LMFDB - Embedded newform 547.8.a.a.1.15

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			1.15
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)

$f(q)$	$=$	$q-19.7400 q^{2} -43.2832 q^{3} +261.668 q^{4} -352.760 q^{5} +854.411 q^{6} -1491.16 q^{7} -2638.61 q^{8} -313.564 q^{9} +O(q^{10})$	\(q-19.7400 q^{2} -43.2832 q^{3} +261.668 q^{4} -352.760 q^{5} +854.411 q^{6} -1491.16 q^{7} -2638.61 q^{8} -313.564 q^{9} +6963.48 q^{10} +8411.59 q^{11} -11325.8 q^{12} -14676.9 q^{13} +29435.5 q^{14} +15268.6 q^{15} +18592.7 q^{16} -32014.2 q^{17} +6189.76 q^{18} -25624.5 q^{19} -92306.0 q^{20} +64542.2 q^{21} -166045. q^{22} +23718.7 q^{23} +114207. q^{24} +46314.5 q^{25} +289723. q^{26} +108232. q^{27} -390189. q^{28} -236883. q^{29} -301402. q^{30} -72430.4 q^{31} -29277.4 q^{32} -364081. q^{33} +631960. q^{34} +526022. q^{35} -82049.8 q^{36} -476959. q^{37} +505828. q^{38} +635265. q^{39} +930795. q^{40} +621232. q^{41} -1.27406e6 q^{42} -675581. q^{43} +2.20105e6 q^{44} +110613. q^{45} -468207. q^{46} -765868. q^{47} -804750. q^{48} +1.40002e6 q^{49} -914249. q^{50} +1.38568e6 q^{51} -3.84049e6 q^{52} -590513. q^{53} -2.13651e6 q^{54} -2.96727e6 q^{55} +3.93459e6 q^{56} +1.10911e6 q^{57} +4.67606e6 q^{58} +83278.3 q^{59} +3.99530e6 q^{60} +1.49686e6 q^{61} +1.42978e6 q^{62} +467575. q^{63} -1.80192e6 q^{64} +5.17743e6 q^{65} +7.18696e6 q^{66} -3.00021e6 q^{67} -8.37708e6 q^{68} -1.02662e6 q^{69} -1.03837e7 q^{70} -1.55307e6 q^{71} +827374. q^{72} +657646. q^{73} +9.41517e6 q^{74} -2.00464e6 q^{75} -6.70511e6 q^{76} -1.25430e7 q^{77} -1.25401e7 q^{78} -3.59582e6 q^{79} -6.55875e6 q^{80} -3.99888e6 q^{81} -1.22631e7 q^{82} -545510. q^{83} +1.68886e7 q^{84} +1.12933e7 q^{85} +1.33360e7 q^{86} +1.02530e7 q^{87} -2.21949e7 q^{88} -1.31179e6 q^{89} -2.18350e6 q^{90} +2.18857e7 q^{91} +6.20642e6 q^{92} +3.13502e6 q^{93} +1.51182e7 q^{94} +9.03929e6 q^{95} +1.26722e6 q^{96} -343213. q^{97} -2.76364e7 q^{98} -2.63757e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−19.7400	−1.74479	−0.872394	−	0.488804i	$-0.837433\pi$
$2$	−19.7400	−1.74479	−0.872394	+	0.488804i	$0.837433\pi$
$3$	−43.2832	−0.925540	−0.462770	−	0.886478i	$-0.653144\pi$
$3$	−43.2832	−0.925540	−0.462770	+	0.886478i	$0.653144\pi$
$4$	261.668	2.04428
$5$	−352.760	−1.26207	−0.631036	−	0.775754i	$-0.717370\pi$
$5$	−352.760	−1.26207	−0.631036	+	0.775754i	$0.717370\pi$
$6$	854.411	1.61487
$7$	−1491.16	−1.64317	−0.821583	−	0.570089i	$-0.806909\pi$
$7$	−1491.16	−1.64317	−0.821583	+	0.570089i	$0.806909\pi$
$8$	−2638.61	−1.82205
$9$	−313.564	−0.143376
$10$	6963.48	2.20205
$11$	8411.59	1.90548	0.952739	−	0.303791i	$-0.0982523\pi$
$11$	8411.59	1.90548	0.952739	+	0.303791i	$0.0982523\pi$
$12$	−11325.8	−1.89206
$13$	−14676.9	−1.85282	−0.926411	−	0.376514i	$-0.877123\pi$
$13$	−14676.9	−1.85282	−0.926411	+	0.376514i	$0.877123\pi$
$14$	29435.5	2.86697
$15$	15268.6	1.16810
$16$	18592.7	1.13481
$17$	−32014.2	−1.58041	−0.790207	−	0.612840i	$-0.790027\pi$
$17$	−32014.2	−1.58041	−0.790207	+	0.612840i	$0.790027\pi$
$18$	6189.76	0.250161
$19$	−25624.5	−0.857073	−0.428536	−	0.903524i	$-0.640971\pi$
$19$	−25624.5	−0.857073	−0.428536	+	0.903524i	$0.640971\pi$
$20$	−92306.0	−2.58003
$21$	64542.2	1.52081
$22$	−166045.	−3.32465
$23$	23718.7	0.406483	0.203242	−	0.979129i	$-0.434852\pi$
$23$	23718.7	0.406483	0.203242	+	0.979129i	$0.434852\pi$
$24$	114207.	1.68638
$25$	46314.5	0.592826
$26$	289723.	3.23278
$27$	108232.	1.05824
$28$	−390189.	−3.35909
$29$	−236883.	−1.80360	−0.901800	−	0.432154i	$-0.857754\pi$
$29$	−236883.	−1.80360	−0.901800	+	0.432154i	$0.857754\pi$
$30$	−301402.	−2.03808
$31$	−72430.4	−0.436672	−0.218336	−	0.975874i	$-0.570063\pi$
$31$	−72430.4	−0.436672	−0.218336	+	0.975874i	$0.570063\pi$
$32$	−29277.4	−0.157946
$33$	−364081.	−1.76360
$34$	631960.	2.75749
$35$	526022.	2.07379
$36$	−82049.8	−0.293102
$37$	−476959.	−1.54801	−0.774007	−	0.633177i	$-0.781751\pi$
$37$	−476959.	−1.54801	−0.774007	+	0.633177i	$0.781751\pi$
$38$	505828.	1.49541
$39$	635265.	1.71486
$40$	930795.	2.29956
$41$	621232.	1.40770	0.703850	−	0.710349i	$-0.251463\pi$
$41$	621232.	1.40770	0.703850	+	0.710349i	$0.251463\pi$
$42$	−1.27406e6	−2.65350
$43$	−675581.	−1.29580	−0.647900	−	0.761725i	$-0.724353\pi$
$43$	−675581.	−1.29580	−0.647900	+	0.761725i	$0.724353\pi$
$44$	2.20105e6	3.89533
$45$	110613.	0.180951
$46$	−468207.	−0.709227
$47$	−765868.	−1.07600	−0.537999	−	0.842946i	$-0.680820\pi$
$47$	−765868.	−1.07600	−0.537999	+	0.842946i	$0.680820\pi$
$48$	−804750.	−1.05031
$49$	1.40002e6	1.69999
$50$	−914249.	−1.03436
$51$	1.38568e6	1.46274
$52$	−3.84049e6	−3.78769
$53$	−590513.	−0.544834	−0.272417	−	0.962179i	$-0.587823\pi$
$53$	−590513.	−0.544834	−0.272417	+	0.962179i	$0.587823\pi$
$54$	−2.13651e6	−1.84640
$55$	−2.96727e6	−2.40485
$56$	3.93459e6	2.99393
$57$	1.10911e6	0.793255
$58$	4.67606e6	3.14690
$59$	83278.3	0.0527898	0.0263949	−	0.999652i	$-0.491597\pi$
$59$	83278.3	0.0527898	0.0263949	+	0.999652i	$0.491597\pi$
$60$	3.99530e6	2.38792
$61$	1.49686e6	0.844357	0.422178	−	0.906513i	$-0.361266\pi$
$61$	1.49686e6	0.844357	0.422178	+	0.906513i	$0.361266\pi$
$62$	1.42978e6	0.761899
$63$	467575.	0.235591
$64$	−1.80192e6	−0.859224
$65$	5.17743e6	2.33839
$66$	7.18696e6	3.07710
$67$	−3.00021e6	−1.21868	−0.609340	−	0.792909i	$-0.708566\pi$
$67$	−3.00021e6	−1.21868	−0.609340	+	0.792909i	$0.708566\pi$
$68$	−8.37708e6	−3.23081
$69$	−1.02662e6	−0.376217
$70$	−1.03837e7	−3.61833
$71$	−1.55307e6	−0.514976	−0.257488	−	0.966281i	$-0.582895\pi$
$71$	−1.55307e6	−0.514976	−0.257488	+	0.966281i	$0.582895\pi$
$72$	827374.	0.261239
$73$	657646.	0.197862	0.0989309	−	0.995094i	$-0.468458\pi$
$73$	657646.	0.197862	0.0989309	+	0.995094i	$0.468458\pi$
$74$	9.41517e6	2.70096
$75$	−2.00464e6	−0.548684
$76$	−6.70511e6	−1.75210
$77$	−1.25430e7	−3.13102
$78$	−1.25401e7	−2.99207
$79$	−3.59582e6	−0.820546	−0.410273	−	0.911963i	$-0.634567\pi$
$79$	−3.59582e6	−0.820546	−0.410273	+	0.911963i	$0.634567\pi$
$80$	−6.55875e6	−1.43221
$81$	−3.99888e6	−0.836067
$82$	−1.22631e7	−2.45614
$83$	−545510.	−0.104720	−0.0523599	−	0.998628i	$-0.516674\pi$
$83$	−545510.	−0.104720	−0.0523599	+	0.998628i	$0.516674\pi$
$84$	1.68886e7	3.10897
$85$	1.12933e7	1.99460
$86$	1.33360e7	2.26089
$87$	1.02530e7	1.66930
$88$	−2.21949e7	−3.47187
$89$	−1.31179e6	−0.197242	−0.0986210	−	0.995125i	$-0.531443\pi$
$89$	−1.31179e6	−0.197242	−0.0986210	+	0.995125i	$0.531443\pi$
$90$	−2.18350e6	−0.315722
$91$	2.18857e7	3.04449
$92$	6.20642e6	0.830967
$93$	3.13502e6	0.404157
$94$	1.51182e7	1.87739
$95$	9.03929e6	1.08169
$96$	1.26722e6	0.146185
$97$	−343213.	−0.0381823	−0.0190912	−	0.999818i	$-0.506077\pi$
$97$	−343213.	−0.0381823	−0.0190912	+	0.999818i	$0.506077\pi$
$98$	−2.76364e7	−2.96613
$99$	−2.63757e6	−0.273201
$100$	1.21190e7	1.21190
$101$	−6.88778e6	−0.665203	−0.332602	−	0.943067i	$-0.607926\pi$
$101$	−6.88778e6	−0.665203	−0.332602	+	0.943067i	$0.607926\pi$
$102$	−2.73533e7	−2.55216
$103$	2.16480e7	1.95203	0.976016	−	0.217698i	$-0.0698548\pi$
$103$	2.16480e7	1.95203	0.976016	+	0.217698i	$0.0698548\pi$
$104$	3.87267e7	3.37593
$105$	−2.27679e7	−1.91938
$106$	1.16567e7	0.950619
$107$	6.33338e6	0.499795	0.249898	−	0.968272i	$-0.419603\pi$
$107$	6.33338e6	0.499795	0.249898	+	0.968272i	$0.419603\pi$
$108$	2.83210e7	2.16334
$109$	5.26757e6	0.389599	0.194799	−	0.980843i	$-0.437594\pi$
$109$	5.26757e6	0.389599	0.194799	+	0.980843i	$0.437594\pi$
$110$	5.85740e7	4.19595
$111$	2.06443e7	1.43275
$112$	−2.77247e7	−1.86467
$113$	1.27154e7	0.829005	0.414503	−	0.910048i	$-0.363956\pi$
$113$	1.27154e7	0.829005	0.414503	+	0.910048i	$0.363956\pi$
$114$	−2.18939e7	−1.38406
$115$	−8.36700e6	−0.513011
$116$	−6.19846e7	−3.68707
$117$	4.60216e6	0.265651
$118$	−1.64392e6	−0.0921070
$119$	4.77383e7	2.59688
$120$	−4.02878e7	−2.12833
$121$	5.12677e7	2.63085
$122$	−2.95480e7	−1.47322
$123$	−2.68889e7	−1.30288
$124$	−1.89527e7	−0.892680
$125$	1.12215e7	0.513883
$126$	−9.22993e6	−0.411057
$127$	3.19372e7	1.38352	0.691758	−	0.722130i	$-0.256837\pi$
$127$	3.19372e7	1.38352	0.691758	+	0.722130i	$0.256837\pi$
$128$	3.93175e7	1.65711
$129$	2.92413e7	1.19931
$130$	−1.02203e8	−4.08000
$131$	1.44368e7	0.561076	0.280538	−	0.959843i	$-0.409487\pi$
$131$	1.44368e7	0.561076	0.280538	+	0.959843i	$0.409487\pi$
$132$	−9.52683e7	−3.60529
$133$	3.82102e7	1.40831
$134$	5.92242e7	2.12634
$135$	−3.81801e7	−1.33558
$136$	8.44729e7	2.87959
$137$	3.02818e7	1.00614	0.503071	−	0.864245i	$-0.332203\pi$
$137$	3.02818e7	1.00614	0.503071	+	0.864245i	$0.332203\pi$
$138$	2.02655e7	0.656418
$139$	−3.32116e7	−1.04891	−0.524455	−	0.851438i	$-0.675731\pi$
$139$	−3.32116e7	−1.04891	−0.524455	+	0.851438i	$0.675731\pi$
$140$	1.37643e8	4.23942
$141$	3.31492e7	0.995878
$142$	3.06576e7	0.898524
$143$	−1.23456e8	−3.53051
$144$	−5.82999e6	−0.162704
$145$	8.35627e7	2.27627
$146$	−1.29819e7	−0.345227
$147$	−6.05973e7	−1.57341
$148$	−1.24805e8	−3.16458
$149$	4.39436e7	1.08829	0.544144	−	0.838992i	$-0.316855\pi$
$149$	4.39436e7	1.08829	0.544144	+	0.838992i	$0.316855\pi$
$150$	3.95716e7	0.957337
$151$	−4.95692e6	−0.117164	−0.0585818	−	0.998283i	$-0.518658\pi$
$151$	−4.95692e6	−0.117164	−0.0585818	+	0.998283i	$0.518658\pi$
$152$	6.76130e7	1.56163
$153$	1.00385e7	0.226594
$154$	2.47600e8	5.46296
$155$	2.55505e7	0.551111
$156$	1.66228e8	3.50566
$157$	1.79990e7	0.371192	0.185596	−	0.982626i	$-0.440578\pi$
$157$	1.79990e7	0.371192	0.185596	+	0.982626i	$0.440578\pi$
$158$	7.09815e7	1.43168
$159$	2.55593e7	0.504265
$160$	1.03279e7	0.199339
$161$	−3.53684e7	−0.667920
$162$	7.89380e7	1.45876
$163$	2.11409e7	0.382355	0.191177	−	0.981555i	$-0.438769\pi$
$163$	2.11409e7	0.382355	0.191177	+	0.981555i	$0.438769\pi$
$164$	1.62556e8	2.87773
$165$	1.28433e8	2.22578
$166$	1.07684e7	0.182714
$167$	−2.70117e7	−0.448791	−0.224395	−	0.974498i	$-0.572041\pi$
$167$	−2.70117e7	−0.448791	−0.224395	+	0.974498i	$0.572041\pi$
$168$	−1.70302e8	−2.77100
$169$	1.52664e8	2.43295
$170$	−2.22930e8	−3.48015
$171$	8.03493e6	0.122884
$172$	−1.76778e8	−2.64898
$173$	6.77527e7	0.994867	0.497433	−	0.867502i	$-0.334276\pi$
$173$	6.77527e7	0.994867	0.497433	+	0.867502i	$0.334276\pi$
$174$	−2.02395e8	−2.91258
$175$	−6.90624e7	−0.974111
$176$	1.56394e8	2.16235
$177$	−3.60455e6	−0.0488591
$178$	2.58948e7	0.344145
$179$	−3.61396e7	−0.470975	−0.235488	−	0.971877i	$-0.575669\pi$
$179$	−3.61396e7	−0.470975	−0.235488	+	0.971877i	$0.575669\pi$
$180$	2.89439e7	0.369916
$181$	−9.60059e7	−1.20344	−0.601718	−	0.798709i	$-0.705517\pi$
$181$	−9.60059e7	−1.20344	−0.601718	+	0.798709i	$0.705517\pi$
$182$	−4.32023e8	−5.31199
$183$	−6.47888e7	−0.781486
$184$	−6.25843e7	−0.740633
$185$	1.68252e8	1.95371
$186$	−6.18853e7	−0.705168
$187$	−2.69290e8	−3.01144
$188$	−2.00403e8	−2.19964
$189$	−1.61392e8	−1.73886
$190$	−1.78436e8	−1.88731
$191$	−1.52473e8	−1.58335	−0.791674	−	0.610944i	$-0.790790\pi$
$191$	−1.52473e8	−1.58335	−0.791674	+	0.610944i	$0.790790\pi$
$192$	7.79931e7	0.795246
$193$	6.90000e7	0.690873	0.345437	−	0.938442i	$-0.387731\pi$
$193$	6.90000e7	0.690873	0.345437	+	0.938442i	$0.387731\pi$
$194$	6.77503e6	0.0666201
$195$	−2.24096e8	−2.16428
$196$	3.66340e8	3.47527
$197$	−1.10124e8	−1.02625	−0.513124	−	0.858315i	$-0.671512\pi$
$197$	−1.10124e8	−1.02625	−0.513124	+	0.858315i	$0.671512\pi$
$198$	5.20658e7	0.476677
$199$	−5.80306e6	−0.0522001	−0.0261001	−	0.999659i	$-0.508309\pi$
$199$	−5.80306e6	−0.0522001	−0.0261001	+	0.999659i	$0.508309\pi$
$200$	−1.22206e8	−1.08016
$201$	1.29859e8	1.12794
$202$	1.35965e8	1.16064
$203$	3.53230e8	2.96361
$204$	3.62587e8	2.99024
$205$	−2.19146e8	−1.77662
$206$	−4.27331e8	−3.40588
$207$	−7.43733e6	−0.0582802
$208$	−2.72883e8	−2.10259
$209$	−2.15543e8	−1.63313
$210$	4.49439e8	3.34891
$211$	1.70538e8	1.24978	0.624888	−	0.780714i	$-0.285144\pi$
$211$	1.70538e8	1.24978	0.624888	+	0.780714i	$0.285144\pi$
$212$	−1.54518e8	−1.11379
$213$	6.72219e7	0.476631
$214$	−1.25021e8	−0.872036
$215$	2.38318e8	1.63539
$216$	−2.85583e8	−1.92817
$217$	1.08005e8	0.717524
$218$	−1.03982e8	−0.679767
$219$	−2.84650e7	−0.183129
$220$	−7.76440e8	−4.91619
$221$	4.69870e8	2.92823
$222$	−4.07519e8	−2.49984
$223$	−3.29132e7	−0.198748	−0.0993740	−	0.995050i	$-0.531684\pi$
$223$	−3.29132e7	−0.198748	−0.0993740	+	0.995050i	$0.531684\pi$
$224$	4.36574e7	0.259531
$225$	−1.45226e7	−0.0849973
$226$	−2.51003e8	−1.44644
$227$	−2.50348e8	−1.42054	−0.710270	−	0.703930i	$-0.751427\pi$
$227$	−2.50348e8	−1.42054	−0.710270	+	0.703930i	$0.751427\pi$
$228$	2.90219e8	1.62164
$229$	6.12837e7	0.337226	0.168613	−	0.985682i	$-0.446071\pi$
$229$	6.12837e7	0.337226	0.168613	+	0.985682i	$0.446071\pi$
$230$	1.65165e8	0.895096
$231$	5.42903e8	2.89788
$232$	6.25040e8	3.28625
$233$	2.28557e8	1.18372	0.591858	−	0.806042i	$-0.298394\pi$
$233$	2.28557e8	1.18372	0.591858	+	0.806042i	$0.298394\pi$
$234$	−9.08467e7	−0.463504
$235$	2.70167e8	1.35799
$236$	2.17913e7	0.107917
$237$	1.55638e8	0.759447
$238$	−9.42354e8	−4.53101
$239$	1.98009e8	0.938193	0.469097	−	0.883147i	$-0.344580\pi$
$239$	1.98009e8	0.938193	0.469097	+	0.883147i	$0.344580\pi$
$240$	2.83884e8	1.32556
$241$	−6.24761e7	−0.287511	−0.143755	−	0.989613i	$-0.545918\pi$
$241$	−6.24761e7	−0.287511	−0.143755	+	0.989613i	$0.545918\pi$
$242$	−1.01203e9	−4.59026
$243$	−6.36199e7	−0.284427
$244$	3.91680e8	1.72610
$245$	−4.93870e8	−2.14551
$246$	5.30787e8	2.27325
$247$	3.76089e8	1.58800
$248$	1.91116e8	0.795637
$249$	2.36114e7	0.0969224
$250$	−2.21512e8	−0.896616
$251$	−1.52621e8	−0.609195	−0.304598	−	0.952481i	$-0.598522\pi$
$251$	−1.52621e8	−0.609195	−0.304598	+	0.952481i	$0.598522\pi$
$252$	1.22349e8	0.481615
$253$	1.99512e8	0.774545
$254$	−6.30441e8	−2.41394
$255$	−4.88811e8	−1.84608
$256$	−5.45482e8	−2.03208
$257$	−4.20606e8	−1.54564	−0.772822	−	0.634623i	$-0.781155\pi$
$257$	−4.20606e8	−1.54564	−0.772822	+	0.634623i	$0.781155\pi$
$258$	−5.77224e8	−2.09255
$259$	7.11222e8	2.54364
$260$	1.35477e9	4.78034
$261$	7.42779e7	0.258594
$262$	−2.84983e8	−0.978959
$263$	3.16639e8	1.07329	0.536647	−	0.843807i	$-0.319691\pi$
$263$	3.16639e8	1.07329	0.536647	+	0.843807i	$0.319691\pi$
$264$	9.60667e8	3.21336
$265$	2.08309e8	0.687619
$266$	−7.54271e8	−2.45721
$267$	5.67785e7	0.182555
$268$	−7.85059e8	−2.49133
$269$	1.16868e8	0.366070	0.183035	−	0.983106i	$-0.441408\pi$
$269$	1.16868e8	0.366070	0.183035	+	0.983106i	$0.441408\pi$
$270$	7.53675e8	2.33029
$271$	−4.94256e8	−1.50855	−0.754275	−	0.656558i	$-0.772012\pi$
$271$	−4.94256e8	−1.50855	−0.754275	+	0.656558i	$0.772012\pi$
$272$	−5.95229e8	−1.79346
$273$	−9.47282e8	−2.81780
$274$	−5.97763e8	−1.75550
$275$	3.89579e8	1.12962
$276$	−2.68634e8	−0.769093
$277$	1.01478e8	0.286874	0.143437	−	0.989659i	$-0.454185\pi$
$277$	1.01478e8	0.286874	0.143437	+	0.989659i	$0.454185\pi$
$278$	6.55598e8	1.83013
$279$	2.27116e7	0.0626084
$280$	−1.38797e9	−3.77855
$281$	5.61245e8	1.50897	0.754485	−	0.656318i	$-0.227887\pi$
$281$	5.61245e8	1.50897	0.754485	+	0.656318i	$0.227887\pi$
$282$	−6.54366e8	−1.73760
$283$	−2.10007e8	−0.550785	−0.275392	−	0.961332i	$-0.588808\pi$
$283$	−2.10007e8	−0.550785	−0.275392	+	0.961332i	$0.588808\pi$
$284$	−4.06389e8	−1.05276
$285$	−3.91250e8	−1.00114
$286$	2.43703e9	6.15999
$287$	−9.26356e8	−2.31308
$288$	9.18035e6	0.0226457
$289$	6.14568e8	1.49771
$290$	−1.64953e9	−3.97161
$291$	1.48554e7	0.0353393
$292$	1.72085e8	0.404485
$293$	−4.96234e8	−1.15252	−0.576262	−	0.817265i	$-0.695489\pi$
$293$	−4.96234e8	−1.15252	−0.576262	+	0.817265i	$0.695489\pi$
$294$	1.19619e9	2.74527
$295$	−2.93773e7	−0.0666245
$296$	1.25851e9	2.82056
$297$	9.10407e8	2.01645
$298$	−8.67447e8	−1.89883
$299$	−3.48117e8	−0.753141
$300$	−5.24551e8	−1.12166
$301$	1.00740e9	2.12921
$302$	9.78497e7	0.204426
$303$	2.98125e8	0.615672
$304$	−4.76428e8	−0.972612
$305$	−5.28031e8	−1.06564
$306$	−1.98160e8	−0.395359
$307$	4.07021e8	0.802846	0.401423	−	0.915893i	$-0.368516\pi$
$307$	4.07021e8	0.802846	0.401423	+	0.915893i	$0.368516\pi$
$308$	−3.28211e9	−6.40068
$309$	−9.36994e8	−1.80668
$310$	−5.04368e8	−0.961572
$311$	−6.40470e7	−0.120736	−0.0603681	−	0.998176i	$-0.519227\pi$
$311$	−6.40470e7	−0.120736	−0.0603681	+	0.998176i	$0.519227\pi$
$312$	−1.67622e9	−3.12456
$313$	−4.69412e8	−0.865265	−0.432633	−	0.901570i	$-0.642415\pi$
$313$	−4.69412e8	−0.865265	−0.432633	+	0.901570i	$0.642415\pi$
$314$	−3.55300e8	−0.647651
$315$	−1.64942e8	−0.297333
$316$	−9.40910e8	−1.67743
$317$	−4.32592e8	−0.762730	−0.381365	−	0.924425i	$-0.624546\pi$
$317$	−4.32592e8	−0.762730	−0.381365	+	0.924425i	$0.624546\pi$
$318$	−5.04541e8	−0.879835
$319$	−1.99256e9	−3.43672
$320$	6.35647e8	1.08440
$321$	−2.74129e8	−0.462580
$322$	6.98172e8	1.16538
$323$	8.20347e8	1.35453
$324$	−1.04638e9	−1.70916
$325$	−6.79755e8	−1.09840
$326$	−4.17321e8	−0.667128
$327$	−2.27997e8	−0.360589
$328$	−1.63919e9	−2.56490
$329$	1.14203e9	1.76804
$330$	−2.53527e9	−3.88352
$331$	−5.07422e8	−0.769080	−0.384540	−	0.923108i	$-0.625640\pi$
$331$	−5.07422e8	−0.769080	−0.384540	+	0.923108i	$0.625640\pi$
$332$	−1.42742e8	−0.214077
$333$	1.49557e8	0.221949
$334$	5.33211e8	0.783044
$335$	1.05835e9	1.53806
$336$	1.20001e9	1.72583
$337$	9.60912e8	1.36766	0.683831	−	0.729640i	$-0.260312\pi$
$337$	9.60912e8	1.36766	0.683831	+	0.729640i	$0.260312\pi$
$338$	−3.01359e9	−4.24498
$339$	−5.50365e8	−0.767277
$340$	2.95510e9	4.07752
$341$	−6.09255e8	−0.832068
$342$	−1.58610e8	−0.214407
$343$	−8.59617e8	−1.15021
$344$	1.78259e9	2.36101
$345$	3.62150e8	0.474812
$346$	−1.33744e9	−1.73583
$347$	−8.93972e8	−1.14860	−0.574302	−	0.818643i	$-0.694727\pi$
$347$	−8.93972e8	−1.14860	−0.574302	+	0.818643i	$0.694727\pi$
$348$	2.68289e9	3.41252
$349$	−5.33051e8	−0.671243	−0.335621	−	0.941997i	$-0.608946\pi$
$349$	−5.33051e8	−0.671243	−0.335621	+	0.941997i	$0.608946\pi$
$350$	1.36329e9	1.69962
$351$	−1.58852e9	−1.96073
$352$	−2.46270e8	−0.300962
$353$	2.47878e8	0.299934	0.149967	−	0.988691i	$-0.452083\pi$
$353$	2.47878e8	0.299934	0.149967	+	0.988691i	$0.452083\pi$
$354$	7.11539e7	0.0852486
$355$	5.47861e8	0.649937
$356$	−3.43254e8	−0.403218
$357$	−2.06627e9	−2.40352
$358$	7.13396e8	0.821751
$359$	7.30862e8	0.833690	0.416845	−	0.908977i	$-0.363136\pi$
$359$	7.30862e8	0.833690	0.416845	+	0.908977i	$0.363136\pi$
$360$	−2.91864e8	−0.329702
$361$	−2.37257e8	−0.265426
$362$	1.89516e9	2.09974
$363$	−2.21903e9	−2.43495
$364$	5.72678e9	6.22380
$365$	−2.31991e8	−0.249716
$366$	1.27893e9	1.36353
$367$	1.95056e8	0.205982	0.102991	−	0.994682i	$-0.467159\pi$
$367$	1.95056e8	0.205982	0.102991	+	0.994682i	$0.467159\pi$
$368$	4.40993e8	0.461280
$369$	−1.94796e8	−0.201831
$370$	−3.32130e9	−3.40880
$371$	8.80550e8	0.895252
$372$	8.20335e8	0.826211
$373$	−4.57447e8	−0.456415	−0.228208	−	0.973613i	$-0.573286\pi$
$373$	−4.57447e8	−0.456415	−0.228208	+	0.973613i	$0.573286\pi$
$374$	5.31579e9	5.25433
$375$	−4.85701e8	−0.475619
$376$	2.02083e9	1.96052
$377$	3.47671e9	3.34175
$378$	3.18588e9	3.03395
$379$	1.73912e9	1.64094	0.820471	−	0.571688i	$-0.193711\pi$
$379$	1.73912e9	1.64094	0.820471	+	0.571688i	$0.193711\pi$
$380$	2.36529e9	2.21127
$381$	−1.38234e9	−1.28050
$382$	3.00982e9	2.76260
$383$	−2.45142e8	−0.222957	−0.111479	−	0.993767i	$-0.535559\pi$
$383$	−2.45142e8	−0.222957	−0.111479	+	0.993767i	$0.535559\pi$
$384$	−1.70179e9	−1.53372
$385$	4.42468e9	3.95157
$386$	−1.36206e9	−1.20543
$387$	2.11838e8	0.185787
$388$	−8.98079e7	−0.0780555
$389$	−1.42786e9	−1.22988	−0.614941	−	0.788573i	$-0.710820\pi$
$389$	−1.42786e9	−1.22988	−0.614941	+	0.788573i	$0.710820\pi$
$390$	4.42366e9	3.77620
$391$	−7.59333e8	−0.642412
$392$	−3.69410e9	−3.09747
$393$	−6.24872e8	−0.519298
$394$	2.17386e9	1.79058
$395$	1.26846e9	1.03559
$396$	−6.90169e8	−0.558499
$397$	4.81907e8	0.386541	0.193271	−	0.981145i	$-0.438090\pi$
$397$	4.81907e8	0.386541	0.193271	+	0.981145i	$0.438090\pi$
$398$	1.14553e8	0.0910781
$399$	−1.65386e9	−1.30345
$400$	8.61111e8	0.672743
$401$	−2.07317e9	−1.60557	−0.802787	−	0.596266i	$-0.796651\pi$
$401$	−2.07317e9	−1.60557	−0.802787	+	0.596266i	$0.796651\pi$
$402$	−2.56341e9	−1.96801
$403$	1.06306e9	0.809075
$404$	−1.80231e9	−1.35986
$405$	1.41064e9	1.05518
$406$	−6.97276e9	−5.17087
$407$	−4.01198e9	−2.94971
$408$	−3.65626e9	−2.66518
$409$	−6.07245e8	−0.438866	−0.219433	−	0.975628i	$-0.570421\pi$
$409$	−6.07245e8	−0.438866	−0.219433	+	0.975628i	$0.570421\pi$
$410$	4.32594e9	3.09982
$411$	−1.31069e9	−0.931225
$412$	5.66458e9	3.99050
$413$	−1.24181e8	−0.0867424
$414$	1.46813e8	0.101686
$415$	1.92434e8	0.132164
$416$	4.29703e8	0.292645
$417$	1.43751e9	0.970808
$418$	4.25482e9	2.84947
$419$	1.21116e9	0.804364	0.402182	−	0.915560i	$-0.368252\pi$
$419$	1.21116e9	0.804364	0.402182	+	0.915560i	$0.368252\pi$
$420$	−5.95763e9	−3.92375
$421$	3.33352e8	0.217729	0.108864	−	0.994057i	$-0.465279\pi$
$421$	3.33352e8	0.217729	0.108864	+	0.994057i	$0.465279\pi$
$422$	−3.36642e9	−2.18059
$423$	2.40149e8	0.154273
$424$	1.55813e9	0.992714
$425$	−1.48272e9	−0.936911
$426$	−1.32696e9	−0.831619
$427$	−2.23206e9	−1.38742
$428$	1.65724e9	1.02172
$429$	5.34359e9	3.26763
$430$	−4.70440e9	−2.85341
$431$	−2.09768e9	−1.26203	−0.631013	−	0.775772i	$-0.717361\pi$
$431$	−2.09768e9	−1.26203	−0.631013	+	0.775772i	$0.717361\pi$
$432$	2.01233e9	1.20090
$433$	1.13986e9	0.674753	0.337377	−	0.941370i	$-0.390460\pi$
$433$	1.13986e9	0.674753	0.337377	+	0.941370i	$0.390460\pi$
$434$	−2.13203e9	−1.25193
$435$	−3.61686e9	−2.10678
$436$	1.37836e9	0.796450
$437$	−6.07779e8	−0.348386
$438$	5.61900e8	0.319521
$439$	2.71525e9	1.53174	0.765868	−	0.642998i	$-0.222310\pi$
$439$	2.71525e9	1.53174	0.765868	+	0.642998i	$0.222310\pi$
$440$	7.82947e9	4.38176
$441$	−4.38996e8	−0.243739
$442$	−9.27524e9	−5.10913
$443$	1.13621e9	0.620933	0.310466	−	0.950584i	$-0.399515\pi$
$443$	1.13621e9	0.620933	0.310466	+	0.950584i	$0.399515\pi$
$444$	5.40196e9	2.92894
$445$	4.62747e8	0.248934
$446$	6.49706e8	0.346773
$447$	−1.90202e9	−1.00725
$448$	2.68696e9	1.41185
$449$	−7.72762e7	−0.0402887	−0.0201444	−	0.999797i	$-0.506413\pi$
$449$	−7.72762e7	−0.0402887	−0.0201444	+	0.999797i	$0.506413\pi$
$450$	2.86676e8	0.148302
$451$	5.22555e9	2.68234
$452$	3.32723e9	1.69472
$453$	2.14551e8	0.108440
$454$	4.94187e9	2.47854
$455$	−7.72039e9	−3.84237
$456$	−2.92651e9	−1.44535
$457$	5.25050e8	0.257332	0.128666	−	0.991688i	$-0.458930\pi$
$457$	5.25050e8	0.257332	0.128666	+	0.991688i	$0.458930\pi$
$458$	−1.20974e9	−0.588387
$459$	−3.46497e9	−1.67246
$460$	−2.18938e9	−1.04874
$461$	−3.22403e9	−1.53266	−0.766330	−	0.642447i	$-0.777919\pi$
$461$	−3.22403e9	−1.53266	−0.766330	+	0.642447i	$0.777919\pi$
$462$	−1.07169e10	−5.05618
$463$	−1.04337e9	−0.488544	−0.244272	−	0.969707i	$-0.578549\pi$
$463$	−1.04337e9	−0.488544	−0.244272	+	0.969707i	$0.578549\pi$
$464$	−4.40428e9	−2.04674
$465$	−1.10591e9	−0.510075
$466$	−4.51171e9	−2.06533
$467$	−9.66598e8	−0.439174	−0.219587	−	0.975593i	$-0.570471\pi$
$467$	−9.66598e8	−0.439174	−0.219587	+	0.975593i	$0.570471\pi$
$468$	1.20424e9	0.543065
$469$	4.47380e9	2.00249
$470$	−5.33311e9	−2.36940
$471$	−7.79053e8	−0.343553
$472$	−2.19739e8	−0.0961856
$473$	−5.68271e9	−2.46912
$474$	−3.07230e9	−1.32507
$475$	−1.18679e9	−0.508095
$476$	1.24916e10	5.30876
$477$	1.85164e8	0.0781163
$478$	−3.90870e9	−1.63695
$479$	−6.05019e6	−0.00251533	−0.00125766	−	0.999999i	$-0.500400\pi$
$479$	−6.05019e6	−0.00251533	−0.00125766	+	0.999999i	$0.500400\pi$
$480$	−4.47025e8	−0.184496
$481$	7.00030e9	2.86819
$482$	1.23328e9	0.501645
$483$	1.53086e9	0.618186
$484$	1.34151e10	5.37819
$485$	1.21072e8	0.0481889
$486$	1.25586e9	0.496265
$487$	−3.16320e8	−0.124101	−0.0620506	−	0.998073i	$-0.519764\pi$
$487$	−3.16320e8	−0.124101	−0.0620506	+	0.998073i	$0.519764\pi$
$488$	−3.94962e9	−1.53846
$489$	−9.15045e8	−0.353885
$490$	9.74900e9	3.74347
$491$	6.56718e8	0.250377	0.125188	−	0.992133i	$-0.460047\pi$
$491$	6.56718e8	0.250377	0.125188	+	0.992133i	$0.460047\pi$
$492$	−7.03596e9	−2.66346
$493$	7.58360e9	2.85043
$494$	−7.42400e9	−2.77073
$495$	9.30431e8	0.344799
$496$	−1.34667e9	−0.495538
$497$	2.31588e9	0.846191
$498$	−4.66089e8	−0.169109
$499$	−2.36816e9	−0.853216	−0.426608	−	0.904437i	$-0.640292\pi$
$499$	−2.36816e9	−0.853216	−0.426608	+	0.904437i	$0.640292\pi$
$500$	2.93630e9	1.05052
$501$	1.16915e9	0.415374
$502$	3.01274e9	1.06292
$503$	8.01298e8	0.280741	0.140371	−	0.990099i	$-0.455171\pi$
$503$	8.01298e8	0.280741	0.140371	+	0.990099i	$0.455171\pi$
$504$	−1.23375e9	−0.429259
$505$	2.42973e9	0.839535
$506$	−3.93837e9	−1.35142
$507$	−6.60778e9	−2.25179
$508$	8.35695e9	2.82829
$509$	−4.45664e8	−0.149794	−0.0748971	−	0.997191i	$-0.523863\pi$
$509$	−4.45664e8	−0.149794	−0.0748971	+	0.997191i	$0.523863\pi$
$510$	9.64913e9	3.22101
$511$	−9.80655e8	−0.325120
$512$	5.73518e9	1.88843
$513$	−2.77340e9	−0.906989
$514$	8.30276e9	2.69682
$515$	−7.63654e9	−2.46361
$516$	7.65152e9	2.45174
$517$	−6.44217e9	−2.05029
$518$	−1.40395e10	−4.43812
$519$	−2.93255e9	−0.920789
$520$	−1.36612e10	−4.26067
$521$	−2.86920e9	−0.888852	−0.444426	−	0.895816i	$-0.646592\pi$
$521$	−2.86920e9	−0.888852	−0.444426	+	0.895816i	$0.646592\pi$
$522$	−1.46625e9	−0.451191
$523$	1.01985e9	0.311732	0.155866	−	0.987778i	$-0.450183\pi$
$523$	1.01985e9	0.311732	0.155866	+	0.987778i	$0.450183\pi$
$524$	3.77765e9	1.14700
$525$	2.98924e9	0.901579
$526$	−6.25045e9	−1.87267
$527$	2.31880e9	0.690122
$528$	−6.76923e9	−2.00134
$529$	−2.84225e9	−0.834771
$530$	−4.11203e9	−1.19975
$531$	−2.61131e7	−0.00756881
$532$	9.99840e9	2.87899
$533$	−9.11777e9	−2.60822
$534$	−1.12081e9	−0.318520
$535$	−2.23416e9	−0.630778
$536$	7.91638e9	2.22050
$537$	1.56424e9	0.435906
$538$	−2.30698e9	−0.638714
$539$	1.17764e10	3.23930
$540$	−9.99050e9	−2.73029
$541$	2.07515e9	0.563455	0.281728	−	0.959494i	$-0.409093\pi$
$541$	2.07515e9	0.563455	0.281728	+	0.959494i	$0.409093\pi$
$542$	9.75663e9	2.63210
$543$	4.15544e9	1.11383
$544$	9.37292e8	0.249620
$545$	−1.85819e9	−0.491702
$546$	1.86994e10	4.91646
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	7.92378e9	2.05684
$549$	−4.69361e8	−0.121061
$550$	−7.69029e9	−1.97094
$551$	6.07000e9	1.54582
$552$	2.70885e9	0.685485
$553$	5.36194e9	1.34829
$554$	−2.00317e9	−0.500534
$555$	−7.28248e9	−1.80823
$556$	−8.69043e9	−2.14427
$557$	−6.27607e9	−1.53884	−0.769422	−	0.638740i	$-0.779456\pi$
$557$	−6.27607e9	−1.53884	−0.769422	+	0.638740i	$0.779456\pi$
$558$	−4.48327e8	−0.109238
$559$	9.91546e9	2.40089
$560$	9.78015e9	2.35335
$561$	1.16557e10	2.78721
$562$	−1.10790e10	−2.63283
$563$	−6.09416e9	−1.43924	−0.719622	−	0.694366i	$-0.755685\pi$
$563$	−6.09416e9	−1.43924	−0.719622	+	0.694366i	$0.755685\pi$
$564$	8.67409e9	2.03586
$565$	−4.48550e9	−1.04626
$566$	4.14555e9	0.961002
$567$	5.96298e9	1.37380
$568$	4.09795e9	0.938312
$569$	2.14854e9	0.488933	0.244467	−	0.969658i	$-0.421387\pi$
$569$	2.14854e9	0.488933	0.244467	+	0.969658i	$0.421387\pi$
$570$	7.72327e9	1.74678
$571$	2.65390e9	0.596565	0.298283	−	0.954478i	$-0.403586\pi$
$571$	2.65390e9	0.596565	0.298283	+	0.954478i	$0.403586\pi$
$572$	−3.23046e10	−7.21736
$573$	6.59952e9	1.46545
$574$	1.82863e10	4.03584
$575$	1.09852e9	0.240974
$576$	5.65019e8	0.123193
$577$	−5.49127e9	−1.19003	−0.595015	−	0.803715i	$-0.702854\pi$
$577$	−5.49127e9	−1.19003	−0.595015	+	0.803715i	$0.702854\pi$
$578$	−1.21316e10	−2.61318
$579$	−2.98654e9	−0.639431
$580$	2.18657e10	4.65334
$581$	8.13443e8	0.172072
$582$	−2.93245e8	−0.0616595
$583$	−4.96716e9	−1.03817
$584$	−1.73527e9	−0.360514
$585$	−1.62346e9	−0.335271
$586$	9.79566e9	2.01091
$587$	3.06922e9	0.626318	0.313159	−	0.949701i	$-0.398613\pi$
$587$	3.06922e9	0.626318	0.313159	+	0.949701i	$0.398613\pi$
$588$	−1.58564e10	−3.21650
$589$	1.85599e9	0.374259
$590$	5.79907e8	0.116246
$591$	4.76654e9	0.949833
$592$	−8.86794e9	−1.75670
$593$	4.64413e9	0.914562	0.457281	−	0.889322i	$-0.348823\pi$
$593$	4.64413e9	0.914562	0.457281	+	0.889322i	$0.348823\pi$
$594$	−1.79714e10	−3.51828
$595$	−1.68401e10	−3.27745
$596$	1.14986e10	2.22477
$597$	2.51175e8	0.0483133
$598$	6.87184e9	1.31407
$599$	−5.26143e9	−1.00025	−0.500127	−	0.865952i	$-0.666713\pi$
$599$	−5.26143e9	−1.00025	−0.500127	+	0.865952i	$0.666713\pi$
$600$	5.28946e9	0.999729
$601$	−7.24116e9	−1.36065	−0.680327	−	0.732909i	$-0.738162\pi$
$601$	−7.24116e9	−1.36065	−0.680327	+	0.732909i	$0.738162\pi$
$602$	−1.98861e10	−3.71502
$603$	9.40759e8	0.174730
$604$	−1.29707e9	−0.239515
$605$	−1.80852e10	−3.32032
$606$	−5.88500e9	−1.07422
$607$	7.02793e9	1.27546	0.637731	−	0.770259i	$-0.279873\pi$
$607$	7.02793e9	1.27546	0.637731	+	0.770259i	$0.279873\pi$
$608$	7.50219e8	0.135371
$609$	−1.52889e10	−2.74294
$610$	1.04233e10	1.85931
$611$	1.12406e10	1.99363
$612$	2.62675e9	0.463222
$613$	4.90128e9	0.859405	0.429703	−	0.902970i	$-0.358618\pi$
$613$	4.90128e9	0.859405	0.429703	+	0.902970i	$0.358618\pi$
$614$	−8.03459e9	−1.40079
$615$	9.48532e9	1.64433
$616$	3.30962e10	5.70486
$617$	8.27523e8	0.141834	0.0709172	−	0.997482i	$-0.477407\pi$
$617$	8.27523e8	0.141834	0.0709172	+	0.997482i	$0.477407\pi$
$618$	1.84963e10	3.15228
$619$	6.92228e9	1.17309	0.586546	−	0.809916i	$-0.300487\pi$
$619$	6.92228e9	1.17309	0.586546	+	0.809916i	$0.300487\pi$
$620$	6.68576e9	1.12663
$621$	2.56713e9	0.430157
$622$	1.26429e9	0.210659
$623$	1.95609e9	0.324101
$624$	1.18113e10	1.94603
$625$	−7.57680e9	−1.24138
$626$	9.26620e9	1.50970
$627$	9.32938e9	1.51153
$628$	4.70975e9	0.758821
$629$	1.52694e10	2.44650
$630$	3.25595e9	0.518783
$631$	−6.57631e9	−1.04203	−0.521014	−	0.853548i	$-0.674446\pi$
$631$	−6.57631e9	−1.04203	−0.521014	+	0.853548i	$0.674446\pi$
$632$	9.48795e9	1.49507
$633$	−7.38143e9	−1.15672
$634$	8.53937e9	1.33080
$635$	−1.12662e10	−1.74610
$636$	6.68805e9	1.03086
$637$	−2.05480e10	−3.14978
$638$	3.93331e10	5.99634
$639$	4.86988e8	0.0738354
$640$	−1.38696e10	−2.09139
$641$	−4.47959e9	−0.671792	−0.335896	−	0.941899i	$-0.609039\pi$
$641$	−4.47959e9	−0.671792	−0.335896	+	0.941899i	$0.609039\pi$
$642$	5.41131e9	0.807104
$643$	−2.56167e9	−0.380001	−0.190000	−	0.981784i	$-0.560849\pi$
$643$	−2.56167e9	−0.380001	−0.190000	+	0.981784i	$0.560849\pi$
$644$	−9.25477e9	−1.36542
$645$	−1.03152e10	−1.51362
$646$	−1.61937e10	−2.36337
$647$	−6.05649e9	−0.879136	−0.439568	−	0.898209i	$-0.644868\pi$
$647$	−6.05649e9	−0.879136	−0.439568	+	0.898209i	$0.644868\pi$
$648$	1.05515e10	1.52335
$649$	7.00504e8	0.100590
$650$	1.34184e10	1.91648
$651$	−4.67482e9	−0.664097
$652$	5.53190e9	0.781641
$653$	1.25389e10	1.76223	0.881113	−	0.472905i	$-0.156795\pi$
$653$	1.25389e10	1.76223	0.881113	+	0.472905i	$0.156795\pi$
$654$	4.50067e9	0.629151
$655$	−5.09273e9	−0.708119
$656$	1.15503e10	1.59747
$657$	−2.06214e8	−0.0283687
$658$	−2.25437e10	−3.08486
$659$	8.74003e9	1.18964	0.594818	−	0.803861i	$-0.297224\pi$
$659$	8.74003e9	1.18964	0.594818	+	0.803861i	$0.297224\pi$
$660$	3.36068e10	4.55013
$661$	1.32866e8	0.0178940	0.00894700	−	0.999960i	$-0.497152\pi$
$661$	1.32866e8	0.0178940	0.00894700	+	0.999960i	$0.497152\pi$
$662$	1.00165e10	1.34188
$663$	−2.03375e10	−2.71019
$664$	1.43939e9	0.190805
$665$	−1.34790e10	−1.77739
$666$	−2.95226e9	−0.387253
$667$	−5.61854e9	−0.733133
$668$	−7.06809e9	−0.917455
$669$	1.42459e9	0.183949
$670$	−2.08919e10	−2.68359
$671$	1.25910e10	1.60890
$672$	−1.88963e9	−0.240206
$673$	9.70310e9	1.22704	0.613519	−	0.789680i	$-0.289754\pi$
$673$	9.70310e9	1.22704	0.613519	+	0.789680i	$0.289754\pi$
$674$	−1.89684e10	−2.38628
$675$	5.01273e9	0.627352
$676$	3.99473e10	4.97363
$677$	3.76975e9	0.466930	0.233465	−	0.972365i	$-0.424994\pi$
$677$	3.76975e9	0.466930	0.233465	+	0.972365i	$0.424994\pi$
$678$	1.08642e10	1.33873
$679$	5.11786e8	0.0627399
$680$	−2.97986e10	−3.63425
$681$	1.08359e10	1.31477
$682$	1.20267e10	1.45178
$683$	3.96005e9	0.475585	0.237793	−	0.971316i	$-0.423576\pi$
$683$	3.96005e9	0.475585	0.237793	+	0.971316i	$0.423576\pi$
$684$	2.10248e9	0.251210
$685$	−1.06822e10	−1.26982
$686$	1.69688e10	2.00686
$687$	−2.65255e9	−0.312116
$688$	−1.25609e10	−1.47048
$689$	8.66692e9	1.00948
$690$	−7.14885e9	−0.828447
$691$	−6.84479e9	−0.789200	−0.394600	−	0.918853i	$-0.629117\pi$
$691$	−6.84479e9	−0.789200	−0.394600	+	0.918853i	$0.629117\pi$
$692$	1.77287e10	2.03379
$693$	3.93305e9	0.448914
$694$	1.76470e10	2.00407
$695$	1.17157e10	1.32380
$696$	−2.70538e10	−3.04155
$697$	−1.98882e10	−2.22475
$698$	1.05224e10	1.17118
$699$	−9.89266e9	−1.09558
$700$	−1.80714e10	−1.99136
$701$	−4.73134e8	−0.0518766	−0.0259383	−	0.999664i	$-0.508257\pi$
$701$	−4.73134e8	−0.0518766	−0.0259383	+	0.999664i	$0.508257\pi$
$702$	3.13574e10	3.42106
$703$	1.22218e10	1.32676
$704$	−1.51571e10	−1.63723
$705$	−1.16937e10	−1.25687
$706$	−4.89311e9	−0.523322
$707$	1.02708e10	1.09304
$708$	−9.43197e8	−0.0998817
$709$	1.18980e10	1.25375	0.626875	−	0.779120i	$-0.284334\pi$
$709$	1.18980e10	1.25375	0.626875	+	0.779120i	$0.284334\pi$
$710$	−1.08148e10	−1.13400
$711$	1.12752e9	0.117647
$712$	3.46130e9	0.359385
$713$	−1.71795e9	−0.177500
$714$	4.07881e10	4.19363
$715$	4.35505e10	4.45576
$716$	−9.45658e9	−0.962806
$717$	−8.57046e9	−0.868335
$718$	−1.44272e10	−1.45461
$719$	4.80159e9	0.481764	0.240882	−	0.970554i	$-0.422563\pi$
$719$	4.80159e9	0.481764	0.240882	+	0.970554i	$0.422563\pi$
$720$	2.05659e9	0.205345
$721$	−3.22806e10	−3.20751
$722$	4.68345e9	0.463112
$723$	2.70417e9	0.266103
$724$	−2.51217e10	−2.46016
$725$	−1.09711e10	−1.06922
$726$	4.38037e10	4.24847
$727$	−1.36579e10	−1.31829	−0.659147	−	0.752014i	$-0.729082\pi$
$727$	−1.36579e10	−1.31829	−0.659147	+	0.752014i	$0.729082\pi$
$728$	−5.77477e10	−5.54722
$729$	1.14992e10	1.09932
$730$	4.57950e9	0.435701
$731$	2.16282e10	2.04790
$732$	−1.69532e10	−1.59758
$733$	1.97682e9	0.185397	0.0926984	−	0.995694i	$-0.470451\pi$
$733$	1.97682e9	0.185397	0.0926984	+	0.995694i	$0.470451\pi$
$734$	−3.85042e9	−0.359395
$735$	2.13763e10	1.98576
$736$	−6.94422e8	−0.0642023
$737$	−2.52365e10	−2.32217
$738$	3.84528e9	0.352152
$739$	7.03640e9	0.641350	0.320675	−	0.947189i	$-0.396090\pi$
$739$	7.03640e9	0.641350	0.320675	+	0.947189i	$0.396090\pi$
$740$	4.40262e10	3.99392
$741$	−1.62783e10	−1.46976
$742$	−1.73821e10	−1.56202
$743$	1.69518e10	1.51620	0.758099	−	0.652140i	$-0.226128\pi$
$743$	1.69518e10	1.51620	0.758099	+	0.652140i	$0.226128\pi$
$744$	−8.27209e9	−0.736394
$745$	−1.55015e10	−1.37350
$746$	9.03001e9	0.796347
$747$	1.71052e8	0.0150144
$748$	−7.04646e10	−6.15624
$749$	−9.44408e9	−0.821246
$750$	9.58774e9	0.829854
$751$	1.21402e10	1.04589	0.522947	−	0.852365i	$-0.324833\pi$
$751$	1.21402e10	1.04589	0.522947	+	0.852365i	$0.324833\pi$
$752$	−1.42395e10	−1.22105
$753$	6.60593e9	0.563834
$754$	−6.86303e10	−5.83064
$755$	1.74860e9	0.147869
$756$	−4.22311e10	−3.55473
$757$	−5.46586e7	−0.00457955	−0.00228978	−	0.999997i	$-0.500729\pi$
$757$	−5.46586e7	−0.00457955	−0.00228978	+	0.999997i	$0.500729\pi$
$758$	−3.43303e10	−2.86309
$759$	−8.63551e9	−0.716872
$760$	−2.38512e10	−1.97089
$761$	−5.69485e9	−0.468420	−0.234210	−	0.972186i	$-0.575250\pi$
$761$	−5.69485e9	−0.468420	−0.234210	+	0.972186i	$0.575250\pi$
$762$	2.72875e10	2.23420
$763$	−7.85480e9	−0.640175
$764$	−3.98973e10	−3.23681
$765$	−3.54118e9	−0.285978
$766$	4.83910e9	0.389013
$767$	−1.22227e9	−0.0978101
$768$	2.36102e10	1.88077
$769$	1.21937e10	0.966924	0.483462	−	0.875365i	$-0.339379\pi$
$769$	1.21937e10	0.966924	0.483462	+	0.875365i	$0.339379\pi$
$770$	−8.73433e10	−6.89464
$771$	1.82052e10	1.43055
$772$	1.80551e10	1.41234
$773$	6.17805e9	0.481086	0.240543	−	0.970638i	$-0.422674\pi$
$773$	6.17805e9	0.481086	0.240543	+	0.970638i	$0.422674\pi$
$774$	−4.18169e9	−0.324159
$775$	−3.35458e9	−0.258870
$776$	9.05605e8	0.0695701
$777$	−3.07840e10	−2.35424
$778$	2.81861e10	2.14588
$779$	−1.59187e10	−1.20650
$780$	−5.86387e10	−4.42439
$781$	−1.30638e10	−0.981275
$782$	1.49893e10	1.12087
$783$	−2.56384e10	−1.90864
$784$	2.60301e10	1.92916
$785$	−6.34931e9	−0.468471
$786$	1.23350e10	0.906065
$787$	−1.90730e10	−1.39478	−0.697391	−	0.716691i	$-0.745656\pi$
$787$	−1.90730e10	−1.39478	−0.697391	+	0.716691i	$0.745656\pi$
$788$	−2.88161e10	−2.09794
$789$	−1.37051e10	−0.993377
$790$	−2.50394e10	−1.80688
$791$	−1.89608e10	−1.36219
$792$	6.95953e9	0.497785
$793$	−2.19693e10	−1.56444
$794$	−9.51284e9	−0.674432
$795$	−9.01629e9	−0.636419
$796$	−1.51848e9	−0.106712
$797$	1.38372e9	0.0968151	0.0484075	−	0.998828i	$-0.484585\pi$
$797$	1.38372e9	0.0968151	0.0484075	+	0.998828i	$0.484585\pi$
$798$	3.26473e10	2.27424
$799$	2.45186e10	1.70052
$800$	−1.35597e9	−0.0936343
$801$	4.11331e8	0.0282799
$802$	4.09245e10	2.80139
$803$	5.53185e9	0.377021
$804$	3.39799e10	2.30582
$805$	1.24765e10	0.842963
$806$	−2.09847e10	−1.41166
$807$	−5.05844e9	−0.338812
$808$	1.81742e10	1.21203
$809$	1.14755e9	0.0761995	0.0380997	−	0.999274i	$-0.487870\pi$
$809$	1.14755e9	0.0761995	0.0380997	+	0.999274i	$0.487870\pi$
$810$	−2.78461e10	−1.84106
$811$	−1.53037e10	−1.00745	−0.503725	−	0.863864i	$-0.668038\pi$
$811$	−1.53037e10	−1.00745	−0.503725	+	0.863864i	$0.668038\pi$
$812$	9.24290e10	6.05846
$813$	2.13930e10	1.39622
$814$	7.91966e10	5.14661
$815$	−7.45766e9	−0.482559
$816$	2.57634e10	1.65992
$817$	1.73114e10	1.11059
$818$	1.19870e10	0.765728
$819$	−6.86256e9	−0.436509
$820$	−5.73434e10	−3.63191
$821$	−1.08209e10	−0.682436	−0.341218	−	0.939984i	$-0.610839\pi$
$821$	−1.08209e10	−0.682436	−0.341218	+	0.939984i	$0.610839\pi$
$822$	2.58731e10	1.62479
$823$	−1.53192e10	−0.957933	−0.478967	−	0.877833i	$-0.658989\pi$
$823$	−1.53192e10	−0.957933	−0.478967	+	0.877833i	$0.658989\pi$
$824$	−5.71205e10	−3.55670
$825$	−1.68622e10	−1.04551
$826$	2.45134e9	0.151347
$827$	2.93374e10	1.80365	0.901826	−	0.432100i	$-0.142227\pi$
$827$	2.93374e10	1.80365	0.901826	+	0.432100i	$0.142227\pi$
$828$	−1.94611e9	−0.119141
$829$	−4.74896e9	−0.289506	−0.144753	−	0.989468i	$-0.546239\pi$
$829$	−4.74896e9	−0.289506	−0.144753	+	0.989468i	$0.546239\pi$
$830$	−3.79865e9	−0.230598
$831$	−4.39227e9	−0.265513
$832$	2.64467e10	1.59199
$833$	−4.48204e10	−2.68669
$834$	−2.83764e10	−1.69385
$835$	9.52864e9	0.566406
$836$	−5.64007e10	−3.33858
$837$	−7.83932e9	−0.462103
$838$	−2.39083e10	−1.40344
$839$	1.67102e10	0.976819	0.488409	−	0.872615i	$-0.337577\pi$
$839$	1.67102e10	0.976819	0.488409	+	0.872615i	$0.337577\pi$
$840$	6.00756e10	3.49720
$841$	3.88635e10	2.25297
$842$	−6.58037e9	−0.379890
$843$	−2.42925e10	−1.39661
$844$	4.46243e10	2.55490
$845$	−5.38537e10	−3.07056
$846$	−4.74054e9	−0.269173
$847$	−7.64484e10	−4.32291
$848$	−1.09792e10	−0.618281
$849$	9.08979e9	0.509773
$850$	2.92689e10	1.63471
$851$	−1.13128e10	−0.629242
$852$	1.75898e10	0.974368
$853$	2.01411e10	1.11112	0.555561	−	0.831476i	$-0.312504\pi$
$853$	2.01411e10	1.11112	0.555561	+	0.831476i	$0.312504\pi$
$854$	4.40608e10	2.42075
$855$	−2.83440e9	−0.155089
$856$	−1.67113e10	−0.910651
$857$	3.10159e10	1.68326	0.841629	−	0.540056i	$-0.181597\pi$
$857$	3.10159e10	1.68326	0.841629	+	0.540056i	$0.181597\pi$
$858$	−1.05483e11	−5.70131
$859$	9.41811e9	0.506976	0.253488	−	0.967339i	$-0.418422\pi$
$859$	9.41811e9	0.506976	0.253488	+	0.967339i	$0.418422\pi$
$860$	6.23602e10	3.34320
$861$	4.00957e10	2.14085
$862$	4.14082e10	2.20197
$863$	4.01081e9	0.212419	0.106210	−	0.994344i	$-0.466129\pi$
$863$	4.01081e9	0.212419	0.106210	+	0.994344i	$0.466129\pi$
$864$	−3.16877e9	−0.167145
$865$	−2.39004e10	−1.25559
$866$	−2.25009e10	−1.17730
$867$	−2.66005e10	−1.38619
$868$	2.82616e10	1.46682
$869$	−3.02465e10	−1.56353
$870$	7.13968e10	3.67588
$871$	4.40339e10	2.25800
$872$	−1.38991e10	−0.709868
$873$	1.07619e8	0.00547445
$874$	1.19976e10	0.607859
$875$	−1.67330e10	−0.844395
$876$	−7.44838e9	−0.374367
$877$	2.87644e10	1.43998	0.719991	−	0.693983i	$-0.244146\pi$
$877$	2.87644e10	1.43998	0.719991	+	0.693983i	$0.244146\pi$
$878$	−5.35990e10	−2.67255
$879$	2.14786e10	1.06671
$880$	−5.51695e10	−2.72904
$881$	−3.18025e10	−1.56691	−0.783457	−	0.621446i	$-0.786545\pi$
$881$	−3.18025e10	−1.56691	−0.783457	+	0.621446i	$0.786545\pi$
$882$	8.66578e9	0.425273
$883$	−1.42313e10	−0.695638	−0.347819	−	0.937562i	$-0.613078\pi$
$883$	−1.42313e10	−0.695638	−0.347819	+	0.937562i	$0.613078\pi$
$884$	1.22950e11	5.98612
$885$	1.27154e9	0.0616636
$886$	−2.24288e10	−1.08340
$887$	−9.41210e8	−0.0452849	−0.0226425	−	0.999744i	$-0.507208\pi$
$887$	−9.41210e8	−0.0452849	−0.0226425	+	0.999744i	$0.507208\pi$
$888$	−5.44723e10	−2.61054
$889$	−4.76235e10	−2.27334
$890$	−9.13463e9	−0.434336
$891$	−3.36370e10	−1.59311
$892$	−8.61232e9	−0.406297
$893$	1.96250e10	0.922208
$894$	3.75459e10	1.75744
$895$	1.27486e10	0.594405
$896$	−5.86287e10	−2.72291
$897$	1.50676e10	0.697062
$898$	1.52543e9	0.0702952
$899$	1.71575e10	0.787581
$900$	−3.80010e9	−0.173758
$901$	1.89048e10	0.861063
$902$	−1.03152e11	−4.68011
$903$	−4.36035e10	−1.97067
$904$	−3.35511e10	−1.51049
$905$	3.38670e10	1.51882
$906$	−4.23525e9	−0.189204
$907$	1.55463e9	0.0691833	0.0345917	−	0.999402i	$-0.488987\pi$
$907$	1.55463e9	0.0691833	0.0345917	+	0.999402i	$0.488987\pi$
$908$	−6.55080e10	−2.90398
$909$	2.15976e9	0.0953745
$910$	1.52401e11	6.70412
$911$	−1.84456e10	−0.808310	−0.404155	−	0.914691i	$-0.632434\pi$
$911$	−1.84456e10	−0.808310	−0.404155	+	0.914691i	$0.632434\pi$
$912$	2.06213e10	0.900191
$913$	−4.58861e9	−0.199541
$914$	−1.03645e10	−0.448990
$915$	2.28549e10	0.986291
$916$	1.60360e10	0.689384
$917$	−2.15276e10	−0.921941
$918$	6.83986e10	2.91808
$919$	−3.40182e9	−0.144580	−0.0722898	−	0.997384i	$-0.523031\pi$
$919$	−3.40182e9	−0.144580	−0.0722898	+	0.997384i	$0.523031\pi$
$920$	2.20772e10	0.934732
$921$	−1.76172e10	−0.743066
$922$	6.36424e10	2.67417
$923$	2.27943e10	0.954159
$924$	1.42060e11	5.92408
$925$	−2.20901e10	−0.917703
$926$	2.05961e10	0.852406
$927$	−6.78803e9	−0.279875
$928$	6.93531e9	0.284871
$929$	−1.94903e10	−0.797560	−0.398780	−	0.917047i	$-0.630566\pi$
$929$	−1.94903e10	−0.797560	−0.398780	+	0.917047i	$0.630566\pi$
$930$	2.18307e10	0.889973
$931$	−3.58748e10	−1.45702
$932$	5.98059e10	2.41985
$933$	2.77216e9	0.111746
$934$	1.90807e10	0.766266
$935$	9.49948e10	3.80066
$936$	−1.21433e10	−0.484029
$937$	3.06307e10	1.21638	0.608189	−	0.793793i	$-0.291896\pi$
$937$	3.06307e10	1.21638	0.608189	+	0.793793i	$0.291896\pi$
$938$	−8.83128e10	−3.49393
$939$	2.03177e10	0.800837
$940$	7.06942e10	2.77611
$941$	3.29024e10	1.28725	0.643627	−	0.765339i	$-0.277429\pi$
$941$	3.29024e10	1.28725	0.643627	+	0.765339i	$0.277429\pi$
$942$	1.53785e10	0.599427
$943$	1.47348e10	0.572207
$944$	1.54837e9	0.0599062
$945$	5.69326e10	2.19457
$946$	1.12177e11	4.30808
$947$	3.98675e9	0.152544	0.0762718	−	0.997087i	$-0.475698\pi$
$947$	3.98675e9	0.152544	0.0762718	+	0.997087i	$0.475698\pi$
$948$	4.07256e10	1.55252
$949$	−9.65222e9	−0.366603
$950$	2.34272e10	0.886518
$951$	1.87240e10	0.705937
$952$	−1.25963e11	−4.73165
$953$	−1.61485e10	−0.604376	−0.302188	−	0.953248i	$-0.597717\pi$
$953$	−1.61485e10	−0.604376	−0.302188	+	0.953248i	$0.597717\pi$
$954$	−3.65514e9	−0.136296
$955$	5.37864e10	1.99830
$956$	5.18126e10	1.91793
$957$	8.62444e10	3.18082
$958$	1.19431e8	0.00438871
$959$	−4.51550e10	−1.65326
$960$	−2.75128e10	−1.00366
$961$	−2.22664e10	−0.809318
$962$	−1.38186e11	−5.00439
$963$	−1.98592e9	−0.0716589
$964$	−1.63480e10	−0.587753
$965$	−2.43404e10	−0.871932
$966$	−3.02191e10	−1.07860
$967$	1.83050e10	0.650993	0.325496	−	0.945543i	$-0.394469\pi$
$967$	1.83050e10	0.650993	0.325496	+	0.945543i	$0.394469\pi$
$968$	−1.35275e11	−4.79353
$969$	−3.55072e10	−1.25367
$970$	−2.38996e9	−0.0840793
$971$	5.89623e9	0.206684	0.103342	−	0.994646i	$-0.467046\pi$
$971$	5.89623e9	0.206684	0.103342	+	0.994646i	$0.467046\pi$
$972$	−1.66473e10	−0.581449
$973$	4.95239e10	1.72353
$974$	6.24417e9	0.216530
$975$	2.94220e10	1.01661
$976$	2.78306e10	0.958181
$977$	−1.57848e10	−0.541513	−0.270756	−	0.962648i	$-0.587274\pi$
$977$	−1.57848e10	−0.541513	−0.270756	+	0.962648i	$0.587274\pi$
$978$	1.80630e10	0.617453
$979$	−1.10342e10	−0.375840
$980$	−1.29230e11	−4.38604
$981$	−1.65172e9	−0.0558593
$982$	−1.29636e10	−0.436854
$983$	2.97004e10	0.997298	0.498649	−	0.866804i	$-0.333830\pi$
$983$	2.97004e10	0.997298	0.498649	+	0.866804i	$0.333830\pi$
$984$	7.09493e10	2.37391
$985$	3.88475e10	1.29520
$986$	−1.49700e11	−4.97340
$987$	−4.94308e10	−1.63639
$988$	9.84105e10	3.24633
$989$	−1.60239e10	−0.526721
$990$	−1.83667e10	−0.601601
$991$	4.61728e9	0.150705	0.0753526	−	0.997157i	$-0.475992\pi$
$991$	4.61728e9	0.150705	0.0753526	+	0.997157i	$0.475992\pi$
$992$	2.12058e9	0.0689704
$993$	2.19629e10	0.711814
$994$	−4.57155e10	−1.47642
$995$	2.04709e9	0.0658803
$996$	6.17835e9	0.198137
$997$	−5.60258e10	−1.79042	−0.895210	−	0.445645i	$-0.852974\pi$
$997$	−5.60258e10	−1.79042	−0.895210	+	0.445645i	$0.852974\pi$
$998$	4.67475e10	1.48868
$999$	−5.16224e10	−1.63817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.15	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-19.7400 q^{2} -43.2832 q^{3} +261.668 q^{4} -352.760 q^{5} +854.411 q^{6} -1491.16 q^{7} -2638.61 q^{8} -313.564 q^{9} +O(q^{10})\)	\(q-19.7400 q^{2} -43.2832 q^{3} +261.668 q^{4} -352.760 q^{5} +854.411 q^{6} -1491.16 q^{7} -2638.61 q^{8} -313.564 q^{9} +6963.48 q^{10} +8411.59 q^{11} -11325.8 q^{12} -14676.9 q^{13} +29435.5 q^{14} +15268.6 q^{15} +18592.7 q^{16} -32014.2 q^{17} +6189.76 q^{18} -25624.5 q^{19} -92306.0 q^{20} +64542.2 q^{21} -166045. q^{22} +23718.7 q^{23} +114207. q^{24} +46314.5 q^{25} +289723. q^{26} +108232. q^{27} -390189. q^{28} -236883. q^{29} -301402. q^{30} -72430.4 q^{31} -29277.4 q^{32} -364081. q^{33} +631960. q^{34} +526022. q^{35} -82049.8 q^{36} -476959. q^{37} +505828. q^{38} +635265. q^{39} +930795. q^{40} +621232. q^{41} -1.27406e6 q^{42} -675581. q^{43} +2.20105e6 q^{44} +110613. q^{45} -468207. q^{46} -765868. q^{47} -804750. q^{48} +1.40002e6 q^{49} -914249. q^{50} +1.38568e6 q^{51} -3.84049e6 q^{52} -590513. q^{53} -2.13651e6 q^{54} -2.96727e6 q^{55} +3.93459e6 q^{56} +1.10911e6 q^{57} +4.67606e6 q^{58} +83278.3 q^{59} +3.99530e6 q^{60} +1.49686e6 q^{61} +1.42978e6 q^{62} +467575. q^{63} -1.80192e6 q^{64} +5.17743e6 q^{65} +7.18696e6 q^{66} -3.00021e6 q^{67} -8.37708e6 q^{68} -1.02662e6 q^{69} -1.03837e7 q^{70} -1.55307e6 q^{71} +827374. q^{72} +657646. q^{73} +9.41517e6 q^{74} -2.00464e6 q^{75} -6.70511e6 q^{76} -1.25430e7 q^{77} -1.25401e7 q^{78} -3.59582e6 q^{79} -6.55875e6 q^{80} -3.99888e6 q^{81} -1.22631e7 q^{82} -545510. q^{83} +1.68886e7 q^{84} +1.12933e7 q^{85} +1.33360e7 q^{86} +1.02530e7 q^{87} -2.21949e7 q^{88} -1.31179e6 q^{89} -2.18350e6 q^{90} +2.18857e7 q^{91} +6.20642e6 q^{92} +3.13502e6 q^{93} +1.51182e7 q^{94} +9.03929e6 q^{95} +1.26722e6 q^{96} -343213. q^{97} -2.76364e7 q^{98} -2.63757e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 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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