LMFDB - Embedded newform 7.8.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,8,Mod(1,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, 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("7.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	7.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:	$2.18669517839$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{865}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 216 $ x^2 - x - 216
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$15.2054$ of defining polynomial
Character	$\chi$	$=$	7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.2054 q^{2} +76.4109 q^{3} +134.616 q^{4} +312.054 q^{5} -1238.27 q^{6} -343.000 q^{7} -107.220 q^{8} +3651.62 q^{9} +O(q^{10})$	\(q-16.2054 q^{2} +76.4109 q^{3} +134.616 q^{4} +312.054 q^{5} -1238.27 q^{6} -343.000 q^{7} -107.220 q^{8} +3651.62 q^{9} -5056.98 q^{10} -283.831 q^{11} +10286.2 q^{12} -11703.2 q^{13} +5558.47 q^{14} +23844.4 q^{15} -15493.3 q^{16} +4020.56 q^{17} -59176.2 q^{18} +3787.73 q^{19} +42007.6 q^{20} -26208.9 q^{21} +4599.61 q^{22} -2582.14 q^{23} -8192.81 q^{24} +19253.0 q^{25} +189656. q^{26} +111913. q^{27} -46173.4 q^{28} -127617. q^{29} -386408. q^{30} -159037. q^{31} +264801. q^{32} -21687.8 q^{33} -65155.0 q^{34} -107035. q^{35} +491568. q^{36} +583390. q^{37} -61381.9 q^{38} -894252. q^{39} -33458.6 q^{40} +18577.8 q^{41} +424727. q^{42} -323000. q^{43} -38208.3 q^{44} +1.13951e6 q^{45} +41844.7 q^{46} -1923.22 q^{47} -1.18386e6 q^{48} +117649. q^{49} -312003. q^{50} +307215. q^{51} -1.57544e6 q^{52} +1.35319e6 q^{53} -1.81360e6 q^{54} -88570.8 q^{55} +36776.6 q^{56} +289424. q^{57} +2.06809e6 q^{58} +868620. q^{59} +3.20984e6 q^{60} -1.27874e6 q^{61} +2.57726e6 q^{62} -1.25251e6 q^{63} -2.30806e6 q^{64} -3.65203e6 q^{65} +351460. q^{66} +584595. q^{67} +541233. q^{68} -197304. q^{69} +1.73454e6 q^{70} -5.67464e6 q^{71} -391529. q^{72} +4.97301e6 q^{73} -9.45409e6 q^{74} +1.47114e6 q^{75} +509890. q^{76} +97354.1 q^{77} +1.44917e7 q^{78} +870364. q^{79} -4.83476e6 q^{80} +565282. q^{81} -301061. q^{82} +3.87968e6 q^{83} -3.52815e6 q^{84} +1.25463e6 q^{85} +5.23436e6 q^{86} -9.75133e6 q^{87} +30432.5 q^{88} +1.02269e7 q^{89} -1.84662e7 q^{90} +4.01420e6 q^{91} -347598. q^{92} -1.21521e7 q^{93} +31166.6 q^{94} +1.18198e6 q^{95} +2.02336e7 q^{96} +3.98924e6 q^{97} -1.90655e6 q^{98} -1.03644e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 94 q^{3} + 181 q^{4} + 330 q^{5} - 1006 q^{6} - 686 q^{7} - 1185 q^{8} + 1774 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 94 * q^3 + 181 * q^4 + 330 * q^5 - 1006 * q^6 - 686 * q^7 - 1185 * q^8 + 1774 * q^9	\( 2 q - 3 q^{2} + 94 q^{3} + 181 q^{4} + 330 q^{5} - 1006 q^{6} - 686 q^{7} - 1185 q^{8} + 1774 q^{9} - 4820 q^{10} + 2844 q^{11} + 11102 q^{12} + 2534 q^{13} + 1029 q^{14} + 24160 q^{15} - 35663 q^{16} - 1488 q^{17} - 83971 q^{18} + 32810 q^{19} + 42840 q^{20} - 32242 q^{21} + 45904 q^{22} - 6576 q^{23} - 27150 q^{24} - 58550 q^{25} + 377664 q^{26} + 40420 q^{27} - 62083 q^{28} + 20640 q^{29} - 382240 q^{30} - 391836 q^{31} + 136407 q^{32} + 33328 q^{33} - 137898 q^{34} - 113190 q^{35} + 404477 q^{36} + 367392 q^{37} + 321870 q^{38} - 643832 q^{39} - 52800 q^{40} + 734664 q^{41} + 345058 q^{42} - 480476 q^{43} + 106872 q^{44} + 1105810 q^{45} - 10896 q^{46} - 1089108 q^{47} - 1538626 q^{48} + 235298 q^{49} - 1339425 q^{50} + 210324 q^{51} - 915068 q^{52} + 2858844 q^{53} - 2757700 q^{54} - 32440 q^{55} + 406455 q^{56} + 799900 q^{57} + 4025890 q^{58} + 160170 q^{59} + 3224480 q^{60} - 864646 q^{61} - 496956 q^{62} - 608482 q^{63} - 1421839 q^{64} - 3396540 q^{65} + 1077968 q^{66} - 328648 q^{67} + 285726 q^{68} - 267552 q^{69} + 1653260 q^{70} - 7500216 q^{71} + 1632135 q^{72} + 4301244 q^{73} - 12306438 q^{74} + 102650 q^{75} + 1856050 q^{76} - 975492 q^{77} + 17798648 q^{78} - 6408440 q^{79} - 5196720 q^{80} + 3414142 q^{81} + 9155174 q^{82} + 11659074 q^{83} - 3807986 q^{84} + 1155780 q^{85} + 3154824 q^{86} - 7143620 q^{87} - 3340680 q^{88} + 9772260 q^{89} - 18911140 q^{90} - 869162 q^{91} - 532848 q^{92} - 16246872 q^{93} - 14325588 q^{94} + 1702800 q^{95} + 17975314 q^{96} + 10762752 q^{97} - 352947 q^{98} - 6909332 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 94 * q^3 + 181 * q^4 + 330 * q^5 - 1006 * q^6 - 686 * q^7 - 1185 * q^8 + 1774 * q^9 - 4820 * q^10 + 2844 * q^11 + 11102 * q^12 + 2534 * q^13 + 1029 * q^14 + 24160 * q^15 - 35663 * q^16 - 1488 * q^17 - 83971 * q^18 + 32810 * q^19 + 42840 * q^20 - 32242 * q^21 + 45904 * q^22 - 6576 * q^23 - 27150 * q^24 - 58550 * q^25 + 377664 * q^26 + 40420 * q^27 - 62083 * q^28 + 20640 * q^29 - 382240 * q^30 - 391836 * q^31 + 136407 * q^32 + 33328 * q^33 - 137898 * q^34 - 113190 * q^35 + 404477 * q^36 + 367392 * q^37 + 321870 * q^38 - 643832 * q^39 - 52800 * q^40 + 734664 * q^41 + 345058 * q^42 - 480476 * q^43 + 106872 * q^44 + 1105810 * q^45 - 10896 * q^46 - 1089108 * q^47 - 1538626 * q^48 + 235298 * q^49 - 1339425 * q^50 + 210324 * q^51 - 915068 * q^52 + 2858844 * q^53 - 2757700 * q^54 - 32440 * q^55 + 406455 * q^56 + 799900 * q^57 + 4025890 * q^58 + 160170 * q^59 + 3224480 * q^60 - 864646 * q^61 - 496956 * q^62 - 608482 * q^63 - 1421839 * q^64 - 3396540 * q^65 + 1077968 * q^66 - 328648 * q^67 + 285726 * q^68 - 267552 * q^69 + 1653260 * q^70 - 7500216 * q^71 + 1632135 * q^72 + 4301244 * q^73 - 12306438 * q^74 + 102650 * q^75 + 1856050 * q^76 - 975492 * q^77 + 17798648 * q^78 - 6408440 * q^79 - 5196720 * q^80 + 3414142 * q^81 + 9155174 * q^82 + 11659074 * q^83 - 3807986 * q^84 + 1155780 * q^85 + 3154824 * q^86 - 7143620 * q^87 - 3340680 * q^88 + 9772260 * q^89 - 18911140 * q^90 - 869162 * q^91 - 532848 * q^92 - 16246872 * q^93 - 14325588 * q^94 + 1702800 * q^95 + 17975314 * q^96 + 10762752 * q^97 - 352947 * q^98 - 6909332 * 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 $

$2$	−16.2054	−1.43237	−0.716186	−	0.697909i	$-0.754114\pi$
$2$	−16.2054	−1.43237	−0.716186	+	0.697909i	$0.754114\pi$
$3$	76.4109	1.63392	0.816960	−	0.576694i	$-0.195658\pi$
$3$	76.4109	1.63392	0.816960	+	0.576694i	$0.195658\pi$
$4$	134.616	1.05169
$5$	312.054	1.11644	0.558220	−	0.829693i	$-0.311485\pi$
$5$	312.054	1.11644	0.558220	+	0.829693i	$0.311485\pi$
$6$	−1238.27	−2.34038
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−107.220	−0.0740394
$9$	3651.62	1.66969
$10$	−5056.98	−1.59916
$11$	−283.831	−0.0642963	−0.0321481	−	0.999483i	$-0.510235\pi$
$11$	−283.831	−0.0642963	−0.0321481	+	0.999483i	$0.510235\pi$
$12$	10286.2	1.71838
$13$	−11703.2	−1.47742	−0.738708	−	0.674025i	$-0.764564\pi$
$13$	−11703.2	−1.47742	−0.738708	+	0.674025i	$0.764564\pi$
$14$	5558.47	0.541386
$15$	23844.4	1.82417
$16$	−15493.3	−0.945638
$17$	4020.56	0.198479	0.0992397	−	0.995064i	$-0.468359\pi$
$17$	4020.56	0.198479	0.0992397	+	0.995064i	$0.468359\pi$
$18$	−59176.2	−2.39162
$19$	3787.73	0.126690	0.0633449	−	0.997992i	$-0.479823\pi$
$19$	3787.73	0.126690	0.0633449	+	0.997992i	$0.479823\pi$
$20$	42007.6	1.17415
$21$	−26208.9	−0.617564
$22$	4599.61	0.0920962
$23$	−2582.14	−0.0442519	−0.0221260	−	0.999755i	$-0.507043\pi$
$23$	−2582.14	−0.0442519	−0.0221260	+	0.999755i	$0.507043\pi$
$24$	−8192.81	−0.120974
$25$	19253.0	0.246438
$26$	189656.	2.11621
$27$	111913.	1.09423
$28$	−46173.4	−0.397501
$29$	−127617.	−0.971663	−0.485832	−	0.874052i	$-0.661483\pi$
$29$	−127617.	−0.971663	−0.485832	+	0.874052i	$0.661483\pi$
$30$	−386408.	−2.61290
$31$	−159037.	−0.958808	−0.479404	−	0.877594i	$-0.659147\pi$
$31$	−159037.	−0.958808	−0.479404	+	0.877594i	$0.659147\pi$
$32$	264801.	1.42855
$33$	−21687.8	−0.105055
$34$	−65155.0	−0.284297
$35$	−107035.	−0.421975
$36$	491568.	1.75600
$37$	583390.	1.89345	0.946723	−	0.322049i	$-0.104372\pi$
$37$	583390.	1.89345	0.946723	+	0.322049i	$0.104372\pi$
$38$	−61381.9	−0.181467
$39$	−894252.	−2.41398
$40$	−33458.6	−0.0826605
$41$	18577.8	0.0420969	0.0210484	−	0.999778i	$-0.493300\pi$
$41$	18577.8	0.0420969	0.0210484	+	0.999778i	$0.493300\pi$
$42$	424727.	0.884581
$43$	−323000.	−0.619531	−0.309766	−	0.950813i	$-0.600251\pi$
$43$	−323000.	−0.619531	−0.309766	+	0.950813i	$0.600251\pi$
$44$	−38208.3	−0.0676197
$45$	1.13951e6	1.86411
$46$	41844.7	0.0633852
$47$	−1923.22	−0.00270201	−0.00135100	−	0.999999i	$-0.500430\pi$
$47$	−1923.22	−0.00270201	−0.00135100	+	0.999999i	$0.500430\pi$
$48$	−1.18386e6	−1.54510
$49$	117649.	0.142857
$50$	−312003.	−0.352991
$51$	307215.	0.324300
$52$	−1.57544e6	−1.55378
$53$	1.35319e6	1.24851	0.624256	−	0.781220i	$-0.285402\pi$
$53$	1.35319e6	1.24851	0.624256	+	0.781220i	$0.285402\pi$
$54$	−1.81360e6	−1.56734
$55$	−88570.8	−0.0717829
$56$	36776.6	0.0279842
$57$	289424.	0.207001
$58$	2.06809e6	1.39178
$59$	868620.	0.550615	0.275307	−	0.961356i	$-0.411220\pi$
$59$	868620.	0.550615	0.275307	+	0.961356i	$0.411220\pi$
$60$	3.20984e6	1.91847
$61$	−1.27874e6	−0.721319	−0.360660	−	0.932698i	$-0.617448\pi$
$61$	−1.27874e6	−0.721319	−0.360660	+	0.932698i	$0.617448\pi$
$62$	2.57726e6	1.37337
$63$	−1.25251e6	−0.631085
$64$	−2.30806e6	−1.10057
$65$	−3.65203e6	−1.64945
$66$	351460.	0.150478
$67$	584595.	0.237461	0.118731	−	0.992926i	$-0.462117\pi$
$67$	584595.	0.237461	0.118731	+	0.992926i	$0.462117\pi$
$68$	541233.	0.208739
$69$	−197304.	−0.0723041
$70$	1.73454e6	0.604425
$71$	−5.67464e6	−1.88163	−0.940814	−	0.338922i	$-0.889938\pi$
$71$	−5.67464e6	−1.88163	−0.940814	+	0.338922i	$0.889938\pi$
$72$	−391529.	−0.123623
$73$	4.97301e6	1.49620	0.748099	−	0.663587i	$-0.230967\pi$
$73$	4.97301e6	1.49620	0.748099	+	0.663587i	$0.230967\pi$
$74$	−9.45409e6	−2.71212
$75$	1.47114e6	0.402660
$76$	509890.	0.133238
$77$	97354.1	0.0243017
$78$	1.44917e7	3.45772
$79$	870364.	0.198612	0.0993061	−	0.995057i	$-0.468338\pi$
$79$	870364.	0.198612	0.0993061	+	0.995057i	$0.468338\pi$
$80$	−4.83476e6	−1.05575
$81$	565282.	0.118186
$82$	−301061.	−0.0602984
$83$	3.87968e6	0.744771	0.372386	−	0.928078i	$-0.378540\pi$
$83$	3.87968e6	0.744771	0.372386	+	0.928078i	$0.378540\pi$
$84$	−3.52815e6	−0.649486
$85$	1.25463e6	0.221590
$86$	5.23436e6	0.887399
$87$	−9.75133e6	−1.58762
$88$	30432.5	0.00476045
$89$	1.02269e7	1.53773	0.768864	−	0.639412i	$-0.220822\pi$
$89$	1.02269e7	1.53773	0.768864	+	0.639412i	$0.220822\pi$
$90$	−1.84662e7	−2.67010
$91$	4.01420e6	0.558411
$92$	−347598.	−0.0465393
$93$	−1.21521e7	−1.56662
$94$	31166.6	0.00387028
$95$	1.18198e6	0.141442
$96$	2.02336e7	2.33413
$97$	3.98924e6	0.443802	0.221901	−	0.975069i	$-0.428774\pi$
$97$	3.98924e6	0.443802	0.221901	+	0.975069i	$0.428774\pi$
$98$	−1.90655e6	−0.204625
$99$	−1.03644e6	−0.107355
$100$	2.59176e6	0.259176
$101$	−61325.9	−0.00592270	−0.00296135	−	0.999996i	$-0.500943\pi$
$101$	−61325.9	−0.00592270	−0.00296135	+	0.999996i	$0.500943\pi$
$102$	−4.97855e6	−0.464518
$103$	−1.86031e7	−1.67747	−0.838736	−	0.544539i	$-0.816705\pi$
$103$	−1.86031e7	−1.67747	−0.838736	+	0.544539i	$0.816705\pi$
$104$	1.25482e6	0.109387
$105$	−8.17861e6	−0.689473
$106$	−2.19290e7	−1.78833
$107$	6.70845e6	0.529394	0.264697	−	0.964332i	$-0.414728\pi$
$107$	6.70845e6	0.529394	0.264697	+	0.964332i	$0.414728\pi$
$108$	1.50653e7	1.15079
$109$	1.34334e7	0.993555	0.496778	−	0.867878i	$-0.334516\pi$
$109$	1.34334e7	0.993555	0.496778	+	0.867878i	$0.334516\pi$
$110$	1.43533e6	0.102820
$111$	4.45773e7	3.09374
$112$	5.31421e6	0.357418
$113$	2.59915e7	1.69456	0.847280	−	0.531147i	$-0.178239\pi$
$113$	2.59915e7	1.69456	0.847280	+	0.531147i	$0.178239\pi$
$114$	−4.69024e6	−0.296502
$115$	−805768.	−0.0494046
$116$	−1.71793e7	−1.02189
$117$	−4.27357e7	−2.46683
$118$	−1.40764e7	−0.788685
$119$	−1.37905e6	−0.0750182
$120$	−2.55660e6	−0.135061
$121$	−1.94066e7	−0.995866
$122$	2.07225e7	1.03320
$123$	1.41954e6	0.0687829
$124$	−2.14089e7	−1.00837
$125$	−1.83713e7	−0.841307
$126$	2.02974e7	0.903949
$127$	−3.26332e7	−1.41367	−0.706833	−	0.707380i	$-0.749877\pi$
$127$	−3.26332e7	−1.41367	−0.706833	+	0.707380i	$0.749877\pi$
$128$	3.50871e6	0.147881
$129$	−2.46807e7	−1.01226
$130$	5.91828e7	2.36262
$131$	4.40185e7	1.71075	0.855373	−	0.518013i	$-0.173328\pi$
$131$	4.40185e7	1.71075	0.855373	+	0.518013i	$0.173328\pi$
$132$	−2.91953e6	−0.110485
$133$	−1.29919e6	−0.0478842
$134$	−9.47362e6	−0.340133
$135$	3.49230e7	1.22164
$136$	−431087.	−0.0146953
$137$	7.19777e6	0.239153	0.119576	−	0.992825i	$-0.461846\pi$
$137$	7.19777e6	0.239153	0.119576	+	0.992825i	$0.461846\pi$
$138$	3.19739e6	0.103566
$139$	−2.50479e7	−0.791079	−0.395539	−	0.918449i	$-0.629442\pi$
$139$	−2.50479e7	−0.791079	−0.395539	+	0.918449i	$0.629442\pi$
$140$	−1.44086e7	−0.443786
$141$	−146955.	−0.00441487
$142$	9.19600e7	2.69519
$143$	3.32173e6	0.0949923
$144$	−5.65758e7	−1.57893
$145$	−3.98235e7	−1.08480
$146$	−8.05898e7	−2.14311
$147$	8.98966e6	0.233417
$148$	7.85338e7	1.99132
$149$	−38001.6	−0.000941130 0	−0.000470565	−	1.00000i	$-0.500150\pi$
$149$	−38001.6	−0.000941130 0	−0.000470565		1.00000i	$0.500150\pi$
$150$	−2.38404e7	−0.576759
$151$	8.26640e6	0.195388	0.0976939	−	0.995217i	$-0.468853\pi$
$151$	8.26640e6	0.195388	0.0976939	+	0.995217i	$0.468853\pi$
$152$	−406122.	−0.00938003
$153$	1.46816e7	0.331400
$154$	−1.57767e6	−0.0348091
$155$	−4.96281e7	−1.07045
$156$	−1.20381e8	−2.53876
$157$	4.00357e7	0.825656	0.412828	−	0.910809i	$-0.364541\pi$
$157$	4.00357e7	0.825656	0.412828	+	0.910809i	$0.364541\pi$
$158$	−1.41046e7	−0.284487
$159$	1.03398e8	2.03997
$160$	8.26322e7	1.59488
$161$	885674.	0.0167257
$162$	−9.16064e6	−0.169287
$163$	−7.43567e7	−1.34482	−0.672409	−	0.740180i	$-0.734740\pi$
$163$	−7.43567e7	−1.34482	−0.672409	+	0.740180i	$0.734740\pi$
$164$	2.50087e6	0.0442729
$165$	−6.76777e6	−0.117288
$166$	−6.28720e7	−1.06679
$167$	6.14875e7	1.02160	0.510798	−	0.859701i	$-0.329350\pi$
$167$	6.14875e7	1.02160	0.510798	+	0.859701i	$0.329350\pi$
$168$	2.81013e6	0.0457240
$169$	7.42164e7	1.18276
$170$	−2.03319e7	−0.317400
$171$	1.38314e7	0.211533
$172$	−4.34811e7	−0.651555
$173$	−1.75888e7	−0.258271	−0.129135	−	0.991627i	$-0.541220\pi$
$173$	−1.75888e7	−0.258271	−0.129135	+	0.991627i	$0.541220\pi$
$174$	1.58025e8	2.27406
$175$	−6.60376e6	−0.0931447
$176$	4.39749e6	0.0608010
$177$	6.63720e7	0.899661
$178$	−1.65732e8	−2.20260
$179$	−1.07789e8	−1.40472	−0.702360	−	0.711822i	$-0.747870\pi$
$179$	−1.07789e8	−1.40472	−0.702360	+	0.711822i	$0.747870\pi$
$180$	1.53396e8	1.96047
$181$	−7.06656e7	−0.885794	−0.442897	−	0.896572i	$-0.646049\pi$
$181$	−7.06656e7	−0.885794	−0.442897	+	0.896572i	$0.646049\pi$
$182$	−6.50518e7	−0.799852
$183$	−9.77096e7	−1.17858
$184$	276858.	0.00327638
$185$	1.82049e8	2.11392
$186$	1.96931e8	2.24398
$187$	−1.14116e6	−0.0127615
$188$	−258897.	−0.00284168
$189$	−3.83862e7	−0.413579
$190$	−1.91545e7	−0.202597
$191$	−7.26186e7	−0.754103	−0.377052	−	0.926192i	$-0.623062\pi$
$191$	−7.26186e7	−0.754103	−0.377052	+	0.926192i	$0.623062\pi$
$192$	−1.76361e8	−1.79824
$193$	3.46942e6	0.0347382	0.0173691	−	0.999849i	$-0.494471\pi$
$193$	3.46942e6	0.0347382	0.0173691	+	0.999849i	$0.494471\pi$
$194$	−6.46474e7	−0.635690
$195$	−2.79055e8	−2.69506
$196$	1.58375e7	0.150241
$197$	6.22429e7	0.580040	0.290020	−	0.957021i	$-0.406338\pi$
$197$	6.22429e7	0.580040	0.290020	+	0.957021i	$0.406338\pi$
$198$	1.67960e7	0.153773
$199$	6.07528e7	0.546488	0.273244	−	0.961945i	$-0.411903\pi$
$199$	6.07528e7	0.546488	0.273244	+	0.961945i	$0.411903\pi$
$200$	−2.06431e6	−0.0182461
$201$	4.46694e7	0.387993
$202$	993814.	0.00848351
$203$	4.37726e7	0.367254
$204$	4.13561e7	0.341063
$205$	5.79727e6	0.0469986
$206$	3.01471e8	2.40276
$207$	−9.42900e6	−0.0738872
$208$	1.81322e8	1.39710
$209$	−1.07508e6	−0.00814568
$210$	1.32538e8	0.987582
$211$	1.46897e8	1.07653	0.538264	−	0.842776i	$-0.319080\pi$
$211$	1.46897e8	1.07653	0.538264	+	0.842776i	$0.319080\pi$
$212$	1.82161e8	1.31305
$213$	−4.33604e8	−3.07443
$214$	−1.08713e8	−0.758289
$215$	−1.00794e8	−0.691669
$216$	−1.19994e7	−0.0810159
$217$	5.45496e7	0.362395
$218$	−2.17694e8	−1.42314
$219$	3.79992e8	2.44467
$220$	−1.19231e7	−0.0754934
$221$	−4.70534e7	−0.293237
$222$	−7.22395e8	−4.43139
$223$	1.41501e8	0.854461	0.427230	−	0.904143i	$-0.359489\pi$
$223$	1.41501e8	0.854461	0.427230	+	0.904143i	$0.359489\pi$
$224$	−9.08266e7	−0.539939
$225$	7.03045e7	0.411476
$226$	−4.21204e8	−2.42724
$227$	3.40504e7	0.193211	0.0966054	−	0.995323i	$-0.469202\pi$
$227$	3.40504e7	0.193211	0.0966054	+	0.995323i	$0.469202\pi$
$228$	3.89612e7	0.217701
$229$	1.56200e8	0.859524	0.429762	−	0.902942i	$-0.358597\pi$
$229$	1.56200e8	0.859524	0.429762	+	0.902942i	$0.358597\pi$
$230$	1.30578e7	0.0707658
$231$	7.43891e6	0.0397070
$232$	1.36832e7	0.0719413
$233$	1.91857e8	0.993645	0.496822	−	0.867852i	$-0.334500\pi$
$233$	1.91857e8	0.993645	0.496822	+	0.867852i	$0.334500\pi$
$234$	6.92550e8	3.53343
$235$	−600150.	−0.00301663
$236$	1.16930e8	0.579076
$237$	6.65053e7	0.324516
$238$	2.23482e7	0.107454
$239$	−3.07750e8	−1.45816	−0.729081	−	0.684427i	$-0.760052\pi$
$239$	−3.07750e8	−1.45816	−0.729081	+	0.684427i	$0.760052\pi$
$240$	−3.69429e8	−1.72501
$241$	−2.14502e8	−0.987124	−0.493562	−	0.869711i	$-0.664305\pi$
$241$	−2.14502e8	−0.987124	−0.493562	+	0.869711i	$0.664305\pi$
$242$	3.14493e8	1.42645
$243$	−2.01560e8	−0.901121
$244$	−1.72139e8	−0.758604
$245$	3.67129e7	0.159491
$246$	−2.30043e7	−0.0985227
$247$	−4.43286e7	−0.187174
$248$	1.70520e7	0.0709895
$249$	2.96450e8	1.21690
$250$	2.97715e8	1.20506
$251$	−1.60485e8	−0.640585	−0.320293	−	0.947319i	$-0.603781\pi$
$251$	−1.60485e8	−0.640585	−0.320293	+	0.947319i	$0.603781\pi$
$252$	−1.68608e8	−0.663706
$253$	732891.	0.00284523
$254$	5.28836e8	2.02490
$255$	9.58677e7	0.362061
$256$	2.38572e8	0.888750
$257$	1.34126e7	0.0492887	0.0246444	−	0.999696i	$-0.492155\pi$
$257$	1.34126e7	0.0492887	0.0246444	+	0.999696i	$0.492155\pi$
$258$	3.99962e8	1.44994
$259$	−2.00103e8	−0.715655
$260$	−4.91624e8	−1.73471
$261$	−4.66009e8	−1.62238
$262$	−7.13339e8	−2.45043
$263$	−1.49544e8	−0.506900	−0.253450	−	0.967348i	$-0.581565\pi$
$263$	−1.49544e8	−0.506900	−0.253450	+	0.967348i	$0.581565\pi$
$264$	2.32537e6	0.00777820
$265$	4.22269e8	1.39389
$266$	2.10540e7	0.0685880
$267$	7.81447e8	2.51252
$268$	7.86960e7	0.249736
$269$	−2.02126e8	−0.633125	−0.316562	−	0.948572i	$-0.602529\pi$
$269$	−2.02126e8	−0.633125	−0.316562	+	0.948572i	$0.602529\pi$
$270$	−5.65942e8	−1.74984
$271$	1.59103e7	0.0485608	0.0242804	−	0.999705i	$-0.492271\pi$
$271$	1.59103e7	0.0485608	0.0242804	+	0.999705i	$0.492271\pi$
$272$	−6.22919e7	−0.187690
$273$	3.06728e8	0.912399
$274$	−1.16643e8	−0.342556
$275$	−5.46459e6	−0.0158450
$276$	−2.65603e7	−0.0760415
$277$	−2.83666e8	−0.801915	−0.400958	−	0.916097i	$-0.631323\pi$
$277$	−2.83666e8	−0.801915	−0.400958	+	0.916097i	$0.631323\pi$
$278$	4.05912e8	1.13312
$279$	−5.80742e8	−1.60092
$280$	1.14763e7	0.0312427
$281$	1.42010e8	0.381811	0.190905	−	0.981608i	$-0.438858\pi$
$281$	1.42010e8	0.381811	0.190905	+	0.981608i	$0.438858\pi$
$282$	2.38147e6	0.00632373
$283$	2.00581e8	0.526063	0.263031	−	0.964787i	$-0.415278\pi$
$283$	2.00581e8	0.526063	0.263031	+	0.964787i	$0.415278\pi$
$284$	−7.63899e8	−1.97889
$285$	9.03160e7	0.231104
$286$	−5.38301e7	−0.136064
$287$	−6.37217e6	−0.0159111
$288$	9.66952e8	2.38523
$289$	−3.94174e8	−0.960606
$290$	6.45357e8	1.55384
$291$	3.04821e8	0.725137
$292$	6.69448e8	1.57354
$293$	−5.15499e8	−1.19727	−0.598633	−	0.801023i	$-0.704289\pi$
$293$	−5.15499e8	−1.19727	−0.598633	+	0.801023i	$0.704289\pi$
$294$	−1.45681e8	−0.334340
$295$	2.71057e8	0.614728
$296$	−6.25513e7	−0.140190
$297$	−3.17644e7	−0.0703548
$298$	615832.	0.00134805
$299$	3.02193e7	0.0653785
$300$	1.98039e8	0.423473
$301$	1.10789e8	0.234161
$302$	−1.33961e8	−0.279868
$303$	−4.68597e6	−0.00967721
$304$	−5.86846e7	−0.119803
$305$	−3.99036e8	−0.805309
$306$	−2.37921e8	−0.474688
$307$	7.65707e8	1.51035	0.755176	−	0.655522i	$-0.227552\pi$
$307$	7.65707e8	1.51035	0.755176	+	0.655522i	$0.227552\pi$
$308$	1.31055e7	0.0255579
$309$	−1.42148e9	−2.74085
$310$	8.04246e8	1.53328
$311$	1.59867e8	0.301367	0.150684	−	0.988582i	$-0.451853\pi$
$311$	1.59867e8	0.301367	0.150684	+	0.988582i	$0.451853\pi$
$312$	9.58821e7	0.178730
$313$	−2.07759e8	−0.382961	−0.191480	−	0.981496i	$-0.561329\pi$
$313$	−2.07759e8	−0.382961	−0.191480	+	0.981496i	$0.561329\pi$
$314$	−6.48797e8	−1.18265
$315$	−3.90850e8	−0.704569
$316$	1.17165e8	0.208878
$317$	5.47705e7	0.0965693	0.0482847	−	0.998834i	$-0.484625\pi$
$317$	5.47705e7	0.0965693	0.0482847	+	0.998834i	$0.484625\pi$
$318$	−1.67562e9	−2.92200
$319$	3.62217e7	0.0624743
$320$	−7.20241e8	−1.22872
$321$	5.12598e8	0.864987
$322$	−1.43527e7	−0.0239574
$323$	1.52288e7	0.0251453
$324$	7.60961e7	0.124295
$325$	−2.25321e8	−0.364091
$326$	1.20498e9	1.92628
$327$	1.02646e9	1.62339
$328$	−1.99192e6	−0.00311683
$329$	659665.	0.00102126
$330$	1.09675e8	0.167999
$331$	−2.41167e8	−0.365527	−0.182763	−	0.983157i	$-0.558504\pi$
$331$	−2.41167e8	−0.365527	−0.182763	+	0.983157i	$0.558504\pi$
$332$	5.22269e8	0.783269
$333$	2.13032e9	3.16148
$334$	−9.96432e8	−1.46331
$335$	1.82425e8	0.265111
$336$	4.06064e8	0.583992
$337$	−7.24589e8	−1.03130	−0.515652	−	0.856798i	$-0.672450\pi$
$337$	−7.24589e8	−1.03130	−0.515652	+	0.856798i	$0.672450\pi$
$338$	−1.20271e9	−1.69415
$339$	1.98603e9	2.76877
$340$	1.68894e8	0.233044
$341$	4.51396e7	0.0616478
$342$	−2.24143e8	−0.302994
$343$	−4.03536e7	−0.0539949
$344$	3.46322e7	0.0458697
$345$	−6.15694e7	−0.0807232
$346$	2.85035e8	0.369940
$347$	−9.93073e8	−1.27593	−0.637966	−	0.770064i	$-0.720224\pi$
$347$	−9.93073e8	−1.27593	−0.637966	+	0.770064i	$0.720224\pi$
$348$	−1.31269e9	−1.66968
$349$	5.45485e8	0.686901	0.343450	−	0.939171i	$-0.388404\pi$
$349$	5.45485e8	0.686901	0.343450	+	0.939171i	$0.388404\pi$
$350$	1.07017e8	0.133418
$351$	−1.30974e9	−1.61663
$352$	−7.51586e7	−0.0918501
$353$	−3.78963e8	−0.458549	−0.229274	−	0.973362i	$-0.573635\pi$
$353$	−3.78963e8	−0.458549	−0.229274	+	0.973362i	$0.573635\pi$
$354$	−1.07559e9	−1.28865
$355$	−1.77080e9	−2.10073
$356$	1.37671e9	1.61721
$357$	−1.05375e8	−0.122574
$358$	1.74677e9	2.01208
$359$	1.23744e9	1.41155	0.705773	−	0.708438i	$-0.250600\pi$
$359$	1.23744e9	1.41155	0.705773	+	0.708438i	$0.250600\pi$
$360$	−1.22178e8	−0.138018
$361$	−8.79525e8	−0.983950
$362$	1.14517e9	1.26879
$363$	−1.48288e9	−1.62717
$364$	5.40376e8	0.587275
$365$	1.55185e9	1.67042
$366$	1.58343e9	1.68816
$367$	8.13553e8	0.859122	0.429561	−	0.903038i	$-0.358668\pi$
$367$	8.13553e8	0.859122	0.429561	+	0.903038i	$0.358668\pi$
$368$	4.00059e7	0.0418463
$369$	6.78390e7	0.0702889
$370$	−2.95019e9	−3.02792
$371$	−4.64144e8	−0.471893
$372$	−1.63588e9	−1.64759
$373$	7.99709e8	0.797905	0.398952	−	0.916972i	$-0.369374\pi$
$373$	7.99709e8	0.797905	0.398952	+	0.916972i	$0.369374\pi$
$374$	1.84930e7	0.0182792
$375$	−1.40377e9	−1.37463
$376$	206209.	0.000200055 0
$377$	1.49353e9	1.43555
$378$	6.22065e8	0.592400
$379$	−1.27251e9	−1.20067	−0.600334	−	0.799749i	$-0.704966\pi$
$379$	−1.27251e9	−1.20067	−0.600334	+	0.799749i	$0.704966\pi$
$380$	1.59114e8	0.148753
$381$	−2.49353e9	−2.30982
$382$	1.17682e9	1.08016
$383$	−3.29059e8	−0.299280	−0.149640	−	0.988741i	$-0.547812\pi$
$383$	−3.29059e8	−0.299280	−0.149640	+	0.988741i	$0.547812\pi$
$384$	2.68103e8	0.241626
$385$	3.03798e7	0.0271314
$386$	−5.62236e7	−0.0497580
$387$	−1.17948e9	−1.03443
$388$	5.37017e8	0.466742
$389$	9.37771e8	0.807743	0.403872	−	0.914816i	$-0.367664\pi$
$389$	9.37771e8	0.807743	0.403872	+	0.914816i	$0.367664\pi$
$390$	4.52221e9	3.86033
$391$	−1.03817e7	−0.00878310
$392$	−1.26144e7	−0.0105771
$393$	3.36349e9	2.79522
$394$	−1.00867e9	−0.830833
$395$	2.71601e8	0.221739
$396$	−1.39522e8	−0.112904
$397$	−1.00184e9	−0.803588	−0.401794	−	0.915730i	$-0.631613\pi$
$397$	−1.00184e9	−0.803588	−0.401794	+	0.915730i	$0.631613\pi$
$398$	−9.84526e8	−0.782774
$399$	−9.92724e7	−0.0782390
$400$	−2.98292e8	−0.233041
$401$	−1.31207e9	−1.01614	−0.508068	−	0.861317i	$-0.669640\pi$
$401$	−1.31207e9	−1.01614	−0.508068	+	0.861317i	$0.669640\pi$
$402$	−7.23887e8	−0.555750
$403$	1.86124e9	1.41656
$404$	−8.25547e6	−0.00622884
$405$	1.76399e8	0.131948
$406$	−7.09355e8	−0.526045
$407$	−1.65584e8	−0.121741
$408$	−3.29397e7	−0.0240109
$409$	8.61243e8	0.622435	0.311217	−	0.950339i	$-0.399263\pi$
$409$	8.61243e8	0.622435	0.311217	+	0.950339i	$0.399263\pi$
$410$	−9.39473e7	−0.0673195
$411$	5.49988e8	0.390757
$412$	−2.50428e9	−1.76418
$413$	−2.97937e8	−0.208113
$414$	1.52801e8	0.105834
$415$	1.21067e9	0.831492
$416$	−3.09901e9	−2.11056
$417$	−1.91393e9	−1.29256
$418$	1.74221e7	0.0116676
$419$	4.12403e8	0.273888	0.136944	−	0.990579i	$-0.456272\pi$
$419$	4.12403e8	0.273888	0.136944	+	0.990579i	$0.456272\pi$
$420$	−1.10097e9	−0.725112
$421$	−9.13691e8	−0.596777	−0.298389	−	0.954444i	$-0.596449\pi$
$421$	−9.13691e8	−0.596777	−0.298389	+	0.954444i	$0.596449\pi$
$422$	−2.38054e9	−1.54199
$423$	−7.02288e6	−0.00451153
$424$	−1.45090e8	−0.0924391
$425$	7.74077e7	0.0489129
$426$	7.02675e9	4.40373
$427$	4.38607e8	0.272633
$428$	9.03067e8	0.556758
$429$	2.53817e8	0.155210
$430$	1.63341e9	0.990728
$431$	−6.54101e8	−0.393527	−0.196764	−	0.980451i	$-0.563043\pi$
$431$	−6.54101e8	−0.393527	−0.196764	+	0.980451i	$0.563043\pi$
$432$	−1.73391e9	−1.03474
$433$	2.14647e9	1.27062	0.635312	−	0.772256i	$-0.280872\pi$
$433$	2.14647e9	1.27062	0.635312	+	0.772256i	$0.280872\pi$
$434$	−8.84000e8	−0.519085
$435$	−3.04295e9	−1.77248
$436$	1.80835e9	1.04491
$437$	−9.78045e6	−0.00560627
$438$	−6.15794e9	−3.50168
$439$	3.11978e9	1.75994	0.879970	−	0.475029i	$-0.157562\pi$
$439$	3.11978e9	1.75994	0.879970	+	0.475029i	$0.157562\pi$
$440$	9.49660e6	0.00531476
$441$	4.29610e8	0.238528
$442$	7.62522e8	0.420024
$443$	−1.99049e9	−1.08780	−0.543898	−	0.839151i	$-0.683052\pi$
$443$	−1.99049e9	−1.08780	−0.543898	+	0.839151i	$0.683052\pi$
$444$	6.00084e9	3.25365
$445$	3.19135e9	1.71678
$446$	−2.29308e9	−1.22391
$447$	−2.90373e6	−0.00153773
$448$	7.91666e8	0.415976
$449$	1.83855e9	0.958547	0.479274	−	0.877666i	$-0.340900\pi$
$449$	1.83855e9	0.958547	0.479274	+	0.877666i	$0.340900\pi$
$450$	−1.13932e9	−0.589387
$451$	−5.27295e6	−0.00270667
$452$	3.49888e9	1.78215
$453$	6.31643e8	0.319248
$454$	−5.51801e8	−0.276750
$455$	1.25265e9	0.623432
$456$	−3.10322e7	−0.0153262
$457$	−3.51474e9	−1.72261	−0.861304	−	0.508091i	$-0.830351\pi$
$457$	−3.51474e9	−1.72261	−0.861304	+	0.508091i	$0.830351\pi$
$458$	−2.53130e9	−1.23116
$459$	4.49954e8	0.217182
$460$	−1.08470e8	−0.0519583
$461$	−2.98808e9	−1.42049	−0.710247	−	0.703953i	$-0.751417\pi$
$461$	−2.98808e9	−1.42049	−0.710247	+	0.703953i	$0.751417\pi$
$462$	−1.20551e8	−0.0568753
$463$	−1.77331e9	−0.830330	−0.415165	−	0.909746i	$-0.636276\pi$
$463$	−1.77331e9	−0.830330	−0.415165	+	0.909746i	$0.636276\pi$
$464$	1.97721e9	0.918842
$465$	−3.79213e9	−1.74903
$466$	−3.10912e9	−1.42327
$467$	1.97100e9	0.895524	0.447762	−	0.894153i	$-0.352221\pi$
$467$	1.97100e9	0.895524	0.447762	+	0.894153i	$0.352221\pi$
$468$	−5.75292e9	−2.59435
$469$	−2.00516e8	−0.0897520
$470$	9.72569e6	0.00432094
$471$	3.05917e9	1.34906
$472$	−9.31338e7	−0.0407672
$473$	9.16775e7	0.0398335
$474$	−1.07775e9	−0.464828
$475$	7.29250e7	0.0312212
$476$	−1.85643e8	−0.0788959
$477$	4.94134e9	2.08464
$478$	4.98723e9	2.08863
$479$	−2.43401e9	−1.01193	−0.505963	−	0.862555i	$-0.668863\pi$
$479$	−2.43401e9	−1.01193	−0.505963	+	0.862555i	$0.668863\pi$
$480$	6.31400e9	2.60591
$481$	−6.82753e9	−2.79741
$482$	3.47610e9	1.41393
$483$	6.76751e7	0.0273284
$484$	−2.61245e9	−1.04734
$485$	1.24486e9	0.495478
$486$	3.26637e9	1.29074
$487$	−1.38401e9	−0.542983	−0.271492	−	0.962441i	$-0.587517\pi$
$487$	−1.38401e9	−0.542983	−0.271492	+	0.962441i	$0.587517\pi$
$488$	1.37107e8	0.0534060
$489$	−5.68166e9	−2.19732
$490$	−5.94949e8	−0.228451
$491$	2.40004e9	0.915025	0.457512	−	0.889203i	$-0.348741\pi$
$491$	2.40004e9	0.915025	0.457512	+	0.889203i	$0.348741\pi$
$492$	1.91094e8	0.0723383
$493$	−5.13092e8	−0.192855
$494$	7.18364e8	0.268102
$495$	−3.23427e8	−0.119856
$496$	2.46401e9	0.906685
$497$	1.94640e9	0.711189
$498$	−4.80410e9	−1.74305
$499$	1.27349e9	0.458823	0.229411	−	0.973330i	$-0.426320\pi$
$499$	1.27349e9	0.458823	0.229411	+	0.973330i	$0.426320\pi$
$500$	−2.47307e9	−0.884794
$501$	4.69831e9	1.66921
$502$	2.60073e9	0.917556
$503$	−2.82372e9	−0.989313	−0.494657	−	0.869089i	$-0.664706\pi$
$503$	−2.82372e9	−0.989313	−0.494657	+	0.869089i	$0.664706\pi$
$504$	1.34294e8	0.0467252
$505$	−1.91370e7	−0.00661233
$506$	−1.18768e7	−0.00407543
$507$	5.67094e9	1.93253
$508$	−4.39296e9	−1.48674
$509$	3.73735e9	1.25618	0.628090	−	0.778141i	$-0.283837\pi$
$509$	3.73735e9	1.25618	0.628090	+	0.778141i	$0.283837\pi$
$510$	−1.55358e9	−0.518606
$511$	−1.70574e9	−0.565510
$512$	−4.31528e9	−1.42090
$513$	4.23897e8	0.138628
$514$	−2.17357e8	−0.0705998
$515$	−5.80518e9	−1.87280
$516$	−3.32243e9	−1.06459
$517$	545870.	0.000173729 0
$518$	3.24275e9	1.02508
$519$	−1.34398e9	−0.421994
$520$	3.91573e8	0.122124
$521$	3.50738e9	1.08655	0.543276	−	0.839554i	$-0.317184\pi$
$521$	3.50738e9	1.08655	0.543276	+	0.839554i	$0.317184\pi$
$522$	7.55189e9	2.32385
$523$	3.36763e9	1.02936	0.514682	−	0.857381i	$-0.327910\pi$
$523$	3.36763e9	1.02936	0.514682	+	0.857381i	$0.327910\pi$
$524$	5.92561e9	1.79917
$525$	−5.04599e8	−0.152191
$526$	2.42342e9	0.726070
$527$	−6.39417e8	−0.190304
$528$	3.36016e8	0.0993440
$529$	−3.39816e9	−0.998042
$530$	−6.84305e9	−1.99657
$531$	3.17187e9	0.919359
$532$	−1.74892e8	−0.0503594
$533$	−2.17419e8	−0.0621946
$534$	−1.26637e10	−3.59887
$535$	2.09340e9	0.591036
$536$	−6.26805e7	−0.0175815
$537$	−8.23627e9	−2.29520
$538$	3.27554e9	0.906870
$539$	−3.33925e7	−0.00918518
$540$	4.70120e9	1.28479
$541$	−4.50424e9	−1.22301	−0.611506	−	0.791239i	$-0.709436\pi$
$541$	−4.50424e9	−1.22301	−0.611506	+	0.791239i	$0.709436\pi$
$542$	−2.57834e8	−0.0695572
$543$	−5.39962e9	−1.44732
$544$	1.06465e9	0.283537
$545$	4.19194e9	1.10924
$546$	−4.97067e9	−1.30689
$547$	−2.31422e9	−0.604574	−0.302287	−	0.953217i	$-0.597750\pi$
$547$	−2.31422e9	−0.604574	−0.302287	+	0.953217i	$0.597750\pi$
$548$	9.68937e8	0.251515
$549$	−4.66947e9	−1.20438
$550$	8.85561e7	0.0226960
$551$	−4.83379e8	−0.123100
$552$	2.11550e7	0.00535335
$553$	−2.98535e8	−0.0750684
$554$	4.59694e9	1.14864
$555$	1.39106e10	3.45397
$556$	−3.37186e9	−0.831969
$557$	5.61006e9	1.37554	0.687771	−	0.725927i	$-0.258589\pi$
$557$	5.61006e9	1.37554	0.687771	+	0.725927i	$0.258589\pi$
$558$	9.41118e9	2.29311
$559$	3.78014e9	0.915306
$560$	1.65832e9	0.399035
$561$	−8.71971e7	−0.0208513
$562$	−2.30134e9	−0.546895
$563$	−4.02844e9	−0.951388	−0.475694	−	0.879611i	$-0.657803\pi$
$563$	−4.02844e9	−0.951388	−0.475694	+	0.879611i	$0.657803\pi$
$564$	−1.97825e7	−0.00464307
$565$	8.11076e9	1.89187
$566$	−3.25051e9	−0.753518
$567$	−1.93892e8	−0.0446702
$568$	6.08437e8	0.139315
$569$	1.35716e9	0.308843	0.154421	−	0.988005i	$-0.450649\pi$
$569$	1.35716e9	0.308843	0.154421	+	0.988005i	$0.450649\pi$
$570$	−1.46361e9	−0.331027
$571$	3.08298e9	0.693017	0.346509	−	0.938047i	$-0.387367\pi$
$571$	3.08298e9	0.693017	0.346509	+	0.938047i	$0.387367\pi$
$572$	4.47159e8	0.0999025
$573$	−5.54885e9	−1.23214
$574$	1.03264e8	0.0227906
$575$	−4.97138e7	−0.0109053
$576$	−8.42817e9	−1.83762
$577$	2.33045e9	0.505039	0.252519	−	0.967592i	$-0.418741\pi$
$577$	2.33045e9	0.505039	0.252519	+	0.967592i	$0.418741\pi$
$578$	6.38776e9	1.37595
$579$	2.65102e8	0.0567594
$580$	−5.36089e9	−1.14088
$581$	−1.33073e9	−0.281497
$582$	−4.93977e9	−1.03867
$583$	−3.84077e8	−0.0802747
$584$	−5.33208e8	−0.110778
$585$	−1.33359e10	−2.75407
$586$	8.35389e9	1.71493
$587$	−6.77557e9	−1.38265	−0.691325	−	0.722544i	$-0.742973\pi$
$587$	−6.77557e9	−1.38265	−0.691325	+	0.722544i	$0.742973\pi$
$588$	1.21016e9	0.245483
$589$	−6.02389e8	−0.121471
$590$	−4.39259e9	−0.880520
$591$	4.75603e9	0.947739
$592$	−9.03865e9	−1.79051
$593$	7.09723e9	1.39765	0.698824	−	0.715294i	$-0.253707\pi$
$593$	7.09723e9	1.39765	0.698824	+	0.715294i	$0.253707\pi$
$594$	5.14757e8	0.100774
$595$	−4.30340e8	−0.0837533
$596$	−5.11563e6	−0.000989777 0
$597$	4.64218e9	0.892918
$598$	−4.89717e8	−0.0936464
$599$	5.44979e9	1.03606	0.518032	−	0.855361i	$-0.326665\pi$
$599$	5.44979e9	1.03606	0.518032	+	0.855361i	$0.326665\pi$
$600$	−1.57736e8	−0.0298127
$601$	7.81035e8	0.146761	0.0733804	−	0.997304i	$-0.476621\pi$
$601$	7.81035e8	0.146761	0.0733804	+	0.997304i	$0.476621\pi$
$602$	−1.79539e9	−0.335405
$603$	2.13472e9	0.396488
$604$	1.11279e9	0.205487
$605$	−6.05592e9	−1.11182
$606$	7.59382e7	0.0138614
$607$	−3.70105e9	−0.671683	−0.335841	−	0.941919i	$-0.609021\pi$
$607$	−3.70105e9	−0.671683	−0.335841	+	0.941919i	$0.609021\pi$
$608$	1.00299e9	0.180982
$609$	3.34471e9	0.600064
$610$	6.46656e9	1.15350
$611$	2.25078e7	0.00399199
$612$	1.97638e9	0.348530
$613$	−1.01586e8	−0.0178125	−0.00890623	−	0.999960i	$-0.502835\pi$
$613$	−1.01586e8	−0.0178125	−0.00890623	+	0.999960i	$0.502835\pi$
$614$	−1.24086e10	−2.16339
$615$	4.42975e8	0.0767920
$616$	−1.04383e7	−0.00179928
$617$	−2.48425e9	−0.425791	−0.212896	−	0.977075i	$-0.568289\pi$
$617$	−2.48425e9	−0.425791	−0.212896	+	0.977075i	$0.568289\pi$
$618$	2.30357e10	3.92592
$619$	−6.89160e9	−1.16789	−0.583946	−	0.811792i	$-0.698492\pi$
$619$	−6.89160e9	−1.16789	−0.583946	+	0.811792i	$0.698492\pi$
$620$	−6.68076e9	−1.12578
$621$	−2.88975e8	−0.0484217
$622$	−2.59071e9	−0.431670
$623$	−3.50783e9	−0.581206
$624$	1.38549e10	2.28275
$625$	−7.23698e9	−1.18571
$626$	3.36682e9	0.548542
$627$	−8.21475e7	−0.0133094
$628$	5.38946e9	0.868334
$629$	2.34556e9	0.375810
$630$	6.33390e9	1.00920
$631$	1.97310e9	0.312641	0.156321	−	0.987706i	$-0.450037\pi$
$631$	1.97310e9	0.312641	0.156321	+	0.987706i	$0.450037\pi$
$632$	−9.33208e7	−0.0147051
$633$	1.12246e10	1.75896
$634$	−8.87580e8	−0.138323
$635$	−1.01833e10	−1.57827
$636$	1.39191e10	2.14542
$637$	−1.37687e9	−0.211059
$638$	−5.86989e8	−0.0894864
$639$	−2.07216e10	−3.14175
$640$	1.09491e9	0.165100
$641$	3.79593e9	0.569266	0.284633	−	0.958637i	$-0.408128\pi$
$641$	3.79593e9	0.569266	0.284633	+	0.958637i	$0.408128\pi$
$642$	−8.30688e9	−1.23898
$643$	−1.07326e10	−1.59208	−0.796042	−	0.605241i	$-0.793077\pi$
$643$	−1.07326e10	−1.59208	−0.796042	+	0.605241i	$0.793077\pi$
$644$	1.19226e8	0.0175902
$645$	−7.70173e9	−1.13013
$646$	−2.46790e8	−0.0360175
$647$	5.28221e9	0.766744	0.383372	−	0.923594i	$-0.374763\pi$
$647$	5.28221e9	0.766744	0.383372	+	0.923594i	$0.374763\pi$
$648$	−6.06098e7	−0.00875044
$649$	−2.46541e8	−0.0354025
$650$	3.65143e9	0.521514
$651$	4.16818e9	0.592125
$652$	−1.00096e10	−1.41433
$653$	9.46338e8	0.133000	0.0664998	−	0.997786i	$-0.478817\pi$
$653$	9.46338e8	0.133000	0.0664998	+	0.997786i	$0.478817\pi$
$654$	−1.66342e10	−2.32530
$655$	1.37362e10	1.90994
$656$	−2.87831e8	−0.0398084
$657$	1.81595e10	2.49819
$658$	−1.06902e7	−0.00146283
$659$	−4.19089e9	−0.570436	−0.285218	−	0.958463i	$-0.592066\pi$
$659$	−4.19089e9	−0.570436	−0.285218	+	0.958463i	$0.592066\pi$
$660$	−9.11052e8	−0.123350
$661$	9.39353e9	1.26510	0.632548	−	0.774521i	$-0.282009\pi$
$661$	9.39353e9	1.26510	0.632548	+	0.774521i	$0.282009\pi$
$662$	3.90821e9	0.523570
$663$	−3.59540e9	−0.479126
$664$	−4.15981e8	−0.0551424
$665$	−4.05419e8	−0.0534599
$666$	−3.45228e10	−4.52841
$667$	3.29525e8	0.0429980
$668$	8.27722e9	1.07440
$669$	1.08122e10	1.39612
$670$	−2.95628e9	−0.379738
$671$	3.62946e8	0.0463781
$672$	−6.94014e9	−0.882218
$673$	9.73932e9	1.23162	0.615809	−	0.787895i	$-0.288829\pi$
$673$	9.73932e9	1.23162	0.615809	+	0.787895i	$0.288829\pi$
$674$	1.17423e10	1.47721
$675$	2.15466e9	0.269659
$676$	9.99073e9	1.24390
$677$	7.93402e9	0.982727	0.491364	−	0.870955i	$-0.336499\pi$
$677$	7.93402e9	0.982727	0.491364	+	0.870955i	$0.336499\pi$
$678$	−3.21845e10	−3.96592
$679$	−1.36831e9	−0.167741
$680$	−1.34522e8	−0.0164064
$681$	2.60182e9	0.315691
$682$	−7.31507e8	−0.0883025
$683$	−1.11816e10	−1.34286	−0.671432	−	0.741067i	$-0.734320\pi$
$683$	−1.11816e10	−1.34286	−0.671432	+	0.741067i	$0.734320\pi$
$684$	1.86193e9	0.222467
$685$	2.24609e9	0.267000
$686$	6.53948e8	0.0773408
$687$	1.19354e10	1.40439
$688$	5.00435e9	0.585852
$689$	−1.58366e10	−1.84457
$690$	9.97760e8	0.115626
$691$	−7.53867e9	−0.869204	−0.434602	−	0.900623i	$-0.643111\pi$
$691$	−7.53867e9	−0.869204	−0.434602	+	0.900623i	$0.643111\pi$
$692$	−2.36774e9	−0.271621
$693$	3.55500e8	0.0405764
$694$	1.60932e10	1.82761
$695$	−7.81631e9	−0.883192
$696$	1.04554e9	0.117546
$697$	7.46930e7	0.00835536
$698$	−8.83983e9	−0.983897
$699$	1.46599e10	1.62354
$700$	−8.88974e8	−0.0979594
$701$	−1.21953e10	−1.33714	−0.668572	−	0.743647i	$-0.733094\pi$
$701$	−1.21953e10	−1.33714	−0.668572	+	0.743647i	$0.733094\pi$
$702$	2.12249e10	2.31562
$703$	2.20972e9	0.239880
$704$	6.55100e8	0.0707625
$705$	−4.58580e7	−0.00492893
$706$	6.14127e9	0.656813
$707$	2.10348e7	0.00223857
$708$	8.93476e9	0.946164
$709$	1.22512e10	1.29097	0.645484	−	0.763774i	$-0.276656\pi$
$709$	1.22512e10	1.29097	0.645484	+	0.763774i	$0.276656\pi$
$710$	2.86965e10	3.00902
$711$	3.17824e9	0.331622
$712$	−1.09653e9	−0.113852
$713$	4.10655e8	0.0424291
$714$	1.70764e9	0.175571
$715$	1.03656e9	0.106053
$716$	−1.45102e10	−1.47733
$717$	−2.35155e10	−2.38252
$718$	−2.00533e10	−2.02186
$719$	8.02518e9	0.805200	0.402600	−	0.915376i	$-0.368107\pi$
$719$	8.02518e9	0.805200	0.402600	+	0.915376i	$0.368107\pi$
$720$	−1.76547e10	−1.76278
$721$	6.38086e9	0.634024
$722$	1.42531e10	1.40938
$723$	−1.63903e10	−1.61288
$724$	−9.51274e9	−0.931581
$725$	−2.45701e9	−0.239455
$726$	2.40307e10	2.33071
$727$	3.03346e9	0.292797	0.146399	−	0.989226i	$-0.453232\pi$
$727$	3.03346e9	0.292797	0.146399	+	0.989226i	$0.453232\pi$
$728$	−4.30404e8	−0.0413444
$729$	−1.66377e10	−1.59055
$730$	−2.51484e10	−2.39266
$731$	−1.29864e9	−0.122964
$732$	−1.31533e10	−1.23950
$733$	−1.96893e10	−1.84657	−0.923285	−	0.384116i	$-0.874506\pi$
$733$	−1.96893e10	−1.84657	−0.923285	+	0.384116i	$0.874506\pi$
$734$	−1.31840e10	−1.23058
$735$	2.80526e9	0.260596
$736$	−6.83752e8	−0.0632159
$737$	−1.65926e8	−0.0152679
$738$	−1.09936e9	−0.100680
$739$	5.69524e9	0.519106	0.259553	−	0.965729i	$-0.416425\pi$
$739$	5.69524e9	0.519106	0.259553	+	0.965729i	$0.416425\pi$
$740$	2.45068e10	2.22319
$741$	−3.38719e9	−0.305827
$742$	7.52166e9	0.675927
$743$	2.15270e10	1.92540	0.962702	−	0.270563i	$-0.0872098\pi$
$743$	2.15270e10	1.92540	0.962702	+	0.270563i	$0.0872098\pi$
$744$	1.30296e9	0.115991
$745$	−1.18586e7	−0.00105071
$746$	−1.29596e10	−1.14290
$747$	1.41671e10	1.24354
$748$	−1.53619e8	−0.0134211
$749$	−2.30100e9	−0.200092
$750$	2.27486e10	1.96898
$751$	1.14509e10	0.986507	0.493254	−	0.869886i	$-0.335807\pi$
$751$	1.14509e10	0.986507	0.493254	+	0.869886i	$0.335807\pi$
$752$	2.97971e7	0.00255512
$753$	−1.22628e10	−1.04666
$754$	−2.42033e10	−2.05624
$755$	2.57957e9	0.218139
$756$	−5.16741e9	−0.434957
$757$	−1.65342e10	−1.38531	−0.692655	−	0.721269i	$-0.743559\pi$
$757$	−1.65342e10	−1.38531	−0.692655	+	0.721269i	$0.743559\pi$
$758$	2.06215e10	1.71980
$759$	5.60009e7	0.00464888
$760$	−1.26732e8	−0.0104722
$761$	9.30606e9	0.765455	0.382728	−	0.923861i	$-0.374985\pi$
$761$	9.30606e9	0.765455	0.382728	+	0.923861i	$0.374985\pi$
$762$	4.04088e10	3.30852
$763$	−4.60764e9	−0.375529
$764$	−9.77564e9	−0.793083
$765$	4.58145e9	0.369988
$766$	5.33255e9	0.428681
$767$	−1.01656e10	−0.813487
$768$	1.82295e10	1.45215
$769$	4.85159e9	0.384717	0.192359	−	0.981325i	$-0.438386\pi$
$769$	4.85159e9	0.384717	0.192359	+	0.981325i	$0.438386\pi$
$770$	−4.92318e8	−0.0388622
$771$	1.02487e9	0.0805339
$772$	4.67041e8	0.0365338
$773$	2.04661e10	1.59370	0.796852	−	0.604175i	$-0.206497\pi$
$773$	2.04661e10	1.59370	0.796852	+	0.604175i	$0.206497\pi$
$774$	1.91139e10	1.48169
$775$	−3.06193e9	−0.236287
$776$	−4.27728e8	−0.0328588
$777$	−1.52900e10	−1.16932
$778$	−1.51970e10	−1.15699
$779$	7.03676e7	0.00533324
$780$	−3.75654e10	−2.83437
$781$	1.61064e9	0.120982
$782$	1.68239e8	0.0125807
$783$	−1.42820e10	−1.06322
$784$	−1.82278e9	−0.135091
$785$	1.24933e10	0.921795
$786$	−5.45069e10	−4.00380
$787$	−1.69075e10	−1.23642	−0.618211	−	0.786012i	$-0.712142\pi$
$787$	−1.69075e10	−1.23642	−0.618211	+	0.786012i	$0.712142\pi$
$788$	8.37891e9	0.610022
$789$	−1.14268e10	−0.828235
$790$	−4.40141e9	−0.317612
$791$	−8.91508e9	−0.640483
$792$	1.11128e8	0.00794851
$793$	1.49653e10	1.06569
$794$	1.62353e10	1.15104
$795$	3.22659e10	2.27750
$796$	8.17832e9	0.574736
$797$	−1.04945e10	−0.734273	−0.367136	−	0.930167i	$-0.619662\pi$
$797$	−1.04945e10	−0.734273	−0.367136	+	0.930167i	$0.619662\pi$
$798$	1.60875e9	0.112067
$799$	−7.73243e6	−0.000536293 0
$800$	5.09819e9	0.352048
$801$	3.73448e10	2.56754
$802$	2.12627e10	1.45549
$803$	−1.41149e9	−0.0961999
$804$	6.01323e9	0.408048
$805$	2.76378e8	0.0186732
$806$	−3.01622e10	−2.02904
$807$	−1.54446e10	−1.03448
$808$	6.57540e6	0.000438513 0
$809$	−1.97682e10	−1.31265	−0.656324	−	0.754479i	$-0.727889\pi$
$809$	−1.97682e10	−1.31265	−0.656324	+	0.754479i	$0.727889\pi$
$810$	−2.85862e9	−0.188999
$811$	1.15699e10	0.761653	0.380826	−	0.924647i	$-0.375640\pi$
$811$	1.15699e10	0.761653	0.380826	+	0.924647i	$0.375640\pi$
$812$	5.89251e9	0.386237
$813$	1.21572e9	0.0793445
$814$	2.68337e9	0.174379
$815$	−2.32033e10	−1.50141
$816$	−4.75978e9	−0.306670
$817$	−1.22344e9	−0.0784883
$818$	−1.39568e10	−0.891559
$819$	1.46583e10	0.932376
$820$	7.80407e8	0.0494280
$821$	−8.26784e9	−0.521424	−0.260712	−	0.965417i	$-0.583957\pi$
$821$	−8.26784e9	−0.521424	−0.260712	+	0.965417i	$0.583957\pi$
$822$	−8.91279e9	−0.559709
$823$	7.82205e9	0.489126	0.244563	−	0.969633i	$-0.421355\pi$
$823$	7.82205e9	0.489126	0.244563	+	0.969633i	$0.421355\pi$
$824$	1.99463e9	0.124199
$825$	−4.17554e8	−0.0258895
$826$	4.82820e9	0.298095
$827$	−6.32518e9	−0.388869	−0.194435	−	0.980915i	$-0.562287\pi$
$827$	−6.32518e9	−0.388869	−0.194435	+	0.980915i	$0.562287\pi$
$828$	−1.26930e9	−0.0777064
$829$	−2.15011e8	−0.0131075	−0.00655376	−	0.999979i	$-0.502086\pi$
$829$	−2.15011e8	−0.0131075	−0.00655376	+	0.999979i	$0.502086\pi$
$830$	−1.96195e10	−1.19101
$831$	−2.16752e10	−1.31027
$832$	2.70117e10	1.62600
$833$	4.73015e8	0.0283542
$834$	3.10161e10	1.85143
$835$	1.91874e10	1.14055
$836$	−1.44723e8	−0.00856673
$837$	−1.77983e10	−1.04915
$838$	−6.68318e9	−0.392310
$839$	2.80409e10	1.63917	0.819587	−	0.572955i	$-0.194203\pi$
$839$	2.80409e10	1.63917	0.819587	+	0.572955i	$0.194203\pi$
$840$	8.76915e8	0.0510481
$841$	−9.63768e8	−0.0558710
$842$	1.48068e10	0.854807
$843$	1.08511e10	0.623848
$844$	1.97748e10	1.13217
$845$	2.31595e10	1.32048
$846$	1.13809e8	0.00646219
$847$	6.65647e9	0.376402
$848$	−2.09654e10	−1.18064
$849$	1.53266e10	0.859545
$850$	−1.25443e9	−0.0700614
$851$	−1.50639e9	−0.0837886
$852$	−5.83702e10	−3.23335
$853$	−3.24393e10	−1.78957	−0.894786	−	0.446495i	$-0.852672\pi$
$853$	−3.24393e10	−1.78957	−0.894786	+	0.446495i	$0.852672\pi$
$854$	−7.10783e9	−0.390512
$855$	4.31614e9	0.236164
$856$	−7.19283e8	−0.0391960
$857$	1.73118e10	0.939525	0.469762	−	0.882793i	$-0.344340\pi$
$857$	1.73118e10	0.939525	0.469762	+	0.882793i	$0.344340\pi$
$858$	−4.11321e9	−0.222318
$859$	7.48729e9	0.403040	0.201520	−	0.979484i	$-0.435412\pi$
$859$	7.48729e9	0.403040	0.201520	+	0.979484i	$0.435412\pi$
$860$	−1.35685e10	−0.727422
$861$	−4.86903e8	−0.0259975
$862$	1.06000e10	0.563677
$863$	2.23774e10	1.18514	0.592572	−	0.805517i	$-0.298113\pi$
$863$	2.23774e10	1.18514	0.592572	+	0.805517i	$0.298113\pi$
$864$	2.96347e10	1.56315
$865$	−5.48867e9	−0.288344
$866$	−3.47845e10	−1.82001
$867$	−3.01192e10	−1.56955
$868$	7.34327e9	0.381128
$869$	−2.47036e8	−0.0127700
$870$	4.93123e10	2.53885
$871$	−6.84163e9	−0.350829
$872$	−1.44033e9	−0.0735622
$873$	1.45672e10	0.741014
$874$	1.58496e8	0.00803026
$875$	6.30135e9	0.317984
$876$	5.11531e10	2.57103
$877$	−2.95004e10	−1.47683	−0.738414	−	0.674348i	$-0.764425\pi$
$877$	−2.95004e10	−1.47683	−0.738414	+	0.674348i	$0.764425\pi$
$878$	−5.05574e10	−2.52089
$879$	−3.93897e10	−1.95624
$880$	1.37226e9	0.0678806
$881$	−2.42854e10	−1.19655	−0.598273	−	0.801293i	$-0.704146\pi$
$881$	−2.42854e10	−1.19655	−0.598273	+	0.801293i	$0.704146\pi$
$882$	−6.96202e9	−0.341661
$883$	−2.14449e10	−1.04824	−0.524120	−	0.851644i	$-0.675606\pi$
$883$	−2.14449e10	−1.04824	−0.524120	+	0.851644i	$0.675606\pi$
$884$	−6.33416e9	−0.308394
$885$	2.07117e10	1.00442
$886$	3.22568e10	1.55813
$887$	3.53723e10	1.70189	0.850943	−	0.525258i	$-0.176031\pi$
$887$	3.53723e10	1.70189	0.850943	+	0.525258i	$0.176031\pi$
$888$	−4.77960e9	−0.229058
$889$	1.11932e10	0.534316
$890$	−5.17173e10	−2.45907
$891$	−1.60445e8	−0.00759894
$892$	1.90483e10	0.898628
$893$	−7.28464e6	−0.000342317 0
$894$	4.70563e7	0.00220260
$895$	−3.36361e10	−1.56829
$896$	−1.20349e9	−0.0558937
$897$	2.30908e9	0.106823
$898$	−2.97945e10	−1.37300
$899$	2.02958e10	0.931638
$900$	9.46414e9	0.432745
$901$	5.44058e9	0.247804
$902$	8.54504e7	0.00387696
$903$	8.46549e9	0.382600
$904$	−2.78682e9	−0.125464
$905$	−2.20515e10	−0.988936
$906$	−1.02361e10	−0.457282
$907$	1.03301e10	0.459703	0.229852	−	0.973226i	$-0.426176\pi$
$907$	1.03301e10	0.459703	0.229852	+	0.973226i	$0.426176\pi$
$908$	4.58374e9	0.203198
$909$	−2.23939e8	−0.00988910
$910$	−2.02997e10	−0.892987
$911$	−7.15628e9	−0.313598	−0.156799	−	0.987631i	$-0.550117\pi$
$911$	−7.15628e9	−0.313598	−0.156799	+	0.987631i	$0.550117\pi$
$912$	−4.48414e9	−0.195748
$913$	−1.10118e9	−0.0478860
$914$	5.69579e10	2.46741
$915$	−3.04907e10	−1.31581
$916$	2.10271e10	0.903953
$917$	−1.50983e10	−0.646601
$918$	−7.29170e9	−0.311085
$919$	1.78768e10	0.759776	0.379888	−	0.925032i	$-0.375962\pi$
$919$	1.78768e10	0.759776	0.379888	+	0.925032i	$0.375962\pi$
$920$	8.63948e7	0.00365789
$921$	5.85083e10	2.46779
$922$	4.84232e10	2.03468
$923$	6.64114e10	2.77995
$924$	1.00140e9	0.0417595
$925$	1.12320e10	0.466617
$926$	2.87372e10	1.18934
$927$	−6.79315e10	−2.80086
$928$	−3.37931e10	−1.38806
$929$	−8.30589e9	−0.339884	−0.169942	−	0.985454i	$-0.554358\pi$
$929$	−8.30589e9	−0.339884	−0.169942	+	0.985454i	$0.554358\pi$
$930$	6.14531e10	2.50526
$931$	4.45623e8	0.0180985
$932$	2.58270e10	1.04501
$933$	1.22155e10	0.492410
$934$	−3.19409e10	−1.28272
$935$	−3.56104e8	−0.0142474
$936$	4.58214e9	0.182643
$937$	−1.89534e10	−0.752660	−0.376330	−	0.926486i	$-0.622814\pi$
$937$	−1.89534e10	−0.752660	−0.376330	+	0.926486i	$0.622814\pi$
$938$	3.24945e9	0.128558
$939$	−1.58750e10	−0.625727
$940$	−8.07899e7	−0.00317256
$941$	1.85991e9	0.0727659	0.0363830	−	0.999338i	$-0.488416\pi$
$941$	1.85991e9	0.0727659	0.0363830	+	0.999338i	$0.488416\pi$
$942$	−4.95751e10	−1.93235
$943$	−4.79703e7	−0.00186287
$944$	−1.34578e10	−0.520682
$945$	−1.19786e10	−0.461736
$946$	−1.48567e9	−0.0570565
$947$	−2.17737e10	−0.833121	−0.416561	−	0.909108i	$-0.636765\pi$
$947$	−2.17737e10	−0.833121	−0.416561	+	0.909108i	$0.636765\pi$
$948$	8.95269e9	0.341291
$949$	−5.82001e10	−2.21051
$950$	−1.18178e9	−0.0447203
$951$	4.18506e9	0.157787
$952$	1.47863e8	0.00555430
$953$	2.45189e10	0.917646	0.458823	−	0.888528i	$-0.348271\pi$
$953$	2.45189e10	0.917646	0.458823	+	0.888528i	$0.348271\pi$
$954$	−8.00765e10	−2.98597
$955$	−2.26609e10	−0.841911
$956$	−4.14282e10	−1.53353
$957$	2.76773e9	0.102078
$958$	3.94443e10	1.44946
$959$	−2.46883e9	−0.0903913
$960$	−5.50343e10	−2.00763
$961$	−2.21993e9	−0.0806875
$962$	1.10643e11	4.00693
$963$	2.44967e10	0.883926
$964$	−2.88755e10	−1.03815
$965$	1.08265e9	0.0387831
$966$	−1.09670e9	−0.0391444
$967$	3.75735e10	1.33625	0.668127	−	0.744047i	$-0.267096\pi$
$967$	3.75735e10	1.33625	0.668127	+	0.744047i	$0.267096\pi$
$968$	2.08079e9	0.0737333
$969$	1.16365e9	0.0410854
$970$	−2.01735e10	−0.709709
$971$	−3.61803e10	−1.26825	−0.634125	−	0.773231i	$-0.718639\pi$
$971$	−3.61803e10	−1.26825	−0.634125	+	0.773231i	$0.718639\pi$
$972$	−2.71333e10	−0.947700
$973$	8.59143e9	0.299000
$974$	2.24284e10	0.777754
$975$	−1.72170e10	−0.594896
$976$	1.98119e10	0.682107
$977$	4.30992e10	1.47856	0.739279	−	0.673399i	$-0.235166\pi$
$977$	4.30992e10	1.47856	0.739279	+	0.673399i	$0.235166\pi$
$978$	9.20738e10	3.14739
$979$	−2.90272e9	−0.0988701
$980$	4.94215e9	0.167736
$981$	4.90536e10	1.65893
$982$	−3.88937e10	−1.31066
$983$	−2.72338e10	−0.914472	−0.457236	−	0.889345i	$-0.651161\pi$
$983$	−2.72338e10	−0.914472	−0.457236	+	0.889345i	$0.651161\pi$
$984$	−1.52204e8	−0.00509264
$985$	1.94232e10	0.647580
$986$	8.31489e9	0.276240
$987$	5.04056e7	0.00166866
$988$	−5.96735e9	−0.196849
$989$	8.34031e8	0.0274155
$990$	5.24128e9	0.171678
$991$	−4.11594e10	−1.34342	−0.671709	−	0.740815i	$-0.734439\pi$
$991$	−4.11594e10	−1.34342	−0.671709	+	0.740815i	$0.734439\pi$
$992$	−4.21130e10	−1.36970
$993$	−1.84278e10	−0.597242
$994$	−3.15423e10	−1.01869
$995$	1.89582e10	0.610121
$996$	3.99070e10	1.27980
$997$	4.76679e10	1.52333	0.761663	−	0.647973i	$-0.224383\pi$
$997$	4.76679e10	1.52333	0.761663	+	0.647973i	$0.224383\pi$
$998$	−2.06375e10	−0.657205
$999$	6.52890e10	2.07186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.8.a.b.1.1	✓	2
3.2	odd	2		63.8.a.e.1.2		2
4.3	odd	2		112.8.a.f.1.1		2
5.2	odd	4		175.8.b.b.99.1		4
5.3	odd	4		175.8.b.b.99.4		4
5.4	even	2		175.8.a.c.1.2		2
7.2	even	3		49.8.c.e.18.2		4
7.3	odd	6		49.8.c.f.30.2		4
7.4	even	3		49.8.c.e.30.2		4
7.5	odd	6		49.8.c.f.18.2		4
7.6	odd	2		49.8.a.c.1.1		2
8.3	odd	2		448.8.a.t.1.2		2
8.5	even	2		448.8.a.k.1.1		2
21.20	even	2		441.8.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.a.b.1.1	✓	2	1.1	even	1	trivial
49.8.a.c.1.1		2	7.6	odd	2
49.8.c.e.18.2		4	7.2	even	3
49.8.c.e.30.2		4	7.4	even	3
49.8.c.f.18.2		4	7.5	odd	6
49.8.c.f.30.2		4	7.3	odd	6
63.8.a.e.1.2		2	3.2	odd	2
112.8.a.f.1.1		2	4.3	odd	2
175.8.a.c.1.2		2	5.4	even	2
175.8.b.b.99.1		4	5.2	odd	4
175.8.b.b.99.4		4	5.3	odd	4
441.8.a.l.1.2		2	21.20	even	2
448.8.a.k.1.1		2	8.5	even	2
448.8.a.t.1.2		2	8.3	odd	2

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q-16.2054 q^{2} +76.4109 q^{3} +134.616 q^{4} +312.054 q^{5} -1238.27 q^{6} -343.000 q^{7} -107.220 q^{8} +3651.62 q^{9} +O(q^{10})\)	\(q-16.2054 q^{2} +76.4109 q^{3} +134.616 q^{4} +312.054 q^{5} -1238.27 q^{6} -343.000 q^{7} -107.220 q^{8} +3651.62 q^{9} -5056.98 q^{10} -283.831 q^{11} +10286.2 q^{12} -11703.2 q^{13} +5558.47 q^{14} +23844.4 q^{15} -15493.3 q^{16} +4020.56 q^{17} -59176.2 q^{18} +3787.73 q^{19} +42007.6 q^{20} -26208.9 q^{21} +4599.61 q^{22} -2582.14 q^{23} -8192.81 q^{24} +19253.0 q^{25} +189656. q^{26} +111913. q^{27} -46173.4 q^{28} -127617. q^{29} -386408. q^{30} -159037. q^{31} +264801. q^{32} -21687.8 q^{33} -65155.0 q^{34} -107035. q^{35} +491568. q^{36} +583390. q^{37} -61381.9 q^{38} -894252. q^{39} -33458.6 q^{40} +18577.8 q^{41} +424727. q^{42} -323000. q^{43} -38208.3 q^{44} +1.13951e6 q^{45} +41844.7 q^{46} -1923.22 q^{47} -1.18386e6 q^{48} +117649. q^{49} -312003. q^{50} +307215. q^{51} -1.57544e6 q^{52} +1.35319e6 q^{53} -1.81360e6 q^{54} -88570.8 q^{55} +36776.6 q^{56} +289424. q^{57} +2.06809e6 q^{58} +868620. q^{59} +3.20984e6 q^{60} -1.27874e6 q^{61} +2.57726e6 q^{62} -1.25251e6 q^{63} -2.30806e6 q^{64} -3.65203e6 q^{65} +351460. q^{66} +584595. q^{67} +541233. q^{68} -197304. q^{69} +1.73454e6 q^{70} -5.67464e6 q^{71} -391529. q^{72} +4.97301e6 q^{73} -9.45409e6 q^{74} +1.47114e6 q^{75} +509890. q^{76} +97354.1 q^{77} +1.44917e7 q^{78} +870364. q^{79} -4.83476e6 q^{80} +565282. q^{81} -301061. q^{82} +3.87968e6 q^{83} -3.52815e6 q^{84} +1.25463e6 q^{85} +5.23436e6 q^{86} -9.75133e6 q^{87} +30432.5 q^{88} +1.02269e7 q^{89} -1.84662e7 q^{90} +4.01420e6 q^{91} -347598. q^{92} -1.21521e7 q^{93} +31166.6 q^{94} +1.18198e6 q^{95} +2.02336e7 q^{96} +3.98924e6 q^{97} -1.90655e6 q^{98} -1.03644e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 94 q^{3} + 181 q^{4} + 330 q^{5} - 1006 q^{6} - 686 q^{7} - 1185 q^{8} + 1774 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 94 * q^3 + 181 * q^4 + 330 * q^5 - 1006 * q^6 - 686 * q^7 - 1185 * q^8 + 1774 * q^9	\( 2 q - 3 q^{2} + 94 q^{3} + 181 q^{4} + 330 q^{5} - 1006 q^{6} - 686 q^{7} - 1185 q^{8} + 1774 q^{9} - 4820 q^{10} + 2844 q^{11} + 11102 q^{12} + 2534 q^{13} + 1029 q^{14} + 24160 q^{15} - 35663 q^{16} - 1488 q^{17} - 83971 q^{18} + 32810 q^{19} + 42840 q^{20} - 32242 q^{21} + 45904 q^{22} - 6576 q^{23} - 27150 q^{24} - 58550 q^{25} + 377664 q^{26} + 40420 q^{27} - 62083 q^{28} + 20640 q^{29} - 382240 q^{30} - 391836 q^{31} + 136407 q^{32} + 33328 q^{33} - 137898 q^{34} - 113190 q^{35} + 404477 q^{36} + 367392 q^{37} + 321870 q^{38} - 643832 q^{39} - 52800 q^{40} + 734664 q^{41} + 345058 q^{42} - 480476 q^{43} + 106872 q^{44} + 1105810 q^{45} - 10896 q^{46} - 1089108 q^{47} - 1538626 q^{48} + 235298 q^{49} - 1339425 q^{50} + 210324 q^{51} - 915068 q^{52} + 2858844 q^{53} - 2757700 q^{54} - 32440 q^{55} + 406455 q^{56} + 799900 q^{57} + 4025890 q^{58} + 160170 q^{59} + 3224480 q^{60} - 864646 q^{61} - 496956 q^{62} - 608482 q^{63} - 1421839 q^{64} - 3396540 q^{65} + 1077968 q^{66} - 328648 q^{67} + 285726 q^{68} - 267552 q^{69} + 1653260 q^{70} - 7500216 q^{71} + 1632135 q^{72} + 4301244 q^{73} - 12306438 q^{74} + 102650 q^{75} + 1856050 q^{76} - 975492 q^{77} + 17798648 q^{78} - 6408440 q^{79} - 5196720 q^{80} + 3414142 q^{81} + 9155174 q^{82} + 11659074 q^{83} - 3807986 q^{84} + 1155780 q^{85} + 3154824 q^{86} - 7143620 q^{87} - 3340680 q^{88} + 9772260 q^{89} - 18911140 q^{90} - 869162 q^{91} - 532848 q^{92} - 16246872 q^{93} - 14325588 q^{94} + 1702800 q^{95} + 17975314 q^{96} + 10762752 q^{97} - 352947 q^{98} - 6909332 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 94 * q^3 + 181 * q^4 + 330 * q^5 - 1006 * q^6 - 686 * q^7 - 1185 * q^8 + 1774 * q^9 - 4820 * q^10 + 2844 * q^11 + 11102 * q^12 + 2534 * q^13 + 1029 * q^14 + 24160 * q^15 - 35663 * q^16 - 1488 * q^17 - 83971 * q^18 + 32810 * q^19 + 42840 * q^20 - 32242 * q^21 + 45904 * q^22 - 6576 * q^23 - 27150 * q^24 - 58550 * q^25 + 377664 * q^26 + 40420 * q^27 - 62083 * q^28 + 20640 * q^29 - 382240 * q^30 - 391836 * q^31 + 136407 * q^32 + 33328 * q^33 - 137898 * q^34 - 113190 * q^35 + 404477 * q^36 + 367392 * q^37 + 321870 * q^38 - 643832 * q^39 - 52800 * q^40 + 734664 * q^41 + 345058 * q^42 - 480476 * q^43 + 106872 * q^44 + 1105810 * q^45 - 10896 * q^46 - 1089108 * q^47 - 1538626 * q^48 + 235298 * q^49 - 1339425 * q^50 + 210324 * q^51 - 915068 * q^52 + 2858844 * q^53 - 2757700 * q^54 - 32440 * q^55 + 406455 * q^56 + 799900 * q^57 + 4025890 * q^58 + 160170 * q^59 + 3224480 * q^60 - 864646 * q^61 - 496956 * q^62 - 608482 * q^63 - 1421839 * q^64 - 3396540 * q^65 + 1077968 * q^66 - 328648 * q^67 + 285726 * q^68 - 267552 * q^69 + 1653260 * q^70 - 7500216 * q^71 + 1632135 * q^72 + 4301244 * q^73 - 12306438 * q^74 + 102650 * q^75 + 1856050 * q^76 - 975492 * q^77 + 17798648 * q^78 - 6408440 * q^79 - 5196720 * q^80 + 3414142 * q^81 + 9155174 * q^82 + 11659074 * q^83 - 3807986 * q^84 + 1155780 * q^85 + 3154824 * q^86 - 7143620 * q^87 - 3340680 * q^88 + 9772260 * q^89 - 18911140 * q^90 - 869162 * q^91 - 532848 * q^92 - 16246872 * q^93 - 14325588 * q^94 + 1702800 * q^95 + 17975314 * q^96 + 10762752 * q^97 - 352947 * q^98 - 6909332 * q^99

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