LMFDB - Embedded newform 425.2.n.c.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.6
Character	$\chi$	$=$	425.49
Dual form			425.2.n.c.399.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44607 - 1.44607i) q^{2} +(-2.95240 + 1.22292i) q^{3} -2.18224i q^{4} +(-2.50094 + 6.03781i) q^{6} +(-0.450584 + 1.08781i) q^{7} +(-0.263530 - 0.263530i) q^{8} +(5.09981 - 5.09981i) q^{9} +O(q^{10})$	\(q+(1.44607 - 1.44607i) q^{2} +(-2.95240 + 1.22292i) q^{3} -2.18224i q^{4} +(-2.50094 + 6.03781i) q^{6} +(-0.450584 + 1.08781i) q^{7} +(-0.263530 - 0.263530i) q^{8} +(5.09981 - 5.09981i) q^{9} +(1.88376 - 4.54781i) q^{11} +(2.66871 + 6.44284i) q^{12} +2.46296 q^{13} +(0.921468 + 2.22462i) q^{14} +3.60231 q^{16} +(3.89141 - 1.36268i) q^{17} -14.7494i q^{18} +(1.44372 + 1.44372i) q^{19} -3.76267i q^{21} +(-3.85240 - 9.30051i) q^{22} +(0.109963 + 0.0455480i) q^{23} +(1.10032 + 0.455769i) q^{24} +(3.56162 - 3.56162i) q^{26} +(-5.15122 + 12.4361i) q^{27} +(2.37385 + 0.983282i) q^{28} +(-0.984309 + 0.407714i) q^{29} +(1.06989 + 2.58295i) q^{31} +(5.73626 - 5.73626i) q^{32} +15.7307i q^{33} +(3.65672 - 7.59779i) q^{34} +(-11.1290 - 11.1290i) q^{36} +(-2.13857 + 0.885823i) q^{37} +4.17544 q^{38} +(-7.27165 + 3.01202i) q^{39} +(-0.662952 - 0.274604i) q^{41} +(-5.44108 - 5.44108i) q^{42} +(-7.13881 - 7.13881i) q^{43} +(-9.92441 - 4.11082i) q^{44} +(0.224879 - 0.0931480i) q^{46} -3.39482 q^{47} +(-10.6355 + 4.40535i) q^{48} +(3.96945 + 3.96945i) q^{49} +(-9.82256 + 8.78209i) q^{51} -5.37477i q^{52} +(9.84581 - 9.84581i) q^{53} +(10.5345 + 25.4326i) q^{54} +(0.405412 - 0.167927i) q^{56} +(-6.02800 - 2.49688i) q^{57} +(-0.833797 + 2.01296i) q^{58} +(-1.07276 + 1.07276i) q^{59} +(7.46606 + 3.09254i) q^{61} +(5.28228 + 2.18799i) q^{62} +(3.24971 + 7.84549i) q^{63} -9.38544i q^{64} +(22.7476 + 22.7476i) q^{66} +4.92534i q^{67} +(-2.97370 - 8.49199i) q^{68} -0.380355 q^{69} +(2.53962 + 6.13119i) q^{71} -2.68790 q^{72} +(-1.40336 - 3.38802i) q^{73} +(-1.81155 + 4.37348i) q^{74} +(3.15054 - 3.15054i) q^{76} +(4.09834 + 4.09834i) q^{77} +(-6.15973 + 14.8709i) q^{78} +(-3.13055 + 7.55781i) q^{79} -21.3794i q^{81} +(-1.35577 + 0.561579i) q^{82} +(-4.30539 + 4.30539i) q^{83} -8.21104 q^{84} -20.6464 q^{86} +(2.40747 - 2.40747i) q^{87} +(-1.69491 + 0.702056i) q^{88} -8.46170i q^{89} +(-1.10977 + 2.67922i) q^{91} +(0.0993966 - 0.239965i) q^{92} +(-6.31751 - 6.31751i) q^{93} +(-4.90915 + 4.90915i) q^{94} +(-9.92072 + 23.9507i) q^{96} +(-1.71804 - 4.14772i) q^{97} +11.4802 q^{98} +(-13.5861 - 32.7998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} + 16 q^{41} - 24 q^{42} - 8 q^{43} - 16 q^{44} + 8 q^{46} - 64 q^{47} - 8 q^{48} - 56 q^{51} + 24 q^{53} + 32 q^{54} + 64 q^{56} + 16 q^{57} + 56 q^{58} - 32 q^{59} + 32 q^{61} - 32 q^{62} + 80 q^{63} + 96 q^{66} + 24 q^{68} - 96 q^{69} - 24 q^{71} - 24 q^{72} - 64 q^{73} + 64 q^{74} - 8 q^{76} + 24 q^{77} + 8 q^{78} - 16 q^{82} - 96 q^{83} + 64 q^{84} - 16 q^{86} + 48 q^{87} + 8 q^{88} - 24 q^{91} + 112 q^{92} - 64 q^{93} - 56 q^{94} - 168 q^{96} + 48 q^{97} + 120 q^{98} + 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	1.44607	−	1.44607i	1.02253	−	1.02253i	0.0227858	−	0.999740i	$-0.492746\pi$
$2$	1.44607	−	1.44607i	1.02253	−	1.02253i	0.999740	−	0.0227858i	$-0.00725356\pi$
$3$	−2.95240	+	1.22292i	−1.70457	+	0.706056i	−0.999994	−	0.00357297i	$-0.998863\pi$
$3$	−2.95240	+	1.22292i	−1.70457	+	0.706056i	−0.704576	+	0.709629i	$0.748863\pi$
$4$		−	2.18224i		−	1.09112i
$5$		0			0
$5$		0			0
$6$	−2.50094	+	6.03781i	−1.02101	+	2.46493i
$7$	−0.450584	+	1.08781i	−0.170305	+	0.411152i	−0.985870	−	0.167513i	$-0.946426\pi$
$7$	−0.450584	+	1.08781i	−0.170305	+	0.411152i	0.815565	+	0.578665i	$0.196426\pi$
$8$	−0.263530	−	0.263530i	−0.0931719	−	0.0931719i
$9$	5.09981	−	5.09981i	1.69994	−	1.69994i
$10$		0			0
$11$	1.88376	−	4.54781i	0.567976	−	1.37122i	−0.335281	−	0.942118i	$-0.608831\pi$
$11$	1.88376	−	4.54781i	0.567976	−	1.37122i	0.903258	−	0.429098i	$-0.141169\pi$
$12$	2.66871	+	6.44284i	0.770391	+	1.85989i
$13$	2.46296			0.683103			0.341551	−	0.939863i	$-0.389048\pi$
$13$	2.46296			0.683103			0.341551	+	0.939863i	$0.389048\pi$
$14$	0.921468	+	2.22462i	0.246273	+	0.594555i
$15$		0			0
$16$	3.60231			0.900578
$17$	3.89141	−	1.36268i	0.943806	−	0.330499i
$17$	3.89141	−	1.36268i	0.943806	−	0.330499i
$18$		−	14.7494i		−	3.47646i
$19$	1.44372	+	1.44372i	0.331212	+	0.331212i	0.853047	−	0.521834i	$-0.174752\pi$
$19$	1.44372	+	1.44372i	0.331212	+	0.331212i	−0.521834	+	0.853047i	$0.674752\pi$
$20$		0			0
$21$		−	3.76267i		−	0.821082i
$22$	−3.85240	−	9.30051i	−0.821334	−	1.98288i
$23$	0.109963	+	0.0455480i	0.0229288	+	0.00949741i	0.394118	−	0.919060i	$-0.371050\pi$
$23$	0.109963	+	0.0455480i	0.0229288	+	0.00949741i	−0.371190	+	0.928557i	$0.621050\pi$
$24$	1.10032	+	0.455769i	0.224603	+	0.0930334i
$25$		0			0
$26$	3.56162	−	3.56162i	0.698491	−	0.698491i
$27$	−5.15122	+	12.4361i	−0.991353	+	2.39334i
$28$	2.37385	+	0.983282i	0.448616	+	0.185823i
$29$	−0.984309	+	0.407714i	−0.182782	+	0.0757106i	−0.472197	−	0.881493i	$-0.656539\pi$
$29$	−0.984309	+	0.407714i	−0.182782	+	0.0757106i	0.289416	+	0.957204i	$0.406539\pi$
$30$		0			0
$31$	1.06989	+	2.58295i	0.192159	+	0.463912i	0.990367	−	0.138470i	$-0.0442184\pi$
$31$	1.06989	+	2.58295i	0.192159	+	0.463912i	−0.798208	+	0.602382i	$0.794218\pi$
$32$	5.73626	−	5.73626i	1.01404	−	1.01404i
$33$			15.7307i			2.73836i
$34$	3.65672	−	7.59779i	0.627123	−	1.30301i
$35$		0			0
$36$	−11.1290	−	11.1290i	−1.85483	−	1.85483i
$37$	−2.13857	+	0.885823i	−0.351578	+	0.145628i	−0.551481	−	0.834187i	$-0.685937\pi$
$37$	−2.13857	+	0.885823i	−0.351578	+	0.145628i	0.199903	+	0.979816i	$0.435937\pi$
$38$	4.17544			0.677346
$39$	−7.27165	+	3.01202i	−1.16440	+	0.482309i
$40$		0			0
$41$	−0.662952	−	0.274604i	−0.103536	−	0.0428859i	0.330314	−	0.943871i	$-0.392845\pi$
$41$	−0.662952	−	0.274604i	−0.103536	−	0.0428859i	−0.433850	+	0.900985i	$0.642845\pi$
$42$	−5.44108	−	5.44108i	−0.839577	−	0.839577i
$43$	−7.13881	−	7.13881i	−1.08866	−	1.08866i	−0.995667	−	0.0929914i	$-0.970357\pi$
$43$	−7.13881	−	7.13881i	−1.08866	−	1.08866i	−0.0929914	−	0.995667i	$-0.529643\pi$
$44$	−9.92441	−	4.11082i	−1.49616	−	0.619730i
$45$		0			0
$46$	0.224879	−	0.0931480i	0.0331566	−	0.0137339i
$47$	−3.39482			−0.495186			−0.247593	−	0.968864i	$-0.579640\pi$
$47$	−3.39482			−0.495186			−0.247593	+	0.968864i	$0.579640\pi$
$48$	−10.6355	+	4.40535i	−1.53510	+	0.635858i
$49$	3.96945	+	3.96945i	0.567065	+	0.567065i
$50$		0			0
$51$	−9.82256	+	8.78209i	−1.37543	+	1.22974i
$52$		−	5.37477i		−	0.745347i
$53$	9.84581	−	9.84581i	1.35243	−	1.35243i	0.469487	−	0.882940i	$-0.344439\pi$
$53$	9.84581	−	9.84581i	1.35243	−	1.35243i	0.882940	−	0.469487i	$-0.155561\pi$
$54$	10.5345	+	25.4326i	1.43357	+	3.46093i
$55$		0			0
$56$	0.405412	−	0.167927i	0.0541754	−	0.0224402i
$57$	−6.02800	−	2.49688i	−0.798429	−	0.330720i
$58$	−0.833797	+	2.01296i	−0.109483	+	0.264315i
$59$	−1.07276	+	1.07276i	−0.139661	+	0.139661i	−0.773481	−	0.633820i	$-0.781486\pi$
$59$	−1.07276	+	1.07276i	−0.139661	+	0.139661i	0.633820	+	0.773481i	$0.281486\pi$
$60$		0			0
$61$	7.46606	+	3.09254i	0.955931	+	0.395959i	0.805457	−	0.592655i	$-0.201920\pi$
$61$	7.46606	+	3.09254i	0.955931	+	0.395959i	0.150474	+	0.988614i	$0.451920\pi$
$62$	5.28228	+	2.18799i	0.670850	+	0.277875i
$63$	3.24971	+	7.84549i	0.409425	+	0.988439i
$64$		−	9.38544i		−	1.17318i
$65$		0			0
$66$	22.7476	+	22.7476i	2.80004	+	2.80004i
$67$			4.92534i			0.601726i	0.953667	+	0.300863i	$0.0972747\pi$
$67$			4.92534i			0.601726i	−0.953667	+	0.300863i	$0.902725\pi$
$68$	−2.97370	−	8.49199i	−0.360614	−	1.02981i
$69$	−0.380355			−0.0457894
$70$		0			0
$71$	2.53962	+	6.13119i	0.301398	+	0.727639i	0.999927	+	0.0120574i	$0.00383809\pi$
$71$	2.53962	+	6.13119i	0.301398	+	0.727639i	−0.698530	+	0.715581i	$0.746162\pi$
$72$	−2.68790			−0.316773
$73$	−1.40336	−	3.38802i	−0.164251	−	0.396537i	0.820228	−	0.572036i	$-0.193846\pi$
$73$	−1.40336	−	3.38802i	−0.164251	−	0.396537i	−0.984480	+	0.175499i	$0.943846\pi$
$74$	−1.81155	+	4.37348i	−0.210589	+	0.508407i
$75$		0			0
$76$	3.15054	−	3.15054i	0.361392	−	0.361392i
$77$	4.09834	+	4.09834i	0.467049	+	0.467049i
$78$	−6.15973	+	14.8709i	−0.697452	+	1.68380i
$79$	−3.13055	+	7.55781i	−0.352214	+	0.850320i	0.644132	+	0.764914i	$0.277219\pi$
$79$	−3.13055	+	7.55781i	−0.352214	+	0.850320i	−0.996346	+	0.0854058i	$0.972781\pi$
$80$		0			0
$81$		−	21.3794i		−	2.37549i
$82$	−1.35577	+	0.561579i	−0.149720	+	0.0620160i
$83$	−4.30539	+	4.30539i	−0.472578	+	0.472578i	−0.902748	−	0.430170i	$-0.858454\pi$
$83$	−4.30539	+	4.30539i	−0.472578	+	0.472578i	0.430170	+	0.902748i	$0.358454\pi$
$84$	−8.21104			−0.895898
$85$		0			0
$86$	−20.6464			−2.22636
$87$	2.40747	−	2.40747i	0.258108	−	0.258108i
$88$	−1.69491	+	0.702056i	−0.180678	+	0.0748394i
$89$		−	8.46170i		−	0.896938i	−0.893798	−	0.448469i	$-0.851969\pi$
$89$		−	8.46170i		−	0.896938i	0.893798	−	0.448469i	$-0.148031\pi$
$90$		0			0
$91$	−1.10977	+	2.67922i	−0.116336	+	0.280859i
$92$	0.0993966	−	0.239965i	0.0103628	−	0.0250180i
$93$	−6.31751	−	6.31751i	−0.655096	−	0.655096i
$94$	−4.90915	+	4.90915i	−0.506341	+	0.506341i
$95$		0			0
$96$	−9.92072	+	23.9507i	−1.01253	+	2.44446i
$97$	−1.71804	−	4.14772i	−0.174441	−	0.421137i	0.812343	−	0.583180i	$-0.198192\pi$
$97$	−1.71804	−	4.14772i	−0.174441	−	0.421137i	−0.986784	+	0.162043i	$0.948192\pi$
$98$	11.4802			1.15968
$99$	−13.5861	−	32.7998i	−1.36546	−	3.29650i
$100$		0			0
$101$	−17.7855			−1.76972			−0.884861	−	0.465854i	$-0.845747\pi$
$101$	−17.7855			−1.76972			−0.884861	+	0.465854i	$0.845747\pi$
$102$	−1.50459	+	26.9036i	−0.148977	+	2.66386i
$103$			11.3352i			1.11689i	0.829542	+	0.558445i	$0.188602\pi$
$103$			11.3352i			1.11689i	−0.829542	+	0.558445i	$0.811398\pi$
$104$	−0.649065	−	0.649065i	−0.0636460	−	0.0636460i
$105$		0			0
$106$		−	28.4755i		−	2.76578i
$107$	−4.93146	−	11.9056i	−0.476742	−	1.15096i	−0.961128	−	0.276102i	$-0.910957\pi$
$107$	−4.93146	−	11.9056i	−0.476742	−	1.15096i	0.484386	−	0.874854i	$-0.339043\pi$
$108$	27.1386	+	11.2412i	2.61142	+	1.08168i
$109$	−10.4593	−	4.33237i	−1.00182	−	0.414966i	−0.179354	−	0.983785i	$-0.557401\pi$
$109$	−10.4593	−	4.33237i	−1.00182	−	0.414966i	−0.822463	+	0.568819i	$0.807401\pi$
$110$		0			0
$111$	5.23061	−	5.23061i	0.496467	−	0.496467i
$112$	−1.62314	+	3.91862i	−0.153373	+	0.370274i
$113$	5.40551	+	2.23904i	0.508508	+	0.210631i	0.622161	−	0.782890i	$-0.286255\pi$
$113$	5.40551	+	2.23904i	0.508508	+	0.210631i	−0.113653	+	0.993521i	$0.536255\pi$
$114$	−12.3276	+	5.10625i	−1.15458	+	0.478244i
$115$		0			0
$116$	0.889730	+	2.14800i	0.0826093	+	0.199437i
$117$	12.5606	−	12.5606i	1.16123	−	1.16123i
$118$			3.10257i			0.285615i
$119$	−0.271076	+	4.84710i	−0.0248495	+	0.444333i
$120$		0			0
$121$	−9.35583	−	9.35583i	−0.850530	−	0.850530i
$122$	15.2685	−	6.32441i	1.38234	−	0.572585i
$123$	2.29312			0.206764
$124$	5.63662	−	2.33477i	0.506184	−	0.209668i
$125$		0			0
$126$	16.0444	+	6.64582i	1.42935	+	0.592057i
$127$	−4.81114	−	4.81114i	−0.426920	−	0.426920i	0.460658	−	0.887578i	$-0.347613\pi$
$127$	−4.81114	−	4.81114i	−0.426920	−	0.426920i	−0.887578	+	0.460658i	$0.847613\pi$
$128$	−2.09949	−	2.09949i	−0.185570	−	0.185570i
$129$	29.8069	+	12.3464i	2.62435	+	1.08704i
$130$		0			0
$131$	1.75560	−	0.727194i	0.153388	−	0.0635352i	−0.304669	−	0.952458i	$-0.598546\pi$
$131$	1.75560	−	0.727194i	0.153388	−	0.0635352i	0.458056	+	0.888923i	$0.348546\pi$
$132$	34.3281			2.98787
$133$	−2.22101	+	0.919971i	−0.192586	+	0.0797716i
$134$	7.12239	+	7.12239i	0.615281	+	0.615281i
$135$		0			0
$136$	−1.38461	−	0.666397i	−0.118729	−	0.0571431i
$137$			19.3637i			1.65435i	0.561946	+	0.827174i	$0.310053\pi$
$137$			19.3637i			1.65435i	−0.561946	+	0.827174i	$0.689947\pi$
$138$	−0.550021	+	0.550021i	−0.0468209	+	0.0468209i
$139$	−3.16744	−	7.64688i	−0.268659	−	0.648600i	0.730762	−	0.682632i	$-0.239165\pi$
$139$	−3.16744	−	7.64688i	−0.268659	−	0.648600i	−0.999421	+	0.0340327i	$0.989165\pi$
$140$		0			0
$141$	10.0229	−	4.15161i	0.844079	−	0.349629i
$142$	12.5386	+	5.19366i	1.05222	+	0.435842i
$143$	4.63964	−	11.2011i	0.387986	−	0.936682i
$144$	18.3711	−	18.3711i	1.53092	−	1.53092i
$145$		0			0
$146$	−6.92867	−	2.86995i	−0.573421	−	0.237519i
$147$	−16.5738	−	6.86507i	−1.36698	−	0.566222i
$148$	1.93308	+	4.66686i	0.158898	+	0.383614i
$149$			4.93485i			0.404279i	0.979357	+	0.202139i	$0.0647894\pi$
$149$			4.93485i			0.404279i	−0.979357	+	0.202139i	$0.935211\pi$
$150$		0			0
$151$	−0.503992	−	0.503992i	−0.0410142	−	0.0410142i	0.686302	−	0.727316i	$-0.259233\pi$
$151$	−0.503992	−	0.503992i	−0.0410142	−	0.0410142i	−0.727316	+	0.686302i	$0.759233\pi$
$152$		−	0.760928i		−	0.0617194i
$153$	12.8960	−	26.7949i	1.04258	−	2.16624i
$154$	11.8530			0.955140
$155$		0			0
$156$	6.57294	+	15.8685i	0.526256	+	1.27050i
$157$	−5.88566			−0.469727			−0.234863	−	0.972028i	$-0.575464\pi$
$157$	−5.88566			−0.469727			−0.234863	+	0.972028i	$0.575464\pi$
$158$	6.40213	+	15.4561i	0.509326	+	1.22962i
$159$	−17.0281	+	41.1095i	−1.35042	+	3.26019i
$160$		0			0
$161$	−0.0990947	+	0.0990947i	−0.00780976	+	0.00780976i
$162$	−30.9161	−	30.9161i	−2.42900	−	2.42900i
$163$	2.25638	−	5.44737i	0.176733	−	0.426671i	−0.810545	−	0.585677i	$-0.800829\pi$
$163$	2.25638	−	5.44737i	0.176733	−	0.426671i	0.987278	+	0.159006i	$0.0508288\pi$
$164$	−0.599251	+	1.44672i	−0.0467936	+	0.112970i
$165$		0			0
$166$			12.4518i			0.966446i
$167$	9.94871	−	4.12089i	0.769854	−	0.318884i	0.0370408	−	0.999314i	$-0.488207\pi$
$167$	9.94871	−	4.12089i	0.769854	−	0.318884i	0.732813	+	0.680430i	$0.238207\pi$
$168$	−0.991576	+	0.991576i	−0.0765018	+	0.0765018i
$169$	−6.93382			−0.533371
$170$		0			0
$171$	14.7254			1.12608
$172$	−15.5786	+	15.5786i	−1.18786	+	1.18786i
$173$	8.95884	−	3.71087i	0.681128	−	0.282132i	−0.0151704	−	0.999885i	$-0.504829\pi$
$173$	8.95884	−	3.71087i	0.681128	−	0.282132i	0.696298	+	0.717753i	$0.254829\pi$
$174$		−	6.96274i		−	0.527844i
$175$		0			0
$176$	6.78591	−	16.3826i	0.511507	−	1.23489i
$177$	1.85531	−	4.47912i	0.139454	−	0.336671i
$178$	−12.2362	−	12.2362i	−0.917143	−	0.917143i
$179$	11.1126	−	11.1126i	0.830594	−	0.830594i	−0.157004	−	0.987598i	$-0.550183\pi$
$179$	11.1126	−	11.1126i	0.830594	−	0.830594i	0.987598	+	0.157004i	$0.0501834\pi$
$180$		0			0
$181$	−1.52658	+	3.68550i	−0.113470	+	0.273941i	−0.970405	−	0.241484i	$-0.922366\pi$
$181$	−1.52658	+	3.68550i	−0.113470	+	0.273941i	0.856935	+	0.515425i	$0.172366\pi$
$182$	2.26954	+	5.47915i	0.168230	+	0.406142i
$183$	−25.8247			−1.90902
$184$	−0.0169752	−	0.0409817i	−0.00125143	−	0.00302121i
$185$		0			0
$186$	−18.2711			−1.33970
$187$	1.13329	−	20.2644i	0.0828745	−	1.48188i
$188$			7.40832i			0.540307i
$189$	−11.2071	−	11.2071i	−0.815193	−	0.815193i
$190$		0			0
$191$			19.2007i			1.38931i	0.719343	+	0.694655i	$0.244443\pi$
$191$			19.2007i			1.38931i	−0.719343	+	0.694655i	$0.755557\pi$
$192$	11.4777	+	27.7096i	0.828330	+	1.99977i
$193$	10.8643	+	4.50016i	0.782033	+	0.323929i	0.737736	−	0.675090i	$-0.235895\pi$
$193$	10.8643	+	4.50016i	0.782033	+	0.323929i	0.0442973	+	0.999018i	$0.485895\pi$
$194$	−8.48231	−	3.51349i	−0.608994	−	0.252254i
$195$		0			0
$196$	8.66229	−	8.66229i	0.618735	−	0.618735i
$197$	−7.32418	+	17.6821i	−0.521826	+	1.25980i	0.414942	+	0.909848i	$0.363802\pi$
$197$	−7.32418	+	17.6821i	−0.521826	+	1.25980i	−0.936768	+	0.349952i	$0.886198\pi$
$198$	−67.0773	−	27.7843i	−4.76697	−	1.97455i
$199$	−9.65379	+	3.99873i	−0.684339	+	0.283463i	−0.697640	−	0.716449i	$-0.745766\pi$
$199$	−9.65379	+	3.99873i	−0.684339	+	0.283463i	0.0133003	+	0.999912i	$0.495766\pi$
$200$		0			0
$201$	−6.02332	−	14.5416i	−0.424852	−	1.02568i
$202$	−25.7191	+	25.7191i	−1.80959	+	1.80959i
$203$		−	1.25445i		−	0.0880449i
$204$	19.1646	+	21.4352i	1.34179	+	1.50076i
$205$		0			0
$206$	16.3915	+	16.3915i	1.14205	+	1.14205i
$207$	0.793074	−	0.328502i	0.0551224	−	0.0228325i
$208$	8.87236			0.615187
$209$	9.28540	−	3.84614i	0.642284	−	0.266043i
$210$		0			0
$211$	−20.1248	−	8.33599i	−1.38545	−	0.573873i	−0.439518	−	0.898234i	$-0.644851\pi$
$211$	−20.1248	−	8.33599i	−1.38545	−	0.573873i	−0.945933	+	0.324361i	$0.894851\pi$
$212$	−21.4859	−	21.4859i	−1.47566	−	1.47566i
$213$	−14.9960	−	14.9960i	−1.02751	−	1.02751i
$214$	−24.3476	−	10.0851i	−1.66436	−	0.689402i
$215$		0			0
$216$	4.63480	−	1.91980i	0.315358	−	0.130626i
$217$	−3.29183			−0.223464
$218$	−21.3898	+	8.85993i	−1.44870	+	0.600070i
$219$	8.28658	+	8.28658i	0.559955	+	0.559955i
$220$		0			0
$221$	9.58440	−	3.35623i	0.644717	−	0.225765i
$222$		−	15.1277i		−	1.01530i
$223$	−14.1552	+	14.1552i	−0.947905	+	0.947905i	−0.998709	−	0.0508034i	$-0.983822\pi$
$223$	−14.1552	+	14.1552i	−0.947905	+	0.947905i	0.0508034	+	0.998709i	$0.483822\pi$
$224$	3.65527	+	8.82460i	0.244228	+	0.589618i
$225$		0			0
$226$	11.0546	−	4.57895i	0.735338	−	0.304587i
$227$	12.7313	+	5.27349i	0.845008	+	0.350014i	0.762826	−	0.646604i	$-0.223811\pi$
$227$	12.7313	+	5.27349i	0.845008	+	0.350014i	0.0821817	+	0.996617i	$0.473811\pi$
$228$	−5.44879	+	13.1545i	−0.360855	+	0.871181i
$229$	−2.57403	+	2.57403i	−0.170096	+	0.170096i	−0.787022	−	0.616925i	$-0.788378\pi$
$229$	−2.57403	+	2.57403i	−0.170096	+	0.170096i	0.616925	+	0.787022i	$0.288378\pi$
$230$		0			0
$231$	−17.1119	−	7.08798i	−1.12588	−	0.466355i
$232$	0.366840	+	0.151950i	0.0240842	+	0.00997601i
$233$	−5.41909	−	13.0828i	−0.355016	−	0.857085i	−0.995985	−	0.0895185i	$-0.971467\pi$
$233$	−5.41909	−	13.0828i	−0.355016	−	0.857085i	0.640969	−	0.767567i	$-0.278533\pi$
$234$		−	36.3271i		−	2.37478i
$235$		0			0
$236$	2.34102	+	2.34102i	0.152387	+	0.152387i
$237$		−	26.1421i		−	1.69811i
$238$	6.61726	+	7.40125i	0.428933	+	0.479752i
$239$	22.6621			1.46589			0.732944	−	0.680289i	$-0.238146\pi$
$239$	22.6621			1.46589			0.732944	+	0.680289i	$0.238146\pi$
$240$		0			0
$241$	2.31331	+	5.58483i	0.149014	+	0.359751i	0.980707	−	0.195485i	$-0.0626281\pi$
$241$	2.31331	+	5.58483i	0.149014	+	0.359751i	−0.831693	+	0.555236i	$0.812628\pi$
$242$	−27.0584			−1.73938
$243$	10.6917	+	25.8121i	0.685875	+	1.65585i
$244$	6.74866	−	16.2927i	0.432039	−	1.04303i
$245$		0			0
$246$	3.31601	−	3.31601i	0.211421	−	0.211421i
$247$	3.55583	+	3.55583i	0.226252	+	0.226252i
$248$	0.398737	−	0.962635i	0.0253198	−	0.0611274i
$249$	7.44607	−	17.9764i	0.471875	−	1.13921i
$250$		0			0
$251$			0.706952i			0.0446224i	0.999751	+	0.0223112i	$0.00710247\pi$
$251$			0.706952i			0.0446224i	−0.999751	+	0.0223112i	$0.992898\pi$
$252$	17.1207	−	7.09164i	1.07850	−	0.446731i
$253$	0.414287	−	0.414287i	0.0260460	−	0.0260460i
$254$	−13.9145			−0.873073
$255$		0			0
$256$	12.6989			0.793679
$257$	−10.6578	+	10.6578i	−0.664817	+	0.664817i	−0.956511	−	0.291695i	$-0.905781\pi$
$257$	−10.6578	+	10.6578i	−0.664817	+	0.664817i	0.291695	+	0.956511i	$0.405781\pi$
$258$	60.9566	−	25.2490i	3.79499	−	1.57194i
$259$		−	2.72548i		−	0.169353i
$260$		0			0
$261$	−2.94052	+	7.09905i	−0.182014	+	0.439420i
$262$	1.48715	−	3.59030i	0.0918764	−	0.221809i
$263$	10.2737	+	10.2737i	0.633504	+	0.633504i	0.948945	−	0.315441i	$-0.102152\pi$
$263$	10.2737	+	10.2737i	0.633504	+	0.633504i	−0.315441	+	0.948945i	$0.602152\pi$
$264$	4.14550	−	4.14550i	0.255138	−	0.255138i
$265$		0			0
$266$	−1.88139	+	4.54207i	−0.115355	+	0.278492i
$267$	10.3480	+	24.9823i	0.633289	+	1.52889i
$268$	10.7483			0.656555
$269$	10.8530	+	26.2015i	0.661720	+	1.59753i	0.795107	+	0.606470i	$0.207415\pi$
$269$	10.8530	+	26.2015i	0.661720	+	1.59753i	−0.133387	+	0.991064i	$0.542585\pi$
$270$		0			0
$271$	−9.29673			−0.564736			−0.282368	−	0.959306i	$-0.591120\pi$
$271$	−9.29673			−0.564736			−0.282368	+	0.959306i	$0.591120\pi$
$272$	14.0181	−	4.90880i	0.849971	−	0.297640i
$273$		−	9.26731i		−	0.560883i
$274$	28.0012	+	28.0012i	1.69161	+	1.69161i
$275$		0			0
$276$			0.830026i			0.0499617i
$277$	−8.57453	−	20.7007i	−0.515193	−	1.24379i	−0.940826	−	0.338891i	$-0.889948\pi$
$277$	−8.57453	−	20.7007i	−0.515193	−	1.24379i	0.425632	−	0.904896i	$-0.360052\pi$
$278$	−15.6383	−	6.47758i	−0.937921	−	0.388500i
$279$	18.6288	+	7.71631i	1.11528	+	0.461963i
$280$		0			0
$281$	−22.0979	+	22.0979i	−1.31825	+	1.31825i	−0.403085	+	0.915162i	$0.632062\pi$
$281$	−22.0979	+	22.0979i	−1.31825	+	1.31825i	−0.915162	+	0.403085i	$0.867938\pi$
$282$	8.49027	−	20.4973i	0.505588	−	1.22060i
$283$	−10.8514	−	4.49480i	−0.645050	−	0.267188i	0.0360824	−	0.999349i	$-0.488512\pi$
$283$	−10.8514	−	4.49480i	−0.645050	−	0.267188i	−0.681132	+	0.732160i	$0.738512\pi$
$284$	13.3797	−	5.54206i	0.793941	−	0.328861i
$285$		0			0
$286$	−9.48831	−	22.9068i	−0.561055	−	1.35451i
$287$	0.597431	−	0.597431i	0.0352652	−	0.0352652i
$288$		−	58.5076i		−	3.44759i
$289$	13.2862	−	10.6055i	0.781541	−	0.623854i
$290$		0			0
$291$	10.1447	+	10.1447i	0.594693	+	0.594693i
$292$	−7.39346	+	3.06247i	−0.432670	+	0.179218i
$293$	−26.5905			−1.55344			−0.776718	−	0.629848i	$-0.783117\pi$
$293$	−26.5905			−1.55344			−0.776718	+	0.629848i	$0.783117\pi$
$294$	−33.8942	+	14.0394i	−1.97675	+	0.818796i
$295$		0			0
$296$	0.797017	+	0.330135i	0.0463257	+	0.0191887i
$297$	46.8535	+	46.8535i	2.71872	+	2.71872i
$298$	7.13614	+	7.13614i	0.413386	+	0.413386i
$299$	0.270834	+	0.112183i	0.0156627	+	0.00648771i
$300$		0			0
$301$	10.9823	−	4.54901i	0.633008	−	0.262200i
$302$	−1.45761			−0.0838763
$303$	52.5099	−	21.7503i	3.01662	−	1.24952i
$304$	5.20073	+	5.20073i	0.298282	+	0.298282i
$305$		0			0
$306$	−20.0987	−	57.3958i	−1.14896	−	3.28110i
$307$			18.6981i			1.06715i	0.845751	+	0.533577i	$0.179153\pi$
$307$			18.6981i			1.06715i	−0.845751	+	0.533577i	$0.820847\pi$
$308$	8.94356	−	8.94356i	0.509606	−	0.509606i
$309$	−13.8621	−	33.4660i	−0.788586	−	1.90382i
$310$		0			0
$311$	7.35993	−	3.04858i	0.417343	−	0.172869i	−0.164123	−	0.986440i	$-0.552479\pi$
$311$	7.35993	−	3.04858i	0.417343	−	0.172869i	0.581466	+	0.813571i	$0.302479\pi$
$312$	2.71006	+	1.12254i	0.153427	+	0.0635514i
$313$	−3.05672	+	7.37958i	−0.172776	+	0.417118i	−0.986419	−	0.164246i	$-0.947481\pi$
$313$	−3.05672	+	7.37958i	−0.172776	+	0.417118i	0.813643	+	0.581364i	$0.197481\pi$
$314$	−8.51107	+	8.51107i	−0.480308	+	0.480308i
$315$		0			0
$316$	16.4929	+	6.83160i	0.927801	+	0.384308i
$317$	14.4421	+	5.98211i	0.811149	+	0.335989i	0.749412	−	0.662104i	$-0.230336\pi$
$317$	14.4421	+	5.98211i	0.811149	+	0.335989i	0.0617365	+	0.998092i	$0.480336\pi$
$318$	34.8234	+	84.0710i	1.95280	+	4.71447i
$319$			5.24449i			0.293635i
$320$		0			0
$321$	29.1193	+	29.1193i	1.62528	+	1.62528i
$322$			0.286596i			0.0159714i
$323$	7.58545	+	3.65078i	0.422066	+	0.203135i
$324$	−46.6550			−2.59194
$325$		0			0
$326$	−4.61441	−	11.1402i	−0.255568	−	0.616996i
$327$	36.1781			2.00065
$328$	0.102341	+	0.247074i	0.00565086	+	0.0136424i
$329$	1.52965	−	3.69291i	0.0843325	−	0.203597i
$330$		0			0
$331$	−3.13284	+	3.13284i	−0.172197	+	0.172197i	−0.787944	−	0.615747i	$-0.788854\pi$
$331$	−3.13284	+	3.13284i	−0.172197	+	0.172197i	0.615747	+	0.787944i	$0.288854\pi$
$332$	9.39539	+	9.39539i	0.515639	+	0.515639i
$333$	−6.38875	+	15.4238i	−0.350101	+	0.845219i
$334$	8.42743	−	20.3456i	0.461129	−	1.11326i
$335$		0			0
$336$		−	13.5543i		−	0.739448i
$337$	−5.57660	+	2.30990i	−0.303777	+	0.125828i	−0.529365	−	0.848394i	$-0.677570\pi$
$337$	−5.57660	+	2.30990i	−0.303777	+	0.125828i	0.225588	+	0.974223i	$0.427570\pi$
$338$	−10.0268	+	10.0268i	−0.545385	+	0.545385i
$339$	−18.6974			−1.01550
$340$		0			0
$341$	13.7622			0.745266
$342$	21.2940	−	21.2940i	1.15145	−	1.15145i
$343$	−13.7212	+	5.68351i	−0.740875	+	0.306881i
$344$			3.76258i			0.202865i
$345$		0			0
$346$	7.58893	−	18.3213i	0.407983	−	0.984959i
$347$	−0.0356264	+	0.0860097i	−0.00191253	+	0.00461724i	−0.924833	−	0.380374i	$-0.875795\pi$
$347$	−0.0356264	+	0.0860097i	−0.00191253	+	0.00461724i	0.922920	+	0.384991i	$0.125795\pi$
$348$	−5.25368	−	5.25368i	−0.281627	−	0.281627i
$349$	6.74736	−	6.74736i	0.361178	−	0.361178i	−0.503069	−	0.864247i	$-0.667796\pi$
$349$	6.74736	−	6.74736i	0.361178	−	0.361178i	0.864247	+	0.503069i	$0.167796\pi$
$350$		0			0
$351$	−12.6873	+	30.6298i	−0.677196	+	1.63490i
$352$	−15.2816	−	36.8932i	−0.814515	−	1.96641i
$353$	−17.2138			−0.916197			−0.458099	−	0.888901i	$-0.651469\pi$
$353$	−17.2138			−0.916197			−0.458099	+	0.888901i	$0.651469\pi$
$354$	−3.79421	−	9.16003i	−0.201660	−	0.486850i
$355$		0			0
$356$	−18.4655			−0.978667
$357$	−5.12732	−	14.6421i	−0.271366	−	0.774942i
$358$		−	32.1392i		−	1.69861i
$359$	−12.5475	−	12.5475i	−0.662232	−	0.662232i	0.293673	−	0.955906i	$-0.405122\pi$
$359$	−12.5475	−	12.5475i	−0.662232	−	0.662232i	−0.955906	+	0.293673i	$0.905122\pi$
$360$		0			0
$361$		−	14.8313i		−	0.780597i
$362$	3.12194	+	7.53704i	0.164086	+	0.396138i
$363$	39.0637	+	16.1807i	2.05031	+	0.849266i
$364$	5.84671	+	2.42179i	0.306451	+	0.126936i
$365$		0			0
$366$	−37.3444	+	37.3444i	−1.95202	+	1.95202i
$367$	13.8930	−	33.5406i	0.725208	−	1.75081i	0.0672686	−	0.997735i	$-0.478572\pi$
$367$	13.8930	−	33.5406i	0.725208	−	1.75081i	0.657939	−	0.753071i	$-0.271428\pi$
$368$	0.396119	+	0.164078i	0.0206492	+	0.00855316i
$369$	−4.78135	+	1.98050i	−0.248907	+	0.103101i
$370$		0			0
$371$	6.27397	+	15.1467i	0.325728	+	0.786377i
$372$	−13.7863	+	13.7863i	−0.714788	+	0.714788i
$373$			5.89146i			0.305048i	0.988300	+	0.152524i	$0.0487402\pi$
$373$			5.89146i			0.305048i	−0.988300	+	0.152524i	$0.951260\pi$
$374$	−27.6649	−	30.9425i	−1.43052	−	1.60000i
$375$		0			0
$376$	0.894638	+	0.894638i	0.0461374	+	0.0461374i
$377$	−2.42432	+	1.00418i	−0.124859	+	0.0517181i
$378$	−32.4124			−1.66711
$379$	−27.0452	+	11.2025i	−1.38922	+	0.575432i	−0.946929	−	0.321442i	$-0.895833\pi$
$379$	−27.0452	+	11.2025i	−1.38922	+	0.575432i	−0.442287	+	0.896874i	$0.645833\pi$
$380$		0			0
$381$	20.0881	+	8.32075i	1.02914	+	0.426285i
$382$	27.7655	+	27.7655i	1.42061	+	1.42061i
$383$	8.70178	+	8.70178i	0.444640	+	0.444640i	0.893568	−	0.448928i	$-0.148194\pi$
$383$	8.70178	+	8.70178i	0.444640	+	0.444640i	−0.448928	+	0.893568i	$0.648194\pi$
$384$	8.76605	+	3.63102i	0.447340	+	0.185294i
$385$		0			0
$386$	22.2182	−	9.20306i	1.13087	−	0.468424i
$387$	−72.8131			−3.70130
$388$	−9.05132	+	3.74918i	−0.459511	+	0.190336i
$389$	1.50316	+	1.50316i	0.0762134	+	0.0762134i	0.744186	−	0.667973i	$-0.232838\pi$
$389$	1.50316	+	1.50316i	0.0762134	+	0.0762134i	−0.667973	+	0.744186i	$0.732838\pi$
$390$		0			0
$391$	0.489977	+	0.0274021i	0.0247792	+	0.00138578i
$392$		−	2.09214i		−	0.105669i
$393$	−4.29394	+	4.29394i	−0.216600	+	0.216600i
$394$	14.9783	+	36.1609i	0.754597	+	1.82176i
$395$		0			0
$396$	−71.5770	+	29.6481i	−3.59688	+	1.48988i
$397$	−23.2802	−	9.64298i	−1.16840	−	0.483968i	−0.287737	−	0.957709i	$-0.592903\pi$
$397$	−23.2802	−	9.64298i	−1.16840	−	0.483968i	−0.880664	+	0.473742i	$0.842903\pi$
$398$	−8.17762	+	19.7425i	−0.409907	+	0.989603i
$399$	5.43224	−	5.43224i	0.271952	−	0.271952i
$400$		0			0
$401$	30.3662	+	12.5781i	1.51641	+	0.628119i	0.976869	−	0.213838i	$-0.0685964\pi$
$401$	30.3662	+	12.5781i	1.51641	+	0.628119i	0.539545	+	0.841957i	$0.318596\pi$
$402$	−29.7383	−	12.3180i	−1.48321	−	0.614366i
$403$	2.63511	+	6.36172i	0.131264	+	0.316900i
$404$			38.8122i			1.93098i
$405$		0			0
$406$	−1.81402	−	1.81402i	−0.0900282	−	0.0900282i
$407$			11.3945i			0.564803i
$408$	4.90288	+	0.274195i	0.242729	+	0.0135747i
$409$	16.5721			0.819437			0.409719	−	0.912212i	$-0.365627\pi$
$409$	16.5721			0.819437			0.409719	+	0.912212i	$0.365627\pi$
$410$		0			0
$411$	−23.6803	−	57.1693i	−1.16806	−	2.81995i
$412$	24.7361			1.21866
$413$	−0.683586	−	1.65032i	−0.0336371	−	0.0812070i
$414$	0.671804	−	1.62188i	0.0330173	−	0.0797109i
$415$		0			0
$416$	14.1282	−	14.1282i	0.692691	−	0.692691i
$417$	18.7031	+	18.7031i	0.915895	+	0.915895i
$418$	7.86555	−	18.9891i	0.384717	−	0.928789i
$419$	−2.03536	+	4.91380i	−0.0994339	+	0.240055i	−0.965767	−	0.259413i	$-0.916471\pi$
$419$	−2.03536	+	4.91380i	−0.0994339	+	0.240055i	0.866333	+	0.499468i	$0.166471\pi$
$420$		0			0
$421$		−	3.72116i		−	0.181358i	−0.995880	−	0.0906791i	$-0.971096\pi$
$421$		−	3.72116i		−	0.181358i	0.995880	−	0.0906791i	$-0.0289037\pi$
$422$	−41.1564	+	17.0475i	−2.00346	+	0.829861i
$423$	−17.3129	+	17.3129i	−0.841784	+	0.841784i
$424$	−5.18933			−0.252016
$425$		0			0
$426$	−43.3705			−2.10131
$427$	−6.72817	+	6.72817i	−0.325599	+	0.325599i
$428$	−25.9808	+	10.7616i	−1.25583	+	0.520182i
$429$			38.7440i			1.87058i
$430$		0			0
$431$	0.249747	−	0.602943i	0.0120299	−	0.0290428i	−0.917750	−	0.397158i	$-0.869997\pi$
$431$	0.249747	−	0.602943i	0.0120299	−	0.0290428i	0.929780	+	0.368115i	$0.119997\pi$
$432$	−18.5563	+	44.7989i	−0.892790	+	2.15539i
$433$	−3.75811	−	3.75811i	−0.180603	−	0.180603i	0.611016	−	0.791619i	$-0.290761\pi$
$433$	−3.75811	−	3.75811i	−0.180603	−	0.180603i	−0.791619	+	0.611016i	$0.790761\pi$
$434$	−4.76022	+	4.76022i	−0.228498	+	0.228498i
$435$		0			0
$436$	−9.45427	+	22.8246i	−0.452777	+	1.09310i
$437$	0.0929967	+	0.224514i	0.00444863	+	0.0107400i
$438$	23.9660			1.14514
$439$	2.11850	+	5.11452i	0.101111	+	0.244103i	0.966337	−	0.257278i	$-0.0828256\pi$
$439$	2.11850	+	5.11452i	0.101111	+	0.244103i	−0.865227	+	0.501381i	$0.832826\pi$
$440$		0			0
$441$	40.4869			1.92795
$442$	9.00637	−	18.7131i	0.428390	−	0.890090i
$443$		−	14.9894i		−	0.712169i	−0.934454	−	0.356084i	$-0.884112\pi$
$443$		−	14.9894i		−	0.712169i	0.934454	−	0.356084i	$-0.115888\pi$
$444$	−11.4144	−	11.4144i	−0.541705	−	0.541705i
$445$		0			0
$446$			40.9390i			1.93852i
$447$	−6.03495	−	14.5697i	−0.285443	−	0.689121i
$448$	10.2095	+	4.22893i	0.482355	+	0.199798i
$449$	19.1997	+	7.95276i	0.906088	+	0.375314i	0.786558	−	0.617517i	$-0.211861\pi$
$449$	19.1997	+	7.95276i	0.906088	+	0.375314i	0.119530	+	0.992831i	$0.461861\pi$
$450$		0			0
$451$	−2.49769	+	2.49769i	−0.117612	+	0.117612i
$452$	4.88611	−	11.7961i	0.229823	−	0.554843i
$453$	2.10433	+	0.871641i	0.0988700	+	0.0409533i
$454$	26.0362	−	10.7846i	1.22194	−	0.506144i
$455$		0			0
$456$	0.930557	+	2.24656i	0.0435773	+	0.105205i
$457$	−11.0623	+	11.0623i	−0.517472	+	0.517472i	−0.916806	−	0.399334i	$-0.869242\pi$
$457$	−11.0623	+	11.0623i	−0.517472	+	0.517472i	0.399334	+	0.916806i	$0.369242\pi$
$458$			7.44445i			0.347856i
$459$	−3.09902	+	55.4137i	−0.144650	+	2.58649i
$460$		0			0
$461$	5.22808	+	5.22808i	0.243496	+	0.243496i	0.818295	−	0.574799i	$-0.194920\pi$
$461$	5.22808	+	5.22808i	0.243496	+	0.243496i	−0.574799	+	0.818295i	$0.694920\pi$
$462$	−34.9947	+	14.4953i	−1.62810	+	0.674382i
$463$	17.2150			0.800049			0.400025	−	0.916504i	$-0.369002\pi$
$463$	17.2150			0.800049			0.400025	+	0.916504i	$0.369002\pi$
$464$	−3.54579	+	1.46871i	−0.164609	+	0.0681833i
$465$		0			0
$466$	−26.7551	−	11.0823i	−1.23941	−	0.513379i
$467$	−25.6956	−	25.6956i	−1.18905	−	1.18905i	−0.977330	−	0.211722i	$-0.932093\pi$
$467$	−25.6956	−	25.6956i	−1.18905	−	1.18905i	−0.211722	−	0.977330i	$-0.567907\pi$
$468$	−27.4103	−	27.4103i	−1.26704	−	1.26704i
$469$	−5.35781	−	2.21928i	−0.247401	−	0.102477i
$470$		0			0
$471$	17.3768	−	7.19771i	0.800681	−	0.331653i
$472$	0.565409			0.0260250
$473$	−45.9138	+	19.0181i	−2.11112	+	0.874454i
$474$	−37.8033	−	37.8033i	−1.73636	−	1.73636i
$475$		0			0
$476$	10.5775	+	0.591552i	0.484821	+	0.0271137i
$477$		−	100.423i		−	4.59807i
$478$	32.7709	−	32.7709i	1.49891	−	1.49891i
$479$	−11.6213	−	28.0562i	−0.530989	−	1.28192i	−0.930869	−	0.365353i	$-0.880948\pi$
$479$	−11.6213	−	28.0562i	−0.530989	−	1.28192i	0.399880	−	0.916567i	$-0.369052\pi$
$480$		0			0
$481$	−5.26721	+	2.18175i	−0.240164	+	0.0994792i
$482$	11.4213	+	4.73084i	0.520225	+	0.215484i
$483$	0.171382	−	0.413753i	0.00779815	−	0.0188264i
$484$	−20.4167	+	20.4167i	−0.928030	+	0.928030i
$485$		0			0
$486$	52.7871	+	21.8651i	2.39447	+	0.991823i
$487$	23.3587	+	9.67548i	1.05848	+	0.438438i	0.842912	−	0.538051i	$-0.180839\pi$
$487$	23.3587	+	9.67548i	1.05848	+	0.438438i	0.215570	+	0.976488i	$0.430839\pi$
$488$	−1.15255	−	2.78251i	−0.0521736	−	0.125958i
$489$			18.8422i			0.852074i
$490$		0			0
$491$	−20.3605	−	20.3605i	−0.918857	−	0.918857i	0.0780890	−	0.996946i	$-0.475118\pi$
$491$	−20.3605	−	20.3605i	−0.918857	−	0.918857i	−0.996946	+	0.0780890i	$0.975118\pi$
$492$		−	5.00413i		−	0.225604i
$493$	−3.27477	+	2.92788i	−0.147488	+	0.131865i
$494$	10.2840			0.462697
$495$		0			0
$496$	3.85409	+	9.30460i	0.173054	+	0.417789i
$497$	−7.81386			−0.350500
$498$	−15.2276	−	36.7627i	−0.682365	−	1.64737i
$499$	5.72345	−	13.8176i	0.256217	−	0.618562i	−0.742465	−	0.669885i	$-0.766344\pi$
$499$	5.72345	−	13.8176i	0.256217	−	0.618562i	0.998682	+	0.0513222i	$0.0163436\pi$
$500$		0			0
$501$	−24.3330	+	24.3330i	−1.08712	+	1.08712i
$502$	1.02230	+	1.02230i	0.0456276	+	0.0456276i
$503$	−12.4672	+	30.0985i	−0.555886	+	1.34203i	0.357112	+	0.934062i	$0.383761\pi$
$503$	−12.4672	+	30.0985i	−0.555886	+	1.34203i	−0.912998	+	0.407965i	$0.866239\pi$
$504$	1.21113	−	2.92392i	0.0539479	−	0.130242i
$505$		0			0
$506$		−	1.19818i		−	0.0532655i
$507$	20.4714	−	8.47953i	0.909167	−	0.376589i
$508$	−10.4991	+	10.4991i	−0.465820	+	0.465820i
$509$	−33.1868			−1.47098			−0.735490	−	0.677535i	$-0.763048\pi$
$509$	−33.1868			−1.47098			−0.735490	+	0.677535i	$0.763048\pi$
$510$		0			0
$511$	4.31784			0.191010
$512$	22.5624	−	22.5624i	0.997127	−	0.997127i
$513$	−25.3912	+	10.5174i	−1.12105	+	0.464355i
$514$			30.8239i			1.35958i
$515$		0			0
$516$	26.9428	−	65.0457i	1.18609	−	2.86348i
$517$	−6.39505	+	15.4390i	−0.281254	+	0.679007i
$518$	−3.94124	−	3.94124i	−0.173168	−	0.173168i
$519$	−21.9120	+	21.9120i	−0.961829	+	0.961829i
$520$		0			0
$521$	10.9704	−	26.4849i	0.480622	−	1.16032i	−0.478692	−	0.877983i	$-0.658889\pi$
$521$	10.9704	−	26.4849i	0.480622	−	1.16032i	0.959314	−	0.282341i	$-0.0911109\pi$
$522$	6.01352	+	14.5179i	0.263205	+	0.635432i
$523$	42.6141			1.86338			0.931692	−	0.363248i	$-0.118332\pi$
$523$	42.6141			1.86338			0.931692	+	0.363248i	$0.118332\pi$
$524$	−1.58691	−	3.83114i	−0.0693245	−	0.167364i
$525$		0			0
$526$	29.7130			1.29555
$527$	7.68314	+	8.59342i	0.334683	+	0.374335i
$528$			56.6667i			2.46610i
$529$	−16.2534	−	16.2534i	−0.706671	−	0.706671i
$530$		0			0
$531$			10.9417i			0.474831i
$532$	2.00760	+	4.84676i	0.0870403	+	0.210134i
$533$	−1.63283	−	0.676339i	−0.0707255	−	0.0292955i
$534$	51.0902	+	21.1622i	2.21089	+	0.915780i
$535$		0			0
$536$	1.29797	−	1.29797i	0.0560640	−	0.0560640i
$537$	−19.2190	+	46.3987i	−0.829360	+	2.00225i
$538$	53.5834	+	22.1950i	2.31015	+	0.956894i
$539$	25.5298	−	10.5748i	1.09965	−	0.455489i
$540$		0			0
$541$	−8.45588	−	20.4143i	−0.363547	−	0.877679i	−0.994776	−	0.102083i	$-0.967449\pi$
$541$	−8.45588	−	20.4143i	−0.363547	−	0.877679i	0.631229	−	0.775596i	$-0.282551\pi$
$542$	−13.4437	+	13.4437i	−0.577457	+	0.577457i
$543$		−	12.7480i		−	0.547068i
$544$	14.5055	−	30.1388i	0.621916	−	1.29219i
$545$		0			0
$546$	−13.4012	−	13.4012i	−0.573518	−	0.573518i
$547$	35.7403	−	14.8041i	1.52815	−	0.632979i	0.548942	−	0.835860i	$-0.315031\pi$
$547$	35.7403	−	14.8041i	1.52815	−	0.632979i	0.979203	+	0.202882i	$0.0650307\pi$
$548$	42.2561			1.80509
$549$	53.8468	−	22.3041i	2.29813	−	0.951915i
$550$		0			0
$551$	−2.00969	−	0.832442i	−0.0856158	−	0.0354632i
$552$	0.100235	+	0.100235i	0.00426629	+	0.00426629i
$553$	−6.81085	−	6.81085i	−0.289627	−	0.289627i
$554$	−42.3341	−	17.5354i	−1.79860	−	0.745006i
$555$		0			0
$556$	−16.6873	+	6.91211i	−0.707700	+	0.293139i
$557$	33.9638			1.43909			0.719546	−	0.694445i	$-0.244350\pi$
$557$	33.9638			1.43909			0.719546	+	0.694445i	$0.244350\pi$
$558$	38.0969	−	15.7803i	1.61277	−	0.668031i
$559$	−17.5826	−	17.5826i	−0.743666	−	0.743666i
$560$		0			0
$561$	21.4359	+	61.2145i	0.905023	+	2.58448i
$562$			63.9101i			2.69589i
$563$	1.60778	−	1.60778i	0.0677597	−	0.0677597i	−0.672415	−	0.740175i	$-0.734743\pi$
$563$	1.60778	−	1.60778i	0.0677597	−	0.0677597i	0.740175	+	0.672415i	$0.234743\pi$
$564$	−9.05981	−	21.8723i	−0.381487	−	0.920991i
$565$		0			0
$566$	−22.1917	+	9.19211i	−0.932787	+	0.386373i
$567$	23.2566	+	9.63321i	0.976687	+	0.404557i
$568$	0.946486	−	2.28502i	0.0397137	−	0.0958773i
$569$	4.01656	−	4.01656i	0.168383	−	0.168383i	−0.617885	−	0.786268i	$-0.712010\pi$
$569$	4.01656	−	4.01656i	0.168383	−	0.168383i	0.786268	+	0.617885i	$0.212010\pi$
$570$		0			0
$571$	11.9760	+	4.96060i	0.501178	+	0.207595i	0.618927	−	0.785449i	$-0.287568\pi$
$571$	11.9760	+	4.96060i	0.501178	+	0.207595i	−0.117749	+	0.993043i	$0.537568\pi$
$572$	−24.4434	−	10.1248i	−1.02203	−	0.423339i
$573$	−23.4810	−	56.6880i	−0.980931	−	2.36818i
$574$		−	1.72785i		−	0.0721193i
$575$		0			0
$576$	−47.8639	−	47.8639i	−1.99433	−	1.99433i
$577$		−	27.7816i		−	1.15656i	−0.815838	−	0.578281i	$-0.803724\pi$
$577$		−	27.7816i		−	1.15656i	0.815838	−	0.578281i	$-0.196276\pi$
$578$	3.87646	−	34.5491i	0.161239	−	1.43705i
$579$	−37.5793			−1.56174
$580$		0			0
$581$	−2.74349	−	6.62337i	−0.113819	−	0.274784i
$582$	29.3399			1.21618
$583$	−26.2297	−	63.3241i	−1.08632	−	2.62262i
$584$	−0.523016	+	1.26267i	−0.0216426	+	0.0522498i
$585$		0			0
$586$	−38.4518	+	38.4518i	−1.58843	+	1.58843i
$587$	4.87317	+	4.87317i	0.201137	+	0.201137i	0.800487	−	0.599350i	$-0.204574\pi$
$587$	4.87317	+	4.87317i	0.201137	+	0.201137i	−0.599350	+	0.800487i	$0.704574\pi$
$588$	−14.9812	+	36.1679i	−0.617815	+	1.49154i
$589$	−2.18444	+	5.27369i	−0.0900081	+	0.217299i
$590$		0			0
$591$		−	61.1617i		−	2.51585i
$592$	−7.70378	+	3.19101i	−0.316623	+	0.131150i
$593$	−9.84816	+	9.84816i	−0.404416	+	0.404416i	−0.879786	−	0.475370i	$-0.842314\pi$
$593$	−9.84816	+	9.84816i	−0.404416	+	0.404416i	0.475370	+	0.879786i	$0.342314\pi$
$594$	135.507			5.55992
$595$		0			0
$596$	10.7690			0.441117
$597$	23.6117	−	23.6117i	0.966363	−	0.966363i
$598$	0.553869	−	0.229420i	0.0226494	−	0.00938168i
$599$		−	19.3270i		−	0.789681i	−0.918750	−	0.394841i	$-0.870800\pi$
$599$		−	19.3270i		−	0.789681i	0.918750	−	0.394841i	$-0.129200\pi$
$600$		0			0
$601$	−16.1400	+	38.9654i	−0.658365	+	1.58943i	0.141964	+	0.989872i	$0.454658\pi$
$601$	−16.1400	+	38.9654i	−0.658365	+	1.58943i	−0.800329	+	0.599561i	$0.795342\pi$
$602$	9.30295	−	22.4593i	0.379160	−	0.915374i
$603$	25.1183	+	25.1183i	1.02290	+	1.02290i
$604$	−1.09983	+	1.09983i	−0.0447514	+	0.0447514i
$605$		0			0
$606$	44.4805	−	107.386i	1.80690	−	4.36224i
$607$	7.21286	+	17.4134i	0.292761	+	0.706787i	1.00000		0.000187126i	$-5.95642e-5\pi$
$607$	7.21286	+	17.4134i	0.292761	+	0.706787i	−0.707239	+	0.706974i	$0.750060\pi$
$608$	16.5631			0.671723
$609$	1.53409	+	3.70363i	0.0621646	+	0.150079i
$610$		0			0
$611$	−8.36132			−0.338263
$612$	−58.4728	−	28.1422i	−2.36362	−	1.13758i
$613$		−	16.1284i		−	0.651420i	−0.945470	−	0.325710i	$-0.894397\pi$
$613$		−	16.1284i		−	0.651420i	0.945470	−	0.325710i	$-0.105603\pi$
$614$	27.0387	+	27.0387i	1.09119	+	1.09119i
$615$		0			0
$616$		−	2.16007i		−	0.0870318i
$617$	14.4466	+	34.8772i	0.581598	+	1.40410i	0.891364	+	0.453289i	$0.149749\pi$
$617$	14.4466	+	34.8772i	0.581598	+	1.40410i	−0.309766	+	0.950813i	$0.600251\pi$
$618$	−68.4398	−	28.3487i	−2.75305	−	1.14035i
$619$	−45.0105	−	18.6439i	−1.80912	−	0.749363i	−0.982409	−	0.186742i	$-0.940207\pi$
$619$	−45.0105	−	18.6439i	−1.80912	−	0.749363i	−0.826714	−	0.562622i	$-0.809793\pi$
$620$		0			0
$621$	−1.13288	+	1.13288i	−0.0454610	+	0.0454610i
$622$	6.23451	−	15.0514i	0.249981	−	0.603508i
$623$	9.20469	+	3.81271i	0.368778	+	0.152753i
$624$	−26.1948	+	10.8502i	−1.04863	+	0.434357i
$625$		0			0
$626$	6.25115	+	15.0916i	0.249846	+	0.603183i
$627$	−22.7107	+	22.7107i	−0.906977	+	0.906977i
$628$			12.8439i			0.512528i
$629$	−7.11495	+	6.36129i	−0.283692	+	0.253641i
$630$		0			0
$631$	27.6845	+	27.6845i	1.10210	+	1.10210i	0.994157	+	0.107944i	$0.0344268\pi$
$631$	27.6845	+	27.6845i	1.10210	+	1.10210i	0.107944	+	0.994157i	$0.465573\pi$
$632$	2.81670	−	1.16672i	0.112042	−	0.0464095i
$633$	69.6109			2.76678
$634$	29.5348	−	12.2337i	1.17298	−	0.485863i
$635$		0			0
$636$	89.7107	+	37.1594i	3.55726	+	1.47347i
$637$	9.77661	+	9.77661i	0.387363	+	0.387363i
$638$	7.58390	+	7.58390i	0.300249	+	0.300249i
$639$	44.2195	+	18.3163i	1.74930	+	0.724582i
$640$		0			0
$641$	−46.1341	+	19.1094i	−1.82219	+	0.754775i	−0.847647	+	0.530560i	$0.821982\pi$
$641$	−46.1341	+	19.1094i	−1.82219	+	0.754775i	−0.974540	+	0.224214i	$0.928018\pi$
$642$	84.2170			3.32378
$643$	−14.4479	+	5.98451i	−0.569769	+	0.236006i	−0.648920	−	0.760856i	$-0.724779\pi$
$643$	−14.4479	+	5.98451i	−0.569769	+	0.236006i	0.0791509	+	0.996863i	$0.474779\pi$
$644$	0.216248	+	0.216248i	0.00852138	+	0.00852138i
$645$		0			0
$646$	16.2484	−	5.68980i	0.639284	−	0.223862i
$647$		−	24.8287i		−	0.976118i	−0.872811	−	0.488059i	$-0.837705\pi$
$647$		−	24.8287i		−	0.976118i	0.872811	−	0.488059i	$-0.162295\pi$
$648$	−5.63411	+	5.63411i	−0.221329	+	0.221329i
$649$	2.85788	+	6.89953i	0.112182	+	0.270830i
$650$		0			0
$651$	9.71880	−	4.02566i	0.380910	−	0.157778i
$652$	−11.8875	−	4.92395i	−0.465549	−	0.192837i
$653$	6.42926	−	15.5216i	0.251596	−	0.607408i	−0.746737	−	0.665120i	$-0.768381\pi$
$653$	6.42926	−	15.5216i	0.251596	−	0.607408i	0.998333	+	0.0577120i	$0.0183805\pi$
$654$	52.3161	−	52.3161i	2.04572	−	2.04572i
$655$		0			0
$656$	−2.38816	−	0.989208i	−0.0932420	−	0.0386221i
$657$	−24.4351	−	10.1214i	−0.953304	−	0.394872i
$658$	−3.12822	−	7.55219i	−0.121951	−	0.294415i
$659$			13.1974i			0.514097i	0.966399	+	0.257048i	$0.0827500\pi$
$659$			13.1974i			0.514097i	−0.966399	+	0.257048i	$0.917250\pi$
$660$		0			0
$661$	−27.0038	−	27.0038i	−1.05033	−	1.05033i	−0.998665	−	0.0516626i	$-0.983548\pi$
$661$	−27.0038	−	27.0038i	−1.05033	−	1.05033i	−0.0516626	−	0.998665i	$-0.516452\pi$
$662$			9.06062i			0.352151i
$663$	−24.1926	+	21.6299i	−0.939562	+	0.840038i
$664$	2.26920			0.0880620
$665$		0			0
$666$	13.0653	+	31.5425i	0.506271	+	1.22225i
$667$	−0.126808			−0.00491001
$668$	−8.99276	−	21.7105i	−0.347941	−	0.840003i
$669$	24.4812	−	59.1027i	0.946496	−	2.28504i
$670$		0			0
$671$	28.1286	−	28.1286i	1.08589	−	1.08589i
$672$	−21.5836	−	21.5836i	−0.832607	−	0.832607i
$673$	−9.32426	+	22.5107i	−0.359424	+	0.867726i	0.635958	+	0.771724i	$0.280605\pi$
$673$	−9.32426	+	22.5107i	−0.359424	+	0.867726i	−0.995381	+	0.0960015i	$0.969395\pi$
$674$	−4.72387	+	11.4044i	−0.181957	+	0.439283i
$675$		0			0
$676$			15.1312i			0.581971i
$677$	−42.7449	+	17.7055i	−1.64282	+	0.680478i	−0.996578	−	0.0826551i	$-0.973660\pi$
$677$	−42.7449	+	17.7055i	−1.64282	+	0.680478i	−0.646241	+	0.763133i	$0.723660\pi$
$678$	−27.0378	+	27.0378i	−1.03838	+	1.03838i
$679$	5.28604			0.202859
$680$		0			0
$681$	−44.0371			−1.68750
$682$	19.9011	−	19.9011i	0.762054	−	0.762054i
$683$	15.2368	−	6.31128i	0.583019	−	0.241495i	−0.0716249	−	0.997432i	$-0.522818\pi$
$683$	15.2368	−	6.31128i	0.583019	−	0.241495i	0.654644	+	0.755937i	$0.272818\pi$
$684$		−	32.1343i		−	1.22869i
$685$		0			0
$686$	−11.6231	+	28.0606i	−0.443771	+	1.07136i
$687$	4.45172	−	10.7474i	0.169844	−	0.410039i
$688$	−25.7162	−	25.7162i	−0.980422	−	0.980422i
$689$	24.2499	−	24.2499i	0.923846	−	0.923846i
$690$		0			0
$691$	−9.89442	+	23.8872i	−0.376401	+	0.908713i	0.616233	+	0.787564i	$0.288658\pi$
$691$	−9.89442	+	23.8872i	−0.376401	+	0.908713i	−0.992634	+	0.121149i	$0.961342\pi$
$692$	−8.09801	−	19.5503i	−0.307840	−	0.743192i
$693$	41.8015			1.58791
$694$	0.0728579	+	0.175894i	0.00276565	+	0.00667686i
$695$		0			0
$696$	−1.26888			−0.0480968
$697$	−2.95402	−	0.165204i	−0.111891	−	0.00625756i
$698$		−	19.5143i		−	0.738628i
$699$	31.9987	+	31.9987i	1.21030	+	1.21030i
$700$		0			0
$701$			8.67606i			0.327690i	0.986486	+	0.163845i	$0.0523897\pi$
$701$			8.67606i			0.327690i	−0.986486	+	0.163845i	$0.947610\pi$
$702$	25.9461	+	62.6395i	0.979273	+	2.36417i
$703$	−4.36637	−	1.80861i	−0.164681	−	0.0682131i
$704$	−42.6832	−	17.6800i	−1.60868	−	0.666338i
$705$		0			0
$706$	−24.8923	+	24.8923i	−0.936835	+	0.936835i
$707$	8.01386	−	19.3472i	0.301392	−	0.727625i
$708$	−9.77451	−	4.04873i	−0.367349	−	0.152161i
$709$	−33.1887	+	13.7472i	−1.24643	+	0.516287i	−0.905718	−	0.423881i	$-0.860667\pi$
$709$	−33.1887	+	13.7472i	−1.24643	+	0.516287i	−0.340710	+	0.940168i	$0.610667\pi$
$710$		0			0
$711$	22.5782	+	54.5085i	0.846748	+	2.04423i
$712$	−2.22991	+	2.22991i	−0.0835695	+	0.0835695i
$713$			0.332760i			0.0124620i
$714$	−28.5880	−	13.7590i	−1.06988	−	0.514919i
$715$		0			0
$716$	−24.2503	−	24.2503i	−0.906278	−	0.906278i
$717$	−66.9075	+	27.7140i	−2.49871	+	1.03500i
$718$	−36.2892			−1.35430
$719$	9.01058	−	3.73231i	0.336038	−	0.139192i	−0.208283	−	0.978069i	$-0.566787\pi$
$719$	9.01058	−	3.73231i	0.336038	−	0.139192i	0.544321	+	0.838877i	$0.316787\pi$
$720$		0			0
$721$	−12.3305	−	5.10745i	−0.459211	−	0.190212i
$722$	−21.4472	−	21.4472i	−0.798181	−	0.798181i
$723$	−13.6597	−	13.6597i	−0.508008	−	0.508008i
$724$	8.04264	+	3.33137i	0.298902	+	0.123809i
$725$		0			0
$726$	79.8872	−	33.0904i	2.96489	−	1.22810i
$727$	−11.0694			−0.410542			−0.205271	−	0.978705i	$-0.565808\pi$
$727$	−11.0694			−0.410542			−0.205271	+	0.978705i	$0.565808\pi$
$728$	0.998514	−	0.413598i	0.0370074	−	0.0153290i
$729$	−17.7800	−	17.7800i	−0.658518	−	0.658518i
$730$		0			0
$731$	−37.5080	−	18.0521i	−1.38728	−	0.667682i
$732$			56.3557i			2.08297i
$733$	−29.8140	+	29.8140i	−1.10121	+	1.10121i	−0.106940	+	0.994266i	$0.534105\pi$
$733$	−29.8140	+	29.8140i	−1.10121	+	1.10121i	−0.994266	+	0.106940i	$0.965895\pi$
$734$	−28.4119	−	68.5923i	−1.04870	−	2.53179i
$735$		0			0
$736$	0.892048	−	0.369499i	0.0328813	−	0.0136199i
$737$	22.3995	+	9.27818i	0.825097	+	0.341766i
$738$	−4.05023	+	9.77812i	−0.149091	+	0.359937i
$739$	−33.3484	+	33.3484i	−1.22674	+	1.22674i	−0.261549	+	0.965190i	$0.584233\pi$
$739$	−33.3484	+	33.3484i	−1.22674	+	1.22674i	−0.965190	+	0.261549i	$0.915767\pi$
$740$		0			0
$741$	−14.8467	−	6.14972i	−0.545409	−	0.225916i
$742$	30.9758	+	12.8306i	1.13716	+	0.471026i
$743$	−12.1500	−	29.3327i	−0.445740	−	1.07611i	−0.973902	−	0.226969i	$-0.927118\pi$
$743$	−12.1500	−	29.3327i	−0.445740	−	1.07611i	0.528162	−	0.849144i	$-0.322882\pi$
$744$			3.32971i			0.122073i
$745$		0			0
$746$	8.51946	+	8.51946i	0.311920	+	0.311920i
$747$			43.9133i			1.60670i
$748$	−44.2217	−	2.47311i	−1.61691	−	0.0904259i
$749$	15.1730			0.554409
$750$		0			0
$751$	−8.49116	−	20.4995i	−0.309847	−	0.748036i	−0.999710	−	0.0240961i	$-0.992329\pi$
$751$	−8.49116	−	20.4995i	−0.309847	−	0.748036i	0.689863	−	0.723940i	$-0.257671\pi$
$752$	−12.2292			−0.445954
$753$	−0.864549	−	2.08721i	−0.0315059	−	0.0760620i
$754$	−2.05361	+	4.95785i	−0.0747881	+	0.180554i
$755$		0			0
$756$	−24.4565	+	24.4565i	−0.889473	+	0.889473i
$757$	9.23768	+	9.23768i	0.335749	+	0.335749i	0.854765	−	0.519016i	$-0.173701\pi$
$757$	9.23768	+	9.23768i	0.335749	+	0.335749i	−0.519016	+	0.854765i	$0.673701\pi$
$758$	−22.9096	+	55.3088i	−0.832115	+	2.00890i
$759$	−0.716500	+	1.72978i	−0.0260073	+	0.0627872i
$760$		0			0
$761$		−	18.9811i		−	0.688065i	−0.938958	−	0.344033i	$-0.888207\pi$
$761$		−	18.9811i		−	0.688065i	0.938958	−	0.344033i	$-0.111793\pi$
$762$	41.0812	−	17.0164i	1.48821	−	0.616438i
$763$	9.42556	−	9.42556i	0.341228	−	0.341228i
$764$	41.9004			1.51590
$765$		0			0
$766$	25.1668			0.909313
$767$	−2.64217	+	2.64217i	−0.0954031	+	0.0954031i
$768$	−37.4921	+	15.5297i	−1.35288	+	0.560381i
$769$			22.0057i			0.793544i	0.917917	+	0.396772i	$0.129870\pi$
$769$			22.0057i			0.793544i	−0.917917	+	0.396772i	$0.870130\pi$
$770$		0			0
$771$	18.4325	−	44.4999i	0.663829	−	1.60262i
$772$	9.82043	−	23.7086i	0.353445	−	0.853291i
$773$	9.36282	+	9.36282i	0.336757	+	0.336757i	0.855145	−	0.518388i	$-0.173468\pi$
$773$	9.36282	+	9.36282i	0.336757	+	0.336757i	−0.518388	+	0.855145i	$0.673468\pi$
$774$	−105.293	+	105.293i	−3.78467	+	3.78467i
$775$		0			0
$776$	−0.640293	+	1.54580i	−0.0229852	+	0.0554912i
$777$	3.33306	+	8.04672i	0.119573	+	0.288674i
$778$	4.34736			0.155860
$779$	−0.560667	−	1.35357i	−0.0200880	−	0.0484966i
$780$		0			0
$781$	32.6676			1.16894
$782$	0.748167	−	0.668916i	0.0267544	−	0.0239204i
$783$		−	14.3412i		−	0.512514i
$784$	14.2992	+	14.2992i	0.510686	+	0.510686i
$785$		0			0
$786$			12.4187i			0.442959i
$787$	−4.58697	−	11.0739i	−0.163508	−	0.394743i	0.820797	−	0.571220i	$-0.193530\pi$
$787$	−4.58697	−	11.0739i	−0.163508	−	0.394743i	−0.984305	+	0.176477i	$0.943530\pi$
$788$	38.5866	+	15.9831i	1.37459	+	0.569375i
$789$	−42.8961	−	17.7681i	−1.52714	−	0.632563i
$790$		0			0
$791$	−4.87128	+	4.87128i	−0.173203	+	0.173203i
$792$	−5.06338	+	12.2241i	−0.179919	+	0.434364i
$793$	18.3886	+	7.61681i	0.652999	+	0.270481i
$794$	−47.6093	+	19.7204i	−1.68959	+	0.699851i
$795$		0			0
$796$	8.72619	+	21.0669i	0.309292	+	0.746696i
$797$	16.4888	−	16.4888i	0.584062	−	0.584062i	−0.351955	−	0.936017i	$-0.614483\pi$
$797$	16.4888	−	16.4888i	0.584062	−	0.584062i	0.936017	+	0.351955i	$0.114483\pi$
$798$		−	15.7108i		−	0.556157i
$799$	−13.2107	+	4.62606i	−0.467360	+	0.163658i
$800$		0			0
$801$	−43.1530	−	43.1530i	−1.52474	−	1.52474i
$802$	62.1004	−	25.7228i	2.19284	−	0.908305i
$803$	−18.0517			−0.637030
$804$	−31.7332	+	13.1443i	−1.11914	+	0.463564i
$805$		0			0
$806$	13.0100	+	5.38894i	0.458259	+	0.189817i
$807$	−64.0849	−	64.0849i	−2.25590	−	2.25590i
$808$	4.68701	+	4.68701i	0.164889	+	0.164889i
$809$	28.4685	+	11.7920i	1.00090	+	0.414586i	0.822127	−	0.569304i	$-0.192787\pi$
$809$	28.4685	+	11.7920i	1.00090	+	0.414586i	0.178772	+	0.983890i	$0.442787\pi$
$810$		0			0
$811$	35.6681	−	14.7742i	1.25248	−	0.518793i	0.344885	−	0.938645i	$-0.387918\pi$
$811$	35.6681	−	14.7742i	1.25248	−	0.518793i	0.907593	+	0.419852i	$0.137918\pi$
$812$	−2.73750			−0.0960675
$813$	27.4477	−	11.3692i	0.962632	−	0.398735i
$814$	16.4772	+	16.4772i	0.577526	+	0.577526i
$815$		0			0
$816$	−35.3839	+	31.6358i	−1.23868	+	1.10747i
$817$		−	20.6129i		−	0.721154i
$818$	23.9644	−	23.9644i	0.837896	−	0.837896i
$819$	8.00391	+	19.3231i	0.279679	+	0.675205i
$820$		0			0
$821$	19.9465	−	8.26210i	0.696137	−	0.288349i	−0.00641740	−	0.999979i	$-0.502043\pi$
$821$	19.9465	−	8.26210i	0.696137	−	0.288349i	0.702554	+	0.711630i	$0.252043\pi$
$822$	−116.914	−	48.4274i	−4.07785	−	1.68910i
$823$	−9.72219	+	23.4714i	−0.338894	+	0.818163i	0.658928	+	0.752206i	$0.271010\pi$
$823$	−9.72219	+	23.4714i	−0.338894	+	0.818163i	−0.997822	+	0.0659572i	$0.978990\pi$
$824$	2.98716	−	2.98716i	0.104063	−	0.104063i
$825$		0			0
$826$	−3.37500	−	1.39797i	−0.117431	−	0.0486416i
$827$	13.7494	+	5.69519i	0.478113	+	0.198041i	0.608707	−	0.793395i	$-0.291688\pi$
$827$	13.7494	+	5.69519i	0.478113	+	0.198041i	−0.130594	+	0.991436i	$0.541688\pi$
$828$	−0.716870	−	1.73068i	−0.0249129	−	0.0601452i
$829$		−	29.8580i		−	1.03701i	−0.855075	−	0.518505i	$-0.826489\pi$
$829$		−	29.8580i		−	1.03701i	0.855075	−	0.518505i	$-0.173511\pi$
$830$		0			0
$831$	50.6309	+	50.6309i	1.75637	+	1.75637i
$832$		−	23.1160i		−	0.801402i
$833$	20.8559	+	10.0377i	0.722613	+	0.347785i
$834$	54.0920			1.87305
$835$		0			0
$836$	−8.39319	−	20.2630i	−0.290285	−	0.700809i
$837$	−37.6333			−1.30080
$838$	4.16242	+	10.0490i	0.143788	+	0.347136i
$839$	12.3297	−	29.7664i	0.425667	−	1.02765i	−0.554979	−	0.831864i	$-0.687274\pi$
$839$	12.3297	−	29.7664i	0.425667	−	1.02765i	0.980646	−	0.195787i	$-0.0627261\pi$
$840$		0			0
$841$	−19.7035	+	19.7035i	−0.679430	+	0.679430i
$842$	−5.38106	−	5.38106i	−0.185443	−	0.185443i
$843$	38.2177	−	92.2658i	1.31629	−	3.17780i
$844$	−18.1911	+	43.9172i	−0.626164	+	1.51169i
$845$		0			0
$846$			50.0715i			1.72149i
$847$	14.3929	−	5.96174i	0.494547	−	0.204848i
$848$	35.4677	−	35.4677i	1.21797	−	1.21797i
$849$	37.5345			1.28818
$850$		0			0
$851$	−0.275510			−0.00944435
$852$	−32.7248	+	32.7248i	−1.12113	+	1.12113i
$853$	−6.13944	+	2.54304i	−0.210210	+	0.0870719i	−0.485304	−	0.874345i	$-0.661291\pi$
$853$	−6.13944	+	2.54304i	−0.210210	+	0.0870719i	0.275094	+	0.961417i	$0.411291\pi$
$854$			19.4588i			0.665867i
$855$		0			0
$856$	−1.83789	+	4.43707i	−0.0628179	+	0.151656i
$857$	13.2139	−	31.9012i	0.451378	−	1.08972i	−0.520420	−	0.853910i	$-0.674225\pi$
$857$	13.2139	−	31.9012i	0.451378	−	1.08972i	0.971798	−	0.235813i	$-0.0757754\pi$
$858$	56.0266	+	56.0266i	1.91272	+	1.91272i
$859$	33.0671	−	33.0671i	1.12823	−	1.12823i	0.137770	−	0.990464i	$-0.456007\pi$
$859$	33.0671	−	33.0671i	1.12823	−	1.12823i	0.990464	−	0.137770i	$-0.0439935\pi$
$860$		0			0
$861$	−1.03324	+	2.49447i	−0.0352128	+	0.0850113i
$862$	−0.510746	−	1.23305i	−0.0173961	−	0.0419979i
$863$	40.3468			1.37342			0.686711	−	0.726930i	$-0.259054\pi$
$863$	40.3468			1.37342			0.686711	+	0.726930i	$0.259054\pi$
$864$	41.7882	+	100.886i	1.42166	+	3.43220i
$865$		0			0
$866$	−10.8690			−0.369343
$867$	−26.2564	+	47.5597i	−0.891716	+	1.61521i
$868$			7.18356i			0.243826i
$869$	28.4743	+	28.4743i	0.965923	+	0.965923i
$870$		0			0
$871$			12.1309i			0.411041i
$872$	1.61462	+	3.89804i	0.0546780	+	0.132004i
$873$	−29.9143	−	12.3909i	−1.01244	−	0.419368i
$874$	0.459143	+	0.190183i	0.0155307	+	0.00643304i
$875$		0			0
$876$	18.0833	−	18.0833i	0.610978	−	0.610978i
$877$	−5.94444	+	14.3511i	−0.200729	+	0.484604i	−0.991904	−	0.126986i	$-0.959470\pi$
$877$	−5.94444	+	14.3511i	−0.200729	+	0.484604i	0.791175	+	0.611590i	$0.209470\pi$
$878$	10.4595	+	4.33245i	0.352990	+	0.146213i
$879$	78.5060	−	32.5182i	2.64794	−	1.09681i
$880$		0			0
$881$	−12.7047	−	30.6719i	−0.428033	−	1.03336i	−0.979911	−	0.199437i	$-0.936089\pi$
$881$	−12.7047	−	30.6719i	−0.428033	−	1.03336i	0.551878	−	0.833925i	$-0.313911\pi$
$882$	58.5469	−	58.5469i	1.97138	−	1.97138i
$883$			34.1078i			1.14782i	0.818919	+	0.573909i	$0.194574\pi$
$883$			34.1078i			1.14782i	−0.818919	+	0.573909i	$0.805426\pi$
$884$	−7.32410	−	20.9155i	−0.246336	−	0.703463i
$885$		0			0
$886$	−21.6758	−	21.6758i	−0.728211	−	0.728211i
$887$	−29.8882	+	12.3801i	−1.00355	+	0.415683i	−0.823097	−	0.567901i	$-0.807756\pi$
$887$	−29.8882	+	12.3801i	−1.00355	+	0.415683i	−0.180451	+	0.983584i	$0.557756\pi$
$888$	−2.75685			−0.0925137
$889$	7.40141	−	3.06576i	0.248235	−	0.102822i
$890$		0			0
$891$	−97.2295	−	40.2738i	−3.25731	−	1.34922i
$892$	30.8901	+	30.8901i	1.03428	+	1.03428i
$893$	−4.90118	−	4.90118i	−0.164012	−	0.164012i
$894$	−29.7957	−	12.3418i	−0.996518	−	0.412771i
$895$		0			0
$896$	3.22983	−	1.33784i	0.107901	−	0.0446941i
$897$	−0.936801			−0.0312789
$898$	39.2643	−	16.2638i	1.31027	−	0.542730i
$899$	−2.10621	−	2.10621i	−0.0702461	−	0.0702461i
$900$		0			0
$901$	24.8974	−	51.7308i	0.829453	−	1.72340i
$902$			7.22367i			0.240522i
$903$	−26.8610	+	26.8610i	−0.893877	+	0.893877i
$904$	−0.834462	−	2.01457i	−0.0277538	−	0.0670036i
$905$		0			0
$906$	4.30346	−	1.78255i	0.142973	−	0.0592213i
$907$	25.8300	+	10.6991i	0.857670	+	0.355259i	0.767796	−	0.640694i	$-0.221353\pi$
$907$	25.8300	+	10.6991i	0.857670	+	0.355259i	0.0898744	+	0.995953i	$0.471353\pi$
$908$	11.5080	−	27.7828i	0.381907	−	0.922004i
$909$	−90.7026	+	90.7026i	−3.00841	+	3.00841i
$910$		0			0
$911$	11.3723	+	4.71057i	0.376782	+	0.156068i	0.563034	−	0.826434i	$-0.309634\pi$
$911$	11.3723	+	4.71057i	0.376782	+	0.156068i	−0.186252	+	0.982502i	$0.559634\pi$
$912$	−21.7147	−	8.99454i	−0.719047	−	0.297839i
$913$	11.4698	+	27.6904i	0.379593	+	0.916420i
$914$			31.9937i			1.05826i
$915$		0			0
$916$	5.61714	+	5.61714i	0.185596	+	0.185596i
$917$			2.23742i			0.0738860i
$918$	75.6506	+	84.6135i	2.49684	+	2.79266i
$919$	−20.0893			−0.662683			−0.331342	−	0.943511i	$-0.607501\pi$
$919$	−20.0893			−0.662683			−0.331342	+	0.943511i	$0.607501\pi$
$920$		0			0
$921$	−22.8663	−	55.2042i	−0.753471	−	1.81904i
$922$	15.1203			0.497962
$923$	6.25500	+	15.1009i	0.205886	+	0.497052i
$924$	−15.4677	+	37.3423i	−0.508849	+	1.22847i
$925$		0			0
$926$	24.8941	−	24.8941i	0.818071	−	0.818071i
$927$	57.8073	+	57.8073i	1.89864	+	1.89864i
$928$	−3.30750	+	7.98500i	−0.108574	+	0.262120i
$929$	−2.31962	+	5.60006i	−0.0761043	+	0.183732i	−0.957353	−	0.288921i	$-0.906704\pi$
$929$	−2.31962	+	5.60006i	−0.0761043	+	0.183732i	0.881249	+	0.472653i	$0.156704\pi$
$930$		0			0
$931$			11.4616i			0.375638i
$932$	−28.5499	+	11.8257i	−0.935183	+	0.387365i
$933$	−18.0013	+	18.0013i	−0.589335	+	0.589335i
$934$	−74.3154			−2.43167
$935$		0			0
$936$	−6.62021			−0.216388
$937$	−24.1663	+	24.1663i	−0.789479	+	0.789479i	−0.981409	−	0.191929i	$-0.938526\pi$
$937$	−24.1663	+	24.1663i	−0.789479	+	0.789479i	0.191929	+	0.981409i	$0.438526\pi$
$938$	−10.9570	+	4.53854i	−0.357759	+	0.148189i
$939$		−	25.5256i		−	0.832997i
$940$		0			0
$941$	13.7852	−	33.2804i	0.449385	−	1.08491i	−0.523168	−	0.852229i	$-0.675250\pi$
$941$	13.7852	−	33.2804i	0.449385	−	1.08491i	0.972553	−	0.232681i	$-0.0747499\pi$
$942$	14.7197	−	35.5365i	0.479594	−	1.15784i
$943$	−0.0603923	−	0.0603923i	−0.00196664	−	0.00196664i
$944$	−3.86441	+	3.86441i	−0.125776	+	0.125776i
$945$		0			0
$946$	−38.8930	+	93.8961i	−1.26452	+	3.05283i
$947$	−15.0836	−	36.4150i	−0.490151	−	1.18333i	−0.954643	−	0.297752i	$-0.903763\pi$
$947$	−15.0836	−	36.4150i	−0.490151	−	1.18333i	0.464492	−	0.885577i	$-0.346237\pi$
$948$	−57.0483			−1.85284
$949$	−3.45643	−	8.34456i	−0.112200	−	0.270876i
$950$		0			0
$951$	−49.9545			−1.61989
$952$	1.34879	−	1.20592i	0.0437147	−	0.0390841i
$953$			6.36027i			0.206029i	0.994680	+	0.103015i	$0.0328489\pi$
$953$			6.36027i			0.206029i	−0.994680	+	0.103015i	$0.967151\pi$
$954$	−145.219	−	145.219i	−4.70165	−	4.70165i
$955$		0			0
$956$		−	49.4540i		−	1.59946i
$957$	−6.41361	−	15.4838i	−0.207323	−	0.500521i
$958$	−57.3764	−	23.7661i	−1.85375	−	0.767847i
$959$	−21.0639	−	8.72495i	−0.680189	−	0.281743i
$960$		0			0
$961$	16.3933	−	16.3933i	0.528817	−	0.528817i
$962$	−4.46179	+	10.7717i	−0.143854	+	0.347294i
$963$	−85.8657	−	35.5667i	−2.76698	−	1.14612i
$964$	12.1874	−	5.04820i	0.392531	−	0.162592i
$965$		0			0
$966$	−0.350485	−	0.846146i	−0.0112767	−	0.0272243i
$967$	−24.2838	+	24.2838i	−0.780913	+	0.780913i	−0.979985	−	0.199072i	$-0.936207\pi$
$967$	−24.2838	+	24.2838i	−0.780913	+	0.780913i	0.199072	+	0.979985i	$0.436207\pi$
$968$			4.93109i			0.158491i
$969$	−26.8599	−	1.50215i	−0.862865	−	0.0482559i
$970$		0			0
$971$	5.64699	+	5.64699i	0.181221	+	0.181221i	0.791888	−	0.610667i	$-0.209099\pi$
$971$	5.64699	+	5.64699i	0.181221	+	0.181221i	−0.610667	+	0.791888i	$0.709099\pi$
$972$	56.3282	−	23.3319i	1.80673	−	0.748371i
$973$	9.74552			0.312427
$974$	47.7697	−	19.7869i	1.53064	−	0.634012i
$975$		0			0
$976$	26.8951	+	11.1403i	0.860890	+	0.356592i
$977$	−10.6765	−	10.6765i	−0.341572	−	0.341572i	0.515386	−	0.856958i	$-0.327649\pi$
$977$	−10.6765	−	10.6765i	−0.341572	−	0.341572i	−0.856958	+	0.515386i	$0.827649\pi$
$978$	27.2472	+	27.2472i	0.871268	+	0.871268i
$979$	−38.4822	−	15.9399i	−1.22990	−	0.509440i
$980$		0			0
$981$	−75.4345	+	31.2460i	−2.40844	+	0.997608i
$982$	−58.8855			−1.87911
$983$	46.4649	−	19.2464i	1.48200	−	0.613864i	0.512440	−	0.858723i	$-0.328742\pi$
$983$	46.4649	−	19.2464i	1.48200	−	0.613864i	0.969559	+	0.244859i	$0.0787416\pi$
$984$	−0.604306	−	0.604306i	−0.0192646	−	0.0192646i
$985$		0			0
$986$	−0.501620	+	8.96947i	−0.0159748	+	0.285646i
$987$			12.7736i			0.406588i
$988$	7.75967	−	7.75967i	0.246868	−	0.246868i
$989$	−0.459844	−	1.11016i	−0.0146222	−	0.0353010i
$990$		0			0
$991$	−12.0211	+	4.97931i	−0.381863	+	0.158173i	−0.565354	−	0.824849i	$-0.691260\pi$
$991$	−12.0211	+	4.97931i	−0.381863	+	0.158173i	0.183490	+	0.983021i	$0.441260\pi$
$992$	20.9537	+	8.67929i	0.665280	+	0.275568i
$993$	5.41817	−	13.0806i	0.171941	−	0.415101i
$994$	−11.2994	+	11.2994i	−0.358395	+	0.358395i
$995$		0			0
$996$	−39.2288	−	16.2491i	−1.24301	−	0.514872i
$997$	8.63721	+	3.57765i	0.273543	+	0.113305i	0.515238	−	0.857047i	$-0.327703\pi$
$997$	8.63721	+	3.57765i	0.273543	+	0.113305i	−0.241695	+	0.970352i	$0.577703\pi$
$998$	−11.7048	−	28.2578i	−0.370508	−	0.894485i
$999$		−	31.1586i		−	0.985814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.c.49.6		24
5.2	odd	4		425.2.m.b.151.6		24
5.3	odd	4		85.2.l.a.66.1	✓	24
5.4	even	2		425.2.n.f.49.1		24
15.8	even	4		765.2.be.b.406.6		24
17.8	even	8		425.2.n.f.399.1		24
85.3	even	16		1445.2.d.j.866.4		24
85.8	odd	8		85.2.l.a.76.1	yes	24
85.12	even	16		7225.2.a.bs.1.2		12
85.22	even	16		7225.2.a.bq.1.2		12
85.42	odd	8		425.2.m.b.76.6		24
85.48	even	16		1445.2.d.j.866.3		24
85.59	even	8	inner	425.2.n.c.399.6		24
85.63	even	16		1445.2.a.p.1.11		12
85.73	even	16		1445.2.a.q.1.11		12
255.8	even	8		765.2.be.b.586.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.1	✓	24	5.3	odd	4
85.2.l.a.76.1	yes	24	85.8	odd	8
425.2.m.b.76.6		24	85.42	odd	8
425.2.m.b.151.6		24	5.2	odd	4
425.2.n.c.49.6		24	1.1	even	1	trivial
425.2.n.c.399.6		24	85.59	even	8	inner
425.2.n.f.49.1		24	5.4	even	2
425.2.n.f.399.1		24	17.8	even	8
765.2.be.b.406.6		24	15.8	even	4
765.2.be.b.586.6		24	255.8	even	8
1445.2.a.p.1.11		12	85.63	even	16
1445.2.a.q.1.11		12	85.73	even	16
1445.2.d.j.866.3		24	85.48	even	16
1445.2.d.j.866.4		24	85.3	even	16
7225.2.a.bq.1.2		12	85.22	even	16
7225.2.a.bs.1.2		12	85.12	even	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.44607 - 1.44607i) q^{2} +(-2.95240 + 1.22292i) q^{3} -2.18224i q^{4} +(-2.50094 + 6.03781i) q^{6} +(-0.450584 + 1.08781i) q^{7} +(-0.263530 - 0.263530i) q^{8} +(5.09981 - 5.09981i) q^{9} +O(q^{10})\)	\(q+(1.44607 - 1.44607i) q^{2} +(-2.95240 + 1.22292i) q^{3} -2.18224i q^{4} +(-2.50094 + 6.03781i) q^{6} +(-0.450584 + 1.08781i) q^{7} +(-0.263530 - 0.263530i) q^{8} +(5.09981 - 5.09981i) q^{9} +(1.88376 - 4.54781i) q^{11} +(2.66871 + 6.44284i) q^{12} +2.46296 q^{13} +(0.921468 + 2.22462i) q^{14} +3.60231 q^{16} +(3.89141 - 1.36268i) q^{17} -14.7494i q^{18} +(1.44372 + 1.44372i) q^{19} -3.76267i q^{21} +(-3.85240 - 9.30051i) q^{22} +(0.109963 + 0.0455480i) q^{23} +(1.10032 + 0.455769i) q^{24} +(3.56162 - 3.56162i) q^{26} +(-5.15122 + 12.4361i) q^{27} +(2.37385 + 0.983282i) q^{28} +(-0.984309 + 0.407714i) q^{29} +(1.06989 + 2.58295i) q^{31} +(5.73626 - 5.73626i) q^{32} +15.7307i q^{33} +(3.65672 - 7.59779i) q^{34} +(-11.1290 - 11.1290i) q^{36} +(-2.13857 + 0.885823i) q^{37} +4.17544 q^{38} +(-7.27165 + 3.01202i) q^{39} +(-0.662952 - 0.274604i) q^{41} +(-5.44108 - 5.44108i) q^{42} +(-7.13881 - 7.13881i) q^{43} +(-9.92441 - 4.11082i) q^{44} +(0.224879 - 0.0931480i) q^{46} -3.39482 q^{47} +(-10.6355 + 4.40535i) q^{48} +(3.96945 + 3.96945i) q^{49} +(-9.82256 + 8.78209i) q^{51} -5.37477i q^{52} +(9.84581 - 9.84581i) q^{53} +(10.5345 + 25.4326i) q^{54} +(0.405412 - 0.167927i) q^{56} +(-6.02800 - 2.49688i) q^{57} +(-0.833797 + 2.01296i) q^{58} +(-1.07276 + 1.07276i) q^{59} +(7.46606 + 3.09254i) q^{61} +(5.28228 + 2.18799i) q^{62} +(3.24971 + 7.84549i) q^{63} -9.38544i q^{64} +(22.7476 + 22.7476i) q^{66} +4.92534i q^{67} +(-2.97370 - 8.49199i) q^{68} -0.380355 q^{69} +(2.53962 + 6.13119i) q^{71} -2.68790 q^{72} +(-1.40336 - 3.38802i) q^{73} +(-1.81155 + 4.37348i) q^{74} +(3.15054 - 3.15054i) q^{76} +(4.09834 + 4.09834i) q^{77} +(-6.15973 + 14.8709i) q^{78} +(-3.13055 + 7.55781i) q^{79} -21.3794i q^{81} +(-1.35577 + 0.561579i) q^{82} +(-4.30539 + 4.30539i) q^{83} -8.21104 q^{84} -20.6464 q^{86} +(2.40747 - 2.40747i) q^{87} +(-1.69491 + 0.702056i) q^{88} -8.46170i q^{89} +(-1.10977 + 2.67922i) q^{91} +(0.0993966 - 0.239965i) q^{92} +(-6.31751 - 6.31751i) q^{93} +(-4.90915 + 4.90915i) q^{94} +(-9.92072 + 23.9507i) q^{96} +(-1.71804 - 4.14772i) q^{97} +11.4802 q^{98} +(-13.5861 - 32.7998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} + 16 q^{41} - 24 q^{42} - 8 q^{43} - 16 q^{44} + 8 q^{46} - 64 q^{47} - 8 q^{48} - 56 q^{51} + 24 q^{53} + 32 q^{54} + 64 q^{56} + 16 q^{57} + 56 q^{58} - 32 q^{59} + 32 q^{61} - 32 q^{62} + 80 q^{63} + 96 q^{66} + 24 q^{68} - 96 q^{69} - 24 q^{71} - 24 q^{72} - 64 q^{73} + 64 q^{74} - 8 q^{76} + 24 q^{77} + 8 q^{78} - 16 q^{82} - 96 q^{83} + 64 q^{84} - 16 q^{86} + 48 q^{87} + 8 q^{88} - 24 q^{91} + 112 q^{92} - 64 q^{93} - 56 q^{94} - 168 q^{96} + 48 q^{97} + 120 q^{98} + 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more