LMFDB - Embedded newform 6.28.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,28,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, 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("6.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	6.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$27.7113344903$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3386644380 $ x^2 - x - 3386644380
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$58195.4$ of defining polynomial
Character	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} -4.07783e9 q^{5} +1.30607e10 q^{6} -1.89573e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} +O(q^{10})$	\(q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} -4.07783e9 q^{5} +1.30607e10 q^{6} -1.89573e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} +3.34056e13 q^{10} -1.71190e14 q^{11} -1.06993e14 q^{12} -1.80233e15 q^{13} +1.55298e15 q^{14} +6.50138e15 q^{15} +4.50360e15 q^{16} -7.39745e16 q^{17} -2.08230e16 q^{18} +5.50896e16 q^{19} -2.73659e17 q^{20} +3.02241e17 q^{21} +1.40239e18 q^{22} -1.48002e18 q^{23} +8.76488e17 q^{24} +9.17813e18 q^{25} +1.47647e19 q^{26} -4.05256e18 q^{27} -1.27220e19 q^{28} +6.45864e19 q^{29} -5.32593e19 q^{30} +6.82617e19 q^{31} -3.68935e19 q^{32} +2.72932e20 q^{33} +6.05999e20 q^{34} +7.73047e20 q^{35} +1.70582e20 q^{36} +5.98039e20 q^{37} -4.51294e20 q^{38} +2.87350e21 q^{39} +2.24181e21 q^{40} -7.95137e20 q^{41} -2.47596e21 q^{42} -8.17465e21 q^{43} -1.14884e22 q^{44} -1.03653e22 q^{45} +1.21243e22 q^{46} -2.61691e22 q^{47} -7.18019e21 q^{48} -2.97744e22 q^{49} -7.51872e22 q^{50} +1.17939e23 q^{51} -1.20952e23 q^{52} -2.61076e23 q^{53} +3.31985e22 q^{54} +6.98084e23 q^{55} +1.04219e23 q^{56} -8.78307e22 q^{57} -5.29092e23 q^{58} +3.67862e23 q^{59} +4.36300e23 q^{60} +9.65474e22 q^{61} -5.59200e23 q^{62} -4.81869e23 q^{63} +3.02231e23 q^{64} +7.34960e24 q^{65} -2.23586e24 q^{66} +8.38584e24 q^{67} -4.96435e24 q^{68} +2.35963e24 q^{69} -6.33280e24 q^{70} -1.34455e25 q^{71} -1.39741e24 q^{72} -1.30358e25 q^{73} -4.89913e24 q^{74} -1.46329e25 q^{75} +3.69700e24 q^{76} +3.24530e25 q^{77} -2.35397e25 q^{78} -2.90459e25 q^{79} -1.83649e25 q^{80} +6.46108e24 q^{81} +6.51376e24 q^{82} +5.64509e24 q^{83} +2.02830e25 q^{84} +3.01656e26 q^{85} +6.69667e25 q^{86} -1.02972e26 q^{87} +9.41127e25 q^{88} -3.97135e26 q^{89} +8.49125e25 q^{90} +3.41673e26 q^{91} -9.93224e25 q^{92} -1.08831e26 q^{93} +2.14377e26 q^{94} -2.24646e26 q^{95} +5.88201e25 q^{96} +2.01474e26 q^{97} +2.43912e26 q^{98} -4.35142e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9}+O(q^{10}) $ 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9	$ 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9} - 2387484966912 q^{10} - 231807361766376 q^{11} - 213986410758144 q^{12} - 11\!\cdots\!64 q^{13}+ \cdots - 58\!\cdots\!04 q^{99}+O(q^{100}) $ 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9 - 2387484966912 * q^10 - 231807361766376 * q^11 - 213986410758144 * q^12 - 1155759271611764 * q^13 - 996526451326976 * q^14 - 464651146838628 * q^15 + 9007199254740992 * q^16 - 46125175777027452 * q^17 - 41645929731342336 * q^18 - 268519854753239000 * q^19 + 19558276848943104 * q^20 - 193943486506222944 * q^21 + 1898965907590152192 * q^22 + 1299561926005929936 * q^23 + 1752976676930715648 * q^24 + 20818087556919436046 * q^25 + 9467979953043570688 * q^26 - 8105110306037952534 * q^27 + 8163544689270587392 * q^28 + 60178362995785587900 * q^29 + 3806422194902040576 * q^30 + 203575085639304966544 * q^31 - 73786976294838206464 * q^32 + 369575808433453883448 * q^33 + 377857439965408886784 * q^34 + 2132849735738606710464 * q^35 + 341163456359156416512 * q^36 + 3022337597514982851388 * q^37 + 2199714650138533888000 * q^38 + 1842653589193882415772 * q^39 - 160221403946541907968 * q^40 - 10870375798082518905516 * q^41 + 1588785041458978357248 * q^42 - 1299568293415606314344 * q^43 - 15556328714978526756864 * q^44 + 740804010381201908844 * q^45 - 10646011297840578035712 * q^46 - 99372996476917699213632 * q^47 - 14360384937416422588416 * q^48 + 1370785920275118717906 * q^49 - 170541773266284020088832 * q^50 + 73538428620357738354996 * q^51 - 77561691775332931076096 * q^52 - 35770850049954566775924 * q^53 + 66397063627062907158528 * q^54 + 433229958906724722129552 * q^55 - 66875758094504651915264 * q^56 + 428107380389748262197000 * q^57 - 492981149661475536076800 * q^58 + 299672958231389705557080 * q^59 - 31182210620637516398592 * q^60 + 2165599091776519863171724 * q^61 - 1667687101557186285928448 * q^62 + 309208561237060882746912 * q^63 + 604462909807314587353088 * q^64 + 10174637395564415468537928 * q^65 - 3027565022686854213206016 * q^66 + 13568283837486181949525608 * q^67 - 3095408148196629600534528 * q^68 - 2071921468555552233353328 * q^69 - 17472305035170666172121088 * q^70 - 4319907418871433623040336 * q^71 - 2794811034494209364066304 * q^72 - 20032895180752990538485964 * q^73 - 24758989598842739518570496 * q^74 - 33190755808010466035166858 * q^75 - 18020062413934869610496000 * q^76 + 13587711578810985760484736 * q^77 - 15095018202676284750004224 * q^78 + 5633936436869082596599600 * q^79 + 1312533741130071310073856 * q^80 + 12922163778453346597864482 * q^81 + 89050118537891994873987072 * q^82 - 46762236922353070723154904 * q^83 - 13015327059631950702575616 * q^84 + 423336865613342459682869784 * q^85 + 10646063459660646927106048 * q^86 - 95943748226529865857491700 * q^87 + 127437444833104091192229888 * q^88 - 191930414076503127699406380 * q^89 - 6068666453042806037250048 * q^90 + 542898500680491813749530304 * q^91 + 87212124551910015268552704 * q^92 - 324564441261713612175329712 * q^93 + 814063587138909791958073344 * q^94 - 1638584179808499075287277840 * q^95 + 117640273407315333844303872 * q^96 + 544725669490755670759486468 * q^97 - 11229478258893772537085952 * q^98 - 589223211629049495820465704 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−1.59432e6	−0.577350
$3$	−1.59432e6	−0.577350
$4$	6.71089e7	0.500000
$5$	−4.07783e9	−1.49394	−0.746972	−	0.664856i	$-0.768493\pi$
$5$	−4.07783e9	−1.49394	−0.746972	+	0.664856i	$0.768493\pi$
$6$	1.30607e10	0.408248
$7$	−1.89573e11	−0.739526	−0.369763	−	0.929126i	$-0.620561\pi$
$7$	−1.89573e11	−0.739526	−0.369763	+	0.929126i	$0.620561\pi$
$8$	−5.49756e11	−0.353553
$9$	2.54187e12	0.333333
$10$	3.34056e13	1.05638
$11$	−1.71190e14	−1.49512	−0.747562	−	0.664192i	$-0.768776\pi$
$11$	−1.71190e14	−1.49512	−0.747562	+	0.664192i	$0.768776\pi$
$12$	−1.06993e14	−0.288675
$13$	−1.80233e15	−1.65044	−0.825218	−	0.564814i	$-0.808948\pi$
$13$	−1.80233e15	−1.65044	−0.825218	+	0.564814i	$0.808948\pi$
$14$	1.55298e15	0.522924
$15$	6.50138e15	0.862529
$16$	4.50360e15	0.250000
$17$	−7.39745e16	−1.81143	−0.905715	−	0.423887i	$-0.860665\pi$
$17$	−7.39745e16	−1.81143	−0.905715	+	0.423887i	$0.860665\pi$
$18$	−2.08230e16	−0.235702
$19$	5.50896e16	0.300536	0.150268	−	0.988645i	$-0.451986\pi$
$19$	5.50896e16	0.300536	0.150268	+	0.988645i	$0.451986\pi$
$20$	−2.73659e17	−0.746972
$21$	3.02241e17	0.426965
$22$	1.40239e18	1.05721
$23$	−1.48002e18	−0.612268	−0.306134	−	0.951988i	$-0.599036\pi$
$23$	−1.48002e18	−0.612268	−0.306134	+	0.951988i	$0.599036\pi$
$24$	8.76488e17	0.204124
$25$	9.17813e18	1.23187
$26$	1.47647e19	1.16704
$27$	−4.05256e18	−0.192450
$28$	−1.27220e19	−0.369763
$29$	6.45864e19	1.16888	0.584438	−	0.811439i	$-0.301315\pi$
$29$	6.45864e19	1.16888	0.584438	+	0.811439i	$0.301315\pi$
$30$	−5.32593e19	−0.609900
$31$	6.82617e19	0.502105	0.251052	−	0.967974i	$-0.419223\pi$
$31$	6.82617e19	0.502105	0.251052	+	0.967974i	$0.419223\pi$
$32$	−3.68935e19	−0.176777
$33$	2.72932e20	0.863210
$34$	6.05999e20	1.28087
$35$	7.73047e20	1.10481
$36$	1.70582e20	0.166667
$37$	5.98039e20	0.403651	0.201825	−	0.979422i	$-0.435313\pi$
$37$	5.98039e20	0.403651	0.201825	+	0.979422i	$0.435313\pi$
$38$	−4.51294e20	−0.212511
$39$	2.87350e21	0.952880
$40$	2.24181e21	0.528189
$41$	−7.95137e20	−0.134233	−0.0671166	−	0.997745i	$-0.521380\pi$
$41$	−7.95137e20	−0.134233	−0.0671166	+	0.997745i	$0.521380\pi$
$42$	−2.47596e21	−0.301910
$43$	−8.17465e21	−0.725513	−0.362756	−	0.931884i	$-0.618164\pi$
$43$	−8.17465e21	−0.725513	−0.362756	+	0.931884i	$0.618164\pi$
$44$	−1.14884e22	−0.747562
$45$	−1.03653e22	−0.497981
$46$	1.21243e22	0.432939
$47$	−2.61691e22	−0.698984	−0.349492	−	0.936939i	$-0.613646\pi$
$47$	−2.61691e22	−0.698984	−0.349492	+	0.936939i	$0.613646\pi$
$48$	−7.18019e21	−0.144338
$49$	−2.97744e22	−0.453102
$50$	−7.51872e22	−0.871062
$51$	1.17939e23	1.04583
$52$	−1.20952e23	−0.825218
$53$	−2.61076e23	−1.37735	−0.688673	−	0.725072i	$-0.741806\pi$
$53$	−2.61076e23	−1.37735	−0.688673	+	0.725072i	$0.741806\pi$
$54$	3.31985e22	0.136083
$55$	6.98084e23	2.23363
$56$	1.04219e23	0.261462
$57$	−8.78307e22	−0.173514
$58$	−5.29092e23	−0.826520
$59$	3.67862e23	0.456229	0.228115	−	0.973634i	$-0.426744\pi$
$59$	3.67862e23	0.456229	0.228115	+	0.973634i	$0.426744\pi$
$60$	4.36300e23	0.431264
$61$	9.65474e22	0.0763462	0.0381731	−	0.999271i	$-0.487846\pi$
$61$	9.65474e22	0.0763462	0.0381731	+	0.999271i	$0.487846\pi$
$62$	−5.59200e23	−0.355042
$63$	−4.81869e23	−0.246509
$64$	3.02231e23	0.125000
$65$	7.34960e24	2.46566
$66$	−2.23586e24	−0.610382
$67$	8.38584e24	1.86869	0.934344	−	0.356373i	$-0.115987\pi$
$67$	8.38584e24	1.86869	0.934344	+	0.356373i	$0.115987\pi$
$68$	−4.96435e24	−0.905715
$69$	2.35963e24	0.353493
$70$	−6.33280e24	−0.781218
$71$	−1.34455e25	−1.36959	−0.684793	−	0.728737i	$-0.740108\pi$
$71$	−1.34455e25	−1.36959	−0.684793	+	0.728737i	$0.740108\pi$
$72$	−1.39741e24	−0.117851
$73$	−1.30358e25	−0.912598	−0.456299	−	0.889827i	$-0.650825\pi$
$73$	−1.30358e25	−0.912598	−0.456299	+	0.889827i	$0.650825\pi$
$74$	−4.89913e24	−0.285424
$75$	−1.46329e25	−0.711219
$76$	3.69700e24	0.150268
$77$	3.24530e25	1.10568
$78$	−2.35397e25	−0.673788
$79$	−2.90459e25	−0.700035	−0.350018	−	0.936743i	$-0.613824\pi$
$79$	−2.90459e25	−0.700035	−0.350018	+	0.936743i	$0.613824\pi$
$80$	−1.83649e25	−0.373486
$81$	6.46108e24	0.111111
$82$	6.51376e24	0.0949172
$83$	5.64509e24	0.0698420	0.0349210	−	0.999390i	$-0.488882\pi$
$83$	5.64509e24	0.0698420	0.0349210	+	0.999390i	$0.488882\pi$
$84$	2.02830e25	0.213483
$85$	3.01656e26	2.70617
$86$	6.69667e25	0.513015
$87$	−1.02972e26	−0.674850
$88$	9.41127e25	0.528606
$89$	−3.97135e26	−1.91502	−0.957510	−	0.288399i	$-0.906877\pi$
$89$	−3.97135e26	−1.91502	−0.957510	+	0.288399i	$0.906877\pi$
$90$	8.49125e25	0.352126
$91$	3.41673e26	1.22054
$92$	−9.93224e25	−0.306134
$93$	−1.08831e26	−0.289890
$94$	2.14377e26	0.494257
$95$	−2.24646e26	−0.448984
$96$	5.88201e25	0.102062
$97$	2.01474e26	0.303948	0.151974	−	0.988384i	$-0.451437\pi$
$97$	2.01474e26	0.303948	0.151974	+	0.988384i	$0.451437\pi$
$98$	2.43912e26	0.320391
$99$	−4.35142e26	−0.498375
$100$	6.15934e26	0.615934
$101$	−1.53743e27	−1.34417	−0.672087	−	0.740472i	$-0.734602\pi$
$101$	−1.53743e27	−1.34417	−0.672087	+	0.740472i	$0.734602\pi$
$102$	−9.66158e26	−0.739513
$103$	−1.23787e27	−0.830561	−0.415281	−	0.909693i	$-0.636317\pi$
$103$	−1.23787e27	−0.830561	−0.415281	+	0.909693i	$0.636317\pi$
$104$	9.90841e26	0.583518
$105$	−1.23249e27	−0.637862
$106$	2.13874e27	0.973930
$107$	−1.16223e27	−0.466242	−0.233121	−	0.972448i	$-0.574894\pi$
$107$	−1.16223e27	−0.466242	−0.233121	+	0.972448i	$0.574894\pi$
$108$	−2.71962e26	−0.0962250
$109$	3.94134e27	1.23136	0.615682	−	0.787995i	$-0.288881\pi$
$109$	3.94134e27	1.23136	0.615682	+	0.787995i	$0.288881\pi$
$110$	−5.71870e27	−1.57942
$111$	−9.53467e26	−0.233048
$112$	−8.53762e26	−0.184881
$113$	3.04033e27	0.583931	0.291965	−	0.956429i	$-0.405691\pi$
$113$	3.04033e27	0.583931	0.291965	+	0.956429i	$0.405691\pi$
$114$	7.19509e26	0.122693
$115$	6.03527e27	0.914693
$116$	4.33432e27	0.584438
$117$	−4.58128e27	−0.550146
$118$	−3.01353e27	−0.322603
$119$	1.40236e28	1.33960
$120$	−3.57417e27	−0.304950
$121$	1.61960e28	1.23539
$122$	−7.90916e26	−0.0539849
$123$	1.26770e27	0.0774995
$124$	4.58097e27	0.251052
$125$	−7.04464e27	−0.346397
$126$	3.94747e27	0.174308
$127$	−1.43469e28	−0.569389	−0.284694	−	0.958618i	$-0.591892\pi$
$127$	−1.43469e28	−0.569389	−0.284694	+	0.958618i	$0.591892\pi$
$128$	−2.47588e27	−0.0883883
$129$	1.30330e28	0.418875
$130$	−6.02079e28	−1.74348
$131$	−1.70578e28	−0.445410	−0.222705	−	0.974886i	$-0.571489\pi$
$131$	−1.70578e28	−0.445410	−0.222705	+	0.974886i	$0.571489\pi$
$132$	1.83162e28	0.431605
$133$	−1.04435e28	−0.222254
$134$	−6.86968e28	−1.32136
$135$	1.65256e28	0.287510
$136$	4.06679e28	0.640437
$137$	−8.35348e28	−1.19163	−0.595813	−	0.803123i	$-0.703170\pi$
$137$	−8.35348e28	−1.19163	−0.595813	+	0.803123i	$0.703170\pi$
$138$	−1.93301e28	−0.249957
$139$	−8.43351e28	−0.989255	−0.494628	−	0.869105i	$-0.664696\pi$
$139$	−8.43351e28	−0.989255	−0.494628	+	0.869105i	$0.664696\pi$
$140$	5.18783e28	0.552405
$141$	4.17220e28	0.403559
$142$	1.10146e29	0.968444
$143$	3.08541e29	2.46761
$144$	1.14475e28	0.0833333
$145$	−2.63372e29	−1.74623
$146$	1.06789e29	0.645304
$147$	4.74700e28	0.261598
$148$	4.01337e28	0.201825
$149$	2.11568e29	0.971485	0.485743	−	0.874102i	$-0.338549\pi$
$149$	2.11568e29	0.971485	0.485743	+	0.874102i	$0.338549\pi$
$150$	1.19873e29	0.502908
$151$	−3.00158e29	−1.15123	−0.575613	−	0.817722i	$-0.695237\pi$
$151$	−3.00158e29	−1.15123	−0.575613	+	0.817722i	$0.695237\pi$
$152$	−3.02858e28	−0.106255
$153$	−1.88033e29	−0.603810
$154$	−2.65855e29	−0.781835
$155$	−2.78360e29	−0.750116
$156$	1.92837e29	0.476440
$157$	5.53083e29	1.25356	0.626779	−	0.779197i	$-0.284373\pi$
$157$	5.53083e29	1.25356	0.626779	+	0.779197i	$0.284373\pi$
$158$	2.37944e29	0.495000
$159$	4.16240e29	0.795211
$160$	1.50445e29	0.264094
$161$	2.80572e29	0.452788
$162$	−5.29292e28	−0.0785674
$163$	−1.37408e30	−1.87706	−0.938532	−	0.345193i	$-0.887813\pi$
$163$	−1.37408e30	−1.87706	−0.938532	+	0.345193i	$0.887813\pi$
$164$	−5.33607e28	−0.0671166
$165$	−1.11297e30	−1.28959
$166$	−4.62446e28	−0.0493858
$167$	−2.02652e29	−0.199562	−0.0997811	−	0.995009i	$-0.531814\pi$
$167$	−2.02652e29	−0.199562	−0.0997811	+	0.995009i	$0.531814\pi$
$168$	−1.66159e29	−0.150955
$169$	2.05586e30	1.72394
$170$	−2.47116e30	−1.91355
$171$	1.40030e29	0.100179
$172$	−5.48592e29	−0.362756
$173$	9.35884e29	0.572268	0.286134	−	0.958190i	$-0.407630\pi$
$173$	9.35884e29	0.572268	0.286134	+	0.958190i	$0.407630\pi$
$174$	8.43543e29	0.477191
$175$	−1.73993e30	−0.910998
$176$	−7.70971e29	−0.373781
$177$	−5.86492e29	−0.263404
$178$	3.25333e30	1.35412
$179$	1.71682e30	0.662536	0.331268	−	0.943537i	$-0.392524\pi$
$179$	1.71682e30	0.662536	0.331268	+	0.943537i	$0.392524\pi$
$180$	−6.95604e29	−0.248991
$181$	2.33832e30	0.776680	0.388340	−	0.921516i	$-0.373049\pi$
$181$	2.33832e30	0.776680	0.388340	+	0.921516i	$0.373049\pi$
$182$	−2.79899e30	−0.863052
$183$	−1.53928e29	−0.0440785
$184$	8.13649e29	0.216469
$185$	−2.43870e30	−0.603032
$186$	8.91545e29	0.204983
$187$	1.26637e31	2.70831
$188$	−1.75618e30	−0.349492
$189$	7.68256e29	0.142322
$190$	1.84030e30	0.317479
$191$	6.87404e30	1.10474	0.552372	−	0.833598i	$-0.313723\pi$
$191$	6.87404e30	1.10474	0.552372	+	0.833598i	$0.313723\pi$
$192$	−4.81855e29	−0.0721688
$193$	−6.83466e30	−0.954319	−0.477159	−	0.878817i	$-0.658334\pi$
$193$	−6.83466e30	−0.954319	−0.477159	+	0.878817i	$0.658334\pi$
$194$	−1.65047e30	−0.214924
$195$	−1.17176e31	−1.42355
$196$	−1.99813e30	−0.226551
$197$	7.95884e30	0.842472	0.421236	−	0.906951i	$-0.361596\pi$
$197$	7.95884e30	0.842472	0.421236	+	0.906951i	$0.361596\pi$
$198$	3.56468e30	0.352404
$199$	−1.94643e31	−1.79772	−0.898861	−	0.438233i	$-0.855604\pi$
$199$	−1.94643e31	−1.79772	−0.898861	+	0.438233i	$0.855604\pi$
$200$	−5.04573e30	−0.435531
$201$	−1.33697e31	−1.07889
$202$	1.25946e31	0.950475
$203$	−1.22438e31	−0.864413
$204$	7.91477e30	0.522915
$205$	3.24243e30	0.200537
$206$	1.01406e31	0.587295
$207$	−3.76201e30	−0.204089
$208$	−8.11697e30	−0.412609
$209$	−9.43079e30	−0.449338
$210$	1.00965e31	0.451037
$211$	−2.28623e31	−0.957872	−0.478936	−	0.877850i	$-0.658977\pi$
$211$	−2.28623e31	−0.957872	−0.478936	+	0.877850i	$0.658977\pi$
$212$	−1.75205e31	−0.688673
$213$	2.14365e31	0.790731
$214$	9.52099e30	0.329683
$215$	3.33348e31	1.08388
$216$	2.22792e30	0.0680414
$217$	−1.29406e31	−0.371319
$218$	−3.22875e31	−0.870706
$219$	2.07833e31	0.526889
$220$	4.68476e31	1.11682
$221$	1.33326e32	2.98965
$222$	7.81080e30	0.164790
$223$	−5.73791e31	−1.13930	−0.569650	−	0.821887i	$-0.692921\pi$
$223$	−5.73791e31	−1.13930	−0.569650	+	0.821887i	$0.692921\pi$
$224$	6.99401e30	0.130731
$225$	2.33296e31	0.410622
$226$	−2.49064e31	−0.412901
$227$	−6.71643e31	−1.04903	−0.524517	−	0.851400i	$-0.675754\pi$
$227$	−6.71643e31	−1.04903	−0.524517	+	0.851400i	$0.675754\pi$
$228$	−5.89422e30	−0.0867572
$229$	−8.82668e30	−0.122467	−0.0612334	−	0.998123i	$-0.519503\pi$
$229$	−8.82668e30	−0.122467	−0.0612334	+	0.998123i	$0.519503\pi$
$230$	−4.94409e31	−0.646786
$231$	−5.17406e31	−0.638366
$232$	−3.55068e31	−0.413260
$233$	4.34961e30	0.0477689	0.0238844	−	0.999715i	$-0.492397\pi$
$233$	4.34961e30	0.0477689	0.0238844	+	0.999715i	$0.492397\pi$
$234$	3.75298e31	0.389012
$235$	1.06713e32	1.04424
$236$	2.46868e31	0.228115
$237$	4.63086e31	0.404165
$238$	−1.14881e32	−0.947240
$239$	3.77518e31	0.294148	0.147074	−	0.989126i	$-0.453014\pi$
$239$	3.77518e31	0.294148	0.147074	+	0.989126i	$0.453014\pi$
$240$	2.92796e31	0.215632
$241$	−1.26869e32	−0.883333	−0.441667	−	0.897179i	$-0.645613\pi$
$241$	−1.26869e32	−0.883333	−0.441667	+	0.897179i	$0.645613\pi$
$242$	−1.32678e32	−0.873556
$243$	−1.03011e31	−0.0641500
$244$	6.47918e30	0.0381731
$245$	1.21415e32	0.676908
$246$	−1.03850e31	−0.0548004
$247$	−9.92897e31	−0.496015
$248$	−3.75273e31	−0.177521
$249$	−9.00010e30	−0.0403233
$250$	5.77097e31	0.244940
$251$	−1.90550e32	−0.766327	−0.383164	−	0.923681i	$-0.625165\pi$
$251$	−1.90550e32	−0.766327	−0.383164	+	0.923681i	$0.625165\pi$
$252$	−3.23377e31	−0.123254
$253$	2.53364e32	0.915416
$254$	1.17530e32	0.402619
$255$	−4.80936e32	−1.56241
$256$	2.02824e31	0.0625000
$257$	3.24261e32	0.947977	0.473988	−	0.880531i	$-0.342814\pi$
$257$	3.24261e32	0.947977	0.473988	+	0.880531i	$0.342814\pi$
$258$	−1.06767e32	−0.296189
$259$	−1.13372e32	−0.298510
$260$	4.93223e32	1.23283
$261$	1.64170e32	0.389625
$262$	1.39737e32	0.314952
$263$	−7.44444e32	−1.59378	−0.796892	−	0.604122i	$-0.793524\pi$
$263$	−7.44444e32	−1.59378	−0.796892	+	0.604122i	$0.793524\pi$
$264$	−1.50046e32	−0.305191
$265$	1.06462e33	2.05768
$266$	8.55533e31	0.157157
$267$	6.33162e32	1.10564
$268$	5.62764e32	0.934344
$269$	2.00142e31	0.0315997	0.0157998	−	0.999875i	$-0.494971\pi$
$269$	2.00142e31	0.0315997	0.0157998	+	0.999875i	$0.494971\pi$
$270$	−1.35378e32	−0.203300
$271$	3.53965e32	0.505679	0.252839	−	0.967508i	$-0.418636\pi$
$271$	3.53965e32	0.505679	0.252839	+	0.967508i	$0.418636\pi$
$272$	−3.33152e32	−0.452858
$273$	−5.44738e32	−0.704679
$274$	6.84317e32	0.842607
$275$	−1.57120e33	−1.84179
$276$	1.58352e32	0.176746
$277$	−8.41079e32	−0.894046	−0.447023	−	0.894522i	$-0.647516\pi$
$277$	−8.41079e32	−0.894046	−0.447023	+	0.894522i	$0.647516\pi$
$278$	6.90873e32	0.699509
$279$	1.73512e32	0.167368
$280$	−4.24987e32	−0.390609
$281$	−9.52021e32	−0.833895	−0.416947	−	0.908931i	$-0.636900\pi$
$281$	−9.52021e32	−0.833895	−0.416947	+	0.908931i	$0.636900\pi$
$282$	−3.41786e32	−0.285359
$283$	−1.19491e33	−0.951082	−0.475541	−	0.879694i	$-0.657748\pi$
$283$	−1.19491e33	−0.951082	−0.475541	+	0.879694i	$0.657748\pi$
$284$	−9.02313e32	−0.684793
$285$	3.58159e32	0.259221
$286$	−2.52757e33	−1.74486
$287$	1.50737e32	0.0992688
$288$	−9.37783e31	−0.0589256
$289$	3.80452e33	2.28128
$290$	2.15755e33	1.23477
$291$	−3.21214e32	−0.175485
$292$	−8.74818e32	−0.456299
$293$	1.47485e32	0.0734571	0.0367285	−	0.999325i	$-0.488306\pi$
$293$	1.47485e32	0.0734571	0.0367285	+	0.999325i	$0.488306\pi$
$294$	−3.88874e32	−0.184978
$295$	−1.50008e33	−0.681581
$296$	−3.28775e32	−0.142712
$297$	6.93757e32	0.287737
$298$	−1.73317e33	−0.686944
$299$	2.66748e33	1.01051
$300$	−9.81997e32	−0.355609
$301$	1.54969e33	0.536535
$302$	2.45889e33	0.814040
$303$	2.45115e33	0.776060
$304$	2.48102e32	0.0751340
$305$	−3.93704e32	−0.114057
$306$	1.54037e33	0.426958
$307$	−5.22105e33	−1.38481	−0.692404	−	0.721510i	$-0.743448\pi$
$307$	−5.22105e33	−1.38481	−0.692404	+	0.721510i	$0.743448\pi$
$308$	2.17789e33	0.552841
$309$	1.97356e33	0.479525
$310$	2.28032e33	0.530412
$311$	2.16869e33	0.482983	0.241491	−	0.970403i	$-0.422363\pi$
$311$	2.16869e33	0.482983	0.241491	+	0.970403i	$0.422363\pi$
$312$	−1.57972e33	−0.336894
$313$	6.47741e33	1.32298	0.661490	−	0.749954i	$-0.269925\pi$
$313$	6.47741e33	1.32298	0.661490	+	0.749954i	$0.269925\pi$
$314$	−4.53085e33	−0.886400
$315$	1.96498e33	0.368270
$316$	−1.94924e33	−0.350018
$317$	2.77239e33	0.477040	0.238520	−	0.971138i	$-0.423338\pi$
$317$	2.77239e33	0.477040	0.238520	+	0.971138i	$0.423338\pi$
$318$	−3.40984e33	−0.562299
$319$	−1.10565e34	−1.74761
$320$	−1.23245e33	−0.186743
$321$	1.85297e33	0.269185
$322$	−2.29844e33	−0.320169
$323$	−4.07523e33	−0.544400
$324$	4.33596e32	0.0555556
$325$	−1.65420e34	−2.03312
$326$	1.12565e34	1.32728
$327$	−6.28377e33	−0.710928
$328$	4.37131e32	0.0474586
$329$	4.96096e33	0.516917
$330$	9.11746e33	0.911876
$331$	1.57643e34	1.51355	0.756773	−	0.653678i	$-0.226775\pi$
$331$	1.57643e34	1.51355	0.756773	+	0.653678i	$0.226775\pi$
$332$	3.78836e32	0.0349210
$333$	1.52013e33	0.134550
$334$	1.66012e33	0.141112
$335$	−3.41960e34	−2.79171
$336$	1.36117e33	0.106741
$337$	6.45721e33	0.486453	0.243227	−	0.969969i	$-0.421794\pi$
$337$	6.45721e33	0.486453	0.243227	+	0.969969i	$0.421794\pi$
$338$	−1.68416e34	−1.21901
$339$	−4.84726e33	−0.337133
$340$	2.02438e34	1.35309
$341$	−1.16857e34	−0.750708
$342$	−1.14713e33	−0.0708370
$343$	1.81017e34	1.07461
$344$	4.49406e33	0.256508
$345$	−9.62216e33	−0.528099
$346$	−7.66676e33	−0.404655
$347$	2.76635e34	1.40430	0.702150	−	0.712029i	$-0.252224\pi$
$347$	2.76635e34	1.40430	0.702150	+	0.712029i	$0.252224\pi$
$348$	−6.91031e33	−0.337425
$349$	−1.31401e34	−0.617241	−0.308620	−	0.951185i	$-0.599867\pi$
$349$	−1.31401e34	−0.617241	−0.308620	+	0.951185i	$0.599867\pi$
$350$	1.42535e34	0.644173
$351$	7.30404e33	0.317627
$352$	6.31580e33	0.264303
$353$	4.59717e33	0.185154	0.0925769	−	0.995706i	$-0.470490\pi$
$353$	4.59717e33	0.185154	0.0925769	+	0.995706i	$0.470490\pi$
$354$	4.80454e33	0.186255
$355$	5.48285e34	2.04609
$356$	−2.66513e34	−0.957510
$357$	−2.23581e34	−0.773418
$358$	−1.40642e34	−0.468484
$359$	4.07811e34	1.30823	0.654114	−	0.756396i	$-0.273042\pi$
$359$	4.07811e34	1.30823	0.654114	+	0.756396i	$0.273042\pi$
$360$	5.69838e33	0.176063
$361$	−3.05657e34	−0.909678
$362$	−1.91555e34	−0.549196
$363$	−2.58217e34	−0.713255
$364$	2.29293e34	0.610270
$365$	5.31578e34	1.36337
$366$	1.26098e33	0.0311682
$367$	−2.64528e34	−0.630201	−0.315100	−	0.949058i	$-0.602038\pi$
$367$	−2.64528e34	−0.630201	−0.315100	+	0.949058i	$0.602038\pi$
$368$	−6.66541e33	−0.153067
$369$	−2.02113e33	−0.0447444
$370$	1.99778e34	0.426408
$371$	4.94930e34	1.01858
$372$	−7.30354e33	−0.144945
$373$	2.34862e34	0.449515	0.224758	−	0.974415i	$-0.427841\pi$
$373$	2.34862e34	0.449515	0.224758	+	0.974415i	$0.427841\pi$
$374$	−1.03741e35	−1.91507
$375$	1.12314e34	0.199992
$376$	1.43866e34	0.247128
$377$	−1.16406e35	−1.92915
$378$	−6.29355e33	−0.100637
$379$	−3.74474e34	−0.577819	−0.288910	−	0.957356i	$-0.593293\pi$
$379$	−3.74474e34	−0.577819	−0.288910	+	0.957356i	$0.593293\pi$
$380$	−1.50758e34	−0.224492
$381$	2.28736e34	0.328737
$382$	−5.63121e34	−0.781172
$383$	−2.21824e34	−0.297047	−0.148524	−	0.988909i	$-0.547452\pi$
$383$	−2.21824e34	−0.297047	−0.148524	+	0.988909i	$0.547452\pi$
$384$	3.94735e33	0.0510310
$385$	−1.32338e35	−1.65183
$386$	5.59895e34	0.674805
$387$	−2.07789e34	−0.241838
$388$	1.35207e34	0.151974
$389$	−5.78779e30	−6.28338e−5 0	−3.14169e−5	−	1.00000i	$-0.500010\pi$
$389$	−5.78779e30	−6.28338e−5 0	−3.14169e−5		1.00000i	$0.500010\pi$
$390$	9.59908e34	1.00660
$391$	1.09484e35	1.10908
$392$	1.63686e34	0.160196
$393$	2.71956e34	0.257157
$394$	−6.51988e34	−0.595718
$395$	1.18444e35	1.04581
$396$	−2.92019e34	−0.249187
$397$	6.37883e34	0.526101	0.263050	−	0.964782i	$-0.415271\pi$
$397$	6.37883e34	0.526101	0.263050	+	0.964782i	$0.415271\pi$
$398$	1.59452e35	1.27118
$399$	1.66503e34	0.128318
$400$	4.13346e34	0.307967
$401$	1.67281e35	1.20503	0.602516	−	0.798107i	$-0.294165\pi$
$401$	1.67281e35	1.20503	0.602516	+	0.798107i	$0.294165\pi$
$402$	1.09525e35	0.762889
$403$	−1.23030e35	−0.828692
$404$	−1.03175e35	−0.672087
$405$	−2.63472e34	−0.165994
$406$	1.00302e35	0.611232
$407$	−1.02378e35	−0.603508
$408$	−6.48378e34	−0.369757
$409$	−2.01106e35	−1.10959	−0.554793	−	0.831988i	$-0.687203\pi$
$409$	−2.01106e35	−1.10959	−0.554793	+	0.831988i	$0.687203\pi$
$410$	−2.65620e34	−0.141801
$411$	1.33182e35	0.687986
$412$	−8.30719e34	−0.415281
$413$	−6.97368e34	−0.337393
$414$	3.08184e34	0.144313
$415$	−2.30197e34	−0.104340
$416$	6.64942e34	0.291759
$417$	1.34457e35	0.571147
$418$	7.72571e34	0.317730
$419$	6.51976e34	0.259623	0.129811	−	0.991539i	$-0.458563\pi$
$419$	6.51976e34	0.259623	0.129811	+	0.991539i	$0.458563\pi$
$420$	−8.27108e34	−0.318931
$421$	−2.44051e35	−0.911323	−0.455661	−	0.890153i	$-0.650597\pi$
$421$	−2.44051e35	−0.911323	−0.455661	+	0.890153i	$0.650597\pi$
$422$	1.87288e35	0.677317
$423$	−6.65183e34	−0.232995
$424$	1.43528e35	0.486965
$425$	−6.78947e35	−2.23144
$426$	−1.75608e35	−0.559131
$427$	−1.83028e34	−0.0564600
$428$	−7.79960e34	−0.233121
$429$	−4.91914e35	−1.42467
$430$	−2.73079e35	−0.766416
$431$	6.35341e35	1.72808	0.864040	−	0.503423i	$-0.167926\pi$
$431$	6.35341e35	1.72808	0.864040	+	0.503423i	$0.167926\pi$
$432$	−1.82511e34	−0.0481125
$433$	4.67419e35	1.19432	0.597158	−	0.802123i	$-0.296296\pi$
$433$	4.67419e35	1.19432	0.597158	+	0.802123i	$0.296296\pi$
$434$	1.06009e35	0.262562
$435$	4.19901e35	1.00819
$436$	2.64499e35	0.615682
$437$	−8.15337e34	−0.184008
$438$	−1.70257e35	−0.372567
$439$	−6.01466e34	−0.127626	−0.0638131	−	0.997962i	$-0.520326\pi$
$439$	−6.01466e34	−0.127626	−0.0638131	+	0.997962i	$0.520326\pi$
$440$	−3.83776e35	−0.789708
$441$	−7.56825e34	−0.151034
$442$	−1.09221e36	−2.11400
$443$	−1.05159e35	−0.197422	−0.0987111	−	0.995116i	$-0.531472\pi$
$443$	−1.05159e35	−0.197422	−0.0987111	+	0.995116i	$0.531472\pi$
$444$	−6.39861e34	−0.116524
$445$	1.61945e36	2.86093
$446$	4.70050e35	0.805607
$447$	−3.37308e35	−0.560887
$448$	−5.72950e34	−0.0924407
$449$	−1.91098e35	−0.299178	−0.149589	−	0.988748i	$-0.547795\pi$
$449$	−1.91098e35	−0.299178	−0.149589	+	0.988748i	$0.547795\pi$
$450$	−1.91116e35	−0.290354
$451$	1.36119e35	0.200695
$452$	2.04033e35	0.291965
$453$	4.78548e35	0.664661
$454$	5.50210e35	0.741779
$455$	−1.39329e36	−1.82342
$456$	4.82854e34	0.0613466
$457$	6.98861e35	0.862030	0.431015	−	0.902345i	$-0.358156\pi$
$457$	6.98861e35	0.862030	0.431015	+	0.902345i	$0.358156\pi$
$458$	7.23082e34	0.0865972
$459$	2.99786e35	0.348610
$460$	4.05020e35	0.457347
$461$	3.84481e35	0.421611	0.210805	−	0.977528i	$-0.432391\pi$
$461$	3.84481e35	0.421611	0.210805	+	0.977528i	$0.432391\pi$
$462$	4.23859e35	0.451393
$463$	9.75069e35	1.00854	0.504268	−	0.863547i	$-0.331762\pi$
$463$	9.75069e35	1.00854	0.504268	+	0.863547i	$0.331762\pi$
$464$	2.90871e35	0.292219
$465$	4.43795e35	0.433080
$466$	−3.56320e34	−0.0337777
$467$	−1.69510e36	−1.56106	−0.780528	−	0.625121i	$-0.785050\pi$
$467$	−1.69510e36	−1.56106	−0.780528	+	0.625121i	$0.785050\pi$
$468$	−3.07444e35	−0.275073
$469$	−1.58973e36	−1.38194
$470$	−8.74194e35	−0.738391
$471$	−8.81792e35	−0.723742
$472$	−2.02235e35	−0.161301
$473$	1.39942e36	1.08473
$474$	−3.79360e35	−0.285788
$475$	5.05620e35	0.370220
$476$	9.41106e35	0.669800
$477$	−6.63620e35	−0.459115
$478$	−3.09262e35	−0.207994
$479$	7.97318e35	0.521317	0.260659	−	0.965431i	$-0.416060\pi$
$479$	7.97318e35	0.521317	0.260659	+	0.965431i	$0.416060\pi$
$480$	−2.39859e35	−0.152475
$481$	−1.07786e36	−0.666200
$482$	1.03931e36	0.624611
$483$	−4.47322e35	−0.261417
$484$	1.08690e36	0.617697
$485$	−8.21576e35	−0.454082
$486$	8.43862e34	0.0453609
$487$	−2.96190e36	−1.54857	−0.774283	−	0.632840i	$-0.781889\pi$
$487$	−2.96190e36	−1.54857	−0.774283	+	0.632840i	$0.781889\pi$
$488$	−5.30775e34	−0.0269925
$489$	2.19073e36	1.08372
$490$	−9.94631e35	−0.478647
$491$	−2.31819e36	−1.08530	−0.542650	−	0.839959i	$-0.682579\pi$
$491$	−2.31819e36	−1.08530	−0.542650	+	0.839959i	$0.682579\pi$
$492$	8.50742e34	0.0387498
$493$	−4.77775e36	−2.11734
$494$	8.13381e35	0.350736
$495$	1.77444e36	0.744543
$496$	3.07423e35	0.125526
$497$	2.54891e36	1.01284
$498$	7.37288e34	0.0285129
$499$	−2.39251e36	−0.900528	−0.450264	−	0.892896i	$-0.648670\pi$
$499$	−2.39251e36	−0.900528	−0.450264	+	0.892896i	$0.648670\pi$
$500$	−4.72758e35	−0.173198
$501$	3.23092e35	0.115217
$502$	1.56099e36	0.541875
$503$	2.04264e36	0.690279	0.345140	−	0.938551i	$-0.387832\pi$
$503$	2.04264e36	0.690279	0.345140	+	0.938551i	$0.387832\pi$
$504$	2.64911e35	0.0871539
$505$	6.26937e36	2.00812
$506$	−2.07556e36	−0.647297
$507$	−3.27770e36	−0.995319
$508$	−9.62806e35	−0.284694
$509$	5.16626e36	1.48760	0.743800	−	0.668402i	$-0.233021\pi$
$509$	5.16626e36	1.48760	0.743800	+	0.668402i	$0.233021\pi$
$510$	3.93983e36	1.10479
$511$	2.47124e36	0.674890
$512$	−1.66153e35	−0.0441942
$513$	−2.23254e35	−0.0578381
$514$	−2.65635e36	−0.670321
$515$	5.04781e36	1.24081
$516$	8.74632e35	0.209438
$517$	4.47988e36	1.04507
$518$	9.28744e35	0.211079
$519$	−1.49210e36	−0.330399
$520$	−4.04048e36	−0.871742
$521$	−2.37289e36	−0.498847	−0.249424	−	0.968394i	$-0.580241\pi$
$521$	−2.37289e36	−0.498847	−0.249424	+	0.968394i	$0.580241\pi$
$522$	−1.34488e36	−0.275507
$523$	−7.05965e36	−1.40932	−0.704661	−	0.709544i	$-0.748901\pi$
$523$	−7.05965e36	−1.40932	−0.704661	+	0.709544i	$0.748901\pi$
$524$	−1.14473e36	−0.222705
$525$	2.77400e36	0.525965
$526$	6.09848e36	1.12698
$527$	−5.04963e36	−0.909528
$528$	1.22918e36	0.215802
$529$	−3.65276e36	−0.625128
$530$	−8.72140e36	−1.45500
$531$	9.35057e35	0.152076
$532$	−7.00852e35	−0.111127
$533$	1.43310e36	0.221543
$534$	−5.18686e36	−0.781804
$535$	4.73938e36	0.696539
$536$	−4.61016e36	−0.660681
$537$	−2.73717e36	−0.382516
$538$	−1.63956e35	−0.0223443
$539$	5.09708e36	0.677443
$540$	1.10902e36	0.143755
$541$	4.19962e36	0.530942	0.265471	−	0.964119i	$-0.414473\pi$
$541$	4.19962e36	0.530942	0.265471	+	0.964119i	$0.414473\pi$
$542$	−2.89968e36	−0.357569
$543$	−3.72803e36	−0.448417
$544$	2.72918e36	0.320219
$545$	−1.60721e37	−1.83959
$546$	4.46249e36	0.498284
$547$	−8.01701e36	−0.873340	−0.436670	−	0.899622i	$-0.643842\pi$
$547$	−8.01701e36	−0.873340	−0.436670	+	0.899622i	$0.643842\pi$
$548$	−5.60593e36	−0.595813
$549$	2.45410e35	0.0254487
$550$	1.28713e37	1.30234
$551$	3.55804e36	0.351289
$552$	−1.29722e36	−0.124979
$553$	5.50633e36	0.517694
$554$	6.89012e36	0.632186
$555$	3.88808e36	0.348161
$556$	−5.65963e36	−0.494628
$557$	8.47920e36	0.723286	0.361643	−	0.932317i	$-0.382216\pi$
$557$	8.47920e36	0.723286	0.361643	+	0.932317i	$0.382216\pi$
$558$	−1.42141e36	−0.118347
$559$	1.47334e37	1.19741
$560$	3.48150e36	0.276202
$561$	−2.01900e37	−1.56364
$562$	7.79896e36	0.589653
$563$	1.57024e37	1.15905	0.579527	−	0.814953i	$-0.303237\pi$
$563$	1.57024e37	1.15905	0.579527	+	0.814953i	$0.303237\pi$
$564$	2.79991e36	0.201779
$565$	−1.23979e37	−0.872360
$566$	9.78869e36	0.672517
$567$	−1.22485e36	−0.0821695
$568$	7.39175e36	0.484222
$569$	−6.61307e36	−0.423046	−0.211523	−	0.977373i	$-0.567842\pi$
$569$	−6.61307e36	−0.423046	−0.211523	+	0.977373i	$0.567842\pi$
$570$	−2.93404e36	−0.183297
$571$	−1.10258e37	−0.672703	−0.336351	−	0.941737i	$-0.609193\pi$
$571$	−1.10258e37	−0.672703	−0.336351	+	0.941737i	$0.609193\pi$
$572$	2.07058e37	1.23380
$573$	−1.09594e37	−0.637824
$574$	−1.23483e36	−0.0701937
$575$	−1.35838e37	−0.754233
$576$	7.68232e35	0.0416667
$577$	5.92894e36	0.314126	0.157063	−	0.987589i	$-0.449798\pi$
$577$	5.92894e36	0.314126	0.157063	+	0.987589i	$0.449798\pi$
$578$	−3.11666e37	−1.61311
$579$	1.08967e37	0.550976
$580$	−1.76746e37	−0.873117
$581$	−1.07016e36	−0.0516500
$582$	2.63139e36	0.124086
$583$	4.46936e37	2.05930
$584$	7.16651e36	0.322652
$585$	1.86817e37	0.821887
$586$	−1.20819e36	−0.0519420
$587$	2.78941e36	0.117192	0.0585960	−	0.998282i	$-0.481338\pi$
$587$	2.78941e36	0.117192	0.0585960	+	0.998282i	$0.481338\pi$
$588$	3.18566e36	0.130799
$589$	3.76051e36	0.150900
$590$	1.22887e37	0.481951
$591$	−1.26890e37	−0.486402
$592$	2.69333e36	0.100913
$593$	−1.73393e37	−0.635030	−0.317515	−	0.948253i	$-0.602848\pi$
$593$	−1.73393e37	−0.635030	−0.317515	+	0.948253i	$0.602848\pi$
$594$	−5.68326e36	−0.203461
$595$	−5.71858e37	−2.00129
$596$	1.41981e37	0.485743
$597$	3.10324e37	1.03792
$598$	−2.18520e37	−0.714538
$599$	−7.25738e36	−0.232016	−0.116008	−	0.993248i	$-0.537010\pi$
$599$	−7.25738e36	−0.232016	−0.116008	+	0.993248i	$0.537010\pi$
$600$	8.04452e36	0.251454
$601$	−3.01715e37	−0.922128	−0.461064	−	0.887367i	$-0.652532\pi$
$601$	−3.01715e37	−0.922128	−0.461064	+	0.887367i	$0.652532\pi$
$602$	−1.26951e37	−0.379388
$603$	2.13157e37	0.622896
$604$	−2.01432e37	−0.575613
$605$	−6.60446e37	−1.84561
$606$	−2.00799e37	−0.548757
$607$	−2.67043e37	−0.713731	−0.356866	−	0.934156i	$-0.616155\pi$
$607$	−2.67043e37	−0.713731	−0.356866	+	0.934156i	$0.616155\pi$
$608$	−2.03245e36	−0.0531277
$609$	1.95206e37	0.499069
$610$	3.22522e36	0.0806505
$611$	4.71653e37	1.15363
$612$	−1.26187e37	−0.301905
$613$	2.42647e37	0.567882	0.283941	−	0.958842i	$-0.408358\pi$
$613$	2.42647e37	0.567882	0.283941	+	0.958842i	$0.408358\pi$
$614$	4.27708e37	0.979207
$615$	−5.16949e36	−0.115780
$616$	−1.78412e37	−0.390918
$617$	4.06856e37	0.872150	0.436075	−	0.899910i	$-0.356368\pi$
$617$	4.06856e37	0.872150	0.436075	+	0.899910i	$0.356368\pi$
$618$	−1.61674e37	−0.339075
$619$	5.00474e37	1.02697	0.513485	−	0.858098i	$-0.328354\pi$
$619$	5.00474e37	1.02697	0.513485	+	0.858098i	$0.328354\pi$
$620$	−1.86804e37	−0.375058
$621$	5.99786e36	0.117831
$622$	−1.77659e37	−0.341521
$623$	7.52862e37	1.41621
$624$	1.29411e37	0.238220
$625$	−3.96555e37	−0.714370
$626$	−5.30630e37	−0.935488
$627$	1.50357e37	0.259426
$628$	3.71167e37	0.626779
$629$	−4.42396e37	−0.731186
$630$	−1.60971e37	−0.260406
$631$	3.08165e37	0.487964	0.243982	−	0.969780i	$-0.421546\pi$
$631$	3.08165e37	0.487964	0.243982	+	0.969780i	$0.421546\pi$
$632$	1.59682e37	0.247500
$633$	3.64499e37	0.553027
$634$	−2.27114e37	−0.337318
$635$	5.85044e37	0.850634
$636$	2.79334e37	0.397605
$637$	5.36633e37	0.747816
$638$	9.05752e37	1.23575
$639$	−3.41767e37	−0.456529
$640$	1.00962e37	0.132047
$641$	−8.17226e37	−1.04655	−0.523274	−	0.852165i	$-0.675290\pi$
$641$	−8.17226e37	−1.04655	−0.523274	+	0.852165i	$0.675290\pi$
$642$	−1.51795e37	−0.190342
$643$	5.72750e37	0.703262	0.351631	−	0.936139i	$-0.385627\pi$
$643$	5.72750e37	0.703262	0.351631	+	0.936139i	$0.385627\pi$
$644$	1.88289e37	0.226394
$645$	−5.31465e37	−0.625776
$646$	3.33843e37	0.384949
$647$	−1.57953e38	−1.78370	−0.891848	−	0.452335i	$-0.850591\pi$
$647$	−1.57953e38	−1.78370	−0.891848	+	0.452335i	$0.850591\pi$
$648$	−3.55202e36	−0.0392837
$649$	−6.29744e37	−0.682119
$650$	1.35512e38	1.43763
$651$	2.06315e37	0.214381
$652$	−9.22129e37	−0.938532
$653$	−3.34681e37	−0.333659	−0.166830	−	0.985986i	$-0.553353\pi$
$653$	−3.34681e37	−0.333659	−0.166830	+	0.985986i	$0.553353\pi$
$654$	5.14767e37	0.502702
$655$	6.95587e37	0.665417
$656$	−3.58098e36	−0.0335583
$657$	−3.31353e37	−0.304199
$658$	−4.06401e37	−0.365515
$659$	1.52900e37	0.134727	0.0673635	−	0.997728i	$-0.478541\pi$
$659$	1.52900e37	0.134727	0.0673635	+	0.997728i	$0.478541\pi$
$660$	−7.46902e37	−0.644793
$661$	−1.36410e38	−1.15379	−0.576896	−	0.816817i	$-0.695736\pi$
$661$	−1.36410e38	−1.15379	−0.576896	+	0.816817i	$0.695736\pi$
$662$	−1.29141e38	−1.07024
$663$	−2.12565e38	−1.72608
$664$	−3.10342e36	−0.0246929
$665$	4.25869e37	0.332035
$666$	−1.24529e37	−0.0951414
$667$	−9.55891e37	−0.715665
$668$	−1.35997e37	−0.0997811
$669$	9.14809e37	0.657775
$670$	2.80134e38	1.97404
$671$	−1.65279e37	−0.114147
$672$	−1.11507e37	−0.0754775
$673$	1.74357e38	1.15674	0.578371	−	0.815774i	$-0.303689\pi$
$673$	1.74357e38	1.15674	0.578371	+	0.815774i	$0.303689\pi$
$674$	−5.28975e37	−0.343975
$675$	−3.71949e37	−0.237073
$676$	1.37966e38	0.861971
$677$	−1.87754e38	−1.14985	−0.574927	−	0.818205i	$-0.694969\pi$
$677$	−1.87754e38	−1.14985	−0.574927	+	0.818205i	$0.694969\pi$
$678$	3.97088e37	0.238389
$679$	−3.81940e37	−0.224778
$680$	−1.65837e38	−0.956777
$681$	1.07082e38	0.605660
$682$	9.57294e37	0.530831
$683$	−1.57801e38	−0.857885	−0.428943	−	0.903332i	$-0.641114\pi$
$683$	−1.57801e38	−0.857885	−0.428943	+	0.903332i	$0.641114\pi$
$684$	9.39728e36	0.0500893
$685$	3.40641e38	1.78022
$686$	−1.48289e38	−0.759861
$687$	1.40726e37	0.0707063
$688$	−3.68154e37	−0.181378
$689$	4.70545e38	2.27322
$690$	7.88248e37	0.373422
$691$	−1.14657e38	−0.532654	−0.266327	−	0.963883i	$-0.585810\pi$
$691$	−1.14657e38	−0.532654	−0.266327	+	0.963883i	$0.585810\pi$
$692$	6.28061e37	0.286134
$693$	8.24912e37	0.368561
$694$	−2.26620e38	−0.992990
$695$	3.43904e38	1.47789
$696$	5.66092e37	0.238596
$697$	5.88198e37	0.243154
$698$	1.07643e38	0.436455
$699$	−6.93468e36	−0.0275794
$700$	−1.16764e38	−0.455499
$701$	−1.51443e38	−0.579504	−0.289752	−	0.957102i	$-0.593573\pi$
$701$	−1.51443e38	−0.579504	−0.289752	+	0.957102i	$0.593573\pi$
$702$	−5.98347e37	−0.224596
$703$	3.29457e37	0.121312
$704$	−5.17390e37	−0.186890
$705$	−1.70135e38	−0.602894
$706$	−3.76600e37	−0.130923
$707$	2.91455e38	0.994052
$708$	−3.93588e37	−0.131702
$709$	1.93052e38	0.633797	0.316898	−	0.948460i	$-0.397359\pi$
$709$	1.93052e38	0.633797	0.316898	+	0.948460i	$0.397359\pi$
$710$	−4.49155e38	−1.44680
$711$	−7.38309e37	−0.233345
$712$	2.18327e38	0.677062
$713$	−1.01029e38	−0.307422
$714$	1.83158e38	0.546889
$715$	−1.25818e39	−3.68647
$716$	1.15214e38	0.331268
$717$	−6.01885e37	−0.169826
$718$	−3.34079e38	−0.925057
$719$	2.23169e38	0.606450	0.303225	−	0.952919i	$-0.401937\pi$
$719$	2.23169e38	0.606450	0.303225	+	0.952919i	$0.401937\pi$
$720$	−4.66812e37	−0.124495
$721$	2.34666e38	0.614221
$722$	2.50395e38	0.643240
$723$	2.02270e38	0.509993
$724$	1.56922e38	0.388340
$725$	5.92782e38	1.43990
$726$	2.11531e38	0.504348
$727$	−6.80926e38	−1.59362	−0.796812	−	0.604228i	$-0.793482\pi$
$727$	−6.80926e38	−1.59362	−0.796812	+	0.604228i	$0.793482\pi$
$728$	−1.87837e38	−0.431526
$729$	1.64232e37	0.0370370
$730$	−4.35469e38	−0.964048
$731$	6.04716e38	1.31422
$732$	−1.03299e37	−0.0220393
$733$	5.94424e38	1.24507	0.622534	−	0.782593i	$-0.286103\pi$
$733$	5.94424e38	1.24507	0.622534	+	0.782593i	$0.286103\pi$
$734$	2.16701e38	0.445619
$735$	−1.93575e38	−0.390813
$736$	5.46030e37	0.108235
$737$	−1.43557e39	−2.79392
$738$	1.65571e37	0.0316391
$739$	1.39799e38	0.262304	0.131152	−	0.991362i	$-0.458132\pi$
$739$	1.39799e38	0.262304	0.131152	+	0.991362i	$0.458132\pi$
$740$	−1.63658e38	−0.301516
$741$	1.58300e38	0.286375
$742$	−4.05447e38	−0.720246
$743$	−6.17947e38	−1.07796	−0.538979	−	0.842319i	$-0.681190\pi$
$743$	−6.17947e38	−1.07796	−0.538979	+	0.842319i	$0.681190\pi$
$744$	5.98306e37	0.102492
$745$	−8.62740e38	−1.45134
$746$	−1.92399e38	−0.317855
$747$	1.43491e37	0.0232807
$748$	8.49846e38	1.35416
$749$	2.20328e38	0.344798
$750$	−9.20079e37	−0.141416
$751$	9.81933e38	1.48232	0.741161	−	0.671327i	$-0.234275\pi$
$751$	9.81933e38	1.48232	0.741161	+	0.671327i	$0.234275\pi$
$752$	−1.17855e38	−0.174746
$753$	3.03799e38	0.442439
$754$	9.53598e38	1.36412
$755$	1.22399e39	1.71987
$756$	5.15568e37	0.0711609
$757$	−1.21343e39	−1.64520	−0.822601	−	0.568619i	$-0.807478\pi$
$757$	−1.21343e39	−1.64520	−0.822601	+	0.568619i	$0.807478\pi$
$758$	3.06769e38	0.408580
$759$	−4.03945e38	−0.528516
$760$	1.23501e38	0.158740
$761$	−8.53798e37	−0.107811	−0.0539054	−	0.998546i	$-0.517167\pi$
$761$	−8.53798e37	−0.107811	−0.0539054	+	0.998546i	$0.517167\pi$
$762$	−1.87381e38	−0.232452
$763$	−7.47173e38	−0.910625
$764$	4.61309e38	0.552372
$765$	7.66768e38	0.902058
$766$	1.81718e38	0.210044
$767$	−6.63009e38	−0.752978
$768$	−3.23367e37	−0.0360844
$769$	1.34859e39	1.47868	0.739342	−	0.673330i	$-0.235137\pi$
$769$	1.34859e39	1.47868	0.739342	+	0.673330i	$0.235137\pi$
$770$	1.08411e39	1.16802
$771$	−5.16977e38	−0.547315
$772$	−4.58666e38	−0.477159
$773$	−3.49887e38	−0.357688	−0.178844	−	0.983877i	$-0.557236\pi$
$773$	−3.49887e38	−0.357688	−0.178844	+	0.983877i	$0.557236\pi$
$774$	1.70220e38	0.171005
$775$	6.26515e38	0.618526
$776$	−1.10761e38	−0.107462
$777$	1.80752e38	0.172345
$778$	4.74136e34	4.44302e−5 0
$779$	−4.38038e37	−0.0403419
$780$	−7.86357e38	−0.711775
$781$	2.30174e39	2.04770
$782$	−8.96890e38	−0.784238
$783$	−2.61740e38	−0.224950
$784$	−1.34092e38	−0.113275
$785$	−2.25538e39	−1.87275
$786$	−2.22786e38	−0.181838
$787$	7.49672e38	0.601468	0.300734	−	0.953708i	$-0.402768\pi$
$787$	7.49672e38	0.601468	0.300734	+	0.953708i	$0.402768\pi$
$788$	5.34109e38	0.421236
$789$	1.18688e39	0.920171
$790$	−9.70297e38	−0.739501
$791$	−5.76364e38	−0.431832
$792$	2.39222e38	0.176202
$793$	−1.74010e38	−0.126005
$794$	−5.22553e38	−0.372009
$795$	−1.69736e39	−1.18800
$796$	−1.30623e39	−0.898861
$797$	−2.08690e39	−1.41194	−0.705968	−	0.708243i	$-0.749488\pi$
$797$	−2.08690e39	−1.41194	−0.705968	+	0.708243i	$0.749488\pi$
$798$	−1.36400e38	−0.0907348
$799$	1.93584e39	1.26616
$800$	−3.38613e38	−0.217765
$801$	−1.00946e39	−0.638340
$802$	−1.37037e39	−0.852086
$803$	2.23160e39	1.36445
$804$	−8.97228e38	−0.539444
$805$	−1.14412e39	−0.676439
$806$	1.00786e39	0.585974
$807$	−3.19091e37	−0.0182441
$808$	8.45209e38	0.475238
$809$	−3.04435e39	−1.68341	−0.841703	−	0.539941i	$-0.818447\pi$
$809$	−3.04435e39	−1.68341	−0.841703	+	0.539941i	$0.818447\pi$
$810$	2.15836e38	0.117375
$811$	−5.48000e38	−0.293089	−0.146544	−	0.989204i	$-0.546815\pi$
$811$	−5.48000e38	−0.293089	−0.146544	+	0.989204i	$0.546815\pi$
$812$	−8.21671e38	−0.432207
$813$	−5.64335e38	−0.291954
$814$	8.38682e38	0.426745
$815$	5.60326e39	2.80423
$816$	5.31151e38	0.261457
$817$	−4.50339e38	−0.218043
$818$	1.64746e39	0.784596
$819$	8.68488e38	0.406847
$820$	2.17596e38	0.100268
$821$	3.55165e39	1.60989	0.804947	−	0.593347i	$-0.202194\pi$
$821$	3.55165e39	1.60989	0.804947	+	0.593347i	$0.202194\pi$
$822$	−1.09102e39	−0.486479
$823$	−3.38913e38	−0.148659	−0.0743295	−	0.997234i	$-0.523682\pi$
$823$	−3.38913e38	−0.148659	−0.0743295	+	0.997234i	$0.523682\pi$
$824$	6.80525e38	0.293648
$825$	2.50501e39	1.06336
$826$	5.71284e38	0.238573
$827$	−4.33147e39	−1.77955	−0.889776	−	0.456398i	$-0.849139\pi$
$827$	−4.33147e39	−1.77955	−0.889776	+	0.456398i	$0.849139\pi$
$828$	−2.52464e38	−0.102045
$829$	−1.12963e39	−0.449210	−0.224605	−	0.974450i	$-0.572109\pi$
$829$	−1.12963e39	−0.449210	−0.224605	+	0.974450i	$0.572109\pi$
$830$	1.88578e38	0.0737796
$831$	1.34095e39	0.516178
$832$	−5.44721e38	−0.206305
$833$	2.20255e39	0.820762
$834$	−1.10147e39	−0.403862
$835$	8.26380e38	0.298135
$836$	−6.32890e38	−0.224669
$837$	−2.76634e38	−0.0966301
$838$	−5.34099e38	−0.183581
$839$	3.16991e39	1.07216	0.536081	−	0.844167i	$-0.319904\pi$
$839$	3.16991e39	1.07216	0.536081	+	0.844167i	$0.319904\pi$
$840$	6.77567e38	0.225518
$841$	1.11827e39	0.366269
$842$	1.99927e39	0.644402
$843$	1.51783e39	0.481449
$844$	−1.53426e39	−0.478936
$845$	−8.38344e39	−2.57547
$846$	5.44918e38	0.164752
$847$	−3.07033e39	−0.913606
$848$	−1.17578e39	−0.344336
$849$	1.90507e39	0.549107
$850$	5.56194e39	1.57787
$851$	−8.85108e38	−0.247142
$852$	1.43858e39	0.395366
$853$	−2.38143e39	−0.644207	−0.322104	−	0.946704i	$-0.604390\pi$
$853$	−2.38143e39	−0.644207	−0.322104	+	0.946704i	$0.604390\pi$
$854$	1.49936e38	0.0399233
$855$	−5.71021e38	−0.149661
$856$	6.38943e38	0.164841
$857$	−4.37377e39	−1.11075	−0.555374	−	0.831601i	$-0.687425\pi$
$857$	−4.37377e39	−1.11075	−0.555374	+	0.831601i	$0.687425\pi$
$858$	4.02976e39	1.00740
$859$	2.25574e39	0.555113	0.277556	−	0.960709i	$-0.410475\pi$
$859$	2.25574e39	0.555113	0.277556	+	0.960709i	$0.410475\pi$
$860$	2.23706e39	0.541938
$861$	−2.40323e38	−0.0573129
$862$	−5.20472e39	−1.22194
$863$	4.17296e39	0.964493	0.482246	−	0.876036i	$-0.339821\pi$
$863$	4.17296e39	0.964493	0.482246	+	0.876036i	$0.339821\pi$
$864$	1.49513e38	0.0340207
$865$	−3.81638e39	−0.854936
$866$	−3.82910e39	−0.844510
$867$	−6.06563e39	−1.31710
$868$	−8.68428e38	−0.185660
$869$	4.97237e39	1.04664
$870$	−3.43983e39	−0.712897
$871$	−1.51140e40	−3.08415
$872$	−2.16678e39	−0.435353
$873$	5.12119e38	0.101316
$874$	6.67924e38	0.130114
$875$	1.33548e39	0.256169
$876$	1.39474e39	0.263444
$877$	4.78308e39	0.889637	0.444819	−	0.895621i	$-0.353268\pi$
$877$	4.78308e39	0.889637	0.444819	+	0.895621i	$0.353268\pi$
$878$	4.92721e38	0.0902454
$879$	−2.35138e38	−0.0424105
$880$	3.14389e39	0.558408
$881$	−3.65274e39	−0.638917	−0.319459	−	0.947600i	$-0.603501\pi$
$881$	−3.65274e39	−0.638917	−0.319459	+	0.947600i	$0.603501\pi$
$882$	6.19991e38	0.106797
$883$	6.82091e39	1.15710	0.578552	−	0.815645i	$-0.303618\pi$
$883$	6.82091e39	1.15710	0.578552	+	0.815645i	$0.303618\pi$
$884$	8.94739e39	1.49483
$885$	2.39161e39	0.393511
$886$	8.61462e38	0.139599
$887$	1.10574e40	1.76476	0.882379	−	0.470539i	$-0.155940\pi$
$887$	1.10574e40	1.76476	0.882379	+	0.470539i	$0.155940\pi$
$888$	5.24174e38	0.0823949
$889$	2.71979e39	0.421078
$890$	−1.32665e40	−2.02298
$891$	−1.10607e39	−0.166125
$892$	−3.85065e39	−0.569650
$893$	−1.44165e39	−0.210070
$894$	2.76323e39	0.396607
$895$	−7.00092e39	−0.989792
$896$	4.69360e38	0.0653655
$897$	−4.25283e39	−0.583418
$898$	1.56547e39	0.211551
$899$	4.40878e39	0.586898
$900$	1.56562e39	0.205311
$901$	1.93130e40	2.49497
$902$	−1.11509e39	−0.141913
$903$	−2.47071e39	−0.309769
$904$	−1.67144e39	−0.206451
$905$	−9.53526e39	−1.16032
$906$	−3.92027e39	−0.469986
$907$	−1.78298e39	−0.210595	−0.105297	−	0.994441i	$-0.533579\pi$
$907$	−1.78298e39	−0.210595	−0.105297	+	0.994441i	$0.533579\pi$
$908$	−4.50732e39	−0.524517
$909$	−3.90793e39	−0.448058
$910$	1.14138e40	1.28935
$911$	9.95944e39	1.10850	0.554252	−	0.832349i	$-0.313005\pi$
$911$	9.95944e39	1.10850	0.554252	+	0.832349i	$0.313005\pi$
$912$	−3.95554e38	−0.0433786
$913$	−9.66383e38	−0.104422
$914$	−5.72507e39	−0.609547
$915$	6.27691e38	0.0658508
$916$	−5.92349e38	−0.0612334
$917$	3.23369e39	0.329392
$918$	−2.45584e39	−0.246504
$919$	5.16258e39	0.510631	0.255316	−	0.966858i	$-0.417821\pi$
$919$	5.16258e39	0.510631	0.255316	+	0.966858i	$0.417821\pi$
$920$	−3.31792e39	−0.323393
$921$	8.32403e39	0.799519
$922$	−3.14966e39	−0.298124
$923$	2.42332e40	2.26042
$924$	−3.47225e39	−0.319183
$925$	5.48887e39	0.497244
$926$	−7.98776e39	−0.713143
$927$	−3.14649e39	−0.276854
$928$	−2.38282e39	−0.206630
$929$	6.71129e39	0.573580	0.286790	−	0.957993i	$-0.407412\pi$
$929$	6.71129e39	0.573580	0.286790	+	0.957993i	$0.407412\pi$
$930$	−3.63557e39	−0.306234
$931$	−1.64026e39	−0.136173
$932$	2.91897e38	0.0238844
$933$	−3.45759e39	−0.278850
$934$	1.38863e40	1.10383
$935$	−5.16404e40	−4.04607
$936$	2.51859e39	0.194506
$937$	−8.79137e39	−0.669225	−0.334613	−	0.942356i	$-0.608605\pi$
$937$	−8.79137e39	−0.669225	−0.334613	+	0.942356i	$0.608605\pi$
$938$	1.30231e40	0.977181
$939$	−1.03271e40	−0.763822
$940$	7.16140e39	0.522122
$941$	9.62477e39	0.691720	0.345860	−	0.938286i	$-0.387587\pi$
$941$	9.62477e39	0.691720	0.345860	+	0.938286i	$0.387587\pi$
$942$	7.22364e39	0.511763
$943$	1.17682e39	0.0821866
$944$	1.65671e39	0.114057
$945$	−3.13282e39	−0.212621
$946$	−1.14640e40	−0.767021
$947$	−2.79419e40	−1.84303	−0.921514	−	0.388345i	$-0.873047\pi$
$947$	−2.79419e40	−1.84303	−0.921514	+	0.388345i	$0.873047\pi$
$948$	3.10772e39	0.202083
$949$	2.34948e40	1.50619
$950$	−4.14204e39	−0.261785
$951$	−4.42009e39	−0.275419
$952$	−7.70954e39	−0.473620
$953$	−1.71770e40	−1.04039	−0.520193	−	0.854049i	$-0.674140\pi$
$953$	−1.71770e40	−1.04039	−0.520193	+	0.854049i	$0.674140\pi$
$954$	5.43638e39	0.324643
$955$	−2.80312e40	−1.65042
$956$	2.53348e39	0.147074
$957$	1.76277e40	1.00898
$958$	−6.53163e39	−0.368627
$959$	1.58360e40	0.881238
$960$	1.96492e39	0.107816
$961$	−1.38231e40	−0.747891
$962$	8.82985e39	0.471075
$963$	−2.95423e39	−0.155414
$964$	−8.51402e39	−0.441667
$965$	2.78706e40	1.42570
$966$	3.66446e39	0.184850
$967$	−2.43617e40	−1.21186	−0.605928	−	0.795520i	$-0.707198\pi$
$967$	−2.43617e40	−1.21186	−0.605928	+	0.795520i	$0.707198\pi$
$968$	−8.90385e39	−0.436778
$969$	6.49723e39	0.314309
$970$	6.73035e39	0.321084
$971$	−3.36431e40	−1.58284	−0.791419	−	0.611274i	$-0.790657\pi$
$971$	−3.36431e40	−1.58284	−0.791419	+	0.611274i	$0.790657\pi$
$972$	−6.91292e38	−0.0320750
$973$	1.59877e40	0.731580
$974$	2.42639e40	1.09500
$975$	2.63733e40	1.17382
$976$	4.34811e38	0.0190866
$977$	6.68476e39	0.289407	0.144704	−	0.989475i	$-0.453777\pi$
$977$	6.68476e39	0.289407	0.144704	+	0.989475i	$0.453777\pi$
$978$	−1.79464e40	−0.766308
$979$	6.79856e40	2.86319
$980$	8.14802e39	0.338454
$981$	1.00184e40	0.410455
$982$	1.89906e40	0.767422
$983$	1.58448e40	0.631558	0.315779	−	0.948833i	$-0.397734\pi$
$983$	1.58448e40	0.631558	0.315779	+	0.948833i	$0.397734\pi$
$984$	−6.96928e38	−0.0274002
$985$	−3.24548e40	−1.25861
$986$	3.91393e40	1.49718
$987$	−7.90936e39	−0.298442
$988$	−6.66322e39	−0.248008
$989$	1.20986e40	0.444208
$990$	−1.45362e40	−0.526472
$991$	−1.77796e40	−0.635226	−0.317613	−	0.948221i	$-0.602881\pi$
$991$	−1.77796e40	−0.635226	−0.317613	+	0.948221i	$0.602881\pi$
$992$	−2.51841e39	−0.0887604
$993$	−2.51333e40	−0.873846
$994$	−2.08806e40	−0.716189
$995$	7.93722e40	2.68570
$996$	−6.03987e38	−0.0201617
$997$	−3.86472e40	−1.27272	−0.636360	−	0.771392i	$-0.719561\pi$
$997$	−3.86472e40	−1.27272	−0.636360	+	0.771392i	$0.719561\pi$
$998$	1.95995e40	0.636769
$999$	−2.42358e39	−0.0776827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.28.a.d.1.1	✓	2
3.2	odd	2		18.28.a.g.1.2		2
4.3	odd	2		48.28.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.28.a.d.1.1	✓	2	1.1	even	1	trivial
18.28.a.g.1.2		2	3.2	odd	2
48.28.a.g.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

\(f(q)\)	\(=\)	\(q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} -4.07783e9 q^{5} +1.30607e10 q^{6} -1.89573e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} +O(q^{10})\)	\(q-8192.00 q^{2} -1.59432e6 q^{3} +6.71089e7 q^{4} -4.07783e9 q^{5} +1.30607e10 q^{6} -1.89573e11 q^{7} -5.49756e11 q^{8} +2.54187e12 q^{9} +3.34056e13 q^{10} -1.71190e14 q^{11} -1.06993e14 q^{12} -1.80233e15 q^{13} +1.55298e15 q^{14} +6.50138e15 q^{15} +4.50360e15 q^{16} -7.39745e16 q^{17} -2.08230e16 q^{18} +5.50896e16 q^{19} -2.73659e17 q^{20} +3.02241e17 q^{21} +1.40239e18 q^{22} -1.48002e18 q^{23} +8.76488e17 q^{24} +9.17813e18 q^{25} +1.47647e19 q^{26} -4.05256e18 q^{27} -1.27220e19 q^{28} +6.45864e19 q^{29} -5.32593e19 q^{30} +6.82617e19 q^{31} -3.68935e19 q^{32} +2.72932e20 q^{33} +6.05999e20 q^{34} +7.73047e20 q^{35} +1.70582e20 q^{36} +5.98039e20 q^{37} -4.51294e20 q^{38} +2.87350e21 q^{39} +2.24181e21 q^{40} -7.95137e20 q^{41} -2.47596e21 q^{42} -8.17465e21 q^{43} -1.14884e22 q^{44} -1.03653e22 q^{45} +1.21243e22 q^{46} -2.61691e22 q^{47} -7.18019e21 q^{48} -2.97744e22 q^{49} -7.51872e22 q^{50} +1.17939e23 q^{51} -1.20952e23 q^{52} -2.61076e23 q^{53} +3.31985e22 q^{54} +6.98084e23 q^{55} +1.04219e23 q^{56} -8.78307e22 q^{57} -5.29092e23 q^{58} +3.67862e23 q^{59} +4.36300e23 q^{60} +9.65474e22 q^{61} -5.59200e23 q^{62} -4.81869e23 q^{63} +3.02231e23 q^{64} +7.34960e24 q^{65} -2.23586e24 q^{66} +8.38584e24 q^{67} -4.96435e24 q^{68} +2.35963e24 q^{69} -6.33280e24 q^{70} -1.34455e25 q^{71} -1.39741e24 q^{72} -1.30358e25 q^{73} -4.89913e24 q^{74} -1.46329e25 q^{75} +3.69700e24 q^{76} +3.24530e25 q^{77} -2.35397e25 q^{78} -2.90459e25 q^{79} -1.83649e25 q^{80} +6.46108e24 q^{81} +6.51376e24 q^{82} +5.64509e24 q^{83} +2.02830e25 q^{84} +3.01656e26 q^{85} +6.69667e25 q^{86} -1.02972e26 q^{87} +9.41127e25 q^{88} -3.97135e26 q^{89} +8.49125e25 q^{90} +3.41673e26 q^{91} -9.93224e25 q^{92} -1.08831e26 q^{93} +2.14377e26 q^{94} -2.24646e26 q^{95} +5.88201e25 q^{96} +2.01474e26 q^{97} +2.43912e26 q^{98} -4.35142e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9}+O(q^{10}) \) 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9	\( 2 q - 16384 q^{2} - 3188646 q^{3} + 134217728 q^{4} + 291441036 q^{5} + 26121388032 q^{6} + 121646295328 q^{7} - 1099511627776 q^{8} + 5083731656658 q^{9} - 2387484966912 q^{10} - 231807361766376 q^{11} - 213986410758144 q^{12} - 11\!\cdots\!64 q^{13}+ \cdots - 58\!\cdots\!04 q^{99}+O(q^{100}) \) 2 * q - 16384 * q^2 - 3188646 * q^3 + 134217728 * q^4 + 291441036 * q^5 + 26121388032 * q^6 + 121646295328 * q^7 - 1099511627776 * q^8 + 5083731656658 * q^9 - 2387484966912 * q^10 - 231807361766376 * q^11 - 213986410758144 * q^12 - 1155759271611764 * q^13 - 996526451326976 * q^14 - 464651146838628 * q^15 + 9007199254740992 * q^16 - 46125175777027452 * q^17 - 41645929731342336 * q^18 - 268519854753239000 * q^19 + 19558276848943104 * q^20 - 193943486506222944 * q^21 + 1898965907590152192 * q^22 + 1299561926005929936 * q^23 + 1752976676930715648 * q^24 + 20818087556919436046 * q^25 + 9467979953043570688 * q^26 - 8105110306037952534 * q^27 + 8163544689270587392 * q^28 + 60178362995785587900 * q^29 + 3806422194902040576 * q^30 + 203575085639304966544 * q^31 - 73786976294838206464 * q^32 + 369575808433453883448 * q^33 + 377857439965408886784 * q^34 + 2132849735738606710464 * q^35 + 341163456359156416512 * q^36 + 3022337597514982851388 * q^37 + 2199714650138533888000 * q^38 + 1842653589193882415772 * q^39 - 160221403946541907968 * q^40 - 10870375798082518905516 * q^41 + 1588785041458978357248 * q^42 - 1299568293415606314344 * q^43 - 15556328714978526756864 * q^44 + 740804010381201908844 * q^45 - 10646011297840578035712 * q^46 - 99372996476917699213632 * q^47 - 14360384937416422588416 * q^48 + 1370785920275118717906 * q^49 - 170541773266284020088832 * q^50 + 73538428620357738354996 * q^51 - 77561691775332931076096 * q^52 - 35770850049954566775924 * q^53 + 66397063627062907158528 * q^54 + 433229958906724722129552 * q^55 - 66875758094504651915264 * q^56 + 428107380389748262197000 * q^57 - 492981149661475536076800 * q^58 + 299672958231389705557080 * q^59 - 31182210620637516398592 * q^60 + 2165599091776519863171724 * q^61 - 1667687101557186285928448 * q^62 + 309208561237060882746912 * q^63 + 604462909807314587353088 * q^64 + 10174637395564415468537928 * q^65 - 3027565022686854213206016 * q^66 + 13568283837486181949525608 * q^67 - 3095408148196629600534528 * q^68 - 2071921468555552233353328 * q^69 - 17472305035170666172121088 * q^70 - 4319907418871433623040336 * q^71 - 2794811034494209364066304 * q^72 - 20032895180752990538485964 * q^73 - 24758989598842739518570496 * q^74 - 33190755808010466035166858 * q^75 - 18020062413934869610496000 * q^76 + 13587711578810985760484736 * q^77 - 15095018202676284750004224 * q^78 + 5633936436869082596599600 * q^79 + 1312533741130071310073856 * q^80 + 12922163778453346597864482 * q^81 + 89050118537891994873987072 * q^82 - 46762236922353070723154904 * q^83 - 13015327059631950702575616 * q^84 + 423336865613342459682869784 * q^85 + 10646063459660646927106048 * q^86 - 95943748226529865857491700 * q^87 + 127437444833104091192229888 * q^88 - 191930414076503127699406380 * q^89 - 6068666453042806037250048 * q^90 + 542898500680491813749530304 * q^91 + 87212124551910015268552704 * q^92 - 324564441261713612175329712 * q^93 + 814063587138909791958073344 * q^94 - 1638584179808499075287277840 * q^95 + 117640273407315333844303872 * q^96 + 544725669490755670759486468 * q^97 - 11229478258893772537085952 * q^98 - 589223211629049495820465704 * q^99

Introduction

L-functions

Modular forms

Varieties

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