LMFDB - Embedded newform 13.12.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,12,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, 12, names="a")

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

chi := DirichletCharacter("13.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 12 $
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:	$9.98846134727$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 13546x^{4} + 130998x^{3} + 49403509x^{2} - 776207317x - 22123683244 $ x^6 - x^5 - 13546x^4 + 130998x^3 + 49403509x^2 - 776207317x - 22123683244
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-89.6176$ 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)

$f(q)$	$=$	$q-80.6176 q^{2} +827.494 q^{3} +4451.20 q^{4} +7679.45 q^{5} -66710.6 q^{6} -6800.32 q^{7} -193740. q^{8} +507599. q^{9} +O(q^{10})$	\(q-80.6176 q^{2} +827.494 q^{3} +4451.20 q^{4} +7679.45 q^{5} -66710.6 q^{6} -6800.32 q^{7} -193740. q^{8} +507599. q^{9} -619099. q^{10} -190123. q^{11} +3.68334e6 q^{12} -371293. q^{13} +548226. q^{14} +6.35470e6 q^{15} +6.50279e6 q^{16} +1.79386e6 q^{17} -4.09214e7 q^{18} -4.42713e6 q^{19} +3.41827e7 q^{20} -5.62723e6 q^{21} +1.53273e7 q^{22} +3.40776e7 q^{23} -1.60318e8 q^{24} +1.01458e7 q^{25} +2.99327e7 q^{26} +2.73447e8 q^{27} -3.02696e7 q^{28} -2.81168e7 q^{29} -5.12300e8 q^{30} +5.00665e7 q^{31} -1.27460e8 q^{32} -1.57326e8 q^{33} -1.44616e8 q^{34} -5.22227e7 q^{35} +2.25942e9 q^{36} -6.15386e8 q^{37} +3.56904e8 q^{38} -3.07243e8 q^{39} -1.48781e9 q^{40} +1.02950e9 q^{41} +4.53653e8 q^{42} -6.48133e8 q^{43} -8.46277e8 q^{44} +3.89808e9 q^{45} -2.74725e9 q^{46} -4.20854e8 q^{47} +5.38102e9 q^{48} -1.93108e9 q^{49} -8.17929e8 q^{50} +1.48440e9 q^{51} -1.65270e9 q^{52} +6.06539e8 q^{53} -2.20446e10 q^{54} -1.46004e9 q^{55} +1.31749e9 q^{56} -3.66342e9 q^{57} +2.26671e9 q^{58} +1.34999e9 q^{59} +2.82860e10 q^{60} +8.08774e9 q^{61} -4.03624e9 q^{62} -3.45184e9 q^{63} -3.04220e9 q^{64} -2.85133e9 q^{65} +1.26832e10 q^{66} +7.48725e9 q^{67} +7.98480e9 q^{68} +2.81990e10 q^{69} +4.21007e9 q^{70} -1.30504e10 q^{71} -9.83421e10 q^{72} -2.83920e10 q^{73} +4.96109e10 q^{74} +8.39558e9 q^{75} -1.97060e10 q^{76} +1.29290e9 q^{77} +2.47692e10 q^{78} -5.07884e10 q^{79} +4.99378e10 q^{80} +1.36356e11 q^{81} -8.29957e10 q^{82} -6.12205e9 q^{83} -2.50479e10 q^{84} +1.37758e10 q^{85} +5.22509e10 q^{86} -2.32665e10 q^{87} +3.68345e10 q^{88} -4.29532e10 q^{89} -3.14254e11 q^{90} +2.52491e9 q^{91} +1.51686e11 q^{92} +4.14297e10 q^{93} +3.39282e10 q^{94} -3.39979e10 q^{95} -1.05472e11 q^{96} +1.36974e11 q^{97} +1.55679e11 q^{98} -9.65065e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9}+O(q^{10}) $ 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9	\( 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9} + 997497 q^{10} + 275060 q^{11} + 3949049 q^{12} - 2227758 q^{13} + 6462587 q^{14} + 5951652 q^{15} + 25038945 q^{16} + 18470848 q^{17} + 1544758 q^{18} + 2382612 q^{19} + 37821799 q^{20} - 67640772 q^{21} - 52649718 q^{22} + 25001944 q^{23} - 243039615 q^{24} - 14063202 q^{25} - 20421115 q^{26} + 77250908 q^{27} - 340836927 q^{28} - 142876028 q^{29} - 838796927 q^{30} - 158397468 q^{31} + 739784589 q^{32} - 115057792 q^{33} - 668802009 q^{34} + 1377003692 q^{35} + 3099344006 q^{36} + 47994456 q^{37} + 2673019714 q^{38} - 176735468 q^{39} + 242886231 q^{40} + 112037548 q^{41} - 5282633557 q^{42} + 1399191924 q^{43} - 1571975050 q^{44} + 7736061780 q^{45} - 2701412412 q^{46} - 3383597640 q^{47} + 1090782789 q^{48} + 7189538970 q^{49} - 12848613144 q^{50} + 8959562860 q^{51} - 5684124537 q^{52} + 546961604 q^{53} - 38372021519 q^{54} - 7803526248 q^{55} - 6807872407 q^{56} + 918537576 q^{57} + 5714690406 q^{58} + 10067834260 q^{59} + 2453022955 q^{60} + 15731821572 q^{61} - 7829475572 q^{62} + 29876175732 q^{63} + 2237284569 q^{64} - 1229722416 q^{65} + 12031833058 q^{66} + 50546073444 q^{67} + 15412804265 q^{68} + 10879166680 q^{69} + 2924449065 q^{70} - 2646136112 q^{71} - 8720745402 q^{72} + 4198695060 q^{73} + 5050454541 q^{74} - 7695720336 q^{75} + 59928748062 q^{76} + 9015828840 q^{77} + 21459621521 q^{78} - 92124930312 q^{79} + 89421404931 q^{80} + 67208776622 q^{81} - 150798850248 q^{82} + 20440296092 q^{83} - 419349915667 q^{84} - 124095891228 q^{85} + 116436457677 q^{86} - 161197597808 q^{87} - 158617438842 q^{88} + 20540234076 q^{89} - 279059693450 q^{90} + 1550519568 q^{91} + 446253814012 q^{92} + 142195723000 q^{93} + 92592053391 q^{94} + 82521342544 q^{95} - 2651637759 q^{96} - 203942467020 q^{97} + 711378915442 q^{98} - 235408311580 q^{99}+O(q^{100}) \) 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9 + 997497 * q^10 + 275060 * q^11 + 3949049 * q^12 - 2227758 * q^13 + 6462587 * q^14 + 5951652 * q^15 + 25038945 * q^16 + 18470848 * q^17 + 1544758 * q^18 + 2382612 * q^19 + 37821799 * q^20 - 67640772 * q^21 - 52649718 * q^22 + 25001944 * q^23 - 243039615 * q^24 - 14063202 * q^25 - 20421115 * q^26 + 77250908 * q^27 - 340836927 * q^28 - 142876028 * q^29 - 838796927 * q^30 - 158397468 * q^31 + 739784589 * q^32 - 115057792 * q^33 - 668802009 * q^34 + 1377003692 * q^35 + 3099344006 * q^36 + 47994456 * q^37 + 2673019714 * q^38 - 176735468 * q^39 + 242886231 * q^40 + 112037548 * q^41 - 5282633557 * q^42 + 1399191924 * q^43 - 1571975050 * q^44 + 7736061780 * q^45 - 2701412412 * q^46 - 3383597640 * q^47 + 1090782789 * q^48 + 7189538970 * q^49 - 12848613144 * q^50 + 8959562860 * q^51 - 5684124537 * q^52 + 546961604 * q^53 - 38372021519 * q^54 - 7803526248 * q^55 - 6807872407 * q^56 + 918537576 * q^57 + 5714690406 * q^58 + 10067834260 * q^59 + 2453022955 * q^60 + 15731821572 * q^61 - 7829475572 * q^62 + 29876175732 * q^63 + 2237284569 * q^64 - 1229722416 * q^65 + 12031833058 * q^66 + 50546073444 * q^67 + 15412804265 * q^68 + 10879166680 * q^69 + 2924449065 * q^70 - 2646136112 * q^71 - 8720745402 * q^72 + 4198695060 * q^73 + 5050454541 * q^74 - 7695720336 * q^75 + 59928748062 * q^76 + 9015828840 * q^77 + 21459621521 * q^78 - 92124930312 * q^79 + 89421404931 * q^80 + 67208776622 * q^81 - 150798850248 * q^82 + 20440296092 * q^83 - 419349915667 * q^84 - 124095891228 * q^85 + 116436457677 * q^86 - 161197597808 * q^87 - 158617438842 * q^88 + 20540234076 * q^89 - 279059693450 * q^90 + 1550519568 * q^91 + 446253814012 * q^92 + 142195723000 * q^93 + 92592053391 * q^94 + 82521342544 * q^95 - 2651637759 * q^96 - 203942467020 * q^97 + 711378915442 * q^98 - 235408311580 * 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 $

$2$	−80.6176	−1.78141	−0.890707	−	0.454578i	$-0.849790\pi$
$2$	−80.6176	−1.78141	−0.890707	+	0.454578i	$0.849790\pi$
$3$	827.494	1.96606	0.983032	−	0.183432i	$-0.0587206\pi$
$3$	827.494	1.96606	0.983032	+	0.183432i	$0.0587206\pi$
$4$	4451.20	2.17344
$5$	7679.45	1.09899	0.549497	−	0.835496i	$-0.314820\pi$
$5$	7679.45	1.09899	0.549497	+	0.835496i	$0.314820\pi$
$6$	−66710.6	−3.50238
$7$	−6800.32	−0.152929	−0.0764646	−	0.997072i	$-0.524363\pi$
$7$	−6800.32	−0.152929	−0.0764646	+	0.997072i	$0.524363\pi$
$8$	−193740.	−2.09037
$9$	507599.	2.86541
$10$	−619099.	−1.95776
$11$	−190123.	−0.355939	−0.177970	−	0.984036i	$-0.556953\pi$
$11$	−190123.	−0.355939	−0.177970	+	0.984036i	$0.556953\pi$
$12$	3.68334e6	4.27311
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	548226.	0.272430
$15$	6.35470e6	2.16069
$16$	6.50279e6	1.55039
$17$	1.79386e6	0.306421	0.153210	−	0.988194i	$-0.451039\pi$
$17$	1.79386e6	0.306421	0.153210	+	0.988194i	$0.451039\pi$
$18$	−4.09214e7	−5.10448
$19$	−4.42713e6	−0.410182	−0.205091	−	0.978743i	$-0.565749\pi$
$19$	−4.42713e6	−0.410182	−0.205091	+	0.978743i	$0.565749\pi$
$20$	3.41827e7	2.38859
$21$	−5.62723e6	−0.300669
$22$	1.53273e7	0.634075
$23$	3.40776e7	1.10399	0.551995	−	0.833847i	$-0.313867\pi$
$23$	3.40776e7	1.10399	0.551995	+	0.833847i	$0.313867\pi$
$24$	−1.60318e8	−4.10981
$25$	1.01458e7	0.207786
$26$	2.99327e7	0.494075
$27$	2.73447e8	3.66752
$28$	−3.02696e7	−0.332382
$29$	−2.81168e7	−0.254553	−0.127276	−	0.991867i	$-0.540623\pi$
$29$	−2.81168e7	−0.254553	−0.127276	+	0.991867i	$0.540623\pi$
$30$	−5.12300e8	−3.84909
$31$	5.00665e7	0.314093	0.157046	−	0.987591i	$-0.449803\pi$
$31$	5.00665e7	0.314093	0.157046	+	0.987591i	$0.449803\pi$
$32$	−1.27460e8	−0.671504
$33$	−1.57326e8	−0.699800
$34$	−1.44616e8	−0.545862
$35$	−5.22227e7	−0.168068
$36$	2.25942e9	6.22779
$37$	−6.15386e8	−1.45894	−0.729471	−	0.684012i	$-0.760234\pi$
$37$	−6.15386e8	−1.45894	−0.729471	+	0.684012i	$0.760234\pi$
$38$	3.56904e8	0.730705
$39$	−3.07243e8	−0.545288
$40$	−1.48781e9	−2.29731
$41$	1.02950e9	1.38776	0.693880	−	0.720091i	$-0.255900\pi$
$41$	1.02950e9	1.38776	0.693880	+	0.720091i	$0.255900\pi$
$42$	4.53653e8	0.535615
$43$	−6.48133e8	−0.672338	−0.336169	−	0.941802i	$-0.609131\pi$
$43$	−6.48133e8	−0.672338	−0.336169	+	0.941802i	$0.609131\pi$
$44$	−8.46277e8	−0.773611
$45$	3.89808e9	3.14907
$46$	−2.74725e9	−1.96666
$47$	−4.20854e8	−0.267666	−0.133833	−	0.991004i	$-0.542729\pi$
$47$	−4.20854e8	−0.267666	−0.133833	+	0.991004i	$0.542729\pi$
$48$	5.38102e9	3.04816
$49$	−1.93108e9	−0.976613
$50$	−8.17929e8	−0.370153
$51$	1.48440e9	0.602443
$52$	−1.65270e9	−0.602802
$53$	6.06539e8	0.199224	0.0996120	−	0.995026i	$-0.468240\pi$
$53$	6.06539e8	0.199224	0.0996120	+	0.995026i	$0.468240\pi$
$54$	−2.20446e10	−6.53337
$55$	−1.46004e9	−0.391175
$56$	1.31749e9	0.319679
$57$	−3.66342e9	−0.806445
$58$	2.26671e9	0.453463
$59$	1.34999e9	0.245836	0.122918	−	0.992417i	$-0.460775\pi$
$59$	1.34999e9	0.245836	0.122918	+	0.992417i	$0.460775\pi$
$60$	2.82860e10	4.69612
$61$	8.08774e9	1.22606	0.613032	−	0.790058i	$-0.289950\pi$
$61$	8.08774e9	1.22606	0.613032	+	0.790058i	$0.289950\pi$
$62$	−4.03624e9	−0.559529
$63$	−3.45184e9	−0.438205
$64$	−3.04220e9	−0.354159
$65$	−2.85133e9	−0.304806
$66$	1.26832e10	1.24663
$67$	7.48725e9	0.677502	0.338751	−	0.940876i	$-0.389996\pi$
$67$	7.48725e9	0.677502	0.338751	+	0.940876i	$0.389996\pi$
$68$	7.98480e9	0.665986
$69$	2.81990e10	2.17052
$70$	4.21007e9	0.299399
$71$	−1.30504e10	−0.858423	−0.429212	−	0.903204i	$-0.641209\pi$
$71$	−1.30504e10	−0.858423	−0.429212	+	0.903204i	$0.641209\pi$
$72$	−9.83421e10	−5.98978
$73$	−2.83920e10	−1.60295	−0.801476	−	0.598027i	$-0.795951\pi$
$73$	−2.83920e10	−1.60295	−0.801476	+	0.598027i	$0.795951\pi$
$74$	4.96109e10	2.59898
$75$	8.39558e9	0.408520
$76$	−1.97060e10	−0.891505
$77$	1.29290e9	0.0544335
$78$	2.47692e10	0.971384
$79$	−5.07884e10	−1.85701	−0.928507	−	0.371315i	$-0.878907\pi$
$79$	−5.07884e10	−1.85701	−0.928507	+	0.371315i	$0.878907\pi$
$80$	4.99378e10	1.70386
$81$	1.36356e11	4.34517
$82$	−8.29957e10	−2.47218
$83$	−6.12205e9	−0.170595	−0.0852977	−	0.996356i	$-0.527184\pi$
$83$	−6.12205e9	−0.170595	−0.0852977	+	0.996356i	$0.527184\pi$
$84$	−2.50479e10	−0.653484
$85$	1.37758e10	0.336754
$86$	5.22509e10	1.19771
$87$	−2.32665e10	−0.500467
$88$	3.68345e10	0.744046
$89$	−4.29532e10	−0.815361	−0.407681	−	0.913125i	$-0.633662\pi$
$89$	−4.29532e10	−0.815361	−0.407681	+	0.913125i	$0.633662\pi$
$90$	−3.14254e11	−5.60979
$91$	2.52491e9	0.0424149
$92$	1.51686e11	2.39945
$93$	4.14297e10	0.617526
$94$	3.39282e10	0.476824
$95$	−3.39979e10	−0.450788
$96$	−1.05472e11	−1.32022
$97$	1.36974e11	1.61955	0.809775	−	0.586740i	$-0.199589\pi$
$97$	1.36974e11	1.61955	0.809775	+	0.586740i	$0.199589\pi$
$98$	1.55679e11	1.73975
$99$	−9.65065e10	−1.01991
$100$	4.51609e10	0.451609
$101$	−1.63102e11	−1.54416	−0.772079	−	0.635527i	$-0.780783\pi$
$101$	−1.63102e11	−1.54416	−0.772079	+	0.635527i	$0.780783\pi$
$102$	−1.19669e11	−1.07320
$103$	−6.38269e10	−0.542499	−0.271250	−	0.962509i	$-0.587437\pi$
$103$	−6.38269e10	−0.542499	−0.271250	+	0.962509i	$0.587437\pi$
$104$	7.19342e10	0.579765
$105$	−4.32140e10	−0.330433
$106$	−4.88977e10	−0.354900
$107$	5.30957e10	0.365973	0.182986	−	0.983115i	$-0.441424\pi$
$107$	5.30957e10	0.365973	0.182986	+	0.983115i	$0.441424\pi$
$108$	1.21717e12	7.97112
$109$	−7.63773e10	−0.475465	−0.237733	−	0.971331i	$-0.576404\pi$
$109$	−7.63773e10	−0.475465	−0.237733	+	0.971331i	$0.576404\pi$
$110$	1.17705e11	0.696844
$111$	−5.09228e11	−2.86837
$112$	−4.42211e10	−0.237099
$113$	−1.84561e11	−0.942342	−0.471171	−	0.882042i	$-0.656169\pi$
$113$	−1.84561e11	−0.942342	−0.471171	+	0.882042i	$0.656169\pi$
$114$	2.95336e11	1.43661
$115$	2.61697e11	1.21328
$116$	−1.25153e11	−0.553253
$117$	−1.88468e11	−0.794722
$118$	−1.08833e11	−0.437936
$119$	−1.21988e10	−0.0468607
$120$	−1.23116e12	−4.51665
$121$	−2.49165e11	−0.873307
$122$	−6.52014e11	−2.18413
$123$	8.51904e11	2.72843
$124$	2.22856e11	0.682660
$125$	−2.97059e11	−0.870638
$126$	2.78279e11	0.780624
$127$	3.29376e11	0.884651	0.442326	−	0.896855i	$-0.354154\pi$
$127$	3.29376e11	0.884651	0.442326	+	0.896855i	$0.354154\pi$
$128$	5.06293e11	1.30241
$129$	−5.36326e11	−1.32186
$130$	2.29867e11	0.542985
$131$	−2.15645e11	−0.488367	−0.244184	−	0.969729i	$-0.578520\pi$
$131$	−2.15645e11	−0.488367	−0.244184	+	0.969729i	$0.578520\pi$
$132$	−7.00289e11	−1.52097
$133$	3.01059e10	0.0627289
$134$	−6.03604e11	−1.20691
$135$	2.09992e12	4.03058
$136$	−3.47541e11	−0.640534
$137$	6.22172e11	1.10141	0.550703	−	0.834701i	$-0.314360\pi$
$137$	6.22172e11	1.10141	0.550703	+	0.834701i	$0.314360\pi$
$138$	−2.27333e12	−3.86659
$139$	5.90997e11	0.966059	0.483030	−	0.875604i	$-0.339536\pi$
$139$	5.90997e11	0.966059	0.483030	+	0.875604i	$0.339536\pi$
$140$	−2.32454e11	−0.365285
$141$	−3.48254e11	−0.526248
$142$	1.05209e12	1.52921
$143$	7.05915e10	0.0987198
$144$	3.30081e12	4.44249
$145$	−2.15922e11	−0.279751
$146$	2.28889e12	2.85552
$147$	−1.59796e12	−1.92008
$148$	−2.73920e12	−3.17092
$149$	6.62582e11	0.739121	0.369560	−	0.929207i	$-0.379508\pi$
$149$	6.62582e11	0.739121	0.369560	+	0.929207i	$0.379508\pi$
$150$	−6.76831e11	−0.727744
$151$	−4.62765e11	−0.479719	−0.239860	−	0.970808i	$-0.577101\pi$
$151$	−4.62765e11	−0.479719	−0.239860	+	0.970808i	$0.577101\pi$
$152$	8.57710e11	0.857434
$153$	9.10559e11	0.878022
$154$	−1.04231e11	−0.0969686
$155$	3.84483e11	0.345186
$156$	−1.36760e12	−1.18515
$157$	−1.21379e12	−1.01554	−0.507770	−	0.861493i	$-0.669530\pi$
$157$	−1.21379e12	−1.01554	−0.507770	+	0.861493i	$0.669530\pi$
$158$	4.09443e12	3.30811
$159$	5.01907e11	0.391687
$160$	−9.78821e11	−0.737978
$161$	−2.31738e11	−0.168832
$162$	−1.09927e13	−7.74055
$163$	1.38105e12	0.940107	0.470053	−	0.882638i	$-0.344235\pi$
$163$	1.38105e12	0.940107	0.470053	+	0.882638i	$0.344235\pi$
$164$	4.58250e12	3.01621
$165$	−1.20818e12	−0.769075
$166$	4.93545e11	0.303901
$167$	1.59345e12	0.949288	0.474644	−	0.880178i	$-0.342577\pi$
$167$	1.59345e12	0.949288	0.474644	+	0.880178i	$0.342577\pi$
$168$	1.09022e12	0.628510
$169$	1.37858e11	0.0769231
$170$	−1.11057e12	−0.599899
$171$	−2.24720e12	−1.17534
$172$	−2.88497e12	−1.46128
$173$	−1.01020e12	−0.495628	−0.247814	−	0.968808i	$-0.579712\pi$
$173$	−1.01020e12	−0.495628	−0.247814	+	0.968808i	$0.579712\pi$
$174$	1.87569e12	0.891538
$175$	−6.89947e10	−0.0317765
$176$	−1.23633e12	−0.551843
$177$	1.11711e12	0.483330
$178$	3.46278e12	1.45250
$179$	−3.51420e12	−1.42934	−0.714668	−	0.699464i	$-0.753422\pi$
$179$	−3.51420e12	−1.42934	−0.714668	+	0.699464i	$0.753422\pi$
$180$	1.73511e13	6.84429
$181$	−1.51716e12	−0.580497	−0.290248	−	0.956951i	$-0.593738\pi$
$181$	−1.51716e12	−0.580497	−0.290248	+	0.956951i	$0.593738\pi$
$182$	−2.03552e11	−0.0755585
$183$	6.69255e12	2.41052
$184$	−6.60218e12	−2.30775
$185$	−4.72582e12	−1.60337
$186$	−3.33996e12	−1.10007
$187$	−3.41054e11	−0.109067
$188$	−1.87330e12	−0.581754
$189$	−1.85953e12	−0.560871
$190$	2.74083e12	0.803039
$191$	−1.86562e12	−0.531056	−0.265528	−	0.964103i	$-0.585546\pi$
$191$	−1.86562e12	−0.531056	−0.265528	+	0.964103i	$0.585546\pi$
$192$	−2.51740e12	−0.696299
$193$	−1.77157e12	−0.476205	−0.238103	−	0.971240i	$-0.576525\pi$
$193$	−1.77157e12	−0.476205	−0.238103	+	0.971240i	$0.576525\pi$
$194$	−1.10425e13	−2.88509
$195$	−2.35945e12	−0.599268
$196$	−8.59562e12	−2.12260
$197$	4.35896e12	1.04669	0.523345	−	0.852121i	$-0.324684\pi$
$197$	4.35896e12	1.04669	0.523345	+	0.852121i	$0.324684\pi$
$198$	7.78012e12	1.81689
$199$	3.26369e12	0.741340	0.370670	−	0.928765i	$-0.379128\pi$
$199$	3.26369e12	0.741340	0.370670	+	0.928765i	$0.379128\pi$
$200$	−1.96564e12	−0.434350
$201$	6.19565e12	1.33201
$202$	1.31489e13	2.75078
$203$	1.91204e11	0.0389285
$204$	6.60737e12	1.30937
$205$	7.90598e12	1.52514
$206$	5.14557e12	0.966416
$207$	1.72977e13	3.16339
$208$	−2.41444e12	−0.429999
$209$	8.41700e11	0.146000
$210$	3.48381e12	0.588638
$211$	−1.87281e12	−0.308276	−0.154138	−	0.988049i	$-0.549260\pi$
$211$	−1.87281e12	−0.308276	−0.154138	+	0.988049i	$0.549260\pi$
$212$	2.69982e12	0.433000
$213$	−1.07991e13	−1.68772
$214$	−4.28045e12	−0.651949
$215$	−4.97730e12	−0.738895
$216$	−5.29776e13	−7.66649
$217$	−3.40468e11	−0.0480339
$218$	6.15735e12	0.847000
$219$	−2.34942e13	−3.15151
$220$	−6.49894e12	−0.850193
$221$	−6.66046e11	−0.0849859
$222$	4.10527e13	5.10976
$223$	−4.09388e12	−0.497117	−0.248559	−	0.968617i	$-0.579957\pi$
$223$	−4.09388e12	−0.497117	−0.248559	+	0.968617i	$0.579957\pi$
$224$	8.66768e11	0.102693
$225$	5.14999e12	0.595392
$226$	1.48789e13	1.67870
$227$	−1.90529e12	−0.209807	−0.104903	−	0.994482i	$-0.533453\pi$
$227$	−1.90529e12	−0.209807	−0.104903	+	0.994482i	$0.533453\pi$
$228$	−1.63066e13	−1.75276
$229$	−7.09401e12	−0.744384	−0.372192	−	0.928156i	$-0.621394\pi$
$229$	−7.09401e12	−0.744384	−0.372192	+	0.928156i	$0.621394\pi$
$230$	−2.10974e13	−2.16135
$231$	1.06987e12	0.107020
$232$	5.44735e12	0.532110
$233$	2.77211e11	0.0264456	0.0132228	−	0.999913i	$-0.495791\pi$
$233$	2.77211e11	0.0264456	0.0132228	+	0.999913i	$0.495791\pi$
$234$	1.51938e13	1.41573
$235$	−3.23192e12	−0.294163
$236$	6.00908e12	0.534309
$237$	−4.20270e13	−3.65101
$238$	9.83438e11	0.0834783
$239$	−1.54095e13	−1.27821	−0.639104	−	0.769121i	$-0.720695\pi$
$239$	−1.54095e13	−1.27821	−0.639104	+	0.769121i	$0.720695\pi$
$240$	4.13232e13	3.34990
$241$	1.99082e13	1.57738	0.788692	−	0.614788i	$-0.210759\pi$
$241$	1.99082e13	1.57738	0.788692	+	0.614788i	$0.210759\pi$
$242$	2.00871e13	1.55572
$243$	6.43935e13	4.87537
$244$	3.60001e13	2.66477
$245$	−1.48296e13	−1.07329
$246$	−6.86784e13	−4.86046
$247$	1.64376e12	0.113764
$248$	−9.69987e12	−0.656571
$249$	−5.06596e12	−0.335401
$250$	2.39482e13	1.55097
$251$	2.02324e13	1.28186	0.640931	−	0.767598i	$-0.278548\pi$
$251$	2.02324e13	1.28186	0.640931	+	0.767598i	$0.278548\pi$
$252$	−1.53648e13	−0.952410
$253$	−6.47894e12	−0.392954
$254$	−2.65535e13	−1.57593
$255$	1.13994e13	0.662081
$256$	−3.45857e13	−1.96597
$257$	1.61645e13	0.899355	0.449678	−	0.893191i	$-0.351539\pi$
$257$	1.61645e13	0.899355	0.449678	+	0.893191i	$0.351539\pi$
$258$	4.32373e13	2.35478
$259$	4.18482e12	0.223115
$260$	−1.26918e13	−0.662476
$261$	−1.42721e13	−0.729398
$262$	1.73848e13	0.869984
$263$	4.74365e11	0.0232464	0.0116232	−	0.999932i	$-0.496300\pi$
$263$	4.74365e11	0.0232464	0.0116232	+	0.999932i	$0.496300\pi$
$264$	3.04803e13	1.46284
$265$	4.65789e12	0.218946
$266$	−2.42706e12	−0.111746
$267$	−3.55435e13	−1.60305
$268$	3.33272e13	1.47251
$269$	−2.28160e13	−0.987647	−0.493824	−	0.869562i	$-0.664401\pi$
$269$	−2.28160e13	−0.987647	−0.493824	+	0.869562i	$0.664401\pi$
$270$	−1.69291e14	−7.18013
$271$	2.15094e13	0.893918	0.446959	−	0.894554i	$-0.352507\pi$
$271$	2.15094e13	0.893918	0.446959	+	0.894554i	$0.352507\pi$
$272$	1.16651e13	0.475070
$273$	2.08935e12	0.0833905
$274$	−5.01580e13	−1.96206
$275$	−1.92895e12	−0.0739591
$276$	1.25519e14	4.71748
$277$	3.16079e13	1.16455	0.582273	−	0.812993i	$-0.302163\pi$
$277$	3.16079e13	1.16455	0.582273	+	0.812993i	$0.302163\pi$
$278$	−4.76447e13	−1.72095
$279$	2.54137e13	0.900004
$280$	1.01176e13	0.351325
$281$	−2.38637e13	−0.812557	−0.406279	−	0.913749i	$-0.633174\pi$
$281$	−2.38637e13	−0.812557	−0.406279	+	0.913749i	$0.633174\pi$
$282$	2.80754e13	0.937466
$283$	3.82123e13	1.25135	0.625673	−	0.780085i	$-0.284824\pi$
$283$	3.82123e13	1.25135	0.625673	+	0.780085i	$0.284824\pi$
$284$	−5.80897e13	−1.86573
$285$	−2.81330e13	−0.886278
$286$	−5.69092e12	−0.175861
$287$	−7.00092e12	−0.212229
$288$	−6.46985e13	−1.92414
$289$	−3.10540e13	−0.906106
$290$	1.74071e13	0.498353
$291$	1.13345e14	3.18414
$292$	−1.26378e14	−3.48391
$293$	3.29421e13	0.891208	0.445604	−	0.895230i	$-0.352989\pi$
$293$	3.29421e13	0.891208	0.445604	+	0.895230i	$0.352989\pi$
$294$	1.28824e14	3.42046
$295$	1.03672e13	0.270172
$296$	1.19225e14	3.04973
$297$	−5.19887e13	−1.30541
$298$	−5.34158e13	−1.31668
$299$	−1.26528e13	−0.306192
$300$	3.73704e13	0.887893
$301$	4.40751e12	0.102820
$302$	3.73070e13	0.854578
$303$	−1.34966e14	−3.03591
$304$	−2.87887e13	−0.635941
$305$	6.21094e13	1.34744
$306$	−7.34071e13	−1.56412
$307$	7.33775e13	1.53568	0.767842	−	0.640640i	$-0.221331\pi$
$307$	7.33775e13	1.53568	0.767842	+	0.640640i	$0.221331\pi$
$308$	5.75495e12	0.118308
$309$	−5.28164e13	−1.06659
$310$	−3.09961e13	−0.614918
$311$	1.27675e12	0.0248843	0.0124421	−	0.999923i	$-0.496039\pi$
$311$	1.27675e12	0.0248843	0.0124421	+	0.999923i	$0.496039\pi$
$312$	5.95251e13	1.13986
$313$	9.59462e13	1.80524	0.902618	−	0.430443i	$-0.141642\pi$
$313$	9.59462e13	1.80524	0.902618	+	0.430443i	$0.141642\pi$
$314$	9.78531e13	1.80910
$315$	−2.65082e13	−0.481584
$316$	−2.26069e14	−4.03610
$317$	−1.44103e13	−0.252841	−0.126420	−	0.991977i	$-0.540349\pi$
$317$	−1.44103e13	−0.252841	−0.126420	+	0.991977i	$0.540349\pi$
$318$	−4.04626e13	−0.697757
$319$	5.34567e12	0.0906052
$320$	−2.33624e13	−0.389218
$321$	4.39364e13	0.719526
$322$	1.86822e13	0.300760
$323$	−7.94162e12	−0.125688
$324$	6.06948e14	9.44395
$325$	−3.76706e12	−0.0576294
$326$	−1.11337e14	−1.67472
$327$	−6.32017e13	−0.934795
$328$	−1.99455e14	−2.90094
$329$	2.86194e12	0.0409339
$330$	9.74003e13	1.37004
$331$	1.62434e13	0.224710	0.112355	−	0.993668i	$-0.464161\pi$
$331$	1.62434e13	0.224710	0.112355	+	0.993668i	$0.464161\pi$
$332$	−2.72504e13	−0.370778
$333$	−3.12369e14	−4.18047
$334$	−1.28460e14	−1.69108
$335$	5.74979e13	0.744570
$336$	−3.65926e13	−0.466152
$337$	−6.10462e13	−0.765058	−0.382529	−	0.923943i	$-0.624947\pi$
$337$	−6.10462e13	−0.765058	−0.382529	+	0.923943i	$0.624947\pi$
$338$	−1.11138e13	−0.137032
$339$	−1.52723e14	−1.85271
$340$	6.13189e13	0.731914
$341$	−9.51881e12	−0.111798
$342$	1.81164e14	2.09377
$343$	2.65784e13	0.302282
$344$	1.25569e14	1.40544
$345$	2.16552e14	2.38538
$346$	8.14403e13	0.882919
$347$	1.62881e14	1.73803	0.869017	−	0.494783i	$-0.164752\pi$
$347$	1.62881e14	1.73803	0.869017	+	0.494783i	$0.164752\pi$
$348$	−1.03564e14	−1.08773
$349$	−5.18682e13	−0.536243	−0.268121	−	0.963385i	$-0.586403\pi$
$349$	−5.18682e13	−0.536243	−0.268121	+	0.963385i	$0.586403\pi$
$350$	5.56218e12	0.0566071
$351$	−1.01529e14	−1.01719
$352$	2.42331e13	0.239015
$353$	8.51060e13	0.826417	0.413208	−	0.910637i	$-0.364408\pi$
$353$	8.51060e13	0.826417	0.413208	+	0.910637i	$0.364408\pi$
$354$	−9.00588e13	−0.861010
$355$	−1.00220e14	−0.943401
$356$	−1.91193e14	−1.77213
$357$	−1.00944e13	−0.0921312
$358$	2.83306e14	2.54624
$359$	1.10550e14	0.978456	0.489228	−	0.872156i	$-0.337279\pi$
$359$	1.10550e14	0.978456	0.489228	+	0.872156i	$0.337279\pi$
$360$	−7.55213e14	−6.58273
$361$	−9.68908e13	−0.831750
$362$	1.22310e14	1.03410
$363$	−2.06182e14	−1.71698
$364$	1.12389e13	0.0921861
$365$	−2.18035e14	−1.76163
$366$	−5.39537e14	−4.29413
$367$	1.10642e14	0.867471	0.433735	−	0.901040i	$-0.357195\pi$
$367$	1.10642e14	0.867471	0.433735	+	0.901040i	$0.357195\pi$
$368$	2.21599e14	1.71161
$369$	5.22572e14	3.97650
$370$	3.80984e14	2.85626
$371$	−4.12466e12	−0.0304672
$372$	1.84412e14	1.34215
$373$	1.72159e11	0.00123461	0.000617307	−	1.00000i	$-0.499804\pi$
$373$	1.72159e11	0.00123461	0.000617307		1.00000i	$0.499804\pi$
$374$	2.74950e13	0.194294
$375$	−2.45814e14	−1.71173
$376$	8.15361e13	0.559521
$377$	1.04396e13	0.0706002
$378$	1.49911e14	0.999143
$379$	3.01174e13	0.197835	0.0989173	−	0.995096i	$-0.468462\pi$
$379$	3.01174e13	0.197835	0.0989173	+	0.995096i	$0.468462\pi$
$380$	−1.51331e14	−0.979758
$381$	2.72557e14	1.73928
$382$	1.50402e14	0.946030
$383$	−2.09126e14	−1.29662	−0.648312	−	0.761375i	$-0.724525\pi$
$383$	−2.09126e14	−1.29662	−0.648312	+	0.761375i	$0.724525\pi$
$384$	4.18954e14	2.56062
$385$	9.92877e12	0.0598220
$386$	1.42820e14	0.848319
$387$	−3.28992e14	−1.92652
$388$	6.09699e14	3.51999
$389$	2.57389e14	1.46510	0.732551	−	0.680712i	$-0.238330\pi$
$389$	2.57389e14	1.46510	0.732551	+	0.680712i	$0.238330\pi$
$390$	1.90213e14	1.06754
$391$	6.11302e13	0.338286
$392$	3.74127e14	2.04149
$393$	−1.78445e14	−0.960162
$394$	−3.51409e14	−1.86459
$395$	−3.90026e14	−2.04085
$396$	−4.29569e14	−2.21671
$397$	−2.33715e14	−1.18943	−0.594714	−	0.803938i	$-0.702735\pi$
$397$	−2.33715e14	−1.18943	−0.594714	+	0.803938i	$0.702735\pi$
$398$	−2.63111e14	−1.32063
$399$	2.49124e13	0.123329
$400$	6.59759e13	0.322148
$401$	2.55407e14	1.23009	0.615047	−	0.788490i	$-0.289137\pi$
$401$	2.55407e14	1.23009	0.615047	+	0.788490i	$0.289137\pi$
$402$	−4.99478e14	−2.37287
$403$	−1.85893e13	−0.0871136
$404$	−7.25999e14	−3.35613
$405$	1.04714e15	4.77531
$406$	−1.54144e13	−0.0693478
$407$	1.16999e14	0.519295
$408$	−2.87588e14	−1.25933
$409$	6.08758e13	0.263007	0.131503	−	0.991316i	$-0.458020\pi$
$409$	6.08758e13	0.263007	0.131503	+	0.991316i	$0.458020\pi$
$410$	−6.37361e14	−2.71690
$411$	5.14844e14	2.16544
$412$	−2.84106e14	−1.17909
$413$	−9.18039e12	−0.0375955
$414$	−1.39450e15	−5.63530
$415$	−4.70139e13	−0.187483
$416$	4.73250e13	0.186242
$417$	4.89046e14	1.89934
$418$	−6.78559e13	−0.260086
$419$	1.47931e14	0.559605	0.279803	−	0.960058i	$-0.409731\pi$
$419$	1.47931e14	0.559605	0.279803	+	0.960058i	$0.409731\pi$
$420$	−1.92354e14	−0.718174
$421$	−3.16159e14	−1.16507	−0.582537	−	0.812804i	$-0.697940\pi$
$421$	−3.16159e14	−1.16507	−0.582537	+	0.812804i	$0.697940\pi$
$422$	1.50981e14	0.549167
$423$	−2.13625e14	−0.766973
$424$	−1.17511e14	−0.416452
$425$	1.82001e13	0.0636699
$426$	8.70596e14	3.00652
$427$	−5.49992e13	−0.187501
$428$	2.36339e14	0.795418
$429$	5.84140e13	0.194090
$430$	4.01258e14	1.31628
$431$	3.33650e14	1.08060	0.540302	−	0.841471i	$-0.318310\pi$
$431$	3.33650e14	1.08060	0.540302	+	0.841471i	$0.318310\pi$
$432$	1.77817e15	5.68607
$433$	−3.59934e14	−1.13642	−0.568210	−	0.822884i	$-0.692364\pi$
$433$	−3.59934e14	−1.13642	−0.568210	+	0.822884i	$0.692364\pi$
$434$	2.74477e13	0.0855683
$435$	−1.78674e14	−0.550010
$436$	−3.39970e14	−1.03339
$437$	−1.50866e14	−0.452837
$438$	1.89405e15	5.61414
$439$	−3.20285e14	−0.937523	−0.468762	−	0.883325i	$-0.655300\pi$
$439$	−3.20285e14	−0.937523	−0.468762	+	0.883325i	$0.655300\pi$
$440$	2.82868e14	0.817702
$441$	−9.80216e14	−2.79840
$442$	5.36950e13	0.151395
$443$	2.47990e14	0.690579	0.345290	−	0.938496i	$-0.387781\pi$
$443$	2.47990e14	0.690579	0.345290	+	0.938496i	$0.387781\pi$
$444$	−2.26667e15	−6.23423
$445$	−3.29857e14	−0.896076
$446$	3.30039e14	0.885572
$447$	5.48283e14	1.45316
$448$	2.06879e13	0.0541612
$449$	−2.25177e14	−0.582330	−0.291165	−	0.956673i	$-0.594043\pi$
$449$	−2.25177e14	−0.582330	−0.291165	+	0.956673i	$0.594043\pi$
$450$	−4.15180e14	−1.06064
$451$	−1.95732e14	−0.493958
$452$	−8.21517e14	−2.04812
$453$	−3.82935e14	−0.943159
$454$	1.53600e14	0.373753
$455$	1.93899e13	0.0466137
$456$	7.09750e14	1.68577
$457$	−5.30339e14	−1.24456	−0.622278	−	0.782796i	$-0.713793\pi$
$457$	−5.30339e14	−1.24456	−0.622278	+	0.782796i	$0.713793\pi$
$458$	5.71902e14	1.32606
$459$	4.90524e14	1.12380
$460$	1.16486e15	2.63698
$461$	−5.20324e14	−1.16391	−0.581954	−	0.813222i	$-0.697712\pi$
$461$	−5.20324e14	−1.16391	−0.581954	+	0.813222i	$0.697712\pi$
$462$	−8.62501e13	−0.190647
$463$	4.51776e14	0.986796	0.493398	−	0.869804i	$-0.335755\pi$
$463$	4.51776e14	0.986796	0.493398	+	0.869804i	$0.335755\pi$
$464$	−1.82838e14	−0.394654
$465$	3.18157e14	0.678657
$466$	−2.23481e13	−0.0471105
$467$	3.14303e14	0.654796	0.327398	−	0.944887i	$-0.393828\pi$
$467$	3.14303e14	0.654796	0.327398	+	0.944887i	$0.393828\pi$
$468$	−8.38908e14	−1.72728
$469$	−5.09157e13	−0.103610
$470$	2.60550e14	0.524026
$471$	−1.00441e15	−1.99662
$472$	−2.61547e14	−0.513889
$473$	1.23225e14	0.239311
$474$	3.38812e15	6.50396
$475$	−4.49167e13	−0.0852301
$476$	−5.42992e13	−0.101849
$477$	3.07879e14	0.570859
$478$	1.24228e15	2.27702
$479$	−1.29429e14	−0.234524	−0.117262	−	0.993101i	$-0.537412\pi$
$479$	−1.29429e14	−0.234524	−0.117262	+	0.993101i	$0.537412\pi$
$480$	−8.09969e14	−1.45091
$481$	2.28488e14	0.404638
$482$	−1.60495e15	−2.80997
$483$	−1.91762e14	−0.331935
$484$	−1.10908e15	−1.89808
$485$	1.05189e15	1.77988
$486$	−5.19125e15	−8.68505
$487$	−8.39205e14	−1.38822	−0.694111	−	0.719868i	$-0.744202\pi$
$487$	−8.39205e14	−1.38822	−0.694111	+	0.719868i	$0.744202\pi$
$488$	−1.56692e15	−2.56293
$489$	1.14281e15	1.84831
$490$	1.19553e15	1.91197
$491$	−2.26495e14	−0.358187	−0.179093	−	0.983832i	$-0.557316\pi$
$491$	−2.26495e14	−0.358187	−0.179093	+	0.983832i	$0.557316\pi$
$492$	3.79199e15	5.93006
$493$	−5.04375e13	−0.0780002
$494$	−1.32516e14	−0.202661
$495$	−7.41117e14	−1.12088
$496$	3.25572e14	0.486964
$497$	8.87466e13	0.131278
$498$	4.08405e14	0.597489
$499$	9.50555e14	1.37539	0.687693	−	0.726002i	$-0.258624\pi$
$499$	9.50555e14	1.37539	0.687693	+	0.726002i	$0.258624\pi$
$500$	−1.32227e15	−1.89228
$501$	1.31857e15	1.86636
$502$	−1.63109e15	−2.28353
$503$	8.25749e14	1.14347	0.571734	−	0.820439i	$-0.306271\pi$
$503$	8.25749e14	1.14347	0.571734	+	0.820439i	$0.306271\pi$
$504$	6.68758e14	0.916012
$505$	−1.25253e15	−1.69702
$506$	5.22317e14	0.700013
$507$	1.14077e14	0.151236
$508$	1.46612e15	1.92273
$509$	1.83171e14	0.237635	0.118817	−	0.992916i	$-0.462090\pi$
$509$	1.83171e14	0.237635	0.118817	+	0.992916i	$0.462090\pi$
$510$	−9.18993e14	−1.17944
$511$	1.93075e14	0.245138
$512$	1.75133e15	2.19979
$513$	−1.21058e15	−1.50435
$514$	−1.30315e15	−1.60212
$515$	−4.90155e14	−0.596203
$516$	−2.38729e15	−2.87298
$517$	8.00142e13	0.0952728
$518$	−3.37370e14	−0.397460
$519$	−8.35938e14	−0.974437
$520$	5.52415e14	0.637158
$521$	1.51978e15	1.73450	0.867250	−	0.497874i	$-0.165886\pi$
$521$	1.51978e15	1.73450	0.867250	+	0.497874i	$0.165886\pi$
$522$	1.15058e15	1.29936
$523$	−5.06543e14	−0.566053	−0.283027	−	0.959112i	$-0.591338\pi$
$523$	−5.06543e14	−0.566053	−0.283027	+	0.959112i	$0.591338\pi$
$524$	−9.59877e14	−1.06143
$525$	−5.70927e13	−0.0624747
$526$	−3.82422e13	−0.0414115
$527$	8.98120e13	0.0962445
$528$	−1.02306e15	−1.08496
$529$	2.08470e14	0.218795
$530$	−3.75507e14	−0.390033
$531$	6.85255e14	0.704421
$532$	1.34007e14	0.136337
$533$	−3.82246e14	−0.384895
$534$	2.86543e15	2.85570
$535$	4.07746e14	0.402201
$536$	−1.45058e15	−1.41623
$537$	−2.90797e15	−2.81017
$538$	1.83937e15	1.75941
$539$	3.67144e14	0.347615
$540$	9.34716e15	8.76020
$541$	−7.15249e14	−0.663548	−0.331774	−	0.943359i	$-0.607647\pi$
$541$	−7.15249e14	−0.663548	−0.331774	+	0.943359i	$0.607647\pi$
$542$	−1.73404e15	−1.59244
$543$	−1.25544e15	−1.14129
$544$	−2.28645e14	−0.205763
$545$	−5.86535e14	−0.522533
$546$	−1.68438e14	−0.148553
$547$	−2.48926e14	−0.217340	−0.108670	−	0.994078i	$-0.534659\pi$
$547$	−2.48926e14	−0.217340	−0.108670	+	0.994078i	$0.534659\pi$
$548$	2.76941e15	2.39383
$549$	4.10533e15	3.51318
$550$	1.55508e14	0.131752
$551$	1.24477e14	0.104413
$552$	−5.46326e15	−4.53719
$553$	3.45377e14	0.283992
$554$	−2.54815e15	−2.07454
$555$	−3.91059e15	−3.15232
$556$	2.63064e15	2.09967
$557$	1.42621e15	1.12714	0.563572	−	0.826067i	$-0.309427\pi$
$557$	1.42621e15	1.12714	0.563572	+	0.826067i	$0.309427\pi$
$558$	−2.04879e15	−1.60328
$559$	2.40647e14	0.186473
$560$	−3.39593e14	−0.260570
$561$	−2.82220e14	−0.214433
$562$	1.92384e15	1.44750
$563$	1.87050e15	1.39367	0.696837	−	0.717230i	$-0.254590\pi$
$563$	1.87050e15	1.39367	0.696837	+	0.717230i	$0.254590\pi$
$564$	−1.55015e15	−1.14377
$565$	−1.41733e15	−1.03563
$566$	−3.08058e15	−2.22917
$567$	−9.27265e14	−0.664503
$568$	2.52837e15	1.79442
$569$	5.17569e14	0.363790	0.181895	−	0.983318i	$-0.441777\pi$
$569$	5.17569e14	0.363790	0.181895	+	0.983318i	$0.441777\pi$
$570$	2.26802e15	1.57883
$571$	1.58321e15	1.09154	0.545771	−	0.837935i	$-0.316237\pi$
$571$	1.58321e15	1.09154	0.545771	+	0.837935i	$0.316237\pi$
$572$	3.14217e14	0.214561
$573$	−1.54379e15	−1.04409
$574$	5.64397e14	0.378068
$575$	3.45744e14	0.229394
$576$	−1.54422e15	−1.01481
$577$	2.03426e14	0.132416	0.0662079	−	0.997806i	$-0.478910\pi$
$577$	2.03426e14	0.132416	0.0662079	+	0.997806i	$0.478910\pi$
$578$	2.50350e15	1.61415
$579$	−1.46597e15	−0.936251
$580$	−9.61110e14	−0.608022
$581$	4.16319e13	0.0260890
$582$	−9.13763e15	−5.67227
$583$	−1.15317e14	−0.0709116
$584$	5.50066e15	3.35077
$585$	−1.44733e15	−0.873394
$586$	−2.65571e15	−1.58761
$587$	−2.47792e14	−0.146750	−0.0733750	−	0.997304i	$-0.523377\pi$
$587$	−2.47792e14	−0.146750	−0.0733750	+	0.997304i	$0.523377\pi$
$588$	−7.11283e15	−4.17318
$589$	−2.21651e14	−0.128835
$590$	−8.35779e14	−0.481288
$591$	3.60701e15	2.05786
$592$	−4.00172e15	−2.26192
$593$	−3.75390e14	−0.210224	−0.105112	−	0.994460i	$-0.533520\pi$
$593$	−3.75390e14	−0.210224	−0.105112	+	0.994460i	$0.533520\pi$
$594$	4.19120e15	2.32548
$595$	−9.36800e13	−0.0514996
$596$	2.94928e15	1.60643
$597$	2.70068e15	1.45752
$598$	1.02003e15	0.545454
$599$	−1.20541e15	−0.638686	−0.319343	−	0.947639i	$-0.603462\pi$
$599$	−1.20541e15	−0.638686	−0.319343	+	0.947639i	$0.603462\pi$
$600$	−1.62656e15	−0.853960
$601$	1.63974e15	0.853032	0.426516	−	0.904480i	$-0.359741\pi$
$601$	1.63974e15	0.853032	0.426516	+	0.904480i	$0.359741\pi$
$602$	−3.55323e14	−0.183165
$603$	3.80052e15	1.94132
$604$	−2.05986e15	−1.04264
$605$	−1.91345e15	−0.959759
$606$	1.08806e16	5.40822
$607$	−1.17507e15	−0.578797	−0.289398	−	0.957209i	$-0.593455\pi$
$607$	−1.17507e15	−0.578797	−0.289398	+	0.957209i	$0.593455\pi$
$608$	5.64281e14	0.275439
$609$	1.58220e14	0.0765360
$610$	−5.00711e15	−2.40034
$611$	1.56260e14	0.0742371
$612$	4.05308e15	1.90832
$613$	−1.49286e15	−0.696605	−0.348302	−	0.937382i	$-0.613242\pi$
$613$	−1.49286e15	−0.696605	−0.348302	+	0.937382i	$0.613242\pi$
$614$	−5.91551e15	−2.73569
$615$	6.54215e15	2.99852
$616$	−2.50486e14	−0.113786
$617$	−4.17198e14	−0.187834	−0.0939170	−	0.995580i	$-0.529939\pi$
$617$	−4.17198e14	−0.187834	−0.0939170	+	0.995580i	$0.529939\pi$
$618$	4.25793e15	1.90004
$619$	−2.36168e15	−1.04453	−0.522267	−	0.852782i	$-0.674914\pi$
$619$	−2.36168e15	−1.04453	−0.522267	+	0.852782i	$0.674914\pi$
$620$	1.71141e15	0.750238
$621$	9.31841e15	4.04891
$622$	−1.02929e14	−0.0443292
$623$	2.92095e14	0.124693
$624$	−1.99793e15	−0.845407
$625$	−2.77665e15	−1.16461
$626$	−7.73495e15	−3.21587
$627$	6.96502e14	0.287046
$628$	−5.40283e15	−2.20721
$629$	−1.10391e15	−0.447050
$630$	2.13703e15	0.857901
$631$	4.41315e15	1.75625	0.878126	−	0.478429i	$-0.158794\pi$
$631$	4.41315e15	1.75625	0.878126	+	0.478429i	$0.158794\pi$
$632$	9.83972e15	3.88185
$633$	−1.54974e15	−0.606090
$634$	1.16172e15	0.450414
$635$	2.52943e15	0.972226
$636$	2.23409e15	0.851307
$637$	7.16997e14	0.270864
$638$	−4.30955e14	−0.161405
$639$	−6.62435e15	−2.45974
$640$	3.88805e15	1.43134
$641$	−3.61321e15	−1.31878	−0.659392	−	0.751799i	$-0.729186\pi$
$641$	−3.61321e15	−1.31878	−0.659392	+	0.751799i	$0.729186\pi$
$642$	−3.54204e15	−1.28177
$643$	2.73707e15	0.982033	0.491017	−	0.871150i	$-0.336625\pi$
$643$	2.73707e15	0.982033	0.491017	+	0.871150i	$0.336625\pi$
$644$	−1.03151e15	−0.366946
$645$	−4.11869e15	−1.45271
$646$	6.40234e14	0.223903
$647$	3.29364e15	1.14209	0.571047	−	0.820917i	$-0.306537\pi$
$647$	3.29364e15	1.14209	0.571047	+	0.820917i	$0.306537\pi$
$648$	−2.64176e16	−9.08303
$649$	−2.56665e14	−0.0875027
$650$	3.03691e14	0.102662
$651$	−2.81735e14	−0.0944378
$652$	6.14732e15	2.04326
$653$	−2.77047e15	−0.913125	−0.456563	−	0.889691i	$-0.650920\pi$
$653$	−2.77047e15	−0.913125	−0.456563	+	0.889691i	$0.650920\pi$
$654$	5.09517e15	1.66526
$655$	−1.65603e15	−0.536712
$656$	6.69461e15	2.15156
$657$	−1.44118e16	−4.59312
$658$	−2.30723e14	−0.0729202
$659$	1.75878e15	0.551240	0.275620	−	0.961267i	$-0.411117\pi$
$659$	1.75878e15	0.551240	0.275620	+	0.961267i	$0.411117\pi$
$660$	−5.37783e15	−1.67153
$661$	−2.49010e15	−0.767555	−0.383777	−	0.923426i	$-0.625377\pi$
$661$	−2.49010e15	−0.767555	−0.383777	+	0.923426i	$0.625377\pi$
$662$	−1.30950e15	−0.400301
$663$	−5.51149e14	−0.167088
$664$	1.18608e15	0.356608
$665$	2.31197e14	0.0689386
$666$	2.51825e16	7.44715
$667$	−9.58153e14	−0.281024
$668$	7.09276e15	2.06322
$669$	−3.38766e15	−0.977365
$670$	−4.63534e15	−1.32639
$671$	−1.53767e15	−0.436404
$672$	7.17245e14	0.201900
$673$	2.61428e14	0.0729909	0.0364954	−	0.999334i	$-0.488381\pi$
$673$	2.61428e14	0.0729909	0.0364954	+	0.999334i	$0.488381\pi$
$674$	4.92140e15	1.36289
$675$	2.77434e15	0.762059
$676$	6.13635e14	0.167187
$677$	4.41872e15	1.19415	0.597076	−	0.802185i	$-0.296329\pi$
$677$	4.41872e15	1.19415	0.597076	+	0.802185i	$0.296329\pi$
$678$	1.23122e16	3.30044
$679$	−9.31470e14	−0.247677
$680$	−2.66892e15	−0.703943
$681$	−1.57662e15	−0.412494
$682$	7.67384e14	0.199158
$683$	7.13796e15	1.83764	0.918819	−	0.394678i	$-0.129144\pi$
$683$	7.13796e15	1.83764	0.918819	+	0.394678i	$0.129144\pi$
$684$	−1.00027e16	−2.55453
$685$	4.77794e15	1.21044
$686$	−2.14269e15	−0.538489
$687$	−5.87025e15	−1.46351
$688$	−4.21467e15	−1.04238
$689$	−2.25204e14	−0.0552548
$690$	−1.74579e16	−4.24935
$691$	4.59401e15	1.10933	0.554667	−	0.832072i	$-0.312846\pi$
$691$	4.59401e15	1.10933	0.554667	+	0.832072i	$0.312846\pi$
$692$	−4.49662e15	−1.07722
$693$	6.56275e14	0.155974
$694$	−1.31311e16	−3.09616
$695$	4.53853e15	1.06169
$696$	4.50765e15	1.04616
$697$	1.84677e15	0.425239
$698$	4.18149e15	0.955270
$699$	2.29390e14	0.0519937
$700$	−3.07109e14	−0.0690642
$701$	−7.00318e15	−1.56259	−0.781297	−	0.624159i	$-0.785442\pi$
$701$	−7.00318e15	−1.56259	−0.781297	+	0.624159i	$0.785442\pi$
$702$	8.18502e15	1.81203
$703$	2.72439e15	0.598432
$704$	5.78394e14	0.126059
$705$	−2.67440e15	−0.578343
$706$	−6.86104e15	−1.47219
$707$	1.10915e15	0.236147
$708$	4.97248e15	1.05049
$709$	−2.31965e15	−0.486260	−0.243130	−	0.969994i	$-0.578174\pi$
$709$	−2.31965e15	−0.486260	−0.243130	+	0.969994i	$0.578174\pi$
$710$	8.07946e15	1.68059
$711$	−2.57801e16	−5.32111
$712$	8.32174e15	1.70441
$713$	1.70614e15	0.346755
$714$	8.13789e14	0.164124
$715$	5.42104e14	0.108492
$716$	−1.56424e16	−3.10657
$717$	−1.27513e16	−2.51304
$718$	−8.91231e15	−1.74303
$719$	2.33755e15	0.453682	0.226841	−	0.973932i	$-0.427160\pi$
$719$	2.33755e15	0.453682	0.226841	+	0.973932i	$0.427160\pi$
$720$	2.53484e16	4.88227
$721$	4.34044e14	0.0829640
$722$	7.81110e15	1.48169
$723$	1.64739e16	3.10124
$724$	−6.75318e15	−1.26167
$725$	−2.85268e14	−0.0528924
$726$	1.66219e16	3.05865
$727$	4.34203e15	0.792964	0.396482	−	0.918042i	$-0.370231\pi$
$727$	4.34203e15	0.792964	0.396482	+	0.918042i	$0.370231\pi$
$728$	−4.89176e14	−0.0886630
$729$	2.91302e16	5.24012
$730$	1.75774e16	3.13820
$731$	−1.16266e15	−0.206018
$732$	2.97899e16	5.23911
$733$	2.28839e15	0.399446	0.199723	−	0.979852i	$-0.435996\pi$
$733$	2.28839e15	0.399446	0.199723	+	0.979852i	$0.435996\pi$
$734$	−8.91965e15	−1.54532
$735$	−1.22714e16	−2.11016
$736$	−4.34352e15	−0.741334
$737$	−1.42350e15	−0.241150
$738$	−4.21285e16	−7.08380
$739$	−3.96465e15	−0.661698	−0.330849	−	0.943684i	$-0.607335\pi$
$739$	−3.96465e15	−0.661698	−0.330849	+	0.943684i	$0.607335\pi$
$740$	−2.10356e16	−3.48481
$741$	1.36020e15	0.223668
$742$	3.32520e14	0.0542746
$743$	−1.15398e16	−1.86964	−0.934821	−	0.355119i	$-0.884440\pi$
$743$	−1.15398e16	−1.86964	−0.934821	+	0.355119i	$0.884440\pi$
$744$	−8.02658e15	−1.29086
$745$	5.08827e15	0.812289
$746$	−1.38790e13	−0.00219936
$747$	−3.10754e15	−0.488826
$748$	−1.51810e15	−0.237051
$749$	−3.61068e14	−0.0559679
$750$	1.98170e16	3.04930
$751$	6.70009e15	1.02344	0.511719	−	0.859153i	$-0.329009\pi$
$751$	6.70009e15	1.02344	0.511719	+	0.859153i	$0.329009\pi$
$752$	−2.73672e15	−0.414985
$753$	1.67422e16	2.52022
$754$	−8.41614e14	−0.125768
$755$	−3.55378e15	−0.527208
$756$	−8.27712e15	−1.21902
$757$	3.02082e15	0.441670	0.220835	−	0.975311i	$-0.429122\pi$
$757$	3.02082e15	0.441670	0.220835	+	0.975311i	$0.429122\pi$
$758$	−2.42799e15	−0.352425
$759$	−5.36128e15	−0.772572
$760$	6.58674e15	0.942315
$761$	6.55745e15	0.931364	0.465682	−	0.884952i	$-0.345809\pi$
$761$	6.55745e15	0.931364	0.465682	+	0.884952i	$0.345809\pi$
$762$	−2.19729e16	−3.09838
$763$	5.19390e14	0.0727125
$764$	−8.30425e15	−1.15422
$765$	6.99259e15	0.964940
$766$	1.68592e16	2.30982
$767$	−5.01243e14	−0.0681827
$768$	−2.86194e16	−3.86522
$769$	6.49137e15	0.870446	0.435223	−	0.900323i	$-0.356670\pi$
$769$	6.49137e15	0.870446	0.435223	+	0.900323i	$0.356670\pi$
$770$	−8.00433e14	−0.106568
$771$	1.33761e16	1.76819
$772$	−7.88563e15	−1.03500
$773$	−1.20236e16	−1.56692	−0.783460	−	0.621442i	$-0.786547\pi$
$773$	−1.20236e16	−1.56692	−0.783460	+	0.621442i	$0.786547\pi$
$774$	2.65225e16	3.43194
$775$	5.07964e14	0.0652640
$776$	−2.65374e16	−3.38547
$777$	3.46292e15	0.438658
$778$	−2.07501e16	−2.60995
$779$	−4.55772e15	−0.569235
$780$	−1.05024e16	−1.30247
$781$	2.48118e15	0.305547
$782$	−4.92817e15	−0.602627
$783$	−7.68846e15	−0.933576
$784$	−1.25574e16	−1.51413
$785$	−9.32126e15	−1.11607
$786$	1.43858e16	1.71045
$787$	−1.37929e15	−0.162853	−0.0814264	−	0.996679i	$-0.525948\pi$
$787$	−1.37929e15	−0.162853	−0.0814264	+	0.996679i	$0.525948\pi$
$788$	1.94026e16	2.27491
$789$	3.92534e14	0.0457040
$790$	3.14430e16	3.63559
$791$	1.25507e15	0.144112
$792$	1.86971e16	2.13200
$793$	−3.00292e15	−0.340049
$794$	1.88415e16	2.11886
$795$	3.85437e15	0.430462
$796$	1.45273e16	1.61125
$797$	1.17675e15	0.129617	0.0648087	−	0.997898i	$-0.479356\pi$
$797$	1.17675e15	0.129617	0.0648087	+	0.997898i	$0.479356\pi$
$798$	−2.00838e15	−0.219700
$799$	−7.54951e14	−0.0820184
$800$	−1.29318e15	−0.139529
$801$	−2.18030e16	−2.33635
$802$	−2.05903e16	−2.19131
$803$	5.39799e15	0.570553
$804$	2.75781e16	2.89504
$805$	−1.77962e15	−0.185546
$806$	1.49863e15	0.155185
$807$	−1.88801e16	−1.94178
$808$	3.15993e16	3.22787
$809$	9.80169e15	0.994453	0.497226	−	0.867621i	$-0.334352\pi$
$809$	9.80169e15	0.994453	0.497226	+	0.867621i	$0.334352\pi$
$810$	−8.44179e16	−8.50681
$811$	5.92177e15	0.592703	0.296351	−	0.955079i	$-0.404230\pi$
$811$	5.92177e15	0.592703	0.296351	+	0.955079i	$0.404230\pi$
$812$	8.51084e14	0.0846086
$813$	1.77989e16	1.75750
$814$	−9.43220e15	−0.925079
$815$	1.06057e16	1.03317
$816$	9.65276e15	0.934019
$817$	2.86937e15	0.275781
$818$	−4.90766e15	−0.468524
$819$	1.28164e15	0.121536
$820$	3.51911e16	3.31479
$821$	−1.78148e16	−1.66684	−0.833418	−	0.552643i	$-0.813619\pi$
$821$	−1.78148e16	−1.66684	−0.833418	+	0.552643i	$0.813619\pi$
$822$	−4.15054e16	−3.85754
$823$	−1.93020e16	−1.78199	−0.890993	−	0.454018i	$-0.849990\pi$
$823$	−1.93020e16	−1.78199	−0.890993	+	0.454018i	$0.849990\pi$
$824$	1.23658e16	1.13403
$825$	−1.59620e15	−0.145408
$826$	7.40101e14	0.0669732
$827$	8.68345e15	0.780570	0.390285	−	0.920694i	$-0.372376\pi$
$827$	8.68345e15	0.780570	0.390285	+	0.920694i	$0.372376\pi$
$828$	7.69956e16	6.87542
$829$	1.35553e16	1.20243	0.601213	−	0.799089i	$-0.294684\pi$
$829$	1.35553e16	1.20243	0.601213	+	0.799089i	$0.294684\pi$
$830$	3.79015e15	0.333985
$831$	2.61553e16	2.28958
$832$	1.12955e15	0.0982260
$833$	−3.46408e15	−0.299255
$834$	−3.94257e16	−3.38350
$835$	1.22368e16	1.04326
$836$	3.74657e15	0.317322
$837$	1.36905e16	1.15194
$838$	−1.19258e16	−0.996889
$839$	−1.24391e16	−1.03300	−0.516499	−	0.856288i	$-0.672765\pi$
$839$	−1.24391e16	−1.03300	−0.516499	+	0.856288i	$0.672765\pi$
$840$	8.37227e15	0.690728
$841$	−1.14100e16	−0.935203
$842$	2.54879e16	2.07548
$843$	−1.97471e16	−1.59754
$844$	−8.33623e15	−0.670017
$845$	1.05868e15	0.0845379
$846$	1.72219e16	1.36630
$847$	1.69440e15	0.133554
$848$	3.94419e15	0.308874
$849$	3.16204e16	2.46023
$850$	−1.46725e15	−0.113422
$851$	−2.09708e16	−1.61066
$852$	−4.80688e16	−3.66814
$853$	−1.96232e16	−1.48782	−0.743911	−	0.668278i	$-0.767031\pi$
$853$	−1.96232e16	−1.48782	−0.743911	+	0.668278i	$0.767031\pi$
$854$	4.43390e15	0.334017
$855$	−1.72573e16	−1.29169
$856$	−1.02867e16	−0.765019
$857$	−1.81142e16	−1.33852	−0.669260	−	0.743028i	$-0.733389\pi$
$857$	−1.81142e16	−1.33852	−0.669260	+	0.743028i	$0.733389\pi$
$858$	−4.70920e15	−0.345754
$859$	−2.39903e16	−1.75014	−0.875070	−	0.483997i	$-0.839185\pi$
$859$	−2.39903e16	−1.75014	−0.875070	+	0.483997i	$0.839185\pi$
$860$	−2.21549e16	−1.60594
$861$	−5.79322e15	−0.417256
$862$	−2.68981e16	−1.92500
$863$	2.45591e16	1.74644	0.873218	−	0.487329i	$-0.162029\pi$
$863$	2.45591e16	1.74644	0.873218	+	0.487329i	$0.162029\pi$
$864$	−3.48535e16	−2.46275
$865$	−7.75782e15	−0.544692
$866$	2.90170e16	2.02443
$867$	−2.56970e16	−1.78146
$868$	−1.51549e15	−0.104399
$869$	9.65606e15	0.660984
$870$	1.44043e16	0.979795
$871$	−2.77996e15	−0.187905
$872$	1.47973e16	0.993899
$873$	6.95280e16	4.64068
$874$	1.21624e16	0.806691
$875$	2.02010e15	0.133146
$876$	−1.04577e17	−6.84959
$877$	−1.54180e16	−1.00353	−0.501765	−	0.865004i	$-0.667316\pi$
$877$	−1.54180e16	−1.00353	−0.501765	+	0.865004i	$0.667316\pi$
$878$	2.58206e16	1.67012
$879$	2.72594e16	1.75217
$880$	−9.49435e15	−0.606472
$881$	−7.65477e15	−0.485920	−0.242960	−	0.970036i	$-0.578118\pi$
$881$	−7.65477e15	−0.485920	−0.242960	+	0.970036i	$0.578118\pi$
$882$	7.90226e16	4.98510
$883$	1.39715e15	0.0875909	0.0437955	−	0.999041i	$-0.486055\pi$
$883$	1.39715e15	0.0875909	0.0437955	+	0.999041i	$0.486055\pi$
$884$	−2.96470e15	−0.184711
$885$	8.57880e15	0.531176
$886$	−1.99924e16	−1.23021
$887$	3.96850e15	0.242687	0.121343	−	0.992611i	$-0.461280\pi$
$887$	3.96850e15	0.242687	0.121343	+	0.992611i	$0.461280\pi$
$888$	9.86577e16	5.99597
$889$	−2.23987e15	−0.135289
$890$	2.65922e16	1.59628
$891$	−2.59245e16	−1.54662
$892$	−1.82227e16	−1.08045
$893$	1.86317e15	0.109792
$894$	−4.42012e16	−2.58868
$895$	−2.69871e16	−1.57083
$896$	−3.44295e15	−0.199176
$897$	−1.04701e16	−0.601993
$898$	1.81532e16	1.03737
$899$	−1.40771e15	−0.0799530
$900$	2.29236e16	1.29405
$901$	1.08804e15	0.0610464
$902$	1.57794e16	0.879944
$903$	3.64719e15	0.202151
$904$	3.57568e16	1.96985
$905$	−1.16510e16	−0.637962
$906$	3.08713e16	1.68016
$907$	−2.06793e16	−1.11866	−0.559328	−	0.828946i	$-0.688941\pi$
$907$	−2.06793e16	−1.11866	−0.559328	+	0.828946i	$0.688941\pi$
$908$	−8.48083e15	−0.456002
$909$	−8.27904e16	−4.42465
$910$	−1.56317e15	−0.0830383
$911$	−1.35138e16	−0.713552	−0.356776	−	0.934190i	$-0.616124\pi$
$911$	−1.35138e16	−0.713552	−0.356776	+	0.934190i	$0.616124\pi$
$912$	−2.38224e16	−1.25030
$913$	1.16394e15	0.0607216
$914$	4.27547e16	2.21707
$915$	5.13951e16	2.64915
$916$	−3.15768e16	−1.61787
$917$	1.46645e15	0.0746856
$918$	−3.95449e16	−2.00196
$919$	2.79491e16	1.40648	0.703239	−	0.710953i	$-0.251736\pi$
$919$	2.79491e16	1.40648	0.703239	+	0.710953i	$0.251736\pi$
$920$	−5.07011e16	−2.53620
$921$	6.07194e16	3.01925
$922$	4.19473e16	2.07340
$923$	4.84551e15	0.238084
$924$	4.76219e15	0.232601
$925$	−6.24358e15	−0.303147
$926$	−3.64211e16	−1.75789
$927$	−3.23985e16	−1.55448
$928$	3.58377e15	0.170933
$929$	2.45428e16	1.16369	0.581845	−	0.813300i	$-0.302331\pi$
$929$	2.45428e16	1.16369	0.581845	+	0.813300i	$0.302331\pi$
$930$	−2.56491e16	−1.20897
$931$	8.54914e15	0.400589
$932$	1.23392e15	0.0574777
$933$	1.05651e15	0.0489241
$934$	−2.53384e16	−1.16646
$935$	−2.61911e15	−0.119864
$936$	3.65137e16	1.66127
$937$	−1.50982e16	−0.682901	−0.341451	−	0.939900i	$-0.610918\pi$
$937$	−1.50982e16	−0.682901	−0.341451	+	0.939900i	$0.610918\pi$
$938$	4.10470e15	0.184572
$939$	7.93949e16	3.54921
$940$	−1.43859e16	−0.639344
$941$	−2.28006e14	−0.0100740	−0.00503701	−	0.999987i	$-0.501603\pi$
$941$	−2.28006e14	−0.0100740	−0.00503701	+	0.999987i	$0.501603\pi$
$942$	8.09728e16	3.55680
$943$	3.50828e16	1.53207
$944$	8.77872e15	0.381141
$945$	−1.42801e16	−0.616393
$946$	−9.93412e15	−0.426313
$947$	9.07029e15	0.386987	0.193494	−	0.981102i	$-0.438018\pi$
$947$	9.07029e15	0.386987	0.193494	+	0.981102i	$0.438018\pi$
$948$	−1.87071e17	−7.93523
$949$	1.05418e16	0.444579
$950$	3.62108e15	0.151830
$951$	−1.19244e16	−0.497101
$952$	2.36339e15	0.0979564
$953$	−6.30557e15	−0.259844	−0.129922	−	0.991524i	$-0.541473\pi$
$953$	−6.30557e15	−0.259844	−0.129922	+	0.991524i	$0.541473\pi$
$954$	−2.48204e16	−1.01694
$955$	−1.43269e16	−0.583627
$956$	−6.85909e16	−2.77810
$957$	4.42351e15	0.178136
$958$	1.04343e16	0.417784
$959$	−4.23097e15	−0.168437
$960$	−1.93323e16	−0.765228
$961$	−2.29018e16	−0.901346
$962$	−1.84202e16	−0.720827
$963$	2.69513e16	1.04866
$964$	8.86151e16	3.42834
$965$	−1.36047e16	−0.523346
$966$	1.54594e16	0.591314
$967$	1.15613e16	0.439705	0.219852	−	0.975533i	$-0.429442\pi$
$967$	1.15613e16	0.439705	0.219852	+	0.975533i	$0.429442\pi$
$968$	4.82731e16	1.82554
$969$	−6.57164e15	−0.247112
$970$	−8.48006e16	−3.17069
$971$	7.47877e15	0.278051	0.139026	−	0.990289i	$-0.455603\pi$
$971$	7.47877e15	0.278051	0.139026	+	0.990289i	$0.455603\pi$
$972$	2.86628e17	10.5963
$973$	−4.01897e15	−0.147739
$974$	6.76547e16	2.47300
$975$	−3.11722e15	−0.113303
$976$	5.25928e16	1.90087
$977$	−8.78218e15	−0.315633	−0.157816	−	0.987468i	$-0.550445\pi$
$977$	−8.78218e15	−0.315633	−0.157816	+	0.987468i	$0.550445\pi$
$978$	−9.21305e16	−3.29261
$979$	8.16640e15	0.290219
$980$	−6.60096e16	−2.33273
$981$	−3.87690e16	−1.36240
$982$	1.82594e16	0.638079
$983$	−1.52932e16	−0.531439	−0.265720	−	0.964050i	$-0.585610\pi$
$983$	−1.52932e16	−0.531439	−0.265720	+	0.964050i	$0.585610\pi$
$984$	−1.65048e17	−5.70343
$985$	3.34744e16	1.15031
$986$	4.06615e15	0.138951
$987$	2.36824e15	0.0804787
$988$	7.31670e15	0.247259
$989$	−2.20868e16	−0.742254
$990$	5.97470e16	1.99675
$991$	−1.56887e16	−0.521413	−0.260706	−	0.965418i	$-0.583955\pi$
$991$	−1.56887e16	−0.521413	−0.260706	+	0.965418i	$0.583955\pi$
$992$	−6.38147e15	−0.210914
$993$	1.34413e16	0.441794
$994$	−7.15454e15	−0.233860
$995$	2.50633e16	0.814727
$996$	−2.25496e16	−0.728973
$997$	5.36897e16	1.72611	0.863053	−	0.505113i	$-0.168549\pi$
$997$	5.36897e16	1.72611	0.863053	+	0.505113i	$0.168549\pi$
$998$	−7.66315e16	−2.45013
$999$	−1.68275e17	−5.35070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.12.a.b.1.1	✓	6
3.2	odd	2		117.12.a.d.1.6		6
4.3	odd	2		208.12.a.h.1.1		6
13.12	even	2		169.12.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.12.a.b.1.1	✓	6	1.1	even	1	trivial
117.12.a.d.1.6		6	3.2	odd	2
169.12.a.c.1.6		6	13.12	even	2
208.12.a.h.1.1		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	13.a (trivial)

\(f(q)\)	\(=\)	\(q-80.6176 q^{2} +827.494 q^{3} +4451.20 q^{4} +7679.45 q^{5} -66710.6 q^{6} -6800.32 q^{7} -193740. q^{8} +507599. q^{9} +O(q^{10})\)	\(q-80.6176 q^{2} +827.494 q^{3} +4451.20 q^{4} +7679.45 q^{5} -66710.6 q^{6} -6800.32 q^{7} -193740. q^{8} +507599. q^{9} -619099. q^{10} -190123. q^{11} +3.68334e6 q^{12} -371293. q^{13} +548226. q^{14} +6.35470e6 q^{15} +6.50279e6 q^{16} +1.79386e6 q^{17} -4.09214e7 q^{18} -4.42713e6 q^{19} +3.41827e7 q^{20} -5.62723e6 q^{21} +1.53273e7 q^{22} +3.40776e7 q^{23} -1.60318e8 q^{24} +1.01458e7 q^{25} +2.99327e7 q^{26} +2.73447e8 q^{27} -3.02696e7 q^{28} -2.81168e7 q^{29} -5.12300e8 q^{30} +5.00665e7 q^{31} -1.27460e8 q^{32} -1.57326e8 q^{33} -1.44616e8 q^{34} -5.22227e7 q^{35} +2.25942e9 q^{36} -6.15386e8 q^{37} +3.56904e8 q^{38} -3.07243e8 q^{39} -1.48781e9 q^{40} +1.02950e9 q^{41} +4.53653e8 q^{42} -6.48133e8 q^{43} -8.46277e8 q^{44} +3.89808e9 q^{45} -2.74725e9 q^{46} -4.20854e8 q^{47} +5.38102e9 q^{48} -1.93108e9 q^{49} -8.17929e8 q^{50} +1.48440e9 q^{51} -1.65270e9 q^{52} +6.06539e8 q^{53} -2.20446e10 q^{54} -1.46004e9 q^{55} +1.31749e9 q^{56} -3.66342e9 q^{57} +2.26671e9 q^{58} +1.34999e9 q^{59} +2.82860e10 q^{60} +8.08774e9 q^{61} -4.03624e9 q^{62} -3.45184e9 q^{63} -3.04220e9 q^{64} -2.85133e9 q^{65} +1.26832e10 q^{66} +7.48725e9 q^{67} +7.98480e9 q^{68} +2.81990e10 q^{69} +4.21007e9 q^{70} -1.30504e10 q^{71} -9.83421e10 q^{72} -2.83920e10 q^{73} +4.96109e10 q^{74} +8.39558e9 q^{75} -1.97060e10 q^{76} +1.29290e9 q^{77} +2.47692e10 q^{78} -5.07884e10 q^{79} +4.99378e10 q^{80} +1.36356e11 q^{81} -8.29957e10 q^{82} -6.12205e9 q^{83} -2.50479e10 q^{84} +1.37758e10 q^{85} +5.22509e10 q^{86} -2.32665e10 q^{87} +3.68345e10 q^{88} -4.29532e10 q^{89} -3.14254e11 q^{90} +2.52491e9 q^{91} +1.51686e11 q^{92} +4.14297e10 q^{93} +3.39282e10 q^{94} -3.39979e10 q^{95} -1.05472e11 q^{96} +1.36974e11 q^{97} +1.55679e11 q^{98} -9.65065e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9}+O(q^{10}) \) 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9	\( 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9} + 997497 q^{10} + 275060 q^{11} + 3949049 q^{12} - 2227758 q^{13} + 6462587 q^{14} + 5951652 q^{15} + 25038945 q^{16} + 18470848 q^{17} + 1544758 q^{18} + 2382612 q^{19} + 37821799 q^{20} - 67640772 q^{21} - 52649718 q^{22} + 25001944 q^{23} - 243039615 q^{24} - 14063202 q^{25} - 20421115 q^{26} + 77250908 q^{27} - 340836927 q^{28} - 142876028 q^{29} - 838796927 q^{30} - 158397468 q^{31} + 739784589 q^{32} - 115057792 q^{33} - 668802009 q^{34} + 1377003692 q^{35} + 3099344006 q^{36} + 47994456 q^{37} + 2673019714 q^{38} - 176735468 q^{39} + 242886231 q^{40} + 112037548 q^{41} - 5282633557 q^{42} + 1399191924 q^{43} - 1571975050 q^{44} + 7736061780 q^{45} - 2701412412 q^{46} - 3383597640 q^{47} + 1090782789 q^{48} + 7189538970 q^{49} - 12848613144 q^{50} + 8959562860 q^{51} - 5684124537 q^{52} + 546961604 q^{53} - 38372021519 q^{54} - 7803526248 q^{55} - 6807872407 q^{56} + 918537576 q^{57} + 5714690406 q^{58} + 10067834260 q^{59} + 2453022955 q^{60} + 15731821572 q^{61} - 7829475572 q^{62} + 29876175732 q^{63} + 2237284569 q^{64} - 1229722416 q^{65} + 12031833058 q^{66} + 50546073444 q^{67} + 15412804265 q^{68} + 10879166680 q^{69} + 2924449065 q^{70} - 2646136112 q^{71} - 8720745402 q^{72} + 4198695060 q^{73} + 5050454541 q^{74} - 7695720336 q^{75} + 59928748062 q^{76} + 9015828840 q^{77} + 21459621521 q^{78} - 92124930312 q^{79} + 89421404931 q^{80} + 67208776622 q^{81} - 150798850248 q^{82} + 20440296092 q^{83} - 419349915667 q^{84} - 124095891228 q^{85} + 116436457677 q^{86} - 161197597808 q^{87} - 158617438842 q^{88} + 20540234076 q^{89} - 279059693450 q^{90} + 1550519568 q^{91} + 446253814012 q^{92} + 142195723000 q^{93} + 92592053391 q^{94} + 82521342544 q^{95} - 2651637759 q^{96} - 203942467020 q^{97} + 711378915442 q^{98} - 235408311580 q^{99}+O(q^{100}) \) 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9 + 997497 * q^10 + 275060 * q^11 + 3949049 * q^12 - 2227758 * q^13 + 6462587 * q^14 + 5951652 * q^15 + 25038945 * q^16 + 18470848 * q^17 + 1544758 * q^18 + 2382612 * q^19 + 37821799 * q^20 - 67640772 * q^21 - 52649718 * q^22 + 25001944 * q^23 - 243039615 * q^24 - 14063202 * q^25 - 20421115 * q^26 + 77250908 * q^27 - 340836927 * q^28 - 142876028 * q^29 - 838796927 * q^30 - 158397468 * q^31 + 739784589 * q^32 - 115057792 * q^33 - 668802009 * q^34 + 1377003692 * q^35 + 3099344006 * q^36 + 47994456 * q^37 + 2673019714 * q^38 - 176735468 * q^39 + 242886231 * q^40 + 112037548 * q^41 - 5282633557 * q^42 + 1399191924 * q^43 - 1571975050 * q^44 + 7736061780 * q^45 - 2701412412 * q^46 - 3383597640 * q^47 + 1090782789 * q^48 + 7189538970 * q^49 - 12848613144 * q^50 + 8959562860 * q^51 - 5684124537 * q^52 + 546961604 * q^53 - 38372021519 * q^54 - 7803526248 * q^55 - 6807872407 * q^56 + 918537576 * q^57 + 5714690406 * q^58 + 10067834260 * q^59 + 2453022955 * q^60 + 15731821572 * q^61 - 7829475572 * q^62 + 29876175732 * q^63 + 2237284569 * q^64 - 1229722416 * q^65 + 12031833058 * q^66 + 50546073444 * q^67 + 15412804265 * q^68 + 10879166680 * q^69 + 2924449065 * q^70 - 2646136112 * q^71 - 8720745402 * q^72 + 4198695060 * q^73 + 5050454541 * q^74 - 7695720336 * q^75 + 59928748062 * q^76 + 9015828840 * q^77 + 21459621521 * q^78 - 92124930312 * q^79 + 89421404931 * q^80 + 67208776622 * q^81 - 150798850248 * q^82 + 20440296092 * q^83 - 419349915667 * q^84 - 124095891228 * q^85 + 116436457677 * q^86 - 161197597808 * q^87 - 158617438842 * q^88 + 20540234076 * q^89 - 279059693450 * q^90 + 1550519568 * q^91 + 446253814012 * q^92 + 142195723000 * q^93 + 92592053391 * q^94 + 82521342544 * q^95 - 2651637759 * q^96 - 203942467020 * q^97 + 711378915442 * q^98 - 235408311580 * q^99

Introduction

L-functions

Modular forms

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