LMFDB - Embedded newform 29.18.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,18,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	29.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:	$53.1344053299$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 1610997 x^{16} - 28978880 x^{15} + 1054878119348 x^{14} + 33471007935200 x^{13} + \cdots - 13\!\cdots\!24 $ x^18 - 1610997x^16 - 28978880x^15 + 1054878119348x^14 + 33471007935200x^13 - 361118629330503872x^12 - 14867597249727884800x^11 + 69075461759211999549440x^10 + 3136429534292709271797760x^9 - 7293684107327839501793427456x^8 - 310705174164268019482139033600x^7 + 392089226833876108917621043232768x^6 + 11987811702756552456984769970831360x^5 - 8875073388959894229615422940880306176x^4 - 110123126416280653106554268008725872640x^3 + 38261887665727248243207924189998746697728x^2 - 570869901591701973911550639846099485982720x - 1366002559879573583573099965753694433050624
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{14}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$54.5616$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+54.5616 q^{2} -10196.6 q^{3} -128095. q^{4} -1.33117e6 q^{5} -556341. q^{6} +2.01292e7 q^{7} -1.41406e7 q^{8} -2.51701e7 q^{9} +O(q^{10})$	\(q+54.5616 q^{2} -10196.6 q^{3} -128095. q^{4} -1.33117e6 q^{5} -556341. q^{6} +2.01292e7 q^{7} -1.41406e7 q^{8} -2.51701e7 q^{9} -7.26309e7 q^{10} +2.80767e8 q^{11} +1.30613e9 q^{12} +9.57014e8 q^{13} +1.09828e9 q^{14} +1.35734e10 q^{15} +1.60181e10 q^{16} +5.38562e10 q^{17} -1.37332e9 q^{18} -4.43543e10 q^{19} +1.70517e11 q^{20} -2.05249e11 q^{21} +1.53191e10 q^{22} -6.01447e11 q^{23} +1.44185e11 q^{24} +1.00908e12 q^{25} +5.22162e10 q^{26} +1.57344e12 q^{27} -2.57845e12 q^{28} -5.00246e11 q^{29} +7.40586e11 q^{30} +2.83601e12 q^{31} +2.72741e12 q^{32} -2.86286e12 q^{33} +2.93848e12 q^{34} -2.67955e13 q^{35} +3.22416e12 q^{36} -1.36128e13 q^{37} -2.42004e12 q^{38} -9.75827e12 q^{39} +1.88235e13 q^{40} -1.86675e13 q^{41} -1.11987e13 q^{42} +2.11163e13 q^{43} -3.59649e13 q^{44} +3.35057e13 q^{45} -3.28159e13 q^{46} +7.40600e13 q^{47} -1.63330e14 q^{48} +1.72554e14 q^{49} +5.50572e13 q^{50} -5.49149e14 q^{51} -1.22589e14 q^{52} +4.25173e14 q^{53} +8.58491e13 q^{54} -3.73750e14 q^{55} -2.84638e14 q^{56} +4.52262e14 q^{57} -2.72942e13 q^{58} +1.17870e15 q^{59} -1.73869e15 q^{60} -2.42023e15 q^{61} +1.54737e14 q^{62} -5.06654e14 q^{63} -1.95072e15 q^{64} -1.27395e15 q^{65} -1.56202e14 q^{66} +4.35045e14 q^{67} -6.89871e15 q^{68} +6.13270e15 q^{69} -1.46200e15 q^{70} -5.22292e15 q^{71} +3.55919e14 q^{72} -6.64010e15 q^{73} -7.42733e14 q^{74} -1.02892e16 q^{75} +5.68157e15 q^{76} +5.65162e15 q^{77} -5.32426e14 q^{78} +3.89746e15 q^{79} -2.13229e16 q^{80} -1.27932e16 q^{81} -1.01853e15 q^{82} +1.53250e16 q^{83} +2.62914e16 q^{84} -7.16920e16 q^{85} +1.15214e15 q^{86} +5.10080e15 q^{87} -3.97021e15 q^{88} +5.58798e16 q^{89} +1.82813e15 q^{90} +1.92639e16 q^{91} +7.70423e16 q^{92} -2.89175e16 q^{93} +4.04083e15 q^{94} +5.90433e16 q^{95} -2.78102e16 q^{96} -1.24003e17 q^{97} +9.41484e15 q^{98} -7.06694e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) $ 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * 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 $

$2$	54.5616	0.150706	0.0753532	−	0.997157i	$-0.475992\pi$
$2$	54.5616	0.150706	0.0753532	+	0.997157i	$0.475992\pi$
$3$	−10196.6	−0.897271	−0.448635	−	0.893715i	$-0.648090\pi$
$3$	−10196.6	−0.897271	−0.448635	+	0.893715i	$0.648090\pi$
$4$	−128095.	−0.977288
$5$	−1.33117e6	−1.52402	−0.762008	−	0.647567i	$-0.775786\pi$
$5$	−1.33117e6	−1.52402	−0.762008	+	0.647567i	$0.775786\pi$
$6$	−556341.	−0.135225
$7$	2.01292e7	1.31975	0.659877	−	0.751373i	$-0.270608\pi$
$7$	2.01292e7	1.31975	0.659877	+	0.751373i	$0.270608\pi$
$8$	−1.41406e7	−0.297990
$9$	−2.51701e7	−0.194905
$10$	−7.26309e7	−0.229679
$11$	2.80767e8	0.394920	0.197460	−	0.980311i	$-0.436731\pi$
$11$	2.80767e8	0.394920	0.197460	+	0.980311i	$0.436731\pi$
$12$	1.30613e9	0.876892
$13$	9.57014e8	0.325387	0.162693	−	0.986677i	$-0.447982\pi$
$13$	9.57014e8	0.325387	0.162693	+	0.986677i	$0.447982\pi$
$14$	1.09828e9	0.198896
$15$	1.35734e10	1.36746
$16$	1.60181e10	0.932379
$17$	5.38562e10	1.87249	0.936246	−	0.351345i	$-0.114276\pi$
$17$	5.38562e10	1.87249	0.936246	+	0.351345i	$0.114276\pi$
$18$	−1.37332e9	−0.0293735
$19$	−4.43543e10	−0.599143	−0.299572	−	0.954074i	$-0.596844\pi$
$19$	−4.43543e10	−0.599143	−0.299572	+	0.954074i	$0.596844\pi$
$20$	1.70517e11	1.48940
$21$	−2.05249e11	−1.18418
$22$	1.53191e10	0.0595169
$23$	−6.01447e11	−1.60144	−0.800720	−	0.599039i	$-0.795549\pi$
$23$	−6.01447e11	−1.60144	−0.800720	+	0.599039i	$0.795549\pi$
$24$	1.44185e11	0.267378
$25$	1.00908e12	1.32263
$26$	5.22162e10	0.0490379
$27$	1.57344e12	1.07215
$28$	−2.57845e12	−1.28978
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	7.40586e11	0.206084
$31$	2.83601e12	0.597218	0.298609	−	0.954376i	$-0.403477\pi$
$31$	2.83601e12	0.597218	0.298609	+	0.954376i	$0.403477\pi$
$32$	2.72741e12	0.438506
$33$	−2.86286e12	−0.354350
$34$	2.93848e12	0.282197
$35$	−2.67955e13	−2.01133
$36$	3.22416e12	0.190478
$37$	−1.36128e13	−0.637135	−0.318567	−	0.947900i	$-0.603202\pi$
$37$	−1.36128e13	−0.637135	−0.318567	+	0.947900i	$0.603202\pi$
$38$	−2.42004e12	−0.0902947
$39$	−9.75827e12	−0.291960
$40$	1.88235e13	0.454142
$41$	−1.86675e13	−0.365110	−0.182555	−	0.983196i	$-0.558437\pi$
$41$	−1.86675e13	−0.365110	−0.182555	+	0.983196i	$0.558437\pi$
$42$	−1.11987e13	−0.178463
$43$	2.11163e13	0.275510	0.137755	−	0.990466i	$-0.456011\pi$
$43$	2.11163e13	0.275510	0.137755	+	0.990466i	$0.456011\pi$
$44$	−3.59649e13	−0.385950
$45$	3.35057e13	0.297039
$46$	−3.28159e13	−0.241347
$47$	7.40600e13	0.453683	0.226841	−	0.973932i	$-0.427160\pi$
$47$	7.40600e13	0.453683	0.226841	+	0.973932i	$0.427160\pi$
$48$	−1.63330e14	−0.836596
$49$	1.72554e14	0.741753
$50$	5.50572e13	0.199328
$51$	−5.49149e14	−1.68013
$52$	−1.22589e14	−0.317996
$53$	4.25173e14	0.938039	0.469019	−	0.883188i	$-0.344607\pi$
$53$	4.25173e14	0.938039	0.469019	+	0.883188i	$0.344607\pi$
$54$	8.58491e13	0.161580
$55$	−3.73750e14	−0.601864
$56$	−2.84638e14	−0.393274
$57$	4.52262e14	0.537594
$58$	−2.72942e13	−0.0279855
$59$	1.17870e15	1.04511	0.522556	−	0.852605i	$-0.324979\pi$
$59$	1.17870e15	1.04511	0.522556	+	0.852605i	$0.324979\pi$
$60$	−1.73869e15	−1.33640
$61$	−2.42023e15	−1.61642	−0.808209	−	0.588896i	$-0.799563\pi$
$61$	−2.42023e15	−1.61642	−0.808209	+	0.588896i	$0.799563\pi$
$62$	1.54737e14	0.0900046
$63$	−5.06654e14	−0.257227
$64$	−1.95072e15	−0.866293
$65$	−1.27395e15	−0.495895
$66$	−1.56202e14	−0.0534028
$67$	4.35045e14	0.130888	0.0654438	−	0.997856i	$-0.479154\pi$
$67$	4.35045e14	0.130888	0.0654438	+	0.997856i	$0.479154\pi$
$68$	−6.89871e15	−1.82996
$69$	6.13270e15	1.43693
$70$	−1.46200e15	−0.303120
$71$	−5.22292e15	−0.959880	−0.479940	−	0.877301i	$-0.659342\pi$
$71$	−5.22292e15	−0.959880	−0.479940	+	0.877301i	$0.659342\pi$
$72$	3.55919e14	0.0580798
$73$	−6.64010e15	−0.963674	−0.481837	−	0.876261i	$-0.660030\pi$
$73$	−6.64010e15	−0.963674	−0.481837	+	0.876261i	$0.660030\pi$
$74$	−7.42733e14	−0.0960203
$75$	−1.02892e16	−1.18675
$76$	5.68157e15	0.585535
$77$	5.65162e15	0.521197
$78$	−5.32426e14	−0.0440003
$79$	3.89746e15	0.289036	0.144518	−	0.989502i	$-0.453837\pi$
$79$	3.89746e15	0.289036	0.144518	+	0.989502i	$0.453837\pi$
$80$	−2.13229e16	−1.42096
$81$	−1.27932e16	−0.767107
$82$	−1.01853e15	−0.0550245
$83$	1.53250e16	0.746857	0.373428	−	0.927659i	$-0.378182\pi$
$83$	1.53250e16	0.746857	0.373428	+	0.927659i	$0.378182\pi$
$84$	2.62914e16	1.15728
$85$	−7.16920e16	−2.85371
$86$	1.15214e15	0.0415211
$87$	5.10080e15	0.166619
$88$	−3.97021e15	−0.117682
$89$	5.58798e16	1.50466	0.752332	−	0.658784i	$-0.228929\pi$
$89$	5.58798e16	1.50466	0.752332	+	0.658784i	$0.228929\pi$
$90$	1.82813e15	0.0447656
$91$	1.92639e16	0.429431
$92$	7.70423e16	1.56507
$93$	−2.89175e16	−0.535866
$94$	4.04083e15	0.0683729
$95$	5.90433e16	0.913104
$96$	−2.78102e16	−0.393458
$97$	−1.24003e17	−1.60648	−0.803238	−	0.595659i	$-0.796891\pi$
$97$	−1.24003e17	−1.60648	−0.803238	+	0.595659i	$0.796891\pi$
$98$	9.41484e15	0.111787
$99$	−7.06694e15	−0.0769719
$100$	−1.29259e17	−1.29259
$101$	7.97192e16	0.732540	0.366270	−	0.930509i	$-0.380635\pi$
$101$	7.97192e16	0.732540	0.366270	+	0.930509i	$0.380635\pi$
$102$	−2.99624e16	−0.253207
$103$	2.37203e16	0.184503	0.0922516	−	0.995736i	$-0.470594\pi$
$103$	2.37203e16	0.184503	0.0922516	+	0.995736i	$0.470594\pi$
$104$	−1.35327e16	−0.0969620
$105$	2.73222e17	1.80471
$106$	2.31981e16	0.141368
$107$	−2.45155e17	−1.37936	−0.689681	−	0.724114i	$-0.742249\pi$
$107$	−2.45155e17	−1.37936	−0.689681	+	0.724114i	$0.742249\pi$
$108$	−2.01549e17	−1.04780
$109$	5.94577e16	0.285814	0.142907	−	0.989736i	$-0.454355\pi$
$109$	5.94577e16	0.285814	0.142907	+	0.989736i	$0.454355\pi$
$110$	−2.03924e16	−0.0907048
$111$	1.38803e17	0.571682
$112$	3.22432e17	1.23051
$113$	4.69951e17	1.66297	0.831487	−	0.555544i	$-0.187490\pi$
$113$	4.69951e17	1.66297	0.831487	+	0.555544i	$0.187490\pi$
$114$	2.46761e16	0.0810188
$115$	8.00630e17	2.44062
$116$	6.40791e16	0.181478
$117$	−2.40881e16	−0.0634196
$118$	6.43119e16	0.157505
$119$	1.08408e18	2.47123
$120$	−1.91936e17	−0.407488
$121$	−4.26617e17	−0.844038
$122$	−1.32052e17	−0.243605
$123$	1.90345e17	0.327603
$124$	−3.63278e17	−0.583653
$125$	−3.27661e17	−0.491688
$126$	−2.76438e16	−0.0387658
$127$	−7.77869e15	−0.0101994	−0.00509970	−	0.999987i	$-0.501623\pi$
$127$	−7.77869e15	−0.0101994	−0.00509970	+	0.999987i	$0.501623\pi$
$128$	−4.63921e17	−0.569061
$129$	−2.15314e17	−0.247207
$130$	−6.95088e16	−0.0747346
$131$	−1.04138e18	−1.04907	−0.524536	−	0.851388i	$-0.675761\pi$
$131$	−1.04138e18	−1.04907	−0.524536	+	0.851388i	$0.675761\pi$
$132$	3.66719e17	0.346302
$133$	−8.92818e17	−0.790722
$134$	2.37367e16	0.0197256
$135$	−2.09452e18	−1.63398
$136$	−7.61557e17	−0.557984
$137$	−1.29271e18	−0.889971	−0.444985	−	0.895538i	$-0.646791\pi$
$137$	−1.29271e18	−0.889971	−0.444985	+	0.895538i	$0.646791\pi$
$138$	3.34610e17	0.216554
$139$	2.14711e18	1.30686	0.653429	−	0.756988i	$-0.273330\pi$
$139$	2.14711e18	1.30686	0.653429	+	0.756988i	$0.273330\pi$
$140$	3.43237e18	1.96565
$141$	−7.55158e17	−0.407076
$142$	−2.84971e17	−0.144660
$143$	2.68698e17	0.128502
$144$	−4.03178e17	−0.181725
$145$	6.65915e17	0.283003
$146$	−3.62294e17	−0.145232
$147$	−1.75946e18	−0.665553
$148$	1.74373e18	0.622664
$149$	−1.63127e18	−0.550102	−0.275051	−	0.961430i	$-0.588695\pi$
$149$	−1.63127e18	−0.550102	−0.275051	+	0.961430i	$0.588695\pi$
$150$	−5.61395e17	−0.178852
$151$	4.05526e18	1.22100	0.610498	−	0.792018i	$-0.290969\pi$
$151$	4.05526e18	1.22100	0.610498	+	0.792018i	$0.290969\pi$
$152$	6.27195e17	0.178539
$153$	−1.35556e18	−0.364958
$154$	3.08361e17	0.0785478
$155$	−3.77522e18	−0.910170
$156$	1.24999e18	0.285329
$157$	1.71961e18	0.371778	0.185889	−	0.982571i	$-0.440484\pi$
$157$	1.71961e18	0.371778	0.185889	+	0.982571i	$0.440484\pi$
$158$	2.12651e17	0.0435595
$159$	−4.33531e18	−0.841675
$160$	−3.63065e18	−0.668290
$161$	−1.21066e19	−2.11351
$162$	−6.98016e17	−0.115608
$163$	−8.61988e18	−1.35490	−0.677449	−	0.735570i	$-0.736914\pi$
$163$	−8.61988e18	−1.35490	−0.677449	+	0.735570i	$0.736914\pi$
$164$	2.39122e18	0.356818
$165$	3.81097e18	0.540035
$166$	8.36158e17	0.112556
$167$	9.15181e18	1.17062	0.585312	−	0.810808i	$-0.300972\pi$
$167$	9.15181e18	1.17062	0.585312	+	0.810808i	$0.300972\pi$
$168$	2.90233e18	0.352873
$169$	−7.73454e18	−0.894123
$170$	−3.91163e18	−0.430072
$171$	1.11640e18	0.116776
$172$	−2.70490e18	−0.269252
$173$	−1.41333e19	−1.33922	−0.669609	−	0.742714i	$-0.733538\pi$
$173$	−1.41333e19	−1.33922	−0.669609	+	0.742714i	$0.733538\pi$
$174$	2.78308e17	0.0251106
$175$	2.03121e19	1.74554
$176$	4.49737e18	0.368215
$177$	−1.20187e19	−0.937748
$178$	3.04889e18	0.226763
$179$	−7.13771e18	−0.506184	−0.253092	−	0.967442i	$-0.581447\pi$
$179$	−7.13771e18	−0.506184	−0.253092	+	0.967442i	$0.581447\pi$
$180$	−4.29192e18	−0.290292
$181$	−4.09192e18	−0.264034	−0.132017	−	0.991247i	$-0.542145\pi$
$181$	−4.09192e18	−0.264034	−0.132017	+	0.991247i	$0.542145\pi$
$182$	1.05107e18	0.0647180
$183$	2.46781e19	1.45036
$184$	8.50479e18	0.477213
$185$	1.81209e19	0.971004
$186$	−1.57779e18	−0.0807585
$187$	1.51211e19	0.739484
$188$	−9.48672e18	−0.443378
$189$	3.16720e19	1.41498
$190$	3.22150e18	0.137611
$191$	3.69987e19	1.51148	0.755740	−	0.654871i	$-0.227277\pi$
$191$	3.69987e19	1.51148	0.755740	+	0.654871i	$0.227277\pi$
$192$	1.98906e19	0.777299
$193$	−2.83391e19	−1.05962	−0.529809	−	0.848117i	$-0.677736\pi$
$193$	−2.83391e19	−1.05962	−0.529809	+	0.848117i	$0.677736\pi$
$194$	−6.76582e18	−0.242106
$195$	1.29899e19	0.444952
$196$	−2.21034e19	−0.724906
$197$	−5.31846e19	−1.67041	−0.835204	−	0.549940i	$-0.814651\pi$
$197$	−5.31846e19	−1.67041	−0.835204	+	0.549940i	$0.814651\pi$
$198$	−3.85583e17	−0.0116002
$199$	3.85647e19	1.11158	0.555788	−	0.831324i	$-0.312417\pi$
$199$	3.85647e19	1.11158	0.555788	+	0.831324i	$0.312417\pi$
$200$	−1.42690e19	−0.394129
$201$	−4.43597e18	−0.117442
$202$	4.34961e18	0.110399
$203$	−1.00696e19	−0.245072
$204$	7.03432e19	1.64197
$205$	2.48497e19	0.556434
$206$	1.29422e18	0.0278058
$207$	1.51385e19	0.312129
$208$	1.53296e19	0.303384
$209$	−1.24532e19	−0.236613
$210$	1.49074e19	0.271981
$211$	−4.95264e19	−0.867833	−0.433917	−	0.900953i	$-0.642869\pi$
$211$	−4.95264e19	−0.867833	−0.433917	+	0.900953i	$0.642869\pi$
$212$	−5.44625e19	−0.916733
$213$	5.32558e19	0.861273
$214$	−1.33760e19	−0.207879
$215$	−2.81095e19	−0.419881
$216$	−2.22493e19	−0.319491
$217$	5.70865e19	0.788181
$218$	3.24411e18	0.0430740
$219$	6.77063e19	0.864677
$220$	4.78755e19	0.588194
$221$	5.15412e19	0.609284
$222$	7.57333e18	0.0861562
$223$	−1.49577e20	−1.63785	−0.818926	−	0.573900i	$-0.805430\pi$
$223$	−1.49577e20	−1.63785	−0.818926	+	0.573900i	$0.805430\pi$
$224$	5.49005e19	0.578720
$225$	−2.53987e19	−0.257787
$226$	2.56412e19	0.250621
$227$	−1.52819e20	−1.43865	−0.719327	−	0.694672i	$-0.755550\pi$
$227$	−1.52819e20	−1.43865	−0.719327	+	0.694672i	$0.755550\pi$
$228$	−5.79325e19	−0.525383
$229$	−1.32057e20	−1.15388	−0.576940	−	0.816787i	$-0.695753\pi$
$229$	−1.32057e20	−1.15388	−0.576940	+	0.816787i	$0.695753\pi$
$230$	4.36836e19	0.367817
$231$	−5.76272e19	−0.467655
$232$	7.07376e18	0.0553354
$233$	−3.44465e19	−0.259788	−0.129894	−	0.991528i	$-0.541464\pi$
$233$	−3.44465e19	−0.259788	−0.129894	+	0.991528i	$0.541464\pi$
$234$	−1.31429e18	−0.00955774
$235$	−9.85868e19	−0.691420
$236$	−1.50986e20	−1.02137
$237$	−3.97407e19	−0.259343
$238$	5.91493e19	0.372430
$239$	1.41339e20	0.858773	0.429387	−	0.903121i	$-0.358730\pi$
$239$	1.41339e20	0.858773	0.429387	+	0.903121i	$0.358730\pi$
$240$	2.17421e20	1.27499
$241$	−3.15012e20	−1.78313	−0.891563	−	0.452897i	$-0.850391\pi$
$241$	−3.15012e20	−1.78313	−0.891563	+	0.452897i	$0.850391\pi$
$242$	−2.32769e19	−0.127202
$243$	−7.27471e19	−0.383851
$244$	3.10020e20	1.57970
$245$	−2.29700e20	−1.13044
$246$	1.03855e19	0.0493719
$247$	−4.24477e19	−0.194953
$248$	−4.01027e19	−0.177965
$249$	−1.56263e20	−0.670133
$250$	−1.78777e19	−0.0741005
$251$	−3.11813e20	−1.24930	−0.624651	−	0.780904i	$-0.714759\pi$
$251$	−3.11813e20	−1.24930	−0.624651	+	0.780904i	$0.714759\pi$
$252$	6.48998e19	0.251385
$253$	−1.68867e20	−0.632440
$254$	−4.24417e17	−0.00153712
$255$	7.31012e20	2.56055
$256$	2.30372e20	0.780532
$257$	5.18518e20	1.69954	0.849772	−	0.527151i	$-0.176740\pi$
$257$	5.18518e20	1.69954	0.849772	+	0.527151i	$0.176740\pi$
$258$	−1.17479e19	−0.0372557
$259$	−2.74014e20	−0.840862
$260$	1.63187e20	0.484632
$261$	1.25912e19	0.0361930
$262$	−5.68196e19	−0.158102
$263$	−5.38268e19	−0.145002	−0.0725011	−	0.997368i	$-0.523098\pi$
$263$	−5.38268e19	−0.145002	−0.0725011	+	0.997368i	$0.523098\pi$
$264$	4.04825e19	0.105593
$265$	−5.65979e20	−1.42959
$266$	−4.87135e19	−0.119167
$267$	−5.69782e20	−1.35009
$268$	−5.57271e19	−0.127915
$269$	−2.56014e20	−0.569337	−0.284668	−	0.958626i	$-0.591883\pi$
$269$	−2.56014e20	−0.569337	−0.284668	+	0.958626i	$0.591883\pi$
$270$	−1.14280e20	−0.246251
$271$	3.96803e20	0.828582	0.414291	−	0.910144i	$-0.364030\pi$
$271$	3.96803e20	0.828582	0.414291	+	0.910144i	$0.364030\pi$
$272$	8.62676e20	1.74587
$273$	−1.96426e20	−0.385316
$274$	−7.05322e19	−0.134124
$275$	2.83318e20	0.522331
$276$	−7.85568e20	−1.40429
$277$	−8.88278e20	−1.53982	−0.769911	−	0.638151i	$-0.779700\pi$
$277$	−8.88278e20	−1.53982	−0.769911	+	0.638151i	$0.779700\pi$
$278$	1.17150e20	0.196952
$279$	−7.13825e19	−0.116401
$280$	3.78903e20	0.599356
$281$	1.00610e21	1.54396	0.771979	−	0.635648i	$-0.219267\pi$
$281$	1.00610e21	1.54396	0.771979	+	0.635648i	$0.219267\pi$
$282$	−4.12026e19	−0.0613490
$283$	1.97445e20	0.285274	0.142637	−	0.989775i	$-0.454442\pi$
$283$	1.97445e20	0.285274	0.142637	+	0.989775i	$0.454442\pi$
$284$	6.69030e20	0.938079
$285$	−6.02040e20	−0.819301
$286$	1.46606e19	0.0193660
$287$	−3.75763e20	−0.481856
$288$	−6.86490e19	−0.0854670
$289$	2.07325e21	2.50623
$290$	3.63334e19	0.0426503
$291$	1.26441e21	1.44144
$292$	8.50564e20	0.941787
$293$	1.92638e19	0.0207189	0.0103595	−	0.999946i	$-0.496702\pi$
$293$	1.92638e19	0.0207189	0.0103595	+	0.999946i	$0.496702\pi$
$294$	−9.59991e19	−0.100303
$295$	−1.56906e21	−1.59277
$296$	1.92492e20	0.189860
$297$	4.41769e20	0.423414
$298$	−8.90047e19	−0.0829039
$299$	−5.75593e20	−0.521087
$300$	1.31799e21	1.15980
$301$	4.25055e20	0.363605
$302$	2.21261e20	0.184012
$303$	−8.12863e20	−0.657287
$304$	−7.10474e20	−0.558628
$305$	3.22175e21	2.46345
$306$	−7.39618e19	−0.0550016
$307$	2.58288e20	0.186822	0.0934112	−	0.995628i	$-0.470223\pi$
$307$	2.58288e20	0.186822	0.0934112	+	0.995628i	$0.470223\pi$
$308$	−7.23945e20	−0.509359
$309$	−2.41866e20	−0.165549
$310$	−2.05982e20	−0.137168
$311$	−2.59032e21	−1.67838	−0.839190	−	0.543838i	$-0.816971\pi$
$311$	−2.59032e21	−1.67838	−0.839190	+	0.543838i	$0.816971\pi$
$312$	1.37987e20	0.0870012
$313$	−4.79687e20	−0.294328	−0.147164	−	0.989112i	$-0.547014\pi$
$313$	−4.79687e20	−0.294328	−0.147164	+	0.989112i	$0.547014\pi$
$314$	9.38248e19	0.0560293
$315$	6.74444e20	0.392018
$316$	−4.99245e20	−0.282471
$317$	−3.00176e21	−1.65338	−0.826688	−	0.562660i	$-0.809778\pi$
$317$	−3.00176e21	−1.65338	−0.826688	+	0.562660i	$0.809778\pi$
$318$	−2.36541e20	−0.126846
$319$	−1.40453e20	−0.0733347
$320$	2.59674e21	1.32024
$321$	2.49974e21	1.23766
$322$	−6.60558e20	−0.318519
$323$	−2.38876e21	−1.12189
$324$	1.63874e21	0.749684
$325$	9.65708e20	0.430365
$326$	−4.70314e20	−0.204192
$327$	−6.06265e20	−0.256452
$328$	2.63969e20	0.108799
$329$	1.49077e21	0.598750
$330$	2.07932e20	0.0813868
$331$	−2.57286e21	−0.981474	−0.490737	−	0.871308i	$-0.663272\pi$
$331$	−2.57286e21	−0.981474	−0.490737	+	0.871308i	$0.663272\pi$
$332$	−1.96306e21	−0.729894
$333$	3.42634e20	0.124181
$334$	4.99337e20	0.176421
$335$	−5.79120e20	−0.199475
$336$	−3.28771e21	−1.10410
$337$	−3.59632e21	−1.17762	−0.588809	−	0.808272i	$-0.700403\pi$
$337$	−3.59632e21	−1.17762	−0.588809	+	0.808272i	$0.700403\pi$
$338$	−4.22009e20	−0.134750
$339$	−4.79189e21	−1.49214
$340$	9.18338e21	2.78889
$341$	7.96258e20	0.235853
$342$	6.09127e19	0.0175989
$343$	−1.20928e21	−0.340823
$344$	−2.98597e20	−0.0820991
$345$	−8.16368e21	−2.18990
$346$	−7.71134e20	−0.201829
$347$	−2.96489e21	−0.757195	−0.378598	−	0.925561i	$-0.623594\pi$
$347$	−2.96489e21	−0.757195	−0.378598	+	0.925561i	$0.623594\pi$
$348$	−6.53387e20	−0.162835
$349$	5.14599e21	1.25156	0.625781	−	0.779999i	$-0.284780\pi$
$349$	5.14599e21	1.25156	0.625781	+	0.779999i	$0.284780\pi$
$350$	1.10826e21	0.263065
$351$	1.50580e21	0.348865
$352$	7.65767e20	0.173174
$353$	2.45796e21	0.542613	0.271306	−	0.962493i	$-0.412544\pi$
$353$	2.45796e21	0.542613	0.271306	+	0.962493i	$0.412544\pi$
$354$	−6.55761e20	−0.141325
$355$	6.95261e21	1.46287
$356$	−7.15792e21	−1.47049
$357$	−1.10539e22	−2.21736
$358$	−3.89445e20	−0.0762852
$359$	−1.16618e21	−0.223082	−0.111541	−	0.993760i	$-0.535579\pi$
$359$	−1.16618e21	−0.223082	−0.111541	+	0.993760i	$0.535579\pi$
$360$	−4.73790e20	−0.0885146
$361$	−3.51308e21	−0.641028
$362$	−2.23262e20	−0.0397916
$363$	4.35003e21	0.757331
$364$	−2.46761e21	−0.419677
$365$	8.83913e21	1.46866
$366$	1.34647e21	0.218579
$367$	7.64959e21	1.21332	0.606662	−	0.794960i	$-0.292508\pi$
$367$	7.64959e21	1.21332	0.606662	+	0.794960i	$0.292508\pi$
$368$	−9.63406e21	−1.49315
$369$	4.69863e20	0.0711619
$370$	9.88707e20	0.146337
$371$	8.55839e21	1.23798
$372$	3.70419e21	0.523695
$373$	1.02472e22	1.41605	0.708025	−	0.706187i	$-0.249586\pi$
$373$	1.02472e22	1.41605	0.708025	+	0.706187i	$0.249586\pi$
$374$	8.25029e20	0.111445
$375$	3.34102e21	0.441177
$376$	−1.04725e21	−0.135193
$377$	−4.78743e20	−0.0604228
$378$	1.72807e21	0.213247
$379$	−8.25826e21	−0.996449	−0.498225	−	0.867048i	$-0.666015\pi$
$379$	−8.25826e21	−0.996449	−0.498225	+	0.867048i	$0.666015\pi$
$380$	−7.56316e21	−0.892365
$381$	7.93159e19	0.00915162
$382$	2.01871e21	0.227790
$383$	−9.47841e21	−1.04603	−0.523017	−	0.852322i	$-0.675194\pi$
$383$	−9.47841e21	−1.04603	−0.523017	+	0.852322i	$0.675194\pi$
$384$	4.73040e21	0.510602
$385$	−7.52329e21	−0.794313
$386$	−1.54623e21	−0.159691
$387$	−5.31500e20	−0.0536982
$388$	1.58842e22	1.56999
$389$	−2.62513e21	−0.253851	−0.126926	−	0.991912i	$-0.540511\pi$
$389$	−2.62513e21	−0.253851	−0.126926	+	0.991912i	$0.540511\pi$
$390$	7.08752e20	0.0670571
$391$	−3.23916e22	−2.99868
$392$	−2.44002e21	−0.221035
$393$	1.06185e22	0.941301
$394$	−2.90183e21	−0.251741
$395$	−5.18819e21	−0.440495
$396$	9.05239e20	0.0752236
$397$	1.37249e22	1.11633	0.558163	−	0.829731i	$-0.311506\pi$
$397$	1.37249e22	1.11633	0.558163	+	0.829731i	$0.311506\pi$
$398$	2.10415e21	0.167522
$399$	9.10368e21	0.709492
$400$	1.61636e22	1.23319
$401$	1.41780e22	1.05898	0.529492	−	0.848315i	$-0.322383\pi$
$401$	1.41780e22	1.05898	0.529492	+	0.848315i	$0.322383\pi$
$402$	−2.42033e20	−0.0176992
$403$	2.71410e21	0.194327
$404$	−1.02116e22	−0.715902
$405$	1.70299e22	1.16908
$406$	−5.49411e20	−0.0369340
$407$	−3.82202e21	−0.251617
$408$	7.76527e21	0.500663
$409$	1.60961e21	0.101642	0.0508211	−	0.998708i	$-0.483816\pi$
$409$	1.60961e21	0.101642	0.0508211	+	0.998708i	$0.483816\pi$
$410$	1.35584e21	0.0838582
$411$	1.31812e22	0.798545
$412$	−3.03845e21	−0.180313
$413$	2.37264e22	1.37929
$414$	8.25978e20	0.0470398
$415$	−2.04003e22	−1.13822
$416$	2.61017e21	0.142684
$417$	−2.18932e22	−1.17261
$418$	−6.79469e20	−0.0356592
$419$	1.46158e22	0.751630	0.375815	−	0.926695i	$-0.377363\pi$
$419$	1.46158e22	0.751630	0.375815	+	0.926695i	$0.377363\pi$
$420$	−3.49984e22	−1.76372
$421$	2.38420e22	1.17746	0.588728	−	0.808331i	$-0.299629\pi$
$421$	2.38420e22	1.17746	0.588728	+	0.808331i	$0.299629\pi$
$422$	−2.70224e21	−0.130788
$423$	−1.86410e21	−0.0884250
$424$	−6.01218e21	−0.279526
$425$	5.43454e22	2.47661
$426$	2.90572e21	0.129799
$427$	−4.87174e22	−2.13327
$428$	3.14031e22	1.34803
$429$	−2.73980e21	−0.115301
$430$	−1.53370e21	−0.0632788
$431$	4.26671e22	1.72598	0.862992	−	0.505218i	$-0.168588\pi$
$431$	4.26671e22	1.72598	0.862992	+	0.505218i	$0.168588\pi$
$432$	2.52035e22	0.999653
$433$	−2.28136e22	−0.887251	−0.443625	−	0.896212i	$-0.646308\pi$
$433$	−2.28136e22	−0.887251	−0.443625	+	0.896212i	$0.646308\pi$
$434$	3.11473e21	0.118784
$435$	−6.79005e21	−0.253930
$436$	−7.61624e21	−0.279322
$437$	2.66768e22	0.959491
$438$	3.69416e21	0.130312
$439$	−4.34798e22	−1.50432	−0.752158	−	0.658983i	$-0.770987\pi$
$439$	−4.34798e22	−1.50432	−0.752158	+	0.658983i	$0.770987\pi$
$440$	5.28504e21	0.179349
$441$	−4.34321e21	−0.144571
$442$	2.81217e21	0.0918231
$443$	−1.08055e22	−0.346111	−0.173055	−	0.984912i	$-0.555364\pi$
$443$	−1.08055e22	−0.346111	−0.173055	+	0.984912i	$0.555364\pi$
$444$	−1.77800e22	−0.558698
$445$	−7.43857e22	−2.29313
$446$	−8.16117e21	−0.246835
$447$	1.66334e22	0.493590
$448$	−3.92664e22	−1.14329
$449$	−1.15443e22	−0.329818	−0.164909	−	0.986309i	$-0.552733\pi$
$449$	−1.15443e22	−0.329818	−0.164909	+	0.986309i	$0.552733\pi$
$450$	−1.38579e21	−0.0388501
$451$	−5.24123e21	−0.144189
$452$	−6.01983e22	−1.62520
$453$	−4.13497e22	−1.09556
$454$	−8.33802e21	−0.216814
$455$	−2.56436e22	−0.654460
$456$	−6.39524e21	−0.160198
$457$	4.55840e22	1.12079	0.560395	−	0.828225i	$-0.310649\pi$
$457$	4.55840e22	1.12079	0.560395	+	0.828225i	$0.310649\pi$
$458$	−7.20525e21	−0.173897
$459$	8.47393e22	2.00760
$460$	−1.02557e23	−2.38519
$461$	−2.19053e22	−0.500140	−0.250070	−	0.968228i	$-0.580454\pi$
$461$	−2.19053e22	−0.500140	−0.250070	+	0.968228i	$0.580454\pi$
$462$	−3.14423e21	−0.0704786
$463$	5.60234e22	1.23291	0.616454	−	0.787391i	$-0.288568\pi$
$463$	5.60234e22	1.23291	0.616454	+	0.787391i	$0.288568\pi$
$464$	−8.01302e21	−0.173138
$465$	3.84943e22	0.816669
$466$	−1.87945e21	−0.0391518
$467$	−2.61181e22	−0.534254	−0.267127	−	0.963661i	$-0.586074\pi$
$467$	−2.61181e22	−0.534254	−0.267127	+	0.963661i	$0.586074\pi$
$468$	3.08557e21	0.0619791
$469$	8.75711e21	0.172740
$470$	−5.37905e21	−0.104201
$471$	−1.75342e22	−0.333585
$472$	−1.66675e22	−0.311433
$473$	5.92878e21	0.108804
$474$	−2.16832e21	−0.0390847
$475$	−4.47572e22	−0.792442
$476$	−1.38866e23	−2.41510
$477$	−1.07016e22	−0.182829
$478$	7.71166e21	0.129423
$479$	8.06478e22	1.32966	0.664830	−	0.746994i	$-0.268504\pi$
$479$	8.06478e22	1.32966	0.664830	+	0.746994i	$0.268504\pi$
$480$	3.70202e22	0.599637
$481$	−1.30276e22	−0.207315
$482$	−1.71875e22	−0.268729
$483$	1.23446e23	1.89639
$484$	5.46475e22	0.824868
$485$	1.65070e23	2.44829
$486$	−3.96920e21	−0.0578488
$487$	2.04288e22	0.292581	0.146290	−	0.989242i	$-0.453267\pi$
$487$	2.04288e22	0.292581	0.146290	+	0.989242i	$0.453267\pi$
$488$	3.42234e22	0.481676
$489$	8.78932e22	1.21571
$490$	−1.25328e22	−0.170365
$491$	6.26855e22	0.837480	0.418740	−	0.908106i	$-0.362472\pi$
$491$	6.26855e22	0.837480	0.418740	+	0.908106i	$0.362472\pi$
$492$	−2.43822e22	−0.320162
$493$	−2.69414e22	−0.347713
$494$	−2.31602e21	−0.0293807
$495$	9.40732e21	0.117306
$496$	4.54275e22	0.556833
$497$	−1.05133e23	−1.26681
$498$	−8.52594e21	−0.100993
$499$	−2.31609e21	−0.0269712	−0.0134856	−	0.999909i	$-0.504293\pi$
$499$	−2.31609e21	−0.0269712	−0.0134856	+	0.999909i	$0.504293\pi$
$500$	4.19717e22	0.480520
$501$	−9.33171e22	−1.05037
$502$	−1.70130e22	−0.188278
$503$	−1.05866e23	−1.15194	−0.575968	−	0.817472i	$-0.695375\pi$
$503$	−1.05866e23	−1.15194	−0.575968	+	0.817472i	$0.695375\pi$
$504$	7.16437e21	0.0766511
$505$	−1.06120e23	−1.11640
$506$	−9.21363e21	−0.0953128
$507$	7.88658e22	0.802271
$508$	9.96411e20	0.00996775
$509$	−3.24347e22	−0.319087	−0.159543	−	0.987191i	$-0.551002\pi$
$509$	−3.24347e22	−0.319087	−0.159543	+	0.987191i	$0.551002\pi$
$510$	3.98852e22	0.385891
$511$	−1.33660e23	−1.27181
$512$	7.33765e22	0.686693
$513$	−6.97887e22	−0.642373
$514$	2.82911e22	0.256132
$515$	−3.15759e22	−0.281186
$516$	2.75807e22	0.241592
$517$	2.07936e22	0.179168
$518$	−1.49506e22	−0.126723
$519$	1.44111e23	1.20164
$520$	1.80144e22	0.147772
$521$	−1.04361e23	−0.842203	−0.421101	−	0.907014i	$-0.638356\pi$
$521$	−1.04361e23	−0.842203	−0.421101	+	0.907014i	$0.638356\pi$
$522$	6.86998e20	0.00545452
$523$	−9.75879e22	−0.762310	−0.381155	−	0.924511i	$-0.624474\pi$
$523$	−9.75879e22	−0.762310	−0.381155	+	0.924511i	$0.624474\pi$
$524$	1.33396e23	1.02524
$525$	−2.07113e23	−1.56622
$526$	−2.93687e21	−0.0218528
$527$	1.52736e23	1.11829
$528$	−4.58578e22	−0.330388
$529$	2.20688e23	1.56461
$530$	−3.08807e22	−0.215448
$531$	−2.96681e22	−0.203698
$532$	1.14366e23	0.772763
$533$	−1.78651e22	−0.118802
$534$	−3.10882e22	−0.203468
$535$	3.26343e23	2.10217
$536$	−6.15178e21	−0.0390032
$537$	7.27802e22	0.454184
$538$	−1.39685e22	−0.0858027
$539$	4.84476e22	0.292933
$540$	2.68297e23	1.59687
$541$	−4.74231e22	−0.277852	−0.138926	−	0.990303i	$-0.544365\pi$
$541$	−4.74231e22	−0.277852	−0.138926	+	0.990303i	$0.544365\pi$
$542$	2.16502e22	0.124873
$543$	4.17236e22	0.236910
$544$	1.46888e23	0.821098
$545$	−7.91485e22	−0.435585
$546$	−1.07173e22	−0.0580696
$547$	−2.64811e22	−0.141268	−0.0706341	−	0.997502i	$-0.522502\pi$
$547$	−2.64811e22	−0.141268	−0.0706341	+	0.997502i	$0.522502\pi$
$548$	1.65590e23	0.869757
$549$	6.09174e22	0.315048
$550$	1.54583e22	0.0787187
$551$	2.21881e22	0.111258
$552$	−8.67198e22	−0.428189
$553$	7.84527e22	0.381456
$554$	−4.84658e22	−0.232061
$555$	−1.84771e23	−0.871253
$556$	−2.75034e23	−1.27718
$557$	3.54293e23	1.62029	0.810146	−	0.586228i	$-0.199388\pi$
$557$	3.54293e23	1.62029	0.810146	+	0.586228i	$0.199388\pi$
$558$	−3.89474e21	−0.0175424
$559$	2.02086e22	0.0896472
$560$	−4.29214e23	−1.87532
$561$	−1.54183e23	−0.663517
$562$	5.48941e22	0.232684
$563$	4.60238e22	0.192159	0.0960797	−	0.995374i	$-0.469370\pi$
$563$	4.60238e22	0.192159	0.0960797	+	0.995374i	$0.469370\pi$
$564$	9.67320e22	0.397830
$565$	−6.25586e23	−2.53440
$566$	1.07729e22	0.0429927
$567$	−2.57517e23	−1.01239
$568$	7.38550e22	0.286035
$569$	2.76984e22	0.105682	0.0528409	−	0.998603i	$-0.483172\pi$
$569$	2.76984e22	0.105682	0.0528409	+	0.998603i	$0.483172\pi$
$570$	−3.28482e22	−0.123474
$571$	1.13123e23	0.418934	0.209467	−	0.977816i	$-0.432827\pi$
$571$	1.13123e23	0.418934	0.209467	+	0.977816i	$0.432827\pi$
$572$	−3.44189e22	−0.125583
$573$	−3.77260e23	−1.35621
$574$	−2.05022e22	−0.0726189
$575$	−6.06910e23	−2.11811
$576$	4.90997e22	0.168845
$577$	6.86089e22	0.232480	0.116240	−	0.993221i	$-0.462916\pi$
$577$	6.86089e22	0.232480	0.116240	+	0.993221i	$0.462916\pi$
$578$	1.13120e23	0.377704
$579$	2.88962e23	0.950764
$580$	−8.53004e22	−0.276575
$581$	3.08481e23	0.985668
$582$	6.89882e22	0.217235
$583$	1.19375e23	0.370450
$584$	9.38948e22	0.287165
$585$	3.20655e22	0.0966525
$586$	1.05106e21	0.00312247
$587$	−3.27296e22	−0.0958333	−0.0479166	−	0.998851i	$-0.515258\pi$
$587$	−3.27296e22	−0.0958333	−0.0479166	+	0.998851i	$0.515258\pi$
$588$	2.25379e23	0.650437
$589$	−1.25789e23	−0.357819
$590$	−8.56103e22	−0.240040
$591$	5.42300e23	1.49881
$592$	−2.18051e23	−0.594051
$593$	6.38213e23	1.71396	0.856981	−	0.515349i	$-0.172338\pi$
$593$	6.38213e23	1.71396	0.856981	+	0.515349i	$0.172338\pi$
$594$	2.41036e22	0.0638113
$595$	−1.44310e24	−3.76620
$596$	2.08958e23	0.537608
$597$	−3.93228e23	−0.997385
$598$	−3.14053e22	−0.0785312
$599$	−4.65201e23	−1.14687	−0.573433	−	0.819252i	$-0.694389\pi$
$599$	−4.65201e23	−1.14687	−0.573433	+	0.819252i	$0.694389\pi$
$600$	1.45495e23	0.353641
$601$	−3.53845e23	−0.847970	−0.423985	−	0.905669i	$-0.639369\pi$
$601$	−3.53845e23	−0.847970	−0.423985	+	0.905669i	$0.639369\pi$
$602$	2.31917e22	0.0547977
$603$	−1.09501e22	−0.0255107
$604$	−5.19458e23	−1.19326
$605$	5.67901e23	1.28633
$606$	−4.43511e22	−0.0990574
$607$	7.57097e23	1.66743	0.833715	−	0.552195i	$-0.186210\pi$
$607$	7.57097e23	1.66743	0.833715	+	0.552195i	$0.186210\pi$
$608$	−1.20972e23	−0.262728
$609$	1.02675e23	0.219896
$610$	1.75784e23	0.371257
$611$	7.08765e22	0.147622
$612$	1.73641e23	0.356669
$613$	−9.38083e23	−1.90032	−0.950161	−	0.311758i	$-0.899082\pi$
$613$	−9.38083e23	−1.90032	−0.950161	+	0.311758i	$0.899082\pi$
$614$	1.40926e22	0.0281553
$615$	−2.53382e23	−0.499272
$616$	−7.99171e22	−0.155312
$617$	8.45123e23	1.61993	0.809964	−	0.586479i	$-0.199486\pi$
$617$	8.45123e23	1.61993	0.809964	+	0.586479i	$0.199486\pi$
$618$	−1.31966e22	−0.0249494
$619$	−6.66868e23	−1.24357	−0.621783	−	0.783189i	$-0.713592\pi$
$619$	−6.66868e23	−1.24357	−0.621783	+	0.783189i	$0.713592\pi$
$620$	4.83586e23	0.889497
$621$	−9.46338e23	−1.71699
$622$	−1.41332e23	−0.252943
$623$	1.12482e24	1.98579
$624$	−1.56309e23	−0.272217
$625$	−3.33696e23	−0.573286
$626$	−2.61725e22	−0.0443571
$627$	1.26980e23	0.212306
$628$	−2.20274e23	−0.363334
$629$	−7.33131e23	−1.19303
$630$	3.67987e22	0.0590797
$631$	−2.23701e23	−0.354338	−0.177169	−	0.984180i	$-0.556694\pi$
$631$	−2.23701e23	−0.354338	−0.177169	+	0.984180i	$0.556694\pi$
$632$	−5.51122e22	−0.0861297
$633$	5.05000e23	0.778681
$634$	−1.63781e23	−0.249175
$635$	1.03548e22	0.0155441
$636$	5.55331e23	0.822558
$637$	1.65137e23	0.241357
$638$	−7.66333e21	−0.0110520
$639$	1.31461e23	0.187086
$640$	6.17559e23	0.867259
$641$	−1.98512e23	−0.275101	−0.137551	−	0.990495i	$-0.543923\pi$
$641$	−1.98512e23	−0.275101	−0.137551	+	0.990495i	$0.543923\pi$
$642$	1.36390e23	0.186523
$643$	−7.72836e23	−1.04302	−0.521512	−	0.853244i	$-0.674632\pi$
$643$	−7.72836e23	−1.04302	−0.521512	+	0.853244i	$0.674632\pi$
$644$	1.55080e24	2.06551
$645$	2.86621e23	0.376747
$646$	−1.30334e23	−0.169076
$647$	1.99065e23	0.254863	0.127432	−	0.991847i	$-0.459327\pi$
$647$	1.99065e23	0.254863	0.127432	+	0.991847i	$0.459327\pi$
$648$	1.80903e23	0.228590
$649$	3.30941e23	0.412735
$650$	5.26905e22	0.0648588
$651$	−5.82087e23	−0.707212
$652$	1.10416e24	1.32412
$653$	3.19799e23	0.378543	0.189272	−	0.981925i	$-0.439387\pi$
$653$	3.19799e23	0.378543	0.189272	+	0.981925i	$0.439387\pi$
$654$	−3.30788e22	−0.0386490
$655$	1.38626e24	1.59880
$656$	−2.99019e23	−0.340421
$657$	1.67132e23	0.187825
$658$	8.13387e22	0.0902355
$659$	8.08739e23	0.885692	0.442846	−	0.896598i	$-0.353969\pi$
$659$	8.08739e23	0.885692	0.442846	+	0.896598i	$0.353969\pi$
$660$	−4.88166e23	−0.527770
$661$	−1.02936e24	−1.09864	−0.549322	−	0.835611i	$-0.685114\pi$
$661$	−1.02936e24	−1.09864	−0.549322	+	0.835611i	$0.685114\pi$
$662$	−1.40380e23	−0.147915
$663$	−5.25543e23	−0.546693
$664$	−2.16704e23	−0.222556
$665$	1.18850e24	1.20507
$666$	1.86947e22	0.0187149
$667$	3.00872e23	0.297380
$668$	−1.17230e24	−1.14404
$669$	1.52518e24	1.46960
$670$	−3.15977e22	−0.0300621
$671$	−6.79522e23	−0.638355
$672$	−5.59797e23	−0.519268
$673$	−4.29117e23	−0.393050	−0.196525	−	0.980499i	$-0.562966\pi$
$673$	−4.29117e23	−0.393050	−0.196525	+	0.980499i	$0.562966\pi$
$674$	−1.96221e23	−0.177475
$675$	1.58773e24	1.41806
$676$	9.90756e23	0.873816
$677$	4.23067e22	0.0368473	0.0184237	−	0.999830i	$-0.494135\pi$
$677$	4.23067e22	0.0368473	0.0184237	+	0.999830i	$0.494135\pi$
$678$	−2.61453e23	−0.224875
$679$	−2.49609e24	−2.12015
$680$	1.01376e24	0.850377
$681$	1.55822e24	1.29086
$682$	4.34451e22	0.0355446
$683$	−2.15416e24	−1.74061	−0.870307	−	0.492510i	$-0.836079\pi$
$683$	−2.15416e24	−1.74061	−0.870307	+	0.492510i	$0.836079\pi$
$684$	−1.43006e23	−0.114124
$685$	1.72082e24	1.35633
$686$	−6.59804e22	−0.0513642
$687$	1.34653e24	1.03534
$688$	3.38245e23	0.256879
$689$	4.06897e23	0.305225
$690$	−4.45423e23	−0.330032
$691$	−1.89661e24	−1.38808	−0.694039	−	0.719937i	$-0.744171\pi$
$691$	−1.89661e24	−1.38808	−0.694039	+	0.719937i	$0.744171\pi$
$692$	1.81040e24	1.30880
$693$	−1.42252e23	−0.101584
$694$	−1.61769e23	−0.114114
$695$	−2.85818e24	−1.99167
$696$	−7.21282e22	−0.0496508
$697$	−1.00536e24	−0.683666
$698$	2.80773e23	0.188619
$699$	3.51236e23	0.233100
$700$	−2.60187e24	−1.70590
$701$	−1.32717e23	−0.0859656	−0.0429828	−	0.999076i	$-0.513686\pi$
$701$	−1.32717e23	−0.0859656	−0.0429828	+	0.999076i	$0.513686\pi$
$702$	8.21588e22	0.0525762
$703$	6.03785e23	0.381735
$704$	−5.47698e23	−0.342116
$705$	1.00525e24	0.620391
$706$	1.34110e23	0.0817753
$707$	1.60468e24	0.966773
$708$	1.53954e24	0.916449
$709$	−3.42005e23	−0.201159	−0.100580	−	0.994929i	$-0.532070\pi$
$709$	−3.42005e23	−0.201159	−0.100580	+	0.994929i	$0.532070\pi$
$710$	3.79345e23	0.220464
$711$	−9.80993e22	−0.0563345
$712$	−7.90171e23	−0.448375
$713$	−1.70571e24	−0.956408
$714$	−6.03120e23	−0.334171
$715$	−3.57684e23	−0.195839
$716$	9.14305e23	0.494687
$717$	−1.44117e24	−0.770552
$718$	−6.36288e22	−0.0336198
$719$	−2.62203e24	−1.36912	−0.684560	−	0.728957i	$-0.740006\pi$
$719$	−2.62203e24	−1.36912	−0.684560	+	0.728957i	$0.740006\pi$
$720$	5.36700e23	0.276952
$721$	4.77471e23	0.243499
$722$	−1.91679e23	−0.0966070
$723$	3.21204e24	1.59995
$724$	5.24155e23	0.258037
$725$	−5.04791e23	−0.245606
$726$	2.37344e23	0.114135
$727$	−4.69281e23	−0.223044	−0.111522	−	0.993762i	$-0.535573\pi$
$727$	−4.69281e23	−0.223044	−0.111522	+	0.993762i	$0.535573\pi$
$728$	−2.72403e23	−0.127966
$729$	2.39388e24	1.11153
$730$	4.82277e23	0.221336
$731$	1.13725e24	0.515890
$732$	−3.16114e24	−1.41742
$733$	−2.74389e24	−1.21614	−0.608070	−	0.793883i	$-0.708056\pi$
$733$	−2.74389e24	−1.21614	−0.608070	+	0.793883i	$0.708056\pi$
$734$	4.17374e23	0.182856
$735$	2.34215e24	1.01431
$736$	−1.64039e24	−0.702240
$737$	1.22146e23	0.0516901
$738$	2.56365e22	0.0107246
$739$	−2.42358e24	−1.00226	−0.501129	−	0.865373i	$-0.667082\pi$
$739$	−2.42358e24	−1.00226	−0.501129	+	0.865373i	$0.667082\pi$
$740$	−2.32120e24	−0.948950
$741$	4.32821e23	0.174926
$742$	4.66959e23	0.186572
$743$	2.73717e24	1.08118	0.540588	−	0.841288i	$-0.318202\pi$
$743$	2.73717e24	1.08118	0.540588	+	0.841288i	$0.318202\pi$
$744$	4.08910e23	0.159683
$745$	2.17151e24	0.838364
$746$	5.59102e23	0.213408
$747$	−3.85732e23	−0.145566
$748$	−1.93693e24	−0.722688
$749$	−4.93477e24	−1.82042
$750$	1.82291e23	0.0664883
$751$	−1.88497e24	−0.679774	−0.339887	−	0.940466i	$-0.610389\pi$
$751$	−1.88497e24	−0.679774	−0.339887	+	0.940466i	$0.610389\pi$
$752$	1.18630e24	0.423004
$753$	3.17942e24	1.12096
$754$	−2.61210e22	−0.00910611
$755$	−5.39825e24	−1.86082
$756$	−4.05703e24	−1.38284
$757$	1.54720e24	0.521472	0.260736	−	0.965410i	$-0.416035\pi$
$757$	1.54720e24	0.521472	0.260736	+	0.965410i	$0.416035\pi$
$758$	−4.50584e23	−0.150171
$759$	1.72186e24	0.567470
$760$	−8.34906e23	−0.272096
$761$	1.28984e24	0.415688	0.207844	−	0.978162i	$-0.433355\pi$
$761$	1.28984e24	0.415688	0.207844	+	0.978162i	$0.433355\pi$
$762$	4.32760e21	0.00137921
$763$	1.19684e24	0.377204
$764$	−4.73935e24	−1.47715
$765$	1.80449e24	0.556202
$766$	−5.17157e23	−0.157644
$767$	1.12804e24	0.340065
$768$	−2.34901e24	−0.700348
$769$	−5.27736e24	−1.55612	−0.778060	−	0.628190i	$-0.783796\pi$
$769$	−5.27736e24	−1.55612	−0.778060	+	0.628190i	$0.783796\pi$
$770$	−4.10483e23	−0.119708
$771$	−5.28710e24	−1.52495
$772$	3.63010e24	1.03555
$773$	2.63433e24	0.743267	0.371633	−	0.928380i	$-0.378798\pi$
$773$	2.63433e24	0.743267	0.371633	+	0.928380i	$0.378798\pi$
$774$	−2.89995e22	−0.00809267
$775$	2.86177e24	0.789896
$776$	1.75348e24	0.478714
$777$	2.79400e24	0.754481
$778$	−1.43231e23	−0.0382570
$779$	8.27986e23	0.218753
$780$	−1.66395e24	−0.434846
$781$	−1.46642e24	−0.379076
$782$	−1.76734e24	−0.451921
$783$	−7.87105e23	−0.199094
$784$	2.76400e24	0.691595
$785$	−2.28910e24	−0.566596
$786$	5.79365e23	0.141860
$787$	3.35616e24	0.812937	0.406469	−	0.913665i	$-0.366760\pi$
$787$	3.35616e24	0.812937	0.406469	+	0.913665i	$0.366760\pi$
$788$	6.81268e24	1.63247
$789$	5.48848e23	0.130106
$790$	−2.83076e23	−0.0663854
$791$	9.45973e24	2.19472
$792$	9.99304e22	0.0229368
$793$	−2.31620e24	−0.525961
$794$	7.48855e23	0.168238
$795$	5.77105e24	1.28273
$796$	−4.93995e24	−1.08633
$797$	−7.78898e24	−1.69467	−0.847335	−	0.531059i	$-0.821794\pi$
$797$	−7.78898e24	−1.69467	−0.847335	+	0.531059i	$0.821794\pi$
$798$	4.96711e23	0.106925
$799$	3.98859e24	0.849517
$800$	2.75218e24	0.579979
$801$	−1.40650e24	−0.293267
$802$	7.73576e23	0.159596
$803$	−1.86432e24	−0.380574
$804$	5.68225e23	0.114774
$805$	1.61160e25	3.22102
$806$	1.48085e23	0.0292863
$807$	2.61046e24	0.510849
$808$	−1.12727e24	−0.218290
$809$	6.02211e24	1.15395	0.576974	−	0.816763i	$-0.304234\pi$
$809$	6.02211e24	1.15395	0.576974	+	0.816763i	$0.304234\pi$
$810$	9.29181e23	0.176188
$811$	−1.83705e24	−0.344702	−0.172351	−	0.985036i	$-0.555136\pi$
$811$	−1.83705e24	−0.344702	−0.172351	+	0.985036i	$0.555136\pi$
$812$	1.28986e24	0.239506
$813$	−4.04603e24	−0.743462
$814$	−2.08535e23	−0.0379203
$815$	1.14746e25	2.06489
$816$	−8.79634e24	−1.56652
$817$	−9.36601e23	−0.165070
$818$	8.78231e22	0.0153181
$819$	−4.84875e23	−0.0836983
$820$	−3.18313e24	−0.543796
$821$	−4.64950e24	−0.786122	−0.393061	−	0.919512i	$-0.628584\pi$
$821$	−4.64950e24	−0.786122	−0.393061	+	0.919512i	$0.628584\pi$
$822$	7.19187e23	0.120346
$823$	−6.25356e24	−1.03569	−0.517844	−	0.855475i	$-0.673265\pi$
$823$	−6.25356e24	−1.03569	−0.517844	+	0.855475i	$0.673265\pi$
$824$	−3.35418e23	−0.0549801
$825$	−2.88887e24	−0.468672
$826$	1.29455e24	0.207868
$827$	3.57046e24	0.567450	0.283725	−	0.958906i	$-0.408430\pi$
$827$	3.57046e24	0.567450	0.283725	+	0.958906i	$0.408430\pi$
$828$	−1.93916e24	−0.305040
$829$	6.27247e24	0.976619	0.488309	−	0.872671i	$-0.337614\pi$
$829$	6.27247e24	0.976619	0.488309	+	0.872671i	$0.337614\pi$
$830$	−1.11307e24	−0.171537
$831$	9.05739e24	1.38164
$832$	−1.86687e24	−0.281880
$833$	9.29313e24	1.38893
$834$	−1.19453e24	−0.176719
$835$	−1.21827e25	−1.78405
$836$	1.59520e24	0.231239
$837$	4.46227e24	0.640309
$838$	7.97462e23	0.113275
$839$	−1.29316e25	−1.81834	−0.909168	−	0.416430i	$-0.863281\pi$
$839$	−1.29316e25	−1.81834	−0.909168	+	0.416430i	$0.863281\pi$
$840$	−3.86351e24	−0.537784
$841$	2.50246e23	0.0344828
$842$	1.30086e24	0.177450
$843$	−1.02587e25	−1.38535
$844$	6.34409e24	0.848123
$845$	1.02960e25	1.36266
$846$	−1.01708e23	−0.0133262
$847$	−8.58746e24	−1.11392
$848$	6.81048e24	0.874607
$849$	−2.01327e24	−0.255968
$850$	2.96517e24	0.373241
$851$	8.18735e24	1.02033
$852$	−6.82181e24	−0.841711
$853$	−1.02613e25	−1.25353	−0.626767	−	0.779207i	$-0.715622\pi$
$853$	−1.02613e25	−1.25353	−0.626767	+	0.779207i	$0.715622\pi$
$854$	−2.65810e24	−0.321498
$855$	−1.48613e24	−0.177969
$856$	3.46662e24	0.411036
$857$	−9.58828e24	−1.12565	−0.562826	−	0.826576i	$-0.690286\pi$
$857$	−9.58828e24	−1.12565	−0.562826	+	0.826576i	$0.690286\pi$
$858$	−1.49488e23	−0.0173766
$859$	1.15681e25	1.33143	0.665716	−	0.746206i	$-0.268126\pi$
$859$	1.15681e25	1.33143	0.665716	+	0.746206i	$0.268126\pi$
$860$	3.60069e24	0.410345
$861$	3.83149e24	0.432355
$862$	2.32799e24	0.260117
$863$	−4.68727e24	−0.518595	−0.259298	−	0.965797i	$-0.583491\pi$
$863$	−4.68727e24	−0.518595	−0.259298	+	0.965797i	$0.583491\pi$
$864$	4.29140e24	0.470145
$865$	1.88139e25	2.04099
$866$	−1.24474e24	−0.133714
$867$	−2.11400e25	−2.24876
$868$	−7.31250e24	−0.770280
$869$	1.09428e24	0.114146
$870$	−3.70476e23	−0.0382689
$871$	4.16344e23	0.0425891
$872$	−8.40765e23	−0.0851696
$873$	3.12118e24	0.313110
$874$	1.45553e24	0.144602
$875$	−6.59555e24	−0.648907
$876$	−8.67284e24	−0.845038
$877$	6.13694e23	0.0592182	0.0296091	−	0.999562i	$-0.490574\pi$
$877$	6.13694e23	0.0592182	0.0296091	+	0.999562i	$0.490574\pi$
$878$	−2.37233e24	−0.226710
$879$	−1.96425e23	−0.0185905
$880$	−5.98678e24	−0.561165
$881$	7.13273e23	0.0662157	0.0331078	−	0.999452i	$-0.489460\pi$
$881$	7.13273e23	0.0662157	0.0331078	+	0.999452i	$0.489460\pi$
$882$	−2.36972e23	−0.0217879
$883$	−1.97665e25	−1.79996	−0.899982	−	0.435928i	$-0.856420\pi$
$883$	−1.97665e25	−1.79996	−0.899982	+	0.435928i	$0.856420\pi$
$884$	−6.60217e24	−0.595446
$885$	1.59990e25	1.42914
$886$	−5.89568e23	−0.0521611
$887$	−2.00652e25	−1.75830	−0.879149	−	0.476547i	$-0.841888\pi$
$887$	−2.00652e25	−1.75830	−0.879149	+	0.476547i	$0.841888\pi$
$888$	−1.96276e24	−0.170356
$889$	−1.56579e23	−0.0134607
$890$	−4.05860e24	−0.345590
$891$	−3.59191e24	−0.302946
$892$	1.91601e25	1.60065
$893$	−3.28488e24	−0.271821
$894$	9.07543e23	0.0743872
$895$	9.50153e24	0.771432
$896$	−9.33836e24	−0.751022
$897$	5.86908e24	0.467556
$898$	−6.29877e23	−0.0497057
$899$	−1.41870e24	−0.110901
$900$	3.25345e24	0.251932
$901$	2.28982e25	1.75647
$902$	−2.85970e23	−0.0217303
$903$	−4.33411e24	−0.326252
$904$	−6.64537e24	−0.495550
$905$	5.44706e24	0.402392
$906$	−2.25611e24	−0.165109
$907$	−2.27726e25	−1.65101	−0.825507	−	0.564391i	$-0.809111\pi$
$907$	−2.27726e25	−1.65101	−0.825507	+	0.564391i	$0.809111\pi$
$908$	1.95753e25	1.40598
$909$	−2.00654e24	−0.142776
$910$	−1.39916e24	−0.0986313
$911$	1.81814e25	1.26976	0.634878	−	0.772612i	$-0.281050\pi$
$911$	1.81814e25	1.26976	0.634878	+	0.772612i	$0.281050\pi$
$912$	7.24440e24	0.501241
$913$	4.30277e24	0.294948
$914$	2.48713e24	0.168910
$915$	−3.28508e25	−2.21038
$916$	1.69159e25	1.12767
$917$	−2.09622e25	−1.38452
$918$	4.62351e24	0.302558
$919$	5.51452e24	0.357541	0.178771	−	0.983891i	$-0.442788\pi$
$919$	5.51452e24	0.357541	0.178771	+	0.983891i	$0.442788\pi$
$920$	−1.13214e25	−0.727281
$921$	−2.63366e24	−0.167630
$922$	−1.19519e24	−0.0753743
$923$	−4.99841e24	−0.312332
$924$	7.38176e24	0.457033
$925$	−1.37364e25	−0.842691
$926$	3.05672e24	0.185807
$927$	−5.97042e23	−0.0359606
$928$	−1.36438e24	−0.0814284
$929$	2.31103e25	1.36670	0.683349	−	0.730091i	$-0.260523\pi$
$929$	2.31103e25	1.36670	0.683349	+	0.730091i	$0.260523\pi$
$930$	2.10031e24	0.123077
$931$	−7.65354e24	−0.444416
$932$	4.41242e24	0.253888
$933$	2.64124e25	1.50596
$934$	−1.42504e24	−0.0805155
$935$	−2.01288e25	−1.12699
$936$	3.40620e23	0.0188984
$937$	−1.90821e25	−1.04915	−0.524577	−	0.851363i	$-0.675777\pi$
$937$	−1.90821e25	−1.04915	−0.524577	+	0.851363i	$0.675777\pi$
$938$	4.77802e23	0.0260330
$939$	4.89116e24	0.264092
$940$	1.26285e25	0.675716
$941$	6.67066e24	0.353718	0.176859	−	0.984236i	$-0.443406\pi$
$941$	6.67066e24	0.353718	0.176859	+	0.984236i	$0.443406\pi$
$942$	−9.56691e23	−0.0502735
$943$	1.12275e25	0.584702
$944$	1.88806e25	0.974439
$945$	−4.21609e25	−2.15645
$946$	3.23484e23	0.0163975
$947$	−4.42838e24	−0.222470	−0.111235	−	0.993794i	$-0.535481\pi$
$947$	−4.42838e24	−0.222470	−0.111235	+	0.993794i	$0.535481\pi$
$948$	5.09059e24	0.253453
$949$	−6.35467e24	−0.313567
$950$	−2.44203e24	−0.119426
$951$	3.06076e25	1.48353
$952$	−1.53295e25	−0.736402
$953$	−2.91907e25	−1.38981	−0.694903	−	0.719103i	$-0.744553\pi$
$953$	−2.91907e25	−1.38981	−0.694903	+	0.719103i	$0.744553\pi$
$954$	−5.83898e23	−0.0275534
$955$	−4.92517e25	−2.30352
$956$	−1.81048e25	−0.839269
$957$	1.43214e24	0.0658011
$958$	4.40027e24	0.200388
$959$	−2.60212e25	−1.17454
$960$	−2.64779e25	−1.18462
$961$	−1.45072e25	−0.643331
$962$	−7.10806e23	−0.0312437
$963$	6.17056e24	0.268845
$964$	4.03514e25	1.74263
$965$	3.77243e25	1.61487
$966$	6.73542e24	0.285798
$967$	4.44805e25	1.87087	0.935437	−	0.353493i	$-0.115006\pi$
$967$	4.44805e25	1.87087	0.935437	+	0.353493i	$0.115006\pi$
$968$	6.03260e24	0.251515
$969$	2.43571e25	1.00664
$970$	9.00649e24	0.368974
$971$	−6.79651e24	−0.276009	−0.138004	−	0.990432i	$-0.544069\pi$
$971$	−6.79651e24	−0.276009	−0.138004	+	0.990432i	$0.544069\pi$
$972$	9.31855e24	0.375133
$973$	4.32196e25	1.72473
$974$	1.11463e24	0.0440938
$975$	−9.84691e24	−0.386154
$976$	−3.87676e25	−1.50711
$977$	−1.45129e25	−0.559305	−0.279653	−	0.960101i	$-0.590219\pi$
$977$	−1.45129e25	−0.559305	−0.279653	+	0.960101i	$0.590219\pi$
$978$	4.79559e24	0.183215
$979$	1.56892e25	0.594221
$980$	2.94234e25	1.10477
$981$	−1.49656e24	−0.0557065
$982$	3.42022e24	0.126214
$983$	1.62259e24	0.0593613	0.0296807	−	0.999559i	$-0.490551\pi$
$983$	1.62259e24	0.0593613	0.0296807	+	0.999559i	$0.490551\pi$
$984$	−2.69158e24	−0.0976224
$985$	7.07979e25	2.54573
$986$	−1.46996e24	−0.0524026
$987$	−1.52007e25	−0.537241
$988$	5.43734e24	0.190525
$989$	−1.27004e25	−0.441212
$990$	5.13278e23	0.0176788
$991$	3.15126e25	1.07611	0.538057	−	0.842908i	$-0.319159\pi$
$991$	3.15126e25	1.07611	0.538057	+	0.842908i	$0.319159\pi$
$992$	7.73494e24	0.261883
$993$	2.62344e25	0.880648
$994$	−5.73623e24	−0.190916
$995$	−5.13364e25	−1.69406
$996$	2.00165e25	0.654913
$997$	2.08948e25	0.677842	0.338921	−	0.940815i	$-0.389938\pi$
$997$	2.08948e25	0.677842	0.338921	+	0.940815i	$0.389938\pi$
$998$	−1.26369e23	−0.00406474
$999$	−2.14188e25	−0.683106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.11	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.11	✓	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+54.5616 q^{2} -10196.6 q^{3} -128095. q^{4} -1.33117e6 q^{5} -556341. q^{6} +2.01292e7 q^{7} -1.41406e7 q^{8} -2.51701e7 q^{9} +O(q^{10})\)	\(q+54.5616 q^{2} -10196.6 q^{3} -128095. q^{4} -1.33117e6 q^{5} -556341. q^{6} +2.01292e7 q^{7} -1.41406e7 q^{8} -2.51701e7 q^{9} -7.26309e7 q^{10} +2.80767e8 q^{11} +1.30613e9 q^{12} +9.57014e8 q^{13} +1.09828e9 q^{14} +1.35734e10 q^{15} +1.60181e10 q^{16} +5.38562e10 q^{17} -1.37332e9 q^{18} -4.43543e10 q^{19} +1.70517e11 q^{20} -2.05249e11 q^{21} +1.53191e10 q^{22} -6.01447e11 q^{23} +1.44185e11 q^{24} +1.00908e12 q^{25} +5.22162e10 q^{26} +1.57344e12 q^{27} -2.57845e12 q^{28} -5.00246e11 q^{29} +7.40586e11 q^{30} +2.83601e12 q^{31} +2.72741e12 q^{32} -2.86286e12 q^{33} +2.93848e12 q^{34} -2.67955e13 q^{35} +3.22416e12 q^{36} -1.36128e13 q^{37} -2.42004e12 q^{38} -9.75827e12 q^{39} +1.88235e13 q^{40} -1.86675e13 q^{41} -1.11987e13 q^{42} +2.11163e13 q^{43} -3.59649e13 q^{44} +3.35057e13 q^{45} -3.28159e13 q^{46} +7.40600e13 q^{47} -1.63330e14 q^{48} +1.72554e14 q^{49} +5.50572e13 q^{50} -5.49149e14 q^{51} -1.22589e14 q^{52} +4.25173e14 q^{53} +8.58491e13 q^{54} -3.73750e14 q^{55} -2.84638e14 q^{56} +4.52262e14 q^{57} -2.72942e13 q^{58} +1.17870e15 q^{59} -1.73869e15 q^{60} -2.42023e15 q^{61} +1.54737e14 q^{62} -5.06654e14 q^{63} -1.95072e15 q^{64} -1.27395e15 q^{65} -1.56202e14 q^{66} +4.35045e14 q^{67} -6.89871e15 q^{68} +6.13270e15 q^{69} -1.46200e15 q^{70} -5.22292e15 q^{71} +3.55919e14 q^{72} -6.64010e15 q^{73} -7.42733e14 q^{74} -1.02892e16 q^{75} +5.68157e15 q^{76} +5.65162e15 q^{77} -5.32426e14 q^{78} +3.89746e15 q^{79} -2.13229e16 q^{80} -1.27932e16 q^{81} -1.01853e15 q^{82} +1.53250e16 q^{83} +2.62914e16 q^{84} -7.16920e16 q^{85} +1.15214e15 q^{86} +5.10080e15 q^{87} -3.97021e15 q^{88} +5.58798e16 q^{89} +1.82813e15 q^{90} +1.92639e16 q^{91} +7.70423e16 q^{92} -2.89175e16 q^{93} +4.04083e15 q^{94} +5.90433e16 q^{95} -2.78102e16 q^{96} -1.24003e17 q^{97} +9.41484e15 q^{98} -7.06694e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Introduction

L-functions

Modular forms

Varieties

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