LMFDB - Embedded newform 354.8.a.e.1.8

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 260588 x^{7} - 2627755 x^{6} + 16696953355 x^{5} + 808091684078 x^{4} + \cdots + 15\!\cdots\!00 $ x^9 - 4x^8 - 260588x^7 - 2627755x^6 + 16696953355x^5 + 808091684078x^4 - 191825159847522x^3 - 12153827093891319x^2 + 237398587398357570x + 15300107670464479800
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-36.9079$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +290.127 q^{5} +216.000 q^{6} -1124.72 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +290.127 q^{5} +216.000 q^{6} -1124.72 q^{7} -512.000 q^{8} +729.000 q^{9} -2321.02 q^{10} -7255.10 q^{11} -1728.00 q^{12} +14357.2 q^{13} +8997.76 q^{14} -7833.44 q^{15} +4096.00 q^{16} -13473.9 q^{17} -5832.00 q^{18} +50223.1 q^{19} +18568.2 q^{20} +30367.4 q^{21} +58040.8 q^{22} -43036.2 q^{23} +13824.0 q^{24} +6048.97 q^{25} -114858. q^{26} -19683.0 q^{27} -71982.1 q^{28} +192583. q^{29} +62667.5 q^{30} -222471. q^{31} -32768.0 q^{32} +195888. q^{33} +107791. q^{34} -326312. q^{35} +46656.0 q^{36} +100018. q^{37} -401785. q^{38} -387645. q^{39} -148545. q^{40} -372023. q^{41} -242940. q^{42} +347558. q^{43} -464327. q^{44} +211503. q^{45} +344289. q^{46} -303059. q^{47} -110592. q^{48} +441452. q^{49} -48391.7 q^{50} +363794. q^{51} +918862. q^{52} +1.26970e6 q^{53} +157464. q^{54} -2.10490e6 q^{55} +575857. q^{56} -1.35602e6 q^{57} -1.54066e6 q^{58} +205379. q^{59} -501340. q^{60} +393792. q^{61} +1.77977e6 q^{62} -819921. q^{63} +262144. q^{64} +4.16542e6 q^{65} -1.56710e6 q^{66} -1.10830e6 q^{67} -862328. q^{68} +1.16198e6 q^{69} +2.61050e6 q^{70} +5.52317e6 q^{71} -373248. q^{72} -2.07574e6 q^{73} -800148. q^{74} -163322. q^{75} +3.21428e6 q^{76} +8.15996e6 q^{77} +3.10116e6 q^{78} +6.23393e6 q^{79} +1.18836e6 q^{80} +531441. q^{81} +2.97618e6 q^{82} +41087.5 q^{83} +1.94352e6 q^{84} -3.90914e6 q^{85} -2.78046e6 q^{86} -5.19974e6 q^{87} +3.71461e6 q^{88} -9.58940e6 q^{89} -1.69202e6 q^{90} -1.61478e7 q^{91} -2.75432e6 q^{92} +6.00673e6 q^{93} +2.42447e6 q^{94} +1.45711e7 q^{95} +884736. q^{96} +1.36028e7 q^{97} -3.53162e6 q^{98} -5.28897e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) $ 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * 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
$5$	290.127	1.03799	0.518996	−	0.854777i	$-0.326306\pi$
$5$	290.127	1.03799	0.518996	+	0.854777i	$0.326306\pi$
$6$	216.000	0.408248
$7$	−1124.72	−1.23937	−0.619685	−	0.784850i	$-0.712740\pi$
$7$	−1124.72	−1.23937	−0.619685	+	0.784850i	$0.712740\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−2321.02	−0.733971
$11$	−7255.10	−1.64350	−0.821749	−	0.569850i	$-0.807001\pi$
$11$	−7255.10	−1.64350	−0.821749	+	0.569850i	$0.807001\pi$
$12$	−1728.00	−0.288675
$13$	14357.2	1.81246	0.906230	−	0.422785i	$-0.138947\pi$
$13$	14357.2	1.81246	0.906230	+	0.422785i	$0.138947\pi$
$14$	8997.76	0.876368
$15$	−7833.44	−0.599285
$16$	4096.00	0.250000
$17$	−13473.9	−0.665152	−0.332576	−	0.943076i	$-0.607918\pi$
$17$	−13473.9	−0.665152	−0.332576	+	0.943076i	$0.607918\pi$
$18$	−5832.00	−0.235702
$19$	50223.1	1.67983	0.839917	−	0.542715i	$-0.182604\pi$
$19$	50223.1	1.67983	0.839917	+	0.542715i	$0.182604\pi$
$20$	18568.2	0.518996
$21$	30367.4	0.715551
$22$	58040.8	1.16213
$23$	−43036.2	−0.737541	−0.368771	−	0.929520i	$-0.620221\pi$
$23$	−43036.2	−0.737541	−0.368771	+	0.929520i	$0.620221\pi$
$24$	13824.0	0.204124
$25$	6048.97	0.0774268
$26$	−114858.	−1.28160
$27$	−19683.0	−0.192450
$28$	−71982.1	−0.619685
$29$	192583.	1.46631	0.733153	−	0.680063i	$-0.238048\pi$
$29$	192583.	1.46631	0.733153	+	0.680063i	$0.238048\pi$
$30$	62667.5	0.423758
$31$	−222471.	−1.34125	−0.670623	−	0.741799i	$-0.733973\pi$
$31$	−222471.	−1.34125	−0.670623	+	0.741799i	$0.733973\pi$
$32$	−32768.0	−0.176777
$33$	195888.	0.948874
$34$	107791.	0.470334
$35$	−326312.	−1.28646
$36$	46656.0	0.166667
$37$	100018.	0.324619	0.162310	−	0.986740i	$-0.448106\pi$
$37$	100018.	0.324619	0.162310	+	0.986740i	$0.448106\pi$
$38$	−401785.	−1.18782
$39$	−387645.	−1.04642
$40$	−148545.	−0.366985
$41$	−372023.	−0.842997	−0.421498	−	0.906829i	$-0.638496\pi$
$41$	−372023.	−0.842997	−0.421498	+	0.906829i	$0.638496\pi$
$42$	−242940.	−0.505971
$43$	347558.	0.666634	0.333317	−	0.942815i	$-0.391832\pi$
$43$	347558.	0.666634	0.333317	+	0.942815i	$0.391832\pi$
$44$	−464327.	−0.821749
$45$	211503.	0.345997
$46$	344289.	0.521520
$47$	−303059.	−0.425779	−0.212890	−	0.977076i	$-0.568287\pi$
$47$	−303059.	−0.425779	−0.212890	+	0.977076i	$0.568287\pi$
$48$	−110592.	−0.144338
$49$	441452.	0.536040
$50$	−48391.7	−0.0547490
$51$	363794.	0.384026
$52$	918862.	0.906230
$53$	1.26970e6	1.17148	0.585740	−	0.810499i	$-0.300804\pi$
$53$	1.26970e6	1.17148	0.585740	+	0.810499i	$0.300804\pi$
$54$	157464.	0.136083
$55$	−2.10490e6	−1.70594
$56$	575857.	0.438184
$57$	−1.35602e6	−0.969852
$58$	−1.54066e6	−1.03684
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−501340.	−0.299642
$61$	393792.	0.222132	0.111066	−	0.993813i	$-0.464573\pi$
$61$	393792.	0.222132	0.111066	+	0.993813i	$0.464573\pi$
$62$	1.77977e6	0.948404
$63$	−819921.	−0.413124
$64$	262144.	0.125000
$65$	4.16542e6	1.88132
$66$	−1.56710e6	−0.670955
$67$	−1.10830e6	−0.450188	−0.225094	−	0.974337i	$-0.572269\pi$
$67$	−1.10830e6	−0.450188	−0.225094	+	0.974337i	$0.572269\pi$
$68$	−862328.	−0.332576
$69$	1.16198e6	0.425820
$70$	2.61050e6	0.909662
$71$	5.52317e6	1.83140	0.915702	−	0.401859i	$-0.131636\pi$
$71$	5.52317e6	1.83140	0.915702	+	0.401859i	$0.131636\pi$
$72$	−373248.	−0.117851
$73$	−2.07574e6	−0.624514	−0.312257	−	0.949998i	$-0.601085\pi$
$73$	−2.07574e6	−0.624514	−0.312257	+	0.949998i	$0.601085\pi$
$74$	−800148.	−0.229540
$75$	−163322.	−0.0447024
$76$	3.21428e6	0.839917
$77$	8.15996e6	2.03690
$78$	3.10116e6	0.739934
$79$	6.23393e6	1.42255	0.711274	−	0.702915i	$-0.248118\pi$
$79$	6.23393e6	1.42255	0.711274	+	0.702915i	$0.248118\pi$
$80$	1.18836e6	0.259498
$81$	531441.	0.111111
$82$	2.97618e6	0.596089
$83$	41087.5	0.00788744	0.00394372	−	0.999992i	$-0.498745\pi$
$83$	41087.5	0.00788744	0.00394372	+	0.999992i	$0.498745\pi$
$84$	1.94352e6	0.357776
$85$	−3.90914e6	−0.690423
$86$	−2.78046e6	−0.471381
$87$	−5.19974e6	−0.846573
$88$	3.71461e6	0.581064
$89$	−9.58940e6	−1.44187	−0.720935	−	0.693002i	$-0.756288\pi$
$89$	−9.58940e6	−1.44187	−0.720935	+	0.693002i	$0.756288\pi$
$90$	−1.69202e6	−0.244657
$91$	−1.61478e7	−2.24631
$92$	−2.75432e6	−0.368771
$93$	6.00673e6	0.774368
$94$	2.42447e6	0.301071
$95$	1.45711e7	1.74365
$96$	884736.	0.102062
$97$	1.36028e7	1.51331	0.756654	−	0.653816i	$-0.226833\pi$
$97$	1.36028e7	1.51331	0.756654	+	0.653816i	$0.226833\pi$
$98$	−3.53162e6	−0.379038
$99$	−5.28897e6	−0.547833
$100$	387134.	0.0387134
$101$	−6.17709e6	−0.596567	−0.298283	−	0.954477i	$-0.596414\pi$
$101$	−6.17709e6	−0.596567	−0.298283	+	0.954477i	$0.596414\pi$
$102$	−2.91036e6	−0.271547
$103$	−5.05786e6	−0.456075	−0.228038	−	0.973652i	$-0.573231\pi$
$103$	−5.05786e6	−0.456075	−0.228038	+	0.973652i	$0.573231\pi$
$104$	−7.35089e6	−0.640801
$105$	8.81043e6	0.742736
$106$	−1.01576e7	−0.828361
$107$	−6.07039e6	−0.479041	−0.239521	−	0.970891i	$-0.576990\pi$
$107$	−6.07039e6	−0.479041	−0.239521	+	0.970891i	$0.576990\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.76806e7	−1.30769	−0.653845	−	0.756628i	$-0.726845\pi$
$109$	−1.76806e7	−1.30769	−0.653845	+	0.756628i	$0.726845\pi$
$110$	1.68392e7	1.20628
$111$	−2.70050e6	−0.187419
$112$	−4.60685e6	−0.309843
$113$	1.02177e7	0.666162	0.333081	−	0.942898i	$-0.391912\pi$
$113$	1.02177e7	0.666162	0.333081	+	0.942898i	$0.391912\pi$
$114$	1.08482e7	0.685789
$115$	−1.24860e7	−0.765562
$116$	1.23253e7	0.733153
$117$	1.04664e7	0.604153
$118$	−1.64303e6	−0.0920575
$119$	1.51543e7	0.824370
$120$	4.01072e6	0.211879
$121$	3.31493e7	1.70108
$122$	−3.15033e6	−0.157071
$123$	1.00446e7	0.486704
$124$	−1.42382e7	−0.670623
$125$	−2.09112e7	−0.957623
$126$	6.55937e6	0.292123
$127$	8.94133e6	0.387337	0.193669	−	0.981067i	$-0.437961\pi$
$127$	8.94133e6	0.387337	0.193669	+	0.981067i	$0.437961\pi$
$128$	−2.09715e6	−0.0883883
$129$	−9.38406e6	−0.384881
$130$	−3.33234e7	−1.33029
$131$	−4.62058e7	−1.79576	−0.897878	−	0.440245i	$-0.854892\pi$
$131$	−4.62058e7	−1.79576	−0.897878	+	0.440245i	$0.854892\pi$
$132$	1.25368e7	0.474437
$133$	−5.64870e7	−2.08194
$134$	8.86636e6	0.318331
$135$	−5.71058e6	−0.199762
$136$	6.89862e6	0.235167
$137$	1.96343e7	0.652371	0.326185	−	0.945306i	$-0.394237\pi$
$137$	1.96343e7	0.652371	0.326185	+	0.945306i	$0.394237\pi$
$138$	−9.29582e6	−0.301100
$139$	−2.74373e7	−0.866540	−0.433270	−	0.901264i	$-0.642640\pi$
$139$	−2.74373e7	−0.866540	−0.433270	+	0.901264i	$0.642640\pi$
$140$	−2.08840e7	−0.643228
$141$	8.18259e6	0.245824
$142$	−4.41853e7	−1.29500
$143$	−1.04163e8	−2.97877
$144$	2.98598e6	0.0833333
$145$	5.58736e7	1.52201
$146$	1.66059e7	0.441598
$147$	−1.19192e7	−0.309483
$148$	6.40118e6	0.162310
$149$	−4.66432e7	−1.15515	−0.577573	−	0.816339i	$-0.696000\pi$
$149$	−4.66432e7	−1.15515	−0.577573	+	0.816339i	$0.696000\pi$
$150$	1.30658e6	0.0316093
$151$	−3.30324e7	−0.780766	−0.390383	−	0.920652i	$-0.627657\pi$
$151$	−3.30324e7	−0.780766	−0.390383	+	0.920652i	$0.627657\pi$
$152$	−2.57142e7	−0.593911
$153$	−9.82245e6	−0.221717
$154$	−6.52797e7	−1.44031
$155$	−6.45451e7	−1.39220
$156$	−2.48093e7	−0.523212
$157$	5.67822e7	1.17102	0.585509	−	0.810666i	$-0.300895\pi$
$157$	5.67822e7	1.17102	0.585509	+	0.810666i	$0.300895\pi$
$158$	−4.98714e7	−1.00589
$159$	−3.42818e7	−0.676354
$160$	−9.50690e6	−0.183493
$161$	4.84037e7	0.914087
$162$	−4.25153e6	−0.0785674
$163$	−3.03320e7	−0.548585	−0.274293	−	0.961646i	$-0.588444\pi$
$163$	−3.03320e7	−0.548585	−0.274293	+	0.961646i	$0.588444\pi$
$164$	−2.38094e7	−0.421498
$165$	5.68324e7	0.984923
$166$	−328700.	−0.00557726
$167$	−9.74477e7	−1.61906	−0.809532	−	0.587075i	$-0.800279\pi$
$167$	−9.74477e7	−1.61906	−0.809532	+	0.587075i	$0.800279\pi$
$168$	−1.55481e7	−0.252986
$169$	1.43381e8	2.28501
$170$	3.12731e7	0.488202
$171$	3.66127e7	0.559945
$172$	2.22437e7	0.333317
$173$	−5.18119e7	−0.760796	−0.380398	−	0.924823i	$-0.624213\pi$
$173$	−5.18119e7	−0.760796	−0.380398	+	0.924823i	$0.624213\pi$
$174$	4.15979e7	0.598617
$175$	−6.80339e6	−0.0959605
$176$	−2.97169e7	−0.410874
$177$	−5.54523e6	−0.0751646
$178$	7.67152e7	1.01956
$179$	−9.32171e7	−1.21481	−0.607407	−	0.794390i	$-0.707790\pi$
$179$	−9.32171e7	−1.21481	−0.607407	+	0.794390i	$0.707790\pi$
$180$	1.35362e7	0.172999
$181$	9.69388e7	1.21513	0.607565	−	0.794270i	$-0.292147\pi$
$181$	9.69388e7	1.21513	0.607565	+	0.794270i	$0.292147\pi$
$182$	1.29183e8	1.58838
$183$	−1.06324e7	−0.128248
$184$	2.20345e7	0.260760
$185$	2.90181e7	0.336952
$186$	−4.80538e7	−0.547561
$187$	9.77543e7	1.09318
$188$	−1.93958e7	−0.212890
$189$	2.21379e7	0.238517
$190$	−1.16569e8	−1.23295
$191$	1.27140e8	1.32027	0.660137	−	0.751145i	$-0.270498\pi$
$191$	1.27140e8	1.32027	0.660137	+	0.751145i	$0.270498\pi$
$192$	−7.07789e6	−0.0721688
$193$	2.55061e6	0.0255384	0.0127692	−	0.999918i	$-0.495935\pi$
$193$	2.55061e6	0.0255384	0.0127692	+	0.999918i	$0.495935\pi$
$194$	−1.08822e8	−1.07007
$195$	−1.12466e8	−1.08618
$196$	2.82529e7	0.268020
$197$	8.57668e7	0.799259	0.399629	−	0.916677i	$-0.369139\pi$
$197$	8.57668e7	0.799259	0.399629	+	0.916677i	$0.369139\pi$
$198$	4.23118e7	0.387376
$199$	−3.27789e7	−0.294855	−0.147427	−	0.989073i	$-0.547099\pi$
$199$	−3.27789e7	−0.294855	−0.147427	+	0.989073i	$0.547099\pi$
$200$	−3.09707e6	−0.0273745
$201$	2.99240e7	0.259916
$202$	4.94167e7	0.421836
$203$	−2.16602e8	−1.81730
$204$	2.32828e7	0.192013
$205$	−1.07934e8	−0.875023
$206$	4.04629e7	0.322494
$207$	−3.13734e7	−0.245847
$208$	5.88071e7	0.453115
$209$	−3.64374e8	−2.76080
$210$	−7.04834e7	−0.525194
$211$	−2.03426e8	−1.49080	−0.745398	−	0.666620i	$-0.767741\pi$
$211$	−2.03426e8	−1.49080	−0.745398	+	0.666620i	$0.767741\pi$
$212$	8.12607e7	0.585740
$213$	−1.49126e8	−1.05736
$214$	4.85631e7	0.338733
$215$	1.00836e8	0.691960
$216$	1.00777e7	0.0680414
$217$	2.50218e8	1.66230
$218$	1.41445e8	0.924677
$219$	5.60449e7	0.360563
$220$	−1.34714e8	−0.852969
$221$	−1.93447e8	−1.20556
$222$	2.16040e7	0.132525
$223$	−2.06959e8	−1.24974	−0.624868	−	0.780731i	$-0.714847\pi$
$223$	−2.06959e8	−1.24974	−0.624868	+	0.780731i	$0.714847\pi$
$224$	3.68548e7	0.219092
$225$	4.40970e6	0.0258089
$226$	−8.17418e7	−0.471047
$227$	9.48324e7	0.538104	0.269052	−	0.963126i	$-0.413290\pi$
$227$	9.48324e7	0.538104	0.269052	+	0.963126i	$0.413290\pi$
$228$	−8.67856e7	−0.484926
$229$	−8.40568e7	−0.462539	−0.231270	−	0.972890i	$-0.574288\pi$
$229$	−8.40568e7	−0.462539	−0.231270	+	0.972890i	$0.574288\pi$
$230$	9.98878e7	0.541334
$231$	−2.20319e8	−1.17601
$232$	−9.86025e7	−0.518418
$233$	−2.52419e8	−1.30730	−0.653652	−	0.756796i	$-0.726764\pi$
$233$	−2.52419e8	−1.30730	−0.653652	+	0.756796i	$0.726764\pi$
$234$	−8.37313e7	−0.427201
$235$	−8.79257e7	−0.441955
$236$	1.31443e7	0.0650945
$237$	−1.68316e8	−0.821309
$238$	−1.21235e8	−0.582918
$239$	−9.91242e7	−0.469664	−0.234832	−	0.972036i	$-0.575454\pi$
$239$	−9.91242e7	−0.469664	−0.234832	+	0.972036i	$0.575454\pi$
$240$	−3.20858e7	−0.149821
$241$	−3.70091e8	−1.70314	−0.851568	−	0.524245i	$-0.824348\pi$
$241$	−3.70091e8	−1.70314	−0.851568	+	0.524245i	$0.824348\pi$
$242$	−2.65195e8	−1.20285
$243$	−1.43489e7	−0.0641500
$244$	2.52027e7	0.111066
$245$	1.28077e8	0.556405
$246$	−8.03569e7	−0.344152
$247$	7.21064e8	3.04463
$248$	1.13905e8	0.474202
$249$	−1.10936e6	−0.00455381
$250$	1.67290e8	0.677142
$251$	−3.98931e8	−1.59235	−0.796177	−	0.605063i	$-0.793148\pi$
$251$	−3.98931e8	−1.59235	−0.796177	+	0.605063i	$0.793148\pi$
$252$	−5.24749e7	−0.206562
$253$	3.12232e8	1.21215
$254$	−7.15307e7	−0.273889
$255$	1.05547e8	0.398616
$256$	1.67772e7	0.0625000
$257$	−5.11567e8	−1.87991	−0.939953	−	0.341303i	$-0.889132\pi$
$257$	−5.11567e8	−1.87991	−0.939953	+	0.341303i	$0.889132\pi$
$258$	7.50725e7	0.272152
$259$	−1.12493e8	−0.402324
$260$	2.66587e8	0.940659
$261$	1.40393e8	0.488769
$262$	3.69647e8	1.26979
$263$	−2.71150e7	−0.0919104	−0.0459552	−	0.998944i	$-0.514633\pi$
$263$	−2.71150e7	−0.0919104	−0.0459552	+	0.998944i	$0.514633\pi$
$264$	−1.00295e8	−0.335478
$265$	3.68374e8	1.21599
$266$	4.51896e8	1.47215
$267$	2.58914e8	0.832465
$268$	−7.09309e7	−0.225094
$269$	−1.47275e8	−0.461315	−0.230657	−	0.973035i	$-0.574088\pi$
$269$	−1.47275e8	−0.461315	−0.230657	+	0.973035i	$0.574088\pi$
$270$	4.56846e7	0.141253
$271$	1.51434e8	0.462201	0.231101	−	0.972930i	$-0.425767\pi$
$271$	1.51434e8	0.462201	0.231101	+	0.972930i	$0.425767\pi$
$272$	−5.51890e7	−0.166288
$273$	4.35992e8	1.29691
$274$	−1.57075e8	−0.461296
$275$	−4.38859e7	−0.127251
$276$	7.43665e7	0.212910
$277$	−6.04479e8	−1.70884	−0.854421	−	0.519582i	$-0.826088\pi$
$277$	−6.04479e8	−1.70884	−0.854421	+	0.519582i	$0.826088\pi$
$278$	2.19498e8	0.612737
$279$	−1.62182e8	−0.447082
$280$	1.67072e8	0.454831
$281$	3.33773e8	0.897384	0.448692	−	0.893686i	$-0.351890\pi$
$281$	3.33773e8	0.897384	0.448692	+	0.893686i	$0.351890\pi$
$282$	−6.54607e7	−0.173824
$283$	−4.10438e8	−1.07645	−0.538227	−	0.842800i	$-0.680906\pi$
$283$	−4.10438e8	−1.07645	−0.538227	+	0.842800i	$0.680906\pi$
$284$	3.53483e8	0.915702
$285$	−3.93420e8	−1.00670
$286$	8.33304e8	2.10631
$287$	4.18421e8	1.04479
$288$	−2.38879e7	−0.0589256
$289$	−2.28794e8	−0.557572
$290$	−4.46989e8	−1.07623
$291$	−3.67276e8	−0.873709
$292$	−1.32847e8	−0.312257
$293$	1.50658e8	0.349908	0.174954	−	0.984577i	$-0.444022\pi$
$293$	1.50658e8	0.349908	0.174954	+	0.984577i	$0.444022\pi$
$294$	9.53537e7	0.218838
$295$	5.95861e7	0.135135
$296$	−5.12095e7	−0.114770
$297$	1.42802e8	0.316291
$298$	3.73146e8	0.816811
$299$	−6.17880e8	−1.33676
$300$	−1.04526e7	−0.0223512
$301$	−3.90905e8	−0.826206
$302$	2.64259e8	0.552085
$303$	1.66781e8	0.344428
$304$	2.05714e8	0.419958
$305$	1.14250e8	0.230572
$306$	7.85796e7	0.156778
$307$	3.79025e8	0.747624	0.373812	−	0.927505i	$-0.378051\pi$
$307$	3.79025e8	0.747624	0.373812	+	0.927505i	$0.378051\pi$
$308$	5.22237e8	1.01845
$309$	1.36562e8	0.263315
$310$	5.16361e8	0.984435
$311$	−3.77563e8	−0.711752	−0.355876	−	0.934533i	$-0.615817\pi$
$311$	−3.77563e8	−0.711752	−0.355876	+	0.934533i	$0.615817\pi$
$312$	1.98474e8	0.369967
$313$	−3.86727e8	−0.712852	−0.356426	−	0.934323i	$-0.616005\pi$
$313$	−3.86727e8	−0.712852	−0.356426	+	0.934323i	$0.616005\pi$
$314$	−4.54258e8	−0.828035
$315$	−2.37882e8	−0.428819
$316$	3.98972e8	0.711274
$317$	−3.81383e8	−0.672440	−0.336220	−	0.941784i	$-0.609149\pi$
$317$	−3.81383e8	−0.672440	−0.336220	+	0.941784i	$0.609149\pi$
$318$	2.74255e8	0.478255
$319$	−1.39721e9	−2.40987
$320$	7.60552e7	0.129749
$321$	1.63900e8	0.276575
$322$	−3.87229e8	−0.646357
$323$	−6.76700e8	−1.11735
$324$	3.40122e7	0.0555556
$325$	8.68463e7	0.140333
$326$	2.42656e8	0.387908
$327$	4.77377e8	0.754996
$328$	1.90476e8	0.298044
$329$	3.40856e8	0.527698
$330$	−4.54659e8	−0.696446
$331$	1.17093e9	1.77473	0.887366	−	0.461065i	$-0.152533\pi$
$331$	1.17093e9	1.77473	0.887366	+	0.461065i	$0.152533\pi$
$332$	2.62960e6	0.00394372
$333$	7.29135e7	0.108206
$334$	7.79582e8	1.14485
$335$	−3.21547e8	−0.467291
$336$	1.24385e8	0.178888
$337$	−7.75907e8	−1.10434	−0.552172	−	0.833730i	$-0.686201\pi$
$337$	−7.75907e8	−1.10434	−0.552172	+	0.833730i	$0.686201\pi$
$338$	−1.14705e9	−1.61575
$339$	−2.75879e8	−0.384609
$340$	−2.50185e8	−0.345211
$341$	1.61405e9	2.20433
$342$	−2.92901e8	−0.395941
$343$	4.29745e8	0.575018
$344$	−1.77950e8	−0.235691
$345$	3.37121e8	0.441997
$346$	4.14495e8	0.537964
$347$	−1.05696e8	−0.135802	−0.0679009	−	0.997692i	$-0.521630\pi$
$347$	−1.05696e8	−0.135802	−0.0679009	+	0.997692i	$0.521630\pi$
$348$	−3.32783e8	−0.423286
$349$	7.84247e8	0.987561	0.493781	−	0.869587i	$-0.335615\pi$
$349$	7.84247e8	0.987561	0.493781	+	0.869587i	$0.335615\pi$
$350$	5.44271e7	0.0678543
$351$	−2.82593e8	−0.348808
$352$	2.37735e8	0.290532
$353$	−5.91802e8	−0.716086	−0.358043	−	0.933705i	$-0.616556\pi$
$353$	−5.91802e8	−0.716086	−0.358043	+	0.933705i	$0.616556\pi$
$354$	4.43619e7	0.0531494
$355$	1.60242e9	1.90098
$356$	−6.13722e8	−0.720935
$357$	−4.09167e8	−0.475951
$358$	7.45737e8	0.859004
$359$	1.48030e9	1.68857	0.844284	−	0.535896i	$-0.180026\pi$
$359$	1.48030e9	1.68857	0.844284	+	0.535896i	$0.180026\pi$
$360$	−1.08290e8	−0.122328
$361$	1.62849e9	1.82184
$362$	−7.75510e8	−0.859226
$363$	−8.95032e8	−0.982122
$364$	−1.03346e9	−1.12316
$365$	−6.02228e8	−0.648240
$366$	8.50590e7	0.0906852
$367$	−1.28041e9	−1.35213	−0.676063	−	0.736844i	$-0.736315\pi$
$367$	−1.28041e9	−1.35213	−0.676063	+	0.736844i	$0.736315\pi$
$368$	−1.76276e8	−0.184385
$369$	−2.71204e8	−0.280999
$370$	−2.32145e8	−0.238261
$371$	−1.42805e9	−1.45190
$372$	3.84431e8	0.387184
$373$	1.37269e9	1.36959	0.684796	−	0.728735i	$-0.259891\pi$
$373$	1.37269e9	1.36959	0.684796	+	0.728735i	$0.259891\pi$
$374$	−7.82034e8	−0.772992
$375$	5.64603e8	0.552884
$376$	1.55166e8	0.150536
$377$	2.76495e9	2.65762
$378$	−1.77103e8	−0.168657
$379$	1.29892e8	0.122559	0.0612793	−	0.998121i	$-0.480482\pi$
$379$	1.29892e8	0.122559	0.0612793	+	0.998121i	$0.480482\pi$
$380$	9.32551e8	0.871827
$381$	−2.41416e8	−0.223629
$382$	−1.01712e9	−0.933575
$383$	1.92717e9	1.75276	0.876382	−	0.481616i	$-0.159950\pi$
$383$	1.92717e9	1.75276	0.876382	+	0.481616i	$0.159950\pi$
$384$	5.66231e7	0.0510310
$385$	2.36743e9	2.11429
$386$	−2.04049e7	−0.0180584
$387$	2.53370e8	0.222211
$388$	8.70579e8	0.756654
$389$	−8.95785e8	−0.771579	−0.385789	−	0.922587i	$-0.626071\pi$
$389$	−8.95785e8	−0.771579	−0.385789	+	0.922587i	$0.626071\pi$
$390$	8.99731e8	0.768045
$391$	5.79864e8	0.490577
$392$	−2.26024e8	−0.189519
$393$	1.24756e9	1.03678
$394$	−6.86134e8	−0.565161
$395$	1.80863e9	1.47659
$396$	−3.38494e8	−0.273916
$397$	−1.10513e9	−0.886433	−0.443217	−	0.896415i	$-0.646163\pi$
$397$	−1.10513e9	−0.886433	−0.443217	+	0.896415i	$0.646163\pi$
$398$	2.62231e8	0.208494
$399$	1.52515e9	1.20201
$400$	2.47766e7	0.0193567
$401$	6.50948e8	0.504128	0.252064	−	0.967711i	$-0.418891\pi$
$401$	6.50948e8	0.504128	0.252064	+	0.967711i	$0.418891\pi$
$402$	−2.39392e8	−0.183788
$403$	−3.19407e9	−2.43095
$404$	−3.95334e8	−0.298283
$405$	1.54186e8	0.115332
$406$	1.73282e9	1.28502
$407$	−7.25644e8	−0.533511
$408$	−1.86263e8	−0.135774
$409$	−1.62091e9	−1.17146	−0.585730	−	0.810507i	$-0.699192\pi$
$409$	−1.62091e9	−1.17146	−0.585730	+	0.810507i	$0.699192\pi$
$410$	8.63472e8	0.618735
$411$	−5.30127e8	−0.376646
$412$	−3.23703e8	−0.228038
$413$	−2.30994e8	−0.161352
$414$	2.50987e8	0.173840
$415$	1.19206e7	0.00818710
$416$	−4.70457e8	−0.320401
$417$	7.40806e8	0.500297
$418$	2.91499e9	1.95218
$419$	−1.01382e9	−0.673307	−0.336653	−	0.941629i	$-0.609295\pi$
$419$	−1.01382e9	−0.673307	−0.336653	+	0.941629i	$0.609295\pi$
$420$	5.63868e8	0.371368
$421$	6.58023e8	0.429787	0.214894	−	0.976637i	$-0.431059\pi$
$421$	6.58023e8	0.429787	0.214894	+	0.976637i	$0.431059\pi$
$422$	1.62741e9	1.05415
$423$	−2.20930e8	−0.141926
$424$	−6.50085e8	−0.414181
$425$	−8.15030e7	−0.0515006
$426$	1.19300e9	0.747667
$427$	−4.42905e8	−0.275305
$428$	−3.88505e8	−0.239521
$429$	2.81240e9	1.71980
$430$	−8.06688e8	−0.489290
$431$	−5.39243e7	−0.0324425	−0.0162212	−	0.999868i	$-0.505164\pi$
$431$	−5.39243e7	−0.0324425	−0.0162212	+	0.999868i	$0.505164\pi$
$432$	−8.06216e7	−0.0481125
$433$	−8.32678e8	−0.492912	−0.246456	−	0.969154i	$-0.579266\pi$
$433$	−8.32678e8	−0.492912	−0.246456	+	0.969154i	$0.579266\pi$
$434$	−2.00174e9	−1.17542
$435$	−1.50859e9	−0.878735
$436$	−1.13156e9	−0.653845
$437$	−2.16141e9	−1.23895
$438$	−4.48359e8	−0.254957
$439$	−9.05452e8	−0.510786	−0.255393	−	0.966837i	$-0.582205\pi$
$439$	−9.05452e8	−0.510786	−0.255393	+	0.966837i	$0.582205\pi$
$440$	1.07771e9	0.603140
$441$	3.21819e8	0.178680
$442$	1.54758e9	0.852461
$443$	−1.10161e9	−0.602026	−0.301013	−	0.953620i	$-0.597325\pi$
$443$	−1.10161e9	−0.602026	−0.301013	+	0.953620i	$0.597325\pi$
$444$	−1.72832e8	−0.0937095
$445$	−2.78215e9	−1.49665
$446$	1.65568e9	0.883697
$447$	1.25937e9	0.666924
$448$	−2.94839e8	−0.154921
$449$	−1.19812e9	−0.624652	−0.312326	−	0.949975i	$-0.601108\pi$
$449$	−1.19812e9	−0.624652	−0.312326	+	0.949975i	$0.601108\pi$
$450$	−3.52776e7	−0.0182497
$451$	2.69906e9	1.38546
$452$	6.53934e8	0.333081
$453$	8.91875e8	0.450776
$454$	−7.58659e8	−0.380497
$455$	−4.68493e9	−2.33165
$456$	6.94285e8	0.342895
$457$	2.89956e8	0.142110	0.0710550	−	0.997472i	$-0.477363\pi$
$457$	2.89956e8	0.142110	0.0710550	+	0.997472i	$0.477363\pi$
$458$	6.72454e8	0.327065
$459$	2.65206e8	0.128009
$460$	−7.99103e8	−0.382781
$461$	1.34150e8	0.0637732	0.0318866	−	0.999491i	$-0.489848\pi$
$461$	1.34150e8	0.0637732	0.0318866	+	0.999491i	$0.489848\pi$
$462$	1.76255e9	0.831562
$463$	2.18608e9	1.02360	0.511802	−	0.859103i	$-0.328978\pi$
$463$	2.18608e9	1.02360	0.511802	+	0.859103i	$0.328978\pi$
$464$	7.88820e8	0.366577
$465$	1.74272e9	0.803788
$466$	2.01935e9	0.924403
$467$	−1.87710e9	−0.852861	−0.426431	−	0.904520i	$-0.640229\pi$
$467$	−1.87710e9	−0.852861	−0.426431	+	0.904520i	$0.640229\pi$
$468$	6.69850e8	0.302077
$469$	1.24652e9	0.557950
$470$	7.03405e8	0.312509
$471$	−1.53312e9	−0.676088
$472$	−1.05154e8	−0.0460287
$473$	−2.52157e9	−1.09561
$474$	1.34653e9	0.580753
$475$	3.03798e8	0.130064
$476$	9.69877e8	0.412185
$477$	9.25610e8	0.390493
$478$	7.92993e8	0.332102
$479$	−2.44802e9	−1.01775	−0.508874	−	0.860841i	$-0.669938\pi$
$479$	−2.44802e9	−1.01775	−0.508874	+	0.860841i	$0.669938\pi$
$480$	2.56686e8	0.105940
$481$	1.43599e9	0.588359
$482$	2.96073e9	1.20430
$483$	−1.30690e9	−0.527748
$484$	2.12156e9	0.850542
$485$	3.94655e9	1.57080
$486$	1.14791e8	0.0453609
$487$	1.14034e9	0.447388	0.223694	−	0.974659i	$-0.428188\pi$
$487$	1.14034e9	0.447388	0.223694	+	0.974659i	$0.428188\pi$
$488$	−2.01621e8	−0.0785357
$489$	8.18963e8	0.316726
$490$	−1.02462e9	−0.393438
$491$	−3.22543e9	−1.22971	−0.614855	−	0.788640i	$-0.710786\pi$
$491$	−3.22543e9	−1.22971	−0.614855	+	0.788640i	$0.710786\pi$
$492$	6.42855e8	0.243352
$493$	−2.59484e9	−0.975317
$494$	−5.76851e9	−2.15288
$495$	−1.53448e9	−0.568646
$496$	−9.11243e8	−0.335311
$497$	−6.21202e9	−2.26979
$498$	8.87489e6	0.00322003
$499$	−1.59600e9	−0.575018	−0.287509	−	0.957778i	$-0.592827\pi$
$499$	−1.59600e9	−0.575018	−0.287509	+	0.957778i	$0.592827\pi$
$500$	−1.33832e9	−0.478812
$501$	2.63109e9	0.934767
$502$	3.19145e9	1.12596
$503$	3.64537e9	1.27719	0.638593	−	0.769545i	$-0.279517\pi$
$503$	3.64537e9	1.27719	0.638593	+	0.769545i	$0.279517\pi$
$504$	4.19800e8	0.146061
$505$	−1.79214e9	−0.619231
$506$	−2.49786e9	−0.857118
$507$	−3.87129e9	−1.31925
$508$	5.72245e8	0.193669
$509$	1.85551e8	0.0623666	0.0311833	−	0.999514i	$-0.490072\pi$
$509$	1.85551e8	0.0623666	0.0311833	+	0.999514i	$0.490072\pi$
$510$	−8.44374e8	−0.281864
$511$	2.33462e9	0.774004
$512$	−1.34218e8	−0.0441942
$513$	−9.88542e8	−0.323284
$514$	4.09253e9	1.32929
$515$	−1.46742e9	−0.473402
$516$	−6.00580e8	−0.192441
$517$	2.19872e9	0.699767
$518$	8.99942e8	0.284486
$519$	1.39892e9	0.439246
$520$	−2.13270e9	−0.665146
$521$	−8.06175e6	−0.00249745	−0.00124873	−	0.999999i	$-0.500397\pi$
$521$	−8.06175e6	−0.00249745	−0.00124873	+	0.999999i	$0.500397\pi$
$522$	−1.12314e9	−0.345612
$523$	7.12168e8	0.217684	0.108842	−	0.994059i	$-0.465286\pi$
$523$	7.12168e8	0.217684	0.108842	+	0.994059i	$0.465286\pi$
$524$	−2.95717e9	−0.897878
$525$	1.83692e8	0.0554028
$526$	2.16920e8	0.0649905
$527$	2.99755e9	0.892133
$528$	8.02356e8	0.237218
$529$	−1.55271e9	−0.456033
$530$	−2.94699e9	−0.859832
$531$	1.49721e8	0.0433963
$532$	−3.61517e9	−1.04097
$533$	−5.34121e9	−1.52790
$534$	−2.07131e9	−0.588641
$535$	−1.76119e9	−0.497241
$536$	5.67447e8	0.159165
$537$	2.51686e9	0.701374
$538$	1.17820e9	0.326199
$539$	−3.20278e9	−0.880981
$540$	−3.65477e8	−0.0998808
$541$	−5.85862e8	−0.159076	−0.0795380	−	0.996832i	$-0.525344\pi$
$541$	−5.85862e8	−0.159076	−0.0795380	+	0.996832i	$0.525344\pi$
$542$	−1.21147e9	−0.326826
$543$	−2.61735e9	−0.701555
$544$	4.41512e8	0.117583
$545$	−5.12964e9	−1.35737
$546$	−3.48793e9	−0.917052
$547$	4.00131e9	1.04531	0.522657	−	0.852543i	$-0.324941\pi$
$547$	4.00131e9	1.04531	0.522657	+	0.852543i	$0.324941\pi$
$548$	1.25660e9	0.326185
$549$	2.87074e8	0.0740442
$550$	3.51087e8	0.0899798
$551$	9.67212e9	2.46315
$552$	−5.94932e8	−0.150550
$553$	−7.01143e9	−1.76307
$554$	4.83583e9	1.20833
$555$	−7.83489e8	−0.194539
$556$	−1.75598e9	−0.433270
$557$	3.50068e9	0.858341	0.429170	−	0.903224i	$-0.358806\pi$
$557$	3.50068e9	0.858341	0.429170	+	0.903224i	$0.358806\pi$
$558$	1.29745e9	0.316135
$559$	4.98996e9	1.20825
$560$	−1.33657e9	−0.321614
$561$	−2.63937e9	−0.631146
$562$	−2.67018e9	−0.634547
$563$	−1.26943e9	−0.299797	−0.149899	−	0.988701i	$-0.547895\pi$
$563$	−1.26943e9	−0.299797	−0.149899	+	0.988701i	$0.547895\pi$
$564$	5.23686e8	0.122912
$565$	2.96444e9	0.691470
$566$	3.28351e9	0.761168
$567$	−5.97722e8	−0.137708
$568$	−2.82786e9	−0.647499
$569$	−1.70568e9	−0.388155	−0.194077	−	0.980986i	$-0.562171\pi$
$569$	−1.70568e9	−0.388155	−0.194077	+	0.980986i	$0.562171\pi$
$570$	3.14736e9	0.711843
$571$	7.30684e9	1.64249	0.821246	−	0.570574i	$-0.193279\pi$
$571$	7.30684e9	1.64249	0.821246	+	0.570574i	$0.193279\pi$
$572$	−6.66643e9	−1.48939
$573$	−3.43277e9	−0.762261
$574$	−3.34737e9	−0.738775
$575$	−2.60324e8	−0.0571054
$576$	1.91103e8	0.0416667
$577$	1.70127e9	0.368688	0.184344	−	0.982862i	$-0.440984\pi$
$577$	1.70127e9	0.368688	0.184344	+	0.982862i	$0.440984\pi$
$578$	1.83035e9	0.394263
$579$	−6.88665e7	−0.0147446
$580$	3.57591e9	0.761007
$581$	−4.62119e7	−0.00977546
$582$	2.93820e9	0.617805
$583$	−9.21179e9	−1.92532
$584$	1.06278e9	0.220799
$585$	3.03659e9	0.627106
$586$	−1.20526e9	−0.247423
$587$	8.66094e9	1.76739	0.883693	−	0.468067i	$-0.155049\pi$
$587$	8.66094e9	1.76739	0.883693	+	0.468067i	$0.155049\pi$
$588$	−7.62829e8	−0.154742
$589$	−1.11732e10	−2.25307
$590$	−4.76689e8	−0.0955549
$591$	−2.31570e9	−0.461452
$592$	4.09676e8	0.0811548
$593$	−7.17495e9	−1.41295	−0.706476	−	0.707737i	$-0.749716\pi$
$593$	−7.17495e9	−1.41295	−0.706476	+	0.707737i	$0.749716\pi$
$594$	−1.14242e9	−0.223652
$595$	4.39669e9	0.855690
$596$	−2.98517e9	−0.577573
$597$	8.85029e8	0.170234
$598$	4.94304e9	0.945235
$599$	−9.82065e9	−1.86701	−0.933505	−	0.358566i	$-0.883266\pi$
$599$	−9.82065e9	−1.86701	−0.933505	+	0.358566i	$0.883266\pi$
$600$	8.36209e7	0.0158047
$601$	6.65145e9	1.24984	0.624922	−	0.780687i	$-0.285131\pi$
$601$	6.65145e9	1.24984	0.624922	+	0.780687i	$0.285131\pi$
$602$	3.12724e9	0.584216
$603$	−8.07947e8	−0.150063
$604$	−2.11407e9	−0.390383
$605$	9.61753e9	1.76571
$606$	−1.33425e9	−0.243547
$607$	−2.57316e9	−0.466988	−0.233494	−	0.972358i	$-0.575016\pi$
$607$	−2.57316e9	−0.466988	−0.233494	+	0.972358i	$0.575016\pi$
$608$	−1.64571e9	−0.296955
$609$	5.84825e9	1.04922
$610$	−9.13998e8	−0.163039
$611$	−4.35108e9	−0.771708
$612$	−6.28637e8	−0.110859
$613$	−9.66126e8	−0.169403	−0.0847017	−	0.996406i	$-0.526994\pi$
$613$	−9.66126e8	−0.169403	−0.0847017	+	0.996406i	$0.526994\pi$
$614$	−3.03220e9	−0.528650
$615$	2.91422e9	0.505195
$616$	−4.17790e9	−0.720154
$617$	−5.30533e9	−0.909315	−0.454658	−	0.890666i	$-0.650238\pi$
$617$	−5.30533e9	−0.909315	−0.454658	+	0.890666i	$0.650238\pi$
$618$	−1.09250e9	−0.186192
$619$	2.97571e9	0.504282	0.252141	−	0.967691i	$-0.418865\pi$
$619$	2.97571e9	0.504282	0.252141	+	0.967691i	$0.418865\pi$
$620$	−4.13088e9	−0.696101
$621$	8.47081e8	0.141940
$622$	3.02051e9	0.503285
$623$	1.07854e10	1.78701
$624$	−1.58779e9	−0.261606
$625$	−6.53950e9	−1.07143
$626$	3.09382e9	0.504063
$627$	9.83810e9	1.59395
$628$	3.63406e9	0.585509
$629$	−1.34764e9	−0.215921
$630$	1.90305e9	0.303221
$631$	−4.18252e9	−0.662728	−0.331364	−	0.943503i	$-0.607509\pi$
$631$	−4.18252e9	−0.662728	−0.331364	+	0.943503i	$0.607509\pi$
$632$	−3.19177e9	−0.502947
$633$	5.49251e9	0.860712
$634$	3.05106e9	0.475487
$635$	2.59413e9	0.402053
$636$	−2.19404e9	−0.338177
$637$	6.33802e9	0.971552
$638$	1.11777e10	1.70404
$639$	4.02639e9	0.610468
$640$	−6.08441e8	−0.0917464
$641$	−7.35319e9	−1.10274	−0.551369	−	0.834261i	$-0.685894\pi$
$641$	−7.35319e9	−1.10274	−0.551369	+	0.834261i	$0.685894\pi$
$642$	−1.31120e9	−0.195568
$643$	2.99811e9	0.444744	0.222372	−	0.974962i	$-0.428620\pi$
$643$	2.99811e9	0.444744	0.222372	+	0.974962i	$0.428620\pi$
$644$	3.09783e9	0.457044
$645$	−2.72257e9	−0.399503
$646$	5.41360e9	0.790082
$647$	7.70739e9	1.11877	0.559387	−	0.828907i	$-0.311037\pi$
$647$	7.70739e9	1.11877	0.559387	+	0.828907i	$0.311037\pi$
$648$	−2.72098e8	−0.0392837
$649$	−1.49005e9	−0.213965
$650$	−6.94770e8	−0.0992303
$651$	−6.75589e9	−0.959730
$652$	−1.94125e9	−0.274293
$653$	3.20326e8	0.0450190	0.0225095	−	0.999747i	$-0.492834\pi$
$653$	3.20326e8	0.0450190	0.0225095	+	0.999747i	$0.492834\pi$
$654$	−3.81902e9	−0.533863
$655$	−1.34056e10	−1.86398
$656$	−1.52380e9	−0.210749
$657$	−1.51321e9	−0.208171
$658$	−2.72685e9	−0.373139
$659$	−1.15631e10	−1.57390	−0.786948	−	0.617020i	$-0.788340\pi$
$659$	−1.15631e10	−1.57390	−0.786948	+	0.617020i	$0.788340\pi$
$660$	3.63728e9	0.492462
$661$	−6.08067e9	−0.818929	−0.409464	−	0.912326i	$-0.634284\pi$
$661$	−6.08067e9	−0.818929	−0.409464	+	0.912326i	$0.634284\pi$
$662$	−9.36744e9	−1.25493
$663$	5.22307e9	0.696032
$664$	−2.10368e7	−0.00278863
$665$	−1.63884e10	−2.16103
$666$	−5.83308e8	−0.0765135
$667$	−8.28804e9	−1.08146
$668$	−6.23666e9	−0.809532
$669$	5.58790e9	0.721535
$670$	2.57238e9	0.330425
$671$	−2.85700e9	−0.365074
$672$	−9.95080e8	−0.126493
$673$	2.42217e9	0.306303	0.153151	−	0.988203i	$-0.451058\pi$
$673$	2.42217e9	0.306303	0.153151	+	0.988203i	$0.451058\pi$
$674$	6.20725e9	0.780890
$675$	−1.19062e8	−0.0149008
$676$	9.17639e9	1.14251
$677$	−4.51255e8	−0.0558935	−0.0279468	−	0.999609i	$-0.508897\pi$
$677$	−4.51255e8	−0.0558935	−0.0279468	+	0.999609i	$0.508897\pi$
$678$	2.20703e9	0.271959
$679$	−1.52993e10	−1.87555
$680$	2.00148e9	0.244101
$681$	−2.56048e9	−0.310675
$682$	−1.29124e10	−1.55870
$683$	5.23433e9	0.628621	0.314311	−	0.949320i	$-0.398227\pi$
$683$	5.23433e9	0.628621	0.314311	+	0.949320i	$0.398227\pi$
$684$	2.34321e9	0.279972
$685$	5.69646e9	0.677155
$686$	−3.43796e9	−0.406599
$687$	2.26953e9	0.267047
$688$	1.42360e9	0.166658
$689$	1.82293e10	2.12326
$690$	−2.69697e9	−0.312539
$691$	−1.26972e10	−1.46397	−0.731987	−	0.681318i	$-0.761407\pi$
$691$	−1.26972e10	−1.46397	−0.731987	+	0.681318i	$0.761407\pi$
$692$	−3.31596e9	−0.380398
$693$	5.94861e9	0.678968
$694$	8.45569e8	0.0960264
$695$	−7.96030e9	−0.899462
$696$	2.66227e9	0.299309
$697$	5.01258e9	0.560721
$698$	−6.27398e9	−0.698311
$699$	6.81531e9	0.754772
$700$	−4.35417e8	−0.0479802
$701$	−1.98360e9	−0.217491	−0.108746	−	0.994070i	$-0.534683\pi$
$701$	−1.98360e9	−0.217491	−0.108746	+	0.994070i	$0.534683\pi$
$702$	2.26074e9	0.246645
$703$	5.02324e9	0.545306
$704$	−1.90188e9	−0.205437
$705$	2.37399e9	0.255163
$706$	4.73442e9	0.506349
$707$	6.94749e9	0.739367
$708$	−3.54895e8	−0.0375823
$709$	1.28318e10	1.35215	0.676075	−	0.736833i	$-0.263680\pi$
$709$	1.28318e10	1.35215	0.676075	+	0.736833i	$0.263680\pi$
$710$	−1.28194e10	−1.34420
$711$	4.54453e9	0.474183
$712$	4.90977e9	0.509778
$713$	9.57432e9	0.989224
$714$	3.27334e9	0.336548
$715$	−3.02206e10	−3.09194
$716$	−5.96590e9	−0.607407
$717$	2.67635e9	0.271160
$718$	−1.18424e10	−1.19400
$719$	4.60612e9	0.462151	0.231076	−	0.972936i	$-0.425776\pi$
$719$	4.60612e9	0.462151	0.231076	+	0.972936i	$0.425776\pi$
$720$	8.66316e8	0.0864993
$721$	5.68868e9	0.565246
$722$	−1.30279e10	−1.28824
$723$	9.99246e9	0.983305
$724$	6.20408e9	0.607565
$725$	1.16493e9	0.113531
$726$	7.16026e9	0.694465
$727$	1.72140e10	1.66154	0.830772	−	0.556614i	$-0.187900\pi$
$727$	1.72140e10	1.66154	0.830772	+	0.556614i	$0.187900\pi$
$728$	8.26770e9	0.794191
$729$	3.87420e8	0.0370370
$730$	4.81782e9	0.458375
$731$	−4.68295e9	−0.443413
$732$	−6.80472e8	−0.0641241
$733$	1.67712e10	1.57290	0.786450	−	0.617654i	$-0.211917\pi$
$733$	1.67712e10	1.57290	0.786450	+	0.617654i	$0.211917\pi$
$734$	1.02433e10	0.956098
$735$	−3.45809e9	−0.321241
$736$	1.41021e9	0.130380
$737$	8.04079e9	0.739883
$738$	2.16964e9	0.198696
$739$	8.06153e9	0.734788	0.367394	−	0.930065i	$-0.380250\pi$
$739$	8.06153e9	0.734788	0.367394	+	0.930065i	$0.380250\pi$
$740$	1.85716e9	0.168476
$741$	−1.94687e10	−1.75782
$742$	1.14244e10	1.02665
$743$	−1.67118e10	−1.49473	−0.747364	−	0.664414i	$-0.768681\pi$
$743$	−1.67118e10	−1.49473	−0.747364	+	0.664414i	$0.768681\pi$
$744$	−3.07544e9	−0.273781
$745$	−1.35325e10	−1.19903
$746$	−1.09815e10	−0.968448
$747$	2.99528e7	0.00262915
$748$	6.25627e9	0.546588
$749$	6.82749e9	0.593710
$750$	−4.51683e9	−0.390948
$751$	3.37188e9	0.290490	0.145245	−	0.989396i	$-0.453603\pi$
$751$	3.37188e9	0.290490	0.145245	+	0.989396i	$0.453603\pi$
$752$	−1.24133e9	−0.106445
$753$	1.07711e10	0.919346
$754$	−2.21196e10	−1.87922
$755$	−9.58361e9	−0.810429
$756$	1.41682e9	0.119259
$757$	1.82033e10	1.52515	0.762577	−	0.646897i	$-0.223934\pi$
$757$	1.82033e10	1.52515	0.762577	+	0.646897i	$0.223934\pi$
$758$	−1.03913e9	−0.0866620
$759$	−8.43026e9	−0.699834
$760$	−7.46041e9	−0.616475
$761$	−1.36217e10	−1.12043	−0.560216	−	0.828347i	$-0.689282\pi$
$761$	−1.36217e10	−1.12043	−0.560216	+	0.828347i	$0.689282\pi$
$762$	1.93133e9	0.158130
$763$	1.98858e10	1.62071
$764$	8.13694e9	0.660137
$765$	−2.84976e9	−0.230141
$766$	−1.54173e10	−1.23939
$767$	2.94867e9	0.235962
$768$	−4.52985e8	−0.0360844
$769$	−5.68023e9	−0.450426	−0.225213	−	0.974310i	$-0.572308\pi$
$769$	−5.68023e9	−0.450426	−0.225213	+	0.974310i	$0.572308\pi$
$770$	−1.89394e10	−1.49503
$771$	1.38123e10	1.08536
$772$	1.63239e8	0.0127692
$773$	−1.48227e10	−1.15425	−0.577123	−	0.816658i	$-0.695825\pi$
$773$	−1.48227e10	−1.15425	−0.577123	+	0.816658i	$0.695825\pi$
$774$	−2.02696e9	−0.157127
$775$	−1.34572e9	−0.103848
$776$	−6.96463e9	−0.535035
$777$	3.03731e9	0.232282
$778$	7.16628e9	0.545589
$779$	−1.86841e10	−1.41609
$780$	−7.19785e9	−0.543090
$781$	−4.00711e10	−3.00991
$782$	−4.63891e9	−0.346891
$783$	−3.79061e9	−0.282191
$784$	1.80819e9	0.134010
$785$	1.64741e10	1.21551
$786$	−9.98046e9	−0.733114
$787$	−1.39582e10	−1.02075	−0.510373	−	0.859953i	$-0.670493\pi$
$787$	−1.39582e10	−1.02075	−0.510373	+	0.859953i	$0.670493\pi$
$788$	5.48907e9	0.399629
$789$	7.32105e8	0.0530645
$790$	−1.44691e10	−1.04411
$791$	−1.14921e10	−0.825621
$792$	2.70795e9	0.193688
$793$	5.65375e9	0.402606
$794$	8.84103e9	0.626803
$795$	−9.94611e9	−0.702050
$796$	−2.09785e9	−0.147427
$797$	2.10634e10	1.47375	0.736877	−	0.676027i	$-0.236300\pi$
$797$	2.10634e10	1.47375	0.736877	+	0.676027i	$0.236300\pi$
$798$	−1.22012e10	−0.849947
$799$	4.08337e9	0.283208
$800$	−1.98212e8	−0.0136872
$801$	−6.99067e9	−0.480624
$802$	−5.20758e9	−0.356472
$803$	1.50597e10	1.02639
$804$	1.91513e9	0.129958
$805$	1.40432e10	0.948815
$806$	2.55526e10	1.71894
$807$	3.97644e9	0.266340
$808$	3.16267e9	0.210918
$809$	1.97653e10	1.31245	0.656227	−	0.754563i	$-0.272151\pi$
$809$	1.97653e10	1.31245	0.656227	+	0.754563i	$0.272151\pi$
$810$	−1.23349e9	−0.0815523
$811$	1.77973e10	1.17160	0.585802	−	0.810454i	$-0.300780\pi$
$811$	1.77973e10	1.17160	0.585802	+	0.810454i	$0.300780\pi$
$812$	−1.38625e10	−0.908649
$813$	−4.08872e9	−0.266852
$814$	5.80516e9	0.377249
$815$	−8.80014e9	−0.569427
$816$	1.49010e9	0.0960065
$817$	1.74554e10	1.11983
$818$	1.29673e10	0.828347
$819$	−1.17718e10	−0.748770
$820$	−6.90778e9	−0.437512
$821$	−8.54691e9	−0.539024	−0.269512	−	0.962997i	$-0.586862\pi$
$821$	−8.54691e9	−0.539024	−0.269512	+	0.962997i	$0.586862\pi$
$822$	4.24102e9	0.266329
$823$	1.83996e10	1.15056	0.575280	−	0.817957i	$-0.304893\pi$
$823$	1.83996e10	1.15056	0.575280	+	0.817957i	$0.304893\pi$
$824$	2.58962e9	0.161247
$825$	1.18492e9	0.0734682
$826$	1.84795e9	0.114093
$827$	−1.36755e10	−0.840761	−0.420381	−	0.907348i	$-0.638103\pi$
$827$	−1.36755e10	−0.840761	−0.420381	+	0.907348i	$0.638103\pi$
$828$	−2.00790e9	−0.122924
$829$	−2.10633e10	−1.28406	−0.642032	−	0.766678i	$-0.721908\pi$
$829$	−2.10633e10	−1.28406	−0.642032	+	0.766678i	$0.721908\pi$
$830$	−9.53648e7	−0.00578915
$831$	1.63209e10	0.986600
$832$	3.76366e9	0.226557
$833$	−5.94807e9	−0.356548
$834$	−5.92645e9	−0.353764
$835$	−2.82723e10	−1.68058
$836$	−2.33199e10	−1.38040
$837$	4.37890e9	0.258123
$838$	8.11059e9	0.476100
$839$	2.49143e10	1.45640	0.728202	−	0.685362i	$-0.240356\pi$
$839$	2.49143e10	1.45640	0.728202	+	0.685362i	$0.240356\pi$
$840$	−4.51094e9	−0.262597
$841$	1.98383e10	1.15006
$842$	−5.26418e9	−0.303906
$843$	−9.01186e9	−0.518105
$844$	−1.30193e10	−0.745398
$845$	4.15988e10	2.37182
$846$	1.76744e9	0.100357
$847$	−3.72837e10	−2.10828
$848$	5.20068e9	0.292870
$849$	1.10818e10	0.621491
$850$	6.52024e8	0.0364164
$851$	−4.30441e9	−0.239420
$852$	−9.54403e9	−0.528681
$853$	1.84798e10	1.01947	0.509737	−	0.860330i	$-0.329743\pi$
$853$	1.84798e10	1.01947	0.509737	+	0.860330i	$0.329743\pi$
$854$	3.54324e9	0.194670
$855$	1.06223e10	0.581218
$856$	3.10804e9	0.169367
$857$	−7.07535e9	−0.383986	−0.191993	−	0.981396i	$-0.561495\pi$
$857$	−7.07535e9	−0.383986	−0.191993	+	0.981396i	$0.561495\pi$
$858$	−2.24992e10	−1.21608
$859$	1.62502e10	0.874747	0.437374	−	0.899280i	$-0.355909\pi$
$859$	1.62502e10	0.874747	0.437374	+	0.899280i	$0.355909\pi$
$860$	6.45351e9	0.345980
$861$	−1.12974e10	−0.603207
$862$	4.31395e8	0.0229403
$863$	−2.08226e10	−1.10280	−0.551401	−	0.834240i	$-0.685907\pi$
$863$	−2.08226e10	−1.10280	−0.551401	+	0.834240i	$0.685907\pi$
$864$	6.44973e8	0.0340207
$865$	−1.50321e10	−0.789700
$866$	6.66142e9	0.348541
$867$	6.17742e9	0.321915
$868$	1.60140e10	0.831150
$869$	−4.52278e10	−2.33796
$870$	1.20687e10	0.621360
$871$	−1.59120e10	−0.815947
$872$	9.05248e9	0.462339
$873$	9.91644e9	0.504436
$874$	1.72913e10	0.876067
$875$	2.35193e10	1.18685
$876$	3.58687e9	0.180282
$877$	3.49612e10	1.75020	0.875101	−	0.483940i	$-0.160795\pi$
$877$	3.49612e10	1.75020	0.875101	+	0.483940i	$0.160795\pi$
$878$	7.24361e9	0.361181
$879$	−4.06775e9	−0.202020
$880$	−8.62169e9	−0.426484
$881$	−1.53635e10	−0.756962	−0.378481	−	0.925609i	$-0.623553\pi$
$881$	−1.53635e10	−0.756962	−0.378481	+	0.925609i	$0.623553\pi$
$882$	−2.57455e9	−0.126346
$883$	−2.95536e9	−0.144460	−0.0722300	−	0.997388i	$-0.523012\pi$
$883$	−2.95536e9	−0.144460	−0.0722300	+	0.997388i	$0.523012\pi$
$884$	−1.23806e10	−0.602781
$885$	−1.60882e9	−0.0780202
$886$	8.81289e9	0.425697
$887$	2.45124e10	1.17938	0.589689	−	0.807630i	$-0.299250\pi$
$887$	2.45124e10	1.17938	0.589689	+	0.807630i	$0.299250\pi$
$888$	1.38266e9	0.0662626
$889$	−1.00565e10	−0.480055
$890$	2.22572e10	1.05829
$891$	−3.85566e9	−0.182611
$892$	−1.32454e10	−0.624868
$893$	−1.52206e10	−0.715238
$894$	−1.00749e10	−0.471586
$895$	−2.70449e10	−1.26097
$896$	2.35871e9	0.109546
$897$	1.66827e10	0.771781
$898$	9.58496e9	0.441695
$899$	−4.28442e10	−1.96668
$900$	2.82221e8	0.0129045
$901$	−1.71077e10	−0.779213
$902$	−2.15925e10	−0.979670
$903$	1.05544e10	0.477011
$904$	−5.23147e9	−0.235524
$905$	2.81246e10	1.26129
$906$	−7.13500e9	−0.318747
$907$	−3.05677e10	−1.36031	−0.680154	−	0.733070i	$-0.738087\pi$
$907$	−3.05677e10	−1.36031	−0.680154	+	0.733070i	$0.738087\pi$
$908$	6.06928e9	0.269052
$909$	−4.50310e9	−0.198856
$910$	3.74795e10	1.64873
$911$	7.01582e9	0.307442	0.153721	−	0.988114i	$-0.450874\pi$
$911$	7.01582e9	0.307442	0.153721	+	0.988114i	$0.450874\pi$
$912$	−5.55428e9	−0.242463
$913$	−2.98094e8	−0.0129630
$914$	−2.31965e9	−0.100487
$915$	−3.08474e9	−0.133121
$916$	−5.37963e9	−0.231270
$917$	5.19686e10	2.22561
$918$	−2.12165e9	−0.0905158
$919$	3.61821e10	1.53777	0.768883	−	0.639390i	$-0.220813\pi$
$919$	3.61821e10	1.53777	0.768883	+	0.639390i	$0.220813\pi$
$920$	6.39282e9	0.270667
$921$	−1.02337e10	−0.431641
$922$	−1.07320e9	−0.0450945
$923$	7.92973e10	3.31935
$924$	−1.41004e10	−0.588003
$925$	6.05008e8	0.0251342
$926$	−1.74886e10	−0.723798
$927$	−3.68718e9	−0.152025
$928$	−6.31056e9	−0.259209
$929$	−5.41546e9	−0.221606	−0.110803	−	0.993842i	$-0.535342\pi$
$929$	−5.41546e9	−0.221606	−0.110803	+	0.993842i	$0.535342\pi$
$930$	−1.39417e10	−0.568364
$931$	2.21711e10	0.900458
$932$	−1.61548e10	−0.653652
$933$	1.01942e10	0.410930
$934$	1.50168e10	0.603064
$935$	2.83612e10	1.13471
$936$	−5.35880e9	−0.213600
$937$	−2.46820e9	−0.0980149	−0.0490075	−	0.998798i	$-0.515606\pi$
$937$	−2.46820e9	−0.0980149	−0.0490075	+	0.998798i	$0.515606\pi$
$938$	−9.97218e9	−0.394530
$939$	1.04416e10	0.411566
$940$	−5.62724e9	−0.220978
$941$	−4.36716e10	−1.70858	−0.854290	−	0.519797i	$-0.826008\pi$
$941$	−4.36716e10	−1.70858	−0.854290	+	0.519797i	$0.826008\pi$
$942$	1.22650e10	0.478066
$943$	1.60104e10	0.621745
$944$	8.41232e8	0.0325472
$945$	6.42280e9	0.247579
$946$	2.01725e10	0.774714
$947$	1.89527e10	0.725182	0.362591	−	0.931948i	$-0.381892\pi$
$947$	1.89527e10	0.725182	0.362591	+	0.931948i	$0.381892\pi$
$948$	−1.07722e10	−0.410654
$949$	−2.98018e10	−1.13191
$950$	−2.43038e9	−0.0919692
$951$	1.02973e10	0.388233
$952$	−7.75902e9	−0.291459
$953$	3.87561e10	1.45049	0.725245	−	0.688491i	$-0.241726\pi$
$953$	3.87561e10	1.45049	0.725245	+	0.688491i	$0.241726\pi$
$954$	−7.40488e9	−0.276120
$955$	3.68867e10	1.37043
$956$	−6.34395e9	−0.234832
$957$	3.77246e10	1.39134
$958$	1.95841e10	0.719656
$959$	−2.20831e10	−0.808529
$960$	−2.05349e9	−0.0749106
$961$	2.19809e10	0.798940
$962$	−1.14879e10	−0.416033
$963$	−4.42531e9	−0.159680
$964$	−2.36858e10	−0.851568
$965$	7.40003e8	0.0265087
$966$	1.04552e10	0.373175
$967$	3.03103e9	0.107795	0.0538973	−	0.998546i	$-0.482836\pi$
$967$	3.03103e9	0.107795	0.0538973	+	0.998546i	$0.482836\pi$
$968$	−1.69725e10	−0.601424
$969$	1.82709e10	0.645100
$970$	−3.15724e10	−1.11072
$971$	−3.86376e10	−1.35439	−0.677194	−	0.735805i	$-0.736804\pi$
$971$	−3.86376e10	−1.35439	−0.677194	+	0.735805i	$0.736804\pi$
$972$	−9.18330e8	−0.0320750
$973$	3.08592e10	1.07396
$974$	−9.12275e9	−0.316351
$975$	−2.34485e9	−0.0810212
$976$	1.61297e9	0.0555331
$977$	−8.77414e9	−0.301005	−0.150502	−	0.988610i	$-0.548089\pi$
$977$	−8.77414e9	−0.301005	−0.150502	+	0.988610i	$0.548089\pi$
$978$	−6.55171e9	−0.223959
$979$	6.95721e10	2.36971
$980$	8.19696e9	0.278203
$981$	−1.28892e10	−0.435897
$982$	2.58035e10	0.869537
$983$	3.61692e10	1.21451	0.607255	−	0.794507i	$-0.292271\pi$
$983$	3.61692e10	1.21451	0.607255	+	0.794507i	$0.292271\pi$
$984$	−5.14284e9	−0.172076
$985$	2.48833e10	0.829624
$986$	2.07587e10	0.689654
$987$	−9.20312e9	−0.304667
$988$	4.61481e10	1.52232
$989$	−1.49576e10	−0.491670
$990$	1.22758e10	0.402093
$991$	−6.47096e9	−0.211208	−0.105604	−	0.994408i	$-0.533678\pi$
$991$	−6.47096e9	−0.211208	−0.105604	+	0.994408i	$0.533678\pi$
$992$	7.28994e9	0.237101
$993$	−3.16151e10	−1.02464
$994$	4.96961e10	1.60498
$995$	−9.51005e9	−0.306057
$996$	−7.09991e7	−0.00227691
$997$	3.40191e10	1.08715	0.543576	−	0.839360i	$-0.317070\pi$
$997$	3.40191e10	1.08715	0.543576	+	0.839360i	$0.317070\pi$
$998$	1.27680e10	0.406599
$999$	−1.96866e9	−0.0624730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.e.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.e.1.8	✓	9	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +290.127 q^{5} +216.000 q^{6} -1124.72 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +290.127 q^{5} +216.000 q^{6} -1124.72 q^{7} -512.000 q^{8} +729.000 q^{9} -2321.02 q^{10} -7255.10 q^{11} -1728.00 q^{12} +14357.2 q^{13} +8997.76 q^{14} -7833.44 q^{15} +4096.00 q^{16} -13473.9 q^{17} -5832.00 q^{18} +50223.1 q^{19} +18568.2 q^{20} +30367.4 q^{21} +58040.8 q^{22} -43036.2 q^{23} +13824.0 q^{24} +6048.97 q^{25} -114858. q^{26} -19683.0 q^{27} -71982.1 q^{28} +192583. q^{29} +62667.5 q^{30} -222471. q^{31} -32768.0 q^{32} +195888. q^{33} +107791. q^{34} -326312. q^{35} +46656.0 q^{36} +100018. q^{37} -401785. q^{38} -387645. q^{39} -148545. q^{40} -372023. q^{41} -242940. q^{42} +347558. q^{43} -464327. q^{44} +211503. q^{45} +344289. q^{46} -303059. q^{47} -110592. q^{48} +441452. q^{49} -48391.7 q^{50} +363794. q^{51} +918862. q^{52} +1.26970e6 q^{53} +157464. q^{54} -2.10490e6 q^{55} +575857. q^{56} -1.35602e6 q^{57} -1.54066e6 q^{58} +205379. q^{59} -501340. q^{60} +393792. q^{61} +1.77977e6 q^{62} -819921. q^{63} +262144. q^{64} +4.16542e6 q^{65} -1.56710e6 q^{66} -1.10830e6 q^{67} -862328. q^{68} +1.16198e6 q^{69} +2.61050e6 q^{70} +5.52317e6 q^{71} -373248. q^{72} -2.07574e6 q^{73} -800148. q^{74} -163322. q^{75} +3.21428e6 q^{76} +8.15996e6 q^{77} +3.10116e6 q^{78} +6.23393e6 q^{79} +1.18836e6 q^{80} +531441. q^{81} +2.97618e6 q^{82} +41087.5 q^{83} +1.94352e6 q^{84} -3.90914e6 q^{85} -2.78046e6 q^{86} -5.19974e6 q^{87} +3.71461e6 q^{88} -9.58940e6 q^{89} -1.69202e6 q^{90} -1.61478e7 q^{91} -2.75432e6 q^{92} +6.00673e6 q^{93} +2.42447e6 q^{94} +1.45711e7 q^{95} +884736. q^{96} +1.36028e7 q^{97} -3.53162e6 q^{98} -5.28897e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Introduction

L-functions

Modular forms

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