LMFDB - Embedded newform 74.8.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(1,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("74.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 10621x^{4} + 102052x^{3} + 31004503x^{2} - 305547358x - 22608804936 $ x^6 - 2x^5 - 10621x^4 + 102052x^3 + 31004503x^2 - 305547358*x - 22608804936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-85.7890$ of defining polynomial
Character	$\chi$	$=$	74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +90.7890 q^{3} +64.0000 q^{4} +133.163 q^{5} -726.312 q^{6} -948.062 q^{7} -512.000 q^{8} +6055.64 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +90.7890 q^{3} +64.0000 q^{4} +133.163 q^{5} -726.312 q^{6} -948.062 q^{7} -512.000 q^{8} +6055.64 q^{9} -1065.31 q^{10} +4655.78 q^{11} +5810.49 q^{12} -1049.71 q^{13} +7584.49 q^{14} +12089.8 q^{15} +4096.00 q^{16} +37870.8 q^{17} -48445.1 q^{18} -37462.0 q^{19} +8522.46 q^{20} -86073.6 q^{21} -37246.3 q^{22} +40596.4 q^{23} -46483.9 q^{24} -60392.5 q^{25} +8397.65 q^{26} +351229. q^{27} -60676.0 q^{28} -66725.4 q^{29} -96718.2 q^{30} +220090. q^{31} -32768.0 q^{32} +422694. q^{33} -302966. q^{34} -126247. q^{35} +387561. q^{36} -50653.0 q^{37} +299696. q^{38} -95301.7 q^{39} -68179.7 q^{40} -101084. q^{41} +688588. q^{42} +816690. q^{43} +297970. q^{44} +806389. q^{45} -324771. q^{46} -1.00197e6 q^{47} +371872. q^{48} +75278.3 q^{49} +483140. q^{50} +3.43825e6 q^{51} -67181.2 q^{52} +1.40417e6 q^{53} -2.80984e6 q^{54} +619980. q^{55} +485408. q^{56} -3.40113e6 q^{57} +533804. q^{58} +686480. q^{59} +773745. q^{60} -2.33880e6 q^{61} -1.76072e6 q^{62} -5.74112e6 q^{63} +262144. q^{64} -139782. q^{65} -3.38155e6 q^{66} -8039.60 q^{67} +2.42373e6 q^{68} +3.68571e6 q^{69} +1.00998e6 q^{70} -1.08288e6 q^{71} -3.10049e6 q^{72} +142983. q^{73} +405224. q^{74} -5.48297e6 q^{75} -2.39757e6 q^{76} -4.41397e6 q^{77} +762414. q^{78} -844178. q^{79} +545437. q^{80} +1.86441e7 q^{81} +808676. q^{82} -8.33149e6 q^{83} -5.50871e6 q^{84} +5.04300e6 q^{85} -6.53352e6 q^{86} -6.05793e6 q^{87} -2.38376e6 q^{88} +8.29467e6 q^{89} -6.45112e6 q^{90} +995186. q^{91} +2.59817e6 q^{92} +1.99818e7 q^{93} +8.01580e6 q^{94} -4.98857e6 q^{95} -2.97497e6 q^{96} +4.06489e6 q^{97} -602226. q^{98} +2.81937e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) $ 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9} + 112 q^{10} + 2956 q^{11} + 1792 q^{12} + 2394 q^{13} + 7840 q^{14} - 28820 q^{15} + 24576 q^{16} - 45108 q^{17} - 66032 q^{18} + 11764 q^{19} - 896 q^{20} - 135378 q^{21} - 23648 q^{22} + 21052 q^{23} - 14336 q^{24} + 194744 q^{25} - 19152 q^{26} + 439240 q^{27} - 62720 q^{28} + 288454 q^{29} + 230560 q^{30} + 578868 q^{31} - 196608 q^{32} + 980174 q^{33} + 360864 q^{34} + 1243052 q^{35} + 528256 q^{36} - 303918 q^{37} - 94112 q^{38} + 1735296 q^{39} + 7168 q^{40} + 1176840 q^{41} + 1083024 q^{42} + 2669236 q^{43} + 189184 q^{44} + 2560692 q^{45} - 168416 q^{46} - 131044 q^{47} + 114688 q^{48} + 2460856 q^{49} - 1557952 q^{50} + 2899732 q^{51} + 153216 q^{52} + 983190 q^{53} - 3513920 q^{54} - 1200168 q^{55} + 501760 q^{56} - 163216 q^{57} - 2307632 q^{58} - 1215568 q^{59} - 1844480 q^{60} + 3136358 q^{61} - 4630944 q^{62} - 1444880 q^{63} + 1572864 q^{64} - 1302836 q^{65} - 7841392 q^{66} + 2179276 q^{67} - 2886912 q^{68} - 929514 q^{69} - 9944416 q^{70} + 325164 q^{71} - 4226048 q^{72} + 5011444 q^{73} + 2431344 q^{74} - 9374520 q^{75} + 752896 q^{76} - 26500426 q^{77} - 13882368 q^{78} + 3173032 q^{79} - 57344 q^{80} - 2565226 q^{81} - 9414720 q^{82} - 22567048 q^{83} - 8664192 q^{84} + 1486476 q^{85} - 21353888 q^{86} - 157228 q^{87} - 1513472 q^{88} + 26836996 q^{89} - 20485536 q^{90} + 17942380 q^{91} + 1347328 q^{92} + 16734948 q^{93} + 1048352 q^{94} - 4252048 q^{95} - 917504 q^{96} + 295792 q^{97} - 19686848 q^{98} + 25990712 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9 + 112 * q^10 + 2956 * q^11 + 1792 * q^12 + 2394 * q^13 + 7840 * q^14 - 28820 * q^15 + 24576 * q^16 - 45108 * q^17 - 66032 * q^18 + 11764 * q^19 - 896 * q^20 - 135378 * q^21 - 23648 * q^22 + 21052 * q^23 - 14336 * q^24 + 194744 * q^25 - 19152 * q^26 + 439240 * q^27 - 62720 * q^28 + 288454 * q^29 + 230560 * q^30 + 578868 * q^31 - 196608 * q^32 + 980174 * q^33 + 360864 * q^34 + 1243052 * q^35 + 528256 * q^36 - 303918 * q^37 - 94112 * q^38 + 1735296 * q^39 + 7168 * q^40 + 1176840 * q^41 + 1083024 * q^42 + 2669236 * q^43 + 189184 * q^44 + 2560692 * q^45 - 168416 * q^46 - 131044 * q^47 + 114688 * q^48 + 2460856 * q^49 - 1557952 * q^50 + 2899732 * q^51 + 153216 * q^52 + 983190 * q^53 - 3513920 * q^54 - 1200168 * q^55 + 501760 * q^56 - 163216 * q^57 - 2307632 * q^58 - 1215568 * q^59 - 1844480 * q^60 + 3136358 * q^61 - 4630944 * q^62 - 1444880 * q^63 + 1572864 * q^64 - 1302836 * q^65 - 7841392 * q^66 + 2179276 * q^67 - 2886912 * q^68 - 929514 * q^69 - 9944416 * q^70 + 325164 * q^71 - 4226048 * q^72 + 5011444 * q^73 + 2431344 * q^74 - 9374520 * q^75 + 752896 * q^76 - 26500426 * q^77 - 13882368 * q^78 + 3173032 * q^79 - 57344 * q^80 - 2565226 * q^81 - 9414720 * q^82 - 22567048 * q^83 - 8664192 * q^84 + 1486476 * q^85 - 21353888 * q^86 - 157228 * q^87 - 1513472 * q^88 + 26836996 * q^89 - 20485536 * q^90 + 17942380 * q^91 + 1347328 * q^92 + 16734948 * q^93 + 1048352 * q^94 - 4252048 * q^95 - 917504 * q^96 + 295792 * q^97 - 19686848 * q^98 + 25990712 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	90.7890	1.94137	0.970686	−	0.240352i	$-0.0772629\pi$
$3$	90.7890	1.94137	0.970686	+	0.240352i	$0.0772629\pi$
$4$	64.0000	0.500000
$5$	133.163	0.476420	0.238210	−	0.971214i	$-0.423439\pi$
$5$	133.163	0.476420	0.238210	+	0.971214i	$0.423439\pi$
$6$	−726.312	−1.37276
$7$	−948.062	−1.04470	−0.522352	−	0.852730i	$-0.674945\pi$
$7$	−948.062	−1.04470	−0.522352	+	0.852730i	$0.674945\pi$
$8$	−512.000	−0.353553
$9$	6055.64	2.76892
$10$	−1065.31	−0.336880
$11$	4655.78	1.05467	0.527337	−	0.849656i	$-0.323190\pi$
$11$	4655.78	1.05467	0.527337	+	0.849656i	$0.323190\pi$
$12$	5810.49	0.970686
$13$	−1049.71	−0.132515	−0.0662576	−	0.997803i	$-0.521106\pi$
$13$	−1049.71	−0.132515	−0.0662576	+	0.997803i	$0.521106\pi$
$14$	7584.49	0.738718
$15$	12089.8	0.924908
$16$	4096.00	0.250000
$17$	37870.8	1.86953	0.934766	−	0.355264i	$-0.115609\pi$
$17$	37870.8	1.86953	0.934766	+	0.355264i	$0.115609\pi$
$18$	−48445.1	−1.95792
$19$	−37462.0	−1.25301	−0.626503	−	0.779419i	$-0.715514\pi$
$19$	−37462.0	−1.25301	−0.626503	+	0.779419i	$0.715514\pi$
$20$	8522.46	0.238210
$21$	−86073.6	−2.02816
$22$	−37246.3	−0.745767
$23$	40596.4	0.695729	0.347865	−	0.937545i	$-0.386907\pi$
$23$	40596.4	0.695729	0.347865	+	0.937545i	$0.386907\pi$
$24$	−46483.9	−0.686379
$25$	−60392.5	−0.773024
$26$	8397.65	0.0937025
$27$	351229.	3.43414
$28$	−60676.0	−0.522352
$29$	−66725.4	−0.508041	−0.254020	−	0.967199i	$-0.581753\pi$
$29$	−66725.4	−0.508041	−0.254020	+	0.967199i	$0.581753\pi$
$30$	−96718.2	−0.654009
$31$	220090.	1.32689	0.663446	−	0.748224i	$-0.269093\pi$
$31$	220090.	1.32689	0.663446	+	0.748224i	$0.269093\pi$
$32$	−32768.0	−0.176777
$33$	422694.	2.04752
$34$	−302966.	−1.32196
$35$	−126247.	−0.497718
$36$	387561.	1.38446
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	299696.	0.886009
$39$	−95301.7	−0.257261
$40$	−68179.7	−0.168440
$41$	−101084.	−0.229056	−0.114528	−	0.993420i	$-0.536536\pi$
$41$	−101084.	−0.229056	−0.114528	+	0.993420i	$0.536536\pi$
$42$	688588.	1.43413
$43$	816690.	1.56645	0.783227	−	0.621736i	$-0.213572\pi$
$43$	816690.	1.56645	0.783227	+	0.621736i	$0.213572\pi$
$44$	297970.	0.527337
$45$	806389.	1.31917
$46$	−324771.	−0.491955
$47$	−1.00197e6	−1.40771	−0.703857	−	0.710342i	$-0.748540\pi$
$47$	−1.00197e6	−1.40771	−0.703857	+	0.710342i	$0.748540\pi$
$48$	371872.	0.485343
$49$	75278.3	0.0914078
$50$	483140.	0.546610
$51$	3.43825e6	3.62946
$52$	−67181.2	−0.0662576
$53$	1.40417e6	1.29555	0.647776	−	0.761830i	$-0.275699\pi$
$53$	1.40417e6	1.29555	0.647776	+	0.761830i	$0.275699\pi$
$54$	−2.80984e6	−2.42830
$55$	619980.	0.502468
$56$	485408.	0.369359
$57$	−3.40113e6	−2.43255
$58$	533804.	0.359239
$59$	686480.	0.435157	0.217578	−	0.976043i	$-0.430184\pi$
$59$	686480.	0.435157	0.217578	+	0.976043i	$0.430184\pi$
$60$	773745.	0.462454
$61$	−2.33880e6	−1.31929	−0.659644	−	0.751578i	$-0.729293\pi$
$61$	−2.33880e6	−1.31929	−0.659644	+	0.751578i	$0.729293\pi$
$62$	−1.76072e6	−0.938254
$63$	−5.74112e6	−2.89271
$64$	262144.	0.125000
$65$	−139782.	−0.0631329
$66$	−3.38155e6	−1.44781
$67$	−8039.60	−0.00326567	−0.00163284	−	0.999999i	$-0.500520\pi$
$67$	−8039.60	−0.00326567	−0.00163284	+	0.999999i	$0.500520\pi$
$68$	2.42373e6	0.934766
$69$	3.68571e6	1.35067
$70$	1.00998e6	0.351940
$71$	−1.08288e6	−0.359066	−0.179533	−	0.983752i	$-0.557459\pi$
$71$	−1.08288e6	−0.359066	−0.179533	+	0.983752i	$0.557459\pi$
$72$	−3.10049e6	−0.978962
$73$	142983.	0.0430184	0.0215092	−	0.999769i	$-0.493153\pi$
$73$	142983.	0.0430184	0.0215092	+	0.999769i	$0.493153\pi$
$74$	405224.	0.116248
$75$	−5.48297e6	−1.50073
$76$	−2.39757e6	−0.626503
$77$	−4.41397e6	−1.10182
$78$	762414.	0.181911
$79$	−844178.	−0.192637	−0.0963183	−	0.995351i	$-0.530707\pi$
$79$	−844178.	−0.192637	−0.0963183	+	0.995351i	$0.530707\pi$
$80$	545437.	0.119105
$81$	1.86441e7	3.89801
$82$	808676.	0.161967
$83$	−8.33149e6	−1.59937	−0.799685	−	0.600419i	$-0.795000\pi$
$83$	−8.33149e6	−1.59937	−0.799685	+	0.600419i	$0.795000\pi$
$84$	−5.50871e6	−1.01408
$85$	5.04300e6	0.890683
$86$	−6.53352e6	−1.10765
$87$	−6.05793e6	−0.986296
$88$	−2.38376e6	−0.372884
$89$	8.29467e6	1.24719	0.623597	−	0.781746i	$-0.285671\pi$
$89$	8.29467e6	1.24719	0.623597	+	0.781746i	$0.285671\pi$
$90$	−6.45112e6	−0.932795
$91$	995186.	0.138439
$92$	2.59817e6	0.347865
$93$	1.99818e7	2.57599
$94$	8.01580e6	0.995404
$95$	−4.98857e6	−0.596957
$96$	−2.97497e6	−0.343189
$97$	4.06489e6	0.452218	0.226109	−	0.974102i	$-0.427399\pi$
$97$	4.06489e6	0.452218	0.226109	+	0.974102i	$0.427399\pi$
$98$	−602226.	−0.0646351
$99$	2.81937e7	2.92031
$100$	−3.86512e6	−0.386512
$101$	51781.2	0.00500089	0.00250045	−	0.999997i	$-0.499204\pi$
$101$	51781.2	0.00500089	0.00250045	+	0.999997i	$0.499204\pi$
$102$	−2.75060e7	−2.56641
$103$	−8.90574e6	−0.803045	−0.401522	−	0.915849i	$-0.631519\pi$
$103$	−8.90574e6	−0.803045	−0.401522	+	0.915849i	$0.631519\pi$
$104$	537449.	0.0468512
$105$	−1.14619e7	−0.966256
$106$	−1.12334e7	−0.916094
$107$	23216.9	0.00183215	0.000916075	−	1.00000i	$-0.499708\pi$
$107$	23216.9	0.00183215	0.000916075		1.00000i	$0.499708\pi$
$108$	2.24787e7	1.71707
$109$	−8.81772e6	−0.652174	−0.326087	−	0.945340i	$-0.605730\pi$
$109$	−8.81772e6	−0.652174	−0.326087	+	0.945340i	$0.605730\pi$
$110$	−4.95984e6	−0.355299
$111$	−4.59873e6	−0.319160
$112$	−3.88326e6	−0.261176
$113$	−2.36821e7	−1.54399	−0.771997	−	0.635626i	$-0.780742\pi$
$113$	−2.36821e7	−1.54399	−0.771997	+	0.635626i	$0.780742\pi$
$114$	2.72091e7	1.72007
$115$	5.40596e6	0.331459
$116$	−4.27043e6	−0.254020
$117$	−6.35664e6	−0.366925
$118$	−5.49184e6	−0.307702
$119$	−3.59038e7	−1.95311
$120$	−6.18996e6	−0.327004
$121$	2.18916e6	0.112338
$122$	1.87104e7	0.932877
$123$	−9.17735e6	−0.444682
$124$	1.40858e7	0.663446
$125$	−1.84455e7	−0.844704
$126$	4.59289e7	2.04545
$127$	−30304.1	−0.00131277	−0.000656384	−	1.00000i	$-0.500209\pi$
$127$	−30304.1	−0.00131277	−0.000656384		1.00000i	$0.500209\pi$
$128$	−2.09715e6	−0.0883883
$129$	7.41464e7	3.04107
$130$	1.11826e6	0.0446417
$131$	1.27920e7	0.497150	0.248575	−	0.968613i	$-0.420038\pi$
$131$	1.27920e7	0.497150	0.248575	+	0.968613i	$0.420038\pi$
$132$	2.70524e7	1.02376
$133$	3.55163e7	1.30902
$134$	64316.8	0.00230918
$135$	4.67709e7	1.63609
$136$	−1.93898e7	−0.660980
$137$	−4.45086e7	−1.47884	−0.739422	−	0.673242i	$-0.764901\pi$
$137$	−4.45086e7	−1.47884	−0.739422	+	0.673242i	$0.764901\pi$
$138$	−2.94856e7	−0.955067
$139$	3.36501e6	0.106276	0.0531379	−	0.998587i	$-0.483078\pi$
$139$	3.36501e6	0.106276	0.0531379	+	0.998587i	$0.483078\pi$
$140$	−8.07982e6	−0.248859
$141$	−9.09682e7	−2.73289
$142$	8.66300e6	0.253898
$143$	−4.88720e6	−0.139760
$144$	2.48039e7	0.692231
$145$	−8.88539e6	−0.242041
$146$	−1.14386e6	−0.0304186
$147$	6.83444e6	0.177457
$148$	−3.24179e6	−0.0821995
$149$	−3.75616e7	−0.930234	−0.465117	−	0.885249i	$-0.653988\pi$
$149$	−3.75616e7	−0.930234	−0.465117	+	0.885249i	$0.653988\pi$
$150$	4.38638e7	1.06117
$151$	−7.66361e7	−1.81140	−0.905699	−	0.423922i	$-0.860653\pi$
$151$	−7.66361e7	−1.81140	−0.905699	+	0.423922i	$0.860653\pi$
$152$	1.91805e7	0.443004
$153$	2.29332e8	5.17659
$154$	3.53118e7	0.779107
$155$	2.93080e7	0.632158
$156$	−6.09931e6	−0.128631
$157$	−3.83181e7	−0.790233	−0.395116	−	0.918631i	$-0.629296\pi$
$157$	−3.83181e7	−0.790233	−0.395116	+	0.918631i	$0.629296\pi$
$158$	6.75342e6	0.136215
$159$	1.27483e8	2.51515
$160$	−4.36350e6	−0.0842200
$161$	−3.84879e7	−0.726831
$162$	−1.49153e8	−2.75631
$163$	4.20835e7	0.761123	0.380562	−	0.924756i	$-0.375731\pi$
$163$	4.20835e7	0.761123	0.380562	+	0.924756i	$0.375731\pi$
$164$	−6.46941e6	−0.114528
$165$	5.62874e7	0.975477
$166$	6.66519e7	1.13093
$167$	−1.08504e8	−1.80276	−0.901378	−	0.433033i	$-0.857443\pi$
$167$	−1.08504e8	−1.80276	−0.901378	+	0.433033i	$0.857443\pi$
$168$	4.40697e7	0.717063
$169$	−6.16466e7	−0.982440
$170$	−4.03440e7	−0.629808
$171$	−2.26856e8	−3.46948
$172$	5.22681e7	0.783227
$173$	−3.54173e7	−0.520060	−0.260030	−	0.965601i	$-0.583732\pi$
$173$	−3.54173e7	−0.520060	−0.260030	+	0.965601i	$0.583732\pi$
$174$	4.84635e7	0.697416
$175$	5.72558e7	0.807582
$176$	1.90701e7	0.263669
$177$	6.23248e7	0.844801
$178$	−6.63573e7	−0.881899
$179$	4.27586e7	0.557235	0.278617	−	0.960402i	$-0.410124\pi$
$179$	4.27586e7	0.557235	0.278617	+	0.960402i	$0.410124\pi$
$180$	5.16089e7	0.659585
$181$	−7.04378e7	−0.882940	−0.441470	−	0.897276i	$-0.645543\pi$
$181$	−7.04378e7	−0.882940	−0.441470	+	0.897276i	$0.645543\pi$
$182$	−7.96149e6	−0.0978914
$183$	−2.12338e8	−2.56123
$184$	−2.07854e7	−0.245977
$185$	−6.74513e6	−0.0783230
$186$	−1.59854e8	−1.82150
$187$	1.76318e8	1.97175
$188$	−6.41264e7	−0.703857
$189$	−3.32987e8	−3.58766
$190$	3.99085e7	0.422112
$191$	1.29769e8	1.34758	0.673788	−	0.738925i	$-0.264666\pi$
$191$	1.29769e8	1.34758	0.673788	+	0.738925i	$0.264666\pi$
$192$	2.37998e7	0.242671
$193$	5.09514e7	0.510159	0.255079	−	0.966920i	$-0.417898\pi$
$193$	5.09514e7	0.510159	0.255079	+	0.966920i	$0.417898\pi$
$194$	−3.25191e7	−0.319766
$195$	−1.26907e7	−0.122564
$196$	4.81781e6	0.0457039
$197$	−1.80715e6	−0.0168408	−0.00842039	−	0.999965i	$-0.502680\pi$
$197$	−1.80715e6	−0.0168408	−0.00842039	+	0.999965i	$0.502680\pi$
$198$	−2.25550e8	−2.06497
$199$	4.75898e7	0.428083	0.214041	−	0.976825i	$-0.431337\pi$
$199$	4.75898e7	0.428083	0.214041	+	0.976825i	$0.431337\pi$
$200$	3.09210e7	0.273305
$201$	−729907.	−0.00633989
$202$	−414250.	−0.00353617
$203$	6.32598e7	0.530752
$204$	2.20048e8	1.81473
$205$	−1.34608e7	−0.109127
$206$	7.12459e7	0.567838
$207$	2.45837e8	1.92642
$208$	−4.29960e6	−0.0331288
$209$	−1.74415e8	−1.32151
$210$	9.16948e7	0.683246
$211$	−5.04805e7	−0.369943	−0.184972	−	0.982744i	$-0.559219\pi$
$211$	−5.04805e7	−0.369943	−0.184972	+	0.982744i	$0.559219\pi$
$212$	8.98671e7	0.647776
$213$	−9.83131e7	−0.697080
$214$	−185735.	−0.00129553
$215$	1.08753e8	0.746290
$216$	−1.79829e8	−1.21415
$217$	−2.08659e8	−1.38621
$218$	7.05417e7	0.461157
$219$	1.29813e7	0.0835146
$220$	3.96787e7	0.251234
$221$	−3.97532e7	−0.247742
$222$	3.67899e7	0.225680
$223$	1.34484e8	0.812089	0.406044	−	0.913853i	$-0.366908\pi$
$223$	1.34484e8	0.812089	0.406044	+	0.913853i	$0.366908\pi$
$224$	3.10661e7	0.184679
$225$	−3.65715e8	−2.14044
$226$	1.89457e8	1.09177
$227$	1.82525e8	1.03569	0.517847	−	0.855473i	$-0.326734\pi$
$227$	1.82525e8	1.03569	0.517847	+	0.855473i	$0.326734\pi$
$228$	−2.17673e8	−1.21627
$229$	1.55708e8	0.856816	0.428408	−	0.903585i	$-0.359075\pi$
$229$	1.55708e8	0.856816	0.428408	+	0.903585i	$0.359075\pi$
$230$	−4.32477e7	−0.234377
$231$	−4.00740e8	−2.13905
$232$	3.41634e7	0.179619
$233$	6.82458e7	0.353452	0.176726	−	0.984260i	$-0.443449\pi$
$233$	6.82458e7	0.353452	0.176726	+	0.984260i	$0.443449\pi$
$234$	5.08531e7	0.259455
$235$	−1.33426e8	−0.670663
$236$	4.39347e7	0.217578
$237$	−7.66420e7	−0.373979
$238$	2.87231e8	1.38106
$239$	−1.59910e8	−0.757677	−0.378838	−	0.925463i	$-0.623676\pi$
$239$	−1.59910e8	−0.757677	−0.378838	+	0.925463i	$0.623676\pi$
$240$	4.95197e7	0.231227
$241$	2.46558e8	1.13465	0.567323	−	0.823496i	$-0.307979\pi$
$241$	2.46558e8	1.13465	0.567323	+	0.823496i	$0.307979\pi$
$242$	−1.75132e7	−0.0794352
$243$	9.24538e8	4.13336
$244$	−1.49683e8	−0.659644
$245$	1.00243e7	0.0435485
$246$	7.34188e7	0.314438
$247$	3.93241e7	0.166042
$248$	−1.12686e8	−0.469127
$249$	−7.56407e8	−3.10497
$250$	1.47564e8	0.597296
$251$	−3.82771e8	−1.52785	−0.763926	−	0.645304i	$-0.776731\pi$
$251$	−3.82771e8	−1.52785	−0.763926	+	0.645304i	$0.776731\pi$
$252$	−3.67432e8	−1.44635
$253$	1.89008e8	0.733768
$254$	242433.	0.000928267 0
$255$	4.57849e8	1.72915
$256$	1.67772e7	0.0625000
$257$	1.28126e8	0.470837	0.235419	−	0.971894i	$-0.424354\pi$
$257$	1.28126e8	0.470837	0.235419	+	0.971894i	$0.424354\pi$
$258$	−5.93171e8	−2.15036
$259$	4.80222e7	0.171748
$260$	−8.94608e6	−0.0315665
$261$	−4.04065e8	−1.40673
$262$	−1.02336e8	−0.351538
$263$	1.53745e8	0.521142	0.260571	−	0.965455i	$-0.416089\pi$
$263$	1.53745e8	0.521142	0.260571	+	0.965455i	$0.416089\pi$
$264$	−2.16419e8	−0.723906
$265$	1.86985e8	0.617227
$266$	−2.84130e8	−0.925618
$267$	7.53064e8	2.42127
$268$	−514535.	−0.00163284
$269$	4.21270e8	1.31956	0.659778	−	0.751461i	$-0.270650\pi$
$269$	4.21270e8	1.31956	0.659778	+	0.751461i	$0.270650\pi$
$270$	−3.74167e8	−1.15689
$271$	5.02799e8	1.53462	0.767312	−	0.641274i	$-0.221594\pi$
$271$	5.02799e8	1.53462	0.767312	+	0.641274i	$0.221594\pi$
$272$	1.55119e8	0.467383
$273$	9.03519e7	0.268762
$274$	3.56069e8	1.04570
$275$	−2.81174e8	−0.815289
$276$	2.35885e8	0.675334
$277$	3.20002e8	0.904636	0.452318	−	0.891857i	$-0.350597\pi$
$277$	3.20002e8	0.904636	0.452318	+	0.891857i	$0.350597\pi$
$278$	−2.69201e7	−0.0751483
$279$	1.33279e9	3.67406
$280$	6.46386e7	0.175970
$281$	−4.74241e8	−1.27505	−0.637524	−	0.770430i	$-0.720042\pi$
$281$	−4.74241e8	−1.27505	−0.637524	+	0.770430i	$0.720042\pi$
$282$	7.27746e8	1.93245
$283$	−5.32308e8	−1.39608	−0.698040	−	0.716058i	$-0.745944\pi$
$283$	−5.32308e8	−1.39608	−0.698040	+	0.716058i	$0.745944\pi$
$284$	−6.93040e7	−0.179533
$285$	−4.52907e8	−1.15892
$286$	3.90976e7	0.0988256
$287$	9.58343e7	0.239295
$288$	−1.98431e8	−0.489481
$289$	1.02386e9	2.49515
$290$	7.10831e7	0.171149
$291$	3.69047e8	0.877923
$292$	9.15090e6	0.0215092
$293$	−2.15803e8	−0.501211	−0.250606	−	0.968089i	$-0.580630\pi$
$293$	−2.15803e8	−0.501211	−0.250606	+	0.968089i	$0.580630\pi$
$294$	−5.46755e7	−0.125481
$295$	9.14140e7	0.207317
$296$	2.59343e7	0.0581238
$297$	1.63525e9	3.62190
$298$	3.00493e8	0.657775
$299$	−4.26143e7	−0.0921947
$300$	−3.50910e8	−0.750363
$301$	−7.74272e8	−1.63648
$302$	6.13088e8	1.28085
$303$	4.70116e6	0.00970859
$304$	−1.53444e8	−0.313251
$305$	−3.11443e8	−0.628535
$306$	−1.83465e9	−3.66040
$307$	−5.97092e8	−1.17776	−0.588881	−	0.808220i	$-0.700431\pi$
$307$	−5.97092e8	−1.17776	−0.588881	+	0.808220i	$0.700431\pi$
$308$	−2.82494e8	−0.550912
$309$	−8.08543e8	−1.55901
$310$	−2.34464e8	−0.447003
$311$	2.38042e8	0.448738	0.224369	−	0.974504i	$-0.427968\pi$
$311$	2.38042e8	0.448738	0.224369	+	0.974504i	$0.427968\pi$
$312$	4.87945e7	0.0909556
$313$	3.27112e8	0.602964	0.301482	−	0.953472i	$-0.402519\pi$
$313$	3.27112e8	0.602964	0.301482	+	0.953472i	$0.402519\pi$
$314$	3.06545e8	0.558779
$315$	−7.64507e8	−1.37814
$316$	−5.40274e7	−0.0963183
$317$	−8.33077e8	−1.46885	−0.734426	−	0.678689i	$-0.762548\pi$
$317$	−8.33077e8	−1.46885	−0.734426	+	0.678689i	$0.762548\pi$
$318$	−1.01987e9	−1.77848
$319$	−3.10659e8	−0.535817
$320$	3.49080e7	0.0595525
$321$	2.10784e6	0.00355688
$322$	3.07903e8	0.513947
$323$	−1.41871e9	−2.34253
$324$	1.19322e9	1.94901
$325$	6.33944e7	0.102437
$326$	−3.36668e8	−0.538196
$327$	−8.00551e8	−1.26611
$328$	5.17552e7	0.0809834
$329$	9.49934e8	1.47064
$330$	−4.50299e8	−0.689767
$331$	−4.86383e8	−0.737192	−0.368596	−	0.929590i	$-0.620161\pi$
$331$	−4.86383e8	−0.737192	−0.368596	+	0.929590i	$0.620161\pi$
$332$	−5.33215e8	−0.799685
$333$	−3.06736e8	−0.455208
$334$	8.68030e8	1.27474
$335$	−1.07058e6	−0.00155583
$336$	−3.52557e8	−0.507040
$337$	−9.74289e8	−1.38670	−0.693351	−	0.720600i	$-0.743867\pi$
$337$	−9.74289e8	−1.38670	−0.693351	+	0.720600i	$0.743867\pi$
$338$	4.93173e8	0.694690
$339$	−2.15007e9	−2.99747
$340$	3.22752e8	0.445341
$341$	1.02469e9	1.39944
$342$	1.81485e9	2.45329
$343$	7.09401e8	0.949210
$344$	−4.18145e8	−0.553825
$345$	4.90801e8	0.643486
$346$	2.83338e8	0.367738
$347$	8.61556e8	1.10696	0.553478	−	0.832864i	$-0.313300\pi$
$347$	8.61556e8	1.10696	0.553478	+	0.832864i	$0.313300\pi$
$348$	−3.87708e8	−0.493148
$349$	1.30969e9	1.64923	0.824613	−	0.565697i	$-0.191393\pi$
$349$	1.30969e9	1.64923	0.824613	+	0.565697i	$0.191393\pi$
$350$	−4.58047e8	−0.571047
$351$	−3.68688e8	−0.455076
$352$	−1.52561e8	−0.186442
$353$	−8.77420e8	−1.06169	−0.530843	−	0.847470i	$-0.678125\pi$
$353$	−8.77420e8	−1.06169	−0.530843	+	0.847470i	$0.678125\pi$
$354$	−4.98598e8	−0.597365
$355$	−1.44199e8	−0.171066
$356$	5.30859e8	0.623597
$357$	−3.25967e9	−3.79171
$358$	−3.42069e8	−0.394025
$359$	1.49791e9	1.70866	0.854331	−	0.519729i	$-0.173967\pi$
$359$	1.49791e9	1.70866	0.854331	+	0.519729i	$0.173967\pi$
$360$	−4.12871e8	−0.466397
$361$	5.09528e8	0.570023
$362$	5.63503e8	0.624333
$363$	1.98751e8	0.218090
$364$	6.36919e7	0.0692197
$365$	1.90401e7	0.0204948
$366$	1.69870e9	1.81106
$367$	−1.40720e9	−1.48602	−0.743008	−	0.669283i	$-0.766602\pi$
$367$	−1.40720e9	−1.48602	−0.743008	+	0.669283i	$0.766602\pi$
$368$	1.66283e8	0.173932
$369$	−6.12131e8	−0.634237
$370$	5.39610e7	0.0553827
$371$	−1.33124e9	−1.35347
$372$	1.27883e9	1.28799
$373$	−6.79783e8	−0.678249	−0.339125	−	0.940741i	$-0.610131\pi$
$373$	−6.79783e8	−0.678249	−0.339125	+	0.940741i	$0.610131\pi$
$374$	−1.41055e9	−1.39424
$375$	−1.67464e9	−1.63988
$376$	5.13011e8	0.497702
$377$	7.00421e7	0.0673231
$378$	2.66390e9	2.53686
$379$	1.91260e9	1.80462	0.902310	−	0.431087i	$-0.141870\pi$
$379$	1.91260e9	1.80462	0.902310	+	0.431087i	$0.141870\pi$
$380$	−3.19268e8	−0.298479
$381$	−2.75127e6	−0.00254857
$382$	−1.03815e9	−0.952879
$383$	1.45283e9	1.32135	0.660676	−	0.750671i	$-0.270270\pi$
$383$	1.45283e9	1.32135	0.660676	+	0.750671i	$0.270270\pi$
$384$	−1.90398e8	−0.171595
$385$	−5.87780e8	−0.524931
$386$	−4.07611e8	−0.360737
$387$	4.94558e9	4.33739
$388$	2.60153e8	0.226109
$389$	−9.78824e8	−0.843104	−0.421552	−	0.906804i	$-0.638514\pi$
$389$	−9.78824e8	−0.843104	−0.421552	+	0.906804i	$0.638514\pi$
$390$	1.01526e8	0.0866662
$391$	1.53742e9	1.30069
$392$	−3.85425e7	−0.0323176
$393$	1.16137e9	0.965154
$394$	1.44572e7	0.0119082
$395$	−1.12414e8	−0.0917760
$396$	1.80440e9	1.46016
$397$	−1.37188e9	−1.10039	−0.550197	−	0.835035i	$-0.685447\pi$
$397$	−1.37188e9	−1.10039	−0.550197	+	0.835035i	$0.685447\pi$
$398$	−3.80718e8	−0.302700
$399$	3.22449e9	2.54130
$400$	−2.47368e8	−0.193256
$401$	3.44789e8	0.267022	0.133511	−	0.991047i	$-0.457375\pi$
$401$	3.44789e8	0.267022	0.133511	+	0.991047i	$0.457375\pi$
$402$	5.83926e6	0.00448298
$403$	−2.31030e8	−0.175833
$404$	3.31400e6	0.00250045
$405$	2.48271e9	1.85709
$406$	−5.06079e8	−0.375299
$407$	−2.35829e8	−0.173387
$408$	−1.76038e9	−1.28321
$409$	5.43183e8	0.392568	0.196284	−	0.980547i	$-0.437113\pi$
$409$	5.43183e8	0.392568	0.196284	+	0.980547i	$0.437113\pi$
$410$	1.07686e8	0.0771642
$411$	−4.04089e9	−2.87099
$412$	−5.69967e8	−0.401522
$413$	−6.50825e8	−0.454610
$414$	−1.96670e9	−1.36219
$415$	−1.10945e9	−0.761972
$416$	3.43968e7	0.0234256
$417$	3.05506e8	0.206321
$418$	1.39532e9	0.934451
$419$	2.19669e9	1.45888	0.729439	−	0.684046i	$-0.239781\pi$
$419$	2.19669e9	1.45888	0.729439	+	0.684046i	$0.239781\pi$
$420$	−7.33559e8	−0.483128
$421$	1.69532e9	1.10730	0.553650	−	0.832749i	$-0.313234\pi$
$421$	1.69532e9	1.10730	0.553650	+	0.832749i	$0.313234\pi$
$422$	4.03844e8	0.261589
$423$	−6.06759e9	−3.89785
$424$	−7.18937e8	−0.458047
$425$	−2.28711e9	−1.44519
$426$	7.86505e8	0.492910
$427$	2.21733e9	1.37827
$428$	1.48588e6	0.000916075 0
$429$	−4.43704e8	−0.271327
$430$	−8.70026e8	−0.527707
$431$	−6.19918e8	−0.372962	−0.186481	−	0.982459i	$-0.559708\pi$
$431$	−6.19918e8	−0.372962	−0.186481	+	0.982459i	$0.559708\pi$
$432$	1.43864e9	0.858535
$433$	2.69875e9	1.59755	0.798777	−	0.601627i	$-0.205481\pi$
$433$	2.69875e9	1.59755	0.798777	+	0.601627i	$0.205481\pi$
$434$	1.66928e9	0.980198
$435$	−8.06695e8	−0.469891
$436$	−5.64334e8	−0.326087
$437$	−1.52082e9	−0.871752
$438$	−1.03850e8	−0.0590537
$439$	−1.55515e9	−0.877297	−0.438648	−	0.898659i	$-0.644543\pi$
$439$	−1.55515e9	−0.877297	−0.438648	+	0.898659i	$0.644543\pi$
$440$	−3.17430e8	−0.177649
$441$	4.55858e8	0.253101
$442$	3.18025e8	0.175180
$443$	9.06288e8	0.495283	0.247641	−	0.968852i	$-0.420345\pi$
$443$	9.06288e8	0.495283	0.247641	+	0.968852i	$0.420345\pi$
$444$	−2.94319e8	−0.159580
$445$	1.10455e9	0.594188
$446$	−1.07587e9	−0.574233
$447$	−3.41018e9	−1.80593
$448$	−2.48529e8	−0.130588
$449$	4.68202e8	0.244102	0.122051	−	0.992524i	$-0.461053\pi$
$449$	4.68202e8	0.244102	0.122051	+	0.992524i	$0.461053\pi$
$450$	2.92572e9	1.51352
$451$	−4.70627e8	−0.241579
$452$	−1.51565e9	−0.771997
$453$	−6.95771e9	−3.51660
$454$	−1.46020e9	−0.732346
$455$	1.32522e8	0.0659553
$456$	1.74138e9	0.860036
$457$	−6.95216e8	−0.340732	−0.170366	−	0.985381i	$-0.554495\pi$
$457$	−6.95216e8	−0.340732	−0.170366	+	0.985381i	$0.554495\pi$
$458$	−1.24567e9	−0.605861
$459$	1.33013e10	6.42023
$460$	3.45981e8	0.165730
$461$	4.09996e8	0.194906	0.0974532	−	0.995240i	$-0.468930\pi$
$461$	4.09996e8	0.194906	0.0974532	+	0.995240i	$0.468930\pi$
$462$	3.20592e9	1.51254
$463$	−1.35529e9	−0.634600	−0.317300	−	0.948325i	$-0.602776\pi$
$463$	−1.35529e9	−0.634600	−0.317300	+	0.948325i	$0.602776\pi$
$464$	−2.73307e8	−0.127010
$465$	2.66084e9	1.22725
$466$	−5.45966e8	−0.249928
$467$	−7.26978e8	−0.330303	−0.165151	−	0.986268i	$-0.552811\pi$
$467$	−7.26978e8	−0.330303	−0.165151	+	0.986268i	$0.552811\pi$
$468$	−4.06825e8	−0.183462
$469$	7.62204e6	0.00341167
$470$	1.06741e9	0.474230
$471$	−3.47886e9	−1.53414
$472$	−3.51478e8	−0.153851
$473$	3.80233e9	1.65210
$474$	6.13136e8	0.264443
$475$	2.26242e9	0.968603
$476$	−2.29785e9	−0.976555
$477$	8.50316e9	3.58729
$478$	1.27928e9	0.535759
$479$	2.16041e9	0.898175	0.449087	−	0.893488i	$-0.351749\pi$
$479$	2.16041e9	0.898175	0.449087	+	0.893488i	$0.351749\pi$
$480$	−3.96158e8	−0.163502
$481$	5.31708e7	0.0217854
$482$	−1.97247e9	−0.802315
$483$	−3.49428e9	−1.41105
$484$	1.40106e8	0.0561691
$485$	5.41295e8	0.215446
$486$	−7.39631e9	−2.92272
$487$	−9.09190e7	−0.0356700	−0.0178350	−	0.999841i	$-0.505677\pi$
$487$	−9.09190e7	−0.0356700	−0.0178350	+	0.999841i	$0.505677\pi$
$488$	1.19747e9	0.466439
$489$	3.82072e9	1.47762
$490$	−8.01945e7	−0.0307935
$491$	−4.35917e9	−1.66195	−0.830976	−	0.556308i	$-0.812218\pi$
$491$	−4.35917e9	−1.66195	−0.830976	+	0.556308i	$0.812218\pi$
$492$	−5.87351e8	−0.222341
$493$	−2.52694e9	−0.949798
$494$	−3.14592e8	−0.117410
$495$	3.75437e9	1.39130
$496$	9.01491e8	0.331723
$497$	1.02663e9	0.375118
$498$	6.05126e9	2.19555
$499$	3.39355e9	1.22265	0.611326	−	0.791379i	$-0.290636\pi$
$499$	3.39355e9	1.22265	0.611326	+	0.791379i	$0.290636\pi$
$500$	−1.18051e9	−0.422352
$501$	−9.85094e9	−3.49982
$502$	3.06217e9	1.08035
$503$	4.26413e9	1.49397	0.746986	−	0.664840i	$-0.231500\pi$
$503$	4.26413e9	1.49397	0.746986	+	0.664840i	$0.231500\pi$
$504$	2.93945e9	1.02273
$505$	6.89537e6	0.00238253
$506$	−1.51206e9	−0.518852
$507$	−5.59683e9	−1.90728
$508$	−1.93946e6	−0.000656384 0
$509$	−4.85962e9	−1.63339	−0.816695	−	0.577070i	$-0.804196\pi$
$509$	−4.85962e9	−1.63339	−0.816695	+	0.577070i	$0.804196\pi$
$510$	−3.66279e9	−1.22269
$511$	−1.35557e8	−0.0449415
$512$	−1.34218e8	−0.0441942
$513$	−1.31577e10	−4.30299
$514$	−1.02501e9	−0.332932
$515$	−1.18592e9	−0.382587
$516$	4.74537e9	1.52053
$517$	−4.66498e9	−1.48468
$518$	−3.84177e8	−0.121444
$519$	−3.21550e9	−1.00963
$520$	7.15686e7	0.0223209
$521$	4.97824e8	0.154221	0.0771106	−	0.997023i	$-0.475431\pi$
$521$	4.97824e8	0.154221	0.0771106	+	0.997023i	$0.475431\pi$
$522$	3.23252e9	0.994705
$523$	3.00519e9	0.918579	0.459289	−	0.888287i	$-0.348104\pi$
$523$	3.00519e9	0.918579	0.459289	+	0.888287i	$0.348104\pi$
$524$	8.18686e8	0.248575
$525$	5.19820e9	1.56782
$526$	−1.22996e9	−0.368503
$527$	8.33500e9	2.48067
$528$	1.73135e9	0.511879
$529$	−1.75676e9	−0.515961
$530$	−1.49588e9	−0.436446
$531$	4.15707e9	1.20492
$532$	2.27304e9	0.654510
$533$	1.06109e8	0.0303534
$534$	−6.02451e9	−1.71209
$535$	3.09164e6	0.000872873 0
$536$	4.11628e6	0.00115459
$537$	3.88201e9	1.08180
$538$	−3.37016e9	−0.933066
$539$	3.50479e8	0.0964055
$540$	2.99334e9	0.818046
$541$	−2.61020e9	−0.708734	−0.354367	−	0.935106i	$-0.615304\pi$
$541$	−2.61020e9	−0.708734	−0.354367	+	0.935106i	$0.615304\pi$
$542$	−4.02239e9	−1.08514
$543$	−6.39498e9	−1.71411
$544$	−1.24095e9	−0.330490
$545$	−1.17420e9	−0.310709
$546$	−7.22815e8	−0.190044
$547$	6.31955e8	0.165094	0.0825468	−	0.996587i	$-0.473695\pi$
$547$	6.31955e8	0.165094	0.0825468	+	0.996587i	$0.473695\pi$
$548$	−2.84855e9	−0.739422
$549$	−1.41629e10	−3.65301
$550$	2.24940e9	0.576496
$551$	2.49967e9	0.636578
$552$	−1.88708e9	−0.477533
$553$	8.00333e8	0.201248
$554$	−2.56002e9	−0.639674
$555$	−6.12383e8	−0.152054
$556$	2.15361e8	0.0531379
$557$	3.22387e9	0.790468	0.395234	−	0.918580i	$-0.370663\pi$
$557$	3.22387e9	0.790468	0.395234	+	0.918580i	$0.370663\pi$
$558$	−1.06623e10	−2.59795
$559$	−8.57284e8	−0.207579
$560$	−5.17108e8	−0.124430
$561$	1.60077e10	3.82790
$562$	3.79393e9	0.901596
$563$	3.75859e9	0.887658	0.443829	−	0.896112i	$-0.353620\pi$
$563$	3.75859e9	0.887658	0.443829	+	0.896112i	$0.353620\pi$
$564$	−5.82197e9	−1.36645
$565$	−3.15359e9	−0.735589
$566$	4.25847e9	0.987178
$567$	−1.76757e10	−4.07227
$568$	5.54432e8	0.126949
$569$	3.16154e8	0.0719459	0.0359730	−	0.999353i	$-0.488547\pi$
$569$	3.16154e8	0.0719459	0.0359730	+	0.999353i	$0.488547\pi$
$570$	3.62325e9	0.819477
$571$	5.14375e9	1.15625	0.578127	−	0.815947i	$-0.303784\pi$
$571$	5.14375e9	1.15625	0.578127	+	0.815947i	$0.303784\pi$
$572$	−3.12781e8	−0.0698802
$573$	1.17816e10	2.61614
$574$	−7.66675e8	−0.169207
$575$	−2.45172e9	−0.537815
$576$	1.58745e9	0.346115
$577$	2.95737e8	0.0640900	0.0320450	−	0.999486i	$-0.489798\pi$
$577$	2.95737e8	0.0640900	0.0320450	+	0.999486i	$0.489798\pi$
$578$	−8.19086e9	−1.76434
$579$	4.62582e9	0.990408
$580$	−5.68665e8	−0.121020
$581$	7.89876e9	1.67087
$582$	−2.95238e9	−0.620785
$583$	6.53753e9	1.36639
$584$	−7.32072e7	−0.0152093
$585$	−8.46472e8	−0.174810
$586$	1.72642e9	0.354410
$587$	1.01541e9	0.207209	0.103604	−	0.994619i	$-0.466962\pi$
$587$	1.01541e9	0.207209	0.103604	+	0.994619i	$0.466962\pi$
$588$	4.37404e8	0.0887283
$589$	−8.24502e9	−1.66260
$590$	−7.31312e8	−0.146596
$591$	−1.64069e8	−0.0326942
$592$	−2.07475e8	−0.0410997
$593$	−3.96291e9	−0.780409	−0.390205	−	0.920728i	$-0.627596\pi$
$593$	−3.96291e9	−0.780409	−0.390205	+	0.920728i	$0.627596\pi$
$594$	−1.30820e10	−2.56107
$595$	−4.78108e9	−0.930500
$596$	−2.40394e9	−0.465117
$597$	4.32063e9	0.831068
$598$	3.40914e8	0.0651915
$599$	9.42097e9	1.79103	0.895513	−	0.445036i	$-0.146809\pi$
$599$	9.42097e9	1.79103	0.895513	+	0.445036i	$0.146809\pi$
$600$	2.80728e9	0.530587
$601$	3.58702e8	0.0674021	0.0337010	−	0.999432i	$-0.489271\pi$
$601$	3.58702e8	0.0674021	0.0337010	+	0.999432i	$0.489271\pi$
$602$	6.19418e9	1.15717
$603$	−4.86849e7	−0.00904240
$604$	−4.90471e9	−0.905699
$605$	2.91515e8	0.0535202
$606$	−3.76093e7	−0.00686501
$607$	6.29066e9	1.14166	0.570829	−	0.821069i	$-0.306622\pi$
$607$	6.29066e9	1.14166	0.570829	+	0.821069i	$0.306622\pi$
$608$	1.22755e9	0.221502
$609$	5.74330e9	1.03039
$610$	2.49155e9	0.444441
$611$	1.05178e9	0.186544
$612$	1.46772e10	2.58830
$613$	3.78212e9	0.663168	0.331584	−	0.943426i	$-0.392417\pi$
$613$	3.78212e9	0.663168	0.331584	+	0.943426i	$0.392417\pi$
$614$	4.77674e9	0.832803
$615$	−1.22209e9	−0.211855
$616$	2.25995e9	0.389553
$617$	−2.05900e9	−0.352905	−0.176452	−	0.984309i	$-0.556462\pi$
$617$	−2.05900e9	−0.352905	−0.176452	+	0.984309i	$0.556462\pi$
$618$	6.46834e9	1.10239
$619$	1.93114e9	0.327263	0.163632	−	0.986522i	$-0.447679\pi$
$619$	1.93114e9	0.327263	0.163632	+	0.986522i	$0.447679\pi$
$620$	1.87571e9	0.316079
$621$	1.42587e10	2.38923
$622$	−1.90434e9	−0.317306
$623$	−7.86386e9	−1.30295
$624$	−3.90356e8	−0.0643153
$625$	2.26190e9	0.370590
$626$	−2.61690e9	−0.426360
$627$	−1.58349e10	−2.56555
$628$	−2.45236e9	−0.395116
$629$	−1.91827e9	−0.307349
$630$	6.11606e9	0.974495
$631$	1.64426e9	0.260537	0.130268	−	0.991479i	$-0.458416\pi$
$631$	1.64426e9	0.260537	0.130268	+	0.991479i	$0.458416\pi$
$632$	4.32219e8	0.0681074
$633$	−4.58307e9	−0.718197
$634$	6.66462e9	1.03864
$635$	−4.03539e6	−0.000625429 0
$636$	8.15894e9	1.25757
$637$	−7.90201e7	−0.0121129
$638$	2.48527e9	0.378880
$639$	−6.55750e9	−0.994226
$640$	−2.79264e8	−0.0421100
$641$	−1.79601e9	−0.269344	−0.134672	−	0.990890i	$-0.542998\pi$
$641$	−1.79601e9	−0.269344	−0.134672	+	0.990890i	$0.542998\pi$
$642$	−1.68627e7	−0.00251510
$643$	6.06484e9	0.899666	0.449833	−	0.893113i	$-0.351484\pi$
$643$	6.06484e9	0.899666	0.449833	+	0.893113i	$0.351484\pi$
$644$	−2.46323e9	−0.363416
$645$	9.87359e9	1.44883
$646$	1.13497e10	1.65642
$647$	−8.83053e9	−1.28180	−0.640902	−	0.767622i	$-0.721440\pi$
$647$	−8.83053e9	−1.28180	−0.640902	+	0.767622i	$0.721440\pi$
$648$	−9.54577e9	−1.37816
$649$	3.19610e9	0.458949
$650$	−5.07155e8	−0.0724342
$651$	−1.89440e10	−2.69115
$652$	2.69334e9	0.380562
$653$	1.00013e10	1.40560	0.702800	−	0.711388i	$-0.251933\pi$
$653$	1.00013e10	1.40560	0.702800	+	0.711388i	$0.251933\pi$
$654$	6.40441e9	0.895276
$655$	1.70342e9	0.236852
$656$	−4.14042e8	−0.0572639
$657$	8.65852e8	0.119115
$658$	−7.59947e9	−1.03990
$659$	−4.00313e9	−0.544880	−0.272440	−	0.962173i	$-0.587831\pi$
$659$	−4.00313e9	−0.544880	−0.272440	+	0.962173i	$0.587831\pi$
$660$	3.60239e9	0.487739
$661$	1.12552e10	1.51582	0.757910	−	0.652359i	$-0.226221\pi$
$661$	1.12552e10	1.51582	0.757910	+	0.652359i	$0.226221\pi$
$662$	3.89107e9	0.521274
$663$	−3.60915e9	−0.480958
$664$	4.26572e9	0.565463
$665$	4.72947e9	0.623644
$666$	2.45389e9	0.321881
$667$	−2.70881e9	−0.353459
$668$	−6.94424e9	−0.901378
$669$	1.22097e10	1.57657
$670$	8.56465e6	0.00110014
$671$	−1.08890e10	−1.39142
$672$	2.82046e9	0.358531
$673$	−1.10405e10	−1.39616	−0.698080	−	0.716020i	$-0.745962\pi$
$673$	−1.10405e10	−1.39616	−0.698080	+	0.716020i	$0.745962\pi$
$674$	7.79431e9	0.980547
$675$	−2.12116e10	−2.65467
$676$	−3.94538e9	−0.491220
$677$	−5.08333e9	−0.629634	−0.314817	−	0.949152i	$-0.601943\pi$
$677$	−5.08333e9	−0.629634	−0.314817	+	0.949152i	$0.601943\pi$
$678$	1.72006e10	2.11953
$679$	−3.85377e9	−0.472434
$680$	−2.58202e9	−0.314904
$681$	1.65712e10	2.01067
$682$	−8.19755e9	−0.989552
$683$	−4.62507e9	−0.555451	−0.277725	−	0.960661i	$-0.589581\pi$
$683$	−4.62507e9	−0.555451	−0.277725	+	0.960661i	$0.589581\pi$
$684$	−1.45188e10	−1.73474
$685$	−5.92692e9	−0.704551
$686$	−5.67521e9	−0.671193
$687$	1.41366e10	1.66340
$688$	3.34516e9	0.391613
$689$	−1.47397e9	−0.171681
$690$	−3.92641e9	−0.455013
$691$	−1.38457e10	−1.59640	−0.798200	−	0.602393i	$-0.794214\pi$
$691$	−1.38457e10	−1.59640	−0.798200	+	0.602393i	$0.794214\pi$
$692$	−2.26670e9	−0.260030
$693$	−2.67294e10	−3.05086
$694$	−6.89245e9	−0.782736
$695$	4.48096e8	0.0506319
$696$	3.10166e9	0.348708
$697$	−3.82815e9	−0.428227
$698$	−1.04775e10	−1.16618
$699$	6.19597e9	0.686181
$700$	3.66437e9	0.403791
$701$	1.30053e10	1.42596	0.712980	−	0.701184i	$-0.247345\pi$
$701$	1.30053e10	1.42596	0.712980	+	0.701184i	$0.247345\pi$
$702$	2.94950e9	0.321787
$703$	1.89756e9	0.205993
$704$	1.22049e9	0.131834
$705$	−1.21136e10	−1.30201
$706$	7.01936e9	0.750725
$707$	−4.90918e7	−0.00522446
$708$	3.98879e9	0.422401
$709$	−1.83890e10	−1.93774	−0.968872	−	0.247564i	$-0.920370\pi$
$709$	−1.83890e10	−1.93774	−0.968872	+	0.247564i	$0.920370\pi$
$710$	1.15360e9	0.120962
$711$	−5.11203e9	−0.533396
$712$	−4.24687e9	−0.440950
$713$	8.93488e9	0.923157
$714$	2.60774e10	2.68114
$715$	−6.50797e8	−0.0665847
$716$	2.73655e9	0.278617
$717$	−1.45181e10	−1.47093
$718$	−1.19833e10	−1.20821
$719$	1.56639e9	0.157162	0.0785811	−	0.996908i	$-0.474961\pi$
$719$	1.56639e9	0.157162	0.0785811	+	0.996908i	$0.474961\pi$
$720$	3.30297e9	0.329793
$721$	8.44319e9	0.838945
$722$	−4.07622e9	−0.403067
$723$	2.23848e10	2.20277
$724$	−4.50802e9	−0.441470
$725$	4.02972e9	0.392728
$726$	−1.59001e9	−0.154213
$727$	−1.22967e10	−1.18691	−0.593456	−	0.804867i	$-0.702237\pi$
$727$	−1.22967e10	−1.18691	−0.593456	+	0.804867i	$0.702237\pi$
$728$	−5.09535e8	−0.0489457
$729$	4.31633e10	4.12637
$730$	−1.52321e8	−0.0144920
$731$	3.09287e10	2.92854
$732$	−1.35896e10	−1.28061
$733$	−8.41188e9	−0.788913	−0.394456	−	0.918915i	$-0.629067\pi$
$733$	−8.41188e9	−0.788913	−0.394456	+	0.918915i	$0.629067\pi$
$734$	1.12576e10	1.05077
$735$	9.10097e8	0.0845439
$736$	−1.33026e9	−0.122989
$737$	−3.74307e7	−0.00344422
$738$	4.89705e9	0.448474
$739$	4.83992e9	0.441147	0.220573	−	0.975370i	$-0.429207\pi$
$739$	4.83992e9	0.441147	0.220573	+	0.975370i	$0.429207\pi$
$740$	−4.31688e8	−0.0391615
$741$	3.57019e9	0.322350
$742$	1.06499e10	0.957048
$743$	5.87021e8	0.0525040	0.0262520	−	0.999655i	$-0.491643\pi$
$743$	5.87021e8	0.0525040	0.0262520	+	0.999655i	$0.491643\pi$
$744$	−1.02307e10	−0.910750
$745$	−5.00184e9	−0.443182
$746$	5.43826e9	0.479595
$747$	−5.04524e10	−4.42854
$748$	1.12844e10	0.985874
$749$	−2.20111e7	−0.00191406
$750$	1.33972e10	1.15957
$751$	−2.24897e9	−0.193751	−0.0968753	−	0.995297i	$-0.530885\pi$
$751$	−2.24897e9	−0.193751	−0.0968753	+	0.995297i	$0.530885\pi$
$752$	−4.10409e9	−0.351928
$753$	−3.47514e10	−2.96613
$754$	−5.60337e8	−0.0476047
$755$	−1.02051e10	−0.862986
$756$	−2.13112e10	−1.79383
$757$	−1.99556e10	−1.67197	−0.835985	−	0.548752i	$-0.815103\pi$
$757$	−1.99556e10	−1.67197	−0.835985	+	0.548752i	$0.815103\pi$
$758$	−1.53008e10	−1.27606
$759$	1.71598e10	1.42452
$760$	2.55415e9	0.211056
$761$	−5.23703e9	−0.430764	−0.215382	−	0.976530i	$-0.569100\pi$
$761$	−5.23703e9	−0.430764	−0.215382	+	0.976530i	$0.569100\pi$
$762$	2.20102e7	0.00180211
$763$	8.35974e9	0.681329
$764$	8.30519e9	0.673788
$765$	3.05386e10	2.46623
$766$	−1.16226e10	−0.934337
$767$	−7.20602e8	−0.0576649
$768$	1.52319e9	0.121336
$769$	−7.11248e9	−0.564000	−0.282000	−	0.959414i	$-0.590998\pi$
$769$	−7.11248e9	−0.564000	−0.282000	+	0.959414i	$0.590998\pi$
$770$	4.70224e9	0.371182
$771$	1.16324e10	0.914070
$772$	3.26089e9	0.255079
$773$	5.47777e9	0.426556	0.213278	−	0.976992i	$-0.431586\pi$
$773$	5.47777e9	0.426556	0.213278	+	0.976992i	$0.431586\pi$
$774$	−3.95646e10	−3.06700
$775$	−1.32918e10	−1.02572
$776$	−2.08122e9	−0.159883
$777$	4.35988e9	0.333427
$778$	7.83059e9	0.596164
$779$	3.78682e9	0.287008
$780$	−8.12205e8	−0.0612822
$781$	−5.04163e9	−0.378698
$782$	−1.22993e10	−0.919725
$783$	−2.34359e10	−1.74468
$784$	3.08340e8	0.0228520
$785$	−5.10257e9	−0.376483
$786$	−9.29096e9	−0.682467
$787$	−1.97867e10	−1.44698	−0.723488	−	0.690337i	$-0.757462\pi$
$787$	−1.97867e10	−1.44698	−0.723488	+	0.690337i	$0.757462\pi$
$788$	−1.15658e8	−0.00842039
$789$	1.39584e10	1.01173
$790$	8.99309e8	0.0648954
$791$	2.24521e10	1.61302
$792$	−1.44352e10	−1.03249
$793$	2.45506e9	0.174826
$794$	1.09750e10	0.778096
$795$	1.69761e10	1.19827
$796$	3.04575e9	0.214041
$797$	−1.91992e10	−1.34332	−0.671661	−	0.740859i	$-0.734419\pi$
$797$	−1.91992e10	−1.34332	−0.671661	+	0.740859i	$0.734419\pi$
$798$	−2.57959e10	−1.79697
$799$	−3.79456e10	−2.63177
$800$	1.97894e9	0.136653
$801$	5.02295e10	3.45338
$802$	−2.75831e9	−0.188813
$803$	6.65697e8	0.0453704
$804$	−4.67141e7	−0.00316994
$805$	−5.12518e9	−0.346277
$806$	1.84824e9	0.124333
$807$	3.82467e10	2.56175
$808$	−2.65120e7	−0.00176808
$809$	9.47189e8	0.0628951	0.0314476	−	0.999505i	$-0.489988\pi$
$809$	9.47189e8	0.0628951	0.0314476	+	0.999505i	$0.489988\pi$
$810$	−1.98617e10	−1.31316
$811$	−1.41110e9	−0.0928931	−0.0464466	−	0.998921i	$-0.514790\pi$
$811$	−1.41110e9	−0.0928931	−0.0464466	+	0.998921i	$0.514790\pi$
$812$	4.04863e9	0.265376
$813$	4.56486e10	2.97928
$814$	1.88664e9	0.122603
$815$	5.60398e9	0.362614
$816$	1.40831e10	0.907364
$817$	−3.05948e10	−1.96278
$818$	−4.34546e9	−0.277587
$819$	6.02649e9	0.383328
$820$	−8.61488e8	−0.0545633
$821$	2.01870e7	0.00127313	0.000636563	−	1.00000i	$-0.499797\pi$
$821$	2.01870e7	0.00127313	0.000636563		1.00000i	$0.499797\pi$
$822$	3.23271e10	2.03009
$823$	−2.14990e9	−0.134437	−0.0672185	−	0.997738i	$-0.521412\pi$
$823$	−2.14990e9	−0.134437	−0.0672185	+	0.997738i	$0.521412\pi$
$824$	4.55974e9	0.283919
$825$	−2.55275e10	−1.58278
$826$	5.20660e9	0.321458
$827$	1.71093e10	1.05187	0.525937	−	0.850524i	$-0.323715\pi$
$827$	1.71093e10	1.05187	0.525937	+	0.850524i	$0.323715\pi$
$828$	1.57336e10	0.963210
$829$	−7.25127e8	−0.0442052	−0.0221026	−	0.999756i	$-0.507036\pi$
$829$	−7.25127e8	−0.0442052	−0.0221026	+	0.999756i	$0.507036\pi$
$830$	8.87560e9	0.538796
$831$	2.90527e10	1.75623
$832$	−2.75174e8	−0.0165644
$833$	2.85085e9	0.170890
$834$	−2.44405e9	−0.145891
$835$	−1.44487e10	−0.858869
$836$	−1.11626e10	−0.660757
$837$	7.73023e10	4.55673
$838$	−1.75735e10	−1.03158
$839$	1.09113e9	0.0637839	0.0318920	−	0.999491i	$-0.489847\pi$
$839$	1.09113e9	0.0637839	0.0318920	+	0.999491i	$0.489847\pi$
$840$	5.86847e9	0.341623
$841$	−1.27976e10	−0.741895
$842$	−1.35626e10	−0.782980
$843$	−4.30558e10	−2.47534
$844$	−3.23075e9	−0.184972
$845$	−8.20908e9	−0.468054
$846$	4.85408e10	2.75620
$847$	−2.07545e9	−0.117360
$848$	5.75149e9	0.323888
$849$	−4.83277e10	−2.71031
$850$	1.82969e10	1.02191
$851$	−2.05633e9	−0.114377
$852$	−6.29204e9	−0.348540
$853$	1.53367e10	0.846076	0.423038	−	0.906112i	$-0.360964\pi$
$853$	1.53367e10	0.846076	0.423038	+	0.906112i	$0.360964\pi$
$854$	−1.77386e10	−0.974581
$855$	−3.02089e10	−1.65293
$856$	−1.18871e7	−0.000647763 0
$857$	−1.85211e10	−1.00516	−0.502578	−	0.864532i	$-0.667615\pi$
$857$	−1.85211e10	−1.00516	−0.502578	+	0.864532i	$0.667615\pi$
$858$	3.54963e9	0.191857
$859$	−8.76910e6	−0.000472040 0	−0.000236020	−	1.00000i	$-0.500075\pi$
$859$	−8.76910e6	−0.000472040 0	−0.000236020		1.00000i	$0.500075\pi$
$860$	6.96021e9	0.373145
$861$	8.70070e9	0.464561
$862$	4.95935e9	0.263724
$863$	−1.82668e10	−0.967443	−0.483721	−	0.875222i	$-0.660715\pi$
$863$	−1.82668e10	−0.967443	−0.483721	+	0.875222i	$0.660715\pi$
$864$	−1.15091e10	−0.607076
$865$	−4.71628e9	−0.247767
$866$	−2.15900e10	−1.12964
$867$	9.29549e10	4.84402
$868$	−1.33542e10	−0.693105
$869$	−3.93031e9	−0.203169
$870$	6.45356e9	0.332263
$871$	8.43922e6	0.000432752 0
$872$	4.51467e9	0.230578
$873$	2.46155e10	1.25216
$874$	1.21666e10	0.616422
$875$	1.74874e10	0.882466
$876$	8.30801e8	0.0417573
$877$	−2.99806e10	−1.50086	−0.750432	−	0.660948i	$-0.770154\pi$
$877$	−2.99806e10	−1.50086	−0.750432	+	0.660948i	$0.770154\pi$
$878$	1.24412e10	0.620342
$879$	−1.95925e10	−0.973037
$880$	2.53944e9	0.125617
$881$	3.82446e8	0.0188432	0.00942160	−	0.999956i	$-0.497001\pi$
$881$	3.82446e8	0.0188432	0.00942160	+	0.999956i	$0.497001\pi$
$882$	−3.64686e9	−0.178970
$883$	−5.12232e9	−0.250382	−0.125191	−	0.992133i	$-0.539954\pi$
$883$	−5.12232e9	−0.250382	−0.125191	+	0.992133i	$0.539954\pi$
$884$	−2.54420e9	−0.123871
$885$	8.29939e9	0.402480
$886$	−7.25030e9	−0.350218
$887$	2.34581e10	1.12865	0.564326	−	0.825552i	$-0.309136\pi$
$887$	2.34581e10	1.12865	0.564326	+	0.825552i	$0.309136\pi$
$888$	2.35455e9	0.112840
$889$	2.87301e7	0.00137145
$890$	−8.83637e9	−0.420154
$891$	8.68028e10	4.11114
$892$	8.60697e9	0.406044
$893$	3.75360e10	1.76387
$894$	2.72814e10	1.27699
$895$	5.69389e9	0.265478
$896$	1.98823e9	0.0923397
$897$	−3.86891e9	−0.178984
$898$	−3.74561e9	−0.172606
$899$	−1.46856e10	−0.674115
$900$	−2.34058e10	−1.07022
$901$	5.31771e10	2.42208
$902$	3.76502e9	0.170822
$903$	−7.02954e10	−3.17702
$904$	1.21252e10	0.545884
$905$	−9.37975e9	−0.420650
$906$	5.56617e10	2.48661
$907$	2.54092e10	1.13075	0.565373	−	0.824835i	$-0.308732\pi$
$907$	2.54092e10	1.13075	0.565373	+	0.824835i	$0.308732\pi$
$908$	1.16816e10	0.517847
$909$	3.13568e8	0.0138471
$910$	−1.06018e9	−0.0466374
$911$	7.96177e9	0.348895	0.174448	−	0.984666i	$-0.444186\pi$
$911$	7.96177e9	0.348895	0.174448	+	0.984666i	$0.444186\pi$
$912$	−1.39310e10	−0.608137
$913$	−3.87896e10	−1.68682
$914$	5.56173e9	0.240934
$915$	−2.82756e10	−1.22022
$916$	9.96533e9	0.428408
$917$	−1.21276e10	−0.519375
$918$	−1.06411e11	−4.53979
$919$	2.30253e10	0.978588	0.489294	−	0.872119i	$-0.337254\pi$
$919$	2.30253e10	0.978588	0.489294	+	0.872119i	$0.337254\pi$
$920$	−2.76785e9	−0.117189
$921$	−5.42094e10	−2.28647
$922$	−3.27997e9	−0.137820
$923$	1.13670e9	0.0475817
$924$	−2.56474e10	−1.06952
$925$	3.05906e9	0.127084
$926$	1.08424e10	0.448730
$927$	−5.39299e10	−2.22357
$928$	2.18646e9	0.0898097
$929$	3.32878e10	1.36217	0.681083	−	0.732206i	$-0.261509\pi$
$929$	3.32878e10	1.36217	0.681083	+	0.732206i	$0.261509\pi$
$930$	−2.12867e10	−0.867799
$931$	−2.82007e9	−0.114535
$932$	4.36773e9	0.176726
$933$	2.16116e10	0.871167
$934$	5.81582e9	0.233559
$935$	2.34791e10	0.939380
$936$	3.25460e9	0.129727
$937$	1.77970e10	0.706737	0.353369	−	0.935484i	$-0.385036\pi$
$937$	1.77970e10	0.706737	0.353369	+	0.935484i	$0.385036\pi$
$938$	−6.09763e7	−0.00241241
$939$	2.96982e10	1.17058
$940$	−8.53929e9	−0.335331
$941$	−3.32182e10	−1.29961	−0.649803	−	0.760102i	$-0.725149\pi$
$941$	−3.32182e10	−1.29961	−0.649803	+	0.760102i	$0.725149\pi$
$942$	2.78309e10	1.08480
$943$	−4.10367e9	−0.159361
$944$	2.81182e9	0.108789
$945$	−4.43417e10	−1.70923
$946$	−3.04186e10	−1.16821
$947$	1.50372e10	0.575364	0.287682	−	0.957726i	$-0.407115\pi$
$947$	1.50372e10	0.575364	0.287682	+	0.957726i	$0.407115\pi$
$948$	−4.90509e9	−0.186990
$949$	−1.50090e8	−0.00570059
$950$	−1.80994e10	−0.684906
$951$	−7.56342e10	−2.85159
$952$	1.83828e10	0.690528
$953$	−1.27447e10	−0.476983	−0.238492	−	0.971145i	$-0.576653\pi$
$953$	−1.27447e10	−0.476983	−0.238492	+	0.971145i	$0.576653\pi$
$954$	−6.80253e10	−2.53659
$955$	1.72804e10	0.642012
$956$	−1.02343e10	−0.378838
$957$	−2.82044e10	−1.04022
$958$	−1.72832e10	−0.635106
$959$	4.21969e10	1.54496
$960$	3.16926e9	0.115614
$961$	2.09272e10	0.760640
$962$	−4.25366e8	−0.0154046
$963$	1.40593e8	0.00507308
$964$	1.57797e10	0.567323
$965$	6.78486e9	0.243050
$966$	2.79542e10	0.997763
$967$	2.50300e10	0.890161	0.445080	−	0.895491i	$-0.353175\pi$
$967$	2.50300e10	0.890161	0.445080	+	0.895491i	$0.353175\pi$
$968$	−1.12085e9	−0.0397176
$969$	−1.28804e11	−4.54773
$970$	−4.33036e9	−0.152343
$971$	1.01634e10	0.356265	0.178132	−	0.984007i	$-0.442994\pi$
$971$	1.01634e10	0.356265	0.178132	+	0.984007i	$0.442994\pi$
$972$	5.91704e10	2.06668
$973$	−3.19024e9	−0.111027
$974$	7.27352e8	0.0252225
$975$	5.75551e9	0.198869
$976$	−9.57974e9	−0.329822
$977$	3.59483e10	1.23324	0.616620	−	0.787261i	$-0.288502\pi$
$977$	3.59483e10	1.23324	0.616620	+	0.787261i	$0.288502\pi$
$978$	−3.05657e10	−1.04484
$979$	3.86182e10	1.31538
$980$	6.41556e8	0.0217743
$981$	−5.33969e10	−1.80582
$982$	3.48734e10	1.17518
$983$	2.69073e10	0.903510	0.451755	−	0.892142i	$-0.350798\pi$
$983$	2.69073e10	0.903510	0.451755	+	0.892142i	$0.350798\pi$
$984$	4.69881e9	0.157219
$985$	−2.40646e8	−0.00802328
$986$	2.02156e10	0.671609
$987$	8.62435e10	2.85507
$988$	2.51674e9	0.0830212
$989$	3.31547e10	1.08983
$990$	−3.00350e10	−0.983795
$991$	−1.91531e10	−0.625147	−0.312573	−	0.949894i	$-0.601191\pi$
$991$	−1.91531e10	−0.625147	−0.312573	+	0.949894i	$0.601191\pi$
$992$	−7.21192e9	−0.234563
$993$	−4.41582e10	−1.43116
$994$	−8.21306e9	−0.265248
$995$	6.33722e9	0.203947
$996$	−4.84100e10	−1.55249
$997$	−2.26750e10	−0.724625	−0.362313	−	0.932057i	$-0.618013\pi$
$997$	−2.26750e10	−0.724625	−0.362313	+	0.932057i	$0.618013\pi$
$998$	−2.71484e10	−0.864545
$999$	−1.77908e10	−0.564569

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.a.c.1.6	✓	6
4.3	odd	2		592.8.a.c.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.a.c.1.6	✓	6	1.1	even	1	trivial
592.8.a.c.1.1		6	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +90.7890 q^{3} +64.0000 q^{4} +133.163 q^{5} -726.312 q^{6} -948.062 q^{7} -512.000 q^{8} +6055.64 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +90.7890 q^{3} +64.0000 q^{4} +133.163 q^{5} -726.312 q^{6} -948.062 q^{7} -512.000 q^{8} +6055.64 q^{9} -1065.31 q^{10} +4655.78 q^{11} +5810.49 q^{12} -1049.71 q^{13} +7584.49 q^{14} +12089.8 q^{15} +4096.00 q^{16} +37870.8 q^{17} -48445.1 q^{18} -37462.0 q^{19} +8522.46 q^{20} -86073.6 q^{21} -37246.3 q^{22} +40596.4 q^{23} -46483.9 q^{24} -60392.5 q^{25} +8397.65 q^{26} +351229. q^{27} -60676.0 q^{28} -66725.4 q^{29} -96718.2 q^{30} +220090. q^{31} -32768.0 q^{32} +422694. q^{33} -302966. q^{34} -126247. q^{35} +387561. q^{36} -50653.0 q^{37} +299696. q^{38} -95301.7 q^{39} -68179.7 q^{40} -101084. q^{41} +688588. q^{42} +816690. q^{43} +297970. q^{44} +806389. q^{45} -324771. q^{46} -1.00197e6 q^{47} +371872. q^{48} +75278.3 q^{49} +483140. q^{50} +3.43825e6 q^{51} -67181.2 q^{52} +1.40417e6 q^{53} -2.80984e6 q^{54} +619980. q^{55} +485408. q^{56} -3.40113e6 q^{57} +533804. q^{58} +686480. q^{59} +773745. q^{60} -2.33880e6 q^{61} -1.76072e6 q^{62} -5.74112e6 q^{63} +262144. q^{64} -139782. q^{65} -3.38155e6 q^{66} -8039.60 q^{67} +2.42373e6 q^{68} +3.68571e6 q^{69} +1.00998e6 q^{70} -1.08288e6 q^{71} -3.10049e6 q^{72} +142983. q^{73} +405224. q^{74} -5.48297e6 q^{75} -2.39757e6 q^{76} -4.41397e6 q^{77} +762414. q^{78} -844178. q^{79} +545437. q^{80} +1.86441e7 q^{81} +808676. q^{82} -8.33149e6 q^{83} -5.50871e6 q^{84} +5.04300e6 q^{85} -6.53352e6 q^{86} -6.05793e6 q^{87} -2.38376e6 q^{88} +8.29467e6 q^{89} -6.45112e6 q^{90} +995186. q^{91} +2.59817e6 q^{92} +1.99818e7 q^{93} +8.01580e6 q^{94} -4.98857e6 q^{95} -2.97497e6 q^{96} +4.06489e6 q^{97} -602226. q^{98} +2.81937e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9} + 112 q^{10} + 2956 q^{11} + 1792 q^{12} + 2394 q^{13} + 7840 q^{14} - 28820 q^{15} + 24576 q^{16} - 45108 q^{17} - 66032 q^{18} + 11764 q^{19} - 896 q^{20} - 135378 q^{21} - 23648 q^{22} + 21052 q^{23} - 14336 q^{24} + 194744 q^{25} - 19152 q^{26} + 439240 q^{27} - 62720 q^{28} + 288454 q^{29} + 230560 q^{30} + 578868 q^{31} - 196608 q^{32} + 980174 q^{33} + 360864 q^{34} + 1243052 q^{35} + 528256 q^{36} - 303918 q^{37} - 94112 q^{38} + 1735296 q^{39} + 7168 q^{40} + 1176840 q^{41} + 1083024 q^{42} + 2669236 q^{43} + 189184 q^{44} + 2560692 q^{45} - 168416 q^{46} - 131044 q^{47} + 114688 q^{48} + 2460856 q^{49} - 1557952 q^{50} + 2899732 q^{51} + 153216 q^{52} + 983190 q^{53} - 3513920 q^{54} - 1200168 q^{55} + 501760 q^{56} - 163216 q^{57} - 2307632 q^{58} - 1215568 q^{59} - 1844480 q^{60} + 3136358 q^{61} - 4630944 q^{62} - 1444880 q^{63} + 1572864 q^{64} - 1302836 q^{65} - 7841392 q^{66} + 2179276 q^{67} - 2886912 q^{68} - 929514 q^{69} - 9944416 q^{70} + 325164 q^{71} - 4226048 q^{72} + 5011444 q^{73} + 2431344 q^{74} - 9374520 q^{75} + 752896 q^{76} - 26500426 q^{77} - 13882368 q^{78} + 3173032 q^{79} - 57344 q^{80} - 2565226 q^{81} - 9414720 q^{82} - 22567048 q^{83} - 8664192 q^{84} + 1486476 q^{85} - 21353888 q^{86} - 157228 q^{87} - 1513472 q^{88} + 26836996 q^{89} - 20485536 q^{90} + 17942380 q^{91} + 1347328 q^{92} + 16734948 q^{93} + 1048352 q^{94} - 4252048 q^{95} - 917504 q^{96} + 295792 q^{97} - 19686848 q^{98} + 25990712 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9 + 112 * q^10 + 2956 * q^11 + 1792 * q^12 + 2394 * q^13 + 7840 * q^14 - 28820 * q^15 + 24576 * q^16 - 45108 * q^17 - 66032 * q^18 + 11764 * q^19 - 896 * q^20 - 135378 * q^21 - 23648 * q^22 + 21052 * q^23 - 14336 * q^24 + 194744 * q^25 - 19152 * q^26 + 439240 * q^27 - 62720 * q^28 + 288454 * q^29 + 230560 * q^30 + 578868 * q^31 - 196608 * q^32 + 980174 * q^33 + 360864 * q^34 + 1243052 * q^35 + 528256 * q^36 - 303918 * q^37 - 94112 * q^38 + 1735296 * q^39 + 7168 * q^40 + 1176840 * q^41 + 1083024 * q^42 + 2669236 * q^43 + 189184 * q^44 + 2560692 * q^45 - 168416 * q^46 - 131044 * q^47 + 114688 * q^48 + 2460856 * q^49 - 1557952 * q^50 + 2899732 * q^51 + 153216 * q^52 + 983190 * q^53 - 3513920 * q^54 - 1200168 * q^55 + 501760 * q^56 - 163216 * q^57 - 2307632 * q^58 - 1215568 * q^59 - 1844480 * q^60 + 3136358 * q^61 - 4630944 * q^62 - 1444880 * q^63 + 1572864 * q^64 - 1302836 * q^65 - 7841392 * q^66 + 2179276 * q^67 - 2886912 * q^68 - 929514 * q^69 - 9944416 * q^70 + 325164 * q^71 - 4226048 * q^72 + 5011444 * q^73 + 2431344 * q^74 - 9374520 * q^75 + 752896 * q^76 - 26500426 * q^77 - 13882368 * q^78 + 3173032 * q^79 - 57344 * q^80 - 2565226 * q^81 - 9414720 * q^82 - 22567048 * q^83 - 8664192 * q^84 + 1486476 * q^85 - 21353888 * q^86 - 157228 * q^87 - 1513472 * q^88 + 26836996 * q^89 - 20485536 * q^90 + 17942380 * q^91 + 1347328 * q^92 + 16734948 * q^93 + 1048352 * q^94 - 4252048 * q^95 - 917504 * q^96 + 295792 * q^97 - 19686848 * q^98 + 25990712 * q^99

Introduction

L-functions

Modular forms

Varieties

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