LMFDB - Embedded newform 40.6.k.a.27.11

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			27.11
Character	$\chi$	$=$	40.27
Dual form			40.6.k.a.3.11

$q$-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 $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

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	−0.279843	−	0.960046i	$-0.590282\pi$
$3$	10.6033	−	10.6033i	0.680203	−	0.680203i	0.960046	+	0.279843i	$0.0902823\pi$
$4$	−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	0.271187	−	0.962527i	$-0.412584\pi$
$7$	159.941	−	159.941i	1.23371	−	1.23371i	0.962527	−	0.271187i	$-0.0874162\pi$
$8$	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	0.817830	−	0.575459i	$-0.195177\pi$
$13$	147.686	+	147.686i	0.242371	+	0.242371i	−0.575459	+	0.817830i	$0.695177\pi$
$14$	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	0.973905	−	0.226957i	$-0.0728777\pi$
$17$	890.046	+	890.046i	0.746948	+	0.746948i	−0.226957	+	0.973905i	$0.572878\pi$
$18$	−92.0575	−	45.3268i	−0.0669697	−	0.0329742i
$19$		−	1009.77i		−	0.641709i	−0.947128	−	0.320854i	$-0.896030\pi$
$19$		−	1009.77i		−	0.641709i	0.947128	−	0.320854i	$-0.103970\pi$
$20$	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	0.241922	−	0.970296i	$-0.422222\pi$
$23$	−1847.88	−	1847.88i	−0.728374	−	0.728374i	−0.970296	+	0.241922i	$0.922222\pi$
$24$	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	$-0.846138\pi$
$31$		−	4973.59i		−	0.929535i	0.885433	−	0.464767i	$-0.153862\pi$
$32$	−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	−0.517269	−	0.855823i	$-0.673051\pi$
$37$	2819.25	−	2819.25i	0.338555	−	0.338555i	0.855823	+	0.517269i	$0.173051\pi$
$38$	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	−0.999805	−	0.0197274i	$-0.993720\pi$
$43$	−11883.2	+	11883.2i	−0.980078	+	0.980078i	0.0197274	+	0.999805i	$0.493720\pi$
$44$	−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	−0.981014	−	0.193935i	$-0.937875\pi$
$47$	−11919.6	+	11919.6i	−0.787080	+	0.787080i	0.193935	+	0.981014i	$0.437875\pi$
$48$	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	0.919525	−	0.393031i	$-0.128573\pi$
$53$	10766.7	+	10766.7i	0.526494	+	0.526494i	−0.393031	+	0.919525i	$0.628573\pi$
$54$	−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	$-0.950567\pi$
$59$		−	8271.39i		−	0.309349i	0.987965	−	0.154674i	$-0.0494329\pi$
$60$	10644.8	−	24622.0i	0.381732	−	0.882968i
$61$			28492.9i			0.980420i	0.871604	+	0.490210i	$0.163080\pi$
$61$			28492.9i			0.980420i	−0.871604	+	0.490210i	$0.836920\pi$
$62$	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	0.821769	−	0.569820i	$-0.192987\pi$
$67$	9257.64	+	9257.64i	0.251949	+	0.251949i	−0.569820	+	0.821769i	$0.692987\pi$
$68$	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	$-0.929871\pi$
$71$		−	18565.5i		−	0.437079i	0.975828	−	0.218539i	$-0.0701292\pi$
$72$	646.581	+	3219.28i	0.0146991	+	0.0731858i
$73$	−58309.9	+	58309.9i	−1.28066	+	1.28066i	−0.340375	+	0.940290i	$0.610554\pi$
$73$	−58309.9	+	58309.9i	−1.28066	+	1.28066i	−0.940290	+	0.340375i	$0.889446\pi$
$74$	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	−0.599179	−	0.800615i	$-0.704506\pi$
$83$	12642.5	−	12642.5i	0.201436	−	0.201436i	0.800615	+	0.599179i	$0.204506\pi$
$84$	−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	$-0.854417\pi$
$89$		−	65996.0i		−	0.883166i	0.897220	−	0.441583i	$-0.145583\pi$
$90$	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	0.781442	−	0.623978i	$-0.214485\pi$
$97$	14591.8	+	14591.8i	0.157464	+	0.157464i	−0.623978	+	0.781442i	$0.714485\pi$
$98$	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	$0.171768\pi$
$101$			105351.i			1.02763i	−0.857901	+	0.513814i	$0.828232\pi$
$102$	−47164.9	+	95790.6i	−0.448867	+	0.911638i
$103$	−95388.9	−	95388.9i	−0.885941	−	0.885941i	0.108189	−	0.994130i	$-0.465495\pi$
$103$	−95388.9	−	95388.9i	−0.885941	−	0.885941i	−0.994130	+	0.108189i	$0.965495\pi$
$104$	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	0.157876	−	0.987459i	$-0.449535\pi$
$107$	−98246.9	−	98246.9i	−0.829582	−	0.829582i	−0.987459	+	0.157876i	$0.949535\pi$
$108$	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	−0.853371	−	0.521304i	$-0.825446\pi$
$113$	−45073.6	+	45073.6i	−0.332067	+	0.332067i	0.521304	+	0.853371i	$0.325446\pi$
$114$	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	−0.887774	−	0.460280i	$-0.847749\pi$
$127$	−77703.2	+	77703.2i	−0.427494	+	0.427494i	0.460280	+	0.887774i	$0.347749\pi$
$128$	−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	0.760762	−	0.649031i	$-0.224826\pi$
$137$	24545.6	+	24545.6i	0.111731	+	0.111731i	−0.649031	+	0.760762i	$0.724826\pi$
$138$	97921.9	−	198877.i	0.437706	−	0.888969i
$139$		−	318666.i		−	1.39894i	−0.714662	−	0.699470i	$-0.753419\pi$
$139$		−	318666.i		−	1.39894i	0.714662	−	0.699470i	$-0.246581\pi$
$140$	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	$-0.854923\pi$
$151$		−	246649.i		−	0.880313i	0.897921	−	0.440157i	$-0.145077\pi$
$152$	−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	−0.879646	−	0.475629i	$-0.842220\pi$
$157$	−124781.	+	124781.i	−0.404017	+	0.404017i	0.475629	+	0.879646i	$0.342220\pi$
$158$	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	−0.956517	−	0.291676i	$-0.905787\pi$
$163$	−225521.	+	225521.i	−0.664841	+	0.664841i	0.291676	+	0.956517i	$0.405787\pi$
$164$	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	−0.641688	−	0.766966i	$-0.721765\pi$
$167$	45151.0	−	45151.0i	0.125278	−	0.125278i	0.766966	+	0.641688i	$0.221765\pi$
$168$	−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	0.425329	−	0.905039i	$-0.360158\pi$
$173$	−188840.	−	188840.i	−0.479710	−	0.479710i	−0.905039	+	0.425329i	$0.860158\pi$
$174$	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	$0.108584\pi$
$179$			286829.i			0.669098i	−0.942378	+	0.334549i	$0.891416\pi$
$180$	11955.6	+	30165.8i	0.0275035	+	0.0693959i
$181$			120295.i			0.272930i	0.990645	+	0.136465i	$0.0435741\pi$
$181$			120295.i			0.272930i	−0.990645	+	0.136465i	$0.956426\pi$
$182$	−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	$0.162537\pi$
$191$			492807.i			0.977448i	−0.872439	+	0.488724i	$0.837463\pi$
$192$	186348.	−	454661.i	0.364815	−	0.890092i
$193$	662231.	−	662231.i	1.27972	−	1.27972i	0.338902	−	0.940822i	$-0.389945\pi$
$193$	662231.	−	662231.i	1.27972	−	1.27972i	0.940822	−	0.338902i	$-0.110055\pi$
$194$	−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	−0.308036	−	0.951375i	$-0.599672\pi$
$197$	350433.	−	350433.i	0.643339	−	0.643339i	0.951375	+	0.308036i	$0.0996717\pi$
$198$	−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	0.905389	−	0.424582i	$-0.139579\pi$
$223$	357053.	+	357053.i	0.480807	+	0.480807i	−0.424582	+	0.905389i	$0.639579\pi$
$224$	−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	0.998498	+	0.0547891i	$0.0174486\pi$
$227$	817733.	+	817733.i	1.05329	+	1.05329i	0.0547891	+	0.998498i	$0.482551\pi$
$228$	−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	−0.138774	+	0.990324i	$0.544316\pi$
$233$	−935667.	+	935667.i	−1.12910	+	1.12910i	−0.990324	+	0.138774i	$0.955684\pi$
$234$	−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	0.996890	+	0.0788094i	$0.0251118\pi$
$257$	1.13900e6	+	1.13900e6i	1.07570	+	1.07570i	0.0788094	+	0.996890i	$0.474888\pi$
$258$	−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	0.994627	−	0.103522i	$-0.0330112\pi$
$263$	999582.	+	999582.i	0.891105	+	0.891105i	−0.103522	+	0.994627i	$0.533011\pi$
$264$	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	$-0.930513\pi$
$271$		−	523663.i		−	0.433141i	0.976267	−	0.216570i	$-0.0694870\pi$
$272$	−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	−0.216200	−	0.976349i	$-0.569366\pi$
$277$	970729.	−	970729.i	0.760149	−	0.760149i	0.976349	+	0.216200i	$0.0693663\pi$
$278$	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	−0.880167	−	0.474664i	$-0.842570\pi$
$283$	−546336.	+	546336.i	−0.405503	+	0.405503i	0.474664	+	0.880167i	$0.342570\pi$
$284$	−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	0.967288	−	0.253680i	$-0.0816410\pi$
$293$	1.04865e6	+	1.04865e6i	0.713608	+	0.713608i	−0.253680	+	0.967288i	$0.581641\pi$
$294$	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	0.576341	−	0.817210i	$-0.304480\pi$
$307$	−397765.	−	397765.i	−0.240869	−	0.240869i	−0.817210	+	0.576341i	$0.804480\pi$
$308$	−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	$-0.766603\pi$
$311$		−	2.28317e6i		−	1.33856i	0.743011	−	0.669279i	$-0.233397\pi$
$312$	555838.	−	111638.i	0.323267	−	0.0649271i
$313$	2.40862e6	−	2.40862e6i	1.38965	−	1.38965i	0.563621	−	0.826034i	$-0.309408\pi$
$313$	2.40862e6	−	2.40862e6i	1.38965	−	1.38965i	0.826034	−	0.563621i	$-0.190592\pi$
$314$	−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	−0.307473	+	0.951557i	$0.599484\pi$
$317$	−2.25260e6	+	2.25260e6i	−1.25903	+	1.25903i	−0.951557	+	0.307473i	$0.900516\pi$
$318$	−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	0.886617	−	0.462504i	$-0.153049\pi$
$337$	884212.	+	884212.i	0.424113	+	0.424113i	−0.462504	+	0.886617i	$0.653049\pi$
$338$	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	0.375125	−	0.926974i	$-0.377600\pi$
$347$	−1.23778e6	−	1.23778e6i	−0.551849	−	0.551849i	−0.926974	+	0.375125i	$0.877600\pi$
$348$	−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	−0.872918	−	0.487866i	$-0.837775\pi$
$353$	−901480.	+	901480.i	−0.385052	+	0.385052i	0.487866	+	0.872918i	$0.337775\pi$
$354$	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	−0.986142	−	0.165903i	$-0.946946\pi$
$367$	−2.11644e6	+	2.11644e6i	−0.820239	+	0.820239i	0.165903	+	0.986142i	$0.446946\pi$
$368$	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	0.925073	−	0.379790i	$-0.124004\pi$
$373$	1.46519e6	+	1.46519e6i	0.545283	+	0.545283i	−0.379790	+	0.925073i	$0.624004\pi$
$374$	−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	$0.0295625\pi$
$379$			518674.i			0.185480i	−0.995690	+	0.0927399i	$0.970437\pi$
$380$	−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	0.976849	+	0.213930i	$0.0686266\pi$
$383$	3.41844e6	+	3.41844e6i	1.19078	+	1.19078i	0.213930	+	0.976849i	$0.431373\pi$
$384$	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	−0.509085	−	0.860716i	$-0.670016\pi$
$397$	1.10424e6	−	1.10424e6i	0.351631	−	0.351631i	0.860716	+	0.509085i	$0.170016\pi$
$398$	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	$-0.849359\pi$
$409$		−	3.08388e6i		−	0.911569i	0.890090	−	0.455784i	$-0.150641\pi$
$410$	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	$0.0916820\pi$
$419$			2.04163e6i			0.568123i	−0.958806	+	0.284061i	$0.908318\pi$
$420$	−2.23553e6	−	5.64060e6i	−0.618382	−	1.56028i
$421$			2.04322e6i			0.561836i	0.959732	+	0.280918i	$0.0906389\pi$
$421$			2.04322e6i			0.561836i	−0.959732	+	0.280918i	$0.909361\pi$
$422$	−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	$0.0724116\pi$
$431$			1.73952e6i			0.451061i	−0.974236	+	0.225531i	$0.927588\pi$
$432$	−3.46766e6	+	2.01354e6i	−0.893978	+	0.519099i
$433$	395725.	−	395725.i	0.101432	−	0.101432i	−0.654570	−	0.756002i	$-0.727150\pi$
$433$	395725.	−	395725.i	0.101432	−	0.101432i	0.756002	+	0.654570i	$0.227150\pi$
$434$	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	−0.554580	−	0.832130i	$-0.687121\pi$
$443$	1.14644e6	−	1.14644e6i	0.277550	−	0.277550i	0.832130	+	0.554580i	$0.187121\pi$
$444$	−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	$-0.736514\pi$
$449$		−	6.29177e6i		−	1.47284i	0.676522	−	0.736422i	$-0.263486\pi$
$450$	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	0.204198	−	0.978930i	$-0.434541\pi$
$457$	−3.45893e6	−	3.45893e6i	−0.774732	−	0.774732i	−0.978930	+	0.204198i	$0.934541\pi$
$458$	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	$-0.867003\pi$
$461$		−	3.70309e6i		−	0.811544i	0.913974	−	0.405772i	$-0.132997\pi$
$462$	8.88758e6	+	4.37602e6i	1.93722	+	0.953838i
$463$	−2.86396e6	−	2.86396e6i	−0.620889	−	0.620889i	0.324870	−	0.945759i	$-0.394680\pi$
$463$	−2.86396e6	−	2.86396e6i	−0.620889	−	0.620889i	−0.945759	+	0.324870i	$0.894680\pi$
$464$	−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	0.640633	−	0.767847i	$-0.278672\pi$
$467$	−599549.	−	599549.i	−0.127213	−	0.127213i	−0.767847	+	0.640633i	$0.778672\pi$
$468$	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	−0.100986	−	0.994888i	$-0.532200\pi$
$487$	4.67856e6	−	4.67856e6i	0.893902	−	0.893902i	0.994888	+	0.100986i	$0.0321996\pi$
$488$	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	$-0.952692\pi$
$499$		−	1.64729e6i		−	0.296154i	0.988976	−	0.148077i	$-0.0473084\pi$
$500$	−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	−0.939753	−	0.341854i	$-0.888945\pi$
$503$	−7.27235e6	−	7.27235e6i	−1.28161	−	1.28161i	−0.341854	−	0.939753i	$-0.611055\pi$
$504$	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	−0.946161	−	0.323696i	$-0.895074\pi$
$523$	−3.89376e6	+	3.89376e6i	−0.622465	+	0.622465i	0.323696	+	0.946161i	$0.395074\pi$
$524$	−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	$-0.696971\pi$
$541$		−	1.10906e7i		−	1.62915i	0.580060	−	0.814574i	$-0.303029\pi$
$542$	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	0.569368	−	0.822083i	$-0.307188\pi$
$547$	−1.76847e6	−	1.76847e6i	−0.252714	−	0.252714i	−0.822083	+	0.569368i	$0.807188\pi$
$548$	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	−0.469747	−	0.882801i	$-0.655655\pi$
$557$	3.02444e6	−	3.02444e6i	0.413054	−	0.413054i	0.882801	+	0.469747i	$0.155655\pi$
$558$	−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	−0.632745	−	0.774360i	$-0.718072\pi$
$563$	1.06508e6	−	1.06508e6i	0.141616	−	0.141616i	0.774360	+	0.632745i	$0.218072\pi$
$564$	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	$0.136872\pi$
$569$			6.43884e6i			0.833733i	−0.908968	+	0.416866i	$0.863128\pi$
$570$	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	0.949028	+	0.315191i	$0.102069\pi$
$577$	1.01103e7	+	1.01103e7i	1.26422	+	1.26422i	0.315191	+	0.949028i	$0.397931\pi$
$578$	−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	0.922590	−	0.385781i	$-0.126068\pi$
$587$	4.48142e6	+	4.48142e6i	0.536810	+	0.536810i	−0.385781	+	0.922590i	$0.626068\pi$
$588$	−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	−0.937161	−	0.348898i	$-0.886556\pi$
$593$	−5.03742e6	+	5.03742e6i	−0.588263	+	0.588263i	0.348898	+	0.937161i	$0.386556\pi$
$594$	−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	0.215458	−	0.976513i	$-0.430875\pi$
$607$	1.08203e7	−	1.08203e7i	1.19197	−	1.19197i	0.976513	−	0.215458i	$-0.0691246\pi$
$608$	−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	0.805429	−	0.592692i	$-0.201935\pi$
$613$	1.97923e6	+	1.97923e6i	0.212738	+	0.212738i	−0.592692	+	0.805429i	$0.701935\pi$
$614$	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	0.467244	−	0.884128i	$-0.345247\pi$
$617$	−3.94210e6	−	3.94210e6i	−0.416884	−	0.416884i	−0.884128	+	0.467244i	$0.845247\pi$
$618$	5.05480e6	−	1.02662e7i	0.532394	−	1.08128i
$619$			3.91209e6i			0.410377i	0.978723	+	0.205188i	$0.0657807\pi$
$619$			3.91209e6i			0.410377i	−0.978723	+	0.205188i	$0.934219\pi$
$620$	−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	$0.0858045\pi$
$631$			5.32710e6i			0.532620i	−0.963887	+	0.266310i	$0.914195\pi$
$632$	−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	−0.441312	−	0.897354i	$-0.645487\pi$
$643$	4.78115e6	−	4.78115e6i	0.456042	−	0.456042i	0.897354	+	0.441312i	$0.145487\pi$
$644$	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	−0.0546725	+	0.998504i	$0.517411\pi$
$647$	−1.12140e7	+	1.12140e7i	−1.05318	+	1.05318i	−0.998504	+	0.0546725i	$0.982589\pi$
$648$	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	0.719486	−	0.694507i	$-0.244377\pi$
$653$	272189.	+	272189.i	0.0249797	+	0.0249797i	−0.694507	+	0.719486i	$0.744377\pi$
$654$	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	$0.136541\pi$
$659$			9.27375e6i			0.831844i	−0.909400	+	0.415922i	$0.863459\pi$
$660$	5.49605e6	−	1.27127e7i	0.491124	−	1.13600i
$661$			1.18368e7i			1.05374i	0.849947	+	0.526868i	$0.176634\pi$
$661$			1.18368e7i			1.05374i	−0.849947	+	0.526868i	$0.823366\pi$
$662$	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	−0.551323	−	0.834292i	$-0.685877\pi$
$673$	3.32488e6	−	3.32488e6i	0.282969	−	0.282969i	0.834292	+	0.551323i	$0.185877\pi$
$674$	−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	−0.122567	+	0.992460i	$0.539113\pi$
$677$	−1.32971e7	+	1.32971e7i	−1.11503	+	1.11503i	−0.992460	+	0.122567i	$0.960887\pi$
$678$	−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	−0.146316	−	0.989238i	$-0.546742\pi$
$683$	1.02763e7	−	1.02763e7i	0.842921	−	0.842921i	0.989238	+	0.146316i	$0.0467418\pi$
$684$	−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	$-0.982507\pi$
$701$		−	1.42933e6i		−	0.109859i	0.998490	−	0.0549297i	$-0.0174935\pi$
$702$	−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	−0.829141	−	0.559040i	$-0.811170\pi$
$727$	−3.84912e6	+	3.84912e6i	−0.270101	+	0.270101i	0.559040	+	0.829141i	$0.311170\pi$
$728$	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	0.999580	−	0.0289819i	$-0.00922652\pi$
$733$	1.41189e7	+	1.41189e7i	0.970598	+	0.970598i	−0.0289819	+	0.999580i	$0.509227\pi$
$734$	−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	$-0.973501\pi$
$739$		−	2.46897e6i		−	0.166305i	0.996537	−	0.0831525i	$-0.0264989\pi$
$740$	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	0.477565	−	0.878597i	$-0.341520\pi$
$743$	−6.03463e6	−	6.03463e6i	−0.401032	−	0.401032i	−0.878597	+	0.477565i	$0.841520\pi$
$744$	−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	$-0.844534\pi$
$751$		−	1.45047e7i		−	0.938444i	0.883080	−	0.469222i	$-0.155466\pi$
$752$	−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	−0.592461	−	0.805599i	$-0.701843\pi$
$757$	3.36048e6	−	3.36048e6i	0.213138	−	0.213138i	0.805599	+	0.592461i	$0.201843\pi$
$758$	−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	$0.00386832\pi$
$769$			398573.i			0.0243048i	−0.999926	+	0.0121524i	$0.996132\pi$
$770$	−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	0.760518	−	0.649317i	$-0.224945\pi$
$773$	1.84740e6	+	1.84740e6i	0.111202	+	0.111202i	−0.649317	+	0.760518i	$0.724945\pi$
$774$	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	0.402323	−	0.915498i	$-0.368203\pi$
$787$	−8.91667e6	−	8.91667e6i	−0.513175	−	0.513175i	−0.915498	+	0.402323i	$0.868203\pi$
$788$	−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	−0.298211	−	0.954500i	$-0.596390\pi$
$797$	1.17690e7	−	1.17690e7i	0.656289	−	0.656289i	0.954500	+	0.298211i	$0.0963900\pi$
$798$	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	$-0.876890\pi$
$809$		−	1.40431e7i		−	0.754380i	0.926136	−	0.377190i	$-0.123110\pi$
$810$	−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	$-0.884595\pi$
$821$		−	1.36995e7i		−	0.709327i	0.934994	−	0.354664i	$-0.115405\pi$
$822$	−1.30071e6	+	2.64170e6i	−0.0671429	+	0.136365i
$823$	−1.16517e7	−	1.16517e7i	−0.599641	−	0.599641i	0.340576	−	0.940217i	$-0.389378\pi$
$823$	−1.16517e7	−	1.16517e7i	−0.599641	−	0.599641i	−0.940217	+	0.340576i	$0.889378\pi$
$824$	−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	0.915944	−	0.401306i	$-0.131444\pi$
$827$	1.01220e7	+	1.01220e7i	0.514638	+	0.514638i	−0.401306	+	0.915944i	$0.631444\pi$
$828$	−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	0.837256	−	0.546812i	$-0.184159\pi$
$853$	6.17213e6	+	6.17213e6i	0.290444	+	0.290444i	−0.546812	+	0.837256i	$0.684159\pi$
$854$	−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	0.970929	−	0.239369i	$-0.0769407\pi$
$857$	1.57290e7	+	1.57290e7i	0.731559	+	0.731559i	−0.239369	+	0.970929i	$0.576941\pi$
$858$	−4.04072e6	+	8.20659e6i	−0.187387	+	0.380579i
$859$			2.09256e7i			0.967597i	0.875179	+	0.483799i	$0.160743\pi$
$859$			2.09256e7i			0.967597i	−0.875179	+	0.483799i	$0.839257\pi$
$860$	−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	0.768679	−	0.639635i	$-0.220914\pi$
$863$	2.82335e6	+	2.82335e6i	0.129044	+	0.129044i	−0.639635	+	0.768679i	$0.720914\pi$
$864$	−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	−0.137807	+	0.990459i	$0.544005\pi$
$877$	−2.56987e7	+	2.56987e7i	−1.12827	+	1.12827i	−0.990459	+	0.137807i	$0.955995\pi$
$878$	−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	0.0296818	−	0.999559i	$-0.490551\pi$
$883$	2.38462e7	−	2.38462e7i	1.02924	−	1.02924i	0.999559	−	0.0296818i	$-0.00944941\pi$
$884$	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	−0.737765	−	0.675058i	$-0.764119\pi$
$887$	−1.46935e6	+	1.46935e6i	−0.0627070	+	0.0627070i	0.675058	+	0.737765i	$0.264119\pi$
$888$	−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	0.413819	−	0.910359i	$-0.364195\pi$
$907$	−1.23019e7	−	1.23019e7i	−0.496541	−	0.496541i	−0.910359	+	0.413819i	$0.864195\pi$
$908$	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	$-0.733660\pi$
$911$		−	3.71961e7i		−	1.48491i	0.669894	−	0.742457i	$-0.266340\pi$
$912$	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	$0.0254810\pi$
$929$			4.20699e6i			0.159931i	−0.996798	+	0.0799655i	$0.974519\pi$
$930$	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	0.861120	−	0.508401i	$-0.169763\pi$
$937$	9.47934e6	+	9.47934e6i	0.352719	+	0.352719i	−0.508401	+	0.861120i	$0.669763\pi$
$938$	−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	$-0.907995\pi$
$941$		−	1.54846e7i		−	0.570068i	0.958517	−	0.285034i	$-0.0920049\pi$
$942$	−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	0.0909198	−	0.995858i	$-0.471019\pi$
$947$	−2.49743e7	−	2.49743e7i	−0.904938	−	0.904938i	−0.995858	+	0.0909198i	$0.971019\pi$
$948$	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	−0.993946	−	0.109866i	$-0.964958\pi$
$953$	−2.47870e7	+	2.47870e7i	−0.884080	+	0.884080i	0.109866	+	0.993946i	$0.464958\pi$
$954$	−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	−0.829141	−	0.559039i	$-0.811170\pi$
$967$	−7.85405e6	+	7.85405e6i	−0.270102	+	0.270102i	0.559039	+	0.829141i	$0.311170\pi$
$968$	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	0.907153	−	0.420801i	$-0.138251\pi$
$977$	1.45106e7	+	1.45106e7i	0.486352	+	0.486352i	−0.420801	+	0.907153i	$0.638251\pi$
$978$	−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	0.658313	−	0.752744i	$-0.271270\pi$
$983$	−2.86088e6	−	2.86088e6i	−0.0944312	−	0.0944312i	−0.752744	+	0.658313i	$0.771270\pi$
$984$	−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	$-0.765349\pi$
$991$		−	4.15637e7i		−	1.34440i	0.740368	−	0.672202i	$-0.234651\pi$
$992$	−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	−0.893382	−	0.449299i	$-0.851674\pi$
$997$	−1.39380e7	+	1.39380e7i	−0.444083	+	0.444083i	0.449299	+	0.893382i	$0.351674\pi$
$998$	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.27.11	yes	56
4.3	odd	2		160.6.o.a.47.8		56
5.3	odd	4	inner	40.6.k.a.3.24	yes	56
8.3	odd	2	inner	40.6.k.a.27.24	yes	56
8.5	even	2		160.6.o.a.47.7		56
20.3	even	4		160.6.o.a.143.7		56
40.3	even	4	inner	40.6.k.a.3.11	✓	56
40.13	odd	4		160.6.o.a.143.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.11	✓	56	40.3	even	4	inner
40.6.k.a.3.24	yes	56	5.3	odd	4	inner
40.6.k.a.27.11	yes	56	1.1	even	1	trivial
40.6.k.a.27.24	yes	56	8.3	odd	2	inner
160.6.o.a.47.7		56	8.5	even	2
160.6.o.a.47.8		56	4.3	odd	2
160.6.o.a.143.7		56	20.3	even	4
160.6.o.a.143.8		56	40.13	odd	4

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

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