LMFDB - Embedded newform 40.6.k.a.3.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, 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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.11
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49882 - 5.07503i) q^{2} +(10.6033 + 10.6033i) q^{3} +(-19.5118 + 25.3631i) q^{4} +(-15.3629 - 53.7493i) q^{5} +(27.3164 - 80.3079i) q^{6} +(159.941 + 159.941i) q^{7} +(177.475 + 35.6453i) q^{8} -18.1393i q^{9} +O(q^{10})$	\(q+(-2.49882 - 5.07503i) q^{2} +(10.6033 + 10.6033i) q^{3} +(-19.5118 + 25.3631i) q^{4} +(-15.3629 - 53.7493i) q^{5} +(27.3164 - 80.3079i) q^{6} +(159.941 + 159.941i) q^{7} +(177.475 + 35.6453i) q^{8} -18.1393i q^{9} +(-234.390 + 212.276i) q^{10} +516.314 q^{11} +(-475.823 + 62.0432i) q^{12} +(147.686 - 147.686i) q^{13} +(412.042 - 1211.37i) q^{14} +(407.023 - 732.818i) q^{15} +(-262.577 - 989.762i) q^{16} +(890.046 - 890.046i) q^{17} +(-92.0575 + 45.3268i) q^{18} +1009.77i q^{19} +(1663.01 + 659.096i) q^{20} +3391.81i q^{21} +(-1290.17 - 2620.31i) q^{22} +(-1847.88 + 1847.88i) q^{23} +(1503.87 + 2259.78i) q^{24} +(-2652.97 + 1651.48i) q^{25} +(-1118.55 - 380.470i) q^{26} +(2768.94 - 2768.94i) q^{27} +(-7177.34 + 935.862i) q^{28} +1847.15 q^{29} +(-4736.15 - 234.477i) q^{30} +4973.59i q^{31} +(-4366.94 + 3805.82i) q^{32} +(5474.64 + 5474.64i) q^{33} +(-6741.07 - 2292.95i) q^{34} +(6139.55 - 11053.9i) q^{35} +(460.070 + 353.931i) q^{36} +(2819.25 + 2819.25i) q^{37} +(5124.61 - 2523.23i) q^{38} +3131.92 q^{39} +(-810.617 - 10086.8i) q^{40} -12472.0 q^{41} +(17213.5 - 8475.51i) q^{42} +(-11883.2 - 11883.2i) q^{43} +(-10074.2 + 13095.3i) q^{44} +(-974.975 + 278.672i) q^{45} +(13995.6 + 4760.53i) q^{46} +(-11919.6 - 11919.6i) q^{47} +(7710.58 - 13278.9i) q^{48} +34355.2i q^{49} +(15010.6 + 9337.12i) q^{50} +18874.9 q^{51} +(864.154 + 6627.39i) q^{52} +(10766.7 - 10766.7i) q^{53} +(-20971.5 - 7133.38i) q^{54} +(-7932.06 - 27751.5i) q^{55} +(22684.4 + 34086.7i) q^{56} +(-10706.9 + 10706.9i) q^{57} +(-4615.69 - 9374.33i) q^{58} +8271.39i q^{59} +(10644.8 + 24622.0i) q^{60} -28492.9i q^{61} +(25241.1 - 12428.1i) q^{62} +(2901.22 - 2901.22i) q^{63} +(30226.8 + 12652.3i) q^{64} +(-10206.9 - 5669.13i) q^{65} +(14103.8 - 41464.1i) q^{66} +(9257.64 - 9257.64i) q^{67} +(5207.93 + 39940.8i) q^{68} -39187.3 q^{69} +(-71440.2 - 3536.86i) q^{70} +18565.5i q^{71} +(646.581 - 3219.28i) q^{72} +(-58309.9 - 58309.9i) q^{73} +(7262.98 - 21352.5i) q^{74} +(-45641.4 - 10619.0i) q^{75} +(-25610.9 - 19702.4i) q^{76} +(82579.7 + 82579.7i) q^{77} +(-7826.09 - 15894.6i) q^{78} -10581.9 q^{79} +(-49165.1 + 29318.9i) q^{80} +54312.1 q^{81} +(31165.4 + 63296.0i) q^{82} +(12642.5 + 12642.5i) q^{83} +(-86026.9 - 66180.4i) q^{84} +(-61513.0 - 34165.7i) q^{85} +(-30613.5 + 90001.2i) q^{86} +(19585.9 + 19585.9i) q^{87} +(91632.9 + 18404.2i) q^{88} +65996.0i q^{89} +(3850.55 + 4251.67i) q^{90} +47242.0 q^{91} +(-10812.5 - 82923.6i) q^{92} +(-52736.5 + 52736.5i) q^{93} +(-30707.5 + 90277.5i) q^{94} +(54274.3 - 15512.9i) q^{95} +(-86658.4 - 5949.75i) q^{96} +(14591.8 - 14591.8i) q^{97} +(174353. - 85847.3i) q^{98} -9365.58i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	−2.49882	−	5.07503i	−0.441733	−	0.897147i
$2$	−2.49882	−	5.07503i	−0.441733	−	0.897147i
$3$	10.6033	+	10.6033i	0.680203	+	0.680203i	0.960046	−	0.279843i	$-0.0902823\pi$
$3$	10.6033	+	10.6033i	0.680203	+	0.680203i	−0.279843	+	0.960046i	$0.590282\pi$
$4$	−19.5118	+	25.3631i	−0.609745	+	0.792598i
$5$	−15.3629	−	53.7493i	−0.274819	−	0.961496i
$5$	−15.3629	−	53.7493i	−0.274819	−	0.961496i
$6$	27.3164	−	80.3079i	0.309774	−	0.910710i
$7$	159.941	+	159.941i	1.23371	+	1.23371i	0.962527	+	0.271187i	$0.0874162\pi$
$7$	159.941	+	159.941i	1.23371	+	1.23371i	0.271187	+	0.962527i	$0.412584\pi$
$8$	177.475	+	35.6453i	0.980421	+	0.196914i
$9$		−	18.1393i		−	0.0746474i
$10$	−234.390	+	212.276i	−0.741206	+	0.671277i
$11$	516.314			1.28657			0.643283	−	0.765628i	$-0.277572\pi$
$11$	516.314			1.28657			0.643283	+	0.765628i	$0.277572\pi$
$12$	−475.823	+	62.0432i	−0.953878	+	0.124377i
$13$	147.686	−	147.686i	0.242371	−	0.242371i	−0.575459	−	0.817830i	$-0.695177\pi$
$13$	147.686	−	147.686i	0.242371	−	0.242371i	0.817830	+	0.575459i	$0.195177\pi$
$14$	412.042	−	1211.37i	0.561851	−	1.65179i
$15$	407.023	−	732.818i	0.467080	−	0.840945i
$16$	−262.577	−	989.762i	−0.256423	−	0.966565i
$17$	890.046	−	890.046i	0.746948	−	0.746948i	−0.226957	−	0.973905i	$-0.572878\pi$
$17$	890.046	−	890.046i	0.746948	−	0.746948i	0.973905	+	0.226957i	$0.0728777\pi$
$18$	−92.0575	+	45.3268i	−0.0669697	+	0.0329742i
$19$			1009.77i			0.641709i	0.947128	+	0.320854i	$0.103970\pi$
$19$			1009.77i			0.641709i	−0.947128	+	0.320854i	$0.896030\pi$
$20$	1663.01	+	659.096i	0.929649	+	0.368446i
$21$			3391.81i			1.67835i
$22$	−1290.17	−	2620.31i	−0.568318	−	1.15424i
$23$	−1847.88	+	1847.88i	−0.728374	+	0.728374i	−0.970296	−	0.241922i	$-0.922222\pi$
$23$	−1847.88	+	1847.88i	−0.728374	+	0.728374i	0.241922	+	0.970296i	$0.422222\pi$
$24$	1503.87	+	2259.78i	0.532944	+	0.800827i
$25$	−2652.97	+	1651.48i	−0.848949	+	0.528475i
$26$	−1118.55	−	380.470i	−0.324505	−	0.110379i
$27$	2768.94	−	2768.94i	0.730979	−	0.730979i
$28$	−7177.34	+	935.862i	−1.73009	+	0.225588i
$29$	1847.15			0.407856			0.203928	−	0.978986i	$-0.434629\pi$
$29$	1847.15			0.407856			0.203928	+	0.978986i	$0.434629\pi$
$30$	−4736.15	−	234.477i	−0.960776	−	0.0475661i
$31$			4973.59i			0.929535i	0.885433	+	0.464767i	$0.153862\pi$
$31$			4973.59i			0.929535i	−0.885433	+	0.464767i	$0.846138\pi$
$32$	−4366.94	+	3805.82i	−0.753880	+	0.657012i
$33$	5474.64	+	5474.64i	0.875126	+	0.875126i
$34$	−6741.07	−	2292.95i	−1.00007	−	0.340171i
$35$	6139.55	−	11053.9i	0.847162	−	1.52526i
$36$	460.070	+	353.931i	0.0591654	+	0.0455158i
$37$	2819.25	+	2819.25i	0.338555	+	0.338555i	0.855823	−	0.517269i	$-0.173051\pi$
$37$	2819.25	+	2819.25i	0.338555	+	0.338555i	−0.517269	+	0.855823i	$0.673051\pi$
$38$	5124.61	−	2523.23i	0.575707	−	0.283464i
$39$	3131.92			0.329723
$40$	−810.617	−	10086.8i	−0.0801061	−	0.996786i
$41$	−12472.0			−1.15872			−0.579359	−	0.815072i	$-0.696697\pi$
$41$	−12472.0			−1.15872			−0.579359	+	0.815072i	$0.696697\pi$
$42$	17213.5	−	8475.51i	1.50573	−	0.741383i
$43$	−11883.2	−	11883.2i	−0.980078	−	0.980078i	0.0197274	−	0.999805i	$-0.493720\pi$
$43$	−11883.2	−	11883.2i	−0.980078	−	0.980078i	−0.999805	+	0.0197274i	$0.993720\pi$
$44$	−10074.2	+	13095.3i	−0.784477	+	1.01973i
$45$	−974.975	+	278.672i	−0.0717732	+	0.0205145i
$46$	13995.6	+	4760.53i	0.975205	+	0.331712i
$47$	−11919.6	−	11919.6i	−0.787080	−	0.787080i	0.193935	−	0.981014i	$-0.437875\pi$
$47$	−11919.6	−	11919.6i	−0.787080	−	0.787080i	−0.981014	+	0.193935i	$0.937875\pi$
$48$	7710.58	−	13278.9i	0.483041	−	0.831880i
$49$			34355.2i			2.04410i
$50$	15010.6	+	9337.12i	0.849128	+	0.528187i
$51$	18874.9			1.01615
$52$	864.154	+	6627.39i	0.0443182	+	0.339887i
$53$	10766.7	−	10766.7i	0.526494	−	0.526494i	−0.393031	−	0.919525i	$-0.628573\pi$
$53$	10766.7	−	10766.7i	0.526494	−	0.526494i	0.919525	+	0.393031i	$0.128573\pi$
$54$	−20971.5	−	7133.38i	−0.978692	−	0.332898i
$55$	−7932.06	−	27751.5i	−0.353573	−	1.23703i
$56$	22684.4	+	34086.7i	0.966623	+	1.45249i
$57$	−10706.9	+	10706.9i	−0.436492	+	0.436492i
$58$	−4615.69	−	9374.33i	−0.180163	−	0.365907i
$59$			8271.39i			0.309349i	0.987965	+	0.154674i	$0.0494329\pi$
$59$			8271.39i			0.309349i	−0.987965	+	0.154674i	$0.950567\pi$
$60$	10644.8	+	24622.0i	0.381732	+	0.882968i
$61$		−	28492.9i		−	0.980420i	−0.871604	−	0.490210i	$-0.836920\pi$
$61$		−	28492.9i		−	0.980420i	0.871604	−	0.490210i	$-0.163080\pi$
$62$	25241.1	−	12428.1i	0.833929	−	0.410606i
$63$	2901.22	−	2901.22i	0.0920935	−	0.0920935i
$64$	30226.8	+	12652.3i	0.922450	+	0.386118i
$65$	−10206.9	−	5669.13i	−0.299647	−	0.166430i
$66$	14103.8	−	41464.1i	0.398545	−	1.17169i
$67$	9257.64	−	9257.64i	0.251949	−	0.251949i	−0.569820	−	0.821769i	$-0.692987\pi$
$67$	9257.64	−	9257.64i	0.251949	−	0.251949i	0.821769	+	0.569820i	$0.192987\pi$
$68$	5207.93	+	39940.8i	0.136582	+	1.04748i
$69$	−39187.3			−0.990884
$70$	−71440.2	−	3536.86i	−1.74260	−	0.0862727i
$71$			18565.5i			0.437079i	0.975828	+	0.218539i	$0.0701292\pi$
$71$			18565.5i			0.437079i	−0.975828	+	0.218539i	$0.929871\pi$
$72$	646.581	−	3219.28i	0.0146991	−	0.0731858i
$73$	−58309.9	−	58309.9i	−1.28066	−	1.28066i	−0.940290	−	0.340375i	$-0.889446\pi$
$73$	−58309.9	−	58309.9i	−1.28066	−	1.28066i	−0.340375	−	0.940290i	$-0.610554\pi$
$74$	7262.98	−	21352.5i	0.154183	−	0.453284i
$75$	−45641.4	−	10619.0i	−0.936928	−	0.217987i
$76$	−25610.9	−	19702.4i	−0.508617	−	0.391279i
$77$	82579.7	+	82579.7i	1.58725	+	1.58725i
$78$	−7826.09	−	15894.6i	−0.145649	−	0.295810i
$79$	−10581.9			−0.190764			−0.0953822	−	0.995441i	$-0.530407\pi$
$79$	−10581.9			−0.190764			−0.0953822	+	0.995441i	$0.530407\pi$
$80$	−49165.1	+	29318.9i	−0.858878	+	0.512180i
$81$	54312.1			0.919780
$82$	31165.4	+	63296.0i	0.511844	+	1.03954i
$83$	12642.5	+	12642.5i	0.201436	+	0.201436i	0.800615	−	0.599179i	$-0.204506\pi$
$83$	12642.5	+	12642.5i	0.201436	+	0.201436i	−0.599179	+	0.800615i	$0.704506\pi$
$84$	−86026.9	−	66180.4i	−1.33026	−	1.02337i
$85$	−61513.0	−	34165.7i	−0.923463	−	0.512912i
$86$	−30613.5	+	90001.2i	−0.446342	+	1.31221i
$87$	19585.9	+	19585.9i	0.277425	+	0.277425i
$88$	91632.9	+	18404.2i	1.26138	+	0.253343i
$89$			65996.0i			0.883166i	0.897220	+	0.441583i	$0.145583\pi$
$89$			65996.0i			0.883166i	−0.897220	+	0.441583i	$0.854417\pi$
$90$	3850.55	+	4251.67i	0.0501091	+	0.0553291i
$91$	47242.0			0.598032
$92$	−10812.5	−	82923.6i	−0.133185	−	1.02143i
$93$	−52736.5	+	52736.5i	−0.632272	+	0.632272i
$94$	−30707.5	+	90277.5i	−0.358447	+	1.05380i
$95$	54274.3	−	15512.9i	0.617001	−	0.176354i
$96$	−86658.4	−	5949.75i	−0.959693	−	0.0658902i
$97$	14591.8	−	14591.8i	0.157464	−	0.157464i	−0.623978	−	0.781442i	$-0.714485\pi$
$97$	14591.8	−	14591.8i	0.157464	−	0.157464i	0.781442	+	0.623978i	$0.214485\pi$
$98$	174353.	−	85847.3i	1.83386	−	0.902945i
$99$		−	9365.58i		−	0.0960388i
$100$	9877.39	−	99511.0i	0.0987739	−	0.995110i
$101$		−	105351.i		−	1.02763i	−0.857901	−	0.513814i	$-0.828232\pi$
$101$		−	105351.i		−	1.02763i	0.857901	−	0.513814i	$-0.171768\pi$
$102$	−47164.9	−	95790.6i	−0.448867	−	0.911638i
$103$	−95388.9	+	95388.9i	−0.885941	+	0.885941i	−0.994130	−	0.108189i	$-0.965495\pi$
$103$	−95388.9	+	95388.9i	−0.885941	+	0.885941i	0.108189	+	0.994130i	$0.465495\pi$
$104$	31474.9	−	20946.2i	0.285352	−	0.189899i
$105$	182307.	−	52107.9i	1.61373	−	0.461243i
$106$	−81545.5	−	27737.4i	−0.704912	−	0.239773i
$107$	−98246.9	+	98246.9i	−0.829582	+	0.829582i	−0.987459	−	0.157876i	$-0.949535\pi$
$107$	−98246.9	+	98246.9i	−0.829582	+	0.829582i	0.157876	+	0.987459i	$0.449535\pi$
$108$	16201.9	+	124256.i	0.133662	+	1.02508i
$109$	90675.6			0.731012			0.365506	−	0.930809i	$-0.380896\pi$
$109$	90675.6			0.731012			0.365506	+	0.930809i	$0.380896\pi$
$110$	−121019.	+	109601.i	−0.953611	+	0.863642i
$111$			59786.7i			0.460572i
$112$	116307.	−	200300.i	0.876112	−	1.50882i
$113$	−45073.6	−	45073.6i	−0.332067	−	0.332067i	0.521304	−	0.853371i	$-0.325446\pi$
$113$	−45073.6	−	45073.6i	−0.332067	−	0.332067i	−0.853371	+	0.521304i	$0.825446\pi$
$114$	81092.4	+	27583.3i	0.584411	+	0.198785i
$115$	127711.	+	70933.5i	0.900500	+	0.500157i
$116$	−36041.3	+	46849.5i	−0.248688	+	0.323266i
$117$	−2678.92	−	2678.92i	−0.0180923	−	0.0180923i
$118$	41977.6	−	20668.7i	0.277531	−	0.136649i
$119$	284709.			1.84304
$120$	98358.0	−	115548.i	0.623529	−	0.732506i
$121$	105529.			0.655252
$122$	−144602.	+	71198.6i	−0.879581	+	0.433084i
$123$	−132245.	−	132245.i	−0.788164	−	0.788164i
$124$	−126146.	−	97043.8i	−0.736747	−	0.566779i
$125$	129523.	+	117223.i	0.741434	+	0.671026i
$126$	−21973.4	−	7474.15i	−0.123302	−	0.0419407i
$127$	−77703.2	−	77703.2i	−0.427494	−	0.427494i	0.460280	−	0.887774i	$-0.347749\pi$
$127$	−77703.2	−	77703.2i	−0.427494	−	0.427494i	−0.887774	+	0.460280i	$0.847749\pi$
$128$	−11320.5	−	185018.i	−0.0610717	−	0.998133i
$129$		−	252002.i		−	1.33330i
$130$	−3265.86	+	65966.3i	−0.0169488	+	0.342345i
$131$	11817.8			0.0601671			0.0300836	−	0.999547i	$-0.490423\pi$
$131$	11817.8			0.0601671			0.0300836	+	0.999547i	$0.490423\pi$
$132$	−245674.	+	32033.8i	−1.22723	+	0.160020i
$133$	−161503.	+	161503.i	−0.791685	+	0.791685i
$134$	−70115.9	−	23849.6i	−0.337330	−	0.114741i
$135$	−191368.	−	106290.i	−0.903720	−	0.501946i
$136$	189687.	−	126235.i	0.879408	−	0.585238i
$137$	24545.6	−	24545.6i	0.111731	−	0.111731i	−0.649031	−	0.760762i	$-0.724826\pi$
$137$	24545.6	−	24545.6i	0.111731	−	0.111731i	0.760762	+	0.649031i	$0.224826\pi$
$138$	97921.9	+	198877.i	0.437706	+	0.888969i
$139$			318666.i			1.39894i	0.714662	+	0.699470i	$0.246581\pi$
$139$			318666.i			1.39894i	−0.714662	+	0.699470i	$0.753419\pi$
$140$	160566.	+	371399.i	0.692364	+	1.60148i
$141$		−	252776.i		−	1.07075i
$142$	94220.2	−	46391.7i	0.392124	−	0.193072i
$143$	76252.2	−	76252.2i	0.311826	−	0.311826i
$144$	−17953.6	+	4762.96i	−0.0721515	+	0.0191413i
$145$	−28377.5	−	99282.9i	−0.112087	−	0.392152i
$146$	−150219.	+	441631.i	−0.583233	+	1.71466i
$147$	−364279.	+	364279.i	−1.39040	+	1.39040i
$148$	−126514.	+	16496.3i	−0.474769	+	0.0619057i
$149$	−355298.			−1.31108			−0.655538	−	0.755162i	$-0.727558\pi$
$149$	−355298.			−1.31108			−0.655538	+	0.755162i	$0.727558\pi$
$150$	60157.8	+	258167.i	0.218305	+	0.936854i
$151$			246649.i			0.880313i	0.897921	+	0.440157i	$0.145077\pi$
$151$			246649.i			0.880313i	−0.897921	+	0.440157i	$0.854923\pi$
$152$	−35993.5	+	179209.i	−0.126362	+	0.629145i
$153$	−16144.8	−	16144.8i	−0.0557577	−	0.0557577i
$154$	212743.	−	625446.i	0.722858	−	2.12514i
$155$	267327.	−	76408.5i	0.893744	−	0.255454i
$156$	−61109.5	+	79435.3i	−0.201047	+	0.261338i
$157$	−124781.	−	124781.i	−0.404017	−	0.404017i	0.475629	−	0.879646i	$-0.342220\pi$
$157$	−124781.	−	124781.i	−0.404017	−	0.404017i	−0.879646	+	0.475629i	$0.842220\pi$
$158$	26442.3	+	53703.6i	0.0842668	+	0.171144i
$159$	228326.			0.716246
$160$	271649.	+	176252.i	0.838895	+	0.544293i
$161$	−591103.			−1.79721
$162$	−135716.	−	275636.i	−0.406297	−	0.825178i
$163$	−225521.	−	225521.i	−0.664841	−	0.664841i	0.291676	−	0.956517i	$-0.405787\pi$
$163$	−225521.	−	225521.i	−0.664841	−	0.664841i	−0.956517	+	0.291676i	$0.905787\pi$
$164$	243352.	−	316330.i	0.706523	−	0.918398i
$165$	210152.	−	378364.i	0.600929	−	1.08193i
$166$	32569.7	−	95752.3i	0.0917369	−	0.269699i
$167$	45151.0	+	45151.0i	0.125278	+	0.125278i	0.766966	−	0.641688i	$-0.221765\pi$
$167$	45151.0	+	45151.0i	0.125278	+	0.125278i	−0.641688	+	0.766966i	$0.721765\pi$
$168$	−120902.	+	601961.i	−0.330491	+	1.64549i
$169$			327671.i			0.882513i
$170$	−19682.1	+	397554.i	−0.0522335	+	1.05505i
$171$	18316.5			0.0479019
$172$	533256.	−	69531.9i	1.37441	−	0.179210i
$173$	−188840.	+	188840.i	−0.479710	+	0.479710i	−0.905039	−	0.425329i	$-0.860158\pi$
$173$	−188840.	+	188840.i	−0.479710	+	0.479710i	0.425329	+	0.905039i	$0.360158\pi$
$174$	50457.4	−	148341.i	0.126343	−	0.371438i
$175$	−688457.	−	160178.i	−1.69935	−	0.395373i
$176$	−135572.	−	511028.i	−0.329905	−	1.24355i
$177$	−87704.2	+	87704.2i	−0.210420	+	0.210420i
$178$	334931.	−	164912.i	0.792330	−	0.390123i
$179$		−	286829.i		−	0.669098i	−0.942378	−	0.334549i	$-0.891416\pi$
$179$		−	286829.i		−	0.669098i	0.942378	−	0.334549i	$-0.108584\pi$
$180$	11955.6	−	30165.8i	0.0275035	−	0.0693959i
$181$		−	120295.i		−	0.272930i	−0.990645	−	0.136465i	$-0.956426\pi$
$181$		−	120295.i		−	0.272930i	0.990645	−	0.136465i	$-0.0435741\pi$
$182$	−118049.	−	239754.i	−0.264170	−	0.536523i
$183$	302119.	−	302119.i	0.666885	−	0.666885i
$184$	−393821.	+	262085.i	−0.857540	+	0.570686i
$185$	108221.	−	194844.i	0.232478	−	0.418560i
$186$	399418.	+	135860.i	0.846536	+	0.287946i
$187$	459543.	−	459543.i	0.960998	−	0.960998i
$188$	534894.	−	69745.4i	1.10376	−	0.143920i
$189$	885734.			1.80364
$190$	−214350.	−	236680.i	−0.430765	−	0.475639i
$191$		−	492807.i		−	0.977448i	−0.872439	−	0.488724i	$-0.837463\pi$
$191$		−	492807.i		−	0.977448i	0.872439	−	0.488724i	$-0.162537\pi$
$192$	186348.	+	454661.i	0.364815	+	0.890092i
$193$	662231.	+	662231.i	1.27972	+	1.27972i	0.940822	+	0.338902i	$0.110055\pi$
$193$	662231.	+	662231.i	1.27972	+	1.27972i	0.338902	+	0.940822i	$0.389945\pi$
$194$	−110516.	−	37591.7i	−0.210825	−	0.0717113i
$195$	−48115.2	−	168338.i	−0.0906141	−	0.317027i
$196$	−871355.	−	670332.i	−1.62015	−	1.24638i
$197$	350433.	+	350433.i	0.643339	+	0.643339i	0.951375	−	0.308036i	$-0.0996717\pi$
$197$	350433.	+	350433.i	0.643339	+	0.643339i	−0.308036	+	0.951375i	$0.599672\pi$
$198$	−47530.6	+	23402.9i	−0.0861609	+	0.0424235i
$199$	−95737.5			−0.171376			−0.0856879	−	0.996322i	$-0.527309\pi$
$199$	−95737.5			−0.171376			−0.0856879	+	0.996322i	$0.527309\pi$
$200$	−529703.	+	198532.i	−0.936391	+	0.350958i
$201$	196323.			0.342754
$202$	−534660.	+	263253.i	−0.921934	+	0.453937i
$203$	295435.	+	295435.i	0.503177	+	0.503177i
$204$	−368284.	+	478726.i	−0.619593	+	0.805400i
$205$	191606.	+	670363.i	0.318438	+	1.11410i
$206$	722461.	+	245742.i	1.18617	+	0.403470i
$207$	33519.3	+	33519.3i	0.0543712	+	0.0543712i
$208$	−184953.	−	107395.i	−0.296416	−	0.172118i
$209$			521358.i			0.825601i
$210$	−720001.	−	795006.i	−1.12664	−	1.24401i
$211$	30783.5			0.0476006			0.0238003	−	0.999717i	$-0.492423\pi$
$211$	30783.5			0.0476006			0.0238003	+	0.999717i	$0.492423\pi$
$212$	62999.3	+	483156.i	0.0962711	+	0.738325i
$213$	−196855.	+	196855.i	−0.297302	+	0.297302i
$214$	744107.	+	253105.i	1.11071	+	0.377804i
$215$	−456152.	+	821270.i	−0.672997	+	1.21169i
$216$	590118.	−	392719.i	0.860607	−	0.572726i
$217$	−795480.	+	795480.i	−1.14678	+	1.14678i
$218$	−226582.	−	460181.i	−0.322912	−	0.655825i
$219$		−	1.23656e6i		−	1.74222i
$220$	858634.	+	340301.i	1.19606	+	0.474030i
$221$		−	262894.i		−	0.362077i
$222$	303419.	−	149396.i	0.413200	−	0.203450i
$223$	357053.	−	357053.i	0.480807	−	0.480807i	−0.424582	−	0.905389i	$-0.639579\pi$
$223$	357053.	−	357053.i	0.480807	−	0.480807i	0.905389	+	0.424582i	$0.139579\pi$
$224$	−1.30716e6	−	89746.3i	−1.74064	−	0.119508i
$225$	29956.8	+	48123.0i	0.0394493	+	0.0633718i
$226$	−116119.	+	341381.i	−0.151228	+	0.444598i
$227$	817733.	−	817733.i	1.05329	−	1.05329i	0.0547891	−	0.998498i	$-0.482551\pi$
$227$	817733.	−	817733.i	1.05329	−	1.05329i	0.998498	−	0.0547891i	$-0.0174486\pi$
$228$	−62649.3	−	480472.i	−0.0798140	−	0.612112i
$229$	−1.37993e6			−1.73888			−0.869440	−	0.494039i	$-0.835520\pi$
$229$	−1.37993e6			−1.73888			−0.869440	+	0.494039i	$0.835520\pi$
$230$	40863.2	−	825386.i	0.0509346	−	1.02882i
$231$			1.75124e6i			2.15931i
$232$	327823.	+	65842.2i	0.399870	+	0.0803127i
$233$	−935667.	−	935667.i	−1.12910	−	1.12910i	−0.990324	−	0.138774i	$-0.955684\pi$
$233$	−935667.	−	935667.i	−1.12910	−	1.12910i	−0.138774	−	0.990324i	$-0.544316\pi$
$234$	−6901.46	+	20289.7i	−0.00823951	+	0.0242235i
$235$	−457552.	+	823792.i	−0.540469	+	0.973078i
$236$	−209788.	−	161390.i	−0.245189	−	0.188624i
$237$	−112204.	−	112204.i	−0.129759	−	0.129759i
$238$	−711437.	−	1.44491e6i	−0.814130	−	1.65348i
$239$	−141812.			−0.160590			−0.0802951	−	0.996771i	$-0.525586\pi$
$239$	−141812.			−0.160590			−0.0802951	+	0.996771i	$0.525586\pi$
$240$	−832190.	−	210435.i	−0.932598	−	0.235825i
$241$	353109.			0.391621			0.195811	−	0.980642i	$-0.437266\pi$
$241$	353109.			0.391621			0.195811	+	0.980642i	$0.437266\pi$
$242$	−263698.	−	535563.i	−0.289446	−	0.587858i
$243$	−96964.6	−	96964.6i	−0.105341	−	0.105341i
$244$	722670.	+	555949.i	0.777079	+	0.597806i
$245$	1.84656e6	−	527794.i	1.96539	−	0.561758i
$246$	−340691.	+	1.00160e6i	−0.358941	+	1.05526i
$247$	149129.	+	149129.i	0.155532	+	0.155532i
$248$	−177285.	+	882688.i	−0.183039	+	0.911335i
$249$			268105.i			0.274035i
$250$	271257.	−	950254.i	0.274493	−	0.961589i
$251$	1.19095e6			1.19319			0.596596	−	0.802542i	$-0.296519\pi$
$251$	1.19095e6			1.19319			0.596596	+	0.802542i	$0.296519\pi$
$252$	16975.9	+	130192.i	0.0168396	+	0.129147i
$253$	−954086.	+	954086.i	−0.937101	+	0.937101i
$254$	−200180.	+	588512.i	−0.194687	+	0.572362i
$255$	−289972.	−	1.01451e6i	−0.279258	−	0.977026i
$256$	−910683.	+	519777.i	−0.868495	+	0.495698i
$257$	1.13900e6	−	1.13900e6i	1.07570	−	1.07570i	0.0788094	−	0.996890i	$-0.474888\pi$
$257$	1.13900e6	−	1.13900e6i	1.07570	−	1.07570i	0.996890	−	0.0788094i	$-0.0251118\pi$
$258$	−1.27892e6	+	629706.i	−1.19617	+	0.588964i
$259$			901825.i			0.835359i
$260$	342942.	−	148263.i	0.314620	−	0.136019i
$261$		−	33506.0i		−	0.0304454i
$262$	−29530.6	−	59975.8i	−0.0265778	−	0.0539787i
$263$	999582.	−	999582.i	0.891105	−	0.891105i	−0.103522	−	0.994627i	$-0.533011\pi$
$263$	999582.	−	999582.i	0.891105	−	0.891105i	0.994627	+	0.103522i	$0.0330112\pi$
$264$	776467.	+	1.16676e6i	0.685667	+	1.03032i
$265$	−744111.	−	413296.i	−0.650913	−	0.361531i
$266$	1.22320e6	+	416067.i	1.05997	+	0.360545i
$267$	−699776.	+	699776.i	−0.600732	+	0.600732i
$268$	54169.2	+	415436.i	0.0460697	+	0.353319i
$269$	−1.07177e6			−0.903072			−0.451536	−	0.892253i	$-0.649124\pi$
$269$	−1.07177e6			−0.903072			−0.451536	+	0.892253i	$0.649124\pi$
$270$	−61231.2	+	1.23679e6i	−0.0511168	+	1.03250i
$271$			523663.i			0.433141i	0.976267	+	0.216570i	$0.0694870\pi$
$271$			523663.i			0.433141i	−0.976267	+	0.216570i	$0.930513\pi$
$272$	−1.11464e6	−	647229.i	−0.913508	−	0.530439i
$273$	500922.	+	500922.i	0.406783	+	0.406783i
$274$	−185905.	−	63234.6i	−0.149594	−	0.0508837i
$275$	−1.36976e6	+	852684.i	−1.09223	+	0.679918i
$276$	764617.	−	993913.i	0.604187	−	0.785373i
$277$	970729.	+	970729.i	0.760149	+	0.760149i	0.976349	−	0.216200i	$-0.0693663\pi$
$277$	970729.	+	970729.i	0.760149	+	0.760149i	−0.216200	+	0.976349i	$0.569366\pi$
$278$	1.61724e6	−	796289.i	1.25506	−	0.617958i
$279$	90217.5			0.0693873
$280$	1.48364e6	−	1.74294e6i	1.13092	−	1.32858i
$281$	−571060.			−0.431435			−0.215718	−	0.976456i	$-0.569209\pi$
$281$	−571060.			−0.431435			−0.215718	+	0.976456i	$0.569209\pi$
$282$	−1.28284e6	+	631640.i	−0.960618	+	0.472984i
$283$	−546336.	−	546336.i	−0.405503	−	0.405503i	0.474664	−	0.880167i	$-0.342570\pi$
$283$	−546336.	−	546336.i	−0.405503	−	0.405503i	−0.880167	+	0.474664i	$0.842570\pi$
$284$	−470878.	−	362246.i	−0.346428	−	0.266506i
$285$	739977.	+	410999.i	0.539642	+	0.299729i
$286$	−577523.	−	196442.i	−0.417497	−	0.142010i
$287$	−1.99479e6	−	1.99479e6i	−1.42953	−	1.42953i
$288$	69034.9	+	79213.3i	0.0490442	+	0.0562752i
$289$		−	164507.i		−	0.115862i
$290$	−432953.	+	392106.i	−0.302305	+	0.273784i
$291$	309444.			0.214215
$292$	2.61666e6	−	341189.i	1.79593	−	0.234174i
$293$	1.04865e6	−	1.04865e6i	0.713608	−	0.713608i	−0.253680	−	0.967288i	$-0.581641\pi$
$293$	1.04865e6	−	1.04865e6i	0.713608	−	0.713608i	0.967288	+	0.253680i	$0.0816410\pi$
$294$	2.75899e6	+	938459.i	1.86158	+	0.633209i
$295$	444581.	−	127072.i	0.297438	−	0.0850150i
$296$	399853.	+	600839.i	0.265260	+	0.398592i
$297$	1.42964e6	−	1.42964e6i	0.940452	−	0.940452i
$298$	887826.	+	1.80315e6i	0.579145	+	1.17623i
$299$			545811.i			0.353073i
$300$	1.15988e6	−	950413.i	0.744063	−	0.609691i
$301$		−	3.80120e6i		−	2.41827i
$302$	1.25175e6	−	616331.i	0.789770	−	0.388863i
$303$	1.11707e6	−	1.11707e6i	0.698996	−	0.698996i
$304$	999432.	−	265142.i	0.620253	−	0.164549i
$305$	−1.53147e6	+	437733.i	−0.942670	+	0.269438i
$306$	−41592.5	+	122278.i	−0.0253928	+	0.0746528i
$307$	−397765.	+	397765.i	−0.240869	+	0.240869i	−0.817210	−	0.576341i	$-0.804480\pi$
$307$	−397765.	+	397765.i	−0.240869	+	0.240869i	0.576341	+	0.817210i	$0.304480\pi$
$308$	−3.70576e6	+	483198.i	−2.22587	+	0.290234i
$309$	−2.02288e6			−1.20524
$310$	−1.05578e6	−	1.16576e6i	−0.623975	−	0.688977i
$311$			2.28317e6i			1.33856i	0.743011	+	0.669279i	$0.233397\pi$
$311$			2.28317e6i			1.33856i	−0.743011	+	0.669279i	$0.766603\pi$
$312$	555838.	+	111638.i	0.323267	+	0.0649271i
$313$	2.40862e6	+	2.40862e6i	1.38965	+	1.38965i	0.826034	+	0.563621i	$0.190592\pi$
$313$	2.40862e6	+	2.40862e6i	1.38965	+	1.38965i	0.563621	+	0.826034i	$0.309408\pi$
$314$	−321462.	+	945072.i	−0.183995	+	0.540929i
$315$	−200509.	−	111367.i	−0.113857	−	0.0632385i
$316$	206473.	−	268391.i	0.116318	−	0.151199i
$317$	−2.25260e6	−	2.25260e6i	−1.25903	−	1.25903i	−0.951557	−	0.307473i	$-0.900516\pi$
$317$	−2.25260e6	−	2.25260e6i	−1.25903	−	1.25903i	−0.307473	−	0.951557i	$-0.599484\pi$
$318$	−570545.	−	1.15876e6i	−0.316389	−	0.642578i
$319$	953708.			0.524734
$320$	215682.	−	1.81904e6i	0.117744	−	0.993044i
$321$	−2.08349e6			−1.12857
$322$	1.47706e6	+	2.99987e6i	0.793886	+	1.61236i
$323$	898741.	+	898741.i	0.479323	+	0.479323i
$324$	−1.05973e6	+	1.37753e6i	−0.560831	+	0.729016i
$325$	−147904.	+	635706.i	−0.0776735	+	0.333847i
$326$	−580990.	+	1.70806e6i	−0.302778	+	0.890142i
$327$	961462.	+	961462.i	0.497236	+	0.497236i
$328$	−2.21348e6	−	444570.i	−1.13603	−	0.228168i
$329$		−	3.81288e6i		−	1.94206i
$330$	−2.44534e6	−	121064.i	−1.23610	−	0.0611969i
$331$	−3.68065e6			−1.84652			−0.923262	−	0.384171i	$-0.874487\pi$
$331$	−3.68065e6			−1.84652			−0.923262	+	0.384171i	$0.874487\pi$
$332$	−567331.	+	73975.0i	−0.282483	+	0.0368332i
$333$	51139.2	−	51139.2i	0.0252722	−	0.0252722i
$334$	116319.	−	341967.i	0.0570536	−	0.167733i
$335$	−639815.	−	355367.i	−0.311489	−	0.173008i
$336$	3.35708e6	−	890610.i	1.62224	−	0.430367i
$337$	884212.	−	884212.i	0.424113	−	0.424113i	−0.462504	−	0.886617i	$-0.653049\pi$
$337$	884212.	−	884212.i	0.424113	−	0.424113i	0.886617	+	0.462504i	$0.153049\pi$
$338$	1.66294e6	−	818789.i	0.791744	−	0.389835i
$339$		−	955860.i		−	0.451747i
$340$	2.06678e6	−	893527.i	0.969609	−	0.419189i
$341$			2.56793e6i			1.19591i
$342$	−45769.6	−	92956.9i	−0.0211598	−	0.0429750i
$343$	−2.80667e6	+	2.80667e6i	−1.28812	+	1.28812i
$344$	−1.68539e6	−	2.53254e6i	−0.767897	−	1.15388i
$345$	602029.	+	2.10629e6i	0.272314	+	0.952731i
$346$	1.43025e6	+	486492.i	0.642274	+	0.218467i
$347$	−1.23778e6	+	1.23778e6i	−0.551849	+	0.551849i	−0.926974	−	0.375125i	$-0.877600\pi$
$347$	−1.23778e6	+	1.23778e6i	−0.551849	+	0.551849i	0.375125	+	0.926974i	$0.377600\pi$
$348$	−878917.	+	114603.i	−0.389045	+	0.0507280i
$349$	101130.			0.0444442			0.0222221	−	0.999753i	$-0.492926\pi$
$349$	101130.			0.0444442			0.0222221	+	0.999753i	$0.492926\pi$
$350$	907422.	+	3.89420e6i	0.395949	+	1.69921i
$351$		−	817867.i		−	0.354336i
$352$	−2.25471e6	+	1.96500e6i	−0.969917	+	0.845289i
$353$	−901480.	−	901480.i	−0.385052	−	0.385052i	0.487866	−	0.872918i	$-0.337775\pi$
$353$	−901480.	−	901480.i	−0.385052	−	0.385052i	−0.872918	+	0.487866i	$0.837775\pi$
$354$	664258.	+	225945.i	0.281727	+	0.0958283i
$355$	997879.	−	285218.i	0.420249	−	0.120118i
$356$	−1.67386e6	−	1.28770e6i	−0.699996	−	0.538506i
$357$	3.01886e6	+	3.01886e6i	1.25364	+	1.25364i
$358$	−1.45566e6	+	716732.i	−0.600279	+	0.295562i
$359$	3.32311e6			1.36084			0.680422	−	0.732820i	$-0.261796\pi$
$359$	3.32311e6			1.36084			0.680422	+	0.732820i	$0.261796\pi$
$360$	−182967.	+	14704.0i	−0.0744075	+	0.00597971i
$361$	1.45647e6			0.588210
$362$	−610501.	+	300595.i	−0.244858	+	0.120562i
$363$	1.11896e6	+	1.11896e6i	0.445705	+	0.445705i
$364$	−921778.	+	1.19820e6i	−0.364647	+	0.473999i
$365$	−2.23831e6	+	4.02992e6i	−0.879403	+	1.58331i
$366$	−2.28821e6	−	778324.i	−0.892879	−	0.303709i
$367$	−2.11644e6	−	2.11644e6i	−0.820239	−	0.820239i	0.165903	−	0.986142i	$-0.446946\pi$
$367$	−2.11644e6	−	2.11644e6i	−0.820239	−	0.820239i	−0.986142	+	0.165903i	$0.946946\pi$
$368$	2.31417e6	+	1.34375e6i	0.890792	+	0.517249i
$369$			226234.i			0.0864953i
$370$	−1.25926e6	−	62343.6i	−0.478203	−	0.0236749i
$371$	3.44408e6			1.29909
$372$	−308577.	−	2.36655e6i	−0.115613	−	0.886662i
$373$	1.46519e6	−	1.46519e6i	0.545283	−	0.545283i	−0.379790	−	0.925073i	$-0.624004\pi$
$373$	1.46519e6	−	1.46519e6i	0.545283	−	0.545283i	0.925073	+	0.379790i	$0.124004\pi$
$374$	−3.48051e6	−	1.18388e6i	−1.28666	−	0.437652i
$375$	130419.	+	2.61633e6i	0.0478919	+	0.960760i
$376$	−1.69056e6	−	2.54032e6i	−0.616682	−	0.926656i
$377$	272798.	−	272798.i	0.0988524	−	0.0988524i
$378$	−2.21329e6	−	4.49513e6i	−0.796725	−	1.61813i
$379$		−	518674.i		−	0.185480i	−0.995690	−	0.0927399i	$-0.970437\pi$
$379$		−	518674.i		−	0.185480i	0.995690	−	0.0927399i	$-0.0295625\pi$
$380$	−665535.	+	1.67925e6i	−0.236435	+	0.596564i
$381$		−	1.64782e6i		−	0.581565i
$382$	−2.50101e6	+	1.23143e6i	−0.876914	+	0.431770i
$383$	3.41844e6	−	3.41844e6i	1.19078	−	1.19078i	0.213930	−	0.976849i	$-0.431373\pi$
$383$	3.41844e6	−	3.41844e6i	1.19078	−	1.19078i	0.976849	−	0.213930i	$-0.0686266\pi$
$384$	1.84177e6	−	2.08184e6i	0.637392	−	0.720475i
$385$	3.16994e6	−	5.70726e6i	1.08993	−	1.96235i
$386$	1.70605e6	−	5.01563e6i	0.582804	−	1.71340i
$387$	−215552.	+	215552.i	−0.0731603	+	0.0731603i
$388$	85381.2	+	654808.i	0.0287927	+	0.220818i
$389$	682389.			0.228643			0.114322	−	0.993444i	$-0.463531\pi$
$389$	682389.			0.228643			0.114322	+	0.993444i	$0.463531\pi$
$390$	−734091.	+	664833.i	−0.244393	+	0.221335i
$391$			3.28940e6i			1.08811i
$392$	−1.22460e6	+	6.09719e6i	−0.402512	+	2.00408i
$393$	125308.	+	125308.i	0.0409259	+	0.0409259i
$394$	902790.	−	2.65413e6i	0.292986	−	0.861353i
$395$	162569.	+	568771.i	0.0524257	+	0.183419i
$396$	237540.	+	182740.i	0.0761201	+	0.0585591i
$397$	1.10424e6	+	1.10424e6i	0.351631	+	0.351631i	0.860716	−	0.509085i	$-0.170016\pi$
$397$	1.10424e6	+	1.10424e6i	0.351631	+	0.351631i	−0.509085	+	0.860716i	$0.670016\pi$
$398$	239230.	+	485870.i	0.0757022	+	0.153749i
$399$	−3.42494e6			−1.07701
$400$	2.33118e6	+	2.19216e6i	0.728495	+	0.685051i
$401$	−2.52254e6			−0.783390			−0.391695	−	0.920095i	$-0.628111\pi$
$401$	−2.52254e6			−0.783390			−0.391695	+	0.920095i	$0.628111\pi$
$402$	−490576.	−	996347.i	−0.151405	−	0.307500i
$403$	734528.	+	734528.i	0.225292	+	0.225292i
$404$	2.67204e6	+	2.05560e6i	0.814496	+	0.626591i
$405$	−834389.	−	2.91924e6i	−0.252773	−	0.884365i
$406$	761102.	−	2.23758e6i	0.229154	−	0.673694i
$407$	1.45562e6	+	1.45562e6i	0.435573	+	0.435573i
$408$	3.34982e6	+	672801.i	0.996257	+	0.200095i
$409$			3.08388e6i			0.911569i	0.890090	+	0.455784i	$0.150641\pi$
$409$			3.08388e6i			0.911569i	−0.890090	+	0.455784i	$0.849359\pi$
$410$	2.92332e6	−	2.64752e6i	0.858850	−	0.777821i
$411$	520529.			0.151999
$412$	−558149.	−	4.28057e6i	−0.161997	−	1.24239i
$413$	−1.32293e6	+	1.32293e6i	−0.381648	+	0.381648i
$414$	86352.8	−	253870.i	0.0247614	−	0.0727965i
$415$	485300.	−	873750.i	0.138322	−	0.249039i
$416$	−82869.7	+	1.20700e6i	−0.0234781	+	0.341959i
$417$	−3.37892e6	+	3.37892e6i	−0.951564	+	0.951564i
$418$	2.64591e6	−	1.30278e6i	0.740685	−	0.364695i
$419$		−	2.04163e6i		−	0.568123i	−0.958806	−	0.284061i	$-0.908318\pi$
$419$		−	2.04163e6i		−	0.568123i	0.958806	−	0.284061i	$-0.0916820\pi$
$420$	−2.23553e6	+	5.64060e6i	−0.618382	+	1.56028i
$421$		−	2.04322e6i		−	0.561836i	−0.959732	−	0.280918i	$-0.909361\pi$
$421$		−	2.04322e6i		−	0.561836i	0.959732	−	0.280918i	$-0.0906389\pi$
$422$	−76922.4	−	156227.i	−0.0210267	−	0.0427047i
$423$	−216214.	+	216214.i	−0.0587534	+	0.0587534i
$424$	2.29461e6	−	1.52704e6i	0.619860	−	0.412512i
$425$	−891364.	+	3.83116e6i	−0.239377	+	1.02886i
$426$	1.49095e6	+	507141.i	0.398052	+	0.135396i
$427$	4.55718e6	−	4.55718e6i	1.20956	−	1.20956i
$428$	−574872.	−	4.40883e6i	−0.151692	−	1.16336i
$429$	1.61705e6			0.424210
$430$	5.30781e6	+	262779.i	1.38434	+	0.0685361i
$431$		−	1.73952e6i		−	0.451061i	−0.974236	−	0.225531i	$-0.927588\pi$
$431$		−	1.73952e6i		−	0.451061i	0.974236	−	0.225531i	$-0.0724116\pi$
$432$	−3.46766e6	−	2.01354e6i	−0.893978	−	0.519099i
$433$	395725.	+	395725.i	0.101432	+	0.101432i	0.756002	−	0.654570i	$-0.227150\pi$
$433$	395725.	+	395725.i	0.101432	+	0.101432i	−0.654570	+	0.756002i	$0.727150\pi$
$434$	6.02484e6	+	2.04933e6i	1.53540	+	0.522260i
$435$	751832.	−	1.35362e6i	0.190501	−	0.342985i
$436$	−1.76925e6	+	2.29982e6i	−0.445730	+	0.579398i
$437$	−1.86593e6	−	1.86593e6i	−0.467404	−	0.467404i
$438$	−6.27557e6	+	3.08993e6i	−1.56303	+	0.769597i
$439$	484857.			0.120075			0.0600375	−	0.998196i	$-0.480878\pi$
$439$	484857.			0.120075			0.0600375	+	0.998196i	$0.480878\pi$
$440$	−418533.	−	5.20794e6i	−0.103062	−	1.28243i
$441$	623179.			0.152587
$442$	−1.33420e6	+	656925.i	−0.324836	+	0.159941i
$443$	1.14644e6	+	1.14644e6i	0.277550	+	0.277550i	0.832130	−	0.554580i	$-0.187121\pi$
$443$	1.14644e6	+	1.14644e6i	0.277550	+	0.277550i	−0.554580	+	0.832130i	$0.687121\pi$
$444$	−1.51638e6	−	1.16655e6i	−0.365048	−	0.280831i
$445$	3.54723e6	−	1.01389e6i	0.849161	−	0.242711i
$446$	−2.70427e6	−	919845.i	−0.643743	−	0.218966i
$447$	−3.76734e6	−	3.76734e6i	−0.891798	−	0.891798i
$448$	2.81088e6	+	6.85813e6i	0.661680	+	1.61440i
$449$			6.29177e6i			1.47284i	0.676522	+	0.736422i	$0.263486\pi$
$449$			6.29177e6i			1.47284i	−0.676522	+	0.736422i	$0.736514\pi$
$450$	169369.	−	272282.i	0.0394278	−	0.0633852i
$451$	−6.43949e6			−1.49077
$452$	2.02268e6	−	263739.i	0.465672	−	0.0607195i
$453$	−2.61530e6	+	2.61530e6i	−0.598792	+	0.598792i
$454$	−6.19338e6	−	2.10665e6i	−1.41022	−	0.479682i
$455$	−725772.	−	2.53922e6i	−0.164351	−	0.575006i
$456$	−2.28186e6	+	1.51856e6i	−0.513898	+	0.341995i
$457$	−3.45893e6	+	3.45893e6i	−0.774732	+	0.774732i	−0.978930	−	0.204198i	$-0.934541\pi$
$457$	−3.45893e6	+	3.45893e6i	−0.774732	+	0.774732i	0.204198	+	0.978930i	$0.434541\pi$
$458$	3.44820e6	+	7.00320e6i	0.768120	+	1.56003i
$459$		−	4.92897e6i		−	1.09201i
$460$	−4.29097e6	+	1.85511e6i	−0.945499	+	0.408766i
$461$			3.70309e6i			0.811544i	0.913974	+	0.405772i	$0.132997\pi$
$461$			3.70309e6i			0.811544i	−0.913974	+	0.405772i	$0.867003\pi$
$462$	8.88758e6	−	4.37602e6i	1.93722	−	0.953838i
$463$	−2.86396e6	+	2.86396e6i	−0.620889	+	0.620889i	−0.945759	−	0.324870i	$-0.894680\pi$
$463$	−2.86396e6	+	2.86396e6i	−0.620889	+	0.620889i	0.324870	+	0.945759i	$0.394680\pi$
$464$	−485018.	−	1.82824e6i	−0.104584	−	0.394219i
$465$	3.64473e6	+	2.02437e6i	0.781688	+	0.434167i
$466$	−2.41048e6	+	7.08660e6i	−0.514207	+	1.51173i
$467$	−599549.	+	599549.i	−0.127213	+	0.127213i	−0.767847	−	0.640633i	$-0.778672\pi$
$467$	−599549.	+	599549.i	−0.127213	+	0.127213i	0.640633	+	0.767847i	$0.278672\pi$
$468$	120216.	−	15675.2i	0.0253717	−	0.00330824i
$469$	2.96135e6			0.621667
$470$	5.32411e6	+	263586.i	1.11174	+	0.0550399i
$471$		−	2.64618e6i		−	0.549627i
$472$	−294836.	+	1.46797e6i	−0.0609152	+	0.303292i
$473$	−6.13544e6	−	6.13544e6i	−1.26094	−	1.26094i
$474$	−289060.	+	849813.i	−0.0590939	+	0.173731i
$475$	−1.66762e6	−	2.67888e6i	−0.339127	−	0.544778i
$476$	−5.55520e6	+	7.22112e6i	−1.12378	+	1.46079i
$477$	−195301.	−	195301.i	−0.0393014	−	0.0393014i
$478$	354363.	+	719701.i	0.0709379	+	0.144073i
$479$	70233.6			0.0139864			0.00699321	−	0.999976i	$-0.497774\pi$
$479$	70233.6			0.0139864			0.00699321	+	0.999976i	$0.497774\pi$
$480$	1.01153e6	+	4.74923e6i	0.200389	+	0.940849i
$481$	832725.			0.164111
$482$	−882355.	−	1.79204e6i	−0.172992	−	0.351342i
$483$	−6.26766e6	−	6.26766e6i	−1.22247	−	1.22247i
$484$	−2.05907e6	+	2.67655e6i	−0.399537	+	0.519352i
$485$	−1.00847e6	−	560128.i	−0.194675	−	0.108127i
$486$	−249801.	+	734395.i	−0.0479738	+	0.141039i
$487$	4.67856e6	+	4.67856e6i	0.893902	+	0.893902i	0.994888	−	0.100986i	$-0.0321996\pi$
$487$	4.67856e6	+	4.67856e6i	0.893902	+	0.893902i	−0.100986	+	0.994888i	$0.532200\pi$
$488$	1.01564e6	−	5.05678e6i	0.193059	−	0.961224i
$489$		−	4.78254e6i		−	0.904454i
$490$	−7.29279e6	−	8.05251e6i	−1.37216	−	1.51510i
$491$	7.83994e6			1.46760			0.733802	−	0.679363i	$-0.237744\pi$
$491$	7.83994e6			1.46760			0.733802	+	0.679363i	$0.237744\pi$
$492$	5.93449e6	−	773805.i	1.10528	−	0.144118i
$493$	1.64405e6	−	1.64405e6i	0.304647	−	0.304647i
$494$	384187.	−	1.12948e6i	0.0708313	−	0.208238i
$495$	−503393.	+	143882.i	−0.0923409	+	0.0263933i
$496$	4.92267e6	−	1.30595e6i	0.898455	−	0.238354i
$497$	−2.96937e6	+	2.96937e6i	−0.539230	+	0.539230i
$498$	1.36064e6	−	669945.i	0.245850	−	0.121050i
$499$			1.64729e6i			0.296154i	0.988976	+	0.148077i	$0.0473084\pi$
$499$			1.64729e6i			0.296154i	−0.988976	+	0.148077i	$0.952692\pi$
$500$	−5.50039e6	+	997871.i	−0.983939	+	0.178505i
$501$			957501.i			0.170430i
$502$	−2.97597e6	−	6.04412e6i	−0.527072	−	1.07047i
$503$	−7.27235e6	+	7.27235e6i	−1.28161	+	1.28161i	−0.341854	+	0.939753i	$0.611055\pi$
$503$	−7.27235e6	+	7.27235e6i	−1.28161	+	1.28161i	−0.939753	+	0.341854i	$0.888945\pi$
$504$	618309.	−	411479.i	0.108425	−	0.0721558i
$505$	−5.66255e6	+	1.61850e6i	−0.988061	+	0.282412i
$506$	7.22610e6	+	2.45793e6i	1.25467	+	0.426769i
$507$	−3.47440e6	+	3.47440e6i	−0.600288	+	0.600288i
$508$	3.48693e6	−	454665.i	0.599492	−	0.0781685i
$509$	6.59314e6			1.12797			0.563985	−	0.825785i	$-0.309268\pi$
$509$	6.59314e6			1.12797			0.563985	+	0.825785i	$0.309268\pi$
$510$	−4.42408e6	+	4.00669e6i	−0.753179	+	0.682120i
$511$		−	1.86523e7i		−	3.15995i
$512$	4.91351e6	+	3.32291e6i	0.828356	+	0.560201i
$513$	2.79599e6	+	2.79599e6i	0.469075	+	0.469075i
$514$	−8.62661e6	−	2.93430e6i	−1.44023	−	0.489889i
$515$	6.59253e6	+	3.66164e6i	1.09530	+	0.608355i
$516$	6.39155e6	+	4.91702e6i	1.05677	+	0.812975i
$517$	−6.15428e6	−	6.15428e6i	−1.01263	−	1.01263i
$518$	4.57679e6	−	2.25350e6i	0.749439	−	0.369005i
$519$	−4.00466e6			−0.652601
$520$	−1.60939e6	−	1.36996e6i	−0.261007	−	0.222177i
$521$	4.60672e6			0.743529			0.371765	−	0.928327i	$-0.378753\pi$
$521$	4.60672e6			0.743529			0.371765	+	0.928327i	$0.378753\pi$
$522$	−170044.	+	83725.4i	−0.0273140	+	0.0134487i
$523$	−3.89376e6	−	3.89376e6i	−0.622465	−	0.622465i	0.323696	−	0.946161i	$-0.395074\pi$
$523$	−3.89376e6	−	3.89376e6i	−0.622465	−	0.622465i	−0.946161	+	0.323696i	$0.895074\pi$
$524$	−230587.	+	299737.i	−0.0366866	+	0.0476883i
$525$	−5.60152e6	−	8.99835e6i	−0.886967	−	1.42483i
$526$	−7.57068e6	−	2.57514e6i	−1.19308	−	0.405822i
$527$	4.42672e6	+	4.42672e6i	0.694314	+	0.694314i
$528$	3.98108e6	−	6.85611e6i	0.621464	−	1.07027i
$529$		−	392982.i		−	0.0610568i
$530$	−238091.	+	4.80913e6i	−0.0368174	+	0.743665i
$531$	150037.			0.0230921
$532$	−945004.	−	7.24746e6i	−0.144762	−	1.11021i
$533$	−1.84194e6	+	1.84194e6i	−0.280840	+	0.280840i
$534$	5.30000e6	+	1.80277e6i	0.804308	+	0.273582i
$535$	6.79005e6	+	3.77135e6i	1.02563	+	0.569655i
$536$	1.97299e6	−	1.31301e6i	0.296629	−	0.197404i
$537$	3.04133e6	−	3.04133e6i	0.455123	−	0.455123i
$538$	2.67817e6	+	5.43928e6i	0.398916	+	0.810188i
$539$			1.77381e7i			2.62987i
$540$	6.42977e6	−	2.77977e6i	0.948880	−	0.410227i
$541$			1.10906e7i			1.62915i	0.580060	+	0.814574i	$0.303029\pi$
$541$			1.10906e7i			1.62915i	−0.580060	+	0.814574i	$0.696971\pi$
$542$	2.65761e6	−	1.30854e6i	0.388591	−	0.191332i
$543$	1.27553e6	−	1.27553e6i	0.185648	−	0.185648i
$544$	−499424.	+	7.27413e6i	−0.0723556	+	1.05386i
$545$	−1.39304e6	−	4.87375e6i	−0.200896	−	0.702865i
$546$	1.29048e6	−	3.79390e6i	0.185255	−	0.544634i
$547$	−1.76847e6	+	1.76847e6i	−0.252714	+	0.252714i	−0.822083	−	0.569368i	$-0.807188\pi$
$547$	−1.76847e6	+	1.76847e6i	−0.252714	+	0.252714i	0.569368	+	0.822083i	$0.307188\pi$
$548$	143624.	+	1.10148e6i	0.0204303	+	0.156685i
$549$	−516842.			−0.0731858
$550$	7.75018e6	+	4.82088e6i	1.09246	+	0.679548i
$551$			1.86519e6i			0.261725i
$552$	−6.95478e6	−	1.39684e6i	−0.971483	−	0.195119i
$553$	−1.69248e6	−	1.69248e6i	−0.235349	−	0.235349i
$554$	2.50081e6	−	7.35215e6i	0.346183	−	1.01775i
$555$	3.21349e6	−	918495.i	0.442838	−	0.126574i
$556$	−8.08238e6	−	6.21777e6i	−1.10880	−	0.852997i
$557$	3.02444e6	+	3.02444e6i	0.413054	+	0.413054i	0.882801	−	0.469747i	$-0.155655\pi$
$557$	3.02444e6	+	3.02444e6i	0.413054	+	0.413054i	−0.469747	+	0.882801i	$0.655655\pi$
$558$	−225437.	−	457856.i	−0.0306506	−	0.0622506i
$559$	−3.50995e6			−0.475085
$560$	−1.25528e7	−	3.17421e6i	−1.69149	−	0.427726i
$561$	9.74536e6			1.30735
$562$	1.42697e6	+	2.89814e6i	0.190579	+	0.387061i
$563$	1.06508e6	+	1.06508e6i	0.141616	+	0.141616i	0.774360	−	0.632745i	$-0.218072\pi$
$563$	1.06508e6	+	1.06508e6i	0.141616	+	0.141616i	−0.632745	+	0.774360i	$0.718072\pi$
$564$	6.41118e6	+	4.93211e6i	0.848672	+	0.652883i
$565$	−1.73021e6	+	3.11513e6i	−0.228023	+	0.410540i
$566$	−1.40748e6	+	4.13787e6i	−0.184672	+	0.542920i
$567$	8.68673e6	+	8.68673e6i	1.13475	+	1.13475i
$568$	−661771.	+	3.29491e6i	−0.0860670	+	0.428521i
$569$		−	6.43884e6i		−	0.833733i	−0.908968	−	0.416866i	$-0.863128\pi$
$569$		−	6.43884e6i		−	0.833733i	0.908968	−	0.416866i	$-0.136872\pi$
$570$	236768.	−	4.78242e6i	0.0305236	−	0.616538i
$571$	1.08005e6			0.138629			0.0693144	−	0.997595i	$-0.477919\pi$
$571$	1.08005e6			0.138629			0.0693144	+	0.997595i	$0.477919\pi$
$572$	446175.	+	3.42182e6i	0.0570184	+	0.437287i
$573$	5.22539e6	−	5.22539e6i	0.664863	−	0.664863i
$574$	−5.13900e6	+	1.51082e7i	−0.651027	+	1.91396i
$575$	1.85062e6	−	7.95411e6i	0.233425	−	1.00328i
$576$	229504.	−	548294.i	0.0288227	−	0.0688584i
$577$	1.01103e7	−	1.01103e7i	1.26422	−	1.26422i	0.315191	−	0.949028i	$-0.397931\pi$
$577$	1.01103e7	−	1.01103e7i	1.26422	−	1.26422i	0.949028	−	0.315191i	$-0.102069\pi$
$578$	−834877.	+	411072.i	−0.103945	+	0.0511798i
$579$			1.40437e7i			1.74094i
$580$	3.07182e6	+	1.21745e6i	0.379163	+	0.150273i
$581$			4.04410e6i			0.497029i
$582$	−773243.	−	1.57044e6i	−0.0946256	−	0.192182i
$583$	5.55901e6	−	5.55901e6i	0.677370	−	0.677370i
$584$	−8.27009e6	−	1.24270e7i	−1.00341	−	1.50777i
$585$	−102834.	+	185146.i	−0.0124236	+	0.0223678i
$586$	−7.94228e6	−	2.70153e6i	−0.955435	−	0.324987i
$587$	4.48142e6	−	4.48142e6i	0.536810	−	0.536810i	−0.385781	−	0.922590i	$-0.626068\pi$
$587$	4.48142e6	−	4.48142e6i	0.536810	−	0.536810i	0.922590	+	0.385781i	$0.126068\pi$
$588$	−2.13150e6	−	1.63470e7i	−0.254239	−	1.94982i
$589$	−5.02218e6			−0.596491
$590$	−1.75582e6	−	1.93873e6i	−0.207659	−	0.229291i
$591$			7.43151e6i			0.875202i
$592$	2.05011e6	−	3.53065e6i	0.240422	−	0.414048i
$593$	−5.03742e6	−	5.03742e6i	−0.588263	−	0.588263i	0.348898	−	0.937161i	$-0.386556\pi$
$593$	−5.03742e6	−	5.03742e6i	−0.588263	−	0.588263i	−0.937161	+	0.348898i	$0.886556\pi$
$594$	−1.08279e7	−	3.68307e6i	−1.25915	−	0.428295i
$595$	−4.37395e6	−	1.53029e7i	−0.506502	−	1.77207i
$596$	6.93252e6	−	9.01148e6i	0.799421	−	1.03916i
$597$	−1.01513e6	−	1.01513e6i	−0.116570	−	0.116570i
$598$	2.77001e6	−	1.36388e6i	0.316758	−	0.155964i
$599$	−4.33756e6			−0.493945			−0.246973	−	0.969022i	$-0.579436\pi$
$599$	−4.33756e6			−0.493945			−0.246973	+	0.969022i	$0.579436\pi$
$600$	−7.72170e6	−	3.51151e6i	−0.875659	−	0.398214i
$601$	8.62330e6			0.973839			0.486920	−	0.873447i	$-0.338120\pi$
$601$	8.62330e6			0.973839			0.486920	+	0.873447i	$0.338120\pi$
$602$	−1.92912e7	+	9.49851e6i	−2.16954	+	1.06823i
$603$	−167927.	−	167927.i	−0.0188074	−	0.0188074i
$604$	−6.25579e6	−	4.81258e6i	−0.697734	−	0.536766i
$605$	−1.62123e6	−	5.67211e6i	−0.180076	−	0.630023i
$606$	−8.46053e6	−	2.87782e6i	−0.935871	−	0.318333i
$607$	1.08203e7	+	1.08203e7i	1.19197	+	1.19197i	0.976513	+	0.215458i	$0.0691246\pi$
$607$	1.08203e7	+	1.08203e7i	1.19197	+	1.19197i	0.215458	+	0.976513i	$0.430875\pi$
$608$	−3.84300e6	−	4.40960e6i	−0.421610	−	0.483772i
$609$			6.26517e6i			0.684526i
$610$	6.04838e6	+	6.67846e6i	0.658134	+	0.726694i
$611$	−3.52072e6			−0.381530
$612$	724498.	−	94468.2i	0.0781914	−	0.0101955i
$613$	1.97923e6	−	1.97923e6i	0.212738	−	0.212738i	−0.592692	−	0.805429i	$-0.701935\pi$
$613$	1.97923e6	−	1.97923e6i	0.212738	−	0.212738i	0.805429	+	0.592692i	$0.201935\pi$
$614$	3.01261e6	+	1.02473e6i	0.322494	+	0.109695i
$615$	−5.07641e6	+	9.13973e6i	−0.541214	+	0.974419i
$616$	1.17123e7	+	1.75994e7i	1.24362	+	1.86873i
$617$	−3.94210e6	+	3.94210e6i	−0.416884	+	0.416884i	−0.884128	−	0.467244i	$-0.845247\pi$
$617$	−3.94210e6	+	3.94210e6i	−0.416884	+	0.416884i	0.467244	+	0.884128i	$0.345247\pi$
$618$	5.05480e6	+	1.02662e7i	0.532394	+	1.08128i
$619$		−	3.91209e6i		−	0.410377i	−0.978723	−	0.205188i	$-0.934219\pi$
$619$		−	3.91209e6i		−	0.410377i	0.978723	−	0.205188i	$-0.0657807\pi$
$620$	−3.27807e6	+	8.27111e6i	−0.342483	+	0.864141i
$621$			1.02334e7i			1.06485i
$622$	1.15871e7	−	5.70522e6i	1.20088	−	0.591285i
$623$	−1.05555e7	+	1.05555e7i	−1.08957	+	1.08957i
$624$	−822369.	−	3.09985e6i	−0.0845484	−	0.318698i
$625$	4.31082e6	−	8.76266e6i	0.441428	−	0.897297i
$626$	6.20511e6	−	1.82425e7i	0.632868	−	1.86058i
$627$	−5.52812e6	+	5.52812e6i	−0.561576	+	0.561576i
$628$	5.59954e6	−	730131.i	0.566570	−	0.0738757i
$629$	5.01852e6			0.505765
$630$	−64156.3	+	1.29588e6i	−0.00644003	+	0.130081i
$631$		−	5.32710e6i		−	0.532620i	−0.963887	−	0.266310i	$-0.914195\pi$
$631$		−	5.32710e6i		−	0.532620i	0.963887	−	0.266310i	$-0.0858045\pi$
$632$	−1.87803e6	−	377196.i	−0.187029	−	0.0375642i
$633$	326408.	+	326408.i	0.0323781	+	0.0323781i
$634$	−5.80318e6	+	1.70609e7i	−0.573380	+	1.68569i
$635$	−2.98275e6	+	5.37023e6i	−0.293550	+	0.528517i
$636$	−4.45506e6	+	5.79106e6i	−0.436727	+	0.567695i
$637$	5.07377e6	+	5.07377e6i	0.495430	+	0.495430i
$638$	−2.38314e6	−	4.84010e6i	−0.231792	−	0.470763i
$639$	336765.			0.0326268
$640$	−9.77065e6	+	3.45087e6i	−0.942918	+	0.333026i
$641$	−1.83912e7			−1.76793			−0.883966	−	0.467550i	$-0.845137\pi$
$641$	−1.83912e7			−1.76793			−0.883966	+	0.467550i	$0.845137\pi$
$642$	5.20625e6	+	1.05738e7i	0.498526	+	1.01249i
$643$	4.78115e6	+	4.78115e6i	0.456042	+	0.456042i	0.897354	−	0.441312i	$-0.145487\pi$
$643$	4.78115e6	+	4.78115e6i	0.456042	+	0.456042i	−0.441312	+	0.897354i	$0.645487\pi$
$644$	1.15335e7	−	1.49922e7i	1.09584	−	1.42446i
$645$	−1.35449e7	+	3.87147e6i	−1.28197	+	0.366418i
$646$	2.31535e6	−	6.80693e6i	0.218291	−	0.641756i
$647$	−1.12140e7	−	1.12140e7i	−1.05318	−	1.05318i	−0.998504	−	0.0546725i	$-0.982589\pi$
$647$	−1.12140e7	−	1.12140e7i	−1.05318	−	1.05318i	−0.0546725	−	0.998504i	$-0.517411\pi$
$648$	9.63905e6	+	1.93597e6i	0.901772	+	0.181118i
$649$			4.27064e6i			0.397998i
$650$	3.59581e6	−	837893.i	0.333821	−	0.0777867i
$651$	−1.68695e7			−1.56009
$652$	1.01202e7	−	1.31959e6i	0.932335	−	0.121568i
$653$	272189.	−	272189.i	0.0249797	−	0.0249797i	−0.694507	−	0.719486i	$-0.744377\pi$
$653$	272189.	−	272189.i	0.0249797	−	0.0249797i	0.719486	+	0.694507i	$0.244377\pi$
$654$	2.47693e6	−	7.28197e6i	0.226449	−	0.665739i
$655$	−181556.	−	635199.i	−0.0165351	−	0.0578504i
$656$	3.27487e6	+	1.23444e7i	0.297122	+	1.11998i
$657$	−1.05770e6	+	1.05770e6i	−0.0955983	+	0.0955983i
$658$	−1.93505e7	+	9.52768e6i	−1.74231	+	0.857872i
$659$		−	9.27375e6i		−	0.831844i	−0.909400	−	0.415922i	$-0.863459\pi$
$659$		−	9.27375e6i		−	0.831844i	0.909400	−	0.415922i	$-0.136541\pi$
$660$	5.49605e6	+	1.27127e7i	0.491124	+	1.13600i
$661$		−	1.18368e7i		−	1.05374i	−0.849947	−	0.526868i	$-0.823366\pi$
$661$		−	1.18368e7i		−	1.05374i	0.849947	−	0.526868i	$-0.176634\pi$
$662$	9.19728e6	+	1.86794e7i	0.815670	+	1.65660i
$663$	2.78755e6	−	2.78755e6i	0.246286	−	0.246286i
$664$	1.79308e6	+	2.69437e6i	0.157827	+	0.237158i
$665$	1.11618e7	+	6.19953e6i	0.978772	+	0.543632i
$666$	−387320.	−	131745.i	−0.0338364	−	0.0115093i
$667$	−3.41331e6	+	3.41331e6i	−0.297072	+	0.297072i
$668$	−2.02615e6	+	264192.i	−0.175683	+	0.0229076i
$669$	7.57190e6			0.654093
$670$	−204720.	+	4.13508e6i	−0.0176186	+	0.355874i
$671$		−	1.47113e7i		−	1.26138i
$672$	−1.29086e7	−	1.48118e7i	−1.10270	−	1.26528i
$673$	3.32488e6	+	3.32488e6i	0.282969	+	0.282969i	0.834292	−	0.551323i	$-0.185877\pi$
$673$	3.32488e6	+	3.32488e6i	0.282969	+	0.282969i	−0.551323	+	0.834292i	$0.685877\pi$
$674$	−6.69689e6	−	2.27792e6i	−0.567836	−	0.193147i
$675$	−2.77304e6	+	1.19188e7i	−0.234259	+	1.00687i
$676$	−8.31076e6	−	6.39346e6i	−0.699478	−	0.538108i
$677$	−1.32971e7	−	1.32971e7i	−1.11503	−	1.11503i	−0.992460	−	0.122567i	$-0.960887\pi$
$677$	−1.32971e7	−	1.32971e7i	−1.11503	−	1.11503i	−0.122567	−	0.992460i	$-0.539113\pi$
$678$	−4.85101e6	+	2.38852e6i	−0.405283	+	0.199551i
$679$	4.66766e6			0.388530
$680$	−9.69917e6	−	8.25620e6i	−0.804382	−	0.684712i
$681$	1.73414e7			1.43290
$682$	1.30323e7	−	6.41679e6i	1.07290	−	0.528271i
$683$	1.02763e7	+	1.02763e7i	0.842921	+	0.842921i	0.989238	−	0.146316i	$-0.0467418\pi$
$683$	1.02763e7	+	1.02763e7i	0.842921	+	0.842921i	−0.146316	+	0.989238i	$0.546742\pi$
$684$	−357389.	+	464564.i	−0.0292079	+	0.0379669i
$685$	−1.69640e6	−	942217.i	−0.138134	−	0.0767228i
$686$	2.12573e7	+	7.23058e6i	1.72464	+	0.586628i
$687$	−1.46319e7	−	1.46319e7i	−1.18279	−	1.18279i
$688$	−8.64126e6	+	1.48817e7i	−0.695995	+	1.19862i
$689$		−	3.18018e6i		−	0.255214i
$690$	9.18512e6	−	8.31855e6i	0.734450	−	0.665158i
$691$	6.84499e6			0.545353			0.272676	−	0.962106i	$-0.412091\pi$
$691$	6.84499e6			0.545353			0.272676	+	0.962106i	$0.412091\pi$
$692$	−1.10496e6	−	8.47419e6i	−0.0877165	−	0.672718i
$693$	1.49794e6	−	1.49794e6i	0.118484	−	0.118484i
$694$	9.37476e6	+	3.18879e6i	0.738859	+	0.251320i
$695$	1.71281e7	−	4.89563e6i	1.34508	−	0.384456i
$696$	2.77786e6	+	4.17416e6i	0.217364	+	0.326622i
$697$	−1.11007e7	+	1.11007e7i	−0.865502	+	0.865502i
$698$	−252705.	−	513237.i	−0.0196325	−	0.0398730i
$699$		−	1.98424e7i		−	1.53603i
$700$	1.74957e7	−	1.43361e7i	1.34954	−	1.10582i
$701$			1.42933e6i			0.109859i	0.998490	+	0.0549297i	$0.0174935\pi$
$701$			1.42933e6i			0.109859i	−0.998490	+	0.0549297i	$0.982507\pi$
$702$	−4.15070e6	+	2.04370e6i	−0.317891	+	0.156522i
$703$	−2.84679e6	+	2.84679e6i	−0.217254	+	0.217254i
$704$	1.56065e7	+	6.53256e6i	1.18679	+	0.496766i
$705$	−1.35865e7	+	3.88335e6i	−1.02952	+	0.294262i
$706$	−2.32240e6	+	6.82767e6i	−0.175358	+	0.515538i
$707$	1.68500e7	−	1.68500e7i	1.26780	−	1.26780i
$708$	−513183.	−	3.93572e6i	−0.0384760	−	0.295081i
$709$	1.95653e7			1.46174			0.730870	−	0.682517i	$-0.239115\pi$
$709$	1.95653e7			1.46174			0.730870	+	0.682517i	$0.239115\pi$
$710$	−3.94101e6	−	4.35156e6i	−0.293401	−	0.323966i
$711$			191949.i			0.0142401i
$712$	−2.35245e6	+	1.17126e7i	−0.173908	+	0.865874i
$713$	−9.19060e6	−	9.19060e6i	−0.677049	−	0.677049i
$714$	7.77724e6	−	2.28644e7i	0.570926	−	1.67847i
$715$	−5.26995e6	−	2.92705e6i	−0.385515	−	0.214124i
$716$	7.27487e6	+	5.59655e6i	0.530326	+	0.407979i
$717$	−1.50368e6	−	1.50368e6i	−0.109234	−	0.109234i
$718$	−8.30384e6	−	1.68649e7i	−0.601129	−	1.22088i
$719$	4.68265e6			0.337807			0.168904	−	0.985633i	$-0.445977\pi$
$719$	4.68265e6			0.337807			0.168904	+	0.985633i	$0.445977\pi$
$720$	531824.	+	891820.i	0.0382329	+	0.0641130i
$721$	−3.05132e7			−2.18600
$722$	−3.63944e6	−	7.39160e6i	−0.259831	−	0.527710i
$723$	3.74413e6	+	3.74413e6i	0.266382	+	0.266382i
$724$	3.05106e6	+	2.34718e6i	0.216324	+	0.166418i
$725$	−4.90042e6	+	3.05054e6i	−0.346249	+	0.215542i
$726$	2.88267e6	−	8.47482e6i	0.202980	−	0.596745i
$727$	−3.84912e6	−	3.84912e6i	−0.270101	−	0.270101i	0.559040	−	0.829141i	$-0.311170\pi$
$727$	−3.84912e6	−	3.84912e6i	−0.270101	−	0.270101i	−0.829141	+	0.559040i	$0.811170\pi$
$728$	8.38428e6	+	1.68395e6i	0.586323	+	0.117761i
$729$		−	1.52541e7i		−	1.06309i
$730$	2.60451e7	+	1.28944e6i	1.80892	+	0.0895559i
$731$	−2.11531e7			−1.46413
$732$	1.76779e6	+	1.35576e7i	0.121942	+	0.935201i
$733$	1.41189e7	−	1.41189e7i	0.970598	−	0.970598i	−0.0289819	−	0.999580i	$-0.509227\pi$
$733$	1.41189e7	−	1.41189e7i	0.970598	−	0.970598i	0.999580	+	0.0289819i	$0.00922652\pi$
$734$	−5.45239e6	+	1.60296e7i	−0.373548	+	1.09820i
$735$	2.51761e7	+	1.39833e7i	1.71898	+	0.954757i
$736$	1.03689e6	−	1.51023e7i	0.0705564	−	1.02766i
$737$	4.77985e6	−	4.77985e6i	0.324150	−	0.324150i
$738$	1.14815e6	−	565318.i	0.0775990	−	0.0382078i
$739$			2.46897e6i			0.166305i	0.996537	+	0.0831525i	$0.0264989\pi$
$739$			2.46897e6i			0.166305i	−0.996537	+	0.0831525i	$0.973501\pi$
$740$	2.83027e6	+	6.54658e6i	0.189998	+	0.439476i
$741$			3.16251e6i			0.211586i
$742$	−8.60612e6	−	1.74788e7i	−0.573849	−	1.16547i
$743$	−6.03463e6	+	6.03463e6i	−0.401032	+	0.401032i	−0.878597	−	0.477565i	$-0.841520\pi$
$743$	−6.03463e6	+	6.03463e6i	−0.401032	+	0.401032i	0.477565	+	0.878597i	$0.341520\pi$
$744$	−1.12392e7	+	7.47961e6i	−0.744396	+	0.495389i
$745$	5.45840e6	+	1.90970e7i	0.360309	+	1.26059i
$746$	−1.10971e7	−	3.77464e6i	−0.730068	−	0.248330i
$747$	229326.	−	229326.i	0.0150367	−	0.0150367i
$748$	2.68892e6	+	2.06220e7i	0.175721	+	1.34765i
$749$	−3.14274e7			−2.04693
$750$	1.29521e7	−	7.19961e6i	0.840787	−	0.467365i
$751$			1.45047e7i			0.938444i	0.883080	+	0.469222i	$0.155466\pi$
$751$			1.45047e7i			0.938444i	−0.883080	+	0.469222i	$0.844534\pi$
$752$	−8.66779e6	+	1.49274e7i	−0.558938	+	0.962588i
$753$	1.26281e7	+	1.26281e7i	0.811613	+	0.811613i
$754$	−2.06613e6	−	702784.i	−0.132351	−	0.0450188i
$755$	1.32572e7	−	3.78924e6i	0.846417	−	0.241927i
$756$	−1.72823e7	+	2.24650e7i	−1.09976	+	1.42956i
$757$	3.36048e6	+	3.36048e6i	0.213138	+	0.213138i	0.805599	−	0.592461i	$-0.201843\pi$
$757$	3.36048e6	+	3.36048e6i	0.213138	+	0.213138i	−0.592461	+	0.805599i	$0.701843\pi$
$758$	−2.63229e6	+	1.29607e6i	−0.166403	+	0.0819325i
$759$	−2.02330e7			−1.27484
$760$	1.01853e7	−	818536.i	0.639647	−	0.0514048i
$761$	9.65654e6			0.604449			0.302225	−	0.953237i	$-0.402271\pi$
$761$	9.65654e6			0.604449			0.302225	+	0.953237i	$0.402271\pi$
$762$	−8.36275e6	+	4.11761e6i	−0.521749	+	0.256896i
$763$	1.45027e7	+	1.45027e7i	0.901859	+	0.901859i
$764$	1.24991e7	+	9.61557e6i	0.774723	+	0.595994i
$765$	−619742.	+	1.11580e6i	−0.0382875	+	0.0689341i
$766$	−2.58908e7	−	8.80663e6i	−1.59431	−	0.542298i
$767$	1.22157e6	+	1.22157e6i	0.0749771	+	0.0749771i
$768$	−1.51676e7	−	4.14490e6i	−0.927928	−	0.253577i
$769$		−	398573.i		−	0.0243048i	−0.999926	−	0.0121524i	$-0.996132\pi$
$769$		−	398573.i		−	0.0243048i	0.999926	−	0.0121524i	$-0.00386832\pi$
$770$	−3.68856e7	−	1.82613e6i	−2.24197	−	0.110996i
$771$	2.41544e7			1.46339
$772$	−2.97176e7	+	3.87491e6i	−1.79461	+	0.234001i
$773$	1.84740e6	−	1.84740e6i	0.111202	−	0.111202i	−0.649317	−	0.760518i	$-0.724945\pi$
$773$	1.84740e6	−	1.84740e6i	0.111202	−	0.111202i	0.760518	+	0.649317i	$0.224945\pi$
$774$	1.63256e6	+	555308.i	0.0979528	+	0.0333182i
$775$	−8.21380e6	−	1.31948e7i	−0.491236	−	0.789127i
$776$	3.10982e6	−	2.06956e6i	0.185388	−	0.123374i
$777$	−9.56234e6	+	9.56234e6i	−0.568214	+	0.568214i
$778$	−1.70517e6	−	3.46314e6i	−0.100999	−	0.205126i
$779$		−	1.25939e7i		−	0.743560i
$780$	5.20840e6	+	2.06424e6i	0.306526	+	0.121485i
$781$			9.58560e6i			0.562331i
$782$	1.66938e7	−	8.21960e6i	0.976198	−	0.480655i
$783$	5.11465e6	−	5.11465e6i	0.298134	−	0.298134i
$784$	3.40034e7	−	9.02087e6i	1.97575	−	0.524153i
$785$	−4.78989e6	+	8.62387e6i	−0.277429	+	0.499492i
$786$	322820.	−	949064.i	0.0186382	−	0.0547948i
$787$	−8.91667e6	+	8.91667e6i	−0.513175	+	0.513175i	−0.915498	−	0.402323i	$-0.868203\pi$
$787$	−8.91667e6	+	8.91667e6i	−0.513175	+	0.513175i	0.402323	+	0.915498i	$0.368203\pi$
$788$	−1.57257e7	+	2.05049e6i	−0.902181	+	0.117636i
$789$	2.11978e7			1.21227
$790$	2.48030e6	−	2.24630e6i	0.141396	−	0.128056i
$791$		−	1.44182e7i		−	0.819352i
$792$	333839.	−	1.66216e6i	0.0189114	−	0.0941584i
$793$	−4.20800e6	−	4.20800e6i	−0.237625	−	0.237625i
$794$	2.84475e6	−	8.36333e6i	0.160138	−	0.470791i
$795$	−3.50774e6	−	1.22723e7i	−0.196838	−	0.688668i
$796$	1.86801e6	−	2.42820e6i	0.104495	−	0.135832i
$797$	1.17690e7	+	1.17690e7i	0.656289	+	0.656289i	0.954500	−	0.298211i	$-0.0963900\pi$
$797$	1.17690e7	+	1.17690e7i	0.656289	+	0.656289i	−0.298211	+	0.954500i	$0.596390\pi$
$798$	8.55830e6	+	1.73817e7i	0.475752	+	0.966239i
$799$	−2.12181e7			−1.17581
$800$	5.30009e6	−	1.73086e7i	0.292791	−	0.956176i
$801$	1.19712e6			0.0659260
$802$	6.30338e6	+	1.28020e7i	0.346049	+	0.702816i
$803$	−3.01062e7	−	3.01062e7i	−1.64766	−	1.64766i
$804$	−3.83063e6	+	4.97938e6i	−0.208992	+	0.271666i
$805$	9.08104e6	+	3.17714e7i	0.493908	+	1.72801i
$806$	1.89230e6	−	5.56320e6i	0.102601	−	0.301639i
$807$	−1.13644e7	−	1.13644e7i	−0.614272	−	0.614272i
$808$	3.75528e6	−	1.86972e7i	0.202355	−	1.00751i
$809$			1.40431e7i			0.754380i	0.926136	+	0.377190i	$0.123110\pi$
$809$			1.40431e7i			0.754380i	−0.926136	+	0.377190i	$0.876890\pi$
$810$	−1.27302e7	+	1.15292e7i	−0.681747	+	0.617428i
$811$	1.59685e7			0.852536			0.426268	−	0.904597i	$-0.359828\pi$
$811$	1.59685e7			0.852536			0.426268	+	0.904597i	$0.359828\pi$
$812$	−1.32576e7	+	1.72868e6i	−0.705627	+	0.0920076i
$813$	−5.55257e6	+	5.55257e6i	−0.294624	+	0.294624i
$814$	3.74998e6	−	1.10246e7i	0.198366	−	0.583179i
$815$	−8.65694e6	+	1.55862e7i	−0.456531	+	0.821953i
$816$	−4.95611e6	−	1.86816e7i	−0.260564	−	0.982177i
$817$	1.19992e7	−	1.19992e7i	0.628925	−	0.628925i
$818$	1.56508e7	−	7.70606e6i	0.817811	−	0.402670i
$819$		−	856937.i		−	0.0446415i
$820$	−2.07411e7	−	8.22028e6i	−1.07720	−	0.426925i
$821$			1.36995e7i			0.709327i	0.934994	+	0.354664i	$0.115405\pi$
$821$			1.36995e7i			0.709327i	−0.934994	+	0.354664i	$0.884595\pi$
$822$	−1.30071e6	−	2.64170e6i	−0.0671429	−	0.136365i
$823$	−1.16517e7	+	1.16517e7i	−0.599641	+	0.599641i	−0.940217	−	0.340576i	$-0.889378\pi$
$823$	−1.16517e7	+	1.16517e7i	−0.599641	+	0.599641i	0.340576	+	0.940217i	$0.389378\pi$
$824$	−2.03293e7	+	1.35290e7i	−1.04305	+	0.694141i
$825$	−2.35653e7	−	5.48275e6i	−1.20542	−	0.280455i
$826$	1.00197e7	+	3.40816e6i	0.510981	+	0.173808i
$827$	1.01220e7	−	1.01220e7i	0.514638	−	0.514638i	−0.401306	−	0.915944i	$-0.631444\pi$
$827$	1.01220e7	−	1.01220e7i	0.514638	−	0.514638i	0.915944	+	0.401306i	$0.131444\pi$
$828$	−1.50418e6	+	196131.i	−0.0762470	+	0.00994194i
$829$	−3.25318e7			−1.64407			−0.822037	−	0.569434i	$-0.807162\pi$
$829$	−3.25318e7			−1.64407			−0.822037	+	0.569434i	$0.807162\pi$
$830$	−5.64698e6	−	279571.i	−0.284525	−	0.0140863i
$831$			2.05859e7i			1.03411i
$832$	6.33264e6	−	2.59551e6i	0.317158	−	0.129991i
$833$	3.05777e7	+	3.05777e7i	1.52683	+	1.52683i
$834$	2.55914e7	+	8.70482e6i	1.27403	+	0.433356i
$835$	1.73319e6	−	3.12048e6i	0.0860258	−	0.154884i
$836$	−1.32233e7	−	1.01726e7i	−0.654370	−	0.503406i
$837$	1.37716e7	+	1.37716e7i	0.679470	+	0.679470i
$838$	−1.03613e7	+	5.10166e6i	−0.509690	+	0.250958i
$839$	3.86903e7			1.89757			0.948784	−	0.315925i	$-0.102315\pi$
$839$	3.86903e7			1.89757			0.948784	+	0.315925i	$0.102315\pi$
$840$	3.42124e7	−	2.74946e6i	1.67296	−	0.134446i
$841$	−1.70992e7			−0.833654
$842$	−1.03694e7	+	5.10563e6i	−0.504049	+	0.248181i
$843$	−6.05513e6	−	6.05513e6i	−0.293464	−	0.293464i
$844$	−600643.	+	780767.i	−0.0290242	+	0.0377281i
$845$	1.76121e7	−	5.03396e6i	0.848532	−	0.242531i
$846$	1.63757e6	+	557014.i	0.0786637	+	0.0267571i
$847$	1.68784e7	+	1.68784e7i	0.808394	+	0.808394i
$848$	−1.34836e7	−	7.82940e6i	−0.643896	−	0.373886i
$849$		−	1.15860e7i		−	0.551649i
$850$	2.16706e7	−	5.04966e6i	1.02878	−	0.239726i
$851$	−1.04193e7			−0.493189
$852$	−1.15186e6	−	8.83388e6i	−0.0543626	−	0.416920i
$853$	6.17213e6	−	6.17213e6i	0.290444	−	0.290444i	−0.546812	−	0.837256i	$-0.684159\pi$
$853$	6.17213e6	−	6.17213e6i	0.290444	−	0.290444i	0.837256	+	0.546812i	$0.184159\pi$
$854$	−3.45154e7	−	1.17403e7i	−1.61945	−	0.550850i
$855$	−281394.	−	984499.i	−0.0131644	−	0.0460575i
$856$	−2.09384e7	+	1.39343e7i	−0.976696	+	0.649983i
$857$	1.57290e7	−	1.57290e7i	0.731559	−	0.731559i	−0.239369	−	0.970929i	$-0.576941\pi$
$857$	1.57290e7	−	1.57290e7i	0.731559	−	0.731559i	0.970929	+	0.239369i	$0.0769407\pi$
$858$	−4.04072e6	−	8.20659e6i	−0.187387	−	0.380579i
$859$		−	2.09256e7i		−	0.967597i	−0.875179	−	0.483799i	$-0.839257\pi$
$859$		−	2.09256e7i		−	0.967597i	0.875179	−	0.483799i	$-0.160743\pi$
$860$	−1.19296e7	−	2.75939e7i	−0.550023	−	1.27223i
$861$		−	4.23028e7i		−	1.94474i
$862$	−8.82810e6	+	4.34674e6i	−0.404668	+	0.199248i
$863$	2.82335e6	−	2.82335e6i	0.129044	−	0.129044i	−0.639635	−	0.768679i	$-0.720914\pi$
$863$	2.82335e6	−	2.82335e6i	0.129044	−	0.129044i	0.768679	+	0.639635i	$0.220914\pi$
$864$	−1.55371e6	+	2.26299e7i	−0.0708087	+	1.03133i
$865$	1.30511e7	+	7.24889e6i	0.593073	+	0.329406i
$866$	1.01947e6	−	2.99716e6i	0.0461935	−	0.135805i
$867$	1.74432e6	−	1.74432e6i	0.0788094	−	0.0788094i
$868$	−4.65459e6	−	3.56971e7i	−0.209692	−	1.60818i
$869$	−5.46360e6			−0.245431
$870$	−8.74837e6	−	433114.i	−0.391858	−	0.0194001i
$871$		−	2.73444e6i		−	0.122130i
$872$	1.60927e7	+	3.23216e6i	0.716699	+	0.143947i
$873$	−264686.	−	264686.i	−0.0117543	−	0.0117543i
$874$	−4.80704e6	+	1.41323e7i	−0.212862	+	0.625798i
$875$	1.96724e6	+	3.94649e7i	0.0868636	+	1.74257i
$876$	3.13630e7	+	2.41275e7i	1.38088	+	1.06231i
$877$	−2.56987e7	−	2.56987e7i	−1.12827	−	1.12827i	−0.990459	−	0.137807i	$-0.955995\pi$
$877$	−2.56987e7	−	2.56987e7i	−1.12827	−	1.12827i	−0.137807	−	0.990459i	$-0.544005\pi$
$878$	−1.21157e6	−	2.46066e6i	−0.0530410	−	0.107725i
$879$	2.22383e7			0.970797
$880$	−2.53846e7	+	1.51377e7i	−1.10500	+	0.658953i
$881$	1.37523e7			0.596945			0.298473	−	0.954418i	$-0.403523\pi$
$881$	1.37523e7			0.596945			0.298473	+	0.954418i	$0.403523\pi$
$882$	−1.55721e6	−	3.16265e6i	−0.0674025	−	0.136893i
$883$	2.38462e7	+	2.38462e7i	1.02924	+	1.02924i	0.999559	+	0.0296818i	$0.00944941\pi$
$883$	2.38462e7	+	2.38462e7i	1.02924	+	1.02924i	0.0296818	+	0.999559i	$0.490551\pi$
$884$	6.66782e6	+	5.12955e6i	0.286981	+	0.220774i
$885$	6.06142e6	+	3.36665e6i	0.260146	+	0.144491i
$886$	2.95346e6	−	8.68293e6i	0.126400	−	0.371605i
$887$	−1.46935e6	−	1.46935e6i	−0.0627070	−	0.0627070i	0.675058	−	0.737765i	$-0.264119\pi$
$887$	−1.46935e6	−	1.46935e6i	−0.0627070	−	0.0627070i	−0.737765	+	0.675058i	$0.764119\pi$
$888$	−2.13112e6	+	1.06107e7i	−0.0906932	+	0.451554i
$889$		−	2.48558e7i		−	1.05481i
$890$	−1.40094e7	−	1.54688e7i	−0.592849	−	0.654608i
$891$	2.80421e7			1.18336
$892$	2.08923e6	+	1.60228e7i	0.0879171	+	0.674256i
$893$	1.20361e7	−	1.20361e7i	0.505076	−	0.505076i
$894$	−9.70547e6	+	2.85333e7i	−0.406137	+	1.19401i
$895$	−1.54168e7	+	4.40651e6i	−0.643335	+	0.183881i
$896$	2.77813e7	−	3.14025e7i	1.15607	−	1.30676i
$897$	−5.78741e6	+	5.78741e6i	−0.240161	+	0.240161i
$898$	3.19309e7	−	1.57220e7i	1.32136	−	0.650603i
$899$			9.18696e6i			0.379116i
$900$	−1.80506e6	−	179169.i	−0.0742823	−	0.00737321i
$901$		−	1.91658e7i		−	0.786527i
$902$	1.60911e7	+	3.26806e7i	0.658521	+	1.33744i
$903$	4.03054e7	−	4.03054e7i	1.64492	−	1.64492i
$904$	−6.39278e6	−	9.60611e6i	−0.260177	−	0.390955i
$905$	−6.46577e6	+	1.84808e6i	−0.262421	+	0.0750064i
$906$	1.98079e7	+	6.73756e6i	0.801710	+	0.272698i
$907$	−1.23019e7	+	1.23019e7i	−0.496541	+	0.496541i	−0.910359	−	0.413819i	$-0.864195\pi$
$907$	−1.23019e7	+	1.23019e7i	−0.496541	+	0.496541i	0.413819	+	0.910359i	$0.364195\pi$
$908$	4.78480e6	+	3.66957e7i	0.192597	+	1.47707i
$909$	−1.91100e6			−0.0767098
$910$	−1.10731e7	+	1.00284e7i	−0.443265	+	0.401445i
$911$			3.71961e7i			1.48491i	0.669894	+	0.742457i	$0.266340\pi$
$911$			3.71961e7i			1.48491i	−0.669894	+	0.742457i	$0.733660\pi$
$912$	1.34087e7	+	7.78591e6i	0.533825	+	0.309972i
$913$	6.52750e6	+	6.52750e6i	0.259161	+	0.259161i
$914$	2.61974e7	+	8.91094e6i	1.03727	+	0.352824i
$915$	−2.08801e7	−	1.15973e7i	−0.824480	−	0.457934i
$916$	2.69250e7	−	3.49994e7i	1.06027	−	1.37823i
$917$	1.89015e6	+	1.89015e6i	0.0742290	+	0.0742290i
$918$	−2.50147e7	+	1.23166e7i	−0.979689	+	0.482374i
$919$	−4.30763e7			−1.68248			−0.841240	−	0.540663i	$-0.818174\pi$
$919$	−4.30763e7			−1.68248			−0.841240	+	0.540663i	$0.818174\pi$
$920$	2.01371e7	+	1.71412e7i	0.784380	+	0.667686i
$921$	−8.43526e6			−0.327680
$922$	1.87933e7	−	9.25335e6i	0.728074	−	0.358485i
$923$	2.74185e6	+	2.74185e6i	0.105935	+	0.105935i
$924$	−4.44169e7	−	3.41699e7i	−1.71146	−	1.31663i
$925$	−1.21353e7	−	2.82342e6i	−0.466333	−	0.108498i
$926$	2.16912e7	+	7.37816e6i	0.831295	+	0.282762i
$927$	1.73029e6	+	1.73029e6i	0.0661332	+	0.0661332i
$928$	−8.06639e6	+	7.02991e6i	−0.307475	+	0.267966i
$929$		−	4.20699e6i		−	0.159931i	−0.996798	−	0.0799655i	$-0.974519\pi$
$929$		−	4.20699e6i		−	0.159931i	0.996798	−	0.0799655i	$-0.0254810\pi$
$930$	1.16619e6	−	2.35556e7i	0.0442143	−	0.893074i
$931$	−3.46908e7			−1.31172
$932$	4.19880e7	−	5.47487e6i	1.58338	−	0.206459i
$933$	−2.42092e7	+	2.42092e7i	−0.910491	+	0.910491i
$934$	4.54089e6	+	1.54457e6i	0.170323	+	0.0579348i
$935$	−3.17600e7	−	1.76402e7i	−1.18810	−	0.659895i
$936$	−379951.	−	570932.i	−0.0141755	−	0.0213008i
$937$	9.47934e6	−	9.47934e6i	0.352719	−	0.352719i	−0.508401	−	0.861120i	$-0.669763\pi$
$937$	9.47934e6	−	9.47934e6i	0.352719	−	0.352719i	0.861120	+	0.508401i	$0.169763\pi$
$938$	−7.39987e6	−	1.50289e7i	−0.274610	−	0.557726i
$939$			5.10787e7i			1.89049i
$940$	−1.19663e7	−	2.76786e7i	−0.441711	−	1.02170i
$941$			1.54846e7i			0.570068i	0.958517	+	0.285034i	$0.0920049\pi$
$941$			1.54846e7i			0.570068i	−0.958517	+	0.285034i	$0.907995\pi$
$942$	−1.34295e7	+	6.61233e6i	−0.493096	+	0.242788i
$943$	2.30468e7	−	2.30468e7i	0.843980	−	0.843980i
$944$	8.18671e6	−	2.17188e6i	0.299006	−	0.0793241i
$945$	−1.36074e7	−	4.76076e7i	−0.495674	−	1.73419i
$946$	−1.58062e7	+	4.64689e7i	−0.574248	+	1.68824i
$947$	−2.49743e7	+	2.49743e7i	−0.904938	+	0.904938i	−0.995858	−	0.0909198i	$-0.971019\pi$
$947$	−2.49743e7	+	2.49743e7i	−0.904938	+	0.904938i	0.0909198	+	0.995858i	$0.471019\pi$
$948$	5.03513e6	−	656537.i	0.181966	−	0.0237268i
$949$	−1.72231e7			−0.620792
$950$	−9.42833e6	+	1.51572e7i	−0.338942	+	0.544893i
$951$		−	4.77701e7i		−	1.71279i
$952$	5.05288e7	+	1.01486e7i	1.80695	+	0.362921i
$953$	−2.47870e7	−	2.47870e7i	−0.884080	−	0.884080i	0.109866	−	0.993946i	$-0.464958\pi$
$953$	−2.47870e7	−	2.47870e7i	−0.884080	−	0.884080i	−0.993946	+	0.109866i	$0.964958\pi$
$954$	−503137.	+	1.47918e6i	−0.0178984	+	0.0526199i
$955$	−2.64880e7	+	7.57093e6i	−0.939812	+	0.268621i
$956$	2.76702e6	−	3.59680e6i	0.0979190	−	0.127283i
$957$	1.01125e7	+	1.01125e7i	0.356925	+	0.356925i
$958$	−175501.	−	356438.i	−0.00617825	−	0.0125479i
$959$	7.85169e6			0.275687
$960$	2.15749e7	−	1.70010e7i	0.755561	−	0.595382i
$961$	3.89258e6			0.135965
$962$	−2.08083e6	−	4.22610e6i	−0.0724934	−	0.147232i
$963$	1.78213e6	+	1.78213e6i	0.0619262	+	0.0619262i
$964$	−6.88981e6	+	8.95596e6i	−0.238789	+	0.310398i
$965$	2.54207e7	−	4.57682e7i	0.878756	−	1.58214i
$966$	−1.61468e7	+	4.74703e7i	−0.556729	+	1.63674i
$967$	−7.85405e6	−	7.85405e6i	−0.270102	−	0.270102i	0.559039	−	0.829141i	$-0.311170\pi$
$967$	−7.85405e6	−	7.85405e6i	−0.270102	−	0.270102i	−0.829141	+	0.559039i	$0.811170\pi$
$968$	1.87288e7	+	3.76161e6i	0.642423	+	0.129029i
$969$			1.90593e7i			0.652074i
$970$	−322678.	+	6.51769e6i	−0.0110113	+	0.222415i
$971$	−5.25604e7			−1.78900			−0.894501	−	0.447066i	$-0.852469\pi$
$971$	−5.25604e7			−1.78900			−0.894501	+	0.447066i	$0.852469\pi$
$972$	4.35128e6	−	567369.i	0.147724	−	0.0192619i
$973$	−5.09678e7	+	5.09678e7i	−1.72589	+	1.72589i
$974$	1.20530e7	−	3.54347e7i	0.407096	−	1.19683i
$975$	−8.30887e6	+	5.17231e6i	−0.279918	+	0.174250i
$976$	−2.82012e7	+	7.48158e6i	−0.947640	+	0.251402i
$977$	1.45106e7	−	1.45106e7i	0.486352	−	0.486352i	−0.420801	−	0.907153i	$-0.638251\pi$
$977$	1.45106e7	−	1.45106e7i	0.486352	−	0.486352i	0.907153	+	0.420801i	$0.138251\pi$
$978$	−2.42715e7	+	1.19507e7i	−0.811428	+	0.399527i
$979$			3.40746e7i			1.13625i
$980$	−2.26434e7	+	5.71329e7i	−0.753140	+	1.90029i
$981$		−	1.64479e6i		−	0.0545681i
$982$	−1.95906e7	−	3.97879e7i	−0.648289	−	1.31666i
$983$	−2.86088e6	+	2.86088e6i	−0.0944312	+	0.0944312i	−0.752744	−	0.658313i	$-0.771270\pi$
$983$	−2.86088e6	+	2.86088e6i	−0.0944312	+	0.0944312i	0.658313	+	0.752744i	$0.271270\pi$
$984$	−1.87563e7	−	2.81841e7i	−0.617532	−	0.927933i
$985$	1.34519e7	−	2.42192e7i	0.441766	−	0.795369i
$986$	−1.24518e7	−	4.23541e6i	−0.407886	−	0.138741i
$987$	4.04291e7	−	4.04291e7i	1.32100	−	1.32100i
$988$	−6.69214e6	+	872596.i	−0.218108	+	0.0284394i
$989$	4.39173e7			1.42773
$990$	1.98809e6	+	2.19520e6i	0.0644686	+	0.0711846i
$991$			4.15637e7i			1.34440i	0.740368	+	0.672202i	$0.234651\pi$
$991$			4.15637e7i			1.34440i	−0.740368	+	0.672202i	$0.765349\pi$
$992$	−1.89286e7	−	2.17194e7i	−0.610715	−	0.700758i
$993$	−3.90271e7	−	3.90271e7i	−1.25601	−	1.25601i
$994$	2.24896e7	+	7.64974e6i	0.721964	+	0.245573i
$995$	1.47080e6	+	5.14582e6i	0.0470973	+	0.164777i
$996$	−6.79998e6	−	5.23122e6i	−0.217200	−	0.167091i
$997$	−1.39380e7	−	1.39380e7i	−0.444083	−	0.444083i	0.449299	−	0.893382i	$-0.351674\pi$
$997$	−1.39380e7	−	1.39380e7i	−0.444083	−	0.444083i	−0.893382	+	0.449299i	$0.851674\pi$
$998$	8.36004e6	−	4.11627e6i	0.265694	−	0.130821i
$999$	1.56127e7			0.494952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.11	✓	56
4.3	odd	2		160.6.o.a.143.8		56
5.2	odd	4	inner	40.6.k.a.27.24	yes	56
8.3	odd	2	inner	40.6.k.a.3.24	yes	56
8.5	even	2		160.6.o.a.143.7		56
20.7	even	4		160.6.o.a.47.7		56
40.27	even	4	inner	40.6.k.a.27.11	yes	56
40.37	odd	4		160.6.o.a.47.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.11	✓	56	1.1	even	1	trivial
40.6.k.a.3.24	yes	56	8.3	odd	2	inner
40.6.k.a.27.11	yes	56	40.27	even	4	inner
40.6.k.a.27.24	yes	56	5.2	odd	4	inner
160.6.o.a.47.7		56	20.7	even	4
160.6.o.a.47.8		56	40.37	odd	4
160.6.o.a.143.7		56	8.5	even	2
160.6.o.a.143.8		56	4.3	odd	2

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.49882 - 5.07503i) q^{2} +(10.6033 + 10.6033i) q^{3} +(-19.5118 + 25.3631i) q^{4} +(-15.3629 - 53.7493i) q^{5} +(27.3164 - 80.3079i) q^{6} +(159.941 + 159.941i) q^{7} +(177.475 + 35.6453i) q^{8} -18.1393i q^{9} +O(q^{10})\)	\(q+(-2.49882 - 5.07503i) q^{2} +(10.6033 + 10.6033i) q^{3} +(-19.5118 + 25.3631i) q^{4} +(-15.3629 - 53.7493i) q^{5} +(27.3164 - 80.3079i) q^{6} +(159.941 + 159.941i) q^{7} +(177.475 + 35.6453i) q^{8} -18.1393i q^{9} +(-234.390 + 212.276i) q^{10} +516.314 q^{11} +(-475.823 + 62.0432i) q^{12} +(147.686 - 147.686i) q^{13} +(412.042 - 1211.37i) q^{14} +(407.023 - 732.818i) q^{15} +(-262.577 - 989.762i) q^{16} +(890.046 - 890.046i) q^{17} +(-92.0575 + 45.3268i) q^{18} +1009.77i q^{19} +(1663.01 + 659.096i) q^{20} +3391.81i q^{21} +(-1290.17 - 2620.31i) q^{22} +(-1847.88 + 1847.88i) q^{23} +(1503.87 + 2259.78i) q^{24} +(-2652.97 + 1651.48i) q^{25} +(-1118.55 - 380.470i) q^{26} +(2768.94 - 2768.94i) q^{27} +(-7177.34 + 935.862i) q^{28} +1847.15 q^{29} +(-4736.15 - 234.477i) q^{30} +4973.59i q^{31} +(-4366.94 + 3805.82i) q^{32} +(5474.64 + 5474.64i) q^{33} +(-6741.07 - 2292.95i) q^{34} +(6139.55 - 11053.9i) q^{35} +(460.070 + 353.931i) q^{36} +(2819.25 + 2819.25i) q^{37} +(5124.61 - 2523.23i) q^{38} +3131.92 q^{39} +(-810.617 - 10086.8i) q^{40} -12472.0 q^{41} +(17213.5 - 8475.51i) q^{42} +(-11883.2 - 11883.2i) q^{43} +(-10074.2 + 13095.3i) q^{44} +(-974.975 + 278.672i) q^{45} +(13995.6 + 4760.53i) q^{46} +(-11919.6 - 11919.6i) q^{47} +(7710.58 - 13278.9i) q^{48} +34355.2i q^{49} +(15010.6 + 9337.12i) q^{50} +18874.9 q^{51} +(864.154 + 6627.39i) q^{52} +(10766.7 - 10766.7i) q^{53} +(-20971.5 - 7133.38i) q^{54} +(-7932.06 - 27751.5i) q^{55} +(22684.4 + 34086.7i) q^{56} +(-10706.9 + 10706.9i) q^{57} +(-4615.69 - 9374.33i) q^{58} +8271.39i q^{59} +(10644.8 + 24622.0i) q^{60} -28492.9i q^{61} +(25241.1 - 12428.1i) q^{62} +(2901.22 - 2901.22i) q^{63} +(30226.8 + 12652.3i) q^{64} +(-10206.9 - 5669.13i) q^{65} +(14103.8 - 41464.1i) q^{66} +(9257.64 - 9257.64i) q^{67} +(5207.93 + 39940.8i) q^{68} -39187.3 q^{69} +(-71440.2 - 3536.86i) q^{70} +18565.5i q^{71} +(646.581 - 3219.28i) q^{72} +(-58309.9 - 58309.9i) q^{73} +(7262.98 - 21352.5i) q^{74} +(-45641.4 - 10619.0i) q^{75} +(-25610.9 - 19702.4i) q^{76} +(82579.7 + 82579.7i) q^{77} +(-7826.09 - 15894.6i) q^{78} -10581.9 q^{79} +(-49165.1 + 29318.9i) q^{80} +54312.1 q^{81} +(31165.4 + 63296.0i) q^{82} +(12642.5 + 12642.5i) q^{83} +(-86026.9 - 66180.4i) q^{84} +(-61513.0 - 34165.7i) q^{85} +(-30613.5 + 90001.2i) q^{86} +(19585.9 + 19585.9i) q^{87} +(91632.9 + 18404.2i) q^{88} +65996.0i q^{89} +(3850.55 + 4251.67i) q^{90} +47242.0 q^{91} +(-10812.5 - 82923.6i) q^{92} +(-52736.5 + 52736.5i) q^{93} +(-30707.5 + 90277.5i) q^{94} +(54274.3 - 15512.9i) q^{95} +(-86658.4 - 5949.75i) q^{96} +(14591.8 - 14591.8i) q^{97} +(174353. - 85847.3i) q^{98} -9365.58i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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