LMFDB - Embedded newform 1260.2.c.e.811.3

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			811.3
Root			$1.10145 - 0.887017i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.e.811.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10145 - 0.887017i) q^{2} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-0.391948 + 2.61656i) q^{7} +(1.26358 - 2.53049i) q^{8} +O(q^{10})$	\(q+(-1.10145 - 0.887017i) q^{2} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-0.391948 + 2.61656i) q^{7} +(1.26358 - 2.53049i) q^{8} +(-0.887017 + 1.10145i) q^{10} +0.770756i q^{11} -5.60576i q^{13} +(2.75264 - 2.53435i) q^{14} +(-3.63636 + 1.66639i) q^{16} +0.503042i q^{17} -1.63506 q^{19} +(1.95402 - 0.426402i) q^{20} +(0.683673 - 0.848952i) q^{22} -1.42475i q^{23} -1.00000 q^{25} +(-4.97240 + 6.17449i) q^{26} +(-5.27993 + 0.349833i) q^{28} -5.03595 q^{29} +8.23212 q^{31} +(5.48341 + 1.39006i) q^{32} +(0.446206 - 0.554077i) q^{34} +(2.61656 + 0.391948i) q^{35} +10.1403 q^{37} +(1.80094 + 1.45033i) q^{38} +(-2.53049 - 1.26358i) q^{40} -5.07885i q^{41} -9.06204i q^{43} +(-1.50607 + 0.328652i) q^{44} +(-1.26378 + 1.56930i) q^{46} +4.64967 q^{47} +(-6.69275 - 2.05111i) q^{49} +(1.10145 + 0.887017i) q^{50} +(10.9537 - 2.39031i) q^{52} -0.455805 q^{53} +0.770756 q^{55} +(6.12590 + 4.29806i) q^{56} +(5.54687 + 4.46697i) q^{58} +10.4908 q^{59} -3.32394i q^{61} +(-9.06730 - 7.30202i) q^{62} +(-4.80671 - 6.39496i) q^{64} -5.60576 q^{65} -8.70791i q^{67} +(-0.982952 + 0.214498i) q^{68} +(-2.53435 - 2.75264i) q^{70} +10.8176i q^{71} +2.29564i q^{73} +(-11.1691 - 8.99464i) q^{74} +(-0.697193 - 3.19494i) q^{76} +(-2.01673 - 0.302096i) q^{77} +2.56336i q^{79} +(1.66639 + 3.63636i) q^{80} +(-4.50503 + 5.59412i) q^{82} +13.9979 q^{83} +0.503042 q^{85} +(-8.03818 + 9.98142i) q^{86} +(1.95039 + 0.973914i) q^{88} -2.98877i q^{89} +(14.6678 + 2.19717i) q^{91} +(2.78399 - 0.607518i) q^{92} +(-5.12139 - 4.12433i) q^{94} +1.63506i q^{95} -15.5818i q^{97} +(5.55239 + 8.19579i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.10145	−	0.887017i	−0.778846	−	0.627216i
$2$	−1.10145	−	0.887017i	−0.778846	−	0.627216i
$3$		0			0
$3$		0			0
$4$	0.426402	+	1.95402i	0.213201	+	0.977008i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−0.391948	+	2.61656i	−0.148142	+	0.988966i
$7$	−0.391948	+	2.61656i	−0.148142	+	0.988966i
$8$	1.26358	−	2.53049i	0.446744	−	0.894662i
$9$		0			0
$10$	−0.887017	+	1.10145i	−0.280499	+	0.348310i
$11$			0.770756i			0.232392i	0.993226	+	0.116196i	$0.0370700\pi$
$11$			0.770756i			0.232392i	−0.993226	+	0.116196i	$0.962930\pi$
$12$		0			0
$13$		−	5.60576i		−	1.55476i	−0.629032	−	0.777379i	$-0.716549\pi$
$13$		−	5.60576i		−	1.55476i	0.629032	−	0.777379i	$-0.283451\pi$
$14$	2.75264	−	2.53435i	0.735675	−	0.677335i
$15$		0			0
$16$	−3.63636	+	1.66639i	−0.909091	+	0.416598i
$17$			0.503042i			0.122005i	0.998138	+	0.0610027i	$0.0194298\pi$
$17$			0.503042i			0.122005i	−0.998138	+	0.0610027i	$0.980570\pi$
$18$		0			0
$19$	−1.63506			−0.375109			−0.187554	−	0.982254i	$-0.560056\pi$
$19$	−1.63506			−0.375109			−0.187554	+	0.982254i	$0.560056\pi$
$20$	1.95402	−	0.426402i	0.436931	−	0.0953464i
$21$		0			0
$22$	0.683673	−	0.848952i	0.145760	−	0.180997i
$23$		−	1.42475i		−	0.297082i	−0.988906	−	0.148541i	$-0.952542\pi$
$23$		−	1.42475i		−	0.297082i	0.988906	−	0.148541i	$-0.0474577\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−4.97240	+	6.17449i	−0.975169	+	1.21092i
$27$		0			0
$28$	−5.27993	+	0.349833i	−0.997812	+	0.0661123i
$29$	−5.03595			−0.935152			−0.467576	−	0.883953i	$-0.654873\pi$
$29$	−5.03595			−0.935152			−0.467576	+	0.883953i	$0.654873\pi$
$30$		0			0
$31$	8.23212			1.47853			0.739266	−	0.673414i	$-0.235173\pi$
$31$	8.23212			1.47853			0.739266	+	0.673414i	$0.235173\pi$
$32$	5.48341	+	1.39006i	0.969338	+	0.245730i
$33$		0			0
$34$	0.446206	−	0.554077i	0.0765238	−	0.0950235i
$35$	2.61656	+	0.391948i	0.442279	+	0.0662513i
$36$		0			0
$37$	10.1403			1.66706			0.833530	−	0.552475i	$-0.186316\pi$
$37$	10.1403			1.66706			0.833530	+	0.552475i	$0.186316\pi$
$38$	1.80094	+	1.45033i	0.292152	+	0.235274i
$39$		0			0
$40$	−2.53049	−	1.26358i	−0.400105	−	0.199790i
$41$		−	5.07885i		−	0.793184i	−0.917995	−	0.396592i	$-0.870193\pi$
$41$		−	5.07885i		−	0.793184i	0.917995	−	0.396592i	$-0.129807\pi$
$42$		0			0
$43$		−	9.06204i		−	1.38195i	−0.722880	−	0.690974i	$-0.757182\pi$
$43$		−	9.06204i		−	1.38195i	0.722880	−	0.690974i	$-0.242818\pi$
$44$	−1.50607	+	0.328652i	−0.227049	+	0.0495461i
$45$		0			0
$46$	−1.26378	+	1.56930i	−0.186334	+	0.231381i
$47$	4.64967			0.678223			0.339112	−	0.940746i	$-0.389874\pi$
$47$	4.64967			0.678223			0.339112	+	0.940746i	$0.389874\pi$
$48$		0			0
$49$	−6.69275	−	2.05111i	−0.956108	−	0.293016i
$50$	1.10145	+	0.887017i	0.155769	+	0.125443i
$51$		0			0
$52$	10.9537	−	2.39031i	1.51901	−	0.331476i
$53$	−0.455805			−0.0626096			−0.0313048	−	0.999510i	$-0.509966\pi$
$53$	−0.455805			−0.0626096			−0.0313048	+	0.999510i	$0.509966\pi$
$54$		0			0
$55$	0.770756			0.103929
$56$	6.12590	+	4.29806i	0.818608	+	0.574352i
$57$		0			0
$58$	5.54687	+	4.46697i	0.728339	+	0.586542i
$59$	10.4908			1.36578			0.682890	−	0.730521i	$-0.260723\pi$
$59$	10.4908			1.36578			0.682890	+	0.730521i	$0.260723\pi$
$60$		0			0
$61$		−	3.32394i		−	0.425587i	−0.977097	−	0.212794i	$-0.931744\pi$
$61$		−	3.32394i		−	0.425587i	0.977097	−	0.212794i	$-0.0682562\pi$
$62$	−9.06730	−	7.30202i	−1.15155	−	0.927358i
$63$		0			0
$64$	−4.80671	−	6.39496i	−0.600839	−	0.799370i
$65$	−5.60576			−0.695309
$66$		0			0
$67$		−	8.70791i		−	1.06384i	−0.846794	−	0.531920i	$-0.821471\pi$
$67$		−	8.70791i		−	1.06384i	0.846794	−	0.531920i	$-0.178529\pi$
$68$	−0.982952	+	0.214498i	−0.119200	+	0.0260117i
$69$		0			0
$70$	−2.53435	−	2.75264i	−0.302913	−	0.329004i
$71$			10.8176i			1.28382i	0.766781	+	0.641909i	$0.221857\pi$
$71$			10.8176i			1.28382i	−0.766781	+	0.641909i	$0.778143\pi$
$72$		0			0
$73$			2.29564i			0.268685i	0.990935	+	0.134342i	$0.0428922\pi$
$73$			2.29564i			0.268685i	−0.990935	+	0.134342i	$0.957108\pi$
$74$	−11.1691	−	8.99464i	−1.29838	−	1.04561i
$75$		0			0
$76$	−0.697193	−	3.19494i	−0.0799736	−	0.366484i
$77$	−2.01673	−	0.302096i	−0.229827	−	0.0344270i
$78$		0			0
$79$			2.56336i			0.288400i	0.989549	+	0.144200i	$0.0460609\pi$
$79$			2.56336i			0.288400i	−0.989549	+	0.144200i	$0.953939\pi$
$80$	1.66639	+	3.63636i	0.186309	+	0.406558i
$81$		0			0
$82$	−4.50503	+	5.59412i	−0.497497	+	0.617768i
$83$	13.9979			1.53646			0.768232	−	0.640171i	$-0.221137\pi$
$83$	13.9979			1.53646			0.768232	+	0.640171i	$0.221137\pi$
$84$		0			0
$85$	0.503042			0.0545625
$86$	−8.03818	+	9.98142i	−0.866779	+	1.07632i
$87$		0			0
$88$	1.95039	+	0.973914i	0.207912	+	0.103820i
$89$		−	2.98877i		−	0.316809i	−0.987374	−	0.158404i	$-0.949365\pi$
$89$		−	2.98877i		−	0.316809i	0.987374	−	0.158404i	$-0.0506349\pi$
$90$		0			0
$91$	14.6678	+	2.19717i	1.53760	+	0.230326i
$92$	2.78399	−	0.607518i	0.290251	−	0.0633382i
$93$		0			0
$94$	−5.12139	−	4.12433i	−0.528231	−	0.425392i
$95$			1.63506i			0.167754i
$96$		0			0
$97$		−	15.5818i		−	1.58209i	−0.611756	−	0.791046i	$-0.709537\pi$
$97$		−	15.5818i		−	1.58209i	0.611756	−	0.791046i	$-0.290463\pi$
$98$	5.55239	+	8.19579i	0.560876	+	0.827900i
$99$		0			0
$100$	−0.426402	−	1.95402i	−0.0426402	−	0.195402i
$101$		−	18.9661i		−	1.88719i	−0.331097	−	0.943597i	$-0.607419\pi$
$101$		−	18.9661i		−	1.88719i	0.331097	−	0.943597i	$-0.392581\pi$
$102$		0			0
$103$	−8.23760			−0.811675			−0.405837	−	0.913945i	$-0.633020\pi$
$103$	−8.23760			−0.811675			−0.405837	+	0.913945i	$0.633020\pi$
$104$	−14.1853	−	7.08335i	−1.39098	−	0.694579i
$105$		0			0
$106$	0.502048	+	0.404306i	0.0487632	+	0.0392697i
$107$		−	11.8042i		−	1.14115i	−0.821244	−	0.570577i	$-0.806720\pi$
$107$		−	11.8042i		−	1.14115i	0.821244	−	0.570577i	$-0.193280\pi$
$108$		0			0
$109$	−9.80783			−0.939419			−0.469710	−	0.882821i	$-0.655641\pi$
$109$	−9.80783			−0.939419			−0.469710	+	0.882821i	$0.655641\pi$
$110$	−0.848952	−	0.683673i	−0.0809444	−	0.0651857i
$111$		0			0
$112$	−2.93495	−	10.1679i	−0.277327	−	0.960776i
$113$	10.0104			0.941702			0.470851	−	0.882213i	$-0.343947\pi$
$113$	10.0104			0.941702			0.470851	+	0.882213i	$0.343947\pi$
$114$		0			0
$115$	−1.42475			−0.132859
$116$	−2.14734	−	9.84033i	−0.199376	−	0.913652i
$117$		0			0
$118$	−11.5551	−	9.30548i	−1.06373	−	0.856638i
$119$	−1.31624	−	0.197166i	−0.120659	−	0.0180742i
$120$		0			0
$121$	10.4059			0.945994
$122$	−2.94839	+	3.66117i	−0.266935	+	0.331467i
$123$		0			0
$124$	3.51019	+	16.0857i	0.315225	+	1.44454i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			3.09530i			0.274663i	0.990525	+	0.137332i	$0.0438526\pi$
$127$			3.09530i			0.274663i	−0.990525	+	0.137332i	$0.956147\pi$
$128$	−0.378061	+	11.3074i	−0.0334162	+	0.999442i
$129$		0			0
$130$	6.17449	+	4.97240i	0.541538	+	0.436109i
$131$	−17.5001			−1.52899			−0.764495	−	0.644630i	$-0.777011\pi$
$131$	−17.5001			−1.52899			−0.764495	+	0.644630i	$0.777011\pi$
$132$		0			0
$133$	0.640859	−	4.27823i	0.0555695	−	0.370970i
$134$	−7.72407	+	9.59137i	−0.667258	+	0.828568i
$135$		0			0
$136$	1.27294	+	0.635635i	0.109154	+	0.0545052i
$137$	15.6542			1.33742			0.668712	−	0.743521i	$-0.266846\pi$
$137$	15.6542			1.33742			0.668712	+	0.743521i	$0.266846\pi$
$138$		0			0
$139$	−1.13095			−0.0959261			−0.0479630	−	0.998849i	$-0.515273\pi$
$139$	−1.13095			−0.0959261			−0.0479630	+	0.998849i	$0.515273\pi$
$140$	0.349833	+	5.27993i	0.0295663	+	0.446235i
$141$		0			0
$142$	9.59542	−	11.9151i	0.805230	−	0.999895i
$143$	4.32067			0.361313
$144$		0			0
$145$			5.03595i			0.418213i
$146$	2.03627	−	2.52855i	0.168523	−	0.209264i
$147$		0			0
$148$	4.32386	+	19.8144i	0.355419	+	1.62873i
$149$	−21.3643			−1.75023			−0.875117	−	0.483911i	$-0.839216\pi$
$149$	−21.3643			−1.75023			−0.875117	+	0.483911i	$0.839216\pi$
$150$		0			0
$151$			2.83045i			0.230339i	0.993346	+	0.115169i	$0.0367411\pi$
$151$			2.83045i			0.230339i	−0.993346	+	0.115169i	$0.963259\pi$
$152$	−2.06604	+	4.13750i	−0.167578	+	0.335595i
$153$		0			0
$154$	1.95337	+	2.12162i	0.157407	+	0.170965i
$155$		−	8.23212i		−	0.661219i
$156$		0			0
$157$		−	18.7903i		−	1.49963i	−0.661649	−	0.749814i	$-0.730143\pi$
$157$		−	18.7903i		−	1.49963i	0.661649	−	0.749814i	$-0.269857\pi$
$158$	2.27374	−	2.82342i	0.180889	−	0.224619i
$159$		0			0
$160$	1.39006	−	5.48341i	0.109894	−	0.433501i
$161$	3.72795	+	0.558430i	0.293804	+	0.0440104i
$162$		0			0
$163$			7.40744i			0.580195i	0.956997	+	0.290098i	$0.0936878\pi$
$163$			7.40744i			0.580195i	−0.956997	+	0.290098i	$0.906312\pi$
$164$	9.92417	−	2.16563i	0.774947	−	0.169108i
$165$		0			0
$166$	−15.4180	−	12.4163i	−1.19667	−	0.963694i
$167$	−2.96147			−0.229165			−0.114583	−	0.993414i	$-0.536553\pi$
$167$	−2.96147			−0.229165			−0.114583	+	0.993414i	$0.536553\pi$
$168$		0			0
$169$	−18.4246			−1.41727
$170$	−0.554077	−	0.446206i	−0.0424958	−	0.0342225i
$171$		0			0
$172$	17.7074	−	3.86407i	1.35017	−	0.294633i
$173$		−	15.0215i		−	1.14206i	−0.820928	−	0.571031i	$-0.806543\pi$
$173$		−	15.0215i		−	1.14206i	0.820928	−	0.571031i	$-0.193457\pi$
$174$		0			0
$175$	0.391948	−	2.61656i	0.0296285	−	0.197793i
$176$	−1.28438	−	2.80275i	−0.0968140	−	0.211265i
$177$		0			0
$178$	−2.65109	+	3.29199i	−0.198707	+	0.246745i
$179$			4.82936i			0.360963i	0.983578	+	0.180482i	$0.0577656\pi$
$179$			4.82936i			0.360963i	−0.983578	+	0.180482i	$0.942234\pi$
$180$		0			0
$181$			18.2050i			1.35316i	0.736367	+	0.676582i	$0.236540\pi$
$181$			18.2050i			1.35316i	−0.736367	+	0.676582i	$0.763460\pi$
$182$	−14.2070	−	15.4307i	−1.05309	−	1.14380i
$183$		0			0
$184$	−3.60532	−	1.80030i	−0.265788	−	0.132720i
$185$		−	10.1403i		−	0.745532i
$186$		0			0
$187$	−0.387722			−0.0283531
$188$	1.98263	+	9.08552i	0.144598	+	0.662630i
$189$		0			0
$190$	1.45033	−	1.80094i	0.105218	−	0.130654i
$191$		−	5.65184i		−	0.408953i	−0.978871	−	0.204476i	$-0.934451\pi$
$191$		−	5.65184i		−	0.408953i	0.978871	−	0.204476i	$-0.0655492\pi$
$192$		0			0
$193$	−16.0978			−1.15874			−0.579372	−	0.815063i	$-0.696702\pi$
$193$	−16.0978			−1.15874			−0.579372	+	0.815063i	$0.696702\pi$
$194$	−13.8213	+	17.1626i	−0.992313	+	1.23221i
$195$		0			0
$196$	1.15410	−	13.9523i	0.0824355	−	0.996596i
$197$	12.2972			0.876141			0.438071	−	0.898941i	$-0.355662\pi$
$197$	12.2972			0.876141			0.438071	+	0.898941i	$0.355662\pi$
$198$		0			0
$199$	16.8234			1.19258			0.596290	−	0.802769i	$-0.296641\pi$
$199$	16.8234			1.19258			0.596290	+	0.802769i	$0.296641\pi$
$200$	−1.26358	+	2.53049i	−0.0893488	+	0.178932i
$201$		0			0
$202$	−16.8232	+	20.8902i	−1.18368	+	1.46983i
$203$	1.97383	−	13.1769i	0.138536	−	0.924834i
$204$		0			0
$205$	−5.07885			−0.354723
$206$	9.07333	+	7.30689i	0.632169	+	0.509095i
$207$		0			0
$208$	9.34141	+	20.3846i	0.647710	+	1.41342i
$209$		−	1.26023i		−	0.0871721i
$210$		0			0
$211$			9.19446i			0.632973i	0.948597	+	0.316486i	$0.102503\pi$
$211$			9.19446i			0.632973i	−0.948597	+	0.316486i	$0.897497\pi$
$212$	−0.194356	−	0.890650i	−0.0133484	−	0.0611701i
$213$		0			0
$214$	−10.4705	+	13.0018i	−0.715749	+	0.888782i
$215$	−9.06204			−0.618026
$216$		0			0
$217$	−3.22656	+	21.5398i	−0.219033	+	1.46222i
$218$	10.8029	+	8.69971i	0.731663	+	0.589219i
$219$		0			0
$220$	0.328652	+	1.50607i	0.0221577	+	0.101539i
$221$	2.81993			0.189689
$222$		0			0
$223$	−22.8560			−1.53055			−0.765275	−	0.643704i	$-0.777397\pi$
$223$	−22.8560			−1.53055			−0.765275	+	0.643704i	$0.777397\pi$
$224$	−5.78638	+	13.8028i	−0.386619	+	0.922240i
$225$		0			0
$226$	−11.0260	−	8.87942i	−0.733440	−	0.590650i
$227$	17.4680			1.15939			0.579697	−	0.814832i	$-0.303171\pi$
$227$	17.4680			1.15939			0.579697	+	0.814832i	$0.303171\pi$
$228$		0			0
$229$		−	12.6233i		−	0.834169i	−0.908868	−	0.417085i	$-0.863052\pi$
$229$		−	12.6233i		−	0.834169i	0.908868	−	0.417085i	$-0.136948\pi$
$230$	1.56930	+	1.26378i	0.103477	+	0.0833313i
$231$		0			0
$232$	−6.36334	+	12.7434i	−0.417774	+	0.836645i
$233$	3.89410			0.255111			0.127555	−	0.991831i	$-0.459287\pi$
$233$	3.89410			0.255111			0.127555	+	0.991831i	$0.459287\pi$
$234$		0			0
$235$		−	4.64967i		−	0.303311i
$236$	4.47328	+	20.4991i	0.291186	+	1.33438i
$237$		0			0
$238$	1.27489	+	1.38469i	0.0826386	+	0.0897564i
$239$		−	11.6497i		−	0.753559i	−0.926303	−	0.376779i	$-0.877032\pi$
$239$		−	11.6497i		−	0.753559i	0.926303	−	0.376779i	$-0.122968\pi$
$240$		0			0
$241$			21.0259i			1.35440i	0.735799	+	0.677200i	$0.236807\pi$
$241$			21.0259i			1.35440i	−0.735799	+	0.677200i	$0.763193\pi$
$242$	−11.4617	−	9.23024i	−0.736783	−	0.593342i
$243$		0			0
$244$	6.49504	−	1.41734i	0.415802	−	0.0907357i
$245$	−2.05111	+	6.69275i	−0.131041	+	0.427584i
$246$		0			0
$247$			9.16576i			0.583203i
$248$	10.4020	−	20.8312i	0.660525	−	1.32279i
$249$		0			0
$250$	0.887017	−	1.10145i	0.0560999	−	0.0696621i
$251$	1.36484			0.0861478			0.0430739	−	0.999072i	$-0.486285\pi$
$251$	1.36484			0.0861478			0.0430739	+	0.999072i	$0.486285\pi$
$252$		0			0
$253$	1.09814			0.0690393
$254$	2.74558	−	3.40933i	0.172273	−	0.213920i
$255$		0			0
$256$	10.4463	−	12.1192i	0.652891	−	0.757452i
$257$			4.44214i			0.277093i	0.990356	+	0.138547i	$0.0442431\pi$
$257$			4.44214i			0.277093i	−0.990356	+	0.138547i	$0.955757\pi$
$258$		0			0
$259$	−3.97448	+	26.5328i	−0.246962	+	1.64866i
$260$	−2.39031	−	10.9537i	−0.148241	−	0.679323i
$261$		0			0
$262$	19.2755	+	15.5229i	1.19085	+	0.959006i
$263$			4.92839i			0.303898i	0.988388	+	0.151949i	$0.0485549\pi$
$263$			4.92839i			0.303898i	−0.988388	+	0.151949i	$0.951445\pi$
$264$		0			0
$265$			0.455805i			0.0279999i
$266$	−4.50074	+	4.14382i	−0.275958	+	0.254074i
$267$		0			0
$268$	17.0154	−	3.71307i	1.03938	−	0.226812i
$269$			25.0193i			1.52546i	0.646719	+	0.762728i	$0.276141\pi$
$269$			25.0193i			1.52546i	−0.646719	+	0.762728i	$0.723859\pi$
$270$		0			0
$271$	−12.1353			−0.737170			−0.368585	−	0.929594i	$-0.620158\pi$
$271$	−12.1353			−0.737170			−0.368585	+	0.929594i	$0.620158\pi$
$272$	−0.838265	−	1.82924i	−0.0508273	−	0.110914i
$273$		0			0
$274$	−17.2423	−	13.8855i	−1.04165	−	0.838854i
$275$		−	0.770756i		−	0.0464783i
$276$		0			0
$277$	19.4692			1.16979			0.584896	−	0.811108i	$-0.301135\pi$
$277$	19.4692			1.16979			0.584896	+	0.811108i	$0.301135\pi$
$278$	1.24569	+	1.00317i	0.0747116	+	0.0601663i
$279$		0			0
$280$	4.29806	−	6.12590i	0.256858	−	0.366093i
$281$	17.7452			1.05859			0.529296	−	0.848437i	$-0.322456\pi$
$281$	17.7452			1.05859			0.529296	+	0.848437i	$0.322456\pi$
$282$		0			0
$283$	29.4942			1.75325			0.876623	−	0.481177i	$-0.159791\pi$
$283$	29.4942			1.75325			0.876623	+	0.481177i	$0.159791\pi$
$284$	−21.1378	+	4.61266i	−1.25430	+	0.273711i
$285$		0			0
$286$	−4.75902	−	3.83251i	−0.281407	−	0.226621i
$287$	13.2891	+	1.99065i	0.784432	+	0.117504i
$288$		0			0
$289$	16.7469			0.985115
$290$	4.46697	−	5.54687i	0.262310	−	0.325723i
$291$		0			0
$292$	−4.48573	+	0.978867i	−0.262507	+	0.0572839i
$293$			19.8780i			1.16129i	0.814158	+	0.580643i	$0.197199\pi$
$293$			19.8780i			1.16129i	−0.814158	+	0.580643i	$0.802801\pi$
$294$		0			0
$295$		−	10.4908i		−	0.610795i
$296$	12.8131	−	25.6599i	0.744749	−	1.49145i
$297$		0			0
$298$	23.5318	+	18.9505i	1.36316	+	1.09777i
$299$	−7.98683			−0.461890
$300$		0			0
$301$	23.7114	+	3.55185i	1.36670	+	0.204725i
$302$	2.51065	−	3.11761i	0.144472	−	0.179398i
$303$		0			0
$304$	5.94567	−	2.72466i	0.341008	−	0.156270i
$305$	−3.32394			−0.190328
$306$		0			0
$307$	−2.12425			−0.121238			−0.0606188	−	0.998161i	$-0.519307\pi$
$307$	−2.12425			−0.121238			−0.0606188	+	0.998161i	$0.519307\pi$
$308$	−0.269636	−	4.06953i	−0.0153639	−	0.231883i
$309$		0			0
$310$	−7.30202	+	9.06730i	−0.414727	+	0.514988i
$311$	10.2870			0.583323			0.291661	−	0.956522i	$-0.405792\pi$
$311$	10.2870			0.583323			0.291661	+	0.956522i	$0.405792\pi$
$312$		0			0
$313$			17.8800i			1.01064i	0.862932	+	0.505320i	$0.168626\pi$
$313$			17.8800i			1.01064i	−0.862932	+	0.505320i	$0.831374\pi$
$314$	−16.6673	+	20.6966i	−0.940590	+	1.16798i
$315$		0			0
$316$	−5.00884	+	1.09302i	−0.281769	+	0.0614872i
$317$	−12.3840			−0.695557			−0.347778	−	0.937577i	$-0.613064\pi$
$317$	−12.3840			−0.695557			−0.347778	+	0.937577i	$0.613064\pi$
$318$		0			0
$319$		−	3.88149i		−	0.217322i
$320$	−6.39496	+	4.80671i	−0.357489	+	0.268703i
$321$		0			0
$322$	−3.61083	−	3.92184i	−0.201224	−	0.218556i
$323$		−	0.822503i		−	0.0457653i
$324$		0			0
$325$			5.60576i			0.310952i
$326$	6.57052	−	8.15895i	0.363908	−	0.451883i
$327$		0			0
$328$	−12.8520	−	6.41756i	−0.709631	−	0.354350i
$329$	−1.82243	+	12.1661i	−0.100474	+	0.670740i
$330$		0			0
$331$			21.3000i			1.17075i	0.810762	+	0.585376i	$0.199053\pi$
$331$			21.3000i			1.17075i	−0.810762	+	0.585376i	$0.800947\pi$
$332$	5.96872	+	27.3520i	0.327576	+	1.50114i
$333$		0			0
$334$	3.26192	+	2.62687i	0.178484	+	0.143736i
$335$	−8.70791			−0.475764
$336$		0			0
$337$	−0.875789			−0.0477073			−0.0238536	−	0.999715i	$-0.507594\pi$
$337$	−0.875789			−0.0477073			−0.0238536	+	0.999715i	$0.507594\pi$
$338$	20.2938	+	16.3429i	1.10384	+	0.888936i
$339$		0			0
$340$	0.214498	+	0.982952i	0.0116328	+	0.0533080i
$341$			6.34495i			0.343598i
$342$		0			0
$343$	7.99006	−	16.7081i	0.431423	−	0.902150i
$344$	−22.9314	−	11.4506i	−1.23638	−	0.617377i
$345$		0			0
$346$	−13.3243	+	16.5455i	−0.716320	+	0.889491i
$347$			34.9081i			1.87396i	0.349379	+	0.936981i	$0.386392\pi$
$347$			34.9081i			1.87396i	−0.349379	+	0.936981i	$0.613608\pi$
$348$		0			0
$349$			21.1880i			1.13417i	0.823660	+	0.567084i	$0.191929\pi$
$349$			21.1880i			1.13417i	−0.823660	+	0.567084i	$0.808071\pi$
$350$	−2.75264	+	2.53435i	−0.147135	+	0.135467i
$351$		0			0
$352$	−1.07140	+	4.22637i	−0.0571056	+	0.225266i
$353$		−	7.69915i		−	0.409785i	−0.978785	−	0.204892i	$-0.934316\pi$
$353$		−	7.69915i		−	0.409785i	0.978785	−	0.204892i	$-0.0656844\pi$
$354$		0			0
$355$	10.8176			0.574140
$356$	5.84010	−	1.27442i	0.309525	−	0.0675439i
$357$		0			0
$358$	4.28372	−	5.31931i	0.226402	−	0.281134i
$359$			2.14821i			0.113378i	0.998392	+	0.0566890i	$0.0180543\pi$
$359$			2.14821i			0.113378i	−0.998392	+	0.0566890i	$0.981946\pi$
$360$		0			0
$361$	−16.3266			−0.859294
$362$	16.1481	−	20.0519i	0.848726	−	1.05391i
$363$		0			0
$364$	1.96108	+	29.5980i	0.102789	+	1.55136i
$365$	2.29564			0.120159
$366$		0			0
$367$	−26.6962			−1.39353			−0.696764	−	0.717300i	$-0.745378\pi$
$367$	−26.6962			−1.39353			−0.696764	+	0.717300i	$0.745378\pi$
$368$	2.37420	+	5.18092i	0.123764	+	0.270074i
$369$		0			0
$370$	−8.99464	+	11.1691i	−0.467609	+	0.580654i
$371$	0.178652	−	1.19264i	0.00927513	−	0.0619187i
$372$		0			0
$373$	−8.51430			−0.440854			−0.220427	−	0.975403i	$-0.570745\pi$
$373$	−8.51430			−0.440854			−0.220427	+	0.975403i	$0.570745\pi$
$374$	0.427058	+	0.343916i	0.0220826	+	0.0177835i
$375$		0			0
$376$	5.87524	−	11.7659i	0.302992	−	0.606781i
$377$			28.2303i			1.45394i
$378$		0			0
$379$		−	31.1693i		−	1.60106i	−0.599295	−	0.800529i	$-0.704552\pi$
$379$		−	31.1693i		−	1.60106i	0.599295	−	0.800529i	$-0.295448\pi$
$380$	−3.19494	+	0.697193i	−0.163897	+	0.0357653i
$381$		0			0
$382$	−5.01328	+	6.22524i	−0.256502	+	0.318511i
$383$	−33.7311			−1.72358			−0.861788	−	0.507268i	$-0.830655\pi$
$383$	−33.7311			−1.72358			−0.861788	+	0.507268i	$0.830655\pi$
$384$		0			0
$385$	−0.302096	+	2.01673i	−0.0153962	+	0.102782i
$386$	17.7310	+	14.2790i	0.902483	+	0.726783i
$387$		0			0
$388$	30.4471	−	6.64412i	1.54572	−	0.337304i
$389$	−25.9912			−1.31780			−0.658902	−	0.752228i	$-0.728979\pi$
$389$	−25.9912			−1.31780			−0.658902	+	0.752228i	$0.728979\pi$
$390$		0			0
$391$	0.716711			0.0362456
$392$	−13.6472	+	14.3442i	−0.689285	+	0.724490i
$393$		0			0
$394$	−13.5448	−	10.9078i	−0.682379	−	0.549529i
$395$	2.56336			0.128977
$396$		0			0
$397$			1.63535i			0.0820760i	0.999158	+	0.0410380i	$0.0130665\pi$
$397$			1.63535i			0.0820760i	−0.999158	+	0.0410380i	$0.986934\pi$
$398$	−18.5302	−	14.9226i	−0.928835	−	0.748004i
$399$		0			0
$400$	3.63636	−	1.66639i	0.181818	−	0.0833197i
$401$	11.7906			0.588797			0.294398	−	0.955683i	$-0.404881\pi$
$401$	11.7906			0.588797			0.294398	+	0.955683i	$0.404881\pi$
$402$		0			0
$403$		−	46.1473i		−	2.29876i
$404$	37.0600	−	8.08717i	1.84380	−	0.402352i
$405$		0			0
$406$	−13.8622	+	12.7629i	−0.687968	+	0.633411i
$407$			7.81571i			0.387411i
$408$		0			0
$409$		−	9.74926i		−	0.482070i	−0.970516	−	0.241035i	$-0.922513\pi$
$409$		−	9.74926i		−	0.482070i	0.970516	−	0.241035i	$-0.0774868\pi$
$410$	5.59412	+	4.50503i	0.276274	+	0.222488i
$411$		0			0
$412$	−3.51253	−	16.0964i	−0.173050	−	0.793013i
$413$	−4.11183	+	27.4497i	−0.202330	+	1.35071i
$414$		0			0
$415$		−	13.9979i		−	0.687128i
$416$	7.79233	−	30.7387i	0.382051	−	1.50709i
$417$		0			0
$418$	−1.11785	+	1.38809i	−0.0546757	+	0.0678936i
$419$	15.3501			0.749902			0.374951	−	0.927045i	$-0.377659\pi$
$419$	15.3501			0.749902			0.374951	+	0.927045i	$0.377659\pi$
$420$		0			0
$421$	36.0738			1.75813			0.879064	−	0.476703i	$-0.158168\pi$
$421$	36.0738			1.75813			0.879064	+	0.476703i	$0.158168\pi$
$422$	8.15564	−	10.1273i	0.397011	−	0.492988i
$423$		0			0
$424$	−0.575947	+	1.15341i	−0.0279705	+	0.0560144i
$425$		−	0.503042i		−	0.0244011i
$426$		0			0
$427$	8.69729	+	1.30281i	0.420891	+	0.0630475i
$428$	23.0656	−	5.03333i	1.11492	−	0.243295i
$429$		0			0
$430$	9.98142	+	8.03818i	0.481347	+	0.387635i
$431$			20.9842i			1.01077i	0.862893	+	0.505387i	$0.168650\pi$
$431$			20.9842i			1.01077i	−0.862893	+	0.505387i	$0.831350\pi$
$432$		0			0
$433$			10.4424i			0.501828i	0.968009	+	0.250914i	$0.0807312\pi$
$433$			10.4424i			0.501828i	−0.968009	+	0.250914i	$0.919269\pi$
$434$	22.6601	−	20.8631i	1.08772	−	1.00146i
$435$		0			0
$436$	−4.18208	−	19.1647i	−0.200285	−	0.917821i
$437$			2.32956i			0.111438i
$438$		0			0
$439$	−36.2996			−1.73249			−0.866243	−	0.499624i	$-0.833472\pi$
$439$	−36.2996			−1.73249			−0.866243	+	0.499624i	$0.833472\pi$
$440$	0.973914	−	1.95039i	0.0464295	−	0.0929810i
$441$		0			0
$442$	−3.10602	−	2.50133i	−0.147738	−	0.118976i
$443$			3.71212i			0.176368i	0.996104	+	0.0881842i	$0.0281064\pi$
$443$			3.71212i			0.176368i	−0.996104	+	0.0881842i	$0.971894\pi$
$444$		0			0
$445$	−2.98877			−0.141681
$446$	25.1748	+	20.2736i	1.19206	+	0.959985i
$447$		0			0
$448$	18.6168	−	10.0706i	0.879559	−	0.475789i
$449$	−8.56515			−0.404215			−0.202107	−	0.979363i	$-0.564779\pi$
$449$	−8.56515			−0.404215			−0.202107	+	0.979363i	$0.564779\pi$
$450$		0			0
$451$	3.91456			0.184329
$452$	4.26847	+	19.5605i	0.200772	+	0.920051i
$453$		0			0
$454$	−19.2402	−	15.4944i	−0.902989	−	0.727190i
$455$	2.19717	−	14.6678i	0.103005	−	0.687637i
$456$		0			0
$457$	−14.6705			−0.686259			−0.343129	−	0.939288i	$-0.611487\pi$
$457$	−14.6705			−0.686259			−0.343129	+	0.939288i	$0.611487\pi$
$458$	−11.1971	+	13.9040i	−0.523204	+	0.649689i
$459$		0			0
$460$	−0.607518	−	2.78399i	−0.0283257	−	0.129804i
$461$		−	19.3683i		−	0.902072i	−0.892506	−	0.451036i	$-0.851055\pi$
$461$		−	19.3683i		−	0.902072i	0.892506	−	0.451036i	$-0.148945\pi$
$462$		0			0
$463$			4.34277i			0.201826i	0.994895	+	0.100913i	$0.0321763\pi$
$463$			4.34277i			0.201826i	−0.994895	+	0.100913i	$0.967824\pi$
$464$	18.3125	−	8.39188i	0.850138	−	0.389583i
$465$		0			0
$466$	−4.28917	−	3.45413i	−0.198692	−	0.160009i
$467$	−15.4501			−0.714943			−0.357472	−	0.933924i	$-0.616361\pi$
$467$	−15.4501			−0.714943			−0.357472	+	0.933924i	$0.616361\pi$
$468$		0			0
$469$	22.7848	+	3.41305i	1.05210	+	0.157600i
$470$	−4.12433	+	5.12139i	−0.190241	+	0.236232i
$471$		0			0
$472$	13.2559	−	26.5467i	0.610154	−	1.22191i
$473$	6.98462			0.321153
$474$		0			0
$475$	1.63506			0.0750217
$476$	−0.175981	−	2.65602i	−0.00806606	−	0.121739i
$477$		0			0
$478$	−10.3335	+	12.8316i	−0.472644	+	0.586906i
$479$	−22.4129			−1.02407			−0.512035	−	0.858964i	$-0.671108\pi$
$479$	−22.4129			−1.02407			−0.512035	+	0.858964i	$0.671108\pi$
$480$		0			0
$481$		−	56.8442i		−	2.59187i
$482$	18.6504	−	23.1591i	0.849501	−	1.05487i
$483$		0			0
$484$	4.43711	+	20.3334i	0.201687	+	0.924244i
$485$	−15.5818			−0.707533
$486$		0			0
$487$			14.7901i			0.670202i	0.942182	+	0.335101i	$0.108770\pi$
$487$			14.7901i			0.670202i	−0.942182	+	0.335101i	$0.891230\pi$
$488$	−8.41119	−	4.20008i	−0.380757	−	0.190129i
$489$		0			0
$490$	8.19579	−	5.55239i	0.370248	−	0.250832i
$491$			18.0235i			0.813388i	0.913565	+	0.406694i	$0.133318\pi$
$491$			18.0235i			0.813388i	−0.913565	+	0.406694i	$0.866682\pi$
$492$		0			0
$493$		−	2.53329i		−	0.114094i
$494$	8.13018	−	10.0957i	0.365794	−	0.454225i
$495$		0			0
$496$	−29.9350	+	13.7179i	−1.34412	+	0.615954i
$497$	−28.3050	−	4.23995i	−1.26965	−	0.190188i
$498$		0			0
$499$		−	13.6272i		−	0.610036i	−0.952347	−	0.305018i	$-0.901338\pi$
$499$		−	13.6272i		−	0.610036i	0.952347	−	0.305018i	$-0.0986625\pi$
$500$	−1.95402	+	0.426402i	−0.0873863	+	0.0190693i
$501$		0			0
$502$	−1.50331	−	1.21063i	−0.0670959	−	0.0540333i
$503$	−23.8378			−1.06287			−0.531436	−	0.847098i	$-0.678348\pi$
$503$	−23.8378			−1.06287			−0.531436	+	0.847098i	$0.678348\pi$
$504$		0			0
$505$	−18.9661			−0.843979
$506$	−1.20955	−	0.974067i	−0.0537710	−	0.0433025i
$507$		0			0
$508$	−6.04827	+	1.31984i	−0.268348	+	0.0585585i
$509$		−	35.2475i		−	1.56232i	−0.624332	−	0.781159i	$-0.714629\pi$
$509$		−	35.2475i		−	1.56232i	0.624332	−	0.781159i	$-0.285371\pi$
$510$		0			0
$511$	−6.00668	−	0.899773i	−0.265720	−	0.0398036i
$512$	−22.2560	+	4.08276i	−0.983587	+	0.180434i
$513$		0			0
$514$	3.94026	−	4.89282i	0.173797	−	0.215813i
$515$			8.23760i			0.362992i
$516$		0			0
$517$			3.58376i			0.157613i
$518$	27.9127	−	25.6992i	1.22641	−	1.12916i
$519$		0			0
$520$	−7.08335	+	14.1853i	−0.310625	+	0.622066i
$521$			5.38270i			0.235820i	0.993024	+	0.117910i	$0.0376195\pi$
$521$			5.38270i			0.235820i	−0.993024	+	0.117910i	$0.962381\pi$
$522$		0			0
$523$	−0.0967711			−0.00423150			−0.00211575	−	0.999998i	$-0.500673\pi$
$523$	−0.0967711			−0.00423150			−0.00211575	+	0.999998i	$0.500673\pi$
$524$	−7.46207	−	34.1954i	−0.325982	−	1.49384i
$525$		0			0
$526$	4.37156	−	5.42839i	0.190609	−	0.236689i
$527$			4.14110i			0.180389i
$528$		0			0
$529$	20.9701			0.911742
$530$	0.404306	−	0.502048i	0.0175619	−	0.0218076i
$531$		0			0
$532$	8.63300	−	0.571999i	0.374288	−	0.0247993i
$533$	−28.4708			−1.23321
$534$		0			0
$535$	−11.8042			−0.510339
$536$	−22.0352	−	11.0032i	−0.951778	−	0.475265i
$537$		0			0
$538$	22.1926	−	27.5577i	0.956790	−	1.18810i
$539$	1.58090	−	5.15848i	0.0680944	−	0.222191i
$540$		0			0
$541$	2.76915			0.119055			0.0595275	−	0.998227i	$-0.481041\pi$
$541$	2.76915			0.119055			0.0595275	+	0.998227i	$0.481041\pi$
$542$	13.3665	+	10.7643i	0.574141	+	0.462364i
$543$		0			0
$544$	−0.699257	+	2.75838i	−0.0299804	+	0.118265i
$545$			9.80783i			0.420121i
$546$		0			0
$547$			25.1688i			1.07614i	0.842900	+	0.538071i	$0.180847\pi$
$547$			25.1688i			1.07614i	−0.842900	+	0.538071i	$0.819153\pi$
$548$	6.67497	+	30.5885i	0.285140	+	1.30668i
$549$		0			0
$550$	−0.683673	+	0.848952i	−0.0291519	+	0.0361994i
$551$	8.23408			0.350784
$552$		0			0
$553$	−6.70717	−	1.00470i	−0.285218	−	0.0427243i
$554$	−21.4445	−	17.2695i	−0.911088	−	0.733712i
$555$		0			0
$556$	−0.482240	−	2.20990i	−0.0204515	−	0.0937206i
$557$	39.1885			1.66047			0.830235	−	0.557413i	$-0.188206\pi$
$557$	39.1885			1.66047			0.830235	+	0.557413i	$0.188206\pi$
$558$		0			0
$559$	−50.7996			−2.14859
$560$	−10.1679	+	2.93495i	−0.429672	+	0.124024i
$561$		0			0
$562$	−19.5455	−	15.7403i	−0.824479	−	0.663965i
$563$	−23.3400			−0.983665			−0.491832	−	0.870690i	$-0.663673\pi$
$563$	−23.3400			−0.983665			−0.491832	+	0.870690i	$0.663673\pi$
$564$		0			0
$565$		−	10.0104i		−	0.421142i
$566$	−32.4865	−	26.1618i	−1.36551	−	1.09966i
$567$		0			0
$568$	27.3739	+	13.6690i	1.14858	+	0.573538i
$569$	35.0677			1.47011			0.735057	−	0.678005i	$-0.237155\pi$
$569$	35.0677			1.47011			0.735057	+	0.678005i	$0.237155\pi$
$570$		0			0
$571$			8.01227i			0.335303i	0.985846	+	0.167651i	$0.0536183\pi$
$571$			8.01227i			0.335303i	−0.985846	+	0.167651i	$0.946382\pi$
$572$	1.84234	+	8.44266i	0.0770323	+	0.353006i
$573$		0			0
$574$	−12.8716	−	13.9803i	−0.537251	−	0.583525i
$575$			1.42475i			0.0594164i
$576$		0			0
$577$		−	27.1156i		−	1.12884i	−0.825489	−	0.564418i	$-0.809100\pi$
$577$		−	27.1156i		−	1.12884i	0.825489	−	0.564418i	$-0.190900\pi$
$578$	−18.4460	−	14.8548i	−0.767252	−	0.617879i
$579$		0			0
$580$	−9.84033	+	2.14734i	−0.408598	+	0.0891634i
$581$	−5.48643	+	36.6262i	−0.227615	+	1.51951i
$582$		0			0
$583$		−	0.351314i		−	0.0145499i
$584$	5.80909	+	2.90074i	0.240382	+	0.120033i
$585$		0			0
$586$	17.6321	−	21.8947i	0.728377	−	0.904463i
$587$	−44.6409			−1.84253			−0.921264	−	0.388939i	$-0.872842\pi$
$587$	−44.6409			−1.84253			−0.921264	+	0.388939i	$0.872842\pi$
$588$		0			0
$589$	−13.4600			−0.554610
$590$	−9.30548	+	11.5551i	−0.383100	+	0.475715i
$591$		0			0
$592$	−36.8739	+	16.8978i	−1.51551	+	0.694494i
$593$		−	42.8848i		−	1.76107i	−0.473984	−	0.880534i	$-0.657184\pi$
$593$		−	42.8848i		−	1.76107i	0.473984	−	0.880534i	$-0.342816\pi$
$594$		0			0
$595$	−0.197166	+	1.31624i	−0.00808302	+	0.0539605i
$596$	−9.10980	−	41.7463i	−0.373152	−	1.70999i
$597$		0			0
$598$	8.79713	+	7.08445i	0.359741	+	0.289705i
$599$		−	17.8050i		−	0.727492i	−0.931498	−	0.363746i	$-0.881498\pi$
$599$		−	17.8050i		−	0.727492i	0.931498	−	0.363746i	$-0.118502\pi$
$600$		0			0
$601$		−	7.15463i		−	0.291843i	−0.989296	−	0.145922i	$-0.953385\pi$
$601$		−	7.15463i		−	0.291843i	0.989296	−	0.145922i	$-0.0466148\pi$
$602$	−22.9664	−	24.9446i	−0.936041	−	1.01666i
$603$		0			0
$604$	−5.53074	+	1.20691i	−0.225043	+	0.0491084i
$605$		−	10.4059i		−	0.423061i
$606$		0			0
$607$	−11.8573			−0.481272			−0.240636	−	0.970615i	$-0.577356\pi$
$607$	−11.8573			−0.481272			−0.240636	+	0.970615i	$0.577356\pi$
$608$	−8.96570	−	2.27283i	−0.363607	−	0.0921754i
$609$		0			0
$610$	3.66117	+	2.94839i	0.148236	+	0.119377i
$611$		−	26.0649i		−	1.05447i
$612$		0			0
$613$	−22.6111			−0.913254			−0.456627	−	0.889658i	$-0.650943\pi$
$613$	−22.6111			−0.913254			−0.456627	+	0.889658i	$0.650943\pi$
$614$	2.33977	+	1.88425i	0.0944254	+	0.0760421i
$615$		0			0
$616$	−3.31275	+	4.72158i	−0.133475	+	0.190238i
$617$	−18.4097			−0.741146			−0.370573	−	0.928803i	$-0.620839\pi$
$617$	−18.4097			−0.741146			−0.370573	+	0.928803i	$0.620839\pi$
$618$		0			0
$619$	33.4715			1.34533			0.672667	−	0.739946i	$-0.265149\pi$
$619$	33.4715			1.34533			0.672667	+	0.739946i	$0.265149\pi$
$620$	16.0857	−	3.51019i	0.646017	−	0.140973i
$621$		0			0
$622$	−11.3307	−	9.12475i	−0.454318	−	0.365869i
$623$	7.82028	+	1.17144i	0.313313	+	0.0469328i
$624$		0			0
$625$	1.00000			0.0400000
$626$	15.8599	−	19.6941i	0.633889	−	0.787133i
$627$		0			0
$628$	36.7165	−	8.01221i	1.46515	−	0.319722i
$629$			5.10101i			0.203390i
$630$		0			0
$631$			43.0583i			1.71412i	0.515213	+	0.857062i	$0.327713\pi$
$631$			43.0583i			1.71412i	−0.515213	+	0.857062i	$0.672287\pi$
$632$	6.48654	+	3.23902i	0.258021	+	0.128841i
$633$		0			0
$634$	13.6404	+	10.9848i	0.541731	+	0.436264i
$635$	3.09530			0.122833
$636$		0			0
$637$	−11.4980	+	37.5180i	−0.455568	+	1.48652i
$638$	−3.44294	+	4.27528i	−0.136307	+	0.169260i
$639$		0			0
$640$	11.3074	+	0.378061i	0.446964	+	0.0149442i
$641$	12.3471			0.487681			0.243841	−	0.969815i	$-0.421593\pi$
$641$	12.3471			0.487681			0.243841	+	0.969815i	$0.421593\pi$
$642$		0			0
$643$	9.21215			0.363292			0.181646	−	0.983364i	$-0.441858\pi$
$643$	9.21215			0.363292			0.181646	+	0.983364i	$0.441858\pi$
$644$	0.498427	+	7.52260i	0.0196408	+	0.296432i
$645$		0			0
$646$	−0.729574	+	0.905950i	−0.0287047	+	0.0356441i
$647$	−19.8210			−0.779243			−0.389622	−	0.920975i	$-0.627394\pi$
$647$	−19.8210			−0.779243			−0.389622	+	0.920975i	$0.627394\pi$
$648$		0			0
$649$			8.08581i			0.317396i
$650$	4.97240	−	6.17449i	0.195034	−	0.242183i
$651$		0			0
$652$	−14.4743	+	3.15855i	−0.566856	+	0.123698i
$653$	19.0538			0.745635			0.372817	−	0.927905i	$-0.378392\pi$
$653$	19.0538			0.745635			0.372817	+	0.927905i	$0.378392\pi$
$654$		0			0
$655$			17.5001i			0.683785i
$656$	8.46337	+	18.4686i	0.330439	+	0.721076i
$657$		0			0
$658$	12.7989	−	11.7839i	0.498952	−	0.459384i
$659$			10.4331i			0.406416i	0.979136	+	0.203208i	$0.0651367\pi$
$659$			10.4331i			0.406416i	−0.979136	+	0.203208i	$0.934863\pi$
$660$		0			0
$661$			9.84122i			0.382779i	0.981514	+	0.191389i	$0.0612994\pi$
$661$			9.84122i			0.382779i	−0.981514	+	0.191389i	$0.938701\pi$
$662$	18.8934	−	23.4609i	0.734314	−	0.911836i
$663$		0			0
$664$	17.6875	−	35.4214i	0.686406	−	1.37462i
$665$	−4.27823	−	0.640859i	−0.165903	−	0.0248514i
$666$		0			0
$667$			7.17499i			0.277817i
$668$	−1.26278	−	5.78676i	−0.0488583	−	0.223896i
$669$		0			0
$670$	9.59137	+	7.72407i	0.370547	+	0.298407i
$671$	2.56195			0.0989029
$672$		0			0
$673$	5.51471			0.212577			0.106288	−	0.994335i	$-0.466103\pi$
$673$	5.51471			0.212577			0.106288	+	0.994335i	$0.466103\pi$
$674$	0.964641	+	0.776840i	0.0371566	+	0.0299227i
$675$		0			0
$676$	−7.85627	−	36.0019i	−0.302164	−	1.38469i
$677$		−	44.8711i		−	1.72454i	−0.506451	−	0.862269i	$-0.669043\pi$
$677$		−	44.8711i		−	1.72454i	0.506451	−	0.862269i	$-0.330957\pi$
$678$		0			0
$679$	40.7707	+	6.10726i	1.56464	+	0.234375i
$680$	0.635635	−	1.27294i	0.0243755	−	0.0488150i
$681$		0			0
$682$	5.62808	−	6.98867i	0.215510	−	0.267610i
$683$		−	34.0718i		−	1.30372i	−0.758338	−	0.651862i	$-0.773988\pi$
$683$		−	34.0718i		−	1.30372i	0.758338	−	0.651862i	$-0.226012\pi$
$684$		0			0
$685$		−	15.6542i		−	0.598115i
$686$	−23.6210	+	11.3158i	−0.901854	+	0.432041i
$687$		0			0
$688$	15.1009	+	32.9529i	0.575717	+	1.25632i
$689$			2.55513i			0.0973428i
$690$		0			0
$691$	0.264224			0.0100515			0.00502577	−	0.999987i	$-0.498400\pi$
$691$	0.264224			0.0100515			0.00502577	+	0.999987i	$0.498400\pi$
$692$	29.3522	−	6.40520i	1.11581	−	0.243489i
$693$		0			0
$694$	30.9640	−	38.4496i	1.17538	−	1.45953i
$695$			1.13095i			0.0428994i
$696$		0			0
$697$	2.55487			0.0967728
$698$	18.7941	−	23.3376i	0.711368	−	0.883342i
$699$		0			0
$700$	5.27993	−	0.349833i	0.199562	−	0.0132225i
$701$	−17.5109			−0.661376			−0.330688	−	0.943740i	$-0.607281\pi$
$701$	−17.5109			−0.661376			−0.330688	+	0.943740i	$0.607281\pi$
$702$		0			0
$703$	−16.5800			−0.625328
$704$	4.92895	−	3.70480i	0.185767	−	0.139630i
$705$		0			0
$706$	−6.82928	+	8.48026i	−0.257023	+	0.319159i
$707$	49.6258	+	7.43371i	1.86637	+	0.279573i
$708$		0			0
$709$	−13.0797			−0.491219			−0.245610	−	0.969369i	$-0.578988\pi$
$709$	−13.0797			−0.491219			−0.245610	+	0.969369i	$0.578988\pi$
$710$	−11.9151	−	9.59542i	−0.447167	−	0.360110i
$711$		0			0
$712$	−7.56303	−	3.77656i	−0.283437	−	0.141532i
$713$		−	11.7287i		−	0.439245i
$714$		0			0
$715$		−	4.32067i		−	0.161584i
$716$	−9.43664	+	2.05925i	−0.352664	+	0.0769577i
$717$		0			0
$718$	1.90549	−	2.36615i	0.0711124	−	0.0883039i
$719$	−16.9650			−0.632689			−0.316345	−	0.948644i	$-0.602456\pi$
$719$	−16.9650			−0.632689			−0.316345	+	0.948644i	$0.602456\pi$
$720$		0			0
$721$	3.22871	−	21.5542i	0.120243	−	0.802719i
$722$	17.9830	+	14.4819i	0.669257	+	0.538962i
$723$		0			0
$724$	−35.5728	+	7.76264i	−1.32205	+	0.288496i
$725$	5.03595			0.187030
$726$		0			0
$727$	32.4836			1.20475			0.602375	−	0.798213i	$-0.294221\pi$
$727$	32.4836			1.20475			0.602375	+	0.798213i	$0.294221\pi$
$728$	24.0939	−	34.3403i	0.892979	−	1.27274i
$729$		0			0
$730$	−2.52855	−	2.03627i	−0.0935857	−	0.0753659i
$731$	4.55858			0.168605
$732$		0			0
$733$		−	35.8223i		−	1.32313i	−0.749890	−	0.661563i	$-0.769894\pi$
$733$		−	35.8223i		−	1.32313i	0.749890	−	0.661563i	$-0.230106\pi$
$734$	29.4046	+	23.6799i	1.08534	+	0.874043i
$735$		0			0
$736$	1.98049	−	7.81251i	0.0730019	−	0.287973i
$737$	6.71167			0.247228
$738$		0			0
$739$			21.8037i			0.802060i	0.916065	+	0.401030i	$0.131348\pi$
$739$			21.8037i			0.802060i	−0.916065	+	0.401030i	$0.868652\pi$
$740$	19.8144	−	4.32386i	0.728391	−	0.158948i
$741$		0			0
$742$	−1.25467	+	1.15517i	−0.0460603	+	0.0424076i
$743$		−	23.4618i		−	0.860731i	−0.902655	−	0.430365i	$-0.858385\pi$
$743$		−	23.4618i		−	0.860731i	0.902655	−	0.430365i	$-0.141615\pi$
$744$		0			0
$745$			21.3643i			0.782729i
$746$	9.37811	+	7.55233i	0.343357	+	0.276510i
$747$		0			0
$748$	−0.165326	−	0.757616i	−0.00604490	−	0.0277012i
$749$	30.8863	+	4.62662i	1.12856	+	0.169053i
$750$		0			0
$751$		−	15.9484i		−	0.581965i	−0.956728	−	0.290983i	$-0.906018\pi$
$751$		−	15.9484i		−	0.581965i	0.956728	−	0.290983i	$-0.0939822\pi$
$752$	−16.9079	+	7.74817i	−0.616567	+	0.282547i
$753$		0			0
$754$	25.0408	−	31.0944i	0.911931	−	1.13239i
$755$	2.83045			0.103011
$756$		0			0
$757$	27.9746			1.01675			0.508377	−	0.861135i	$-0.330246\pi$
$757$	27.9746			1.01675			0.508377	+	0.861135i	$0.330246\pi$
$758$	−27.6477	+	34.3315i	−1.00421	+	1.24698i
$759$		0			0
$760$	4.13750	+	2.06604i	0.150083	+	0.0749430i
$761$			17.5525i			0.636277i	0.948044	+	0.318138i	$0.103058\pi$
$761$			17.5525i			0.636277i	−0.948044	+	0.318138i	$0.896942\pi$
$762$		0			0
$763$	3.84416	−	25.6627i	0.139168	−	0.929054i
$764$	11.0438	−	2.40996i	0.399550	−	0.0871892i
$765$		0			0
$766$	37.1532	+	29.9200i	1.34240	+	1.08105i
$767$		−	58.8087i		−	2.12346i
$768$		0			0
$769$			5.74365i			0.207121i	0.994623	+	0.103561i	$0.0330236\pi$
$769$			5.74365i			0.207121i	−0.994623	+	0.103561i	$0.966976\pi$
$770$	2.12162	−	1.95337i	0.0764577	−	0.0703945i
$771$		0			0
$772$	−6.86414	−	31.4554i	−0.247046	−	1.13210i
$773$			46.0638i			1.65680i	0.560138	+	0.828399i	$0.310748\pi$
$773$			46.0638i			1.65680i	−0.560138	+	0.828399i	$0.689252\pi$
$774$		0			0
$775$	−8.23212			−0.295706
$776$	−39.4295	−	19.6889i	−1.41544	−	0.706791i
$777$		0			0
$778$	28.6281	+	23.0546i	1.02637	+	0.826548i
$779$			8.30423i			0.297530i
$780$		0			0
$781$	−8.33775			−0.298348
$782$	−0.789424	−	0.635734i	−0.0282297	−	0.0227338i
$783$		0			0
$784$	27.7552	−	3.69419i	0.991258	−	0.131935i
$785$	−18.7903			−0.670654
$786$		0			0
$787$	26.5373			0.945951			0.472976	−	0.881075i	$-0.343180\pi$
$787$	26.5373			0.945951			0.472976	+	0.881075i	$0.343180\pi$
$788$	5.24356	+	24.0290i	0.186794	+	0.855997i
$789$		0			0
$790$	−2.82342	−	2.27374i	−0.100453	−	0.0808961i
$791$	−3.92357	+	26.1929i	−0.139506	+	0.931311i
$792$		0			0
$793$	−18.6332			−0.661685
$794$	1.45059	−	1.80127i	0.0514794	−	0.0639245i
$795$		0			0
$796$	7.17353	+	32.8732i	0.254259	+	1.16516i
$797$			29.3245i			1.03873i	0.854553	+	0.519364i	$0.173831\pi$
$797$			29.3245i			1.03873i	−0.854553	+	0.519364i	$0.826169\pi$
$798$		0			0
$799$			2.33898i			0.0827470i
$800$	−5.48341	−	1.39006i	−0.193868	−	0.0491460i
$801$		0			0
$802$	−12.9869	−	10.4585i	−0.458582	−	0.369302i
$803$	−1.76938			−0.0624401
$804$		0			0
$805$	0.558430	−	3.72795i	0.0196821	−	0.131393i
$806$	−40.9334	+	50.8291i	−1.44182	+	1.79038i
$807$		0			0
$808$	−47.9933	−	23.9652i	−1.68840	−	0.843093i
$809$	15.6127			0.548913			0.274456	−	0.961600i	$-0.411502\pi$
$809$	15.6127			0.548913			0.274456	+	0.961600i	$0.411502\pi$
$810$		0			0
$811$	−24.0925			−0.846004			−0.423002	−	0.906129i	$-0.639024\pi$
$811$	−24.0925			−0.846004			−0.423002	+	0.906129i	$0.639024\pi$
$812$	26.5894	−	1.76174i	0.933107	−	0.0618251i
$813$		0			0
$814$	6.93267	−	8.60865i	0.242990	−	0.301733i
$815$	7.40744			0.259471
$816$		0			0
$817$			14.8170i			0.518381i
$818$	−8.64776	+	10.7384i	−0.302362	+	0.375458i
$819$		0			0
$820$	−2.16563	−	9.92417i	−0.0756272	−	0.346567i
$821$	47.2309			1.64837			0.824185	−	0.566321i	$-0.191634\pi$
$821$	47.2309			1.64837			0.824185	+	0.566321i	$0.191634\pi$
$822$		0			0
$823$		−	15.0076i		−	0.523133i	−0.965185	−	0.261566i	$-0.915761\pi$
$823$		−	15.0076i		−	0.523133i	0.965185	−	0.261566i	$-0.0842390\pi$
$824$	−10.4089	+	20.8451i	−0.362611	+	0.726174i
$825$		0			0
$826$	28.8773	−	26.5873i	1.00477	−	0.925090i
$827$			8.53837i			0.296908i	0.988919	+	0.148454i	$0.0474297\pi$
$827$			8.53837i			0.296908i	−0.988919	+	0.148454i	$0.952570\pi$
$828$		0			0
$829$		−	19.3755i		−	0.672941i	−0.941694	−	0.336470i	$-0.890767\pi$
$829$		−	19.3755i		−	0.672941i	0.941694	−	0.336470i	$-0.109233\pi$
$830$	−12.4163	+	15.4180i	−0.430977	+	0.535166i
$831$		0			0
$832$	−35.8486	+	26.9453i	−1.24283	+	0.934160i
$833$	1.03179	−	3.36673i	0.0357495	−	0.116650i
$834$		0			0
$835$			2.96147i			0.102486i
$836$	2.46251	−	0.537366i	0.0851679	−	0.0185852i
$837$		0			0
$838$	−16.9074	−	13.6158i	−0.584058	−	0.470350i
$839$	33.8009			1.16693			0.583467	−	0.812137i	$-0.301696\pi$
$839$	33.8009			1.16693			0.583467	+	0.812137i	$0.301696\pi$
$840$		0			0
$841$	−3.63920			−0.125490
$842$	−39.7336	−	31.9981i	−1.36931	−	1.10273i
$843$		0			0
$844$	−17.9661	+	3.92054i	−0.618420	+	0.134951i
$845$			18.4246i			0.633824i
$846$		0			0
$847$	−4.07858	+	27.2277i	−0.140142	+	0.935556i
$848$	1.65747	−	0.759550i	0.0569178	−	0.0260831i
$849$		0			0
$850$	−0.446206	+	0.554077i	−0.0153048	+	0.0190047i
$851$		−	14.4475i		−	0.495253i
$852$		0			0
$853$			20.5520i			0.703688i	0.936059	+	0.351844i	$0.114445\pi$
$853$			20.5520i			0.703688i	−0.936059	+	0.351844i	$0.885555\pi$
$854$	−8.42405	−	9.14963i	−0.288265	−	0.313094i
$855$		0			0
$856$	−29.8703	−	14.9156i	−1.02095	−	0.509803i
$857$		−	12.0420i		−	0.411346i	−0.978621	−	0.205673i	$-0.934062\pi$
$857$		−	12.0420i		−	0.411346i	0.978621	−	0.205673i	$-0.0659384\pi$
$858$		0			0
$859$	19.0195			0.648938			0.324469	−	0.945896i	$-0.394814\pi$
$859$	19.0195			0.648938			0.324469	+	0.945896i	$0.394814\pi$
$860$	−3.86407	−	17.7074i	−0.131764	−	0.603816i
$861$		0			0
$862$	18.6133	−	23.1131i	0.633973	−	0.787236i
$863$			51.7910i			1.76299i	0.472198	+	0.881493i	$0.343461\pi$
$863$			51.7910i			1.76299i	−0.472198	+	0.881493i	$0.656539\pi$
$864$		0			0
$865$	−15.0215			−0.510746
$866$	9.26256	−	11.5018i	0.314755	−	0.390847i
$867$		0			0
$868$	−43.4650	+	2.87987i	−1.47530	+	0.0977491i
$869$	−1.97572			−0.0670218
$870$		0			0
$871$	−48.8145			−1.65402
$872$	−12.3930	+	24.8186i	−0.419680	+	0.840463i
$873$		0			0
$874$	2.06636	−	2.56590i	0.0698956	−	0.0867930i
$875$	−2.61656	−	0.391948i	−0.0884558	−	0.0132503i
$876$		0			0
$877$	−46.5940			−1.57337			−0.786683	−	0.617357i	$-0.788204\pi$
$877$	−46.5940			−1.57337			−0.786683	+	0.617357i	$0.788204\pi$
$878$	39.9823	+	32.1984i	1.34934	+	1.08664i
$879$		0			0
$880$	−2.80275	+	1.28438i	−0.0944806	+	0.0432965i
$881$			53.7772i			1.81180i	0.423491	+	0.905901i	$0.360805\pi$
$881$			53.7772i			1.81180i	−0.423491	+	0.905901i	$0.639195\pi$
$882$		0			0
$883$		−	17.0329i		−	0.573202i	−0.958050	−	0.286601i	$-0.907475\pi$
$883$		−	17.0329i		−	0.573202i	0.958050	−	0.286601i	$-0.0925255\pi$
$884$	1.20242	+	5.51019i	0.0404419	+	0.185328i
$885$		0			0
$886$	3.29272	−	4.08873i	0.110621	−	0.137364i
$887$	−47.8749			−1.60748			−0.803741	−	0.594980i	$-0.797160\pi$
$887$	−47.8749			−1.60748			−0.803741	+	0.594980i	$0.797160\pi$
$888$		0			0
$889$	−8.09903	−	1.21320i	−0.271633	−	0.0406893i
$890$	3.29199	+	2.65109i	0.110348	+	0.0888646i
$891$		0			0
$892$	−9.74584	−	44.6610i	−0.326315	−	1.49536i
$893$	−7.60249			−0.254407
$894$		0			0
$895$	4.82936			0.161428
$896$	−29.4383	−	5.42113i	−0.983463	−	0.181107i
$897$		0			0
$898$	9.43412	+	7.59744i	0.314821	+	0.253530i
$899$	−41.4565			−1.38265
$900$		0			0
$901$		−	0.229289i		−	0.00763871i
$902$	−4.31170	−	3.47228i	−0.143564	−	0.115614i
$903$		0			0
$904$	12.6490	−	25.3312i	0.420700	−	0.842505i
$905$	18.2050			0.605154
$906$		0			0
$907$		−	22.5992i		−	0.750395i	−0.926945	−	0.375197i	$-0.877575\pi$
$907$		−	22.5992i		−	0.750395i	0.926945	−	0.375197i	$-0.122425\pi$
$908$	7.44841	+	34.1328i	0.247184	+	1.13274i
$909$		0			0
$910$	−15.4307	+	14.2070i	−0.511521	+	0.470957i
$911$			38.2369i			1.26685i	0.773806	+	0.633423i	$0.218350\pi$
$911$			38.2369i			1.26685i	−0.773806	+	0.633423i	$0.781650\pi$
$912$		0			0
$913$			10.7889i			0.357061i
$914$	16.1589	+	13.0130i	0.534490	+	0.430432i
$915$		0			0
$916$	24.6661	−	5.38259i	0.814990	−	0.177846i
$917$	6.85912	−	45.7900i	0.226508	−	1.51212i
$918$		0			0
$919$		−	17.0673i		−	0.562999i	−0.959561	−	0.281500i	$-0.909168\pi$
$919$		−	17.0673i		−	0.562999i	0.959561	−	0.281500i	$-0.0908318\pi$
$920$	−1.80030	+	3.60532i	−0.0593540	+	0.118864i
$921$		0			0
$922$	−17.1800	+	21.3333i	−0.565794	+	0.702575i
$923$	60.6411			1.99603
$924$		0			0
$925$	−10.1403			−0.333412
$926$	3.85211	−	4.78336i	0.126588	−	0.157191i
$927$		0			0
$928$	−27.6142	−	7.00027i	−0.906479	−	0.229795i
$929$		−	19.7796i		−	0.648947i	−0.945895	−	0.324473i	$-0.894813\pi$
$929$		−	19.7796i		−	0.648947i	0.945895	−	0.324473i	$-0.105187\pi$
$930$		0			0
$931$	10.9431	+	3.35369i	0.358644	+	0.109913i
$932$	1.66045	+	7.60913i	0.0543899	+	0.249245i
$933$		0			0
$934$	17.0175	+	13.7045i	0.556830	+	0.448424i
$935$			0.387722i			0.0126799i
$936$		0			0
$937$		−	21.4491i		−	0.700712i	−0.936617	−	0.350356i	$-0.886061\pi$
$937$		−	21.4491i		−	0.700712i	0.936617	−	0.350356i	$-0.113939\pi$
$938$	−22.0689	−	23.9698i	−0.720576	−	0.782641i
$939$		0			0
$940$	9.08552	−	1.98263i	0.296337	−	0.0646662i
$941$		−	42.2481i		−	1.37725i	−0.725119	−	0.688624i	$-0.758215\pi$
$941$		−	42.2481i		−	1.37725i	0.725119	−	0.688624i	$-0.241785\pi$
$942$		0			0
$943$	−7.23612			−0.235640
$944$	−38.1482	+	17.4817i	−1.24162	+	0.568982i
$945$		0			0
$946$	−7.69324	−	6.19547i	−0.250129	−	0.201432i
$947$		−	17.0774i		−	0.554939i	−0.960734	−	0.277470i	$-0.910504\pi$
$947$		−	17.0774i		−	0.554939i	0.960734	−	0.277470i	$-0.0894958\pi$
$948$		0			0
$949$	12.8688			0.417740
$950$	−1.80094	−	1.45033i	−0.0584303	−	0.0470548i
$951$		0			0
$952$	−2.16210	+	3.08158i	−0.0700741	+	0.0998747i
$953$	9.75364			0.315951			0.157976	−	0.987443i	$-0.449503\pi$
$953$	9.75364			0.315951			0.157976	+	0.987443i	$0.449503\pi$
$954$		0			0
$955$	−5.65184			−0.182889
$956$	22.7638	−	4.96747i	0.736233	−	0.160659i
$957$		0			0
$958$	24.6868	+	19.8806i	0.797593	+	0.642313i
$959$	−6.13561	+	40.9600i	−0.198129	+	1.32267i
$960$		0			0
$961$	36.7677			1.18606
$962$	−50.4218	+	62.6113i	−1.62566	+	2.01867i
$963$		0			0
$964$	−41.0850	+	8.96551i	−1.32326	+	0.288759i
$965$			16.0978i			0.518206i
$966$		0			0
$967$		−	24.1757i		−	0.777437i	−0.921356	−	0.388719i	$-0.872918\pi$
$967$		−	24.1757i		−	0.777437i	0.921356	−	0.388719i	$-0.127082\pi$
$968$	13.1488	−	26.3321i	0.422617	−	0.846345i
$969$		0			0
$970$	17.1626	+	13.8213i	0.551059	+	0.443776i
$971$	30.5804			0.981373			0.490686	−	0.871336i	$-0.336746\pi$
$971$	30.5804			0.981373			0.490686	+	0.871336i	$0.336746\pi$
$972$		0			0
$973$	0.443274	−	2.95920i	0.0142107	−	0.0948676i
$974$	13.1190	−	16.2906i	0.420361	−	0.521984i
$975$		0			0
$976$	5.53900	+	12.0871i	0.177299	+	0.386897i
$977$	−26.4757			−0.847031			−0.423516	−	0.905889i	$-0.639204\pi$
$977$	−26.4757			−0.847031			−0.423516	+	0.905889i	$0.639204\pi$
$978$		0			0
$979$	2.30361			0.0736237
$980$	−13.9523	−	1.15410i	−0.445691	−	0.0368663i
$981$		0			0
$982$	15.9871	−	19.8520i	0.510169	−	0.633503i
$983$	1.44944			0.0462300			0.0231150	−	0.999733i	$-0.492642\pi$
$983$	1.44944			0.0462300			0.0231150	+	0.999733i	$0.492642\pi$
$984$		0			0
$985$		−	12.2972i		−	0.391822i
$986$	−2.24707	+	2.79031i	−0.0715614	+	0.0888614i
$987$		0			0
$988$	−17.9100	+	3.90830i	−0.569794	+	0.124340i
$989$	−12.9112			−0.410552
$990$		0			0
$991$			43.1709i			1.37137i	0.727899	+	0.685684i	$0.240497\pi$
$991$			43.1709i			1.37137i	−0.727899	+	0.685684i	$0.759503\pi$
$992$	45.1400	+	11.4431i	1.43320	+	0.363319i
$993$		0			0
$994$	27.4157	+	29.7771i	0.869574	+	0.944472i
$995$		−	16.8234i		−	0.533338i
$996$		0			0
$997$			59.0825i			1.87116i	0.353114	+	0.935580i	$0.385123\pi$
$997$			59.0825i			1.87116i	−0.353114	+	0.935580i	$0.614877\pi$
$998$	−12.0875	+	15.0097i	−0.382624	+	0.475124i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.e.811.3		16
3.2	odd	2		420.2.c.b.391.14	yes	16
4.3	odd	2		1260.2.c.d.811.4		16
7.6	odd	2		1260.2.c.d.811.3		16
12.11	even	2		420.2.c.a.391.13	✓	16
21.20	even	2		420.2.c.a.391.14	yes	16
28.27	even	2	inner	1260.2.c.e.811.4		16
84.83	odd	2		420.2.c.b.391.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.13	✓	16	12.11	even	2
420.2.c.a.391.14	yes	16	21.20	even	2
420.2.c.b.391.13	yes	16	84.83	odd	2
420.2.c.b.391.14	yes	16	3.2	odd	2
1260.2.c.d.811.3		16	7.6	odd	2
1260.2.c.d.811.4		16	4.3	odd	2
1260.2.c.e.811.3		16	1.1	even	1	trivial
1260.2.c.e.811.4		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)

\(f(q)\)	\(=\)	\(q+(-1.10145 - 0.887017i) q^{2} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-0.391948 + 2.61656i) q^{7} +(1.26358 - 2.53049i) q^{8} +O(q^{10})\)	\(q+(-1.10145 - 0.887017i) q^{2} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-0.391948 + 2.61656i) q^{7} +(1.26358 - 2.53049i) q^{8} +(-0.887017 + 1.10145i) q^{10} +0.770756i q^{11} -5.60576i q^{13} +(2.75264 - 2.53435i) q^{14} +(-3.63636 + 1.66639i) q^{16} +0.503042i q^{17} -1.63506 q^{19} +(1.95402 - 0.426402i) q^{20} +(0.683673 - 0.848952i) q^{22} -1.42475i q^{23} -1.00000 q^{25} +(-4.97240 + 6.17449i) q^{26} +(-5.27993 + 0.349833i) q^{28} -5.03595 q^{29} +8.23212 q^{31} +(5.48341 + 1.39006i) q^{32} +(0.446206 - 0.554077i) q^{34} +(2.61656 + 0.391948i) q^{35} +10.1403 q^{37} +(1.80094 + 1.45033i) q^{38} +(-2.53049 - 1.26358i) q^{40} -5.07885i q^{41} -9.06204i q^{43} +(-1.50607 + 0.328652i) q^{44} +(-1.26378 + 1.56930i) q^{46} +4.64967 q^{47} +(-6.69275 - 2.05111i) q^{49} +(1.10145 + 0.887017i) q^{50} +(10.9537 - 2.39031i) q^{52} -0.455805 q^{53} +0.770756 q^{55} +(6.12590 + 4.29806i) q^{56} +(5.54687 + 4.46697i) q^{58} +10.4908 q^{59} -3.32394i q^{61} +(-9.06730 - 7.30202i) q^{62} +(-4.80671 - 6.39496i) q^{64} -5.60576 q^{65} -8.70791i q^{67} +(-0.982952 + 0.214498i) q^{68} +(-2.53435 - 2.75264i) q^{70} +10.8176i q^{71} +2.29564i q^{73} +(-11.1691 - 8.99464i) q^{74} +(-0.697193 - 3.19494i) q^{76} +(-2.01673 - 0.302096i) q^{77} +2.56336i q^{79} +(1.66639 + 3.63636i) q^{80} +(-4.50503 + 5.59412i) q^{82} +13.9979 q^{83} +0.503042 q^{85} +(-8.03818 + 9.98142i) q^{86} +(1.95039 + 0.973914i) q^{88} -2.98877i q^{89} +(14.6678 + 2.19717i) q^{91} +(2.78399 - 0.607518i) q^{92} +(-5.12139 - 4.12433i) q^{94} +1.63506i q^{95} -15.5818i q^{97} +(5.55239 + 8.19579i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 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

L-functions

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