LMFDB - Embedded newform 547.8.a.a.1.7

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			1.7
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)

$f(q)$	$=$	$q-21.1072 q^{2} +70.0639 q^{3} +317.514 q^{4} +140.672 q^{5} -1478.85 q^{6} -431.091 q^{7} -4000.10 q^{8} +2721.94 q^{9} +O(q^{10})$	\(q-21.1072 q^{2} +70.0639 q^{3} +317.514 q^{4} +140.672 q^{5} -1478.85 q^{6} -431.091 q^{7} -4000.10 q^{8} +2721.94 q^{9} -2969.18 q^{10} +5251.35 q^{11} +22246.2 q^{12} -2663.50 q^{13} +9099.11 q^{14} +9856.00 q^{15} +43789.1 q^{16} -1523.22 q^{17} -57452.6 q^{18} -54944.4 q^{19} +44665.1 q^{20} -30203.9 q^{21} -110841. q^{22} -25819.7 q^{23} -280262. q^{24} -58336.5 q^{25} +56219.1 q^{26} +37480.3 q^{27} -136877. q^{28} +196009. q^{29} -208032. q^{30} +62242.4 q^{31} -412253. q^{32} +367930. q^{33} +32150.9 q^{34} -60642.2 q^{35} +864254. q^{36} +305892. q^{37} +1.15972e6 q^{38} -186615. q^{39} -562700. q^{40} +833769. q^{41} +637519. q^{42} -836061. q^{43} +1.66737e6 q^{44} +382900. q^{45} +544982. q^{46} -1.07693e6 q^{47} +3.06804e6 q^{48} -637704. q^{49} +1.23132e6 q^{50} -106723. q^{51} -845698. q^{52} -1.31730e6 q^{53} -791104. q^{54} +738716. q^{55} +1.72440e6 q^{56} -3.84961e6 q^{57} -4.13721e6 q^{58} +411011. q^{59} +3.12941e6 q^{60} +2.69399e6 q^{61} -1.31376e6 q^{62} -1.17340e6 q^{63} +3.09649e6 q^{64} -374679. q^{65} -7.76596e6 q^{66} -1.95729e6 q^{67} -483643. q^{68} -1.80903e6 q^{69} +1.27999e6 q^{70} -977592. q^{71} -1.08880e7 q^{72} -61108.1 q^{73} -6.45653e6 q^{74} -4.08728e6 q^{75} -1.74456e7 q^{76} -2.26381e6 q^{77} +3.93892e6 q^{78} +7.94442e6 q^{79} +6.15989e6 q^{80} -3.32688e6 q^{81} -1.75985e7 q^{82} +3.27160e6 q^{83} -9.59014e6 q^{84} -214274. q^{85} +1.76469e7 q^{86} +1.37332e7 q^{87} -2.10059e7 q^{88} -4.59392e6 q^{89} -8.08195e6 q^{90} +1.14821e6 q^{91} -8.19811e6 q^{92} +4.36094e6 q^{93} +2.27309e7 q^{94} -7.72911e6 q^{95} -2.88840e7 q^{96} -1.53384e7 q^{97} +1.34601e7 q^{98} +1.42939e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−21.1072	−1.86563	−0.932815	−	0.360356i	$-0.882655\pi$
$2$	−21.1072	−1.86563	−0.932815	+	0.360356i	$0.882655\pi$
$3$	70.0639	1.49820	0.749100	−	0.662457i	$-0.230486\pi$
$3$	70.0639	1.49820	0.749100	+	0.662457i	$0.230486\pi$
$4$	317.514	2.48057
$5$	140.672	0.503282	0.251641	−	0.967821i	$-0.419030\pi$
$5$	140.672	0.503282	0.251641	+	0.967821i	$0.419030\pi$
$6$	−1478.85	−2.79509
$7$	−431.091	−0.475035	−0.237517	−	0.971383i	$-0.576334\pi$
$7$	−431.091	−0.475035	−0.237517	+	0.971383i	$0.576334\pi$
$8$	−4000.10	−2.76220
$9$	2721.94	1.24460
$10$	−2969.18	−0.938938
$11$	5251.35	1.18959	0.594794	−	0.803878i	$-0.297234\pi$
$11$	5251.35	1.18959	0.594794	+	0.803878i	$0.297234\pi$
$12$	22246.2	3.71640
$13$	−2663.50	−0.336242	−0.168121	−	0.985766i	$-0.553770\pi$
$13$	−2663.50	−0.336242	−0.168121	+	0.985766i	$0.553770\pi$
$14$	9099.11	0.886239
$15$	9856.00	0.754017
$16$	43789.1	2.67268
$17$	−1523.22	−0.0751954	−0.0375977	−	0.999293i	$-0.511971\pi$
$17$	−1523.22	−0.0751954	−0.0375977	+	0.999293i	$0.511971\pi$
$18$	−57452.6	−2.32197
$19$	−54944.4	−1.83775	−0.918873	−	0.394553i	$-0.870899\pi$
$19$	−54944.4	−1.83775	−0.918873	+	0.394553i	$0.870899\pi$
$20$	44665.1	1.24843
$21$	−30203.9	−0.711697
$22$	−110841.	−2.21933
$23$	−25819.7	−0.442491	−0.221245	−	0.975218i	$-0.571012\pi$
$23$	−25819.7	−0.442491	−0.221245	+	0.975218i	$0.571012\pi$
$24$	−280262.	−4.13833
$25$	−58336.5	−0.746707
$26$	56219.1	0.627302
$27$	37480.3	0.366463
$28$	−136877.	−1.17836
$29$	196009.	1.49240	0.746198	−	0.665724i	$-0.231877\pi$
$29$	196009.	1.49240	0.746198	+	0.665724i	$0.231877\pi$
$30$	−208032.	−1.40672
$31$	62242.4	0.375250	0.187625	−	0.982241i	$-0.439921\pi$
$31$	62242.4	0.375250	0.187625	+	0.982241i	$0.439921\pi$
$32$	−412253.	−2.22402
$33$	367930.	1.78224
$34$	32150.9	0.140287
$35$	−60642.2	−0.239076
$36$	864254.	3.08733
$37$	305892.	0.992802	0.496401	−	0.868093i	$-0.334655\pi$
$37$	305892.	0.992802	0.496401	+	0.868093i	$0.334655\pi$
$38$	1.15972e6	3.42855
$39$	−186615.	−0.503757
$40$	−562700.	−1.39017
$41$	833769.	1.88930	0.944652	−	0.328073i	$-0.106399\pi$
$41$	833769.	1.88930	0.944652	+	0.328073i	$0.106399\pi$
$42$	637519.	1.32776
$43$	−836061.	−1.60361	−0.801804	−	0.597587i	$-0.796126\pi$
$43$	−836061.	−1.60361	−0.801804	+	0.597587i	$0.796126\pi$
$44$	1.66737e6	2.95086
$45$	382900.	0.626386
$46$	544982.	0.825524
$47$	−1.07693e6	−1.51301	−0.756507	−	0.653985i	$-0.773096\pi$
$47$	−1.07693e6	−1.51301	−0.756507	+	0.653985i	$0.773096\pi$
$48$	3.06804e6	4.00420
$49$	−637704.	−0.774342
$50$	1.23132e6	1.39308
$51$	−106723.	−0.112658
$52$	−845698.	−0.834072
$53$	−1.31730e6	−1.21540	−0.607702	−	0.794165i	$-0.707908\pi$
$53$	−1.31730e6	−1.21540	−0.607702	+	0.794165i	$0.707908\pi$
$54$	−791104.	−0.683684
$55$	738716.	0.598698
$56$	1.72440e6	1.31214
$57$	−3.84961e6	−2.75331
$58$	−4.13721e6	−2.78426
$59$	411011.	0.260538	0.130269	−	0.991479i	$-0.458416\pi$
$59$	411011.	0.260538	0.130269	+	0.991479i	$0.458416\pi$
$60$	3.12941e6	1.87040
$61$	2.69399e6	1.51964	0.759822	−	0.650131i	$-0.225286\pi$
$61$	2.69399e6	1.51964	0.759822	+	0.650131i	$0.225286\pi$
$62$	−1.31376e6	−0.700077
$63$	−1.17340e6	−0.591229
$64$	3.09649e6	1.47652
$65$	−374679.	−0.169224
$66$	−7.76596e6	−3.32500
$67$	−1.95729e6	−0.795048	−0.397524	−	0.917592i	$-0.630130\pi$
$67$	−1.95729e6	−0.795048	−0.397524	+	0.917592i	$0.630130\pi$
$68$	−483643.	−0.186528
$69$	−1.80903e6	−0.662940
$70$	1.27999e6	0.446028
$71$	−977592.	−0.324155	−0.162078	−	0.986778i	$-0.551820\pi$
$71$	−977592.	−0.324155	−0.162078	+	0.986778i	$0.551820\pi$
$72$	−1.08880e7	−3.43785
$73$	−61108.1	−0.0183852	−0.00919260	−	0.999958i	$-0.502926\pi$
$73$	−61108.1	−0.0183852	−0.00919260	+	0.999958i	$0.502926\pi$
$74$	−6.45653e6	−1.85220
$75$	−4.08728e6	−1.11872
$76$	−1.74456e7	−4.55867
$77$	−2.26381e6	−0.565095
$78$	3.93892e6	0.939824
$79$	7.94442e6	1.81287	0.906437	−	0.422341i	$-0.138792\pi$
$79$	7.94442e6	1.81287	0.906437	+	0.422341i	$0.138792\pi$
$80$	6.15989e6	1.34511
$81$	−3.32688e6	−0.695568
$82$	−1.75985e7	−3.52474
$83$	3.27160e6	0.628039	0.314019	−	0.949417i	$-0.398324\pi$
$83$	3.27160e6	0.628039	0.314019	+	0.949417i	$0.398324\pi$
$84$	−9.59014e6	−1.76542
$85$	−214274.	−0.0378445
$86$	1.76469e7	2.99174
$87$	1.37332e7	2.23591
$88$	−2.10059e7	−3.28588
$89$	−4.59392e6	−0.690746	−0.345373	−	0.938466i	$-0.612248\pi$
$89$	−4.59392e6	−0.690746	−0.345373	+	0.938466i	$0.612248\pi$
$90$	−8.08195e6	−1.16860
$91$	1.14821e6	0.159726
$92$	−8.19811e6	−1.09763
$93$	4.36094e6	0.562199
$94$	2.27309e7	2.82272
$95$	−7.72911e6	−0.924905
$96$	−2.88840e7	−3.33203
$97$	−1.53384e7	−1.70639	−0.853197	−	0.521589i	$-0.825340\pi$
$97$	−1.53384e7	−1.70639	−0.853197	+	0.521589i	$0.825340\pi$
$98$	1.34601e7	1.44464
$99$	1.42939e7	1.48056
$100$	−1.85226e7	−1.85226
$101$	−3.72109e6	−0.359373	−0.179686	−	0.983724i	$-0.557508\pi$
$101$	−3.72109e6	−0.359373	−0.179686	+	0.983724i	$0.557508\pi$
$102$	2.25262e6	0.210178
$103$	−1.51009e7	−1.36167	−0.680835	−	0.732437i	$-0.738383\pi$
$103$	−1.51009e7	−1.36167	−0.680835	+	0.732437i	$0.738383\pi$
$104$	1.06543e7	0.928768
$105$	−4.24883e6	−0.358184
$106$	2.78046e7	2.26749
$107$	−1.60887e7	−1.26963	−0.634814	−	0.772665i	$-0.718923\pi$
$107$	−1.60887e7	−1.26963	−0.634814	+	0.772665i	$0.718923\pi$
$108$	1.19005e7	0.909038
$109$	−2.46687e7	−1.82454	−0.912268	−	0.409593i	$-0.865671\pi$
$109$	−2.46687e7	−1.82454	−0.912268	+	0.409593i	$0.865671\pi$
$110$	−1.55922e7	−1.11695
$111$	2.14320e7	1.48742
$112$	−1.88771e7	−1.26961
$113$	5.74126e6	0.374311	0.187156	−	0.982330i	$-0.440073\pi$
$113$	5.74126e6	0.374311	0.187156	+	0.982330i	$0.440073\pi$
$114$	8.12546e7	5.13666
$115$	−3.63210e6	−0.222698
$116$	6.22357e7	3.70200
$117$	−7.24991e6	−0.418487
$118$	−8.67528e6	−0.486068
$119$	656646.	0.0357204
$120$	−3.94250e7	−2.08275
$121$	8.08947e6	0.415118
$122$	−5.68626e7	−2.83509
$123$	5.84171e7	2.83056
$124$	1.97628e7	0.930835
$125$	−1.91963e7	−0.879086
$126$	2.47673e7	1.10301
$127$	2.29444e6	0.0993947	0.0496974	−	0.998764i	$-0.484174\pi$
$127$	2.29444e6	0.0993947	0.0496974	+	0.998764i	$0.484174\pi$
$128$	−1.25899e7	−0.530623
$129$	−5.85776e7	−2.40253
$130$	7.90843e6	0.315710
$131$	−1.84750e7	−0.718015	−0.359008	−	0.933335i	$-0.616885\pi$
$131$	−1.84750e7	−0.718015	−0.359008	+	0.933335i	$0.616885\pi$
$132$	1.16823e8	4.42098
$133$	2.36860e7	0.872993
$134$	4.13129e7	1.48326
$135$	5.27241e6	0.184434
$136$	6.09303e6	0.207705
$137$	−2.54743e7	−0.846410	−0.423205	−	0.906034i	$-0.639095\pi$
$137$	−2.54743e7	−0.846410	−0.423205	+	0.906034i	$0.639095\pi$
$138$	3.81835e7	1.23680
$139$	1.31428e7	0.415083	0.207541	−	0.978226i	$-0.433454\pi$
$139$	1.31428e7	0.415083	0.207541	+	0.978226i	$0.433454\pi$
$140$	−1.92547e7	−0.593047
$141$	−7.54535e7	−2.26680
$142$	2.06342e7	0.604754
$143$	−1.39870e7	−0.399989
$144$	1.19192e8	3.32642
$145$	2.75730e7	0.751096
$146$	1.28982e6	0.0343000
$147$	−4.46800e7	−1.16012
$148$	9.71250e7	2.46272
$149$	−1.49351e7	−0.369875	−0.184938	−	0.982750i	$-0.559208\pi$
$149$	−1.49351e7	−0.369875	−0.184938	+	0.982750i	$0.559208\pi$
$150$	8.62710e7	2.08711
$151$	4.89135e7	1.15614	0.578069	−	0.815988i	$-0.303806\pi$
$151$	4.89135e7	1.15614	0.578069	+	0.815988i	$0.303806\pi$
$152$	2.19783e8	5.07623
$153$	−4.14612e6	−0.0935884
$154$	4.77826e7	1.05426
$155$	8.75574e6	0.188857
$156$	−5.92529e7	−1.24961
$157$	9.53493e7	1.96639	0.983193	−	0.182570i	$-0.0584415\pi$
$157$	9.53493e7	1.96639	0.983193	+	0.182570i	$0.0584415\pi$
$158$	−1.67684e8	−3.38215
$159$	−9.22954e7	−1.82092
$160$	−5.79923e7	−1.11931
$161$	1.11306e7	0.210198
$162$	7.02211e7	1.29767
$163$	2.55496e7	0.462091	0.231045	−	0.972943i	$-0.425785\pi$
$163$	2.55496e7	0.462091	0.231045	+	0.972943i	$0.425785\pi$
$164$	2.64733e8	4.68656
$165$	5.17573e7	0.896969
$166$	−6.90542e7	−1.17169
$167$	−1.04846e7	−0.174198	−0.0870990	−	0.996200i	$-0.527760\pi$
$167$	−1.04846e7	−0.174198	−0.0870990	+	0.996200i	$0.527760\pi$
$168$	1.20818e8	1.96585
$169$	−5.56543e7	−0.886942
$170$	4.52272e6	0.0706039
$171$	−1.49556e8	−2.28726
$172$	−2.65461e8	−3.97787
$173$	−1.00814e8	−1.48033	−0.740165	−	0.672426i	$-0.765252\pi$
$173$	−1.00814e8	−1.48033	−0.740165	+	0.672426i	$0.765252\pi$
$174$	−2.89869e8	−4.17138
$175$	2.51483e7	0.354712
$176$	2.29952e8	3.17938
$177$	2.87970e7	0.390338
$178$	9.69647e7	1.28868
$179$	1.48753e8	1.93856	0.969280	−	0.245958i	$-0.0791027\pi$
$179$	1.48753e8	1.93856	0.969280	+	0.245958i	$0.0791027\pi$
$180$	1.21576e8	1.55380
$181$	−1.10745e8	−1.38819	−0.694094	−	0.719884i	$-0.744195\pi$
$181$	−1.10745e8	−1.38819	−0.694094	+	0.719884i	$0.744195\pi$
$182$	−2.42355e7	−0.297990
$183$	1.88752e8	2.27673
$184$	1.03281e8	1.22225
$185$	4.30304e7	0.499660
$186$	−9.20473e7	−1.04886
$187$	−7.99896e6	−0.0894515
$188$	−3.41938e8	−3.75314
$189$	−1.61574e7	−0.174083
$190$	1.63140e8	1.72553
$191$	−8.99345e7	−0.933920	−0.466960	−	0.884278i	$-0.654651\pi$
$191$	−8.99345e7	−0.933920	−0.466960	+	0.884278i	$0.654651\pi$
$192$	2.16952e8	2.21212
$193$	1.33433e8	1.33602	0.668012	−	0.744151i	$-0.267146\pi$
$193$	1.33433e8	1.33602	0.668012	+	0.744151i	$0.267146\pi$
$194$	3.23751e8	3.18350
$195$	−2.62515e7	−0.253532
$196$	−2.02480e8	−1.92081
$197$	2.25266e7	0.209925	0.104963	−	0.994476i	$-0.466528\pi$
$197$	2.25266e7	0.209925	0.104963	+	0.994476i	$0.466528\pi$
$198$	−3.01704e8	−2.76218
$199$	1.32382e8	1.19082	0.595408	−	0.803424i	$-0.296991\pi$
$199$	1.32382e8	1.19082	0.595408	+	0.803424i	$0.296991\pi$
$200$	2.33352e8	2.06256
$201$	−1.37135e8	−1.19114
$202$	7.85417e7	0.670456
$203$	−8.44978e7	−0.708940
$204$	−3.38859e7	−0.279456
$205$	1.17288e8	0.950853
$206$	3.18737e8	2.54037
$207$	−7.02799e7	−0.550725
$208$	−1.16632e8	−0.898665
$209$	−2.88532e8	−2.18616
$210$	8.96808e7	0.668239
$211$	1.98830e7	0.145711	0.0728557	−	0.997342i	$-0.476789\pi$
$211$	1.98830e7	0.145711	0.0728557	+	0.997342i	$0.476789\pi$
$212$	−4.18262e8	−3.01490
$213$	−6.84939e7	−0.485650
$214$	3.39586e8	2.36866
$215$	−1.17610e8	−0.807067
$216$	−1.49925e8	−1.01225
$217$	−2.68321e7	−0.178257
$218$	5.20686e8	3.40391
$219$	−4.28147e6	−0.0275447
$220$	2.34552e8	1.48512
$221$	4.05710e6	0.0252838
$222$	−4.52369e8	−2.77497
$223$	−1.60835e8	−0.971213	−0.485607	−	0.874177i	$-0.661401\pi$
$223$	−1.60835e8	−0.971213	−0.485607	+	0.874177i	$0.661401\pi$
$224$	1.77718e8	1.05649
$225$	−1.58789e8	−0.929353
$226$	−1.21182e8	−0.698326
$227$	−1.19782e8	−0.679673	−0.339837	−	0.940485i	$-0.610372\pi$
$227$	−1.19782e8	−0.679673	−0.339837	+	0.940485i	$0.610372\pi$
$228$	−1.22230e9	−6.82979
$229$	−4.53521e6	−0.0249559	−0.0124779	−	0.999922i	$-0.503972\pi$
$229$	−4.53521e6	−0.0249559	−0.0124779	+	0.999922i	$0.503972\pi$
$230$	7.66635e7	0.415471
$231$	−1.58611e8	−0.846625
$232$	−7.84057e8	−4.12230
$233$	4.75521e7	0.246277	0.123138	−	0.992390i	$-0.460704\pi$
$233$	4.75521e7	0.246277	0.123138	+	0.992390i	$0.460704\pi$
$234$	1.53025e8	0.780742
$235$	−1.51493e8	−0.761473
$236$	1.30502e8	0.646284
$237$	5.56617e8	2.71605
$238$	−1.38599e7	−0.0666411
$239$	−2.39346e8	−1.13405	−0.567027	−	0.823699i	$-0.691906\pi$
$239$	−2.39346e8	−1.13405	−0.567027	+	0.823699i	$0.691906\pi$
$240$	4.31585e8	2.01524
$241$	−1.63106e8	−0.750604	−0.375302	−	0.926903i	$-0.622461\pi$
$241$	−1.63106e8	−0.750604	−0.375302	+	0.926903i	$0.622461\pi$
$242$	−1.70746e8	−0.774456
$243$	−3.15063e8	−1.40856
$244$	8.55379e8	3.76959
$245$	−8.97069e7	−0.389713
$246$	−1.23302e9	−5.28077
$247$	1.46344e8	0.617927
$248$	−2.48976e8	−1.03652
$249$	2.29221e8	0.940927
$250$	4.05179e8	1.64005
$251$	1.43288e8	0.571941	0.285970	−	0.958238i	$-0.407684\pi$
$251$	1.43288e8	0.571941	0.285970	+	0.958238i	$0.407684\pi$
$252$	−3.72572e8	−1.46659
$253$	−1.35588e8	−0.526381
$254$	−4.84291e7	−0.185434
$255$	−1.50129e7	−0.0566986
$256$	−1.30614e8	−0.486576
$257$	4.91469e7	0.180605	0.0903025	−	0.995914i	$-0.471217\pi$
$257$	4.91469e7	0.180605	0.0903025	+	0.995914i	$0.471217\pi$
$258$	1.23641e9	4.48222
$259$	−1.31867e8	−0.471615
$260$	−1.18966e8	−0.419774
$261$	5.33527e8	1.85744
$262$	3.89954e8	1.33955
$263$	−1.24542e8	−0.422153	−0.211077	−	0.977470i	$-0.567697\pi$
$263$	−1.24542e8	−0.422153	−0.211077	+	0.977470i	$0.567697\pi$
$264$	−1.47176e9	−4.92291
$265$	−1.85307e8	−0.611691
$266$	−4.99945e8	−1.62868
$267$	−3.21868e8	−1.03488
$268$	−6.21466e8	−1.97218
$269$	1.19532e8	0.374412	0.187206	−	0.982321i	$-0.440057\pi$
$269$	1.19532e8	0.374412	0.187206	+	0.982321i	$0.440057\pi$
$270$	−1.11286e8	−0.344086
$271$	1.79816e8	0.548826	0.274413	−	0.961612i	$-0.411516\pi$
$271$	1.79816e8	0.548826	0.274413	+	0.961612i	$0.411516\pi$
$272$	−6.67005e7	−0.200973
$273$	8.04481e7	0.239302
$274$	5.37692e8	1.57909
$275$	−3.06345e8	−0.888273
$276$	−5.74391e8	−1.64447
$277$	4.18448e8	1.18294	0.591469	−	0.806327i	$-0.298548\pi$
$277$	4.18448e8	1.18294	0.591469	+	0.806327i	$0.298548\pi$
$278$	−2.77407e8	−0.774391
$279$	1.69420e8	0.467037
$280$	2.42575e8	0.660378
$281$	−1.64963e8	−0.443521	−0.221761	−	0.975101i	$-0.571180\pi$
$281$	−1.64963e8	−0.443521	−0.221761	+	0.975101i	$0.571180\pi$
$282$	1.59261e9	4.22900
$283$	−2.06524e8	−0.541649	−0.270824	−	0.962629i	$-0.587296\pi$
$283$	−2.06524e8	−0.541649	−0.270824	+	0.962629i	$0.587296\pi$
$284$	−3.10399e8	−0.804092
$285$	−5.41532e8	−1.38569
$286$	2.95226e8	0.746231
$287$	−3.59430e8	−0.897485
$288$	−1.12213e9	−2.76802
$289$	−4.08018e8	−0.994346
$290$	−5.81988e8	−1.40127
$291$	−1.07467e9	−2.55652
$292$	−1.94026e7	−0.0456059
$293$	−5.50317e8	−1.27813	−0.639067	−	0.769151i	$-0.720679\pi$
$293$	−5.50317e8	−1.27813	−0.639067	+	0.769151i	$0.720679\pi$
$294$	9.43069e8	2.16435
$295$	5.78176e7	0.131124
$296$	−1.22360e9	−2.74232
$297$	1.96822e8	0.435939
$298$	3.15237e8	0.690050
$299$	6.87709e7	0.148784
$300$	−1.29777e9	−2.77506
$301$	3.60418e8	0.761769
$302$	−1.03243e9	−2.15693
$303$	−2.60714e8	−0.538412
$304$	−2.40597e9	−4.91170
$305$	3.78968e8	0.764810
$306$	8.75130e7	0.174601
$307$	8.24524e8	1.62637	0.813184	−	0.582007i	$-0.197732\pi$
$307$	8.24524e8	1.62637	0.813184	+	0.582007i	$0.197732\pi$
$308$	−7.18789e8	−1.40176
$309$	−1.05803e9	−2.04005
$310$	−1.84809e8	−0.352336
$311$	9.61316e8	1.81219	0.906097	−	0.423069i	$-0.139047\pi$
$311$	9.61316e8	1.81219	0.906097	+	0.423069i	$0.139047\pi$
$312$	7.46480e8	1.39148
$313$	3.62749e8	0.668653	0.334326	−	0.942457i	$-0.391491\pi$
$313$	3.62749e8	0.668653	0.334326	+	0.942457i	$0.391491\pi$
$314$	−2.01256e9	−3.66855
$315$	−1.65065e8	−0.297555
$316$	2.52246e9	4.49697
$317$	9.12812e8	1.60944	0.804718	−	0.593657i	$-0.202316\pi$
$317$	9.12812e8	1.60944	0.804718	+	0.593657i	$0.202316\pi$
$318$	1.94810e9	3.39716
$319$	1.02931e9	1.77534
$320$	4.35588e8	0.743107
$321$	−1.12723e9	−1.90216
$322$	−2.34937e8	−0.392153
$323$	8.36924e7	0.138190
$324$	−1.05633e9	−1.72541
$325$	1.55379e8	0.251074
$326$	−5.39280e8	−0.862091
$327$	−1.72838e9	−2.73352
$328$	−3.33516e9	−5.21865
$329$	4.64252e8	0.718734
$330$	−1.09245e9	−1.67341
$331$	1.01949e8	0.154521	0.0772604	−	0.997011i	$-0.475383\pi$
$331$	1.01949e8	0.154521	0.0772604	+	0.997011i	$0.475383\pi$
$332$	1.03878e9	1.55790
$333$	8.32622e8	1.23564
$334$	2.21300e8	0.324989
$335$	−2.75335e8	−0.400133
$336$	−1.32260e9	−1.90213
$337$	−1.22430e9	−1.74255	−0.871274	−	0.490797i	$-0.836706\pi$
$337$	−1.22430e9	−1.74255	−0.871274	+	0.490797i	$0.836706\pi$
$338$	1.17471e9	1.65470
$339$	4.02255e8	0.560793
$340$	−6.80349e7	−0.0938761
$341$	3.26857e8	0.446392
$342$	3.15670e9	4.26719
$343$	6.29930e8	0.842874
$344$	3.34433e9	4.42949
$345$	−2.54479e8	−0.333646
$346$	2.12789e9	2.76175
$347$	5.20408e8	0.668638	0.334319	−	0.942460i	$-0.391494\pi$
$347$	5.20408e8	0.668638	0.334319	+	0.942460i	$0.391494\pi$
$348$	4.36047e9	5.54633
$349$	6.13710e8	0.772812	0.386406	−	0.922329i	$-0.373716\pi$
$349$	6.13710e8	0.772812	0.386406	+	0.922329i	$0.373716\pi$
$350$	−5.30810e8	−0.661761
$351$	−9.98289e7	−0.123220
$352$	−2.16488e9	−2.64567
$353$	−1.13963e9	−1.37897	−0.689483	−	0.724302i	$-0.742162\pi$
$353$	−1.13963e9	−1.37897	−0.689483	+	0.724302i	$0.742162\pi$
$354$	−6.07824e8	−0.728226
$355$	−1.37519e8	−0.163142
$356$	−1.45863e9	−1.71345
$357$	4.60071e7	0.0535163
$358$	−3.13975e9	−3.61664
$359$	6.63688e8	0.757065	0.378533	−	0.925588i	$-0.376429\pi$
$359$	6.63688e8	0.757065	0.378533	+	0.925588i	$0.376429\pi$
$360$	−1.53164e9	−1.73021
$361$	2.12501e9	2.37731
$362$	2.33751e9	2.58985
$363$	5.66780e8	0.621930
$364$	3.64572e8	0.396213
$365$	−8.59617e6	−0.00925295
$366$	−3.98402e9	−4.24754
$367$	−1.29942e9	−1.37220	−0.686099	−	0.727508i	$-0.740678\pi$
$367$	−1.29942e9	−1.37220	−0.686099	+	0.727508i	$0.740678\pi$
$368$	−1.13062e9	−1.18263
$369$	2.26947e9	2.35143
$370$	−9.08251e8	−0.932180
$371$	5.67877e8	0.577359
$372$	1.38466e9	1.39458
$373$	−1.01330e9	−1.01101	−0.505506	−	0.862823i	$-0.668694\pi$
$373$	−1.01330e9	−1.01101	−0.505506	+	0.862823i	$0.668694\pi$
$374$	1.68836e8	0.166883
$375$	−1.34496e9	−1.31705
$376$	4.30781e9	4.17925
$377$	−5.22072e8	−0.501806
$378$	3.41037e8	0.324774
$379$	−1.08418e9	−1.02298	−0.511488	−	0.859290i	$-0.670906\pi$
$379$	−1.08418e9	−1.02298	−0.511488	+	0.859290i	$0.670906\pi$
$380$	−2.45410e9	−2.29430
$381$	1.60757e8	0.148913
$382$	1.89827e9	1.74235
$383$	6.07008e8	0.552075	0.276038	−	0.961147i	$-0.410979\pi$
$383$	6.07008e8	0.552075	0.276038	+	0.961147i	$0.410979\pi$
$384$	−8.82094e8	−0.794979
$385$	−3.18453e8	−0.284402
$386$	−2.81641e9	−2.49253
$387$	−2.27571e9	−1.99585
$388$	−4.87015e9	−4.23284
$389$	−2.16314e9	−1.86321	−0.931605	−	0.363473i	$-0.881591\pi$
$389$	−2.16314e9	−1.86321	−0.931605	+	0.363473i	$0.881591\pi$
$390$	5.54095e8	0.472997
$391$	3.93291e7	0.0332733
$392$	2.55088e9	2.13889
$393$	−1.29443e9	−1.07573
$394$	−4.75474e8	−0.391642
$395$	1.11755e9	0.912387
$396$	4.53850e9	3.67265
$397$	−4.18266e8	−0.335495	−0.167747	−	0.985830i	$-0.553649\pi$
$397$	−4.18266e8	−0.335495	−0.167747	+	0.985830i	$0.553649\pi$
$398$	−2.79422e9	−2.22162
$399$	1.65953e9	1.30792
$400$	−2.55450e9	−1.99571
$401$	−1.73065e9	−1.34030	−0.670151	−	0.742224i	$-0.733771\pi$
$401$	−1.73065e9	−1.34030	−0.670151	+	0.742224i	$0.733771\pi$
$402$	2.89454e9	2.22223
$403$	−1.65783e8	−0.126175
$404$	−1.18150e9	−0.891450
$405$	−4.67997e8	−0.350067
$406$	1.78351e9	1.32262
$407$	1.60635e9	1.18102
$408$	4.26901e8	0.311184
$409$	−6.20919e8	−0.448749	−0.224375	−	0.974503i	$-0.572034\pi$
$409$	−6.20919e8	−0.448749	−0.224375	+	0.974503i	$0.572034\pi$
$410$	−2.47561e9	−1.77394
$411$	−1.78483e9	−1.26809
$412$	−4.79473e9	−3.37772
$413$	−1.77183e8	−0.123765
$414$	1.48341e9	1.02745
$415$	4.60221e8	0.316081
$416$	1.09804e9	0.747808
$417$	9.20833e8	0.621877
$418$	6.09010e9	4.07856
$419$	−1.25339e8	−0.0832408	−0.0416204	−	0.999133i	$-0.513252\pi$
$419$	−1.25339e8	−0.0832408	−0.0416204	+	0.999133i	$0.513252\pi$
$420$	−1.34906e9	−0.888503
$421$	−2.92707e9	−1.91181	−0.955906	−	0.293671i	$-0.905123\pi$
$421$	−2.92707e9	−1.91181	−0.955906	+	0.293671i	$0.905123\pi$
$422$	−4.19675e8	−0.271844
$423$	−2.93133e9	−1.88310
$424$	5.26935e9	3.35719
$425$	8.88593e7	0.0561490
$426$	1.44571e9	0.906042
$427$	−1.16135e9	−0.721884
$428$	−5.10836e9	−3.14941
$429$	−9.79981e8	−0.599263
$430$	2.48242e9	1.50569
$431$	−2.20458e8	−0.132634	−0.0663172	−	0.997799i	$-0.521125\pi$
$431$	−2.20458e8	−0.132634	−0.0663172	+	0.997799i	$0.521125\pi$
$432$	1.64123e9	0.979436
$433$	−1.31134e9	−0.776261	−0.388131	−	0.921604i	$-0.626879\pi$
$433$	−1.31134e9	−0.776261	−0.388131	+	0.921604i	$0.626879\pi$
$434$	5.66351e8	0.332561
$435$	1.93187e9	1.12529
$436$	−7.83263e9	−4.52590
$437$	1.41865e9	0.813186
$438$	9.03698e7	0.0513882
$439$	−2.53463e9	−1.42984	−0.714922	−	0.699204i	$-0.753538\pi$
$439$	−2.53463e9	−1.42984	−0.714922	+	0.699204i	$0.753538\pi$
$440$	−2.95494e9	−1.65373
$441$	−1.73580e9	−0.963748
$442$	−8.56340e7	−0.0471703
$443$	−1.91827e9	−1.04833	−0.524164	−	0.851617i	$-0.675622\pi$
$443$	−1.91827e9	−1.04833	−0.524164	+	0.851617i	$0.675622\pi$
$444$	6.80495e9	3.68965
$445$	−6.46234e8	−0.347640
$446$	3.39478e9	1.81192
$447$	−1.04641e9	−0.554147
$448$	−1.33487e9	−0.701399
$449$	−1.41494e9	−0.737694	−0.368847	−	0.929490i	$-0.620247\pi$
$449$	−1.41494e9	−0.737694	−0.368847	+	0.929490i	$0.620247\pi$
$450$	3.35158e9	1.73383
$451$	4.37841e9	2.24749
$452$	1.82293e9	0.928507
$453$	3.42707e9	1.73213
$454$	2.52826e9	1.26802
$455$	1.61521e8	0.0803874
$456$	1.53988e10	7.60521
$457$	9.22607e8	0.452178	0.226089	−	0.974107i	$-0.427406\pi$
$457$	9.22607e8	0.452178	0.226089	+	0.974107i	$0.427406\pi$
$458$	9.57255e7	0.0465585
$459$	−5.70907e7	−0.0275563
$460$	−1.15324e9	−0.552418
$461$	−2.95993e9	−1.40711	−0.703554	−	0.710641i	$-0.748405\pi$
$461$	−2.95993e9	−1.40711	−0.703554	+	0.710641i	$0.748405\pi$
$462$	3.34783e9	1.57949
$463$	2.71598e9	1.27173	0.635863	−	0.771802i	$-0.280644\pi$
$463$	2.71598e9	1.27173	0.635863	+	0.771802i	$0.280644\pi$
$464$	8.58308e9	3.98869
$465$	6.13461e8	0.282945
$466$	−1.00369e9	−0.459462
$467$	−2.84268e9	−1.29157	−0.645787	−	0.763518i	$-0.723470\pi$
$467$	−2.84268e9	−1.29157	−0.645787	+	0.763518i	$0.723470\pi$
$468$	−2.30194e9	−1.03809
$469$	8.43769e8	0.377675
$470$	3.19759e9	1.42063
$471$	6.68054e9	2.94604
$472$	−1.64408e9	−0.719659
$473$	−4.39044e9	−1.90763
$474$	−1.17486e10	−5.06714
$475$	3.20526e9	1.37226
$476$	2.08494e8	0.0886072
$477$	−3.58563e9	−1.51269
$478$	5.05192e9	2.11572
$479$	−5.93721e8	−0.246836	−0.123418	−	0.992355i	$-0.539386\pi$
$479$	−5.93721e8	−0.246836	−0.123418	+	0.992355i	$0.539386\pi$
$480$	−4.06316e9	−1.67695
$481$	−8.14745e8	−0.333821
$482$	3.44271e9	1.40035
$483$	7.79856e8	0.314919
$484$	2.56852e9	1.02973
$485$	−2.15768e9	−0.858798
$486$	6.65010e9	2.62786
$487$	1.21772e9	0.477746	0.238873	−	0.971051i	$-0.423222\pi$
$487$	1.21772e9	0.477746	0.238873	+	0.971051i	$0.423222\pi$
$488$	−1.07762e10	−4.19757
$489$	1.79010e9	0.692304
$490$	1.89346e9	0.727059
$491$	−9.17266e7	−0.0349712	−0.0174856	−	0.999847i	$-0.505566\pi$
$491$	−9.17266e7	−0.0349712	−0.0174856	+	0.999847i	$0.505566\pi$
$492$	1.85482e10	7.02141
$493$	−2.98566e8	−0.112221
$494$	−3.08892e9	−1.15282
$495$	2.01074e9	0.745141
$496$	2.72554e9	1.00292
$497$	4.21431e8	0.153985
$498$	−4.83820e9	−1.75542
$499$	1.84939e9	0.666309	0.333155	−	0.942872i	$-0.391887\pi$
$499$	1.84939e9	0.666309	0.333155	+	0.942872i	$0.391887\pi$
$500$	−6.09507e9	−2.18064
$501$	−7.34590e8	−0.260983
$502$	−3.02440e9	−1.06703
$503$	−9.18482e8	−0.321797	−0.160899	−	0.986971i	$-0.551439\pi$
$503$	−9.18482e8	−0.321797	−0.160899	+	0.986971i	$0.551439\pi$
$504$	4.69373e9	1.63310
$505$	−5.23451e8	−0.180866
$506$	2.86189e9	0.982033
$507$	−3.89935e9	−1.32882
$508$	7.28515e8	0.246556
$509$	3.03376e9	1.01969	0.509845	−	0.860266i	$-0.329703\pi$
$509$	3.03376e9	1.01969	0.509845	+	0.860266i	$0.329703\pi$
$510$	3.16879e8	0.105779
$511$	2.63431e7	0.00873361
$512$	4.36840e9	1.43839
$513$	−2.05933e9	−0.673466
$514$	−1.03735e9	−0.336942
$515$	−2.12427e9	−0.685304
$516$	−1.85992e10	−5.95964
$517$	−5.65531e9	−1.79986
$518$	2.78335e9	0.879860
$519$	−7.06340e9	−2.21783
$520$	1.49875e9	0.467432
$521$	4.00810e9	1.24167	0.620836	−	0.783941i	$-0.286793\pi$
$521$	4.00810e9	1.24167	0.620836	+	0.783941i	$0.286793\pi$
$522$	−1.12613e10	−3.46529
$523$	−7.05665e8	−0.215696	−0.107848	−	0.994167i	$-0.534396\pi$
$523$	−7.05665e8	−0.215696	−0.107848	+	0.994167i	$0.534396\pi$
$524$	−5.86605e9	−1.78109
$525$	1.76199e9	0.531429
$526$	2.62873e9	0.787582
$527$	−9.48089e7	−0.0282171
$528$	1.61113e10	4.76335
$529$	−2.73817e9	−0.804202
$530$	3.91132e9	1.14119
$531$	1.11875e9	0.324266
$532$	7.52062e9	2.16552
$533$	−2.22074e9	−0.635263
$534$	6.79372e9	1.93069
$535$	−2.26322e9	−0.638981
$536$	7.82935e9	2.19608
$537$	1.04222e10	2.90435
$538$	−2.52298e9	−0.698514
$539$	−3.34880e9	−0.921147
$540$	1.67406e9	0.457503
$541$	2.60536e9	0.707420	0.353710	−	0.935355i	$-0.384920\pi$
$541$	2.60536e9	0.707420	0.353710	+	0.935355i	$0.384920\pi$
$542$	−3.79540e9	−1.02391
$543$	−7.75921e9	−2.07978
$544$	6.27952e8	0.167236
$545$	−3.47018e9	−0.918257
$546$	−1.69803e9	−0.446449
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	−8.08845e9	−2.09958
$549$	7.33290e9	1.89135
$550$	6.46609e9	1.65719
$551$	−1.07696e10	−2.74265
$552$	7.23630e9	1.83117
$553$	−3.42477e9	−0.861178
$554$	−8.83226e9	−2.20693
$555$	3.01488e9	0.748590
$556$	4.17301e9	1.02964
$557$	4.38703e9	1.07567	0.537833	−	0.843051i	$-0.319243\pi$
$557$	4.38703e9	1.07567	0.537833	+	0.843051i	$0.319243\pi$
$558$	−3.57599e9	−0.871318
$559$	2.22685e9	0.539200
$560$	−2.65547e9	−0.638974
$561$	−5.60438e8	−0.134016
$562$	3.48190e9	0.827446
$563$	−6.11158e9	−1.44336	−0.721679	−	0.692228i	$-0.756629\pi$
$563$	−6.11158e9	−1.44336	−0.721679	+	0.692228i	$0.756629\pi$
$564$	−2.39575e10	−5.62296
$565$	8.07632e8	0.188384
$566$	4.35914e9	1.01052
$567$	1.43419e9	0.330419
$568$	3.91046e9	0.895383
$569$	3.42797e9	0.780088	0.390044	−	0.920796i	$-0.372460\pi$
$569$	3.42797e9	0.780088	0.390044	+	0.920796i	$0.372460\pi$
$570$	1.14302e10	2.58519
$571$	7.15242e9	1.60778	0.803890	−	0.594777i	$-0.202760\pi$
$571$	7.15242e9	1.60778	0.803890	+	0.594777i	$0.202760\pi$
$572$	−4.44105e9	−0.992202
$573$	−6.30116e9	−1.39920
$574$	7.58655e9	1.67438
$575$	1.50623e9	0.330411
$576$	8.42848e9	1.83768
$577$	6.65506e9	1.44224	0.721118	−	0.692812i	$-0.243628\pi$
$577$	6.65506e9	1.44224	0.721118	+	0.692812i	$0.243628\pi$
$578$	8.61212e9	1.85508
$579$	9.34886e9	2.00163
$580$	8.75479e9	1.86315
$581$	−1.41035e9	−0.298340
$582$	2.26832e10	4.76952
$583$	−6.91762e9	−1.44583
$584$	2.44438e8	0.0507837
$585$	−1.01986e9	−0.210617
$586$	1.16157e10	2.38453
$587$	−3.07861e8	−0.0628234	−0.0314117	−	0.999507i	$-0.510000\pi$
$587$	−3.07861e8	−0.0628234	−0.0314117	+	0.999507i	$0.510000\pi$
$588$	−1.41865e10	−2.87776
$589$	−3.41987e9	−0.689614
$590$	−1.22037e9	−0.244629
$591$	1.57830e9	0.314510
$592$	1.33948e10	2.65344
$593$	7.23934e9	1.42563	0.712816	−	0.701351i	$-0.247419\pi$
$593$	7.23934e9	1.42563	0.712816	+	0.701351i	$0.247419\pi$
$594$	−4.15436e9	−0.813302
$595$	9.23714e7	0.0179775
$596$	−4.74208e9	−0.917503
$597$	9.27522e9	1.78408
$598$	−1.45156e9	−0.277575
$599$	−4.30119e9	−0.817702	−0.408851	−	0.912601i	$-0.634070\pi$
$599$	−4.30119e9	−0.817702	−0.408851	+	0.912601i	$0.634070\pi$
$600$	1.63495e10	3.09012
$601$	−1.32718e9	−0.249384	−0.124692	−	0.992196i	$-0.539794\pi$
$601$	−1.32718e9	−0.249384	−0.124692	+	0.992196i	$0.539794\pi$
$602$	−7.60741e9	−1.42118
$603$	−5.32763e9	−0.989518
$604$	1.55307e10	2.86789
$605$	1.13796e9	0.208921
$606$	5.50293e9	1.00448
$607$	−2.43612e9	−0.442118	−0.221059	−	0.975260i	$-0.570951\pi$
$607$	−2.43612e9	−0.442118	−0.221059	+	0.975260i	$0.570951\pi$
$608$	2.26510e10	4.08718
$609$	−5.92024e9	−1.06213
$610$	−7.99896e9	−1.42685
$611$	2.86839e9	0.508738
$612$	−1.31645e9	−0.232153
$613$	1.99883e8	0.0350481	0.0175240	−	0.999846i	$-0.494422\pi$
$613$	1.99883e8	0.0350481	0.0175240	+	0.999846i	$0.494422\pi$
$614$	−1.74034e10	−3.03420
$615$	8.21762e9	1.42457
$616$	9.05545e9	1.56091
$617$	−3.55739e9	−0.609724	−0.304862	−	0.952397i	$-0.598610\pi$
$617$	−3.55739e9	−0.609724	−0.304862	+	0.952397i	$0.598610\pi$
$618$	2.23320e10	3.80599
$619$	−6.32261e9	−1.07147	−0.535734	−	0.844387i	$-0.679965\pi$
$619$	−6.32261e9	−1.07147	−0.535734	+	0.844387i	$0.679965\pi$
$620$	2.78007e9	0.468473
$621$	−9.67731e8	−0.162156
$622$	−2.02907e10	−3.38088
$623$	1.98040e9	0.328128
$624$	−8.17172e9	−1.34638
$625$	1.85717e9	0.304279
$626$	−7.65660e9	−1.24746
$627$	−2.02157e10	−3.27530
$628$	3.02747e10	4.87777
$629$	−4.65942e8	−0.0746542
$630$	3.48405e9	0.555128
$631$	−4.23711e8	−0.0671378	−0.0335689	−	0.999436i	$-0.510687\pi$
$631$	−4.23711e8	−0.0671378	−0.0335689	+	0.999436i	$0.510687\pi$
$632$	−3.17785e10	−5.00753
$633$	1.39308e9	0.218305
$634$	−1.92669e10	−3.00261
$635$	3.22762e8	0.0500236
$636$	−2.93050e10	−4.51692
$637$	1.69853e9	0.260366
$638$	−2.17259e10	−3.31212
$639$	−2.66095e9	−0.403445
$640$	−1.77104e9	−0.267053
$641$	−4.57127e9	−0.685542	−0.342771	−	0.939419i	$-0.611365\pi$
$641$	−4.57127e9	−0.685542	−0.342771	+	0.939419i	$0.611365\pi$
$642$	2.37927e10	3.54872
$643$	1.66407e9	0.246850	0.123425	−	0.992354i	$-0.460612\pi$
$643$	1.66407e9	0.246850	0.123425	+	0.992354i	$0.460612\pi$
$644$	3.53413e9	0.521413
$645$	−8.24021e9	−1.20915
$646$	−1.76651e9	−0.257812
$647$	−9.61513e8	−0.139569	−0.0697847	−	0.997562i	$-0.522231\pi$
$647$	−9.61513e8	−0.139569	−0.0697847	+	0.997562i	$0.522231\pi$
$648$	1.33078e10	1.92130
$649$	2.15836e9	0.309933
$650$	−3.27962e9	−0.468411
$651$	−1.87996e9	−0.267064
$652$	8.11234e9	1.14625
$653$	−9.77163e9	−1.37332	−0.686659	−	0.726980i	$-0.740923\pi$
$653$	−9.77163e9	−1.37332	−0.686659	+	0.726980i	$0.740923\pi$
$654$	3.64813e10	5.09974
$655$	−2.59890e9	−0.361364
$656$	3.65100e10	5.04950
$657$	−1.66333e8	−0.0228823
$658$	−9.79906e9	−1.34089
$659$	−2.92835e8	−0.0398587	−0.0199294	−	0.999801i	$-0.506344\pi$
$659$	−2.92835e8	−0.0398587	−0.0199294	+	0.999801i	$0.506344\pi$
$660$	1.64336e10	2.22500
$661$	6.07869e9	0.818662	0.409331	−	0.912386i	$-0.365762\pi$
$661$	6.07869e9	0.818662	0.409331	+	0.912386i	$0.365762\pi$
$662$	−2.15187e9	−0.288279
$663$	2.84256e8	0.0378802
$664$	−1.30867e10	−1.73477
$665$	3.33195e9	0.439362
$666$	−1.75743e10	−2.30525
$667$	−5.06091e9	−0.660371
$668$	−3.32900e9	−0.432111
$669$	−1.12687e10	−1.45507
$670$	5.81155e9	0.746501
$671$	1.41471e10	1.80775
$672$	1.24516e10	1.58283
$673$	−7.74984e9	−0.980032	−0.490016	−	0.871713i	$-0.663009\pi$
$673$	−7.74984e9	−0.980032	−0.490016	+	0.871713i	$0.663009\pi$
$674$	2.58416e10	3.25095
$675$	−2.18647e9	−0.273640
$676$	−1.76710e10	−2.20012
$677$	−5.84316e9	−0.723749	−0.361874	−	0.932227i	$-0.617863\pi$
$677$	−5.84316e9	−0.723749	−0.361874	+	0.932227i	$0.617863\pi$
$678$	−8.49047e9	−1.04623
$679$	6.61224e9	0.810596
$680$	8.57117e8	0.104534
$681$	−8.39237e9	−1.01829
$682$	−6.89902e9	−0.832803
$683$	1.00062e10	1.20171	0.600853	−	0.799360i	$-0.294828\pi$
$683$	1.00062e10	1.20171	0.600853	+	0.799360i	$0.294828\pi$
$684$	−4.74859e10	−5.67373
$685$	−3.58352e9	−0.425983
$686$	−1.32960e10	−1.57249
$687$	−3.17754e8	−0.0373889
$688$	−3.66104e10	−4.28592
$689$	3.50864e9	0.408669
$690$	5.37134e9	0.622459
$691$	6.04369e8	0.0696834	0.0348417	−	0.999393i	$-0.488907\pi$
$691$	6.04369e8	0.0696834	0.0348417	+	0.999393i	$0.488907\pi$
$692$	−3.20097e10	−3.67207
$693$	−6.16195e9	−0.703319
$694$	−1.09844e10	−1.24743
$695$	1.84881e9	0.208904
$696$	−5.49341e10	−6.17603
$697$	−1.27001e9	−0.142067
$698$	−1.29537e10	−1.44178
$699$	3.33168e9	0.368972
$700$	7.98493e9	0.879889
$701$	4.49700e8	0.0493071	0.0246535	−	0.999696i	$-0.492152\pi$
$701$	4.49700e8	0.0493071	0.0246535	+	0.999696i	$0.492152\pi$
$702$	2.10711e9	0.229883
$703$	−1.68071e10	−1.82452
$704$	1.62607e10	1.75645
$705$	−1.06142e10	−1.14084
$706$	2.40544e10	2.57264
$707$	1.60412e9	0.170714
$708$	9.14344e9	0.968263
$709$	−1.64388e10	−1.73225	−0.866123	−	0.499831i	$-0.833395\pi$
$709$	−1.64388e10	−1.73225	−0.866123	+	0.499831i	$0.833395\pi$
$710$	2.90265e9	0.304362
$711$	2.16243e10	2.25631
$712$	1.83761e10	1.90798
$713$	−1.60708e9	−0.166045
$714$	−9.71081e8	−0.0998417
$715$	−1.96757e9	−0.201307
$716$	4.72310e10	4.80874
$717$	−1.67695e10	−1.69904
$718$	−1.40086e10	−1.41240
$719$	1.71902e10	1.72476	0.862380	−	0.506261i	$-0.168973\pi$
$719$	1.71902e10	1.72476	0.862380	+	0.506261i	$0.168973\pi$
$720$	1.67669e10	1.67413
$721$	6.50985e9	0.646841
$722$	−4.48530e10	−4.43518
$723$	−1.14279e10	−1.12455
$724$	−3.51630e10	−3.44351
$725$	−1.14345e10	−1.11438
$726$	−1.19631e10	−1.16029
$727$	−4.59068e9	−0.443105	−0.221552	−	0.975149i	$-0.571112\pi$
$727$	−4.59068e9	−0.443105	−0.221552	+	0.975149i	$0.571112\pi$
$728$	−4.59296e9	−0.441197
$729$	−1.47987e10	−1.41474
$730$	1.81441e8	0.0172626
$731$	1.27350e9	0.120584
$732$	5.99312e10	5.64760
$733$	3.44443e9	0.323037	0.161519	−	0.986870i	$-0.448361\pi$
$733$	3.44443e9	0.323037	0.161519	+	0.986870i	$0.448361\pi$
$734$	2.74270e10	2.56001
$735$	−6.28521e9	−0.583867
$736$	1.06443e10	0.984108
$737$	−1.02784e10	−0.945779
$738$	−4.79022e10	−4.38690
$739$	−9.16784e9	−0.835625	−0.417812	−	0.908533i	$-0.637203\pi$
$739$	−9.16784e9	−0.835625	−0.417812	+	0.908533i	$0.637203\pi$
$740$	1.36627e10	1.23944
$741$	1.02535e10	0.925777
$742$	−1.19863e10	−1.07714
$743$	1.51817e10	1.35787	0.678936	−	0.734197i	$-0.262441\pi$
$743$	1.51817e10	1.35787	0.678936	+	0.734197i	$0.262441\pi$
$744$	−1.74442e10	−1.55291
$745$	−2.10094e9	−0.186152
$746$	2.13879e10	1.88617
$747$	8.90510e9	0.781658
$748$	−2.53978e9	−0.221891
$749$	6.93566e9	0.603117
$750$	2.83884e10	2.45712
$751$	−4.76500e9	−0.410510	−0.205255	−	0.978709i	$-0.565802\pi$
$751$	−4.76500e9	−0.410510	−0.205255	+	0.978709i	$0.565802\pi$
$752$	−4.71576e10	−4.04380
$753$	1.00393e10	0.856881
$754$	1.10195e10	0.936183
$755$	6.88075e9	0.581864
$756$	−5.13019e9	−0.431825
$757$	−1.35703e10	−1.13698	−0.568490	−	0.822690i	$-0.692472\pi$
$757$	−1.35703e10	−1.13698	−0.568490	+	0.822690i	$0.692472\pi$
$758$	2.28841e10	1.90850
$759$	−9.49984e9	−0.788624
$760$	3.09172e10	2.55478
$761$	1.34492e9	0.110624	0.0553121	−	0.998469i	$-0.482385\pi$
$761$	1.34492e9	0.110624	0.0553121	+	0.998469i	$0.482385\pi$
$762$	−3.39313e9	−0.277817
$763$	1.06344e10	0.866718
$764$	−2.85554e10	−2.31666
$765$	−5.83242e8	−0.0471014
$766$	−1.28122e10	−1.02997
$767$	−1.09473e9	−0.0876037
$768$	−9.15133e9	−0.728987
$769$	−7.51194e9	−0.595676	−0.297838	−	0.954616i	$-0.596265\pi$
$769$	−7.51194e9	−0.595676	−0.297838	+	0.954616i	$0.596265\pi$
$770$	6.72165e9	0.530589
$771$	3.44342e9	0.270582
$772$	4.23669e10	3.31411
$773$	−1.39698e10	−1.08783	−0.543915	−	0.839141i	$-0.683058\pi$
$773$	−1.39698e10	−1.08783	−0.543915	+	0.839141i	$0.683058\pi$
$774$	4.80339e10	3.72352
$775$	−3.63100e9	−0.280202
$776$	6.13552e10	4.71341
$777$	−9.23913e9	−0.706574
$778$	4.56579e10	3.47606
$779$	−4.58109e10	−3.47206
$780$	−8.33520e9	−0.628905
$781$	−5.13367e9	−0.385611
$782$	−8.30127e8	−0.0620756
$783$	7.34649e9	0.546908
$784$	−2.79245e10	−2.06957
$785$	1.34129e10	0.989647
$786$	2.73217e10	2.00691
$787$	1.41141e10	1.03214	0.516072	−	0.856545i	$-0.327394\pi$
$787$	1.41141e10	1.03214	0.516072	+	0.856545i	$0.327394\pi$
$788$	7.15251e9	0.520735
$789$	−8.72588e9	−0.632470
$790$	−2.35884e10	−1.70218
$791$	−2.47500e9	−0.177811
$792$	−5.71769e10	−4.08962
$793$	−7.17546e9	−0.510968
$794$	8.82842e9	0.625909
$795$	−1.29833e10	−0.916435
$796$	4.20332e10	2.95391
$797$	−1.38596e10	−0.969717	−0.484859	−	0.874593i	$-0.661129\pi$
$797$	−1.38596e10	−0.969717	−0.484859	+	0.874593i	$0.661129\pi$
$798$	−3.50281e10	−2.44009
$799$	1.64039e9	0.113772
$800$	2.40494e10	1.66069
$801$	−1.25044e10	−0.859704
$802$	3.65291e10	2.50051
$803$	−3.20900e8	−0.0218708
$804$	−4.35423e10	−2.95471
$805$	1.56577e9	0.105789
$806$	3.49921e9	0.235395
$807$	8.37484e9	0.560944
$808$	1.48847e10	0.992660
$809$	−2.79598e10	−1.85658	−0.928290	−	0.371858i	$-0.878721\pi$
$809$	−2.79598e10	−1.85658	−0.928290	+	0.371858i	$0.878721\pi$
$810$	9.87811e9	0.653095
$811$	1.23493e10	0.812959	0.406479	−	0.913660i	$-0.366756\pi$
$811$	1.23493e10	0.812959	0.406479	+	0.913660i	$0.366756\pi$
$812$	−2.68292e10	−1.75858
$813$	1.25986e10	0.822251
$814$	−3.39055e10	−2.20336
$815$	3.59410e9	0.232562
$816$	−4.67329e9	−0.301098
$817$	4.59368e10	2.94702
$818$	1.31059e10	0.837200
$819$	3.12537e9	0.198796
$820$	3.72404e10	2.35866
$821$	2.79047e9	0.175986	0.0879928	−	0.996121i	$-0.471955\pi$
$821$	2.79047e9	0.175986	0.0879928	+	0.996121i	$0.471955\pi$
$822$	3.76728e10	2.36579
$823$	1.99832e10	1.24959	0.624793	−	0.780791i	$-0.285183\pi$
$823$	1.99832e10	1.24959	0.624793	+	0.780791i	$0.285183\pi$
$824$	6.04050e10	3.76121
$825$	−2.14637e10	−1.33081
$826$	3.73983e9	0.230899
$827$	−1.35359e10	−0.832181	−0.416091	−	0.909323i	$-0.636600\pi$
$827$	−1.35359e10	−0.832181	−0.416091	+	0.909323i	$0.636600\pi$
$828$	−2.23148e10	−1.36611
$829$	−8.91486e9	−0.543467	−0.271734	−	0.962372i	$-0.587597\pi$
$829$	−8.91486e9	−0.543467	−0.271734	+	0.962372i	$0.587597\pi$
$830$	−9.71397e9	−0.589689
$831$	2.93181e10	1.77228
$832$	−8.24751e9	−0.496468
$833$	9.71363e8	0.0582270
$834$	−1.94362e10	−1.16019
$835$	−1.47488e9	−0.0876708
$836$	−9.16128e10	−5.42293
$837$	2.33286e9	0.137515
$838$	2.64555e9	0.155297
$839$	1.42434e10	0.832618	0.416309	−	0.909223i	$-0.363324\pi$
$839$	1.42434e10	0.832618	0.416309	+	0.909223i	$0.363324\pi$
$840$	1.69957e10	0.989378
$841$	2.11698e10	1.22725
$842$	6.17822e10	3.56674
$843$	−1.15579e10	−0.664483
$844$	6.31313e9	0.361448
$845$	−7.82898e9	−0.446382
$846$	6.18722e10	3.51317
$847$	−3.48730e9	−0.197195
$848$	−5.76836e10	−3.24838
$849$	−1.44699e10	−0.811498
$850$	−1.87557e9	−0.104753
$851$	−7.89806e9	−0.439306
$852$	−2.17477e10	−1.20469
$853$	−3.97551e9	−0.219317	−0.109658	−	0.993969i	$-0.534976\pi$
$853$	−3.97551e9	−0.219317	−0.109658	+	0.993969i	$0.534976\pi$
$854$	2.45129e10	1.34677
$855$	−2.10382e10	−1.15114
$856$	6.43562e10	3.50697
$857$	−1.19416e10	−0.648083	−0.324041	−	0.946043i	$-0.605042\pi$
$857$	−1.19416e10	−0.648083	−0.324041	+	0.946043i	$0.605042\pi$
$858$	2.06847e10	1.11800
$859$	−2.48651e9	−0.133849	−0.0669244	−	0.997758i	$-0.521319\pi$
$859$	−2.48651e9	−0.133849	−0.0669244	+	0.997758i	$0.521319\pi$
$860$	−3.73428e10	−2.00199
$861$	−2.51830e10	−1.34461
$862$	4.65326e9	0.247447
$863$	−2.03521e10	−1.07788	−0.538941	−	0.842343i	$-0.681176\pi$
$863$	−2.03521e10	−1.07788	−0.538941	+	0.842343i	$0.681176\pi$
$864$	−1.54514e10	−0.815020
$865$	−1.41816e10	−0.745023
$866$	2.76787e10	1.44822
$867$	−2.85874e10	−1.48973
$868$	−8.51956e9	−0.442179
$869$	4.17189e10	2.15657
$870$	−4.07763e10	−2.09938
$871$	5.21324e9	0.267328
$872$	9.86770e10	5.03974
$873$	−4.17503e10	−2.12378
$874$	−2.99437e10	−1.51710
$875$	8.27533e9	0.417597
$876$	−1.35942e9	−0.0683267
$877$	2.01054e10	1.00650	0.503250	−	0.864141i	$-0.332137\pi$
$877$	2.01054e10	1.00650	0.503250	+	0.864141i	$0.332137\pi$
$878$	5.34989e10	2.66756
$879$	−3.85574e10	−1.91490
$880$	3.23477e10	1.60013
$881$	−1.34779e10	−0.664061	−0.332031	−	0.943269i	$-0.607734\pi$
$881$	−1.34779e10	−0.664061	−0.332031	+	0.943269i	$0.607734\pi$
$882$	3.66378e10	1.79800
$883$	6.90901e9	0.337717	0.168859	−	0.985640i	$-0.445992\pi$
$883$	6.90901e9	0.337717	0.168859	+	0.985640i	$0.445992\pi$
$884$	1.28818e9	0.0627184
$885$	4.05092e9	0.196450
$886$	4.04894e10	1.95579
$887$	1.74120e10	0.837752	0.418876	−	0.908043i	$-0.362424\pi$
$887$	1.74120e10	0.837752	0.418876	+	0.908043i	$0.362424\pi$
$888$	−8.57301e10	−4.10855
$889$	−9.89110e8	−0.0472159
$890$	1.36402e10	0.648568
$891$	−1.74706e10	−0.827438
$892$	−5.10674e10	−2.40917
$893$	5.91710e10	2.78054
$894$	2.20867e10	1.03383
$895$	2.09253e10	0.975643
$896$	5.42737e9	0.252064
$897$	4.81836e9	0.222908
$898$	2.98654e10	1.37626
$899$	1.22001e10	0.560021
$900$	−5.04176e10	−2.30533
$901$	2.00654e9	0.0913928
$902$	−9.24159e10	−4.19299
$903$	2.52523e10	1.14128
$904$	−2.29656e10	−1.03392
$905$	−1.55787e10	−0.698651
$906$	−7.23359e10	−3.23151
$907$	1.18574e10	0.527670	0.263835	−	0.964568i	$-0.415013\pi$
$907$	1.18574e10	0.527670	0.263835	+	0.964568i	$0.415013\pi$
$908$	−3.80323e10	−1.68598
$909$	−1.01286e10	−0.447276
$910$	−3.40925e9	−0.149973
$911$	−2.86141e10	−1.25391	−0.626955	−	0.779056i	$-0.715699\pi$
$911$	−2.86141e10	−1.25391	−0.626955	+	0.779056i	$0.715699\pi$
$912$	−1.68571e11	−7.35871
$913$	1.71803e10	0.747107
$914$	−1.94736e10	−0.843598
$915$	2.65520e10	1.14584
$916$	−1.43999e9	−0.0619050
$917$	7.96438e9	0.341082
$918$	1.20503e9	0.0514099
$919$	−1.07853e9	−0.0458384	−0.0229192	−	0.999737i	$-0.507296\pi$
$919$	−1.07853e9	−0.0458384	−0.0229192	+	0.999737i	$0.507296\pi$
$920$	1.45288e10	0.615137
$921$	5.77693e10	2.43662
$922$	6.24757e10	2.62514
$923$	2.60382e9	0.108995
$924$	−5.03611e10	−2.10012
$925$	−1.78447e10	−0.741332
$926$	−5.73268e10	−2.37257
$927$	−4.11038e10	−1.69474
$928$	−8.08054e10	−3.31912
$929$	9.77774e9	0.400114	0.200057	−	0.979784i	$-0.435887\pi$
$929$	9.77774e9	0.400114	0.200057	+	0.979784i	$0.435887\pi$
$930$	−1.29484e10	−0.527870
$931$	3.50382e10	1.42304
$932$	1.50984e10	0.610908
$933$	6.73535e10	2.71503
$934$	6.00010e10	2.40960
$935$	−1.12523e9	−0.0450194
$936$	2.90003e10	1.15595
$937$	1.71271e10	0.680136	0.340068	−	0.940401i	$-0.389550\pi$
$937$	1.71271e10	0.680136	0.340068	+	0.940401i	$0.389550\pi$
$938$	−1.78096e10	−0.704602
$939$	2.54156e10	1.00177
$940$	−4.81010e10	−1.88889
$941$	−2.06958e10	−0.809691	−0.404846	−	0.914385i	$-0.632675\pi$
$941$	−2.06958e10	−0.809691	−0.404846	+	0.914385i	$0.632675\pi$
$942$	−1.41007e11	−5.49622
$943$	−2.15277e10	−0.836000
$944$	1.79978e10	0.696334
$945$	−2.27289e9	−0.0876126
$946$	9.26700e10	3.55893
$947$	3.87248e10	1.48171	0.740857	−	0.671663i	$-0.234420\pi$
$947$	3.87248e10	1.48171	0.740857	+	0.671663i	$0.234420\pi$
$948$	1.76733e11	6.73736
$949$	1.62762e8	0.00618187
$950$	−6.76541e10	−2.56013
$951$	6.39551e10	2.41126
$952$	−2.62665e9	−0.0986671
$953$	4.81094e10	1.80055	0.900274	−	0.435323i	$-0.143366\pi$
$953$	4.81094e10	1.80055	0.900274	+	0.435323i	$0.143366\pi$
$954$	7.56826e10	2.82213
$955$	−1.26512e10	−0.470025
$956$	−7.59956e10	−2.81311
$957$	7.21177e10	2.65981
$958$	1.25318e10	0.460504
$959$	1.09817e10	0.402074
$960$	3.05190e10	1.11332
$961$	−2.36385e10	−0.859188
$962$	1.71970e10	0.622787
$963$	−4.37924e10	−1.58018
$964$	−5.17884e10	−1.86193
$965$	1.87703e10	0.672397
$966$	−1.64606e10	−0.587523
$967$	−1.17223e10	−0.416889	−0.208445	−	0.978034i	$-0.566840\pi$
$967$	−1.17223e10	−0.416889	−0.208445	+	0.978034i	$0.566840\pi$
$968$	−3.23587e10	−1.14664
$969$	5.86381e9	0.207036
$970$	4.55426e10	1.60220
$971$	−1.00998e9	−0.0354036	−0.0177018	−	0.999843i	$-0.505635\pi$
$971$	−1.00998e9	−0.0354036	−0.0177018	+	0.999843i	$0.505635\pi$
$972$	−1.00037e11	−3.49404
$973$	−5.66572e9	−0.197179
$974$	−2.57027e10	−0.891296
$975$	1.08865e10	0.376159
$976$	1.17968e11	4.06152
$977$	7.38272e9	0.253271	0.126635	−	0.991949i	$-0.459582\pi$
$977$	7.38272e9	0.253271	0.126635	+	0.991949i	$0.459582\pi$
$978$	−3.77841e10	−1.29158
$979$	−2.41243e10	−0.821703
$980$	−2.84831e10	−0.966711
$981$	−6.71467e10	−2.27082
$982$	1.93609e9	0.0652432
$983$	−3.48349e10	−1.16971	−0.584854	−	0.811138i	$-0.698848\pi$
$983$	−3.48349e10	−1.16971	−0.584854	+	0.811138i	$0.698848\pi$
$984$	−2.33674e11	−7.81857
$985$	3.16886e9	0.105652
$986$	6.30188e9	0.209364
$987$	3.25273e10	1.07681
$988$	4.64663e10	1.53281
$989$	2.15869e10	0.709582
$990$	−4.24411e10	−1.39016
$991$	−4.17165e10	−1.36160	−0.680800	−	0.732469i	$-0.738368\pi$
$991$	−4.17165e10	−1.36160	−0.680800	+	0.732469i	$0.738368\pi$
$992$	−2.56596e10	−0.834563
$993$	7.14297e9	0.231503
$994$	−8.89521e9	−0.287279
$995$	1.86224e10	0.599316
$996$	7.27807e10	2.33404
$997$	1.20242e10	0.384258	0.192129	−	0.981370i	$-0.438461\pi$
$997$	1.20242e10	0.384258	0.192129	+	0.981370i	$0.438461\pi$
$998$	−3.90354e10	−1.24309
$999$	1.14649e10	0.363825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.7	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-21.1072 q^{2} +70.0639 q^{3} +317.514 q^{4} +140.672 q^{5} -1478.85 q^{6} -431.091 q^{7} -4000.10 q^{8} +2721.94 q^{9} +O(q^{10})\)	\(q-21.1072 q^{2} +70.0639 q^{3} +317.514 q^{4} +140.672 q^{5} -1478.85 q^{6} -431.091 q^{7} -4000.10 q^{8} +2721.94 q^{9} -2969.18 q^{10} +5251.35 q^{11} +22246.2 q^{12} -2663.50 q^{13} +9099.11 q^{14} +9856.00 q^{15} +43789.1 q^{16} -1523.22 q^{17} -57452.6 q^{18} -54944.4 q^{19} +44665.1 q^{20} -30203.9 q^{21} -110841. q^{22} -25819.7 q^{23} -280262. q^{24} -58336.5 q^{25} +56219.1 q^{26} +37480.3 q^{27} -136877. q^{28} +196009. q^{29} -208032. q^{30} +62242.4 q^{31} -412253. q^{32} +367930. q^{33} +32150.9 q^{34} -60642.2 q^{35} +864254. q^{36} +305892. q^{37} +1.15972e6 q^{38} -186615. q^{39} -562700. q^{40} +833769. q^{41} +637519. q^{42} -836061. q^{43} +1.66737e6 q^{44} +382900. q^{45} +544982. q^{46} -1.07693e6 q^{47} +3.06804e6 q^{48} -637704. q^{49} +1.23132e6 q^{50} -106723. q^{51} -845698. q^{52} -1.31730e6 q^{53} -791104. q^{54} +738716. q^{55} +1.72440e6 q^{56} -3.84961e6 q^{57} -4.13721e6 q^{58} +411011. q^{59} +3.12941e6 q^{60} +2.69399e6 q^{61} -1.31376e6 q^{62} -1.17340e6 q^{63} +3.09649e6 q^{64} -374679. q^{65} -7.76596e6 q^{66} -1.95729e6 q^{67} -483643. q^{68} -1.80903e6 q^{69} +1.27999e6 q^{70} -977592. q^{71} -1.08880e7 q^{72} -61108.1 q^{73} -6.45653e6 q^{74} -4.08728e6 q^{75} -1.74456e7 q^{76} -2.26381e6 q^{77} +3.93892e6 q^{78} +7.94442e6 q^{79} +6.15989e6 q^{80} -3.32688e6 q^{81} -1.75985e7 q^{82} +3.27160e6 q^{83} -9.59014e6 q^{84} -214274. q^{85} +1.76469e7 q^{86} +1.37332e7 q^{87} -2.10059e7 q^{88} -4.59392e6 q^{89} -8.08195e6 q^{90} +1.14821e6 q^{91} -8.19811e6 q^{92} +4.36094e6 q^{93} +2.27309e7 q^{94} -7.72911e6 q^{95} -2.88840e7 q^{96} -1.53384e7 q^{97} +1.34601e7 q^{98} +1.42939e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 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

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Database

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