LMFDB - Embedded newform 10.28.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,28,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, 28, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 28 $
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:	$46.1855574838$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{711649}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 177912 $ x^2 - x - 177912
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$422.296$ 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)

$f(q)$	$=$	\(q+8192.00 q^{2} -5.48964e6 q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} -4.49712e10 q^{6} -8.15752e10 q^{7} +5.49756e11 q^{8} +2.25106e13 q^{9} -1.00000e13 q^{10} +1.33950e13 q^{11} -3.68404e14 q^{12} +5.64686e14 q^{13} -6.68264e14 q^{14} +6.70123e15 q^{15} +4.50360e15 q^{16} -1.28911e16 q^{17} +1.84407e17 q^{18} +3.07151e17 q^{19} -8.19200e16 q^{20} +4.47819e17 q^{21} +1.09732e17 q^{22} -1.99871e18 q^{23} -3.01796e18 q^{24} +1.49012e18 q^{25} +4.62590e18 q^{26} -8.17133e19 q^{27} -5.47442e18 q^{28} -8.80094e19 q^{29} +5.48964e19 q^{30} +2.22760e20 q^{31} +3.68935e19 q^{32} -7.35337e19 q^{33} -1.05604e20 q^{34} +9.95791e19 q^{35} +1.51066e21 q^{36} -1.61882e21 q^{37} +2.51618e21 q^{38} -3.09992e21 q^{39} -6.71089e20 q^{40} -9.68899e21 q^{41} +3.66853e21 q^{42} +9.33483e21 q^{43} +8.98922e20 q^{44} -2.74787e22 q^{45} -1.63734e22 q^{46} +1.20564e22 q^{47} -2.47232e22 q^{48} -5.90579e22 q^{49} +1.22070e22 q^{50} +7.07676e22 q^{51} +3.78954e22 q^{52} -8.75697e21 q^{53} -6.69395e23 q^{54} -1.63513e22 q^{55} -4.48464e22 q^{56} -1.68615e24 q^{57} -7.20973e23 q^{58} +3.03895e23 q^{59} +4.49712e23 q^{60} +1.15214e24 q^{61} +1.82485e24 q^{62} -1.83631e24 q^{63} +3.02231e23 q^{64} -6.89313e23 q^{65} -6.02388e23 q^{66} -1.86933e24 q^{67} -8.65108e23 q^{68} +1.09722e25 q^{69} +8.15752e23 q^{70} -8.93880e24 q^{71} +1.23753e25 q^{72} -2.18673e25 q^{73} -1.32614e25 q^{74} -8.18021e24 q^{75} +2.06126e25 q^{76} -1.09270e24 q^{77} -2.53946e25 q^{78} +1.05795e25 q^{79} -5.49756e24 q^{80} +2.76920e26 q^{81} -7.93722e25 q^{82} +2.25868e25 q^{83} +3.00526e25 q^{84} +1.57362e25 q^{85} +7.64710e25 q^{86} +4.83140e26 q^{87} +7.36397e24 q^{88} -1.78891e26 q^{89} -2.25106e26 q^{90} -4.60643e25 q^{91} -1.34131e26 q^{92} -1.22287e27 q^{93} +9.87663e25 q^{94} -3.74941e26 q^{95} -2.02532e26 q^{96} +8.87997e26 q^{97} -4.83802e26 q^{98} +3.01529e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16384 q^{2} - 4702956 q^{3} + 134217728 q^{4} - 2441406250 q^{5} - 38526615552 q^{6} - 57185041508 q^{7} + 1099511627776 q^{8} + 15503869642194 q^{9} - 20000000000000 q^{10} + 169851430699104 q^{11}+ \cdots - 79\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 16384 * q^2 - 4702956 * q^3 + 134217728 * q^4 - 2441406250 * q^5 - 38526615552 * q^6 - 57185041508 * q^7 + 1099511627776 * q^8 + 15503869642194 * q^9 - 20000000000000 * q^10 + 169851430699104 * q^11 - 315610034601984 * q^12 - 1039094991262796 * q^13 - 468459860033536 * q^14 + 5740913085937500 * q^15 + 9007199254740992 * q^16 - 50445145609767948 * q^17 + 127007700108853248 * q^18 + 446863730094123400 * q^19 - 163840000000000000 * q^20 + 467006108827766424 * q^21 + 1391422920287059968 * q^22 - 6647307932323726956 * q^23 - 2585477403459452928 * q^24 + 2980232238769531250 * q^25 - 8512266168424824832 * q^26 - 93224365905702240360 * q^27 - 3837623173394726912 * q^28 - 47997399844470169380 * q^29 + 47029560000000000000 * q^30 + 33574730315678836744 * q^31 + 73786976294838206464 * q^32 + 49548682554417655488 * q^33 - 413246632835219030016 * q^34 + 69805958872070312500 * q^35 + 1040447079291725807616 * q^36 - 1349929187895125662508 * q^37 + 3660707676931058892800 * q^38 - 4361597048598395237112 * q^39 - 1342177280000000000000 * q^40 - 1182957469635679236756 * q^41 + 3825714043517062545408 * q^42 - 3918269768563513059836 * q^43 + 11398536562991595257856 * q^44 - 18925622121818847656250 * q^45 - 54454746581595971223552 * q^46 - 32027326481691215437428 * q^47 - 21180230889139838386176 * q^48 - 124175335159331248585254 * q^49 + 24414062500000000000000 * q^50 + 41224319062757865329544 * q^51 - 69732484451736165023744 * q^52 - 338645206816246511641596 * q^53 - 763694005499512753029120 * q^54 - 207338172240117187500000 * q^55 - 31437809036449602863104 * q^56 - 1576241472518493550388400 * q^57 - 393194699525899627560960 * q^58 - 343725486206796714375960 * q^59 + 385266155520000000000000 * q^60 + 228063235764015707336884 * q^61 + 275044190746041030606848 * q^62 - 2007200379545784196719876 * q^63 + 604462909807314587353088 * q^64 + 1268426503006342773437500 * q^65 + 405902807485789433757696 * q^66 - 3973383158722681594905428 * q^67 - 3385316416186114293891072 * q^68 + 7315190141287874962404168 * q^69 + 571850415080000000000000 * q^70 - 2414614414513749020227176 * q^71 + 8523342473557817815990272 * q^72 - 12422599244545503708131996 * q^73 - 11058619907236869427265536 * q^74 - 7007950544357299804687500 * q^75 + 29988517289419234449817600 * q^76 + 2723296993852627128197184 * q^77 - 35730203022118053782421504 * q^78 + 14197635994550588853149680 * q^79 - 10995116277760000000000000 * q^80 + 321295031247975610705880202 * q^81 - 9690787591255484307505152 * q^82 + 113637606793167338211169284 * q^83 + 31340249444491776371982336 * q^84 + 61578546886923764648437500 * q^85 - 32098465944072298986176512 * q^86 + 514617127953054957365529240 * q^87 + 93376811524027148352356352 * q^88 + 139217760348347863809112020 * q^89 - 155038696421940000000000000 * q^90 - 85180767378984078493944616 * q^91 - 446093283996434196263337984 * q^92 - 1371703352271155402043821232 * q^93 - 262367858538014436863410176 * q^94 - 545487951775052978515625000 * q^95 - 173508451443833556059553792 * q^96 + 1199842643269565667896244292 * q^97 - 1017244345625241588410400768 * q^98 - 794717627905923529800830112 * 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 $

$2$	8192.00	0.707107
$2$	8192.00	0.707107
$3$	−5.48964e6	−1.98796	−0.993979	−	0.109571i	$-0.965052\pi$
$3$	−5.48964e6	−1.98796	−0.993979	+	0.109571i	$0.965052\pi$
$4$	6.71089e7	0.500000
$5$	−1.22070e9	−0.447214
$5$	−1.22070e9	−0.447214
$6$	−4.49712e10	−1.40570
$7$	−8.15752e10	−0.318225	−0.159113	−	0.987260i	$-0.550863\pi$
$7$	−8.15752e10	−0.318225	−0.159113	+	0.987260i	$0.550863\pi$
$8$	5.49756e11	0.353553
$9$	2.25106e13	2.95198
$10$	−1.00000e13	−0.316228
$11$	1.33950e13	0.116988	0.0584939	−	0.998288i	$-0.481370\pi$
$11$	1.33950e13	0.116988	0.0584939	+	0.998288i	$0.481370\pi$
$12$	−3.68404e14	−0.993979
$13$	5.64686e14	0.517096	0.258548	−	0.965998i	$-0.416756\pi$
$13$	5.64686e14	0.517096	0.258548	+	0.965998i	$0.416756\pi$
$14$	−6.68264e14	−0.225019
$15$	6.70123e15	0.889042
$16$	4.50360e15	0.250000
$17$	−1.28911e16	−0.315668	−0.157834	−	0.987466i	$-0.550451\pi$
$17$	−1.28911e16	−0.315668	−0.157834	+	0.987466i	$0.550451\pi$
$18$	1.84407e17	2.08736
$19$	3.07151e17	1.67563	0.837816	−	0.545952i	$-0.183832\pi$
$19$	3.07151e17	1.67563	0.837816	+	0.545952i	$0.183832\pi$
$20$	−8.19200e16	−0.223607
$21$	4.47819e17	0.632618
$22$	1.09732e17	0.0827229
$23$	−1.99871e18	−0.826843	−0.413422	−	0.910540i	$-0.635666\pi$
$23$	−1.99871e18	−0.826843	−0.413422	+	0.910540i	$0.635666\pi$
$24$	−3.01796e18	−0.702849
$25$	1.49012e18	0.200000
$26$	4.62590e18	0.365642
$27$	−8.17133e19	−3.88045
$28$	−5.47442e18	−0.159113
$29$	−8.80094e19	−1.59278	−0.796390	−	0.604783i	$-0.793260\pi$
$29$	−8.80094e19	−1.59278	−0.796390	+	0.604783i	$0.793260\pi$
$30$	5.48964e19	0.628648
$31$	2.22760e20	1.63853	0.819265	−	0.573415i	$-0.194382\pi$
$31$	2.22760e20	1.63853	0.819265	+	0.573415i	$0.194382\pi$
$32$	3.68935e19	0.176777
$33$	−7.35337e19	−0.232567
$34$	−1.05604e20	−0.223211
$35$	9.95791e19	0.142315
$36$	1.51066e21	1.47599
$37$	−1.61882e21	−1.09264	−0.546319	−	0.837577i	$-0.683971\pi$
$37$	−1.61882e21	−1.09264	−0.546319	+	0.837577i	$0.683971\pi$
$38$	2.51618e21	1.18485
$39$	−3.09992e21	−1.02797
$40$	−6.71089e20	−0.158114
$41$	−9.68899e21	−1.63567	−0.817837	−	0.575450i	$-0.804827\pi$
$41$	−9.68899e21	−1.63567	−0.817837	+	0.575450i	$0.804827\pi$
$42$	3.66853e21	0.447329
$43$	9.33483e21	0.828481	0.414240	−	0.910167i	$-0.364047\pi$
$43$	9.33483e21	0.828481	0.414240	+	0.910167i	$0.364047\pi$
$44$	8.98922e20	0.0584939
$45$	−2.74787e22	−1.32016
$46$	−1.63734e22	−0.584667
$47$	1.20564e22	0.322031	0.161016	−	0.986952i	$-0.448523\pi$
$47$	1.20564e22	0.322031	0.161016	+	0.986952i	$0.448523\pi$
$48$	−2.47232e22	−0.496990
$49$	−5.90579e22	−0.898733
$50$	1.22070e22	0.141421
$51$	7.07676e22	0.627534
$52$	3.78954e22	0.258548
$53$	−8.75697e21	−0.0461987	−0.0230993	−	0.999733i	$-0.507353\pi$
$53$	−8.75697e21	−0.0461987	−0.0230993	+	0.999733i	$0.507353\pi$
$54$	−6.69395e23	−2.74389
$55$	−1.63513e22	−0.0523186
$56$	−4.48464e22	−0.112510
$57$	−1.68615e24	−3.33109
$58$	−7.20973e23	−1.12627
$59$	3.03895e23	0.376896	0.188448	−	0.982083i	$-0.439654\pi$
$59$	3.03895e23	0.376896	0.188448	+	0.982083i	$0.439654\pi$
$60$	4.49712e23	0.444521
$61$	1.15214e24	0.911070	0.455535	−	0.890218i	$-0.349448\pi$
$61$	1.15214e24	0.911070	0.455535	+	0.890218i	$0.349448\pi$
$62$	1.82485e24	1.15862
$63$	−1.83631e24	−0.939393
$64$	3.02231e23	0.125000
$65$	−6.89313e23	−0.231253
$66$	−6.02388e23	−0.164450
$67$	−1.86933e24	−0.416559	−0.208280	−	0.978069i	$-0.566786\pi$
$67$	−1.86933e24	−0.416559	−0.208280	+	0.978069i	$0.566786\pi$
$68$	−8.65108e23	−0.157834
$69$	1.09722e25	1.64373
$70$	8.15752e23	0.100632
$71$	−8.93880e24	−0.910524	−0.455262	−	0.890357i	$-0.650454\pi$
$71$	−8.93880e24	−0.910524	−0.455262	+	0.890357i	$0.650454\pi$
$72$	1.23753e25	1.04368
$73$	−2.18673e25	−1.53086	−0.765432	−	0.643517i	$-0.777475\pi$
$73$	−2.18673e25	−1.53086	−0.765432	+	0.643517i	$0.777475\pi$
$74$	−1.32614e25	−0.772612
$75$	−8.18021e24	−0.397592
$76$	2.06126e25	0.837816
$77$	−1.09270e24	−0.0372285
$78$	−2.53946e25	−0.726882
$79$	1.05795e25	0.254975	0.127488	−	0.991840i	$-0.459309\pi$
$79$	1.05795e25	0.254975	0.127488	+	0.991840i	$0.459309\pi$
$80$	−5.49756e24	−0.111803
$81$	2.76920e26	4.76219
$82$	−7.93722e25	−1.15660
$83$	2.25868e25	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$83$	2.25868e25	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$84$	3.00526e25	0.316309
$85$	1.57362e25	0.141171
$86$	7.64710e25	0.585824
$87$	4.83140e26	3.16638
$88$	7.36397e24	0.0413615
$89$	−1.78891e26	−0.862626	−0.431313	−	0.902202i	$-0.641950\pi$
$89$	−1.78891e26	−0.862626	−0.431313	+	0.902202i	$0.641950\pi$
$90$	−2.25106e26	−0.933497
$91$	−4.60643e25	−0.164553
$92$	−1.34131e26	−0.413422
$93$	−1.22287e27	−3.25733
$94$	9.87663e25	0.227710
$95$	−3.74941e26	−0.749366
$96$	−2.02532e26	−0.351425
$97$	8.87997e26	1.33966	0.669828	−	0.742517i	$-0.266368\pi$
$97$	8.87997e26	1.33966	0.669828	+	0.742517i	$0.266368\pi$
$98$	−4.83802e26	−0.635500
$99$	3.01529e26	0.345346
$100$	1.00000e26	0.100000
$101$	5.69733e26	0.498119	0.249059	−	0.968488i	$-0.419879\pi$
$101$	5.69733e26	0.498119	0.249059	+	0.968488i	$0.419879\pi$
$102$	5.79728e26	0.443733
$103$	−1.77162e27	−1.18869	−0.594343	−	0.804212i	$-0.702588\pi$
$103$	−1.77162e27	−1.18869	−0.594343	+	0.804212i	$0.702588\pi$
$104$	3.10439e26	0.182821
$105$	−5.46654e26	−0.282915
$106$	−7.17371e25	−0.0326674
$107$	−2.46061e27	−0.987102	−0.493551	−	0.869717i	$-0.664301\pi$
$107$	−2.46061e27	−0.987102	−0.493551	+	0.869717i	$0.664301\pi$
$108$	−5.48369e27	−1.94022
$109$	3.19335e27	0.997674	0.498837	−	0.866696i	$-0.333761\pi$
$109$	3.19335e27	0.997674	0.498837	+	0.866696i	$0.333761\pi$
$110$	−1.33950e26	−0.0369948
$111$	8.88677e27	2.17212
$112$	−3.67382e26	−0.0795563
$113$	−7.75073e26	−0.148862	−0.0744310	−	0.997226i	$-0.523714\pi$
$113$	−7.75073e26	−0.148862	−0.0744310	+	0.997226i	$0.523714\pi$
$114$	−1.38130e28	−2.35543
$115$	2.43983e27	0.369776
$116$	−5.90621e27	−0.796390
$117$	1.27114e28	1.52646
$118$	2.48951e27	0.266506
$119$	1.05159e27	0.100453
$120$	3.68404e27	0.314324
$121$	−1.29306e28	−0.986314
$122$	9.43831e27	0.644224
$123$	5.31891e28	3.25165
$124$	1.49492e28	0.819265
$125$	−1.81899e27	−0.0894427
$126$	−1.50430e28	−0.664251
$127$	1.11798e28	0.443695	0.221848	−	0.975081i	$-0.428791\pi$
$127$	1.11798e28	0.443695	0.221848	+	0.975081i	$0.428791\pi$
$128$	2.47588e27	0.0883883
$129$	−5.12449e28	−1.64699
$130$	−5.64686e27	−0.163520
$131$	8.48344e27	0.221518	0.110759	−	0.993847i	$-0.464672\pi$
$131$	8.48344e27	0.221518	0.110759	+	0.993847i	$0.464672\pi$
$132$	−4.93476e27	−0.116283
$133$	−2.50559e28	−0.533228
$134$	−1.53136e28	−0.294552
$135$	9.97477e28	1.73539
$136$	−7.08696e27	−0.111605
$137$	−8.14420e28	−1.16177	−0.580886	−	0.813985i	$-0.697294\pi$
$137$	−8.14420e28	−1.16177	−0.580886	+	0.813985i	$0.697294\pi$
$138$	8.98842e28	1.16229
$139$	−4.14318e28	−0.485997	−0.242999	−	0.970027i	$-0.578131\pi$
$139$	−4.14318e28	−0.485997	−0.242999	+	0.970027i	$0.578131\pi$
$140$	6.68264e27	0.0711573
$141$	−6.61855e28	−0.640184
$142$	−7.32267e28	−0.643838
$143$	7.56395e27	0.0604940
$144$	1.01379e29	0.737994
$145$	1.07433e29	0.712313
$146$	−1.79137e29	−1.08248
$147$	3.24207e29	1.78664
$148$	−1.08637e29	−0.546319
$149$	−2.60623e29	−1.19674	−0.598368	−	0.801221i	$-0.704184\pi$
$149$	−2.60623e29	−1.19674	−0.598368	+	0.801221i	$0.704184\pi$
$150$	−6.70123e28	−0.281140
$151$	−2.46658e29	−0.946034	−0.473017	−	0.881053i	$-0.656835\pi$
$151$	−2.46658e29	−0.946034	−0.473017	+	0.881053i	$0.656835\pi$
$152$	1.68858e29	0.592426
$153$	−2.90187e29	−0.931843
$154$	−8.95138e27	−0.0263245
$155$	−2.71924e29	−0.732773
$156$	−2.08032e29	−0.513983
$157$	−6.53188e29	−1.48045	−0.740223	−	0.672361i	$-0.765280\pi$
$157$	−6.53188e29	−1.48045	−0.740223	+	0.672361i	$0.765280\pi$
$158$	8.66671e28	0.180295
$159$	4.80726e28	0.0918410
$160$	−4.50360e28	−0.0790569
$161$	1.63045e29	0.263122
$162$	2.26853e30	3.36738
$163$	−4.95480e29	−0.676851	−0.338426	−	0.940993i	$-0.609894\pi$
$163$	−4.95480e29	−0.676851	−0.338426	+	0.940993i	$0.609894\pi$
$164$	−6.50217e29	−0.817837
$165$	8.97628e28	0.104007
$166$	1.85031e29	0.197600
$167$	−3.99121e29	−0.393036	−0.196518	−	0.980500i	$-0.562963\pi$
$167$	−3.99121e29	−0.393036	−0.196518	+	0.980500i	$0.562963\pi$
$168$	2.46191e29	0.223664
$169$	−8.73663e29	−0.732611
$170$	1.28911e29	0.0998228
$171$	6.91416e30	4.94643
$172$	6.26450e29	0.414240
$173$	−1.45903e30	−0.892160	−0.446080	−	0.894993i	$-0.647180\pi$
$173$	−1.45903e30	−0.892160	−0.446080	+	0.894993i	$0.647180\pi$
$174$	3.95788e30	2.23897
$175$	−1.21556e29	−0.0636450
$176$	6.03256e28	0.0292470
$177$	−1.66828e30	−0.749254
$178$	−1.46547e30	−0.609969
$179$	3.95662e29	0.152689	0.0763446	−	0.997081i	$-0.475675\pi$
$179$	3.95662e29	0.152689	0.0763446	+	0.997081i	$0.475675\pi$
$180$	−1.84407e30	−0.660082
$181$	−1.52183e30	−0.505481	−0.252740	−	0.967534i	$-0.581332\pi$
$181$	−1.52183e30	−0.505481	−0.252740	+	0.967534i	$0.581332\pi$
$182$	−3.77359e29	−0.116357
$183$	−6.32483e30	−1.81117
$184$	−1.09880e30	−0.292333
$185$	1.97610e30	0.488643
$186$	−1.00178e31	−2.30328
$187$	−1.72676e29	−0.0369293
$188$	8.09094e29	0.161016
$189$	6.66578e30	1.23486
$190$	−3.07151e30	−0.529882
$191$	2.06556e29	0.0331961	0.0165980	−	0.999862i	$-0.494716\pi$
$191$	2.06556e29	0.0331961	0.0165980	+	0.999862i	$0.494716\pi$
$192$	−1.65914e30	−0.248495
$193$	8.12733e30	1.13481	0.567407	−	0.823438i	$-0.307947\pi$
$193$	8.12733e30	1.13481	0.567407	+	0.823438i	$0.307947\pi$
$194$	7.27447e30	0.947279
$195$	3.78409e30	0.459720
$196$	−3.96331e30	−0.449366
$197$	−1.15879e31	−1.22662	−0.613311	−	0.789841i	$-0.710163\pi$
$197$	−1.15879e31	−1.22662	−0.613311	+	0.789841i	$0.710163\pi$
$198$	2.47012e30	0.244196
$199$	−1.61914e31	−1.49543	−0.747717	−	0.664018i	$-0.768850\pi$
$199$	−1.61914e31	−1.49543	−0.747717	+	0.664018i	$0.768850\pi$
$200$	8.19200e29	0.0707107
$201$	1.02620e31	0.828103
$202$	4.66725e30	0.352223
$203$	7.17938e30	0.506863
$204$	4.74913e30	0.313767
$205$	1.18274e31	0.731495
$206$	−1.45131e31	−0.840528
$207$	−4.49921e31	−2.44082
$208$	2.54312e30	0.129274
$209$	4.11429e30	0.196029
$210$	−4.47819e30	−0.200051
$211$	−8.13808e30	−0.340964	−0.170482	−	0.985361i	$-0.554532\pi$
$211$	−8.13808e30	−0.340964	−0.170482	+	0.985361i	$0.554532\pi$
$212$	−5.87670e29	−0.0230993
$213$	4.90708e31	1.81008
$214$	−2.01573e31	−0.697986
$215$	−1.13951e31	−0.370508
$216$	−4.49224e31	−1.37195
$217$	−1.81717e31	−0.521422
$218$	2.61599e31	0.705462
$219$	1.20044e32	3.04329
$220$	−1.09732e30	−0.0261593
$221$	−7.27943e30	−0.163231
$222$	7.28004e31	1.53592
$223$	−4.12421e31	−0.818890	−0.409445	−	0.912335i	$-0.634278\pi$
$223$	−4.12421e31	−0.818890	−0.409445	+	0.912335i	$0.634278\pi$
$224$	−3.00959e30	−0.0562548
$225$	3.35434e31	0.590395
$226$	−6.34940e30	−0.105261
$227$	8.27912e31	1.29311	0.646555	−	0.762868i	$-0.276209\pi$
$227$	8.27912e31	1.29311	0.646555	+	0.762868i	$0.276209\pi$
$228$	−1.13156e32	−1.66554
$229$	9.00491e31	1.24940	0.624698	−	0.780866i	$-0.285222\pi$
$229$	9.00491e31	1.24940	0.624698	+	0.780866i	$0.285222\pi$
$230$	1.99871e31	0.261471
$231$	5.99852e30	0.0740087
$232$	−4.83837e31	−0.563133
$233$	3.39840e31	0.373224	0.186612	−	0.982434i	$-0.440249\pi$
$233$	3.39840e31	0.373224	0.186612	+	0.982434i	$0.440249\pi$
$234$	1.04132e32	1.07937
$235$	−1.47173e31	−0.144017
$236$	2.03941e31	0.188448
$237$	−5.80775e31	−0.506880
$238$	8.61467e30	0.0710313
$239$	−1.37775e32	−1.07349	−0.536747	−	0.843743i	$-0.680347\pi$
$239$	−1.37775e32	−1.07349	−0.536747	+	0.843743i	$0.680347\pi$
$240$	3.01796e31	0.222260
$241$	−8.67658e31	−0.604114	−0.302057	−	0.953290i	$-0.597673\pi$
$241$	−8.67658e31	−0.604114	−0.302057	+	0.953290i	$0.597673\pi$
$242$	−1.05927e32	−0.697429
$243$	−8.97081e32	−5.58659
$244$	7.73187e31	0.455535
$245$	7.20921e31	0.401926
$246$	4.35725e32	2.29926
$247$	1.73444e32	0.866464
$248$	1.22464e32	0.579308
$249$	−1.23994e32	−0.555531
$250$	−1.49012e31	−0.0632456
$251$	4.76708e32	1.91716	0.958578	−	0.284829i	$-0.0919367\pi$
$251$	4.76708e32	1.91716	0.958578	+	0.284829i	$0.0919367\pi$
$252$	−1.23232e32	−0.469697
$253$	−2.67726e31	−0.0967307
$254$	9.15852e31	0.313740
$255$	−8.63862e31	−0.280642
$256$	2.02824e31	0.0625000
$257$	3.36363e32	0.983357	0.491678	−	0.870777i	$-0.336384\pi$
$257$	3.36363e32	0.983357	0.491678	+	0.870777i	$0.336384\pi$
$258$	−4.19798e32	−1.16459
$259$	1.32056e32	0.347705
$260$	−4.62590e31	−0.115626
$261$	−1.98114e33	−4.70185
$262$	6.94964e31	0.156637
$263$	−1.96857e32	−0.421453	−0.210726	−	0.977545i	$-0.567583\pi$
$263$	−1.96857e32	−0.421453	−0.210726	+	0.977545i	$0.567583\pi$
$264$	−4.04256e31	−0.0822248
$265$	1.06897e31	0.0206607
$266$	−2.05258e32	−0.377049
$267$	9.82046e32	1.71486
$268$	−1.25449e32	−0.208280
$269$	9.12489e32	1.44069	0.720347	−	0.693613i	$-0.243982\pi$
$269$	9.12489e32	1.44069	0.720347	+	0.693613i	$0.243982\pi$
$270$	8.17133e32	1.22711
$271$	3.57579e32	0.510841	0.255421	−	0.966830i	$-0.417786\pi$
$271$	3.57579e32	0.510841	0.255421	+	0.966830i	$0.417786\pi$
$272$	−5.80564e31	−0.0789169
$273$	2.52877e32	0.327125
$274$	−6.67173e32	−0.821496
$275$	1.99601e31	0.0233976
$276$	7.36331e32	0.821865
$277$	−1.49389e33	−1.58797	−0.793986	−	0.607936i	$-0.791998\pi$
$277$	−1.49389e33	−1.58797	−0.793986	+	0.607936i	$0.791998\pi$
$278$	−3.39409e32	−0.343652
$279$	5.01446e33	4.83690
$280$	5.47442e31	0.0503158
$281$	−6.43291e32	−0.563472	−0.281736	−	0.959492i	$-0.590910\pi$
$281$	−6.43291e32	−0.563472	−0.281736	+	0.959492i	$0.590910\pi$
$282$	−5.42192e32	−0.452679
$283$	4.79228e32	0.381439	0.190720	−	0.981645i	$-0.438918\pi$
$283$	4.79228e32	0.381439	0.190720	+	0.981645i	$0.438918\pi$
$284$	−5.99873e32	−0.455262
$285$	2.05829e33	1.48971
$286$	6.19639e31	0.0427757
$287$	7.90381e32	0.520512
$288$	8.30494e32	0.521841
$289$	−1.50153e33	−0.900354
$290$	8.80094e32	0.503682
$291$	−4.87479e33	−2.66318
$292$	−1.46749e33	−0.765432
$293$	−3.27376e32	−0.163055	−0.0815275	−	0.996671i	$-0.525980\pi$
$293$	−3.27376e32	−0.163055	−0.0815275	+	0.996671i	$0.525980\pi$
$294$	2.65590e33	1.26335
$295$	−3.70966e32	−0.168553
$296$	−8.89958e32	−0.386306
$297$	−1.09455e33	−0.453965
$298$	−2.13503e33	−0.846221
$299$	−1.12864e33	−0.427558
$300$	−5.48964e32	−0.198796
$301$	−7.61491e32	−0.263643
$302$	−2.02062e33	−0.668947
$303$	−3.12763e33	−0.990239
$304$	1.38329e33	0.418908
$305$	−1.40642e33	−0.407443
$306$	−2.37721e33	−0.658913
$307$	8.73502e32	0.231684	0.115842	−	0.993268i	$-0.463043\pi$
$307$	8.73502e32	0.231684	0.115842	+	0.993268i	$0.463043\pi$
$308$	−7.33297e31	−0.0186142
$309$	9.72554e33	2.36306
$310$	−2.22760e33	−0.518149
$311$	3.78077e33	0.842005	0.421002	−	0.907059i	$-0.361678\pi$
$311$	3.78077e33	0.842005	0.421002	+	0.907059i	$0.361678\pi$
$312$	−1.70420e33	−0.363441
$313$	−1.46656e33	−0.299537	−0.149769	−	0.988721i	$-0.547853\pi$
$313$	−1.46656e33	−0.299537	−0.149769	+	0.988721i	$0.547853\pi$
$314$	−5.35091e33	−1.04683
$315$	2.24158e33	0.420110
$316$	7.09976e32	0.127488
$317$	−7.26388e31	−0.0124988	−0.00624940	−	0.999980i	$-0.501989\pi$
$317$	−7.26388e31	−0.0124988	−0.00624940	+	0.999980i	$0.501989\pi$
$318$	3.93811e32	0.0649414
$319$	−1.17888e33	−0.186336
$320$	−3.68935e32	−0.0559017
$321$	1.35079e34	1.96232
$322$	1.33566e33	0.186056
$323$	−3.95952e33	−0.528943
$324$	1.85838e34	2.38110
$325$	8.41447e32	0.103419
$326$	−4.05897e33	−0.478606
$327$	−1.75303e34	−1.98333
$328$	−5.32658e33	−0.578298
$329$	−9.83506e32	−0.102478
$330$	7.35337e32	0.0735441
$331$	1.22753e34	1.17857	0.589284	−	0.807926i	$-0.299410\pi$
$331$	1.22753e34	1.17857	0.589284	+	0.807926i	$0.299410\pi$
$332$	1.51578e33	0.139724
$333$	−3.64407e34	−3.22544
$334$	−3.26960e33	−0.277918
$335$	2.28190e33	0.186291
$336$	2.01680e33	0.158155
$337$	3.74086e33	0.281817	0.140909	−	0.990023i	$-0.454998\pi$
$337$	3.74086e33	0.281817	0.140909	+	0.990023i	$0.454998\pi$
$338$	−7.15705e33	−0.518034
$339$	4.25487e33	0.295931
$340$	1.05604e33	0.0705854
$341$	2.98387e33	0.191688
$342$	5.66408e34	3.49765
$343$	1.01782e34	0.604225
$344$	5.13188e33	0.292912
$345$	−1.33938e34	−0.735098
$346$	−1.19524e34	−0.630852
$347$	−5.08016e33	−0.257887	−0.128943	−	0.991652i	$-0.541159\pi$
$347$	−5.08016e33	−0.257887	−0.128943	+	0.991652i	$0.541159\pi$
$348$	3.24230e34	1.58319
$349$	3.72143e34	1.74810	0.874050	−	0.485835i	$-0.161485\pi$
$349$	3.72143e34	1.74810	0.874050	+	0.485835i	$0.161485\pi$
$350$	−9.95791e32	−0.0450038
$351$	−4.61423e34	−2.00657
$352$	4.94188e32	0.0206807
$353$	1.32758e34	0.534690	0.267345	−	0.963601i	$-0.413854\pi$
$353$	1.32758e34	0.534690	0.267345	+	0.963601i	$0.413854\pi$
$354$	−1.36665e34	−0.529803
$355$	1.09116e34	0.407199
$356$	−1.20052e34	−0.431313
$357$	−5.77288e33	−0.199697
$358$	3.24126e33	0.107968
$359$	−4.06074e34	−1.30266	−0.651329	−	0.758795i	$-0.725788\pi$
$359$	−4.06074e34	−1.30266	−0.651329	+	0.758795i	$0.725788\pi$
$360$	−1.51066e34	−0.466749
$361$	6.07413e34	1.80774
$362$	−1.24668e34	−0.357429
$363$	7.09842e34	1.96075
$364$	−3.09132e33	−0.0822765
$365$	2.66935e34	0.684623
$366$	−5.18130e34	−1.28069
$367$	4.81487e33	0.114708	0.0573539	−	0.998354i	$-0.481734\pi$
$367$	4.81487e33	0.114708	0.0573539	+	0.998354i	$0.481734\pi$
$368$	−9.00137e33	−0.206711
$369$	−2.18105e35	−4.82847
$370$	1.61882e34	0.345523
$371$	7.14351e32	0.0147016
$372$	−8.20657e34	−1.62866
$373$	−2.48819e34	−0.476228	−0.238114	−	0.971237i	$-0.576529\pi$
$373$	−2.48819e34	−0.476228	−0.238114	+	0.971237i	$0.576529\pi$
$374$	−1.41456e33	−0.0261129
$375$	9.98560e33	0.177808
$376$	6.62810e33	0.113855
$377$	−4.96976e34	−0.823621
$378$	5.46061e34	0.873175
$379$	2.13394e34	0.329270	0.164635	−	0.986355i	$-0.447355\pi$
$379$	2.13394e34	0.329270	0.164635	+	0.986355i	$0.447355\pi$
$380$	−2.51618e34	−0.374683
$381$	−6.13733e34	−0.882048
$382$	1.69210e33	0.0234732
$383$	9.26670e34	1.24091	0.620457	−	0.784241i	$-0.286947\pi$
$383$	9.26670e34	1.24091	0.620457	+	0.784241i	$0.286947\pi$
$384$	−1.35917e34	−0.175712
$385$	1.33386e33	0.0166491
$386$	6.65791e34	0.802434
$387$	2.10133e35	2.44566
$388$	5.95925e34	0.669828
$389$	2.66544e34	0.289368	0.144684	−	0.989478i	$-0.453784\pi$
$389$	2.66544e34	0.289368	0.144684	+	0.989478i	$0.453784\pi$
$390$	3.09992e34	0.325071
$391$	2.57656e34	0.261008
$392$	−3.24674e34	−0.317750
$393$	−4.65711e34	−0.440369
$394$	−9.49281e34	−0.867353
$395$	−1.29144e34	−0.114028
$396$	2.02353e34	0.172673
$397$	6.20560e34	0.511814	0.255907	−	0.966701i	$-0.417626\pi$
$397$	6.20560e34	0.511814	0.255907	+	0.966701i	$0.417626\pi$
$398$	−1.32640e35	−1.05743
$399$	1.37548e35	1.06004
$400$	6.71089e33	0.0500000
$401$	−3.83625e34	−0.276349	−0.138174	−	0.990408i	$-0.544123\pi$
$401$	−3.83625e34	−0.276349	−0.138174	+	0.990408i	$0.544123\pi$
$402$	8.40661e34	0.585557
$403$	1.25789e35	0.847278
$404$	3.82341e34	0.249059
$405$	−3.38037e35	−2.12972
$406$	5.88135e34	0.358406
$407$	−2.16841e34	−0.127825
$408$	3.89049e34	0.221867
$409$	6.77841e33	0.0373993	0.0186996	−	0.999825i	$-0.494047\pi$
$409$	6.77841e33	0.0373993	0.0186996	+	0.999825i	$0.494047\pi$
$410$	9.68899e34	0.517245
$411$	4.47087e35	2.30955
$412$	−1.18891e35	−0.594343
$413$	−2.47903e34	−0.119938
$414$	−3.68575e35	−1.72592
$415$	−2.75718e34	−0.124973
$416$	2.08332e34	0.0914106
$417$	2.27446e35	0.966142
$418$	3.37042e34	0.138613
$419$	−1.94310e35	−0.773760	−0.386880	−	0.922130i	$-0.626447\pi$
$419$	−1.94310e35	−0.773760	−0.386880	+	0.922130i	$0.626447\pi$
$420$	−3.66853e34	−0.141458
$421$	1.96151e35	0.732457	0.366229	−	0.930525i	$-0.380649\pi$
$421$	1.96151e35	0.732457	0.366229	+	0.930525i	$0.380649\pi$
$422$	−6.66671e34	−0.241098
$423$	2.71397e35	0.950629
$424$	−4.81419e33	−0.0163337
$425$	−1.92093e34	−0.0631335
$426$	4.01988e35	1.27992
$427$	−9.39859e34	−0.289925
$428$	−1.65129e35	−0.493551
$429$	−4.15234e34	−0.120260
$430$	−9.33483e34	−0.261989
$431$	−4.47018e33	−0.0121585	−0.00607927	−	0.999982i	$-0.501935\pi$
$431$	−4.47018e33	−0.0121585	−0.00607927	+	0.999982i	$0.501935\pi$
$432$	−3.68004e35	−0.970112
$433$	−3.75519e35	−0.959501	−0.479751	−	0.877405i	$-0.659273\pi$
$433$	−3.75519e35	−0.959501	−0.479751	+	0.877405i	$0.659273\pi$
$434$	−1.48863e35	−0.368701
$435$	−5.89771e35	−1.41605
$436$	2.14302e35	0.498837
$437$	−6.13905e35	−1.38549
$438$	9.83398e35	2.15193
$439$	−2.32360e35	−0.493050	−0.246525	−	0.969136i	$-0.579289\pi$
$439$	−2.32360e35	−0.493050	−0.246525	+	0.969136i	$0.579289\pi$
$440$	−8.98922e33	−0.0184974
$441$	−1.32943e36	−2.65304
$442$	−5.96331e34	−0.115421
$443$	−9.07441e35	−1.70360	−0.851801	−	0.523865i	$-0.824490\pi$
$443$	−9.07441e35	−1.70360	−0.851801	+	0.523865i	$0.824490\pi$
$444$	5.96381e35	1.08606
$445$	2.18372e35	0.385778
$446$	−3.37855e35	−0.579042
$447$	1.43073e36	2.37906
$448$	−2.46546e34	−0.0397781
$449$	−7.86327e35	−1.23106	−0.615528	−	0.788115i	$-0.711057\pi$
$449$	−7.86327e35	−1.23106	−0.615528	+	0.788115i	$0.711057\pi$
$450$	2.74787e35	0.417473
$451$	−1.29784e35	−0.191354
$452$	−5.20143e34	−0.0744310
$453$	1.35407e36	1.88068
$454$	6.78226e35	0.914366
$455$	5.62309e34	0.0735904
$456$	−9.26972e35	−1.17772
$457$	−7.49955e35	−0.925053	−0.462526	−	0.886606i	$-0.653057\pi$
$457$	−7.49955e35	−0.925053	−0.462526	+	0.886606i	$0.653057\pi$
$458$	7.37682e35	0.883457
$459$	1.05338e36	1.22493
$460$	1.63734e35	0.184888
$461$	−1.56743e35	−0.171880	−0.0859399	−	0.996300i	$-0.527389\pi$
$461$	−1.56743e35	−0.171880	−0.0859399	+	0.996300i	$0.527389\pi$
$462$	4.91399e34	0.0523320
$463$	−5.52219e35	−0.571173	−0.285587	−	0.958353i	$-0.592188\pi$
$463$	−5.52219e35	−0.571173	−0.285587	+	0.958353i	$0.592188\pi$
$464$	−3.96359e35	−0.398195
$465$	1.49277e36	1.45672
$466$	2.78397e35	0.263909
$467$	−1.27404e36	−1.17329	−0.586643	−	0.809845i	$-0.699551\pi$
$467$	−1.27404e36	−1.17329	−0.586643	+	0.809845i	$0.699551\pi$
$468$	8.53048e35	0.763228
$469$	1.52491e35	0.132560
$470$	−1.20564e35	−0.101835
$471$	3.58577e36	2.94306
$472$	1.67068e35	0.133253
$473$	1.25040e35	0.0969222
$474$	−4.75771e35	−0.358419
$475$	4.57691e35	0.335127
$476$	7.05713e34	0.0502267
$477$	−1.97125e35	−0.136377
$478$	−1.12866e36	−0.759076
$479$	−9.37975e35	−0.613285	−0.306642	−	0.951825i	$-0.599206\pi$
$479$	−9.37975e35	−0.613285	−0.306642	+	0.951825i	$0.599206\pi$
$480$	2.47232e35	0.157162
$481$	−9.14127e35	−0.564999
$482$	−7.10786e35	−0.427173
$483$	−8.95058e35	−0.523076
$484$	−8.67756e35	−0.493157
$485$	−1.08398e36	−0.599112
$486$	−7.34888e36	−3.95032
$487$	1.24632e35	0.0651610	0.0325805	−	0.999469i	$-0.489627\pi$
$487$	1.24632e35	0.0651610	0.0325805	+	0.999469i	$0.489627\pi$
$488$	6.33395e35	0.322112
$489$	2.72001e36	1.34555
$490$	5.90579e35	0.284204
$491$	2.13166e36	0.997972	0.498986	−	0.866610i	$-0.333706\pi$
$491$	2.13166e36	0.997972	0.498986	+	0.866610i	$0.333706\pi$
$492$	3.56946e36	1.62583
$493$	1.13454e36	0.502789
$494$	1.42085e36	0.612682
$495$	−3.68077e35	−0.154443
$496$	1.00322e36	0.409633
$497$	7.29184e35	0.289752
$498$	−1.01576e36	−0.392820
$499$	1.17967e36	0.444020	0.222010	−	0.975044i	$-0.428738\pi$
$499$	1.17967e36	0.444020	0.222010	+	0.975044i	$0.428738\pi$
$500$	−1.22070e35	−0.0447214
$501$	2.19103e36	0.781338
$502$	3.90520e36	1.35563
$503$	−4.40912e36	−1.48999	−0.744996	−	0.667069i	$-0.767548\pi$
$503$	−4.40912e36	−1.48999	−0.744996	+	0.667069i	$0.767548\pi$
$504$	−1.00952e36	−0.332126
$505$	−6.95475e35	−0.222765
$506$	−2.19321e35	−0.0683989
$507$	4.79610e36	1.45640
$508$	7.50266e35	0.221848
$509$	−1.66203e36	−0.478574	−0.239287	−	0.970949i	$-0.576914\pi$
$509$	−1.66203e36	−0.478574	−0.239287	+	0.970949i	$0.576914\pi$
$510$	−7.07676e35	−0.198444
$511$	1.78383e36	0.487160
$512$	1.66153e35	0.0441942
$513$	−2.50984e37	−6.50221
$514$	2.75549e36	0.695338
$515$	2.16262e36	0.531596
$516$	−3.43899e36	−0.823493
$517$	1.61496e35	0.0376737
$518$	1.08180e36	0.245865
$519$	8.00957e36	1.77358
$520$	−3.78954e35	−0.0817601
$521$	−1.69142e36	−0.355583	−0.177792	−	0.984068i	$-0.556895\pi$
$521$	−1.69142e36	−0.355583	−0.177792	+	0.984068i	$0.556895\pi$
$522$	−1.62295e37	−3.32471
$523$	4.63272e36	0.924832	0.462416	−	0.886663i	$-0.346983\pi$
$523$	4.63272e36	0.924832	0.462416	+	0.886663i	$0.346983\pi$
$524$	5.69314e35	0.110759
$525$	6.67302e35	0.126524
$526$	−1.61265e36	−0.298012
$527$	−2.87163e36	−0.517231
$528$	−3.31166e35	−0.0581417
$529$	−1.84838e36	−0.316330
$530$	8.75697e34	0.0146093
$531$	6.84086e36	1.11259
$532$	−1.68147e36	−0.266614
$533$	−5.47124e36	−0.845801
$534$	8.04492e36	1.21259
$535$	3.00368e36	0.441445
$536$	−1.02768e36	−0.147276
$537$	−2.17204e36	−0.303540
$538$	7.47511e36	1.01873
$539$	−7.91079e35	−0.105141
$540$	6.69395e36	0.867695
$541$	1.22619e37	1.55022	0.775112	−	0.631823i	$-0.217693\pi$
$541$	1.22619e37	1.55022	0.775112	+	0.631823i	$0.217693\pi$
$542$	2.92928e36	0.361219
$543$	8.35429e36	1.00487
$544$	−4.75598e35	−0.0558027
$545$	−3.89813e36	−0.446173
$546$	2.07157e36	0.231312
$547$	1.26741e37	1.38066	0.690330	−	0.723494i	$-0.257465\pi$
$547$	1.26741e37	1.38066	0.690330	+	0.723494i	$0.257465\pi$
$548$	−5.46548e36	−0.580886
$549$	2.59353e37	2.68946
$550$	1.63513e35	0.0165446
$551$	−2.70322e37	−2.66892
$552$	6.03202e36	0.581146
$553$	−8.63023e35	−0.0811396
$554$	−1.22380e37	−1.12287
$555$	−1.08481e37	−0.971401
$556$	−2.78044e36	−0.242999
$557$	−5.14205e36	−0.438623	−0.219312	−	0.975655i	$-0.570381\pi$
$557$	−5.14205e36	−0.438623	−0.219312	+	0.975655i	$0.570381\pi$
$558$	4.10785e37	3.42021
$559$	5.27125e36	0.428404
$560$	4.48464e35	0.0355787
$561$	9.47931e35	0.0734139
$562$	−5.26984e36	−0.398435
$563$	1.08130e37	0.798147	0.399074	−	0.916919i	$-0.369332\pi$
$563$	1.08130e37	0.798147	0.399074	+	0.916919i	$0.369332\pi$
$564$	−4.44164e36	−0.320092
$565$	9.46134e35	0.0665731
$566$	3.92583e36	0.269718
$567$	−2.25898e37	−1.51545
$568$	−4.91416e36	−0.321919
$569$	−1.71706e37	−1.09843	−0.549213	−	0.835682i	$-0.685073\pi$
$569$	−1.71706e37	−1.09843	−0.549213	+	0.835682i	$0.685073\pi$
$570$	1.68615e37	1.05338
$571$	−2.73444e37	−1.66833	−0.834163	−	0.551518i	$-0.814049\pi$
$571$	−2.73444e37	−1.66833	−0.834163	+	0.551518i	$0.814049\pi$
$572$	5.07608e35	0.0302470
$573$	−1.13392e36	−0.0659924
$574$	6.47480e36	0.368058
$575$	−2.97831e36	−0.165369
$576$	6.80341e36	0.368997
$577$	−3.20240e36	−0.169669	−0.0848345	−	0.996395i	$-0.527036\pi$
$577$	−3.20240e36	−0.169669	−0.0848345	+	0.996395i	$0.527036\pi$
$578$	−1.23005e37	−0.636646
$579$	−4.46162e37	−2.25596
$580$	7.20973e36	0.356157
$581$	−1.84253e36	−0.0889275
$582$	−3.99343e37	−1.88315
$583$	−1.17299e35	−0.00540469
$584$	−1.20217e37	−0.541242
$585$	−1.55169e37	−0.682652
$586$	−2.68186e36	−0.115297
$587$	−5.30209e36	−0.222758	−0.111379	−	0.993778i	$-0.535527\pi$
$587$	−5.30209e36	−0.222758	−0.111379	+	0.993778i	$0.535527\pi$
$588$	2.17571e37	0.893321
$589$	6.84211e37	2.74558
$590$	−3.03895e36	−0.119185
$591$	6.36135e37	2.43847
$592$	−7.29054e36	−0.273160
$593$	−1.26381e37	−0.462855	−0.231428	−	0.972852i	$-0.574340\pi$
$593$	−1.26381e37	−0.462855	−0.231428	+	0.972852i	$0.574340\pi$
$594$	−8.96654e36	−0.321002
$595$	−1.28369e36	−0.0449241
$596$	−1.74901e37	−0.598368
$597$	8.88849e37	2.97286
$598$	−9.24583e36	−0.302329
$599$	−2.17161e37	−0.694255	−0.347128	−	0.937818i	$-0.612843\pi$
$599$	−2.17161e37	−0.694255	−0.347128	+	0.937818i	$0.612843\pi$
$600$	−4.49712e36	−0.140570
$601$	−2.82821e37	−0.864382	−0.432191	−	0.901782i	$-0.642259\pi$
$601$	−2.82821e37	−0.864382	−0.432191	+	0.901782i	$0.642259\pi$
$602$	−6.23813e36	−0.186424
$603$	−4.20798e37	−1.22967
$604$	−1.65529e37	−0.473017
$605$	1.57844e37	0.441093
$606$	−2.56215e37	−0.700204
$607$	4.82470e37	1.28951	0.644753	−	0.764391i	$-0.276960\pi$
$607$	4.82470e37	1.28951	0.644753	+	0.764391i	$0.276960\pi$
$608$	1.13319e37	0.296213
$609$	−3.94122e37	−1.00762
$610$	−1.15214e37	−0.288106
$611$	6.80810e36	0.166521
$612$	−1.94741e37	−0.465922
$613$	−4.26300e37	−0.997698	−0.498849	−	0.866689i	$-0.666244\pi$
$613$	−4.26300e37	−0.997698	−0.498849	+	0.866689i	$0.666244\pi$
$614$	7.15573e36	0.163825
$615$	−6.49281e37	−1.45418
$616$	−6.00717e35	−0.0131623
$617$	7.03658e37	1.50838	0.754192	−	0.656655i	$-0.228029\pi$
$617$	7.03658e37	1.50838	0.754192	+	0.656655i	$0.228029\pi$
$618$	7.96716e37	1.67093
$619$	−6.05562e37	−1.24261	−0.621305	−	0.783569i	$-0.713397\pi$
$619$	−6.05562e37	−1.24261	−0.621305	+	0.783569i	$0.713397\pi$
$620$	−1.82485e37	−0.366387
$621$	1.63321e38	3.20852
$622$	3.09720e37	0.595387
$623$	1.45930e37	0.274509
$624$	−1.39608e37	−0.256991
$625$	2.22045e36	0.0400000
$626$	−1.20140e37	−0.211805
$627$	−2.25860e37	−0.389697
$628$	−4.38347e37	−0.740223
$629$	2.08684e37	0.344910
$630$	1.83631e37	0.297062
$631$	9.89033e37	1.56608	0.783041	−	0.621970i	$-0.213668\pi$
$631$	9.89033e37	1.56608	0.783041	+	0.621970i	$0.213668\pi$
$632$	5.81613e36	0.0901474
$633$	4.46751e37	0.677822
$634$	−5.95057e35	−0.00883799
$635$	−1.36473e37	−0.198427
$636$	3.22610e36	0.0459205
$637$	−3.33491e37	−0.464731
$638$	−9.65742e36	−0.131759
$639$	−2.01218e38	−2.68785
$640$	−3.02231e36	−0.0395285
$641$	5.95420e37	0.762500	0.381250	−	0.924472i	$-0.375494\pi$
$641$	5.95420e37	0.762500	0.381250	+	0.924472i	$0.375494\pi$
$642$	1.10657e38	1.38757
$643$	2.01207e36	0.0247056	0.0123528	−	0.999924i	$-0.496068\pi$
$643$	2.01207e36	0.0247056	0.0123528	+	0.999924i	$0.496068\pi$
$644$	1.09418e37	0.131561
$645$	6.25548e37	0.736554
$646$	−3.24364e37	−0.374019
$647$	3.99414e37	0.451040	0.225520	−	0.974239i	$-0.427592\pi$
$647$	3.99414e37	0.451040	0.225520	+	0.974239i	$0.427592\pi$
$648$	1.52238e38	1.68369
$649$	4.07067e36	0.0440923
$650$	6.89313e36	0.0731285
$651$	9.97561e37	1.03656
$652$	−3.32511e37	−0.338426
$653$	1.78987e37	0.178440	0.0892201	−	0.996012i	$-0.471563\pi$
$653$	1.78987e37	0.178440	0.0892201	+	0.996012i	$0.471563\pi$
$654$	−1.43609e38	−1.40243
$655$	−1.03558e37	−0.0990660
$656$	−4.36353e37	−0.408918
$657$	−4.92246e38	−4.51908
$658$	−8.05688e36	−0.0724632
$659$	−5.06340e36	−0.0446159	−0.0223079	−	0.999751i	$-0.507101\pi$
$659$	−5.06340e36	−0.0446159	−0.0223079	+	0.999751i	$0.507101\pi$
$660$	6.02388e36	0.0520036
$661$	−2.02410e38	−1.71203	−0.856016	−	0.516949i	$-0.827068\pi$
$661$	−2.02410e38	−1.71203	−0.856016	+	0.516949i	$0.827068\pi$
$662$	1.00559e38	0.833373
$663$	3.99615e37	0.324495
$664$	1.24173e37	0.0987999
$665$	3.05858e37	0.238467
$666$	−2.98522e38	−2.28073
$667$	1.75905e38	1.31698
$668$	−2.67845e37	−0.196518
$669$	2.26405e38	1.62792
$670$	1.86933e37	0.131728
$671$	1.54329e37	0.106584
$672$	1.65216e37	0.111832
$673$	7.53924e36	0.0500178	0.0250089	−	0.999687i	$-0.492039\pi$
$673$	7.53924e36	0.0500178	0.0250089	+	0.999687i	$0.492039\pi$
$674$	3.06451e37	0.199275
$675$	−1.21762e38	−0.776090
$676$	−5.86306e37	−0.366306
$677$	1.83489e38	1.12373	0.561866	−	0.827228i	$-0.310084\pi$
$677$	1.83489e38	1.12373	0.561866	+	0.827228i	$0.310084\pi$
$678$	3.48559e37	0.209255
$679$	−7.24385e37	−0.426312
$680$	8.65108e36	0.0499114
$681$	−4.54494e38	−2.57065
$682$	2.44438e37	0.135544
$683$	2.34491e38	1.27481	0.637407	−	0.770527i	$-0.280007\pi$
$683$	2.34491e38	1.27481	0.637407	+	0.770527i	$0.280007\pi$
$684$	4.64001e38	2.47321
$685$	9.94165e37	0.519560
$686$	8.33794e37	0.427251
$687$	−4.94337e38	−2.48375
$688$	4.20404e37	0.207120
$689$	−4.94493e36	−0.0238892
$690$	−1.09722e38	−0.519793
$691$	6.34902e37	0.294953	0.147477	−	0.989066i	$-0.452885\pi$
$691$	6.34902e37	0.294953	0.147477	+	0.989066i	$0.452885\pi$
$692$	−9.79141e37	−0.446080
$693$	−2.45973e37	−0.109898
$694$	−4.16166e37	−0.182354
$695$	5.05759e37	0.217345
$696$	2.65609e38	1.11948
$697$	1.24902e38	0.516329
$698$	3.04859e38	1.23609
$699$	−1.86560e38	−0.741953
$700$	−8.15752e36	−0.0318225
$701$	2.26958e38	0.868465	0.434233	−	0.900801i	$-0.357020\pi$
$701$	2.26958e38	0.868465	0.434233	+	0.900801i	$0.357020\pi$
$702$	−3.77998e38	−1.41886
$703$	−4.97224e38	−1.83086
$704$	4.04838e36	0.0146235
$705$	8.07929e37	0.286299
$706$	1.08755e38	0.378083
$707$	−4.64761e37	−0.158514
$708$	−1.11956e38	−0.374627
$709$	−4.92739e37	−0.161768	−0.0808840	−	0.996724i	$-0.525774\pi$
$709$	−4.92739e37	−0.161768	−0.0808840	+	0.996724i	$0.525774\pi$
$710$	8.93880e37	0.287933
$711$	2.38150e38	0.752682
$712$	−9.83462e37	−0.304984
$713$	−4.45232e38	−1.35481
$714$	−4.72914e37	−0.141207
$715$	−9.23334e36	−0.0270537
$716$	2.65524e37	0.0763446
$717$	7.56338e38	2.13406
$718$	−3.32656e38	−0.921118
$719$	−1.73047e38	−0.470246	−0.235123	−	0.971966i	$-0.575549\pi$
$719$	−1.73047e38	−0.470246	−0.235123	+	0.971966i	$0.575549\pi$
$720$	−1.23753e38	−0.330041
$721$	1.44520e38	0.378270
$722$	4.97593e38	1.27827
$723$	4.76314e38	1.20095
$724$	−1.02128e38	−0.252740
$725$	−1.31144e38	−0.318556
$726$	5.81503e38	1.38646
$727$	7.52465e37	0.176105	0.0880525	−	0.996116i	$-0.471936\pi$
$727$	7.52465e37	0.176105	0.0880525	+	0.996116i	$0.471936\pi$
$728$	−2.53241e37	−0.0581783
$729$	2.81297e39	6.34371
$730$	2.18673e38	0.484102
$731$	−1.20336e38	−0.261525
$732$	−4.24452e38	−0.905584
$733$	−5.84393e37	−0.122406	−0.0612028	−	0.998125i	$-0.519494\pi$
$733$	−5.84393e37	−0.122406	−0.0612028	+	0.998125i	$0.519494\pi$
$734$	3.94434e37	0.0811106
$735$	−3.95760e38	−0.799011
$736$	−7.37393e37	−0.146167
$737$	−2.50397e37	−0.0487324
$738$	−1.78672e39	−3.41424
$739$	−2.75465e38	−0.516851	−0.258426	−	0.966031i	$-0.583204\pi$
$739$	−2.75465e38	−0.516851	−0.258426	+	0.966031i	$0.583204\pi$
$740$	1.32614e38	0.244321
$741$	−9.52145e38	−1.72249
$742$	5.85197e36	0.0103956
$743$	6.91625e38	1.20648	0.603242	−	0.797558i	$-0.293875\pi$
$743$	6.91625e38	1.20648	0.603242	+	0.797558i	$0.293875\pi$
$744$	−6.72282e38	−1.15164
$745$	3.18144e38	0.535197
$746$	−2.03833e38	−0.336744
$747$	5.08443e38	0.824925
$748$	−1.15881e37	−0.0184646
$749$	2.00725e38	0.314121
$750$	8.18021e37	0.125730
$751$	−9.44712e38	−1.42613	−0.713067	−	0.701096i	$-0.752694\pi$
$751$	−9.44712e38	−1.42613	−0.713067	+	0.701096i	$0.752694\pi$
$752$	5.42974e37	0.0805078
$753$	−2.61696e39	−3.81123
$754$	−4.07123e38	−0.582388
$755$	3.01096e38	0.423079
$756$	4.47333e38	0.617428
$757$	−1.05837e39	−1.43497	−0.717484	−	0.696575i	$-0.754706\pi$
$757$	−1.05837e39	−1.43497	−0.717484	+	0.696575i	$0.754706\pi$
$758$	1.74812e38	0.232829
$759$	1.46972e38	0.192296
$760$	−2.06126e38	−0.264941
$761$	6.48621e38	0.819026	0.409513	−	0.912304i	$-0.365699\pi$
$761$	6.48621e38	0.819026	0.409513	+	0.912304i	$0.365699\pi$
$762$	−5.02770e38	−0.623702
$763$	−2.60498e38	−0.317485
$764$	1.38617e37	0.0165980
$765$	3.54232e38	0.416733
$766$	7.59128e38	0.877458
$767$	1.71605e38	0.194892
$768$	−1.11343e38	−0.124247
$769$	−5.73159e38	−0.628449	−0.314224	−	0.949349i	$-0.601744\pi$
$769$	−5.73159e38	−0.628449	−0.314224	+	0.949349i	$0.601744\pi$
$770$	1.09270e37	0.0117727
$771$	−1.84651e39	−1.95487
$772$	5.45416e38	0.567407
$773$	−7.89580e38	−0.807185	−0.403592	−	0.914939i	$-0.632239\pi$
$773$	−7.89580e38	−0.807185	−0.403592	+	0.914939i	$0.632239\pi$
$774$	1.72141e39	1.72934
$775$	3.31938e38	0.327706
$776$	4.88181e38	0.473640
$777$	−7.24940e38	−0.691223
$778$	2.18353e38	0.204614
$779$	−2.97599e39	−2.74079
$780$	2.53946e38	0.229860
$781$	−1.19735e38	−0.106520
$782$	2.11071e38	0.184560
$783$	7.19154e39	6.18070
$784$	−2.65973e38	−0.224683
$785$	7.97348e38	0.662076
$786$	−3.81510e38	−0.311388
$787$	1.73852e39	1.39483	0.697414	−	0.716668i	$-0.254334\pi$
$787$	1.73852e39	1.39483	0.697414	+	0.716668i	$0.254334\pi$
$788$	−7.77651e38	−0.613311
$789$	1.08068e39	0.837830
$790$	−1.05795e38	−0.0806303
$791$	6.32267e37	0.0473716
$792$	1.65767e38	0.122098
$793$	6.50596e38	0.471111
$794$	5.08363e38	0.361907
$795$	−5.86824e37	−0.0410726
$796$	−1.08658e39	−0.747717
$797$	1.88301e39	1.27399	0.636994	−	0.770869i	$-0.280178\pi$
$797$	1.88301e39	1.27399	0.636994	+	0.770869i	$0.280178\pi$
$798$	1.12679e39	0.749559
$799$	−1.55421e38	−0.101655
$800$	5.49756e37	0.0353553
$801$	−4.02693e39	−2.54645
$802$	−3.14265e38	−0.195408
$803$	−2.92912e38	−0.179093
$804$	6.88669e38	0.414051
$805$	−1.99029e38	−0.117672
$806$	1.03047e39	0.599116
$807$	−5.00924e39	−2.86404
$808$	3.13214e38	0.176111
$809$	−1.60495e38	−0.0887474	−0.0443737	−	0.999015i	$-0.514129\pi$
$809$	−1.60495e38	−0.0887474	−0.0443737	+	0.999015i	$0.514129\pi$
$810$	−2.76920e39	−1.50594
$811$	2.12672e39	1.13744	0.568721	−	0.822531i	$-0.307439\pi$
$811$	2.12672e39	1.13744	0.568721	+	0.822531i	$0.307439\pi$
$812$	4.81800e38	0.253431
$813$	−1.96298e39	−1.01553
$814$	−1.77636e38	−0.0903862
$815$	6.04834e38	0.302697
$816$	3.18709e38	0.156883
$817$	2.86721e39	1.38823
$818$	5.55287e37	0.0264453
$819$	−1.03694e39	−0.485757
$820$	7.93722e38	0.365748
$821$	−2.13403e39	−0.967317	−0.483658	−	0.875257i	$-0.660692\pi$
$821$	−2.13403e39	−0.967317	−0.483658	+	0.875257i	$0.660692\pi$
$822$	3.66254e39	1.63310
$823$	1.46819e39	0.643997	0.321998	−	0.946740i	$-0.395645\pi$
$823$	1.46819e39	0.643997	0.321998	+	0.946740i	$0.395645\pi$
$824$	−9.73956e38	−0.420264
$825$	−1.09574e38	−0.0465134
$826$	−2.03082e38	−0.0848089
$827$	1.74523e39	0.717016	0.358508	−	0.933527i	$-0.383286\pi$
$827$	1.74523e39	0.717016	0.358508	+	0.933527i	$0.383286\pi$
$828$	−3.01937e39	−1.22041
$829$	−1.03362e39	−0.411031	−0.205515	−	0.978654i	$-0.565887\pi$
$829$	−1.03362e39	−0.411031	−0.205515	+	0.978654i	$0.565887\pi$
$830$	−2.25868e38	−0.0883693
$831$	8.20094e39	3.15682
$832$	1.70666e38	0.0646370
$833$	7.61321e38	0.283701
$834$	1.86323e39	0.683165
$835$	4.87208e38	0.175771
$836$	2.76105e38	0.0980144
$837$	−1.82025e40	−6.35823
$838$	−1.59179e39	−0.547131
$839$	1.58461e39	0.535966	0.267983	−	0.963424i	$-0.413643\pi$
$839$	1.58461e39	0.535966	0.267983	+	0.963424i	$0.413643\pi$
$840$	−3.00526e38	−0.100026
$841$	4.69252e39	1.53695
$842$	1.60687e39	0.517926
$843$	3.53144e39	1.12016
$844$	−5.46137e38	−0.170482
$845$	1.06648e39	0.327634
$846$	2.22329e39	0.672196
$847$	1.05481e39	0.313870
$848$	−3.94379e37	−0.0115497
$849$	−2.63079e39	−0.758285
$850$	−1.57362e38	−0.0446421
$851$	3.23556e39	0.903441
$852$	3.29309e39	0.905042
$853$	−4.84028e39	−1.30936	−0.654679	−	0.755907i	$-0.727196\pi$
$853$	−4.84028e39	−1.30936	−0.654679	+	0.755907i	$0.727196\pi$
$854$	−7.69932e38	−0.205008
$855$	−8.44013e39	−2.21211
$856$	−1.35274e39	−0.348993
$857$	1.36798e38	0.0347406	0.0173703	−	0.999849i	$-0.494471\pi$
$857$	1.36798e38	0.0347406	0.0173703	+	0.999849i	$0.494471\pi$
$858$	−3.40160e38	−0.0850363
$859$	−4.42921e39	−1.08998	−0.544990	−	0.838442i	$-0.683467\pi$
$859$	−4.42921e39	−1.08998	−0.544990	+	0.838442i	$0.683467\pi$
$860$	−7.64710e38	−0.185254
$861$	−4.33891e39	−1.03476
$862$	−3.66197e37	−0.00859739
$863$	−7.25613e39	−1.67710	−0.838550	−	0.544824i	$-0.816596\pi$
$863$	−7.25613e39	−1.67710	−0.838550	+	0.544824i	$0.816596\pi$
$864$	−3.01469e39	−0.685973
$865$	1.78105e39	0.398986
$866$	−3.07625e39	−0.678470
$867$	8.24287e39	1.78987
$868$	−1.21948e39	−0.260711
$869$	1.41712e38	0.0298290
$870$	−4.83140e39	−1.00130
$871$	−1.05559e39	−0.215401
$872$	1.75556e39	0.352731
$873$	1.99893e40	3.95463
$874$	−5.02911e39	−0.979686
$875$	1.48384e38	0.0284629
$876$	8.05600e39	1.52165
$877$	7.76731e39	1.44470	0.722348	−	0.691530i	$-0.243063\pi$
$877$	7.76731e39	1.44470	0.722348	+	0.691530i	$0.243063\pi$
$878$	−1.90350e39	−0.348639
$879$	1.79718e39	0.324146
$880$	−7.36397e37	−0.0130796
$881$	−3.34645e39	−0.585341	−0.292671	−	0.956213i	$-0.594544\pi$
$881$	−3.34645e39	−0.585341	−0.292671	+	0.956213i	$0.594544\pi$
$882$	−1.08907e40	−1.87598
$883$	5.35163e39	0.907856	0.453928	−	0.891038i	$-0.350022\pi$
$883$	5.35163e39	0.907856	0.453928	+	0.891038i	$0.350022\pi$
$884$	−4.88514e38	−0.0816153
$885$	2.03647e39	0.335077
$886$	−7.43376e39	−1.20463
$887$	9.27354e38	0.148005	0.0740026	−	0.997258i	$-0.476423\pi$
$887$	9.27354e38	0.148005	0.0740026	+	0.997258i	$0.476423\pi$
$888$	4.88555e39	0.767960
$889$	−9.11997e38	−0.141195
$890$	1.78891e39	0.272786
$891$	3.70934e39	0.557119
$892$	−2.76771e39	−0.409445
$893$	3.70315e39	0.539606
$894$	1.17205e40	1.68225
$895$	−4.82986e38	−0.0682847
$896$	−2.01970e38	−0.0281274
$897$	6.19584e39	0.849967
$898$	−6.44159e39	−0.870488
$899$	−1.96050e40	−2.60982
$900$	2.25106e39	0.295198
$901$	1.12887e38	0.0145834
$902$	−1.06319e39	−0.135308
$903$	4.18031e39	0.524112
$904$	−4.26101e38	−0.0526306
$905$	1.85770e39	0.226058
$906$	1.10925e40	1.32984
$907$	1.06013e40	1.25217	0.626083	−	0.779756i	$-0.284657\pi$
$907$	1.06013e40	1.25217	0.626083	+	0.779756i	$0.284657\pi$
$908$	5.55602e39	0.646555
$909$	1.28250e40	1.47043
$910$	4.60643e38	0.0520362
$911$	−1.34212e40	−1.49381	−0.746903	−	0.664933i	$-0.768460\pi$
$911$	−1.34212e40	−1.49381	−0.746903	+	0.664933i	$0.768460\pi$
$912$	−7.59375e39	−0.832772
$913$	3.02550e38	0.0326921
$914$	−6.14363e39	−0.654111
$915$	7.72074e39	0.809979
$916$	6.04309e39	0.624698
$917$	−6.92038e38	−0.0704927
$918$	8.62925e39	0.866158
$919$	6.48496e39	0.641428	0.320714	−	0.947176i	$-0.396077\pi$
$919$	6.48496e39	0.641428	0.320714	+	0.947176i	$0.396077\pi$
$920$	1.34131e39	0.130735
$921$	−4.79521e39	−0.460578
$922$	−1.28404e39	−0.121537
$923$	−5.04761e39	−0.470829
$924$	4.02554e38	0.0370043
$925$	−2.41224e39	−0.218528
$926$	−4.52378e39	−0.403881
$927$	−3.98801e40	−3.50897
$928$	−3.24697e39	−0.281567
$929$	4.31118e39	0.368454	0.184227	−	0.982884i	$-0.441022\pi$
$929$	4.31118e39	0.368454	0.184227	+	0.982884i	$0.441022\pi$
$930$	1.22287e40	1.03006
$931$	−1.81397e40	−1.50595
$932$	2.28063e39	0.186612
$933$	−2.07551e40	−1.67387
$934$	−1.04369e40	−0.829639
$935$	2.10786e38	0.0165153
$936$	6.98817e39	0.539684
$937$	1.66692e40	1.26891	0.634453	−	0.772962i	$-0.281226\pi$
$937$	1.66692e40	1.26891	0.634453	+	0.772962i	$0.281226\pi$
$938$	1.24921e39	0.0937339
$939$	8.05088e39	0.595467
$940$	−9.87663e38	−0.0720084
$941$	−2.51285e40	−1.80596	−0.902978	−	0.429687i	$-0.858624\pi$
$941$	−2.51285e40	−1.80596	−0.902978	+	0.429687i	$0.858624\pi$
$942$	2.93746e40	2.08106
$943$	1.93655e40	1.35245
$944$	1.36862e39	0.0942241
$945$	−8.13694e39	−0.552245
$946$	1.02433e39	0.0685344
$947$	1.74731e40	1.15251	0.576257	−	0.817268i	$-0.304513\pi$
$947$	1.74731e40	1.15251	0.576257	+	0.817268i	$0.304513\pi$
$948$	−3.89752e39	−0.253440
$949$	−1.23482e40	−0.791604
$950$	3.74941e39	0.236970
$951$	3.98761e38	0.0248471
$952$	5.78120e38	0.0355156
$953$	−1.34477e40	−0.814504	−0.407252	−	0.913316i	$-0.633513\pi$
$953$	−1.34477e40	−0.814504	−0.407252	+	0.913316i	$0.633513\pi$
$954$	−1.61484e39	−0.0964334
$955$	−2.52143e38	−0.0148457
$956$	−9.24595e39	−0.536747
$957$	6.47165e39	0.370428
$958$	−7.68389e39	−0.433658
$959$	6.64365e39	0.369705
$960$	2.02532e39	0.111130
$961$	3.11393e40	1.68478
$962$	−7.48853e39	−0.399515
$963$	−5.53898e40	−2.91390
$964$	−5.82276e39	−0.302057
$965$	−9.92106e39	−0.507504
$966$	−7.33232e39	−0.369871
$967$	−6.46684e38	−0.0321688	−0.0160844	−	0.999871i	$-0.505120\pi$
$967$	−6.46684e38	−0.0321688	−0.0160844	+	0.999871i	$0.505120\pi$
$968$	−7.10866e39	−0.348715
$969$	2.17364e40	1.05152
$970$	−8.87997e39	−0.423636
$971$	9.04161e38	0.0425389	0.0212694	−	0.999774i	$-0.493229\pi$
$971$	9.04161e38	0.0425389	0.0212694	+	0.999774i	$0.493229\pi$
$972$	−6.02021e40	−2.79329
$973$	3.37980e39	0.154657
$974$	1.02098e39	0.0460758
$975$	−4.61924e39	−0.205593
$976$	5.18877e39	0.227767
$977$	−2.22532e40	−0.963420	−0.481710	−	0.876331i	$-0.659984\pi$
$977$	−2.22532e40	−0.963420	−0.481710	+	0.876331i	$0.659984\pi$
$978$	2.22823e40	0.951449
$979$	−2.39624e39	−0.100917
$980$	4.83802e39	0.200963
$981$	7.18842e40	2.94511
$982$	1.74626e40	0.705673
$983$	−2.74028e40	−1.09225	−0.546126	−	0.837703i	$-0.683898\pi$
$983$	−2.74028e40	−1.09225	−0.546126	+	0.837703i	$0.683898\pi$
$984$	2.92410e40	1.14963
$985$	1.41454e40	0.548562
$986$	9.29414e39	0.355526
$987$	5.39910e39	0.203723
$988$	1.16396e40	0.433232
$989$	−1.86576e40	−0.685024
$990$	−3.01529e39	−0.109208
$991$	1.63958e40	0.585786	0.292893	−	0.956145i	$-0.405382\pi$
$991$	1.63958e40	0.585786	0.292893	+	0.956145i	$0.405382\pi$
$992$	8.21840e39	0.289654
$993$	−6.73871e40	−2.34294
$994$	5.97348e39	0.204885
$995$	1.97649e40	0.668778
$996$	−8.32108e39	−0.277766
$997$	3.56689e40	1.17464	0.587320	−	0.809355i	$-0.300183\pi$
$997$	3.56689e40	1.17464	0.587320	+	0.809355i	$0.300183\pi$
$998$	9.66385e39	0.313970
$999$	1.32279e41	4.23993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.a.c.1.1	✓	2
5.2	odd	4		50.28.b.c.49.4		4
5.3	odd	4		50.28.b.c.49.1		4
5.4	even	2		50.28.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.a.c.1.1	✓	2	1.1	even	1	trivial
50.28.a.c.1.2		2	5.4	even	2
50.28.b.c.49.1		4	5.3	odd	4
50.28.b.c.49.4		4	5.2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+8192.00 q^{2} -5.48964e6 q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} -4.49712e10 q^{6} -8.15752e10 q^{7} +5.49756e11 q^{8} +2.25106e13 q^{9} -1.00000e13 q^{10} +1.33950e13 q^{11} -3.68404e14 q^{12} +5.64686e14 q^{13} -6.68264e14 q^{14} +6.70123e15 q^{15} +4.50360e15 q^{16} -1.28911e16 q^{17} +1.84407e17 q^{18} +3.07151e17 q^{19} -8.19200e16 q^{20} +4.47819e17 q^{21} +1.09732e17 q^{22} -1.99871e18 q^{23} -3.01796e18 q^{24} +1.49012e18 q^{25} +4.62590e18 q^{26} -8.17133e19 q^{27} -5.47442e18 q^{28} -8.80094e19 q^{29} +5.48964e19 q^{30} +2.22760e20 q^{31} +3.68935e19 q^{32} -7.35337e19 q^{33} -1.05604e20 q^{34} +9.95791e19 q^{35} +1.51066e21 q^{36} -1.61882e21 q^{37} +2.51618e21 q^{38} -3.09992e21 q^{39} -6.71089e20 q^{40} -9.68899e21 q^{41} +3.66853e21 q^{42} +9.33483e21 q^{43} +8.98922e20 q^{44} -2.74787e22 q^{45} -1.63734e22 q^{46} +1.20564e22 q^{47} -2.47232e22 q^{48} -5.90579e22 q^{49} +1.22070e22 q^{50} +7.07676e22 q^{51} +3.78954e22 q^{52} -8.75697e21 q^{53} -6.69395e23 q^{54} -1.63513e22 q^{55} -4.48464e22 q^{56} -1.68615e24 q^{57} -7.20973e23 q^{58} +3.03895e23 q^{59} +4.49712e23 q^{60} +1.15214e24 q^{61} +1.82485e24 q^{62} -1.83631e24 q^{63} +3.02231e23 q^{64} -6.89313e23 q^{65} -6.02388e23 q^{66} -1.86933e24 q^{67} -8.65108e23 q^{68} +1.09722e25 q^{69} +8.15752e23 q^{70} -8.93880e24 q^{71} +1.23753e25 q^{72} -2.18673e25 q^{73} -1.32614e25 q^{74} -8.18021e24 q^{75} +2.06126e25 q^{76} -1.09270e24 q^{77} -2.53946e25 q^{78} +1.05795e25 q^{79} -5.49756e24 q^{80} +2.76920e26 q^{81} -7.93722e25 q^{82} +2.25868e25 q^{83} +3.00526e25 q^{84} +1.57362e25 q^{85} +7.64710e25 q^{86} +4.83140e26 q^{87} +7.36397e24 q^{88} -1.78891e26 q^{89} -2.25106e26 q^{90} -4.60643e25 q^{91} -1.34131e26 q^{92} -1.22287e27 q^{93} +9.87663e25 q^{94} -3.74941e26 q^{95} -2.02532e26 q^{96} +8.87997e26 q^{97} -4.83802e26 q^{98} +3.01529e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16384 q^{2} - 4702956 q^{3} + 134217728 q^{4} - 2441406250 q^{5} - 38526615552 q^{6} - 57185041508 q^{7} + 1099511627776 q^{8} + 15503869642194 q^{9} - 20000000000000 q^{10} + 169851430699104 q^{11}+ \cdots - 79\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 16384 * q^2 - 4702956 * q^3 + 134217728 * q^4 - 2441406250 * q^5 - 38526615552 * q^6 - 57185041508 * q^7 + 1099511627776 * q^8 + 15503869642194 * q^9 - 20000000000000 * q^10 + 169851430699104 * q^11 - 315610034601984 * q^12 - 1039094991262796 * q^13 - 468459860033536 * q^14 + 5740913085937500 * q^15 + 9007199254740992 * q^16 - 50445145609767948 * q^17 + 127007700108853248 * q^18 + 446863730094123400 * q^19 - 163840000000000000 * q^20 + 467006108827766424 * q^21 + 1391422920287059968 * q^22 - 6647307932323726956 * q^23 - 2585477403459452928 * q^24 + 2980232238769531250 * q^25 - 8512266168424824832 * q^26 - 93224365905702240360 * q^27 - 3837623173394726912 * q^28 - 47997399844470169380 * q^29 + 47029560000000000000 * q^30 + 33574730315678836744 * q^31 + 73786976294838206464 * q^32 + 49548682554417655488 * q^33 - 413246632835219030016 * q^34 + 69805958872070312500 * q^35 + 1040447079291725807616 * q^36 - 1349929187895125662508 * q^37 + 3660707676931058892800 * q^38 - 4361597048598395237112 * q^39 - 1342177280000000000000 * q^40 - 1182957469635679236756 * q^41 + 3825714043517062545408 * q^42 - 3918269768563513059836 * q^43 + 11398536562991595257856 * q^44 - 18925622121818847656250 * q^45 - 54454746581595971223552 * q^46 - 32027326481691215437428 * q^47 - 21180230889139838386176 * q^48 - 124175335159331248585254 * q^49 + 24414062500000000000000 * q^50 + 41224319062757865329544 * q^51 - 69732484451736165023744 * q^52 - 338645206816246511641596 * q^53 - 763694005499512753029120 * q^54 - 207338172240117187500000 * q^55 - 31437809036449602863104 * q^56 - 1576241472518493550388400 * q^57 - 393194699525899627560960 * q^58 - 343725486206796714375960 * q^59 + 385266155520000000000000 * q^60 + 228063235764015707336884 * q^61 + 275044190746041030606848 * q^62 - 2007200379545784196719876 * q^63 + 604462909807314587353088 * q^64 + 1268426503006342773437500 * q^65 + 405902807485789433757696 * q^66 - 3973383158722681594905428 * q^67 - 3385316416186114293891072 * q^68 + 7315190141287874962404168 * q^69 + 571850415080000000000000 * q^70 - 2414614414513749020227176 * q^71 + 8523342473557817815990272 * q^72 - 12422599244545503708131996 * q^73 - 11058619907236869427265536 * q^74 - 7007950544357299804687500 * q^75 + 29988517289419234449817600 * q^76 + 2723296993852627128197184 * q^77 - 35730203022118053782421504 * q^78 + 14197635994550588853149680 * q^79 - 10995116277760000000000000 * q^80 + 321295031247975610705880202 * q^81 - 9690787591255484307505152 * q^82 + 113637606793167338211169284 * q^83 + 31340249444491776371982336 * q^84 + 61578546886923764648437500 * q^85 - 32098465944072298986176512 * q^86 + 514617127953054957365529240 * q^87 + 93376811524027148352356352 * q^88 + 139217760348347863809112020 * q^89 - 155038696421940000000000000 * q^90 - 85180767378984078493944616 * q^91 - 446093283996434196263337984 * q^92 - 1371703352271155402043821232 * q^93 - 262367858538014436863410176 * q^94 - 545487951775052978515625000 * q^95 - 173508451443833556059553792 * q^96 + 1199842643269565667896244292 * q^97 - 1017244345625241588410400768 * q^98 - 794717627905923529800830112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more