LMFDB - Embedded newform 547.8.a.b.1.4

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:	$0$
Dimension:	$162$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-21.7039 q^{2} +18.5452 q^{3} +343.061 q^{4} +347.311 q^{5} -402.503 q^{6} -741.863 q^{7} -4667.67 q^{8} -1843.08 q^{9} +O(q^{10})$	\(q-21.7039 q^{2} +18.5452 q^{3} +343.061 q^{4} +347.311 q^{5} -402.503 q^{6} -741.863 q^{7} -4667.67 q^{8} -1843.08 q^{9} -7538.02 q^{10} +4381.24 q^{11} +6362.12 q^{12} -8523.32 q^{13} +16101.4 q^{14} +6440.94 q^{15} +57395.0 q^{16} +5005.38 q^{17} +40002.0 q^{18} -4595.58 q^{19} +119149. q^{20} -13758.0 q^{21} -95090.1 q^{22} -57829.7 q^{23} -86562.7 q^{24} +42499.9 q^{25} +184990. q^{26} -74738.5 q^{27} -254504. q^{28} -209992. q^{29} -139794. q^{30} -27259.7 q^{31} -648236. q^{32} +81250.8 q^{33} -108637. q^{34} -257657. q^{35} -632288. q^{36} +138457. q^{37} +99742.1 q^{38} -158066. q^{39} -1.62113e6 q^{40} -614751. q^{41} +298602. q^{42} +629021. q^{43} +1.50303e6 q^{44} -640121. q^{45} +1.25513e6 q^{46} +754131. q^{47} +1.06440e6 q^{48} -273182. q^{49} -922416. q^{50} +92825.7 q^{51} -2.92402e6 q^{52} -1.98562e6 q^{53} +1.62212e6 q^{54} +1.52165e6 q^{55} +3.46277e6 q^{56} -85225.7 q^{57} +4.55766e6 q^{58} +2.20513e6 q^{59} +2.20964e6 q^{60} -1.17845e6 q^{61} +591643. q^{62} +1.36731e6 q^{63} +6.72271e6 q^{64} -2.96024e6 q^{65} -1.76346e6 q^{66} +3.19854e6 q^{67} +1.71715e6 q^{68} -1.07246e6 q^{69} +5.59218e6 q^{70} +2.97974e6 q^{71} +8.60287e6 q^{72} -2.30687e6 q^{73} -3.00507e6 q^{74} +788168. q^{75} -1.57656e6 q^{76} -3.25028e6 q^{77} +3.43066e6 q^{78} +2.17251e6 q^{79} +1.99339e7 q^{80} +2.64477e6 q^{81} +1.33425e7 q^{82} +4.61850e6 q^{83} -4.71983e6 q^{84} +1.73842e6 q^{85} -1.36522e7 q^{86} -3.89434e6 q^{87} -2.04502e7 q^{88} -9.59280e6 q^{89} +1.38931e7 q^{90} +6.32314e6 q^{91} -1.98391e7 q^{92} -505536. q^{93} -1.63676e7 q^{94} -1.59609e6 q^{95} -1.20216e7 q^{96} +4.07353e6 q^{97} +5.92912e6 q^{98} -8.07495e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) $ 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * 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 $

$2$	−21.7039	−1.91838	−0.959188	−	0.282770i	$-0.908747\pi$
$2$	−21.7039	−1.91838	−0.959188	+	0.282770i	$0.908747\pi$
$3$	18.5452	0.396558	0.198279	−	0.980146i	$-0.436465\pi$
$3$	18.5452	0.396558	0.198279	+	0.980146i	$0.436465\pi$
$4$	343.061	2.68016
$5$	347.311	1.24258	0.621289	−	0.783582i	$-0.286609\pi$
$5$	347.311	1.24258	0.621289	+	0.783582i	$0.286609\pi$
$6$	−402.503	−0.760746
$7$	−741.863	−0.817487	−0.408743	−	0.912649i	$-0.634033\pi$
$7$	−741.863	−0.817487	−0.408743	+	0.912649i	$0.634033\pi$
$8$	−4667.67	−3.22318
$9$	−1843.08	−0.842742
$10$	−7538.02	−2.38373
$11$	4381.24	0.992481	0.496241	−	0.868185i	$-0.334713\pi$
$11$	4381.24	0.992481	0.496241	+	0.868185i	$0.334713\pi$
$12$	6362.12	1.06284
$13$	−8523.32	−1.07599	−0.537994	−	0.842949i	$-0.680818\pi$
$13$	−8523.32	−1.07599	−0.537994	+	0.842949i	$0.680818\pi$
$14$	16101.4	1.56825
$15$	6440.94	0.492754
$16$	57395.0	3.50311
$17$	5005.38	0.247096	0.123548	−	0.992339i	$-0.460573\pi$
$17$	5005.38	0.247096	0.123548	+	0.992339i	$0.460573\pi$
$18$	40002.0	1.61670
$19$	−4595.58	−0.153710	−0.0768550	−	0.997042i	$-0.524488\pi$
$19$	−4595.58	−0.153710	−0.0768550	+	0.997042i	$0.524488\pi$
$20$	119149.	3.33031
$21$	−13758.0	−0.324181
$22$	−95090.1	−1.90395
$23$	−57829.7	−0.991068	−0.495534	−	0.868588i	$-0.665028\pi$
$23$	−57829.7	−0.991068	−0.495534	+	0.868588i	$0.665028\pi$
$24$	−86562.7	−1.27818
$25$	42499.9	0.543999
$26$	184990.	2.06415
$27$	−74738.5	−0.730754
$28$	−254504.	−2.19100
$29$	−209992.	−1.59886	−0.799430	−	0.600760i	$-0.794865\pi$
$29$	−209992.	−1.59886	−0.799430	+	0.600760i	$0.794865\pi$
$30$	−139794.	−0.945287
$31$	−27259.7	−0.164344	−0.0821722	−	0.996618i	$-0.526186\pi$
$31$	−27259.7	−0.164344	−0.0821722	+	0.996618i	$0.526186\pi$
$32$	−648236.	−3.49710
$33$	81250.8	0.393576
$34$	−108637.	−0.474023
$35$	−257657.	−1.01579
$36$	−632288.	−2.25869
$37$	138457.	0.449376	0.224688	−	0.974431i	$-0.427864\pi$
$37$	138457.	0.449376	0.224688	+	0.974431i	$0.427864\pi$
$38$	99742.1	0.294874
$39$	−158066.	−0.426691
$40$	−1.62113e6	−4.00506
$41$	−614751.	−1.39301	−0.696507	−	0.717550i	$-0.745264\pi$
$41$	−614751.	−1.39301	−0.696507	+	0.717550i	$0.745264\pi$
$42$	298602.	0.621900
$43$	629021.	1.20650	0.603248	−	0.797554i	$-0.293873\pi$
$43$	629021.	1.20650	0.603248	+	0.797554i	$0.293873\pi$
$44$	1.50303e6	2.66001
$45$	−640121.	−1.04717
$46$	1.25513e6	1.90124
$47$	754131.	1.05951	0.529754	−	0.848151i	$-0.322284\pi$
$47$	754131.	1.05951	0.529754	+	0.848151i	$0.322284\pi$
$48$	1.06440e6	1.38919
$49$	−273182.	−0.331715
$50$	−922416.	−1.04359
$51$	92825.7	0.0979879
$52$	−2.92402e6	−2.88382
$53$	−1.98562e6	−1.83202	−0.916012	−	0.401152i	$-0.868610\pi$
$53$	−1.98562e6	−1.83202	−0.916012	+	0.401152i	$0.868610\pi$
$54$	1.62212e6	1.40186
$55$	1.52165e6	1.23323
$56$	3.46277e6	2.63491
$57$	−85225.7	−0.0609549
$58$	4.55766e6	3.06721
$59$	2.20513e6	1.39782	0.698912	−	0.715208i	$-0.253668\pi$
$59$	2.20513e6	1.39782	0.698912	+	0.715208i	$0.253668\pi$
$60$	2.20964e6	1.32066
$61$	−1.17845e6	−0.664746	−0.332373	−	0.943148i	$-0.607849\pi$
$61$	−1.17845e6	−0.664746	−0.332373	+	0.943148i	$0.607849\pi$
$62$	591643.	0.315274
$63$	1.36731e6	0.688930
$64$	6.72271e6	3.20564
$65$	−2.96024e6	−1.33700
$66$	−1.76346e6	−0.755027
$67$	3.19854e6	1.29924	0.649621	−	0.760258i	$-0.274927\pi$
$67$	3.19854e6	1.29924	0.649621	+	0.760258i	$0.274927\pi$
$68$	1.71715e6	0.662258
$69$	−1.07246e6	−0.393016
$70$	5.59218e6	1.94867
$71$	2.97974e6	0.988041	0.494020	−	0.869450i	$-0.335527\pi$
$71$	2.97974e6	0.988041	0.494020	+	0.869450i	$0.335527\pi$
$72$	8.60287e6	2.71631
$73$	−2.30687e6	−0.694054	−0.347027	−	0.937855i	$-0.612809\pi$
$73$	−2.30687e6	−0.694054	−0.347027	+	0.937855i	$0.612809\pi$
$74$	−3.00507e6	−0.862071
$75$	788168.	0.215727
$76$	−1.57656e6	−0.411968
$77$	−3.25028e6	−0.811340
$78$	3.43066e6	0.818554
$79$	2.17251e6	0.495755	0.247878	−	0.968791i	$-0.420267\pi$
$79$	2.17251e6	0.495755	0.247878	+	0.968791i	$0.420267\pi$
$80$	1.99339e7	4.35289
$81$	2.64477e6	0.552956
$82$	1.33425e7	2.67232
$83$	4.61850e6	0.886599	0.443300	−	0.896373i	$-0.353808\pi$
$83$	4.61850e6	0.886599	0.443300	+	0.896373i	$0.353808\pi$
$84$	−4.71983e6	−0.868857
$85$	1.73842e6	0.307036
$86$	−1.36522e7	−2.31451
$87$	−3.89434e6	−0.634040
$88$	−2.04502e7	−3.19895
$89$	−9.59280e6	−1.44238	−0.721191	−	0.692736i	$-0.756405\pi$
$89$	−9.59280e6	−1.44238	−0.721191	+	0.692736i	$0.756405\pi$
$90$	1.38931e7	2.00887
$91$	6.32314e6	0.879606
$92$	−1.98391e7	−2.65623
$93$	−505536.	−0.0651721
$94$	−1.63676e7	−2.03253
$95$	−1.59609e6	−0.190997
$96$	−1.20216e7	−1.38680
$97$	4.07353e6	0.453179	0.226590	−	0.973990i	$-0.427242\pi$
$97$	4.07353e6	0.453179	0.226590	+	0.973990i	$0.427242\pi$
$98$	5.92912e6	0.636354
$99$	−8.07495e6	−0.836406
$100$	1.45801e7	1.45801
$101$	−1.24988e7	−1.20710	−0.603550	−	0.797325i	$-0.706247\pi$
$101$	−1.24988e7	−1.20710	−0.603550	+	0.797325i	$0.706247\pi$
$102$	−2.01468e6	−0.187978
$103$	1.23873e7	1.11698	0.558490	−	0.829511i	$-0.311381\pi$
$103$	1.23873e7	1.11698	0.558490	+	0.829511i	$0.311381\pi$
$104$	3.97841e7	3.46811
$105$	−4.77830e6	−0.402820
$106$	4.30958e7	3.51451
$107$	2.44838e7	1.93213	0.966063	−	0.258308i	$-0.0831648\pi$
$107$	2.44838e7	1.93213	0.966063	+	0.258308i	$0.0831648\pi$
$108$	−2.56398e7	−1.95854
$109$	9.77133e6	0.722705	0.361352	−	0.932429i	$-0.382315\pi$
$109$	9.77133e6	0.722705	0.361352	+	0.932429i	$0.382315\pi$
$110$	−3.30258e7	−2.36581
$111$	2.56771e6	0.178203
$112$	−4.25793e7	−2.86375
$113$	1.24157e7	0.809459	0.404730	−	0.914436i	$-0.367366\pi$
$113$	1.24157e7	0.809459	0.404730	+	0.914436i	$0.367366\pi$
$114$	1.84973e6	0.116934
$115$	−2.00849e7	−1.23148
$116$	−7.20401e7	−4.28520
$117$	1.57091e7	0.906780
$118$	−4.78601e7	−2.68155
$119$	−3.71331e6	−0.201998
$120$	−3.00642e7	−1.58824
$121$	−291938.	−0.0149810
$122$	2.55769e7	1.27523
$123$	−1.14007e7	−0.552411
$124$	−9.35174e6	−0.440470
$125$	−1.23730e7	−0.566617
$126$	−2.96760e7	−1.32163
$127$	−1.38717e7	−0.600921	−0.300461	−	0.953794i	$-0.597140\pi$
$127$	−1.38717e7	−0.600921	−0.300461	+	0.953794i	$0.597140\pi$
$128$	−6.29351e7	−2.65252
$129$	1.16653e7	0.478445
$130$	6.42489e7	2.56486
$131$	1.92949e7	0.749883	0.374942	−	0.927048i	$-0.377663\pi$
$131$	1.92949e7	0.749883	0.374942	+	0.927048i	$0.377663\pi$
$132$	2.78740e7	1.05485
$133$	3.40929e6	0.125656
$134$	−6.94210e7	−2.49243
$135$	−2.59575e7	−0.908018
$136$	−2.33635e7	−0.796437
$137$	3.93568e7	1.30767	0.653835	−	0.756637i	$-0.273159\pi$
$137$	3.93568e7	1.30767	0.653835	+	0.756637i	$0.273159\pi$
$138$	2.32766e7	0.753952
$139$	−3.71144e6	−0.117217	−0.0586085	−	0.998281i	$-0.518666\pi$
$139$	−3.71144e6	−0.117217	−0.0586085	+	0.998281i	$0.518666\pi$
$140$	−8.83922e7	−2.72249
$141$	1.39855e7	0.420156
$142$	−6.46722e7	−1.89543
$143$	−3.73427e7	−1.06790
$144$	−1.05783e8	−2.95222
$145$	−7.29326e7	−1.98671
$146$	5.00682e7	1.33146
$147$	−5.06620e6	−0.131544
$148$	4.74992e7	1.20440
$149$	2.43060e7	0.601953	0.300976	−	0.953632i	$-0.402688\pi$
$149$	2.43060e7	0.601953	0.300976	+	0.953632i	$0.402688\pi$
$150$	−1.71064e7	−0.413845
$151$	6.04288e7	1.42832	0.714158	−	0.699985i	$-0.246810\pi$
$151$	6.04288e7	1.42832	0.714158	+	0.699985i	$0.246810\pi$
$152$	2.14506e7	0.495436
$153$	−9.22531e6	−0.208238
$154$	7.05439e7	1.55646
$155$	−9.46759e6	−0.204211
$156$	−5.42264e7	−1.14360
$157$	5.69964e7	1.17543	0.587717	−	0.809066i	$-0.300027\pi$
$157$	5.69964e7	1.17543	0.587717	+	0.809066i	$0.300027\pi$
$158$	−4.71521e7	−0.951045
$159$	−3.68237e7	−0.726503
$160$	−2.25139e8	−4.34542
$161$	4.29017e7	0.810185
$162$	−5.74020e7	−1.06078
$163$	−5.68011e7	−1.02731	−0.513653	−	0.857998i	$-0.671708\pi$
$163$	−5.68011e7	−1.02731	−0.513653	+	0.857998i	$0.671708\pi$
$164$	−2.10897e8	−3.73351
$165$	2.82193e7	0.489049
$166$	−1.00240e8	−1.70083
$167$	9.77723e7	1.62446	0.812229	−	0.583339i	$-0.198254\pi$
$167$	9.77723e7	1.62446	0.812229	+	0.583339i	$0.198254\pi$
$168$	6.42177e7	1.04489
$169$	9.89852e6	0.157749
$170$	−3.77307e7	−0.589011
$171$	8.47000e6	0.129538
$172$	2.15793e8	3.23361
$173$	−7.82480e7	−1.14898	−0.574489	−	0.818512i	$-0.694799\pi$
$173$	−7.82480e7	−1.14898	−0.574489	+	0.818512i	$0.694799\pi$
$174$	8.45225e7	1.21633
$175$	−3.15291e7	−0.444712
$176$	2.51461e8	3.47677
$177$	4.08945e7	0.554318
$178$	2.08202e8	2.76703
$179$	−1.04264e8	−1.35879	−0.679393	−	0.733775i	$-0.737757\pi$
$179$	−1.04264e8	−1.35879	−0.679393	+	0.733775i	$0.737757\pi$
$180$	−2.19600e8	−2.80659
$181$	6.45777e7	0.809483	0.404741	−	0.914431i	$-0.367362\pi$
$181$	6.45777e7	0.809483	0.404741	+	0.914431i	$0.367362\pi$
$182$	−1.37237e8	−1.68741
$183$	−2.18545e7	−0.263610
$184$	2.69930e8	3.19440
$185$	4.80877e7	0.558384
$186$	1.09721e7	0.125024
$187$	2.19298e7	0.245238
$188$	2.58713e8	2.83965
$189$	5.54457e7	0.597381
$190$	3.46415e7	0.366403
$191$	−8.70951e7	−0.904434	−0.452217	−	0.891908i	$-0.649367\pi$
$191$	−8.70951e7	−0.904434	−0.452217	+	0.891908i	$0.649367\pi$
$192$	1.24674e8	1.27122
$193$	6.03473e7	0.604236	0.302118	−	0.953270i	$-0.402306\pi$
$193$	6.03473e7	0.604236	0.302118	+	0.953270i	$0.402306\pi$
$194$	−8.84116e7	−0.869368
$195$	−5.48982e7	−0.530197
$196$	−9.37180e7	−0.889051
$197$	3.56807e7	0.332508	0.166254	−	0.986083i	$-0.446833\pi$
$197$	3.56807e7	0.332508	0.166254	+	0.986083i	$0.446833\pi$
$198$	1.75258e8	1.60454
$199$	5.98465e6	0.0538336	0.0269168	−	0.999638i	$-0.491431\pi$
$199$	5.98465e6	0.0538336	0.0269168	+	0.999638i	$0.491431\pi$
$200$	−1.98376e8	−1.75341
$201$	5.93175e7	0.515225
$202$	2.71273e8	2.31567
$203$	1.55786e8	1.30705
$204$	3.18449e7	0.262624
$205$	−2.13510e8	−1.73093
$206$	−2.68853e8	−2.14279
$207$	1.06585e8	0.835215
$208$	−4.89196e8	−3.76931
$209$	−2.01343e7	−0.152554
$210$	1.03708e8	0.772759
$211$	−2.60567e8	−1.90955	−0.954773	−	0.297336i	$-0.903902\pi$
$211$	−2.60567e8	−1.90955	−0.954773	+	0.297336i	$0.903902\pi$
$212$	−6.81189e8	−4.91012
$213$	5.52599e7	0.391815
$214$	−5.31395e8	−3.70654
$215$	2.18466e8	1.49916
$216$	3.48854e8	2.35535
$217$	2.02230e7	0.134349
$218$	−2.12076e8	−1.38642
$219$	−4.27813e7	−0.275232
$220$	5.22019e8	3.30527
$221$	−4.26625e7	−0.265872
$222$	−5.57295e7	−0.341861
$223$	8.69411e7	0.524999	0.262499	−	0.964932i	$-0.415453\pi$
$223$	8.69411e7	0.524999	0.262499	+	0.964932i	$0.415453\pi$
$224$	4.80903e8	2.85883
$225$	−7.83306e7	−0.458451
$226$	−2.69469e8	−1.55285
$227$	−5.61654e7	−0.318697	−0.159349	−	0.987222i	$-0.550939\pi$
$227$	−5.61654e7	−0.318697	−0.159349	+	0.987222i	$0.550939\pi$
$228$	−2.92376e7	−0.163369
$229$	9.64290e7	0.530620	0.265310	−	0.964163i	$-0.414526\pi$
$229$	9.64290e7	0.530620	0.265310	+	0.964163i	$0.414526\pi$
$230$	4.35921e8	2.36244
$231$	−6.02770e7	−0.321743
$232$	9.80174e8	5.15342
$233$	1.02025e8	0.528399	0.264200	−	0.964468i	$-0.414892\pi$
$233$	1.02025e8	0.528399	0.264200	+	0.964468i	$0.414892\pi$
$234$	−3.40950e8	−1.73954
$235$	2.61918e8	1.31652
$236$	7.56495e8	3.74640
$237$	4.02896e7	0.196596
$238$	8.05935e7	0.387508
$239$	−4.79738e7	−0.227306	−0.113653	−	0.993520i	$-0.536255\pi$
$239$	−4.79738e7	−0.227306	−0.113653	+	0.993520i	$0.536255\pi$
$240$	3.69678e8	1.72617
$241$	−3.18651e8	−1.46641	−0.733205	−	0.680008i	$-0.761976\pi$
$241$	−3.18651e8	−1.46641	−0.733205	+	0.680008i	$0.761976\pi$
$242$	6.33620e6	0.0287392
$243$	2.12501e8	0.950033
$244$	−4.04279e8	−1.78163
$245$	−9.48790e7	−0.412182
$246$	2.47439e8	1.05973
$247$	3.91696e7	0.165390
$248$	1.27239e8	0.529713
$249$	8.56508e7	0.351588
$250$	2.68542e8	1.08698
$251$	1.46598e8	0.585156	0.292578	−	0.956242i	$-0.405487\pi$
$251$	1.46598e8	0.585156	0.292578	+	0.956242i	$0.405487\pi$
$252$	4.69071e8	1.84645
$253$	−2.53366e8	−0.983617
$254$	3.01071e8	1.15279
$255$	3.22394e7	0.121758
$256$	5.05433e8	1.88289
$257$	1.91446e8	0.703528	0.351764	−	0.936089i	$-0.385582\pi$
$257$	1.91446e8	0.703528	0.351764	+	0.936089i	$0.385582\pi$
$258$	−2.53183e8	−0.917837
$259$	−1.02716e8	−0.367359
$260$	−1.01554e9	−3.58337
$261$	3.87032e8	1.34743
$262$	−4.18776e8	−1.43856
$263$	−7.16770e7	−0.242960	−0.121480	−	0.992594i	$-0.538764\pi$
$263$	−7.16770e7	−0.242960	−0.121480	+	0.992594i	$0.538764\pi$
$264$	−3.79252e8	−1.26857
$265$	−6.89628e8	−2.27643
$266$	−7.39950e7	−0.241055
$267$	−1.77900e8	−0.571988
$268$	1.09729e9	3.48218
$269$	1.66055e7	0.0520139	0.0260069	−	0.999662i	$-0.491721\pi$
$269$	1.66055e7	0.0520139	0.0260069	+	0.999662i	$0.491721\pi$
$270$	5.63380e8	1.74192
$271$	−3.78978e8	−1.15670	−0.578350	−	0.815789i	$-0.696303\pi$
$271$	−3.78978e8	−1.15670	−0.578350	+	0.815789i	$0.696303\pi$
$272$	2.87284e8	0.865606
$273$	1.17264e8	0.348814
$274$	−8.54198e8	−2.50860
$275$	1.86202e8	0.539909
$276$	−3.67920e8	−1.05335
$277$	5.63421e7	0.159277	0.0796386	−	0.996824i	$-0.474623\pi$
$277$	5.63421e7	0.159277	0.0796386	+	0.996824i	$0.474623\pi$
$278$	8.05528e7	0.224866
$279$	5.02417e7	0.138500
$280$	1.20266e9	3.27408
$281$	4.81539e8	1.29467	0.647335	−	0.762206i	$-0.275884\pi$
$281$	4.81539e8	1.29467	0.647335	+	0.762206i	$0.275884\pi$
$282$	−3.03540e8	−0.806017
$283$	−1.68909e8	−0.442997	−0.221498	−	0.975161i	$-0.571095\pi$
$283$	−1.68909e8	−0.442997	−0.221498	+	0.975161i	$0.571095\pi$
$284$	1.02223e9	2.64811
$285$	−2.95998e7	−0.0757412
$286$	8.10484e8	2.04863
$287$	4.56061e8	1.13877
$288$	1.19475e9	2.94715
$289$	−3.85285e8	−0.938943
$290$	1.58292e9	3.81125
$291$	7.55443e7	0.179712
$292$	−7.91397e8	−1.86018
$293$	3.93103e8	0.912998	0.456499	−	0.889724i	$-0.349103\pi$
$293$	3.93103e8	0.912998	0.456499	+	0.889724i	$0.349103\pi$
$294$	1.09957e8	0.252351
$295$	7.65867e8	1.73691
$296$	−6.46272e8	−1.44842
$297$	−3.27447e8	−0.725259
$298$	−5.27537e8	−1.15477
$299$	4.92901e8	1.06638
$300$	2.70390e8	0.578184
$301$	−4.66648e8	−0.986294
$302$	−1.31154e9	−2.74005
$303$	−2.31792e8	−0.478684
$304$	−2.63763e8	−0.538464
$305$	−4.09288e8	−0.825998
$306$	2.00225e8	0.399479
$307$	1.82975e8	0.360917	0.180458	−	0.983583i	$-0.442242\pi$
$307$	1.82975e8	0.360917	0.180458	+	0.983583i	$0.442242\pi$
$308$	−1.11504e9	−2.17452
$309$	2.29724e8	0.442947
$310$	2.05484e8	0.391753
$311$	6.72049e8	1.26689	0.633446	−	0.773787i	$-0.281640\pi$
$311$	6.72049e8	1.26689	0.633446	+	0.773787i	$0.281640\pi$
$312$	7.37802e8	1.37530
$313$	−3.73633e8	−0.688716	−0.344358	−	0.938838i	$-0.611903\pi$
$313$	−3.73633e8	−0.688716	−0.344358	+	0.938838i	$0.611903\pi$
$314$	−1.23705e9	−2.25492
$315$	4.74882e8	0.856050
$316$	7.45304e8	1.32871
$317$	1.25346e8	0.221006	0.110503	−	0.993876i	$-0.464754\pi$
$317$	1.25346e8	0.221006	0.110503	+	0.993876i	$0.464754\pi$
$318$	7.99219e8	1.39371
$319$	−9.20026e8	−1.58684
$320$	2.33487e9	3.98326
$321$	4.54056e8	0.766199
$322$	−9.31137e8	−1.55424
$323$	−2.30026e7	−0.0379812
$324$	9.07318e8	1.48201
$325$	−3.62241e8	−0.585336
$326$	1.23281e9	1.97076
$327$	1.81211e8	0.286594
$328$	2.86945e9	4.48994
$329$	−5.59462e8	−0.866134
$330$	−6.12470e8	−0.938179
$331$	7.52273e8	1.14019	0.570095	−	0.821579i	$-0.306906\pi$
$331$	7.52273e8	1.14019	0.570095	+	0.821579i	$0.306906\pi$
$332$	1.58443e9	2.37623
$333$	−2.55187e8	−0.378708
$334$	−2.12204e9	−3.11632
$335$	1.11089e9	1.61441
$336$	−7.89639e8	−1.13564
$337$	−1.20087e9	−1.70919	−0.854596	−	0.519294i	$-0.826195\pi$
$337$	−1.20087e9	−1.70919	−0.854596	+	0.519294i	$0.826195\pi$
$338$	−2.14837e8	−0.302622
$339$	2.30250e8	0.320997
$340$	5.96386e8	0.822907
$341$	−1.19431e8	−0.163109
$342$	−1.83832e8	−0.248502
$343$	8.13620e8	1.08866
$344$	−2.93606e9	−3.88876
$345$	−3.72478e8	−0.488353
$346$	1.69829e9	2.20417
$347$	−9.13542e8	−1.17375	−0.586875	−	0.809678i	$-0.699642\pi$
$347$	−9.13542e8	−1.17375	−0.586875	+	0.809678i	$0.699642\pi$
$348$	−1.33600e9	−1.69933
$349$	2.71556e8	0.341956	0.170978	−	0.985275i	$-0.445307\pi$
$349$	2.71556e8	0.341956	0.170978	+	0.985275i	$0.445307\pi$
$350$	6.84306e8	0.853125
$351$	6.37020e8	0.786282
$352$	−2.84008e9	−3.47081
$353$	1.56770e9	1.89693	0.948465	−	0.316883i	$-0.102636\pi$
$353$	1.56770e9	1.89693	0.948465	+	0.316883i	$0.102636\pi$
$354$	−8.87573e8	−1.06339
$355$	1.03490e9	1.22772
$356$	−3.29092e9	−3.86582
$357$	−6.88640e7	−0.0801038
$358$	2.26295e9	2.60666
$359$	−1.23443e9	−1.40810	−0.704051	−	0.710149i	$-0.748627\pi$
$359$	−1.23443e9	−1.40810	−0.704051	+	0.710149i	$0.748627\pi$
$360$	2.98787e9	3.37523
$361$	−8.72752e8	−0.976373
$362$	−1.40159e9	−1.55289
$363$	−5.41404e6	−0.00594085
$364$	2.16922e9	2.35749
$365$	−8.01201e8	−0.862416
$366$	4.74329e8	0.505703
$367$	−6.73989e8	−0.711740	−0.355870	−	0.934535i	$-0.615815\pi$
$367$	−6.73989e8	−0.711740	−0.355870	+	0.934535i	$0.615815\pi$
$368$	−3.31914e9	−3.47182
$369$	1.13303e9	1.17395
$370$	−1.04369e9	−1.07119
$371$	1.47306e9	1.49766
$372$	−1.73430e8	−0.174672
$373$	1.92179e9	1.91745	0.958726	−	0.284331i	$-0.0917716\pi$
$373$	1.92179e9	1.91745	0.958726	+	0.284331i	$0.0917716\pi$
$374$	−4.75962e8	−0.470459
$375$	−2.29459e8	−0.224696
$376$	−3.52003e9	−3.41499
$377$	1.78983e9	1.72035
$378$	−1.20339e9	−1.14600
$379$	1.08467e8	0.102343	0.0511717	−	0.998690i	$-0.483704\pi$
$379$	1.08467e8	0.102343	0.0511717	+	0.998690i	$0.483704\pi$
$380$	−5.47558e8	−0.511902
$381$	−2.57254e8	−0.238300
$382$	1.89031e9	1.73504
$383$	7.40674e8	0.673646	0.336823	−	0.941568i	$-0.390648\pi$
$383$	7.40674e8	0.673646	0.336823	+	0.941568i	$0.390648\pi$
$384$	−1.16714e9	−1.05188
$385$	−1.12886e9	−1.00815
$386$	−1.30977e9	−1.15915
$387$	−1.15933e9	−1.01676
$388$	1.39747e9	1.21459
$389$	1.88337e9	1.62223	0.811115	−	0.584886i	$-0.198861\pi$
$389$	1.88337e9	1.62223	0.811115	+	0.584886i	$0.198861\pi$
$390$	1.19151e9	1.01712
$391$	−2.89460e8	−0.244889
$392$	1.27512e9	1.06918
$393$	3.57828e8	0.297372
$394$	−7.74412e8	−0.637874
$395$	7.54538e8	0.616015
$396$	−2.77020e9	−2.24170
$397$	4.98557e8	0.399897	0.199948	−	0.979806i	$-0.435923\pi$
$397$	4.98557e8	0.399897	0.199948	+	0.979806i	$0.435923\pi$
$398$	−1.29891e8	−0.103273
$399$	6.32258e7	0.0498298
$400$	2.43928e9	1.90569
$401$	−2.75148e8	−0.213089	−0.106544	−	0.994308i	$-0.533979\pi$
$401$	−2.75148e8	−0.213089	−0.106544	+	0.994308i	$0.533979\pi$
$402$	−1.28742e9	−0.988394
$403$	2.32343e8	0.176833
$404$	−4.28784e9	−3.23522
$405$	9.18558e8	0.687091
$406$	−3.38116e9	−2.50741
$407$	6.06614e8	0.445997
$408$	−4.33280e8	−0.315833
$409$	−1.22263e9	−0.883615	−0.441807	−	0.897110i	$-0.645663\pi$
$409$	−1.22263e9	−0.883615	−0.441807	+	0.897110i	$0.645663\pi$
$410$	4.63400e9	3.32057
$411$	7.29879e8	0.518567
$412$	4.24959e9	2.99369
$413$	−1.63591e9	−1.14270
$414$	−2.31331e9	−1.60226
$415$	1.60405e9	1.10167
$416$	5.52512e9	3.76284
$417$	−6.88292e7	−0.0464833
$418$	4.36994e8	0.292657
$419$	1.79367e9	1.19122	0.595612	−	0.803272i	$-0.296910\pi$
$419$	1.79367e9	1.19122	0.595612	+	0.803272i	$0.296910\pi$
$420$	−1.63925e9	−1.07962
$421$	3.26365e8	0.213165	0.106582	−	0.994304i	$-0.466009\pi$
$421$	3.26365e8	0.213165	0.106582	+	0.994304i	$0.466009\pi$
$422$	5.65532e9	3.66323
$423$	−1.38992e9	−0.892892
$424$	9.26823e9	5.90495
$425$	2.12728e8	0.134420
$426$	−1.19936e9	−0.751648
$427$	8.74247e8	0.543421
$428$	8.39943e9	5.17841
$429$	−6.92527e8	−0.423483
$430$	−4.74157e9	−2.87596
$431$	−1.35044e9	−0.812463	−0.406231	−	0.913770i	$-0.633157\pi$
$431$	−1.35044e9	−0.812463	−0.406231	+	0.913770i	$0.633157\pi$
$432$	−4.28961e9	−2.55991
$433$	−1.18374e9	−0.700724	−0.350362	−	0.936614i	$-0.613941\pi$
$433$	−1.18374e9	−0.700724	−0.350362	+	0.936614i	$0.613941\pi$
$434$	−4.38918e8	−0.257733
$435$	−1.35255e9	−0.787844
$436$	3.35216e9	1.93697
$437$	2.65761e8	0.152337
$438$	9.28523e8	0.527999
$439$	−2.77248e9	−1.56402	−0.782011	−	0.623264i	$-0.785806\pi$
$439$	−2.77248e9	−1.56402	−0.782011	+	0.623264i	$0.785806\pi$
$440$	−7.10257e9	−3.97494
$441$	5.03495e8	0.279550
$442$	9.25944e8	0.510043
$443$	2.17313e9	1.18760	0.593802	−	0.804611i	$-0.297626\pi$
$443$	2.17313e9	1.18760	0.593802	+	0.804611i	$0.297626\pi$
$444$	8.80882e8	0.477614
$445$	−3.33169e9	−1.79227
$446$	−1.88696e9	−1.00714
$447$	4.50760e8	0.238709
$448$	−4.98733e9	−2.62057
$449$	2.91993e8	0.152233	0.0761166	−	0.997099i	$-0.475748\pi$
$449$	2.91993e8	0.152233	0.0761166	+	0.997099i	$0.475748\pi$
$450$	1.70008e9	0.879481
$451$	−2.69337e9	−1.38254
$452$	4.25933e9	2.16948
$453$	1.12066e9	0.566410
$454$	1.21901e9	0.611381
$455$	2.19610e9	1.09298
$456$	3.97806e8	0.196469
$457$	1.75107e9	0.858218	0.429109	−	0.903253i	$-0.358828\pi$
$457$	1.75107e9	0.858218	0.429109	+	0.903253i	$0.358828\pi$
$458$	−2.09289e9	−1.01793
$459$	−3.74095e8	−0.180566
$460$	−6.89034e9	−3.30057
$461$	1.89652e8	0.0901578	0.0450789	−	0.998983i	$-0.485646\pi$
$461$	1.89652e8	0.0901578	0.0450789	+	0.998983i	$0.485646\pi$
$462$	1.30825e9	0.617224
$463$	1.31527e9	0.615861	0.307930	−	0.951409i	$-0.400364\pi$
$463$	1.31527e9	0.615861	0.307930	+	0.951409i	$0.400364\pi$
$464$	−1.20525e10	−5.60099
$465$	−1.75578e8	−0.0809814
$466$	−2.21435e9	−1.01367
$467$	−2.34371e9	−1.06487	−0.532434	−	0.846472i	$-0.678722\pi$
$467$	−2.34371e9	−1.06487	−0.532434	+	0.846472i	$0.678722\pi$
$468$	5.38919e9	2.43032
$469$	−2.37288e9	−1.06211
$470$	−5.68465e9	−2.52558
$471$	1.05701e9	0.466128
$472$	−1.02928e10	−4.50545
$473$	2.75589e9	1.19742
$474$	−8.74443e8	−0.377144
$475$	−1.95312e8	−0.0836181
$476$	−1.27389e9	−0.541387
$477$	3.65965e9	1.54392
$478$	1.04122e9	0.436059
$479$	1.91654e9	0.796791	0.398395	−	0.917214i	$-0.369567\pi$
$479$	1.91654e9	0.796791	0.398395	+	0.917214i	$0.369567\pi$
$480$	−4.17525e9	−1.72321
$481$	−1.18012e9	−0.483522
$482$	6.91597e9	2.81312
$483$	7.95620e8	0.321285
$484$	−1.00153e8	−0.0401516
$485$	1.41478e9	0.563110
$486$	−4.61210e9	−1.82252
$487$	3.62921e9	1.42384	0.711920	−	0.702261i	$-0.247826\pi$
$487$	3.62921e9	1.42384	0.711920	+	0.702261i	$0.247826\pi$
$488$	5.50060e9	2.14260
$489$	−1.05339e9	−0.407386
$490$	2.05925e9	0.790720
$491$	1.16688e9	0.444876	0.222438	−	0.974947i	$-0.428598\pi$
$491$	1.16688e9	0.444876	0.222438	+	0.974947i	$0.428598\pi$
$492$	−3.91112e9	−1.48055
$493$	−1.05109e9	−0.395072
$494$	−8.50134e8	−0.317280
$495$	−2.80452e9	−1.03930
$496$	−1.56457e9	−0.575717
$497$	−2.21056e9	−0.807710
$498$	−1.85896e9	−0.674477
$499$	2.37888e9	0.857077	0.428538	−	0.903524i	$-0.359029\pi$
$499$	2.37888e9	0.857077	0.428538	+	0.903524i	$0.359029\pi$
$500$	−4.24469e9	−1.51862
$501$	1.81320e9	0.644191
$502$	−3.18176e9	−1.12255
$503$	−1.18084e9	−0.413718	−0.206859	−	0.978371i	$-0.566324\pi$
$503$	−1.18084e9	−0.413718	−0.206859	+	0.978371i	$0.566324\pi$
$504$	−6.38216e9	−2.22055
$505$	−4.34097e9	−1.49991
$506$	5.49903e9	1.88695
$507$	1.83570e8	0.0625566
$508$	−4.75885e9	−1.61057
$509$	−3.76164e9	−1.26434	−0.632172	−	0.774828i	$-0.717836\pi$
$509$	−3.76164e9	−1.26434	−0.632172	+	0.774828i	$0.717836\pi$
$510$	−6.99721e8	−0.233577
$511$	1.71138e9	0.567380
$512$	−2.91419e9	−0.959563
$513$	3.43466e8	0.112324
$514$	−4.15514e9	−1.34963
$515$	4.30224e9	1.38794
$516$	4.00191e9	1.28231
$517$	3.30403e9	1.05154
$518$	2.22935e9	0.704732
$519$	−1.45112e9	−0.455636
$520$	1.38174e10	4.30939
$521$	1.79651e9	0.556543	0.278271	−	0.960502i	$-0.410239\pi$
$521$	1.79651e9	0.556543	0.278271	+	0.960502i	$0.410239\pi$
$522$	−8.40011e9	−2.58487
$523$	−4.83752e9	−1.47866	−0.739328	−	0.673345i	$-0.764857\pi$
$523$	−4.83752e9	−1.47866	−0.739328	+	0.673345i	$0.764857\pi$
$524$	6.61934e9	2.00981
$525$	−5.84713e8	−0.176354
$526$	1.55567e9	0.466088
$527$	−1.36445e8	−0.0406089
$528$	4.66339e9	1.37874
$529$	−6.05497e7	−0.0177835
$530$	1.49677e10	4.36705
$531$	−4.06423e9	−1.17801
$532$	1.16959e9	0.336779
$533$	5.23972e9	1.49887
$534$	3.86113e9	1.09729
$535$	8.50349e9	2.40082
$536$	−1.49297e10	−4.18770
$537$	−1.93360e9	−0.538837
$538$	−3.60405e8	−0.0997821
$539$	−1.19687e9	−0.329221
$540$	−8.90500e9	−2.43364
$541$	−1.20863e9	−0.328174	−0.164087	−	0.986446i	$-0.552468\pi$
$541$	−1.20863e9	−0.328174	−0.164087	+	0.986446i	$0.552468\pi$
$542$	8.22531e9	2.21899
$543$	1.19760e9	0.321007
$544$	−3.24467e9	−0.864121
$545$	3.39369e9	0.898017
$546$	−2.54508e9	−0.669157
$547$	−1.63667e8	−0.0427569
$547$	−1.63667e8	−0.0427569
$548$	1.35018e10	3.50477
$549$	2.17197e9	0.560209
$550$	−4.04132e9	−1.03575
$551$	9.65035e8	0.245761
$552$	5.00590e9	1.26676
$553$	−1.61171e9	−0.405274
$554$	−1.22284e9	−0.305553
$555$	8.91794e8	0.221431
$556$	−1.27325e9	−0.314160
$557$	4.20567e9	1.03120	0.515599	−	0.856830i	$-0.327569\pi$
$557$	4.20567e9	1.03120	0.515599	+	0.856830i	$0.327569\pi$
$558$	−1.09044e9	−0.265695
$559$	−5.36135e9	−1.29817
$560$	−1.47882e10	−3.55843
$561$	4.06691e8	0.0972512
$562$	−1.04513e10	−2.48366
$563$	1.53651e9	0.362873	0.181437	−	0.983403i	$-0.441925\pi$
$563$	1.53651e9	0.362873	0.181437	+	0.983403i	$0.441925\pi$
$564$	4.79787e9	1.12609
$565$	4.31209e9	1.00582
$566$	3.66599e9	0.849834
$567$	−1.96206e9	−0.452034
$568$	−1.39085e10	−3.18464
$569$	3.24818e8	0.0739174	0.0369587	−	0.999317i	$-0.488233\pi$
$569$	3.24818e8	0.0739174	0.0369587	+	0.999317i	$0.488233\pi$
$570$	6.42433e8	0.145300
$571$	6.70744e9	1.50775	0.753877	−	0.657015i	$-0.228181\pi$
$571$	6.70744e9	1.50775	0.753877	+	0.657015i	$0.228181\pi$
$572$	−1.28108e10	−2.86214
$573$	−1.61519e9	−0.358660
$574$	−9.89832e9	−2.18459
$575$	−2.45776e9	−0.539140
$576$	−1.23905e10	−2.70153
$577$	−1.69952e9	−0.368308	−0.184154	−	0.982897i	$-0.558955\pi$
$577$	−1.69952e9	−0.368308	−0.184154	+	0.982897i	$0.558955\pi$
$578$	8.36220e9	1.80125
$579$	1.11915e9	0.239615
$580$	−2.50203e10	−5.32470
$581$	−3.42629e9	−0.724783
$582$	−1.63961e9	−0.344754
$583$	−8.69948e9	−1.81825
$584$	1.07677e10	2.23706
$585$	5.45596e9	1.12674
$586$	−8.53189e9	−1.75147
$587$	−9.62265e8	−0.196364	−0.0981819	−	0.995168i	$-0.531303\pi$
$587$	−9.62265e8	−0.196364	−0.0981819	+	0.995168i	$0.531303\pi$
$588$	−1.73802e9	−0.352560
$589$	1.25274e8	0.0252614
$590$	−1.66223e10	−3.33204
$591$	6.61705e8	0.131858
$592$	7.94675e9	1.57421
$593$	−4.08906e9	−0.805252	−0.402626	−	0.915365i	$-0.631902\pi$
$593$	−4.08906e9	−0.805252	−0.402626	+	0.915365i	$0.631902\pi$
$594$	7.10689e9	1.39132
$595$	−1.28967e9	−0.250998
$596$	8.33845e9	1.61333
$597$	1.10986e8	0.0213481
$598$	−1.06979e10	−2.04571
$599$	−4.43182e8	−0.0842535	−0.0421268	−	0.999112i	$-0.513413\pi$
$599$	−4.43182e8	−0.0842535	−0.0421268	+	0.999112i	$0.513413\pi$
$600$	−3.67891e9	−0.695328
$601$	−1.82531e9	−0.342986	−0.171493	−	0.985185i	$-0.554859\pi$
$601$	−1.82531e9	−0.342986	−0.171493	+	0.985185i	$0.554859\pi$
$602$	1.01281e10	1.89208
$603$	−5.89516e9	−1.09493
$604$	2.07307e10	3.82812
$605$	−1.01393e8	−0.0186151
$606$	5.03080e9	0.918296
$607$	−6.58318e9	−1.19475	−0.597373	−	0.801964i	$-0.703789\pi$
$607$	−6.58318e9	−1.19475	−0.597373	+	0.801964i	$0.703789\pi$
$608$	2.97902e9	0.537540
$609$	2.88907e9	0.518319
$610$	8.88315e9	1.58458
$611$	−6.42770e9	−1.14002
$612$	−3.16484e9	−0.558113
$613$	−2.04744e8	−0.0359004	−0.0179502	−	0.999839i	$-0.505714\pi$
$613$	−2.04744e8	−0.0359004	−0.0179502	+	0.999839i	$0.505714\pi$
$614$	−3.97127e9	−0.692374
$615$	−3.95957e9	−0.686413
$616$	1.51712e10	2.61510
$617$	4.43693e9	0.760473	0.380237	−	0.924889i	$-0.375843\pi$
$617$	4.43693e9	0.760473	0.380237	+	0.924889i	$0.375843\pi$
$618$	−4.98592e9	−0.849739
$619$	5.20840e9	0.882647	0.441324	−	0.897348i	$-0.354509\pi$
$619$	5.20840e9	0.882647	0.441324	+	0.897348i	$0.354509\pi$
$620$	−3.24796e9	−0.547318
$621$	4.32210e9	0.724227
$622$	−1.45861e10	−2.43038
$623$	7.11655e9	1.17913
$624$	−9.07223e9	−1.49475
$625$	−7.61758e9	−1.24806
$626$	8.10930e9	1.32121
$627$	−3.73394e8	−0.0604966
$628$	1.95532e10	3.15036
$629$	6.93031e8	0.111039
$630$	−1.03068e10	−1.64222
$631$	8.95070e9	1.41825	0.709127	−	0.705081i	$-0.249089\pi$
$631$	8.95070e9	1.41825	0.709127	+	0.705081i	$0.249089\pi$
$632$	−1.01406e10	−1.59791
$633$	−4.83225e9	−0.757245
$634$	−2.72051e9	−0.423973
$635$	−4.81780e9	−0.746691
$636$	−1.26328e10	−1.94715
$637$	2.32842e9	0.356921
$638$	1.99682e10	3.04415
$639$	−5.49190e9	−0.832663
$640$	−2.18581e10	−3.29596
$641$	−3.04411e9	−0.456517	−0.228259	−	0.973601i	$-0.573303\pi$
$641$	−3.04411e9	−0.456517	−0.228259	+	0.973601i	$0.573303\pi$
$642$	−9.85480e9	−1.46986
$643$	1.42689e9	0.211666	0.105833	−	0.994384i	$-0.466249\pi$
$643$	1.42689e9	0.211666	0.105833	+	0.994384i	$0.466249\pi$
$644$	1.47179e10	2.17143
$645$	4.05149e9	0.594505
$646$	4.99247e8	0.0728622
$647$	3.01088e9	0.437047	0.218524	−	0.975832i	$-0.429876\pi$
$647$	3.01088e9	0.437047	0.218524	+	0.975832i	$0.429876\pi$
$648$	−1.23449e10	−1.78228
$649$	9.66121e9	1.38731
$650$	7.86205e9	1.12289
$651$	3.75038e8	0.0532773
$652$	−1.94862e10	−2.75335
$653$	4.88250e9	0.686193	0.343097	−	0.939300i	$-0.388524\pi$
$653$	4.88250e9	0.686193	0.343097	+	0.939300i	$0.388524\pi$
$654$	−3.93299e9	−0.549795
$655$	6.70134e9	0.931788
$656$	−3.52836e10	−4.87989
$657$	4.25174e9	0.584908
$658$	1.21425e10	1.66157
$659$	1.27442e10	1.73465	0.867327	−	0.497738i	$-0.165836\pi$
$659$	1.27442e10	1.73465	0.867327	+	0.497738i	$0.165836\pi$
$660$	9.68093e9	1.31073
$661$	5.21268e9	0.702030	0.351015	−	0.936370i	$-0.385837\pi$
$661$	5.21268e9	0.702030	0.351015	+	0.936370i	$0.385837\pi$
$662$	−1.63273e10	−2.18731
$663$	−7.91183e8	−0.105434
$664$	−2.15576e10	−2.85767
$665$	1.18408e9	0.156137
$666$	5.53857e9	0.726503
$667$	1.21438e10	1.58458
$668$	3.35419e10	4.35381
$669$	1.61234e9	0.208192
$670$	−2.41107e10	−3.09704
$671$	−5.16306e9	−0.659748
$672$	8.91842e9	1.13369
$673$	−1.05298e10	−1.33158	−0.665788	−	0.746141i	$-0.731904\pi$
$673$	−1.05298e10	−1.33158	−0.665788	+	0.746141i	$0.731904\pi$
$674$	2.60636e10	3.27887
$675$	−3.17638e9	−0.397529
$676$	3.39579e9	0.422793
$677$	−4.95535e7	−0.00613782	−0.00306891	−	0.999995i	$-0.500977\pi$
$677$	−4.95535e7	−0.00613782	−0.00306891	+	0.999995i	$0.500977\pi$
$678$	−4.99734e9	−0.615793
$679$	−3.02200e9	−0.370468
$680$	−8.11439e9	−0.989634
$681$	−1.04160e9	−0.126382
$682$	2.59213e9	0.312904
$683$	−1.13628e10	−1.36463	−0.682314	−	0.731059i	$-0.739026\pi$
$683$	−1.13628e10	−1.36463	−0.682314	+	0.731059i	$0.739026\pi$
$684$	2.90573e9	0.347183
$685$	1.36691e10	1.62488
$686$	−1.76588e10	−2.08846
$687$	1.78829e9	0.210421
$688$	3.61027e10	4.22649
$689$	1.69241e10	1.97123
$690$	8.08423e9	0.936844
$691$	1.10382e10	1.27270	0.636350	−	0.771401i	$-0.280444\pi$
$691$	1.10382e10	1.27270	0.636350	+	0.771401i	$0.280444\pi$
$692$	−2.68438e10	−3.07945
$693$	5.99051e9	0.683751
$694$	1.98275e10	2.25169
$695$	−1.28902e9	−0.145651
$696$	1.81775e10	2.04363
$697$	−3.07706e9	−0.344209
$698$	−5.89384e9	−0.656000
$699$	1.89208e9	0.209541
$700$	−1.08164e10	−1.19190
$701$	1.45377e10	1.59398	0.796989	−	0.603993i	$-0.206425\pi$
$701$	1.45377e10	1.59398	0.796989	+	0.603993i	$0.206425\pi$
$702$	−1.38258e10	−1.50838
$703$	−6.36290e8	−0.0690736
$704$	2.94538e10	3.18154
$705$	4.85731e9	0.522077
$706$	−3.40252e10	−3.63902
$707$	9.27239e9	0.986788
$708$	1.40293e10	1.48566
$709$	1.04044e9	0.109637	0.0548183	−	0.998496i	$-0.482542\pi$
$709$	1.04044e9	0.109637	0.0548183	+	0.998496i	$0.482542\pi$
$710$	−2.24614e10	−2.35522
$711$	−4.00411e9	−0.417794
$712$	4.47760e10	4.64906
$713$	1.57642e9	0.162877
$714$	1.49462e9	0.153669
$715$	−1.29695e10	−1.32695
$716$	−3.57691e10	−3.64177
$717$	−8.89682e8	−0.0901401
$718$	2.67919e10	2.70127
$719$	6.02817e9	0.604832	0.302416	−	0.953176i	$-0.402207\pi$
$719$	6.02817e9	0.604832	0.302416	+	0.953176i	$0.402207\pi$
$720$	−3.67397e10	−3.66836
$721$	−9.18967e9	−0.913117
$722$	1.89422e10	1.87305
$723$	−5.90943e9	−0.581516
$724$	2.21541e10	2.16955
$725$	−8.92466e9	−0.869778
$726$	1.17506e8	0.0113968
$727$	1.87004e10	1.80502	0.902508	−	0.430674i	$-0.141724\pi$
$727$	1.87004e10	1.80502	0.902508	+	0.430674i	$0.141724\pi$
$728$	−2.95143e10	−2.83513
$729$	−1.84325e9	−0.176213
$730$	1.73892e10	1.65444
$731$	3.14849e9	0.298121
$732$	−7.49743e9	−0.706518
$733$	9.38136e9	0.879837	0.439918	−	0.898038i	$-0.355007\pi$
$733$	9.38136e9	0.879837	0.439918	+	0.898038i	$0.355007\pi$
$734$	1.46282e10	1.36538
$735$	−1.75955e9	−0.163454
$736$	3.74873e10	3.46587
$737$	1.40136e10	1.28947
$738$	−2.45913e10	−2.25208
$739$	2.80909e9	0.256041	0.128020	−	0.991772i	$-0.459138\pi$
$739$	2.80909e9	0.256041	0.128020	+	0.991772i	$0.459138\pi$
$740$	1.64970e10	1.49656
$741$	7.26406e8	0.0655867
$742$	−3.19712e10	−2.87306
$743$	7.92119e9	0.708484	0.354242	−	0.935154i	$-0.384739\pi$
$743$	7.92119e9	0.708484	0.354242	+	0.935154i	$0.384739\pi$
$744$	2.35967e9	0.210062
$745$	8.44175e9	0.747973
$746$	−4.17104e10	−3.67839
$747$	−8.51224e9	−0.747174
$748$	7.52325e9	0.657279
$749$	−1.81636e10	−1.57949
$750$	4.98016e9	0.431052
$751$	1.87978e10	1.61945	0.809725	−	0.586810i	$-0.199616\pi$
$751$	1.87978e10	1.61945	0.809725	+	0.586810i	$0.199616\pi$
$752$	4.32834e10	3.71158
$753$	2.71869e9	0.232048
$754$	−3.88464e10	−3.30028
$755$	2.09876e10	1.77479
$756$	1.90213e10	1.60108
$757$	−1.65649e8	−0.0138788	−0.00693940	−	0.999976i	$-0.502209\pi$
$757$	−1.65649e8	−0.0138788	−0.00693940	+	0.999976i	$0.502209\pi$
$758$	−2.35416e9	−0.196333
$759$	−4.69871e9	−0.390061
$760$	7.45004e9	0.615618
$761$	−2.36169e9	−0.194257	−0.0971286	−	0.995272i	$-0.530966\pi$
$761$	−2.36169e9	−0.194257	−0.0971286	+	0.995272i	$0.530966\pi$
$762$	5.58342e9	0.457149
$763$	−7.24899e9	−0.590802
$764$	−2.98789e10	−2.42403
$765$	−3.20405e9	−0.258752
$766$	−1.60755e10	−1.29231
$767$	−1.87951e10	−1.50404
$768$	9.37334e9	0.746673
$769$	1.43196e10	1.13550	0.567751	−	0.823200i	$-0.307814\pi$
$769$	1.43196e10	1.13550	0.567751	+	0.823200i	$0.307814\pi$
$770$	2.45007e10	1.93402
$771$	3.55040e9	0.278989
$772$	2.07028e10	1.61945
$773$	2.00337e10	1.56003	0.780014	−	0.625762i	$-0.215212\pi$
$773$	2.00337e10	1.56003	0.780014	+	0.625762i	$0.215212\pi$
$774$	2.51621e10	1.95054
$775$	−1.15854e9	−0.0894033
$776$	−1.90139e10	−1.46068
$777$	−1.90489e9	−0.145679
$778$	−4.08766e10	−3.11205
$779$	2.82513e9	0.214120
$780$	−1.88334e10	−1.42101
$781$	1.30550e10	0.980612
$782$	6.28242e9	0.469789
$783$	1.56945e10	1.16837
$784$	−1.56793e10	−1.16204
$785$	1.97955e10	1.46057
$786$	−7.76627e9	−0.570471
$787$	−1.40347e10	−1.02634	−0.513169	−	0.858287i	$-0.671529\pi$
$787$	−1.40347e10	−1.02634	−0.513169	+	0.858287i	$0.671529\pi$
$788$	1.22407e10	0.891175
$789$	−1.32926e9	−0.0963476
$790$	−1.63764e10	−1.18175
$791$	−9.21072e9	−0.661722
$792$	3.76912e10	2.69589
$793$	1.00443e10	0.715258
$794$	−1.08206e10	−0.767152
$795$	−1.27893e10	−0.902736
$796$	2.05310e9	0.144283
$797$	1.82522e10	1.27706	0.638531	−	0.769596i	$-0.279543\pi$
$797$	1.82522e10	1.27706	0.638531	+	0.769596i	$0.279543\pi$
$798$	−1.37225e9	−0.0955923
$799$	3.77471e9	0.261800
$800$	−2.75500e10	−1.90242
$801$	1.76803e10	1.21556
$802$	5.97179e9	0.408784
$803$	−1.01069e10	−0.688835
$804$	2.03495e10	1.38089
$805$	1.49002e10	1.00672
$806$	−5.04276e9	−0.339231
$807$	3.07952e8	0.0206265
$808$	5.83402e10	3.89070
$809$	1.69528e10	1.12570	0.562849	−	0.826559i	$-0.309705\pi$
$809$	1.69528e10	1.12570	0.562849	+	0.826559i	$0.309705\pi$
$810$	−1.99363e10	−1.31810
$811$	1.57454e10	1.03653	0.518265	−	0.855220i	$-0.326578\pi$
$811$	1.57454e10	1.03653	0.518265	+	0.855220i	$0.326578\pi$
$812$	5.34439e10	3.50310
$813$	−7.02820e9	−0.458699
$814$	−1.31659e10	−0.855589
$815$	−1.97276e10	−1.27651
$816$	5.32773e9	0.343263
$817$	−2.89072e9	−0.185451
$818$	2.65358e10	1.69510
$819$	−1.16540e10	−0.741281
$820$	−7.32468e10	−4.63917
$821$	−1.40935e10	−0.888825	−0.444413	−	0.895822i	$-0.646588\pi$
$821$	−1.40935e10	−0.888825	−0.444413	+	0.895822i	$0.646588\pi$
$822$	−1.58412e10	−0.994805
$823$	1.51503e10	0.947373	0.473687	−	0.880694i	$-0.342923\pi$
$823$	1.51503e10	0.947373	0.473687	+	0.880694i	$0.342923\pi$
$824$	−5.78197e10	−3.60023
$825$	3.45315e9	0.214105
$826$	3.55056e10	2.19213
$827$	−2.51047e10	−1.54342	−0.771711	−	0.635973i	$-0.780599\pi$
$827$	−2.51047e10	−1.54342	−0.771711	+	0.635973i	$0.780599\pi$
$828$	3.65650e10	2.23851
$829$	1.69163e10	1.03125	0.515626	−	0.856814i	$-0.327559\pi$
$829$	1.69163e10	1.03125	0.515626	+	0.856814i	$0.327559\pi$
$830$	−3.48143e10	−2.11341
$831$	1.04487e9	0.0631626
$832$	−5.72999e10	−3.44923
$833$	−1.36738e9	−0.0819656
$834$	1.49387e9	0.0891723
$835$	3.39574e10	2.01851
$836$	−6.90729e9	−0.408871
$837$	2.03735e9	0.120095
$838$	−3.89297e10	−2.28521
$839$	2.23392e10	1.30587	0.652937	−	0.757412i	$-0.273537\pi$
$839$	2.23392e10	1.30587	0.652937	+	0.757412i	$0.273537\pi$
$840$	2.23035e10	1.29836
$841$	2.68469e10	1.55635
$842$	−7.08340e9	−0.408930
$843$	8.93021e9	0.513411
$844$	−8.93902e10	−5.11789
$845$	3.43786e9	0.196015
$846$	3.01668e10	1.71290
$847$	2.16578e8	0.0122468
$848$	−1.13965e11	−6.41779
$849$	−3.13245e9	−0.175674
$850$	−4.61704e9	−0.257868
$851$	−8.00694e9	−0.445362
$852$	1.89575e10	1.05013
$853$	3.03756e10	1.67573	0.837863	−	0.545881i	$-0.183805\pi$
$853$	3.03756e10	1.67573	0.837863	+	0.545881i	$0.183805\pi$
$854$	−1.89746e10	−1.04249
$855$	2.94172e9	0.160961
$856$	−1.14282e11	−6.22760
$857$	−1.17411e10	−0.637198	−0.318599	−	0.947890i	$-0.603212\pi$
$857$	−1.17411e10	−0.637198	−0.318599	+	0.947890i	$0.603212\pi$
$858$	1.50306e10	0.812399
$859$	−2.32620e10	−1.25219	−0.626096	−	0.779746i	$-0.715348\pi$
$859$	−2.32620e10	−1.25219	−0.626096	+	0.779746i	$0.715348\pi$
$860$	7.49472e10	4.01801
$861$	8.45773e9	0.451588
$862$	2.93098e10	1.55861
$863$	−8.69964e9	−0.460748	−0.230374	−	0.973102i	$-0.573995\pi$
$863$	−8.69964e9	−0.460748	−0.230374	+	0.973102i	$0.573995\pi$
$864$	4.84482e10	2.55552
$865$	−2.71764e10	−1.42769
$866$	2.56917e10	1.34425
$867$	−7.14517e9	−0.372345
$868$	6.93771e9	0.360079
$869$	9.51829e9	0.492028
$870$	2.93556e10	1.51138
$871$	−2.72622e10	−1.39797
$872$	−4.56093e10	−2.32941
$873$	−7.50783e9	−0.381913
$874$	−5.76806e9	−0.292240
$875$	9.17906e9	0.463202
$876$	−1.46766e10	−0.737668
$877$	−2.14606e10	−1.07434	−0.537172	−	0.843472i	$-0.680508\pi$
$877$	−2.14606e10	−1.07434	−0.537172	+	0.843472i	$0.680508\pi$
$878$	6.01738e10	3.00038
$879$	7.29017e9	0.362057
$880$	8.73352e10	4.32016
$881$	1.87633e9	0.0924473	0.0462236	−	0.998931i	$-0.485281\pi$
$881$	1.87633e9	0.0924473	0.0462236	+	0.998931i	$0.485281\pi$
$882$	−1.09278e10	−0.536282
$883$	−1.37195e9	−0.0670617	−0.0335308	−	0.999438i	$-0.510675\pi$
$883$	−1.37195e9	−0.0670617	−0.0335308	+	0.999438i	$0.510675\pi$
$884$	−1.46358e10	−0.712582
$885$	1.42031e10	0.688783
$886$	−4.71654e10	−2.27827
$887$	1.10299e10	0.530687	0.265343	−	0.964154i	$-0.414515\pi$
$887$	1.10299e10	0.530687	0.265343	+	0.964154i	$0.414515\pi$
$888$	−1.19852e10	−0.574382
$889$	1.02909e10	0.491245
$890$	7.23107e10	3.43825
$891$	1.15874e10	0.548798
$892$	2.98261e10	1.40708
$893$	−3.46567e9	−0.162857
$894$	−9.78326e9	−0.457933
$895$	−3.62122e10	−1.68840
$896$	4.66893e10	2.16840
$897$	9.14094e9	0.422880
$898$	−6.33739e9	−0.292041
$899$	5.72433e9	0.262764
$900$	−2.68722e10	−1.22872
$901$	−9.93880e9	−0.452686
$902$	5.84567e10	2.65223
$903$	−8.65406e9	−0.391123
$904$	−5.79522e10	−2.60904
$905$	2.24285e10	1.00585
$906$	−2.43228e10	−1.08659
$907$	−3.36059e10	−1.49551	−0.747756	−	0.663974i	$-0.768869\pi$
$907$	−3.36059e10	−1.49551	−0.747756	+	0.663974i	$0.768869\pi$
$908$	−1.92681e10	−0.854160
$909$	2.30362e10	1.01727
$910$	−4.76639e10	−2.09674
$911$	−1.12124e10	−0.491343	−0.245671	−	0.969353i	$-0.579008\pi$
$911$	−1.12124e10	−0.491343	−0.245671	+	0.969353i	$0.579008\pi$
$912$	−4.89153e9	−0.213532
$913$	2.02347e10	0.879933
$914$	−3.80052e10	−1.64638
$915$	−7.59031e9	−0.327556
$916$	3.30810e10	1.42215
$917$	−1.43142e10	−0.613020
$918$	8.11933e9	0.346394
$919$	−1.87602e10	−0.797322	−0.398661	−	0.917098i	$-0.630525\pi$
$919$	−1.87602e10	−0.797322	−0.398661	+	0.917098i	$0.630525\pi$
$920$	9.37496e10	3.96928
$921$	3.39330e9	0.143124
$922$	−4.11619e9	−0.172957
$923$	−2.53973e10	−1.06312
$924$	−2.06787e10	−0.862325
$925$	5.88442e9	0.244460
$926$	−2.85466e10	−1.18145
$927$	−2.28307e10	−0.941326
$928$	1.36125e11	5.59137
$929$	−3.35622e10	−1.37339	−0.686697	−	0.726944i	$-0.740940\pi$
$929$	−3.35622e10	−1.37339	−0.686697	+	0.726944i	$0.740940\pi$
$930$	3.81074e9	0.155353
$931$	1.25543e9	0.0509880
$932$	3.50009e10	1.41620
$933$	1.24633e10	0.502396
$934$	5.08678e10	2.04281
$935$	7.61645e9	0.304728
$936$	−7.33251e10	−2.92272
$937$	−4.09812e10	−1.62741	−0.813704	−	0.581279i	$-0.802552\pi$
$937$	−4.09812e10	−1.62741	−0.813704	+	0.581279i	$0.802552\pi$
$938$	5.15009e10	2.03753
$939$	−6.92908e9	−0.273115
$940$	8.98538e10	3.52849
$941$	1.88633e10	0.737997	0.368999	−	0.929430i	$-0.379701\pi$
$941$	1.88633e10	0.737997	0.368999	+	0.929430i	$0.379701\pi$
$942$	−2.29412e10	−0.894208
$943$	3.55509e10	1.38057
$944$	1.26564e11	4.89674
$945$	1.92569e10	0.742293
$946$	−5.98137e10	−2.29711
$947$	2.32362e10	0.889079	0.444540	−	0.895759i	$-0.353367\pi$
$947$	2.32362e10	0.889079	0.444540	+	0.895759i	$0.353367\pi$
$948$	1.38218e10	0.526908
$949$	1.96622e10	0.746793
$950$	4.23903e9	0.160411
$951$	2.32457e9	0.0876418
$952$	1.73325e10	0.651076
$953$	−4.79456e10	−1.79442	−0.897208	−	0.441607i	$-0.854408\pi$
$953$	−4.79456e10	−1.79442	−0.897208	+	0.441607i	$0.854408\pi$
$954$	−7.94289e10	−2.96182
$955$	−3.02491e10	−1.12383
$956$	−1.64579e10	−0.609218
$957$	−1.70620e10	−0.629273
$958$	−4.15965e10	−1.52854
$959$	−2.91974e10	−1.06900
$960$	4.33006e10	1.57959
$961$	−2.67695e10	−0.972991
$962$	2.56131e10	0.927577
$963$	−4.51255e10	−1.62828
$964$	−1.09317e11	−3.93022
$965$	2.09593e10	0.750811
$966$	−1.72681e10	−0.616346
$967$	−3.30920e10	−1.17688	−0.588438	−	0.808543i	$-0.700257\pi$
$967$	−3.30920e10	−1.17688	−0.588438	+	0.808543i	$0.700257\pi$
$968$	1.36267e9	0.0482866
$969$	−4.26587e8	−0.0150617
$970$	−3.07063e10	−1.08026
$971$	−2.59003e10	−0.907898	−0.453949	−	0.891028i	$-0.649985\pi$
$971$	−2.59003e10	−0.907898	−0.453949	+	0.891028i	$0.649985\pi$
$972$	7.29007e10	2.54624
$973$	2.75338e9	0.0958233
$974$	−7.87682e10	−2.73146
$975$	−6.71781e9	−0.232120
$976$	−6.76370e10	−2.32868
$977$	−2.30381e10	−0.790344	−0.395172	−	0.918607i	$-0.629315\pi$
$977$	−2.30381e10	−0.790344	−0.395172	+	0.918607i	$0.629315\pi$
$978$	2.28626e10	0.781519
$979$	−4.20283e10	−1.43154
$980$	−3.25493e10	−1.10471
$981$	−1.80093e10	−0.609054
$982$	−2.53258e10	−0.853440
$983$	−1.51665e10	−0.509269	−0.254635	−	0.967037i	$-0.581955\pi$
$983$	−1.51665e10	−0.509269	−0.254635	+	0.967037i	$0.581955\pi$
$984$	5.32145e10	1.78052
$985$	1.23923e10	0.413166
$986$	2.28128e10	0.757897
$987$	−1.03753e10	−0.343472
$988$	1.34376e10	0.443273
$989$	−3.63761e10	−1.19572
$990$	6.08691e10	1.99377
$991$	2.59162e10	0.845889	0.422944	−	0.906156i	$-0.360997\pi$
$991$	2.59162e10	0.845889	0.422944	+	0.906156i	$0.360997\pi$
$992$	1.76707e10	0.574729
$993$	1.39510e10	0.452151
$994$	4.79779e10	1.54949
$995$	2.07854e9	0.0668924
$996$	2.93834e10	0.942313
$997$	−5.34864e9	−0.170927	−0.0854635	−	0.996341i	$-0.527237\pi$
$997$	−5.34864e9	−0.170927	−0.0854635	+	0.996341i	$0.527237\pi$
$998$	−5.16310e10	−1.64419
$999$	−1.03481e10	−0.328383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.b.1.4	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.b.1.4	✓	162	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)

\(f(q)\)	\(=\)	\(q-21.7039 q^{2} +18.5452 q^{3} +343.061 q^{4} +347.311 q^{5} -402.503 q^{6} -741.863 q^{7} -4667.67 q^{8} -1843.08 q^{9} +O(q^{10})\)	\(q-21.7039 q^{2} +18.5452 q^{3} +343.061 q^{4} +347.311 q^{5} -402.503 q^{6} -741.863 q^{7} -4667.67 q^{8} -1843.08 q^{9} -7538.02 q^{10} +4381.24 q^{11} +6362.12 q^{12} -8523.32 q^{13} +16101.4 q^{14} +6440.94 q^{15} +57395.0 q^{16} +5005.38 q^{17} +40002.0 q^{18} -4595.58 q^{19} +119149. q^{20} -13758.0 q^{21} -95090.1 q^{22} -57829.7 q^{23} -86562.7 q^{24} +42499.9 q^{25} +184990. q^{26} -74738.5 q^{27} -254504. q^{28} -209992. q^{29} -139794. q^{30} -27259.7 q^{31} -648236. q^{32} +81250.8 q^{33} -108637. q^{34} -257657. q^{35} -632288. q^{36} +138457. q^{37} +99742.1 q^{38} -158066. q^{39} -1.62113e6 q^{40} -614751. q^{41} +298602. q^{42} +629021. q^{43} +1.50303e6 q^{44} -640121. q^{45} +1.25513e6 q^{46} +754131. q^{47} +1.06440e6 q^{48} -273182. q^{49} -922416. q^{50} +92825.7 q^{51} -2.92402e6 q^{52} -1.98562e6 q^{53} +1.62212e6 q^{54} +1.52165e6 q^{55} +3.46277e6 q^{56} -85225.7 q^{57} +4.55766e6 q^{58} +2.20513e6 q^{59} +2.20964e6 q^{60} -1.17845e6 q^{61} +591643. q^{62} +1.36731e6 q^{63} +6.72271e6 q^{64} -2.96024e6 q^{65} -1.76346e6 q^{66} +3.19854e6 q^{67} +1.71715e6 q^{68} -1.07246e6 q^{69} +5.59218e6 q^{70} +2.97974e6 q^{71} +8.60287e6 q^{72} -2.30687e6 q^{73} -3.00507e6 q^{74} +788168. q^{75} -1.57656e6 q^{76} -3.25028e6 q^{77} +3.43066e6 q^{78} +2.17251e6 q^{79} +1.99339e7 q^{80} +2.64477e6 q^{81} +1.33425e7 q^{82} +4.61850e6 q^{83} -4.71983e6 q^{84} +1.73842e6 q^{85} -1.36522e7 q^{86} -3.89434e6 q^{87} -2.04502e7 q^{88} -9.59280e6 q^{89} +1.38931e7 q^{90} +6.32314e6 q^{91} -1.98391e7 q^{92} -505536. q^{93} -1.63676e7 q^{94} -1.59609e6 q^{95} -1.20216e7 q^{96} +4.07353e6 q^{97} +5.92912e6 q^{98} -8.07495e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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