LMFDB - Embedded newform 547.8.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,8,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	547.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:	$170.874608940$
Analytic rank:	$1$
Dimension:	$156$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.1152 q^{2} +83.7935 q^{3} +361.080 q^{4} -144.371 q^{5} -1853.11 q^{6} +55.2475 q^{7} -5154.61 q^{8} +4834.35 q^{9} +O(q^{10})$	\(q-22.1152 q^{2} +83.7935 q^{3} +361.080 q^{4} -144.371 q^{5} -1853.11 q^{6} +55.2475 q^{7} -5154.61 q^{8} +4834.35 q^{9} +3192.79 q^{10} -1873.51 q^{11} +30256.2 q^{12} +9324.01 q^{13} -1221.81 q^{14} -12097.4 q^{15} +67776.6 q^{16} -26294.4 q^{17} -106912. q^{18} +12609.1 q^{19} -52129.6 q^{20} +4629.38 q^{21} +41433.0 q^{22} +26042.8 q^{23} -431922. q^{24} -57281.9 q^{25} -206202. q^{26} +221830. q^{27} +19948.8 q^{28} -197155. q^{29} +267535. q^{30} -103133. q^{31} -839102. q^{32} -156988. q^{33} +581506. q^{34} -7976.16 q^{35} +1.74559e6 q^{36} +1185.12 q^{37} -278853. q^{38} +781291. q^{39} +744177. q^{40} +322567. q^{41} -102380. q^{42} +812182. q^{43} -676487. q^{44} -697941. q^{45} -575941. q^{46} +986058. q^{47} +5.67924e6 q^{48} -820491. q^{49} +1.26680e6 q^{50} -2.20330e6 q^{51} +3.36672e6 q^{52} -1.82870e6 q^{53} -4.90581e6 q^{54} +270481. q^{55} -284779. q^{56} +1.05656e6 q^{57} +4.36012e6 q^{58} -1.81447e6 q^{59} -4.36812e6 q^{60} -490694. q^{61} +2.28081e6 q^{62} +267086. q^{63} +9.88146e6 q^{64} -1.34612e6 q^{65} +3.47181e6 q^{66} +481203. q^{67} -9.49440e6 q^{68} +2.18222e6 q^{69} +176394. q^{70} -3.84299e6 q^{71} -2.49191e7 q^{72} +1.49449e6 q^{73} -26209.0 q^{74} -4.79985e6 q^{75} +4.55291e6 q^{76} -103507. q^{77} -1.72784e7 q^{78} -4.34780e6 q^{79} -9.78500e6 q^{80} +8.01522e6 q^{81} -7.13363e6 q^{82} +3.27067e6 q^{83} +1.67158e6 q^{84} +3.79616e6 q^{85} -1.79615e7 q^{86} -1.65203e7 q^{87} +9.65720e6 q^{88} +6.12067e6 q^{89} +1.54351e7 q^{90} +515129. q^{91} +9.40355e6 q^{92} -8.64189e6 q^{93} -2.18068e7 q^{94} -1.82040e6 q^{95} -7.03112e7 q^{96} -1.54355e7 q^{97} +1.81453e7 q^{98} -9.05719e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) $ 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9} - 10570 q^{10} - 20090 q^{11} - 58311 q^{12} - 63021 q^{13} - 45057 q^{14} - 36391 q^{15} + 574338 q^{16} - 232394 q^{17} - 92277 q^{18} - 43100 q^{19} - 485568 q^{20} - 231868 q^{21} - 225008 q^{22} - 401950 q^{23} - 503569 q^{24} + 2076291 q^{25} - 530768 q^{26} - 959873 q^{27} - 617816 q^{28} - 1275618 q^{29} - 778474 q^{30} - 485945 q^{31} - 1903692 q^{32} - 1050846 q^{33} - 466263 q^{34} - 1826209 q^{35} + 5276156 q^{36} - 2129902 q^{37} - 2480555 q^{38} - 974653 q^{39} - 937648 q^{40} - 2309325 q^{41} - 2803500 q^{42} - 1756918 q^{43} - 3314520 q^{44} - 7492064 q^{45} - 1323786 q^{46} - 6203828 q^{47} - 7957494 q^{48} + 15095175 q^{49} - 5758152 q^{50} - 1556293 q^{51} - 7587898 q^{52} - 13775068 q^{53} - 6848423 q^{54} - 4045669 q^{55} - 8326655 q^{56} - 9421556 q^{57} - 4938892 q^{58} - 7755758 q^{59} - 5358502 q^{60} - 11693582 q^{61} - 14895366 q^{62} - 9477805 q^{63} + 31311690 q^{64} - 15629670 q^{65} - 5969892 q^{66} - 9560716 q^{67} - 34045735 q^{68} - 17825946 q^{69} - 4291177 q^{70} - 13661197 q^{71} - 21516953 q^{72} - 17125972 q^{73} - 19749599 q^{74} - 21752079 q^{75} - 15479244 q^{76} - 55632329 q^{77} - 12746879 q^{78} - 9534338 q^{79} - 61267539 q^{80} + 58468208 q^{81} - 29265046 q^{82} - 38447793 q^{83} - 33520873 q^{84} - 22365109 q^{85} - 21208733 q^{86} - 27018273 q^{87} - 40855385 q^{88} - 62436196 q^{89} - 19477679 q^{90} - 20640165 q^{91} - 78867734 q^{92} - 77801528 q^{93} + 2996793 q^{94} - 30557422 q^{95} - 82397286 q^{96} - 56264748 q^{97} - 72954494 q^{98} - 43444577 q^{99}+O(q^{100}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9 - 10570 * q^10 - 20090 * q^11 - 58311 * q^12 - 63021 * q^13 - 45057 * q^14 - 36391 * q^15 + 574338 * q^16 - 232394 * q^17 - 92277 * q^18 - 43100 * q^19 - 485568 * q^20 - 231868 * q^21 - 225008 * q^22 - 401950 * q^23 - 503569 * q^24 + 2076291 * q^25 - 530768 * q^26 - 959873 * q^27 - 617816 * q^28 - 1275618 * q^29 - 778474 * q^30 - 485945 * q^31 - 1903692 * q^32 - 1050846 * q^33 - 466263 * q^34 - 1826209 * q^35 + 5276156 * q^36 - 2129902 * q^37 - 2480555 * q^38 - 974653 * q^39 - 937648 * q^40 - 2309325 * q^41 - 2803500 * q^42 - 1756918 * q^43 - 3314520 * q^44 - 7492064 * q^45 - 1323786 * q^46 - 6203828 * q^47 - 7957494 * q^48 + 15095175 * q^49 - 5758152 * q^50 - 1556293 * q^51 - 7587898 * q^52 - 13775068 * q^53 - 6848423 * q^54 - 4045669 * q^55 - 8326655 * q^56 - 9421556 * q^57 - 4938892 * q^58 - 7755758 * q^59 - 5358502 * q^60 - 11693582 * q^61 - 14895366 * q^62 - 9477805 * q^63 + 31311690 * q^64 - 15629670 * q^65 - 5969892 * q^66 - 9560716 * q^67 - 34045735 * q^68 - 17825946 * q^69 - 4291177 * q^70 - 13661197 * q^71 - 21516953 * q^72 - 17125972 * q^73 - 19749599 * q^74 - 21752079 * q^75 - 15479244 * q^76 - 55632329 * q^77 - 12746879 * q^78 - 9534338 * q^79 - 61267539 * q^80 + 58468208 * q^81 - 29265046 * q^82 - 38447793 * q^83 - 33520873 * q^84 - 22365109 * q^85 - 21208733 * q^86 - 27018273 * q^87 - 40855385 * q^88 - 62436196 * q^89 - 19477679 * q^90 - 20640165 * q^91 - 78867734 * q^92 - 77801528 * q^93 + 2996793 * q^94 - 30557422 * q^95 - 82397286 * q^96 - 56264748 * q^97 - 72954494 * q^98 - 43444577 * 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 $

$2$	−22.1152	−1.95472	−0.977361	−	0.211578i	$-0.932140\pi$
$2$	−22.1152	−1.95472	−0.977361	+	0.211578i	$0.932140\pi$
$3$	83.7935	1.79178	0.895892	−	0.444271i	$-0.146537\pi$
$3$	83.7935	1.79178	0.895892	+	0.444271i	$0.146537\pi$
$4$	361.080	2.82094
$5$	−144.371	−0.516519	−0.258259	−	0.966076i	$-0.583149\pi$
$5$	−144.371	−0.516519	−0.258259	+	0.966076i	$0.583149\pi$
$6$	−1853.11	−3.50244
$7$	55.2475	0.0608793	0.0304397	−	0.999537i	$-0.490309\pi$
$7$	55.2475	0.0608793	0.0304397	+	0.999537i	$0.490309\pi$
$8$	−5154.61	−3.55943
$9$	4834.35	2.21049
$10$	3192.79	1.00965
$11$	−1873.51	−0.424406	−0.212203	−	0.977226i	$-0.568064\pi$
$11$	−1873.51	−0.424406	−0.212203	+	0.977226i	$0.568064\pi$
$12$	30256.2	5.05452
$13$	9324.01	1.17707	0.588533	−	0.808473i	$-0.299706\pi$
$13$	9324.01	1.17707	0.588533	+	0.808473i	$0.299706\pi$
$14$	−1221.81	−0.119002
$15$	−12097.4	−0.925490
$16$	67776.6	4.13676
$17$	−26294.4	−1.29805	−0.649027	−	0.760766i	$-0.724824\pi$
$17$	−26294.4	−1.29805	−0.649027	+	0.760766i	$0.724824\pi$
$18$	−106912.	−4.32090
$19$	12609.1	0.421743	0.210872	−	0.977514i	$-0.432370\pi$
$19$	12609.1	0.421743	0.210872	+	0.977514i	$0.432370\pi$
$20$	−52129.6	−1.45707
$21$	4629.38	0.109083
$22$	41433.0	0.829596
$23$	26042.8	0.446314	0.223157	−	0.974782i	$-0.428364\pi$
$23$	26042.8	0.446314	0.223157	+	0.974782i	$0.428364\pi$
$24$	−431922.	−6.37773
$25$	−57281.9	−0.733209
$26$	−206202.	−2.30084
$27$	221830.	2.16894
$28$	19948.8	0.171737
$29$	−197155.	−1.50112	−0.750561	−	0.660802i	$-0.770216\pi$
$29$	−197155.	−1.50112	−0.750561	+	0.660802i	$0.770216\pi$
$30$	267535.	1.80908
$31$	−103133.	−0.621774	−0.310887	−	0.950447i	$-0.600626\pi$
$31$	−103133.	−0.621774	−0.310887	+	0.950447i	$0.600626\pi$
$32$	−839102.	−4.52678
$33$	−156988.	−0.760444
$34$	581506.	2.53733
$35$	−7976.16	−0.0314453
$36$	1.74559e6	6.23566
$37$	1185.12	0.00384640	0.00192320	−	0.999998i	$-0.499388\pi$
$37$	1185.12	0.00384640	0.00192320	+	0.999998i	$0.499388\pi$
$38$	−278853.	−0.824391
$39$	781291.	2.10905
$40$	744177.	1.83851
$41$	322567.	0.730932	0.365466	−	0.930825i	$-0.380910\pi$
$41$	322567.	0.730932	0.365466	+	0.930825i	$0.380910\pi$
$42$	−102380.	−0.213226
$43$	812182.	1.55781	0.778904	−	0.627144i	$-0.215776\pi$
$43$	812182.	1.55781	0.778904	+	0.627144i	$0.215776\pi$
$44$	−676487.	−1.19722
$45$	−697941.	−1.14176
$46$	−575941.	−0.872420
$47$	986058.	1.38535	0.692676	−	0.721249i	$-0.256432\pi$
$47$	986058.	1.38535	0.692676	+	0.721249i	$0.256432\pi$
$48$	5.67924e6	7.41218
$49$	−820491.	−0.996294
$50$	1.26680e6	1.43322
$51$	−2.20330e6	−2.32583
$52$	3.36672e6	3.32043
$53$	−1.82870e6	−1.68724	−0.843619	−	0.536943i	$-0.819579\pi$
$53$	−1.82870e6	−1.68724	−0.843619	+	0.536943i	$0.819579\pi$
$54$	−4.90581e6	−4.23968
$55$	270481.	0.219214
$56$	−284779.	−0.216696
$57$	1.05656e6	0.755673
$58$	4.36012e6	2.93427
$59$	−1.81447e6	−1.15019	−0.575093	−	0.818088i	$-0.695034\pi$
$59$	−1.81447e6	−1.15019	−0.575093	+	0.818088i	$0.695034\pi$
$60$	−4.36812e6	−2.61075
$61$	−490694.	−0.276794	−0.138397	−	0.990377i	$-0.544195\pi$
$61$	−490694.	−0.276794	−0.138397	+	0.990377i	$0.544195\pi$
$62$	2.28081e6	1.21540
$63$	267086.	0.134573
$64$	9.88146e6	4.71184
$65$	−1.34612e6	−0.607977
$66$	3.47181e6	1.48646
$67$	481203.	0.195464	0.0977320	−	0.995213i	$-0.468841\pi$
$67$	481203.	0.195464	0.0977320	+	0.995213i	$0.468841\pi$
$68$	−9.49440e6	−3.66173
$69$	2.18222e6	0.799699
$70$	176394.	0.0614668
$71$	−3.84299e6	−1.27428	−0.637140	−	0.770748i	$-0.719883\pi$
$71$	−3.84299e6	−1.27428	−0.637140	+	0.770748i	$0.719883\pi$
$72$	−2.49191e7	−7.86809
$73$	1.49449e6	0.449637	0.224818	−	0.974401i	$-0.427821\pi$
$73$	1.49449e6	0.449637	0.224818	+	0.974401i	$0.427821\pi$
$74$	−26209.0	−0.00751865
$75$	−4.79985e6	−1.31375
$76$	4.55291e6	1.18971
$77$	−103507.	−0.0258375
$78$	−1.72784e7	−4.12261
$79$	−4.34780e6	−0.992144	−0.496072	−	0.868281i	$-0.665225\pi$
$79$	−4.34780e6	−0.992144	−0.496072	+	0.868281i	$0.665225\pi$
$80$	−9.78500e6	−2.13671
$81$	8.01522e6	1.67578
$82$	−7.13363e6	−1.42877
$83$	3.27067e6	0.627861	0.313931	−	0.949446i	$-0.398354\pi$
$83$	3.27067e6	0.627861	0.313931	+	0.949446i	$0.398354\pi$
$84$	1.67158e6	0.307715
$85$	3.79616e6	0.670469
$86$	−1.79615e7	−3.04508
$87$	−1.65203e7	−2.68969
$88$	9.65720e6	1.51064
$89$	6.12067e6	0.920309	0.460155	−	0.887839i	$-0.347794\pi$
$89$	6.12067e6	0.920309	0.460155	+	0.887839i	$0.347794\pi$
$90$	1.54351e7	2.23182
$91$	515129.	0.0716590
$92$	9.40355e6	1.25903
$93$	−8.64189e6	−1.11409
$94$	−2.18068e7	−2.70798
$95$	−1.82040e6	−0.217838
$96$	−7.03112e7	−8.11102
$97$	−1.54355e7	−1.71719	−0.858595	−	0.512654i	$-0.828662\pi$
$97$	−1.54355e7	−1.71719	−0.858595	+	0.512654i	$0.828662\pi$
$98$	1.81453e7	1.94748
$99$	−9.05719e6	−0.938146
$100$	−2.06834e7	−2.06834
$101$	−1.41345e7	−1.36507	−0.682536	−	0.730852i	$-0.739123\pi$
$101$	−1.41345e7	−1.36507	−0.682536	+	0.730852i	$0.739123\pi$
$102$	4.87264e7	4.54636
$103$	−2.73657e6	−0.246761	−0.123380	−	0.992359i	$-0.539374\pi$
$103$	−2.73657e6	−0.246761	−0.123380	+	0.992359i	$0.539374\pi$
$104$	−4.80616e7	−4.18969
$105$	−668350.	−0.0563432
$106$	4.04419e7	3.29808
$107$	2.01046e6	0.158655	0.0793274	−	0.996849i	$-0.474723\pi$
$107$	2.01046e6	0.158655	0.0793274	+	0.996849i	$0.474723\pi$
$108$	8.00985e7	6.11845
$109$	1.67977e7	1.24239	0.621196	−	0.783656i	$-0.286647\pi$
$109$	1.67977e7	1.24239	0.621196	+	0.783656i	$0.286647\pi$
$110$	−5.98173e6	−0.428502
$111$	99304.9	0.00689192
$112$	3.74449e6	0.251843
$113$	1.56095e7	1.01769	0.508845	−	0.860858i	$-0.330073\pi$
$113$	1.56095e7	1.01769	0.508845	+	0.860858i	$0.330073\pi$
$114$	−2.33661e7	−1.47713
$115$	−3.75984e6	−0.230530
$116$	−7.11889e7	−4.23457
$117$	4.50755e7	2.60190
$118$	4.01273e7	2.24830
$119$	−1.45270e6	−0.0790246
$120$	6.23572e7	3.29422
$121$	−1.59771e7	−0.819880
$122$	1.08518e7	0.541055
$123$	2.70290e7	1.30967
$124$	−3.72394e7	−1.75399
$125$	1.95489e7	0.895234
$126$	−5.90664e6	−0.263053
$127$	2.15295e7	0.932657	0.466328	−	0.884612i	$-0.345576\pi$
$127$	2.15295e7	0.932657	0.466328	+	0.884612i	$0.345576\pi$
$128$	−1.11125e8	−4.68357
$129$	6.80555e7	2.79125
$130$	2.97697e7	1.18843
$131$	−4.48048e7	−1.74131	−0.870653	−	0.491897i	$-0.836303\pi$
$131$	−4.48048e7	−1.74131	−0.870653	+	0.491897i	$0.836303\pi$
$132$	−5.66852e7	−2.14517
$133$	696625.	0.0256754
$134$	−1.06419e7	−0.382078
$135$	−3.20259e7	−1.12030
$136$	1.35537e8	4.62033
$137$	−2.83710e7	−0.942654	−0.471327	−	0.881959i	$-0.656225\pi$
$137$	−2.83710e7	−0.942654	−0.471327	+	0.881959i	$0.656225\pi$
$138$	−4.82601e7	−1.56319
$139$	2.07099e7	0.654072	0.327036	−	0.945012i	$-0.393950\pi$
$139$	2.07099e7	0.654072	0.327036	+	0.945012i	$0.393950\pi$
$140$	−2.88003e6	−0.0887053
$141$	8.26252e7	2.48225
$142$	8.49883e7	2.49086
$143$	−1.74686e7	−0.499554
$144$	3.27656e8	9.14427
$145$	2.84636e7	0.775357
$146$	−3.30508e7	−0.878915
$147$	−6.87518e7	−1.78514
$148$	427922.	0.0108505
$149$	7.03782e7	1.74295	0.871477	−	0.490436i	$-0.163162\pi$
$149$	7.03782e7	1.74295	0.871477	+	0.490436i	$0.163162\pi$
$150$	1.06149e8	2.56802
$151$	−6.06676e7	−1.43396	−0.716981	−	0.697092i	$-0.754477\pi$
$151$	−6.06676e7	−1.43396	−0.716981	+	0.697092i	$0.754477\pi$
$152$	−6.49952e7	−1.50117
$153$	−1.27116e8	−2.86934
$154$	2.28907e6	0.0505052
$155$	1.48895e7	0.321158
$156$	2.82109e8	5.94950
$157$	−2.76711e6	−0.0570660	−0.0285330	−	0.999593i	$-0.509084\pi$
$157$	−2.76711e6	−0.0570660	−0.0285330	+	0.999593i	$0.509084\pi$
$158$	9.61523e7	1.93937
$159$	−1.53233e8	−3.02317
$160$	1.21142e8	2.33817
$161$	1.43880e6	0.0271713
$162$	−1.77258e8	−3.27569
$163$	−6.04572e7	−1.09343	−0.546716	−	0.837318i	$-0.684122\pi$
$163$	−6.04572e7	−1.09343	−0.546716	+	0.837318i	$0.684122\pi$
$164$	1.16473e8	2.06191
$165$	2.26645e7	0.392783
$166$	−7.23314e7	−1.22729
$167$	−2.42683e7	−0.403210	−0.201605	−	0.979467i	$-0.564616\pi$
$167$	−2.42683e7	−0.403210	−0.201605	+	0.979467i	$0.564616\pi$
$168$	−2.38626e7	−0.388272
$169$	2.41887e7	0.385487
$170$	−8.39527e7	−1.31058
$171$	6.09570e7	0.932260
$172$	2.93263e8	4.39448
$173$	−8.33508e7	−1.22391	−0.611954	−	0.790894i	$-0.709616\pi$
$173$	−8.33508e7	−1.22391	−0.611954	+	0.790894i	$0.709616\pi$
$174$	3.65350e8	5.25759
$175$	−3.16469e6	−0.0446372
$176$	−1.26980e8	−1.75566
$177$	−1.52041e8	−2.06089
$178$	−1.35360e8	−1.79895
$179$	−5.81542e7	−0.757871	−0.378936	−	0.925423i	$-0.623710\pi$
$179$	−5.81542e7	−0.757871	−0.378936	+	0.925423i	$0.623710\pi$
$180$	−2.52013e8	−3.22084
$181$	4.16808e6	0.0522470	0.0261235	−	0.999659i	$-0.491684\pi$
$181$	4.16808e6	0.0522470	0.0261235	+	0.999659i	$0.491684\pi$
$182$	−1.13922e7	−0.140074
$183$	−4.11170e7	−0.495955
$184$	−1.34240e8	−1.58862
$185$	−171097.	−0.00198674
$186$	1.91117e8	2.17773
$187$	4.92629e7	0.550902
$188$	3.56046e8	3.90799
$189$	1.22556e7	0.132044
$190$	4.02584e7	0.425813
$191$	−8.76681e6	−0.0910385	−0.0455192	−	0.998963i	$-0.514494\pi$
$191$	−8.76681e6	−0.0910385	−0.0455192	+	0.998963i	$0.514494\pi$
$192$	8.28001e8	8.44261
$193$	−5.10748e7	−0.511395	−0.255697	−	0.966757i	$-0.582305\pi$
$193$	−5.10748e7	−0.511395	−0.255697	+	0.966757i	$0.582305\pi$
$194$	3.41358e8	3.35663
$195$	−1.12796e8	−1.08936
$196$	−2.96263e8	−2.81048
$197$	−8.66188e7	−0.807199	−0.403599	−	0.914936i	$-0.632241\pi$
$197$	−8.66188e7	−0.807199	−0.403599	+	0.914936i	$0.632241\pi$
$198$	2.00301e8	1.83381
$199$	5.50425e7	0.495122	0.247561	−	0.968872i	$-0.420371\pi$
$199$	5.50425e7	0.495122	0.247561	+	0.968872i	$0.420371\pi$
$200$	2.95266e8	2.60980
$201$	4.03217e7	0.350229
$202$	3.12586e8	2.66833
$203$	−1.08924e7	−0.0913872
$204$	−7.95569e8	−6.56103
$205$	−4.65695e7	−0.377540
$206$	6.05197e7	0.482349
$207$	1.25900e8	0.986574
$208$	6.31950e8	4.86924
$209$	−2.36234e7	−0.178990
$210$	1.47807e7	0.110135
$211$	−4.84688e7	−0.355201	−0.177600	−	0.984103i	$-0.556833\pi$
$211$	−4.84688e7	−0.355201	−0.177600	+	0.984103i	$0.556833\pi$
$212$	−6.60306e8	−4.75959
$213$	−3.22017e8	−2.28324
$214$	−4.44617e7	−0.310126
$215$	−1.17256e8	−0.804636
$216$	−1.14345e9	−7.72019
$217$	−5.69786e6	−0.0378532
$218$	−3.71485e8	−2.42853
$219$	1.25228e8	0.805652
$220$	9.76653e7	0.618388
$221$	−2.45170e8	−1.52790
$222$	−2.19614e6	−0.0134718
$223$	−3.29767e7	−0.199131	−0.0995657	−	0.995031i	$-0.531745\pi$
$223$	−3.29767e7	−0.199131	−0.0995657	+	0.995031i	$0.531745\pi$
$224$	−4.63583e7	−0.275587
$225$	−2.76921e8	−1.62075
$226$	−3.45207e8	−1.98930
$227$	1.11772e8	0.634223	0.317112	−	0.948388i	$-0.397287\pi$
$227$	1.11772e8	0.634223	0.317112	+	0.948388i	$0.397287\pi$
$228$	3.81504e8	2.13171
$229$	7.09489e7	0.390411	0.195205	−	0.980762i	$-0.437463\pi$
$229$	7.09489e7	0.390411	0.195205	+	0.980762i	$0.437463\pi$
$230$	8.31494e7	0.450621
$231$	−8.67319e6	−0.0462953
$232$	1.01626e9	5.34314
$233$	3.03367e8	1.57117	0.785584	−	0.618755i	$-0.212363\pi$
$233$	3.03367e8	1.57117	0.785584	+	0.618755i	$0.212363\pi$
$234$	−9.96852e8	−5.08599
$235$	−1.42358e8	−0.715560
$236$	−6.55170e8	−3.24461
$237$	−3.64317e8	−1.77771
$238$	3.21268e7	0.154471
$239$	2.67779e8	1.26877	0.634385	−	0.773017i	$-0.281253\pi$
$239$	2.67779e8	1.26877	0.634385	+	0.773017i	$0.281253\pi$
$240$	−8.19919e8	−3.82853
$241$	2.83175e8	1.30315	0.651577	−	0.758583i	$-0.274108\pi$
$241$	2.83175e8	1.30315	0.651577	+	0.758583i	$0.274108\pi$
$242$	3.53337e8	1.60264
$243$	1.86480e8	0.833701
$244$	−1.77180e8	−0.780819
$245$	1.18455e8	0.514604
$246$	−5.97751e8	−2.56005
$247$	1.17568e8	0.496420
$248$	5.31611e8	2.21316
$249$	2.74061e8	1.12499
$250$	−4.32326e8	−1.74993
$251$	−3.78457e8	−1.51063	−0.755315	−	0.655361i	$-0.772516\pi$
$251$	−3.78457e8	−1.51063	−0.755315	+	0.655361i	$0.772516\pi$
$252$	9.64394e7	0.379623
$253$	−4.87915e7	−0.189418
$254$	−4.76129e8	−1.82309
$255$	3.18094e8	1.20134
$256$	1.19272e9	4.44322
$257$	−2.07176e6	−0.00761330	−0.00380665	−	0.999993i	$-0.501212\pi$
$257$	−2.07176e6	−0.00761330	−0.00380665	+	0.999993i	$0.501212\pi$
$258$	−1.50506e9	−5.45613
$259$	65474.7	0.000234166 0
$260$	−4.86057e8	−1.71507
$261$	−9.53118e8	−3.31822
$262$	9.90866e8	3.40377
$263$	3.61538e8	1.22549	0.612743	−	0.790282i	$-0.290066\pi$
$263$	3.61538e8	1.22549	0.612743	+	0.790282i	$0.290066\pi$
$264$	8.09210e8	2.70675
$265$	2.64011e8	0.871489
$266$	−1.54060e7	−0.0501884
$267$	5.12872e8	1.64900
$268$	1.73753e8	0.551392
$269$	2.09991e8	0.657760	0.328880	−	0.944372i	$-0.393329\pi$
$269$	2.09991e8	0.657760	0.328880	+	0.944372i	$0.393329\pi$
$270$	7.08259e8	2.18987
$271$	6.32837e7	0.193152	0.0965761	−	0.995326i	$-0.469211\pi$
$271$	6.32837e7	0.193152	0.0965761	+	0.995326i	$0.469211\pi$
$272$	−1.78215e9	−5.36973
$273$	4.31644e7	0.128398
$274$	6.27428e8	1.84263
$275$	1.07318e8	0.311178
$276$	7.87956e8	2.25590
$277$	−5.85931e8	−1.65641	−0.828205	−	0.560426i	$-0.810637\pi$
$277$	−5.85931e8	−1.65641	−0.828205	+	0.560426i	$0.810637\pi$
$278$	−4.58002e8	−1.27853
$279$	−4.98582e8	−1.37443
$280$	4.11140e7	0.111927
$281$	3.34788e8	0.900115	0.450058	−	0.893000i	$-0.351403\pi$
$281$	3.34788e8	0.900115	0.450058	+	0.893000i	$0.351403\pi$
$282$	−1.82727e9	−4.85211
$283$	−4.04721e8	−1.06146	−0.530729	−	0.847541i	$-0.678082\pi$
$283$	−4.04721e8	−1.06146	−0.530729	+	0.847541i	$0.678082\pi$
$284$	−1.38763e9	−3.59467
$285$	−1.52538e8	−0.390319
$286$	3.86321e8	0.976490
$287$	1.78210e7	0.0444986
$288$	−4.05651e9	−10.0064
$289$	2.81059e8	0.684943
$290$	−6.29477e8	−1.51561
$291$	−1.29339e9	−3.07683
$292$	5.39629e8	1.26840
$293$	1.82647e8	0.424206	0.212103	−	0.977247i	$-0.431969\pi$
$293$	1.82647e8	0.424206	0.212103	+	0.977247i	$0.431969\pi$
$294$	1.52046e9	3.48946
$295$	2.61958e8	0.594093
$296$	−6.10880e6	−0.0136910
$297$	−4.15601e8	−0.920511
$298$	−1.55642e9	−3.40699
$299$	2.42824e8	0.525342
$300$	−1.73313e9	−3.70601
$301$	4.48711e7	0.0948382
$302$	1.34167e9	2.80300
$303$	−1.18438e9	−2.44591
$304$	8.54606e8	1.74465
$305$	7.08422e7	0.142969
$306$	2.81120e9	5.60876
$307$	−3.76919e8	−0.743471	−0.371735	−	0.928339i	$-0.621237\pi$
$307$	−3.76919e8	−0.743471	−0.371735	+	0.928339i	$0.621237\pi$
$308$	−3.73743e7	−0.0728861
$309$	−2.29307e8	−0.442142
$310$	−3.29283e8	−0.627775
$311$	−1.96416e8	−0.370267	−0.185133	−	0.982713i	$-0.559272\pi$
$311$	−1.96416e8	−0.370267	−0.185133	+	0.982713i	$0.559272\pi$
$312$	−4.02725e9	−7.50702
$313$	−9.61087e8	−1.77157	−0.885784	−	0.464098i	$-0.846378\pi$
$313$	−9.61087e8	−1.77157	−0.885784	+	0.464098i	$0.846378\pi$
$314$	6.11950e7	0.111548
$315$	−3.85595e7	−0.0695096
$316$	−1.56991e9	−2.79878
$317$	−1.04330e8	−0.183951	−0.0919754	−	0.995761i	$-0.529318\pi$
$317$	−1.04330e8	−0.183951	−0.0919754	+	0.995761i	$0.529318\pi$
$318$	3.38877e9	5.90945
$319$	3.69372e8	0.637085
$320$	−1.42660e9	−2.43376
$321$	1.68464e8	0.284275
$322$	−3.18193e7	−0.0531124
$323$	−3.31550e8	−0.547445
$324$	2.89414e9	4.72728
$325$	−5.34097e8	−0.863036
$326$	1.33702e9	2.13735
$327$	1.40754e9	2.22610
$328$	−1.66271e9	−2.60170
$329$	5.44773e7	0.0843392
$330$	−5.01230e8	−0.767783
$331$	9.41130e8	1.42643	0.713217	−	0.700943i	$-0.247237\pi$
$331$	9.41130e8	1.42643	0.713217	+	0.700943i	$0.247237\pi$
$332$	1.18098e9	1.77116
$333$	5.72926e6	0.00850244
$334$	5.36696e8	0.788163
$335$	−6.94720e7	−0.100961
$336$	3.13764e8	0.451249
$337$	8.77550e8	1.24901	0.624507	−	0.781019i	$-0.285300\pi$
$337$	8.77550e8	1.24901	0.624507	+	0.781019i	$0.285300\pi$
$338$	−5.34937e8	−0.753519
$339$	1.30798e9	1.82348
$340$	1.37072e9	1.89135
$341$	1.93221e8	0.263885
$342$	−1.34807e9	−1.82231
$343$	−9.08288e7	−0.121533
$344$	−4.18648e9	−5.54491
$345$	−3.15050e8	−0.413059
$346$	1.84332e9	2.39240
$347$	4.15250e8	0.533527	0.266763	−	0.963762i	$-0.414046\pi$
$347$	4.15250e8	0.533527	0.266763	+	0.963762i	$0.414046\pi$
$348$	−5.96517e9	−7.58744
$349$	7.03324e7	0.0885659	0.0442829	−	0.999019i	$-0.485900\pi$
$349$	7.03324e7	0.0885659	0.0442829	+	0.999019i	$0.485900\pi$
$350$	6.99875e7	0.0872534
$351$	2.06835e9	2.55299
$352$	1.57206e9	1.92119
$353$	1.22348e8	0.148042	0.0740212	−	0.997257i	$-0.476417\pi$
$353$	1.22348e8	0.148042	0.0740212	+	0.997257i	$0.476417\pi$
$354$	3.36241e9	4.02846
$355$	5.54817e8	0.658189
$356$	2.21005e9	2.59614
$357$	−1.21727e8	−0.141595
$358$	1.28609e9	1.48143
$359$	4.44828e8	0.507413	0.253706	−	0.967281i	$-0.418350\pi$
$359$	4.44828e8	0.507413	0.253706	+	0.967281i	$0.418350\pi$
$360$	3.59761e9	4.06402
$361$	−7.34881e8	−0.822133
$362$	−9.21778e7	−0.102128
$363$	−1.33878e9	−1.46905
$364$	1.86003e8	0.202146
$365$	−2.15761e8	−0.232246
$366$	9.09308e8	0.969454
$367$	−6.94137e8	−0.733016	−0.366508	−	0.930415i	$-0.619447\pi$
$367$	−6.94137e8	−0.733016	−0.366508	+	0.930415i	$0.619447\pi$
$368$	1.76510e9	1.84629
$369$	1.55940e9	1.61572
$370$	3.78383e6	0.00388352
$371$	−1.01031e8	−0.102718
$372$	−3.12042e9	−3.14277
$373$	−1.41208e9	−1.40890	−0.704449	−	0.709755i	$-0.748806\pi$
$373$	−1.41208e9	−1.40890	−0.704449	+	0.709755i	$0.748806\pi$
$374$	−1.08946e9	−1.07686
$375$	1.63807e9	1.60407
$376$	−5.08274e9	−4.93106
$377$	−1.83828e9	−1.76692
$378$	−2.71034e8	−0.258109
$379$	−7.73009e7	−0.0729369	−0.0364685	−	0.999335i	$-0.511611\pi$
$379$	−7.73009e7	−0.0729369	−0.0364685	+	0.999335i	$0.511611\pi$
$380$	−6.57310e8	−0.614508
$381$	1.80404e9	1.67112
$382$	1.93879e8	0.177955
$383$	−1.33734e9	−1.21631	−0.608157	−	0.793816i	$-0.708091\pi$
$383$	−1.33734e9	−1.21631	−0.608157	+	0.793816i	$0.708091\pi$
$384$	−9.31154e9	−8.39194
$385$	1.49434e7	0.0133456
$386$	1.12953e9	0.999635
$387$	3.92637e9	3.44352
$388$	−5.57344e9	−4.84409
$389$	−9.04465e7	−0.0779055	−0.0389528	−	0.999241i	$-0.512402\pi$
$389$	−9.04465e7	−0.0779055	−0.0389528	+	0.999241i	$0.512402\pi$
$390$	2.49450e9	2.12940
$391$	−6.84781e8	−0.579340
$392$	4.22931e9	3.54624
$393$	−3.75435e9	−3.12005
$394$	1.91559e9	1.57785
$395$	6.27698e8	0.512461
$396$	−3.27037e9	−2.64645
$397$	1.77779e9	1.42598	0.712990	−	0.701174i	$-0.247341\pi$
$397$	1.77779e9	1.42598	0.712990	+	0.701174i	$0.247341\pi$
$398$	−1.21727e9	−0.967826
$399$	5.83726e7	0.0460049
$400$	−3.88238e9	−3.03311
$401$	−4.72695e8	−0.366080	−0.183040	−	0.983106i	$-0.558594\pi$
$401$	−4.72695e8	−0.366080	−0.183040	+	0.983106i	$0.558594\pi$
$402$	−8.91721e8	−0.684601
$403$	−9.61616e8	−0.731870
$404$	−5.10368e9	−3.85078
$405$	−1.15717e9	−0.865573
$406$	2.40886e8	0.178637
$407$	−2.22032e6	−0.00163244
$408$	1.13572e10	8.27864
$409$	−2.14044e9	−1.54693	−0.773465	−	0.633839i	$-0.781478\pi$
$409$	−2.14044e9	−1.54693	−0.773465	+	0.633839i	$0.781478\pi$
$410$	1.02989e9	0.737985
$411$	−2.37730e9	−1.68903
$412$	−9.88121e8	−0.696097
$413$	−1.00245e8	−0.0700226
$414$	−2.78430e9	−1.92848
$415$	−4.72191e8	−0.324302
$416$	−7.82380e9	−5.32833
$417$	1.73535e9	1.17196
$418$	5.22434e8	0.349876
$419$	3.98664e8	0.264763	0.132382	−	0.991199i	$-0.457738\pi$
$419$	3.98664e8	0.264763	0.132382	+	0.991199i	$0.457738\pi$
$420$	−2.41328e8	−0.158941
$421$	3.34129e8	0.218236	0.109118	−	0.994029i	$-0.465197\pi$
$421$	3.34129e8	0.218236	0.109118	+	0.994029i	$0.465197\pi$
$422$	1.07190e9	0.694318
$423$	4.76694e9	3.06231
$424$	9.42621e9	6.00560
$425$	1.50620e9	0.951744
$426$	7.12147e9	4.46309
$427$	−2.71097e7	−0.0168510
$428$	7.25939e8	0.447556
$429$	−1.46376e9	−0.895093
$430$	2.59313e9	1.57284
$431$	−1.96528e9	−1.18237	−0.591185	−	0.806536i	$-0.701340\pi$
$431$	−1.96528e9	−1.18237	−0.591185	+	0.806536i	$0.701340\pi$
$432$	1.50349e10	8.97238
$433$	−2.44502e9	−1.44735	−0.723677	−	0.690138i	$-0.757550\pi$
$433$	−2.44502e9	−1.44735	−0.723677	+	0.690138i	$0.757550\pi$
$434$	1.26009e8	0.0739925
$435$	2.38506e9	1.38927
$436$	6.06533e9	3.50471
$437$	3.28378e8	0.188230
$438$	−2.76944e9	−1.57483
$439$	−2.40830e9	−1.35858	−0.679289	−	0.733871i	$-0.737712\pi$
$439$	−2.40830e9	−1.35858	−0.679289	+	0.733871i	$0.737712\pi$
$440$	−1.39422e9	−0.780275
$441$	−3.96654e9	−2.20230
$442$	5.42197e9	2.98661
$443$	−2.88642e9	−1.57742	−0.788708	−	0.614768i	$-0.789249\pi$
$443$	−2.88642e9	−1.57742	−0.788708	+	0.614768i	$0.789249\pi$
$444$	3.58570e7	0.0194417
$445$	−8.83649e8	−0.475357
$446$	7.29284e8	0.389247
$447$	5.89723e9	3.12300
$448$	5.45926e8	0.286854
$449$	1.19368e9	0.622338	0.311169	−	0.950355i	$-0.399279\pi$
$449$	1.19368e9	0.622338	0.311169	+	0.950355i	$0.399279\pi$
$450$	6.12414e9	3.16812
$451$	−6.04333e8	−0.310212
$452$	5.63629e9	2.87084
$453$	−5.08355e9	−2.56935
$454$	−2.47185e9	−1.23973
$455$	−7.43698e7	−0.0370132
$456$	−5.44617e9	−2.68977
$457$	4.81159e8	0.235821	0.117910	−	0.993024i	$-0.462380\pi$
$457$	4.81159e8	0.235821	0.117910	+	0.993024i	$0.462380\pi$
$458$	−1.56905e9	−0.763144
$459$	−5.83290e9	−2.81540
$460$	−1.35760e9	−0.650310
$461$	−3.14817e9	−1.49660	−0.748299	−	0.663362i	$-0.769129\pi$
$461$	−3.14817e9	−1.49660	−0.748299	+	0.663362i	$0.769129\pi$
$462$	1.91809e8	0.0904945
$463$	2.04254e9	0.956393	0.478196	−	0.878253i	$-0.341291\pi$
$463$	2.04254e9	0.956393	0.478196	+	0.878253i	$0.341291\pi$
$464$	−1.33625e10	−6.20977
$465$	1.24764e9	0.575446
$466$	−6.70901e9	−3.07120
$467$	−3.18102e9	−1.44530	−0.722648	−	0.691216i	$-0.757075\pi$
$467$	−3.18102e9	−1.44530	−0.722648	+	0.691216i	$0.757075\pi$
$468$	1.62759e10	7.33979
$469$	2.65853e7	0.0118997
$470$	3.14828e9	1.39872
$471$	−2.31866e8	−0.102250
$472$	9.35289e9	4.09401
$473$	−1.52163e9	−0.661143
$474$	8.05694e9	3.47493
$475$	−7.22276e8	−0.309226
$476$	−5.24542e8	−0.222924
$477$	−8.84055e9	−3.72962
$478$	−5.92197e9	−2.48009
$479$	−1.56737e9	−0.651623	−0.325811	−	0.945435i	$-0.605637\pi$
$479$	−1.56737e9	−0.651623	−0.325811	+	0.945435i	$0.605637\pi$
$480$	1.01509e10	4.18949
$481$	1.10500e7	0.00452747
$482$	−6.26246e9	−2.54730
$483$	1.20562e8	0.0486851
$484$	−5.76903e9	−2.31283
$485$	2.22844e9	0.886961
$486$	−4.12404e9	−1.62965
$487$	−4.31452e9	−1.69270	−0.846352	−	0.532624i	$-0.821206\pi$
$487$	−4.31452e9	−1.69270	−0.846352	+	0.532624i	$0.821206\pi$
$488$	2.52934e9	0.985229
$489$	−5.06592e9	−1.95919
$490$	−2.61966e9	−1.00591
$491$	2.18196e9	0.831882	0.415941	−	0.909392i	$-0.363452\pi$
$491$	2.18196e9	0.831882	0.415941	+	0.909392i	$0.363452\pi$
$492$	9.75965e9	3.69451
$493$	5.18409e9	1.94854
$494$	−2.60003e9	−0.970363
$495$	1.30760e9	0.484570
$496$	−6.99003e9	−2.57213
$497$	−2.12316e8	−0.0775773
$498$	−6.06090e9	−2.19905
$499$	−5.47763e8	−0.197351	−0.0986757	−	0.995120i	$-0.531461\pi$
$499$	−5.47763e8	−0.197351	−0.0986757	+	0.995120i	$0.531461\pi$
$500$	7.05871e9	2.52540
$501$	−2.03352e9	−0.722465
$502$	8.36963e9	2.95286
$503$	−1.14481e9	−0.401094	−0.200547	−	0.979684i	$-0.564272\pi$
$503$	−1.14481e9	−0.401094	−0.200547	+	0.979684i	$0.564272\pi$
$504$	−1.37672e9	−0.479004
$505$	2.04061e9	0.705085
$506$	1.07903e9	0.370260
$507$	2.02686e9	0.690709
$508$	7.77389e9	2.63097
$509$	3.00091e9	1.00865	0.504325	−	0.863514i	$-0.331741\pi$
$509$	3.00091e9	1.00865	0.504325	+	0.863514i	$0.331741\pi$
$510$	−7.03469e9	−2.34828
$511$	8.25667e7	0.0273736
$512$	−1.21532e10	−4.00170
$513$	2.79709e9	0.914736
$514$	4.58172e7	0.0148819
$515$	3.95082e8	0.127457
$516$	2.45735e10	7.87396
$517$	−1.84739e9	−0.587951
$518$	−1.44798e6	−0.000457730 0
$519$	−6.98425e9	−2.19298
$520$	6.93872e9	2.16405
$521$	−2.78691e9	−0.863358	−0.431679	−	0.902027i	$-0.642079\pi$
$521$	−2.78691e9	−0.863358	−0.431679	+	0.902027i	$0.642079\pi$
$522$	2.10783e10	6.48619
$523$	6.03218e9	1.84382	0.921909	−	0.387406i	$-0.126629\pi$
$523$	6.03218e9	1.84382	0.921909	+	0.387406i	$0.126629\pi$
$524$	−1.61781e10	−4.91212
$525$	−2.65180e8	−0.0799803
$526$	−7.99546e9	−2.39548
$527$	2.71183e9	0.807096
$528$	−1.06401e10	−3.14577
$529$	−2.72660e9	−0.800804
$530$	−5.83865e9	−1.70352
$531$	−8.77179e9	−2.54248
$532$	2.51537e8	0.0724289
$533$	3.00762e9	0.860356
$534$	−1.13422e10	−3.22333
$535$	−2.90253e8	−0.0819482
$536$	−2.48041e9	−0.695741
$537$	−4.87294e9	−1.35794
$538$	−4.64398e9	−1.28574
$539$	1.53720e9	0.422833
$540$	−1.15639e10	−3.16029
$541$	3.58578e9	0.973629	0.486815	−	0.873505i	$-0.338159\pi$
$541$	3.58578e9	0.973629	0.486815	+	0.873505i	$0.338159\pi$
$542$	−1.39953e9	−0.377559
$543$	3.49258e8	0.0936153
$544$	2.20637e10	5.87601
$545$	−2.42511e9	−0.641718
$546$	−9.54588e8	−0.250982
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	−1.02442e10	−2.65917
$549$	−2.37219e9	−0.611851
$550$	−2.37336e9	−0.608267
$551$	−2.48596e9	−0.633088
$552$	−1.12485e10	−2.84647
$553$	−2.40205e8	−0.0604011
$554$	1.29580e10	3.23782
$555$	−1.43368e7	−0.00355981
$556$	7.47793e9	1.84510
$557$	−3.82099e9	−0.936878	−0.468439	−	0.883496i	$-0.655183\pi$
$557$	−3.82099e9	−0.936878	−0.468439	+	0.883496i	$0.655183\pi$
$558$	1.10262e10	2.68662
$559$	7.57279e9	1.83364
$560$	−5.40597e8	−0.130082
$561$	4.12791e9	0.987097
$562$	−7.40389e9	−1.75947
$563$	−5.77471e9	−1.36380	−0.681900	−	0.731445i	$-0.738846\pi$
$563$	−5.77471e9	−1.36380	−0.681900	+	0.731445i	$0.738846\pi$
$564$	2.98343e10	7.00228
$565$	−2.25357e9	−0.525656
$566$	8.95047e9	2.07486
$567$	4.42821e8	0.102021
$568$	1.98091e10	4.53571
$569$	5.37675e9	1.22356	0.611782	−	0.791026i	$-0.290453\pi$
$569$	5.37675e9	1.22356	0.611782	+	0.791026i	$0.290453\pi$
$570$	3.37339e9	0.762966
$571$	6.19668e9	1.39294	0.696471	−	0.717585i	$-0.254753\pi$
$571$	6.19668e9	1.39294	0.696471	+	0.717585i	$0.254753\pi$
$572$	−6.30757e9	−1.40921
$573$	−7.34602e8	−0.163121
$574$	−3.94115e8	−0.0869825
$575$	−1.49178e9	−0.327241
$576$	4.77704e10	10.4155
$577$	9.04519e8	0.196021	0.0980105	−	0.995185i	$-0.468752\pi$
$577$	9.04519e8	0.196021	0.0980105	+	0.995185i	$0.468752\pi$
$578$	−6.21565e9	−1.33887
$579$	−4.27974e9	−0.916309
$580$	1.02776e10	2.18723
$581$	1.80697e8	0.0382238
$582$	2.86035e10	6.01436
$583$	3.42608e9	0.716073
$584$	−7.70348e9	−1.60045
$585$	−6.50761e9	−1.34393
$586$	−4.03927e9	−0.829204
$587$	4.86703e9	0.993187	0.496593	−	0.867983i	$-0.334584\pi$
$587$	4.86703e9	0.993187	0.496593	+	0.867983i	$0.334584\pi$
$588$	−2.48249e10	−5.03578
$589$	−1.30042e9	−0.262229
$590$	−5.79324e9	−1.16129
$591$	−7.25809e9	−1.44633
$592$	8.03231e7	0.0159116
$593$	−3.25317e9	−0.640643	−0.320321	−	0.947309i	$-0.603791\pi$
$593$	−3.25317e9	−0.640643	−0.320321	+	0.947309i	$0.603791\pi$
$594$	9.19109e9	1.79934
$595$	2.09729e8	0.0408177
$596$	2.54122e10	4.91677
$597$	4.61220e9	0.887152
$598$	−5.37008e9	−1.02690
$599$	5.81135e9	1.10480	0.552399	−	0.833580i	$-0.313712\pi$
$599$	5.81135e9	1.10480	0.552399	+	0.833580i	$0.313712\pi$
$600$	2.47413e10	4.67621
$601$	3.14526e9	0.591011	0.295506	−	0.955341i	$-0.404512\pi$
$601$	3.14526e9	0.591011	0.295506	+	0.955341i	$0.404512\pi$
$602$	−9.92330e8	−0.185382
$603$	2.32630e9	0.432072
$604$	−2.19059e10	−4.04512
$605$	2.30664e9	0.423483
$606$	2.61927e10	4.78108
$607$	1.97323e9	0.358111	0.179056	−	0.983839i	$-0.442696\pi$
$607$	1.97323e9	0.358111	0.179056	+	0.983839i	$0.442696\pi$
$608$	−1.05804e10	−1.90914
$609$	−9.12708e8	−0.163746
$610$	−1.56669e9	−0.279465
$611$	9.19402e9	1.63065
$612$	−4.58992e10	−8.09422
$613$	−4.13370e9	−0.724816	−0.362408	−	0.932020i	$-0.618045\pi$
$613$	−4.13370e9	−0.724816	−0.362408	+	0.932020i	$0.618045\pi$
$614$	8.33563e9	1.45328
$615$	−3.90222e9	−0.676470
$616$	5.33537e8	0.0919669
$617$	−3.40143e9	−0.582993	−0.291496	−	0.956572i	$-0.594153\pi$
$617$	−3.40143e9	−0.582993	−0.291496	+	0.956572i	$0.594153\pi$
$618$	5.07115e9	0.864265
$619$	−1.11268e10	−1.88561	−0.942806	−	0.333343i	$-0.891823\pi$
$619$	−1.11268e10	−1.88561	−0.942806	+	0.333343i	$0.891823\pi$
$620$	5.37630e9	0.905967
$621$	5.77709e9	0.968029
$622$	4.34376e9	0.723769
$623$	3.38152e8	0.0560278
$624$	5.29533e10	8.72463
$625$	1.65285e9	0.270803
$626$	2.12546e10	3.46292
$627$	−1.97948e9	−0.320712
$628$	−9.99148e8	−0.160980
$629$	−3.11619e7	−0.00499284
$630$	8.52750e8	0.135872
$631$	−1.14542e10	−1.81494	−0.907472	−	0.420112i	$-0.861991\pi$
$631$	−1.14542e10	−1.81494	−0.907472	+	0.420112i	$0.861991\pi$
$632$	2.24112e10	3.53147
$633$	−4.06137e9	−0.636443
$634$	2.30727e9	0.359573
$635$	−3.10825e9	−0.481735
$636$	−5.53293e10	−8.52817
$637$	−7.65027e9	−1.17270
$638$	−8.16873e9	−1.24532
$639$	−1.85783e10	−2.81679
$640$	1.60433e10	2.41915
$641$	−3.19906e9	−0.479755	−0.239878	−	0.970803i	$-0.577107\pi$
$641$	−3.19906e9	−0.479755	−0.239878	+	0.970803i	$0.577107\pi$
$642$	−3.72560e9	−0.555679
$643$	9.13627e9	1.35529	0.677643	−	0.735391i	$-0.263002\pi$
$643$	9.13627e9	1.35529	0.677643	+	0.735391i	$0.263002\pi$
$644$	5.19523e8	0.0766486
$645$	−9.82527e9	−1.44173
$646$	7.33229e9	1.07010
$647$	−4.71016e9	−0.683708	−0.341854	−	0.939753i	$-0.611055\pi$
$647$	−4.71016e9	−0.683708	−0.341854	+	0.939753i	$0.611055\pi$
$648$	−4.13153e10	−5.96483
$649$	3.39943e9	0.488146
$650$	1.18116e10	1.68699
$651$	−4.77443e8	−0.0678248
$652$	−2.18299e10	−3.08450
$653$	−1.14338e10	−1.60691	−0.803457	−	0.595362i	$-0.797009\pi$
$653$	−1.14338e10	−1.60691	−0.803457	+	0.595362i	$0.797009\pi$
$654$	−3.11280e10	−4.35140
$655$	6.46853e9	0.899417
$656$	2.18625e10	3.02369
$657$	7.22486e9	0.993918
$658$	−1.20477e9	−0.164860
$659$	−4.89573e8	−0.0666375	−0.0333188	−	0.999445i	$-0.510608\pi$
$659$	−4.89573e8	−0.0666375	−0.0333188	+	0.999445i	$0.510608\pi$
$660$	8.18372e9	1.10802
$661$	2.17404e9	0.292794	0.146397	−	0.989226i	$-0.453232\pi$
$661$	2.17404e9	0.292794	0.146397	+	0.989226i	$0.453232\pi$
$662$	−2.08132e10	−2.78828
$663$	−2.05436e10	−2.73766
$664$	−1.68590e10	−2.23483
$665$	−1.00573e8	−0.0132618
$666$	−1.26703e8	−0.0166199
$667$	−5.13448e9	−0.669972
$668$	−8.76279e9	−1.13743
$669$	−2.76323e9	−0.356801
$670$	1.53638e9	0.197350
$671$	9.19320e8	0.117473
$672$	−3.88452e9	−0.493793
$673$	1.46066e10	1.84712	0.923560	−	0.383453i	$-0.125265\pi$
$673$	1.46066e10	1.84712	0.923560	+	0.383453i	$0.125265\pi$
$674$	−1.94072e10	−2.44148
$675$	−1.27069e10	−1.59029
$676$	8.73406e9	1.08743
$677$	−1.24567e10	−1.54292	−0.771458	−	0.636281i	$-0.780472\pi$
$677$	−1.24567e10	−1.54292	−0.771458	+	0.636281i	$0.780472\pi$
$678$	−2.89261e10	−3.56440
$679$	−8.52771e8	−0.104541
$680$	−1.95677e10	−2.38649
$681$	9.36576e9	1.13639
$682$	−4.27311e9	−0.515821
$683$	2.69865e9	0.324096	0.162048	−	0.986783i	$-0.448190\pi$
$683$	2.69865e9	0.324096	0.162048	+	0.986783i	$0.448190\pi$
$684$	2.20104e10	2.62985
$685$	4.09595e9	0.486898
$686$	2.00869e9	0.237563
$687$	5.94506e9	0.699532
$688$	5.50470e10	6.44427
$689$	−1.70508e10	−1.98599
$690$	6.96738e9	0.807416
$691$	−1.62653e10	−1.87538	−0.937689	−	0.347476i	$-0.887039\pi$
$691$	−1.62653e10	−1.87538	−0.937689	+	0.347476i	$0.887039\pi$
$692$	−3.00963e10	−3.45257
$693$	−5.00388e8	−0.0571137
$694$	−9.18332e9	−1.04290
$695$	−2.98991e9	−0.337840
$696$	8.51558e10	9.57375
$697$	−8.48172e9	−0.948788
$698$	−1.55541e9	−0.173122
$699$	2.54202e10	2.81519
$700$	−1.14271e9	−0.125919
$701$	−2.46654e9	−0.270443	−0.135222	−	0.990815i	$-0.543175\pi$
$701$	−2.46654e9	−0.270443	−0.135222	+	0.990815i	$0.543175\pi$
$702$	−4.57419e10	−4.99038
$703$	1.49433e7	0.00162219
$704$	−1.85130e10	−1.99973
$705$	−1.19287e10	−1.28213
$706$	−2.70575e9	−0.289382
$707$	−7.80896e8	−0.0831046
$708$	−5.48990e10	−5.81364
$709$	4.06873e9	0.428743	0.214371	−	0.976752i	$-0.431230\pi$
$709$	4.06873e9	0.428743	0.214371	+	0.976752i	$0.431230\pi$
$710$	−1.22699e10	−1.28658
$711$	−2.10188e10	−2.19313
$712$	−3.15496e10	−3.27578
$713$	−2.68588e9	−0.277507
$714$	2.69201e9	0.276779
$715$	2.52197e9	0.258029
$716$	−2.09983e10	−2.13791
$717$	2.24381e10	2.27336
$718$	−9.83744e9	−0.991851
$719$	−3.48940e9	−0.350106	−0.175053	−	0.984559i	$-0.556010\pi$
$719$	−3.48940e9	−0.350106	−0.175053	+	0.984559i	$0.556010\pi$
$720$	−4.73041e10	−4.72319
$721$	−1.51189e8	−0.0150226
$722$	1.62520e10	1.60704
$723$	2.37282e10	2.33497
$724$	1.50501e9	0.147386
$725$	1.12934e10	1.10063
$726$	2.96073e10	2.87158
$727$	−1.36792e10	−1.32035	−0.660175	−	0.751111i	$-0.729518\pi$
$727$	−1.36792e10	−1.32035	−0.660175	+	0.751111i	$0.729518\pi$
$728$	−2.65529e9	−0.255065
$729$	−1.90347e9	−0.181970
$730$	4.77159e9	0.453976
$731$	−2.13559e10	−2.02212
$732$	−1.48465e10	−1.39906
$733$	−4.66545e9	−0.437552	−0.218776	−	0.975775i	$-0.570206\pi$
$733$	−4.66545e9	−0.437552	−0.218776	+	0.975775i	$0.570206\pi$
$734$	1.53509e10	1.43284
$735$	9.92578e9	0.922060
$736$	−2.18526e10	−2.02037
$737$	−9.01539e8	−0.0829561
$738$	−3.44864e10	−3.15828
$739$	−1.35896e10	−1.23866	−0.619331	−	0.785130i	$-0.712596\pi$
$739$	−1.35896e10	−1.23866	−0.619331	+	0.785130i	$0.712596\pi$
$740$	−6.17796e7	−0.00560447
$741$	9.85142e9	0.889478
$742$	2.23432e9	0.200785
$743$	−1.94086e10	−1.73593	−0.867967	−	0.496621i	$-0.834574\pi$
$743$	−1.94086e10	−1.73593	−0.867967	+	0.496621i	$0.834574\pi$
$744$	4.45455e10	3.96551
$745$	−1.01606e10	−0.900268
$746$	3.12284e10	2.75400
$747$	1.58116e10	1.38788
$748$	1.77878e10	1.55406
$749$	1.11073e8	0.00965880
$750$	−3.62261e10	−3.13551
$751$	3.15071e8	0.0271437	0.0135718	−	0.999908i	$-0.495680\pi$
$751$	3.15071e8	0.0271437	0.0135718	+	0.999908i	$0.495680\pi$
$752$	6.68317e10	5.73086
$753$	−3.17122e10	−2.70673
$754$	4.06538e10	3.45384
$755$	8.75867e9	0.740668
$756$	4.42525e9	0.372487
$757$	4.94779e9	0.414549	0.207274	−	0.978283i	$-0.433541\pi$
$757$	4.94779e9	0.414549	0.207274	+	0.978283i	$0.433541\pi$
$758$	1.70952e9	0.142571
$759$	−4.08841e9	−0.339397
$760$	9.38344e9	0.775380
$761$	1.33957e10	1.10184	0.550920	−	0.834558i	$-0.314277\pi$
$761$	1.33957e10	1.10184	0.550920	+	0.834558i	$0.314277\pi$
$762$	−3.98965e10	−3.26658
$763$	9.28034e8	0.0756359
$764$	−3.16552e9	−0.256814
$765$	1.83520e10	1.48207
$766$	2.95755e10	2.37756
$767$	−1.69182e10	−1.35385
$768$	9.99421e10	7.96130
$769$	1.64284e10	1.30273	0.651364	−	0.758765i	$-0.274197\pi$
$769$	1.64284e10	1.30273	0.651364	+	0.758765i	$0.274197\pi$
$770$	−3.30476e8	−0.0260869
$771$	−1.73600e8	−0.0136414
$772$	−1.84421e10	−1.44261
$773$	2.12610e10	1.65560	0.827799	−	0.561025i	$-0.189593\pi$
$773$	2.12610e10	1.65560	0.827799	+	0.561025i	$0.189593\pi$
$774$	−8.68322e10	−6.73113
$775$	5.90767e9	0.455890
$776$	7.95637e10	6.11222
$777$	5.48635e6	0.000419576 0
$778$	2.00024e9	0.152284
$779$	4.06730e9	0.308266
$780$	−4.07284e10	−3.07303
$781$	7.19988e9	0.540812
$782$	1.51440e10	1.13245
$783$	−4.37351e10	−3.25584
$784$	−5.56101e10	−4.12143
$785$	3.99491e8	0.0294756
$786$	8.30281e10	6.09882
$787$	−1.31631e10	−0.962602	−0.481301	−	0.876555i	$-0.659836\pi$
$787$	−1.31631e10	−0.962602	−0.481301	+	0.876555i	$0.659836\pi$
$788$	−3.12763e10	−2.27706
$789$	3.02945e10	2.19581
$790$	−1.38816e10	−1.00172
$791$	8.62389e8	0.0619563
$792$	4.66862e10	3.33926
$793$	−4.57524e9	−0.325805
$794$	−3.93161e10	−2.78739
$795$	2.21224e10	1.56152
$796$	1.98747e10	1.39671
$797$	−7.44867e9	−0.521164	−0.260582	−	0.965452i	$-0.583914\pi$
$797$	−7.44867e9	−0.521164	−0.260582	+	0.965452i	$0.583914\pi$
$798$	−1.29092e9	−0.0899268
$799$	−2.59278e10	−1.79826
$800$	4.80654e10	3.31908
$801$	2.95894e10	2.03434
$802$	1.04537e10	0.715584
$803$	−2.79993e9	−0.190828
$804$	1.45594e10	0.987976
$805$	−2.07722e8	−0.0140345
$806$	2.12663e10	1.43060
$807$	1.75959e10	1.17856
$808$	7.28577e10	4.85888
$809$	2.17029e10	1.44111	0.720555	−	0.693398i	$-0.243887\pi$
$809$	2.17029e10	1.44111	0.720555	+	0.693398i	$0.243887\pi$
$810$	2.55909e10	1.69196
$811$	1.74034e10	1.14568	0.572838	−	0.819669i	$-0.305843\pi$
$811$	1.74034e10	1.14568	0.572838	+	0.819669i	$0.305843\pi$
$812$	−3.93301e9	−0.257798
$813$	5.30276e9	0.346087
$814$	4.91028e7	0.00319096
$815$	8.72829e9	0.564778
$816$	−1.49332e11	−9.62141
$817$	1.02409e10	0.656995
$818$	4.73361e10	3.02382
$819$	2.49031e9	0.158402
$820$	−1.68153e10	−1.06502
$821$	−2.33489e10	−1.47254	−0.736268	−	0.676690i	$-0.763414\pi$
$821$	−2.33489e10	−1.47254	−0.736268	+	0.676690i	$0.763414\pi$
$822$	5.25744e10	3.30159
$823$	1.93298e9	0.120873	0.0604364	−	0.998172i	$-0.480751\pi$
$823$	1.93298e9	0.120873	0.0604364	+	0.998172i	$0.480751\pi$
$824$	1.41059e10	0.878328
$825$	8.99257e9	0.557564
$826$	2.21694e9	0.136875
$827$	−1.05115e10	−0.646241	−0.323120	−	0.946358i	$-0.604732\pi$
$827$	−1.05115e10	−0.646241	−0.323120	+	0.946358i	$0.604732\pi$
$828$	4.54600e10	2.78306
$829$	4.17438e9	0.254479	0.127239	−	0.991872i	$-0.459388\pi$
$829$	4.17438e9	0.254479	0.127239	+	0.991872i	$0.459388\pi$
$830$	1.04426e10	0.633920
$831$	−4.90972e10	−2.96793
$832$	9.21348e10	5.54616
$833$	2.15743e10	1.29324
$834$	−3.83776e10	−2.29085
$835$	3.50364e9	0.208265
$836$	−8.52993e9	−0.504921
$837$	−2.28781e10	−1.34859
$838$	−8.81651e9	−0.517538
$839$	−2.04056e10	−1.19284	−0.596420	−	0.802673i	$-0.703411\pi$
$839$	−2.04056e10	−1.19284	−0.596420	+	0.802673i	$0.703411\pi$
$840$	3.44508e9	0.200550
$841$	2.16204e10	1.25336
$842$	−7.38931e9	−0.426591
$843$	2.80531e10	1.61281
$844$	−1.75011e10	−1.00200
$845$	−3.49216e9	−0.199111
$846$	−1.05422e11	−5.98596
$847$	−8.82697e8	−0.0499137
$848$	−1.23943e11	−6.97969
$849$	−3.39130e10	−1.90191
$850$	−3.33098e10	−1.86040
$851$	3.08638e7	0.00171670
$852$	−1.16274e11	−6.44087
$853$	−2.47572e10	−1.36578	−0.682888	−	0.730523i	$-0.739276\pi$
$853$	−2.47572e10	−1.36578	−0.682888	+	0.730523i	$0.739276\pi$
$854$	5.99534e8	0.0329391
$855$	−8.80044e9	−0.481530
$856$	−1.03632e10	−0.564721
$857$	1.28010e9	0.0694724	0.0347362	−	0.999397i	$-0.488941\pi$
$857$	1.28010e9	0.0694724	0.0347362	+	0.999397i	$0.488941\pi$
$858$	3.23712e10	1.74966
$859$	2.68276e10	1.44413	0.722065	−	0.691826i	$-0.243193\pi$
$859$	2.68276e10	1.44413	0.722065	+	0.691826i	$0.243193\pi$
$860$	−4.23387e10	−2.26983
$861$	1.49329e9	0.0797320
$862$	4.34624e10	2.31120
$863$	2.63322e10	1.39460	0.697300	−	0.716780i	$-0.254385\pi$
$863$	2.63322e10	1.39460	0.697300	+	0.716780i	$0.254385\pi$
$864$	−1.86138e11	−9.81833
$865$	1.20335e10	0.632171
$866$	5.40720e10	2.82918
$867$	2.35509e10	1.22727
$868$	−2.05738e9	−0.106782
$869$	8.14565e9	0.421072
$870$	−5.27460e10	−2.71564
$871$	4.48675e9	0.230074
$872$	−8.65858e10	−4.42220
$873$	−7.46203e10	−3.79584
$874$	−7.26213e9	−0.367937
$875$	1.08003e9	0.0545013
$876$	4.52174e10	2.27270
$877$	2.49785e10	1.25045	0.625226	−	0.780443i	$-0.285007\pi$
$877$	2.49785e10	1.25045	0.625226	+	0.780443i	$0.285007\pi$
$878$	5.32599e10	2.65564
$879$	1.53046e10	0.760085
$880$	1.83323e10	0.906833
$881$	2.46572e10	1.21487	0.607433	−	0.794371i	$-0.292199\pi$
$881$	2.46572e10	1.21487	0.607433	+	0.794371i	$0.292199\pi$
$882$	8.77206e10	4.30488
$883$	4.02409e10	1.96700	0.983501	−	0.180903i	$-0.0579021\pi$
$883$	4.02409e10	1.96700	0.983501	+	0.180903i	$0.0579021\pi$
$884$	−8.85259e10	−4.31010
$885$	2.19504e10	1.06449
$886$	6.38336e10	3.08341
$887$	2.76204e10	1.32892	0.664458	−	0.747325i	$-0.268662\pi$
$887$	2.76204e10	1.32892	0.664458	+	0.747325i	$0.268662\pi$
$888$	−5.11878e8	−0.0245313
$889$	1.18945e9	0.0567795
$890$	1.95420e10	0.929191
$891$	−1.50166e10	−0.711212
$892$	−1.19072e10	−0.561738
$893$	1.24333e10	0.584263
$894$	−1.30418e11	−6.10460
$895$	8.39580e9	0.391455
$896$	−6.13938e9	−0.285132
$897$	2.03470e10	0.941299
$898$	−2.63985e10	−1.21650
$899$	2.03333e10	0.933359
$900$	−9.99906e10	−4.57204
$901$	4.80845e10	2.19012
$902$	1.33649e10	0.606378
$903$	3.75990e9	0.169930
$904$	−8.04610e10	−3.62240
$905$	−6.01751e8	−0.0269865
$906$	1.12424e11	5.02237
$907$	−6.91605e9	−0.307774	−0.153887	−	0.988088i	$-0.549179\pi$
$907$	−6.91605e9	−0.307774	−0.153887	+	0.988088i	$0.549179\pi$
$908$	4.03586e10	1.78910
$909$	−6.83310e10	−3.01748
$910$	1.64470e9	0.0723506
$911$	1.85014e10	0.810758	0.405379	−	0.914149i	$-0.367140\pi$
$911$	1.85014e10	0.810758	0.405379	+	0.914149i	$0.367140\pi$
$912$	7.16104e10	3.12604
$913$	−6.12764e9	−0.266468
$914$	−1.06409e10	−0.460964
$915$	5.93611e9	0.256170
$916$	2.56183e10	1.10132
$917$	−2.47536e9	−0.106010
$918$	1.28996e11	5.50333
$919$	1.06473e10	0.452516	0.226258	−	0.974067i	$-0.427351\pi$
$919$	1.06473e10	0.452516	0.226258	+	0.974067i	$0.427351\pi$
$920$	1.93805e10	0.820554
$921$	−3.15834e10	−1.33214
$922$	6.96223e10	2.92543
$923$	−3.58321e10	−1.49991
$924$	−3.13172e9	−0.130596
$925$	−6.78857e7	−0.00282021
$926$	−4.51710e10	−1.86948
$927$	−1.32295e10	−0.545463
$928$	1.65433e11	6.79525
$929$	−1.34280e9	−0.0549487	−0.0274744	−	0.999623i	$-0.508746\pi$
$929$	−1.34280e9	−0.0549487	−0.0274744	+	0.999623i	$0.508746\pi$
$930$	−2.75918e10	−1.12484
$931$	−1.03457e10	−0.420180
$932$	1.09540e11	4.43217
$933$	−1.64583e10	−0.663438
$934$	7.03487e10	2.82515
$935$	−7.11214e9	−0.284551
$936$	−2.32346e11	−9.26127
$937$	−1.46188e10	−0.580529	−0.290265	−	0.956946i	$-0.593743\pi$
$937$	−1.46188e10	−0.580529	−0.290265	+	0.956946i	$0.593743\pi$
$938$	−5.87938e8	−0.0232606
$939$	−8.05329e10	−3.17427
$940$	−5.14028e10	−2.01855
$941$	2.43376e10	0.952169	0.476085	−	0.879399i	$-0.342056\pi$
$941$	2.43376e10	0.952169	0.476085	+	0.879399i	$0.342056\pi$
$942$	5.12774e9	0.199870
$943$	8.40056e9	0.326225
$944$	−1.22979e11	−4.75804
$945$	−1.76935e9	−0.0682030
$946$	3.36511e10	1.29235
$947$	−4.38594e9	−0.167818	−0.0839089	−	0.996473i	$-0.526740\pi$
$947$	−4.38594e9	−0.167818	−0.0839089	+	0.996473i	$0.526740\pi$
$948$	−1.31548e11	−5.01481
$949$	1.39346e10	0.529253
$950$	1.59733e10	0.604451
$951$	−8.74217e9	−0.329600
$952$	7.48811e9	0.281283
$953$	−1.91167e10	−0.715462	−0.357731	−	0.933825i	$-0.616450\pi$
$953$	−1.91167e10	−0.715462	−0.357731	+	0.933825i	$0.616450\pi$
$954$	1.95510e11	7.29038
$955$	1.26568e9	0.0470231
$956$	9.66895e10	3.57913
$957$	3.09510e10	1.14152
$958$	3.46626e10	1.27374
$959$	−1.56743e9	−0.0573881
$960$	−1.19540e11	−4.36077
$961$	−1.68761e10	−0.613397
$962$	−2.44373e8	−0.00884995
$963$	9.71928e9	0.350705
$964$	1.02249e11	3.67612
$965$	7.37374e9	0.264145
$966$	−2.66625e9	−0.0951659
$967$	7.46976e9	0.265653	0.132826	−	0.991139i	$-0.457595\pi$
$967$	7.46976e9	0.265653	0.132826	+	0.991139i	$0.457595\pi$
$968$	8.23558e10	2.91830
$969$	−2.77818e10	−0.980904
$970$	−4.92822e10	−1.73376
$971$	−5.14735e10	−1.80433	−0.902166	−	0.431390i	$-0.858023\pi$
$971$	−5.14735e10	−1.80433	−0.902166	+	0.431390i	$0.858023\pi$
$972$	6.73343e10	2.35182
$973$	1.14417e9	0.0398195
$974$	9.54163e10	3.30877
$975$	−4.47539e10	−1.54637
$976$	−3.32576e10	−1.14503
$977$	−4.55341e10	−1.56209	−0.781044	−	0.624476i	$-0.785312\pi$
$977$	−4.55341e10	−1.56209	−0.781044	+	0.624476i	$0.785312\pi$
$978$	1.12034e11	3.82968
$979$	−1.14671e10	−0.390585
$980$	4.27719e10	1.45167
$981$	8.12061e10	2.74630
$982$	−4.82544e10	−1.62610
$983$	4.86762e9	0.163448	0.0817240	−	0.996655i	$-0.473957\pi$
$983$	4.86762e9	0.163448	0.0817240	+	0.996655i	$0.473957\pi$
$984$	−1.39324e11	−4.66169
$985$	1.25053e10	0.416933
$986$	−1.14647e11	−3.80885
$987$	4.56484e9	0.151118
$988$	4.24514e10	1.40037
$989$	2.11515e10	0.695271
$990$	−2.89178e10	−0.947199
$991$	−4.51418e10	−1.47340	−0.736700	−	0.676220i	$-0.763617\pi$
$991$	−4.51418e10	−1.47340	−0.736700	+	0.676220i	$0.763617\pi$
$992$	8.65393e10	2.81464
$993$	7.88606e10	2.55586
$994$	4.69540e9	0.151642
$995$	−7.94655e9	−0.255740
$996$	9.89580e10	3.17353
$997$	−1.22204e10	−0.390527	−0.195264	−	0.980751i	$-0.562556\pi$
$997$	−1.22204e10	−0.390527	−0.195264	+	0.980751i	$0.562556\pi$
$998$	1.21139e10	0.385767
$999$	2.62895e8	0.00834262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.1	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.1	✓	156	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-22.1152 q^{2} +83.7935 q^{3} +361.080 q^{4} -144.371 q^{5} -1853.11 q^{6} +55.2475 q^{7} -5154.61 q^{8} +4834.35 q^{9} +O(q^{10})\)	\(q-22.1152 q^{2} +83.7935 q^{3} +361.080 q^{4} -144.371 q^{5} -1853.11 q^{6} +55.2475 q^{7} -5154.61 q^{8} +4834.35 q^{9} +3192.79 q^{10} -1873.51 q^{11} +30256.2 q^{12} +9324.01 q^{13} -1221.81 q^{14} -12097.4 q^{15} +67776.6 q^{16} -26294.4 q^{17} -106912. q^{18} +12609.1 q^{19} -52129.6 q^{20} +4629.38 q^{21} +41433.0 q^{22} +26042.8 q^{23} -431922. q^{24} -57281.9 q^{25} -206202. q^{26} +221830. q^{27} +19948.8 q^{28} -197155. q^{29} +267535. q^{30} -103133. q^{31} -839102. q^{32} -156988. q^{33} +581506. q^{34} -7976.16 q^{35} +1.74559e6 q^{36} +1185.12 q^{37} -278853. q^{38} +781291. q^{39} +744177. q^{40} +322567. q^{41} -102380. q^{42} +812182. q^{43} -676487. q^{44} -697941. q^{45} -575941. q^{46} +986058. q^{47} +5.67924e6 q^{48} -820491. q^{49} +1.26680e6 q^{50} -2.20330e6 q^{51} +3.36672e6 q^{52} -1.82870e6 q^{53} -4.90581e6 q^{54} +270481. q^{55} -284779. q^{56} +1.05656e6 q^{57} +4.36012e6 q^{58} -1.81447e6 q^{59} -4.36812e6 q^{60} -490694. q^{61} +2.28081e6 q^{62} +267086. q^{63} +9.88146e6 q^{64} -1.34612e6 q^{65} +3.47181e6 q^{66} +481203. q^{67} -9.49440e6 q^{68} +2.18222e6 q^{69} +176394. q^{70} -3.84299e6 q^{71} -2.49191e7 q^{72} +1.49449e6 q^{73} -26209.0 q^{74} -4.79985e6 q^{75} +4.55291e6 q^{76} -103507. q^{77} -1.72784e7 q^{78} -4.34780e6 q^{79} -9.78500e6 q^{80} +8.01522e6 q^{81} -7.13363e6 q^{82} +3.27067e6 q^{83} +1.67158e6 q^{84} +3.79616e6 q^{85} -1.79615e7 q^{86} -1.65203e7 q^{87} +9.65720e6 q^{88} +6.12067e6 q^{89} +1.54351e7 q^{90} +515129. q^{91} +9.40355e6 q^{92} -8.64189e6 q^{93} -2.18068e7 q^{94} -1.82040e6 q^{95} -7.03112e7 q^{96} -1.54355e7 q^{97} +1.81453e7 q^{98} -9.05719e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9} - 10570 q^{10} - 20090 q^{11} - 58311 q^{12} - 63021 q^{13} - 45057 q^{14} - 36391 q^{15} + 574338 q^{16} - 232394 q^{17} - 92277 q^{18} - 43100 q^{19} - 485568 q^{20} - 231868 q^{21} - 225008 q^{22} - 401950 q^{23} - 503569 q^{24} + 2076291 q^{25} - 530768 q^{26} - 959873 q^{27} - 617816 q^{28} - 1275618 q^{29} - 778474 q^{30} - 485945 q^{31} - 1903692 q^{32} - 1050846 q^{33} - 466263 q^{34} - 1826209 q^{35} + 5276156 q^{36} - 2129902 q^{37} - 2480555 q^{38} - 974653 q^{39} - 937648 q^{40} - 2309325 q^{41} - 2803500 q^{42} - 1756918 q^{43} - 3314520 q^{44} - 7492064 q^{45} - 1323786 q^{46} - 6203828 q^{47} - 7957494 q^{48} + 15095175 q^{49} - 5758152 q^{50} - 1556293 q^{51} - 7587898 q^{52} - 13775068 q^{53} - 6848423 q^{54} - 4045669 q^{55} - 8326655 q^{56} - 9421556 q^{57} - 4938892 q^{58} - 7755758 q^{59} - 5358502 q^{60} - 11693582 q^{61} - 14895366 q^{62} - 9477805 q^{63} + 31311690 q^{64} - 15629670 q^{65} - 5969892 q^{66} - 9560716 q^{67} - 34045735 q^{68} - 17825946 q^{69} - 4291177 q^{70} - 13661197 q^{71} - 21516953 q^{72} - 17125972 q^{73} - 19749599 q^{74} - 21752079 q^{75} - 15479244 q^{76} - 55632329 q^{77} - 12746879 q^{78} - 9534338 q^{79} - 61267539 q^{80} + 58468208 q^{81} - 29265046 q^{82} - 38447793 q^{83} - 33520873 q^{84} - 22365109 q^{85} - 21208733 q^{86} - 27018273 q^{87} - 40855385 q^{88} - 62436196 q^{89} - 19477679 q^{90} - 20640165 q^{91} - 78867734 q^{92} - 77801528 q^{93} + 2996793 q^{94} - 30557422 q^{95} - 82397286 q^{96} - 56264748 q^{97} - 72954494 q^{98} - 43444577 q^{99}+O(q^{100}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9 - 10570 * q^10 - 20090 * q^11 - 58311 * q^12 - 63021 * q^13 - 45057 * q^14 - 36391 * q^15 + 574338 * q^16 - 232394 * q^17 - 92277 * q^18 - 43100 * q^19 - 485568 * q^20 - 231868 * q^21 - 225008 * q^22 - 401950 * q^23 - 503569 * q^24 + 2076291 * q^25 - 530768 * q^26 - 959873 * q^27 - 617816 * q^28 - 1275618 * q^29 - 778474 * q^30 - 485945 * q^31 - 1903692 * q^32 - 1050846 * q^33 - 466263 * q^34 - 1826209 * q^35 + 5276156 * q^36 - 2129902 * q^37 - 2480555 * q^38 - 974653 * q^39 - 937648 * q^40 - 2309325 * q^41 - 2803500 * q^42 - 1756918 * q^43 - 3314520 * q^44 - 7492064 * q^45 - 1323786 * q^46 - 6203828 * q^47 - 7957494 * q^48 + 15095175 * q^49 - 5758152 * q^50 - 1556293 * q^51 - 7587898 * q^52 - 13775068 * q^53 - 6848423 * q^54 - 4045669 * q^55 - 8326655 * q^56 - 9421556 * q^57 - 4938892 * q^58 - 7755758 * q^59 - 5358502 * q^60 - 11693582 * q^61 - 14895366 * q^62 - 9477805 * q^63 + 31311690 * q^64 - 15629670 * q^65 - 5969892 * q^66 - 9560716 * q^67 - 34045735 * q^68 - 17825946 * q^69 - 4291177 * q^70 - 13661197 * q^71 - 21516953 * q^72 - 17125972 * q^73 - 19749599 * q^74 - 21752079 * q^75 - 15479244 * q^76 - 55632329 * q^77 - 12746879 * q^78 - 9534338 * q^79 - 61267539 * q^80 + 58468208 * q^81 - 29265046 * q^82 - 38447793 * q^83 - 33520873 * q^84 - 22365109 * q^85 - 21208733 * q^86 - 27018273 * q^87 - 40855385 * q^88 - 62436196 * q^89 - 19477679 * q^90 - 20640165 * q^91 - 78867734 * q^92 - 77801528 * q^93 + 2996793 * q^94 - 30557422 * q^95 - 82397286 * q^96 - 56264748 * q^97 - 72954494 * q^98 - 43444577 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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