LMFDB - Embedded newform 74.8.a.c.1.4

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			1.4
Root			$-26.0193$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} +31.0193 q^{3} +64.0000 q^{4} -544.510 q^{5} -248.154 q^{6} -1685.44 q^{7} -512.000 q^{8} -1224.80 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +31.0193 q^{3} +64.0000 q^{4} -544.510 q^{5} -248.154 q^{6} -1685.44 q^{7} -512.000 q^{8} -1224.80 q^{9} +4356.08 q^{10} +5629.72 q^{11} +1985.23 q^{12} +5228.81 q^{13} +13483.5 q^{14} -16890.3 q^{15} +4096.00 q^{16} -12575.5 q^{17} +9798.43 q^{18} +18367.1 q^{19} -34848.6 q^{20} -52281.0 q^{21} -45037.7 q^{22} +40252.9 q^{23} -15881.9 q^{24} +218366. q^{25} -41830.5 q^{26} -105832. q^{27} -107868. q^{28} +18705.8 q^{29} +135123. q^{30} -169281. q^{31} -32768.0 q^{32} +174630. q^{33} +100604. q^{34} +917737. q^{35} -78387.4 q^{36} -50653.0 q^{37} -146937. q^{38} +162194. q^{39} +278789. q^{40} -26437.9 q^{41} +418248. q^{42} +406992. q^{43} +360302. q^{44} +666918. q^{45} -322024. q^{46} +175342. q^{47} +127055. q^{48} +2.01715e6 q^{49} -1.74693e6 q^{50} -390084. q^{51} +334644. q^{52} -1.82314e6 q^{53} +846654. q^{54} -3.06544e6 q^{55} +862943. q^{56} +569735. q^{57} -149646. q^{58} -1.24173e6 q^{59} -1.08098e6 q^{60} +3.25092e6 q^{61} +1.35425e6 q^{62} +2.06433e6 q^{63} +262144. q^{64} -2.84714e6 q^{65} -1.39704e6 q^{66} -1.66755e6 q^{67} -804834. q^{68} +1.24862e6 q^{69} -7.34189e6 q^{70} +262493. q^{71} +627099. q^{72} +2.68612e6 q^{73} +405224. q^{74} +6.77356e6 q^{75} +1.17550e6 q^{76} -9.48853e6 q^{77} -1.29755e6 q^{78} +363284. q^{79} -2.23031e6 q^{80} -604180. q^{81} +211503. q^{82} -6.71044e6 q^{83} -3.34599e6 q^{84} +6.84750e6 q^{85} -3.25594e6 q^{86} +580239. q^{87} -2.88241e6 q^{88} +1.16083e7 q^{89} -5.33534e6 q^{90} -8.81283e6 q^{91} +2.57619e6 q^{92} -5.25097e6 q^{93} -1.40274e6 q^{94} -1.00011e7 q^{95} -1.01644e6 q^{96} +1.63488e7 q^{97} -1.61372e7 q^{98} -6.89530e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	31.0193	0.663296	0.331648	−	0.943403i	$-0.392395\pi$
$3$	31.0193	0.663296	0.331648	+	0.943403i	$0.392395\pi$
$4$	64.0000	0.500000
$5$	−544.510	−1.94810	−0.974049	−	0.226337i	$-0.927325\pi$
$5$	−544.510	−1.94810	−0.974049	+	0.226337i	$0.927325\pi$
$6$	−248.154	−0.469021
$7$	−1685.44	−1.85724	−0.928622	−	0.371026i	$-0.879006\pi$
$7$	−1685.44	−1.85724	−0.928622	+	0.371026i	$0.879006\pi$
$8$	−512.000	−0.353553
$9$	−1224.80	−0.560038
$10$	4356.08	1.37751
$11$	5629.72	1.27530	0.637650	−	0.770327i	$-0.279907\pi$
$11$	5629.72	1.27530	0.637650	+	0.770327i	$0.279907\pi$
$12$	1985.23	0.331648
$13$	5228.81	0.660087	0.330044	−	0.943966i	$-0.392937\pi$
$13$	5228.81	0.660087	0.330044	+	0.943966i	$0.392937\pi$
$14$	13483.5	1.31327
$15$	−16890.3	−1.29217
$16$	4096.00	0.250000
$17$	−12575.5	−0.620805	−0.310402	−	0.950605i	$-0.600464\pi$
$17$	−12575.5	−0.620805	−0.310402	+	0.950605i	$0.600464\pi$
$18$	9798.43	0.396007
$19$	18367.1	0.614332	0.307166	−	0.951656i	$-0.400619\pi$
$19$	18367.1	0.614332	0.307166	+	0.951656i	$0.400619\pi$
$20$	−34848.6	−0.974049
$21$	−52281.0	−1.23190
$22$	−45037.7	−0.901773
$23$	40252.9	0.689843	0.344921	−	0.938632i	$-0.387906\pi$
$23$	40252.9	0.689843	0.344921	+	0.938632i	$0.387906\pi$
$24$	−15881.9	−0.234511
$25$	218366.	2.79509
$26$	−41830.5	−0.466752
$27$	−105832.	−1.03477
$28$	−107868.	−0.928622
$29$	18705.8	0.142424	0.0712118	−	0.997461i	$-0.477313\pi$
$29$	18705.8	0.142424	0.0712118	+	0.997461i	$0.477313\pi$
$30$	135123.	0.913699
$31$	−169281.	−1.02057	−0.510284	−	0.860006i	$-0.670460\pi$
$31$	−169281.	−1.02057	−0.510284	+	0.860006i	$0.670460\pi$
$32$	−32768.0	−0.176777
$33$	174630.	0.845901
$34$	100604.	0.438975
$35$	917737.	3.61809
$36$	−78387.4	−0.280019
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	−146937.	−0.434399
$39$	162194.	0.437833
$40$	278789.	0.688757
$41$	−26437.9	−0.0599078	−0.0299539	−	0.999551i	$-0.509536\pi$
$41$	−26437.9	−0.0599078	−0.0299539	+	0.999551i	$0.509536\pi$
$42$	418248.	0.871087
$43$	406992.	0.780632	0.390316	−	0.920681i	$-0.372366\pi$
$43$	406992.	0.780632	0.390316	+	0.920681i	$0.372366\pi$
$44$	360302.	0.637650
$45$	666918.	1.09101
$46$	−322024.	−0.487793
$47$	175342.	0.246345	0.123173	−	0.992385i	$-0.460693\pi$
$47$	175342.	0.246345	0.123173	+	0.992385i	$0.460693\pi$
$48$	127055.	0.165824
$49$	2.01715e6	2.44936
$50$	−1.74693e6	−1.97642
$51$	−390084.	−0.411778
$52$	334644.	0.330044
$53$	−1.82314e6	−1.68211	−0.841056	−	0.540949i	$-0.818065\pi$
$53$	−1.82314e6	−1.68211	−0.841056	+	0.540949i	$0.818065\pi$
$54$	846654.	0.731691
$55$	−3.06544e6	−2.48441
$56$	862943.	0.656635
$57$	569735.	0.407484
$58$	−149646.	−0.100709
$59$	−1.24173e6	−0.787131	−0.393565	−	0.919297i	$-0.628758\pi$
$59$	−1.24173e6	−0.787131	−0.393565	+	0.919297i	$0.628758\pi$
$60$	−1.08098e6	−0.646083
$61$	3.25092e6	1.83380	0.916899	−	0.399120i	$-0.130684\pi$
$61$	3.25092e6	1.83380	0.916899	+	0.399120i	$0.130684\pi$
$62$	1.35425e6	0.721651
$63$	2.06433e6	1.04013
$64$	262144.	0.125000
$65$	−2.84714e6	−1.28592
$66$	−1.39704e6	−0.598142
$67$	−1.66755e6	−0.677357	−0.338678	−	0.940902i	$-0.609980\pi$
$67$	−1.66755e6	−0.677357	−0.338678	+	0.940902i	$0.609980\pi$
$68$	−804834.	−0.310402
$69$	1.24862e6	0.457570
$70$	−7.34189e6	−2.55838
$71$	262493.	0.0870388	0.0435194	−	0.999053i	$-0.486143\pi$
$71$	262493.	0.0870388	0.0435194	+	0.999053i	$0.486143\pi$
$72$	627099.	0.198003
$73$	2.68612e6	0.808157	0.404078	−	0.914724i	$-0.367592\pi$
$73$	2.68612e6	0.808157	0.404078	+	0.914724i	$0.367592\pi$
$74$	405224.	0.116248
$75$	6.77356e6	1.85397
$76$	1.17550e6	0.307166
$77$	−9.48853e6	−2.36854
$78$	−1.29755e6	−0.309595
$79$	363284.	0.0828993	0.0414497	−	0.999141i	$-0.486802\pi$
$79$	363284.	0.0828993	0.0414497	+	0.999141i	$0.486802\pi$
$80$	−2.23031e6	−0.487025
$81$	−604180.	−0.126319
$82$	211503.	0.0423612
$83$	−6.71044e6	−1.28818	−0.644091	−	0.764948i	$-0.722764\pi$
$83$	−6.71044e6	−1.28818	−0.644091	+	0.764948i	$0.722764\pi$
$84$	−3.34599e6	−0.615952
$85$	6.84750e6	1.20939
$86$	−3.25594e6	−0.551990
$87$	580239.	0.0944691
$88$	−2.88241e6	−0.450886
$89$	1.16083e7	1.74543	0.872715	−	0.488229i	$-0.162357\pi$
$89$	1.16083e7	1.74543	0.872715	+	0.488229i	$0.162357\pi$
$90$	−5.33534e6	−0.771460
$91$	−8.81283e6	−1.22594
$92$	2.57619e6	0.344921
$93$	−5.25097e6	−0.676939
$94$	−1.40274e6	−0.174192
$95$	−1.00011e7	−1.19678
$96$	−1.01644e6	−0.117255
$97$	1.63488e7	1.81880	0.909400	−	0.415923i	$-0.136541\pi$
$97$	1.63488e7	1.81880	0.909400	+	0.415923i	$0.136541\pi$
$98$	−1.61372e7	−1.73196
$99$	−6.89530e6	−0.714216
$100$	1.39754e7	1.39754
$101$	7.79452e6	0.752774	0.376387	−	0.926462i	$-0.377166\pi$
$101$	7.79452e6	0.752774	0.376387	+	0.926462i	$0.377166\pi$
$102$	3.12067e6	0.291171
$103$	8.12543e6	0.732683	0.366341	−	0.930481i	$-0.380610\pi$
$103$	8.12543e6	0.732683	0.366341	+	0.930481i	$0.380610\pi$
$104$	−2.67715e6	−0.233376
$105$	2.84675e7	2.39987
$106$	1.45851e7	1.18943
$107$	1.15348e6	0.0910264	0.0455132	−	0.998964i	$-0.485508\pi$
$107$	1.15348e6	0.0910264	0.0455132	+	0.998964i	$0.485508\pi$
$108$	−6.77323e6	−0.517384
$109$	−8.60358e6	−0.636336	−0.318168	−	0.948034i	$-0.603068\pi$
$109$	−8.60358e6	−0.636336	−0.318168	+	0.948034i	$0.603068\pi$
$110$	2.45235e7	1.75674
$111$	−1.57122e6	−0.109045
$112$	−6.90355e6	−0.464311
$113$	−7.76780e6	−0.506435	−0.253217	−	0.967409i	$-0.581489\pi$
$113$	−7.76780e6	−0.506435	−0.253217	+	0.967409i	$0.581489\pi$
$114$	−4.55788e6	−0.288135
$115$	−2.19181e7	−1.34388
$116$	1.19717e6	0.0712118
$117$	−6.40427e6	−0.369674
$118$	9.93388e6	0.556585
$119$	2.11953e7	1.15299
$120$	8.64784e6	0.456850
$121$	1.22065e7	0.626388
$122$	−2.60073e7	−1.29669
$123$	−820084.	−0.0397366
$124$	−1.08340e7	−0.510284
$125$	−7.63627e7	−3.49700
$126$	−1.65146e7	−0.735481
$127$	4.49536e6	0.194738	0.0973691	−	0.995248i	$-0.468957\pi$
$127$	4.49536e6	0.194738	0.0973691	+	0.995248i	$0.468957\pi$
$128$	−2.09715e6	−0.0883883
$129$	1.26246e7	0.517791
$130$	2.27771e7	0.909279
$131$	−1.57640e7	−0.612656	−0.306328	−	0.951926i	$-0.599100\pi$
$131$	−1.57640e7	−0.612656	−0.306328	+	0.951926i	$0.599100\pi$
$132$	1.11763e7	0.422951
$133$	−3.09566e7	−1.14097
$134$	1.33404e7	0.478963
$135$	5.76264e7	2.01583
$136$	6.43867e6	0.219488
$137$	−9.27787e6	−0.308267	−0.154133	−	0.988050i	$-0.549259\pi$
$137$	−9.27787e6	−0.308267	−0.154133	+	0.988050i	$0.549259\pi$
$138$	−9.98894e6	−0.323551
$139$	5.30404e7	1.67515	0.837577	−	0.546319i	$-0.183972\pi$
$139$	5.30404e7	1.67515	0.837577	+	0.546319i	$0.183972\pi$
$140$	5.87351e7	1.80905
$141$	5.43899e6	0.163400
$142$	−2.09994e6	−0.0615457
$143$	2.94367e7	0.841809
$144$	−5.01680e6	−0.140010
$145$	−1.01855e7	−0.277455
$146$	−2.14890e7	−0.571453
$147$	6.25706e7	1.62465
$148$	−3.24179e6	−0.0821995
$149$	2.61358e7	0.647267	0.323633	−	0.946183i	$-0.395096\pi$
$149$	2.61358e7	0.647267	0.323633	+	0.946183i	$0.395096\pi$
$150$	−5.41885e7	−1.31095
$151$	−3.32760e7	−0.786523	−0.393261	−	0.919427i	$-0.628653\pi$
$151$	−3.32760e7	−0.786523	−0.393261	+	0.919427i	$0.628653\pi$
$152$	−9.40396e6	−0.217199
$153$	1.54026e7	0.347674
$154$	7.59082e7	1.67481
$155$	9.21751e7	1.98817
$156$	1.03804e7	0.218917
$157$	−2.08133e7	−0.429232	−0.214616	−	0.976698i	$-0.568850\pi$
$157$	−2.08133e7	−0.429232	−0.214616	+	0.976698i	$0.568850\pi$
$158$	−2.90627e6	−0.0586187
$159$	−5.65525e7	−1.11574
$160$	1.78425e7	0.344378
$161$	−6.78438e7	−1.28121
$162$	4.83344e6	0.0893211
$163$	4.00702e7	0.724711	0.362355	−	0.932040i	$-0.381973\pi$
$163$	4.00702e7	0.724711	0.362355	+	0.932040i	$0.381973\pi$
$164$	−1.69202e6	−0.0299539
$165$	−9.50877e7	−1.64790
$166$	5.36835e7	0.910883
$167$	4.26523e7	0.708656	0.354328	−	0.935121i	$-0.384710\pi$
$167$	4.26523e7	0.708656	0.354328	+	0.935121i	$0.384710\pi$
$168$	2.67679e7	0.435544
$169$	−3.54080e7	−0.564285
$170$	−5.47800e7	−0.855167
$171$	−2.24961e7	−0.344050
$172$	2.60475e7	0.390316
$173$	7.13528e6	0.104773	0.0523865	−	0.998627i	$-0.483317\pi$
$173$	7.13528e6	0.104773	0.0523865	+	0.998627i	$0.483317\pi$
$174$	−4.64191e6	−0.0667997
$175$	−3.68042e8	−5.19116
$176$	2.30593e7	0.318825
$177$	−3.85177e7	−0.522101
$178$	−9.28662e7	−1.23421
$179$	1.39174e8	1.81373	0.906866	−	0.421419i	$-0.138468\pi$
$179$	1.39174e8	1.81373	0.906866	+	0.421419i	$0.138468\pi$
$180$	4.26827e7	0.545505
$181$	−6.11153e7	−0.766082	−0.383041	−	0.923731i	$-0.625123\pi$
$181$	−6.11153e7	−0.766082	−0.383041	+	0.923731i	$0.625123\pi$
$182$	7.05026e7	0.866873
$183$	1.00841e8	1.21635
$184$	−2.06095e7	−0.243896
$185$	2.75811e7	0.320265
$186$	4.20078e7	0.478668
$187$	−7.07967e7	−0.791712
$188$	1.12219e7	0.123173
$189$	1.78373e8	1.92182
$190$	8.00086e7	0.846251
$191$	−1.77318e8	−1.84135	−0.920676	−	0.390329i	$-0.872361\pi$
$191$	−1.77318e8	−1.84135	−0.920676	+	0.390329i	$0.872361\pi$
$192$	8.13152e6	0.0829120
$193$	−6.75041e7	−0.675896	−0.337948	−	0.941165i	$-0.609733\pi$
$193$	−6.75041e7	−0.675896	−0.337948	+	0.941165i	$0.609733\pi$
$194$	−1.30790e8	−1.28609
$195$	−8.83163e7	−0.852943
$196$	1.29098e8	1.22468
$197$	−1.03097e8	−0.960761	−0.480380	−	0.877060i	$-0.659501\pi$
$197$	−1.03097e8	−0.960761	−0.480380	+	0.877060i	$0.659501\pi$
$198$	5.51624e7	0.505027
$199$	1.78780e8	1.60817	0.804086	−	0.594512i	$-0.202655\pi$
$199$	1.78780e8	1.60817	0.804086	+	0.594512i	$0.202655\pi$
$200$	−1.11803e8	−0.988212
$201$	−5.17263e7	−0.449288
$202$	−6.23562e7	−0.532292
$203$	−3.15273e7	−0.264516
$204$	−2.49654e7	−0.205889
$205$	1.43957e7	0.116706
$206$	−6.50034e7	−0.518085
$207$	−4.93019e7	−0.386338
$208$	2.14172e7	0.165022
$209$	1.03402e8	0.783458
$210$	−2.27740e8	−1.69696
$211$	2.20832e8	1.61836	0.809178	−	0.587564i	$-0.199913\pi$
$211$	2.20832e8	1.61836	0.809178	+	0.587564i	$0.199913\pi$
$212$	−1.16681e8	−0.841056
$213$	8.14233e6	0.0577325
$214$	−9.22786e6	−0.0643654
$215$	−2.21611e8	−1.52075
$216$	5.41858e7	0.365846
$217$	2.85312e8	1.89544
$218$	6.88286e7	0.449957
$219$	8.33216e7	0.536047
$220$	−1.96188e8	−1.24220
$221$	−6.57551e7	−0.409786
$222$	1.25698e7	0.0771066
$223$	2.27015e8	1.37085	0.685423	−	0.728146i	$-0.259618\pi$
$223$	2.27015e8	1.37085	0.685423	+	0.728146i	$0.259618\pi$
$224$	5.52284e7	0.328318
$225$	−2.67456e8	−1.56535
$226$	6.21424e7	0.358103
$227$	−2.27056e8	−1.28838	−0.644188	−	0.764867i	$-0.722805\pi$
$227$	−2.27056e8	−1.28838	−0.644188	+	0.764867i	$0.722805\pi$
$228$	3.64630e7	0.203742
$229$	1.74743e8	0.961557	0.480778	−	0.876842i	$-0.340354\pi$
$229$	1.74743e8	0.961557	0.480778	+	0.876842i	$0.340354\pi$
$230$	1.75345e8	0.950268
$231$	−2.94327e8	−1.57105
$232$	−9.57735e6	−0.0503544
$233$	2.66617e8	1.38083	0.690417	−	0.723411i	$-0.257427\pi$
$233$	2.66617e8	1.38083	0.690417	+	0.723411i	$0.257427\pi$
$234$	5.12342e7	0.261399
$235$	−9.54755e7	−0.479904
$236$	−7.94710e7	−0.393565
$237$	1.12688e7	0.0549868
$238$	−1.69562e8	−0.815285
$239$	7.94730e7	0.376554	0.188277	−	0.982116i	$-0.439710\pi$
$239$	7.94730e7	0.376554	0.188277	+	0.982116i	$0.439710\pi$
$240$	−6.91827e7	−0.323042
$241$	5.79710e7	0.266779	0.133389	−	0.991064i	$-0.457414\pi$
$241$	5.79710e7	0.266779	0.133389	+	0.991064i	$0.457414\pi$
$242$	−9.76523e7	−0.442923
$243$	2.12713e8	0.950980
$244$	2.08059e8	0.916899
$245$	−1.09836e9	−4.77159
$246$	6.56067e6	0.0280980
$247$	9.60382e7	0.405513
$248$	8.66718e7	0.360825
$249$	−2.08153e8	−0.854447
$250$	6.10901e8	2.47275
$251$	3.14343e8	1.25472	0.627358	−	0.778731i	$-0.284136\pi$
$251$	3.14343e8	1.25472	0.627358	+	0.778731i	$0.284136\pi$
$252$	1.32117e8	0.520064
$253$	2.26613e8	0.879756
$254$	−3.59629e7	−0.137701
$255$	2.12405e8	0.802183
$256$	1.67772e7	0.0625000
$257$	3.09191e8	1.13622	0.568108	−	0.822954i	$-0.307675\pi$
$257$	3.09191e8	1.13622	0.568108	+	0.822954i	$0.307675\pi$
$258$	−1.00997e8	−0.366133
$259$	8.53724e7	0.305329
$260$	−1.82217e8	−0.642958
$261$	−2.29109e7	−0.0797627
$262$	1.26112e8	0.433213
$263$	−3.09539e8	−1.04923	−0.524614	−	0.851340i	$-0.675790\pi$
$263$	−3.09539e8	−1.04923	−0.524614	+	0.851340i	$0.675790\pi$
$264$	−8.94105e7	−0.299071
$265$	9.92718e8	3.27692
$266$	2.47653e8	0.806784
$267$	3.60080e8	1.15774
$268$	−1.06723e8	−0.338678
$269$	−2.59451e8	−0.812686	−0.406343	−	0.913721i	$-0.633196\pi$
$269$	−2.59451e8	−0.812686	−0.406343	+	0.913721i	$0.633196\pi$
$270$	−4.61011e8	−1.42541
$271$	7.90601e7	0.241304	0.120652	−	0.992695i	$-0.461501\pi$
$271$	7.90601e7	0.241304	0.120652	+	0.992695i	$0.461501\pi$
$272$	−5.15094e7	−0.155201
$273$	−2.73368e8	−0.813164
$274$	7.42230e7	0.217977
$275$	1.22934e9	3.56457
$276$	7.99115e7	0.228785
$277$	2.41348e8	0.682283	0.341142	−	0.940012i	$-0.389186\pi$
$277$	2.41348e8	0.682283	0.341142	+	0.940012i	$0.389186\pi$
$278$	−4.24323e8	−1.18451
$279$	2.07336e8	0.571557
$280$	−4.69881e8	−1.27919
$281$	−1.24454e8	−0.334609	−0.167304	−	0.985905i	$-0.553506\pi$
$281$	−1.24454e8	−0.334609	−0.167304	+	0.985905i	$0.553506\pi$
$282$	−4.35119e7	−0.115541
$283$	4.05747e8	1.06415	0.532074	−	0.846698i	$-0.321413\pi$
$283$	4.05747e8	1.06415	0.532074	+	0.846698i	$0.321413\pi$
$284$	1.67995e7	0.0435194
$285$	−3.10226e8	−0.793819
$286$	−2.35494e8	−0.595249
$287$	4.45593e7	0.111263
$288$	4.01344e7	0.0990017
$289$	−2.52195e8	−0.614601
$290$	8.14837e7	0.196191
$291$	5.07128e8	1.20640
$292$	1.71912e8	0.404078
$293$	4.99201e8	1.15941	0.579707	−	0.814825i	$-0.303167\pi$
$293$	4.99201e8	1.15941	0.579707	+	0.814825i	$0.303167\pi$
$294$	−5.00565e8	−1.14880
$295$	6.76137e8	1.53341
$296$	2.59343e7	0.0581238
$297$	−5.95803e8	−1.31964
$298$	−2.09086e8	−0.457687
$299$	2.10475e8	0.455357
$300$	4.33508e8	0.926985
$301$	−6.85959e8	−1.44983
$302$	2.66208e8	0.556156
$303$	2.41781e8	0.499312
$304$	7.52317e7	0.153583
$305$	−1.77016e9	−3.57242
$306$	−1.23220e8	−0.245843
$307$	−3.21540e8	−0.634235	−0.317118	−	0.948386i	$-0.602715\pi$
$307$	−3.21540e8	−0.634235	−0.317118	+	0.948386i	$0.602715\pi$
$308$	−6.07266e8	−1.18427
$309$	2.52045e8	0.485986
$310$	−7.37401e8	−1.40585
$311$	−1.03297e8	−0.194726	−0.0973631	−	0.995249i	$-0.531041\pi$
$311$	−1.03297e8	−0.194726	−0.0973631	+	0.995249i	$0.531041\pi$
$312$	−8.30434e7	−0.154798
$313$	5.25918e8	0.969422	0.484711	−	0.874674i	$-0.338925\pi$
$313$	5.25918e8	0.969422	0.484711	+	0.874674i	$0.338925\pi$
$314$	1.66507e8	0.303513
$315$	−1.12405e9	−2.02627
$316$	2.32502e7	0.0414497
$317$	−6.26026e7	−0.110379	−0.0551893	−	0.998476i	$-0.517576\pi$
$317$	−6.26026e7	−0.110379	−0.0551893	+	0.998476i	$0.517576\pi$
$318$	4.52420e8	0.788946
$319$	1.05308e8	0.181633
$320$	−1.42740e8	−0.243512
$321$	3.57802e7	0.0603775
$322$	5.42750e8	0.905950
$323$	−2.30976e8	−0.381381
$324$	−3.86675e7	−0.0631595
$325$	1.14180e9	1.84500
$326$	−3.20562e8	−0.512448
$327$	−2.66877e8	−0.422079
$328$	1.35362e7	0.0211806
$329$	−2.95528e8	−0.457523
$330$	7.60701e8	1.16524
$331$	−3.10780e8	−0.471037	−0.235518	−	0.971870i	$-0.575679\pi$
$331$	−3.10780e8	−0.471037	−0.235518	+	0.971870i	$0.575679\pi$
$332$	−4.29468e8	−0.644091
$333$	6.20400e7	0.0920697
$334$	−3.41219e8	−0.501095
$335$	9.07998e8	1.31956
$336$	−2.14143e8	−0.307976
$337$	−9.56000e8	−1.36067	−0.680335	−	0.732901i	$-0.738166\pi$
$337$	−9.56000e8	−1.36067	−0.680335	+	0.732901i	$0.738166\pi$
$338$	2.83264e8	0.399009
$339$	−2.40952e8	−0.335916
$340$	4.38240e8	0.604694
$341$	−9.53003e8	−1.30153
$342$	1.79969e8	0.243280
$343$	−2.01175e9	−2.69181
$344$	−2.08380e8	−0.275995
$345$	−6.79885e8	−0.891392
$346$	−5.70822e7	−0.0740858
$347$	1.37536e9	1.76711	0.883555	−	0.468327i	$-0.155143\pi$
$347$	1.37536e9	1.76711	0.883555	+	0.468327i	$0.155143\pi$
$348$	3.71353e7	0.0472345
$349$	−1.38134e9	−1.73945	−0.869725	−	0.493537i	$-0.835704\pi$
$349$	−1.38134e9	−1.73945	−0.869725	+	0.493537i	$0.835704\pi$
$350$	2.94434e9	3.67070
$351$	−5.53374e8	−0.683037
$352$	−1.84475e8	−0.225443
$353$	−6.48672e8	−0.784899	−0.392450	−	0.919774i	$-0.628372\pi$
$353$	−6.48672e8	−0.784899	−0.392450	+	0.919774i	$0.628372\pi$
$354$	3.08142e8	0.369181
$355$	−1.42930e8	−0.169560
$356$	7.42929e8	0.872715
$357$	6.57462e8	0.764772
$358$	−1.11339e9	−1.28250
$359$	3.64068e8	0.415291	0.207645	−	0.978204i	$-0.433420\pi$
$359$	3.64068e8	0.415291	0.207645	+	0.978204i	$0.433420\pi$
$360$	−3.41462e8	−0.385730
$361$	−5.56521e8	−0.622596
$362$	4.88922e8	0.541701
$363$	3.78638e8	0.415481
$364$	−5.64021e8	−0.612972
$365$	−1.46262e9	−1.57437
$366$	−8.06729e8	−0.860090
$367$	3.90647e8	0.412528	0.206264	−	0.978496i	$-0.433869\pi$
$367$	3.90647e8	0.412528	0.206264	+	0.978496i	$0.433869\pi$
$368$	1.64876e8	0.172461
$369$	3.23812e7	0.0335506
$370$	−2.20649e8	−0.226462
$371$	3.07279e9	3.12409
$372$	−3.36062e8	−0.338469
$373$	−8.58735e7	−0.0856797	−0.0428399	−	0.999082i	$-0.513641\pi$
$373$	−8.58735e7	−0.0856797	−0.0428399	+	0.999082i	$0.513641\pi$
$374$	5.66373e8	0.559825
$375$	−2.36872e9	−2.31955
$376$	−8.97752e7	−0.0870961
$377$	9.78089e7	0.0940121
$378$	−1.42698e9	−1.35893
$379$	3.53330e8	0.333383	0.166691	−	0.986009i	$-0.446692\pi$
$379$	3.53330e8	0.333383	0.166691	+	0.986009i	$0.446692\pi$
$380$	−6.40069e8	−0.598390
$381$	1.39443e8	0.129169
$382$	1.41855e9	1.30203
$383$	−4.90315e8	−0.445943	−0.222971	−	0.974825i	$-0.571576\pi$
$383$	−4.90315e8	−0.445943	−0.222971	+	0.974825i	$0.571576\pi$
$384$	−6.50522e7	−0.0586277
$385$	5.16660e9	4.61415
$386$	5.40033e8	0.477931
$387$	−4.98486e8	−0.437184
$388$	1.04632e9	0.909400
$389$	9.97474e7	0.0859168	0.0429584	−	0.999077i	$-0.486322\pi$
$389$	9.97474e7	0.0859168	0.0429584	+	0.999077i	$0.486322\pi$
$390$	7.06530e8	0.603121
$391$	−5.06202e8	−0.428258
$392$	−1.03278e9	−0.865979
$393$	−4.88988e8	−0.406372
$394$	8.24778e8	0.679361
$395$	−1.97812e8	−0.161496
$396$	−4.41299e8	−0.357108
$397$	−2.09994e8	−0.168438	−0.0842189	−	0.996447i	$-0.526839\pi$
$397$	−2.09994e8	−0.168438	−0.0842189	+	0.996447i	$0.526839\pi$
$398$	−1.43024e9	−1.13715
$399$	−9.60252e8	−0.756798
$400$	8.94428e8	0.698772
$401$	5.55414e8	0.430141	0.215071	−	0.976598i	$-0.431002\pi$
$401$	5.55414e8	0.430141	0.215071	+	0.976598i	$0.431002\pi$
$402$	4.13810e8	0.317695
$403$	−8.85138e8	−0.673664
$404$	4.98849e8	0.376387
$405$	3.28982e8	0.246082
$406$	2.52219e8	0.187041
$407$	−2.85162e8	−0.209658
$408$	1.99723e8	0.145585
$409$	1.80096e9	1.30158	0.650792	−	0.759256i	$-0.274437\pi$
$409$	1.80096e9	1.30158	0.650792	+	0.759256i	$0.274437\pi$
$410$	−1.15165e8	−0.0825237
$411$	−2.87793e8	−0.204472
$412$	5.20027e8	0.366341
$413$	2.09286e9	1.46189
$414$	3.94416e8	0.273182
$415$	3.65390e9	2.50951
$416$	−1.71338e8	−0.116688
$417$	1.64527e9	1.11112
$418$	−8.27213e8	−0.553988
$419$	−1.69929e7	−0.0112854	−0.00564272	−	0.999984i	$-0.501796\pi$
$419$	−1.69929e7	−0.0112854	−0.00564272	+	0.999984i	$0.501796\pi$
$420$	1.82192e9	1.19993
$421$	2.76374e9	1.80514	0.902568	−	0.430548i	$-0.141680\pi$
$421$	2.76374e9	1.80514	0.902568	+	0.430548i	$0.141680\pi$
$422$	−1.76666e9	−1.14435
$423$	−2.14760e8	−0.137963
$424$	9.33448e8	0.594716
$425$	−2.74607e9	−1.73520
$426$	−6.51387e7	−0.0408230
$427$	−5.47921e9	−3.40581
$428$	7.38228e7	0.0455132
$429$	9.13107e8	0.558369
$430$	1.77289e9	1.07533
$431$	−2.95133e9	−1.77561	−0.887804	−	0.460222i	$-0.847770\pi$
$431$	−2.95133e9	−1.77561	−0.887804	+	0.460222i	$0.847770\pi$
$432$	−4.33487e8	−0.258692
$433$	−2.29366e9	−1.35776	−0.678878	−	0.734251i	$-0.737533\pi$
$433$	−2.29366e9	−1.35776	−0.678878	+	0.734251i	$0.737533\pi$
$434$	−2.28250e9	−1.34028
$435$	−3.15946e8	−0.184035
$436$	−5.50629e8	−0.318168
$437$	7.39331e8	0.423793
$438$	−6.66573e8	−0.379043
$439$	2.21394e9	1.24893	0.624467	−	0.781052i	$-0.285316\pi$
$439$	2.21394e9	1.24893	0.624467	+	0.781052i	$0.285316\pi$
$440$	1.56950e9	0.878371
$441$	−2.47061e9	−1.37173
$442$	5.26041e8	0.289762
$443$	−2.80148e9	−1.53100	−0.765498	−	0.643438i	$-0.777507\pi$
$443$	−2.80148e9	−1.53100	−0.765498	+	0.643438i	$0.777507\pi$
$444$	−1.00558e8	−0.0545226
$445$	−6.32082e9	−3.40027
$446$	−1.81612e9	−0.969334
$447$	8.10713e8	0.429330
$448$	−4.41827e8	−0.232156
$449$	−1.24071e9	−0.646856	−0.323428	−	0.946253i	$-0.604835\pi$
$449$	−1.24071e9	−0.646856	−0.323428	+	0.946253i	$0.604835\pi$
$450$	2.13964e9	1.10687
$451$	−1.48838e8	−0.0764003
$452$	−4.97139e8	−0.253217
$453$	−1.03220e9	−0.521698
$454$	1.81645e9	0.911020
$455$	4.79867e9	2.38826
$456$	−2.91704e8	−0.144067
$457$	8.16764e8	0.400304	0.200152	−	0.979765i	$-0.435856\pi$
$457$	8.16764e8	0.400304	0.200152	+	0.979765i	$0.435856\pi$
$458$	−1.39794e9	−0.679923
$459$	1.33089e9	0.642389
$460$	−1.40276e9	−0.671941
$461$	1.07694e9	0.511962	0.255981	−	0.966682i	$-0.417601\pi$
$461$	1.07694e9	0.511962	0.255981	+	0.966682i	$0.417601\pi$
$462$	2.35462e9	1.11090
$463$	3.16535e9	1.48214	0.741068	−	0.671430i	$-0.234320\pi$
$463$	3.16535e9	1.48214	0.741068	+	0.671430i	$0.234320\pi$
$464$	7.66188e7	0.0356059
$465$	2.85921e9	1.31874
$466$	−2.13293e9	−0.976398
$467$	2.37777e9	1.08034	0.540171	−	0.841555i	$-0.318360\pi$
$467$	2.37777e9	1.08034	0.540171	+	0.841555i	$0.318360\pi$
$468$	−4.09873e8	−0.184837
$469$	2.81055e9	1.25802
$470$	7.63804e8	0.339344
$471$	−6.45614e8	−0.284708
$472$	6.35768e8	0.278293
$473$	2.29125e9	0.995540
$474$	−9.01504e7	−0.0388816
$475$	4.01076e9	1.71711
$476$	1.35650e9	0.576493
$477$	2.23299e9	0.942047
$478$	−6.35784e8	−0.266264
$479$	3.68467e9	1.53188	0.765939	−	0.642914i	$-0.222275\pi$
$479$	3.68467e9	1.53188	0.765939	+	0.642914i	$0.222275\pi$
$480$	5.53462e8	0.228425
$481$	−2.64855e8	−0.108518
$482$	−4.63768e8	−0.188641
$483$	−2.10447e9	−0.849820
$484$	7.81218e8	0.313194
$485$	−8.90209e9	−3.54320
$486$	−1.70170e9	−0.672445
$487$	−1.99019e9	−0.780807	−0.390404	−	0.920644i	$-0.627665\pi$
$487$	−1.99019e9	−0.780807	−0.390404	+	0.920644i	$0.627665\pi$
$488$	−1.66447e9	−0.648345
$489$	1.24295e9	0.480698
$490$	8.78687e9	3.37402
$491$	−1.03457e9	−0.394433	−0.197217	−	0.980360i	$-0.563190\pi$
$491$	−1.03457e9	−0.394433	−0.197217	+	0.980360i	$0.563190\pi$
$492$	−5.24854e7	−0.0198683
$493$	−2.35235e8	−0.0884173
$494$	−7.68306e8	−0.286741
$495$	3.75456e9	1.39136
$496$	−6.93374e8	−0.255142
$497$	−4.42414e8	−0.161652
$498$	1.66522e9	0.604185
$499$	−1.69821e9	−0.611843	−0.305922	−	0.952057i	$-0.598965\pi$
$499$	−1.69821e9	−0.611843	−0.305922	+	0.952057i	$0.598965\pi$
$500$	−4.88721e9	−1.74850
$501$	1.32305e9	0.470049
$502$	−2.51474e9	−0.887218
$503$	9.98691e8	0.349899	0.174950	−	0.984577i	$-0.444024\pi$
$503$	9.98691e8	0.349899	0.174950	+	0.984577i	$0.444024\pi$
$504$	−1.05694e9	−0.367741
$505$	−4.24420e9	−1.46648
$506$	−1.81290e9	−0.622082
$507$	−1.09833e9	−0.374288
$508$	2.87703e8	0.0973691
$509$	4.86581e9	1.63547	0.817735	−	0.575594i	$-0.195229\pi$
$509$	4.86581e9	1.63547	0.817735	+	0.575594i	$0.195229\pi$
$510$	−1.69924e9	−0.567229
$511$	−4.52729e9	−1.50094
$512$	−1.34218e8	−0.0441942
$513$	−1.94382e9	−0.635691
$514$	−2.47353e9	−0.803427
$515$	−4.42438e9	−1.42734
$516$	8.07975e8	0.258895
$517$	9.87127e8	0.314164
$518$	−6.82979e8	−0.215900
$519$	2.21331e8	0.0694956
$520$	1.45774e9	0.454640
$521$	−2.29363e9	−0.710544	−0.355272	−	0.934763i	$-0.615612\pi$
$521$	−2.29363e9	−0.710544	−0.355272	+	0.934763i	$0.615612\pi$
$522$	1.83287e8	0.0564007
$523$	−1.41986e8	−0.0434000	−0.0217000	−	0.999765i	$-0.506908\pi$
$523$	−1.41986e8	−0.0434000	−0.0217000	+	0.999765i	$0.506908\pi$
$524$	−1.00890e9	−0.306328
$525$	−1.14164e10	−3.44328
$526$	2.47631e9	0.741916
$527$	2.12880e9	0.633574
$528$	7.15284e8	0.211475
$529$	−1.78453e9	−0.524117
$530$	−7.94175e9	−2.31713
$531$	1.52088e9	0.440823
$532$	−1.98122e9	−0.570483
$533$	−1.38239e8	−0.0395444
$534$	−2.88064e9	−0.818644
$535$	−6.28082e8	−0.177328
$536$	8.53786e8	0.239482
$537$	4.31709e9	1.20304
$538$	2.07561e9	0.574656
$539$	1.13560e10	3.12366
$540$	3.68809e9	1.00791
$541$	6.73035e9	1.82746	0.913729	−	0.406324i	$-0.133190\pi$
$541$	6.73035e9	1.82746	0.913729	+	0.406324i	$0.133190\pi$
$542$	−6.32481e8	−0.170628
$543$	−1.89575e9	−0.508139
$544$	4.12075e8	0.109744
$545$	4.68474e9	1.23964
$546$	2.18694e9	0.574994
$547$	−2.10936e9	−0.551056	−0.275528	−	0.961293i	$-0.588853\pi$
$547$	−2.10936e9	−0.551056	−0.275528	+	0.961293i	$0.588853\pi$
$548$	−5.93784e8	−0.154133
$549$	−3.98173e9	−1.02700
$550$	−9.83471e9	−2.52053
$551$	3.43571e8	0.0874955
$552$	−6.39292e8	−0.161775
$553$	−6.12291e8	−0.153964
$554$	−1.93078e9	−0.482447
$555$	8.55545e8	0.212431
$556$	3.39458e9	0.837577
$557$	−5.46338e9	−1.33958	−0.669790	−	0.742551i	$-0.733616\pi$
$557$	−5.46338e9	−1.33958	−0.669790	+	0.742551i	$0.733616\pi$
$558$	−1.65869e9	−0.404152
$559$	2.12809e9	0.515286
$560$	3.75905e9	0.904524
$561$	−2.19606e9	−0.525140
$562$	9.95634e8	0.236604
$563$	−2.38438e9	−0.563113	−0.281557	−	0.959545i	$-0.590851\pi$
$563$	−2.38438e9	−0.563113	−0.281557	+	0.959545i	$0.590851\pi$
$564$	3.48095e8	0.0816999
$565$	4.22964e9	0.986584
$566$	−3.24597e9	−0.752467
$567$	1.01831e9	0.234605
$568$	−1.34396e8	−0.0307729
$569$	4.69886e9	1.06930	0.534650	−	0.845073i	$-0.320443\pi$
$569$	4.69886e9	1.06930	0.534650	+	0.845073i	$0.320443\pi$
$570$	2.48181e9	0.561315
$571$	2.04617e9	0.459954	0.229977	−	0.973196i	$-0.426135\pi$
$571$	2.04617e9	0.459954	0.229977	+	0.973196i	$0.426135\pi$
$572$	1.88395e9	0.420905
$573$	−5.50029e9	−1.22136
$574$	−3.56475e8	−0.0786751
$575$	8.78988e9	1.92817
$576$	−3.21075e8	−0.0700048
$577$	−6.13969e9	−1.33055	−0.665274	−	0.746599i	$-0.731685\pi$
$577$	−6.13969e9	−1.33055	−0.665274	+	0.746599i	$0.731685\pi$
$578$	2.01756e9	0.434589
$579$	−2.09393e9	−0.448319
$580$	−6.51870e8	−0.138728
$581$	1.13100e10	2.39247
$582$	−4.05703e9	−0.853056
$583$	−1.02638e10	−2.14520
$584$	−1.37529e9	−0.285727
$585$	3.48719e9	0.720161
$586$	−3.99360e9	−0.819829
$587$	−1.29772e9	−0.264819	−0.132410	−	0.991195i	$-0.542271\pi$
$587$	−1.29772e9	−0.264819	−0.132410	+	0.991195i	$0.542271\pi$
$588$	4.00452e9	0.812325
$589$	−3.10920e9	−0.626968
$590$	−5.40910e9	−1.08428
$591$	−3.19800e9	−0.637269
$592$	−2.07475e8	−0.0410997
$593$	−1.01765e9	−0.200404	−0.100202	−	0.994967i	$-0.531949\pi$
$593$	−1.01765e9	−0.200404	−0.100202	+	0.994967i	$0.531949\pi$
$594$	4.76642e9	0.933125
$595$	−1.15410e10	−2.24613
$596$	1.67269e9	0.323633
$597$	5.54562e9	1.06670
$598$	−1.68380e9	−0.321986
$599$	1.36024e9	0.258595	0.129298	−	0.991606i	$-0.458728\pi$
$599$	1.36024e9	0.258595	0.129298	+	0.991606i	$0.458728\pi$
$600$	−3.46806e9	−0.655477
$601$	5.83436e9	1.09631	0.548154	−	0.836378i	$-0.315331\pi$
$601$	5.83436e9	1.09631	0.548154	+	0.836378i	$0.315331\pi$
$602$	5.48768e9	1.02518
$603$	2.04242e9	0.379346
$604$	−2.12966e9	−0.393261
$605$	−6.64658e9	−1.22027
$606$	−1.93424e9	−0.353067
$607$	4.09613e9	0.743384	0.371692	−	0.928356i	$-0.378778\pi$
$607$	4.09613e9	0.743384	0.371692	+	0.928356i	$0.378778\pi$
$608$	−6.01854e8	−0.108600
$609$	−9.77956e8	−0.175452
$610$	1.41613e10	2.52608
$611$	9.16831e8	0.162609
$612$	9.85764e8	0.173837
$613$	−5.20044e8	−0.0911861	−0.0455930	−	0.998960i	$-0.514518\pi$
$613$	−5.20044e8	−0.0911861	−0.0455930	+	0.998960i	$0.514518\pi$
$614$	2.57232e9	0.448472
$615$	4.46544e8	0.0774108
$616$	4.85813e9	0.837406
$617$	3.87499e9	0.664160	0.332080	−	0.943251i	$-0.392250\pi$
$617$	3.87499e9	0.664160	0.332080	+	0.943251i	$0.392250\pi$
$618$	−2.01636e9	−0.343644
$619$	−6.93110e9	−1.17459	−0.587293	−	0.809375i	$-0.699806\pi$
$619$	−6.93110e9	−1.17459	−0.587293	+	0.809375i	$0.699806\pi$
$620$	5.89921e9	0.994083
$621$	−4.26004e9	−0.713827
$622$	8.26372e8	0.137692
$623$	−1.95650e10	−3.24169
$624$	6.64347e8	0.109458
$625$	2.45204e10	4.01742
$626$	−4.20734e9	−0.685485
$627$	3.20745e9	0.519665
$628$	−1.33205e9	−0.214616
$629$	6.36988e8	0.102060
$630$	8.99238e9	1.43279
$631$	1.27564e9	0.202128	0.101064	−	0.994880i	$-0.467775\pi$
$631$	1.27564e9	0.202128	0.101064	+	0.994880i	$0.467775\pi$
$632$	−1.86001e8	−0.0293093
$633$	6.85006e9	1.07345
$634$	5.00821e8	0.0780494
$635$	−2.44777e9	−0.379369
$636$	−3.61936e9	−0.557869
$637$	1.05473e10	1.61679
$638$	−8.42465e8	−0.128434
$639$	−3.21502e8	−0.0487450
$640$	1.14192e9	0.172189
$641$	8.45969e9	1.26868	0.634339	−	0.773055i	$-0.281272\pi$
$641$	8.45969e9	1.26868	0.634339	+	0.773055i	$0.281272\pi$
$642$	−2.86242e8	−0.0426933
$643$	−2.53383e9	−0.375871	−0.187935	−	0.982181i	$-0.560180\pi$
$643$	−2.53383e9	−0.375871	−0.187935	+	0.982181i	$0.560180\pi$
$644$	−4.34200e9	−0.640604
$645$	−6.87423e9	−1.00871
$646$	1.84781e9	0.269677
$647$	−9.30854e8	−0.135119	−0.0675595	−	0.997715i	$-0.521521\pi$
$647$	−9.30854e8	−0.135119	−0.0675595	+	0.997715i	$0.521521\pi$
$648$	3.09340e8	0.0446605
$649$	−6.99061e9	−1.00383
$650$	−9.13437e9	−1.30461
$651$	8.85018e9	1.25724
$652$	2.56449e9	0.362355
$653$	4.54702e9	0.639044	0.319522	−	0.947579i	$-0.396478\pi$
$653$	4.54702e9	0.639044	0.319522	+	0.947579i	$0.396478\pi$
$654$	2.13502e9	0.298455
$655$	8.58365e9	1.19351
$656$	−1.08290e8	−0.0149769
$657$	−3.28997e9	−0.452599
$658$	2.36422e9	0.323518
$659$	5.26043e9	0.716015	0.358007	−	0.933719i	$-0.383456\pi$
$659$	5.26043e9	0.716015	0.358007	+	0.933719i	$0.383456\pi$
$660$	−6.08561e9	−0.823949
$661$	−9.97829e8	−0.134385	−0.0671925	−	0.997740i	$-0.521404\pi$
$661$	−9.97829e8	−0.134385	−0.0671925	+	0.997740i	$0.521404\pi$
$662$	2.48624e9	0.333073
$663$	−2.03968e9	−0.271809
$664$	3.43574e9	0.455441
$665$	1.68562e10	2.22271
$666$	−4.96320e8	−0.0651031
$667$	7.52962e8	0.0982500
$668$	2.72975e9	0.354328
$669$	7.04186e9	0.909276
$670$	−7.26399e9	−0.933068
$671$	1.83017e10	2.33864
$672$	1.71314e9	0.217772
$673$	−2.48723e9	−0.314530	−0.157265	−	0.987556i	$-0.550268\pi$
$673$	−2.48723e9	−0.314530	−0.157265	+	0.987556i	$0.550268\pi$
$674$	7.64800e9	0.962140
$675$	−2.31101e10	−2.89226
$676$	−2.26611e9	−0.282142
$677$	−6.47115e9	−0.801532	−0.400766	−	0.916180i	$-0.631256\pi$
$677$	−6.47115e9	−0.801532	−0.400766	+	0.916180i	$0.631256\pi$
$678$	1.92761e9	0.237529
$679$	−2.75549e10	−3.37796
$680$	−3.50592e9	−0.427584
$681$	−7.04312e9	−0.854575
$682$	7.62403e9	0.920320
$683$	−4.86398e9	−0.584143	−0.292071	−	0.956397i	$-0.594345\pi$
$683$	−4.86398e9	−0.584143	−0.292071	+	0.956397i	$0.594345\pi$
$684$	−1.43975e9	−0.172025
$685$	5.05189e9	0.600533
$686$	1.60940e10	1.90340
$687$	5.42040e9	0.637797
$688$	1.66704e9	0.195158
$689$	−9.53287e9	−1.11034
$690$	5.43908e9	0.630309
$691$	7.51546e9	0.866527	0.433264	−	0.901267i	$-0.357362\pi$
$691$	7.51546e9	0.866527	0.433264	+	0.901267i	$0.357362\pi$
$692$	4.56658e8	0.0523865
$693$	1.16216e10	1.32647
$694$	−1.10029e10	−1.24954
$695$	−2.88810e10	−3.26336
$696$	−2.97082e8	−0.0333999
$697$	3.32470e8	0.0371910
$698$	1.10507e10	1.22998
$699$	8.27026e9	0.915902
$700$	−2.35547e10	−2.59558
$701$	−1.02509e10	−1.12396	−0.561978	−	0.827152i	$-0.689960\pi$
$701$	−1.02509e10	−1.12396	−0.561978	+	0.827152i	$0.689960\pi$
$702$	4.42700e9	0.482980
$703$	−9.30350e8	−0.100996
$704$	1.47580e9	0.159412
$705$	−2.96158e9	−0.318319
$706$	5.18938e9	0.555007
$707$	−1.31372e10	−1.39809
$708$	−2.46513e9	−0.261050
$709$	5.01078e9	0.528012	0.264006	−	0.964521i	$-0.414956\pi$
$709$	5.01078e9	0.528012	0.264006	+	0.964521i	$0.414956\pi$
$710$	1.14344e9	0.119897
$711$	−4.44951e8	−0.0464268
$712$	−5.94344e9	−0.617103
$713$	−6.81405e9	−0.704032
$714$	−5.25969e9	−0.540775
$715$	−1.60286e10	−1.63993
$716$	8.90715e9	0.906866
$717$	2.46520e9	0.249767
$718$	−2.91255e9	−0.293655
$719$	1.55089e10	1.55607	0.778035	−	0.628221i	$-0.216217\pi$
$719$	1.55089e10	1.55607	0.778035	+	0.628221i	$0.216217\pi$
$720$	2.73169e9	0.272752
$721$	−1.36949e10	−1.36077
$722$	4.45217e9	0.440242
$723$	1.79822e9	0.176953
$724$	−3.91138e9	−0.383041
$725$	4.08470e9	0.398086
$726$	−3.02911e9	−0.293789
$727$	−9.09964e8	−0.0878322	−0.0439161	−	0.999035i	$-0.513983\pi$
$727$	−9.09964e8	−0.0878322	−0.0439161	+	0.999035i	$0.513983\pi$
$728$	4.51217e9	0.433437
$729$	7.91954e9	0.757101
$730$	1.17010e10	1.11325
$731$	−5.11814e9	−0.484620
$732$	6.45383e9	0.608176
$733$	−6.80412e9	−0.638128	−0.319064	−	0.947733i	$-0.603369\pi$
$733$	−6.80412e9	−0.638128	−0.319064	+	0.947733i	$0.603369\pi$
$734$	−3.12518e9	−0.291701
$735$	−3.40703e10	−3.16498
$736$	−1.31901e9	−0.121948
$737$	−9.38784e9	−0.863832
$738$	−2.59050e8	−0.0237239
$739$	9.88530e9	0.901020	0.450510	−	0.892771i	$-0.351242\pi$
$739$	9.88530e9	0.901020	0.450510	+	0.892771i	$0.351242\pi$
$740$	1.76519e9	0.160133
$741$	2.97904e9	0.268975
$742$	−2.45823e10	−2.20907
$743$	−1.40609e10	−1.25763	−0.628814	−	0.777556i	$-0.716459\pi$
$743$	−1.40609e10	−1.25763	−0.628814	+	0.777556i	$0.716459\pi$
$744$	2.68850e9	0.239334
$745$	−1.42312e10	−1.26094
$746$	6.86988e8	0.0605847
$747$	8.21897e9	0.721432
$748$	−4.53099e9	−0.395856
$749$	−1.94412e9	−0.169058
$750$	1.89497e10	1.64017
$751$	1.89107e10	1.62918	0.814590	−	0.580038i	$-0.196962\pi$
$751$	1.89107e10	1.62918	0.814590	+	0.580038i	$0.196962\pi$
$752$	7.18201e8	0.0615863
$753$	9.75069e9	0.832248
$754$	−7.82471e8	−0.0664766
$755$	1.81191e10	1.53222
$756$	1.14158e10	0.960908
$757$	−1.68703e9	−0.141348	−0.0706738	−	0.997499i	$-0.522515\pi$
$757$	−1.68703e9	−0.141348	−0.0706738	+	0.997499i	$0.522515\pi$
$758$	−2.82664e9	−0.235737
$759$	7.02936e9	0.583539
$760$	5.12055e9	0.423126
$761$	1.35093e10	1.11118	0.555591	−	0.831456i	$-0.312492\pi$
$761$	1.35093e10	1.11118	0.555591	+	0.831456i	$0.312492\pi$
$762$	−1.11554e9	−0.0913363
$763$	1.45008e10	1.18183
$764$	−1.13484e10	−0.920676
$765$	−8.38685e9	−0.677304
$766$	3.92252e9	0.315329
$767$	−6.49280e9	−0.519575
$768$	5.20417e8	0.0414560
$769$	−2.04375e10	−1.62064	−0.810318	−	0.585990i	$-0.800706\pi$
$769$	−2.04375e10	−1.62064	−0.810318	+	0.585990i	$0.800706\pi$
$770$	−4.13328e10	−3.26270
$771$	9.59089e9	0.753648
$772$	−4.32026e9	−0.337948
$773$	−3.22437e9	−0.251083	−0.125541	−	0.992088i	$-0.540067\pi$
$773$	−3.22437e9	−0.251083	−0.125541	+	0.992088i	$0.540067\pi$
$774$	3.98788e9	0.309136
$775$	−3.69652e10	−2.85258
$776$	−8.37059e9	−0.643043
$777$	2.64819e9	0.202524
$778$	−7.97979e8	−0.0607524
$779$	−4.85588e8	−0.0368033
$780$	−5.65224e9	−0.426471
$781$	1.47776e9	0.111000
$782$	4.04962e9	0.302824
$783$	−1.97966e9	−0.147375
$784$	8.26225e9	0.612339
$785$	1.13331e10	0.836187
$786$	3.91190e9	0.287349
$787$	−1.34167e10	−0.981147	−0.490574	−	0.871400i	$-0.663213\pi$
$787$	−1.34167e10	−0.981147	−0.490574	+	0.871400i	$0.663213\pi$
$788$	−6.59822e9	−0.480380
$789$	−9.60167e9	−0.695949
$790$	1.58249e9	0.114195
$791$	1.30921e10	0.940573
$792$	3.53039e9	0.252514
$793$	1.69984e10	1.21047
$794$	1.67995e9	0.119104
$795$	3.07934e10	2.17357
$796$	1.14419e10	0.804086
$797$	1.04838e10	0.733528	0.366764	−	0.930314i	$-0.380466\pi$
$797$	1.04838e10	0.733528	0.366764	+	0.930314i	$0.380466\pi$
$798$	7.68201e9	0.535137
$799$	−2.20502e9	−0.152932
$800$	−7.15542e9	−0.494106
$801$	−1.42179e10	−0.977508
$802$	−4.44331e9	−0.304156
$803$	1.51221e10	1.03064
$804$	−3.31048e9	−0.224644
$805$	3.69416e10	2.49592
$806$	7.08110e9	0.476352
$807$	−8.04800e9	−0.539052
$808$	−3.99080e9	−0.266146
$809$	8.66031e9	0.575060	0.287530	−	0.957772i	$-0.407166\pi$
$809$	8.66031e9	0.575060	0.287530	+	0.957772i	$0.407166\pi$
$810$	−2.63186e9	−0.174006
$811$	7.78352e9	0.512393	0.256196	−	0.966625i	$-0.417531\pi$
$811$	7.78352e9	0.512393	0.256196	+	0.966625i	$0.417531\pi$
$812$	−2.01775e9	−0.132258
$813$	2.45239e9	0.160056
$814$	2.28130e9	0.148251
$815$	−2.18186e10	−1.41181
$816$	−1.59778e9	−0.102944
$817$	7.47528e9	0.479568
$818$	−1.44077e10	−0.920359
$819$	1.07940e10	0.686575
$820$	9.21324e8	0.0583531
$821$	7.91243e9	0.499009	0.249505	−	0.968374i	$-0.419732\pi$
$821$	7.91243e9	0.499009	0.249505	+	0.968374i	$0.419732\pi$
$822$	2.30234e9	0.144584
$823$	−4.48091e9	−0.280199	−0.140100	−	0.990137i	$-0.544742\pi$
$823$	−4.48091e9	−0.280199	−0.140100	+	0.990137i	$0.544742\pi$
$824$	−4.16022e9	−0.259042
$825$	3.81332e10	2.36437
$826$	−1.67429e10	−1.03372
$827$	−7.15443e8	−0.0439851	−0.0219926	−	0.999758i	$-0.507001\pi$
$827$	−7.15443e8	−0.0439851	−0.0219926	+	0.999758i	$0.507001\pi$
$828$	−3.15532e9	−0.193169
$829$	−2.36866e10	−1.44398	−0.721990	−	0.691903i	$-0.756773\pi$
$829$	−2.36866e10	−1.44398	−0.721990	+	0.691903i	$0.756773\pi$
$830$	−2.92312e10	−1.77449
$831$	7.48645e9	0.452556
$832$	1.37070e9	0.0825109
$833$	−2.53668e10	−1.52057
$834$	−1.31622e10	−0.785683
$835$	−2.32246e10	−1.38053
$836$	6.61771e9	0.391729
$837$	1.79153e10	1.05605
$838$	1.35943e8	0.00798002
$839$	2.37629e10	1.38909	0.694547	−	0.719447i	$-0.255605\pi$
$839$	2.37629e10	1.38909	0.694547	+	0.719447i	$0.255605\pi$
$840$	−1.45754e10	−0.848482
$841$	−1.69000e10	−0.979715
$842$	−2.21099e10	−1.27642
$843$	−3.86048e9	−0.221945
$844$	1.41333e10	0.809178
$845$	1.92800e10	1.09928
$846$	1.71808e9	0.0975543
$847$	−2.05733e10	−1.16336
$848$	−7.46759e9	−0.420528
$849$	1.25860e10	0.705846
$850$	2.19686e10	1.22697
$851$	−2.03893e9	−0.113409
$852$	5.21109e8	0.0288662
$853$	−3.28503e10	−1.81225	−0.906126	−	0.423009i	$-0.860974\pi$
$853$	−3.28503e10	−1.81225	−0.906126	+	0.423009i	$0.860974\pi$
$854$	4.38337e10	2.40827
$855$	1.22494e10	0.670242
$856$	−5.90583e8	−0.0321827
$857$	−5.67832e9	−0.308168	−0.154084	−	0.988058i	$-0.549243\pi$
$857$	−5.67832e9	−0.308168	−0.154084	+	0.988058i	$0.549243\pi$
$858$	−7.30485e9	−0.394826
$859$	−1.22964e10	−0.661914	−0.330957	−	0.943646i	$-0.607372\pi$
$859$	−1.22964e10	−0.661914	−0.330957	+	0.943646i	$0.607372\pi$
$860$	−1.41831e10	−0.760374
$861$	1.38220e9	0.0738006
$862$	2.36106e10	1.25554
$863$	1.75550e10	0.929743	0.464871	−	0.885378i	$-0.346101\pi$
$863$	1.75550e10	0.929743	0.464871	+	0.885378i	$0.346101\pi$
$864$	3.46789e9	0.182923
$865$	−3.88523e9	−0.204108
$866$	1.83493e10	0.960078
$867$	−7.82290e9	−0.407663
$868$	1.82600e10	0.947722
$869$	2.04518e9	0.105721
$870$	2.52757e9	0.130132
$871$	−8.71931e9	−0.447115
$872$	4.40503e9	0.224979
$873$	−2.00241e10	−1.01860
$874$	−5.91465e9	−0.299667
$875$	1.28704e11	6.49479
$876$	5.33258e9	0.268024
$877$	−9.75144e7	−0.00488169	−0.00244084	−	0.999997i	$-0.500777\pi$
$877$	−9.75144e7	−0.00488169	−0.00244084	+	0.999997i	$0.500777\pi$
$878$	−1.77115e10	−0.883129
$879$	1.54848e10	0.769035
$880$	−1.25560e10	−0.621102
$881$	−1.68618e10	−0.830786	−0.415393	−	0.909642i	$-0.636356\pi$
$881$	−1.68618e10	−0.830786	−0.415393	+	0.909642i	$0.636356\pi$
$882$	1.97649e10	0.969962
$883$	2.81287e10	1.37495	0.687476	−	0.726207i	$-0.258719\pi$
$883$	2.81287e10	1.37495	0.687476	+	0.726207i	$0.258719\pi$
$884$	−4.20833e9	−0.204893
$885$	2.09733e10	1.01710
$886$	2.24118e10	1.08258
$887$	1.49073e10	0.717241	0.358621	−	0.933483i	$-0.383247\pi$
$887$	1.49073e10	0.717241	0.358621	+	0.933483i	$0.383247\pi$
$888$	8.04465e8	0.0385533
$889$	−7.57664e9	−0.361676
$890$	5.05666e10	2.40435
$891$	−3.40136e9	−0.161095
$892$	1.45290e10	0.685423
$893$	3.22053e9	0.151338
$894$	−6.48570e9	−0.303582
$895$	−7.57817e10	−3.53333
$896$	3.53462e9	0.164159
$897$	6.52879e9	0.302036
$898$	9.92567e9	0.457396
$899$	−3.16653e9	−0.145353
$900$	−1.71172e10	−0.782677
$901$	2.29270e10	1.04426
$902$	1.19070e9	0.0540232
$903$	−2.12780e10	−0.961664
$904$	3.97711e9	0.179052
$905$	3.32779e10	1.49240
$906$	8.25757e9	0.368896
$907$	2.00171e10	0.890790	0.445395	−	0.895334i	$-0.353063\pi$
$907$	2.00171e10	0.890790	0.445395	+	0.895334i	$0.353063\pi$
$908$	−1.45316e10	−0.644188
$909$	−9.54676e9	−0.421582
$910$	−3.83894e10	−1.68875
$911$	−1.55429e10	−0.681113	−0.340556	−	0.940224i	$-0.610615\pi$
$911$	−1.55429e10	−0.681113	−0.340556	+	0.940224i	$0.610615\pi$
$912$	2.33363e9	0.101871
$913$	−3.77779e10	−1.64282
$914$	−6.53412e9	−0.283058
$915$	−5.49090e10	−2.36957
$916$	1.11835e10	0.480778
$917$	2.65692e10	1.13785
$918$	−1.06471e10	−0.454237
$919$	−7.07850e9	−0.300841	−0.150420	−	0.988622i	$-0.548063\pi$
$919$	−7.07850e9	−0.300841	−0.150420	+	0.988622i	$0.548063\pi$
$920$	1.12221e10	0.475134
$921$	−9.97394e9	−0.420686
$922$	−8.61552e9	−0.362012
$923$	1.37252e9	0.0574532
$924$	−1.88370e10	−0.785523
$925$	−1.10609e10	−0.459509
$926$	−2.53228e10	−1.04803
$927$	−9.95205e9	−0.410330
$928$	−6.12950e8	−0.0251772
$929$	−9.26783e9	−0.379248	−0.189624	−	0.981857i	$-0.560727\pi$
$929$	−9.26783e9	−0.379248	−0.189624	+	0.981857i	$0.560727\pi$
$930$	−2.28737e10	−0.932492
$931$	3.70493e10	1.50472
$932$	1.70635e10	0.690417
$933$	−3.20419e9	−0.129161
$934$	−1.90222e10	−0.763917
$935$	3.85495e10	1.54233
$936$	3.27899e9	0.130700
$937$	−2.95508e10	−1.17349	−0.586746	−	0.809771i	$-0.699591\pi$
$937$	−2.95508e10	−1.17349	−0.586746	+	0.809771i	$0.699591\pi$
$938$	−2.24844e10	−0.889552
$939$	1.63136e10	0.643014
$940$	−6.11043e9	−0.239952
$941$	1.39298e10	0.544979	0.272489	−	0.962159i	$-0.412153\pi$
$941$	1.39298e10	0.544979	0.272489	+	0.962159i	$0.412153\pi$
$942$	5.16492e9	0.201319
$943$	−1.06420e9	−0.0413269
$944$	−5.08615e9	−0.196783
$945$	−9.71257e10	−3.74389
$946$	−1.83300e10	−0.703953
$947$	−2.48316e10	−0.950122	−0.475061	−	0.879953i	$-0.657574\pi$
$947$	−2.48316e10	−0.950122	−0.475061	+	0.879953i	$0.657574\pi$
$948$	7.21203e8	0.0274934
$949$	1.40452e10	0.533454
$950$	−3.20860e10	−1.21418
$951$	−1.94189e9	−0.0732137
$952$	−1.08520e10	−0.407642
$953$	−3.01791e10	−1.12949	−0.564744	−	0.825266i	$-0.691025\pi$
$953$	−3.01791e10	−1.12949	−0.564744	+	0.825266i	$0.691025\pi$
$954$	−1.78639e10	−0.666127
$955$	9.65515e10	3.58713
$956$	5.08627e9	0.188277
$957$	3.26658e9	0.120476
$958$	−2.94773e10	−1.08320
$959$	1.56373e10	0.572526
$960$	−4.42769e9	−0.161521
$961$	1.14339e9	0.0415589
$962$	2.11884e9	0.0767336
$963$	−1.41279e9	−0.0509783
$964$	3.71015e9	0.133389
$965$	3.67567e10	1.31671
$966$	1.68357e10	0.600913
$967$	−2.93661e10	−1.04437	−0.522184	−	0.852833i	$-0.674882\pi$
$967$	−2.93661e10	−1.04437	−0.522184	+	0.852833i	$0.674882\pi$
$968$	−6.24975e9	−0.221462
$969$	−7.16472e9	−0.252968
$970$	7.12167e10	2.50542
$971$	−2.39542e10	−0.839683	−0.419841	−	0.907598i	$-0.637914\pi$
$971$	−2.39542e10	−0.839683	−0.419841	+	0.907598i	$0.637914\pi$
$972$	1.36136e10	0.475490
$973$	−8.93961e10	−3.11117
$974$	1.59215e10	0.552114
$975$	3.54177e10	1.22378
$976$	1.33158e10	0.458449
$977$	2.91663e10	1.00058	0.500289	−	0.865859i	$-0.333227\pi$
$977$	2.91663e10	1.00058	0.500289	+	0.865859i	$0.333227\pi$
$978$	−9.94359e9	−0.339905
$979$	6.53513e10	2.22595
$980$	−7.02950e10	−2.38579
$981$	1.05377e10	0.356372
$982$	8.27654e9	0.278906
$983$	4.44637e9	0.149303	0.0746514	−	0.997210i	$-0.476216\pi$
$983$	4.44637e9	0.149303	0.0746514	+	0.997210i	$0.476216\pi$
$984$	4.19883e8	0.0140490
$985$	5.61375e10	1.87166
$986$	1.88188e9	0.0625205
$987$	−9.16707e9	−0.303473
$988$	6.14645e9	0.202757
$989$	1.63826e10	0.538514
$990$	−3.00365e10	−0.983842
$991$	3.36917e10	1.09968	0.549838	−	0.835271i	$-0.314689\pi$
$991$	3.36917e10	1.09968	0.549838	+	0.835271i	$0.314689\pi$
$992$	5.54700e9	0.180413
$993$	−9.64017e9	−0.312437
$994$	3.53931e9	0.114305
$995$	−9.73474e10	−3.13288
$996$	−1.33218e10	−0.427223
$997$	−7.98360e9	−0.255132	−0.127566	−	0.991830i	$-0.540717\pi$
$997$	−7.98360e9	−0.255132	−0.127566	+	0.991830i	$0.540717\pi$
$998$	1.35857e10	0.432638
$999$	5.36069e9	0.170115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.a.c.1.4	✓	6
4.3	odd	2		592.8.a.c.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.a.c.1.4	✓	6	1.1	even	1	trivial
592.8.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +31.0193 q^{3} +64.0000 q^{4} -544.510 q^{5} -248.154 q^{6} -1685.44 q^{7} -512.000 q^{8} -1224.80 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +31.0193 q^{3} +64.0000 q^{4} -544.510 q^{5} -248.154 q^{6} -1685.44 q^{7} -512.000 q^{8} -1224.80 q^{9} +4356.08 q^{10} +5629.72 q^{11} +1985.23 q^{12} +5228.81 q^{13} +13483.5 q^{14} -16890.3 q^{15} +4096.00 q^{16} -12575.5 q^{17} +9798.43 q^{18} +18367.1 q^{19} -34848.6 q^{20} -52281.0 q^{21} -45037.7 q^{22} +40252.9 q^{23} -15881.9 q^{24} +218366. q^{25} -41830.5 q^{26} -105832. q^{27} -107868. q^{28} +18705.8 q^{29} +135123. q^{30} -169281. q^{31} -32768.0 q^{32} +174630. q^{33} +100604. q^{34} +917737. q^{35} -78387.4 q^{36} -50653.0 q^{37} -146937. q^{38} +162194. q^{39} +278789. q^{40} -26437.9 q^{41} +418248. q^{42} +406992. q^{43} +360302. q^{44} +666918. q^{45} -322024. q^{46} +175342. q^{47} +127055. q^{48} +2.01715e6 q^{49} -1.74693e6 q^{50} -390084. q^{51} +334644. q^{52} -1.82314e6 q^{53} +846654. q^{54} -3.06544e6 q^{55} +862943. q^{56} +569735. q^{57} -149646. q^{58} -1.24173e6 q^{59} -1.08098e6 q^{60} +3.25092e6 q^{61} +1.35425e6 q^{62} +2.06433e6 q^{63} +262144. q^{64} -2.84714e6 q^{65} -1.39704e6 q^{66} -1.66755e6 q^{67} -804834. q^{68} +1.24862e6 q^{69} -7.34189e6 q^{70} +262493. q^{71} +627099. q^{72} +2.68612e6 q^{73} +405224. q^{74} +6.77356e6 q^{75} +1.17550e6 q^{76} -9.48853e6 q^{77} -1.29755e6 q^{78} +363284. q^{79} -2.23031e6 q^{80} -604180. q^{81} +211503. q^{82} -6.71044e6 q^{83} -3.34599e6 q^{84} +6.84750e6 q^{85} -3.25594e6 q^{86} +580239. q^{87} -2.88241e6 q^{88} +1.16083e7 q^{89} -5.33534e6 q^{90} -8.81283e6 q^{91} +2.57619e6 q^{92} -5.25097e6 q^{93} -1.40274e6 q^{94} -1.00011e7 q^{95} -1.01644e6 q^{96} +1.63488e7 q^{97} -1.61372e7 q^{98} -6.89530e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) \) 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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Database

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