LMFDB - Embedded newform 13.10.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,10,Mod(1,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("13.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	13.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:	$6.69546587013$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 $ x^5 - 1438x^3 - 4164x^2 + 396957*x - 59580
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.150341$ of defining polynomial
Character	$\chi$	$=$	13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.15034 q^{2} -136.532 q^{3} -502.075 q^{4} +2554.62 q^{5} -430.124 q^{6} +9399.91 q^{7} -3194.68 q^{8} -1041.89 q^{9} +O(q^{10})$	\(q+3.15034 q^{2} -136.532 q^{3} -502.075 q^{4} +2554.62 q^{5} -430.124 q^{6} +9399.91 q^{7} -3194.68 q^{8} -1041.89 q^{9} +8047.92 q^{10} +44094.1 q^{11} +68549.6 q^{12} +28561.0 q^{13} +29612.9 q^{14} -348788. q^{15} +246998. q^{16} +28289.4 q^{17} -3282.30 q^{18} +273836. q^{19} -1.28261e6 q^{20} -1.28339e6 q^{21} +138911. q^{22} -1.12921e6 q^{23} +436178. q^{24} +4.57295e6 q^{25} +89976.9 q^{26} +2.82962e6 q^{27} -4.71947e6 q^{28} -1.63691e6 q^{29} -1.09880e6 q^{30} +6.65402e6 q^{31} +2.41381e6 q^{32} -6.02028e6 q^{33} +89121.2 q^{34} +2.40132e7 q^{35} +523105. q^{36} -1.71193e7 q^{37} +862677. q^{38} -3.89950e6 q^{39} -8.16119e6 q^{40} -5.15179e6 q^{41} -4.04313e6 q^{42} -1.97275e7 q^{43} -2.21386e7 q^{44} -2.66162e6 q^{45} -3.55739e6 q^{46} +4.82947e7 q^{47} -3.37233e7 q^{48} +4.80048e7 q^{49} +1.44063e7 q^{50} -3.86242e6 q^{51} -1.43398e7 q^{52} -3.06731e7 q^{53} +8.91427e6 q^{54} +1.12644e8 q^{55} -3.00298e7 q^{56} -3.73875e7 q^{57} -5.15683e6 q^{58} -1.15154e7 q^{59} +1.75118e8 q^{60} -3.62567e7 q^{61} +2.09624e7 q^{62} -9.79364e6 q^{63} -1.18859e8 q^{64} +7.29624e7 q^{65} -1.89659e7 q^{66} -6.48390e7 q^{67} -1.42034e7 q^{68} +1.54174e8 q^{69} +7.56497e7 q^{70} -1.47071e8 q^{71} +3.32850e6 q^{72} -3.37321e8 q^{73} -5.39317e7 q^{74} -6.24356e8 q^{75} -1.37486e8 q^{76} +4.14481e8 q^{77} -1.22848e7 q^{78} -2.04060e8 q^{79} +6.30986e8 q^{80} -3.65828e8 q^{81} -1.62299e7 q^{82} +7.61700e8 q^{83} +6.44360e8 q^{84} +7.22685e7 q^{85} -6.21484e7 q^{86} +2.23491e8 q^{87} -1.40867e8 q^{88} -8.29058e8 q^{89} -8.38502e6 q^{90} +2.68471e8 q^{91} +5.66948e8 q^{92} -9.08490e8 q^{93} +1.52145e8 q^{94} +6.99547e8 q^{95} -3.29563e8 q^{96} +1.00647e9 q^{97} +1.51231e8 q^{98} -4.59410e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9}+O(q^{10}) $ 5 * q + 15 * q^2 + 161 * q^3 + 361 * q^4 + 1803 * q^5 + 5693 * q^6 + 10099 * q^7 + 23151 * q^8 + 61060 * q^9	\( 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9} + 84505 q^{10} + 121746 q^{11} + 113389 q^{12} + 142805 q^{13} + 8475 q^{14} + 105973 q^{15} - 322463 q^{16} - 495669 q^{17} - 656228 q^{18} - 840738 q^{19} - 1595607 q^{20} - 1599467 q^{21} - 2023594 q^{22} - 592152 q^{23} - 2295657 q^{24} + 1670362 q^{25} + 428415 q^{26} + 6847883 q^{27} + 2587955 q^{28} + 10678182 q^{29} + 5491201 q^{30} + 12885296 q^{31} + 3282927 q^{32} + 17278298 q^{33} - 9934079 q^{34} + 8380731 q^{35} - 20483302 q^{36} + 7171823 q^{37} - 25568814 q^{38} + 4598321 q^{39} - 54359445 q^{40} + 9294012 q^{41} - 69520457 q^{42} + 12831975 q^{43} - 41479074 q^{44} + 26135198 q^{45} - 59319696 q^{46} + 43354215 q^{47} - 86874671 q^{48} + 25249488 q^{49} - 16270770 q^{50} + 16905901 q^{51} + 10310521 q^{52} + 93231780 q^{53} + 58983719 q^{54} + 99448846 q^{55} + 199599225 q^{56} + 90173382 q^{57} + 151020970 q^{58} + 246496182 q^{59} + 90097913 q^{60} - 132232612 q^{61} + 158135724 q^{62} - 416955202 q^{63} + 91019105 q^{64} + 51495483 q^{65} - 323733130 q^{66} - 369388534 q^{67} + 238172073 q^{68} - 579986760 q^{69} - 144857425 q^{70} + 212150457 q^{71} - 415774278 q^{72} - 252729806 q^{73} + 192105957 q^{74} - 752457788 q^{75} - 953775990 q^{76} + 449666118 q^{77} + 162597773 q^{78} - 1247271728 q^{79} + 900649725 q^{80} - 317713115 q^{81} + 169559388 q^{82} + 1696894296 q^{83} + 1247983739 q^{84} - 775363765 q^{85} + 3291621459 q^{86} - 614530466 q^{87} - 220227222 q^{88} - 753854382 q^{89} + 2296265882 q^{90} + 288437539 q^{91} + 13876128 q^{92} - 892784668 q^{93} + 272071215 q^{94} + 1442632962 q^{95} + 930612847 q^{96} + 3824606 q^{97} + 1570614816 q^{98} + 3016199848 q^{99}+O(q^{100}) \) 5 * q + 15 * q^2 + 161 * q^3 + 361 * q^4 + 1803 * q^5 + 5693 * q^6 + 10099 * q^7 + 23151 * q^8 + 61060 * q^9 + 84505 * q^10 + 121746 * q^11 + 113389 * q^12 + 142805 * q^13 + 8475 * q^14 + 105973 * q^15 - 322463 * q^16 - 495669 * q^17 - 656228 * q^18 - 840738 * q^19 - 1595607 * q^20 - 1599467 * q^21 - 2023594 * q^22 - 592152 * q^23 - 2295657 * q^24 + 1670362 * q^25 + 428415 * q^26 + 6847883 * q^27 + 2587955 * q^28 + 10678182 * q^29 + 5491201 * q^30 + 12885296 * q^31 + 3282927 * q^32 + 17278298 * q^33 - 9934079 * q^34 + 8380731 * q^35 - 20483302 * q^36 + 7171823 * q^37 - 25568814 * q^38 + 4598321 * q^39 - 54359445 * q^40 + 9294012 * q^41 - 69520457 * q^42 + 12831975 * q^43 - 41479074 * q^44 + 26135198 * q^45 - 59319696 * q^46 + 43354215 * q^47 - 86874671 * q^48 + 25249488 * q^49 - 16270770 * q^50 + 16905901 * q^51 + 10310521 * q^52 + 93231780 * q^53 + 58983719 * q^54 + 99448846 * q^55 + 199599225 * q^56 + 90173382 * q^57 + 151020970 * q^58 + 246496182 * q^59 + 90097913 * q^60 - 132232612 * q^61 + 158135724 * q^62 - 416955202 * q^63 + 91019105 * q^64 + 51495483 * q^65 - 323733130 * q^66 - 369388534 * q^67 + 238172073 * q^68 - 579986760 * q^69 - 144857425 * q^70 + 212150457 * q^71 - 415774278 * q^72 - 252729806 * q^73 + 192105957 * q^74 - 752457788 * q^75 - 953775990 * q^76 + 449666118 * q^77 + 162597773 * q^78 - 1247271728 * q^79 + 900649725 * q^80 - 317713115 * q^81 + 169559388 * q^82 + 1696894296 * q^83 + 1247983739 * q^84 - 775363765 * q^85 + 3291621459 * q^86 - 614530466 * q^87 - 220227222 * q^88 - 753854382 * q^89 + 2296265882 * q^90 + 288437539 * q^91 + 13876128 * q^92 - 892784668 * q^93 + 272071215 * q^94 + 1442632962 * q^95 + 930612847 * q^96 + 3824606 * q^97 + 1570614816 * q^98 + 3016199848 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.15034	0.139227	0.0696134	−	0.997574i	$-0.477823\pi$
$2$	3.15034	0.139227	0.0696134	+	0.997574i	$0.477823\pi$
$3$	−136.532	−0.973174	−0.486587	−	0.873632i	$-0.661758\pi$
$3$	−136.532	−0.973174	−0.486587	+	0.873632i	$0.661758\pi$
$4$	−502.075	−0.980616
$5$	2554.62	1.82794	0.913968	−	0.405787i	$-0.133002\pi$
$5$	2554.62	1.82794	0.913968	+	0.405787i	$0.133002\pi$
$6$	−430.124	−0.135492
$7$	9399.91	1.47973	0.739865	−	0.672755i	$-0.234889\pi$
$7$	9399.91	1.47973	0.739865	+	0.672755i	$0.234889\pi$
$8$	−3194.68	−0.275755
$9$	−1041.89	−0.0529333
$10$	8047.92	0.254498
$11$	44094.1	0.908058	0.454029	−	0.890987i	$-0.349986\pi$
$11$	44094.1	0.908058	0.454029	+	0.890987i	$0.349986\pi$
$12$	68549.6	0.954309
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	29612.9	0.206018
$15$	−348788.	−1.77890
$16$	246998.	0.942223
$17$	28289.4	0.0821492	0.0410746	−	0.999156i	$-0.486922\pi$
$17$	28289.4	0.0821492	0.0410746	+	0.999156i	$0.486922\pi$
$18$	−3282.30	−0.00736973
$19$	273836.	0.482058	0.241029	−	0.970518i	$-0.422515\pi$
$19$	273836.	0.482058	0.241029	+	0.970518i	$0.422515\pi$
$20$	−1.28261e6	−1.79250
$21$	−1.28339e6	−1.44003
$22$	138911.	0.126426
$23$	−1.12921e6	−0.841393	−0.420697	−	0.907201i	$-0.638214\pi$
$23$	−1.12921e6	−0.841393	−0.420697	+	0.907201i	$0.638214\pi$
$24$	436178.	0.268357
$25$	4.57295e6	2.34135
$26$	89976.9	0.0386145
$27$	2.82962e6	1.02469
$28$	−4.71947e6	−1.45105
$29$	−1.63691e6	−0.429768	−0.214884	−	0.976640i	$-0.568937\pi$
$29$	−1.63691e6	−0.429768	−0.214884	+	0.976640i	$0.568937\pi$
$30$	−1.09880e6	−0.247670
$31$	6.65402e6	1.29407	0.647033	−	0.762462i	$-0.276009\pi$
$31$	6.65402e6	1.29407	0.647033	+	0.762462i	$0.276009\pi$
$32$	2.41381e6	0.406937
$33$	−6.02028e6	−0.883698
$34$	89121.2	0.0114374
$35$	2.40132e7	2.70485
$36$	523105.	0.0519073
$37$	−1.71193e7	−1.50169	−0.750843	−	0.660481i	$-0.770352\pi$
$37$	−1.71193e7	−1.50169	−0.750843	+	0.660481i	$0.770352\pi$
$38$	862677.	0.0671154
$39$	−3.89950e6	−0.269910
$40$	−8.16119e6	−0.504062
$41$	−5.15179e6	−0.284728	−0.142364	−	0.989814i	$-0.545470\pi$
$41$	−5.15179e6	−0.284728	−0.142364	+	0.989814i	$0.545470\pi$
$42$	−4.04313e6	−0.200491
$43$	−1.97275e7	−0.879962	−0.439981	−	0.898007i	$-0.645015\pi$
$43$	−1.97275e7	−0.879962	−0.439981	+	0.898007i	$0.645015\pi$
$44$	−2.21386e7	−0.890456
$45$	−2.66162e6	−0.0967587
$46$	−3.55739e6	−0.117144
$47$	4.82947e7	1.44364	0.721821	−	0.692080i	$-0.243305\pi$
$47$	4.82947e7	1.44364	0.721821	+	0.692080i	$0.243305\pi$
$48$	−3.37233e7	−0.916947
$49$	4.80048e7	1.18960
$50$	1.44063e7	0.325978
$51$	−3.86242e6	−0.0799454
$52$	−1.43398e7	−0.271974
$53$	−3.06731e7	−0.533970	−0.266985	−	0.963701i	$-0.586027\pi$
$53$	−3.06731e7	−0.533970	−0.266985	+	0.963701i	$0.586027\pi$
$54$	8.91427e6	0.142664
$55$	1.12644e8	1.65987
$56$	−3.00298e7	−0.408043
$57$	−3.73875e7	−0.469126
$58$	−5.15683e6	−0.0598352
$59$	−1.15154e7	−0.123722	−0.0618609	−	0.998085i	$-0.519704\pi$
$59$	−1.15154e7	−0.123722	−0.0618609	+	0.998085i	$0.519704\pi$
$60$	1.75118e8	1.74442
$61$	−3.62567e7	−0.335277	−0.167639	−	0.985849i	$-0.553614\pi$
$61$	−3.62567e7	−0.335277	−0.167639	+	0.985849i	$0.553614\pi$
$62$	2.09624e7	0.180169
$63$	−9.79364e6	−0.0783271
$64$	−1.18859e8	−0.885567
$65$	7.29624e7	0.506978
$66$	−1.89659e7	−0.123034
$67$	−6.48390e7	−0.393097	−0.196548	−	0.980494i	$-0.562973\pi$
$67$	−6.48390e7	−0.393097	−0.196548	+	0.980494i	$0.562973\pi$
$68$	−1.42034e7	−0.0805568
$69$	1.54174e8	0.818822
$70$	7.56497e7	0.376588
$71$	−1.47071e8	−0.686853	−0.343427	−	0.939180i	$-0.611588\pi$
$71$	−1.47071e8	−0.686853	−0.343427	+	0.939180i	$0.611588\pi$
$72$	3.32850e6	0.0145966
$73$	−3.37321e8	−1.39024	−0.695122	−	0.718892i	$-0.744650\pi$
$73$	−3.37321e8	−1.39024	−0.695122	+	0.718892i	$0.744650\pi$
$74$	−5.39317e7	−0.209075
$75$	−6.24356e8	−2.27854
$76$	−1.37486e8	−0.472714
$77$	4.14481e8	1.34368
$78$	−1.22848e7	−0.0375787
$79$	−2.04060e8	−0.589436	−0.294718	−	0.955584i	$-0.595226\pi$
$79$	−2.04060e8	−0.589436	−0.294718	+	0.955584i	$0.595226\pi$
$80$	6.30986e8	1.72232
$81$	−3.65828e8	−0.944265
$82$	−1.62299e7	−0.0396418
$83$	7.61700e8	1.76170	0.880851	−	0.473394i	$-0.156971\pi$
$83$	7.61700e8	1.76170	0.880851	+	0.473394i	$0.156971\pi$
$84$	6.44360e8	1.41212
$85$	7.22685e7	0.150163
$86$	−6.21484e7	−0.122514
$87$	2.23491e8	0.418239
$88$	−1.40867e8	−0.250401
$89$	−8.29058e8	−1.40065	−0.700326	−	0.713823i	$-0.746962\pi$
$89$	−8.29058e8	−1.40065	−0.700326	+	0.713823i	$0.746962\pi$
$90$	−8.38502e6	−0.0134714
$91$	2.68471e8	0.410403
$92$	5.66948e8	0.825084
$93$	−9.08490e8	−1.25935
$94$	1.52145e8	0.200994
$95$	6.99547e8	0.881172
$96$	−3.29563e8	−0.396021
$97$	1.00647e9	1.15432	0.577161	−	0.816631i	$-0.304161\pi$
$97$	1.00647e9	1.15432	0.577161	+	0.816631i	$0.304161\pi$
$98$	1.51231e8	0.165625
$99$	−4.59410e7	−0.0480665
$100$	−2.29596e9	−2.29596
$101$	1.59054e9	1.52089	0.760446	−	0.649401i	$-0.224980\pi$
$101$	1.59054e9	1.52089	0.760446	+	0.649401i	$0.224980\pi$
$102$	−1.21679e7	−0.0111305
$103$	1.13889e9	0.997040	0.498520	−	0.866878i	$-0.333877\pi$
$103$	1.13889e9	0.997040	0.498520	+	0.866878i	$0.333877\pi$
$104$	−9.12434e7	−0.0764806
$105$	−3.27858e9	−2.63229
$106$	−9.66309e7	−0.0743429
$107$	−7.21432e8	−0.532069	−0.266035	−	0.963963i	$-0.585714\pi$
$107$	−7.21432e8	−0.532069	−0.266035	+	0.963963i	$0.585714\pi$
$108$	−1.42068e9	−1.00482
$109$	−6.86462e8	−0.465798	−0.232899	−	0.972501i	$-0.574821\pi$
$109$	−6.86462e8	−0.465798	−0.232899	+	0.972501i	$0.574821\pi$
$110$	3.54866e8	0.231098
$111$	2.33734e9	1.46140
$112$	2.32176e9	1.39424
$113$	−8.33795e8	−0.481068	−0.240534	−	0.970641i	$-0.577323\pi$
$113$	−8.33795e8	−0.481068	−0.240534	+	0.970641i	$0.577323\pi$
$114$	−1.17783e8	−0.0653149
$115$	−2.88470e9	−1.53801
$116$	8.21852e8	0.421437
$117$	−2.97573e7	−0.0146811
$118$	−3.62775e7	−0.0172254
$119$	2.65918e8	0.121559
$120$	1.11427e9	0.490540
$121$	−4.13658e8	−0.175431
$122$	−1.14221e8	−0.0466796
$123$	7.03386e8	0.277090
$124$	−3.34082e9	−1.26898
$125$	6.69264e9	2.45190
$126$	−3.08533e7	−0.0109052
$127$	−4.01307e8	−0.136886	−0.0684431	−	0.997655i	$-0.521803\pi$
$127$	−4.01307e8	−0.136886	−0.0684431	+	0.997655i	$0.521803\pi$
$128$	−1.61031e9	−0.530232
$129$	2.69344e9	0.856356
$130$	2.29857e8	0.0705849
$131$	−3.78377e9	−1.12255	−0.561273	−	0.827631i	$-0.689688\pi$
$131$	−3.78377e9	−1.12255	−0.561273	+	0.827631i	$0.689688\pi$
$132$	3.02263e9	0.866568
$133$	2.57404e9	0.713317
$134$	−2.04265e8	−0.0547296
$135$	7.22860e9	1.87306
$136$	−9.03756e7	−0.0226530
$137$	1.45518e9	0.352919	0.176459	−	0.984308i	$-0.443536\pi$
$137$	1.45518e9	0.352919	0.176459	+	0.984308i	$0.443536\pi$
$138$	4.85700e8	0.114002
$139$	1.50381e9	0.341685	0.170842	−	0.985298i	$-0.445351\pi$
$139$	1.50381e9	0.341685	0.170842	+	0.985298i	$0.445351\pi$
$140$	−1.20564e10	−2.65242
$141$	−6.59380e9	−1.40491
$142$	−4.63323e8	−0.0956283
$143$	1.25937e9	0.251850
$144$	−2.57344e8	−0.0498750
$145$	−4.18168e9	−0.785588
$146$	−1.06268e9	−0.193559
$147$	−6.55421e9	−1.15769
$148$	8.59520e9	1.47258
$149$	−4.28624e9	−0.712423	−0.356212	−	0.934405i	$-0.615932\pi$
$149$	−4.28624e9	−0.712423	−0.356212	+	0.934405i	$0.615932\pi$
$150$	−1.96693e9	−0.317233
$151$	4.79918e8	0.0751226	0.0375613	−	0.999294i	$-0.488041\pi$
$151$	4.79918e8	0.0751226	0.0375613	+	0.999294i	$0.488041\pi$
$152$	−8.74820e8	−0.132930
$153$	−2.94743e7	−0.00434843
$154$	1.30576e9	0.187076
$155$	1.69985e10	2.36547
$156$	1.95784e9	0.264678
$157$	−8.24624e9	−1.08320	−0.541598	−	0.840637i	$-0.682181\pi$
$157$	−8.24624e9	−1.08320	−0.541598	+	0.840637i	$0.682181\pi$
$158$	−6.42860e8	−0.0820652
$159$	4.18788e9	0.519646
$160$	6.16635e9	0.743855
$161$	−1.06145e10	−1.24504
$162$	−1.15248e9	−0.131467
$163$	−5.93537e9	−0.658573	−0.329286	−	0.944230i	$-0.606808\pi$
$163$	−5.93537e9	−0.658573	−0.329286	+	0.944230i	$0.606808\pi$
$164$	2.58659e9	0.279209
$165$	−1.53795e10	−1.61534
$166$	2.39961e9	0.245276
$167$	−7.41172e9	−0.737386	−0.368693	−	0.929551i	$-0.620195\pi$
$167$	−7.41172e9	−0.737386	−0.368693	+	0.929551i	$0.620195\pi$
$168$	4.10004e9	0.397096
$169$	8.15731e8	0.0769231
$170$	2.27671e8	0.0209068
$171$	−2.85306e8	−0.0255169
$172$	9.90469e9	0.862905
$173$	5.63923e9	0.478643	0.239322	−	0.970940i	$-0.423075\pi$
$173$	5.63923e9	0.478643	0.239322	+	0.970940i	$0.423075\pi$
$174$	7.04074e8	0.0582300
$175$	4.29853e10	3.46457
$176$	1.08912e10	0.855593
$177$	1.57223e9	0.120403
$178$	−2.61182e9	−0.195008
$179$	1.23881e10	0.901916	0.450958	−	0.892545i	$-0.351082\pi$
$179$	1.23881e10	0.901916	0.450958	+	0.892545i	$0.351082\pi$
$180$	1.33633e9	0.0948831
$181$	−2.45852e10	−1.70263	−0.851314	−	0.524657i	$-0.824194\pi$
$181$	−2.45852e10	−1.70263	−0.851314	+	0.524657i	$0.824194\pi$
$182$	8.45775e8	0.0571391
$183$	4.95022e9	0.326283
$184$	3.60746e9	0.232018
$185$	−4.37334e10	−2.74499
$186$	−2.86205e9	−0.175335
$187$	1.24739e9	0.0745962
$188$	−2.42476e10	−1.41566
$189$	2.65982e10	1.51626
$190$	2.20381e9	0.122683
$191$	−1.06604e10	−0.579592	−0.289796	−	0.957088i	$-0.593587\pi$
$191$	−1.06604e10	−0.579592	−0.289796	+	0.957088i	$0.593587\pi$
$192$	1.62281e10	0.861810
$193$	−2.09640e10	−1.08759	−0.543797	−	0.839217i	$-0.683014\pi$
$193$	−2.09640e10	−1.08759	−0.543797	+	0.839217i	$0.683014\pi$
$194$	3.17071e9	0.160712
$195$	−9.96174e9	−0.493378
$196$	−2.41020e10	−1.16654
$197$	1.27051e10	0.601009	0.300504	−	0.953780i	$-0.402845\pi$
$197$	1.27051e10	0.601009	0.300504	+	0.953780i	$0.402845\pi$
$198$	−1.44730e8	−0.00669214
$199$	2.57825e9	0.116543	0.0582715	−	0.998301i	$-0.481441\pi$
$199$	2.57825e9	0.116543	0.0582715	+	0.998301i	$0.481441\pi$
$200$	−1.46091e10	−0.645638
$201$	8.85262e9	0.382551
$202$	5.01075e9	0.211749
$203$	−1.53868e10	−0.635941
$204$	1.93922e9	0.0783957
$205$	−1.31608e10	−0.520465
$206$	3.58788e9	0.138815
$207$	1.17651e9	0.0445377
$208$	7.05452e9	0.261326
$209$	1.20746e10	0.437737
$210$	−1.03286e10	−0.366485
$211$	1.94301e10	0.674846	0.337423	−	0.941353i	$-0.390445\pi$
$211$	1.94301e10	0.674846	0.337423	+	0.941353i	$0.390445\pi$
$212$	1.54002e10	0.523620
$213$	2.00799e10	0.668427
$214$	−2.27276e9	−0.0740783
$215$	−5.03962e10	−1.60851
$216$	−9.03974e9	−0.282562
$217$	6.25472e10	1.91487
$218$	−2.16259e9	−0.0648515
$219$	4.60553e10	1.35295
$220$	−5.65556e10	−1.62770
$221$	8.07973e8	0.0227841
$222$	7.36343e9	0.203466
$223$	9.56077e9	0.258893	0.129447	−	0.991586i	$-0.458680\pi$
$223$	9.56077e9	0.258893	0.129447	+	0.991586i	$0.458680\pi$
$224$	2.26896e10	0.602158
$225$	−4.76449e9	−0.123935
$226$	−2.62674e9	−0.0669775
$227$	−2.02032e10	−0.505015	−0.252507	−	0.967595i	$-0.581255\pi$
$227$	−2.02032e10	−0.505015	−0.252507	+	0.967595i	$0.581255\pi$
$228$	1.87714e10	0.460033
$229$	−2.45816e10	−0.590678	−0.295339	−	0.955392i	$-0.595433\pi$
$229$	−2.45816e10	−0.590678	−0.295339	+	0.955392i	$0.595433\pi$
$230$	−9.08778e9	−0.214132
$231$	−5.65901e10	−1.30763
$232$	5.22941e9	0.118510
$233$	7.93260e10	1.76325	0.881625	−	0.471951i	$-0.156450\pi$
$233$	7.93260e10	1.76325	0.881625	+	0.471951i	$0.156450\pi$
$234$	−9.37457e7	−0.00204400
$235$	1.23375e11	2.63888
$236$	5.78161e9	0.121324
$237$	2.78609e10	0.573623
$238$	8.37732e8	0.0169242
$239$	−2.62515e10	−0.520431	−0.260215	−	0.965551i	$-0.583794\pi$
$239$	−2.62515e10	−0.520431	−0.260215	+	0.965551i	$0.583794\pi$
$240$	−8.61501e10	−1.67612
$241$	−1.00766e11	−1.92415	−0.962074	−	0.272787i	$-0.912055\pi$
$241$	−1.00766e11	−1.92415	−0.962074	+	0.272787i	$0.912055\pi$
$242$	−1.30316e9	−0.0244247
$243$	−5.74808e9	−0.105753
$244$	1.82036e10	0.328778
$245$	1.22634e11	2.17452
$246$	2.21591e9	0.0385783
$247$	7.82103e9	0.133699
$248$	−2.12575e10	−0.356845
$249$	−1.03997e11	−1.71444
$250$	2.10841e10	0.341370
$251$	−8.72780e10	−1.38795	−0.693973	−	0.720001i	$-0.744142\pi$
$251$	−8.72780e10	−1.38795	−0.693973	+	0.720001i	$0.744142\pi$
$252$	4.91715e9	0.0768088
$253$	−4.97914e10	−0.764034
$254$	−1.26425e9	−0.0190582
$255$	−9.86700e9	−0.146135
$256$	5.57827e10	0.811744
$257$	4.84205e10	0.692358	0.346179	−	0.938169i	$-0.387479\pi$
$257$	4.84205e10	0.692358	0.346179	+	0.938169i	$0.387479\pi$
$258$	8.48527e9	0.119228
$259$	−1.60920e11	−2.22209
$260$	−3.66326e10	−0.497151
$261$	1.70547e9	0.0227490
$262$	−1.19202e10	−0.156288
$263$	−4.40656e9	−0.0567935	−0.0283968	−	0.999597i	$-0.509040\pi$
$263$	−4.40656e9	−0.0567935	−0.0283968	+	0.999597i	$0.509040\pi$
$264$	1.92329e10	0.243684
$265$	−7.83582e10	−0.976063
$266$	8.10909e9	0.0993127
$267$	1.13193e11	1.36308
$268$	3.25540e10	0.385477
$269$	1.41879e11	1.65209	0.826045	−	0.563604i	$-0.190586\pi$
$269$	1.41879e11	1.65209	0.826045	+	0.563604i	$0.190586\pi$
$270$	2.27725e10	0.260780
$271$	−7.09707e10	−0.799313	−0.399657	−	0.916665i	$-0.630871\pi$
$271$	−7.09707e10	−0.799313	−0.399657	+	0.916665i	$0.630871\pi$
$272$	6.98743e9	0.0774029
$273$	−3.66550e10	−0.399394
$274$	4.58432e9	0.0491357
$275$	2.01640e11	2.12608
$276$	−7.74068e10	−0.802950
$277$	1.22293e11	1.24808	0.624039	−	0.781393i	$-0.285491\pi$
$277$	1.22293e11	1.24808	0.624039	+	0.781393i	$0.285491\pi$
$278$	4.73751e9	0.0475717
$279$	−6.93274e9	−0.0684992
$280$	−7.67145e10	−0.745876
$281$	−9.91936e10	−0.949085	−0.474543	−	0.880233i	$-0.657387\pi$
$281$	−9.91936e10	−0.949085	−0.474543	+	0.880233i	$0.657387\pi$
$282$	−2.07727e10	−0.195602
$283$	1.89673e11	1.75779	0.878893	−	0.477019i	$-0.158283\pi$
$283$	1.89673e11	1.75779	0.878893	+	0.477019i	$0.158283\pi$
$284$	7.38406e10	0.673539
$285$	−9.55108e10	−0.857533
$286$	3.96745e9	0.0350642
$287$	−4.84264e10	−0.421321
$288$	−2.51491e9	−0.0215405
$289$	−1.17788e11	−0.993252
$290$	−1.31737e10	−0.109375
$291$	−1.37415e11	−1.12336
$292$	1.69361e11	1.36329
$293$	1.95772e11	1.55183	0.775917	−	0.630835i	$-0.217287\pi$
$293$	1.95772e11	1.55183	0.775917	+	0.630835i	$0.217287\pi$
$294$	−2.06480e10	−0.161181
$295$	−2.94175e10	−0.226155
$296$	5.46908e10	0.414097
$297$	1.24770e11	0.930475
$298$	−1.35031e10	−0.0991884
$299$	−3.22513e10	−0.233360
$300$	3.13474e11	2.23437
$301$	−1.85437e11	−1.30211
$302$	1.51190e9	0.0104591
$303$	−2.17160e11	−1.48009
$304$	6.76370e10	0.454207
$305$	−9.26220e10	−0.612865
$306$	−9.28542e7	−0.000605417 0
$307$	−7.17504e10	−0.461001	−0.230500	−	0.973072i	$-0.574036\pi$
$307$	−7.17504e10	−0.461001	−0.230500	+	0.973072i	$0.574036\pi$
$308$	−2.08101e11	−1.31763
$309$	−1.55495e11	−0.970293
$310$	5.35510e10	0.329337
$311$	2.11023e10	0.127911	0.0639554	−	0.997953i	$-0.479628\pi$
$311$	2.11023e10	0.127911	0.0639554	+	0.997953i	$0.479628\pi$
$312$	1.24577e10	0.0744289
$313$	−1.44667e11	−0.851963	−0.425982	−	0.904732i	$-0.640071\pi$
$313$	−1.44667e11	−0.851963	−0.425982	+	0.904732i	$0.640071\pi$
$314$	−2.59785e10	−0.150810
$315$	−2.50190e10	−0.143177
$316$	1.02454e11	0.578010
$317$	5.78709e10	0.321880	0.160940	−	0.986964i	$-0.448547\pi$
$317$	5.78709e10	0.321880	0.160940	+	0.986964i	$0.448547\pi$
$318$	1.31933e10	0.0723485
$319$	−7.21781e10	−0.390254
$320$	−3.03639e11	−1.61876
$321$	9.84988e10	0.517796
$322$	−3.34392e10	−0.173342
$323$	7.74665e9	0.0396007
$324$	1.83673e11	0.925961
$325$	1.30608e11	0.649373
$326$	−1.86984e10	−0.0916909
$327$	9.37244e10	0.453302
$328$	1.64583e10	0.0785151
$329$	4.53966e11	2.13620
$330$	−4.84507e10	−0.224899
$331$	−1.00283e11	−0.459199	−0.229600	−	0.973285i	$-0.573742\pi$
$331$	−1.00283e11	−0.459199	−0.229600	+	0.973285i	$0.573742\pi$
$332$	−3.82431e11	−1.72755
$333$	1.78364e10	0.0794892
$334$	−2.33495e10	−0.102664
$335$	−1.65639e11	−0.718555
$336$	−3.16996e11	−1.35683
$337$	−5.73297e10	−0.242128	−0.121064	−	0.992645i	$-0.538631\pi$
$337$	−5.73297e10	−0.242128	−0.121064	+	0.992645i	$0.538631\pi$
$338$	2.56983e9	0.0107097
$339$	1.13840e11	0.468163
$340$	−3.62843e10	−0.147253
$341$	2.93403e11	1.17509
$342$	−8.98812e8	−0.00355264
$343$	7.19204e10	0.280562
$344$	6.30231e10	0.242654
$345$	3.93855e11	1.49675
$346$	1.77655e10	0.0666399
$347$	−2.34072e10	−0.0866695	−0.0433347	−	0.999061i	$-0.513798\pi$
$347$	−2.34072e10	−0.0866695	−0.0433347	+	0.999061i	$0.513798\pi$
$348$	−1.12210e11	−0.410131
$349$	3.92804e11	1.41730	0.708649	−	0.705562i	$-0.249305\pi$
$349$	3.92804e11	1.41730	0.708649	+	0.705562i	$0.249305\pi$
$350$	1.35418e11	0.482360
$351$	8.08168e10	0.284197
$352$	1.06435e11	0.369523
$353$	2.16422e11	0.741849	0.370925	−	0.928663i	$-0.379041\pi$
$353$	2.16422e11	0.741849	0.370925	+	0.928663i	$0.379041\pi$
$354$	4.95306e9	0.0167633
$355$	−3.75710e11	−1.25552
$356$	4.16250e11	1.37350
$357$	−3.63064e10	−0.118298
$358$	3.90267e10	0.125571
$359$	3.49576e11	1.11075	0.555376	−	0.831600i	$-0.312574\pi$
$359$	3.49576e11	1.11075	0.555376	+	0.831600i	$0.312574\pi$
$360$	8.50304e9	0.0266817
$361$	−2.47701e11	−0.767620
$362$	−7.74517e10	−0.237051
$363$	5.64778e10	0.170725
$364$	−1.34793e11	−0.402448
$365$	−8.61727e11	−2.54128
$366$	1.55949e10	0.0454273
$367$	−1.83237e9	−0.00527248	−0.00263624	−	0.999997i	$-0.500839\pi$
$367$	−1.83237e9	−0.00527248	−0.00263624	+	0.999997i	$0.500839\pi$
$368$	−2.78913e11	−0.792780
$369$	5.36758e9	0.0150716
$370$	−1.37775e11	−0.382175
$371$	−2.88325e11	−0.790132
$372$	4.56130e11	1.23494
$373$	5.52030e10	0.147663	0.0738317	−	0.997271i	$-0.476477\pi$
$373$	5.52030e10	0.147663	0.0738317	+	0.997271i	$0.476477\pi$
$374$	3.92972e9	0.0103858
$375$	−9.13763e11	−2.38612
$376$	−1.54286e11	−0.398091
$377$	−4.67518e10	−0.119196
$378$	8.37934e10	0.211104
$379$	2.25258e11	0.560795	0.280397	−	0.959884i	$-0.409534\pi$
$379$	2.25258e11	0.560795	0.280397	+	0.959884i	$0.409534\pi$
$380$	−3.51225e11	−0.864091
$381$	5.47914e10	0.133214
$382$	−3.35838e10	−0.0806947
$383$	4.64079e11	1.10204	0.551020	−	0.834492i	$-0.314239\pi$
$383$	4.64079e11	1.10204	0.551020	+	0.834492i	$0.314239\pi$
$384$	2.19860e11	0.516008
$385$	1.05884e12	2.45616
$386$	−6.60438e10	−0.151422
$387$	2.05538e10	0.0465793
$388$	−5.05322e11	−1.13195
$389$	−2.63061e11	−0.582482	−0.291241	−	0.956650i	$-0.594068\pi$
$389$	−2.63061e11	−0.582482	−0.291241	+	0.956650i	$0.594068\pi$
$390$	−3.13829e10	−0.0686914
$391$	−3.19446e10	−0.0691198
$392$	−1.53360e11	−0.328039
$393$	5.16608e11	1.09243
$394$	4.00255e10	0.0836765
$395$	−5.21296e11	−1.07745
$396$	2.30659e10	0.0471348
$397$	−1.80382e10	−0.0364449	−0.0182224	−	0.999834i	$-0.505801\pi$
$397$	−1.80382e10	−0.0364449	−0.0182224	+	0.999834i	$0.505801\pi$
$398$	8.12236e9	0.0162259
$399$	−3.51440e11	−0.694181
$400$	1.12951e12	2.20607
$401$	7.18792e10	0.138821	0.0694103	−	0.997588i	$-0.477888\pi$
$401$	7.18792e10	0.138821	0.0694103	+	0.997588i	$0.477888\pi$
$402$	2.78888e10	0.0532614
$403$	1.90046e11	0.358910
$404$	−7.98571e11	−1.49141
$405$	−9.34549e11	−1.72606
$406$	−4.84737e10	−0.0885399
$407$	−7.54862e11	−1.36362
$408$	1.23392e10	0.0220453
$409$	5.31862e11	0.939819	0.469910	−	0.882715i	$-0.344287\pi$
$409$	5.31862e11	0.939819	0.469910	+	0.882715i	$0.344287\pi$
$410$	−4.14612e10	−0.0724626
$411$	−1.98680e11	−0.343451
$412$	−5.71806e11	−0.977713
$413$	−1.08244e11	−0.183075
$414$	3.70640e9	0.00620084
$415$	1.94585e12	3.22028
$416$	6.89407e10	0.112864
$417$	−2.05319e11	−0.332519
$418$	3.80390e10	0.0609446
$419$	1.45942e11	0.231322	0.115661	−	0.993289i	$-0.463101\pi$
$419$	1.45942e11	0.231322	0.115661	+	0.993289i	$0.463101\pi$
$420$	1.64609e12	2.58127
$421$	3.66247e11	0.568204	0.284102	−	0.958794i	$-0.408305\pi$
$421$	3.66247e11	0.568204	0.284102	+	0.958794i	$0.408305\pi$
$422$	6.12115e10	0.0939565
$423$	−5.03176e10	−0.0764168
$424$	9.79910e10	0.147245
$425$	1.29366e11	0.192340
$426$	6.32587e10	0.0930629
$427$	−3.40810e11	−0.496120
$428$	3.62213e11	0.521756
$429$	−1.71945e11	−0.245094
$430$	−1.58765e11	−0.223948
$431$	7.66389e11	1.06980	0.534899	−	0.844916i	$-0.320350\pi$
$431$	7.66389e11	1.06980	0.534899	+	0.844916i	$0.320350\pi$
$432$	6.98911e11	0.965484
$433$	−1.24176e12	−1.69763	−0.848813	−	0.528694i	$-0.822682\pi$
$433$	−1.24176e12	−1.69763	−0.848813	+	0.528694i	$0.822682\pi$
$434$	1.97045e11	0.266601
$435$	5.70935e11	0.764513
$436$	3.44656e11	0.456769
$437$	−3.09218e11	−0.405601
$438$	1.45090e11	0.188367
$439$	−1.48429e12	−1.90734	−0.953671	−	0.300852i	$-0.902729\pi$
$439$	−1.48429e12	−1.90734	−0.953671	+	0.300852i	$0.902729\pi$
$440$	−3.59861e11	−0.457717
$441$	−5.00155e10	−0.0629696
$442$	2.54539e9	0.00317215
$443$	1.03343e12	1.27487	0.637433	−	0.770506i	$-0.279996\pi$
$443$	1.03343e12	1.27487	0.637433	+	0.770506i	$0.279996\pi$
$444$	−1.17352e12	−1.43307
$445$	−2.11793e12	−2.56030
$446$	3.01197e10	0.0360449
$447$	5.85211e11	0.693312
$448$	−1.11726e12	−1.31040
$449$	−5.83072e11	−0.677039	−0.338519	−	0.940959i	$-0.609926\pi$
$449$	−5.83072e11	−0.677039	−0.338519	+	0.940959i	$0.609926\pi$
$450$	−1.50098e10	−0.0172551
$451$	−2.27163e11	−0.258550
$452$	4.18628e11	0.471743
$453$	−6.55244e10	−0.0731073
$454$	−6.36470e10	−0.0703116
$455$	6.85841e11	0.750191
$456$	1.19441e11	0.129364
$457$	7.39681e11	0.793271	0.396635	−	0.917976i	$-0.370178\pi$
$457$	7.39681e11	0.793271	0.396635	+	0.917976i	$0.370178\pi$
$458$	−7.74405e10	−0.0822382
$459$	8.00482e10	0.0841772
$460$	1.44834e12	1.50820
$461$	1.45843e12	1.50394	0.751971	−	0.659197i	$-0.229104\pi$
$461$	1.45843e12	1.50394	0.751971	+	0.659197i	$0.229104\pi$
$462$	−1.78278e11	−0.182058
$463$	−1.63194e12	−1.65040	−0.825200	−	0.564841i	$-0.808937\pi$
$463$	−1.63194e12	−1.65040	−0.825200	+	0.564841i	$0.808937\pi$
$464$	−4.04314e11	−0.404937
$465$	−2.32084e12	−2.30201
$466$	2.49904e11	0.245492
$467$	−8.24440e11	−0.802109	−0.401054	−	0.916054i	$-0.631356\pi$
$467$	−8.24440e11	−0.802109	−0.401054	+	0.916054i	$0.631356\pi$
$468$	1.49404e10	0.0143965
$469$	−6.09481e11	−0.581677
$470$	3.88672e11	0.367403
$471$	1.12588e12	1.05414
$472$	3.67882e10	0.0341169
$473$	−8.69866e11	−0.799056
$474$	8.77712e10	0.0798637
$475$	1.25224e12	1.12867
$476$	−1.33511e11	−0.119202
$477$	3.19579e10	0.0282648
$478$	−8.27011e10	−0.0724579
$479$	−1.80073e11	−0.156293	−0.0781463	−	0.996942i	$-0.524900\pi$
$479$	−1.80073e11	−0.156293	−0.0781463	+	0.996942i	$0.524900\pi$
$480$	−8.41907e11	−0.723900
$481$	−4.88945e11	−0.416493
$482$	−3.17448e11	−0.267893
$483$	1.44922e12	1.21164
$484$	2.07688e11	0.172031
$485$	2.57114e12	2.11003
$486$	−1.81084e10	−0.0147237
$487$	−7.22045e11	−0.581680	−0.290840	−	0.956772i	$-0.593935\pi$
$487$	−7.22045e11	−0.581680	−0.290840	+	0.956772i	$0.593935\pi$
$488$	1.15829e11	0.0924543
$489$	8.10371e11	0.640905
$490$	3.86339e11	0.302751
$491$	1.98313e12	1.53987	0.769937	−	0.638119i	$-0.220287\pi$
$491$	1.98313e12	1.53987	0.769937	+	0.638119i	$0.220287\pi$
$492$	−3.53153e11	−0.271719
$493$	−4.63072e10	−0.0353051
$494$	2.46389e10	0.0186145
$495$	−1.17362e11	−0.0878625
$496$	1.64353e12	1.21930
$497$	−1.38245e12	−1.01636
$498$	−3.27625e11	−0.238696
$499$	−8.27327e11	−0.597344	−0.298672	−	0.954356i	$-0.596544\pi$
$499$	−8.27327e11	−0.597344	−0.298672	+	0.954356i	$0.596544\pi$
$500$	−3.36021e12	−2.40437
$501$	1.01194e12	0.717605
$502$	−2.74955e11	−0.193239
$503$	4.94554e11	0.344475	0.172238	−	0.985055i	$-0.444900\pi$
$503$	4.94554e11	0.344475	0.172238	+	0.985055i	$0.444900\pi$
$504$	3.12876e10	0.0215991
$505$	4.06322e12	2.78009
$506$	−1.56860e11	−0.106374
$507$	−1.11374e11	−0.0748595
$508$	2.01486e11	0.134233
$509$	−2.31118e12	−1.52617	−0.763087	−	0.646296i	$-0.776317\pi$
$509$	−2.31118e12	−1.52617	−0.763087	+	0.646296i	$0.776317\pi$
$510$	−3.10844e10	−0.0203459
$511$	−3.17079e12	−2.05719
$512$	1.00022e12	0.643248
$513$	7.74852e11	0.493959
$514$	1.52541e11	0.0963947
$515$	2.90942e12	1.82252
$516$	−1.35231e12	−0.839756
$517$	2.12951e12	1.31091
$518$	−5.06954e11	−0.309374
$519$	−7.69937e11	−0.465803
$520$	−2.33092e11	−0.139802
$521$	2.20997e12	1.31406	0.657031	−	0.753864i	$-0.271812\pi$
$521$	2.20997e12	1.31406	0.657031	+	0.753864i	$0.271812\pi$
$522$	5.37283e9	0.00316727
$523$	2.43867e12	1.42527	0.712633	−	0.701537i	$-0.247503\pi$
$523$	2.43867e12	1.42527	0.712633	+	0.701537i	$0.247503\pi$
$524$	1.89974e12	1.10079
$525$	−5.86889e12	−3.37162
$526$	−1.38822e10	−0.00790718
$527$	1.88238e11	0.106307
$528$	−1.48700e12	−0.832641
$529$	−5.26040e11	−0.292057
$530$	−2.46855e11	−0.135894
$531$	1.19978e10	0.00654900
$532$	−1.29236e12	−0.699490
$533$	−1.47140e11	−0.0789694
$534$	3.56598e11	0.189777
$535$	−1.84298e12	−0.972588
$536$	2.07140e11	0.108398
$537$	−1.69138e12	−0.877720
$538$	4.46968e11	0.230015
$539$	2.11673e12	1.08023
$540$	−3.62930e12	−1.83675
$541$	−1.84418e12	−0.925585	−0.462792	−	0.886467i	$-0.653152\pi$
$541$	−1.84418e12	−0.925585	−0.462792	+	0.886467i	$0.653152\pi$
$542$	−2.23582e11	−0.111286
$543$	3.35667e12	1.65695
$544$	6.82851e10	0.0334296
$545$	−1.75365e12	−0.851448
$546$	−1.15476e11	−0.0556063
$547$	−2.62022e12	−1.25140	−0.625698	−	0.780065i	$-0.715186\pi$
$547$	−2.62022e12	−1.25140	−0.625698	+	0.780065i	$0.715186\pi$
$548$	−7.30611e11	−0.346078
$549$	3.77754e10	0.0177473
$550$	6.35235e11	0.296007
$551$	−4.48245e11	−0.207173
$552$	−4.92536e11	−0.225794
$553$	−1.91815e12	−0.872206
$554$	3.85264e11	0.173766
$555$	5.97102e12	2.67135
$556$	−7.55025e11	−0.335062
$557$	2.45908e12	1.08249	0.541245	−	0.840865i	$-0.317953\pi$
$557$	2.45908e12	1.08249	0.541245	+	0.840865i	$0.317953\pi$
$558$	−2.18405e10	−0.00953692
$559$	−5.63437e11	−0.244058
$560$	5.93122e12	2.54858
$561$	−1.70310e11	−0.0725950
$562$	−3.12494e11	−0.132138
$563$	−1.30659e12	−0.548091	−0.274046	−	0.961717i	$-0.588362\pi$
$563$	−1.30659e12	−0.548091	−0.274046	+	0.961717i	$0.588362\pi$
$564$	3.31058e12	1.37768
$565$	−2.13003e12	−0.879361
$566$	5.97534e11	0.244731
$567$	−3.43875e12	−1.39726
$568$	4.69845e11	0.189403
$569$	−2.68810e12	−1.07508	−0.537539	−	0.843239i	$-0.680646\pi$
$569$	−2.68810e12	−1.07508	−0.537539	+	0.843239i	$0.680646\pi$
$570$	−3.00892e11	−0.119391
$571$	2.99602e12	1.17946	0.589729	−	0.807601i	$-0.299235\pi$
$571$	2.99602e12	1.17946	0.589729	+	0.807601i	$0.299235\pi$
$572$	−6.32299e11	−0.246968
$573$	1.45549e12	0.564044
$574$	−1.52560e11	−0.0586592
$575$	−5.16381e12	−1.97000
$576$	1.23837e11	0.0468760
$577$	6.04343e11	0.226982	0.113491	−	0.993539i	$-0.463797\pi$
$577$	6.04343e11	0.226982	0.113491	+	0.993539i	$0.463797\pi$
$578$	−3.71071e11	−0.138287
$579$	2.86227e12	1.05842
$580$	2.09952e12	0.770360
$581$	7.15991e12	2.60684
$582$	−4.32905e11	−0.156401
$583$	−1.35250e12	−0.484876
$584$	1.07763e12	0.383366
$585$	−7.60186e10	−0.0268360
$586$	6.16747e11	0.216057
$587$	−7.41276e11	−0.257697	−0.128848	−	0.991664i	$-0.541128\pi$
$587$	−7.41276e11	−0.257697	−0.128848	+	0.991664i	$0.541128\pi$
$588$	3.29071e12	1.13525
$589$	1.82211e12	0.623816
$590$	−9.26752e10	−0.0314869
$591$	−1.73466e12	−0.584886
$592$	−4.22845e12	−1.41492
$593$	−5.55536e12	−1.84487	−0.922435	−	0.386152i	$-0.873804\pi$
$593$	−5.55536e12	−1.84487	−0.922435	+	0.386152i	$0.873804\pi$
$594$	3.93067e11	0.129547
$595$	6.79318e11	0.222201
$596$	2.15201e12	0.698614
$597$	−3.52015e11	−0.113417
$598$	−1.01603e11	−0.0324900
$599$	−3.35363e12	−1.06437	−0.532187	−	0.846627i	$-0.678630\pi$
$599$	−3.35363e12	−1.06437	−0.532187	+	0.846627i	$0.678630\pi$
$600$	1.99462e12	0.628318
$601$	1.88646e12	0.589809	0.294905	−	0.955527i	$-0.404712\pi$
$601$	1.88646e12	0.589809	0.294905	+	0.955527i	$0.404712\pi$
$602$	−5.84189e11	−0.181288
$603$	6.75548e10	0.0208079
$604$	−2.40955e11	−0.0736664
$605$	−1.05674e12	−0.320677
$606$	−6.84129e11	−0.206068
$607$	1.01740e12	0.304188	0.152094	−	0.988366i	$-0.451398\pi$
$607$	1.01740e12	0.304188	0.152094	+	0.988366i	$0.451398\pi$
$608$	6.60987e11	0.196168
$609$	2.10080e12	0.618881
$610$	−2.91791e11	−0.0853272
$611$	1.37935e12	0.400394
$612$	1.47983e10	0.00426414
$613$	−5.21446e11	−0.149155	−0.0745774	−	0.997215i	$-0.523761\pi$
$613$	−5.21446e11	−0.149155	−0.0745774	+	0.997215i	$0.523761\pi$
$614$	−2.26038e11	−0.0641836
$615$	1.79688e12	0.506503
$616$	−1.32413e12	−0.370526
$617$	1.14541e12	0.318183	0.159092	−	0.987264i	$-0.449143\pi$
$617$	1.14541e12	0.318183	0.159092	+	0.987264i	$0.449143\pi$
$618$	−4.89862e11	−0.135091
$619$	−1.10612e12	−0.302827	−0.151414	−	0.988470i	$-0.548383\pi$
$619$	−1.10612e12	−0.302827	−0.151414	+	0.988470i	$0.548383\pi$
$620$	−8.53452e12	−2.31962
$621$	−3.19523e12	−0.862165
$622$	6.64793e10	0.0178086
$623$	−7.79308e12	−2.07259
$624$	−9.63171e11	−0.254315
$625$	8.16561e12	2.14057
$626$	−4.55751e11	−0.118616
$627$	−1.64857e12	−0.425994
$628$	4.14023e12	1.06220
$629$	−4.84295e11	−0.123362
$630$	−7.88184e10	−0.0199340
$631$	3.20443e12	0.804671	0.402336	−	0.915492i	$-0.368198\pi$
$631$	3.20443e12	0.804671	0.402336	+	0.915492i	$0.368198\pi$
$632$	6.51908e11	0.162540
$633$	−2.65284e12	−0.656742
$634$	1.82313e11	0.0448143
$635$	−1.02518e12	−0.250219
$636$	−2.10263e12	−0.509573
$637$	1.37106e12	0.329937
$638$	−2.27386e11	−0.0543338
$639$	1.53231e11	0.0363574
$640$	−4.11374e12	−0.969230
$641$	−4.90467e12	−1.14749	−0.573745	−	0.819034i	$-0.694510\pi$
$641$	−4.90467e12	−1.14749	−0.573745	+	0.819034i	$0.694510\pi$
$642$	3.10305e11	0.0720910
$643$	1.53529e12	0.354194	0.177097	−	0.984193i	$-0.443329\pi$
$643$	1.53529e12	0.354194	0.177097	+	0.984193i	$0.443329\pi$
$644$	5.32926e12	1.22090
$645$	6.88072e12	1.56536
$646$	2.44046e10	0.00551347
$647$	−6.61326e11	−0.148370	−0.0741850	−	0.997244i	$-0.523636\pi$
$647$	−6.61326e11	−0.148370	−0.0741850	+	0.997244i	$0.523636\pi$
$648$	1.16870e12	0.260385
$649$	−5.07763e11	−0.112347
$650$	4.11460e11	0.0904101
$651$	−8.53973e12	−1.86350
$652$	2.98000e12	0.645807
$653$	4.61469e12	0.993192	0.496596	−	0.867982i	$-0.334583\pi$
$653$	4.61469e12	0.993192	0.496596	+	0.867982i	$0.334583\pi$
$654$	2.95264e11	0.0631118
$655$	−9.66610e12	−2.05194
$656$	−1.27248e12	−0.268278
$657$	3.51450e11	0.0735902
$658$	1.43015e12	0.297416
$659$	−9.04687e12	−1.86859	−0.934294	−	0.356502i	$-0.883969\pi$
$659$	−9.04687e12	−1.86859	−0.934294	+	0.356502i	$0.883969\pi$
$660$	7.72167e12	1.58403
$661$	3.59295e12	0.732057	0.366028	−	0.930604i	$-0.380717\pi$
$661$	3.59295e12	0.732057	0.366028	+	0.930604i	$0.380717\pi$
$662$	−3.15926e11	−0.0639328
$663$	−1.10315e11	−0.0221729
$664$	−2.43339e12	−0.485797
$665$	6.57568e12	1.30390
$666$	5.61907e10	0.0110670
$667$	1.84841e12	0.361604
$668$	3.72124e12	0.723093
$669$	−1.30536e12	−0.251948
$670$	−5.21819e11	−0.100042
$671$	−1.59871e12	−0.304451
$672$	−3.09786e12	−0.586004
$673$	2.13714e12	0.401573	0.200786	−	0.979635i	$-0.435650\pi$
$673$	2.13714e12	0.401573	0.200786	+	0.979635i	$0.435650\pi$
$674$	−1.80608e11	−0.0337107
$675$	1.29397e13	2.39915
$676$	−4.09558e11	−0.0754320
$677$	−2.55166e12	−0.466847	−0.233423	−	0.972375i	$-0.574993\pi$
$677$	−2.55166e12	−0.466847	−0.233423	+	0.972375i	$0.574993\pi$
$678$	3.58635e11	0.0651808
$679$	9.46070e12	1.70809
$680$	−2.30875e11	−0.0414083
$681$	2.75840e12	0.491467
$682$	9.24320e11	0.163604
$683$	7.63188e12	1.34196	0.670978	−	0.741477i	$-0.265874\pi$
$683$	7.63188e12	1.34196	0.670978	+	0.741477i	$0.265874\pi$
$684$	1.43245e11	0.0250223
$685$	3.71743e12	0.645113
$686$	2.26574e11	0.0390617
$687$	3.35619e12	0.574832
$688$	−4.87266e12	−0.829121
$689$	−8.76056e11	−0.148097
$690$	1.24078e12	0.208388
$691$	−2.36970e12	−0.395405	−0.197703	−	0.980262i	$-0.563348\pi$
$691$	−2.36970e12	−0.395405	−0.197703	+	0.980262i	$0.563348\pi$
$692$	−2.83132e12	−0.469365
$693$	−4.31842e11	−0.0711255
$694$	−7.37405e10	−0.0120667
$695$	3.84165e12	0.624578
$696$	−7.13984e11	−0.115331
$697$	−1.45741e11	−0.0233902
$698$	1.23747e12	0.197326
$699$	−1.08306e13	−1.71595
$700$	−2.15819e13	−3.39741
$701$	−1.72803e12	−0.270284	−0.135142	−	0.990826i	$-0.543149\pi$
$701$	−1.72803e12	−0.270284	−0.135142	+	0.990826i	$0.543149\pi$
$702$	2.54600e11	0.0395678
$703$	−4.68789e12	−0.723900
$704$	−5.24097e12	−0.804146
$705$	−1.68446e13	−2.56809
$706$	6.81804e11	0.103285
$707$	1.49509e13	2.25051
$708$	−7.89378e11	−0.118069
$709$	−3.26440e12	−0.485172	−0.242586	−	0.970130i	$-0.577996\pi$
$709$	−3.26440e12	−0.485172	−0.242586	+	0.970130i	$0.577996\pi$
$710$	−1.18361e12	−0.174802
$711$	2.12608e11	0.0312008
$712$	2.64858e12	0.386236
$713$	−7.51378e12	−1.08882
$714$	−1.14378e11	−0.0164702
$715$	3.21721e12	0.460365
$716$	−6.21976e12	−0.884433
$717$	3.58418e12	0.506469
$718$	1.10128e12	0.154646
$719$	−6.17850e11	−0.0862191	−0.0431095	−	0.999070i	$-0.513726\pi$
$719$	−6.17850e11	−0.0862191	−0.0431095	+	0.999070i	$0.513726\pi$
$720$	−6.57416e11	−0.0911683
$721$	1.07054e13	1.47535
$722$	−7.80344e11	−0.106873
$723$	1.37579e13	1.87253
$724$	1.23436e13	1.66962
$725$	−7.48550e12	−1.00624
$726$	1.77924e11	0.0237695
$727$	5.84000e12	0.775368	0.387684	−	0.921792i	$-0.373275\pi$
$727$	5.84000e12	0.775368	0.387684	+	0.921792i	$0.373275\pi$
$728$	−8.57680e11	−0.113171
$729$	7.98538e12	1.04718
$730$	−2.71473e12	−0.353813
$731$	−5.58079e11	−0.0722882
$732$	−2.48538e12	−0.319958
$733$	−7.18908e10	−0.00919826	−0.00459913	−	0.999989i	$-0.501464\pi$
$733$	−7.18908e10	−0.00919826	−0.00459913	+	0.999989i	$0.501464\pi$
$734$	−5.77258e9	−0.000734070 0
$735$	−1.67435e13	−2.11618
$736$	−2.72569e12	−0.342394
$737$	−2.85902e12	−0.356954
$738$	1.69097e10	0.00209837
$739$	−1.01033e13	−1.24613	−0.623067	−	0.782168i	$-0.714114\pi$
$739$	−1.01033e13	−1.24613	−0.623067	+	0.782168i	$0.714114\pi$
$740$	2.19574e13	2.69178
$741$	−1.06783e12	−0.130112
$742$	−9.08322e11	−0.110007
$743$	−6.09193e12	−0.733340	−0.366670	−	0.930351i	$-0.619502\pi$
$743$	−6.09193e12	−0.733340	−0.366670	+	0.930351i	$0.619502\pi$
$744$	2.90234e12	0.347272
$745$	−1.09497e13	−1.30226
$746$	1.73908e11	0.0205587
$747$	−7.93604e11	−0.0932527
$748$	−6.26286e11	−0.0731502
$749$	−6.78139e12	−0.787319
$750$	−2.87867e12	−0.332212
$751$	−1.43572e13	−1.64698	−0.823491	−	0.567330i	$-0.807976\pi$
$751$	−1.43572e13	−1.64698	−0.823491	+	0.567330i	$0.807976\pi$
$752$	1.19287e13	1.36023
$753$	1.19163e13	1.35071
$754$	−1.47284e11	−0.0165953
$755$	1.22601e12	0.137319
$756$	−1.33543e13	−1.48687
$757$	1.33786e13	1.48074	0.740370	−	0.672200i	$-0.234651\pi$
$757$	1.33786e13	1.48074	0.740370	+	0.672200i	$0.234651\pi$
$758$	7.09640e11	0.0780776
$759$	6.79815e12	0.743537
$760$	−2.23483e12	−0.242987
$761$	1.00649e13	1.08788	0.543938	−	0.839126i	$-0.316933\pi$
$761$	1.00649e13	1.08788	0.543938	+	0.839126i	$0.316933\pi$
$762$	1.72611e11	0.0185469
$763$	−6.45269e12	−0.689255
$764$	5.35231e12	0.568357
$765$	−7.52956e10	−0.00794865
$766$	1.46201e12	0.153433
$767$	−3.28892e11	−0.0343142
$768$	−7.61614e12	−0.789968
$769$	4.34623e12	0.448172	0.224086	−	0.974569i	$-0.428060\pi$
$769$	4.34623e12	0.448172	0.224086	+	0.974569i	$0.428060\pi$
$770$	3.33571e12	0.341963
$771$	−6.61097e12	−0.673784
$772$	1.05255e13	1.06651
$773$	2.50017e12	0.251862	0.125931	−	0.992039i	$-0.459808\pi$
$773$	2.50017e12	0.251862	0.125931	+	0.992039i	$0.459808\pi$
$774$	6.47515e10	0.00648509
$775$	3.04285e13	3.02986
$776$	−3.21534e12	−0.318310
$777$	2.19708e13	2.16248
$778$	−8.28731e11	−0.0810971
$779$	−1.41075e12	−0.137256
$780$	5.00154e12	0.483814
$781$	−6.48495e12	−0.623702
$782$	−1.00636e11	−0.00962332
$783$	−4.63183e12	−0.440377
$784$	1.18571e13	1.12087
$785$	−2.10660e13	−1.98001
$786$	1.62749e12	0.152096
$787$	−1.47010e13	−1.36603	−0.683013	−	0.730406i	$-0.739331\pi$
$787$	−1.47010e13	−1.36603	−0.683013	+	0.730406i	$0.739331\pi$
$788$	−6.37893e12	−0.589359
$789$	6.01639e11	0.0552700
$790$	−1.64226e12	−0.150010
$791$	−7.83761e12	−0.711851
$792$	1.46767e11	0.0132546
$793$	−1.03553e12	−0.0929892
$794$	−5.68266e10	−0.00507410
$795$	1.06984e13	0.949879
$796$	−1.29448e12	−0.114284
$797$	8.96898e12	0.787373	0.393687	−	0.919245i	$-0.371199\pi$
$797$	8.96898e12	0.787373	0.393687	+	0.919245i	$0.371199\pi$
$798$	−1.10715e12	−0.0966485
$799$	1.36623e12	0.118594
$800$	1.10382e13	0.952782
$801$	8.63785e11	0.0741411
$802$	2.26444e11	0.0193275
$803$	−1.48739e13	−1.26242
$804$	−4.44468e12	−0.375136
$805$	−2.71159e13	−2.27584
$806$	5.98708e11	0.0499698
$807$	−1.93711e13	−1.60777
$808$	−5.08127e12	−0.419393
$809$	1.74450e13	1.43187	0.715934	−	0.698168i	$-0.246001\pi$
$809$	1.74450e13	1.43187	0.715934	+	0.698168i	$0.246001\pi$
$810$	−2.94415e12	−0.240313
$811$	−8.34611e12	−0.677470	−0.338735	−	0.940882i	$-0.609999\pi$
$811$	−8.34611e12	−0.677470	−0.338735	+	0.940882i	$0.609999\pi$
$812$	7.72534e12	0.623614
$813$	9.68980e12	0.777871
$814$	−2.37807e12	−0.189852
$815$	−1.51626e13	−1.20383
$816$	−9.54010e11	−0.0753264
$817$	−5.40210e12	−0.424193
$818$	1.67555e12	0.130848
$819$	−2.79716e11	−0.0217240
$820$	6.60774e12	0.510376
$821$	1.88288e13	1.44637	0.723183	−	0.690657i	$-0.242678\pi$
$821$	1.88288e13	1.44637	0.723183	+	0.690657i	$0.242678\pi$
$822$	−6.25909e11	−0.0478176
$823$	4.02178e12	0.305576	0.152788	−	0.988259i	$-0.451175\pi$
$823$	4.02178e12	0.305576	0.152788	+	0.988259i	$0.451175\pi$
$824$	−3.63838e12	−0.274938
$825$	−2.75304e13	−2.06904
$826$	−3.41006e11	−0.0254889
$827$	3.84013e12	0.285477	0.142738	−	0.989760i	$-0.454409\pi$
$827$	3.84013e12	0.285477	0.142738	+	0.989760i	$0.454409\pi$
$828$	−5.90695e11	−0.0436744
$829$	1.81041e13	1.33132	0.665660	−	0.746255i	$-0.268150\pi$
$829$	1.81041e13	1.33132	0.665660	+	0.746255i	$0.268150\pi$
$830$	6.13010e12	0.448349
$831$	−1.66969e13	−1.21460
$832$	−3.39473e12	−0.245612
$833$	1.35803e12	0.0977249
$834$	−6.46824e11	−0.0462955
$835$	−1.89341e13	−1.34789
$836$	−6.06234e12	−0.429252
$837$	1.88284e13	1.32601
$838$	4.59766e11	0.0322062
$839$	1.83543e13	1.27882	0.639410	−	0.768866i	$-0.279179\pi$
$839$	1.83543e13	1.27882	0.639410	+	0.768866i	$0.279179\pi$
$840$	1.04740e13	0.725867
$841$	−1.18277e13	−0.815300
$842$	1.15380e12	0.0791092
$843$	1.35431e13	0.923625
$844$	−9.75538e12	−0.661764
$845$	2.08388e12	0.140610
$846$	−1.58518e11	−0.0106393
$847$	−3.88835e12	−0.259591
$848$	−7.57621e12	−0.503119
$849$	−2.58965e13	−1.71063
$850$	4.07546e11	0.0267789
$851$	1.93313e13	1.26351
$852$	−1.00816e13	−0.655470
$853$	−1.20116e13	−0.776835	−0.388418	−	0.921483i	$-0.626978\pi$
$853$	−1.20116e13	−0.776835	−0.388418	+	0.921483i	$0.626978\pi$
$854$	−1.07367e12	−0.0690732
$855$	−7.28848e11	−0.0466433
$856$	2.30475e12	0.146721
$857$	−6.17723e12	−0.391183	−0.195592	−	0.980685i	$-0.562663\pi$
$857$	−6.17723e12	−0.391183	−0.195592	+	0.980685i	$0.562663\pi$
$858$	−5.41686e11	−0.0341236
$859$	2.76160e13	1.73058	0.865291	−	0.501269i	$-0.167133\pi$
$859$	2.76160e13	1.73058	0.865291	+	0.501269i	$0.167133\pi$
$860$	2.53027e13	1.57733
$861$	6.61177e12	0.410019
$862$	2.41439e12	0.148944
$863$	9.27582e12	0.569251	0.284626	−	0.958639i	$-0.408131\pi$
$863$	9.27582e12	0.569251	0.284626	+	0.958639i	$0.408131\pi$
$864$	6.83016e12	0.416983
$865$	1.44061e13	0.874929
$866$	−3.91197e12	−0.236355
$867$	1.60818e13	0.966606
$868$	−3.14034e13	−1.87775
$869$	−8.99785e12	−0.535242
$870$	1.79864e12	0.106441
$871$	−1.85187e12	−0.109025
$872$	2.19303e12	0.128446
$873$	−1.04862e12	−0.0611021
$874$	−9.74143e11	−0.0564704
$875$	6.29103e13	3.62815
$876$	−2.31232e13	−1.32672
$877$	−2.19078e13	−1.25055	−0.625274	−	0.780405i	$-0.715013\pi$
$877$	−2.19078e13	−1.25055	−0.625274	+	0.780405i	$0.715013\pi$
$878$	−4.67602e12	−0.265553
$879$	−2.67292e13	−1.51020
$880$	2.78228e13	1.56397
$881$	2.92416e12	0.163534	0.0817672	−	0.996651i	$-0.473944\pi$
$881$	2.92416e12	0.163534	0.0817672	+	0.996651i	$0.473944\pi$
$882$	−1.57566e11	−0.00876706
$883$	3.35851e13	1.85919	0.929594	−	0.368585i	$-0.120158\pi$
$883$	3.35851e13	1.85919	0.929594	+	0.368585i	$0.120158\pi$
$884$	−4.05663e11	−0.0223424
$885$	4.01645e12	0.220089
$886$	3.25566e12	0.177495
$887$	−3.31699e13	−1.79924	−0.899619	−	0.436676i	$-0.856156\pi$
$887$	−3.31699e13	−1.79924	−0.899619	+	0.436676i	$0.856156\pi$
$888$	−7.46708e12	−0.402988
$889$	−3.77225e12	−0.202555
$890$	−6.67219e12	−0.356462
$891$	−1.61308e13	−0.857447
$892$	−4.80023e12	−0.253875
$893$	1.32248e13	0.695920
$894$	1.84361e12	0.0965275
$895$	3.16469e13	1.64864
$896$	−1.51368e13	−0.784601
$897$	4.40335e12	0.227100
$898$	−1.83688e12	−0.0942619
$899$	−1.08920e13	−0.556148
$900$	2.39213e12	0.121533
$901$	−8.67724e11	−0.0438652
$902$	−7.15642e11	−0.0359970
$903$	2.53181e13	1.26718
$904$	2.66371e12	0.132657
$905$	−6.28057e13	−3.11229
$906$	−2.06424e11	−0.0101785
$907$	2.27086e13	1.11418	0.557092	−	0.830451i	$-0.311917\pi$
$907$	2.27086e13	1.11418	0.557092	+	0.830451i	$0.311917\pi$
$908$	1.01435e13	0.495226
$909$	−1.65716e12	−0.0805059
$910$	2.16063e12	0.104447
$911$	4.92090e12	0.236707	0.118354	−	0.992972i	$-0.462238\pi$
$911$	4.92090e12	0.236707	0.118354	+	0.992972i	$0.462238\pi$
$912$	−9.23465e12	−0.442022
$913$	3.35865e13	1.59973
$914$	2.33025e12	0.110444
$915$	1.26459e13	0.596424
$916$	1.23418e13	0.579229
$917$	−3.55671e13	−1.66107
$918$	2.52179e11	0.0117197
$919$	−9.41621e12	−0.435468	−0.217734	−	0.976008i	$-0.569867\pi$
$919$	−9.41621e12	−0.435468	−0.217734	+	0.976008i	$0.569867\pi$
$920$	9.21569e12	0.424114
$921$	9.79626e12	0.448634
$922$	4.59455e12	0.209389
$923$	−4.20049e12	−0.190499
$924$	2.84125e13	1.28229
$925$	−7.82858e13	−3.51597
$926$	−5.14116e12	−0.229780
$927$	−1.18659e12	−0.0527766
$928$	−3.95118e12	−0.174889
$929$	−3.87518e13	−1.70695	−0.853476	−	0.521131i	$-0.825510\pi$
$929$	−3.87518e13	−1.70695	−0.853476	+	0.521131i	$0.825510\pi$
$930$	−7.31145e12	−0.320502
$931$	1.31454e13	0.573458
$932$	−3.98276e13	−1.72907
$933$	−2.88114e12	−0.124479
$934$	−2.59727e12	−0.111675
$935$	3.18662e12	0.136357
$936$	9.50652e10	0.00404837
$937$	1.41425e13	0.599373	0.299687	−	0.954038i	$-0.403118\pi$
$937$	1.41425e13	0.599373	0.299687	+	0.954038i	$0.403118\pi$
$938$	−1.92007e12	−0.0809850
$939$	1.97518e13	0.829108
$940$	−6.19433e13	−2.58773
$941$	−2.29704e13	−0.955027	−0.477514	−	0.878624i	$-0.658462\pi$
$941$	−2.29704e13	−0.955027	−0.477514	+	0.878624i	$0.658462\pi$
$942$	3.54690e12	0.146764
$943$	5.81744e12	0.239568
$944$	−2.84429e12	−0.116574
$945$	6.79482e13	2.77163
$946$	−2.74038e12	−0.111250
$947$	−1.50510e12	−0.0608120	−0.0304060	−	0.999538i	$-0.509680\pi$
$947$	−1.50510e12	−0.0608120	−0.0304060	+	0.999538i	$0.509680\pi$
$948$	−1.39882e13	−0.562504
$949$	−9.63423e12	−0.385584
$950$	3.94498e12	0.157141
$951$	−7.90126e12	−0.313245
$952$	−8.49523e11	−0.0335204
$953$	2.42253e13	0.951373	0.475686	−	0.879615i	$-0.342200\pi$
$953$	2.42253e13	0.951373	0.475686	+	0.879615i	$0.342200\pi$
$954$	1.00678e11	0.00393522
$955$	−2.72332e13	−1.05946
$956$	1.31802e13	0.510343
$957$	9.85465e12	0.379785
$958$	−5.67291e11	−0.0217601
$959$	1.36786e13	0.522225
$960$	4.14565e13	1.57533
$961$	1.78364e13	0.674608
$962$	−1.54034e12	−0.0579869
$963$	7.51650e11	0.0281642
$964$	5.05923e13	1.88685
$965$	−5.35551e13	−1.98805
$966$	4.56554e12	0.168692
$967$	2.41172e13	0.886967	0.443484	−	0.896282i	$-0.353742\pi$
$967$	2.41172e13	0.886967	0.443484	+	0.896282i	$0.353742\pi$
$968$	1.32151e12	0.0483760
$969$	−1.05767e12	−0.0385383
$970$	8.09996e12	0.293772
$971$	3.13584e13	1.13206	0.566028	−	0.824386i	$-0.308479\pi$
$971$	3.13584e13	1.13206	0.566028	+	0.824386i	$0.308479\pi$
$972$	2.88597e12	0.103703
$973$	1.41357e13	0.505602
$974$	−2.27469e12	−0.0809854
$975$	−1.78322e13	−0.631953
$976$	−8.95534e12	−0.315906
$977$	4.44366e13	1.56033	0.780163	−	0.625576i	$-0.215136\pi$
$977$	4.44366e13	1.56033	0.780163	+	0.625576i	$0.215136\pi$
$978$	2.55294e12	0.0892312
$979$	−3.65566e13	−1.27187
$980$	−6.15714e13	−2.13237
$981$	7.15216e11	0.0246562
$982$	6.24755e12	0.214392
$983$	1.53216e13	0.523376	0.261688	−	0.965153i	$-0.415721\pi$
$983$	1.53216e13	0.523376	0.261688	+	0.965153i	$0.415721\pi$
$984$	−2.24710e12	−0.0764089
$985$	3.24567e13	1.09861
$986$	−1.45883e11	−0.00491541
$987$	−6.19812e13	−2.07889
$988$	−3.92675e12	−0.131107
$989$	2.22765e13	0.740394
$990$	−3.69730e11	−0.0122328
$991$	2.32887e13	0.767034	0.383517	−	0.923534i	$-0.374713\pi$
$991$	2.32887e13	0.767034	0.383517	+	0.923534i	$0.374713\pi$
$992$	1.60615e13	0.526604
$993$	1.36919e13	0.446881
$994$	−4.35520e12	−0.141504
$995$	6.58644e12	0.213033
$996$	5.22142e13	1.68121
$997$	−1.12247e13	−0.359788	−0.179894	−	0.983686i	$-0.557575\pi$
$997$	−1.12247e13	−0.359788	−0.179894	+	0.983686i	$0.557575\pi$
$998$	−2.60636e12	−0.0831663
$999$	−4.84412e13	−1.53876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.a.b.1.3	✓	5
3.2	odd	2		117.10.a.e.1.3		5
4.3	odd	2		208.10.a.h.1.4		5
5.4	even	2		325.10.a.b.1.3		5
13.12	even	2		169.10.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.3	✓	5	1.1	even	1	trivial
117.10.a.e.1.3		5	3.2	odd	2
169.10.a.b.1.3		5	13.12	even	2
208.10.a.h.1.4		5	4.3	odd	2
325.10.a.b.1.3		5	5.4	even	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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	13.a (trivial)

\(f(q)\)	\(=\)	\(q+3.15034 q^{2} -136.532 q^{3} -502.075 q^{4} +2554.62 q^{5} -430.124 q^{6} +9399.91 q^{7} -3194.68 q^{8} -1041.89 q^{9} +O(q^{10})\)	\(q+3.15034 q^{2} -136.532 q^{3} -502.075 q^{4} +2554.62 q^{5} -430.124 q^{6} +9399.91 q^{7} -3194.68 q^{8} -1041.89 q^{9} +8047.92 q^{10} +44094.1 q^{11} +68549.6 q^{12} +28561.0 q^{13} +29612.9 q^{14} -348788. q^{15} +246998. q^{16} +28289.4 q^{17} -3282.30 q^{18} +273836. q^{19} -1.28261e6 q^{20} -1.28339e6 q^{21} +138911. q^{22} -1.12921e6 q^{23} +436178. q^{24} +4.57295e6 q^{25} +89976.9 q^{26} +2.82962e6 q^{27} -4.71947e6 q^{28} -1.63691e6 q^{29} -1.09880e6 q^{30} +6.65402e6 q^{31} +2.41381e6 q^{32} -6.02028e6 q^{33} +89121.2 q^{34} +2.40132e7 q^{35} +523105. q^{36} -1.71193e7 q^{37} +862677. q^{38} -3.89950e6 q^{39} -8.16119e6 q^{40} -5.15179e6 q^{41} -4.04313e6 q^{42} -1.97275e7 q^{43} -2.21386e7 q^{44} -2.66162e6 q^{45} -3.55739e6 q^{46} +4.82947e7 q^{47} -3.37233e7 q^{48} +4.80048e7 q^{49} +1.44063e7 q^{50} -3.86242e6 q^{51} -1.43398e7 q^{52} -3.06731e7 q^{53} +8.91427e6 q^{54} +1.12644e8 q^{55} -3.00298e7 q^{56} -3.73875e7 q^{57} -5.15683e6 q^{58} -1.15154e7 q^{59} +1.75118e8 q^{60} -3.62567e7 q^{61} +2.09624e7 q^{62} -9.79364e6 q^{63} -1.18859e8 q^{64} +7.29624e7 q^{65} -1.89659e7 q^{66} -6.48390e7 q^{67} -1.42034e7 q^{68} +1.54174e8 q^{69} +7.56497e7 q^{70} -1.47071e8 q^{71} +3.32850e6 q^{72} -3.37321e8 q^{73} -5.39317e7 q^{74} -6.24356e8 q^{75} -1.37486e8 q^{76} +4.14481e8 q^{77} -1.22848e7 q^{78} -2.04060e8 q^{79} +6.30986e8 q^{80} -3.65828e8 q^{81} -1.62299e7 q^{82} +7.61700e8 q^{83} +6.44360e8 q^{84} +7.22685e7 q^{85} -6.21484e7 q^{86} +2.23491e8 q^{87} -1.40867e8 q^{88} -8.29058e8 q^{89} -8.38502e6 q^{90} +2.68471e8 q^{91} +5.66948e8 q^{92} -9.08490e8 q^{93} +1.52145e8 q^{94} +6.99547e8 q^{95} -3.29563e8 q^{96} +1.00647e9 q^{97} +1.51231e8 q^{98} -4.59410e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9}+O(q^{10}) \) 5 * q + 15 * q^2 + 161 * q^3 + 361 * q^4 + 1803 * q^5 + 5693 * q^6 + 10099 * q^7 + 23151 * q^8 + 61060 * q^9	\( 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9} + 84505 q^{10} + 121746 q^{11} + 113389 q^{12} + 142805 q^{13} + 8475 q^{14} + 105973 q^{15} - 322463 q^{16} - 495669 q^{17} - 656228 q^{18} - 840738 q^{19} - 1595607 q^{20} - 1599467 q^{21} - 2023594 q^{22} - 592152 q^{23} - 2295657 q^{24} + 1670362 q^{25} + 428415 q^{26} + 6847883 q^{27} + 2587955 q^{28} + 10678182 q^{29} + 5491201 q^{30} + 12885296 q^{31} + 3282927 q^{32} + 17278298 q^{33} - 9934079 q^{34} + 8380731 q^{35} - 20483302 q^{36} + 7171823 q^{37} - 25568814 q^{38} + 4598321 q^{39} - 54359445 q^{40} + 9294012 q^{41} - 69520457 q^{42} + 12831975 q^{43} - 41479074 q^{44} + 26135198 q^{45} - 59319696 q^{46} + 43354215 q^{47} - 86874671 q^{48} + 25249488 q^{49} - 16270770 q^{50} + 16905901 q^{51} + 10310521 q^{52} + 93231780 q^{53} + 58983719 q^{54} + 99448846 q^{55} + 199599225 q^{56} + 90173382 q^{57} + 151020970 q^{58} + 246496182 q^{59} + 90097913 q^{60} - 132232612 q^{61} + 158135724 q^{62} - 416955202 q^{63} + 91019105 q^{64} + 51495483 q^{65} - 323733130 q^{66} - 369388534 q^{67} + 238172073 q^{68} - 579986760 q^{69} - 144857425 q^{70} + 212150457 q^{71} - 415774278 q^{72} - 252729806 q^{73} + 192105957 q^{74} - 752457788 q^{75} - 953775990 q^{76} + 449666118 q^{77} + 162597773 q^{78} - 1247271728 q^{79} + 900649725 q^{80} - 317713115 q^{81} + 169559388 q^{82} + 1696894296 q^{83} + 1247983739 q^{84} - 775363765 q^{85} + 3291621459 q^{86} - 614530466 q^{87} - 220227222 q^{88} - 753854382 q^{89} + 2296265882 q^{90} + 288437539 q^{91} + 13876128 q^{92} - 892784668 q^{93} + 272071215 q^{94} + 1442632962 q^{95} + 930612847 q^{96} + 3824606 q^{97} + 1570614816 q^{98} + 3016199848 q^{99}+O(q^{100}) \) 5 * q + 15 * q^2 + 161 * q^3 + 361 * q^4 + 1803 * q^5 + 5693 * q^6 + 10099 * q^7 + 23151 * q^8 + 61060 * q^9 + 84505 * q^10 + 121746 * q^11 + 113389 * q^12 + 142805 * q^13 + 8475 * q^14 + 105973 * q^15 - 322463 * q^16 - 495669 * q^17 - 656228 * q^18 - 840738 * q^19 - 1595607 * q^20 - 1599467 * q^21 - 2023594 * q^22 - 592152 * q^23 - 2295657 * q^24 + 1670362 * q^25 + 428415 * q^26 + 6847883 * q^27 + 2587955 * q^28 + 10678182 * q^29 + 5491201 * q^30 + 12885296 * q^31 + 3282927 * q^32 + 17278298 * q^33 - 9934079 * q^34 + 8380731 * q^35 - 20483302 * q^36 + 7171823 * q^37 - 25568814 * q^38 + 4598321 * q^39 - 54359445 * q^40 + 9294012 * q^41 - 69520457 * q^42 + 12831975 * q^43 - 41479074 * q^44 + 26135198 * q^45 - 59319696 * q^46 + 43354215 * q^47 - 86874671 * q^48 + 25249488 * q^49 - 16270770 * q^50 + 16905901 * q^51 + 10310521 * q^52 + 93231780 * q^53 + 58983719 * q^54 + 99448846 * q^55 + 199599225 * q^56 + 90173382 * q^57 + 151020970 * q^58 + 246496182 * q^59 + 90097913 * q^60 - 132232612 * q^61 + 158135724 * q^62 - 416955202 * q^63 + 91019105 * q^64 + 51495483 * q^65 - 323733130 * q^66 - 369388534 * q^67 + 238172073 * q^68 - 579986760 * q^69 - 144857425 * q^70 + 212150457 * q^71 - 415774278 * q^72 - 252729806 * q^73 + 192105957 * q^74 - 752457788 * q^75 - 953775990 * q^76 + 449666118 * q^77 + 162597773 * q^78 - 1247271728 * q^79 + 900649725 * q^80 - 317713115 * q^81 + 169559388 * q^82 + 1696894296 * q^83 + 1247983739 * q^84 - 775363765 * q^85 + 3291621459 * q^86 - 614530466 * q^87 - 220227222 * q^88 - 753854382 * q^89 + 2296265882 * q^90 + 288437539 * q^91 + 13876128 * q^92 - 892784668 * q^93 + 272071215 * q^94 + 1442632962 * q^95 + 930612847 * q^96 + 3824606 * q^97 + 1570614816 * q^98 + 3016199848 * q^99

Introduction

L-functions

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