LMFDB - Embedded newform 13.10.a.b.1.2

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			1.2
Root			$-24.3176$ 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)

$f(q)$	$=$	$q-21.3176 q^{2} -195.094 q^{3} -57.5590 q^{4} -1277.14 q^{5} +4158.93 q^{6} -2277.98 q^{7} +12141.6 q^{8} +18378.5 q^{9} +O(q^{10})$	\(q-21.3176 q^{2} -195.094 q^{3} -57.5590 q^{4} -1277.14 q^{5} +4158.93 q^{6} -2277.98 q^{7} +12141.6 q^{8} +18378.5 q^{9} +27225.6 q^{10} -7177.94 q^{11} +11229.4 q^{12} +28561.0 q^{13} +48561.1 q^{14} +249162. q^{15} -229361. q^{16} -447890. q^{17} -391786. q^{18} -528333. q^{19} +73510.8 q^{20} +444419. q^{21} +153017. q^{22} +2.24354e6 q^{23} -2.36876e6 q^{24} -322041. q^{25} -608853. q^{26} +254496. q^{27} +131118. q^{28} +5.98542e6 q^{29} -5.31153e6 q^{30} +169630. q^{31} -1.32709e6 q^{32} +1.40037e6 q^{33} +9.54795e6 q^{34} +2.90930e6 q^{35} -1.05785e6 q^{36} +1.26336e7 q^{37} +1.12628e7 q^{38} -5.57207e6 q^{39} -1.55066e7 q^{40} -2.76549e7 q^{41} -9.47396e6 q^{42} -2.27606e7 q^{43} +413155. q^{44} -2.34719e7 q^{45} -4.78270e7 q^{46} +5.32103e7 q^{47} +4.47468e7 q^{48} -3.51644e7 q^{49} +6.86516e6 q^{50} +8.73804e7 q^{51} -1.64394e6 q^{52} +3.18756e7 q^{53} -5.42525e6 q^{54} +9.16722e6 q^{55} -2.76584e7 q^{56} +1.03074e8 q^{57} -1.27595e8 q^{58} +1.14800e8 q^{59} -1.43415e7 q^{60} -7.80352e7 q^{61} -3.61610e6 q^{62} -4.18659e7 q^{63} +1.45723e8 q^{64} -3.64764e7 q^{65} -2.98526e7 q^{66} +8.40538e7 q^{67} +2.57801e7 q^{68} -4.37700e8 q^{69} -6.20193e7 q^{70} +1.25752e8 q^{71} +2.23145e8 q^{72} -1.88250e8 q^{73} -2.69318e8 q^{74} +6.28282e7 q^{75} +3.04103e7 q^{76} +1.63512e7 q^{77} +1.18783e8 q^{78} -4.28673e8 q^{79} +2.92926e8 q^{80} -4.11395e8 q^{81} +5.89536e8 q^{82} +2.43067e8 q^{83} -2.55803e7 q^{84} +5.72018e8 q^{85} +4.85202e8 q^{86} -1.16772e9 q^{87} -8.71520e7 q^{88} +2.92716e8 q^{89} +5.00366e8 q^{90} -6.50614e7 q^{91} -1.29136e8 q^{92} -3.30937e7 q^{93} -1.13432e9 q^{94} +6.74754e8 q^{95} +2.58908e8 q^{96} +1.14275e9 q^{97} +7.49622e8 q^{98} -1.31920e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−21.3176	−0.942115	−0.471057	−	0.882103i	$-0.656128\pi$
$2$	−21.3176	−0.942115	−0.471057	+	0.882103i	$0.656128\pi$
$3$	−195.094	−1.39058	−0.695292	−	0.718727i	$-0.744725\pi$
$3$	−195.094	−1.39058	−0.695292	+	0.718727i	$0.744725\pi$
$4$	−57.5590	−0.112420
$5$	−1277.14	−0.913846	−0.456923	−	0.889506i	$-0.651049\pi$
$5$	−1277.14	−0.913846	−0.456923	+	0.889506i	$0.651049\pi$
$6$	4158.93	1.31009
$7$	−2277.98	−0.358599	−0.179299	−	0.983795i	$-0.557383\pi$
$7$	−2277.98	−0.358599	−0.179299	+	0.983795i	$0.557383\pi$
$8$	12141.6	1.04803
$9$	18378.5	0.933725
$10$	27225.6	0.860948
$11$	−7177.94	−0.147820	−0.0739099	−	0.997265i	$-0.523548\pi$
$11$	−7177.94	−0.147820	−0.0739099	+	0.997265i	$0.523548\pi$
$12$	11229.4	0.156329
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	48561.1	0.337841
$15$	249162.	1.27078
$16$	−229361.	−0.874942
$17$	−447890.	−1.30062	−0.650311	−	0.759668i	$-0.725361\pi$
$17$	−447890.	−1.30062	−0.650311	+	0.759668i	$0.725361\pi$
$18$	−391786.	−0.879677
$19$	−528333.	−0.930071	−0.465036	−	0.885292i	$-0.653959\pi$
$19$	−528333.	−0.930071	−0.465036	+	0.885292i	$0.653959\pi$
$20$	73510.8	0.102734
$21$	444419.	0.498662
$22$	153017.	0.139263
$23$	2.24354e6	1.67170	0.835851	−	0.548957i	$-0.184975\pi$
$23$	2.24354e6	1.67170	0.835851	+	0.548957i	$0.184975\pi$
$24$	−2.36876e6	−1.45737
$25$	−322041.	−0.164885
$26$	−608853.	−0.261296
$27$	254496.	0.0921603
$28$	131118.	0.0403136
$29$	5.98542e6	1.57146	0.785730	−	0.618569i	$-0.212287\pi$
$29$	5.98542e6	1.57146	0.785730	+	0.618569i	$0.212287\pi$
$30$	−5.31153e6	−1.19722
$31$	169630.	0.0329894	0.0164947	−	0.999864i	$-0.494749\pi$
$31$	169630.	0.0329894	0.0164947	+	0.999864i	$0.494749\pi$
$32$	−1.32709e6	−0.223731
$33$	1.40037e6	0.205556
$34$	9.54795e6	1.22534
$35$	2.90930e6	0.327704
$36$	−1.05785e6	−0.104969
$37$	1.26336e7	1.10820	0.554100	−	0.832450i	$-0.313062\pi$
$37$	1.26336e7	1.10820	0.554100	+	0.832450i	$0.313062\pi$
$38$	1.12628e7	0.876234
$39$	−5.57207e6	−0.385679
$40$	−1.55066e7	−0.957736
$41$	−2.76549e7	−1.52843	−0.764213	−	0.644964i	$-0.776872\pi$
$41$	−2.76549e7	−1.52843	−0.764213	+	0.644964i	$0.776872\pi$
$42$	−9.47396e6	−0.469796
$43$	−2.27606e7	−1.01526	−0.507628	−	0.861576i	$-0.669478\pi$
$43$	−2.27606e7	−1.01526	−0.507628	+	0.861576i	$0.669478\pi$
$44$	413155.	0.0166179
$45$	−2.34719e7	−0.853281
$46$	−4.78270e7	−1.57493
$47$	5.32103e7	1.59058	0.795289	−	0.606230i	$-0.207319\pi$
$47$	5.32103e7	1.59058	0.795289	+	0.606230i	$0.207319\pi$
$48$	4.47468e7	1.21668
$49$	−3.51644e7	−0.871407
$50$	6.86516e6	0.155341
$51$	8.73804e7	1.80862
$52$	−1.64394e6	−0.0311797
$53$	3.18756e7	0.554904	0.277452	−	0.960740i	$-0.410510\pi$
$53$	3.18756e7	0.554904	0.277452	+	0.960740i	$0.410510\pi$
$54$	−5.42525e6	−0.0868256
$55$	9.16722e6	0.135085
$56$	−2.76584e7	−0.375821
$57$	1.03074e8	1.29334
$58$	−1.27595e8	−1.48050
$59$	1.14800e8	1.23341	0.616705	−	0.787194i	$-0.288467\pi$
$59$	1.14800e8	1.23341	0.616705	+	0.787194i	$0.288467\pi$
$60$	−1.43415e7	−0.142861
$61$	−7.80352e7	−0.721616	−0.360808	−	0.932640i	$-0.617499\pi$
$61$	−7.80352e7	−0.721616	−0.360808	+	0.932640i	$0.617499\pi$
$62$	−3.61610e6	−0.0310798
$63$	−4.18659e7	−0.334833
$64$	1.45723e8	1.08572
$65$	−3.64764e7	−0.253455
$66$	−2.98526e7	−0.193657
$67$	8.40538e7	0.509590	0.254795	−	0.966995i	$-0.417992\pi$
$67$	8.40538e7	0.509590	0.254795	+	0.966995i	$0.417992\pi$
$68$	2.57801e7	0.146216
$69$	−4.37700e8	−2.32464
$70$	−6.20193e7	−0.308735
$71$	1.25752e8	0.587288	0.293644	−	0.955915i	$-0.405132\pi$
$71$	1.25752e8	0.587288	0.293644	+	0.955915i	$0.405132\pi$
$72$	2.23145e8	0.978570
$73$	−1.88250e8	−0.775859	−0.387929	−	0.921689i	$-0.626810\pi$
$73$	−1.88250e8	−0.775859	−0.387929	+	0.921689i	$0.626810\pi$
$74$	−2.69318e8	−1.04405
$75$	6.28282e7	0.229287
$76$	3.04103e7	0.104558
$77$	1.63512e7	0.0530080
$78$	1.18783e8	0.363354
$79$	−4.28673e8	−1.23824	−0.619120	−	0.785297i	$-0.712510\pi$
$79$	−4.28673e8	−1.23824	−0.619120	+	0.785297i	$0.712510\pi$
$80$	2.92926e8	0.799562
$81$	−4.11395e8	−1.06188
$82$	5.89536e8	1.43995
$83$	2.43067e8	0.562180	0.281090	−	0.959681i	$-0.409304\pi$
$83$	2.43067e8	0.562180	0.281090	+	0.959681i	$0.409304\pi$
$84$	−2.55803e7	−0.0560594
$85$	5.72018e8	1.18857
$86$	4.85202e8	0.956488
$87$	−1.16772e9	−2.18525
$88$	−8.71520e7	−0.154919
$89$	2.92716e8	0.494529	0.247265	−	0.968948i	$-0.420468\pi$
$89$	2.92716e8	0.494529	0.247265	+	0.968948i	$0.420468\pi$
$90$	5.00366e8	0.803889
$91$	−6.50614e7	−0.0994573
$92$	−1.29136e8	−0.187932
$93$	−3.30937e7	−0.0458746
$94$	−1.13432e9	−1.49851
$95$	6.74754e8	0.849942
$96$	2.58908e8	0.311117
$97$	1.14275e9	1.31063	0.655313	−	0.755358i	$-0.272537\pi$
$97$	1.14275e9	1.31063	0.655313	+	0.755358i	$0.272537\pi$
$98$	7.49622e8	0.820965
$99$	−1.31920e8	−0.138023
$100$	1.85364e7	0.0185364
$101$	−8.98629e8	−0.859279	−0.429640	−	0.903000i	$-0.641359\pi$
$101$	−8.98629e8	−0.859279	−0.429640	+	0.903000i	$0.641359\pi$
$102$	−1.86274e9	−1.70393
$103$	6.13518e8	0.537106	0.268553	−	0.963265i	$-0.413455\pi$
$103$	6.13518e8	0.537106	0.268553	+	0.963265i	$0.413455\pi$
$104$	3.46777e8	0.290670
$105$	−5.67585e8	−0.455700
$106$	−6.79513e8	−0.522783
$107$	1.46257e9	1.07868	0.539338	−	0.842090i	$-0.318675\pi$
$107$	1.46257e9	1.07868	0.539338	+	0.842090i	$0.318675\pi$
$108$	−1.46485e7	−0.0103607
$109$	7.17715e8	0.487005	0.243502	−	0.969900i	$-0.421704\pi$
$109$	7.17715e8	0.487005	0.243502	+	0.969900i	$0.421704\pi$
$110$	−1.95423e8	−0.127265
$111$	−2.46473e9	−1.54105
$112$	5.22479e8	0.313753
$113$	9.27444e7	0.0535099	0.0267550	−	0.999642i	$-0.491483\pi$
$113$	9.27444e7	0.0535099	0.0267550	+	0.999642i	$0.491483\pi$
$114$	−2.19730e9	−1.21848
$115$	−2.86531e9	−1.52768
$116$	−3.44514e8	−0.176663
$117$	5.24909e8	0.258969
$118$	−2.44726e9	−1.16201
$119$	1.02028e9	0.466401
$120$	3.02523e9	1.33181
$121$	−2.30642e9	−0.978149
$122$	1.66352e9	0.679845
$123$	5.39529e9	2.12540
$124$	−9.76371e6	−0.00370866
$125$	2.90570e9	1.06453
$126$	8.92481e8	0.315451
$127$	4.40060e9	1.50105	0.750524	−	0.660843i	$-0.229801\pi$
$127$	4.40060e9	1.50105	0.750524	+	0.660843i	$0.229801\pi$
$128$	−2.42700e9	−0.799144
$129$	4.44045e9	1.41180
$130$	7.77589e8	0.238784
$131$	−1.21951e9	−0.361798	−0.180899	−	0.983502i	$-0.557901\pi$
$131$	−1.21951e9	−0.361798	−0.180899	+	0.983502i	$0.557901\pi$
$132$	−8.06038e7	−0.0231086
$133$	1.20353e9	0.333522
$134$	−1.79183e9	−0.480092
$135$	−3.25027e8	−0.0842204
$136$	−5.43812e9	−1.36309
$137$	−6.73258e9	−1.63282	−0.816411	−	0.577472i	$-0.804039\pi$
$137$	−6.73258e9	−1.63282	−0.816411	+	0.577472i	$0.804039\pi$
$138$	9.33073e9	2.19008
$139$	4.12694e8	0.0937695	0.0468847	−	0.998900i	$-0.485071\pi$
$139$	4.12694e8	0.0937695	0.0468847	+	0.998900i	$0.485071\pi$
$140$	−1.67456e8	−0.0368404
$141$	−1.03810e10	−2.21183
$142$	−2.68073e9	−0.553293
$143$	−2.05009e8	−0.0409978
$144$	−4.21531e9	−0.816956
$145$	−7.64421e9	−1.43607
$146$	4.01305e9	0.730948
$147$	6.86035e9	1.21177
$148$	−7.27175e8	−0.124584
$149$	7.17339e9	1.19230	0.596151	−	0.802872i	$-0.296696\pi$
$149$	7.17339e9	1.19230	0.596151	+	0.802872i	$0.296696\pi$
$150$	−1.33935e9	−0.216015
$151$	9.30445e9	1.45645	0.728223	−	0.685340i	$-0.240346\pi$
$151$	9.30445e9	1.45645	0.728223	+	0.685340i	$0.240346\pi$
$152$	−6.41483e9	−0.974740
$153$	−8.23155e9	−1.21442
$154$	−3.48569e8	−0.0499396
$155$	−2.16641e8	−0.0301472
$156$	3.20722e8	0.0433579
$157$	−5.86131e9	−0.769921	−0.384961	−	0.922933i	$-0.625785\pi$
$157$	−5.86131e9	−0.769921	−0.384961	+	0.922933i	$0.625785\pi$
$158$	9.13830e9	1.16656
$159$	−6.21873e9	−0.771640
$160$	1.69488e9	0.204456
$161$	−5.11074e9	−0.599470
$162$	8.76996e9	1.00041
$163$	1.60676e10	1.78282	0.891409	−	0.453199i	$-0.149717\pi$
$163$	1.60676e10	1.78282	0.891409	+	0.453199i	$0.149717\pi$
$164$	1.59179e9	0.171825
$165$	−1.78847e9	−0.187847
$166$	−5.18162e9	−0.529638
$167$	−1.49042e9	−0.148281	−0.0741404	−	0.997248i	$-0.523621\pi$
$167$	−1.49042e9	−0.148281	−0.0741404	+	0.997248i	$0.523621\pi$
$168$	5.39598e9	0.522611
$169$	8.15731e8	0.0769231
$170$	−1.21941e10	−1.11977
$171$	−9.70997e9	−0.868431
$172$	1.31008e9	0.114135
$173$	−6.62250e9	−0.562101	−0.281050	−	0.959693i	$-0.590683\pi$
$173$	−6.62250e9	−0.562101	−0.281050	+	0.959693i	$0.590683\pi$
$174$	2.48930e10	2.05876
$175$	7.33604e8	0.0591276
$176$	1.64634e9	0.129334
$177$	−2.23967e10	−1.71516
$178$	−6.24002e9	−0.465903
$179$	1.41019e10	1.02669	0.513344	−	0.858183i	$-0.328406\pi$
$179$	1.41019e10	1.02669	0.513344	+	0.858183i	$0.328406\pi$
$180$	1.35102e9	0.0959257
$181$	2.38898e10	1.65447	0.827234	−	0.561857i	$-0.189913\pi$
$181$	2.38898e10	1.65447	0.827234	+	0.561857i	$0.189913\pi$
$182$	1.38695e9	0.0937002
$183$	1.52242e10	1.00347
$184$	2.72403e10	1.75199
$185$	−1.61348e10	−1.01272
$186$	7.05479e8	0.0432191
$187$	3.21493e9	0.192258
$188$	−3.06273e9	−0.178813
$189$	−5.79737e8	−0.0330486
$190$	−1.43842e10	−0.800743
$191$	−2.32674e10	−1.26502	−0.632509	−	0.774553i	$-0.717975\pi$
$191$	−2.32674e10	−1.26502	−0.632509	+	0.774553i	$0.717975\pi$
$192$	−2.84297e10	−1.50979
$193$	8.87539e9	0.460447	0.230224	−	0.973138i	$-0.426054\pi$
$193$	8.87539e9	0.460447	0.230224	+	0.973138i	$0.426054\pi$
$194$	−2.43607e10	−1.23476
$195$	7.11631e9	0.352451
$196$	2.02403e9	0.0979634
$197$	−9.96936e9	−0.471595	−0.235798	−	0.971802i	$-0.575770\pi$
$197$	−9.96936e9	−0.471595	−0.235798	+	0.971802i	$0.575770\pi$
$198$	2.81222e9	0.130034
$199$	−5.92044e9	−0.267618	−0.133809	−	0.991007i	$-0.542721\pi$
$199$	−5.92044e9	−0.267618	−0.133809	+	0.991007i	$0.542721\pi$
$200$	−3.91011e9	−0.172804
$201$	−1.63984e10	−0.708628
$202$	1.91566e10	0.809540
$203$	−1.36347e10	−0.563524
$204$	−5.02953e9	−0.203325
$205$	3.53191e10	1.39675
$206$	−1.30787e10	−0.506015
$207$	4.12330e10	1.56091
$208$	−6.55077e9	−0.242665
$209$	3.79234e9	0.137483
$210$	1.20996e10	0.429322
$211$	−3.18290e10	−1.10548	−0.552741	−	0.833353i	$-0.686418\pi$
$211$	−3.18290e10	−1.10548	−0.552741	+	0.833353i	$0.686418\pi$
$212$	−1.83473e9	−0.0623822
$213$	−2.45334e10	−0.816674
$214$	−3.11786e10	−1.01624
$215$	2.90685e10	0.927788
$216$	3.09000e9	0.0965865
$217$	−3.86413e8	−0.0118300
$218$	−1.53000e10	−0.458814
$219$	3.67264e10	1.07890
$220$	−5.27656e8	−0.0151862
$221$	−1.27922e10	−0.360728
$222$	5.25422e10	1.45184
$223$	−2.33567e10	−0.632470	−0.316235	−	0.948681i	$-0.602419\pi$
$223$	−2.33567e10	−0.632470	−0.316235	+	0.948681i	$0.602419\pi$
$224$	3.02309e9	0.0802298
$225$	−5.91865e9	−0.153958
$226$	−1.97709e9	−0.0504125
$227$	2.96928e10	0.742223	0.371112	−	0.928588i	$-0.378977\pi$
$227$	2.96928e10	0.742223	0.371112	+	0.928588i	$0.378977\pi$
$228$	−5.93285e9	−0.145397
$229$	4.24937e10	1.02109	0.510546	−	0.859850i	$-0.329443\pi$
$229$	4.24937e10	1.02109	0.510546	+	0.859850i	$0.329443\pi$
$230$	6.10817e10	1.43925
$231$	−3.19001e9	−0.0737121
$232$	7.26728e10	1.64693
$233$	−3.84693e10	−0.855092	−0.427546	−	0.903994i	$-0.640622\pi$
$233$	−3.84693e10	−0.855092	−0.427546	+	0.903994i	$0.640622\pi$
$234$	−1.11898e10	−0.243978
$235$	−6.79569e10	−1.45354
$236$	−6.60776e9	−0.138660
$237$	8.36314e10	1.72188
$238$	−2.17500e10	−0.439403
$239$	−1.98946e10	−0.394407	−0.197203	−	0.980363i	$-0.563186\pi$
$239$	−1.98946e10	−0.394407	−0.197203	+	0.980363i	$0.563186\pi$
$240$	−5.71479e10	−1.11186
$241$	−5.31240e10	−1.01441	−0.507206	−	0.861825i	$-0.669322\pi$
$241$	−5.31240e10	−1.01441	−0.507206	+	0.861825i	$0.669322\pi$
$242$	4.91675e10	0.921529
$243$	7.52513e10	1.38448
$244$	4.49162e9	0.0811240
$245$	4.49098e10	0.796332
$246$	−1.15015e11	−2.00238
$247$	−1.50897e10	−0.257955
$248$	2.05958e9	0.0345738
$249$	−4.74209e10	−0.781758
$250$	−6.19427e10	−1.00291
$251$	1.26269e10	0.200801	0.100400	−	0.994947i	$-0.467988\pi$
$251$	1.26269e10	0.200801	0.100400	+	0.994947i	$0.467988\pi$
$252$	2.40976e9	0.0376418
$253$	−1.61040e10	−0.247111
$254$	−9.38102e10	−1.41416
$255$	−1.11597e11	−1.65280
$256$	−2.28724e10	−0.332837
$257$	1.11000e11	1.58717	0.793583	−	0.608461i	$-0.208213\pi$
$257$	1.11000e11	1.58717	0.793583	+	0.608461i	$0.208213\pi$
$258$	−9.46598e10	−1.33008
$259$	−2.87790e10	−0.397399
$260$	2.09954e9	0.0284934
$261$	1.10003e11	1.46731
$262$	2.59971e10	0.340855
$263$	7.01020e10	0.903503	0.451752	−	0.892144i	$-0.350799\pi$
$263$	7.01020e10	0.903503	0.451752	+	0.892144i	$0.350799\pi$
$264$	1.70028e10	0.215428
$265$	−4.07096e10	−0.507097
$266$	−2.56564e10	−0.314216
$267$	−5.71071e10	−0.687685
$268$	−4.83805e9	−0.0572880
$269$	7.41364e10	0.863269	0.431635	−	0.902049i	$-0.357937\pi$
$269$	7.41364e10	0.863269	0.431635	+	0.902049i	$0.357937\pi$
$270$	6.92880e9	0.0793453
$271$	8.92477e10	1.00516	0.502580	−	0.864531i	$-0.332384\pi$
$271$	8.92477e10	1.00516	0.502580	+	0.864531i	$0.332384\pi$
$272$	1.02728e11	1.13797
$273$	1.26931e10	0.138304
$274$	1.43523e11	1.53831
$275$	2.31159e9	0.0243733
$276$	2.51936e10	0.261336
$277$	−6.68313e10	−0.682057	−0.341028	−	0.940053i	$-0.610775\pi$
$277$	−6.68313e10	−0.682057	−0.341028	+	0.940053i	$0.610775\pi$
$278$	−8.79765e9	−0.0883416
$279$	3.11754e9	0.0308031
$280$	3.53236e10	0.343443
$281$	−8.13670e10	−0.778520	−0.389260	−	0.921128i	$-0.627269\pi$
$281$	−8.13670e10	−0.778520	−0.389260	+	0.921128i	$0.627269\pi$
$282$	2.21298e11	2.08380
$283$	−1.19236e11	−1.10502	−0.552508	−	0.833507i	$-0.686329\pi$
$283$	−1.19236e11	−1.10502	−0.552508	+	0.833507i	$0.686329\pi$
$284$	−7.23814e9	−0.0660229
$285$	−1.31640e11	−1.18192
$286$	4.37031e9	0.0386247
$287$	6.29972e10	0.548091
$288$	−2.43900e10	−0.208904
$289$	8.20174e10	0.691617
$290$	1.62956e11	1.35295
$291$	−2.22943e11	−1.82254
$292$	1.08355e10	0.0872219
$293$	−6.95594e10	−0.551381	−0.275690	−	0.961246i	$-0.588906\pi$
$293$	−6.95594e10	−0.551381	−0.275690	+	0.961246i	$0.588906\pi$
$294$	−1.46246e11	−1.14162
$295$	−1.46615e11	−1.12715
$296$	1.53392e11	1.16142
$297$	−1.82676e9	−0.0136231
$298$	−1.52920e11	−1.12328
$299$	6.40778e10	0.463647
$300$	−3.61633e9	−0.0257764
$301$	5.18482e10	0.364069
$302$	−1.98349e11	−1.37214
$303$	1.75317e11	1.19490
$304$	1.21179e11	0.813759
$305$	9.96618e10	0.659446
$306$	1.75477e11	1.14413
$307$	−4.02660e10	−0.258711	−0.129356	−	0.991598i	$-0.541291\pi$
$307$	−4.02660e10	−0.258711	−0.129356	+	0.991598i	$0.541291\pi$
$308$	−9.41157e8	−0.00595915
$309$	−1.19693e11	−0.746891
$310$	4.61827e9	0.0284022
$311$	−1.78556e11	−1.08231	−0.541157	−	0.840921i	$-0.682014\pi$
$311$	−1.78556e11	−1.08231	−0.541157	+	0.840921i	$0.682014\pi$
$312$	−6.76541e10	−0.404202
$313$	9.44550e9	0.0556257	0.0278128	−	0.999613i	$-0.491146\pi$
$313$	9.44550e9	0.0556257	0.0278128	+	0.999613i	$0.491146\pi$
$314$	1.24949e11	0.725354
$315$	5.34685e10	0.305985
$316$	2.46740e10	0.139203
$317$	5.42593e10	0.301792	0.150896	−	0.988550i	$-0.451784\pi$
$317$	5.42593e10	0.301792	0.150896	+	0.988550i	$0.451784\pi$
$318$	1.32569e11	0.726974
$319$	−4.29630e10	−0.232293
$320$	−1.86109e11	−0.992183
$321$	−2.85339e11	−1.49999
$322$	1.08949e11	0.564769
$323$	2.36635e11	1.20967
$324$	2.36795e10	0.119377
$325$	−9.19783e9	−0.0457309
$326$	−3.42523e11	−1.67962
$327$	−1.40022e11	−0.677221
$328$	−3.35776e11	−1.60183
$329$	−1.21212e11	−0.570379
$330$	3.81259e10	0.176973
$331$	6.66790e10	0.305325	0.152663	−	0.988278i	$-0.451215\pi$
$331$	6.66790e10	0.305325	0.152663	+	0.988278i	$0.451215\pi$
$332$	−1.39907e10	−0.0632001
$333$	2.32186e11	1.03476
$334$	3.17722e10	0.139697
$335$	−1.07348e11	−0.465687
$336$	−1.01932e11	−0.436300
$337$	2.13457e11	0.901522	0.450761	−	0.892645i	$-0.351153\pi$
$337$	2.13457e11	0.901522	0.450761	+	0.892645i	$0.351153\pi$
$338$	−1.73894e10	−0.0724704
$339$	−1.80938e10	−0.0744101
$340$	−3.29247e10	−0.133619
$341$	−1.21759e9	−0.00487649
$342$	2.06994e11	0.818162
$343$	1.72028e11	0.671084
$344$	−2.76351e11	−1.06402
$345$	5.59004e11	2.12437
$346$	1.41176e11	0.529564
$347$	−9.49978e10	−0.351748	−0.175874	−	0.984413i	$-0.556275\pi$
$347$	−9.49978e10	−0.351748	−0.175874	+	0.984413i	$0.556275\pi$
$348$	6.72126e10	0.245665
$349$	2.52647e11	0.911590	0.455795	−	0.890085i	$-0.349355\pi$
$349$	2.52647e11	0.911590	0.455795	+	0.890085i	$0.349355\pi$
$350$	−1.56387e10	−0.0557050
$351$	7.26866e9	0.0255607
$352$	9.52580e9	0.0330719
$353$	4.50376e11	1.54379	0.771896	−	0.635749i	$-0.219309\pi$
$353$	4.50376e11	1.54379	0.771896	+	0.635749i	$0.219309\pi$
$354$	4.77445e11	1.61588
$355$	−1.60602e11	−0.536691
$356$	−1.68485e10	−0.0555949
$357$	−1.99051e11	−0.648570
$358$	−3.00619e11	−0.967258
$359$	3.93740e11	1.25108	0.625539	−	0.780193i	$-0.284879\pi$
$359$	3.93740e11	1.25108	0.625539	+	0.780193i	$0.284879\pi$
$360$	−2.84988e11	−0.894262
$361$	−4.35522e10	−0.134967
$362$	−5.09273e11	−1.55870
$363$	4.49969e11	1.36020
$364$	3.74486e9	0.0111810
$365$	2.40422e11	0.709015
$366$	−3.24543e11	−0.945382
$367$	−2.26305e11	−0.651173	−0.325586	−	0.945512i	$-0.605562\pi$
$367$	−2.26305e11	−0.651173	−0.325586	+	0.945512i	$0.605562\pi$
$368$	−5.14580e11	−1.46264
$369$	−5.08255e11	−1.42713
$370$	3.43956e11	0.954103
$371$	−7.26120e10	−0.198988
$372$	1.90484e9	0.00515721
$373$	4.75023e11	1.27065	0.635323	−	0.772246i	$-0.280867\pi$
$373$	4.75023e11	1.27065	0.635323	+	0.772246i	$0.280867\pi$
$374$	−6.85346e10	−0.181129
$375$	−5.66884e11	−1.48031
$376$	6.46060e11	1.66697
$377$	1.70950e11	0.435845
$378$	1.23586e10	0.0311355
$379$	−1.67293e11	−0.416486	−0.208243	−	0.978077i	$-0.566775\pi$
$379$	−1.67293e11	−0.416486	−0.208243	+	0.978077i	$0.566775\pi$
$380$	−3.88381e10	−0.0955504
$381$	−8.58528e11	−2.08733
$382$	4.96005e11	1.19179
$383$	−5.36589e11	−1.27423	−0.637114	−	0.770769i	$-0.719872\pi$
$383$	−5.36589e11	−1.27423	−0.637114	+	0.770769i	$0.719872\pi$
$384$	4.73492e11	1.11128
$385$	−2.08827e10	−0.0484411
$386$	−1.89202e11	−0.433794
$387$	−4.18306e11	−0.947971
$388$	−6.57755e10	−0.147340
$389$	5.95613e11	1.31884	0.659418	−	0.751776i	$-0.270803\pi$
$389$	5.95613e11	1.31884	0.659418	+	0.751776i	$0.270803\pi$
$390$	−1.51703e11	−0.332049
$391$	−1.00486e12	−2.17425
$392$	−4.26954e11	−0.913258
$393$	2.37919e11	0.503110
$394$	2.12523e11	0.444297
$395$	5.47475e11	1.13156
$396$	7.59317e9	0.0155165
$397$	−6.68797e11	−1.35125	−0.675627	−	0.737243i	$-0.736127\pi$
$397$	−6.68797e11	−1.35125	−0.675627	+	0.737243i	$0.736127\pi$
$398$	1.26210e11	0.252127
$399$	−2.34801e11	−0.463791
$400$	7.38637e10	0.144265
$401$	4.27579e11	0.825785	0.412892	−	0.910780i	$-0.364519\pi$
$401$	4.27579e11	0.825785	0.412892	+	0.910780i	$0.364519\pi$
$402$	3.49574e11	0.667609
$403$	4.84480e9	0.00914962
$404$	5.17241e10	0.0966000
$405$	5.25408e11	0.970397
$406$	2.90658e11	0.530904
$407$	−9.06830e10	−0.163814
$408$	1.06094e12	1.89549
$409$	−4.37893e10	−0.0773772	−0.0386886	−	0.999251i	$-0.512318\pi$
$409$	−4.37893e10	−0.0773772	−0.0386886	+	0.999251i	$0.512318\pi$
$410$	−7.52919e11	−1.31589
$411$	1.31348e12	2.27058
$412$	−3.53135e10	−0.0603813
$413$	−2.61512e11	−0.442299
$414$	−8.78989e11	−1.47056
$415$	−3.10431e11	−0.513746
$416$	−3.79031e10	−0.0620519
$417$	−8.05139e10	−0.130394
$418$	−8.08437e10	−0.129525
$419$	−1.14243e11	−0.181079	−0.0905395	−	0.995893i	$-0.528859\pi$
$419$	−1.14243e11	−0.181079	−0.0905395	+	0.995893i	$0.528859\pi$
$420$	3.26696e10	0.0512297
$421$	−5.06520e11	−0.785828	−0.392914	−	0.919575i	$-0.628533\pi$
$421$	−5.06520e11	−0.785828	−0.392914	+	0.919575i	$0.628533\pi$
$422$	6.78518e11	1.04149
$423$	9.77926e11	1.48516
$424$	3.87023e11	0.581554
$425$	1.44239e11	0.214453
$426$	5.22993e11	0.769401
$427$	1.77763e11	0.258770
$428$	−8.41842e10	−0.121264
$429$	3.99960e10	0.0570110
$430$	−6.19670e11	−0.874083
$431$	−1.32605e11	−0.185103	−0.0925513	−	0.995708i	$-0.529502\pi$
$431$	−1.32605e11	−0.185103	−0.0925513	+	0.995708i	$0.529502\pi$
$432$	−5.83714e10	−0.0806350
$433$	1.21346e12	1.65894	0.829469	−	0.558553i	$-0.188643\pi$
$433$	1.21346e12	1.65894	0.829469	+	0.558553i	$0.188643\pi$
$434$	8.23741e9	0.0111452
$435$	1.49134e12	1.99698
$436$	−4.13110e10	−0.0547490
$437$	−1.18534e12	−1.55480
$438$	−7.82920e11	−1.01644
$439$	−7.26961e11	−0.934159	−0.467079	−	0.884215i	$-0.654694\pi$
$439$	−7.26961e11	−0.934159	−0.467079	+	0.884215i	$0.654694\pi$
$440$	1.11305e11	0.141572
$441$	−6.46270e11	−0.813655
$442$	2.72699e11	0.339847
$443$	−1.02161e12	−1.26028	−0.630142	−	0.776480i	$-0.717003\pi$
$443$	−1.02161e12	−1.26028	−0.630142	+	0.776480i	$0.717003\pi$
$444$	1.41867e11	0.173244
$445$	−3.73840e11	−0.451924
$446$	4.97910e11	0.595859
$447$	−1.39948e12	−1.65800
$448$	−3.31954e11	−0.389339
$449$	5.91722e11	0.687083	0.343542	−	0.939137i	$-0.388373\pi$
$449$	5.91722e11	0.687083	0.343542	+	0.939137i	$0.388373\pi$
$450$	1.26171e11	0.145046
$451$	1.98505e11	0.225932
$452$	−5.33827e9	−0.00601558
$453$	−1.81524e12	−2.02531
$454$	−6.32979e11	−0.699259
$455$	8.30924e10	0.0908887
$456$	1.25149e12	1.35546
$457$	−8.30664e11	−0.890845	−0.445423	−	0.895320i	$-0.646947\pi$
$457$	−8.30664e11	−0.890845	−0.445423	+	0.895320i	$0.646947\pi$
$458$	−9.05865e11	−0.961986
$459$	−1.13986e11	−0.119866
$460$	1.64924e11	0.171741
$461$	8.73246e11	0.900497	0.450249	−	0.892903i	$-0.351335\pi$
$461$	8.73246e11	0.900497	0.450249	+	0.892903i	$0.351335\pi$
$462$	6.80035e10	0.0694452
$463$	7.70415e11	0.779130	0.389565	−	0.920999i	$-0.372625\pi$
$463$	7.70415e11	0.779130	0.389565	+	0.920999i	$0.372625\pi$
$464$	−1.37282e12	−1.37494
$465$	4.22652e10	0.0419223
$466$	8.20074e11	0.805595
$467$	4.50995e11	0.438779	0.219390	−	0.975637i	$-0.429593\pi$
$467$	4.50995e11	0.438779	0.219390	+	0.975637i	$0.429593\pi$
$468$	−3.02132e10	−0.0291132
$469$	−1.91473e11	−0.182738
$470$	1.44868e12	1.36940
$471$	1.14350e12	1.07064
$472$	1.39386e12	1.29265
$473$	1.63374e11	0.150075
$474$	−1.78282e12	−1.62221
$475$	1.70145e11	0.153355
$476$	−5.87265e10	−0.0524327
$477$	5.85827e11	0.518128
$478$	4.24105e11	0.371576
$479$	−5.26966e11	−0.457376	−0.228688	−	0.973500i	$-0.573444\pi$
$479$	−5.26966e11	−0.457376	−0.228688	+	0.973500i	$0.573444\pi$
$480$	−3.30661e11	−0.284313
$481$	3.60827e11	0.307360
$482$	1.13248e12	0.955692
$483$	9.97072e11	0.833613
$484$	1.32755e11	0.109963
$485$	−1.45945e12	−1.19771
$486$	−1.60418e12	−1.30434
$487$	1.88076e12	1.51514	0.757570	−	0.652754i	$-0.226386\pi$
$487$	1.88076e12	1.51514	0.757570	+	0.652754i	$0.226386\pi$
$488$	−9.47475e11	−0.756273
$489$	−3.13469e12	−2.47916
$490$	−9.57371e11	−0.750236
$491$	1.68889e12	1.31140	0.655699	−	0.755022i	$-0.272374\pi$
$491$	1.68889e12	1.31140	0.655699	+	0.755022i	$0.272374\pi$
$492$	−3.10547e11	−0.238938
$493$	−2.68081e12	−2.04388
$494$	3.21677e11	0.243024
$495$	1.68480e11	0.126132
$496$	−3.89064e10	−0.0288638
$497$	−2.86460e11	−0.210601
$498$	1.01090e12	0.736506
$499$	1.60699e12	1.16027	0.580137	−	0.814519i	$-0.302999\pi$
$499$	1.60699e12	1.16027	0.580137	+	0.814519i	$0.302999\pi$
$500$	−1.67249e11	−0.119674
$501$	2.90772e11	0.206197
$502$	−2.69176e11	−0.189177
$503$	2.73565e12	1.90548	0.952740	−	0.303786i	$-0.0982507\pi$
$503$	2.73565e12	1.90548	0.952740	+	0.303786i	$0.0982507\pi$
$504$	−5.08321e11	−0.350914
$505$	1.14767e12	0.785249
$506$	3.43299e11	0.232807
$507$	−1.59144e11	−0.106968
$508$	−2.53294e11	−0.168748
$509$	7.49256e11	0.494766	0.247383	−	0.968918i	$-0.420429\pi$
$509$	7.49256e11	0.494766	0.247383	+	0.968918i	$0.420429\pi$
$510$	2.37898e12	1.55713
$511$	4.28830e11	0.278222
$512$	1.73021e12	1.11271
$513$	−1.34459e11	−0.0857157
$514$	−2.36625e12	−1.49529
$515$	−7.83548e11	−0.490832
$516$	−2.55588e11	−0.158714
$517$	−3.81940e11	−0.235119
$518$	6.13500e11	0.374396
$519$	1.29201e12	0.781649
$520$	−4.42883e11	−0.265628
$521$	1.07862e12	0.641355	0.320678	−	0.947188i	$-0.396089\pi$
$521$	1.07862e12	0.641355	0.320678	+	0.947188i	$0.396089\pi$
$522$	−2.34501e12	−1.38238
$523$	−2.69236e12	−1.57353	−0.786765	−	0.617253i	$-0.788246\pi$
$523$	−2.69236e12	−1.57353	−0.786765	+	0.617253i	$0.788246\pi$
$524$	7.01939e10	0.0406732
$525$	−1.43121e11	−0.0822219
$526$	−1.49441e12	−0.851204
$527$	−7.59755e10	−0.0429067
$528$	−3.21190e11	−0.179850
$529$	3.23232e12	1.79459
$530$	8.67832e11	0.477743
$531$	2.10985e12	1.15167
$532$	−6.92740e10	−0.0374945
$533$	−7.89851e11	−0.423909
$534$	1.21739e12	0.647878
$535$	−1.86791e12	−0.985743
$536$	1.02055e12	0.534064
$537$	−2.75119e12	−1.42770
$538$	−1.58041e12	−0.813299
$539$	2.52408e11	0.128811
$540$	1.87082e10	0.00946804
$541$	1.94584e12	0.976604	0.488302	−	0.872675i	$-0.337616\pi$
$541$	1.94584e12	0.976604	0.488302	+	0.872675i	$0.337616\pi$
$542$	−1.90255e12	−0.946976
$543$	−4.66074e12	−2.30068
$544$	5.94392e11	0.290990
$545$	−9.16622e11	−0.445047
$546$	−2.70586e11	−0.130298
$547$	−7.49274e11	−0.357847	−0.178924	−	0.983863i	$-0.557261\pi$
$547$	−7.49274e11	−0.357847	−0.178924	+	0.983863i	$0.557261\pi$
$548$	3.87520e11	0.183562
$549$	−1.43417e12	−0.673791
$550$	−4.92777e10	−0.0229625
$551$	−3.16229e12	−1.46157
$552$	−5.31440e12	−2.43629
$553$	9.76509e11	0.444031
$554$	1.42468e12	0.642576
$555$	3.14780e12	1.40828
$556$	−2.37542e10	−0.0105415
$557$	2.43252e12	1.07080	0.535399	−	0.844599i	$-0.320161\pi$
$557$	2.43252e12	1.07080	0.535399	+	0.844599i	$0.320161\pi$
$558$	−6.64586e10	−0.0290200
$559$	−6.50066e11	−0.281581
$560$	−6.67278e11	−0.286722
$561$	−6.27212e11	−0.267351
$562$	1.73455e12	0.733455
$563$	−2.26566e12	−0.950401	−0.475200	−	0.879878i	$-0.657624\pi$
$563$	−2.26566e12	−0.950401	−0.475200	+	0.879878i	$0.657624\pi$
$564$	5.97518e11	0.248654
$565$	−1.18447e11	−0.0488999
$566$	2.54183e12	1.04105
$567$	9.37149e11	0.380789
$568$	1.52683e12	0.615494
$569$	4.39567e12	1.75800	0.879002	−	0.476817i	$-0.158210\pi$
$569$	4.39567e12	1.75800	0.879002	+	0.476817i	$0.158210\pi$
$570$	2.80626e12	1.11350
$571$	2.81010e12	1.10626	0.553132	−	0.833094i	$-0.313433\pi$
$571$	2.81010e12	1.10626	0.553132	+	0.833094i	$0.313433\pi$
$572$	1.18001e10	0.00460897
$573$	4.53931e12	1.75912
$574$	−1.34295e12	−0.516365
$575$	−7.22513e11	−0.275639
$576$	2.67818e12	1.01377
$577$	−3.06576e12	−1.15146	−0.575728	−	0.817642i	$-0.695281\pi$
$577$	−3.06576e12	−1.15146	−0.575728	+	0.817642i	$0.695281\pi$
$578$	−1.74842e12	−0.651583
$579$	−1.73153e12	−0.640291
$580$	4.39993e11	0.161443
$581$	−5.53702e11	−0.201597
$582$	4.75262e12	1.71704
$583$	−2.28801e11	−0.0820257
$584$	−2.28567e12	−0.813121
$585$	−6.70381e11	−0.236658
$586$	1.48284e12	0.519464
$587$	1.53677e12	0.534240	0.267120	−	0.963663i	$-0.413928\pi$
$587$	1.53677e12	0.534240	0.267120	+	0.963663i	$0.413928\pi$
$588$	−3.94875e11	−0.136226
$589$	−8.96210e10	−0.0306825
$590$	3.12549e12	1.06190
$591$	1.94496e12	0.655793
$592$	−2.89765e12	−0.969611
$593$	−3.34336e12	−1.11029	−0.555146	−	0.831753i	$-0.687338\pi$
$593$	−3.34336e12	−1.11029	−0.555146	+	0.831753i	$0.687338\pi$
$594$	3.89421e10	0.0128345
$595$	−1.30304e12	−0.426219
$596$	−4.12893e11	−0.134038
$597$	1.15504e12	0.372145
$598$	−1.36599e12	−0.436808
$599$	−9.97101e11	−0.316460	−0.158230	−	0.987402i	$-0.550579\pi$
$599$	−9.97101e11	−0.316460	−0.158230	+	0.987402i	$0.550579\pi$
$600$	7.62838e11	0.240299
$601$	−2.24332e12	−0.701386	−0.350693	−	0.936491i	$-0.614054\pi$
$601$	−2.24332e12	−0.701386	−0.350693	+	0.936491i	$0.614054\pi$
$602$	−1.10528e12	−0.342995
$603$	1.54478e12	0.475817
$604$	−5.35555e11	−0.163733
$605$	2.94562e12	0.893878
$606$	−3.73734e12	−1.12573
$607$	−5.75690e12	−1.72123	−0.860617	−	0.509253i	$-0.829922\pi$
$607$	−5.75690e12	−1.72123	−0.860617	+	0.509253i	$0.829922\pi$
$608$	7.01147e11	0.208086
$609$	2.66003e12	0.783627
$610$	−2.12455e12	−0.621274
$611$	1.51974e12	0.441147
$612$	4.73799e11	0.136525
$613$	3.44873e12	0.986479	0.493239	−	0.869894i	$-0.335813\pi$
$613$	3.44873e12	0.986479	0.493239	+	0.869894i	$0.335813\pi$
$614$	8.58375e11	0.243736
$615$	−6.89053e12	−1.94229
$616$	1.98530e11	0.0555538
$617$	−5.13402e12	−1.42618	−0.713089	−	0.701073i	$-0.752705\pi$
$617$	−5.13402e12	−1.42618	−0.713089	+	0.701073i	$0.752705\pi$
$618$	2.55158e12	0.703657
$619$	1.83851e12	0.503336	0.251668	−	0.967814i	$-0.419021\pi$
$619$	1.83851e12	0.503336	0.251668	+	0.967814i	$0.419021\pi$
$620$	1.24696e10	0.00338915
$621$	5.70972e11	0.154065
$622$	3.80640e12	1.01966
$623$	−6.66802e11	−0.177338
$624$	1.27801e12	0.337447
$625$	−3.08200e12	−0.807928
$626$	−2.01356e11	−0.0524058
$627$	−7.39861e11	−0.191182
$628$	3.37371e11	0.0865544
$629$	−5.65845e12	−1.44135
$630$	−1.13982e12	−0.288273
$631$	3.01780e12	0.757805	0.378903	−	0.925437i	$-0.376301\pi$
$631$	3.01780e12	0.757805	0.378903	+	0.925437i	$0.376301\pi$
$632$	−5.20480e12	−1.29771
$633$	6.20963e12	1.53727
$634$	−1.15668e12	−0.284322
$635$	−5.62017e12	−1.37173
$636$	3.57944e11	0.0867477
$637$	−1.00433e12	−0.241685
$638$	9.15868e11	0.218847
$639$	2.31113e12	0.548366
$640$	3.09962e12	0.730295
$641$	2.47728e12	0.579580	0.289790	−	0.957090i	$-0.406415\pi$
$641$	2.47728e12	0.579580	0.289790	+	0.957090i	$0.406415\pi$
$642$	6.08274e12	1.41316
$643$	5.96725e12	1.37665	0.688327	−	0.725401i	$-0.258346\pi$
$643$	5.96725e12	1.37665	0.688327	+	0.725401i	$0.258346\pi$
$644$	2.94169e11	0.0673923
$645$	−5.67107e12	−1.29017
$646$	−5.04449e12	−1.13965
$647$	−4.85153e12	−1.08845	−0.544227	−	0.838938i	$-0.683177\pi$
$647$	−4.85153e12	−1.08845	−0.544227	+	0.838938i	$0.683177\pi$
$648$	−4.99501e12	−1.11288
$649$	−8.24027e11	−0.182322
$650$	1.96076e11	0.0430838
$651$	7.53867e10	0.0164506
$652$	−9.24835e11	−0.200424
$653$	−1.50523e12	−0.323961	−0.161980	−	0.986794i	$-0.551788\pi$
$653$	−1.50523e12	−0.323961	−0.161980	+	0.986794i	$0.551788\pi$
$654$	2.98493e12	0.638020
$655$	1.55749e12	0.330628
$656$	6.34294e12	1.33728
$657$	−3.45976e12	−0.724439
$658$	2.58395e12	0.537362
$659$	−3.29009e12	−0.679552	−0.339776	−	0.940506i	$-0.610351\pi$
$659$	−3.29009e12	−0.679552	−0.339776	+	0.940506i	$0.610351\pi$
$660$	1.02942e11	0.0211177
$661$	7.79224e12	1.58765	0.793827	−	0.608144i	$-0.208086\pi$
$661$	7.79224e12	1.58765	0.793827	+	0.608144i	$0.208086\pi$
$662$	−1.42144e12	−0.287652
$663$	2.49567e12	0.501622
$664$	2.95124e12	0.589179
$665$	−1.53708e12	−0.304788
$666$	−4.94966e12	−0.974858
$667$	1.34285e13	2.62701
$668$	8.57871e10	0.0166697
$669$	4.55675e12	0.879503
$670$	2.28841e12	0.438730
$671$	5.60132e11	0.106669
$672$	−5.89786e11	−0.111566
$673$	−6.76161e12	−1.27052	−0.635261	−	0.772297i	$-0.719108\pi$
$673$	−6.76161e12	−1.27052	−0.635261	+	0.772297i	$0.719108\pi$
$674$	−4.55040e12	−0.849337
$675$	−8.19583e10	−0.0151959
$676$	−4.69526e10	−0.00864768
$677$	6.04459e12	1.10590	0.552952	−	0.833213i	$-0.313501\pi$
$677$	6.04459e12	1.10590	0.552952	+	0.833213i	$0.313501\pi$
$678$	3.85718e11	0.0701029
$679$	−2.60316e12	−0.469988
$680$	6.94523e12	1.24565
$681$	−5.79287e12	−1.03212
$682$	2.59562e10	0.00459421
$683$	3.24587e12	0.570740	0.285370	−	0.958417i	$-0.407884\pi$
$683$	3.24587e12	0.570740	0.285370	+	0.958417i	$0.407884\pi$
$684$	5.58896e11	0.0976289
$685$	8.59843e12	1.49215
$686$	−3.66724e12	−0.632238
$687$	−8.29025e12	−1.41992
$688$	5.22039e12	0.888290
$689$	9.10400e11	0.153903
$690$	−1.19166e13	−2.00140
$691$	−4.14584e12	−0.691769	−0.345885	−	0.938277i	$-0.612421\pi$
$691$	−4.14584e12	−0.691769	−0.345885	+	0.938277i	$0.612421\pi$
$692$	3.81184e11	0.0631913
$693$	3.00511e11	0.0494949
$694$	2.02513e12	0.331387
$695$	−5.27067e11	−0.0856908
$696$	−1.41780e13	−2.29020
$697$	1.23863e13	1.98790
$698$	−5.38583e12	−0.858822
$699$	7.50512e12	1.18908
$700$	−4.22255e10	−0.00664711
$701$	−5.47240e12	−0.855947	−0.427974	−	0.903791i	$-0.640772\pi$
$701$	−5.47240e12	−0.855947	−0.427974	+	0.903791i	$0.640772\pi$
$702$	−1.54951e11	−0.0240811
$703$	−6.67473e12	−1.03071
$704$	−1.04599e12	−0.160491
$705$	1.32580e13	2.02128
$706$	−9.60094e12	−1.45443
$707$	2.04706e12	0.308136
$708$	1.28913e12	0.192818
$709$	1.68810e12	0.250895	0.125447	−	0.992100i	$-0.459963\pi$
$709$	1.68810e12	0.250895	0.125447	+	0.992100i	$0.459963\pi$
$710$	3.42366e12	0.505625
$711$	−7.87838e12	−1.15618
$712$	3.55406e12	0.518280
$713$	3.80571e11	0.0551484
$714$	4.24329e12	0.611028
$715$	2.61825e11	0.0374657
$716$	−8.11690e11	−0.115420
$717$	3.88131e12	0.548456
$718$	−8.39360e12	−1.17866
$719$	−3.99409e12	−0.557363	−0.278681	−	0.960384i	$-0.589897\pi$
$719$	−3.99409e12	−0.557363	−0.278681	+	0.960384i	$0.589897\pi$
$720$	5.38354e12	0.746572
$721$	−1.39758e12	−0.192605
$722$	9.28430e11	0.127154
$723$	1.03642e13	1.41062
$724$	−1.37507e12	−0.185995
$725$	−1.92755e12	−0.259111
$726$	−9.59226e12	−1.28146
$727$	−1.96928e12	−0.261459	−0.130730	−	0.991418i	$-0.541732\pi$
$727$	−1.96928e12	−0.261459	−0.130730	+	0.991418i	$0.541732\pi$
$728$	−7.89952e11	−0.104234
$729$	−6.58356e12	−0.863350
$730$	−5.12522e12	−0.667974
$731$	1.01942e13	1.32046
$732$	−8.76287e11	−0.112810
$733$	2.48265e12	0.317649	0.158825	−	0.987307i	$-0.449230\pi$
$733$	2.48265e12	0.317649	0.158825	+	0.987307i	$0.449230\pi$
$734$	4.82428e12	0.613479
$735$	−8.76162e12	−1.10737
$736$	−2.97739e12	−0.374012
$737$	−6.03333e11	−0.0753275
$738$	1.08348e13	1.34452
$739$	−8.83198e12	−1.08933	−0.544664	−	0.838655i	$-0.683343\pi$
$739$	−8.83198e12	−1.08933	−0.544664	+	0.838655i	$0.683343\pi$
$740$	9.28704e11	0.113850
$741$	2.94391e12	0.358709
$742$	1.54792e12	0.187469
$743$	5.88065e12	0.707906	0.353953	−	0.935263i	$-0.384837\pi$
$743$	5.88065e12	0.707906	0.353953	+	0.935263i	$0.384837\pi$
$744$	−4.01812e11	−0.0480778
$745$	−9.16141e12	−1.08958
$746$	−1.01264e13	−1.19710
$747$	4.46722e12	0.524921
$748$	−1.85048e11	−0.0216136
$749$	−3.33171e12	−0.386811
$750$	1.20846e13	1.39462
$751$	−9.39265e12	−1.07748	−0.538739	−	0.842473i	$-0.681099\pi$
$751$	−9.39265e12	−1.07748	−0.538739	+	0.842473i	$0.681099\pi$
$752$	−1.22043e13	−1.39166
$753$	−2.46343e12	−0.279230
$754$	−3.64424e12	−0.410616
$755$	−1.18831e13	−1.33097
$756$	3.33690e10	0.00371531
$757$	1.20690e13	1.33579	0.667897	−	0.744254i	$-0.267195\pi$
$757$	1.20690e13	1.33579	0.667897	+	0.744254i	$0.267195\pi$
$758$	3.56628e12	0.392378
$759$	3.14179e12	0.343628
$760$	8.19263e12	0.890762
$761$	1.73414e12	0.187436	0.0937182	−	0.995599i	$-0.470125\pi$
$761$	1.73414e12	0.187436	0.0937182	+	0.995599i	$0.470125\pi$
$762$	1.83018e13	1.96651
$763$	−1.63494e12	−0.174639
$764$	1.33924e12	0.142213
$765$	1.05128e13	1.10980
$766$	1.14388e13	1.20047
$767$	3.27880e12	0.342086
$768$	4.46226e12	0.462839
$769$	−1.87490e13	−1.93335	−0.966675	−	0.256006i	$-0.917593\pi$
$769$	−1.87490e13	−1.93335	−0.966675	+	0.256006i	$0.917593\pi$
$770$	4.45170e11	0.0456371
$771$	−2.16553e13	−2.20709
$772$	−5.10858e11	−0.0517634
$773$	−2.23308e12	−0.224956	−0.112478	−	0.993654i	$-0.535879\pi$
$773$	−2.23308e12	−0.224956	−0.112478	+	0.993654i	$0.535879\pi$
$774$	8.91729e12	0.893097
$775$	−5.46278e10	−0.00543947
$776$	1.38749e13	1.37357
$777$	5.61460e12	0.552617
$778$	−1.26971e13	−1.24250
$779$	1.46110e13	1.42154
$780$	−4.09607e11	−0.0396225
$781$	−9.02638e11	−0.0868129
$782$	2.14212e13	2.04839
$783$	1.52327e12	0.144826
$784$	8.06534e12	0.762431
$785$	7.48571e12	0.703590
$786$	−5.07188e12	−0.473988
$787$	7.05497e12	0.655555	0.327777	−	0.944755i	$-0.393700\pi$
$787$	7.05497e12	0.655555	0.327777	+	0.944755i	$0.393700\pi$
$788$	5.73826e11	0.0530166
$789$	−1.36765e13	−1.25640
$790$	−1.16709e13	−1.06606
$791$	−2.11270e11	−0.0191886
$792$	−1.60172e12	−0.144652
$793$	−2.22876e12	−0.200140
$794$	1.42572e13	1.27304
$795$	7.94219e12	0.705161
$796$	3.40774e11	0.0300855
$797$	1.16654e13	1.02409	0.512045	−	0.858959i	$-0.328888\pi$
$797$	1.16654e13	1.02409	0.512045	+	0.858959i	$0.328888\pi$
$798$	5.00540e12	0.436944
$799$	−2.38323e13	−2.06874
$800$	4.27379e11	0.0368900
$801$	5.37969e12	0.461755
$802$	−9.11497e12	−0.777984
$803$	1.35125e12	0.114687
$804$	9.43873e11	0.0796638
$805$	6.52712e12	0.547823
$806$	−1.03280e11	−0.00861999
$807$	−1.44635e13	−1.20045
$808$	−1.09108e13	−0.900548
$809$	−1.37043e13	−1.12483	−0.562415	−	0.826855i	$-0.690128\pi$
$809$	−1.37043e13	−1.12483	−0.562415	+	0.826855i	$0.690128\pi$
$810$	−1.12005e13	−0.914225
$811$	2.07440e12	0.168383	0.0841917	−	0.996450i	$-0.473169\pi$
$811$	2.07440e12	0.168383	0.0841917	+	0.996450i	$0.473169\pi$
$812$	7.84797e11	0.0633512
$813$	−1.74117e13	−1.39776
$814$	1.93315e12	0.154332
$815$	−2.05206e13	−1.62922
$816$	−2.00416e13	−1.58244
$817$	1.20252e13	0.944261
$818$	9.33483e11	0.0728982
$819$	−1.19573e12	−0.0928658
$820$	−2.03293e12	−0.157022
$821$	−1.51952e13	−1.16724	−0.583622	−	0.812026i	$-0.698365\pi$
$821$	−1.51952e13	−1.16724	−0.583622	+	0.812026i	$0.698365\pi$
$822$	−2.80003e13	−2.13914
$823$	8.32881e12	0.632825	0.316412	−	0.948622i	$-0.397522\pi$
$823$	8.32881e12	0.632825	0.316412	+	0.948622i	$0.397522\pi$
$824$	7.44912e12	0.562901
$825$	−4.50977e11	−0.0338931
$826$	5.57481e12	0.416697
$827$	−1.50997e13	−1.12252	−0.561258	−	0.827641i	$-0.689683\pi$
$827$	−1.50997e13	−1.12252	−0.561258	+	0.827641i	$0.689683\pi$
$828$	−2.37333e12	−0.175477
$829$	−9.65383e12	−0.709912	−0.354956	−	0.934883i	$-0.615504\pi$
$829$	−9.65383e12	−0.709912	−0.354956	+	0.934883i	$0.615504\pi$
$830$	6.61764e12	0.484007
$831$	1.30384e13	0.948458
$832$	4.16200e12	0.301125
$833$	1.57498e13	1.13337
$834$	1.71637e12	0.122846
$835$	1.90347e12	0.135506
$836$	−2.18283e11	−0.0154558
$837$	4.31701e10	0.00304032
$838$	2.43540e12	0.170597
$839$	1.96235e13	1.36725	0.683623	−	0.729835i	$-0.260403\pi$
$839$	1.96235e13	1.36725	0.683623	+	0.729835i	$0.260403\pi$
$840$	−6.89141e12	−0.477586
$841$	2.13181e13	1.46949
$842$	1.07978e13	0.740340
$843$	1.58742e13	1.08260
$844$	1.83204e12	0.124278
$845$	−1.04180e12	−0.0702959
$846$	−2.08471e13	−1.39919
$847$	5.25399e12	0.350763
$848$	−7.31102e12	−0.485508
$849$	2.32622e13	1.53662
$850$	−3.07483e12	−0.202040
$851$	2.83439e13	1.85258
$852$	1.41211e12	0.0918104
$853$	−1.66671e13	−1.07793	−0.538963	−	0.842329i	$-0.681184\pi$
$853$	−1.66671e13	−1.07793	−0.538963	+	0.842329i	$0.681184\pi$
$854$	−3.78947e12	−0.243791
$855$	1.24010e13	0.793613
$856$	1.77580e13	1.13048
$857$	−8.56434e12	−0.542351	−0.271175	−	0.962530i	$-0.587412\pi$
$857$	−8.56434e12	−0.542351	−0.271175	+	0.962530i	$0.587412\pi$
$858$	−8.52619e11	−0.0537109
$859$	1.87649e12	0.117592	0.0587958	−	0.998270i	$-0.481274\pi$
$859$	1.87649e12	0.117592	0.0587958	+	0.998270i	$0.481274\pi$
$860$	−1.67315e12	−0.104302
$861$	−1.22904e13	−0.762167
$862$	2.82683e12	0.174388
$863$	2.54184e11	0.0155991	0.00779956	−	0.999970i	$-0.497517\pi$
$863$	2.54184e11	0.0155991	0.00779956	+	0.999970i	$0.497517\pi$
$864$	−3.37740e11	−0.0206192
$865$	8.45785e12	0.513674
$866$	−2.58681e13	−1.56291
$867$	−1.60011e13	−0.961753
$868$	2.22415e10	0.00132992
$869$	3.07699e12	0.183036
$870$	−3.17918e13	−1.88139
$871$	2.40066e12	0.141335
$872$	8.71425e12	0.510394
$873$	2.10021e13	1.22376
$874$	2.52685e13	1.46480
$875$	−6.61913e12	−0.381737
$876$	−2.11393e12	−0.121289
$877$	−2.88730e13	−1.64814	−0.824069	−	0.566490i	$-0.808301\pi$
$877$	−2.88730e13	−1.64814	−0.824069	+	0.566490i	$0.808301\pi$
$878$	1.54971e13	0.880085
$879$	1.35706e13	0.766742
$880$	−2.10260e12	−0.118191
$881$	−1.43284e13	−0.801317	−0.400659	−	0.916227i	$-0.631219\pi$
$881$	−1.43284e13	−0.801317	−0.400659	+	0.916227i	$0.631219\pi$
$882$	1.37769e13	0.766556
$883$	3.54065e12	0.196001	0.0980007	−	0.995186i	$-0.468755\pi$
$883$	3.54065e12	0.196001	0.0980007	+	0.995186i	$0.468755\pi$
$884$	7.36305e11	0.0405529
$885$	2.86037e13	1.56739
$886$	2.17783e13	1.18733
$887$	1.07018e13	0.580497	0.290249	−	0.956951i	$-0.406262\pi$
$887$	1.07018e13	0.580497	0.290249	+	0.956951i	$0.406262\pi$
$888$	−2.99259e13	−1.61506
$889$	−1.00245e13	−0.538274
$890$	7.96937e12	0.425764
$891$	2.95297e12	0.156967
$892$	1.34439e12	0.0711022
$893$	−2.81127e13	−1.47935
$894$	2.98336e13	1.56202
$895$	−1.80101e13	−0.938235
$896$	5.52866e12	0.286572
$897$	−1.25012e13	−0.644740
$898$	−1.26141e13	−0.647311
$899$	1.01531e12	0.0518416
$900$	3.40671e11	0.0173079
$901$	−1.42768e13	−0.721720
$902$	−4.23165e12	−0.212853
$903$	−1.01152e13	−0.506269
$904$	1.12607e12	0.0560799
$905$	−3.05106e13	−1.51193
$906$	3.86966e13	1.90808
$907$	2.74516e13	1.34690	0.673448	−	0.739234i	$-0.264812\pi$
$907$	2.74516e13	1.34690	0.673448	+	0.739234i	$0.264812\pi$
$908$	−1.70909e12	−0.0834406
$909$	−1.65155e13	−0.802331
$910$	−1.77133e12	−0.0856276
$911$	1.57903e13	0.759550	0.379775	−	0.925079i	$-0.376001\pi$
$911$	1.57903e13	0.759550	0.379775	+	0.925079i	$0.376001\pi$
$912$	−2.36412e13	−1.13160
$913$	−1.74472e12	−0.0831013
$914$	1.77078e13	0.839279
$915$	−1.94434e13	−0.917016
$916$	−2.44589e12	−0.114791
$917$	2.77803e12	0.129740
$918$	2.42991e12	0.112927
$919$	3.33575e13	1.54267	0.771335	−	0.636429i	$-0.219589\pi$
$919$	3.33575e13	1.54267	0.771335	+	0.636429i	$0.219589\pi$
$920$	−3.47896e13	−1.60105
$921$	7.85564e12	0.359760
$922$	−1.86155e13	−0.848372
$923$	3.59160e12	0.162885
$924$	1.83614e11	0.00828670
$925$	−4.06853e12	−0.182726
$926$	−1.64234e13	−0.734030
$927$	1.12756e13	0.501509
$928$	−7.94322e12	−0.351585
$929$	−5.90953e12	−0.260305	−0.130152	−	0.991494i	$-0.541547\pi$
$929$	−5.90953e12	−0.260305	−0.130152	+	0.991494i	$0.541547\pi$
$930$	−9.00994e11	−0.0394956
$931$	1.85785e13	0.810471
$932$	2.21425e12	0.0961293
$933$	3.48352e13	1.50505
$934$	−9.61415e12	−0.413380
$935$	−4.10591e12	−0.175694
$936$	6.37326e12	0.271406
$937$	2.94135e13	1.24657	0.623287	−	0.781993i	$-0.285797\pi$
$937$	2.94135e13	1.24657	0.623287	+	0.781993i	$0.285797\pi$
$938$	4.08175e12	0.172160
$939$	−1.84276e12	−0.0773522
$940$	3.91153e12	0.163407
$941$	−1.78277e13	−0.741212	−0.370606	−	0.928790i	$-0.620850\pi$
$941$	−1.78277e13	−0.741212	−0.370606	+	0.928790i	$0.620850\pi$
$942$	−2.43768e13	−1.00867
$943$	−6.20448e13	−2.55507
$944$	−2.63306e13	−1.07916
$945$	7.40404e11	0.0302013
$946$	−3.48275e12	−0.141388
$947$	−2.20380e13	−0.890427	−0.445213	−	0.895425i	$-0.646872\pi$
$947$	−2.20380e13	−0.890427	−0.445213	+	0.895425i	$0.646872\pi$
$948$	−4.81374e12	−0.193573
$949$	−5.37661e12	−0.215184
$950$	−3.62709e12	−0.144478
$951$	−1.05856e13	−0.419667
$952$	1.23879e13	0.488801
$953$	3.10318e13	1.21868	0.609340	−	0.792909i	$-0.291435\pi$
$953$	3.10318e13	1.21868	0.609340	+	0.792909i	$0.291435\pi$
$954$	−1.24884e13	−0.488136
$955$	2.97156e13	1.15603
$956$	1.14511e12	0.0443391
$957$	8.38180e12	0.323023
$958$	1.12337e13	0.430900
$959$	1.53367e13	0.585527
$960$	3.63086e13	1.37971
$961$	−2.64108e13	−0.998912
$962$	−7.69198e12	−0.289568
$963$	2.68799e13	1.00719
$964$	3.05776e12	0.114040
$965$	−1.13351e13	−0.420778
$966$	−2.12552e13	−0.785359
$967$	3.86641e13	1.42196	0.710982	−	0.703210i	$-0.248251\pi$
$967$	3.86641e13	1.42196	0.710982	+	0.703210i	$0.248251\pi$
$968$	−2.80038e13	−1.02513
$969$	−4.61660e13	−1.68215
$970$	3.11120e13	1.12838
$971$	2.91204e13	1.05126	0.525631	−	0.850713i	$-0.323829\pi$
$971$	2.91204e13	1.05126	0.525631	+	0.850713i	$0.323829\pi$
$972$	−4.33138e12	−0.155643
$973$	−9.40108e11	−0.0336256
$974$	−4.00933e13	−1.42744
$975$	1.79444e12	0.0635927
$976$	1.78982e13	0.631372
$977$	−2.43957e13	−0.856618	−0.428309	−	0.903632i	$-0.640891\pi$
$977$	−2.43957e13	−0.856618	−0.428309	+	0.903632i	$0.640891\pi$
$978$	6.68241e13	2.33565
$979$	−2.10110e12	−0.0731012
$980$	−2.58496e12	−0.0895235
$981$	1.31905e13	0.454729
$982$	−3.60031e13	−1.23549
$983$	1.65480e13	0.565268	0.282634	−	0.959228i	$-0.408792\pi$
$983$	1.65480e13	0.565268	0.282634	+	0.959228i	$0.408792\pi$
$984$	6.55077e13	2.22748
$985$	1.27323e13	0.430965
$986$	5.71485e13	1.92557
$987$	2.36477e13	0.793160
$988$	8.68548e11	0.0289993
$989$	−5.10643e13	−1.69721
$990$	−3.59159e12	−0.118831
$991$	−6.37548e12	−0.209982	−0.104991	−	0.994473i	$-0.533481\pi$
$991$	−6.37548e12	−0.209982	−0.104991	+	0.994473i	$0.533481\pi$
$992$	−2.25115e11	−0.00738077
$993$	−1.30086e13	−0.424581
$994$	6.10664e12	0.198410
$995$	7.56122e12	0.244561
$996$	2.72950e12	0.0878851
$997$	1.52049e13	0.487366	0.243683	−	0.969855i	$-0.421644\pi$
$997$	1.52049e13	0.487366	0.243683	+	0.969855i	$0.421644\pi$
$998$	−3.42572e13	−1.09311
$999$	3.21519e12	0.102132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.a.b.1.2	✓	5
3.2	odd	2		117.10.a.e.1.4		5
4.3	odd	2		208.10.a.h.1.5		5
5.4	even	2		325.10.a.b.1.4		5
13.12	even	2		169.10.a.b.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.2	✓	5	1.1	even	1	trivial
117.10.a.e.1.4		5	3.2	odd	2
169.10.a.b.1.4		5	13.12	even	2
208.10.a.h.1.5		5	4.3	odd	2
325.10.a.b.1.4		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)

\(f(q)\)	\(=\)	\(q-21.3176 q^{2} -195.094 q^{3} -57.5590 q^{4} -1277.14 q^{5} +4158.93 q^{6} -2277.98 q^{7} +12141.6 q^{8} +18378.5 q^{9} +O(q^{10})\)	\(q-21.3176 q^{2} -195.094 q^{3} -57.5590 q^{4} -1277.14 q^{5} +4158.93 q^{6} -2277.98 q^{7} +12141.6 q^{8} +18378.5 q^{9} +27225.6 q^{10} -7177.94 q^{11} +11229.4 q^{12} +28561.0 q^{13} +48561.1 q^{14} +249162. q^{15} -229361. q^{16} -447890. q^{17} -391786. q^{18} -528333. q^{19} +73510.8 q^{20} +444419. q^{21} +153017. q^{22} +2.24354e6 q^{23} -2.36876e6 q^{24} -322041. q^{25} -608853. q^{26} +254496. q^{27} +131118. q^{28} +5.98542e6 q^{29} -5.31153e6 q^{30} +169630. q^{31} -1.32709e6 q^{32} +1.40037e6 q^{33} +9.54795e6 q^{34} +2.90930e6 q^{35} -1.05785e6 q^{36} +1.26336e7 q^{37} +1.12628e7 q^{38} -5.57207e6 q^{39} -1.55066e7 q^{40} -2.76549e7 q^{41} -9.47396e6 q^{42} -2.27606e7 q^{43} +413155. q^{44} -2.34719e7 q^{45} -4.78270e7 q^{46} +5.32103e7 q^{47} +4.47468e7 q^{48} -3.51644e7 q^{49} +6.86516e6 q^{50} +8.73804e7 q^{51} -1.64394e6 q^{52} +3.18756e7 q^{53} -5.42525e6 q^{54} +9.16722e6 q^{55} -2.76584e7 q^{56} +1.03074e8 q^{57} -1.27595e8 q^{58} +1.14800e8 q^{59} -1.43415e7 q^{60} -7.80352e7 q^{61} -3.61610e6 q^{62} -4.18659e7 q^{63} +1.45723e8 q^{64} -3.64764e7 q^{65} -2.98526e7 q^{66} +8.40538e7 q^{67} +2.57801e7 q^{68} -4.37700e8 q^{69} -6.20193e7 q^{70} +1.25752e8 q^{71} +2.23145e8 q^{72} -1.88250e8 q^{73} -2.69318e8 q^{74} +6.28282e7 q^{75} +3.04103e7 q^{76} +1.63512e7 q^{77} +1.18783e8 q^{78} -4.28673e8 q^{79} +2.92926e8 q^{80} -4.11395e8 q^{81} +5.89536e8 q^{82} +2.43067e8 q^{83} -2.55803e7 q^{84} +5.72018e8 q^{85} +4.85202e8 q^{86} -1.16772e9 q^{87} -8.71520e7 q^{88} +2.92716e8 q^{89} +5.00366e8 q^{90} -6.50614e7 q^{91} -1.29136e8 q^{92} -3.30937e7 q^{93} -1.13432e9 q^{94} +6.74754e8 q^{95} +2.58908e8 q^{96} +1.14275e9 q^{97} +7.49622e8 q^{98} -1.31920e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9}+O(q^{10}) \) 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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