LMFDB - Embedded newform 210.12.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,12,Mod(1,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("210.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	210.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:	$161.352067918$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2535805712x^{2} - 66934369575900x - 478525314115194389 $ x^4 - 2535805712x^2 - 66934369575900x - 478525314115194389
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-24753.1$ of defining polynomial
Character	$\chi$	$=$	210.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +100000. q^{10} +496107. q^{11} +248832. q^{12} +1.71068e6 q^{13} +537824. q^{14} +759375. q^{15} +1.04858e6 q^{16} -2.89443e6 q^{17} +1.88957e6 q^{18} -2.50747e6 q^{19} +3.20000e6 q^{20} +4.08410e6 q^{21} +1.58754e7 q^{22} +5.66907e7 q^{23} +7.96262e6 q^{24} +9.76562e6 q^{25} +5.47417e7 q^{26} +1.43489e7 q^{27} +1.72104e7 q^{28} -1.71822e7 q^{29} +2.43000e7 q^{30} -1.19955e8 q^{31} +3.35544e7 q^{32} +1.20554e8 q^{33} -9.26219e7 q^{34} +5.25219e7 q^{35} +6.04662e7 q^{36} -3.06527e8 q^{37} -8.02389e7 q^{38} +4.15695e8 q^{39} +1.02400e8 q^{40} -1.35196e9 q^{41} +1.30691e8 q^{42} +1.34023e9 q^{43} +5.08014e8 q^{44} +1.84528e8 q^{45} +1.81410e9 q^{46} +8.36693e8 q^{47} +2.54804e8 q^{48} +2.82475e8 q^{49} +3.12500e8 q^{50} -7.03348e8 q^{51} +1.75173e9 q^{52} +1.38347e9 q^{53} +4.59165e8 q^{54} +1.55034e9 q^{55} +5.50732e8 q^{56} -6.09314e8 q^{57} -5.49831e8 q^{58} +2.55059e9 q^{59} +7.77600e8 q^{60} -9.78656e9 q^{61} -3.83857e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +5.34587e9 q^{65} +3.85773e9 q^{66} +1.94212e9 q^{67} -2.96390e9 q^{68} +1.37759e10 q^{69} +1.68070e9 q^{70} -2.88416e9 q^{71} +1.93492e9 q^{72} +1.79708e10 q^{73} -9.80886e9 q^{74} +2.37305e9 q^{75} -2.56764e9 q^{76} +8.33808e9 q^{77} +1.33022e10 q^{78} +1.96210e9 q^{79} +3.27680e9 q^{80} +3.48678e9 q^{81} -4.32626e10 q^{82} +8.31418e9 q^{83} +4.18212e9 q^{84} -9.04511e9 q^{85} +4.28874e10 q^{86} -4.17528e9 q^{87} +1.62564e10 q^{88} +1.33895e10 q^{89} +5.90490e9 q^{90} +2.87514e10 q^{91} +5.80513e10 q^{92} -2.91491e10 q^{93} +2.67742e10 q^{94} -7.83583e9 q^{95} +8.15373e9 q^{96} -1.69301e10 q^{97} +9.03921e9 q^{98} +2.92946e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 128 q^{2} + 972 q^{3} + 4096 q^{4} + 12500 q^{5} + 31104 q^{6} + 67228 q^{7} + 131072 q^{8} + 236196 q^{9}+O(q^{10}) $ 4 * q + 128 * q^2 + 972 * q^3 + 4096 * q^4 + 12500 * q^5 + 31104 * q^6 + 67228 * q^7 + 131072 * q^8 + 236196 * q^9	\( 4 q + 128 q^{2} + 972 q^{3} + 4096 q^{4} + 12500 q^{5} + 31104 q^{6} + 67228 q^{7} + 131072 q^{8} + 236196 q^{9} + 400000 q^{10} + 458260 q^{11} + 995328 q^{12} + 1574316 q^{13} + 2151296 q^{14} + 3037500 q^{15} + 4194304 q^{16} + 8678072 q^{17} + 7558272 q^{18} + 12442004 q^{19} + 12800000 q^{20} + 16336404 q^{21} + 14664320 q^{22} + 513088 q^{23} + 31850496 q^{24} + 39062500 q^{25} + 50378112 q^{26} + 57395628 q^{27} + 68841472 q^{28} + 58476696 q^{29} + 97200000 q^{30} + 145189572 q^{31} + 134217728 q^{32} + 111357180 q^{33} + 277698304 q^{34} + 210087500 q^{35} + 241864704 q^{36} + 340912752 q^{37} + 398144128 q^{38} + 382558788 q^{39} + 409600000 q^{40} + 915147368 q^{41} + 522764928 q^{42} + 462244024 q^{43} + 469258240 q^{44} + 738112500 q^{45} + 16418816 q^{46} + 901710040 q^{47} + 1019215872 q^{48} + 1129900996 q^{49} + 1250000000 q^{50} + 2108771496 q^{51} + 1612099584 q^{52} - 157945788 q^{53} + 1836660096 q^{54} + 1432062500 q^{55} + 2202927104 q^{56} + 3023406972 q^{57} + 1871254272 q^{58} + 2706989128 q^{59} + 3110400000 q^{60} + 8740846920 q^{61} + 4646066304 q^{62} + 3969746172 q^{63} + 4294967296 q^{64} + 4919737500 q^{65} + 3563429760 q^{66} + 5883134368 q^{67} + 8886345728 q^{68} + 124680384 q^{69} + 6722800000 q^{70} + 344015372 q^{71} + 7739670528 q^{72} + 10549706244 q^{73} + 10909208064 q^{74} + 9492187500 q^{75} + 12740612096 q^{76} + 7701975820 q^{77} + 12241881216 q^{78} - 430177976 q^{79} + 13107200000 q^{80} + 13947137604 q^{81} + 29284715776 q^{82} + 28504941432 q^{83} + 16728477696 q^{84} + 27118975000 q^{85} + 14791808768 q^{86} + 14209837128 q^{87} + 15016263680 q^{88} + 26763786680 q^{89} + 23619600000 q^{90} + 26459529012 q^{91} + 525402112 q^{92} + 35281065996 q^{93} + 28854721280 q^{94} + 38881262500 q^{95} + 32614907904 q^{96} + 62389990476 q^{97} + 36156831872 q^{98} + 27059794740 q^{99}+O(q^{100}) \) 4 * q + 128 * q^2 + 972 * q^3 + 4096 * q^4 + 12500 * q^5 + 31104 * q^6 + 67228 * q^7 + 131072 * q^8 + 236196 * q^9 + 400000 * q^10 + 458260 * q^11 + 995328 * q^12 + 1574316 * q^13 + 2151296 * q^14 + 3037500 * q^15 + 4194304 * q^16 + 8678072 * q^17 + 7558272 * q^18 + 12442004 * q^19 + 12800000 * q^20 + 16336404 * q^21 + 14664320 * q^22 + 513088 * q^23 + 31850496 * q^24 + 39062500 * q^25 + 50378112 * q^26 + 57395628 * q^27 + 68841472 * q^28 + 58476696 * q^29 + 97200000 * q^30 + 145189572 * q^31 + 134217728 * q^32 + 111357180 * q^33 + 277698304 * q^34 + 210087500 * q^35 + 241864704 * q^36 + 340912752 * q^37 + 398144128 * q^38 + 382558788 * q^39 + 409600000 * q^40 + 915147368 * q^41 + 522764928 * q^42 + 462244024 * q^43 + 469258240 * q^44 + 738112500 * q^45 + 16418816 * q^46 + 901710040 * q^47 + 1019215872 * q^48 + 1129900996 * q^49 + 1250000000 * q^50 + 2108771496 * q^51 + 1612099584 * q^52 - 157945788 * q^53 + 1836660096 * q^54 + 1432062500 * q^55 + 2202927104 * q^56 + 3023406972 * q^57 + 1871254272 * q^58 + 2706989128 * q^59 + 3110400000 * q^60 + 8740846920 * q^61 + 4646066304 * q^62 + 3969746172 * q^63 + 4294967296 * q^64 + 4919737500 * q^65 + 3563429760 * q^66 + 5883134368 * q^67 + 8886345728 * q^68 + 124680384 * q^69 + 6722800000 * q^70 + 344015372 * q^71 + 7739670528 * q^72 + 10549706244 * q^73 + 10909208064 * q^74 + 9492187500 * q^75 + 12740612096 * q^76 + 7701975820 * q^77 + 12241881216 * q^78 - 430177976 * q^79 + 13107200000 * q^80 + 13947137604 * q^81 + 29284715776 * q^82 + 28504941432 * q^83 + 16728477696 * q^84 + 27118975000 * q^85 + 14791808768 * q^86 + 14209837128 * q^87 + 15016263680 * q^88 + 26763786680 * q^89 + 23619600000 * q^90 + 26459529012 * q^91 + 525402112 * q^92 + 35281065996 * q^93 + 28854721280 * q^94 + 38881262500 * q^95 + 32614907904 * q^96 + 62389990476 * q^97 + 36156831872 * q^98 + 27059794740 * 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 $

$2$	32.0000	0.707107
$2$	32.0000	0.707107
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	1024.00	0.500000
$5$	3125.00	0.447214
$5$	3125.00	0.447214
$6$	7776.00	0.408248
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	32768.0	0.353553
$9$	59049.0	0.333333
$10$	100000.	0.316228
$11$	496107.	0.928787	0.464393	−	0.885629i	$-0.346272\pi$
$11$	496107.	0.928787	0.464393	+	0.885629i	$0.346272\pi$
$12$	248832.	0.288675
$13$	1.71068e6	1.27785	0.638925	−	0.769269i	$-0.279379\pi$
$13$	1.71068e6	1.27785	0.638925	+	0.769269i	$0.279379\pi$
$14$	537824.	0.267261
$15$	759375.	0.258199
$16$	1.04858e6	0.250000
$17$	−2.89443e6	−0.494418	−0.247209	−	0.968962i	$-0.579513\pi$
$17$	−2.89443e6	−0.494418	−0.247209	+	0.968962i	$0.579513\pi$
$18$	1.88957e6	0.235702
$19$	−2.50747e6	−0.232322	−0.116161	−	0.993230i	$-0.537059\pi$
$19$	−2.50747e6	−0.232322	−0.116161	+	0.993230i	$0.537059\pi$
$20$	3.20000e6	0.223607
$21$	4.08410e6	0.218218
$22$	1.58754e7	0.656751
$23$	5.66907e7	1.83658	0.918288	−	0.395912i	$-0.129572\pi$
$23$	5.66907e7	1.83658	0.918288	+	0.395912i	$0.129572\pi$
$24$	7.96262e6	0.204124
$25$	9.76562e6	0.200000
$26$	5.47417e7	0.903576
$27$	1.43489e7	0.192450
$28$	1.72104e7	0.188982
$29$	−1.71822e7	−0.155557	−0.0777786	−	0.996971i	$-0.524783\pi$
$29$	−1.71822e7	−0.155557	−0.0777786	+	0.996971i	$0.524783\pi$
$30$	2.43000e7	0.182574
$31$	−1.19955e8	−0.752541	−0.376270	−	0.926510i	$-0.622794\pi$
$31$	−1.19955e8	−0.752541	−0.376270	+	0.926510i	$0.622794\pi$
$32$	3.35544e7	0.176777
$33$	1.20554e8	0.536235
$34$	−9.26219e7	−0.349607
$35$	5.25219e7	0.169031
$36$	6.04662e7	0.166667
$37$	−3.06527e8	−0.726707	−0.363353	−	0.931651i	$-0.618368\pi$
$37$	−3.06527e8	−0.726707	−0.363353	+	0.931651i	$0.618368\pi$
$38$	−8.02389e7	−0.164276
$39$	4.15695e8	0.737767
$40$	1.02400e8	0.158114
$41$	−1.35196e9	−1.82243	−0.911217	−	0.411928i	$-0.864856\pi$
$41$	−1.35196e9	−1.82243	−0.911217	+	0.411928i	$0.864856\pi$
$42$	1.30691e8	0.154303
$43$	1.34023e9	1.39028	0.695142	−	0.718872i	$-0.255341\pi$
$43$	1.34023e9	1.39028	0.695142	+	0.718872i	$0.255341\pi$
$44$	5.08014e8	0.464393
$45$	1.84528e8	0.149071
$46$	1.81410e9	1.29866
$47$	8.36693e8	0.532143	0.266071	−	0.963953i	$-0.414274\pi$
$47$	8.36693e8	0.532143	0.266071	+	0.963953i	$0.414274\pi$
$48$	2.54804e8	0.144338
$49$	2.82475e8	0.142857
$50$	3.12500e8	0.141421
$51$	−7.03348e8	−0.285453
$52$	1.75173e9	0.638925
$53$	1.38347e9	0.454416	0.227208	−	0.973846i	$-0.427040\pi$
$53$	1.38347e9	0.454416	0.227208	+	0.973846i	$0.427040\pi$
$54$	4.59165e8	0.136083
$55$	1.55034e9	0.415366
$56$	5.50732e8	0.133631
$57$	−6.09314e8	−0.134131
$58$	−5.49831e8	−0.109996
$59$	2.55059e9	0.464466	0.232233	−	0.972660i	$-0.425397\pi$
$59$	2.55059e9	0.464466	0.232233	+	0.972660i	$0.425397\pi$
$60$	7.77600e8	0.129099
$61$	−9.78656e9	−1.48360	−0.741798	−	0.670623i	$-0.766027\pi$
$61$	−9.78656e9	−1.48360	−0.741798	+	0.670623i	$0.766027\pi$
$62$	−3.83857e9	−0.532127
$63$	9.92437e8	0.125988
$64$	1.07374e9	0.125000
$65$	5.34587e9	0.571472
$66$	3.85773e9	0.379176
$67$	1.94212e9	0.175737	0.0878686	−	0.996132i	$-0.471994\pi$
$67$	1.94212e9	0.175737	0.0878686	+	0.996132i	$0.471994\pi$
$68$	−2.96390e9	−0.247209
$69$	1.37759e10	1.06035
$70$	1.68070e9	0.119523
$71$	−2.88416e9	−0.189714	−0.0948568	−	0.995491i	$-0.530239\pi$
$71$	−2.88416e9	−0.189714	−0.0948568	+	0.995491i	$0.530239\pi$
$72$	1.93492e9	0.117851
$73$	1.79708e10	1.01459	0.507295	−	0.861772i	$-0.330645\pi$
$73$	1.79708e10	1.01459	0.507295	+	0.861772i	$0.330645\pi$
$74$	−9.80886e9	−0.513859
$75$	2.37305e9	0.115470
$76$	−2.56764e9	−0.116161
$77$	8.33808e9	0.351048
$78$	1.33022e10	0.521680
$79$	1.96210e9	0.0717419	0.0358710	−	0.999356i	$-0.488579\pi$
$79$	1.96210e9	0.0717419	0.0358710	+	0.999356i	$0.488579\pi$
$80$	3.27680e9	0.111803
$81$	3.48678e9	0.111111
$82$	−4.32626e10	−1.28865
$83$	8.31418e9	0.231681	0.115840	−	0.993268i	$-0.463044\pi$
$83$	8.31418e9	0.231681	0.115840	+	0.993268i	$0.463044\pi$
$84$	4.18212e9	0.109109
$85$	−9.04511e9	−0.221111
$86$	4.28874e10	0.983079
$87$	−4.17528e9	−0.0898110
$88$	1.62564e10	0.328376
$89$	1.33895e10	0.254167	0.127083	−	0.991892i	$-0.459438\pi$
$89$	1.33895e10	0.254167	0.127083	+	0.991892i	$0.459438\pi$
$90$	5.90490e9	0.105409
$91$	2.87514e10	0.482982
$92$	5.80513e10	0.918288
$93$	−2.91491e10	−0.434480
$94$	2.67742e10	0.376282
$95$	−7.83583e9	−0.103898
$96$	8.15373e9	0.102062
$97$	−1.69301e10	−0.200177	−0.100089	−	0.994979i	$-0.531913\pi$
$97$	−1.69301e10	−0.200177	−0.100089	+	0.994979i	$0.531913\pi$
$98$	9.03921e9	0.101015
$99$	2.92946e10	0.309596
$100$	1.00000e10	0.100000
$101$	−1.02358e11	−0.969071	−0.484536	−	0.874772i	$-0.661011\pi$
$101$	−1.02358e11	−0.969071	−0.484536	+	0.874772i	$0.661011\pi$
$102$	−2.25071e10	−0.201845
$103$	−1.74730e10	−0.148512	−0.0742562	−	0.997239i	$-0.523658\pi$
$103$	−1.74730e10	−0.148512	−0.0742562	+	0.997239i	$0.523658\pi$
$104$	5.60555e10	0.451788
$105$	1.27628e10	0.0975900
$106$	4.42711e10	0.321320
$107$	9.88046e10	0.681031	0.340515	−	0.940239i	$-0.389399\pi$
$107$	9.88046e10	0.681031	0.340515	+	0.940239i	$0.389399\pi$
$108$	1.46933e10	0.0962250
$109$	6.32757e10	0.393905	0.196953	−	0.980413i	$-0.436896\pi$
$109$	6.32757e10	0.393905	0.196953	+	0.980413i	$0.436896\pi$
$110$	4.96107e10	0.293708
$111$	−7.44861e10	−0.419564
$112$	1.76234e10	0.0944911
$113$	4.94630e10	0.252551	0.126276	−	0.991995i	$-0.459698\pi$
$113$	4.94630e10	0.252551	0.126276	+	0.991995i	$0.459698\pi$
$114$	−1.94981e10	−0.0948450
$115$	1.77159e11	0.821342
$116$	−1.75946e10	−0.0777786
$117$	1.01014e11	0.425950
$118$	8.16188e10	0.328427
$119$	−4.86468e10	−0.186873
$120$	2.48832e10	0.0912871
$121$	−3.91892e10	−0.137356
$122$	−3.13170e11	−1.04906
$123$	−3.28525e11	−1.05218
$124$	−1.22834e11	−0.376270
$125$	3.05176e10	0.0894427
$126$	3.17580e10	0.0890871
$127$	5.19274e11	1.39468	0.697342	−	0.716738i	$-0.254366\pi$
$127$	5.19274e11	1.39468	0.697342	+	0.716738i	$0.254366\pi$
$128$	3.43597e10	0.0883883
$129$	3.25676e11	0.802681
$130$	1.71068e11	0.404092
$131$	2.26241e11	0.512364	0.256182	−	0.966629i	$-0.417535\pi$
$131$	2.26241e11	0.512364	0.256182	+	0.966629i	$0.417535\pi$
$132$	1.23447e11	0.268118
$133$	−4.21430e10	−0.0878094
$134$	6.21477e10	0.124265
$135$	4.48403e10	0.0860663
$136$	−9.48448e10	−0.174803
$137$	−6.00451e11	−1.06295	−0.531477	−	0.847073i	$-0.678363\pi$
$137$	−6.00451e11	−1.06295	−0.531477	+	0.847073i	$0.678363\pi$
$138$	4.40827e11	0.749779
$139$	−2.17075e11	−0.354836	−0.177418	−	0.984136i	$-0.556774\pi$
$139$	−2.17075e11	−0.354836	−0.177418	+	0.984136i	$0.556774\pi$
$140$	5.37824e10	0.0845154
$141$	2.03316e11	0.307233
$142$	−9.22931e10	−0.134148
$143$	8.48680e11	1.18685
$144$	6.19174e10	0.0833333
$145$	−5.36944e10	−0.0695673
$146$	5.75064e11	0.717424
$147$	6.86415e10	0.0824786
$148$	−3.13884e11	−0.363353
$149$	9.78724e10	0.109178	0.0545891	−	0.998509i	$-0.482615\pi$
$149$	9.78724e10	0.109178	0.0545891	+	0.998509i	$0.482615\pi$
$150$	7.59375e10	0.0816497
$151$	−1.09383e12	−1.13390	−0.566950	−	0.823752i	$-0.691877\pi$
$151$	−1.09383e12	−1.13390	−0.566950	+	0.823752i	$0.691877\pi$
$152$	−8.21646e10	−0.0821382
$153$	−1.70913e11	−0.164806
$154$	2.66818e11	0.248229
$155$	−3.74860e11	−0.336546
$156$	4.25671e11	0.368883
$157$	1.74847e12	1.46288	0.731442	−	0.681903i	$-0.238848\pi$
$157$	1.74847e12	1.46288	0.731442	+	0.681903i	$0.238848\pi$
$158$	6.27873e10	0.0507292
$159$	3.36184e11	0.262357
$160$	1.04858e11	0.0790569
$161$	9.52801e11	0.694161
$162$	1.11577e11	0.0785674
$163$	−1.23611e12	−0.841445	−0.420723	−	0.907189i	$-0.638223\pi$
$163$	−1.23611e12	−0.841445	−0.420723	+	0.907189i	$0.638223\pi$
$164$	−1.38440e12	−0.911217
$165$	3.76732e11	0.239812
$166$	2.66054e11	0.163823
$167$	−6.16294e11	−0.367153	−0.183576	−	0.983005i	$-0.558767\pi$
$167$	−6.16294e11	−0.367153	−0.183576	+	0.983005i	$0.558767\pi$
$168$	1.33828e11	0.0771517
$169$	1.13426e12	0.632900
$170$	−2.89443e11	−0.156349
$171$	−1.48063e11	−0.0774406
$172$	1.37240e12	0.695142
$173$	2.97769e11	0.146092	0.0730460	−	0.997329i	$-0.476728\pi$
$173$	2.97769e11	0.146092	0.0730460	+	0.997329i	$0.476728\pi$
$174$	−1.33609e11	−0.0635060
$175$	1.64131e11	0.0755929
$176$	5.20206e11	0.232197
$177$	6.19792e11	0.268160
$178$	4.28463e11	0.179723
$179$	1.61951e12	0.658707	0.329353	−	0.944207i	$-0.393169\pi$
$179$	1.61951e12	0.658707	0.329353	+	0.944207i	$0.393169\pi$
$180$	1.88957e11	0.0745356
$181$	−1.98574e11	−0.0759784	−0.0379892	−	0.999278i	$-0.512095\pi$
$181$	−1.98574e11	−0.0759784	−0.0379892	+	0.999278i	$0.512095\pi$
$182$	9.20044e11	0.341520
$183$	−2.37813e12	−0.856555
$184$	1.85764e12	0.649328
$185$	−9.57897e11	−0.324993
$186$	−9.32772e11	−0.307223
$187$	−1.43595e12	−0.459209
$188$	8.56774e11	0.266071
$189$	2.41162e11	0.0727393
$190$	−2.50747e11	−0.0734666
$191$	5.64271e12	1.60622	0.803108	−	0.595833i	$-0.203178\pi$
$191$	5.64271e12	1.60622	0.803108	+	0.595833i	$0.203178\pi$
$192$	2.60919e11	0.0721688
$193$	3.10117e12	0.833604	0.416802	−	0.908997i	$-0.363151\pi$
$193$	3.10117e12	0.833604	0.416802	+	0.908997i	$0.363151\pi$
$194$	−5.41763e11	−0.141547
$195$	1.29905e12	0.329939
$196$	2.89255e11	0.0714286
$197$	−7.53912e11	−0.181032	−0.0905162	−	0.995895i	$-0.528852\pi$
$197$	−7.53912e11	−0.181032	−0.0905162	+	0.995895i	$0.528852\pi$
$198$	9.37429e11	0.218917
$199$	−3.89504e12	−0.884750	−0.442375	−	0.896830i	$-0.645864\pi$
$199$	−3.89504e12	−0.884750	−0.442375	+	0.896830i	$0.645864\pi$
$200$	3.20000e11	0.0707107
$201$	4.71934e11	0.101462
$202$	−3.27547e12	−0.685237
$203$	−2.88781e11	−0.0587951
$204$	−7.20228e11	−0.142726
$205$	−4.22486e12	−0.815017
$206$	−5.59136e11	−0.105014
$207$	3.34753e12	0.612192
$208$	1.79378e12	0.319462
$209$	−1.24397e12	−0.215777
$210$	4.08410e11	0.0690066
$211$	3.43669e12	0.565701	0.282851	−	0.959164i	$-0.408720\pi$
$211$	3.43669e12	0.565701	0.282851	+	0.959164i	$0.408720\pi$
$212$	1.41668e12	0.227208
$213$	−7.00851e11	−0.109531
$214$	3.16175e12	0.481561
$215$	4.18823e12	0.621754
$216$	4.70185e11	0.0680414
$217$	−2.01609e12	−0.284434
$218$	2.02482e12	0.278533
$219$	4.36689e12	0.585774
$220$	1.58754e12	0.207683
$221$	−4.95145e12	−0.631792
$222$	−2.38355e12	−0.296677
$223$	1.14836e13	1.39444	0.697220	−	0.716857i	$-0.254420\pi$
$223$	1.14836e13	1.39444	0.697220	+	0.716857i	$0.254420\pi$
$224$	5.63949e11	0.0668153
$225$	5.76650e11	0.0666667
$226$	1.58282e12	0.178581
$227$	6.21327e12	0.684192	0.342096	−	0.939665i	$-0.388863\pi$
$227$	6.21327e12	0.684192	0.342096	+	0.939665i	$0.388863\pi$
$228$	−6.23938e11	−0.0670656
$229$	1.82978e12	0.192001	0.0960007	−	0.995381i	$-0.469395\pi$
$229$	1.82978e12	0.192001	0.0960007	+	0.995381i	$0.469395\pi$
$230$	5.66907e12	0.580777
$231$	2.02615e12	0.202678
$232$	−5.63027e11	−0.0549978
$233$	−1.23710e13	−1.18018	−0.590090	−	0.807338i	$-0.700908\pi$
$233$	−1.23710e13	−1.18018	−0.590090	+	0.807338i	$0.700908\pi$
$234$	3.23244e12	0.301192
$235$	2.61467e12	0.237981
$236$	2.61180e12	0.232233
$237$	4.76791e11	0.0414202
$238$	−1.55670e12	−0.132139
$239$	2.88475e12	0.239287	0.119644	−	0.992817i	$-0.461825\pi$
$239$	2.88475e12	0.239287	0.119644	+	0.992817i	$0.461825\pi$
$240$	7.96262e11	0.0645497
$241$	4.73102e12	0.374853	0.187426	−	0.982279i	$-0.439985\pi$
$241$	4.73102e12	0.374853	0.187426	+	0.982279i	$0.439985\pi$
$242$	−1.25405e12	−0.0971251
$243$	8.47289e11	0.0641500
$244$	−1.00214e13	−0.741798
$245$	8.82735e11	0.0638877
$246$	−1.05128e13	−0.744005
$247$	−4.28947e12	−0.296873
$248$	−3.93069e12	−0.266063
$249$	2.02035e12	0.133761
$250$	9.76562e11	0.0632456
$251$	−8.74937e12	−0.554334	−0.277167	−	0.960822i	$-0.589396\pi$
$251$	−8.74937e12	−0.554334	−0.277167	+	0.960822i	$0.589396\pi$
$252$	1.01626e12	0.0629941
$253$	2.81247e13	1.70579
$254$	1.66168e13	0.986191
$255$	−2.19796e12	−0.127658
$256$	1.09951e12	0.0625000
$257$	4.74252e12	0.263862	0.131931	−	0.991259i	$-0.457882\pi$
$257$	4.74252e12	0.263862	0.131931	+	0.991259i	$0.457882\pi$
$258$	1.04216e13	0.567581
$259$	−5.15180e12	−0.274669
$260$	5.47417e12	0.285736
$261$	−1.01459e12	−0.0518524
$262$	7.23970e12	0.362296
$263$	9.14876e12	0.448338	0.224169	−	0.974550i	$-0.428033\pi$
$263$	9.14876e12	0.448338	0.224169	+	0.974550i	$0.428033\pi$
$264$	3.95032e12	0.189588
$265$	4.32335e12	0.203221
$266$	−1.34858e12	−0.0620906
$267$	3.25364e12	0.146743
$268$	1.98873e12	0.0878686
$269$	1.05149e12	0.0455165	0.0227583	−	0.999741i	$-0.492755\pi$
$269$	1.05149e12	0.0455165	0.0227583	+	0.999741i	$0.492755\pi$
$270$	1.43489e12	0.0608581
$271$	−1.86750e13	−0.776123	−0.388061	−	0.921633i	$-0.626855\pi$
$271$	−1.86750e13	−0.776123	−0.388061	+	0.921633i	$0.626855\pi$
$272$	−3.03503e12	−0.123605
$273$	6.98658e12	0.278850
$274$	−1.92144e13	−0.751622
$275$	4.84480e12	0.185757
$276$	1.41065e13	0.530174
$277$	2.75523e13	1.01512	0.507562	−	0.861615i	$-0.330547\pi$
$277$	2.75523e13	1.01512	0.507562	+	0.861615i	$0.330547\pi$
$278$	−6.94639e12	−0.250907
$279$	−7.08324e12	−0.250847
$280$	1.72104e12	0.0597614
$281$	3.01818e13	1.02769	0.513843	−	0.857884i	$-0.328221\pi$
$281$	3.01818e13	1.02769	0.513843	+	0.857884i	$0.328221\pi$
$282$	6.50613e12	0.217246
$283$	−1.42882e13	−0.467898	−0.233949	−	0.972249i	$-0.575165\pi$
$283$	−1.42882e13	−0.467898	−0.233949	+	0.972249i	$0.575165\pi$
$284$	−2.95338e12	−0.0948568
$285$	−1.90411e12	−0.0599853
$286$	2.71578e13	0.839230
$287$	−2.27223e13	−0.688815
$288$	1.98136e12	0.0589256
$289$	−2.58941e13	−0.755550
$290$	−1.71822e12	−0.0491915
$291$	−4.11402e12	−0.115573
$292$	1.84021e13	0.507295
$293$	1.66342e13	0.450018	0.225009	−	0.974357i	$-0.427759\pi$
$293$	1.66342e13	0.450018	0.225009	+	0.974357i	$0.427759\pi$
$294$	2.19653e12	0.0583212
$295$	7.97058e12	0.207716
$296$	−1.00443e13	−0.256930
$297$	7.11860e12	0.178745
$298$	3.13192e12	0.0772006
$299$	9.69796e13	2.34687
$300$	2.43000e12	0.0577350
$301$	2.25253e13	0.525478
$302$	−3.50024e13	−0.801788
$303$	−2.48731e13	−0.559494
$304$	−2.62927e12	−0.0580805
$305$	−3.05830e13	−0.663485
$306$	−5.46923e12	−0.116536
$307$	−3.44652e13	−0.721306	−0.360653	−	0.932700i	$-0.617446\pi$
$307$	−3.44652e13	−0.721306	−0.360653	+	0.932700i	$0.617446\pi$
$308$	8.53819e12	0.175524
$309$	−4.24594e12	−0.0857437
$310$	−1.19955e13	−0.237974
$311$	8.69277e13	1.69424	0.847122	−	0.531398i	$-0.178333\pi$
$311$	8.69277e13	1.69424	0.847122	+	0.531398i	$0.178333\pi$
$312$	1.36215e13	0.260840
$313$	−3.11922e13	−0.586885	−0.293442	−	0.955977i	$-0.594801\pi$
$313$	−3.11922e13	−0.586885	−0.293442	+	0.955977i	$0.594801\pi$
$314$	5.59510e13	1.03442
$315$	3.10136e12	0.0563436
$316$	2.00919e12	0.0358710
$317$	−2.19358e12	−0.0384881	−0.0192441	−	0.999815i	$-0.506126\pi$
$317$	−2.19358e12	−0.0384881	−0.0192441	+	0.999815i	$0.506126\pi$
$318$	1.07579e13	0.185514
$319$	−8.52422e12	−0.144479
$320$	3.35544e12	0.0559017
$321$	2.40095e13	0.393193
$322$	3.04896e13	0.490846
$323$	7.25769e12	0.114864
$324$	3.57047e12	0.0555556
$325$	1.67058e13	0.255570
$326$	−3.95556e13	−0.594992
$327$	1.53760e13	0.227421
$328$	−4.43009e13	−0.644327
$329$	1.40623e13	0.201131
$330$	1.20554e13	0.169572
$331$	1.16918e13	0.161743	0.0808717	−	0.996725i	$-0.474230\pi$
$331$	1.16918e13	0.161743	0.0808717	+	0.996725i	$0.474230\pi$
$332$	8.51372e12	0.115840
$333$	−1.81001e13	−0.242236
$334$	−1.97214e13	−0.259616
$335$	6.06911e12	0.0785921
$336$	4.28249e12	0.0545545
$337$	−6.57715e13	−0.824277	−0.412138	−	0.911121i	$-0.635218\pi$
$337$	−6.57715e13	−0.824277	−0.412138	+	0.911121i	$0.635218\pi$
$338$	3.62963e13	0.447528
$339$	1.20195e13	0.145810
$340$	−9.26219e12	−0.110555
$341$	−5.95107e13	−0.698950
$342$	−4.73803e12	−0.0547588
$343$	4.74756e12	0.0539949
$344$	4.39167e13	0.491540
$345$	4.30495e13	0.474202
$346$	9.52862e12	0.103303
$347$	−5.13489e13	−0.547922	−0.273961	−	0.961741i	$-0.588334\pi$
$347$	−5.13489e13	−0.547922	−0.273961	+	0.961741i	$0.588334\pi$
$348$	−4.27548e12	−0.0449055
$349$	−1.96254e13	−0.202899	−0.101449	−	0.994841i	$-0.532348\pi$
$349$	−1.96254e13	−0.202899	−0.101449	+	0.994841i	$0.532348\pi$
$350$	5.25219e12	0.0534522
$351$	2.45464e13	0.245922
$352$	1.66466e13	0.164188
$353$	1.56942e13	0.152398	0.0761988	−	0.997093i	$-0.475722\pi$
$353$	1.56942e13	0.152398	0.0761988	+	0.997093i	$0.475722\pi$
$354$	1.98334e13	0.189617
$355$	−9.01300e12	−0.0848425
$356$	1.37108e13	0.127083
$357$	−1.18212e13	−0.107891
$358$	5.18243e13	0.465776
$359$	−1.36337e14	−1.20669	−0.603344	−	0.797481i	$-0.706165\pi$
$359$	−1.36337e14	−1.20669	−0.603344	+	0.797481i	$0.706165\pi$
$360$	6.04662e12	0.0527046
$361$	−1.10203e14	−0.946027
$362$	−6.35436e12	−0.0537248
$363$	−9.52296e12	−0.0793023
$364$	2.94414e13	0.241491
$365$	5.61586e13	0.453739
$366$	−7.61003e13	−0.605676
$367$	−1.51557e14	−1.18826	−0.594131	−	0.804369i	$-0.702504\pi$
$367$	−1.51557e14	−1.18826	−0.594131	+	0.804369i	$0.702504\pi$
$368$	5.94446e13	0.459144
$369$	−7.98317e13	−0.607478
$370$	−3.06527e13	−0.229805
$371$	2.32520e13	0.171753
$372$	−2.98487e13	−0.217240
$373$	2.07413e14	1.48743	0.743716	−	0.668495i	$-0.233061\pi$
$373$	2.07413e14	1.48743	0.743716	+	0.668495i	$0.233061\pi$
$374$	−4.59504e13	−0.324710
$375$	7.41577e12	0.0516398
$376$	2.74168e13	0.188141
$377$	−2.93932e13	−0.198779
$378$	7.71719e12	0.0514344
$379$	−3.01215e14	−1.97861	−0.989306	−	0.145854i	$-0.953407\pi$
$379$	−3.01215e14	−1.97861	−0.989306	+	0.145854i	$0.953407\pi$
$380$	−8.02389e12	−0.0519488
$381$	1.26184e14	0.805222
$382$	1.80567e14	1.13577
$383$	3.10956e14	1.92800	0.963998	−	0.265908i	$-0.0856716\pi$
$383$	3.10956e14	1.92800	0.963998	+	0.265908i	$0.0856716\pi$
$384$	8.34942e12	0.0510310
$385$	2.60565e13	0.156994
$386$	9.92374e13	0.589447
$387$	7.91394e13	0.463428
$388$	−1.73364e13	−0.100089
$389$	−2.52476e14	−1.43714	−0.718568	−	0.695457i	$-0.755202\pi$
$389$	−2.52476e14	−1.43714	−0.718568	+	0.695457i	$0.755202\pi$
$390$	4.15695e13	0.233302
$391$	−1.64088e14	−0.908037
$392$	9.25615e12	0.0505076
$393$	5.49765e13	0.295813
$394$	−2.41252e13	−0.128009
$395$	6.13158e12	0.0320840
$396$	2.99977e13	0.154798
$397$	2.38011e13	0.121129	0.0605646	−	0.998164i	$-0.480710\pi$
$397$	2.38011e13	0.121129	0.0605646	+	0.998164i	$0.480710\pi$
$398$	−1.24641e14	−0.625612
$399$	−1.02407e13	−0.0506968
$400$	1.02400e13	0.0500000
$401$	−1.84767e14	−0.889880	−0.444940	−	0.895560i	$-0.646775\pi$
$401$	−1.84767e14	−0.889880	−0.444940	+	0.895560i	$0.646775\pi$
$402$	1.51019e13	0.0717444
$403$	−2.05205e14	−0.961634
$404$	−1.04815e14	−0.484536
$405$	1.08962e13	0.0496904
$406$	−9.24101e12	−0.0415744
$407$	−1.52070e14	−0.674956
$408$	−2.30473e13	−0.100923
$409$	−3.75636e14	−1.62289	−0.811445	−	0.584429i	$-0.801319\pi$
$409$	−3.75636e14	−1.62289	−0.811445	+	0.584429i	$0.801319\pi$
$410$	−1.35196e14	−0.576304
$411$	−1.45910e14	−0.613697
$412$	−1.78924e13	−0.0742562
$413$	4.28677e13	0.175552
$414$	1.07121e14	0.432885
$415$	2.59818e13	0.103611
$416$	5.74008e13	0.225894
$417$	−5.27492e13	−0.204865
$418$	−3.98071e13	−0.152578
$419$	−2.99525e14	−1.13307	−0.566534	−	0.824039i	$-0.691716\pi$
$419$	−2.99525e14	−1.13307	−0.566534	+	0.824039i	$0.691716\pi$
$420$	1.30691e13	0.0487950
$421$	−2.55954e14	−0.943215	−0.471608	−	0.881808i	$-0.656326\pi$
$421$	−2.55954e14	−0.943215	−0.471608	+	0.881808i	$0.656326\pi$
$422$	1.09974e14	0.400011
$423$	4.94059e13	0.177381
$424$	4.53336e13	0.160660
$425$	−2.82660e13	−0.0988837
$426$	−2.24272e13	−0.0774503
$427$	−1.64483e14	−0.560747
$428$	1.01176e14	0.340515
$429$	2.06229e14	0.685228
$430$	1.34023e14	0.439646
$431$	−4.39767e14	−1.42429	−0.712143	−	0.702034i	$-0.752275\pi$
$431$	−4.39767e14	−1.42429	−0.712143	+	0.702034i	$0.752275\pi$
$432$	1.50459e13	0.0481125
$433$	−4.80229e14	−1.51623	−0.758114	−	0.652122i	$-0.773879\pi$
$433$	−4.80229e14	−1.51623	−0.758114	+	0.652122i	$0.773879\pi$
$434$	−6.45148e13	−0.201125
$435$	−1.30477e13	−0.0401647
$436$	6.47944e13	0.196953
$437$	−1.42150e14	−0.426677
$438$	1.39741e14	0.414205
$439$	5.81580e14	1.70237	0.851187	−	0.524863i	$-0.175883\pi$
$439$	5.81580e14	1.70237	0.851187	+	0.524863i	$0.175883\pi$
$440$	5.08014e13	0.146854
$441$	1.66799e13	0.0476190
$442$	−1.58446e14	−0.446745
$443$	−5.48931e14	−1.52861	−0.764305	−	0.644854i	$-0.776918\pi$
$443$	−5.48931e14	−1.52861	−0.764305	+	0.644854i	$0.776918\pi$
$444$	−7.62737e13	−0.209782
$445$	4.18421e13	0.113667
$446$	3.67474e14	0.986018
$447$	2.37830e13	0.0630340
$448$	1.80464e13	0.0472456
$449$	−3.76834e14	−0.974529	−0.487265	−	0.873254i	$-0.662005\pi$
$449$	−3.76834e14	−0.974529	−0.487265	+	0.873254i	$0.662005\pi$
$450$	1.84528e13	0.0471405
$451$	−6.70716e14	−1.69265
$452$	5.06501e13	0.126276
$453$	−2.65800e14	−0.654657
$454$	1.98825e14	0.483797
$455$	8.98480e13	0.215996
$456$	−1.99660e13	−0.0474225
$457$	3.17612e14	0.745347	0.372673	−	0.927963i	$-0.378441\pi$
$457$	3.17612e14	0.745347	0.372673	+	0.927963i	$0.378441\pi$
$458$	5.85531e13	0.135766
$459$	−4.15320e13	−0.0951509
$460$	1.81410e14	0.410671
$461$	−7.98215e14	−1.78552	−0.892760	−	0.450533i	$-0.851234\pi$
$461$	−7.98215e14	−1.78552	−0.892760	+	0.450533i	$0.851234\pi$
$462$	6.48369e13	0.143315
$463$	−5.49117e14	−1.19941	−0.599707	−	0.800220i	$-0.704716\pi$
$463$	−5.49117e14	−1.19941	−0.599707	+	0.800220i	$0.704716\pi$
$464$	−1.80169e13	−0.0388893
$465$	−9.10910e13	−0.194305
$466$	−3.95873e14	−0.834513
$467$	−8.18400e13	−0.170499	−0.0852497	−	0.996360i	$-0.527169\pi$
$467$	−8.18400e13	−0.170499	−0.0852497	+	0.996360i	$0.527169\pi$
$468$	1.03438e14	0.212975
$469$	3.26411e13	0.0664224
$470$	8.36693e13	0.168278
$471$	4.24878e14	0.844597
$472$	8.35776e13	0.164214
$473$	6.64899e14	1.29128
$474$	1.52573e13	0.0292885
$475$	−2.44870e13	−0.0464644
$476$	−4.98143e13	−0.0934363
$477$	8.16927e13	0.151472
$478$	9.23120e13	0.169202
$479$	−4.42175e14	−0.801214	−0.400607	−	0.916250i	$-0.631201\pi$
$479$	−4.42175e14	−0.801214	−0.400607	+	0.916250i	$0.631201\pi$
$480$	2.54804e13	0.0456435
$481$	−5.24369e14	−0.928622
$482$	1.51393e14	0.265061
$483$	2.31531e14	0.400774
$484$	−4.01297e13	−0.0686778
$485$	−5.29066e13	−0.0895221
$486$	2.71132e13	0.0453609
$487$	6.81973e14	1.12813	0.564063	−	0.825731i	$-0.309237\pi$
$487$	6.81973e14	1.12813	0.564063	+	0.825731i	$0.309237\pi$
$488$	−3.20686e14	−0.524531
$489$	−3.00375e14	−0.485809
$490$	2.82475e13	0.0451754
$491$	−7.26590e14	−1.14906	−0.574528	−	0.818485i	$-0.694814\pi$
$491$	−7.26590e14	−1.14906	−0.574528	+	0.818485i	$0.694814\pi$
$492$	−3.36410e14	−0.526091
$493$	4.97328e13	0.0769103
$494$	−1.37263e14	−0.209921
$495$	9.15458e13	0.138455
$496$	−1.25782e14	−0.188135
$497$	−4.84741e13	−0.0717050
$498$	6.46511e13	0.0945833
$499$	−2.68992e14	−0.389212	−0.194606	−	0.980882i	$-0.562343\pi$
$499$	−2.68992e14	−0.389212	−0.194606	+	0.980882i	$0.562343\pi$
$500$	3.12500e13	0.0447214
$501$	−1.49759e14	−0.211976
$502$	−2.79980e14	−0.391973
$503$	2.45124e13	0.0339440	0.0169720	−	0.999856i	$-0.494597\pi$
$503$	2.45124e13	0.0339440	0.0169720	+	0.999856i	$0.494597\pi$
$504$	3.25202e13	0.0445435
$505$	−3.19870e14	−0.433382
$506$	8.99990e14	1.20617
$507$	2.75625e14	0.365405
$508$	5.31736e14	0.697342
$509$	−1.11428e15	−1.44559	−0.722794	−	0.691063i	$-0.757143\pi$
$509$	−1.11428e15	−1.44559	−0.722794	+	0.691063i	$0.757143\pi$
$510$	−7.03348e13	−0.0902680
$511$	3.02035e14	0.383479
$512$	3.51844e13	0.0441942
$513$	−3.59794e13	−0.0447104
$514$	1.51761e14	0.186579
$515$	−5.46032e13	−0.0664168
$516$	3.33493e14	0.401340
$517$	4.15090e14	0.494247
$518$	−1.64858e14	−0.194221
$519$	7.23580e13	0.0843463
$520$	1.75173e14	0.202046
$521$	−1.24928e15	−1.42578	−0.712889	−	0.701277i	$-0.752614\pi$
$521$	−1.24928e15	−1.42578	−0.712889	+	0.701277i	$0.752614\pi$
$522$	−3.24670e13	−0.0366652
$523$	−9.62331e14	−1.07539	−0.537694	−	0.843140i	$-0.680704\pi$
$523$	−9.62331e14	−1.07539	−0.537694	+	0.843140i	$0.680704\pi$
$524$	2.31670e14	0.256182
$525$	3.98838e13	0.0436436
$526$	2.92760e14	0.317023
$527$	3.47203e14	0.372070
$528$	1.26410e14	0.134059
$529$	2.26103e15	2.37301
$530$	1.38347e14	0.143699
$531$	1.50610e14	0.154822
$532$	−4.31544e13	−0.0439047
$533$	−2.31276e15	−2.32880
$534$	1.04117e14	0.103763
$535$	3.08765e14	0.304566
$536$	6.36392e13	0.0621325
$537$	3.93541e14	0.380304
$538$	3.36478e13	0.0321850
$539$	1.40138e14	0.132684
$540$	4.59165e13	0.0430331
$541$	1.36072e15	1.26236	0.631182	−	0.775635i	$-0.282570\pi$
$541$	1.36072e15	1.26236	0.631182	+	0.775635i	$0.282570\pi$
$542$	−5.97601e14	−0.548802
$543$	−4.82535e13	−0.0438661
$544$	−9.71211e13	−0.0874016
$545$	1.97737e14	0.176160
$546$	2.23571e14	0.197177
$547$	1.75346e15	1.53097	0.765484	−	0.643455i	$-0.222500\pi$
$547$	1.75346e15	1.53097	0.765484	+	0.643455i	$0.222500\pi$
$548$	−6.14862e14	−0.531477
$549$	−5.77886e14	−0.494532
$550$	1.55034e14	0.131350
$551$	4.30838e13	0.0361393
$552$	4.51407e14	0.374890
$553$	3.29771e13	0.0271159
$554$	8.81674e14	0.717802
$555$	−2.32769e14	−0.187635
$556$	−2.22285e14	−0.177418
$557$	−3.42029e13	−0.0270308	−0.0135154	−	0.999909i	$-0.504302\pi$
$557$	−3.42029e13	−0.0270308	−0.0135154	+	0.999909i	$0.504302\pi$
$558$	−2.26664e14	−0.177376
$559$	2.29271e15	1.77657
$560$	5.50732e13	0.0422577
$561$	−3.48936e14	−0.265125
$562$	9.65818e14	0.726684
$563$	−3.31050e14	−0.246660	−0.123330	−	0.992366i	$-0.539357\pi$
$563$	−3.31050e14	−0.246660	−0.123330	+	0.992366i	$0.539357\pi$
$564$	2.08196e14	0.153616
$565$	1.54572e14	0.112944
$566$	−4.57222e14	−0.330854
$567$	5.86024e13	0.0419961
$568$	−9.45082e13	−0.0670739
$569$	8.51591e14	0.598568	0.299284	−	0.954164i	$-0.403252\pi$
$569$	8.51591e14	0.598568	0.299284	+	0.954164i	$0.403252\pi$
$570$	−6.09314e13	−0.0424160
$571$	1.07412e15	0.740550	0.370275	−	0.928922i	$-0.379263\pi$
$571$	1.07412e15	0.740550	0.370275	+	0.928922i	$0.379263\pi$
$572$	8.69048e14	0.593425
$573$	1.37118e15	0.927350
$574$	−7.27115e14	−0.487066
$575$	5.53621e14	0.367315
$576$	6.34034e13	0.0416667
$577$	1.95031e15	1.26951	0.634757	−	0.772712i	$-0.281100\pi$
$577$	1.95031e15	1.26951	0.634757	+	0.772712i	$0.281100\pi$
$578$	−8.28613e14	−0.534255
$579$	7.53584e14	0.481282
$580$	−5.49831e13	−0.0347836
$581$	1.39736e14	0.0875671
$582$	−1.31649e14	−0.0817221
$583$	6.86351e14	0.422055
$584$	5.88866e14	0.358712
$585$	3.15668e14	0.190491
$586$	5.32295e14	0.318211
$587$	2.57996e15	1.52793	0.763965	−	0.645258i	$-0.223250\pi$
$587$	2.57996e15	1.52793	0.763965	+	0.645258i	$0.223250\pi$
$588$	7.02889e13	0.0412393
$589$	3.00784e14	0.174832
$590$	2.55059e14	0.146877
$591$	−1.83201e14	−0.104519
$592$	−3.21417e14	−0.181677
$593$	1.58670e14	0.0888576	0.0444288	−	0.999013i	$-0.485853\pi$
$593$	1.58670e14	0.0888576	0.0444288	+	0.999013i	$0.485853\pi$
$594$	2.27795e14	0.126392
$595$	−1.52021e14	−0.0835720
$596$	1.00221e14	0.0545891
$597$	−9.46496e14	−0.510810
$598$	3.10335e15	1.65949
$599$	−2.90890e15	−1.54128	−0.770641	−	0.637270i	$-0.780064\pi$
$599$	−2.90890e15	−1.54128	−0.770641	+	0.637270i	$0.780064\pi$
$600$	7.77600e13	0.0408248
$601$	−4.50791e14	−0.234512	−0.117256	−	0.993102i	$-0.537410\pi$
$601$	−4.50791e14	−0.234512	−0.117256	+	0.993102i	$0.537410\pi$
$602$	7.20809e14	0.371569
$603$	1.14680e14	0.0585791
$604$	−1.12008e15	−0.566950
$605$	−1.22466e14	−0.0614273
$606$	−7.95938e14	−0.395622
$607$	−1.57972e15	−0.778114	−0.389057	−	0.921214i	$-0.627199\pi$
$607$	−1.57972e15	−0.778114	−0.389057	+	0.921214i	$0.627199\pi$
$608$	−8.41366e13	−0.0410691
$609$	−7.01739e13	−0.0339454
$610$	−9.78656e14	−0.469154
$611$	1.43131e15	0.679998
$612$	−1.75015e14	−0.0824031
$613$	−2.75862e15	−1.28724	−0.643619	−	0.765346i	$-0.722568\pi$
$613$	−2.75862e15	−1.28724	−0.643619	+	0.765346i	$0.722568\pi$
$614$	−1.10289e15	−0.510040
$615$	−1.02664e15	−0.470550
$616$	2.73222e14	0.124114
$617$	−1.63125e15	−0.734433	−0.367217	−	0.930135i	$-0.619689\pi$
$617$	−1.63125e15	−0.734433	−0.367217	+	0.930135i	$0.619689\pi$
$618$	−1.35870e14	−0.0606300
$619$	−1.49326e15	−0.660443	−0.330222	−	0.943903i	$-0.607123\pi$
$619$	−1.49326e15	−0.660443	−0.330222	+	0.943903i	$0.607123\pi$
$620$	−3.83857e14	−0.168273
$621$	8.13450e14	0.353449
$622$	2.78169e15	1.19801
$623$	2.25037e14	0.0960660
$624$	4.35888e14	0.184442
$625$	9.53674e13	0.0400000
$626$	−9.98152e14	−0.414990
$627$	−3.02285e14	−0.124579
$628$	1.79043e15	0.731442
$629$	8.87222e14	0.359297
$630$	9.92437e13	0.0398410
$631$	4.62905e15	1.84217	0.921087	−	0.389357i	$-0.127303\pi$
$631$	4.62905e15	1.84217	0.921087	+	0.389357i	$0.127303\pi$
$632$	6.42942e13	0.0253646
$633$	8.35116e14	0.326608
$634$	−7.01944e13	−0.0272152
$635$	1.62273e15	0.623722
$636$	3.44252e14	0.131179
$637$	4.83224e14	0.182550
$638$	−2.72775e14	−0.102162
$639$	−1.70307e14	−0.0632379
$640$	1.07374e14	0.0395285
$641$	2.80109e15	1.02237	0.511185	−	0.859471i	$-0.329207\pi$
$641$	2.80109e15	1.02237	0.511185	+	0.859471i	$0.329207\pi$
$642$	7.68305e14	0.278030
$643$	−7.59484e14	−0.272495	−0.136247	−	0.990675i	$-0.543504\pi$
$643$	−7.59484e14	−0.272495	−0.136247	+	0.990675i	$0.543504\pi$
$644$	9.75669e14	0.347080
$645$	1.01774e15	0.358970
$646$	2.32246e14	0.0812213
$647$	3.99398e15	1.38494	0.692471	−	0.721445i	$-0.256522\pi$
$647$	3.99398e15	1.38494	0.692471	+	0.721445i	$0.256522\pi$
$648$	1.14255e14	0.0392837
$649$	1.26536e15	0.431390
$650$	5.34587e14	0.180715
$651$	−4.89909e14	−0.164218
$652$	−1.26578e15	−0.420723
$653$	1.28898e15	0.424837	0.212418	−	0.977179i	$-0.431866\pi$
$653$	1.28898e15	0.424837	0.212418	+	0.977179i	$0.431866\pi$
$654$	4.92032e14	0.160811
$655$	7.07002e14	0.229136
$656$	−1.41763e15	−0.455608
$657$	1.06116e15	0.338197
$658$	4.49994e14	0.142221
$659$	−3.02120e15	−0.946913	−0.473456	−	0.880817i	$-0.656994\pi$
$659$	−3.02120e15	−0.946913	−0.473456	+	0.880817i	$0.656994\pi$
$660$	3.85773e14	0.119906
$661$	−4.57318e15	−1.40965	−0.704823	−	0.709383i	$-0.748974\pi$
$661$	−4.57318e15	−1.40965	−0.704823	+	0.709383i	$0.748974\pi$
$662$	3.74137e14	0.114370
$663$	−1.20320e15	−0.364766
$664$	2.72439e14	0.0819115
$665$	−1.31697e14	−0.0392696
$666$	−5.79204e14	−0.171286
$667$	−9.74072e14	−0.285693
$668$	−6.31085e14	−0.183576
$669$	2.79050e15	0.805080
$670$	1.94212e14	0.0555730
$671$	−4.85518e15	−1.37794
$672$	1.37040e14	0.0385758
$673$	−8.72326e14	−0.243554	−0.121777	−	0.992557i	$-0.538859\pi$
$673$	−8.72326e14	−0.243554	−0.121777	+	0.992557i	$0.538859\pi$
$674$	−2.10469e15	−0.582852
$675$	1.40126e14	0.0384900
$676$	1.16148e15	0.316450
$677$	−7.00525e15	−1.89315	−0.946577	−	0.322477i	$-0.895484\pi$
$677$	−7.00525e15	−1.89315	−0.946577	+	0.322477i	$0.895484\pi$
$678$	3.84624e14	0.103104
$679$	−2.84544e14	−0.0756600
$680$	−2.96390e14	−0.0781744
$681$	1.50983e15	0.395019
$682$	−1.90434e15	−0.494232
$683$	1.49164e15	0.384018	0.192009	−	0.981393i	$-0.438500\pi$
$683$	1.49164e15	0.384018	0.192009	+	0.981393i	$0.438500\pi$
$684$	−1.51617e14	−0.0387203
$685$	−1.87641e15	−0.475367
$686$	1.51922e14	0.0381802
$687$	4.44637e14	0.110852
$688$	1.40534e15	0.347571
$689$	2.36668e15	0.580675
$690$	1.37759e15	0.335312
$691$	1.50425e15	0.363238	0.181619	−	0.983369i	$-0.441866\pi$
$691$	1.50425e15	0.363238	0.181619	+	0.983369i	$0.441866\pi$
$692$	3.04916e14	0.0730460
$693$	4.92355e14	0.117016
$694$	−1.64316e15	−0.387440
$695$	−6.78359e14	−0.158688
$696$	−1.36815e14	−0.0317530
$697$	3.91315e15	0.901044
$698$	−6.28014e14	−0.143471
$699$	−3.00616e15	−0.681377
$700$	1.68070e14	0.0377964
$701$	−6.87996e15	−1.53510	−0.767550	−	0.640989i	$-0.778525\pi$
$701$	−6.87996e15	−1.53510	−0.767550	+	0.640989i	$0.778525\pi$
$702$	7.85484e14	0.173893
$703$	7.68606e14	0.168830
$704$	5.32691e14	0.116098
$705$	6.35364e14	0.137399
$706$	5.02214e14	0.107761
$707$	−1.72034e15	−0.366274
$708$	6.34667e14	0.134080
$709$	5.68948e15	1.19267	0.596333	−	0.802737i	$-0.296624\pi$
$709$	5.68948e15	1.19267	0.596333	+	0.802737i	$0.296624\pi$
$710$	−2.88416e14	−0.0599927
$711$	1.15860e14	0.0239140
$712$	4.38747e14	0.0898615
$713$	−6.80035e15	−1.38210
$714$	−3.78277e14	−0.0762904
$715$	2.65212e15	0.530775
$716$	1.65838e15	0.329353
$717$	7.00995e14	0.138153
$718$	−4.36279e15	−0.853257
$719$	−9.71834e15	−1.88618	−0.943090	−	0.332538i	$-0.892095\pi$
$719$	−9.71834e15	−1.88618	−0.943090	+	0.332538i	$0.892095\pi$
$720$	1.93492e14	0.0372678
$721$	−2.93669e14	−0.0561324
$722$	−3.52649e15	−0.668942
$723$	1.14964e15	0.216421
$724$	−2.03340e14	−0.0379892
$725$	−1.67795e14	−0.0311114
$726$	−3.04735e14	−0.0560752
$727$	9.64375e15	1.76119	0.880596	−	0.473867i	$-0.157142\pi$
$727$	9.64375e15	1.76119	0.880596	+	0.473867i	$0.157142\pi$
$728$	9.42125e14	0.170760
$729$	2.05891e14	0.0370370
$730$	1.79708e15	0.320842
$731$	−3.87921e15	−0.687382
$732$	−2.43521e15	−0.428277
$733$	5.72664e14	0.0999604	0.0499802	−	0.998750i	$-0.484084\pi$
$733$	5.72664e14	0.0999604	0.0499802	+	0.998750i	$0.484084\pi$
$734$	−4.84982e15	−0.840228
$735$	2.14505e14	0.0368856
$736$	1.90223e15	0.324664
$737$	9.63498e14	0.163222
$738$	−2.55461e15	−0.429552
$739$	−6.36585e14	−0.106246	−0.0531230	−	0.998588i	$-0.516918\pi$
$739$	−6.36585e14	−0.106246	−0.0531230	+	0.998588i	$0.516918\pi$
$740$	−9.80886e14	−0.162497
$741$	−1.04234e15	−0.171399
$742$	7.44065e14	0.121448
$743$	−5.55205e15	−0.899529	−0.449764	−	0.893147i	$-0.648492\pi$
$743$	−5.55205e15	−0.899529	−0.449764	+	0.893147i	$0.648492\pi$
$744$	−9.55159e14	−0.153612
$745$	3.05851e14	0.0488260
$746$	6.63721e15	1.05177
$747$	4.90944e14	0.0772269
$748$	−1.47041e15	−0.229605
$749$	1.66061e15	0.257405
$750$	2.37305e14	0.0365148
$751$	6.39847e15	0.977364	0.488682	−	0.872462i	$-0.337478\pi$
$751$	6.39847e15	0.977364	0.488682	+	0.872462i	$0.337478\pi$
$752$	8.77336e14	0.133036
$753$	−2.12610e15	−0.320045
$754$	−9.40583e14	−0.140558
$755$	−3.41820e15	−0.507096
$756$	2.46950e14	0.0363696
$757$	2.59150e15	0.378900	0.189450	−	0.981890i	$-0.439330\pi$
$757$	2.59150e15	0.378900	0.189450	+	0.981890i	$0.439330\pi$
$758$	−9.63887e15	−1.39909
$759$	6.83430e15	0.984837
$760$	−2.56764e14	−0.0367333
$761$	−7.14556e15	−1.01489	−0.507447	−	0.861683i	$-0.669411\pi$
$761$	−7.14556e15	−1.01489	−0.507447	+	0.861683i	$0.669411\pi$
$762$	4.03787e15	0.569378
$763$	1.06348e15	0.148882
$764$	5.77813e15	0.803108
$765$	−5.34105e14	−0.0737035
$766$	9.95061e15	1.36330
$767$	4.36323e15	0.593518
$768$	2.67181e14	0.0360844
$769$	9.93769e15	1.33257	0.666286	−	0.745697i	$-0.267883\pi$
$769$	9.93769e15	1.33257	0.666286	+	0.745697i	$0.267883\pi$
$770$	8.33808e14	0.111011
$771$	1.15243e15	0.152341
$772$	3.17560e15	0.416802
$773$	−1.37799e16	−1.79581	−0.897904	−	0.440192i	$-0.854910\pi$
$773$	−1.37799e16	−1.79581	−0.897904	+	0.440192i	$0.854910\pi$
$774$	2.53246e15	0.327693
$775$	−1.17144e15	−0.150508
$776$	−5.54766e14	−0.0707734
$777$	−1.25189e15	−0.158580
$778$	−8.07924e15	−1.01621
$779$	3.38998e15	0.423391
$780$	1.33022e15	0.164970
$781$	−1.43085e15	−0.176203
$782$	−5.25080e15	−0.642079
$783$	−2.46546e14	−0.0299370
$784$	2.96197e14	0.0357143
$785$	5.46397e15	0.654222
$786$	1.75925e15	0.209172
$787$	7.51570e15	0.887377	0.443688	−	0.896181i	$-0.353670\pi$
$787$	7.51570e15	0.887377	0.443688	+	0.896181i	$0.353670\pi$
$788$	−7.72006e14	−0.0905162
$789$	2.22315e15	0.258848
$790$	1.96210e14	0.0226868
$791$	8.31325e14	0.0954553
$792$	9.59927e14	0.109459
$793$	−1.67416e16	−1.89581
$794$	7.61635e14	0.0856513
$795$	1.05057e15	0.117330
$796$	−3.98852e15	−0.442375
$797$	2.47331e14	0.0272432	0.0136216	−	0.999907i	$-0.495664\pi$
$797$	2.47331e14	0.0272432	0.0136216	+	0.999907i	$0.495664\pi$
$798$	−3.27704e14	−0.0358480
$799$	−2.42175e15	−0.263101
$800$	3.27680e14	0.0353553
$801$	7.90635e14	0.0847222
$802$	−5.91256e15	−0.629240
$803$	8.91543e15	0.942338
$804$	4.83261e14	0.0507310
$805$	2.97750e15	0.310438
$806$	−6.56656e15	−0.679978
$807$	2.55513e14	0.0262790
$808$	−3.35408e15	−0.342618
$809$	1.17402e16	1.19113	0.595564	−	0.803308i	$-0.296929\pi$
$809$	1.17402e16	1.19113	0.595564	+	0.803308i	$0.296929\pi$
$810$	3.48678e14	0.0351364
$811$	1.68265e16	1.68414	0.842072	−	0.539365i	$-0.181336\pi$
$811$	1.68265e16	1.68414	0.842072	+	0.539365i	$0.181336\pi$
$812$	−2.95712e14	−0.0293975
$813$	−4.53804e15	−0.448095
$814$	−4.86625e15	−0.477266
$815$	−3.86285e15	−0.376306
$816$	−7.37513e14	−0.0713631
$817$	−3.36059e15	−0.322993
$818$	−1.20204e16	−1.14756
$819$	1.69774e15	0.160994
$820$	−4.32626e15	−0.407508
$821$	1.41300e16	1.32207	0.661037	−	0.750353i	$-0.270116\pi$
$821$	1.41300e16	1.32207	0.661037	+	0.750353i	$0.270116\pi$
$822$	−4.66911e15	−0.433949
$823$	2.06859e16	1.90975	0.954873	−	0.297015i	$-0.0959913\pi$
$823$	2.06859e16	1.90975	0.954873	+	0.297015i	$0.0959913\pi$
$824$	−5.72556e14	−0.0525071
$825$	1.17729e15	0.107247
$826$	1.37177e15	0.124134
$827$	4.03864e15	0.363041	0.181520	−	0.983387i	$-0.441898\pi$
$827$	4.03864e15	0.363041	0.181520	+	0.983387i	$0.441898\pi$
$828$	3.42787e15	0.306096
$829$	−5.49340e15	−0.487294	−0.243647	−	0.969864i	$-0.578344\pi$
$829$	−5.49340e15	−0.487294	−0.243647	+	0.969864i	$0.578344\pi$
$830$	8.31418e14	0.0732639
$831$	6.69521e15	0.586082
$832$	1.83683e15	0.159731
$833$	−8.17606e14	−0.0706312
$834$	−1.68797e15	−0.144861
$835$	−1.92592e15	−0.164196
$836$	−1.27383e15	−0.107889
$837$	−1.72123e15	−0.144827
$838$	−9.58480e15	−0.801200
$839$	1.12948e16	0.937965	0.468982	−	0.883207i	$-0.344621\pi$
$839$	1.12948e16	0.937965	0.468982	+	0.883207i	$0.344621\pi$
$840$	4.18212e14	0.0345033
$841$	−1.19053e16	−0.975802
$842$	−8.19054e15	−0.666954
$843$	7.33418e15	0.593335
$844$	3.51917e15	0.282851
$845$	3.54456e15	0.283042
$846$	1.58099e15	0.125427
$847$	−6.58652e14	−0.0519155
$848$	1.45068e15	0.113604
$849$	−3.47203e15	−0.270141
$850$	−9.04511e14	−0.0699213
$851$	−1.73772e16	−1.33465
$852$	−7.17671e14	−0.0547656
$853$	2.76258e14	0.0209457	0.0104728	−	0.999945i	$-0.496666\pi$
$853$	2.76258e14	0.0209457	0.0104728	+	0.999945i	$0.496666\pi$
$854$	−5.26345e15	−0.396508
$855$	−4.62698e14	−0.0346325
$856$	3.23763e15	0.240781
$857$	−1.03136e16	−0.762105	−0.381052	−	0.924553i	$-0.624438\pi$
$857$	−1.03136e16	−0.762105	−0.381052	+	0.924553i	$0.624438\pi$
$858$	6.59934e15	0.484529
$859$	−1.01097e16	−0.737520	−0.368760	−	0.929525i	$-0.620218\pi$
$859$	−1.01097e16	−0.737520	−0.368760	+	0.929525i	$0.620218\pi$
$860$	4.28874e15	0.310877
$861$	−5.52153e15	−0.397687
$862$	−1.40725e16	−1.00712
$863$	−2.21303e16	−1.57372	−0.786860	−	0.617132i	$-0.788294\pi$
$863$	−2.21303e16	−1.57372	−0.786860	+	0.617132i	$0.788294\pi$
$864$	4.81469e14	0.0340207
$865$	9.30529e14	0.0653343
$866$	−1.53673e16	−1.07214
$867$	−6.29228e15	−0.436217
$868$	−2.06447e15	−0.142217
$869$	9.73414e14	0.0666329
$870$	−4.17528e14	−0.0284007
$871$	3.32233e15	0.224566
$872$	2.07342e15	0.139266
$873$	−9.99706e14	−0.0667258
$874$	−4.54880e15	−0.301706
$875$	5.12909e14	0.0338062
$876$	4.47170e15	0.292887
$877$	−2.19146e15	−0.142638	−0.0713191	−	0.997454i	$-0.522721\pi$
$877$	−2.19146e15	−0.142638	−0.0713191	+	0.997454i	$0.522721\pi$
$878$	1.86106e16	1.20376
$879$	4.04211e15	0.259818
$880$	1.62564e15	0.103841
$881$	−8.02603e15	−0.509487	−0.254743	−	0.967009i	$-0.581991\pi$
$881$	−8.02603e15	−0.509487	−0.254743	+	0.967009i	$0.581991\pi$
$882$	5.33756e14	0.0336718
$883$	9.26414e15	0.580793	0.290396	−	0.956906i	$-0.406213\pi$
$883$	9.26414e15	0.580793	0.290396	+	0.956906i	$0.406213\pi$
$884$	−5.07028e15	−0.315896
$885$	1.93685e15	0.119925
$886$	−1.75658e16	−1.08089
$887$	−1.23230e16	−0.753592	−0.376796	−	0.926296i	$-0.622974\pi$
$887$	−1.23230e16	−0.753592	−0.376796	+	0.926296i	$0.622974\pi$
$888$	−2.44076e15	−0.148338
$889$	8.72744e15	0.527141
$890$	1.33895e15	0.0803746
$891$	1.72982e15	0.103199
$892$	1.17592e16	0.697220
$893$	−2.09798e15	−0.123628
$894$	7.61056e14	0.0445718
$895$	5.06097e15	0.294583
$896$	5.77484e14	0.0334077
$897$	2.35660e16	1.35497
$898$	−1.20587e16	−0.689096
$899$	2.06110e15	0.117063
$900$	5.90490e14	0.0333333
$901$	−4.00437e15	−0.224671
$902$	−2.14629e16	−1.19689
$903$	5.47364e15	0.303385
$904$	1.62080e15	0.0892903
$905$	−6.20543e14	−0.0339786
$906$	−8.50559e15	−0.462913
$907$	−4.10687e15	−0.222162	−0.111081	−	0.993811i	$-0.535431\pi$
$907$	−4.10687e15	−0.222162	−0.111081	+	0.993811i	$0.535431\pi$
$908$	6.36239e15	0.342096
$909$	−6.04416e15	−0.323024
$910$	2.87514e15	0.152732
$911$	−1.18583e16	−0.626138	−0.313069	−	0.949730i	$-0.601357\pi$
$911$	−1.18583e16	−0.626138	−0.313069	+	0.949730i	$0.601357\pi$
$912$	−6.38912e14	−0.0335328
$913$	4.12473e15	0.215182
$914$	1.01636e16	0.527040
$915$	−7.43167e15	−0.383063
$916$	1.87370e15	0.0960007
$917$	3.80243e15	0.193655
$918$	−1.32902e15	−0.0672818
$919$	4.13291e15	0.207980	0.103990	−	0.994578i	$-0.466839\pi$
$919$	4.13291e15	0.207980	0.103990	+	0.994578i	$0.466839\pi$
$920$	5.80513e15	0.290388
$921$	−8.37504e15	−0.416446
$922$	−2.55429e16	−1.26255
$923$	−4.93387e15	−0.242426
$924$	2.07478e15	0.101339
$925$	−2.99343e15	−0.145341
$926$	−1.75717e16	−0.848114
$927$	−1.03176e15	−0.0495042
$928$	−5.76539e14	−0.0274989
$929$	5.30391e15	0.251484	0.125742	−	0.992063i	$-0.459869\pi$
$929$	5.30391e15	0.251484	0.125742	+	0.992063i	$0.459869\pi$
$930$	−2.91491e15	−0.137395
$931$	−7.08297e14	−0.0331888
$932$	−1.26679e16	−0.590090
$933$	2.11234e16	0.978173
$934$	−2.61888e15	−0.120561
$935$	−4.48734e15	−0.205365
$936$	3.31002e15	0.150596
$937$	−2.53212e16	−1.14529	−0.572646	−	0.819803i	$-0.694083\pi$
$937$	−2.53212e16	−1.14529	−0.572646	+	0.819803i	$0.694083\pi$
$938$	1.04452e15	0.0469677
$939$	−7.57972e15	−0.338838
$940$	2.67742e15	0.118991
$941$	−1.15457e15	−0.0510126	−0.0255063	−	0.999675i	$-0.508120\pi$
$941$	−1.15457e15	−0.0510126	−0.0255063	+	0.999675i	$0.508120\pi$
$942$	1.35961e16	0.597220
$943$	−7.66434e16	−3.34704
$944$	2.67448e15	0.116116
$945$	7.53631e14	0.0325300
$946$	2.12768e16	0.913071
$947$	−1.88371e16	−0.803690	−0.401845	−	0.915708i	$-0.631631\pi$
$947$	−1.88371e16	−0.803690	−0.401845	+	0.915708i	$0.631631\pi$
$948$	4.88234e14	0.0207101
$949$	3.07422e16	1.29649
$950$	−7.83583e14	−0.0328553
$951$	−5.33039e14	−0.0222211
$952$	−1.59406e15	−0.0660694
$953$	−8.66522e15	−0.357083	−0.178541	−	0.983932i	$-0.557138\pi$
$953$	−8.66522e15	−0.357083	−0.178541	+	0.983932i	$0.557138\pi$
$954$	2.61417e15	0.107107
$955$	1.76335e16	0.718322
$956$	2.95399e15	0.119644
$957$	−2.07139e15	−0.0834152
$958$	−1.41496e16	−0.566544
$959$	−1.00918e16	−0.401759
$960$	8.15373e14	0.0322749
$961$	−1.10192e16	−0.433682
$962$	−1.67798e16	−0.656635
$963$	5.83432e15	0.227010
$964$	4.84456e15	0.187426
$965$	9.69115e15	0.372799
$966$	7.40898e15	0.283390
$967$	1.26740e16	0.482022	0.241011	−	0.970522i	$-0.422521\pi$
$967$	1.26740e16	0.482022	0.241011	+	0.970522i	$0.422521\pi$
$968$	−1.28415e15	−0.0485625
$969$	1.76362e15	0.0663169
$970$	−1.69301e15	−0.0633017
$971$	−3.09799e16	−1.15179	−0.575897	−	0.817523i	$-0.695347\pi$
$971$	−3.09799e16	−1.15179	−0.575897	+	0.817523i	$0.695347\pi$
$972$	8.67624e14	0.0320750
$973$	−3.64838e15	−0.134115
$974$	2.18231e16	0.797706
$975$	4.05952e15	0.147553
$976$	−1.02619e16	−0.370899
$977$	1.45630e16	0.523396	0.261698	−	0.965150i	$-0.415718\pi$
$977$	1.45630e16	0.523396	0.261698	+	0.965150i	$0.415718\pi$
$978$	−9.61201e15	−0.343519
$979$	6.64262e15	0.236067
$980$	9.03921e14	0.0319438
$981$	3.73637e15	0.131302
$982$	−2.32509e16	−0.812505
$983$	−1.90451e16	−0.661820	−0.330910	−	0.943662i	$-0.607356\pi$
$983$	−1.90451e16	−0.661820	−0.330910	+	0.943662i	$0.607356\pi$
$984$	−1.07651e16	−0.372003
$985$	−2.35597e15	−0.0809601
$986$	1.59145e15	0.0543838
$987$	3.41714e15	0.116123
$988$	−4.39241e15	−0.148436
$989$	7.59788e16	2.55336
$990$	2.92946e15	0.0979027
$991$	−9.74803e15	−0.323975	−0.161988	−	0.986793i	$-0.551790\pi$
$991$	−9.74803e15	−0.323975	−0.161988	+	0.986793i	$0.551790\pi$
$992$	−4.02503e15	−0.133032
$993$	2.84110e15	0.0933826
$994$	−1.55117e15	−0.0507031
$995$	−1.21720e16	−0.395672
$996$	2.06883e15	0.0668805
$997$	−1.75038e16	−0.562741	−0.281371	−	0.959599i	$-0.590789\pi$
$997$	−1.75038e16	−0.562741	−0.281371	+	0.959599i	$0.590789\pi$
$998$	−8.60774e15	−0.275214
$999$	−4.39833e15	−0.139855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.12.a.p.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.12.a.p.1.3	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	210.a (trivial)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +100000. q^{10} +496107. q^{11} +248832. q^{12} +1.71068e6 q^{13} +537824. q^{14} +759375. q^{15} +1.04858e6 q^{16} -2.89443e6 q^{17} +1.88957e6 q^{18} -2.50747e6 q^{19} +3.20000e6 q^{20} +4.08410e6 q^{21} +1.58754e7 q^{22} +5.66907e7 q^{23} +7.96262e6 q^{24} +9.76562e6 q^{25} +5.47417e7 q^{26} +1.43489e7 q^{27} +1.72104e7 q^{28} -1.71822e7 q^{29} +2.43000e7 q^{30} -1.19955e8 q^{31} +3.35544e7 q^{32} +1.20554e8 q^{33} -9.26219e7 q^{34} +5.25219e7 q^{35} +6.04662e7 q^{36} -3.06527e8 q^{37} -8.02389e7 q^{38} +4.15695e8 q^{39} +1.02400e8 q^{40} -1.35196e9 q^{41} +1.30691e8 q^{42} +1.34023e9 q^{43} +5.08014e8 q^{44} +1.84528e8 q^{45} +1.81410e9 q^{46} +8.36693e8 q^{47} +2.54804e8 q^{48} +2.82475e8 q^{49} +3.12500e8 q^{50} -7.03348e8 q^{51} +1.75173e9 q^{52} +1.38347e9 q^{53} +4.59165e8 q^{54} +1.55034e9 q^{55} +5.50732e8 q^{56} -6.09314e8 q^{57} -5.49831e8 q^{58} +2.55059e9 q^{59} +7.77600e8 q^{60} -9.78656e9 q^{61} -3.83857e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +5.34587e9 q^{65} +3.85773e9 q^{66} +1.94212e9 q^{67} -2.96390e9 q^{68} +1.37759e10 q^{69} +1.68070e9 q^{70} -2.88416e9 q^{71} +1.93492e9 q^{72} +1.79708e10 q^{73} -9.80886e9 q^{74} +2.37305e9 q^{75} -2.56764e9 q^{76} +8.33808e9 q^{77} +1.33022e10 q^{78} +1.96210e9 q^{79} +3.27680e9 q^{80} +3.48678e9 q^{81} -4.32626e10 q^{82} +8.31418e9 q^{83} +4.18212e9 q^{84} -9.04511e9 q^{85} +4.28874e10 q^{86} -4.17528e9 q^{87} +1.62564e10 q^{88} +1.33895e10 q^{89} +5.90490e9 q^{90} +2.87514e10 q^{91} +5.80513e10 q^{92} -2.91491e10 q^{93} +2.67742e10 q^{94} -7.83583e9 q^{95} +8.15373e9 q^{96} -1.69301e10 q^{97} +9.03921e9 q^{98} +2.92946e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 128 q^{2} + 972 q^{3} + 4096 q^{4} + 12500 q^{5} + 31104 q^{6} + 67228 q^{7} + 131072 q^{8} + 236196 q^{9}+O(q^{10}) \) 4 * q + 128 * q^2 + 972 * q^3 + 4096 * q^4 + 12500 * q^5 + 31104 * q^6 + 67228 * q^7 + 131072 * q^8 + 236196 * q^9	\( 4 q + 128 q^{2} + 972 q^{3} + 4096 q^{4} + 12500 q^{5} + 31104 q^{6} + 67228 q^{7} + 131072 q^{8} + 236196 q^{9} + 400000 q^{10} + 458260 q^{11} + 995328 q^{12} + 1574316 q^{13} + 2151296 q^{14} + 3037500 q^{15} + 4194304 q^{16} + 8678072 q^{17} + 7558272 q^{18} + 12442004 q^{19} + 12800000 q^{20} + 16336404 q^{21} + 14664320 q^{22} + 513088 q^{23} + 31850496 q^{24} + 39062500 q^{25} + 50378112 q^{26} + 57395628 q^{27} + 68841472 q^{28} + 58476696 q^{29} + 97200000 q^{30} + 145189572 q^{31} + 134217728 q^{32} + 111357180 q^{33} + 277698304 q^{34} + 210087500 q^{35} + 241864704 q^{36} + 340912752 q^{37} + 398144128 q^{38} + 382558788 q^{39} + 409600000 q^{40} + 915147368 q^{41} + 522764928 q^{42} + 462244024 q^{43} + 469258240 q^{44} + 738112500 q^{45} + 16418816 q^{46} + 901710040 q^{47} + 1019215872 q^{48} + 1129900996 q^{49} + 1250000000 q^{50} + 2108771496 q^{51} + 1612099584 q^{52} - 157945788 q^{53} + 1836660096 q^{54} + 1432062500 q^{55} + 2202927104 q^{56} + 3023406972 q^{57} + 1871254272 q^{58} + 2706989128 q^{59} + 3110400000 q^{60} + 8740846920 q^{61} + 4646066304 q^{62} + 3969746172 q^{63} + 4294967296 q^{64} + 4919737500 q^{65} + 3563429760 q^{66} + 5883134368 q^{67} + 8886345728 q^{68} + 124680384 q^{69} + 6722800000 q^{70} + 344015372 q^{71} + 7739670528 q^{72} + 10549706244 q^{73} + 10909208064 q^{74} + 9492187500 q^{75} + 12740612096 q^{76} + 7701975820 q^{77} + 12241881216 q^{78} - 430177976 q^{79} + 13107200000 q^{80} + 13947137604 q^{81} + 29284715776 q^{82} + 28504941432 q^{83} + 16728477696 q^{84} + 27118975000 q^{85} + 14791808768 q^{86} + 14209837128 q^{87} + 15016263680 q^{88} + 26763786680 q^{89} + 23619600000 q^{90} + 26459529012 q^{91} + 525402112 q^{92} + 35281065996 q^{93} + 28854721280 q^{94} + 38881262500 q^{95} + 32614907904 q^{96} + 62389990476 q^{97} + 36156831872 q^{98} + 27059794740 q^{99}+O(q^{100}) \) 4 * q + 128 * q^2 + 972 * q^3 + 4096 * q^4 + 12500 * q^5 + 31104 * q^6 + 67228 * q^7 + 131072 * q^8 + 236196 * q^9 + 400000 * q^10 + 458260 * q^11 + 995328 * q^12 + 1574316 * q^13 + 2151296 * q^14 + 3037500 * q^15 + 4194304 * q^16 + 8678072 * q^17 + 7558272 * q^18 + 12442004 * q^19 + 12800000 * q^20 + 16336404 * q^21 + 14664320 * q^22 + 513088 * q^23 + 31850496 * q^24 + 39062500 * q^25 + 50378112 * q^26 + 57395628 * q^27 + 68841472 * q^28 + 58476696 * q^29 + 97200000 * q^30 + 145189572 * q^31 + 134217728 * q^32 + 111357180 * q^33 + 277698304 * q^34 + 210087500 * q^35 + 241864704 * q^36 + 340912752 * q^37 + 398144128 * q^38 + 382558788 * q^39 + 409600000 * q^40 + 915147368 * q^41 + 522764928 * q^42 + 462244024 * q^43 + 469258240 * q^44 + 738112500 * q^45 + 16418816 * q^46 + 901710040 * q^47 + 1019215872 * q^48 + 1129900996 * q^49 + 1250000000 * q^50 + 2108771496 * q^51 + 1612099584 * q^52 - 157945788 * q^53 + 1836660096 * q^54 + 1432062500 * q^55 + 2202927104 * q^56 + 3023406972 * q^57 + 1871254272 * q^58 + 2706989128 * q^59 + 3110400000 * q^60 + 8740846920 * q^61 + 4646066304 * q^62 + 3969746172 * q^63 + 4294967296 * q^64 + 4919737500 * q^65 + 3563429760 * q^66 + 5883134368 * q^67 + 8886345728 * q^68 + 124680384 * q^69 + 6722800000 * q^70 + 344015372 * q^71 + 7739670528 * q^72 + 10549706244 * q^73 + 10909208064 * q^74 + 9492187500 * q^75 + 12740612096 * q^76 + 7701975820 * q^77 + 12241881216 * q^78 - 430177976 * q^79 + 13107200000 * q^80 + 13947137604 * q^81 + 29284715776 * q^82 + 28504941432 * q^83 + 16728477696 * q^84 + 27118975000 * q^85 + 14791808768 * q^86 + 14209837128 * q^87 + 15016263680 * q^88 + 26763786680 * q^89 + 23619600000 * q^90 + 26459529012 * q^91 + 525402112 * q^92 + 35281065996 * q^93 + 28854721280 * q^94 + 38881262500 * q^95 + 32614907904 * q^96 + 62389990476 * q^97 + 36156831872 * q^98 + 27059794740 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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