LMFDB - Embedded newform 354.8.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2 x^{6} - 77333 x^{5} - 3585829 x^{4} + 1295511138 x^{3} + 69321224657 x^{2} + \cdots - 316178833801950 $ x^7 - 2x^6 - 77333x^5 - 3585829x^4 + 1295511138x^3 + 69321224657x^2 - 5554636281450x - 316178833801950
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$83.8682$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +407.599 q^{5} -216.000 q^{6} -513.363 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +407.599 q^{5} -216.000 q^{6} -513.363 q^{7} -512.000 q^{8} +729.000 q^{9} -3260.79 q^{10} +1818.44 q^{11} +1728.00 q^{12} -2646.21 q^{13} +4106.90 q^{14} +11005.2 q^{15} +4096.00 q^{16} -25663.4 q^{17} -5832.00 q^{18} +8069.39 q^{19} +26086.3 q^{20} -13860.8 q^{21} -14547.5 q^{22} -32390.7 q^{23} -13824.0 q^{24} +88011.7 q^{25} +21169.7 q^{26} +19683.0 q^{27} -32855.2 q^{28} +61928.0 q^{29} -88041.3 q^{30} -249059. q^{31} -32768.0 q^{32} +49097.8 q^{33} +205307. q^{34} -209246. q^{35} +46656.0 q^{36} +9485.58 q^{37} -64555.1 q^{38} -71447.6 q^{39} -208691. q^{40} -343416. q^{41} +110886. q^{42} -464183. q^{43} +116380. q^{44} +297139. q^{45} +259125. q^{46} -1.17480e6 q^{47} +110592. q^{48} -560001. q^{49} -704094. q^{50} -692911. q^{51} -169357. q^{52} -1.23035e6 q^{53} -157464. q^{54} +741193. q^{55} +262842. q^{56} +217874. q^{57} -495424. q^{58} -205379. q^{59} +704331. q^{60} +514481. q^{61} +1.99247e6 q^{62} -374242. q^{63} +262144. q^{64} -1.07859e6 q^{65} -392782. q^{66} +3.37364e6 q^{67} -1.64246e6 q^{68} -874548. q^{69} +1.67397e6 q^{70} -2.75210e6 q^{71} -373248. q^{72} +3.45596e6 q^{73} -75884.6 q^{74} +2.37632e6 q^{75} +516441. q^{76} -933518. q^{77} +571581. q^{78} +1.22905e6 q^{79} +1.66952e6 q^{80} +531441. q^{81} +2.74733e6 q^{82} +5.58635e6 q^{83} -887091. q^{84} -1.04604e7 q^{85} +3.71346e6 q^{86} +1.67206e6 q^{87} -931040. q^{88} +2.11586e6 q^{89} -2.37712e6 q^{90} +1.35846e6 q^{91} -2.07300e6 q^{92} -6.72460e6 q^{93} +9.39838e6 q^{94} +3.28907e6 q^{95} -884736. q^{96} +3.63915e6 q^{97} +4.48001e6 q^{98} +1.32564e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) $ 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9} + 1264 q^{10} - 2201 q^{11} + 12096 q^{12} - 8421 q^{13} + 4648 q^{14} - 4266 q^{15} + 28672 q^{16} - 2425 q^{17} - 40824 q^{18} - 37084 q^{19} - 10112 q^{20} - 15687 q^{21} + 17608 q^{22} + 99364 q^{23} - 96768 q^{24} + 101361 q^{25} + 67368 q^{26} + 137781 q^{27} - 37184 q^{28} + 2498 q^{29} + 34128 q^{30} - 57962 q^{31} - 229376 q^{32} - 59427 q^{33} + 19400 q^{34} + 190586 q^{35} + 326592 q^{36} - 6497 q^{37} + 296672 q^{38} - 227367 q^{39} + 80896 q^{40} - 319165 q^{41} + 125496 q^{42} - 633743 q^{43} - 140864 q^{44} - 115182 q^{45} - 794912 q^{46} - 1626560 q^{47} + 774144 q^{48} - 3846354 q^{49} - 810888 q^{50} - 65475 q^{51} - 538944 q^{52} - 1215602 q^{53} - 1102248 q^{54} - 3329556 q^{55} + 297472 q^{56} - 1001268 q^{57} - 19984 q^{58} - 1437653 q^{59} - 273024 q^{60} - 3180086 q^{61} + 463696 q^{62} - 423549 q^{63} + 1835008 q^{64} + 544086 q^{65} + 475416 q^{66} - 5349632 q^{67} - 155200 q^{68} + 2682828 q^{69} - 1524688 q^{70} + 1752423 q^{71} - 2612736 q^{72} - 1843424 q^{73} + 51976 q^{74} + 2736747 q^{75} - 2373376 q^{76} - 3885063 q^{77} + 1818936 q^{78} - 4769243 q^{79} - 647168 q^{80} + 3720087 q^{81} + 2553320 q^{82} + 5154441 q^{83} - 1003968 q^{84} - 4594902 q^{85} + 5069944 q^{86} + 67446 q^{87} + 1126912 q^{88} + 20086462 q^{89} + 921456 q^{90} + 6733847 q^{91} + 6359296 q^{92} - 1564974 q^{93} + 13012480 q^{94} + 12936212 q^{95} - 6193152 q^{96} + 6244248 q^{97} + 30770832 q^{98} - 1604529 q^{99}+O(q^{100}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9 + 1264 * q^10 - 2201 * q^11 + 12096 * q^12 - 8421 * q^13 + 4648 * q^14 - 4266 * q^15 + 28672 * q^16 - 2425 * q^17 - 40824 * q^18 - 37084 * q^19 - 10112 * q^20 - 15687 * q^21 + 17608 * q^22 + 99364 * q^23 - 96768 * q^24 + 101361 * q^25 + 67368 * q^26 + 137781 * q^27 - 37184 * q^28 + 2498 * q^29 + 34128 * q^30 - 57962 * q^31 - 229376 * q^32 - 59427 * q^33 + 19400 * q^34 + 190586 * q^35 + 326592 * q^36 - 6497 * q^37 + 296672 * q^38 - 227367 * q^39 + 80896 * q^40 - 319165 * q^41 + 125496 * q^42 - 633743 * q^43 - 140864 * q^44 - 115182 * q^45 - 794912 * q^46 - 1626560 * q^47 + 774144 * q^48 - 3846354 * q^49 - 810888 * q^50 - 65475 * q^51 - 538944 * q^52 - 1215602 * q^53 - 1102248 * q^54 - 3329556 * q^55 + 297472 * q^56 - 1001268 * q^57 - 19984 * q^58 - 1437653 * q^59 - 273024 * q^60 - 3180086 * q^61 + 463696 * q^62 - 423549 * q^63 + 1835008 * q^64 + 544086 * q^65 + 475416 * q^66 - 5349632 * q^67 - 155200 * q^68 + 2682828 * q^69 - 1524688 * q^70 + 1752423 * q^71 - 2612736 * q^72 - 1843424 * q^73 + 51976 * q^74 + 2736747 * q^75 - 2373376 * q^76 - 3885063 * q^77 + 1818936 * q^78 - 4769243 * q^79 - 647168 * q^80 + 3720087 * q^81 + 2553320 * q^82 + 5154441 * q^83 - 1003968 * q^84 - 4594902 * q^85 + 5069944 * q^86 + 67446 * q^87 + 1126912 * q^88 + 20086462 * q^89 + 921456 * q^90 + 6733847 * q^91 + 6359296 * q^92 - 1564974 * q^93 + 13012480 * q^94 + 12936212 * q^95 - 6193152 * q^96 + 6244248 * q^97 + 30770832 * q^98 - 1604529 * 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
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	407.599	1.45827	0.729135	−	0.684370i	$-0.239923\pi$
$5$	407.599	1.45827	0.729135	+	0.684370i	$0.239923\pi$
$6$	−216.000	−0.408248
$7$	−513.363	−0.565694	−0.282847	−	0.959165i	$-0.591279\pi$
$7$	−513.363	−0.565694	−0.282847	+	0.959165i	$0.591279\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−3260.79	−1.03115
$11$	1818.44	0.411930	0.205965	−	0.978559i	$-0.433967\pi$
$11$	1818.44	0.411930	0.205965	+	0.978559i	$0.433967\pi$
$12$	1728.00	0.288675
$13$	−2646.21	−0.334058	−0.167029	−	0.985952i	$-0.553417\pi$
$13$	−2646.21	−0.334058	−0.167029	+	0.985952i	$0.553417\pi$
$14$	4106.90	0.400006
$15$	11005.2	0.841932
$16$	4096.00	0.250000
$17$	−25663.4	−1.26690	−0.633450	−	0.773784i	$-0.718362\pi$
$17$	−25663.4	−1.26690	−0.633450	+	0.773784i	$0.718362\pi$
$18$	−5832.00	−0.235702
$19$	8069.39	0.269900	0.134950	−	0.990852i	$-0.456913\pi$
$19$	8069.39	0.269900	0.134950	+	0.990852i	$0.456913\pi$
$20$	26086.3	0.729135
$21$	−13860.8	−0.326603
$22$	−14547.5	−0.291279
$23$	−32390.7	−0.555102	−0.277551	−	0.960711i	$-0.589523\pi$
$23$	−32390.7	−0.555102	−0.277551	+	0.960711i	$0.589523\pi$
$24$	−13824.0	−0.204124
$25$	88011.7	1.12655
$26$	21169.7	0.236215
$27$	19683.0	0.192450
$28$	−32855.2	−0.282847
$29$	61928.0	0.471513	0.235757	−	0.971812i	$-0.424243\pi$
$29$	61928.0	0.471513	0.235757	+	0.971812i	$0.424243\pi$
$30$	−88041.3	−0.595336
$31$	−249059.	−1.50154	−0.750770	−	0.660564i	$-0.770317\pi$
$31$	−249059.	−1.50154	−0.750770	+	0.660564i	$0.770317\pi$
$32$	−32768.0	−0.176777
$33$	49097.8	0.237828
$34$	205307.	0.895834
$35$	−209246.	−0.824934
$36$	46656.0	0.166667
$37$	9485.58	0.0307863	0.0153932	−	0.999882i	$-0.495100\pi$
$37$	9485.58	0.0307863	0.0153932	+	0.999882i	$0.495100\pi$
$38$	−64555.1	−0.190848
$39$	−71447.6	−0.192869
$40$	−208691.	−0.515576
$41$	−343416.	−0.778175	−0.389087	−	0.921201i	$-0.627210\pi$
$41$	−343416.	−0.778175	−0.389087	+	0.921201i	$0.627210\pi$
$42$	110886.	0.230943
$43$	−464183.	−0.890326	−0.445163	−	0.895449i	$-0.646854\pi$
$43$	−464183.	−0.890326	−0.445163	+	0.895449i	$0.646854\pi$
$44$	116380.	0.205965
$45$	297139.	0.486090
$46$	259125.	0.392516
$47$	−1.17480e6	−1.65052	−0.825260	−	0.564753i	$-0.808971\pi$
$47$	−1.17480e6	−1.65052	−0.825260	+	0.564753i	$0.808971\pi$
$48$	110592.	0.144338
$49$	−560001.	−0.679991
$50$	−704094.	−0.796591
$51$	−692911.	−0.731445
$52$	−169357.	−0.167029
$53$	−1.23035e6	−1.13518	−0.567590	−	0.823311i	$-0.692124\pi$
$53$	−1.23035e6	−1.13518	−0.567590	+	0.823311i	$0.692124\pi$
$54$	−157464.	−0.136083
$55$	741193.	0.600706
$56$	262842.	0.200003
$57$	217874.	0.155827
$58$	−495424.	−0.333410
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	704331.	0.420966
$61$	514481.	0.290212	0.145106	−	0.989416i	$-0.453648\pi$
$61$	514481.	0.290212	0.145106	+	0.989416i	$0.453648\pi$
$62$	1.99247e6	1.06175
$63$	−374242.	−0.188565
$64$	262144.	0.125000
$65$	−1.07859e6	−0.487147
$66$	−392782.	−0.168170
$67$	3.37364e6	1.37037	0.685183	−	0.728371i	$-0.259722\pi$
$67$	3.37364e6	1.37037	0.685183	+	0.728371i	$0.259722\pi$
$68$	−1.64246e6	−0.633450
$69$	−874548.	−0.320488
$70$	1.67397e6	0.583316
$71$	−2.75210e6	−0.912558	−0.456279	−	0.889837i	$-0.650818\pi$
$71$	−2.75210e6	−0.912558	−0.456279	+	0.889837i	$0.650818\pi$
$72$	−373248.	−0.117851
$73$	3.45596e6	1.03977	0.519886	−	0.854236i	$-0.325974\pi$
$73$	3.45596e6	1.03977	0.519886	+	0.854236i	$0.325974\pi$
$74$	−75884.6	−0.0217692
$75$	2.37632e6	0.650414
$76$	516441.	0.134950
$77$	−933518.	−0.233026
$78$	571581.	0.136379
$79$	1.22905e6	0.280462	0.140231	−	0.990119i	$-0.455215\pi$
$79$	1.22905e6	0.280462	0.140231	+	0.990119i	$0.455215\pi$
$80$	1.66952e6	0.364567
$81$	531441.	0.111111
$82$	2.74733e6	0.550253
$83$	5.58635e6	1.07239	0.536197	−	0.844093i	$-0.319860\pi$
$83$	5.58635e6	1.07239	0.536197	+	0.844093i	$0.319860\pi$
$84$	−887091.	−0.163302
$85$	−1.04604e7	−1.84748
$86$	3.71346e6	0.629556
$87$	1.67206e6	0.272228
$88$	−931040.	−0.145639
$89$	2.11586e6	0.318142	0.159071	−	0.987267i	$-0.449150\pi$
$89$	2.11586e6	0.318142	0.159071	+	0.987267i	$0.449150\pi$
$90$	−2.37712e6	−0.343717
$91$	1.35846e6	0.188975
$92$	−2.07300e6	−0.277551
$93$	−6.72460e6	−0.866914
$94$	9.39838e6	1.16709
$95$	3.28907e6	0.393587
$96$	−884736.	−0.102062
$97$	3.63915e6	0.404854	0.202427	−	0.979297i	$-0.435117\pi$
$97$	3.63915e6	0.404854	0.202427	+	0.979297i	$0.435117\pi$
$98$	4.48001e6	0.480826
$99$	1.32564e6	0.137310
$100$	5.63275e6	0.563275
$101$	−2.66791e6	−0.257660	−0.128830	−	0.991667i	$-0.541122\pi$
$101$	−2.66791e6	−0.257660	−0.128830	+	0.991667i	$0.541122\pi$
$102$	5.54329e6	0.517210
$103$	−2.55372e6	−0.230273	−0.115137	−	0.993350i	$-0.536731\pi$
$103$	−2.55372e6	−0.230273	−0.115137	+	0.993350i	$0.536731\pi$
$104$	1.35486e6	0.118107
$105$	−5.64964e6	−0.476276
$106$	9.84284e6	0.802693
$107$	3.83509e6	0.302644	0.151322	−	0.988485i	$-0.451647\pi$
$107$	3.83509e6	0.302644	0.151322	+	0.988485i	$0.451647\pi$
$108$	1.25971e6	0.0962250
$109$	237316.	0.0175523	0.00877616	−	0.999961i	$-0.497206\pi$
$109$	237316.	0.0175523	0.00877616	+	0.999961i	$0.497206\pi$
$110$	−5.92954e6	−0.424763
$111$	256111.	0.0177745
$112$	−2.10273e6	−0.141423
$113$	−7.89601e6	−0.514794	−0.257397	−	0.966306i	$-0.582865\pi$
$113$	−7.89601e6	−0.514794	−0.257397	+	0.966306i	$0.582865\pi$
$114$	−1.74299e6	−0.110186
$115$	−1.32024e7	−0.809488
$116$	3.96339e6	0.235757
$117$	−1.92908e6	−0.111353
$118$	1.64303e6	0.0920575
$119$	1.31746e7	0.716677
$120$	−5.63465e6	−0.297668
$121$	−1.61805e7	−0.830313
$122$	−4.11585e6	−0.205211
$123$	−9.27224e6	−0.449280
$124$	−1.59398e7	−0.750770
$125$	4.02982e6	0.184544
$126$	2.99393e6	0.133335
$127$	6.56501e6	0.284395	0.142198	−	0.989838i	$-0.454583\pi$
$127$	6.56501e6	0.284395	0.142198	+	0.989838i	$0.454583\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.25329e7	−0.514030
$130$	8.62872e6	0.344465
$131$	1.40909e7	0.547634	0.273817	−	0.961782i	$-0.411714\pi$
$131$	1.40909e7	0.547634	0.273817	+	0.961782i	$0.411714\pi$
$132$	3.14226e6	0.118914
$133$	−4.14253e6	−0.152681
$134$	−2.69891e7	−0.968996
$135$	8.02277e6	0.280644
$136$	1.31396e7	0.447917
$137$	1.53477e7	0.509943	0.254971	−	0.966949i	$-0.417934\pi$
$137$	1.53477e7	0.509943	0.254971	+	0.966949i	$0.417934\pi$
$138$	6.99639e6	0.226619
$139$	−4.07922e7	−1.28832	−0.644162	−	0.764889i	$-0.722794\pi$
$139$	−4.07922e7	−1.28832	−0.644162	+	0.764889i	$0.722794\pi$
$140$	−1.33917e7	−0.412467
$141$	−3.17195e7	−0.952928
$142$	2.20168e7	0.645276
$143$	−4.81196e6	−0.137609
$144$	2.98598e6	0.0833333
$145$	2.52418e7	0.687594
$146$	−2.76477e7	−0.735230
$147$	−1.51200e7	−0.392593
$148$	607077.	0.0153932
$149$	−2.58104e7	−0.639210	−0.319605	−	0.947551i	$-0.603550\pi$
$149$	−2.58104e7	−0.639210	−0.319605	+	0.947551i	$0.603550\pi$
$150$	−1.90105e7	−0.459912
$151$	−6.60315e7	−1.56074	−0.780372	−	0.625316i	$-0.784970\pi$
$151$	−6.60315e7	−1.56074	−0.780372	+	0.625316i	$0.784970\pi$
$152$	−4.13153e6	−0.0954241
$153$	−1.87086e7	−0.422300
$154$	7.46815e6	0.164775
$155$	−1.01516e8	−2.18965
$156$	−4.57265e6	−0.0964343
$157$	2.29712e7	0.473733	0.236867	−	0.971542i	$-0.423880\pi$
$157$	2.29712e7	0.473733	0.236867	+	0.971542i	$0.423880\pi$
$158$	−9.83239e6	−0.198317
$159$	−3.32196e7	−0.655396
$160$	−1.33562e7	−0.257788
$161$	1.66282e7	0.314018
$162$	−4.25153e6	−0.0785674
$163$	−1.25687e7	−0.227318	−0.113659	−	0.993520i	$-0.536257\pi$
$163$	−1.25687e7	−0.227318	−0.113659	+	0.993520i	$0.536257\pi$
$164$	−2.19786e7	−0.389087
$165$	2.00122e7	0.346818
$166$	−4.46908e7	−0.758297
$167$	7.70796e7	1.28065	0.640327	−	0.768102i	$-0.278799\pi$
$167$	7.70796e7	1.28065	0.640327	+	0.768102i	$0.278799\pi$
$168$	7.09673e6	0.115472
$169$	−5.57461e7	−0.888405
$170$	8.36828e7	1.30637
$171$	5.88259e6	0.0899667
$172$	−2.97077e7	−0.445163
$173$	5.75174e7	0.844575	0.422287	−	0.906462i	$-0.361227\pi$
$173$	5.75174e7	0.844575	0.422287	+	0.906462i	$0.361227\pi$
$174$	−1.33764e7	−0.192495
$175$	−4.51820e7	−0.637282
$176$	7.44832e6	0.102983
$177$	−5.54523e6	−0.0751646
$178$	−1.69269e7	−0.224960
$179$	9.57510e6	0.124784	0.0623919	−	0.998052i	$-0.480127\pi$
$179$	9.57510e6	0.124784	0.0623919	+	0.998052i	$0.480127\pi$
$180$	1.90169e7	0.243045
$181$	1.30692e8	1.63822	0.819112	−	0.573634i	$-0.194467\pi$
$181$	1.30692e8	1.63822	0.819112	+	0.573634i	$0.194467\pi$
$182$	−1.08677e7	−0.133625
$183$	1.38910e7	0.167554
$184$	1.65840e7	0.196258
$185$	3.86631e6	0.0448948
$186$	5.37968e7	0.613001
$187$	−4.66672e7	−0.521875
$188$	−7.51871e7	−0.825260
$189$	−1.01045e7	−0.108868
$190$	−2.63126e7	−0.278308
$191$	−8.28061e7	−0.859895	−0.429947	−	0.902854i	$-0.641468\pi$
$191$	−8.28061e7	−0.859895	−0.429947	+	0.902854i	$0.641468\pi$
$192$	7.07789e6	0.0721688
$193$	−4.08145e7	−0.408662	−0.204331	−	0.978902i	$-0.565502\pi$
$193$	−4.08145e7	−0.408662	−0.204331	+	0.978902i	$0.565502\pi$
$194$	−2.91132e7	−0.286275
$195$	−2.91219e7	−0.281254
$196$	−3.58401e7	−0.339995
$197$	−2.46646e7	−0.229849	−0.114925	−	0.993374i	$-0.536663\pi$
$197$	−2.46646e7	−0.229849	−0.114925	+	0.993374i	$0.536663\pi$
$198$	−1.06051e7	−0.0970929
$199$	−9.91120e7	−0.891539	−0.445769	−	0.895148i	$-0.647070\pi$
$199$	−9.91120e7	−0.891539	−0.445769	+	0.895148i	$0.647070\pi$
$200$	−4.50620e7	−0.398296
$201$	9.10883e7	0.791182
$202$	2.13433e7	0.182193
$203$	−3.17915e7	−0.266732
$204$	−4.43463e7	−0.365723
$205$	−1.39976e8	−1.13479
$206$	2.04298e7	0.162828
$207$	−2.36128e7	−0.185034
$208$	−1.08389e7	−0.0835145
$209$	1.46737e7	0.111180
$210$	4.51972e7	0.336778
$211$	−1.66067e8	−1.21701	−0.608505	−	0.793550i	$-0.708230\pi$
$211$	−1.66067e8	−1.21701	−0.608505	+	0.793550i	$0.708230\pi$
$212$	−7.87427e7	−0.567590
$213$	−7.43068e7	−0.526865
$214$	−3.06807e7	−0.214002
$215$	−1.89200e8	−1.29834
$216$	−1.00777e7	−0.0680414
$217$	1.27858e8	0.849411
$218$	−1.89853e6	−0.0124114
$219$	9.33108e7	0.600313
$220$	4.74363e7	0.300353
$221$	6.79106e7	0.423218
$222$	−2.04889e6	−0.0125685
$223$	−3.13802e8	−1.89491	−0.947457	−	0.319884i	$-0.896356\pi$
$223$	−3.13802e8	−1.89491	−0.947457	+	0.319884i	$0.896356\pi$
$224$	1.68219e7	0.100001
$225$	6.41606e7	0.375517
$226$	6.31681e7	0.364014
$227$	−1.10635e8	−0.627771	−0.313886	−	0.949461i	$-0.601631\pi$
$227$	−1.10635e8	−0.627771	−0.313886	+	0.949461i	$0.601631\pi$
$228$	1.39439e7	0.0779135
$229$	−1.90713e8	−1.04944	−0.524719	−	0.851275i	$-0.675830\pi$
$229$	−1.90713e8	−1.04944	−0.524719	+	0.851275i	$0.675830\pi$
$230$	1.05619e8	0.572395
$231$	−2.52050e7	−0.134538
$232$	−3.17071e7	−0.166705
$233$	3.33567e8	1.72758	0.863789	−	0.503853i	$-0.168085\pi$
$233$	3.33567e8	1.72758	0.863789	+	0.503853i	$0.168085\pi$
$234$	1.54327e7	0.0787383
$235$	−4.78846e8	−2.40690
$236$	−1.31443e7	−0.0650945
$237$	3.31843e7	0.161925
$238$	−1.05397e8	−0.506767
$239$	2.74731e8	1.30171	0.650857	−	0.759200i	$-0.274410\pi$
$239$	2.74731e8	1.30171	0.650857	+	0.759200i	$0.274410\pi$
$240$	4.50772e7	0.210483
$241$	−3.53161e8	−1.62522	−0.812611	−	0.582806i	$-0.801955\pi$
$241$	−3.53161e8	−1.62522	−0.812611	+	0.582806i	$0.801955\pi$
$242$	1.29444e8	0.587120
$243$	1.43489e7	0.0641500
$244$	3.29268e7	0.145106
$245$	−2.28256e8	−0.991610
$246$	7.41779e7	0.317689
$247$	−2.13533e7	−0.0901623
$248$	1.27518e8	0.530874
$249$	1.50831e8	0.619147
$250$	−3.22386e7	−0.130493
$251$	1.58920e7	0.0634339	0.0317170	−	0.999497i	$-0.489902\pi$
$251$	1.58920e7	0.0634339	0.0317170	+	0.999497i	$0.489902\pi$
$252$	−2.39515e7	−0.0942823
$253$	−5.89004e7	−0.228663
$254$	−5.25200e7	−0.201098
$255$	−2.82430e8	−1.06664
$256$	1.67772e7	0.0625000
$257$	−3.05623e7	−0.112311	−0.0561553	−	0.998422i	$-0.517884\pi$
$257$	−3.05623e7	−0.112311	−0.0561553	+	0.998422i	$0.517884\pi$
$258$	1.00263e8	0.363474
$259$	−4.86955e6	−0.0174156
$260$	−6.90298e7	−0.243573
$261$	4.51455e7	0.157171
$262$	−1.12727e8	−0.387235
$263$	−6.48670e7	−0.219876	−0.109938	−	0.993938i	$-0.535065\pi$
$263$	−6.48670e7	−0.219876	−0.109938	+	0.993938i	$0.535065\pi$
$264$	−2.51381e7	−0.0840850
$265$	−5.01491e8	−1.65540
$266$	3.31402e7	0.107962
$267$	5.71281e7	0.183679
$268$	2.15913e8	0.685183
$269$	−1.18028e8	−0.369702	−0.184851	−	0.982767i	$-0.559180\pi$
$269$	−1.18028e8	−0.369702	−0.184851	+	0.982767i	$0.559180\pi$
$270$	−6.41821e7	−0.198445
$271$	−5.59144e8	−1.70660	−0.853299	−	0.521422i	$-0.825402\pi$
$271$	−5.59144e8	−1.70660	−0.853299	+	0.521422i	$0.825402\pi$
$272$	−1.05117e8	−0.316725
$273$	3.66785e7	0.109105
$274$	−1.22782e8	−0.360584
$275$	1.60044e8	0.464060
$276$	−5.59711e7	−0.160244
$277$	−2.56045e8	−0.723832	−0.361916	−	0.932211i	$-0.617877\pi$
$277$	−2.56045e8	−0.723832	−0.361916	+	0.932211i	$0.617877\pi$
$278$	3.26337e8	0.910983
$279$	−1.81564e8	−0.500513
$280$	1.07134e8	0.291658
$281$	−1.88164e8	−0.505899	−0.252950	−	0.967479i	$-0.581401\pi$
$281$	−1.88164e8	−0.505899	−0.252950	+	0.967479i	$0.581401\pi$
$282$	2.53756e8	0.673822
$283$	5.03627e8	1.32086	0.660429	−	0.750889i	$-0.270374\pi$
$283$	5.03627e8	1.32086	0.660429	+	0.750889i	$0.270374\pi$
$284$	−1.76135e8	−0.456279
$285$	8.88050e7	0.227238
$286$	3.84957e7	0.0973041
$287$	1.76297e8	0.440209
$288$	−2.38879e7	−0.0589256
$289$	2.48269e8	0.605036
$290$	−2.01934e8	−0.486202
$291$	9.82570e7	0.233743
$292$	2.21181e8	0.519886
$293$	−4.11649e7	−0.0956071	−0.0478035	−	0.998857i	$-0.515222\pi$
$293$	−4.11649e7	−0.0956071	−0.0478035	+	0.998857i	$0.515222\pi$
$294$	1.20960e8	0.277605
$295$	−8.37122e7	−0.189851
$296$	−4.85662e6	−0.0108846
$297$	3.57923e7	0.0792761
$298$	2.06483e8	0.451990
$299$	8.57125e7	0.185436
$300$	1.52084e8	0.325207
$301$	2.38294e8	0.503652
$302$	5.28252e8	1.10361
$303$	−7.20335e7	−0.148760
$304$	3.30522e7	0.0674750
$305$	2.09702e8	0.423207
$306$	1.49669e8	0.298611
$307$	4.88206e8	0.962984	0.481492	−	0.876451i	$-0.340095\pi$
$307$	4.88206e8	0.962984	0.481492	+	0.876451i	$0.340095\pi$
$308$	−5.97452e7	−0.116513
$309$	−6.89505e7	−0.132948
$310$	8.12130e8	1.54832
$311$	5.83054e7	0.109913	0.0549563	−	0.998489i	$-0.482498\pi$
$311$	5.83054e7	0.109913	0.0549563	+	0.998489i	$0.482498\pi$
$312$	3.65812e7	0.0681893
$313$	8.19110e8	1.50986	0.754930	−	0.655805i	$-0.227671\pi$
$313$	8.19110e8	1.50986	0.754930	+	0.655805i	$0.227671\pi$
$314$	−1.83769e8	−0.334980
$315$	−1.52540e8	−0.274978
$316$	7.86591e7	0.140231
$317$	5.58726e8	0.985126	0.492563	−	0.870277i	$-0.336060\pi$
$317$	5.58726e8	0.985126	0.492563	+	0.870277i	$0.336060\pi$
$318$	2.65757e8	0.463435
$319$	1.12612e8	0.194231
$320$	1.06850e8	0.182284
$321$	1.03547e8	0.174731
$322$	−1.33025e8	−0.222044
$323$	−2.07088e8	−0.341936
$324$	3.40122e7	0.0555556
$325$	−2.32897e8	−0.376333
$326$	1.00549e8	0.160738
$327$	6.40754e6	0.0101338
$328$	1.75829e8	0.275126
$329$	6.03098e8	0.933689
$330$	−1.60098e8	−0.245237
$331$	5.26629e8	0.798191	0.399095	−	0.916909i	$-0.369324\pi$
$331$	5.26629e8	0.798191	0.399095	+	0.916909i	$0.369324\pi$
$332$	3.57526e8	0.536197
$333$	6.91499e6	0.0102621
$334$	−6.16637e8	−0.905560
$335$	1.37509e9	1.99836
$336$	−5.67738e7	−0.0816509
$337$	4.69018e8	0.667552	0.333776	−	0.942652i	$-0.391677\pi$
$337$	4.69018e8	0.667552	0.333776	+	0.942652i	$0.391677\pi$
$338$	4.45969e8	0.628197
$339$	−2.13192e8	−0.297216
$340$	−6.69463e8	−0.923741
$341$	−4.52899e8	−0.618530
$342$	−4.70607e7	−0.0636161
$343$	7.10260e8	0.950360
$344$	2.37662e8	0.314778
$345$	−3.56465e8	−0.467358
$346$	−4.60139e8	−0.597205
$347$	−4.49557e8	−0.577606	−0.288803	−	0.957389i	$-0.593257\pi$
$347$	−4.49557e8	−0.577606	−0.288803	+	0.957389i	$0.593257\pi$
$348$	1.07012e8	0.136114
$349$	4.97045e8	0.625902	0.312951	−	0.949769i	$-0.398682\pi$
$349$	4.97045e8	0.625902	0.312951	+	0.949769i	$0.398682\pi$
$350$	3.61456e8	0.450627
$351$	−5.20853e7	−0.0642895
$352$	−5.95866e7	−0.0728197
$353$	3.48864e8	0.422129	0.211064	−	0.977472i	$-0.432307\pi$
$353$	3.48864e8	0.422129	0.211064	+	0.977472i	$0.432307\pi$
$354$	4.43619e7	0.0531494
$355$	−1.12175e9	−1.33076
$356$	1.35415e8	0.159071
$357$	3.55715e8	0.413774
$358$	−7.66008e7	−0.0882354
$359$	−4.25031e8	−0.484831	−0.242415	−	0.970173i	$-0.577940\pi$
$359$	−4.25031e8	−0.484831	−0.242415	+	0.970173i	$0.577940\pi$
$360$	−1.52135e8	−0.171859
$361$	−8.28757e8	−0.927154
$362$	−1.04553e9	−1.15840
$363$	−4.36872e8	−0.479382
$364$	8.69417e7	0.0944873
$365$	1.40864e9	1.51627
$366$	−1.11128e8	−0.118478
$367$	6.26777e8	0.661884	0.330942	−	0.943651i	$-0.392634\pi$
$367$	6.26777e8	0.661884	0.330942	+	0.943651i	$0.392634\pi$
$368$	−1.32672e8	−0.138775
$369$	−2.50350e8	−0.259392
$370$	−3.09305e7	−0.0317454
$371$	6.31618e8	0.642164
$372$	−4.30374e8	−0.433457
$373$	−3.93191e8	−0.392303	−0.196152	−	0.980574i	$-0.562845\pi$
$373$	−3.93191e8	−0.392303	−0.196152	+	0.980574i	$0.562845\pi$
$374$	3.73338e8	0.369021
$375$	1.08805e8	0.106547
$376$	6.01497e8	0.583547
$377$	−1.63874e8	−0.157513
$378$	8.08362e7	0.0769812
$379$	−1.73913e9	−1.64095	−0.820473	−	0.571686i	$-0.806290\pi$
$379$	−1.73913e9	−1.64095	−0.820473	+	0.571686i	$0.806290\pi$
$380$	2.10501e8	0.196794
$381$	1.77255e8	0.164196
$382$	6.62448e8	0.608037
$383$	3.21570e8	0.292469	0.146234	−	0.989250i	$-0.453285\pi$
$383$	3.21570e8	0.292469	0.146234	+	0.989250i	$0.453285\pi$
$384$	−5.66231e7	−0.0510310
$385$	−3.80501e8	−0.339815
$386$	3.26516e8	0.288968
$387$	−3.38389e8	−0.296775
$388$	2.32906e8	0.202427
$389$	−5.46124e8	−0.470400	−0.235200	−	0.971947i	$-0.575575\pi$
$389$	−5.46124e8	−0.470400	−0.235200	+	0.971947i	$0.575575\pi$
$390$	2.32976e8	0.198877
$391$	8.31254e8	0.703259
$392$	2.86721e8	0.240413
$393$	3.80455e8	0.316176
$394$	1.97317e8	0.162528
$395$	5.00959e8	0.408989
$396$	8.48410e7	0.0686551
$397$	6.75722e8	0.542003	0.271001	−	0.962579i	$-0.412645\pi$
$397$	6.75722e8	0.542003	0.271001	+	0.962579i	$0.412645\pi$
$398$	7.92896e8	0.630413
$399$	−1.11848e8	−0.0881503
$400$	3.60496e8	0.281638
$401$	−3.72002e8	−0.288098	−0.144049	−	0.989571i	$-0.546012\pi$
$401$	−3.72002e8	−0.288098	−0.144049	+	0.989571i	$0.546012\pi$
$402$	−7.28706e8	−0.559450
$403$	6.59062e8	0.501601
$404$	−1.70746e8	−0.128830
$405$	2.16615e8	0.162030
$406$	2.54332e8	0.188608
$407$	1.72489e7	0.0126818
$408$	3.54770e8	0.258605
$409$	−7.34148e8	−0.530582	−0.265291	−	0.964168i	$-0.585468\pi$
$409$	−7.34148e8	−0.530582	−0.265291	+	0.964168i	$0.585468\pi$
$410$	1.11981e9	0.802417
$411$	4.14388e8	0.294416
$412$	−1.63438e8	−0.115137
$413$	1.05434e8	0.0736471
$414$	1.88902e8	0.130839
$415$	2.27699e9	1.56384
$416$	8.67109e7	0.0590537
$417$	−1.10139e9	−0.743814
$418$	−1.17389e8	−0.0786162
$419$	1.02210e9	0.678807	0.339403	−	0.940641i	$-0.389775\pi$
$419$	1.02210e9	0.678807	0.339403	+	0.940641i	$0.389775\pi$
$420$	−3.61577e8	−0.238138
$421$	−3.57327e7	−0.0233388	−0.0116694	−	0.999932i	$-0.503715\pi$
$421$	−3.57327e7	−0.0233388	−0.0116694	+	0.999932i	$0.503715\pi$
$422$	1.32853e9	0.860556
$423$	−8.56428e8	−0.550173
$424$	6.29942e8	0.401347
$425$	−2.25868e9	−1.42723
$426$	5.94454e8	0.372550
$427$	−2.64115e8	−0.164171
$428$	2.45445e8	0.151322
$429$	−1.29923e8	−0.0794484
$430$	1.51360e9	0.918062
$431$	−3.07253e9	−1.84853	−0.924263	−	0.381758i	$-0.875319\pi$
$431$	−3.07253e9	−1.84853	−0.924263	+	0.381758i	$0.875319\pi$
$432$	8.06216e7	0.0481125
$433$	−8.35814e8	−0.494769	−0.247384	−	0.968917i	$-0.579571\pi$
$433$	−8.35814e8	−0.494769	−0.247384	+	0.968917i	$0.579571\pi$
$434$	−1.02286e9	−0.600625
$435$	6.81528e8	0.396982
$436$	1.51882e7	0.00877616
$437$	−2.61373e8	−0.149822
$438$	−7.46487e8	−0.424485
$439$	−2.63711e9	−1.48765	−0.743827	−	0.668372i	$-0.766991\pi$
$439$	−2.63711e9	−1.48765	−0.743827	+	0.668372i	$0.766991\pi$
$440$	−3.79491e8	−0.212382
$441$	−4.08241e8	−0.226664
$442$	−5.43285e8	−0.299260
$443$	−7.12823e8	−0.389555	−0.194778	−	0.980847i	$-0.562398\pi$
$443$	−7.12823e8	−0.389555	−0.194778	+	0.980847i	$0.562398\pi$
$444$	1.63911e7	0.00888725
$445$	8.62420e8	0.463937
$446$	2.51042e9	1.33991
$447$	−6.96882e8	−0.369048
$448$	−1.34575e8	−0.0707117
$449$	1.60893e9	0.838832	0.419416	−	0.907794i	$-0.362235\pi$
$449$	1.60893e9	0.838832	0.419416	+	0.907794i	$0.362235\pi$
$450$	−5.13284e8	−0.265530
$451$	−6.24481e8	−0.320554
$452$	−5.05345e8	−0.257397
$453$	−1.78285e9	−0.901096
$454$	8.85079e8	0.443901
$455$	5.53708e8	0.275576
$456$	−1.11551e8	−0.0550931
$457$	2.91579e9	1.42906	0.714529	−	0.699606i	$-0.246641\pi$
$457$	2.91579e9	1.42906	0.714529	+	0.699606i	$0.246641\pi$
$458$	1.52571e9	0.742065
$459$	−5.05132e8	−0.243815
$460$	−8.44954e8	−0.404744
$461$	−2.09634e8	−0.0996570	−0.0498285	−	0.998758i	$-0.515867\pi$
$461$	−2.09634e8	−0.0996570	−0.0498285	+	0.998758i	$0.515867\pi$
$462$	2.01640e8	0.0951327
$463$	−2.41333e9	−1.13001	−0.565006	−	0.825087i	$-0.691126\pi$
$463$	−2.41333e9	−1.13001	−0.565006	+	0.825087i	$0.691126\pi$
$464$	2.53657e8	0.117878
$465$	−2.74094e9	−1.26419
$466$	−2.66854e9	−1.22158
$467$	−5.27531e8	−0.239684	−0.119842	−	0.992793i	$-0.538239\pi$
$467$	−5.27531e8	−0.239684	−0.119842	+	0.992793i	$0.538239\pi$
$468$	−1.23461e8	−0.0556764
$469$	−1.73190e9	−0.775208
$470$	3.83077e9	1.70194
$471$	6.20221e8	0.273510
$472$	1.05154e8	0.0460287
$473$	−8.44087e8	−0.366753
$474$	−2.65474e8	−0.114498
$475$	7.10201e8	0.304056
$476$	8.43176e8	0.358339
$477$	−8.96928e8	−0.378393
$478$	−2.19785e9	−0.920451
$479$	4.07792e9	1.69537	0.847684	−	0.530501i	$-0.177996\pi$
$479$	4.07792e9	1.69537	0.847684	+	0.530501i	$0.177996\pi$
$480$	−3.60617e8	−0.148834
$481$	−2.51008e7	−0.0102844
$482$	2.82529e9	1.14921
$483$	4.48961e8	0.181298
$484$	−1.03555e9	−0.415157
$485$	1.48331e9	0.590387
$486$	−1.14791e8	−0.0453609
$487$	6.20552e8	0.243459	0.121730	−	0.992563i	$-0.461156\pi$
$487$	6.20552e8	0.243459	0.121730	+	0.992563i	$0.461156\pi$
$488$	−2.63414e8	−0.102605
$489$	−3.39354e8	−0.131242
$490$	1.82605e9	0.701174
$491$	−9.22705e7	−0.0351785	−0.0175893	−	0.999845i	$-0.505599\pi$
$491$	−9.22705e7	−0.0351785	−0.0175893	+	0.999845i	$0.505599\pi$
$492$	−5.93423e8	−0.224640
$493$	−1.58928e9	−0.597360
$494$	1.70826e8	0.0637544
$495$	5.40330e8	0.200235
$496$	−1.02015e9	−0.375385
$497$	1.41283e9	0.516228
$498$	−1.20665e9	−0.437803
$499$	2.59284e9	0.934164	0.467082	−	0.884214i	$-0.345305\pi$
$499$	2.59284e9	0.934164	0.467082	+	0.884214i	$0.345305\pi$
$500$	2.57909e8	0.0922722
$501$	2.08115e9	0.739386
$502$	−1.27136e8	−0.0448546
$503$	−2.91117e9	−1.01995	−0.509977	−	0.860188i	$-0.670346\pi$
$503$	−2.91117e9	−1.01995	−0.509977	+	0.860188i	$0.670346\pi$
$504$	1.91612e8	0.0666676
$505$	−1.08744e9	−0.375737
$506$	4.71203e8	0.161689
$507$	−1.50514e9	−0.512921
$508$	4.20160e8	0.142198
$509$	−1.31863e9	−0.443212	−0.221606	−	0.975136i	$-0.571130\pi$
$509$	−1.31863e9	−0.443212	−0.221606	+	0.975136i	$0.571130\pi$
$510$	2.25944e9	0.754231
$511$	−1.77416e9	−0.588193
$512$	−1.34218e8	−0.0441942
$513$	1.58830e8	0.0519423
$514$	2.44499e8	0.0794156
$515$	−1.04089e9	−0.335800
$516$	−8.02108e8	−0.257015
$517$	−2.13630e9	−0.679899
$518$	3.89564e7	0.0123147
$519$	1.55297e9	0.487616
$520$	5.52238e8	0.172232
$521$	8.35183e8	0.258732	0.129366	−	0.991597i	$-0.458706\pi$
$521$	8.35183e8	0.258732	0.129366	+	0.991597i	$0.458706\pi$
$522$	−3.61164e8	−0.111137
$523$	−3.68007e9	−1.12486	−0.562432	−	0.826844i	$-0.690134\pi$
$523$	−3.68007e9	−1.12486	−0.562432	+	0.826844i	$0.690134\pi$
$524$	9.01820e8	0.273817
$525$	−1.21991e9	−0.367935
$526$	5.18936e8	0.155476
$527$	6.39170e9	1.90230
$528$	2.01105e8	0.0594570
$529$	−2.35567e9	−0.691862
$530$	4.01193e9	1.17054
$531$	−1.49721e8	−0.0433963
$532$	−2.65122e8	−0.0763404
$533$	9.08750e8	0.259956
$534$	−4.57025e8	−0.129881
$535$	1.56318e9	0.441336
$536$	−1.72730e9	−0.484498
$537$	2.58528e8	0.0720439
$538$	9.44223e8	0.261419
$539$	−1.01833e9	−0.280109
$540$	5.13457e8	0.140322
$541$	4.67597e9	1.26964	0.634821	−	0.772659i	$-0.281074\pi$
$541$	4.67597e9	1.26964	0.634821	+	0.772659i	$0.281074\pi$
$542$	4.47315e9	1.20675
$543$	3.52868e9	0.945829
$544$	8.40937e8	0.223958
$545$	9.67298e7	0.0255960
$546$	−2.93428e8	−0.0771486
$547$	−1.82602e9	−0.477036	−0.238518	−	0.971138i	$-0.576662\pi$
$547$	−1.82602e9	−0.477036	−0.238518	+	0.971138i	$0.576662\pi$
$548$	9.82253e8	0.254971
$549$	3.75057e8	0.0967372
$550$	−1.28035e9	−0.328140
$551$	4.99721e8	0.127262
$552$	4.47769e8	0.113310
$553$	−6.30948e8	−0.158656
$554$	2.04836e9	0.511827
$555$	1.04390e8	0.0259200
$556$	−2.61070e9	−0.644162
$557$	4.46770e8	0.109545	0.0547723	−	0.998499i	$-0.482557\pi$
$557$	4.46770e8	0.109545	0.0547723	+	0.998499i	$0.482557\pi$
$558$	1.45251e9	0.353916
$559$	1.22832e9	0.297421
$560$	−8.57072e8	−0.206233
$561$	−1.26001e9	−0.301304
$562$	1.50531e9	0.357725
$563$	4.97740e7	0.0117550	0.00587751	−	0.999983i	$-0.498129\pi$
$563$	4.97740e7	0.0117550	0.00587751	+	0.999983i	$0.498129\pi$
$564$	−2.03005e9	−0.476464
$565$	−3.21840e9	−0.750708
$566$	−4.02901e9	−0.933987
$567$	−2.72822e8	−0.0628549
$568$	1.40908e9	0.322638
$569$	3.03191e9	0.689959	0.344979	−	0.938610i	$-0.387886\pi$
$569$	3.03191e9	0.689959	0.344979	+	0.938610i	$0.387886\pi$
$570$	−7.10440e8	−0.160681
$571$	−2.00184e9	−0.449990	−0.224995	−	0.974360i	$-0.572237\pi$
$571$	−2.00184e9	−0.449990	−0.224995	+	0.974360i	$0.572237\pi$
$572$	−3.07966e8	−0.0688044
$573$	−2.23576e9	−0.496460
$574$	−1.41038e9	−0.311275
$575$	−2.85076e9	−0.625350
$576$	1.91103e8	0.0416667
$577$	−7.78825e9	−1.68781	−0.843907	−	0.536489i	$-0.819750\pi$
$577$	−7.78825e9	−1.68781	−0.843907	+	0.536489i	$0.819750\pi$
$578$	−1.98616e9	−0.427825
$579$	−1.10199e9	−0.235941
$580$	1.61547e9	0.343797
$581$	−2.86782e9	−0.606647
$582$	−7.86056e8	−0.165281
$583$	−2.23732e9	−0.467615
$584$	−1.76945e9	−0.367615
$585$	−7.86293e8	−0.162382
$586$	3.29319e8	0.0676044
$587$	−3.42081e9	−0.698065	−0.349032	−	0.937111i	$-0.613490\pi$
$587$	−3.42081e9	−0.698065	−0.349032	+	0.937111i	$0.613490\pi$
$588$	−9.67683e8	−0.196296
$589$	−2.00976e9	−0.405266
$590$	6.69698e8	0.134245
$591$	−6.65945e8	−0.132703
$592$	3.88529e7	0.00769658
$593$	3.43345e9	0.676144	0.338072	−	0.941120i	$-0.390225\pi$
$593$	3.43345e9	0.676144	0.338072	+	0.941120i	$0.390225\pi$
$594$	−2.86338e8	−0.0560566
$595$	5.36996e9	1.04511
$596$	−1.65187e9	−0.319605
$597$	−2.67602e9	−0.514730
$598$	−6.85700e8	−0.131123
$599$	5.18336e9	0.985412	0.492706	−	0.870196i	$-0.336008\pi$
$599$	5.18336e9	0.985412	0.492706	+	0.870196i	$0.336008\pi$
$600$	−1.21667e9	−0.229956
$601$	1.38094e9	0.259487	0.129743	−	0.991548i	$-0.458585\pi$
$601$	1.38094e9	0.259487	0.129743	+	0.991548i	$0.458585\pi$
$602$	−1.90635e9	−0.356136
$603$	2.45938e9	0.456789
$604$	−4.22601e9	−0.780372
$605$	−6.59513e9	−1.21082
$606$	5.76268e8	0.105189
$607$	8.55417e9	1.55245	0.776224	−	0.630457i	$-0.217132\pi$
$607$	8.55417e9	1.55245	0.776224	+	0.630457i	$0.217132\pi$
$608$	−2.64418e8	−0.0477121
$609$	−8.58371e8	−0.153998
$610$	−1.67761e9	−0.299252
$611$	3.10876e9	0.551369
$612$	−1.19735e9	−0.211150
$613$	3.63703e9	0.637727	0.318863	−	0.947801i	$-0.396699\pi$
$613$	3.63703e9	0.637727	0.318863	+	0.947801i	$0.396699\pi$
$614$	−3.90565e9	−0.680932
$615$	−3.77935e9	−0.655171
$616$	4.77961e8	0.0823873
$617$	3.04232e9	0.521443	0.260721	−	0.965414i	$-0.416040\pi$
$617$	3.04232e9	0.521443	0.260721	+	0.965414i	$0.416040\pi$
$618$	5.51604e8	0.0940086
$619$	−3.61336e9	−0.612341	−0.306171	−	0.951977i	$-0.599048\pi$
$619$	−3.61336e9	−0.612341	−0.306171	+	0.951977i	$0.599048\pi$
$620$	−6.49704e9	−1.09482
$621$	−6.37546e8	−0.106829
$622$	−4.66443e8	−0.0777199
$623$	−1.08620e9	−0.179971
$624$	−2.92649e8	−0.0482171
$625$	−5.23337e9	−0.857435
$626$	−6.55288e9	−1.06763
$627$	3.96189e8	0.0641899
$628$	1.47015e9	0.236867
$629$	−2.43432e8	−0.0390032
$630$	1.22032e9	0.194439
$631$	4.91130e9	0.778205	0.389102	−	0.921195i	$-0.372785\pi$
$631$	4.91130e9	0.778205	0.389102	+	0.921195i	$0.372785\pi$
$632$	−6.29273e8	−0.0991583
$633$	−4.48380e9	−0.702641
$634$	−4.46981e9	−0.696589
$635$	2.67589e9	0.414725
$636$	−2.12605e9	−0.327698
$637$	1.48188e9	0.227156
$638$	−9.00897e8	−0.137342
$639$	−2.00628e9	−0.304186
$640$	−8.54797e8	−0.128894
$641$	1.32687e10	1.98987	0.994935	−	0.100519i	$-0.0320502\pi$
$641$	1.32687e10	1.98987	0.994935	+	0.100519i	$0.0320502\pi$
$642$	−8.28378e8	−0.123554
$643$	3.40231e9	0.504702	0.252351	−	0.967636i	$-0.418796\pi$
$643$	3.40231e9	0.504702	0.252351	+	0.967636i	$0.418796\pi$
$644$	1.06420e9	0.157009
$645$	−5.10841e9	−0.749595
$646$	1.65670e9	0.241786
$647$	−2.61998e9	−0.380306	−0.190153	−	0.981754i	$-0.560898\pi$
$647$	−2.61998e9	−0.380306	−0.190153	+	0.981754i	$0.560898\pi$
$648$	−2.72098e8	−0.0392837
$649$	−3.73469e8	−0.0536288
$650$	1.86318e9	0.266108
$651$	3.45216e9	0.490408
$652$	−8.04396e8	−0.113659
$653$	−2.43123e9	−0.341688	−0.170844	−	0.985298i	$-0.554649\pi$
$653$	−2.43123e9	−0.341688	−0.170844	+	0.985298i	$0.554649\pi$
$654$	−5.12603e7	−0.00716570
$655$	5.74345e9	0.798598
$656$	−1.40663e9	−0.194544
$657$	2.51939e9	0.346591
$658$	−4.82478e9	−0.660217
$659$	9.78306e9	1.33161	0.665803	−	0.746127i	$-0.268089\pi$
$659$	9.78306e9	1.33161	0.665803	+	0.746127i	$0.268089\pi$
$660$	1.28078e9	0.173409
$661$	2.07257e9	0.279128	0.139564	−	0.990213i	$-0.455430\pi$
$661$	2.07257e9	0.279128	0.139564	+	0.990213i	$0.455430\pi$
$662$	−4.21303e9	−0.564406
$663$	1.83359e9	0.244345
$664$	−2.86021e9	−0.379149
$665$	−1.68849e9	−0.222650
$666$	−5.53199e7	−0.00725641
$667$	−2.00589e9	−0.261738
$668$	4.93310e9	0.640327
$669$	−8.47267e9	−1.09403
$670$	−1.10007e10	−1.41306
$671$	9.35551e8	0.119547
$672$	4.54191e8	0.0577359
$673$	5.12966e9	0.648688	0.324344	−	0.945939i	$-0.394857\pi$
$673$	5.12966e9	0.648688	0.324344	+	0.945939i	$0.394857\pi$
$674$	−3.75214e9	−0.472030
$675$	1.73234e9	0.216805
$676$	−3.56775e9	−0.444203
$677$	−9.28348e9	−1.14987	−0.574937	−	0.818198i	$-0.694973\pi$
$677$	−9.28348e9	−1.14987	−0.574937	+	0.818198i	$0.694973\pi$
$678$	1.70554e9	0.210164
$679$	−1.86820e9	−0.229024
$680$	5.35570e9	0.653183
$681$	−2.98714e9	−0.362444
$682$	3.62319e9	0.437367
$683$	−1.77999e9	−0.213769	−0.106885	−	0.994271i	$-0.534088\pi$
$683$	−1.77999e9	−0.213769	−0.106885	+	0.994271i	$0.534088\pi$
$684$	3.76485e8	0.0449834
$685$	6.25571e9	0.743634
$686$	−5.68208e9	−0.672006
$687$	−5.14926e9	−0.605893
$688$	−1.90129e9	−0.222582
$689$	3.25577e9	0.379216
$690$	2.85172e9	0.330472
$691$	8.59780e8	0.0991321	0.0495661	−	0.998771i	$-0.484216\pi$
$691$	8.59780e8	0.0991321	0.0495661	+	0.998771i	$0.484216\pi$
$692$	3.68112e9	0.422287
$693$	−6.80535e8	−0.0776755
$694$	3.59646e9	0.408429
$695$	−1.66268e10	−1.87872
$696$	−8.56093e8	−0.0962473
$697$	8.81321e9	0.985870
$698$	−3.97636e9	−0.442580
$699$	9.00632e9	0.997418
$700$	−2.89165e9	−0.318641
$701$	1.15166e10	1.26273	0.631363	−	0.775487i	$-0.282496\pi$
$701$	1.15166e10	1.26273	0.631363	+	0.775487i	$0.282496\pi$
$702$	4.16682e8	0.0454596
$703$	7.65428e7	0.00830923
$704$	4.76692e8	0.0514913
$705$	−1.29288e10	−1.38963
$706$	−2.79091e9	−0.298490
$707$	1.36961e9	0.145756
$708$	−3.54895e8	−0.0375823
$709$	−1.24761e9	−0.131467	−0.0657334	−	0.997837i	$-0.520939\pi$
$709$	−1.24761e9	−0.131467	−0.0657334	+	0.997837i	$0.520939\pi$
$710$	8.97403e9	0.940986
$711$	8.95976e8	0.0934874
$712$	−1.08332e9	−0.112480
$713$	8.06720e9	0.833507
$714$	−2.84572e9	−0.292582
$715$	−1.96135e9	−0.200671
$716$	6.12807e8	0.0623919
$717$	7.41774e9	0.751545
$718$	3.40025e9	0.342827
$719$	−2.09386e8	−0.0210086	−0.0105043	−	0.999945i	$-0.503344\pi$
$719$	−2.09386e8	−0.0210086	−0.0105043	+	0.999945i	$0.503344\pi$
$720$	1.21708e9	0.121522
$721$	1.31099e9	0.130264
$722$	6.63005e9	0.655597
$723$	−9.53534e9	−0.938323
$724$	8.36427e9	0.819112
$725$	5.45039e9	0.531184
$726$	3.49498e9	0.338974
$727$	3.16813e9	0.305796	0.152898	−	0.988242i	$-0.451139\pi$
$727$	3.16813e9	0.305796	0.152898	+	0.988242i	$0.451139\pi$
$728$	−6.95534e8	−0.0668126
$729$	3.87420e8	0.0370370
$730$	−1.12692e10	−1.07216
$731$	1.19125e10	1.12795
$732$	8.89023e8	0.0837769
$733$	1.33707e10	1.25398	0.626989	−	0.779028i	$-0.284287\pi$
$733$	1.33707e10	1.25398	0.626989	+	0.779028i	$0.284287\pi$
$734$	−5.01421e9	−0.468022
$735$	−6.16291e9	−0.572506
$736$	1.06138e9	0.0981291
$737$	6.13475e9	0.564496
$738$	2.00280e9	0.183418
$739$	−9.84355e9	−0.897215	−0.448607	−	0.893729i	$-0.648080\pi$
$739$	−9.84355e9	−0.897215	−0.448607	+	0.893729i	$0.648080\pi$
$740$	2.47444e8	0.0224474
$741$	−5.76538e8	−0.0520553
$742$	−5.05295e9	−0.454079
$743$	−9.61176e9	−0.859691	−0.429845	−	0.902902i	$-0.641432\pi$
$743$	−9.61176e9	−0.859691	−0.429845	+	0.902902i	$0.641432\pi$
$744$	3.44299e9	0.306500
$745$	−1.05203e10	−0.932140
$746$	3.14552e9	0.277400
$747$	4.07245e9	0.357465
$748$	−2.98670e9	−0.260937
$749$	−1.96879e9	−0.171204
$750$	−8.70442e8	−0.0753400
$751$	−5.19039e9	−0.447157	−0.223579	−	0.974686i	$-0.571774\pi$
$751$	−5.19039e9	−0.447157	−0.223579	+	0.974686i	$0.571774\pi$
$752$	−4.81197e9	−0.412630
$753$	4.29085e8	0.0366236
$754$	1.31099e9	0.111378
$755$	−2.69143e10	−2.27599
$756$	−6.46689e8	−0.0544339
$757$	−2.04164e9	−0.171058	−0.0855290	−	0.996336i	$-0.527258\pi$
$757$	−2.04164e9	−0.171058	−0.0855290	+	0.996336i	$0.527258\pi$
$758$	1.39130e10	1.16032
$759$	−1.59031e9	−0.132019
$760$	−1.68401e9	−0.139154
$761$	6.45045e9	0.530572	0.265286	−	0.964170i	$-0.414534\pi$
$761$	6.45045e9	0.530572	0.265286	+	0.964170i	$0.414534\pi$
$762$	−1.41804e9	−0.116104
$763$	−1.21829e8	−0.00992924
$764$	−5.29959e9	−0.429947
$765$	−7.62560e9	−0.615827
$766$	−2.57256e9	−0.206807
$767$	5.43475e8	0.0434907
$768$	4.52985e8	0.0360844
$769$	2.33813e9	0.185407	0.0927034	−	0.995694i	$-0.470449\pi$
$769$	2.33813e9	0.185407	0.0927034	+	0.995694i	$0.470449\pi$
$770$	3.04401e9	0.240286
$771$	−8.25183e8	−0.0648426
$772$	−2.61213e9	−0.204331
$773$	−2.01517e10	−1.56922	−0.784608	−	0.619992i	$-0.787136\pi$
$773$	−2.01517e10	−1.56922	−0.784608	+	0.619992i	$0.787136\pi$
$774$	2.70711e9	0.209852
$775$	−2.19201e10	−1.69156
$776$	−1.86324e9	−0.143138
$777$	−1.31478e8	−0.0100549
$778$	4.36899e9	0.332623
$779$	−2.77116e9	−0.210030
$780$	−1.86380e9	−0.140627
$781$	−5.00453e9	−0.375910
$782$	−6.65003e9	−0.497279
$783$	1.21893e9	0.0907428
$784$	−2.29377e9	−0.169998
$785$	9.36301e9	0.690831
$786$	−3.04364e9	−0.223571
$787$	−7.42971e9	−0.543326	−0.271663	−	0.962392i	$-0.587574\pi$
$787$	−7.42971e9	−0.543326	−0.271663	+	0.962392i	$0.587574\pi$
$788$	−1.57854e9	−0.114925
$789$	−1.75141e9	−0.126946
$790$	−4.00767e9	−0.289199
$791$	4.05352e9	0.291216
$792$	−6.78728e8	−0.0485465
$793$	−1.36142e9	−0.0969476
$794$	−5.40578e9	−0.383254
$795$	−1.35403e10	−0.955745
$796$	−6.34317e9	−0.445769
$797$	9.35369e9	0.654453	0.327227	−	0.944946i	$-0.393886\pi$
$797$	9.35369e9	0.654453	0.327227	+	0.944946i	$0.393886\pi$
$798$	8.94786e8	0.0623317
$799$	3.01493e10	2.09104
$800$	−2.88397e9	−0.199148
$801$	1.54246e9	0.106047
$802$	2.97602e9	0.203716
$803$	6.28444e9	0.428314
$804$	5.82965e9	0.395591
$805$	6.77762e9	0.457922
$806$	−5.27250e9	−0.354686
$807$	−3.18675e9	−0.213447
$808$	1.36597e9	0.0910964
$809$	1.38334e9	0.0918560	0.0459280	−	0.998945i	$-0.485376\pi$
$809$	1.38334e9	0.0918560	0.0459280	+	0.998945i	$0.485376\pi$
$810$	−1.73292e9	−0.114572
$811$	1.24625e10	0.820415	0.410208	−	0.911992i	$-0.365456\pi$
$811$	1.24625e10	0.820415	0.410208	+	0.911992i	$0.365456\pi$
$812$	−2.03466e9	−0.133366
$813$	−1.50969e10	−0.985304
$814$	−1.37991e8	−0.00896741
$815$	−5.12298e9	−0.331490
$816$	−2.83816e9	−0.182861
$817$	−3.74567e9	−0.240299
$818$	5.87319e9	0.375178
$819$	9.90321e8	0.0629915
$820$	−8.95846e9	−0.567394
$821$	1.03565e10	0.653149	0.326575	−	0.945171i	$-0.394106\pi$
$821$	1.03565e10	0.653149	0.326575	+	0.945171i	$0.394106\pi$
$822$	−3.31511e9	−0.208183
$823$	2.32179e10	1.45186	0.725929	−	0.687770i	$-0.241410\pi$
$823$	2.32179e10	1.45186	0.725929	+	0.687770i	$0.241410\pi$
$824$	1.30751e9	0.0814139
$825$	4.32118e9	0.267925
$826$	−8.43472e8	−0.0520763
$827$	2.26448e10	1.39220	0.696098	−	0.717947i	$-0.254918\pi$
$827$	2.26448e10	1.39220	0.696098	+	0.717947i	$0.254918\pi$
$828$	−1.51122e9	−0.0925170
$829$	−1.80027e10	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$829$	−1.80027e10	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$830$	−1.82159e10	−1.10580
$831$	−6.91323e9	−0.417905
$832$	−6.93687e8	−0.0417573
$833$	1.43715e10	0.861480
$834$	8.81111e9	0.525956
$835$	3.14176e10	1.86754
$836$	9.39115e8	0.0555900
$837$	−4.90223e9	−0.288971
$838$	−8.17683e9	−0.479989
$839$	−7.41594e9	−0.433510	−0.216755	−	0.976226i	$-0.569547\pi$
$839$	−7.41594e9	−0.433510	−0.216755	+	0.976226i	$0.569547\pi$
$840$	2.89262e9	0.168389
$841$	−1.34148e10	−0.777675
$842$	2.85861e8	0.0165030
$843$	−5.08043e9	−0.292081
$844$	−1.06283e10	−0.608505
$845$	−2.27220e10	−1.29553
$846$	6.85142e9	0.389031
$847$	8.30645e9	0.469703
$848$	−5.03953e9	−0.283795
$849$	1.35979e10	0.762598
$850$	1.80694e10	1.00920
$851$	−3.07244e8	−0.0170895
$852$	−4.75563e9	−0.263433
$853$	3.91993e9	0.216250	0.108125	−	0.994137i	$-0.465515\pi$
$853$	3.91993e9	0.216250	0.108125	+	0.994137i	$0.465515\pi$
$854$	2.11292e9	0.116086
$855$	2.39773e9	0.131196
$856$	−1.96356e9	−0.107001
$857$	2.17765e9	0.118183	0.0590916	−	0.998253i	$-0.481180\pi$
$857$	2.17765e9	0.118183	0.0590916	+	0.998253i	$0.481180\pi$
$858$	1.03938e9	0.0561785
$859$	−2.19729e10	−1.18280	−0.591400	−	0.806378i	$-0.701425\pi$
$859$	−2.19729e10	−1.18280	−0.591400	+	0.806378i	$0.701425\pi$
$860$	−1.21088e10	−0.649168
$861$	4.76002e9	0.254155
$862$	2.45802e10	1.30710
$863$	−8.08075e9	−0.427971	−0.213985	−	0.976837i	$-0.568644\pi$
$863$	−8.08075e9	−0.427971	−0.213985	+	0.976837i	$0.568644\pi$
$864$	−6.44973e8	−0.0340207
$865$	2.34440e10	1.23162
$866$	6.68651e9	0.349854
$867$	6.70328e9	0.349317
$868$	8.18290e9	0.424706
$869$	2.23495e9	0.115531
$870$	−5.45222e9	−0.280709
$871$	−8.92735e9	−0.457782
$872$	−1.21506e8	−0.00620568
$873$	2.65294e9	0.134951
$874$	2.09098e9	0.105940
$875$	−2.06876e9	−0.104396
$876$	5.97189e9	0.300156
$877$	2.40515e10	1.20405	0.602023	−	0.798478i	$-0.294361\pi$
$877$	2.40515e10	1.20405	0.602023	+	0.798478i	$0.294361\pi$
$878$	2.10968e10	1.05193
$879$	−1.11145e9	−0.0551988
$880$	3.03593e9	0.150176
$881$	4.44088e7	0.00218803	0.00109402	−	0.999999i	$-0.499652\pi$
$881$	4.44088e7	0.00218803	0.00109402	+	0.999999i	$0.499652\pi$
$882$	3.26593e9	0.160275
$883$	−2.73742e10	−1.33807	−0.669034	−	0.743231i	$-0.733292\pi$
$883$	−2.73742e10	−1.33807	−0.669034	+	0.743231i	$0.733292\pi$
$884$	4.34628e9	0.211609
$885$	−2.26023e9	−0.109610
$886$	5.70259e9	0.275457
$887$	1.44062e10	0.693135	0.346567	−	0.938025i	$-0.387347\pi$
$887$	1.44062e10	0.693135	0.346567	+	0.938025i	$0.387347\pi$
$888$	−1.31129e8	−0.00628423
$889$	−3.37023e9	−0.160881
$890$	−6.89936e9	−0.328053
$891$	9.66392e8	0.0457701
$892$	−2.00834e10	−0.947457
$893$	−9.47990e9	−0.445475
$894$	5.57505e9	0.260956
$895$	3.90280e9	0.181968
$896$	1.07660e9	0.0500007
$897$	2.31424e9	0.107062
$898$	−1.28714e10	−0.593144
$899$	−1.54237e10	−0.707996
$900$	4.10628e9	0.187758
$901$	3.15750e10	1.43816
$902$	4.99585e9	0.226666
$903$	6.43394e9	0.290784
$904$	4.04276e9	0.182007
$905$	5.32698e10	2.38897
$906$	1.42628e10	0.637171
$907$	1.76764e10	0.786628	0.393314	−	0.919404i	$-0.371328\pi$
$907$	1.76764e10	0.786628	0.393314	+	0.919404i	$0.371328\pi$
$908$	−7.08063e9	−0.313886
$909$	−1.94491e9	−0.0858865
$910$	−4.42967e9	−0.194862
$911$	2.22276e10	0.974043	0.487022	−	0.873390i	$-0.338083\pi$
$911$	2.22276e10	0.974043	0.487022	+	0.873390i	$0.338083\pi$
$912$	8.92410e8	0.0389567
$913$	1.01584e10	0.441752
$914$	−2.33263e10	−1.01050
$915$	5.66195e9	0.244339
$916$	−1.22057e10	−0.524719
$917$	−7.23376e9	−0.309793
$918$	4.04106e9	0.172403
$919$	−1.42607e10	−0.606091	−0.303045	−	0.952976i	$-0.598003\pi$
$919$	−1.42607e10	−0.606091	−0.303045	+	0.952976i	$0.598003\pi$
$920$	6.75963e9	0.286197
$921$	1.31816e10	0.555979
$922$	1.67707e9	0.0704682
$923$	7.28263e9	0.304847
$924$	−1.61312e9	−0.0672690
$925$	8.34842e8	0.0346823
$926$	1.93066e10	0.799039
$927$	−1.86166e9	−0.0767577
$928$	−2.02926e9	−0.0833526
$929$	−9.14525e9	−0.374232	−0.187116	−	0.982338i	$-0.559914\pi$
$929$	−9.14525e9	−0.374232	−0.187116	+	0.982338i	$0.559914\pi$
$930$	2.19275e10	0.893921
$931$	−4.51887e9	−0.183530
$932$	2.13483e10	0.863789
$933$	1.57425e9	0.0634580
$934$	4.22024e9	0.169482
$935$	−1.90215e10	−0.761034
$936$	9.87691e8	0.0393691
$937$	−1.09169e9	−0.0433522	−0.0216761	−	0.999765i	$-0.506900\pi$
$937$	−1.09169e9	−0.0433522	−0.0216761	+	0.999765i	$0.506900\pi$
$938$	1.38552e10	0.548155
$939$	2.21160e10	0.871718
$940$	−3.06462e10	−1.20345
$941$	2.99308e10	1.17100	0.585498	−	0.810674i	$-0.300899\pi$
$941$	2.99308e10	1.17100	0.585498	+	0.810674i	$0.300899\pi$
$942$	−4.96177e9	−0.193401
$943$	1.11235e10	0.431966
$944$	−8.41232e8	−0.0325472
$945$	−4.11859e9	−0.158759
$946$	6.75270e9	0.259333
$947$	−3.11683e10	−1.19258	−0.596291	−	0.802768i	$-0.703360\pi$
$947$	−3.11683e10	−1.19258	−0.596291	+	0.802768i	$0.703360\pi$
$948$	2.12380e9	0.0809624
$949$	−9.14518e9	−0.347344
$950$	−5.68161e9	−0.215000
$951$	1.50856e10	0.568763
$952$	−6.74540e9	−0.253384
$953$	5.15442e10	1.92910	0.964550	−	0.263899i	$-0.0850086\pi$
$953$	5.15442e10	1.92910	0.964550	+	0.263899i	$0.0850086\pi$
$954$	7.17543e9	0.267564
$955$	−3.37516e10	−1.25396
$956$	1.75828e10	0.650857
$957$	3.04053e9	0.112139
$958$	−3.26233e10	−1.19881
$959$	−7.87895e9	−0.288472
$960$	2.88494e9	0.105242
$961$	3.45179e10	1.25462
$962$	2.00806e8	0.00727219
$963$	2.79578e9	0.100881
$964$	−2.26023e10	−0.812611
$965$	−1.66360e10	−0.595939
$966$	−3.59169e9	−0.128197
$967$	−2.43610e9	−0.0866368	−0.0433184	−	0.999061i	$-0.513793\pi$
$967$	−2.43610e9	−0.0866368	−0.0433184	+	0.999061i	$0.513793\pi$
$968$	8.28439e9	0.293560
$969$	−5.59137e9	−0.197417
$970$	−1.18665e10	−0.417466
$971$	−3.65480e10	−1.28114	−0.640570	−	0.767900i	$-0.721302\pi$
$971$	−3.65480e10	−1.28114	−0.640570	+	0.767900i	$0.721302\pi$
$972$	9.18330e8	0.0320750
$973$	2.09412e10	0.728797
$974$	−4.96441e9	−0.172152
$975$	−6.28823e9	−0.217276
$976$	2.10731e9	0.0725529
$977$	4.17412e10	1.43197	0.715985	−	0.698116i	$-0.245978\pi$
$977$	4.17412e10	1.43197	0.715985	+	0.698116i	$0.245978\pi$
$978$	2.71484e9	0.0928020
$979$	3.84755e9	0.131052
$980$	−1.46084e10	−0.495805
$981$	1.73003e8	0.00585077
$982$	7.38164e8	0.0248750
$983$	5.67608e10	1.90595	0.952974	−	0.303051i	$-0.0980052\pi$
$983$	5.67608e10	1.90595	0.952974	+	0.303051i	$0.0980052\pi$
$984$	4.74739e9	0.158844
$985$	−1.00533e10	−0.335182
$986$	1.27142e10	0.422397
$987$	1.62836e10	0.539065
$988$	−1.36661e9	−0.0450812
$989$	1.50352e10	0.494222
$990$	−4.32264e9	−0.141588
$991$	1.89646e10	0.618992	0.309496	−	0.950901i	$-0.399840\pi$
$991$	1.89646e10	0.618992	0.309496	+	0.950901i	$0.399840\pi$
$992$	8.16117e9	0.265437
$993$	1.42190e10	0.460836
$994$	−1.13026e10	−0.365028
$995$	−4.03979e10	−1.30010
$996$	9.65320e9	0.309574
$997$	2.12555e10	0.679263	0.339631	−	0.940559i	$-0.389698\pi$
$997$	2.12555e10	0.679263	0.339631	+	0.940559i	$0.389698\pi$
$998$	−2.07427e10	−0.660554
$999$	1.86705e8	0.00592483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.c.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.c.1.7	✓	7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +407.599 q^{5} -216.000 q^{6} -513.363 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +407.599 q^{5} -216.000 q^{6} -513.363 q^{7} -512.000 q^{8} +729.000 q^{9} -3260.79 q^{10} +1818.44 q^{11} +1728.00 q^{12} -2646.21 q^{13} +4106.90 q^{14} +11005.2 q^{15} +4096.00 q^{16} -25663.4 q^{17} -5832.00 q^{18} +8069.39 q^{19} +26086.3 q^{20} -13860.8 q^{21} -14547.5 q^{22} -32390.7 q^{23} -13824.0 q^{24} +88011.7 q^{25} +21169.7 q^{26} +19683.0 q^{27} -32855.2 q^{28} +61928.0 q^{29} -88041.3 q^{30} -249059. q^{31} -32768.0 q^{32} +49097.8 q^{33} +205307. q^{34} -209246. q^{35} +46656.0 q^{36} +9485.58 q^{37} -64555.1 q^{38} -71447.6 q^{39} -208691. q^{40} -343416. q^{41} +110886. q^{42} -464183. q^{43} +116380. q^{44} +297139. q^{45} +259125. q^{46} -1.17480e6 q^{47} +110592. q^{48} -560001. q^{49} -704094. q^{50} -692911. q^{51} -169357. q^{52} -1.23035e6 q^{53} -157464. q^{54} +741193. q^{55} +262842. q^{56} +217874. q^{57} -495424. q^{58} -205379. q^{59} +704331. q^{60} +514481. q^{61} +1.99247e6 q^{62} -374242. q^{63} +262144. q^{64} -1.07859e6 q^{65} -392782. q^{66} +3.37364e6 q^{67} -1.64246e6 q^{68} -874548. q^{69} +1.67397e6 q^{70} -2.75210e6 q^{71} -373248. q^{72} +3.45596e6 q^{73} -75884.6 q^{74} +2.37632e6 q^{75} +516441. q^{76} -933518. q^{77} +571581. q^{78} +1.22905e6 q^{79} +1.66952e6 q^{80} +531441. q^{81} +2.74733e6 q^{82} +5.58635e6 q^{83} -887091. q^{84} -1.04604e7 q^{85} +3.71346e6 q^{86} +1.67206e6 q^{87} -931040. q^{88} +2.11586e6 q^{89} -2.37712e6 q^{90} +1.35846e6 q^{91} -2.07300e6 q^{92} -6.72460e6 q^{93} +9.39838e6 q^{94} +3.28907e6 q^{95} -884736. q^{96} +3.63915e6 q^{97} +4.48001e6 q^{98} +1.32564e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9} + 1264 q^{10} - 2201 q^{11} + 12096 q^{12} - 8421 q^{13} + 4648 q^{14} - 4266 q^{15} + 28672 q^{16} - 2425 q^{17} - 40824 q^{18} - 37084 q^{19} - 10112 q^{20} - 15687 q^{21} + 17608 q^{22} + 99364 q^{23} - 96768 q^{24} + 101361 q^{25} + 67368 q^{26} + 137781 q^{27} - 37184 q^{28} + 2498 q^{29} + 34128 q^{30} - 57962 q^{31} - 229376 q^{32} - 59427 q^{33} + 19400 q^{34} + 190586 q^{35} + 326592 q^{36} - 6497 q^{37} + 296672 q^{38} - 227367 q^{39} + 80896 q^{40} - 319165 q^{41} + 125496 q^{42} - 633743 q^{43} - 140864 q^{44} - 115182 q^{45} - 794912 q^{46} - 1626560 q^{47} + 774144 q^{48} - 3846354 q^{49} - 810888 q^{50} - 65475 q^{51} - 538944 q^{52} - 1215602 q^{53} - 1102248 q^{54} - 3329556 q^{55} + 297472 q^{56} - 1001268 q^{57} - 19984 q^{58} - 1437653 q^{59} - 273024 q^{60} - 3180086 q^{61} + 463696 q^{62} - 423549 q^{63} + 1835008 q^{64} + 544086 q^{65} + 475416 q^{66} - 5349632 q^{67} - 155200 q^{68} + 2682828 q^{69} - 1524688 q^{70} + 1752423 q^{71} - 2612736 q^{72} - 1843424 q^{73} + 51976 q^{74} + 2736747 q^{75} - 2373376 q^{76} - 3885063 q^{77} + 1818936 q^{78} - 4769243 q^{79} - 647168 q^{80} + 3720087 q^{81} + 2553320 q^{82} + 5154441 q^{83} - 1003968 q^{84} - 4594902 q^{85} + 5069944 q^{86} + 67446 q^{87} + 1126912 q^{88} + 20086462 q^{89} + 921456 q^{90} + 6733847 q^{91} + 6359296 q^{92} - 1564974 q^{93} + 13012480 q^{94} + 12936212 q^{95} - 6193152 q^{96} + 6244248 q^{97} + 30770832 q^{98} - 1604529 q^{99}+O(q^{100}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9 + 1264 * q^10 - 2201 * q^11 + 12096 * q^12 - 8421 * q^13 + 4648 * q^14 - 4266 * q^15 + 28672 * q^16 - 2425 * q^17 - 40824 * q^18 - 37084 * q^19 - 10112 * q^20 - 15687 * q^21 + 17608 * q^22 + 99364 * q^23 - 96768 * q^24 + 101361 * q^25 + 67368 * q^26 + 137781 * q^27 - 37184 * q^28 + 2498 * q^29 + 34128 * q^30 - 57962 * q^31 - 229376 * q^32 - 59427 * q^33 + 19400 * q^34 + 190586 * q^35 + 326592 * q^36 - 6497 * q^37 + 296672 * q^38 - 227367 * q^39 + 80896 * q^40 - 319165 * q^41 + 125496 * q^42 - 633743 * q^43 - 140864 * q^44 - 115182 * q^45 - 794912 * q^46 - 1626560 * q^47 + 774144 * q^48 - 3846354 * q^49 - 810888 * q^50 - 65475 * q^51 - 538944 * q^52 - 1215602 * q^53 - 1102248 * q^54 - 3329556 * q^55 + 297472 * q^56 - 1001268 * q^57 - 19984 * q^58 - 1437653 * q^59 - 273024 * q^60 - 3180086 * q^61 + 463696 * q^62 - 423549 * q^63 + 1835008 * q^64 + 544086 * q^65 + 475416 * q^66 - 5349632 * q^67 - 155200 * q^68 + 2682828 * q^69 - 1524688 * q^70 + 1752423 * q^71 - 2612736 * q^72 - 1843424 * q^73 + 51976 * q^74 + 2736747 * q^75 - 2373376 * q^76 - 3885063 * q^77 + 1818936 * q^78 - 4769243 * q^79 - 647168 * q^80 + 3720087 * q^81 + 2553320 * q^82 + 5154441 * q^83 - 1003968 * q^84 - 4594902 * q^85 + 5069944 * q^86 + 67446 * q^87 + 1126912 * q^88 + 20086462 * q^89 + 921456 * q^90 + 6733847 * q^91 + 6359296 * q^92 - 1564974 * q^93 + 13012480 * q^94 + 12936212 * q^95 - 6193152 * q^96 + 6244248 * q^97 + 30770832 * q^98 - 1604529 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more