LMFDB - Embedded newform 425.3.t.e.199.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(24,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.24"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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			199.12
Character	$\chi$	$=$	425.199
Dual form			425.3.t.e.299.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.38065 - 1.40031i) q^{2} +(-3.15183 - 4.71704i) q^{3} +(6.63952 - 6.63952i) q^{4} +(-17.2606 - 11.5332i) q^{6} +(-1.04150 - 5.23596i) q^{7} +(7.54727 - 18.2207i) q^{8} +(-8.87234 + 21.4197i) q^{9} +(2.84290 - 4.25470i) q^{11} +(-52.2455 - 10.3923i) q^{12} +(3.48556 - 3.48556i) q^{13} +(-10.8529 - 16.2426i) q^{14} -34.6077i q^{16} +(-0.237334 + 16.9983i) q^{17} +84.8367i q^{18} +(3.46526 + 8.36588i) q^{19} +(-21.4157 + 21.4157i) q^{21} +(3.65295 - 18.3646i) q^{22} +(20.0759 - 30.0458i) q^{23} +(-109.736 + 21.8278i) q^{24} +(6.90260 - 16.6644i) q^{26} +(78.9247 - 15.6991i) q^{27} +(-41.6793 - 27.8492i) q^{28} +(-0.381842 + 1.91965i) q^{29} +(3.40793 + 5.10033i) q^{31} +(-18.2725 - 44.1137i) q^{32} -29.0299 q^{33} +(23.0007 + 57.7979i) q^{34} +(83.3086 + 201.125i) q^{36} +(-7.93518 - 11.8758i) q^{37} +(23.4297 + 23.4297i) q^{38} +(-27.4274 - 5.45566i) q^{39} +(-64.9302 + 12.9154i) q^{41} +(-42.4103 + 102.388i) q^{42} +(-10.5616 - 4.37477i) q^{43} +(-9.37368 - 47.1247i) q^{44} +(25.7963 - 129.687i) q^{46} +(1.67827 - 1.67827i) q^{47} +(-163.246 + 109.077i) q^{48} +(18.9395 - 7.84500i) q^{49} +(80.9300 - 52.4564i) q^{51} -46.2849i q^{52} +(50.9049 - 21.0855i) q^{53} +(244.833 - 163.592i) q^{54} +(-103.263 - 20.5404i) q^{56} +(28.5403 - 42.7136i) q^{57} +(1.39723 + 7.02437i) q^{58} +(-38.2228 - 15.8324i) q^{59} +(5.85814 + 29.4509i) q^{61} +(18.6631 + 12.4703i) q^{62} +(121.393 + 24.1466i) q^{63} +(-25.6607 - 25.6607i) q^{64} +(-98.1402 + 40.6510i) q^{66} -83.0052 q^{67} +(111.285 + 114.437i) q^{68} -205.003 q^{69} +(77.2000 - 51.5834i) q^{71} +(323.321 + 323.321i) q^{72} +(10.1112 - 50.8326i) q^{73} +(-43.4560 - 29.0364i) q^{74} +(78.5531 + 32.5378i) q^{76} +(-25.2383 - 10.4541i) q^{77} +(-100.362 + 19.9633i) q^{78} +(53.4837 - 80.0441i) q^{79} +(-175.265 - 175.265i) q^{81} +(-201.421 + 134.585i) q^{82} +(37.2261 + 89.8717i) q^{83} +284.379i q^{84} -41.8312 q^{86} +(10.2586 - 4.24924i) q^{87} +(-56.0675 - 83.9110i) q^{88} +(-6.35442 + 6.35442i) q^{89} +(-21.8805 - 14.6201i) q^{91} +(-66.1949 - 332.784i) q^{92} +(13.3173 - 32.1507i) q^{93} +(3.32355 - 8.02376i) q^{94} +(-150.494 + 225.231i) q^{96} +(70.8202 + 14.0870i) q^{97} +(53.0424 - 53.0424i) q^{98} +(65.9113 + 98.6432i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 48 q^{13} + 64 q^{14} + 128 q^{17} - 48 q^{19} + 96 q^{22} + 144 q^{23} - 240 q^{24} - 224 q^{26} - 64 q^{31} - 400 q^{32} - 512 q^{33} - 64 q^{34} + 192 q^{36} + 144 q^{37} - 208 q^{38} - 16 q^{39}+ \cdots + 592 q^{99}+O(q^{100}) $ 96 * q - 48 * q^13 + 64 * q^14 + 128 * q^17 - 48 * q^19 + 96 * q^22 + 144 * q^23 - 240 * q^24 - 224 * q^26 - 64 * q^31 - 400 * q^32 - 512 * q^33 - 64 * q^34 + 192 * q^36 + 144 * q^37 - 208 * q^38 - 16 * q^39 - 432 * q^41 - 496 * q^42 - 128 * q^43 + 32 * q^44 - 48 * q^46 + 32 * q^49 + 64 * q^51 - 208 * q^53 + 976 * q^54 + 80 * q^56 + 672 * q^57 + 256 * q^58 + 224 * q^59 - 224 * q^61 + 304 * q^62 + 512 * q^63 - 160 * q^64 + 48 * q^66 - 288 * q^67 + 1040 * q^68 - 384 * q^69 + 48 * q^71 + 1040 * q^72 - 672 * q^74 + 496 * q^76 - 720 * q^77 - 1184 * q^78 - 768 * q^79 + 1424 * q^81 + 576 * q^82 - 1680 * q^83 + 64 * q^86 - 768 * q^87 + 1152 * q^88 + 1152 * q^89 + 336 * q^91 + 640 * q^92 + 1344 * q^94 + 768 * q^96 - 1440 * q^97 - 816 * q^98 + 592 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	3.38065	−	1.40031i	1.69033	−	0.700156i	0.690594	−	0.723243i	$-0.257349\pi$
$2$	3.38065	−	1.40031i	1.69033	−	0.700156i	0.999733	+	0.0230865i	$0.00734933\pi$
$3$	−3.15183	−	4.71704i	−1.05061	−	1.57235i	−0.795993	−	0.605306i	$-0.793051\pi$
$3$	−3.15183	−	4.71704i	−1.05061	−	1.57235i	−0.254617	−	0.967042i	$-0.581949\pi$
$4$	6.63952	−	6.63952i	1.65988	−	1.65988i
$5$		0			0
$5$		0			0
$6$	−17.2606	−	11.5332i	−2.87676	−	1.92219i
$7$	−1.04150	−	5.23596i	−0.148785	−	0.747995i	−0.981071	−	0.193648i	$-0.937968\pi$
$7$	−1.04150	−	5.23596i	−0.148785	−	0.747995i	0.832286	−	0.554347i	$-0.187032\pi$
$8$	7.54727	−	18.2207i	0.943408	−	2.27759i
$9$	−8.87234	+	21.4197i	−0.985815	+	2.37997i
$10$		0			0
$11$	2.84290	−	4.25470i	0.258445	−	0.386791i	−0.679443	−	0.733728i	$-0.737778\pi$
$11$	2.84290	−	4.25470i	0.258445	−	0.386791i	0.937888	+	0.346938i	$0.112778\pi$
$12$	−52.2455	−	10.3923i	−4.35380	−	0.866024i
$13$	3.48556	−	3.48556i	0.268120	−	0.268120i	−0.560222	−	0.828342i	$-0.689284\pi$
$13$	3.48556	−	3.48556i	0.268120	−	0.268120i	0.828342	+	0.560222i	$0.189284\pi$
$14$	−10.8529	−	16.2426i	−0.775209	−	1.16018i
$15$		0			0
$16$		−	34.6077i		−	2.16298i
$17$	−0.237334	+	16.9983i	−0.0139608	+	0.999903i
$17$	−0.237334	+	16.9983i	−0.0139608	+	0.999903i
$18$			84.8367i			4.71315i
$19$	3.46526	+	8.36588i	0.182382	+	0.440309i	0.988457	−	0.151505i	$-0.0484119\pi$
$19$	3.46526	+	8.36588i	0.182382	+	0.440309i	−0.806074	+	0.591814i	$0.798412\pi$
$20$		0			0
$21$	−21.4157	+	21.4157i	−1.01979	+	1.01979i
$22$	3.65295	−	18.3646i	0.166043	−	0.834755i
$23$	20.0759	−	30.0458i	0.872867	−	1.30634i	−0.0780686	−	0.996948i	$-0.524875\pi$
$23$	20.0759	−	30.0458i	0.872867	−	1.30634i	0.950935	−	0.309390i	$-0.100125\pi$
$24$	−109.736	+	21.8278i	−4.57232	+	0.909490i
$25$		0			0
$26$	6.90260	−	16.6644i	0.265485	−	0.640937i
$27$	78.9247	−	15.6991i	2.92314	−	0.581448i
$28$	−41.6793	−	27.8492i	−1.48855	−	0.994616i
$29$	−0.381842	+	1.91965i	−0.0131670	+	0.0661948i	−0.986810	−	0.161882i	$-0.948244\pi$
$29$	−0.381842	+	1.91965i	−0.0131670	+	0.0661948i	0.973643	+	0.228077i	$0.0732437\pi$
$30$		0			0
$31$	3.40793	+	5.10033i	0.109933	+	0.164527i	0.882357	−	0.470581i	$-0.155956\pi$
$31$	3.40793	+	5.10033i	0.109933	+	0.164527i	−0.772423	+	0.635108i	$0.780956\pi$
$32$	−18.2725	−	44.1137i	−0.571015	−	1.37855i
$33$	−29.0299			−0.879695
$34$	23.0007	+	57.7979i	0.676490	+	1.69994i
$35$		0			0
$36$	83.3086	+	201.125i	2.31413	+	5.58680i
$37$	−7.93518	−	11.8758i	−0.214464	−	0.320969i	0.708603	−	0.705608i	$-0.249326\pi$
$37$	−7.93518	−	11.8758i	−0.214464	−	0.320969i	−0.923067	+	0.384639i	$0.874326\pi$
$38$	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	−0.906950	−	0.421237i	$-0.861596\pi$
$41$	−64.9302	+	12.9154i	−1.58366	+	0.315010i	−0.676712	+	0.736247i	$0.736596\pi$
$42$	−42.4103	+	102.388i	−1.00977	+	2.43780i
$43$	−10.5616	−	4.37477i	−0.245619	−	0.101739i	0.256478	−	0.966550i	$-0.417438\pi$
$43$	−10.5616	−	4.37477i	−0.245619	−	0.101739i	−0.502097	+	0.864811i	$0.667438\pi$
$44$	−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	$0.241962\pi$
$48$	−163.246	+	109.077i	−3.40096	+	2.27245i
$49$	18.9395	−	7.84500i	0.386520	−	0.160102i
$50$		0			0
$51$	80.9300	−	52.4564i	1.58686	−	1.02856i
$52$		−	46.2849i		−	0.890094i
$53$	50.9049	−	21.0855i	0.960469	−	0.397839i	0.153313	−	0.988178i	$-0.451006\pi$
$53$	50.9049	−	21.0855i	0.960469	−	0.397839i	0.807156	+	0.590338i	$0.201006\pi$
$54$	244.833	−	163.592i	4.53395	−	3.02949i
$55$		0			0
$56$	−103.263	−	20.5404i	−1.84399	−	0.366792i
$57$	28.5403	−	42.7136i	0.500707	−	0.749362i
$58$	1.39723	+	7.02437i	0.0240902	+	0.121110i
$59$	−38.2228	−	15.8324i	−0.647844	−	0.268346i	0.0344693	−	0.999406i	$-0.489026\pi$
$59$	−38.2228	−	15.8324i	−0.647844	−	0.268346i	−0.682313	+	0.731060i	$0.739026\pi$
$60$		0			0
$61$	5.85814	+	29.4509i	0.0960351	+	0.482801i	0.998631	+	0.0523118i	$0.0166590\pi$
$61$	5.85814	+	29.4509i	0.0960351	+	0.482801i	−0.902596	+	0.430489i	$0.858341\pi$
$62$	18.6631	+	12.4703i	0.301018	+	0.201134i
$63$	121.393	+	24.1466i	1.92688	+	0.383280i
$64$	−25.6607	−	25.6607i	−0.400948	−	0.400948i
$65$		0			0
$66$	−98.1402	+	40.6510i	−1.48697	+	0.615924i
$67$	−83.0052			−1.23888			−0.619442	−	0.785042i	$-0.712641\pi$
$67$	−83.0052			−1.23888			−0.619442	+	0.785042i	$0.712641\pi$
$68$	111.285	+	114.437i	1.63654	+	1.68289i
$69$	−205.003			−2.97106
$70$		0			0
$71$	77.2000	−	51.5834i	1.08732	−	0.726526i	0.123307	−	0.992369i	$-0.460650\pi$
$71$	77.2000	−	51.5834i	1.08732	−	0.726526i	0.964017	+	0.265842i	$0.0856500\pi$
$72$	323.321	+	323.321i	4.49056	+	4.49056i
$73$	10.1112	−	50.8326i	0.138510	−	0.696337i	−0.847652	−	0.530553i	$-0.821984\pi$
$73$	10.1112	−	50.8326i	0.138510	−	0.696337i	0.986162	−	0.165784i	$-0.0530156\pi$
$74$	−43.4560	−	29.0364i	−0.587243	−	0.392383i
$75$		0			0
$76$	78.5531	+	32.5378i	1.03359	+	0.428128i
$77$	−25.2383	−	10.4541i	−0.327770	−	0.135767i
$78$	−100.362	+	19.9633i	−1.28670	+	0.255940i
$79$	53.4837	−	80.0441i	0.677009	−	1.01322i	−0.320806	−	0.947145i	$-0.603954\pi$
$79$	53.4837	−	80.0441i	0.677009	−	1.01322i	0.997815	−	0.0660709i	$-0.0210463\pi$
$80$		0			0
$81$	−175.265	−	175.265i	−2.16376	−	2.16376i
$82$	−201.421	+	134.585i	−2.45635	+	1.64128i
$83$	37.2261	+	89.8717i	0.448507	+	1.08279i	0.972881	+	0.231304i	$0.0742993\pi$
$83$	37.2261	+	89.8717i	0.448507	+	1.08279i	−0.524374	+	0.851488i	$0.675701\pi$
$84$			284.379i			3.38547i
$85$		0			0
$86$	−41.8312			−0.486410
$87$	10.2586	−	4.24924i	0.117915	−	0.0488418i
$88$	−56.0675	−	83.9110i	−0.637131	−	0.953534i
$89$	−6.35442	+	6.35442i	−0.0713979	+	0.0713979i	−0.741904	−	0.670506i	$-0.766077\pi$
$89$	−6.35442	+	6.35442i	−0.0713979	+	0.0713979i	0.670506	+	0.741904i	$0.266077\pi$
$90$		0			0
$91$	−21.8805	−	14.6201i	−0.240445	−	0.160660i
$92$	−66.1949	−	332.784i	−0.719509	−	3.61722i
$93$	13.3173	−	32.1507i	0.143197	−	0.345707i
$94$	3.32355	−	8.02376i	0.0353569	−	0.0853592i
$95$		0			0
$96$	−150.494	+	225.231i	−1.56765	+	2.34616i
$97$	70.8202	+	14.0870i	0.730105	+	0.145227i	0.546126	−	0.837703i	$-0.316102\pi$
$97$	70.8202	+	14.0870i	0.730105	+	0.145227i	0.183979	+	0.982930i	$0.441102\pi$
$98$	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	$-0.864620\pi$
$101$		−	83.3457i		−	0.825205i	0.910911	−	0.412602i	$-0.135380\pi$
$102$	200.141	−	290.664i	1.96217	−	2.84965i
$103$			5.01201i			0.0486603i	0.999704	+	0.0243302i	$0.00774530\pi$
$103$			5.01201i			0.0486603i	−0.999704	+	0.0243302i	$0.992255\pi$
$104$	−37.2029	−	89.8158i	−0.357721	−	0.863614i
$105$		0			0
$106$	142.565	−	142.565i	1.34496	−	1.34496i
$107$	−17.6714	+	88.8403i	−0.165154	+	0.830284i	0.806016	+	0.591894i	$0.201620\pi$
$107$	−17.6714	+	88.8403i	−0.165154	+	0.830284i	−0.971170	+	0.238390i	$0.923380\pi$
$108$	419.787	−	628.256i	3.88692	−	5.81719i
$109$	149.579	−	29.7531i	1.37228	−	0.272964i	0.546740	−	0.837302i	$-0.315868\pi$
$109$	149.579	−	29.7531i	1.37228	−	0.272964i	0.825544	+	0.564338i	$0.190868\pi$
$110$		0			0
$111$	−31.0085	+	74.8612i	−0.279356	+	0.674425i
$112$	−181.204	+	36.0438i	−1.61790	+	0.321820i
$113$	−176.235	−	117.757i	−1.55961	−	1.04210i	−0.972592	−	0.232518i	$-0.925304\pi$
$113$	−176.235	−	117.757i	−1.55961	−	1.04210i	−0.587013	−	0.809577i	$-0.699696\pi$
$114$	36.6725	−	184.365i	0.321689	−	1.61724i
$115$		0			0
$116$	10.2103	+	15.2808i	0.0880198	+	0.131731i
$117$	43.7347	+	105.585i	0.373801	+	0.902434i
$118$	−151.388			−1.28295
$119$	89.2499	−	16.4611i	0.749999	−	0.138328i
$120$		0			0
$121$	36.2843	+	87.5981i	0.299870	+	0.723951i
$122$	61.0448	+	91.3600i	0.500367	+	0.748852i
$123$	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
$127$	51.5570	−	124.469i	0.405960	−	0.980075i	−0.580229	−	0.814453i	$-0.697037\pi$
$127$	51.5570	−	124.469i	0.405960	−	0.980075i	0.986189	−	0.165621i	$-0.0529630\pi$
$128$	53.7719	+	22.2730i	0.420093	+	0.174008i
$129$	12.6524	+	63.6081i	0.0980810	+	0.493086i
$130$		0			0
$131$	−22.1681	+	111.446i	−0.169222	+	0.850736i	0.799132	+	0.601155i	$0.205293\pi$
$131$	−22.1681	+	111.446i	−0.169222	+	0.850736i	−0.968354	+	0.249581i	$0.919707\pi$
$132$	−192.745	+	192.745i	−1.46019	+	1.46019i
$133$	40.1944	−	26.8570i	0.302213	−	0.201933i
$134$	−280.612	+	116.233i	−2.09412	+	0.867413i
$135$		0			0
$136$	307.931	+	132.615i	2.26420	+	0.975113i
$137$		−	16.2847i		−	0.118867i	−0.998232	−	0.0594333i	$-0.981071\pi$
$137$		−	16.2847i		−	0.118867i	0.998232	−	0.0594333i	$-0.0189294\pi$
$138$	−693.045	+	287.069i	−5.02206	+	2.08021i
$139$	42.9869	−	28.7229i	0.309258	−	0.206640i	−0.391249	−	0.920285i	$-0.627957\pi$
$139$	42.9869	−	28.7229i	0.309258	−	0.206640i	0.700507	+	0.713645i	$0.252957\pi$
$140$		0			0
$141$	−13.2061	−	2.62686i	−0.0936604	−	0.0186302i
$142$	188.754	−	282.490i	1.32925	−	1.98936i
$143$	−4.92092	−	24.7391i	−0.0344120	−	0.173001i
$144$	741.286	+	307.051i	5.14782	+	2.13230i
$145$		0			0
$146$	−36.9990	−	186.006i	−0.253418	−	1.27402i
$147$	−96.6993	−	64.6124i	−0.657818	−	0.439540i
$148$	−131.536	−	26.1641i	−0.888754	−	0.176784i
$149$	178.810	+	178.810i	1.20007	+	1.20007i	0.974145	+	0.225924i	$0.0725401\pi$
$149$	178.810	+	178.810i	1.20007	+	1.20007i	0.225924	+	0.974145i	$0.427460\pi$
$150$		0			0
$151$	38.4098	−	15.9098i	0.254369	−	0.105363i	−0.251855	−	0.967765i	$-0.581041\pi$
$151$	38.4098	−	15.9098i	0.254369	−	0.105363i	0.506225	+	0.862402i	$0.331041\pi$
$152$	178.586			1.17490
$153$	−361.994	−	155.899i	−2.36597	−	1.01895i
$154$	−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	0.819541	−	0.573020i	$-0.194228\pi$
$157$	38.7039	+	38.7039i	0.246522	+	0.246522i	−0.573020	+	0.819541i	$0.694228\pi$
$158$	68.7233	−	345.495i	0.434957	−	2.18668i
$159$	−259.905	−	173.663i	−1.63462	−	1.09222i
$160$		0			0
$161$	−178.228	−	73.8243i	−1.10700	−	0.458536i
$162$	−837.935	−	347.084i	−5.17244	−	2.14250i
$163$	235.503	−	46.8445i	1.44481	−	0.287390i	0.590448	−	0.807076i	$-0.298951\pi$
$163$	235.503	−	46.8445i	1.44481	−	0.287390i	0.854357	+	0.519686i	$0.173951\pi$
$164$	−345.353	+	516.857i	−2.10581	+	3.15157i
$165$		0			0
$166$	251.697	+	251.697i	1.51625	+	1.51625i
$167$	−85.3608	+	57.0363i	−0.511143	+	0.341535i	−0.784246	−	0.620450i	$-0.786950\pi$
$167$	−85.3608	+	57.0363i	−0.511143	+	0.341535i	0.273103	+	0.961985i	$0.411950\pi$
$168$	228.579	+	551.838i	1.36059	+	3.28475i
$169$			144.702i			0.856223i
$170$		0			0
$171$	−209.940			−1.22772
$172$	−99.1704	+	41.0777i	−0.576572	+	0.238824i
$173$	17.4964	+	26.1852i	0.101135	+	0.151360i	0.878586	−	0.477584i	$-0.158487\pi$
$173$	17.4964	+	26.1852i	0.101135	+	0.151360i	−0.777451	+	0.628944i	$0.783487\pi$
$174$	28.7304	−	28.7304i	0.165117	−	0.165117i
$175$		0			0
$176$	−147.245	−	98.3861i	−0.836620	−	0.559012i
$177$	45.7895	+	230.200i	0.258698	+	1.30056i
$178$	−12.5839	+	30.3803i	−0.0706961	+	0.170676i
$179$	−121.040	+	292.217i	−0.676202	+	1.63250i	0.0946731	+	0.995508i	$0.469819\pi$
$179$	−121.040	+	292.217i	−0.676202	+	1.63250i	−0.770875	+	0.636987i	$0.780181\pi$
$180$		0			0
$181$	−168.125	+	251.617i	−0.928869	+	1.39015i	−0.00813199	+	0.999967i	$0.502589\pi$
$181$	−168.125	+	251.617i	−0.928869	+	1.39015i	−0.920737	+	0.390184i	$0.872411\pi$
$182$	−94.4430	−	18.7859i	−0.518917	−	0.103219i
$183$	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
$187$	71.6481	+	49.3344i	0.383145	+	0.263820i
$188$		−	22.2858i		−	0.118542i
$189$	−164.400	−	396.896i	−0.869840	−	2.09998i
$190$		0			0
$191$	−5.18071	+	5.18071i	−0.0271241	+	0.0271241i	−0.720539	−	0.693415i	$-0.756105\pi$
$191$	−5.18071	+	5.18071i	−0.0271241	+	0.0271241i	0.693415	+	0.720539i	$0.256105\pi$
$192$	−40.1645	+	201.921i	−0.209190	+	1.05167i
$193$	−170.929	+	255.813i	−0.885642	+	1.32546i	0.0593066	+	0.998240i	$0.481111\pi$
$193$	−170.929	+	255.813i	−0.885642	+	1.32546i	−0.944949	+	0.327218i	$0.893889\pi$
$194$	259.145	−	51.5471i	1.33580	−	0.265707i
$195$		0			0
$196$	73.6622	−	177.836i	0.375827	−	0.907328i
$197$	45.9352	−	9.13709i	0.233174	−	0.0463811i	−0.0771202	−	0.997022i	$-0.524573\pi$
$197$	45.9352	−	9.13709i	0.233174	−	0.0463811i	0.310294	+	0.950641i	$0.399573\pi$
$198$	360.955	+	241.182i	1.82300	+	1.21809i
$199$	−10.2205	+	51.3818i	−0.0513591	+	0.258200i	−0.997931	−	0.0642930i	$-0.979521\pi$
$199$	−10.2205	+	51.3818i	−0.0513591	+	0.258200i	0.946572	+	0.322493i	$0.104521\pi$
$200$		0			0
$201$	261.618	+	391.539i	1.30158	+	1.94796i
$202$	−116.710	−	281.763i	−0.577772	−	1.39487i
$203$	10.4489			0.0514724
$204$	189.051	−	885.621i	0.926722	−	4.34128i
$205$		0			0
$206$	7.01839	+	16.9439i	0.0340698	+	0.0822519i
$207$	465.451	+	696.597i	2.24856	+	3.36520i
$208$	−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	−0.636051	−	0.771647i	$-0.719433\pi$
$211$	−195.890	+	38.9649i	−0.928388	+	0.184668i	−0.292337	+	0.956315i	$0.594433\pi$
$212$	197.986	−	477.981i	0.933898	−	2.25463i
$213$	−486.642	−	201.574i	−2.28471	−	0.946356i
$214$	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
$218$	464.011	−	310.042i	2.12849	−	1.42221i
$219$	−271.649	+	112.521i	−1.24040	+	0.513792i
$220$		0			0
$221$	58.4215	+	60.0760i	0.264351	+	0.271837i
$222$			296.501i			1.33559i
$223$	−101.785	+	42.1607i	−0.456435	+	0.189062i	−0.599042	−	0.800718i	$-0.704452\pi$
$223$	−101.785	+	42.1607i	−0.456435	+	0.189062i	0.142607	+	0.989779i	$0.454452\pi$
$224$	−211.947	+	141.618i	−0.946191	+	0.632225i
$225$		0			0
$226$	−760.687	−	151.310i	−3.36587	−	0.669514i
$227$	−142.623	+	213.450i	−0.628294	+	0.940309i	0.371635	+	0.928379i	$0.378797\pi$
$227$	−142.623	+	213.450i	−0.628294	+	0.940309i	−0.999929	+	0.0119297i	$0.996203\pi$
$228$	−94.1038	−	473.092i	−0.412736	−	2.07496i
$229$	−28.1869	−	11.6754i	−0.123087	−	0.0509842i	0.320290	−	0.947320i	$-0.396220\pi$
$229$	−28.1869	−	11.6754i	−0.123087	−	0.0509842i	−0.443377	+	0.896335i	$0.646220\pi$
$230$		0			0
$231$	30.2346	+	152.000i	0.130886	+	0.658007i
$232$	32.0955	+	21.4455i	0.138343	+	0.0924376i
$233$	137.146	+	27.2801i	0.588611	+	0.117082i	0.480405	−	0.877047i	$-0.340490\pi$
$233$	137.146	+	27.2801i	0.588611	+	0.117082i	0.108205	+	0.994129i	$0.465490\pi$
$234$	295.704	+	295.704i	1.26369	+	1.26369i
$235$		0			0
$236$	−358.900	+	148.661i	−1.52076	+	0.629921i
$237$	−546.143			−2.30440
$238$	278.672	−	180.627i	1.17089	−	0.758937i
$239$	439.887			1.84053			0.920265	−	0.391295i	$-0.127973\pi$
$239$	439.887			1.84053			0.920265	+	0.391295i	$0.127973\pi$
$240$		0			0
$241$	−21.9897	+	14.6931i	−0.0912437	+	0.0609671i	−0.600355	−	0.799734i	$-0.704974\pi$
$241$	−21.9897	+	14.6931i	−0.0912437	+	0.0609671i	0.509111	+	0.860701i	$0.329974\pi$
$242$	245.329	+	245.329i	1.01376	+	1.01376i
$243$	−133.036	+	668.815i	−0.547471	+	2.75232i
$244$	234.435	+	156.644i	0.960799	+	0.641985i
$245$		0			0
$246$	1269.69	+	525.922i	5.16133	+	2.13789i
$247$	41.2382	+	17.0814i	0.166956	+	0.0691555i
$248$	118.652	−	23.6014i	0.478436	−	0.0951669i
$249$	306.599	−	458.857i	1.23132	−	1.84280i
$250$		0			0
$251$	166.889	+	166.889i	0.664897	+	0.664897i	0.956530	−	0.291634i	$-0.0941988\pi$
$251$	166.889	+	166.889i	0.664897	+	0.664897i	−0.291634	+	0.956530i	$0.594199\pi$
$252$	966.316	−	645.672i	3.83459	−	2.56219i
$253$	−70.7618	−	170.834i	−0.279691	−	0.675234i
$254$		−	492.984i		−	1.94088i
$255$		0			0
$256$	358.132			1.39895
$257$	380.517	−	157.615i	1.48061	−	0.613289i	0.511361	−	0.859366i	$-0.329141\pi$
$257$	380.517	−	157.615i	1.48061	−	0.613289i	0.969250	+	0.246077i	$0.0791415\pi$
$258$	131.845	+	197.320i	0.511027	+	0.764805i
$259$	−53.9170	+	53.9170i	−0.208174	+	0.208174i
$260$		0			0
$261$	−37.7305	−	25.2107i	−0.144561	−	0.0965928i
$262$	81.1173	+	407.804i	0.309608	+	1.55650i
$263$	109.341	−	263.972i	0.415745	−	1.00370i	−0.567822	−	0.823151i	$-0.692214\pi$
$263$	109.341	−	263.972i	0.415745	−	1.00370i	0.983567	−	0.180545i	$-0.0577861\pi$
$264$	−219.097	+	528.946i	−0.829912	+	2.00358i
$265$		0			0
$266$	98.2751	−	147.079i	0.369455	−	0.552929i
$267$	50.0021	+	9.94604i	0.187274	+	0.0372511i
$268$	−551.115	+	551.115i	−2.05640	+	2.05640i
$269$	152.969	+	228.934i	0.568657	+	0.851055i	0.998659	−	0.0517731i	$-0.0164873\pi$
$269$	152.969	+	228.934i	0.568657	+	0.851055i	−0.430002	+	0.902828i	$0.641487\pi$
$270$		0			0
$271$		−	89.0741i		−	0.328687i	−0.986403	−	0.164343i	$-0.947449\pi$
$271$		−	89.0741i		−	0.328687i	0.986403	−	0.164343i	$-0.0525505\pi$
$272$	588.273	+	8.21356i	2.16277	+	0.0301969i
$273$			149.291i			0.546854i
$274$	−22.8037	−	55.0530i	−0.0832252	−	0.200923i
$275$		0			0
$276$	−1361.12	+	1361.12i	−4.93160	+	4.93160i
$277$	39.7079	−	199.625i	0.143350	−	0.720667i	−0.840520	−	0.541781i	$-0.817750\pi$
$277$	39.7079	−	199.625i	0.143350	−	0.720667i	0.983870	−	0.178887i	$-0.0572496\pi$
$278$	105.103	−	157.297i	0.378067	−	0.565817i
$279$	−139.484	+	27.7451i	−0.499943	+	0.0994448i
$280$		0			0
$281$	−10.2241	+	24.6831i	−0.0363847	+	0.0878404i	−0.941027	−	0.338331i	$-0.890138\pi$
$281$	−10.2241	+	24.6831i	−0.0363847	+	0.0878404i	0.904643	+	0.426171i	$0.140138\pi$
$282$	−48.3237	+	9.61219i	−0.171361	+	0.0340858i
$283$	105.177	+	70.2769i	0.371649	+	0.248328i	0.727343	−	0.686275i	$-0.240755\pi$
$283$	105.177	+	70.2769i	0.371649	+	0.248328i	−0.355693	+	0.934603i	$0.615755\pi$
$284$	170.082	−	855.060i	0.598880	−	3.01077i
$285$		0			0
$286$	−51.2784	−	76.7436i	−0.179295	−	0.268334i
$287$	135.249	+	326.521i	0.471252	+	1.13770i
$288$	1107.02			3.84383
$289$	−288.887	−	8.06856i	−0.999610	−	0.0279189i
$290$		0			0
$291$	−156.764	−	378.462i	−0.538708	−	1.30056i
$292$	−270.370	−	404.638i	−0.925926	−	1.38575i
$293$	−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
$297$	157.580	−	380.432i	0.530572	−	1.28091i
$298$	854.886	+	354.105i	2.86874	+	1.18827i
$299$	−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
$303$	−393.145	+	262.691i	−1.29751	+	0.866968i
$304$	289.523	−	119.925i	0.952380	−	0.394489i
$305$		0			0
$306$	−1442.08	−	20.1346i	−4.71269	−	0.0657994i
$307$		−	237.767i		−	0.774485i	−0.921978	−	0.387242i	$-0.873428\pi$
$307$		−	237.767i		−	0.774485i	0.921978	−	0.387242i	$-0.126572\pi$
$308$	−236.980	+	98.1605i	−0.769417	+	0.318703i
$309$	23.6419	−	15.7970i	0.0765110	−	0.0511230i
$310$		0			0
$311$	61.0589	+	12.1454i	0.196331	+	0.0390526i	0.292276	−	0.956334i	$-0.405587\pi$
$311$	61.0589	+	12.1454i	0.196331	+	0.0390526i	−0.0959453	+	0.995387i	$0.530587\pi$
$312$	−306.408	+	458.572i	−0.982077	+	1.46978i
$313$	−36.7577	−	184.794i	−0.117437	−	0.590395i	−0.994025	−	0.109153i	$-0.965186\pi$
$313$	−36.7577	−	184.794i	−0.117437	−	0.590395i	0.876588	−	0.481242i	$-0.159814\pi$
$314$	185.042	+	76.6469i	0.589306	+	0.244098i
$315$		0			0
$316$	−176.348	−	886.560i	−0.558063	−	2.80557i
$317$	−391.135	−	261.348i	−1.23386	−	0.824442i	−0.244464	−	0.969658i	$-0.578612\pi$
$317$	−391.135	−	261.348i	−1.23386	−	0.824442i	−0.989400	+	0.145217i	$0.953612\pi$
$318$	−1121.83	−	223.146i	−3.52777	−	0.701716i
$319$	7.08199	+	7.08199i	0.0222006	+	0.0222006i
$320$		0			0
$321$	474.761	−	196.653i	1.47901	−	0.612625i
$322$	−705.903			−2.19224
$323$	−143.029	+	56.9182i	−0.442813	+	0.176217i
$324$	−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
$328$	−254.717	+	1280.55i	−0.776577	+	3.90412i
$329$	−10.5353	−	7.03946i	−0.0320222	−	0.0213965i
$330$		0			0
$331$	193.036	+	79.9583i	0.583191	+	0.241566i	0.654718	−	0.755873i	$-0.272787\pi$
$331$	193.036	+	79.9583i	0.583191	+	0.241566i	−0.0715270	+	0.997439i	$0.522787\pi$
$332$	843.869	+	349.542i	2.54177	+	1.05284i
$333$	324.781	−	64.6029i	0.975317	−	0.194003i
$334$	−208.707	+	312.352i	−0.624871	+	0.935185i
$335$		0			0
$336$	741.146	+	741.146i	2.20579	+	2.20579i
$337$	−199.913	+	133.577i	−0.593212	+	0.396372i	−0.815625	−	0.578581i	$-0.803607\pi$
$337$	−199.913	+	133.577i	−0.593212	+	0.396372i	0.222413	+	0.974953i	$0.428607\pi$
$338$	202.628	+	489.187i	0.599490	+	1.44730i
$339$			1202.46i			3.54708i
$340$		0			0
$341$	31.3888			0.0920492
$342$	−709.734	+	293.981i	−2.07524	+	0.859595i
$343$	−206.132	−	308.499i	−0.600969	−	0.899414i
$344$	−159.423	+	159.423i	−0.463438	+	0.463438i
$345$		0			0
$346$	95.8168	+	64.0228i	0.276927	+	0.185037i
$347$	63.7204	+	320.344i	0.183632	+	0.923182i	0.957191	+	0.289457i	$0.0934748\pi$
$347$	63.7204	+	320.344i	0.183632	+	0.923182i	−0.773559	+	0.633725i	$0.781525\pi$
$348$	39.8991	−	96.3249i	0.114653	−	0.276796i
$349$	22.5880	−	54.5323i	0.0647221	−	0.156253i	−0.888209	−	0.459439i	$-0.848050\pi$
$349$	22.5880	−	54.5323i	0.0647221	−	0.156253i	0.952931	+	0.303186i	$0.0980504\pi$
$350$		0			0
$351$	220.377	−	329.817i	0.627853	−	0.939649i
$352$	−239.637	−	47.6668i	−0.680788	−	0.135417i
$353$	−279.425	+	279.425i	−0.791571	+	0.791571i	−0.981750	−	0.190178i	$-0.939093\pi$
$353$	−279.425	+	279.425i	−0.791571	+	0.791571i	0.190178	+	0.981750i	$0.439093\pi$
$354$	477.150	+	714.106i	1.34788	+	2.01725i
$355$		0			0
$356$			84.3806i			0.237024i
$357$	−358.948	−	369.113i	−1.00546	−	1.03393i
$358$			1157.38i			3.23290i
$359$	53.3154	+	128.715i	0.148511	+	0.358537i	0.980576	−	0.196142i	$-0.0628412\pi$
$359$	53.3154	+	128.715i	0.148511	+	0.358537i	−0.832065	+	0.554679i	$0.812841\pi$
$360$		0			0
$361$	197.286	−	197.286i	0.546498	−	0.546498i
$362$	−216.031	+	1086.06i	−0.596770	+	3.00016i
$363$	298.842	−	447.249i	0.823256	−	1.23209i
$364$	−242.346	+	48.2056i	−0.665786	+	0.132433i
$365$		0			0
$366$	238.546	−	575.902i	0.651766	−	1.57350i
$367$	−477.255	+	94.9319i	−1.30042	+	0.258670i	−0.796268	−	0.604944i	$-0.793195\pi$
$367$	−477.255	+	94.9319i	−1.30042	+	0.258670i	−0.504154	+	0.863614i	$0.668195\pi$
$368$	−1039.81	−	694.781i	−2.82558	−	1.88799i
$369$	299.438	−	1505.38i	0.811485	−	4.07961i
$370$		0			0
$371$	−163.420	−	244.576i	−0.440486	−	0.659233i
$372$	−125.045	−	301.886i	−0.336143	−	0.811521i
$373$	−176.006			−0.471867			−0.235933	−	0.971769i	$-0.575815\pi$
$373$	−176.006			−0.471867			−0.235933	+	0.971769i	$0.575815\pi$
$374$	311.301	+	66.4526i	0.832356	+	0.177681i
$375$		0			0
$376$	−17.9129	−	43.2457i	−0.0476408	−	0.115015i
$377$	5.36012	+	8.02199i	0.0142178	+	0.0212785i
$378$	−1111.56	−	1111.56i	−2.94063	−	2.94063i
$379$	−434.443	−	86.4160i	−1.14629	−	0.228011i	−0.414830	−	0.909899i	$-0.636159\pi$
$379$	−434.443	−	86.4160i	−1.14629	−	0.228011i	−0.731456	+	0.681888i	$0.761159\pi$
$380$		0			0
$381$	−749.627	+	149.110i	−1.96752	+	0.391365i
$382$	−10.2596	+	24.7688i	−0.0268575	+	0.0648397i
$383$	538.287	+	222.966i	1.40545	+	0.582157i	0.951160	−	0.308697i	$-0.0998930\pi$
$383$	538.287	+	222.966i	1.40545	+	0.582157i	0.454290	+	0.890854i	$0.349893\pi$
$384$	−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
$388$	563.743	−	376.681i	1.45295	−	0.970827i
$389$	358.440	−	148.471i	0.921441	−	0.381673i	0.129016	−	0.991643i	$-0.458818\pi$
$389$	358.440	−	148.471i	0.921441	−	0.381673i	0.792425	+	0.609969i	$0.208818\pi$
$390$		0			0
$391$	505.963	+	348.389i	1.29402	+	0.891019i
$392$		−	404.299i		−	1.03138i
$393$	595.568	−	246.692i	1.51544	−	0.627716i
$394$	142.496	−	95.2130i	0.361666	−	0.241657i
$395$		0			0
$396$	1092.56	+	217.324i	2.75900	+	0.548799i
$397$	53.1910	−	79.6060i	0.133982	−	0.200519i	−0.758412	−	0.651776i	$-0.774024\pi$
$397$	53.1910	−	79.6060i	0.133982	−	0.200519i	0.892394	+	0.451257i	$0.149024\pi$
$398$	37.3987	+	188.016i	0.0939665	+	0.472401i
$399$	−253.372	−	104.950i	−0.635017	−	0.263032i
$400$		0			0
$401$	−15.3440	−	77.1397i	−0.0382644	−	0.192368i	0.956925	−	0.290334i	$-0.0937664\pi$
$401$	−15.3440	−	77.1397i	−0.0382644	−	0.192368i	−0.995190	+	0.0979657i	$0.968766\pi$
$402$	1432.72	+	957.312i	3.56398	+	2.38137i
$403$	29.6561	+	5.89896i	0.0735883	+	0.0146376i
$404$	−553.375	−	553.375i	−1.36974	−	1.36974i
$405$		0			0
$406$	35.3241	−	14.6317i	0.0870052	−	0.0360387i
$407$	−73.0870			−0.179575
$408$	−344.992	−	1870.50i	−0.845568	−	4.58457i
$409$	41.8341			0.102284			0.0511420	−	0.998691i	$-0.483714\pi$
$409$	41.8341			0.102284			0.0511420	+	0.998691i	$0.483714\pi$
$410$		0			0
$411$	−76.8157	+	51.3266i	−0.186900	+	0.124882i
$412$	33.2774	+	33.2774i	0.0807703	+	0.0807703i
$413$	−43.0889	+	216.623i	−0.104331	+	0.524510i
$414$	2548.98	+	1703.18i	6.15697	+	4.11395i
$415$		0			0
$416$	−217.451	−	90.0711i	−0.522718	−	0.216517i
$417$	−270.974	−	112.241i	−0.649819	−	0.269164i
$418$	166.295	−	33.0781i	0.397834	−	0.0791341i
$419$	−141.224	+	211.357i	−0.337051	+	0.504432i	−0.960819	−	0.277177i	$-0.910601\pi$
$419$	−141.224	+	211.357i	−0.337051	+	0.504432i	0.623768	+	0.781610i	$0.285601\pi$
$420$		0			0
$421$	23.1007	+	23.1007i	0.0548710	+	0.0548710i	0.734010	−	0.679139i	$-0.237647\pi$
$421$	23.1007	+	23.1007i	0.0548710	+	0.0548710i	−0.679139	+	0.734010i	$0.737647\pi$
$422$	−607.673	+	406.034i	−1.43998	+	0.962166i
$423$	21.0579	+	50.8383i	0.0497823	+	0.120185i
$424$		−	1086.66i		−	2.56288i
$425$		0			0
$426$	−1927.44			−4.52450
$427$	148.102	−	61.3460i	0.346844	−	0.143668i
$428$	472.527	+	707.187i	1.10404	+	1.65231i
$429$	−101.186	+	101.186i	−0.235864	+	0.235864i
$430$		0			0
$431$	505.056	+	337.468i	1.17182	+	0.782987i	0.980108	−	0.198463i	$-0.0635950\pi$
$431$	505.056	+	337.468i	1.17182	+	0.782987i	0.191715	+	0.981451i	$0.438595\pi$
$432$	−543.309	−	2731.40i	−1.25766	−	6.32268i
$433$	90.2325	−	217.841i	0.208389	−	0.503096i	−0.784781	−	0.619774i	$-0.787224\pi$
$433$	90.2325	−	217.841i	0.208389	−	0.503096i	0.993170	+	0.116678i	$0.0372244\pi$
$434$	45.8564	−	110.707i	0.105660	−	0.255086i
$435$		0			0
$436$	795.586	−	1190.68i	1.82474	−	2.73092i
$437$	320.928	+	63.8365i	0.734388	+	0.146079i
$438$	−760.786	+	760.786i	−1.73695	+	1.73695i
$439$	−372.897	−	558.080i	−0.849424	−	1.27125i	−0.960735	−	0.277467i	$-0.910505\pi$
$439$	−372.897	−	558.080i	−0.849424	−	1.27125i	0.111311	−	0.993786i	$-0.464495\pi$
$440$		0			0
$441$			475.282i			1.07774i
$442$	281.628	+	121.288i	0.637168	+	0.274407i
$443$		−	310.122i		−	0.700049i	−0.936741	−	0.350024i	$-0.886173\pi$
$443$		−	310.122i		−	0.700049i	0.936741	−	0.350024i	$-0.113827\pi$
$444$	291.161	+	702.924i	0.655767	+	1.58316i
$445$		0			0
$446$	−285.062	+	285.062i	−0.639152	+	0.639152i
$447$	279.877	−	1407.04i	0.626122	−	3.14773i
$448$	−107.633	+	161.084i	−0.240252	+	0.359562i
$449$	−172.129	+	34.2385i	−0.383360	+	0.0762551i	−0.383008	−	0.923745i	$-0.625112\pi$
$449$	−172.129	+	34.2385i	−0.383360	+	0.0762551i	−0.000351796		1.00000i	$0.500112\pi$
$450$		0			0
$451$	−129.639	+	312.976i	−0.287447	+	0.693959i
$452$	−1951.97	+	388.270i	−4.31851	+	0.859005i
$453$	−196.108	−	131.035i	−0.432910	−	0.289262i
$454$	−183.261	+	921.318i	−0.403660	+	2.02933i
$455$		0			0
$456$	−562.871	−	842.396i	−1.23437	−	1.84736i
$457$	238.465	+	575.705i	0.521805	+	1.25975i	0.936781	+	0.349917i	$0.113790\pi$
$457$	238.465	+	575.705i	0.521805	+	1.25975i	−0.414976	+	0.909832i	$0.636210\pi$
$458$	−111.639			−0.243754
$459$	248.127	+	1345.31i	0.540582	+	2.93097i
$460$		0			0
$461$	−269.146	−	649.777i	−0.583831	−	1.40949i	−0.889314	−	0.457296i	$-0.848818\pi$
$461$	−269.146	−	649.777i	−0.583831	−	1.40949i	0.305483	−	0.952198i	$-0.401182\pi$
$462$	315.060	+	471.521i	0.681948	+	1.02061i
$463$	−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
$467$	204.048	−	492.616i	0.436934	−	1.05485i	−0.540068	−	0.841621i	$-0.681602\pi$
$467$	204.048	−	492.616i	0.436934	−	1.05485i	0.977002	−	0.213230i	$-0.0683984\pi$
$468$	991.410	+	410.655i	2.11840	+	0.877469i
$469$	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
$473$	−48.6389	+	32.4995i	−0.102831	+	0.0687093i
$474$	−1846.32	+	764.771i	−3.89519	+	1.61344i
$475$		0			0
$476$	483.283	−	701.870i	1.01530	−	1.47452i
$477$			1277.45i			2.67808i
$478$	1487.11	−	615.979i	3.11110	−	1.28866i
$479$	632.407	−	422.561i	1.32027	−	0.882173i	0.322345	−	0.946622i	$-0.395529\pi$
$479$	632.407	−	422.561i	1.32027	−	0.882173i	0.997921	+	0.0644488i	$0.0205289\pi$
$480$		0			0
$481$	−69.0525	−	13.7354i	−0.143560	−	0.0285559i
$482$	−53.7648	+	80.4646i	−0.111545	+	0.166939i
$483$	213.510	+	1073.39i	0.442050	+	2.22234i
$484$	822.519	+	340.699i	1.69942	+	0.703923i
$485$		0			0
$486$	486.803	+	2447.32i	1.00165	+	5.03565i
$487$	−304.140	−	203.220i	−0.624518	−	0.417289i	0.202645	−	0.979252i	$-0.435046\pi$
$487$	−304.140	−	203.220i	−0.624518	−	0.417289i	−0.827162	+	0.561963i	$0.810046\pi$
$488$	580.829	+	115.534i	1.19022	+	0.236750i
$489$	−963.234	−	963.234i	−1.96980	−	1.96980i
$490$		0			0
$491$	−543.876	+	225.281i	−1.10769	+	0.458820i	−0.860142	−	0.510055i	$-0.829625\pi$
$491$	−543.876	+	225.281i	−1.10769	+	0.458820i	−0.247548	+	0.968876i	$0.579625\pi$
$492$	3526.53			7.16775
$493$	−32.5402	−	6.94628i	−0.0660045	−	0.0140898i
$494$	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
$498$	393.960	−	1980.57i	0.791085	−	3.97705i
$499$	−242.463	−	162.009i	−0.485898	−	0.324666i	0.288376	−	0.957517i	$-0.406885\pi$
$499$	−242.463	−	162.009i	−0.485898	−	0.324666i	−0.774274	+	0.632851i	$0.781885\pi$
$500$		0			0
$501$	538.085	+	222.882i	1.07402	+	0.444875i
$502$	797.891	+	330.497i	1.58942	+	0.658361i
$503$	−615.564	+	122.443i	−1.22379	+	0.243426i	−0.764360	−	0.644790i	$-0.776945\pi$
$503$	−615.564	+	122.443i	−1.22379	+	0.243426i	−0.459426	+	0.888216i	$0.651945\pi$
$504$	1356.16	−	2029.63i	2.69079	−	4.02705i
$505$		0			0
$506$	−478.443	−	478.443i	−0.945539	−	0.945539i
$507$	682.565	−	456.075i	1.34628	−	0.899556i
$508$	−484.104	−	1168.73i	−0.952961	−	2.30065i
$509$			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
$512$	995.633	−	412.405i	1.94460	−	0.805478i
$513$	404.831	+	605.873i	0.789145	+	1.18104i
$514$	1065.69	−	1065.69i	2.07332	−	2.07332i
$515$		0			0
$516$	506.334	+	338.321i	0.981267	+	0.655662i
$517$	−2.36939	−	11.9117i	−0.00458295	−	0.0230400i
$518$	−106.774	+	257.775i	−0.206127	+	0.497636i
$519$	68.3712	−	165.063i	0.131736	−	0.318040i
$520$		0			0
$521$	−500.960	+	749.739i	−0.961535	+	1.43904i	−0.0640736	+	0.997945i	$0.520409\pi$
$521$	−500.960	+	749.739i	−0.961535	+	1.43904i	−0.897461	+	0.441093i	$0.854591\pi$
$522$	−162.857	−	32.3942i	−0.311986	−	0.0620579i
$523$	33.6388	−	33.6388i	0.0643190	−	0.0643190i	−0.674216	−	0.738535i	$-0.735518\pi$
$523$	33.6388	−	33.6388i	0.0643190	−	0.0643190i	0.738535	+	0.674216i	$0.235518\pi$
$524$	592.765	+	887.136i	1.13123	+	1.69301i
$525$		0			0
$526$		−	1045.51i		−	1.98766i
$527$	−87.5060	+	56.7187i	−0.166046	+	0.107626i
$528$			1004.66i			1.90276i
$529$	−297.265	−	717.661i	−0.561938	−	1.35664i
$530$		0			0
$531$	678.251	−	678.251i	1.27731	−	1.27731i
$532$	88.5536	−	445.189i	0.166454	−	0.836822i
$533$	−181.301	+	271.336i	−0.340151	+	0.509072i
$534$	182.967	−	36.3945i	0.342636	−	0.0681544i
$535$		0			0
$536$	−626.463	+	1512.41i	−1.16877	+	2.82167i
$537$	1759.90	−	350.065i	3.27727	−	0.651891i
$538$	837.713	+	559.742i	1.55709	+	1.04041i
$539$	20.4650	−	102.884i	0.0379684	−	0.190880i
$540$		0			0
$541$	−193.644	−	289.809i	−0.357937	−	0.535691i	0.608178	−	0.793800i	$-0.291901\pi$
$541$	−193.644	−	289.809i	−0.357937	−	0.535691i	−0.966116	+	0.258109i	$0.916901\pi$
$542$	−124.732	−	301.129i	−0.230132	−	0.555588i
$543$	1716.79			3.16168
$544$	754.196	−	300.132i	1.38639	−	0.551714i
$545$		0			0
$546$	209.054	+	504.702i	0.382883	+	0.924362i
$547$	−121.428	−	181.730i	−0.221989	−	0.332230i	0.703712	−	0.710485i	$-0.251524\pi$
$547$	−121.428	−	181.730i	−0.221989	−	0.332230i	−0.925702	+	0.378255i	$0.876524\pi$
$548$	−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
$552$	−1547.21	+	3735.30i	−2.80292	+	6.76685i
$553$	−474.811	−	196.673i	−0.858609	−	0.355648i
$554$	−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	$0.439282\pi$
$558$	−432.695	+	289.118i	−0.775440	+	0.518132i
$559$	−52.0617	+	21.5647i	−0.0931336	+	0.0385772i
$560$		0			0
$561$	6.88978	−	493.461i	0.0122813	−	0.879609i
$562$			97.7621i			0.173954i
$563$	−342.135	+	141.717i	−0.607700	+	0.251718i	−0.665245	−	0.746625i	$-0.731673\pi$
$563$	−342.135	+	141.717i	−0.607700	+	0.251718i	0.0575448	+	0.998343i	$0.481673\pi$
$564$	−105.123	+	70.2412i	−0.186389	+	0.124541i
$565$		0			0
$566$	453.976	+	90.3014i	0.802078	+	0.159543i
$567$	−735.142	+	1100.22i	−1.29655	+	1.94042i
$568$	−357.237	−	1795.95i	−0.628938	−	3.16189i
$569$	891.706	+	369.357i	1.56715	+	0.649133i	0.986312	−	0.164889i	$-0.0527264\pi$
$569$	891.706	+	369.357i	1.56715	+	0.649133i	0.580834	+	0.814022i	$0.302726\pi$
$570$		0			0
$571$	−62.0643	−	312.018i	−0.108694	−	0.546442i	−0.996308	−	0.0858532i	$-0.972638\pi$
$571$	−62.0643	−	312.018i	−0.108694	−	0.546442i	0.887614	−	0.460589i	$-0.152362\pi$
$572$	−196.928	−	131.583i	−0.344280	−	0.230041i
$573$	40.7663	+	8.10893i	0.0711454	+	0.0141517i
$574$	914.462	+	914.462i	1.59314	+	1.59314i
$575$		0			0
$576$	777.315	−	321.974i	1.34950	−	0.558983i
$577$	−163.289			−0.282996			−0.141498	−	0.989939i	$-0.545192\pi$
$577$	−163.289			−0.282996			−0.141498	+	0.989939i	$0.545192\pi$
$578$	−987.927	+	377.256i	−1.70922	+	0.652691i
$579$	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
$583$	55.0050	−	276.529i	0.0943482	−	0.474321i
$584$	−849.894	−	567.881i	−1.45530	−	0.972399i
$585$		0			0
$586$	−1313.06	−	543.887i	−2.24072	−	0.928135i
$587$	−52.3344	−	21.6776i	−0.0891557	−	0.0369295i	0.337660	−	0.941268i	$-0.390365\pi$
$587$	−52.3344	−	21.6776i	−0.0891557	−	0.0369295i	−0.426816	+	0.904339i	$0.640365\pi$
$588$	−1071.03	+	213.041i	−1.82148	+	0.362315i
$589$	−30.8594	+	46.1843i	−0.0523929	+	0.0784114i
$590$		0			0
$591$	−187.880	−	187.880i	−0.317902	−	0.317902i
$592$	−410.995	+	274.618i	−0.694248	+	0.463882i
$593$	−310.327	−	749.195i	−0.523316	−	1.26340i	−0.935832	−	0.352447i	$-0.885350\pi$
$593$	−310.327	−	749.195i	−0.523316	−	1.26340i	0.412515	−	0.910951i	$-0.364650\pi$
$594$		−	1506.77i		−	2.53665i
$595$		0			0
$596$	2374.43			3.98394
$597$	274.583	−	113.736i	0.459938	−	0.190513i
$598$	−362.117	−	541.946i	−0.605547	−	0.906265i
$599$	−453.053	+	453.053i	−0.756349	+	0.756349i	−0.975656	−	0.219307i	$-0.929620\pi$
$599$	−453.053	+	453.053i	−0.756349	+	0.756349i	0.219307	+	0.975656i	$0.429620\pi$
$600$		0			0
$601$	−332.402	−	222.104i	−0.553081	−	0.369557i	0.247401	−	0.968913i	$-0.420423\pi$
$601$	−332.402	−	222.104i	−0.553081	−	0.369557i	−0.800483	+	0.599356i	$0.795423\pi$
$602$	43.5671	+	219.027i	0.0723707	+	0.363832i
$603$	736.451	−	1777.95i	1.22131	−	2.94851i
$604$	149.389	−	360.656i	0.247332	−	0.597113i
$605$		0			0
$606$	−961.238	+	1438.59i	−1.58620	+	2.37392i
$607$	900.705	+	179.161i	1.48386	+	0.295159i	0.869527	−	0.493886i	$-0.164424\pi$
$607$	900.705	+	179.161i	1.48386	+	0.295159i	0.614336	+	0.789045i	$0.289424\pi$
$608$	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
$612$	−3438.56	+	1368.37i	−5.61856	+	2.23591i
$613$			1.10159i			0.00179704i	1.00000		0.000898520i	$0.000286008\pi$
$613$			1.10159i			0.00179704i	−1.00000		0.000898520i	$0.999714\pi$
$614$	−332.948	−	803.807i	−0.542260	−	1.30913i
$615$		0			0
$616$	−380.961	+	380.961i	−0.618443	+	0.618443i
$617$	−151.416	+	761.218i	−0.245406	+	1.23374i	0.639800	+	0.768541i	$0.279017\pi$
$617$	−151.416	+	761.218i	−0.245406	+	1.23374i	−0.885206	+	0.465199i	$0.845983\pi$
$618$	57.8043	−	86.5103i	0.0935345	−	0.139984i
$619$	835.815	−	166.254i	1.35027	−	0.268585i	0.533620	−	0.845724i	$-0.320831\pi$
$619$	835.815	−	166.254i	1.35027	−	0.268585i	0.816646	+	0.577139i	$0.195831\pi$
$620$		0			0
$621$	1112.80	−	2686.53i	1.79194	−	4.32613i
$622$	223.426	−	44.4423i	0.359206	−	0.0714506i
$623$	39.8896	+	26.6534i	0.0640283	+	0.0427823i
$624$	−188.807	+	949.199i	−0.302576	+	1.52115i
$625$		0			0
$626$	−383.034	−	573.251i	−0.611876	−	0.915736i
$627$	−100.596	−	242.861i	−0.160441	−	0.387338i
$628$	513.951			0.818393
$629$	203.753	−	132.066i	0.323931	−	0.209962i
$630$		0			0
$631$	−1.11445	−	2.69052i	−0.00176616	−	0.00426390i	0.922994	−	0.384814i	$-0.125735\pi$
$631$	−1.11445	−	2.69052i	−0.00176616	−	0.00426390i	−0.924760	+	0.380550i	$0.875735\pi$
$632$	−1054.80	−	1578.63i	−1.66899	−	2.49782i
$633$	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
$637$	38.6706	−	93.3590i	0.0607073	−	0.146560i
$638$	33.8588	+	14.0248i	0.0530702	+	0.0219824i
$639$	419.957	+	2111.27i	0.657210	+	3.30402i
$640$		0			0
$641$	−49.4146	+	248.424i	−0.0770898	+	0.387557i	0.922907	+	0.385023i	$0.125806\pi$
$641$	−49.4146	+	248.424i	−0.0770898	+	0.387557i	−0.999997	+	0.00253359i	$0.999194\pi$
$642$	1329.63	−	1329.63i	2.07107	−	2.07107i
$643$	−704.026	+	470.415i	−1.09491	+	0.731595i	−0.965606	−	0.260010i	$-0.916274\pi$
$643$	−704.026	+	470.415i	−1.09491	+	0.731595i	−0.129303	+	0.991605i	$0.541274\pi$
$644$	−1673.50	+	693.188i	−2.59861	+	1.07638i
$645$		0			0
$646$	−403.827	+	392.705i	−0.625119	+	0.607903i
$647$			631.331i			0.975783i	0.872904	+	0.487891i	$0.162234\pi$
$647$			631.331i			0.975783i	−0.872904	+	0.487891i	$0.837766\pi$
$648$	−4516.22	+	1870.68i	−6.96948	+	2.88685i
$649$	−176.026	+	117.617i	−0.271226	+	0.181227i
$650$		0			0
$651$	−182.210	−	36.2438i	−0.279893	−	0.0556741i
$652$	1252.60	−	1874.65i	1.92117	−	2.87524i
$653$	204.845	+	1029.82i	0.313698	+	1.57707i	0.740077	+	0.672522i	$0.234789\pi$
$653$	204.845	+	1029.82i	0.313698	+	1.57707i	−0.426379	+	0.904545i	$0.640211\pi$
$654$	−2924.97	−	1211.56i	−4.47243	−	1.85254i
$655$		0			0
$656$	446.972	+	2247.08i	0.681360	+	3.42543i
$657$	999.110	+	667.584i	1.52072	+	1.01611i
$658$	−45.4736	−	9.04526i	−0.0691088	−	0.0137466i
$659$	−494.059	−	494.059i	−0.749711	−	0.749711i	0.224714	−	0.974425i	$-0.427855\pi$
$659$	−494.059	−	494.059i	−0.749711	−	0.749711i	−0.974425	+	0.224714i	$0.927855\pi$
$660$		0			0
$661$	399.021	−	165.280i	0.603663	−	0.250046i	−0.0598532	−	0.998207i	$-0.519063\pi$
$661$	399.021	−	165.280i	0.603663	−	0.250046i	0.663516	+	0.748162i	$0.269063\pi$
$662$	764.556			1.15492
$663$	99.2466	−	464.926i	0.149693	−	0.701246i
$664$	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
$668$	−188.061	+	945.448i	−0.281529	+	1.41534i
$669$	519.683	+	347.241i	0.776806	+	0.519045i
$670$		0			0
$671$	141.959	+	58.8012i	0.211563	+	0.0876322i
$672$	1336.04	+	553.406i	1.98816	+	0.823521i
$673$	693.283	−	137.903i	1.03014	−	0.204907i	0.349047	−	0.937105i	$-0.386505\pi$
$673$	693.283	−	137.903i	1.03014	−	0.204907i	0.681092	+	0.732198i	$0.261505\pi$
$674$	−488.785	+	731.519i	−0.725201	+	1.08534i
$675$		0			0
$676$	960.750	+	960.750i	1.42123	+	1.42123i
$677$	−710.811	+	474.949i	−1.04994	+	0.701549i	−0.955802	−	0.294010i	$-0.905010\pi$
$677$	−710.811	+	474.949i	−1.04994	+	0.701549i	−0.0941403	+	0.995559i	$0.530010\pi$
$678$	1683.82	+	4065.10i	2.48351	+	5.99572i
$679$		−	385.483i		−	0.567722i
$680$		0			0
$681$	1456.38			2.13858
$682$	106.115	−	43.9541i	0.155593	−	0.0644489i
$683$	595.659	+	891.467i	0.872122	+	1.30522i	0.951270	+	0.308360i	$0.0997801\pi$
$683$	595.659	+	891.467i	0.872122	+	1.30522i	−0.0791477	+	0.996863i	$0.525220\pi$
$684$	−1393.90	+	1393.90i	−2.03786	+	2.03786i
$685$		0			0
$686$	−1128.86	−	754.278i	−1.64556	−	1.09953i
$687$	33.7669	+	169.758i	0.0491512	+	0.247100i
$688$	−151.400	+	365.513i	−0.220059	+	0.531269i
$689$	103.937	−	250.927i	0.150852	−	0.364190i
$690$		0			0
$691$	−30.8540	+	46.1763i	−0.0446512	+	0.0668253i	−0.853124	−	0.521709i	$-0.825295\pi$
$691$	−30.8540	+	46.1763i	−0.0446512	+	0.0668253i	0.808472	+	0.588534i	$0.200295\pi$
$692$	290.025	+	57.6896i	0.419111	+	0.0833664i
$693$	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
$697$	−204.131	−	1106.77i	−0.292870	−	1.58791i
$698$		−	215.985i		−	0.309434i
$699$	−303.580	−	732.907i	−0.434306	−	1.04851i
$700$		0			0
$701$	−234.497	+	234.497i	−0.334518	+	0.334518i	−0.854299	−	0.519781i	$-0.826013\pi$
$701$	−234.497	+	234.497i	−0.334518	+	0.334518i	0.519781	+	0.854299i	$0.326013\pi$
$702$	283.170	−	1423.59i	0.403376	−	2.02791i
$703$	71.8544	−	107.538i	0.102211	−	0.152970i
$704$	−182.129	+	36.2277i	−0.258706	+	0.0514599i
$705$		0			0
$706$	−553.356	+	1335.92i	−0.783791	+	1.89224i
$707$	−436.395	+	86.8043i	−0.617249	+	0.122778i
$708$	1832.44	+	1224.39i	2.58819	+	1.72937i
$709$	−6.19721	+	31.1555i	−0.00874077	+	0.0439428i	−0.984910	−	0.173070i	$-0.944631\pi$
$709$	−6.19721	+	31.1555i	−0.00874077	+	0.0439428i	0.976169	+	0.217013i	$0.0696313\pi$
$710$		0			0
$711$	1240.00	+	1855.78i	1.74402	+	2.61010i
$712$	67.8235	+	163.740i	0.0952577	+	0.229973i
$713$	221.661			0.310885
$714$	−1730.35	−	745.205i	−2.42346	−	1.04370i
$715$		0			0
$716$	1136.53	+	2743.83i	1.58733	+	3.83216i
$717$	−1386.45	−	2074.97i	−1.93368	−	2.89396i
$718$	360.482	+	360.482i	0.502064	+	0.502064i
$719$	495.464	+	98.5540i	0.689102	+	0.137071i	0.527207	−	0.849737i	$-0.323239\pi$
$719$	495.464	+	98.5540i	0.689102	+	0.137071i	0.161895	+	0.986808i	$0.448239\pi$
$720$		0			0
$721$	26.2427	−	5.22000i	0.0363977	−	0.00723995i
$722$	390.693	−	943.216i	0.541126	−	1.30639i
$723$	138.616	+	57.4165i	0.191723	+	0.0794142i
$724$	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	$0.232254\pi$
$728$	−431.526	+	288.336i	−0.592755	+	0.396066i
$729$	1513.18	−	626.782i	2.07570	−	0.859783i
$730$		0			0
$731$	76.8704	−	178.492i	0.105158	−	0.244175i
$732$		−	1599.56i		−	2.18519i
$733$	−831.666	+	344.487i	−1.13461	+	0.469969i	−0.869344	−	0.494207i	$-0.835458\pi$
$733$	−831.666	+	344.487i	−1.13461	+	0.469969i	−0.265262	+	0.964176i	$0.585458\pi$
$734$	−1480.50	+	989.238i	−2.01703	+	1.34774i
$735$		0			0
$736$	−1692.27	−	336.613i	−2.29928	−	0.457354i
$737$	−235.976	+	353.162i	−0.320184	+	0.479189i
$738$	−1095.70	−	5508.46i	−1.48469	−	7.46404i
$739$	−726.586	−	300.962i	−0.983201	−	0.407255i	−0.167591	−	0.985857i	$-0.553599\pi$
$739$	−726.586	−	300.962i	−0.983201	−	0.407255i	−0.815611	+	0.578601i	$0.803599\pi$
$740$		0			0
$741$	−49.4019	−	248.360i	−0.0666692	−	0.335169i
$742$	−894.949	−	597.986i	−1.20613	−	0.805911i
$743$	−588.634	−	117.087i	−0.792239	−	0.157586i	−0.217649	−	0.976027i	$-0.569839\pi$
$743$	−588.634	−	117.087i	−0.792239	−	0.157586i	−0.574591	+	0.818441i	$0.694839\pi$
$744$	−485.300	−	485.300i	−0.652286	−	0.652286i
$745$		0			0
$746$	−595.016	+	246.464i	−0.797609	+	0.330380i
$747$	−2255.31			−3.01916
$748$	803.266	−	148.153i	1.07388	−	0.198065i
$749$	483.570			0.645620
$750$		0			0
$751$	−134.595	+	89.9336i	−0.179221	+	0.119752i	−0.641945	−	0.766751i	$-0.721872\pi$
$751$	−134.595	+	89.9336i	−0.179221	+	0.119752i	0.462724	+	0.886503i	$0.346872\pi$
$752$	−58.0811	−	58.0811i	−0.0772355	−	0.0772355i
$753$	261.217	−	1313.23i	0.346902	−	1.74400i
$754$	29.3540	+	19.6137i	0.0389310	+	0.0260129i
$755$		0			0
$756$	−3726.74	−	1543.66i	−4.92954	−	2.04188i
$757$	−419.645	−	173.822i	−0.554352	−	0.229620i	0.0878790	−	0.996131i	$-0.471991\pi$
$757$	−419.645	−	173.822i	−0.554352	−	0.229620i	−0.642231	+	0.766511i	$0.721991\pi$
$758$	−1589.71	+	316.213i	−2.09724	+	0.417168i
$759$	−582.803	+	872.227i	−0.767857	+	1.14918i
$760$		0			0
$761$	−395.123	−	395.123i	−0.519215	−	0.519215i	0.398119	−	0.917334i	$-0.369663\pi$
$761$	−395.123	−	395.123i	−0.519215	−	0.519215i	−0.917334	+	0.398119i	$0.869663\pi$
$762$	−2325.43	+	1553.80i	−3.05174	+	2.03911i
$763$	−311.572	−	752.202i	−0.408352	−	0.985848i
$764$			68.7948i			0.0900456i
$765$		0			0
$766$	2131.99			2.78327
$767$	−188.413	+	78.0431i	−0.245649	+	0.101751i
$768$	−1128.77	−	1689.33i	−1.46975	−	2.19964i
$769$	568.899	−	568.899i	0.739790	−	0.739790i	−0.232747	−	0.972537i	$-0.574771\pi$
$769$	568.899	−	568.899i	0.739790	−	0.739790i	0.972537	+	0.232747i	$0.0747714\pi$
$770$		0			0
$771$	−1942.80	−	1298.14i	−2.51985	−	1.68371i
$772$	563.591	+	2833.36i	0.730040	+	3.67016i
$773$	−497.404	+	1200.84i	−0.643472	+	1.55348i	0.178493	+	0.983941i	$0.442878\pi$
$773$	−497.404	+	1200.84i	−0.643472	+	1.55348i	−0.821965	+	0.569538i	$0.807122\pi$
$774$	371.141	−	896.013i	0.479510	−	1.15764i
$775$		0			0
$776$	791.174	−	1184.08i	1.01955	−	1.52587i
$777$	424.266	+	84.3917i	0.546031	+	0.108612i
$778$	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
$782$	2198.34	+	469.274i	2.81118	+	0.600095i
$783$			157.502i			0.201152i
$784$	−271.497	−	655.452i	−0.346297	−	0.836035i
$785$		0			0
$786$	1667.96	−	1667.96i	2.12209	−	2.12209i
$787$	6.61174	−	33.2395i	0.00840120	−	0.0422357i	−0.976357	−	0.216163i	$-0.930646\pi$
$787$	6.61174	−	33.2395i	0.00840120	−	0.0422357i	0.984759	+	0.173927i	$0.0556458\pi$
$788$	244.322	−	365.654i	0.310053	−	0.464028i
$789$	−1589.79	+	316.229i	−2.01495	+	0.400797i
$790$		0			0
$791$	−433.021	+	1045.41i	−0.547435	+	1.32163i
$792$	2294.80	−	456.464i	2.89747	−	0.576344i
$793$	123.072	+	82.2339i	0.155198	+	0.103700i
$794$	68.3472	−	343.604i	0.0860796	−	0.432751i
$795$		0			0
$796$	273.291	+	409.009i	0.343331	+	0.513831i
$797$	−28.4474	−	68.6780i	−0.0356931	−	0.0861707i	0.905028	−	0.425352i	$-0.139850\pi$
$797$	−28.4474	−	68.6780i	−0.0356931	−	0.0861707i	−0.940721	+	0.339182i	$0.889850\pi$
$798$	−1003.52			−1.25755
$799$	28.1295	+	28.9262i	0.0352059	+	0.0362030i
$800$		0			0
$801$	−79.7313	−	192.488i	−0.0995397	−	0.240310i
$802$	−159.893	−	239.296i	−0.199367	−	0.298374i
$803$	−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
$807$	597.760	−	1443.12i	0.740718	−	1.78825i
$808$	−1518.62	−	629.032i	−1.87948	−	0.778505i
$809$	−64.3000	−	323.258i	−0.0794809	−	0.399577i	−0.999961	−	0.00878888i	$-0.997202\pi$
$809$	−64.3000	−	323.258i	−0.0794809	−	0.399577i	0.920480	−	0.390789i	$-0.127798\pi$
$810$		0			0
$811$	47.8095	−	240.355i	0.0589513	−	0.296368i	−0.940051	−	0.341035i	$-0.889223\pi$
$811$	47.8095	−	240.355i	0.0589513	−	0.296368i	0.999002	+	0.0446666i	$0.0142225\pi$
$812$	69.3757	−	69.3757i	0.0854380	−	0.0854380i
$813$	−420.167	+	280.746i	−0.516810	+	0.345322i
$814$	−247.082	+	102.345i	−0.303541	+	0.125731i
$815$		0			0
$816$	−1815.39	−	2800.80i	−2.22474	−	3.43235i
$817$		−	103.517i		−	0.126704i
$818$	141.427	−	58.5809i	0.172893	−	0.0716148i
$819$	507.289	−	338.959i	0.619400	−	0.413870i
$820$		0			0
$821$	613.444	+	122.022i	0.747191	+	0.148625i	0.553978	−	0.832531i	$-0.313109\pi$
$821$	613.444	+	122.022i	0.747191	+	0.148625i	0.193213	+	0.981157i	$0.438109\pi$
$822$	−187.814	+	281.084i	−0.228484	+	0.341951i
$823$	115.470	+	580.505i	0.140303	+	0.705352i	0.985334	+	0.170635i	$0.0545819\pi$
$823$	115.470	+	580.505i	0.140303	+	0.705352i	−0.845031	+	0.534717i	$0.820418\pi$
$824$	91.3225	+	37.8270i	0.110828	+	0.0459066i
$825$		0			0
$826$	157.671	+	792.664i	0.190885	+	0.959641i
$827$	12.4759	+	8.33614i	0.0150858	+	0.0100800i	0.563090	−	0.826395i	$-0.309612\pi$
$827$	12.4759	+	8.33614i	0.0150858	+	0.0100800i	−0.548004	+	0.836475i	$0.684612\pi$
$828$	7715.44	+	1534.70i	9.31817	+	1.85350i
$829$	360.941	+	360.941i	0.435393	+	0.435393i	0.890458	−	0.455065i	$-0.150384\pi$
$829$	360.941	+	360.941i	0.435393	+	0.435393i	−0.455065	+	0.890458i	$0.650384\pi$
$830$		0			0
$831$	−1066.79	+	441.880i	−1.28374	+	0.531744i
$832$	−178.884			−0.215004
$833$	128.857	+	323.802i	0.154690	+	0.388718i
$834$	−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
$838$	−181.464	+	912.283i	−0.216545	+	1.08864i
$839$	−1028.00	−	686.885i	−1.22526	−	0.818695i	−0.237008	−	0.971508i	$-0.576167\pi$
$839$	−1028.00	−	686.885i	−1.22526	−	0.818695i	−0.988255	+	0.152813i	$0.951167\pi$
$840$		0			0
$841$	773.443	+	320.371i	0.919671	+	0.380940i
$842$	110.444	+	45.7472i	0.131168	+	0.0543316i
$843$	148.656	−	29.5695i	0.176342	−	0.0350765i
$844$	−1041.91	+	1559.32i	−1.23449	+	1.84754i
$845$		0			0
$846$	142.379	+	142.379i	0.168297	+	0.168297i
$847$	420.870	−	281.216i	0.496895	−	0.332015i
$848$	−729.719	−	1761.70i	−0.860518	−	2.07747i
$849$		−	717.624i		−	0.845258i
$850$		0			0
$851$	−516.125			−0.606492
$852$	−4569.42	+	1892.72i	−5.36317	+	2.22150i
$853$	−360.989	−	540.259i	−0.423200	−	0.633363i	0.557201	−	0.830378i	$-0.311875\pi$
$853$	−360.989	−	540.259i	−0.423200	−	0.633363i	−0.980401	+	0.197014i	$0.936875\pi$
$854$	414.779	−	414.779i	0.485690	−	0.485690i
$855$		0			0
$856$	1485.36	+	992.488i	1.73524	+	1.15945i
$857$	156.735	+	787.962i	0.182888	+	0.919442i	0.957814	+	0.287389i	$0.0927874\pi$
$857$	156.735	+	787.962i	0.182888	+	0.919442i	−0.774925	+	0.632053i	$0.782213\pi$
$858$	−200.382	+	483.765i	−0.233546	+	0.563829i
$859$	348.417	−	841.152i	0.405607	−	0.979222i	−0.580672	−	0.814137i	$-0.697210\pi$
$859$	348.417	−	841.152i	0.405607	−	0.979222i	0.986279	−	0.165085i	$-0.0527898\pi$
$860$		0			0
$861$	1113.93	−	1667.11i	1.29376	−	1.93625i
$862$	2179.98	+	433.625i	2.52898	+	0.503045i
$863$	634.157	−	634.157i	0.734828	−	0.734828i	−0.236744	−	0.971572i	$-0.576080\pi$
$863$	634.157	−	634.157i	0.734828	−	0.734828i	0.971572	+	0.236744i	$0.0760802\pi$
$864$	−2134.69	−	3194.80i	−2.47071	−	3.69768i
$865$		0			0
$866$		−	862.797i		−	0.996302i
$867$	872.464	+	1388.13i	1.00630	+	1.60107i
$868$		−	307.487i		−	0.354247i
$869$	−188.515	−	455.114i	−0.216933	−	0.523722i
$870$		0			0
$871$	−289.320	+	289.320i	−0.332170	+	0.332170i
$872$	586.789	−	2949.99i	0.672924	−	3.38302i
$873$	−930.080	+	1391.96i	−1.06538	+	1.59446i
$874$	1174.34	−	233.590i	1.34363	−	0.267265i
$875$		0			0
$876$	−1056.53	+	2550.70i	−1.20609	+	2.91176i
$877$	−215.684	+	42.9023i	−0.245934	+	0.0489193i	−0.316518	−	0.948587i	$-0.602514\pi$
$877$	−215.684	+	42.9023i	−0.245934	+	0.0489193i	0.0705838	+	0.997506i	$0.477514\pi$
$878$	−2042.12	−	1364.50i	−2.32588	−	1.55410i
$879$	−429.876	+	2161.13i	−0.489051	+	2.45863i
$880$		0			0
$881$	−21.8952	−	32.7685i	−0.0248527	−	0.0371947i	0.818835	−	0.574029i	$-0.194620\pi$
$881$	−21.8952	−	32.7685i	−0.0248527	−	0.0371947i	−0.843688	+	0.536834i	$0.819620\pi$
$882$	665.544	+	1606.76i	0.754585	+	1.82173i
$883$	−1402.81			−1.58869			−0.794343	−	0.607469i	$-0.792185\pi$
$883$	−1402.81			−1.58869			−0.794343	+	0.607469i	$0.792185\pi$
$884$	786.767	+	10.9850i	0.890008	+	0.0124264i
$885$		0			0
$886$	−434.267	−	1048.41i	−0.490144	−	1.18331i
$887$	547.484	+	819.368i	0.617231	+	0.923751i	1.00000		9.26296e-5i	$-2.94849e-5\pi$
$887$	547.484	+	819.368i	0.617231	+	0.923751i	−0.382769	+	0.923844i	$0.625029\pi$
$888$	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
$892$	−395.877	+	955.731i	−0.443808	+	1.07145i
$893$	19.8559	+	8.22457i	0.0222350	+	0.00921005i
$894$	−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
$898$	−533.963	+	356.783i	−0.594614	+	0.397308i
$899$	−11.0921	+	4.59451i	−0.0123383	+	0.00511069i
$900$		0			0
$901$	346.337	+	870.303i	0.384392	+	0.965930i
$902$			1239.60i			1.37428i
$903$	319.872	−	132.496i	0.354233	−	0.146728i
$904$	−3475.71	+	2322.39i	−3.84481	+	2.56902i
$905$		0			0
$906$	−846.465	−	168.372i	−0.934289	−	0.185842i
$907$	44.9747	−	67.3094i	0.0495863	−	0.0742111i	−0.805848	−	0.592122i	$-0.798290\pi$
$907$	44.9747	−	67.3094i	0.0495863	−	0.0742111i	0.855434	+	0.517911i	$0.173290\pi$
$908$	470.259	+	2364.15i	0.517907	+	2.60369i
$909$	1785.24	+	739.471i	1.96396	+	0.813499i
$910$		0			0
$911$	286.067	+	1438.15i	0.314014	+	1.57866i	0.739160	+	0.673530i	$0.235223\pi$
$911$	286.067	+	1438.15i	0.314014	+	1.57866i	−0.425146	+	0.905125i	$0.639777\pi$
$912$	−1478.22	−	987.714i	−1.62085	−	1.08302i
$913$	488.207	+	97.1105i	0.534729	+	0.106364i
$914$	1612.34	+	1612.34i	1.76404	+	1.76404i
$915$		0			0
$916$	−264.666	+	109.628i	−0.288937	+	0.119682i
$917$	606.617			0.661524
$918$	2722.69	+	4200.59i	2.96590	+	4.57580i
$919$	−1285.69			−1.39901			−0.699504	−	0.714629i	$-0.746596\pi$
$919$	−1285.69			−1.39901			−0.699504	+	0.714629i	$0.746596\pi$
$920$		0			0
$921$	−1121.56	+	749.400i	−1.21776	+	0.813681i
$922$	−1819.78	−	1819.78i	−1.97373	−	1.97373i
$923$	89.2882	−	448.882i	0.0967370	−	0.486330i
$924$	1209.95	+	808.462i	1.30947	+	0.874959i
$925$		0			0
$926$	−1281.95	−	531.000i	−1.38439	−	0.573434i
$927$	−107.356	−	44.4683i	−0.115810	−	0.0479701i
$928$	91.6600	−	18.2323i	0.0987715	−	0.0196469i
$929$	965.295	−	1444.67i	1.03907	−	1.55508i	0.224957	−	0.974369i	$-0.427776\pi$
$929$	965.295	−	1444.67i	1.03907	−	1.55508i	0.814112	−	0.580708i	$-0.197224\pi$
$930$		0			0
$931$	131.261	+	131.261i	0.140989	+	0.140989i
$932$	1091.71	−	729.459i	1.17136	−	0.782681i
$933$	−135.157	−	326.298i	−0.144863	−	0.349730i
$934$		−	1951.09i		−	2.08897i
$935$		0			0
$936$	2253.91			2.40802
$937$	1509.10	−	625.091i	1.61057	−	0.667119i	0.617708	−	0.786407i	$-0.288061\pi$
$937$	1509.10	−	625.091i	1.61057	−	0.667119i	0.992860	+	0.119288i	$0.0380612\pi$
$938$	900.850	+	1348.22i	0.960395	+	1.43733i
$939$	−755.826	+	755.826i	−0.804926	+	0.804926i
$940$		0			0
$941$	−237.401	−	158.626i	−0.252286	−	0.168572i	0.422997	−	0.906131i	$-0.360978\pi$
$941$	−237.401	−	158.626i	−0.252286	−	0.168572i	−0.675282	+	0.737559i	$0.735978\pi$
$942$	−221.674	−	1114.43i	−0.235323	−	1.18305i
$943$	−915.481	+	2210.17i	−0.970817	+	2.34376i
$944$	−547.922	+	1322.80i	−0.580426	+	1.40127i
$945$		0			0
$946$	−118.922	+	177.979i	−0.125710	+	0.188139i
$947$	15.8796	+	3.15865i	0.0167683	+	0.00333543i	0.203467	−	0.979082i	$-0.434779\pi$
$947$	15.8796	+	3.15865i	0.0167683	+	0.00333543i	−0.186699	+	0.982417i	$0.559779\pi$
$948$	−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
$952$	373.660	−	1750.43i	0.392500	−	1.83869i
$953$			1030.31i			1.08112i	0.841306	+	0.540560i	$0.181788\pi$
$953$			1030.31i			1.08112i	−0.841306	+	0.540560i	$0.818212\pi$
$954$	1788.82	+	4318.60i	1.87508	+	4.52684i
$955$		0			0
$956$	2920.64	−	2920.64i	3.05506	−	3.05506i
$957$	11.0848	−	55.7273i	0.0115829	−	0.0582312i
$958$	1546.23	−	2314.10i	1.61402	−	2.41555i
$959$	−85.2662	+	16.9605i	−0.0889116	+	0.0176856i
$960$		0			0
$961$	353.359	−	853.085i	0.367700	−	0.887706i
$962$	−252.677	+	50.2605i	−0.262657	+	0.0522458i
$963$	−1746.15	−	1166.74i	−1.81324	−	1.21157i
$964$	−48.4463	+	243.556i	−0.0502555	+	0.252652i
$965$		0			0
$966$	2224.88	+	3329.78i	2.30319	+	3.44697i
$967$	−184.118	−	444.501i	−0.190402	−	0.459670i	0.799634	−	0.600488i	$-0.205027\pi$
$967$	−184.118	−	444.501i	−0.190402	−	0.459670i	−0.990036	+	0.140818i	$0.955027\pi$
$968$	1869.95			1.93176
$969$	719.287	+	495.276i	0.742298	+	0.511120i
$970$		0			0
$971$	347.780	+	839.615i	0.358167	+	0.864691i	0.995558	+	0.0941509i	$0.0300136\pi$
$971$	347.780	+	839.615i	0.358167	+	0.864691i	−0.637391	+	0.770541i	$0.719986\pi$
$972$	3557.32	+	5323.90i	3.65979	+	5.47727i
$973$	−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
$977$	−328.742	+	793.653i	−0.336481	+	0.812337i	0.661567	+	0.749886i	$0.269892\pi$
$977$	−328.742	+	793.653i	−0.336481	+	0.812337i	−0.998048	+	0.0624510i	$0.980108\pi$
$978$	−4605.19	−	1907.53i	−4.70878	−	1.95044i
$979$	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
$983$	1349.84	−	901.935i	1.37319	−	0.917533i	0.373237	−	0.927736i	$-0.378248\pi$
$983$	1349.84	−	901.935i	1.37319	−	0.917533i	0.999948	+	0.0102031i	$0.00324780\pi$
$984$	6843.24	−	2834.56i	6.95451	−	2.88065i
$985$		0			0
$986$	−119.734	+	22.0835i	−0.121434	+	0.0223971i
$987$			71.8826i			0.0728294i
$988$	387.214	−	160.389i	0.391917	−	0.162337i
$989$	−343.478	+	229.504i	−0.347298	+	0.232057i
$990$		0			0
$991$	−1713.25	−	340.786i	−1.72881	−	0.343881i	−0.772226	−	0.635348i	$-0.780857\pi$
$991$	−1713.25	−	340.786i	−1.72881	−	0.343881i	−0.956581	+	0.291467i	$0.905857\pi$
$992$	162.723	−	243.532i	0.164035	−	0.245496i
$993$	−231.251	−	1162.58i	−0.232881	−	1.17077i
$994$	−1675.69	−	694.094i	−1.68581	−	0.698284i
$995$		0			0
$996$	−1010.92	−	5082.26i	−1.01498	−	5.10267i
$997$	−449.374	−	300.262i	−0.450726	−	0.301165i	0.309411	−	0.950928i	$-0.399868\pi$
$997$	−449.374	−	300.262i	−0.450726	−	0.301165i	−0.760137	+	0.649763i	$0.774868\pi$
$998$	−1046.55	−	208.171i	−1.04864	−	0.208588i
$999$	−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.t.e.199.12		96
5.2	odd	4		425.3.u.e.301.12		96
5.3	odd	4		85.3.q.a.46.1	✓	96
5.4	even	2		425.3.t.h.199.1		96
17.10	odd	16		425.3.t.h.299.1		96
85.27	even	16		425.3.u.e.401.12		96
85.44	odd	16	inner	425.3.t.e.299.12		96
85.78	even	16		85.3.q.a.61.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.q.a.46.1	✓	96	5.3	odd	4
85.3.q.a.61.1	yes	96	85.78	even	16
425.3.t.e.199.12		96	1.1	even	1	trivial
425.3.t.e.299.12		96	85.44	odd	16	inner
425.3.t.h.199.1		96	5.4	even	2
425.3.t.h.299.1		96	17.10	odd	16
425.3.u.e.301.12		96	5.2	odd	4
425.3.u.e.401.12		96	85.27	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.38065 - 1.40031i) q^{2} +(-3.15183 - 4.71704i) q^{3} +(6.63952 - 6.63952i) q^{4} +(-17.2606 - 11.5332i) q^{6} +(-1.04150 - 5.23596i) q^{7} +(7.54727 - 18.2207i) q^{8} +(-8.87234 + 21.4197i) q^{9} +(2.84290 - 4.25470i) q^{11} +(-52.2455 - 10.3923i) q^{12} +(3.48556 - 3.48556i) q^{13} +(-10.8529 - 16.2426i) q^{14} -34.6077i q^{16} +(-0.237334 + 16.9983i) q^{17} +84.8367i q^{18} +(3.46526 + 8.36588i) q^{19} +(-21.4157 + 21.4157i) q^{21} +(3.65295 - 18.3646i) q^{22} +(20.0759 - 30.0458i) q^{23} +(-109.736 + 21.8278i) q^{24} +(6.90260 - 16.6644i) q^{26} +(78.9247 - 15.6991i) q^{27} +(-41.6793 - 27.8492i) q^{28} +(-0.381842 + 1.91965i) q^{29} +(3.40793 + 5.10033i) q^{31} +(-18.2725 - 44.1137i) q^{32} -29.0299 q^{33} +(23.0007 + 57.7979i) q^{34} +(83.3086 + 201.125i) q^{36} +(-7.93518 - 11.8758i) q^{37} +(23.4297 + 23.4297i) q^{38} +(-27.4274 - 5.45566i) q^{39} +(-64.9302 + 12.9154i) q^{41} +(-42.4103 + 102.388i) q^{42} +(-10.5616 - 4.37477i) q^{43} +(-9.37368 - 47.1247i) q^{44} +(25.7963 - 129.687i) q^{46} +(1.67827 - 1.67827i) q^{47} +(-163.246 + 109.077i) q^{48} +(18.9395 - 7.84500i) q^{49} +(80.9300 - 52.4564i) q^{51} -46.2849i q^{52} +(50.9049 - 21.0855i) q^{53} +(244.833 - 163.592i) q^{54} +(-103.263 - 20.5404i) q^{56} +(28.5403 - 42.7136i) q^{57} +(1.39723 + 7.02437i) q^{58} +(-38.2228 - 15.8324i) q^{59} +(5.85814 + 29.4509i) q^{61} +(18.6631 + 12.4703i) q^{62} +(121.393 + 24.1466i) q^{63} +(-25.6607 - 25.6607i) q^{64} +(-98.1402 + 40.6510i) q^{66} -83.0052 q^{67} +(111.285 + 114.437i) q^{68} -205.003 q^{69} +(77.2000 - 51.5834i) q^{71} +(323.321 + 323.321i) q^{72} +(10.1112 - 50.8326i) q^{73} +(-43.4560 - 29.0364i) q^{74} +(78.5531 + 32.5378i) q^{76} +(-25.2383 - 10.4541i) q^{77} +(-100.362 + 19.9633i) q^{78} +(53.4837 - 80.0441i) q^{79} +(-175.265 - 175.265i) q^{81} +(-201.421 + 134.585i) q^{82} +(37.2261 + 89.8717i) q^{83} +284.379i q^{84} -41.8312 q^{86} +(10.2586 - 4.24924i) q^{87} +(-56.0675 - 83.9110i) q^{88} +(-6.35442 + 6.35442i) q^{89} +(-21.8805 - 14.6201i) q^{91} +(-66.1949 - 332.784i) q^{92} +(13.3173 - 32.1507i) q^{93} +(3.32355 - 8.02376i) q^{94} +(-150.494 + 225.231i) q^{96} +(70.8202 + 14.0870i) q^{97} +(53.0424 - 53.0424i) q^{98} +(65.9113 + 98.6432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 48 q^{13} + 64 q^{14} + 128 q^{17} - 48 q^{19} + 96 q^{22} + 144 q^{23} - 240 q^{24} - 224 q^{26} - 64 q^{31} - 400 q^{32} - 512 q^{33} - 64 q^{34} + 192 q^{36} + 144 q^{37} - 208 q^{38} - 16 q^{39}+ \cdots + 592 q^{99}+O(q^{100}) \) 96 * q - 48 * q^13 + 64 * q^14 + 128 * q^17 - 48 * q^19 + 96 * q^22 + 144 * q^23 - 240 * q^24 - 224 * q^26 - 64 * q^31 - 400 * q^32 - 512 * q^33 - 64 * q^34 + 192 * q^36 + 144 * q^37 - 208 * q^38 - 16 * q^39 - 432 * q^41 - 496 * q^42 - 128 * q^43 + 32 * q^44 - 48 * q^46 + 32 * q^49 + 64 * q^51 - 208 * q^53 + 976 * q^54 + 80 * q^56 + 672 * q^57 + 256 * q^58 + 224 * q^59 - 224 * q^61 + 304 * q^62 + 512 * q^63 - 160 * q^64 + 48 * q^66 - 288 * q^67 + 1040 * q^68 - 384 * q^69 + 48 * q^71 + 1040 * q^72 - 672 * q^74 + 496 * q^76 - 720 * q^77 - 1184 * q^78 - 768 * q^79 + 1424 * q^81 + 576 * q^82 - 1680 * q^83 + 64 * q^86 - 768 * q^87 + 1152 * q^88 + 1152 * q^89 + 336 * q^91 + 640 * q^92 + 1344 * q^94 + 768 * q^96 - 1440 * q^97 - 816 * q^98 + 592 * q^99

Introduction

L-functions

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