LMFDB - Embedded newform 21.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,10,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	21.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:	$10.8157525594$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{345}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 86 $ x^2 - x - 86
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$9.78709$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57418 q^{2} -81.0000 q^{3} -499.225 q^{4} -736.192 q^{5} +289.508 q^{6} +2401.00 q^{7} +3614.30 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-3.57418 q^{2} -81.0000 q^{3} -499.225 q^{4} -736.192 q^{5} +289.508 q^{6} +2401.00 q^{7} +3614.30 q^{8} +6561.00 q^{9} +2631.28 q^{10} +4731.57 q^{11} +40437.2 q^{12} +60742.8 q^{13} -8581.60 q^{14} +59631.6 q^{15} +242685. q^{16} +224563. q^{17} -23450.2 q^{18} +187155. q^{19} +367526. q^{20} -194481. q^{21} -16911.4 q^{22} +1.28626e6 q^{23} -292758. q^{24} -1.41115e6 q^{25} -217106. q^{26} -531441. q^{27} -1.19864e6 q^{28} +1.36690e6 q^{29} -213134. q^{30} -6.11017e6 q^{31} -2.71792e6 q^{32} -383257. q^{33} -802628. q^{34} -1.76760e6 q^{35} -3.27542e6 q^{36} +87025.6 q^{37} -668927. q^{38} -4.92017e6 q^{39} -2.66082e6 q^{40} +2.07024e7 q^{41} +695109. q^{42} +7.12910e6 q^{43} -2.36212e6 q^{44} -4.83016e6 q^{45} -4.59731e6 q^{46} +5.70542e7 q^{47} -1.96575e7 q^{48} +5.76480e6 q^{49} +5.04368e6 q^{50} -1.81896e7 q^{51} -3.03244e7 q^{52} +8.39231e7 q^{53} +1.89946e6 q^{54} -3.48334e6 q^{55} +8.67793e6 q^{56} -1.51596e7 q^{57} -4.88554e6 q^{58} +8.82114e7 q^{59} -2.97696e7 q^{60} +4.69813e7 q^{61} +2.18388e7 q^{62} +1.57530e7 q^{63} -1.14541e8 q^{64} -4.47184e7 q^{65} +1.36983e6 q^{66} -9.64796e7 q^{67} -1.12108e8 q^{68} -1.04187e8 q^{69} +6.31770e6 q^{70} -3.36368e8 q^{71} +2.37134e7 q^{72} -1.32482e8 q^{73} -311045. q^{74} +1.14303e8 q^{75} -9.34327e7 q^{76} +1.13605e7 q^{77} +1.75856e7 q^{78} +6.00622e8 q^{79} -1.78663e8 q^{80} +4.30467e7 q^{81} -7.39941e7 q^{82} +7.73006e8 q^{83} +9.70898e7 q^{84} -1.65322e8 q^{85} -2.54807e7 q^{86} -1.10719e8 q^{87} +1.71013e7 q^{88} +9.98519e7 q^{89} +1.72638e7 q^{90} +1.45844e8 q^{91} -6.42132e8 q^{92} +4.94924e8 q^{93} -2.03922e8 q^{94} -1.37782e8 q^{95} +2.20151e8 q^{96} +8.94470e8 q^{97} -2.06044e7 q^{98} +3.10438e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 30 q^{2} - 162 q^{3} + 116 q^{4} + 1128 q^{5} - 2430 q^{6} + 4802 q^{7} + 7080 q^{8} + 13122 q^{9}+O(q^{10}) $ 2 * q + 30 * q^2 - 162 * q^3 + 116 * q^4 + 1128 * q^5 - 2430 * q^6 + 4802 * q^7 + 7080 * q^8 + 13122 * q^9	\( 2 q + 30 q^{2} - 162 q^{3} + 116 q^{4} + 1128 q^{5} - 2430 q^{6} + 4802 q^{7} + 7080 q^{8} + 13122 q^{9} + 65220 q^{10} + 73284 q^{11} - 9396 q^{12} + 141100 q^{13} + 72030 q^{14} - 91368 q^{15} + 44048 q^{16} - 101784 q^{17} + 196830 q^{18} + 481744 q^{19} + 1514424 q^{20} - 388962 q^{21} + 2284680 q^{22} - 982212 q^{23} - 573480 q^{24} + 110942 q^{25} + 2480820 q^{26} - 1062882 q^{27} + 278516 q^{28} - 2550924 q^{29} - 5282820 q^{30} - 4935848 q^{31} - 11161440 q^{32} - 5936004 q^{33} - 11759460 q^{34} + 2708328 q^{35} + 761076 q^{36} - 16256516 q^{37} + 9221640 q^{38} - 11429100 q^{39} + 3799920 q^{40} + 48707856 q^{41} - 5834430 q^{42} + 7989640 q^{43} + 39813072 q^{44} + 7400808 q^{45} - 80759280 q^{46} + 85572408 q^{47} - 3567888 q^{48} + 11529602 q^{49} + 56146530 q^{50} + 8244504 q^{51} + 19113400 q^{52} + 26565324 q^{53} - 15943230 q^{54} + 124311576 q^{55} + 16999080 q^{56} - 39021264 q^{57} - 136423260 q^{58} + 115200960 q^{59} - 122668344 q^{60} - 142820204 q^{61} + 61265760 q^{62} + 31505922 q^{63} - 296322496 q^{64} + 105082800 q^{65} - 185059080 q^{66} + 27521392 q^{67} - 312884472 q^{68} + 79559172 q^{69} + 156593220 q^{70} + 38070180 q^{71} + 46451880 q^{72} - 2095316 q^{73} - 549031980 q^{74} - 8986302 q^{75} + 87805552 q^{76} + 175954884 q^{77} - 200946420 q^{78} + 435097048 q^{79} - 548960928 q^{80} + 86093442 q^{81} + 866264940 q^{82} + 264288744 q^{83} - 22559796 q^{84} - 773695176 q^{85} + 3411240 q^{86} + 206624844 q^{87} + 254683680 q^{88} + 642673776 q^{89} + 427908420 q^{90} + 338781100 q^{91} - 2037751296 q^{92} + 399803688 q^{93} + 753552960 q^{94} + 411387216 q^{95} + 904076640 q^{96} + 345361228 q^{97} + 172944030 q^{98} + 480816324 q^{99}+O(q^{100}) \) 2 * q + 30 * q^2 - 162 * q^3 + 116 * q^4 + 1128 * q^5 - 2430 * q^6 + 4802 * q^7 + 7080 * q^8 + 13122 * q^9 + 65220 * q^10 + 73284 * q^11 - 9396 * q^12 + 141100 * q^13 + 72030 * q^14 - 91368 * q^15 + 44048 * q^16 - 101784 * q^17 + 196830 * q^18 + 481744 * q^19 + 1514424 * q^20 - 388962 * q^21 + 2284680 * q^22 - 982212 * q^23 - 573480 * q^24 + 110942 * q^25 + 2480820 * q^26 - 1062882 * q^27 + 278516 * q^28 - 2550924 * q^29 - 5282820 * q^30 - 4935848 * q^31 - 11161440 * q^32 - 5936004 * q^33 - 11759460 * q^34 + 2708328 * q^35 + 761076 * q^36 - 16256516 * q^37 + 9221640 * q^38 - 11429100 * q^39 + 3799920 * q^40 + 48707856 * q^41 - 5834430 * q^42 + 7989640 * q^43 + 39813072 * q^44 + 7400808 * q^45 - 80759280 * q^46 + 85572408 * q^47 - 3567888 * q^48 + 11529602 * q^49 + 56146530 * q^50 + 8244504 * q^51 + 19113400 * q^52 + 26565324 * q^53 - 15943230 * q^54 + 124311576 * q^55 + 16999080 * q^56 - 39021264 * q^57 - 136423260 * q^58 + 115200960 * q^59 - 122668344 * q^60 - 142820204 * q^61 + 61265760 * q^62 + 31505922 * q^63 - 296322496 * q^64 + 105082800 * q^65 - 185059080 * q^66 + 27521392 * q^67 - 312884472 * q^68 + 79559172 * q^69 + 156593220 * q^70 + 38070180 * q^71 + 46451880 * q^72 - 2095316 * q^73 - 549031980 * q^74 - 8986302 * q^75 + 87805552 * q^76 + 175954884 * q^77 - 200946420 * q^78 + 435097048 * q^79 - 548960928 * q^80 + 86093442 * q^81 + 866264940 * q^82 + 264288744 * q^83 - 22559796 * q^84 - 773695176 * q^85 + 3411240 * q^86 + 206624844 * q^87 + 254683680 * q^88 + 642673776 * q^89 + 427908420 * q^90 + 338781100 * q^91 - 2037751296 * q^92 + 399803688 * q^93 + 753552960 * q^94 + 411387216 * q^95 + 904076640 * q^96 + 345361228 * q^97 + 172944030 * q^98 + 480816324 * 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 $

$2$	−3.57418	−0.157958	−0.0789789	−	0.996876i	$-0.525166\pi$
$2$	−3.57418	−0.157958	−0.0789789	+	0.996876i	$0.525166\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−499.225	−0.975049
$5$	−736.192	−0.526776	−0.263388	−	0.964690i	$-0.584840\pi$
$5$	−736.192	−0.526776	−0.263388	+	0.964690i	$0.584840\pi$
$6$	289.508	0.0911969
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	3614.30	0.311974
$9$	6561.00	0.333333
$10$	2631.28	0.0832084
$11$	4731.57	0.0974401	0.0487201	−	0.998812i	$-0.484486\pi$
$11$	4731.57	0.0974401	0.0487201	+	0.998812i	$0.484486\pi$
$12$	40437.2	0.562945
$13$	60742.8	0.589861	0.294931	−	0.955519i	$-0.404703\pi$
$13$	60742.8	0.589861	0.294931	+	0.955519i	$0.404703\pi$
$14$	−8581.60	−0.0597024
$15$	59631.6	0.304134
$16$	242685.	0.925771
$17$	224563.	0.652106	0.326053	−	0.945352i	$-0.394281\pi$
$17$	224563.	0.652106	0.326053	+	0.945352i	$0.394281\pi$
$18$	−23450.2	−0.0526526
$19$	187155.	0.329467	0.164733	−	0.986338i	$-0.447324\pi$
$19$	187155.	0.329467	0.164733	+	0.986338i	$0.447324\pi$
$20$	367526.	0.513633
$21$	−194481.	−0.218218
$22$	−16911.4	−0.0153914
$23$	1.28626e6	0.958412	0.479206	−	0.877702i	$-0.340925\pi$
$23$	1.28626e6	0.958412	0.479206	+	0.877702i	$0.340925\pi$
$24$	−292758.	−0.180118
$25$	−1.41115e6	−0.722507
$26$	−217106.	−0.0931732
$27$	−531441.	−0.192450
$28$	−1.19864e6	−0.368534
$29$	1.36690e6	0.358877	0.179439	−	0.983769i	$-0.442572\pi$
$29$	1.36690e6	0.358877	0.179439	+	0.983769i	$0.442572\pi$
$30$	−213134.	−0.0480404
$31$	−6.11017e6	−1.18830	−0.594150	−	0.804355i	$-0.702511\pi$
$31$	−6.11017e6	−1.18830	−0.594150	+	0.804355i	$0.702511\pi$
$32$	−2.71792e6	−0.458207
$33$	−383257.	−0.0562571
$34$	−802628.	−0.103005
$35$	−1.76760e6	−0.199103
$36$	−3.27542e6	−0.325016
$37$	87025.6	0.00763377	0.00381689	−	0.999993i	$-0.498785\pi$
$37$	87025.6	0.00763377	0.00381689	+	0.999993i	$0.498785\pi$
$38$	−668927.	−0.0520418
$39$	−4.92017e6	−0.340557
$40$	−2.66082e6	−0.164341
$41$	2.07024e7	1.14418	0.572090	−	0.820191i	$-0.306133\pi$
$41$	2.07024e7	1.14418	0.572090	+	0.820191i	$0.306133\pi$
$42$	695109.	0.0344692
$43$	7.12910e6	0.318000	0.159000	−	0.987279i	$-0.449173\pi$
$43$	7.12910e6	0.318000	0.159000	+	0.987279i	$0.449173\pi$
$44$	−2.36212e6	−0.0950089
$45$	−4.83016e6	−0.175592
$46$	−4.59731e6	−0.151389
$47$	5.70542e7	1.70548	0.852741	−	0.522333i	$-0.174938\pi$
$47$	5.70542e7	1.70548	0.852741	+	0.522333i	$0.174938\pi$
$48$	−1.96575e7	−0.534494
$49$	5.76480e6	0.142857
$50$	5.04368e6	0.114126
$51$	−1.81896e7	−0.376493
$52$	−3.03244e7	−0.575144
$53$	8.39231e7	1.46097	0.730483	−	0.682931i	$-0.239295\pi$
$53$	8.39231e7	1.46097	0.730483	+	0.682931i	$0.239295\pi$
$54$	1.89946e6	0.0303990
$55$	−3.48334e6	−0.0513292
$56$	8.67793e6	0.117915
$57$	−1.51596e7	−0.190218
$58$	−4.88554e6	−0.0566874
$59$	8.82114e7	0.947743	0.473872	−	0.880594i	$-0.342856\pi$
$59$	8.82114e7	0.947743	0.473872	+	0.880594i	$0.342856\pi$
$60$	−2.97696e7	−0.296546
$61$	4.69813e7	0.434451	0.217226	−	0.976121i	$-0.430299\pi$
$61$	4.69813e7	0.434451	0.217226	+	0.976121i	$0.430299\pi$
$62$	2.18388e7	0.187701
$63$	1.57530e7	0.125988
$64$	−1.14541e8	−0.853393
$65$	−4.47184e7	−0.310725
$66$	1.36983e6	0.00888624
$67$	−9.64796e7	−0.584923	−0.292462	−	0.956277i	$-0.594474\pi$
$67$	−9.64796e7	−0.584923	−0.292462	+	0.956277i	$0.594474\pi$
$68$	−1.12108e8	−0.635835
$69$	−1.04187e8	−0.553340
$70$	6.31770e6	0.0314498
$71$	−3.36368e8	−1.57091	−0.785457	−	0.618916i	$-0.787572\pi$
$71$	−3.36368e8	−1.57091	−0.785457	+	0.618916i	$0.787572\pi$
$72$	2.37134e7	0.103991
$73$	−1.32482e8	−0.546013	−0.273007	−	0.962012i	$-0.588018\pi$
$73$	−1.32482e8	−0.546013	−0.273007	+	0.962012i	$0.588018\pi$
$74$	−311045.	−0.00120581
$75$	1.14303e8	0.417139
$76$	−9.34327e7	−0.321246
$77$	1.13605e7	0.0368289
$78$	1.75856e7	0.0537936
$79$	6.00622e8	1.73492	0.867460	−	0.497506i	$-0.165751\pi$
$79$	6.00622e8	1.73492	0.867460	+	0.497506i	$0.165751\pi$
$80$	−1.78663e8	−0.487674
$81$	4.30467e7	0.111111
$82$	−7.39941e7	−0.180732
$83$	7.73006e8	1.78785	0.893926	−	0.448214i	$-0.147940\pi$
$83$	7.73006e8	1.78785	0.893926	+	0.448214i	$0.147940\pi$
$84$	9.70898e7	0.212773
$85$	−1.65322e8	−0.343514
$86$	−2.54807e7	−0.0502305
$87$	−1.10719e8	−0.207198
$88$	1.71013e7	0.0303988
$89$	9.98519e7	0.168695	0.0843473	−	0.996436i	$-0.473119\pi$
$89$	9.98519e7	0.168695	0.0843473	+	0.996436i	$0.473119\pi$
$90$	1.72638e7	0.0277361
$91$	1.45844e8	0.222947
$92$	−6.42132e8	−0.934499
$93$	4.94924e8	0.686065
$94$	−2.03922e8	−0.269394
$95$	−1.37782e8	−0.173555
$96$	2.20151e8	0.264546
$97$	8.94470e8	1.02587	0.512936	−	0.858427i	$-0.328558\pi$
$97$	8.94470e8	1.02587	0.512936	+	0.858427i	$0.328558\pi$
$98$	−2.06044e7	−0.0225654
$99$	3.10438e7	0.0324800
$100$	7.04480e8	0.704480
$101$	−1.06158e9	−1.01509	−0.507546	−	0.861624i	$-0.669447\pi$
$101$	−1.06158e9	−1.01509	−0.507546	+	0.861624i	$0.669447\pi$
$102$	6.50128e7	0.0594701
$103$	1.59262e9	1.39426	0.697131	−	0.716943i	$-0.254459\pi$
$103$	1.59262e9	1.39426	0.697131	+	0.716943i	$0.254459\pi$
$104$	2.19543e8	0.184022
$105$	1.43175e8	0.114952
$106$	−2.99956e8	−0.230771
$107$	−1.06928e9	−0.788611	−0.394306	−	0.918979i	$-0.629015\pi$
$107$	−1.06928e9	−0.788611	−0.394306	+	0.918979i	$0.629015\pi$
$108$	2.65309e8	0.187648
$109$	−1.42904e9	−0.969672	−0.484836	−	0.874605i	$-0.661121\pi$
$109$	−1.42904e9	−0.969672	−0.484836	+	0.874605i	$0.661121\pi$
$110$	1.24501e7	0.00810784
$111$	−7.04907e6	−0.00440736
$112$	5.82687e8	0.349908
$113$	−3.16896e9	−1.82837	−0.914184	−	0.405299i	$-0.867167\pi$
$113$	−3.16896e9	−1.82837	−0.914184	+	0.405299i	$0.867167\pi$
$114$	5.41831e7	0.0300463
$115$	−9.46932e8	−0.504869
$116$	−6.82391e8	−0.349923
$117$	3.98534e8	0.196620
$118$	−3.15283e8	−0.149703
$119$	5.39176e8	0.246473
$120$	2.15526e8	0.0948821
$121$	−2.33556e9	−0.990505
$122$	−1.67919e8	−0.0686249
$123$	−1.67690e9	−0.660592
$124$	3.05035e9	1.15865
$125$	2.47675e9	0.907376
$126$	−5.63038e7	−0.0199008
$127$	−4.81195e9	−1.64136	−0.820680	−	0.571387i	$-0.806405\pi$
$127$	−4.81195e9	−1.64136	−0.820680	+	0.571387i	$0.806405\pi$
$128$	1.80096e9	0.593007
$129$	−5.77457e8	−0.183597
$130$	1.59831e8	0.0490814
$131$	3.82371e9	1.13439	0.567197	−	0.823582i	$-0.308028\pi$
$131$	3.82371e9	1.13439	0.567197	+	0.823582i	$0.308028\pi$
$132$	1.91332e8	0.0548534
$133$	4.49360e8	0.124527
$134$	3.44835e8	0.0923932
$135$	3.91243e8	0.101378
$136$	8.11637e8	0.203440
$137$	6.90619e8	0.167493	0.0837464	−	0.996487i	$-0.473311\pi$
$137$	6.90619e8	0.167493	0.0837464	+	0.996487i	$0.473311\pi$
$138$	3.72382e8	0.0874043
$139$	2.06821e9	0.469925	0.234962	−	0.972004i	$-0.424503\pi$
$139$	2.06821e9	0.469925	0.234962	+	0.972004i	$0.424503\pi$
$140$	8.82429e8	0.194135
$141$	−4.62139e9	−0.984661
$142$	1.20224e9	0.248138
$143$	2.87409e8	0.0574762
$144$	1.59226e9	0.308590
$145$	−1.00630e9	−0.189048
$146$	4.73513e8	0.0862470
$147$	−4.66949e8	−0.0824786
$148$	−4.34454e7	−0.00744330
$149$	7.98764e9	1.32764	0.663820	−	0.747893i	$-0.268934\pi$
$149$	7.98764e9	1.32764	0.663820	+	0.747893i	$0.268934\pi$
$150$	−4.08538e8	−0.0658904
$151$	5.68409e8	0.0889743	0.0444872	−	0.999010i	$-0.485835\pi$
$151$	5.68409e8	0.0889743	0.0444872	+	0.999010i	$0.485835\pi$
$152$	6.76435e8	0.102785
$153$	1.47336e9	0.217369
$154$	−4.06044e7	−0.00581741
$155$	4.49826e9	0.625968
$156$	2.45627e9	0.332060
$157$	−3.35804e9	−0.441101	−0.220550	−	0.975376i	$-0.570785\pi$
$157$	−3.35804e9	−0.441101	−0.220550	+	0.975376i	$0.570785\pi$
$158$	−2.14673e9	−0.274044
$159$	−6.79777e9	−0.843489
$160$	2.00091e9	0.241373
$161$	3.08830e9	0.362246
$162$	−1.53857e8	−0.0175509
$163$	−8.35779e8	−0.0927358	−0.0463679	−	0.998924i	$-0.514765\pi$
$163$	−8.35779e8	−0.0927358	−0.0463679	+	0.998924i	$0.514765\pi$
$164$	−1.03352e10	−1.11563
$165$	2.82151e8	0.0296349
$166$	−2.76286e9	−0.282405
$167$	8.98432e8	0.0893843	0.0446922	−	0.999001i	$-0.485769\pi$
$167$	8.98432e8	0.0893843	0.0446922	+	0.999001i	$0.485769\pi$
$168$	−7.02912e8	−0.0680784
$169$	−6.91481e9	−0.652064
$170$	5.90888e8	0.0542607
$171$	1.22793e9	0.109822
$172$	−3.55903e9	−0.310065
$173$	−6.00377e9	−0.509585	−0.254792	−	0.966996i	$-0.582007\pi$
$173$	−6.00377e9	−0.509585	−0.254792	+	0.966996i	$0.582007\pi$
$174$	3.95729e8	0.0327285
$175$	−3.38816e9	−0.273082
$176$	1.14828e9	0.0902072
$177$	−7.14512e9	−0.547180
$178$	−3.56888e8	−0.0266466
$179$	1.12088e10	0.816055	0.408027	−	0.912970i	$-0.366217\pi$
$179$	1.12088e10	0.816055	0.408027	+	0.912970i	$0.366217\pi$
$180$	2.41134e9	0.171211
$181$	−2.52832e9	−0.175097	−0.0875483	−	0.996160i	$-0.527903\pi$
$181$	−2.52832e9	−0.175097	−0.0875483	+	0.996160i	$0.527903\pi$
$182$	−5.21270e8	−0.0352161
$183$	−3.80549e9	−0.250831
$184$	4.64891e9	0.299000
$185$	−6.40676e7	−0.00402129
$186$	−1.76894e9	−0.108369
$187$	1.06253e9	0.0635413
$188$	−2.84829e10	−1.66293
$189$	−1.27599e9	−0.0727393
$190$	4.92459e8	0.0274144
$191$	−5.10445e9	−0.277523	−0.138761	−	0.990326i	$-0.544312\pi$
$191$	−5.10445e9	−0.277523	−0.138761	+	0.990326i	$0.544312\pi$
$192$	9.27778e9	0.492707
$193$	3.93871e9	0.204337	0.102168	−	0.994767i	$-0.467422\pi$
$193$	3.93871e9	0.204337	0.102168	+	0.994767i	$0.467422\pi$
$194$	−3.19699e9	−0.162044
$195$	3.62219e9	0.179397
$196$	−2.87793e9	−0.139293
$197$	2.08841e10	0.987909	0.493955	−	0.869488i	$-0.335551\pi$
$197$	2.08841e10	0.987909	0.493955	+	0.869488i	$0.335551\pi$
$198$	−1.10956e8	−0.00513047
$199$	3.42370e10	1.54759	0.773796	−	0.633435i	$-0.218356\pi$
$199$	3.42370e10	1.54759	0.773796	+	0.633435i	$0.218356\pi$
$200$	−5.10030e9	−0.225404
$201$	7.81485e9	0.337706
$202$	3.79427e9	0.160342
$203$	3.28193e9	0.135643
$204$	9.08071e9	0.367100
$205$	−1.52410e10	−0.602726
$206$	−5.69230e9	−0.220235
$207$	8.43913e9	0.319471
$208$	1.47414e10	0.546076
$209$	8.85539e8	0.0321033
$210$	−5.11734e8	−0.0181576
$211$	5.31186e10	1.84491	0.922455	−	0.386104i	$-0.126179\pi$
$211$	5.31186e10	1.84491	0.922455	+	0.386104i	$0.126179\pi$
$212$	−4.18965e10	−1.42451
$213$	2.72458e10	0.906968
$214$	3.82178e9	0.124567
$215$	−5.24839e9	−0.167515
$216$	−1.92079e9	−0.0600395
$217$	−1.46705e10	−0.449135
$218$	5.10764e9	0.153167
$219$	1.07310e10	0.315241
$220$	1.73897e9	0.0500485
$221$	1.36406e10	0.384652
$222$	2.51946e7	0.000696177 0
$223$	−2.09206e10	−0.566504	−0.283252	−	0.959046i	$-0.591413\pi$
$223$	−2.09206e10	−0.566504	−0.283252	+	0.959046i	$0.591413\pi$
$224$	−6.52572e9	−0.173186
$225$	−9.25853e9	−0.240836
$226$	1.13264e10	0.288805
$227$	−1.31489e10	−0.328681	−0.164340	−	0.986404i	$-0.552550\pi$
$227$	−1.31489e10	−0.328681	−0.164340	+	0.986404i	$0.552550\pi$
$228$	7.56805e9	0.185472
$229$	−3.98559e10	−0.957707	−0.478854	−	0.877895i	$-0.658948\pi$
$229$	−3.98559e10	−0.957707	−0.478854	+	0.877895i	$0.658948\pi$
$230$	3.38450e9	0.0797480
$231$	−9.20200e8	−0.0212632
$232$	4.94038e9	0.111960
$233$	−4.84866e10	−1.07775	−0.538877	−	0.842384i	$-0.681151\pi$
$233$	−4.84866e10	−1.07775	−0.538877	+	0.842384i	$0.681151\pi$
$234$	−1.42443e9	−0.0310577
$235$	−4.20029e10	−0.898408
$236$	−4.40374e10	−0.924096
$237$	−4.86504e10	−1.00166
$238$	−1.92711e9	−0.0389323
$239$	8.42010e10	1.66927	0.834635	−	0.550803i	$-0.185679\pi$
$239$	8.42010e10	1.66927	0.834635	+	0.550803i	$0.185679\pi$
$240$	1.44717e10	0.281559
$241$	2.20823e9	0.0421665	0.0210832	−	0.999778i	$-0.493289\pi$
$241$	2.20823e9	0.0421665	0.0210832	+	0.999778i	$0.493289\pi$
$242$	8.34770e9	0.156458
$243$	−3.48678e9	−0.0641500
$244$	−2.34543e10	−0.423611
$245$	−4.24400e9	−0.0752538
$246$	5.99352e9	0.104346
$247$	1.13684e10	0.194340
$248$	−2.20840e10	−0.370719
$249$	−6.26135e10	−1.03222
$250$	−8.85234e9	−0.143327
$251$	6.67124e10	1.06090	0.530450	−	0.847716i	$-0.322023\pi$
$251$	6.67124e10	1.06090	0.530450	+	0.847716i	$0.322023\pi$
$252$	−7.86428e9	−0.122845
$253$	6.08601e9	0.0933878
$254$	1.71987e10	0.259266
$255$	1.33910e10	0.198328
$256$	5.22078e10	0.759723
$257$	−7.89414e10	−1.12877	−0.564385	−	0.825512i	$-0.690887\pi$
$257$	−7.89414e10	−1.12877	−0.564385	+	0.825512i	$0.690887\pi$
$258$	2.06393e9	0.0290006
$259$	2.08948e8	0.00288529
$260$	2.23246e10	0.302972
$261$	8.96823e9	0.119626
$262$	−1.36666e10	−0.179186
$263$	9.06073e10	1.16778	0.583892	−	0.811831i	$-0.301529\pi$
$263$	9.06073e10	1.16778	0.583892	+	0.811831i	$0.301529\pi$
$264$	−1.38520e9	−0.0175508
$265$	−6.17835e10	−0.769602
$266$	−1.60609e9	−0.0196699
$267$	−8.08801e9	−0.0973959
$268$	4.81651e10	0.570329
$269$	−4.19023e10	−0.487924	−0.243962	−	0.969785i	$-0.578447\pi$
$269$	−4.19023e10	−0.487924	−0.243962	+	0.969785i	$0.578447\pi$
$270$	−1.39837e9	−0.0160135
$271$	−2.16540e10	−0.243880	−0.121940	−	0.992537i	$-0.538912\pi$
$271$	−2.16540e10	−0.243880	−0.121940	+	0.992537i	$0.538912\pi$
$272$	5.44981e10	0.603700
$273$	−1.18133e10	−0.128718
$274$	−2.46839e9	−0.0264568
$275$	−6.67693e9	−0.0704011
$276$	5.20127e10	0.539533
$277$	−9.35582e10	−0.954823	−0.477412	−	0.878680i	$-0.658425\pi$
$277$	−9.35582e10	−0.954823	−0.477412	+	0.878680i	$0.658425\pi$
$278$	−7.39215e9	−0.0742282
$279$	−4.00888e10	−0.396100
$280$	−6.38862e9	−0.0621149
$281$	3.38510e10	0.323886	0.161943	−	0.986800i	$-0.448224\pi$
$281$	3.38510e10	0.323886	0.161943	+	0.986800i	$0.448224\pi$
$282$	1.65177e10	0.155535
$283$	2.00632e11	1.85935	0.929674	−	0.368383i	$-0.120089\pi$
$283$	2.00632e11	1.85935	0.929674	+	0.368383i	$0.120089\pi$
$284$	1.67924e11	1.53172
$285$	1.11604e10	0.100202
$286$	−1.02725e9	−0.00907881
$287$	4.97065e10	0.432459
$288$	−1.78323e10	−0.152736
$289$	−6.81593e10	−0.574758
$290$	3.59670e9	0.0298616
$291$	−7.24521e10	−0.592287
$292$	6.61382e10	0.532390
$293$	1.03467e11	0.820156	0.410078	−	0.912051i	$-0.365502\pi$
$293$	1.03467e11	0.820156	0.410078	+	0.912051i	$0.365502\pi$
$294$	1.66896e9	0.0130281
$295$	−6.49405e10	−0.499249
$296$	3.14536e8	0.00238154
$297$	−2.51455e9	−0.0187524
$298$	−2.85492e10	−0.209711
$299$	7.81309e10	0.565331
$300$	−5.70629e10	−0.406732
$301$	1.71170e10	0.120193
$302$	−2.03159e9	−0.0140542
$303$	8.59878e10	0.586064
$304$	4.54199e10	0.305010
$305$	−3.45873e10	−0.228859
$306$	−5.26604e9	−0.0343351
$307$	−1.50688e11	−0.968178	−0.484089	−	0.875019i	$-0.660849\pi$
$307$	−1.50688e11	−0.968178	−0.484089	+	0.875019i	$0.660849\pi$
$308$	−5.67144e9	−0.0359100
$309$	−1.29002e11	−0.804978
$310$	−1.60776e10	−0.0988765
$311$	−2.83127e11	−1.71617	−0.858083	−	0.513512i	$-0.828344\pi$
$311$	−2.83127e11	−1.71617	−0.858083	+	0.513512i	$0.828344\pi$
$312$	−1.77830e10	−0.106245
$313$	1.13782e11	0.670075	0.335038	−	0.942205i	$-0.391251\pi$
$313$	1.13782e11	0.670075	0.335038	+	0.942205i	$0.391251\pi$
$314$	1.20022e10	0.0696753
$315$	−1.15972e10	−0.0663676
$316$	−2.99846e11	−1.69163
$317$	−2.76476e11	−1.53777	−0.768884	−	0.639388i	$-0.779188\pi$
$317$	−2.76476e11	−1.53777	−0.768884	+	0.639388i	$0.779188\pi$
$318$	2.42964e10	0.133236
$319$	6.46758e9	0.0349690
$320$	8.43238e10	0.449547
$321$	8.66114e10	0.455305
$322$	−1.10381e10	−0.0572195
$323$	4.20282e10	0.214847
$324$	−2.14900e10	−0.108339
$325$	−8.57170e10	−0.426179
$326$	2.98722e9	0.0146483
$327$	1.15752e11	0.559840
$328$	7.48247e10	0.356954
$329$	1.36987e11	0.644612
$330$	−1.00846e9	−0.00468106
$331$	2.25382e11	1.03203	0.516016	−	0.856579i	$-0.327415\pi$
$331$	2.25382e11	1.03203	0.516016	+	0.856579i	$0.327415\pi$
$332$	−3.85904e11	−1.74324
$333$	5.70975e8	0.00254459
$334$	−3.21115e9	−0.0141189
$335$	7.10276e10	0.308124
$336$	−4.71977e10	−0.202020
$337$	−1.32007e11	−0.557521	−0.278761	−	0.960361i	$-0.589924\pi$
$337$	−1.32007e11	−0.557521	−0.278761	+	0.960361i	$0.589924\pi$
$338$	2.47147e10	0.102998
$339$	2.56686e11	1.05561
$340$	8.25327e10	0.334943
$341$	−2.89107e10	−0.115788
$342$	−4.38883e9	−0.0173473
$343$	1.38413e10	0.0539949
$344$	2.57667e10	0.0992077
$345$	7.67015e10	0.291486
$346$	2.14585e10	0.0804929
$347$	−3.20699e11	−1.18745	−0.593724	−	0.804669i	$-0.702343\pi$
$347$	−3.20699e11	−1.18745	−0.593724	+	0.804669i	$0.702343\pi$
$348$	5.52737e10	0.202028
$349$	4.55225e11	1.64253	0.821263	−	0.570550i	$-0.193270\pi$
$349$	4.55225e11	1.64253	0.821263	+	0.570550i	$0.193270\pi$
$350$	1.21099e10	0.0431354
$351$	−3.22812e10	−0.113519
$352$	−1.28600e10	−0.0446477
$353$	−5.24416e11	−1.79759	−0.898793	−	0.438373i	$-0.855555\pi$
$353$	−5.24416e11	−1.79759	−0.898793	+	0.438373i	$0.855555\pi$
$354$	2.55379e10	0.0864313
$355$	2.47632e11	0.827521
$356$	−4.98486e10	−0.164486
$357$	−4.36732e10	−0.142301
$358$	−4.00621e10	−0.128902
$359$	1.84903e11	0.587516	0.293758	−	0.955880i	$-0.405094\pi$
$359$	1.84903e11	0.587516	0.293758	+	0.955880i	$0.405094\pi$
$360$	−1.74576e10	−0.0547802
$361$	−2.87661e11	−0.891452
$362$	9.03664e9	0.0276579
$363$	1.89180e11	0.571869
$364$	−7.28088e10	−0.217384
$365$	9.75320e10	0.287627
$366$	1.36015e10	0.0396206
$367$	3.00165e11	0.863699	0.431849	−	0.901946i	$-0.357861\pi$
$367$	3.00165e11	0.863699	0.431849	+	0.901946i	$0.357861\pi$
$368$	3.12156e11	0.887270
$369$	1.35829e11	0.381393
$370$	2.28989e8	0.000635194 0
$371$	2.01499e11	0.552193
$372$	−2.47079e11	−0.668947
$373$	6.13858e11	1.64202	0.821009	−	0.570915i	$-0.193411\pi$
$373$	6.13858e11	1.64202	0.821009	+	0.570915i	$0.193411\pi$
$374$	−3.79769e9	−0.0100368
$375$	−2.00617e11	−0.523874
$376$	2.06211e11	0.532067
$377$	8.30294e10	0.211688
$378$	4.56061e9	0.0114897
$379$	−2.53423e11	−0.630912	−0.315456	−	0.948940i	$-0.602158\pi$
$379$	−2.53423e11	−0.630912	−0.315456	+	0.948940i	$0.602158\pi$
$380$	6.87845e10	0.169225
$381$	3.89768e11	0.947640
$382$	1.82442e10	0.0438368
$383$	−1.99672e11	−0.474159	−0.237079	−	0.971490i	$-0.576190\pi$
$383$	−1.99672e11	−0.474159	−0.237079	+	0.971490i	$0.576190\pi$
$384$	−1.45878e11	−0.342373
$385$	−8.36351e9	−0.0194006
$386$	−1.40777e10	−0.0322766
$387$	4.67740e10	0.106000
$388$	−4.46542e11	−1.00028
$389$	3.20524e11	0.709720	0.354860	−	0.934920i	$-0.384529\pi$
$389$	3.20524e11	0.709720	0.354860	+	0.934920i	$0.384529\pi$
$390$	−1.29463e10	−0.0283372
$391$	2.88846e11	0.624986
$392$	2.08357e10	0.0445678
$393$	−3.09720e11	−0.654942
$394$	−7.46433e10	−0.156048
$395$	−4.42174e11	−0.913915
$396$	−1.54979e10	−0.0316696
$397$	−7.99985e11	−1.61631	−0.808154	−	0.588971i	$-0.799533\pi$
$397$	−7.99985e11	−1.61631	−0.808154	+	0.588971i	$0.799533\pi$
$398$	−1.22369e11	−0.244454
$399$	−3.63982e10	−0.0718955
$400$	−3.42464e11	−0.668875
$401$	−4.02474e11	−0.777299	−0.388649	−	0.921386i	$-0.627058\pi$
$401$	−4.02474e11	−0.777299	−0.388649	+	0.921386i	$0.627058\pi$
$402$	−2.79316e10	−0.0533432
$403$	−3.71149e11	−0.700932
$404$	5.29967e11	0.989766
$405$	−3.16907e10	−0.0585307
$406$	−1.17302e10	−0.0214258
$407$	4.11767e8	0.000743836 0
$408$	−6.57426e10	−0.117456
$409$	8.85365e11	1.56447	0.782235	−	0.622983i	$-0.214079\pi$
$409$	8.85365e11	1.56447	0.782235	+	0.622983i	$0.214079\pi$
$410$	5.44739e10	0.0952053
$411$	−5.59402e10	−0.0967020
$412$	−7.95076e11	−1.35947
$413$	2.11796e11	0.358213
$414$	−3.01629e10	−0.0504629
$415$	−5.69081e11	−0.941798
$416$	−1.65094e11	−0.270279
$417$	−1.67525e11	−0.271311
$418$	−3.16507e9	−0.00507096
$419$	3.48424e11	0.552262	0.276131	−	0.961120i	$-0.410948\pi$
$419$	3.48424e11	0.552262	0.276131	+	0.961120i	$0.410948\pi$
$420$	−7.14768e10	−0.112084
$421$	−3.84281e10	−0.0596183	−0.0298091	−	0.999556i	$-0.509490\pi$
$421$	−3.84281e10	−0.0596183	−0.0298091	+	0.999556i	$0.509490\pi$
$422$	−1.89855e11	−0.291418
$423$	3.74333e11	0.568494
$424$	3.03323e11	0.455784
$425$	−3.16891e11	−0.471151
$426$	−9.73814e10	−0.143263
$427$	1.12802e11	0.164207
$428$	5.33810e11	0.768935
$429$	−2.32801e10	−0.0331839
$430$	1.87587e10	0.0264602
$431$	−8.93745e10	−0.124757	−0.0623786	−	0.998053i	$-0.519869\pi$
$431$	−8.93745e10	−0.124757	−0.0623786	+	0.998053i	$0.519869\pi$
$432$	−1.28973e11	−0.178165
$433$	−3.63248e11	−0.496601	−0.248300	−	0.968683i	$-0.579872\pi$
$433$	−3.63248e11	−0.496601	−0.248300	+	0.968683i	$0.579872\pi$
$434$	5.24350e10	0.0709443
$435$	8.15104e10	0.109147
$436$	7.13412e11	0.945478
$437$	2.40730e11	0.315765
$438$	−3.83545e10	−0.0497947
$439$	1.83669e11	0.236018	0.118009	−	0.993013i	$-0.462349\pi$
$439$	1.83669e11	0.236018	0.118009	+	0.993013i	$0.462349\pi$
$440$	−1.25898e10	−0.0160134
$441$	3.78229e10	0.0476190
$442$	−4.87539e10	−0.0607588
$443$	−6.12188e11	−0.755211	−0.377606	−	0.925967i	$-0.623252\pi$
$443$	−6.12188e11	−0.755211	−0.377606	+	0.925967i	$0.623252\pi$
$444$	3.51907e9	0.00429739
$445$	−7.35102e10	−0.0888644
$446$	7.47740e10	0.0894837
$447$	−6.46998e11	−0.766513
$448$	−2.75012e11	−0.322552
$449$	1.65704e12	1.92408	0.962041	−	0.272906i	$-0.0879847\pi$
$449$	1.65704e12	1.92408	0.962041	+	0.272906i	$0.0879847\pi$
$450$	3.30916e10	0.0380418
$451$	9.79549e10	0.111489
$452$	1.58202e12	1.78275
$453$	−4.60411e10	−0.0513694
$454$	4.69966e10	0.0519177
$455$	−1.07369e11	−0.117443
$456$	−5.47913e10	−0.0593430
$457$	−7.94449e11	−0.852007	−0.426004	−	0.904721i	$-0.640079\pi$
$457$	−7.94449e11	−0.852007	−0.426004	+	0.904721i	$0.640079\pi$
$458$	1.42452e11	0.151277
$459$	−1.19342e11	−0.125498
$460$	4.72733e11	0.492272
$461$	1.36339e12	1.40593	0.702967	−	0.711222i	$-0.251858\pi$
$461$	1.36339e12	1.40593	0.702967	+	0.711222i	$0.251858\pi$
$462$	3.28896e9	0.00335868
$463$	9.86724e11	0.997887	0.498943	−	0.866635i	$-0.333722\pi$
$463$	9.86724e11	0.997887	0.498943	+	0.866635i	$0.333722\pi$
$464$	3.31726e11	0.332238
$465$	−3.64359e11	−0.361403
$466$	1.73300e11	0.170240
$467$	−1.71683e12	−1.67032	−0.835161	−	0.550005i	$-0.814626\pi$
$467$	−1.71683e12	−1.67032	−0.835161	+	0.550005i	$0.814626\pi$
$468$	−1.98958e11	−0.191715
$469$	−2.31648e11	−0.221080
$470$	1.50126e11	0.141911
$471$	2.72002e11	0.254670
$472$	3.18822e11	0.295672
$473$	3.37318e10	0.0309859
$474$	1.73885e11	0.158219
$475$	−2.64104e11	−0.238042
$476$	−2.69170e11	−0.240323
$477$	5.50619e11	0.486989
$478$	−3.00949e11	−0.263674
$479$	−1.12271e11	−0.0974450	−0.0487225	−	0.998812i	$-0.515515\pi$
$479$	−1.12271e11	−0.0974450	−0.0487225	+	0.998812i	$0.515515\pi$
$480$	−1.62074e11	−0.139357
$481$	5.28618e9	0.00450287
$482$	−7.89260e9	−0.00666052
$483$	−2.50153e11	−0.209143
$484$	1.16597e12	0.965792
$485$	−6.58502e11	−0.540405
$486$	1.24624e10	0.0101330
$487$	−1.95765e12	−1.57709	−0.788543	−	0.614979i	$-0.789164\pi$
$487$	−1.95765e12	−1.57709	−0.788543	+	0.614979i	$0.789164\pi$
$488$	1.69804e11	0.135538
$489$	6.76981e10	0.0535410
$490$	1.51688e10	0.0118869
$491$	−4.47693e11	−0.347627	−0.173814	−	0.984779i	$-0.555609\pi$
$491$	−4.47693e11	−0.347627	−0.173814	+	0.984779i	$0.555609\pi$
$492$	8.37149e11	0.644110
$493$	3.06955e11	0.234026
$494$	−4.06325e10	−0.0306974
$495$	−2.28542e10	−0.0171097
$496$	−1.48285e12	−1.10009
$497$	−8.07621e11	−0.593750
$498$	2.23792e11	0.163047
$499$	6.72766e11	0.485749	0.242874	−	0.970058i	$-0.421910\pi$
$499$	6.72766e11	0.485749	0.242874	+	0.970058i	$0.421910\pi$
$500$	−1.23646e12	−0.884736
$501$	−7.27730e10	−0.0516061
$502$	−2.38442e11	−0.167577
$503$	−9.04614e11	−0.630097	−0.315048	−	0.949076i	$-0.602021\pi$
$503$	−9.04614e11	−0.630097	−0.315048	+	0.949076i	$0.602021\pi$
$504$	5.69359e10	0.0393051
$505$	7.81526e11	0.534727
$506$	−2.17525e10	−0.0147513
$507$	5.60099e11	0.376469
$508$	2.40225e12	1.60041
$509$	−1.28097e12	−0.845880	−0.422940	−	0.906158i	$-0.639002\pi$
$509$	−1.28097e12	−0.845880	−0.422940	+	0.906158i	$0.639002\pi$
$510$	−4.78620e10	−0.0313274
$511$	−3.18089e11	−0.206374
$512$	−1.10869e12	−0.713011
$513$	−9.94621e10	−0.0634059
$514$	2.82150e11	0.178298
$515$	−1.17247e12	−0.734465
$516$	2.88281e11	0.179016
$517$	2.69956e11	0.166182
$518$	−7.46818e8	−0.000455755 0
$519$	4.86305e11	0.294209
$520$	−1.61626e11	−0.0969382
$521$	1.05853e12	0.629408	0.314704	−	0.949190i	$-0.398095\pi$
$521$	1.05853e12	0.629408	0.314704	+	0.949190i	$0.398095\pi$
$522$	−3.20540e10	−0.0188958
$523$	−5.23137e11	−0.305744	−0.152872	−	0.988246i	$-0.548852\pi$
$523$	−5.23137e11	−0.305744	−0.152872	+	0.988246i	$0.548852\pi$
$524$	−1.90889e12	−1.10609
$525$	2.74441e11	0.157664
$526$	−3.23847e11	−0.184460
$527$	−1.37212e12	−0.774897
$528$	−9.30108e10	−0.0520812
$529$	−1.46696e11	−0.0814456
$530$	2.20825e11	0.121565
$531$	5.78755e11	0.315914
$532$	−2.24332e11	−0.121420
$533$	1.25752e12	0.674907
$534$	2.89080e10	0.0153844
$535$	7.87193e11	0.415422
$536$	−3.48706e11	−0.182481
$537$	−9.07910e11	−0.471149
$538$	1.49766e11	0.0770714
$539$	2.72765e10	0.0139200
$540$	−1.95318e11	−0.0988487
$541$	−1.26755e12	−0.636178	−0.318089	−	0.948061i	$-0.603041\pi$
$541$	−1.26755e12	−0.636178	−0.318089	+	0.948061i	$0.603041\pi$
$542$	7.73953e10	0.0385228
$543$	2.04794e11	0.101092
$544$	−6.10344e11	−0.298799
$545$	1.05205e12	0.510800
$546$	4.22229e10	0.0203321
$547$	1.41292e12	0.674798	0.337399	−	0.941362i	$-0.390453\pi$
$547$	1.41292e12	0.674798	0.337399	+	0.941362i	$0.390453\pi$
$548$	−3.44775e11	−0.163314
$549$	3.08244e11	0.144817
$550$	2.38645e10	0.0111204
$551$	2.55823e11	0.118238
$552$	−3.76562e11	−0.172628
$553$	1.44209e12	0.655738
$554$	3.34394e11	0.150822
$555$	5.18947e9	0.00232169
$556$	−1.03250e12	−0.458200
$557$	1.78189e12	0.784389	0.392195	−	0.919882i	$-0.371716\pi$
$557$	1.78189e12	0.784389	0.392195	+	0.919882i	$0.371716\pi$
$558$	1.43285e11	0.0625670
$559$	4.33042e11	0.187576
$560$	−4.28970e11	−0.184323
$561$	−8.60653e10	−0.0366856
$562$	−1.20989e11	−0.0511603
$563$	3.60578e12	1.51256	0.756278	−	0.654251i	$-0.227016\pi$
$563$	3.60578e12	1.51256	0.756278	+	0.654251i	$0.227016\pi$
$564$	2.30712e12	0.960093
$565$	2.33296e12	0.963141
$566$	−7.17093e11	−0.293698
$567$	1.03355e11	0.0419961
$568$	−1.21574e12	−0.490085
$569$	3.16798e12	1.26700	0.633501	−	0.773742i	$-0.281617\pi$
$569$	3.16798e12	1.26700	0.633501	+	0.773742i	$0.281617\pi$
$570$	−3.98891e10	−0.0158277
$571$	1.83575e12	0.722687	0.361343	−	0.932433i	$-0.382318\pi$
$571$	1.83575e12	0.722687	0.361343	+	0.932433i	$0.382318\pi$
$572$	−1.43482e11	−0.0560421
$573$	4.13460e11	0.160228
$574$	−1.77660e11	−0.0683102
$575$	−1.81510e12	−0.692459
$576$	−7.51500e11	−0.284464
$577$	−2.26172e12	−0.849471	−0.424736	−	0.905317i	$-0.639633\pi$
$577$	−2.26172e12	−0.849471	−0.424736	+	0.905317i	$0.639633\pi$
$578$	2.43613e11	0.0907875
$579$	−3.19036e11	−0.117974
$580$	5.02371e11	0.184331
$581$	1.85599e12	0.675745
$582$	2.58957e11	0.0935564
$583$	3.97088e11	0.142357
$584$	−4.78828e11	−0.170342
$585$	−2.93397e11	−0.103575
$586$	−3.69808e11	−0.129550
$587$	−1.41600e12	−0.492257	−0.246128	−	0.969237i	$-0.579158\pi$
$587$	−1.41600e12	−0.492257	−0.246128	+	0.969237i	$0.579158\pi$
$588$	2.33113e11	0.0804207
$589$	−1.14355e12	−0.391505
$590$	2.32109e11	0.0788602
$591$	−1.69161e12	−0.570370
$592$	2.11198e10	0.00706712
$593$	3.01897e12	1.00257	0.501283	−	0.865283i	$-0.332861\pi$
$593$	3.01897e12	1.00257	0.501283	+	0.865283i	$0.332861\pi$
$594$	8.98744e9	0.00296208
$595$	−3.96937e11	−0.129836
$596$	−3.98763e12	−1.29451
$597$	−2.77319e12	−0.893502
$598$	−2.79254e11	−0.0892983
$599$	−4.80027e12	−1.52351	−0.761754	−	0.647867i	$-0.775661\pi$
$599$	−4.80027e12	−1.52351	−0.761754	+	0.647867i	$0.775661\pi$
$600$	4.13124e11	0.130137
$601$	3.98912e12	1.24722	0.623609	−	0.781737i	$-0.285666\pi$
$601$	3.98912e12	1.24722	0.623609	+	0.781737i	$0.285666\pi$
$602$	−6.11791e10	−0.0189853
$603$	−6.33003e11	−0.194974
$604$	−2.83764e11	−0.0867544
$605$	1.71942e12	0.521775
$606$	−3.07336e11	−0.0925734
$607$	−3.78440e12	−1.13148	−0.565741	−	0.824583i	$-0.691410\pi$
$607$	−3.78440e12	−1.13148	−0.565741	+	0.824583i	$0.691410\pi$
$608$	−5.08674e11	−0.150964
$609$	−2.65836e11	−0.0783134
$610$	1.23621e11	0.0361500
$611$	3.46563e12	1.00600
$612$	−7.35538e11	−0.211945
$613$	−3.69582e12	−1.05715	−0.528577	−	0.848885i	$-0.677274\pi$
$613$	−3.69582e12	−1.05715	−0.528577	+	0.848885i	$0.677274\pi$
$614$	5.38585e11	0.152931
$615$	1.23452e12	0.347984
$616$	4.10602e10	0.0114897
$617$	8.82859e11	0.245250	0.122625	−	0.992453i	$-0.460869\pi$
$617$	8.82859e11	0.245250	0.122625	+	0.992453i	$0.460869\pi$
$618$	4.61077e11	0.127152
$619$	−3.15553e12	−0.863902	−0.431951	−	0.901897i	$-0.642175\pi$
$619$	−3.15553e12	−0.863902	−0.431951	+	0.901897i	$0.642175\pi$
$620$	−2.24565e12	−0.610350
$621$	−6.83570e11	−0.184447
$622$	1.01194e12	0.271082
$623$	2.39744e11	0.0637606
$624$	−1.19405e12	−0.315277
$625$	9.32780e11	0.244523
$626$	−4.06676e11	−0.105844
$627$	−7.17286e10	−0.0185348
$628$	1.67642e12	0.430095
$629$	1.95427e10	0.00497803
$630$	4.14505e10	0.0104833
$631$	−4.86495e12	−1.22165	−0.610825	−	0.791766i	$-0.709162\pi$
$631$	−4.86495e12	−1.22165	−0.610825	+	0.791766i	$0.709162\pi$
$632$	2.17083e12	0.541251
$633$	−4.30260e12	−1.06516
$634$	9.88174e11	0.242902
$635$	3.54252e12	0.864630
$636$	3.39362e12	0.822443
$637$	3.50170e11	0.0842659
$638$	−2.31163e10	−0.00552363
$639$	−2.20691e12	−0.523638
$640$	−1.32585e12	−0.312382
$641$	−1.28546e12	−0.300744	−0.150372	−	0.988629i	$-0.548047\pi$
$641$	−1.28546e12	−0.300744	−0.150372	+	0.988629i	$0.548047\pi$
$642$	−3.09564e11	−0.0719189
$643$	7.55834e11	0.174372	0.0871861	−	0.996192i	$-0.472213\pi$
$643$	7.55834e11	0.174372	0.0871861	+	0.996192i	$0.472213\pi$
$644$	−1.54176e12	−0.353208
$645$	4.25120e11	0.0967147
$646$	−1.50216e11	−0.0339368
$647$	4.12274e12	0.924946	0.462473	−	0.886633i	$-0.346962\pi$
$647$	4.12274e12	0.924946	0.462473	+	0.886633i	$0.346962\pi$
$648$	1.55584e11	0.0346638
$649$	4.17378e11	0.0923482
$650$	3.06368e11	0.0673182
$651$	1.18831e12	0.259308
$652$	4.17242e11	0.0904220
$653$	5.69239e12	1.22514	0.612570	−	0.790417i	$-0.290136\pi$
$653$	5.69239e12	1.22514	0.612570	+	0.790417i	$0.290136\pi$
$654$	−4.13718e11	−0.0884311
$655$	−2.81498e12	−0.597572
$656$	5.02417e12	1.05925
$657$	−8.69213e11	−0.182004
$658$	−4.89616e11	−0.101821
$659$	−5.47295e12	−1.13041	−0.565206	−	0.824950i	$-0.691203\pi$
$659$	−5.47295e12	−1.13041	−0.565206	+	0.824950i	$0.691203\pi$
$660$	−1.40857e11	−0.0288955
$661$	−4.53574e12	−0.924149	−0.462075	−	0.886841i	$-0.652895\pi$
$661$	−4.53574e12	−0.924149	−0.462075	+	0.886841i	$0.652895\pi$
$662$	−8.05555e11	−0.163017
$663$	−1.10489e12	−0.222079
$664$	2.79387e12	0.557764
$665$	−3.30816e11	−0.0655977
$666$	−2.04076e9	−0.000401938 0
$667$	1.75818e12	0.343952
$668$	−4.48520e11	−0.0871541
$669$	1.69457e12	0.327071
$670$	−2.53865e11	−0.0486705
$671$	2.22295e11	0.0423330
$672$	5.28584e11	0.0999890
$673$	8.65957e11	0.162715	0.0813576	−	0.996685i	$-0.474074\pi$
$673$	8.65957e11	0.162715	0.0813576	+	0.996685i	$0.474074\pi$
$674$	4.71815e11	0.0880648
$675$	7.49941e11	0.139046
$676$	3.45205e12	0.635794
$677$	5.00114e12	0.914998	0.457499	−	0.889210i	$-0.348745\pi$
$677$	5.00114e12	0.914998	0.457499	+	0.889210i	$0.348745\pi$
$678$	−9.17440e11	−0.166742
$679$	2.14762e12	0.387743
$680$	−5.97521e11	−0.107168
$681$	1.06506e12	0.189764
$682$	1.03332e11	0.0182896
$683$	−3.52112e12	−0.619138	−0.309569	−	0.950877i	$-0.600185\pi$
$683$	−3.52112e12	−0.619138	−0.309569	+	0.950877i	$0.600185\pi$
$684$	−6.13012e11	−0.107082
$685$	−5.08428e11	−0.0882312
$686$	−4.94712e10	−0.00852892
$687$	3.22833e12	0.552933
$688$	1.73013e12	0.294395
$689$	5.09773e12	0.861767
$690$	−2.74145e11	−0.0460425
$691$	9.05704e12	1.51125	0.755623	−	0.655007i	$-0.227334\pi$
$691$	9.05704e12	1.51125	0.755623	+	0.655007i	$0.227334\pi$
$692$	2.99723e12	0.496870
$693$	7.45362e10	0.0122763
$694$	1.14623e12	0.187567
$695$	−1.52260e12	−0.247545
$696$	−4.00171e11	−0.0646404
$697$	4.64900e12	0.746126
$698$	−1.62706e12	−0.259450
$699$	3.92741e12	0.622242
$700$	1.69146e12	0.266268
$701$	−1.07978e13	−1.68891	−0.844453	−	0.535630i	$-0.820074\pi$
$701$	−1.07978e13	−1.68891	−0.844453	+	0.535630i	$0.820074\pi$
$702$	1.15379e11	0.0179312
$703$	1.62873e10	0.00251507
$704$	−5.41956e11	−0.0831547
$705$	3.40223e12	0.518696
$706$	1.87435e12	0.283943
$707$	−2.54885e12	−0.383669
$708$	3.56703e12	0.533527
$709$	−1.08715e13	−1.61578	−0.807888	−	0.589336i	$-0.799389\pi$
$709$	−1.08715e13	−1.61578	−0.807888	+	0.589336i	$0.799389\pi$
$710$	−8.85080e11	−0.130713
$711$	3.94068e12	0.578307
$712$	3.60894e11	0.0526284
$713$	−7.85925e12	−1.13888
$714$	1.56096e11	0.0224776
$715$	−2.11588e11	−0.0302771
$716$	−5.59570e12	−0.795694
$717$	−6.82028e12	−0.963754
$718$	−6.60877e11	−0.0928027
$719$	−1.01264e13	−1.41311	−0.706553	−	0.707660i	$-0.749751\pi$
$719$	−1.01264e13	−1.41311	−0.706553	+	0.707660i	$0.749751\pi$
$720$	−1.17221e12	−0.162558
$721$	3.82388e12	0.526982
$722$	1.02815e12	0.140812
$723$	−1.78866e11	−0.0243448
$724$	1.26220e12	0.170728
$725$	−1.92890e12	−0.259291
$726$	−6.76164e11	−0.0903311
$727$	−3.11988e12	−0.414222	−0.207111	−	0.978317i	$-0.566406\pi$
$727$	−3.11988e12	−0.414222	−0.207111	+	0.978317i	$0.566406\pi$
$728$	5.27122e11	0.0695536
$729$	2.82430e11	0.0370370
$730$	−3.48597e11	−0.0454329
$731$	1.60093e12	0.207369
$732$	1.89980e12	0.244572
$733$	−1.31337e13	−1.68043	−0.840214	−	0.542255i	$-0.817570\pi$
$733$	−1.31337e13	−1.68043	−0.840214	+	0.542255i	$0.817570\pi$
$734$	−1.07284e12	−0.136428
$735$	3.43764e11	0.0434478
$736$	−3.49594e12	−0.439151
$737$	−4.56500e11	−0.0569950
$738$	−4.85475e11	−0.0602440
$739$	9.53784e12	1.17639	0.588193	−	0.808720i	$-0.299839\pi$
$739$	9.53784e12	1.17639	0.588193	+	0.808720i	$0.299839\pi$
$740$	3.19841e10	0.00392096
$741$	−9.20837e11	−0.112202
$742$	−7.20194e11	−0.0872232
$743$	−8.26771e12	−0.995257	−0.497629	−	0.867390i	$-0.665796\pi$
$743$	−8.26771e12	−0.995257	−0.497629	+	0.867390i	$0.665796\pi$
$744$	1.78880e12	0.214035
$745$	−5.88044e12	−0.699369
$746$	−2.19404e12	−0.259369
$747$	5.07170e12	0.595951
$748$	−5.30444e11	−0.0619559
$749$	−2.56733e12	−0.298067
$750$	7.17040e11	0.0827499
$751$	4.70427e12	0.539651	0.269825	−	0.962909i	$-0.413034\pi$
$751$	4.70427e12	0.539651	0.269825	+	0.962909i	$0.413034\pi$
$752$	1.38462e13	1.57889
$753$	−5.40370e12	−0.612511
$754$	−2.96762e11	−0.0334377
$755$	−4.18458e11	−0.0468696
$756$	6.37006e11	0.0709244
$757$	1.64258e13	1.81801	0.909005	−	0.416785i	$-0.136843\pi$
$757$	1.64258e13	1.81801	0.909005	+	0.416785i	$0.136843\pi$
$758$	9.05777e11	0.0996575
$759$	−4.92967e11	−0.0539175
$760$	−4.97987e11	−0.0541448
$761$	−5.22426e12	−0.564669	−0.282334	−	0.959316i	$-0.591109\pi$
$761$	−5.22426e12	−0.564669	−0.282334	+	0.959316i	$0.591109\pi$
$762$	−1.39310e12	−0.149687
$763$	−3.43112e12	−0.366501
$764$	2.54827e12	0.270598
$765$	−1.08467e12	−0.114505
$766$	7.13665e11	0.0748970
$767$	5.35821e12	0.559037
$768$	−4.22883e12	−0.438626
$769$	−1.72013e13	−1.77375	−0.886877	−	0.462006i	$-0.847130\pi$
$769$	−1.72013e13	−1.77375	−0.886877	+	0.462006i	$0.847130\pi$
$770$	2.98926e10	0.00306447
$771$	6.39425e12	0.651696
$772$	−1.96631e12	−0.199238
$773$	4.25719e12	0.428859	0.214430	−	0.976739i	$-0.431211\pi$
$773$	4.25719e12	0.428859	0.214430	+	0.976739i	$0.431211\pi$
$774$	−1.67179e11	−0.0167435
$775$	8.62234e12	0.858554
$776$	3.23288e12	0.320046
$777$	−1.69248e10	−0.00166583
$778$	−1.14561e12	−0.112106
$779$	3.87457e12	0.376969
$780$	−1.80829e12	−0.174921
$781$	−1.59155e12	−0.153070
$782$	−1.03239e12	−0.0987214
$783$	−7.26427e11	−0.0690659
$784$	1.39903e12	0.132253
$785$	2.47217e12	0.232362
$786$	1.10699e12	0.103453
$787$	9.98835e12	0.928127	0.464063	−	0.885802i	$-0.346391\pi$
$787$	9.98835e12	0.928127	0.464063	+	0.885802i	$0.346391\pi$
$788$	−1.04259e13	−0.963260
$789$	−7.33919e12	−0.674220
$790$	1.58041e12	0.144360
$791$	−7.60867e12	−0.691058
$792$	1.12202e11	0.0101329
$793$	2.85378e12	0.256266
$794$	2.85929e12	0.255308
$795$	5.00447e12	0.444330
$796$	−1.70920e13	−1.50898
$797$	6.83407e12	0.599953	0.299976	−	0.953947i	$-0.403021\pi$
$797$	6.83407e12	0.599953	0.299976	+	0.953947i	$0.403021\pi$
$798$	1.30094e11	0.0113565
$799$	1.28123e13	1.11216
$800$	3.83538e12	0.331058
$801$	6.55128e11	0.0562316
$802$	1.43851e12	0.122780
$803$	−6.26846e11	−0.0532036
$804$	−3.90137e12	−0.329280
$805$	−2.27358e12	−0.190823
$806$	1.32655e12	0.110718
$807$	3.39408e12	0.281703
$808$	−3.83686e12	−0.316683
$809$	1.29163e13	1.06016	0.530079	−	0.847948i	$-0.322162\pi$
$809$	1.29163e13	1.06016	0.530079	+	0.847948i	$0.322162\pi$
$810$	1.13268e11	0.00924538
$811$	1.64453e13	1.33489	0.667447	−	0.744657i	$-0.267387\pi$
$811$	1.64453e13	1.33489	0.667447	+	0.744657i	$0.267387\pi$
$812$	−1.63842e12	−0.132258
$813$	1.75398e12	0.140804
$814$	−1.47173e9	−0.000117495 0
$815$	6.15294e11	0.0488510
$816$	−4.41435e12	−0.348547
$817$	1.33425e12	0.104770
$818$	−3.16445e12	−0.247120
$819$	9.56880e11	0.0743156
$820$	7.60868e12	0.587688
$821$	−2.83436e12	−0.217727	−0.108863	−	0.994057i	$-0.534721\pi$
$821$	−2.83436e12	−0.217727	−0.108863	+	0.994057i	$0.534721\pi$
$822$	1.99940e11	0.0152748
$823$	4.76712e12	0.362207	0.181103	−	0.983464i	$-0.442033\pi$
$823$	4.76712e12	0.362207	0.181103	+	0.983464i	$0.442033\pi$
$824$	5.75620e12	0.434974
$825$	5.40831e11	0.0406461
$826$	−7.56994e11	−0.0565825
$827$	1.94033e13	1.44245	0.721224	−	0.692702i	$-0.243580\pi$
$827$	1.94033e13	1.44245	0.721224	+	0.692702i	$0.243580\pi$
$828$	−4.21303e12	−0.311500
$829$	−2.32572e12	−0.171026	−0.0855129	−	0.996337i	$-0.527253\pi$
$829$	−2.32572e12	−0.171026	−0.0855129	+	0.996337i	$0.527253\pi$
$830$	2.03400e12	0.148764
$831$	7.57822e12	0.551268
$832$	−6.95751e12	−0.503384
$833$	1.29456e12	0.0931580
$834$	5.98764e11	0.0428557
$835$	−6.61419e11	−0.0470855
$836$	−4.42083e11	−0.0313023
$837$	3.24720e12	0.228688
$838$	−1.24533e12	−0.0872340
$839$	−1.08642e13	−0.756956	−0.378478	−	0.925610i	$-0.623552\pi$
$839$	−1.08642e13	−0.756956	−0.378478	+	0.925610i	$0.623552\pi$
$840$	5.17478e11	0.0358621
$841$	−1.26387e13	−0.871207
$842$	1.37349e11	0.00941716
$843$	−2.74193e12	−0.186996
$844$	−2.65181e13	−1.79888
$845$	5.09063e12	0.343492
$846$	−1.33793e12	−0.0897981
$847$	−5.60768e12	−0.374376
$848$	2.03669e13	1.35252
$849$	−1.62512e13	−1.07350
$850$	1.13262e12	0.0744219
$851$	1.11937e11	0.00731630
$852$	−1.36018e13	−0.884339
$853$	−7.25439e12	−0.469170	−0.234585	−	0.972096i	$-0.575373\pi$
$853$	−7.25439e12	−0.469170	−0.234585	+	0.972096i	$0.575373\pi$
$854$	−4.03175e11	−0.0259378
$855$	−9.03990e11	−0.0578517
$856$	−3.86468e12	−0.246026
$857$	8.31045e12	0.526273	0.263136	−	0.964759i	$-0.415243\pi$
$857$	8.31045e12	0.526273	0.263136	+	0.964759i	$0.415243\pi$
$858$	8.32072e10	0.00524165
$859$	−1.36529e13	−0.855573	−0.427786	−	0.903880i	$-0.640706\pi$
$859$	−1.36529e13	−0.855573	−0.427786	+	0.903880i	$0.640706\pi$
$860$	2.62013e12	0.163335
$861$	−4.02623e12	−0.249680
$862$	3.19440e11	0.0197064
$863$	−1.01066e13	−0.620238	−0.310119	−	0.950698i	$-0.600369\pi$
$863$	−1.01066e13	−0.620238	−0.310119	+	0.950698i	$0.600369\pi$
$864$	1.44441e12	0.0881820
$865$	4.41993e12	0.268437
$866$	1.29831e12	0.0784420
$867$	5.52091e12	0.331837
$868$	7.32389e12	0.437929
$869$	2.84188e12	0.169051
$870$	−2.91333e11	−0.0172406
$871$	−5.86045e12	−0.345024
$872$	−5.16497e12	−0.302513
$873$	5.86862e12	0.341957
$874$	−8.60411e11	−0.0498775
$875$	5.94668e12	0.342956
$876$	−5.35720e12	−0.307375
$877$	−1.65582e13	−0.945182	−0.472591	−	0.881282i	$-0.656681\pi$
$877$	−1.65582e13	−0.945182	−0.472591	+	0.881282i	$0.656681\pi$
$878$	−6.56465e11	−0.0372809
$879$	−8.38080e12	−0.473517
$880$	−8.45356e11	−0.0475190
$881$	−9.60228e12	−0.537010	−0.268505	−	0.963278i	$-0.586530\pi$
$881$	−9.60228e12	−0.537010	−0.268505	+	0.963278i	$0.586530\pi$
$882$	−1.35186e11	−0.00752180
$883$	1.49031e13	0.824998	0.412499	−	0.910958i	$-0.364656\pi$
$883$	1.49031e13	0.824998	0.412499	+	0.910958i	$0.364656\pi$
$884$	−6.80973e12	−0.375055
$885$	5.26018e12	0.288241
$886$	2.18807e12	0.119291
$887$	−1.19352e13	−0.647400	−0.323700	−	0.946160i	$-0.604927\pi$
$887$	−1.19352e13	−0.647400	−0.323700	+	0.946160i	$0.604927\pi$
$888$	−2.54774e10	−0.00137498
$889$	−1.15535e13	−0.620376
$890$	2.62738e11	0.0140368
$891$	2.03678e11	0.0108267
$892$	1.04441e13	0.552369
$893$	1.06780e13	0.561900
$894$	2.31249e12	0.121077
$895$	−8.25181e12	−0.429878
$896$	4.32411e12	0.224136
$897$	−6.32860e12	−0.326394
$898$	−5.92254e12	−0.303924
$899$	−8.35199e12	−0.426453
$900$	4.62209e12	0.234827
$901$	1.88460e13	0.952704
$902$	−3.50108e11	−0.0176105
$903$	−1.38647e12	−0.0693932
$904$	−1.14536e13	−0.570404
$905$	1.86133e12	0.0922367
$906$	1.64559e11	0.00811419
$907$	2.06113e13	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$907$	2.06113e13	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$908$	6.56428e12	0.320480
$909$	−6.96501e12	−0.338364
$910$	3.83755e11	0.0185510
$911$	−2.98428e13	−1.43551	−0.717755	−	0.696296i	$-0.754830\pi$
$911$	−2.98428e13	−1.43551	−0.717755	+	0.696296i	$0.754830\pi$
$912$	−3.67901e12	−0.176098
$913$	3.65753e12	0.174209
$914$	2.83950e12	0.134581
$915$	2.80157e12	0.132132
$916$	1.98971e13	0.933812
$917$	9.18072e12	0.428760
$918$	4.26549e11	0.0198234
$919$	1.29175e13	0.597393	0.298696	−	0.954348i	$-0.403448\pi$
$919$	1.29175e13	0.597393	0.298696	+	0.954348i	$0.403448\pi$
$920$	−3.42249e12	−0.157506
$921$	1.22057e13	0.558978
$922$	−4.87299e12	−0.222078
$923$	−2.04320e13	−0.926622
$924$	4.59387e11	0.0207326
$925$	−1.22806e11	−0.00551545
$926$	−3.52673e12	−0.157624
$927$	1.04492e13	0.464754
$928$	−3.71512e12	−0.164440
$929$	−2.23197e12	−0.0983144	−0.0491572	−	0.998791i	$-0.515654\pi$
$929$	−2.23197e12	−0.0983144	−0.0491572	+	0.998791i	$0.515654\pi$
$930$	1.30228e12	0.0570864
$931$	1.07891e12	0.0470667
$932$	2.42057e13	1.05086
$933$	2.29333e13	0.990828
$934$	6.13624e12	0.263840
$935$	−7.82230e11	−0.0334720
$936$	1.44042e12	0.0613405
$937$	1.30181e13	0.551723	0.275861	−	0.961197i	$-0.411037\pi$
$937$	1.30181e13	0.551723	0.275861	+	0.961197i	$0.411037\pi$
$938$	8.27949e11	0.0349213
$939$	−9.21633e12	−0.386868
$940$	2.09689e13	0.875992
$941$	−3.23429e13	−1.34470	−0.672351	−	0.740232i	$-0.734715\pi$
$941$	−3.23429e13	−1.34470	−0.672351	+	0.740232i	$0.734715\pi$
$942$	−9.72182e11	−0.0402271
$943$	2.66286e13	1.09660
$944$	2.14076e13	0.877393
$945$	9.39374e11	0.0383173
$946$	−1.20563e11	−0.00489447
$947$	2.58612e13	1.04490	0.522450	−	0.852670i	$-0.325018\pi$
$947$	2.58612e13	1.04490	0.522450	+	0.852670i	$0.325018\pi$
$948$	2.42875e13	0.976665
$949$	−8.04732e12	−0.322072
$950$	9.43953e11	0.0376005
$951$	2.23946e13	0.887831
$952$	1.94874e12	0.0768932
$953$	−6.95786e12	−0.273248	−0.136624	−	0.990623i	$-0.543625\pi$
$953$	−6.95786e12	−0.273248	−0.136624	+	0.990623i	$0.543625\pi$
$954$	−1.96801e12	−0.0769236
$955$	3.75785e12	0.146192
$956$	−4.20353e13	−1.62762
$957$	−5.23874e11	−0.0201894
$958$	4.01278e11	0.0153922
$959$	1.65818e12	0.0633063
$960$	−6.83023e12	−0.259546
$961$	1.08946e13	0.412055
$962$	−1.88937e10	−0.000711263 0
$963$	−7.01552e12	−0.262870
$964$	−1.10240e12	−0.0411144
$965$	−2.89965e12	−0.107640
$966$	8.94089e11	0.0330357
$967$	−4.99450e13	−1.83685	−0.918424	−	0.395598i	$-0.870537\pi$
$967$	−4.99450e13	−1.83685	−0.918424	+	0.395598i	$0.870537\pi$
$968$	−8.44141e12	−0.309012
$969$	−3.40428e12	−0.124042
$970$	2.35360e12	0.0853612
$971$	−2.24431e13	−0.810208	−0.405104	−	0.914271i	$-0.632765\pi$
$971$	−2.24431e13	−0.810208	−0.405104	+	0.914271i	$0.632765\pi$
$972$	1.74069e12	0.0625494
$973$	4.96577e12	0.177615
$974$	6.99700e12	0.249113
$975$	6.94308e12	0.246054
$976$	1.14017e13	0.402202
$977$	3.68084e13	1.29247	0.646236	−	0.763137i	$-0.276342\pi$
$977$	3.68084e13	1.29247	0.646236	+	0.763137i	$0.276342\pi$
$978$	−2.41965e11	−0.00845722
$979$	4.72456e11	0.0164376
$980$	2.11871e12	0.0733761
$981$	−9.37592e12	−0.323224
$982$	1.60013e12	0.0549104
$983$	−5.76358e13	−1.96880	−0.984399	−	0.175951i	$-0.943700\pi$
$983$	−5.76358e13	−1.96880	−0.984399	+	0.175951i	$0.943700\pi$
$984$	−6.06080e12	−0.206088
$985$	−1.53747e13	−0.520407
$986$	−1.09711e12	−0.0369662
$987$	−1.10960e13	−0.372167
$988$	−5.67537e12	−0.189491
$989$	9.16985e12	0.304775
$990$	8.16850e10	0.00270261
$991$	−1.26349e13	−0.416141	−0.208070	−	0.978114i	$-0.566718\pi$
$991$	−1.26349e13	−0.416141	−0.208070	+	0.978114i	$0.566718\pi$
$992$	1.66070e13	0.544487
$993$	−1.82559e13	−0.595844
$994$	2.88658e12	0.0937874
$995$	−2.52050e13	−0.815235
$996$	3.12583e13	1.00646
$997$	−2.82899e12	−0.0906782	−0.0453391	−	0.998972i	$-0.514437\pi$
$997$	−2.82899e12	−0.0906782	−0.0453391	+	0.998972i	$0.514437\pi$
$998$	−2.40458e12	−0.0767278
$999$	−4.62490e10	−0.00146912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.10.a.c.1.1	✓	2
3.2	odd	2		63.10.a.b.1.2		2
4.3	odd	2		336.10.a.l.1.1		2
7.6	odd	2		147.10.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.10.a.c.1.1	✓	2	1.1	even	1	trivial
63.10.a.b.1.2		2	3.2	odd	2
147.10.a.e.1.1		2	7.6	odd	2
336.10.a.l.1.1		2	4.3	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q-3.57418 q^{2} -81.0000 q^{3} -499.225 q^{4} -736.192 q^{5} +289.508 q^{6} +2401.00 q^{7} +3614.30 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-3.57418 q^{2} -81.0000 q^{3} -499.225 q^{4} -736.192 q^{5} +289.508 q^{6} +2401.00 q^{7} +3614.30 q^{8} +6561.00 q^{9} +2631.28 q^{10} +4731.57 q^{11} +40437.2 q^{12} +60742.8 q^{13} -8581.60 q^{14} +59631.6 q^{15} +242685. q^{16} +224563. q^{17} -23450.2 q^{18} +187155. q^{19} +367526. q^{20} -194481. q^{21} -16911.4 q^{22} +1.28626e6 q^{23} -292758. q^{24} -1.41115e6 q^{25} -217106. q^{26} -531441. q^{27} -1.19864e6 q^{28} +1.36690e6 q^{29} -213134. q^{30} -6.11017e6 q^{31} -2.71792e6 q^{32} -383257. q^{33} -802628. q^{34} -1.76760e6 q^{35} -3.27542e6 q^{36} +87025.6 q^{37} -668927. q^{38} -4.92017e6 q^{39} -2.66082e6 q^{40} +2.07024e7 q^{41} +695109. q^{42} +7.12910e6 q^{43} -2.36212e6 q^{44} -4.83016e6 q^{45} -4.59731e6 q^{46} +5.70542e7 q^{47} -1.96575e7 q^{48} +5.76480e6 q^{49} +5.04368e6 q^{50} -1.81896e7 q^{51} -3.03244e7 q^{52} +8.39231e7 q^{53} +1.89946e6 q^{54} -3.48334e6 q^{55} +8.67793e6 q^{56} -1.51596e7 q^{57} -4.88554e6 q^{58} +8.82114e7 q^{59} -2.97696e7 q^{60} +4.69813e7 q^{61} +2.18388e7 q^{62} +1.57530e7 q^{63} -1.14541e8 q^{64} -4.47184e7 q^{65} +1.36983e6 q^{66} -9.64796e7 q^{67} -1.12108e8 q^{68} -1.04187e8 q^{69} +6.31770e6 q^{70} -3.36368e8 q^{71} +2.37134e7 q^{72} -1.32482e8 q^{73} -311045. q^{74} +1.14303e8 q^{75} -9.34327e7 q^{76} +1.13605e7 q^{77} +1.75856e7 q^{78} +6.00622e8 q^{79} -1.78663e8 q^{80} +4.30467e7 q^{81} -7.39941e7 q^{82} +7.73006e8 q^{83} +9.70898e7 q^{84} -1.65322e8 q^{85} -2.54807e7 q^{86} -1.10719e8 q^{87} +1.71013e7 q^{88} +9.98519e7 q^{89} +1.72638e7 q^{90} +1.45844e8 q^{91} -6.42132e8 q^{92} +4.94924e8 q^{93} -2.03922e8 q^{94} -1.37782e8 q^{95} +2.20151e8 q^{96} +8.94470e8 q^{97} -2.06044e7 q^{98} +3.10438e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 30 q^{2} - 162 q^{3} + 116 q^{4} + 1128 q^{5} - 2430 q^{6} + 4802 q^{7} + 7080 q^{8} + 13122 q^{9}+O(q^{10}) \) 2 * q + 30 * q^2 - 162 * q^3 + 116 * q^4 + 1128 * q^5 - 2430 * q^6 + 4802 * q^7 + 7080 * q^8 + 13122 * q^9	\( 2 q + 30 q^{2} - 162 q^{3} + 116 q^{4} + 1128 q^{5} - 2430 q^{6} + 4802 q^{7} + 7080 q^{8} + 13122 q^{9} + 65220 q^{10} + 73284 q^{11} - 9396 q^{12} + 141100 q^{13} + 72030 q^{14} - 91368 q^{15} + 44048 q^{16} - 101784 q^{17} + 196830 q^{18} + 481744 q^{19} + 1514424 q^{20} - 388962 q^{21} + 2284680 q^{22} - 982212 q^{23} - 573480 q^{24} + 110942 q^{25} + 2480820 q^{26} - 1062882 q^{27} + 278516 q^{28} - 2550924 q^{29} - 5282820 q^{30} - 4935848 q^{31} - 11161440 q^{32} - 5936004 q^{33} - 11759460 q^{34} + 2708328 q^{35} + 761076 q^{36} - 16256516 q^{37} + 9221640 q^{38} - 11429100 q^{39} + 3799920 q^{40} + 48707856 q^{41} - 5834430 q^{42} + 7989640 q^{43} + 39813072 q^{44} + 7400808 q^{45} - 80759280 q^{46} + 85572408 q^{47} - 3567888 q^{48} + 11529602 q^{49} + 56146530 q^{50} + 8244504 q^{51} + 19113400 q^{52} + 26565324 q^{53} - 15943230 q^{54} + 124311576 q^{55} + 16999080 q^{56} - 39021264 q^{57} - 136423260 q^{58} + 115200960 q^{59} - 122668344 q^{60} - 142820204 q^{61} + 61265760 q^{62} + 31505922 q^{63} - 296322496 q^{64} + 105082800 q^{65} - 185059080 q^{66} + 27521392 q^{67} - 312884472 q^{68} + 79559172 q^{69} + 156593220 q^{70} + 38070180 q^{71} + 46451880 q^{72} - 2095316 q^{73} - 549031980 q^{74} - 8986302 q^{75} + 87805552 q^{76} + 175954884 q^{77} - 200946420 q^{78} + 435097048 q^{79} - 548960928 q^{80} + 86093442 q^{81} + 866264940 q^{82} + 264288744 q^{83} - 22559796 q^{84} - 773695176 q^{85} + 3411240 q^{86} + 206624844 q^{87} + 254683680 q^{88} + 642673776 q^{89} + 427908420 q^{90} + 338781100 q^{91} - 2037751296 q^{92} + 399803688 q^{93} + 753552960 q^{94} + 411387216 q^{95} + 904076640 q^{96} + 345361228 q^{97} + 172944030 q^{98} + 480816324 q^{99}+O(q^{100}) \) 2 * q + 30 * q^2 - 162 * q^3 + 116 * q^4 + 1128 * q^5 - 2430 * q^6 + 4802 * q^7 + 7080 * q^8 + 13122 * q^9 + 65220 * q^10 + 73284 * q^11 - 9396 * q^12 + 141100 * q^13 + 72030 * q^14 - 91368 * q^15 + 44048 * q^16 - 101784 * q^17 + 196830 * q^18 + 481744 * q^19 + 1514424 * q^20 - 388962 * q^21 + 2284680 * q^22 - 982212 * q^23 - 573480 * q^24 + 110942 * q^25 + 2480820 * q^26 - 1062882 * q^27 + 278516 * q^28 - 2550924 * q^29 - 5282820 * q^30 - 4935848 * q^31 - 11161440 * q^32 - 5936004 * q^33 - 11759460 * q^34 + 2708328 * q^35 + 761076 * q^36 - 16256516 * q^37 + 9221640 * q^38 - 11429100 * q^39 + 3799920 * q^40 + 48707856 * q^41 - 5834430 * q^42 + 7989640 * q^43 + 39813072 * q^44 + 7400808 * q^45 - 80759280 * q^46 + 85572408 * q^47 - 3567888 * q^48 + 11529602 * q^49 + 56146530 * q^50 + 8244504 * q^51 + 19113400 * q^52 + 26565324 * q^53 - 15943230 * q^54 + 124311576 * q^55 + 16999080 * q^56 - 39021264 * q^57 - 136423260 * q^58 + 115200960 * q^59 - 122668344 * q^60 - 142820204 * q^61 + 61265760 * q^62 + 31505922 * q^63 - 296322496 * q^64 + 105082800 * q^65 - 185059080 * q^66 + 27521392 * q^67 - 312884472 * q^68 + 79559172 * q^69 + 156593220 * q^70 + 38070180 * q^71 + 46451880 * q^72 - 2095316 * q^73 - 549031980 * q^74 - 8986302 * q^75 + 87805552 * q^76 + 175954884 * q^77 - 200946420 * q^78 + 435097048 * q^79 - 548960928 * q^80 + 86093442 * q^81 + 866264940 * q^82 + 264288744 * q^83 - 22559796 * q^84 - 773695176 * q^85 + 3411240 * q^86 + 206624844 * q^87 + 254683680 * q^88 + 642673776 * q^89 + 427908420 * q^90 + 338781100 * q^91 - 2037751296 * q^92 + 399803688 * q^93 + 753552960 * q^94 + 411387216 * q^95 + 904076640 * q^96 + 345361228 * q^97 + 172944030 * q^98 + 480816324 * q^99

Introduction

L-functions

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