LMFDB - Embedded newform 1148.2.k.b.337.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.6
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.898855 - 0.898855i) q^{3} +3.17533i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.38412i q^{9} +O(q^{10})$	\(q+(-0.898855 - 0.898855i) q^{3} +3.17533i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.38412i q^{9} +(-3.23064 - 3.23064i) q^{11} +(3.60315 + 3.60315i) q^{13} +(2.85416 - 2.85416i) q^{15} +(-4.90397 + 4.90397i) q^{17} +(1.76734 - 1.76734i) q^{19} +1.27117i q^{21} +7.82290 q^{23} -5.08271 q^{25} +(-3.94069 + 3.94069i) q^{27} +(-1.94379 - 1.94379i) q^{29} -10.1342 q^{31} +5.80775i q^{33} +(2.24530 - 2.24530i) q^{35} -10.4792 q^{37} -6.47742i q^{39} +(-6.28688 + 1.21455i) q^{41} -2.44432i q^{43} +4.39504 q^{45} +(-3.19148 + 3.19148i) q^{47} +1.00000i q^{49} +8.81592 q^{51} +(-0.796549 - 0.796549i) q^{53} +(10.2583 - 10.2583i) q^{55} -3.17716 q^{57} -11.7853 q^{59} -14.3630i q^{61} +(-0.978721 + 0.978721i) q^{63} +(-11.4412 + 11.4412i) q^{65} +(-4.45771 + 4.45771i) q^{67} +(-7.03165 - 7.03165i) q^{69} +(0.431860 + 0.431860i) q^{71} +6.43168i q^{73} +(4.56862 + 4.56862i) q^{75} +4.56881i q^{77} +(0.490820 + 0.490820i) q^{79} +2.93185 q^{81} -2.68754 q^{83} +(-15.5717 - 15.5717i) q^{85} +3.49437i q^{87} +(9.23786 + 9.23786i) q^{89} -5.09563i q^{91} +(9.10915 + 9.10915i) q^{93} +(5.61187 + 5.61187i) q^{95} +(5.19074 - 5.19074i) q^{97} +(-4.47159 + 4.47159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.898855	−	0.898855i	−0.518954	−	0.518954i	0.398301	−	0.917255i	$-0.369600\pi$
$3$	−0.898855	−	0.898855i	−0.518954	−	0.518954i	−0.917255	+	0.398301i	$0.869600\pi$
$4$		0			0
$5$			3.17533i			1.42005i	0.704177	+	0.710025i	$0.251316\pi$
$5$			3.17533i			1.42005i	−0.704177	+	0.710025i	$0.748684\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$		−	1.38412i		−	0.461373i
$10$		0			0
$11$	−3.23064	−	3.23064i	−0.974074	−	0.974074i	0.0255985	−	0.999672i	$-0.491851\pi$
$11$	−3.23064	−	3.23064i	−0.974074	−	0.974074i	−0.999672	+	0.0255985i	$0.991851\pi$
$12$		0			0
$13$	3.60315	+	3.60315i	0.999335	+	0.999335i	1.00000		0.000664865i	$-0.000211633\pi$
$13$	3.60315	+	3.60315i	0.999335	+	0.999335i	−0.000664865		1.00000i	$0.500212\pi$
$14$		0			0
$15$	2.85416	−	2.85416i	0.736941	−	0.736941i
$16$		0			0
$17$	−4.90397	+	4.90397i	−1.18939	+	1.18939i	−0.212151	+	0.977237i	$0.568047\pi$
$17$	−4.90397	+	4.90397i	−1.18939	+	1.18939i	−0.977237	+	0.212151i	$0.931953\pi$
$18$		0			0
$19$	1.76734	−	1.76734i	0.405455	−	0.405455i	−0.474695	−	0.880150i	$-0.657442\pi$
$19$	1.76734	−	1.76734i	0.405455	−	0.405455i	0.880150	+	0.474695i	$0.157442\pi$
$20$		0			0
$21$			1.27117i			0.277393i
$22$		0			0
$23$	7.82290			1.63119			0.815593	−	0.578625i	$-0.196411\pi$
$23$	7.82290			1.63119			0.815593	+	0.578625i	$0.196411\pi$
$24$		0			0
$25$	−5.08271			−1.01654
$26$		0			0
$27$	−3.94069	+	3.94069i	−0.758386	+	0.758386i
$28$		0			0
$29$	−1.94379	−	1.94379i	−0.360953	−	0.360953i	0.503211	−	0.864164i	$-0.332152\pi$
$29$	−1.94379	−	1.94379i	−0.360953	−	0.360953i	−0.864164	+	0.503211i	$0.832152\pi$
$30$		0			0
$31$	−10.1342			−1.82015			−0.910075	−	0.414443i	$-0.863977\pi$
$31$	−10.1342			−1.82015			−0.910075	+	0.414443i	$0.863977\pi$
$32$		0			0
$33$			5.80775i			1.01100i
$34$		0			0
$35$	2.24530	−	2.24530i	0.379524	−	0.379524i
$36$		0			0
$37$	−10.4792			−1.72277			−0.861387	−	0.507949i	$-0.830404\pi$
$37$	−10.4792			−1.72277			−0.861387	+	0.507949i	$0.830404\pi$
$38$		0			0
$39$		−	6.47742i		−	1.03722i
$40$		0			0
$41$	−6.28688	+	1.21455i	−0.981846	+	0.189680i
$41$	−6.28688	+	1.21455i	−0.981846	+	0.189680i
$42$		0			0
$43$		−	2.44432i		−	0.372755i	−0.982478	−	0.186378i	$-0.940325\pi$
$43$		−	2.44432i		−	0.372755i	0.982478	−	0.186378i	$-0.0596748\pi$
$44$		0			0
$45$	4.39504			0.655173
$46$		0			0
$47$	−3.19148	+	3.19148i	−0.465525	+	0.465525i	−0.900461	−	0.434936i	$-0.856771\pi$
$47$	−3.19148	+	3.19148i	−0.465525	+	0.465525i	0.434936	+	0.900461i	$0.356771\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	8.81592			1.23448
$52$		0			0
$53$	−0.796549	−	0.796549i	−0.109414	−	0.109414i	0.650280	−	0.759695i	$-0.274652\pi$
$53$	−0.796549	−	0.796549i	−0.109414	−	0.109414i	−0.759695	+	0.650280i	$0.774652\pi$
$54$		0			0
$55$	10.2583	−	10.2583i	1.38323	−	1.38323i
$56$		0			0
$57$	−3.17716			−0.420825
$58$		0			0
$59$	−11.7853			−1.53431			−0.767156	−	0.641461i	$-0.778329\pi$
$59$	−11.7853			−1.53431			−0.767156	+	0.641461i	$0.778329\pi$
$60$		0			0
$61$		−	14.3630i		−	1.83899i	−0.393101	−	0.919495i	$-0.628598\pi$
$61$		−	14.3630i		−	1.83899i	0.393101	−	0.919495i	$-0.371402\pi$
$62$		0			0
$63$	−0.978721	+	0.978721i	−0.123307	+	0.123307i
$64$		0			0
$65$	−11.4412	+	11.4412i	−1.41911	+	1.41911i
$66$		0			0
$67$	−4.45771	+	4.45771i	−0.544596	+	0.544596i	−0.924873	−	0.380276i	$-0.875829\pi$
$67$	−4.45771	+	4.45771i	−0.544596	+	0.544596i	0.380276	+	0.924873i	$0.375829\pi$
$68$		0			0
$69$	−7.03165	−	7.03165i	−0.846511	−	0.846511i
$70$		0			0
$71$	0.431860	+	0.431860i	0.0512524	+	0.0512524i	0.732268	−	0.681016i	$-0.238462\pi$
$71$	0.431860	+	0.431860i	0.0512524	+	0.0512524i	−0.681016	+	0.732268i	$0.738462\pi$
$72$		0			0
$73$			6.43168i			0.752772i	0.926463	+	0.376386i	$0.122833\pi$
$73$			6.43168i			0.752772i	−0.926463	+	0.376386i	$0.877167\pi$
$74$		0			0
$75$	4.56862	+	4.56862i	0.527538	+	0.527538i
$76$		0			0
$77$			4.56881i			0.520664i
$78$		0			0
$79$	0.490820	+	0.490820i	0.0552215	+	0.0552215i	0.734178	−	0.678957i	$-0.237568\pi$
$79$	0.490820	+	0.490820i	0.0552215	+	0.0552215i	−0.678957	+	0.734178i	$0.737568\pi$
$80$		0			0
$81$	2.93185			0.325761
$82$		0			0
$83$	−2.68754			−0.294996			−0.147498	−	0.989062i	$-0.547122\pi$
$83$	−2.68754			−0.294996			−0.147498	+	0.989062i	$0.547122\pi$
$84$		0			0
$85$	−15.5717	−	15.5717i	−1.68899	−	1.68899i
$86$		0			0
$87$			3.49437i			0.374636i
$88$		0			0
$89$	9.23786	+	9.23786i	0.979211	+	0.979211i	0.999788	−	0.0205770i	$-0.00655032\pi$
$89$	9.23786	+	9.23786i	0.979211	+	0.979211i	−0.0205770	+	0.999788i	$0.506550\pi$
$90$		0			0
$91$		−	5.09563i		−	0.534167i
$92$		0			0
$93$	9.10915	+	9.10915i	0.944575	+	0.944575i
$94$		0			0
$95$	5.61187	+	5.61187i	0.575766	+	0.575766i
$96$		0			0
$97$	5.19074	−	5.19074i	0.527040	−	0.527040i	−0.392649	−	0.919689i	$-0.628441\pi$
$97$	5.19074	−	5.19074i	0.527040	−	0.527040i	0.919689	+	0.392649i	$0.128441\pi$
$98$		0			0
$99$	−4.47159	+	4.47159i	−0.449412	+	0.449412i
$100$		0			0
$101$	−9.45064	+	9.45064i	−0.940374	+	0.940374i	−0.998320	−	0.0579460i	$-0.981545\pi$
$101$	−9.45064	+	9.45064i	−0.940374	+	0.940374i	0.0579460	+	0.998320i	$0.481545\pi$
$102$		0			0
$103$		−	4.04846i		−	0.398906i	−0.979907	−	0.199453i	$-0.936083\pi$
$103$		−	4.04846i		−	0.398906i	0.979907	−	0.199453i	$-0.0639165\pi$
$104$		0			0
$105$	−4.03639			−0.393911
$106$		0			0
$107$	−17.4119			−1.68327			−0.841634	−	0.540048i	$-0.818406\pi$
$107$	−17.4119			−1.68327			−0.841634	+	0.540048i	$0.818406\pi$
$108$		0			0
$109$	0.978729	−	0.978729i	0.0937452	−	0.0937452i	−0.658679	−	0.752424i	$-0.728884\pi$
$109$	0.978729	−	0.978729i	0.0937452	−	0.0937452i	0.752424	+	0.658679i	$0.228884\pi$
$110$		0			0
$111$	9.41930	+	9.41930i	0.894041	+	0.894041i
$112$		0			0
$113$	5.12924			0.482518			0.241259	−	0.970461i	$-0.422440\pi$
$113$	5.12924			0.482518			0.241259	+	0.970461i	$0.422440\pi$
$114$		0			0
$115$			24.8403i			2.31637i
$116$		0			0
$117$	4.98720	−	4.98720i	0.461066	−	0.461066i
$118$		0			0
$119$	6.93527			0.635755
$120$		0			0
$121$			9.87403i			0.897639i
$122$		0			0
$123$	6.74270	+	4.55929i	0.607968	+	0.411098i
$124$		0			0
$125$		−	0.262626i		−	0.0234900i
$126$		0			0
$127$	−0.889564			−0.0789360			−0.0394680	−	0.999221i	$-0.512566\pi$
$127$	−0.889564			−0.0789360			−0.0394680	+	0.999221i	$0.512566\pi$
$128$		0			0
$129$	−2.19709	+	2.19709i	−0.193443	+	0.193443i
$130$		0			0
$131$			10.6279i			0.928565i	0.885687	+	0.464283i	$0.153688\pi$
$131$			10.6279i			0.928565i	−0.885687	+	0.464283i	$0.846312\pi$
$132$		0			0
$133$	−2.49939			−0.216725
$134$		0			0
$135$	−12.5130	−	12.5130i	−1.07695	−	1.07695i
$136$		0			0
$137$	0.0781818	−	0.0781818i	0.00667952	−	0.00667952i	−0.703759	−	0.710439i	$-0.748497\pi$
$137$	0.0781818	−	0.0781818i	0.00667952	−	0.00667952i	0.710439	+	0.703759i	$0.248497\pi$
$138$		0			0
$139$	9.09143			0.771125			0.385563	−	0.922682i	$-0.374007\pi$
$139$	9.09143			0.771125			0.385563	+	0.922682i	$0.374007\pi$
$140$		0			0
$141$	5.73735			0.483172
$142$		0			0
$143$		−	23.2810i		−	1.94685i
$144$		0			0
$145$	6.17217	−	6.17217i	0.512571	−	0.512571i
$146$		0			0
$147$	0.898855	−	0.898855i	0.0741363	−	0.0741363i
$148$		0			0
$149$	−11.3092	+	11.3092i	−0.926484	+	0.926484i	−0.997477	−	0.0709928i	$-0.977383\pi$
$149$	−11.3092	+	11.3092i	−0.926484	+	0.926484i	0.0709928	+	0.997477i	$0.477383\pi$
$150$		0			0
$151$	−1.64619	−	1.64619i	−0.133965	−	0.133965i	0.636945	−	0.770910i	$-0.280198\pi$
$151$	−1.64619	−	1.64619i	−0.133965	−	0.133965i	−0.770910	+	0.636945i	$0.780198\pi$
$152$		0			0
$153$	6.78769	+	6.78769i	0.548752	+	0.548752i
$154$		0			0
$155$		−	32.1793i		−	2.58471i
$156$		0			0
$157$	7.30693	+	7.30693i	0.583157	+	0.583157i	0.935769	−	0.352613i	$-0.114707\pi$
$157$	7.30693	+	7.30693i	0.583157	+	0.583157i	−0.352613	+	0.935769i	$0.614707\pi$
$158$		0			0
$159$			1.43196i			0.113562i
$160$		0			0
$161$	−5.53162	−	5.53162i	−0.435953	−	0.435953i
$162$		0			0
$163$	−3.53525			−0.276902			−0.138451	−	0.990369i	$-0.544212\pi$
$163$	−3.53525			−0.276902			−0.138451	+	0.990369i	$0.544212\pi$
$164$		0			0
$165$	−18.4415			−1.43567
$166$		0			0
$167$	10.1679	+	10.1679i	0.786816	+	0.786816i	0.980971	−	0.194155i	$-0.0621964\pi$
$167$	10.1679	+	10.1679i	0.786816	+	0.786816i	−0.194155	+	0.980971i	$0.562196\pi$
$168$		0			0
$169$			12.9654i			0.997341i
$170$		0			0
$171$	−2.44621	−	2.44621i	−0.187066	−	0.187066i
$172$		0			0
$173$		−	11.5873i		−	0.880964i	−0.897761	−	0.440482i	$-0.854807\pi$
$173$		−	11.5873i		−	0.880964i	0.897761	−	0.440482i	$-0.145193\pi$
$174$		0			0
$175$	3.59402	+	3.59402i	0.271682	+	0.271682i
$176$		0			0
$177$	10.5932	+	10.5932i	0.796237	+	0.796237i
$178$		0			0
$179$	11.3428	−	11.3428i	0.847797	−	0.847797i	−0.142061	−	0.989858i	$-0.545373\pi$
$179$	11.3428	−	11.3428i	0.847797	−	0.847797i	0.989858	+	0.142061i	$0.0453728\pi$
$180$		0			0
$181$	11.4097	−	11.4097i	0.848076	−	0.848076i	−0.141817	−	0.989893i	$-0.545294\pi$
$181$	11.4097	−	11.4097i	0.848076	−	0.848076i	0.989893	+	0.141817i	$0.0452944\pi$
$182$		0			0
$183$	−12.9102	+	12.9102i	−0.954351	+	0.954351i
$184$		0			0
$185$		−	33.2750i		−	2.44643i
$186$		0			0
$187$	31.6859			2.31710
$188$		0			0
$189$	5.57297			0.405374
$190$		0			0
$191$	10.7086	−	10.7086i	0.774846	−	0.774846i	−0.204103	−	0.978949i	$-0.565428\pi$
$191$	10.7086	−	10.7086i	0.774846	−	0.774846i	0.978949	+	0.204103i	$0.0654279\pi$
$192$		0			0
$193$	−1.24930	−	1.24930i	−0.0899268	−	0.0899268i	0.660712	−	0.750639i	$-0.270254\pi$
$193$	−1.24930	−	1.24930i	−0.0899268	−	0.0899268i	−0.750639	+	0.660712i	$0.770254\pi$
$194$		0			0
$195$	20.5679			1.47290
$196$		0			0
$197$		−	8.32237i		−	0.592945i	−0.955041	−	0.296472i	$-0.904190\pi$
$197$		−	8.32237i		−	0.592945i	0.955041	−	0.296472i	$-0.0958103\pi$
$198$		0			0
$199$	16.7332	−	16.7332i	1.18619	−	1.18619i	0.208073	−	0.978113i	$-0.433281\pi$
$199$	16.7332	−	16.7332i	1.18619	−	1.18619i	0.978113	−	0.208073i	$-0.0667190\pi$
$200$		0			0
$201$	8.01368			0.565241
$202$		0			0
$203$			2.74893i			0.192937i
$204$		0			0
$205$	−3.85659	−	19.9629i	−0.269356	−	1.39427i
$206$		0			0
$207$		−	10.8278i		−	0.752586i
$208$		0			0
$209$	−11.4192			−0.789886
$210$		0			0
$211$	−8.31690	+	8.31690i	−0.572559	+	0.572559i	−0.932843	−	0.360284i	$-0.882680\pi$
$211$	−8.31690	+	8.31690i	−0.572559	+	0.572559i	0.360284	+	0.932843i	$0.382680\pi$
$212$		0			0
$213$		−	0.776360i		−	0.0531953i
$214$		0			0
$215$	7.76151			0.529331
$216$		0			0
$217$	7.16594	+	7.16594i	0.486456	+	0.486456i
$218$		0			0
$219$	5.78115	−	5.78115i	0.390654	−	0.390654i
$220$		0			0
$221$	−35.3395			−2.37719
$222$		0			0
$223$	−7.07610			−0.473851			−0.236925	−	0.971528i	$-0.576140\pi$
$223$	−7.07610			−0.473851			−0.236925	+	0.971528i	$0.576140\pi$
$224$		0			0
$225$			7.03508i			0.469005i
$226$		0			0
$227$	15.8504	−	15.8504i	1.05203	−	1.05203i	0.0534569	−	0.998570i	$-0.482976\pi$
$227$	15.8504	−	15.8504i	1.05203	−	1.05203i	0.998570	−	0.0534569i	$-0.0170240\pi$
$228$		0			0
$229$	−10.9365	+	10.9365i	−0.722704	+	0.722704i	−0.969155	−	0.246452i	$-0.920735\pi$
$229$	−10.9365	+	10.9365i	−0.722704	+	0.722704i	0.246452	+	0.969155i	$0.420735\pi$
$230$		0			0
$231$	4.10670	−	4.10670i	0.270201	−	0.270201i
$232$		0			0
$233$	7.18801	+	7.18801i	0.470902	+	0.470902i	0.902207	−	0.431304i	$-0.141946\pi$
$233$	7.18801	+	7.18801i	0.470902	+	0.470902i	−0.431304	+	0.902207i	$0.641946\pi$
$234$		0			0
$235$	−10.1340	−	10.1340i	−0.661068	−	0.661068i
$236$		0			0
$237$		−	0.882351i		−	0.0573149i
$238$		0			0
$239$	12.0190	+	12.0190i	0.777445	+	0.777445i	0.979396	−	0.201950i	$-0.0647279\pi$
$239$	12.0190	+	12.0190i	0.777445	+	0.777445i	−0.201950	+	0.979396i	$0.564728\pi$
$240$		0			0
$241$		−	29.2447i		−	1.88382i	−0.335870	−	0.941908i	$-0.609030\pi$
$241$		−	29.2447i		−	1.88382i	0.335870	−	0.941908i	$-0.390970\pi$
$242$		0			0
$243$	9.18675	+	9.18675i	0.589330	+	0.589330i
$244$		0			0
$245$	−3.17533			−0.202864
$246$		0			0
$247$	12.7360			0.810370
$248$		0			0
$249$	2.41571	+	2.41571i	0.153089	+	0.153089i
$250$		0			0
$251$			12.0031i			0.757632i	0.925472	+	0.378816i	$0.123669\pi$
$251$			12.0031i			0.757632i	−0.925472	+	0.378816i	$0.876331\pi$
$252$		0			0
$253$	−25.2729	−	25.2729i	−1.58890	−	1.58890i
$254$		0			0
$255$			27.9934i			1.75302i
$256$		0			0
$257$	1.48650	+	1.48650i	0.0927255	+	0.0927255i	0.751948	−	0.659222i	$-0.229114\pi$
$257$	1.48650	+	1.48650i	0.0927255	+	0.0927255i	−0.659222	+	0.751948i	$0.729114\pi$
$258$		0			0
$259$	7.40993	+	7.40993i	0.460431	+	0.460431i
$260$		0			0
$261$	−2.69044	+	2.69044i	−0.166534	+	0.166534i
$262$		0			0
$263$	−9.58843	+	9.58843i	−0.591248	+	0.591248i	−0.937968	−	0.346721i	$-0.887295\pi$
$263$	−9.58843	+	9.58843i	−0.591248	+	0.591248i	0.346721	+	0.937968i	$0.387295\pi$
$264$		0			0
$265$	2.52930	−	2.52930i	0.155374	−	0.155374i
$266$		0			0
$267$		−	16.6070i		−	1.01633i
$268$		0			0
$269$	−22.9772			−1.40095			−0.700474	−	0.713678i	$-0.747028\pi$
$269$	−22.9772			−1.40095			−0.700474	+	0.713678i	$0.747028\pi$
$270$		0			0
$271$	−13.5441			−0.822743			−0.411371	−	0.911468i	$-0.634950\pi$
$271$	−13.5441			−0.822743			−0.411371	+	0.911468i	$0.634950\pi$
$272$		0			0
$273$	−4.58023	+	4.58023i	−0.277208	+	0.277208i
$274$		0			0
$275$	16.4204	+	16.4204i	0.990187	+	0.990187i
$276$		0			0
$277$	32.8570			1.97419			0.987094	−	0.160145i	$-0.0511961\pi$
$277$	32.8570			1.97419			0.987094	+	0.160145i	$0.0511961\pi$
$278$		0			0
$279$			14.0269i			0.839769i
$280$		0			0
$281$	−4.67777	+	4.67777i	−0.279053	+	0.279053i	−0.832731	−	0.553678i	$-0.813224\pi$
$281$	−4.67777	+	4.67777i	−0.279053	+	0.279053i	0.553678	+	0.832731i	$0.313224\pi$
$282$		0			0
$283$	−3.80539			−0.226207			−0.113103	−	0.993583i	$-0.536079\pi$
$283$	−3.80539			−0.226207			−0.113103	+	0.993583i	$0.536079\pi$
$284$		0			0
$285$		−	10.0885i		−	0.597592i
$286$		0			0
$287$	5.30431	+	3.58668i	0.313104	+	0.211715i
$288$		0			0
$289$		−	31.0979i		−	1.82929i
$290$		0			0
$291$	−9.33145			−0.547019
$292$		0			0
$293$	−5.65650	+	5.65650i	−0.330456	+	0.330456i	−0.852760	−	0.522303i	$-0.825073\pi$
$293$	−5.65650	+	5.65650i	−0.330456	+	0.330456i	0.522303	+	0.852760i	$0.325073\pi$
$294$		0			0
$295$		−	37.4221i		−	2.17880i
$296$		0			0
$297$	25.4619			1.47745
$298$		0			0
$299$	28.1871	+	28.1871i	1.63010	+	1.63010i
$300$		0			0
$301$	−1.72839	+	1.72839i	−0.0996230	+	0.0996230i
$302$		0			0
$303$	16.9895			0.976022
$304$		0			0
$305$	45.6072			2.61146
$306$		0			0
$307$		−	8.30419i		−	0.473945i	−0.971516	−	0.236973i	$-0.923845\pi$
$307$		−	8.30419i		−	0.473945i	0.971516	−	0.236973i	$-0.0761552\pi$
$308$		0			0
$309$	−3.63897	+	3.63897i	−0.207014	+	0.207014i
$310$		0			0
$311$	−6.99226	+	6.99226i	−0.396495	+	0.396495i	−0.876995	−	0.480500i	$-0.840455\pi$
$311$	−6.99226	+	6.99226i	−0.396495	+	0.396495i	0.480500	+	0.876995i	$0.340455\pi$
$312$		0			0
$313$	5.57929	−	5.57929i	0.315360	−	0.315360i	−0.531622	−	0.846982i	$-0.678417\pi$
$313$	5.57929	−	5.57929i	0.315360	−	0.315360i	0.846982	+	0.531622i	$0.178417\pi$
$314$		0			0
$315$	−3.10776	−	3.10776i	−0.175102	−	0.175102i
$316$		0			0
$317$	−2.94928	−	2.94928i	−0.165648	−	0.165648i	0.619415	−	0.785064i	$-0.287370\pi$
$317$	−2.94928	−	2.94928i	−0.165648	−	0.165648i	−0.785064	+	0.619415i	$0.787370\pi$
$318$		0			0
$319$			12.5594i			0.703189i
$320$		0			0
$321$	15.6507	+	15.6507i	0.873539	+	0.873539i
$322$		0			0
$323$			17.3339i			0.964486i
$324$		0			0
$325$	−18.3138	−	18.3138i	−1.01587	−	1.01587i
$326$		0			0
$327$	−1.75947			−0.0972990
$328$		0			0
$329$	4.51343			0.248833
$330$		0			0
$331$	18.1383	+	18.1383i	0.996970	+	0.996970i	0.999995	−	0.00302502i	$-0.000962895\pi$
$331$	18.1383	+	18.1383i	0.996970	+	0.996970i	−0.00302502	+	0.999995i	$0.500963\pi$
$332$		0			0
$333$			14.5045i			0.794842i
$334$		0			0
$335$	−14.1547	−	14.1547i	−0.773354	−	0.773354i
$336$		0			0
$337$		−	0.453144i		−	0.0246843i	−0.999924	−	0.0123422i	$-0.996071\pi$
$337$		−	0.453144i		−	0.0246843i	0.999924	−	0.0123422i	$-0.00392873\pi$
$338$		0			0
$339$	−4.61044	−	4.61044i	−0.250405	−	0.250405i
$340$		0			0
$341$	32.7398	+	32.7398i	1.77296	+	1.77296i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	22.3278	−	22.3278i	1.20209	−	1.20209i
$346$		0			0
$347$	−17.0961	+	17.0961i	−0.917767	+	0.917767i	−0.996867	−	0.0790998i	$-0.974795\pi$
$347$	−17.0961	+	17.0961i	−0.917767	+	0.917767i	0.0790998	+	0.996867i	$0.474795\pi$
$348$		0			0
$349$			27.1989i			1.45592i	0.685618	+	0.727962i	$0.259532\pi$
$349$			27.1989i			1.45592i	−0.685618	+	0.727962i	$0.740468\pi$
$350$		0			0
$351$	−28.3978			−1.51576
$352$		0			0
$353$	−18.1032			−0.963536			−0.481768	−	0.876299i	$-0.660005\pi$
$353$	−18.1032			−0.963536			−0.481768	+	0.876299i	$0.660005\pi$
$354$		0			0
$355$	−1.37130	+	1.37130i	−0.0727810	+	0.0727810i
$356$		0			0
$357$	−6.23380	−	6.23380i	−0.329927	−	0.329927i
$358$		0			0
$359$	16.1281			0.851209			0.425605	−	0.904909i	$-0.360061\pi$
$359$	16.1281			0.851209			0.425605	+	0.904909i	$0.360061\pi$
$360$		0			0
$361$			12.7530i			0.671213i
$362$		0			0
$363$	8.87532	−	8.87532i	0.465834	−	0.465834i
$364$		0			0
$365$	−20.4227			−1.06897
$366$		0			0
$367$		−	30.5280i		−	1.59355i	−0.604278	−	0.796774i	$-0.706538\pi$
$367$		−	30.5280i		−	1.59355i	0.604278	−	0.796774i	$-0.293462\pi$
$368$		0			0
$369$	1.68108	+	8.70180i	0.0875135	+	0.452998i
$370$		0			0
$371$			1.12649i			0.0584844i
$372$		0			0
$373$	17.4217			0.902060			0.451030	−	0.892509i	$-0.351057\pi$
$373$	17.4217			0.902060			0.451030	+	0.892509i	$0.351057\pi$
$374$		0			0
$375$	−0.236063	+	0.236063i	−0.0121902	+	0.0121902i
$376$		0			0
$377$		−	14.0075i		−	0.721425i
$378$		0			0
$379$	−31.9163			−1.63943			−0.819715	−	0.572772i	$-0.805868\pi$
$379$	−31.9163			−1.63943			−0.819715	+	0.572772i	$0.805868\pi$
$380$		0			0
$381$	0.799589	+	0.799589i	0.0409642	+	0.0409642i
$382$		0			0
$383$	−3.59095	+	3.59095i	−0.183489	+	0.183489i	−0.792874	−	0.609385i	$-0.791416\pi$
$383$	−3.59095	+	3.59095i	−0.183489	+	0.183489i	0.609385	+	0.792874i	$0.291416\pi$
$384$		0			0
$385$	−14.5075			−0.739369
$386$		0			0
$387$	−3.38323			−0.171979
$388$		0			0
$389$			25.4500i			1.29037i	0.764028	+	0.645183i	$0.223219\pi$
$389$			25.4500i			1.29037i	−0.764028	+	0.645183i	$0.776781\pi$
$390$		0			0
$391$	−38.3633	+	38.3633i	−1.94011	+	1.94011i
$392$		0			0
$393$	9.55295	−	9.55295i	0.481883	−	0.481883i
$394$		0			0
$395$	−1.55851	+	1.55851i	−0.0784173	+	0.0784173i
$396$		0			0
$397$	−4.45110	−	4.45110i	−0.223394	−	0.223394i	0.586532	−	0.809926i	$-0.300493\pi$
$397$	−4.45110	−	4.45110i	−0.223394	−	0.223394i	−0.809926	+	0.586532i	$0.800493\pi$
$398$		0			0
$399$	2.24659	+	2.24659i	0.112470	+	0.112470i
$400$		0			0
$401$			25.9816i			1.29746i	0.761019	+	0.648730i	$0.224700\pi$
$401$			25.9816i			1.29746i	−0.761019	+	0.648730i	$0.775300\pi$
$402$		0			0
$403$	−36.5150	−	36.5150i	−1.81894	−	1.81894i
$404$		0			0
$405$			9.30959i			0.462597i
$406$		0			0
$407$	33.8546	+	33.8546i	1.67811	+	1.67811i
$408$		0			0
$409$	−29.9120			−1.47905			−0.739527	−	0.673127i	$-0.764951\pi$
$409$	−29.9120			−1.47905			−0.739527	+	0.673127i	$0.764951\pi$
$410$		0			0
$411$	−0.140548			−0.00693273
$412$		0			0
$413$	8.33344	+	8.33344i	0.410062	+	0.410062i
$414$		0			0
$415$		−	8.53382i		−	0.418909i
$416$		0			0
$417$	−8.17188	−	8.17188i	−0.400179	−	0.400179i
$418$		0			0
$419$		−	27.6599i		−	1.35127i	−0.737235	−	0.675637i	$-0.763869\pi$
$419$		−	27.6599i		−	1.35127i	0.737235	−	0.675637i	$-0.236131\pi$
$420$		0			0
$421$	−1.33229	−	1.33229i	−0.0649320	−	0.0649320i	0.673895	−	0.738827i	$-0.264620\pi$
$421$	−1.33229	−	1.33229i	−0.0649320	−	0.0649320i	−0.738827	+	0.673895i	$0.764620\pi$
$422$		0			0
$423$	4.41739	+	4.41739i	0.214781	+	0.214781i
$424$		0			0
$425$	24.9255	−	24.9255i	1.20906	−	1.20906i
$426$		0			0
$427$	−10.1562	+	10.1562i	−0.491491	+	0.491491i
$428$		0			0
$429$	−20.9262	+	20.9262i	−1.01033	+	1.01033i
$430$		0			0
$431$		−	3.34284i		−	0.161019i	−0.996754	−	0.0805095i	$-0.974345\pi$
$431$		−	3.34284i		−	0.161019i	0.996754	−	0.0805095i	$-0.0256547\pi$
$432$		0			0
$433$	5.36464			0.257808			0.128904	−	0.991657i	$-0.458854\pi$
$433$	5.36464			0.257808			0.128904	+	0.991657i	$0.458854\pi$
$434$		0			0
$435$	−11.0958			−0.532002
$436$		0			0
$437$	13.8257	−	13.8257i	0.661373	−	0.661373i
$438$		0			0
$439$	−20.1275	−	20.1275i	−0.960635	−	0.960635i	0.0386189	−	0.999254i	$-0.487704\pi$
$439$	−20.1275	−	20.1275i	−0.960635	−	0.960635i	−0.999254	+	0.0386189i	$0.987704\pi$
$440$		0			0
$441$	1.38412			0.0659105
$442$		0			0
$443$		−	17.5644i		−	0.834511i	−0.908789	−	0.417256i	$-0.862992\pi$
$443$		−	17.5644i		−	0.834511i	0.908789	−	0.417256i	$-0.137008\pi$
$444$		0			0
$445$	−29.3332	+	29.3332i	−1.39053	+	1.39053i
$446$		0			0
$447$	20.3306			0.961605
$448$		0			0
$449$		−	6.11739i		−	0.288698i	−0.989527	−	0.144349i	$-0.953891\pi$
$449$		−	6.11739i		−	0.288698i	0.989527	−	0.144349i	$-0.0461087\pi$
$450$		0			0
$451$	24.2344	+	16.3869i	1.14115	+	0.771628i
$452$		0			0
$453$			2.95937i			0.139043i
$454$		0			0
$455$	16.1803			0.758544
$456$		0			0
$457$	−4.69840	+	4.69840i	−0.219782	+	0.219782i	−0.808406	−	0.588625i	$-0.799670\pi$
$457$	−4.69840	+	4.69840i	−0.219782	+	0.219782i	0.588625	+	0.808406i	$0.299670\pi$
$458$		0			0
$459$		−	38.6500i		−	1.80403i
$460$		0			0
$461$	22.9832			1.07044			0.535218	−	0.844714i	$-0.320229\pi$
$461$	22.9832			1.07044			0.535218	+	0.844714i	$0.320229\pi$
$462$		0			0
$463$	13.7403	+	13.7403i	0.638568	+	0.638568i	0.950202	−	0.311634i	$-0.100876\pi$
$463$	13.7403	+	13.7403i	0.638568	+	0.638568i	−0.311634	+	0.950202i	$0.600876\pi$
$464$		0			0
$465$	−28.9245	+	28.9245i	−1.34134	+	1.34134i
$466$		0			0
$467$	−31.9109			−1.47666			−0.738329	−	0.674440i	$-0.764385\pi$
$467$	−31.9109			−1.47666			−0.738329	+	0.674440i	$0.764385\pi$
$468$		0			0
$469$	6.30416			0.291099
$470$		0			0
$471$		−	13.1357i		−	0.605263i
$472$		0			0
$473$	−7.89671	+	7.89671i	−0.363091	+	0.363091i
$474$		0			0
$475$	−8.98286	+	8.98286i	−0.412162	+	0.412162i
$476$		0			0
$477$	−1.10252	+	1.10252i	−0.0504809	+	0.0504809i
$478$		0			0
$479$	20.0784	+	20.0784i	0.917405	+	0.917405i	0.996840	−	0.0794347i	$-0.0253115\pi$
$479$	20.0784	+	20.0784i	0.917405	+	0.917405i	−0.0794347	+	0.996840i	$0.525312\pi$
$480$		0			0
$481$	−37.7583	−	37.7583i	−1.72163	−	1.72163i
$482$		0			0
$483$			9.94425i			0.452479i
$484$		0			0
$485$	16.4823	+	16.4823i	0.748423	+	0.748423i
$486$		0			0
$487$		−	30.1236i		−	1.36503i	−0.730872	−	0.682515i	$-0.760886\pi$
$487$		−	30.1236i		−	1.36503i	0.730872	−	0.682515i	$-0.239114\pi$
$488$		0			0
$489$	3.17767	+	3.17767i	0.143699	+	0.143699i
$490$		0			0
$491$	−5.91261			−0.266832			−0.133416	−	0.991060i	$-0.542595\pi$
$491$	−5.91261			−0.266832			−0.133416	+	0.991060i	$0.542595\pi$
$492$		0			0
$493$	19.0646			0.858626
$494$		0			0
$495$	−14.1988	−	14.1988i	−0.638187	−	0.638187i
$496$		0			0
$497$		−	0.610743i		−	0.0273956i
$498$		0			0
$499$	0.844691	+	0.844691i	0.0378136	+	0.0378136i	0.725761	−	0.687947i	$-0.241488\pi$
$499$	0.844691	+	0.844691i	0.0378136	+	0.0378136i	−0.687947	+	0.725761i	$0.741488\pi$
$500$		0			0
$501$		−	18.2789i		−	0.816643i
$502$		0			0
$503$	10.5141	+	10.5141i	0.468800	+	0.468800i	0.901526	−	0.432725i	$-0.142448\pi$
$503$	10.5141	+	10.5141i	0.468800	+	0.468800i	−0.432725	+	0.901526i	$0.642448\pi$
$504$		0			0
$505$	−30.0089	−	30.0089i	−1.33538	−	1.33538i
$506$		0			0
$507$	11.6540	−	11.6540i	0.517574	−	0.517574i
$508$		0			0
$509$	−0.254782	+	0.254782i	−0.0112930	+	0.0112930i	−0.712731	−	0.701438i	$-0.752542\pi$
$509$	−0.254782	+	0.254782i	−0.0112930	+	0.0112930i	0.701438	+	0.712731i	$0.252542\pi$
$510$		0			0
$511$	4.54789	−	4.54789i	0.201187	−	0.201187i
$512$		0			0
$513$			13.9290i			0.614982i
$514$		0			0
$515$	12.8552			0.566467
$516$		0			0
$517$	20.6210			0.906911
$518$		0			0
$519$	−10.4153	+	10.4153i	−0.457180	+	0.457180i
$520$		0			0
$521$	11.0165	+	11.0165i	0.482644	+	0.482644i	0.905975	−	0.423331i	$-0.139139\pi$
$521$	11.0165	+	11.0165i	0.482644	+	0.482644i	−0.423331	+	0.905975i	$0.639139\pi$
$522$		0			0
$523$	−24.4937			−1.07104			−0.535518	−	0.844524i	$-0.679884\pi$
$523$	−24.4937			−1.07104			−0.535518	+	0.844524i	$0.679884\pi$
$524$		0			0
$525$		−	6.46100i		−	0.281981i
$526$		0			0
$527$	49.6977	−	49.6977i	2.16487	−	2.16487i
$528$		0			0
$529$	38.1977			1.66077
$530$		0			0
$531$			16.3122i			0.707890i
$532$		0			0
$533$	−27.0288	−	18.2764i	−1.17075	−	0.791639i
$534$		0			0
$535$		−	55.2884i		−	2.39032i
$536$		0			0
$537$	−20.3910			−0.879936
$538$		0			0
$539$	3.23064	−	3.23064i	0.139153	−	0.139153i
$540$		0			0
$541$		−	40.7307i		−	1.75115i	−0.483084	−	0.875574i	$-0.660484\pi$
$541$		−	40.7307i		−	1.75115i	0.483084	−	0.875574i	$-0.339516\pi$
$542$		0			0
$543$	−20.5113			−0.880225
$544$		0			0
$545$	3.10779	+	3.10779i	0.133123	+	0.133123i
$546$		0			0
$547$	1.83965	−	1.83965i	0.0786578	−	0.0786578i	−0.666683	−	0.745341i	$-0.732287\pi$
$547$	1.83965	−	1.83965i	0.0786578	−	0.0786578i	0.745341	+	0.666683i	$0.232287\pi$
$548$		0			0
$549$	−19.8801			−0.848461
$550$		0			0
$551$	−6.87066			−0.292700
$552$		0			0
$553$		−	0.694124i		−	0.0295171i
$554$		0			0
$555$	−29.9094	+	29.9094i	−1.26958	+	1.26958i
$556$		0			0
$557$	8.99669	−	8.99669i	0.381202	−	0.381202i	−0.490333	−	0.871535i	$-0.663125\pi$
$557$	8.99669	−	8.99669i	0.381202	−	0.381202i	0.871535	+	0.490333i	$0.163125\pi$
$558$		0			0
$559$	8.80725	−	8.80725i	0.372507	−	0.372507i
$560$		0			0
$561$	−28.4810	−	28.4810i	−1.20247	−	1.20247i
$562$		0			0
$563$	−9.11108	−	9.11108i	−0.383986	−	0.383986i	0.488550	−	0.872536i	$-0.337526\pi$
$563$	−9.11108	−	9.11108i	−0.383986	−	0.383986i	−0.872536	+	0.488550i	$0.837526\pi$
$564$		0			0
$565$			16.2870i			0.685199i
$566$		0			0
$567$	−2.07313	−	2.07313i	−0.0870634	−	0.0870634i
$568$		0			0
$569$			23.8699i			1.00068i	0.865830	+	0.500339i	$0.166791\pi$
$569$			23.8699i			1.00068i	−0.865830	+	0.500339i	$0.833209\pi$
$570$		0			0
$571$	18.4625	+	18.4625i	0.772632	+	0.772632i	0.978566	−	0.205934i	$-0.0660232\pi$
$571$	18.4625	+	18.4625i	0.772632	+	0.772632i	−0.205934	+	0.978566i	$0.566023\pi$
$572$		0			0
$573$	−19.2509			−0.804219
$574$		0			0
$575$	−39.7615			−1.65817
$576$		0			0
$577$	16.2481	+	16.2481i	0.676416	+	0.676416i	0.959187	−	0.282772i	$-0.0912538\pi$
$577$	16.2481	+	16.2481i	0.676416	+	0.676416i	−0.282772	+	0.959187i	$0.591254\pi$
$578$		0			0
$579$			2.24588i			0.0933357i
$580$		0			0
$581$	1.90038	+	1.90038i	0.0788410	+	0.0788410i
$582$		0			0
$583$			5.14672i			0.213155i
$584$		0			0
$585$	15.8360	+	15.8360i	0.654737	+	0.654737i
$586$		0			0
$587$	−25.6552	−	25.6552i	−1.05890	−	1.05890i	−0.998153	−	0.0607512i	$-0.980650\pi$
$587$	−25.6552	−	25.6552i	−1.05890	−	1.05890i	−0.0607512	−	0.998153i	$-0.519350\pi$
$588$		0			0
$589$	−17.9105	+	17.9105i	−0.737989	+	0.737989i
$590$		0			0
$591$	−7.48061	+	7.48061i	−0.307711	+	0.307711i
$592$		0			0
$593$	32.9511	−	32.9511i	1.35314	−	1.35314i	0.471013	−	0.882126i	$-0.343888\pi$
$593$	32.9511	−	32.9511i	1.35314	−	1.35314i	0.882126	−	0.471013i	$-0.156112\pi$
$594$		0			0
$595$			22.0217i			0.902803i
$596$		0			0
$597$	−30.0815			−1.23115
$598$		0			0
$599$	1.28943			0.0526846			0.0263423	−	0.999653i	$-0.491614\pi$
$599$	1.28943			0.0526846			0.0263423	+	0.999653i	$0.491614\pi$
$600$		0			0
$601$	12.2813	−	12.2813i	0.500966	−	0.500966i	−0.410772	−	0.911738i	$-0.634741\pi$
$601$	12.2813	−	12.2813i	0.500966	−	0.500966i	0.911738	+	0.410772i	$0.134741\pi$
$602$		0			0
$603$	6.17001	+	6.17001i	0.251262	+	0.251262i
$604$		0			0
$605$	−31.3533			−1.27469
$606$		0			0
$607$		−	7.06614i		−	0.286806i	−0.989664	−	0.143403i	$-0.954196\pi$
$607$		−	7.06614i		−	0.286806i	0.989664	−	0.143403i	$-0.0458045\pi$
$608$		0			0
$609$	2.47089	−	2.47089i	0.100126	−	0.100126i
$610$		0			0
$611$	−22.9988			−0.930430
$612$		0			0
$613$			19.8614i			0.802194i	0.916036	+	0.401097i	$0.131371\pi$
$613$			19.8614i			0.802194i	−0.916036	+	0.401097i	$0.868629\pi$
$614$		0			0
$615$	−14.4772	+	21.4103i	−0.583779	+	0.863345i
$616$		0			0
$617$			33.9650i			1.36738i	0.729773	+	0.683690i	$0.239626\pi$
$617$			33.9650i			1.36738i	−0.729773	+	0.683690i	$0.760374\pi$
$618$		0			0
$619$	−18.9560			−0.761905			−0.380953	−	0.924595i	$-0.624404\pi$
$619$	−18.9560			−0.761905			−0.380953	+	0.924595i	$0.624404\pi$
$620$		0			0
$621$	−30.8276	+	30.8276i	−1.23707	+	1.23707i
$622$		0			0
$623$		−	13.0643i		−	0.523410i
$624$		0			0
$625$	−24.5796			−0.983185
$626$		0			0
$627$	10.2642	+	10.2642i	0.409914	+	0.409914i
$628$		0			0
$629$	51.3898	−	51.3898i	2.04905	−	2.04905i
$630$		0			0
$631$	−24.9884			−0.994772			−0.497386	−	0.867529i	$-0.665707\pi$
$631$	−24.9884			−0.994772			−0.497386	+	0.867529i	$0.665707\pi$
$632$		0			0
$633$	14.9514			0.594264
$634$		0			0
$635$		−	2.82466i		−	0.112093i
$636$		0			0
$637$	−3.60315	+	3.60315i	−0.142762	+	0.142762i
$638$		0			0
$639$	0.597747	−	0.597747i	0.0236465	−	0.0236465i
$640$		0			0
$641$	2.92515	−	2.92515i	0.115536	−	0.115536i	−0.646975	−	0.762511i	$-0.723966\pi$
$641$	2.92515	−	2.92515i	0.115536	−	0.115536i	0.762511	+	0.646975i	$0.223966\pi$
$642$		0			0
$643$	8.25587	+	8.25587i	0.325580	+	0.325580i	0.850903	−	0.525323i	$-0.176056\pi$
$643$	8.25587	+	8.25587i	0.325580	+	0.325580i	−0.525323	+	0.850903i	$0.676056\pi$
$644$		0			0
$645$	−6.97647	−	6.97647i	−0.274698	−	0.274698i
$646$		0			0
$647$		−	24.7889i		−	0.974553i	−0.873248	−	0.487276i	$-0.837990\pi$
$647$		−	24.7889i		−	0.974553i	0.873248	−	0.487276i	$-0.162010\pi$
$648$		0			0
$649$	38.0739	+	38.0739i	1.49453	+	1.49453i
$650$		0			0
$651$		−	12.8823i		−	0.504896i
$652$		0			0
$653$	29.9864	+	29.9864i	1.17346	+	1.17346i	0.981380	+	0.192077i	$0.0615223\pi$
$653$	29.9864	+	29.9864i	1.17346	+	1.17346i	0.192077	+	0.981380i	$0.438478\pi$
$654$		0			0
$655$	−33.7471			−1.31861
$656$		0			0
$657$	8.90222			0.347309
$658$		0			0
$659$	13.6460	+	13.6460i	0.531574	+	0.531574i	0.921041	−	0.389467i	$-0.127341\pi$
$659$	13.6460	+	13.6460i	0.531574	+	0.531574i	−0.389467	+	0.921041i	$0.627341\pi$
$660$		0			0
$661$			37.0565i			1.44133i	0.693284	+	0.720665i	$0.256163\pi$
$661$			37.0565i			1.44133i	−0.693284	+	0.720665i	$0.743837\pi$
$662$		0			0
$663$	31.7651	+	31.7651i	1.23365	+	1.23365i
$664$		0			0
$665$		−	7.93639i		−	0.307760i
$666$		0			0
$667$	−15.2061	−	15.2061i	−0.588781	−	0.588781i
$668$		0			0
$669$	6.36038	+	6.36038i	0.245907	+	0.245907i
$670$		0			0
$671$	−46.4016	+	46.4016i	−1.79131	+	1.79131i
$672$		0			0
$673$	−17.9693	+	17.9693i	−0.692665	+	0.692665i	−0.962817	−	0.270153i	$-0.912926\pi$
$673$	−17.9693	+	17.9693i	−0.692665	+	0.692665i	0.270153	+	0.962817i	$0.412926\pi$
$674$		0			0
$675$	20.0294	−	20.0294i	0.770931	−	0.770931i
$676$		0			0
$677$			48.3118i			1.85678i	0.371613	+	0.928388i	$0.378805\pi$
$677$			48.3118i			1.85678i	−0.371613	+	0.928388i	$0.621195\pi$
$678$		0			0
$679$	−7.34082			−0.281715
$680$		0			0
$681$	−28.4944			−1.09191
$682$		0			0
$683$	19.6184	−	19.6184i	0.750677	−	0.750677i	−0.223928	−	0.974606i	$-0.571888\pi$
$683$	19.6184	−	19.6184i	0.750677	−	0.750677i	0.974606	+	0.223928i	$0.0718882\pi$
$684$		0			0
$685$	0.248253	+	0.248253i	0.00948525	+	0.00948525i
$686$		0			0
$687$	19.6606			0.750100
$688$		0			0
$689$		−	5.74017i		−	0.218683i
$690$		0			0
$691$	−20.2232	+	20.2232i	−0.769328	+	0.769328i	−0.977988	−	0.208660i	$-0.933090\pi$
$691$	−20.2232	+	20.2232i	−0.769328	+	0.769328i	0.208660	+	0.977988i	$0.433090\pi$
$692$		0			0
$693$	6.32378			0.240221
$694$		0			0
$695$			28.8683i			1.09504i
$696$		0			0
$697$	24.8746	−	36.7868i	0.942192	−	1.39340i
$698$		0			0
$699$		−	12.9220i		−	0.488754i
$700$		0			0
$701$	−17.0207			−0.642862			−0.321431	−	0.946933i	$-0.604164\pi$
$701$	−17.0207			−0.642862			−0.321431	+	0.946933i	$0.604164\pi$
$702$		0			0
$703$	−18.5203	+	18.5203i	−0.698507	+	0.698507i
$704$		0			0
$705$			18.2180i			0.686128i
$706$		0			0
$707$	13.3652			0.502651
$708$		0			0
$709$	−30.7522	−	30.7522i	−1.15492	−	1.15492i	−0.985552	−	0.169370i	$-0.945827\pi$
$709$	−30.7522	−	30.7522i	−1.15492	−	1.15492i	−0.169370	−	0.985552i	$-0.554173\pi$
$710$		0			0
$711$	0.679353	−	0.679353i	0.0254777	−	0.0254777i
$712$		0			0
$713$	−79.2786			−2.96901
$714$		0			0
$715$	73.9247			2.76463
$716$		0			0
$717$		−	21.6067i		−	0.806917i
$718$		0			0
$719$	−14.5626	+	14.5626i	−0.543093	+	0.543093i	−0.924434	−	0.381341i	$-0.875462\pi$
$719$	−14.5626	+	14.5626i	−0.543093	+	0.543093i	0.381341	+	0.924434i	$0.375462\pi$
$720$		0			0
$721$	−2.86269	+	2.86269i	−0.106612	+	0.106612i
$722$		0			0
$723$	−26.2867	+	26.2867i	−0.977614	+	0.977614i
$724$		0			0
$725$	9.87972	+	9.87972i	0.366924	+	0.366924i
$726$		0			0
$727$	13.3854	+	13.3854i	0.496437	+	0.496437i	0.910327	−	0.413890i	$-0.135830\pi$
$727$	13.3854	+	13.3854i	0.496437	+	0.496437i	−0.413890	+	0.910327i	$0.635830\pi$
$728$		0			0
$729$		−	25.3107i		−	0.937432i
$730$		0			0
$731$	11.9869	+	11.9869i	0.443350	+	0.443350i
$732$		0			0
$733$			18.6444i			0.688647i	0.938851	+	0.344323i	$0.111892\pi$
$733$			18.6444i			0.688647i	−0.938851	+	0.344323i	$0.888108\pi$
$734$		0			0
$735$	2.85416	+	2.85416i	0.105277	+	0.105277i
$736$		0			0
$737$	28.8025			1.06095
$738$		0			0
$739$	12.9718			0.477176			0.238588	−	0.971121i	$-0.423315\pi$
$739$	12.9718			0.477176			0.238588	+	0.971121i	$0.423315\pi$
$740$		0			0
$741$	−11.4478	−	11.4478i	−0.420545	−	0.420545i
$742$		0			0
$743$		−	19.7381i		−	0.724119i	−0.932155	−	0.362060i	$-0.882074\pi$
$743$		−	19.7381i		−	0.724119i	0.932155	−	0.362060i	$-0.117926\pi$
$744$		0			0
$745$	−35.9104	−	35.9104i	−1.31565	−	1.31565i
$746$		0			0
$747$			3.71988i			0.136103i
$748$		0			0
$749$	12.3120	+	12.3120i	0.449872	+	0.449872i
$750$		0			0
$751$	0.359210	+	0.359210i	0.0131077	+	0.0131077i	0.713630	−	0.700523i	$-0.247050\pi$
$751$	0.359210	+	0.359210i	0.0131077	+	0.0131077i	−0.700523	+	0.713630i	$0.747050\pi$
$752$		0			0
$753$	10.7891	−	10.7891i	0.393176	−	0.393176i
$754$		0			0
$755$	5.22719	−	5.22719i	0.190237	−	0.190237i
$756$		0			0
$757$	16.3008	−	16.3008i	0.592463	−	0.592463i	−0.345833	−	0.938296i	$-0.612404\pi$
$757$	16.3008	−	16.3008i	0.592463	−	0.592463i	0.938296	+	0.345833i	$0.112404\pi$
$758$		0			0
$759$			45.4334i			1.64913i
$760$		0			0
$761$	23.1815			0.840328			0.420164	−	0.907448i	$-0.361972\pi$
$761$	23.1815			0.840328			0.420164	+	0.907448i	$0.361972\pi$
$762$		0			0
$763$	−1.38413			−0.0501089
$764$		0			0
$765$	−21.5531	+	21.5531i	−0.779255	+	0.779255i
$766$		0			0
$767$	−42.4641	−	42.4641i	−1.53329	−	1.53329i
$768$		0			0
$769$	27.0527			0.975546			0.487773	−	0.872971i	$-0.337809\pi$
$769$	27.0527			0.975546			0.487773	+	0.872971i	$0.337809\pi$
$770$		0			0
$771$		−	2.67230i		−	0.0962405i
$772$		0			0
$773$	−33.0614	+	33.0614i	−1.18913	+	1.18913i	−0.211827	+	0.977307i	$0.567941\pi$
$773$	−33.0614	+	33.0614i	−1.18913	+	1.18913i	−0.977307	+	0.211827i	$0.932059\pi$
$774$		0			0
$775$	51.5090			1.85026
$776$		0			0
$777$		−	13.3209i		−	0.477885i
$778$		0			0
$779$	−8.96452	+	13.2575i	−0.321187	+	0.475001i
$780$		0			0
$781$		−	2.79037i		−	0.0998472i
$782$		0			0
$783$	15.3197			0.547483
$784$		0			0
$785$	−23.2019	+	23.2019i	−0.828112	+	0.828112i
$786$		0			0
$787$			26.7178i			0.952385i	0.879341	+	0.476193i	$0.157983\pi$
$787$			26.7178i			0.952385i	−0.879341	+	0.476193i	$0.842017\pi$
$788$		0			0
$789$	17.2372			0.613661
$790$		0			0
$791$	−3.62692	−	3.62692i	−0.128958	−	0.128958i
$792$		0			0
$793$	51.7520	−	51.7520i	1.83777	−	1.83777i
$794$		0			0
$795$	−4.54695			−0.161264
$796$		0			0
$797$	−10.7130			−0.379475			−0.189738	−	0.981835i	$-0.560764\pi$
$797$	−10.7130			−0.379475			−0.189738	+	0.981835i	$0.560764\pi$
$798$		0			0
$799$		−	31.3018i		−	1.10738i
$800$		0			0
$801$	12.7863	−	12.7863i	0.451782	−	0.451782i
$802$		0			0
$803$	20.7784	−	20.7784i	0.733255	−	0.733255i
$804$		0			0
$805$	17.5647	−	17.5647i	0.619075	−	0.619075i
$806$		0			0
$807$	20.6532	+	20.6532i	0.727027	+	0.727027i
$808$		0			0
$809$	−9.59317	−	9.59317i	−0.337278	−	0.337278i	0.518064	−	0.855342i	$-0.326653\pi$
$809$	−9.59317	−	9.59317i	−0.337278	−	0.337278i	−0.855342	+	0.518064i	$0.826653\pi$
$810$		0			0
$811$		−	4.79179i		−	0.168263i	−0.996455	−	0.0841313i	$-0.973188\pi$
$811$		−	4.79179i		−	0.168263i	0.996455	−	0.0841313i	$-0.0268115\pi$
$812$		0			0
$813$	12.1741	+	12.1741i	0.426966	+	0.426966i
$814$		0			0
$815$		−	11.2256i		−	0.393215i
$816$		0			0
$817$	−4.31993	−	4.31993i	−0.151135	−	0.151135i
$818$		0			0
$819$	−7.05296			−0.246450
$820$		0			0
$821$	−40.7246			−1.42130			−0.710650	−	0.703546i	$-0.751599\pi$
$821$	−40.7246			−1.42130			−0.710650	+	0.703546i	$0.751599\pi$
$822$		0			0
$823$	3.97041	+	3.97041i	0.138400	+	0.138400i	0.772912	−	0.634513i	$-0.218799\pi$
$823$	3.97041	+	3.97041i	0.138400	+	0.138400i	−0.634513	+	0.772912i	$0.718799\pi$
$824$		0			0
$825$		−	29.5191i		−	1.02772i
$826$		0			0
$827$	−17.1726	−	17.1726i	−0.597149	−	0.597149i	0.342404	−	0.939553i	$-0.388759\pi$
$827$	−17.1726	−	17.1726i	−0.597149	−	0.597149i	−0.939553	+	0.342404i	$0.888759\pi$
$828$		0			0
$829$			3.67582i			0.127666i	0.997961	+	0.0638332i	$0.0203326\pi$
$829$			3.67582i			0.127666i	−0.997961	+	0.0638332i	$0.979667\pi$
$830$		0			0
$831$	−29.5337	−	29.5337i	−1.02451	−	1.02451i
$832$		0			0
$833$	−4.90397	−	4.90397i	−0.169913	−	0.169913i
$834$		0			0
$835$	−32.2864	+	32.2864i	−1.11732	+	1.11732i
$836$		0			0
$837$	39.9356	−	39.9356i	1.38038	−	1.38038i
$838$		0			0
$839$	5.97990	−	5.97990i	0.206449	−	0.206449i	−0.596307	−	0.802756i	$-0.703366\pi$
$839$	5.97990	−	5.97990i	0.206449	−	0.206449i	0.802756	+	0.596307i	$0.203366\pi$
$840$		0			0
$841$		−	21.4434i		−	0.739426i
$842$		0			0
$843$	8.40928			0.289631
$844$		0			0
$845$	−41.1695			−1.41627
$846$		0			0
$847$	6.98200	−	6.98200i	0.239904	−	0.239904i
$848$		0			0
$849$	3.42049	+	3.42049i	0.117391	+	0.117391i
$850$		0			0
$851$	−81.9779			−2.81017
$852$		0			0
$853$		−	21.8056i		−	0.746611i	−0.927709	−	0.373305i	$-0.878224\pi$
$853$		−	21.8056i		−	0.746611i	0.927709	−	0.373305i	$-0.121776\pi$
$854$		0			0
$855$	7.76751	−	7.76751i	0.265643	−	0.265643i
$856$		0			0
$857$	33.5611			1.14643			0.573213	−	0.819406i	$-0.305697\pi$
$857$	33.5611			1.14643			0.573213	+	0.819406i	$0.305697\pi$
$858$		0			0
$859$			13.6710i			0.466449i	0.972423	+	0.233225i	$0.0749277\pi$
$859$			13.6710i			0.466449i	−0.972423	+	0.233225i	$0.925072\pi$
$860$		0			0
$861$	−1.54390	−	7.99171i	−0.0526159	−	0.272357i
$862$		0			0
$863$		−	28.4151i		−	0.967262i	−0.875272	−	0.483631i	$-0.839318\pi$
$863$		−	28.4151i		−	0.967262i	0.875272	−	0.483631i	$-0.160682\pi$
$864$		0			0
$865$	36.7934			1.25101
$866$		0			0
$867$	−27.9525	+	27.9525i	−0.949317	+	0.949317i
$868$		0			0
$869$		−	3.17132i		−	0.107580i
$870$		0			0
$871$	−32.1237			−1.08847
$872$		0			0
$873$	−7.18461	−	7.18461i	−0.243162	−	0.243162i
$874$		0			0
$875$	−0.185705	+	0.185705i	−0.00627797	+	0.00627797i
$876$		0			0
$877$	39.4630			1.33257			0.666285	−	0.745698i	$-0.267884\pi$
$877$	39.4630			1.33257			0.666285	+	0.745698i	$0.267884\pi$
$878$		0			0
$879$	10.1688			0.342983
$880$		0			0
$881$			32.6407i			1.09969i	0.835266	+	0.549846i	$0.185314\pi$
$881$			32.6407i			1.09969i	−0.835266	+	0.549846i	$0.814686\pi$
$882$		0			0
$883$	−7.66914	+	7.66914i	−0.258087	+	0.258087i	−0.824276	−	0.566189i	$-0.808417\pi$
$883$	−7.66914	+	7.66914i	−0.258087	+	0.258087i	0.566189	+	0.824276i	$0.308417\pi$
$884$		0			0
$885$	−33.6370	+	33.6370i	−1.13070	+	1.13070i
$886$		0			0
$887$	−28.6160	+	28.6160i	−0.960830	+	0.960830i	−0.999261	−	0.0384312i	$-0.987764\pi$
$887$	−28.6160	+	28.6160i	−0.960830	+	0.960830i	0.0384312	+	0.999261i	$0.487764\pi$
$888$		0			0
$889$	0.629017	+	0.629017i	0.0210965	+	0.0210965i
$890$		0			0
$891$	−9.47175	−	9.47175i	−0.317316	−	0.317316i
$892$		0			0
$893$			11.2808i			0.377499i
$894$		0			0
$895$	36.0170	+	36.0170i	1.20391	+	1.20391i
$896$		0			0
$897$		−	50.6722i		−	1.69190i
$898$		0			0
$899$	19.6987	+	19.6987i	0.656988	+	0.656988i
$900$		0			0
$901$	7.81251			0.260272
$902$		0			0
$903$	3.10715			0.103400
$904$		0			0
$905$	36.2295	+	36.2295i	1.20431	+	1.20431i
$906$		0			0
$907$		−	17.4492i		−	0.579391i	−0.957119	−	0.289696i	$-0.906446\pi$
$907$		−	17.4492i		−	0.579391i	0.957119	−	0.289696i	$-0.0935541\pi$
$908$		0			0
$909$	13.0808	+	13.0808i	0.433863	+	0.433863i
$910$		0			0
$911$		−	29.3132i		−	0.971190i	−0.874184	−	0.485595i	$-0.838603\pi$
$911$		−	29.3132i		−	0.971190i	0.874184	−	0.485595i	$-0.161397\pi$
$912$		0			0
$913$	8.68247	+	8.68247i	0.287348	+	0.287348i
$914$		0			0
$915$	−40.9942	−	40.9942i	−1.35523	−	1.35523i
$916$		0			0
$917$	7.51507	−	7.51507i	0.248169	−	0.248169i
$918$		0			0
$919$	−27.1640	+	27.1640i	−0.896057	+	0.896057i	−0.995085	−	0.0990275i	$-0.968427\pi$
$919$	−27.1640	+	27.1640i	−0.896057	+	0.896057i	0.0990275	+	0.995085i	$0.468427\pi$
$920$		0			0
$921$	−7.46426	+	7.46426i	−0.245956	+	0.245956i
$922$		0			0
$923$			3.11212i			0.102437i
$924$		0			0
$925$	53.2628			1.75127
$926$		0			0
$927$	−5.60355			−0.184045
$928$		0			0
$929$	11.9878	−	11.9878i	0.393306	−	0.393306i	−0.482558	−	0.875864i	$-0.660292\pi$
$929$	11.9878	−	11.9878i	0.393306	−	0.393306i	0.875864	+	0.482558i	$0.160292\pi$
$930$		0			0
$931$	1.76734	+	1.76734i	0.0579221	+	0.0579221i
$932$		0			0
$933$	12.5701			0.411525
$934$		0			0
$935$			100.613i			3.29040i
$936$		0			0
$937$	−17.2777	+	17.2777i	−0.564437	+	0.564437i	−0.930565	−	0.366128i	$-0.880683\pi$
$937$	−17.2777	+	17.2777i	−0.564437	+	0.564437i	0.366128	+	0.930565i	$0.380683\pi$
$938$		0			0
$939$	−10.0299			−0.327315
$940$		0			0
$941$		−	36.4971i		−	1.18977i	−0.803810	−	0.594886i	$-0.797197\pi$
$941$		−	36.4971i		−	1.18977i	0.803810	−	0.594886i	$-0.202803\pi$
$942$		0			0
$943$	−49.1816	+	9.50128i	−1.60157	+	0.309404i
$944$		0			0
$945$			17.6960i			0.575652i
$946$		0			0
$947$	−37.7447			−1.22654			−0.613269	−	0.789874i	$-0.710146\pi$
$947$	−37.7447			−1.22654			−0.613269	+	0.789874i	$0.710146\pi$
$948$		0			0
$949$	−23.1743	+	23.1743i	−0.752271	+	0.752271i
$950$		0			0
$951$			5.30196i			0.171928i
$952$		0			0
$953$	19.3829			0.627873			0.313936	−	0.949444i	$-0.398352\pi$
$953$	19.3829			0.627873			0.313936	+	0.949444i	$0.398352\pi$
$954$		0			0
$955$	34.0033	+	34.0033i	1.10032	+	1.10032i
$956$		0			0
$957$	11.2890	−	11.2890i	0.364923	−	0.364923i
$958$		0			0
$959$	−0.110566			−0.00357035
$960$		0			0
$961$	71.7014			2.31295
$962$		0			0
$963$			24.1001i			0.776615i
$964$		0			0
$965$	3.96695	−	3.96695i	0.127700	−	0.127700i
$966$		0			0
$967$	28.5554	−	28.5554i	0.918281	−	0.918281i	−0.0786231	−	0.996904i	$-0.525052\pi$
$967$	28.5554	−	28.5554i	0.918281	−	0.918281i	0.996904	+	0.0786231i	$0.0250524\pi$
$968$		0			0
$969$	15.5807	−	15.5807i	0.500524	−	0.500524i
$970$		0			0
$971$	−9.66813	−	9.66813i	−0.310265	−	0.310265i	0.534747	−	0.845012i	$-0.320407\pi$
$971$	−9.66813	−	9.66813i	−0.310265	−	0.310265i	−0.845012	+	0.534747i	$0.820407\pi$
$972$		0			0
$973$	−6.42861	−	6.42861i	−0.206092	−	0.206092i
$974$		0			0
$975$			32.9229i			1.05438i
$976$		0			0
$977$	−1.94524	−	1.94524i	−0.0622337	−	0.0622337i	0.675305	−	0.737539i	$-0.264012\pi$
$977$	−1.94524	−	1.94524i	−0.0622337	−	0.0622337i	−0.737539	+	0.675305i	$0.764012\pi$
$978$		0			0
$979$		−	59.6884i		−	1.90765i
$980$		0			0
$981$	−1.35468	−	1.35468i	−0.0432516	−	0.0432516i
$982$		0			0
$983$	8.10783			0.258600			0.129300	−	0.991606i	$-0.458727\pi$
$983$	8.10783			0.258600			0.129300	+	0.991606i	$0.458727\pi$
$984$		0			0
$985$	26.4263			0.842011
$986$		0			0
$987$	−4.05692	−	4.05692i	−0.129133	−	0.129133i
$988$		0			0
$989$		−	19.1217i		−	0.608033i
$990$		0			0
$991$	3.72547	+	3.72547i	0.118344	+	0.118344i	0.763798	−	0.645455i	$-0.223332\pi$
$991$	3.72547	+	3.72547i	0.118344	+	0.118344i	−0.645455	+	0.763798i	$0.723332\pi$
$992$		0			0
$993$		−	32.6074i		−	1.03476i
$994$		0			0
$995$	53.1334	+	53.1334i	1.68444	+	1.68444i
$996$		0			0
$997$	−25.2823	−	25.2823i	−0.800697	−	0.800697i	0.182507	−	0.983205i	$-0.441579\pi$
$997$	−25.2823	−	25.2823i	−0.800697	−	0.800697i	−0.983205	+	0.182507i	$0.941579\pi$
$998$		0			0
$999$	41.2954	−	41.2954i	1.30653	−	1.30653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.6	✓	36
41.32	even	4	inner	1148.2.k.b.729.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.6	✓	36	1.1	even	1	trivial
1148.2.k.b.729.6	yes	36	41.32	even	4	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.898855 - 0.898855i) q^{3} +3.17533i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.38412i q^{9} +O(q^{10})\)	\(q+(-0.898855 - 0.898855i) q^{3} +3.17533i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.38412i q^{9} +(-3.23064 - 3.23064i) q^{11} +(3.60315 + 3.60315i) q^{13} +(2.85416 - 2.85416i) q^{15} +(-4.90397 + 4.90397i) q^{17} +(1.76734 - 1.76734i) q^{19} +1.27117i q^{21} +7.82290 q^{23} -5.08271 q^{25} +(-3.94069 + 3.94069i) q^{27} +(-1.94379 - 1.94379i) q^{29} -10.1342 q^{31} +5.80775i q^{33} +(2.24530 - 2.24530i) q^{35} -10.4792 q^{37} -6.47742i q^{39} +(-6.28688 + 1.21455i) q^{41} -2.44432i q^{43} +4.39504 q^{45} +(-3.19148 + 3.19148i) q^{47} +1.00000i q^{49} +8.81592 q^{51} +(-0.796549 - 0.796549i) q^{53} +(10.2583 - 10.2583i) q^{55} -3.17716 q^{57} -11.7853 q^{59} -14.3630i q^{61} +(-0.978721 + 0.978721i) q^{63} +(-11.4412 + 11.4412i) q^{65} +(-4.45771 + 4.45771i) q^{67} +(-7.03165 - 7.03165i) q^{69} +(0.431860 + 0.431860i) q^{71} +6.43168i q^{73} +(4.56862 + 4.56862i) q^{75} +4.56881i q^{77} +(0.490820 + 0.490820i) q^{79} +2.93185 q^{81} -2.68754 q^{83} +(-15.5717 - 15.5717i) q^{85} +3.49437i q^{87} +(9.23786 + 9.23786i) q^{89} -5.09563i q^{91} +(9.10915 + 9.10915i) q^{93} +(5.61187 + 5.61187i) q^{95} +(5.19074 - 5.19074i) q^{97} +(-4.47159 + 4.47159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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