LMFDB - Embedded newform 35.5.i.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	35.19
Dual form			35.5.i.a.24.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.03175 - 1.75038i) q^{2} +(-7.77475 - 13.4663i) q^{3} +(-1.87234 - 3.24299i) q^{4} +(-2.74588 + 24.8487i) q^{5} +54.4351i q^{6} +(37.0452 - 32.0727i) q^{7} +69.1214i q^{8} +(-80.3936 + 139.246i) q^{9} +O(q^{10})$	\(q+(-3.03175 - 1.75038i) q^{2} +(-7.77475 - 13.4663i) q^{3} +(-1.87234 - 3.24299i) q^{4} +(-2.74588 + 24.8487i) q^{5} +54.4351i q^{6} +(37.0452 - 32.0727i) q^{7} +69.1214i q^{8} +(-80.3936 + 139.246i) q^{9} +(51.8195 - 70.5288i) q^{10} +(-47.6201 - 82.4804i) q^{11} +(-29.1140 + 50.4270i) q^{12} -194.691 q^{13} +(-168.451 + 32.3932i) q^{14} +(355.968 - 156.216i) q^{15} +(91.0312 - 157.671i) q^{16} +(117.330 + 203.222i) q^{17} +(487.466 - 281.438i) q^{18} +(-87.8739 - 50.7340i) q^{19} +(85.7256 - 37.6205i) q^{20} +(-719.916 - 249.503i) q^{21} +333.413i q^{22} +(-365.097 - 210.789i) q^{23} +(930.807 - 537.402i) q^{24} +(-609.920 - 136.463i) q^{25} +(590.252 + 340.782i) q^{26} +1240.65 q^{27} +(-173.373 - 60.0861i) q^{28} -62.2893 q^{29} +(-1352.64 - 149.472i) q^{30} +(-1295.68 + 748.063i) q^{31} +(405.807 - 234.293i) q^{32} +(-740.469 + 1282.53i) q^{33} -821.491i q^{34} +(695.244 + 1008.59i) q^{35} +602.097 q^{36} +(-161.932 - 93.4914i) q^{37} +(177.608 + 307.625i) q^{38} +(1513.67 + 2621.76i) q^{39} +(-1717.58 - 189.799i) q^{40} -395.108i q^{41} +(1745.88 + 2016.56i) q^{42} -3510.40i q^{43} +(-178.322 + 308.863i) q^{44} +(-3239.33 - 2380.03i) q^{45} +(737.921 + 1278.12i) q^{46} +(-607.404 + 1052.05i) q^{47} -2830.98 q^{48} +(343.686 - 2376.27i) q^{49} +(1610.26 + 1481.31i) q^{50} +(1824.43 - 3160.01i) q^{51} +(364.528 + 631.380i) q^{52} +(1894.49 - 1093.78i) q^{53} +(-3761.34 - 2171.61i) q^{54} +(2180.29 - 956.818i) q^{55} +(2216.91 + 2560.61i) q^{56} +1577.78i q^{57} +(188.845 + 109.030i) q^{58} +(-1529.09 + 882.820i) q^{59} +(-1173.10 - 861.913i) q^{60} +(-1334.20 - 770.300i) q^{61} +5237.58 q^{62} +(1487.79 + 7736.82i) q^{63} -4553.40 q^{64} +(534.597 - 4837.82i) q^{65} +(4489.83 - 2592.20i) q^{66} +(4141.09 - 2390.86i) q^{67} +(439.366 - 761.004i) q^{68} +6555.32i q^{69} +(-342.384 - 4274.74i) q^{70} -329.707 q^{71} +(-9624.86 - 5556.91i) q^{72} +(387.130 + 670.528i) q^{73} +(327.291 + 566.884i) q^{74} +(2904.33 + 9274.32i) q^{75} +379.966i q^{76} +(-4409.46 - 1528.20i) q^{77} -10598.0i q^{78} +(2502.85 - 4335.06i) q^{79} +(3667.96 + 2694.95i) q^{80} +(-3133.87 - 5428.02i) q^{81} +(-691.589 + 1197.87i) q^{82} -12492.1 q^{83} +(538.794 + 2801.84i) q^{84} +(-5372.00 + 2357.49i) q^{85} +(-6144.53 + 10642.6i) q^{86} +(484.284 + 838.804i) q^{87} +(5701.16 - 3291.57i) q^{88} +(4892.96 + 2824.95i) q^{89} +(5654.87 + 12885.7i) q^{90} +(-7212.34 + 6244.25i) q^{91} +1578.68i q^{92} +(20147.2 + 11632.0i) q^{93} +(3682.99 - 2126.37i) q^{94} +(1501.97 - 2044.25i) q^{95} +(-6310.10 - 3643.14i) q^{96} -5033.05 q^{97} +(-5201.35 + 6602.68i) q^{98} +15313.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−3.03175	−	1.75038i	−0.757937	−	0.437595i	0.0706179	−	0.997503i	$-0.477503\pi$
$2$	−3.03175	−	1.75038i	−0.757937	−	0.437595i	−0.828554	+	0.559909i	$0.810836\pi$
$3$	−7.77475	−	13.4663i	−0.863861	−	1.49625i	−0.868173	−	0.496261i	$-0.834706\pi$
$3$	−7.77475	−	13.4663i	−0.863861	−	1.49625i	0.00431192	−	0.999991i	$-0.498627\pi$
$4$	−1.87234	−	3.24299i	−0.117021	−	0.202687i
$5$	−2.74588	+	24.8487i	−0.109835	+	0.993950i
$5$	−2.74588	+	24.8487i	−0.109835	+	0.993950i
$6$			54.4351i			1.51209i
$7$	37.0452	−	32.0727i	0.756023	−	0.654544i
$7$	37.0452	−	32.0727i	0.756023	−	0.654544i
$8$			69.1214i			1.08002i
$9$	−80.3936	+	139.246i	−0.992513	+	1.71908i
$10$	51.8195	−	70.5288i	0.518195	−	0.705288i
$11$	−47.6201	−	82.4804i	−0.393554	−	0.681656i	0.599361	−	0.800479i	$-0.295421\pi$
$11$	−47.6201	−	82.4804i	−0.393554	−	0.681656i	−0.992916	+	0.118823i	$0.962088\pi$
$12$	−29.1140	+	50.4270i	−0.202181	+	0.350187i
$13$	−194.691			−1.15202			−0.576008	−	0.817444i	$-0.695390\pi$
$13$	−194.691			−1.15202			−0.576008	+	0.817444i	$0.695390\pi$
$14$	−168.451	+	32.3932i	−0.859443	+	0.165271i
$15$	355.968	−	156.216i	1.58208	−	0.694294i
$16$	91.0312	−	157.671i	0.355590	−	0.615901i
$17$	117.330	+	203.222i	0.405988	+	0.703192i	0.994436	−	0.105343i	$-0.0335942\pi$
$17$	117.330	+	203.222i	0.405988	+	0.703192i	−0.588448	+	0.808535i	$0.700261\pi$
$18$	487.466	−	281.438i	1.50452	−	0.868637i
$19$	−87.8739	−	50.7340i	−0.243418	−	0.140537i	0.373329	−	0.927699i	$-0.378216\pi$
$19$	−87.8739	−	50.7340i	−0.243418	−	0.140537i	−0.616747	+	0.787162i	$0.711550\pi$
$20$	85.7256	−	37.6205i	0.214314	−	0.0940513i
$21$	−719.916	−	249.503i	−1.63246	−	0.565766i
$22$			333.413i			0.688869i
$23$	−365.097	−	210.789i	−0.690164	−	0.398467i	0.113509	−	0.993537i	$-0.463791\pi$
$23$	−365.097	−	210.789i	−0.690164	−	0.398467i	−0.803674	+	0.595070i	$0.797124\pi$
$24$	930.807	−	537.402i	1.61598	−	0.932989i
$25$	−609.920	−	136.463i	−0.975872	−	0.218341i
$26$	590.252	+	340.782i	0.873154	+	0.504116i
$27$	1240.65			1.70185
$28$	−173.373	−	60.0861i	−0.221139	−	0.0766405i
$29$	−62.2893			−0.0740657			−0.0370329	−	0.999314i	$-0.511791\pi$
$29$	−62.2893			−0.0740657			−0.0370329	+	0.999314i	$0.511791\pi$
$30$	−1352.64	−	149.472i	−1.50294	−	0.166080i
$31$	−1295.68	+	748.063i	−1.34827	+	0.778422i	−0.988004	−	0.154429i	$-0.950646\pi$
$31$	−1295.68	+	748.063i	−1.34827	+	0.778422i	−0.360262	+	0.932851i	$0.617313\pi$
$32$	405.807	−	234.293i	0.396296	−	0.228802i
$33$	−740.469	+	1282.53i	−0.679953	+	1.17771i
$34$		−	821.491i		−	0.710633i
$35$	695.244	+	1008.59i	0.567546	+	0.823341i
$36$	602.097			0.464581
$37$	−161.932	−	93.4914i	−0.118285	−	0.0682918i	0.439690	−	0.898149i	$-0.355088\pi$
$37$	−161.932	−	93.4914i	−0.118285	−	0.0682918i	−0.557975	+	0.829858i	$0.688422\pi$
$38$	177.608	+	307.625i	0.122997	+	0.213037i
$39$	1513.67	+	2621.76i	0.995181	+	1.72370i
$40$	−1717.58	−	189.799i	−1.07349	−	0.118624i
$41$		−	395.108i		−	0.235043i	−0.993070	−	0.117522i	$-0.962505\pi$
$41$		−	395.108i		−	0.235043i	0.993070	−	0.117522i	$-0.0374950\pi$
$42$	1745.88	+	2016.56i	0.989727	+	1.14317i
$43$		−	3510.40i		−	1.89854i	−0.314465	−	0.949269i	$-0.601825\pi$
$43$		−	3510.40i		−	1.89854i	0.314465	−	0.949269i	$-0.398175\pi$
$44$	−178.322	+	308.863i	−0.0921086	+	0.159537i
$45$	−3239.33	−	2380.03i	−1.59967	−	1.17532i
$46$	737.921	+	1278.12i	0.348734	+	0.604025i
$47$	−607.404	+	1052.05i	−0.274968	+	0.476258i	−0.970127	−	0.242598i	$-0.922000\pi$
$47$	−607.404	+	1052.05i	−0.274968	+	0.476258i	0.695159	+	0.718856i	$0.255334\pi$
$48$	−2830.98			−1.22872
$49$	343.686	−	2376.27i	0.143143	−	0.989702i
$50$	1610.26	+	1481.31i	0.644104	+	0.592526i
$51$	1824.43	−	3160.01i	0.701434	−	1.21492i
$52$	364.528	+	631.380i	0.134811	+	0.233499i
$53$	1894.49	−	1093.78i	0.674436	−	0.389386i	−0.123319	−	0.992367i	$-0.539354\pi$
$53$	1894.49	−	1093.78i	0.674436	−	0.389386i	0.797755	+	0.602981i	$0.206021\pi$
$54$	−3761.34	−	2171.61i	−1.28990	−	0.744722i
$55$	2180.29	−	956.818i	0.720758	−	0.316303i
$56$	2216.91	+	2560.61i	0.706922	+	0.816522i
$57$			1577.78i			0.485620i
$58$	188.845	+	109.030i	0.0561371	+	0.0324108i
$59$	−1529.09	+	882.820i	−0.439267	+	0.253611i	−0.703287	−	0.710906i	$-0.748285\pi$
$59$	−1529.09	+	882.820i	−0.439267	+	0.253611i	0.264020	+	0.964517i	$0.414952\pi$
$60$	−1173.10	−	861.913i	−0.325862	−	0.239420i
$61$	−1334.20	−	770.300i	−0.358559	−	0.207014i	0.309889	−	0.950773i	$-0.399708\pi$
$61$	−1334.20	−	770.300i	−0.358559	−	0.207014i	−0.668449	+	0.743758i	$0.733041\pi$
$62$	5237.58			1.36253
$63$	1487.79	+	7736.82i	0.374853	+	1.94931i
$64$	−4553.40			−1.11167
$65$	534.597	−	4837.82i	0.126532	−	1.14505i
$66$	4489.83	−	2592.20i	1.03072	−	0.595088i
$67$	4141.09	−	2390.86i	0.922498	−	0.532604i	0.0380666	−	0.999275i	$-0.487880\pi$
$67$	4141.09	−	2390.86i	0.922498	−	0.532604i	0.884431	+	0.466671i	$0.154547\pi$
$68$	439.366	−	761.004i	0.0950186	−	0.164577i
$69$			6555.32i			1.37688i
$70$	−342.384	−	4274.74i	−0.0698742	−	0.872396i
$71$	−329.707			−0.0654050			−0.0327025	−	0.999465i	$-0.510411\pi$
$71$	−329.707			−0.0654050			−0.0327025	+	0.999465i	$0.510411\pi$
$72$	−9624.86	−	5556.91i	−1.85665	−	1.07194i
$73$	387.130	+	670.528i	0.0726458	+	0.125826i	0.900060	−	0.435766i	$-0.143522\pi$
$73$	387.130	+	670.528i	0.0726458	+	0.125826i	−0.827414	+	0.561592i	$0.810189\pi$
$74$	327.291	+	566.884i	0.0597682	+	0.103522i
$75$	2904.33	+	9274.32i	0.516325	+	1.64877i
$76$			379.966i			0.0657836i
$77$	−4409.46	−	1528.20i	−0.743711	−	0.257749i
$78$		−	10598.0i		−	1.74195i
$79$	2502.85	−	4335.06i	0.401033	−	0.694609i	−0.592818	−	0.805337i	$-0.701985\pi$
$79$	2502.85	−	4335.06i	0.401033	−	0.694609i	0.993851	+	0.110727i	$0.0353180\pi$
$80$	3667.96	+	2694.95i	0.573118	+	0.421087i
$81$	−3133.87	−	5428.02i	−0.477651	−	0.827316i
$82$	−691.589	+	1197.87i	−0.102854	+	0.178148i
$83$	−12492.1			−1.81335			−0.906673	−	0.421834i	$-0.861386\pi$
$83$	−12492.1			−1.81335			−0.906673	+	0.421834i	$0.861386\pi$
$84$	538.794	+	2801.84i	0.0763598	+	0.397086i
$85$	−5372.00	+	2357.49i	−0.743529	+	0.326296i
$86$	−6144.53	+	10642.6i	−0.830791	+	1.43897i
$87$	484.284	+	838.804i	0.0639825	+	0.110821i
$88$	5701.16	−	3291.57i	0.736203	−	0.425047i
$89$	4892.96	+	2824.95i	0.617720	+	0.356641i	0.775981	−	0.630756i	$-0.217255\pi$
$89$	4892.96	+	2824.95i	0.617720	+	0.356641i	−0.158261	+	0.987397i	$0.550589\pi$
$90$	5654.87	+	12885.7i	0.698132	+	1.59083i
$91$	−7212.34	+	6244.25i	−0.870951	+	0.754045i
$92$			1578.68i			0.186517i
$93$	20147.2	+	11632.0i	2.32943	+	1.34490i
$94$	3682.99	−	2126.37i	0.416816	−	0.240649i
$95$	1501.97	−	2044.25i	0.166423	−	0.226509i
$96$	−6310.10	−	3643.14i	−0.684690	−	0.395306i
$97$	−5033.05			−0.534918			−0.267459	−	0.963569i	$-0.586184\pi$
$97$	−5033.05			−0.534918			−0.267459	+	0.963569i	$0.586184\pi$
$98$	−5201.35	+	6602.68i	−0.541582	+	0.687493i
$99$	15313.4			1.56243
$100$	699.431	+	2233.47i	0.0699431	+	0.223347i
$101$	5530.54	−	3193.06i	0.542156	−	0.313014i	−0.203796	−	0.979013i	$-0.565328\pi$
$101$	5530.54	−	3193.06i	0.542156	−	0.313014i	0.745952	+	0.665999i	$0.231995\pi$
$102$	−11062.4	+	6386.89i	−1.06329	+	0.613888i
$103$	−2607.52	+	4516.36i	−0.245784	+	0.425710i	−0.962352	−	0.271807i	$-0.912379\pi$
$103$	−2607.52	+	4516.36i	−0.245784	+	0.425710i	0.716568	+	0.697517i	$0.245712\pi$
$104$		−	13457.3i		−	1.24420i
$105$	8176.63	−	17203.9i	0.741645	−	1.56045i
$106$	−7658.15			−0.681573
$107$	−14530.6	−	8389.26i	−1.26916	−	0.732750i	−0.294331	−	0.955703i	$-0.595097\pi$
$107$	−14530.6	−	8389.26i	−1.26916	−	0.732750i	−0.974829	+	0.222953i	$0.928430\pi$
$108$	−2322.92	−	4023.42i	−0.199153	−	0.344944i
$109$	−3987.93	−	6907.29i	−0.335656	−	0.581373i	0.647955	−	0.761679i	$-0.275625\pi$
$109$	−3987.93	−	6907.29i	−0.335656	−	0.581373i	−0.983611	+	0.180306i	$0.942291\pi$
$110$	−8284.89	−	915.511i	−0.684702	−	0.0756621i
$111$			2907.49i			0.235978i
$112$	−1684.66	−	8760.54i	−0.134300	−	0.698385i
$113$		−	6194.94i		−	0.485154i	−0.970132	−	0.242577i	$-0.922007\pi$
$113$		−	6194.94i		−	0.485154i	0.970132	−	0.242577i	$-0.0779928\pi$
$114$	2761.71	−	4783.42i	0.212505	−	0.368069i
$115$	6240.35	−	8493.40i	0.471860	−	0.642223i
$116$	116.627	+	202.004i	0.00866728	+	0.0150122i
$117$	15651.9	−	27109.8i	1.14339	−	1.98041i
$118$	6181.08			0.443915
$119$	10864.4	+	3765.30i	0.767206	+	0.265892i
$120$	10797.9	+	24605.0i	0.749852	+	1.70868i
$121$	2785.16	−	4824.03i	0.190230	−	0.329488i
$122$	2696.64	+	4670.71i	0.181177	+	0.313807i
$123$	−5320.63	+	3071.87i	−0.351684	+	0.203045i
$124$	4851.93	+	2801.26i	0.315552	+	0.182184i
$125$	5065.71	−	14781.0i	0.324205	−	0.945987i
$126$	9031.76	−	26060.3i	0.568894	−	1.64149i
$127$			12064.2i			0.747981i	0.927432	+	0.373991i	$0.122011\pi$
$127$			12064.2i			0.747981i	−0.927432	+	0.373991i	$0.877989\pi$
$128$	7311.85	+	4221.50i	0.446280	+	0.257660i
$129$	−47271.9	+	27292.5i	−2.84069	+	1.64007i
$130$	−10088.8	+	13731.3i	−0.596969	+	0.812502i
$131$	16541.4	+	9550.18i	0.963894	+	0.556505i	0.897369	−	0.441280i	$-0.145475\pi$
$131$	16541.4	+	9550.18i	0.963894	+	0.556505i	0.0665249	+	0.997785i	$0.478809\pi$
$132$	5545.65			0.318276
$133$	−4882.48	+	938.902i	−0.276018	+	0.0530783i
$134$	−16739.7			−0.932260
$135$	−3406.67	+	30828.6i	−0.186923	+	1.69156i
$136$	−14047.0	+	8110.05i	−0.759462	+	0.438476i
$137$	−833.531	+	481.239i	−0.0444100	+	0.0256401i	−0.522041	−	0.852921i	$-0.674829\pi$
$137$	−833.531	+	481.239i	−0.0444100	+	0.0256401i	0.477631	+	0.878561i	$0.341496\pi$
$138$	11474.3	−	19874.1i	0.602515	−	1.04359i
$139$		−	31248.3i		−	1.61732i	−0.588273	−	0.808662i	$-0.700192\pi$
$139$		−	31248.3i		−	1.61732i	0.588273	−	0.808662i	$-0.299808\pi$
$140$	1969.13	−	4143.11i	0.100466	−	0.211383i
$141$	18889.7			0.950136
$142$	999.587	+	577.112i	0.0495728	+	0.0286209i
$143$	9271.18	+	16058.2i	0.453381	+	0.785278i
$144$	14636.6	+	25351.4i	0.705856	+	1.22258i
$145$	171.039	−	1547.81i	0.00813502	−	0.0736176i
$146$		−	2710.50i		−	0.127158i
$147$	−34671.6	+	13846.8i	−1.60450	+	0.640787i
$148$			700.192i			0.0319664i
$149$	−11796.5	+	20432.2i	−0.531351	+	0.920328i	0.467979	+	0.883740i	$0.344982\pi$
$149$	−11796.5	+	20432.2i	−0.531351	+	0.920328i	−0.999330	+	0.0365881i	$0.988351\pi$
$150$	7428.39	−	33201.1i	0.330151	−	1.47560i
$151$	14204.2	+	24602.4i	0.622964	+	1.07901i	0.988931	+	0.148377i	$0.0474050\pi$
$151$	14204.2	+	24602.4i	0.622964	+	1.07901i	−0.365967	+	0.930628i	$0.619262\pi$
$152$	3506.81	−	6073.97i	0.151784	−	0.262897i
$153$	−37730.5			−1.61179
$154$	10693.4	+	12351.3i	0.450896	+	0.520801i
$155$	−15030.6	−	34250.2i	−0.625625	−	1.42561i
$156$	5668.22	−	9817.65i	0.232915	−	0.403421i
$157$	−133.458	−	231.157i	−0.00541436	−	0.00937794i	0.863306	−	0.504682i	$-0.168390\pi$
$157$	−133.458	−	231.157i	−0.00541436	−	0.00937794i	−0.868720	+	0.495304i	$0.835057\pi$
$158$	−15176.0	+	8761.86i	−0.607915	+	0.350980i
$159$	−29458.4	−	17007.8i	−1.16524	−	0.672751i
$160$	4707.59	+	10727.1i	0.183890	+	0.419029i
$161$	−20285.6	+	3900.93i	−0.782594	+	0.150493i
$162$			21941.8i			0.836071i
$163$	15750.3	+	9093.46i	0.592809	+	0.342258i	0.766207	−	0.642593i	$-0.222142\pi$
$163$	15750.3	+	9093.46i	0.592809	+	0.342258i	−0.173399	+	0.984852i	$0.555475\pi$
$164$	−1281.33	+	739.778i	−0.0476403	+	0.0275051i
$165$	−29836.0	−	21921.4i	−1.09590	−	0.805193i
$166$	37873.0	+	21866.0i	1.37440	+	0.793511i
$167$	41682.1			1.49457			0.747286	−	0.664502i	$-0.231356\pi$
$167$	41682.1			1.49457			0.747286	+	0.664502i	$0.231356\pi$
$168$	17246.0	−	49761.6i	0.611039	−	1.76310i
$169$	9343.42			0.327139
$170$	20413.0	+	2255.72i	0.706333	+	0.0780524i
$171$	14129.0	−	8157.38i	0.483191	−	0.278971i
$172$	−11384.2	+	6572.67i	−0.384809	+	0.222170i
$173$	−6070.72	+	10514.8i	−0.202837	+	0.351324i	−0.949441	−	0.313944i	$-0.898350\pi$
$173$	−6070.72	+	10514.8i	−0.202837	+	0.351324i	0.746604	+	0.665268i	$0.231683\pi$
$174$		−	3390.72i		−	0.111994i
$175$	−26971.3	+	14506.5i	−0.880697	+	0.473681i
$176$	−17339.6			−0.559777
$177$	23776.6	+	13727.4i	0.758932	+	0.438169i
$178$	−9889.48	−	17129.1i	−0.312128	−	0.540622i
$179$	−745.566	−	1291.36i	−0.0232691	−	0.0403033i	0.854156	−	0.520016i	$-0.174074\pi$
$179$	−745.566	−	1291.36i	−0.0232691	−	0.0403033i	−0.877425	+	0.479713i	$0.840741\pi$
$180$	−1653.29	+	14961.4i	−0.0510274	+	0.461771i
$181$			13647.2i			0.416568i	0.978068	+	0.208284i	$0.0667878\pi$
$181$			13647.2i			0.416568i	−0.978068	+	0.208284i	$0.933212\pi$
$182$	32795.8	−	6306.64i	0.990092	−	0.190395i
$183$			23955.6i			0.715327i
$184$	14570.0	−	25236.0i	0.430352	−	0.745392i
$185$	2767.79	−	3767.09i	0.0808704	−	0.110068i
$186$	−40720.9	−	70530.6i	−1.17704	−	2.03869i
$187$	11174.6	−	19354.9i	0.319557	−	0.553488i
$188$	4549.07			0.128709
$189$	45960.1	−	39791.0i	1.28664	−	1.11394i
$190$	−8131.79	+	3568.62i	−0.225257	+	0.0988538i
$191$	−11367.0	+	19688.1i	−0.311586	+	0.539682i	−0.978706	−	0.205268i	$-0.934193\pi$
$191$	−11367.0	+	19688.1i	−0.311586	+	0.539682i	0.667120	+	0.744950i	$0.267527\pi$
$192$	35401.6	+	61317.3i	0.960329	+	1.66334i
$193$	9645.61	−	5568.90i	0.258949	−	0.149505i	−0.364906	−	0.931044i	$-0.618899\pi$
$193$	9645.61	−	5568.90i	0.258949	−	0.149505i	0.623855	+	0.781540i	$0.285565\pi$
$194$	15258.9	+	8809.74i	0.405434	+	0.234077i
$195$	−69303.7	+	30413.8i	−1.82258	+	0.799837i
$196$	−8349.74	+	3334.63i	−0.217351	+	0.0868031i
$197$		−	24817.1i		−	0.639467i	−0.947508	−	0.319733i	$-0.896407\pi$
$197$		−	24817.1i		−	0.639467i	0.947508	−	0.319733i	$-0.103593\pi$
$198$	−46426.3	−	26804.2i	−1.18422	−	0.683712i
$199$	51236.6	−	29581.4i	1.29382	−	0.746987i	0.314491	−	0.949261i	$-0.398166\pi$
$199$	51236.6	−	29581.4i	1.29382	−	0.746987i	0.979329	+	0.202273i	$0.0648329\pi$
$200$	9432.53	−	42158.5i	0.235813	−	1.05396i
$201$	−64391.9	−	37176.7i	−1.59382	−	0.920192i
$202$	−22356.3			−0.547894
$203$	−2307.52	+	1997.78i	−0.0559954	+	0.0484793i
$204$	−13663.8			−0.328332
$205$	9817.94	+	1084.92i	0.233621	+	0.0258160i
$206$	15810.7	−	9128.31i	0.372577	−	0.215108i
$207$	58702.9	−	33892.1i	1.36999	−	0.790966i
$208$	−17722.9	+	30697.0i	−0.409646	+	0.709527i
$209$			9663.83i			0.221237i
$210$	−54902.8	+	37845.7i	−1.24496	+	0.858179i
$211$	3198.70			0.0718471			0.0359235	−	0.999355i	$-0.488563\pi$
$211$	3198.70			0.0718471			0.0359235	+	0.999355i	$0.488563\pi$
$212$	−7094.27	−	4095.88i	−0.157847	−	0.0911330i
$213$	2563.39	+	4439.92i	0.0565009	+	0.0978624i
$214$	29368.8	+	50868.2i	0.641295	+	1.11076i
$215$	87229.0	+	9639.13i	1.88705	+	0.208526i
$216$			85755.5i			1.83804i
$217$	−24006.4	+	69268.2i	−0.509809	+	1.47101i
$218$			27921.5i			0.587525i
$219$	6019.68	−	10426.4i	0.125512	−	0.217393i
$220$	−7185.21	−	5279.19i	−0.148455	−	0.109074i
$221$	−22843.1	−	39565.5i	−0.467704	−	0.810087i
$222$	5089.21	−	8814.77i	0.103263	−	0.178857i
$223$	77124.7			1.55090			0.775450	−	0.631409i	$-0.217523\pi$
$223$	77124.7			1.55090			0.775450	+	0.631409i	$0.217523\pi$
$224$	7518.79	−	21694.7i	0.149848	−	0.432373i
$225$	68035.6	−	73958.0i	1.34391	−	1.46090i
$226$	−10843.5	+	18781.5i	−0.212301	+	0.367716i
$227$	2271.76	+	3934.81i	0.0440871	+	0.0763610i	0.887227	−	0.461333i	$-0.152629\pi$
$227$	2271.76	+	3934.81i	0.0440871	+	0.0763610i	−0.843140	+	0.537694i	$0.819295\pi$
$228$	5116.73	−	2954.14i	0.0984288	−	0.0568279i
$229$	−27870.3	−	16090.9i	−0.531460	−	0.306839i	0.210151	−	0.977669i	$-0.432605\pi$
$229$	−27870.3	−	16090.9i	−0.531460	−	0.306839i	−0.741611	+	0.670830i	$0.765938\pi$
$230$	−33785.8	+	14826.9i	−0.638673	+	0.280281i
$231$	13703.4	+	71260.3i	0.256805	+	1.33544i
$232$		−	4305.52i		−	0.0799926i
$233$	−56853.7	−	32824.5i	−1.04724	−	0.604625i	−0.125365	−	0.992111i	$-0.540010\pi$
$233$	−56853.7	−	32824.5i	−1.04724	−	0.604625i	−0.921876	+	0.387486i	$0.873344\pi$
$234$	−94905.0	+	54793.4i	−1.73323	+	1.00068i
$235$	−24474.4	−	17982.0i	−0.443175	−	0.325614i
$236$	5725.96	+	3305.88i	0.102807	+	0.0593559i
$237$	−77836.0			−1.38575
$238$	−26347.4	−	30432.3i	−0.465141	−	0.537255i
$239$	−100919.			−1.76675			−0.883376	−	0.468665i	$-0.844735\pi$
$239$	−100919.			−1.76675			−0.883376	+	0.468665i	$0.844735\pi$
$240$	7773.52	−	70346.3i	0.134957	−	1.22129i
$241$	32559.4	−	18798.2i	0.560587	−	0.323655i	−0.192794	−	0.981239i	$-0.561755\pi$
$241$	32559.4	−	18798.2i	0.560587	−	0.323655i	0.753381	+	0.657584i	$0.228422\pi$
$242$	−16887.8	+	9750.16i	−0.288364	+	0.166487i
$243$	1516.21	−	2626.15i	0.0256772	−	0.0444742i
$244$			5769.07i			0.0969005i
$245$	58103.7	+	15065.1i	0.967992	+	0.250981i
$246$	21507.7			0.355406
$247$	17108.2	+	9877.44i	0.280421	+	0.161901i
$248$	−51707.2	−	89559.5i	−0.840712	−	1.45616i
$249$	97123.3	+	168222.i	1.56648	+	2.71322i
$250$	−41230.4	+	35945.5i	−0.659686	+	0.575127i
$251$		−	96648.4i		−	1.53408i	−0.641601	−	0.767039i	$-0.721729\pi$
$251$		−	96648.4i		−	1.53408i	0.641601	−	0.767039i	$-0.278271\pi$
$252$	22304.8	−	19310.9i	0.351234	−	0.304089i
$253$			40151.1i			0.627273i
$254$	21116.9	−	36575.6i	0.327313	−	0.566922i
$255$	73512.5	+	54011.8i	1.13053	+	0.830632i
$256$	21648.8	+	37496.8i	0.330334	+	0.572156i
$257$	−53064.1	+	91909.8i	−0.803406	+	1.39154i	0.113957	+	0.993486i	$0.463648\pi$
$257$	−53064.1	+	91909.8i	−0.803406	+	1.39154i	−0.917362	+	0.398054i	$0.869686\pi$
$258$	191089.			2.87075
$259$	−8997.31	+	1730.19i	−0.134126	+	0.0257925i
$260$	−16690.0	+	7324.36i	−0.246893	+	0.108349i
$261$	5007.66	−	8673.52i	0.0735112	−	0.127325i
$262$	−33432.9	−	57907.4i	−0.487047	−	0.843590i
$263$	−89505.9	+	51676.3i	−1.29402	+	0.747102i	−0.979364	−	0.202105i	$-0.935222\pi$
$263$	−89505.9	+	51676.3i	−1.29402	+	0.747102i	−0.314654	+	0.949206i	$0.601888\pi$
$264$	−88650.2	−	51182.2i	−1.27196	−	0.734364i
$265$	21977.1	+	50079.1i	0.312953	+	0.713124i
$266$	16445.9	+	5699.68i	0.232431	+	0.0805540i
$267$		−	87853.2i		−	1.23235i
$268$	−15507.1	−	8953.02i	−0.215904	−	0.124652i
$269$	−83430.8	+	48168.8i	−1.15298	+	0.665674i	−0.949612	−	0.313429i	$-0.898522\pi$
$269$	−83430.8	+	48168.8i	−1.15298	+	0.665674i	−0.203369	+	0.979102i	$0.565189\pi$
$270$	64289.9	−	87501.5i	0.881892	−	1.20030i
$271$	−47103.2	−	27195.0i	−0.641374	−	0.370298i	0.143770	−	0.989611i	$-0.454078\pi$
$271$	−47103.2	−	27195.0i	−0.641374	−	0.370298i	−0.785144	+	0.619314i	$0.787411\pi$
$272$	42722.9			0.577462
$273$	140161.	+	48575.8i	1.88062	+	0.651771i
$274$	3369.41			0.0448799
$275$	17788.9	+	56804.9i	0.235225	+	0.751139i
$276$	21258.9	−	12273.8i	0.279076	−	0.161124i
$277$	78180.1	−	45137.3i	1.01891	−	0.588269i	0.105123	−	0.994459i	$-0.466476\pi$
$277$	78180.1	−	45137.3i	1.01891	−	0.588269i	0.913789	+	0.406190i	$0.133143\pi$
$278$	−54696.4	+	94737.0i	−0.707733	+	1.22583i
$279$		−	240558.i		−	3.09037i
$280$	−69715.4	+	48056.3i	−0.889227	+	0.612962i
$281$	97744.9			1.23789			0.618944	−	0.785435i	$-0.287561\pi$
$281$	97744.9			1.23789			0.618944	+	0.785435i	$0.287561\pi$
$282$	−57268.6	−	33064.1i	−0.720143	−	0.415775i
$283$	−12293.0	−	21292.1i	−0.153492	−	0.265856i	0.779017	−	0.627003i	$-0.215719\pi$
$283$	−12293.0	−	21292.1i	−0.153492	−	0.265856i	−0.932509	+	0.361147i	$0.882385\pi$
$284$	617.324	+	1069.24i	0.00765379	+	0.0132568i
$285$	−39205.8	−	4332.39i	−0.482681	−	0.0533381i
$286$		−	64912.3i		−	0.793588i
$287$	−12672.2	−	14636.8i	−0.153846	−	0.177698i
$288$			75342.6i			0.908355i
$289$	14227.6	−	24643.0i	0.170348	−	0.295051i
$290$	−3227.80	+	4393.19i	−0.0383805	+	0.0522376i
$291$	39130.7	+	67776.3i	0.462095	+	0.800372i
$292$	1449.68	−	2510.92i	0.0170022	−	0.0294488i
$293$	−71689.1			−0.835060			−0.417530	−	0.908663i	$-0.637104\pi$
$293$	−71689.1			−0.835060			−0.417530	+	0.908663i	$0.637104\pi$
$294$	129353.	+	18708.6i	1.49651	+	0.216444i
$295$	−17738.3	−	40420.0i	−0.203830	−	0.464465i
$296$	6462.26	−	11193.0i	0.0737566	−	0.127750i
$297$	−59079.9	−	102329.i	−0.669771	−	1.16008i
$298$	71528.2	−	41296.8i	0.805461	−	0.465033i
$299$	71080.9	+	41038.6i	0.795080	+	0.459039i
$300$	24638.7	−	26783.4i	0.273763	−	0.297594i
$301$	−112588.	−	130043.i	−1.24268	−	1.43534i
$302$		−	99451.0i		−	1.09042i
$303$	−85997.1	−	49650.5i	−0.936696	−	0.540802i
$304$	−15998.5	+	9236.75i	−0.173114	+	0.0999476i
$305$	22804.5	−	31038.0i	0.245144	−	0.333653i
$306$	114389.	+	66042.6i	1.22164	+	0.705312i
$307$	−69302.3			−0.735311			−0.367656	−	0.929962i	$-0.619839\pi$
$307$	−69302.3			−0.735311			−0.367656	+	0.929962i	$0.619839\pi$
$308$	3300.10	+	17161.2i	0.0347877	+	0.180903i
$309$	81091.4			0.849293
$310$	−14381.8	+	130147.i	−0.149654	+	1.35429i
$311$	−44261.2	+	25554.2i	−0.457617	+	0.264205i	−0.711042	−	0.703150i	$-0.751776\pi$
$311$	−44261.2	+	25554.2i	−0.457617	+	0.264205i	0.253425	+	0.967355i	$0.418443\pi$
$312$	−181219.	+	104627.i	−1.86164	+	1.07482i
$313$	72869.4	−	126214.i	0.743801	−	1.28830i	−0.206952	−	0.978351i	$-0.566354\pi$
$313$	72869.4	−	126214.i	0.743801	−	1.28830i	0.950753	−	0.309950i	$-0.100312\pi$
$314$			934.412i			0.00947718i
$315$	−196335.	+	15725.4i	−1.97869	+	0.158482i
$316$	−18744.8			−0.187718
$317$	−10732.1	−	6196.18i	−0.106799	−	0.0616603i	0.445649	−	0.895208i	$-0.352973\pi$
$317$	−10732.1	−	6196.18i	−0.106799	−	0.0616603i	−0.552448	+	0.833547i	$0.686306\pi$
$318$	59540.2	+	103127.i	0.588784	+	1.01980i
$319$	2966.22	+	5137.64i	0.0291489	+	0.0504874i
$320$	12503.1	−	113146.i	0.122101	−	1.10494i
$321$			260898.i			2.53198i
$322$	68329.0	+	23680.9i	0.659012	+	0.228395i
$323$		−	23810.6i		−	0.228226i
$324$	−11735.4	+	20326.2i	−0.111791	+	0.193628i
$325$	118746.	+	26568.1i	1.12422	+	0.251532i
$326$	−31834.0	−	55138.1i	−0.299541	−	0.518820i
$327$	−62010.3	+	107405.i	−0.579920	+	1.00445i
$328$	27310.4			0.253852
$329$	11240.8	+	58454.6i	0.103850	+	0.540041i
$330$	52084.5	+	118684.i	0.478278	+	1.08985i
$331$	20740.4	−	35923.4i	0.189304	−	0.327885i	−0.755714	−	0.654902i	$-0.772710\pi$
$331$	20740.4	−	35923.4i	0.189304	−	0.327885i	0.945019	+	0.327017i	$0.106043\pi$
$332$	23389.6	+	40511.9i	0.212200	+	0.367542i
$333$	26036.6	−	15032.2i	0.234798	−	0.135561i
$334$	−126370.	−	72959.6i	−1.13279	−	0.654017i
$335$	48038.9	+	109466.i	0.428059	+	0.975415i
$336$	−104874.	+	90797.1i	−0.928944	+	0.804254i
$337$			178430.i			1.57112i	0.618786	+	0.785560i	$0.287625\pi$
$337$			178430.i			1.57112i	−0.618786	+	0.785560i	$0.712375\pi$
$338$	−28326.9	−	16354.5i	−0.247951	−	0.143154i
$339$	−83422.7	+	48164.1i	−0.725913	+	0.419106i
$340$	17703.6	+	13007.3i	0.153145	+	0.112520i
$341$	123401.	+	71245.7i	1.06123	+	0.612703i
$342$	−57114.0			−0.488304
$343$	−63481.6	−	99052.4i	−0.539584	−	0.841931i
$344$	242644.			2.05046
$345$	−162892.	−	18000.1i	−1.36855	−	0.151230i
$346$	36809.7	−	21252.1i	0.307476	−	0.177521i
$347$	127561.	−	73647.6i	1.05940	−	0.611646i	0.134135	−	0.990963i	$-0.457175\pi$
$347$	127561.	−	73647.6i	1.05940	−	0.611646i	0.925267	+	0.379318i	$0.123841\pi$
$348$	1813.49	−	3141.06i	0.0149747	−	0.0259369i
$349$			81566.9i			0.669673i	0.942276	+	0.334837i	$0.108681\pi$
$349$			81566.9i			0.669673i	−0.942276	+	0.334837i	$0.891319\pi$
$350$	107162.	+	3230.12i	0.874792	+	0.0263683i
$351$	−241543.			−1.96056
$352$	−38649.2	−	22314.1i	−0.311928	−	0.180092i
$353$	89444.2	+	154922.i	0.717799	+	1.24326i	0.961870	+	0.273507i	$0.0881835\pi$
$353$	89444.2	+	154922.i	0.717799	+	1.24326i	−0.244071	+	0.969757i	$0.578483\pi$
$354$	−48056.3	−	83236.0i	−0.383481	−	0.664209i
$355$	905.334	−	8192.80i	0.00718377	−	0.0650093i
$356$		−	21157.1i		−	0.166939i
$357$	−33763.6	−	175577.i	−0.264918	−	1.37763i
$358$			5220.09i			0.0407298i
$359$	15387.2	−	26651.3i	0.119390	−	0.206790i	−0.800136	−	0.599819i	$-0.795239\pi$
$359$	15387.2	−	26651.3i	0.119390	−	0.206790i	0.919526	+	0.393029i	$0.128573\pi$
$360$	164511.	−	223907.i	1.26938	−	1.72768i
$361$	−60012.6	−	103945.i	−0.460498	−	0.797607i
$362$	23887.8	−	41374.8i	0.182288	−	0.315732i
$363$	−86615.6			−0.657329
$364$	33754.0	+	11698.2i	0.254755	+	0.0882910i
$365$	−17724.8	+	7778.50i	−0.133044	+	0.0583862i
$366$	41931.4	−	72627.2i	0.313023	−	0.542172i
$367$	−117206.	−	203006.i	−0.870196	−	1.50722i	−0.861793	−	0.507259i	$-0.830659\pi$
$367$	−117206.	−	203006.i	−0.870196	−	1.50722i	−0.00840272	−	0.999965i	$-0.502675\pi$
$368$	−66470.4	+	38376.7i	−0.490832	+	0.283382i
$369$	55017.1	+	31764.1i	0.404059	+	0.233284i
$370$	−14985.1	+	6576.17i	−0.109460	+	0.0480363i
$371$	35101.1	−	101281.i	0.255019	−	0.735833i
$372$		−	87116.5i		−	0.629527i
$373$	156364.	+	90276.8i	1.12388	+	0.648871i	0.942388	−	0.334522i	$-0.108575\pi$
$373$	156364.	+	90276.8i	1.12388	+	0.648871i	0.181490	+	0.983393i	$0.441908\pi$
$374$	−67756.9	+	39119.5i	−0.484407	+	0.279673i
$375$	−238430.	+	46702.8i	−1.69550	+	0.332109i
$376$	−72719.4	−	41984.6i	−0.514369	−	0.296971i
$377$	12127.1			0.0853249
$378$	−208989.	+	40188.6i	−1.46264	+	0.281267i
$379$	−165867.			−1.15473			−0.577367	−	0.816485i	$-0.695920\pi$
$379$	−165867.			−1.15473			−0.577367	+	0.816485i	$0.695920\pi$
$380$	−9441.68	−	1043.34i	−0.0653856	−	0.00722535i
$381$	162460.	−	93796.1i	1.11917	−	0.646152i
$382$	68923.4	−	39793.0i	0.472324	−	0.272697i
$383$	−2588.32	+	4483.11i	−0.0176450	+	0.0305620i	−0.874713	−	0.484641i	$-0.838950\pi$
$383$	−2588.32	+	4483.11i	−0.0176450	+	0.0305620i	0.857068	+	0.515203i	$0.172284\pi$
$384$		−	131284.i		−	0.890329i
$385$	50081.6	−	105373.i	0.337875	−	0.710901i
$386$	−38990.7			−0.261690
$387$	488808.	+	282213.i	3.26375	+	1.88432i
$388$	9423.59	+	16322.1i	0.0625969	+	0.108421i
$389$	−25536.9	−	44231.3i	−0.168760	−	0.292301i	0.769224	−	0.638979i	$-0.220643\pi$
$389$	−25536.9	−	44231.3i	−0.168760	−	0.292301i	−0.937984	+	0.346678i	$0.887310\pi$
$390$	263347.	+	29100.8i	1.73141	+	0.191327i
$391$		−	98927.8i		−	0.647090i
$392$	164251.	+	23756.1i	1.06890	+	0.154598i
$393$		−	297001.i		−	1.92297i
$394$	−43439.3	+	75239.0i	−0.279827	+	0.484675i
$395$	100848.	+	74096.1i	0.646359	+	0.474899i
$396$	−28671.9	−	49661.2i	−0.182838	−	0.316685i
$397$	−53287.2	+	92296.2i	−0.338098	+	0.585602i	−0.984075	−	0.177754i	$-0.943117\pi$
$397$	−53287.2	+	92296.2i	−0.338098	+	0.585602i	0.645977	+	0.763357i	$0.276450\pi$
$398$	−207115.			−1.30751
$399$	50603.6	+	58449.0i	0.317860	+	0.367140i
$400$	−77038.0	+	83744.1i	−0.481487	+	0.523401i
$401$	−132592.	+	229656.i	−0.824573	+	1.42820i	0.0776729	+	0.996979i	$0.475251\pi$
$401$	−132592.	+	229656.i	−0.824573	+	1.42820i	−0.902246	+	0.431223i	$0.858082\pi$
$402$	130147.	+	225421.i	0.805343	+	1.39489i
$403$	252257.	−	145641.i	1.55322	−	0.896754i
$404$	−20710.1	−	11957.0i	−0.126888	−	0.0732588i
$405$	143485.	−	62968.0i	0.874774	−	0.383893i
$406$	10492.7	−	2017.75i	0.0636553	−	0.0122409i
$407$			17808.3i			0.107506i
$408$	218424.	+	126107.i	1.31214	+	0.757564i
$409$	−176854.	+	102107.i	−1.05723	+	0.610390i	−0.924664	−	0.380785i	$-0.875654\pi$
$409$	−176854.	+	102107.i	−1.05723	+	0.610390i	−0.132563	+	0.991175i	$0.542321\pi$
$410$	−27866.5	−	20474.3i	−0.165773	−	0.121798i
$411$	12961.0	+	7483.03i	0.0767281	+	0.0442990i
$412$	19528.7			0.115048
$413$	−28330.9	+	81746.1i	−0.166097	+	0.479256i
$414$	−237296.			−1.38449
$415$	34301.9	−	310414.i	0.199169	−	1.80237i
$416$	−79006.9	+	45614.6i	−0.456539	+	0.263583i
$417$	−420798.	+	242948.i	−2.41993	+	1.39714i
$418$	16915.4	−	29298.3i	0.0968120	−	0.167683i
$419$			120103.i			0.684109i	0.939680	+	0.342054i	$0.111123\pi$
$419$			120103.i			0.684109i	−0.939680	+	0.342054i	$0.888877\pi$
$420$	−71101.6	+	5694.86i	−0.403071	+	0.0322838i
$421$	219953.			1.24098			0.620492	−	0.784212i	$-0.286933\pi$
$421$	219953.			1.24098			0.620492	+	0.784212i	$0.286933\pi$
$422$	−9697.66	−	5598.94i	−0.0544555	−	0.0314399i
$423$	−97662.7	−	169157.i	−0.545818	−	0.945385i
$424$	75603.9	+	130950.i	0.420545	+	0.728405i
$425$	−43829.9	−	139961.i	−0.242657	−	0.774869i
$426$		−	17947.6i		−	0.0988979i
$427$	−74131.2	+	14255.5i	−0.406579	+	0.0781853i
$428$			62830.3i			0.342990i
$429$	144162.	−	249696.i	0.783316	−	1.35674i
$430$	−247584.	−	181907.i	−1.33902	−	0.983814i
$431$	40694.2	+	70484.5i	0.219068	+	0.379436i	0.954523	−	0.298137i	$-0.0963651\pi$
$431$	40694.2	+	70484.5i	0.219068	+	0.379436i	−0.735456	+	0.677573i	$0.763032\pi$
$432$	112938.	−	195614.i	0.605162	−	1.04817i
$433$	−296669.			−1.58233			−0.791164	−	0.611605i	$-0.790524\pi$
$433$	−296669.			−1.58233			−0.791164	+	0.611605i	$0.790524\pi$
$434$	194027.	−	167983.i	1.03011	−	0.891839i
$435$	−22173.0	+	9730.59i	−0.117178	+	0.0514234i
$436$	−14933.5	+	25865.6i	−0.0785579	+	0.136066i
$437$	21388.3	+	37045.7i	0.111999	+	0.193988i
$438$	−36500.3	+	21073.4i	−0.190260	+	0.109847i
$439$	48562.1	+	28037.3i	0.251981	+	0.145481i	0.620671	−	0.784071i	$-0.286860\pi$
$439$	48562.1	+	28037.3i	0.251981	+	0.145481i	−0.368690	+	0.929552i	$0.620194\pi$
$440$	66136.6	+	150705.i	0.341615	+	0.778434i
$441$	303256.	+	238894.i	1.55931	+	1.22837i
$442$			159937.i			0.818660i
$443$	−101750.	−	58745.2i	−0.518472	−	0.299340i	0.217837	−	0.975985i	$-0.430100\pi$
$443$	−101750.	−	58745.2i	−0.518472	−	0.299340i	−0.736309	+	0.676645i	$0.763433\pi$
$444$	9428.98	−	5443.82i	0.0478298	−	0.0276145i
$445$	−83632.0	+	113827.i	−0.422330	+	0.574811i
$446$	−233822.	−	134997.i	−1.17548	−	0.678666i
$447$	366861.			1.83606
$448$	−168682.	+	146040.i	−0.840449	+	0.727638i
$449$	−34432.0			−0.170793			−0.0853963	−	0.996347i	$-0.527216\pi$
$449$	−34432.0			−0.170793			−0.0853963	+	0.996347i	$0.527216\pi$
$450$	−335721.	+	105134.i	−1.65788	+	0.519180i
$451$	−32588.7	+	18815.1i	−0.160219	+	0.0925024i
$452$	−20090.1	+	11599.0i	−0.0983346	+	0.0567735i
$453$	220868.	−	382555.i	1.07631	−	1.86422i
$454$		−	15905.8i		−	0.0771691i
$455$	−135358.	−	196364.i	−0.653822	−	0.948502i
$456$	−109058.			−0.524480
$457$	−22887.5	−	13214.1i	−0.109589	−	0.0632710i	0.444204	−	0.895926i	$-0.353487\pi$
$457$	−22887.5	−	13214.1i	−0.109589	−	0.0632710i	−0.553792	+	0.832655i	$0.686820\pi$
$458$	56330.5	+	97567.2i	0.268542	+	0.465129i
$459$	145566.	+	252128.i	0.690931	+	1.19673i
$460$	−39228.1	−	4334.85i	−0.185388	−	0.0204861i
$461$		−	104131.i		−	0.489978i	−0.969526	−	0.244989i	$-0.921216\pi$
$461$		−	104131.i		−	0.489978i	0.969526	−	0.244989i	$-0.0787844\pi$
$462$	83187.4	−	240029.i	0.389739	−	1.12455i
$463$			126336.i			0.589337i	0.955600	+	0.294668i	$0.0952092\pi$
$463$			126336.i			0.589337i	−0.955600	+	0.294668i	$0.904791\pi$
$464$	−5670.27	+	9821.19i	−0.0263371	+	0.0456171i
$465$	−344363.	+	468694.i	−1.59261	+	2.16762i
$466$	114911.	+	199031.i	0.529161	+	0.916534i
$467$	25586.7	−	44317.5i	0.117322	−	0.203208i	−0.801383	−	0.598151i	$-0.795902\pi$
$467$	25586.7	−	44317.5i	0.117322	−	0.203208i	0.918706	+	0.394943i	$0.129236\pi$
$468$	−117223.			−0.535205
$469$	76726.1	−	221386.i	0.348817	−	1.00648i
$470$	42724.7	+	97356.4i	0.193412	+	0.440726i
$471$	−2075.21	+	3594.37i	−0.00935451	+	0.0162025i
$472$	−61021.7	−	105693.i	−0.273905	−	0.474418i
$473$	−289539.	+	167165.i	−1.29415	+	0.747178i
$474$	235979.	+	136243.i	1.05031	+	0.606396i
$475$	46672.8	+	42935.3i	0.206860	+	0.190295i
$476$	−8131.06	−	42283.2i	−0.0358867	−	0.186618i
$477$			351733.i			1.54588i
$478$	305960.	+	176646.i	1.33909	+	0.773121i
$479$	239065.	−	138024.i	1.04195	−	0.601568i	0.121562	−	0.992584i	$-0.461210\pi$
$479$	239065.	−	138024.i	1.04195	−	0.601568i	0.920384	+	0.391016i	$0.127876\pi$
$480$	107854.	−	146795.i	0.468117	−	0.637129i
$481$	31526.6	+	18201.9i	0.136266	+	0.0786731i
$482$	−131616.			−0.566519
$483$	210247.	+	242843.i	0.901229	+	1.04095i
$484$	−20859.1			−0.0890439
$485$	13820.1	−	125065.i	0.0587528	−	0.531682i
$486$	−9193.53	+	5307.89i	−0.0389233	+	0.0224724i
$487$	312155.	−	180223.i	1.31617	−	0.759891i	0.333060	−	0.942906i	$-0.391919\pi$
$487$	312155.	−	180223.i	1.31617	−	0.759891i	0.983110	+	0.183015i	$0.0585856\pi$
$488$	53244.2	−	92221.7i	0.223580	−	0.387252i
$489$		−	282798.i		−	1.18265i
$490$	−149786.	−	147377.i	−0.623848	−	0.613816i
$491$	203453.			0.843919			0.421960	−	0.906615i	$-0.361342\pi$
$491$	203453.			0.843919			0.421960	+	0.906615i	$0.361342\pi$
$492$	19924.1	+	11503.2i	0.0823092	+	0.0475212i
$493$	−7308.43	−	12658.6i	−0.0300698	−	0.0520824i
$494$	−34578.5	−	59891.8i	−0.141694	−	0.245422i
$495$	−42048.7	+	380519.i	−0.171610	+	1.55298i
$496$			272388.i			1.10720i
$497$	−12214.0	+	10574.6i	−0.0494477	+	0.0428105i
$498$		−	680011.i		−	2.74193i
$499$	−165969.	+	287467.i	−0.666541	+	1.15448i	0.312325	+	0.949975i	$0.398892\pi$
$499$	−165969.	+	287467.i	−0.666541	+	1.15448i	−0.978865	+	0.204507i	$0.934441\pi$
$500$	−57419.6	+	11247.1i	−0.229678	+	0.0449885i
$501$	−324068.	−	561303.i	−1.29110	−	2.23626i
$502$	−169171.	+	293013.i	−0.671304	+	1.16273i
$503$	−16418.1			−0.0648913			−0.0324457	−	0.999474i	$-0.510330\pi$
$503$	−16418.1			−0.0648913			−0.0324457	+	0.999474i	$0.510330\pi$
$504$	−534779.	+	102838.i	−2.10530	+	0.404849i
$505$	64157.3	+	146195.i	0.251573	+	0.573256i
$506$	70279.7	−	121728.i	0.274491	−	0.475433i
$507$	−72642.8	−	125821.i	−0.282603	−	0.489482i
$508$	39124.1	−	22588.3i	0.151606	−	0.0875299i
$509$	−324430.	−	187310.i	−1.25224	−	0.722978i	−0.280682	−	0.959801i	$-0.590561\pi$
$509$	−324430.	−	187310.i	−1.25224	−	0.722978i	−0.971553	+	0.236822i	$0.923894\pi$
$510$	−128330.	−	292425.i	−0.493388	−	1.12428i
$511$	35846.9	+	12423.5i	0.137281	+	0.0475777i
$512$		−	286662.i		−	1.09353i
$513$	−109021.	−	62943.2i	−0.414261	−	0.239174i
$514$	321754.	−	185765.i	1.21786	−	0.703132i
$515$	−105066.	−	77195.0i	−0.396139	−	0.291055i
$516$	177019.	+	102202.i	0.664844	+	0.383848i
$517$	115698.			0.432859
$518$	30306.0	+	10503.2i	0.112946	+	0.0391438i
$519$	188793.			0.700893
$520$	334397.	+	36952.1i	1.23667	+	0.136657i
$521$	46755.3	−	26994.2i	0.172248	−	0.0994476i	−0.411397	−	0.911456i	$-0.634959\pi$
$521$	46755.3	−	26994.2i	0.172248	−	0.0994476i	0.583646	+	0.812009i	$0.301626\pi$
$522$	−30363.9	+	17530.6i	−0.111434	+	0.0643363i
$523$	−109296.	+	189307.i	−0.399578	+	0.692090i	−0.993674	−	0.112305i	$-0.964177\pi$
$523$	−109296.	+	189307.i	−0.399578	+	0.692090i	0.594096	+	0.804394i	$0.297510\pi$
$524$		−	71524.8i		−	0.260492i
$525$	405044.	+	250419.i	1.46955	+	0.908549i
$526$	361812.			1.30771
$527$	−304046.	−	175541.i	−1.09476	−	0.632059i
$528$	134811.	+	233500.i	0.483569	+	0.837567i
$529$	−51056.7	−	88432.8i	−0.182449	−	0.316011i
$530$	21028.4	−	190295.i	0.0748606	−	0.677449i
$531$		−	283892.i		−	1.00685i
$532$	12186.5	+	14075.9i	0.0430583	+	0.0497340i
$533$			76923.8i			0.270774i
$534$	−153776.	+	266349.i	−0.539271	+	0.934045i
$535$	248362.	−	338032.i	0.867715	−	1.18100i
$536$	165260.	+	286238.i	0.575224	+	0.996317i
$537$	−11593.2	+	20080.0i	−0.0402026	+	0.0696330i
$538$	337255.			1.16518
$539$	−212362.	+	84811.0i	−0.730971	+	0.291927i
$540$	106355.	−	46673.9i	0.364731	−	0.160061i
$541$	−202993.	+	351594.i	−0.693564	+	1.20129i	0.277098	+	0.960842i	$0.410627\pi$
$541$	−202993.	+	351594.i	−0.693564	+	1.20129i	−0.970662	+	0.240447i	$0.922706\pi$
$542$	95203.2	+	164897.i	0.324081	+	0.561324i
$543$	183777.	−	106103.i	0.623291	−	0.359857i
$544$	95227.1	+	54979.4i	0.321783	+	0.185781i
$545$	182588.	−	80128.4i	0.614722	−	0.269770i
$546$	−339906.	−	392604.i	−1.14018	−	1.31695i
$547$			119849.i			0.400554i	0.979739	+	0.200277i	$0.0641842\pi$
$547$			119849.i			0.400554i	−0.979739	+	0.200277i	$0.935816\pi$
$548$	3121.31	+	1802.09i	0.0103938	+	0.00600089i
$549$	214522.	−	123854.i	0.711750	−	0.410929i
$550$	45498.6	−	203355.i	0.150409	−	0.672249i
$551$	5473.60	+	3160.19i	0.0180289	+	0.0104090i
$552$	−453113.			−1.48706
$553$	−46318.6	−	240866.i	−0.151462	−	0.787635i
$554$	−316030.			−1.02969
$555$	−72247.5	−	7983.62i	−0.234551	−	0.0259187i
$556$	−101338.	+	58507.6i	−0.327811	+	0.189262i
$557$	115141.	−	66476.8i	0.371125	−	0.214269i	−0.302825	−	0.953046i	$-0.597930\pi$
$557$	115141.	−	66476.8i	0.371125	−	0.214269i	0.673950	+	0.738777i	$0.264596\pi$
$558$	−421068.	+	729310.i	−1.35233	+	2.34231i
$559$			683441.i			2.18715i
$560$	222314.	−	17806.2i	0.708911	−	0.0567799i
$561$	−347518.			−1.10421
$562$	−296338.	−	171091.i	−0.938241	−	0.541693i
$563$	−92431.4	−	160096.i	−0.291610	−	0.505084i	0.682580	−	0.730810i	$-0.260858\pi$
$563$	−92431.4	−	160096.i	−0.291610	−	0.505084i	−0.974191	+	0.225727i	$0.927524\pi$
$564$	−35367.9	−	61259.0i	−0.111186	−	0.192580i
$565$	153936.	+	17010.5i	0.482219	+	0.0532870i
$566$			86069.8i			0.268669i
$567$	−290186.	−	100570.i	−0.902631	−	0.312826i
$568$		−	22789.8i		−	0.0706388i
$569$	53457.9	−	92591.8i	0.165115	−	0.285988i	−0.771581	−	0.636131i	$-0.780534\pi$
$569$	53457.9	−	92591.8i	0.165115	−	0.285988i	0.936696	+	0.350143i	$0.113867\pi$
$570$	111279.	+	81759.7i	0.342501	+	0.251646i
$571$	43978.7	+	76173.4i	0.134887	+	0.233631i	0.925554	−	0.378615i	$-0.123599\pi$
$571$	43978.7	+	76173.4i	0.134887	+	0.233631i	−0.790667	+	0.612246i	$0.790266\pi$
$572$	34717.7	−	60132.8i	0.106111	−	0.183789i
$573$	353501.			1.07667
$574$	12798.8	+	66556.3i	0.0388459	+	0.202006i
$575$	193915.	+	178387.i	0.586511	+	0.539544i
$576$	366064.	−	634042.i	1.10335	−	1.91105i
$577$	−52122.4	−	90278.6i	−0.156557	−	0.271165i	0.777068	−	0.629417i	$-0.216706\pi$
$577$	−52122.4	−	90278.6i	−0.156557	−	0.271165i	−0.933625	+	0.358252i	$0.883373\pi$
$578$	−86269.0	+	49807.5i	−0.258226	+	0.149087i
$579$	−149984.	−	86593.6i	−0.447393	−	0.258302i
$580$	−5339.78	+	2343.36i	−0.0158733	+	0.00696598i
$581$	−462773.	+	400656.i	−1.37093	+	1.18692i
$582$		−	273974.i		−	0.808842i
$583$	−180432.	−	104172.i	−0.530854	−	0.306489i
$584$	−46347.8	+	26758.9i	−0.135895	+	0.0784591i
$585$	630667.	+	463370.i	1.84284	+	1.35399i
$586$	217343.	+	125483.i	0.632922	+	0.365418i
$587$	90836.0			0.263622			0.131811	−	0.991275i	$-0.457921\pi$
$587$	90836.0			0.263622			0.131811	+	0.991275i	$0.457921\pi$
$588$	109822.	+	86514.0i	0.317640	+	0.250225i
$589$	151809.			0.437590
$590$	−16972.5	+	153592.i	−0.0487575	+	0.441230i
$591$	−334193.	+	192947.i	−0.956803	+	0.552411i
$592$	−29481.7	+	17021.3i	−0.0841219	+	0.0485678i
$593$	172701.	−	299126.i	0.491116	−	0.850639i	−0.508831	−	0.860866i	$-0.669922\pi$
$593$	172701.	−	299126.i	0.491116	−	0.850639i	0.999948	+	0.0102276i	$0.00325561\pi$
$594$			413649.i			1.17235i
$595$	−123395.	+	259628.i	−0.348550	+	0.733360i
$596$	88348.7			0.248718
$597$	−796703.	−	459977.i	−2.23536	−	1.29059i
$598$	−143666.	−	248837.i	−0.401747	−	0.695846i
$599$	−210132.	−	363960.i	−0.585651	−	1.01438i	−0.994794	−	0.101907i	$-0.967506\pi$
$599$	−210132.	−	363960.i	−0.585651	−	1.01438i	0.409143	−	0.912470i	$-0.365828\pi$
$600$	−641054.	+	200751.i	−1.78070	+	0.557642i
$601$			6051.66i			0.0167543i	0.999965	+	0.00837713i	$0.00266655\pi$
$601$			6051.66i			0.0167543i	−0.999965	+	0.00837713i	$0.997333\pi$
$602$	113713.	+	591329.i	0.313774	+	1.63169i
$603$			768839.i			2.11447i
$604$	53190.3	−	92128.3i	0.145800	−	0.252534i
$605$	112223.	+	82453.8i	0.306601	+	0.225268i
$606$	173814.	+	301055.i	0.473304	+	0.819787i
$607$	−2519.33	+	4363.60i	−0.00683765	+	0.0118432i	−0.869424	−	0.494067i	$-0.835510\pi$
$607$	−2519.33	+	4363.60i	−0.00683765	+	0.0118432i	0.862586	+	0.505910i	$0.168843\pi$
$608$	−47546.5			−0.128621
$609$	44843.1	+	15541.3i	0.120910	+	0.0419039i
$610$	−123466.	+	54182.8i	−0.331808	+	0.145614i
$611$	118256.	−	204825.i	0.316767	−	0.548656i
$612$	70644.4	+	122360.i	0.188614	+	0.326690i
$613$	274927.	−	158729.i	0.731637	−	0.422411i	−0.0873834	−	0.996175i	$-0.527851\pi$
$613$	274927.	−	158729.i	0.731637	−	0.422411i	0.819021	+	0.573764i	$0.194517\pi$
$614$	210107.	+	121305.i	0.557319	+	0.321768i
$615$	−61722.2	−	140646.i	−0.163189	−	0.371858i
$616$	105631.	−	304788.i	0.278375	−	0.803224i
$617$		−	526834.i		−	1.38390i	−0.721947	−	0.691948i	$-0.756753\pi$
$617$		−	526834.i		−	1.38390i	0.721947	−	0.691948i	$-0.243247\pi$
$618$	−245848.	−	141941.i	−0.643710	−	0.371646i
$619$	−67509.0	+	38976.3i	−0.176190	+	0.101723i	−0.585501	−	0.810672i	$-0.699102\pi$
$619$	−67509.0	+	38976.3i	−0.176190	+	0.101723i	0.409312	+	0.912395i	$0.365769\pi$
$620$	−82930.7	+	112872.i	−0.215741	+	0.293633i
$621$	−452957.	−	261515.i	−1.17456	−	0.678131i
$622$	178918.			0.462460
$623$	271864.	−	52279.6i	0.700448	−	0.134696i
$624$	551165.			1.41551
$625$	353381.	+	166463.i	0.904654	+	0.426146i
$626$	−441843.	+	255098.i	−1.12751	+	0.650967i
$627$	130136.	−	75133.9i	0.331026	−	0.191118i
$628$	−499.760	+	865.610i	−0.00126719	+	0.00219484i
$629$		−	43877.6i		−	0.110902i
$630$	622765.	+	295986.i	1.56907	+	0.745745i
$631$	−607987.			−1.52699			−0.763494	−	0.645815i	$-0.776518\pi$
$631$	−607987.			−1.52699			−0.763494	+	0.645815i	$0.776518\pi$
$632$	299645.	+	173000.i	0.750193	+	0.433124i
$633$	−24869.1	−	43074.6i	−0.0620659	−	0.107501i
$634$	21691.3	+	37570.5i	0.0539644	+	0.0934691i
$635$	−299780.	−	33126.8i	−0.743456	−	0.0821546i
$636$			127378.i			0.314905i
$637$	−66912.5	+	462638.i	−0.164903	+	1.14015i
$638$		−	20768.0i		−	0.0510216i
$639$	26506.3	−	45910.2i	0.0649153	−	0.112437i
$640$	−124976.	+	170098.i	−0.305118	+	0.415279i
$641$	105614.	+	182928.i	0.257042	+	0.445210i	0.965448	−	0.260595i	$-0.0839188\pi$
$641$	105614.	+	182928.i	0.257042	+	0.445210i	−0.708406	+	0.705805i	$0.750585\pi$
$642$	456670.	−	790975.i	1.10798	−	1.91908i
$643$	−197749.			−0.478291			−0.239145	−	0.970984i	$-0.576867\pi$
$643$	−197749.			−0.478291			−0.239145	+	0.970984i	$0.576867\pi$
$644$	50632.4	+	58482.3i	0.122083	+	0.141011i
$645$	−548381.	−	1.24959e6i	−1.31814	−	3.00364i
$646$	−41677.6	+	72187.7i	−0.0998705	+	0.172981i
$647$	447.688	+	775.418i	0.00106946	+	0.00185237i	0.866560	−	0.499074i	$-0.166326\pi$
$647$	447.688	+	775.418i	0.00106946	+	0.00185237i	−0.865490	+	0.500926i	$0.832993\pi$
$648$	375192.	−	216617.i	0.893519	−	0.515874i
$649$	145631.	+	84079.9i	0.345751	+	0.199619i
$650$	−313503.	−	288398.i	−0.742018	−	0.682599i
$651$	1.11943e6	−	215266.i	2.64140	−	0.507942i
$652$		−	68104.3i		−	0.160206i
$653$	171343.	+	98924.8i	0.401827	+	0.231995i	0.687272	−	0.726400i	$-0.258808\pi$
$653$	171343.	+	98924.8i	0.401827	+	0.231995i	−0.285445	+	0.958395i	$0.592141\pi$
$654$	375999.	−	217083.i	0.879085	−	0.507540i
$655$	−282731.	+	384809.i	−0.659007	+	0.896939i
$656$	−62296.9	−	35967.1i	−0.144763	−	0.0835792i
$657$	−124491.			−0.288408
$658$	68238.3	−	196895.i	0.157607	−	0.454761i
$659$	656212.			1.51103			0.755515	−	0.655131i	$-0.227386\pi$
$659$	656212.			1.51103			0.755515	+	0.655131i	$0.227386\pi$
$660$	−15227.7	+	137802.i	−0.0349579	+	0.316351i
$661$	528853.	−	305334.i	1.21041	−	0.698830i	0.247561	−	0.968872i	$-0.420371\pi$
$661$	528853.	−	305334.i	1.21041	−	0.698830i	0.962848	+	0.270042i	$0.0870377\pi$
$662$	−125759.	+	72607.1i	−0.286961	+	0.165677i
$663$	−355199.	+	615224.i	−0.808063	+	1.39961i
$664$		−	863474.i		−	1.95845i
$665$	−9923.85	−	123902.i	−0.0224407	−	0.280178i
$666$	−105248.			−0.237283
$667$	22741.6	+	13129.9i	0.0511175	+	0.0295127i
$668$	−78043.3	−	135175.i	−0.174897	−	0.302931i
$669$	−599625.	−	1.03858e6i	−1.33976	−	2.32054i
$670$	45965.1	−	415959.i	0.102395	−	0.926619i
$671$			146727.i			0.325886i
$672$	−350604.	+	67421.3i	−0.776387	+	0.149299i
$673$			529223.i			1.16845i	0.811593	+	0.584223i	$0.198601\pi$
$673$			529223.i			1.16845i	−0.811593	+	0.584223i	$0.801399\pi$
$674$	312321.	−	540956.i	0.687514	−	1.19081i
$675$	−756698.	−	169303.i	−1.66079	−	0.371584i
$676$	−17494.1	−	30300.7i	−0.0382823	−	0.0663069i
$677$	−296942.	+	514318.i	−0.647879	+	1.12216i	0.335749	+	0.941951i	$0.391011\pi$
$677$	−296942.	+	514318.i	−0.647879	+	1.12216i	−0.983628	+	0.180209i	$0.942323\pi$
$678$	337222.			0.733595
$679$	−186450.	+	161423.i	−0.404411	+	0.350128i
$680$	−162953.	−	371320.i	−0.352407	−	0.803027i
$681$	35324.8	−	61184.3i	0.0761702	−	0.131931i
$682$	−249414.	−	431998.i	−0.536231	−	0.928779i
$683$	−390870.	+	225669.i	−0.837897	+	0.483760i	−0.856549	−	0.516066i	$-0.827396\pi$
$683$	−390870.	+	225669.i	−0.837897	+	0.483760i	0.0186520	+	0.999826i	$0.494063\pi$
$684$	−52908.7	−	30546.8i	−0.113087	−	0.0652911i
$685$	−9669.42	−	22033.6i	−0.0206072	−	0.0469575i
$686$	19080.7	+	411419.i	0.0405459	+	0.874250i
$687$			500412.i			1.06026i
$688$	−553486.	−	319556.i	−1.16931	−	0.675102i
$689$	−368839.	+	212950.i	−0.776960	+	0.448578i
$690$	462339.	+	339694.i	0.971096	+	0.713493i
$691$	−428518.	−	247405.i	−0.897455	−	0.518146i	−0.0210812	−	0.999778i	$-0.506711\pi$
$691$	−428518.	−	247405.i	−0.897455	−	0.518146i	−0.876374	+	0.481632i	$0.840044\pi$
$692$	45465.9			0.0949453
$693$	567287.	−	491141.i	1.18123	−	1.02268i
$694$	−515645.			−1.07061
$695$	776482.	+	85804.1i	1.60754	+	0.177639i
$696$	−57979.3	+	33474.4i	−0.119689	+	0.0691025i
$697$	80294.8	−	46358.2i	0.165281	−	0.0954248i
$698$	142773.	−	247290.i	0.293046	−	0.507570i
$699$			1.02081e6i			2.08925i
$700$	97544.0	+	60306.8i	0.199069	+	0.123075i
$701$	151008.			0.307301			0.153650	−	0.988125i	$-0.450897\pi$
$701$	151008.			0.307301			0.153650	+	0.988125i	$0.450897\pi$
$702$	732297.	+	422792.i	1.48598	+	0.857931i
$703$	9486.39	+	16430.9i	0.0191951	+	0.0332469i
$704$	216833.	+	375567.i	0.437503	+	0.757777i
$705$	−51868.7	+	469384.i	−0.104358	+	0.944387i
$706$		−	626245.i		−	1.25642i
$707$	102470.	−	295666.i	0.205001	−	0.591512i
$708$		−	102810.i		−	0.205101i
$709$	171500.	−	297047.i	0.341171	−	0.590925i	−0.643480	−	0.765463i	$-0.722510\pi$
$709$	171500.	−	297047.i	0.341171	−	0.590925i	0.984650	+	0.174538i	$0.0558432\pi$
$710$	−17085.2	+	23253.8i	−0.0338926	+	0.0461293i
$711$	402425.	+	697021.i	0.796061	+	1.37882i
$712$	−195265.	+	338208.i	−0.385180	+	0.667151i
$713$	630733.			1.24070
$714$	−204964.	+	591405.i	−0.402052	+	1.16008i
$715$	−424483.	+	186283.i	−0.830324	+	0.364386i
$716$	−2791.91	+	4835.73i	−0.00544598	+	0.00943271i
$717$	784617.	+	1.35900e6i	1.52623	+	2.64351i
$718$	−93299.9	+	53866.7i	−0.180981	+	0.104489i
$719$	263267.	+	151997.i	0.509259	+	0.294021i	0.732529	−	0.680736i	$-0.238340\pi$
$719$	263267.	+	151997.i	0.509259	+	0.294021i	−0.223270	+	0.974757i	$0.571673\pi$
$720$	−670141.	+	294090.i	−1.29271	+	0.567304i
$721$	48255.7	+	250939.i	0.0928279	+	0.482724i
$722$			420179.i			0.806047i
$723$	−506283.	−	292303.i	−0.968538	−	0.559186i
$724$	44257.7	−	25552.2i	0.0844330	−	0.0487474i
$725$	37991.5	+	8500.20i	0.0722787	+	0.0161716i
$726$	262597.	+	151610.i	0.498214	+	0.287644i
$727$	745592.			1.41069			0.705346	−	0.708863i	$-0.250791\pi$
$727$	745592.			1.41069			0.705346	+	0.708863i	$0.250791\pi$
$728$	−431611.	−	498527.i	−0.814385	−	0.940646i
$729$	−554839.			−1.04403
$730$	67352.4	+	7442.69i	0.126388	+	0.0139664i
$731$	713391.	−	411877.i	1.33504	−	0.770783i
$732$	77687.8	−	44853.1i	0.144988	−	0.0837086i
$733$	−233073.	+	403695.i	−0.433795	+	0.751356i	−0.997196	−	0.0748280i	$-0.976159\pi$
$733$	−233073.	+	403695.i	−0.433795	+	0.751356i	0.563401	+	0.826183i	$0.309493\pi$
$734$			820619.i			1.52317i
$735$	−248871.	−	899568.i	−0.460680	−	1.66517i
$736$	−197545.			−0.364679
$737$	−394398.	−	227706.i	−0.726106	−	0.419217i
$738$	−111199.	−	192602.i	−0.204167	−	0.353628i
$739$	−217896.	−	377407.i	−0.398988	−	0.691068i	0.594613	−	0.804012i	$-0.297305\pi$
$739$	−217896.	−	377407.i	−0.398988	−	0.691068i	−0.993601	+	0.112944i	$0.963972\pi$
$740$	−17398.9	−	1922.64i	−0.0317730	−	0.00351104i
$741$		−	307179.i		−	0.559441i
$742$	−283697.	+	245617.i	−0.515285	+	0.446120i
$743$		−	190248.i		−	0.344621i	−0.985043	−	0.172311i	$-0.944877\pi$
$743$		−	190248.i		−	0.344621i	0.985043	−	0.172311i	$-0.0551233\pi$
$744$	−804021.	+	1.39261e6i	−1.45252	+	2.51583i
$745$	−475323.	−	349233.i	−0.856399	−	0.629221i
$746$	−316037.	−	547393.i	−0.567885	−	0.983606i
$747$	1.00429e6	−	1.73948e6i	1.79977	−	3.11729i
$748$	−83690.6			−0.149580
$749$	−807355.	+	155255.i	−1.43913	+	0.276746i
$750$	804607.	+	275752.i	1.43041	+	0.490226i
$751$	−422514.	+	731817.i	−0.749138	+	1.29754i	0.199099	+	0.979979i	$0.436199\pi$
$751$	−422514.	+	731817.i	−0.749138	+	1.29754i	−0.948236	+	0.317565i	$0.897135\pi$
$752$	110585.	+	191539.i	0.195552	+	0.338706i
$753$	−1.30149e6	+	751417.i	−2.29537	+	1.32523i
$754$	−36766.4	−	21227.1i	−0.0646708	−	0.0373377i
$755$	−650342.	+	285401.i	−1.14090	+	0.500682i
$756$	−215095.	−	74545.9i	−0.376345	−	0.130431i
$757$		−	1.02470e6i		−	1.78815i	−0.447917	−	0.894075i	$-0.647834\pi$
$757$		−	1.02470e6i		−	1.78815i	0.447917	−	0.894075i	$-0.352166\pi$
$758$	502867.	+	290330.i	0.875215	+	0.505306i
$759$	540686.	−	312165.i	0.938558	−	0.541877i
$760$	141301.	+	103818.i	0.244635	+	0.179741i
$761$	538597.	+	310959.i	0.930026	+	0.536951i	0.886820	−	0.462116i	$-0.152909\pi$
$761$	538597.	+	310959.i	0.930026	+	0.536951i	0.0432061	+	0.999066i	$0.486243\pi$
$762$	−656715.			−1.13101
$763$	−369269.	−	127978.i	−0.634298	−	0.219830i
$764$	85131.4			0.145849
$765$	103603.	−	937555.i	0.177031	−	1.60204i
$766$	15694.3	−	9061.09i	0.0267475	−	0.0154427i
$767$	297699.	−	171877.i	0.506042	−	0.292164i
$768$	336628.	−	583057.i	0.570726	−	0.988527i
$769$		−	117784.i		−	0.199174i	−0.995029	−	0.0995871i	$-0.968248\pi$
$769$		−	117784.i		−	0.199174i	0.995029	−	0.0995871i	$-0.0317522\pi$
$770$	−336278.	+	231803.i	−0.567175	+	0.390965i
$771$	1.65024e6			2.77612
$772$	−36119.8	−	20853.8i	−0.0606053	−	0.0349905i
$773$	115668.	+	200344.i	0.193578	+	0.335287i	0.946433	−	0.322899i	$-0.104657\pi$
$773$	115668.	+	200344.i	0.193578	+	0.335287i	−0.752855	+	0.658186i	$0.771324\pi$
$774$	−987961.	−	1.71120e6i	−1.64914	−	2.85640i
$775$	892347.	−	279446.i	1.48570	−	0.465258i
$776$		−	347891.i		−	0.577723i
$777$	93251.0	+	107708.i	0.154458	+	0.178405i
$778$			178797.i			0.295394i
$779$	−20045.4	+	34719.7i	−0.0330324	+	0.0572138i
$780$	228392.	+	167806.i	0.375398	+	0.275816i
$781$	15700.7	+	27194.3i	0.0257404	+	0.0445837i
$782$	−173161.	+	299924.i	−0.283163	+	0.490453i
$783$	−77279.2			−0.126049
$784$	−343382.	−	270504.i	−0.558658	−	0.440091i
$785$	6110.42	−	2681.55i	0.00991589	−	0.00435157i
$786$	−519864.	+	900432.i	−0.841482	+	1.45749i
$787$	160277.	+	277608.i	0.258775	+	0.448211i	0.965914	−	0.258863i	$-0.0833479\pi$
$787$	160277.	+	277608.i	0.258775	+	0.448211i	−0.707139	+	0.707074i	$0.750015\pi$
$788$	−80481.6	+	46466.1i	−0.129612	+	0.0748313i
$789$	1.39177e6	+	803540.i	2.23570	+	1.29078i
$790$	−176050.	−	401163.i	−0.282086	−	0.642787i
$791$	−198688.	−	229492.i	−0.317555	−	0.366788i
$792$			1.05848e6i			1.68746i
$793$	259756.	+	149970.i	0.413066	+	0.238484i
$794$	323107.	−	186546.i	0.512513	−	0.295900i
$795$	503512.	−	685303.i	0.796664	−	1.08430i
$796$	−191865.	−	110773.i	−0.302809	−	0.174827i
$797$	−570129.			−0.897546			−0.448773	−	0.893646i	$-0.648139\pi$
$797$	−570129.			−0.897546			−0.448773	+	0.893646i	$0.648139\pi$
$798$	−51109.2	−	265778.i	−0.0802589	−	0.417362i
$799$	−285068.			−0.446534
$800$	−279483.	+	87522.2i	−0.436691	+	0.136754i
$801$	−786725.	+	454216.i	−1.22619	+	0.707941i
$802$	803971.	−	464173.i	1.24995	−	0.721657i
$803$	36870.3	−	63861.2i	0.0571802	−	0.0990390i
$804$			278430.i			0.430729i
$805$	−41231.4	−	514784.i	−0.0636263	−	0.794389i
$806$	−1.01971e6			−1.56966
$807$	1.29731e6	+	749001.i	1.99203	+	1.15010i
$808$	220709.	+	382278.i	0.338062	+	0.585541i
$809$	511147.	+	885333.i	0.780997	+	1.35273i	0.931362	+	0.364095i	$0.118622\pi$
$809$	511147.	+	885333.i	0.780997	+	1.35273i	−0.150365	+	0.988631i	$0.548045\pi$
$810$	−545227.	−	60249.6i	−0.831012	−	0.0918300i
$811$			86272.7i			0.131169i	0.997847	+	0.0655845i	$0.0208912\pi$
$811$			86272.7i			0.131169i	−0.997847	+	0.0655845i	$0.979109\pi$
$812$	10799.3	+	3742.72i	0.0163788	+	0.00567643i
$813$			845738.i			1.27954i
$814$	31171.2	−	53990.2i	0.0470441	−	0.0814828i
$815$	−269210.	+	366407.i	−0.405299	+	0.551630i
$816$	−332160.	−	575318.i	−0.498847	−	0.864028i
$817$	−178097.	+	308472.i	−0.266816	+	0.462139i
$818$	714901.			1.06841
$819$	−289659.	−	1.50629e6i	−0.431836	−	2.24564i
$820$	−14864.2	−	33870.9i	−0.0221061	−	0.0503731i
$821$	383079.	−	663512.i	0.568331	−	0.984379i	−0.428400	−	0.903589i	$-0.640922\pi$
$821$	383079.	−	663512.i	0.568331	−	0.984379i	0.996731	−	0.0807896i	$-0.0257442\pi$
$822$	−26196.3	−	45373.3i	−0.0387700	−	0.0671517i
$823$	792924.	−	457795.i	1.17066	−	0.675883i	0.216827	−	0.976210i	$-0.430429\pi$
$823$	792924.	−	457795.i	1.17066	−	0.675883i	0.953836	+	0.300327i	$0.0970959\pi$
$824$	−312177.	−	180236.i	−0.459776	−	0.265452i
$825$	626645.	−	681194.i	0.920691	−	1.00084i
$826$	228979.	−	198244.i	0.335610	−	0.290562i
$827$			792892.i			1.15932i	0.814859	+	0.579659i	$0.196814\pi$
$827$			792892.i			1.15932i	−0.814859	+	0.579659i	$0.803186\pi$
$828$	−219824.	−	126915.i	−0.320637	−	0.185120i
$829$	921879.	−	532247.i	1.34142	−	0.774469i	0.354404	−	0.935092i	$-0.384684\pi$
$829$	921879.	−	532247.i	1.34142	−	0.774469i	0.987016	+	0.160623i	$0.0513505\pi$
$830$	−647337.	+	881055.i	−0.939668	+	1.27893i
$831$	−1.21566e6	−	701863.i	−1.76040	−	1.01637i
$832$	886505.			1.28066
$833$	523237.	−	208965.i	0.754064	−	0.301150i
$834$	1.70100e6			2.44553
$835$	−114454.	+	1.03575e6i	−0.164157	+	1.48553i
$836$	31339.8	−	18094.0i	0.0448418	−	0.0258894i
$837$	−1.60749e6	+	928085.i	−2.29455	+	1.32476i
$838$	210226.	−	364121.i	0.299363	−	0.518511i
$839$		−	589508.i		−	0.837464i	−0.908110	−	0.418732i	$-0.862475\pi$
$839$		−	589508.i		−	0.837464i	0.908110	−	0.418732i	$-0.137525\pi$
$840$	1.18916e6	+	565180.i	1.68531	+	0.800992i
$841$	−703401.			−0.994514
$842$	−666843.	−	385002.i	−0.940588	−	0.543049i
$843$	−759942.	−	1.31626e6i	−1.06936	−	1.85219i
$844$	−5989.07	−	10373.4i	−0.00840765	−	0.0145625i
$845$	−25655.9	+	232172.i	−0.0359314	+	0.325160i
$846$			683787.i			0.955389i
$847$	−51543.1	−	268034.i	−0.0718462	−	0.373615i
$848$		−	398274.i		−	0.553847i
$849$	−191150.	+	331082.i	−0.265192	+	0.459325i
$850$	−112103.	+	501044.i	−0.155160	+	0.693487i
$851$	39413.9	+	68266.8i	0.0544240	+	0.0942651i
$852$	9599.08	−	16626.1i	0.0132236	−	0.0229040i
$853$	−978175.			−1.34437			−0.672184	−	0.740384i	$-0.734644\pi$
$853$	−978175.			−1.34437			−0.672184	+	0.740384i	$0.734644\pi$
$854$	249699.	+	86538.8i	0.342375	+	0.118658i
$855$	163904.	+	373487.i	0.224211	+	0.510909i
$856$	579877.	−	1.00438e6i	0.791386	−	1.37072i
$857$	−397460.	−	688422.i	−0.541168	−	0.937331i	−0.998837	−	0.0482081i	$-0.984649\pi$
$857$	−397460.	−	688422.i	−0.541168	−	0.937331i	0.457669	−	0.889123i	$-0.348684\pi$
$858$	−874127.	+	504677.i	−1.18741	+	0.685550i
$859$	27946.5	+	16134.9i	0.0378740	+	0.0218665i	0.518817	−	0.854885i	$-0.326372\pi$
$859$	27946.5	+	16134.9i	0.0378740	+	0.0218665i	−0.480943	+	0.876752i	$0.659706\pi$
$860$	−132063.	−	300931.i	−0.178560	−	0.406883i
$861$	−98580.5	+	284445.i	−0.132980	+	0.383700i
$862$		−	284921.i		−	0.383451i
$863$	814498.	+	470250.i	1.09362	+	0.631404i	0.934539	−	0.355860i	$-0.115812\pi$
$863$	814498.	+	470250.i	1.09362	+	0.631404i	0.159085	+	0.987265i	$0.449145\pi$
$864$	503465.	−	290676.i	0.674438	−	0.389387i
$865$	−244610.	−	179722.i	−0.326920	−	0.240198i
$866$	899425.	+	519283.i	1.19930	+	0.692418i
$867$	−442465.			−0.588628
$868$	269584.	−	51841.2i	0.357812	−	0.0688074i
$869$	−476743.			−0.631313
$870$	84255.2	+	9310.51i	0.111316	+	0.0123008i
$871$	−806232.	+	465478.i	−1.06273	+	0.613568i
$872$	477442.	−	275651.i	0.627895	−	0.362516i
$873$	404624.	−	700830.i	0.530913	−	0.919569i
$874$		−	149751.i		−	0.196041i
$875$	−286408.	−	710037.i	−0.374084	−	0.927395i
$876$	−45083.6			−0.0587503
$877$	106052.	+	61229.0i	0.137885	+	0.0796082i	0.567356	−	0.823473i	$-0.307966\pi$
$877$	106052.	+	61229.0i	0.137885	+	0.0796082i	−0.429470	+	0.903081i	$0.641300\pi$
$878$	−98151.9	−	170004.i	−0.127324	−	0.220531i
$879$	557365.	+	965384.i	0.721376	+	1.24946i
$880$	47612.6	−	430868.i	0.0614832	−	0.556390i
$881$		−	1.13387e6i		−	1.46087i	−0.682981	−	0.730436i	$-0.739317\pi$
$881$		−	1.13387e6i		−	1.46087i	0.682981	−	0.730436i	$-0.260683\pi$
$882$	−501240.	−	1.25508e6i	−0.644330	−	1.61337i
$883$			508083.i			0.651648i	0.945430	+	0.325824i	$0.105642\pi$
$883$			508083.i			0.651648i	−0.945430	+	0.325824i	$0.894358\pi$
$884$	−85540.4	+	148160.i	−0.109463	+	0.189595i
$885$	−406396.	+	553124.i	−0.518876	+	0.706214i
$886$	205653.	+	356201.i	0.261979	+	0.453761i
$887$	−93351.2	+	161689.i	−0.118651	+	0.205510i	−0.919233	−	0.393713i	$-0.871190\pi$
$887$	−93351.2	+	161689.i	−0.118651	+	0.205510i	0.800582	+	0.599223i	$0.204524\pi$
$888$	−200970.			−0.254862
$889$	386931.	+	446920.i	0.489587	+	0.565491i
$890$	452791.	−	198707.i	0.571634	−	0.250861i
$891$	−298470.	+	516966.i	−0.375963	+	0.651188i
$892$	−144404.	−	250115.i	−0.181489	−	0.314347i
$893$	106750.	−	61632.1i	0.133864	−	0.0772865i
$894$	−1.11223e6	−	642145.i	−1.39161	−	0.803449i
$895$	34135.9	−	14980.5i	0.0426152	−	0.0187016i
$896$	406263.	−	78124.5i	0.506048	−	0.0973131i
$897$		−	1.27626e6i		−	1.58619i
$898$	104389.	+	60269.0i	0.129450	+	0.0747380i
$899$	80707.2	−	46596.3i	0.0998603	−	0.0576544i
$900$	−367231.	−	82164.2i	−0.453372	−	0.101437i
$901$	444563.	+	256669.i	0.547625	+	0.316172i
$902$	131734.			0.161914
$903$	−875854.	+	2.52719e6i	−1.07413	+	3.09929i
$904$	428203.			0.523977
$905$	−339115.	−	37473.5i	−0.414048	−	0.0457538i
$906$	−1.33923e6	+	773207.i	−1.63155	+	0.941974i
$907$	−890151.	+	513929.i	−1.08205	+	0.624725i	−0.931450	−	0.363869i	$-0.881455\pi$
$907$	−890151.	+	513929.i	−1.08205	+	0.624725i	−0.150605	+	0.988594i	$0.548122\pi$
$908$	8507.04	−	14734.6i	0.0103183	−	0.0178718i
$909$			1.02681e6i			1.24268i
$910$	66658.9	+	832252.i	0.0804961	+	1.00501i
$911$	−729324.			−0.878787			−0.439394	−	0.898295i	$-0.644807\pi$
$911$	−729324.			−0.878787			−0.439394	+	0.898295i	$0.644807\pi$
$912$	248769.	+	143627.i	0.299093	+	0.172682i
$913$	594877.	+	1.03036e6i	0.713650	+	1.23608i
$914$	46259.3	+	80123.5i	0.0553741	+	0.0959108i
$915$	−595266.	−	65779.1i	−0.710999	−	0.0785680i
$916$			120511.i			0.143627i
$917$	919078.	−	176739.i	1.09298	−	0.210181i
$918$		−	1.01918e6i		−	1.20939i
$919$	−185501.	+	321297.i	−0.219642	+	0.380431i	−0.954698	−	0.297575i	$-0.903822\pi$
$919$	−185501.	+	321297.i	−0.219642	+	0.380431i	0.735057	+	0.678006i	$0.237155\pi$
$920$	587076.	+	431342.i	0.693615	+	0.509619i
$921$	538808.	+	933244.i	0.635207	+	1.10021i
$922$	−182268.	+	315698.i	−0.214412	+	0.371373i
$923$	64190.8			0.0753476
$924$	205439.	−	177864.i	0.240624	−	0.208326i
$925$	86007.4	+	79120.1i	0.100520	+	0.0924705i
$926$	221135.	−	383017.i	0.257891	−	0.446680i
$927$	−419256.	−	726173.i	−0.487888	−	0.845046i
$928$	−25277.4	+	14593.9i	−0.0293520	+	0.0169464i
$929$	−1537.52	−	887.686i	−0.00178151	−	0.00102856i	0.499109	−	0.866539i	$-0.333661\pi$
$929$	−1537.52	−	887.686i	−0.00178151	−	0.00102856i	−0.500890	+	0.865511i	$0.666994\pi$
$930$	1.86441e6	−	818194.i	2.15564	−	0.945999i
$931$	−150759.	+	191376.i	−0.173934	+	0.220794i
$932$			245835.i			0.283016i
$933$	688240.	+	397355.i	0.790636	+	0.456474i
$934$	−155145.	+	89572.8i	−0.177846	+	0.102679i
$935$	450262.	+	330820.i	0.515041	+	0.378416i
$936$	1.87387e6	+	1.08188e6i	2.13889	+	1.23489i
$937$	−309575.			−0.352603			−0.176302	−	0.984336i	$-0.556413\pi$
$937$	−309575.			−0.352603			−0.176302	+	0.984336i	$0.556413\pi$
$938$	−620123.	+	536885.i	−0.704810	+	0.610205i
$939$	−2.26617e6			−2.57016
$940$	−12491.2	+	113039.i	−0.0141367	+	0.127930i
$941$	351332.	−	202842.i	0.396770	−	0.229075i	−0.288320	−	0.957534i	$-0.593097\pi$
$941$	351332.	−	202842.i	0.396770	−	0.229075i	0.685089	+	0.728459i	$0.259763\pi$
$942$	12583.0	−	7264.82i	0.0141802	−	0.00818697i
$943$	−83284.3	+	144253.i	−0.0936569	+	0.162219i
$944$			321456.i			0.360726i
$945$	862555.	+	1.25131e6i	0.965880	+	1.40121i
$946$	1.17041e6			1.30785
$947$	−1.35533e6	−	782498.i	−1.51128	−	0.872536i	−0.999913	−	0.0131713i	$-0.995807\pi$
$947$	−1.35533e6	−	782498.i	−1.51128	−	0.872536i	−0.511363	−	0.859365i	$-0.670859\pi$
$948$	145736.	+	252422.i	0.162162	+	0.280873i
$949$	−75370.5	−	130546.i	−0.0836891	−	0.144954i
$950$	−66346.9	−	211864.i	−0.0735146	−	0.234752i
$951$			192695.i			0.213064i
$952$	−260263.	+	750963.i	−0.287169	+	0.828600i
$953$		−	1.14512e6i		−	1.26086i	−0.776247	−	0.630429i	$-0.782879\pi$
$953$		−	1.14512e6i		−	1.26086i	0.776247	−	0.630429i	$-0.217121\pi$
$954$	615666.	−	1.06636e6i	0.676470	−	1.17168i
$955$	−458013.	−	336516.i	−0.502194	−	0.368977i
$956$	188954.	+	327279.i	0.206748	+	0.358098i
$957$	46123.3	−	79887.8i	0.0503612	−	0.0872282i
$958$	−966380.			−1.05297
$959$	−15443.6	+	44561.2i	−0.0167924	+	0.0484528i
$960$	−1.62087e6	+	711315.i	−1.75875	+	0.771826i
$961$	657437.	−	1.13871e6i	0.711881	−	1.23301i
$962$	−63720.5	−	110367.i	−0.0688539	−	0.119259i
$963$	2.33634e6	−	1.34888e6i	2.51932	−	1.45453i
$964$	−121925.	−	70393.4i	−0.131201	−	0.0757491i
$965$	111894.	+	254973.i	0.120158	+	0.273804i
$966$	−212348.	−	1.10425e6i	−0.227558	−	1.18335i
$967$		−	1.15709e6i		−	1.23741i	−0.785622	−	0.618707i	$-0.787657\pi$
$967$		−	1.15709e6i		−	1.23741i	0.785622	−	0.618707i	$-0.212343\pi$
$968$	333444.	+	192514.i	0.355854	+	0.205452i
$969$	−320640.	+	185121.i	−0.341484	+	0.197156i
$970$	−260810.	+	354974.i	−0.277192	+	0.377271i
$971$	−1.45668e6	−	841015.i	−1.54499	−	0.892000i	−0.998512	−	0.0545268i	$-0.982635\pi$
$971$	−1.45668e6	−	841015.i	−1.54499	−	0.892000i	−0.546478	−	0.837474i	$-0.684032\pi$
$972$	−11355.5			−0.0120191
$973$	−1.00222e6	−	1.15760e6i	−1.05861	−	1.22274i
$974$	−1.26183e6			−1.33010
$975$	−565445.	−	1.80562e6i	−0.594814	−	1.89941i
$976$	−242907.	+	140243.i	−0.255001	+	0.147225i
$977$	−593106.	+	342430.i	−0.621360	+	0.358742i	−0.777398	−	0.629009i	$-0.783461\pi$
$977$	−593106.	+	342430.i	−0.621360	+	0.358742i	0.156038	+	0.987751i	$0.450128\pi$
$978$	−495003.	+	857371.i	−0.517524	+	0.896377i
$979$		−	538098.i		−	0.561430i
$980$	−59934.0	−	216637.i	−0.0624052	−	0.225570i
$981$	1.28241e6			1.33257
$982$	−616817.	−	356120.i	−0.639637	−	0.369295i
$983$	373630.	+	647145.i	0.386664	+	0.669722i	0.991999	−	0.126249i	$-0.0402938\pi$
$983$	373630.	+	647145.i	0.386664	+	0.669722i	−0.605334	+	0.795971i	$0.706960\pi$
$984$	−212332.	−	367769.i	−0.219293	−	0.379827i
$985$	616673.	+	68144.6i	0.635598	+	0.0702359i
$986$			51170.1i			0.0526335i
$987$	699770.	−	605842.i	0.718325	−	0.621906i
$988$		−	73975.8i		−	0.0757837i
$989$	−739952.	+	1.28164e6i	−0.756504	+	1.31030i
$990$	793533.	−	1.08003e6i	0.809645	−	1.10196i
$991$	−788259.	−	1.36530e6i	−0.802641	−	1.39022i	−0.917872	−	0.396876i	$-0.870094\pi$
$991$	−788259.	−	1.36530e6i	−0.802641	−	1.39022i	0.115231	−	0.993339i	$-0.463239\pi$
$992$	−350532.	+	607139.i	−0.356208	+	0.616971i
$993$	−645005.			−0.654131
$994$	55539.4	−	10680.2i	0.0562119	−	0.0108096i
$995$	594372.	+	1.35439e6i	0.600361	+	1.36804i
$996$	363696.	−	629941.i	0.366624	−	0.635011i
$997$	346433.	+	600039.i	0.348521	+	0.603655i	0.985987	−	0.166823i	$-0.0533508\pi$
$997$	346433.	+	600039.i	0.348521	+	0.603655i	−0.637466	+	0.770478i	$0.720017\pi$
$998$	1.00635e6	−	581018.i	1.01039	−	0.583349i
$999$	−200901.	−	115990.i	−0.201303	−	0.116222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.i.a.19.5	✓	28
5.2	odd	4		175.5.i.e.26.10		28
5.3	odd	4		175.5.i.e.26.5		28
5.4	even	2	inner	35.5.i.a.19.10	yes	28
7.2	even	3		245.5.c.a.244.26		28
7.3	odd	6	inner	35.5.i.a.24.10	yes	28
7.5	odd	6		245.5.c.a.244.4		28
35.3	even	12		175.5.i.e.101.5		28
35.9	even	6		245.5.c.a.244.3		28
35.17	even	12		175.5.i.e.101.10		28
35.19	odd	6		245.5.c.a.244.25		28
35.24	odd	6	inner	35.5.i.a.24.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.i.a.19.5	✓	28	1.1	even	1	trivial
35.5.i.a.19.10	yes	28	5.4	even	2	inner
35.5.i.a.24.5	yes	28	35.24	odd	6	inner
35.5.i.a.24.10	yes	28	7.3	odd	6	inner
175.5.i.e.26.5		28	5.3	odd	4
175.5.i.e.26.10		28	5.2	odd	4
175.5.i.e.101.5		28	35.3	even	12
175.5.i.e.101.10		28	35.17	even	12
245.5.c.a.244.3		28	35.9	even	6
245.5.c.a.244.4		28	7.5	odd	6
245.5.c.a.244.25		28	35.19	odd	6
245.5.c.a.244.26		28	7.2	even	3

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.03175 - 1.75038i) q^{2} +(-7.77475 - 13.4663i) q^{3} +(-1.87234 - 3.24299i) q^{4} +(-2.74588 + 24.8487i) q^{5} +54.4351i q^{6} +(37.0452 - 32.0727i) q^{7} +69.1214i q^{8} +(-80.3936 + 139.246i) q^{9} +O(q^{10})\)	\(q+(-3.03175 - 1.75038i) q^{2} +(-7.77475 - 13.4663i) q^{3} +(-1.87234 - 3.24299i) q^{4} +(-2.74588 + 24.8487i) q^{5} +54.4351i q^{6} +(37.0452 - 32.0727i) q^{7} +69.1214i q^{8} +(-80.3936 + 139.246i) q^{9} +(51.8195 - 70.5288i) q^{10} +(-47.6201 - 82.4804i) q^{11} +(-29.1140 + 50.4270i) q^{12} -194.691 q^{13} +(-168.451 + 32.3932i) q^{14} +(355.968 - 156.216i) q^{15} +(91.0312 - 157.671i) q^{16} +(117.330 + 203.222i) q^{17} +(487.466 - 281.438i) q^{18} +(-87.8739 - 50.7340i) q^{19} +(85.7256 - 37.6205i) q^{20} +(-719.916 - 249.503i) q^{21} +333.413i q^{22} +(-365.097 - 210.789i) q^{23} +(930.807 - 537.402i) q^{24} +(-609.920 - 136.463i) q^{25} +(590.252 + 340.782i) q^{26} +1240.65 q^{27} +(-173.373 - 60.0861i) q^{28} -62.2893 q^{29} +(-1352.64 - 149.472i) q^{30} +(-1295.68 + 748.063i) q^{31} +(405.807 - 234.293i) q^{32} +(-740.469 + 1282.53i) q^{33} -821.491i q^{34} +(695.244 + 1008.59i) q^{35} +602.097 q^{36} +(-161.932 - 93.4914i) q^{37} +(177.608 + 307.625i) q^{38} +(1513.67 + 2621.76i) q^{39} +(-1717.58 - 189.799i) q^{40} -395.108i q^{41} +(1745.88 + 2016.56i) q^{42} -3510.40i q^{43} +(-178.322 + 308.863i) q^{44} +(-3239.33 - 2380.03i) q^{45} +(737.921 + 1278.12i) q^{46} +(-607.404 + 1052.05i) q^{47} -2830.98 q^{48} +(343.686 - 2376.27i) q^{49} +(1610.26 + 1481.31i) q^{50} +(1824.43 - 3160.01i) q^{51} +(364.528 + 631.380i) q^{52} +(1894.49 - 1093.78i) q^{53} +(-3761.34 - 2171.61i) q^{54} +(2180.29 - 956.818i) q^{55} +(2216.91 + 2560.61i) q^{56} +1577.78i q^{57} +(188.845 + 109.030i) q^{58} +(-1529.09 + 882.820i) q^{59} +(-1173.10 - 861.913i) q^{60} +(-1334.20 - 770.300i) q^{61} +5237.58 q^{62} +(1487.79 + 7736.82i) q^{63} -4553.40 q^{64} +(534.597 - 4837.82i) q^{65} +(4489.83 - 2592.20i) q^{66} +(4141.09 - 2390.86i) q^{67} +(439.366 - 761.004i) q^{68} +6555.32i q^{69} +(-342.384 - 4274.74i) q^{70} -329.707 q^{71} +(-9624.86 - 5556.91i) q^{72} +(387.130 + 670.528i) q^{73} +(327.291 + 566.884i) q^{74} +(2904.33 + 9274.32i) q^{75} +379.966i q^{76} +(-4409.46 - 1528.20i) q^{77} -10598.0i q^{78} +(2502.85 - 4335.06i) q^{79} +(3667.96 + 2694.95i) q^{80} +(-3133.87 - 5428.02i) q^{81} +(-691.589 + 1197.87i) q^{82} -12492.1 q^{83} +(538.794 + 2801.84i) q^{84} +(-5372.00 + 2357.49i) q^{85} +(-6144.53 + 10642.6i) q^{86} +(484.284 + 838.804i) q^{87} +(5701.16 - 3291.57i) q^{88} +(4892.96 + 2824.95i) q^{89} +(5654.87 + 12885.7i) q^{90} +(-7212.34 + 6244.25i) q^{91} +1578.68i q^{92} +(20147.2 + 11632.0i) q^{93} +(3682.99 - 2126.37i) q^{94} +(1501.97 - 2044.25i) q^{95} +(-6310.10 - 3643.14i) q^{96} -5033.05 q^{97} +(-5201.35 + 6602.68i) q^{98} +15313.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Introduction

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