LMFDB - Embedded newform 425.3.u.e.401.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.12
Character	$\chi$	$=$	425.401
Dual form			425.3.u.e.301.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40031 - 3.38065i) q^{2} +(-4.71704 - 3.15183i) q^{3} +(-6.63952 - 6.63952i) q^{4} +(-17.2606 + 11.5332i) q^{6} +(5.23596 + 1.04150i) q^{7} +(-18.2207 + 7.54727i) q^{8} +(8.87234 + 21.4197i) q^{9} +(2.84290 + 4.25470i) q^{11} +(10.3923 + 52.2455i) q^{12} +(-3.48556 + 3.48556i) q^{13} +(10.8529 - 16.2426i) q^{14} +34.6077i q^{16} +(-16.9983 + 0.237334i) q^{17} +84.8367 q^{18} +(-3.46526 + 8.36588i) q^{19} +(-21.4157 - 21.4157i) q^{21} +(18.3646 - 3.65295i) q^{22} +(-30.0458 + 20.0759i) q^{23} +(109.736 + 21.8278i) q^{24} +(6.90260 + 16.6644i) q^{26} +(15.6991 - 78.9247i) q^{27} +(-27.8492 - 41.6793i) q^{28} +(0.381842 + 1.91965i) q^{29} +(3.40793 - 5.10033i) q^{31} +(44.1137 + 18.2725i) q^{32} -29.0299i q^{33} +(-23.0007 + 57.7979i) q^{34} +(83.3086 - 201.125i) q^{36} +(11.8758 + 7.93518i) q^{37} +(23.4297 + 23.4297i) q^{38} +(27.4274 - 5.45566i) q^{39} +(-64.9302 - 12.9154i) q^{41} +(-102.388 + 42.4103i) q^{42} +(-4.37477 - 10.5616i) q^{43} +(9.37368 - 47.1247i) q^{44} +(25.7963 + 129.687i) q^{46} +(1.67827 - 1.67827i) q^{47} +(109.077 - 163.246i) q^{48} +(-18.9395 - 7.84500i) q^{49} +(80.9300 + 52.4564i) q^{51} +46.2849 q^{52} +(-21.0855 + 50.9049i) q^{53} +(-244.833 - 163.592i) q^{54} +(-103.263 + 20.5404i) q^{56} +(42.7136 - 28.5403i) q^{57} +(7.02437 + 1.39723i) q^{58} +(38.2228 - 15.8324i) q^{59} +(5.85814 - 29.4509i) q^{61} +(-12.4703 - 18.6631i) q^{62} +(24.1466 + 121.393i) q^{63} +(25.6607 - 25.6607i) q^{64} +(-98.1402 - 40.6510i) q^{66} +83.0052i q^{67} +(114.437 + 111.285i) q^{68} +205.003 q^{69} +(77.2000 + 51.5834i) q^{71} +(-323.321 - 323.321i) q^{72} +(-50.8326 + 10.1112i) q^{73} +(43.4560 - 29.0364i) q^{74} +(78.5531 - 32.5378i) q^{76} +(10.4541 + 25.2383i) q^{77} +(19.9633 - 100.362i) q^{78} +(-53.4837 - 80.0441i) q^{79} +(-175.265 + 175.265i) q^{81} +(-134.585 + 201.421i) q^{82} +(89.8717 + 37.2261i) q^{83} +284.379i q^{84} -41.8312 q^{86} +(4.24924 - 10.2586i) q^{87} +(-83.9110 - 56.0675i) q^{88} +(6.35442 + 6.35442i) q^{89} +(-21.8805 + 14.6201i) q^{91} +(332.784 + 66.1949i) q^{92} +(-32.1507 + 13.3173i) q^{93} +(-3.32355 - 8.02376i) q^{94} +(-150.494 - 225.231i) q^{96} +(-14.0870 - 70.8202i) q^{97} +(-53.0424 + 53.0424i) q^{98} +(-65.9113 + 98.6432i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) $ 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	1.40031	−	3.38065i	0.700156	−	1.69033i	−0.0230865	−	0.999733i	$-0.507349\pi$
$2$	1.40031	−	3.38065i	0.700156	−	1.69033i	0.723243	−	0.690594i	$-0.242651\pi$
$3$	−4.71704	−	3.15183i	−1.57235	−	1.05061i	−0.967042	−	0.254617i	$-0.918051\pi$
$3$	−4.71704	−	3.15183i	−1.57235	−	1.05061i	−0.605306	−	0.795993i	$-0.706949\pi$
$4$	−6.63952	−	6.63952i	−1.65988	−	1.65988i
$5$		0			0
$5$		0			0
$6$	−17.2606	+	11.5332i	−2.87676	+	1.92219i
$7$	5.23596	+	1.04150i	0.747995	+	0.148785i	0.554347	−	0.832286i	$-0.312968\pi$
$7$	5.23596	+	1.04150i	0.747995	+	0.148785i	0.193648	+	0.981071i	$0.437968\pi$
$8$	−18.2207	+	7.54727i	−2.27759	+	0.943408i
$9$	8.87234	+	21.4197i	0.985815	+	2.37997i
$10$		0			0
$11$	2.84290	+	4.25470i	0.258445	+	0.386791i	0.937888	−	0.346938i	$-0.112778\pi$
$11$	2.84290	+	4.25470i	0.258445	+	0.386791i	−0.679443	+	0.733728i	$0.737778\pi$
$12$	10.3923	+	52.2455i	0.866024	+	4.35380i
$13$	−3.48556	+	3.48556i	−0.268120	+	0.268120i	−0.828342	−	0.560222i	$-0.810716\pi$
$13$	−3.48556	+	3.48556i	−0.268120	+	0.268120i	0.560222	+	0.828342i	$0.310716\pi$
$14$	10.8529	−	16.2426i	0.775209	−	1.16018i
$15$		0			0
$16$			34.6077i			2.16298i
$17$	−16.9983	+	0.237334i	−0.999903	+	0.0139608i
$17$	−16.9983	+	0.237334i	−0.999903	+	0.0139608i
$18$	84.8367			4.71315
$19$	−3.46526	+	8.36588i	−0.182382	+	0.440309i	−0.988457	−	0.151505i	$-0.951588\pi$
$19$	−3.46526	+	8.36588i	−0.182382	+	0.440309i	0.806074	+	0.591814i	$0.201588\pi$
$20$		0			0
$21$	−21.4157	−	21.4157i	−1.01979	−	1.01979i
$22$	18.3646	−	3.65295i	0.834755	−	0.166043i
$23$	−30.0458	+	20.0759i	−1.30634	+	0.872867i	−0.996948	−	0.0780686i	$-0.975125\pi$
$23$	−30.0458	+	20.0759i	−1.30634	+	0.872867i	−0.309390	+	0.950935i	$0.600125\pi$
$24$	109.736	+	21.8278i	4.57232	+	0.909490i
$25$		0			0
$26$	6.90260	+	16.6644i	0.265485	+	0.640937i
$27$	15.6991	−	78.9247i	0.581448	−	2.92314i
$28$	−27.8492	−	41.6793i	−0.994616	−	1.48855i
$29$	0.381842	+	1.91965i	0.0131670	+	0.0661948i	0.986810	−	0.161882i	$-0.0517563\pi$
$29$	0.381842	+	1.91965i	0.0131670	+	0.0661948i	−0.973643	+	0.228077i	$0.926756\pi$
$30$		0			0
$31$	3.40793	−	5.10033i	0.109933	−	0.164527i	−0.772423	−	0.635108i	$-0.780956\pi$
$31$	3.40793	−	5.10033i	0.109933	−	0.164527i	0.882357	+	0.470581i	$0.155956\pi$
$32$	44.1137	+	18.2725i	1.37855	+	0.571015i
$33$		−	29.0299i		−	0.879695i
$34$	−23.0007	+	57.7979i	−0.676490	+	1.69994i
$35$		0			0
$36$	83.3086	−	201.125i	2.31413	−	5.58680i
$37$	11.8758	+	7.93518i	0.320969	+	0.214464i	0.705608	−	0.708603i	$-0.250674\pi$
$37$	11.8758	+	7.93518i	0.320969	+	0.214464i	−0.384639	+	0.923067i	$0.625674\pi$
$38$	23.4297	+	23.4297i	0.616571	+	0.616571i
$39$	27.4274	−	5.45566i	0.703268	−	0.139889i
$40$		0			0
$41$	−64.9302	−	12.9154i	−1.58366	−	0.315010i	−0.676712	−	0.736247i	$-0.736596\pi$
$41$	−64.9302	−	12.9154i	−1.58366	−	0.315010i	−0.906950	+	0.421237i	$0.861596\pi$
$42$	−102.388	+	42.4103i	−2.43780	+	1.00977i
$43$	−4.37477	−	10.5616i	−0.101739	−	0.245619i	0.864811	−	0.502097i	$-0.167438\pi$
$43$	−4.37477	−	10.5616i	−0.101739	−	0.245619i	−0.966550	+	0.256478i	$0.917438\pi$
$44$	9.37368	−	47.1247i	0.213038	−	1.07101i
$45$		0			0
$46$	25.7963	+	129.687i	0.560790	+	2.81928i
$47$	1.67827	−	1.67827i	0.0357079	−	0.0357079i	−0.689027	−	0.724735i	$-0.741962\pi$
$47$	1.67827	−	1.67827i	0.0357079	−	0.0357079i	0.724735	+	0.689027i	$0.241962\pi$
$48$	109.077	−	163.246i	2.27245	−	3.40096i
$49$	−18.9395	−	7.84500i	−0.386520	−	0.160102i
$50$		0			0
$51$	80.9300	+	52.4564i	1.58686	+	1.02856i
$52$	46.2849			0.890094
$53$	−21.0855	+	50.9049i	−0.397839	+	0.960469i	0.590338	+	0.807156i	$0.298994\pi$
$53$	−21.0855	+	50.9049i	−0.397839	+	0.960469i	−0.988178	+	0.153313i	$0.951006\pi$
$54$	−244.833	−	163.592i	−4.53395	−	3.02949i
$55$		0			0
$56$	−103.263	+	20.5404i	−1.84399	+	0.366792i
$57$	42.7136	−	28.5403i	0.749362	−	0.500707i
$58$	7.02437	+	1.39723i	0.121110	+	0.0240902i
$59$	38.2228	−	15.8324i	0.647844	−	0.268346i	−0.0344693	−	0.999406i	$-0.510974\pi$
$59$	38.2228	−	15.8324i	0.647844	−	0.268346i	0.682313	+	0.731060i	$0.260974\pi$
$60$		0			0
$61$	5.85814	−	29.4509i	0.0960351	−	0.482801i	−0.902596	−	0.430489i	$-0.858341\pi$
$61$	5.85814	−	29.4509i	0.0960351	−	0.482801i	0.998631	−	0.0523118i	$-0.0166590\pi$
$62$	−12.4703	−	18.6631i	−0.201134	−	0.301018i
$63$	24.1466	+	121.393i	0.383280	+	1.92688i
$64$	25.6607	−	25.6607i	0.400948	−	0.400948i
$65$		0			0
$66$	−98.1402	−	40.6510i	−1.48697	−	0.615924i
$67$			83.0052i			1.23888i	0.785042	+	0.619442i	$0.212641\pi$
$67$			83.0052i			1.23888i	−0.785042	+	0.619442i	$0.787359\pi$
$68$	114.437	+	111.285i	1.68289	+	1.63654i
$69$	205.003			2.97106
$70$		0			0
$71$	77.2000	+	51.5834i	1.08732	+	0.726526i	0.964017	−	0.265842i	$-0.0856500\pi$
$71$	77.2000	+	51.5834i	1.08732	+	0.726526i	0.123307	+	0.992369i	$0.460650\pi$
$72$	−323.321	−	323.321i	−4.49056	−	4.49056i
$73$	−50.8326	+	10.1112i	−0.696337	+	0.138510i	−0.530553	−	0.847652i	$-0.678016\pi$
$73$	−50.8326	+	10.1112i	−0.696337	+	0.138510i	−0.165784	+	0.986162i	$0.553016\pi$
$74$	43.4560	−	29.0364i	0.587243	−	0.392383i
$75$		0			0
$76$	78.5531	−	32.5378i	1.03359	−	0.428128i
$77$	10.4541	+	25.2383i	0.135767	+	0.327770i
$78$	19.9633	−	100.362i	0.255940	−	1.28670i
$79$	−53.4837	−	80.0441i	−0.677009	−	1.01322i	−0.997815	−	0.0660709i	$-0.978954\pi$
$79$	−53.4837	−	80.0441i	−0.677009	−	1.01322i	0.320806	−	0.947145i	$-0.396046\pi$
$80$		0			0
$81$	−175.265	+	175.265i	−2.16376	+	2.16376i
$82$	−134.585	+	201.421i	−1.64128	+	2.45635i
$83$	89.8717	+	37.2261i	1.08279	+	0.448507i	0.851488	−	0.524374i	$-0.175701\pi$
$83$	89.8717	+	37.2261i	1.08279	+	0.448507i	0.231304	+	0.972881i	$0.425701\pi$
$84$			284.379i			3.38547i
$85$		0			0
$86$	−41.8312			−0.486410
$87$	4.24924	−	10.2586i	0.0488418	−	0.117915i
$88$	−83.9110	−	56.0675i	−0.953534	−	0.637131i
$89$	6.35442	+	6.35442i	0.0713979	+	0.0713979i	0.741904	−	0.670506i	$-0.233923\pi$
$89$	6.35442	+	6.35442i	0.0713979	+	0.0713979i	−0.670506	+	0.741904i	$0.733923\pi$
$90$		0			0
$91$	−21.8805	+	14.6201i	−0.240445	+	0.160660i
$92$	332.784	+	66.1949i	3.61722	+	0.719509i
$93$	−32.1507	+	13.3173i	−0.345707	+	0.143197i
$94$	−3.32355	−	8.02376i	−0.0353569	−	0.0853592i
$95$		0			0
$96$	−150.494	−	225.231i	−1.56765	−	2.34616i
$97$	−14.0870	−	70.8202i	−0.145227	−	0.730105i	−0.982930	−	0.183979i	$-0.941102\pi$
$97$	−14.0870	−	70.8202i	−0.145227	−	0.730105i	0.837703	−	0.546126i	$-0.183898\pi$
$98$	−53.0424	+	53.0424i	−0.541249	+	0.541249i
$99$	−65.9113	+	98.6432i	−0.665771	+	0.996396i
$100$		0			0
$101$			83.3457i			0.825205i	0.910911	+	0.412602i	$0.135380\pi$
$101$			83.3457i			0.825205i	−0.910911	+	0.412602i	$0.864620\pi$
$102$	290.664	−	200.141i	2.84965	−	1.96217i
$103$	5.01201			0.0486603			0.0243302	−	0.999704i	$-0.492255\pi$
$103$	5.01201			0.0486603			0.0243302	+	0.999704i	$0.492255\pi$
$104$	37.2029	−	89.8158i	0.357721	−	0.863614i
$105$		0			0
$106$	142.565	+	142.565i	1.34496	+	1.34496i
$107$	−88.8403	+	17.6714i	−0.830284	+	0.165154i	−0.591894	−	0.806016i	$-0.701620\pi$
$107$	−88.8403	+	17.6714i	−0.830284	+	0.165154i	−0.238390	+	0.971170i	$0.576620\pi$
$108$	−628.256	+	419.787i	−5.81719	+	3.88692i
$109$	−149.579	−	29.7531i	−1.37228	−	0.272964i	−0.546740	−	0.837302i	$-0.684132\pi$
$109$	−149.579	−	29.7531i	−1.37228	−	0.272964i	−0.825544	+	0.564338i	$0.809132\pi$
$110$		0			0
$111$	−31.0085	−	74.8612i	−0.279356	−	0.674425i
$112$	−36.0438	+	181.204i	−0.321820	+	1.61790i
$113$	−117.757	−	176.235i	−1.04210	−	1.55961i	−0.809577	−	0.587013i	$-0.800304\pi$
$113$	−117.757	−	176.235i	−1.04210	−	1.55961i	−0.232518	−	0.972592i	$-0.574696\pi$
$114$	−36.6725	−	184.365i	−0.321689	−	1.61724i
$115$		0			0
$116$	10.2103	−	15.2808i	0.0880198	−	0.131731i
$117$	−105.585	−	43.7347i	−0.902434	−	0.373801i
$118$		−	151.388i		−	1.28295i
$119$	−89.2499	−	16.4611i	−0.749999	−	0.138328i
$120$		0			0
$121$	36.2843	−	87.5981i	0.299870	−	0.723951i
$122$	−91.3600	−	61.0448i	−0.748852	−	0.500367i
$123$	265.571	+	265.571i	2.15912	+	2.15912i
$124$	−56.4908	+	11.2367i	−0.455571	+	0.0906187i
$125$		0			0
$126$	444.202	+	88.3573i	3.52541	+	0.701248i
$127$	124.469	−	51.5570i	0.980075	−	0.405960i	0.165621	−	0.986189i	$-0.447037\pi$
$127$	124.469	−	51.5570i	0.980075	−	0.405960i	0.814453	+	0.580229i	$0.197037\pi$
$128$	22.2730	+	53.7719i	0.174008	+	0.420093i
$129$	−12.6524	+	63.6081i	−0.0980810	+	0.493086i
$130$		0			0
$131$	−22.1681	−	111.446i	−0.169222	−	0.850736i	−0.968354	−	0.249581i	$-0.919707\pi$
$131$	−22.1681	−	111.446i	−0.169222	−	0.850736i	0.799132	−	0.601155i	$-0.205293\pi$
$132$	−192.745	+	192.745i	−1.46019	+	1.46019i
$133$	−26.8570	+	40.1944i	−0.201933	+	0.302213i
$134$	280.612	+	116.233i	2.09412	+	0.867413i
$135$		0			0
$136$	307.931	−	132.615i	2.26420	−	0.975113i
$137$	16.2847			0.118867			0.0594333	−	0.998232i	$-0.481071\pi$
$137$	16.2847			0.118867			0.0594333	+	0.998232i	$0.481071\pi$
$138$	287.069	−	693.045i	2.08021	−	5.02206i
$139$	−42.9869	−	28.7229i	−0.309258	−	0.206640i	0.391249	−	0.920285i	$-0.372043\pi$
$139$	−42.9869	−	28.7229i	−0.309258	−	0.206640i	−0.700507	+	0.713645i	$0.747043\pi$
$140$		0			0
$141$	−13.2061	+	2.62686i	−0.0936604	+	0.0186302i
$142$	282.490	−	188.754i	1.98936	−	1.32925i
$143$	−24.7391	−	4.92092i	−0.173001	−	0.0344120i
$144$	−741.286	+	307.051i	−5.14782	+	2.13230i
$145$		0			0
$146$	−36.9990	+	186.006i	−0.253418	+	1.27402i
$147$	64.6124	+	96.6993i	0.439540	+	0.657818i
$148$	−26.1641	−	131.536i	−0.176784	−	0.888754i
$149$	−178.810	+	178.810i	−1.20007	+	1.20007i	−0.225924	+	0.974145i	$0.572540\pi$
$149$	−178.810	+	178.810i	−1.20007	+	1.20007i	−0.974145	+	0.225924i	$0.927460\pi$
$150$		0			0
$151$	38.4098	+	15.9098i	0.254369	+	0.105363i	0.506225	−	0.862402i	$-0.331041\pi$
$151$	38.4098	+	15.9098i	0.254369	+	0.105363i	−0.251855	+	0.967765i	$0.581041\pi$
$152$		−	178.586i		−	1.17490i
$153$	−155.899	−	361.994i	−1.01895	−	2.36597i
$154$	99.9610			0.649097
$155$		0			0
$156$	−218.328	−	145.882i	−1.39954	−	0.935142i
$157$	−38.7039	−	38.7039i	−0.246522	−	0.246522i	0.573020	−	0.819541i	$-0.305772\pi$
$157$	−38.7039	−	38.7039i	−0.246522	−	0.246522i	−0.819541	+	0.573020i	$0.805772\pi$
$158$	−345.495	+	68.7233i	−2.18668	+	0.434957i
$159$	259.905	−	173.663i	1.63462	−	1.09222i
$160$		0			0
$161$	−178.228	+	73.8243i	−1.10700	+	0.458536i
$162$	347.084	+	837.935i	2.14250	+	5.17244i
$163$	−46.8445	+	235.503i	−0.287390	+	1.44481i	0.519686	+	0.854357i	$0.326049\pi$
$163$	−46.8445	+	235.503i	−0.287390	+	1.44481i	−0.807076	+	0.590448i	$0.798951\pi$
$164$	345.353	+	516.857i	2.10581	+	3.15157i
$165$		0			0
$166$	251.697	−	251.697i	1.51625	−	1.51625i
$167$	−57.0363	+	85.3608i	−0.341535	+	0.511143i	−0.961985	−	0.273103i	$-0.911950\pi$
$167$	−57.0363	+	85.3608i	−0.341535	+	0.511143i	0.620450	+	0.784246i	$0.286950\pi$
$168$	551.838	+	228.579i	3.28475	+	1.36059i
$169$			144.702i			0.856223i
$170$		0			0
$171$	−209.940			−1.22772
$172$	−41.0777	+	99.1704i	−0.238824	+	0.576572i
$173$	26.1852	+	17.4964i	0.151360	+	0.101135i	0.628944	−	0.777451i	$-0.283487\pi$
$173$	26.1852	+	17.4964i	0.151360	+	0.101135i	−0.477584	+	0.878586i	$0.658487\pi$
$174$	−28.7304	−	28.7304i	−0.165117	−	0.165117i
$175$		0			0
$176$	−147.245	+	98.3861i	−0.836620	+	0.559012i
$177$	−230.200	−	45.7895i	−1.30056	−	0.258698i
$178$	30.3803	−	12.5839i	0.170676	−	0.0706961i
$179$	121.040	+	292.217i	0.676202	+	1.63250i	0.770875	+	0.636987i	$0.219819\pi$
$179$	121.040	+	292.217i	0.676202	+	1.63250i	−0.0946731	+	0.995508i	$0.530181\pi$
$180$		0			0
$181$	−168.125	−	251.617i	−0.928869	−	1.39015i	−0.920737	−	0.390184i	$-0.872411\pi$
$181$	−168.125	−	251.617i	−0.928869	−	1.39015i	−0.00813199	−	0.999967i	$-0.502589\pi$
$182$	18.7859	+	94.4430i	0.103219	+	0.518917i
$183$	−120.457	+	120.457i	−0.658236	+	0.658236i
$184$	395.937	−	592.561i	2.15183	−	3.22044i
$185$		0			0
$186$			127.339i			0.684618i
$187$	−49.3344	−	71.6481i	−0.263820	−	0.383145i
$188$	−22.2858			−0.118542
$189$	164.400	−	396.896i	0.869840	−	2.09998i
$190$		0			0
$191$	−5.18071	−	5.18071i	−0.0271241	−	0.0271241i	0.693415	−	0.720539i	$-0.256105\pi$
$191$	−5.18071	−	5.18071i	−0.0271241	−	0.0271241i	−0.720539	+	0.693415i	$0.756105\pi$
$192$	−201.921	+	40.1645i	−1.05167	+	0.209190i
$193$	255.813	−	170.929i	1.32546	−	0.885642i	0.327218	−	0.944949i	$-0.393889\pi$
$193$	255.813	−	170.929i	1.32546	−	0.885642i	0.998240	+	0.0593066i	$0.0188890\pi$
$194$	−259.145	−	51.5471i	−1.33580	−	0.265707i
$195$		0			0
$196$	73.6622	+	177.836i	0.375827	+	0.907328i
$197$	9.13709	−	45.9352i	0.0463811	−	0.233174i	−0.950641	−	0.310294i	$-0.899573\pi$
$197$	9.13709	−	45.9352i	0.0463811	−	0.233174i	0.997022	+	0.0771202i	$0.0245725\pi$
$198$	241.182	+	360.955i	1.21809	+	1.82300i
$199$	10.2205	+	51.3818i	0.0513591	+	0.258200i	0.997931	−	0.0642930i	$-0.0204792\pi$
$199$	10.2205	+	51.3818i	0.0513591	+	0.258200i	−0.946572	+	0.322493i	$0.895479\pi$
$200$		0			0
$201$	261.618	−	391.539i	1.30158	−	1.94796i
$202$	281.763	+	116.710i	1.39487	+	0.577772i
$203$			10.4489i			0.0514724i
$204$	−189.051	−	885.621i	−0.926722	−	4.34128i
$205$		0			0
$206$	7.01839	−	16.9439i	0.0340698	−	0.0822519i
$207$	−696.597	−	465.451i	−3.36520	−	2.24856i
$208$	−120.627	−	120.627i	−0.579938	−	0.579938i
$209$	−45.4457	+	9.03971i	−0.217444	+	0.0432522i
$210$		0			0
$211$	−195.890	−	38.9649i	−0.928388	−	0.184668i	−0.292337	−	0.956315i	$-0.594433\pi$
$211$	−195.890	−	38.9649i	−0.928388	−	0.184668i	−0.636051	+	0.771647i	$0.719433\pi$
$212$	477.981	−	197.986i	2.25463	−	0.933898i
$213$	−201.574	−	486.642i	−0.946356	−	2.28471i
$214$	−64.6632	+	325.084i	−0.302165	+	1.51908i
$215$		0			0
$216$	309.617	+	1556.55i	1.43341	+	7.20624i
$217$	23.1558	−	23.1558i	0.106709	−	0.106709i
$218$	−310.042	+	464.011i	−1.42221	+	2.12849i
$219$	271.649	+	112.521i	1.24040	+	0.513792i
$220$		0			0
$221$	58.4215	−	60.0760i	0.264351	−	0.271837i
$222$	−296.501			−1.33559
$223$	42.1607	−	101.785i	0.189062	−	0.456435i	−0.800718	−	0.599042i	$-0.795548\pi$
$223$	42.1607	−	101.785i	0.189062	−	0.456435i	0.989779	+	0.142607i	$0.0455484\pi$
$224$	211.947	+	141.618i	0.946191	+	0.632225i
$225$		0			0
$226$	−760.687	+	151.310i	−3.36587	+	0.669514i
$227$	−213.450	+	142.623i	−0.940309	+	0.628294i	−0.928379	−	0.371635i	$-0.878797\pi$
$227$	−213.450	+	142.623i	−0.940309	+	0.628294i	−0.0119297	+	0.999929i	$0.503797\pi$
$228$	−473.092	−	94.1038i	−2.07496	−	0.412736i
$229$	28.1869	−	11.6754i	0.123087	−	0.0509842i	−0.320290	−	0.947320i	$-0.603780\pi$
$229$	28.1869	−	11.6754i	0.123087	−	0.0509842i	0.443377	+	0.896335i	$0.353780\pi$
$230$		0			0
$231$	30.2346	−	152.000i	0.130886	−	0.658007i
$232$	−21.4455	−	32.0955i	−0.0924376	−	0.138343i
$233$	27.2801	+	137.146i	0.117082	+	0.588611i	0.994129	+	0.108205i	$0.0345104\pi$
$233$	27.2801	+	137.146i	0.117082	+	0.588611i	−0.877047	+	0.480405i	$0.840490\pi$
$234$	−295.704	+	295.704i	−1.26369	+	1.26369i
$235$		0			0
$236$	−358.900	−	148.661i	−1.52076	−	0.629921i
$237$			546.143i			2.30440i
$238$	−180.627	+	278.672i	−0.758937	+	1.17089i
$239$	−439.887			−1.84053			−0.920265	−	0.391295i	$-0.872027\pi$
$239$	−439.887			−1.84053			−0.920265	+	0.391295i	$0.872027\pi$
$240$		0			0
$241$	−21.9897	−	14.6931i	−0.0912437	−	0.0609671i	0.509111	−	0.860701i	$-0.329974\pi$
$241$	−21.9897	−	14.6931i	−0.0912437	−	0.0609671i	−0.600355	+	0.799734i	$0.704974\pi$
$242$	−245.329	−	245.329i	−1.01376	−	1.01376i
$243$	668.815	−	133.036i	2.75232	−	0.547471i
$244$	−234.435	+	156.644i	−0.960799	+	0.641985i
$245$		0			0
$246$	1269.69	−	525.922i	5.16133	−	2.13789i
$247$	−17.0814	−	41.2382i	−0.0691555	−	0.166956i
$248$	−23.6014	+	118.652i	−0.0951669	+	0.478436i
$249$	−306.599	−	458.857i	−1.23132	−	1.84280i
$250$		0			0
$251$	166.889	−	166.889i	0.664897	−	0.664897i	−0.291634	−	0.956530i	$-0.594199\pi$
$251$	166.889	−	166.889i	0.664897	−	0.664897i	0.956530	+	0.291634i	$0.0941988\pi$
$252$	645.672	−	966.316i	2.56219	−	3.83459i
$253$	−170.834	−	70.7618i	−0.675234	−	0.279691i
$254$		−	492.984i		−	1.94088i
$255$		0			0
$256$	358.132			1.39895
$257$	157.615	−	380.517i	0.613289	−	1.48061i	−0.246077	−	0.969250i	$-0.579141\pi$
$257$	157.615	−	380.517i	0.613289	−	1.48061i	0.859366	−	0.511361i	$-0.170859\pi$
$258$	197.320	+	131.845i	0.764805	+	0.511027i
$259$	53.9170	+	53.9170i	0.208174	+	0.208174i
$260$		0			0
$261$	−37.7305	+	25.2107i	−0.144561	+	0.0965928i
$262$	−407.804	−	81.1173i	−1.55650	−	0.309608i
$263$	−263.972	+	109.341i	−1.00370	+	0.415745i	−0.823151	−	0.567822i	$-0.807786\pi$
$263$	−263.972	+	109.341i	−1.00370	+	0.415745i	−0.180545	+	0.983567i	$0.557786\pi$
$264$	219.097	+	528.946i	0.829912	+	2.00358i
$265$		0			0
$266$	98.2751	+	147.079i	0.369455	+	0.552929i
$267$	−9.94604	−	50.0021i	−0.0372511	−	0.187274i
$268$	551.115	−	551.115i	2.05640	−	2.05640i
$269$	−152.969	+	228.934i	−0.568657	+	0.851055i	−0.998659	−	0.0517731i	$-0.983513\pi$
$269$	−152.969	+	228.934i	−0.568657	+	0.851055i	0.430002	+	0.902828i	$0.358513\pi$
$270$		0			0
$271$			89.0741i			0.328687i	0.986403	+	0.164343i	$0.0525505\pi$
$271$			89.0741i			0.328687i	−0.986403	+	0.164343i	$0.947449\pi$
$272$	−8.21356	−	588.273i	−0.0301969	−	2.16277i
$273$	149.291			0.546854
$274$	22.8037	−	55.0530i	0.0832252	−	0.200923i
$275$		0			0
$276$	−1361.12	−	1361.12i	−4.93160	−	4.93160i
$277$	199.625	−	39.7079i	0.720667	−	0.143350i	0.178887	−	0.983870i	$-0.442750\pi$
$277$	199.625	−	39.7079i	0.720667	−	0.143350i	0.541781	+	0.840520i	$0.317750\pi$
$278$	−157.297	+	105.103i	−0.565817	+	0.378067i
$279$	139.484	+	27.7451i	0.499943	+	0.0994448i
$280$		0			0
$281$	−10.2241	−	24.6831i	−0.0363847	−	0.0878404i	0.904643	−	0.426171i	$-0.140138\pi$
$281$	−10.2241	−	24.6831i	−0.0363847	−	0.0878404i	−0.941027	+	0.338331i	$0.890138\pi$
$282$	−9.61219	+	48.3237i	−0.0340858	+	0.171361i
$283$	70.2769	+	105.177i	0.248328	+	0.371649i	0.934603	−	0.355693i	$-0.115755\pi$
$283$	70.2769	+	105.177i	0.248328	+	0.371649i	−0.686275	+	0.727343i	$0.740755\pi$
$284$	−170.082	−	855.060i	−0.598880	−	3.01077i
$285$		0			0
$286$	−51.2784	+	76.7436i	−0.179295	+	0.268334i
$287$	−326.521	−	135.249i	−1.13770	−	0.471252i
$288$			1107.02i			3.84383i
$289$	288.887	−	8.06856i	0.999610	−	0.0279189i
$290$		0			0
$291$	−156.764	+	378.462i	−0.538708	+	1.30056i
$292$	404.638	+	270.370i	1.38575	+	0.925926i
$293$	−274.643	−	274.643i	−0.937349	−	0.937349i	0.0608010	−	0.998150i	$-0.480635\pi$
$293$	−274.643	−	274.643i	−0.937349	−	0.937349i	−0.998150	+	0.0608010i	$0.980635\pi$
$294$	417.384	−	83.0229i	1.41967	−	0.282391i
$295$		0			0
$296$	−276.275	−	54.9545i	−0.933362	−	0.185657i
$297$	380.432	−	157.580i	1.28091	−	0.530572i
$298$	354.105	+	854.886i	1.18827	+	2.86874i
$299$	34.7504	−	174.702i	0.116222	−	0.584288i
$300$		0			0
$301$	−11.9062	−	59.8566i	−0.0395555	−	0.198859i
$302$	107.571	−	107.571i	0.356197	−	0.356197i
$303$	262.691	−	393.145i	0.866968	−	1.29751i
$304$	−289.523	−	119.925i	−0.952380	−	0.394489i
$305$		0			0
$306$	−1442.08	+	20.1346i	−4.71269	+	0.0657994i
$307$	237.767			0.774485			0.387242	−	0.921978i	$-0.373428\pi$
$307$	237.767			0.774485			0.387242	+	0.921978i	$0.373428\pi$
$308$	98.1605	−	236.980i	0.318703	−	0.769417i
$309$	−23.6419	−	15.7970i	−0.0765110	−	0.0511230i
$310$		0			0
$311$	61.0589	−	12.1454i	0.196331	−	0.0390526i	−0.0959453	−	0.995387i	$-0.530587\pi$
$311$	61.0589	−	12.1454i	0.196331	−	0.0390526i	0.292276	+	0.956334i	$0.405587\pi$
$312$	−458.572	+	306.408i	−1.46978	+	0.982077i
$313$	−184.794	−	36.7577i	−0.590395	−	0.117437i	−0.109153	−	0.994025i	$-0.534814\pi$
$313$	−184.794	−	36.7577i	−0.590395	−	0.117437i	−0.481242	+	0.876588i	$0.659814\pi$
$314$	−185.042	+	76.6469i	−0.589306	+	0.244098i
$315$		0			0
$316$	−176.348	+	886.560i	−0.558063	+	2.80557i
$317$	261.348	+	391.135i	0.824442	+	1.23386i	0.969658	+	0.244464i	$0.0786121\pi$
$317$	261.348	+	391.135i	0.824442	+	1.23386i	−0.145217	+	0.989400i	$0.546388\pi$
$318$	−223.146	−	1121.83i	−0.701716	−	3.52777i
$319$	−7.08199	+	7.08199i	−0.0222006	+	0.0222006i
$320$		0			0
$321$	474.761	+	196.653i	1.47901	+	0.612625i
$322$			705.903i			2.19224i
$323$	56.9182	−	143.029i	0.176217	−	0.442813i
$324$	2327.35			7.18318
$325$		0			0
$326$	730.558	+	488.143i	2.24098	+	1.49737i
$327$	611.794	+	611.794i	1.87093	+	1.87093i
$328$	1280.55	−	254.717i	3.90412	−	0.776577i
$329$	10.5353	−	7.03946i	0.0320222	−	0.0213965i
$330$		0			0
$331$	193.036	−	79.9583i	0.583191	−	0.241566i	−0.0715270	−	0.997439i	$-0.522787\pi$
$331$	193.036	−	79.9583i	0.583191	−	0.241566i	0.654718	+	0.755873i	$0.272787\pi$
$332$	−349.542	−	843.869i	−1.05284	−	2.54177i
$333$	−64.6029	+	324.781i	−0.194003	+	0.975317i
$334$	208.707	+	312.352i	0.624871	+	0.935185i
$335$		0			0
$336$	741.146	−	741.146i	2.20579	−	2.20579i
$337$	−133.577	+	199.913i	−0.396372	+	0.593212i	−0.974953	−	0.222413i	$-0.928607\pi$
$337$	−133.577	+	199.913i	−0.396372	+	0.593212i	0.578581	+	0.815625i	$0.303607\pi$
$338$	489.187	+	202.628i	1.44730	+	0.599490i
$339$			1202.46i			3.54708i
$340$		0			0
$341$	31.3888			0.0920492
$342$	−293.981	+	709.734i	−0.859595	+	2.07524i
$343$	−308.499	−	206.132i	−0.899414	−	0.600969i
$344$	159.423	+	159.423i	0.463438	+	0.463438i
$345$		0			0
$346$	95.8168	−	64.0228i	0.276927	−	0.185037i
$347$	−320.344	−	63.7204i	−0.923182	−	0.183632i	−0.289457	−	0.957191i	$-0.593475\pi$
$347$	−320.344	−	63.7204i	−0.923182	−	0.183632i	−0.633725	+	0.773559i	$0.718475\pi$
$348$	−96.3249	+	39.8991i	−0.276796	+	0.114653i
$349$	−22.5880	−	54.5323i	−0.0647221	−	0.156253i	0.888209	−	0.459439i	$-0.151950\pi$
$349$	−22.5880	−	54.5323i	−0.0647221	−	0.156253i	−0.952931	+	0.303186i	$0.901950\pi$
$350$		0			0
$351$	220.377	+	329.817i	0.627853	+	0.939649i
$352$	47.6668	+	239.637i	0.135417	+	0.680788i
$353$	279.425	−	279.425i	0.791571	−	0.791571i	−0.190178	−	0.981750i	$-0.560907\pi$
$353$	279.425	−	279.425i	0.791571	−	0.791571i	0.981750	+	0.190178i	$0.0609066\pi$
$354$	−477.150	+	714.106i	−1.34788	+	2.01725i
$355$		0			0
$356$		−	84.3806i		−	0.237024i
$357$	369.113	+	358.948i	1.03393	+	1.00546i
$358$	1157.38			3.23290
$359$	−53.3154	+	128.715i	−0.148511	+	0.358537i	−0.980576	−	0.196142i	$-0.937159\pi$
$359$	−53.3154	+	128.715i	−0.148511	+	0.358537i	0.832065	+	0.554679i	$0.187159\pi$
$360$		0			0
$361$	197.286	+	197.286i	0.546498	+	0.546498i
$362$	−1086.06	+	216.031i	−3.00016	+	0.596770i
$363$	−447.249	+	298.842i	−1.23209	+	0.823256i
$364$	242.346	+	48.2056i	0.665786	+	0.132433i
$365$		0			0
$366$	238.546	+	575.902i	0.651766	+	1.57350i
$367$	−94.9319	+	477.255i	−0.258670	+	1.30042i	0.604944	+	0.796268i	$0.293195\pi$
$367$	−94.9319	+	477.255i	−0.258670	+	1.30042i	−0.863614	+	0.504154i	$0.831805\pi$
$368$	−694.781	−	1039.81i	−1.88799	−	2.82558i
$369$	−299.438	−	1505.38i	−0.811485	−	4.07961i
$370$		0			0
$371$	−163.420	+	244.576i	−0.440486	+	0.659233i
$372$	301.886	+	125.045i	0.811521	+	0.336143i
$373$		−	176.006i		−	0.471867i	−0.971769	−	0.235933i	$-0.924185\pi$
$373$		−	176.006i		−	0.471867i	0.971769	−	0.235933i	$-0.0758147\pi$
$374$	−311.301	+	66.4526i	−0.832356	+	0.177681i
$375$		0			0
$376$	−17.9129	+	43.2457i	−0.0476408	+	0.115015i
$377$	−8.02199	−	5.36012i	−0.0212785	−	0.0142178i
$378$	−1111.56	−	1111.56i	−2.94063	−	2.94063i
$379$	434.443	−	86.4160i	1.14629	−	0.228011i	0.414830	−	0.909899i	$-0.363841\pi$
$379$	434.443	−	86.4160i	1.14629	−	0.228011i	0.731456	+	0.681888i	$0.238841\pi$
$380$		0			0
$381$	−749.627	−	149.110i	−1.96752	−	0.391365i
$382$	−24.7688	+	10.2596i	−0.0648397	+	0.0268575i
$383$	222.966	+	538.287i	0.582157	+	1.40545i	0.890854	+	0.454290i	$0.150107\pi$
$383$	222.966	+	538.287i	0.582157	+	1.40545i	−0.308697	+	0.951160i	$0.599893\pi$
$384$	64.4168	−	323.845i	0.167752	−	0.843347i
$385$		0			0
$386$	−219.633	−	1104.17i	−0.568998	−	2.86055i
$387$	187.413	−	187.413i	0.484270	−	0.484270i
$388$	−376.681	+	563.743i	−0.970827	+	1.45295i
$389$	−358.440	−	148.471i	−0.921441	−	0.381673i	−0.129016	−	0.991643i	$-0.541182\pi$
$389$	−358.440	−	148.471i	−0.921441	−	0.381673i	−0.792425	+	0.609969i	$0.791182\pi$
$390$		0			0
$391$	505.963	−	348.389i	1.29402	−	0.891019i
$392$	404.299			1.03138
$393$	−246.692	+	595.568i	−0.627716	+	1.51544i
$394$	−142.496	−	95.2130i	−0.361666	−	0.241657i
$395$		0			0
$396$	1092.56	−	217.324i	2.75900	−	0.548799i
$397$	79.6060	−	53.1910i	0.200519	−	0.133982i	−0.451257	−	0.892394i	$-0.649024\pi$
$397$	79.6060	−	53.1910i	0.200519	−	0.133982i	0.651776	+	0.758412i	$0.274024\pi$
$398$	188.016	+	37.3987i	0.472401	+	0.0939665i
$399$	253.372	−	104.950i	0.635017	−	0.263032i
$400$		0			0
$401$	−15.3440	+	77.1397i	−0.0382644	+	0.192368i	−0.995190	−	0.0979657i	$-0.968766\pi$
$401$	−15.3440	+	77.1397i	−0.0382644	+	0.192368i	0.956925	+	0.290334i	$0.0937664\pi$
$402$	−957.312	−	1432.72i	−2.38137	−	3.56398i
$403$	5.89896	+	29.6561i	0.0146376	+	0.0735883i
$404$	553.375	−	553.375i	1.36974	−	1.36974i
$405$		0			0
$406$	35.3241	+	14.6317i	0.0870052	+	0.0360387i
$407$			73.0870i			0.179575i
$408$	−1870.50	−	344.992i	−4.58457	−	0.845568i
$409$	−41.8341			−0.102284			−0.0511420	−	0.998691i	$-0.516286\pi$
$409$	−41.8341			−0.102284			−0.0511420	+	0.998691i	$0.516286\pi$
$410$		0			0
$411$	−76.8157	−	51.3266i	−0.186900	−	0.124882i
$412$	−33.2774	−	33.2774i	−0.0807703	−	0.0807703i
$413$	216.623	−	43.0889i	0.524510	−	0.104331i
$414$	−2548.98	+	1703.18i	−6.15697	+	4.11395i
$415$		0			0
$416$	−217.451	+	90.0711i	−0.522718	+	0.216517i
$417$	112.241	+	270.974i	0.269164	+	0.649819i
$418$	−33.0781	+	166.295i	−0.0791341	+	0.397834i
$419$	141.224	+	211.357i	0.337051	+	0.504432i	0.960819	−	0.277177i	$-0.0893990\pi$
$419$	141.224	+	211.357i	0.337051	+	0.504432i	−0.623768	+	0.781610i	$0.714399\pi$
$420$		0			0
$421$	23.1007	−	23.1007i	0.0548710	−	0.0548710i	−0.679139	−	0.734010i	$-0.737647\pi$
$421$	23.1007	−	23.1007i	0.0548710	−	0.0548710i	0.734010	+	0.679139i	$0.237647\pi$
$422$	−406.034	+	607.673i	−0.962166	+	1.43998i
$423$	50.8383	+	21.0579i	0.120185	+	0.0497823i
$424$		−	1086.66i		−	2.56288i
$425$		0			0
$426$	−1927.44			−4.52450
$427$	61.3460	−	148.102i	0.143668	−	0.346844i
$428$	707.187	+	472.527i	1.65231	+	1.10404i
$429$	101.186	+	101.186i	0.235864	+	0.235864i
$430$		0			0
$431$	505.056	−	337.468i	1.17182	−	0.782987i	0.191715	−	0.981451i	$-0.438595\pi$
$431$	505.056	−	337.468i	1.17182	−	0.782987i	0.980108	+	0.198463i	$0.0635950\pi$
$432$	2731.40	+	543.309i	6.32268	+	1.25766i
$433$	−217.841	+	90.2325i	−0.503096	+	0.208389i	−0.619774	−	0.784781i	$-0.712776\pi$
$433$	−217.841	+	90.2325i	−0.503096	+	0.208389i	0.116678	+	0.993170i	$0.462776\pi$
$434$	−45.8564	−	110.707i	−0.105660	−	0.255086i
$435$		0			0
$436$	795.586	+	1190.68i	1.82474	+	2.73092i
$437$	−63.8365	−	320.928i	−0.146079	−	0.734388i
$438$	760.786	−	760.786i	1.73695	−	1.73695i
$439$	372.897	−	558.080i	0.849424	−	1.27125i	−0.111311	−	0.993786i	$-0.535505\pi$
$439$	372.897	−	558.080i	0.849424	−	1.27125i	0.960735	−	0.277467i	$-0.0894950\pi$
$440$		0			0
$441$		−	475.282i		−	1.07774i
$442$	−121.288	−	281.628i	−0.274407	−	0.637168i
$443$	−310.122			−0.700049			−0.350024	−	0.936741i	$-0.613827\pi$
$443$	−310.122			−0.700049			−0.350024	+	0.936741i	$0.613827\pi$
$444$	−291.161	+	702.924i	−0.655767	+	1.58316i
$445$		0			0
$446$	−285.062	−	285.062i	−0.639152	−	0.639152i
$447$	1407.04	−	279.877i	3.14773	−	0.626122i
$448$	161.084	−	107.633i	0.359562	−	0.240252i
$449$	172.129	+	34.2385i	0.383360	+	0.0762551i	0.383008	−	0.923745i	$-0.374888\pi$
$449$	172.129	+	34.2385i	0.383360	+	0.0762551i	0.000351796		1.00000i	$0.499888\pi$
$450$		0			0
$451$	−129.639	−	312.976i	−0.287447	−	0.693959i
$452$	−388.270	+	1951.97i	−0.859005	+	4.31851i
$453$	−131.035	−	196.108i	−0.289262	−	0.432910i
$454$	183.261	+	921.318i	0.403660	+	2.02933i
$455$		0			0
$456$	−562.871	+	842.396i	−1.23437	+	1.84736i
$457$	−575.705	−	238.465i	−1.25975	−	0.521805i	−0.349917	−	0.936781i	$-0.613790\pi$
$457$	−575.705	−	238.465i	−1.25975	−	0.521805i	−0.909832	+	0.414976i	$0.863790\pi$
$458$		−	111.639i		−	0.243754i
$459$	−248.127	+	1345.31i	−0.540582	+	2.93097i
$460$		0			0
$461$	−269.146	+	649.777i	−0.583831	+	1.40949i	0.305483	+	0.952198i	$0.401182\pi$
$461$	−269.146	+	649.777i	−0.583831	+	1.40949i	−0.889314	+	0.457296i	$0.848818\pi$
$462$	−471.521	−	315.060i	−1.02061	−	0.681948i
$463$	−268.136	−	268.136i	−0.579127	−	0.579127i	0.355536	−	0.934663i	$-0.384298\pi$
$463$	−268.136	−	268.136i	−0.579127	−	0.579127i	−0.934663	+	0.355536i	$0.884298\pi$
$464$	−66.4346	+	13.2147i	−0.143178	+	0.0284799i
$465$		0			0
$466$	501.845	+	99.8231i	1.07692	+	0.214213i
$467$	492.616	−	204.048i	1.05485	−	0.436934i	0.213230	−	0.977002i	$-0.431602\pi$
$467$	492.616	−	204.048i	1.05485	−	0.436934i	0.841621	+	0.540068i	$0.181602\pi$
$468$	410.655	+	991.410i	0.877469	+	2.11840i
$469$	−86.4498	+	434.612i	−0.184328	+	0.926679i
$470$		0			0
$471$	60.5800	+	304.556i	0.128620	+	0.646616i
$472$	−576.955	+	576.955i	−1.22236	+	1.22236i
$473$	32.4995	−	48.6389i	0.0687093	−	0.102831i
$474$	1846.32	+	764.771i	3.89519	+	1.61344i
$475$		0			0
$476$	483.283	+	701.870i	1.01530	+	1.47452i
$477$	−1277.45			−2.67808
$478$	−615.979	+	1487.11i	−1.28866	+	3.11110i
$479$	−632.407	−	422.561i	−1.32027	−	0.882173i	−0.322345	−	0.946622i	$-0.604471\pi$
$479$	−632.407	−	422.561i	−1.32027	−	0.882173i	−0.997921	+	0.0644488i	$0.979471\pi$
$480$		0			0
$481$	−69.0525	+	13.7354i	−0.143560	+	0.0285559i
$482$	−80.4646	+	53.7648i	−0.166939	+	0.111545i
$483$	1073.39	+	213.510i	2.22234	+	0.442050i
$484$	−822.519	+	340.699i	−1.69942	+	0.703923i
$485$		0			0
$486$	486.803	−	2447.32i	1.00165	−	5.03565i
$487$	203.220	+	304.140i	0.417289	+	0.624518i	0.979252	−	0.202645i	$-0.0649537\pi$
$487$	203.220	+	304.140i	0.417289	+	0.624518i	−0.561963	+	0.827162i	$0.689954\pi$
$488$	115.534	+	580.829i	0.236750	+	1.19022i
$489$	963.234	−	963.234i	1.96980	−	1.96980i
$490$		0			0
$491$	−543.876	−	225.281i	−1.10769	−	0.458820i	−0.247548	−	0.968876i	$-0.579625\pi$
$491$	−543.876	−	225.281i	−1.10769	−	0.458820i	−0.860142	+	0.510055i	$0.829625\pi$
$492$		−	3526.53i		−	7.16775i
$493$	−6.94628	−	32.5402i	−0.0140898	−	0.0660045i
$494$	−163.331			−0.330630
$495$		0			0
$496$	176.511	+	117.941i	0.355868	+	0.237783i
$497$	350.492	+	350.492i	0.705216	+	0.705216i
$498$	−1980.57	+	393.960i	−3.97705	+	0.791085i
$499$	242.463	−	162.009i	0.485898	−	0.324666i	−0.288376	−	0.957517i	$-0.593115\pi$
$499$	242.463	−	162.009i	0.485898	−	0.324666i	0.774274	+	0.632851i	$0.218115\pi$
$500$		0			0
$501$	538.085	−	222.882i	1.07402	−	0.444875i
$502$	−330.497	−	797.891i	−0.658361	−	1.58942i
$503$	122.443	−	615.564i	0.243426	−	1.22379i	−0.644790	−	0.764360i	$-0.723055\pi$
$503$	122.443	−	615.564i	0.243426	−	1.22379i	0.888216	−	0.459426i	$-0.151945\pi$
$504$	−1356.16	−	2029.63i	−2.69079	−	4.02705i
$505$		0			0
$506$	−478.443	+	478.443i	−0.945539	+	0.945539i
$507$	456.075	−	682.565i	0.899556	−	1.34628i
$508$	−1168.73	−	484.104i	−2.30065	−	0.952961i
$509$			905.441i			1.77886i	0.457069	+	0.889431i	$0.348899\pi$
$509$			905.441i			1.77886i	−0.457069	+	0.889431i	$0.651101\pi$
$510$		0			0
$511$	−276.688			−0.541465
$512$	412.405	−	995.633i	0.805478	−	1.94460i
$513$	605.873	+	404.831i	1.18104	+	0.789145i
$514$	−1065.69	−	1065.69i	−2.07332	−	2.07332i
$515$		0			0
$516$	506.334	−	338.321i	0.981267	−	0.655662i
$517$	11.9117	+	2.36939i	0.0230400	+	0.00458295i
$518$	257.775	−	106.774i	0.497636	−	0.206127i
$519$	−68.3712	−	165.063i	−0.131736	−	0.318040i
$520$		0			0
$521$	−500.960	−	749.739i	−0.961535	−	1.43904i	−0.897461	−	0.441093i	$-0.854591\pi$
$521$	−500.960	−	749.739i	−0.961535	−	1.43904i	−0.0640736	−	0.997945i	$-0.520409\pi$
$522$	32.3942	+	162.857i	0.0620579	+	0.311986i
$523$	−33.6388	+	33.6388i	−0.0643190	+	0.0643190i	−0.738535	−	0.674216i	$-0.764482\pi$
$523$	−33.6388	+	33.6388i	−0.0643190	+	0.0643190i	0.674216	+	0.738535i	$0.264482\pi$
$524$	−592.765	+	887.136i	−1.13123	+	1.69301i
$525$		0			0
$526$			1045.51i			1.98766i
$527$	−56.7187	+	87.5060i	−0.107626	+	0.166046i
$528$	1004.66			1.90276
$529$	297.265	−	717.661i	0.561938	−	1.35664i
$530$		0			0
$531$	678.251	+	678.251i	1.27731	+	1.27731i
$532$	445.189	−	88.5536i	0.836822	−	0.166454i
$533$	271.336	−	181.301i	0.509072	−	0.340151i
$534$	−182.967	−	36.3945i	−0.342636	−	0.0681544i
$535$		0			0
$536$	−626.463	−	1512.41i	−1.16877	−	2.82167i
$537$	350.065	−	1759.90i	0.651891	−	3.27727i
$538$	559.742	+	837.713i	1.04041	+	1.55709i
$539$	−20.4650	−	102.884i	−0.0379684	−	0.190880i
$540$		0			0
$541$	−193.644	+	289.809i	−0.357937	+	0.535691i	−0.966116	−	0.258109i	$-0.916901\pi$
$541$	−193.644	+	289.809i	−0.357937	+	0.535691i	0.608178	+	0.793800i	$0.291901\pi$
$542$	301.129	+	124.732i	0.555588	+	0.230132i
$543$			1716.79i			3.16168i
$544$	−754.196	−	300.132i	−1.38639	−	0.551714i
$545$		0			0
$546$	209.054	−	504.702i	0.382883	−	0.924362i
$547$	181.730	+	121.428i	0.332230	+	0.221989i	0.710485	−	0.703712i	$-0.248476\pi$
$547$	181.730	+	121.428i	0.332230	+	0.221989i	−0.378255	+	0.925702i	$0.623476\pi$
$548$	−108.123	−	108.123i	−0.197304	−	0.197304i
$549$	682.805	−	135.818i	1.24372	−	0.247392i
$550$		0			0
$551$	−17.3827	−	3.45764i	−0.0315476	−	0.00627521i
$552$	−3735.30	+	1547.21i	−6.76685	+	2.80292i
$553$	−196.673	−	474.811i	−0.355648	−	0.858609i
$554$	145.299	−	730.466i	0.262272	−	1.31853i
$555$		0			0
$556$	94.7058	+	476.118i	0.170334	+	0.856328i
$557$	−441.292	+	441.292i	−0.792267	+	0.792267i	−0.981862	−	0.189596i	$-0.939282\pi$
$557$	−441.292	+	441.292i	−0.792267	+	0.792267i	0.189596	+	0.981862i	$0.439282\pi$
$558$	289.118	−	432.695i	0.518132	−	0.775440i
$559$	52.0617	+	21.5647i	0.0931336	+	0.0385772i
$560$		0			0
$561$	6.88978	+	493.461i	0.0122813	+	0.879609i
$562$	−97.7621			−0.173954
$563$	141.717	−	342.135i	0.251718	−	0.607700i	−0.746625	−	0.665245i	$-0.768327\pi$
$563$	141.717	−	342.135i	0.251718	−	0.607700i	0.998343	+	0.0575448i	$0.0183272\pi$
$564$	105.123	+	70.2412i	0.186389	+	0.124541i
$565$		0			0
$566$	453.976	−	90.3014i	0.802078	−	0.159543i
$567$	−1100.22	+	735.142i	−1.94042	+	1.29655i
$568$	−1795.95	−	357.237i	−3.16189	−	0.628938i
$569$	−891.706	+	369.357i	−1.56715	+	0.649133i	−0.986312	−	0.164889i	$-0.947274\pi$
$569$	−891.706	+	369.357i	−1.56715	+	0.649133i	−0.580834	+	0.814022i	$0.697274\pi$
$570$		0			0
$571$	−62.0643	+	312.018i	−0.108694	+	0.546442i	0.887614	+	0.460589i	$0.152362\pi$
$571$	−62.0643	+	312.018i	−0.108694	+	0.546442i	−0.996308	+	0.0858532i	$0.972638\pi$
$572$	131.583	+	196.928i	0.230041	+	0.344280i
$573$	8.10893	+	40.7663i	0.0141517	+	0.0711454i
$574$	−914.462	+	914.462i	−1.59314	+	1.59314i
$575$		0			0
$576$	777.315	+	321.974i	1.34950	+	0.558983i
$577$			163.289i			0.282996i	0.989939	+	0.141498i	$0.0451919\pi$
$577$			163.289i			0.282996i	−0.989939	+	0.141498i	$0.954808\pi$
$578$	377.256	−	987.927i	0.652691	−	1.70922i
$579$	−1745.42			−3.01455
$580$		0			0
$581$	431.794	+	288.516i	0.743192	+	0.496585i
$582$	1059.93	+	1059.93i	1.82119	+	1.82119i
$583$	−276.529	+	55.0050i	−0.474321	+	0.0943482i
$584$	849.894	−	567.881i	1.45530	−	0.972399i
$585$		0			0
$586$	−1313.06	+	543.887i	−2.24072	+	0.928135i
$587$	21.6776	+	52.3344i	0.0369295	+	0.0891557i	0.941268	−	0.337660i	$-0.109635\pi$
$587$	21.6776	+	52.3344i	0.0369295	+	0.0891557i	−0.904339	+	0.426816i	$0.859635\pi$
$588$	213.041	−	1071.03i	0.362315	−	1.82148i
$589$	30.8594	+	46.1843i	0.0523929	+	0.0784114i
$590$		0			0
$591$	−187.880	+	187.880i	−0.317902	+	0.317902i
$592$	−274.618	+	410.995i	−0.463882	+	0.694248i
$593$	−749.195	−	310.327i	−1.26340	−	0.523316i	−0.352447	−	0.935832i	$-0.614650\pi$
$593$	−749.195	−	310.327i	−1.26340	−	0.523316i	−0.910951	+	0.412515i	$0.864650\pi$
$594$		−	1506.77i		−	2.53665i
$595$		0			0
$596$	2374.43			3.98394
$597$	113.736	−	274.583i	0.190513	−	0.459938i
$598$	−541.946	−	362.117i	−0.906265	−	0.605547i
$599$	453.053	+	453.053i	0.756349	+	0.756349i	0.975656	−	0.219307i	$-0.0703795\pi$
$599$	453.053	+	453.053i	0.756349	+	0.756349i	−0.219307	+	0.975656i	$0.570380\pi$
$600$		0			0
$601$	−332.402	+	222.104i	−0.553081	+	0.369557i	−0.800483	−	0.599356i	$-0.795423\pi$
$601$	−332.402	+	222.104i	−0.553081	+	0.369557i	0.247401	+	0.968913i	$0.420423\pi$
$602$	−219.027	−	43.5671i	−0.363832	−	0.0723707i
$603$	−1777.95	+	736.451i	−2.94851	+	1.22131i
$604$	−149.389	−	360.656i	−0.247332	−	0.597113i
$605$		0			0
$606$	−961.238	−	1438.59i	−1.58620	−	2.37392i
$607$	−179.161	−	900.705i	−0.295159	−	1.48386i	−0.789045	−	0.614336i	$-0.789424\pi$
$607$	−179.161	−	900.705i	−0.295159	−	1.48386i	0.493886	−	0.869527i	$-0.335576\pi$
$608$	−305.731	+	305.731i	−0.502847	+	0.502847i
$609$	32.9331	−	49.2879i	0.0540774	−	0.0809326i
$610$		0			0
$611$			11.6994i			0.0191480i
$612$	−1368.37	+	3438.56i	−2.23591	+	5.61856i
$613$	1.10159			0.00179704			0.000898520	−	1.00000i	$-0.499714\pi$
$613$	1.10159			0.00179704			0.000898520		1.00000i	$0.499714\pi$
$614$	332.948	−	803.807i	0.542260	−	1.30913i
$615$		0			0
$616$	−380.961	−	380.961i	−0.618443	−	0.618443i
$617$	−761.218	+	151.416i	−1.23374	+	0.245406i	−0.768541	−	0.639800i	$-0.779017\pi$
$617$	−761.218	+	151.416i	−1.23374	+	0.245406i	−0.465199	+	0.885206i	$0.654017\pi$
$618$	−86.5103	+	57.8043i	−0.139984	+	0.0935345i
$619$	−835.815	−	166.254i	−1.35027	−	0.268585i	−0.533620	−	0.845724i	$-0.679169\pi$
$619$	−835.815	−	166.254i	−1.35027	−	0.268585i	−0.816646	+	0.577139i	$0.804169\pi$
$620$		0			0
$621$	1112.80	+	2686.53i	1.79194	+	4.32613i
$622$	44.4423	−	223.426i	0.0714506	−	0.359206i
$623$	26.6534	+	39.8896i	0.0427823	+	0.0640283i
$624$	188.807	+	949.199i	0.302576	+	1.52115i
$625$		0			0
$626$	−383.034	+	573.251i	−0.611876	+	0.915736i
$627$	242.861	+	100.596i	0.387338	+	0.160441i
$628$			513.951i			0.818393i
$629$	−203.753	−	132.066i	−0.323931	−	0.209962i
$630$		0			0
$631$	−1.11445	+	2.69052i	−0.00176616	+	0.00426390i	−0.924760	−	0.380550i	$-0.875735\pi$
$631$	−1.11445	+	2.69052i	−0.00176616	+	0.00426390i	0.922994	+	0.384814i	$0.125735\pi$
$632$	1578.63	+	1054.80i	2.49782	+	1.66899i
$633$	801.211	+	801.211i	1.26574	+	1.26574i
$634$	1688.26	−	335.816i	2.66287	−	0.529678i
$635$		0			0
$636$	−2878.68	−	572.605i	−4.52622	−	0.900322i
$637$	93.3590	−	38.6706i	0.146560	−	0.0607073i
$638$	14.0248	+	33.8588i	0.0219824	+	0.0530702i
$639$	−419.957	+	2111.27i	−0.657210	+	3.30402i
$640$		0			0
$641$	−49.4146	−	248.424i	−0.0770898	−	0.387557i	−0.999997	−	0.00253359i	$-0.999194\pi$
$641$	−49.4146	−	248.424i	−0.0770898	−	0.387557i	0.922907	−	0.385023i	$-0.125806\pi$
$642$	1329.63	−	1329.63i	2.07107	−	2.07107i
$643$	470.415	−	704.026i	0.731595	−	1.09491i	−0.260010	−	0.965606i	$-0.583726\pi$
$643$	470.415	−	704.026i	0.731595	−	1.09491i	0.991605	−	0.129303i	$-0.0412740\pi$
$644$	1673.50	+	693.188i	2.59861	+	1.07638i
$645$		0			0
$646$	−403.827	−	392.705i	−0.625119	−	0.607903i
$647$	−631.331			−0.975783			−0.487891	−	0.872904i	$-0.662234\pi$
$647$	−631.331			−0.975783			−0.487891	+	0.872904i	$0.662234\pi$
$648$	1870.68	−	4516.22i	2.88685	−	6.96948i
$649$	176.026	+	117.617i	0.271226	+	0.181227i
$650$		0			0
$651$	−182.210	+	36.2438i	−0.279893	+	0.0556741i
$652$	1874.65	−	1252.60i	2.87524	−	1.92117i
$653$	1029.82	+	204.845i	1.57707	+	0.313698i	0.904545	−	0.426379i	$-0.140211\pi$
$653$	1029.82	+	204.845i	1.57707	+	0.313698i	0.672522	+	0.740077i	$0.265211\pi$
$654$	2924.97	−	1211.56i	4.47243	−	1.85254i
$655$		0			0
$656$	446.972	−	2247.08i	0.681360	−	3.42543i
$657$	−667.584	−	999.110i	−1.01611	−	1.52072i
$658$	−9.04526	−	45.4736i	−0.0137466	−	0.0691088i
$659$	494.059	−	494.059i	0.749711	−	0.749711i	−0.224714	−	0.974425i	$-0.572145\pi$
$659$	494.059	−	494.059i	0.749711	−	0.749711i	0.974425	+	0.224714i	$0.0721448\pi$
$660$		0			0
$661$	399.021	+	165.280i	0.603663	+	0.250046i	0.663516	−	0.748162i	$-0.269063\pi$
$661$	399.021	+	165.280i	0.603663	+	0.250046i	−0.0598532	+	0.998207i	$0.519063\pi$
$662$		−	764.556i		−	1.15492i
$663$	−464.926	+	99.2466i	−0.701246	+	0.149693i
$664$	−1918.48			−2.88928
$665$		0			0
$666$	1007.51	+	673.195i	1.51277	+	1.01080i
$667$	−50.0115	−	50.0115i	−0.0749797	−	0.0749797i
$668$	945.448	−	188.061i	1.41534	−	0.281529i
$669$	−519.683	+	347.241i	−0.776806	+	0.519045i
$670$		0			0
$671$	141.959	−	58.8012i	0.211563	−	0.0876322i
$672$	−553.406	−	1336.04i	−0.823521	−	1.98816i
$673$	−137.903	+	693.283i	−0.204907	+	1.03014i	0.732198	+	0.681092i	$0.238495\pi$
$673$	−137.903	+	693.283i	−0.204907	+	1.03014i	−0.937105	+	0.349047i	$0.886505\pi$
$674$	488.785	+	731.519i	0.725201	+	1.08534i
$675$		0			0
$676$	960.750	−	960.750i	1.42123	−	1.42123i
$677$	−474.949	+	710.811i	−0.701549	+	1.04994i	0.294010	+	0.955802i	$0.405010\pi$
$677$	−474.949	+	710.811i	−0.701549	+	1.04994i	−0.995559	+	0.0941403i	$0.969990\pi$
$678$	4065.10	+	1683.82i	5.99572	+	2.48351i
$679$		−	385.483i		−	0.567722i
$680$		0			0
$681$	1456.38			2.13858
$682$	43.9541	−	106.115i	0.0644489	−	0.155593i
$683$	891.467	+	595.659i	1.30522	+	0.872122i	0.996863	−	0.0791477i	$-0.0252199\pi$
$683$	891.467	+	595.659i	1.30522	+	0.872122i	0.308360	+	0.951270i	$0.400220\pi$
$684$	1393.90	+	1393.90i	2.03786	+	2.03786i
$685$		0			0
$686$	−1128.86	+	754.278i	−1.64556	+	1.09953i
$687$	−169.758	−	33.7669i	−0.247100	−	0.0491512i
$688$	365.513	−	151.400i	0.531269	−	0.220059i
$689$	−103.937	−	250.927i	−0.150852	−	0.364190i
$690$		0			0
$691$	−30.8540	−	46.1763i	−0.0446512	−	0.0668253i	0.808472	−	0.588534i	$-0.200295\pi$
$691$	−30.8540	−	46.1763i	−0.0446512	−	0.0668253i	−0.853124	+	0.521709i	$0.825295\pi$
$692$	−57.6896	−	290.025i	−0.0833664	−	0.419111i
$693$	−447.846	+	447.846i	−0.646242	+	0.646242i
$694$	−663.999	+	993.744i	−0.956770	+	1.43191i
$695$		0			0
$696$			218.989i			0.314639i
$697$	1106.77	+	204.131i	1.58791	+	0.292870i
$698$	−215.985			−0.309434
$699$	303.580	−	732.907i	0.434306	−	1.04851i
$700$		0			0
$701$	−234.497	−	234.497i	−0.334518	−	0.334518i	0.519781	−	0.854299i	$-0.326013\pi$
$701$	−234.497	−	234.497i	−0.334518	−	0.334518i	−0.854299	+	0.519781i	$0.826013\pi$
$702$	1423.59	−	283.170i	2.02791	−	0.403376i
$703$	−107.538	+	71.8544i	−0.152970	+	0.102211i
$704$	182.129	+	36.2277i	0.258706	+	0.0514599i
$705$		0			0
$706$	−553.356	−	1335.92i	−0.783791	−	1.89224i
$707$	−86.8043	+	436.395i	−0.122778	+	0.617249i
$708$	1224.39	+	1832.44i	1.72937	+	2.58819i
$709$	6.19721	+	31.1555i	0.00874077	+	0.0439428i	0.984910	−	0.173070i	$-0.0553687\pi$
$709$	6.19721	+	31.1555i	0.00874077	+	0.0439428i	−0.976169	+	0.217013i	$0.930369\pi$
$710$		0			0
$711$	1240.00	−	1855.78i	1.74402	−	2.61010i
$712$	−163.740	−	67.8235i	−0.229973	−	0.0952577i
$713$			221.661i			0.310885i
$714$	1730.35	−	745.205i	2.42346	−	1.04370i
$715$		0			0
$716$	1136.53	−	2743.83i	1.58733	−	3.83216i
$717$	2074.97	+	1386.45i	2.89396	+	1.93368i
$718$	360.482	+	360.482i	0.502064	+	0.502064i
$719$	−495.464	+	98.5540i	−0.689102	+	0.137071i	−0.527207	−	0.849737i	$-0.676761\pi$
$719$	−495.464	+	98.5540i	−0.689102	+	0.137071i	−0.161895	+	0.986808i	$0.551761\pi$
$720$		0			0
$721$	26.2427	+	5.22000i	0.0363977	+	0.00723995i
$722$	943.216	−	390.693i	1.30639	−	0.541126i
$723$	57.4165	+	138.616i	0.0794142	+	0.191723i
$724$	−554.347	+	2786.89i	−0.765672	+	3.84929i
$725$		0			0
$726$	383.994	+	1930.47i	0.528917	+	2.65904i
$727$	57.2885	−	57.2885i	0.0788013	−	0.0788013i	−0.666608	−	0.745409i	$-0.732254\pi$
$727$	57.2885	−	57.2885i	0.0788013	−	0.0788013i	0.745409	+	0.666608i	$0.232254\pi$
$728$	288.336	−	431.526i	0.396066	−	0.592755i
$729$	−1513.18	−	626.782i	−2.07570	−	0.859783i
$730$		0			0
$731$	76.8704	+	178.492i	0.105158	+	0.244175i
$732$	1599.56			2.18519
$733$	344.487	−	831.666i	0.469969	−	1.13461i	−0.494207	−	0.869344i	$-0.664542\pi$
$733$	344.487	−	831.666i	0.469969	−	1.13461i	0.964176	−	0.265262i	$-0.0854584\pi$
$734$	1480.50	+	989.238i	2.01703	+	1.34774i
$735$		0			0
$736$	−1692.27	+	336.613i	−2.29928	+	0.457354i
$737$	−353.162	+	235.976i	−0.479189	+	0.320184i
$738$	−5508.46	−	1095.70i	−7.46404	−	1.48469i
$739$	726.586	−	300.962i	0.983201	−	0.407255i	0.167591	−	0.985857i	$-0.446401\pi$
$739$	726.586	−	300.962i	0.983201	−	0.407255i	0.815611	+	0.578601i	$0.196401\pi$
$740$		0			0
$741$	−49.4019	+	248.360i	−0.0666692	+	0.335169i
$742$	597.986	+	894.949i	0.805911	+	1.20613i
$743$	−117.087	−	588.634i	−0.157586	−	0.792239i	−0.976027	−	0.217649i	$-0.930161\pi$
$743$	−117.087	−	588.634i	−0.157586	−	0.792239i	0.818441	−	0.574591i	$-0.194839\pi$
$744$	485.300	−	485.300i	0.652286	−	0.652286i
$745$		0			0
$746$	−595.016	−	246.464i	−0.797609	−	0.330380i
$747$			2255.31i			3.01916i
$748$	−148.153	+	803.266i	−0.198065	+	1.07388i
$749$	−483.570			−0.645620
$750$		0			0
$751$	−134.595	−	89.9336i	−0.179221	−	0.119752i	0.462724	−	0.886503i	$-0.346872\pi$
$751$	−134.595	−	89.9336i	−0.179221	−	0.119752i	−0.641945	+	0.766751i	$0.721872\pi$
$752$	58.0811	+	58.0811i	0.0772355	+	0.0772355i
$753$	−1313.23	+	261.217i	−1.74400	+	0.346902i
$754$	−29.3540	+	19.6137i	−0.0389310	+	0.0260129i
$755$		0			0
$756$	−3726.74	+	1543.66i	−4.92954	+	2.04188i
$757$	173.822	+	419.645i	0.229620	+	0.554352i	0.996131	−	0.0878790i	$-0.0280089\pi$
$757$	173.822	+	419.645i	0.229620	+	0.554352i	−0.766511	+	0.642231i	$0.778009\pi$
$758$	316.213	−	1589.71i	0.417168	−	2.09724i
$759$	582.803	+	872.227i	0.767857	+	1.14918i
$760$		0			0
$761$	−395.123	+	395.123i	−0.519215	+	0.519215i	−0.917334	−	0.398119i	$-0.869663\pi$
$761$	−395.123	+	395.123i	−0.519215	+	0.519215i	0.398119	+	0.917334i	$0.369663\pi$
$762$	−1553.80	+	2325.43i	−2.03911	+	3.05174i
$763$	−752.202	−	311.572i	−0.985848	−	0.408352i
$764$			68.7948i			0.0900456i
$765$		0			0
$766$	2131.99			2.78327
$767$	−78.0431	+	188.413i	−0.101751	+	0.245649i
$768$	−1689.33	−	1128.77i	−2.19964	−	1.46975i
$769$	−568.899	−	568.899i	−0.739790	−	0.739790i	0.232747	−	0.972537i	$-0.425229\pi$
$769$	−568.899	−	568.899i	−0.739790	−	0.739790i	−0.972537	+	0.232747i	$0.925229\pi$
$770$		0			0
$771$	−1942.80	+	1298.14i	−2.51985	+	1.68371i
$772$	−2833.36	−	563.591i	−3.67016	−	0.730040i
$773$	1200.84	−	497.404i	1.55348	−	0.643472i	0.569538	−	0.821965i	$-0.307122\pi$
$773$	1200.84	−	497.404i	1.55348	−	0.643472i	0.983941	+	0.178493i	$0.0571221\pi$
$774$	−371.141	−	896.013i	−0.479510	−	1.15764i
$775$		0			0
$776$	791.174	+	1184.08i	1.01955	+	1.52587i
$777$	−84.3917	−	424.266i	−0.108612	−	0.546031i
$778$	−1003.86	+	1003.86i	−1.29031	+	1.29031i
$779$	333.049	−	498.443i	0.427534	−	0.639850i
$780$		0			0
$781$			475.109i			0.608334i
$782$	−469.274	−	2198.34i	−0.600095	−	2.81118i
$783$	157.502			0.201152
$784$	271.497	−	655.452i	0.346297	−	0.836035i
$785$		0			0
$786$	1667.96	+	1667.96i	2.12209	+	2.12209i
$787$	33.2395	−	6.61174i	0.0422357	−	0.00840120i	−0.173927	−	0.984759i	$-0.555646\pi$
$787$	33.2395	−	6.61174i	0.0422357	−	0.00840120i	0.216163	+	0.976357i	$0.430646\pi$
$788$	−365.654	+	244.322i	−0.464028	+	0.310053i
$789$	1589.79	+	316.229i	2.01495	+	0.400797i
$790$		0			0
$791$	−433.021	−	1045.41i	−0.547435	−	1.32163i
$792$	456.464	−	2294.80i	0.576344	−	2.89747i
$793$	82.2339	+	123.072i	0.103700	+	0.155198i
$794$	−68.3472	−	343.604i	−0.0860796	−	0.432751i
$795$		0			0
$796$	273.291	−	409.009i	0.343331	−	0.513831i
$797$	68.6780	+	28.4474i	0.0861707	+	0.0356931i	0.425352	−	0.905028i	$-0.360150\pi$
$797$	68.6780	+	28.4474i	0.0861707	+	0.0356931i	−0.339182	+	0.940721i	$0.610150\pi$
$798$		−	1003.52i		−	1.25755i
$799$	−28.1295	+	28.9262i	−0.0352059	+	0.0362030i
$800$		0			0
$801$	−79.7313	+	192.488i	−0.0995397	+	0.240310i
$802$	239.296	+	159.893i	0.298374	+	0.199367i
$803$	−187.532	−	187.532i	−0.233540	−	0.233540i
$804$	−4336.65	+	862.614i	−5.39385	+	1.07290i
$805$		0			0
$806$	108.517	+	21.5854i	0.134637	+	0.0267809i
$807$	1443.12	−	597.760i	1.78825	−	0.740718i
$808$	−629.032	−	1518.62i	−0.778505	−	1.87948i
$809$	64.3000	−	323.258i	0.0794809	−	0.399577i	−0.920480	−	0.390789i	$-0.872202\pi$
$809$	64.3000	−	323.258i	0.0794809	−	0.399577i	0.999961	−	0.00878888i	$-0.00279762\pi$
$810$		0			0
$811$	47.8095	+	240.355i	0.0589513	+	0.296368i	0.999002	−	0.0446666i	$-0.0142225\pi$
$811$	47.8095	+	240.355i	0.0589513	+	0.296368i	−0.940051	+	0.341035i	$0.889223\pi$
$812$	69.3757	−	69.3757i	0.0854380	−	0.0854380i
$813$	280.746	−	420.167i	0.345322	−	0.516810i
$814$	247.082	+	102.345i	0.303541	+	0.125731i
$815$		0			0
$816$	−1815.39	+	2800.80i	−2.22474	+	3.43235i
$817$	103.517			0.126704
$818$	−58.5809	+	141.427i	−0.0716148	+	0.172893i
$819$	−507.289	−	338.959i	−0.619400	−	0.413870i
$820$		0			0
$821$	613.444	−	122.022i	0.747191	−	0.148625i	0.193213	−	0.981157i	$-0.438109\pi$
$821$	613.444	−	122.022i	0.747191	−	0.148625i	0.553978	+	0.832531i	$0.313109\pi$
$822$	−281.084	+	187.814i	−0.341951	+	0.228484i
$823$	580.505	+	115.470i	0.705352	+	0.140303i	0.534717	−	0.845031i	$-0.320418\pi$
$823$	580.505	+	115.470i	0.705352	+	0.140303i	0.170635	+	0.985334i	$0.445418\pi$
$824$	−91.3225	+	37.8270i	−0.110828	+	0.0459066i
$825$		0			0
$826$	157.671	−	792.664i	0.190885	−	0.959641i
$827$	−8.33614	−	12.4759i	−0.0100800	−	0.0150858i	0.826395	−	0.563090i	$-0.190388\pi$
$827$	−8.33614	−	12.4759i	−0.0100800	−	0.0150858i	−0.836475	+	0.548004i	$0.815388\pi$
$828$	1534.70	+	7715.44i	1.85350	+	9.31817i
$829$	−360.941	+	360.941i	−0.435393	+	0.435393i	−0.890458	−	0.455065i	$-0.849616\pi$
$829$	−360.941	+	360.941i	−0.435393	+	0.435393i	0.455065	+	0.890458i	$0.349616\pi$
$830$		0			0
$831$	−1066.79	−	441.880i	−1.28374	−	0.531744i
$832$			178.884i			0.215004i
$833$	323.802	+	128.857i	0.388718	+	0.154690i
$834$	1073.24			1.28686
$835$		0			0
$836$	361.757	+	241.718i	0.432724	+	0.289137i
$837$	−349.041	−	349.041i	−0.417014	−	0.417014i
$838$	912.283	−	181.464i	1.08864	−	0.216545i
$839$	1028.00	−	686.885i	1.22526	−	0.818695i	0.237008	−	0.971508i	$-0.423833\pi$
$839$	1028.00	−	686.885i	1.22526	−	0.818695i	0.988255	+	0.152813i	$0.0488333\pi$
$840$		0			0
$841$	773.443	−	320.371i	0.919671	−	0.380940i
$842$	−45.7472	−	110.444i	−0.0543316	−	0.131168i
$843$	−29.5695	+	148.656i	−0.0350765	+	0.176342i
$844$	1041.91	+	1559.32i	1.23449	+	1.84754i
$845$		0			0
$846$	142.379	−	142.379i	0.168297	−	0.168297i
$847$	281.216	−	420.870i	0.332015	−	0.496895i
$848$	−1761.70	−	729.719i	−2.07747	−	0.860518i
$849$		−	717.624i		−	0.845258i
$850$		0			0
$851$	−516.125			−0.606492
$852$	−1892.72	+	4569.42i	−2.22150	+	5.36317i
$853$	−540.259	−	360.989i	−0.633363	−	0.423200i	0.197014	−	0.980401i	$-0.436875\pi$
$853$	−540.259	−	360.989i	−0.633363	−	0.423200i	−0.830378	+	0.557201i	$0.811875\pi$
$854$	−414.779	−	414.779i	−0.485690	−	0.485690i
$855$		0			0
$856$	1485.36	−	992.488i	1.73524	−	1.15945i
$857$	−787.962	−	156.735i	−0.919442	−	0.182888i	−0.287389	−	0.957814i	$-0.592787\pi$
$857$	−787.962	−	156.735i	−0.919442	−	0.182888i	−0.632053	+	0.774925i	$0.717787\pi$
$858$	483.765	−	200.382i	0.563829	−	0.233546i
$859$	−348.417	−	841.152i	−0.405607	−	0.979222i	−0.986279	−	0.165085i	$-0.947210\pi$
$859$	−348.417	−	841.152i	−0.405607	−	0.979222i	0.580672	−	0.814137i	$-0.302790\pi$
$860$		0			0
$861$	1113.93	+	1667.11i	1.29376	+	1.93625i
$862$	−433.625	−	2179.98i	−0.503045	−	2.52898i
$863$	−634.157	+	634.157i	−0.734828	+	0.734828i	−0.971572	−	0.236744i	$-0.923920\pi$
$863$	−634.157	+	634.157i	−0.734828	+	0.734828i	0.236744	+	0.971572i	$0.423920\pi$
$864$	2134.69	−	3194.80i	2.47071	−	3.69768i
$865$		0			0
$866$			862.797i			0.996302i
$867$	−1388.13	−	872.464i	−1.60107	−	1.00630i
$868$	−307.487			−0.354247
$869$	188.515	−	455.114i	0.216933	−	0.523722i
$870$		0			0
$871$	−289.320	−	289.320i	−0.332170	−	0.332170i
$872$	2949.99	−	586.789i	3.38302	−	0.672924i
$873$	1391.96	−	930.080i	1.59446	−	1.06538i
$874$	−1174.34	−	233.590i	−1.34363	−	0.267265i
$875$		0			0
$876$	−1056.53	−	2550.70i	−1.20609	−	2.91176i
$877$	−42.9023	+	215.684i	−0.0489193	+	0.245934i	−0.997506	−	0.0705838i	$-0.977514\pi$
$877$	−42.9023	+	215.684i	−0.0489193	+	0.245934i	0.948587	+	0.316518i	$0.102514\pi$
$878$	−1364.50	−	2042.12i	−1.55410	−	2.32588i
$879$	429.876	+	2161.13i	0.489051	+	2.45863i
$880$		0			0
$881$	−21.8952	+	32.7685i	−0.0248527	+	0.0371947i	−0.843688	−	0.536834i	$-0.819620\pi$
$881$	−21.8952	+	32.7685i	−0.0248527	+	0.0371947i	0.818835	+	0.574029i	$0.194620\pi$
$882$	−1606.76	−	665.544i	−1.82173	−	0.754585i
$883$		−	1402.81i		−	1.58869i	−0.607469	−	0.794343i	$-0.707815\pi$
$883$		−	1402.81i		−	1.58869i	0.607469	−	0.794343i	$-0.292185\pi$
$884$	−786.767	+	10.9850i	−0.890008	+	0.0124264i
$885$		0			0
$886$	−434.267	+	1048.41i	−0.490144	+	1.18331i
$887$	−819.368	−	547.484i	−0.923751	−	0.617231i	9.26296e−5	−	1.00000i	$-0.499971\pi$
$887$	−819.368	−	547.484i	−0.923751	−	0.617231i	−0.923844	+	0.382769i	$0.874971\pi$
$888$	1129.99	+	1129.99i	1.27252	+	1.27252i
$889$	705.414	−	140.316i	0.793492	−	0.157835i
$890$		0			0
$891$	−1243.96	−	247.439i	−1.39614	−	0.277709i
$892$	−955.731	+	395.877i	−1.07145	+	0.443808i
$893$	8.22457	+	19.8559i	0.00921005	+	0.0222350i
$894$	1024.12	−	5148.61i	1.14555	−	5.75908i
$895$		0			0
$896$	60.6175	+	304.745i	0.0676535	+	0.340117i
$897$	−714.551	+	714.551i	−0.796601	+	0.796601i
$898$	356.783	−	533.963i	0.397308	−	0.594614i
$899$	11.0921	+	4.59451i	0.0123383	+	0.00511069i
$900$		0			0
$901$	346.337	−	870.303i	0.384392	−	0.965930i
$902$	−1239.60			−1.37428
$903$	−132.496	+	319.872i	−0.146728	+	0.354233i
$904$	3475.71	+	2322.39i	3.84481	+	2.56902i
$905$		0			0
$906$	−846.465	+	168.372i	−0.934289	+	0.185842i
$907$	67.3094	−	44.9747i	0.0742111	−	0.0495863i	−0.517911	−	0.855434i	$-0.673290\pi$
$907$	67.3094	−	44.9747i	0.0742111	−	0.0495863i	0.592122	+	0.805848i	$0.298290\pi$
$908$	2364.15	+	470.259i	2.60369	+	0.517907i
$909$	−1785.24	+	739.471i	−1.96396	+	0.813499i
$910$		0			0
$911$	286.067	−	1438.15i	0.314014	−	1.57866i	−0.425146	−	0.905125i	$-0.639777\pi$
$911$	286.067	−	1438.15i	0.314014	−	1.57866i	0.739160	−	0.673530i	$-0.235223\pi$
$912$	987.714	+	1478.22i	1.08302	+	1.62085i
$913$	97.1105	+	488.207i	0.106364	+	0.534729i
$914$	−1612.34	+	1612.34i	−1.76404	+	1.76404i
$915$		0			0
$916$	−264.666	−	109.628i	−0.288937	−	0.119682i
$917$		−	606.617i		−	0.661524i
$918$	4200.59	+	2722.69i	4.57580	+	2.96590i
$919$	1285.69			1.39901			0.699504	−	0.714629i	$-0.253404\pi$
$919$	1285.69			1.39901			0.699504	+	0.714629i	$0.253404\pi$
$920$		0			0
$921$	−1121.56	−	749.400i	−1.21776	−	0.813681i
$922$	1819.78	+	1819.78i	1.97373	+	1.97373i
$923$	−448.882	+	89.2882i	−0.486330	+	0.0967370i
$924$	−1209.95	+	808.462i	−1.30947	+	0.874959i
$925$		0			0
$926$	−1281.95	+	531.000i	−1.38439	+	0.573434i
$927$	44.4683	+	107.356i	0.0479701	+	0.115810i
$928$	−18.2323	+	91.6600i	−0.0196469	+	0.0987715i
$929$	−965.295	−	1444.67i	−1.03907	−	1.55508i	−0.814112	−	0.580708i	$-0.802776\pi$
$929$	−965.295	−	1444.67i	−1.03907	−	1.55508i	−0.224957	−	0.974369i	$-0.572224\pi$
$930$		0			0
$931$	131.261	−	131.261i	0.140989	−	0.140989i
$932$	729.459	−	1091.71i	0.782681	−	1.17136i
$933$	−326.298	−	135.157i	−0.349730	−	0.144863i
$934$		−	1951.09i		−	2.08897i
$935$		0			0
$936$	2253.91			2.40802
$937$	625.091	−	1509.10i	0.667119	−	1.61057i	−0.119288	−	0.992860i	$-0.538061\pi$
$937$	625.091	−	1509.10i	0.667119	−	1.61057i	0.786407	−	0.617708i	$-0.211939\pi$
$938$	1348.22	+	900.850i	1.43733	+	0.960395i
$939$	755.826	+	755.826i	0.804926	+	0.804926i
$940$		0			0
$941$	−237.401	+	158.626i	−0.252286	+	0.168572i	−0.675282	−	0.737559i	$-0.735978\pi$
$941$	−237.401	+	158.626i	−0.252286	+	0.168572i	0.422997	+	0.906131i	$0.360978\pi$
$942$	1114.43	+	221.674i	1.18305	+	0.235323i
$943$	2210.17	−	915.481i	2.34376	−	0.970817i
$944$	547.922	+	1322.80i	0.580426	+	1.40127i
$945$		0			0
$946$	−118.922	−	177.979i	−0.125710	−	0.188139i
$947$	−3.15865	−	15.8796i	−0.00333543	−	0.0167683i	0.979082	−	0.203467i	$-0.0652211\pi$
$947$	−3.15865	−	15.8796i	−0.00333543	−	0.0167683i	−0.982417	+	0.186699i	$0.940221\pi$
$948$	3626.13	−	3626.13i	3.82503	−	3.82503i
$949$	141.937	−	212.423i	0.149565	−	0.223839i
$950$		0			0
$951$		−	2668.73i		−	2.80623i
$952$	1750.43	−	373.660i	1.83869	−	0.392500i
$953$	1030.31			1.08112			0.540560	−	0.841306i	$-0.318212\pi$
$953$	1030.31			1.08112			0.540560	+	0.841306i	$0.318212\pi$
$954$	−1788.82	+	4318.60i	−1.87508	+	4.52684i
$955$		0			0
$956$	2920.64	+	2920.64i	3.05506	+	3.05506i
$957$	55.7273	−	11.0848i	0.0582312	−	0.0115829i
$958$	−2314.10	+	1546.23i	−2.41555	+	1.61402i
$959$	85.2662	+	16.9605i	0.0889116	+	0.0176856i
$960$		0			0
$961$	353.359	+	853.085i	0.367700	+	0.887706i
$962$	−50.2605	+	252.677i	−0.0522458	+	0.262657i
$963$	−1166.74	−	1746.15i	−1.21157	−	1.81324i
$964$	48.4463	+	243.556i	0.0502555	+	0.252652i
$965$		0			0
$966$	2224.88	−	3329.78i	2.30319	−	3.44697i
$967$	444.501	+	184.118i	0.459670	+	0.190402i	0.600488	−	0.799634i	$-0.294973\pi$
$967$	444.501	+	184.118i	0.459670	+	0.190402i	−0.140818	+	0.990036i	$0.544973\pi$
$968$			1869.95i			1.93176i
$969$	−719.287	+	495.276i	−0.742298	+	0.511120i
$970$		0			0
$971$	347.780	−	839.615i	0.358167	−	0.864691i	−0.637391	−	0.770541i	$-0.719986\pi$
$971$	347.780	−	839.615i	0.358167	−	0.864691i	0.995558	−	0.0941509i	$-0.0300136\pi$
$972$	−5323.90	−	3557.32i	−5.47727	−	3.65979i
$973$	−195.163	−	195.163i	−0.200578	−	0.200578i
$974$	1312.76	−	261.125i	1.34781	−	0.268095i
$975$		0			0
$976$	1019.23	+	202.737i	1.04429	+	0.207722i
$977$	−793.653	+	328.742i	−0.812337	+	0.336481i	−0.749886	−	0.661567i	$-0.769892\pi$
$977$	−793.653	+	328.742i	−0.812337	+	0.336481i	−0.0624510	+	0.998048i	$0.519892\pi$
$978$	−1907.53	−	4605.19i	−1.95044	−	4.70878i
$979$	−8.97117	+	45.1011i	−0.00916360	+	0.0460685i
$980$		0			0
$981$	−689.812	−	3467.92i	−0.703172	−	3.53509i
$982$	−1523.19	+	1523.19i	−1.55111	+	1.55111i
$983$	−901.935	+	1349.84i	−0.917533	+	1.37319i	0.0102031	+	0.999948i	$0.496752\pi$
$983$	−901.935	+	1349.84i	−0.917533	+	1.37319i	−0.927736	+	0.373237i	$0.878248\pi$
$984$	−6843.24	−	2834.56i	−6.95451	−	2.88065i
$985$		0			0
$986$	−119.734	−	22.0835i	−0.121434	−	0.0223971i
$987$	−71.8826			−0.0728294
$988$	−160.389	+	387.214i	−0.162337	+	0.391917i
$989$	343.478	+	229.504i	0.347298	+	0.232057i
$990$		0			0
$991$	−1713.25	+	340.786i	−1.72881	+	0.343881i	−0.956581	−	0.291467i	$-0.905857\pi$
$991$	−1713.25	+	340.786i	−1.72881	+	0.343881i	−0.772226	+	0.635348i	$0.780857\pi$
$992$	243.532	−	162.723i	0.245496	−	0.164035i
$993$	−1162.58	−	231.251i	−1.17077	−	0.232881i
$994$	1675.69	−	694.094i	1.68581	−	0.698284i
$995$		0			0
$996$	−1010.92	+	5082.26i	−1.01498	+	5.10267i
$997$	300.262	+	449.374i	0.301165	+	0.450726i	0.950928	−	0.309411i	$-0.100132\pi$
$997$	300.262	+	449.374i	0.301165	+	0.450726i	−0.649763	+	0.760137i	$0.725132\pi$
$998$	−208.171	−	1046.55i	−0.208588	−	1.04864i
$999$	812.721	−	812.721i	0.813535	−	0.813535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.e.401.12		96
5.2	odd	4		425.3.t.e.299.12		96
5.3	odd	4		425.3.t.h.299.1		96
5.4	even	2		85.3.q.a.61.1	yes	96
17.12	odd	16	inner	425.3.u.e.301.12		96
85.12	even	16		425.3.t.h.199.1		96
85.29	odd	16		85.3.q.a.46.1	✓	96
85.63	even	16		425.3.t.e.199.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.q.a.46.1	✓	96	85.29	odd	16
85.3.q.a.61.1	yes	96	5.4	even	2
425.3.t.e.199.12		96	85.63	even	16
425.3.t.e.299.12		96	5.2	odd	4
425.3.t.h.199.1		96	85.12	even	16
425.3.t.h.299.1		96	5.3	odd	4
425.3.u.e.301.12		96	17.12	odd	16	inner
425.3.u.e.401.12		96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40031 - 3.38065i) q^{2} +(-4.71704 - 3.15183i) q^{3} +(-6.63952 - 6.63952i) q^{4} +(-17.2606 + 11.5332i) q^{6} +(5.23596 + 1.04150i) q^{7} +(-18.2207 + 7.54727i) q^{8} +(8.87234 + 21.4197i) q^{9} +(2.84290 + 4.25470i) q^{11} +(10.3923 + 52.2455i) q^{12} +(-3.48556 + 3.48556i) q^{13} +(10.8529 - 16.2426i) q^{14} +34.6077i q^{16} +(-16.9983 + 0.237334i) q^{17} +84.8367 q^{18} +(-3.46526 + 8.36588i) q^{19} +(-21.4157 - 21.4157i) q^{21} +(18.3646 - 3.65295i) q^{22} +(-30.0458 + 20.0759i) q^{23} +(109.736 + 21.8278i) q^{24} +(6.90260 + 16.6644i) q^{26} +(15.6991 - 78.9247i) q^{27} +(-27.8492 - 41.6793i) q^{28} +(0.381842 + 1.91965i) q^{29} +(3.40793 - 5.10033i) q^{31} +(44.1137 + 18.2725i) q^{32} -29.0299i q^{33} +(-23.0007 + 57.7979i) q^{34} +(83.3086 - 201.125i) q^{36} +(11.8758 + 7.93518i) q^{37} +(23.4297 + 23.4297i) q^{38} +(27.4274 - 5.45566i) q^{39} +(-64.9302 - 12.9154i) q^{41} +(-102.388 + 42.4103i) q^{42} +(-4.37477 - 10.5616i) q^{43} +(9.37368 - 47.1247i) q^{44} +(25.7963 + 129.687i) q^{46} +(1.67827 - 1.67827i) q^{47} +(109.077 - 163.246i) q^{48} +(-18.9395 - 7.84500i) q^{49} +(80.9300 + 52.4564i) q^{51} +46.2849 q^{52} +(-21.0855 + 50.9049i) q^{53} +(-244.833 - 163.592i) q^{54} +(-103.263 + 20.5404i) q^{56} +(42.7136 - 28.5403i) q^{57} +(7.02437 + 1.39723i) q^{58} +(38.2228 - 15.8324i) q^{59} +(5.85814 - 29.4509i) q^{61} +(-12.4703 - 18.6631i) q^{62} +(24.1466 + 121.393i) q^{63} +(25.6607 - 25.6607i) q^{64} +(-98.1402 - 40.6510i) q^{66} +83.0052i q^{67} +(114.437 + 111.285i) q^{68} +205.003 q^{69} +(77.2000 + 51.5834i) q^{71} +(-323.321 - 323.321i) q^{72} +(-50.8326 + 10.1112i) q^{73} +(43.4560 - 29.0364i) q^{74} +(78.5531 - 32.5378i) q^{76} +(10.4541 + 25.2383i) q^{77} +(19.9633 - 100.362i) q^{78} +(-53.4837 - 80.0441i) q^{79} +(-175.265 + 175.265i) q^{81} +(-134.585 + 201.421i) q^{82} +(89.8717 + 37.2261i) q^{83} +284.379i q^{84} -41.8312 q^{86} +(4.24924 - 10.2586i) q^{87} +(-83.9110 - 56.0675i) q^{88} +(6.35442 + 6.35442i) q^{89} +(-21.8805 + 14.6201i) q^{91} +(332.784 + 66.1949i) q^{92} +(-32.1507 + 13.3173i) q^{93} +(-3.32355 - 8.02376i) q^{94} +(-150.494 - 225.231i) q^{96} +(-14.0870 - 70.8202i) q^{97} +(-53.0424 + 53.0424i) q^{98} +(-65.9113 + 98.6432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) \) 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

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