$	2.34972			0.148313			0.0741564	+	0.997247i	$0.476374\pi$
$252$		0			0
$253$	5.80530			0.364976
$254$	−7.15688	+	1.60358i	−0.449063	+	0.100618i
$255$		0			0
$256$	−3.06211	−	15.7043i	−0.191382	−	0.981516i
$257$			6.47150i			0.403681i	0.979418	+	0.201840i	$0.0646922\pi$
$257$			6.47150i			0.403681i	−0.979418	+	0.201840i	$0.935308\pi$
$258$		0			0
$259$	21.8685	+	0.649320i	1.35884	+	0.0403468i
$260$	−8.48605	+	4.00380i	−0.526283	+	0.248305i
$261$		0			0
$262$	−3.51309	−	15.6792i	−0.217040	−	0.968662i
$263$			2.38076i			0.146804i	0.997302	+	0.0734018i	$0.0233856\pi$
$263$			2.38076i			0.146804i	−0.997302	+	0.0734018i	$0.976614\pi$
$264$		0			0
$265$		−	8.35002i		−	0.512938i
$266$	0.158822	+	0.822550i	0.00973799	+	0.0504338i
$267$		0			0
$268$	6.69684	+	14.1940i	0.409075	+	0.867034i
$269$		−	9.44894i		−	0.576112i	−0.957614	−	0.288056i	$-0.906991\pi$
$269$		−	9.44894i		−	0.576112i	0.957614	−	0.288056i	$-0.0930089\pi$
$270$		0			0
$271$	−22.1827			−1.34750			−0.673752	−	0.738958i	$-0.735318\pi$
$271$	−22.1827			−1.34750			−0.673752	+	0.738958i	$0.735318\pi$
$272$	−12.1493	−	10.0091i	−0.736657	−	0.606892i
$273$		0			0
$274$	−1.81172	−	8.08583i	−0.109450	−	0.488483i
$275$			0.987080i			0.0595232i
$276$		0			0
$277$	−26.7718			−1.60856			−0.804281	−	0.594249i	$-0.797449\pi$
$277$	−26.7718			−1.60856			−0.804281	+	0.594249i	$0.797449\pi$
$278$	5.61082	+	25.0414i	0.336514	+	1.50189i
$279$		0			0
$280$	6.03976	−	4.41830i	0.360944	−	0.264044i
$281$	8.64183			0.515529			0.257764	−	0.966208i	$-0.417014\pi$
$281$	8.64183			0.515529			0.257764	+	0.966208i	$0.417014\pi$
$282$		0			0
$283$	5.92047			0.351935			0.175968	−	0.984396i	$-0.443695\pi$
$283$	5.92047			0.351935			0.175968	+	0.984396i	$0.443695\pi$
$284$	7.25289	+	15.3725i	0.430380	+	0.912191i
$285$		0			0
$286$	−1.43191	−	6.39071i	−0.0846707	−	0.377891i
$287$	−0.577075	+	19.4353i	−0.0340637	+	1.14723i
$288$		0			0
$289$	1.51332			0.0890186
$290$	−14.1453	+	3.16941i	−0.830640	+	0.186114i
$291$		0			0
$292$	12.3458	+	26.1669i	0.722482	+	1.53130i
$293$		−	26.2654i		−	1.53444i	−0.641382	−	0.767221i	$-0.721639\pi$
$293$		−	26.2654i		−	1.53444i	0.641382	−	0.767221i	$-0.278361\pi$
$294$		0			0
$295$			13.9829i			0.814116i
$296$	14.3633	+	18.4588i	0.834850	+	1.07289i
$297$		0			0
$298$	4.78454	+	21.3537i	0.277161	+	1.23699i
$299$	−27.5925			−1.59571
$300$		0			0
$301$	0.339470	−	11.4330i	0.0195667	−	0.658988i
$302$	15.9144	−	3.56579i	0.915768	−	0.205188i
$303$		0			0
$304$	−0.569460	+	0.691221i	−0.0326608	+	0.0396443i
$305$	4.93374			0.282505
$306$		0			0
$307$	18.5432			1.05832			0.529158	−	0.848524i	$-0.322508\pi$
$307$	18.5432			1.05832			0.529158	+	0.848524i	$0.322508\pi$
$308$	2.08754	+	4.78783i	0.118949	+	0.272812i
$309$		0			0
$310$	−3.82865	+	0.857851i	−0.217453	+	0.0487227i
$311$	−30.8370			−1.74861			−0.874304	−	0.485379i	$-0.838682\pi$
$311$	−30.8370			−1.74861			−0.874304	+	0.485379i	$0.838682\pi$
$312$		0			0
$313$		−	20.8250i		−	1.17710i	−0.808461	−	0.588550i	$-0.799699\pi$
$313$		−	20.8250i		−	1.17710i	0.808461	−	0.588550i	$-0.200301\pi$
$314$	−1.11330	+	0.249448i	−0.0628274	+	0.0140772i
$315$		0			0
$316$	9.82975	+	20.8342i	0.552967	+	1.17201i
$317$	−5.41152			−0.303941			−0.151971	−	0.988385i	$-0.548562\pi$
$317$	−5.41152			−0.303941			−0.151971	+	0.988385i	$0.548562\pi$
$318$		0			0
$319$		−	10.1178i		−	0.566488i
$320$	7.75471	+	1.96583i	0.433501	+	0.109893i
$321$		0			0
$322$	21.6067	−	4.17192i	1.20409	−	0.232492i
$323$			0.881101i			0.0490258i
$324$		0			0
$325$		−	4.69157i		−	0.260242i
$326$	8.94613	−	2.00448i	0.495480	−	0.111018i
$327$		0			0
$328$	−16.4050	+	12.7652i	−0.905814	+	0.704841i
$329$	−6.36760	−	0.189067i	−0.351057	−	0.0104236i
$330$		0			0
$331$		−	1.77494i		−	0.0975597i	−0.998810	−	0.0487799i	$-0.984467\pi$
$331$		−	1.77494i		−	0.0975597i	0.998810	−	0.0487799i	$-0.0155333\pi$
$332$	−3.02273	+	1.42615i	−0.165894	+	0.0782702i
$333$		0			0
$334$	−2.36751	−	10.5663i	−0.129544	−	0.578164i
$335$	−7.84723			−0.428740
$336$		0			0
$337$	22.3668			1.21839			0.609197	−	0.793019i	$-0.291492\pi$
$337$	22.3668			1.21839			0.609197	+	0.793019i	$0.291492\pi$
$338$	2.78620	+	12.4350i	0.151549	+	0.676374i
$339$		0			0
$340$	7.11814	−	3.35840i	0.386035	−	0.182135i
$341$		−	2.73854i		−	0.148300i
$342$		0			0
$343$	18.4469	+	1.64705i	0.996038	+	0.0889324i
$344$	9.65039	−	7.50925i	0.520314	−	0.404872i
$345$		0			0
$346$	9.82569	−	2.20156i	0.528232	−	0.118356i
$347$		−	0.606084i		−	0.0325363i	−0.999868	−	0.0162681i	$-0.994821\pi$
$347$		−	0.606084i		−	0.0325363i	0.999868	−	0.0162681i	$-0.00517854\pi$
$348$		0			0
$349$			31.6682i			1.69516i	0.530668	+	0.847580i	$0.321941\pi$
$349$			31.6682i			1.69516i	−0.530668	+	0.847580i	$0.678059\pi$
$350$	0.709355	+	3.67380i	0.0379166	+	0.196373i
$351$		0			0
$352$	−2.52230	+	4.98161i	−0.134439	+	0.265521i
$353$			4.06901i			0.216572i	0.994120	+	0.108286i	$0.0345362\pi$
$353$			4.06901i			0.216572i	−0.994120	+	0.108286i	$0.965464\pi$
$354$		0			0
$355$	−8.49881			−0.451070
$356$	0.421047	+	0.892410i	0.0223154	+	0.0472976i
$357$		0			0
$358$	28.7645	−	6.44500i	1.52025	−	0.340629i
$359$			11.0427i			0.582809i	0.956600	+	0.291405i	$0.0941226\pi$
$359$			11.0427i			0.582809i	−0.956600	+	0.291405i	$0.905877\pi$
$360$		0			0
$361$	−18.9499			−0.997362
$362$	33.7310	−	7.55782i	1.77286	−	0.397230i
$363$		0			0
$364$	−9.92203	−	22.7565i	−0.520056	−	1.19276i
$365$	−14.4665			−0.757214
$366$		0			0
$367$	−0.0725720			−0.00378823			−0.00189411	−	0.999998i	$-0.500603\pi$
$367$	−0.0725720			−0.00378823			−0.00189411	+	0.999998i	$0.500603\pi$
$368$	18.1569	+	14.9585i	0.946496	+	0.779767i
$369$		0			0
$370$	−11.4114	+	2.55685i	−0.593251	+	0.132924i
$371$	22.0824	+	0.655671i	1.14646	+	0.0340407i
$372$		0			0
$373$	22.4132			1.16051			0.580257	−	0.814433i	$-0.302952\pi$
$373$	22.4132			1.16051			0.580257	+	0.814433i	$0.302952\pi$
$374$	1.20109	+	5.36056i	0.0621071	+	0.277188i
$375$		0			0
$376$	−4.18227	−	5.37477i	−0.215684	−	0.277183i
$377$			48.0897i			2.47675i
$378$		0			0
$379$			26.9969i			1.38674i	0.720584	+	0.693368i	$0.243874\pi$
$379$			26.9969i			1.38674i	−0.720584	+	0.693368i	$0.756126\pi$
$380$	−0.191073	−	0.404980i	−0.00980185	−	0.0207750i
$381$		0			0
$382$	−26.6404	+	5.96909i	−1.36304	+	0.305405i
$383$	−19.7866			−1.01105			−0.505523	−	0.862813i	$-0.668701\pi$
$383$	−19.7866			−1.01105			−0.505523	+	0.862813i	$0.668701\pi$
$384$		0			0
$385$	−2.61042	−	0.0775087i	−0.133039	−	0.00395021i
$386$	4.71553	+	21.0457i	0.240014	+	1.07120i
$387$		0			0
$388$	3.67846	+	7.79651i	0.186746	+	0.395808i
$389$	29.6119			1.50138			0.750690	−	0.660654i	$-0.229721\pi$
$389$	29.6119			1.50138			0.750690	+	0.660654i	$0.229721\pi$
$390$		0			0
$391$	23.1447			1.17048
$392$	11.2103	+	16.3196i	0.566206	+	0.824264i
$393$		0			0
$394$	0.929865	+	4.15005i	0.0468459	+	0.209076i
$395$	−11.5183			−0.579549
$396$		0			0
$397$			21.2555i			1.06678i	0.845868	+	0.533392i	$0.179083\pi$
$397$			21.2555i			1.06678i	−0.845868	+	0.533392i	$0.820917\pi$
$398$	6.85156	+	30.5790i	0.343438	+	1.53279i
$399$		0			0
$400$	−2.54341	+	3.08724i	−0.127171	+	0.154362i
$401$	−24.5750			−1.22722			−0.613608	−	0.789610i	$-0.710283\pi$
$401$	−24.5750			−1.22722			−0.613608	+	0.789610i	$0.710283\pi$
$402$		0			0
$403$			13.0162i			0.648385i
$404$	5.15174	+	10.9191i	0.256309	+	0.543246i
$405$		0			0
$406$	−7.27104	−	37.6573i	−0.360856	−	1.86890i
$407$		−	8.16231i		−	0.404591i
$408$		0			0
$409$		−	34.9158i		−	1.72648i	−0.504797	−	0.863238i	$-0.668433\pi$
$409$		−	34.9158i		−	1.72648i	0.504797	−	0.863238i	$-0.331567\pi$
$410$	−2.27237	−	10.1417i	−0.112224	−	0.500865i
$411$		0			0
$412$	−14.1644	+	6.68290i	−0.697831	+	0.329243i
$413$	−36.9790	−	1.09798i	−1.81962	−	0.0540282i
$414$		0			0
$415$		−	1.67114i		−	0.0820329i
$416$	11.9885	−	23.6775i	0.587782	−	1.16089i
$417$		0			0
$418$	0.304984	−	0.0683351i	0.0149173	−	0.00334238i
$419$	−2.32360			−0.113515			−0.0567577	−	0.998388i	$-0.518076\pi$
$419$	−2.32360			−0.113515			−0.0567577	+	0.998388i	$0.518076\pi$
$420$		0			0
$421$	−22.9539			−1.11870			−0.559352	−	0.828930i	$-0.688950\pi$
$421$	−22.9539			−1.11870			−0.559352	+	0.828930i	$0.688950\pi$
$422$	17.4941	−	3.91975i	0.851599	−	0.190810i
$423$		0			0
$424$	14.5038	+	18.6393i	0.704366	+	0.905204i
$425$			3.93531i			0.190891i
$426$		0			0
$427$	−0.387413	+	13.0477i	−0.0187482	+	0.631422i
$428$	−11.9357	−	25.2977i	−0.576932	−	1.22281i
$429$		0			0
$430$	1.33674	+	5.96597i	0.0644635	+	0.287705i
$431$			0.0761033i			0.00366577i	0.999998	+	0.00183288i	$0.000583425\pi$
$431$			0.0761033i			0.00366577i	−0.999998	+	0.00183288i	$0.999417\pi$
$432$		0			0
$433$			9.43899i			0.453609i	0.973940	+	0.226805i	$0.0728278\pi$
$433$			9.43899i			0.453609i	−0.973940	+	0.226805i	$0.927172\pi$
$434$	−1.96802	−	10.1925i	−0.0944682	−	0.489258i
$435$		0			0
$436$	−7.35414	+	3.46975i	−0.352199	+	0.166171i
$437$		−	1.31680i		−	0.0629909i
$438$		0			0
$439$	−4.35512			−0.207858			−0.103929	−	0.994585i	$-0.533142\pi$
$439$	−4.35512			−0.207858			−0.103929	+	0.994585i	$0.533142\pi$
$440$	−1.71453	−	2.20340i	−0.0817372	−	0.105043i
$441$		0			0
$442$	−5.70878	−	25.4786i	−0.271539	−	1.21190i
$443$		−	35.6619i		−	1.69435i	−0.531315	−	0.847174i	$-0.678302\pi$
$443$		−	35.6619i		−	1.69435i	0.531315	−	0.847174i	$-0.321698\pi$
$444$		0			0
$445$	−0.493375			−0.0233882
$446$	1.99632	+	8.90970i	0.0945284	+	0.421886i
$447$		0			0
$448$	−5.80774	+	20.3536i	−0.274390	+	0.961619i
$449$	−15.1046			−0.712832			−0.356416	−	0.934327i	$-0.616001\pi$
$449$	−15.1046			−0.712832			−0.356416	+	0.934327i	$0.616001\pi$
$450$		0			0
$451$	7.25415			0.341585
$452$	−15.6715	+	7.39397i	−0.737127	+	0.347783i
$453$		0			0
$454$	−4.35613	−	19.4417i	−0.204443	−	0.912443i
$455$	12.4073	+	0.368398i	0.581662	+	0.0172707i
$456$		0			0
$457$	−23.3917			−1.09422			−0.547109	−	0.837061i	$-0.684272\pi$
$457$	−23.3917			−1.09422			−0.547109	+	0.837061i	$0.684272\pi$
$458$	13.4540	−	3.01453i	0.628666	−	0.140860i
$459$		0			0
$460$	−10.6380	+	5.01910i	−0.495999	+	0.234017i
$461$			22.6568i			1.05523i	0.849482	+	0.527617i	$0.176914\pi$
$461$			22.6568i			1.05523i	−0.849482	+	0.527617i	$0.823086\pi$
$462$		0			0
$463$		−	31.9975i		−	1.48705i	−0.668707	−	0.743526i	$-0.733152\pi$
$463$		−	31.9975i		−	1.48705i	0.668707	−	0.743526i	$-0.266848\pi$
$464$	26.0705	−	31.6449i	1.21029	−	1.46908i
$465$		0			0
$466$	0.507807	+	2.26638i	0.0235237	+	0.104988i
$467$	−42.6816			−1.97507			−0.987533	−	0.157409i	$-0.949686\pi$
$467$	−42.6816			−1.97507			−0.987533	+	0.157409i	$0.949686\pi$
$468$		0			0
$469$	0.616190	−	20.7527i	0.0284530	−	0.958270i
$470$	3.32274	−	0.744498i	0.153267	−	0.0343411i
$471$		0			0
$472$	−24.2880	−	31.2133i	−1.11794	−	1.43671i
$473$	−4.26732			−0.196212
$474$		0			0
$475$	0.223896			0.0102731
$476$	8.32264	+	19.0882i	0.381468	+	0.874908i
$477$		0			0
$478$	13.4926	−	3.02316i	0.617136	−	0.138276i
$479$	0.259729			0.0118673			0.00593366	−	0.999982i	$-0.498111\pi$
$479$	0.259729			0.0118673			0.00593366	+	0.999982i	$0.498111\pi$
$480$		0			0
$481$			38.7953i			1.76891i
$482$	9.44064	−	2.11528i	0.430009	−	0.0963484i
$483$		0			0
$484$	−18.1343	+	8.55592i	−0.824286	+	0.388906i
$485$	−4.31036			−0.195723
$486$		0			0
$487$		−	29.8196i		−	1.35126i	−0.737242	−	0.675628i	$-0.763872\pi$
$487$		−	29.8196i		−	1.35126i	0.737242	−	0.675628i	$-0.236128\pi$
$488$	−11.0133	+	8.56978i	−0.498549	+	0.387936i
$489$		0			0
$490$	−9.77138	+	1.58747i	−0.441426	+	0.0717146i
$491$			25.9448i			1.17087i	0.810718	+	0.585437i	$0.199077\pi$
$491$			25.9448i			1.17087i	−0.810718	+	0.585437i	$0.800923\pi$
$492$		0			0
$493$		−	40.3378i		−	1.81672i
$494$	−1.44958	+	0.324796i	−0.0652199	+	0.0146132i
$495$		0			0
$496$	7.05641	−	8.56520i	0.316842	−	0.384589i
$497$	0.667354	−	22.4758i	0.0299349	−	1.00818i
$498$		0			0
$499$			22.9135i			1.02575i	0.858464	+	0.512874i	$0.171419\pi$
$499$			22.9135i			1.02575i	−0.858464	+	0.512874i	$0.828581\pi$
$500$	−0.853401	−	1.80879i	−0.0381653	−	0.0808914i
$501$		0			0
$502$	−0.726541	−	3.24260i	−0.0324271	−	0.144724i
$503$	29.7060			1.32453			0.662263	−	0.749271i	$-0.269596\pi$
$503$	29.7060			1.32453			0.662263	+	0.749271i	$0.269596\pi$
$504$		0			0
$505$	−6.03671			−0.268630
$506$	−1.79502	−	8.01130i	−0.0797984	−	0.356146i
$507$		0			0
$508$	4.42587	+	9.38064i	0.196366	+	0.416199i
$509$		−	15.8710i		−	0.703470i	−0.936100	−	0.351735i	$-0.885592\pi$
$509$		−	15.8710i		−	0.703470i	0.936100	−	0.351735i	$-0.114408\pi$
$510$		0			0
$511$	1.13596	−	38.2580i	0.0502519	−	1.69244i
$512$	−20.7250	+	9.08152i	−0.915925	+	0.401350i
$513$		0			0
$514$	8.93065	−	2.00101i	0.393914	−	0.0882609i
$515$		−	7.83090i		−	0.345071i
$516$		0			0
$517$			2.37668i			0.104526i
$518$	−5.86576	−	30.3792i	−0.257727	−	1.33479i
$519$		0			0
$520$	8.14915	+	10.4727i	0.357364	+	0.459260i
$521$		−	10.0748i		−	0.441387i	−0.975343	−	0.220693i	$-0.929168\pi$
$521$		−	10.0748i		−	0.441387i	0.975343	−	0.220693i	$-0.0708320\pi$
$522$		0			0
$523$	15.4083			0.673759			0.336880	−	0.941548i	$-0.390628\pi$
$523$	15.4083			0.673759			0.336880	+	0.941548i	$0.390628\pi$
$524$	−20.5509	+	9.69612i	−0.897772	+	0.423577i
$525$		0			0
$526$	3.28544	−	0.736139i	0.143252	−	0.0320972i
$527$		−	10.9181i		−	0.475599i
$528$		0			0
$529$	−11.5895			−0.503891
$530$	−11.5230	+	2.58186i	−0.500528	+	0.112149i
$531$		0			0
$532$	1.08601	−	0.473509i	0.0470844	−	0.0205292i
$533$	−34.4788			−1.49344
$534$		0			0
$535$	13.9860			0.604667
$536$	17.5169	−	13.6305i	0.756617	−	0.588746i
$537$		0			0
$538$	−13.0395	+	2.92165i	−0.562173	+	0.125961i
$539$	0.409957	−	6.89739i	0.0176581	−	0.297092i
$540$		0			0
$541$	−11.4549			−0.492486			−0.246243	−	0.969208i	$-0.579196\pi$
$541$	−11.4549			−0.492486			−0.246243	+	0.969208i	$0.579196\pi$
$542$	6.85898	+	30.6121i	0.294619	+	1.31490i
$543$		0			0
$544$	−10.0560	+	19.8608i	−0.431146	+	0.851525i
$545$		−	4.06579i		−	0.174159i
$546$		0			0
$547$		−	25.1553i		−	1.07556i	−0.843085	−	0.537781i	$-0.819263\pi$
$547$		−	25.1553i		−	1.07556i	0.843085	−	0.537781i	$-0.180737\pi$
$548$	−10.5982	+	5.00034i	−0.452734	+	0.213604i
$549$		0			0
$550$	1.36217	−	0.305209i	0.0580830	−	0.0130142i
$551$	−2.29499			−0.0977697
$552$		0			0
$553$	0.904455	−	30.4612i	0.0384614	−	1.29534i
$554$	8.27795	+	36.9450i	0.351696	+	1.56964i
$555$		0			0
$556$	32.8222	−	15.4858i	1.39197	−	0.656745i
$557$	−26.6942			−1.13107			−0.565534	−	0.824725i	$-0.691330\pi$
$557$	−26.6942			−1.13107			−0.565534	+	0.824725i	$0.691330\pi$
$558$		0			0
$559$	20.2825			0.857859
$560$	−7.96476	−	6.96869i	−0.336572	−	0.294481i
$561$		0			0
$562$	−2.67209	−	11.9257i	−0.112715	−	0.503056i
$563$	10.8180			0.455923			0.227962	−	0.973670i	$-0.426794\pi$
$563$	10.8180			0.455923			0.227962	+	0.973670i	$0.426794\pi$
$564$		0			0
$565$		−	8.66412i		−	0.364502i
$566$	−1.83063	−	8.17023i	−0.0769472	−	0.343420i
$567$		0			0
$568$	18.9714	−	14.7622i	0.796023	−	0.619409i
$569$	−15.0833			−0.632323			−0.316162	−	0.948705i	$-0.602394\pi$
$569$	−15.0833			−0.632323			−0.316162	+	0.948705i	$0.602394\pi$
$570$		0			0
$571$			11.4509i			0.479206i	0.970871	+	0.239603i	$0.0770174\pi$
$571$			11.4509i			0.479206i	−0.970871	+	0.239603i	$0.922983\pi$
$572$	−8.37642	+	3.95207i	−0.350236	+	0.165244i
$573$		0			0
$574$	26.9991	−	5.21312i	1.12692	−	0.217591i
$575$		−	5.88128i		−	0.245267i
$576$		0			0
$577$			27.7622i			1.15576i	0.816123	+	0.577878i	$0.196119\pi$
$577$			27.7622i			1.15576i	−0.816123	+	0.577878i	$0.803881\pi$
$578$	−0.467923	−	2.08837i	−0.0194630	−	0.0868648i
$579$		0			0
$580$	8.74756	+	18.5405i	0.363223	+	0.769851i
$581$	4.41946	+	0.131223i	0.183350	+	0.00544405i
$582$		0			0
$583$		−	8.24214i		−	0.341355i
$584$	32.2929	−	25.1280i	1.33629	−	1.03981i
$585$		0			0
$586$	−36.2462	+	8.12137i	−1.49732	+	0.335491i
$587$	4.20086			0.173388			0.0866941	−	0.996235i	$-0.472370\pi$
$587$	4.20086			0.173388			0.0866941	+	0.996235i	$0.472370\pi$
$588$		0			0
$589$	−0.621174			−0.0255950
$590$	19.2964	−	4.32357i	0.794419	−	0.177999i
$591$		0			0
$592$	21.0319	−	25.5289i	0.864404	−	1.04923i
$593$		−	12.2323i		−	0.502321i	−0.967945	−	0.251161i	$-0.919188\pi$
$593$		−	12.2323i		−	0.502321i	0.967945	−	0.251161i	$-0.0808123\pi$
$594$		0			0
$595$	−10.4073	−	0.309013i	−0.426657	−	0.0126683i
$596$	27.9887	−	13.2053i	1.14646	−	0.540911i
$597$		0			0
$598$	8.53171	+	38.0776i	0.348887	+	1.55711i
$599$		−	43.8944i		−	1.79348i	−0.442562	−	0.896738i	$-0.645930\pi$
$599$		−	43.8944i		−	1.79348i	0.442562	−	0.896738i	$-0.354070\pi$
$600$		0			0
$601$			5.44570i			0.222135i	0.993813	+	0.111067i	$0.0354269\pi$
$601$			5.44570i			0.222135i	−0.993813	+	0.111067i	$0.964573\pi$
$602$	−15.8825	+	3.06667i	−0.647322	+	0.124988i
$603$		0			0
$604$	−9.84156	−	20.8592i	−0.400447	−	0.848749i
$605$		−	10.0257i		−	0.407602i
$606$		0			0
$607$	−29.7406			−1.20713			−0.603567	−	0.797312i	$-0.706255\pi$
$607$	−29.7406			−1.20713			−0.603567	+	0.797312i	$0.706255\pi$
$608$	1.12996	+	0.572125i	0.0458260	+	0.0232027i
$609$		0			0
$610$	−1.52553	−	6.80855i	−0.0617670	−	0.275670i
$611$		−	11.2963i		−	0.457000i
$612$		0			0
$613$	26.7046			1.07859			0.539295	−	0.842117i	$-0.318691\pi$
$613$	26.7046			1.07859			0.539295	+	0.842117i	$0.318691\pi$
$614$	−5.73363	−	25.5895i	−0.231390	−	1.03271i
$615$		0			0
$616$	5.96172	−	4.36121i	0.240205	−	0.175718i
$617$	18.7712			0.755701			0.377851	−	0.925867i	$-0.376663\pi$
$617$	18.7712			0.755701			0.377851	+	0.925867i	$0.376663\pi$
$618$		0			0
$619$	−6.00143			−0.241218			−0.120609	−	0.992700i	$-0.538485\pi$
$619$	−6.00143			−0.241218			−0.120609	+	0.992700i	$0.538485\pi$
$620$	2.36767	+	5.01827i	0.0950877	+	0.201539i
$621$		0			0
$622$	9.53493	+	42.5550i	0.382316	+	1.70630i
$623$	0.0387414	−	1.30477i	0.00155214	−	0.0522746i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−28.7385	+	6.43918i	−1.14862	+	0.257361i
$627$		0			0
$628$	0.688476	+	1.45923i	0.0274732	+	0.0582294i
$629$		−	32.5417i		−	1.29752i
$630$		0			0
$631$		−	42.7851i		−	1.70325i	−0.524154	−	0.851623i	$-0.675619\pi$
$631$		−	42.7851i		−	1.70325i	0.524154	−	0.851623i	$-0.324381\pi$
$632$	25.7117	−	20.0070i	1.02276	−	0.795837i
$633$		0			0
$634$	1.67326	+	7.46788i	0.0664538	+	0.296587i
$635$	−5.18615			−0.205806
$636$		0			0
$637$	−1.94852	+	32.7832i	−0.0772031	+	1.29892i
$638$	−13.9625	+	3.12846i	−0.552782	+	0.123857i
$639$		0			0
$640$	0.315057	−	11.3093i	0.0124537	−	0.447040i
$641$	−32.5398			−1.28525			−0.642623	−	0.766182i	$-0.722154\pi$
$641$	−32.5398			−1.28525			−0.642623	+	0.766182i	$0.722154\pi$
$642$		0			0
$643$	10.1954			0.402068			0.201034	−	0.979584i	$-0.435570\pi$
$643$	10.1954			0.402068			0.201034	+	0.979584i	$0.435570\pi$
$644$	−12.4381	−	28.5272i	−0.490130	−	1.12413i
$645$		0			0
$646$	1.21592	−	0.272440i	0.0478396	−	0.0107190i
$647$	32.1295			1.26314			0.631571	−	0.775318i	$-0.282410\pi$
$647$	32.1295			1.26314			0.631571	+	0.775318i	$0.282410\pi$
$648$		0			0
$649$			13.8023i			0.541786i
$650$	−6.47436	+	1.45065i	−0.253945	+	0.0568993i
$651$		0			0
$652$	−5.53236	−	11.7258i	−0.216664	−	0.459220i
$653$	25.0805			0.981476			0.490738	−	0.871307i	$-0.336727\pi$
$653$	25.0805			0.981476			0.490738	+	0.871307i	$0.336727\pi$
$654$		0			0
$655$		−	11.3617i		−	0.443940i
$656$	22.6884	+	18.6918i	0.885835	+	0.729792i
$657$		0			0
$658$	1.70798	+	8.84574i	0.0665838	+	0.344843i
$659$		−	8.80669i		−	0.343060i	−0.985179	−	0.171530i	$-0.945129\pi$
$659$		−	8.80669i		−	0.343060i	0.985179	−	0.171530i	$-0.0548710\pi$
$660$		0			0
$661$			43.1173i			1.67707i	0.544849	+	0.838534i	$0.316587\pi$
$661$			43.1173i			1.67707i	−0.544849	+	0.838534i	$0.683413\pi$
$662$	−2.44942	+	0.548820i	−0.0951993	+	0.0213305i
$663$		0			0
$664$	2.90272	+	3.73039i	0.112648	+	0.144767i
$665$	−0.0175810	+	0.592112i	−0.000681764	+	0.0229611i
$666$		0			0
$667$			60.2845i			2.33422i
$668$	−13.8495	+	6.53430i	−0.535852	+	0.252820i
$669$		0			0
$670$	2.42640	+	10.8292i	0.0937399	+	0.418367i
$671$	4.87000			0.188004
$672$		0			0
$673$	−12.2583			−0.472524			−0.236262	−	0.971689i	$-0.575922\pi$
$673$	−12.2583			−0.472524			−0.236262	+	0.971689i	$0.575922\pi$
$674$	−6.91589	−	30.8661i	−0.266390	−	1.18892i
$675$		0			0
$676$	16.2987	−	7.68989i	0.626875	−	0.295765i
$677$		−	29.7024i		−	1.14155i	−0.821105	−	0.570777i	$-0.806642\pi$
$677$		−	29.7024i		−	1.14155i	0.821105	−	0.570777i	$-0.193358\pi$
$678$		0			0
$679$	0.338463	−	11.3991i	0.0129890	−	0.437458i
$680$	−6.83554	−	8.78458i	−0.262131	−	0.336873i
$681$		0			0
$682$	−3.77918	+	0.846768i	−0.144712	+	0.0324244i
$683$			35.1749i			1.34593i	0.739674	+	0.672965i	$0.234980\pi$
$683$			35.1749i			1.34593i	−0.739674	+	0.672965i	$0.765020\pi$
$684$		0			0
$685$		−	5.85931i		−	0.223873i
$686$	−3.43092	−	25.9659i	−0.130993	−	0.991383i
$687$		0			0
$688$	−13.3467	−	10.9956i	−0.508838	−	0.419204i
$689$			39.1748i			1.49244i
$690$		0			0
$691$	−42.9454			−1.63372			−0.816860	−	0.576836i	$-0.804287\pi$
$691$	−42.9454			−1.63372			−0.816860	+	0.576836i	$0.804287\pi$
$692$	−6.07628	−	12.8787i	−0.230986	−	0.489574i
$693$		0			0
$694$	−0.836394	+	0.187403i	−0.0317491	+	0.00711374i
$695$			18.1460i			0.688317i
$696$		0			0
$697$	28.9210			1.09546
$698$	43.7020	−	9.79193i	1.65415	−	0.370630i
$699$		0			0
$700$	4.85050	−	2.11486i	0.183332	−	0.0799343i
$701$	9.37675			0.354155			0.177077	−	0.984197i	$-0.443336\pi$
$701$	9.37675			0.354155			0.177077	+	0.984197i	$0.443336\pi$
$702$		0			0
$703$	−1.85143			−0.0698280
$704$	7.65452	+	1.94043i	0.288491	+	0.0731329i
$705$		0			0
$706$	5.61523	−	1.25815i	0.211332	−	0.0473513i
$707$	0.474022	−	15.9646i	0.0178274	−	0.600411i
$708$		0			0
$709$	−27.6729			−1.03928			−0.519638	−	0.854386i	$-0.673933\pi$
$709$	−27.6729			−1.03928			−0.519638	+	0.854386i	$0.673933\pi$
$710$	2.62786	+	11.7283i	0.0986220	+	0.440156i
$711$		0			0
$712$	1.10133	−	0.856980i	0.0412742	−	0.0321167i
$713$			16.3170i			0.611075i
$714$		0			0
$715$		−	4.63096i		−	0.173188i
$716$	−17.7882	−	37.7021i	−0.664776	−	1.40899i
$717$		0			0
$718$	15.2388	−	3.41443i	0.568708	−	0.127426i
$719$	−9.24786			−0.344887			−0.172444	−	0.985019i	$-0.555166\pi$
$719$	−9.24786			−0.344887			−0.172444	+	0.985019i	$0.555166\pi$
$720$		0			0
$721$	20.7095	+	0.614908i	0.771262	+	0.0229004i
$722$	5.85938	+	26.1508i	0.218063	+	0.973231i
$723$		0			0
$724$	−20.8595	−	44.2118i	−0.775239	−	1.64312i
$725$	−10.2502			−0.380684
$726$		0			0
$727$	−34.7371			−1.28833			−0.644163	−	0.764888i	$-0.722794\pi$
$727$	−34.7371			−1.28833			−0.644163	+	0.764888i	$0.722794\pi$
$728$	−28.3360	+	20.7288i	−1.05020	+	0.768259i
$729$		0			0
$730$	4.47311	+	19.9638i	0.165557	+	0.738893i
$731$	−17.0131			−0.629250
$732$		0			0
$733$		−	38.6871i		−	1.42894i	−0.699666	−	0.714470i	$-0.746668\pi$
$733$		−	38.6871i		−	1.42894i	0.699666	−	0.714470i	$-0.253332\pi$
$734$	0.0224396	+	0.100149i	0.000828259	+	0.00369657i
$735$		0			0
$736$	15.0285	−	29.6818i	0.553959	−	1.09408i
$737$	−7.74585			−0.285322
$738$		0			0
$739$		−	40.4228i		−	1.48698i	−0.668748	−	0.743489i	$-0.733170\pi$
$739$		−	40.4228i		−	1.48698i	0.668748	−	0.743489i	$-0.266830\pi$
$740$	7.05690	+	14.9571i	0.259417	+	0.549835i
$741$		0			0
$742$	−5.92313	−	30.6763i	−0.217445	−	1.12616i
$743$		−	25.5119i		−	0.935941i	−0.883744	−	0.467970i	$-0.844985\pi$
$743$		−	25.5119i		−	0.935941i	0.883744	−	0.467970i	$-0.155015\pi$
$744$		0			0
$745$			15.4737i			0.566914i
$746$	−6.93026	−	30.9302i	−0.253735	−	1.13244i
$747$		0			0
$748$	7.02617	−	3.31501i	0.256902	−	0.121209i
$749$	−1.09823	+	36.9872i	−0.0401283	+	1.35148i
$750$		0			0
$751$		−	31.4000i		−	1.14580i	−0.819625	−	0.572901i	$-0.805818\pi$
$751$		−	31.4000i		−	1.14580i	0.819625	−	0.572901i	$-0.194182\pi$
$752$	−6.12400	+	7.43342i	−0.223319	+	0.271069i
$753$		0			0
$754$	66.3637	−	14.8695i	2.41682	−	0.541516i
$755$	11.5322			0.419698
$756$		0			0
$757$	−32.9674			−1.19822			−0.599111	−	0.800666i	$-0.704479\pi$
$757$	−32.9674			−1.19822			−0.599111	+	0.800666i	$0.704479\pi$
$758$	37.2556	−	8.34754i	1.35318	−	0.303196i
$759$		0			0
$760$	−0.499791	+	0.388902i	−0.0181293	+	0.0141070i
$761$			45.0372i			1.63260i	0.577631	+	0.816298i	$0.303977\pi$
$761$			45.0372i			1.63260i	−0.577631	+	0.816298i	$0.696023\pi$
$762$		0			0
$763$	10.7523	+	0.319259i	0.389260	+	0.0115579i
$764$	16.4747	+	34.9181i	0.596032	+	1.26329i
$765$		0			0
$766$	6.11809	+	27.3054i	0.221056	+	0.986585i
$767$		−	65.6019i		−	2.36875i
$768$		0			0
$769$			16.6023i			0.598694i	0.954144	+	0.299347i	$0.0967688\pi$
$769$			16.6023i			0.598694i	−0.954144	+	0.299347i	$0.903231\pi$
$770$	0.700190	+	3.62634i	0.0252331	+	0.130684i
$771$		0			0
$772$	27.5850	−	13.0148i	0.992804	−	0.468414i
$773$		−	23.1862i		−	0.833951i	−0.908918	−	0.416975i	$-0.863090\pi$
$773$		−	23.1862i		−	0.833951i	0.908918	−	0.416975i	$-0.136910\pi$
$774$		0			0
$775$	−2.77439			−0.0996589
$776$	9.62177	−	7.48698i	0.345401	−	0.268767i
$777$		0			0
$778$	−9.15610	−	40.8643i	−0.328262	−	1.46506i
$779$		−	1.64543i		−	0.0589538i
$780$		0			0
$781$	−8.38900			−0.300182
$782$	−7.15643	−	31.9396i	−0.255913	−	1.14216i
$783$		0			0
$784$	19.0547	−	20.5163i	0.680526	−	0.732724i
$785$	−0.806743			−0.0287939
$786$		0			0
$787$	−45.5418			−1.62339			−0.811695	−	0.584081i	$-0.801455\pi$
$787$	−45.5418			−1.62339			−0.811695	+	0.584081i	$0.801455\pi$
$788$	5.43954	−	2.56642i	0.193775	−	0.0914250i
$789$		0			0
$790$	3.56151	+	15.8952i	0.126713	+	0.565528i
$791$	22.9130	+	0.680334i	0.814692	+	0.0241899i
$792$		0			0
$793$	−23.1470			−0.821974
$794$	29.3326	−	6.57229i	1.04097	−	0.233242i
$795$		0			0
$796$	40.0804	−	18.9103i	1.42061	−	0.670257i
$797$			53.9376i			1.91057i	0.295688	+	0.955284i	$0.404451\pi$
$797$			53.9376i			1.91057i	−0.295688	+	0.955284i	$0.595549\pi$
$798$		0			0
$799$			9.47540i			0.335216i
$800$	5.04682	+	2.55532i	0.178432	+	0.0903440i
$801$		0			0
$802$	7.59869	+	33.9134i	0.268319	+	1.19752i
$803$	−14.2796			−0.503918
$804$		0			0
$805$	15.5536	+	0.461817i	0.548191	+	0.0162769i
$806$	17.9624	−	4.02467i	0.632698	−	0.141763i
$807$		0			0
$808$	13.4754	−	10.4856i	0.474064	−	0.368883i
$809$	−14.1973			−0.499151			−0.249576	−	0.968355i	$-0.580291\pi$
$809$	−14.1973			−0.499151			−0.249576	+	0.968355i	$0.580291\pi$
$810$		0			0
$811$	−23.5815			−0.828059			−0.414029	−	0.910264i	$-0.635879\pi$
$811$	−23.5815			−0.828059			−0.414029	+	0.910264i	$0.635879\pi$
$812$	−49.7187	+	21.6778i	−1.74479	+	0.760742i
$813$		0			0
$814$	−11.2640	+	2.52382i	−0.394802	+	0.0884598i
$815$	6.48272			0.227080
$816$		0			0
$817$			0.967942i			0.0338640i
$818$	−48.1837	+	10.7961i	−1.68471	+	0.377477i
$819$		0			0
$820$	−13.2929	+	6.27173i	−0.464210	+	0.219018i
$821$	8.67229			0.302665			0.151332	−	0.988483i	$-0.451644\pi$
$821$	8.67229			0.302665			0.151332	+	0.988483i	$0.451644\pi$
$822$		0			0
$823$			28.4926i			0.993191i	0.867982	+	0.496595i	$0.165417\pi$
$823$			28.4926i			0.993191i	−0.867982	+	0.496595i	$0.834583\pi$
$824$	13.6021	+	17.4805i	0.473851	+	0.608962i
$825$		0			0
$826$	9.91884	+	51.3704i	0.345121	+	1.78741i
$827$			26.7340i			0.929634i	0.885407	+	0.464817i	$0.153880\pi$
$827$			26.7340i			0.929634i	−0.885407	+	0.464817i	$0.846120\pi$
$828$		0			0
$829$		−	50.3223i		−	1.74777i	−0.486137	−	0.873883i	$-0.661594\pi$
$829$		−	50.3223i		−	1.74777i	0.486137	−	0.873883i	$-0.338406\pi$
$830$	−2.30616	+	0.516722i	−0.0800481	+	0.0179357i
$831$		0			0
$832$	−36.3818	−	9.22285i	−1.26131	−	0.319745i
$833$	1.63443	−	27.4987i	0.0566295	−	0.952772i
$834$		0			0
$835$		−	7.65678i		−	0.264974i
$836$	−0.188605	−	0.399748i	−0.00652303	−	0.0138256i
$837$		0			0
$838$	0.718467	+	3.20656i	0.0248190	+	0.110769i
$839$	37.9994			1.31188			0.655942	−	0.754811i	$-0.272271\pi$
$839$	37.9994			1.31188			0.655942	+	0.754811i	$0.272271\pi$
$840$		0			0
$841$	76.0671			2.62300
$842$	7.09743	+	31.6763i	0.244594	+	1.09164i
$843$		0			0
$844$	−10.8185	−	22.9298i	−0.372388	−	0.789276i
$845$			9.01087i			0.309983i
$846$		0			0
$847$	26.5138	+	0.787248i	0.911023	+	0.0270502i
$848$	21.2376	−	25.7785i	0.729300	−	0.885238i
$849$		0			0
$850$	5.43072	−	1.21681i	0.186272	−	0.0417364i
$851$			48.6332i			1.66713i
$852$		0			0
$853$		−	19.8625i		−	0.680078i	−0.940411	−	0.340039i	$-0.889560\pi$
$853$		−	19.8625i		−	0.680078i	0.940411	−	0.340039i	$-0.110440\pi$
$854$	18.1256	−	3.49977i	0.620244	−	0.119760i
$855$		0			0
$856$	−31.2202	+	24.2933i	−1.06708	+	0.830329i
$857$		−	21.4344i		−	0.732187i	−0.930578	−	0.366093i	$-0.880695\pi$
$857$		−	21.4344i		−	0.732187i	0.930578	−	0.366093i	$-0.119305\pi$
$858$		0			0
$859$	−12.6251			−0.430764			−0.215382	−	0.976530i	$-0.569100\pi$
$859$	−12.6251			−0.430764			−0.215382	+	0.976530i	$0.569100\pi$
$860$	7.81970	−	3.68941i	0.266650	−	0.125808i
$861$		0			0
$862$	0.105022	−	0.0235314i	0.00357707	−	0.000801484i
$863$			17.9610i			0.611400i	0.952128	+	0.305700i	$0.0988904\pi$
$863$			17.9610i			0.611400i	−0.952128	+	0.305700i	$0.901110\pi$
$864$		0			0
$865$	7.12007			0.242090
$866$	13.0258	−	2.91857i	0.442634	−	0.0991772i
$867$		0			0
$868$	−13.4572	+	5.86744i	−0.456766	+	0.199154i
$869$	−11.3695			−0.385684
$870$		0			0
$871$	36.8159			1.24746
$872$	7.06218	+	9.07584i	0.239155	+	0.307347i
$873$		0			0
$874$	−1.81718	+	0.407159i	−0.0614669	+	0.0137724i
$875$	−0.0785232	+	2.64459i	−0.00265457	+	0.0894033i
$876$		0			0
$877$	12.0637			0.407361			0.203681	−	0.979037i	$-0.434710\pi$
$877$	12.0637			0.407361			0.203681	+	0.979037i	$0.434710\pi$
$878$	1.34662	+	6.01005i	0.0454462	+	0.202829i
$879$		0			0
$880$	−2.51055	+	3.04735i	−0.0846307	+	0.102726i
$881$		−	18.8245i		−	0.634213i	−0.948390	−	0.317107i	$-0.897289\pi$
$881$		−	18.8245i		−	0.634213i	0.948390	−	0.317107i	$-0.102711\pi$
$882$		0			0
$883$		−	12.8758i		−	0.433305i	−0.976249	−	0.216652i	$-0.930486\pi$
$883$		−	12.8758i		−	0.433305i	0.976249	−	0.216652i	$-0.0695138\pi$
$884$	−33.3953	+	15.7562i	−1.12320	+	0.529938i
$885$		0			0
$886$	−49.2134	+	11.0268i	−1.65336	+	0.370453i
$887$	−44.5236			−1.49496			−0.747478	−	0.664286i	$-0.768736\pi$
$887$	−44.5236			−1.49496			−0.747478	+	0.664286i	$0.768736\pi$
$888$		0			0
$889$	0.407233	−	13.7152i	0.0136582	−	0.459994i
$890$	0.152554	+	0.680856i	0.00511361	+	0.0228224i
$891$		0			0
$892$	11.6781	−	5.50983i	0.391011	−	0.184483i
$893$	0.539095			0.0180401
$894$		0			0
$895$	20.8439			0.696733
$896$	29.8837	+	1.72124i	0.998345	+	0.0575026i
$897$		0			0
$898$	4.67042	+	20.8444i	0.155854	+	0.695586i
$899$	28.4381			0.948463
$900$		0			0
$901$		−	32.8600i		−	1.09472i
$902$	−2.24301	−	10.0107i	−0.0746841	−	0.333320i
$903$		0			0
$904$	15.0494	+	19.3404i	0.500534	+	0.643253i
$905$	24.4428			0.812507
$906$		0			0
$907$			18.9911i			0.630589i	0.948994	+	0.315295i	$0.102103\pi$
$907$			18.9911i			0.630589i	−0.948994	+	0.315295i	$0.897897\pi$
$908$	−25.4825	+	12.0229i	−0.845667	+	0.398993i
$909$		0			0
$910$	−3.32799	−	17.2359i	−0.110322	−	0.571365i
$911$			27.0080i			0.894816i	0.894330	+	0.447408i	$0.147653\pi$
$911$			27.0080i			0.894816i	−0.894330	+	0.447408i	$0.852347\pi$
$912$		0			0
$913$		−	1.64955i		−	0.0545920i
$914$	7.23281	+	32.2805i	0.239240	+	1.06774i
$915$		0			0
$916$	−8.32008	−	17.6344i	−0.274903	−	0.582658i
$917$	30.0471	+	0.892160i	0.992242	+	0.0294617i
$918$		0			0
$919$		−	13.2985i		−	0.438677i	−0.975649	−	0.219338i	$-0.929610\pi$
$919$		−	13.2985i		−	0.438677i	0.975649	−	0.219338i	$-0.0703898\pi$
$920$	10.2156	+	13.1285i	0.336800	+	0.432833i
$921$		0			0
$922$	31.2664	−	7.00559i	1.02970	−	0.230717i
$923$	39.8728			1.31243
$924$		0			0
$925$	−8.26915			−0.271888
$926$	−44.1565	+	9.89377i	−1.45107	+	0.325129i
$927$		0			0
$928$	−51.7310	−	26.1926i	−1.69815	−	0.859813i
$929$		−	30.1489i		−	0.989152i	−0.869134	−	0.494576i	$-0.835323\pi$
$929$		−	30.1489i		−	0.989152i	0.869134	−	0.494576i	$-0.164677\pi$
$930$		0			0
$931$	−1.56451	−	0.0929892i	−0.0512748	−	0.00304760i
$932$	2.97058	−	1.40155i	0.0973045	−	0.0459092i
$933$		0			0
$934$	13.1973	+	58.9004i	0.431829	+	1.92728i
$935$			3.88447i			0.127036i
$936$		0			0
$937$		−	21.3618i		−	0.697859i	−0.937149	−	0.348929i	$-0.886545\pi$
$937$		−	21.3618i		−	0.697859i	0.937149	−	0.348929i	$-0.113455\pi$
$938$	−28.8292	+	5.56647i	−0.941306	+	0.181752i
$939$		0			0
$940$	−2.05481	−	4.35517i	−0.0670205	−	0.142050i
$941$			48.5491i			1.58266i	0.611391	+	0.791328i	$0.290610\pi$
$941$			48.5491i			1.58266i	−0.611391	+	0.791328i	$0.709390\pi$
$942$		0			0
$943$	−43.2221			−1.40751
$944$	−35.5643	+	43.1686i	−1.15752	+	1.40502i
$945$		0			0
$946$	1.31947	+	5.88889i	0.0428998	+	0.191464i
$947$		−	5.19386i		−	0.168778i	−0.996433	−	0.0843888i	$-0.973106\pi$
$947$		−	5.19386i		−	0.168778i	0.996433	−	0.0843888i	$-0.0268938\pi$
$948$		0			0
$949$	67.8709			2.20318
$950$	−0.0692296	−	0.308976i	−0.00224610	−	0.0100245i
$951$		0			0
$952$	23.7683	−	17.3874i	0.770336	−	0.563528i
$953$	8.36814			0.271071			0.135535	−	0.990773i	$-0.456725\pi$
$953$	8.36814			0.271071			0.135535	+	0.990773i	$0.456725\pi$
$954$		0			0
$955$	−19.3047			−0.624685
$956$	−8.34391	−	17.6849i	−0.269861	−	0.571972i
$957$		0			0
$958$	−0.0803092	−	0.358425i	−0.00259467	−	0.0115802i
$959$	15.4954	+	0.460092i	0.500374	+	0.0148571i
$960$		0			0
$961$	−23.3028			−0.751703
$962$	53.5375	−	11.9957i	1.72612	−	0.386756i
$963$		0			0
$964$	−5.83817	−	12.3740i	−0.188035	−	0.398540i
$965$			15.2505i			0.490932i
$966$		0			0
$967$			53.7808i			1.72947i	0.502225	+	0.864737i	$0.332515\pi$
$967$			53.7808i			1.72947i	−0.502225	+	0.864737i	$0.667485\pi$
$968$	17.4143	+	22.3798i	0.559718	+	0.719313i
$969$		0			0
$970$	1.33278	+	5.94828i	0.0427930	+	0.190988i
$971$	−27.9111			−0.895709			−0.447855	−	0.894106i	$-0.647812\pi$
$971$	−27.9111			−0.895709			−0.447855	+	0.894106i	$0.647812\pi$
$972$		0			0
$973$	−47.9887	−	1.42488i	−1.53845	−	0.0456796i
$974$	−41.1510	+	9.22035i	−1.31856	+	0.295439i
$975$		0			0
$976$	15.2316	+	12.5485i	0.487553	+	0.401669i
$977$	−16.8294			−0.538422			−0.269211	−	0.963081i	$-0.586763\pi$
$977$	−16.8294			−0.538422			−0.269211	+	0.963081i	$0.586763\pi$
$978$		0			0
$979$	−0.487001			−0.0155646
$980$	5.21206	+	12.9936i	0.166493	+	0.415066i
$981$		0			0
$982$	35.8038	−	8.02225i	1.14255	−	0.256000i
$983$	−34.1214			−1.08830			−0.544151	−	0.838987i	$-0.683148\pi$
$983$	−34.1214			−1.08830			−0.544151	+	0.838987i	$0.683148\pi$
$984$		0			0
$985$			3.00729i			0.0958201i
$986$	−55.6661	+	12.4726i	−1.77277	+	0.397209i
$987$		0			0
$988$	0.896434	+	1.89999i	0.0285194	+	0.0604469i
$989$	25.4258			0.808494
$990$		0			0
$991$			56.2777i			1.78772i	0.448346	+	0.893860i	$0.352013\pi$
$991$			56.2777i			1.78772i	−0.448346	+	0.893860i	$0.647987\pi$
$992$	−14.0018	−	7.08943i	−0.444558	−	0.225090i
$993$		0			0
$994$	−31.2229	+	6.02867i	−0.990331	+	0.191218i
$995$			22.1587i			0.702478i
$996$		0			0
$997$			20.1636i			0.638589i	0.947656	+	0.319295i	$0.103446\pi$
$997$			20.1636i			0.638589i	−0.947656	+	0.319295i	$0.896554\pi$
$998$	31.6205	−	7.08493i	1.00093	−	0.224270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.e.811.7		16
3.2	odd	2		420.2.c.b.391.10	yes	16
4.3	odd	2		1260.2.c.d.811.8		16
7.6	odd	2		1260.2.c.d.811.7		16
12.11	even	2		420.2.c.a.391.9	✓	16
21.20	even	2		420.2.c.a.391.10	yes	16
28.27	even	2	inner	1260.2.c.e.811.8		16
84.83	odd	2		420.2.c.b.391.9	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.9	✓	16	12.11	even	2
420.2.c.a.391.10	yes	16	21.20	even	2
420.2.c.b.391.9	yes	16	84.83	odd	2
420.2.c.b.391.10	yes	16	3.2	odd	2
1260.2.c.d.811.7		16	7.6	odd	2
1260.2.c.d.811.8		16	4.3	odd	2
1260.2.c.e.811.7		16	1.1	even	1	trivial
1260.2.c.e.811.8		16	28.27	even	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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} -1.00000i q^{5} +(2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +O(q^{10})\)	\(q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} -1.00000i q^{5} +(2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +(-1.38000 + 0.309204i) q^{10} -0.987080i q^{11} +4.69157i q^{13} +(-0.709355 - 3.67380i) q^{14} +(2.54341 - 3.08724i) q^{16} -3.93531i q^{17} -0.223896 q^{19} +(0.853401 + 1.80879i) q^{20} +(-1.36217 + 0.305209i) q^{22} +5.88128i q^{23} -1.00000 q^{25} +(6.47436 - 1.45065i) q^{26} +(-4.85050 + 2.11486i) q^{28} +10.2502 q^{29} +2.77439 q^{31} +(-5.04682 - 2.55532i) q^{32} +(-5.43072 + 1.21681i) q^{34} +(0.0785232 - 2.64459i) q^{35} +8.26915 q^{37} +(0.0692296 + 0.308976i) q^{38} +(2.23224 - 1.73698i) q^{40} +7.34910i q^{41} -4.32318i q^{43} +(0.842376 + 1.78542i) q^{44} +(8.11616 - 1.81852i) q^{46} -2.40779 q^{47} +(6.98767 + 0.415323i) q^{49} +(0.309204 + 1.38000i) q^{50} +(-4.00380 - 8.48605i) q^{52} +8.35002 q^{53} -0.987080 q^{55} +(4.41830 + 6.03976i) q^{56} +(-3.16941 - 14.1453i) q^{58} -13.9829 q^{59} +4.93374i q^{61} +(-0.857851 - 3.82865i) q^{62} +(-1.96583 + 7.75471i) q^{64} +4.69157 q^{65} -7.84723i q^{67} +(3.35840 + 7.11814i) q^{68} +(-3.67380 + 0.709355i) q^{70} -8.49881i q^{71} -14.4665i q^{73} +(-2.55685 - 11.4114i) q^{74} +(0.404980 - 0.191073i) q^{76} +(0.0775087 - 2.61042i) q^{77} -11.5183i q^{79} +(-3.08724 - 2.54341i) q^{80} +(10.1417 - 2.27237i) q^{82} +1.67114 q^{83} -3.93531 q^{85} +(-5.96597 + 1.33674i) q^{86} +(2.20340 - 1.71453i) q^{88} -0.493375i q^{89} +(-0.368398 + 12.4073i) q^{91} +(-5.01910 - 10.6380i) q^{92} +(0.744498 + 3.32274i) q^{94} +0.223896i q^{95} -4.31036i q^{97} +(-1.58747 - 9.77138i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Introduction

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