LMFDB - Embedded newform 74.8.a.c.1.5

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			1.5
Root			$-57.0201$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} +62.0201 q^{3} +64.0000 q^{4} +42.8650 q^{5} -496.161 q^{6} +819.178 q^{7} -512.000 q^{8} +1659.49 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +62.0201 q^{3} +64.0000 q^{4} +42.8650 q^{5} -496.161 q^{6} +819.178 q^{7} -512.000 q^{8} +1659.49 q^{9} -342.920 q^{10} +728.856 q^{11} +3969.29 q^{12} +14302.8 q^{13} -6553.43 q^{14} +2658.49 q^{15} +4096.00 q^{16} -34889.7 q^{17} -13275.9 q^{18} +38798.5 q^{19} +2743.36 q^{20} +50805.5 q^{21} -5830.85 q^{22} -61429.2 q^{23} -31754.3 q^{24} -76287.6 q^{25} -114423. q^{26} -32716.2 q^{27} +52427.4 q^{28} +197556. q^{29} -21267.9 q^{30} +255264. q^{31} -32768.0 q^{32} +45203.7 q^{33} +279117. q^{34} +35114.1 q^{35} +106207. q^{36} -50653.0 q^{37} -310388. q^{38} +887064. q^{39} -21946.9 q^{40} +797332. q^{41} -406444. q^{42} +141543. q^{43} +46646.8 q^{44} +71134.1 q^{45} +491434. q^{46} +643617. q^{47} +254034. q^{48} -152490. q^{49} +610301. q^{50} -2.16386e6 q^{51} +915382. q^{52} +994805. q^{53} +261729. q^{54} +31242.4 q^{55} -419419. q^{56} +2.40629e6 q^{57} -1.58045e6 q^{58} -2.48495e6 q^{59} +170143. q^{60} -649593. q^{61} -2.04211e6 q^{62} +1.35942e6 q^{63} +262144. q^{64} +613091. q^{65} -361630. q^{66} -818509. q^{67} -2.23294e6 q^{68} -3.80985e6 q^{69} -280913. q^{70} -2.77796e6 q^{71} -849659. q^{72} +4.46812e6 q^{73} +405224. q^{74} -4.73136e6 q^{75} +2.48310e6 q^{76} +597063. q^{77} -7.09651e6 q^{78} +3.61377e6 q^{79} +175575. q^{80} -5.65837e6 q^{81} -6.37866e6 q^{82} -2.47637e6 q^{83} +3.25155e6 q^{84} -1.49555e6 q^{85} -1.13235e6 q^{86} +1.22525e7 q^{87} -373174. q^{88} +6.02437e6 q^{89} -569072. q^{90} +1.17166e7 q^{91} -3.93147e6 q^{92} +1.58315e7 q^{93} -5.14894e6 q^{94} +1.66310e6 q^{95} -2.03227e6 q^{96} -1.02401e7 q^{97} +1.21992e6 q^{98} +1.20953e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	62.0201	1.32620	0.663098	−	0.748532i	$-0.269241\pi$
$3$	62.0201	1.32620	0.663098	+	0.748532i	$0.269241\pi$
$4$	64.0000	0.500000
$5$	42.8650	0.153358	0.0766792	−	0.997056i	$-0.475568\pi$
$5$	42.8650	0.153358	0.0766792	+	0.997056i	$0.475568\pi$
$6$	−496.161	−0.937763
$7$	819.178	0.902683	0.451341	−	0.892351i	$-0.350946\pi$
$7$	819.178	0.902683	0.451341	+	0.892351i	$0.350946\pi$
$8$	−512.000	−0.353553
$9$	1659.49	0.758798
$10$	−342.920	−0.108441
$11$	728.856	0.165108	0.0825538	−	0.996587i	$-0.473692\pi$
$11$	728.856	0.165108	0.0825538	+	0.996587i	$0.473692\pi$
$12$	3969.29	0.663098
$13$	14302.8	1.80560	0.902798	−	0.430065i	$-0.141509\pi$
$13$	14302.8	1.80560	0.902798	+	0.430065i	$0.141509\pi$
$14$	−6553.43	−0.638293
$15$	2658.49	0.203384
$16$	4096.00	0.250000
$17$	−34889.7	−1.72237	−0.861183	−	0.508295i	$-0.830276\pi$
$17$	−34889.7	−1.72237	−0.861183	+	0.508295i	$0.830276\pi$
$18$	−13275.9	−0.536551
$19$	38798.5	1.29771	0.648854	−	0.760913i	$-0.275248\pi$
$19$	38798.5	1.29771	0.648854	+	0.760913i	$0.275248\pi$
$20$	2743.36	0.0766792
$21$	50805.5	1.19714
$22$	−5830.85	−0.116749
$23$	−61429.2	−1.05276	−0.526378	−	0.850251i	$-0.676450\pi$
$23$	−61429.2	−1.05276	−0.526378	+	0.850251i	$0.676450\pi$
$24$	−31754.3	−0.468881
$25$	−76287.6	−0.976481
$26$	−114423.	−1.27675
$27$	−32716.2	−0.319882
$28$	52427.4	0.451341
$29$	197556.	1.50417	0.752086	−	0.659065i	$-0.229048\pi$
$29$	197556.	1.50417	0.752086	+	0.659065i	$0.229048\pi$
$30$	−21267.9	−0.143814
$31$	255264.	1.53895	0.769474	−	0.638678i	$-0.220519\pi$
$31$	255264.	1.53895	0.769474	+	0.638678i	$0.220519\pi$
$32$	−32768.0	−0.176777
$33$	45203.7	0.218965
$34$	279117.	1.21790
$35$	35114.1	0.138434
$36$	106207.	0.379399
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	−310388.	−0.917618
$39$	887064.	2.39458
$40$	−21946.9	−0.0542204
$41$	797332.	1.80674	0.903370	−	0.428861i	$-0.141085\pi$
$41$	797332.	1.80674	0.903370	+	0.428861i	$0.141085\pi$
$42$	−406444.	−0.846502
$43$	141543.	0.271487	0.135744	−	0.990744i	$-0.456658\pi$
$43$	141543.	0.271487	0.135744	+	0.990744i	$0.456658\pi$
$44$	46646.8	0.0825538
$45$	71134.1	0.116368
$46$	491434.	0.744411
$47$	643617.	0.904243	0.452121	−	0.891956i	$-0.350667\pi$
$47$	643617.	0.904243	0.452121	+	0.891956i	$0.350667\pi$
$48$	254034.	0.331549
$49$	−152490.	−0.185163
$50$	610301.	0.690476
$51$	−2.16386e6	−2.28420
$52$	915382.	0.902798
$53$	994805.	0.917852	0.458926	−	0.888475i	$-0.348234\pi$
$53$	994805.	0.917852	0.458926	+	0.888475i	$0.348234\pi$
$54$	261729.	0.226191
$55$	31242.4	0.0253207
$56$	−419419.	−0.319147
$57$	2.40629e6	1.72102
$58$	−1.58045e6	−1.06361
$59$	−2.48495e6	−1.57520	−0.787601	−	0.616185i	$-0.788677\pi$
$59$	−2.48495e6	−1.57520	−0.787601	+	0.616185i	$0.788677\pi$
$60$	170143.	0.101692
$61$	−649593.	−0.366426	−0.183213	−	0.983073i	$-0.558650\pi$
$61$	−649593.	−0.366426	−0.183213	+	0.983073i	$0.558650\pi$
$62$	−2.04211e6	−1.08820
$63$	1.35942e6	0.684954
$64$	262144.	0.125000
$65$	613091.	0.276904
$66$	−361630.	−0.154832
$67$	−818509.	−0.332477	−0.166239	−	0.986086i	$-0.553162\pi$
$67$	−818509.	−0.332477	−0.166239	+	0.986086i	$0.553162\pi$
$68$	−2.23294e6	−0.861183
$69$	−3.80985e6	−1.39616
$70$	−280913.	−0.0978877
$71$	−2.77796e6	−0.921132	−0.460566	−	0.887625i	$-0.652354\pi$
$71$	−2.77796e6	−0.921132	−0.460566	+	0.887625i	$0.652354\pi$
$72$	−849659.	−0.268276
$73$	4.46812e6	1.34430	0.672148	−	0.740416i	$-0.265372\pi$
$73$	4.46812e6	1.34430	0.672148	+	0.740416i	$0.265372\pi$
$74$	405224.	0.116248
$75$	−4.73136e6	−1.29501
$76$	2.48310e6	0.648854
$77$	597063.	0.149040
$78$	−7.09651e6	−1.69322
$79$	3.61377e6	0.824643	0.412321	−	0.911038i	$-0.364718\pi$
$79$	3.61377e6	0.824643	0.412321	+	0.911038i	$0.364718\pi$
$80$	175575.	0.0383396
$81$	−5.65837e6	−1.18302
$82$	−6.37866e6	−1.27756
$83$	−2.47637e6	−0.475382	−0.237691	−	0.971341i	$-0.576391\pi$
$83$	−2.47637e6	−0.475382	−0.237691	+	0.971341i	$0.576391\pi$
$84$	3.25155e6	0.598568
$85$	−1.49555e6	−0.264139
$86$	−1.13235e6	−0.191970
$87$	1.22525e7	1.99483
$88$	−373174.	−0.0583744
$89$	6.02437e6	0.905829	0.452915	−	0.891554i	$-0.350384\pi$
$89$	6.02437e6	0.905829	0.452915	+	0.891554i	$0.350384\pi$
$90$	−569072.	−0.0822846
$91$	1.17166e7	1.62988
$92$	−3.93147e6	−0.526378
$93$	1.58315e7	2.04095
$94$	−5.14894e6	−0.639396
$95$	1.66310e6	0.199015
$96$	−2.03227e6	−0.234441
$97$	−1.02401e7	−1.13921	−0.569603	−	0.821920i	$-0.692903\pi$
$97$	−1.02401e7	−1.13921	−0.569603	+	0.821920i	$0.692903\pi$
$98$	1.21992e6	0.130930
$99$	1.20953e6	0.125283
$100$	−4.88241e6	−0.488241
$101$	−9.80284e6	−0.946732	−0.473366	−	0.880866i	$-0.656961\pi$
$101$	−9.80284e6	−0.946732	−0.473366	+	0.880866i	$0.656961\pi$
$102$	1.73109e7	1.61517
$103$	−8.87773e6	−0.800519	−0.400260	−	0.916402i	$-0.631080\pi$
$103$	−8.87773e6	−0.800519	−0.400260	+	0.916402i	$0.631080\pi$
$104$	−7.32306e6	−0.638375
$105$	2.17778e6	0.183591
$106$	−7.95844e6	−0.649019
$107$	−2.13471e7	−1.68459	−0.842297	−	0.539014i	$-0.818797\pi$
$107$	−2.13471e7	−1.68459	−0.842297	+	0.539014i	$0.818797\pi$
$108$	−2.09384e6	−0.159941
$109$	4.53326e6	0.335288	0.167644	−	0.985848i	$-0.446384\pi$
$109$	4.53326e6	0.335288	0.167644	+	0.985848i	$0.446384\pi$
$110$	−249939.	−0.0179044
$111$	−3.14150e6	−0.218025
$112$	3.35535e6	0.225671
$113$	1.86207e7	1.21401	0.607003	−	0.794700i	$-0.292372\pi$
$113$	1.86207e7	1.21401	0.607003	+	0.794700i	$0.292372\pi$
$114$	−1.92503e7	−1.21694
$115$	−2.63316e6	−0.161449
$116$	1.26436e7	0.752086
$117$	2.37354e7	1.37008
$118$	1.98796e7	1.11384
$119$	−2.85809e7	−1.55475
$120$	−1.36115e6	−0.0719069
$121$	−1.89559e7	−0.972739
$122$	5.19674e6	0.259103
$123$	4.94506e7	2.39609
$124$	1.63369e7	0.769474
$125$	−6.61890e6	−0.303110
$126$	−1.08753e7	−0.484335
$127$	−3.19197e7	−1.38276	−0.691378	−	0.722494i	$-0.742996\pi$
$127$	−3.19197e7	−1.38276	−0.691378	+	0.722494i	$0.742996\pi$
$128$	−2.09715e6	−0.0883883
$129$	8.77852e6	0.360045
$130$	−4.90473e6	−0.195800
$131$	4.29915e6	0.167083	0.0835417	−	0.996504i	$-0.473377\pi$
$131$	4.29915e6	0.167083	0.0835417	+	0.996504i	$0.473377\pi$
$132$	2.89304e6	0.109483
$133$	3.17829e7	1.17142
$134$	6.54807e6	0.235097
$135$	−1.40238e6	−0.0490566
$136$	1.78635e7	0.608948
$137$	−2.11879e7	−0.703990	−0.351995	−	0.936002i	$-0.614497\pi$
$137$	−2.11879e7	−0.703990	−0.351995	+	0.936002i	$0.614497\pi$
$138$	3.04788e7	0.987235
$139$	−4.55730e7	−1.43932	−0.719658	−	0.694329i	$-0.755701\pi$
$139$	−4.55730e7	−1.43932	−0.719658	+	0.694329i	$0.755701\pi$
$140$	2.24730e6	0.0692170
$141$	3.99172e7	1.19920
$142$	2.22237e7	0.651339
$143$	1.04247e7	0.298118
$144$	6.79727e6	0.189699
$145$	8.46825e6	0.230678
$146$	−3.57450e7	−0.950561
$147$	−9.45745e6	−0.245563
$148$	−3.24179e6	−0.0821995
$149$	−9.31111e6	−0.230595	−0.115297	−	0.993331i	$-0.536782\pi$
$149$	−9.31111e6	−0.230595	−0.115297	+	0.993331i	$0.536782\pi$
$150$	3.78509e7	0.915708
$151$	3.37665e7	0.798118	0.399059	−	0.916925i	$-0.369337\pi$
$151$	3.37665e7	0.798118	0.399059	+	0.916925i	$0.369337\pi$
$152$	−1.98648e7	−0.458809
$153$	−5.78991e7	−1.30693
$154$	−4.77650e6	−0.105387
$155$	1.09419e7	0.236011
$156$	5.67721e7	1.19729
$157$	−4.56700e7	−0.941852	−0.470926	−	0.882173i	$-0.656080\pi$
$157$	−4.56700e7	−0.941852	−0.470926	+	0.882173i	$0.656080\pi$
$158$	−2.89102e7	−0.583110
$159$	6.16979e7	1.21725
$160$	−1.40460e6	−0.0271102
$161$	−5.03215e7	−0.950305
$162$	4.52669e7	0.836524
$163$	7.19023e7	1.30043	0.650214	−	0.759751i	$-0.274679\pi$
$163$	7.19023e7	1.30043	0.650214	+	0.759751i	$0.274679\pi$
$164$	5.10293e7	0.903370
$165$	1.93766e6	0.0335802
$166$	1.98110e7	0.336146
$167$	−1.35765e7	−0.225569	−0.112785	−	0.993619i	$-0.535977\pi$
$167$	−1.35765e7	−0.225569	−0.112785	+	0.993619i	$0.535977\pi$
$168$	−2.60124e7	−0.423251
$169$	1.41823e8	2.26018
$170$	1.19644e7	0.186775
$171$	6.43857e7	0.984698
$172$	9.05876e6	0.135744
$173$	−7.10807e7	−1.04374	−0.521868	−	0.853027i	$-0.674764\pi$
$173$	−7.10807e7	−1.04374	−0.521868	+	0.853027i	$0.674764\pi$
$174$	−9.80196e7	−1.41056
$175$	−6.24931e7	−0.881453
$176$	2.98539e6	0.0412769
$177$	−1.54117e8	−2.08903
$178$	−4.81949e7	−0.640518
$179$	−1.03698e8	−1.35141	−0.675704	−	0.737173i	$-0.736160\pi$
$179$	−1.03698e8	−1.35141	−0.675704	+	0.737173i	$0.736160\pi$
$180$	4.55258e6	0.0581840
$181$	1.19620e7	0.149944	0.0749721	−	0.997186i	$-0.476113\pi$
$181$	1.19620e7	0.149944	0.0749721	+	0.997186i	$0.476113\pi$
$182$	−9.37326e7	−1.15250
$183$	−4.02878e7	−0.485954
$184$	3.14518e7	0.372205
$185$	−2.17124e6	−0.0252120
$186$	−1.26652e8	−1.44317
$187$	−2.54295e7	−0.284376
$188$	4.11915e7	0.452121
$189$	−2.68004e7	−0.288752
$190$	−1.33048e7	−0.140725
$191$	−6.85614e7	−0.711972	−0.355986	−	0.934491i	$-0.615855\pi$
$191$	−6.85614e7	−0.711972	−0.355986	+	0.934491i	$0.615855\pi$
$192$	1.62582e7	0.165775
$193$	1.14842e7	0.114987	0.0574935	−	0.998346i	$-0.481689\pi$
$193$	1.14842e7	0.114987	0.0574935	+	0.998346i	$0.481689\pi$
$194$	8.19206e7	0.805540
$195$	3.80240e7	0.367229
$196$	−9.75936e6	−0.0925817
$197$	−5.96509e7	−0.555885	−0.277943	−	0.960598i	$-0.589652\pi$
$197$	−5.96509e7	−0.555885	−0.277943	+	0.960598i	$0.589652\pi$
$198$	−9.67624e6	−0.0885887
$199$	2.32794e6	0.0209404	0.0104702	−	0.999945i	$-0.496667\pi$
$199$	2.32794e6	0.0209404	0.0104702	+	0.999945i	$0.496667\pi$
$200$	3.90592e7	0.345238
$201$	−5.07640e7	−0.440930
$202$	7.84227e7	0.669441
$203$	1.61834e8	1.35779
$204$	−1.38487e8	−1.14210
$205$	3.41776e7	0.277079
$206$	7.10218e7	0.566052
$207$	−1.01941e8	−0.798829
$208$	5.85844e7	0.451399
$209$	2.82785e7	0.214262
$210$	−1.74222e7	−0.129818
$211$	−1.21515e8	−0.890512	−0.445256	−	0.895403i	$-0.646887\pi$
$211$	−1.21515e8	−0.890512	−0.445256	+	0.895403i	$0.646887\pi$
$212$	6.36675e7	0.458926
$213$	−1.72289e8	−1.22160
$214$	1.70777e8	1.19119
$215$	6.06725e6	0.0416349
$216$	1.67507e7	0.113095
$217$	2.09107e8	1.38918
$218$	−3.62661e7	−0.237084
$219$	2.77113e8	1.78280
$220$	1.99951e6	0.0126603
$221$	−4.99021e8	−3.10990
$222$	2.51320e7	0.154167
$223$	7.31257e7	0.441574	0.220787	−	0.975322i	$-0.429138\pi$
$223$	7.31257e7	0.441574	0.220787	+	0.975322i	$0.429138\pi$
$224$	−2.68428e7	−0.159573
$225$	−1.26599e8	−0.740952
$226$	−1.48965e8	−0.858431
$227$	2.34452e8	1.33034	0.665171	−	0.746691i	$-0.268359\pi$
$227$	2.34452e8	1.33034	0.665171	+	0.746691i	$0.268359\pi$
$228$	1.54002e8	0.860508
$229$	−1.23358e8	−0.678804	−0.339402	−	0.940641i	$-0.610225\pi$
$229$	−1.23358e8	−0.678804	−0.339402	+	0.940641i	$0.610225\pi$
$230$	2.10653e7	0.114162
$231$	3.70299e7	0.197656
$232$	−1.01149e8	−0.531805
$233$	−1.91129e8	−0.989877	−0.494939	−	0.868928i	$-0.664809\pi$
$233$	−1.91129e8	−0.989877	−0.494939	+	0.868928i	$0.664809\pi$
$234$	−1.89883e8	−0.968795
$235$	2.75886e7	0.138673
$236$	−1.59037e8	−0.787601
$237$	2.24126e8	1.09364
$238$	2.28647e8	1.09937
$239$	3.66027e8	1.73428	0.867142	−	0.498060i	$-0.165954\pi$
$239$	3.66027e8	1.73428	0.867142	+	0.498060i	$0.165954\pi$
$240$	1.08892e7	0.0508459
$241$	−3.34001e8	−1.53705	−0.768526	−	0.639819i	$-0.779009\pi$
$241$	−3.34001e8	−1.53705	−0.768526	+	0.639819i	$0.779009\pi$
$242$	1.51648e8	0.687831
$243$	−2.79382e8	−1.24904
$244$	−4.15739e7	−0.183213
$245$	−6.53649e6	−0.0283964
$246$	−3.95605e8	−1.69429
$247$	5.54929e8	2.34314
$248$	−1.30695e8	−0.544100
$249$	−1.53585e8	−0.630450
$250$	5.29512e7	0.214331
$251$	4.23063e8	1.68868	0.844340	−	0.535808i	$-0.179993\pi$
$251$	4.23063e8	1.68868	0.844340	+	0.535808i	$0.179993\pi$
$252$	8.70028e7	0.342477
$253$	−4.47731e7	−0.173818
$254$	2.55357e8	0.977756
$255$	−9.27538e7	−0.350301
$256$	1.67772e7	0.0625000
$257$	−1.74610e8	−0.641659	−0.320830	−	0.947137i	$-0.603962\pi$
$257$	−1.74610e8	−0.641659	−0.320830	+	0.947137i	$0.603962\pi$
$258$	−7.02281e7	−0.254591
$259$	−4.14938e7	−0.148400
$260$	3.92378e7	0.138452
$261$	3.27843e8	1.14136
$262$	−3.43932e7	−0.118146
$263$	−4.23880e7	−0.143680	−0.0718402	−	0.997416i	$-0.522887\pi$
$263$	−4.23880e7	−0.143680	−0.0718402	+	0.997416i	$0.522887\pi$
$264$	−2.31443e7	−0.0774159
$265$	4.26423e7	0.140760
$266$	−2.54263e8	−0.828319
$267$	3.73632e8	1.20131
$268$	−5.23846e7	−0.166239
$269$	6.79464e6	0.0212830	0.0106415	−	0.999943i	$-0.496613\pi$
$269$	6.79464e6	0.0212830	0.0106415	+	0.999943i	$0.496613\pi$
$270$	1.12190e7	0.0346882
$271$	4.98438e8	1.52131	0.760656	−	0.649155i	$-0.224877\pi$
$271$	4.98438e8	1.52131	0.760656	+	0.649155i	$0.224877\pi$
$272$	−1.42908e8	−0.430592
$273$	7.26663e8	2.16154
$274$	1.69503e8	0.497796
$275$	−5.56027e7	−0.161225
$276$	−2.43830e8	−0.698081
$277$	−1.15197e7	−0.0325659	−0.0162830	−	0.999867i	$-0.505183\pi$
$277$	−1.15197e7	−0.0325659	−0.0162830	+	0.999867i	$0.505183\pi$
$278$	3.64584e8	1.01775
$279$	4.23608e8	1.16775
$280$	−1.79784e7	−0.0489438
$281$	−3.39018e7	−0.0911489	−0.0455744	−	0.998961i	$-0.514512\pi$
$281$	−3.39018e7	−0.0911489	−0.0455744	+	0.998961i	$0.514512\pi$
$282$	−3.19337e8	−0.847965
$283$	8.85427e7	0.232220	0.116110	−	0.993236i	$-0.462957\pi$
$283$	8.85427e7	0.232220	0.116110	+	0.993236i	$0.462957\pi$
$284$	−1.77790e8	−0.460566
$285$	1.03145e8	0.263933
$286$	−8.33977e7	−0.210801
$287$	6.53157e8	1.63091
$288$	−5.43782e7	−0.134138
$289$	8.06950e8	1.96655
$290$	−6.77460e7	−0.163114
$291$	−6.35090e8	−1.51081
$292$	2.85960e8	0.672148
$293$	−2.03644e8	−0.472971	−0.236486	−	0.971635i	$-0.575996\pi$
$293$	−2.03644e8	−0.472971	−0.236486	+	0.971635i	$0.575996\pi$
$294$	7.56596e7	0.173639
$295$	−1.06518e8	−0.241571
$296$	2.59343e7	0.0581238
$297$	−2.38454e7	−0.0528149
$298$	7.44889e7	0.163055
$299$	−8.78613e8	−1.90085
$300$	−3.02807e8	−0.647503
$301$	1.15949e8	0.245067
$302$	−2.70132e8	−0.564355
$303$	−6.07973e8	−1.25555
$304$	1.58919e8	0.324427
$305$	−2.78448e7	−0.0561946
$306$	4.63193e8	0.924137
$307$	6.17625e8	1.21826	0.609130	−	0.793070i	$-0.291519\pi$
$307$	6.17625e8	1.21826	0.609130	+	0.793070i	$0.291519\pi$
$308$	3.82120e7	0.0745200
$309$	−5.50598e8	−1.06165
$310$	−8.75352e7	−0.166885
$311$	−3.12762e8	−0.589593	−0.294796	−	0.955560i	$-0.595252\pi$
$311$	−3.12762e8	−0.589593	−0.294796	+	0.955560i	$0.595252\pi$
$312$	−4.54177e8	−0.846610
$313$	7.83237e8	1.44374	0.721868	−	0.692030i	$-0.243284\pi$
$313$	7.83237e8	1.44374	0.721868	+	0.692030i	$0.243284\pi$
$314$	3.65360e8	0.665990
$315$	5.82715e7	0.105043
$316$	2.31281e8	0.412321
$317$	2.34008e8	0.412594	0.206297	−	0.978489i	$-0.433859\pi$
$317$	2.34008e8	0.412594	0.206297	+	0.978489i	$0.433859\pi$
$318$	−4.93583e8	−0.860727
$319$	1.43990e8	0.248350
$320$	1.12368e7	0.0191698
$321$	−1.32395e9	−2.23410
$322$	4.02572e8	0.671967
$323$	−1.35367e9	−2.23513
$324$	−3.62135e8	−0.591512
$325$	−1.09113e9	−1.76313
$326$	−5.75219e8	−0.919542
$327$	2.81153e8	0.444658
$328$	−4.08234e8	−0.638779
$329$	5.27237e8	0.816244
$330$	−1.55013e7	−0.0237448
$331$	3.12893e8	0.474240	0.237120	−	0.971480i	$-0.423797\pi$
$331$	3.12893e8	0.474240	0.237120	+	0.971480i	$0.423797\pi$
$332$	−1.58488e8	−0.237691
$333$	−8.40582e7	−0.124746
$334$	1.08612e8	0.159502
$335$	−3.50854e7	−0.0509882
$336$	2.08099e8	0.299284
$337$	−1.12815e9	−1.60569	−0.802844	−	0.596189i	$-0.796681\pi$
$337$	−1.12815e9	−1.60569	−0.802844	+	0.596189i	$0.796681\pi$
$338$	−1.13458e9	−1.59819
$339$	1.15485e9	1.61001
$340$	−9.57149e7	−0.132070
$341$	1.86051e8	0.254092
$342$	−5.15086e8	−0.696287
$343$	−7.99545e8	−1.06983
$344$	−7.24701e7	−0.0959852
$345$	−1.63309e8	−0.214113
$346$	5.68646e8	0.738032
$347$	−4.60459e8	−0.591614	−0.295807	−	0.955248i	$-0.595588\pi$
$347$	−4.60459e8	−0.591614	−0.295807	+	0.955248i	$0.595588\pi$
$348$	7.84157e8	0.997414
$349$	−1.49795e8	−0.188629	−0.0943147	−	0.995542i	$-0.530066\pi$
$349$	−1.49795e8	−0.188629	−0.0943147	+	0.995542i	$0.530066\pi$
$350$	4.99945e8	0.623281
$351$	−4.67934e8	−0.577577
$352$	−2.38832e7	−0.0291872
$353$	−6.18632e8	−0.748550	−0.374275	−	0.927318i	$-0.622108\pi$
$353$	−6.18632e8	−0.748550	−0.374275	+	0.927318i	$0.622108\pi$
$354$	1.23294e9	1.47717
$355$	−1.19077e8	−0.141263
$356$	3.85559e8	0.452915
$357$	−1.77259e9	−2.06191
$358$	8.29587e8	0.955589
$359$	5.79596e8	0.661142	0.330571	−	0.943781i	$-0.392759\pi$
$359$	5.79596e8	0.661142	0.330571	+	0.943781i	$0.392759\pi$
$360$	−3.64206e7	−0.0411423
$361$	6.11451e8	0.684047
$362$	−9.56962e7	−0.106027
$363$	−1.17565e9	−1.29004
$364$	7.49861e8	0.814941
$365$	1.91526e8	0.206159
$366$	3.22302e8	0.343621
$367$	−6.40385e8	−0.676254	−0.338127	−	0.941100i	$-0.609793\pi$
$367$	−6.40385e8	−0.676254	−0.338127	+	0.941100i	$0.609793\pi$
$368$	−2.51614e8	−0.263189
$369$	1.32317e9	1.37095
$370$	1.73699e7	0.0178276
$371$	8.14923e8	0.828529
$372$	1.01322e9	1.02047
$373$	−8.49178e8	−0.847263	−0.423631	−	0.905835i	$-0.639245\pi$
$373$	−8.49178e8	−0.847263	−0.423631	+	0.905835i	$0.639245\pi$
$374$	2.03436e8	0.201084
$375$	−4.10504e8	−0.401984
$376$	−3.29532e8	−0.319698
$377$	2.82562e9	2.71593
$378$	2.14403e8	0.204178
$379$	2.68398e7	0.0253246	0.0126623	−	0.999920i	$-0.495969\pi$
$379$	2.68398e7	0.0253246	0.0126623	+	0.999920i	$0.495969\pi$
$380$	1.06438e8	0.0995073
$381$	−1.97966e9	−1.83381
$382$	5.48491e8	0.503440
$383$	−9.40912e8	−0.855762	−0.427881	−	0.903835i	$-0.640740\pi$
$383$	−9.40912e8	−0.855762	−0.427881	+	0.903835i	$0.640740\pi$
$384$	−1.30066e8	−0.117220
$385$	2.55931e7	0.0228565
$386$	−9.18733e7	−0.0813081
$387$	2.34890e8	0.206004
$388$	−6.55365e8	−0.569603
$389$	6.17107e8	0.531541	0.265771	−	0.964036i	$-0.414374\pi$
$389$	6.17107e8	0.531541	0.265771	+	0.964036i	$0.414374\pi$
$390$	−3.04192e8	−0.259670
$391$	2.14325e9	1.81323
$392$	7.80749e7	0.0654652
$393$	2.66634e8	0.221585
$394$	4.77207e8	0.393070
$395$	1.54904e8	0.126466
$396$	7.74099e7	0.0626417
$397$	−5.83027e8	−0.467651	−0.233825	−	0.972279i	$-0.575124\pi$
$397$	−5.83027e8	−0.467651	−0.233825	+	0.972279i	$0.575124\pi$
$398$	−1.86235e7	−0.0148071
$399$	1.97118e9	1.55353
$400$	−3.12474e8	−0.244120
$401$	3.92326e8	0.303838	0.151919	−	0.988393i	$-0.451455\pi$
$401$	3.92326e8	0.303838	0.151919	+	0.988393i	$0.451455\pi$
$402$	4.06112e8	0.311785
$403$	3.65100e9	2.77872
$404$	−6.27382e8	−0.473366
$405$	−2.42546e8	−0.181427
$406$	−1.29467e9	−0.960103
$407$	−3.69187e7	−0.0271435
$408$	1.10790e9	0.807585
$409$	−7.88600e8	−0.569935	−0.284967	−	0.958537i	$-0.591983\pi$
$409$	−7.88600e8	−0.569935	−0.284967	+	0.958537i	$0.591983\pi$
$410$	−2.73421e8	−0.195924
$411$	−1.31408e9	−0.933629
$412$	−5.68175e8	−0.400260
$413$	−2.03562e9	−1.42191
$414$	8.15530e8	0.564857
$415$	−1.06150e8	−0.0729038
$416$	−4.68676e8	−0.319187
$417$	−2.82644e9	−1.90882
$418$	−2.26228e8	−0.151506
$419$	9.25509e8	0.614655	0.307328	−	0.951604i	$-0.400565\pi$
$419$	9.25509e8	0.614655	0.307328	+	0.951604i	$0.400565\pi$
$420$	1.39378e8	0.0917954
$421$	−1.35607e9	−0.885717	−0.442859	−	0.896591i	$-0.646036\pi$
$421$	−1.35607e9	−0.885717	−0.442859	+	0.896591i	$0.646036\pi$
$422$	9.72117e8	0.629687
$423$	1.06808e9	0.686137
$424$	−5.09340e8	−0.324510
$425$	2.66165e9	1.68186
$426$	1.37832e9	0.863803
$427$	−5.32132e8	−0.330767
$428$	−1.36621e9	−0.842297
$429$	6.46542e8	0.395363
$430$	−4.85380e7	−0.0294403
$431$	−1.78683e9	−1.07501	−0.537506	−	0.843260i	$-0.680633\pi$
$431$	−1.78683e9	−1.07501	−0.537506	+	0.843260i	$0.680633\pi$
$432$	−1.34005e8	−0.0799704
$433$	1.29073e9	0.764059	0.382029	−	0.924150i	$-0.375225\pi$
$433$	1.29073e9	0.764059	0.382029	+	0.924150i	$0.375225\pi$
$434$	−1.67285e9	−0.982300
$435$	5.25201e8	0.305924
$436$	2.90129e8	0.167644
$437$	−2.38336e9	−1.36617
$438$	−2.21691e9	−1.26063
$439$	−1.86786e9	−1.05370	−0.526852	−	0.849957i	$-0.676628\pi$
$439$	−1.86786e9	−1.05370	−0.526852	+	0.849957i	$0.676628\pi$
$440$	−1.59961e7	−0.00895221
$441$	−2.53056e8	−0.140502
$442$	3.99217e9	2.19903
$443$	−4.02219e8	−0.219811	−0.109905	−	0.993942i	$-0.535055\pi$
$443$	−4.02219e8	−0.219811	−0.109905	+	0.993942i	$0.535055\pi$
$444$	−2.01056e8	−0.109013
$445$	2.58234e8	0.138917
$446$	−5.85006e8	−0.312240
$447$	−5.77476e8	−0.305814
$448$	2.14743e8	0.112835
$449$	2.85136e8	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$449$	2.85136e8	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$450$	1.01279e9	0.523932
$451$	5.81140e8	0.298307
$452$	1.19172e9	0.607003
$453$	2.09420e9	1.05846
$454$	−1.87562e9	−0.940694
$455$	5.02231e8	0.249956
$456$	−1.23202e9	−0.608471
$457$	3.67397e9	1.80065	0.900325	−	0.435218i	$-0.143329\pi$
$457$	3.67397e9	1.80065	0.900325	+	0.435218i	$0.143329\pi$
$458$	9.86867e8	0.479987
$459$	1.14146e9	0.550953
$460$	−1.68523e8	−0.0807245
$461$	2.42828e9	1.15437	0.577185	−	0.816613i	$-0.304151\pi$
$461$	2.42828e9	1.15437	0.577185	+	0.816613i	$0.304151\pi$
$462$	−2.96239e8	−0.139764
$463$	−5.71932e8	−0.267800	−0.133900	−	0.990995i	$-0.542750\pi$
$463$	−5.71932e8	−0.267800	−0.133900	+	0.990995i	$0.542750\pi$
$464$	8.09190e8	0.376043
$465$	6.78617e8	0.312997
$466$	1.52903e9	0.699949
$467$	7.45718e8	0.338817	0.169409	−	0.985546i	$-0.445814\pi$
$467$	7.45718e8	0.338817	0.169409	+	0.985546i	$0.445814\pi$
$468$	1.51907e9	0.685041
$469$	−6.70505e8	−0.300121
$470$	−2.20709e8	−0.0980568
$471$	−2.83246e9	−1.24908
$472$	1.27230e9	0.556918
$473$	1.03165e8	0.0448246
$474$	−1.79301e9	−0.773319
$475$	−2.95984e9	−1.26719
$476$	−1.82917e9	−0.777375
$477$	1.65087e9	0.696464
$478$	−2.92822e9	−1.22632
$479$	−2.52196e9	−1.04849	−0.524244	−	0.851568i	$-0.675652\pi$
$479$	−2.52196e9	−1.04849	−0.524244	+	0.851568i	$0.675652\pi$
$480$	−8.71134e7	−0.0359535
$481$	−7.24482e8	−0.296838
$482$	2.67201e9	1.08686
$483$	−3.12094e9	−1.26029
$484$	−1.21318e9	−0.486370
$485$	−4.38941e8	−0.174707
$486$	2.23506e9	0.883205
$487$	5.08644e9	1.99555	0.997776	−	0.0666592i	$-0.0212340\pi$
$487$	5.08644e9	1.99555	0.997776	+	0.0666592i	$0.0212340\pi$
$488$	3.32592e8	0.129551
$489$	4.45939e9	1.72462
$490$	5.22919e7	0.0200793
$491$	4.19309e9	1.59863	0.799317	−	0.600909i	$-0.205195\pi$
$491$	4.19309e9	1.59863	0.799317	+	0.600909i	$0.205195\pi$
$492$	3.16484e9	1.19805
$493$	−6.89267e9	−2.59074
$494$	−4.43943e9	−1.65685
$495$	5.18465e7	0.0192133
$496$	1.04556e9	0.384737
$497$	−2.27565e9	−0.831490
$498$	1.22868e9	0.445795
$499$	2.71162e9	0.976960	0.488480	−	0.872575i	$-0.337552\pi$
$499$	2.71162e9	0.976960	0.488480	+	0.872575i	$0.337552\pi$
$500$	−4.23609e8	−0.151555
$501$	−8.42015e8	−0.299149
$502$	−3.38451e9	−1.19408
$503$	−1.10903e8	−0.0388558	−0.0194279	−	0.999811i	$-0.506184\pi$
$503$	−1.10903e8	−0.0388558	−0.0194279	+	0.999811i	$0.506184\pi$
$504$	−6.96022e8	−0.242168
$505$	−4.20199e8	−0.145189
$506$	3.58185e8	0.122908
$507$	8.79586e9	2.99744
$508$	−2.04286e9	−0.691378
$509$	−2.34668e8	−0.0788753	−0.0394377	−	0.999222i	$-0.512557\pi$
$509$	−2.34668e8	−0.0788753	−0.0394377	+	0.999222i	$0.512557\pi$
$510$	7.42031e8	0.247700
$511$	3.66019e9	1.21347
$512$	−1.34218e8	−0.0441942
$513$	−1.26934e9	−0.415113
$514$	1.39688e9	0.453722
$515$	−3.80544e8	−0.122766
$516$	5.61825e8	0.180023
$517$	4.69104e8	0.149297
$518$	3.31951e8	0.104935
$519$	−4.40843e9	−1.38420
$520$	−3.13903e8	−0.0979002
$521$	−4.13958e9	−1.28240	−0.641201	−	0.767373i	$-0.721564\pi$
$521$	−4.13958e9	−1.28240	−0.641201	+	0.767373i	$0.721564\pi$
$522$	−2.62274e9	−0.807065
$523$	−3.44542e9	−1.05314	−0.526570	−	0.850132i	$-0.676522\pi$
$523$	−3.44542e9	−1.05314	−0.526570	+	0.850132i	$0.676522\pi$
$524$	2.75146e8	0.0835417
$525$	−3.87583e9	−1.16898
$526$	3.39104e8	0.101597
$527$	−8.90608e9	−2.65063
$528$	1.85154e8	0.0547413
$529$	3.68727e8	0.108295
$530$	−3.41139e8	−0.0995326
$531$	−4.12376e9	−1.19526
$532$	2.03410e9	0.585710
$533$	1.14041e10	3.26224
$534$	−2.98905e9	−0.849453
$535$	−9.15042e8	−0.258347
$536$	4.19077e8	0.117548
$537$	−6.43138e9	−1.79223
$538$	−5.43571e7	−0.0150494
$539$	−1.11143e8	−0.0305719
$540$	−8.97522e7	−0.0245283
$541$	−1.85339e9	−0.503241	−0.251620	−	0.967826i	$-0.580963\pi$
$541$	−1.85339e9	−0.503241	−0.251620	+	0.967826i	$0.580963\pi$
$542$	−3.98750e9	−1.07573
$543$	7.41886e8	0.198855
$544$	1.14326e9	0.304474
$545$	1.94318e8	0.0514192
$546$	−5.81330e9	−1.52844
$547$	5.68957e9	1.48636	0.743180	−	0.669092i	$-0.233317\pi$
$547$	5.68957e9	1.48636	0.743180	+	0.669092i	$0.233317\pi$
$548$	−1.35603e9	−0.351995
$549$	−1.07799e9	−0.278044
$550$	4.44821e8	0.114003
$551$	7.66488e9	1.95198
$552$	1.95064e9	0.493618
$553$	2.96032e9	0.744391
$554$	9.21579e7	0.0230276
$555$	−1.34661e8	−0.0334360
$556$	−2.91667e9	−0.719658
$557$	−3.33204e9	−0.816991	−0.408495	−	0.912760i	$-0.633946\pi$
$557$	−3.33204e9	−0.816991	−0.408495	+	0.912760i	$0.633946\pi$
$558$	−3.38887e9	−0.825724
$559$	2.02447e9	0.490196
$560$	1.43827e8	0.0346085
$561$	−1.57714e9	−0.377138
$562$	2.71215e8	0.0644520
$563$	−1.06521e9	−0.251569	−0.125785	−	0.992058i	$-0.540145\pi$
$563$	−1.06521e9	−0.251569	−0.125785	+	0.992058i	$0.540145\pi$
$564$	2.55470e9	0.599602
$565$	7.98175e8	0.186178
$566$	−7.08342e8	−0.164205
$567$	−4.63521e9	−1.06790
$568$	1.42232e9	0.325669
$569$	7.06281e9	1.60725	0.803627	−	0.595134i	$-0.202901\pi$
$569$	7.06281e9	1.60725	0.803627	+	0.595134i	$0.202901\pi$
$570$	−8.25163e8	−0.186628
$571$	−4.37500e8	−0.0983448	−0.0491724	−	0.998790i	$-0.515658\pi$
$571$	−4.37500e8	−0.0983448	−0.0491724	+	0.998790i	$0.515658\pi$
$572$	6.67182e8	0.149059
$573$	−4.25218e9	−0.944215
$574$	−5.22526e9	−1.15323
$575$	4.68629e9	1.02800
$576$	4.35026e8	0.0948497
$577$	−3.43823e9	−0.745108	−0.372554	−	0.928011i	$-0.621518\pi$
$577$	−3.43823e9	−0.745108	−0.372554	+	0.928011i	$0.621518\pi$
$578$	−6.45560e9	−1.39056
$579$	7.12249e8	0.152495
$580$	5.41968e8	0.115339
$581$	−2.02859e9	−0.429119
$582$	5.08072e9	1.06830
$583$	7.25070e8	0.151544
$584$	−2.28768e9	−0.475281
$585$	1.01742e9	0.210114
$586$	1.62915e9	0.334441
$587$	−3.05838e9	−0.624106	−0.312053	−	0.950065i	$-0.601017\pi$
$587$	−3.05838e9	−0.624106	−0.312053	+	0.950065i	$0.601017\pi$
$588$	−6.05277e8	−0.122782
$589$	9.90386e9	1.99711
$590$	8.52140e8	0.170816
$591$	−3.69955e9	−0.737213
$592$	−2.07475e8	−0.0410997
$593$	−3.89622e9	−0.767277	−0.383638	−	0.923483i	$-0.625329\pi$
$593$	−3.89622e9	−0.767277	−0.383638	+	0.923483i	$0.625329\pi$
$594$	1.90763e8	0.0373458
$595$	−1.22512e9	−0.238434
$596$	−5.95911e8	−0.115297
$597$	1.44379e8	0.0277711
$598$	7.02890e9	1.34411
$599$	2.62988e8	0.0499968	0.0249984	−	0.999687i	$-0.492042\pi$
$599$	2.62988e8	0.0499968	0.0249984	+	0.999687i	$0.492042\pi$
$600$	2.42246e9	0.457854
$601$	5.90358e9	1.10931	0.554657	−	0.832079i	$-0.312849\pi$
$601$	5.90358e9	1.10931	0.554657	+	0.832079i	$0.312849\pi$
$602$	−9.27593e8	−0.173288
$603$	−1.35831e9	−0.252283
$604$	2.16106e9	0.399059
$605$	−8.12546e8	−0.149178
$606$	4.86378e9	0.887810
$607$	−3.48163e8	−0.0631862	−0.0315931	−	0.999501i	$-0.510058\pi$
$607$	−3.48163e8	−0.0631862	−0.0315931	+	0.999501i	$0.510058\pi$
$608$	−1.27135e9	−0.229405
$609$	1.00369e10	1.80070
$610$	2.22758e8	0.0397356
$611$	9.20555e9	1.63270
$612$	−3.70554e9	−0.653464
$613$	9.95233e9	1.74507	0.872535	−	0.488551i	$-0.162474\pi$
$613$	9.95233e9	1.74507	0.872535	+	0.488551i	$0.162474\pi$
$614$	−4.94100e9	−0.861440
$615$	2.11970e9	0.367461
$616$	−3.05696e8	−0.0526936
$617$	−4.16252e9	−0.713440	−0.356720	−	0.934211i	$-0.616105\pi$
$617$	−4.16252e9	−0.713440	−0.356720	+	0.934211i	$0.616105\pi$
$618$	4.40478e9	0.750697
$619$	−9.02642e9	−1.52967	−0.764836	−	0.644225i	$-0.777180\pi$
$619$	−9.02642e9	−1.52967	−0.764836	+	0.644225i	$0.777180\pi$
$620$	7.00281e8	0.118005
$621$	2.00973e9	0.336757
$622$	2.50209e9	0.416905
$623$	4.93503e9	0.817677
$624$	3.63341e9	0.598644
$625$	5.67625e9	0.929997
$626$	−6.26590e9	−1.02088
$627$	1.75384e9	0.284153
$628$	−2.92288e9	−0.470926
$629$	1.76727e9	0.283155
$630$	−4.66172e8	−0.0742770
$631$	−5.18976e9	−0.822327	−0.411164	−	0.911562i	$-0.634877\pi$
$631$	−5.18976e9	−0.822327	−0.411164	+	0.911562i	$0.634877\pi$
$632$	−1.85025e9	−0.291555
$633$	−7.53635e9	−1.18099
$634$	−1.87206e9	−0.291748
$635$	−1.36824e9	−0.212057
$636$	3.94867e9	0.608626
$637$	−2.18104e9	−0.334330
$638$	−1.15192e9	−0.175610
$639$	−4.61000e9	−0.698953
$640$	−8.98944e7	−0.0135551
$641$	4.63971e9	0.695805	0.347903	−	0.937531i	$-0.386894\pi$
$641$	4.63971e9	0.695805	0.347903	+	0.937531i	$0.386894\pi$
$642$	1.05916e10	1.57975
$643$	−5.83618e9	−0.865746	−0.432873	−	0.901455i	$-0.642500\pi$
$643$	−5.83618e9	−0.865746	−0.432873	+	0.901455i	$0.642500\pi$
$644$	−3.22058e9	−0.475153
$645$	3.76291e8	0.0552160
$646$	1.08293e10	1.58048
$647$	6.91032e9	1.00307	0.501537	−	0.865136i	$-0.332768\pi$
$647$	6.91032e9	1.00307	0.501537	+	0.865136i	$0.332768\pi$
$648$	2.89708e9	0.418262
$649$	−1.81117e9	−0.260078
$650$	8.72904e9	1.24672
$651$	1.29688e10	1.84233
$652$	4.60175e9	0.650214
$653$	1.11911e10	1.57281	0.786404	−	0.617713i	$-0.211941\pi$
$653$	1.11911e10	1.57281	0.786404	+	0.617713i	$0.211941\pi$
$654$	−2.24922e9	−0.314420
$655$	1.84283e8	0.0256237
$656$	3.26587e9	0.451685
$657$	7.41481e9	1.02005
$658$	−4.21790e9	−0.577172
$659$	−6.79949e8	−0.0925501	−0.0462751	−	0.998929i	$-0.514735\pi$
$659$	−6.79949e8	−0.0925501	−0.0462751	+	0.998929i	$0.514735\pi$
$660$	1.24010e8	0.0167901
$661$	−9.88028e9	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$661$	−9.88028e9	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$662$	−2.50314e9	−0.335338
$663$	−3.09493e10	−4.12434
$664$	1.26790e9	0.168073
$665$	1.36237e9	0.179647
$666$	6.72465e8	0.0882084
$667$	−1.21357e10	−1.58353
$668$	−8.68896e8	−0.112785
$669$	4.53526e9	0.585613
$670$	2.80683e8	0.0360541
$671$	−4.73460e8	−0.0604998
$672$	−1.66479e9	−0.211626
$673$	−7.85546e9	−0.993388	−0.496694	−	0.867926i	$-0.665453\pi$
$673$	−7.85546e9	−0.993388	−0.496694	+	0.867926i	$0.665453\pi$
$674$	9.02518e9	1.13539
$675$	2.49584e9	0.312358
$676$	9.07666e9	1.13009
$677$	6.57364e8	0.0814227	0.0407113	−	0.999171i	$-0.487038\pi$
$677$	6.57364e8	0.0814227	0.0407113	+	0.999171i	$0.487038\pi$
$678$	−9.23884e9	−1.13845
$679$	−8.38844e9	−1.02834
$680$	7.65719e8	0.0933874
$681$	1.45407e10	1.76430
$682$	−1.48841e9	−0.179670
$683$	−2.16148e9	−0.259584	−0.129792	−	0.991541i	$-0.541431\pi$
$683$	−2.16148e9	−0.259584	−0.129792	+	0.991541i	$0.541431\pi$
$684$	4.12069e9	0.492349
$685$	−9.08220e8	−0.107963
$686$	6.39636e9	0.756482
$687$	−7.65069e9	−0.900228
$688$	5.79761e8	0.0678718
$689$	1.42285e10	1.65727
$690$	1.30647e9	0.151401
$691$	−2.97140e9	−0.342600	−0.171300	−	0.985219i	$-0.554797\pi$
$691$	−2.97140e9	−0.342600	−0.171300	+	0.985219i	$0.554797\pi$
$692$	−4.54916e9	−0.521868
$693$	9.90820e8	0.113091
$694$	3.68368e9	0.418334
$695$	−1.95349e9	−0.220731
$696$	−6.27326e9	−0.705279
$697$	−2.78187e10	−3.11187
$698$	1.19836e9	0.133381
$699$	−1.18539e10	−1.31277
$700$	−3.99956e9	−0.440726
$701$	−1.11677e9	−0.122448	−0.0612239	−	0.998124i	$-0.519500\pi$
$701$	−1.11677e9	−0.122448	−0.0612239	+	0.998124i	$0.519500\pi$
$702$	3.74347e9	0.408409
$703$	−1.96526e9	−0.213342
$704$	1.91065e8	0.0206385
$705$	1.71105e9	0.183908
$706$	4.94905e9	0.529305
$707$	−8.03027e9	−0.854599
$708$	−9.86349e9	−1.04451
$709$	1.09686e9	0.115582	0.0577909	−	0.998329i	$-0.481594\pi$
$709$	1.09686e9	0.115582	0.0577909	+	0.998329i	$0.481594\pi$
$710$	9.52618e8	0.0998883
$711$	5.99702e9	0.625737
$712$	−3.08448e9	−0.320259
$713$	−1.56807e10	−1.62014
$714$	1.41807e10	1.45799
$715$	4.46855e8	0.0457189
$716$	−6.63670e9	−0.675704
$717$	2.27010e10	2.30000
$718$	−4.63676e9	−0.467498
$719$	1.63850e10	1.64397	0.821987	−	0.569507i	$-0.192866\pi$
$719$	1.63850e10	1.64397	0.821987	+	0.569507i	$0.192866\pi$
$720$	2.91365e8	0.0290920
$721$	−7.27244e9	−0.722615
$722$	−4.89160e9	−0.483694
$723$	−2.07148e10	−2.03843
$724$	7.65569e8	0.0749721
$725$	−1.50711e10	−1.46880
$726$	9.40519e9	0.912199
$727$	1.15403e10	1.11390	0.556951	−	0.830545i	$-0.311971\pi$
$727$	1.15403e10	1.11390	0.556951	+	0.830545i	$0.311971\pi$
$728$	−5.99889e9	−0.576250
$729$	−4.95245e9	−0.473450
$730$	−1.53221e9	−0.145777
$731$	−4.93839e9	−0.467600
$732$	−2.57842e9	−0.242977
$733$	2.54300e9	0.238497	0.119248	−	0.992864i	$-0.461952\pi$
$733$	2.54300e9	0.238497	0.119248	+	0.992864i	$0.461952\pi$
$734$	5.12308e9	0.478184
$735$	−4.05393e8	−0.0376592
$736$	2.01291e9	0.186103
$737$	−5.96575e8	−0.0548945
$738$	−1.05853e10	−0.969409
$739$	4.83951e9	0.441109	0.220554	−	0.975375i	$-0.429213\pi$
$739$	4.83951e9	0.441109	0.220554	+	0.975375i	$0.429213\pi$
$740$	−1.38959e8	−0.0126060
$741$	3.44167e10	3.10746
$742$	−6.51938e9	−0.585859
$743$	1.47376e10	1.31815	0.659075	−	0.752077i	$-0.270948\pi$
$743$	1.47376e10	1.31815	0.659075	+	0.752077i	$0.270948\pi$
$744$	−8.10573e9	−0.721584
$745$	−3.99121e8	−0.0353637
$746$	6.79343e9	0.599105
$747$	−4.10952e9	−0.360719
$748$	−1.62749e9	−0.142188
$749$	−1.74871e10	−1.52065
$750$	3.28404e9	0.284245
$751$	−8.79357e9	−0.757575	−0.378787	−	0.925484i	$-0.623659\pi$
$751$	−8.79357e9	−0.757575	−0.378787	+	0.925484i	$0.623659\pi$
$752$	2.63625e9	0.226061
$753$	2.62384e10	2.23952
$754$	−2.26049e10	−1.92045
$755$	1.44740e9	0.122398
$756$	−1.71522e9	−0.144376
$757$	1.10901e10	0.929176	0.464588	−	0.885527i	$-0.346202\pi$
$757$	1.10901e10	0.929176	0.464588	+	0.885527i	$0.346202\pi$
$758$	−2.14718e8	−0.0179072
$759$	−2.77683e9	−0.230517
$760$	−8.51506e8	−0.0703623
$761$	1.63390e10	1.34394	0.671971	−	0.740578i	$-0.265448\pi$
$761$	1.63390e10	1.34394	0.671971	+	0.740578i	$0.265448\pi$
$762$	1.58373e10	1.29670
$763$	3.71355e9	0.302659
$764$	−4.38793e9	−0.355986
$765$	−2.48184e9	−0.200428
$766$	7.52729e9	0.605115
$767$	−3.55419e10	−2.84418
$768$	1.04052e9	0.0828873
$769$	−2.03601e10	−1.61450	−0.807250	−	0.590210i	$-0.799045\pi$
$769$	−2.03601e10	−1.61450	−0.807250	+	0.590210i	$0.799045\pi$
$770$	−2.04745e8	−0.0161620
$771$	−1.08294e10	−0.850966
$772$	7.34987e8	0.0574935
$773$	−1.48655e10	−1.15758	−0.578791	−	0.815476i	$-0.696475\pi$
$773$	−1.48655e10	−1.15758	−0.578791	+	0.815476i	$0.696475\pi$
$774$	−1.87912e9	−0.145667
$775$	−1.94735e10	−1.50275
$776$	5.24292e9	0.402770
$777$	−2.57345e9	−0.196808
$778$	−4.93686e9	−0.375856
$779$	3.09353e10	2.34462
$780$	2.43353e9	0.183614
$781$	−2.02473e9	−0.152086
$782$	−1.71460e10	−1.28215
$783$	−6.46328e9	−0.481157
$784$	−6.24599e8	−0.0462909
$785$	−1.95765e9	−0.144441
$786$	−2.13307e9	−0.156685
$787$	8.65619e8	0.0633017	0.0316508	−	0.999499i	$-0.489924\pi$
$787$	8.65619e8	0.0633017	0.0316508	+	0.999499i	$0.489924\pi$
$788$	−3.81766e9	−0.277943
$789$	−2.62891e9	−0.190549
$790$	−1.23923e9	−0.0894249
$791$	1.52536e10	1.09586
$792$	−6.19279e8	−0.0442943
$793$	−9.29103e9	−0.661618
$794$	4.66421e9	0.330679
$795$	2.64468e9	0.186676
$796$	1.48988e8	0.0104702
$797$	9.04298e9	0.632714	0.316357	−	0.948640i	$-0.397540\pi$
$797$	9.04298e9	0.632714	0.316357	+	0.948640i	$0.397540\pi$
$798$	−1.57694e10	−1.09851
$799$	−2.24556e10	−1.55744
$800$	2.49979e9	0.172619
$801$	9.99738e9	0.687341
$802$	−3.13861e9	−0.214846
$803$	3.25662e9	0.221954
$804$	−3.24890e9	−0.220465
$805$	−2.15703e9	−0.145737
$806$	−2.92080e10	−1.96485
$807$	4.21404e8	0.0282255
$808$	5.01905e9	0.334720
$809$	1.63192e10	1.08362	0.541812	−	0.840500i	$-0.317738\pi$
$809$	1.63192e10	1.08362	0.541812	+	0.840500i	$0.317738\pi$
$810$	1.94037e9	0.128288
$811$	7.76810e9	0.511378	0.255689	−	0.966759i	$-0.417698\pi$
$811$	7.76810e9	0.511378	0.255689	+	0.966759i	$0.417698\pi$
$812$	1.03574e10	0.678896
$813$	3.09131e10	2.01756
$814$	2.95350e8	0.0191934
$815$	3.08209e9	0.199432
$816$	−8.86317e9	−0.571049
$817$	5.49166e9	0.352311
$818$	6.30880e9	0.403005
$819$	1.94436e10	1.23675
$820$	2.18737e9	0.138539
$821$	−2.01204e10	−1.26892	−0.634461	−	0.772955i	$-0.718778\pi$
$821$	−2.01204e10	−1.26892	−0.634461	+	0.772955i	$0.718778\pi$
$822$	1.05126e10	0.660176
$823$	1.05708e10	0.661012	0.330506	−	0.943804i	$-0.392781\pi$
$823$	1.05708e10	0.661012	0.330506	+	0.943804i	$0.392781\pi$
$824$	4.54540e9	0.283026
$825$	−3.44848e9	−0.213815
$826$	1.62850e10	1.00544
$827$	1.25059e10	0.768855	0.384427	−	0.923155i	$-0.374399\pi$
$827$	1.25059e10	0.768855	0.384427	+	0.923155i	$0.374399\pi$
$828$	−6.52424e9	−0.399414
$829$	−2.45378e10	−1.49587	−0.747935	−	0.663771i	$-0.768955\pi$
$829$	−2.45378e10	−1.49587	−0.747935	+	0.663771i	$0.768955\pi$
$830$	8.49197e8	0.0515508
$831$	−7.14455e8	−0.0431888
$832$	3.74940e9	0.225700
$833$	5.32033e9	0.318919
$834$	2.26115e10	1.34974
$835$	−5.81956e8	−0.0345930
$836$	1.80982e9	0.107131
$837$	−8.35127e9	−0.492281
$838$	−7.40407e9	−0.434627
$839$	1.37816e10	0.805627	0.402814	−	0.915282i	$-0.368032\pi$
$839$	1.37816e10	0.805627	0.402814	+	0.915282i	$0.368032\pi$
$840$	−1.11502e9	−0.0649092
$841$	2.17786e10	1.26254
$842$	1.08486e10	0.626297
$843$	−2.10260e9	−0.120881
$844$	−7.77694e9	−0.445256
$845$	6.07923e9	0.346617
$846$	−8.54461e9	−0.485172
$847$	−1.55283e10	−0.878075
$848$	4.07472e9	0.229463
$849$	5.49143e9	0.307970
$850$	−2.12932e10	−1.18925
$851$	3.11158e9	0.173072
$852$	−1.10265e10	−0.610801
$853$	−1.85710e10	−1.02450	−0.512252	−	0.858835i	$-0.671189\pi$
$853$	−1.85710e10	−1.02450	−0.512252	+	0.858835i	$0.671189\pi$
$854$	4.25706e9	0.233888
$855$	2.75989e9	0.151012
$856$	1.09297e10	0.595594
$857$	−2.10434e10	−1.14204	−0.571021	−	0.820935i	$-0.693453\pi$
$857$	−2.10434e10	−1.14204	−0.571021	+	0.820935i	$0.693453\pi$
$858$	−5.17233e9	−0.279564
$859$	9.00309e9	0.484636	0.242318	−	0.970197i	$-0.422092\pi$
$859$	9.00309e9	0.484636	0.242318	+	0.970197i	$0.422092\pi$
$860$	3.88304e8	0.0208174
$861$	4.05089e10	2.16291
$862$	1.42946e10	0.760148
$863$	−3.43937e9	−0.182155	−0.0910775	−	0.995844i	$-0.529031\pi$
$863$	−3.43937e9	−0.182155	−0.0910775	+	0.995844i	$0.529031\pi$
$864$	1.07204e9	0.0565476
$865$	−3.04687e9	−0.160066
$866$	−1.03258e10	−0.540271
$867$	5.00471e10	2.60803
$868$	1.33828e10	0.694591
$869$	2.63392e9	0.136155
$870$	−4.20161e9	−0.216321
$871$	−1.17070e10	−0.600319
$872$	−2.32103e9	−0.118542
$873$	−1.69933e10	−0.864426
$874$	1.90669e10	0.966028
$875$	−5.42206e9	−0.273612
$876$	1.77353e10	0.891401
$877$	2.84257e10	1.42302	0.711512	−	0.702674i	$-0.248011\pi$
$877$	2.84257e10	1.42302	0.711512	+	0.702674i	$0.248011\pi$
$878$	1.49429e10	0.745081
$879$	−1.26300e10	−0.627253
$880$	1.27969e8	0.00633017
$881$	2.37520e10	1.17027	0.585134	−	0.810937i	$-0.301042\pi$
$881$	2.37520e10	1.17027	0.585134	+	0.810937i	$0.301042\pi$
$882$	2.02445e9	0.0993496
$883$	6.43568e9	0.314581	0.157290	−	0.987552i	$-0.449724\pi$
$883$	6.43568e9	0.314581	0.157290	+	0.987552i	$0.449724\pi$
$884$	−3.19374e10	−1.55495
$885$	−6.60623e9	−0.320370
$886$	3.21775e9	0.155430
$887$	3.32908e10	1.60174	0.800868	−	0.598841i	$-0.204372\pi$
$887$	3.32908e10	1.60174	0.800868	+	0.598841i	$0.204372\pi$
$888$	1.60845e9	0.0770836
$889$	−2.61479e10	−1.24819
$890$	−2.06588e9	−0.0982289
$891$	−4.12413e9	−0.195326
$892$	4.68005e9	0.220787
$893$	2.49714e10	1.17344
$894$	4.61981e9	0.216243
$895$	−4.44503e9	−0.207250
$896$	−1.71794e9	−0.0797867
$897$	−5.44916e10	−2.52090
$898$	−2.28109e9	−0.105118
$899$	5.04290e10	2.31484
$900$	−8.10231e9	−0.370476
$901$	−3.47084e10	−1.58088
$902$	−4.64912e9	−0.210935
$903$	7.19117e9	0.325007
$904$	−9.53378e9	−0.429216
$905$	5.12752e8	0.0229952
$906$	−1.67536e10	−0.748445
$907$	1.75497e10	0.780986	0.390493	−	0.920606i	$-0.372305\pi$
$907$	1.75497e10	0.780986	0.390493	+	0.920606i	$0.372305\pi$
$908$	1.50049e10	0.665171
$909$	−1.62677e10	−0.718378
$910$	−4.01785e9	−0.176746
$911$	2.72922e10	1.19598	0.597991	−	0.801503i	$-0.295966\pi$
$911$	2.72922e10	1.19598	0.597991	+	0.801503i	$0.295966\pi$
$912$	9.85614e9	0.430254
$913$	−1.80492e9	−0.0784892
$914$	−2.93918e10	−1.27325
$915$	−1.72694e9	−0.0745251
$916$	−7.89493e9	−0.339402
$917$	3.52177e9	0.150823
$918$	−9.13165e9	−0.389583
$919$	1.03176e10	0.438504	0.219252	−	0.975668i	$-0.429638\pi$
$919$	1.03176e10	0.438504	0.219252	+	0.975668i	$0.429638\pi$
$920$	1.34818e9	0.0570809
$921$	3.83051e10	1.61565
$922$	−1.94262e10	−0.816263
$923$	−3.97327e10	−1.66319
$924$	2.36991e9	0.0988281
$925$	3.86420e9	0.160533
$926$	4.57546e9	0.189363
$927$	−1.47325e10	−0.607432
$928$	−6.47352e9	−0.265903
$929$	−4.40028e10	−1.80064	−0.900318	−	0.435233i	$-0.856666\pi$
$929$	−4.40028e10	−1.80064	−0.900318	+	0.435233i	$0.856666\pi$
$930$	−5.42894e9	−0.221322
$931$	−5.91638e9	−0.240288
$932$	−1.22323e10	−0.494939
$933$	−1.93975e10	−0.781916
$934$	−5.96574e9	−0.239580
$935$	−1.09004e9	−0.0436115
$936$	−1.21525e10	−0.484397
$937$	−4.05329e10	−1.60960	−0.804802	−	0.593543i	$-0.797729\pi$
$937$	−4.05329e10	−1.60960	−0.804802	+	0.593543i	$0.797729\pi$
$938$	5.36404e9	0.212218
$939$	4.85764e10	1.91468
$940$	1.76567e9	0.0693366
$941$	2.75697e10	1.07862	0.539310	−	0.842107i	$-0.318685\pi$
$941$	2.75697e10	1.07862	0.539310	+	0.842107i	$0.318685\pi$
$942$	2.26597e10	0.883233
$943$	−4.89795e10	−1.90206
$944$	−1.01784e10	−0.393801
$945$	−1.14880e9	−0.0442825
$946$	−8.25317e8	−0.0316958
$947$	2.02210e10	0.773710	0.386855	−	0.922141i	$-0.373561\pi$
$947$	2.02210e10	0.773710	0.386855	+	0.922141i	$0.373561\pi$
$948$	1.43441e10	0.546819
$949$	6.39069e10	2.42726
$950$	2.36787e10	0.896037
$951$	1.45132e10	0.547180
$952$	1.46334e10	0.549687
$953$	−3.99186e10	−1.49400	−0.747000	−	0.664825i	$-0.768506\pi$
$953$	−3.99186e10	−1.49400	−0.747000	+	0.664825i	$0.768506\pi$
$954$	−1.32070e10	−0.492474
$955$	−2.93888e9	−0.109187
$956$	2.34257e10	0.867142
$957$	8.93027e9	0.329362
$958$	2.01756e10	0.741392
$959$	−1.73567e10	−0.635480
$960$	6.96907e8	0.0254229
$961$	3.76472e10	1.36836
$962$	5.79586e9	0.209896
$963$	−3.54253e10	−1.27827
$964$	−2.13761e10	−0.768526
$965$	4.92269e8	0.0176342
$966$	2.49675e10	0.891161
$967$	2.34274e10	0.833164	0.416582	−	0.909098i	$-0.363228\pi$
$967$	2.34274e10	0.833164	0.416582	+	0.909098i	$0.363228\pi$
$968$	9.70544e9	0.343915
$969$	−8.39545e10	−2.96422
$970$	3.51153e9	0.123536
$971$	−8.28673e9	−0.290480	−0.145240	−	0.989396i	$-0.546395\pi$
$971$	−8.28673e9	−0.290480	−0.145240	+	0.989396i	$0.546395\pi$
$972$	−1.78805e10	−0.624520
$973$	−3.73324e10	−1.29925
$974$	−4.06916e10	−1.41107
$975$	−6.76719e10	−2.33826
$976$	−2.66073e9	−0.0916066
$977$	2.09332e8	0.00718132	0.00359066	−	0.999994i	$-0.498857\pi$
$977$	2.09332e8	0.00718132	0.00359066	+	0.999994i	$0.498857\pi$
$978$	−3.56751e10	−1.21949
$979$	4.39090e9	0.149559
$980$	−4.18335e8	−0.0141982
$981$	7.52290e9	0.254416
$982$	−3.35447e10	−1.13041
$983$	−2.56474e10	−0.861204	−0.430602	−	0.902542i	$-0.641699\pi$
$983$	−2.56474e10	−0.861204	−0.430602	+	0.902542i	$0.641699\pi$
$984$	−2.53187e10	−0.847147
$985$	−2.55693e9	−0.0852497
$986$	5.51414e10	1.83193
$987$	3.26993e10	1.08250
$988$	3.55154e10	1.17157
$989$	−8.69489e9	−0.285810
$990$	−4.14772e8	−0.0135858
$991$	−1.00296e10	−0.327360	−0.163680	−	0.986513i	$-0.552337\pi$
$991$	−1.00296e10	−0.327360	−0.163680	+	0.986513i	$0.552337\pi$
$992$	−8.36449e9	−0.272050
$993$	1.94057e10	0.628935
$994$	1.82052e10	0.587952
$995$	9.97871e7	0.00321139
$996$	−9.82943e9	−0.315225
$997$	−5.07634e10	−1.62225	−0.811125	−	0.584872i	$-0.801145\pi$
$997$	−5.07634e10	−1.62225	−0.811125	+	0.584872i	$0.801145\pi$
$998$	−2.16930e10	−0.690815
$999$	1.65717e9	0.0525882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.a.c.1.5	✓	6
4.3	odd	2		592.8.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.a.c.1.5	✓	6	1.1	even	1	trivial
592.8.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +62.0201 q^{3} +64.0000 q^{4} +42.8650 q^{5} -496.161 q^{6} +819.178 q^{7} -512.000 q^{8} +1659.49 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +62.0201 q^{3} +64.0000 q^{4} +42.8650 q^{5} -496.161 q^{6} +819.178 q^{7} -512.000 q^{8} +1659.49 q^{9} -342.920 q^{10} +728.856 q^{11} +3969.29 q^{12} +14302.8 q^{13} -6553.43 q^{14} +2658.49 q^{15} +4096.00 q^{16} -34889.7 q^{17} -13275.9 q^{18} +38798.5 q^{19} +2743.36 q^{20} +50805.5 q^{21} -5830.85 q^{22} -61429.2 q^{23} -31754.3 q^{24} -76287.6 q^{25} -114423. q^{26} -32716.2 q^{27} +52427.4 q^{28} +197556. q^{29} -21267.9 q^{30} +255264. q^{31} -32768.0 q^{32} +45203.7 q^{33} +279117. q^{34} +35114.1 q^{35} +106207. q^{36} -50653.0 q^{37} -310388. q^{38} +887064. q^{39} -21946.9 q^{40} +797332. q^{41} -406444. q^{42} +141543. q^{43} +46646.8 q^{44} +71134.1 q^{45} +491434. q^{46} +643617. q^{47} +254034. q^{48} -152490. q^{49} +610301. q^{50} -2.16386e6 q^{51} +915382. q^{52} +994805. q^{53} +261729. q^{54} +31242.4 q^{55} -419419. q^{56} +2.40629e6 q^{57} -1.58045e6 q^{58} -2.48495e6 q^{59} +170143. q^{60} -649593. q^{61} -2.04211e6 q^{62} +1.35942e6 q^{63} +262144. q^{64} +613091. q^{65} -361630. q^{66} -818509. q^{67} -2.23294e6 q^{68} -3.80985e6 q^{69} -280913. q^{70} -2.77796e6 q^{71} -849659. q^{72} +4.46812e6 q^{73} +405224. q^{74} -4.73136e6 q^{75} +2.48310e6 q^{76} +597063. q^{77} -7.09651e6 q^{78} +3.61377e6 q^{79} +175575. q^{80} -5.65837e6 q^{81} -6.37866e6 q^{82} -2.47637e6 q^{83} +3.25155e6 q^{84} -1.49555e6 q^{85} -1.13235e6 q^{86} +1.22525e7 q^{87} -373174. q^{88} +6.02437e6 q^{89} -569072. q^{90} +1.17166e7 q^{91} -3.93147e6 q^{92} +1.58315e7 q^{93} -5.14894e6 q^{94} +1.66310e6 q^{95} -2.03227e6 q^{96} -1.02401e7 q^{97} +1.21992e6 q^{98} +1.20953e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) \) 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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