LMFDB - Embedded newform 22.12.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,12,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	22.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:	$16.9035499723$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{331}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 331 $ x^2 - 331
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$18.1934$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.0000 q^{2} +223.642 q^{3} +1024.00 q^{4} -6132.36 q^{5} +7156.54 q^{6} -67177.3 q^{7} +32768.0 q^{8} -127131. q^{9} +O(q^{10})$	\(q+32.0000 q^{2} +223.642 q^{3} +1024.00 q^{4} -6132.36 q^{5} +7156.54 q^{6} -67177.3 q^{7} +32768.0 q^{8} -127131. q^{9} -196236. q^{10} -161051. q^{11} +229009. q^{12} +236400. q^{13} -2.14967e6 q^{14} -1.37145e6 q^{15} +1.04858e6 q^{16} +1.46268e6 q^{17} -4.06820e6 q^{18} -8.85857e6 q^{19} -6.27954e6 q^{20} -1.50236e7 q^{21} -5.15363e6 q^{22} +2.18357e7 q^{23} +7.32829e6 q^{24} -1.12223e7 q^{25} +7.56480e6 q^{26} -6.80493e7 q^{27} -6.87896e7 q^{28} -3.83484e7 q^{29} -4.38865e7 q^{30} -2.25578e8 q^{31} +3.35544e7 q^{32} -3.60177e7 q^{33} +4.68056e7 q^{34} +4.11956e8 q^{35} -1.30183e8 q^{36} +5.36528e8 q^{37} -2.83474e8 q^{38} +5.28689e7 q^{39} -2.00945e8 q^{40} -5.70685e8 q^{41} -4.80757e8 q^{42} +1.72681e9 q^{43} -1.64916e8 q^{44} +7.79616e8 q^{45} +6.98741e8 q^{46} +2.62539e9 q^{47} +2.34505e8 q^{48} +2.53546e9 q^{49} -3.59112e8 q^{50} +3.27115e8 q^{51} +2.42074e8 q^{52} -3.63466e9 q^{53} -2.17758e9 q^{54} +9.87623e8 q^{55} -2.20127e9 q^{56} -1.98115e9 q^{57} -1.22715e9 q^{58} -1.73378e8 q^{59} -1.40437e9 q^{60} -5.44417e9 q^{61} -7.21851e9 q^{62} +8.54034e9 q^{63} +1.07374e9 q^{64} -1.44969e9 q^{65} -1.15257e9 q^{66} -1.96293e10 q^{67} +1.49778e9 q^{68} +4.88337e9 q^{69} +1.31826e10 q^{70} -6.50056e9 q^{71} -4.16584e9 q^{72} +9.04153e9 q^{73} +1.71689e10 q^{74} -2.50977e9 q^{75} -9.07118e9 q^{76} +1.08190e10 q^{77} +1.69181e9 q^{78} -1.46795e10 q^{79} -6.43025e9 q^{80} +7.30227e9 q^{81} -1.82619e10 q^{82} +4.83255e9 q^{83} -1.53842e10 q^{84} -8.96965e9 q^{85} +5.52580e10 q^{86} -8.57630e9 q^{87} -5.27732e9 q^{88} +4.77156e10 q^{89} +2.49477e10 q^{90} -1.58807e10 q^{91} +2.23597e10 q^{92} -5.04488e10 q^{93} +8.40124e10 q^{94} +5.43240e10 q^{95} +7.50417e9 q^{96} -1.12120e11 q^{97} +8.11348e10 q^{98} +2.04746e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 64 q^{2} - 426 q^{3} + 2048 q^{4} + 2290 q^{5} - 13632 q^{6} - 86324 q^{7} + 65536 q^{8} + 117756 q^{9}+O(q^{10}) $ 2 * q + 64 * q^2 - 426 * q^3 + 2048 * q^4 + 2290 * q^5 - 13632 * q^6 - 86324 * q^7 + 65536 * q^8 + 117756 * q^9	\( 2 q + 64 q^{2} - 426 q^{3} + 2048 q^{4} + 2290 q^{5} - 13632 q^{6} - 86324 q^{7} + 65536 q^{8} + 117756 q^{9} + 73280 q^{10} - 322102 q^{11} - 436224 q^{12} - 2100184 q^{13} - 2762368 q^{14} - 6842970 q^{15} + 2097152 q^{16} - 2882276 q^{17} + 3768192 q^{18} - 19571712 q^{19} + 2344960 q^{20} - 2585148 q^{21} - 10307264 q^{22} + 12680534 q^{23} - 13959168 q^{24} + 10885800 q^{25} - 67205888 q^{26} - 112056318 q^{27} - 88395776 q^{28} + 45662496 q^{29} - 218975040 q^{30} - 506504170 q^{31} + 67108864 q^{32} + 68607726 q^{33} - 92232832 q^{34} + 250695020 q^{35} + 120582144 q^{36} + 402672518 q^{37} - 626294784 q^{38} + 1570811448 q^{39} + 75038720 q^{40} + 608864016 q^{41} - 82724736 q^{42} + 1100094564 q^{43} - 329832448 q^{44} + 2842145820 q^{45} + 405777088 q^{46} + 1012342272 q^{47} - 446693376 q^{48} + 924731802 q^{49} + 348345600 q^{50} + 3149776692 q^{51} - 2150588416 q^{52} - 68189276 q^{53} - 3585802176 q^{54} - 368806790 q^{55} - 2828664832 q^{56} + 4978554240 q^{57} + 1461199872 q^{58} - 6791617518 q^{59} - 7007201280 q^{60} + 5704046520 q^{61} - 16208133440 q^{62} + 3851555688 q^{63} + 2147483648 q^{64} - 21129248280 q^{65} + 2195447232 q^{66} - 36514311702 q^{67} - 2951450624 q^{68} + 10830919410 q^{69} + 8022240640 q^{70} + 20672196594 q^{71} + 3858628608 q^{72} + 3082870856 q^{73} + 12885520576 q^{74} - 16872083400 q^{75} - 20041433088 q^{76} + 13902566524 q^{77} + 50265966336 q^{78} - 28681382180 q^{79} + 2401239040 q^{80} - 7490027070 q^{81} + 19483648512 q^{82} + 29532640772 q^{83} - 2647191552 q^{84} - 45564404420 q^{85} + 35203026048 q^{86} - 63153261216 q^{87} - 10554638336 q^{88} + 85063742462 q^{89} + 90948666240 q^{90} + 28857167728 q^{91} + 12984866816 q^{92} + 132052307250 q^{93} + 32394952704 q^{94} - 35905936640 q^{95} - 14294188032 q^{96} - 180832449678 q^{97} + 29591417664 q^{98} - 18964721556 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 - 426 * q^3 + 2048 * q^4 + 2290 * q^5 - 13632 * q^6 - 86324 * q^7 + 65536 * q^8 + 117756 * q^9 + 73280 * q^10 - 322102 * q^11 - 436224 * q^12 - 2100184 * q^13 - 2762368 * q^14 - 6842970 * q^15 + 2097152 * q^16 - 2882276 * q^17 + 3768192 * q^18 - 19571712 * q^19 + 2344960 * q^20 - 2585148 * q^21 - 10307264 * q^22 + 12680534 * q^23 - 13959168 * q^24 + 10885800 * q^25 - 67205888 * q^26 - 112056318 * q^27 - 88395776 * q^28 + 45662496 * q^29 - 218975040 * q^30 - 506504170 * q^31 + 67108864 * q^32 + 68607726 * q^33 - 92232832 * q^34 + 250695020 * q^35 + 120582144 * q^36 + 402672518 * q^37 - 626294784 * q^38 + 1570811448 * q^39 + 75038720 * q^40 + 608864016 * q^41 - 82724736 * q^42 + 1100094564 * q^43 - 329832448 * q^44 + 2842145820 * q^45 + 405777088 * q^46 + 1012342272 * q^47 - 446693376 * q^48 + 924731802 * q^49 + 348345600 * q^50 + 3149776692 * q^51 - 2150588416 * q^52 - 68189276 * q^53 - 3585802176 * q^54 - 368806790 * q^55 - 2828664832 * q^56 + 4978554240 * q^57 + 1461199872 * q^58 - 6791617518 * q^59 - 7007201280 * q^60 + 5704046520 * q^61 - 16208133440 * q^62 + 3851555688 * q^63 + 2147483648 * q^64 - 21129248280 * q^65 + 2195447232 * q^66 - 36514311702 * q^67 - 2951450624 * q^68 + 10830919410 * q^69 + 8022240640 * q^70 + 20672196594 * q^71 + 3858628608 * q^72 + 3082870856 * q^73 + 12885520576 * q^74 - 16872083400 * q^75 - 20041433088 * q^76 + 13902566524 * q^77 + 50265966336 * q^78 - 28681382180 * q^79 + 2401239040 * q^80 - 7490027070 * q^81 + 19483648512 * q^82 + 29532640772 * q^83 - 2647191552 * q^84 - 45564404420 * q^85 + 35203026048 * q^86 - 63153261216 * q^87 - 10554638336 * q^88 + 85063742462 * q^89 + 90948666240 * q^90 + 28857167728 * q^91 + 12984866816 * q^92 + 132052307250 * q^93 + 32394952704 * q^94 - 35905936640 * q^95 - 14294188032 * q^96 - 180832449678 * q^97 + 29591417664 * q^98 - 18964721556 * 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
$3$	223.642	0.531356	0.265678	−	0.964062i	$-0.414404\pi$
$3$	223.642	0.531356	0.265678	+	0.964062i	$0.414404\pi$
$4$	1024.00	0.500000
$5$	−6132.36	−0.877592	−0.438796	−	0.898587i	$-0.644595\pi$
$5$	−6132.36	−0.877592	−0.438796	+	0.898587i	$0.644595\pi$
$6$	7156.54	0.375726
$7$	−67177.3	−1.51072	−0.755359	−	0.655311i	$-0.772537\pi$
$7$	−67177.3	−1.51072	−0.755359	+	0.655311i	$0.772537\pi$
$8$	32768.0	0.353553
$9$	−127131.	−0.717660
$10$	−196236.	−0.620551
$11$	−161051.	−0.301511
$11$	−161051.	−0.301511
$12$	229009.	0.265678
$13$	236400.	0.176587	0.0882936	−	0.996094i	$-0.471859\pi$
$13$	236400.	0.176587	0.0882936	+	0.996094i	$0.471859\pi$
$14$	−2.14967e6	−1.06824
$15$	−1.37145e6	−0.466314
$16$	1.04858e6	0.250000
$17$	1.46268e6	0.249850	0.124925	−	0.992166i	$-0.460131\pi$
$17$	1.46268e6	0.249850	0.124925	+	0.992166i	$0.460131\pi$
$18$	−4.06820e6	−0.507462
$19$	−8.85857e6	−0.820765	−0.410383	−	0.911913i	$-0.634605\pi$
$19$	−8.85857e6	−0.820765	−0.410383	+	0.911913i	$0.634605\pi$
$20$	−6.27954e6	−0.438796
$21$	−1.50236e7	−0.802730
$22$	−5.15363e6	−0.213201
$23$	2.18357e7	0.707397	0.353699	−	0.935359i	$-0.384924\pi$
$23$	2.18357e7	0.707397	0.353699	+	0.935359i	$0.384924\pi$
$24$	7.32829e6	0.187863
$25$	−1.12223e7	−0.229832
$26$	7.56480e6	0.124866
$27$	−6.80493e7	−0.912690
$28$	−6.87896e7	−0.755359
$29$	−3.83484e7	−0.347183	−0.173591	−	0.984818i	$-0.555537\pi$
$29$	−3.83484e7	−0.347183	−0.173591	+	0.984818i	$0.555537\pi$
$30$	−4.38865e7	−0.329734
$31$	−2.25578e8	−1.41517	−0.707585	−	0.706629i	$-0.750215\pi$
$31$	−2.25578e8	−1.41517	−0.707585	+	0.706629i	$0.750215\pi$
$32$	3.35544e7	0.176777
$33$	−3.60177e7	−0.160210
$34$	4.68056e7	0.176670
$35$	4.11956e8	1.32579
$36$	−1.30183e8	−0.358830
$37$	5.36528e8	1.27199	0.635994	−	0.771694i	$-0.280590\pi$
$37$	5.36528e8	1.27199	0.635994	+	0.771694i	$0.280590\pi$
$38$	−2.83474e8	−0.580369
$39$	5.28689e7	0.0938307
$40$	−2.00945e8	−0.310276
$41$	−5.70685e8	−0.769281	−0.384641	−	0.923066i	$-0.625675\pi$
$41$	−5.70685e8	−0.769281	−0.384641	+	0.923066i	$0.625675\pi$
$42$	−4.80757e8	−0.567615
$43$	1.72681e9	1.79130	0.895651	−	0.444757i	$-0.146710\pi$
$43$	1.72681e9	1.79130	0.895651	+	0.444757i	$0.146710\pi$
$44$	−1.64916e8	−0.150756
$45$	7.79616e8	0.629813
$46$	6.98741e8	0.500205
$47$	2.62539e9	1.66976	0.834882	−	0.550428i	$-0.185536\pi$
$47$	2.62539e9	1.66976	0.834882	+	0.550428i	$0.185536\pi$
$48$	2.34505e8	0.132839
$49$	2.53546e9	1.28227
$50$	−3.59112e8	−0.162516
$51$	3.27115e8	0.132759
$52$	2.42074e8	0.0882936
$53$	−3.63466e9	−1.19384	−0.596920	−	0.802301i	$-0.703609\pi$
$53$	−3.63466e9	−1.19384	−0.596920	+	0.802301i	$0.703609\pi$
$54$	−2.17758e9	−0.645369
$55$	9.87623e8	0.264604
$56$	−2.20127e9	−0.534119
$57$	−1.98115e9	−0.436119
$58$	−1.22715e9	−0.245495
$59$	−1.73378e8	−0.0315725	−0.0157862	−	0.999875i	$-0.505025\pi$
$59$	−1.73378e8	−0.0315725	−0.0157862	+	0.999875i	$0.505025\pi$
$60$	−1.40437e9	−0.233157
$61$	−5.44417e9	−0.825311	−0.412656	−	0.910887i	$-0.635399\pi$
$61$	−5.44417e9	−0.825311	−0.412656	+	0.910887i	$0.635399\pi$
$62$	−7.21851e9	−1.00068
$63$	8.54034e9	1.08418
$64$	1.07374e9	0.125000
$65$	−1.44969e9	−0.154972
$66$	−1.15257e9	−0.113286
$67$	−1.96293e10	−1.77621	−0.888104	−	0.459643i	$-0.847978\pi$
$67$	−1.96293e10	−1.77621	−0.888104	+	0.459643i	$0.847978\pi$
$68$	1.49778e9	0.124925
$69$	4.88337e9	0.375880
$70$	1.31826e10	0.937478
$71$	−6.50056e9	−0.427592	−0.213796	−	0.976878i	$-0.568583\pi$
$71$	−6.50056e9	−0.427592	−0.213796	+	0.976878i	$0.568583\pi$
$72$	−4.16584e9	−0.253731
$73$	9.04153e9	0.510465	0.255233	−	0.966880i	$-0.417848\pi$
$73$	9.04153e9	0.510465	0.255233	+	0.966880i	$0.417848\pi$
$74$	1.71689e10	0.899432
$75$	−2.50977e9	−0.122123
$76$	−9.07118e9	−0.410383
$77$	1.08190e10	0.455498
$78$	1.69181e9	0.0663484
$79$	−1.46795e10	−0.536737	−0.268368	−	0.963316i	$-0.586484\pi$
$79$	−1.46795e10	−0.536737	−0.268368	+	0.963316i	$0.586484\pi$
$80$	−6.43025e9	−0.219398
$81$	7.30227e9	0.232697
$82$	−1.82619e10	−0.543964
$83$	4.83255e9	0.134663	0.0673313	−	0.997731i	$-0.478552\pi$
$83$	4.83255e9	0.134663	0.0673313	+	0.997731i	$0.478552\pi$
$84$	−1.53842e10	−0.401365
$85$	−8.96965e9	−0.219266
$86$	5.52580e10	1.26664
$87$	−8.57630e9	−0.184478
$88$	−5.27732e9	−0.106600
$89$	4.77156e10	0.905764	0.452882	−	0.891570i	$-0.350396\pi$
$89$	4.77156e10	0.905764	0.452882	+	0.891570i	$0.350396\pi$
$90$	2.49477e10	0.445345
$91$	−1.58807e10	−0.266773
$92$	2.23597e10	0.353699
$93$	−5.04488e10	−0.751959
$94$	8.40124e10	1.18070
$95$	5.43240e10	0.720297
$96$	7.50417e9	0.0939314
$97$	−1.12120e11	−1.32568	−0.662840	−	0.748761i	$-0.730649\pi$
$97$	−1.12120e11	−1.32568	−0.662840	+	0.748761i	$0.730649\pi$
$98$	8.11348e10	0.906700
$99$	2.04746e10	0.216383
$100$	−1.14916e10	−0.114916
$101$	−5.13615e10	−0.486261	−0.243131	−	0.969994i	$-0.578174\pi$
$101$	−5.13615e10	−0.486261	−0.243131	+	0.969994i	$0.578174\pi$
$102$	1.04677e10	0.0938750
$103$	7.70147e10	0.654589	0.327295	−	0.944922i	$-0.393863\pi$
$103$	7.70147e10	0.654589	0.327295	+	0.944922i	$0.393863\pi$
$104$	7.74636e9	0.0624330
$105$	9.21304e10	0.704469
$106$	−1.16309e11	−0.844173
$107$	−1.56088e11	−1.07587	−0.537933	−	0.842987i	$-0.680795\pi$
$107$	−1.56088e11	−1.07587	−0.537933	+	0.842987i	$0.680795\pi$
$108$	−6.96825e10	−0.456345
$109$	1.56923e11	0.976878	0.488439	−	0.872598i	$-0.337566\pi$
$109$	1.56923e11	0.976878	0.488439	+	0.872598i	$0.337566\pi$
$110$	3.16039e10	0.187103
$111$	1.19990e11	0.675879
$112$	−7.04405e10	−0.377679
$113$	−3.15388e11	−1.61032	−0.805162	−	0.593055i	$-0.797922\pi$
$113$	−3.15388e11	−1.61032	−0.805162	+	0.593055i	$0.797922\pi$
$114$	−6.33967e10	−0.308383
$115$	−1.33904e11	−0.620806
$116$	−3.92687e10	−0.173591
$117$	−3.00539e10	−0.126730
$118$	−5.54811e9	−0.0223251
$119$	−9.82586e10	−0.377452
$120$	−4.49397e10	−0.164867
$121$	2.59374e10	0.0909091
$122$	−1.74213e11	−0.583583
$123$	−1.27629e11	−0.408763
$124$	−2.30992e11	−0.707585
$125$	3.68251e11	1.07929
$126$	2.73291e11	0.766633
$127$	−1.15702e11	−0.310757	−0.155378	−	0.987855i	$-0.549660\pi$
$127$	−1.15702e11	−0.310757	−0.155378	+	0.987855i	$0.549660\pi$
$128$	3.43597e10	0.0883883
$129$	3.86188e11	0.951820
$130$	−4.63901e10	−0.109581
$131$	−6.34963e11	−1.43799	−0.718995	−	0.695015i	$-0.755398\pi$
$131$	−6.34963e11	−1.43799	−0.718995	+	0.695015i	$0.755398\pi$
$132$	−3.68821e10	−0.0801050
$133$	5.95095e11	1.23994
$134$	−6.28138e11	−1.25597
$135$	4.17303e11	0.800970
$136$	4.79289e10	0.0883352
$137$	6.15264e11	1.08918	0.544588	−	0.838704i	$-0.316686\pi$
$137$	6.15264e11	1.08918	0.544588	+	0.838704i	$0.316686\pi$
$138$	1.56268e11	0.265787
$139$	−7.88116e11	−1.28828	−0.644138	−	0.764910i	$-0.722784\pi$
$139$	−7.88116e11	−1.28828	−0.644138	+	0.764910i	$0.722784\pi$
$140$	4.21842e11	0.662897
$141$	5.87146e11	0.887240
$142$	−2.08018e11	−0.302353
$143$	−3.80725e10	−0.0532430
$144$	−1.33307e11	−0.179415
$145$	2.35166e11	0.304685
$146$	2.89329e11	0.360953
$147$	5.67035e11	0.681341
$148$	5.49405e11	0.635994
$149$	2.30289e11	0.256891	0.128445	−	0.991717i	$-0.459001\pi$
$149$	2.30289e11	0.256891	0.128445	+	0.991717i	$0.459001\pi$
$150$	−8.03125e10	−0.0863537
$151$	7.28707e11	0.755405	0.377703	−	0.925927i	$-0.376714\pi$
$151$	7.28707e11	0.755405	0.377703	+	0.925927i	$0.376714\pi$
$152$	−2.90278e11	−0.290184
$153$	−1.85952e11	−0.179307
$154$	3.46207e11	0.322086
$155$	1.38333e12	1.24194
$156$	5.41378e10	0.0469154
$157$	8.01237e11	0.670367	0.335184	−	0.942153i	$-0.391202\pi$
$157$	8.01237e11	0.670367	0.335184	+	0.942153i	$0.391202\pi$
$158$	−4.69743e11	−0.379530
$159$	−8.12861e11	−0.634355
$160$	−2.05768e11	−0.155138
$161$	−1.46686e12	−1.06868
$162$	2.33673e11	0.164541
$163$	−2.73048e12	−1.85869	−0.929346	−	0.369210i	$-0.879628\pi$
$163$	−2.73048e12	−1.85869	−0.929346	+	0.369210i	$0.879628\pi$
$164$	−5.84381e11	−0.384641
$165$	2.20874e11	0.140599
$166$	1.54642e11	0.0952208
$167$	−1.47055e12	−0.876070	−0.438035	−	0.898958i	$-0.644325\pi$
$167$	−1.47055e12	−0.876070	−0.438035	+	0.898958i	$0.644325\pi$
$168$	−4.92295e11	−0.283808
$169$	−1.73628e12	−0.968817
$170$	−2.87029e11	−0.155045
$171$	1.12620e12	0.589031
$172$	1.76826e12	0.895651
$173$	−9.04930e11	−0.443978	−0.221989	−	0.975049i	$-0.571255\pi$
$173$	−9.04930e11	−0.443978	−0.221989	+	0.975049i	$0.571255\pi$
$174$	−2.74441e11	−0.130445
$175$	7.53881e11	0.347211
$176$	−1.68874e11	−0.0753778
$177$	−3.87746e10	−0.0167762
$178$	1.52690e12	0.640472
$179$	−2.77941e12	−1.13048	−0.565238	−	0.824928i	$-0.691216\pi$
$179$	−2.77941e12	−1.13048	−0.565238	+	0.824928i	$0.691216\pi$
$180$	7.98326e11	0.314907
$181$	−4.70638e11	−0.180076	−0.0900378	−	0.995938i	$-0.528699\pi$
$181$	−4.70638e11	−0.180076	−0.0900378	+	0.995938i	$0.528699\pi$
$182$	−5.08183e11	−0.188637
$183$	−1.21754e12	−0.438534
$184$	7.15511e11	0.250103
$185$	−3.29019e12	−1.11629
$186$	−1.61436e12	−0.531715
$187$	−2.35565e11	−0.0753325
$188$	2.68840e12	0.834882
$189$	4.57137e12	1.37882
$190$	1.73837e12	0.509327
$191$	−5.18981e12	−1.47730	−0.738649	−	0.674090i	$-0.764536\pi$
$191$	−5.18981e12	−1.47730	−0.738649	+	0.674090i	$0.764536\pi$
$192$	2.40133e11	0.0664196
$193$	7.32616e12	1.96930	0.984648	−	0.174549i	$-0.0558467\pi$
$193$	7.32616e12	1.96930	0.984648	+	0.174549i	$0.0558467\pi$
$194$	−3.58784e12	−0.937398
$195$	−3.24211e11	−0.0823451
$196$	2.59631e12	0.641134
$197$	2.10089e12	0.504473	0.252237	−	0.967666i	$-0.418834\pi$
$197$	2.10089e12	0.504473	0.252237	+	0.967666i	$0.418834\pi$
$198$	6.55188e11	0.153006
$199$	5.92246e11	0.134527	0.0672637	−	0.997735i	$-0.478573\pi$
$199$	5.92246e11	0.134527	0.0672637	+	0.997735i	$0.478573\pi$
$200$	−3.67731e11	−0.0812578
$201$	−4.38993e12	−0.943800
$202$	−1.64357e12	−0.343839
$203$	2.57614e12	0.524495
$204$	3.34966e11	0.0663796
$205$	3.49965e12	0.675115
$206$	2.46447e12	0.462865
$207$	−2.77600e12	−0.507671
$208$	2.47883e11	0.0441468
$209$	1.42668e12	0.247470
$210$	2.94817e12	0.498135
$211$	5.62286e12	0.925558	0.462779	−	0.886474i	$-0.346852\pi$
$211$	5.62286e12	0.925558	0.462779	+	0.886474i	$0.346852\pi$
$212$	−3.72189e12	−0.596920
$213$	−1.45380e12	−0.227204
$214$	−4.99481e12	−0.760753
$215$	−1.05894e13	−1.57203
$216$	−2.22984e12	−0.322685
$217$	1.51538e13	2.13792
$218$	5.02153e12	0.690757
$219$	2.02206e12	0.271239
$220$	1.01133e12	0.132302
$221$	3.45777e11	0.0441203
$222$	3.83968e12	0.477919
$223$	−5.15256e11	−0.0625672	−0.0312836	−	0.999511i	$-0.509959\pi$
$223$	−5.15256e11	−0.0625672	−0.0312836	+	0.999511i	$0.509959\pi$
$224$	−2.25410e12	−0.267060
$225$	1.42670e12	0.164941
$226$	−1.00924e13	−1.13867
$227$	−6.10651e12	−0.672436	−0.336218	−	0.941784i	$-0.609148\pi$
$227$	−6.10651e12	−0.672436	−0.336218	+	0.941784i	$0.609148\pi$
$228$	−2.02869e12	−0.218059
$229$	1.35475e13	1.42156	0.710778	−	0.703416i	$-0.248343\pi$
$229$	1.35475e13	1.42156	0.710778	+	0.703416i	$0.248343\pi$
$230$	−4.28493e12	−0.438976
$231$	2.41957e12	0.242032
$232$	−1.25660e12	−0.122748
$233$	−8.63262e11	−0.0823541	−0.0411770	−	0.999152i	$-0.513111\pi$
$233$	−8.63262e11	−0.0823541	−0.0411770	+	0.999152i	$0.513111\pi$
$234$	−9.61724e11	−0.0896114
$235$	−1.60998e13	−1.46537
$236$	−1.77539e11	−0.0157862
$237$	−3.28294e12	−0.285199
$238$	−3.14427e12	−0.266899
$239$	1.91732e13	1.59040	0.795199	−	0.606348i	$-0.207366\pi$
$239$	1.91732e13	1.59040	0.795199	+	0.606348i	$0.207366\pi$
$240$	−1.43807e12	−0.116579
$241$	1.92619e13	1.52618	0.763091	−	0.646292i	$-0.223681\pi$
$241$	1.92619e13	1.52618	0.763091	+	0.646292i	$0.223681\pi$
$242$	8.29998e11	0.0642824
$243$	1.36878e13	1.03633
$244$	−5.57483e12	−0.412656
$245$	−1.55484e13	−1.12531
$246$	−4.08413e12	−0.289039
$247$	−2.09417e12	−0.144937
$248$	−7.39175e12	−0.500338
$249$	1.08076e12	0.0715538
$250$	1.17840e13	0.763174
$251$	−2.96195e13	−1.87660	−0.938301	−	0.345819i	$-0.887601\pi$
$251$	−2.96195e13	−1.87660	−0.938301	+	0.345819i	$0.887601\pi$
$252$	8.74531e12	0.542091
$253$	−3.51666e12	−0.213288
$254$	−3.70246e12	−0.219738
$255$	−2.00599e12	−0.116508
$256$	1.09951e12	0.0625000
$257$	−3.07684e13	−1.71188	−0.855940	−	0.517075i	$-0.827021\pi$
$257$	−3.07684e13	−1.71188	−0.855940	+	0.517075i	$0.827021\pi$
$258$	1.23580e13	0.673038
$259$	−3.60425e13	−1.92162
$260$	−1.48448e12	−0.0774858
$261$	4.87528e12	0.249159
$262$	−2.03188e13	−1.01681
$263$	−5.84028e12	−0.286205	−0.143103	−	0.989708i	$-0.545708\pi$
$263$	−5.84028e12	−0.286205	−0.143103	+	0.989708i	$0.545708\pi$
$264$	−1.18023e12	−0.0566428
$265$	2.22890e13	1.04771
$266$	1.90430e13	0.876773
$267$	1.06712e13	0.481284
$268$	−2.01004e13	−0.888104
$269$	−2.03663e13	−0.881608	−0.440804	−	0.897603i	$-0.645307\pi$
$269$	−2.03663e13	−0.881608	−0.440804	+	0.897603i	$0.645307\pi$
$270$	1.33537e13	0.566371
$271$	−7.25920e12	−0.301688	−0.150844	−	0.988558i	$-0.548199\pi$
$271$	−7.25920e12	−0.301688	−0.150844	+	0.988558i	$0.548199\pi$
$272$	1.53373e12	0.0624624
$273$	−3.55159e12	−0.141752
$274$	1.96884e13	0.770164
$275$	1.80736e12	0.0692969
$276$	5.00057e12	0.187940
$277$	5.01115e13	1.84628	0.923142	−	0.384459i	$-0.125612\pi$
$277$	5.01115e13	1.84628	0.923142	+	0.384459i	$0.125612\pi$
$278$	−2.52197e13	−0.910948
$279$	2.86781e13	1.01561
$280$	1.34990e13	0.468739
$281$	2.56674e13	0.873973	0.436986	−	0.899468i	$-0.356046\pi$
$281$	2.56674e13	0.873973	0.436986	+	0.899468i	$0.356046\pi$
$282$	1.87887e13	0.627374
$283$	4.10685e13	1.34488	0.672441	−	0.740151i	$-0.265246\pi$
$283$	4.10685e13	1.34488	0.672441	+	0.740151i	$0.265246\pi$
$284$	−6.65657e12	−0.213796
$285$	1.21491e13	0.382735
$286$	−1.21832e12	−0.0376485
$287$	3.83371e13	1.16217
$288$	−4.26582e12	−0.126866
$289$	−3.21325e13	−0.937575
$290$	7.52532e12	0.215445
$291$	−2.50747e13	−0.704409
$292$	9.25853e12	0.255233
$293$	−4.43654e13	−1.20025	−0.600126	−	0.799905i	$-0.704883\pi$
$293$	−4.43654e13	−1.20025	−0.600126	+	0.799905i	$0.704883\pi$
$294$	1.81451e13	0.481781
$295$	1.06322e12	0.0277078
$296$	1.75810e13	0.449716
$297$	1.09594e13	0.275186
$298$	7.36924e12	0.181649
$299$	5.16195e12	0.124917
$300$	−2.57000e12	−0.0610613
$301$	−1.16003e14	−2.70615
$302$	2.33186e13	0.534152
$303$	−1.14866e13	−0.258378
$304$	−9.28889e12	−0.205191
$305$	3.33856e13	0.724287
$306$	−5.95046e12	−0.126789
$307$	−5.64451e12	−0.118131	−0.0590657	−	0.998254i	$-0.518812\pi$
$307$	−5.64451e12	−0.118131	−0.0590657	+	0.998254i	$0.518812\pi$
$308$	1.10786e13	0.227749
$309$	1.72237e13	0.347820
$310$	4.42665e13	0.878185
$311$	3.53475e13	0.688933	0.344467	−	0.938799i	$-0.388060\pi$
$311$	3.53475e13	0.688933	0.344467	+	0.938799i	$0.388060\pi$
$312$	1.73241e12	0.0331742
$313$	−3.27110e13	−0.615460	−0.307730	−	0.951474i	$-0.599569\pi$
$313$	−3.27110e13	−0.615460	−0.307730	+	0.951474i	$0.599569\pi$
$314$	2.56396e13	0.474021
$315$	−5.23725e13	−0.951470
$316$	−1.50318e13	−0.268368
$317$	4.10323e13	0.719945	0.359973	−	0.932963i	$-0.382786\pi$
$317$	4.10323e13	0.719945	0.359973	+	0.932963i	$0.382786\pi$
$318$	−2.60116e13	−0.448557
$319$	6.17604e12	0.104679
$320$	−6.58457e12	−0.109699
$321$	−3.49078e13	−0.571669
$322$	−4.69395e13	−0.755669
$323$	−1.29572e13	−0.205068
$324$	7.47752e12	0.116348
$325$	−2.65294e12	−0.0405854
$326$	−8.73754e13	−1.31429
$327$	3.50945e13	0.519070
$328$	−1.87002e13	−0.271982
$329$	−1.76366e14	−2.52254
$330$	7.06796e12	0.0994185
$331$	2.45292e13	0.339335	0.169668	−	0.985501i	$-0.445731\pi$
$331$	2.45292e13	0.339335	0.169668	+	0.985501i	$0.445731\pi$
$332$	4.94853e12	0.0673313
$333$	−6.82096e13	−0.912856
$334$	−4.70576e13	−0.619475
$335$	1.20374e14	1.55879
$336$	−1.57534e13	−0.200682
$337$	1.23850e14	1.55214	0.776072	−	0.630644i	$-0.217209\pi$
$337$	1.23850e14	1.55214	0.776072	+	0.630644i	$0.217209\pi$
$338$	−5.55608e13	−0.685057
$339$	−7.05338e13	−0.855656
$340$	−9.18492e12	−0.109633
$341$	3.63296e13	0.426690
$342$	3.60385e13	0.416508
$343$	−3.74940e13	−0.426427
$344$	5.65842e13	0.633321
$345$	−2.99466e13	−0.329869
$346$	−2.89578e13	−0.313940
$347$	1.16538e14	1.24353	0.621763	−	0.783206i	$-0.286417\pi$
$347$	1.16538e14	1.24353	0.621763	+	0.783206i	$0.286417\pi$
$348$	−8.78213e12	−0.0922389
$349$	6.30644e13	0.651995	0.325998	−	0.945371i	$-0.394300\pi$
$349$	6.30644e13	0.651995	0.325998	+	0.945371i	$0.394300\pi$
$350$	2.41242e13	0.245515
$351$	−1.60869e13	−0.161169
$352$	−5.40397e12	−0.0533002
$353$	1.30447e13	0.126670	0.0633348	−	0.997992i	$-0.479826\pi$
$353$	1.30447e13	0.126670	0.0633348	+	0.997992i	$0.479826\pi$
$354$	−1.24079e12	−0.0118626
$355$	3.98638e13	0.375252
$356$	4.88608e13	0.452882
$357$	−2.19747e13	−0.200562
$358$	−8.89413e13	−0.799368
$359$	−2.21205e13	−0.195783	−0.0978915	−	0.995197i	$-0.531210\pi$
$359$	−2.21205e13	−0.195783	−0.0978915	+	0.995197i	$0.531210\pi$
$360$	2.55464e13	0.222673
$361$	−3.80159e13	−0.326344
$362$	−1.50604e13	−0.127333
$363$	5.80069e12	0.0483051
$364$	−1.62619e13	−0.133387
$365$	−5.54459e13	−0.447980
$366$	−3.89614e13	−0.310091
$367$	1.08385e14	0.849779	0.424890	−	0.905245i	$-0.360313\pi$
$367$	1.08385e14	0.849779	0.424890	+	0.905245i	$0.360313\pi$
$368$	2.28964e13	0.176849
$369$	7.25520e13	0.552083
$370$	−1.05286e14	−0.789334
$371$	2.44167e14	1.80356
$372$	−5.16595e13	−0.375980
$373$	2.38124e14	1.70767	0.853835	−	0.520543i	$-0.174270\pi$
$373$	2.38124e14	1.70767	0.853835	+	0.520543i	$0.174270\pi$
$374$	−7.53809e12	−0.0532681
$375$	8.23562e13	0.573488
$376$	8.60287e13	0.590351
$377$	−9.06556e12	−0.0613080
$378$	1.46284e14	0.974971
$379$	3.91367e13	0.257080	0.128540	−	0.991704i	$-0.458971\pi$
$379$	3.91367e13	0.257080	0.128540	+	0.991704i	$0.458971\pi$
$380$	5.56278e13	0.360149
$381$	−2.58758e13	−0.165122
$382$	−1.66074e14	−1.04461
$383$	−2.22250e14	−1.37800	−0.688998	−	0.724764i	$-0.741949\pi$
$383$	−2.22250e14	−1.37800	−0.688998	+	0.724764i	$0.741949\pi$
$384$	7.68427e12	0.0469657
$385$	−6.63458e13	−0.399742
$386$	2.34437e14	1.39250
$387$	−2.19532e14	−1.28555
$388$	−1.14811e14	−0.662840
$389$	1.90097e13	0.108206	0.0541031	−	0.998535i	$-0.482770\pi$
$389$	1.90097e13	0.108206	0.0541031	+	0.998535i	$0.482770\pi$
$390$	−1.03748e13	−0.0582268
$391$	3.19385e13	0.176743
$392$	8.30820e13	0.453350
$393$	−1.42004e14	−0.764086
$394$	6.72283e13	0.356716
$395$	9.00199e13	0.471036
$396$	2.09660e13	0.108191
$397$	−1.89536e14	−0.964592	−0.482296	−	0.876008i	$-0.660197\pi$
$397$	−1.89536e14	−0.964592	−0.482296	+	0.876008i	$0.660197\pi$
$398$	1.89519e13	0.0951252
$399$	1.33088e14	0.658853
$400$	−1.17674e13	−0.0574580
$401$	−1.44601e14	−0.696429	−0.348214	−	0.937415i	$-0.613212\pi$
$401$	−1.44601e14	−0.696429	−0.348214	+	0.937415i	$0.613212\pi$
$402$	−1.40478e14	−0.667367
$403$	−5.33268e13	−0.249901
$404$	−5.25941e13	−0.243131
$405$	−4.47802e13	−0.204213
$406$	8.24365e13	0.370874
$407$	−8.64084e13	−0.383519
$408$	1.07189e13	0.0469375
$409$	−2.03810e13	−0.0880538	−0.0440269	−	0.999030i	$-0.514019\pi$
$409$	−2.03810e13	−0.0880538	−0.0440269	+	0.999030i	$0.514019\pi$
$410$	1.11989e14	0.477379
$411$	1.37599e14	0.578741
$412$	7.88631e13	0.327295
$413$	1.16471e13	0.0476971
$414$	−8.88319e13	−0.358978
$415$	−2.96350e13	−0.118179
$416$	7.93227e12	0.0312165
$417$	−1.76256e14	−0.684533
$418$	4.56538e13	0.174988
$419$	6.74431e13	0.255129	0.127565	−	0.991830i	$-0.459284\pi$
$419$	6.74431e13	0.255129	0.127565	+	0.991830i	$0.459284\pi$
$420$	9.43416e13	0.352235
$421$	3.79394e13	0.139810	0.0699052	−	0.997554i	$-0.477730\pi$
$421$	3.79394e13	0.139810	0.0699052	+	0.997554i	$0.477730\pi$
$422$	1.79932e14	0.654469
$423$	−3.33769e14	−1.19832
$424$	−1.19100e14	−0.422086
$425$	−1.64145e13	−0.0574234
$426$	−4.65215e13	−0.160657
$427$	3.65725e14	1.24681
$428$	−1.59834e14	−0.537933
$429$	−8.51459e12	−0.0282910
$430$	−3.38862e14	−1.11160
$431$	−4.64035e14	−1.50288	−0.751442	−	0.659799i	$-0.770641\pi$
$431$	−4.64035e14	−1.50288	−0.751442	+	0.659799i	$0.770641\pi$
$432$	−7.13549e13	−0.228172
$433$	−1.08846e14	−0.343660	−0.171830	−	0.985127i	$-0.554968\pi$
$433$	−1.08846e14	−0.343660	−0.171830	+	0.985127i	$0.554968\pi$
$434$	4.84920e14	1.51174
$435$	5.25930e13	0.161896
$436$	1.60689e14	0.488439
$437$	−1.93433e14	−0.580607
$438$	6.47060e13	0.191795
$439$	8.53107e13	0.249717	0.124859	−	0.992175i	$-0.460152\pi$
$439$	8.53107e13	0.249717	0.124859	+	0.992175i	$0.460152\pi$
$440$	3.23624e13	0.0935516
$441$	−3.22337e14	−0.920233
$442$	1.10648e13	0.0311977
$443$	7.85379e12	0.0218705	0.0109352	−	0.999940i	$-0.496519\pi$
$443$	7.85379e12	0.0218705	0.0109352	+	0.999940i	$0.496519\pi$
$444$	1.22870e14	0.337940
$445$	−2.92609e14	−0.794892
$446$	−1.64882e13	−0.0442417
$447$	5.15022e13	0.136500
$448$	−7.21311e13	−0.188840
$449$	5.91770e14	1.53038	0.765188	−	0.643807i	$-0.222646\pi$
$449$	5.91770e14	1.53038	0.765188	+	0.643807i	$0.222646\pi$
$450$	4.56544e13	0.116631
$451$	9.19094e13	0.231947
$452$	−3.22957e14	−0.805162
$453$	1.62969e14	0.401389
$454$	−1.95408e14	−0.475484
$455$	9.73863e13	0.234118
$456$	−6.49182e13	−0.154191
$457$	−3.15070e14	−0.739380	−0.369690	−	0.929155i	$-0.620536\pi$
$457$	−3.15070e14	−0.739380	−0.369690	+	0.929155i	$0.620536\pi$
$458$	4.33520e14	1.00519
$459$	−9.95341e13	−0.228035
$460$	−1.37118e14	−0.310403
$461$	2.59857e13	0.0581272	0.0290636	−	0.999578i	$-0.490747\pi$
$461$	2.59857e13	0.0581272	0.0290636	+	0.999578i	$0.490747\pi$
$462$	7.74263e13	0.171143
$463$	−7.23059e14	−1.57935	−0.789675	−	0.613526i	$-0.789751\pi$
$463$	−7.23059e14	−1.57935	−0.789675	+	0.613526i	$0.789751\pi$
$464$	−4.02112e13	−0.0867956
$465$	3.09370e14	0.659914
$466$	−2.76244e13	−0.0582331
$467$	−1.72765e14	−0.359926	−0.179963	−	0.983673i	$-0.557598\pi$
$467$	−1.72765e14	−0.359926	−0.179963	+	0.983673i	$0.557598\pi$
$468$	−3.07752e13	−0.0633648
$469$	1.31864e15	2.68335
$470$	−5.15195e14	−1.03617
$471$	1.79190e14	0.356204
$472$	−5.68126e12	−0.0111626
$473$	−2.78105e14	−0.540098
$474$	−1.05054e14	−0.201666
$475$	9.94132e13	0.188638
$476$	−1.00617e14	−0.188726
$477$	4.62079e14	0.856772
$478$	6.13542e14	1.12458
$479$	9.82952e14	1.78109	0.890547	−	0.454891i	$-0.150322\pi$
$479$	9.82952e14	1.78109	0.890547	+	0.454891i	$0.150322\pi$
$480$	−4.60183e13	−0.0824335
$481$	1.26835e14	0.224617
$482$	6.16382e14	1.07917
$483$	−3.28051e14	−0.567849
$484$	2.65599e13	0.0454545
$485$	6.87561e14	1.16341
$486$	4.38011e14	0.732799
$487$	5.83467e14	0.965177	0.482589	−	0.875847i	$-0.339697\pi$
$487$	5.83467e14	0.965177	0.482589	+	0.875847i	$0.339697\pi$
$488$	−1.78395e14	−0.291792
$489$	−6.10650e14	−0.987628
$490$	−4.97548e14	−0.795713
$491$	−5.27245e13	−0.0833804	−0.0416902	−	0.999131i	$-0.513274\pi$
$491$	−5.27245e13	−0.0833804	−0.0416902	+	0.999131i	$0.513274\pi$
$492$	−1.30692e14	−0.204381
$493$	−5.60912e13	−0.0867435
$494$	−6.70134e13	−0.102486
$495$	−1.25558e14	−0.189896
$496$	−2.36536e14	−0.353792
$497$	4.36690e14	0.645971
$498$	3.45843e13	0.0505962
$499$	1.67856e14	0.242876	0.121438	−	0.992599i	$-0.461249\pi$
$499$	1.67856e14	0.242876	0.121438	+	0.992599i	$0.461249\pi$
$500$	3.77089e14	0.539645
$501$	−3.28876e14	−0.465506
$502$	−9.47824e14	−1.32696
$503$	−1.06856e15	−1.47971	−0.739855	−	0.672766i	$-0.765106\pi$
$503$	−1.06856e15	−1.47971	−0.739855	+	0.672766i	$0.765106\pi$
$504$	2.79850e14	0.383316
$505$	3.14967e14	0.426739
$506$	−1.12533e14	−0.150818
$507$	−3.88304e14	−0.514787
$508$	−1.18479e14	−0.155378
$509$	1.36868e15	1.77563	0.887817	−	0.460197i	$-0.152221\pi$
$509$	1.36868e15	1.77563	0.887817	+	0.460197i	$0.152221\pi$
$510$	−6.41916e13	−0.0823839
$511$	−6.07386e14	−0.771169
$512$	3.51844e13	0.0441942
$513$	6.02820e14	0.749104
$514$	−9.84590e14	−1.21048
$515$	−4.72282e14	−0.574463
$516$	3.95456e14	0.475910
$517$	−4.22821e14	−0.503453
$518$	−1.15336e15	−1.35879
$519$	−2.02380e14	−0.235911
$520$	−4.75035e13	−0.0547907
$521$	−1.02353e15	−1.16813	−0.584065	−	0.811707i	$-0.698539\pi$
$521$	−1.02353e15	−1.16813	−0.584065	+	0.811707i	$0.698539\pi$
$522$	1.56009e14	0.176182
$523$	8.46109e14	0.945512	0.472756	−	0.881193i	$-0.343259\pi$
$523$	8.46109e14	0.945512	0.472756	+	0.881193i	$0.343259\pi$
$524$	−6.50202e14	−0.718995
$525$	1.68599e14	0.184493
$526$	−1.86889e14	−0.202378
$527$	−3.29948e14	−0.353580
$528$	−3.77673e13	−0.0400525
$529$	−4.76014e14	−0.499589
$530$	7.13249e14	0.740839
$531$	2.20418e13	0.0226583
$532$	6.09377e14	0.619972
$533$	−1.34910e14	−0.135845
$534$	3.41478e14	0.340319
$535$	9.57188e14	0.944172
$536$	−6.43214e14	−0.627984
$537$	−6.21593e14	−0.600686
$538$	−6.51723e14	−0.623391
$539$	−4.08339e14	−0.386618
$540$	4.27318e14	0.400485
$541$	−1.74330e15	−1.61729	−0.808644	−	0.588298i	$-0.799798\pi$
$541$	−1.74330e15	−1.61729	−0.808644	+	0.588298i	$0.799798\pi$
$542$	−2.32294e14	−0.213325
$543$	−1.05254e14	−0.0956843
$544$	4.90792e13	0.0441676
$545$	−9.62308e14	−0.857301
$546$	−1.13651e14	−0.100234
$547$	−1.31863e15	−1.15131	−0.575655	−	0.817692i	$-0.695253\pi$
$547$	−1.31863e15	−1.15131	−0.575655	+	0.817692i	$0.695253\pi$
$548$	6.30030e14	0.544588
$549$	6.92125e14	0.592293
$550$	5.78354e13	0.0490003
$551$	3.39712e14	0.284955
$552$	1.60018e14	0.132894
$553$	9.86127e14	0.810858
$554$	1.60357e15	1.30552
$555$	−7.35823e14	−0.593146
$556$	−8.07031e14	−0.644138
$557$	6.43699e14	0.508721	0.254360	−	0.967110i	$-0.418135\pi$
$557$	6.43699e14	0.508721	0.254360	+	0.967110i	$0.418135\pi$
$558$	9.17699e14	0.718145
$559$	4.08219e14	0.316321
$560$	4.31967e14	0.331449
$561$	−5.26822e13	−0.0400284
$562$	8.21358e14	0.617992
$563$	−1.69920e15	−1.26604	−0.633022	−	0.774134i	$-0.718186\pi$
$563$	−1.69920e15	−1.26604	−0.633022	+	0.774134i	$0.718186\pi$
$564$	6.01238e14	0.443620
$565$	1.93407e15	1.41321
$566$	1.31419e15	0.950975
$567$	−4.90547e14	−0.351539
$568$	−2.13010e14	−0.151177
$569$	1.77508e15	1.24767	0.623836	−	0.781555i	$-0.285573\pi$
$569$	1.77508e15	1.24767	0.623836	+	0.781555i	$0.285573\pi$
$570$	3.88772e14	0.270634
$571$	−1.64668e14	−0.113530	−0.0567651	−	0.998388i	$-0.518079\pi$
$571$	−1.64668e14	−0.113530	−0.0567651	+	0.998388i	$0.518079\pi$
$572$	−3.89862e13	−0.0266215
$573$	−1.16066e15	−0.784972
$574$	1.22679e15	0.821776
$575$	−2.45045e14	−0.162582
$576$	−1.36506e14	−0.0897075
$577$	2.57019e15	1.67301	0.836505	−	0.547959i	$-0.184595\pi$
$577$	2.57019e15	1.67301	0.836505	+	0.547959i	$0.184595\pi$
$578$	−1.02824e15	−0.662966
$579$	1.63844e15	1.04640
$580$	2.40810e14	0.152342
$581$	−3.24638e14	−0.203437
$582$	−8.02391e14	−0.498092
$583$	5.85365e14	0.359956
$584$	2.96273e14	0.180477
$585$	1.84301e14	0.111217
$586$	−1.41969e15	−0.848707
$587$	−2.65167e15	−1.57040	−0.785199	−	0.619243i	$-0.787440\pi$
$587$	−2.65167e15	−1.57040	−0.785199	+	0.619243i	$0.787440\pi$
$588$	5.80644e14	0.340671
$589$	1.99830e15	1.16152
$590$	3.40230e13	0.0195924
$591$	4.69846e14	0.268055
$592$	5.62591e14	0.317997
$593$	−2.40219e15	−1.34526	−0.672631	−	0.739978i	$-0.734836\pi$
$593$	−2.40219e15	−1.34526	−0.672631	+	0.739978i	$0.734836\pi$
$594$	3.50701e14	0.194586
$595$	6.02557e14	0.331249
$596$	2.35816e14	0.128445
$597$	1.32451e14	0.0714820
$598$	1.65182e14	0.0883298
$599$	−1.40929e15	−0.746709	−0.373355	−	0.927689i	$-0.621793\pi$
$599$	−1.40929e15	−0.746709	−0.373355	+	0.927689i	$0.621793\pi$
$600$	−8.22400e13	−0.0431769
$601$	−7.57379e14	−0.394007	−0.197003	−	0.980403i	$-0.563121\pi$
$601$	−7.57379e14	−0.394007	−0.197003	+	0.980403i	$0.563121\pi$
$602$	−3.71209e15	−1.91354
$603$	2.49550e15	1.27471
$604$	7.46196e14	0.377703
$605$	−1.59058e14	−0.0797811
$606$	−3.67570e14	−0.182701
$607$	−4.02907e15	−1.98458	−0.992288	−	0.123958i	$-0.960441\pi$
$607$	−4.02907e15	−1.98458	−0.992288	+	0.123958i	$0.960441\pi$
$608$	−2.97244e14	−0.145092
$609$	5.76132e14	0.278694
$610$	1.06834e15	0.512148
$611$	6.20642e14	0.294859
$612$	−1.90415e14	−0.0896536
$613$	2.84125e15	1.32579	0.662897	−	0.748710i	$-0.269327\pi$
$613$	2.84125e15	1.32579	0.662897	+	0.748710i	$0.269327\pi$
$614$	−1.80624e14	−0.0835315
$615$	7.82667e14	0.358727
$616$	3.54516e14	0.161043
$617$	−5.00304e14	−0.225250	−0.112625	−	0.993638i	$-0.535926\pi$
$617$	−5.00304e14	−0.225250	−0.112625	+	0.993638i	$0.535926\pi$
$618$	5.51159e14	0.245946
$619$	1.65577e14	0.0732319	0.0366159	−	0.999329i	$-0.488342\pi$
$619$	1.65577e14	0.0732319	0.0366159	+	0.999329i	$0.488342\pi$
$620$	1.41653e15	0.620971
$621$	−1.48590e15	−0.645634
$622$	1.13112e15	0.487149
$623$	−3.20540e15	−1.36835
$624$	5.54371e13	0.0234577
$625$	−1.71028e15	−0.717345
$626$	−1.04675e15	−0.435196
$627$	3.19066e14	0.131495
$628$	8.20466e14	0.335184
$629$	7.84767e14	0.317806
$630$	−1.67592e15	−0.672791
$631$	1.93212e15	0.768903	0.384452	−	0.923145i	$-0.374391\pi$
$631$	1.93212e15	0.768903	0.384452	+	0.923145i	$0.374391\pi$
$632$	−4.81017e14	−0.189765
$633$	1.25751e15	0.491801
$634$	1.31303e15	0.509078
$635$	7.09526e14	0.272718
$636$	−8.32370e14	−0.317177
$637$	5.99383e14	0.226432
$638$	1.97633e14	0.0740196
$639$	8.26425e14	0.306866
$640$	−2.10706e14	−0.0775689
$641$	−2.22364e15	−0.811607	−0.405804	−	0.913960i	$-0.633008\pi$
$641$	−2.22364e15	−0.811607	−0.405804	+	0.913960i	$0.633008\pi$
$642$	−1.11705e15	−0.404231
$643$	−4.41198e15	−1.58297	−0.791486	−	0.611187i	$-0.790692\pi$
$643$	−4.41198e15	−1.58297	−0.791486	+	0.611187i	$0.790692\pi$
$644$	−1.50207e15	−0.534339
$645$	−2.36824e15	−0.835310
$646$	−4.14631e14	−0.145005
$647$	−2.57932e13	−0.00894399	−0.00447200	−	0.999990i	$-0.501423\pi$
$647$	−2.57932e13	−0.00894399	−0.00447200	+	0.999990i	$0.501423\pi$
$648$	2.39281e14	0.0822707
$649$	2.79228e13	0.00951947
$650$	−8.48942e13	−0.0286982
$651$	3.38901e15	1.13600
$652$	−2.79601e15	−0.929346
$653$	−9.39966e14	−0.309806	−0.154903	−	0.987930i	$-0.549506\pi$
$653$	−9.39966e14	−0.309806	−0.154903	+	0.987930i	$0.549506\pi$
$654$	1.12302e15	0.367038
$655$	3.89382e15	1.26197
$656$	−5.98406e14	−0.192320
$657$	−1.14946e15	−0.366341
$658$	−5.64373e15	−1.78371
$659$	3.61970e15	1.13450	0.567248	−	0.823547i	$-0.308008\pi$
$659$	3.61970e15	1.13450	0.567248	+	0.823547i	$0.308008\pi$
$660$	2.26175e14	0.0702995
$661$	2.36068e15	0.727660	0.363830	−	0.931465i	$-0.381469\pi$
$661$	2.36068e15	0.727660	0.363830	+	0.931465i	$0.381469\pi$
$662$	7.84934e14	0.239946
$663$	7.73301e13	0.0234436
$664$	1.58353e14	0.0476104
$665$	−3.64934e15	−1.08817
$666$	−2.18271e15	−0.645486
$667$	−8.37362e14	−0.245596
$668$	−1.50584e15	−0.438035
$669$	−1.15233e14	−0.0332455
$670$	3.85197e15	1.10223
$671$	8.76789e14	0.248841
$672$	−5.04110e14	−0.141904
$673$	−4.47663e15	−1.24988	−0.624939	−	0.780673i	$-0.714876\pi$
$673$	−4.47663e15	−1.24988	−0.624939	+	0.780673i	$0.714876\pi$
$674$	3.96321e15	1.09753
$675$	7.63667e14	0.209765
$676$	−1.77795e15	−0.484408
$677$	5.83286e14	0.157632	0.0788159	−	0.996889i	$-0.474886\pi$
$677$	5.83286e14	0.157632	0.0788159	+	0.996889i	$0.474886\pi$
$678$	−2.25708e15	−0.605040
$679$	7.53192e15	2.00273
$680$	−2.93918e14	−0.0775223
$681$	−1.36567e15	−0.357303
$682$	1.16255e15	0.301715
$683$	4.49866e15	1.15816	0.579080	−	0.815270i	$-0.303412\pi$
$683$	4.49866e15	1.15816	0.579080	+	0.815270i	$0.303412\pi$
$684$	1.15323e15	0.294515
$685$	−3.77302e15	−0.955853
$686$	−1.19981e15	−0.301529
$687$	3.02979e15	0.755353
$688$	1.81070e15	0.447826
$689$	−8.59234e14	−0.210817
$690$	−9.58290e14	−0.233253
$691$	−1.90377e15	−0.459710	−0.229855	−	0.973225i	$-0.573825\pi$
$691$	−1.90377e15	−0.459710	−0.229855	+	0.973225i	$0.573825\pi$
$692$	−9.26648e14	−0.221989
$693$	−1.37543e15	−0.326893
$694$	3.72921e15	0.879305
$695$	4.83301e15	1.13058
$696$	−2.81028e14	−0.0652227
$697$	−8.34727e14	−0.192205
$698$	2.01806e15	0.461030
$699$	−1.93061e14	−0.0437594
$700$	7.71974e14	0.173606
$701$	8.09537e15	1.80629	0.903146	−	0.429334i	$-0.141252\pi$
$701$	8.09537e15	1.80629	0.903146	+	0.429334i	$0.141252\pi$
$702$	−5.14780e14	−0.113964
$703$	−4.75288e15	−1.04400
$704$	−1.72927e14	−0.0376889
$705$	−3.60059e15	−0.778635
$706$	4.17430e14	0.0895690
$707$	3.45032e15	0.734604
$708$	−3.97052e13	−0.00838812
$709$	3.30685e15	0.693203	0.346602	−	0.938012i	$-0.387336\pi$
$709$	3.30685e15	0.693203	0.346602	+	0.938012i	$0.387336\pi$
$710$	1.27564e15	0.265343
$711$	1.86622e15	0.385195
$712$	1.56354e15	0.320236
$713$	−4.92566e15	−1.00109
$714$	−7.03191e14	−0.141819
$715$	2.33474e14	0.0467257
$716$	−2.84612e15	−0.565238
$717$	4.28793e15	0.845069
$718$	−7.07855e14	−0.138440
$719$	−9.78250e15	−1.89863	−0.949316	−	0.314324i	$-0.898222\pi$
$719$	−9.78250e15	−1.89863	−0.949316	+	0.314324i	$0.898222\pi$
$720$	8.17486e14	0.157453
$721$	−5.17364e15	−0.988900
$722$	−1.21651e15	−0.230760
$723$	4.30777e15	0.810946
$724$	−4.81933e14	−0.0900378
$725$	4.30355e14	0.0797936
$726$	1.85622e14	0.0341569
$727$	2.49870e15	0.456325	0.228163	−	0.973623i	$-0.426728\pi$
$727$	2.49870e15	0.456325	0.228163	+	0.973623i	$0.426728\pi$
$728$	−5.20379e14	−0.0943186
$729$	1.76759e15	0.317966
$730$	−1.77427e15	−0.316770
$731$	2.52577e15	0.447556
$732$	−1.24676e15	−0.219267
$733$	3.49691e15	0.610397	0.305198	−	0.952289i	$-0.401277\pi$
$733$	3.49691e15	0.610397	0.305198	+	0.952289i	$0.401277\pi$
$734$	3.46832e15	0.600884
$735$	−3.47726e15	−0.597940
$736$	7.32683e14	0.125051
$737$	3.16132e15	0.535547
$738$	2.32166e15	0.390381
$739$	−3.56268e15	−0.594611	−0.297305	−	0.954782i	$-0.596088\pi$
$739$	−3.56268e15	−0.594611	−0.297305	+	0.954782i	$0.596088\pi$
$740$	−3.36915e15	−0.558144
$741$	−4.68343e14	−0.0770130
$742$	7.81333e15	1.27531
$743$	−8.55809e15	−1.38656	−0.693279	−	0.720669i	$-0.743835\pi$
$743$	−8.55809e15	−1.38656	−0.693279	+	0.720669i	$0.743835\pi$
$744$	−1.65310e15	−0.265858
$745$	−1.41221e15	−0.225445
$746$	7.61996e15	1.20751
$747$	−6.14369e14	−0.0966420
$748$	−2.41219e14	−0.0376663
$749$	1.04856e16	1.62533
$750$	2.63540e15	0.405517
$751$	2.61136e15	0.398884	0.199442	−	0.979910i	$-0.436087\pi$
$751$	2.61136e15	0.398884	0.199442	+	0.979910i	$0.436087\pi$
$752$	2.75292e15	0.417441
$753$	−6.62416e15	−0.997145
$754$	−2.90098e14	−0.0433513
$755$	−4.46870e15	−0.662938
$756$	4.68108e15	0.689408
$757$	2.24153e15	0.327730	0.163865	−	0.986483i	$-0.447604\pi$
$757$	2.24153e15	0.327730	0.163865	+	0.986483i	$0.447604\pi$
$758$	1.25238e15	0.181783
$759$	−7.86471e14	−0.113332
$760$	1.78009e15	0.254664
$761$	−5.35692e15	−0.760851	−0.380425	−	0.924812i	$-0.624222\pi$
$761$	−5.35692e15	−0.760851	−0.380425	+	0.924812i	$0.624222\pi$
$762$	−8.28025e14	−0.116759
$763$	−1.05417e16	−1.47579
$764$	−5.31437e15	−0.738649
$765$	1.14032e15	0.157359
$766$	−7.11199e15	−0.974390
$767$	−4.09867e13	−0.00557530
$768$	2.45897e14	0.0332098
$769$	−9.53280e15	−1.27828	−0.639139	−	0.769091i	$-0.720709\pi$
$769$	−9.53280e15	−1.27828	−0.639139	+	0.769091i	$0.720709\pi$
$770$	−2.12307e15	−0.282660
$771$	−6.88111e15	−0.909619
$772$	7.50199e15	0.984648
$773$	−1.27998e16	−1.66808	−0.834040	−	0.551704i	$-0.813978\pi$
$773$	−1.27998e16	−1.66808	−0.834040	+	0.551704i	$0.813978\pi$
$774$	−7.02503e15	−0.909019
$775$	2.53150e15	0.325251
$776$	−3.67395e15	−0.468699
$777$	−8.06061e15	−1.02106
$778$	6.08310e14	0.0765133
$779$	5.05545e15	0.631399
$780$	−3.31992e14	−0.0411726
$781$	1.04692e15	0.128924
$782$	1.02203e15	0.124976
$783$	2.60958e15	0.316870
$784$	2.65862e15	0.320567
$785$	−4.91347e15	−0.588309
$786$	−4.54413e15	−0.540290
$787$	−1.24619e16	−1.47138	−0.735688	−	0.677320i	$-0.763141\pi$
$787$	−1.24619e16	−1.47138	−0.735688	+	0.677320i	$0.763141\pi$
$788$	2.15131e15	0.252237
$789$	−1.30613e15	−0.152077
$790$	2.88064e15	0.333073
$791$	2.11869e16	2.43274
$792$	6.70913e14	0.0765028
$793$	−1.28700e15	−0.145739
$794$	−6.06515e15	−0.682070
$795$	4.98476e15	0.556705
$796$	6.06460e14	0.0672637
$797$	1.29315e16	1.42439	0.712196	−	0.701981i	$-0.247701\pi$
$797$	1.29315e16	1.42439	0.712196	+	0.701981i	$0.247701\pi$
$798$	4.25882e15	0.465879
$799$	3.84009e15	0.417190
$800$	−3.76557e14	−0.0406289
$801$	−6.06615e15	−0.650031
$802$	−4.62723e15	−0.492449
$803$	−1.45615e15	−0.153911
$804$	−4.49529e15	−0.471900
$805$	8.99532e15	0.937863
$806$	−1.70646e15	−0.176706
$807$	−4.55477e15	−0.468448
$808$	−1.68301e15	−0.171919
$809$	1.41812e16	1.43879	0.719393	−	0.694603i	$-0.244420\pi$
$809$	1.41812e16	1.43879	0.719393	+	0.694603i	$0.244420\pi$
$810$	−1.43297e15	−0.144400
$811$	−1.19017e16	−1.19123	−0.595616	−	0.803270i	$-0.703092\pi$
$811$	−1.19017e16	−1.19123	−0.595616	+	0.803270i	$0.703092\pi$
$812$	2.63797e15	0.262247
$813$	−1.62346e15	−0.160304
$814$	−2.76507e15	−0.271189
$815$	1.67443e16	1.63117
$816$	3.43005e14	0.0331898
$817$	−1.52971e16	−1.47024
$818$	−6.52193e14	−0.0622634
$819$	2.01894e15	0.191453
$820$	3.58364e15	0.337558
$821$	1.13457e16	1.06156	0.530781	−	0.847509i	$-0.321899\pi$
$821$	1.13457e16	1.06156	0.530781	+	0.847509i	$0.321899\pi$
$822$	4.40316e15	0.409232
$823$	−4.11321e15	−0.379736	−0.189868	−	0.981810i	$-0.560806\pi$
$823$	−4.11321e15	−0.379736	−0.189868	+	0.981810i	$0.560806\pi$
$824$	2.52362e15	0.231432
$825$	4.04200e14	0.0368214
$826$	3.72707e14	0.0337270
$827$	1.78386e16	1.60354	0.801771	−	0.597631i	$-0.203891\pi$
$827$	1.78386e16	1.60354	0.801771	+	0.597631i	$0.203891\pi$
$828$	−2.84262e15	−0.253835
$829$	−1.22717e16	−1.08857	−0.544284	−	0.838901i	$-0.683199\pi$
$829$	−1.22717e16	−1.08857	−0.544284	+	0.838901i	$0.683199\pi$
$830$	−9.48319e14	−0.0835651
$831$	1.12070e16	0.981035
$832$	2.53833e14	0.0220734
$833$	3.70856e15	0.320374
$834$	−5.64018e15	−0.484038
$835$	9.01794e15	0.768833
$836$	1.46092e15	0.123735
$837$	1.53505e16	1.29161
$838$	2.15818e15	0.180404
$839$	6.46465e15	0.536851	0.268426	−	0.963300i	$-0.413497\pi$
$839$	6.46465e15	0.536851	0.268426	+	0.963300i	$0.413497\pi$
$840$	3.01893e15	0.249067
$841$	−1.07299e16	−0.879464
$842$	1.21406e15	0.0988608
$843$	5.74031e15	0.464391
$844$	5.75781e15	0.462779
$845$	1.06475e16	0.850226
$846$	−1.06806e16	−0.847343
$847$	−1.74241e15	−0.137338
$848$	−3.81122e15	−0.298460
$849$	9.18464e15	0.714611
$850$	−5.25265e14	−0.0406045
$851$	1.17155e16	0.899801
$852$	−1.48869e15	−0.113602
$853$	2.54947e15	0.193299	0.0966495	−	0.995318i	$-0.469187\pi$
$853$	2.54947e15	0.193299	0.0966495	+	0.995318i	$0.469187\pi$
$854$	1.17032e16	0.881629
$855$	−6.90628e15	−0.516929
$856$	−5.11469e15	−0.380376
$857$	6.68978e15	0.494331	0.247165	−	0.968973i	$-0.420501\pi$
$857$	6.68978e15	0.494331	0.247165	+	0.968973i	$0.420501\pi$
$858$	−2.72467e14	−0.0200048
$859$	−1.45593e16	−1.06213	−0.531066	−	0.847331i	$-0.678208\pi$
$859$	−1.45593e16	−1.06213	−0.531066	+	0.847331i	$0.678208\pi$
$860$	−1.08436e16	−0.786017
$861$	8.57377e15	0.617525
$862$	−1.48491e16	−1.06270
$863$	−8.34062e15	−0.593115	−0.296558	−	0.955015i	$-0.595839\pi$
$863$	−8.34062e15	−0.593115	−0.296558	+	0.955015i	$0.595839\pi$
$864$	−2.28336e15	−0.161342
$865$	5.54936e15	0.389632
$866$	−3.48307e15	−0.243004
$867$	−7.18616e15	−0.498187
$868$	1.55174e16	1.06896
$869$	2.36414e15	0.161832
$870$	1.68297e15	0.114478
$871$	−4.64037e15	−0.313656
$872$	5.14205e15	0.345379
$873$	1.42540e16	0.951388
$874$	−6.18985e15	−0.410551
$875$	−2.47381e16	−1.63050
$876$	2.07059e15	0.135620
$877$	−1.21586e16	−0.791384	−0.395692	−	0.918383i	$-0.629495\pi$
$877$	−1.21586e16	−0.791384	−0.395692	+	0.918383i	$0.629495\pi$
$878$	2.72994e15	0.176577
$879$	−9.92196e15	−0.637762
$880$	1.03560e15	0.0661510
$881$	−1.93966e16	−1.23129	−0.615643	−	0.788025i	$-0.711104\pi$
$881$	−1.93966e16	−1.23129	−0.615643	+	0.788025i	$0.711104\pi$
$882$	−1.03148e16	−0.650703
$883$	−4.07717e15	−0.255608	−0.127804	−	0.991799i	$-0.540793\pi$
$883$	−4.07717e15	−0.255608	−0.127804	+	0.991799i	$0.540793\pi$
$884$	3.54075e14	0.0220601
$885$	2.37780e14	0.0147227
$886$	2.51321e14	0.0154648
$887$	−3.20987e16	−1.96294	−0.981472	−	0.191604i	$-0.938631\pi$
$887$	−3.20987e16	−1.96294	−0.981472	+	0.191604i	$0.938631\pi$
$888$	3.93184e15	0.238959
$889$	7.77255e15	0.469465
$890$	−9.36350e15	−0.562073
$891$	−1.17604e15	−0.0701607
$892$	−5.27622e14	−0.0312836
$893$	−2.32572e16	−1.37049
$894$	1.64807e15	0.0965204
$895$	1.70444e16	0.992098
$896$	−2.30819e15	−0.133530
$897$	1.15443e15	0.0663756
$898$	1.89366e16	1.08214
$899$	8.65057e15	0.491322
$900$	1.46094e15	0.0824706
$901$	−5.31632e15	−0.298281
$902$	2.94110e15	0.164011
$903$	−2.59430e16	−1.43793
$904$	−1.03346e16	−0.569335
$905$	2.88612e15	0.158033
$906$	5.21502e15	0.283825
$907$	2.80672e16	1.51830	0.759151	−	0.650914i	$-0.225614\pi$
$907$	2.80672e16	1.51830	0.759151	+	0.650914i	$0.225614\pi$
$908$	−6.25307e15	−0.336218
$909$	6.52965e15	0.348971
$910$	3.11636e15	0.165547
$911$	−4.20682e14	−0.0222128	−0.0111064	−	0.999938i	$-0.503535\pi$
$911$	−4.20682e14	−0.0222128	−0.0111064	+	0.999938i	$0.503535\pi$
$912$	−2.07738e15	−0.109030
$913$	−7.78287e14	−0.0406023
$914$	−1.00822e16	−0.522820
$915$	7.46642e15	0.384854
$916$	1.38726e16	0.710778
$917$	4.26551e16	2.17240
$918$	−3.18509e15	−0.161245
$919$	−1.00447e16	−0.505478	−0.252739	−	0.967534i	$-0.581331\pi$
$919$	−1.00447e16	−0.505478	−0.252739	+	0.967534i	$0.581331\pi$
$920$	−4.38777e15	−0.219488
$921$	−1.26235e15	−0.0627699
$922$	8.31543e14	0.0411022
$923$	−1.53673e15	−0.0755073
$924$	2.47764e15	0.121016
$925$	−6.02106e15	−0.292344
$926$	−2.31379e16	−1.11677
$927$	−9.79099e15	−0.469773
$928$	−1.28676e15	−0.0613738
$929$	−2.15223e16	−1.02047	−0.510236	−	0.860034i	$-0.670442\pi$
$929$	−2.15223e16	−1.02047	−0.510236	+	0.860034i	$0.670442\pi$
$930$	9.89984e15	0.466629
$931$	−2.24606e16	−1.05244
$932$	−8.83980e14	−0.0411770
$933$	7.90519e15	0.366069
$934$	−5.52849e15	−0.254506
$935$	1.44457e15	0.0661112
$936$	−9.84805e14	−0.0448057
$937$	3.92925e16	1.77722	0.888612	−	0.458660i	$-0.151670\pi$
$937$	3.92925e16	1.77722	0.888612	+	0.458660i	$0.151670\pi$
$938$	4.21966e16	1.89741
$939$	−7.31555e15	−0.327029
$940$	−1.64862e16	−0.732686
$941$	3.48975e15	0.154188	0.0770941	−	0.997024i	$-0.475436\pi$
$941$	3.48975e15	0.154188	0.0770941	+	0.997024i	$0.475436\pi$
$942$	5.73408e15	0.251874
$943$	−1.24613e16	−0.544187
$944$	−1.81800e14	−0.00789312
$945$	−2.80333e16	−1.21004
$946$	−8.89936e15	−0.381907
$947$	−1.09651e16	−0.467829	−0.233915	−	0.972257i	$-0.575154\pi$
$947$	−1.09651e16	−0.467829	−0.233915	+	0.972257i	$0.575154\pi$
$948$	−3.36173e15	−0.142599
$949$	2.13742e15	0.0901416
$950$	3.18122e15	0.133387
$951$	9.17653e15	0.382548
$952$	−3.21974e15	−0.133450
$953$	−1.19556e16	−0.492676	−0.246338	−	0.969184i	$-0.579227\pi$
$953$	−1.19556e16	−0.492676	−0.246338	+	0.969184i	$0.579227\pi$
$954$	1.47865e16	0.605829
$955$	3.18258e16	1.29647
$956$	1.96334e16	0.795199
$957$	1.38122e15	0.0556221
$958$	3.14545e16	1.25942
$959$	−4.13318e16	−1.64544
$960$	−1.47259e15	−0.0582893
$961$	2.54772e16	1.00270
$962$	4.05873e15	0.158828
$963$	1.98437e16	0.772107
$964$	1.97242e16	0.763091
$965$	−4.49267e16	−1.72824
$966$	−1.04976e16	−0.401530
$967$	−9.70974e15	−0.369285	−0.184643	−	0.982806i	$-0.559113\pi$
$967$	−9.70974e15	−0.369285	−0.184643	+	0.982806i	$0.559113\pi$
$968$	8.49918e14	0.0321412
$969$	−2.89777e15	−0.108964
$970$	2.20020e16	0.822653
$971$	6.78078e15	0.252100	0.126050	−	0.992024i	$-0.459770\pi$
$971$	6.78078e15	0.252100	0.126050	+	0.992024i	$0.459770\pi$
$972$	1.40163e16	0.518167
$973$	5.29435e16	1.94622
$974$	1.86709e16	0.682483
$975$	−5.93309e14	−0.0215653
$976$	−5.70863e15	−0.206328
$977$	−2.35356e16	−0.845873	−0.422936	−	0.906159i	$-0.639001\pi$
$977$	−2.35356e16	−0.845873	−0.422936	+	0.906159i	$0.639001\pi$
$978$	−1.95408e16	−0.698358
$979$	−7.68464e15	−0.273098
$980$	−1.59215e16	−0.562654
$981$	−1.99498e16	−0.701067
$982$	−1.68718e15	−0.0589588
$983$	3.93740e16	1.36825	0.684125	−	0.729365i	$-0.260184\pi$
$983$	3.93740e16	1.36825	0.684125	+	0.729365i	$0.260184\pi$
$984$	−4.18215e15	−0.144519
$985$	−1.28834e16	−0.442722
$986$	−1.79492e15	−0.0613369
$987$	−3.94429e16	−1.34037
$988$	−2.14443e15	−0.0724683
$989$	3.77061e16	1.26716
$990$	−4.01785e15	−0.134277
$991$	−3.04982e15	−0.101361	−0.0506804	−	0.998715i	$-0.516139\pi$
$991$	−3.04982e15	−0.101361	−0.0506804	+	0.998715i	$0.516139\pi$
$992$	−7.56916e15	−0.250169
$993$	5.48575e15	0.180308
$994$	1.39741e16	0.456770
$995$	−3.63187e15	−0.118060
$996$	1.10670e15	0.0357769
$997$	2.24261e16	0.720992	0.360496	−	0.932761i	$-0.382607\pi$
$997$	2.24261e16	0.720992	0.360496	+	0.932761i	$0.382607\pi$
$998$	5.37140e15	0.171739
$999$	−3.65104e16	−1.16093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.a.a.1.2	✓	2
3.2	odd	2		198.12.a.c.1.2		2
4.3	odd	2		176.12.a.a.1.1		2
11.10	odd	2		242.12.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.a.a.1.2	✓	2	1.1	even	1	trivial
176.12.a.a.1.1		2	4.3	odd	2
198.12.a.c.1.2		2	3.2	odd	2
242.12.a.a.1.2		2	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} +223.642 q^{3} +1024.00 q^{4} -6132.36 q^{5} +7156.54 q^{6} -67177.3 q^{7} +32768.0 q^{8} -127131. q^{9} +O(q^{10})\)	\(q+32.0000 q^{2} +223.642 q^{3} +1024.00 q^{4} -6132.36 q^{5} +7156.54 q^{6} -67177.3 q^{7} +32768.0 q^{8} -127131. q^{9} -196236. q^{10} -161051. q^{11} +229009. q^{12} +236400. q^{13} -2.14967e6 q^{14} -1.37145e6 q^{15} +1.04858e6 q^{16} +1.46268e6 q^{17} -4.06820e6 q^{18} -8.85857e6 q^{19} -6.27954e6 q^{20} -1.50236e7 q^{21} -5.15363e6 q^{22} +2.18357e7 q^{23} +7.32829e6 q^{24} -1.12223e7 q^{25} +7.56480e6 q^{26} -6.80493e7 q^{27} -6.87896e7 q^{28} -3.83484e7 q^{29} -4.38865e7 q^{30} -2.25578e8 q^{31} +3.35544e7 q^{32} -3.60177e7 q^{33} +4.68056e7 q^{34} +4.11956e8 q^{35} -1.30183e8 q^{36} +5.36528e8 q^{37} -2.83474e8 q^{38} +5.28689e7 q^{39} -2.00945e8 q^{40} -5.70685e8 q^{41} -4.80757e8 q^{42} +1.72681e9 q^{43} -1.64916e8 q^{44} +7.79616e8 q^{45} +6.98741e8 q^{46} +2.62539e9 q^{47} +2.34505e8 q^{48} +2.53546e9 q^{49} -3.59112e8 q^{50} +3.27115e8 q^{51} +2.42074e8 q^{52} -3.63466e9 q^{53} -2.17758e9 q^{54} +9.87623e8 q^{55} -2.20127e9 q^{56} -1.98115e9 q^{57} -1.22715e9 q^{58} -1.73378e8 q^{59} -1.40437e9 q^{60} -5.44417e9 q^{61} -7.21851e9 q^{62} +8.54034e9 q^{63} +1.07374e9 q^{64} -1.44969e9 q^{65} -1.15257e9 q^{66} -1.96293e10 q^{67} +1.49778e9 q^{68} +4.88337e9 q^{69} +1.31826e10 q^{70} -6.50056e9 q^{71} -4.16584e9 q^{72} +9.04153e9 q^{73} +1.71689e10 q^{74} -2.50977e9 q^{75} -9.07118e9 q^{76} +1.08190e10 q^{77} +1.69181e9 q^{78} -1.46795e10 q^{79} -6.43025e9 q^{80} +7.30227e9 q^{81} -1.82619e10 q^{82} +4.83255e9 q^{83} -1.53842e10 q^{84} -8.96965e9 q^{85} +5.52580e10 q^{86} -8.57630e9 q^{87} -5.27732e9 q^{88} +4.77156e10 q^{89} +2.49477e10 q^{90} -1.58807e10 q^{91} +2.23597e10 q^{92} -5.04488e10 q^{93} +8.40124e10 q^{94} +5.43240e10 q^{95} +7.50417e9 q^{96} -1.12120e11 q^{97} +8.11348e10 q^{98} +2.04746e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 64 q^{2} - 426 q^{3} + 2048 q^{4} + 2290 q^{5} - 13632 q^{6} - 86324 q^{7} + 65536 q^{8} + 117756 q^{9}+O(q^{10}) \) 2 * q + 64 * q^2 - 426 * q^3 + 2048 * q^4 + 2290 * q^5 - 13632 * q^6 - 86324 * q^7 + 65536 * q^8 + 117756 * q^9	\( 2 q + 64 q^{2} - 426 q^{3} + 2048 q^{4} + 2290 q^{5} - 13632 q^{6} - 86324 q^{7} + 65536 q^{8} + 117756 q^{9} + 73280 q^{10} - 322102 q^{11} - 436224 q^{12} - 2100184 q^{13} - 2762368 q^{14} - 6842970 q^{15} + 2097152 q^{16} - 2882276 q^{17} + 3768192 q^{18} - 19571712 q^{19} + 2344960 q^{20} - 2585148 q^{21} - 10307264 q^{22} + 12680534 q^{23} - 13959168 q^{24} + 10885800 q^{25} - 67205888 q^{26} - 112056318 q^{27} - 88395776 q^{28} + 45662496 q^{29} - 218975040 q^{30} - 506504170 q^{31} + 67108864 q^{32} + 68607726 q^{33} - 92232832 q^{34} + 250695020 q^{35} + 120582144 q^{36} + 402672518 q^{37} - 626294784 q^{38} + 1570811448 q^{39} + 75038720 q^{40} + 608864016 q^{41} - 82724736 q^{42} + 1100094564 q^{43} - 329832448 q^{44} + 2842145820 q^{45} + 405777088 q^{46} + 1012342272 q^{47} - 446693376 q^{48} + 924731802 q^{49} + 348345600 q^{50} + 3149776692 q^{51} - 2150588416 q^{52} - 68189276 q^{53} - 3585802176 q^{54} - 368806790 q^{55} - 2828664832 q^{56} + 4978554240 q^{57} + 1461199872 q^{58} - 6791617518 q^{59} - 7007201280 q^{60} + 5704046520 q^{61} - 16208133440 q^{62} + 3851555688 q^{63} + 2147483648 q^{64} - 21129248280 q^{65} + 2195447232 q^{66} - 36514311702 q^{67} - 2951450624 q^{68} + 10830919410 q^{69} + 8022240640 q^{70} + 20672196594 q^{71} + 3858628608 q^{72} + 3082870856 q^{73} + 12885520576 q^{74} - 16872083400 q^{75} - 20041433088 q^{76} + 13902566524 q^{77} + 50265966336 q^{78} - 28681382180 q^{79} + 2401239040 q^{80} - 7490027070 q^{81} + 19483648512 q^{82} + 29532640772 q^{83} - 2647191552 q^{84} - 45564404420 q^{85} + 35203026048 q^{86} - 63153261216 q^{87} - 10554638336 q^{88} + 85063742462 q^{89} + 90948666240 q^{90} + 28857167728 q^{91} + 12984866816 q^{92} + 132052307250 q^{93} + 32394952704 q^{94} - 35905936640 q^{95} - 14294188032 q^{96} - 180832449678 q^{97} + 29591417664 q^{98} - 18964721556 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 - 426 * q^3 + 2048 * q^4 + 2290 * q^5 - 13632 * q^6 - 86324 * q^7 + 65536 * q^8 + 117756 * q^9 + 73280 * q^10 - 322102 * q^11 - 436224 * q^12 - 2100184 * q^13 - 2762368 * q^14 - 6842970 * q^15 + 2097152 * q^16 - 2882276 * q^17 + 3768192 * q^18 - 19571712 * q^19 + 2344960 * q^20 - 2585148 * q^21 - 10307264 * q^22 + 12680534 * q^23 - 13959168 * q^24 + 10885800 * q^25 - 67205888 * q^26 - 112056318 * q^27 - 88395776 * q^28 + 45662496 * q^29 - 218975040 * q^30 - 506504170 * q^31 + 67108864 * q^32 + 68607726 * q^33 - 92232832 * q^34 + 250695020 * q^35 + 120582144 * q^36 + 402672518 * q^37 - 626294784 * q^38 + 1570811448 * q^39 + 75038720 * q^40 + 608864016 * q^41 - 82724736 * q^42 + 1100094564 * q^43 - 329832448 * q^44 + 2842145820 * q^45 + 405777088 * q^46 + 1012342272 * q^47 - 446693376 * q^48 + 924731802 * q^49 + 348345600 * q^50 + 3149776692 * q^51 - 2150588416 * q^52 - 68189276 * q^53 - 3585802176 * q^54 - 368806790 * q^55 - 2828664832 * q^56 + 4978554240 * q^57 + 1461199872 * q^58 - 6791617518 * q^59 - 7007201280 * q^60 + 5704046520 * q^61 - 16208133440 * q^62 + 3851555688 * q^63 + 2147483648 * q^64 - 21129248280 * q^65 + 2195447232 * q^66 - 36514311702 * q^67 - 2951450624 * q^68 + 10830919410 * q^69 + 8022240640 * q^70 + 20672196594 * q^71 + 3858628608 * q^72 + 3082870856 * q^73 + 12885520576 * q^74 - 16872083400 * q^75 - 20041433088 * q^76 + 13902566524 * q^77 + 50265966336 * q^78 - 28681382180 * q^79 + 2401239040 * q^80 - 7490027070 * q^81 + 19483648512 * q^82 + 29532640772 * q^83 - 2647191552 * q^84 - 45564404420 * q^85 + 35203026048 * q^86 - 63153261216 * q^87 - 10554638336 * q^88 + 85063742462 * q^89 + 90948666240 * q^90 + 28857167728 * q^91 + 12984866816 * q^92 + 132052307250 * q^93 + 32394952704 * q^94 - 35905936640 * q^95 - 14294188032 * q^96 - 180832449678 * q^97 + 29591417664 * q^98 - 18964721556 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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