LMFDB - Embedded newform 29.18.a.a.1.5

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			1.5
Root			$-415.129$ 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)

$f(q)$	$=$	$q-415.129 q^{2} +11060.0 q^{3} +41259.9 q^{4} +1.55169e6 q^{5} -4.59133e6 q^{6} +5.04285e6 q^{7} +3.72836e7 q^{8} -6.81605e6 q^{9} +O(q^{10})$	\(q-415.129 q^{2} +11060.0 q^{3} +41259.9 q^{4} +1.55169e6 q^{5} -4.59133e6 q^{6} +5.04285e6 q^{7} +3.72836e7 q^{8} -6.81605e6 q^{9} -6.44152e8 q^{10} +2.87649e8 q^{11} +4.56335e8 q^{12} -4.50962e9 q^{13} -2.09343e9 q^{14} +1.71618e10 q^{15} -2.08855e10 q^{16} -5.19130e10 q^{17} +2.82954e9 q^{18} -7.65674e10 q^{19} +6.40226e10 q^{20} +5.57740e10 q^{21} -1.19411e11 q^{22} -4.59448e11 q^{23} +4.12357e11 q^{24} +1.64481e12 q^{25} +1.87207e12 q^{26} -1.50368e12 q^{27} +2.08067e11 q^{28} -5.00246e11 q^{29} -7.12434e12 q^{30} -4.33415e12 q^{31} +3.78334e12 q^{32} +3.18141e12 q^{33} +2.15506e13 q^{34} +7.82495e12 q^{35} -2.81229e11 q^{36} +3.72622e13 q^{37} +3.17853e13 q^{38} -4.98765e13 q^{39} +5.78527e13 q^{40} +3.78955e12 q^{41} -2.31534e13 q^{42} +1.03405e13 q^{43} +1.18684e13 q^{44} -1.05764e13 q^{45} +1.90730e14 q^{46} -1.38762e14 q^{47} -2.30994e14 q^{48} -2.07200e14 q^{49} -6.82808e14 q^{50} -5.74159e14 q^{51} -1.86066e14 q^{52} -2.25950e14 q^{53} +6.24220e14 q^{54} +4.46343e14 q^{55} +1.88016e14 q^{56} -8.46837e14 q^{57} +2.07667e14 q^{58} -1.88191e15 q^{59} +7.08091e14 q^{60} -1.72952e15 q^{61} +1.79923e15 q^{62} -3.43723e13 q^{63} +1.16693e15 q^{64} -6.99754e15 q^{65} -1.32069e15 q^{66} +2.95384e15 q^{67} -2.14192e15 q^{68} -5.08151e15 q^{69} -3.24836e15 q^{70} +2.94095e15 q^{71} -2.54127e14 q^{72} +5.20859e15 q^{73} -1.54686e16 q^{74} +1.81916e16 q^{75} -3.15916e15 q^{76} +1.45057e15 q^{77} +2.07052e16 q^{78} +7.23877e15 q^{79} -3.24079e16 q^{80} -1.57505e16 q^{81} -1.57315e15 q^{82} +3.85013e16 q^{83} +2.30123e15 q^{84} -8.05530e16 q^{85} -4.29264e15 q^{86} -5.53274e15 q^{87} +1.07246e16 q^{88} +2.41093e16 q^{89} +4.39057e15 q^{90} -2.27413e16 q^{91} -1.89568e16 q^{92} -4.79358e16 q^{93} +5.76041e16 q^{94} -1.18809e17 q^{95} +4.18438e16 q^{96} -5.13245e16 q^{97} +8.60147e16 q^{98} -1.96063e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−415.129	−1.14664	−0.573321	−	0.819331i	$-0.694345\pi$
$2$	−415.129	−1.14664	−0.573321	+	0.819331i	$0.694345\pi$
$3$	11060.0	0.973252	0.486626	−	0.873610i	$-0.338227\pi$
$3$	11060.0	0.973252	0.486626	+	0.873610i	$0.338227\pi$
$4$	41259.9	0.314788
$5$	1.55169e6	1.77648	0.888240	−	0.459379i	$-0.151928\pi$
$5$	1.55169e6	1.77648	0.888240	+	0.459379i	$0.151928\pi$
$6$	−4.59133e6	−1.11597
$7$	5.04285e6	0.330630	0.165315	−	0.986241i	$-0.447136\pi$
$7$	5.04285e6	0.330630	0.165315	+	0.986241i	$0.447136\pi$
$8$	3.72836e7	0.785693
$9$	−6.81605e6	−0.0527803
$10$	−6.44152e8	−2.03699
$11$	2.87649e8	0.404600	0.202300	−	0.979324i	$-0.435158\pi$
$11$	2.87649e8	0.404600	0.202300	+	0.979324i	$0.435158\pi$
$12$	4.56335e8	0.306368
$13$	−4.50962e9	−1.53328	−0.766639	−	0.642078i	$-0.778073\pi$
$13$	−4.50962e9	−1.53328	−0.766639	+	0.642078i	$0.778073\pi$
$14$	−2.09343e9	−0.379115
$15$	1.71618e10	1.72896
$16$	−2.08855e10	−1.21570
$17$	−5.19130e10	−1.80493	−0.902465	−	0.430764i	$-0.858244\pi$
$17$	−5.19130e10	−1.80493	−0.902465	+	0.430764i	$0.858244\pi$
$18$	2.82954e9	0.0605201
$19$	−7.65674e10	−1.03428	−0.517140	−	0.855901i	$-0.673003\pi$
$19$	−7.65674e10	−1.03428	−0.517140	+	0.855901i	$0.673003\pi$
$20$	6.40226e10	0.559214
$21$	5.57740e10	0.321787
$22$	−1.19411e11	−0.463931
$23$	−4.59448e11	−1.22335	−0.611674	−	0.791110i	$-0.709504\pi$
$23$	−4.59448e11	−1.22335	−0.611674	+	0.791110i	$0.709504\pi$
$24$	4.12357e11	0.764678
$25$	1.64481e12	2.15588
$26$	1.87207e12	1.75812
$27$	−1.50368e12	−1.02462
$28$	2.08067e11	0.104078
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	−7.12434e12	−1.98250
$31$	−4.33415e12	−0.912704	−0.456352	−	0.889799i	$-0.650844\pi$
$31$	−4.33415e12	−0.912704	−0.456352	+	0.889799i	$0.650844\pi$
$32$	3.78334e12	0.608275
$33$	3.18141e12	0.393777
$34$	2.15506e13	2.06961
$35$	7.82495e12	0.587358
$36$	−2.81229e11	−0.0166146
$37$	3.72622e13	1.74403	0.872014	−	0.489481i	$-0.162814\pi$
$37$	3.72622e13	1.74403	0.872014	+	0.489481i	$0.162814\pi$
$38$	3.17853e13	1.18595
$39$	−4.98765e13	−1.49227
$40$	5.78527e13	1.39577
$41$	3.78955e12	0.0741181	0.0370591	−	0.999313i	$-0.488201\pi$
$41$	3.78955e12	0.0741181	0.0370591	+	0.999313i	$0.488201\pi$
$42$	−2.31534e13	−0.368974
$43$	1.03405e13	0.134915	0.0674575	−	0.997722i	$-0.478511\pi$
$43$	1.03405e13	0.134915	0.0674575	+	0.997722i	$0.478511\pi$
$44$	1.18684e13	0.127363
$45$	−1.05764e13	−0.0937631
$46$	1.90730e14	1.40274
$47$	−1.38762e14	−0.850038	−0.425019	−	0.905184i	$-0.639733\pi$
$47$	−1.38762e14	−0.850038	−0.425019	+	0.905184i	$0.639733\pi$
$48$	−2.30994e14	−1.18318
$49$	−2.07200e14	−0.890684
$50$	−6.82808e14	−2.47203
$51$	−5.74159e14	−1.75665
$52$	−1.86066e14	−0.482657
$53$	−2.25950e14	−0.498503	−0.249252	−	0.968439i	$-0.580185\pi$
$53$	−2.25950e14	−0.498503	−0.249252	+	0.968439i	$0.580185\pi$
$54$	6.24220e14	1.17487
$55$	4.46343e14	0.718764
$56$	1.88016e14	0.259774
$57$	−8.46837e14	−1.00662
$58$	2.07667e14	0.212926
$59$	−1.88191e15	−1.66862	−0.834311	−	0.551295i	$-0.814134\pi$
$59$	−1.88191e15	−1.66862	−0.834311	+	0.551295i	$0.814134\pi$
$60$	7.08091e14	0.544257
$61$	−1.72952e15	−1.15511	−0.577553	−	0.816353i	$-0.695992\pi$
$61$	−1.72952e15	−1.15511	−0.577553	+	0.816353i	$0.695992\pi$
$62$	1.79923e15	1.04654
$63$	−3.43723e13	−0.0174508
$64$	1.16693e15	0.518222
$65$	−6.99754e15	−2.72384
$66$	−1.32069e15	−0.451522
$67$	2.95384e15	0.888692	0.444346	−	0.895855i	$-0.353436\pi$
$67$	2.95384e15	0.888692	0.444346	+	0.895855i	$0.353436\pi$
$68$	−2.14192e15	−0.568170
$69$	−5.08151e15	−1.19063
$70$	−3.24836e15	−0.673490
$71$	2.94095e15	0.540495	0.270248	−	0.962791i	$-0.412894\pi$
$71$	2.94095e15	0.540495	0.270248	+	0.962791i	$0.412894\pi$
$72$	−2.54127e14	−0.0414691
$73$	5.20859e15	0.755920	0.377960	−	0.925822i	$-0.376626\pi$
$73$	5.20859e15	0.755920	0.377960	+	0.925822i	$0.376626\pi$
$74$	−1.54686e16	−1.99978
$75$	1.81916e16	2.09822
$76$	−3.15916e15	−0.325579
$77$	1.45057e15	0.133773
$78$	2.07052e16	1.71110
$79$	7.23877e15	0.536827	0.268414	−	0.963304i	$-0.413501\pi$
$79$	7.23877e15	0.536827	0.268414	+	0.963304i	$0.413501\pi$
$80$	−3.24079e16	−2.15966
$81$	−1.57505e16	−0.944434
$82$	−1.57315e15	−0.0849870
$83$	3.85013e16	1.87634	0.938169	−	0.346177i	$-0.112520\pi$
$83$	3.85013e16	1.87634	0.938169	+	0.346177i	$0.112520\pi$
$84$	2.30123e15	0.101294
$85$	−8.05530e16	−3.20642
$86$	−4.29264e15	−0.154699
$87$	−5.53274e15	−0.180728
$88$	1.07246e16	0.317891
$89$	2.41093e16	0.649186	0.324593	−	0.945854i	$-0.394773\pi$
$89$	2.41093e16	0.649186	0.324593	+	0.945854i	$0.394773\pi$
$90$	4.39057e15	0.107513
$91$	−2.27413e16	−0.506948
$92$	−1.89568e16	−0.385095
$93$	−4.79358e16	−0.888291
$94$	5.76041e16	0.974690
$95$	−1.18809e17	−1.83738
$96$	4.18438e16	0.592005
$97$	−5.13245e16	−0.664913	−0.332457	−	0.943119i	$-0.607878\pi$
$97$	−5.13245e16	−0.664913	−0.332457	+	0.943119i	$0.607878\pi$
$98$	8.60147e16	1.02130
$99$	−1.96063e15	−0.0213549
$100$	6.78646e16	0.678646
$101$	1.39744e17	1.28411	0.642055	−	0.766659i	$-0.278082\pi$
$101$	1.39744e17	1.28411	0.642055	+	0.766659i	$0.278082\pi$
$102$	2.38350e17	2.01425
$103$	−6.70477e16	−0.521516	−0.260758	−	0.965404i	$-0.583972\pi$
$103$	−6.70477e16	−0.521516	−0.260758	+	0.965404i	$0.583972\pi$
$104$	−1.68135e17	−1.20469
$105$	8.65441e16	0.571648
$106$	9.37985e16	0.571605
$107$	−2.99538e16	−0.168535	−0.0842675	−	0.996443i	$-0.526855\pi$
$107$	−2.99538e16	−0.168535	−0.0842675	+	0.996443i	$0.526855\pi$
$108$	−6.20416e16	−0.322538
$109$	3.22165e17	1.54865	0.774324	−	0.632789i	$-0.218090\pi$
$109$	3.22165e17	1.54865	0.774324	+	0.632789i	$0.218090\pi$
$110$	−1.85290e17	−0.824164
$111$	4.12120e17	1.69738
$112$	−1.05322e17	−0.401946
$113$	−5.48364e17	−1.94045	−0.970224	−	0.242210i	$-0.922128\pi$
$113$	−5.48364e17	−1.94045	−0.970224	+	0.242210i	$0.922128\pi$
$114$	3.51546e17	1.15423
$115$	−7.12922e17	−2.17325
$116$	−2.06401e16	−0.0584546
$117$	3.07378e16	0.0809269
$118$	7.81237e17	1.91331
$119$	−2.61789e17	−0.596764
$120$	6.39852e17	1.35844
$121$	−4.22705e17	−0.836299
$122$	7.17973e17	1.32449
$123$	4.19125e16	0.0721356
$124$	−1.78827e17	−0.287308
$125$	1.36839e18	2.05341
$126$	1.42689e16	0.0200098
$127$	5.32344e17	0.698009	0.349004	−	0.937121i	$-0.386520\pi$
$127$	5.32344e17	0.698009	0.349004	+	0.937121i	$0.386520\pi$
$128$	−9.80317e17	−1.20249
$129$	1.14366e17	0.131306
$130$	2.90488e18	3.12327
$131$	4.51342e17	0.454674	0.227337	−	0.973816i	$-0.426998\pi$
$131$	4.51342e17	0.454674	0.227337	+	0.973816i	$0.426998\pi$
$132$	1.31264e17	0.123956
$133$	−3.86118e17	−0.341964
$134$	−1.22622e18	−1.01901
$135$	−2.33325e18	−1.82022
$136$	−1.93550e18	−1.41812
$137$	−6.91889e17	−0.476334	−0.238167	−	0.971224i	$-0.576547\pi$
$137$	−6.91889e17	−0.476334	−0.238167	+	0.971224i	$0.576547\pi$
$138$	2.10948e18	1.36522
$139$	1.03387e18	0.629276	0.314638	−	0.949212i	$-0.398117\pi$
$139$	1.03387e18	0.629276	0.314638	+	0.949212i	$0.398117\pi$
$140$	3.22856e17	0.184893
$141$	−1.53471e18	−0.827302
$142$	−1.22087e18	−0.619755
$143$	−1.29719e18	−0.620364
$144$	1.42357e17	0.0641648
$145$	−7.76228e17	−0.329884
$146$	−2.16224e18	−0.866770
$147$	−2.29164e18	−0.866860
$148$	1.53743e18	0.548999
$149$	8.44547e17	0.284800	0.142400	−	0.989809i	$-0.454518\pi$
$149$	8.44547e17	0.284800	0.142400	+	0.989809i	$0.454518\pi$
$150$	−7.55187e18	−2.40591
$151$	1.82666e18	0.549990	0.274995	−	0.961446i	$-0.411324\pi$
$151$	1.82666e18	0.549990	0.274995	+	0.961446i	$0.411324\pi$
$152$	−2.85471e18	−0.812627
$153$	3.53842e17	0.0952647
$154$	−6.02174e17	−0.153390
$155$	−6.72527e18	−1.62140
$156$	−2.05790e18	−0.469747
$157$	−1.84002e18	−0.397811	−0.198905	−	0.980019i	$-0.563739\pi$
$157$	−1.84002e18	−0.397811	−0.198905	+	0.980019i	$0.563739\pi$
$158$	−3.00502e18	−0.615548
$159$	−2.49902e18	−0.485169
$160$	5.87057e18	1.08059
$161$	−2.31693e18	−0.404476
$162$	6.53848e18	1.08293
$163$	1.05099e18	0.165198	0.0825989	−	0.996583i	$-0.473678\pi$
$163$	1.05099e18	0.165198	0.0825989	+	0.996583i	$0.473678\pi$
$164$	1.56356e17	0.0233315
$165$	4.93657e18	0.699538
$166$	−1.59830e19	−2.15149
$167$	1.33047e19	1.70182	0.850911	−	0.525309i	$-0.176050\pi$
$167$	1.33047e19	1.70182	0.850911	+	0.525309i	$0.176050\pi$
$168$	2.07946e18	0.252826
$169$	1.16862e19	1.35094
$170$	3.34399e19	3.67662
$171$	5.21887e17	0.0545896
$172$	4.26648e17	0.0424696
$173$	−1.27962e19	−1.21252	−0.606262	−	0.795265i	$-0.707332\pi$
$173$	−1.27962e19	−1.21252	−0.606262	+	0.795265i	$0.707332\pi$
$174$	2.29680e18	0.207231
$175$	8.29453e18	0.712801
$176$	−6.00770e18	−0.491870
$177$	−2.08140e19	−1.62399
$178$	−1.00084e19	−0.744384
$179$	1.41130e18	0.100085	0.0500423	−	0.998747i	$-0.484064\pi$
$179$	1.41130e18	0.100085	0.0500423	+	0.998747i	$0.484064\pi$
$180$	−4.36381e17	−0.0295155
$181$	−6.50326e18	−0.419627	−0.209813	−	0.977741i	$-0.567286\pi$
$181$	−6.50326e18	−0.419627	−0.209813	+	0.977741i	$0.567286\pi$
$182$	9.44057e18	0.581288
$183$	−1.91285e19	−1.12421
$184$	−1.71299e19	−0.961176
$185$	5.78194e19	3.09823
$186$	1.98995e19	1.01855
$187$	−1.49327e19	−0.730274
$188$	−5.72530e18	−0.267582
$189$	−7.58283e18	−0.338771
$190$	4.93210e19	2.10682
$191$	1.76902e19	0.722683	0.361342	−	0.932433i	$-0.382319\pi$
$191$	1.76902e19	0.722683	0.361342	+	0.932433i	$0.382319\pi$
$192$	1.29063e19	0.504361
$193$	8.93361e18	0.334033	0.167017	−	0.985954i	$-0.446587\pi$
$193$	8.93361e18	0.334033	0.167017	+	0.985954i	$0.446587\pi$
$194$	2.13063e19	0.762418
$195$	−7.73929e19	−2.65098
$196$	−8.54905e18	−0.280376
$197$	−4.22694e19	−1.32759	−0.663794	−	0.747915i	$-0.731055\pi$
$197$	−4.22694e19	−1.32759	−0.663794	+	0.747915i	$0.731055\pi$
$198$	8.13915e17	0.0244864
$199$	−3.56844e19	−1.02856	−0.514278	−	0.857624i	$-0.671940\pi$
$199$	−3.56844e19	−1.02856	−0.514278	+	0.857624i	$0.671940\pi$
$200$	6.13244e19	1.69386
$201$	3.26695e19	0.864921
$202$	−5.80118e19	−1.47241
$203$	−2.52267e18	−0.0613965
$204$	−2.36897e19	−0.552972
$205$	5.88021e18	0.131669
$206$	2.78334e19	0.597992
$207$	3.13162e18	0.0645686
$208$	9.41856e19	1.86400
$209$	−2.20245e19	−0.418469
$210$	−3.59270e19	−0.655475
$211$	3.52261e19	0.617253	0.308627	−	0.951183i	$-0.400131\pi$
$211$	3.52261e19	0.617253	0.308627	+	0.951183i	$0.400131\pi$
$212$	−9.32268e18	−0.156923
$213$	3.25270e19	0.526038
$214$	1.24347e19	0.193249
$215$	1.60453e19	0.239674
$216$	−5.60626e19	−0.805037
$217$	−2.18565e19	−0.301768
$218$	−1.33740e20	−1.77574
$219$	5.76071e19	0.735701
$220$	1.84161e19	0.226258
$221$	2.34108e20	2.76746
$222$	−1.71083e20	−1.94629
$223$	−1.47245e20	−1.61231	−0.806155	−	0.591704i	$-0.798455\pi$
$223$	−1.47245e20	−1.61231	−0.806155	+	0.591704i	$0.798455\pi$
$224$	1.90788e19	0.201114
$225$	−1.12111e19	−0.113788
$226$	2.27642e20	2.22500
$227$	3.21981e19	0.303117	0.151559	−	0.988448i	$-0.451571\pi$
$227$	3.21981e19	0.303117	0.151559	+	0.988448i	$0.451571\pi$
$228$	−3.49404e19	−0.316870
$229$	−9.50814e19	−0.830795	−0.415398	−	0.909640i	$-0.636358\pi$
$229$	−9.50814e19	−0.830795	−0.415398	+	0.909640i	$0.636358\pi$
$230$	2.95955e20	2.49194
$231$	1.60434e19	0.130195
$232$	−1.86510e19	−0.145900
$233$	1.02997e20	0.776781	0.388391	−	0.921495i	$-0.373031\pi$
$233$	1.02997e20	0.776781	0.388391	+	0.921495i	$0.373031\pi$
$234$	−1.27601e19	−0.0927941
$235$	−2.15316e20	−1.51008
$236$	−7.76475e19	−0.525261
$237$	8.00609e19	0.522468
$238$	1.08676e20	0.684275
$239$	−2.01087e20	−1.22181	−0.610903	−	0.791706i	$-0.709193\pi$
$239$	−2.01087e20	−1.22181	−0.610903	+	0.791706i	$0.709193\pi$
$240$	−3.58432e20	−2.10190
$241$	−2.22284e19	−0.125824	−0.0629120	−	0.998019i	$-0.520039\pi$
$241$	−2.22284e19	−0.125824	−0.0629120	+	0.998019i	$0.520039\pi$
$242$	1.75477e20	0.958936
$243$	1.99845e19	0.105448
$244$	−7.13597e19	−0.363613
$245$	−3.21511e20	−1.58228
$246$	−1.73991e19	−0.0827137
$247$	3.45289e20	1.58584
$248$	−1.61593e20	−0.717105
$249$	4.25825e20	1.82615
$250$	−5.68058e20	−2.35452
$251$	1.00310e20	0.401902	0.200951	−	0.979601i	$-0.435597\pi$
$251$	1.00310e20	0.401902	0.200951	+	0.979601i	$0.435597\pi$
$252$	−1.41820e18	−0.00549328
$253$	−1.32160e20	−0.494966
$254$	−2.20991e20	−0.800366
$255$	−8.90918e20	−3.12066
$256$	2.54005e20	0.860604
$257$	−6.98751e19	−0.229029	−0.114515	−	0.993422i	$-0.536531\pi$
$257$	−6.98751e19	−0.229029	−0.114515	+	0.993422i	$0.536531\pi$
$258$	−4.74767e19	−0.150561
$259$	1.87907e20	0.576628
$260$	−2.88717e20	−0.857432
$261$	3.40971e18	0.00980105
$262$	−1.87365e20	−0.521348
$263$	−1.36314e20	−0.367211	−0.183605	−	0.983000i	$-0.558777\pi$
$263$	−1.36314e20	−0.367211	−0.183605	+	0.983000i	$0.558777\pi$
$264$	1.18614e20	0.309388
$265$	−3.50605e20	−0.885582
$266$	1.60289e20	0.392111
$267$	2.66649e20	0.631821
$268$	1.21875e20	0.279749
$269$	−3.90735e20	−0.868937	−0.434469	−	0.900687i	$-0.643064\pi$
$269$	−3.90735e20	−0.868937	−0.434469	+	0.900687i	$0.643064\pi$
$270$	9.68598e20	2.08714
$271$	3.92062e19	0.0818683	0.0409341	−	0.999162i	$-0.486967\pi$
$271$	3.92062e19	0.0818683	0.0409341	+	0.999162i	$0.486967\pi$
$272$	1.08423e21	2.19425
$273$	−2.51519e20	−0.493389
$274$	2.87223e20	0.546184
$275$	4.73128e20	0.872270
$276$	−2.09662e20	−0.374794
$277$	5.05456e20	0.876203	0.438102	−	0.898925i	$-0.355651\pi$
$277$	5.05456e20	0.876203	0.438102	+	0.898925i	$0.355651\pi$
$278$	−4.29190e20	−0.721554
$279$	2.95418e19	0.0481728
$280$	2.91742e20	0.461483
$281$	5.81280e20	0.892035	0.446017	−	0.895024i	$-0.352842\pi$
$281$	5.81280e20	0.892035	0.446017	+	0.895024i	$0.352842\pi$
$282$	6.37102e20	0.948619
$283$	−9.23686e20	−1.33456	−0.667282	−	0.744805i	$-0.732542\pi$
$283$	−9.23686e20	−1.33456	−0.667282	+	0.744805i	$0.732542\pi$
$284$	1.21343e20	0.170141
$285$	−1.31403e21	−1.78823
$286$	5.38500e20	0.711335
$287$	1.91101e19	0.0245057
$288$	−2.57874e19	−0.0321049
$289$	1.86772e21	2.25777
$290$	3.22235e20	0.378259
$291$	−5.67650e20	−0.647128
$292$	2.14906e20	0.237954
$293$	−2.63360e20	−0.283253	−0.141627	−	0.989920i	$-0.545233\pi$
$293$	−2.63360e20	−0.283253	−0.141627	+	0.989920i	$0.545233\pi$
$294$	9.51325e20	0.993978
$295$	−2.92015e21	−2.96427
$296$	1.38927e21	1.37027
$297$	−4.32532e20	−0.414561
$298$	−3.50596e20	−0.326564
$299$	2.07194e21	1.87573
$300$	7.50584e20	0.660494
$301$	5.21456e19	0.0446070
$302$	−7.58301e20	−0.630642
$303$	1.54557e21	1.24976
$304$	1.59915e21	1.25737
$305$	−2.68368e21	−2.05202
$306$	−1.46890e20	−0.109234
$307$	−1.37187e21	−0.992285	−0.496142	−	0.868241i	$-0.665251\pi$
$307$	−1.37187e21	−0.992285	−0.496142	+	0.868241i	$0.665251\pi$
$308$	5.98504e19	0.0421101
$309$	−7.41549e20	−0.507566
$310$	2.79185e21	1.85917
$311$	−9.99508e19	−0.0647624	−0.0323812	−	0.999476i	$-0.510309\pi$
$311$	−9.99508e19	−0.0647624	−0.0323812	+	0.999476i	$0.510309\pi$
$312$	−1.85957e21	−1.17246
$313$	8.95318e20	0.549351	0.274676	−	0.961537i	$-0.411430\pi$
$313$	8.95318e20	0.549351	0.274676	+	0.961537i	$0.411430\pi$
$314$	7.63847e20	0.456147
$315$	−5.33353e19	−0.0310009
$316$	2.98670e20	0.168987
$317$	−2.55489e20	−0.140724	−0.0703622	−	0.997522i	$-0.522415\pi$
$317$	−2.55489e20	−0.140724	−0.0703622	+	0.997522i	$0.522415\pi$
$318$	1.03741e21	0.556316
$319$	−1.43896e20	−0.0751323
$320$	1.81072e21	0.920612
$321$	−3.31290e20	−0.164027
$322$	9.61823e20	0.463789
$323$	3.97484e21	1.86680
$324$	−6.49863e20	−0.297296
$325$	−7.41746e21	−3.30557
$326$	−4.36296e20	−0.189423
$327$	3.56315e21	1.50722
$328$	1.41288e20	0.0582341
$329$	−6.99755e20	−0.281048
$330$	−2.04931e21	−0.802120
$331$	−5.17929e21	−1.97575	−0.987876	−	0.155242i	$-0.950384\pi$
$331$	−5.17929e21	−1.97575	−0.987876	+	0.155242i	$0.950384\pi$
$332$	1.58856e21	0.590648
$333$	−2.53981e20	−0.0920503
$334$	−5.52315e21	−1.95138
$335$	4.58345e21	1.57874
$336$	−1.16487e21	−0.391195
$337$	1.48278e21	0.485538	0.242769	−	0.970084i	$-0.421944\pi$
$337$	1.48278e21	0.485538	0.242769	+	0.970084i	$0.421944\pi$
$338$	−4.85129e21	−1.54905
$339$	−6.06492e21	−1.88854
$340$	−3.32360e21	−1.00934
$341$	−1.24672e21	−0.369280
$342$	−2.16650e20	−0.0625947
$343$	−2.21800e21	−0.625117
$344$	3.85531e20	0.106002
$345$	−7.88494e21	−2.11512
$346$	5.31208e21	1.39033
$347$	6.08641e21	1.55439	0.777196	−	0.629259i	$-0.216641\pi$
$347$	6.08641e21	1.55439	0.777196	+	0.629259i	$0.216641\pi$
$348$	−2.28280e20	−0.0568911
$349$	−6.58393e21	−1.60129	−0.800643	−	0.599142i	$-0.795509\pi$
$349$	−6.58393e21	−1.60129	−0.800643	+	0.599142i	$0.795509\pi$
$350$	−3.44330e21	−0.817327
$351$	6.78102e21	1.57103
$352$	1.08827e21	0.246108
$353$	−2.92751e21	−0.646270	−0.323135	−	0.946353i	$-0.604737\pi$
$353$	−2.92751e21	−0.646270	−0.323135	+	0.946353i	$0.604737\pi$
$354$	8.64050e21	1.86213
$355$	4.56345e21	0.960180
$356$	9.94745e20	0.204356
$357$	−2.89540e21	−0.580802
$358$	−5.85870e20	−0.114761
$359$	2.87297e21	0.549576	0.274788	−	0.961505i	$-0.411392\pi$
$359$	2.87297e21	0.549576	0.274788	+	0.961505i	$0.411392\pi$
$360$	−3.94327e20	−0.0736691
$361$	3.82173e20	0.0697348
$362$	2.69969e21	0.481161
$363$	−4.67513e21	−0.813930
$364$	−9.38303e20	−0.159581
$365$	8.08213e21	1.34288
$366$	7.94079e21	1.28906
$367$	7.18035e20	0.113890	0.0569448	−	0.998377i	$-0.481864\pi$
$367$	7.18035e20	0.113890	0.0569448	+	0.998377i	$0.481864\pi$
$368$	9.59581e21	1.48722
$369$	−2.58298e19	−0.00391198
$370$	−2.40025e22	−3.55256
$371$	−1.13943e21	−0.164820
$372$	−1.97783e21	−0.279623
$373$	−3.41257e21	−0.471581	−0.235791	−	0.971804i	$-0.575768\pi$
$373$	−3.41257e21	−0.471581	−0.235791	+	0.971804i	$0.575768\pi$
$374$	6.19901e21	0.837363
$375$	1.51344e22	1.99848
$376$	−5.17354e21	−0.667869
$377$	2.25592e21	0.284723
$378$	3.14785e21	0.388449
$379$	−1.04437e22	−1.26015	−0.630075	−	0.776535i	$-0.716976\pi$
$379$	−1.04437e22	−1.26015	−0.630075	+	0.776535i	$0.716976\pi$
$380$	−4.90204e21	−0.578384
$381$	5.88774e21	0.679339
$382$	−7.34369e21	−0.828659
$383$	−9.48338e21	−1.04658	−0.523291	−	0.852154i	$-0.675296\pi$
$383$	−9.48338e21	−1.04658	−0.523291	+	0.852154i	$0.675296\pi$
$384$	−1.08423e22	−1.17033
$385$	2.25084e21	0.237645
$386$	−3.70860e21	−0.383017
$387$	−7.04814e19	−0.00712084
$388$	−2.11764e21	−0.209307
$389$	5.89182e21	0.569742	0.284871	−	0.958566i	$-0.408049\pi$
$389$	5.89182e21	0.569742	0.284871	+	0.958566i	$0.408049\pi$
$390$	3.21280e22	3.03973
$391$	2.38513e22	2.20806
$392$	−7.72517e21	−0.699804
$393$	4.99185e21	0.442512
$394$	1.75473e22	1.52227
$395$	1.12323e22	0.953663
$396$	−8.08954e19	−0.00672225
$397$	1.74947e22	1.42294	0.711470	−	0.702717i	$-0.248030\pi$
$397$	1.74947e22	1.42294	0.711470	+	0.702717i	$0.248030\pi$
$398$	1.48136e22	1.17938
$399$	−4.27047e21	−0.332817
$400$	−3.43527e22	−2.62090
$401$	−1.42397e21	−0.106359	−0.0531794	−	0.998585i	$-0.516936\pi$
$401$	−1.42397e21	−0.106359	−0.0531794	+	0.998585i	$0.516936\pi$
$402$	−1.35621e22	−0.991755
$403$	1.95454e22	1.39943
$404$	5.76582e21	0.404222
$405$	−2.44399e22	−1.67777
$406$	1.04723e21	0.0703998
$407$	1.07184e22	0.705633
$408$	−2.14067e22	−1.38019
$409$	−1.04876e22	−0.662260	−0.331130	−	0.943585i	$-0.607430\pi$
$409$	−1.04876e22	−0.662260	−0.331130	+	0.943585i	$0.607430\pi$
$410$	−2.44104e21	−0.150978
$411$	−7.65231e21	−0.463593
$412$	−2.76638e21	−0.164167
$413$	−9.49021e21	−0.551697
$414$	−1.30003e21	−0.0740371
$415$	5.97421e22	3.33328
$416$	−1.70614e22	−0.932656
$417$	1.14347e22	0.612444
$418$	9.14302e21	0.479834
$419$	−1.78407e22	−0.917471	−0.458735	−	0.888573i	$-0.651697\pi$
$419$	−1.78407e22	−0.917471	−0.458735	+	0.888573i	$0.651697\pi$
$420$	3.57080e21	0.179948
$421$	2.04270e22	1.00881	0.504403	−	0.863469i	$-0.331713\pi$
$421$	2.04270e22	1.00881	0.504403	+	0.863469i	$0.331713\pi$
$422$	−1.46234e22	−0.707768
$423$	9.45809e20	0.0448653
$424$	−8.42424e21	−0.391671
$425$	−8.53870e22	−3.89122
$426$	−1.35029e22	−0.603178
$427$	−8.72170e21	−0.381913
$428$	−1.23589e21	−0.0530527
$429$	−1.43469e22	−0.603771
$430$	−6.66086e21	−0.274820
$431$	−8.54980e21	−0.345859	−0.172930	−	0.984934i	$-0.555323\pi$
$431$	−8.54980e21	−0.345859	−0.172930	+	0.984934i	$0.555323\pi$
$432$	3.14051e22	1.24563
$433$	4.66469e22	1.81416	0.907081	−	0.420957i	$-0.138306\pi$
$433$	4.66469e22	1.81416	0.907081	+	0.420957i	$0.138306\pi$
$434$	9.07325e21	0.346019
$435$	−8.58511e21	−0.321061
$436$	1.32925e22	0.487495
$437$	3.51787e22	1.26528
$438$	−2.39144e22	−0.843585
$439$	−2.94887e21	−0.102025	−0.0510125	−	0.998698i	$-0.516245\pi$
$439$	−2.94887e21	−0.102025	−0.0510125	+	0.998698i	$0.516245\pi$
$440$	1.66413e22	0.564728
$441$	1.41229e21	0.0470105
$442$	−9.71848e22	−3.17329
$443$	2.38802e22	0.764903	0.382452	−	0.923975i	$-0.375080\pi$
$443$	2.38802e22	0.764903	0.382452	+	0.923975i	$0.375080\pi$
$444$	1.70040e22	0.534314
$445$	3.74102e22	1.15327
$446$	6.11256e22	1.84874
$447$	9.34070e21	0.277182
$448$	5.88467e21	0.171340
$449$	7.30017e21	0.208564	0.104282	−	0.994548i	$-0.466746\pi$
$449$	7.30017e21	0.208564	0.104282	+	0.994548i	$0.466746\pi$
$450$	4.65405e21	0.130474
$451$	1.09006e21	0.0299882
$452$	−2.26254e22	−0.610829
$453$	2.02030e22	0.535279
$454$	−1.33664e22	−0.347567
$455$	−3.52875e22	−0.900584
$456$	−3.15731e22	−0.790891
$457$	3.58472e22	0.881389	0.440695	−	0.897657i	$-0.354732\pi$
$457$	3.58472e22	0.881389	0.440695	+	0.897657i	$0.354732\pi$
$458$	3.94710e22	0.952625
$459$	7.80605e22	1.84937
$460$	−2.94151e22	−0.684114
$461$	3.24898e22	0.741805	0.370902	−	0.928672i	$-0.379048\pi$
$461$	3.24898e22	0.741805	0.370902	+	0.928672i	$0.379048\pi$
$462$	−6.66006e21	−0.149287
$463$	−2.49633e22	−0.549367	−0.274684	−	0.961535i	$-0.588573\pi$
$463$	−2.49633e22	−0.549367	−0.274684	+	0.961535i	$0.588573\pi$
$464$	1.04479e22	0.225749
$465$	−7.43817e22	−1.57803
$466$	−4.27570e22	−0.890690
$467$	−1.95425e22	−0.399748	−0.199874	−	0.979822i	$-0.564053\pi$
$467$	−1.95425e22	−0.399748	−0.199874	+	0.979822i	$0.564053\pi$
$468$	1.26824e21	0.0254748
$469$	1.48958e22	0.293828
$470$	8.93838e22	1.73152
$471$	−2.03507e22	−0.387170
$472$	−7.01645e22	−1.31102
$473$	2.97444e21	0.0545865
$474$	−3.32356e22	−0.599084
$475$	−1.25939e23	−2.22979
$476$	−1.08014e22	−0.187854
$477$	1.54009e21	0.0263111
$478$	8.34770e22	1.40097
$479$	−1.10335e23	−1.81913	−0.909563	−	0.415565i	$-0.863584\pi$
$479$	−1.10335e23	−1.81913	−0.909563	+	0.415565i	$0.863584\pi$
$480$	6.49287e22	1.05169
$481$	−1.68038e23	−2.67408
$482$	9.22764e21	0.144275
$483$	−2.56253e22	−0.393657
$484$	−1.74407e22	−0.263257
$485$	−7.96398e22	−1.18121
$486$	−8.29613e21	−0.120911
$487$	−8.98881e22	−1.28738	−0.643689	−	0.765287i	$-0.722597\pi$
$487$	−8.98881e22	−1.28738	−0.643689	+	0.765287i	$0.722597\pi$
$488$	−6.44827e22	−0.907558
$489$	1.16240e22	0.160779
$490$	1.33468e23	1.81431
$491$	9.86228e21	0.131760	0.0658801	−	0.997828i	$-0.479014\pi$
$491$	9.86228e21	0.131760	0.0658801	+	0.997828i	$0.479014\pi$
$492$	1.72930e21	0.0227074
$493$	2.59693e22	0.335167
$494$	−1.43340e23	−1.81839
$495$	−3.04230e21	−0.0379365
$496$	9.05210e22	1.10957
$497$	1.48308e22	0.178704
$498$	−1.76772e23	−2.09394
$499$	4.28557e22	0.499061	0.249531	−	0.968367i	$-0.419724\pi$
$499$	4.28557e22	0.499061	0.249531	+	0.968367i	$0.419724\pi$
$500$	5.64596e22	0.646387
$501$	1.47150e23	1.65630
$502$	−4.16418e22	−0.460837
$503$	−1.45517e22	−0.158338	−0.0791691	−	0.996861i	$-0.525227\pi$
$503$	−1.45517e22	−0.158338	−0.0791691	+	0.996861i	$0.525227\pi$
$504$	−1.28152e21	−0.0137109
$505$	2.16840e23	2.28120
$506$	5.48634e22	0.567549
$507$	1.29250e23	1.31481
$508$	2.19644e22	0.219725
$509$	−2.24819e22	−0.221173	−0.110587	−	0.993866i	$-0.535273\pi$
$509$	−2.24819e22	−0.221173	−0.110587	+	0.993866i	$0.535273\pi$
$510$	3.69846e23	3.57828
$511$	2.62661e22	0.249930
$512$	2.30471e22	0.215686
$513$	1.15133e23	1.05974
$514$	2.90072e22	0.262615
$515$	−1.04037e23	−0.926463
$516$	4.71873e21	0.0413336
$517$	−3.99148e22	−0.343925
$518$	−7.80058e22	−0.661186
$519$	−1.41527e23	−1.18009
$520$	−2.60893e23	−2.14010
$521$	−2.20797e22	−0.178186	−0.0890928	−	0.996023i	$-0.528397\pi$
$521$	−2.20797e22	−0.178186	−0.0890928	+	0.996023i	$0.528397\pi$
$522$	−1.41547e21	−0.0112383
$523$	1.14181e23	0.891924	0.445962	−	0.895052i	$-0.352862\pi$
$523$	1.14181e23	0.891924	0.445962	+	0.895052i	$0.352862\pi$
$524$	1.86223e22	0.143126
$525$	9.17376e22	0.693735
$526$	5.65877e22	0.421059
$527$	2.24999e23	1.64737
$528$	−6.64453e22	−0.478714
$529$	7.00427e22	0.496580
$530$	1.45546e23	1.01545
$531$	1.28272e22	0.0880703
$532$	−1.59312e22	−0.107646
$533$	−1.70894e22	−0.113644
$534$	−1.10694e23	−0.724473
$535$	−4.64791e22	−0.299399
$536$	1.10130e23	0.698239
$537$	1.56090e22	0.0974076
$538$	1.62205e23	0.996360
$539$	−5.96010e22	−0.360370
$540$	−9.62694e22	−0.572983
$541$	1.83494e23	1.07509	0.537545	−	0.843235i	$-0.319352\pi$
$541$	1.83494e23	1.07509	0.537545	+	0.843235i	$0.319352\pi$
$542$	−1.62756e22	−0.0938736
$543$	−7.19262e22	−0.408402
$544$	−1.96404e23	−1.09789
$545$	4.99900e23	2.75114
$546$	1.04413e23	0.565740
$547$	−1.49844e23	−0.799369	−0.399685	−	0.916653i	$-0.630880\pi$
$547$	−1.49844e23	−0.799369	−0.399685	+	0.916653i	$0.630880\pi$
$548$	−2.85472e22	−0.149944
$549$	1.17885e22	0.0609668
$550$	−1.96409e23	−1.00018
$551$	3.83025e22	0.192061
$552$	−1.89457e23	−0.935467
$553$	3.65040e22	0.177491
$554$	−2.09829e23	−1.00469
$555$	6.39484e23	3.01536
$556$	4.26574e22	0.198088
$557$	−1.78508e23	−0.816375	−0.408188	−	0.912898i	$-0.633839\pi$
$557$	−1.78508e23	−0.816375	−0.408188	+	0.912898i	$0.633839\pi$
$558$	−1.22637e22	−0.0552369
$559$	−4.66317e22	−0.206862
$560$	−1.63428e23	−0.714049
$561$	−1.65156e23	−0.710741
$562$	−2.41306e23	−1.02284
$563$	4.53016e23	1.89144	0.945719	−	0.324986i	$-0.105360\pi$
$563$	4.53016e23	1.89144	0.945719	+	0.324986i	$0.105360\pi$
$564$	−6.33219e22	−0.260424
$565$	−8.50892e23	−3.44717
$566$	3.83448e23	1.53027
$567$	−7.94274e22	−0.312258
$568$	1.09649e23	0.424664
$569$	−1.41654e23	−0.540473	−0.270236	−	0.962794i	$-0.587102\pi$
$569$	−1.41654e23	−0.540473	−0.270236	+	0.962794i	$0.587102\pi$
$570$	5.45492e23	2.05046
$571$	−3.72958e23	−1.38119	−0.690595	−	0.723242i	$-0.742651\pi$
$571$	−3.72958e23	−1.38119	−0.690595	+	0.723242i	$0.742651\pi$
$572$	−5.35218e22	−0.195283
$573$	1.95654e23	0.703353
$574$	−7.93316e21	−0.0280993
$575$	−7.55705e23	−2.63740
$576$	−7.95388e21	−0.0273519
$577$	−3.89826e23	−1.32092	−0.660459	−	0.750862i	$-0.729638\pi$
$577$	−3.89826e23	−1.32092	−0.660459	+	0.750862i	$0.729638\pi$
$578$	−7.75344e23	−2.58885
$579$	9.88059e22	0.325099
$580$	−3.20271e22	−0.103843
$581$	1.94156e23	0.620374
$582$	2.35648e23	0.742025
$583$	−6.49944e22	−0.201694
$584$	1.94195e23	0.593921
$585$	4.76956e22	0.143765
$586$	1.09328e23	0.324790
$587$	2.41264e23	0.706429	0.353214	−	0.935542i	$-0.385089\pi$
$587$	2.41264e23	0.706429	0.353214	+	0.935542i	$0.385089\pi$
$588$	−9.45527e22	−0.272877
$589$	3.31855e23	0.943991
$590$	1.21224e24	3.39896
$591$	−4.67501e23	−1.29208
$592$	−7.78239e23	−2.12021
$593$	−2.33031e23	−0.625820	−0.312910	−	0.949783i	$-0.601304\pi$
$593$	−2.33031e23	−0.625820	−0.312910	+	0.949783i	$0.601304\pi$
$594$	1.79557e23	0.475353
$595$	−4.06217e23	−1.06014
$596$	3.48459e22	0.0896516
$597$	−3.94671e23	−1.00104
$598$	−8.60120e23	−2.15079
$599$	−6.65932e23	−1.64173	−0.820865	−	0.571123i	$-0.806508\pi$
$599$	−6.65932e23	−1.64173	−0.820865	+	0.571123i	$0.806508\pi$
$600$	6.78250e23	1.64856
$601$	3.76828e23	0.903046	0.451523	−	0.892259i	$-0.350881\pi$
$601$	3.76828e23	0.903046	0.451523	+	0.892259i	$0.350881\pi$
$602$	−2.16471e22	−0.0511482
$603$	−2.01335e22	−0.0469054
$604$	7.53679e22	0.173130
$605$	−6.55908e23	−1.48567
$606$	−6.41612e23	−1.43303
$607$	−1.91087e23	−0.420850	−0.210425	−	0.977610i	$-0.567485\pi$
$607$	−1.91087e23	−0.420850	−0.210425	+	0.977610i	$0.567485\pi$
$608$	−2.89680e23	−0.629127
$609$	−2.79008e22	−0.0597543
$610$	1.11407e24	2.35293
$611$	6.25763e23	1.30335
$612$	1.45995e22	0.0299881
$613$	−1.84351e23	−0.373450	−0.186725	−	0.982412i	$-0.559787\pi$
$613$	−1.84351e23	−0.373450	−0.186725	+	0.982412i	$0.559787\pi$
$614$	5.69502e23	1.13780
$615$	6.50353e22	0.128148
$616$	5.40825e22	0.105104
$617$	1.48719e21	0.00285064	0.00142532	−	0.999999i	$-0.499546\pi$
$617$	1.48719e21	0.00285064	0.00142532	+	0.999999i	$0.499546\pi$
$618$	3.07838e23	0.581997
$619$	1.15122e23	0.214678	0.107339	−	0.994222i	$-0.465767\pi$
$619$	1.15122e23	0.214678	0.107339	+	0.994222i	$0.465767\pi$
$620$	−2.77484e23	−0.510397
$621$	6.90863e23	1.25347
$622$	4.14924e22	0.0742593
$623$	1.21579e23	0.214640
$624$	1.04170e24	1.81414
$625$	8.68432e23	1.49195
$626$	−3.71672e23	−0.629909
$627$	−2.43592e23	−0.407276
$628$	−7.59191e22	−0.125226
$629$	−1.93439e24	−3.14785
$630$	2.21410e22	0.0355470
$631$	4.16819e23	0.660234	0.330117	−	0.943940i	$-0.392912\pi$
$631$	4.16819e23	0.660234	0.330117	+	0.943940i	$0.392912\pi$
$632$	2.69887e23	0.421781
$633$	3.89601e23	0.600743
$634$	1.06061e23	0.161360
$635$	8.26035e23	1.24000
$636$	−1.03109e23	−0.152725
$637$	9.34393e23	1.36567
$638$	5.97352e22	0.0861498
$639$	−2.00457e22	−0.0285275
$640$	−1.52115e24	−2.13620
$641$	8.83664e23	1.22460	0.612299	−	0.790626i	$-0.290245\pi$
$641$	8.83664e23	1.22460	0.612299	+	0.790626i	$0.290245\pi$
$642$	1.37528e23	0.188080
$643$	−9.29400e23	−1.25432	−0.627161	−	0.778889i	$-0.715783\pi$
$643$	−9.29400e23	−1.25432	−0.627161	+	0.778889i	$0.715783\pi$
$644$	−9.55961e22	−0.127324
$645$	1.77461e23	0.233263
$646$	−1.65007e24	−2.14055
$647$	−7.86599e23	−1.00709	−0.503544	−	0.863970i	$-0.667971\pi$
$647$	−7.86599e23	−1.00709	−0.503544	+	0.863970i	$0.667971\pi$
$648$	−5.87235e23	−0.742035
$649$	−5.41331e23	−0.675123
$650$	3.07920e24	3.79031
$651$	−2.41733e23	−0.293696
$652$	4.33637e22	0.0520022
$653$	1.08686e24	1.28650	0.643251	−	0.765656i	$-0.277585\pi$
$653$	1.08686e24	1.28650	0.643251	+	0.765656i	$0.277585\pi$
$654$	−1.47917e24	−1.72825
$655$	7.00344e23	0.807719
$656$	−7.91466e22	−0.0901051
$657$	−3.55020e22	−0.0398977
$658$	2.90489e23	0.322262
$659$	−9.21823e23	−1.00954	−0.504768	−	0.863255i	$-0.668422\pi$
$659$	−9.21823e23	−1.00954	−0.504768	+	0.863255i	$0.668422\pi$
$660$	2.03682e23	0.220206
$661$	9.28675e23	0.991178	0.495589	−	0.868557i	$-0.334952\pi$
$661$	9.28675e23	0.991178	0.495589	+	0.868557i	$0.334952\pi$
$662$	2.15007e24	2.26548
$663$	2.58924e24	2.69344
$664$	1.43547e24	1.47423
$665$	−5.99136e23	−0.607493
$666$	1.05435e23	0.105549
$667$	2.29837e23	0.227170
$668$	5.48949e23	0.535713
$669$	−1.62853e24	−1.56918
$670$	−1.90272e24	−1.81025
$671$	−4.97495e23	−0.467355
$672$	2.11012e23	0.195735
$673$	−2.04195e24	−1.87033	−0.935163	−	0.354217i	$-0.884747\pi$
$673$	−2.04195e24	−1.87033	−0.935163	+	0.354217i	$0.884747\pi$
$674$	−6.15546e23	−0.556739
$675$	−2.47327e24	−2.20896
$676$	4.82172e23	0.425261
$677$	7.06634e23	0.615447	0.307724	−	0.951476i	$-0.400433\pi$
$677$	7.06634e23	0.615447	0.307724	+	0.951476i	$0.400433\pi$
$678$	2.51772e24	2.16548
$679$	−2.58822e23	−0.219840
$680$	−3.00331e24	−2.51926
$681$	3.56112e23	0.295010
$682$	5.17548e23	0.423431
$683$	2.25862e23	0.182502	0.0912511	−	0.995828i	$-0.470913\pi$
$683$	2.25862e23	0.182502	0.0912511	+	0.995828i	$0.470913\pi$
$684$	2.15330e22	0.0171841
$685$	−1.07360e24	−0.846198
$686$	9.20755e23	0.716786
$687$	−1.05160e24	−0.808573
$688$	−2.15967e23	−0.164016
$689$	1.01895e24	0.764345
$690$	3.27326e24	2.42529
$691$	2.06132e24	1.50863	0.754313	−	0.656515i	$-0.227970\pi$
$691$	2.06132e24	1.50863	0.754313	+	0.656515i	$0.227970\pi$
$692$	−5.27970e23	−0.381687
$693$	−9.88717e21	−0.00706057
$694$	−2.52664e24	−1.78233
$695$	1.60425e24	1.11790
$696$	−2.06280e23	−0.141997
$697$	−1.96727e23	−0.133778
$698$	2.73318e24	1.83610
$699$	1.13915e24	0.756004
$700$	3.42231e23	0.224381
$701$	2.43215e24	1.57539	0.787694	−	0.616067i	$-0.211275\pi$
$701$	2.43215e24	1.57539	0.787694	+	0.616067i	$0.211275\pi$
$702$	−2.81499e24	−1.80141
$703$	−2.85307e24	−1.80381
$704$	3.35667e23	0.209673
$705$	−2.38140e24	−1.46969
$706$	1.21530e24	0.741040
$707$	7.04709e23	0.424565
$708$	−8.58783e23	−0.511212
$709$	−1.96995e24	−1.15868	−0.579339	−	0.815087i	$-0.696689\pi$
$709$	−1.96995e24	−1.15868	−0.579339	+	0.815087i	$0.696689\pi$
$710$	−1.89442e24	−1.10098
$711$	−4.93398e22	−0.0283339
$712$	8.98880e23	0.510061
$713$	1.99132e24	1.11655
$714$	1.20196e24	0.665972
$715$	−2.01284e24	−1.10206
$716$	5.82299e22	0.0315054
$717$	−2.22403e24	−1.18912
$718$	−1.19265e24	−0.630167
$719$	9.41466e23	0.491597	0.245798	−	0.969321i	$-0.420950\pi$
$719$	9.41466e23	0.491597	0.245798	+	0.969321i	$0.420950\pi$
$720$	2.20894e23	0.113988
$721$	−3.38111e23	−0.172429
$722$	−1.58651e23	−0.0799608
$723$	−2.45847e23	−0.122458
$724$	−2.68323e23	−0.132093
$725$	−8.22810e23	−0.400338
$726$	1.94078e24	0.933286
$727$	−2.29094e24	−1.08886	−0.544428	−	0.838808i	$-0.683253\pi$
$727$	−2.29094e24	−1.08886	−0.544428	+	0.838808i	$0.683253\pi$
$728$	−8.47878e23	−0.398306
$729$	2.25505e24	1.04706
$730$	−3.35512e24	−1.53980
$731$	−5.36807e23	−0.243512
$732$	−7.89240e23	−0.353887
$733$	1.52425e24	0.675574	0.337787	−	0.941223i	$-0.390322\pi$
$733$	1.52425e24	0.675574	0.337787	+	0.941223i	$0.390322\pi$
$734$	−2.98077e23	−0.130591
$735$	−3.55592e24	−1.53996
$736$	−1.73825e24	−0.744132
$737$	8.49670e23	0.359564
$738$	1.07227e22	0.00448563
$739$	1.16569e24	0.482063	0.241032	−	0.970517i	$-0.422514\pi$
$739$	1.16569e24	0.482063	0.241032	+	0.970517i	$0.422514\pi$
$740$	2.38562e24	0.975285
$741$	3.81891e24	1.54342
$742$	4.73012e23	0.188990
$743$	−1.23599e24	−0.488215	−0.244108	−	0.969748i	$-0.578495\pi$
$743$	−1.23599e24	−0.488215	−0.244108	+	0.969748i	$0.578495\pi$
$744$	−1.78722e24	−0.697924
$745$	1.31048e24	0.505942
$746$	1.41666e24	0.540735
$747$	−2.62427e23	−0.0990336
$748$	−6.16122e23	−0.229881
$749$	−1.51053e23	−0.0557228
$750$	−6.28274e24	−2.29154
$751$	7.31775e23	0.263899	0.131950	−	0.991256i	$-0.457876\pi$
$751$	7.31775e23	0.263899	0.131950	+	0.991256i	$0.457876\pi$
$752$	2.89811e24	1.03339
$753$	1.10944e24	0.391152
$754$	−9.36497e23	−0.326475
$755$	2.83442e24	0.977047
$756$	−3.12866e23	−0.106641
$757$	1.09821e24	0.370143	0.185072	−	0.982725i	$-0.440748\pi$
$757$	1.09821e24	0.370143	0.185072	+	0.982725i	$0.440748\pi$
$758$	4.33549e24	1.44494
$759$	−1.46169e24	−0.481727
$760$	−4.42963e24	−1.44362
$761$	1.02391e24	0.329982	0.164991	−	0.986295i	$-0.447240\pi$
$761$	1.02391e24	0.329982	0.164991	+	0.986295i	$0.447240\pi$
$762$	−2.44417e24	−0.778958
$763$	1.62463e24	0.512030
$764$	7.29893e23	0.227492
$765$	5.49053e23	0.169236
$766$	3.93682e24	1.20006
$767$	8.48671e24	2.55846
$768$	2.80931e24	0.837585
$769$	−4.53247e24	−1.33647	−0.668237	−	0.743948i	$-0.732951\pi$
$769$	−4.53247e24	−1.33647	−0.668237	+	0.743948i	$0.732951\pi$
$770$	−9.34389e23	−0.272494
$771$	−7.72820e23	−0.222903
$772$	3.68599e23	0.105150
$773$	2.98975e24	0.843548	0.421774	−	0.906701i	$-0.361408\pi$
$773$	2.98975e24	0.843548	0.421774	+	0.906701i	$0.361408\pi$
$774$	2.92589e22	0.00816506
$775$	−7.12886e24	−1.96768
$776$	−1.91356e24	−0.522418
$777$	2.07826e24	0.561205
$778$	−2.44587e24	−0.653290
$779$	−2.90156e23	−0.0766589
$780$	−3.19322e24	−0.834497
$781$	8.45963e23	0.218684
$782$	−9.90137e24	−2.53185
$783$	7.52210e23	0.190267
$784$	4.32748e24	1.08280
$785$	−2.85515e24	−0.706703
$786$	−2.07226e24	−0.507403
$787$	−1.63043e24	−0.394926	−0.197463	−	0.980310i	$-0.563270\pi$
$787$	−1.63043e24	−0.394926	−0.197463	+	0.980310i	$0.563270\pi$
$788$	−1.74403e24	−0.417909
$789$	−1.50763e24	−0.357389
$790$	−4.66287e24	−1.09351
$791$	−2.76532e24	−0.641571
$792$	−7.30994e22	−0.0167784
$793$	7.79946e24	1.77110
$794$	−7.26254e24	−1.63160
$795$	−3.87770e24	−0.861894
$796$	−1.47233e24	−0.323777
$797$	4.24524e24	0.923647	0.461824	−	0.886972i	$-0.347195\pi$
$797$	4.24524e24	0.923647	0.461824	+	0.886972i	$0.347195\pi$
$798$	1.77279e24	0.381622
$799$	7.20355e24	1.53426
$800$	6.22287e24	1.31137
$801$	−1.64330e23	−0.0342642
$802$	5.91131e23	0.121955
$803$	1.49825e24	0.305845
$804$	1.34794e24	0.272266
$805$	−3.59516e24	−0.718544
$806$	−8.11384e24	−1.60464
$807$	−4.32154e24	−0.845695
$808$	5.21017e24	1.00892
$809$	4.95411e24	0.949299	0.474650	−	0.880175i	$-0.342575\pi$
$809$	4.95411e24	0.949299	0.474650	+	0.880175i	$0.342575\pi$
$810$	1.01457e25	1.92380
$811$	8.18309e24	1.53547	0.767733	−	0.640770i	$-0.221385\pi$
$811$	8.18309e24	1.53547	0.767733	+	0.640770i	$0.221385\pi$
$812$	−1.04085e23	−0.0193269
$813$	4.33621e23	0.0796785
$814$	−4.44953e24	−0.809108
$815$	1.63081e24	0.293471
$816$	1.19916e25	2.13555
$817$	−7.91745e23	−0.139540
$818$	4.35371e24	0.759375
$819$	1.55006e23	0.0267569
$820$	2.42617e23	0.0414479
$821$	−7.89641e24	−1.33510	−0.667549	−	0.744566i	$-0.732656\pi$
$821$	−7.89641e24	−1.33510	−0.667549	+	0.744566i	$0.732656\pi$
$822$	3.17669e24	0.531575
$823$	7.86056e23	0.130183	0.0650916	−	0.997879i	$-0.479266\pi$
$823$	7.86056e23	0.130183	0.0650916	+	0.997879i	$0.479266\pi$
$824$	−2.49978e24	−0.409751
$825$	5.23281e24	0.848939
$826$	3.93966e24	0.632599
$827$	−3.45632e24	−0.549310	−0.274655	−	0.961543i	$-0.588564\pi$
$827$	−3.45632e24	−0.549310	−0.274655	+	0.961543i	$0.588564\pi$
$828$	1.29210e23	0.0203254
$829$	5.08460e23	0.0791668	0.0395834	−	0.999216i	$-0.487397\pi$
$829$	5.08460e23	0.0791668	0.0395834	+	0.999216i	$0.487397\pi$
$830$	−2.48007e25	−3.82208
$831$	5.59035e24	0.852767
$832$	−5.26242e24	−0.794579
$833$	1.07564e25	1.60762
$834$	−4.74685e24	−0.702254
$835$	2.06448e25	3.02326
$836$	−9.08730e23	−0.131729
$837$	6.51717e24	0.935175
$838$	7.40618e24	1.05201
$839$	−1.16540e25	−1.63870	−0.819351	−	0.573292i	$-0.805666\pi$
$839$	−1.16540e25	−1.63870	−0.819351	+	0.573292i	$0.805666\pi$
$840$	3.22668e24	0.449140
$841$	2.50246e23	0.0344828
$842$	−8.47984e24	−1.15674
$843$	6.42897e24	0.868175
$844$	1.45342e24	0.194304
$845$	1.81334e25	2.39993
$846$	−3.92632e23	−0.0514444
$847$	−2.13164e24	−0.276506
$848$	4.71909e24	0.606029
$849$	−1.02160e25	−1.29887
$850$	3.54466e25	4.46184
$851$	−1.71200e25	−2.13355
$852$	1.34206e24	0.165590
$853$	−7.67822e24	−0.937980	−0.468990	−	0.883203i	$-0.655382\pi$
$853$	−7.67822e24	−0.937980	−0.468990	+	0.883203i	$0.655382\pi$
$854$	3.62063e24	0.437917
$855$	8.09808e23	0.0969773
$856$	−1.11679e24	−0.132417
$857$	−2.51938e24	−0.295772	−0.147886	−	0.989004i	$-0.547247\pi$
$857$	−2.51938e24	−0.295772	−0.147886	+	0.989004i	$0.547247\pi$
$858$	5.95582e24	0.692309
$859$	−4.18052e24	−0.481159	−0.240580	−	0.970629i	$-0.577338\pi$
$859$	−4.18052e24	−0.481159	−0.240580	+	0.970629i	$0.577338\pi$
$860$	6.62026e23	0.0754463
$861$	2.11358e23	0.0238502
$862$	3.54927e24	0.396577
$863$	−1.22538e25	−1.35574	−0.677872	−	0.735180i	$-0.737097\pi$
$863$	−1.22538e25	−1.35574	−0.677872	+	0.735180i	$0.737097\pi$
$864$	−5.68892e24	−0.623251
$865$	−1.98558e25	−2.15402
$866$	−1.93645e25	−2.08019
$867$	2.06570e25	2.19738
$868$	−9.01795e23	−0.0949927
$869$	2.08223e24	0.217200
$870$	3.56392e24	0.368141
$871$	−1.33207e25	−1.36261
$872$	1.20115e25	1.21676
$873$	3.49831e23	0.0350943
$874$	−1.46037e25	−1.45083
$875$	6.90059e24	0.678919
$876$	2.37686e24	0.231590
$877$	−2.16883e24	−0.209281	−0.104640	−	0.994510i	$-0.533369\pi$
$877$	−2.16883e24	−0.209281	−0.104640	+	0.994510i	$0.533369\pi$
$878$	1.22416e24	0.116986
$879$	−2.91277e24	−0.275677
$880$	−9.32210e24	−0.873798
$881$	−1.45095e25	−1.34697	−0.673484	−	0.739201i	$-0.735203\pi$
$881$	−1.45095e25	−1.34697	−0.673484	+	0.739201i	$0.735203\pi$
$882$	−5.86281e23	−0.0539042
$883$	−2.89183e24	−0.263334	−0.131667	−	0.991294i	$-0.542033\pi$
$883$	−2.89183e24	−0.263334	−0.131667	+	0.991294i	$0.542033\pi$
$884$	9.65925e24	0.871162
$885$	−3.22969e25	−2.88499
$886$	−9.91336e24	−0.877070
$887$	−1.20002e25	−1.05157	−0.525783	−	0.850618i	$-0.676228\pi$
$887$	−1.20002e25	−1.05157	−0.525783	+	0.850618i	$0.676228\pi$
$888$	1.53653e25	1.33362
$889$	2.68453e24	0.230783
$890$	−1.55300e25	−1.32238
$891$	−4.53062e24	−0.382118
$892$	−6.07530e24	−0.507536
$893$	1.06246e25	0.879178
$894$	−3.87759e24	−0.317829
$895$	2.18990e24	0.177799
$896$	−4.94359e24	−0.397580
$897$	2.29157e25	1.82556
$898$	−3.03051e24	−0.239148
$899$	2.16814e24	0.169485
$900$	−4.62569e23	−0.0358191
$901$	1.17298e25	0.899763
$902$	−4.52515e23	−0.0343857
$903$	5.76732e23	0.0434138
$904$	−2.04450e25	−1.52460
$905$	−1.00911e25	−0.745459
$906$	−8.38683e24	−0.613773
$907$	9.85491e24	0.714481	0.357241	−	0.934012i	$-0.383718\pi$
$907$	9.85491e24	0.714481	0.357241	+	0.934012i	$0.383718\pi$
$908$	1.32849e24	0.0954176
$909$	−9.52504e23	−0.0677756
$910$	1.46489e25	1.03265
$911$	2.51467e25	1.75620	0.878100	−	0.478476i	$-0.158811\pi$
$911$	2.51467e25	1.75620	0.878100	+	0.478476i	$0.158811\pi$
$912$	1.76866e25	1.22374
$913$	1.10749e25	0.759166
$914$	−1.48812e25	−1.01064
$915$	−2.96816e25	−1.99714
$916$	−3.92305e24	−0.261524
$917$	2.27605e24	0.150329
$918$	−3.24051e25	−2.12056
$919$	−1.74916e25	−1.13409	−0.567044	−	0.823687i	$-0.691913\pi$
$919$	−1.74916e25	−1.13409	−0.567044	+	0.823687i	$0.691913\pi$
$920$	−2.65803e25	−1.70751
$921$	−1.51729e25	−0.965743
$922$	−1.34875e25	−0.850585
$923$	−1.32626e25	−0.828730
$924$	6.61947e23	0.0409837
$925$	6.12892e25	3.75992
$926$	1.03630e25	0.629927
$927$	4.57001e23	0.0275257
$928$	−1.89260e24	−0.112954
$929$	−2.12686e25	−1.25778	−0.628892	−	0.777493i	$-0.716491\pi$
$929$	−2.12686e25	−1.25778	−0.628892	+	0.777493i	$0.716491\pi$
$930$	3.08780e25	1.80944
$931$	1.58648e25	0.921216
$932$	4.24963e24	0.244521
$933$	−1.10546e24	−0.0630301
$934$	8.11264e24	0.458368
$935$	−2.31710e25	−1.29732
$936$	1.14602e24	0.0635837
$937$	−2.58410e24	−0.142077	−0.0710383	−	0.997474i	$-0.522631\pi$
$937$	−2.58410e24	−0.142077	−0.0710383	+	0.997474i	$0.522631\pi$
$938$	−6.18366e24	−0.336916
$939$	9.90223e24	0.534657
$940$	−8.88390e24	−0.475354
$941$	−1.58858e25	−0.842357	−0.421178	−	0.906978i	$-0.638383\pi$
$941$	−1.58858e25	−0.842357	−0.421178	+	0.906978i	$0.638383\pi$
$942$	8.44817e24	0.443946
$943$	−1.74110e24	−0.0906723
$944$	3.93047e25	2.02854
$945$	−1.17662e25	−0.601820
$946$	−1.23478e24	−0.0625912
$947$	1.43317e25	0.719983	0.359991	−	0.932956i	$-0.382780\pi$
$947$	1.43317e25	0.719983	0.359991	+	0.932956i	$0.382780\pi$
$948$	3.30330e24	0.164467
$949$	−2.34887e25	−1.15904
$950$	5.22808e25	2.55677
$951$	−2.82572e24	−0.136960
$952$	−9.76045e24	−0.468874
$953$	−7.87499e24	−0.374939	−0.187469	−	0.982270i	$-0.560029\pi$
$953$	−7.87499e24	−0.374939	−0.187469	+	0.982270i	$0.560029\pi$
$954$	−6.39335e23	−0.0301695
$955$	2.74497e25	1.28383
$956$	−8.29682e24	−0.384609
$957$	−1.59149e24	−0.0731226
$958$	4.58034e25	2.08589
$959$	−3.48909e24	−0.157490
$960$	2.00266e25	0.895988
$961$	−3.76523e24	−0.166972
$962$	6.97574e25	3.06621
$963$	2.04167e23	0.00889532
$964$	−9.17140e23	−0.0396078
$965$	1.38622e25	0.593404
$966$	1.06378e25	0.451384
$967$	−4.85625e24	−0.204257	−0.102128	−	0.994771i	$-0.532565\pi$
$967$	−4.85625e24	−0.204257	−0.102128	+	0.994771i	$0.532565\pi$
$968$	−1.57600e25	−0.657075
$969$	4.39618e25	1.81687
$970$	3.30608e25	1.35442
$971$	2.82700e25	1.14806	0.574028	−	0.818836i	$-0.305380\pi$
$971$	2.82700e25	1.14806	0.574028	+	0.818836i	$0.305380\pi$
$972$	8.24557e23	0.0331938
$973$	5.21366e24	0.208058
$974$	3.73151e25	1.47616
$975$	−8.20373e25	−3.21716
$976$	3.61219e25	1.40426
$977$	−8.13154e23	−0.0313378	−0.0156689	−	0.999877i	$-0.504988\pi$
$977$	−8.13154e23	−0.0313378	−0.0156689	+	0.999877i	$0.504988\pi$
$978$	−4.82545e24	−0.184356
$979$	6.93501e24	0.262660
$980$	−1.32655e25	−0.498083
$981$	−2.19589e24	−0.0817381
$982$	−4.09411e24	−0.151082
$983$	−2.03883e25	−0.745892	−0.372946	−	0.927853i	$-0.621652\pi$
$983$	−2.03883e25	−0.745892	−0.372946	+	0.927853i	$0.621652\pi$
$984$	1.56265e24	0.0566765
$985$	−6.55892e25	−2.35844
$986$	−1.07806e25	−0.384317
$987$	−7.73931e24	−0.273531
$988$	1.42466e25	0.499203
$989$	−4.75093e24	−0.165048
$990$	1.26295e24	0.0434996
$991$	−3.50648e25	−1.19742	−0.598708	−	0.800967i	$-0.704319\pi$
$991$	−3.50648e25	−1.19742	−0.598708	+	0.800967i	$0.704319\pi$
$992$	−1.63976e25	−0.555175
$993$	−5.72831e25	−1.92291
$994$	−6.15668e24	−0.204910
$995$	−5.53713e25	−1.82721
$996$	1.75695e25	0.574850
$997$	2.11147e25	0.684977	0.342489	−	0.939522i	$-0.388730\pi$
$997$	2.11147e25	0.684977	0.342489	+	0.939522i	$0.388730\pi$
$998$	−1.77906e25	−0.572245
$999$	−5.60303e25	−1.78697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.5	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-415.129 q^{2} +11060.0 q^{3} +41259.9 q^{4} +1.55169e6 q^{5} -4.59133e6 q^{6} +5.04285e6 q^{7} +3.72836e7 q^{8} -6.81605e6 q^{9} +O(q^{10})\)	\(q-415.129 q^{2} +11060.0 q^{3} +41259.9 q^{4} +1.55169e6 q^{5} -4.59133e6 q^{6} +5.04285e6 q^{7} +3.72836e7 q^{8} -6.81605e6 q^{9} -6.44152e8 q^{10} +2.87649e8 q^{11} +4.56335e8 q^{12} -4.50962e9 q^{13} -2.09343e9 q^{14} +1.71618e10 q^{15} -2.08855e10 q^{16} -5.19130e10 q^{17} +2.82954e9 q^{18} -7.65674e10 q^{19} +6.40226e10 q^{20} +5.57740e10 q^{21} -1.19411e11 q^{22} -4.59448e11 q^{23} +4.12357e11 q^{24} +1.64481e12 q^{25} +1.87207e12 q^{26} -1.50368e12 q^{27} +2.08067e11 q^{28} -5.00246e11 q^{29} -7.12434e12 q^{30} -4.33415e12 q^{31} +3.78334e12 q^{32} +3.18141e12 q^{33} +2.15506e13 q^{34} +7.82495e12 q^{35} -2.81229e11 q^{36} +3.72622e13 q^{37} +3.17853e13 q^{38} -4.98765e13 q^{39} +5.78527e13 q^{40} +3.78955e12 q^{41} -2.31534e13 q^{42} +1.03405e13 q^{43} +1.18684e13 q^{44} -1.05764e13 q^{45} +1.90730e14 q^{46} -1.38762e14 q^{47} -2.30994e14 q^{48} -2.07200e14 q^{49} -6.82808e14 q^{50} -5.74159e14 q^{51} -1.86066e14 q^{52} -2.25950e14 q^{53} +6.24220e14 q^{54} +4.46343e14 q^{55} +1.88016e14 q^{56} -8.46837e14 q^{57} +2.07667e14 q^{58} -1.88191e15 q^{59} +7.08091e14 q^{60} -1.72952e15 q^{61} +1.79923e15 q^{62} -3.43723e13 q^{63} +1.16693e15 q^{64} -6.99754e15 q^{65} -1.32069e15 q^{66} +2.95384e15 q^{67} -2.14192e15 q^{68} -5.08151e15 q^{69} -3.24836e15 q^{70} +2.94095e15 q^{71} -2.54127e14 q^{72} +5.20859e15 q^{73} -1.54686e16 q^{74} +1.81916e16 q^{75} -3.15916e15 q^{76} +1.45057e15 q^{77} +2.07052e16 q^{78} +7.23877e15 q^{79} -3.24079e16 q^{80} -1.57505e16 q^{81} -1.57315e15 q^{82} +3.85013e16 q^{83} +2.30123e15 q^{84} -8.05530e16 q^{85} -4.29264e15 q^{86} -5.53274e15 q^{87} +1.07246e16 q^{88} +2.41093e16 q^{89} +4.39057e15 q^{90} -2.27413e16 q^{91} -1.89568e16 q^{92} -4.79358e16 q^{93} +5.76041e16 q^{94} -1.18809e17 q^{95} +4.18438e16 q^{96} -5.13245e16 q^{97} +8.60147e16 q^{98} -1.96063e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 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

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