LMFDB - Embedded newform 210.12.a.p.1.1

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			1.1
Root			$-14006.7$ 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)

$f(q)$	$=$	$q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +100000. q^{10} -802239. q^{11} +248832. q^{12} +1.29587e6 q^{13} +537824. q^{14} +759375. q^{15} +1.04858e6 q^{16} +4.53027e6 q^{17} +1.88957e6 q^{18} +2.73535e6 q^{19} +3.20000e6 q^{20} +4.08410e6 q^{21} -2.56717e7 q^{22} -2.07220e7 q^{23} +7.96262e6 q^{24} +9.76562e6 q^{25} +4.14677e7 q^{26} +1.43489e7 q^{27} +1.72104e7 q^{28} +3.95764e7 q^{29} +2.43000e7 q^{30} -8.36867e7 q^{31} +3.35544e7 q^{32} -1.94944e8 q^{33} +1.44969e8 q^{34} +5.25219e7 q^{35} +6.04662e7 q^{36} +4.45436e8 q^{37} +8.75313e7 q^{38} +3.14896e8 q^{39} +1.02400e8 q^{40} +1.42524e9 q^{41} +1.30691e8 q^{42} +1.63135e9 q^{43} -8.21493e8 q^{44} +1.84528e8 q^{45} -6.63104e8 q^{46} -1.57401e9 q^{47} +2.54804e8 q^{48} +2.82475e8 q^{49} +3.12500e8 q^{50} +1.10086e9 q^{51} +1.32697e9 q^{52} -4.33453e9 q^{53} +4.59165e8 q^{54} -2.50700e9 q^{55} +5.50732e8 q^{56} +6.64691e8 q^{57} +1.26645e9 q^{58} +3.95434e9 q^{59} +7.77600e8 q^{60} +9.07018e9 q^{61} -2.67797e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +4.04958e9 q^{65} -6.23821e9 q^{66} +4.11278e9 q^{67} +4.63899e9 q^{68} -5.03544e9 q^{69} +1.68070e9 q^{70} -2.60303e10 q^{71} +1.93492e9 q^{72} +3.40816e10 q^{73} +1.42539e10 q^{74} +2.37305e9 q^{75} +2.80100e9 q^{76} -1.34832e10 q^{77} +1.00767e10 q^{78} -3.82352e10 q^{79} +3.27680e9 q^{80} +3.48678e9 q^{81} +4.56076e10 q^{82} +4.93129e10 q^{83} +4.18212e9 q^{84} +1.41571e10 q^{85} +5.22033e10 q^{86} +9.61707e9 q^{87} -2.62878e10 q^{88} -2.47455e10 q^{89} +5.90490e9 q^{90} +2.17796e10 q^{91} -2.12193e10 q^{92} -2.03359e10 q^{93} -5.03684e10 q^{94} +8.54798e9 q^{95} +8.15373e9 q^{96} +9.83294e10 q^{97} +9.03921e9 q^{98} -4.73714e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	−802239.	−1.50191	−0.750956	−	0.660353i	$-0.770407\pi$
$11$	−802239.	−1.50191	−0.750956	+	0.660353i	$0.770407\pi$
$12$	248832.	0.288675
$13$	1.29587e6	0.967993	0.483996	−	0.875070i	$-0.339185\pi$
$13$	1.29587e6	0.967993	0.483996	+	0.875070i	$0.339185\pi$
$14$	537824.	0.267261
$15$	759375.	0.258199
$16$	1.04858e6	0.250000
$17$	4.53027e6	0.773847	0.386923	−	0.922112i	$-0.373538\pi$
$17$	4.53027e6	0.773847	0.386923	+	0.922112i	$0.373538\pi$
$18$	1.88957e6	0.235702
$19$	2.73535e6	0.253436	0.126718	−	0.991939i	$-0.459556\pi$
$19$	2.73535e6	0.253436	0.126718	+	0.991939i	$0.459556\pi$
$20$	3.20000e6	0.223607
$21$	4.08410e6	0.218218
$22$	−2.56717e7	−1.06201
$23$	−2.07220e7	−0.671318	−0.335659	−	0.941984i	$-0.608959\pi$
$23$	−2.07220e7	−0.671318	−0.335659	+	0.941984i	$0.608959\pi$
$24$	7.96262e6	0.204124
$25$	9.76562e6	0.200000
$26$	4.14677e7	0.684474
$27$	1.43489e7	0.192450
$28$	1.72104e7	0.188982
$29$	3.95764e7	0.358300	0.179150	−	0.983822i	$-0.442665\pi$
$29$	3.95764e7	0.358300	0.179150	+	0.983822i	$0.442665\pi$
$30$	2.43000e7	0.182574
$31$	−8.36867e7	−0.525010	−0.262505	−	0.964931i	$-0.584549\pi$
$31$	−8.36867e7	−0.525010	−0.262505	+	0.964931i	$0.584549\pi$
$32$	3.35544e7	0.176777
$33$	−1.94944e8	−0.867129
$34$	1.44969e8	0.547192
$35$	5.25219e7	0.169031
$36$	6.04662e7	0.166667
$37$	4.45436e8	1.05603	0.528014	−	0.849236i	$-0.322937\pi$
$37$	4.45436e8	1.05603	0.528014	+	0.849236i	$0.322937\pi$
$38$	8.75313e7	0.179207
$39$	3.14896e8	0.558871
$40$	1.02400e8	0.158114
$41$	1.42524e9	1.92121	0.960607	−	0.277911i	$-0.0896422\pi$
$41$	1.42524e9	1.92121	0.960607	+	0.277911i	$0.0896422\pi$
$42$	1.30691e8	0.154303
$43$	1.63135e9	1.69228	0.846139	−	0.532962i	$-0.178921\pi$
$43$	1.63135e9	1.69228	0.846139	+	0.532962i	$0.178921\pi$
$44$	−8.21493e8	−0.750956
$45$	1.84528e8	0.149071
$46$	−6.63104e8	−0.474694
$47$	−1.57401e9	−1.00108	−0.500541	−	0.865713i	$-0.666866\pi$
$47$	−1.57401e9	−1.00108	−0.500541	+	0.865713i	$0.666866\pi$
$48$	2.54804e8	0.144338
$49$	2.82475e8	0.142857
$50$	3.12500e8	0.141421
$51$	1.10086e9	0.446781
$52$	1.32697e9	0.483996
$53$	−4.33453e9	−1.42372	−0.711861	−	0.702320i	$-0.752147\pi$
$53$	−4.33453e9	−1.42372	−0.711861	+	0.702320i	$0.752147\pi$
$54$	4.59165e8	0.136083
$55$	−2.50700e9	−0.671675
$56$	5.50732e8	0.133631
$57$	6.64691e8	0.146322
$58$	1.26645e9	0.253357
$59$	3.95434e9	0.720092	0.360046	−	0.932935i	$-0.382761\pi$
$59$	3.95434e9	0.720092	0.360046	+	0.932935i	$0.382761\pi$
$60$	7.77600e8	0.129099
$61$	9.07018e9	1.37500	0.687499	−	0.726185i	$-0.258709\pi$
$61$	9.07018e9	1.37500	0.687499	+	0.726185i	$0.258709\pi$
$62$	−2.67797e9	−0.371238
$63$	9.92437e8	0.125988
$64$	1.07374e9	0.125000
$65$	4.04958e9	0.432899
$66$	−6.23821e9	−0.613153
$67$	4.11278e9	0.372155	0.186078	−	0.982535i	$-0.440422\pi$
$67$	4.11278e9	0.372155	0.186078	+	0.982535i	$0.440422\pi$
$68$	4.63899e9	0.386923
$69$	−5.03544e9	−0.387586
$70$	1.68070e9	0.119523
$71$	−2.60303e10	−1.71222	−0.856108	−	0.516797i	$-0.827124\pi$
$71$	−2.60303e10	−1.71222	−0.856108	+	0.516797i	$0.827124\pi$
$72$	1.93492e9	0.117851
$73$	3.40816e10	1.92417	0.962087	−	0.272742i	$-0.0879305\pi$
$73$	3.40816e10	1.92417	0.962087	+	0.272742i	$0.0879305\pi$
$74$	1.42539e10	0.746725
$75$	2.37305e9	0.115470
$76$	2.80100e9	0.126718
$77$	−1.34832e10	−0.567669
$78$	1.00767e10	0.395181
$79$	−3.82352e10	−1.39802	−0.699012	−	0.715110i	$-0.746376\pi$
$79$	−3.82352e10	−1.39802	−0.699012	+	0.715110i	$0.746376\pi$
$80$	3.27680e9	0.111803
$81$	3.48678e9	0.111111
$82$	4.56076e10	1.35850
$83$	4.93129e10	1.37414	0.687071	−	0.726591i	$-0.258896\pi$
$83$	4.93129e10	1.37414	0.687071	+	0.726591i	$0.258896\pi$
$84$	4.18212e9	0.109109
$85$	1.41571e10	0.346075
$86$	5.22033e10	1.19662
$87$	9.61707e9	0.206865
$88$	−2.62878e10	−0.531006
$89$	−2.47455e10	−0.469732	−0.234866	−	0.972028i	$-0.575465\pi$
$89$	−2.47455e10	−0.469732	−0.234866	+	0.972028i	$0.575465\pi$
$90$	5.90490e9	0.105409
$91$	2.17796e10	0.365867
$92$	−2.12193e10	−0.335659
$93$	−2.03359e10	−0.303114
$94$	−5.03684e10	−0.707872
$95$	8.54798e9	0.113340
$96$	8.15373e9	0.102062
$97$	9.83294e10	1.16262	0.581311	−	0.813681i	$-0.302540\pi$
$97$	9.83294e10	1.16262	0.581311	+	0.813681i	$0.302540\pi$
$98$	9.03921e9	0.101015
$99$	−4.73714e10	−0.500637
$100$	1.00000e10	0.100000
$101$	4.05796e10	0.384184	0.192092	−	0.981377i	$-0.438473\pi$
$101$	4.05796e10	0.384184	0.192092	+	0.981377i	$0.438473\pi$
$102$	3.52274e10	0.315922
$103$	1.21733e10	0.103467	0.0517336	−	0.998661i	$-0.483525\pi$
$103$	1.21733e10	0.103467	0.0517336	+	0.998661i	$0.483525\pi$
$104$	4.24630e10	0.342237
$105$	1.27628e10	0.0975900
$106$	−1.38705e11	−1.00672
$107$	−1.63643e11	−1.12794	−0.563972	−	0.825794i	$-0.690727\pi$
$107$	−1.63643e11	−1.12794	−0.563972	+	0.825794i	$0.690727\pi$
$108$	1.46933e10	0.0962250
$109$	−2.80323e11	−1.74507	−0.872535	−	0.488551i	$-0.837526\pi$
$109$	−2.80323e11	−1.74507	−0.872535	+	0.488551i	$0.837526\pi$
$110$	−8.02239e10	−0.474946
$111$	1.08241e11	0.609698
$112$	1.76234e10	0.0944911
$113$	3.81618e11	1.94849	0.974244	−	0.225499i	$-0.0724011\pi$
$113$	3.81618e11	1.94849	0.974244	+	0.225499i	$0.0724011\pi$
$114$	2.12701e10	0.103465
$115$	−6.47562e10	−0.300223
$116$	4.05262e10	0.179150
$117$	7.65197e10	0.322664
$118$	1.26539e11	0.509182
$119$	7.61402e10	0.292487
$120$	2.48832e10	0.0912871
$121$	3.58277e11	1.25574
$122$	2.90246e11	0.972270
$123$	3.46332e11	1.10921
$124$	−8.56952e10	−0.262505
$125$	3.05176e10	0.0894427
$126$	3.17580e10	0.0890871
$127$	−3.71024e11	−0.996511	−0.498255	−	0.867030i	$-0.666026\pi$
$127$	−3.71024e11	−0.996511	−0.498255	+	0.867030i	$0.666026\pi$
$128$	3.43597e10	0.0883883
$129$	3.96419e11	0.977037
$130$	1.29587e11	0.306106
$131$	−6.74168e11	−1.52678	−0.763390	−	0.645938i	$-0.776466\pi$
$131$	−6.74168e11	−1.52678	−0.763390	+	0.645938i	$0.776466\pi$
$132$	−1.99623e11	−0.433564
$133$	4.59731e10	0.0957899
$134$	1.31609e11	0.263154
$135$	4.48403e10	0.0860663
$136$	1.48448e11	0.273596
$137$	8.17540e11	1.44726	0.723629	−	0.690189i	$-0.242473\pi$
$137$	8.17540e11	1.44726	0.723629	+	0.690189i	$0.242473\pi$
$138$	−1.61134e11	−0.274064
$139$	9.75718e11	1.59493	0.797467	−	0.603362i	$-0.206173\pi$
$139$	9.75718e11	1.59493	0.797467	+	0.603362i	$0.206173\pi$
$140$	5.37824e10	0.0845154
$141$	−3.82485e11	−0.577975
$142$	−8.32970e11	−1.21072
$143$	−1.03960e12	−1.45384
$144$	6.19174e10	0.0833333
$145$	1.23676e11	0.160237
$146$	1.09061e12	1.36060
$147$	6.86415e10	0.0824786
$148$	4.56126e11	0.528014
$149$	−8.13920e11	−0.907940	−0.453970	−	0.891017i	$-0.649993\pi$
$149$	−8.13920e11	−0.907940	−0.453970	+	0.891017i	$0.649993\pi$
$150$	7.59375e10	0.0816497
$151$	5.08360e11	0.526985	0.263492	−	0.964662i	$-0.415126\pi$
$151$	5.08360e11	0.526985	0.263492	+	0.964662i	$0.415126\pi$
$152$	8.96321e10	0.0896033
$153$	2.67508e11	0.257949
$154$	−4.31464e11	−0.401403
$155$	−2.61521e11	−0.234791
$156$	3.22453e11	0.279435
$157$	2.64108e11	0.220970	0.110485	−	0.993878i	$-0.464760\pi$
$157$	2.64108e11	0.220970	0.110485	+	0.993878i	$0.464760\pi$
$158$	−1.22353e12	−0.988552
$159$	−1.05329e12	−0.821986
$160$	1.04858e11	0.0790569
$161$	−3.48274e11	−0.253734
$162$	1.11577e11	0.0785674
$163$	−2.22290e11	−0.151317	−0.0756584	−	0.997134i	$-0.524106\pi$
$163$	−2.22290e11	−0.151317	−0.0756584	+	0.997134i	$0.524106\pi$
$164$	1.45944e12	0.960607
$165$	−6.09201e11	−0.387792
$166$	1.57801e12	0.971665
$167$	2.18784e11	0.130339	0.0651697	−	0.997874i	$-0.479241\pi$
$167$	2.18784e11	0.130339	0.0651697	+	0.997874i	$0.479241\pi$
$168$	1.33828e11	0.0771517
$169$	−1.12889e11	−0.0629904
$170$	4.53027e11	0.244712
$171$	1.61520e11	0.0844788
$172$	1.67051e12	0.846139
$173$	1.23399e12	0.605421	0.302711	−	0.953082i	$-0.402108\pi$
$173$	1.23399e12	0.605421	0.302711	+	0.953082i	$0.402108\pi$
$174$	3.07746e11	0.146276
$175$	1.64131e11	0.0755929
$176$	−8.41209e11	−0.375478
$177$	9.60905e11	0.415745
$178$	−7.91855e11	−0.332151
$179$	1.58185e12	0.643388	0.321694	−	0.946844i	$-0.395748\pi$
$179$	1.58185e12	0.643388	0.321694	+	0.946844i	$0.395748\pi$
$180$	1.88957e11	0.0745356
$181$	2.76554e12	1.05815	0.529076	−	0.848574i	$-0.322539\pi$
$181$	2.76554e12	1.05815	0.529076	+	0.848574i	$0.322539\pi$
$182$	6.96948e11	0.258707
$183$	2.20405e12	0.793855
$184$	−6.79018e11	−0.237347
$185$	1.39199e12	0.472270
$186$	−6.50748e11	−0.214334
$187$	−3.63436e12	−1.16225
$188$	−1.61179e12	−0.500541
$189$	2.41162e11	0.0727393
$190$	2.73535e11	0.0801436
$191$	−5.61643e12	−1.59874	−0.799368	−	0.600841i	$-0.794832\pi$
$191$	−5.61643e12	−1.59874	−0.799368	+	0.600841i	$0.794832\pi$
$192$	2.60919e11	0.0721688
$193$	1.52127e12	0.408921	0.204461	−	0.978875i	$-0.434456\pi$
$193$	1.52127e12	0.408921	0.204461	+	0.978875i	$0.434456\pi$
$194$	3.14654e12	0.822099
$195$	9.84049e11	0.249935
$196$	2.89255e11	0.0714286
$197$	5.29870e12	1.27234	0.636172	−	0.771547i	$-0.280517\pi$
$197$	5.29870e12	1.27234	0.636172	+	0.771547i	$0.280517\pi$
$198$	−1.51589e12	−0.354004
$199$	6.78650e12	1.54154	0.770769	−	0.637115i	$-0.219872\pi$
$199$	6.78650e12	1.54154	0.770769	+	0.637115i	$0.219872\pi$
$200$	3.20000e11	0.0707107
$201$	9.99406e11	0.214864
$202$	1.29855e12	0.271659
$203$	6.65161e11	0.135425
$204$	1.12728e12	0.223390
$205$	4.45386e12	0.859193
$206$	3.89545e11	0.0731623
$207$	−1.22361e12	−0.223773
$208$	1.35882e12	0.241998
$209$	−2.19441e12	−0.380639
$210$	4.08410e11	0.0690066
$211$	−1.13489e13	−1.86810	−0.934049	−	0.357145i	$-0.883750\pi$
$211$	−1.13489e13	−1.86810	−0.934049	+	0.357145i	$0.883750\pi$
$212$	−4.43856e12	−0.711861
$213$	−6.32537e12	−0.988548
$214$	−5.23658e12	−0.797576
$215$	5.09798e12	0.756810
$216$	4.70185e11	0.0680414
$217$	−1.40652e12	−0.198435
$218$	−8.97034e12	−1.23395
$219$	8.28183e12	1.11092
$220$	−2.56717e12	−0.335838
$221$	5.87063e12	0.749078
$222$	3.46371e12	0.431122
$223$	−1.40334e12	−0.170406	−0.0852031	−	0.996364i	$-0.527154\pi$
$223$	−1.40334e12	−0.170406	−0.0852031	+	0.996364i	$0.527154\pi$
$224$	5.63949e11	0.0668153
$225$	5.76650e11	0.0666667
$226$	1.22118e13	1.37779
$227$	4.57649e12	0.503954	0.251977	−	0.967733i	$-0.418919\pi$
$227$	4.57649e12	0.503954	0.251977	+	0.967733i	$0.418919\pi$
$228$	6.80644e11	0.0731608
$229$	−1.14316e13	−1.19954	−0.599768	−	0.800174i	$-0.704741\pi$
$229$	−1.14316e13	−1.19954	−0.599768	+	0.800174i	$0.704741\pi$
$230$	−2.07220e12	−0.212289
$231$	−3.27643e12	−0.327744
$232$	1.29684e12	0.126678
$233$	1.41109e13	1.34616	0.673082	−	0.739568i	$-0.264970\pi$
$233$	1.41109e13	1.34616	0.673082	+	0.739568i	$0.264970\pi$
$234$	2.44863e12	0.228158
$235$	−4.91879e12	−0.447698
$236$	4.04924e12	0.360046
$237$	−9.29115e12	−0.807149
$238$	2.43649e12	0.206819
$239$	1.26704e13	1.05100	0.525500	−	0.850794i	$-0.323878\pi$
$239$	1.26704e13	1.05100	0.525500	+	0.850794i	$0.323878\pi$
$240$	7.96262e11	0.0645497
$241$	5.54333e12	0.439215	0.219608	−	0.975588i	$-0.429522\pi$
$241$	5.54333e12	0.439215	0.219608	+	0.975588i	$0.429522\pi$
$242$	1.14648e13	0.887940
$243$	8.47289e11	0.0641500
$244$	9.28787e12	0.687499
$245$	8.82735e11	0.0638877
$246$	1.10826e13	0.784332
$247$	3.54466e12	0.245324
$248$	−2.74225e12	−0.185619
$249$	1.19830e13	0.793361
$250$	9.76562e11	0.0632456
$251$	−2.64538e12	−0.167603	−0.0838017	−	0.996482i	$-0.526706\pi$
$251$	−2.64538e12	−0.167603	−0.0838017	+	0.996482i	$0.526706\pi$
$252$	1.01626e12	0.0629941
$253$	1.66240e13	1.00826
$254$	−1.18728e13	−0.704640
$255$	3.44017e12	0.199806
$256$	1.09951e12	0.0625000
$257$	9.51573e11	0.0529432	0.0264716	−	0.999650i	$-0.491573\pi$
$257$	9.51573e11	0.0529432	0.0264716	+	0.999650i	$0.491573\pi$
$258$	1.26854e13	0.690870
$259$	7.48644e12	0.399141
$260$	4.14677e12	0.216450
$261$	2.33695e12	0.119433
$262$	−2.15734e13	−1.07960
$263$	3.59891e12	0.176366	0.0881829	−	0.996104i	$-0.471894\pi$
$263$	3.59891e12	0.176366	0.0881829	+	0.996104i	$0.471894\pi$
$264$	−6.38793e12	−0.306576
$265$	−1.35454e13	−0.636708
$266$	1.47114e12	0.0677337
$267$	−6.01315e12	−0.271200
$268$	4.21149e12	0.186078
$269$	−2.37982e13	−1.03016	−0.515082	−	0.857141i	$-0.672239\pi$
$269$	−2.37982e13	−1.03016	−0.515082	+	0.857141i	$0.672239\pi$
$270$	1.43489e12	0.0608581
$271$	1.20434e13	0.500516	0.250258	−	0.968179i	$-0.419485\pi$
$271$	1.20434e13	0.500516	0.250258	+	0.968179i	$0.419485\pi$
$272$	4.75033e12	0.193462
$273$	5.29245e12	0.211233
$274$	2.61613e13	1.02337
$275$	−7.83437e12	−0.300382
$276$	−5.15629e12	−0.193793
$277$	−2.43659e13	−0.897725	−0.448863	−	0.893601i	$-0.648171\pi$
$277$	−2.43659e13	−0.897725	−0.448863	+	0.893601i	$0.648171\pi$
$278$	3.12230e13	1.12779
$279$	−4.94162e12	−0.175003
$280$	1.72104e12	0.0597614
$281$	−3.47053e12	−0.118171	−0.0590855	−	0.998253i	$-0.518818\pi$
$281$	−3.47053e12	−0.118171	−0.0590855	+	0.998253i	$0.518818\pi$
$282$	−1.22395e13	−0.408690
$283$	3.34340e13	1.09487	0.547436	−	0.836848i	$-0.315604\pi$
$283$	3.34340e13	1.09487	0.547436	+	0.836848i	$0.315604\pi$
$284$	−2.66550e13	−0.856108
$285$	2.07716e12	0.0654370
$286$	−3.32671e13	−1.02802
$287$	2.39539e13	0.726150
$288$	1.98136e12	0.0589256
$289$	−1.37486e13	−0.401161
$290$	3.95764e12	0.113305
$291$	2.38940e13	0.671241
$292$	3.48996e13	0.962087
$293$	−1.36235e13	−0.368567	−0.184283	−	0.982873i	$-0.558996\pi$
$293$	−1.36235e13	−0.368567	−0.184283	+	0.982873i	$0.558996\pi$
$294$	2.19653e12	0.0583212
$295$	1.23573e13	0.322035
$296$	1.45960e13	0.373362
$297$	−1.15113e13	−0.289043
$298$	−2.60454e13	−0.642011
$299$	−2.68529e13	−0.649831
$300$	2.43000e12	0.0577350
$301$	2.74182e13	0.639621
$302$	1.62675e13	0.372634
$303$	9.86083e12	0.221809
$304$	2.86823e12	0.0633591
$305$	2.83443e13	0.614918
$306$	8.56025e12	0.182397
$307$	3.08085e13	0.644778	0.322389	−	0.946607i	$-0.395514\pi$
$307$	3.08085e13	0.644778	0.322389	+	0.946607i	$0.395514\pi$
$308$	−1.38068e13	−0.283835
$309$	2.95811e12	0.0597368
$310$	−8.36867e12	−0.166023
$311$	8.51097e13	1.65881	0.829406	−	0.558646i	$-0.188679\pi$
$311$	8.51097e13	1.65881	0.829406	+	0.558646i	$0.188679\pi$
$312$	1.03185e13	0.197591
$313$	3.50826e13	0.660082	0.330041	−	0.943967i	$-0.392937\pi$
$313$	3.50826e13	0.660082	0.330041	+	0.943967i	$0.392937\pi$
$314$	8.45145e12	0.156249
$315$	3.10136e12	0.0563436
$316$	−3.91528e13	−0.699012
$317$	6.38797e13	1.12082	0.560411	−	0.828215i	$-0.310643\pi$
$317$	6.38797e13	1.12082	0.560411	+	0.828215i	$0.310643\pi$
$318$	−3.37053e13	−0.581232
$319$	−3.17498e13	−0.538136
$320$	3.35544e12	0.0559017
$321$	−3.97653e13	−0.651218
$322$	−1.11448e13	−0.179417
$323$	1.23919e13	0.196121
$324$	3.57047e12	0.0555556
$325$	1.26550e13	0.193599
$326$	−7.11327e12	−0.106997
$327$	−6.81185e13	−1.00752
$328$	4.67021e13	0.679252
$329$	−2.64544e13	−0.378374
$330$	−1.94944e13	−0.274210
$331$	1.71826e13	0.237702	0.118851	−	0.992912i	$-0.462079\pi$
$331$	1.71826e13	0.237702	0.118851	+	0.992912i	$0.462079\pi$
$332$	5.04965e13	0.687071
$333$	2.63025e13	0.352009
$334$	7.00110e12	0.0921639
$335$	1.28524e13	0.166433
$336$	4.28249e12	0.0545545
$337$	−3.65494e13	−0.458053	−0.229026	−	0.973420i	$-0.573554\pi$
$337$	−3.65494e13	−0.458053	−0.229026	+	0.973420i	$0.573554\pi$
$338$	−3.61245e12	−0.0445410
$339$	9.27332e13	1.12496
$340$	1.44969e13	0.173037
$341$	6.71368e13	0.788518
$342$	5.16864e12	0.0597355
$343$	4.74756e12	0.0539949
$344$	5.34562e13	0.598311
$345$	−1.57358e13	−0.173334
$346$	3.94877e13	0.428098
$347$	−1.55119e14	−1.65521	−0.827606	−	0.561310i	$-0.810298\pi$
$347$	−1.55119e14	−1.65521	−0.827606	+	0.561310i	$0.810298\pi$
$348$	9.84788e12	0.103432
$349$	−1.43948e14	−1.48822	−0.744110	−	0.668057i	$-0.767126\pi$
$349$	−1.43948e14	−1.48822	−0.744110	+	0.668057i	$0.767126\pi$
$350$	5.25219e12	0.0534522
$351$	1.85943e13	0.186290
$352$	−2.69187e13	−0.265503
$353$	−6.28705e13	−0.610501	−0.305250	−	0.952272i	$-0.598740\pi$
$353$	−6.28705e13	−0.610501	−0.305250	+	0.952272i	$0.598740\pi$
$354$	3.07489e13	0.293976
$355$	−8.13447e13	−0.765726
$356$	−2.53394e13	−0.234866
$357$	1.85021e13	0.168867
$358$	5.06191e13	0.454944
$359$	−8.77892e13	−0.777001	−0.388501	−	0.921448i	$-0.627007\pi$
$359$	−8.77892e13	−0.777001	−0.388501	+	0.921448i	$0.627007\pi$
$360$	6.04662e12	0.0527046
$361$	−1.09008e14	−0.935770
$362$	8.84973e13	0.748226
$363$	8.70612e13	0.725000
$364$	2.23023e13	0.182933
$365$	1.06505e14	0.860517
$366$	7.05298e13	0.561341
$367$	1.83489e13	0.143862	0.0719311	−	0.997410i	$-0.477084\pi$
$367$	1.83489e13	0.143862	0.0719311	+	0.997410i	$0.477084\pi$
$368$	−2.17286e13	−0.167830
$369$	8.41588e13	0.640404
$370$	4.45436e13	0.333945
$371$	−7.28505e13	−0.538116
$372$	−2.08239e13	−0.151557
$373$	−2.71056e14	−1.94384	−0.971920	−	0.235312i	$-0.924389\pi$
$373$	−2.71056e14	−1.94384	−0.971920	+	0.235312i	$0.924389\pi$
$374$	−1.16300e14	−0.821834
$375$	7.41577e12	0.0516398
$376$	−5.15772e13	−0.353936
$377$	5.12858e13	0.346832
$378$	7.71719e12	0.0514344
$379$	−1.80900e14	−1.18829	−0.594145	−	0.804358i	$-0.702509\pi$
$379$	−1.80900e14	−1.18829	−0.594145	+	0.804358i	$0.702509\pi$
$380$	8.75313e12	0.0566701
$381$	−9.01589e13	−0.575336
$382$	−1.79726e14	−1.13048
$383$	7.41744e12	0.0459897	0.0229949	−	0.999736i	$-0.492680\pi$
$383$	7.41744e12	0.0459897	0.0229949	+	0.999736i	$0.492680\pi$
$384$	8.34942e12	0.0510310
$385$	−4.21351e13	−0.253869
$386$	4.86805e13	0.289151
$387$	9.63298e13	0.564093
$388$	1.00689e14	0.581311
$389$	2.19156e14	1.24747	0.623735	−	0.781636i	$-0.285614\pi$
$389$	2.19156e14	1.24747	0.623735	+	0.781636i	$0.285614\pi$
$390$	3.14896e13	0.176730
$391$	−9.38762e13	−0.519497
$392$	9.25615e12	0.0505076
$393$	−1.63823e14	−0.881486
$394$	1.69558e14	0.899684
$395$	−1.19485e14	−0.625215
$396$	−4.85084e13	−0.250319
$397$	−2.83927e14	−1.44497	−0.722485	−	0.691387i	$-0.757000\pi$
$397$	−2.83927e14	−1.44497	−0.722485	+	0.691387i	$0.757000\pi$
$398$	2.17168e14	1.09003
$399$	1.11715e13	0.0553043
$400$	1.02400e13	0.0500000
$401$	−2.18476e14	−1.05223	−0.526115	−	0.850414i	$-0.676352\pi$
$401$	−2.18476e14	−1.05223	−0.526115	+	0.850414i	$0.676352\pi$
$402$	3.19810e13	0.151932
$403$	−1.08447e14	−0.508205
$404$	4.15535e13	0.192092
$405$	1.08962e13	0.0496904
$406$	2.12851e13	0.0957598
$407$	−3.57346e14	−1.58606
$408$	3.60728e13	0.157961
$409$	2.10748e14	0.910510	0.455255	−	0.890361i	$-0.349548\pi$
$409$	2.10748e14	0.910510	0.455255	+	0.890361i	$0.349548\pi$
$410$	1.42524e14	0.607541
$411$	1.98662e14	0.835575
$412$	1.24654e13	0.0517336
$413$	6.64606e13	0.272169
$414$	−3.91556e13	−0.158231
$415$	1.54103e14	0.614535
$416$	4.34821e13	0.171119
$417$	2.37100e14	0.920836
$418$	−7.02211e13	−0.269152
$419$	−4.37490e14	−1.65497	−0.827486	−	0.561486i	$-0.810230\pi$
$419$	−4.37490e14	−1.65497	−0.827486	+	0.561486i	$0.810230\pi$
$420$	1.30691e13	0.0487950
$421$	−1.12467e14	−0.414452	−0.207226	−	0.978293i	$-0.566444\pi$
$421$	−1.12467e14	−0.414452	−0.207226	+	0.978293i	$0.566444\pi$
$422$	−3.63164e14	−1.32094
$423$	−9.29439e13	−0.333694
$424$	−1.42034e14	−0.503362
$425$	4.42409e13	0.154769
$426$	−2.02412e14	−0.699009
$427$	1.52443e14	0.519700
$428$	−1.67571e14	−0.563972
$429$	−2.52622e14	−0.839374
$430$	1.63135e14	0.535145
$431$	−2.63173e14	−0.852346	−0.426173	−	0.904642i	$-0.640139\pi$
$431$	−2.63173e14	−0.852346	−0.426173	+	0.904642i	$0.640139\pi$
$432$	1.50459e13	0.0481125
$433$	1.33605e14	0.421833	0.210916	−	0.977504i	$-0.432355\pi$
$433$	1.33605e14	0.421833	0.210916	+	0.977504i	$0.432355\pi$
$434$	−4.50087e13	−0.140315
$435$	3.00533e13	0.0925128
$436$	−2.87051e14	−0.872535
$437$	−5.66820e13	−0.170136
$438$	2.65019e14	0.785541
$439$	−6.37140e14	−1.86501	−0.932503	−	0.361163i	$-0.882380\pi$
$439$	−6.37140e14	−1.86501	−0.932503	+	0.361163i	$0.882380\pi$
$440$	−8.21493e13	−0.237473
$441$	1.66799e13	0.0476190
$442$	1.87860e14	0.529678
$443$	5.14105e14	1.43163	0.715816	−	0.698289i	$-0.246055\pi$
$443$	5.14105e14	1.43163	0.715816	+	0.698289i	$0.246055\pi$
$444$	1.10839e14	0.304849
$445$	−7.73296e13	−0.210071
$446$	−4.49068e13	−0.120495
$447$	−1.97783e14	−0.524199
$448$	1.80464e13	0.0472456
$449$	−6.32872e14	−1.63667	−0.818335	−	0.574741i	$-0.805103\pi$
$449$	−6.32872e14	−1.63667	−0.818335	+	0.574741i	$0.805103\pi$
$450$	1.84528e13	0.0471405
$451$	−1.14338e15	−2.88549
$452$	3.90777e14	0.974244
$453$	1.23531e14	0.304255
$454$	1.46448e14	0.356349
$455$	6.80614e13	0.163621
$456$	2.17806e13	0.0517325
$457$	2.25234e13	0.0528560	0.0264280	−	0.999651i	$-0.491587\pi$
$457$	2.25234e13	0.0528560	0.0264280	+	0.999651i	$0.491587\pi$
$458$	−3.65813e14	−0.848201
$459$	6.50044e13	0.148927
$460$	−6.63104e13	−0.150111
$461$	−6.49823e14	−1.45358	−0.726792	−	0.686858i	$-0.758989\pi$
$461$	−6.49823e14	−1.45358	−0.726792	+	0.686858i	$0.758989\pi$
$462$	−1.04846e14	−0.231750
$463$	−7.46408e14	−1.63035	−0.815175	−	0.579215i	$-0.803359\pi$
$463$	−7.46408e14	−1.63035	−0.815175	+	0.579215i	$0.803359\pi$
$464$	4.14989e13	0.0895751
$465$	−6.35496e13	−0.135557
$466$	4.51549e14	0.951881
$467$	6.12704e14	1.27646	0.638231	−	0.769845i	$-0.279666\pi$
$467$	6.12704e14	1.27646	0.638231	+	0.769845i	$0.279666\pi$
$468$	7.83561e13	0.161332
$469$	6.91235e13	0.140662
$470$	−1.57401e14	−0.316570
$471$	6.41782e13	0.127577
$472$	1.29576e14	0.254591
$473$	−1.30874e15	−2.54165
$474$	−2.97317e14	−0.570741
$475$	2.67124e13	0.0506873
$476$	7.79676e13	0.146243
$477$	−2.55950e14	−0.474574
$478$	4.05453e14	0.743169
$479$	−8.31056e14	−1.50586	−0.752931	−	0.658100i	$-0.771361\pi$
$479$	−8.31056e14	−1.50586	−0.752931	+	0.658100i	$0.771361\pi$
$480$	2.54804e13	0.0456435
$481$	5.77225e14	1.02223
$482$	1.77387e14	0.310572
$483$	−8.46307e13	−0.146494
$484$	3.66875e14	0.627869
$485$	3.07279e14	0.519941
$486$	2.71132e13	0.0453609
$487$	5.83497e14	0.965227	0.482614	−	0.875833i	$-0.339688\pi$
$487$	5.83497e14	0.965227	0.482614	+	0.875833i	$0.339688\pi$
$488$	2.97212e14	0.486135
$489$	−5.40164e13	−0.0873628
$490$	2.82475e13	0.0451754
$491$	−1.08493e15	−1.71575	−0.857875	−	0.513859i	$-0.828215\pi$
$491$	−1.08493e15	−1.71575	−0.857875	+	0.513859i	$0.828215\pi$
$492$	3.54644e14	0.554607
$493$	1.79292e14	0.277270
$494$	1.13429e14	0.173471
$495$	−1.48036e14	−0.223892
$496$	−8.77519e13	−0.131252
$497$	−4.37491e14	−0.647157
$498$	3.83457e14	0.560991
$499$	5.66339e14	0.819451	0.409726	−	0.912209i	$-0.365624\pi$
$499$	5.66339e14	0.819451	0.409726	+	0.912209i	$0.365624\pi$
$500$	3.12500e13	0.0447214
$501$	5.31646e13	0.0752515
$502$	−8.46523e13	−0.118514
$503$	−6.45582e14	−0.893979	−0.446990	−	0.894539i	$-0.647504\pi$
$503$	−6.45582e14	−0.893979	−0.446990	+	0.894539i	$0.647504\pi$
$504$	3.25202e13	0.0445435
$505$	1.26811e14	0.171813
$506$	5.31968e14	0.712948
$507$	−2.74320e13	−0.0363675
$508$	−3.79929e14	−0.498255
$509$	−4.43965e14	−0.575972	−0.287986	−	0.957635i	$-0.592986\pi$
$509$	−4.43965e14	−0.575972	−0.287986	+	0.957635i	$0.592986\pi$
$510$	1.10086e14	0.141284
$511$	5.72810e14	0.727270
$512$	3.51844e13	0.0441942
$513$	3.92493e13	0.0487738
$514$	3.04503e13	0.0374365
$515$	3.80415e13	0.0462719
$516$	4.05933e14	0.488519
$517$	1.26273e15	1.50354
$518$	2.39566e14	0.282235
$519$	2.99859e14	0.349540
$520$	1.32697e14	0.153053
$521$	−6.77706e14	−0.773453	−0.386727	−	0.922194i	$-0.626394\pi$
$521$	−6.77706e14	−0.773453	−0.386727	+	0.922194i	$0.626394\pi$
$522$	7.47823e13	0.0844522
$523$	−5.84032e14	−0.652645	−0.326322	−	0.945259i	$-0.605810\pi$
$523$	−5.84032e14	−0.652645	−0.326322	+	0.945259i	$0.605810\pi$
$524$	−6.90348e14	−0.763390
$525$	3.98838e13	0.0436436
$526$	1.15165e14	0.124709
$527$	−3.79123e14	−0.406277
$528$	−2.04414e14	−0.216782
$529$	−5.23409e14	−0.549332
$530$	−4.33453e14	−0.450220
$531$	2.33500e14	0.240031
$532$	4.70765e13	0.0478950
$533$	1.84692e15	1.85972
$534$	−1.92421e14	−0.191767
$535$	−5.11385e14	−0.504432
$536$	1.34768e14	0.131577
$537$	3.84389e14	0.371460
$538$	−7.61542e14	−0.728436
$539$	−2.26613e14	−0.214559
$540$	4.59165e13	0.0430331
$541$	−6.42310e14	−0.595882	−0.297941	−	0.954584i	$-0.596300\pi$
$541$	−6.42310e14	−0.595882	−0.297941	+	0.954584i	$0.596300\pi$
$542$	3.85389e14	0.353918
$543$	6.72027e14	0.610924
$544$	1.52011e14	0.136798
$545$	−8.76009e14	−0.780419
$546$	1.69358e14	0.149364
$547$	1.90619e15	1.66432	0.832159	−	0.554537i	$-0.187105\pi$
$547$	1.90619e15	1.66432	0.832159	+	0.554537i	$0.187105\pi$
$548$	8.37161e14	0.723629
$549$	5.35585e14	0.458333
$550$	−2.50700e14	−0.212402
$551$	1.08256e14	0.0908063
$552$	−1.65001e14	−0.137032
$553$	−6.42619e14	−0.528403
$554$	−7.79708e14	−0.634788
$555$	3.38253e14	0.272665
$556$	9.99135e14	0.797467
$557$	5.06132e14	0.400000	0.200000	−	0.979796i	$-0.435906\pi$
$557$	5.06132e14	0.400000	0.200000	+	0.979796i	$0.435906\pi$
$558$	−1.58132e14	−0.123746
$559$	2.11402e15	1.63811
$560$	5.50732e13	0.0422577
$561$	−8.83150e14	−0.671025
$562$	−1.11057e14	−0.0835596
$563$	−4.72016e14	−0.351691	−0.175845	−	0.984418i	$-0.556266\pi$
$563$	−4.72016e14	−0.351691	−0.175845	+	0.984418i	$0.556266\pi$
$564$	−3.91665e14	−0.288988
$565$	1.19256e15	0.871390
$566$	1.06989e15	0.774191
$567$	5.86024e13	0.0419961
$568$	−8.52961e14	−0.605360
$569$	1.54164e15	1.08359	0.541797	−	0.840510i	$-0.317744\pi$
$569$	1.54164e15	1.08359	0.541797	+	0.840510i	$0.317744\pi$
$570$	6.64691e13	0.0462709
$571$	−2.54083e14	−0.175177	−0.0875885	−	0.996157i	$-0.527916\pi$
$571$	−2.54083e14	−0.175177	−0.0875885	+	0.996157i	$0.527916\pi$
$572$	−1.06455e15	−0.726919
$573$	−1.36479e15	−0.923031
$574$	7.66526e14	0.513466
$575$	−2.02363e14	−0.134264
$576$	6.34034e13	0.0416667
$577$	2.09702e14	0.136501	0.0682504	−	0.997668i	$-0.478258\pi$
$577$	2.09702e14	0.136501	0.0682504	+	0.997668i	$0.478258\pi$
$578$	−4.39954e14	−0.283664
$579$	3.69668e14	0.236091
$580$	1.26645e14	0.0801184
$581$	8.28803e14	0.519377
$582$	7.64609e14	0.474639
$583$	3.47733e15	2.13830
$584$	1.11679e15	0.680298
$585$	2.39124e14	0.144300
$586$	−4.35951e14	−0.260616
$587$	−8.74129e14	−0.517686	−0.258843	−	0.965919i	$-0.583341\pi$
$587$	−8.74129e14	−0.517686	−0.258843	+	0.965919i	$0.583341\pi$
$588$	7.02889e13	0.0412393
$589$	−2.28913e14	−0.133056
$590$	3.95434e14	0.227713
$591$	1.28758e15	0.734589
$592$	4.67073e14	0.264007
$593$	−1.71234e15	−0.958934	−0.479467	−	0.877560i	$-0.659170\pi$
$593$	−1.71234e15	−0.958934	−0.479467	+	0.877560i	$0.659170\pi$
$594$	−3.68360e14	−0.204384
$595$	2.37938e14	0.130804
$596$	−8.33454e14	−0.453970
$597$	1.64912e15	0.890007
$598$	−8.59294e14	−0.459500
$599$	2.68452e15	1.42239	0.711196	−	0.702993i	$-0.248154\pi$
$599$	2.68452e15	1.42239	0.711196	+	0.702993i	$0.248154\pi$
$600$	7.77600e13	0.0408248
$601$	−5.49447e14	−0.285836	−0.142918	−	0.989735i	$-0.545648\pi$
$601$	−5.49447e14	−0.285836	−0.142918	+	0.989735i	$0.545648\pi$
$602$	8.77381e14	0.452280
$603$	2.42856e14	0.124052
$604$	5.20560e14	0.263492
$605$	1.11961e15	0.561583
$606$	3.15547e14	0.156843
$607$	1.98762e15	0.979030	0.489515	−	0.871995i	$-0.337174\pi$
$607$	1.98762e15	0.979030	0.489515	+	0.871995i	$0.337174\pi$
$608$	9.17833e13	0.0448016
$609$	1.61634e14	0.0781876
$610$	9.07018e14	0.434813
$611$	−2.03971e15	−0.969040
$612$	2.73928e14	0.128974
$613$	−1.19480e14	−0.0557524	−0.0278762	−	0.999611i	$-0.508874\pi$
$613$	−1.19480e14	−0.0557524	−0.0278762	+	0.999611i	$0.508874\pi$
$614$	9.85873e14	0.455927
$615$	1.08229e15	0.496055
$616$	−4.41819e14	−0.200701
$617$	−2.32322e15	−1.04598	−0.522988	−	0.852340i	$-0.675183\pi$
$617$	−2.32322e15	−1.04598	−0.522988	+	0.852340i	$0.675183\pi$
$618$	9.46594e13	0.0422403
$619$	−7.30545e14	−0.323109	−0.161554	−	0.986864i	$-0.551651\pi$
$619$	−7.30545e14	−0.323109	−0.161554	+	0.986864i	$0.551651\pi$
$620$	−2.67797e14	−0.117396
$621$	−2.97338e14	−0.129195
$622$	2.72351e15	1.17296
$623$	−4.15897e14	−0.177542
$624$	3.30192e14	0.139718
$625$	9.53674e13	0.0400000
$626$	1.12264e15	0.466748
$627$	−5.33241e14	−0.219762
$628$	2.70446e14	0.110485
$629$	2.01794e15	0.817204
$630$	9.92437e13	0.0398410
$631$	4.27112e15	1.69973	0.849865	−	0.527001i	$-0.176684\pi$
$631$	4.27112e15	1.69973	0.849865	+	0.527001i	$0.176684\pi$
$632$	−1.25289e15	−0.494276
$633$	−2.75778e15	−1.07855
$634$	2.04415e15	0.792541
$635$	−1.15945e15	−0.445653
$636$	−1.07857e15	−0.410993
$637$	3.66050e14	0.138285
$638$	−1.01599e15	−0.380519
$639$	−1.53706e15	−0.570739
$640$	1.07374e14	0.0395285
$641$	4.95978e14	0.181027	0.0905136	−	0.995895i	$-0.471149\pi$
$641$	4.95978e14	0.181027	0.0905136	+	0.995895i	$0.471149\pi$
$642$	−1.27249e15	−0.460481
$643$	4.01985e15	1.44228	0.721140	−	0.692789i	$-0.243618\pi$
$643$	4.01985e15	1.44228	0.721140	+	0.692789i	$0.243618\pi$
$644$	−3.56633e14	−0.126867
$645$	1.23881e15	0.436944
$646$	3.96540e14	0.138678
$647$	8.80939e14	0.305473	0.152736	−	0.988267i	$-0.451191\pi$
$647$	8.80939e14	0.305473	0.152736	+	0.988267i	$0.451191\pi$
$648$	1.14255e14	0.0392837
$649$	−3.17233e15	−1.08151
$650$	4.04958e14	0.136895
$651$	−3.41785e14	−0.114566
$652$	−2.27625e14	−0.0756584
$653$	−2.70423e15	−0.891296	−0.445648	−	0.895208i	$-0.647027\pi$
$653$	−2.70423e15	−0.891296	−0.445648	+	0.895208i	$0.647027\pi$
$654$	−2.17979e15	−0.712422
$655$	−2.10678e15	−0.682796
$656$	1.49447e15	0.480303
$657$	2.01249e15	0.641392
$658$	−8.46542e14	−0.267551
$659$	−1.28808e15	−0.403713	−0.201857	−	0.979415i	$-0.564697\pi$
$659$	−1.28808e15	−0.403713	−0.201857	+	0.979415i	$0.564697\pi$
$660$	−6.23821e14	−0.193896
$661$	4.74248e14	0.146183	0.0730916	−	0.997325i	$-0.476713\pi$
$661$	4.74248e14	0.146183	0.0730916	+	0.997325i	$0.476713\pi$
$662$	5.49842e14	0.168081
$663$	1.42656e15	0.432480
$664$	1.61589e15	0.485832
$665$	1.43666e14	0.0428386
$666$	8.41681e14	0.248908
$667$	−8.20102e14	−0.240534
$668$	2.24035e14	0.0651697
$669$	−3.41011e14	−0.0983841
$670$	4.11278e14	0.117686
$671$	−7.27646e15	−2.06512
$672$	1.37040e14	0.0385758
$673$	−4.31939e15	−1.20598	−0.602990	−	0.797749i	$-0.706024\pi$
$673$	−4.31939e15	−1.20598	−0.602990	+	0.797749i	$0.706024\pi$
$674$	−1.16958e15	−0.323892
$675$	1.40126e14	0.0384900
$676$	−1.15598e14	−0.0314952
$677$	−1.18502e15	−0.320248	−0.160124	−	0.987097i	$-0.551189\pi$
$677$	−1.18502e15	−0.320248	−0.160124	+	0.987097i	$0.551189\pi$
$678$	2.96746e15	0.795466
$679$	1.65262e15	0.439430
$680$	4.63899e14	0.122356
$681$	1.11209e15	0.290958
$682$	2.14838e15	0.557566
$683$	−1.56907e15	−0.403951	−0.201976	−	0.979391i	$-0.564736\pi$
$683$	−1.56907e15	−0.403951	−0.201976	+	0.979391i	$0.564736\pi$
$684$	1.65396e14	0.0422394
$685$	2.55481e15	0.647234
$686$	1.51922e14	0.0381802
$687$	−2.77789e15	−0.692553
$688$	1.71060e15	0.423070
$689$	−5.61698e15	−1.37815
$690$	−5.03544e14	−0.122565
$691$	3.18443e14	0.0768957	0.0384478	−	0.999261i	$-0.487759\pi$
$691$	3.18443e14	0.0768957	0.0384478	+	0.999261i	$0.487759\pi$
$692$	1.26361e15	0.302711
$693$	−7.96172e14	−0.189223
$694$	−4.96381e15	−1.17041
$695$	3.04912e15	0.713277
$696$	3.15132e14	0.0731378
$697$	6.45670e15	1.48672
$698$	−4.60635e15	−1.05233
$699$	3.42895e15	0.777208
$700$	1.68070e14	0.0377964
$701$	−2.42392e15	−0.540841	−0.270421	−	0.962742i	$-0.587163\pi$
$701$	−2.42392e15	−0.540841	−0.270421	+	0.962742i	$0.587163\pi$
$702$	5.95017e14	0.131727
$703$	1.21842e15	0.267636
$704$	−8.61398e14	−0.187739
$705$	−1.19527e15	−0.258478
$706$	−2.01186e15	−0.431689
$707$	6.82021e14	0.145208
$708$	9.83966e14	0.207873
$709$	−2.29281e15	−0.480632	−0.240316	−	0.970695i	$-0.577251\pi$
$709$	−2.29281e15	−0.480632	−0.240316	+	0.970695i	$0.577251\pi$
$710$	−2.60303e15	−0.541450
$711$	−2.25775e15	−0.466008
$712$	−8.10859e14	−0.166076
$713$	1.73416e15	0.352448
$714$	5.92066e14	0.119407
$715$	−3.24874e15	−0.650177
$716$	1.61981e15	0.321694
$717$	3.07891e15	0.606795
$718$	−2.80926e15	−0.549423
$719$	−9.81800e14	−0.190552	−0.0952761	−	0.995451i	$-0.530373\pi$
$719$	−9.81800e14	−0.190552	−0.0952761	+	0.995451i	$0.530373\pi$
$720$	1.93492e14	0.0372678
$721$	2.04596e14	0.0391069
$722$	−3.48826e15	−0.661689
$723$	1.34703e15	0.253581
$724$	2.83191e15	0.529076
$725$	3.86488e14	0.0716601
$726$	2.78596e15	0.512653
$727$	9.57481e14	0.174860	0.0874301	−	0.996171i	$-0.472135\pi$
$727$	9.57481e14	0.174860	0.0874301	+	0.996171i	$0.472135\pi$
$728$	7.13675e14	0.129353
$729$	2.05891e14	0.0370370
$730$	3.40816e15	0.608477
$731$	7.39047e15	1.30956
$732$	2.25695e15	0.396928
$733$	−5.81504e15	−1.01503	−0.507517	−	0.861642i	$-0.669437\pi$
$733$	−5.81504e15	−1.01503	−0.507517	+	0.861642i	$0.669437\pi$
$734$	5.87165e14	0.101726
$735$	2.14505e14	0.0368856
$736$	−6.95315e14	−0.118673
$737$	−3.29944e15	−0.558944
$738$	2.69308e15	0.452834
$739$	9.30321e15	1.55270	0.776352	−	0.630300i	$-0.217068\pi$
$739$	9.30321e15	1.55270	0.776352	+	0.630300i	$0.217068\pi$
$740$	1.42539e15	0.236135
$741$	8.61351e14	0.141638
$742$	−2.33122e15	−0.380506
$743$	−5.88515e15	−0.953496	−0.476748	−	0.879040i	$-0.658185\pi$
$743$	−5.88515e15	−0.953496	−0.476748	+	0.879040i	$0.658185\pi$
$744$	−6.66366e14	−0.107167
$745$	−2.54350e15	−0.406043
$746$	−8.67379e15	−1.37450
$747$	2.91188e15	0.458047
$748$	−3.72158e15	−0.581124
$749$	−2.75035e15	−0.426323
$750$	2.37305e14	0.0365148
$751$	5.82383e15	0.889588	0.444794	−	0.895633i	$-0.353277\pi$
$751$	5.82383e15	0.889588	0.444794	+	0.895633i	$0.353277\pi$
$752$	−1.65047e15	−0.250271
$753$	−6.42828e14	−0.0967659
$754$	1.64114e15	0.245247
$755$	1.58862e15	0.235675
$756$	2.46950e14	0.0363696
$757$	2.45913e15	0.359546	0.179773	−	0.983708i	$-0.442464\pi$
$757$	2.45913e15	0.359546	0.179773	+	0.983708i	$0.442464\pi$
$758$	−5.78879e15	−0.840248
$759$	4.03963e15	0.582119
$760$	2.80100e14	0.0400718
$761$	−9.25594e15	−1.31463	−0.657317	−	0.753614i	$-0.728309\pi$
$761$	−9.25594e15	−1.31463	−0.657317	+	0.753614i	$0.728309\pi$
$762$	−2.88509e15	−0.406824
$763$	−4.71139e15	−0.659575
$764$	−5.75123e15	−0.799368
$765$	8.35962e14	0.115358
$766$	2.37358e14	0.0325197
$767$	5.12430e15	0.697044
$768$	2.67181e14	0.0360844
$769$	−3.58918e15	−0.481282	−0.240641	−	0.970614i	$-0.577358\pi$
$769$	−3.58918e15	−0.481282	−0.240641	+	0.970614i	$0.577358\pi$
$770$	−1.34832e15	−0.179513
$771$	2.31232e14	0.0305667
$772$	1.55778e15	0.204461
$773$	−7.06972e15	−0.921330	−0.460665	−	0.887574i	$-0.652389\pi$
$773$	−7.06972e15	−0.921330	−0.460665	+	0.887574i	$0.652389\pi$
$774$	3.08255e15	0.398874
$775$	−8.17253e14	−0.105002
$776$	3.22206e15	0.411049
$777$	1.81920e15	0.230444
$778$	7.01299e15	0.882095
$779$	3.89853e15	0.486905
$780$	1.00767e15	0.124967
$781$	2.08825e16	2.57160
$782$	−3.00404e15	−0.367340
$783$	5.67878e14	0.0689550
$784$	2.96197e14	0.0357143
$785$	8.25337e14	0.0988208
$786$	−5.24233e15	−0.623305
$787$	−1.65921e15	−0.195903	−0.0979516	−	0.995191i	$-0.531229\pi$
$787$	−1.65921e15	−0.195903	−0.0979516	+	0.995191i	$0.531229\pi$
$788$	5.42587e15	0.636172
$789$	8.74535e14	0.101825
$790$	−3.82352e15	−0.442094
$791$	6.41386e15	0.736459
$792$	−1.55227e15	−0.177002
$793$	1.17538e16	1.33099
$794$	−9.08566e15	−1.02175
$795$	−3.29154e15	−0.367603
$796$	6.94938e15	0.770769
$797$	6.99192e15	0.770151	0.385075	−	0.922885i	$-0.374175\pi$
$797$	6.99192e15	0.770151	0.385075	+	0.922885i	$0.374175\pi$
$798$	3.57487e14	0.0391061
$799$	−7.13070e15	−0.774684
$800$	3.27680e14	0.0353553
$801$	−1.46119e15	−0.156577
$802$	−6.99124e15	−0.744038
$803$	−2.73416e16	−2.88994
$804$	1.02339e15	0.107432
$805$	−1.08836e15	−0.113473
$806$	−3.47030e15	−0.359355
$807$	−5.78296e15	−0.594765
$808$	1.32971e15	0.135830
$809$	5.72209e15	0.580548	0.290274	−	0.956944i	$-0.406254\pi$
$809$	5.72209e15	0.580548	0.290274	+	0.956944i	$0.406254\pi$
$810$	3.48678e14	0.0351364
$811$	8.66986e15	0.867755	0.433878	−	0.900972i	$-0.357145\pi$
$811$	8.66986e15	0.867755	0.433878	+	0.900972i	$0.357145\pi$
$812$	6.81125e14	0.0677124
$813$	2.92654e15	0.288973
$814$	−1.14351e16	−1.12151
$815$	−6.94655e14	−0.0676710
$816$	1.15433e15	0.111695
$817$	4.46233e15	0.428885
$818$	6.74393e15	0.643828
$819$	1.28607e15	0.121956
$820$	4.56076e15	0.429596
$821$	−6.38864e15	−0.597752	−0.298876	−	0.954292i	$-0.596612\pi$
$821$	−6.38864e15	−0.597752	−0.298876	+	0.954292i	$0.596612\pi$
$822$	6.35719e15	0.590841
$823$	1.85799e15	0.171532	0.0857659	−	0.996315i	$-0.472666\pi$
$823$	1.85799e15	0.171532	0.0857659	+	0.996315i	$0.472666\pi$
$824$	3.98894e14	0.0365812
$825$	−1.90375e15	−0.173426
$826$	2.12674e15	0.192453
$827$	5.28436e15	0.475021	0.237510	−	0.971385i	$-0.423669\pi$
$827$	5.28436e15	0.475021	0.237510	+	0.971385i	$0.423669\pi$
$828$	−1.25298e15	−0.111886
$829$	1.46466e16	1.29923	0.649617	−	0.760262i	$-0.274929\pi$
$829$	1.46466e16	1.29923	0.649617	+	0.760262i	$0.274929\pi$
$830$	4.93129e15	0.434542
$831$	−5.92091e15	−0.518302
$832$	1.39143e15	0.120999
$833$	1.27969e15	0.110550
$834$	7.58718e15	0.651129
$835$	6.83701e14	0.0582896
$836$	−2.24708e15	−0.190319
$837$	−1.20081e15	−0.101038
$838$	−1.39997e16	−1.17024
$839$	−1.35111e16	−1.12202	−0.561009	−	0.827810i	$-0.689587\pi$
$839$	−1.35111e16	−1.12202	−0.561009	+	0.827810i	$0.689587\pi$
$840$	4.18212e14	0.0345033
$841$	−1.06342e16	−0.871621
$842$	−3.59895e15	−0.293062
$843$	−8.43339e14	−0.0682261
$844$	−1.16213e16	−0.934049
$845$	−3.52778e14	−0.0281702
$846$	−2.97420e15	−0.235957
$847$	6.02155e15	0.474624
$848$	−4.54509e15	−0.355930
$849$	8.12447e15	0.632124
$850$	1.41571e15	0.109438
$851$	−9.23031e15	−0.708931
$852$	−6.47717e15	−0.494274
$853$	−1.12294e16	−0.851407	−0.425704	−	0.904863i	$-0.639973\pi$
$853$	−1.12294e16	−0.851407	−0.425704	+	0.904863i	$0.639973\pi$
$854$	4.87816e15	0.367484
$855$	5.04750e14	0.0377801
$856$	−5.36226e15	−0.398788
$857$	1.61495e16	1.19334	0.596672	−	0.802486i	$-0.296490\pi$
$857$	1.61495e16	1.19334	0.596672	+	0.802486i	$0.296490\pi$
$858$	−8.08390e15	−0.593527
$859$	1.48950e16	1.08662	0.543309	−	0.839533i	$-0.317171\pi$
$859$	1.48950e16	1.08662	0.543309	+	0.839533i	$0.317171\pi$
$860$	5.22033e15	0.378405
$861$	5.82081e15	0.419243
$862$	−8.42153e15	−0.602700
$863$	1.50959e16	1.07350	0.536748	−	0.843742i	$-0.319652\pi$
$863$	1.50959e16	1.07350	0.536748	+	0.843742i	$0.319652\pi$
$864$	4.81469e14	0.0340207
$865$	3.85622e15	0.270753
$866$	4.27537e15	0.298281
$867$	−3.34090e15	−0.231611
$868$	−1.44028e15	−0.0992175
$869$	3.06738e16	2.09971
$870$	9.61707e14	0.0654164
$871$	5.32962e15	0.360244
$872$	−9.18562e15	−0.616976
$873$	5.80625e15	0.387541
$874$	−1.81382e15	−0.120305
$875$	5.12909e14	0.0338062
$876$	8.48060e15	0.555461
$877$	−1.88782e16	−1.22875	−0.614374	−	0.789015i	$-0.710591\pi$
$877$	−1.88782e16	−1.22875	−0.614374	+	0.789015i	$0.710591\pi$
$878$	−2.03885e16	−1.31876
$879$	−3.31050e15	−0.212792
$880$	−2.62878e15	−0.167919
$881$	−2.05027e16	−1.30150	−0.650748	−	0.759294i	$-0.725545\pi$
$881$	−2.05027e16	−1.30150	−0.650748	+	0.759294i	$0.725545\pi$
$882$	5.33756e14	0.0336718
$883$	7.55799e15	0.473830	0.236915	−	0.971530i	$-0.423864\pi$
$883$	7.55799e15	0.473830	0.236915	+	0.971530i	$0.423864\pi$
$884$	6.01152e15	0.374539
$885$	3.00283e15	0.185927
$886$	1.64514e16	1.01232
$887$	−2.12273e16	−1.29812	−0.649062	−	0.760736i	$-0.724838\pi$
$887$	−2.12273e16	−1.29812	−0.649062	+	0.760736i	$0.724838\pi$
$888$	3.54684e15	0.215561
$889$	−6.23581e15	−0.376646
$890$	−2.47455e15	−0.148542
$891$	−2.79724e15	−0.166879
$892$	−1.43702e15	−0.0852031
$893$	−4.30548e15	−0.253711
$894$	−6.32904e15	−0.370665
$895$	4.94327e15	0.287732
$896$	5.77484e14	0.0334077
$897$	−6.52527e15	−0.375180
$898$	−2.02519e16	−1.15730
$899$	−3.31202e15	−0.188111
$900$	5.90490e14	0.0333333
$901$	−1.96366e16	−1.10174
$902$	−3.65882e16	−2.04035
$903$	6.66261e15	0.369285
$904$	1.25049e16	0.688894
$905$	8.64232e15	0.473220
$906$	3.95300e15	0.215141
$907$	−8.01086e15	−0.433350	−0.216675	−	0.976244i	$-0.569521\pi$
$907$	−8.01086e15	−0.433350	−0.216675	+	0.976244i	$0.569521\pi$
$908$	4.68633e15	0.251977
$909$	2.39618e15	0.128061
$910$	2.17796e15	0.115697
$911$	−1.34049e16	−0.707801	−0.353901	−	0.935283i	$-0.615145\pi$
$911$	−1.34049e16	−0.707801	−0.353901	+	0.935283i	$0.615145\pi$
$912$	6.96979e14	0.0365804
$913$	−3.95608e16	−2.06384
$914$	7.20748e14	0.0373748
$915$	6.88767e15	0.355023
$916$	−1.17060e16	−0.599768
$917$	−1.13307e16	−0.577068
$918$	2.08014e15	0.105307
$919$	2.74043e16	1.37906	0.689529	−	0.724258i	$-0.257817\pi$
$919$	2.74043e16	1.37906	0.689529	+	0.724258i	$0.257817\pi$
$920$	−2.12193e15	−0.106145
$921$	7.48648e15	0.372263
$922$	−2.07943e16	−1.02784
$923$	−3.37318e16	−1.65741
$924$	−3.35506e15	−0.163872
$925$	4.34996e15	0.211206
$926$	−2.38851e16	−1.15283
$927$	7.18820e14	0.0344891
$928$	1.32796e15	0.0633392
$929$	−1.81506e16	−0.860608	−0.430304	−	0.902684i	$-0.641594\pi$
$929$	−1.81506e16	−0.860608	−0.430304	+	0.902684i	$0.641594\pi$
$930$	−2.03359e15	−0.0958532
$931$	7.72670e14	0.0362052
$932$	1.44496e16	0.673082
$933$	2.06817e16	0.957715
$934$	1.96065e16	0.902595
$935$	−1.13574e16	−0.519774
$936$	2.50740e15	0.114079
$937$	1.47790e16	0.668464	0.334232	−	0.942491i	$-0.391523\pi$
$937$	1.47790e16	0.668464	0.334232	+	0.942491i	$0.391523\pi$
$938$	2.21195e15	0.0994627
$939$	8.52507e15	0.381098
$940$	−5.03684e15	−0.223849
$941$	−2.90263e16	−1.28247	−0.641237	−	0.767343i	$-0.721579\pi$
$941$	−2.90263e16	−1.28247	−0.641237	+	0.767343i	$0.721579\pi$
$942$	2.05370e15	0.0902106
$943$	−2.95337e16	−1.28975
$944$	4.14643e15	0.180023
$945$	7.53631e14	0.0325300
$946$	−4.18796e16	−1.79722
$947$	2.50004e15	0.106665	0.0533324	−	0.998577i	$-0.483016\pi$
$947$	2.50004e15	0.106665	0.0533324	+	0.998577i	$0.483016\pi$
$948$	−9.51414e15	−0.403575
$949$	4.41652e16	1.86259
$950$	8.54798e14	0.0358413
$951$	1.55228e16	0.647107
$952$	2.49496e15	0.103410
$953$	−1.89109e16	−0.779294	−0.389647	−	0.920964i	$-0.627403\pi$
$953$	−1.89109e16	−0.779294	−0.389647	+	0.920964i	$0.627403\pi$
$954$	−8.19040e15	−0.335574
$955$	−1.75513e16	−0.714977
$956$	1.29745e16	0.525500
$957$	−7.71519e15	−0.310693
$958$	−2.65938e16	−1.06480
$959$	1.37404e16	0.547012
$960$	8.15373e14	0.0322749
$961$	−1.84050e16	−0.724365
$962$	1.84712e16	0.722824
$963$	−9.66297e15	−0.375981
$964$	5.67637e15	0.219608
$965$	4.75396e15	0.182875
$966$	−2.70818e15	−0.103587
$967$	−1.20508e16	−0.458322	−0.229161	−	0.973389i	$-0.573598\pi$
$967$	−1.20508e16	−0.458322	−0.229161	+	0.973389i	$0.573598\pi$
$968$	1.17400e16	0.443970
$969$	3.01123e15	0.113230
$970$	9.83294e15	0.367654
$971$	4.18450e16	1.55574	0.777872	−	0.628423i	$-0.216299\pi$
$971$	4.18450e16	1.55574	0.777872	+	0.628423i	$0.216299\pi$
$972$	8.67624e14	0.0320750
$973$	1.63989e16	0.602829
$974$	1.86719e16	0.682519
$975$	3.07515e15	0.111774
$976$	9.51078e15	0.343749
$977$	2.72991e16	0.981133	0.490567	−	0.871404i	$-0.336790\pi$
$977$	2.72991e16	0.981133	0.490567	+	0.871404i	$0.336790\pi$
$978$	−1.72852e15	−0.0617748
$979$	1.98518e16	0.705496
$980$	9.03921e14	0.0319438
$981$	−1.65528e16	−0.581690
$982$	−3.47178e16	−1.21322
$983$	3.24907e16	1.12905	0.564526	−	0.825415i	$-0.309059\pi$
$983$	3.24907e16	1.12905	0.564526	+	0.825415i	$0.309059\pi$
$984$	1.13486e16	0.392166
$985$	1.65584e16	0.569010
$986$	5.73734e15	0.196059
$987$	−6.42843e15	−0.218454
$988$	3.62973e15	0.122662
$989$	−3.38049e16	−1.13606
$990$	−4.73714e15	−0.158315
$991$	−4.04363e16	−1.34390	−0.671949	−	0.740597i	$-0.734543\pi$
$991$	−4.04363e16	−1.34390	−0.671949	+	0.740597i	$0.734543\pi$
$992$	−2.80806e15	−0.0928094
$993$	4.17536e15	0.137238
$994$	−1.39997e16	−0.457609
$995$	2.12078e16	0.689396
$996$	1.22706e16	0.396680
$997$	1.38170e15	0.0444213	0.0222107	−	0.999753i	$-0.492930\pi$
$997$	1.38170e15	0.0444213	0.0222107	+	0.999753i	$0.492930\pi$
$998$	1.81228e16	0.579440
$999$	6.39151e15	0.203233

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.12.a.p.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +100000. q^{10} -802239. q^{11} +248832. q^{12} +1.29587e6 q^{13} +537824. q^{14} +759375. q^{15} +1.04858e6 q^{16} +4.53027e6 q^{17} +1.88957e6 q^{18} +2.73535e6 q^{19} +3.20000e6 q^{20} +4.08410e6 q^{21} -2.56717e7 q^{22} -2.07220e7 q^{23} +7.96262e6 q^{24} +9.76562e6 q^{25} +4.14677e7 q^{26} +1.43489e7 q^{27} +1.72104e7 q^{28} +3.95764e7 q^{29} +2.43000e7 q^{30} -8.36867e7 q^{31} +3.35544e7 q^{32} -1.94944e8 q^{33} +1.44969e8 q^{34} +5.25219e7 q^{35} +6.04662e7 q^{36} +4.45436e8 q^{37} +8.75313e7 q^{38} +3.14896e8 q^{39} +1.02400e8 q^{40} +1.42524e9 q^{41} +1.30691e8 q^{42} +1.63135e9 q^{43} -8.21493e8 q^{44} +1.84528e8 q^{45} -6.63104e8 q^{46} -1.57401e9 q^{47} +2.54804e8 q^{48} +2.82475e8 q^{49} +3.12500e8 q^{50} +1.10086e9 q^{51} +1.32697e9 q^{52} -4.33453e9 q^{53} +4.59165e8 q^{54} -2.50700e9 q^{55} +5.50732e8 q^{56} +6.64691e8 q^{57} +1.26645e9 q^{58} +3.95434e9 q^{59} +7.77600e8 q^{60} +9.07018e9 q^{61} -2.67797e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +4.04958e9 q^{65} -6.23821e9 q^{66} +4.11278e9 q^{67} +4.63899e9 q^{68} -5.03544e9 q^{69} +1.68070e9 q^{70} -2.60303e10 q^{71} +1.93492e9 q^{72} +3.40816e10 q^{73} +1.42539e10 q^{74} +2.37305e9 q^{75} +2.80100e9 q^{76} -1.34832e10 q^{77} +1.00767e10 q^{78} -3.82352e10 q^{79} +3.27680e9 q^{80} +3.48678e9 q^{81} +4.56076e10 q^{82} +4.93129e10 q^{83} +4.18212e9 q^{84} +1.41571e10 q^{85} +5.22033e10 q^{86} +9.61707e9 q^{87} -2.62878e10 q^{88} -2.47455e10 q^{89} +5.90490e9 q^{90} +2.17796e10 q^{91} -2.12193e10 q^{92} -2.03359e10 q^{93} -5.03684e10 q^{94} +8.54798e9 q^{95} +8.15373e9 q^{96} +9.83294e10 q^{97} +9.03921e9 q^{98} -4.73714e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 128 q^{2} + 972 q^{3} + 4096 q^{4} + 12500 q^{5} + 31104 q^{6} + 67228 q^{7} + 131072 q^{8} + 236196 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more