LMFDB - Embedded newform 10.22.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,22,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	10.a (trivial)

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:	yes
Analytic conductor:	$27.9477344287$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{157921}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 39480 $ x^2 - x - 39480
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-198.196$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1024.00 q^{2} +47924.0 q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} -4.90741e7 q^{6} +6.67863e8 q^{7} -1.07374e9 q^{8} -8.16365e9 q^{9} +1.00000e10 q^{10} -1.26793e11 q^{11} +5.02519e10 q^{12} +9.12750e11 q^{13} -6.83892e11 q^{14} -4.68008e11 q^{15} +1.09951e12 q^{16} +8.60406e12 q^{17} +8.35957e12 q^{18} -6.93702e12 q^{19} -1.02400e13 q^{20} +3.20066e13 q^{21} +1.29836e14 q^{22} -3.30974e14 q^{23} -5.14580e13 q^{24} +9.53674e13 q^{25} -9.34656e14 q^{26} -8.92536e14 q^{27} +7.00305e14 q^{28} -3.90534e15 q^{29} +4.79240e14 q^{30} +3.32185e15 q^{31} -1.12590e15 q^{32} -6.07642e15 q^{33} -8.81056e15 q^{34} -6.52210e15 q^{35} -8.56020e15 q^{36} -4.33804e16 q^{37} +7.10351e15 q^{38} +4.37426e16 q^{39} +1.04858e16 q^{40} -9.56620e16 q^{41} -3.27748e16 q^{42} -7.81706e16 q^{43} -1.32952e17 q^{44} +7.97231e16 q^{45} +3.38917e17 q^{46} -2.03634e17 q^{47} +5.26930e16 q^{48} -1.12505e17 q^{49} -9.76562e16 q^{50} +4.12341e17 q^{51} +9.57088e17 q^{52} +1.42121e18 q^{53} +9.13957e17 q^{54} +1.23821e18 q^{55} -7.17112e17 q^{56} -3.32449e17 q^{57} +3.99907e18 q^{58} +2.28919e18 q^{59} -4.90741e17 q^{60} -5.32798e18 q^{61} -3.40158e18 q^{62} -5.45220e18 q^{63} +1.15292e18 q^{64} -8.91357e18 q^{65} +6.22226e18 q^{66} -1.31401e19 q^{67} +9.02201e18 q^{68} -1.58616e19 q^{69} +6.67863e18 q^{70} -2.98159e19 q^{71} +8.76565e18 q^{72} +1.37094e18 q^{73} +4.44215e19 q^{74} +4.57039e18 q^{75} -7.27399e18 q^{76} -8.46803e19 q^{77} -4.47924e19 q^{78} +1.74281e19 q^{79} -1.07374e19 q^{80} +4.26208e19 q^{81} +9.79579e19 q^{82} +3.75717e19 q^{83} +3.35614e19 q^{84} -8.40240e19 q^{85} +8.00467e19 q^{86} -1.87159e20 q^{87} +1.36143e20 q^{88} +2.43231e20 q^{89} -8.16365e19 q^{90} +6.09592e20 q^{91} -3.47051e20 q^{92} +1.59196e20 q^{93} +2.08521e20 q^{94} +6.77443e19 q^{95} -5.39576e19 q^{96} -1.80740e20 q^{97} +1.15205e20 q^{98} +1.03509e21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2048 q^{2} - 126692 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 129732608 q^{6} - 292598684 q^{7} - 2147483648 q^{8} + 11866737826 q^{9} + 20000000000 q^{10} - 41326831776 q^{11} - 132846190592 q^{12}+ \cdots + 27\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 2048 * q^2 - 126692 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 129732608 * q^6 - 292598684 * q^7 - 2147483648 * q^8 + 11866737826 * q^9 + 20000000000 * q^10 - 41326831776 * q^11 - 132846190592 * q^12 + 1887051472228 * q^13 + 299621052416 * q^14 + 1237226562500 * q^15 + 2199023255552 * q^16 - 3100413932364 * q^17 - 12151539533824 * q^18 + 7175794652440 * q^19 - 20480000000000 * q^20 + 199718603894264 * q^21 + 42318675738624 * q^22 - 357559990100052 * q^23 + 136034499166208 * q^24 + 190734863281250 * q^25 - 1932340707561472 * q^26 - 2563616231988920 * q^27 - 306811957673984 * q^28 - 2454584202185940 * q^29 - 1266920000000000 * q^30 - 4310677151243336 * q^31 - 2251799813685248 * q^32 - 21000167846983104 * q^33 + 3174823866740736 * q^34 + 2857409023437500 * q^35 + 12443176482635776 * q^36 - 32389201650205724 * q^37 - 7348013724098560 * q^38 - 126386038156081288 * q^39 + 20971520000000000 * q^40 - 16298035212712116 * q^41 - 204511850387726336 * q^42 - 161845702253479412 * q^43 - 43334323956350976 * q^44 - 115886111582031250 * q^45 + 366141429862453248 * q^46 + 153492993930726996 * q^47 - 139299327146196992 * q^48 + 251436016683357114 * q^49 - 195312500000000000 * q^50 + 2456129297437264344 * q^51 + 1978716884542947328 * q^52 + 604198357317820308 * q^53 + 2625143021556654080 * q^54 + 403582341562500000 * q^55 + 314175444658159616 * q^56 - 2796771718696561840 * q^57 + 2513494223038402560 * q^58 + 3110197357974672120 * q^59 + 1297326080000000000 * q^60 - 791142209760451676 * q^61 + 4414133402873176064 * q^62 - 24690614624666969692 * q^63 + 2305843009213693952 * q^64 - 18428237033476562500 * q^65 + 21504171875310698496 * q^66 - 5111819523383561564 * q^67 - 3251019639542513664 * q^68 - 11219196977510717208 * q^69 - 2925986840000000000 * q^70 - 82388741313238482456 * q^71 - 12741812718219034624 * q^72 + 10657918464992348548 * q^73 + 33166542489810661376 * q^74 - 12082290649414062500 * q^75 + 7524366053476925440 * q^76 - 166767237207340703808 * q^77 + 129419303071827238912 * q^78 + 28314166125451369360 * q^79 - 21474836480000000000 * q^80 + 124893157714537187242 * q^81 + 16689188057817206784 * q^82 - 10427725705926651732 * q^83 + 209420134797031768064 * q^84 + 30277479808242187500 * q^85 + 165729999107562917888 * q^86 - 440484049640705943960 * q^87 + 44374347731303399424 * q^88 + 478501472814113520180 * q^89 + 118667378260000000000 * q^90 - 326187611445407942776 * q^91 - 374928824179152125952 * q^92 + 1491957513759228855056 * q^93 - 157176825785064443904 * q^94 - 70076119652734375000 * q^95 + 142642510997705719808 * q^96 + 545226897779926992196 * q^97 - 257470481083757684736 * q^98 + 2747011580657571215712 * q^99

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 $

$2$	−1024.00	−0.707107
$2$	−1024.00	−0.707107
$3$	47924.0	0.468576	0.234288	−	0.972167i	$-0.424724\pi$
$3$	47924.0	0.468576	0.234288	+	0.972167i	$0.424724\pi$
$4$	1.04858e6	0.500000
$5$	−9.76562e6	−0.447214
$5$	−9.76562e6	−0.447214
$6$	−4.90741e7	−0.331333
$7$	6.67863e8	0.893631	0.446815	−	0.894626i	$-0.352558\pi$
$7$	6.67863e8	0.893631	0.446815	+	0.894626i	$0.352558\pi$
$8$	−1.07374e9	−0.353553
$9$	−8.16365e9	−0.780437
$10$	1.00000e10	0.316228
$11$	−1.26793e11	−1.47391	−0.736957	−	0.675940i	$-0.763738\pi$
$11$	−1.26793e11	−1.47391	−0.736957	+	0.675940i	$0.763738\pi$
$12$	5.02519e10	0.234288
$13$	9.12750e11	1.83631	0.918156	−	0.396219i	$-0.129678\pi$
$13$	9.12750e11	1.83631	0.918156	+	0.396219i	$0.129678\pi$
$14$	−6.83892e11	−0.631892
$15$	−4.68008e11	−0.209553
$16$	1.09951e12	0.250000
$17$	8.60406e12	1.03512	0.517559	−	0.855648i	$-0.326841\pi$
$17$	8.60406e12	1.03512	0.517559	+	0.855648i	$0.326841\pi$
$18$	8.35957e12	0.551852
$19$	−6.93702e12	−0.259573	−0.129787	−	0.991542i	$-0.541429\pi$
$19$	−6.93702e12	−0.259573	−0.129787	+	0.991542i	$0.541429\pi$
$20$	−1.02400e13	−0.223607
$21$	3.20066e13	0.418733
$22$	1.29836e14	1.04221
$23$	−3.30974e14	−1.66591	−0.832955	−	0.553341i	$-0.813352\pi$
$23$	−3.30974e14	−1.66591	−0.832955	+	0.553341i	$0.813352\pi$
$24$	−5.14580e13	−0.165666
$25$	9.53674e13	0.200000
$26$	−9.34656e14	−1.29847
$27$	−8.92536e14	−0.834269
$28$	7.00305e14	0.446815
$29$	−3.90534e15	−1.72377	−0.861886	−	0.507103i	$-0.830716\pi$
$29$	−3.90534e15	−1.72377	−0.861886	+	0.507103i	$0.830716\pi$
$30$	4.79240e14	0.148177
$31$	3.32185e15	0.727918	0.363959	−	0.931415i	$-0.381425\pi$
$31$	3.32185e15	0.727918	0.363959	+	0.931415i	$0.381425\pi$
$32$	−1.12590e15	−0.176777
$33$	−6.07642e15	−0.690640
$34$	−8.81056e15	−0.731939
$35$	−6.52210e15	−0.399644
$36$	−8.56020e15	−0.390218
$37$	−4.33804e16	−1.48312	−0.741558	−	0.670889i	$-0.765913\pi$
$37$	−4.33804e16	−1.48312	−0.741558	+	0.670889i	$0.765913\pi$
$38$	7.10351e15	0.183546
$39$	4.37426e16	0.860451
$40$	1.04858e16	0.158114
$41$	−9.56620e16	−1.11304	−0.556518	−	0.830836i	$-0.687863\pi$
$41$	−9.56620e16	−1.11304	−0.556518	+	0.830836i	$0.687863\pi$
$42$	−3.27748e16	−0.296089
$43$	−7.81706e16	−0.551601	−0.275800	−	0.961215i	$-0.588943\pi$
$43$	−7.81706e16	−0.551601	−0.275800	+	0.961215i	$0.588943\pi$
$44$	−1.32952e17	−0.736957
$45$	7.97231e16	0.349022
$46$	3.38917e17	1.17798
$47$	−2.03634e17	−0.564707	−0.282354	−	0.959310i	$-0.591115\pi$
$47$	−2.03634e17	−0.564707	−0.282354	+	0.959310i	$0.591115\pi$
$48$	5.26930e16	0.117144
$49$	−1.12505e17	−0.201425
$50$	−9.76562e16	−0.141421
$51$	4.12341e17	0.485031
$52$	9.57088e17	0.918156
$53$	1.42121e18	1.11625	0.558127	−	0.829756i	$-0.311520\pi$
$53$	1.42121e18	1.11625	0.558127	+	0.829756i	$0.311520\pi$
$54$	9.13957e17	0.589917
$55$	1.23821e18	0.659154
$56$	−7.17112e17	−0.315946
$57$	−3.32449e17	−0.121630
$58$	3.99907e18	1.21889
$59$	2.28919e18	0.583089	0.291545	−	0.956557i	$-0.405831\pi$
$59$	2.28919e18	0.583089	0.291545	+	0.956557i	$0.405831\pi$
$60$	−4.90741e17	−0.104777
$61$	−5.32798e18	−0.956311	−0.478155	−	0.878275i	$-0.658694\pi$
$61$	−5.32798e18	−0.956311	−0.478155	+	0.878275i	$0.658694\pi$
$62$	−3.40158e18	−0.514716
$63$	−5.45220e18	−0.697422
$64$	1.15292e18	0.125000
$65$	−8.91357e18	−0.821224
$66$	6.22226e18	0.488356
$67$	−1.31401e19	−0.880668	−0.440334	−	0.897834i	$-0.645140\pi$
$67$	−1.31401e19	−0.880668	−0.440334	+	0.897834i	$0.645140\pi$
$68$	9.02201e18	0.517559
$69$	−1.58616e19	−0.780604
$70$	6.67863e18	0.282591
$71$	−2.98159e19	−1.08702	−0.543508	−	0.839404i	$-0.682904\pi$
$71$	−2.98159e19	−1.08702	−0.543508	+	0.839404i	$0.682904\pi$
$72$	8.76565e18	0.275926
$73$	1.37094e18	0.0373361	0.0186681	−	0.999826i	$-0.494057\pi$
$73$	1.37094e18	0.0373361	0.0186681	+	0.999826i	$0.494057\pi$
$74$	4.44215e19	1.04872
$75$	4.57039e18	0.0937151
$76$	−7.27399e18	−0.129787
$77$	−8.46803e19	−1.31713
$78$	−4.47924e19	−0.608431
$79$	1.74281e19	0.207093	0.103546	−	0.994625i	$-0.466981\pi$
$79$	1.74281e19	0.207093	0.103546	+	0.994625i	$0.466981\pi$
$80$	−1.07374e19	−0.111803
$81$	4.26208e19	0.389519
$82$	9.79579e19	0.787035
$83$	3.75717e19	0.265792	0.132896	−	0.991130i	$-0.457572\pi$
$83$	3.75717e19	0.265792	0.132896	+	0.991130i	$0.457572\pi$
$84$	3.35614e19	0.209367
$85$	−8.40240e19	−0.462919
$86$	8.00467e19	0.390040
$87$	−1.87159e20	−0.807717
$88$	1.36143e20	0.521107
$89$	2.43231e20	0.826845	0.413423	−	0.910539i	$-0.364333\pi$
$89$	2.43231e20	0.826845	0.413423	+	0.910539i	$0.364333\pi$
$90$	−8.16365e19	−0.246796
$91$	6.09592e20	1.64098
$92$	−3.47051e20	−0.832955
$93$	1.59196e20	0.341084
$94$	2.08521e20	0.399308
$95$	6.77443e19	0.116085
$96$	−5.39576e19	−0.0828332
$97$	−1.80740e20	−0.248858	−0.124429	−	0.992229i	$-0.539710\pi$
$97$	−1.80740e20	−0.248858	−0.124429	+	0.992229i	$0.539710\pi$
$98$	1.15205e20	0.142429
$99$	1.03509e21	1.15030
$100$	1.00000e20	0.100000
$101$	−4.40260e20	−0.396583	−0.198292	−	0.980143i	$-0.563539\pi$
$101$	−4.40260e20	−0.396583	−0.198292	+	0.980143i	$0.563539\pi$
$102$	−4.22237e20	−0.342969
$103$	−1.91819e21	−1.40637	−0.703186	−	0.711005i	$-0.748240\pi$
$103$	−1.91819e21	−1.40637	−0.703186	+	0.711005i	$0.748240\pi$
$104$	−9.80058e20	−0.649234
$105$	−3.12565e20	−0.187263
$106$	−1.45532e21	−0.789310
$107$	7.55037e20	0.371055	0.185528	−	0.982639i	$-0.440601\pi$
$107$	7.55037e20	0.371055	0.185528	+	0.982639i	$0.440601\pi$
$108$	−9.35892e20	−0.417135
$109$	−9.55072e20	−0.386418	−0.193209	−	0.981158i	$-0.561890\pi$
$109$	−9.55072e20	−0.386418	−0.193209	+	0.981158i	$0.561890\pi$
$110$	−1.26793e21	−0.466092
$111$	−2.07896e21	−0.694952
$112$	7.34323e20	0.223408
$113$	5.50602e21	1.52586	0.762929	−	0.646482i	$-0.223760\pi$
$113$	5.50602e21	1.52586	0.762929	+	0.646482i	$0.223760\pi$
$114$	3.40428e20	0.0860052
$115$	3.23217e21	0.745017
$116$	−4.09504e21	−0.861886
$117$	−7.45137e21	−1.43313
$118$	−2.34413e21	−0.412306
$119$	5.74634e21	0.925013
$120$	5.02519e20	0.0740883
$121$	8.67620e21	1.17242
$122$	5.45585e21	0.676214
$123$	−4.58450e21	−0.521541
$124$	3.48321e21	0.363959
$125$	−9.31323e20	−0.0894427
$126$	5.58305e21	0.493152
$127$	2.04590e22	1.66320	0.831602	−	0.555371i	$-0.187424\pi$
$127$	2.04590e22	1.66320	0.831602	+	0.555371i	$0.187424\pi$
$128$	−1.18059e21	−0.0883883
$129$	−3.74625e21	−0.258467
$130$	9.12750e21	0.580693
$131$	−1.03791e22	−0.609271	−0.304635	−	0.952469i	$-0.598535\pi$
$131$	−1.03791e22	−0.609271	−0.304635	+	0.952469i	$0.598535\pi$
$132$	−6.37159e21	−0.345320
$133$	−4.63298e21	−0.231963
$134$	1.34554e22	0.622727
$135$	8.71617e21	0.373097
$136$	−9.23854e21	−0.365969
$137$	−9.13014e21	−0.334897	−0.167449	−	0.985881i	$-0.553553\pi$
$137$	−9.13014e21	−0.334897	−0.167449	+	0.985881i	$0.553553\pi$
$138$	1.62423e22	0.551971
$139$	−3.18076e22	−1.00202	−0.501009	−	0.865442i	$-0.667038\pi$
$139$	−3.18076e22	−1.00202	−0.501009	+	0.865442i	$0.667038\pi$
$140$	−6.83892e21	−0.199822
$141$	−9.75896e21	−0.264608
$142$	3.05315e22	0.768636
$143$	−1.15730e23	−2.70656
$144$	−8.97602e21	−0.195109
$145$	3.81381e22	0.770894
$146$	−1.40384e21	−0.0264006
$147$	−5.39168e21	−0.0943826
$148$	−4.54876e22	−0.741558
$149$	1.17039e23	1.77777	0.888884	−	0.458133i	$-0.151482\pi$
$149$	1.17039e23	1.77777	0.888884	+	0.458133i	$0.151482\pi$
$150$	−4.68008e21	−0.0662666
$151$	−1.57736e22	−0.208293	−0.104146	−	0.994562i	$-0.533211\pi$
$151$	−1.57736e22	−0.208293	−0.104146	+	0.994562i	$0.533211\pi$
$152$	7.44857e21	0.0917730
$153$	−7.02405e22	−0.807844
$154$	8.67126e22	0.931354
$155$	−3.24399e22	−0.325535
$156$	4.58674e22	0.430226
$157$	−9.37324e22	−0.822135	−0.411068	−	0.911605i	$-0.634844\pi$
$157$	−9.37324e22	−0.822135	−0.411068	+	0.911605i	$0.634844\pi$
$158$	−1.78464e22	−0.146437
$159$	6.81102e22	0.523049
$160$	1.09951e22	0.0790569
$161$	−2.21045e23	−1.48871
$162$	−4.36437e22	−0.275431
$163$	1.15735e23	0.684691	0.342345	−	0.939574i	$-0.388779\pi$
$163$	1.15735e23	0.684691	0.342345	+	0.939574i	$0.388779\pi$
$164$	−1.00309e23	−0.556518
$165$	5.93400e22	0.308863
$166$	−3.84734e22	−0.187943
$167$	1.46022e23	0.669723	0.334862	−	0.942267i	$-0.391310\pi$
$167$	1.46022e23	0.669723	0.334862	+	0.942267i	$0.391310\pi$
$168$	−3.43669e22	−0.148045
$169$	5.86048e23	2.37204
$170$	8.60406e22	0.327333
$171$	5.66314e22	0.202581
$172$	−8.19678e22	−0.275800
$173$	−2.62784e23	−0.831984	−0.415992	−	0.909368i	$-0.636566\pi$
$173$	−2.62784e23	−0.831984	−0.415992	+	0.909368i	$0.636566\pi$
$174$	1.91651e23	0.571142
$175$	6.36924e22	0.178726
$176$	−1.39410e23	−0.368478
$177$	1.09707e23	0.273221
$178$	−2.49069e23	−0.584668
$179$	8.92249e23	1.97483	0.987413	−	0.158160i	$-0.0505562\pi$
$179$	8.92249e23	1.97483	0.987413	+	0.158160i	$0.0505562\pi$
$180$	8.35957e22	0.174511
$181$	2.71393e23	0.534531	0.267266	−	0.963623i	$-0.413880\pi$
$181$	2.71393e23	0.534531	0.267266	+	0.963623i	$0.413880\pi$
$182$	−6.24222e23	−1.16035
$183$	−2.55338e23	−0.448104
$184$	3.55380e23	0.588988
$185$	4.23636e23	0.663269
$186$	−1.63017e23	−0.241183
$187$	−1.09093e24	−1.52567
$188$	−2.13526e23	−0.282354
$189$	−5.96092e23	−0.745528
$190$	−6.93702e22	−0.0820843
$191$	−1.16742e24	−1.30731	−0.653654	−	0.756794i	$-0.726765\pi$
$191$	−1.16742e24	−1.30731	−0.653654	+	0.756794i	$0.726765\pi$
$192$	5.52526e22	0.0585719
$193$	8.18854e22	0.0821968	0.0410984	−	0.999155i	$-0.486914\pi$
$193$	8.18854e22	0.0821968	0.0410984	+	0.999155i	$0.486914\pi$
$194$	1.85078e23	0.175969
$195$	−4.27174e23	−0.384805
$196$	−1.17970e23	−0.100712
$197$	−6.59417e23	−0.533660	−0.266830	−	0.963744i	$-0.585976\pi$
$197$	−6.59417e23	−0.533660	−0.266830	+	0.963744i	$0.585976\pi$
$198$	−1.05993e24	−0.813382
$199$	1.82645e24	1.32938	0.664692	−	0.747117i	$-0.268563\pi$
$199$	1.82645e24	1.32938	0.664692	+	0.747117i	$0.268563\pi$
$200$	−1.02400e23	−0.0707107
$201$	−6.29725e23	−0.412660
$202$	4.50826e23	0.280427
$203$	−2.60823e24	−1.54041
$204$	4.32371e23	0.242515
$205$	9.34199e23	0.497764
$206$	1.96423e24	0.994456
$207$	2.70195e24	1.30014
$208$	1.00358e24	0.459078
$209$	8.79565e23	0.382588
$210$	3.20066e23	0.132415
$211$	−3.36470e24	−1.32428	−0.662140	−	0.749380i	$-0.730352\pi$
$211$	−3.36470e24	−1.32428	−0.662140	+	0.749380i	$0.730352\pi$
$212$	1.49025e24	0.558127
$213$	−1.42890e24	−0.509349
$214$	−7.73158e23	−0.262376
$215$	7.63385e23	0.246683
$216$	9.58353e23	0.294959
$217$	2.21854e24	0.650490
$218$	9.77993e23	0.273239
$219$	6.57010e22	0.0174948
$220$	1.29836e24	0.329577
$221$	7.85336e24	1.90080
$222$	2.12885e24	0.491405
$223$	1.44704e23	0.0318626	0.0159313	−	0.999873i	$-0.494929\pi$
$223$	1.44704e23	0.0318626	0.0159313	+	0.999873i	$0.494929\pi$
$224$	−7.51947e23	−0.157973
$225$	−7.78546e23	−0.156087
$226$	−5.63817e24	−1.07894
$227$	−4.83544e24	−0.883415	−0.441707	−	0.897159i	$-0.645627\pi$
$227$	−4.83544e24	−0.883415	−0.441707	+	0.897159i	$0.645627\pi$
$228$	−3.48598e23	−0.0608148
$229$	−4.35342e24	−0.725367	−0.362684	−	0.931912i	$-0.618139\pi$
$229$	−4.35342e24	−0.725367	−0.362684	+	0.931912i	$0.618139\pi$
$230$	−3.30974e24	−0.526807
$231$	−4.05822e24	−0.617177
$232$	4.19332e24	0.609445
$233$	1.03556e23	0.0143860	0.00719300	−	0.999974i	$-0.497710\pi$
$233$	1.03556e23	0.0143860	0.00719300	+	0.999974i	$0.497710\pi$
$234$	7.63020e24	1.01337
$235$	1.98862e24	0.252545
$236$	2.40039e24	0.291545
$237$	8.35223e23	0.0970387
$238$	−5.88425e24	−0.654083
$239$	−1.45089e25	−1.54332	−0.771660	−	0.636035i	$-0.780573\pi$
$239$	−1.45089e25	−1.54332	−0.771660	+	0.636035i	$0.780573\pi$
$240$	−5.14580e23	−0.0523883
$241$	−2.10504e23	−0.0205155	−0.0102578	−	0.999947i	$-0.503265\pi$
$241$	−2.10504e23	−0.0205155	−0.0102578	+	0.999947i	$0.503265\pi$
$242$	−8.88443e24	−0.829026
$243$	1.13788e25	1.01679
$244$	−5.58679e24	−0.478155
$245$	1.09868e24	0.0900798
$246$	4.69453e24	0.368785
$247$	−6.33176e24	−0.476658
$248$	−3.56681e24	−0.257358
$249$	1.80059e24	0.124543
$250$	9.53674e23	0.0632456
$251$	−8.79823e24	−0.559527	−0.279764	−	0.960069i	$-0.590256\pi$
$251$	−8.79823e24	−0.559527	−0.279764	+	0.960069i	$0.590256\pi$
$252$	−5.71704e24	−0.348711
$253$	4.19651e25	2.45541
$254$	−2.09500e25	−1.17606
$255$	−4.02677e24	−0.216912
$256$	1.20893e24	0.0625000
$257$	2.93954e24	0.145875	0.0729376	−	0.997337i	$-0.476763\pi$
$257$	2.93954e24	0.145875	0.0729376	+	0.997337i	$0.476763\pi$
$258$	3.83616e24	0.182763
$259$	−2.89721e25	−1.32536
$260$	−9.34656e24	−0.410612
$261$	3.18818e25	1.34529
$262$	1.06282e25	0.430820
$263$	−7.06799e23	−0.0275271	−0.0137636	−	0.999905i	$-0.504381\pi$
$263$	−7.06799e23	−0.0275271	−0.0137636	+	0.999905i	$0.504381\pi$
$264$	6.52451e24	0.244178
$265$	−1.38790e25	−0.499204
$266$	4.74417e24	0.164022
$267$	1.16566e25	0.387439
$268$	−1.37784e25	−0.440334
$269$	4.29393e25	1.31964	0.659821	−	0.751423i	$-0.270632\pi$
$269$	4.29393e25	1.31964	0.659821	+	0.751423i	$0.270632\pi$
$270$	−8.92536e24	−0.263819
$271$	1.66203e25	0.472564	0.236282	−	0.971685i	$-0.424071\pi$
$271$	1.66203e25	0.472564	0.236282	+	0.971685i	$0.424071\pi$
$272$	9.46027e24	0.258780
$273$	2.92141e25	0.768925
$274$	9.34927e24	0.236808
$275$	−1.20919e25	−0.294783
$276$	−1.66321e25	−0.390302
$277$	−2.85979e25	−0.646095	−0.323048	−	0.946383i	$-0.604707\pi$
$277$	−2.85979e25	−0.646095	−0.323048	+	0.946383i	$0.604707\pi$
$278$	3.25710e25	0.708534
$279$	−2.71184e25	−0.568094
$280$	7.00305e24	0.141295
$281$	−5.58235e25	−1.08493	−0.542464	−	0.840079i	$-0.682509\pi$
$281$	−5.58235e25	−1.08493	−0.542464	+	0.840079i	$0.682509\pi$
$282$	9.99318e24	0.187106
$283$	6.54228e25	1.18024	0.590121	−	0.807315i	$-0.299080\pi$
$283$	6.54228e25	1.18024	0.590121	+	0.807315i	$0.299080\pi$
$284$	−3.12643e25	−0.543508
$285$	3.24658e24	0.0543944
$286$	1.18508e26	1.91383
$287$	−6.38891e25	−0.994642
$288$	9.19145e24	0.137963
$289$	4.93795e24	0.0714693
$290$	−3.90534e25	−0.545104
$291$	−8.66179e24	−0.116609
$292$	1.43754e24	0.0186681
$293$	−1.10836e25	−0.138858	−0.0694289	−	0.997587i	$-0.522118\pi$
$293$	−1.10836e25	−0.138858	−0.0694289	+	0.997587i	$0.522118\pi$
$294$	5.52108e24	0.0667386
$295$	−2.23553e25	−0.260765
$296$	4.65793e25	0.524361
$297$	1.13167e26	1.22964
$298$	−1.19848e26	−1.25707
$299$	−3.02096e26	−3.05913
$300$	4.79240e24	0.0468576
$301$	−5.22073e25	−0.492927
$302$	1.61522e25	0.147285
$303$	−2.10990e25	−0.185829
$304$	−7.62733e24	−0.0648933
$305$	5.20310e25	0.427675
$306$	7.19263e25	0.571232
$307$	−1.02459e26	−0.786315	−0.393157	−	0.919471i	$-0.628617\pi$
$307$	−1.02459e26	−0.786315	−0.393157	+	0.919471i	$0.628617\pi$
$308$	−8.87937e25	−0.658567
$309$	−9.19272e25	−0.658992
$310$	3.32185e25	0.230188
$311$	−2.17194e26	−1.45500	−0.727502	−	0.686105i	$-0.759319\pi$
$311$	−2.17194e26	−1.45500	−0.727502	+	0.686105i	$0.759319\pi$
$312$	−4.69683e25	−0.304215
$313$	2.19829e26	1.37679	0.688397	−	0.725334i	$-0.258315\pi$
$313$	2.19829e26	1.37679	0.688397	+	0.725334i	$0.258315\pi$
$314$	9.59820e25	0.581337
$315$	5.32441e25	0.311897
$316$	1.82747e25	0.103546
$317$	1.26596e26	0.693901	0.346950	−	0.937883i	$-0.387217\pi$
$317$	1.26596e26	0.693901	0.346950	+	0.937883i	$0.387217\pi$
$318$	−6.97449e25	−0.369852
$319$	4.95169e26	2.54069
$320$	−1.12590e25	−0.0559017
$321$	3.61844e25	0.173867
$322$	2.26350e26	1.05267
$323$	−5.96865e25	−0.268689
$324$	4.46911e25	0.194759
$325$	8.70466e25	0.367262
$326$	−1.18513e26	−0.484150
$327$	−4.57708e25	−0.181066
$328$	1.02716e26	0.393517
$329$	−1.36000e26	−0.504640
$330$	−6.07642e25	−0.218399
$331$	1.93702e26	0.674433	0.337217	−	0.941427i	$-0.390514\pi$
$331$	1.93702e26	0.674433	0.337217	+	0.941427i	$0.390514\pi$
$332$	3.93968e25	0.132896
$333$	3.54142e26	1.15748
$334$	−1.49527e26	−0.473566
$335$	1.28321e26	0.393847
$336$	3.51917e25	0.104683
$337$	1.34839e26	0.388779	0.194389	−	0.980924i	$-0.437727\pi$
$337$	1.34839e26	0.388779	0.194389	+	0.980924i	$0.437727\pi$
$338$	−6.00113e26	−1.67729
$339$	2.63870e26	0.714980
$340$	−8.81056e25	−0.231459
$341$	−4.21187e26	−1.07289
$342$	−5.79905e25	−0.143246
$343$	−4.48170e26	−1.07363
$344$	8.39350e25	0.195020
$345$	1.54898e26	0.349097
$346$	2.69091e26	0.588302
$347$	−6.73325e26	−1.42812	−0.714061	−	0.700084i	$-0.753146\pi$
$347$	−6.73325e26	−1.42812	−0.714061	+	0.700084i	$0.753146\pi$
$348$	−1.96251e26	−0.403859
$349$	9.07724e26	1.81254	0.906268	−	0.422703i	$-0.138919\pi$
$349$	9.07724e26	1.81254	0.906268	+	0.422703i	$0.138919\pi$
$350$	−6.52210e25	−0.126378
$351$	−8.14662e26	−1.53198
$352$	1.42756e26	0.260553
$353$	4.40145e25	0.0779761	0.0389880	−	0.999240i	$-0.487587\pi$
$353$	4.40145e25	0.0779761	0.0389880	+	0.999240i	$0.487587\pi$
$354$	−1.12340e26	−0.193197
$355$	2.91171e26	0.486128
$356$	2.55046e26	0.413423
$357$	2.75387e26	0.433438
$358$	−9.13663e26	−1.39641
$359$	−3.93523e26	−0.584088	−0.292044	−	0.956405i	$-0.594335\pi$
$359$	−3.93523e26	−0.584088	−0.292044	+	0.956405i	$0.594335\pi$
$360$	−8.56020e25	−0.123398
$361$	−6.66087e26	−0.932622
$362$	−2.77906e26	−0.377971
$363$	4.15798e26	0.549367
$364$	6.39203e26	0.820492
$365$	−1.33881e25	−0.0166972
$366$	2.61466e26	0.316857
$367$	1.48020e25	0.0174312	0.00871559	−	0.999962i	$-0.497226\pi$
$367$	1.48020e25	0.0174312	0.00871559	+	0.999962i	$0.497226\pi$
$368$	−3.63910e26	−0.416477
$369$	7.80951e26	0.868654
$370$	−4.33804e26	−0.469002
$371$	9.49176e26	0.997518
$372$	1.66929e26	0.170542
$373$	−1.57080e27	−1.56019	−0.780094	−	0.625662i	$-0.784829\pi$
$373$	−1.57080e27	−1.56019	−0.780094	+	0.625662i	$0.784829\pi$
$374$	1.11712e27	1.07881
$375$	−4.46327e25	−0.0419107
$376$	2.18651e26	0.199654
$377$	−3.56460e27	−3.16538
$378$	6.10398e26	0.527168
$379$	−2.27703e26	−0.191275	−0.0956373	−	0.995416i	$-0.530489\pi$
$379$	−2.27703e26	−0.191275	−0.0956373	+	0.995416i	$0.530489\pi$
$380$	7.10351e25	0.0580423
$381$	9.80478e26	0.779337
$382$	1.19544e27	0.924406
$383$	2.29376e27	1.72569	0.862843	−	0.505472i	$-0.168682\pi$
$383$	2.29376e27	1.72569	0.862843	+	0.505472i	$0.168682\pi$
$384$	−5.65786e25	−0.0414166
$385$	8.26956e26	0.589040
$386$	−8.38506e25	−0.0581219
$387$	6.38157e26	0.430489
$388$	−1.89520e26	−0.124429
$389$	1.10508e27	0.706190	0.353095	−	0.935587i	$-0.385129\pi$
$389$	1.10508e27	0.706190	0.353095	+	0.935587i	$0.385129\pi$
$390$	4.37426e26	0.272099
$391$	−2.84772e27	−1.72441
$392$	1.20801e26	0.0712143
$393$	−4.97407e26	−0.285489
$394$	6.75243e26	0.377355
$395$	−1.70196e26	−0.0926148
$396$	1.08537e27	0.575148
$397$	1.88707e26	0.0973839	0.0486919	−	0.998814i	$-0.484495\pi$
$397$	1.88707e26	0.0973839	0.0486919	+	0.998814i	$0.484495\pi$
$398$	−1.87029e27	−0.940017
$399$	−2.22031e26	−0.108692
$400$	1.04858e26	0.0500000
$401$	−1.74678e27	−0.811376	−0.405688	−	0.914012i	$-0.632968\pi$
$401$	−1.74678e27	−0.811376	−0.405688	+	0.914012i	$0.632968\pi$
$402$	6.44838e26	0.291794
$403$	3.03202e27	1.33668
$404$	−4.61646e26	−0.198292
$405$	−4.16218e26	−0.174198
$406$	2.67083e27	1.08924
$407$	5.50032e27	2.18598
$408$	−4.42748e26	−0.171484
$409$	−2.92958e27	−1.10588	−0.552942	−	0.833219i	$-0.686495\pi$
$409$	−2.92958e27	−1.10588	−0.552942	+	0.833219i	$0.686495\pi$
$410$	−9.56620e26	−0.351973
$411$	−4.37553e26	−0.156925
$412$	−2.01137e27	−0.703186
$413$	1.52886e27	0.521066
$414$	−2.76680e27	−0.919336
$415$	−3.66911e26	−0.118866
$416$	−1.02766e27	−0.324617
$417$	−1.52435e27	−0.469521
$418$	−9.00674e26	−0.270531
$419$	−2.59534e27	−0.760234	−0.380117	−	0.924938i	$-0.624116\pi$
$419$	−2.59534e27	−0.760234	−0.380117	+	0.924938i	$0.624116\pi$
$420$	−3.27748e26	−0.0936316
$421$	−2.08416e27	−0.580723	−0.290362	−	0.956917i	$-0.593776\pi$
$421$	−2.08416e27	−0.580723	−0.290362	+	0.956917i	$0.593776\pi$
$422$	3.44545e27	0.936408
$423$	1.66240e27	0.440718
$424$	−1.52602e27	−0.394655
$425$	8.20547e26	0.207024
$426$	1.46319e27	0.360164
$427$	−3.55836e27	−0.854588
$428$	7.91713e26	0.185528
$429$	−5.54625e27	−1.26823
$430$	−7.81706e26	−0.174431
$431$	1.85265e27	0.403444	0.201722	−	0.979443i	$-0.435346\pi$
$431$	1.85265e27	0.403444	0.201722	+	0.979443i	$0.435346\pi$
$432$	−9.81354e26	−0.208567
$433$	6.31486e26	0.130991	0.0654954	−	0.997853i	$-0.479137\pi$
$433$	6.31486e26	0.130991	0.0654954	+	0.997853i	$0.479137\pi$
$434$	−2.27179e27	−0.459966
$435$	1.82773e27	0.361222
$436$	−1.00147e27	−0.193209
$437$	2.29597e27	0.432425
$438$	−6.72778e25	−0.0123707
$439$	3.19822e27	0.574158	0.287079	−	0.957907i	$-0.407316\pi$
$439$	3.19822e27	0.574158	0.287079	+	0.957907i	$0.407316\pi$
$440$	−1.32952e27	−0.233046
$441$	9.18450e26	0.157199
$442$	−8.04184e27	−1.34407
$443$	7.29283e26	0.119030	0.0595151	−	0.998227i	$-0.481045\pi$
$443$	7.29283e26	0.119030	0.0595151	+	0.998227i	$0.481045\pi$
$444$	−2.17995e27	−0.347476
$445$	−2.37530e27	−0.369776
$446$	−1.48177e26	−0.0225302
$447$	5.60898e27	0.833018
$448$	7.69994e26	0.111704
$449$	−1.59099e27	−0.225466	−0.112733	−	0.993625i	$-0.535961\pi$
$449$	−1.59099e27	−0.225466	−0.112733	+	0.993625i	$0.535961\pi$
$450$	7.97231e26	0.110370
$451$	1.21293e28	1.64052
$452$	5.77348e27	0.762929
$453$	−7.55936e26	−0.0976009
$454$	4.95149e27	0.624669
$455$	−5.95305e27	−0.733871
$456$	3.56965e26	0.0430026
$457$	8.94924e27	1.05358	0.526788	−	0.849997i	$-0.323396\pi$
$457$	8.94924e27	1.05358	0.526788	+	0.849997i	$0.323396\pi$
$458$	4.45790e27	0.512912
$459$	−7.67944e27	−0.863567
$460$	3.38917e27	0.372509
$461$	1.32946e28	1.42829	0.714144	−	0.699999i	$-0.246816\pi$
$461$	1.32946e28	1.42829	0.714144	+	0.699999i	$0.246816\pi$
$462$	4.15561e27	0.436410
$463$	1.29662e28	1.33110	0.665551	−	0.746352i	$-0.268197\pi$
$463$	1.29662e28	1.33110	0.665551	+	0.746352i	$0.268197\pi$
$464$	−4.29396e27	−0.430943
$465$	−1.55465e27	−0.152538
$466$	−1.06042e26	−0.0101724
$467$	−5.02371e27	−0.471191	−0.235595	−	0.971851i	$-0.575704\pi$
$467$	−5.02371e27	−0.471191	−0.235595	+	0.971851i	$0.575704\pi$
$468$	−7.81332e27	−0.716563
$469$	−8.77577e27	−0.786992
$470$	−2.03634e27	−0.178576
$471$	−4.49203e27	−0.385232
$472$	−2.45800e27	−0.206153
$473$	9.91148e27	0.813011
$474$	−8.55269e26	−0.0686167
$475$	−6.61565e26	−0.0519147
$476$	6.02547e27	0.462507
$477$	−1.16023e28	−0.871165
$478$	1.48571e28	1.09129
$479$	1.23595e28	0.888132	0.444066	−	0.895994i	$-0.353536\pi$
$479$	1.23595e28	0.888132	0.444066	+	0.895994i	$0.353536\pi$
$480$	5.26930e26	0.0370441
$481$	−3.95954e28	−2.72346
$482$	2.15556e26	0.0145067
$483$	−1.05934e28	−0.697572
$484$	9.09765e27	0.586210
$485$	1.76504e27	0.111293
$486$	−1.16519e28	−0.718978
$487$	−2.33221e28	−1.40836	−0.704179	−	0.710023i	$-0.748685\pi$
$487$	−2.33221e28	−1.40836	−0.704179	+	0.710023i	$0.748685\pi$
$488$	5.72087e27	0.338107
$489$	5.54648e27	0.320829
$490$	−1.12505e27	−0.0636960
$491$	2.65852e28	1.47328	0.736640	−	0.676286i	$-0.236411\pi$
$491$	2.65852e28	1.47328	0.736640	+	0.676286i	$0.236411\pi$
$492$	−4.80720e27	−0.260771
$493$	−3.36018e28	−1.78431
$494$	6.48372e27	0.337048
$495$	−1.01083e28	−0.514428
$496$	3.65241e27	0.181979
$497$	−1.99130e28	−0.971390
$498$	−1.84380e27	−0.0880655
$499$	−1.38803e28	−0.649148	−0.324574	−	0.945860i	$-0.605221\pi$
$499$	−1.38803e28	−0.649148	−0.324574	+	0.945860i	$0.605221\pi$
$500$	−9.76563e26	−0.0447214
$501$	6.99795e27	0.313816
$502$	9.00939e27	0.395646
$503$	−8.55444e27	−0.367898	−0.183949	−	0.982936i	$-0.558888\pi$
$503$	−8.55444e27	−0.367898	−0.183949	+	0.982936i	$0.558888\pi$
$504$	5.85425e27	0.246576
$505$	4.29941e27	0.177357
$506$	−4.29723e28	−1.73623
$507$	2.80857e28	1.11148
$508$	2.14528e28	0.831602
$509$	3.82946e28	1.45412	0.727060	−	0.686574i	$-0.240886\pi$
$509$	3.82946e28	1.45412	0.727060	+	0.686574i	$0.240886\pi$
$510$	4.12341e27	0.153380
$511$	9.15601e26	0.0333647
$512$	−1.23794e27	−0.0441942
$513$	6.19154e27	0.216554
$514$	−3.01009e27	−0.103149
$515$	1.87323e28	0.628949
$516$	−3.92822e27	−0.129233
$517$	2.58194e28	0.832329
$518$	2.96675e28	0.937169
$519$	−1.25937e28	−0.389847
$520$	9.57088e27	0.290346
$521$	2.56460e28	0.762471	0.381236	−	0.924478i	$-0.375499\pi$
$521$	2.56460e28	0.762471	0.381236	+	0.924478i	$0.375499\pi$
$522$	−3.26470e28	−0.951267
$523$	−4.56980e28	−1.30506	−0.652529	−	0.757764i	$-0.726292\pi$
$523$	−4.56980e28	−1.30506	−0.652529	+	0.757764i	$0.726292\pi$
$524$	−1.08833e28	−0.304635
$525$	3.05239e27	0.0837467
$526$	7.23762e26	0.0194646
$527$	2.85814e28	0.753481
$528$	−6.68110e27	−0.172660
$529$	7.00720e28	1.77525
$530$	1.42121e28	0.352990
$531$	−1.86881e28	−0.455064
$532$	−4.85803e27	−0.115981
$533$	−8.73155e28	−2.04388
$534$	−1.19364e28	−0.273961
$535$	−7.37341e27	−0.165941
$536$	1.41090e28	0.311363
$537$	4.27601e28	0.925356
$538$	−4.39699e28	−0.933128
$539$	1.42648e28	0.296882
$540$	9.13957e27	0.186548
$541$	5.19261e28	1.03948	0.519738	−	0.854326i	$-0.326029\pi$
$541$	5.19261e28	1.03948	0.519738	+	0.854326i	$0.326029\pi$
$542$	−1.70192e28	−0.334153
$543$	1.30062e28	0.250468
$544$	−9.68731e27	−0.182985
$545$	9.32687e27	0.172812
$546$	−2.99152e28	−0.543712
$547$	−4.55529e28	−0.812173	−0.406087	−	0.913835i	$-0.633107\pi$
$547$	−4.55529e28	−0.812173	−0.406087	+	0.913835i	$0.633107\pi$
$548$	−9.57365e27	−0.167449
$549$	4.34957e28	0.746340
$550$	1.23821e28	0.208443
$551$	2.70914e28	0.447445
$552$	1.70312e28	0.275985
$553$	1.16396e28	0.185065
$554$	2.92842e28	0.456858
$555$	2.03023e28	0.310792
$556$	−3.33527e28	−0.501009
$557$	2.98975e28	0.440713	0.220356	−	0.975419i	$-0.429278\pi$
$557$	2.98975e28	0.440713	0.220356	+	0.975419i	$0.429278\pi$
$558$	2.77693e28	0.401703
$559$	−7.13502e28	−1.01291
$560$	−7.17112e27	−0.0999109
$561$	−5.22819e28	−0.714894
$562$	5.71633e28	0.767160
$563$	−4.42316e28	−0.582632	−0.291316	−	0.956627i	$-0.594093\pi$
$563$	−4.42316e28	−0.582632	−0.291316	+	0.956627i	$0.594093\pi$
$564$	−1.02330e28	−0.132304
$565$	−5.37697e28	−0.682385
$566$	−6.69929e28	−0.834558
$567$	2.84648e28	0.348086
$568$	3.20146e28	0.384318
$569$	2.66278e28	0.313803	0.156901	−	0.987614i	$-0.449849\pi$
$569$	2.66278e28	0.313803	0.156901	+	0.987614i	$0.449849\pi$
$570$	−3.32449e27	−0.0384627
$571$	−5.39217e28	−0.612469	−0.306235	−	0.951956i	$-0.599069\pi$
$571$	−5.39217e28	−0.612469	−0.306235	+	0.951956i	$0.599069\pi$
$572$	−1.21352e29	−1.35328
$573$	−5.59475e28	−0.612572
$574$	6.54224e28	0.703318
$575$	−3.15641e28	−0.333182
$576$	−9.41204e27	−0.0975546
$577$	−4.00855e28	−0.407983	−0.203991	−	0.978973i	$-0.565391\pi$
$577$	−4.00855e28	−0.407983	−0.203991	+	0.978973i	$0.565391\pi$
$578$	−5.05646e27	−0.0505364
$579$	3.92427e27	0.0385154
$580$	3.99907e28	0.385447
$581$	2.50928e28	0.237519
$582$	8.86967e27	0.0824548
$583$	−1.80200e29	−1.64526
$584$	−1.47204e27	−0.0132003
$585$	7.27673e28	0.640913
$586$	1.13496e28	0.0981873
$587$	6.52023e28	0.554068	0.277034	−	0.960860i	$-0.410649\pi$
$587$	6.52023e28	0.554068	0.277034	+	0.960860i	$0.410649\pi$
$588$	−5.65358e27	−0.0471913
$589$	−2.30437e28	−0.188948
$590$	2.28919e28	0.184389
$591$	−3.16019e28	−0.250060
$592$	−4.76972e28	−0.370779
$593$	7.72360e28	0.589855	0.294928	−	0.955520i	$-0.404704\pi$
$593$	7.72360e28	0.589855	0.294928	+	0.955520i	$0.404704\pi$
$594$	−1.15883e29	−0.869487
$595$	−5.61166e28	−0.413678
$596$	1.22724e29	0.888884
$597$	8.75308e28	0.622917
$598$	3.09347e29	2.16313
$599$	8.22197e28	0.564930	0.282465	−	0.959278i	$-0.408848\pi$
$599$	8.22197e28	0.564930	0.282465	+	0.959278i	$0.408848\pi$
$600$	−4.90741e27	−0.0331333
$601$	1.57712e29	1.04636	0.523181	−	0.852221i	$-0.324745\pi$
$601$	1.57712e29	1.04636	0.523181	+	0.852221i	$0.324745\pi$
$602$	5.34602e28	0.348552
$603$	1.07271e29	0.687306
$604$	−1.65399e28	−0.104146
$605$	−8.47285e28	−0.524322
$606$	2.16054e28	0.131401
$607$	−3.31059e29	−1.97890	−0.989450	−	0.144877i	$-0.953721\pi$
$607$	−3.31059e29	−1.97890	−0.989450	+	0.144877i	$0.953721\pi$
$608$	7.81039e27	0.0458865
$609$	−1.24997e29	−0.721801
$610$	−5.32798e28	−0.302412
$611$	−1.85867e29	−1.03698
$612$	−7.36525e28	−0.403922
$613$	3.50723e29	1.89073	0.945363	−	0.326018i	$-0.105707\pi$
$613$	3.50723e29	1.89073	0.945363	+	0.326018i	$0.105707\pi$
$614$	1.04918e29	0.556008
$615$	4.47705e28	0.233240
$616$	9.09248e28	0.465677
$617$	−2.45228e28	−0.123474	−0.0617371	−	0.998092i	$-0.519664\pi$
$617$	−2.45228e28	−0.123474	−0.0617371	+	0.998092i	$0.519664\pi$
$618$	9.41335e28	0.465978
$619$	1.47013e28	0.0715492	0.0357746	−	0.999360i	$-0.488610\pi$
$619$	1.47013e28	0.0715492	0.0357746	+	0.999360i	$0.488610\pi$
$620$	−3.40158e28	−0.162767
$621$	2.95406e29	1.38982
$622$	2.22407e29	1.02884
$623$	1.62445e29	0.738894
$624$	4.80955e28	0.215113
$625$	9.09495e27	0.0400000
$626$	−2.25105e29	−0.973541
$627$	4.21522e28	0.179272
$628$	−9.82855e28	−0.411068
$629$	−3.73247e29	−1.53520
$630$	−5.45220e28	−0.220544
$631$	1.42534e29	0.567034	0.283517	−	0.958967i	$-0.408499\pi$
$631$	1.42534e29	0.567034	0.283517	+	0.958967i	$0.408499\pi$
$632$	−1.87133e28	−0.0732184
$633$	−1.61250e29	−0.620526
$634$	−1.29634e29	−0.490662
$635$	−1.99795e29	−0.743808
$636$	7.14187e28	0.261525
$637$	−1.02689e29	−0.369878
$638$	−5.07053e29	−1.79654
$639$	2.43407e29	0.848347
$640$	1.15292e28	0.0395285
$641$	2.82277e28	0.0952064	0.0476032	−	0.998866i	$-0.484842\pi$
$641$	2.82277e28	0.0952064	0.0476032	+	0.998866i	$0.484842\pi$
$642$	−3.70528e28	−0.122943
$643$	1.52966e29	0.499321	0.249661	−	0.968333i	$-0.419681\pi$
$643$	1.52966e29	0.499321	0.249661	+	0.968333i	$0.419681\pi$
$644$	−2.31783e29	−0.744354
$645$	3.65844e28	0.115590
$646$	6.11190e28	0.189992
$647$	−9.19042e28	−0.281087	−0.140543	−	0.990075i	$-0.544885\pi$
$647$	−9.19042e28	−0.281087	−0.140543	+	0.990075i	$0.544885\pi$
$648$	−4.57637e28	−0.137716
$649$	−2.90253e29	−0.859423
$650$	−8.91357e28	−0.259694
$651$	1.06321e29	0.304803
$652$	1.21357e29	0.342345
$653$	−8.26379e28	−0.229399	−0.114699	−	0.993400i	$-0.536590\pi$
$653$	−8.26379e28	−0.229399	−0.114699	+	0.993400i	$0.536590\pi$
$654$	4.68693e28	0.128033
$655$	1.01358e29	0.272474
$656$	−1.05181e29	−0.278259
$657$	−1.11919e28	−0.0291385
$658$	1.39264e29	0.356834
$659$	−7.76286e29	−1.95760	−0.978802	−	0.204807i	$-0.934343\pi$
$659$	−7.76286e29	−1.95760	−0.978802	+	0.204807i	$0.934343\pi$
$660$	6.22226e28	0.154432
$661$	−6.63151e29	−1.61993	−0.809967	−	0.586476i	$-0.800515\pi$
$661$	−6.63151e29	−1.61993	−0.809967	+	0.586476i	$0.800515\pi$
$662$	−1.98350e29	−0.476896
$663$	3.76364e29	0.890668
$664$	−4.03423e28	−0.0939715
$665$	4.52439e28	0.103737
$666$	−3.62641e29	−0.818461
$667$	1.29256e30	2.87165
$668$	1.53115e29	0.334862
$669$	6.93481e27	0.0149300
$670$	−1.31401e29	−0.278492
$671$	6.75550e29	1.40952
$672$	−3.60363e28	−0.0740223
$673$	3.60156e29	0.728337	0.364169	−	0.931333i	$-0.381353\pi$
$673$	3.60156e29	0.728337	0.364169	+	0.931333i	$0.381353\pi$
$674$	−1.38075e29	−0.274908
$675$	−8.51189e28	−0.166854
$676$	6.14516e29	1.18602
$677$	−1.28335e28	−0.0243874	−0.0121937	−	0.999926i	$-0.503881\pi$
$677$	−1.28335e28	−0.0243874	−0.0121937	+	0.999926i	$0.503881\pi$
$678$	−2.70203e29	−0.505567
$679$	−1.20710e29	−0.222387
$680$	9.02201e28	0.163667
$681$	−2.31734e29	−0.413947
$682$	4.31296e29	0.758646
$683$	−2.83065e29	−0.490308	−0.245154	−	0.969484i	$-0.578838\pi$
$683$	−2.83065e29	−0.490308	−0.245154	+	0.969484i	$0.578838\pi$
$684$	5.93823e28	0.101290
$685$	8.91616e28	0.149771
$686$	4.58926e29	0.759171
$687$	−2.08633e29	−0.339889
$688$	−8.59495e28	−0.137900
$689$	1.29721e30	2.04979
$690$	−1.58616e29	−0.246849
$691$	−6.08933e29	−0.933361	−0.466681	−	0.884426i	$-0.654550\pi$
$691$	−6.08933e29	−0.933361	−0.466681	+	0.884426i	$0.654550\pi$
$692$	−2.75549e29	−0.415992
$693$	6.91300e29	1.02794
$694$	6.89485e29	1.00983
$695$	3.10621e29	0.448116
$696$	2.00961e29	0.285571
$697$	−8.23082e29	−1.15212
$698$	−9.29509e29	−1.28166
$699$	4.96284e27	0.00674093
$700$	6.67863e28	0.0893631
$701$	−4.09891e29	−0.540292	−0.270146	−	0.962819i	$-0.587072\pi$
$701$	−4.09891e29	−0.540292	−0.270146	+	0.962819i	$0.587072\pi$
$702$	8.34214e29	1.08327
$703$	3.00930e29	0.384977
$704$	−1.46182e29	−0.184239
$705$	9.53024e28	0.118336
$706$	−4.50709e28	−0.0551374
$707$	−2.94033e29	−0.354399
$708$	1.15036e29	0.136611
$709$	−1.14539e30	−1.34020	−0.670098	−	0.742273i	$-0.733748\pi$
$709$	−1.14539e30	−1.34020	−0.670098	+	0.742273i	$0.733748\pi$
$710$	−2.98159e29	−0.343745
$711$	−1.42277e29	−0.161623
$712$	−2.61168e29	−0.292334
$713$	−1.09945e30	−1.21264
$714$	−2.81996e29	−0.306487
$715$	1.13018e30	1.21041
$716$	9.35590e29	0.987413
$717$	−6.95323e29	−0.723162
$718$	4.02968e29	0.413013
$719$	1.29783e30	1.31088	0.655440	−	0.755247i	$-0.272483\pi$
$719$	1.29783e30	1.31088	0.655440	+	0.755247i	$0.272483\pi$
$720$	8.76565e28	0.0872555
$721$	−1.28109e30	−1.25678
$722$	6.82073e29	0.659463
$723$	−1.00882e28	−0.00961306
$724$	2.84576e29	0.267266
$725$	−3.72442e29	−0.344754
$726$	−4.25777e29	−0.388461
$727$	−1.67396e30	−1.50534	−0.752669	−	0.658399i	$-0.771234\pi$
$727$	−1.67396e30	−1.50534	−0.752669	+	0.658399i	$0.771234\pi$
$728$	−6.54544e29	−0.580176
$729$	9.94890e28	0.0869233
$730$	1.37094e28	0.0118067
$731$	−6.72585e29	−0.570972
$732$	−2.67741e29	−0.224052
$733$	4.12599e29	0.340359	0.170179	−	0.985413i	$-0.445565\pi$
$733$	4.12599e29	0.340359	0.170179	+	0.985413i	$0.445565\pi$
$734$	−1.51573e28	−0.0123257
$735$	5.26531e28	0.0422092
$736$	3.72643e29	0.294494
$737$	1.66607e30	1.29803
$738$	−7.99693e29	−0.614231
$739$	1.73492e30	1.31375	0.656877	−	0.753998i	$-0.271877\pi$
$739$	1.73492e30	1.31375	0.656877	+	0.753998i	$0.271877\pi$
$740$	4.44215e29	0.331635
$741$	−3.03443e29	−0.223350
$742$	−9.71956e29	−0.705352
$743$	−1.36497e30	−0.976656	−0.488328	−	0.872660i	$-0.662393\pi$
$743$	−1.36497e30	−0.976656	−0.488328	+	0.872660i	$0.662393\pi$
$744$	−1.70936e29	−0.120592
$745$	−1.14296e30	−0.795042
$746$	1.60849e30	1.10322
$747$	−3.06722e29	−0.207434
$748$	−1.14393e30	−0.762837
$749$	5.04261e29	0.331586
$750$	4.57039e28	0.0296353
$751$	−1.35372e30	−0.865587	−0.432793	−	0.901493i	$-0.642472\pi$
$751$	−1.35372e30	−0.865587	−0.432793	+	0.901493i	$0.642472\pi$
$752$	−2.23898e29	−0.141177
$753$	−4.21646e29	−0.262181
$754$	3.65015e30	2.23826
$755$	1.54040e29	0.0931514
$756$	−6.25048e29	−0.372764
$757$	−8.02724e29	−0.472128	−0.236064	−	0.971738i	$-0.575857\pi$
$757$	−8.02724e29	−0.472128	−0.236064	+	0.971738i	$0.575857\pi$
$758$	2.33168e29	0.135252
$759$	2.01114e30	1.15054
$760$	−7.27399e28	−0.0410421
$761$	2.59098e29	0.144186	0.0720932	−	0.997398i	$-0.477032\pi$
$761$	2.59098e29	0.144186	0.0720932	+	0.997398i	$0.477032\pi$
$762$	−1.00401e30	−0.551075
$763$	−6.37857e29	−0.345315
$764$	−1.22413e30	−0.653654
$765$	6.85943e29	0.361279
$766$	−2.34882e30	−1.22024
$767$	2.08945e30	1.07073
$768$	5.79365e28	0.0292860
$769$	−9.50454e29	−0.473919	−0.236960	−	0.971519i	$-0.576151\pi$
$769$	−9.50454e29	−0.473919	−0.236960	+	0.971519i	$0.576151\pi$
$770$	−8.46803e29	−0.416514
$771$	1.40874e29	0.0683535
$772$	8.58631e28	0.0410984
$773$	3.15209e30	1.48838	0.744191	−	0.667967i	$-0.232835\pi$
$773$	3.15209e30	1.48838	0.744191	+	0.667967i	$0.232835\pi$
$774$	−6.53473e29	−0.304402
$775$	3.16796e29	0.145584
$776$	1.94068e29	0.0879846
$777$	−1.38846e30	−0.621030
$778$	−1.13160e30	−0.499352
$779$	6.63609e29	0.288914
$780$	−4.47924e29	−0.192403
$781$	3.78045e30	1.60217
$782$	2.91606e30	1.21934
$783$	3.48565e30	1.43809
$784$	−1.23700e29	−0.0503561
$785$	9.15355e29	0.367670
$786$	5.09345e29	0.201872
$787$	−1.06937e30	−0.418211	−0.209105	−	0.977893i	$-0.567055\pi$
$787$	−1.06937e30	−0.418211	−0.209105	+	0.977893i	$0.567055\pi$
$788$	−6.91449e29	−0.266830
$789$	−3.38726e28	−0.0128985
$790$	1.74281e29	0.0654885
$791$	3.67727e30	1.36355
$792$	−1.11142e30	−0.406691
$793$	−4.86311e30	−1.75609
$794$	−1.93236e29	−0.0688608
$795$	−6.65139e29	−0.233915
$796$	1.91517e30	0.664692
$797$	2.66578e30	0.913086	0.456543	−	0.889701i	$-0.349087\pi$
$797$	2.66578e30	0.913086	0.456543	+	0.889701i	$0.349087\pi$
$798$	2.27359e29	0.0768568
$799$	−1.75208e30	−0.584539
$800$	−1.07374e29	−0.0353553
$801$	−1.98565e30	−0.645301
$802$	1.78870e30	0.573730
$803$	−1.73826e29	−0.0550302
$804$	−6.60314e29	−0.206330
$805$	2.15864e30	0.665770
$806$	−3.10479e30	−0.945179
$807$	2.05782e30	0.618352
$808$	4.72725e29	0.140213
$809$	1.67414e30	0.490153	0.245077	−	0.969504i	$-0.421187\pi$
$809$	1.67414e30	0.490153	0.245077	+	0.969504i	$0.421187\pi$
$810$	4.26208e29	0.123177
$811$	−4.62583e30	−1.31969	−0.659843	−	0.751404i	$-0.729377\pi$
$811$	−4.62583e30	−1.31969	−0.659843	+	0.751404i	$0.729377\pi$
$812$	−2.73493e30	−0.770207
$813$	7.96509e29	0.221432
$814$	−5.63233e30	−1.54572
$815$	−1.13022e30	−0.306203
$816$	4.53374e29	0.121258
$817$	5.42271e29	0.143181
$818$	2.99988e30	0.781979
$819$	−4.97649e30	−1.28069
$820$	9.79579e29	0.248882
$821$	−2.81912e30	−0.707147	−0.353573	−	0.935407i	$-0.615034\pi$
$821$	−2.81912e30	−0.707147	−0.353573	+	0.935407i	$0.615034\pi$
$822$	4.48054e29	0.110963
$823$	−8.15621e29	−0.199430	−0.0997149	−	0.995016i	$-0.531793\pi$
$823$	−8.15621e29	−0.199430	−0.0997149	+	0.995016i	$0.531793\pi$
$824$	2.05964e30	0.497228
$825$	−5.79493e29	−0.138128
$826$	−1.56556e30	−0.368450
$827$	−5.27710e30	−1.22627	−0.613137	−	0.789977i	$-0.710093\pi$
$827$	−5.27710e30	−1.22627	−0.613137	+	0.789977i	$0.710093\pi$
$828$	2.83320e30	0.650068
$829$	−5.17029e30	−1.17137	−0.585683	−	0.810540i	$-0.699174\pi$
$829$	−5.17029e30	−1.17137	−0.585683	+	0.810540i	$0.699174\pi$
$830$	3.75717e29	0.0840507
$831$	−1.37052e30	−0.302744
$832$	1.05233e30	0.229539
$833$	−9.67999e29	−0.208498
$834$	1.56093e30	0.332002
$835$	−1.42600e30	−0.299509
$836$	9.22291e29	0.191294
$837$	−2.96487e30	−0.607279
$838$	2.65763e30	0.537567
$839$	−9.14574e30	−1.82692	−0.913458	−	0.406934i	$-0.866598\pi$
$839$	−9.14574e30	−1.82692	−0.913458	+	0.406934i	$0.866598\pi$
$840$	3.35614e29	0.0662076
$841$	1.01188e31	1.97139
$842$	2.13418e30	0.410633
$843$	−2.67529e30	−0.508371
$844$	−3.52814e30	−0.662140
$845$	−5.72312e30	−1.06081
$846$	−1.70230e30	−0.311635
$847$	5.79451e30	1.04771
$848$	1.56264e30	0.279063
$849$	3.13532e30	0.553033
$850$	−8.40240e29	−0.146388
$851$	1.43578e31	2.47074
$852$	−1.49831e30	−0.254674
$853$	9.89405e30	1.66115	0.830576	−	0.556906i	$-0.188011\pi$
$853$	9.89405e30	1.66115	0.830576	+	0.556906i	$0.188011\pi$
$854$	3.64376e30	0.604285
$855$	−5.53041e29	−0.0905968
$856$	−8.10714e29	−0.131188
$857$	5.52749e30	0.883546	0.441773	−	0.897127i	$-0.354350\pi$
$857$	5.52749e30	0.883546	0.441773	+	0.897127i	$0.354350\pi$
$858$	5.67936e30	0.896774
$859$	−3.34705e29	−0.0522076	−0.0261038	−	0.999659i	$-0.508310\pi$
$859$	−3.34705e29	−0.0522076	−0.0261038	+	0.999659i	$0.508310\pi$
$860$	8.00467e29	0.123342
$861$	−3.06182e30	−0.466065
$862$	−1.89712e30	−0.285278
$863$	−4.68654e30	−0.696208	−0.348104	−	0.937456i	$-0.613174\pi$
$863$	−4.68654e30	−0.696208	−0.348104	+	0.937456i	$0.613174\pi$
$864$	1.00491e30	0.147479
$865$	2.56625e30	0.372075
$866$	−6.46641e29	−0.0926244
$867$	2.36646e29	0.0334888
$868$	2.32631e30	0.325245
$869$	−2.20976e30	−0.305237
$870$	−1.87159e30	−0.255423
$871$	−1.19936e31	−1.61718
$872$	1.02550e30	0.136620
$873$	1.47550e30	0.194218
$874$	−2.35107e30	−0.305771
$875$	−6.21996e29	−0.0799287
$876$	6.88925e28	0.00874739
$877$	2.46570e30	0.309346	0.154673	−	0.987966i	$-0.450568\pi$
$877$	2.46570e30	0.309346	0.154673	+	0.987966i	$0.450568\pi$
$878$	−3.27498e30	−0.405991
$879$	−5.31170e29	−0.0650654
$880$	1.36143e30	0.164788
$881$	9.27878e30	1.10980	0.554899	−	0.831918i	$-0.312757\pi$
$881$	9.27878e30	1.10980	0.554899	+	0.831918i	$0.312757\pi$
$882$	−9.40492e29	−0.111157
$883$	1.09864e29	0.0128313	0.00641564	−	0.999979i	$-0.497958\pi$
$883$	1.09864e29	0.0128313	0.00641564	+	0.999979i	$0.497958\pi$
$884$	8.23484e30	0.950400
$885$	−1.07136e30	−0.122188
$886$	−7.46786e29	−0.0841670
$887$	9.09262e30	1.01272	0.506362	−	0.862321i	$-0.330990\pi$
$887$	9.09262e30	1.01272	0.506362	+	0.862321i	$0.330990\pi$
$888$	2.23227e30	0.245703
$889$	1.36638e31	1.48629
$890$	2.43231e30	0.261471
$891$	−5.40401e30	−0.574117
$892$	1.51734e29	0.0159313
$893$	1.41261e30	0.146583
$894$	−5.74359e30	−0.589033
$895$	−8.71337e30	−0.883169
$896$	−7.88474e29	−0.0789865
$897$	−1.44777e31	−1.43343
$898$	1.62918e30	0.159429
$899$	−1.29729e31	−1.25476
$900$	−8.16365e29	−0.0780437
$901$	1.22282e31	1.15545
$902$	−1.24204e31	−1.16002
$903$	−2.50198e30	−0.230974
$904$	−5.91205e30	−0.539472
$905$	−2.65032e30	−0.239050
$906$	7.74078e29	0.0690143
$907$	−4.70059e30	−0.414263	−0.207132	−	0.978313i	$-0.566413\pi$
$907$	−4.70059e30	−0.414263	−0.207132	+	0.978313i	$0.566413\pi$
$908$	−5.07033e30	−0.441707
$909$	3.59412e30	0.309508
$910$	6.09592e30	0.518925
$911$	1.05639e31	0.888960	0.444480	−	0.895789i	$-0.353388\pi$
$911$	1.05639e31	0.888960	0.444480	+	0.895789i	$0.353388\pi$
$912$	−3.65532e29	−0.0304074
$913$	−4.76383e30	−0.391754
$914$	−9.16402e30	−0.744991
$915$	2.49353e30	0.200398
$916$	−4.56489e30	−0.362684
$917$	−6.93181e30	−0.544463
$918$	7.86374e30	0.610634
$919$	2.15821e31	1.65684	0.828421	−	0.560105i	$-0.189239\pi$
$919$	2.15821e31	1.65684	0.828421	+	0.560105i	$0.189239\pi$
$920$	−3.47051e30	−0.263403
$921$	−4.91023e30	−0.368448
$922$	−1.36137e31	−1.00995
$923$	−2.72145e31	−1.99610
$924$	−4.25535e30	−0.308588
$925$	−4.13707e30	−0.296623
$926$	−1.32774e31	−0.941231
$927$	1.56594e31	1.09759
$928$	4.39702e30	0.304723
$929$	8.91027e30	0.610557	0.305278	−	0.952263i	$-0.401250\pi$
$929$	8.91027e30	0.610557	0.305278	+	0.952263i	$0.401250\pi$
$930$	1.59196e30	0.107860
$931$	7.80448e29	0.0522844
$932$	1.08587e29	0.00719300
$933$	−1.04088e31	−0.681780
$934$	5.14427e30	0.333182
$935$	1.06537e31	0.682302
$936$	8.00084e30	0.506687
$937$	8.67478e29	0.0543241	0.0271621	−	0.999631i	$-0.491353\pi$
$937$	8.67478e29	0.0543241	0.0271621	+	0.999631i	$0.491353\pi$
$938$	8.98639e30	0.556487
$939$	1.05351e31	0.645132
$940$	2.08521e30	0.126272
$941$	−1.58550e31	−0.949459	−0.474730	−	0.880132i	$-0.657454\pi$
$941$	−1.58550e31	−0.949459	−0.474730	+	0.880132i	$0.657454\pi$
$942$	4.59984e30	0.272401
$943$	3.16616e31	1.85422
$944$	2.51699e30	0.145772
$945$	5.82121e30	0.333410
$946$	−1.01494e31	−0.574886
$947$	−2.27081e31	−1.27206	−0.636028	−	0.771666i	$-0.719424\pi$
$947$	−2.27081e31	−1.27206	−0.636028	+	0.771666i	$0.719424\pi$
$948$	8.75795e29	0.0485193
$949$	1.25133e30	0.0685607
$950$	6.77443e29	0.0367092
$951$	6.06698e30	0.325145
$952$	−6.17008e30	−0.327041
$953$	−1.88217e31	−0.986696	−0.493348	−	0.869832i	$-0.664227\pi$
$953$	−1.88217e31	−0.986696	−0.493348	+	0.869832i	$0.664227\pi$
$954$	1.18807e31	0.616007
$955$	1.14006e31	0.584646
$956$	−1.52137e31	−0.771660
$957$	2.37305e31	1.19050
$958$	−1.26561e31	−0.628004
$959$	−6.09769e30	−0.299274
$960$	−5.39576e29	−0.0261942
$961$	−9.79081e30	−0.470136
$962$	4.05457e31	1.92578
$963$	−6.16385e30	−0.289585
$964$	−2.20730e29	−0.0102578
$965$	−7.99662e29	−0.0367595
$966$	1.08476e31	0.493258
$967$	1.59166e31	0.715934	0.357967	−	0.933734i	$-0.383470\pi$
$967$	1.59166e31	0.715934	0.357967	+	0.933734i	$0.383470\pi$
$968$	−9.31600e30	−0.414513
$969$	−2.86042e30	−0.125901
$970$	−1.80740e30	−0.0786958
$971$	−1.49572e31	−0.644239	−0.322119	−	0.946699i	$-0.604395\pi$
$971$	−1.49572e31	−0.644239	−0.322119	+	0.946699i	$0.604395\pi$
$972$	1.19315e31	0.508394
$973$	−2.12431e31	−0.895434
$974$	2.38818e31	0.995859
$975$	4.17162e30	0.172090
$976$	−5.85817e30	−0.239078
$977$	2.26547e31	0.914672	0.457336	−	0.889294i	$-0.348804\pi$
$977$	2.26547e31	0.914672	0.457336	+	0.889294i	$0.348804\pi$
$978$	−5.67959e30	−0.226861
$979$	−3.08400e31	−1.21870
$980$	1.15205e30	0.0450399
$981$	7.79687e30	0.301575
$982$	−2.72233e31	−1.04177
$983$	−7.38759e30	−0.279699	−0.139849	−	0.990173i	$-0.544662\pi$
$983$	−7.38759e30	−0.279699	−0.139849	+	0.990173i	$0.544662\pi$
$984$	4.92257e30	0.184393
$985$	6.43962e30	0.238660
$986$	3.44082e31	1.26170
$987$	−6.51765e30	−0.236462
$988$	−6.63933e30	−0.238329
$989$	2.58724e31	0.918916
$990$	1.03509e31	0.363756
$991$	1.82576e31	0.634849	0.317425	−	0.948284i	$-0.397182\pi$
$991$	1.82576e31	0.634849	0.317425	+	0.948284i	$0.397182\pi$
$992$	−3.74007e30	−0.128679
$993$	9.28295e30	0.316023
$994$	2.03909e31	0.686877
$995$	−1.78364e31	−0.594519
$996$	1.88805e30	0.0622717
$997$	−3.18289e31	−1.03878	−0.519389	−	0.854538i	$-0.673840\pi$
$997$	−3.18289e31	−1.03878	−0.519389	+	0.854538i	$0.673840\pi$
$998$	1.42134e31	0.459017
$999$	3.87185e31	1.23732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.a.b.1.2	✓	2
4.3	odd	2		80.22.a.d.1.1		2
5.2	odd	4		50.22.b.f.49.1		4
5.3	odd	4		50.22.b.f.49.4		4
5.4	even	2		50.22.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.a.b.1.2	✓	2	1.1	even	1	trivial
50.22.a.f.1.1		2	5.4	even	2
50.22.b.f.49.1		4	5.2	odd	4
50.22.b.f.49.4		4	5.3	odd	4
80.22.a.d.1.1		2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-1024.00 q^{2} +47924.0 q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} -4.90741e7 q^{6} +6.67863e8 q^{7} -1.07374e9 q^{8} -8.16365e9 q^{9} +1.00000e10 q^{10} -1.26793e11 q^{11} +5.02519e10 q^{12} +9.12750e11 q^{13} -6.83892e11 q^{14} -4.68008e11 q^{15} +1.09951e12 q^{16} +8.60406e12 q^{17} +8.35957e12 q^{18} -6.93702e12 q^{19} -1.02400e13 q^{20} +3.20066e13 q^{21} +1.29836e14 q^{22} -3.30974e14 q^{23} -5.14580e13 q^{24} +9.53674e13 q^{25} -9.34656e14 q^{26} -8.92536e14 q^{27} +7.00305e14 q^{28} -3.90534e15 q^{29} +4.79240e14 q^{30} +3.32185e15 q^{31} -1.12590e15 q^{32} -6.07642e15 q^{33} -8.81056e15 q^{34} -6.52210e15 q^{35} -8.56020e15 q^{36} -4.33804e16 q^{37} +7.10351e15 q^{38} +4.37426e16 q^{39} +1.04858e16 q^{40} -9.56620e16 q^{41} -3.27748e16 q^{42} -7.81706e16 q^{43} -1.32952e17 q^{44} +7.97231e16 q^{45} +3.38917e17 q^{46} -2.03634e17 q^{47} +5.26930e16 q^{48} -1.12505e17 q^{49} -9.76562e16 q^{50} +4.12341e17 q^{51} +9.57088e17 q^{52} +1.42121e18 q^{53} +9.13957e17 q^{54} +1.23821e18 q^{55} -7.17112e17 q^{56} -3.32449e17 q^{57} +3.99907e18 q^{58} +2.28919e18 q^{59} -4.90741e17 q^{60} -5.32798e18 q^{61} -3.40158e18 q^{62} -5.45220e18 q^{63} +1.15292e18 q^{64} -8.91357e18 q^{65} +6.22226e18 q^{66} -1.31401e19 q^{67} +9.02201e18 q^{68} -1.58616e19 q^{69} +6.67863e18 q^{70} -2.98159e19 q^{71} +8.76565e18 q^{72} +1.37094e18 q^{73} +4.44215e19 q^{74} +4.57039e18 q^{75} -7.27399e18 q^{76} -8.46803e19 q^{77} -4.47924e19 q^{78} +1.74281e19 q^{79} -1.07374e19 q^{80} +4.26208e19 q^{81} +9.79579e19 q^{82} +3.75717e19 q^{83} +3.35614e19 q^{84} -8.40240e19 q^{85} +8.00467e19 q^{86} -1.87159e20 q^{87} +1.36143e20 q^{88} +2.43231e20 q^{89} -8.16365e19 q^{90} +6.09592e20 q^{91} -3.47051e20 q^{92} +1.59196e20 q^{93} +2.08521e20 q^{94} +6.77443e19 q^{95} -5.39576e19 q^{96} -1.80740e20 q^{97} +1.15205e20 q^{98} +1.03509e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2048 q^{2} - 126692 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 129732608 q^{6} - 292598684 q^{7} - 2147483648 q^{8} + 11866737826 q^{9} + 20000000000 q^{10} - 41326831776 q^{11} - 132846190592 q^{12}+ \cdots + 27\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 2048 * q^2 - 126692 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 129732608 * q^6 - 292598684 * q^7 - 2147483648 * q^8 + 11866737826 * q^9 + 20000000000 * q^10 - 41326831776 * q^11 - 132846190592 * q^12 + 1887051472228 * q^13 + 299621052416 * q^14 + 1237226562500 * q^15 + 2199023255552 * q^16 - 3100413932364 * q^17 - 12151539533824 * q^18 + 7175794652440 * q^19 - 20480000000000 * q^20 + 199718603894264 * q^21 + 42318675738624 * q^22 - 357559990100052 * q^23 + 136034499166208 * q^24 + 190734863281250 * q^25 - 1932340707561472 * q^26 - 2563616231988920 * q^27 - 306811957673984 * q^28 - 2454584202185940 * q^29 - 1266920000000000 * q^30 - 4310677151243336 * q^31 - 2251799813685248 * q^32 - 21000167846983104 * q^33 + 3174823866740736 * q^34 + 2857409023437500 * q^35 + 12443176482635776 * q^36 - 32389201650205724 * q^37 - 7348013724098560 * q^38 - 126386038156081288 * q^39 + 20971520000000000 * q^40 - 16298035212712116 * q^41 - 204511850387726336 * q^42 - 161845702253479412 * q^43 - 43334323956350976 * q^44 - 115886111582031250 * q^45 + 366141429862453248 * q^46 + 153492993930726996 * q^47 - 139299327146196992 * q^48 + 251436016683357114 * q^49 - 195312500000000000 * q^50 + 2456129297437264344 * q^51 + 1978716884542947328 * q^52 + 604198357317820308 * q^53 + 2625143021556654080 * q^54 + 403582341562500000 * q^55 + 314175444658159616 * q^56 - 2796771718696561840 * q^57 + 2513494223038402560 * q^58 + 3110197357974672120 * q^59 + 1297326080000000000 * q^60 - 791142209760451676 * q^61 + 4414133402873176064 * q^62 - 24690614624666969692 * q^63 + 2305843009213693952 * q^64 - 18428237033476562500 * q^65 + 21504171875310698496 * q^66 - 5111819523383561564 * q^67 - 3251019639542513664 * q^68 - 11219196977510717208 * q^69 - 2925986840000000000 * q^70 - 82388741313238482456 * q^71 - 12741812718219034624 * q^72 + 10657918464992348548 * q^73 + 33166542489810661376 * q^74 - 12082290649414062500 * q^75 + 7524366053476925440 * q^76 - 166767237207340703808 * q^77 + 129419303071827238912 * q^78 + 28314166125451369360 * q^79 - 21474836480000000000 * q^80 + 124893157714537187242 * q^81 + 16689188057817206784 * q^82 - 10427725705926651732 * q^83 + 209420134797031768064 * q^84 + 30277479808242187500 * q^85 + 165729999107562917888 * q^86 - 440484049640705943960 * q^87 + 44374347731303399424 * q^88 + 478501472814113520180 * q^89 + 118667378260000000000 * q^90 - 326187611445407942776 * q^91 - 374928824179152125952 * q^92 + 1491957513759228855056 * q^93 - 157176825785064443904 * q^94 - 70076119652734375000 * q^95 + 142642510997705719808 * q^96 + 545226897779926992196 * q^97 - 257470481083757684736 * q^98 + 2747011580657571215712 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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