LMFDB - Embedded newform 621.2.s.a.287.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [621,2,Mod(17,621)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("621.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(621, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 21])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 621 = 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	621.s (of order $66$, degree $20$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.95870996552$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	no (minimal twist has level 207)
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			287.11
Character	$\chi$	$=$	621.287
Dual form			621.2.s.a.251.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.120000 - 0.232768i) q^{2} +(1.12033 + 1.57329i) q^{4} +(-0.991492 + 4.08698i) q^{5} +(3.50853 + 1.21431i) q^{7} +(1.01908 - 0.146521i) q^{8} +(0.832339 + 0.721226i) q^{10} +(0.185211 - 3.88807i) q^{11} +(-0.0862974 - 0.249340i) q^{13} +(0.703678 - 0.670955i) q^{14} +(-1.17523 + 3.39559i) q^{16} +(-1.22006 - 2.67157i) q^{17} +(1.48734 + 0.679244i) q^{19} +(-7.54080 + 3.01888i) q^{20} +(-0.882791 - 0.509680i) q^{22} +(-0.324837 + 4.78482i) q^{23} +(-11.2762 - 5.81329i) q^{25} +(-0.0683940 - 0.00983357i) q^{26} +(2.02026 + 6.88036i) q^{28} +(2.00588 + 1.42838i) q^{29} +(-0.710211 - 0.284326i) q^{31} +(2.07031 + 2.17128i) q^{32} +(-0.768262 - 0.0365968i) q^{34} +(-8.44156 + 13.1353i) q^{35} +(1.05184 - 3.58222i) q^{37} +(0.336587 - 0.264695i) q^{38} +(-0.411577 + 4.31023i) q^{40} +(-3.88202 - 0.941769i) q^{41} +(-2.64877 - 6.61630i) q^{43} +(6.32454 - 4.06454i) q^{44} +(1.07477 + 0.649790i) q^{46} +(4.75835 - 2.74724i) q^{47} +(5.33286 + 4.19381i) q^{49} +(-2.70629 + 1.92714i) q^{50} +(0.295602 - 0.415114i) q^{52} +(1.42625 + 1.64598i) q^{53} +(15.7068 + 4.61194i) q^{55} +(3.75339 + 0.723407i) q^{56} +(0.573187 - 0.295499i) q^{58} +(9.13745 - 3.16250i) q^{59} +(2.52544 + 3.21135i) q^{61} +(-0.151407 + 0.131195i) q^{62} +(-6.14149 + 1.80331i) q^{64} +(1.10461 - 0.105478i) q^{65} +(-13.3829 + 0.637507i) q^{67} +(2.83626 - 4.91255i) q^{68} +(2.04449 + 3.54117i) q^{70} +(-0.327930 - 0.510270i) q^{71} +(6.89379 - 15.0953i) q^{73} +(-0.707606 - 0.674701i) q^{74} +(0.597666 + 3.10099i) q^{76} +(5.37115 - 13.4165i) q^{77} +(-0.400302 + 2.07696i) q^{79} +(-12.7125 - 8.16984i) q^{80} +(-0.685057 + 0.790598i) q^{82} +(2.85086 + 11.7514i) q^{83} +(12.1283 - 2.33754i) q^{85} +(-1.85791 - 0.177409i) q^{86} +(-0.380940 - 3.98938i) q^{88} +(1.15305 - 8.01966i) q^{89} -0.979609i q^{91} +(-7.89182 + 4.84953i) q^{92} +(-0.0684651 - 1.43726i) q^{94} +(-4.25074 + 5.40526i) q^{95} +(4.17127 - 4.37470i) q^{97} +(1.61613 - 0.738060i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) $ 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/621\mathbb{Z}\right)^\times$.

$n$	$28$	$461$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.120000	−	0.232768i	0.0848529	−	0.164592i	−0.842591	−	0.538554i	$-0.818971\pi$
$2$	0.120000	−	0.232768i	0.0848529	−	0.164592i	0.927444	+	0.373962i	$0.122001\pi$
$3$		0			0
$3$		0			0
$4$	1.12033	+	1.57329i	0.560167	+	0.786644i
$5$	−0.991492	+	4.08698i	−0.443409	+	1.82775i	0.108819	+	0.994062i	$0.465293\pi$
$5$	−0.991492	+	4.08698i	−0.443409	+	1.82775i	−0.552228	+	0.833693i	$0.686222\pi$
$6$		0			0
$7$	3.50853	+	1.21431i	1.32610	+	0.458968i	0.896096	−	0.443859i	$-0.146391\pi$
$7$	3.50853	+	1.21431i	1.32610	+	0.458968i	0.430004	+	0.902827i	$0.358512\pi$
$8$	1.01908	−	0.146521i	0.360299	−	0.0518031i
$9$		0			0
$10$	0.832339	+	0.721226i	0.263209	+	0.228072i
$11$	0.185211	−	3.88807i	0.0558433	−	1.17230i	−0.780884	−	0.624676i	$-0.785231\pi$
$11$	0.185211	−	3.88807i	0.0558433	−	1.17230i	0.836727	−	0.547620i	$-0.184466\pi$
$12$		0			0
$13$	−0.0862974	−	0.249340i	−0.0239346	−	0.0691545i	0.932401	−	0.361426i	$-0.117710\pi$
$13$	−0.0862974	−	0.249340i	−0.0239346	−	0.0691545i	−0.956335	+	0.292272i	$0.905589\pi$
$14$	0.703678	−	0.670955i	0.188066	−	0.179320i
$15$		0			0
$16$	−1.17523	+	3.39559i	−0.293807	+	0.848898i
$17$	−1.22006	−	2.67157i	−0.295909	−	0.647950i	0.702028	−	0.712149i	$-0.252278\pi$
$17$	−1.22006	−	2.67157i	−0.295909	−	0.647950i	−0.997937	+	0.0641992i	$0.979551\pi$
$18$		0			0
$19$	1.48734	+	0.679244i	0.341218	+	0.155829i	0.578652	−	0.815575i	$-0.303579\pi$
$19$	1.48734	+	0.679244i	0.341218	+	0.155829i	−0.237434	+	0.971404i	$0.576306\pi$
$20$	−7.54080	+	3.01888i	−1.68617	+	0.675042i
$21$		0			0
$22$	−0.882791	−	0.509680i	−0.188212	−	0.108664i
$23$	−0.324837	+	4.78482i	−0.0677332	+	0.997703i
$23$	−0.324837	+	4.78482i	−0.0677332	+	0.997703i
$24$		0			0
$25$	−11.2762	−	5.81329i	−2.25524	−	1.16266i
$26$	−0.0683940	−	0.00983357i	−0.0134132	−	0.00192852i
$27$		0			0
$28$	2.02026	+	6.88036i	0.381793	+	1.30027i
$29$	2.00588	+	1.42838i	0.372483	+	0.265244i	0.750934	−	0.660378i	$-0.229604\pi$
$29$	2.00588	+	1.42838i	0.372483	+	0.265244i	−0.378451	+	0.925621i	$0.623543\pi$
$30$		0			0
$31$	−0.710211	−	0.284326i	−0.127558	−	0.0510664i	0.307006	−	0.951708i	$-0.400673\pi$
$31$	−0.710211	−	0.284326i	−0.127558	−	0.0510664i	−0.434563	+	0.900641i	$0.643097\pi$
$32$	2.07031	+	2.17128i	0.365983	+	0.383832i
$33$		0			0
$34$	−0.768262	−	0.0365968i	−0.131756	−	0.00627631i
$35$	−8.44156	+	13.1353i	−1.42688	+	2.22028i
$36$		0			0
$37$	1.05184	−	3.58222i	0.172921	−	0.588914i	−0.826733	−	0.562595i	$-0.809803\pi$
$37$	1.05184	−	3.58222i	0.172921	−	0.588914i	0.999654	−	0.0263193i	$-0.00837867\pi$
$38$	0.336587	−	0.264695i	0.0546016	−	0.0429391i
$39$		0			0
$40$	−0.411577	+	4.31023i	−0.0650761	+	0.681508i
$41$	−3.88202	−	0.941769i	−0.606270	−	0.147080i	−0.0791391	−	0.996864i	$-0.525217\pi$
$41$	−3.88202	−	0.941769i	−0.606270	−	0.147080i	−0.527131	+	0.849784i	$0.676732\pi$
$42$		0			0
$43$	−2.64877	−	6.61630i	−0.403933	−	1.00898i	−0.981299	−	0.192491i	$-0.938343\pi$
$43$	−2.64877	−	6.61630i	−0.403933	−	1.00898i	0.577365	−	0.816486i	$-0.304081\pi$
$44$	6.32454	−	4.06454i	0.953461	−	0.612752i
$45$		0			0
$46$	1.07477	+	0.649790i	0.158466	+	0.0958064i
$47$	4.75835	−	2.74724i	0.694077	−	0.400726i	−0.111061	−	0.993814i	$-0.535425\pi$
$47$	4.75835	−	2.74724i	0.694077	−	0.400726i	0.805138	+	0.593088i	$0.202091\pi$
$48$		0			0
$49$	5.33286	+	4.19381i	0.761837	+	0.599115i
$50$	−2.70629	+	1.92714i	−0.382728	+	0.272539i
$51$		0			0
$52$	0.295602	−	0.415114i	0.0409926	−	0.0575660i
$53$	1.42625	+	1.64598i	0.195910	+	0.226092i	0.845202	−	0.534447i	$-0.179480\pi$
$53$	1.42625	+	1.64598i	0.195910	+	0.226092i	−0.649292	+	0.760539i	$0.724935\pi$
$54$		0			0
$55$	15.7068	+	4.61194i	2.11791	+	0.621874i
$56$	3.75339	+	0.723407i	0.501568	+	0.0966693i
$57$		0			0
$58$	0.573187	−	0.295499i	0.0752632	−	0.0388009i
$59$	9.13745	−	3.16250i	1.18960	−	0.411723i	0.340643	−	0.940193i	$-0.389355\pi$
$59$	9.13745	−	3.16250i	1.18960	−	0.411723i	0.848952	+	0.528470i	$0.177234\pi$
$60$		0			0
$61$	2.52544	+	3.21135i	0.323349	+	0.411172i	0.920367	−	0.391056i	$-0.127890\pi$
$61$	2.52544	+	3.21135i	0.323349	+	0.411172i	−0.597018	+	0.802228i	$0.703648\pi$
$62$	−0.151407	+	0.131195i	−0.0192287	+	0.0166618i
$63$		0			0
$64$	−6.14149	+	1.80331i	−0.767687	+	0.225413i
$65$	1.10461	−	0.105478i	0.137010	−	0.0130829i
$66$		0			0
$67$	−13.3829	+	0.637507i	−1.63498	+	0.0778838i	−0.844833	−	0.535030i	$-0.820300\pi$
$67$	−13.3829	+	0.637507i	−1.63498	+	0.0778838i	−0.790150	+	0.612914i	$0.789997\pi$
$68$	2.83626	−	4.91255i	0.343948	−	0.595735i
$69$		0			0
$70$	2.04449	+	3.54117i	0.244364	+	0.423250i
$71$	−0.327930	−	0.510270i	−0.0389182	−	0.0605579i	0.821249	−	0.570569i	$-0.193277\pi$
$71$	−0.327930	−	0.510270i	−0.0389182	−	0.0605579i	−0.860168	+	0.510012i	$0.829641\pi$
$72$		0			0
$73$	6.89379	−	15.0953i	0.806857	−	1.76677i	0.186492	−	0.982457i	$-0.440288\pi$
$73$	6.89379	−	15.0953i	0.806857	−	1.76677i	0.620365	−	0.784313i	$-0.286984\pi$
$74$	−0.707606	−	0.674701i	−0.0822575	−	0.0784324i
$75$		0			0
$76$	0.597666	+	3.10099i	0.0685570	+	0.355708i
$77$	5.37115	−	13.4165i	0.612100	−	1.52895i
$78$		0			0
$79$	−0.400302	+	2.07696i	−0.0450374	+	0.233676i	−0.997471	−	0.0710685i	$-0.977359\pi$
$79$	−0.400302	+	2.07696i	−0.0450374	+	0.233676i	0.952434	+	0.304745i	$0.0985712\pi$
$80$	−12.7125	−	8.16984i	−1.42130	−	0.913415i
$81$		0			0
$82$	−0.685057	+	0.790598i	−0.0756519	+	0.0873069i
$83$	2.85086	+	11.7514i	0.312922	+	1.28988i	0.883419	+	0.468584i	$0.155236\pi$
$83$	2.85086	+	11.7514i	0.312922	+	1.28988i	−0.570497	+	0.821300i	$0.693249\pi$
$84$		0			0
$85$	12.1283	−	2.33754i	1.31550	−	0.253542i
$86$	−1.85791	−	0.177409i	−0.200344	−	0.0191305i
$87$		0			0
$88$	−0.380940	−	3.98938i	−0.0406083	−	0.425270i
$89$	1.15305	−	8.01966i	0.122223	−	0.850082i	−0.832805	−	0.553567i	$-0.813266\pi$
$89$	1.15305	−	8.01966i	0.122223	−	0.850082i	0.955028	−	0.296515i	$-0.0958246\pi$
$90$		0			0
$91$		−	0.979609i		−	0.102691i
$92$	−7.89182	+	4.84953i	−0.822779	+	0.505598i
$93$		0			0
$94$	−0.0684651	−	1.43726i	−0.00706164	−	0.148242i
$95$	−4.25074	+	5.40526i	−0.436117	+	0.554568i
$96$		0			0
$97$	4.17127	−	4.37470i	0.423528	−	0.444183i	−0.477051	−	0.878876i	$-0.658294\pi$
$97$	4.17127	−	4.37470i	0.423528	−	0.444183i	0.900579	+	0.434692i	$0.143143\pi$
$98$	1.61613	−	0.738060i	0.163253	−	0.0745554i
$99$		0			0
$100$	−3.48713	−	24.2535i	−0.348713	−	2.42535i
$101$	−0.694693	+	0.168531i	−0.0691245	+	0.0167694i	−0.270172	−	0.962812i	$-0.587081\pi$
$101$	−0.694693	+	0.168531i	−0.0691245	+	0.0167694i	0.201048	+	0.979581i	$0.435565\pi$
$102$		0			0
$103$	7.43198	+	14.4160i	0.732295	+	1.42045i	0.900569	+	0.434714i	$0.143151\pi$
$103$	7.43198	+	14.4160i	0.732295	+	1.42045i	−0.168274	+	0.985740i	$0.553819\pi$
$104$	−0.124477	−	0.241453i	−0.0122060	−	0.0236764i
$105$		0			0
$106$	0.554280	−	0.134467i	0.0538365	−	0.0130606i
$107$	1.68209	+	11.6992i	0.162614	+	1.13100i	0.893683	+	0.448700i	$0.148113\pi$
$107$	1.68209	+	11.6992i	0.162614	+	1.13100i	−0.731069	+	0.682304i	$0.760978\pi$
$108$		0			0
$109$	−18.0521	+	8.24414i	−1.72908	+	0.789645i	−0.735372	+	0.677664i	$0.762992\pi$
$109$	−18.0521	+	8.24414i	−1.72908	+	0.789645i	−0.993710	+	0.111981i	$0.964280\pi$
$110$	2.95833	−	3.10261i	0.282066	−	0.295822i
$111$		0			0
$112$	−8.24664	+	10.4865i	−0.779234	+	0.990877i
$113$	−0.0144765	−	0.303898i	−0.00136183	−	0.0285883i	0.998084	−	0.0618712i	$-0.0197068\pi$
$113$	−0.0144765	−	0.303898i	−0.00136183	−	0.0285883i	−0.999446	+	0.0332829i	$0.989404\pi$
$114$		0			0
$115$	−19.2334	−	6.07171i	−1.79352	−	0.566190i
$116$			4.75609i			0.441592i
$117$		0			0
$118$	0.360367	−	2.50641i	0.0331745	−	0.230733i
$119$	−1.03651	−	10.8548i	−0.0950166	−	0.995059i
$120$		0			0
$121$	−4.13256	−	0.394611i	−0.375687	−	0.0358737i
$122$	1.05055	−	0.202477i	0.0951125	−	0.0183314i
$123$		0			0
$124$	−0.348347	−	1.43591i	−0.0312825	−	0.128948i
$125$	21.1689	−	24.4302i	1.89340	−	2.18510i
$126$		0			0
$127$	1.05634	+	0.678868i	0.0937349	+	0.0602398i	0.586669	−	0.809827i	$-0.300439\pi$
$127$	1.05634	+	0.678868i	0.0937349	+	0.0602398i	−0.492934	+	0.870067i	$0.664075\pi$
$128$	−1.45278	+	7.53772i	−0.128409	+	0.666247i
$129$		0			0
$130$	0.108002	−	0.269775i	0.00947238	−	0.0236609i
$131$	−1.32952	−	6.89818i	−0.116160	−	0.602697i	−0.992624	−	0.121230i	$-0.961316\pi$
$131$	−1.32952	−	6.89818i	−0.116160	−	0.602697i	0.876464	−	0.481467i	$-0.159896\pi$
$132$		0			0
$133$	4.39355	+	4.18924i	0.380969	+	0.363253i
$134$	−1.45756	+	3.19161i	−0.125914	+	0.275713i
$135$		0			0
$136$	−1.63478	−	2.54377i	−0.140181	−	0.218127i
$137$	0.000589825		0.00102161i	5.03921e−5		8.72817e-5i	0.866051	−	0.499956i	$-0.166651\pi$
$137$	0.000589825		0.00102161i	5.03921e−5		8.72817e-5i	−0.866000	+	0.500044i	$0.833317\pi$
$138$		0			0
$139$	4.03809	−	6.99418i	0.342507	−	0.593239i	−0.642391	−	0.766377i	$-0.722057\pi$
$139$	4.03809	−	6.99418i	0.342507	−	0.593239i	0.984898	+	0.173138i	$0.0553908\pi$
$140$	−30.1230	+	1.43494i	−2.54586	+	0.121274i
$141$		0			0
$142$	−0.158126	+	0.0150992i	−0.0132696	+	0.00126710i
$143$	−0.985433	+	0.289349i	−0.0824061	+	0.0241966i
$144$		0			0
$145$	−7.82659	+	6.78178i	−0.649963	+	0.563196i
$146$	−2.68644	−	3.41609i	−0.222331	−	0.282717i
$147$		0			0
$148$	6.81428	−	2.35844i	0.560130	−	0.193863i
$149$	2.47861	−	1.27781i	0.203056	−	0.104682i	−0.353700	−	0.935359i	$-0.615076\pi$
$149$	2.47861	−	1.27781i	0.203056	−	0.104682i	0.556755	+	0.830677i	$0.312046\pi$
$150$		0			0
$151$	9.16133	+	1.76570i	0.745538	+	0.143691i	0.547853	−	0.836575i	$-0.315445\pi$
$151$	9.16133	+	1.76570i	0.745538	+	0.143691i	0.197686	+	0.980265i	$0.436657\pi$
$152$	1.61524	+	0.474276i	0.131013	+	0.0384689i
$153$		0			0
$154$	−2.47839	−	2.86021i	−0.199714	−	0.230482i
$155$	1.86620	−	2.62072i	0.149897	−	0.210501i
$156$		0			0
$157$	3.61330	−	2.57302i	0.288373	−	0.205349i	−0.426711	−	0.904388i	$-0.640328\pi$
$157$	3.61330	−	2.57302i	0.288373	−	0.205349i	0.715084	+	0.699039i	$0.246388\pi$
$158$	0.435414	+	0.342413i	0.0346396	+	0.0272409i
$159$		0			0
$160$	−10.9267	+	6.30852i	−0.863830	+	0.498732i
$161$	−6.94997	+	16.3932i	−0.547735	+	1.29197i
$162$		0			0
$163$	0.905001	−	0.581609i	0.0708852	−	0.0455551i	−0.504718	−	0.863284i	$-0.668404\pi$
$163$	0.905001	−	0.581609i	0.0708852	−	0.0455551i	0.575603	+	0.817729i	$0.304767\pi$
$164$	−2.86749	−	7.16263i	−0.223913	−	0.559308i
$165$		0			0
$166$	3.07745	+	0.746581i	0.238856	+	0.0579460i
$167$	1.49547	−	15.6612i	0.115723	−	1.21190i	−0.731941	−	0.681368i	$-0.761385\pi$
$167$	1.49547	−	15.6612i	0.115723	−	1.21190i	0.847664	−	0.530534i	$-0.178008\pi$
$168$		0			0
$169$	10.1640	−	7.99303i	0.781844	−	0.614849i
$170$	0.911296	−	3.10359i	0.0698932	−	0.238035i
$171$		0			0
$172$	7.44184	−	11.5797i	0.567435	−	0.882947i
$173$	17.5284	+	0.834982i	1.33266	+	0.0634825i	0.701778	−	0.712395i	$-0.252390\pi$
$173$	17.5284	+	0.834982i	1.33266	+	0.0634825i	0.630883	+	0.775878i	$0.282693\pi$
$174$		0			0
$175$	−32.5038	−	34.0890i	−2.45705	−	2.57688i
$176$	12.9846	+	5.19826i	0.978753	+	0.391834i
$177$		0			0
$178$	−1.72835	−	1.23075i	−0.129545	−	0.0922489i
$179$	−4.41110	−	15.0228i	−0.329701	−	1.12286i	−0.942940	−	0.332962i	$-0.891952\pi$
$179$	−4.41110	−	15.0228i	−0.329701	−	1.12286i	0.613239	−	0.789898i	$-0.289866\pi$
$180$		0			0
$181$	−2.90054	−	0.417035i	−0.215596	−	0.0309980i	0.0336705	−	0.999433i	$-0.489280\pi$
$181$	−2.90054	−	0.417035i	−0.215596	−	0.0309980i	−0.249266	+	0.968435i	$0.580189\pi$
$182$	−0.228021	−	0.117553i	−0.0169021	−	0.00871363i
$183$		0			0
$184$	0.370044	+	4.92370i	0.0272800	+	0.362980i
$185$	13.5976	+	7.85058i	0.999716	+	0.577186i
$186$		0			0
$187$	−10.6132	+	4.24888i	−0.776113	+	0.310709i
$188$	9.65313	+	4.40844i	0.704027	+	0.321518i
$189$		0			0
$190$	0.748080	+	1.63807i	0.0542714	+	0.118838i
$191$	4.80103	−	13.8717i	0.347390	−	1.00372i	−0.627032	−	0.778994i	$-0.715730\pi$
$191$	4.80103	−	13.8717i	0.347390	−	1.00372i	0.974422	−	0.224725i	$-0.0721484\pi$
$192$		0			0
$193$	−8.74657	+	8.33984i	−0.629592	+	0.600315i	−0.936177	−	0.351528i	$-0.885662\pi$
$193$	−8.74657	+	8.33984i	−0.629592	+	0.600315i	0.306585	+	0.951843i	$0.400814\pi$
$194$	−0.517736	−	1.49590i	−0.0371713	−	0.107399i
$195$		0			0
$196$	−0.623486	+	13.0886i	−0.0445347	+	0.934898i
$197$	3.10535	+	2.69081i	0.221247	+	0.191712i	0.758431	−	0.651753i	$-0.225966\pi$
$197$	3.10535	+	2.69081i	0.221247	+	0.191712i	−0.537184	+	0.843465i	$0.680512\pi$
$198$		0			0
$199$	16.4077	−	2.35908i	1.16311	−	0.167230i	0.466396	−	0.884576i	$-0.345552\pi$
$199$	16.4077	−	2.35908i	1.16311	−	0.167230i	0.696717	+	0.717346i	$0.254643\pi$
$200$	−12.3431	−	4.27199i	−0.872790	−	0.302076i
$201$		0			0
$202$	−0.0441347	+	0.181926i	−0.00310531	+	0.0128003i
$203$	5.30319	+	7.44729i	0.372211	+	0.522697i
$204$		0			0
$205$	7.69799	−	14.9320i	0.537651	−	1.04290i
$206$	4.24743			0.295932
$207$		0			0
$208$	0.948076			0.0657373
$209$	2.91642	−	5.65706i	0.201733	−	0.391307i
$210$		0			0
$211$	−5.99252	−	8.41532i	−0.412542	−	0.579335i	0.555061	−	0.831810i	$-0.312695\pi$
$211$	−5.99252	−	8.41532i	−0.412542	−	0.579335i	−0.967603	+	0.252475i	$0.918755\pi$
$212$	−0.991723	+	4.08794i	−0.0681118	+	0.280761i
$213$		0			0
$214$	2.92505	+	1.01237i	0.199952	+	0.0692041i
$215$	29.6670	−	4.26546i	2.02327	−	0.290902i
$216$		0			0
$217$	−2.14654	−	1.85998i	−0.145716	−	0.126264i
$218$	−0.247290	+	5.19126i	−0.0167486	+	0.351596i
$219$		0			0
$220$	10.3410	+	29.8783i	0.697188	+	2.01439i
$221$	−0.560840	+	0.534760i	−0.0377262	+	0.0359718i
$222$		0			0
$223$	5.86401	−	16.9429i	0.392683	−	1.13458i	−0.559441	−	0.828870i	$-0.688984\pi$
$223$	5.86401	−	16.9429i	0.392683	−	1.13458i	0.952124	−	0.305713i	$-0.0988947\pi$
$224$	4.62713	+	10.1320i	0.309163	+	0.676973i
$225$		0			0
$226$	−0.0724749	−	0.0330982i	−0.00482096	−	0.00220166i
$227$	−17.6478	+	7.06512i	−1.17133	+	0.468929i	−0.874037	−	0.485859i	$-0.838507\pi$
$227$	−17.6478	+	7.06512i	−1.17133	+	0.468929i	−0.297290	+	0.954787i	$0.596083\pi$
$228$		0			0
$229$	13.9991	+	8.08237i	0.925085	+	0.534098i	0.885254	−	0.465108i	$-0.153985\pi$
$229$	13.9991	+	8.08237i	0.925085	+	0.534098i	0.0398315	+	0.999206i	$0.487318\pi$
$230$	−3.72131	+	3.74831i	−0.245376	+	0.247156i
$231$		0			0
$232$	2.25344	+	1.16173i	0.147946	+	0.0762712i
$233$	−12.5681	−	1.80702i	−0.823363	−	0.118382i	−0.282260	−	0.959338i	$-0.591084\pi$
$233$	−12.5681	−	1.80702i	−0.823363	−	0.118382i	−0.541103	+	0.840956i	$0.681993\pi$
$234$		0			0
$235$	6.51004	+	22.1712i	0.424668	+	1.44629i
$236$	15.2125	+	10.8328i	0.990251	+	0.705154i
$237$		0			0
$238$	−2.65103	−	1.06131i	−0.171841	−	0.0687947i
$239$	−3.66511	−	3.84386i	−0.237076	−	0.248638i	0.594439	−	0.804141i	$-0.297374\pi$
$239$	−3.66511	−	3.84386i	−0.237076	−	0.248638i	−0.831515	+	0.555503i	$0.812526\pi$
$240$		0			0
$241$	−5.80880	−	0.276707i	−0.374178	−	0.0178243i	−0.140349	−	0.990102i	$-0.544822\pi$
$241$	−5.80880	−	0.276707i	−0.374178	−	0.0178243i	−0.233829	+	0.972278i	$0.575125\pi$
$242$	−0.587760	+	0.914573i	−0.0377826	+	0.0587910i
$243$		0			0
$244$	−2.22305	+	7.57102i	−0.142316	+	0.484685i
$245$	−22.4275	+	17.6372i	−1.43284	+	1.12680i
$246$		0			0
$247$	0.0410093	−	0.429469i	0.00260936	−	0.0273265i
$248$	−0.765421	−	0.185689i	−0.0486043	−	0.0117913i
$249$		0			0
$250$	−3.14630	−	7.85907i	−0.198989	−	0.497051i
$251$	−9.76049	+	6.27268i	−0.616076	+	0.395928i	−0.811131	−	0.584864i	$-0.801148\pi$
$251$	−9.76049	+	6.27268i	−0.616076	+	0.395928i	0.195055	+	0.980792i	$0.437512\pi$
$252$		0			0
$253$	18.5435	+	2.14919i	1.16582	+	0.135118i
$254$	0.284779	−	0.164417i	0.0178686	−	0.0103165i
$255$		0			0
$256$	−8.48248	−	6.67070i	−0.530155	−	0.416919i
$257$	−0.903074	+	0.643076i	−0.0563322	+	0.0401140i	−0.607876	−	0.794032i	$-0.707978\pi$
$257$	−0.903074	+	0.643076i	−0.0563322	+	0.0401140i	0.551544	+	0.834146i	$0.314039\pi$
$258$		0			0
$259$	8.04035	−	11.2911i	0.499603	−	0.701594i
$260$	1.40348	+	1.61970i	0.0870401	+	0.100450i
$261$		0			0
$262$	−1.76522	−	0.518314i	−0.109055	−	0.0320216i
$263$	−13.4842	−	2.59887i	−0.831473	−	0.160253i	−0.244285	−	0.969704i	$-0.578553\pi$
$263$	−13.4842	−	2.59887i	−0.831473	−	0.160253i	−0.587189	+	0.809450i	$0.699765\pi$
$264$		0			0
$265$	−8.14119	+	4.19708i	−0.500109	+	0.257824i
$266$	1.50235	−	0.519967i	0.0921148	−	0.0318812i
$267$		0			0
$268$	−15.9963	−	20.3409i	−0.977129	−	1.24252i
$269$	−9.11016	+	7.89400i	−0.555456	+	0.481305i	−0.886767	−	0.462216i	$-0.847054\pi$
$269$	−9.11016	+	7.89400i	−0.555456	+	0.481305i	0.331311	+	0.943522i	$0.392509\pi$
$270$		0			0
$271$	−16.1529	+	4.74293i	−0.981222	+	0.288113i	−0.732729	−	0.680521i	$-0.761754\pi$
$271$	−16.1529	+	4.74293i	−0.981222	+	0.288113i	−0.248493	+	0.968634i	$0.579935\pi$
$272$	10.5054	−	1.00314i	0.636984	−	0.0608246i
$273$		0			0
$274$	0.000308576	0	1.46993e-5i	1.86418e−5	0	8.88017e-7i
$275$	−24.6909	+	42.7659i	−1.48892	+	2.57888i
$276$		0			0
$277$	14.1883	+	24.5748i	0.852490	+	1.47656i	0.878954	+	0.476907i	$0.158242\pi$
$277$	14.1883	+	24.5748i	0.852490	+	1.47656i	−0.0264633	+	0.999650i	$0.508425\pi$
$278$	−1.14345	−	1.77924i	−0.0685795	−	0.106712i
$279$		0			0
$280$	−6.67801	+	14.6228i	−0.399087	+	0.873880i
$281$	1.33110	+	1.26920i	0.0794068	+	0.0757142i	0.728743	−	0.684787i	$-0.240105\pi$
$281$	1.33110	+	1.26920i	0.0794068	+	0.0757142i	−0.649336	+	0.760501i	$0.724953\pi$
$282$		0			0
$283$	2.38945	+	12.3977i	0.142038	+	0.736964i	0.981187	+	0.193062i	$0.0618417\pi$
$283$	2.38945	+	12.3977i	0.142038	+	0.736964i	−0.839148	+	0.543902i	$0.816946\pi$
$284$	0.435410	−	1.08760i	0.0258368	−	0.0645372i
$285$		0			0
$286$	−0.0509009	+	0.264099i	−0.00300984	+	0.0156165i
$287$	−12.4766	−	8.01822i	−0.736470	−	0.473301i
$288$		0			0
$289$	5.48392	−	6.32878i	0.322584	−	0.372281i
$290$	0.639388	+	2.63559i	0.0375461	+	0.154767i
$291$		0			0
$292$	31.4726	−	6.06584i	1.84179	−	0.354976i
$293$	−0.235876	−	0.0225234i	−0.0137800	−	0.00131583i	0.0881638	−	0.996106i	$-0.471900\pi$
$293$	−0.235876	−	0.0225234i	−0.0137800	−	0.00131583i	−0.101944	+	0.994790i	$0.532506\pi$
$294$		0			0
$295$	3.86539	+	40.4802i	0.225052	+	2.35685i
$296$	0.547031	−	3.80469i	0.0317955	−	0.221143i
$297$		0			0
$298$		−	0.730278i		−	0.0423039i
$299$	1.22108	−	0.331922i	0.0706168	−	0.0191956i
$300$		0			0
$301$	−1.25901	−	26.4299i	−0.0725683	−	1.52340i
$302$	1.51036	−	1.92058i	0.0869114	−	0.110517i
$303$		0			0
$304$	−4.05439	+	4.25212i	−0.232535	+	0.243876i
$305$	−15.6287	+	7.13739i	−0.894896	+	0.408686i
$306$		0			0
$307$	3.74628	+	26.0559i	0.213811	+	1.48709i	0.760271	+	0.649606i	$0.225066\pi$
$307$	3.74628	+	26.0559i	0.213811	+	1.48709i	−0.546460	+	0.837485i	$0.684025\pi$
$308$	27.1255	−	6.58057i	1.54562	−	0.374963i
$309$		0			0
$310$	−0.386074	−	0.748878i	−0.0219275	−	0.0425334i
$311$	−6.48438	−	12.5779i	−0.367695	−	0.713229i	0.630311	−	0.776343i	$-0.282927\pi$
$311$	−6.48438	−	12.5779i	−0.367695	−	0.713229i	−0.998006	+	0.0631134i	$0.979897\pi$
$312$		0			0
$313$	1.48671	−	0.360673i	0.0840340	−	0.0203864i	−0.193521	−	0.981096i	$-0.561991\pi$
$313$	1.48671	−	0.360673i	0.0840340	−	0.0203864i	0.277555	+	0.960710i	$0.410476\pi$
$314$	−0.165320	−	1.14982i	−0.00932952	−	0.0648883i
$315$		0			0
$316$	−3.71613	+	1.69710i	−0.209049	+	0.0954693i
$317$	−12.9503	+	13.5819i	−0.727362	+	0.762836i	−0.978751	−	0.205050i	$-0.934264\pi$
$317$	−12.9503	+	13.5819i	−0.727362	+	0.762836i	0.251389	+	0.967886i	$0.419113\pi$
$318$		0			0
$319$	5.92515	−	7.53444i	0.331745	−	0.421848i
$320$	−1.28084	−	26.8881i	−0.0716012	−	1.50309i
$321$		0			0
$322$	2.98182	+	3.58492i	0.166170	+	0.199780i
$323$		−	4.80224i		−	0.267204i
$324$		0			0
$325$	−0.476378	+	3.31328i	−0.0264247	+	0.183788i
$326$	−0.0267796	−	0.280448i	−0.00148318	−	0.0155326i
$327$		0			0
$328$	−4.09408	−	0.390937i	−0.226058	−	0.0215859i
$329$	20.0308	−	3.86063i	1.10434	−	0.212843i
$330$		0			0
$331$	−4.48375	−	18.4823i	−0.246449	−	1.01588i	−0.951727	−	0.306947i	$-0.900693\pi$
$331$	−4.48375	−	18.4823i	−0.246449	−	1.01588i	0.705277	−	0.708931i	$-0.250822\pi$
$332$	−15.2944	+	17.6507i	−0.839390	+	0.968708i
$333$		0			0
$334$	−3.46597	−	2.22744i	−0.189650	−	0.121880i
$335$	10.6636	−	55.3278i	0.582613	−	3.02288i
$336$		0			0
$337$	−4.09149	+	10.2200i	−0.222878	+	0.556721i	−0.997092	−	0.0762016i	$-0.975721\pi$
$337$	−4.09149	+	10.2200i	−0.222878	+	0.556721i	0.774215	+	0.632923i	$0.218145\pi$
$338$	−0.640843	−	3.32501i	−0.0348573	−	0.180857i
$339$		0			0
$340$	17.2654	+	16.4625i	0.936348	+	0.892806i
$341$	−1.23702	+	2.70869i	−0.0669882	+	0.146684i
$342$		0			0
$343$	−0.432867	−	0.673554i	−0.0233726	−	0.0363685i
$344$	−3.66873	−	6.35443i	−0.197805	−	0.342608i
$345$		0			0
$346$	2.29777	−	3.97986i	0.123529	−	0.213958i
$347$	−13.0542	+	0.621846i	−0.700784	+	0.0333824i	−0.394950	−	0.918703i	$-0.629238\pi$
$347$	−13.0542	+	0.621846i	−0.700784	+	0.0333824i	−0.305833	+	0.952085i	$0.598935\pi$
$348$		0			0
$349$	2.14597	−	0.204915i	0.114871	−	0.0109688i	−0.0374622	−	0.999298i	$-0.511927\pi$
$349$	2.14597	−	0.204915i	0.114871	−	0.0109688i	0.152333	+	0.988329i	$0.451321\pi$
$350$	−11.8353	+	3.47515i	−0.632622	+	0.185755i
$351$		0			0
$352$	8.82552	−	7.64736i	0.470402	−	0.407605i
$353$	14.6234	+	18.5951i	0.778324	+	0.989719i	0.999894	+	0.0145745i	$0.00463936\pi$
$353$	14.6234	+	18.5951i	0.778324	+	0.989719i	−0.221570	+	0.975144i	$0.571118\pi$
$354$		0			0
$355$	2.41060	−	0.834318i	0.127942	−	0.0442810i
$356$	13.9090	−	7.17061i	0.737178	−	0.380041i
$357$		0			0
$358$	−4.02617	−	0.775980i	−0.212790	−	0.0410118i
$359$	−31.0308	−	9.11147i	−1.63774	−	0.480885i	−0.672037	−	0.740518i	$-0.734580\pi$
$359$	−31.0308	−	9.11147i	−1.63774	−	0.480885i	−0.965707	+	0.259633i	$0.916398\pi$
$360$		0			0
$361$	−10.6916	−	12.3387i	−0.562714	−	0.649406i
$362$	−0.445138	+	0.625109i	−0.0233959	+	0.0328550i
$363$		0			0
$364$	1.54121	−	1.09749i	0.0807812	−	0.0575240i
$365$	54.8591	+	43.1416i	2.87145	+	2.25814i
$366$		0			0
$367$	−11.6368	+	6.71851i	−0.607436	+	0.350703i	−0.771961	−	0.635670i	$-0.780724\pi$
$367$	−11.6368	+	6.71851i	−0.607436	+	0.350703i	0.164525	+	0.986373i	$0.447391\pi$
$368$	−15.8655	−	6.72626i	−0.827048	−	0.350631i
$369$		0			0
$370$	3.45908	−	2.22301i	0.179829	−	0.115569i
$371$	3.00530	+	7.50687i	0.156027	+	0.389737i
$372$		0			0
$373$	−26.1186	−	6.33630i	−1.35237	−	0.328081i	−0.506853	−	0.862032i	$-0.669191\pi$
$373$	−26.1186	−	6.33630i	−1.35237	−	0.328081i	−0.845515	+	0.533951i	$0.820707\pi$
$374$	−0.284582	+	2.98028i	−0.0147154	+	0.154106i
$375$		0			0
$376$	4.44661	−	3.49685i	0.229316	−	0.180336i
$377$	0.183050	−	0.623412i	0.00942757	−	0.0321074i
$378$		0			0
$379$	−10.4054	+	16.1911i	−0.534487	+	0.831679i	−0.998534	−	0.0541323i	$-0.982761\pi$
$379$	−10.4054	+	16.1911i	−0.534487	+	0.831679i	0.464046	+	0.885811i	$0.346397\pi$
$380$	−13.2663	−	0.631950i	−0.680545	−	0.0324184i
$381$		0			0
$382$	−2.65275	−	2.78213i	−0.135727	−	0.142346i
$383$	−17.6050	−	7.04799i	−0.899575	−	0.360135i	−0.124659	−	0.992200i	$-0.539784\pi$
$383$	−17.6050	−	7.04799i	−0.899575	−	0.360135i	−0.774916	+	0.632064i	$0.782208\pi$
$384$		0			0
$385$	49.5075	+	35.2542i	2.52314	+	1.79672i
$386$	0.891656	+	3.03670i	0.0453841	+	0.154564i
$387$		0			0
$388$	11.5559	+	1.66148i	0.586660	+	0.0843490i
$389$	30.9734	+	15.9679i	1.57041	+	0.809604i	0.999931	−	0.0117064i	$-0.00372635\pi$
$389$	30.9734	+	15.9679i	1.57041	+	0.809604i	0.570481	+	0.821311i	$0.306757\pi$
$390$		0			0
$391$	13.1793	−	4.96996i	0.666505	−	0.251341i
$392$	6.04908	+	3.49244i	0.305525	+	0.176395i
$393$		0			0
$394$	0.998976	−	0.399930i	0.0503277	−	0.0201482i
$395$	−8.09161	−	3.69532i	−0.407133	−	0.185932i
$396$		0			0
$397$	10.4790	+	22.9457i	0.525924	+	1.15161i	0.967148	+	0.254215i	$0.0818172\pi$
$397$	10.4790	+	22.9457i	0.525924	+	1.15161i	−0.441224	+	0.897397i	$0.645456\pi$
$398$	1.41981	−	4.10228i	0.0711688	−	0.205629i
$399$		0			0
$400$	32.9917	−	31.4575i	1.64958	−	1.57287i
$401$	−9.35019	−	27.0156i	−0.466926	−	1.34909i	−0.895288	−	0.445487i	$-0.853031\pi$
$401$	−9.35019	−	27.0156i	−0.466926	−	1.34909i	0.428362	−	0.903607i	$-0.359091\pi$
$402$		0			0
$403$	−0.00960437	+	0.201621i	−0.000478428	+	0.0100434i
$404$	−1.04343	−	0.904141i	−0.0519128	−	0.0449827i
$405$		0			0
$406$	2.36987	−	0.340736i	0.117615	−	0.0169105i
$407$	−13.7331	−	4.75308i	−0.680725	−	0.235601i
$408$		0			0
$409$	7.05326	−	29.0739i	0.348761	−	1.43761i	−0.479634	−	0.877469i	$-0.659231\pi$
$409$	7.05326	−	29.0739i	0.348761	−	1.43761i	0.828395	−	0.560144i	$-0.189254\pi$
$410$	−2.55193	−	3.58369i	−0.126031	−	0.176986i
$411$		0			0
$412$	−14.3543	+	27.8434i	−0.707184	+	1.37175i
$413$	35.8993			1.76649
$414$		0			0
$415$	−50.8544			−2.49634
$416$	0.362724	−	0.703587i	0.0177840	−	0.0344962i
$417$		0			0
$418$	−0.966810	−	1.35770i	−0.0472882	−	0.0664070i
$419$	3.06537	−	12.6356i	0.149753	−	0.617292i	−0.846620	−	0.532198i	$-0.821366\pi$
$419$	3.06537	−	12.6356i	0.149753	−	0.617292i	0.996373	−	0.0850932i	$-0.0271188\pi$
$420$		0			0
$421$	3.96346	+	1.37177i	0.193167	+	0.0668557i	0.421939	−	0.906624i	$-0.361350\pi$
$421$	3.96346	+	1.37177i	0.193167	+	0.0668557i	−0.228772	+	0.973480i	$0.573471\pi$
$422$	−2.67792	+	0.385027i	−0.130359	+	0.0187428i
$423$		0			0
$424$	1.69463	+	1.46840i	0.0822984	+	0.0713120i
$425$	−1.77290	+	37.2177i	−0.0859982	+	1.80532i
$426$		0			0
$427$	4.96098	+	14.3338i	0.240078	+	0.693661i
$428$	−16.5217	+	15.7534i	−0.798606	+	0.761469i
$429$		0			0
$430$	2.56718	−	7.41737i	0.123800	−	0.357697i
$431$	8.23138	+	18.0242i	0.396491	+	0.868195i	0.997614	+	0.0690383i	$0.0219931\pi$
$431$	8.23138	+	18.0242i	0.396491	+	0.868195i	−0.601123	+	0.799157i	$0.705280\pi$
$432$		0			0
$433$	−2.39698	−	1.09467i	−0.115192	−	0.0526063i	0.356986	−	0.934110i	$-0.383805\pi$
$433$	−2.39698	−	1.09467i	−0.115192	−	0.0526063i	−0.472177	+	0.881504i	$0.656532\pi$
$434$	−0.690529	+	0.276446i	−0.0331465	+	0.0132698i
$435$		0			0
$436$	−33.1948	−	19.1650i	−1.58974	−	0.917839i
$437$	−3.73320	+	6.89599i	−0.178583	+	0.329880i
$438$		0			0
$439$	−5.25974	−	2.71159i	−0.251034	−	0.129417i	0.328118	−	0.944637i	$-0.393586\pi$
$439$	−5.25974	−	2.71159i	−0.251034	−	0.129417i	−0.579151	+	0.815220i	$0.696616\pi$
$440$	16.6822	+	2.39854i	0.795295	+	0.114346i
$441$		0			0
$442$	0.0571740	+	0.194717i	0.00271949	+	0.00926173i
$443$	−7.76475	−	5.52925i	−0.368914	−	0.262703i	0.380532	−	0.924768i	$-0.375741\pi$
$443$	−7.76475	−	5.52925i	−0.368914	−	0.262703i	−0.749446	+	0.662065i	$0.769680\pi$
$444$		0			0
$445$	31.6330	+	12.6639i	1.49955	+	0.600328i
$446$	−3.24009	−	3.39811i	−0.153423	−	0.160905i
$447$		0			0
$448$	−23.7374	−	1.13075i	−1.12149	−	0.0534230i
$449$	7.65255	−	11.9076i	0.361146	−	0.561954i	−0.612370	−	0.790571i	$-0.709784\pi$
$449$	7.65255	−	11.9076i	0.361146	−	0.561954i	0.973517	+	0.228617i	$0.0734202\pi$
$450$		0			0
$451$	−4.38065	+	14.9191i	−0.206277	+	0.702514i
$452$	0.461901	−	0.363243i	0.0217260	−	0.0170855i
$453$		0			0
$454$	−0.473208	+	4.95566i	−0.0222088	+	0.232581i
$455$	4.00365	+	0.971274i	0.187694	+	0.0455340i
$456$		0			0
$457$	12.7449	+	31.8353i	0.596182	+	1.48919i	0.852568	+	0.522617i	$0.175044\pi$
$457$	12.7449	+	31.8353i	0.596182	+	1.48919i	−0.256386	+	0.966575i	$0.582532\pi$
$458$	3.56121	−	2.28865i	0.166404	−	0.106942i
$459$		0			0
$460$	−11.9953	−	37.0620i	−0.559282	−	1.72803i
$461$	−23.9595	+	13.8330i	−1.11590	+	0.644267i	−0.940352	−	0.340203i	$-0.889504\pi$
$461$	−23.9595	+	13.8330i	−1.11590	+	0.644267i	−0.175551	+	0.984470i	$0.556171\pi$
$462$		0			0
$463$	−0.147261	−	0.115807i	−0.00684378	−	0.00538201i	0.614731	−	0.788737i	$-0.289264\pi$
$463$	−0.147261	−	0.115807i	−0.00684378	−	0.00538201i	−0.621575	+	0.783355i	$0.713507\pi$
$464$	−7.20757	+	5.13249i	−0.334603	+	0.238270i
$465$		0			0
$466$	−1.92879	+	2.70861i	−0.0893494	+	0.125474i
$467$	18.8588	+	21.7643i	0.872683	+	1.00713i	0.999884	+	0.0152530i	$0.00485537\pi$
$467$	18.8588	+	21.7643i	0.872683	+	1.00713i	−0.127201	+	0.991877i	$0.540599\pi$
$468$		0			0
$469$	−47.7285	−	14.0143i	−2.20390	−	0.647122i
$470$	5.94194	+	1.14522i	0.274081	+	0.0528248i
$471$		0			0
$472$	8.84841	−	4.56167i	0.407281	−	0.209968i
$473$	−26.2152	+	9.07317i	−1.20538	+	0.417185i
$474$		0			0
$475$	−12.8229	−	16.3056i	−0.588354	−	0.748153i
$476$	15.9165	−	13.7917i	0.729532	−	0.632143i
$477$		0			0
$478$	−1.33454	+	0.391856i	−0.0610404	+	0.0179231i
$479$	13.9208	−	1.32927i	0.636056	−	0.0607360i	0.227954	−	0.973672i	$-0.426797\pi$
$479$	13.9208	−	1.32927i	0.636056	−	0.0607360i	0.408103	+	0.912936i	$0.366190\pi$
$480$		0			0
$481$	−0.983962	+	0.0468719i	−0.0448648	+	0.00213718i
$482$	−0.761465	+	1.31890i	−0.0346838	+	0.0600741i
$483$		0			0
$484$	−4.00900	−	6.94379i	−0.182227	−	0.315627i
$485$	13.7436	+	21.3854i	0.624062	+	0.971060i
$486$		0			0
$487$	5.80138	−	12.7033i	0.262886	−	0.575639i	−0.731454	−	0.681891i	$-0.761158\pi$
$487$	5.80138	−	12.7033i	0.262886	−	0.575639i	0.994339	+	0.106252i	$0.0338850\pi$
$488$	3.04415	+	2.90259i	0.137802	+	0.131394i
$489$		0			0
$490$	1.41406	+	7.33687i	0.0638809	+	0.331446i
$491$	−5.00205	+	12.4945i	−0.225739	+	0.563869i	−0.997392	−	0.0721748i	$-0.977006\pi$
$491$	−5.00205	+	12.4945i	−0.225739	+	0.563869i	0.771653	+	0.636044i	$0.219430\pi$
$492$		0			0
$493$	1.36871	−	7.10156i	0.0616438	−	0.319838i
$494$	−0.0950455	−	0.0610820i	−0.00427630	−	0.00274821i
$495$		0			0
$496$	1.80011	−	2.07744i	0.0808275	−	0.0932799i
$497$	−0.530926	−	2.18851i	−0.0238153	−	0.0981680i
$498$		0			0
$499$	15.6917	−	3.02432i	0.702456	−	0.135387i	0.174498	−	0.984658i	$-0.444170\pi$
$499$	15.6917	−	3.02432i	0.702456	−	0.135387i	0.527958	+	0.849270i	$0.322958\pi$
$500$	62.1520	+	5.93479i	2.77952	+	0.265412i
$501$		0			0
$502$	0.288819	+	3.02465i	0.0128906	+	0.134997i
$503$	−1.81756	+	12.6414i	−0.0810410	+	0.563653i	0.908332	+	0.418251i	$0.137357\pi$
$503$	−1.81756	+	12.6414i	−0.0810410	+	0.563653i	−0.989373	+	0.145402i	$0.953552\pi$
$504$		0			0
$505$		−	3.00630i		−	0.133778i
$506$	2.72549	−	4.05843i	0.121163	−	0.180419i
$507$		0			0
$508$	0.115397	+	2.42248i	0.00511992	+	0.107480i
$509$	−8.77625	+	11.1599i	−0.389000	+	0.494654i	−0.940629	−	0.339435i	$-0.889764\pi$
$509$	−8.77625	+	11.1599i	−0.389000	+	0.494654i	0.551629	+	0.834090i	$0.314006\pi$
$510$		0			0
$511$	42.5175	−	44.5911i	1.88086	−	1.97259i
$512$	−16.5361	+	7.55178i	−0.730799	+	0.333745i
$513$		0			0
$514$	0.0413184	+	0.287376i	0.00182248	+	0.0126756i
$515$	−66.2869	+	16.0810i	−2.92095	+	0.708614i
$516$		0			0
$517$	−9.80013	−	19.0096i	−0.431009	−	0.836041i
$518$	−1.66336	−	3.22647i	−0.0730838	−	0.141763i
$519$		0			0
$520$	1.11023	−	0.269339i	0.0486869	−	0.0118113i
$521$	−5.63432	−	39.1875i	−0.246844	−	1.71684i	−0.616234	−	0.787563i	$-0.711343\pi$
$521$	−5.63432	−	39.1875i	−0.246844	−	1.71684i	0.369390	−	0.929274i	$-0.379567\pi$
$522$		0			0
$523$	10.2065	−	4.66115i	0.446299	−	0.203818i	−0.179572	−	0.983745i	$-0.557471\pi$
$523$	10.2065	−	4.66115i	0.446299	−	0.203818i	0.625870	+	0.779927i	$0.284744\pi$
$524$	9.36332	−	9.81997i	0.409039	−	0.428987i
$525$		0			0
$526$	−2.22304	+	2.82683i	−0.0969293	+	0.123256i
$527$	0.106908	+	2.24427i	0.00465698	+	0.0977620i
$528$		0			0
$529$	−22.7890	−	3.10857i	−0.990824	−	0.135155i
$530$			2.39866i			0.104191i
$531$		0			0
$532$	−1.66864	+	11.6057i	−0.0723448	+	0.503169i
$533$	0.100188	+	1.04922i	0.00433962	+	0.0454466i
$534$		0			0
$535$	−49.4822	−	4.72498i	−2.13930	−	0.204279i
$536$	−13.5448	+	2.61055i	−0.585048	+	0.112759i
$537$		0			0
$538$	0.744248	+	3.06783i	0.0320868	+	0.132264i
$539$	17.2935	−	19.9578i	0.744884	−	0.859642i
$540$		0			0
$541$	−20.8576	−	13.4044i	−0.896739	−	0.576299i	0.00908220	−	0.999959i	$-0.497109\pi$
$541$	−20.8576	−	13.4044i	−0.896739	−	0.576299i	−0.905822	+	0.423659i	$0.860745\pi$
$542$	−0.834354	+	4.32904i	−0.0358386	+	0.185948i
$543$		0			0
$544$	3.27481	−	8.18007i	0.140406	−	0.350718i
$545$	−15.7951	−	81.9528i	−0.676588	−	3.51047i
$546$		0			0
$547$	−21.2464	−	20.2584i	−0.908429	−	0.866185i	0.0830378	−	0.996546i	$-0.473538\pi$
$547$	−21.2464	−	20.2584i	−0.908429	−	0.866185i	−0.991467	+	0.130361i	$0.958386\pi$
$548$	−0.000946481		0.00207250i	−4.04316e−5		8.85330e-5i
$549$		0			0
$550$	6.99162	+	10.8792i	0.298124	+	0.463889i
$551$	2.01320	+	3.48697i	0.0857652	+	0.148550i
$552$		0			0
$553$	−3.92655	+	6.80099i	−0.166974	+	0.289208i
$554$	7.42282	−	0.353592i	0.315365	−	0.0150227i
$555$		0			0
$556$	15.5279	−	1.48273i	0.658528	−	0.0628818i
$557$	1.53026	−	0.449323i	0.0648390	−	0.0190384i	−0.249152	−	0.968464i	$-0.580152\pi$
$557$	1.53026	−	0.449323i	0.0648390	−	0.0190384i	0.313991	+	0.949426i	$0.398334\pi$
$558$		0			0
$559$	−1.42113	+	1.23141i	−0.0601073	+	0.0520832i
$560$	−34.6815	−	44.1011i	−1.46556	−	1.86361i
$561$		0			0
$562$	0.455162	−	0.157533i	0.0191998	−	0.00664513i
$563$	19.1445	−	9.86969i	0.806846	−	0.415958i	−0.00488607	−	0.999988i	$-0.501555\pi$
$563$	19.1445	−	9.86969i	0.806846	−	0.415958i	0.811732	+	0.584030i	$0.198525\pi$
$564$		0			0
$565$	1.25638	+	0.242148i	0.0528563	+	0.0101872i
$566$	3.17251	+	0.931533i	0.133351	+	0.0391553i
$567$		0			0
$568$	−0.408952	−	0.471956i	−0.0171593	−	0.0198028i
$569$	17.6640	−	24.8057i	0.740515	−	1.03991i	−0.256784	−	0.966469i	$-0.582663\pi$
$569$	17.6640	−	24.8057i	0.740515	−	1.03991i	0.997300	−	0.0734396i	$-0.0233976\pi$
$570$		0			0
$571$	−25.5046	+	18.1617i	−1.06733	+	0.760045i	−0.971901	−	0.235390i	$-0.924363\pi$
$571$	−25.5046	+	18.1617i	−1.06733	+	0.760045i	−0.0954334	+	0.995436i	$0.530424\pi$
$572$	−1.55924	−	1.22620i	−0.0651952	−	0.0512701i
$573$		0			0
$574$	−3.36358	+	1.94196i	−0.140393	+	0.0810559i
$575$	31.4785	−	52.0662i	1.31274	−	2.17131i
$576$		0			0
$577$	26.1902	−	16.8314i	1.09031	−	0.700701i	0.133395	−	0.991063i	$-0.457412\pi$
$577$	26.1902	−	16.8314i	1.09031	−	0.700701i	0.956917	+	0.290362i	$0.0937758\pi$
$578$	−0.815066	−	2.03594i	−0.0339023	−	0.0846838i
$579$		0			0
$580$	−19.4381	−	4.71562i	−0.807122	−	0.195806i
$581$	−4.26757	+	44.6920i	−0.177048	+	1.85414i
$582$		0			0
$583$	6.66382	−	5.24049i	0.275987	−	0.217039i
$584$	4.81353	−	16.3934i	0.199185	−	0.678363i
$585$		0			0
$586$	−0.0335478	+	0.0522014i	−0.00138585	+	0.00215642i
$587$	22.5514	+	1.07426i	0.930796	+	0.0443393i	0.507499	−	0.861652i	$-0.330570\pi$
$587$	22.5514	+	1.07426i	0.930796	+	0.0443393i	0.423296	+	0.905991i	$0.360873\pi$
$588$		0			0
$589$	−0.863196	−	0.905294i	−0.0355674	−	0.0373020i
$590$	9.88634	+	3.95789i	0.407014	+	0.162944i
$591$		0			0
$592$	10.9276	+	7.78153i	0.449123	+	0.319819i
$593$	−0.429753	−	1.46360i	−0.0176478	−	0.0601030i	0.950198	−	0.311646i	$-0.100880\pi$
$593$	−0.429753	−	1.46360i	−0.0176478	−	0.0601030i	−0.967846	+	0.251543i	$0.919062\pi$
$594$		0			0
$595$	45.3911	+	6.52626i	1.86085	+	0.267551i
$596$	4.78724	+	2.46799i	0.196093	+	0.101093i
$597$		0			0
$598$	0.0692688	−	0.324059i	0.00283261	−	0.0132517i
$599$	−24.7668	−	14.2991i	−1.01195	−	0.584247i	−0.100185	−	0.994969i	$-0.531943\pi$
$599$	−24.7668	−	14.2991i	−1.01195	−	0.584247i	−0.911761	+	0.410722i	$0.865277\pi$
$600$		0			0
$601$	8.90427	−	3.56473i	0.363213	−	0.145408i	−0.182876	−	0.983136i	$-0.558541\pi$
$601$	8.90427	−	3.56473i	0.363213	−	0.145408i	0.546088	+	0.837728i	$0.316116\pi$
$602$	−6.30312	−	2.87854i	−0.256896	−	0.117320i
$603$		0			0
$604$	7.48578	+	16.3916i	0.304592	+	0.666964i
$605$	5.71016	−	16.4984i	0.232151	−	0.670757i
$606$		0			0
$607$	−30.4086	+	28.9945i	−1.23425	+	1.17685i	−0.256617	+	0.966513i	$0.582608\pi$
$607$	−30.4086	+	28.9945i	−1.23425	+	1.17685i	−0.977629	+	0.210337i	$0.932544\pi$
$608$	1.60442	+	4.63567i	0.0650678	+	0.188001i
$609$		0			0
$610$	−0.214092	+	4.49434i	−0.00866833	+	0.181971i
$611$	−1.09563	−	0.949368i	−0.0443244	−	0.0384073i
$612$		0			0
$613$	−14.7166	+	2.11593i	−0.594399	+	0.0854617i	−0.432948	−	0.901419i	$-0.642527\pi$
$613$	−14.7166	+	2.11593i	−0.594399	+	0.0854617i	−0.161451	+	0.986881i	$0.551618\pi$
$614$	6.51454	+	2.25470i	0.262905	+	0.0909924i
$615$		0			0
$616$	3.50782	−	14.4595i	0.141334	−	0.582588i
$617$	15.0749	+	21.1697i	0.606892	+	0.852261i	0.997670	−	0.0682241i	$-0.0217333\pi$
$617$	15.0749	+	21.1697i	0.606892	+	0.852261i	−0.390778	+	0.920485i	$0.627794\pi$
$618$		0			0
$619$	−6.85424	+	13.2954i	−0.275495	+	0.534386i	−0.985472	−	0.169839i	$-0.945675\pi$
$619$	−6.85424	+	13.2954i	−0.275495	+	0.534386i	0.709977	+	0.704225i	$0.248705\pi$
$620$	6.21391			0.249557
$621$		0			0
$622$	−3.70586			−0.148592
$623$	13.7839	−	26.7371i	0.552241	−	1.07120i
$624$		0			0
$625$	42.0626	+	59.0687i	1.68251	+	2.36275i
$626$	0.0944529	−	0.389340i	0.00377510	−	0.0155612i
$627$		0			0
$628$	8.09620	+	2.80212i	0.323074	+	0.111817i
$629$	−10.8535	+	1.56049i	−0.432756	+	0.0622209i
$630$		0			0
$631$	1.81259	+	1.57062i	0.0721583	+	0.0625255i	0.690193	−	0.723625i	$-0.257526\pi$
$631$	1.81259	+	1.57062i	0.0721583	+	0.0625255i	−0.618035	+	0.786151i	$0.712071\pi$
$632$	−0.103619	+	2.17524i	−0.00412176	+	0.0865264i
$633$		0			0
$634$	1.60739	+	4.64425i	0.0638376	+	0.184447i
$635$	−3.82187	+	3.64415i	−0.151666	+	0.144614i
$636$		0			0
$637$	0.585472	−	1.69161i	0.0231972	−	0.0670240i
$638$	−1.04276	−	2.28332i	−0.0412831	−	0.0903975i
$639$		0			0
$640$	−29.3661	−	13.4111i	−1.16080	−	0.530119i
$641$	1.13136	−	0.452929i	0.0446861	−	0.0178896i	−0.349212	−	0.937044i	$-0.613551\pi$
$641$	1.13136	−	0.452929i	0.0446861	−	0.0178896i	0.393898	+	0.919154i	$0.371126\pi$
$642$		0			0
$643$	−14.1568	−	8.17341i	−0.558288	−	0.322328i	0.194170	−	0.980968i	$-0.437799\pi$
$643$	−14.1568	−	8.17341i	−0.558288	−	0.322328i	−0.752458	+	0.658640i	$0.771132\pi$
$644$	−33.5775	+	7.43157i	−1.32314	+	0.292845i
$645$		0			0
$646$	−1.11781	−	0.576269i	−0.0439795	−	0.0226730i
$647$	−15.7972	−	2.27130i	−0.621053	−	0.0892939i	−0.175396	−	0.984498i	$-0.556121\pi$
$647$	−15.7972	−	2.27130i	−0.621053	−	0.0892939i	−0.445657	+	0.895204i	$0.647030\pi$
$648$		0			0
$649$	−10.6037	−	36.1128i	−0.416230	−	1.41755i
$650$	0.714060	+	0.508480i	0.0280077	+	0.0199442i
$651$		0			0
$652$	1.92894	+	0.772231i	0.0755431	+	0.0302429i
$653$	−21.3562	−	22.3977i	−0.835732	−	0.876490i	0.158096	−	0.987424i	$-0.449464\pi$
$653$	−21.3562	−	22.3977i	−0.835732	−	0.876490i	−0.993828	+	0.110934i	$0.964616\pi$
$654$		0			0
$655$	29.5110	+	1.40578i	1.15309	+	0.0549284i
$656$	7.76012	−	12.0750i	0.302982	−	0.471449i
$657$		0			0
$658$	1.50507	−	5.12581i	0.0586739	−	0.199825i
$659$	6.62215	−	5.20772i	0.257962	−	0.202864i	−0.480799	−	0.876831i	$-0.659653\pi$
$659$	6.62215	−	5.20772i	0.257962	−	0.202864i	0.738762	+	0.673967i	$0.235411\pi$
$660$		0			0
$661$	1.08578	−	11.3709i	0.0422321	−	0.442275i	−0.949483	−	0.313818i	$-0.898392\pi$
$661$	1.08578	−	11.3709i	0.0422321	−	0.442275i	0.991715	−	0.128456i	$-0.0410023\pi$
$662$	−4.84013	−	1.17420i	−0.188117	−	0.0456367i
$663$		0			0
$664$	4.62708	+	11.5579i	0.179566	+	0.448533i
$665$	−21.4775	+	13.8028i	−0.832863	+	0.535249i
$666$		0			0
$667$	−7.48613	+	9.13379i	−0.289864	+	0.353662i
$668$	26.3150	−	15.1930i	1.01816	−	0.587834i
$669$		0			0
$670$	−11.5989	−	9.12148i	−0.448105	−	0.352394i
$671$	12.9537	−	9.22428i	0.500072	−	0.356099i
$672$		0			0
$673$	10.8534	−	15.2415i	0.418370	−	0.587518i	−0.550578	−	0.834784i	$-0.685593\pi$
$673$	10.8534	−	15.2415i	0.418370	−	0.587518i	0.968948	+	0.247266i	$0.0795321\pi$
$674$	1.88792	+	2.17877i	0.0727199	+	0.0839232i
$675$		0			0
$676$	23.9624	+	7.03599i	0.921629	+	0.270615i
$677$	−42.4299	−	8.17769i	−1.63071	−	0.314294i	−0.709901	−	0.704301i	$-0.751261\pi$
$677$	−42.4299	−	8.17769i	−1.63071	−	0.314294i	−0.920812	+	0.390007i	$0.872473\pi$
$678$		0			0
$679$	19.9473	−	10.2835i	0.765506	−	0.394646i
$680$	12.0172	−	4.15920i	0.460839	−	0.159498i
$681$		0			0
$682$	0.482053	+	0.612980i	0.0184588	+	0.0234722i
$683$	21.8205	−	18.9076i	0.834940	−	0.723479i	−0.128412	−	0.991721i	$-0.540988\pi$
$683$	21.8205	−	18.9076i	0.834940	−	0.723479i	0.963352	+	0.268241i	$0.0864425\pi$
$684$		0			0
$685$	−0.00476010	+	0.00139769i	−0.000181874	+	5.34030e-5i
$686$	−0.208726	+	0.0199309i	−0.00796919	+	0.000760966i
$687$		0			0
$688$	25.5792	−	1.21849i	0.975197	−	0.0464544i
$689$	0.287326	−	0.497664i	0.0109463	−	0.0189595i
$690$		0			0
$691$	7.76050	+	13.4416i	0.295223	+	0.511342i	0.975037	−	0.222043i	$-0.0712726\pi$
$691$	7.76050	+	13.4416i	0.295223	+	0.511342i	−0.679813	+	0.733385i	$0.737939\pi$
$692$	18.3240	+	28.5127i	0.696574	+	1.08389i
$693$		0			0
$694$	−1.42175	+	3.11321i	−0.0539691	+	0.118176i
$695$	24.5814	+	23.4383i	0.932425	+	0.889065i
$696$		0			0
$697$	2.22032	+	11.5201i	0.0841005	+	0.436355i
$698$	0.209819	−	0.524102i	0.00794175	−	0.0198375i
$699$		0			0
$700$	17.2167	−	89.3288i	0.650730	−	3.37631i
$701$	−9.56055	−	6.14419i	−0.361097	−	0.232063i	0.347494	−	0.937682i	$-0.387033\pi$
$701$	−9.56055	−	6.14419i	−0.361097	−	0.232063i	−0.708591	+	0.705619i	$0.750669\pi$
$702$		0			0
$703$	3.99764	−	4.61352i	0.150774	−	0.174002i
$704$	5.87389	+	24.2125i	0.221381	+	0.912544i
$705$		0			0
$706$	6.08315	−	1.17243i	0.228943	−	0.0441251i
$707$	−2.64200	−	0.252280i	−0.0993627	−	0.00948798i
$708$		0			0
$709$	−1.43041	−	14.9799i	−0.0537202	−	0.562584i	−0.981763	−	0.190110i	$-0.939116\pi$
$709$	−1.43041	−	14.9799i	−0.0537202	−	0.562584i	0.928043	−	0.372474i	$-0.121490\pi$
$710$	0.0950704	−	0.661229i	0.00356793	−	0.0248155i
$711$		0			0
$712$		−	8.34161i		−	0.312615i
$713$	1.59115	−	3.30587i	0.0595890	−	0.123806i
$714$		0			0
$715$	−0.205517	−	4.31434i	−0.00768591	−	0.161347i
$716$	18.6933	−	23.7705i	0.698603	−	0.888346i
$717$		0			0
$718$	−5.84456	+	6.12960i	−0.218117	+	0.228755i
$719$	−16.0632	+	7.33582i	−0.599057	+	0.273580i	−0.691776	−	0.722112i	$-0.743171\pi$
$719$	−16.0632	+	7.33582i	−0.599057	+	0.273580i	0.0927192	+	0.995692i	$0.470444\pi$
$720$		0			0
$721$	8.56974	+	59.6039i	0.319154	+	2.21976i
$722$	−4.15504	+	1.00800i	−0.154635	+	0.0375140i
$723$		0			0
$724$	−2.59346	−	5.03061i	−0.0963851	−	0.186961i
$725$	−14.3151	−	27.7675i	−0.531651	−	1.03126i
$726$		0			0
$727$	−38.1723	+	9.26051i	−1.41573	+	0.343453i	−0.869398	−	0.494113i	$-0.835493\pi$
$727$	−38.1723	+	9.26051i	−1.41573	+	0.343453i	−0.546336	+	0.837566i	$0.683978\pi$
$728$	−0.143534	−	0.998299i	−0.00531971	−	0.0369994i
$729$		0			0
$730$	16.6251	−	7.59242i	0.615322	−	0.281008i
$731$	−14.4442	+	15.1487i	−0.534239	+	0.560294i
$732$		0			0
$733$	−11.6877	+	14.8621i	−0.431695	+	0.548945i	−0.952424	−	0.304778i	$-0.901418\pi$
$733$	−11.6877	+	14.8621i	−0.431695	+	0.548945i	0.520729	+	0.853722i	$0.325660\pi$
$734$	0.167435	+	3.51489i	0.00618014	+	0.129737i
$735$		0			0
$736$	−11.0617	+	9.20075i	−0.407739	+	0.339144i
$737$			52.1517i			1.92103i
$738$		0			0
$739$	4.87676	−	33.9186i	0.179394	−	1.24772i	−0.678774	−	0.734347i	$-0.737488\pi$
$739$	4.87676	−	33.9186i	0.179394	−	1.24772i	0.858169	−	0.513368i	$-0.171602\pi$
$740$	2.88263	+	30.1882i	0.105967	+	1.10974i
$741$		0			0
$742$	2.10799	+	0.201289i	0.0773869	+	0.00738955i
$743$	45.1231	−	8.69677i	1.65541	−	0.319054i	0.725884	−	0.687817i	$-0.241431\pi$
$743$	45.1231	−	8.69677i	1.65541	−	0.319054i	0.929523	+	0.368764i	$0.120219\pi$
$744$		0			0
$745$	2.76488	+	11.3970i	0.101297	+	0.417553i
$746$	−4.60912	+	5.31921i	−0.168752	+	0.194750i
$747$		0			0
$748$	−18.5750	−	11.9374i	−0.679170	−	0.436476i
$749$	−8.30483	+	43.0896i	−0.303452	+	1.57446i
$750$		0			0
$751$	−11.1577	+	27.8707i	−0.407152	+	1.01702i	0.573140	+	0.819458i	$0.305725\pi$
$751$	−11.1577	+	27.8707i	−0.407152	+	1.01702i	−0.980291	+	0.197558i	$0.936699\pi$
$752$	3.73636	+	19.3861i	0.136251	+	0.706937i
$753$		0			0
$754$	−0.123144	−	0.117418i	−0.00448465	−	0.00427610i
$755$	−16.2998	+	35.6915i	−0.593210	+	1.29895i
$756$		0			0
$757$	−5.75878	−	8.96084i	−0.209306	−	0.325687i	0.720689	−	0.693259i	$-0.243826\pi$
$757$	−5.75878	−	8.96084i	−0.209306	−	0.325687i	−0.929995	+	0.367572i	$0.880189\pi$
$758$	2.52011	+	4.36496i	0.0915346	+	0.158543i
$759$		0			0
$760$	−3.53985	+	6.13121i	−0.128404	+	0.222402i
$761$	−33.5809	+	1.59966i	−1.21731	+	0.0579875i	−0.646382	−	0.763014i	$-0.723719\pi$
$761$	−33.5809	+	1.59966i	−1.21731	+	0.0579875i	−0.570926	+	0.821002i	$0.693416\pi$
$762$		0			0
$763$	−73.3475	+	7.00384i	−2.65536	+	0.253556i
$764$	27.2029	−	7.98749i	0.984166	−	0.288977i
$765$		0			0
$766$	−3.75315	+	3.25212i	−0.135607	+	0.117504i
$767$	−1.57708	−	2.00542i	−0.0569450	−	0.0724114i
$768$		0			0
$769$	18.7545	−	6.49101i	0.676306	−	0.234072i	0.0327416	−	0.999464i	$-0.489576\pi$
$769$	18.7545	−	6.49101i	0.676306	−	0.234072i	0.643564	+	0.765392i	$0.277455\pi$
$770$	14.1469	−	7.29326i	0.509820	−	0.262831i
$771$		0			0
$772$	−22.9200	−	4.41747i	−0.824910	−	0.158988i
$773$	−3.36480	−	0.987993i	−0.121023	−	0.0355357i	0.220660	−	0.975351i	$-0.429179\pi$
$773$	−3.36480	−	0.987993i	−0.121023	−	0.0355357i	−0.341683	+	0.939815i	$0.610997\pi$
$774$		0			0
$775$	6.35562	+	7.33478i	0.228301	+	0.263473i
$776$	3.60986	−	5.06934i	0.129587	−	0.181979i
$777$		0			0
$778$	7.43362	−	5.29346i	0.266508	−	0.189780i
$779$	−5.13418	−	4.03757i	−0.183951	−	0.144661i
$780$		0			0
$781$	−2.04470	+	1.18051i	−0.0731650	+	0.0422419i
$782$	0.424669	−	3.66411i	0.0151861	−	0.131028i
$783$		0			0
$784$	−20.5078	+	13.1795i	−0.732421	+	0.470698i
$785$	6.93333	+	17.3186i	0.247461	+	0.618129i
$786$		0			0
$787$	−35.1283	−	8.52204i	−1.25219	−	0.303778i	−0.445784	−	0.895141i	$-0.647075\pi$
$787$	−35.1283	−	8.52204i	−1.25219	−	0.303778i	−0.806406	+	0.591363i	$0.798590\pi$
$788$	−0.754379	+	7.90021i	−0.0268736	+	0.281433i
$789$		0			0
$790$	−1.83115	+	1.44003i	−0.0651492	+	0.0512339i
$791$	0.318237	−	1.08382i	0.0113152	−	0.0385360i
$792$		0			0
$793$	0.582780	−	0.906823i	0.0206951	−	0.0322022i
$794$	6.59850	+	0.314325i	0.234172	+	0.0111550i
$795$		0			0
$796$	22.0936	+	23.1711i	0.783088	+	0.821279i
$797$	−26.9123	−	10.7741i	−0.953283	−	0.381637i	−0.157704	−	0.987486i	$-0.550409\pi$
$797$	−26.9123	−	10.7741i	−0.953283	−	0.381637i	−0.795579	+	0.605850i	$0.792833\pi$
$798$		0			0
$799$	−13.1449	−	9.36045i	−0.465034	−	0.331149i
$800$	−10.7230	−	36.5191i	−0.379115	−	1.29115i
$801$		0			0
$802$	−7.41038	−	1.06545i	−0.261670	−	0.0376224i
$803$	−57.4147	−	29.5993i	−2.02612	−	1.04454i
$804$		0			0
$805$	−60.1080	−	44.6582i	−2.11853	−	1.57399i
$806$	0.0457783	+	0.0264301i	0.00161247	+	0.000930960i
$807$		0			0
$808$	−0.683253	+	0.273533i	−0.0240368	+	0.00962287i
$809$	31.5971	+	14.4299i	1.11089	+	0.507328i	0.884422	−	0.466689i	$-0.154553\pi$
$809$	31.5971	+	14.4299i	1.11089	+	0.507328i	0.226473	+	0.974017i	$0.427281\pi$
$810$		0			0
$811$	−2.55975	−	5.60508i	−0.0898851	−	0.196821i	0.859350	−	0.511387i	$-0.170868\pi$
$811$	−2.55975	−	5.60508i	−0.0898851	−	0.196821i	−0.949236	+	0.314566i	$0.898141\pi$
$812$	−5.77539	+	16.6869i	−0.202676	+	0.585595i
$813$		0			0
$814$	−2.75434	+	2.62626i	−0.0965395	+	0.0920502i
$815$	1.47973	+	4.27539i	0.0518325	+	0.149760i
$816$		0			0
$817$	0.554473	−	11.6398i	0.0193986	−	0.407226i
$818$	−5.92108	−	5.13064i	−0.207026	−	0.179389i
$819$		0			0
$820$	32.1167	−	4.61768i	1.12156	−	0.161256i
$821$	18.2645	+	6.32142i	0.637437	+	0.220619i	0.626623	−	0.779323i	$-0.284437\pi$
$821$	18.2645	+	6.32142i	0.637437	+	0.220619i	0.0108136	+	0.999942i	$0.496558\pi$
$822$		0			0
$823$	1.54066	−	6.35067i	0.0537039	−	0.221370i	−0.938636	−	0.344910i	$-0.887909\pi$
$823$	1.54066	−	6.35067i	0.0537039	−	0.221370i	0.992340	+	0.123540i	$0.0394246\pi$
$824$	9.68603	+	13.6021i	0.337429	+	0.473853i
$825$		0			0
$826$	4.30792	−	8.35621i	0.149892	−	0.290750i
$827$	−53.0645			−1.84523			−0.922616	−	0.385719i	$-0.873954\pi$
$827$	−53.0645			−1.84523			−0.922616	+	0.385719i	$0.873954\pi$
$828$		0			0
$829$	50.4138			1.75094			0.875472	−	0.483269i	$-0.160551\pi$
$829$	50.4138			1.75094			0.875472	+	0.483269i	$0.160551\pi$
$830$	−6.10253	+	11.8373i	−0.211822	+	0.410877i
$831$		0			0
$832$	0.979631	+	1.37570i	0.0339626	+	0.0476938i
$833$	4.69760	−	19.3638i	0.162762	−	0.670916i
$834$		0			0
$835$	62.5244	+	21.6399i	2.16375	+	0.748880i
$836$	12.1675	−	1.74943i	0.420823	−	0.0605052i
$837$		0			0
$838$	−2.57333	−	2.22980i	−0.0888941	−	0.0770271i
$839$	−0.888644	+	18.6549i	−0.0306794	+	0.644040i	0.930197	+	0.367061i	$0.119636\pi$
$839$	−0.888644	+	18.6549i	−0.0306794	+	0.644040i	−0.960876	+	0.276978i	$0.910667\pi$
$840$		0			0
$841$	−7.50169	−	21.6747i	−0.258679	−	0.747403i
$842$	0.794918	−	0.757953i	0.0273947	−	0.0261208i
$843$		0			0
$844$	6.52610	−	18.8559i	0.224638	−	0.649048i
$845$	22.5899	+	49.4650i	0.777116	+	1.70165i
$846$		0			0
$847$	−14.0200	−	6.40273i	−0.481734	−	0.220000i
$848$	−7.26523	+	2.90856i	−0.249489	+	0.0998804i
$849$		0			0
$850$	8.45034	+	4.87880i	0.289844	+	0.167342i
$851$	16.7986	+	6.19648i	0.575849	+	0.212413i
$852$		0			0
$853$	−10.8137	−	5.57487i	−0.370255	−	0.190880i	0.263049	−	0.964782i	$-0.415272\pi$
$853$	−10.8137	−	5.57487i	−0.370255	−	0.190880i	−0.633305	+	0.773902i	$0.718302\pi$
$854$	3.93177	+	0.565303i	0.134542	+	0.0193443i
$855$		0			0
$856$	3.42836	+	11.6759i	0.117179	+	0.399075i
$857$	−21.5386	−	15.3376i	−0.735746	−	0.523922i	0.149662	−	0.988737i	$-0.452181\pi$
$857$	−21.5386	−	15.3376i	−0.735746	−	0.523922i	−0.885408	+	0.464815i	$0.846121\pi$
$858$		0			0
$859$	20.8657	+	8.35338i	0.711930	+	0.285014i	0.699221	−	0.714906i	$-0.253530\pi$
$859$	20.8657	+	8.35338i	0.711930	+	0.285014i	0.0127087	+	0.999919i	$0.495955\pi$
$860$	39.9477	+	41.8959i	1.36220	+	1.42864i
$861$		0			0
$862$	5.18322	+	0.246907i	0.176541	+	0.00840969i
$863$	−23.1000	+	35.9442i	−0.786332	+	1.22356i	0.184273	+	0.982875i	$0.441007\pi$
$863$	−23.1000	+	35.9442i	−0.786332	+	1.22356i	−0.970604	+	0.240681i	$0.922629\pi$
$864$		0			0
$865$	−20.7918	+	70.8105i	−0.706944	+	2.40763i
$866$	−0.542442	+	0.426581i	−0.0184329	+	0.0144958i
$867$		0			0
$868$	0.521455	−	5.46092i	0.0176993	−	0.185356i
$869$	8.00122	+	1.94108i	0.271423	+	0.0658465i
$870$		0			0
$871$	1.31387	+	3.28188i	0.0445187	+	0.111202i
$872$	−17.1886	+	11.0465i	−0.582080	+	0.374080i
$873$		0			0
$874$	1.15718	+	1.69649i	0.0391422	+	0.0573846i
$875$	103.938	−	60.0084i	3.51374	−	2.02866i
$876$		0			0
$877$	29.1868	+	22.9528i	0.985569	+	0.775060i	0.974387	−	0.224877i	$-0.0721981\pi$
$877$	29.1868	+	22.9528i	0.985569	+	0.775060i	0.0111822	+	0.999937i	$0.496441\pi$
$878$	−1.26234	+	0.898908i	−0.0426019	+	0.0303367i
$879$		0			0
$880$	−34.1194	+	47.9139i	−1.15016	+	1.61518i
$881$	−25.1322	−	29.0041i	−0.846726	−	0.977174i	0.153213	−	0.988193i	$-0.451038\pi$
$881$	−25.1322	−	29.0041i	−0.846726	−	0.977174i	−0.999939	+	0.0110188i	$0.996493\pi$
$882$		0			0
$883$	8.16884	+	2.39859i	0.274903	+	0.0807189i	0.416278	−	0.909237i	$-0.363334\pi$
$883$	8.16884	+	2.39859i	0.274903	+	0.0807189i	−0.141375	+	0.989956i	$0.545152\pi$
$884$	−1.46966	−	0.283253i	−0.0494300	−	0.00952684i
$885$		0			0
$886$	−2.21880	+	1.14387i	−0.0745422	+	0.0384292i
$887$	8.00288	−	2.76982i	0.268710	−	0.0930016i	−0.189390	−	0.981902i	$-0.560651\pi$
$887$	8.00288	−	2.76982i	0.268710	−	0.0930016i	0.458101	+	0.888900i	$0.348530\pi$
$888$		0			0
$889$	2.88184	+	3.66456i	0.0966537	+	0.122905i
$890$	6.74372	−	5.84347i	0.226050	−	0.195873i
$891$		0			0
$892$	33.2258	−	9.75596i	1.11248	−	0.326654i
$893$	8.94331	−	0.853983i	0.299277	−	0.0285774i
$894$		0			0
$895$	65.7717	−	3.13309i	2.19850	−	0.104728i
$896$	−14.2503	+	24.6822i	−0.476068	+	0.824574i
$897$		0			0
$898$	−1.85340	−	3.21018i	−0.0618487	−	0.107125i
$899$	−1.01847	−	1.58478i	−0.0339680	−	0.0528552i
$900$		0			0
$901$	2.65722	−	5.81851i	0.0885249	−	0.193843i
$902$	2.94701	+	2.80997i	0.0981249	+	0.0935619i
$903$		0			0
$904$	−0.0592803	−	0.307575i	−0.00197163	−	0.0102298i
$905$	4.58028	−	11.4410i	0.152254	−	0.380311i
$906$		0			0
$907$	−8.51160	+	44.1624i	−0.282623	+	1.46639i	0.511843	+	0.859079i	$0.328963\pi$
$907$	−8.51160	+	44.1624i	−0.282623	+	1.46639i	−0.794466	+	0.607309i	$0.792249\pi$
$908$	−30.8869	−	19.8498i	−1.02502	−	0.658739i
$909$		0			0
$910$	0.706520	−	0.815367i	0.0234209	−	0.0270292i
$911$	8.36548	+	34.4830i	0.277161	+	1.14247i	0.924778	+	0.380506i	$0.124250\pi$
$911$	8.36548	+	34.4830i	0.277161	+	1.14247i	−0.647618	+	0.761966i	$0.724235\pi$
$912$		0			0
$913$	46.2182	−	8.90783i	1.52960	−	0.294806i
$914$	8.93962	+	0.853630i	0.295696	+	0.0282356i
$915$		0			0
$916$	2.96774	+	31.0795i	0.0980567	+	1.02690i
$917$	3.71192	−	25.8169i	0.122578	−	0.852550i
$918$		0			0
$919$		−	34.2932i		−	1.13123i	−0.824670	−	0.565614i	$-0.808639\pi$
$919$		−	34.2932i		−	1.13123i	0.824670	−	0.565614i	$-0.191361\pi$
$920$	−20.4900	−	3.36945i	−0.675535	−	0.111087i
$921$		0			0
$922$	0.344738	+	7.23695i	0.0113534	+	0.238336i
$923$	−0.0989310	+	0.125801i	−0.00325636	+	0.00414079i
$924$		0			0
$925$	−32.6852	+	34.2793i	−1.07468	+	1.12710i
$926$	−0.0446274	+	0.0203807i	−0.00146655	+	0.000669750i
$927$		0			0
$928$	1.05138	+	7.31252i	0.0345133	+	0.240045i
$929$	38.2249	−	9.27325i	1.25412	−	0.304245i	0.446945	−	0.894562i	$-0.352512\pi$
$929$	38.2249	−	9.27325i	1.25412	−	0.304245i	0.807172	+	0.590316i	$0.200997\pi$
$930$		0			0
$931$	5.08314	+	9.85991i	0.166593	+	0.323146i
$932$	−11.2375	−	21.7977i	−0.368096	−	0.714007i
$933$		0			0
$934$	7.32908	−	1.77802i	0.239815	−	0.0581785i
$935$	−6.84222	−	47.5887i	−0.223764	−	1.55632i
$936$		0			0
$937$	31.2252	−	14.2601i	1.02008	−	0.465856i	0.166072	−	0.986114i	$-0.446891\pi$
$937$	31.2252	−	14.2601i	1.02008	−	0.465856i	0.854009	+	0.520258i	$0.174164\pi$
$938$	−8.98951	+	9.42793i	−0.293518	+	0.307833i
$939$		0			0
$940$	−27.5882	+	35.0813i	−0.899828	+	1.14422i
$941$	1.02870	+	21.5950i	0.0335346	+	0.703977i	0.951561	+	0.307459i	$0.0994786\pi$
$941$	1.02870	+	21.5950i	0.0335346	+	0.703977i	−0.918027	+	0.396518i	$0.870218\pi$
$942$		0			0
$943$	5.76722	−	18.2689i	0.187806	−	0.594916i
$944$			34.7437i			1.13081i
$945$		0			0
$946$	−1.03389	+	7.19084i	−0.0336145	+	0.233794i
$947$	−0.577523	−	6.04810i	−0.0187670	−	0.196537i	−0.999993	−	0.00367664i	$-0.998830\pi$
$947$	−0.577523	−	6.04810i	−0.0187670	−	0.196537i	0.981226	−	0.192860i	$-0.0617764\pi$
$948$		0			0
$949$	−4.35877	−	0.416212i	−0.141492	−	0.0135108i
$950$	−5.33417	+	1.02808i	−0.173063	+	0.0333552i
$951$		0			0
$952$	−2.64675	−	10.9100i	−0.0857815	−	0.353596i
$953$	−30.1429	+	34.7868i	−0.976424	+	1.12685i	0.0154819	+	0.999880i	$0.495072\pi$
$953$	−30.1429	+	34.7868i	−0.976424	+	1.12685i	−0.991906	+	0.126973i	$0.959474\pi$
$954$		0			0
$955$	51.9331	+	33.3754i	1.68052	+	1.08000i
$956$	1.94135	−	10.0727i	0.0627877	−	0.325773i
$957$		0			0
$958$	1.36108	−	3.39982i	0.0439746	−	0.109843i
$959$	0.000828867		0.00430057i	2.67655e−5		0.000138873i
$960$		0			0
$961$	−22.0122	−	20.9886i	−0.710071	−	0.677051i
$962$	−0.107165	+	0.234659i	−0.00345515	+	0.00756572i
$963$		0			0
$964$	−6.07245	−	9.44891i	−0.195580	−	0.304329i
$965$	−25.4126	−	44.0160i	−0.818062	−	1.41692i
$966$		0			0
$967$	−21.3193	+	36.9261i	−0.685583	+	1.18746i	0.287670	+	0.957729i	$0.407119\pi$
$967$	−21.3193	+	36.9261i	−0.685583	+	1.18746i	−0.973253	+	0.229735i	$0.926214\pi$
$968$	−4.26922	+	0.203368i	−0.137218	+	0.00653649i
$969$		0			0
$970$	6.62706	−	0.632807i	0.212782	−	0.0203182i
$971$	−37.9374	+	11.1394i	−1.21747	+	0.357481i	−0.826508	−	0.562925i	$-0.809676\pi$
$971$	−37.9374	+	11.1394i	−1.21747	+	0.357481i	−0.390962	+	0.920407i	$0.627858\pi$
$972$		0			0
$973$	22.6609	−	19.6358i	0.726475	−	0.629494i
$974$	−2.26074	−	2.87477i	−0.0724388	−	0.0921135i
$975$		0			0
$976$	−13.8724	+	4.80129i	−0.444045	+	0.153685i
$977$	−31.0130	+	15.9883i	−0.992193	+	0.511511i	−0.876308	−	0.481752i	$-0.840001\pi$
$977$	−31.0130	+	15.9883i	−0.992193	+	0.511511i	−0.115885	+	0.993263i	$0.536970\pi$
$978$		0			0
$979$	−30.9674	−	5.96848i	−0.989723	−	0.190753i
$980$	−52.8746	−	15.5254i	−1.68902	−	0.495940i
$981$		0			0
$982$	2.30807	+	2.66366i	0.0736536	+	0.0850007i
$983$	−3.96537	+	5.56859i	−0.126476	+	0.177610i	−0.872959	−	0.487794i	$-0.837802\pi$
$983$	−3.96537	+	5.56859i	−0.126476	+	0.177610i	0.746483	+	0.665405i	$0.231741\pi$
$984$		0			0
$985$	−14.0762	+	10.0236i	−0.448505	+	0.319379i
$986$	−1.48877	−	1.17078i	−0.0474121	−	0.0372853i
$987$		0			0
$988$	0.721623	−	0.416629i	0.0229579	−	0.0132547i
$989$	32.5182	−	10.5247i	1.03402	−	0.334664i
$990$		0			0
$991$	−24.3623	+	15.6567i	−0.773895	+	0.497352i	−0.867002	−	0.498304i	$-0.833956\pi$
$991$	−24.3623	+	15.6567i	−0.773895	+	0.497352i	0.0931073	+	0.995656i	$0.470320\pi$
$992$	−0.853007	−	2.13071i	−0.0270830	−	0.0676501i
$993$		0			0
$994$	−0.573125	−	0.139039i	−0.0181784	−	0.00441004i
$995$	−6.62662	+	69.3971i	−0.210078	+	2.20004i
$996$		0			0
$997$	21.4018	−	16.8306i	0.677802	−	0.533029i	−0.218854	−	0.975758i	$-0.570232\pi$
$997$	21.4018	−	16.8306i	0.677802	−	0.533029i	0.896656	+	0.442729i	$0.145989\pi$
$998$	1.17904	−	4.01544i	0.0373218	−	0.127106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	621.2.s.a.287.11		440
3.2	odd	2		207.2.o.a.149.12	yes	440
9.2	odd	6	inner	621.2.s.a.494.11		440
9.7	even	3		207.2.o.a.11.12	✓	440
23.21	odd	22	inner	621.2.s.a.44.11		440
69.44	even	22		207.2.o.a.113.12	yes	440
207.182	even	66	inner	621.2.s.a.251.11		440
207.205	odd	66		207.2.o.a.182.12	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.12	✓	440	9.7	even	3
207.2.o.a.113.12	yes	440	69.44	even	22
207.2.o.a.149.12	yes	440	3.2	odd	2
207.2.o.a.182.12	yes	440	207.205	odd	66
621.2.s.a.44.11		440	23.21	odd	22	inner
621.2.s.a.251.11		440	207.182	even	66	inner
621.2.s.a.287.11		440	1.1	even	1	trivial
621.2.s.a.494.11		440	9.2	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.s (of order \(66\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.120000 - 0.232768i) q^{2} +(1.12033 + 1.57329i) q^{4} +(-0.991492 + 4.08698i) q^{5} +(3.50853 + 1.21431i) q^{7} +(1.01908 - 0.146521i) q^{8} +(0.832339 + 0.721226i) q^{10} +(0.185211 - 3.88807i) q^{11} +(-0.0862974 - 0.249340i) q^{13} +(0.703678 - 0.670955i) q^{14} +(-1.17523 + 3.39559i) q^{16} +(-1.22006 - 2.67157i) q^{17} +(1.48734 + 0.679244i) q^{19} +(-7.54080 + 3.01888i) q^{20} +(-0.882791 - 0.509680i) q^{22} +(-0.324837 + 4.78482i) q^{23} +(-11.2762 - 5.81329i) q^{25} +(-0.0683940 - 0.00983357i) q^{26} +(2.02026 + 6.88036i) q^{28} +(2.00588 + 1.42838i) q^{29} +(-0.710211 - 0.284326i) q^{31} +(2.07031 + 2.17128i) q^{32} +(-0.768262 - 0.0365968i) q^{34} +(-8.44156 + 13.1353i) q^{35} +(1.05184 - 3.58222i) q^{37} +(0.336587 - 0.264695i) q^{38} +(-0.411577 + 4.31023i) q^{40} +(-3.88202 - 0.941769i) q^{41} +(-2.64877 - 6.61630i) q^{43} +(6.32454 - 4.06454i) q^{44} +(1.07477 + 0.649790i) q^{46} +(4.75835 - 2.74724i) q^{47} +(5.33286 + 4.19381i) q^{49} +(-2.70629 + 1.92714i) q^{50} +(0.295602 - 0.415114i) q^{52} +(1.42625 + 1.64598i) q^{53} +(15.7068 + 4.61194i) q^{55} +(3.75339 + 0.723407i) q^{56} +(0.573187 - 0.295499i) q^{58} +(9.13745 - 3.16250i) q^{59} +(2.52544 + 3.21135i) q^{61} +(-0.151407 + 0.131195i) q^{62} +(-6.14149 + 1.80331i) q^{64} +(1.10461 - 0.105478i) q^{65} +(-13.3829 + 0.637507i) q^{67} +(2.83626 - 4.91255i) q^{68} +(2.04449 + 3.54117i) q^{70} +(-0.327930 - 0.510270i) q^{71} +(6.89379 - 15.0953i) q^{73} +(-0.707606 - 0.674701i) q^{74} +(0.597666 + 3.10099i) q^{76} +(5.37115 - 13.4165i) q^{77} +(-0.400302 + 2.07696i) q^{79} +(-12.7125 - 8.16984i) q^{80} +(-0.685057 + 0.790598i) q^{82} +(2.85086 + 11.7514i) q^{83} +(12.1283 - 2.33754i) q^{85} +(-1.85791 - 0.177409i) q^{86} +(-0.380940 - 3.98938i) q^{88} +(1.15305 - 8.01966i) q^{89} -0.979609i q^{91} +(-7.89182 + 4.84953i) q^{92} +(-0.0684651 - 1.43726i) q^{94} +(-4.25074 + 5.40526i) q^{95} +(4.17127 - 4.37470i) q^{97} +(1.61613 - 0.738060i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) \) 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Introduction

L-functions

Modular forms

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Database

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