LMFDB - Embedded newform 210.12.a.p.1.4

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			1.4
Root			$-22522.1$ 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)

$f(q)$	$=$	$q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +100000. q^{10} +698251. q^{11} +248832. q^{12} +229130. q^{13} +537824. q^{14} +759375. q^{15} +1.04858e6 q^{16} +9.77117e6 q^{17} +1.88957e6 q^{18} +1.20440e7 q^{19} +3.20000e6 q^{20} +4.08410e6 q^{21} +2.23440e7 q^{22} -5.57444e7 q^{23} +7.96262e6 q^{24} +9.76562e6 q^{25} +7.33216e6 q^{26} +1.43489e7 q^{27} +1.72104e7 q^{28} -1.37670e8 q^{29} +2.43000e7 q^{30} +2.54514e8 q^{31} +3.35544e7 q^{32} +1.69675e8 q^{33} +3.12677e8 q^{34} +5.25219e7 q^{35} +6.04662e7 q^{36} -3.03614e8 q^{37} +3.85407e8 q^{38} +5.56786e7 q^{39} +1.02400e8 q^{40} -1.39163e8 q^{41} +1.30691e8 q^{42} -1.85345e9 q^{43} +7.15009e8 q^{44} +1.84528e8 q^{45} -1.78382e9 q^{46} +2.84162e9 q^{47} +2.54804e8 q^{48} +2.82475e8 q^{49} +3.12500e8 q^{50} +2.37439e9 q^{51} +2.34629e8 q^{52} -1.70315e9 q^{53} +4.59165e8 q^{54} +2.18204e9 q^{55} +5.50732e8 q^{56} +2.92669e9 q^{57} -4.40544e9 q^{58} -3.42148e9 q^{59} +7.77600e8 q^{60} +1.08369e10 q^{61} +8.14445e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +7.16031e8 q^{65} +5.42960e9 q^{66} +2.90368e8 q^{67} +1.00057e10 q^{68} -1.35459e10 q^{69} +1.68070e9 q^{70} +3.15656e9 q^{71} +1.93492e9 q^{72} -2.16205e10 q^{73} -9.71566e9 q^{74} +2.37305e9 q^{75} +1.23330e10 q^{76} +1.17355e10 q^{77} +1.78171e9 q^{78} -4.72176e9 q^{79} +3.27680e9 q^{80} +3.48678e9 q^{81} -4.45321e9 q^{82} +8.20464e9 q^{83} +4.18212e9 q^{84} +3.05349e10 q^{85} -5.93105e10 q^{86} -3.34538e10 q^{87} +2.28803e10 q^{88} +7.16987e10 q^{89} +5.90490e9 q^{90} +3.85099e9 q^{91} -5.70823e10 q^{92} +6.18469e10 q^{93} +9.09317e10 q^{94} +3.76374e10 q^{95} +8.15373e9 q^{96} +1.14510e10 q^{97} +9.03921e9 q^{98} +4.12310e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	698251.	1.30723	0.653615	−	0.756827i	$-0.273252\pi$
$11$	698251.	1.30723	0.653615	+	0.756827i	$0.273252\pi$
$12$	248832.	0.288675
$13$	229130.	0.171156	0.0855782	−	0.996331i	$-0.472726\pi$
$13$	229130.	0.171156	0.0855782	+	0.996331i	$0.472726\pi$
$14$	537824.	0.267261
$15$	759375.	0.258199
$16$	1.04858e6	0.250000
$17$	9.77117e6	1.66908	0.834541	−	0.550946i	$-0.185733\pi$
$17$	9.77117e6	1.66908	0.834541	+	0.550946i	$0.185733\pi$
$18$	1.88957e6	0.235702
$19$	1.20440e7	1.11590	0.557950	−	0.829875i	$-0.311588\pi$
$19$	1.20440e7	1.11590	0.557950	+	0.829875i	$0.311588\pi$
$20$	3.20000e6	0.223607
$21$	4.08410e6	0.218218
$22$	2.23440e7	0.924351
$23$	−5.57444e7	−1.80592	−0.902960	−	0.429725i	$-0.858611\pi$
$23$	−5.57444e7	−1.80592	−0.902960	+	0.429725i	$0.858611\pi$
$24$	7.96262e6	0.204124
$25$	9.76562e6	0.200000
$26$	7.33216e6	0.121026
$27$	1.43489e7	0.192450
$28$	1.72104e7	0.188982
$29$	−1.37670e8	−1.24638	−0.623189	−	0.782071i	$-0.714163\pi$
$29$	−1.37670e8	−1.24638	−0.623189	+	0.782071i	$0.714163\pi$
$30$	2.43000e7	0.182574
$31$	2.54514e8	1.59670	0.798348	−	0.602196i	$-0.205707\pi$
$31$	2.54514e8	1.59670	0.798348	+	0.602196i	$0.205707\pi$
$32$	3.35544e7	0.176777
$33$	1.69675e8	0.754730
$34$	3.12677e8	1.18022
$35$	5.25219e7	0.169031
$36$	6.04662e7	0.166667
$37$	−3.03614e8	−0.719802	−0.359901	−	0.932991i	$-0.617190\pi$
$37$	−3.03614e8	−0.719802	−0.359901	+	0.932991i	$0.617190\pi$
$38$	3.85407e8	0.789060
$39$	5.56786e7	0.0988172
$40$	1.02400e8	0.158114
$41$	−1.39163e8	−0.187591	−0.0937955	−	0.995591i	$-0.529900\pi$
$41$	−1.39163e8	−0.187591	−0.0937955	+	0.995591i	$0.529900\pi$
$42$	1.30691e8	0.154303
$43$	−1.85345e9	−1.92267	−0.961336	−	0.275378i	$-0.911197\pi$
$43$	−1.85345e9	−1.92267	−0.961336	+	0.275378i	$0.911197\pi$
$44$	7.15009e8	0.653615
$45$	1.84528e8	0.149071
$46$	−1.78382e9	−1.27698
$47$	2.84162e9	1.80729	0.903643	−	0.428286i	$-0.140882\pi$
$47$	2.84162e9	1.80729	0.903643	+	0.428286i	$0.140882\pi$
$48$	2.54804e8	0.144338
$49$	2.82475e8	0.142857
$50$	3.12500e8	0.141421
$51$	2.37439e9	0.963645
$52$	2.34629e8	0.0855782
$53$	−1.70315e9	−0.559418	−0.279709	−	0.960085i	$-0.590238\pi$
$53$	−1.70315e9	−0.559418	−0.279709	+	0.960085i	$0.590238\pi$
$54$	4.59165e8	0.136083
$55$	2.18204e9	0.584611
$56$	5.50732e8	0.133631
$57$	2.92669e9	0.644265
$58$	−4.40544e9	−0.881323
$59$	−3.42148e9	−0.623057	−0.311529	−	0.950237i	$-0.600841\pi$
$59$	−3.42148e9	−0.623057	−0.311529	+	0.950237i	$0.600841\pi$
$60$	7.77600e8	0.129099
$61$	1.08369e10	1.64282	0.821411	−	0.570337i	$-0.193187\pi$
$61$	1.08369e10	1.64282	0.821411	+	0.570337i	$0.193187\pi$
$62$	8.14445e9	1.12903
$63$	9.92437e8	0.125988
$64$	1.07374e9	0.125000
$65$	7.16031e8	0.0765435
$66$	5.42960e9	0.533674
$67$	2.90368e8	0.0262747	0.0131374	−	0.999914i	$-0.495818\pi$
$67$	2.90368e8	0.0262747	0.0131374	+	0.999914i	$0.495818\pi$
$68$	1.00057e10	0.834541
$69$	−1.35459e10	−1.04265
$70$	1.68070e9	0.119523
$71$	3.15656e9	0.207632	0.103816	−	0.994597i	$-0.466895\pi$
$71$	3.15656e9	0.207632	0.103816	+	0.994597i	$0.466895\pi$
$72$	1.93492e9	0.117851
$73$	−2.16205e10	−1.22064	−0.610322	−	0.792153i	$-0.708960\pi$
$73$	−2.16205e10	−1.22064	−0.610322	+	0.792153i	$0.708960\pi$
$74$	−9.71566e9	−0.508977
$75$	2.37305e9	0.115470
$76$	1.23330e10	0.557950
$77$	1.17355e10	0.494086
$78$	1.78171e9	0.0698743
$79$	−4.72176e9	−0.172645	−0.0863227	−	0.996267i	$-0.527512\pi$
$79$	−4.72176e9	−0.172645	−0.0863227	+	0.996267i	$0.527512\pi$
$80$	3.27680e9	0.111803
$81$	3.48678e9	0.111111
$82$	−4.45321e9	−0.132647
$83$	8.20464e9	0.228628	0.114314	−	0.993445i	$-0.463533\pi$
$83$	8.20464e9	0.228628	0.114314	+	0.993445i	$0.463533\pi$
$84$	4.18212e9	0.109109
$85$	3.05349e10	0.746436
$86$	−5.93105e10	−1.35953
$87$	−3.34538e10	−0.719597
$88$	2.28803e10	0.462176
$89$	7.16987e10	1.36103	0.680513	−	0.732736i	$-0.261757\pi$
$89$	7.16987e10	1.36103	0.680513	+	0.732736i	$0.261757\pi$
$90$	5.90490e9	0.105409
$91$	3.85099e9	0.0646911
$92$	−5.70823e10	−0.902960
$93$	6.18469e10	0.921853
$94$	9.09317e10	1.27794
$95$	3.76374e10	0.499045
$96$	8.15373e9	0.102062
$97$	1.14510e10	0.135394	0.0676972	−	0.997706i	$-0.478435\pi$
$97$	1.14510e10	0.135394	0.0676972	+	0.997706i	$0.478435\pi$
$98$	9.03921e9	0.101015
$99$	4.12310e10	0.435743
$100$	1.00000e10	0.100000
$101$	−3.46305e10	−0.327863	−0.163931	−	0.986472i	$-0.552418\pi$
$101$	−3.46305e10	−0.327863	−0.163931	+	0.986472i	$0.552418\pi$
$102$	7.59806e10	0.681400
$103$	−4.62747e10	−0.393313	−0.196657	−	0.980472i	$-0.563008\pi$
$103$	−4.62747e10	−0.393313	−0.196657	+	0.980472i	$0.563008\pi$
$104$	7.50813e9	0.0605129
$105$	1.27628e10	0.0975900
$106$	−5.45009e10	−0.395568
$107$	3.62165e10	0.249630	0.124815	−	0.992180i	$-0.460166\pi$
$107$	3.62165e10	0.249630	0.124815	+	0.992180i	$0.460166\pi$
$108$	1.46933e10	0.0962250
$109$	4.68152e10	0.291435	0.145717	−	0.989326i	$-0.453451\pi$
$109$	4.68152e10	0.291435	0.145717	+	0.989326i	$0.453451\pi$
$110$	6.98251e10	0.413382
$111$	−7.37783e10	−0.415578
$112$	1.76234e10	0.0944911
$113$	−3.24061e10	−0.165461	−0.0827306	−	0.996572i	$-0.526364\pi$
$113$	−3.24061e10	−0.165461	−0.0827306	+	0.996572i	$0.526364\pi$
$114$	9.36540e10	0.455564
$115$	−1.74201e11	−0.807632
$116$	−1.40974e11	−0.623189
$117$	1.35299e10	0.0570521
$118$	−1.09487e11	−0.440568
$119$	1.64224e11	0.630854
$120$	2.48832e10	0.0912871
$121$	2.02243e11	0.708850
$122$	3.46780e11	1.16165
$123$	−3.38166e10	−0.108306
$124$	2.60622e11	0.798348
$125$	3.05176e10	0.0894427
$126$	3.17580e10	0.0890871
$127$	−1.26152e11	−0.338824	−0.169412	−	0.985545i	$-0.554187\pi$
$127$	−1.26152e11	−0.338824	−0.169412	+	0.985545i	$0.554187\pi$
$128$	3.43597e10	0.0883883
$129$	−4.50389e11	−1.11006
$130$	2.29130e10	0.0541244
$131$	1.95887e11	0.443623	0.221811	−	0.975090i	$-0.428803\pi$
$131$	1.95887e11	0.443623	0.221811	+	0.975090i	$0.428803\pi$
$132$	1.73747e11	0.377365
$133$	2.02423e11	0.421770
$134$	9.29179e9	0.0185790
$135$	4.48403e10	0.0860663
$136$	3.20182e11	0.590109
$137$	−7.36948e11	−1.30459	−0.652294	−	0.757966i	$-0.726193\pi$
$137$	−7.36948e11	−1.30459	−0.652294	+	0.757966i	$0.726193\pi$
$138$	−4.33469e11	−0.737264
$139$	−4.82577e9	−0.00788834	−0.00394417	−	0.999992i	$-0.501255\pi$
$139$	−4.82577e9	−0.00788834	−0.00394417	+	0.999992i	$0.501255\pi$
$140$	5.37824e10	0.0845154
$141$	6.90512e11	1.04344
$142$	1.01010e11	0.146818
$143$	1.59990e11	0.223741
$144$	6.19174e10	0.0833333
$145$	−4.30219e11	−0.557398
$146$	−6.91855e11	−0.863126
$147$	6.86415e10	0.0824786
$148$	−3.10901e11	−0.359901
$149$	1.16005e12	1.29405	0.647025	−	0.762469i	$-0.276013\pi$
$149$	1.16005e12	1.29405	0.647025	+	0.762469i	$0.276013\pi$
$150$	7.59375e10	0.0816497
$151$	1.34371e12	1.39294	0.696468	−	0.717588i	$-0.254754\pi$
$151$	1.34371e12	1.39294	0.696468	+	0.717588i	$0.254754\pi$
$152$	3.94657e11	0.394530
$153$	5.76978e11	0.556360
$154$	3.75536e11	0.349372
$155$	7.95356e11	0.714064
$156$	5.70148e10	0.0494086
$157$	5.38545e11	0.450582	0.225291	−	0.974291i	$-0.427667\pi$
$157$	5.38545e11	0.450582	0.225291	+	0.974291i	$0.427667\pi$
$158$	−1.51096e11	−0.122079
$159$	−4.13866e11	−0.322980
$160$	1.04858e11	0.0790569
$161$	−9.36897e11	−0.682574
$162$	1.11577e11	0.0785674
$163$	1.11506e12	0.759042	0.379521	−	0.925183i	$-0.376089\pi$
$163$	1.11506e12	0.759042	0.379521	+	0.925183i	$0.376089\pi$
$164$	−1.42503e11	−0.0937955
$165$	5.30235e11	0.337525
$166$	2.62548e11	0.161665
$167$	−7.74195e11	−0.461222	−0.230611	−	0.973046i	$-0.574072\pi$
$167$	−7.74195e11	−0.461222	−0.230611	+	0.973046i	$0.574072\pi$
$168$	1.33828e11	0.0771517
$169$	−1.73966e12	−0.970705
$170$	9.77117e11	0.527810
$171$	7.11185e11	0.371966
$172$	−1.89794e12	−0.961336
$173$	−1.68250e12	−0.825469	−0.412735	−	0.910851i	$-0.635426\pi$
$173$	−1.68250e12	−0.825469	−0.412735	+	0.910851i	$0.635426\pi$
$174$	−1.07052e12	−0.508832
$175$	1.64131e11	0.0755929
$176$	7.32170e11	0.326807
$177$	−8.31420e11	−0.359722
$178$	2.29436e12	0.962391
$179$	2.13685e12	0.869125	0.434562	−	0.900642i	$-0.356903\pi$
$179$	2.13685e12	0.869125	0.434562	+	0.900642i	$0.356903\pi$
$180$	1.88957e11	0.0745356
$181$	−3.73590e12	−1.42943	−0.714716	−	0.699415i	$-0.753444\pi$
$181$	−3.73590e12	−1.42943	−0.714716	+	0.699415i	$0.753444\pi$
$182$	1.23232e11	0.0457435
$183$	2.63336e12	0.948483
$184$	−1.82663e12	−0.638489
$185$	−9.48795e11	−0.321905
$186$	1.97910e12	0.651849
$187$	6.82273e12	2.18187
$188$	2.90981e12	0.903643
$189$	2.41162e11	0.0727393
$190$	1.20440e12	0.352878
$191$	−9.81289e11	−0.279327	−0.139664	−	0.990199i	$-0.544602\pi$
$191$	−9.81289e11	−0.279327	−0.139664	+	0.990199i	$0.544602\pi$
$192$	2.60919e11	0.0721688
$193$	−4.08965e12	−1.09931	−0.549656	−	0.835391i	$-0.685241\pi$
$193$	−4.08965e12	−1.09931	−0.549656	+	0.835391i	$0.685241\pi$
$194$	3.66433e11	0.0957383
$195$	1.73995e11	0.0441924
$196$	2.89255e11	0.0714286
$197$	7.13380e12	1.71300	0.856499	−	0.516149i	$-0.172635\pi$
$197$	7.13380e12	1.71300	0.856499	+	0.516149i	$0.172635\pi$
$198$	1.31939e12	0.308117
$199$	−6.66185e12	−1.51322	−0.756611	−	0.653865i	$-0.773146\pi$
$199$	−6.66185e12	−1.51322	−0.756611	+	0.653865i	$0.773146\pi$
$200$	3.20000e11	0.0707107
$201$	7.05595e10	0.0151697
$202$	−1.10818e12	−0.231834
$203$	−2.31382e12	−0.471087
$204$	2.43138e12	0.481822
$205$	−4.34884e11	−0.0838933
$206$	−1.48079e12	−0.278114
$207$	−3.29165e12	−0.601973
$208$	2.40260e11	0.0427891
$209$	8.40972e12	1.45874
$210$	4.08410e11	0.0690066
$211$	6.06104e12	0.997685	0.498842	−	0.866693i	$-0.333759\pi$
$211$	6.06104e12	0.997685	0.498842	+	0.866693i	$0.333759\pi$
$212$	−1.74403e12	−0.279709
$213$	7.67045e11	0.119876
$214$	1.15893e12	0.176515
$215$	−5.79204e12	−0.859845
$216$	4.70185e11	0.0680414
$217$	4.27762e12	0.603495
$218$	1.49809e12	0.206075
$219$	−5.25377e12	−0.704739
$220$	2.23440e12	0.292306
$221$	2.23887e12	0.285674
$222$	−2.36091e12	−0.293858
$223$	6.19318e12	0.752033	0.376016	−	0.926613i	$-0.377294\pi$
$223$	6.19318e12	0.752033	0.376016	+	0.926613i	$0.377294\pi$
$224$	5.63949e11	0.0668153
$225$	5.76650e11	0.0666667
$226$	−1.03700e12	−0.116999
$227$	−2.75775e12	−0.303678	−0.151839	−	0.988405i	$-0.548520\pi$
$227$	−2.75775e12	−0.303678	−0.151839	+	0.988405i	$0.548520\pi$
$228$	2.99693e12	0.322132
$229$	1.35156e13	1.41821	0.709103	−	0.705105i	$-0.249100\pi$
$229$	1.35156e13	1.41821	0.709103	+	0.705105i	$0.249100\pi$
$230$	−5.57444e12	−0.571082
$231$	2.85173e12	0.285261
$232$	−4.51117e12	−0.440661
$233$	6.95838e12	0.663821	0.331910	−	0.943311i	$-0.392307\pi$
$233$	6.95838e12	0.663821	0.331910	+	0.943311i	$0.392307\pi$
$234$	4.32956e11	0.0403420
$235$	8.88005e12	0.808243
$236$	−3.50360e12	−0.311529
$237$	−1.14739e12	−0.0996769
$238$	5.25517e12	0.446081
$239$	−1.58291e13	−1.31301	−0.656503	−	0.754323i	$-0.727965\pi$
$239$	−1.58291e13	−1.31301	−0.656503	+	0.754323i	$0.727965\pi$
$240$	7.96262e11	0.0645497
$241$	1.04009e13	0.824094	0.412047	−	0.911163i	$-0.364814\pi$
$241$	1.04009e13	0.824094	0.412047	+	0.911163i	$0.364814\pi$
$242$	6.47178e12	0.501233
$243$	8.47289e11	0.0641500
$244$	1.10970e13	0.821411
$245$	8.82735e11	0.0638877
$246$	−1.08213e12	−0.0765837
$247$	2.75963e12	0.190993
$248$	8.33991e12	0.564517
$249$	1.99373e12	0.131999
$250$	9.76562e11	0.0632456
$251$	1.41647e13	0.897431	0.448716	−	0.893675i	$-0.351882\pi$
$251$	1.41647e13	0.897431	0.448716	+	0.893675i	$0.351882\pi$
$252$	1.01626e12	0.0629941
$253$	−3.89236e13	−2.36075
$254$	−4.03687e12	−0.239585
$255$	7.41998e12	0.430955
$256$	1.09951e12	0.0625000
$257$	−1.28843e13	−0.716849	−0.358424	−	0.933559i	$-0.616686\pi$
$257$	−1.28843e13	−0.716849	−0.358424	+	0.933559i	$0.616686\pi$
$258$	−1.44125e13	−0.784928
$259$	−5.10285e12	−0.272060
$260$	7.33216e11	0.0382717
$261$	−8.12927e12	−0.415460
$262$	6.26839e12	0.313689
$263$	4.65127e12	0.227937	0.113968	−	0.993484i	$-0.463644\pi$
$263$	4.65127e12	0.227937	0.113968	+	0.993484i	$0.463644\pi$
$264$	5.55991e12	0.266837
$265$	−5.32235e12	−0.250179
$266$	6.47754e12	0.298237
$267$	1.74228e13	0.785789
$268$	2.97337e11	0.0131374
$269$	3.88101e13	1.67999	0.839995	−	0.542594i	$-0.182558\pi$
$269$	3.88101e13	1.67999	0.839995	+	0.542594i	$0.182558\pi$
$270$	1.43489e12	0.0608581
$271$	2.06033e13	0.856262	0.428131	−	0.903717i	$-0.359172\pi$
$271$	2.06033e13	0.856262	0.428131	+	0.903717i	$0.359172\pi$
$272$	1.02458e13	0.417270
$273$	9.35789e11	0.0373494
$274$	−2.35823e13	−0.922484
$275$	6.81886e12	0.261446
$276$	−1.38710e13	−0.521324
$277$	−3.49690e13	−1.28838	−0.644190	−	0.764865i	$-0.722805\pi$
$277$	−3.49690e13	−1.28838	−0.644190	+	0.764865i	$0.722805\pi$
$278$	−1.54425e11	−0.00557790
$279$	1.50288e13	0.532232
$280$	1.72104e12	0.0597614
$281$	1.80584e13	0.614885	0.307443	−	0.951567i	$-0.400527\pi$
$281$	1.80584e13	0.614885	0.307443	+	0.951567i	$0.400527\pi$
$282$	2.20964e13	0.737822
$283$	1.95900e13	0.641518	0.320759	−	0.947161i	$-0.396062\pi$
$283$	1.95900e13	0.641518	0.320759	+	0.947161i	$0.396062\pi$
$284$	3.23232e12	0.103816
$285$	9.14589e12	0.288124
$286$	5.11969e12	0.158209
$287$	−2.33891e12	−0.0709027
$288$	1.98136e12	0.0589256
$289$	6.12039e13	1.78583
$290$	−1.37670e13	−0.394140
$291$	2.78260e12	0.0781700
$292$	−2.21393e13	−0.610322
$293$	2.33197e13	0.630887	0.315444	−	0.948944i	$-0.397847\pi$
$293$	2.33197e13	0.630887	0.315444	+	0.948944i	$0.397847\pi$
$294$	2.19653e12	0.0583212
$295$	−1.06921e13	−0.278640
$296$	−9.94884e12	−0.254488
$297$	1.00191e13	0.251577
$298$	3.71215e13	0.915032
$299$	−1.27727e13	−0.309095
$300$	2.43000e12	0.0577350
$301$	−3.11510e13	−0.726702
$302$	4.29986e13	0.984954
$303$	−8.41522e12	−0.189292
$304$	1.26290e13	0.278975
$305$	3.38653e13	0.734692
$306$	1.84633e13	0.393406
$307$	−1.39550e13	−0.292058	−0.146029	−	0.989280i	$-0.546649\pi$
$307$	−1.39550e13	−0.292058	−0.146029	+	0.989280i	$0.546649\pi$
$308$	1.20172e13	0.247043
$309$	−1.12447e13	−0.227079
$310$	2.54514e13	0.504920
$311$	−6.97251e13	−1.35896	−0.679481	−	0.733693i	$-0.737795\pi$
$311$	−6.97251e13	−1.35896	−0.679481	+	0.733693i	$0.737795\pi$
$312$	1.82447e12	0.0349372
$313$	2.49227e12	0.0468923	0.0234462	−	0.999725i	$-0.492536\pi$
$313$	2.49227e12	0.0468923	0.0234462	+	0.999725i	$0.492536\pi$
$314$	1.72334e13	0.318610
$315$	3.10136e12	0.0563436
$316$	−4.83508e12	−0.0863227
$317$	−9.89070e13	−1.73541	−0.867703	−	0.497084i	$-0.834404\pi$
$317$	−9.89070e13	−1.73541	−0.867703	+	0.497084i	$0.834404\pi$
$318$	−1.32437e13	−0.228381
$319$	−9.61282e13	−1.62930
$320$	3.35544e12	0.0559017
$321$	8.80062e12	0.144124
$322$	−2.99807e13	−0.482652
$323$	1.17684e14	1.86253
$324$	3.57047e12	0.0555556
$325$	2.23760e12	0.0342313
$326$	3.56818e13	0.536723
$327$	1.13761e13	0.168260
$328$	−4.56009e12	−0.0663234
$329$	4.77590e13	0.683090
$330$	1.69675e13	0.238666
$331$	−2.65361e13	−0.367099	−0.183550	−	0.983010i	$-0.558759\pi$
$331$	−2.65361e13	−0.367099	−0.183550	+	0.983010i	$0.558759\pi$
$332$	8.40155e12	0.114314
$333$	−1.79281e13	−0.239934
$334$	−2.47743e13	−0.326133
$335$	9.07401e11	0.0117504
$336$	4.28249e12	0.0545545
$337$	1.14430e14	1.43409	0.717044	−	0.697028i	$-0.245495\pi$
$337$	1.14430e14	1.43409	0.717044	+	0.697028i	$0.245495\pi$
$338$	−5.56691e13	−0.686392
$339$	−7.87469e12	−0.0955290
$340$	3.12677e13	0.373218
$341$	1.77715e14	2.08725
$342$	2.27579e13	0.263020
$343$	4.74756e12	0.0539949
$344$	−6.07340e13	−0.679767
$345$	−4.23309e13	−0.466287
$346$	−5.38399e13	−0.583695
$347$	−6.11142e13	−0.652123	−0.326062	−	0.945349i	$-0.605722\pi$
$347$	−6.11142e13	−0.652123	−0.326062	+	0.945349i	$0.605722\pi$
$348$	−3.42567e13	−0.359799
$349$	−1.43963e14	−1.48837	−0.744185	−	0.667974i	$-0.767162\pi$
$349$	−1.43963e14	−1.48837	−0.744185	+	0.667974i	$0.767162\pi$
$350$	5.25219e12	0.0534522
$351$	3.28776e12	0.0329391
$352$	2.34294e13	0.231088
$353$	3.50413e13	0.340267	0.170133	−	0.985421i	$-0.445580\pi$
$353$	3.50413e13	0.340267	0.170133	+	0.985421i	$0.445580\pi$
$354$	−2.66054e13	−0.254362
$355$	9.86426e12	0.0928557
$356$	7.34195e13	0.680513
$357$	3.99064e13	0.364223
$358$	6.83792e13	0.614564
$359$	−5.27894e13	−0.467226	−0.233613	−	0.972330i	$-0.575055\pi$
$359$	−5.27894e13	−0.467226	−0.233613	+	0.972330i	$0.575055\pi$
$360$	6.04662e12	0.0527046
$361$	2.85671e13	0.245232
$362$	−1.19549e14	−1.01076
$363$	4.91451e13	0.409255
$364$	3.94341e12	0.0323455
$365$	−6.75639e13	−0.545889
$366$	8.42676e13	0.670679
$367$	8.55428e13	0.670688	0.335344	−	0.942096i	$-0.391148\pi$
$367$	8.55428e13	0.670688	0.335344	+	0.942096i	$0.391148\pi$
$368$	−5.84523e13	−0.451480
$369$	−8.21743e12	−0.0625303
$370$	−3.03614e13	−0.227621
$371$	−2.86249e13	−0.211440
$372$	6.33312e13	0.460927
$373$	−1.71926e14	−1.23294	−0.616470	−	0.787378i	$-0.711438\pi$
$373$	−1.71926e14	−1.23294	−0.616470	+	0.787378i	$0.711438\pi$
$374$	2.18327e14	1.54282
$375$	7.41577e12	0.0516398
$376$	9.31140e13	0.638972
$377$	−3.15443e13	−0.213326
$378$	7.71719e12	0.0514344
$379$	−1.21616e14	−0.798866	−0.399433	−	0.916762i	$-0.630793\pi$
$379$	−1.21616e14	−0.798866	−0.399433	+	0.916762i	$0.630793\pi$
$380$	3.85407e13	0.249523
$381$	−3.06550e13	−0.195620
$382$	−3.14012e13	−0.197514
$383$	1.66646e14	1.03324	0.516621	−	0.856214i	$-0.327190\pi$
$383$	1.66646e14	1.03324	0.516621	+	0.856214i	$0.327190\pi$
$384$	8.34942e12	0.0510310
$385$	3.66735e13	0.220962
$386$	−1.30869e14	−0.777331
$387$	−1.09445e14	−0.640891
$388$	1.17259e13	0.0676972
$389$	−2.26666e14	−1.29022	−0.645110	−	0.764090i	$-0.723189\pi$
$389$	−2.26666e14	−1.29022	−0.645110	+	0.764090i	$0.723189\pi$
$390$	5.56786e12	0.0312487
$391$	−5.44688e14	−3.01423
$392$	9.25615e12	0.0505076
$393$	4.76006e13	0.256126
$394$	2.28282e14	1.21127
$395$	−1.47555e13	−0.0772094
$396$	4.22206e13	0.217872
$397$	−8.39773e13	−0.427380	−0.213690	−	0.976902i	$-0.568548\pi$
$397$	−8.39773e13	−0.427380	−0.213690	+	0.976902i	$0.568548\pi$
$398$	−2.13179e14	−1.07001
$399$	4.91888e13	0.243509
$400$	1.02400e13	0.0500000
$401$	1.74120e14	0.838600	0.419300	−	0.907848i	$-0.362276\pi$
$401$	1.74120e14	0.838600	0.419300	+	0.907848i	$0.362276\pi$
$402$	2.25790e12	0.0107266
$403$	5.83168e13	0.273285
$404$	−3.54617e13	−0.163931
$405$	1.08962e13	0.0496904
$406$	−7.40422e13	−0.333109
$407$	−2.11999e14	−0.940947
$408$	7.78042e13	0.340700
$409$	−2.63742e14	−1.13947	−0.569733	−	0.821830i	$-0.692953\pi$
$409$	−2.63742e14	−1.13947	−0.569733	+	0.821830i	$0.692953\pi$
$410$	−1.39163e13	−0.0593215
$411$	−1.79078e14	−0.753205
$412$	−4.73852e13	−0.196657
$413$	−5.75048e13	−0.235494
$414$	−1.05333e14	−0.425659
$415$	2.56395e13	0.102246
$416$	7.68832e12	0.0302565
$417$	−1.17266e12	−0.00455433
$418$	2.69111e14	1.03148
$419$	−2.92581e14	−1.10680	−0.553399	−	0.832916i	$-0.686670\pi$
$419$	−2.92581e14	−1.10680	−0.553399	+	0.832916i	$0.686670\pi$
$420$	1.30691e13	0.0487950
$421$	−4.84338e14	−1.78483	−0.892416	−	0.451213i	$-0.850991\pi$
$421$	−4.84338e14	−1.78483	−0.892416	+	0.451213i	$0.850991\pi$
$422$	1.93953e14	0.705470
$423$	1.67795e14	0.602429
$424$	−5.58089e13	−0.197784
$425$	9.54216e13	0.333816
$426$	2.45454e13	0.0847652
$427$	1.82136e14	0.620928
$428$	3.70857e13	0.124815
$429$	3.88776e13	0.129177
$430$	−1.85345e14	−0.608002
$431$	−2.49252e14	−0.807261	−0.403630	−	0.914922i	$-0.632252\pi$
$431$	−2.49252e14	−0.807261	−0.403630	+	0.914922i	$0.632252\pi$
$432$	1.50459e13	0.0481125
$433$	−7.71314e13	−0.243527	−0.121764	−	0.992559i	$-0.538855\pi$
$433$	−7.71314e13	−0.243527	−0.121764	+	0.992559i	$0.538855\pi$
$434$	1.36884e14	0.426735
$435$	−1.04543e14	−0.321814
$436$	4.79388e13	0.145717
$437$	−6.71385e14	−2.01523
$438$	−1.68121e14	−0.498326
$439$	−5.35983e14	−1.56890	−0.784452	−	0.620190i	$-0.787056\pi$
$439$	−5.35983e14	−1.56890	−0.784452	+	0.620190i	$0.787056\pi$
$440$	7.15009e13	0.206691
$441$	1.66799e13	0.0476190
$442$	7.16437e13	0.202002
$443$	2.12958e14	0.593027	0.296513	−	0.955029i	$-0.404176\pi$
$443$	2.12958e14	0.593027	0.296513	+	0.955029i	$0.404176\pi$
$444$	−7.55490e13	−0.207789
$445$	2.24059e14	0.608669
$446$	1.98182e14	0.531768
$447$	2.81891e14	0.747120
$448$	1.80464e13	0.0472456
$449$	−5.77641e14	−1.49384	−0.746918	−	0.664916i	$-0.768467\pi$
$449$	−5.77641e14	−1.49384	−0.746918	+	0.664916i	$0.768467\pi$
$450$	1.84528e13	0.0471405
$451$	−9.71706e13	−0.245225
$452$	−3.31839e13	−0.0827306
$453$	3.26520e14	0.804211
$454$	−8.82481e13	−0.214733
$455$	1.20343e13	0.0289307
$456$	9.59016e13	0.227782
$457$	−3.81371e14	−0.894970	−0.447485	−	0.894292i	$-0.647680\pi$
$457$	−3.81371e14	−0.894970	−0.447485	+	0.894292i	$0.647680\pi$
$458$	4.32499e14	1.00282
$459$	1.40206e14	0.321215
$460$	−1.78382e14	−0.403816
$461$	−7.85400e14	−1.75685	−0.878427	−	0.477876i	$-0.841407\pi$
$461$	−7.85400e14	−1.75685	−0.878427	+	0.477876i	$0.841407\pi$
$462$	9.12553e13	0.201710
$463$	−3.62598e14	−0.792008	−0.396004	−	0.918249i	$-0.629603\pi$
$463$	−3.62598e14	−0.792008	−0.396004	+	0.918249i	$0.629603\pi$
$464$	−1.44357e14	−0.311595
$465$	1.93272e14	0.412265
$466$	2.22668e14	0.469392
$467$	−2.48902e14	−0.518544	−0.259272	−	0.965804i	$-0.583483\pi$
$467$	−2.48902e14	−0.518544	−0.259272	+	0.965804i	$0.583483\pi$
$468$	1.38546e13	0.0285261
$469$	4.88022e12	0.00993091
$470$	2.84162e14	0.571514
$471$	1.30866e14	0.260144
$472$	−1.12115e14	−0.220284
$473$	−1.29418e15	−2.51337
$474$	−3.67164e13	−0.0704822
$475$	1.17617e14	0.223180
$476$	1.68165e14	0.315427
$477$	−1.00569e14	−0.186473
$478$	−5.06530e14	−0.928436
$479$	−5.80301e13	−0.105150	−0.0525748	−	0.998617i	$-0.516743\pi$
$479$	−5.80301e13	−0.105150	−0.0525748	+	0.998617i	$0.516743\pi$
$480$	2.54804e13	0.0456435
$481$	−6.95671e13	−0.123199
$482$	3.32828e14	0.582723
$483$	−2.27666e14	−0.394084
$484$	2.07097e14	0.354425
$485$	3.57845e13	0.0605502
$486$	2.71132e13	0.0453609
$487$	9.91576e14	1.64028	0.820138	−	0.572166i	$-0.193897\pi$
$487$	9.91576e14	1.64028	0.820138	+	0.572166i	$0.193897\pi$
$488$	3.55103e14	0.580825
$489$	2.70959e14	0.438233
$490$	2.82475e13	0.0451754
$491$	−3.96838e14	−0.627574	−0.313787	−	0.949493i	$-0.601598\pi$
$491$	−3.96838e14	−0.627574	−0.313787	+	0.949493i	$0.601598\pi$
$492$	−3.46282e13	−0.0541529
$493$	−1.34520e15	−2.08031
$494$	8.83083e13	0.135053
$495$	1.28847e14	0.194870
$496$	2.66877e14	0.399174
$497$	5.30523e13	0.0784774
$498$	6.37993e13	0.0933371
$499$	9.37047e14	1.35584	0.677920	−	0.735136i	$-0.262882\pi$
$499$	9.37047e14	1.35584	0.677920	+	0.735136i	$0.262882\pi$
$500$	3.12500e13	0.0447214
$501$	−1.88129e14	−0.266287
$502$	4.53270e14	0.634580
$503$	−1.19254e15	−1.65139	−0.825693	−	0.564119i	$-0.809216\pi$
$503$	−1.19254e15	−1.65139	−0.825693	+	0.564119i	$0.809216\pi$
$504$	3.25202e13	0.0445435
$505$	−1.08220e14	−0.146625
$506$	−1.24556e15	−1.66930
$507$	−4.22737e14	−0.560437
$508$	−1.29180e14	−0.169412
$509$	−1.01218e15	−1.31314	−0.656571	−	0.754264i	$-0.727994\pi$
$509$	−1.01218e15	−1.31314	−0.656571	+	0.754264i	$0.727994\pi$
$510$	2.37439e14	0.304731
$511$	−3.63375e14	−0.461360
$512$	3.51844e13	0.0441942
$513$	1.72818e14	0.214755
$514$	−4.12296e14	−0.506888
$515$	−1.44608e14	−0.175895
$516$	−4.61199e14	−0.555028
$517$	1.98416e15	2.36254
$518$	−1.63291e14	−0.192375
$519$	−4.08847e14	−0.476585
$520$	2.34629e13	0.0270622
$521$	−1.12034e15	−1.27862	−0.639312	−	0.768948i	$-0.720781\pi$
$521$	−1.12034e15	−1.27862	−0.639312	+	0.768948i	$0.720781\pi$
$522$	−2.60137e14	−0.293774
$523$	4.67165e14	0.522049	0.261025	−	0.965332i	$-0.415940\pi$
$523$	4.67165e14	0.522049	0.261025	+	0.965332i	$0.415940\pi$
$524$	2.00588e14	0.221811
$525$	3.98838e13	0.0436436
$526$	1.48840e14	0.161176
$527$	2.48690e15	2.66502
$528$	1.77917e14	0.188682
$529$	2.15463e15	2.26135
$530$	−1.70315e14	−0.176904
$531$	−2.02035e14	−0.207686
$532$	2.07281e14	0.210885
$533$	−3.18864e13	−0.0321074
$534$	5.57529e14	0.555636
$535$	1.13177e14	0.111638
$536$	9.51479e12	0.00928951
$537$	5.19254e14	0.501789
$538$	1.24192e15	1.18793
$539$	1.97239e14	0.186747
$540$	4.59165e13	0.0430331
$541$	1.59411e15	1.47888	0.739441	−	0.673221i	$-0.235090\pi$
$541$	1.59411e15	1.47888	0.739441	+	0.673221i	$0.235090\pi$
$542$	6.59307e14	0.605469
$543$	−9.07825e14	−0.825283
$544$	3.27866e14	0.295055
$545$	1.46297e14	0.130334
$546$	2.99453e13	0.0264100
$547$	−1.15162e15	−1.00549	−0.502746	−	0.864434i	$-0.667677\pi$
$547$	−1.15162e15	−1.00549	−0.502746	+	0.864434i	$0.667677\pi$
$548$	−7.54635e14	−0.652294
$549$	6.39907e14	0.547607
$550$	2.18204e14	0.184870
$551$	−1.65809e15	−1.39083
$552$	−4.43872e14	−0.368632
$553$	−7.93586e13	−0.0652538
$554$	−1.11901e15	−0.911022
$555$	−2.30557e14	−0.185852
$556$	−4.94159e12	−0.00394417
$557$	4.74336e14	0.374872	0.187436	−	0.982277i	$-0.439982\pi$
$557$	4.74336e14	0.374872	0.187436	+	0.982277i	$0.439982\pi$
$558$	4.80922e14	0.376345
$559$	−4.24682e14	−0.329078
$560$	5.50732e13	0.0422577
$561$	1.65792e15	1.25971
$562$	5.77868e14	0.434789
$563$	1.11377e15	0.829850	0.414925	−	0.909856i	$-0.363808\pi$
$563$	1.11377e15	0.829850	0.414925	+	0.909856i	$0.363808\pi$
$564$	7.07085e14	0.521719
$565$	−1.01269e14	−0.0739965
$566$	6.26880e14	0.453622
$567$	5.86024e13	0.0419961
$568$	1.03434e14	0.0734088
$569$	−5.10232e14	−0.358633	−0.179316	−	0.983791i	$-0.557389\pi$
$569$	−5.10232e14	−0.358633	−0.179316	+	0.983791i	$0.557389\pi$
$570$	2.92669e14	0.203734
$571$	6.48966e13	0.0447428	0.0223714	−	0.999750i	$-0.492878\pi$
$571$	6.48966e13	0.0447428	0.0223714	+	0.999750i	$0.492878\pi$
$572$	1.63830e14	0.111870
$573$	−2.38453e14	−0.161270
$574$	−7.48451e13	−0.0501358
$575$	−5.44379e14	−0.361184
$576$	6.34034e13	0.0416667
$577$	−7.14525e14	−0.465104	−0.232552	−	0.972584i	$-0.574708\pi$
$577$	−7.14525e14	−0.465104	−0.232552	+	0.972584i	$0.574708\pi$
$578$	1.95852e15	1.26277
$579$	−9.93785e14	−0.634688
$580$	−4.40544e14	−0.278699
$581$	1.37895e14	0.0864134
$582$	8.90433e13	0.0552745
$583$	−1.18923e15	−0.731288
$584$	−7.08459e14	−0.431563
$585$	4.22809e13	0.0255145
$586$	7.46232e14	0.446105
$587$	1.58543e15	0.938939	0.469470	−	0.882949i	$-0.344445\pi$
$587$	1.58543e15	0.938939	0.469470	+	0.882949i	$0.344445\pi$
$588$	7.02889e13	0.0412393
$589$	3.06536e15	1.78175
$590$	−3.42148e14	−0.197028
$591$	1.73351e15	0.988999
$592$	−3.18363e14	−0.179950
$593$	−1.13151e14	−0.0633660	−0.0316830	−	0.999498i	$-0.510087\pi$
$593$	−1.13151e14	−0.0633660	−0.0316830	+	0.999498i	$0.510087\pi$
$594$	3.20613e14	0.177891
$595$	5.13200e14	0.282126
$596$	1.18789e15	0.647025
$597$	−1.61883e15	−0.873659
$598$	−4.08727e14	−0.218563
$599$	1.60702e15	0.851481	0.425741	−	0.904845i	$-0.360014\pi$
$599$	1.60702e15	0.851481	0.425741	+	0.904845i	$0.360014\pi$
$600$	7.77600e13	0.0408248
$601$	2.58179e15	1.34311	0.671554	−	0.740955i	$-0.265627\pi$
$601$	2.58179e15	1.34311	0.671554	+	0.740955i	$0.265627\pi$
$602$	−9.96832e14	−0.513856
$603$	1.71460e13	0.00875824
$604$	1.37595e15	0.696468
$605$	6.32010e14	0.317007
$606$	−2.69287e14	−0.133849
$607$	−5.58987e13	−0.0275336	−0.0137668	−	0.999905i	$-0.504382\pi$
$607$	−5.58987e13	−0.0275336	−0.0137668	+	0.999905i	$0.504382\pi$
$608$	4.04129e14	0.197265
$609$	−5.62258e14	−0.271982
$610$	1.08369e15	0.519506
$611$	6.51099e14	0.309329
$612$	5.90825e14	0.278180
$613$	2.17636e15	1.01554	0.507772	−	0.861492i	$-0.330469\pi$
$613$	2.17636e15	1.01554	0.507772	+	0.861492i	$0.330469\pi$
$614$	−4.46561e14	−0.206516
$615$	−1.05677e14	−0.0484358
$616$	3.84549e14	0.174686
$617$	1.13746e15	0.512115	0.256057	−	0.966662i	$-0.417576\pi$
$617$	1.13746e15	0.512115	0.256057	+	0.966662i	$0.417576\pi$
$618$	−3.59832e14	−0.160569
$619$	2.74810e15	1.21544	0.607721	−	0.794150i	$-0.292084\pi$
$619$	2.74810e15	1.21544	0.607721	+	0.794150i	$0.292084\pi$
$620$	8.14445e14	0.357032
$621$	−7.99872e14	−0.347549
$622$	−2.23120e15	−0.960931
$623$	1.20504e15	0.514419
$624$	5.83832e13	0.0247043
$625$	9.53674e13	0.0400000
$626$	7.97527e13	0.0331579
$627$	2.04356e15	0.842202
$628$	5.51470e14	0.225291
$629$	−2.96667e15	−1.20141
$630$	9.92437e13	0.0398410
$631$	−3.21025e15	−1.27755	−0.638774	−	0.769394i	$-0.720558\pi$
$631$	−3.21025e15	−1.27755	−0.638774	+	0.769394i	$0.720558\pi$
$632$	−1.54723e14	−0.0610394
$633$	1.47283e15	0.576014
$634$	−3.16502e15	−1.22712
$635$	−3.94226e14	−0.151527
$636$	−4.23799e14	−0.161490
$637$	6.47235e13	0.0244509
$638$	−3.07610e15	−1.15209
$639$	1.86392e14	0.0692105
$640$	1.07374e14	0.0395285
$641$	−3.68541e15	−1.34514	−0.672568	−	0.740036i	$-0.734809\pi$
$641$	−3.68541e15	−1.34514	−0.672568	+	0.740036i	$0.734809\pi$
$642$	2.81620e14	0.101911
$643$	2.28568e15	0.820079	0.410040	−	0.912068i	$-0.365515\pi$
$643$	2.28568e15	0.820079	0.410040	+	0.912068i	$0.365515\pi$
$644$	−9.59382e14	−0.341287
$645$	−1.40747e15	−0.496432
$646$	3.76588e15	1.31701
$647$	−2.62852e15	−0.911459	−0.455730	−	0.890118i	$-0.650622\pi$
$647$	−2.62852e15	−0.911459	−0.455730	+	0.890118i	$0.650622\pi$
$648$	1.14255e14	0.0392837
$649$	−2.38905e15	−0.814479
$650$	7.16031e13	0.0242052
$651$	1.03946e15	0.348428
$652$	1.14182e15	0.379521
$653$	−2.85158e15	−0.939859	−0.469929	−	0.882704i	$-0.655721\pi$
$653$	−2.85158e15	−0.939859	−0.469929	+	0.882704i	$0.655721\pi$
$654$	3.64035e14	0.118978
$655$	6.12147e14	0.198394
$656$	−1.45923e14	−0.0468978
$657$	−1.27667e15	−0.406881
$658$	1.52829e15	0.483018
$659$	−4.82379e15	−1.51189	−0.755943	−	0.654637i	$-0.772821\pi$
$659$	−4.82379e15	−1.51189	−0.755943	+	0.654637i	$0.772821\pi$
$660$	5.42960e14	0.168763
$661$	−3.50550e14	−0.108054	−0.0540272	−	0.998539i	$-0.517206\pi$
$661$	−3.50550e14	−0.108054	−0.0540272	+	0.998539i	$0.517206\pi$
$662$	−8.49156e14	−0.259579
$663$	5.44045e14	0.164934
$664$	2.68850e14	0.0808323
$665$	6.32572e14	0.188621
$666$	−5.73700e14	−0.169659
$667$	7.67433e15	2.25086
$668$	−7.92776e14	−0.230611
$669$	1.50494e15	0.434186
$670$	2.90368e13	0.00830879
$671$	7.56687e15	2.14755
$672$	1.37040e14	0.0385758
$673$	−1.39991e15	−0.390858	−0.195429	−	0.980718i	$-0.562610\pi$
$673$	−1.39991e15	−0.390858	−0.195429	+	0.980718i	$0.562610\pi$
$674$	3.66176e15	1.01405
$675$	1.40126e14	0.0384900
$676$	−1.78141e15	−0.485353
$677$	3.13348e15	0.846816	0.423408	−	0.905939i	$-0.360834\pi$
$677$	3.13348e15	0.846816	0.423408	+	0.905939i	$0.360834\pi$
$678$	−2.51990e14	−0.0675492
$679$	1.92458e14	0.0511743
$680$	1.00057e15	0.263905
$681$	−6.70134e14	−0.175329
$682$	5.68687e15	1.47591
$683$	−6.82080e14	−0.175599	−0.0877993	−	0.996138i	$-0.527983\pi$
$683$	−6.82080e14	−0.175599	−0.0877993	+	0.996138i	$0.527983\pi$
$684$	7.28253e14	0.185983
$685$	−2.30296e15	−0.583430
$686$	1.51922e14	0.0381802
$687$	3.28429e15	0.818802
$688$	−1.94349e15	−0.480668
$689$	−3.90243e14	−0.0957480
$690$	−1.35459e15	−0.329714
$691$	−1.54099e15	−0.372110	−0.186055	−	0.982539i	$-0.559570\pi$
$691$	−1.54099e15	−0.372110	−0.186055	+	0.982539i	$0.559570\pi$
$692$	−1.72288e15	−0.412735
$693$	6.92970e14	0.164695
$694$	−1.95565e15	−0.461121
$695$	−1.50805e13	−0.00352777
$696$	−1.09621e15	−0.254416
$697$	−1.35978e15	−0.313105
$698$	−4.60681e15	−1.05244
$699$	1.69089e15	0.383257
$700$	1.68070e14	0.0377964
$701$	1.15288e14	0.0257238	0.0128619	−	0.999917i	$-0.495906\pi$
$701$	1.15288e14	0.0257238	0.0128619	+	0.999917i	$0.495906\pi$
$702$	1.05208e14	0.0232914
$703$	−3.65673e15	−0.803227
$704$	7.49742e14	0.163404
$705$	2.15785e15	0.466639
$706$	1.12132e15	0.240605
$707$	−5.82036e14	−0.123920
$708$	−8.51374e14	−0.179861
$709$	−7.50195e15	−1.57261	−0.786303	−	0.617841i	$-0.788008\pi$
$709$	−7.50195e15	−1.57261	−0.786303	+	0.617841i	$0.788008\pi$
$710$	3.15656e14	0.0656589
$711$	−2.78815e14	−0.0575485
$712$	2.34942e15	0.481195
$713$	−1.41877e16	−2.88351
$714$	1.27701e15	0.257545
$715$	4.99969e14	0.100060
$716$	2.18813e15	0.434562
$717$	−3.84646e15	−0.758065
$718$	−1.68926e15	−0.330379
$719$	7.56423e14	0.146810	0.0734051	−	0.997302i	$-0.476613\pi$
$719$	7.56423e14	0.146810	0.0734051	+	0.997302i	$0.476613\pi$
$720$	1.93492e14	0.0372678
$721$	−7.77738e14	−0.148658
$722$	9.14147e14	0.173405
$723$	2.52742e15	0.475791
$724$	−3.82557e15	−0.714716
$725$	−1.34443e15	−0.249276
$726$	1.57264e15	0.289387
$727$	4.24718e15	0.775643	0.387821	−	0.921735i	$-0.373228\pi$
$727$	4.24718e15	0.775643	0.387821	+	0.921735i	$0.373228\pi$
$728$	1.26189e14	0.0228717
$729$	2.05891e14	0.0370370
$730$	−2.16205e15	−0.386002
$731$	−1.81104e16	−3.20910
$732$	2.69656e15	0.474242
$733$	4.49872e14	0.0785266	0.0392633	−	0.999229i	$-0.487499\pi$
$733$	4.49872e14	0.0785266	0.0392633	+	0.999229i	$0.487499\pi$
$734$	2.73737e15	0.474248
$735$	2.14505e14	0.0368856
$736$	−1.87047e15	−0.319245
$737$	2.02750e14	0.0343471
$738$	−2.62958e14	−0.0442156
$739$	6.85217e15	1.14363	0.571813	−	0.820384i	$-0.306240\pi$
$739$	6.85217e15	1.14363	0.571813	+	0.820384i	$0.306240\pi$
$740$	−9.71566e14	−0.160953
$741$	6.70591e14	0.110270
$742$	−9.15997e14	−0.149511
$743$	−1.14804e16	−1.86003	−0.930014	−	0.367525i	$-0.880205\pi$
$743$	−1.14804e16	−1.86003	−0.930014	+	0.367525i	$0.880205\pi$
$744$	2.02660e15	0.325924
$745$	3.62515e15	0.578717
$746$	−5.50162e15	−0.871821
$747$	4.84476e14	0.0762094
$748$	6.98648e15	1.09094
$749$	6.08691e14	0.0943511
$750$	2.37305e14	0.0365148
$751$	1.14999e16	1.75661	0.878307	−	0.478098i	$-0.158674\pi$
$751$	1.14999e16	1.75661	0.878307	+	0.478098i	$0.158674\pi$
$752$	2.97965e15	0.451822
$753$	3.44202e15	0.518132
$754$	−1.00942e15	−0.150844
$755$	4.19908e15	0.622939
$756$	2.46950e14	0.0363696
$757$	1.26672e15	0.185205	0.0926026	−	0.995703i	$-0.470481\pi$
$757$	1.26672e15	0.185205	0.0926026	+	0.995703i	$0.470481\pi$
$758$	−3.89170e15	−0.564883
$759$	−9.45844e15	−1.36298
$760$	1.23330e15	0.176439
$761$	3.28324e15	0.466323	0.233161	−	0.972438i	$-0.425093\pi$
$761$	3.28324e15	0.466323	0.233161	+	0.972438i	$0.425093\pi$
$762$	−9.80960e14	−0.138324
$763$	7.86823e14	0.110152
$764$	−1.00484e15	−0.139664
$765$	1.80306e15	0.248812
$766$	5.33268e15	0.730612
$767$	−7.83963e14	−0.106640
$768$	2.67181e14	0.0360844
$769$	9.46420e15	1.26908	0.634540	−	0.772890i	$-0.281190\pi$
$769$	9.46420e15	1.26908	0.634540	+	0.772890i	$0.281190\pi$
$770$	1.17355e15	0.156244
$771$	−3.13088e15	−0.413873
$772$	−4.18780e15	−0.549656
$773$	1.37570e16	1.79282	0.896411	−	0.443224i	$-0.146165\pi$
$773$	1.37570e16	1.79282	0.896411	+	0.443224i	$0.146165\pi$
$774$	−3.50223e15	−0.453178
$775$	2.48549e15	0.319339
$776$	3.75228e14	0.0478691
$777$	−1.23999e15	−0.157074
$778$	−7.25332e15	−0.912324
$779$	−1.67607e15	−0.209333
$780$	1.78171e14	0.0220962
$781$	2.20407e15	0.271422
$782$	−1.74300e16	−2.13138
$783$	−1.97541e15	−0.239866
$784$	2.96197e14	0.0357143
$785$	1.68295e15	0.201507
$786$	1.52322e15	0.181108
$787$	1.68165e16	1.98552	0.992760	−	0.120113i	$-0.0383258\pi$
$787$	1.68165e16	1.98552	0.992760	+	0.120113i	$0.0383258\pi$
$788$	7.30501e15	0.856499
$789$	1.13026e15	0.131599
$790$	−4.72176e14	−0.0545953
$791$	−5.44650e14	−0.0625384
$792$	1.35106e15	0.154059
$793$	2.48305e15	0.281179
$794$	−2.68727e15	−0.302203
$795$	−1.29333e15	−0.144441
$796$	−6.82173e15	−0.756611
$797$	−8.22245e15	−0.905691	−0.452846	−	0.891589i	$-0.649591\pi$
$797$	−8.22245e15	−0.905691	−0.452846	+	0.891589i	$0.649591\pi$
$798$	1.57404e15	0.172187
$799$	2.77659e16	3.01651
$800$	3.27680e14	0.0353553
$801$	4.23374e15	0.453675
$802$	5.57184e15	0.592980
$803$	−1.50965e16	−1.59566
$804$	7.22529e13	0.00758486
$805$	−2.92780e15	−0.305256
$806$	1.86614e15	0.193242
$807$	9.43085e15	0.969943
$808$	−1.13477e15	−0.115917
$809$	8.84793e15	0.897687	0.448843	−	0.893610i	$-0.351836\pi$
$809$	8.84793e15	0.897687	0.448843	+	0.893610i	$0.351836\pi$
$810$	3.48678e14	0.0351364
$811$	3.09259e15	0.309534	0.154767	−	0.987951i	$-0.450537\pi$
$811$	3.09259e15	0.309534	0.154767	+	0.987951i	$0.450537\pi$
$812$	−2.36935e15	−0.235543
$813$	5.00661e15	0.494363
$814$	−6.78397e15	−0.665350
$815$	3.48456e15	0.339454
$816$	2.48973e15	0.240911
$817$	−2.23230e16	−2.14551
$818$	−8.43974e15	−0.805723
$819$	2.27397e14	0.0215637
$820$	−4.45321e14	−0.0419466
$821$	−1.04448e16	−0.977264	−0.488632	−	0.872490i	$-0.662504\pi$
$821$	−1.04448e16	−0.977264	−0.488632	+	0.872490i	$0.662504\pi$
$822$	−5.73051e15	−0.532596
$823$	−1.37142e16	−1.26611	−0.633054	−	0.774108i	$-0.718199\pi$
$823$	−1.37142e16	−1.26611	−0.633054	+	0.774108i	$0.718199\pi$
$824$	−1.51633e15	−0.139057
$825$	1.65698e15	0.150946
$826$	−1.84015e15	−0.166519
$827$	−1.68428e16	−1.51403	−0.757013	−	0.653400i	$-0.773342\pi$
$827$	−1.68428e16	−1.51403	−0.757013	+	0.653400i	$0.773342\pi$
$828$	−3.37065e15	−0.300987
$829$	1.21822e16	1.08063	0.540315	−	0.841463i	$-0.318305\pi$
$829$	1.21822e16	1.08063	0.540315	+	0.841463i	$0.318305\pi$
$830$	8.20464e14	0.0722986
$831$	−8.49746e15	−0.743847
$832$	2.46026e14	0.0213946
$833$	2.76011e15	0.238440
$834$	−3.75252e13	−0.00322040
$835$	−2.41936e15	−0.206265
$836$	8.61156e15	0.729369
$837$	3.65200e15	0.307284
$838$	−9.36258e15	−0.782624
$839$	1.12881e16	0.937412	0.468706	−	0.883354i	$-0.344720\pi$
$839$	1.12881e16	0.937412	0.468706	+	0.883354i	$0.344720\pi$
$840$	4.18212e14	0.0345033
$841$	6.75250e15	0.553460
$842$	−1.54988e16	−1.26207
$843$	4.38819e15	0.355004
$844$	6.20650e15	0.498842
$845$	−5.43644e15	−0.434113
$846$	5.36942e15	0.425982
$847$	3.39910e15	0.267920
$848$	−1.78589e15	−0.139855
$849$	4.76037e15	0.370381
$850$	3.05349e15	0.236044
$851$	1.69248e16	1.29990
$852$	7.85454e14	0.0599381
$853$	−2.11414e16	−1.60293	−0.801463	−	0.598044i	$-0.795945\pi$
$853$	−2.11414e16	−1.60293	−0.801463	+	0.598044i	$0.795945\pi$
$854$	5.82834e15	0.439063
$855$	2.22245e15	0.166348
$856$	1.18674e15	0.0882574
$857$	8.40339e15	0.620955	0.310477	−	0.950581i	$-0.399511\pi$
$857$	8.40339e15	0.620955	0.310477	+	0.950581i	$0.399511\pi$
$858$	1.24408e15	0.0913418
$859$	−4.96563e15	−0.362253	−0.181127	−	0.983460i	$-0.557974\pi$
$859$	−4.96563e15	−0.362253	−0.181127	+	0.983460i	$0.557974\pi$
$860$	−5.93105e15	−0.429923
$861$	−5.68355e14	−0.0409357
$862$	−7.97607e15	−0.570820
$863$	3.65285e15	0.259760	0.129880	−	0.991530i	$-0.458541\pi$
$863$	3.65285e15	0.259760	0.129880	+	0.991530i	$0.458541\pi$
$864$	4.81469e14	0.0340207
$865$	−5.25781e15	−0.369161
$866$	−2.46820e15	−0.172200
$867$	1.48725e16	1.03105
$868$	4.38028e15	0.301747
$869$	−3.29698e15	−0.225687
$870$	−3.34538e15	−0.227557
$871$	6.65321e13	0.00449709
$872$	1.53404e15	0.103038
$873$	6.76173e14	0.0451315
$874$	−2.14843e16	−1.42498
$875$	5.12909e14	0.0338062
$876$	−5.37986e15	−0.352370
$877$	−3.28639e15	−0.213905	−0.106953	−	0.994264i	$-0.534109\pi$
$877$	−3.28639e15	−0.213905	−0.106953	+	0.994264i	$0.534109\pi$
$878$	−1.71515e16	−1.10938
$879$	5.66670e15	0.364243
$880$	2.28803e15	0.146153
$881$	−1.82122e16	−1.15610	−0.578050	−	0.816002i	$-0.696186\pi$
$881$	−1.82122e16	−1.15610	−0.578050	+	0.816002i	$0.696186\pi$
$882$	5.33756e14	0.0336718
$883$	−2.13461e16	−1.33824	−0.669120	−	0.743155i	$-0.733329\pi$
$883$	−2.13461e16	−1.33824	−0.669120	+	0.743155i	$0.733329\pi$
$884$	2.29260e15	0.142837
$885$	−2.59819e15	−0.160873
$886$	6.81467e15	0.419333
$887$	8.32595e15	0.509160	0.254580	−	0.967052i	$-0.418063\pi$
$887$	8.32595e15	0.509160	0.254580	+	0.967052i	$0.418063\pi$
$888$	−2.41757e15	−0.146929
$889$	−2.12024e15	−0.128064
$890$	7.16987e15	0.430394
$891$	2.43465e15	0.145248
$892$	6.34181e15	0.376016
$893$	3.42243e16	2.01675
$894$	9.02053e15	0.528294
$895$	6.67765e15	0.388684
$896$	5.77484e14	0.0334077
$897$	−3.10377e15	−0.178456
$898$	−1.84845e16	−1.05630
$899$	−3.50389e16	−1.99009
$900$	5.90490e14	0.0333333
$901$	−1.66418e16	−0.933714
$902$	−3.10946e15	−0.173400
$903$	−7.56969e15	−0.419561
$904$	−1.06188e15	−0.0584993
$905$	−1.16747e16	−0.639262
$906$	1.04487e16	0.568663
$907$	−1.81148e16	−0.979927	−0.489964	−	0.871743i	$-0.662990\pi$
$907$	−1.81148e16	−0.979927	−0.489964	+	0.871743i	$0.662990\pi$
$908$	−2.82394e15	−0.151839
$909$	−2.04490e15	−0.109288
$910$	3.85099e14	0.0204571
$911$	−1.26930e15	−0.0670212	−0.0335106	−	0.999438i	$-0.510669\pi$
$911$	−1.26930e15	−0.0670212	−0.0335106	+	0.999438i	$0.510669\pi$
$912$	3.06885e15	0.161066
$913$	5.72890e15	0.298870
$914$	−1.22039e16	−0.632839
$915$	8.22926e15	0.424175
$916$	1.38400e16	0.709103
$917$	3.29227e15	0.167674
$918$	4.48658e15	0.227133
$919$	−3.03129e16	−1.52543	−0.762714	−	0.646736i	$-0.776134\pi$
$919$	−3.03129e16	−1.52543	−0.762714	+	0.646736i	$0.776134\pi$
$920$	−5.70823e15	−0.285541
$921$	−3.39107e15	−0.168620
$922$	−2.51328e16	−1.24228
$923$	7.23263e14	0.0355375
$924$	2.92017e15	0.142630
$925$	−2.96499e15	−0.143960
$926$	−1.16031e16	−0.560034
$927$	−2.73247e15	−0.131104
$928$	−4.61944e15	−0.220331
$929$	2.96441e16	1.40557	0.702783	−	0.711404i	$-0.251940\pi$
$929$	2.96441e16	1.40557	0.702783	+	0.711404i	$0.251940\pi$
$930$	6.18469e15	0.291516
$931$	3.40213e15	0.159414
$932$	7.12538e15	0.331910
$933$	−1.69432e16	−0.784597
$934$	−7.96486e15	−0.366666
$935$	2.13210e16	0.975763
$936$	4.43347e14	0.0201710
$937$	3.55888e16	1.60970	0.804852	−	0.593476i	$-0.202245\pi$
$937$	3.55888e16	1.60970	0.804852	+	0.593476i	$0.202245\pi$
$938$	1.56167e14	0.00702221
$939$	6.05622e14	0.0270733
$940$	9.09317e15	0.404122
$941$	−4.26685e16	−1.88523	−0.942615	−	0.333882i	$-0.891641\pi$
$941$	−4.26685e16	−1.88523	−0.942615	+	0.333882i	$0.891641\pi$
$942$	4.18773e15	0.183949
$943$	7.75756e15	0.338774
$944$	−3.58768e15	−0.155764
$945$	7.53631e14	0.0325300
$946$	−4.14136e16	−1.77722
$947$	−1.42763e16	−0.609105	−0.304552	−	0.952496i	$-0.598507\pi$
$947$	−1.42763e16	−0.609105	−0.304552	+	0.952496i	$0.598507\pi$
$948$	−1.17493e15	−0.0498384
$949$	−4.95389e15	−0.208921
$950$	3.76374e15	0.157812
$951$	−2.40344e16	−1.00194
$952$	5.38129e15	0.223040
$953$	3.31137e15	0.136457	0.0682286	−	0.997670i	$-0.478265\pi$
$953$	3.31137e15	0.136457	0.0682286	+	0.997670i	$0.478265\pi$
$954$	−3.21822e15	−0.131856
$955$	−3.06653e15	−0.124919
$956$	−1.62090e16	−0.656503
$957$	−2.33592e16	−0.940679
$958$	−1.85696e15	−0.0743520
$959$	−1.23859e16	−0.493088
$960$	8.15373e14	0.0322749
$961$	3.93689e16	1.54944
$962$	−2.22615e15	−0.0871147
$963$	2.13855e15	0.0832099
$964$	1.06505e16	0.412047
$965$	−1.27802e16	−0.491627
$966$	−7.28531e15	−0.278659
$967$	−1.07347e16	−0.408268	−0.204134	−	0.978943i	$-0.565438\pi$
$967$	−1.07347e16	−0.408268	−0.204134	+	0.978943i	$0.565438\pi$
$968$	6.62711e15	0.250616
$969$	2.85971e16	1.07533
$970$	1.14510e15	0.0428155
$971$	−4.64271e16	−1.72610	−0.863049	−	0.505121i	$-0.831448\pi$
$971$	−4.64271e16	−1.72610	−0.863049	+	0.505121i	$0.831448\pi$
$972$	8.67624e14	0.0320750
$973$	−8.11068e13	−0.00298151
$974$	3.17304e16	1.15985
$975$	5.43736e14	0.0197634
$976$	1.13633e16	0.410705
$977$	−2.46161e16	−0.884708	−0.442354	−	0.896841i	$-0.645857\pi$
$977$	−2.46161e16	−0.884708	−0.442354	+	0.896841i	$0.645857\pi$
$978$	8.67069e15	0.309877
$979$	5.00637e16	1.77917
$980$	9.03921e14	0.0319438
$981$	2.76439e15	0.0971449
$982$	−1.26988e16	−0.443762
$983$	−1.32615e16	−0.460838	−0.230419	−	0.973092i	$-0.574010\pi$
$983$	−1.32615e16	−0.460838	−0.230419	+	0.973092i	$0.574010\pi$
$984$	−1.10810e15	−0.0382919
$985$	2.22931e16	0.766076
$986$	−4.30463e16	−1.47100
$987$	1.16054e16	0.394382
$988$	2.82587e15	0.0954967
$989$	1.03320e17	3.47219
$990$	4.12310e15	0.137794
$991$	5.77211e16	1.91836	0.959178	−	0.282803i	$-0.0912644\pi$
$991$	5.77211e16	1.91836	0.959178	+	0.282803i	$0.0912644\pi$
$992$	8.54007e15	0.282259
$993$	−6.44828e15	−0.211945
$994$	1.69767e15	0.0554919
$995$	−2.08183e16	−0.676734
$996$	2.04158e15	0.0659993
$997$	−2.42042e16	−0.778156	−0.389078	−	0.921205i	$-0.627206\pi$
$997$	−2.42042e16	−0.778156	−0.389078	+	0.921205i	$0.627206\pi$
$998$	2.99855e16	0.958723
$999$	−4.35654e15	−0.138526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.12.a.p.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.12.a.p.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +100000. q^{10} +698251. q^{11} +248832. q^{12} +229130. q^{13} +537824. q^{14} +759375. q^{15} +1.04858e6 q^{16} +9.77117e6 q^{17} +1.88957e6 q^{18} +1.20440e7 q^{19} +3.20000e6 q^{20} +4.08410e6 q^{21} +2.23440e7 q^{22} -5.57444e7 q^{23} +7.96262e6 q^{24} +9.76562e6 q^{25} +7.33216e6 q^{26} +1.43489e7 q^{27} +1.72104e7 q^{28} -1.37670e8 q^{29} +2.43000e7 q^{30} +2.54514e8 q^{31} +3.35544e7 q^{32} +1.69675e8 q^{33} +3.12677e8 q^{34} +5.25219e7 q^{35} +6.04662e7 q^{36} -3.03614e8 q^{37} +3.85407e8 q^{38} +5.56786e7 q^{39} +1.02400e8 q^{40} -1.39163e8 q^{41} +1.30691e8 q^{42} -1.85345e9 q^{43} +7.15009e8 q^{44} +1.84528e8 q^{45} -1.78382e9 q^{46} +2.84162e9 q^{47} +2.54804e8 q^{48} +2.82475e8 q^{49} +3.12500e8 q^{50} +2.37439e9 q^{51} +2.34629e8 q^{52} -1.70315e9 q^{53} +4.59165e8 q^{54} +2.18204e9 q^{55} +5.50732e8 q^{56} +2.92669e9 q^{57} -4.40544e9 q^{58} -3.42148e9 q^{59} +7.77600e8 q^{60} +1.08369e10 q^{61} +8.14445e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +7.16031e8 q^{65} +5.42960e9 q^{66} +2.90368e8 q^{67} +1.00057e10 q^{68} -1.35459e10 q^{69} +1.68070e9 q^{70} +3.15656e9 q^{71} +1.93492e9 q^{72} -2.16205e10 q^{73} -9.71566e9 q^{74} +2.37305e9 q^{75} +1.23330e10 q^{76} +1.17355e10 q^{77} +1.78171e9 q^{78} -4.72176e9 q^{79} +3.27680e9 q^{80} +3.48678e9 q^{81} -4.45321e9 q^{82} +8.20464e9 q^{83} +4.18212e9 q^{84} +3.05349e10 q^{85} -5.93105e10 q^{86} -3.34538e10 q^{87} +2.28803e10 q^{88} +7.16987e10 q^{89} +5.90490e9 q^{90} +3.85099e9 q^{91} -5.70823e10 q^{92} +6.18469e10 q^{93} +9.09317e10 q^{94} +3.76374e10 q^{95} +8.15373e9 q^{96} +1.14510e10 q^{97} +9.03921e9 q^{98} +4.12310e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 128 q^{2} + 972 q^{3} + 4096 q^{4} + 12500 q^{5} + 31104 q^{6} + 67228 q^{7} + 131072 q^{8} + 236196 q^{9}+O(q^{10}) \) 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

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