LMFDB - Embedded newform 28.6.f.a.3.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,6,Mod(3,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("28.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	28.f (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:	$4.49074695476$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.18
Character	$\chi$	$=$	28.3
Dual form			28.6.f.a.19.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.65684 - 0.0122071i) q^{2} +(11.9407 - 20.6819i) q^{3} +(31.9997 - 0.138107i) q^{4} +(-26.3592 + 15.2185i) q^{5} +(67.2942 - 117.140i) q^{6} +(-129.440 + 7.22687i) q^{7} +(181.016 - 1.17187i) q^{8} +(-163.661 - 283.469i) q^{9} +(-148.924 + 86.4103i) q^{10} +(633.622 + 365.822i) q^{11} +(379.243 - 663.464i) q^{12} +555.117i q^{13} +(-732.135 + 42.4613i) q^{14} +726.878i q^{15} +(1023.96 - 8.83875i) q^{16} +(-1120.85 - 647.122i) q^{17} +(-929.264 - 1601.54i) q^{18} +(-387.571 - 671.292i) q^{19} +(-841.385 + 490.627i) q^{20} +(-1396.14 + 2763.36i) q^{21} +(3588.76 + 2061.66i) q^{22} +(-580.550 + 335.181i) q^{23} +(2137.22 - 3757.74i) q^{24} +(-1099.30 + 1904.04i) q^{25} +(6.77634 + 3140.21i) q^{26} -2013.72 q^{27} +(-4141.05 + 249.134i) q^{28} -3196.74 q^{29} +(8.87304 + 4111.83i) q^{30} +(-156.048 + 270.284i) q^{31} +(5792.28 - 62.4990i) q^{32} +(15131.8 - 8736.34i) q^{33} +(-6348.36 - 3646.99i) q^{34} +(3301.96 - 2160.38i) q^{35} +(-5276.25 - 9048.32i) q^{36} +(-2553.96 - 4423.59i) q^{37} +(-2200.62 - 3792.66i) q^{38} +(11480.9 + 6628.48i) q^{39} +(-4753.59 + 2785.67i) q^{40} -4987.32i q^{41} +(-7864.02 + 15649.0i) q^{42} -12746.7i q^{43} +(20326.2 + 11618.7i) q^{44} +(8627.93 + 4981.34i) q^{45} +(-3279.99 + 1903.15i) q^{46} +(-7560.18 - 13094.6i) q^{47} +(12044.0 - 21283.0i) q^{48} +(16702.5 - 1870.90i) q^{49} +(-6195.30 + 10784.2i) q^{50} +(-26767.4 + 15454.2i) q^{51} +(76.6654 + 17763.6i) q^{52} +(-15224.4 + 26369.5i) q^{53} +(-11391.3 + 24.5816i) q^{54} -22269.0 q^{55} +(-23422.2 + 1459.86i) q^{56} -18511.5 q^{57} +(-18083.5 + 39.0228i) q^{58} +(18539.3 - 32111.0i) q^{59} +(100.387 + 23259.9i) q^{60} +(444.534 - 256.652i) q^{61} +(-879.441 + 1530.86i) q^{62} +(23232.9 + 35509.5i) q^{63} +(32765.3 - 424.253i) q^{64} +(-8448.04 - 14632.4i) q^{65} +(85491.5 - 49604.8i) q^{66} +(27712.2 + 15999.7i) q^{67} +(-35956.2 - 20552.9i) q^{68} +16009.2i q^{69} +(18652.3 - 12261.2i) q^{70} +3970.29i q^{71} +(-29957.3 - 51120.5i) q^{72} +(14512.6 + 8378.88i) q^{73} +(-14501.3 - 24992.4i) q^{74} +(26252.7 + 45471.0i) q^{75} +(-12494.9 - 21427.6i) q^{76} +(-84659.9 - 42773.0i) q^{77} +(65026.4 + 37356.1i) q^{78} +(48277.1 - 27872.8i) q^{79} +(-26856.3 + 15816.1i) q^{80} +(15724.3 - 27235.4i) q^{81} +(-60.8805 - 28212.5i) q^{82} -101988. q^{83} +(-44294.5 + 88619.7i) q^{84} +39392.9 q^{85} +(-155.600 - 72106.1i) q^{86} +(-38171.4 + 66114.7i) q^{87} +(115124. + 65476.9i) q^{88} +(-67250.9 + 38827.3i) q^{89} +(48867.7 + 28073.3i) q^{90} +(-4011.76 - 71854.4i) q^{91} +(-18531.1 + 10805.9i) q^{92} +(3726.65 + 6454.75i) q^{93} +(-42926.6 - 73981.8i) q^{94} +(20432.1 + 11796.5i) q^{95} +(67871.3 - 120542. i) q^{96} +94898.6i q^{97} +(94460.8 - 10787.2i) q^{98} -239483. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9} - 804 q^{10} + 1632 q^{12} + 1024 q^{14} + 664 q^{16} - 6 q^{17} - 1780 q^{18} - 4586 q^{21} + 13768 q^{22} + 564 q^{24} + 7612 q^{25} - 8892 q^{26} - 5928 q^{28}+ \cdots + 418676 q^{98}+O(q^{100}) $ 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9 - 804 * q^10 + 1632 * q^12 + 1024 * q^14 + 664 * q^16 - 6 * q^17 - 1780 * q^18 - 4586 * q^21 + 13768 * q^22 + 564 * q^24 + 7612 * q^25 - 8892 * q^26 - 5928 * q^28 + 176 * q^29 - 5836 * q^30 + 1160 * q^32 - 14154 * q^33 - 27920 * q^36 + 11722 * q^37 - 5652 * q^38 + 35052 * q^40 + 23140 * q^42 + 9096 * q^44 + 19152 * q^45 - 1040 * q^46 + 43900 * q^49 - 51168 * q^50 - 61776 * q^52 - 33486 * q^53 - 30996 * q^54 + 19952 * q^56 - 1668 * q^57 - 48436 * q^58 + 14312 * q^60 + 18846 * q^61 + 44544 * q^64 + 15356 * q^65 + 221808 * q^66 + 25020 * q^68 + 81192 * q^70 + 148064 * q^72 - 236562 * q^73 + 17152 * q^74 - 140010 * q^77 + 127704 * q^78 - 277224 * q^80 + 160402 * q^81 - 391836 * q^82 - 379540 * q^84 + 71212 * q^85 - 252496 * q^86 + 55268 * q^88 - 23706 * q^89 - 190176 * q^92 - 165162 * q^93 + 359988 * q^94 + 1061736 * q^96 + 418676 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	5.65684	−	0.0122071i	0.999998	−	0.00215792i
$2$	5.65684	−	0.0122071i	0.999998	−	0.00215792i
$3$	11.9407	−	20.6819i	0.765997	−	1.32674i	−0.173722	−	0.984795i	$-0.555579\pi$
$3$	11.9407	−	20.6819i	0.765997	−	1.32674i	0.939718	−	0.341950i	$-0.111087\pi$
$4$	31.9997	−	0.138107i	0.999991	−	0.00431584i
$5$	−26.3592	+	15.2185i	−0.471528	+	0.272237i	−0.716879	−	0.697198i	$-0.754430\pi$
$5$	−26.3592	+	15.2185i	−0.471528	+	0.272237i	0.245351	+	0.969434i	$0.421097\pi$
$6$	67.2942	−	117.140i	0.763132	−	1.32839i
$7$	−129.440	+	7.22687i	−0.998445	+	0.0557449i
$7$	−129.440	+	7.22687i	−0.998445	+	0.0557449i
$8$	181.016	−	1.17187i	0.999979	−	0.00647373i
$9$	−163.661	−	283.469i	−0.673501	−	1.16654i
$10$	−148.924	+	86.4103i	−0.470939	+	0.273253i
$11$	633.622	+	365.822i	1.57888	+	0.911566i	0.995016	+	0.0997123i	$0.0317923\pi$
$11$	633.622	+	365.822i	1.57888	+	0.911566i	0.583862	+	0.811853i	$0.301541\pi$
$12$	379.243	−	663.464i	0.760263	−	1.33004i
$13$			555.117i			0.911016i	0.890232	+	0.455508i	$0.150542\pi$
$13$			555.117i			0.911016i	−0.890232	+	0.455508i	$0.849458\pi$
$14$	−732.135	+	42.4613i	−0.998322	+	0.0578993i
$15$			726.878i			0.834129i
$16$	1023.96	−	8.83875i	0.999963	−	0.00863159i
$17$	−1120.85	−	647.122i	−0.940643	−	0.543080i	−0.0504810	−	0.998725i	$-0.516075\pi$
$17$	−1120.85	−	647.122i	−0.940643	−	0.543080i	−0.890162	+	0.455645i	$0.849409\pi$
$18$	−929.264	−	1601.54i	−0.676017	−	1.16508i
$19$	−387.571	−	671.292i	−0.246302	−	0.426607i	0.716195	−	0.697900i	$-0.245882\pi$
$19$	−387.571	−	671.292i	−0.246302	−	0.426607i	−0.962497	+	0.271293i	$0.912549\pi$
$20$	−841.385	+	490.627i	−0.470348	+	0.274269i
$21$	−1396.14	+	2763.36i	−0.690846	+	1.36738i
$22$	3588.76	+	2061.66i	1.58084	+	0.908156i
$23$	−580.550	+	335.181i	−0.228834	+	0.132117i	−0.610034	−	0.792375i	$-0.708844\pi$
$23$	−580.550	+	335.181i	−0.228834	+	0.132117i	0.381200	+	0.924492i	$0.375511\pi$
$24$	2137.22	−	3757.74i	0.757391	−	1.33168i
$25$	−1099.30	+	1904.04i	−0.351774	+	0.609291i
$26$	6.77634	+	3140.21i	0.00196590	+	0.911014i
$27$	−2013.72			−0.531606
$28$	−4141.05	+	249.134i	−0.998195	+	0.0600535i
$29$	−3196.74			−0.705851			−0.352925	−	0.935652i	$-0.614813\pi$
$29$	−3196.74			−0.705851			−0.352925	+	0.935652i	$0.614813\pi$
$30$	8.87304	+	4111.83i	0.00179999	+	0.834127i
$31$	−156.048	+	270.284i	−0.0291645	+	0.0505144i	−0.880239	−	0.474530i	$-0.842618\pi$
$31$	−156.048	+	270.284i	−0.0291645	+	0.0505144i	0.851075	+	0.525045i	$0.175951\pi$
$32$	5792.28	−	62.4990i	0.999942	−	0.0107894i
$33$	15131.8	−	8736.34i	2.41883	−	1.39651i
$34$	−6348.36	−	3646.99i	−0.941812	−	0.541049i
$35$	3301.96	−	2160.38i	0.455619	−	0.298099i
$36$	−5276.25	−	9048.32i	−0.678530	−	1.16362i
$37$	−2553.96	−	4423.59i	−0.306697	−	0.531215i	0.670941	−	0.741511i	$-0.265891\pi$
$37$	−2553.96	−	4423.59i	−0.306697	−	0.531215i	−0.977638	+	0.210296i	$0.932557\pi$
$38$	−2200.62	−	3792.66i	−0.247222	−	0.426074i
$39$	11480.9	+	6628.48i	1.20869	+	0.697835i
$40$	−4753.59	+	2785.67i	−0.469755	+	0.275283i
$41$		−	4987.32i		−	0.463349i	−0.972793	−	0.231674i	$-0.925580\pi$
$41$		−	4987.32i		−	0.463349i	0.972793	−	0.231674i	$-0.0744204\pi$
$42$	−7864.02	+	15649.0i	−0.687894	+	1.36887i
$43$		−	12746.7i		−	1.05130i	−0.850701	−	0.525650i	$-0.823822\pi$
$43$		−	12746.7i		−	1.05130i	0.850701	−	0.525650i	$-0.176178\pi$
$44$	20326.2	+	11618.7i	1.58280	+	0.904743i
$45$	8627.93	+	4981.34i	0.635149	+	0.366703i
$46$	−3279.99	+	1903.15i	−0.228548	+	0.132611i
$47$	−7560.18	−	13094.6i	−0.499215	−	0.864665i	0.500785	−	0.865572i	$-0.333045\pi$
$47$	−7560.18	−	13094.6i	−0.499215	−	0.864665i	−1.00000		0.000906592i	$0.999711\pi$
$48$	12044.0	−	21283.0i	0.754516	−	1.33331i
$49$	16702.5	−	1870.90i	0.993785	−	0.111316i
$50$	−6195.30	+	10784.2i	−0.350459	+	0.610049i
$51$	−26767.4	+	15454.2i	−1.44106	+	0.831995i
$52$	76.6654	+	17763.6i	0.00393180	+	0.911007i
$53$	−15224.4	+	26369.5i	−0.744478	+	1.28947i	0.205961	+	0.978560i	$0.433968\pi$
$53$	−15224.4	+	26369.5i	−0.744478	+	1.28947i	−0.950438	+	0.310913i	$0.899365\pi$
$54$	−11391.3	+	24.5816i	−0.531604	+	0.00114716i
$55$	−22269.0			−0.992646
$56$	−23422.2	+	1459.86i	−0.998063	+	0.0622074i
$57$	−18511.5			−0.754664
$58$	−18083.5	+	39.0228i	−0.705849	+	0.00152317i
$59$	18539.3	−	32111.0i	0.693367	−	1.20095i	−0.277361	−	0.960766i	$-0.589460\pi$
$59$	18539.3	−	32111.0i	0.693367	−	1.20095i	0.970728	−	0.240182i	$-0.0772070\pi$
$60$	100.387	+	23259.9i	0.00359996	+	0.834121i
$61$	444.534	−	256.652i	0.0152961	−	0.00883121i	−0.492332	−	0.870407i	$-0.663856\pi$
$61$	444.534	−	256.652i	0.0152961	−	0.00883121i	0.507629	+	0.861576i	$0.330522\pi$
$62$	−879.441	+	1530.86i	−0.0290555	+	0.0505773i
$63$	23232.9	+	35509.5i	0.737483	+	1.12718i
$64$	32765.3	−	424.253i	0.999916	−	0.0129472i
$65$	−8448.04	−	14632.4i	−0.248012	−	0.429569i
$66$	85491.5	−	49604.8i	2.41581	−	1.40173i
$67$	27712.2	+	15999.7i	0.754197	+	0.435436i	0.827208	−	0.561895i	$-0.189928\pi$
$67$	27712.2	+	15999.7i	0.754197	+	0.435436i	−0.0730115	+	0.997331i	$0.523261\pi$
$68$	−35956.2	−	20552.9i	−0.942978	−	0.539016i
$69$			16009.2i			0.404805i
$70$	18652.3	−	12261.2i	0.454974	−	0.299081i
$71$			3970.29i			0.0934708i	0.998907	+	0.0467354i	$0.0148818\pi$
$71$			3970.29i			0.0934708i	−0.998907	+	0.0467354i	$0.985118\pi$
$72$	−29957.3	−	51120.5i	−0.681039	−	1.16215i
$73$	14512.6	+	8378.88i	0.318742	+	0.184026i	0.650832	−	0.759222i	$-0.274420\pi$
$73$	14512.6	+	8378.88i	0.318742	+	0.184026i	−0.332090	+	0.943248i	$0.607754\pi$
$74$	−14501.3	−	24992.4i	−0.307843	−	0.530552i
$75$	26252.7	+	45471.0i	0.538916	+	0.933430i
$76$	−12494.9	−	21427.6i	−0.248140	−	0.425540i
$77$	−84659.9	−	42773.0i	−1.62724	−	0.822134i
$78$	65026.4	+	37356.1i	1.21019	+	0.695225i
$79$	48277.1	−	27872.8i	0.870308	−	0.502473i	0.00285769	−	0.999996i	$-0.499090\pi$
$79$	48277.1	−	27872.8i	0.870308	−	0.502473i	0.867451	+	0.497523i	$0.165757\pi$
$80$	−26856.3	+	15816.1i	−0.469160	+	0.276296i
$81$	15724.3	−	27235.4i	0.266293	−	0.461233i
$82$	−60.8805	−	28212.5i	−0.000999871	−	0.463348i
$83$	−101988.			−1.62500			−0.812500	−	0.582961i	$-0.801894\pi$
$83$	−101988.			−1.62500			−0.812500	+	0.582961i	$0.801894\pi$
$84$	−44294.5	+	88619.7i	−0.684938	+	1.37035i
$85$	39392.9			0.591385
$86$	−155.600	−	72106.1i	−0.00226863	−	1.05130i
$87$	−38171.4	+	66114.7i	−0.540679	+	0.936484i
$88$	115124.	+	65476.9i	1.58475	+	0.901325i
$89$	−67250.9	+	38827.3i	−0.899960	+	0.519592i	−0.877187	−	0.480149i	$-0.840583\pi$
$89$	−67250.9	+	38827.3i	−0.899960	+	0.519592i	−0.0227725	+	0.999741i	$0.507249\pi$
$90$	48867.7	+	28073.3i	0.635939	+	0.365332i
$91$	−4011.76	−	71854.4i	−0.0507845	−	0.909599i
$92$	−18531.1	+	10805.9i	−0.228261	+	0.133104i
$93$	3726.65	+	6454.75i	0.0446799	+	0.0773878i
$94$	−42926.6	−	73981.8i	−0.501079	−	0.863586i
$95$	20432.1	+	11796.5i	0.232276	+	0.134105i
$96$	67871.3	−	120542.i	0.751637	−	1.33493i
$97$			94898.6i			1.02407i	0.858964	+	0.512036i	$0.171109\pi$
$97$			94898.6i			1.02407i	−0.858964	+	0.512036i	$0.828891\pi$
$98$	94460.8	−	10787.2i	0.993542	−	0.113461i
$99$		−	239483.i		−	2.45576i
$100$	−34914.2	+	61080.4i	−0.349142	+	0.610804i
$101$	124038.	+	71613.4i	1.20991	+	0.698539i	0.962739	−	0.270434i	$-0.0871671\pi$
$101$	124038.	+	71613.4i	1.20991	+	0.698539i	0.247167	+	0.968973i	$0.420500\pi$
$102$	−151231.	+	87748.7i	−1.43926	+	0.835103i
$103$	86828.1	+	150391.i	0.806431	+	1.39678i	0.915321	+	0.402725i	$0.131937\pi$
$103$	86828.1	+	150391.i	0.806431	+	1.39678i	−0.108890	+	0.994054i	$0.534730\pi$
$104$	650.525	+	100485.i	0.00589767	+	0.910997i
$105$	−5253.05	−	94087.2i	−0.0464984	−	0.832832i
$106$	−85800.3	+	149354.i	−0.741693	+	1.29108i
$107$	−38954.5	+	22490.4i	−0.328926	+	0.189906i	−0.655364	−	0.755313i	$-0.727485\pi$
$107$	−38954.5	+	22490.4i	−0.328926	+	0.189906i	0.326438	+	0.945219i	$0.394152\pi$
$108$	−64438.4	+	278.108i	−0.531601	+	0.00229432i
$109$	90839.7	−	157339.i	0.732334	−	1.26844i	−0.223549	−	0.974693i	$-0.571764\pi$
$109$	90839.7	−	157339.i	0.732334	−	1.26844i	0.955883	−	0.293747i	$-0.0949024\pi$
$110$	−125972.	+	271.839i	−0.992644	+	0.00214205i
$111$	−121984.			−0.939716
$112$	−132478.	+	8544.13i	−0.997927	+	0.0643610i
$113$	−92207.5			−0.679313			−0.339657	−	0.940550i	$-0.610311\pi$
$113$	−92207.5			−0.679313			−0.339657	+	0.940550i	$0.610311\pi$
$114$	−104716.	+	225.971i	−0.754663	+	0.00162851i
$115$	10201.9	−	17670.2i	0.0719342	−	0.124594i
$116$	−102295.	+	441.492i	−0.705844	+	0.00304634i
$117$	157358.	−	90850.9i	1.06274	−	0.613570i
$118$	104482.	−	181873.i	0.690774	−	1.20244i
$119$	149760.	+	75663.4i	0.969454	+	0.489800i
$120$	851.807	+	131576.i	0.00539993	+	0.834112i
$121$	187126.	+	324111.i	1.16190	+	2.01248i
$122$	2511.53	−	1457.27i	0.0152770	−	0.00886420i
$123$	−103147.	−	59552.1i	−0.614745	−	0.354923i
$124$	−4956.17	+	8670.55i	−0.0289462	+	0.0506398i
$125$		−	162034.i		−	0.927537i
$126$	131858.	+	200588.i	0.739913	+	1.12559i
$127$		−	50719.5i		−	0.279039i	−0.990219	−	0.139520i	$-0.955444\pi$
$127$		−	50719.5i		−	0.279039i	0.990219	−	0.139520i	$-0.0445559\pi$
$128$	185343.	−	2799.90i	0.999886	−	0.0151049i
$129$	−263626.	−	152205.i	−1.39481	−	0.805293i
$130$	−47967.8	−	82670.2i	−0.248938	−	0.429033i
$131$	−45559.7	−	78911.8i	−0.231955	−	0.401757i	0.726429	−	0.687242i	$-0.241179\pi$
$131$	−45559.7	−	78911.8i	−0.231955	−	0.401757i	−0.958383	+	0.285485i	$0.907845\pi$
$132$	483006.	−	281650.i	2.41278	−	1.40694i
$133$	55018.6	+	84091.3i	0.269700	+	0.412213i
$134$	156959.	+	90169.3i	0.755135	+	0.433807i
$135$	53080.0	−	30645.8i	0.250667	−	0.144723i
$136$	−203649.	−	115826.i	−0.944139	−	0.536979i
$137$	21025.0	−	36416.4i	0.0957051	−	0.165766i	−0.814198	−	0.580588i	$-0.802823\pi$
$137$	21025.0	−	36416.4i	0.0957051	−	0.165766i	0.909903	+	0.414822i	$0.136156\pi$
$138$	195.425	+	90561.3i	0.000873538	+	0.404804i
$139$	123064.			0.540248			0.270124	−	0.962826i	$-0.412935\pi$
$139$	123064.			0.540248			0.270124	+	0.962826i	$0.412935\pi$
$140$	105363.	−	69587.5i	0.454328	−	0.300062i
$141$	−361095.			−1.52959
$142$	48.4655	+	22459.3i	0.000201703	+	0.0934706i
$143$	−203074.	+	351734.i	−0.830451	+	1.43838i
$144$	−170088.	−	288815.i	−0.683545	−	1.16068i
$145$	84263.6	−	48649.6i	0.332828	−	0.192158i
$146$	82198.0	+	47220.8i	0.319138	+	0.183337i
$147$	160746.	−	367780.i	0.613547	−	1.40377i
$148$	−82336.9	−	141201.i	−0.308987	−	0.529887i
$149$	−95787.2	−	165908.i	−0.353461	−	0.612213i	0.633392	−	0.773831i	$-0.281662\pi$
$149$	−95787.2	−	165908.i	−0.353461	−	0.612213i	−0.986853	+	0.161618i	$0.948329\pi$
$150$	149063.	+	256902.i	0.540929	+	0.932265i
$151$	−34698.4	−	20033.1i	−0.123842	−	0.0715000i	0.436799	−	0.899559i	$-0.356112\pi$
$151$	−34698.4	−	20033.1i	−0.123842	−	0.0715000i	−0.560641	+	0.828059i	$0.689445\pi$
$152$	−70943.0	−	121060.i	−0.249058	−	0.425003i
$153$			423634.i			1.46306i
$154$	−479430.	−	240926.i	−1.62901	−	0.818620i
$155$		−	9499.28i		−	0.0317586i
$156$	368300.	+	210524.i	1.21169	+	0.692612i
$157$	5566.84	+	3214.02i	0.0180243	+	0.0104064i	0.508985	−	0.860775i	$-0.330021\pi$
$157$	5566.84	+	3214.02i	0.0180243	+	0.0104064i	−0.490961	+	0.871182i	$0.663354\pi$
$158$	272755.	−	158261.i	0.869222	−	0.504350i
$159$	363581.	+	629741.i	1.14053	+	1.97546i
$160$	−151729.	+	89797.2i	−0.468563	+	0.277308i
$161$	72724.2	−	47581.4i	0.221113	−	0.144668i
$162$	88617.7	−	154258.i	0.265297	−	0.461807i
$163$	−225617.	+	130260.i	−0.665123	+	0.384009i	−0.794226	−	0.607622i	$-0.792124\pi$
$163$	−225617.	+	130260.i	−0.665123	+	0.384009i	0.129103	+	0.991631i	$0.458790\pi$
$164$	−688.783	−	159593.i	−0.00199974	−	0.463344i
$165$	−265908.	+	460566.i	−0.760363	+	1.31699i
$166$	−576930.	+	1244.97i	−1.62500	+	0.00350663i
$167$	−45057.9			−0.125020			−0.0625100	−	0.998044i	$-0.519911\pi$
$167$	−45057.9			−0.125020			−0.0625100	+	0.998044i	$0.519911\pi$
$168$	−249485.	+	501848.i	−0.681980	+	1.37183i
$169$	63138.5			0.170050
$170$	222839.	−	480.871i	0.591384	−	0.00127616i
$171$	−126860.	+	219729.i	−0.331769	+	0.574640i
$172$	−1760.41	−	407891.i	−0.00453724	−	1.05129i
$173$	−13511.1	+	7800.63i	−0.0343222	+	0.0198159i	−0.517063	−	0.855947i	$-0.672975\pi$
$173$	−13511.1	+	7800.63i	−0.0343222	+	0.0198159i	0.482741	+	0.875763i	$0.339641\pi$
$174$	−215122.	+	374467.i	−0.538657	+	0.937648i
$175$	128533.	−	254403.i	0.317263	−	0.627954i
$176$	652038.	+	368987.i	1.58669	+	0.897903i
$177$	−442745.	−	766856.i	−1.06223	−	1.83984i
$178$	−379954.	+	220461.i	−0.898836	+	0.521533i
$179$	85691.4	+	49474.0i	0.199896	+	0.115410i	0.596607	−	0.802533i	$-0.296515\pi$
$179$	85691.4	+	49474.0i	0.199896	+	0.115410i	−0.396711	+	0.917944i	$0.629848\pi$
$180$	276779.	+	158210.i	0.636726	+	0.363959i
$181$			671079.i			1.52257i	0.648418	+	0.761285i	$0.275431\pi$
$181$			671079.i			1.52257i	−0.648418	+	0.761285i	$0.724569\pi$
$182$	−23571.0	−	406420.i	−0.0527472	−	0.909487i
$183$		−	12258.4i		−	0.0270587i
$184$	−104696.	+	61353.2i	−0.227974	+	0.133596i
$185$	134641.	+	77734.8i	0.289232	+	0.166988i
$186$	21159.9	+	36468.0i	0.0448467	+	0.0772912i
$187$	−473463.	−	820062.i	−0.990107	−	1.71491i
$188$	−243732.	−	417980.i	−0.502942	−	0.862503i
$189$	260656.	−	14552.9i	0.530779	−	0.0296343i
$190$	115725.	+	66481.4i	0.232565	+	0.133603i
$191$	−72958.4	+	42122.6i	−0.144708	+	0.0835471i	−0.570606	−	0.821224i	$-0.693292\pi$
$191$	−72958.4	+	42122.6i	−0.144708	+	0.0835471i	0.425898	+	0.904771i	$0.359958\pi$
$192$	382466.	−	682714.i	0.748755	−	1.33655i
$193$	207147.	−	358790.i	0.400301	−	0.693341i	−0.593461	−	0.804863i	$-0.702239\pi$
$193$	207147.	−	358790.i	0.400301	−	0.693341i	0.993762	+	0.111521i	$0.0355723\pi$
$194$	1158.43	+	536827.i	0.00220987	+	1.02407i
$195$	−403502.			−0.759905
$196$	534218.	−	62174.8i	0.993295	−	0.115604i
$197$	83038.4			0.152445			0.0762225	−	0.997091i	$-0.475714\pi$
$197$	83038.4			0.152445			0.0762225	+	0.997091i	$0.475714\pi$
$198$	−2923.38	−	1.35472e6i	−0.00529935	−	2.45576i
$199$	316097.	−	547497.i	0.565833	−	0.980051i	−0.431139	−	0.902286i	$-0.641888\pi$
$199$	316097.	−	547497.i	0.565833	−	0.980051i	0.996972	−	0.0777658i	$-0.0247786\pi$
$200$	−196758.	+	345948.i	−0.347823	+	0.611556i
$201$	661807.	−	382095.i	1.15542	−	0.667085i
$202$	702538.	+	403591.i	1.21141	+	0.695927i
$203$	413787.	−	23102.4i	0.704753	−	0.0393476i
$204$	−854416.	+	498226.i	−1.43745	+	0.838207i
$205$	75899.5	+	131462.i	0.126140	+	0.218482i
$206$	493008.	+	849676.i	0.809443	+	1.39504i
$207$	190026.	+	109712.i	0.308239	+	0.177962i
$208$	4906.54	+	568418.i	0.00786352	+	0.910982i
$209$		−	567127.i		−	0.898080i
$210$	−30864.2	−	532172.i	−0.0482955	−	0.832730i
$211$			214819.i			0.332174i	0.986111	+	0.166087i	$0.0531133\pi$
$211$			214819.i			0.332174i	−0.986111	+	0.166087i	$0.946887\pi$
$212$	−483536.	+	845919.i	−0.738906	+	1.29267i
$213$	82113.1	+	47408.0i	0.124012	+	0.0715983i
$214$	−220085.	+	127700.i	−0.328516	+	0.190615i
$215$	193986.	+	335993.i	0.286203	+	0.495717i
$216$	−364515.	+	2359.82i	−0.531595	+	0.00344147i
$217$	18245.6	−	36113.3i	0.0263033	−	0.0520617i
$218$	511945.	−	891150.i	0.729595	−	1.27002i
$219$	346582.	−	200099.i	0.488310	−	0.281926i
$220$	−712602.	+	3075.50i	−0.992637	+	0.00428410i
$221$	359228.	−	622202.i	0.494755	−	0.856940i
$222$	−690046.	+	1489.07i	−0.939714	+	0.00202784i
$223$	276521.			0.372363			0.186181	−	0.982515i	$-0.440389\pi$
$223$	276521.			0.372363			0.186181	+	0.982515i	$0.440389\pi$
$224$	−749303.	+	49949.9i	−0.997785	+	0.0665143i
$225$	719646.			0.947682
$226$	−521603.	+	1125.58i	−0.679311	+	0.00146591i
$227$	−54984.7	+	95236.4i	−0.0708235	+	0.122670i	−0.899262	−	0.437409i	$-0.855896\pi$
$227$	−54984.7	+	95236.4i	−0.0708235	+	0.122670i	0.828439	+	0.560079i	$0.189229\pi$
$228$	−592362.	+	2556.56i	−0.754657	+	0.00325701i
$229$	−1.16662e6	+	673550.i	−1.47008	+	0.848753i	−0.999436	−	0.0335693i	$-0.989313\pi$
$229$	−1.16662e6	+	673550.i	−1.47008	+	0.848753i	−0.470646	+	0.882322i	$0.655979\pi$
$230$	57494.7	−	100082.i	0.0716652	−	0.124749i
$231$	−1.89553e6	+	1.24019e6i	−2.33722	+	1.52918i
$232$	−578660.	+	3746.17i	−0.705836	+	0.00456949i
$233$	383586.	+	664390.i	0.462885	+	0.801740i	0.999103	−	0.0423393i	$-0.0134810\pi$
$233$	383586.	+	664390.i	0.462885	+	0.801740i	−0.536219	+	0.844079i	$0.680148\pi$
$234$	889042.	−	515850.i	1.06141	−	0.615862i
$235$	398560.	+	230109.i	0.470787	+	0.271809i
$236$	588818.	−	1.03010e6i	0.688178	−	1.20393i
$237$		−	1.33128e6i		−	1.53957i
$238$	848090.	+	426188.i	0.970509	+	0.487707i
$239$		−	772641.i		−	0.874950i	−0.899231	−	0.437475i	$-0.855873\pi$
$239$		−	772641.i		−	0.874950i	0.899231	−	0.437475i	$-0.144127\pi$
$240$	6424.69	+	744295.i	0.00719986	+	0.834098i
$241$	565571.	+	326533.i	0.627256	+	0.362146i	0.779688	−	0.626168i	$-0.215377\pi$
$241$	565571.	+	326533.i	0.627256	+	0.362146i	−0.152433	+	0.988314i	$0.548711\pi$
$242$	1.06250e6	+	1.83116e6i	1.16624	+	2.00996i
$243$	−620187.	−	1.07419e6i	−0.673762	−	1.16699i
$244$	14189.5	−	8274.18i	0.0152578	−	0.00889714i
$245$	−411793.	+	303503.i	−0.438293	+	0.323033i
$246$	−584215.	−	335618.i	−0.615510	−	0.353596i
$247$	372646.	−	215147.i	0.388645	−	0.224385i
$248$	−27930.4	+	49108.4i	−0.0288369	+	0.0507022i
$249$	−1.21781e6	+	2.10930e6i	−1.24474	+	2.15596i
$250$	−1977.96	−	916601.i	−0.00200155	−	0.927535i
$251$	915135.			0.916856			0.458428	−	0.888732i	$-0.348413\pi$
$251$	915135.			0.916856			0.458428	+	0.888732i	$0.348413\pi$
$252$	748350.	+	1.13309e6i	0.742341	+	1.12399i
$253$	−490465.			−0.481734
$254$	−619.136	−	286912.i	−0.000602146	−	0.279039i
$255$	470379.	−	814720.i	0.452999	−	0.784617i
$256$	1.04842e6	−	18101.1i	0.999851	−	0.0172625i
$257$	−1.03059e6	+	595012.i	−0.973315	+	0.561944i	−0.900245	−	0.435383i	$-0.856613\pi$
$257$	−1.03059e6	+	595012.i	−0.973315	+	0.561944i	−0.0730698	+	0.997327i	$0.523280\pi$
$258$	−1.49315e6	−	857780.i	−1.39654	−	0.802281i
$259$	362554.	+	554133.i	0.335833	+	0.513292i
$260$	−272355.	−	467067.i	−0.249863	−	0.428495i
$261$	523182.	+	906177.i	0.475391	+	0.823402i
$262$	−258687.	−	445835.i	−0.232821	−	0.401256i
$263$	−1.45863e6	−	842141.i	−1.30034	−	0.750751i	−0.319876	−	0.947459i	$-0.603641\pi$
$263$	−1.45863e6	−	842141.i	−1.30034	−	0.750751i	−0.980462	+	0.196709i	$0.936975\pi$
$264$	2.72885e6	−	1.59915e6i	2.40974	−	1.41214i
$265$		−	926772.i		−	0.810696i
$266$	312258.	+	475020.i	0.270589	+	0.411630i
$267$			1.85450e6i			1.59202i
$268$	888993.	+	508158.i	0.756069	+	0.432177i
$269$	−295973.	−	170880.i	−0.249386	−	0.143983i	0.370097	−	0.928993i	$-0.379324\pi$
$269$	−295973.	−	170880.i	−0.249386	−	0.143983i	−0.619483	+	0.785010i	$0.712658\pi$
$270$	299891.	−	174006.i	0.250354	−	0.145263i
$271$	569405.	+	986238.i	0.470975	+	0.815753i	0.999449	−	0.0331968i	$-0.0105688\pi$
$271$	569405.	+	986238.i	0.470975	+	0.815753i	−0.528474	+	0.848950i	$0.677235\pi$
$272$	−1.15343e6	−	652722.i	−0.945295	−	0.534941i
$273$	−1.53399e6	−	775022.i	−1.24571	−	0.629372i
$274$	118491.	−	206258.i	0.0953472	−	0.165972i
$275$	−1.39308e6	+	804292.i	−1.11082	+	0.641331i
$276$	2210.97	+	512289.i	0.00174707	+	0.404801i
$277$	1.01600e6	−	1.75977e6i	0.795602	−	1.37802i	−0.126854	−	0.991921i	$-0.540488\pi$
$277$	1.01600e6	−	1.75977e6i	0.795602	−	1.37802i	0.922456	−	0.386102i	$-0.126179\pi$
$278$	696152.	−	1502.25i	0.540247	−	0.00116581i
$279$	102156.			0.0785694
$280$	595174.	−	394932.i	0.453679	−	0.301042i
$281$	−117221.			−0.0885607			−0.0442803	−	0.999019i	$-0.514099\pi$
$281$	−117221.			−0.0885607			−0.0442803	+	0.999019i	$0.514099\pi$
$282$	−2.04266e6	+	4407.91i	−1.52958	+	0.00330073i
$283$	453414.	−	785337.i	0.336534	−	0.582894i	−0.647244	−	0.762283i	$-0.724079\pi$
$283$	453414.	−	785337.i	0.336534	−	0.582894i	0.983778	+	0.179389i	$0.0574119\pi$
$284$	548.324	+	127048.i	0.000403405	+	0.0934700i
$285$	487948.	−	281717.i	0.355845	−	0.205447i
$286$	−1.14446e6	+	1.99218e6i	−0.827345	+	1.44017i
$287$	36042.7	+	645560.i	0.0258293	+	0.462628i
$288$	−965686.	−	1.63170e6i	−0.686048	−	1.15920i
$289$	127606.	+	221020.i	0.0898724	+	0.155664i
$290$	476072.	−	276232.i	0.332413	−	0.192876i
$291$	1.96268e6	+	1.13316e6i	1.35868	+	0.784436i
$292$	465557.	+	266117.i	0.319533	+	0.182648i
$293$		−	253739.i		−	0.172670i	−0.996266	−	0.0863352i	$-0.972484\pi$
$293$		−	253739.i		−	0.172670i	0.996266	−	0.0863352i	$-0.0275156\pi$
$294$	904828.	−	2.08244e6i	0.610517	−	1.40509i
$295$			1.12856e6i			0.755040i
$296$	−467490.	−	797745.i	−0.310130	−	0.529219i
$297$	−1.27594e6	−	736663.i	−0.839341	−	0.484593i
$298$	−543878.	−	937348.i	−0.354782	−	0.611449i
$299$	−186064.	−	322273.i	−0.120361	−	0.208471i
$300$	846359.	+	1.45143e6i	0.542940	+	0.931095i
$301$	92118.8	+	1.64994e6i	0.0586047	+	1.04967i
$302$	−196528.	−	112901.i	−0.123996	−	0.0712326i
$303$	2.96220e6	−	1.71023e6i	1.85357	−	1.07016i
$304$	−402791.	−	683952.i	−0.249975	−	0.424465i
$305$	−7811.71	+	13530.3i	−0.00480836	+	0.00832832i
$306$	5171.33	+	2.39643e6i	0.00315717	+	1.46306i
$307$	−404567.			−0.244988			−0.122494	−	0.992469i	$-0.539089\pi$
$307$	−404567.			−0.244988			−0.122494	+	0.992469i	$0.539089\pi$
$308$	−2.71500e6	−	1.35703e6i	−1.63077	−	0.815103i
$309$	4.14715e6			2.47089
$310$	−115.958	−	53735.9i	−6.85326e−5	−	0.0317585i
$311$	999544.	−	1.73126e6i	0.586005	−	1.01499i	−0.408745	−	0.912649i	$-0.634033\pi$
$311$	999544.	−	1.73126e6i	0.586005	−	1.01499i	0.994749	−	0.102341i	$-0.0326333\pi$
$312$	2.08598e6	+	1.18640e6i	1.21318	+	0.689996i
$313$	910246.	−	525531.i	0.525168	−	0.303206i	−0.213879	−	0.976860i	$-0.568610\pi$
$313$	910246.	−	525531.i	0.525168	−	0.303206i	0.739046	+	0.673654i	$0.235276\pi$
$314$	31530.0	+	18113.2i	0.0180468	+	0.0103674i
$315$	−1.15280e6	−	582433.i	−0.654603	−	0.330727i
$316$	1.54100e6	−	898588.i	0.868132	−	0.506224i
$317$	−797354.	−	1.38106e6i	−0.445659	−	0.771904i	0.552439	−	0.833554i	$-0.313697\pi$
$317$	−797354.	−	1.38106e6i	−0.445659	−	0.771904i	−0.998098	+	0.0616492i	$0.980364\pi$
$318$	2.06441e6	+	3.55791e6i	1.14479	+	1.97300i
$319$	−2.02553e6	−	1.16944e6i	−1.11445	−	0.643429i
$320$	−857209.	+	509821.i	−0.467963	+	0.278319i
$321$			1.07421e6i			0.581868i
$322$	410808.	−	270048.i	0.220800	−	0.145145i
$323$			1.00322e6i			0.535046i
$324$	499413.	−	873695.i	0.264300	−	0.462378i
$325$	−1.05696e6	−	610237.i	−0.555074	−	0.320472i
$326$	−1.27469e6	+	739613.i	−0.664293	+	0.385443i
$327$	−2.16938e6	−	3.75748e6i	−1.12193	−	1.94324i
$328$	−5844.50	−	902783.i	−0.00299959	−	0.463339i
$329$	1.07322e6	+	1.64033e6i	0.546639	+	0.835492i
$330$	−1.49858e6	+	2.60859e6i	−0.757520	+	1.31863i
$331$	−2.16225e6	+	1.24837e6i	−1.08476	+	0.626289i	−0.932178	−	0.362001i	$-0.882094\pi$
$331$	−2.16225e6	+	1.24837e6i	−1.08476	+	0.626289i	−0.152587	+	0.988290i	$0.548760\pi$
$332$	−3.26358e6	+	14085.2i	−1.62499	+	0.00701324i
$333$	−835966.	+	1.44794e6i	−0.413122	+	0.715548i
$334$	−254885.	+	550.024i	−0.125020	+	0.000269783i
$335$	−973963.			−0.474166
$336$	−1.40517e6	+	2.84192e6i	−0.679018	+	1.37329i
$337$	−1.35799e6			−0.651363			−0.325682	−	0.945480i	$-0.605594\pi$
$337$	−1.35799e6			−0.651363			−0.325682	+	0.945480i	$0.605594\pi$
$338$	357164.	−	770.735i	0.170050	−	0.000366955i
$339$	−1.10102e6	+	1.90703e6i	−0.520351	+	0.901275i
$340$	1.26056e6	−	5440.42i	0.591380	−	0.00255232i
$341$	−197751.	+	114172.i	−0.0920945	+	0.0531708i
$342$	−714946.	+	1.24452e6i	−0.330528	+	0.575355i
$343$	−2.14846e6	+	362876.i	−0.986034	+	0.166542i
$344$	−14937.5	−	2.30735e6i	−0.00680584	−	1.05128i
$345$	−243635.	−	421989.i	−0.110203	−	0.190877i
$346$	−76334.8	+	44291.8i	−0.0342793	+	0.0198899i
$347$	1.61299e6	+	931259.i	0.719130	+	0.415190i	0.814432	−	0.580259i	$-0.197049\pi$
$347$	1.61299e6	+	931259.i	0.719130	+	0.415190i	−0.0953026	+	0.995448i	$0.530382\pi$
$348$	−1.21234e6	+	2.12092e6i	−0.536632	+	0.938808i
$349$			581463.i			0.255540i	0.991804	+	0.127770i	$0.0407819\pi$
$349$			581463.i			0.255540i	−0.991804	+	0.127770i	$0.959218\pi$
$350$	723984.	−	1.44069e6i	0.315907	−	0.628637i
$351$		−	1.11785e6i		−	0.484301i
$352$	3.69298e6	+	2.07934e6i	1.58862	+	0.894477i
$353$	3.55330e6	+	2.05150e6i	1.51773	+	0.876262i	0.999783	+	0.0208505i	$0.00663740\pi$
$353$	3.55330e6	+	2.05150e6i	1.51773	+	0.876262i	0.517948	+	0.855412i	$0.326696\pi$
$354$	−2.51390e6	−	4.33258e6i	−1.06620	−	1.83755i
$355$	−60421.8	−	104654.i	−0.0254462	−	0.0440741i
$356$	−2.14665e6	+	1.25175e6i	−0.897709	+	0.523471i
$357$	3.35310e6	−	2.19384e6i	1.39244	−	0.911033i
$358$	485347.	+	278820.i	0.200145	+	0.114979i
$359$	1.34053e6	−	773953.i	0.548958	−	0.316941i	−0.199744	−	0.979848i	$-0.564011\pi$
$359$	1.34053e6	−	773953.i	0.548958	−	0.316941i	0.748702	+	0.662907i	$0.230678\pi$
$360$	1.56763e6	+	891589.i	0.637510	+	0.362584i
$361$	937627.	−	1.62402e6i	0.378671	−	0.655878i
$362$	8191.90	+	3.79619e6i	0.00328559	+	1.52257i
$363$	8.93765e6			3.56006
$364$	−138299.	−	2.29877e6i	−0.0547097	−	0.909372i
$365$	−510055.			−0.200394
$366$	−149.639	−	69344.0i	−5.83906e−5	−	0.0270586i
$367$	−692478.	+	1.19941e6i	−0.268374	+	0.464838i	−0.968442	−	0.249238i	$-0.919820\pi$
$367$	−692478.	+	1.19941e6i	−0.268374	+	0.464838i	0.700068	+	0.714076i	$0.253153\pi$
$368$	−591498.	+	348343.i	−0.227685	+	0.134087i
$369$	−1.41375e6	+	816229.i	−0.540514	+	0.312066i
$370$	762590.	+	438090.i	0.289592	+	0.166364i
$371$	1.78009e6	−	3.52330e6i	0.671438	−	1.32897i
$372$	120143.	+	206036.i	0.0450134	+	0.0771942i
$373$	−2.56886e6	−	4.44939e6i	−0.956022	−	1.65588i	−0.732012	−	0.681291i	$-0.761419\pi$
$373$	−2.56886e6	−	4.44939e6i	−0.956022	−	1.65588i	−0.224009	−	0.974587i	$-0.571915\pi$
$374$	−2.68832e6	−	4.63318e6i	−0.993805	−	1.71277i
$375$	−3.35117e6	−	1.93480e6i	−1.23060	−	0.710490i
$376$	−1.38385e6	−	2.36147e6i	−0.504802	−	0.861415i
$377$		−	1.77457e6i		−	0.643041i
$378$	1.47431e6	−	85505.2i	0.530714	−	0.0307796i
$379$			4.59742e6i			1.64405i	0.569449	+	0.822026i	$0.307156\pi$
$379$			4.59742e6i			1.64405i	−0.569449	+	0.822026i	$0.692844\pi$
$380$	655451.	+	374662.i	0.232853	+	0.133101i
$381$	−1.04898e6	−	605626.i	−0.370214	−	0.213743i
$382$	−412200.	+	239171.i	−0.144527	+	0.0838592i
$383$	1.63872e6	+	2.83835e6i	0.570833	+	0.988711i	0.996481	+	0.0838222i	$0.0267128\pi$
$383$	1.63872e6	+	2.83835e6i	0.570833	+	0.988711i	−0.425648	+	0.904889i	$0.639954\pi$
$384$	2.15521e6	−	3.86667e6i	0.745869	−	1.33816i
$385$	2.88251e6	−	160935.i	0.991102	−	0.0553349i
$386$	1.16742e6	−	2.03215e6i	0.398804	−	0.694203i
$387$	−3.61330e6	+	2.08614e6i	−1.22638	+	0.708053i
$388$	13106.1	+	3.03673e6i	0.00441973	+	1.02406i
$389$	−2.74528e6	+	4.75496e6i	−0.919839	+	1.59321i	−0.120182	+	0.992752i	$0.538348\pi$
$389$	−2.74528e6	+	4.75496e6i	−0.919839	+	1.59321i	−0.799657	+	0.600457i	$0.794986\pi$
$390$	−2.28255e6	+	4925.57i	−0.759903	+	0.00163982i
$391$	867611.			0.287001
$392$	3.02123e6	−	358234.i	0.993044	−	0.117748i
$393$	−2.17606e6			−0.710706
$394$	469735.	−	1013.65i	0.152445	−	0.000328965i
$395$	−848363.	+	1.46941e6i	−0.273583	+	0.473860i
$396$	−33074.2	−	7.66338e6i	−0.0105987	−	2.45574i
$397$	−389906.	+	225112.i	−0.124160	+	0.0716841i	−0.560794	−	0.827955i	$-0.689504\pi$
$397$	−389906.	+	225112.i	−0.124160	+	0.0716841i	0.436633	+	0.899640i	$0.356171\pi$
$398$	1.78143e6	−	3.10096e6i	0.563717	−	0.981270i
$399$	2.39613e6	−	133780.i	0.753491	−	0.0420687i
$400$	−1.10881e6	+	1.95938e6i	−0.346502	+	0.612305i
$401$	−254453.	−	440725.i	−0.0790216	−	0.136869i	0.823806	−	0.566871i	$-0.191846\pi$
$401$	−254453.	−	440725.i	−0.0790216	−	0.136869i	−0.902828	+	0.430002i	$0.858513\pi$
$402$	3.73908e6	−	2.16953e6i	1.15398	−	0.669576i
$403$	−150039.	−	86625.0i	−0.0460195	−	0.0265693i
$404$	3.97907e6	+	2.27448e6i	1.21291	+	0.693311i
$405$			957203.i			0.289979i
$406$	2.34045e6	−	135738.i	0.704666	−	0.0408683i
$407$		−	3.73718e6i		−	1.11830i
$408$	−4.82721e6	+	2.82882e6i	−1.43564	+	0.841307i
$409$	−3.92562e6	−	2.26646e6i	−1.16038	−	0.669946i	−0.208985	−	0.977919i	$-0.567016\pi$
$409$	−3.92562e6	−	2.26646e6i	−1.16038	−	0.669946i	−0.951395	+	0.307973i	$0.900349\pi$
$410$	430956.	+	742732.i	0.126612	+	0.218209i
$411$	−502107.	−	869675.i	−0.146620	−	0.253952i
$412$	2.79924e6	+	4.80046e6i	0.812451	+	1.39329i
$413$	−2.16767e6	+	4.29044e6i	−0.625343	+	1.23773i
$414$	1.07629e6	+	618303.i	0.308623	+	0.177297i
$415$	2.68832e6	−	1.55210e6i	0.766233	−	0.442385i
$416$	34694.2	+	3.21539e6i	0.00982933	+	0.910963i
$417$	1.46947e6	−	2.54519e6i	0.413828	−	0.716772i
$418$	−6922.96	−	3.20815e6i	−0.00193799	−	0.898078i
$419$	−6.52483e6			−1.81566			−0.907829	−	0.419341i	$-0.862261\pi$
$419$	−6.52483e6			−1.81566			−0.907829	+	0.419341i	$0.862261\pi$
$420$	−181090.	−	3.01004e6i	−0.0500924	−	0.832624i
$421$	−5.86333e6			−1.61227			−0.806137	−	0.591728i	$-0.798446\pi$
$421$	−5.86333e6			−1.61227			−0.806137	+	0.591728i	$0.798446\pi$
$422$	2622.30	+	1.21520e6i	0.000716807	+	0.332174i
$423$	−2.47461e6	+	4.28615e6i	−0.672444	+	1.16471i
$424$	−2.72496e6	+	4.79113e6i	−0.736114	+	1.29427i
$425$	2.46429e6	−	1.42276e6i	0.661788	−	0.382084i
$426$	465080.	+	267177.i	0.124166	+	0.0713306i
$427$	−55685.8	+	36433.7i	−0.0147800	+	0.00967016i
$428$	−1.24343e6	+	725066.i	−0.328104	+	0.191323i
$429$	4.84969e6	+	8.39991e6i	1.27224	+	2.20359i
$430$	1.10145e6	+	1.89829e6i	0.287272	+	0.495099i
$431$	1.62224e6	+	936601.i	0.420651	+	0.242863i	0.695356	−	0.718666i	$-0.255247\pi$
$431$	1.62224e6	+	936601.i	0.420651	+	0.242863i	−0.274705	+	0.961529i	$0.588580\pi$
$432$	−2.06197e6	+	17798.8i	−0.531586	+	0.00458860i
$433$			5.60224e6i			1.43596i	0.696064	+	0.717980i	$0.254933\pi$
$433$			5.60224e6i			1.43596i	−0.696064	+	0.717980i	$0.745067\pi$
$434$	102772.	−	204510.i	0.0261908	−	0.0521183i
$435$		−	2.32364e6i		−	0.588770i
$436$	2.88511e6	−	5.04734e6i	0.726853	−	1.27159i
$437$	450008.	+	259812.i	0.112724	+	0.0650813i
$438$	1.95812e6	−	1.13616e6i	0.487701	−	0.282979i
$439$	1.36590e6	+	2.36581e6i	0.338265	+	0.585892i	0.984106	−	0.177579i	$-0.0568266\pi$
$439$	1.36590e6	+	2.36581e6i	0.338265	+	0.585892i	−0.645841	+	0.763472i	$0.723493\pi$
$440$	−4.03104e6	+	26096.4i	−0.992625	+	0.00642612i
$441$	−3.26389e6	−	4.42846e6i	−0.799170	−	1.08432i
$442$	2.02450e6	−	3.52408e6i	0.492904	−	0.858006i
$443$	1.07588e6	−	621160.i	0.260468	−	0.150381i	−0.364080	−	0.931368i	$-0.618616\pi$
$443$	1.07588e6	−	621160.i	0.260468	−	0.150381i	0.624548	+	0.780986i	$0.285283\pi$
$444$	−3.90346e6	+	16846.9i	−0.939707	+	0.00405566i
$445$	1.18179e6	−	2.04691e6i	0.282904	−	0.490004i
$446$	1.56424e6	−	3375.51i	0.372362	−	0.000803530i
$447$	−4.57507e6			−1.08300
$448$	−4.23808e6	+	291706.i	−0.997640	+	0.0686673i
$449$	2.81102e6			0.658033			0.329016	−	0.944324i	$-0.393283\pi$
$449$	2.81102e6			0.658033			0.329016	+	0.944324i	$0.393283\pi$
$450$	4.07092e6	−	8784.76i	0.947680	−	0.00204503i
$451$	1.82447e6	−	3.16008e6i	0.422373	−	0.731571i
$452$	−2.95061e6	+	12734.5i	−0.679307	+	0.00293180i
$453$	−828646.	+	478419.i	−0.189725	+	0.109537i
$454$	−309877.	+	539408.i	−0.0705586	+	0.122822i
$455$	1.19926e6	+	1.83297e6i	0.271572	+	0.415076i
$456$	−3.35086e6	+	21693.0i	−0.754649	+	0.00488549i
$457$	1.01638e6	+	1.76042e6i	0.227649	+	0.394299i	0.957111	−	0.289722i	$-0.0935629\pi$
$457$	1.01638e6	+	1.76042e6i	0.227649	+	0.394299i	−0.729462	+	0.684021i	$0.760230\pi$
$458$	−6.59118e6	+	3.82441e6i	−1.46825	+	0.851923i
$459$	2.25708e6	+	1.30312e6i	0.500051	+	0.288705i
$460$	324017.	−	566849.i	0.0713958	−	0.124903i
$461$		−	4.04823e6i		−	0.887182i	−0.896229	−	0.443591i	$-0.853704\pi$
$461$		−	4.04823e6i		−	0.887182i	0.896229	−	0.443591i	$-0.146296\pi$
$462$	−1.07075e7	+	7.03869e6i	−2.33392	+	1.53422i
$463$		−	2.13471e6i		−	0.462792i	−0.972860	−	0.231396i	$-0.925671\pi$
$463$		−	2.13471e6i		−	0.462792i	0.972860	−	0.231396i	$-0.0743292\pi$
$464$	−3.27334e6	+	28255.2i	−0.705824	+	0.00609261i
$465$	−196463.	−	113428.i	−0.0421356	−	0.0243270i
$466$	2.17799e6	+	3.75367e6i	0.464614	+	0.800739i
$467$	1.35705e6	+	2.35047e6i	0.287940	+	0.498727i	0.973318	−	0.229461i	$-0.0736963\pi$
$467$	1.35705e6	+	2.35047e6i	0.287940	+	0.498727i	−0.685378	+	0.728188i	$0.740363\pi$
$468$	5.02287e6	−	2.92893e6i	1.06008	−	0.618151i
$469$	−3.70271e6	−	1.87073e6i	−0.777297	−	0.392716i
$470$	2.25740e6	+	1.29682e6i	0.471372	+	0.270792i
$471$	132944.	−	76755.2i	0.0276132	−	0.0159425i
$472$	3.31827e6	−	5.83432e6i	0.685578	−	1.20541i
$473$	4.66303e6	−	8.07660e6i	0.958330	−	1.65988i
$474$	−16251.0	−	7.53085e6i	−0.00332227	−	1.53957i
$475$	1.70422e6			0.346570
$476$	4.80271e6	+	2.40052e6i	0.971559	+	0.485611i
$477$	9.96658e6			2.00563
$478$	−9431.68	−	4.37071e6i	−0.00188808	−	0.874948i
$479$	1.98192e6	−	3.43278e6i	0.394681	−	0.683608i	−0.598379	−	0.801213i	$-0.704188\pi$
$479$	1.98192e6	−	3.43278e6i	0.394681	−	0.683608i	0.993060	+	0.117605i	$0.0375216\pi$
$480$	45429.1	+	4.21028e6i	0.00899977	+	0.834081i
$481$	2.45561e6	−	1.41775e6i	0.483945	−	0.279406i
$482$	3.20333e6	+	1.84024e6i	0.628036	+	0.360792i
$483$	−115696.	−	2.07223e6i	−0.0225658	−	0.404176i
$484$	6.03273e6	+	1.03456e7i	1.17058	+	2.00744i
$485$	−1.44421e6	−	2.50145e6i	−0.278790	−	0.482878i
$486$	−3.52141e6	−	6.06898e6i	−0.676279	−	1.16553i
$487$	−4.33222e6	−	2.50121e6i	−0.827729	−	0.477890i	0.0253455	−	0.999679i	$-0.491931\pi$
$487$	−4.33222e6	−	2.50121e6i	−0.827729	−	0.477890i	−0.853074	+	0.521789i	$0.825265\pi$
$488$	80166.9	−	46978.9i	0.0152386	−	0.00893005i
$489$			6.22158e6i			1.17660i
$490$	−2.32574e6	+	1.72189e6i	−0.437595	+	0.323978i
$491$		−	3.80572e6i		−	0.712416i	−0.934407	−	0.356208i	$-0.884069\pi$
$491$		−	3.80572e6i		−	0.712416i	0.934407	−	0.356208i	$-0.115931\pi$
$492$	−3.30891e6	−	1.89141e6i	−0.616271	−	0.352267i
$493$	3.58307e6	+	2.06868e6i	0.663953	+	0.383334i
$494$	2.10537e6	−	1.22160e6i	0.388160	−	0.225223i
$495$	3.64457e6	+	6.31257e6i	0.668548	+	1.15796i
$496$	−157399.	+	278139.i	−0.0287274	+	0.0507643i
$497$	−28692.8	−	513915.i	−0.00521052	−	0.0933255i
$498$	−6.86320e6	+	1.19469e7i	−1.24009	+	2.15864i
$499$	−444337.	+	256538.i	−0.0798842	+	0.0461212i	−0.539410	−	0.842043i	$-0.681353\pi$
$499$	−444337.	+	256538.i	−0.0798842	+	0.0461212i	0.459526	+	0.888164i	$0.348019\pi$
$500$	−22378.0	−	5.18504e6i	−0.00400310	−	0.927528i
$501$	−538023.	+	931882.i	−0.0957648	+	0.165870i
$502$	5.17677e6	−	11171.1i	0.916853	−	0.00197850i
$503$	−5.64567e6			−0.994936			−0.497468	−	0.867482i	$-0.665737\pi$
$503$	−5.64567e6			−0.994936			−0.497468	+	0.867482i	$0.665737\pi$
$504$	4.24713e6	+	6.40055e6i	0.744764	+	1.12238i
$505$	−4.35939e6			−0.760672
$506$	−2.77448e6	+	5987.14i	−0.481733	+	0.00103954i
$507$	753918.	−	1.30582e6i	0.130258	−	0.225613i
$508$	−7004.71	−	1.62301e6i	−0.00120429	−	0.279037i
$509$	−1.99611e6	+	1.15245e6i	−0.341499	+	0.197165i	−0.660935	−	0.750443i	$-0.729840\pi$
$509$	−1.99611e6	+	1.15245e6i	−0.341499	+	0.197165i	0.319436	+	0.947608i	$0.396507\pi$
$510$	2.65091e6	−	4.61448e6i	0.451305	−	0.785593i
$511$	−1.93907e6	−	979683.i	−0.328505	−	0.165971i
$512$	5.93052e6	−	115193.i	0.999811	−	0.0194201i
$513$	780459.	+	1.35179e6i	0.130935	+	0.226787i
$514$	−5.82263e6	+	3.37847e6i	−0.972100	+	0.564043i
$515$	−4.57743e6	−	2.64278e6i	−0.760509	−	0.439080i
$516$	−8.45698e6	−	4.83410e6i	−1.39827	−	0.799266i
$517$		−	1.10627e7i		−	1.82027i
$518$	2.05767e6	+	3.13022e6i	0.336940	+	0.512566i
$519$			372580.i			0.0607157i
$520$	−1.54637e6	−	2.63880e6i	−0.250788	−	0.427954i
$521$	3.69878e6	+	2.13549e6i	0.596987	+	0.344670i	0.767855	−	0.640623i	$-0.221324\pi$
$521$	3.69878e6	+	2.13549e6i	0.596987	+	0.344670i	−0.170869	+	0.985294i	$0.554657\pi$
$522$	2.97062e6	+	5.11971e6i	0.477167	+	0.822374i
$523$	−1.32366e6	−	2.29264e6i	−0.211603	−	0.366507i	0.740613	−	0.671931i	$-0.234535\pi$
$523$	−1.32366e6	−	2.29264e6i	−0.211603	−	0.366507i	−0.952216	+	0.305424i	$0.901202\pi$
$524$	−1.46880e6	−	2.51886e6i	−0.233686	−	0.400752i
$525$	−3.72677e6	−	5.69606e6i	−0.590112	−	0.901937i
$526$	−8.26153e6	−	4.74605e6i	−1.30196	−	0.747943i
$527$	349813.	−	201965.i	0.0548668	−	0.0316774i
$528$	1.54172e7	−	9.07943e6i	2.40669	−	1.41734i
$529$	−2.99348e6	+	5.18486e6i	−0.465090	+	0.805560i
$530$	−11313.2	−	5.24260e6i	−0.00174942	−	0.810694i
$531$	−1.21366e7			−1.86794
$532$	1.77219e6	+	2.68330e6i	0.271476	+	0.411045i
$533$	2.76855e6			0.422118
$534$	22638.0	+	1.04906e7i	0.00343546	+	1.59202i
$535$	684540.	−	1.18566e6i	0.103399	−	0.179091i
$536$	5.03510e6	+	2.86371e6i	0.757000	+	0.430544i
$537$	2.04643e6	−	1.18151e6i	0.306240	−	0.176808i
$538$	−1.67636e6	−	963030.i	−0.249696	−	0.143445i
$539$	1.12675e7	+	4.92472e6i	1.67054	+	0.730145i
$540$	1.69431e6	−	987986.i	0.250040	−	0.145803i
$541$	3.36292e6	+	5.82475e6i	0.493996	+	0.855626i	0.999976	−	0.00691879i	$-0.00220234\pi$
$541$	3.36292e6	+	5.82475e6i	0.493996	+	0.855626i	−0.505980	+	0.862545i	$0.668869\pi$
$542$	3.23307e6	+	5.57204e6i	0.472734	+	0.814735i
$543$	1.38792e7	+	8.01315e6i	2.02006	+	1.16628i
$544$	−6.53272e6	−	3.67826e6i	−0.946447	−	0.532900i
$545$			5.52977e6i			0.797473i
$546$	−8.68700e6	−	4.36545e6i	−1.24706	−	0.626682i
$547$		−	8.94593e6i		−	1.27837i	−0.769052	−	0.639186i	$-0.779271\pi$
$547$		−	8.94593e6i		−	1.27837i	0.769052	−	0.639186i	$-0.220729\pi$
$548$	667765.	−	1.16822e6i	0.0949888	−	0.166178i
$549$	−145506.	−	84007.8i	−0.0206039	−	0.0118957i
$550$	−7.87059e6	+	4.56676e6i	−1.10943	+	0.643727i
$551$	1.23896e6	+	2.14595e6i	0.173852	+	0.301121i
$552$	18760.7	+	2.89791e6i	0.00262060	+	0.404797i
$553$	−6.04756e6	+	3.95675e6i	−0.840945	+	0.550207i
$554$	5.72589e6	−	9.96715e6i	0.792627	−	1.37974i
$555$	3.21541e6	−	1.85642e6i	0.443102	−	0.255825i
$556$	3.93801e6	−	16995.9i	0.540243	−	0.00233162i
$557$	−1.80883e6	+	3.13298e6i	−0.247036	+	0.427878i	−0.962702	−	0.270564i	$-0.912790\pi$
$557$	−1.80883e6	+	3.13298e6i	−0.247036	+	0.427878i	0.715666	+	0.698442i	$0.246123\pi$
$558$	577880.	−	1247.02i	0.0785692	−	0.000169547i
$559$	7.07591e6			0.957752
$560$	3.36198e6	−	2.24133e6i	0.453029	−	0.302020i
$561$	−2.26139e7			−3.03367
$562$	−663103.	+	1430.93i	−0.0885605	+	0.000191107i
$563$	−6.72630e6	+	1.16503e7i	−0.894345	+	1.54905i	−0.0597320	+	0.998214i	$0.519025\pi$
$563$	−6.72630e6	+	1.16503e7i	−0.894345	+	1.54905i	−0.834613	+	0.550837i	$0.814309\pi$
$564$	−1.15549e7	+	49869.7i	−1.52957	+	0.00660145i
$565$	2.43051e6	−	1.40326e6i	0.320315	−	0.184934i
$566$	2.55531e6	−	4.44806e6i	0.335276	−	0.583619i
$567$	−1.83854e6	+	3.63899e6i	−0.240168	+	0.475361i
$568$	4652.66	+	718684.i	0.000605105	+	0.0934689i
$569$	−2.19254e6	−	3.79760e6i	−0.283901	−	0.491732i	0.688441	−	0.725293i	$-0.258296\pi$
$569$	−2.19254e6	−	3.79760e6i	−0.283901	−	0.491732i	−0.972342	+	0.233561i	$0.924962\pi$
$570$	2.75680e6	−	1.59958e6i	0.355401	−	0.206215i
$571$	8.28356e6	+	4.78251e6i	1.06323	+	0.613855i	0.926324	−	0.376729i	$-0.122951\pi$
$571$	8.28356e6	+	4.78251e6i	1.06323	+	0.613855i	0.136905	+	0.990584i	$0.456285\pi$
$572$	−6.44972e6	+	1.12834e7i	−0.824235	+	1.44195i
$573$			2.01189e6i			0.255987i
$574$	211768.	+	3.65139e6i	0.0268276	+	0.462571i
$575$		−	1.47385e6i		−	0.185902i
$576$	−5.48265e6	−	9.21850e6i	−0.688548	−	1.15772i
$577$	9.60129e6	+	5.54330e6i	1.20058	+	0.693153i	0.960683	−	0.277646i	$-0.0895543\pi$
$577$	9.60129e6	+	5.54330e6i	1.20058	+	0.693153i	0.239893	+	0.970799i	$0.422888\pi$
$578$	724545.	+	1.24872e6i	0.0902081	+	0.155469i
$579$	−4.94697e6	−	8.56841e6i	−0.613258	−	1.06219i
$580$	2.68969e6	−	1.56841e6i	0.331996	−	0.193593i
$581$	1.32013e7	−	737054.i	1.62247	−	0.0905855i
$582$	1.11164e7	+	6.38613e6i	1.36037	+	0.781502i
$583$	−1.92931e7	+	1.11389e7i	−2.35088	+	1.35728i
$584$	2.63683e6	+	1.49970e6i	0.319927	+	0.181958i
$585$	−2.76523e6	+	4.78951e6i	−0.334073	+	0.578631i
$586$	−3097.41	−	1.43536e6i	−0.000372610	−	0.172670i
$587$	−8.96982e6			−1.07446			−0.537228	−	0.843437i	$-0.680528\pi$
$587$	−8.96982e6			−1.07446			−0.537228	+	0.843437i	$0.680528\pi$
$588$	5.09305e6	−	1.17911e7i	0.607483	−	1.40640i
$589$	241919.			0.0287331
$590$	13776.4	+	6.38409e6i	0.00162932	+	0.755038i
$591$	991537.	−	1.71739e6i	0.116772	−	0.202256i
$592$	−2.65426e6	−	4.50701e6i	−0.311271	−	0.528548i
$593$	−6.92527e6	+	3.99831e6i	−0.808724	+	0.466917i	−0.846512	−	0.532369i	$-0.821302\pi$
$593$	−6.92527e6	+	3.99831e6i	−0.808724	+	0.466917i	0.0377888	+	0.999286i	$0.487969\pi$
$594$	−7.22677e6	−	4.15161e6i	−0.840384	−	0.482781i
$595$	−5.09902e6	+	284687.i	−0.590466	+	0.0329667i
$596$	−3.08808e6	−	5.29579e6i	−0.356100	−	0.610682i
$597$	−7.54885e6	−	1.30750e7i	−0.866852	−	1.50143i
$598$	−1.05647e6	−	1.82077e6i	−0.120810	−	0.208211i
$599$	6.63704e6	+	3.83190e6i	0.755801	+	0.436362i	0.827786	−	0.561044i	$-0.189600\pi$
$599$	6.63704e6	+	3.83190e6i	0.755801	+	0.436362i	−0.0719850	+	0.997406i	$0.522933\pi$
$600$	4.80544e6	+	8.20020e6i	0.544948	+	0.929922i
$601$			2.64361e6i			0.298547i	0.988796	+	0.149273i	$0.0476934\pi$
$601$			2.64361e6i			0.298547i	−0.988796	+	0.149273i	$0.952307\pi$
$602$	541242.	+	9.33231e6i	0.0608696	+	1.04954i
$603$		−	1.04741e7i		−	1.17307i
$604$	−1.11310e6	−	636261.i	−0.124149	−	0.0709648i
$605$	−9.86497e6	−	5.69554e6i	−1.09574	−	0.632625i
$606$	1.67358e7	−	9.71065e6i	1.85125	−	1.07415i
$607$	4.36221e6	+	7.55556e6i	0.480545	+	0.832329i	0.999751	−	0.0223204i	$-0.00710539\pi$
$607$	4.36221e6	+	7.55556e6i	0.480545	+	0.832329i	−0.519205	+	0.854649i	$0.673772\pi$
$608$	−2.28687e6	−	3.86409e6i	−0.250890	−	0.423924i
$609$	4.46311e6	−	8.83377e6i	0.487634	−	0.965168i
$610$	−44024.4	+	76634.0i	−0.00479037	+	0.00833867i
$611$	7.26904e6	−	4.19678e6i	0.787724	−	0.454792i
$612$	58506.8	+	1.35562e7i	0.00631433	+	1.46305i
$613$	−1.74313e6	+	3.01918e6i	−0.187360	+	0.324518i	−0.944369	−	0.328887i	$-0.893327\pi$
$613$	−1.74313e6	+	3.01918e6i	−0.187360	+	0.324518i	0.757009	+	0.653404i	$0.226660\pi$
$614$	−2.28857e6	+	4938.57i	−0.244987	+	0.000528665i
$615$	3.62517e6			0.386493
$616$	−1.53749e7	−	7.64336e6i	−1.63253	−	0.811582i
$617$	410927.			0.0434562			0.0217281	−	0.999764i	$-0.493083\pi$
$617$	410927.			0.0434562			0.0217281	+	0.999764i	$0.493083\pi$
$618$	2.34598e7	−	50624.5i	2.47089	−	0.00533200i
$619$	7.51026e6	−	1.30082e7i	0.787822	−	1.36455i	−0.139476	−	0.990225i	$-0.544542\pi$
$619$	7.51026e6	−	1.30082e7i	0.787822	−	1.36455i	0.927298	−	0.374323i	$-0.122125\pi$
$620$	−1311.91	−	303974.i	−0.000137065	−	0.0317583i
$621$	1.16906e6	−	674960.i	0.121649	−	0.0702342i
$622$	5.63313e6	−	9.80567e6i	0.583813	−	1.01625i
$623$	8.42437e6	−	5.51183e6i	0.869596	−	0.568952i
$624$	1.18146e7	+	6.68584e6i	1.21466	+	0.687376i
$625$	−969386.	−	1.67903e6i	−0.0992651	−	0.171932i
$626$	5.14270e6	−	2.98396e6i	0.524512	−	0.304338i
$627$	−1.17293e7	−	6.77190e6i	−1.19152	−	0.687926i
$628$	178581.	+	102079.i	0.0180691	+	0.0103285i
$629$			6.61090e6i			0.666245i
$630$	−6.52832e6	−	3.28066e6i	−0.655315	−	0.329314i
$631$			8.11471e6i			0.811334i	0.914021	+	0.405667i	$0.132961\pi$
$631$			8.11471e6i			0.811334i	−0.914021	+	0.405667i	$0.867039\pi$
$632$	8.70624e6	−	5.10198e6i	0.867037	−	0.508096i
$633$	4.44286e6	+	2.56509e6i	0.440711	+	0.254444i
$634$	−4.52736e6	−	7.80269e6i	−0.447324	−	0.770941i
$635$	771874.	+	1.33692e6i	0.0759647	+	0.131575i
$636$	1.17215e7	+	2.01013e7i	1.14905	+	1.97052i
$637$	1.03857e6	+	9.27186e6i	0.101411	+	0.905354i
$638$	−1.14724e7	−	6.59060e6i	−1.11584	−	0.641023i
$639$	1.12545e6	−	649781.i	0.109037	−	0.0629527i
$640$	−4.84287e6	+	2.89444e6i	−0.467362	+	0.279328i
$641$	1.17487e6	−	2.03494e6i	0.112939	−	0.195617i	−0.804015	−	0.594609i	$-0.797307\pi$
$641$	1.17487e6	−	2.03494e6i	0.112939	−	0.195617i	0.916954	+	0.398993i	$0.130640\pi$
$642$	13112.9	+	6.07661e6i	0.00125563	+	0.581867i
$643$	2.27215e6			0.216726			0.108363	−	0.994111i	$-0.465439\pi$
$643$	2.27215e6			0.216726			0.108363	+	0.994111i	$0.465439\pi$
$644$	2.32058e6	−	1.53263e6i	0.220486	−	0.145621i
$645$	9.26530e6			0.876921
$646$	12246.4	+	5.67507e6i	0.00115459	+	0.535045i
$647$	−3.35059e6	+	5.80338e6i	−0.314673	+	0.545030i	−0.979368	−	0.202085i	$-0.935228\pi$
$647$	−3.35059e6	+	5.80338e6i	−0.314673	+	0.545030i	0.664695	+	0.747115i	$0.268562\pi$
$648$	2.81444e6	−	4.94845e6i	0.263302	−	0.462948i
$649$	2.34938e7	−	1.35642e7i	2.18948	−	1.26410i
$650$	−5.98651e6	−	3.43911e6i	−0.555764	−	0.319274i
$651$	−529027.	−	808573.i	−0.0489244	−	0.0747768i
$652$	−7.20168e6	+	4.19943e6i	−0.663460	+	0.386876i
$653$	−6.37918e6	−	1.10491e7i	−0.585439	−	1.01401i	−0.994821	−	0.101647i	$-0.967589\pi$
$653$	−6.37918e6	−	1.10491e7i	−0.585439	−	1.01401i	0.409382	−	0.912363i	$-0.365744\pi$
$654$	−1.23177e7	−	2.12290e7i	−1.12612	−	1.94082i
$655$	2.40184e6	+	1.38670e6i	0.218746	+	0.126293i
$656$	−44081.7	−	5.10683e6i	−0.00399944	−	0.463331i
$657$		−	5.48517e6i		−	0.495766i
$658$	6.09108e6	+	9.26600e6i	0.548441	+	0.834310i
$659$			1.26421e7i			1.13398i	0.823724	+	0.566991i	$0.191893\pi$
$659$			1.26421e7i			1.13398i	−0.823724	+	0.566991i	$0.808107\pi$
$660$	−8.44536e6	+	1.47747e7i	−0.754672	+	1.32026i
$661$	2.49179e6	+	1.43863e6i	0.221823	+	0.128070i	0.606794	−	0.794859i	$-0.292455\pi$
$661$	2.49179e6	+	1.43863e6i	0.221823	+	0.128070i	−0.384971	+	0.922929i	$0.625789\pi$
$662$	−1.22163e7	+	7.08825e6i	−1.08341	+	0.628628i
$663$	−8.57888e6	−	1.48591e7i	−0.757961	−	1.31283i
$664$	−1.84614e7	+	119517.i	−1.62497	+	0.0105198i
$665$	−2.72999e6	−	1.37928e6i	−0.239390	−	0.120948i
$666$	−4.71125e6	+	8.20095e6i	−0.411577	+	0.716438i
$667$	1.85587e6	−	1.07149e6i	0.161522	−	0.0932550i
$668$	−1.44184e6	+	6222.79i	−0.125019	+	0.000539566i
$669$	3.30186e6	−	5.71898e6i	0.285228	−	0.494030i
$670$	−5.50956e6	+	11889.2i	−0.474165	+	0.00102321i
$671$	375556.			0.0322009
$672$	−7.91414e6	+	1.60934e7i	−0.676053	+	1.37476i
$673$	2.11054e7			1.79620			0.898102	−	0.439787i	$-0.144946\pi$
$673$	2.11054e7			1.79620			0.898102	+	0.439787i	$0.144946\pi$
$674$	−7.68196e6	+	16577.1i	−0.651362	+	0.00140559i
$675$	2.21367e6	−	3.83419e6i	0.187005	−	0.323903i
$676$	2.02041e6	−	8719.85i	0.170049	−	0.000733909i
$677$	−1.00811e7	+	5.82034e6i	−0.845352	+	0.488064i	−0.859080	−	0.511842i	$-0.828963\pi$
$677$	−1.00811e7	+	5.82034e6i	−0.845352	+	0.488064i	0.0137279	+	0.999906i	$0.495630\pi$
$678$	−6.20503e6	+	1.08012e7i	−0.518405	+	0.902396i
$679$	−685820.	−	1.22837e7i	−0.0570868	−	1.02248i
$680$	7.13073e6	−	46163.4i	0.591373	−	0.00382847i
$681$	1.31311e6	+	2.27438e6i	0.108501	+	0.187929i
$682$	−1.11725e6	+	648266.i	−0.0919795	+	0.0533694i
$683$	−1.17444e7	−	6.78066e6i	−0.963342	−	0.556186i	−0.0661423	−	0.997810i	$-0.521069\pi$
$683$	−1.17444e7	−	6.78066e6i	−0.963342	−	0.556186i	−0.897200	+	0.441624i	$0.854402\pi$
$684$	−4.02915e6	+	7.04877e6i	−0.329286	+	0.576067i
$685$			1.27988e6i			0.104218i
$686$	−1.21491e7	+	2.07896e6i	−0.985673	+	0.168669i
$687$			3.21706e7i			2.60057i
$688$	−112665.	−	1.30521e7i	−0.00907440	−	1.05126i
$689$	−1.46382e7	−	8.45134e6i	−1.17473	−	0.678231i
$690$	−1.38336e6	−	2.38415e6i	−0.110614	−	0.190639i
$691$	1.38001e6	+	2.39025e6i	0.109948	+	0.190436i	0.915749	−	0.401751i	$-0.131598\pi$
$691$	1.38001e6	+	2.39025e6i	0.109948	+	0.190436i	−0.805801	+	0.592187i	$0.798265\pi$
$692$	−431273.	+	251484.i	−0.0342363	+	0.0199639i
$693$	1.73071e6	+	3.09987e7i	0.136896	+	2.45194i
$694$	9.13578e6	+	5.24829e6i	0.720024	+	0.413637i
$695$	−3.24386e6	+	1.87285e6i	−0.254742	+	0.147075i
$696$	−6.83213e6	+	1.20125e7i	−0.534605	+	0.939964i
$697$	−3.22741e6	+	5.59003e6i	−0.251635	+	0.435845i
$698$	7097.96	+	3.28924e6i	0.000551435	+	0.255539i
$699$	1.83211e7			1.41827
$700$	4.07788e6	−	8.15858e6i	0.314550	−	0.629317i
$701$	1.78304e6			0.137046			0.0685230	−	0.997650i	$-0.478171\pi$
$701$	1.78304e6			0.137046			0.0685230	+	0.997650i	$0.478171\pi$
$702$	−13645.7	−	6.32350e6i	−0.00104508	−	0.484300i
$703$	−1.97968e6	+	3.42891e6i	−0.151080	+	0.261678i
$704$	2.09160e7	+	1.17174e7i	1.59055	+	0.891047i
$705$	9.51818e6	−	5.49533e6i	0.721242	−	0.416409i
$706$	2.01255e7	+	1.15616e7i	1.51962	+	0.872985i
$707$	−1.65731e7	−	8.37325e6i	−1.24696	−	0.630007i
$708$	−1.42736e7	−	2.44780e7i	−1.07016	−	1.83524i
$709$	1.29700e7	+	2.24647e7i	0.969001	+	1.67836i	0.698458	+	0.715651i	$0.253870\pi$
$709$	1.29700e7	+	2.24647e7i	0.969001	+	1.67836i	0.270542	+	0.962708i	$0.412797\pi$
$710$	−343074.	−	591271.i	−0.0255412	−	0.0440191i
$711$	−1.58021e7	−	9.12336e6i	−1.17231	−	0.676832i
$712$	−1.21280e7	+	7.10716e6i	−0.896577	+	0.525407i
$713$		−	209217.i		−	0.0154125i
$714$	1.89412e7	−	1.24511e7i	1.39047	−	0.914036i
$715$		−	1.23619e7i		−	0.904316i
$716$	2.74893e6	+	1.57132e6i	0.200393	+	0.114546i
$717$	−1.59797e7	−	9.22588e6i	−1.16084	−	0.670209i
$718$	7.57369e6	−	4.39449e6i	0.548273	−	0.318125i
$719$	−9.60263e6	−	1.66322e7i	−0.692737	−	1.19985i	−0.970938	−	0.239332i	$-0.923072\pi$
$719$	−9.60263e6	−	1.66322e7i	−0.692737	−	1.19985i	0.278201	−	0.960523i	$-0.410262\pi$
$720$	8.87870e6	+	5.02444e6i	0.638290	+	0.361207i
$721$	−1.23259e7	−	1.88391e7i	−0.883040	−	1.34965i
$722$	5.28418e6	−	9.19826e6i	0.377255	−	0.656693i
$723$	1.35066e7	−	7.79806e6i	0.960951	−	0.554805i
$724$	92680.5	+	2.14743e7i	0.00657116	+	1.52256i
$725$	3.51416e6	−	6.08671e6i	0.248300	−	0.430069i
$726$	5.05589e7	−	109102.i	3.56005	−	0.00768233i
$727$	1.64122e7			1.15168			0.575838	−	0.817564i	$-0.304676\pi$
$727$	1.64122e7			1.15168			0.575838	+	0.817564i	$0.304676\pi$
$728$	−810394.	−	1.30021e7i	−0.0566719	−	0.909251i
$729$	−2.19798e7			−1.53181
$730$	−2.88530e6	+	6226.27i	−0.200394	+	0.000432435i
$731$	−8.24868e6	+	1.42871e7i	−0.570941	+	0.988899i
$732$	−1692.97	−	392266.i	−0.000116781	−	0.0270584i
$733$	−1.23321e7	+	7.11994e6i	−0.847768	+	0.489459i	−0.859897	−	0.510467i	$-0.829472\pi$
$733$	−1.23321e7	+	7.11994e6i	−0.847768	+	0.489459i	0.0121290	+	0.999926i	$0.496139\pi$
$734$	−3.90260e6	+	6.79331e6i	−0.267371	+	0.465416i
$735$	1.35991e6	+	1.21407e7i	0.0928523	+	0.828945i
$736$	−3.34176e6	+	1.97774e6i	−0.227395	+	0.134578i
$737$	1.17061e7	+	2.02755e7i	0.793857	+	1.37500i
$738$	−7.98740e6	+	4.63454e6i	−0.539839	+	0.313232i
$739$	−4.71865e6	−	2.72431e6i	−0.317838	−	0.183504i	0.332590	−	0.943071i	$-0.392077\pi$
$739$	−4.71865e6	−	2.72431e6i	−0.317838	−	0.183504i	−0.650429	+	0.759567i	$0.725411\pi$
$740$	4.31920e6	+	2.46890e6i	0.289950	+	0.165739i
$741$		−	1.02760e7i		−	0.687511i
$742$	1.00267e7	−	1.99525e7i	0.668569	−	1.33041i
$743$		−	2.84427e7i		−	1.89016i	−0.326840	−	0.945080i	$-0.605984\pi$
$743$		−	2.84427e7i		−	1.89016i	0.326840	−	0.945080i	$-0.394016\pi$
$744$	682146.	+	1.16404e6i	0.0451799	+	0.0770969i
$745$	5.04975e6	+	2.91547e6i	0.333334	+	0.192450i
$746$	−1.45859e7	−	2.51381e7i	−0.959593	−	1.65381i
$747$	1.66914e7	+	2.89104e7i	1.09444	+	1.89563i
$748$	−1.52639e7	−	2.61763e7i	−0.997499	−	1.71063i
$749$	4.87975e6	−	3.19268e6i	0.317828	−	0.207946i
$750$	−1.89807e7	−	1.09039e7i	−1.23213	−	0.707833i
$751$	1.00642e7	−	5.81055e6i	0.651146	−	0.375939i	−0.137749	−	0.990467i	$-0.543987\pi$
$751$	1.00642e7	−	5.81055e6i	0.651146	−	0.375939i	0.788895	+	0.614528i	$0.210653\pi$
$752$	−7.85707e6	−	1.33416e7i	−0.506660	−	0.860324i
$753$	1.09274e7	−	1.89267e7i	0.702308	−	1.21643i
$754$	−21662.2	−	1.00384e7i	−0.00138763	−	0.643039i
$755$	1.21949e6			0.0778597
$756$	8.33892e6	−	501687.i	0.530646	−	0.0319248i
$757$	532142.			0.0337511			0.0168756	−	0.999858i	$-0.494628\pi$
$757$	532142.			0.0337511			0.0168756	+	0.999858i	$0.494628\pi$
$758$	56120.9	+	2.60069e7i	0.00354774	+	1.64405i
$759$	−5.85650e6	+	1.01438e7i	−0.369006	+	0.639138i
$760$	3.71235e6	+	2.11140e6i	0.233139	+	0.132598i
$761$	−1.86647e7	+	1.07761e7i	−1.16831	+	0.674526i	−0.953282	−	0.302081i	$-0.902319\pi$
$761$	−1.86647e7	+	1.07761e7i	−1.16831	+	0.674526i	−0.215031	+	0.976607i	$0.568985\pi$
$762$	−5.94128e6	−	3.41313e6i	−0.370675	−	0.212944i
$763$	−1.06212e7	+	2.10225e7i	−0.660486	+	1.30729i
$764$	−2.32883e6	+	1.35799e6i	−0.144346	+	0.0841709i
$765$	−6.44707e6	−	1.11667e7i	−0.398299	−	0.689874i
$766$	9.30465e6	+	1.60361e7i	0.572965	+	0.987477i
$767$	1.78254e7	+	1.02915e7i	1.09408	+	0.631669i
$768$	1.21445e7	−	2.18995e7i	0.742979	−	1.33977i
$769$		−	8.36581e6i		−	0.510143i	−0.966922	−	0.255072i	$-0.917901\pi$
$769$		−	8.36581e6i		−	0.510143i	0.966922	−	0.255072i	$-0.0820990\pi$
$770$	1.63039e7	−	945572.i	0.990981	−	0.0574735i
$771$			2.84194e7i			1.72179i
$772$	6.57911e6	−	1.15098e7i	0.397305	−	0.695062i
$773$	−1.05355e7	−	6.08268e6i	−0.634172	−	0.366139i	0.148194	−	0.988958i	$-0.452654\pi$
$773$	−1.05355e7	−	6.08268e6i	−0.634172	−	0.366139i	−0.782366	+	0.622819i	$0.785987\pi$
$774$	−2.04144e7	+	1.18451e7i	−1.22485	+	0.710697i
$775$	−343086.	−	594243.i	−0.0205187	−	0.0355394i
$776$	111209.	+	1.71781e7i	0.00662957	+	1.02405i
$777$	1.57897e7	−	881565.i	0.938255	−	0.0523844i
$778$	−1.54715e7	+	2.69315e7i	−0.916399	+	1.59519i
$779$	−3.34795e6	+	1.93294e6i	−0.197668	+	0.114123i
$780$	−1.29119e7	+	55726.4i	−0.759898	+	0.00327962i
$781$	−1.45242e6	+	2.51566e6i	−0.0852048	+	0.147579i
$782$	4.90794e6	−	10591.0i	0.287000	−	0.000619326i
$783$	6.43735e6			0.375234
$784$	1.70862e7	−	2.06336e6i	0.992787	−	0.119890i
$785$	−195650.			−0.0113320
$786$	−1.23096e7	+	26563.3i	−0.710704	+	0.00153365i
$787$	1.62373e7	−	2.81238e7i	0.934495	−	1.61859i	0.158962	−	0.987285i	$-0.449185\pi$
$787$	1.62373e7	−	2.81238e7i	0.934495	−	1.61859i	0.775533	−	0.631307i	$-0.217481\pi$
$788$	2.65720e6	−	11468.2i	0.152444	−	0.000657928i
$789$	−3.48342e7	+	2.01115e7i	−1.99211	+	1.15014i
$790$	−4.78112e6	+	8.32256e6i	−0.272560	+	0.474449i
$791$	1.19354e7	−	666371.i	0.678257	−	0.0378682i
$792$	−280643.	−	4.33501e7i	−0.0158979	−	2.45571i
$793$	142472.	+	246768.i	0.00804537	+	0.0139350i
$794$	−2.20289e6	+	1.27818e6i	−0.124006	+	0.0719519i
$795$	−1.91674e7	−	1.10663e7i	−1.07559	−	0.620990i
$796$	1.00394e7	−	1.75634e7i	0.561598	−	0.982484i
$797$		−	3.10780e7i		−	1.73303i	−0.499147	−	0.866517i	$-0.666353\pi$
$797$		−	3.10780e7i		−	1.73303i	0.499147	−	0.866517i	$-0.333647\pi$
$798$	1.35529e7	−	786022.i	0.753398	−	0.0436946i
$799$			1.95694e7i			1.08445i
$800$	−6.24843e6	+	1.10974e7i	−0.345180	+	0.613051i
$801$	2.20127e7	+	1.27090e7i	1.21225	+	0.699892i
$802$	−1.44478e6	−	2.49000e6i	−0.0793168	−	0.136699i
$803$	6.13035e6	+	1.06181e7i	0.335503	+	0.581108i
$804$	2.11249e7	−	1.23183e7i	1.15253	−	0.672065i
$805$	−1.19283e6	+	2.36096e6i	−0.0648769	+	0.128410i
$806$	−849804.	−	488193.i	−0.0460767	−	0.0264700i
$807$	−7.06826e6	+	4.08086e6i	−0.382057	+	0.220581i
$808$	2.25367e7	+	1.28178e7i	1.21440	+	0.690692i
$809$	−4.82186e6	+	8.35171e6i	−0.259026	+	0.448646i	−0.965981	−	0.258612i	$-0.916735\pi$
$809$	−4.82186e6	+	8.35171e6i	−0.259026	+	0.448646i	0.706955	+	0.707258i	$0.250068\pi$
$810$	11684.6	+	5.41475e6i	0.000625752	+	0.289978i
$811$	1.36611e7			0.729345			0.364672	−	0.931136i	$-0.381181\pi$
$811$	1.36611e7			0.729345			0.364672	+	0.931136i	$0.381181\pi$
$812$	1.32379e7	−	796418.i	0.704577	−	0.0423888i
$813$	2.71964e7			1.44306
$814$	−45619.9	−	2.11406e7i	−0.00241320	−	1.11830i
$815$	3.96472e6	−	6.86709e6i	0.209083	−	0.362142i
$816$	−2.72722e7	+	1.60611e7i	−1.43382	+	0.844403i
$817$	−8.55677e6	+	4.94025e6i	−0.448492	+	0.258937i
$818$	−2.22343e7	−	1.27731e7i	−1.16182	−	0.667440i
$819$	−1.97119e7	+	1.28970e7i	−1.02688	+	0.671858i
$820$	2.44692e6	+	4.19626e6i	0.127082	+	0.217935i
$821$	5.50398e6	+	9.53317e6i	0.284983	+	0.493605i	0.972605	−	0.232464i	$-0.0746787\pi$
$821$	5.50398e6	+	9.53317e6i	0.284983	+	0.493605i	−0.687622	+	0.726069i	$0.741345\pi$
$822$	−2.85096e6	−	4.91348e6i	−0.147167	−	0.253636i
$823$	−8.49007e6	−	4.90175e6i	−0.436930	−	0.252262i	0.265364	−	0.964148i	$-0.414508\pi$
$823$	−8.49007e6	−	4.90175e6i	−0.436930	−	0.252262i	−0.702295	+	0.711886i	$0.747841\pi$
$824$	1.58935e7	+	2.71213e7i	0.815456	+	1.39153i
$825$			3.84153e7i			1.96503i
$826$	−1.22098e7	+	2.42968e7i	−0.622670	+	1.23908i
$827$		−	7.36261e6i		−	0.374342i	−0.982327	−	0.187171i	$-0.940068\pi$
$827$		−	7.36261e6i		−	0.374342i	0.982327	−	0.187171i	$-0.0599318\pi$
$828$	6.09594e6	+	3.48450e6i	0.309005	+	0.176630i
$829$	−1.73341e6	−	1.00079e6i	−0.0876024	−	0.0505773i	0.455559	−	0.890206i	$-0.349439\pi$
$829$	−1.73341e6	−	1.00079e6i	−0.0876024	−	0.0505773i	−0.543161	+	0.839628i	$0.682773\pi$
$830$	1.51885e7	−	8.81281e6i	0.765276	−	0.444037i
$831$	−2.42636e7	−	4.20258e7i	−1.21886	−	2.11112i
$832$	235510.	+	1.81885e7i	0.0117951	+	0.910939i
$833$	−1.99317e7	−	8.71160e6i	−0.995250	−	0.434996i
$834$	8.28148e6	−	1.44157e7i	0.412281	−	0.717663i
$835$	1.18769e6	−	685712.i	0.0589504	−	0.0340350i
$836$	−78324.1	−	1.81479e7i	−0.00387597	−	0.898072i
$837$	314238.	−	544276.i	0.0155040	−	0.0268538i
$838$	−3.69099e7	+	79648.9i	−1.81565	+	0.00391805i
$839$	−4.47282e6			−0.219370			−0.109685	−	0.993966i	$-0.534984\pi$
$839$	−4.47282e6			−0.219370			−0.109685	+	0.993966i	$0.534984\pi$
$840$	−1.06114e6	−	1.70251e7i	−0.0518890	−	0.832514i
$841$	−1.02920e7			−0.501775
$842$	−3.31679e7	+	71574.0i	−1.61227	+	0.00347917i
$843$	−1.39971e6	+	2.42436e6i	−0.0678372	+	0.117497i
$844$	29667.9	+	6.87414e6i	0.00143361	+	0.332171i
$845$	−1.66428e6	+	960872.i	−0.0801834	+	0.0462939i
$846$	−1.39462e7	+	2.42763e7i	−0.669929	+	1.16615i
$847$	−2.65639e7	−	4.06007e7i	−1.27228	−	1.94458i
$848$	−1.53562e7	+	2.71359e7i	−0.733320	+	1.29585i
$849$	−1.08282e7	−	1.87549e7i	−0.515568	−	0.892990i
$850$	1.39227e7	−	8.07839e6i	0.660962	−	0.383511i
$851$	2.96540e6	+	1.71208e6i	0.140365	+	0.0810399i
$852$	2.63414e6	+	1.50570e6i	0.124320	+	0.0710625i
$853$		−	1.34576e7i		−	0.633279i	−0.948546	−	0.316639i	$-0.897445\pi$
$853$		−	1.34576e7i		−	0.633279i	0.948546	−	0.316639i	$-0.102555\pi$
$854$	−314561.	+	206779.i	−0.0147591	+	0.00970203i
$855$		−	7.72249e6i		−	0.361278i
$856$	−7.02502e6	+	4.11676e6i	−0.327690	+	0.192031i
$857$	1.23825e7	+	7.14906e6i	0.575914	+	0.332504i	0.759508	−	0.650498i	$-0.225440\pi$
$857$	1.23825e7	+	7.14906e6i	0.575914	+	0.332504i	−0.183594	+	0.983002i	$0.558773\pi$
$858$	2.75365e7	+	4.74577e7i	1.27700	+	2.20084i
$859$	4.55033e6	+	7.88139e6i	0.210407	+	0.364435i	0.951842	−	0.306589i	$-0.0991879\pi$
$859$	4.55033e6	+	7.88139e6i	0.210407	+	0.364435i	−0.741435	+	0.671025i	$0.765855\pi$
$860$	6.25389e6	+	1.07249e7i	0.288339	+	0.494478i
$861$	1.37818e7	+	6.96301e6i	0.633575	+	0.320103i
$862$	9.18819e6	+	5.27840e6i	0.421174	+	0.241955i
$863$	1.37994e7	−	7.96708e6i	0.630715	−	0.364143i	−0.150314	−	0.988638i	$-0.548029\pi$
$863$	1.37994e7	−	7.96708e6i	0.630715	−	0.364143i	0.781029	+	0.624495i	$0.214695\pi$
$864$	−1.16640e7	+	125855.i	−0.531575	+	0.00573572i
$865$	237428.	−	411237.i	0.0107892	−	0.0186875i
$866$	68386.9	+	3.16910e7i	0.00309869	+	1.43596i
$867$	6.09482e6			0.275368
$868$	578867.	−	1.15814e6i	0.0260783	−	0.0521747i
$869$	4.07859e7			1.83215
$870$	−28364.8	−	1.31445e7i	−0.00127052	−	0.588769i
$871$	−8.88169e6	+	1.53835e7i	−0.396689	+	0.687085i
$872$	1.62590e7	−	2.85872e7i	0.724107	−	1.27315i
$873$	2.69008e7	−	1.55312e7i	1.19462	−	0.689714i
$874$	2.54880e6	+	1.46422e6i	0.112864	+	0.0648379i
$875$	1.17100e6	+	2.09737e7i	0.0517054	+	0.926094i
$876$	1.10629e7	−	6.45098e6i	0.487089	−	0.284031i
$877$	−3.48992e6	−	6.04472e6i	−0.153220	−	0.265385i	0.779189	−	0.626789i	$-0.215631\pi$
$877$	−3.48992e6	−	6.04472e6i	−0.153220	−	0.265385i	−0.932410	+	0.361403i	$0.882298\pi$
$878$	7.75555e6	+	1.33663e7i	0.339529	+	0.585161i
$879$	−5.24780e6	−	3.02982e6i	−0.229090	−	0.132265i
$880$	−2.28026e7	+	196830.i	−0.992609	+	0.00856812i
$881$			1.32076e7i			0.573304i	0.958035	+	0.286652i	$0.0925423\pi$
$881$			1.32076e7i			0.573304i	−0.958035	+	0.286652i	$0.907458\pi$
$882$	−1.85174e7	−	2.50112e7i	−0.801508	−	1.08259i
$883$			1.97610e7i			0.852917i	0.904507	+	0.426458i	$0.140239\pi$
$883$			1.97610e7i			0.852917i	−0.904507	+	0.426458i	$0.859761\pi$
$884$	1.14093e7	−	1.99599e7i	0.491052	−	0.859068i
$885$	2.33408e7	+	1.34758e7i	1.00175	+	0.578358i
$886$	6.07851e6	−	3.52694e6i	0.260143	−	0.150943i
$887$	−1.61453e7	−	2.79644e7i	−0.689027	−	1.19343i	−0.972153	−	0.234347i	$-0.924705\pi$
$887$	−1.61453e7	−	2.79644e7i	−0.689027	−	1.19343i	0.283126	−	0.959083i	$-0.408629\pi$
$888$	−2.20811e7	+	142950.i	−0.939696	+	0.00608347i
$889$	366543.	+	6.56514e6i	0.0155550	+	0.278606i
$890$	6.66019e6	−	1.15935e7i	0.281846	−	0.490613i
$891$	1.99266e7	−	1.15046e7i	0.840889	−	0.485487i
$892$	8.84859e6	−	38189.4i	0.372359	−	0.00160706i
$893$	−5.86021e6	+	1.01502e7i	−0.245915	+	0.425937i
$894$	−2.58804e7	+	55848.1i	−1.08300	+	0.00233703i
$895$	−3.01168e6			−0.125675
$896$	−2.39706e7	+	1.70187e6i	−0.997489	+	0.0708200i
$897$	−8.88695e6			−0.368784
$898$	1.59015e7	−	34314.2i	0.658031	−	0.00141998i
$899$	498846.	−	864027.i	0.0205858	−	0.0356556i
$900$	2.30285e7	−	99388.0i	0.947674	−	0.00409004i
$901$	3.41286e7	−	1.97041e7i	1.40057	−	0.808622i
$902$	1.02822e7	−	1.78983e7i	0.420793	−	0.732481i
$903$	3.52238e7	+	1.77962e7i	1.43753	+	0.726287i
$904$	−1.66910e7	+	108055.i	−0.679299	+	0.00439769i
$905$	−1.02128e7	−	1.76891e7i	−0.414499	−	0.717934i
$906$	−4.68168e6	+	2.71645e6i	−0.189488	+	0.109947i
$907$	3.18083e7	+	1.83645e7i	1.28387	+	0.741244i	0.977554	−	0.210685i	$-0.0675694\pi$
$907$	3.18083e7	+	1.83645e7i	1.28387	+	0.741244i	0.306319	+	0.951929i	$0.400903\pi$
$908$	−1.74634e6	+	3.05513e6i	−0.0702934	+	0.122974i
$909$		−	4.68812e7i		−	1.88187i
$910$	6.80641e6	+	1.03542e7i	0.272468	+	0.414489i
$911$			2.68584e7i			1.07222i	0.844148	+	0.536110i	$0.180107\pi$
$911$			2.68584e7i			1.07222i	−0.844148	+	0.536110i	$0.819893\pi$
$912$	−1.89550e7	+	163618.i	−0.754636	+	0.00651396i
$913$	−6.46218e7	−	3.73094e7i	−2.56568	−	1.48129i
$914$	5.77099e6	+	9.94601e6i	0.228499	+	0.393807i
$915$	186555.	+	323122.i	0.00736637	+	0.0127589i
$916$	−3.72386e7	+	2.17145e7i	−1.46641	+	0.855089i
$917$	6.46755e6	+	9.88510e6i	0.253990	+	0.388202i
$918$	1.27838e7	+	7.34401e6i	0.500673	+	0.287625i
$919$	−3.76734e7	+	2.17507e7i	−1.47145	+	0.849542i	−0.999485	−	0.0320753i	$-0.989788\pi$
$919$	−3.76734e7	+	2.17507e7i	−1.47145	+	0.849542i	−0.471965	+	0.881617i	$0.656455\pi$
$920$	1.82599e6	−	3.21053e6i	0.0711261	−	0.125057i
$921$	−4.83081e6	+	8.36721e6i	−0.187660	+	0.325036i
$922$	−49417.0	−	2.29002e7i	−0.00191447	−	0.887180i
$923$	−2.20397e6			−0.0851534
$924$	−6.04850e7	+	3.99475e7i	−2.33060	+	1.53925i
$925$	1.12302e7			0.431553
$926$	−26058.5	−	1.20757e7i	−0.000998669	−	0.462790i
$927$	2.84207e7	−	4.92261e7i	1.08626	−	1.88146i
$928$	−1.85164e7	+	199793.i	−0.705809	+	0.00761572i
$929$	3.49084e7	−	2.01544e7i	1.32706	−	0.766179i	0.342218	−	0.939621i	$-0.388822\pi$
$929$	3.49084e7	−	2.01544e7i	1.32706	−	0.766179i	0.984844	+	0.173441i	$0.0554887\pi$
$930$	−1.11275e6	−	639246.i	−0.0421880	−	0.0242360i
$931$	−7.72934e6	−	1.04872e7i	−0.292259	−	0.396538i
$932$	1.23664e7	+	2.12073e7i	0.466341	+	0.799735i
$933$	−2.38705e7	−	4.13450e7i	−0.897755	−	1.55496i
$934$	7.70528e6	+	1.32797e7i	0.289016	+	0.498104i
$935$	2.49602e7	+	1.44108e7i	0.933725	+	0.539086i
$936$	2.83778e7	−	1.66298e7i	1.05874	−	0.620437i
$937$			3.17181e7i			1.18021i	0.807328	+	0.590104i	$0.200913\pi$
$937$			3.17181e7i			1.18021i	−0.807328	+	0.590104i	$0.799087\pi$
$938$	−2.09685e7	−	1.05372e7i	−0.778143	−	0.391038i
$939$		−	2.51008e7i		−	0.929018i
$940$	1.27856e7	+	7.30837e6i	0.471956	+	0.269775i
$941$	3.81217e7	+	2.20096e7i	1.40345	+	0.810285i	0.994745	−	0.102380i	$-0.0326458\pi$
$941$	3.81217e7	+	2.20096e7i	1.40345	+	0.810285i	0.408709	+	0.912665i	$0.365979\pi$
$942$	751106.	−	435815.i	0.0275787	−	0.0160020i
$943$	1.67165e6	+	2.89539e6i	0.0612163	+	0.106030i
$944$	1.86997e7	−	3.30443e7i	0.682975	−	1.20689i
$945$	−6.64922e6	+	4.35040e6i	−0.242209	+	0.158471i
$946$	2.62794e7	−	4.57450e7i	0.954746	−	1.66194i
$947$	−8.29794e6	+	4.79082e6i	−0.300674	+	0.173594i	−0.642745	−	0.766080i	$-0.722205\pi$
$947$	−8.29794e6	+	4.79082e6i	−0.300674	+	0.173594i	0.342072	+	0.939674i	$0.388871\pi$
$948$	−183859.	−	4.26006e7i	−0.00664453	−	1.53956i
$949$	−4.65125e6	+	8.05621e6i	−0.167650	+	0.290379i
$950$	9.64050e6	−	20803.5i	0.346570	−	0.000747872i
$951$	−3.80839e7			−1.36549
$952$	2.71975e7	+	1.35208e7i	0.972604	+	0.483514i
$953$	−4.97720e6			−0.177522			−0.0887611	−	0.996053i	$-0.528291\pi$
$953$	−4.97720e6			−0.177522			−0.0887611	+	0.996053i	$0.528291\pi$
$954$	5.63793e7	−	121663.i	2.00562	−	0.00432799i
$955$	1.28208e6	−	2.22063e6i	0.0454892	−	0.0787896i
$956$	−106707.	−	2.47243e7i	−0.00377614	−	0.874942i
$957$	−4.83724e7	+	2.79278e7i	−1.70733	+	0.985729i
$958$	1.11695e7	−	1.94429e7i	0.393205	−	0.684458i
$959$	−2.45831e6	+	4.86569e6i	−0.0863157	+	0.170843i
$960$	308380.	+	2.38163e7i	0.0107996	+	0.834059i
$961$	1.42659e7	+	2.47092e7i	0.498299	+	0.863079i
$962$	1.38737e7	−	8.04994e6i	0.483341	−	0.280450i
$963$	1.27507e7	+	7.36160e6i	0.443064	+	0.255803i
$964$	1.81432e7	+	1.03708e7i	0.628813	+	0.359436i
$965$			1.26099e7i			0.435906i
$966$	−679771.	−	1.17209e7i	−0.0234379	−	0.404126i
$967$		−	4.04477e7i		−	1.39100i	−0.718525	−	0.695501i	$-0.755182\pi$
$967$		−	4.04477e7i		−	1.39100i	0.718525	−	0.695501i	$-0.244818\pi$
$968$	3.42525e7	+	5.84499e7i	1.17491	+	2.00491i
$969$	2.07486e7	+	1.19792e7i	0.709870	+	0.409843i
$970$	−8.20022e6	−	1.41327e7i	−0.279831	−	0.482276i
$971$	7.64000e6	+	1.32329e7i	0.260043	+	0.450408i	0.966253	−	0.257595i	$-0.0829299\pi$
$971$	7.64000e6	+	1.32329e7i	0.260043	+	0.450408i	−0.706210	+	0.708002i	$0.749597\pi$
$972$	−1.99941e7	−	3.42883e7i	−0.678792	−	1.16407i
$973$	−1.59294e7	+	889366.i	−0.539408	+	0.0301161i
$974$	−2.45372e7	−	1.40961e7i	−0.828758	−	0.476102i
$975$	−2.52417e7	+	1.45733e7i	−0.850369	+	0.490961i
$976$	452918.	−	266731.i	0.0152193	−	0.00896291i
$977$	−1.73202e7	+	2.99995e7i	−0.580520	+	1.00549i	0.414897	+	0.909868i	$0.363818\pi$
$977$	−1.73202e7	+	2.99995e7i	−0.580520	+	1.00549i	−0.995418	+	0.0956225i	$0.969516\pi$
$978$	75947.1	+	3.51945e7i	0.00253901	+	1.17660i
$979$	−5.68155e7			−1.89457
$980$	−1.31354e7	+	9.76887e6i	−0.436894	+	0.324922i
$981$	−5.94676e7			−1.97291
$982$	−46456.7	−	2.15284e7i	−0.00153734	−	0.712414i
$983$	1.19949e7	−	2.07757e7i	0.395924	−	0.685760i	−0.597295	−	0.802022i	$-0.703758\pi$
$983$	1.19949e7	−	2.07757e7i	0.395924	−	0.685760i	0.993219	+	0.116262i	$0.0370911\pi$
$984$	−1.87411e7	−	1.06590e7i	−0.617030	−	0.350936i
$985$	−2.18883e6	+	1.26372e6i	−0.0718821	+	0.0415011i
$986$	2.02941e7	+	1.16585e7i	0.664779	+	0.381900i
$987$	4.67403e7	−	2.60959e6i	1.52721	−	0.0852667i
$988$	1.18948e7	−	6.93611e6i	0.387673	−	0.226060i
$989$	4.27245e6	+	7.40010e6i	0.138895	+	0.240573i
$990$	2.06938e7	+	3.56647e7i	0.671046	+	1.15651i
$991$	8.59867e6	+	4.96445e6i	0.278130	+	0.160578i	0.632576	−	0.774498i	$-0.281997\pi$
$991$	8.59867e6	+	4.96445e6i	0.278130	+	0.160578i	−0.354447	+	0.935076i	$0.615331\pi$
$992$	−886984.	+	1.57531e6i	−0.0286178	+	0.0508262i
$993$			5.96259e7i			1.91894i
$994$	−168584.	−	2.90679e6i	−0.00541190	−	0.0933140i
$995$			1.92421e7i			0.616162i
$996$	−3.86782e7	+	6.76653e7i	−1.23543	+	2.16131i
$997$	−4.72297e7	−	2.72681e7i	−1.50479	−	0.868793i	−0.999985	−	0.00556182i	$-0.998230\pi$
$997$	−4.72297e7	−	2.72681e7i	−1.50479	−	0.868793i	−0.504809	−	0.863231i	$-0.668437\pi$
$998$	−2.51041e6	+	1.45662e6i	−0.0797845	+	0.0462934i
$999$	5.14296e6	+	8.90787e6i	0.163042	+	0.282397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.6.f.a.3.18	yes	36
4.3	odd	2	inner	28.6.f.a.3.6	✓	36
7.3	odd	6		196.6.d.b.195.16		36
7.4	even	3		196.6.d.b.195.15		36
7.5	odd	6	inner	28.6.f.a.19.6	yes	36
28.3	even	6		196.6.d.b.195.13		36
28.11	odd	6		196.6.d.b.195.14		36
28.19	even	6	inner	28.6.f.a.19.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.6	✓	36	4.3	odd	2	inner
28.6.f.a.3.18	yes	36	1.1	even	1	trivial
28.6.f.a.19.6	yes	36	7.5	odd	6	inner
28.6.f.a.19.18	yes	36	28.19	even	6	inner
196.6.d.b.195.13		36	28.3	even	6
196.6.d.b.195.14		36	28.11	odd	6
196.6.d.b.195.15		36	7.4	even	3
196.6.d.b.195.16		36	7.3	odd	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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.65684 - 0.0122071i) q^{2} +(11.9407 - 20.6819i) q^{3} +(31.9997 - 0.138107i) q^{4} +(-26.3592 + 15.2185i) q^{5} +(67.2942 - 117.140i) q^{6} +(-129.440 + 7.22687i) q^{7} +(181.016 - 1.17187i) q^{8} +(-163.661 - 283.469i) q^{9} +(-148.924 + 86.4103i) q^{10} +(633.622 + 365.822i) q^{11} +(379.243 - 663.464i) q^{12} +555.117i q^{13} +(-732.135 + 42.4613i) q^{14} +726.878i q^{15} +(1023.96 - 8.83875i) q^{16} +(-1120.85 - 647.122i) q^{17} +(-929.264 - 1601.54i) q^{18} +(-387.571 - 671.292i) q^{19} +(-841.385 + 490.627i) q^{20} +(-1396.14 + 2763.36i) q^{21} +(3588.76 + 2061.66i) q^{22} +(-580.550 + 335.181i) q^{23} +(2137.22 - 3757.74i) q^{24} +(-1099.30 + 1904.04i) q^{25} +(6.77634 + 3140.21i) q^{26} -2013.72 q^{27} +(-4141.05 + 249.134i) q^{28} -3196.74 q^{29} +(8.87304 + 4111.83i) q^{30} +(-156.048 + 270.284i) q^{31} +(5792.28 - 62.4990i) q^{32} +(15131.8 - 8736.34i) q^{33} +(-6348.36 - 3646.99i) q^{34} +(3301.96 - 2160.38i) q^{35} +(-5276.25 - 9048.32i) q^{36} +(-2553.96 - 4423.59i) q^{37} +(-2200.62 - 3792.66i) q^{38} +(11480.9 + 6628.48i) q^{39} +(-4753.59 + 2785.67i) q^{40} -4987.32i q^{41} +(-7864.02 + 15649.0i) q^{42} -12746.7i q^{43} +(20326.2 + 11618.7i) q^{44} +(8627.93 + 4981.34i) q^{45} +(-3279.99 + 1903.15i) q^{46} +(-7560.18 - 13094.6i) q^{47} +(12044.0 - 21283.0i) q^{48} +(16702.5 - 1870.90i) q^{49} +(-6195.30 + 10784.2i) q^{50} +(-26767.4 + 15454.2i) q^{51} +(76.6654 + 17763.6i) q^{52} +(-15224.4 + 26369.5i) q^{53} +(-11391.3 + 24.5816i) q^{54} -22269.0 q^{55} +(-23422.2 + 1459.86i) q^{56} -18511.5 q^{57} +(-18083.5 + 39.0228i) q^{58} +(18539.3 - 32111.0i) q^{59} +(100.387 + 23259.9i) q^{60} +(444.534 - 256.652i) q^{61} +(-879.441 + 1530.86i) q^{62} +(23232.9 + 35509.5i) q^{63} +(32765.3 - 424.253i) q^{64} +(-8448.04 - 14632.4i) q^{65} +(85491.5 - 49604.8i) q^{66} +(27712.2 + 15999.7i) q^{67} +(-35956.2 - 20552.9i) q^{68} +16009.2i q^{69} +(18652.3 - 12261.2i) q^{70} +3970.29i q^{71} +(-29957.3 - 51120.5i) q^{72} +(14512.6 + 8378.88i) q^{73} +(-14501.3 - 24992.4i) q^{74} +(26252.7 + 45471.0i) q^{75} +(-12494.9 - 21427.6i) q^{76} +(-84659.9 - 42773.0i) q^{77} +(65026.4 + 37356.1i) q^{78} +(48277.1 - 27872.8i) q^{79} +(-26856.3 + 15816.1i) q^{80} +(15724.3 - 27235.4i) q^{81} +(-60.8805 - 28212.5i) q^{82} -101988. q^{83} +(-44294.5 + 88619.7i) q^{84} +39392.9 q^{85} +(-155.600 - 72106.1i) q^{86} +(-38171.4 + 66114.7i) q^{87} +(115124. + 65476.9i) q^{88} +(-67250.9 + 38827.3i) q^{89} +(48867.7 + 28073.3i) q^{90} +(-4011.76 - 71854.4i) q^{91} +(-18531.1 + 10805.9i) q^{92} +(3726.65 + 6454.75i) q^{93} +(-42926.6 - 73981.8i) q^{94} +(20432.1 + 11796.5i) q^{95} +(67871.3 - 120542. i) q^{96} +94898.6i q^{97} +(94460.8 - 10787.2i) q^{98} -239483. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9} - 804 q^{10} + 1632 q^{12} + 1024 q^{14} + 664 q^{16} - 6 q^{17} - 1780 q^{18} - 4586 q^{21} + 13768 q^{22} + 564 q^{24} + 7612 q^{25} - 8892 q^{26} - 5928 q^{28}+ \cdots + 418676 q^{98}+O(q^{100}) \) 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9 - 804 * q^10 + 1632 * q^12 + 1024 * q^14 + 664 * q^16 - 6 * q^17 - 1780 * q^18 - 4586 * q^21 + 13768 * q^22 + 564 * q^24 + 7612 * q^25 - 8892 * q^26 - 5928 * q^28 + 176 * q^29 - 5836 * q^30 + 1160 * q^32 - 14154 * q^33 - 27920 * q^36 + 11722 * q^37 - 5652 * q^38 + 35052 * q^40 + 23140 * q^42 + 9096 * q^44 + 19152 * q^45 - 1040 * q^46 + 43900 * q^49 - 51168 * q^50 - 61776 * q^52 - 33486 * q^53 - 30996 * q^54 + 19952 * q^56 - 1668 * q^57 - 48436 * q^58 + 14312 * q^60 + 18846 * q^61 + 44544 * q^64 + 15356 * q^65 + 221808 * q^66 + 25020 * q^68 + 81192 * q^70 + 148064 * q^72 - 236562 * q^73 + 17152 * q^74 - 140010 * q^77 + 127704 * q^78 - 277224 * q^80 + 160402 * q^81 - 391836 * q^82 - 379540 * q^84 + 71212 * q^85 - 252496 * q^86 + 55268 * q^88 - 23706 * q^89 - 190176 * q^92 - 165162 * q^93 + 359988 * q^94 + 1061736 * q^96 + 418676 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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