LMFDB - Embedded newform 354.8.a.c.1.1

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			1.1
Root			$115.894$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -506.565 q^{5} -216.000 q^{6} -836.150 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -506.565 q^{5} -216.000 q^{6} -836.150 q^{7} -512.000 q^{8} +729.000 q^{9} +4052.52 q^{10} +3379.42 q^{11} +1728.00 q^{12} -3440.15 q^{13} +6689.20 q^{14} -13677.2 q^{15} +4096.00 q^{16} -3241.88 q^{17} -5832.00 q^{18} -7601.23 q^{19} -32420.1 q^{20} -22576.1 q^{21} -27035.3 q^{22} +104257. q^{23} -13824.0 q^{24} +178483. q^{25} +27521.2 q^{26} +19683.0 q^{27} -53513.6 q^{28} -130142. q^{29} +109418. q^{30} -53431.0 q^{31} -32768.0 q^{32} +91244.3 q^{33} +25935.1 q^{34} +423564. q^{35} +46656.0 q^{36} +539897. q^{37} +60809.8 q^{38} -92884.1 q^{39} +259361. q^{40} +713359. q^{41} +180608. q^{42} +403782. q^{43} +216283. q^{44} -369286. q^{45} -834058. q^{46} -264254. q^{47} +110592. q^{48} -124396. q^{49} -1.42786e6 q^{50} -87530.9 q^{51} -220170. q^{52} -1.50152e6 q^{53} -157464. q^{54} -1.71189e6 q^{55} +428109. q^{56} -205233. q^{57} +1.04114e6 q^{58} -205379. q^{59} -875344. q^{60} -1.84759e6 q^{61} +427448. q^{62} -609553. q^{63} +262144. q^{64} +1.74266e6 q^{65} -729954. q^{66} -185438. q^{67} -207481. q^{68} +2.81495e6 q^{69} -3.38851e6 q^{70} +2.13323e6 q^{71} -373248. q^{72} -3.79106e6 q^{73} -4.31918e6 q^{74} +4.81904e6 q^{75} -486479. q^{76} -2.82570e6 q^{77} +743072. q^{78} -2.01576e6 q^{79} -2.07489e6 q^{80} +531441. q^{81} -5.70688e6 q^{82} +5.34167e6 q^{83} -1.44487e6 q^{84} +1.64222e6 q^{85} -3.23026e6 q^{86} -3.51383e6 q^{87} -1.73026e6 q^{88} +8.99421e6 q^{89} +2.95429e6 q^{90} +2.87648e6 q^{91} +6.67246e6 q^{92} -1.44264e6 q^{93} +2.11404e6 q^{94} +3.85051e6 q^{95} -884736. q^{96} +2.43666e6 q^{97} +995168. q^{98} +2.46360e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−506.565	−1.81234	−0.906170	−	0.422913i	$-0.861008\pi$
$5$	−506.565	−1.81234	−0.906170	+	0.422913i	$0.861008\pi$
$6$	−216.000	−0.408248
$7$	−836.150	−0.921385	−0.460692	−	0.887560i	$-0.652399\pi$
$7$	−836.150	−0.921385	−0.460692	+	0.887560i	$0.652399\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	4052.52	1.28152
$11$	3379.42	0.765539	0.382770	−	0.923844i	$-0.374970\pi$
$11$	3379.42	0.765539	0.382770	+	0.923844i	$0.374970\pi$
$12$	1728.00	0.288675
$13$	−3440.15	−0.434286	−0.217143	−	0.976140i	$-0.569674\pi$
$13$	−3440.15	−0.434286	−0.217143	+	0.976140i	$0.569674\pi$
$14$	6689.20	0.651518
$15$	−13677.2	−1.04636
$16$	4096.00	0.250000
$17$	−3241.88	−0.160039	−0.0800196	−	0.996793i	$-0.525498\pi$
$17$	−3241.88	−0.160039	−0.0800196	+	0.996793i	$0.525498\pi$
$18$	−5832.00	−0.235702
$19$	−7601.23	−0.254241	−0.127121	−	0.991887i	$-0.540574\pi$
$19$	−7601.23	−0.254241	−0.127121	+	0.991887i	$0.540574\pi$
$20$	−32420.1	−0.906170
$21$	−22576.1	−0.531962
$22$	−27035.3	−0.541318
$23$	104257.	1.78673	0.893365	−	0.449332i	$-0.148338\pi$
$23$	104257.	1.78673	0.893365	+	0.449332i	$0.148338\pi$
$24$	−13824.0	−0.204124
$25$	178483.	2.28458
$26$	27521.2	0.307086
$27$	19683.0	0.192450
$28$	−53513.6	−0.460692
$29$	−130142.	−0.990887	−0.495444	−	0.868640i	$-0.664994\pi$
$29$	−130142.	−0.990887	−0.495444	+	0.868640i	$0.664994\pi$
$30$	109418.	0.739885
$31$	−53431.0	−0.322127	−0.161064	−	0.986944i	$-0.551492\pi$
$31$	−53431.0	−0.322127	−0.161064	+	0.986944i	$0.551492\pi$
$32$	−32768.0	−0.176777
$33$	91244.3	0.441984
$34$	25935.1	0.113165
$35$	423564.	1.66986
$36$	46656.0	0.166667
$37$	539897.	1.75229	0.876143	−	0.482051i	$-0.160108\pi$
$37$	539897.	1.75229	0.876143	+	0.482051i	$0.160108\pi$
$38$	60809.8	0.179776
$39$	−92884.1	−0.250735
$40$	259361.	0.640759
$41$	713359.	1.61646	0.808230	−	0.588867i	$-0.200426\pi$
$41$	713359.	1.61646	0.808230	+	0.588867i	$0.200426\pi$
$42$	180608.	0.376154
$43$	403782.	0.774475	0.387237	−	0.921980i	$-0.373429\pi$
$43$	403782.	0.774475	0.387237	+	0.921980i	$0.373429\pi$
$44$	216283.	0.382770
$45$	−369286.	−0.604114
$46$	−834058.	−1.26341
$47$	−264254.	−0.371261	−0.185631	−	0.982620i	$-0.559433\pi$
$47$	−264254.	−0.371261	−0.185631	+	0.982620i	$0.559433\pi$
$48$	110592.	0.144338
$49$	−124396.	−0.151050
$50$	−1.42786e6	−1.61544
$51$	−87530.9	−0.0923987
$52$	−220170.	−0.217143
$53$	−1.50152e6	−1.38537	−0.692687	−	0.721239i	$-0.743573\pi$
$53$	−1.50152e6	−1.38537	−0.692687	+	0.721239i	$0.743573\pi$
$54$	−157464.	−0.136083
$55$	−1.71189e6	−1.38742
$56$	428109.	0.325759
$57$	−205233.	−0.146786
$58$	1.04114e6	0.700663
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−875344.	−0.523178
$61$	−1.84759e6	−1.04220	−0.521101	−	0.853495i	$-0.674478\pi$
$61$	−1.84759e6	−1.04220	−0.521101	+	0.853495i	$0.674478\pi$
$62$	427448.	0.227778
$63$	−609553.	−0.307128
$64$	262144.	0.125000
$65$	1.74266e6	0.787074
$66$	−729954.	−0.312530
$67$	−185438.	−0.0753244	−0.0376622	−	0.999291i	$-0.511991\pi$
$67$	−185438.	−0.0753244	−0.0376622	+	0.999291i	$0.511991\pi$
$68$	−207481.	−0.0800196
$69$	2.81495e6	1.03157
$70$	−3.38851e6	−1.18077
$71$	2.13323e6	0.707349	0.353675	−	0.935368i	$-0.384932\pi$
$71$	2.13323e6	0.707349	0.353675	+	0.935368i	$0.384932\pi$
$72$	−373248.	−0.117851
$73$	−3.79106e6	−1.14059	−0.570297	−	0.821439i	$-0.693172\pi$
$73$	−3.79106e6	−1.14059	−0.570297	+	0.821439i	$0.693172\pi$
$74$	−4.31918e6	−1.23905
$75$	4.81904e6	1.31900
$76$	−486479.	−0.127121
$77$	−2.82570e6	−0.705356
$78$	743072.	0.177296
$79$	−2.01576e6	−0.459984	−0.229992	−	0.973192i	$-0.573870\pi$
$79$	−2.01576e6	−0.459984	−0.229992	+	0.973192i	$0.573870\pi$
$80$	−2.07489e6	−0.453085
$81$	531441.	0.111111
$82$	−5.70688e6	−1.14301
$83$	5.34167e6	1.02542	0.512712	−	0.858561i	$-0.328641\pi$
$83$	5.34167e6	1.02542	0.512712	+	0.858561i	$0.328641\pi$
$84$	−1.44487e6	−0.265981
$85$	1.64222e6	0.290046
$86$	−3.23026e6	−0.547636
$87$	−3.51383e6	−0.572089
$88$	−1.73026e6	−0.270659
$89$	8.99421e6	1.35238	0.676188	−	0.736729i	$-0.263630\pi$
$89$	8.99421e6	1.35238	0.676188	+	0.736729i	$0.263630\pi$
$90$	2.95429e6	0.427173
$91$	2.87648e6	0.400144
$92$	6.67246e6	0.893365
$93$	−1.44264e6	−0.185980
$94$	2.11404e6	0.262521
$95$	3.85051e6	0.460772
$96$	−884736.	−0.102062
$97$	2.43666e6	0.271078	0.135539	−	0.990772i	$-0.456723\pi$
$97$	2.43666e6	0.271078	0.135539	+	0.990772i	$0.456723\pi$
$98$	995168.	0.106808
$99$	2.46360e6	0.255180
$100$	1.14229e7	1.14229
$101$	−814985.	−0.0787090	−0.0393545	−	0.999225i	$-0.512530\pi$
$101$	−814985.	−0.0787090	−0.0393545	+	0.999225i	$0.512530\pi$
$102$	700247.	0.0653357
$103$	−7.33883e6	−0.661754	−0.330877	−	0.943674i	$-0.607345\pi$
$103$	−7.33883e6	−0.661754	−0.330877	+	0.943674i	$0.607345\pi$
$104$	1.76136e6	0.153543
$105$	1.14362e7	0.964096
$106$	1.20122e7	0.979607
$107$	6.97920e6	0.550760	0.275380	−	0.961336i	$-0.411196\pi$
$107$	6.97920e6	0.550760	0.275380	+	0.961336i	$0.411196\pi$
$108$	1.25971e6	0.0962250
$109$	−4.89058e6	−0.361716	−0.180858	−	0.983509i	$-0.557887\pi$
$109$	−4.89058e6	−0.361716	−0.180858	+	0.983509i	$0.557887\pi$
$110$	1.36951e7	0.981053
$111$	1.45772e7	1.01168
$112$	−3.42487e6	−0.230346
$113$	−5.44592e6	−0.355056	−0.177528	−	0.984116i	$-0.556810\pi$
$113$	−5.44592e6	−0.355056	−0.177528	+	0.984116i	$0.556810\pi$
$114$	1.64187e6	0.103794
$115$	−5.28130e7	−3.23816
$116$	−8.32908e6	−0.495444
$117$	−2.50787e6	−0.144762
$118$	1.64303e6	0.0920575
$119$	2.71070e6	0.147458
$120$	7.00275e6	0.369943
$121$	−8.06671e6	−0.413950
$122$	1.47807e7	0.736948
$123$	1.92607e7	0.933264
$124$	−3.41958e6	−0.161064
$125$	−5.08377e7	−2.32810
$126$	4.87643e6	0.217173
$127$	−3.69376e7	−1.60013	−0.800066	−	0.599912i	$-0.795202\pi$
$127$	−3.69376e7	−1.60013	−0.800066	+	0.599912i	$0.795202\pi$
$128$	−2.09715e6	−0.0883883
$129$	1.09021e7	0.447143
$130$	−1.39413e7	−0.556545
$131$	2.78320e7	1.08167	0.540836	−	0.841128i	$-0.318108\pi$
$131$	2.78320e7	1.08167	0.540836	+	0.841128i	$0.318108\pi$
$132$	5.83963e6	0.220992
$133$	6.35577e6	0.234254
$134$	1.48350e6	0.0532624
$135$	−9.97071e6	−0.348785
$136$	1.65985e6	0.0565824
$137$	−1.18039e6	−0.0392197	−0.0196099	−	0.999808i	$-0.506242\pi$
$137$	−1.18039e6	−0.0392197	−0.0196099	+	0.999808i	$0.506242\pi$
$138$	−2.25196e7	−0.729429
$139$	2.35518e7	0.743828	0.371914	−	0.928267i	$-0.378702\pi$
$139$	2.35518e7	0.743828	0.371914	+	0.928267i	$0.378702\pi$
$140$	2.71081e7	0.834932
$141$	−7.13487e6	−0.214348
$142$	−1.70659e7	−0.500172
$143$	−1.16257e7	−0.332463
$144$	2.98598e6	0.0833333
$145$	6.59253e7	1.79583
$146$	3.03285e7	0.806522
$147$	−3.35869e6	−0.0872086
$148$	3.45534e7	0.876143
$149$	1.05431e7	0.261106	0.130553	−	0.991441i	$-0.458325\pi$
$149$	1.05431e7	0.261106	0.130553	+	0.991441i	$0.458325\pi$
$150$	−3.85523e7	−0.932676
$151$	−4.51867e7	−1.06805	−0.534025	−	0.845469i	$-0.679321\pi$
$151$	−4.51867e7	−1.06805	−0.534025	+	0.845469i	$0.679321\pi$
$152$	3.89183e6	0.0898879
$153$	−2.36333e6	−0.0533464
$154$	2.26056e7	0.498762
$155$	2.70663e7	0.583804
$156$	−5.94458e6	−0.125368
$157$	−8.61152e7	−1.77595	−0.887976	−	0.459891i	$-0.847889\pi$
$157$	−8.61152e7	−1.77595	−0.887976	+	0.459891i	$0.847889\pi$
$158$	1.61260e7	0.325258
$159$	−4.05412e7	−0.799846
$160$	1.65991e7	0.320380
$161$	−8.71747e7	−1.64627
$162$	−4.25153e6	−0.0785674
$163$	−3.25648e7	−0.588968	−0.294484	−	0.955656i	$-0.595148\pi$
$163$	−3.25648e7	−0.588968	−0.294484	+	0.955656i	$0.595148\pi$
$164$	4.56550e7	0.808230
$165$	−4.62211e7	−0.801026
$166$	−4.27333e7	−0.725084
$167$	−5.01264e7	−0.832836	−0.416418	−	0.909173i	$-0.636715\pi$
$167$	−5.01264e7	−0.832836	−0.416418	+	0.909173i	$0.636715\pi$
$168$	1.15589e7	0.188077
$169$	−5.09139e7	−0.811396
$170$	−1.31378e7	−0.205093
$171$	−5.54129e6	−0.0847471
$172$	2.58420e7	0.387237
$173$	3.26550e7	0.479500	0.239750	−	0.970835i	$-0.422935\pi$
$173$	3.26550e7	0.479500	0.239750	+	0.970835i	$0.422935\pi$
$174$	2.81107e7	0.404528
$175$	−1.49238e8	−2.10498
$176$	1.38421e7	0.191385
$177$	−5.54523e6	−0.0751646
$178$	−7.19536e7	−0.956275
$179$	−2.44729e6	−0.0318934	−0.0159467	−	0.999873i	$-0.505076\pi$
$179$	−2.44729e6	−0.0318934	−0.0159467	+	0.999873i	$0.505076\pi$
$180$	−2.36343e7	−0.302057
$181$	9.41747e7	1.18048	0.590241	−	0.807227i	$-0.299033\pi$
$181$	9.41747e7	1.18048	0.590241	+	0.807227i	$0.299033\pi$
$182$	−2.30119e7	−0.282945
$183$	−4.98850e7	−0.601715
$184$	−5.33797e7	−0.631704
$185$	−2.73493e8	−3.17574
$186$	1.15411e7	0.131508
$187$	−1.09557e7	−0.122516
$188$	−1.69123e7	−0.185631
$189$	−1.64579e7	−0.177321
$190$	−3.08041e7	−0.325815
$191$	1.13760e8	1.18133	0.590666	−	0.806916i	$-0.298865\pi$
$191$	1.13760e8	1.18133	0.590666	+	0.806916i	$0.298865\pi$
$192$	7.07789e6	0.0721688
$193$	2.62170e7	0.262502	0.131251	−	0.991349i	$-0.458101\pi$
$193$	2.62170e7	0.262502	0.131251	+	0.991349i	$0.458101\pi$
$194$	−1.94933e7	−0.191681
$195$	4.70518e7	0.454417
$196$	−7.96134e6	−0.0755249
$197$	−2.46889e7	−0.230075	−0.115037	−	0.993361i	$-0.536699\pi$
$197$	−2.46889e7	−0.230075	−0.115037	+	0.993361i	$0.536699\pi$
$198$	−1.97088e7	−0.180439
$199$	−9.99677e7	−0.899237	−0.449618	−	0.893221i	$-0.648440\pi$
$199$	−9.99677e7	−0.899237	−0.449618	+	0.893221i	$0.648440\pi$
$200$	−9.13832e7	−0.807721
$201$	−5.00681e6	−0.0434886
$202$	6.51988e6	0.0556557
$203$	1.08818e8	0.912988
$204$	−5.60198e6	−0.0461993
$205$	−3.61363e8	−2.92958
$206$	5.87107e7	0.467931
$207$	7.60035e7	0.595577
$208$	−1.40909e7	−0.108571
$209$	−2.56877e7	−0.194632
$210$	−9.14899e7	−0.681719
$211$	−4.13134e7	−0.302763	−0.151381	−	0.988475i	$-0.548372\pi$
$211$	−4.13134e7	−0.302763	−0.151381	+	0.988475i	$0.548372\pi$
$212$	−9.60975e7	−0.692687
$213$	5.75973e7	0.408388
$214$	−5.58336e7	−0.389446
$215$	−2.04542e8	−1.40361
$216$	−1.00777e7	−0.0680414
$217$	4.46763e7	0.296803
$218$	3.91247e7	0.255772
$219$	−1.02359e8	−0.658522
$220$	−1.09561e8	−0.693709
$221$	1.11526e7	0.0695028
$222$	−1.16618e8	−0.715368
$223$	3.41978e7	0.206505	0.103253	−	0.994655i	$-0.467075\pi$
$223$	3.41978e7	0.206505	0.103253	+	0.994655i	$0.467075\pi$
$224$	2.73990e7	0.162879
$225$	1.30114e8	0.761527
$226$	4.35674e7	0.251062
$227$	2.57409e7	0.146061	0.0730304	−	0.997330i	$-0.476733\pi$
$227$	2.57409e7	0.146061	0.0730304	+	0.997330i	$0.476733\pi$
$228$	−1.31349e7	−0.0733931
$229$	−2.20536e8	−1.21354	−0.606771	−	0.794876i	$-0.707536\pi$
$229$	−2.20536e8	−1.21354	−0.606771	+	0.794876i	$0.707536\pi$
$230$	4.22504e8	2.28973
$231$	−7.62939e7	−0.407238
$232$	6.66327e7	0.350331
$233$	−3.55752e8	−1.84248	−0.921239	−	0.388998i	$-0.872821\pi$
$233$	−3.55752e8	−1.84248	−0.921239	+	0.388998i	$0.872821\pi$
$234$	2.00630e7	0.102362
$235$	1.33862e8	0.672852
$236$	−1.31443e7	−0.0650945
$237$	−5.44254e7	−0.265572
$238$	−2.16856e7	−0.104268
$239$	9.30444e7	0.440857	0.220428	−	0.975403i	$-0.429254\pi$
$239$	9.30444e7	0.440857	0.220428	+	0.975403i	$0.429254\pi$
$240$	−5.60220e7	−0.261589
$241$	5.23402e6	0.0240866	0.0120433	−	0.999927i	$-0.496166\pi$
$241$	5.23402e6	0.0240866	0.0120433	+	0.999927i	$0.496166\pi$
$242$	6.45337e7	0.292707
$243$	1.43489e7	0.0641500
$244$	−1.18246e8	−0.521101
$245$	6.30146e7	0.273754
$246$	−1.54086e8	−0.659917
$247$	2.61494e7	0.110413
$248$	2.73567e7	0.113889
$249$	1.44225e8	0.592029
$250$	4.06702e8	1.64621
$251$	−1.29706e8	−0.517728	−0.258864	−	0.965914i	$-0.583348\pi$
$251$	−1.29706e8	−0.517728	−0.258864	+	0.965914i	$0.583348\pi$
$252$	−3.90114e7	−0.153564
$253$	3.52329e8	1.36781
$254$	2.95501e8	1.13146
$255$	4.43401e7	0.167458
$256$	1.67772e7	0.0625000
$257$	−2.55575e8	−0.939189	−0.469594	−	0.882882i	$-0.655600\pi$
$257$	−2.55575e8	−0.939189	−0.469594	+	0.882882i	$0.655600\pi$
$258$	−8.72169e7	−0.316178
$259$	−4.51435e8	−1.61453
$260$	1.11530e8	0.393537
$261$	−9.48734e7	−0.330296
$262$	−2.22656e8	−0.764858
$263$	1.04952e7	0.0355750	0.0177875	−	0.999842i	$-0.494338\pi$
$263$	1.04952e7	0.0355750	0.0177875	+	0.999842i	$0.494338\pi$
$264$	−4.67171e7	−0.156265
$265$	7.60619e8	2.51077
$266$	−5.08461e7	−0.165643
$267$	2.42844e8	0.780795
$268$	−1.18680e7	−0.0376622
$269$	−1.11240e8	−0.348441	−0.174220	−	0.984707i	$-0.555741\pi$
$269$	−1.11240e8	−0.348441	−0.174220	+	0.984707i	$0.555741\pi$
$270$	7.97657e7	0.246628
$271$	2.75020e8	0.839405	0.419702	−	0.907662i	$-0.362134\pi$
$271$	2.75020e8	0.839405	0.419702	+	0.907662i	$0.362134\pi$
$272$	−1.32788e7	−0.0400098
$273$	7.76650e7	0.231024
$274$	9.44314e6	0.0277325
$275$	6.03168e8	1.74894
$276$	1.80157e8	0.515784
$277$	4.14398e8	1.17149	0.585745	−	0.810496i	$-0.300802\pi$
$277$	4.14398e8	1.17149	0.585745	+	0.810496i	$0.300802\pi$
$278$	−1.88414e8	−0.525966
$279$	−3.89512e7	−0.107376
$280$	−2.16865e8	−0.590386
$281$	−5.94992e8	−1.59970	−0.799850	−	0.600200i	$-0.795088\pi$
$281$	−5.94992e8	−1.59970	−0.799850	+	0.600200i	$0.795088\pi$
$282$	5.70790e7	0.151567
$283$	6.23072e8	1.63413	0.817064	−	0.576548i	$-0.195600\pi$
$283$	6.23072e8	1.63413	0.817064	+	0.576548i	$0.195600\pi$
$284$	1.36527e8	0.353675
$285$	1.03964e8	0.266027
$286$	9.30056e7	0.235087
$287$	−5.96476e8	−1.48938
$288$	−2.38879e7	−0.0589256
$289$	−3.99829e8	−0.974387
$290$	−5.27402e8	−1.26984
$291$	6.57899e7	0.156507
$292$	−2.42628e8	−0.570297
$293$	−4.47861e8	−1.04018	−0.520088	−	0.854113i	$-0.674101\pi$
$293$	−4.47861e8	−1.04018	−0.520088	+	0.854113i	$0.674101\pi$
$294$	2.68695e7	0.0616658
$295$	1.04038e8	0.235947
$296$	−2.76427e8	−0.619527
$297$	6.65171e7	0.147328
$298$	−8.43450e7	−0.184630
$299$	−3.58661e8	−0.775951
$300$	3.08418e8	0.659501
$301$	−3.37622e8	−0.713590
$302$	3.61494e8	0.755226
$303$	−2.20046e7	−0.0454427
$304$	−3.11346e7	−0.0635603
$305$	9.35925e8	1.88882
$306$	1.89067e7	0.0377216
$307$	6.13420e8	1.20997	0.604984	−	0.796238i	$-0.293180\pi$
$307$	6.13420e8	1.20997	0.604984	+	0.796238i	$0.293180\pi$
$308$	−1.80845e8	−0.352678
$309$	−1.98148e8	−0.382064
$310$	−2.16530e8	−0.412812
$311$	−1.06314e8	−0.200415	−0.100207	−	0.994967i	$-0.531951\pi$
$311$	−1.06314e8	−0.200415	−0.100207	+	0.994967i	$0.531951\pi$
$312$	4.75566e7	0.0886482
$313$	−1.01502e9	−1.87098	−0.935492	−	0.353349i	$-0.885043\pi$
$313$	−1.01502e9	−1.87098	−0.935492	+	0.353349i	$0.885043\pi$
$314$	6.88922e8	1.25579
$315$	3.08778e8	0.556621
$316$	−1.29008e8	−0.229992
$317$	6.28235e8	1.10768	0.553840	−	0.832623i	$-0.313162\pi$
$317$	6.28235e8	1.10768	0.553840	+	0.832623i	$0.313162\pi$
$318$	3.24329e8	0.565576
$319$	−4.39804e8	−0.758563
$320$	−1.32793e8	−0.226543
$321$	1.88438e8	0.317981
$322$	6.97398e8	1.16409
$323$	2.46423e7	0.0406886
$324$	3.40122e7	0.0555556
$325$	−6.14008e8	−0.992161
$326$	2.60518e8	0.416463
$327$	−1.32046e8	−0.208837
$328$	−3.65240e8	−0.571505
$329$	2.20956e8	0.342075
$330$	3.69769e8	0.566411
$331$	2.31407e8	0.350734	0.175367	−	0.984503i	$-0.443889\pi$
$331$	2.31407e8	0.350734	0.175367	+	0.984503i	$0.443889\pi$
$332$	3.41867e8	0.512712
$333$	3.93585e8	0.584096
$334$	4.01012e8	0.588904
$335$	9.39361e7	0.136514
$336$	−9.24715e7	−0.132990
$337$	−6.97764e8	−0.993125	−0.496562	−	0.868001i	$-0.665405\pi$
$337$	−6.97764e8	−0.993125	−0.496562	+	0.868001i	$0.665405\pi$
$338$	4.07311e8	0.573743
$339$	−1.47040e8	−0.204992
$340$	1.05102e8	0.145023
$341$	−1.80566e8	−0.246601
$342$	4.43304e7	0.0599253
$343$	7.92619e8	1.06056
$344$	−2.06736e8	−0.273818
$345$	−1.42595e9	−1.86955
$346$	−2.61240e8	−0.339058
$347$	1.14974e9	1.47723	0.738614	−	0.674128i	$-0.235480\pi$
$347$	1.14974e9	1.47723	0.738614	+	0.674128i	$0.235480\pi$
$348$	−2.24885e8	−0.286044
$349$	−1.58127e9	−1.99121	−0.995606	−	0.0936437i	$-0.970149\pi$
$349$	−1.58127e9	−1.99121	−0.995606	+	0.0936437i	$0.970149\pi$
$350$	1.19391e9	1.48844
$351$	−6.77125e7	−0.0835783
$352$	−1.10737e8	−0.135329
$353$	−6.67203e8	−0.807322	−0.403661	−	0.914909i	$-0.632262\pi$
$353$	−6.67203e8	−0.807322	−0.403661	+	0.914909i	$0.632262\pi$
$354$	4.43619e7	0.0531494
$355$	−1.08062e9	−1.28196
$356$	5.75629e8	0.676188
$357$	7.31890e7	0.0851347
$358$	1.95783e7	0.0225520
$359$	8.44254e8	0.963036	0.481518	−	0.876436i	$-0.340086\pi$
$359$	8.44254e8	0.963036	0.481518	+	0.876436i	$0.340086\pi$
$360$	1.89074e8	0.213586
$361$	−8.36093e8	−0.935361
$362$	−7.53398e8	−0.834727
$363$	−2.17801e8	−0.238994
$364$	1.84095e8	0.200072
$365$	1.92042e9	2.06714
$366$	3.99080e8	0.425477
$367$	9.51172e8	1.00445	0.502225	−	0.864737i	$-0.332515\pi$
$367$	9.51172e8	1.00445	0.502225	+	0.864737i	$0.332515\pi$
$368$	4.27038e8	0.446682
$369$	5.20039e8	0.538820
$370$	2.18794e9	2.24559
$371$	1.25550e9	1.27646
$372$	−9.23288e7	−0.0929901
$373$	1.70967e9	1.70581	0.852906	−	0.522065i	$-0.174838\pi$
$373$	1.70967e9	1.70581	0.852906	+	0.522065i	$0.174838\pi$
$374$	8.76454e7	0.0866321
$375$	−1.37262e9	−1.34413
$376$	1.35298e8	0.131261
$377$	4.47708e8	0.430328
$378$	1.31664e8	0.125385
$379$	−2.05504e9	−1.93902	−0.969510	−	0.245050i	$-0.921196\pi$
$379$	−2.05504e9	−1.93902	−0.969510	+	0.245050i	$0.921196\pi$
$380$	2.46433e8	0.230386
$381$	−9.97316e8	−0.923837
$382$	−9.10078e8	−0.835328
$383$	−3.34461e8	−0.304194	−0.152097	−	0.988366i	$-0.548603\pi$
$383$	−3.34461e8	−0.304194	−0.152097	+	0.988366i	$0.548603\pi$
$384$	−5.66231e7	−0.0510310
$385$	1.43140e9	1.27835
$386$	−2.09736e8	−0.185617
$387$	2.94357e8	0.258158
$388$	1.55947e8	0.135539
$389$	1.05259e9	0.906639	0.453319	−	0.891348i	$-0.350240\pi$
$389$	1.05259e9	0.906639	0.453319	+	0.891348i	$0.350240\pi$
$390$	−3.76414e8	−0.321322
$391$	−3.37990e8	−0.285947
$392$	6.36907e7	0.0534041
$393$	7.51465e8	0.624504
$394$	1.97511e8	0.162687
$395$	1.02111e9	0.833648
$396$	1.57670e8	0.127590
$397$	−1.32894e9	−1.06595	−0.532976	−	0.846130i	$-0.678927\pi$
$397$	−1.32894e9	−1.06595	−0.532976	+	0.846130i	$0.678927\pi$
$398$	7.99742e8	0.635856
$399$	1.71606e8	0.135247
$400$	7.31065e8	0.571145
$401$	−1.07984e9	−0.836281	−0.418141	−	0.908382i	$-0.637318\pi$
$401$	−1.07984e9	−0.836281	−0.418141	+	0.908382i	$0.637318\pi$
$402$	4.00545e7	0.0307511
$403$	1.83811e8	0.139895
$404$	−5.21590e7	−0.0393545
$405$	−2.69209e8	−0.201371
$406$	−8.70545e8	−0.645580
$407$	1.82454e9	1.34144
$408$	4.48158e7	0.0326679
$409$	−8.68376e8	−0.627591	−0.313795	−	0.949491i	$-0.601601\pi$
$409$	−8.68376e8	−0.627591	−0.313795	+	0.949491i	$0.601601\pi$
$410$	2.89090e9	2.07152
$411$	−3.18706e7	−0.0226435
$412$	−4.69685e8	−0.330877
$413$	1.71728e8	0.119954
$414$	−6.08028e8	−0.421136
$415$	−2.70590e9	−1.85842
$416$	1.12727e8	0.0767716
$417$	6.35899e8	0.429449
$418$	2.05502e8	0.137625
$419$	3.25657e8	0.216278	0.108139	−	0.994136i	$-0.465511\pi$
$419$	3.25657e8	0.216278	0.108139	+	0.994136i	$0.465511\pi$
$420$	7.31919e8	0.482048
$421$	−2.19499e9	−1.43366	−0.716829	−	0.697249i	$-0.754407\pi$
$421$	−2.19499e9	−1.43366	−0.716829	+	0.697249i	$0.754407\pi$
$422$	3.30507e8	0.214085
$423$	−1.92641e8	−0.123754
$424$	7.68780e8	0.489803
$425$	−5.78621e8	−0.365622
$426$	−4.60778e8	−0.288774
$427$	1.54486e9	0.960269
$428$	4.46668e8	0.275380
$429$	−3.13894e8	−0.191947
$430$	1.63633e9	0.992504
$431$	1.66697e9	1.00290	0.501449	−	0.865187i	$-0.332801\pi$
$431$	1.66697e9	1.00290	0.501449	+	0.865187i	$0.332801\pi$
$432$	8.06216e7	0.0481125
$433$	−6.14870e8	−0.363978	−0.181989	−	0.983301i	$-0.558254\pi$
$433$	−6.14870e8	−0.363978	−0.181989	+	0.983301i	$0.558254\pi$
$434$	−3.57411e8	−0.209872
$435$	1.77998e9	1.03682
$436$	−3.12997e8	−0.180858
$437$	−7.92483e8	−0.454261
$438$	8.18870e8	0.465645
$439$	2.20687e9	1.24495	0.622474	−	0.782641i	$-0.286128\pi$
$439$	2.20687e9	1.24495	0.622474	+	0.782641i	$0.286128\pi$
$440$	8.76489e8	0.490526
$441$	−9.06846e7	−0.0503499
$442$	−8.92206e7	−0.0491459
$443$	1.33985e9	0.732224	0.366112	−	0.930571i	$-0.380689\pi$
$443$	1.33985e9	0.732224	0.366112	+	0.930571i	$0.380689\pi$
$444$	9.32943e8	0.505842
$445$	−4.55615e9	−2.45097
$446$	−2.73583e8	−0.146021
$447$	2.84664e8	0.150750
$448$	−2.19192e8	−0.115173
$449$	2.28859e9	1.19318	0.596589	−	0.802547i	$-0.296522\pi$
$449$	2.28859e9	1.19318	0.596589	+	0.802547i	$0.296522\pi$
$450$	−1.04091e9	−0.538481
$451$	2.41074e9	1.23746
$452$	−3.48539e8	−0.177528
$453$	−1.22004e9	−0.616639
$454$	−2.05927e8	−0.103281
$455$	−1.45712e9	−0.725198
$456$	1.05079e8	0.0518968
$457$	2.96429e9	1.45283	0.726414	−	0.687258i	$-0.241186\pi$
$457$	2.96429e9	1.45283	0.726414	+	0.687258i	$0.241186\pi$
$458$	1.76429e9	0.858104
$459$	−6.38100e7	−0.0307996
$460$	−3.38003e9	−1.61908
$461$	−3.36420e9	−1.59930	−0.799649	−	0.600468i	$-0.794981\pi$
$461$	−3.36420e9	−1.59930	−0.799649	+	0.600468i	$0.794981\pi$
$462$	6.10351e8	0.287960
$463$	−2.70896e9	−1.26844	−0.634219	−	0.773154i	$-0.718678\pi$
$463$	−2.70896e9	−1.26844	−0.634219	+	0.773154i	$0.718678\pi$
$464$	−5.33061e8	−0.247722
$465$	7.30789e8	0.337060
$466$	2.84602e9	1.30283
$467$	−3.81919e8	−0.173525	−0.0867625	−	0.996229i	$-0.527652\pi$
$467$	−3.81919e8	−0.173525	−0.0867625	+	0.996229i	$0.527652\pi$
$468$	−1.60504e8	−0.0723810
$469$	1.55054e8	0.0694028
$470$	−1.07090e9	−0.475778
$471$	−2.32511e9	−1.02535
$472$	1.05154e8	0.0460287
$473$	1.36455e9	0.592891
$474$	4.35403e8	0.187788
$475$	−1.35669e9	−0.580835
$476$	1.73485e8	0.0737289
$477$	−1.09461e9	−0.461791
$478$	−7.44355e8	−0.311733
$479$	1.50391e9	0.625241	0.312620	−	0.949878i	$-0.398793\pi$
$479$	1.50391e9	0.625241	0.312620	+	0.949878i	$0.398793\pi$
$480$	4.48176e8	0.184971
$481$	−1.85733e9	−0.760993
$482$	−4.18721e7	−0.0170318
$483$	−2.35372e9	−0.950472
$484$	−5.16269e8	−0.206975
$485$	−1.23433e9	−0.491286
$486$	−1.14791e8	−0.0453609
$487$	1.80300e9	0.707367	0.353684	−	0.935365i	$-0.384929\pi$
$487$	1.80300e9	0.707367	0.353684	+	0.935365i	$0.384929\pi$
$488$	9.45967e8	0.368474
$489$	−8.79250e8	−0.340041
$490$	−5.04117e8	−0.193573
$491$	−2.20948e8	−0.0842375	−0.0421188	−	0.999113i	$-0.513411\pi$
$491$	−2.20948e8	−0.0842375	−0.0421188	+	0.999113i	$0.513411\pi$
$492$	1.23269e9	0.466632
$493$	4.21905e8	0.158581
$494$	−2.09195e8	−0.0780741
$495$	−1.24797e9	−0.462473
$496$	−2.18853e8	−0.0805318
$497$	−1.78370e9	−0.651741
$498$	−1.15380e9	−0.418628
$499$	−2.58497e9	−0.931329	−0.465664	−	0.884961i	$-0.654185\pi$
$499$	−2.58497e9	−0.931329	−0.465664	+	0.884961i	$0.654185\pi$
$500$	−3.25361e9	−1.16405
$501$	−1.35341e9	−0.480838
$502$	1.03765e9	0.366089
$503$	4.62148e9	1.61917	0.809585	−	0.587002i	$-0.199692\pi$
$503$	4.62148e9	1.61917	0.809585	+	0.587002i	$0.199692\pi$
$504$	3.12091e8	0.108586
$505$	4.12842e8	0.142648
$506$	−2.81863e9	−0.967189
$507$	−1.37467e9	−0.468460
$508$	−2.36401e9	−0.800066
$509$	−4.59087e9	−1.54306	−0.771530	−	0.636193i	$-0.780508\pi$
$509$	−4.59087e9	−1.54306	−0.771530	+	0.636193i	$0.780508\pi$
$510$	−3.54720e8	−0.118411
$511$	3.16990e9	1.05093
$512$	−1.34218e8	−0.0441942
$513$	−1.49615e8	−0.0489288
$514$	2.04460e9	0.664107
$515$	3.71759e9	1.19932
$516$	6.97735e8	0.223572
$517$	−8.93026e8	−0.284215
$518$	3.61148e9	1.14165
$519$	8.81686e8	0.276839
$520$	−8.92241e8	−0.278273
$521$	−4.51230e8	−0.139787	−0.0698934	−	0.997554i	$-0.522266\pi$
$521$	−4.51230e8	−0.139787	−0.0698934	+	0.997554i	$0.522266\pi$
$522$	7.58988e8	0.233554
$523$	−4.89074e9	−1.49492	−0.747461	−	0.664305i	$-0.768728\pi$
$523$	−4.89074e9	−1.49492	−0.747461	+	0.664305i	$0.768728\pi$
$524$	1.78125e9	0.540836
$525$	−4.02944e9	−1.21531
$526$	−8.39614e7	−0.0251553
$527$	1.73217e8	0.0515530
$528$	3.73737e8	0.110496
$529$	7.46475e9	2.19240
$530$	−6.08495e9	−1.77538
$531$	−1.49721e8	−0.0433963
$532$	4.06769e8	0.117127
$533$	−2.45406e9	−0.702006
$534$	−1.94275e9	−0.552106
$535$	−3.53541e9	−0.998164
$536$	9.49440e7	0.0266312
$537$	−6.60769e7	−0.0184136
$538$	8.89922e8	0.246385
$539$	−4.20386e8	−0.115634
$540$	−6.38126e8	−0.174393
$541$	2.56729e9	0.697082	0.348541	−	0.937293i	$-0.386677\pi$
$541$	2.56729e9	0.697082	0.348541	+	0.937293i	$0.386677\pi$
$542$	−2.20016e9	−0.593549
$543$	2.54272e9	0.681552
$544$	1.06230e8	0.0282912
$545$	2.47740e9	0.655553
$546$	−6.21320e8	−0.163358
$547$	6.50090e9	1.69831	0.849157	−	0.528140i	$-0.177110\pi$
$547$	6.50090e9	1.69831	0.849157	+	0.528140i	$0.177110\pi$
$548$	−7.55451e7	−0.0196099
$549$	−1.34689e9	−0.347400
$550$	−4.82534e9	−1.23668
$551$	9.89238e8	0.251924
$552$	−1.44125e9	−0.364715
$553$	1.68547e9	0.423823
$554$	−3.31518e9	−0.828368
$555$	−7.38431e9	−1.83351
$556$	1.50732e9	0.371914
$557$	5.02651e9	1.23246	0.616231	−	0.787566i	$-0.288659\pi$
$557$	5.02651e9	1.23246	0.616231	+	0.787566i	$0.288659\pi$
$558$	3.11610e8	0.0759261
$559$	−1.38907e9	−0.336343
$560$	1.73492e9	0.417466
$561$	−2.95803e8	−0.0707348
$562$	4.75993e9	1.13116
$563$	−3.66275e9	−0.865024	−0.432512	−	0.901628i	$-0.642373\pi$
$563$	−3.66275e9	−0.865024	−0.432512	+	0.901628i	$0.642373\pi$
$564$	−4.56632e8	−0.107174
$565$	2.75871e9	0.643482
$566$	−4.98458e9	−1.15550
$567$	−4.44364e8	−0.102376
$568$	−1.09222e9	−0.250086
$569$	−5.59970e9	−1.27430	−0.637151	−	0.770739i	$-0.719887\pi$
$569$	−5.59970e9	−1.27430	−0.637151	+	0.770739i	$0.719887\pi$
$570$	−8.31711e8	−0.188109
$571$	−1.35388e9	−0.304336	−0.152168	−	0.988355i	$-0.548625\pi$
$571$	−1.35388e9	−0.304336	−0.152168	+	0.988355i	$0.548625\pi$
$572$	−7.44045e8	−0.166231
$573$	3.07151e9	0.682042
$574$	4.77181e9	1.05315
$575$	1.86081e10	4.08193
$576$	1.91103e8	0.0416667
$577$	2.35235e9	0.509785	0.254893	−	0.966969i	$-0.417960\pi$
$577$	2.35235e9	0.509785	0.254893	+	0.966969i	$0.417960\pi$
$578$	3.19863e9	0.688996
$579$	7.07859e8	0.151556
$580$	4.21922e9	0.897913
$581$	−4.46644e9	−0.944811
$582$	−5.26320e8	−0.110667
$583$	−5.07428e9	−1.06056
$584$	1.94102e9	0.403261
$585$	1.27040e9	0.262358
$586$	3.58289e9	0.735515
$587$	−2.94267e9	−0.600492	−0.300246	−	0.953862i	$-0.597069\pi$
$587$	−2.94267e9	−0.600492	−0.300246	+	0.953862i	$0.597069\pi$
$588$	−2.14956e8	−0.0436043
$589$	4.06141e8	0.0818980
$590$	−8.32302e8	−0.166840
$591$	−6.66599e8	−0.132834
$592$	2.21142e9	0.438072
$593$	7.16562e9	1.41111	0.705557	−	0.708653i	$-0.250697\pi$
$593$	7.16562e9	1.41111	0.705557	+	0.708653i	$0.250697\pi$
$594$	−5.32137e8	−0.104177
$595$	−1.37315e9	−0.267244
$596$	6.74760e8	0.130553
$597$	−2.69913e9	−0.519174
$598$	2.86928e9	0.548681
$599$	−4.45212e9	−0.846394	−0.423197	−	0.906038i	$-0.639092\pi$
$599$	−4.45212e9	−0.846394	−0.423197	+	0.906038i	$0.639092\pi$
$600$	−2.46735e9	−0.466338
$601$	6.81412e9	1.28041	0.640205	−	0.768204i	$-0.278849\pi$
$601$	6.81412e9	1.28041	0.640205	+	0.768204i	$0.278849\pi$
$602$	2.70098e9	0.504584
$603$	−1.35184e8	−0.0251081
$604$	−2.89195e9	−0.534025
$605$	4.08631e9	0.750218
$606$	1.76037e8	0.0321328
$607$	−7.82449e9	−1.42002	−0.710012	−	0.704190i	$-0.751310\pi$
$607$	−7.82449e9	−1.42002	−0.710012	+	0.704190i	$0.751310\pi$
$608$	2.49077e8	0.0449439
$609$	2.93809e9	0.527114
$610$	−7.48740e9	−1.33560
$611$	9.09075e8	0.161234
$612$	−1.51253e8	−0.0266732
$613$	8.08868e9	1.41829	0.709146	−	0.705061i	$-0.249081\pi$
$613$	8.08868e9	1.41829	0.709146	+	0.705061i	$0.249081\pi$
$614$	−4.90736e9	−0.855576
$615$	−9.75679e9	−1.69139
$616$	1.44676e9	0.249381
$617$	−8.89679e8	−0.152488	−0.0762439	−	0.997089i	$-0.524293\pi$
$617$	−8.89679e8	−0.152488	−0.0762439	+	0.997089i	$0.524293\pi$
$618$	1.58519e9	0.270160
$619$	−3.72186e9	−0.630729	−0.315364	−	0.948971i	$-0.602127\pi$
$619$	−3.72186e9	−0.630729	−0.315364	+	0.948971i	$0.602127\pi$
$620$	1.73224e9	0.291902
$621$	2.05210e9	0.343856
$622$	8.50514e8	0.141715
$623$	−7.52051e9	−1.24606
$624$	−3.80453e8	−0.0626838
$625$	1.18086e10	1.93472
$626$	8.12017e9	1.32298
$627$	−6.93568e8	−0.112371
$628$	−5.51137e9	−0.887976
$629$	−1.75029e9	−0.280435
$630$	−2.47023e9	−0.393591
$631$	6.45037e9	1.02207	0.511036	−	0.859559i	$-0.329262\pi$
$631$	6.45037e9	1.02207	0.511036	+	0.859559i	$0.329262\pi$
$632$	1.03207e9	0.162629
$633$	−1.11546e9	−0.174800
$634$	−5.02588e9	−0.783248
$635$	1.87113e10	2.89998
$636$	−2.59463e9	−0.399923
$637$	4.27941e8	0.0655988
$638$	3.51843e9	0.536385
$639$	1.55513e9	0.235783
$640$	1.06234e9	0.160190
$641$	9.64857e9	1.44697	0.723485	−	0.690340i	$-0.242539\pi$
$641$	9.64857e9	1.44697	0.723485	+	0.690340i	$0.242539\pi$
$642$	−1.50751e9	−0.224847
$643$	−6.95756e9	−1.03209	−0.516046	−	0.856561i	$-0.672597\pi$
$643$	−6.95756e9	−1.03209	−0.516046	+	0.856561i	$0.672597\pi$
$644$	−5.57918e9	−0.823133
$645$	−5.52263e9	−0.810376
$646$	−1.97138e8	−0.0287712
$647$	−9.75805e9	−1.41644	−0.708220	−	0.705992i	$-0.750502\pi$
$647$	−9.75805e9	−1.41644	−0.708220	+	0.705992i	$0.750502\pi$
$648$	−2.72098e8	−0.0392837
$649$	−6.94061e8	−0.0996647
$650$	4.91206e9	0.701563
$651$	1.20626e9	0.171359
$652$	−2.08415e9	−0.294484
$653$	−8.19511e8	−0.115175	−0.0575875	−	0.998340i	$-0.518341\pi$
$653$	−8.19511e8	−0.115175	−0.0575875	+	0.998340i	$0.518341\pi$
$654$	1.05637e9	0.147670
$655$	−1.40987e10	−1.96036
$656$	2.92192e9	0.404115
$657$	−2.76368e9	−0.380198
$658$	−1.76765e9	−0.241883
$659$	−1.05584e10	−1.43714	−0.718572	−	0.695453i	$-0.755204\pi$
$659$	−1.05584e10	−1.43714	−0.718572	+	0.695453i	$0.755204\pi$
$660$	−2.95815e9	−0.400513
$661$	4.30260e9	0.579464	0.289732	−	0.957108i	$-0.406434\pi$
$661$	4.30260e9	0.579464	0.289732	+	0.957108i	$0.406434\pi$
$662$	−1.85125e9	−0.248006
$663$	3.01119e8	0.0401274
$664$	−2.73493e9	−0.362542
$665$	−3.21961e9	−0.424548
$666$	−3.14868e9	−0.413018
$667$	−1.35682e10	−1.77045
$668$	−3.20809e9	−0.416418
$669$	9.23341e8	0.119226
$670$	−7.51489e8	−0.0965297
$671$	−6.24378e9	−0.797846
$672$	7.39772e8	0.0940385
$673$	2.08678e9	0.263890	0.131945	−	0.991257i	$-0.457878\pi$
$673$	2.08678e9	0.263890	0.131945	+	0.991257i	$0.457878\pi$
$674$	5.58211e9	0.702245
$675$	3.51308e9	0.439668
$676$	−3.25849e9	−0.405698
$677$	8.85972e9	1.09739	0.548693	−	0.836024i	$-0.315126\pi$
$677$	8.85972e9	1.09739	0.548693	+	0.836024i	$0.315126\pi$
$678$	1.17632e9	0.144951
$679$	−2.03742e9	−0.249767
$680$	−8.40819e8	−0.102547
$681$	6.95005e8	0.0843282
$682$	1.44453e9	0.174373
$683$	6.44523e9	0.774044	0.387022	−	0.922070i	$-0.373504\pi$
$683$	6.44523e9	0.774044	0.387022	+	0.922070i	$0.373504\pi$
$684$	−3.54643e8	−0.0423736
$685$	5.97945e8	0.0710795
$686$	−6.34095e9	−0.749929
$687$	−5.95447e9	−0.700639
$688$	1.65389e9	0.193619
$689$	5.16547e9	0.601648
$690$	1.14076e10	1.32197
$691$	5.05191e9	0.582482	0.291241	−	0.956650i	$-0.405932\pi$
$691$	5.05191e9	0.582482	0.291241	+	0.956650i	$0.405932\pi$
$692$	2.08992e9	0.239750
$693$	−2.05994e9	−0.235119
$694$	−9.19795e9	−1.04456
$695$	−1.19305e10	−1.34807
$696$	1.79908e9	0.202264
$697$	−2.31263e9	−0.258697
$698$	1.26502e10	1.40800
$699$	−9.60532e9	−1.06375
$700$	−9.55126e9	−1.05249
$701$	−8.81283e9	−0.966279	−0.483139	−	0.875543i	$-0.660504\pi$
$701$	−8.81283e9	−0.966279	−0.483139	+	0.875543i	$0.660504\pi$
$702$	5.41700e8	0.0590988
$703$	−4.10388e9	−0.445504
$704$	8.85894e8	0.0956924
$705$	3.61427e9	0.388471
$706$	5.33763e9	0.570863
$707$	6.81449e8	0.0725213
$708$	−3.54895e8	−0.0375823
$709$	−9.53215e9	−1.00445	−0.502226	−	0.864736i	$-0.667485\pi$
$709$	−9.53215e9	−1.00445	−0.502226	+	0.864736i	$0.667485\pi$
$710$	8.64496e9	0.906481
$711$	−1.46949e9	−0.153328
$712$	−4.60503e9	−0.478137
$713$	−5.57057e9	−0.575554
$714$	−5.85512e8	−0.0601994
$715$	5.88917e9	0.602536
$716$	−1.56627e8	−0.0159467
$717$	2.51220e9	0.254529
$718$	−6.75403e9	−0.680970
$719$	−2.51879e9	−0.252720	−0.126360	−	0.991984i	$-0.540329\pi$
$719$	−2.51879e9	−0.252720	−0.126360	+	0.991984i	$0.540329\pi$
$720$	−1.51259e9	−0.151028
$721$	6.13637e9	0.609730
$722$	6.68874e9	0.661400
$723$	1.41318e8	0.0139064
$724$	6.02718e9	0.590241
$725$	−2.32281e10	−2.26376
$726$	1.74241e9	0.168994
$727$	5.29301e9	0.510895	0.255448	−	0.966823i	$-0.417777\pi$
$727$	5.29301e9	0.510895	0.255448	+	0.966823i	$0.417777\pi$
$728$	−1.47276e9	−0.141472
$729$	3.87420e8	0.0370370
$730$	−1.53633e10	−1.46169
$731$	−1.30901e9	−0.123946
$732$	−3.19264e9	−0.300858
$733$	7.36434e9	0.690669	0.345334	−	0.938480i	$-0.387765\pi$
$733$	7.36434e9	0.690669	0.345334	+	0.938480i	$0.387765\pi$
$734$	−7.60938e9	−0.710253
$735$	1.70139e9	0.158052
$736$	−3.41630e9	−0.315852
$737$	−6.26671e8	−0.0576638
$738$	−4.16031e9	−0.381003
$739$	5.90940e9	0.538626	0.269313	−	0.963053i	$-0.413203\pi$
$739$	5.90940e9	0.538626	0.269313	+	0.963053i	$0.413203\pi$
$740$	−1.75035e10	−1.58787
$741$	7.06033e8	0.0637472
$742$	−1.00440e10	−0.902595
$743$	−1.26701e10	−1.13324	−0.566618	−	0.823980i	$-0.691749\pi$
$743$	−1.26701e10	−1.13324	−0.566618	+	0.823980i	$0.691749\pi$
$744$	7.38630e8	0.0657539
$745$	−5.34078e9	−0.473214
$746$	−1.36773e10	−1.20619
$747$	3.89408e9	0.341808
$748$	−7.01164e8	−0.0612581
$749$	−5.83566e9	−0.507462
$750$	1.09809e10	0.950441
$751$	−1.54488e10	−1.33093	−0.665463	−	0.746431i	$-0.731766\pi$
$751$	−1.54488e10	−1.33093	−0.665463	+	0.746431i	$0.731766\pi$
$752$	−1.08239e9	−0.0928153
$753$	−3.50206e9	−0.298910
$754$	−3.58166e9	−0.304288
$755$	2.28900e10	1.93567
$756$	−1.05331e9	−0.0886603
$757$	−1.24530e10	−1.04337	−0.521687	−	0.853137i	$-0.674697\pi$
$757$	−1.24530e10	−1.04337	−0.521687	+	0.853137i	$0.674697\pi$
$758$	1.64403e10	1.37109
$759$	9.51288e9	0.789706
$760$	−1.97146e9	−0.162907
$761$	1.19378e10	0.981923	0.490962	−	0.871181i	$-0.336646\pi$
$761$	1.19378e10	0.981923	0.490962	+	0.871181i	$0.336646\pi$
$762$	7.97852e9	0.653251
$763$	4.08926e9	0.333280
$764$	7.28063e9	0.590666
$765$	1.19718e9	0.0966819
$766$	2.67569e9	0.215097
$767$	7.06535e8	0.0565392
$768$	4.52985e8	0.0360844
$769$	−1.04459e10	−0.828331	−0.414166	−	0.910202i	$-0.635927\pi$
$769$	−1.04459e10	−0.828331	−0.414166	+	0.910202i	$0.635927\pi$
$770$	−1.14512e10	−0.903927
$771$	−6.90053e9	−0.542241
$772$	1.67789e9	0.131251
$773$	−1.21507e10	−0.946176	−0.473088	−	0.881015i	$-0.656861\pi$
$773$	−1.21507e10	−0.946176	−0.473088	+	0.881015i	$0.656861\pi$
$774$	−2.35486e9	−0.182545
$775$	−9.53651e9	−0.735925
$776$	−1.24757e9	−0.0958406
$777$	−1.21888e10	−0.932150
$778$	−8.42069e9	−0.641090
$779$	−5.42241e9	−0.410971
$780$	3.01131e9	0.227209
$781$	7.20908e9	0.541504
$782$	2.70392e9	0.202195
$783$	−2.56158e9	−0.190696
$784$	−5.09526e8	−0.0377624
$785$	4.36229e10	3.21863
$786$	−6.01172e9	−0.441591
$787$	3.86268e9	0.282473	0.141237	−	0.989976i	$-0.454892\pi$
$787$	3.86268e9	0.282473	0.141237	+	0.989976i	$0.454892\pi$
$788$	−1.58009e9	−0.115037
$789$	2.83370e8	0.0205392
$790$	−8.16889e9	−0.589479
$791$	4.55361e9	0.327143
$792$	−1.26136e9	−0.0902197
$793$	6.35599e9	0.452613
$794$	1.06315e10	0.753742
$795$	2.05367e10	1.44959
$796$	−6.39793e9	−0.449618
$797$	−1.31081e9	−0.0917137	−0.0458569	−	0.998948i	$-0.514602\pi$
$797$	−1.31081e9	−0.0917137	−0.0458569	+	0.998948i	$0.514602\pi$
$798$	−1.37285e9	−0.0956338
$799$	8.56682e8	0.0594164
$800$	−5.84852e9	−0.403860
$801$	6.55678e9	0.450792
$802$	8.63869e9	0.591340
$803$	−1.28116e10	−0.873169
$804$	−3.20436e8	−0.0217443
$805$	4.41596e10	2.98360
$806$	−1.47049e9	−0.0989209
$807$	−3.00349e9	−0.201172
$808$	4.17272e8	0.0278278
$809$	−2.55033e10	−1.69347	−0.846733	−	0.532018i	$-0.821434\pi$
$809$	−2.55033e10	−1.69347	−0.846733	+	0.532018i	$0.821434\pi$
$810$	2.15367e9	0.142391
$811$	1.94674e10	1.28155	0.640773	−	0.767730i	$-0.278614\pi$
$811$	1.94674e10	1.28155	0.640773	+	0.767730i	$0.278614\pi$
$812$	6.96436e9	0.456494
$813$	7.42553e9	0.484630
$814$	−1.45963e10	−0.948544
$815$	1.64962e10	1.06741
$816$	−3.58527e8	−0.0230997
$817$	−3.06924e9	−0.196904
$818$	6.94701e9	0.443774
$819$	2.09696e9	0.133381
$820$	−2.31272e10	−1.46479
$821$	2.26424e10	1.42797	0.713987	−	0.700159i	$-0.246887\pi$
$821$	2.26424e10	1.42797	0.713987	+	0.700159i	$0.246887\pi$
$822$	2.54965e8	0.0160114
$823$	−2.68933e10	−1.68168	−0.840841	−	0.541281i	$-0.817939\pi$
$823$	−2.68933e10	−1.68168	−0.840841	+	0.541281i	$0.817939\pi$
$824$	3.75748e9	0.233965
$825$	1.62855e10	1.00975
$826$	−1.37382e9	−0.0848204
$827$	7.48604e9	0.460239	0.230119	−	0.973162i	$-0.426088\pi$
$827$	7.48604e9	0.460239	0.230119	+	0.973162i	$0.426088\pi$
$828$	4.86423e9	0.297788
$829$	7.00280e9	0.426904	0.213452	−	0.976953i	$-0.431529\pi$
$829$	7.00280e9	0.426904	0.213452	+	0.976953i	$0.431529\pi$
$830$	2.16472e10	1.31410
$831$	1.11887e10	0.676360
$832$	−9.01815e8	−0.0542857
$833$	4.03277e8	0.0241739
$834$	−5.08719e9	−0.303666
$835$	2.53923e10	1.50938
$836$	−1.64401e9	−0.0973158
$837$	−1.05168e9	−0.0619934
$838$	−2.60526e9	−0.152931
$839$	−1.35535e10	−0.792293	−0.396147	−	0.918187i	$-0.629653\pi$
$839$	−1.35535e10	−0.792293	−0.396147	+	0.918187i	$0.629653\pi$
$840$	−5.85535e9	−0.340860
$841$	−3.12962e8	−0.0181429
$842$	1.75599e10	1.01375
$843$	−1.60648e10	−0.923588
$844$	−2.64406e9	−0.151381
$845$	2.57912e10	1.47053
$846$	1.54113e9	0.0875072
$847$	6.74498e9	0.381407
$848$	−6.15024e9	−0.346343
$849$	1.68230e10	0.943464
$850$	4.62897e9	0.258534
$851$	5.62882e10	3.13086
$852$	3.68623e9	0.204194
$853$	1.50496e10	0.830238	0.415119	−	0.909767i	$-0.363740\pi$
$853$	1.50496e10	0.830238	0.415119	+	0.909767i	$0.363740\pi$
$854$	−1.23589e10	−0.679012
$855$	2.80702e9	0.153591
$856$	−3.57335e9	−0.194723
$857$	−2.58332e10	−1.40199	−0.700996	−	0.713165i	$-0.747261\pi$
$857$	−2.58332e10	−1.40199	−0.700996	+	0.713165i	$0.747261\pi$
$858$	2.51115e9	0.135727
$859$	−7.23893e9	−0.389671	−0.194836	−	0.980836i	$-0.562417\pi$
$859$	−7.23893e9	−0.389671	−0.194836	+	0.980836i	$0.562417\pi$
$860$	−1.30907e10	−0.701806
$861$	−1.61048e10	−0.859895
$862$	−1.33357e10	−0.709156
$863$	−1.02812e10	−0.544510	−0.272255	−	0.962225i	$-0.587769\pi$
$863$	−1.02812e10	−0.544510	−0.272255	+	0.962225i	$0.587769\pi$
$864$	−6.44973e8	−0.0340207
$865$	−1.65419e10	−0.869018
$866$	4.91896e9	0.257371
$867$	−1.07954e10	−0.562563
$868$	2.85929e9	0.148402
$869$	−6.81208e9	−0.352136
$870$	−1.42399e10	−0.733143
$871$	6.37933e8	0.0327123
$872$	2.50398e9	0.127886
$873$	1.77633e9	0.0903594
$874$	6.33986e9	0.321211
$875$	4.25080e10	2.14507
$876$	−6.55096e9	−0.329261
$877$	1.92879e10	0.965578	0.482789	−	0.875737i	$-0.339624\pi$
$877$	1.92879e10	0.965578	0.482789	+	0.875737i	$0.339624\pi$
$878$	−1.76550e10	−0.880311
$879$	−1.20922e10	−0.600546
$880$	−7.01192e9	−0.346854
$881$	1.59048e10	0.783631	0.391816	−	0.920044i	$-0.371847\pi$
$881$	1.59048e10	0.783631	0.391816	+	0.920044i	$0.371847\pi$
$882$	7.25477e8	0.0356028
$883$	−1.02556e10	−0.501301	−0.250650	−	0.968078i	$-0.580644\pi$
$883$	−1.02556e10	−0.501301	−0.250650	+	0.968078i	$0.580644\pi$
$884$	7.13765e8	0.0347514
$885$	2.80902e9	0.136224
$886$	−1.07188e10	−0.517761
$887$	4.51587e9	0.217275	0.108637	−	0.994081i	$-0.465351\pi$
$887$	4.51587e9	0.217275	0.108637	+	0.994081i	$0.465351\pi$
$888$	−7.46354e9	−0.357684
$889$	3.08854e10	1.47434
$890$	3.64492e10	1.73310
$891$	1.79596e9	0.0850599
$892$	2.18866e9	0.103253
$893$	2.00866e9	0.0943900
$894$	−2.27732e9	−0.106596
$895$	1.23971e9	0.0578016
$896$	1.75353e9	0.0814397
$897$	−9.68384e9	−0.447996
$898$	−1.83087e10	−0.843704
$899$	6.95361e9	0.319192
$900$	8.32729e9	0.380763
$901$	4.86777e9	0.221714
$902$	−1.92859e10	−0.875019
$903$	−9.11580e9	−0.411991
$904$	2.78831e9	0.125531
$905$	−4.77056e10	−2.13944
$906$	9.76034e9	0.436030
$907$	1.45980e10	0.649633	0.324816	−	0.945777i	$-0.394697\pi$
$907$	1.45980e10	0.649633	0.324816	+	0.945777i	$0.394697\pi$
$908$	1.64742e9	0.0730304
$909$	−5.94124e8	−0.0262363
$910$	1.16570e10	0.512793
$911$	−4.03214e10	−1.76694	−0.883470	−	0.468488i	$-0.844799\pi$
$911$	−4.03214e10	−1.76694	−0.883470	+	0.468488i	$0.844799\pi$
$912$	−8.40635e8	−0.0366966
$913$	1.80517e10	0.785002
$914$	−2.37143e10	−1.02730
$915$	2.52700e10	1.09051
$916$	−1.41143e10	−0.606771
$917$	−2.32718e10	−0.996636
$918$	5.10480e8	0.0217786
$919$	−5.32403e9	−0.226275	−0.113137	−	0.993579i	$-0.536090\pi$
$919$	−5.32403e9	−0.226275	−0.113137	+	0.993579i	$0.536090\pi$
$920$	2.70403e10	1.14486
$921$	1.65623e10	0.698575
$922$	2.69136e10	1.13087
$923$	−7.33864e9	−0.307192
$924$	−4.88281e9	−0.203619
$925$	9.63624e10	4.00324
$926$	2.16717e10	0.896921
$927$	−5.35001e9	−0.220585
$928$	4.26449e9	0.175166
$929$	−3.73324e10	−1.52767	−0.763837	−	0.645410i	$-0.776687\pi$
$929$	−3.73324e10	−1.52767	−0.763837	+	0.645410i	$0.776687\pi$
$930$	−5.84631e9	−0.238337
$931$	9.45562e8	0.0384031
$932$	−2.27682e10	−0.921239
$933$	−2.87048e9	−0.115710
$934$	3.05535e9	0.122701
$935$	5.54976e9	0.222041
$936$	1.28403e9	0.0511811
$937$	−2.95917e10	−1.17512	−0.587559	−	0.809181i	$-0.699911\pi$
$937$	−2.95917e10	−1.17512	−0.587559	+	0.809181i	$0.699911\pi$
$938$	−1.24043e9	−0.0490752
$939$	−2.74056e10	−1.08021
$940$	8.56717e9	0.336426
$941$	−2.98635e10	−1.16836	−0.584181	−	0.811623i	$-0.698584\pi$
$941$	−2.98635e10	−1.16836	−0.584181	+	0.811623i	$0.698584\pi$
$942$	1.86009e10	0.725029
$943$	7.43729e10	2.88818
$944$	−8.41232e8	−0.0325472
$945$	8.33701e9	0.321365
$946$	−1.09164e10	−0.419237
$947$	8.34315e9	0.319231	0.159616	−	0.987179i	$-0.448975\pi$
$947$	8.34315e9	0.319231	0.159616	+	0.987179i	$0.448975\pi$
$948$	−3.48323e9	−0.132786
$949$	1.30418e10	0.495344
$950$	1.08535e10	0.410712
$951$	1.69623e10	0.639520
$952$	−1.38788e9	−0.0521342
$953$	−1.22586e9	−0.0458790	−0.0229395	−	0.999737i	$-0.507303\pi$
$953$	−1.22586e9	−0.0458790	−0.0229395	+	0.999737i	$0.507303\pi$
$954$	8.75689e9	0.326536
$955$	−5.76267e10	−2.14098
$956$	5.95484e9	0.220428
$957$	−1.18747e10	−0.437956
$958$	−1.20313e10	−0.442112
$959$	9.86986e8	0.0361365
$960$	−3.58541e9	−0.130794
$961$	−2.46577e10	−0.896234
$962$	1.48586e10	0.538104
$963$	5.08783e9	0.183587
$964$	3.34977e8	0.0120433
$965$	−1.32806e10	−0.475743
$966$	1.88297e10	0.672085
$967$	2.03807e10	0.724813	0.362407	−	0.932020i	$-0.381955\pi$
$967$	2.03807e10	0.724813	0.362407	+	0.932020i	$0.381955\pi$
$968$	4.13016e9	0.146353
$969$	6.65342e8	0.0234916
$970$	9.87463e9	0.347392
$971$	−5.02103e10	−1.76005	−0.880027	−	0.474924i	$-0.842475\pi$
$971$	−5.02103e10	−1.76005	−0.880027	+	0.474924i	$0.842475\pi$
$972$	9.18330e8	0.0320750
$973$	−1.96928e10	−0.685352
$974$	−1.44240e10	−0.500184
$975$	−1.65782e10	−0.572824
$976$	−7.56774e9	−0.260550
$977$	2.48634e10	0.852960	0.426480	−	0.904497i	$-0.359753\pi$
$977$	2.48634e10	0.852960	0.426480	+	0.904497i	$0.359753\pi$
$978$	7.03400e9	0.240445
$979$	3.03952e10	1.03530
$980$	4.03293e9	0.136877
$981$	−3.56523e9	−0.120572
$982$	1.76759e9	0.0595649
$983$	1.55192e10	0.521113	0.260556	−	0.965459i	$-0.416094\pi$
$983$	1.55192e10	0.521113	0.260556	+	0.965459i	$0.416094\pi$
$984$	−9.86148e9	−0.329959
$985$	1.25065e10	0.416974
$986$	−3.37524e9	−0.112134
$987$	5.96582e9	0.197497
$988$	1.67356e9	0.0552067
$989$	4.20972e10	1.38378
$990$	9.98376e9	0.327018
$991$	−8.32359e9	−0.271677	−0.135838	−	0.990731i	$-0.543373\pi$
$991$	−8.32359e9	−0.271677	−0.135838	+	0.990731i	$0.543373\pi$
$992$	1.75083e9	0.0569446
$993$	6.24798e9	0.202496
$994$	1.42696e10	0.460851
$995$	5.06401e10	1.62972
$996$	9.23040e9	0.296015
$997$	−4.79696e10	−1.53297	−0.766485	−	0.642263i	$-0.777996\pi$
$997$	−4.79696e10	−1.53297	−0.766485	+	0.642263i	$0.777996\pi$
$998$	2.06797e10	0.658549
$999$	1.06268e10	0.337228

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.c.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -506.565 q^{5} -216.000 q^{6} -836.150 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -506.565 q^{5} -216.000 q^{6} -836.150 q^{7} -512.000 q^{8} +729.000 q^{9} +4052.52 q^{10} +3379.42 q^{11} +1728.00 q^{12} -3440.15 q^{13} +6689.20 q^{14} -13677.2 q^{15} +4096.00 q^{16} -3241.88 q^{17} -5832.00 q^{18} -7601.23 q^{19} -32420.1 q^{20} -22576.1 q^{21} -27035.3 q^{22} +104257. q^{23} -13824.0 q^{24} +178483. q^{25} +27521.2 q^{26} +19683.0 q^{27} -53513.6 q^{28} -130142. q^{29} +109418. q^{30} -53431.0 q^{31} -32768.0 q^{32} +91244.3 q^{33} +25935.1 q^{34} +423564. q^{35} +46656.0 q^{36} +539897. q^{37} +60809.8 q^{38} -92884.1 q^{39} +259361. q^{40} +713359. q^{41} +180608. q^{42} +403782. q^{43} +216283. q^{44} -369286. q^{45} -834058. q^{46} -264254. q^{47} +110592. q^{48} -124396. q^{49} -1.42786e6 q^{50} -87530.9 q^{51} -220170. q^{52} -1.50152e6 q^{53} -157464. q^{54} -1.71189e6 q^{55} +428109. q^{56} -205233. q^{57} +1.04114e6 q^{58} -205379. q^{59} -875344. q^{60} -1.84759e6 q^{61} +427448. q^{62} -609553. q^{63} +262144. q^{64} +1.74266e6 q^{65} -729954. q^{66} -185438. q^{67} -207481. q^{68} +2.81495e6 q^{69} -3.38851e6 q^{70} +2.13323e6 q^{71} -373248. q^{72} -3.79106e6 q^{73} -4.31918e6 q^{74} +4.81904e6 q^{75} -486479. q^{76} -2.82570e6 q^{77} +743072. q^{78} -2.01576e6 q^{79} -2.07489e6 q^{80} +531441. q^{81} -5.70688e6 q^{82} +5.34167e6 q^{83} -1.44487e6 q^{84} +1.64222e6 q^{85} -3.23026e6 q^{86} -3.51383e6 q^{87} -1.73026e6 q^{88} +8.99421e6 q^{89} +2.95429e6 q^{90} +2.87648e6 q^{91} +6.67246e6 q^{92} -1.44264e6 q^{93} +2.11404e6 q^{94} +3.85051e6 q^{95} -884736. q^{96} +2.43666e6 q^{97} +995168. q^{98} +2.46360e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) \) 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

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