LMFDB - Embedded newform 10.28.a.c.1.2

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			1.2
Root			$-421.296$ 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)

$f(q)$	$=$	\(q+8192.00 q^{2} +786688. q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} +6.44455e9 q^{6} +2.43901e10 q^{7} +5.49756e11 q^{8} -7.00672e12 q^{9} -1.00000e13 q^{10} +1.56456e14 q^{11} +5.27937e13 q^{12} -1.60378e15 q^{13} +1.99804e14 q^{14} -9.60312e14 q^{15} +4.50360e15 q^{16} -3.75540e16 q^{17} -5.73991e16 q^{18} +1.39712e17 q^{19} -8.19200e16 q^{20} +1.91874e16 q^{21} +1.28169e18 q^{22} -4.64860e18 q^{23} +4.32486e17 q^{24} +1.49012e18 q^{25} -1.31382e19 q^{26} -1.15111e19 q^{27} +1.63679e18 q^{28} +4.00120e19 q^{29} -7.86688e18 q^{30} -1.89185e20 q^{31} +3.68935e19 q^{32} +1.23082e20 q^{33} -3.07643e20 q^{34} -2.97731e19 q^{35} -4.70213e20 q^{36} +2.68895e20 q^{37} +1.14452e21 q^{38} -1.26167e21 q^{39} -6.71089e20 q^{40} +8.50604e21 q^{41} +1.57183e20 q^{42} -1.32531e22 q^{43} +1.04996e22 q^{44} +8.55313e21 q^{45} -3.80813e22 q^{46} -4.40838e22 q^{47} +3.54293e21 q^{48} -6.51175e22 q^{49} +1.22070e22 q^{50} -2.95433e22 q^{51} -1.07628e23 q^{52} -3.29888e23 q^{53} -9.42986e22 q^{54} -1.90987e23 q^{55} +1.34086e22 q^{56} +1.09910e23 q^{57} +3.27778e23 q^{58} -6.47621e23 q^{59} -6.44455e22 q^{60} -9.24075e23 q^{61} -1.54981e24 q^{62} -1.70895e23 q^{63} +3.02231e23 q^{64} +1.95774e24 q^{65} +1.00829e24 q^{66} -2.10405e24 q^{67} -2.52021e24 q^{68} -3.65700e24 q^{69} -2.43901e23 q^{70} +6.52419e24 q^{71} -3.85199e24 q^{72} +9.44471e24 q^{73} +2.20279e24 q^{74} +1.17226e24 q^{75} +9.37594e24 q^{76} +3.81600e24 q^{77} -1.03356e25 q^{78} +3.61816e24 q^{79} -5.49756e24 q^{80} +4.43748e25 q^{81} +6.96814e25 q^{82} +9.10508e25 q^{83} +1.28765e24 q^{84} +4.58423e25 q^{85} -1.08569e26 q^{86} +3.14769e25 q^{87} +8.60128e25 q^{88} +3.18108e26 q^{89} +7.00672e25 q^{90} -3.91164e25 q^{91} -3.11962e26 q^{92} -1.48830e26 q^{93} -3.61134e26 q^{94} -1.70547e26 q^{95} +2.90237e25 q^{96} +3.11846e26 q^{97} -5.33442e26 q^{98} -1.09625e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	786688.	0.284882	0.142441	−	0.989803i	$-0.454505\pi$
$3$	786688.	0.284882	0.142441	+	0.989803i	$0.454505\pi$
$4$	6.71089e7	0.500000
$5$	−1.22070e9	−0.447214
$5$	−1.22070e9	−0.447214
$6$	6.44455e9	0.201442
$7$	2.43901e10	0.0951461	0.0475730	−	0.998868i	$-0.484851\pi$
$7$	2.43901e10	0.0951461	0.0475730	+	0.998868i	$0.484851\pi$
$8$	5.49756e11	0.353553
$9$	−7.00672e12	−0.918842
$10$	−1.00000e13	−0.316228
$11$	1.56456e14	1.36645	0.683223	−	0.730210i	$-0.260578\pi$
$11$	1.56456e14	1.36645	0.683223	+	0.730210i	$0.260578\pi$
$12$	5.27937e13	0.142441
$13$	−1.60378e15	−1.46862	−0.734310	−	0.678814i	$-0.762494\pi$
$13$	−1.60378e15	−1.46862	−0.734310	+	0.678814i	$0.762494\pi$
$14$	1.99804e14	0.0672784
$15$	−9.60312e14	−0.127403
$16$	4.50360e15	0.250000
$17$	−3.75540e16	−0.919594	−0.459797	−	0.888024i	$-0.652078\pi$
$17$	−3.75540e16	−0.919594	−0.459797	+	0.888024i	$0.652078\pi$
$18$	−5.73991e16	−0.649719
$19$	1.39712e17	0.762187	0.381093	−	0.924537i	$-0.375548\pi$
$19$	1.39712e17	0.762187	0.381093	+	0.924537i	$0.375548\pi$
$20$	−8.19200e16	−0.223607
$21$	1.91874e16	0.0271054
$22$	1.28169e18	0.966223
$23$	−4.64860e18	−1.92308	−0.961538	−	0.274671i	$-0.911431\pi$
$23$	−4.64860e18	−1.92308	−0.961538	+	0.274671i	$0.911431\pi$
$24$	4.32486e17	0.100721
$25$	1.49012e18	0.200000
$26$	−1.31382e19	−1.03847
$27$	−1.15111e19	−0.546644
$28$	1.63679e18	0.0475730
$29$	4.00120e19	0.724131	0.362066	−	0.932153i	$-0.382072\pi$
$29$	4.00120e19	0.724131	0.362066	+	0.932153i	$0.382072\pi$
$30$	−7.86688e18	−0.0900877
$31$	−1.89185e20	−1.39157	−0.695784	−	0.718251i	$-0.744943\pi$
$31$	−1.89185e20	−1.39157	−0.695784	+	0.718251i	$0.744943\pi$
$32$	3.68935e19	0.176777
$33$	1.23082e20	0.389276
$34$	−3.07643e20	−0.650251
$35$	−2.97731e19	−0.0425506
$36$	−4.70213e20	−0.459421
$37$	2.68895e20	0.181493	0.0907465	−	0.995874i	$-0.471075\pi$
$37$	2.68895e20	0.181493	0.0907465	+	0.995874i	$0.471075\pi$
$38$	1.14452e21	0.538947
$39$	−1.26167e21	−0.418384
$40$	−6.71089e20	−0.158114
$41$	8.50604e21	1.43597	0.717985	−	0.696059i	$-0.245065\pi$
$41$	8.50604e21	1.43597	0.717985	+	0.696059i	$0.245065\pi$
$42$	1.57183e20	0.0191664
$43$	−1.32531e22	−1.17623	−0.588117	−	0.808776i	$-0.700130\pi$
$43$	−1.32531e22	−1.17623	−0.588117	+	0.808776i	$0.700130\pi$
$44$	1.04996e22	0.683223
$45$	8.55313e21	0.410919
$46$	−3.80813e22	−1.35982
$47$	−4.40838e22	−1.17749	−0.588745	−	0.808318i	$-0.700378\pi$
$47$	−4.40838e22	−1.17749	−0.588745	+	0.808318i	$0.700378\pi$
$48$	3.54293e21	0.0712206
$49$	−6.51175e22	−0.990947
$50$	1.22070e22	0.141421
$51$	−2.95433e22	−0.261976
$52$	−1.07628e23	−0.734310
$53$	−3.29888e23	−1.74037	−0.870187	−	0.492722i	$-0.836002\pi$
$53$	−3.29888e23	−1.74037	−0.870187	+	0.492722i	$0.836002\pi$
$54$	−9.42986e22	−0.386536
$55$	−1.90987e23	−0.611093
$56$	1.34086e22	0.0336392
$57$	1.09910e23	0.217133
$58$	3.27778e23	0.512038
$59$	−6.47621e23	−0.803191	−0.401595	−	0.915817i	$-0.631544\pi$
$59$	−6.47621e23	−0.803191	−0.401595	+	0.915817i	$0.631544\pi$
$60$	−6.44455e22	−0.0637016
$61$	−9.24075e23	−0.730726	−0.365363	−	0.930865i	$-0.619055\pi$
$61$	−9.24075e23	−0.730726	−0.365363	+	0.930865i	$0.619055\pi$
$62$	−1.54981e24	−0.983988
$63$	−1.70895e23	−0.0874242
$64$	3.02231e23	0.125000
$65$	1.95774e24	0.656787
$66$	1.00829e24	0.275260
$67$	−2.10405e24	−0.468863	−0.234432	−	0.972133i	$-0.575323\pi$
$67$	−2.10405e24	−0.468863	−0.234432	+	0.972133i	$0.575323\pi$
$68$	−2.52021e24	−0.459797
$69$	−3.65700e24	−0.547850
$70$	−2.43901e23	−0.0300878
$71$	6.52419e24	0.664567	0.332283	−	0.943180i	$-0.392181\pi$
$71$	6.52419e24	0.664567	0.332283	+	0.943180i	$0.392181\pi$
$72$	−3.85199e24	−0.324860
$73$	9.44471e24	0.661196	0.330598	−	0.943772i	$-0.392750\pi$
$73$	9.44471e24	0.661196	0.330598	+	0.943772i	$0.392750\pi$
$74$	2.20279e24	0.128335
$75$	1.17226e24	0.0569764
$76$	9.37594e24	0.381093
$77$	3.81600e24	0.130012
$78$	−1.03356e25	−0.295842
$79$	3.61816e24	0.0872012	0.0436006	−	0.999049i	$-0.486117\pi$
$79$	3.61816e24	0.0872012	0.0436006	+	0.999049i	$0.486117\pi$
$80$	−5.49756e24	−0.111803
$81$	4.43748e25	0.763113
$82$	6.96814e25	1.01538
$83$	9.10508e25	1.12650	0.563248	−	0.826288i	$-0.309552\pi$
$83$	9.10508e25	1.12650	0.563248	+	0.826288i	$0.309552\pi$
$84$	1.28765e24	0.0135527
$85$	4.58423e25	0.411255
$86$	−1.08569e26	−0.831723
$87$	3.14769e25	0.206292
$88$	8.60128e25	0.483111
$89$	3.18108e26	1.53395	0.766973	−	0.641679i	$-0.221762\pi$
$89$	3.18108e26	1.53395	0.766973	+	0.641679i	$0.221762\pi$
$90$	7.00672e25	0.290563
$91$	−3.91164e25	−0.139733
$92$	−3.11962e26	−0.961538
$93$	−1.48830e26	−0.396433
$94$	−3.61134e26	−0.832612
$95$	−1.70547e26	−0.340860
$96$	2.90237e25	0.0503605
$97$	3.11846e26	0.470459	0.235229	−	0.971940i	$-0.424416\pi$
$97$	3.11846e26	0.470459	0.235229	+	0.971940i	$0.424416\pi$
$98$	−5.33442e26	−0.700706
$99$	−1.09625e27	−1.25555
$100$	1.00000e26	0.100000
$101$	−8.53804e26	−0.746482	−0.373241	−	0.927734i	$-0.621754\pi$
$101$	−8.53804e26	−0.746482	−0.373241	+	0.927734i	$0.621754\pi$
$102$	−2.42019e26	−0.185245
$103$	1.09712e27	0.736123	0.368062	−	0.929801i	$-0.380022\pi$
$103$	1.09712e27	0.736123	0.368062	+	0.929801i	$0.380022\pi$
$104$	−8.81688e26	−0.519236
$105$	−2.34221e25	−0.0121219
$106$	−2.70244e27	−1.23063
$107$	1.02584e27	0.411527	0.205764	−	0.978602i	$-0.434032\pi$
$107$	1.02584e27	0.411527	0.205764	+	0.978602i	$0.434032\pi$
$108$	−7.72494e26	−0.273322
$109$	1.45319e27	0.454008	0.227004	−	0.973894i	$-0.427107\pi$
$109$	1.45319e27	0.454008	0.227004	+	0.973894i	$0.427107\pi$
$110$	−1.56456e27	−0.432108
$111$	2.11537e26	0.0517041
$112$	1.09843e26	0.0237865
$113$	−8.27745e26	−0.158978	−0.0794891	−	0.996836i	$-0.525329\pi$
$113$	−8.27745e26	−0.158978	−0.0794891	+	0.996836i	$0.525329\pi$
$114$	9.00383e26	0.153537
$115$	5.67456e27	0.860026
$116$	2.68516e27	0.362066
$117$	1.12372e28	1.34943
$118$	−5.30531e27	−0.567942
$119$	−9.15948e26	−0.0874957
$120$	−5.27937e26	−0.0450438
$121$	1.13686e28	0.867173
$122$	−7.57002e27	−0.516701
$123$	6.69159e27	0.409082
$124$	−1.26960e28	−0.695784
$125$	−1.81899e27	−0.0894427
$126$	−1.39997e27	−0.0618182
$127$	1.19218e28	0.473144	0.236572	−	0.971614i	$-0.423976\pi$
$127$	1.19218e28	0.473144	0.236572	+	0.971614i	$0.423976\pi$
$128$	2.47588e27	0.0883883
$129$	−1.04261e28	−0.335088
$130$	1.60378e28	0.464419
$131$	3.02913e28	0.790961	0.395481	−	0.918474i	$-0.370578\pi$
$131$	3.02913e28	0.790961	0.395481	+	0.918474i	$0.370578\pi$
$132$	8.25992e27	0.194638
$133$	3.40760e27	0.0725190
$134$	−1.72364e28	−0.331536
$135$	1.40516e28	0.244467
$136$	−2.06455e28	−0.325126
$137$	9.52278e28	1.35843	0.679213	−	0.733941i	$-0.262321\pi$
$137$	9.52278e28	1.35843	0.679213	+	0.733941i	$0.262321\pi$
$138$	−2.99581e28	−0.387389
$139$	3.05255e28	0.358066	0.179033	−	0.983843i	$-0.442703\pi$
$139$	3.05255e28	0.358066	0.179033	+	0.983843i	$0.442703\pi$
$140$	−1.99804e27	−0.0212753
$141$	−3.46802e28	−0.335446
$142$	5.34461e28	0.469920
$143$	−2.50922e29	−2.00679
$144$	−3.15555e28	−0.229711
$145$	−4.88428e28	−0.323841
$146$	7.73710e28	0.467536
$147$	−5.12271e28	−0.282303
$148$	1.80453e28	0.0907465
$149$	−4.28044e29	−1.96550	−0.982751	−	0.184936i	$-0.940792\pi$
$149$	−4.28044e29	−1.96550	−0.982751	+	0.184936i	$0.940792\pi$
$150$	9.60312e27	0.0402884
$151$	−3.33767e29	−1.28013	−0.640066	−	0.768320i	$-0.721093\pi$
$151$	−3.33767e29	−1.28013	−0.640066	+	0.768320i	$0.721093\pi$
$152$	7.68077e28	0.269474
$153$	2.63131e29	0.844962
$154$	3.12606e28	0.0919323
$155$	2.30939e29	0.622328
$156$	−8.46695e28	−0.209192
$157$	−1.69907e29	−0.385093	−0.192546	−	0.981288i	$-0.561675\pi$
$157$	−1.69907e29	−0.385093	−0.192546	+	0.981288i	$0.561675\pi$
$158$	2.96400e28	0.0616605
$159$	−2.59519e29	−0.495802
$160$	−4.50360e28	−0.0790569
$161$	−1.13380e29	−0.182973
$162$	3.63518e29	0.539602
$163$	−5.25888e29	−0.718391	−0.359196	−	0.933262i	$-0.616949\pi$
$163$	−5.25888e29	−0.718391	−0.359196	+	0.933262i	$0.616949\pi$
$164$	5.70830e29	0.717985
$165$	−1.50247e29	−0.174090
$166$	7.45888e29	0.796552
$167$	1.73272e30	1.70630	0.853149	−	0.521667i	$-0.174690\pi$
$167$	1.73272e30	1.70630	0.853149	+	0.521667i	$0.174690\pi$
$168$	1.05484e28	0.00958321
$169$	1.37958e30	1.15685
$170$	3.75540e29	0.290801
$171$	−9.78926e29	−0.700329
$172$	−8.89401e29	−0.588117
$173$	4.42261e29	0.270431	0.135215	−	0.990816i	$-0.456827\pi$
$173$	4.42261e29	0.270431	0.135215	+	0.990816i	$0.456827\pi$
$174$	2.57859e29	0.145871
$175$	3.63441e28	0.0190292
$176$	7.04617e29	0.341611
$177$	−5.09475e29	−0.228815
$178$	2.60594e30	1.08466
$179$	−3.27531e29	−0.126397	−0.0631984	−	0.998001i	$-0.520130\pi$
$179$	−3.27531e29	−0.126397	−0.0631984	+	0.998001i	$0.520130\pi$
$180$	5.73991e29	0.205459
$181$	1.79864e30	0.597424	0.298712	−	0.954343i	$-0.403443\pi$
$181$	1.79864e30	0.597424	0.298712	+	0.954343i	$0.403443\pi$
$182$	−3.20442e29	−0.0988065
$183$	−7.26958e29	−0.208171
$184$	−2.55560e30	−0.679910
$185$	−3.28241e29	−0.0811661
$186$	−1.21921e30	−0.280321
$187$	−5.87557e30	−1.25657
$188$	−2.95841e30	−0.588745
$189$	−2.80756e29	−0.0520110
$190$	−1.39712e30	−0.241025
$191$	6.47244e29	0.104020	0.0520101	−	0.998647i	$-0.483437\pi$
$191$	6.47244e29	0.104020	0.0520101	+	0.998647i	$0.483437\pi$
$192$	2.37762e29	0.0356103
$193$	−6.41550e28	−0.00895791	−0.00447895	−	0.999990i	$-0.501426\pi$
$193$	−6.41550e28	−0.00895791	−0.00447895	+	0.999990i	$0.501426\pi$
$194$	2.55464e30	0.332664
$195$	1.54013e30	0.187107
$196$	−4.36996e30	−0.495474
$197$	−1.36364e31	−1.44346	−0.721732	−	0.692173i	$-0.756653\pi$
$197$	−1.36364e31	−1.44346	−0.721732	+	0.692173i	$0.756653\pi$
$198$	−8.98045e30	−0.887806
$199$	1.77125e31	1.63592	0.817962	−	0.575273i	$-0.195104\pi$
$199$	1.77125e31	1.63592	0.817962	+	0.575273i	$0.195104\pi$
$200$	8.19200e29	0.0707107
$201$	−1.65523e30	−0.133571
$202$	−6.99436e30	−0.527843
$203$	9.75898e29	0.0688982
$204$	−1.98262e30	−0.130988
$205$	−1.03833e31	−0.642185
$206$	8.98758e30	0.520518
$207$	3.25714e31	1.76700
$208$	−7.22279e30	−0.367155
$209$	2.18589e31	1.04149
$210$	−1.91874e29	−0.00857149
$211$	−3.07396e31	−1.28791	−0.643955	−	0.765063i	$-0.722708\pi$
$211$	−3.07396e31	−1.28791	−0.643955	+	0.765063i	$0.722708\pi$
$212$	−2.21384e31	−0.870187
$213$	5.13250e30	0.189323
$214$	8.40368e30	0.290994
$215$	1.61781e31	0.526028
$216$	−6.32827e30	−0.193268
$217$	−4.61426e30	−0.132402
$218$	1.19045e31	0.321032
$219$	7.43004e30	0.188363
$220$	−1.28169e31	−0.305546
$221$	6.02284e31	1.35054
$222$	1.73291e30	0.0365603
$223$	−2.77369e31	−0.550735	−0.275367	−	0.961339i	$-0.588800\pi$
$223$	−2.77369e31	−0.550735	−0.275367	+	0.961339i	$0.588800\pi$
$224$	8.99837e29	0.0168196
$225$	−1.04408e31	−0.183768
$226$	−6.78089e30	−0.112415
$227$	−6.22052e30	−0.0971578	−0.0485789	−	0.998819i	$-0.515469\pi$
$227$	−6.22052e30	−0.0971578	−0.0485789	+	0.998819i	$0.515469\pi$
$228$	7.37594e30	0.108567
$229$	1.25376e32	1.73954	0.869770	−	0.493458i	$-0.164267\pi$
$229$	1.25376e32	1.73954	0.869770	+	0.493458i	$0.164267\pi$
$230$	4.64860e31	0.608130
$231$	3.00200e30	0.0370381
$232$	2.19968e31	0.256019
$233$	−1.22009e32	−1.33994	−0.669970	−	0.742388i	$-0.733693\pi$
$233$	−1.22009e32	−1.33994	−0.669970	+	0.742388i	$0.733693\pi$
$234$	9.20555e31	0.954192
$235$	5.38132e31	0.526590
$236$	−4.34611e31	−0.401595
$237$	2.84636e30	0.0248421
$238$	−7.50345e30	−0.0618688
$239$	−1.02378e32	−0.797690	−0.398845	−	0.917018i	$-0.630589\pi$
$239$	−1.02378e32	−0.797690	−0.398845	+	0.917018i	$0.630589\pi$
$240$	−4.32486e30	−0.0318508
$241$	−2.18292e32	−1.51988	−0.759938	−	0.649995i	$-0.774771\pi$
$241$	−2.18292e32	−1.51988	−0.759938	+	0.649995i	$0.774771\pi$
$242$	9.31318e31	0.613184
$243$	1.22688e32	0.764041
$244$	−6.20136e31	−0.365363
$245$	7.94891e31	0.443165
$246$	5.48175e31	0.289265
$247$	−2.24068e32	−1.11936
$248$	−1.04006e32	−0.491994
$249$	7.16285e31	0.320918
$250$	−1.49012e31	−0.0632456
$251$	−8.02953e31	−0.322920	−0.161460	−	0.986879i	$-0.551620\pi$
$251$	−8.02953e31	−0.322920	−0.161460	+	0.986879i	$0.551620\pi$
$252$	−1.14686e31	−0.0437121
$253$	−7.27304e32	−2.62778
$254$	9.76637e31	0.334563
$255$	3.60636e31	0.117159
$256$	2.02824e31	0.0625000
$257$	−9.14634e29	−0.00267393	−0.00133697	−	0.999999i	$-0.500426\pi$
$257$	−9.14634e29	−0.00267393	−0.00133697	+	0.999999i	$0.500426\pi$
$258$	−8.54102e31	−0.236943
$259$	6.55839e30	0.0172683
$260$	1.31382e32	0.328394
$261$	−2.80353e32	−0.665362
$262$	2.48146e32	0.559294
$263$	−4.16605e32	−0.891912	−0.445956	−	0.895055i	$-0.647136\pi$
$263$	−4.16605e32	−0.891912	−0.445956	+	0.895055i	$0.647136\pi$
$264$	6.76652e31	0.137630
$265$	4.02696e32	0.778319
$266$	2.79151e31	0.0512787
$267$	2.50252e32	0.436994
$268$	−1.41200e32	−0.234432
$269$	9.95223e32	1.57132	0.785660	−	0.618659i	$-0.212324\pi$
$269$	9.95223e32	1.57132	0.785660	+	0.618659i	$0.212324\pi$
$270$	1.15111e32	0.172864
$271$	−3.38305e32	−0.483307	−0.241654	−	0.970363i	$-0.577690\pi$
$271$	−3.38305e32	−0.483307	−0.241654	+	0.970363i	$0.577690\pi$
$272$	−1.69128e32	−0.229899
$273$	−3.07724e31	−0.0398076
$274$	7.80106e32	0.960552
$275$	2.33138e32	0.273289
$276$	−2.45417e32	−0.273925
$277$	1.06018e33	1.12694	0.563472	−	0.826135i	$-0.309465\pi$
$277$	1.06018e33	1.12694	0.563472	+	0.826135i	$0.309465\pi$
$278$	2.50065e32	0.253191
$279$	1.32557e33	1.27863
$280$	−1.63679e31	−0.0150439
$281$	9.26140e32	0.811225	0.405613	−	0.914045i	$-0.367058\pi$
$281$	9.26140e32	0.811225	0.405613	+	0.914045i	$0.367058\pi$
$282$	−2.84100e32	−0.237196
$283$	−4.46833e32	−0.355655	−0.177827	−	0.984062i	$-0.556907\pi$
$283$	−4.46833e32	−0.355655	−0.177827	+	0.984062i	$0.556907\pi$
$284$	4.37831e32	0.332283
$285$	−1.34167e32	−0.0971050
$286$	−2.05555e33	−1.41901
$287$	2.07463e32	0.136627
$288$	−2.58502e32	−0.162430
$289$	−2.57406e32	−0.154347
$290$	−4.00120e32	−0.228990
$291$	2.45325e32	0.134025
$292$	6.33824e32	0.330598
$293$	−3.29906e33	−1.64315	−0.821576	−	0.570098i	$-0.806905\pi$
$293$	−3.29906e33	−1.64315	−0.821576	+	0.570098i	$0.806905\pi$
$294$	−4.19653e32	−0.199619
$295$	7.90553e32	0.359198
$296$	1.47827e32	0.0641674
$297$	−1.80098e33	−0.746959
$298$	−3.50653e33	−1.38982
$299$	7.45534e33	2.82427
$300$	7.86688e31	0.0284882
$301$	−3.23245e32	−0.111914
$302$	−2.73422e33	−0.905190
$303$	−6.71677e32	−0.212660
$304$	6.29209e32	0.190547
$305$	1.12802e33	0.326790
$306$	2.15557e33	0.597478
$307$	−7.19835e33	−1.90926	−0.954629	−	0.297796i	$-0.903748\pi$
$307$	−7.19835e33	−1.90926	−0.954629	+	0.297796i	$0.903748\pi$
$308$	2.56087e32	0.0650059
$309$	8.63089e32	0.209708
$310$	1.89185e33	0.440053
$311$	−7.47510e33	−1.66476	−0.832381	−	0.554204i	$-0.813023\pi$
$311$	−7.47510e33	−1.66476	−0.832381	+	0.554204i	$0.813023\pi$
$312$	−6.93613e32	−0.147921
$313$	2.05380e33	0.419479	0.209740	−	0.977757i	$-0.432738\pi$
$313$	2.05380e33	0.419479	0.209740	+	0.977757i	$0.432738\pi$
$314$	−1.39188e33	−0.272302
$315$	2.08612e32	0.0390973
$316$	2.42811e32	0.0436006
$317$	2.12465e33	0.365583	0.182792	−	0.983152i	$-0.441487\pi$
$317$	2.12465e33	0.365583	0.182792	+	0.983152i	$0.441487\pi$
$318$	−2.12598e33	−0.350585
$319$	6.26013e33	0.989485
$320$	−3.68935e32	−0.0559017
$321$	8.07015e32	0.117237
$322$	−9.28809e32	−0.129382
$323$	−5.24676e33	−0.700902
$324$	2.97794e33	0.381556
$325$	−2.38982e33	−0.293724
$326$	−4.30808e33	−0.507979
$327$	1.14320e33	0.129339
$328$	4.67624e33	0.507692
$329$	−1.07521e33	−0.112034
$330$	−1.23082e33	−0.123100
$331$	1.48960e34	1.43019	0.715093	−	0.699029i	$-0.246384\pi$
$331$	1.48960e34	1.43019	0.715093	+	0.699029i	$0.246384\pi$
$332$	6.11031e33	0.563248
$333$	−1.88407e33	−0.166763
$334$	1.41944e34	1.20654
$335$	2.56842e33	0.209682
$336$	8.64125e31	0.00677636
$337$	−7.49821e33	−0.564877	−0.282439	−	0.959285i	$-0.591143\pi$
$337$	−7.49821e33	−0.564877	−0.282439	+	0.959285i	$0.591143\pi$
$338$	1.13015e34	0.818015
$339$	−6.51177e32	−0.0452901
$340$	3.07643e33	0.205627
$341$	−2.95993e34	−1.90150
$342$	−8.01936e33	−0.495207
$343$	−3.19096e33	−0.189431
$344$	−7.28597e33	−0.415861
$345$	4.46411e33	0.245006
$346$	3.62300e33	0.191223
$347$	2.52764e34	1.28312	0.641560	−	0.767073i	$-0.278287\pi$
$347$	2.52764e34	1.28312	0.641560	+	0.767073i	$0.278287\pi$
$348$	2.11238e33	0.103146
$349$	1.38700e34	0.651529	0.325764	−	0.945451i	$-0.394378\pi$
$349$	1.38700e34	0.651529	0.325764	+	0.945451i	$0.394378\pi$
$350$	2.97731e32	0.0134557
$351$	1.84612e34	0.802813
$352$	5.77222e33	0.241556
$353$	−1.24760e34	−0.502478	−0.251239	−	0.967925i	$-0.580838\pi$
$353$	−1.24760e34	−0.502478	−0.251239	+	0.967925i	$0.580838\pi$
$354$	−4.17362e33	−0.161796
$355$	−7.96409e33	−0.297203
$356$	2.13479e34	0.766973
$357$	−7.20565e32	−0.0249260
$358$	−2.68313e33	−0.0893761
$359$	−4.30170e34	−1.37995	−0.689977	−	0.723831i	$-0.742379\pi$
$359$	−4.30170e34	−1.37995	−0.689977	+	0.723831i	$0.742379\pi$
$360$	4.70213e33	0.145282
$361$	−1.40811e34	−0.419072
$362$	1.47344e34	0.422443
$363$	8.94356e33	0.247042
$364$	−2.62506e33	−0.0698667
$365$	−1.15292e34	−0.295696
$366$	−5.95524e33	−0.147199
$367$	3.46384e34	0.825213	0.412607	−	0.910909i	$-0.364618\pi$
$367$	3.46384e34	0.825213	0.412607	+	0.910909i	$0.364618\pi$
$368$	−2.09354e34	−0.480769
$369$	−5.95994e34	−1.31943
$370$	−2.68895e33	−0.0573931
$371$	−8.04602e33	−0.165590
$372$	−9.98780e33	−0.198217
$373$	4.17174e34	0.798451	0.399226	−	0.916853i	$-0.369279\pi$
$373$	4.17174e34	0.798451	0.399226	+	0.916853i	$0.369279\pi$
$374$	−4.81327e34	−0.888533
$375$	−1.43098e33	−0.0254806
$376$	−2.42353e34	−0.416306
$377$	−6.41705e34	−1.06347
$378$	−2.29996e33	−0.0367773
$379$	−3.57084e34	−0.550987	−0.275494	−	0.961303i	$-0.588841\pi$
$379$	−3.57084e34	−0.550987	−0.275494	+	0.961303i	$0.588841\pi$
$380$	−1.14452e34	−0.170430
$381$	9.37876e33	0.134790
$382$	5.30222e33	0.0735534
$383$	−3.61414e34	−0.483973	−0.241987	−	0.970280i	$-0.577799\pi$
$383$	−3.61414e34	−0.483973	−0.241987	+	0.970280i	$0.577799\pi$
$384$	1.94774e33	0.0251803
$385$	−4.65820e33	−0.0581431
$386$	−5.25557e32	−0.00633420
$387$	9.28608e34	1.08077
$388$	2.09276e34	0.235229
$389$	−2.21108e34	−0.240041	−0.120020	−	0.992771i	$-0.538296\pi$
$389$	−2.21108e34	−0.240041	−0.120020	+	0.992771i	$0.538296\pi$
$390$	1.26167e34	0.132305
$391$	1.74574e35	1.76845
$392$	−3.57987e34	−0.350353
$393$	2.38298e34	0.225331
$394$	−1.11709e35	−1.02068
$395$	−4.41670e33	−0.0389975
$396$	−7.35679e34	−0.627774
$397$	3.17208e34	0.261621	0.130810	−	0.991407i	$-0.458242\pi$
$397$	3.17208e34	0.261621	0.130810	+	0.991407i	$0.458242\pi$
$398$	1.45101e35	1.15677
$399$	2.68072e33	0.0206594
$400$	6.71089e33	0.0500000
$401$	2.56968e35	1.85110	0.925549	−	0.378628i	$-0.123604\pi$
$401$	2.56968e35	1.85110	0.925549	+	0.378628i	$0.123604\pi$
$402$	−1.35596e34	−0.0944488
$403$	3.03412e35	2.04369
$404$	−5.72978e34	−0.373241
$405$	−5.41685e34	−0.341274
$406$	7.99456e33	0.0487184
$407$	4.20704e34	0.248000
$408$	−1.62416e34	−0.0926225
$409$	−1.31563e35	−0.725885	−0.362942	−	0.931812i	$-0.618228\pi$
$409$	−1.31563e35	−0.725885	−0.362942	+	0.931812i	$0.618228\pi$
$410$	−8.50604e34	−0.454093
$411$	7.49145e34	0.386991
$412$	7.36263e34	0.368062
$413$	−1.57956e34	−0.0764204
$414$	2.66825e35	1.24946
$415$	−1.11146e35	−0.503784
$416$	−5.91691e34	−0.259618
$417$	2.40141e34	0.102007
$418$	1.79068e35	0.736442
$419$	−1.77721e35	−0.707702	−0.353851	−	0.935302i	$-0.615128\pi$
$419$	−1.77721e35	−0.707702	−0.353851	+	0.935302i	$0.615128\pi$
$420$	−1.57183e33	−0.00606096
$421$	−4.73825e35	−1.76933	−0.884667	−	0.466223i	$-0.845614\pi$
$421$	−4.73825e35	−1.76933	−0.884667	+	0.466223i	$0.845614\pi$
$422$	−2.51819e35	−0.910690
$423$	3.08883e35	1.08193
$424$	−1.81358e35	−0.615315
$425$	−5.59599e34	−0.183919
$426$	4.20454e34	0.133872
$427$	−2.25383e34	−0.0695257
$428$	6.88429e34	0.205764
$429$	−1.97397e35	−0.571699
$430$	1.32531e35	0.371958
$431$	−2.46508e35	−0.670484	−0.335242	−	0.942132i	$-0.608818\pi$
$431$	−2.46508e35	−0.670484	−0.335242	+	0.942132i	$0.608818\pi$
$432$	−5.18412e34	−0.136661
$433$	−4.00013e35	−1.02209	−0.511043	−	0.859555i	$-0.670741\pi$
$433$	−4.00013e35	−1.02209	−0.511043	+	0.859555i	$0.670741\pi$
$434$	−3.78000e34	−0.0936226
$435$	−3.84240e34	−0.0922566
$436$	9.75217e34	0.227004
$437$	−6.49467e35	−1.46574
$438$	6.08668e34	0.133193
$439$	5.56669e35	1.18121	0.590603	−	0.806962i	$-0.298890\pi$
$439$	5.56669e35	1.18121	0.590603	+	0.806962i	$0.298890\pi$
$440$	−1.04996e35	−0.216054
$441$	4.56260e35	0.910524
$442$	4.93391e35	0.954972
$443$	−9.29221e34	−0.174449	−0.0872246	−	0.996189i	$-0.527800\pi$
$443$	−9.29221e34	−0.174449	−0.0872246	+	0.996189i	$0.527800\pi$
$444$	1.41960e34	0.0258521
$445$	−3.88316e35	−0.686002
$446$	−2.27221e35	−0.389428
$447$	−3.36737e35	−0.559936
$448$	7.37147e33	0.0118933
$449$	−1.08452e36	−1.69789	−0.848946	−	0.528479i	$-0.822762\pi$
$449$	−1.08452e36	−1.69789	−0.848946	+	0.528479i	$0.822762\pi$
$450$	−8.55313e34	−0.129944
$451$	1.33082e36	1.96217
$452$	−5.55490e34	−0.0794891
$453$	−2.62571e35	−0.364687
$454$	−5.09585e34	−0.0687010
$455$	4.77496e34	0.0624907
$456$	6.04237e34	0.0767683
$457$	1.55761e35	0.192128	0.0960640	−	0.995375i	$-0.469375\pi$
$457$	1.55761e35	0.192128	0.0960640	+	0.995375i	$0.469375\pi$
$458$	1.02708e36	1.23004
$459$	4.32287e35	0.502691
$460$	3.80813e35	0.430013
$461$	−1.20864e35	−0.132537	−0.0662683	−	0.997802i	$-0.521109\pi$
$461$	−1.20864e35	−0.132537	−0.0662683	+	0.997802i	$0.521109\pi$
$462$	2.45924e34	0.0261899
$463$	−1.68010e35	−0.173777	−0.0868886	−	0.996218i	$-0.527692\pi$
$463$	−1.68010e35	−0.173777	−0.0868886	+	0.996218i	$0.527692\pi$
$464$	1.80198e35	0.181033
$465$	1.81677e35	0.177290
$466$	−9.99494e35	−0.947480
$467$	4.47847e35	0.412431	0.206216	−	0.978507i	$-0.433885\pi$
$467$	4.47847e35	0.412431	0.206216	+	0.978507i	$0.433885\pi$
$468$	7.54119e35	0.674715
$469$	−5.13181e34	−0.0446105
$470$	4.40838e35	0.372355
$471$	−1.33664e35	−0.109706
$472$	−3.56033e35	−0.283971
$473$	−2.07353e36	−1.60726
$474$	2.33174e34	0.0175660
$475$	2.08188e35	0.152437
$476$	−6.14682e34	−0.0437479
$477$	2.31143e36	1.59913
$478$	−8.38679e35	−0.564052
$479$	2.57973e36	1.68673	0.843364	−	0.537343i	$-0.180572\pi$
$479$	2.57973e36	1.68673	0.843364	+	0.537343i	$0.180572\pi$
$480$	−3.54293e34	−0.0225219
$481$	−4.31249e35	−0.266544
$482$	−1.78825e36	−1.07471
$483$	−8.91947e34	−0.0521258
$484$	7.62936e35	0.433586
$485$	−3.80671e35	−0.210395
$486$	1.00506e36	0.540259
$487$	1.89812e36	0.992390	0.496195	−	0.868211i	$-0.334730\pi$
$487$	1.89812e36	0.992390	0.496195	+	0.868211i	$0.334730\pi$
$488$	−5.08015e35	−0.258351
$489$	−4.13710e35	−0.204657
$490$	6.51175e35	0.313365
$491$	−8.37086e34	−0.0391895	−0.0195947	−	0.999808i	$-0.506238\pi$
$491$	−8.37086e34	−0.0391895	−0.0195947	+	0.999808i	$0.506238\pi$
$492$	4.49065e35	0.204541
$493$	−1.50261e36	−0.665907
$494$	−1.83557e36	−0.791509
$495$	1.33819e36	0.561498
$496$	−8.52015e35	−0.347892
$497$	1.59126e35	0.0632309
$498$	5.86781e35	0.226924
$499$	1.76824e36	0.665554	0.332777	−	0.943005i	$-0.392014\pi$
$499$	1.76824e36	0.665554	0.332777	+	0.943005i	$0.392014\pi$
$500$	−1.22070e35	−0.0447214
$501$	1.36311e36	0.486094
$502$	−6.57779e35	−0.228339
$503$	−3.64441e36	−1.23157	−0.615786	−	0.787913i	$-0.711161\pi$
$503$	−3.64441e36	−1.23157	−0.615786	+	0.787913i	$0.711161\pi$
$504$	−9.39505e34	−0.0309091
$505$	1.04224e36	0.333837
$506$	−5.95807e36	−1.85812
$507$	1.08530e36	0.329565
$508$	8.00061e35	0.236572
$509$	7.64417e35	0.220110	0.110055	−	0.993925i	$-0.464897\pi$
$509$	7.64417e35	0.220110	0.110055	+	0.993925i	$0.464897\pi$
$510$	2.95433e35	0.0828441
$511$	2.30358e35	0.0629101
$512$	1.66153e35	0.0441942
$513$	−1.60824e36	−0.416645
$514$	−7.49268e33	−0.00189076
$515$	−1.33925e36	−0.329204
$516$	−6.99681e35	−0.167544
$517$	−6.89719e36	−1.60898
$518$	5.37263e34	0.0122106
$519$	3.47921e35	0.0770409
$520$	1.07628e36	0.232209
$521$	−7.23178e36	−1.52032	−0.760161	−	0.649734i	$-0.774880\pi$
$521$	−7.23178e36	−1.52032	−0.760161	+	0.649734i	$0.774880\pi$
$522$	−2.29665e36	−0.470482
$523$	−3.07997e36	−0.614856	−0.307428	−	0.951571i	$-0.599468\pi$
$523$	−3.07997e36	−0.614856	−0.307428	+	0.951571i	$0.599468\pi$
$524$	2.03281e36	0.395481
$525$	2.85915e34	0.00542108
$526$	−3.41283e36	−0.630677
$527$	7.10467e36	1.27968
$528$	5.54314e35	0.0973190
$529$	1.57663e37	2.69822
$530$	3.29888e36	0.550355
$531$	4.53770e36	0.738005
$532$	2.28680e35	0.0362595
$533$	−1.36418e37	−2.10889
$534$	2.05006e36	0.309001
$535$	−1.25225e36	−0.184041
$536$	−1.15671e36	−0.165768
$537$	−2.57664e35	−0.0360082
$538$	8.15286e36	1.11109
$539$	−1.01881e37	−1.35408
$540$	9.42986e35	0.122233
$541$	1.36003e37	1.71943	0.859714	−	0.510775i	$-0.170642\pi$
$541$	1.36003e37	1.71943	0.859714	+	0.510775i	$0.170642\pi$
$542$	−2.77140e36	−0.341750
$543$	1.41497e36	0.170196
$544$	−1.38550e36	−0.162563
$545$	−1.77391e36	−0.203039
$546$	−2.52088e35	−0.0281482
$547$	−2.33868e36	−0.254767	−0.127383	−	0.991854i	$-0.540658\pi$
$547$	−2.33868e36	−0.254767	−0.127383	+	0.991854i	$0.540658\pi$
$548$	6.39063e36	0.679213
$549$	6.47473e36	0.671421
$550$	1.90987e36	0.193245
$551$	5.59017e36	0.551923
$552$	−2.01046e36	−0.193694
$553$	8.82475e34	0.00829685
$554$	8.68499e36	0.796870
$555$	−2.58223e35	−0.0231228
$556$	2.04853e36	0.179033
$557$	−1.34839e37	−1.15019	−0.575095	−	0.818087i	$-0.695035\pi$
$557$	−1.34839e37	−1.15019	−0.575095	+	0.818087i	$0.695035\pi$
$558$	1.08591e37	0.904129
$559$	2.12551e37	1.72744
$560$	−1.34086e35	−0.0106377
$561$	−4.62224e36	−0.357976
$562$	7.58694e36	0.573623
$563$	−1.19905e37	−0.885060	−0.442530	−	0.896754i	$-0.645919\pi$
$563$	−1.19905e37	−0.885060	−0.442530	+	0.896754i	$0.645919\pi$
$564$	−2.32735e36	−0.167723
$565$	1.01043e36	0.0710972
$566$	−3.66046e36	−0.251486
$567$	1.08231e36	0.0726072
$568$	3.58671e36	0.234960
$569$	−2.22877e37	−1.42577	−0.712884	−	0.701282i	$-0.752611\pi$
$569$	−2.22877e37	−1.42577	−0.712884	+	0.701282i	$0.752611\pi$
$570$	−1.09910e36	−0.0686636
$571$	1.08564e37	0.662365	0.331182	−	0.943567i	$-0.392552\pi$
$571$	1.08564e37	0.662365	0.331182	+	0.943567i	$0.392552\pi$
$572$	−1.68391e37	−1.00339
$573$	5.09179e35	0.0296335
$574$	1.69954e36	0.0966097
$575$	−6.92696e36	−0.384615
$576$	−2.11765e36	−0.114855
$577$	2.64597e37	1.40188	0.700942	−	0.713218i	$-0.252763\pi$
$577$	2.64597e37	1.40188	0.700942	+	0.713218i	$0.252763\pi$
$578$	−2.10867e36	−0.109140
$579$	−5.04699e34	−0.00255195
$580$	−3.27778e36	−0.161921
$581$	2.22074e36	0.107182
$582$	2.00970e36	0.0947702
$583$	−5.16131e37	−2.37813
$584$	5.19228e36	0.233768
$585$	−1.37173e37	−0.603484
$586$	−2.70259e37	−1.16188
$587$	−2.85761e37	−1.20057	−0.600286	−	0.799785i	$-0.704947\pi$
$587$	−2.85761e37	−1.20057	−0.600286	+	0.799785i	$0.704947\pi$
$588$	−3.43779e36	−0.141152
$589$	−2.64315e37	−1.06063
$590$	6.47621e36	0.253991
$591$	−1.07276e37	−0.411217
$592$	1.21100e36	0.0453732
$593$	5.14830e37	1.88550	0.942748	−	0.333506i	$-0.108232\pi$
$593$	5.14830e37	1.88550	0.942748	+	0.333506i	$0.108232\pi$
$594$	−1.47536e37	−0.528180
$595$	1.11810e36	0.0391293
$596$	−2.87255e37	−0.982751
$597$	1.39342e37	0.466045
$598$	6.10741e37	1.99706
$599$	−2.26841e37	−0.725202	−0.362601	−	0.931944i	$-0.618111\pi$
$599$	−2.26841e37	−0.725202	−0.362601	+	0.931944i	$0.618111\pi$
$600$	6.44455e35	0.0201442
$601$	2.68428e37	0.820395	0.410197	−	0.911997i	$-0.365460\pi$
$601$	2.68428e37	0.820395	0.410197	+	0.911997i	$0.365460\pi$
$602$	−2.64802e36	−0.0791351
$603$	1.47425e37	0.430811
$604$	−2.23987e37	−0.640066
$605$	−1.38777e37	−0.387811
$606$	−5.50238e36	−0.150373
$607$	2.71824e37	0.726508	0.363254	−	0.931690i	$-0.381666\pi$
$607$	2.71824e37	0.726508	0.363254	+	0.931690i	$0.381666\pi$
$608$	5.15448e36	0.134737
$609$	7.67727e35	0.0196279
$610$	9.24075e36	0.231076
$611$	7.07007e37	1.72929
$612$	1.76584e37	0.422481
$613$	−2.70461e36	−0.0632977	−0.0316488	−	0.999499i	$-0.510076\pi$
$613$	−2.70461e36	−0.0632977	−0.0316488	+	0.999499i	$0.510076\pi$
$614$	−5.89689e37	−1.35005
$615$	−8.16845e36	−0.182947
$616$	2.09787e36	0.0459661
$617$	5.25699e37	1.12691	0.563453	−	0.826148i	$-0.309473\pi$
$617$	5.25699e37	1.12691	0.563453	+	0.826148i	$0.309473\pi$
$618$	7.07042e36	0.148286
$619$	−1.09889e37	−0.225492	−0.112746	−	0.993624i	$-0.535965\pi$
$619$	−1.09889e37	−0.225492	−0.112746	+	0.993624i	$0.535965\pi$
$620$	1.54981e37	0.311164
$621$	5.35103e37	1.05124
$622$	−6.12361e37	−1.17716
$623$	7.75871e36	0.145949
$624$	−5.68208e36	−0.104596
$625$	2.22045e36	0.0400000
$626$	1.68248e37	0.296616
$627$	1.71961e37	0.296701
$628$	−1.14022e37	−0.192546
$629$	−1.00981e37	−0.166900
$630$	1.70895e36	0.0276460
$631$	−8.11189e37	−1.28448	−0.642238	−	0.766506i	$-0.721994\pi$
$631$	−8.11189e37	−1.28448	−0.642238	+	0.766506i	$0.721994\pi$
$632$	1.98911e36	0.0308303
$633$	−2.41825e37	−0.366903
$634$	1.74051e37	0.258507
$635$	−1.45530e37	−0.211596
$636$	−1.74160e37	−0.247901
$637$	1.04434e38	1.45533
$638$	5.12830e37	0.699672
$639$	−4.57131e37	−0.610632
$640$	−3.02231e36	−0.0395285
$641$	1.03316e38	1.32308	0.661538	−	0.749912i	$-0.269904\pi$
$641$	1.03316e38	1.32308	0.661538	+	0.749912i	$0.269904\pi$
$642$	6.61107e36	0.0828989
$643$	6.59284e37	0.809514	0.404757	−	0.914424i	$-0.367356\pi$
$643$	6.59284e37	0.809514	0.404757	+	0.914424i	$0.367356\pi$
$644$	−7.60881e36	−0.0914866
$645$	1.27271e37	0.149856
$646$	−4.29815e37	−0.495613
$647$	−3.55430e37	−0.401372	−0.200686	−	0.979656i	$-0.564317\pi$
$647$	−3.55430e37	−0.401372	−0.200686	+	0.979656i	$0.564317\pi$
$648$	2.43953e37	0.269801
$649$	−1.01324e38	−1.09752
$650$	−1.95774e37	−0.207694
$651$	−3.62998e36	−0.0377191
$652$	−3.52918e37	−0.359196
$653$	−2.81161e35	−0.00280303	−0.00140151	−	0.999999i	$-0.500446\pi$
$653$	−2.81161e35	−0.00280303	−0.00140151	+	0.999999i	$0.500446\pi$
$654$	9.36513e36	0.0914564
$655$	−3.69767e37	−0.353729
$656$	3.83078e37	0.358992
$657$	−6.61764e37	−0.607534
$658$	−8.80811e36	−0.0792197
$659$	−9.14262e37	−0.805597	−0.402798	−	0.915289i	$-0.631962\pi$
$659$	−9.14262e37	−0.805597	−0.402798	+	0.915289i	$0.631962\pi$
$660$	−1.00829e37	−0.0870448
$661$	5.68399e37	0.480766	0.240383	−	0.970678i	$-0.422727\pi$
$661$	5.68399e37	0.480766	0.240383	+	0.970678i	$0.422727\pi$
$662$	1.22028e38	1.01129
$663$	4.73810e37	0.384743
$664$	5.00557e37	0.398276
$665$	−4.15967e36	−0.0324315
$666$	−1.54343e37	−0.117920
$667$	−1.86000e38	−1.39256
$668$	1.16281e38	0.853149
$669$	−2.18203e37	−0.156895
$670$	2.10405e37	0.148268
$671$	−1.44577e38	−0.998497
$672$	7.07891e35	0.00479161
$673$	−1.14007e38	−0.756361	−0.378180	−	0.925732i	$-0.623450\pi$
$673$	−1.14007e38	−0.756361	−0.378180	+	0.925732i	$0.623450\pi$
$674$	−6.14254e37	−0.399429
$675$	−1.71528e37	−0.109329
$676$	9.25820e37	0.578424
$677$	1.44663e38	0.885950	0.442975	−	0.896534i	$-0.353923\pi$
$677$	1.44663e38	0.885950	0.442975	+	0.896534i	$0.353923\pi$
$678$	−5.33444e36	−0.0320249
$679$	7.60596e36	0.0447623
$680$	2.52021e37	0.145401
$681$	−4.89361e36	−0.0276785
$682$	−2.42477e38	−1.34457
$683$	−3.65913e38	−1.98929	−0.994645	−	0.103349i	$-0.967044\pi$
$683$	−3.65913e38	−1.98929	−0.994645	+	0.103349i	$0.967044\pi$
$684$	−6.56946e37	−0.350165
$685$	−1.16245e38	−0.607506
$686$	−2.61403e37	−0.133948
$687$	9.86315e37	0.495564
$688$	−5.96867e37	−0.294058
$689$	5.29068e38	2.55595
$690$	3.65700e37	0.173245
$691$	−3.38804e37	−0.157396	−0.0786982	−	0.996898i	$-0.525076\pi$
$691$	−3.38804e37	−0.157396	−0.0786982	+	0.996898i	$0.525076\pi$
$692$	2.96796e37	0.135215
$693$	−2.67376e37	−0.119460
$694$	2.07064e38	0.907303
$695$	−3.72626e37	−0.160132
$696$	1.73046e37	0.0729353
$697$	−3.19436e38	−1.32051
$698$	1.13623e38	0.460701
$699$	−9.59826e37	−0.381725
$700$	2.43901e36	0.00951461
$701$	−1.18033e38	−0.451657	−0.225829	−	0.974167i	$-0.572509\pi$
$701$	−1.18033e38	−0.451657	−0.225829	+	0.974167i	$0.572509\pi$
$702$	1.51234e38	0.567674
$703$	3.75680e37	0.138331
$704$	4.72861e37	0.170806
$705$	4.23342e37	0.150016
$706$	−1.02203e38	−0.355306
$707$	−2.08244e37	−0.0710248
$708$	−3.41903e37	−0.114407
$709$	2.06770e38	0.678832	0.339416	−	0.940636i	$-0.389771\pi$
$709$	2.06770e38	0.678832	0.339416	+	0.940636i	$0.389771\pi$
$710$	−6.52419e37	−0.210154
$711$	−2.53514e37	−0.0801241
$712$	1.74882e38	0.542332
$713$	8.79447e38	2.67609
$714$	−5.90287e36	−0.0176253
$715$	3.06301e38	0.897464
$716$	−2.19802e37	−0.0631984
$717$	−8.05393e37	−0.227248
$718$	−3.52395e38	−0.975775
$719$	4.45988e38	1.21194	0.605972	−	0.795486i	$-0.292784\pi$
$719$	4.45988e38	1.21194	0.605972	+	0.795486i	$0.292784\pi$
$720$	3.85199e37	0.102730
$721$	2.67588e37	0.0700392
$722$	−1.15352e38	−0.296328
$723$	−1.71728e38	−0.432986
$724$	1.20705e38	0.298712
$725$	5.96225e37	0.144826
$726$	7.32656e37	0.174685
$727$	2.82029e38	0.660054	0.330027	−	0.943971i	$-0.392942\pi$
$727$	2.82029e38	0.660054	0.330027	+	0.943971i	$0.392942\pi$
$728$	−2.15045e37	−0.0494032
$729$	−2.41867e38	−0.545451
$730$	−9.44471e37	−0.209088
$731$	4.97708e38	1.08166
$732$	−4.87853e37	−0.104085
$733$	−6.44508e38	−1.34997	−0.674985	−	0.737831i	$-0.735850\pi$
$733$	−6.44508e38	−1.34997	−0.674985	+	0.737831i	$0.735850\pi$
$734$	2.83758e38	0.583514
$735$	6.25331e37	0.126250
$736$	−1.71503e38	−0.339955
$737$	−3.29192e38	−0.640676
$738$	−4.88238e38	−0.932977
$739$	6.59016e38	1.23650	0.618252	−	0.785980i	$-0.287841\pi$
$739$	6.59016e38	1.23650	0.618252	+	0.785980i	$0.287841\pi$
$740$	−2.20279e37	−0.0405831
$741$	−1.76272e38	−0.318887
$742$	−6.59130e37	−0.117090
$743$	−1.94056e38	−0.338515	−0.169258	−	0.985572i	$-0.554137\pi$
$743$	−1.94056e38	−0.338515	−0.169258	+	0.985572i	$0.554137\pi$
$744$	−8.18200e37	−0.140160
$745$	5.22514e38	0.878999
$746$	3.41749e38	0.564590
$747$	−6.37967e38	−1.03507
$748$	−3.94303e38	−0.628287
$749$	2.50204e37	0.0391552
$750$	−1.17226e37	−0.0180175
$751$	−9.80831e38	−1.48066	−0.740329	−	0.672245i	$-0.765330\pi$
$751$	−9.80831e38	−1.48066	−0.740329	+	0.672245i	$0.765330\pi$
$752$	−1.98536e38	−0.294373
$753$	−6.31674e37	−0.0919942
$754$	−5.25684e38	−0.751990
$755$	4.07431e38	0.572493
$756$	−1.88412e37	−0.0260055
$757$	5.73445e38	0.777494	0.388747	−	0.921344i	$-0.372908\pi$
$757$	5.73445e38	0.777494	0.388747	+	0.921344i	$0.372908\pi$
$758$	−2.92524e38	−0.389607
$759$	−5.72161e38	−0.748607
$760$	−9.37594e37	−0.120512
$761$	−1.19199e39	−1.50515	−0.752575	−	0.658507i	$-0.771188\pi$
$761$	−1.19199e39	−1.50515	−0.752575	+	0.658507i	$0.771188\pi$
$762$	7.68308e37	0.0953111
$763$	3.54434e37	0.0431971
$764$	4.34358e37	0.0520101
$765$	−3.21204e38	−0.377878
$766$	−2.96070e38	−0.342221
$767$	1.03864e39	1.17958
$768$	1.59559e37	0.0178051
$769$	−6.10545e38	−0.669441	−0.334721	−	0.942317i	$-0.608642\pi$
$769$	−6.10545e38	−0.669441	−0.334721	+	0.942317i	$0.608642\pi$
$770$	−3.81600e37	−0.0411134
$771$	−7.19531e35	−0.000761756 0
$772$	−4.30537e36	−0.00447895
$773$	−2.79488e38	−0.285720	−0.142860	−	0.989743i	$-0.545630\pi$
$773$	−2.79488e38	−0.285720	−0.142860	+	0.989743i	$0.545630\pi$
$774$	7.60716e38	0.764222
$775$	−2.81908e38	−0.278314
$776$	1.71439e38	0.166332
$777$	5.15941e36	0.00491944
$778$	−1.81132e38	−0.169734
$779$	1.18840e39	1.09448
$780$	1.03356e38	0.0935535
$781$	1.02075e39	0.908094
$782$	1.43011e39	1.25048
$783$	−4.60581e38	−0.395842
$784$	−2.93263e38	−0.247737
$785$	2.07406e38	0.172219
$786$	1.95214e38	0.159333
$787$	−2.69307e38	−0.216067	−0.108033	−	0.994147i	$-0.534455\pi$
$787$	−2.69307e38	−0.216067	−0.108033	+	0.994147i	$0.534455\pi$
$788$	−9.15123e38	−0.721732
$789$	−3.27738e38	−0.254090
$790$	−3.61816e37	−0.0275754
$791$	−2.01888e37	−0.0151262
$792$	−6.02668e38	−0.443903
$793$	1.48201e39	1.07316
$794$	2.59857e38	0.184994
$795$	3.16796e38	0.221729
$796$	1.18866e39	0.817962
$797$	−9.27331e38	−0.627404	−0.313702	−	0.949521i	$-0.601569\pi$
$797$	−9.27331e38	−0.627404	−0.313702	+	0.949521i	$0.601569\pi$
$798$	2.19605e37	0.0146084
$799$	1.65552e39	1.08281
$800$	5.49756e37	0.0353553
$801$	−2.22890e39	−1.40945
$802$	2.10508e39	1.30892
$803$	1.47769e39	0.903488
$804$	−1.11081e38	−0.0667854
$805$	1.38403e38	0.0818281
$806$	2.48555e39	1.44510
$807$	7.82929e38	0.447641
$808$	−4.69384e38	−0.263921
$809$	−2.61826e39	−1.44780	−0.723898	−	0.689907i	$-0.757651\pi$
$809$	−2.61826e39	−1.44780	−0.723898	+	0.689907i	$0.757651\pi$
$810$	−4.43748e38	−0.241317
$811$	−4.92486e38	−0.263398	−0.131699	−	0.991290i	$-0.542043\pi$
$811$	−4.92486e38	−0.263398	−0.131699	+	0.991290i	$0.542043\pi$
$812$	6.54914e37	0.0344491
$813$	−2.66140e38	−0.137686
$814$	3.44641e38	0.175363
$815$	6.41954e38	0.321274
$816$	−1.33051e38	−0.0654940
$817$	−1.85162e39	−0.896509
$818$	−1.07776e39	−0.513278
$819$	2.74078e38	0.128393
$820$	−6.96814e38	−0.321093
$821$	4.69442e38	0.212789	0.106394	−	0.994324i	$-0.466069\pi$
$821$	4.69442e38	0.212789	0.106394	+	0.994324i	$0.466069\pi$
$822$	6.13700e38	0.273644
$823$	2.90035e39	1.27219	0.636095	−	0.771610i	$-0.280548\pi$
$823$	2.90035e39	1.27219	0.636095	+	0.771610i	$0.280548\pi$
$824$	6.03147e38	0.260259
$825$	1.83407e38	0.0778552
$826$	−1.29397e38	−0.0540374
$827$	−3.48558e39	−1.43202	−0.716012	−	0.698088i	$-0.754035\pi$
$827$	−3.48558e39	−1.43202	−0.716012	+	0.698088i	$0.754035\pi$
$828$	2.18583e39	0.883502
$829$	−2.11699e39	−0.841845	−0.420922	−	0.907097i	$-0.638294\pi$
$829$	−2.11699e39	−0.841845	−0.420922	+	0.907097i	$0.638294\pi$
$830$	−9.10508e38	−0.356229
$831$	8.34030e38	0.321046
$832$	−4.84713e38	−0.183578
$833$	2.44542e39	0.911269
$834$	1.96723e38	0.0721296
$835$	−2.11513e39	−0.763080
$836$	1.46693e39	0.520743
$837$	2.17772e39	0.760693
$838$	−1.45589e39	−0.500421
$839$	−4.45636e39	−1.50728	−0.753640	−	0.657287i	$-0.771704\pi$
$839$	−4.45636e39	−1.50728	−0.753640	+	0.657287i	$0.771704\pi$
$840$	−1.28765e37	−0.00428574
$841$	−1.45218e39	−0.475634
$842$	−3.88158e39	−1.25111
$843$	7.28583e38	0.231104
$844$	−2.06290e39	−0.643955
$845$	−1.68406e39	−0.517358
$846$	2.53037e39	0.765039
$847$	2.77282e38	0.0825080
$848$	−1.48568e39	−0.435094
$849$	−3.51518e38	−0.101320
$850$	−4.58423e38	−0.130050
$851$	−1.24999e39	−0.349025
$852$	3.44436e38	0.0946616
$853$	2.08155e39	0.563086	0.281543	−	0.959549i	$-0.409154\pi$
$853$	2.08155e39	0.563086	0.281543	+	0.959549i	$0.409154\pi$
$854$	−1.84634e38	−0.0491621
$855$	1.19498e39	0.313197
$856$	5.63961e38	0.145497
$857$	1.22413e39	0.310876	0.155438	−	0.987846i	$-0.450321\pi$
$857$	1.22413e39	0.310876	0.155438	+	0.987846i	$0.450321\pi$
$858$	−1.61708e39	−0.404252
$859$	2.17470e39	0.535170	0.267585	−	0.963534i	$-0.413774\pi$
$859$	2.17470e39	0.535170	0.267585	+	0.963534i	$0.413774\pi$
$860$	1.08569e39	0.263014
$861$	1.63209e38	0.0389226
$862$	−2.01940e39	−0.474104
$863$	6.48177e39	1.49812	0.749062	−	0.662499i	$-0.230504\pi$
$863$	6.48177e39	1.49812	0.749062	+	0.662499i	$0.230504\pi$
$864$	−4.24683e38	−0.0966339
$865$	−5.39869e38	−0.120940
$866$	−3.27691e39	−0.722724
$867$	−2.02498e38	−0.0439707
$868$	−3.09658e38	−0.0662011
$869$	5.66085e38	0.119156
$870$	−3.14769e38	−0.0652353
$871$	3.37443e39	0.688582
$872$	7.98898e38	0.160516
$873$	−2.18502e39	−0.432277
$874$	−5.32043e39	−1.03644
$875$	−4.43654e37	−0.00851012
$876$	4.98621e38	0.0941814
$877$	−9.35961e39	−1.74086	−0.870429	−	0.492294i	$-0.836158\pi$
$877$	−9.35961e39	−1.74086	−0.870429	+	0.492294i	$0.836158\pi$
$878$	4.56023e39	0.835239
$879$	−2.59533e39	−0.468105
$880$	−8.60128e38	−0.152773
$881$	−5.26507e39	−0.920936	−0.460468	−	0.887676i	$-0.652318\pi$
$881$	−5.26507e39	−0.920936	−0.460468	+	0.887676i	$0.652318\pi$
$882$	3.73768e39	0.643838
$883$	9.76342e39	1.65628	0.828138	−	0.560525i	$-0.189401\pi$
$883$	9.76342e39	1.65628	0.828138	+	0.560525i	$0.189401\pi$
$884$	4.04186e39	0.675268
$885$	6.21918e38	0.102329
$886$	−7.61218e38	−0.123354
$887$	2.93008e39	0.467639	0.233820	−	0.972280i	$-0.424877\pi$
$887$	2.93008e39	0.467639	0.233820	+	0.972280i	$0.424877\pi$
$888$	1.16293e38	0.0182802
$889$	2.90775e38	0.0450177
$890$	−3.18108e39	−0.485076
$891$	6.94273e39	1.04275
$892$	−1.86139e39	−0.275367
$893$	−6.15905e39	−0.897468
$894$	−2.75855e39	−0.395935
$895$	3.99818e38	0.0565264
$896$	6.03871e37	0.00840980
$897$	5.86502e39	0.804584
$898$	−8.88435e39	−1.20059
$899$	−7.56968e39	−1.00768
$900$	−7.00672e38	−0.0918842
$901$	1.23886e40	1.60044
$902$	1.09021e40	1.38747
$903$	−2.54293e38	−0.0318823
$904$	−4.55058e38	−0.0562073
$905$	−2.19560e39	−0.267176
$906$	−2.15098e39	−0.257873
$907$	1.56617e40	1.84987	0.924934	−	0.380128i	$-0.124120\pi$
$907$	1.56617e40	1.84987	0.924934	+	0.380128i	$0.124120\pi$
$908$	−4.17452e38	−0.0485789
$909$	5.98236e39	0.685899
$910$	3.91164e38	0.0441876
$911$	−1.00687e40	−1.12067	−0.560333	−	0.828267i	$-0.689327\pi$
$911$	−1.00687e40	−1.12067	−0.560333	+	0.828267i	$0.689327\pi$
$912$	4.94991e38	0.0542834
$913$	1.42455e40	1.53929
$914$	1.27600e39	0.135855
$915$	8.87400e38	0.0930968
$916$	8.41382e39	0.869770
$917$	7.38809e38	0.0752568
$918$	3.54129e39	0.355456
$919$	7.21315e38	0.0713453	0.0356727	−	0.999364i	$-0.488643\pi$
$919$	7.21315e38	0.0713453	0.0356727	+	0.999364i	$0.488643\pi$
$920$	3.11962e39	0.304065
$921$	−5.66285e39	−0.543914
$922$	−9.90121e38	−0.0937176
$923$	−1.04634e40	−0.975997
$924$	2.01461e38	0.0185190
$925$	4.00685e38	0.0362986
$926$	−1.37634e39	−0.122879
$927$	−7.68719e39	−0.676381
$928$	1.47618e39	0.128009
$929$	−3.23928e39	−0.276845	−0.138422	−	0.990373i	$-0.544203\pi$
$929$	−3.23928e39	−0.276845	−0.138422	+	0.990373i	$0.544203\pi$
$930$	1.48830e39	0.125363
$931$	−9.09772e39	−0.755287
$932$	−8.18785e39	−0.669970
$933$	−5.88057e39	−0.474261
$934$	3.66876e39	0.291633
$935$	7.17233e39	0.561957
$936$	6.17774e39	0.477096
$937$	1.54684e39	0.117750	0.0588752	−	0.998265i	$-0.481249\pi$
$937$	1.54684e39	0.117750	0.0588752	+	0.998265i	$0.481249\pi$
$938$	−4.20398e38	−0.0315444
$939$	1.61570e39	0.119502
$940$	3.61134e39	0.263295
$941$	4.73751e39	0.340479	0.170239	−	0.985403i	$-0.445546\pi$
$941$	4.73751e39	0.340479	0.170239	+	0.985403i	$0.445546\pi$
$942$	−1.09497e39	−0.0775739
$943$	−3.95412e40	−2.76148
$944$	−2.91663e39	−0.200798
$945$	3.42720e38	0.0232600
$946$	−1.69864e40	−1.13650
$947$	−2.32964e40	−1.53661	−0.768306	−	0.640082i	$-0.778900\pi$
$947$	−2.32964e40	−1.53661	−0.768306	+	0.640082i	$0.778900\pi$
$948$	1.91016e38	0.0124210
$949$	−1.51472e40	−0.971046
$950$	1.70547e39	0.107789
$951$	1.67143e39	0.104148
$952$	−5.03548e38	−0.0309344
$953$	−1.13732e40	−0.688856	−0.344428	−	0.938813i	$-0.611927\pi$
$953$	−1.13732e40	−0.688856	−0.344428	+	0.938813i	$0.611927\pi$
$954$	1.89353e40	1.13075
$955$	−7.90093e38	−0.0465193
$956$	−6.87046e39	−0.398845
$957$	4.92477e39	0.281887
$958$	2.11332e40	1.19270
$959$	2.32262e39	0.129249
$960$	−2.90237e38	−0.0159254
$961$	1.73084e40	0.936464
$962$	−3.53279e39	−0.188475
$963$	−7.18777e39	−0.378128
$964$	−1.46493e40	−0.759938
$965$	7.83142e37	0.00400610
$966$	−7.30683e38	−0.0368585
$967$	1.89507e40	0.942689	0.471345	−	0.881949i	$-0.343769\pi$
$967$	1.89507e40	0.942689	0.471345	+	0.881949i	$0.343769\pi$
$968$	6.24997e39	0.306592
$969$	−4.12756e39	−0.199675
$970$	−3.11846e39	−0.148772
$971$	−1.71856e40	−0.808548	−0.404274	−	0.914638i	$-0.632476\pi$
$971$	−1.71856e40	−0.808548	−0.404274	+	0.914638i	$0.632476\pi$
$972$	8.23344e39	0.382021
$973$	7.44522e38	0.0340686
$974$	1.55494e40	0.701726
$975$	−1.88004e39	−0.0836768
$976$	−4.16166e39	−0.182681
$977$	−2.53265e40	−1.09647	−0.548237	−	0.836323i	$-0.684701\pi$
$977$	−2.53265e40	−1.09647	−0.548237	+	0.836323i	$0.684701\pi$
$978$	−3.38911e39	−0.144714
$979$	4.97701e40	2.09605
$980$	5.33442e39	0.221583
$981$	−1.01821e40	−0.417162
$982$	−6.85740e38	−0.0277112
$983$	−2.40137e40	−0.957163	−0.478582	−	0.878043i	$-0.658849\pi$
$983$	−2.40137e40	−0.957163	−0.478582	+	0.878043i	$0.658849\pi$
$984$	3.67874e39	0.144632
$985$	1.66460e40	0.645536
$986$	−1.23094e40	−0.470867
$987$	−8.45854e38	−0.0319164
$988$	−1.50369e40	−0.559682
$989$	6.16084e40	2.26199
$990$	1.09625e40	0.397039
$991$	2.42521e40	0.866471	0.433236	−	0.901281i	$-0.357372\pi$
$991$	2.42521e40	0.866471	0.433236	+	0.901281i	$0.357372\pi$
$992$	−6.97971e39	−0.245997
$993$	1.17185e40	0.407435
$994$	1.30356e39	0.0447110
$995$	−2.16217e40	−0.731607
$996$	4.80691e39	0.160459
$997$	5.33312e40	1.75629	0.878147	−	0.478391i	$-0.158780\pi$
$997$	5.33312e40	1.75629	0.878147	+	0.478391i	$0.158780\pi$
$998$	1.44854e40	0.470618
$999$	−3.09527e39	−0.0992120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.a.c.1.2	✓	2
5.2	odd	4		50.28.b.c.49.3		4
5.3	odd	4		50.28.b.c.49.2		4
5.4	even	2		50.28.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.a.c.1.2	✓	2	1.1	even	1	trivial
50.28.a.c.1.1		2	5.4	even	2
50.28.b.c.49.2		4	5.3	odd	4
50.28.b.c.49.3		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)

\(f(q)\)	\(=\)	\(q+8192.00 q^{2} +786688. q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} +6.44455e9 q^{6} +2.43901e10 q^{7} +5.49756e11 q^{8} -7.00672e12 q^{9} -1.00000e13 q^{10} +1.56456e14 q^{11} +5.27937e13 q^{12} -1.60378e15 q^{13} +1.99804e14 q^{14} -9.60312e14 q^{15} +4.50360e15 q^{16} -3.75540e16 q^{17} -5.73991e16 q^{18} +1.39712e17 q^{19} -8.19200e16 q^{20} +1.91874e16 q^{21} +1.28169e18 q^{22} -4.64860e18 q^{23} +4.32486e17 q^{24} +1.49012e18 q^{25} -1.31382e19 q^{26} -1.15111e19 q^{27} +1.63679e18 q^{28} +4.00120e19 q^{29} -7.86688e18 q^{30} -1.89185e20 q^{31} +3.68935e19 q^{32} +1.23082e20 q^{33} -3.07643e20 q^{34} -2.97731e19 q^{35} -4.70213e20 q^{36} +2.68895e20 q^{37} +1.14452e21 q^{38} -1.26167e21 q^{39} -6.71089e20 q^{40} +8.50604e21 q^{41} +1.57183e20 q^{42} -1.32531e22 q^{43} +1.04996e22 q^{44} +8.55313e21 q^{45} -3.80813e22 q^{46} -4.40838e22 q^{47} +3.54293e21 q^{48} -6.51175e22 q^{49} +1.22070e22 q^{50} -2.95433e22 q^{51} -1.07628e23 q^{52} -3.29888e23 q^{53} -9.42986e22 q^{54} -1.90987e23 q^{55} +1.34086e22 q^{56} +1.09910e23 q^{57} +3.27778e23 q^{58} -6.47621e23 q^{59} -6.44455e22 q^{60} -9.24075e23 q^{61} -1.54981e24 q^{62} -1.70895e23 q^{63} +3.02231e23 q^{64} +1.95774e24 q^{65} +1.00829e24 q^{66} -2.10405e24 q^{67} -2.52021e24 q^{68} -3.65700e24 q^{69} -2.43901e23 q^{70} +6.52419e24 q^{71} -3.85199e24 q^{72} +9.44471e24 q^{73} +2.20279e24 q^{74} +1.17226e24 q^{75} +9.37594e24 q^{76} +3.81600e24 q^{77} -1.03356e25 q^{78} +3.61816e24 q^{79} -5.49756e24 q^{80} +4.43748e25 q^{81} +6.96814e25 q^{82} +9.10508e25 q^{83} +1.28765e24 q^{84} +4.58423e25 q^{85} -1.08569e26 q^{86} +3.14769e25 q^{87} +8.60128e25 q^{88} +3.18108e26 q^{89} +7.00672e25 q^{90} -3.91164e25 q^{91} -3.11962e26 q^{92} -1.48830e26 q^{93} -3.61134e26 q^{94} -1.70547e26 q^{95} +2.90237e25 q^{96} +3.11846e26 q^{97} -5.33442e26 q^{98} -1.09625e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16384 q^{2} - 4702956 q^{3} + 134217728 q^{4} - 2441406250 q^{5} - 38526615552 q^{6} - 57185041508 q^{7} + 1099511627776 q^{8} + 15503869642194 q^{9} - 20000000000000 q^{10} + 169851430699104 q^{11}+ \cdots - 79\!\cdots\!12 q^{99}+O(q^{100}) \) 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

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Database

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