LMFDB - Embedded newform 10.26.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,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, 26, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
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:	$39.5996779952$
Analytic rank:	$1$
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} - 148387471 $ x^2 - 148387471
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-12181.4$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} -701909. q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} +2.87502e9 q^{6} -7.10199e8 q^{7} -6.87195e10 q^{8} -3.54612e11 q^{9} +1.00000e12 q^{10} +6.69047e12 q^{11} -1.17761e13 q^{12} -4.06505e12 q^{13} +2.90898e12 q^{14} +1.71365e14 q^{15} +2.81475e14 q^{16} +2.05623e15 q^{17} +1.45249e15 q^{18} +1.32410e16 q^{19} -4.09600e15 q^{20} +4.98495e14 q^{21} -2.74041e16 q^{22} -2.83334e16 q^{23} +4.82348e16 q^{24} +5.96046e16 q^{25} +1.66504e16 q^{26} +8.43625e17 q^{27} -1.19152e16 q^{28} +8.79820e17 q^{29} -7.01909e17 q^{30} -3.20276e17 q^{31} -1.15292e18 q^{32} -4.69610e18 q^{33} -8.42232e18 q^{34} +1.73388e17 q^{35} -5.94940e18 q^{36} -4.64680e19 q^{37} -5.42350e19 q^{38} +2.85329e18 q^{39} +1.67772e19 q^{40} -1.18387e20 q^{41} -2.04184e18 q^{42} -1.34535e20 q^{43} +1.12247e20 q^{44} +8.65752e19 q^{45} +1.16053e20 q^{46} -7.78716e20 q^{47} -1.97570e20 q^{48} -1.34056e21 q^{49} -2.44141e20 q^{50} -1.44329e21 q^{51} -6.82002e19 q^{52} -3.18129e21 q^{53} -3.45549e21 q^{54} -1.63341e21 q^{55} +4.88045e19 q^{56} -9.29396e21 q^{57} -3.60374e21 q^{58} -2.03629e21 q^{59} +2.87502e21 q^{60} +3.16043e22 q^{61} +1.31185e21 q^{62} +2.51845e20 q^{63} +4.72237e21 q^{64} +9.92443e20 q^{65} +1.92352e22 q^{66} +4.98952e22 q^{67} +3.44978e22 q^{68} +1.98875e22 q^{69} -7.10199e20 q^{70} +1.16862e23 q^{71} +2.43688e22 q^{72} -1.07622e23 q^{73} +1.90333e23 q^{74} -4.18370e22 q^{75} +2.22147e23 q^{76} -4.75156e21 q^{77} -1.16871e22 q^{78} +2.51396e23 q^{79} -6.87195e22 q^{80} -2.91689e23 q^{81} +4.84913e23 q^{82} -1.47962e24 q^{83} +8.36336e21 q^{84} -5.02010e23 q^{85} +5.51054e23 q^{86} -6.17554e23 q^{87} -4.59765e23 q^{88} -1.69758e24 q^{89} -3.54612e23 q^{90} +2.88699e21 q^{91} -4.75355e23 q^{92} +2.24804e23 q^{93} +3.18962e24 q^{94} -3.23266e24 q^{95} +8.09246e23 q^{96} -4.56953e24 q^{97} +5.49095e24 q^{98} -2.37252e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8192 q^{2} + 545212 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 2233188352 q^{6} + 38567856964 q^{7} - 137438953472 q^{8} + 353410472386 q^{9} + 2000000000000 q^{10} - 8379169876416 q^{11} + 9147139489792 q^{12}+ \cdots - 13\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 8192 * q^2 + 545212 * q^3 + 33554432 * q^4 - 488281250 * q^5 - 2233188352 * q^6 + 38567856964 * q^7 - 137438953472 * q^8 + 353410472386 * q^9 + 2000000000000 * q^10 - 8379169876416 * q^11 + 9147139489792 * q^12 - 149443737196988 * q^13 - 157973942124544 * q^14 - 133108398437500 * q^15 + 562949953421312 * q^16 + 3359254299255924 * q^17 - 1447569294893056 * q^18 + 3489461415860920 * q^19 - 8192000000000000 * q^20 + 49482990719617784 * q^21 + 34321079813799936 * q^22 + 72370201928022732 * q^23 - 37466683350188032 * q^24 + 119209289550781250 * q^25 + 612121547558862848 * q^26 + 669943559840926600 * q^27 + 647061266942132224 * q^28 - 537443787959856180 * q^29 + 545212000000000000 * q^30 - 3624027784441312136 * q^31 - 2305843009213693952 * q^32 - 23489760709118906496 * q^33 - 13759505609752264704 * q^34 - 9415980704101562500 * q^35 + 5929243831881957376 * q^36 + 19038572664443645764 * q^37 - 14292833959366328320 * q^38 - 178451546772299045128 * q^39 + 33554432000000000000 * q^40 - 212589580623880771956 * q^41 - 202682329987554443264 * q^42 - 13668418927657846868 * q^43 - 140579142917324537856 * q^44 - 86281853609863281250 * q^45 - 296428347097181110272 * q^46 - 1665681645557377854156 * q^47 + 153463535002370179072 * q^48 - 1138867157350741829766 * q^49 - 488281250000000000000 * q^50 + 181740691723390600344 * q^51 - 2507249858801102225408 * q^52 - 9975823013097020329548 * q^53 - 2744088821108435353600 * q^54 + 2045695770609375000000 * q^55 - 2650362949394973589504 * q^56 - 21455279998725990048880 * q^57 + 2201369755483570913280 * q^58 - 13147506706206800097960 * q^59 - 2233188352000000000000 * q^60 + 114411778307375747524 * q^61 + 14844017805071614509056 * q^62 + 28061596756249158893252 * q^63 + 9444732965739290427392 * q^64 + 36485287401608398437500 * q^65 + 96214059864551041007616 * q^66 + 95143040936399031080644 * q^67 + 56358934977545276227584 * q^68 + 145477011313277750812392 * q^69 + 38567856964000000000000 * q^70 + 83749259495165337742824 * q^71 - 24286182735388497412096 * q^72 + 196631633422897936973572 * q^73 - 77981993633561173049344 * q^74 + 32497167587280273437500 * q^75 + 58543447897564480798720 * q^76 - 596657555842340580669312 * q^77 + 730937535579336888844288 * q^78 + 105871595026057220692240 * q^79 - 137438953472000000000000 * q^80 - 1108190878966022772827798 * q^81 + 870766922235415641931776 * q^82 - 599053017838528107773748 * q^83 + 830186823629022999609344 * q^84 - 820130444154278320312500 * q^85 + 55985843927686540771328 * q^86 - 2385054109175491523609880 * q^87 + 575812169389361307058176 * q^88 - 1877353952181279423739020 * q^89 + 353410472386000000000000 * q^90 - 5707305339748996500897016 * q^91 + 1214170509710053827674112 * q^92 - 3895374854369117044063216 * q^93 + 6822632020203019690622976 * q^94 - 851919290981669921875000 * q^95 - 628586639369708253478912 * q^96 - 11597588153054877446451836 * q^97 + 4664799876508638534721536 * q^98 - 13042162823998039381361088 * 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 $

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	−701909.	−0.762545	−0.381272	−	0.924463i	$-0.624514\pi$
$3$	−701909.	−0.762545	−0.381272	+	0.924463i	$0.624514\pi$
$4$	1.67772e7	0.500000
$5$	−2.44141e8	−0.447214
$5$	−2.44141e8	−0.447214
$6$	2.87502e9	0.539200
$7$	−7.10199e8	−0.0193934	−0.00969672	−	0.999953i	$-0.503087\pi$
$7$	−7.10199e8	−0.0193934	−0.00969672	+	0.999953i	$0.503087\pi$
$8$	−6.87195e10	−0.353553
$9$	−3.54612e11	−0.418526
$10$	1.00000e12	0.316228
$11$	6.69047e12	0.642758	0.321379	−	0.946951i	$-0.395854\pi$
$11$	6.69047e12	0.642758	0.321379	+	0.946951i	$0.395854\pi$
$12$	−1.17761e13	−0.381272
$13$	−4.06505e12	−0.0483920	−0.0241960	−	0.999707i	$-0.507703\pi$
$13$	−4.06505e12	−0.0483920	−0.0241960	+	0.999707i	$0.507703\pi$
$14$	2.90898e12	0.0137132
$15$	1.71365e14	0.341020
$16$	2.81475e14	0.250000
$17$	2.05623e15	0.855974	0.427987	−	0.903785i	$-0.359223\pi$
$17$	2.05623e15	0.855974	0.427987	+	0.903785i	$0.359223\pi$
$18$	1.45249e15	0.295942
$19$	1.32410e16	1.37246	0.686230	−	0.727384i	$-0.259264\pi$
$19$	1.32410e16	1.37246	0.686230	+	0.727384i	$0.259264\pi$
$20$	−4.09600e15	−0.223607
$21$	4.98495e14	0.0147884
$22$	−2.74041e16	−0.454499
$23$	−2.83334e16	−0.269588	−0.134794	−	0.990874i	$-0.543037\pi$
$23$	−2.83334e16	−0.269588	−0.134794	+	0.990874i	$0.543037\pi$
$24$	4.82348e16	0.269600
$25$	5.96046e16	0.200000
$26$	1.66504e16	0.0342183
$27$	8.43625e17	1.08169
$28$	−1.19152e16	−0.00969672
$29$	8.79820e17	0.461763	0.230881	−	0.972982i	$-0.425839\pi$
$29$	8.79820e17	0.461763	0.230881	+	0.972982i	$0.425839\pi$
$30$	−7.01909e17	−0.241138
$31$	−3.20276e17	−0.0730302	−0.0365151	−	0.999333i	$-0.511626\pi$
$31$	−3.20276e17	−0.0730302	−0.0365151	+	0.999333i	$0.511626\pi$
$32$	−1.15292e18	−0.176777
$33$	−4.69610e18	−0.490132
$34$	−8.42232e18	−0.605265
$35$	1.73388e17	0.00867301
$36$	−5.94940e18	−0.209263
$37$	−4.64680e19	−1.16047	−0.580233	−	0.814450i	$-0.697039\pi$
$37$	−4.64680e19	−1.16047	−0.580233	+	0.814450i	$0.697039\pi$
$38$	−5.42350e19	−0.970476
$39$	2.85329e18	0.0369011
$40$	1.67772e19	0.158114
$41$	−1.18387e20	−0.819418	−0.409709	−	0.912216i	$-0.634370\pi$
$41$	−1.18387e20	−0.819418	−0.409709	+	0.912216i	$0.634370\pi$
$42$	−2.04184e18	−0.0104569
$43$	−1.34535e20	−0.513426	−0.256713	−	0.966488i	$-0.582640\pi$
$43$	−1.34535e20	−0.513426	−0.256713	+	0.966488i	$0.582640\pi$
$44$	1.12247e20	0.321379
$45$	8.65752e19	0.187170
$46$	1.16053e20	0.190627
$47$	−7.78716e20	−0.977587	−0.488794	−	0.872399i	$-0.662563\pi$
$47$	−7.78716e20	−0.977587	−0.488794	+	0.872399i	$0.662563\pi$
$48$	−1.97570e20	−0.190636
$49$	−1.34056e21	−0.999624
$50$	−2.44141e20	−0.141421
$51$	−1.44329e21	−0.652718
$52$	−6.82002e19	−0.0241960
$53$	−3.18129e21	−0.889517	−0.444759	−	0.895651i	$-0.646711\pi$
$53$	−3.18129e21	−0.889517	−0.444759	+	0.895651i	$0.646711\pi$
$54$	−3.45549e21	−0.764870
$55$	−1.63341e21	−0.287450
$56$	4.88045e19	0.00685661
$57$	−9.29396e21	−1.04656
$58$	−3.60374e21	−0.326516
$59$	−2.03629e21	−0.149001	−0.0745005	−	0.997221i	$-0.523736\pi$
$59$	−2.03629e21	−0.149001	−0.0745005	+	0.997221i	$0.523736\pi$
$60$	2.87502e21	0.170510
$61$	3.16043e22	1.52448	0.762242	−	0.647292i	$-0.224099\pi$
$61$	3.16043e22	1.52448	0.762242	+	0.647292i	$0.224099\pi$
$62$	1.31185e21	0.0516402
$63$	2.51845e20	0.00811665
$64$	4.72237e21	0.125000
$65$	9.92443e20	0.0216416
$66$	1.92352e22	0.346576
$67$	4.98952e22	0.744945	0.372472	−	0.928043i	$-0.378510\pi$
$67$	4.98952e22	0.744945	0.372472	+	0.928043i	$0.378510\pi$
$68$	3.44978e22	0.427987
$69$	1.98875e22	0.205573
$70$	−7.10199e20	−0.00613274
$71$	1.16862e23	0.845169	0.422585	−	0.906324i	$-0.361123\pi$
$71$	1.16862e23	0.845169	0.422585	+	0.906324i	$0.361123\pi$
$72$	2.43688e22	0.147971
$73$	−1.07622e23	−0.550001	−0.275001	−	0.961444i	$-0.588678\pi$
$73$	−1.07622e23	−0.550001	−0.275001	+	0.961444i	$0.588678\pi$
$74$	1.90333e23	0.820574
$75$	−4.18370e22	−0.152509
$76$	2.22147e23	0.686230
$77$	−4.75156e21	−0.0124653
$78$	−1.16871e22	−0.0260930
$79$	2.51396e23	0.478651	0.239326	−	0.970939i	$-0.423074\pi$
$79$	2.51396e23	0.478651	0.239326	+	0.970939i	$0.423074\pi$
$80$	−6.87195e22	−0.111803
$81$	−2.91689e23	−0.406310
$82$	4.84913e23	0.579416
$83$	−1.47962e24	−1.51941	−0.759703	−	0.650270i	$-0.774656\pi$
$83$	−1.47962e24	−1.51941	−0.759703	+	0.650270i	$0.774656\pi$
$84$	8.36336e21	0.00739418
$85$	−5.02010e23	−0.382803
$86$	5.51054e23	0.363047
$87$	−6.17554e23	−0.352115
$88$	−4.59765e23	−0.227249
$89$	−1.69758e24	−0.728544	−0.364272	−	0.931293i	$-0.618682\pi$
$89$	−1.69758e24	−0.728544	−0.364272	+	0.931293i	$0.618682\pi$
$90$	−3.54612e23	−0.132349
$91$	2.88699e21	0.000938487 0
$92$	−4.75355e23	−0.134794
$93$	2.24804e23	0.0556888
$94$	3.18962e24	0.691259
$95$	−3.23266e24	−0.613783
$96$	8.09246e23	0.134800
$97$	−4.56953e24	−0.668689	−0.334345	−	0.942451i	$-0.608515\pi$
$97$	−4.56953e24	−0.668689	−0.334345	+	0.942451i	$0.608515\pi$
$98$	5.49095e24	0.706841
$99$	−2.37252e24	−0.269011
$100$	1.00000e24	0.100000
$101$	−1.34474e25	−1.18747	−0.593735	−	0.804661i	$-0.702347\pi$
$101$	−1.34474e25	−1.18747	−0.593735	+	0.804661i	$0.702347\pi$
$102$	5.91170e24	0.461541
$103$	−1.45443e25	−1.00514	−0.502571	−	0.864536i	$-0.667612\pi$
$103$	−1.45443e25	−1.00514	−0.502571	+	0.864536i	$0.667612\pi$
$104$	2.79348e23	0.0171092
$105$	−1.21703e23	−0.00661355
$106$	1.30305e25	0.628984
$107$	−3.33812e25	−1.43286	−0.716432	−	0.697657i	$-0.754226\pi$
$107$	−3.33812e25	−1.43286	−0.716432	+	0.697657i	$0.754226\pi$
$108$	1.41537e25	0.540845
$109$	4.20504e25	1.43199	0.715993	−	0.698107i	$-0.245974\pi$
$109$	4.20504e25	1.43199	0.715993	+	0.698107i	$0.245974\pi$
$110$	6.69047e24	0.203258
$111$	3.26163e25	0.884908
$112$	−1.99903e23	−0.00484836
$113$	7.61141e25	1.65190	0.825952	−	0.563741i	$-0.190638\pi$
$113$	7.61141e25	1.65190	0.825952	+	0.563741i	$0.190638\pi$
$114$	3.80681e25	0.740031
$115$	6.91733e24	0.120563
$116$	1.47609e25	0.230881
$117$	1.44152e24	0.0202533
$118$	8.34063e24	0.105360
$119$	−1.46033e24	−0.0166003
$120$	−1.17761e25	−0.120569
$121$	−6.35847e25	−0.586862
$122$	−1.29451e26	−1.07797
$123$	8.30968e25	0.624843
$124$	−5.37333e24	−0.0365151
$125$	−1.45519e25	−0.0894427
$126$	−1.03156e24	−0.00573934
$127$	−2.50269e26	−1.26142	−0.630710	−	0.776018i	$-0.717236\pi$
$127$	−2.50269e26	−1.26142	−0.630710	+	0.776018i	$0.717236\pi$
$128$	−1.93428e25	−0.0883883
$129$	9.44310e25	0.391510
$130$	−4.06505e24	−0.0153029
$131$	−3.42885e26	−1.17289	−0.586445	−	0.809989i	$-0.699473\pi$
$131$	−3.42885e26	−1.17289	−0.586445	+	0.809989i	$0.699473\pi$
$132$	−7.87875e25	−0.245066
$133$	−9.40373e24	−0.0266167
$134$	−2.04371e26	−0.526755
$135$	−2.05963e26	−0.483746
$136$	−1.41303e26	−0.302632
$137$	1.44437e26	0.282274	0.141137	−	0.989990i	$-0.454924\pi$
$137$	1.44437e26	0.282274	0.141137	+	0.989990i	$0.454924\pi$
$138$	−8.14590e25	−0.145362
$139$	4.93300e26	0.804314	0.402157	−	0.915571i	$-0.368261\pi$
$139$	4.93300e26	0.804314	0.402157	+	0.915571i	$0.368261\pi$
$140$	2.90898e24	0.00433650
$141$	5.46588e26	0.745454
$142$	−4.78666e26	−0.597625
$143$	−2.71971e25	−0.0311044
$144$	−9.98144e25	−0.104631
$145$	−2.14800e26	−0.206507
$146$	4.40818e26	0.388910
$147$	9.40954e26	0.762258
$148$	−7.79604e26	−0.580233
$149$	1.50844e27	1.03205	0.516023	−	0.856575i	$-0.327412\pi$
$149$	1.50844e27	1.03205	0.516023	+	0.856575i	$0.327412\pi$
$150$	1.71365e26	0.107840
$151$	1.70083e26	0.0985027	0.0492513	−	0.998786i	$-0.484316\pi$
$151$	1.70083e26	0.0985027	0.0492513	+	0.998786i	$0.484316\pi$
$152$	−9.09913e26	−0.485238
$153$	−7.29164e26	−0.358247
$154$	1.94624e25	0.00881429
$155$	7.81923e25	0.0326601
$156$	4.78703e25	0.0184505
$157$	3.29198e27	1.17142	0.585708	−	0.810522i	$-0.300816\pi$
$157$	3.29198e27	1.17142	0.585708	+	0.810522i	$0.300816\pi$
$158$	−1.02972e27	−0.338458
$159$	2.23297e27	0.678296
$160$	2.81475e26	0.0790569
$161$	2.01223e25	0.00522823
$162$	1.19476e27	0.287305
$163$	5.07392e26	0.112979	0.0564896	−	0.998403i	$-0.482009\pi$
$163$	5.07392e26	0.112979	0.0564896	+	0.998403i	$0.482009\pi$
$164$	−1.98620e27	−0.409709
$165$	1.14651e27	0.219194
$166$	6.06052e27	1.07438
$167$	−8.44897e26	−0.138947	−0.0694733	−	0.997584i	$-0.522132\pi$
$167$	−8.44897e26	−0.138947	−0.0694733	+	0.997584i	$0.522132\pi$
$168$	−3.42563e25	−0.00522847
$169$	−7.03989e27	−0.997658
$170$	2.05623e27	0.270683
$171$	−4.69541e27	−0.574410
$172$	−2.25712e27	−0.256713
$173$	−7.54461e27	−0.798106	−0.399053	−	0.916928i	$-0.630661\pi$
$173$	−7.54461e27	−0.798106	−0.399053	+	0.916928i	$0.630661\pi$
$174$	2.52950e27	0.248983
$175$	−4.23312e25	−0.00387869
$176$	1.88320e27	0.160690
$177$	1.42929e27	0.113620
$178$	6.95330e27	0.515159
$179$	−5.46396e27	−0.377437	−0.188718	−	0.982031i	$-0.560433\pi$
$179$	−5.46396e27	−0.377437	−0.188718	+	0.982031i	$0.560433\pi$
$180$	1.45249e27	0.0935852
$181$	−2.74350e28	−1.64939	−0.824693	−	0.565581i	$-0.808652\pi$
$181$	−2.74350e28	−1.64939	−0.824693	+	0.565581i	$0.808652\pi$
$182$	−1.18251e25	−0.000663611 0
$183$	−2.21833e28	−1.16249
$184$	1.94705e27	0.0953137
$185$	1.13447e28	0.518976
$186$	−9.20799e26	−0.0393779
$187$	1.37571e28	0.550184
$188$	−1.30647e28	−0.488794
$189$	−5.99142e26	−0.0209777
$190$	1.32410e28	0.434010
$191$	−2.53537e28	−0.778258	−0.389129	−	0.921183i	$-0.627224\pi$
$191$	−2.53537e28	−0.778258	−0.389129	+	0.921183i	$0.627224\pi$
$192$	−3.31467e27	−0.0953181
$193$	4.66476e27	0.125708	0.0628540	−	0.998023i	$-0.479980\pi$
$193$	4.66476e27	0.125708	0.0628540	+	0.998023i	$0.479980\pi$
$194$	1.87168e28	0.472835
$195$	−6.96605e26	−0.0165027
$196$	−2.24909e28	−0.499812
$197$	−1.14775e28	−0.239343	−0.119672	−	0.992814i	$-0.538184\pi$
$197$	−1.14775e28	−0.239343	−0.119672	+	0.992814i	$0.538184\pi$
$198$	9.71784e27	0.190219
$199$	1.02205e29	1.87849	0.939243	−	0.343254i	$-0.111529\pi$
$199$	1.02205e29	1.87849	0.939243	+	0.343254i	$0.111529\pi$
$200$	−4.09600e27	−0.0707107
$201$	−3.50219e28	−0.568053
$202$	5.50807e28	0.839668
$203$	−6.24848e26	−0.00895517
$204$	−2.42143e28	−0.326359
$205$	2.89030e28	0.366455
$206$	5.95734e28	0.710742
$207$	1.00474e28	0.112829
$208$	−1.14421e27	−0.0120980
$209$	8.85883e28	0.882161
$210$	4.98495e26	0.00467649
$211$	1.45021e29	1.28204	0.641020	−	0.767524i	$-0.278512\pi$
$211$	1.45021e29	1.28204	0.641020	+	0.767524i	$0.278512\pi$
$212$	−5.33731e28	−0.444759
$213$	−8.20264e28	−0.644479
$214$	1.36729e29	1.01319
$215$	3.28453e28	0.229611
$216$	−5.79735e28	−0.382435
$217$	2.27460e26	0.00141631
$218$	−1.72238e29	−1.01257
$219$	7.55406e28	0.419400
$220$	−2.74041e28	−0.143725
$221$	−8.35868e27	−0.0414223
$222$	−1.33597e29	−0.625724
$223$	−3.26058e29	−1.44372	−0.721861	−	0.692038i	$-0.756713\pi$
$223$	−3.26058e29	−1.44372	−0.721861	+	0.692038i	$0.756713\pi$
$224$	8.18804e26	0.00342831
$225$	−2.11365e28	−0.0837052
$226$	−3.11763e29	−1.16807
$227$	−4.25210e29	−1.50758	−0.753791	−	0.657115i	$-0.771777\pi$
$227$	−4.25210e29	−1.50758	−0.753791	+	0.657115i	$0.771777\pi$
$228$	−1.55927e29	−0.523281
$229$	5.46098e29	1.73511	0.867555	−	0.497342i	$-0.165690\pi$
$229$	5.46098e29	1.73511	0.867555	+	0.497342i	$0.165690\pi$
$230$	−2.83334e28	−0.0852512
$231$	3.33517e27	0.00950534
$232$	−6.04608e28	−0.163258
$233$	−2.50604e29	−0.641268	−0.320634	−	0.947203i	$-0.603896\pi$
$233$	−2.50604e29	−0.641268	−0.320634	+	0.947203i	$0.603896\pi$
$234$	−5.90445e27	−0.0143213
$235$	1.90116e29	0.437190
$236$	−3.41632e28	−0.0745005
$237$	−1.76457e29	−0.364993
$238$	5.98153e27	0.0117382
$239$	6.64864e29	1.23811	0.619055	−	0.785348i	$-0.287516\pi$
$239$	6.64864e29	1.23811	0.619055	+	0.785348i	$0.287516\pi$
$240$	4.82348e28	0.0852551
$241$	2.77555e29	0.465731	0.232866	−	0.972509i	$-0.425190\pi$
$241$	2.77555e29	0.465731	0.232866	+	0.972509i	$0.425190\pi$
$242$	2.60443e29	0.414974
$243$	−5.10055e29	−0.771859
$244$	5.30232e29	0.762242
$245$	3.27286e29	0.447045
$246$	−3.40365e29	−0.441830
$247$	−5.38252e28	−0.0664161
$248$	2.20092e28	0.0258201
$249$	1.03856e30	1.15862
$250$	5.96046e28	0.0632456
$251$	−1.49015e30	−1.50421	−0.752105	−	0.659043i	$-0.770962\pi$
$251$	−1.49015e30	−1.50421	−0.752105	+	0.659043i	$0.770962\pi$
$252$	4.22526e27	0.00405833
$253$	−1.89563e29	−0.173280
$254$	1.02510e30	0.891959
$255$	3.52365e29	0.291904
$256$	7.92282e28	0.0625000
$257$	−7.29296e29	−0.547948	−0.273974	−	0.961737i	$-0.588338\pi$
$257$	−7.29296e29	−0.547948	−0.273974	+	0.961737i	$0.588338\pi$
$258$	−3.86790e29	−0.276840
$259$	3.30016e28	0.0225054
$260$	1.66504e28	0.0108208
$261$	−3.11995e29	−0.193260
$262$	1.40446e30	0.829358
$263$	−5.88360e29	−0.331281	−0.165640	−	0.986186i	$-0.552969\pi$
$263$	−5.88360e29	−0.331281	−0.165640	+	0.986186i	$0.552969\pi$
$264$	3.22713e29	0.173288
$265$	7.76681e29	0.397804
$266$	3.85177e28	0.0188209
$267$	1.19155e30	0.555548
$268$	8.37103e29	0.372472
$269$	1.22413e30	0.519904	0.259952	−	0.965622i	$-0.416293\pi$
$269$	1.22413e30	0.519904	0.259952	+	0.965622i	$0.416293\pi$
$270$	8.43625e29	0.342060
$271$	−1.53605e30	−0.594688	−0.297344	−	0.954770i	$-0.596101\pi$
$271$	−1.53605e30	−0.594688	−0.297344	+	0.954770i	$0.596101\pi$
$272$	5.78778e29	0.213993
$273$	−2.02641e27	−0.000715638 0
$274$	−5.91613e29	−0.199598
$275$	3.98783e29	0.128552
$276$	3.33656e29	0.102786
$277$	−4.32632e29	−0.127386	−0.0636929	−	0.997970i	$-0.520288\pi$
$277$	−4.32632e29	−0.127386	−0.0636929	+	0.997970i	$0.520288\pi$
$278$	−2.02056e30	−0.568736
$279$	1.13574e29	0.0305650
$280$	−1.19152e28	−0.00306637
$281$	−3.63667e30	−0.895107	−0.447554	−	0.894257i	$-0.647705\pi$
$281$	−3.63667e30	−0.895107	−0.447554	+	0.894257i	$0.647705\pi$
$282$	−2.23882e30	−0.527116
$283$	−8.38888e30	−1.88962	−0.944808	−	0.327624i	$-0.893752\pi$
$283$	−8.38888e30	−1.88962	−0.944808	+	0.327624i	$0.893752\pi$
$284$	1.96062e30	0.422585
$285$	2.26903e30	0.468037
$286$	1.11399e29	0.0219941
$287$	8.40783e28	0.0158913
$288$	4.08840e29	0.0739856
$289$	−1.54254e30	−0.267309
$290$	8.79820e29	0.146022
$291$	3.20739e30	0.509906
$292$	−1.80559e30	−0.275001
$293$	−8.70672e30	−1.27060	−0.635301	−	0.772265i	$-0.719124\pi$
$293$	−8.70672e30	−1.27060	−0.635301	+	0.772265i	$0.719124\pi$
$294$	−3.85415e30	−0.538998
$295$	4.97141e29	0.0666352
$296$	3.19326e30	0.410287
$297$	5.64425e30	0.695265
$298$	−6.17856e30	−0.729767
$299$	1.15177e29	0.0130459
$300$	−7.01909e29	−0.0762545
$301$	9.55463e28	0.00995710
$302$	−6.96658e29	−0.0696519
$303$	9.43888e30	0.905498
$304$	3.72700e30	0.343115
$305$	−7.71589e30	−0.681770
$306$	2.98666e30	0.253319
$307$	3.24336e30	0.264098	0.132049	−	0.991243i	$-0.457844\pi$
$307$	3.24336e30	0.264098	0.132049	+	0.991243i	$0.457844\pi$
$308$	−7.97180e28	−0.00623265
$309$	1.02088e31	0.766465
$310$	−3.20276e29	−0.0230942
$311$	−1.24495e30	−0.0862281	−0.0431140	−	0.999070i	$-0.513728\pi$
$311$	−1.24495e30	−0.0862281	−0.0431140	+	0.999070i	$0.513728\pi$
$312$	−1.96077e29	−0.0130465
$313$	2.33420e31	1.49222	0.746112	−	0.665820i	$-0.231918\pi$
$313$	2.33420e31	1.49222	0.746112	+	0.665820i	$0.231918\pi$
$314$	−1.34839e31	−0.828316
$315$	−6.14857e28	−0.00362988
$316$	4.21772e30	0.239326
$317$	2.11447e31	1.15335	0.576674	−	0.816974i	$-0.304350\pi$
$317$	2.11447e31	1.15335	0.576674	+	0.816974i	$0.304350\pi$
$318$	−9.14626e30	−0.479628
$319$	5.88641e30	0.296802
$320$	−1.15292e30	−0.0559017
$321$	2.34306e31	1.09262
$322$	−8.24211e28	−0.00369692
$323$	2.72265e31	1.17479
$324$	−4.89374e30	−0.203155
$325$	−2.42296e29	−0.00967840
$326$	−2.07828e30	−0.0798883
$327$	−2.95156e31	−1.09195
$328$	8.13549e30	0.289708
$329$	5.53043e29	0.0189588
$330$	−4.69610e30	−0.154993
$331$	−4.35367e31	−1.38359	−0.691793	−	0.722096i	$-0.743179\pi$
$331$	−4.35367e31	−1.38359	−0.691793	+	0.722096i	$0.743179\pi$
$332$	−2.48239e31	−0.759703
$333$	1.64781e31	0.485685
$334$	3.46070e30	0.0982501
$335$	−1.21815e31	−0.333149
$336$	1.40314e29	0.00369709
$337$	−5.97252e30	−0.151630	−0.0758148	−	0.997122i	$-0.524156\pi$
$337$	−5.97252e30	−0.151630	−0.0758148	+	0.997122i	$0.524156\pi$
$338$	2.88354e31	0.705451
$339$	−5.34252e31	−1.25965
$340$	−8.42232e30	−0.191402
$341$	−2.14279e30	−0.0469408
$342$	1.92324e31	0.406169
$343$	1.90449e30	0.0387796
$344$	9.24514e30	0.181524
$345$	−4.85534e30	−0.0919349
$346$	3.09027e31	0.564346
$347$	−9.71425e31	−1.71116	−0.855580	−	0.517670i	$-0.826799\pi$
$347$	−9.71425e31	−1.71116	−0.855580	+	0.517670i	$0.826799\pi$
$348$	−1.03608e31	−0.176057
$349$	−7.20784e31	−1.18165	−0.590823	−	0.806801i	$-0.701197\pi$
$349$	−7.20784e31	−1.18165	−0.590823	+	0.806801i	$0.701197\pi$
$350$	1.73388e29	0.00274265
$351$	−3.42938e30	−0.0523451
$352$	−7.71358e30	−0.113625
$353$	6.98207e31	0.992660	0.496330	−	0.868134i	$-0.334681\pi$
$353$	6.98207e31	0.992660	0.496330	+	0.868134i	$0.334681\pi$
$354$	−5.85437e30	−0.0803414
$355$	−2.85307e31	−0.377971
$356$	−2.84807e31	−0.364272
$357$	1.02502e30	0.0126584
$358$	2.23804e31	0.266888
$359$	−1.33870e32	−1.54171	−0.770857	−	0.637009i	$-0.780171\pi$
$359$	−1.33870e32	−1.54171	−0.770857	+	0.637009i	$0.780171\pi$
$360$	−5.94940e30	−0.0661747
$361$	8.22469e31	0.883649
$362$	1.12374e32	1.16629
$363$	4.46307e31	0.447508
$364$	4.84357e28	0.000469244 0
$365$	2.62748e31	0.245968
$366$	9.08629e31	0.822003
$367$	6.63971e31	0.580528	0.290264	−	0.956947i	$-0.406257\pi$
$367$	6.63971e31	0.580528	0.290264	+	0.956947i	$0.406257\pi$
$368$	−7.97514e30	−0.0673970
$369$	4.19814e31	0.342947
$370$	−4.64680e31	−0.366972
$371$	2.25935e30	0.0172508
$372$	3.77159e30	0.0278444
$373$	2.18553e32	1.56026	0.780129	−	0.625619i	$-0.215154\pi$
$373$	2.18553e32	1.56026	0.780129	+	0.625619i	$0.215154\pi$
$374$	−5.63493e31	−0.389039
$375$	1.02141e31	0.0682041
$376$	5.35129e31	0.345629
$377$	−3.57651e30	−0.0223456
$378$	2.45409e30	0.0148334
$379$	−1.48811e32	−0.870253	−0.435126	−	0.900369i	$-0.643296\pi$
$379$	−1.48811e32	−0.870253	−0.435126	+	0.900369i	$0.643296\pi$
$380$	−5.42350e31	−0.306892
$381$	1.75666e32	0.961889
$382$	1.03849e32	0.550311
$383$	−2.09320e32	−1.07356	−0.536779	−	0.843723i	$-0.680359\pi$
$383$	−2.09320e32	−1.07356	−0.536779	+	0.843723i	$0.680359\pi$
$384$	1.35769e31	0.0674001
$385$	1.16005e30	0.00557465
$386$	−1.91068e31	−0.0888889
$387$	4.77076e31	0.214882
$388$	−7.66639e31	−0.334345
$389$	−2.78926e32	−1.17793	−0.588965	−	0.808158i	$-0.700465\pi$
$389$	−2.78926e32	−1.17793	−0.588965	+	0.808158i	$0.700465\pi$
$390$	2.85329e30	0.0116691
$391$	−5.82600e31	−0.230760
$392$	9.21229e31	0.353420
$393$	2.40674e32	0.894381
$394$	4.70120e31	0.169241
$395$	−6.13759e31	−0.214059
$396$	−3.98043e31	−0.134505
$397$	4.22963e32	1.38491	0.692455	−	0.721461i	$-0.256529\pi$
$397$	4.22963e32	1.38491	0.692455	+	0.721461i	$0.256529\pi$
$398$	−4.18631e32	−1.32829
$399$	6.60056e30	0.0202964
$400$	1.67772e31	0.0500000
$401$	−2.59389e32	−0.749284	−0.374642	−	0.927169i	$-0.622234\pi$
$401$	−2.59389e32	−0.749284	−0.374642	+	0.927169i	$0.622234\pi$
$402$	1.43450e32	0.401674
$403$	1.30194e30	0.00353408
$404$	−2.25611e32	−0.593735
$405$	7.12132e31	0.181708
$406$	2.55938e30	0.00633226
$407$	−3.10893e32	−0.745900
$408$	9.91820e31	0.230771
$409$	7.31347e32	1.65037	0.825186	−	0.564861i	$-0.191070\pi$
$409$	7.31347e32	1.65037	0.825186	+	0.564861i	$0.191070\pi$
$410$	−1.18387e32	−0.259123
$411$	−1.01381e32	−0.215246
$412$	−2.44013e32	−0.502571
$413$	1.44617e30	0.00288964
$414$	−4.11540e31	−0.0797825
$415$	3.61235e32	0.679499
$416$	4.68668e30	0.00855458
$417$	−3.46252e32	−0.613325
$418$	−3.62858e32	−0.623782
$419$	−6.24972e32	−1.04276	−0.521381	−	0.853324i	$-0.674583\pi$
$419$	−6.24972e32	−1.04276	−0.521381	+	0.853324i	$0.674583\pi$
$420$	−2.04184e30	−0.00330678
$421$	−2.51168e32	−0.394855	−0.197427	−	0.980318i	$-0.563259\pi$
$421$	−2.51168e32	−0.394855	−0.197427	+	0.980318i	$0.563259\pi$
$422$	−5.94008e32	−0.906539
$423$	2.76142e32	0.409146
$424$	2.18616e32	0.314492
$425$	1.22561e32	0.171195
$426$	3.35980e32	0.455716
$427$	−2.24453e31	−0.0295650
$428$	−5.60044e32	−0.716432
$429$	1.90899e31	0.0237185
$430$	−1.34535e32	−0.162360
$431$	−1.55381e33	−1.82151	−0.910754	−	0.412948i	$-0.864499\pi$
$431$	−1.55381e33	−1.82151	−0.910754	+	0.412948i	$0.864499\pi$
$432$	2.37459e32	0.270422
$433$	1.08349e33	1.19874	0.599370	−	0.800472i	$-0.295418\pi$
$433$	1.08349e33	1.19874	0.599370	+	0.800472i	$0.295418\pi$
$434$	−9.31674e29	−0.00100148
$435$	1.50770e32	0.157471
$436$	7.05489e32	0.715993
$437$	−3.75161e32	−0.369999
$438$	−3.09414e32	−0.296561
$439$	1.66407e33	1.55012	0.775058	−	0.631890i	$-0.217721\pi$
$439$	1.66407e33	1.55012	0.775058	+	0.631890i	$0.217721\pi$
$440$	1.12247e32	0.101629
$441$	4.75380e32	0.418368
$442$	3.42371e31	0.0292900
$443$	3.77416e32	0.313887	0.156944	−	0.987608i	$-0.449836\pi$
$443$	3.77416e32	0.313887	0.156944	+	0.987608i	$0.449836\pi$
$444$	5.47211e32	0.442454
$445$	4.14449e32	0.325815
$446$	1.33553e33	1.02087
$447$	−1.05879e33	−0.786981
$448$	−3.35382e30	−0.00242418
$449$	2.15921e33	1.51781	0.758903	−	0.651204i	$-0.225736\pi$
$449$	2.15921e33	1.51781	0.758903	+	0.651204i	$0.225736\pi$
$450$	8.65752e31	0.0591885
$451$	−7.92063e32	−0.526688
$452$	1.27698e33	0.825952
$453$	−1.19383e32	−0.0751127
$454$	1.74166e33	1.06602
$455$	−7.04832e29	−0.000419704 0
$456$	6.38676e32	0.370016
$457$	8.65127e30	0.00487671	0.00243836	−	0.999997i	$-0.499224\pi$
$457$	8.65127e30	0.00487671	0.00243836	+	0.999997i	$0.499224\pi$
$458$	−2.23682e33	−1.22691
$459$	1.73469e33	0.925897
$460$	1.16053e32	0.0602817
$461$	−3.15151e33	−1.59315	−0.796575	−	0.604539i	$-0.793357\pi$
$461$	−3.15151e33	−1.59315	−0.796575	+	0.604539i	$0.793357\pi$
$462$	−1.36608e31	−0.00672129
$463$	−2.93719e33	−1.40660	−0.703298	−	0.710895i	$-0.748290\pi$
$463$	−2.93719e33	−1.40660	−0.703298	+	0.710895i	$0.748290\pi$
$464$	2.47647e32	0.115441
$465$	−5.48839e31	−0.0249048
$466$	1.02648e33	0.453445
$467$	−2.28078e33	−0.980895	−0.490448	−	0.871471i	$-0.663167\pi$
$467$	−2.28078e33	−0.980895	−0.490448	+	0.871471i	$0.663167\pi$
$468$	2.41846e31	0.0101267
$469$	−3.54356e31	−0.0144470
$470$	−7.78716e32	−0.309140
$471$	−2.31067e33	−0.893257
$472$	1.39933e32	0.0526798
$473$	−9.00099e32	−0.330009
$474$	7.22768e32	0.258089
$475$	7.89224e32	0.274492
$476$	−2.45003e31	−0.00830013
$477$	1.12812e33	0.372286
$478$	−2.72328e33	−0.875476
$479$	−7.97173e32	−0.249666	−0.124833	−	0.992178i	$-0.539839\pi$
$479$	−7.97173e32	−0.249666	−0.124833	+	0.992178i	$0.539839\pi$
$480$	−1.97570e32	−0.0602844
$481$	1.88895e32	0.0561573
$482$	−1.13686e33	−0.329322
$483$	−1.41241e31	−0.00398676
$484$	−1.06677e33	−0.293431
$485$	1.11561e33	0.299047
$486$	2.08918e33	0.545787
$487$	−7.32515e32	−0.186511	−0.0932555	−	0.995642i	$-0.529727\pi$
$487$	−7.32515e32	−0.186511	−0.0932555	+	0.995642i	$0.529727\pi$
$488$	−2.17183e33	−0.538987
$489$	−3.56143e32	−0.0861516
$490$	−1.34056e33	−0.316109
$491$	−2.35651e33	−0.541690	−0.270845	−	0.962623i	$-0.587303\pi$
$491$	−2.35651e33	−0.541690	−0.270845	+	0.962623i	$0.587303\pi$
$492$	1.39413e33	0.312421
$493$	1.80911e33	0.395257
$494$	2.20468e32	0.0469633
$495$	5.79229e32	0.120305
$496$	−9.01496e31	−0.0182576
$497$	−8.29952e31	−0.0163907
$498$	−4.25394e33	−0.819265
$499$	1.11697e33	0.209789	0.104895	−	0.994483i	$-0.466549\pi$
$499$	1.11697e33	0.209789	0.104895	+	0.994483i	$0.466549\pi$
$500$	−2.44141e32	−0.0447214
$501$	5.93041e32	0.105953
$502$	6.10366e33	1.06364
$503$	3.79303e33	0.644743	0.322372	−	0.946613i	$-0.395520\pi$
$503$	3.79303e33	0.644743	0.322372	+	0.946613i	$0.395520\pi$
$504$	−1.73067e31	−0.00286967
$505$	3.28307e33	0.531052
$506$	7.76452e32	0.122527
$507$	4.94136e33	0.760759
$508$	−4.19881e33	−0.630710
$509$	−7.62370e33	−1.11736	−0.558681	−	0.829383i	$-0.688692\pi$
$509$	−7.62370e33	−1.11736	−0.558681	+	0.829383i	$0.688692\pi$
$510$	−1.44329e33	−0.206408
$511$	7.64328e31	0.0106664
$512$	−3.24519e32	−0.0441942
$513$	1.11704e34	1.48458
$514$	2.98720e33	0.387458
$515$	3.55085e33	0.449513
$516$	1.58429e33	0.195755
$517$	−5.20997e33	−0.628353
$518$	−1.35174e32	−0.0159137
$519$	5.29563e33	0.608592
$520$	−6.82002e31	−0.00765145
$521$	5.33662e33	0.584514	0.292257	−	0.956340i	$-0.405594\pi$
$521$	5.33662e33	0.584514	0.292257	+	0.956340i	$0.405594\pi$
$522$	1.27793e33	0.136655
$523$	1.14894e34	1.19957	0.599786	−	0.800160i	$-0.295252\pi$
$523$	1.14894e34	1.19957	0.599786	+	0.800160i	$0.295252\pi$
$524$	−5.75265e33	−0.586445
$525$	2.97126e31	0.00295767
$526$	2.40992e33	0.234251
$527$	−6.58561e32	−0.0625120
$528$	−1.32183e33	−0.122533
$529$	−1.02430e34	−0.927322
$530$	−3.18129e33	−0.281290
$531$	7.22092e32	0.0623607
$532$	−1.57768e32	−0.0133084
$533$	4.81248e32	0.0396533
$534$	−4.88059e33	−0.392831
$535$	8.14971e33	0.640796
$536$	−3.42877e33	−0.263378
$537$	3.83520e33	0.287812
$538$	−5.01403e33	−0.367628
$539$	−8.96900e33	−0.642517
$540$	−3.45549e33	−0.241873
$541$	−2.08461e34	−1.42580	−0.712901	−	0.701265i	$-0.752619\pi$
$541$	−2.08461e34	−1.42580	−0.712901	+	0.701265i	$0.752619\pi$
$542$	6.29167e33	0.420508
$543$	1.92569e34	1.25773
$544$	−2.37067e33	−0.151316
$545$	−1.02662e34	−0.640404
$546$	8.30016e30	0.000506033 0
$547$	−5.82664e33	−0.347197	−0.173599	−	0.984816i	$-0.555540\pi$
$547$	−5.82664e33	−0.347197	−0.173599	+	0.984816i	$0.555540\pi$
$548$	2.42324e33	0.141137
$549$	−1.12073e34	−0.638036
$550$	−1.63341e33	−0.0908998
$551$	1.16497e34	0.633751
$552$	−1.36666e33	−0.0726809
$553$	−1.78541e32	−0.00928270
$554$	1.77206e33	0.0900754
$555$	−7.96297e33	−0.395743
$556$	8.27619e33	0.402157
$557$	−2.41168e34	−1.14586	−0.572928	−	0.819606i	$-0.694193\pi$
$557$	−2.41168e34	−1.14586	−0.572928	+	0.819606i	$0.694193\pi$
$558$	−4.65198e32	−0.0216127
$559$	5.46889e32	0.0248457
$560$	4.88045e31	0.00216825
$561$	−9.65626e33	−0.419540
$562$	1.48958e34	0.632937
$563$	1.42755e34	0.593248	0.296624	−	0.954994i	$-0.404139\pi$
$563$	1.42755e34	0.593248	0.296624	+	0.954994i	$0.404139\pi$
$564$	9.17022e33	0.372727
$565$	−1.85826e34	−0.738754
$566$	3.43609e34	1.33616
$567$	2.07158e32	0.00787975
$568$	−8.03069e33	−0.298812
$569$	−4.47698e34	−1.62960	−0.814802	−	0.579739i	$-0.803154\pi$
$569$	−4.47698e34	−1.62960	−0.814802	+	0.579739i	$0.803154\pi$
$570$	−9.29396e33	−0.330952
$571$	−1.37949e33	−0.0480581	−0.0240291	−	0.999711i	$-0.507649\pi$
$571$	−1.37949e33	−0.0480581	−0.0240291	+	0.999711i	$0.507649\pi$
$572$	−4.56291e32	−0.0155522
$573$	1.77960e34	0.593456
$574$	−3.44385e32	−0.0112369
$575$	−1.68880e33	−0.0539176
$576$	−1.67461e33	−0.0523157
$577$	−2.32241e33	−0.0709973	−0.0354986	−	0.999370i	$-0.511302\pi$
$577$	−2.32241e33	−0.0709973	−0.0354986	+	0.999370i	$0.511302\pi$
$578$	6.31825e33	0.189016
$579$	−3.27424e33	−0.0958579
$580$	−3.60374e33	−0.103253
$581$	1.05082e33	0.0294665
$582$	−1.31375e34	−0.360558
$583$	−2.12843e34	−0.571745
$584$	7.39570e33	0.194455
$585$	−3.51932e32	−0.00905755
$586$	3.56627e34	0.898451
$587$	4.35047e34	1.07290	0.536451	−	0.843931i	$-0.319765\pi$
$587$	4.35047e34	1.07290	0.536451	+	0.843931i	$0.319765\pi$
$588$	1.57866e34	0.381129
$589$	−4.24076e33	−0.100231
$590$	−2.03629e33	−0.0471182
$591$	8.05619e33	0.182510
$592$	−1.30796e34	−0.290117
$593$	5.31713e34	1.15476	0.577382	−	0.816474i	$-0.304074\pi$
$593$	5.31713e34	1.15476	0.577382	+	0.816474i	$0.304074\pi$
$594$	−2.31188e34	−0.491626
$595$	3.56527e32	0.00742387
$596$	2.53074e34	0.516023
$597$	−7.17385e34	−1.43243
$598$	−4.71763e32	−0.00922484
$599$	7.13123e34	1.36562	0.682809	−	0.730597i	$-0.260758\pi$
$599$	7.13123e34	1.36562	0.682809	+	0.730597i	$0.260758\pi$
$600$	2.87502e33	0.0539200
$601$	3.07608e34	0.565023	0.282512	−	0.959264i	$-0.408832\pi$
$601$	3.07608e34	0.565023	0.282512	+	0.959264i	$0.408832\pi$
$602$	−3.91358e32	−0.00704073
$603$	−1.76935e34	−0.311779
$604$	2.85351e33	0.0492513
$605$	1.55236e34	0.262452
$606$	−3.86617e34	−0.640284
$607$	2.76184e34	0.448064	0.224032	−	0.974582i	$-0.428078\pi$
$607$	2.76184e34	0.448064	0.224032	+	0.974582i	$0.428078\pi$
$608$	−1.52658e34	−0.242619
$609$	4.38586e32	0.00682871
$610$	3.16043e34	0.482084
$611$	3.16552e33	0.0473074
$612$	−1.22333e34	−0.179124
$613$	4.94974e34	0.710112	0.355056	−	0.934845i	$-0.384462\pi$
$613$	4.94974e34	0.710112	0.355056	+	0.934845i	$0.384462\pi$
$614$	−1.32848e34	−0.186746
$615$	−2.02873e34	−0.279438
$616$	3.26525e32	0.00440715
$617$	1.12825e35	1.49225	0.746126	−	0.665805i	$-0.231912\pi$
$617$	1.12825e35	1.49225	0.746126	+	0.665805i	$0.231912\pi$
$618$	−4.18151e34	−0.541973
$619$	5.35184e34	0.679782	0.339891	−	0.940465i	$-0.389610\pi$
$619$	5.35184e34	0.679782	0.339891	+	0.940465i	$0.389610\pi$
$620$	1.31185e33	0.0163301
$621$	−2.39027e34	−0.291610
$622$	5.09934e33	0.0609725
$623$	1.20562e33	0.0141290
$624$	8.03131e32	0.00922527
$625$	3.55271e33	0.0400000
$626$	−9.56089e34	−1.05516
$627$	−6.21809e34	−0.672687
$628$	5.52302e34	0.585708
$629$	−9.55490e34	−0.993329
$630$	2.51845e32	0.00256671
$631$	−9.73214e34	−0.972392	−0.486196	−	0.873850i	$-0.661616\pi$
$631$	−9.73214e34	−0.972392	−0.486196	+	0.873850i	$0.661616\pi$
$632$	−1.72758e34	−0.169229
$633$	−1.01792e35	−0.977612
$634$	−8.66087e34	−0.815541
$635$	6.11007e34	0.564124
$636$	3.74631e34	0.339148
$637$	5.44946e33	0.0483738
$638$	−2.41107e34	−0.209871
$639$	−4.14406e34	−0.353725
$640$	4.72237e33	0.0395285
$641$	−2.79912e34	−0.229772	−0.114886	−	0.993379i	$-0.536650\pi$
$641$	−2.79912e34	−0.229772	−0.114886	+	0.993379i	$0.536650\pi$
$642$	−9.59717e34	−0.772601
$643$	−1.80728e35	−1.42688	−0.713442	−	0.700714i	$-0.752865\pi$
$643$	−1.80728e35	−1.42688	−0.713442	+	0.700714i	$0.752865\pi$
$644$	3.37597e32	0.00261412
$645$	−2.30545e34	−0.175089
$646$	−1.11520e35	−0.830702
$647$	7.31933e34	0.534771	0.267385	−	0.963590i	$-0.413840\pi$
$647$	7.31933e34	0.534771	0.267385	+	0.963590i	$0.413840\pi$
$648$	2.00447e34	0.143652
$649$	−1.36237e34	−0.0957716
$650$	9.92443e32	0.00684367
$651$	−1.59656e32	−0.00108000
$652$	8.51262e33	0.0564896
$653$	−7.32271e32	−0.00476713	−0.00238357	−	0.999997i	$-0.500759\pi$
$653$	−7.32271e32	−0.00476713	−0.00238357	+	0.999997i	$0.500759\pi$
$654$	1.20896e35	0.772128
$655$	8.37121e34	0.524532
$656$	−3.33229e34	−0.204854
$657$	3.81639e34	0.230190
$658$	−2.26526e33	−0.0134059
$659$	3.37009e35	1.95692	0.978460	−	0.206434i	$-0.0661860\pi$
$659$	3.37009e35	1.95692	0.978460	+	0.206434i	$0.0661860\pi$
$660$	1.92352e34	0.109597
$661$	1.22749e34	0.0686275	0.0343138	−	0.999411i	$-0.489075\pi$
$661$	1.22749e34	0.0686275	0.0343138	+	0.999411i	$0.489075\pi$
$662$	1.78326e35	0.978343
$663$	5.86703e33	0.0315863
$664$	1.01679e35	0.537191
$665$	2.29583e33	0.0119034
$666$	−6.74944e34	−0.343431
$667$	−2.49283e34	−0.124486
$668$	−1.41750e34	−0.0694733
$669$	2.28863e35	1.10090
$670$	4.98952e34	0.235572
$671$	2.11447e35	0.979875
$672$	−5.74726e32	−0.00261424
$673$	−4.17789e35	−1.86538	−0.932692	−	0.360673i	$-0.882547\pi$
$673$	−4.17789e35	−1.86538	−0.932692	+	0.360673i	$0.882547\pi$
$674$	2.44634e34	0.107218
$675$	5.02840e34	0.216338
$676$	−1.18110e35	−0.498829
$677$	2.87478e35	1.19192	0.595959	−	0.803014i	$-0.296772\pi$
$677$	2.87478e35	1.19192	0.595959	+	0.803014i	$0.296772\pi$
$678$	2.18830e35	0.890707
$679$	3.24527e33	0.0129682
$680$	3.44978e34	0.135341
$681$	2.98459e35	1.14960
$682$	8.77688e33	0.0331922
$683$	−3.52227e35	−1.30787	−0.653935	−	0.756551i	$-0.726883\pi$
$683$	−3.52227e35	−1.30787	−0.653935	+	0.756551i	$0.726883\pi$
$684$	−7.87759e34	−0.287205
$685$	−3.52629e34	−0.126237
$686$	−7.80081e33	−0.0274213
$687$	−3.83311e35	−1.32310
$688$	−3.78681e34	−0.128357
$689$	1.29321e34	0.0430455
$690$	1.98875e34	0.0650078
$691$	−1.41869e35	−0.455421	−0.227711	−	0.973729i	$-0.573124\pi$
$691$	−1.41869e35	−0.455421	−0.227711	+	0.973729i	$0.573124\pi$
$692$	−1.26578e35	−0.399053
$693$	1.68496e33	0.00521705
$694$	3.97896e35	1.20997
$695$	−1.20434e35	−0.359700
$696$	4.24380e34	0.124491
$697$	−2.43431e35	−0.701400
$698$	2.95233e35	0.835550
$699$	1.75901e35	0.488995
$700$	−7.10199e32	−0.00193934
$701$	4.11949e35	1.10502	0.552508	−	0.833508i	$-0.313671\pi$
$701$	4.11949e35	1.10502	0.552508	+	0.833508i	$0.313671\pi$
$702$	1.40467e34	0.0370136
$703$	−6.15282e35	−1.59270
$704$	3.15948e34	0.0803448
$705$	−1.33444e35	−0.333377
$706$	−2.85986e35	−0.701917
$707$	9.55036e33	0.0230291
$708$	2.39795e34	0.0568099
$709$	−3.69515e35	−0.860110	−0.430055	−	0.902803i	$-0.641506\pi$
$709$	−3.69515e35	−0.860110	−0.430055	+	0.902803i	$0.641506\pi$
$710$	1.16862e35	0.267266
$711$	−8.91480e34	−0.200328
$712$	1.16657e35	0.257579
$713$	9.07449e33	0.0196881
$714$	−4.19849e33	−0.00895087
$715$	6.63991e33	0.0139103
$716$	−9.16700e34	−0.188718
$717$	−4.66674e35	−0.944114
$718$	5.48333e35	1.09016
$719$	2.40654e35	0.470200	0.235100	−	0.971971i	$-0.424458\pi$
$719$	2.40654e35	0.470200	0.235100	+	0.971971i	$0.424458\pi$
$720$	2.43688e34	0.0467926
$721$	1.03293e34	0.0194931
$722$	−3.36883e35	−0.624834
$723$	−1.94818e35	−0.355141
$724$	−4.60282e35	−0.824693
$725$	5.24414e34	0.0923526
$726$	−1.82807e35	−0.316436
$727$	−2.82511e34	−0.0480680	−0.0240340	−	0.999711i	$-0.507651\pi$
$727$	−2.82511e34	−0.0480680	−0.0240340	+	0.999711i	$0.507651\pi$
$728$	−1.98393e32	−0.000331805 0
$729$	6.05157e35	0.994888
$730$	−1.07622e35	−0.173926
$731$	−2.76634e35	−0.439479
$732$	−3.72175e35	−0.581244
$733$	1.13647e36	1.74486	0.872428	−	0.488743i	$-0.162544\pi$
$733$	1.13647e36	1.74486	0.872428	+	0.488743i	$0.162544\pi$
$734$	−2.71963e35	−0.410495
$735$	−2.29725e35	−0.340892
$736$	3.26662e34	0.0476568
$737$	3.33822e35	0.478819
$738$	−1.71956e35	−0.242500
$739$	−7.59548e35	−1.05317	−0.526587	−	0.850121i	$-0.676528\pi$
$739$	−7.59548e35	−1.05317	−0.526587	+	0.850121i	$0.676528\pi$
$740$	1.90333e35	0.259488
$741$	3.77804e34	0.0506453
$742$	−9.25428e33	−0.0121982
$743$	−2.06273e35	−0.267352	−0.133676	−	0.991025i	$-0.542678\pi$
$743$	−2.06273e35	−0.267352	−0.133676	+	0.991025i	$0.542678\pi$
$744$	−1.54484e34	−0.0196890
$745$	−3.68271e35	−0.461545
$746$	−8.95193e35	−1.10327
$747$	5.24691e35	0.635911
$748$	2.30807e35	0.275092
$749$	2.37073e34	0.0277881
$750$	−4.18370e34	−0.0482276
$751$	−7.61805e34	−0.0863664	−0.0431832	−	0.999067i	$-0.513750\pi$
$751$	−7.61805e34	−0.0863664	−0.0431832	+	0.999067i	$0.513750\pi$
$752$	−2.19189e35	−0.244397
$753$	1.04595e36	1.14703
$754$	1.46494e34	0.0158008
$755$	−4.15241e34	−0.0440517
$756$	−1.00519e34	−0.0104888
$757$	1.93605e36	1.98709	0.993546	−	0.113428i	$-0.0361831\pi$
$757$	1.93605e36	1.98709	0.993546	+	0.113428i	$0.0361831\pi$
$758$	6.09530e35	0.615362
$759$	1.33056e35	0.132134
$760$	2.22147e35	0.217005
$761$	1.19339e36	1.14677	0.573383	−	0.819288i	$-0.305631\pi$
$761$	1.19339e36	1.14677	0.573383	+	0.819288i	$0.305631\pi$
$762$	−7.19527e35	−0.680158
$763$	−2.98642e34	−0.0277711
$764$	−4.25364e35	−0.389129
$765$	1.78019e35	0.160213
$766$	8.57374e35	0.759121
$767$	8.27761e33	0.00721046
$768$	−5.56110e34	−0.0476590
$769$	−9.68810e35	−0.816882	−0.408441	−	0.912785i	$-0.633927\pi$
$769$	−9.68810e35	−0.816882	−0.408441	+	0.912785i	$0.633927\pi$
$770$	−4.75156e33	−0.00394187
$771$	5.11899e35	0.417835
$772$	7.82616e34	0.0628540
$773$	−8.25175e35	−0.652082	−0.326041	−	0.945356i	$-0.605715\pi$
$773$	−8.25175e35	−0.652082	−0.326041	+	0.945356i	$0.605715\pi$
$774$	−1.95410e35	−0.151945
$775$	−1.90899e34	−0.0146060
$776$	3.14015e35	0.236417
$777$	−2.31641e34	−0.0171614
$778$	1.14248e36	0.832923
$779$	−1.56756e36	−1.12462
$780$	−1.16871e34	−0.00825133
$781$	7.81861e35	0.543240
$782$	2.38633e35	0.163172
$783$	7.42239e35	0.499484
$784$	−3.77335e35	−0.249906
$785$	−8.03706e35	−0.523873
$786$	−9.85801e35	−0.632423
$787$	8.02076e35	0.506444	0.253222	−	0.967408i	$-0.418510\pi$
$787$	8.02076e35	0.506444	0.253222	+	0.967408i	$0.418510\pi$
$788$	−1.92561e35	−0.119672
$789$	4.12975e35	0.252616
$790$	2.51396e35	0.151363
$791$	−5.40562e34	−0.0320361
$792$	1.63038e35	0.0951097
$793$	−1.28473e35	−0.0737729
$794$	−1.73246e36	−0.979279
$795$	−5.45160e35	−0.303343
$796$	1.71471e36	0.939243
$797$	8.65699e35	0.466807	0.233404	−	0.972380i	$-0.425014\pi$
$797$	8.65699e35	0.466807	0.233404	+	0.972380i	$0.425014\pi$
$798$	−2.70359e34	−0.0143518
$799$	−1.60122e36	−0.836789
$800$	−6.87195e34	−0.0353553
$801$	6.01984e35	0.304915
$802$	1.06246e36	0.529824
$803$	−7.20038e35	−0.353518
$804$	−5.87570e35	−0.284027
$805$	−4.91268e33	−0.00233814
$806$	−5.33273e33	−0.00249897
$807$	−8.59226e35	−0.396450
$808$	9.24101e35	0.419834
$809$	−3.72457e36	−1.66617	−0.833086	−	0.553144i	$-0.813428\pi$
$809$	−3.72457e36	−1.66617	−0.833086	+	0.553144i	$0.813428\pi$
$810$	−2.91689e35	−0.128487
$811$	6.42225e35	0.278565	0.139282	−	0.990253i	$-0.455520\pi$
$811$	6.42225e35	0.278565	0.139282	+	0.990253i	$0.455520\pi$
$812$	−1.04832e34	−0.00447758
$813$	1.07817e36	0.453476
$814$	1.27342e36	0.527431
$815$	−1.23875e35	−0.0505258
$816$	−4.06249e35	−0.163180
$817$	−1.78137e36	−0.704657
$818$	−2.99560e36	−1.16699
$819$	−1.02376e33	−0.000392781 0
$820$	4.84913e35	0.183227
$821$	−2.68244e36	−0.998254	−0.499127	−	0.866529i	$-0.666346\pi$
$821$	−2.68244e36	−0.998254	−0.499127	+	0.866529i	$0.666346\pi$
$822$	4.15258e35	0.152202
$823$	−8.11664e35	−0.293007	−0.146504	−	0.989210i	$-0.546802\pi$
$823$	−8.11664e35	−0.293007	−0.146504	+	0.989210i	$0.546802\pi$
$824$	9.99476e35	0.355371
$825$	−2.79909e35	−0.0980264
$826$	−5.92351e33	−0.00204328
$827$	−1.42939e36	−0.485661	−0.242830	−	0.970069i	$-0.578076\pi$
$827$	−1.42939e36	−0.485661	−0.242830	+	0.970069i	$0.578076\pi$
$828$	1.68567e35	0.0564147
$829$	−1.47702e36	−0.486915	−0.243458	−	0.969912i	$-0.578282\pi$
$829$	−1.47702e36	−0.486915	−0.243458	+	0.969912i	$0.578282\pi$
$830$	−1.47962e36	−0.480478
$831$	3.03668e35	0.0971374
$832$	−1.91966e34	−0.00604900
$833$	−2.75651e36	−0.855652
$834$	1.41825e36	0.433687
$835$	2.06274e35	0.0621388
$836$	1.48626e36	0.441080
$837$	−2.70193e35	−0.0789960
$838$	2.55989e36	0.737344
$839$	3.59874e36	1.02124	0.510618	−	0.859808i	$-0.329417\pi$
$839$	3.59874e36	1.02124	0.510618	+	0.859808i	$0.329417\pi$
$840$	8.36336e33	0.00233824
$841$	−2.85628e36	−0.786775
$842$	1.02878e36	0.279204
$843$	2.55261e36	0.682559
$844$	2.43306e36	0.641020
$845$	1.71872e36	0.446166
$846$	−1.13108e36	−0.289310
$847$	4.51578e34	0.0113813
$848$	−8.95452e35	−0.222379
$849$	5.88823e36	1.44092
$850$	−5.02010e35	−0.121053
$851$	1.31660e36	0.312848
$852$	−1.37618e36	−0.322240
$853$	2.51059e36	0.579312	0.289656	−	0.957131i	$-0.406459\pi$
$853$	2.51059e36	0.579312	0.289656	+	0.957131i	$0.406459\pi$
$854$	9.19361e34	0.0209056
$855$	1.14634e36	0.256884
$856$	2.29394e36	0.506594
$857$	−1.62785e36	−0.354286	−0.177143	−	0.984185i	$-0.556686\pi$
$857$	−1.62785e36	−0.354286	−0.177143	+	0.984185i	$0.556686\pi$
$858$	−7.81921e34	−0.0167715
$859$	1.44920e36	0.306348	0.153174	−	0.988199i	$-0.451051\pi$
$859$	1.44920e36	0.306348	0.153174	+	0.988199i	$0.451051\pi$
$860$	5.51054e35	0.114806
$861$	−5.90153e34	−0.0121178
$862$	6.36440e36	1.28800
$863$	5.15478e36	1.02819	0.514097	−	0.857732i	$-0.328127\pi$
$863$	5.15478e36	1.02819	0.514097	+	0.857732i	$0.328127\pi$
$864$	−9.72634e35	−0.191217
$865$	1.84195e36	0.356924
$866$	−4.43796e36	−0.847637
$867$	1.08272e36	0.203835
$868$	3.81614e33	0.000708154 0
$869$	1.68196e36	0.307657
$870$	−6.17554e35	−0.111348
$871$	−2.02826e35	−0.0360494
$872$	−2.88968e36	−0.506284
$873$	1.62041e36	0.279864
$874$	1.53666e36	0.261629
$875$	1.03348e34	0.00173460
$876$	1.26736e36	0.209700
$877$	−1.01431e37	−1.65453	−0.827266	−	0.561810i	$-0.810105\pi$
$877$	−1.01431e37	−1.65453	−0.827266	+	0.561810i	$0.810105\pi$
$878$	−6.81602e36	−1.09610
$879$	6.11132e36	0.968890
$880$	−4.59765e35	−0.0718626
$881$	−3.63479e36	−0.560120	−0.280060	−	0.959983i	$-0.590354\pi$
$881$	−3.63479e36	−0.560120	−0.280060	+	0.959983i	$0.590354\pi$
$882$	−1.94716e36	−0.295831
$883$	4.65240e36	0.696896	0.348448	−	0.937328i	$-0.386709\pi$
$883$	4.65240e36	0.696896	0.348448	+	0.937328i	$0.386709\pi$
$884$	−1.40235e35	−0.0207111
$885$	−3.48947e35	−0.0508123
$886$	−1.54589e36	−0.221952
$887$	9.05035e35	0.128121	0.0640604	−	0.997946i	$-0.479595\pi$
$887$	9.05035e35	0.128121	0.0640604	+	0.997946i	$0.479595\pi$
$888$	−2.24138e36	−0.312862
$889$	1.77741e35	0.0244633
$890$	−1.69758e36	−0.230386
$891$	−1.95154e36	−0.261159
$892$	−5.47034e36	−0.721861
$893$	−1.03110e37	−1.34170
$894$	4.33679e36	0.556480
$895$	1.33397e36	0.168795
$896$	1.37373e34	0.00171415
$897$	−8.08434e34	−0.00994808
$898$	−8.84413e36	−1.07325
$899$	−2.81785e35	−0.0337227
$900$	−3.54612e35	−0.0418526
$901$	−6.54146e36	−0.761403
$902$	3.24429e36	0.372424
$903$	−6.70648e34	−0.00759273
$904$	−5.23052e36	−0.584036
$905$	6.69799e36	0.737628
$906$	4.88991e35	0.0531127
$907$	−3.58423e36	−0.383977	−0.191988	−	0.981397i	$-0.561494\pi$
$907$	−3.58423e36	−0.383977	−0.191988	+	0.981397i	$0.561494\pi$
$908$	−7.13385e36	−0.753791
$909$	4.76862e36	0.496986
$910$	2.88699e33	0.000296776 0
$911$	5.15388e36	0.522582	0.261291	−	0.965260i	$-0.415852\pi$
$911$	5.15388e36	0.522582	0.261291	+	0.965260i	$0.415852\pi$
$912$	−2.61602e36	−0.261641
$913$	−9.89934e36	−0.976611
$914$	−3.54356e34	−0.00344836
$915$	5.41585e36	0.519880
$916$	9.16200e36	0.867555
$917$	2.43517e35	0.0227464
$918$	−7.10528e36	−0.654708
$919$	1.45442e36	0.132205	0.0661023	−	0.997813i	$-0.478944\pi$
$919$	1.45442e36	0.132205	0.0661023	+	0.997813i	$0.478944\pi$
$920$	−4.75355e35	−0.0426256
$921$	−2.27655e36	−0.201387
$922$	1.29086e37	1.12653
$923$	−4.75049e35	−0.0408994
$924$	5.59548e34	0.00475267
$925$	−2.76971e36	−0.232093
$926$	1.20307e37	0.994614
$927$	5.15758e36	0.420678
$928$	−1.01436e36	−0.0816289
$929$	1.48492e37	1.17898	0.589491	−	0.807775i	$-0.299328\pi$
$929$	1.48492e37	1.17898	0.589491	+	0.807775i	$0.299328\pi$
$930$	2.24804e35	0.0176103
$931$	−1.77504e37	−1.37194
$932$	−4.20444e36	−0.320634
$933$	8.73845e35	0.0657528
$934$	9.34208e36	0.693598
$935$	−3.35868e36	−0.246050
$936$	−9.90602e34	−0.00716063
$937$	4.13990e36	0.295288	0.147644	−	0.989041i	$-0.452831\pi$
$937$	4.13990e36	0.295288	0.147644	+	0.989041i	$0.452831\pi$
$938$	1.45144e35	0.0102156
$939$	−1.63840e37	−1.13789
$940$	3.18962e36	0.218595
$941$	3.04574e36	0.205979	0.102989	−	0.994682i	$-0.467159\pi$
$941$	3.04574e36	0.205979	0.102989	+	0.994682i	$0.467159\pi$
$942$	9.46450e36	0.631628
$943$	3.35430e36	0.220905
$944$	−5.73164e35	−0.0372502
$945$	1.46275e35	0.00938150
$946$	3.68680e36	0.233352
$947$	1.93836e37	1.21076	0.605382	−	0.795935i	$-0.293020\pi$
$947$	1.93836e37	1.21076	0.605382	+	0.795935i	$0.293020\pi$
$948$	−2.96046e36	−0.182497
$949$	4.37487e35	0.0266157
$950$	−3.23266e36	−0.194095
$951$	−1.48417e37	−0.879480
$952$	1.00353e35	0.00586908
$953$	−7.72509e35	−0.0445905	−0.0222952	−	0.999751i	$-0.507097\pi$
$953$	−7.72509e35	−0.0445905	−0.0222952	+	0.999751i	$0.507097\pi$
$954$	−4.62079e36	−0.263246
$955$	6.18986e36	0.348048
$956$	1.11546e37	0.619055
$957$	−4.13172e36	−0.226325
$958$	3.26522e36	0.176540
$959$	−1.02579e35	−0.00547425
$960$	8.09246e35	0.0426275
$961$	−1.91302e37	−0.994667
$962$	−7.73713e35	−0.0397092
$963$	1.18374e37	0.599690
$964$	4.65659e36	0.232866
$965$	−1.13886e36	−0.0562183
$966$	5.78521e34	0.00281907
$967$	−6.95372e36	−0.334492	−0.167246	−	0.985915i	$-0.553487\pi$
$967$	−6.95372e36	−0.334492	−0.167246	+	0.985915i	$0.553487\pi$
$968$	4.36951e36	0.207487
$969$	−1.91105e37	−0.895830
$970$	−4.56953e36	−0.211458
$971$	2.67539e37	1.22221	0.611106	−	0.791549i	$-0.290725\pi$
$971$	2.67539e37	1.22221	0.611106	+	0.791549i	$0.290725\pi$
$972$	−8.55729e36	−0.385930
$973$	−3.50341e35	−0.0155984
$974$	3.00038e36	0.131883
$975$	1.70070e35	0.00738021
$976$	8.89581e36	0.381121
$977$	2.82491e37	1.19488	0.597438	−	0.801915i	$-0.296185\pi$
$977$	2.82491e37	1.19488	0.597438	+	0.801915i	$0.296185\pi$
$978$	1.45876e36	0.0609184
$979$	−1.13576e37	−0.468278
$980$	5.49095e36	0.223523
$981$	−1.49116e37	−0.599323
$982$	9.65226e36	0.383032
$983$	3.52532e37	1.38127	0.690636	−	0.723203i	$-0.257331\pi$
$983$	3.52532e37	1.38127	0.690636	+	0.723203i	$0.257331\pi$
$984$	−5.71037e36	−0.220915
$985$	2.80213e36	0.107037
$986$	−7.41013e36	−0.279489
$987$	−3.88186e35	−0.0144569
$988$	−9.03037e35	−0.0332081
$989$	3.81182e36	0.138413
$990$	−2.37252e36	−0.0850687
$991$	−1.01549e36	−0.0359547	−0.0179774	−	0.999838i	$-0.505723\pi$
$991$	−1.01549e36	−0.0359547	−0.0179774	+	0.999838i	$0.505723\pi$
$992$	3.69253e35	0.0129100
$993$	3.05588e37	1.05505
$994$	3.39948e35	0.0115900
$995$	−2.49523e37	−0.840084
$996$	1.74241e37	0.579308
$997$	−5.04007e37	−1.65481	−0.827403	−	0.561608i	$-0.810183\pi$
$997$	−5.04007e37	−1.65481	−0.827403	+	0.561608i	$0.810183\pi$
$998$	−4.57509e36	−0.148343
$999$	−3.92016e37	−1.25526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.a.c.1.1	✓	2
5.2	odd	4		50.26.b.c.49.2		4
5.3	odd	4		50.26.b.c.49.3		4
5.4	even	2		50.26.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.c.1.1	✓	2	1.1	even	1	trivial
50.26.a.e.1.2		2	5.4	even	2
50.26.b.c.49.2		4	5.2	odd	4
50.26.b.c.49.3		4	5.3	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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} -701909. q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} +2.87502e9 q^{6} -7.10199e8 q^{7} -6.87195e10 q^{8} -3.54612e11 q^{9} +1.00000e12 q^{10} +6.69047e12 q^{11} -1.17761e13 q^{12} -4.06505e12 q^{13} +2.90898e12 q^{14} +1.71365e14 q^{15} +2.81475e14 q^{16} +2.05623e15 q^{17} +1.45249e15 q^{18} +1.32410e16 q^{19} -4.09600e15 q^{20} +4.98495e14 q^{21} -2.74041e16 q^{22} -2.83334e16 q^{23} +4.82348e16 q^{24} +5.96046e16 q^{25} +1.66504e16 q^{26} +8.43625e17 q^{27} -1.19152e16 q^{28} +8.79820e17 q^{29} -7.01909e17 q^{30} -3.20276e17 q^{31} -1.15292e18 q^{32} -4.69610e18 q^{33} -8.42232e18 q^{34} +1.73388e17 q^{35} -5.94940e18 q^{36} -4.64680e19 q^{37} -5.42350e19 q^{38} +2.85329e18 q^{39} +1.67772e19 q^{40} -1.18387e20 q^{41} -2.04184e18 q^{42} -1.34535e20 q^{43} +1.12247e20 q^{44} +8.65752e19 q^{45} +1.16053e20 q^{46} -7.78716e20 q^{47} -1.97570e20 q^{48} -1.34056e21 q^{49} -2.44141e20 q^{50} -1.44329e21 q^{51} -6.82002e19 q^{52} -3.18129e21 q^{53} -3.45549e21 q^{54} -1.63341e21 q^{55} +4.88045e19 q^{56} -9.29396e21 q^{57} -3.60374e21 q^{58} -2.03629e21 q^{59} +2.87502e21 q^{60} +3.16043e22 q^{61} +1.31185e21 q^{62} +2.51845e20 q^{63} +4.72237e21 q^{64} +9.92443e20 q^{65} +1.92352e22 q^{66} +4.98952e22 q^{67} +3.44978e22 q^{68} +1.98875e22 q^{69} -7.10199e20 q^{70} +1.16862e23 q^{71} +2.43688e22 q^{72} -1.07622e23 q^{73} +1.90333e23 q^{74} -4.18370e22 q^{75} +2.22147e23 q^{76} -4.75156e21 q^{77} -1.16871e22 q^{78} +2.51396e23 q^{79} -6.87195e22 q^{80} -2.91689e23 q^{81} +4.84913e23 q^{82} -1.47962e24 q^{83} +8.36336e21 q^{84} -5.02010e23 q^{85} +5.51054e23 q^{86} -6.17554e23 q^{87} -4.59765e23 q^{88} -1.69758e24 q^{89} -3.54612e23 q^{90} +2.88699e21 q^{91} -4.75355e23 q^{92} +2.24804e23 q^{93} +3.18962e24 q^{94} -3.23266e24 q^{95} +8.09246e23 q^{96} -4.56953e24 q^{97} +5.49095e24 q^{98} -2.37252e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8192 q^{2} + 545212 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 2233188352 q^{6} + 38567856964 q^{7} - 137438953472 q^{8} + 353410472386 q^{9} + 2000000000000 q^{10} - 8379169876416 q^{11} + 9147139489792 q^{12}+ \cdots - 13\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 8192 * q^2 + 545212 * q^3 + 33554432 * q^4 - 488281250 * q^5 - 2233188352 * q^6 + 38567856964 * q^7 - 137438953472 * q^8 + 353410472386 * q^9 + 2000000000000 * q^10 - 8379169876416 * q^11 + 9147139489792 * q^12 - 149443737196988 * q^13 - 157973942124544 * q^14 - 133108398437500 * q^15 + 562949953421312 * q^16 + 3359254299255924 * q^17 - 1447569294893056 * q^18 + 3489461415860920 * q^19 - 8192000000000000 * q^20 + 49482990719617784 * q^21 + 34321079813799936 * q^22 + 72370201928022732 * q^23 - 37466683350188032 * q^24 + 119209289550781250 * q^25 + 612121547558862848 * q^26 + 669943559840926600 * q^27 + 647061266942132224 * q^28 - 537443787959856180 * q^29 + 545212000000000000 * q^30 - 3624027784441312136 * q^31 - 2305843009213693952 * q^32 - 23489760709118906496 * q^33 - 13759505609752264704 * q^34 - 9415980704101562500 * q^35 + 5929243831881957376 * q^36 + 19038572664443645764 * q^37 - 14292833959366328320 * q^38 - 178451546772299045128 * q^39 + 33554432000000000000 * q^40 - 212589580623880771956 * q^41 - 202682329987554443264 * q^42 - 13668418927657846868 * q^43 - 140579142917324537856 * q^44 - 86281853609863281250 * q^45 - 296428347097181110272 * q^46 - 1665681645557377854156 * q^47 + 153463535002370179072 * q^48 - 1138867157350741829766 * q^49 - 488281250000000000000 * q^50 + 181740691723390600344 * q^51 - 2507249858801102225408 * q^52 - 9975823013097020329548 * q^53 - 2744088821108435353600 * q^54 + 2045695770609375000000 * q^55 - 2650362949394973589504 * q^56 - 21455279998725990048880 * q^57 + 2201369755483570913280 * q^58 - 13147506706206800097960 * q^59 - 2233188352000000000000 * q^60 + 114411778307375747524 * q^61 + 14844017805071614509056 * q^62 + 28061596756249158893252 * q^63 + 9444732965739290427392 * q^64 + 36485287401608398437500 * q^65 + 96214059864551041007616 * q^66 + 95143040936399031080644 * q^67 + 56358934977545276227584 * q^68 + 145477011313277750812392 * q^69 + 38567856964000000000000 * q^70 + 83749259495165337742824 * q^71 - 24286182735388497412096 * q^72 + 196631633422897936973572 * q^73 - 77981993633561173049344 * q^74 + 32497167587280273437500 * q^75 + 58543447897564480798720 * q^76 - 596657555842340580669312 * q^77 + 730937535579336888844288 * q^78 + 105871595026057220692240 * q^79 - 137438953472000000000000 * q^80 - 1108190878966022772827798 * q^81 + 870766922235415641931776 * q^82 - 599053017838528107773748 * q^83 + 830186823629022999609344 * q^84 - 820130444154278320312500 * q^85 + 55985843927686540771328 * q^86 - 2385054109175491523609880 * q^87 + 575812169389361307058176 * q^88 - 1877353952181279423739020 * q^89 + 353410472386000000000000 * q^90 - 5707305339748996500897016 * q^91 + 1214170509710053827674112 * q^92 - 3895374854369117044063216 * q^93 + 6822632020203019690622976 * q^94 - 851919290981669921875000 * q^95 - 628586639369708253478912 * q^96 - 11597588153054877446451836 * q^97 + 4664799876508638534721536 * q^98 - 13042162823998039381361088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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