LMFDB - Embedded newform 392.3.j.e.325.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(117,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.117");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			325.4
Character	$\chi$	$=$	392.325
Dual form			392.3.j.e.117.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61426 - 1.18075i) q^{2} +(0.455431 - 0.788830i) q^{3} +(1.21166 + 3.81207i) q^{4} +(-3.17251 - 5.49495i) q^{5} +(-1.66660 + 0.735624i) q^{6} +(2.54518 - 7.58433i) q^{8} +(4.08516 + 7.07571i) q^{9} +O(q^{10})$	\(q+(-1.61426 - 1.18075i) q^{2} +(0.455431 - 0.788830i) q^{3} +(1.21166 + 3.81207i) q^{4} +(-3.17251 - 5.49495i) q^{5} +(-1.66660 + 0.735624i) q^{6} +(2.54518 - 7.58433i) q^{8} +(4.08516 + 7.07571i) q^{9} +(-1.36692 + 12.6162i) q^{10} +(11.4442 + 6.60732i) q^{11} +(3.55890 + 0.780346i) q^{12} +19.4243 q^{13} -5.77945 q^{15} +(-13.0638 + 9.23784i) q^{16} +(-13.7930 - 7.96338i) q^{17} +(1.76014 - 16.2456i) q^{18} +(8.22725 + 14.2500i) q^{19} +(17.1032 - 18.7518i) q^{20} +(-10.6723 - 24.1787i) q^{22} +(-11.9607 - 20.7166i) q^{23} +(-4.82359 - 5.46186i) q^{24} +(-7.62967 + 13.2150i) q^{25} +(-31.3559 - 22.9353i) q^{26} +15.6398 q^{27} -16.6618i q^{29} +(9.32952 + 6.82409i) q^{30} +(11.1360 + 6.42939i) q^{31} +(31.9959 + 0.512817i) q^{32} +(10.4241 - 6.01837i) q^{33} +(12.8627 + 29.1410i) q^{34} +(-22.0233 + 24.1463i) q^{36} +(41.1844 - 23.7778i) q^{37} +(3.54481 - 32.7175i) q^{38} +(8.84646 - 15.3225i) q^{39} +(-49.7502 + 10.0757i) q^{40} -6.49499i q^{41} -33.2928i q^{43} +(-11.3211 + 51.6320i) q^{44} +(25.9205 - 44.8956i) q^{45} +(-5.15343 + 47.5645i) q^{46} +(18.9713 - 10.9531i) q^{47} +(1.33743 + 14.5123i) q^{48} +(27.9198 - 12.3236i) q^{50} +(-12.5635 + 7.25355i) q^{51} +(23.5356 + 74.0470i) q^{52} +(-32.2028 - 18.5923i) q^{53} +(-25.2467 - 18.4667i) q^{54} -83.8473i q^{55} +14.9878 q^{57} +(-19.6734 + 26.8964i) q^{58} +(27.3428 - 47.3591i) q^{59} +(-7.00270 - 22.0317i) q^{60} +(5.12340 + 8.87399i) q^{61} +(-10.3849 - 23.5276i) q^{62} +(-51.0441 - 38.6070i) q^{64} +(-61.6240 - 106.736i) q^{65} +(-23.9334 - 2.59309i) q^{66} +(-14.8386 - 8.56706i) q^{67} +(13.6446 - 62.2287i) q^{68} -21.7892 q^{69} +32.0568 q^{71} +(64.0620 - 12.9743i) q^{72} +(-92.8082 - 53.5828i) q^{73} +(-94.5579 - 10.2450i) q^{74} +(6.94958 + 12.0370i) q^{75} +(-44.3535 + 48.6290i) q^{76} +(-32.3725 + 14.2890i) q^{78} +(29.1542 + 50.4965i) q^{79} +(92.2065 + 42.4777i) q^{80} +(-29.6436 + 51.3443i) q^{81} +(-7.66897 + 10.4846i) q^{82} +36.3441 q^{83} +101.056i q^{85} +(-39.3105 + 53.7432i) q^{86} +(-13.1433 - 7.58829i) q^{87} +(79.2397 - 69.9799i) q^{88} +(-0.929882 + 0.536867i) q^{89} +(-94.8528 + 41.8674i) q^{90} +(64.4808 - 70.6965i) q^{92} +(10.1434 - 5.85629i) q^{93} +(-43.5575 - 4.71928i) q^{94} +(52.2021 - 90.4167i) q^{95} +(14.9765 - 25.0058i) q^{96} +169.517i q^{97} +107.968i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 28 * q^15 + 16 * q^16 + 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 + 30 * q^24 - 32 * q^25 + 30 * q^26 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 136 * q^71 + 96 * q^72 - 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 - 276 * q^80 - 18 * q^81 + 642 * q^82 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.61426	−	1.18075i	−0.807129	−	0.590375i
$2$	−1.61426	−	1.18075i	−0.807129	−	0.590375i
$3$	0.455431	−	0.788830i	0.151810	−	0.262943i	−0.780083	−	0.625677i	$-0.784823\pi$
$3$	0.455431	−	0.788830i	0.151810	−	0.262943i	0.931893	+	0.362733i	$0.118156\pi$
$4$	1.21166	+	3.81207i	0.302914	+	0.953018i
$5$	−3.17251	−	5.49495i	−0.634503	−	1.09899i	−0.986620	−	0.163035i	$-0.947872\pi$
$5$	−3.17251	−	5.49495i	−0.634503	−	1.09899i	0.352118	−	0.935956i	$-0.385462\pi$
$6$	−1.66660	+	0.735624i	−0.277766	+	0.122604i
$7$		0			0
$7$		0			0
$8$	2.54518	−	7.58433i	0.318148	−	0.948041i
$9$	4.08516	+	7.07571i	0.453907	+	0.786190i
$10$	−1.36692	+	12.6162i	−0.136692	+	1.26162i
$11$	11.4442	+	6.60732i	1.04038	+	0.600666i	0.919942	−	0.392054i	$-0.128236\pi$
$11$	11.4442	+	6.60732i	1.04038	+	0.600666i	0.120442	+	0.992720i	$0.461569\pi$
$12$	3.55890	+	0.780346i	0.296575	+	0.0650289i
$13$	19.4243			1.49418			0.747090	−	0.664723i	$-0.231450\pi$
$13$	19.4243			1.49418			0.747090	+	0.664723i	$0.231450\pi$
$14$		0			0
$15$	−5.77945			−0.385296
$16$	−13.0638	+	9.23784i	−0.816486	+	0.577365i
$17$	−13.7930	−	7.96338i	−0.811352	−	0.468434i	0.0360732	−	0.999349i	$-0.488515\pi$
$17$	−13.7930	−	7.96338i	−0.811352	−	0.468434i	−0.847425	+	0.530915i	$0.821848\pi$
$18$	1.76014	−	16.2456i	0.0977858	−	0.902532i
$19$	8.22725	+	14.2500i	0.433013	+	0.750001i	0.997131	−	0.0756934i	$-0.0241170\pi$
$19$	8.22725	+	14.2500i	0.433013	+	0.750001i	−0.564118	+	0.825694i	$0.690784\pi$
$20$	17.1032	−	18.7518i	0.855158	−	0.937592i
$21$		0			0
$22$	−10.6723	−	24.1787i	−0.485105	−	1.09903i
$23$	−11.9607	−	20.7166i	−0.520032	−	0.900721i	−0.999729	−	0.0232870i	$-0.992587\pi$
$23$	−11.9607	−	20.7166i	−0.520032	−	0.900721i	0.479697	−	0.877434i	$-0.340746\pi$
$24$	−4.82359	−	5.46186i	−0.200983	−	0.227577i
$25$	−7.62967	+	13.2150i	−0.305187	+	0.528599i
$26$	−31.3559	−	22.9353i	−1.20600	−	0.882127i
$27$	15.6398			0.579252
$28$		0			0
$29$		−	16.6618i		−	0.574544i	−0.957849	−	0.287272i	$-0.907252\pi$
$29$		−	16.6618i		−	0.574544i	0.957849	−	0.287272i	$-0.0927483\pi$
$30$	9.32952	+	6.82409i	0.310984	+	0.227470i
$31$	11.1360	+	6.42939i	0.359227	+	0.207400i	0.668741	−	0.743495i	$-0.266833\pi$
$31$	11.1360	+	6.42939i	0.359227	+	0.207400i	−0.309515	+	0.950895i	$0.600167\pi$
$32$	31.9959	+	0.512817i	0.999872	+	0.0160255i
$33$	10.4241	−	6.01837i	0.315882	−	0.182375i
$34$	12.8627	+	29.1410i	0.378314	+	0.857089i
$35$		0			0
$36$	−22.0233	+	24.1463i	−0.611759	+	0.670730i
$37$	41.1844	−	23.7778i	1.11309	−	0.642644i	0.173463	−	0.984840i	$-0.444504\pi$
$37$	41.1844	−	23.7778i	1.11309	−	0.642644i	0.939628	+	0.342196i	$0.111171\pi$
$38$	3.54481	−	32.7175i	0.0932845	−	0.860987i
$39$	8.84646	−	15.3225i	0.226832	−	0.392885i
$40$	−49.7502	+	10.0757i	−1.24375	+	0.251893i
$41$		−	6.49499i		−	0.158415i	−0.996858	−	0.0792073i	$-0.974761\pi$
$41$		−	6.49499i		−	0.158415i	0.996858	−	0.0792073i	$-0.0252389\pi$
$42$		0			0
$43$		−	33.2928i		−	0.774252i	−0.922027	−	0.387126i	$-0.873468\pi$
$43$		−	33.2928i		−	0.774252i	0.922027	−	0.387126i	$-0.126532\pi$
$44$	−11.3211	+	51.6320i	−0.257299	+	1.17345i
$45$	25.9205	−	44.8956i	0.576010	−	0.997679i
$46$	−5.15343	+	47.5645i	−0.112031	+	1.03401i
$47$	18.9713	−	10.9531i	0.403645	−	0.233045i	−0.284411	−	0.958703i	$-0.591798\pi$
$47$	18.9713	−	10.9531i	0.403645	−	0.233045i	0.688056	+	0.725658i	$0.258465\pi$
$48$	1.33743	+	14.5123i	0.0278631	+	0.302340i
$49$		0			0
$50$	27.9198	−	12.3236i	0.558397	−	0.246473i
$51$	−12.5635	+	7.25355i	−0.246343	+	0.142226i
$52$	23.5356	+	74.0470i	0.452608	+	1.42398i
$53$	−32.2028	−	18.5923i	−0.607601	−	0.350798i	0.164425	−	0.986390i	$-0.447423\pi$
$53$	−32.2028	−	18.5923i	−0.607601	−	0.350798i	−0.772026	+	0.635591i	$0.780756\pi$
$54$	−25.2467	−	18.4667i	−0.467531	−	0.341976i
$55$		−	83.8473i		−	1.52450i
$56$		0			0
$57$	14.9878			0.262944
$58$	−19.6734	+	26.8964i	−0.339196	+	0.463731i
$59$	27.3428	−	47.3591i	0.463437	−	0.802696i	−0.535693	−	0.844413i	$-0.679949\pi$
$59$	27.3428	−	47.3591i	0.463437	−	0.802696i	0.999129	+	0.0417169i	$0.0132827\pi$
$60$	−7.00270	−	22.0317i	−0.116712	−	0.367194i
$61$	5.12340	+	8.87399i	0.0839902	+	0.145475i	0.904960	−	0.425496i	$-0.139900\pi$
$61$	5.12340	+	8.87399i	0.0839902	+	0.145475i	−0.820970	+	0.570971i	$0.806567\pi$
$62$	−10.3849	−	23.5276i	−0.167499	−	0.379477i
$63$		0			0
$64$	−51.0441	−	38.6070i	−0.797564	−	0.603234i
$65$	−61.6240	−	106.736i	−0.948061	−	1.64209i
$66$	−23.9334	−	2.59309i	−0.362627	−	0.0392892i
$67$	−14.8386	−	8.56706i	−0.221471	−	0.127867i	0.385160	−	0.922850i	$-0.374146\pi$
$67$	−14.8386	−	8.56706i	−0.221471	−	0.127867i	−0.606631	+	0.794983i	$0.707480\pi$
$68$	13.6446	−	62.2287i	0.200656	−	0.915128i
$69$	−21.7892			−0.315785
$70$		0			0
$71$	32.0568			0.451505			0.225752	−	0.974185i	$-0.427516\pi$
$71$	32.0568			0.451505			0.225752	+	0.974185i	$0.427516\pi$
$72$	64.0620	−	12.9743i	0.889750	−	0.180198i
$73$	−92.8082	−	53.5828i	−1.27135	−	0.734011i	−0.296104	−	0.955156i	$-0.595687\pi$
$73$	−92.8082	−	53.5828i	−1.27135	−	0.734011i	−0.975241	+	0.221144i	$0.929021\pi$
$74$	−94.5579	−	10.2450i	−1.27781	−	0.138446i
$75$	6.94958	+	12.0370i	0.0926611	+	0.160494i
$76$	−44.3535	+	48.6290i	−0.583598	+	0.639855i
$77$		0			0
$78$	−32.3725	+	14.2890i	−0.415032	+	0.183193i
$79$	29.1542	+	50.4965i	0.369040	+	0.639196i	0.989416	−	0.145109i	$-0.0463532\pi$
$79$	29.1542	+	50.4965i	0.369040	+	0.639196i	−0.620376	+	0.784305i	$0.713020\pi$
$80$	92.2065	+	42.4777i	1.15258	+	0.530971i
$81$	−29.6436	+	51.3443i	−0.365971	+	0.633880i
$82$	−7.66897	+	10.4846i	−0.0935240	+	0.127861i
$83$	36.3441			0.437880			0.218940	−	0.975738i	$-0.429740\pi$
$83$	36.3441			0.437880			0.218940	+	0.975738i	$0.429740\pi$
$84$		0			0
$85$			101.056i			1.18889i
$86$	−39.3105	+	53.7432i	−0.457099	+	0.624921i
$87$	−13.1433	−	7.58829i	−0.151072	−	0.0872217i
$88$	79.2397	−	69.9799i	0.900452	−	0.795226i
$89$	−0.929882	+	0.536867i	−0.0104481	+	0.00603222i	−0.505215	−	0.862994i	$-0.668587\pi$
$89$	−0.929882	+	0.536867i	−0.0104481	+	0.00603222i	0.494767	+	0.869026i	$0.335253\pi$
$90$	−94.8528	+	41.8674i	−1.05392	+	0.465193i
$91$		0			0
$92$	64.4808	−	70.6965i	0.700878	−	0.768440i
$93$	10.1434	−	5.85629i	0.109069	−	0.0629709i
$94$	−43.5575	−	4.71928i	−0.463377	−	0.0502051i
$95$	52.2021	−	90.4167i	0.549496	−	0.951755i
$96$	14.9765	−	25.0058i	0.156005	−	0.260477i
$97$			169.517i			1.74760i	0.486286	+	0.873799i	$0.338351\pi$
$97$			169.517i			1.74760i	−0.486286	+	0.873799i	$0.661649\pi$
$98$		0			0
$99$			107.968i			1.09059i
$100$	−59.6210	−	13.0728i	−0.596210	−	0.130728i
$101$	14.0630	−	24.3579i	0.139238	−	0.241167i	−0.787971	−	0.615713i	$-0.788868\pi$
$101$	14.0630	−	24.3579i	0.139238	−	0.241167i	0.927208	+	0.374546i	$0.122201\pi$
$102$	28.8454	+	3.12528i	0.282798	+	0.0306400i
$103$	144.029	−	83.1551i	1.39834	−	0.807331i	0.404120	−	0.914706i	$-0.367578\pi$
$103$	144.029	−	83.1551i	1.39834	−	0.807331i	0.994219	+	0.107374i	$0.0342444\pi$
$104$	49.4385	−	147.321i	0.475370	−	1.41654i
$105$		0			0
$106$	30.0308	+	68.0363i	0.283309	+	0.641852i
$107$	171.112	−	98.7918i	1.59918	−	0.923288i	0.607536	−	0.794292i	$-0.292158\pi$
$107$	171.112	−	98.7918i	1.59918	−	0.923288i	0.991645	−	0.128996i	$-0.0411753\pi$
$108$	18.9501	+	59.6201i	0.175464	+	0.552038i
$109$	9.97643	+	5.75990i	0.0915269	+	0.0528431i	0.545065	−	0.838394i	$-0.316505\pi$
$109$	9.97643	+	5.75990i	0.0915269	+	0.0528431i	−0.453538	+	0.891237i	$0.649838\pi$
$110$	−99.0027	+	135.351i	−0.900025	+	1.23046i
$111$		−	43.3167i		−	0.390240i
$112$		0			0
$113$	−14.7908			−0.130892			−0.0654460	−	0.997856i	$-0.520847\pi$
$113$	−14.7908			−0.130892			−0.0654460	+	0.997856i	$0.520847\pi$
$114$	−24.1942	−	17.6968i	−0.212229	−	0.155235i
$115$	−75.8911	+	131.447i	−0.659923	+	1.14302i
$116$	63.5158	−	20.1883i	0.547550	−	0.174037i
$117$	79.3516	+	137.441i	0.678219	+	1.17471i
$118$	−100.058	+	44.1648i	−0.847945	+	0.374278i
$119$		0			0
$120$	−14.7097	+	43.8332i	−0.122581	+	0.365277i
$121$	26.8135	+	46.4423i	0.221599	+	0.383821i
$122$	2.20748	−	20.3744i	0.0180941	−	0.167003i
$123$	−5.12345	−	2.95802i	−0.0416541	−	0.0240490i
$124$	−11.0163	+	50.2415i	−0.0888408	+	0.405174i
$125$	−61.8047			−0.494438
$126$		0			0
$127$	−70.2656			−0.553272			−0.276636	−	0.960975i	$-0.589220\pi$
$127$	−70.2656			−0.553272			−0.276636	+	0.960975i	$0.589220\pi$
$128$	36.8131	+	122.592i	0.287602	+	0.957750i
$129$	−26.2624	−	15.1626i	−0.203584	−	0.117540i
$130$	−26.5515	+	245.062i	−0.204242	+	1.88509i
$131$	71.0646	+	123.088i	0.542478	+	0.939600i	0.998761	+	0.0497649i	$0.0158472\pi$
$131$	71.0646	+	123.088i	0.542478	+	0.939600i	−0.456283	+	0.889835i	$0.650819\pi$
$132$	35.5729	+	32.4453i	0.269492	+	0.245798i
$133$		0			0
$134$	13.8377	+	31.3501i	0.103267	+	0.233956i
$135$	−49.6175	−	85.9400i	−0.367537	−	0.636593i
$136$	−95.5026	+	84.3423i	−0.702225	+	0.620164i
$137$	−126.537	+	219.168i	−0.923626	+	1.59977i	−0.129870	+	0.991531i	$0.541456\pi$
$137$	−126.537	+	219.168i	−0.923626	+	1.59977i	−0.793756	+	0.608236i	$0.791877\pi$
$138$	35.1733	+	25.7276i	0.254879	+	0.186432i
$139$	49.1909			0.353892			0.176946	−	0.984221i	$-0.443378\pi$
$139$	49.1909			0.353892			0.176946	+	0.984221i	$0.443378\pi$
$140$		0			0
$141$		−	19.9535i		−	0.141514i
$142$	−51.7480	−	37.8511i	−0.364423	−	0.266557i
$143$	222.296	+	128.343i	1.55452	+	0.897503i
$144$	−118.732	−	54.6975i	−0.824528	−	0.379844i
$145$	−91.5556	+	52.8597i	−0.631418	+	0.364549i
$146$	86.5484	+	196.080i	0.592797	+	1.34301i
$147$		0			0
$148$	140.544	+	128.187i	0.949622	+	0.866131i
$149$	−36.1077	+	20.8468i	−0.242334	+	0.139911i	−0.616249	−	0.787551i	$-0.711348\pi$
$149$	−36.1077	+	20.8468i	−0.242334	+	0.139911i	0.373915	+	0.927463i	$0.378015\pi$
$150$	2.99431	−	27.6366i	0.0199621	−	0.184244i
$151$	48.8145	−	84.5492i	0.323275	−	0.559928i	−0.657887	−	0.753117i	$-0.728550\pi$
$151$	48.8145	−	84.5492i	0.323275	−	0.559928i	0.981162	+	0.193188i	$0.0618829\pi$
$152$	129.017	−	26.1293i	0.848794	−	0.171903i
$153$		−	130.127i		−	0.850503i
$154$		0			0
$155$		−	81.5892i		−	0.526382i
$156$	69.1294	+	15.1577i	0.443137	+	0.0971648i
$157$	14.0827	−	24.3919i	0.0896986	−	0.155363i	−0.817685	−	0.575666i	$-0.804743\pi$
$157$	14.0827	−	24.3919i	0.0896986	−	0.155363i	0.907384	+	0.420303i	$0.138076\pi$
$158$	12.5614	−	115.938i	0.0795027	−	0.733786i
$159$	−29.3324	+	16.9350i	−0.184480	+	0.106510i
$160$	−98.6895	−	177.443i	−0.616809	−	1.10902i
$161$		0			0
$162$	108.477	−	47.8811i	0.669612	−	0.295563i
$163$	−209.952	+	121.216i	−1.28805	+	0.743655i	−0.978306	−	0.207165i	$-0.933576\pi$
$163$	−209.952	+	121.216i	−1.28805	+	0.743655i	−0.309743	+	0.950820i	$0.600243\pi$
$164$	24.7594	−	7.86970i	0.150972	−	0.0479860i
$165$	−66.1413	−	38.1867i	−0.400856	−	0.231434i
$166$	−58.6687	−	42.9133i	−0.353426	−	0.258514i
$167$			60.1108i			0.359945i	0.983672	+	0.179972i	$0.0576008\pi$
$167$			60.1108i			0.359945i	−0.983672	+	0.179972i	$0.942399\pi$
$168$		0			0
$169$	208.305			1.23257
$170$	119.322	−	163.130i	0.701892	−	0.959588i
$171$	−67.2193	+	116.427i	−0.393096	+	0.680861i
$172$	126.915	−	40.3395i	0.737876	−	0.234532i
$173$	−69.6820	−	120.693i	−0.402786	−	0.697646i	0.591275	−	0.806470i	$-0.298625\pi$
$173$	−69.6820	−	120.693i	−0.402786	−	0.697646i	−0.994061	+	0.108824i	$0.965292\pi$
$174$	12.2568	+	27.7684i	0.0704414	+	0.159589i
$175$		0			0
$176$	−210.542	+	19.4032i	−1.19626	+	0.110246i
$177$	−24.9055	−	43.1376i	−0.140709	−	0.243715i
$178$	2.13498	+	0.231316i	0.0119942	+	0.00129953i
$179$	252.643	+	145.863i	1.41141	+	0.814879i	0.995522	−	0.0945354i	$-0.0301365\pi$
$179$	252.643	+	145.863i	1.41141	+	0.814879i	0.415891	+	0.909415i	$0.363470\pi$
$180$	202.552	+	44.4127i	1.12529	+	0.246737i
$181$	−166.844			−0.921791			−0.460895	−	0.887455i	$-0.652472\pi$
$181$	−166.844			−0.921791			−0.460895	+	0.887455i	$0.652472\pi$
$182$		0			0
$183$	9.33343			0.0510024
$184$	−187.564	+	37.9866i	−1.01937	+	0.206449i
$185$	−261.316	−	150.871i	−1.41252	−	0.815518i
$186$	−23.2889	−	2.52325i	−0.125209	−	0.0135659i
$187$	−105.233	−	182.269i	−0.562745	−	0.974703i
$188$	64.7407	+	59.0486i	0.344365	+	0.314088i
$189$		0			0
$190$	−191.027	+	84.3182i	−1.00541	+	0.443780i
$191$	65.6781	+	113.758i	0.343864	+	0.595590i	0.985147	−	0.171715i	$-0.0549307\pi$
$191$	65.6781	+	113.758i	0.343864	+	0.595590i	−0.641283	+	0.767305i	$0.721597\pi$
$192$	−53.7014	+	22.6823i	−0.279695	+	0.118137i
$193$	40.7196	−	70.5284i	0.210982	−	0.365432i	−0.741040	−	0.671461i	$-0.765667\pi$
$193$	40.7196	−	70.5284i	0.210982	−	0.365432i	0.952022	+	0.306029i	$0.0990004\pi$
$194$	200.157	−	273.644i	1.03174	−	1.41054i
$195$	−112.262			−0.575702
$196$		0			0
$197$		−	2.09549i		−	0.0106370i	−0.999986	−	0.00531851i	$-0.998307\pi$
$197$		−	2.09549i		−	0.0106370i	0.999986	−	0.00531851i	$-0.00169294\pi$
$198$	127.483	−	174.288i	0.643855	−	0.880244i
$199$	109.937	+	63.4721i	0.552447	+	0.318955i	0.750108	−	0.661315i	$-0.230001\pi$
$199$	109.937	+	63.4721i	0.552447	+	0.318955i	−0.197662	+	0.980270i	$0.563335\pi$
$200$	80.8079	+	91.5005i	0.404039	+	0.457502i
$201$	−13.5159	+	7.80341i	−0.0672433	+	0.0388230i
$202$	−51.4619	+	22.7149i	−0.254762	+	0.112450i
$203$		0			0
$204$	−42.8737	−	39.1042i	−0.210165	−	0.191687i
$205$	−35.6897	+	20.6055i	−0.174096	+	0.100514i
$206$	−330.685	−	35.8284i	−1.60527	−	0.173924i
$207$	97.7231	−	169.261i	0.472092	−	0.817687i
$208$	−253.755	+	179.439i	−1.21998	+	0.862687i
$209$			217.440i			1.04038i
$210$		0			0
$211$			7.16822i			0.0339726i	0.999856	+	0.0169863i	$0.00540717\pi$
$211$			7.16822i			0.0339726i	−0.999856	+	0.0169863i	$0.994593\pi$
$212$	31.8565	−	145.287i	0.150266	−	0.685316i
$213$	14.5997	−	25.2874i	0.0685432	−	0.118720i
$214$	−392.868	−	42.5657i	−1.83583	−	0.198905i
$215$	−182.943	+	105.622i	−0.850896	+	0.491265i
$216$	39.8062	−	118.617i	0.184288	−	0.549155i
$217$		0			0
$218$	−9.30353	−	21.0776i	−0.0426768	−	0.0966864i
$219$	−84.5355	+	48.8066i	−0.386007	+	0.222861i
$220$	319.632	−	101.594i	1.45287	−	0.461791i
$221$	−267.920	−	154.683i	−1.21231	−	0.699925i
$222$	−51.1462	+	69.9243i	−0.230388	+	0.314974i
$223$		−	279.720i		−	1.25435i	−0.778878	−	0.627175i	$-0.784211\pi$
$223$		−	279.720i		−	1.25435i	0.778878	−	0.627175i	$-0.215789\pi$
$224$		0			0
$225$	−124.674			−0.554106
$226$	23.8762	+	17.4642i	0.105647	+	0.0772754i
$227$	152.392	−	263.950i	0.671330	−	1.16278i	−0.306198	−	0.951968i	$-0.599057\pi$
$227$	152.392	−	263.950i	0.671330	−	1.16278i	0.977527	−	0.210809i	$-0.0676098\pi$
$228$	18.1600	+	57.1345i	0.0796493	+	0.250590i
$229$	−207.344	−	359.130i	−0.905433	−	1.56826i	−0.820335	−	0.571883i	$-0.806213\pi$
$229$	−207.344	−	359.130i	−0.905433	−	1.56826i	−0.0850971	−	0.996373i	$-0.527120\pi$
$230$	277.714	−	122.581i	1.20745	−	0.532962i
$231$		0			0
$232$	−126.368	−	42.4072i	−0.544691	−	0.182790i
$233$	82.4628	+	142.830i	0.353918	+	0.613004i	0.986932	−	0.161136i	$-0.0515159\pi$
$233$	82.4628	+	142.830i	0.353918	+	0.613004i	−0.633014	+	0.774140i	$0.718183\pi$
$234$	34.1896	−	315.560i	0.146110	−	1.34855i
$235$	−120.373	−	69.4976i	−0.512227	−	0.295735i
$236$	213.666	+	46.8497i	0.905365	+	0.198516i
$237$	53.1109			0.224097
$238$		0			0
$239$	−19.1182			−0.0799926			−0.0399963	−	0.999200i	$-0.512735\pi$
$239$	−19.1182			−0.0799926			−0.0399963	+	0.999200i	$0.512735\pi$
$240$	75.5014	−	53.3896i	0.314589	−	0.222457i
$241$	303.376	+	175.154i	1.25882	+	0.726780i	0.972845	−	0.231457i	$-0.0743492\pi$
$241$	303.376	+	175.154i	1.25882	+	0.726780i	0.285975	+	0.958237i	$0.407683\pi$
$242$	11.5529	−	106.630i	0.0477393	−	0.440619i
$243$	97.3804	+	168.668i	0.400743	+	0.694106i
$244$	−27.6205	+	30.2830i	−0.113199	+	0.124111i
$245$		0			0
$246$	4.77788	+	10.8245i	0.0194223	+	0.0440022i
$247$	159.809	+	276.797i	0.647000	+	1.12064i
$248$	77.1058	−	68.0953i	0.310910	−	0.274578i
$249$	16.5522	−	28.6693i	0.0664748	−	0.115138i
$250$	99.7687	+	72.9760i	0.399075	+	0.291904i
$251$	88.3204			0.351874			0.175937	−	0.984401i	$-0.443704\pi$
$251$	88.3204			0.351874			0.175937	+	0.984401i	$0.443704\pi$
$252$		0			0
$253$		−	316.114i		−	1.24946i
$254$	113.427	+	82.9661i	0.446562	+	0.326638i
$255$	79.7158	+	46.0240i	0.312611	+	0.180486i
$256$	85.3247	−	241.362i	0.333300	−	0.942821i
$257$	−74.5499	+	43.0414i	−0.290077	+	0.167476i	−0.637977	−	0.770056i	$-0.720228\pi$
$257$	−74.5499	+	43.0414i	−0.290077	+	0.167476i	0.347899	+	0.937532i	$0.386895\pi$
$258$	24.4910	+	55.4857i	0.0949265	+	0.215061i
$259$		0			0
$260$	332.218	−	364.242i	1.27776	−	1.40093i
$261$	117.894	−	68.0661i	0.451701	−	0.260789i
$262$	30.6191	−	282.605i	0.116867	−	1.07864i
$263$	−159.605	+	276.444i	−0.606863	+	1.05112i	0.384891	+	0.922962i	$0.374239\pi$
$263$	−159.605	+	276.444i	−0.606863	+	1.05112i	−0.991754	+	0.128156i	$0.959094\pi$
$264$	−19.1140	−	94.3778i	−0.0724015	−	0.357492i
$265$			235.937i			0.890330i
$266$		0			0
$267$			0.978025i			0.00366302i
$268$	14.6790	−	66.9461i	0.0547723	−	0.249799i
$269$	−28.7340	+	49.7687i	−0.106818	+	0.185014i	−0.914479	−	0.404632i	$-0.867399\pi$
$269$	−28.7340	+	49.7687i	−0.106818	+	0.185014i	0.807662	+	0.589646i	$0.200733\pi$
$270$	−21.3783	+	197.315i	−0.0791790	+	0.730797i
$271$	−26.7398	+	15.4382i	−0.0986709	+	0.0569677i	−0.548523	−	0.836135i	$-0.684810\pi$
$271$	−26.7398	+	15.4382i	−0.0986709	+	0.0569677i	0.449853	+	0.893103i	$0.351477\pi$
$272$	253.753	−	23.3855i	0.932915	−	0.0859759i
$273$		0			0
$274$	463.046	−	204.385i	1.68995	−	0.745932i
$275$	−174.631	+	100.823i	−0.635023	+	0.366631i
$276$	−26.4010	−	83.0618i	−0.0956557	−	0.300949i
$277$	308.465	+	178.092i	1.11359	+	0.642933i	0.939757	−	0.341842i	$-0.111051\pi$
$277$	308.465	+	178.092i	1.11359	+	0.642933i	0.173834	+	0.984775i	$0.444384\pi$
$278$	−79.4068	−	58.0822i	−0.285636	−	0.208929i
$279$			105.060i			0.376561i
$280$		0			0
$281$	−294.160			−1.04683			−0.523416	−	0.852077i	$-0.675343\pi$
$281$	−294.160			−1.04683			−0.523416	+	0.852077i	$0.675343\pi$
$282$	−23.5601	+	32.2101i	−0.0835466	+	0.114220i
$283$	−207.501	+	359.402i	−0.733219	+	1.26997i	0.222282	+	0.974982i	$0.428649\pi$
$283$	−207.501	+	359.402i	−0.733219	+	1.26997i	−0.955501	+	0.294989i	$0.904684\pi$
$284$	38.8419	+	122.203i	0.136767	+	0.430292i
$285$	−47.5490	−	82.3572i	−0.166838	−	0.288973i
$286$	−207.303	−	469.655i	−0.724835	−	1.64215i
$287$		0			0
$288$	127.080	+	228.489i	0.441250	+	0.793363i
$289$	−17.6691	−	30.6037i	−0.0611386	−	0.105895i
$290$	210.208	+	22.7752i	0.724857	+	0.0785353i
$291$	133.720	+	77.2034i	0.459520	+	0.265304i
$292$	91.8100	−	418.715i	0.314418	−	1.43396i
$293$	370.564			1.26472			0.632362	−	0.774673i	$-0.282085\pi$
$293$	370.564			1.26472			0.632362	+	0.774673i	$0.282085\pi$
$294$		0			0
$295$	−346.981			−1.17621
$296$	−75.5171	−	372.875i	−0.255125	−	1.25971i
$297$	178.986	+	103.337i	0.602645	+	0.347937i
$298$	82.9021	+	8.98210i	0.278195	+	0.0301413i
$299$	−232.329	−	402.406i	−0.777021	−	1.34584i
$300$	−37.4655	+	41.0770i	−0.124885	+	0.136923i
$301$		0			0
$302$	−178.631	+	78.8464i	−0.591492	+	0.261081i
$303$	−12.8095	−	22.1867i	−0.0422755	−	0.0732233i
$304$	−239.118	−	110.157i	−0.786573	−	0.362359i
$305$	32.5081	−	56.3057i	0.106584	−	0.184609i
$306$	−153.647	+	210.058i	−0.502116	+	0.686465i
$307$	160.327			0.522239			0.261120	−	0.965306i	$-0.415908\pi$
$307$	160.327			0.522239			0.261120	+	0.965306i	$0.415908\pi$
$308$		0			0
$309$		−	151.486i		−	0.490245i
$310$	−96.3366	+	131.706i	−0.310763	+	0.424858i
$311$	−409.490	−	236.419i	−1.31669	−	0.760191i	−0.333495	−	0.942752i	$-0.608228\pi$
$311$	−409.490	−	236.419i	−1.31669	−	0.760191i	−0.983195	+	0.182561i	$0.941561\pi$
$312$	−93.6951	−	106.093i	−0.300305	−	0.340042i
$313$	−200.063	+	115.506i	−0.639179	+	0.369030i	−0.784298	−	0.620384i	$-0.786977\pi$
$313$	−200.063	+	115.506i	−0.639179	+	0.369030i	0.145119	+	0.989414i	$0.453643\pi$
$314$	−51.5339	+	22.7467i	−0.164121	+	0.0724418i
$315$		0			0
$316$	−157.171	+	172.322i	−0.497378	+	0.545323i
$317$	−195.132	+	112.659i	−0.615557	+	0.355392i	−0.775137	−	0.631793i	$-0.782319\pi$
$317$	−195.132	+	112.659i	−0.615557	+	0.355392i	0.159580	+	0.987185i	$0.448986\pi$
$318$	67.3461	+	7.29667i	0.211780	+	0.0229455i
$319$	110.090	−	190.681i	0.345109	−	0.597746i
$320$	−50.2055	+	402.966i	−0.156892	+	1.25927i
$321$		−	179.972i		−	0.560659i
$322$		0			0
$323$		−	262.067i		−	0.811353i
$324$	−231.646	−	50.7920i	−0.714956	−	0.156766i
$325$	−148.201	+	256.692i	−0.456004	+	0.789822i
$326$	482.042	+	52.2273i	1.47866	+	0.160207i
$327$	9.08716	−	5.24648i	0.0277895	−	0.0160443i
$328$	−49.2602	−	16.5309i	−0.150183	−	0.0503992i
$329$		0			0
$330$	61.6801	+	139.740i	0.186909	+	0.423453i
$331$	17.9257	−	10.3494i	0.0541561	−	0.0312671i	−0.472677	−	0.881236i	$-0.656712\pi$
$331$	17.9257	−	10.3494i	0.0541561	−	0.0312671i	0.526834	+	0.849968i	$0.323379\pi$
$332$	44.0365	+	138.546i	0.132640	+	0.417308i
$333$	336.490	+	194.273i	1.01048	+	0.583401i
$334$	70.9758	−	97.0343i	0.212503	−	0.290522i
$335$			108.716i			0.324527i
$336$		0			0
$337$	34.9645			0.103752			0.0518762	−	0.998654i	$-0.483480\pi$
$337$	34.9645			0.103752			0.0518762	+	0.998654i	$0.483480\pi$
$338$	−336.258	−	245.956i	−0.994846	−	0.727682i
$339$	−6.73619	+	11.6674i	−0.0198708	+	0.0344172i
$340$	−385.232	+	122.445i	−1.13303	+	0.360132i
$341$	84.9621	+	147.159i	0.249156	+	0.431550i
$342$	245.981	−	108.574i	0.719243	−	0.317469i
$343$		0			0
$344$	−252.504	−	84.7363i	−0.734023	−	0.246326i
$345$	69.1264	+	119.730i	0.200366	+	0.347045i
$346$	−30.0234	+	277.106i	−0.0867727	+	0.800886i
$347$	−379.958	−	219.369i	−1.09498	−	0.632188i	−0.160083	−	0.987104i	$-0.551176\pi$
$347$	−379.958	−	219.369i	−1.09498	−	0.632188i	−0.934898	+	0.354916i	$0.884509\pi$
$348$	13.0019	−	59.2976i	0.0373619	−	0.170395i
$349$	−435.121			−1.24677			−0.623383	−	0.781917i	$-0.714242\pi$
$349$	−435.121			−1.24677			−0.623383	+	0.781917i	$0.714242\pi$
$350$		0			0
$351$	303.793			0.865507
$352$	362.780	+	217.276i	1.03062	+	0.617261i
$353$	−243.447	−	140.554i	−0.689653	−	0.398171i	0.113829	−	0.993500i	$-0.463688\pi$
$353$	−243.447	−	140.554i	−0.689653	−	0.398171i	−0.803482	+	0.595329i	$0.797022\pi$
$354$	−10.7309	+	99.0424i	−0.0303131	+	0.279781i
$355$	−101.701	−	176.151i	−0.286481	−	0.496200i
$356$	−3.17327	−	2.89428i	−0.00891369	−	0.00812999i
$357$		0			0
$358$	−235.602	−	533.769i	−0.658107	−	1.49098i
$359$	−131.965	−	228.570i	−0.367590	−	0.636685i	0.621598	−	0.783336i	$-0.286484\pi$
$359$	−131.965	−	228.570i	−0.367590	−	0.636685i	−0.989188	+	0.146652i	$0.953150\pi$
$360$	−274.531	−	310.857i	−0.762585	−	0.863491i
$361$	45.1247	−	78.1583i	0.124999	−	0.216505i
$362$	269.329	+	197.001i	0.744004	+	0.544202i
$363$	48.8468			0.134564
$364$		0			0
$365$			679.969i			1.86293i
$366$	−15.0666	−	11.0205i	−0.0411655	−	0.0301105i
$367$	134.181	+	77.4694i	0.365615	+	0.211088i	0.671541	−	0.740967i	$-0.265633\pi$
$367$	134.181	+	77.4694i	0.365615	+	0.211088i	−0.305926	+	0.952055i	$0.598966\pi$
$368$	347.629	+	160.146i	0.944643	+	0.435178i
$369$	45.9567	−	26.5331i	0.124544	−	0.0719055i
$370$	243.691	+	552.094i	0.658623	+	1.49214i
$371$		0			0
$372$	34.6149	+	31.5715i	0.0930508	+	0.0848697i
$373$	−506.505	+	292.431i	−1.35792	+	0.783997i	−0.989344	−	0.145600i	$-0.953489\pi$
$373$	−506.505	+	292.431i	−1.35792	+	0.783997i	−0.368579	+	0.929597i	$0.620155\pi$
$374$	−45.3411	+	418.484i	−0.121233	+	1.11894i
$375$	−28.1478	+	48.7534i	−0.0750608	+	0.130009i
$376$	−34.7864	−	171.762i	−0.0925171	−	0.456815i
$377$		−	323.644i		−	0.858472i
$378$		0			0
$379$		−	128.176i		−	0.338195i	−0.985599	−	0.169098i	$-0.945915\pi$
$379$		−	128.176i		−	0.338195i	0.985599	−	0.169098i	$-0.0540853\pi$
$380$	407.926	+	89.4442i	1.07349	+	0.235380i
$381$	−32.0011	+	55.4276i	−0.0839925	+	0.145479i
$382$	28.2982	−	261.184i	0.0740791	−	0.683727i
$383$	216.437	−	124.960i	0.565110	−	0.326266i	−0.190084	−	0.981768i	$-0.560876\pi$
$383$	216.437	−	124.960i	0.565110	−	0.326266i	0.755194	+	0.655502i	$0.227543\pi$
$384$	113.470	+	26.7929i	0.295495	+	0.0697733i
$385$		0			0
$386$	−149.008	+	65.7713i	−0.386032	+	0.170392i
$387$	235.571	−	136.007i	0.608709	−	0.351439i
$388$	−646.211	+	205.396i	−1.66549	+	0.529372i
$389$	−187.428	−	108.212i	−0.481821	−	0.278179i	0.239354	−	0.970932i	$-0.423064\pi$
$389$	−187.428	−	108.212i	−0.481821	−	0.278179i	−0.721175	+	0.692753i	$0.756398\pi$
$390$	181.220	+	132.553i	0.464666	+	0.339880i
$391$			380.991i			0.974402i
$392$		0			0
$393$	129.460			0.329415
$394$	−2.47425	+	3.38266i	−0.00627983	+	0.00858544i
$395$	184.984	−	320.401i	0.468314	−	0.811143i
$396$	−411.582	+	130.820i	−1.03935	+	0.330354i
$397$	349.941	+	606.116i	0.881463	+	1.52674i	0.849714	+	0.527244i	$0.176774\pi$
$397$	349.941	+	606.116i	0.881463	+	1.52674i	0.0317493	+	0.999496i	$0.489892\pi$
$398$	−102.522	−	232.268i	−0.257592	−	0.583589i
$399$		0			0
$400$	−22.4055	−	243.119i	−0.0560137	−	0.607798i
$401$	90.4903	+	156.734i	0.225662	+	0.390858i	0.956518	−	0.291674i	$-0.0942123\pi$
$401$	90.4903	+	156.734i	0.225662	+	0.390858i	−0.730856	+	0.682532i	$0.760879\pi$
$402$	31.0320	+	3.36220i	0.0771941	+	0.00836368i
$403$	216.310	+	124.887i	0.536749	+	0.309892i
$404$	109.893	+	24.0959i	0.272013	+	0.0596433i
$405$	376.179			0.928837
$406$		0			0
$407$	628.431			1.54406
$408$	23.0369	+	113.747i	0.0564629	+	0.278793i
$409$	310.767	+	179.421i	0.759821	+	0.438683i	0.829232	−	0.558905i	$-0.188778\pi$
$409$	310.767	+	179.421i	0.759821	+	0.438683i	−0.0694104	+	0.997588i	$0.522112\pi$
$410$	81.9423	+	8.87812i	0.199859	+	0.0216539i
$411$	115.258	+	199.632i	0.280432	+	0.485723i
$412$	491.507	+	448.293i	1.19298	+	1.08809i
$413$		0			0
$414$	−357.606	+	157.845i	−0.863782	+	0.381268i
$415$	−115.302	−	199.709i	−0.277836	−	0.481226i
$416$	621.499	+	9.96114i	1.49399	+	0.0239450i
$417$	22.4031	−	38.8033i	0.0537245	−	0.0930535i
$418$	256.743	−	351.005i	0.614218	−	0.839725i
$419$	−780.890			−1.86370			−0.931849	−	0.362846i	$-0.881805\pi$
$419$	−780.890			−1.86370			−0.931849	+	0.362846i	$0.881805\pi$
$420$		0			0
$421$			114.961i			0.273068i	0.990635	+	0.136534i	$0.0435962\pi$
$421$			114.961i			0.273068i	−0.990635	+	0.136534i	$0.956404\pi$
$422$	8.46388	−	11.5714i	0.0200566	−	0.0274203i
$423$	155.002	+	89.4904i	0.366435	+	0.211561i
$424$	−222.972	+	196.916i	−0.525878	+	0.464425i
$425$	210.472	−	121.516i	0.495228	−	0.285920i
$426$	−53.4258	+	23.5818i	−0.125413	+	0.0553563i
$427$		0			0
$428$	583.931	+	532.591i	1.36432	+	1.24437i
$429$	202.482	−	116.903i	0.471985	−	0.272501i
$430$	420.030	+	45.5085i	0.976813	+	0.105834i
$431$	−154.856	+	268.219i	−0.359295	+	0.622317i	−0.987843	−	0.155453i	$-0.950316\pi$
$431$	−154.856	+	268.219i	−0.359295	+	0.622317i	0.628548	+	0.777771i	$0.283649\pi$
$432$	−204.315	+	144.478i	−0.472952	+	0.334440i
$433$		−	595.775i		−	1.37592i	−0.725747	−	0.687962i	$-0.758506\pi$
$433$		−	595.775i		−	1.37592i	0.725747	−	0.687962i	$-0.241494\pi$
$434$		0			0
$435$			96.2958i			0.221370i
$436$	−9.86914	+	45.0099i	−0.0226356	+	0.103234i
$437$	196.808	−	340.881i	0.450361	−	0.780048i
$438$	194.091	+	21.0289i	0.443129	+	0.0480113i
$439$	−698.796	+	403.450i	−1.59179	+	0.919020i	−0.598789	+	0.800907i	$0.704351\pi$
$439$	−698.796	+	403.450i	−1.59179	+	0.919020i	−0.993000	+	0.118113i	$0.962315\pi$
$440$	−635.925	−	213.407i	−1.44529	−	0.485015i
$441$		0			0
$442$	249.849	+	566.045i	0.565269	+	1.28065i
$443$	385.214	−	222.403i	0.869557	−	0.502039i	0.00235617	−	0.999997i	$-0.499250\pi$
$443$	385.214	−	222.403i	0.869557	−	0.502039i	0.867201	+	0.497958i	$0.165917\pi$
$444$	165.126	−	52.4849i	0.371906	−	0.118209i
$445$	5.90012	+	3.40644i	0.0132587	+	0.00765491i
$446$	−330.280	+	451.540i	−0.740538	+	1.01242i
$447$			37.9772i			0.0849601i
$448$		0			0
$449$	262.420			0.584455			0.292228	−	0.956349i	$-0.405604\pi$
$449$	262.420			0.584455			0.292228	+	0.956349i	$0.405604\pi$
$450$	201.256	+	147.209i	0.447235	+	0.327131i
$451$	42.9145	−	74.3302i	0.0951542	−	0.164812i
$452$	−17.9213	−	56.3836i	−0.0396490	−	0.124742i
$453$	−44.4633	−	77.0127i	−0.0981530	−	0.170006i
$454$	−557.659	+	246.147i	−1.22832	+	0.542174i
$455$		0			0
$456$	38.1466	−	113.672i	0.0836549	−	0.249281i
$457$	−194.738	−	337.296i	−0.426122	−	0.738065i	0.570403	−	0.821365i	$-0.306787\pi$
$457$	−194.738	−	337.296i	−0.426122	−	0.738065i	−0.996524	+	0.0833004i	$0.973454\pi$
$458$	−89.3368	+	824.551i	−0.195058	+	1.80033i
$459$	−215.720	−	124.546i	−0.469978	−	0.271342i
$460$	−593.040	−	130.034i	−1.28922	−	0.282682i
$461$	−158.714			−0.344283			−0.172141	−	0.985072i	$-0.555069\pi$
$461$	−158.714			−0.344283			−0.172141	+	0.985072i	$0.555069\pi$
$462$		0			0
$463$	−528.844			−1.14221			−0.571106	−	0.820877i	$-0.693485\pi$
$463$	−528.844			−1.14221			−0.571106	+	0.820877i	$0.693485\pi$
$464$	153.919	+	217.666i	0.331721	+	0.469107i
$465$	−64.3601	−	37.1583i	−0.138409	−	0.0799103i
$466$	35.5301	−	327.932i	0.0762449	−	0.703717i
$467$	218.449	+	378.365i	0.467771	+	0.810203i	0.999322	−	0.0368236i	$-0.0117240\pi$
$467$	218.449	+	378.365i	0.467771	+	0.810203i	−0.531551	+	0.847026i	$0.678391\pi$
$468$	−427.788	+	469.025i	−0.914078	+	1.00219i
$469$		0			0
$470$	112.254	+	254.318i	0.238839	+	0.541102i
$471$	−12.8274	−	22.2177i	−0.0272344	−	0.0471713i
$472$	−289.595	−	327.914i	−0.613548	−	0.694733i
$473$	219.977	−	381.011i	0.465067	−	0.805519i
$474$	−85.7346	−	62.7107i	−0.180875	−	0.132301i
$475$	−251.085			−0.528600
$476$		0			0
$477$		−	303.811i		−	0.636920i
$478$	30.8617	+	22.5739i	0.0645643	+	0.0472256i
$479$	−472.737	−	272.935i	−0.986925	−	0.569802i	−0.0825716	−	0.996585i	$-0.526313\pi$
$479$	−472.737	−	272.935i	−0.986925	−	0.569802i	−0.904354	+	0.426783i	$0.859647\pi$
$480$	−184.919	−	2.96380i	−0.385247	−	0.00617458i
$481$	799.980	−	461.869i	1.66316	−	0.960226i
$482$	−282.913	−	640.955i	−0.586957	−	1.32978i
$483$		0			0
$484$	−144.553	+	158.487i	−0.298663	+	0.327453i
$485$	931.488	−	537.795i	1.92059	−	1.10886i
$486$	41.9576	−	387.255i	0.0863324	−	0.796822i
$487$	−324.115	+	561.384i	−0.665534	+	1.15274i	0.313606	+	0.949553i	$0.398463\pi$
$487$	−324.115	+	561.384i	−0.665534	+	1.15274i	−0.979140	+	0.203185i	$0.934871\pi$
$488$	80.3433	−	16.2716i	0.164638	−	0.0333435i
$489$			220.822i			0.451579i
$490$		0			0
$491$			732.074i			1.49098i	0.666514	+	0.745492i	$0.267786\pi$
$491$			732.074i			1.49098i	−0.666514	+	0.745492i	$0.732214\pi$
$492$	5.06834	−	23.1151i	0.0103015	−	0.0469818i
$493$	−132.684	+	229.815i	−0.269136	+	0.466157i
$494$	68.8557	−	635.516i	0.139384	−	1.28647i
$495$	593.279	−	342.530i	1.19854	−	0.691980i
$496$	−204.872	+	18.8807i	−0.413049	+	0.0380659i
$497$		0			0
$498$	−60.5709	+	26.7356i	−0.121628	+	0.0536859i
$499$	23.1264	−	13.3520i	0.0463454	−	0.0267575i	−0.476648	−	0.879094i	$-0.658148\pi$
$499$	23.1264	−	13.3520i	0.0463454	−	0.0267575i	0.522994	+	0.852337i	$0.324815\pi$
$500$	−74.8860	−	235.604i	−0.149772	−	0.471208i
$501$	47.4172	+	27.3763i	0.0946451	+	0.0546434i
$502$	−142.572	−	104.284i	−0.284008	−	0.207738i
$503$			616.414i			1.22548i	0.790286	+	0.612738i	$0.209932\pi$
$503$			616.414i			1.22548i	−0.790286	+	0.612738i	$0.790068\pi$
$504$		0			0
$505$	−178.460			−0.353387
$506$	−373.251	+	510.289i	−0.737651	+	1.00848i
$507$	94.8687	−	164.317i	0.187118	−	0.324097i
$508$	−85.1377	−	267.857i	−0.167594	−	0.527278i
$509$	66.3763	+	114.967i	0.130405	+	0.225869i	0.923833	−	0.382796i	$-0.125039\pi$
$509$	66.3763	+	114.967i	0.130405	+	0.225869i	−0.793428	+	0.608665i	$0.791705\pi$
$510$	−74.3391	−	168.419i	−0.145763	−	0.330233i
$511$		0			0
$512$	−422.725	+	288.874i	−0.825634	+	0.564206i
$513$	128.673	+	222.868i	0.250824	+	0.434440i
$514$	171.164	+	18.5449i	0.333004	+	0.0360796i
$515$	−913.867	−	527.621i	−1.77450	−	1.02451i
$516$	25.9799	−	118.486i	0.0503487	−	0.229624i
$517$	289.483			0.559928
$518$		0			0
$519$	−126.942			−0.244589
$520$	−966.364	+	195.714i	−1.85839	+	0.376374i
$521$	585.480	+	338.027i	1.12376	+	0.648804i	0.942359	−	0.334605i	$-0.108603\pi$
$521$	585.480	+	338.027i	1.12376	+	0.648804i	0.181403	+	0.983409i	$0.441936\pi$
$522$	−270.680	−	29.3271i	−0.518544	−	0.0561822i
$523$	186.224	+	322.550i	0.356069	+	0.616730i	0.987300	−	0.158865i	$-0.0507833\pi$
$523$	186.224	+	322.550i	0.356069	+	0.616730i	−0.631231	+	0.775595i	$0.717450\pi$
$524$	−383.113	+	420.043i	−0.731131	+	0.801609i
$525$		0			0
$526$	584.055	−	257.798i	1.11037	−	0.490110i
$527$	−102.399	−	177.361i	−0.194306	−	0.336548i
$528$	−80.5817	+	174.919i	−0.152617	+	0.331286i
$529$	−21.6179	+	37.4433i	−0.0408656	+	0.0707813i
$530$	278.583	−	380.864i	0.525629	−	0.718611i
$531$	446.799			0.841429
$532$		0			0
$533$		−	126.161i		−	0.236700i
$534$	1.15480	−	1.57878i	0.00216255	−	0.00295653i
$535$	−1085.71	−	626.836i	−2.02937	−	1.17166i
$536$	−102.742	+	90.7360i	−0.191683	+	0.169284i
$537$	230.123	−	132.862i	0.428534	−	0.247414i
$538$	105.148	−	46.4119i	0.195443	−	0.0862674i
$539$		0			0
$540$	267.490	−	293.275i	0.495352	−	0.543102i
$541$	−60.3373	+	34.8357i	−0.111529	+	0.0643914i	−0.554727	−	0.832032i	$-0.687177\pi$
$541$	−60.3373	+	34.8357i	−0.111529	+	0.0643914i	0.443198	+	0.896424i	$0.353844\pi$
$542$	61.3936	+	6.65176i	0.113272	+	0.0122726i
$543$	−75.9860	+	131.612i	−0.139937	+	0.242379i
$544$	−437.235	−	261.869i	−0.803741	−	0.481377i
$545$		−	73.0934i		−	0.134116i
$546$		0			0
$547$			466.463i			0.852765i	0.904543	+	0.426383i	$0.140212\pi$
$547$			466.463i			0.852765i	−0.904543	+	0.426383i	$0.859788\pi$
$548$	−988.803	−	216.811i	−1.80439	−	0.395640i
$549$	−41.8599	+	72.5034i	−0.0762475	+	0.132065i
$550$	400.947	+	43.4410i	0.728995	+	0.0789837i
$551$	237.430	−	137.081i	0.430908	−	0.248785i
$552$	−55.4574	+	165.256i	−0.100466	+	0.299377i
$553$		0			0
$554$	−287.659	−	651.707i	−0.519241	−	1.17637i
$555$	−238.023	+	137.423i	−0.428870	+	0.247608i
$556$	59.6025	+	187.519i	0.107199	+	0.337265i
$557$	−118.835	−	68.6094i	−0.213348	−	0.123177i	0.389518	−	0.921019i	$-0.372642\pi$
$557$	−118.835	−	68.6094i	−0.213348	−	0.123177i	−0.602866	+	0.797842i	$0.705975\pi$
$558$	124.050	−	169.595i	0.222312	−	0.303933i
$559$		−	646.692i		−	1.15687i
$560$		0			0
$561$	−191.706			−0.341722
$562$	474.850	+	347.329i	0.844929	+	0.618024i
$563$	84.5632	−	146.468i	0.150201	−	0.260156i	−0.781100	−	0.624406i	$-0.785341\pi$
$563$	84.5632	−	146.468i	0.150201	−	0.260156i	0.931301	+	0.364250i	$0.118675\pi$
$564$	76.0643	−	24.1768i	0.134866	−	0.0428667i
$565$	46.9240	+	81.2747i	0.0830513	+	0.143849i
$566$	759.324	−	335.161i	1.34156	−	0.592157i
$567$		0			0
$568$	81.5905	−	243.130i	0.143645	−	0.428045i
$569$	−372.466	−	645.129i	−0.654597	−	1.13379i	−0.981995	−	0.188908i	$-0.939505\pi$
$569$	−372.466	−	645.129i	−0.654597	−	1.13379i	0.327398	−	0.944887i	$-0.393828\pi$
$570$	−20.4871	+	189.089i	−0.0359422	+	0.331735i
$571$	767.828	+	443.306i	1.34471	+	0.776367i	0.987494	−	0.157655i	$-0.0503935\pi$
$571$	767.828	+	443.306i	1.34471	+	0.776367i	0.357213	+	0.934023i	$0.383727\pi$
$572$	−219.906	+	1002.92i	−0.384450	+	1.75335i
$573$	119.647			0.208809
$574$		0			0
$575$	365.026			0.634827
$576$	64.6484	−	518.889i	0.112237	−	0.900849i
$577$	207.900	+	120.031i	0.360311	+	0.208026i	0.669217	−	0.743067i	$-0.266630\pi$
$577$	207.900	+	120.031i	0.360311	+	0.208026i	−0.308906	+	0.951093i	$0.599963\pi$
$578$	−7.61293	+	70.2650i	−0.0131712	+	0.121566i
$579$	−37.0900	−	64.2417i	−0.0640586	−	0.110953i
$580$	−312.439	−	284.969i	−0.538687	−	0.491326i
$581$		0			0
$582$	−124.701	−	282.516i	−0.214263	−	0.485423i
$583$	−245.691	−	425.549i	−0.421425	−	0.729930i
$584$	−642.604	+	567.510i	−1.10035	+	0.971763i
$585$	503.488	−	872.067i	0.860663	−	1.49071i
$586$	−598.186	−	437.544i	−1.02080	−	0.746662i
$587$	−190.873			−0.325168			−0.162584	−	0.986695i	$-0.551983\pi$
$587$	−190.873			−0.325168			−0.162584	+	0.986695i	$0.551983\pi$
$588$		0			0
$589$			211.585i			0.359227i
$590$	560.117	+	409.698i	0.949351	+	0.694404i
$591$	−1.65299	−	0.954353i	−0.00279693	−	0.00161481i
$592$	−318.368	+	691.083i	−0.537784	+	1.16737i
$593$	−637.548	+	368.089i	−1.07512	+	0.620723i	−0.929577	−	0.368629i	$-0.879827\pi$
$593$	−637.548	+	368.089i	−1.07512	+	0.620723i	−0.145547	+	0.989351i	$0.546494\pi$
$594$	−166.913	−	378.150i	−0.280998	−	0.636617i
$595$		0			0
$596$	−123.220	−	112.386i	−0.206744	−	0.188567i
$597$	100.137	−	57.8144i	0.167734	−	0.0968415i
$598$	−100.102	+	923.910i	−0.167395	+	1.54500i
$599$	−558.330	+	967.057i	−0.932104	+	1.61445i	−0.152386	+	0.988321i	$0.548696\pi$
$599$	−558.330	+	967.057i	−0.932104	+	1.61445i	−0.779718	+	0.626131i	$0.784638\pi$
$600$	108.981	−	22.0715i	0.181635	−	0.0367858i
$601$			183.100i			0.304659i	0.988330	+	0.152329i	$0.0486774\pi$
$601$			183.100i			0.304659i	−0.988330	+	0.152329i	$0.951323\pi$
$602$		0			0
$603$		−	139.991i		−	0.232158i
$604$	381.454	+	83.6398i	0.631546	+	0.138477i
$605$	170.132	−	294.678i	0.281210	−	0.487071i
$606$	−5.51912	+	50.9398i	−0.00910746	+	0.0840591i
$607$	−394.026	+	227.491i	−0.649136	+	0.374779i	−0.788125	−	0.615515i	$-0.788948\pi$
$607$	−394.026	+	227.491i	−0.649136	+	0.374779i	0.138989	+	0.990294i	$0.455615\pi$
$608$	255.931	+	460.161i	0.420938	+	0.756844i
$609$		0			0
$610$	−118.959	+	52.5079i	−0.195015	+	0.0860786i
$611$	368.505	−	212.757i	0.603118	−	0.348211i
$612$	496.053	−	157.669i	0.810544	−	0.257629i
$613$	232.853	+	134.438i	0.379859	+	0.219312i	0.677757	−	0.735286i	$-0.262952\pi$
$613$	232.853	+	134.438i	0.379859	+	0.219312i	−0.297898	+	0.954598i	$0.596286\pi$
$614$	−258.810	−	189.307i	−0.421514	−	0.308317i
$615$			37.5375i			0.0610366i
$616$		0			0
$617$	−184.934			−0.299731			−0.149866	−	0.988706i	$-0.547884\pi$
$617$	−184.934			−0.299731			−0.149866	+	0.988706i	$0.547884\pi$
$618$	−178.867	+	244.537i	−0.289429	+	0.395691i
$619$	496.809	−	860.498i	0.802599	−	1.39014i	−0.115301	−	0.993331i	$-0.536783\pi$
$619$	496.809	−	860.498i	0.802599	−	1.39014i	0.917900	−	0.396812i	$-0.129884\pi$
$620$	311.024	−	98.8581i	0.501652	−	0.159449i
$621$	−187.064	−	324.004i	−0.301229	−	0.521745i
$622$	381.871	+	865.148i	0.613940	+	1.39091i
$623$		0			0
$624$	25.9787	+	281.892i	0.0416325	+	0.451750i
$625$	386.818	+	669.988i	0.618909	+	1.07198i
$626$	459.337	+	49.7674i	0.733766	+	0.0795006i
$627$	171.524	+	99.0292i	0.273562	+	0.157941i
$628$	110.047	+	24.1296i	0.175234	+	0.0384229i
$629$	−757.408			−1.20415
$630$		0			0
$631$	805.857			1.27711			0.638555	−	0.769576i	$-0.279532\pi$
$631$	805.857			1.27711			0.638555	+	0.769576i	$0.279532\pi$
$632$	457.185	−	92.5920i	0.723393	−	0.146506i
$633$	5.65451	+	3.26463i	0.00893287	+	0.00515740i
$634$	448.015	+	48.5406i	0.706648	+	0.0765625i
$635$	222.918	+	386.106i	0.351053	+	0.608041i
$636$	−100.098	−	91.2976i	−0.157387	−	0.143550i
$637$		0			0
$638$	−402.860	+	177.820i	−0.631442	+	0.278714i
$639$	130.957	+	226.825i	0.204941	+	0.354969i
$640$	556.847	−	591.211i	0.870074	−	0.923767i
$641$	−2.75221	+	4.76696i	−0.00429361	+	0.00743676i	−0.868164	−	0.496277i	$-0.834700\pi$
$641$	−2.75221	+	4.76696i	−0.00429361	+	0.00743676i	0.863871	+	0.503714i	$0.168033\pi$
$642$	−212.501	+	290.520i	−0.330999	+	0.452524i
$643$	1024.08			1.59266			0.796331	−	0.604861i	$-0.206771\pi$
$643$	1024.08			1.59266			0.796331	+	0.604861i	$0.206771\pi$
$644$		0			0
$645$			192.414i			0.298317i
$646$	−309.436	+	423.044i	−0.479003	+	0.654866i
$647$	−395.404	−	228.287i	−0.611134	−	0.352839i	0.162275	−	0.986746i	$-0.448117\pi$
$647$	−395.404	−	228.287i	−0.611134	−	0.352839i	−0.773409	+	0.633907i	$0.781450\pi$
$648$	313.963	+	355.507i	0.484511	+	0.548623i
$649$	625.834	−	361.325i	0.964304	−	0.556741i
$650$	542.325	−	239.379i	0.834346	−	0.368275i
$651$		0			0
$652$	−716.473	−	653.480i	−1.09888	−	1.00227i
$653$	−24.4603	+	14.1222i	−0.0374584	+	0.0216266i	−0.518612	−	0.855010i	$-0.673551\pi$
$653$	−24.4603	+	14.1222i	−0.0374584	+	0.0216266i	0.481154	+	0.876636i	$0.340218\pi$
$654$	−20.8638	−	2.26051i	−0.0319018	−	0.00345644i
$655$	450.907	−	780.994i	0.688407	−	1.19236i
$656$	59.9997	+	84.8492i	0.0914630	+	0.129343i
$657$		−	875.579i		−	1.33269i
$658$		0			0
$659$		−	132.188i		−	0.200589i	−0.994958	−	0.100295i	$-0.968021\pi$
$659$		−	132.188i		−	0.200589i	0.994958	−	0.100295i	$-0.0319785\pi$
$660$	65.4299	−	298.404i	0.0991362	−	0.452128i
$661$	−346.924	+	600.889i	−0.524847	+	0.909061i	0.474735	+	0.880129i	$0.342544\pi$
$661$	−346.924	+	600.889i	−0.524847	+	0.909061i	−0.999581	+	0.0289321i	$0.990789\pi$
$662$	−41.1567	−	4.45917i	−0.0621703	−	0.00673590i
$663$	−244.038	+	140.895i	−0.368082	+	0.212512i
$664$	92.5022	−	275.645i	0.139311	−	0.415129i
$665$		0			0
$666$	−313.794	−	710.917i	−0.471162	−	1.06744i
$667$	−345.175	+	199.287i	−0.517504	+	0.298781i
$668$	−229.147	+	72.8336i	−0.343034	+	0.109032i
$669$	−220.652	−	127.393i	−0.329823	−	0.190424i
$670$	128.367	−	175.496i	0.191592	−	0.261935i
$671$			135.408i			0.201800i
$672$		0			0
$673$	532.137			0.790694			0.395347	−	0.918532i	$-0.370624\pi$
$673$	532.137			0.790694			0.395347	+	0.918532i	$0.370624\pi$
$674$	−56.4418	−	41.2844i	−0.0837415	−	0.0612528i
$675$	−119.327	+	206.680i	−0.176780	+	0.306192i
$676$	252.394	+	794.074i	0.373364	+	1.17467i
$677$	143.115	+	247.883i	0.211396	+	0.366149i	0.952152	−	0.305626i	$-0.0988657\pi$
$677$	143.115	+	247.883i	0.211396	+	0.366149i	−0.740756	+	0.671775i	$0.765532\pi$
$678$	24.6503	−	10.8805i	0.0363573	−	0.0160479i
$679$		0			0
$680$	766.440	+	257.205i	1.12712	+	0.378243i
$681$	−138.808	−	240.423i	−0.203830	−	0.353043i
$682$	36.6070	−	337.871i	0.0536759	−	0.495412i
$683$	387.838	+	223.918i	0.567844	+	0.327845i	0.756288	−	0.654239i	$-0.227011\pi$
$683$	387.838	+	223.918i	0.567844	+	0.327845i	−0.188443	+	0.982084i	$0.560344\pi$
$684$	−525.276	−	115.175i	−0.767947	−	0.168385i
$685$	1605.76			2.34417
$686$		0			0
$687$	−377.724			−0.549817
$688$	307.554	+	434.930i	0.447026	+	0.632166i
$689$	−625.519	−	361.143i	−0.907865	−	0.524156i
$690$	29.7840	−	274.897i	0.0431652	−	0.398401i
$691$	−510.366	−	883.980i	−0.738591	−	1.27928i	−0.953130	−	0.302561i	$-0.902158\pi$
$691$	−510.366	−	883.980i	−0.738591	−	1.27928i	0.214539	−	0.976715i	$-0.431175\pi$
$692$	375.659	−	411.871i	0.542860	−	0.595189i
$693$		0			0
$694$	354.331	+	802.754i	0.510563	+	1.15671i
$695$	−156.059	−	270.302i	−0.224545	−	0.388924i
$696$	−91.0042	+	80.3696i	−0.130753	+	0.115474i
$697$	−51.7221	+	89.5854i	−0.0742068	+	0.128530i
$698$	702.398	+	513.770i	1.00630	+	0.736060i
$699$	150.225			0.214914
$700$		0			0
$701$		−	1311.02i		−	1.87021i	−0.354369	−	0.935106i	$-0.615304\pi$
$701$		−	1311.02i		−	1.87021i	0.354369	−	0.935106i	$-0.384696\pi$
$702$	−490.400	−	358.704i	−0.698576	−	0.510974i
$703$	677.669	+	391.252i	0.963967	+	0.556546i
$704$	−329.071	−	779.092i	−0.467431	−	1.10666i
$705$	−109.644	+	63.3028i	−0.155523	+	0.0897912i
$706$	227.027	+	514.342i	0.321568	+	0.728530i
$707$		0			0
$708$	134.267	−	147.210i	0.189642	−	0.207923i
$709$	−465.495	+	268.754i	−0.656552	+	0.379061i	−0.790962	−	0.611865i	$-0.790419\pi$
$709$	−465.495	+	268.754i	−0.656552	+	0.379061i	0.134410	+	0.990926i	$0.457086\pi$
$710$	−43.8190	+	404.436i	−0.0617169	+	0.569628i
$711$	−238.199	+	412.573i	−0.335020	+	0.580271i
$712$	1.70506	+	8.41895i	0.00239475	+	0.0118244i
$713$		−	307.601i		−	0.431417i
$714$		0			0
$715$		−	1628.68i		−	2.27787i
$716$	−249.926	+	1139.83i	−0.349058	+	1.59194i
$717$	−8.70704	+	15.0810i	−0.0121437	+	0.0210335i
$718$	−56.8587	+	524.788i	−0.0791904	+	0.730903i
$719$	233.275	−	134.681i	0.324443	−	0.187318i	−0.328928	−	0.944355i	$-0.606687\pi$
$719$	233.275	−	134.681i	0.324443	−	0.187318i	0.653371	+	0.757037i	$0.273354\pi$
$720$	76.1187	+	825.955i	0.105720	+	1.14716i
$721$		0			0
$722$	−165.128	+	72.8866i	−0.228710	+	0.100951i
$723$	276.334	−	159.541i	0.382204	−	0.220666i
$724$	−202.158	−	636.022i	−0.279223	−	0.878483i
$725$	220.185	+	127.124i	0.303703	+	0.175343i
$726$	−78.8513	−	57.6759i	−0.108611	−	0.0794434i
$727$			460.316i			0.633172i	0.948564	+	0.316586i	$0.102537\pi$
$727$			460.316i			0.633172i	−0.948564	+	0.316586i	$0.897463\pi$
$728$		0			0
$729$	−356.185			−0.488594
$730$	802.874	−	1097.64i	1.09983	−	1.50362i
$731$	−265.124	+	459.208i	−0.362686	+	0.628191i
$732$	11.3089	+	35.5797i	0.0154493	+	0.0486062i
$733$	33.3410	+	57.7484i	0.0454857	+	0.0787836i	0.887872	−	0.460091i	$-0.152183\pi$
$733$	33.3410	+	57.7484i	0.0454857	+	0.0787836i	−0.842386	+	0.538874i	$0.818850\pi$
$734$	−125.130	−	283.490i	−0.170478	−	0.386226i
$735$		0			0
$736$	−372.070	−	668.979i	−0.505530	−	0.908939i
$737$	−113.211	−	196.087i	−0.153610	−	0.266061i
$738$	−105.515	−	11.4321i	−0.142974	−	0.0154907i
$739$	−808.772	−	466.944i	−1.09441	−	0.631860i	−0.159665	−	0.987171i	$-0.551042\pi$
$739$	−808.772	−	466.944i	−1.09441	−	0.631860i	−0.934748	+	0.355311i	$0.884375\pi$
$740$	258.506	−	1178.96i	0.349332	−	1.59319i
$741$	291.128			0.392885
$742$		0			0
$743$	−1198.23			−1.61269			−0.806345	−	0.591446i	$-0.798557\pi$
$743$	−1198.23			−1.61269			−0.806345	+	0.591446i	$0.798557\pi$
$744$	−18.5993	−	91.8361i	−0.0249990	−	0.123436i
$745$	229.104	+	132.273i	0.307523	+	0.177548i
$746$	1162.92	+	125.997i	1.55887	+	0.168897i
$747$	148.471	+	257.160i	0.198757	+	0.344257i
$748$	567.318	−	622.005i	0.758446	−	0.831557i
$749$		0			0
$750$	103.003	−	45.4651i	0.137338	−	0.0606201i
$751$	84.2993	+	146.011i	0.112249	+	0.194422i	0.916677	−	0.399629i	$-0.130861\pi$
$751$	84.2993	+	146.011i	0.112249	+	0.194422i	−0.804427	+	0.594051i	$0.797528\pi$
$752$	−146.654	+	318.343i	−0.195019	+	0.423328i
$753$	40.2239	−	69.6698i	0.0534182	−	0.0925230i
$754$	−382.143	+	522.445i	−0.506821	+	0.692897i
$755$	−619.458			−0.820474
$756$		0			0
$757$			209.207i			0.276364i	0.990407	+	0.138182i	$0.0441259\pi$
$757$			209.207i			0.276364i	−0.990407	+	0.138182i	$0.955874\pi$
$758$	−151.344	+	206.909i	−0.199662	+	0.272967i
$759$	−249.360	−	143.968i	−0.328538	−	0.189681i
$760$	−552.886	−	626.045i	−0.727482	−	0.823743i
$761$	−479.127	+	276.624i	−0.629602	+	0.363501i	−0.780598	−	0.625033i	$-0.785085\pi$
$761$	−479.127	+	276.624i	−0.629602	+	0.363501i	0.150996	+	0.988534i	$0.451752\pi$
$762$	117.104	−	51.6891i	0.153680	−	0.0678334i
$763$		0			0
$764$	−354.073	+	388.205i	−0.463447	+	0.508121i
$765$	−715.041	+	412.829i	−0.934695	+	0.539646i
$766$	−496.932	−	53.8405i	−0.648736	−	0.0702879i
$767$	531.115	−	919.919i	0.692458	−	1.19937i
$768$	−151.534	−	177.231i	−0.197310	−	0.230769i
$769$		−	219.524i		−	0.285467i	−0.989761	−	0.142734i	$-0.954411\pi$
$769$		−	219.524i		−	0.285467i	0.989761	−	0.142734i	$-0.0455892\pi$
$770$		0			0
$771$			78.4096i			0.101699i
$772$	318.197	+	69.7698i	0.412173	+	0.0903755i
$773$	333.337	−	577.357i	0.431225	−	0.746904i	−0.565754	−	0.824574i	$-0.691415\pi$
$773$	333.337	−	577.357i	0.431225	−	0.746904i	0.996979	+	0.0776701i	$0.0247481\pi$
$774$	−540.862	−	58.6002i	−0.698788	−	0.0757108i
$775$	−169.928	+	98.1082i	−0.219262	+	0.126591i
$776$	1285.67	+	431.452i	1.65680	+	0.555995i
$777$		0			0
$778$	174.786	+	395.988i	0.224661	+	0.508981i
$779$	92.5538	−	53.4359i	0.118811	−	0.0685956i
$780$	−136.023	−	427.951i	−0.174388	−	0.548655i
$781$	366.866	+	211.810i	0.469738	+	0.271204i
$782$	449.856	−	615.018i	0.575263	−	0.786468i
$783$		−	260.587i		−	0.332806i
$784$		0			0
$785$	−178.710			−0.227656
$786$	−208.982	−	152.860i	−0.265881	−	0.194479i
$787$	−459.932	+	796.626i	−0.584412	+	1.01223i	0.410536	+	0.911844i	$0.365341\pi$
$787$	−459.932	+	796.626i	−0.584412	+	1.01223i	−0.994948	+	0.100387i	$0.967992\pi$
$788$	7.98816	−	2.53901i	0.0101373	−	0.00322210i
$789$	145.378	+	251.803i	0.184256	+	0.319141i
$790$	−676.926	+	298.791i	−0.856868	+	0.378216i
$791$		0			0
$792$	818.865	+	274.798i	1.03392	+	0.346967i
$793$	99.5187	+	172.371i	0.125496	+	0.217366i
$794$	150.776	−	1391.62i	0.189895	−	1.75267i
$795$	186.115	+	107.453i	0.234106	+	0.135161i
$796$	−108.755	+	495.994i	−0.136626	+	0.623108i
$797$	−1016.13			−1.27494			−0.637470	−	0.770476i	$-0.720019\pi$
$797$	−1016.13			−1.27494			−0.637470	+	0.770476i	$0.720019\pi$
$798$		0			0
$799$	−348.895			−0.436664
$800$	−250.895	+	418.912i	−0.313619	+	0.523640i
$801$	−7.59744	−	4.38638i	−0.00948494	−	0.00547613i
$802$	38.9889	−	359.855i	0.0486146	−	0.448697i
$803$	−708.078	−	1226.43i	−0.881791	−	1.52731i
$804$	−46.1238	−	42.0686i	−0.0573679	−	0.0523241i
$805$		0			0
$806$	−201.720	−	457.007i	−0.250273	−	0.567007i
$807$	26.1727	+	45.3325i	0.0324321	+	0.0561741i
$808$	−148.945	−	168.654i	−0.184338	−	0.208730i
$809$	−565.950	+	980.254i	−0.699567	+	1.21169i	0.269049	+	0.963126i	$0.413291\pi$
$809$	−565.950	+	980.254i	−0.699567	+	1.21169i	−0.968617	+	0.248560i	$0.920043\pi$
$810$	−607.250	−	444.174i	−0.749691	−	0.548362i
$811$	−481.066			−0.593176			−0.296588	−	0.955006i	$-0.595849\pi$
$811$	−481.066			−0.593176			−0.296588	+	0.955006i	$0.595849\pi$
$812$		0			0
$813$			28.1242i			0.0345931i
$814$	−1014.45	−	742.021i	−1.24625	−	0.911573i
$815$	1332.15	+	769.117i	1.63454	+	0.943702i
$816$	97.1199	−	210.818i	0.119019	−	0.258356i
$817$	474.423	−	273.908i	0.580690	−	0.335261i
$818$	−289.806	−	656.570i	−0.354286	−	0.802653i
$819$		0			0
$820$	−121.793	−	111.085i	−0.148528	−	0.135469i
$821$	−630.185	+	363.838i	−0.767582	+	0.443164i	−0.832011	−	0.554758i	$-0.812811\pi$
$821$	−630.185	+	363.838i	−0.767582	+	0.443164i	0.0644292	+	0.997922i	$0.479477\pi$
$822$	49.6602	−	458.348i	0.0604138	−	0.557601i
$823$	313.323	−	542.692i	0.380709	−	0.659407i	−0.610455	−	0.792051i	$-0.709013\pi$
$823$	313.323	−	542.692i	0.380709	−	0.659407i	0.991164	+	0.132644i	$0.0423468\pi$
$824$	−264.096	−	1304.01i	−0.320505	−	1.58253i
$825$			183.673i			0.222633i
$826$		0			0
$827$			1468.52i			1.77572i	0.460116	+	0.887859i	$0.347808\pi$
$827$			1468.52i			1.77572i	−0.460116	+	0.887859i	$0.652192\pi$
$828$	763.643	+	167.441i	0.922274	+	0.202223i
$829$	409.352	−	709.019i	0.493790	−	0.855270i	−0.506184	−	0.862425i	$-0.668944\pi$
$829$	409.352	−	709.019i	0.493790	−	0.855270i	0.999974	+	0.00715566i	$0.00227774\pi$
$830$	−49.6793	+	458.525i	−0.0598546	+	0.552439i
$831$	280.969	−	162.218i	0.338110	−	0.195208i
$832$	−991.498	−	749.915i	−1.19170	−	0.901341i
$833$		0			0
$834$	−81.9814	+	36.1861i	−0.0982990	+	0.0433886i
$835$	330.306	−	190.702i	0.395576	−	0.228386i
$836$	−828.899	+	263.463i	−0.991505	+	0.315147i
$837$	174.165	+	100.554i	0.208083	+	0.120137i
$838$	1260.56	+	922.036i	1.50424	+	1.10028i
$839$			1108.84i			1.32162i	0.750555	+	0.660808i	$0.229786\pi$
$839$			1108.84i			1.32162i	−0.750555	+	0.660808i	$0.770214\pi$
$840$		0			0
$841$	563.386			0.669900
$842$	135.741	−	185.577i	0.161212	−	0.220401i
$843$	−133.970	+	232.042i	−0.158920	+	0.275258i
$844$	−27.3258	+	8.68541i	−0.0323765	+	0.0102908i
$845$	−660.850	−	1144.63i	−0.782072	−	1.35459i
$846$	−144.547	−	327.479i	−0.170860	−	0.387091i
$847$		0			0
$848$	592.443	−	54.5986i	0.698636	−	0.0643852i
$849$	189.005	+	327.366i	0.222621	+	0.385590i
$850$	−483.236	−	52.3567i	−0.568513	−	0.0615961i
$851$	−985.191	−	568.800i	−1.15769	−	0.668390i
$852$	114.087	+	25.0154i	0.133905	+	0.0293608i
$853$	−610.400			−0.715592			−0.357796	−	0.933800i	$-0.616472\pi$
$853$	−610.400			−0.715592			−0.357796	+	0.933800i	$0.616472\pi$
$854$		0			0
$855$	853.017			0.997680
$856$	−313.757	−	1549.22i	−0.366539	−	1.80983i
$857$	−384.614	−	222.057i	−0.448791	−	0.259110i	0.258529	−	0.966004i	$-0.416762\pi$
$857$	−384.614	−	222.057i	−0.448791	−	0.259110i	−0.707319	+	0.706894i	$0.750096\pi$
$858$	−464.891	−	50.3690i	−0.541830	−	0.0587052i
$859$	−40.7547	−	70.5892i	−0.0474443	−	0.0821760i	0.841328	−	0.540525i	$-0.181774\pi$
$859$	−40.7547	−	70.5892i	−0.0474443	−	0.0821760i	−0.888772	+	0.458349i	$0.848441\pi$
$860$	−624.302	−	569.413i	−0.725932	−	0.662108i
$861$		0			0
$862$	566.677	−	250.128i	0.657398	−	0.290171i
$863$	525.730	+	910.592i	0.609189	+	1.05515i	0.991374	+	0.131061i	$0.0418384\pi$
$863$	525.730	+	910.592i	0.609189	+	1.05515i	−0.382185	+	0.924086i	$0.624828\pi$
$864$	500.410	+	8.02036i	0.579178	+	0.00928283i
$865$	−442.134	+	765.799i	−0.511138	+	0.885317i
$866$	−703.462	+	961.734i	−0.812311	+	1.11055i
$867$	−32.1882			−0.0371259
$868$		0			0
$869$			770.524i			0.886679i
$870$	113.701	−	155.446i	0.130691	−	0.178674i
$871$	−288.230	−	166.409i	−0.330918	−	0.191056i
$872$	69.0768	−	61.0046i	0.0792165	−	0.0699594i
$873$	−1199.45	+	692.505i	−1.37395	+	0.793248i
$874$	−720.194	+	317.889i	−0.824020	+	0.363717i
$875$		0			0
$876$	−288.482	−	263.119i	−0.329318	−	0.300364i
$877$	1350.68	−	779.814i	1.54011	−	0.889183i	0.541280	−	0.840842i	$-0.317940\pi$
$877$	1350.68	−	779.814i	1.54011	−	0.889183i	0.998831	−	0.0483410i	$-0.0153934\pi$
$878$	1604.41	+	173.831i	1.82735	+	0.197986i
$879$	168.767	−	292.312i	0.191998	−	0.332551i
$880$	774.568	+	1095.36i	0.880190	+	1.24473i
$881$			1515.22i			1.71989i	0.510389	+	0.859944i	$0.329501\pi$
$881$			1515.22i			1.71989i	−0.510389	+	0.859944i	$0.670499\pi$
$882$		0			0
$883$		−	763.828i		−	0.865037i	−0.901625	−	0.432519i	$-0.857625\pi$
$883$		−	763.828i		−	0.865037i	0.901625	−	0.432519i	$-0.142375\pi$
$884$	265.038	−	1208.75i	0.299817	−	1.36737i
$885$	−158.026	+	273.709i	−0.178561	+	0.309276i
$886$	−884.437	−	95.8252i	−0.998236	−	0.108155i
$887$	−496.554	+	286.686i	−0.559813	+	0.323208i	−0.753070	−	0.657940i	$-0.771428\pi$
$887$	−496.554	+	286.686i	−0.559813	+	0.323208i	0.193258	+	0.981148i	$0.438095\pi$
$888$	−328.528	−	110.249i	−0.369964	−	0.124154i
$889$		0			0
$890$	−5.50216	−	12.4654i	−0.00618221	−	0.0140061i
$891$	−678.496	+	391.730i	−0.761500	+	0.439652i
$892$	1066.31	−	338.925i	1.19542	−	0.379960i
$893$	312.163	+	180.228i	0.349567	+	0.201823i
$894$	44.8416	−	61.3049i	0.0501583	−	0.0685737i
$895$		−	1851.01i		−	2.06817i
$896$		0			0
$897$	−423.240			−0.471840
$898$	−423.614	−	309.853i	−0.471731	−	0.345048i
$899$	107.125	−	185.546i	0.119160	−	0.206391i
$900$	−151.062	−	475.266i	−0.167846	−	0.528073i
$901$	296.115	+	512.887i	0.328652	+	0.569242i
$902$	−157.041	+	69.3167i	−0.174103	+	0.0768477i
$903$		0			0
$904$	−37.6452	+	112.178i	−0.0416430	+	0.124091i
$905$	529.315	+	916.800i	0.584878	+	1.01304i
$906$	−19.1576	+	176.818i	−0.0211452	+	0.195164i
$907$	885.036	+	510.976i	0.975784	+	0.563369i	0.900995	−	0.433830i	$-0.142838\pi$
$907$	885.036	+	510.976i	0.975784	+	0.563369i	0.0747894	+	0.997199i	$0.476172\pi$
$908$	1190.84	+	261.112i	1.31150	+	0.287568i
$909$	229.799			0.252804
$910$		0			0
$911$	630.111			0.691669			0.345835	−	0.938295i	$-0.387596\pi$
$911$	630.111			0.691669			0.345835	+	0.938295i	$0.387596\pi$
$912$	−195.797	+	138.455i	−0.214690	+	0.151814i
$913$	415.930	+	240.137i	0.455564	+	0.263020i
$914$	−83.9052	+	774.419i	−0.0918000	+	0.847285i
$915$	−29.6104	−	51.2868i	−0.0323611	−	0.0560511i
$916$	1117.80	−	1225.55i	1.22031	−	1.33794i
$917$		0			0
$918$	201.170	+	455.760i	0.219139	+	0.496471i
$919$	421.489	+	730.041i	0.458639	+	0.794386i	0.998889	−	0.0471182i	$-0.0150038\pi$
$919$	421.489	+	730.041i	0.458639	+	0.794386i	−0.540250	+	0.841504i	$0.681670\pi$
$920$	803.783	+	910.140i	0.873677	+	0.989283i
$921$	73.0182	−	126.471i	0.0792814	−	0.137319i
$922$	256.206	+	187.402i	0.277881	+	0.203256i
$923$	622.683			0.674630
$924$		0			0
$925$			725.668i			0.784506i
$926$	853.690	+	624.433i	0.921911	+	0.674333i
$927$	1176.76	+	679.405i	1.26943	+	0.732907i
$928$	8.54444	−	533.108i	0.00920737	−	0.574470i
$929$	−670.867	+	387.325i	−0.722139	+	0.416927i	−0.815540	−	0.578701i	$-0.803560\pi$
$929$	−670.867	+	387.325i	−0.722139	+	0.416927i	0.0934003	+	0.995629i	$0.470226\pi$
$930$	60.0190	+	135.976i	0.0645366	+	0.146211i
$931$		0			0
$932$	−444.561	+	487.415i	−0.476997	+	0.522977i
$933$	−372.990	+	215.346i	−0.399774	+	0.230810i
$934$	94.1214	−	868.712i	0.100772	−	0.930098i
$935$	−667.708	+	1156.50i	−0.714126	+	1.23690i
$936$	1244.36	−	252.016i	1.32945	−	0.269248i
$937$			1586.27i			1.69293i	0.532447	+	0.846463i	$0.321273\pi$
$937$			1586.27i			1.69293i	−0.532447	+	0.846463i	$0.678727\pi$
$938$		0			0
$939$			210.421i			0.224090i
$940$	119.079	−	543.079i	0.126680	−	0.577744i
$941$	−410.023	+	710.181i	−0.435731	+	0.754708i	−0.997355	−	0.0726842i	$-0.976843\pi$
$941$	−410.023	+	710.181i	−0.435731	+	0.754708i	0.561624	+	0.827393i	$0.310177\pi$
$942$	−5.52684	+	51.0110i	−0.00586713	+	0.0541518i
$943$	−134.554	+	77.6849i	−0.142687	+	0.0823805i
$944$	80.2954	+	871.277i	0.0850587	+	0.922963i
$945$		0			0
$946$	−804.977	+	355.312i	−0.850928	+	0.375594i
$947$	−551.949	+	318.668i	−0.582839	+	0.336502i	−0.762261	−	0.647270i	$-0.775911\pi$
$947$	−551.949	+	318.668i	−0.582839	+	0.336502i	0.179422	+	0.983772i	$0.442577\pi$
$948$	64.3521	+	202.462i	0.0678820	+	0.213568i
$949$	−1802.74	−	1040.81i	−1.89962	−	1.09675i
$950$	405.316	+	296.469i	0.426648	+	0.312072i
$951$			205.234i			0.215809i
$952$		0			0
$953$	−350.626			−0.367918			−0.183959	−	0.982934i	$-0.558891\pi$
$953$	−350.626			−0.367918			−0.183959	+	0.982934i	$0.558891\pi$
$954$	−358.725	+	490.429i	−0.376022	+	0.514076i
$955$	416.729	−	721.796i	0.436365	−	0.755807i
$956$	−23.1647	−	72.8801i	−0.0242309	−	0.0762344i
$957$	−100.277	−	173.684i	−0.104782	−	0.181488i
$958$	440.852	+	998.772i	0.460179	+	1.04256i
$959$		0			0
$960$	295.007	+	223.127i	0.307299	+	0.232424i
$961$	−397.826	−	689.055i	−0.413971	−	0.717019i
$962$	−1836.73	−	199.002i	−1.90928	−	0.206863i
$963$	1398.04	+	807.161i	1.45176	+	0.838174i
$964$	−300.113	+	1368.72i	−0.311320	+	1.41983i
$965$	−516.734			−0.535475
$966$		0			0
$967$	−649.816			−0.671992			−0.335996	−	0.941863i	$-0.609073\pi$
$967$	−649.816			−0.671992			−0.335996	+	0.941863i	$0.609073\pi$
$968$	420.479	−	85.1582i	0.434379	−	0.0879733i
$969$	−206.726	−	119.354i	−0.213340	−	0.123172i
$970$	−2138.66	−	231.716i	−2.20481	−	0.238882i
$971$	485.305	+	840.573i	0.499799	+	0.865677i	1.00000		0.000232071i	$-7.38706e-5\pi$
$971$	485.305	+	840.573i	0.499799	+	0.865677i	−0.500201	+	0.865909i	$0.666741\pi$
$972$	−524.982	+	575.589i	−0.540105	+	0.592169i
$973$		0			0
$974$	1186.06	−	523.519i	1.21772	−	0.537494i
$975$	134.991	+	233.811i	0.138452	+	0.239807i
$976$	−148.907	−	68.5987i	−0.152569	−	0.0702856i
$977$	300.437	−	520.373i	0.307510	−	0.532623i	−0.670307	−	0.742084i	$-0.733838\pi$
$977$	300.437	−	520.373i	0.307510	−	0.532623i	0.977817	+	0.209461i	$0.0671709\pi$
$978$	260.736	−	356.464i	0.266601	−	0.364482i
$979$	−14.1890			−0.0144934
$980$		0			0
$981$			94.1205i			0.0959434i
$982$	864.396	−	1181.76i	0.880241	−	1.20342i
$983$	−1098.66	−	634.311i	−1.11766	−	0.645281i	−0.176857	−	0.984236i	$-0.556593\pi$
$983$	−1098.66	−	634.311i	−1.11766	−	0.645281i	−0.940802	+	0.338955i	$0.889926\pi$
$984$	−35.4747	+	31.3292i	−0.0360516	+	0.0318386i
$985$	−11.5146	+	6.64797i	−0.0116900	+	0.00674921i
$986$	485.541	−	214.315i	0.492435	−	0.217358i
$987$		0			0
$988$	−861.537	+	944.586i	−0.872001	+	0.956059i
$989$	−689.714	+	398.207i	−0.697385	+	0.402636i
$990$	−1362.15	−	147.583i	−1.37591	−	0.149074i
$991$	774.555	−	1341.57i	0.781590	−	1.35375i	−0.149426	−	0.988773i	$-0.547742\pi$
$991$	774.555	−	1341.57i	0.781590	−	1.35375i	0.931015	−	0.364980i	$-0.118924\pi$
$992$	353.010	+	211.425i	0.355857	+	0.213130i
$993$		−	18.8538i		−	0.0189867i
$994$		0			0
$995$		−	805.464i		−	0.809512i
$996$	129.345	+	28.3610i	0.129864	+	0.0284749i
$997$	−470.469	+	814.876i	−0.471885	+	0.817328i	−0.999483	−	0.0321661i	$-0.989759\pi$
$997$	−470.469	+	814.876i	−0.471885	+	0.817328i	0.527598	+	0.849494i	$0.323093\pi$
$998$	−53.0973	−	5.75288i	−0.0532037	−	0.00576441i
$999$	644.116	−	371.881i	0.644761	−	0.372253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.j.e.325.4		28
7.2	even	3		56.3.j.a.5.6	yes	28
7.3	odd	6		392.3.h.a.293.26		28
7.4	even	3		392.3.h.a.293.25		28
7.5	odd	6	inner	392.3.j.e.117.6		28
7.6	odd	2		56.3.j.a.45.4	yes	28
8.5	even	2	inner	392.3.j.e.325.6		28
28.3	even	6		1568.3.h.a.881.11		28
28.11	odd	6		1568.3.h.a.881.17		28
28.23	odd	6		224.3.n.a.145.6		28
28.27	even	2		224.3.n.a.17.9		28
56.3	even	6		1568.3.h.a.881.18		28
56.5	odd	6	inner	392.3.j.e.117.4		28
56.11	odd	6		1568.3.h.a.881.12		28
56.13	odd	2		56.3.j.a.45.6	yes	28
56.27	even	2		224.3.n.a.17.6		28
56.37	even	6		56.3.j.a.5.4	✓	28
56.45	odd	6		392.3.h.a.293.27		28
56.51	odd	6		224.3.n.a.145.9		28
56.53	even	6		392.3.h.a.293.28		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.4	✓	28	56.37	even	6
56.3.j.a.5.6	yes	28	7.2	even	3
56.3.j.a.45.4	yes	28	7.6	odd	2
56.3.j.a.45.6	yes	28	56.13	odd	2
224.3.n.a.17.6		28	56.27	even	2
224.3.n.a.17.9		28	28.27	even	2
224.3.n.a.145.6		28	28.23	odd	6
224.3.n.a.145.9		28	56.51	odd	6
392.3.h.a.293.25		28	7.4	even	3
392.3.h.a.293.26		28	7.3	odd	6
392.3.h.a.293.27		28	56.45	odd	6
392.3.h.a.293.28		28	56.53	even	6
392.3.j.e.117.4		28	56.5	odd	6	inner
392.3.j.e.117.6		28	7.5	odd	6	inner
392.3.j.e.325.4		28	1.1	even	1	trivial
392.3.j.e.325.6		28	8.5	even	2	inner
1568.3.h.a.881.11		28	28.3	even	6
1568.3.h.a.881.12		28	56.11	odd	6
1568.3.h.a.881.17		28	28.11	odd	6
1568.3.h.a.881.18		28	56.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61426 - 1.18075i) q^{2} +(0.455431 - 0.788830i) q^{3} +(1.21166 + 3.81207i) q^{4} +(-3.17251 - 5.49495i) q^{5} +(-1.66660 + 0.735624i) q^{6} +(2.54518 - 7.58433i) q^{8} +(4.08516 + 7.07571i) q^{9} +O(q^{10})\)	\(q+(-1.61426 - 1.18075i) q^{2} +(0.455431 - 0.788830i) q^{3} +(1.21166 + 3.81207i) q^{4} +(-3.17251 - 5.49495i) q^{5} +(-1.66660 + 0.735624i) q^{6} +(2.54518 - 7.58433i) q^{8} +(4.08516 + 7.07571i) q^{9} +(-1.36692 + 12.6162i) q^{10} +(11.4442 + 6.60732i) q^{11} +(3.55890 + 0.780346i) q^{12} +19.4243 q^{13} -5.77945 q^{15} +(-13.0638 + 9.23784i) q^{16} +(-13.7930 - 7.96338i) q^{17} +(1.76014 - 16.2456i) q^{18} +(8.22725 + 14.2500i) q^{19} +(17.1032 - 18.7518i) q^{20} +(-10.6723 - 24.1787i) q^{22} +(-11.9607 - 20.7166i) q^{23} +(-4.82359 - 5.46186i) q^{24} +(-7.62967 + 13.2150i) q^{25} +(-31.3559 - 22.9353i) q^{26} +15.6398 q^{27} -16.6618i q^{29} +(9.32952 + 6.82409i) q^{30} +(11.1360 + 6.42939i) q^{31} +(31.9959 + 0.512817i) q^{32} +(10.4241 - 6.01837i) q^{33} +(12.8627 + 29.1410i) q^{34} +(-22.0233 + 24.1463i) q^{36} +(41.1844 - 23.7778i) q^{37} +(3.54481 - 32.7175i) q^{38} +(8.84646 - 15.3225i) q^{39} +(-49.7502 + 10.0757i) q^{40} -6.49499i q^{41} -33.2928i q^{43} +(-11.3211 + 51.6320i) q^{44} +(25.9205 - 44.8956i) q^{45} +(-5.15343 + 47.5645i) q^{46} +(18.9713 - 10.9531i) q^{47} +(1.33743 + 14.5123i) q^{48} +(27.9198 - 12.3236i) q^{50} +(-12.5635 + 7.25355i) q^{51} +(23.5356 + 74.0470i) q^{52} +(-32.2028 - 18.5923i) q^{53} +(-25.2467 - 18.4667i) q^{54} -83.8473i q^{55} +14.9878 q^{57} +(-19.6734 + 26.8964i) q^{58} +(27.3428 - 47.3591i) q^{59} +(-7.00270 - 22.0317i) q^{60} +(5.12340 + 8.87399i) q^{61} +(-10.3849 - 23.5276i) q^{62} +(-51.0441 - 38.6070i) q^{64} +(-61.6240 - 106.736i) q^{65} +(-23.9334 - 2.59309i) q^{66} +(-14.8386 - 8.56706i) q^{67} +(13.6446 - 62.2287i) q^{68} -21.7892 q^{69} +32.0568 q^{71} +(64.0620 - 12.9743i) q^{72} +(-92.8082 - 53.5828i) q^{73} +(-94.5579 - 10.2450i) q^{74} +(6.94958 + 12.0370i) q^{75} +(-44.3535 + 48.6290i) q^{76} +(-32.3725 + 14.2890i) q^{78} +(29.1542 + 50.4965i) q^{79} +(92.2065 + 42.4777i) q^{80} +(-29.6436 + 51.3443i) q^{81} +(-7.66897 + 10.4846i) q^{82} +36.3441 q^{83} +101.056i q^{85} +(-39.3105 + 53.7432i) q^{86} +(-13.1433 - 7.58829i) q^{87} +(79.2397 - 69.9799i) q^{88} +(-0.929882 + 0.536867i) q^{89} +(-94.8528 + 41.8674i) q^{90} +(64.4808 - 70.6965i) q^{92} +(10.1434 - 5.85629i) q^{93} +(-43.5575 - 4.71928i) q^{94} +(52.2021 - 90.4167i) q^{95} +(14.9765 - 25.0058i) q^{96} +169.517i q^{97} +107.968i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 28 * q^15 + 16 * q^16 + 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 + 30 * q^24 - 32 * q^25 + 30 * q^26 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 136 * q^71 + 96 * q^72 - 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 - 276 * q^80 - 18 * q^81 + 642 * q^82 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Introduction

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