LMFDB - Embedded newform 29.18.a.a.1.1

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			1.1
Root			$-615.069$ 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)

$f(q)$	$=$	$q-615.069 q^{2} -9589.87 q^{3} +247238. q^{4} +540648. q^{5} +5.89843e6 q^{6} +1.54300e7 q^{7} -7.14501e7 q^{8} -3.71746e7 q^{9} +O(q^{10})$	\(q-615.069 q^{2} -9589.87 q^{3} +247238. q^{4} +540648. q^{5} +5.89843e6 q^{6} +1.54300e7 q^{7} -7.14501e7 q^{8} -3.71746e7 q^{9} -3.32536e8 q^{10} +4.98361e7 q^{11} -2.37098e9 q^{12} -1.90169e9 q^{13} -9.49051e9 q^{14} -5.18475e9 q^{15} +1.15408e10 q^{16} -9.27691e9 q^{17} +2.28649e10 q^{18} +1.60351e10 q^{19} +1.33669e11 q^{20} -1.47972e11 q^{21} -3.06526e10 q^{22} +1.02479e11 q^{23} +6.85197e11 q^{24} -4.70639e11 q^{25} +1.16967e12 q^{26} +1.59494e12 q^{27} +3.81488e12 q^{28} -5.00246e11 q^{29} +3.18898e12 q^{30} +6.11884e12 q^{31} +2.26673e12 q^{32} -4.77921e11 q^{33} +5.70594e12 q^{34} +8.34220e12 q^{35} -9.19097e12 q^{36} -2.81110e13 q^{37} -9.86269e12 q^{38} +1.82369e13 q^{39} -3.86294e13 q^{40} +1.19930e13 q^{41} +9.10127e13 q^{42} +4.35110e12 q^{43} +1.23214e13 q^{44} -2.00984e13 q^{45} -6.30320e13 q^{46} +1.36005e14 q^{47} -1.10675e14 q^{48} +5.45393e12 q^{49} +2.89475e14 q^{50} +8.89644e13 q^{51} -4.70169e14 q^{52} -1.75625e14 q^{53} -9.80996e14 q^{54} +2.69438e13 q^{55} -1.10247e15 q^{56} -1.53774e14 q^{57} +3.07686e14 q^{58} -7.83735e14 q^{59} -1.28187e15 q^{60} -5.56644e13 q^{61} -3.76351e15 q^{62} -5.73603e14 q^{63} -2.90687e15 q^{64} -1.02814e15 q^{65} +2.93955e14 q^{66} -1.15479e15 q^{67} -2.29361e15 q^{68} -9.82765e14 q^{69} -5.13103e15 q^{70} +5.64491e15 q^{71} +2.65613e15 q^{72} +6.92692e15 q^{73} +1.72902e16 q^{74} +4.51336e15 q^{75} +3.96448e15 q^{76} +7.68970e14 q^{77} -1.12170e16 q^{78} -7.04213e15 q^{79} +6.23951e15 q^{80} -1.04945e16 q^{81} -7.37654e15 q^{82} +6.03501e15 q^{83} -3.65842e16 q^{84} -5.01555e15 q^{85} -2.67623e15 q^{86} +4.79730e15 q^{87} -3.56079e15 q^{88} +3.99565e16 q^{89} +1.23619e16 q^{90} -2.93430e16 q^{91} +2.53368e16 q^{92} -5.86789e16 q^{93} -8.36525e16 q^{94} +8.66935e15 q^{95} -2.17377e16 q^{96} -2.91975e16 q^{97} -3.35455e15 q^{98} -1.85264e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−615.069	−1.69890	−0.849452	−	0.527666i	$-0.823067\pi$
$2$	−615.069	−1.69890	−0.849452	+	0.527666i	$0.823067\pi$
$3$	−9589.87	−0.843882	−0.421941	−	0.906623i	$-0.638651\pi$
$3$	−9589.87	−0.843882	−0.421941	+	0.906623i	$0.638651\pi$
$4$	247238.	1.88628
$5$	540648.	0.618970	0.309485	−	0.950904i	$-0.399843\pi$
$5$	540648.	0.618970	0.309485	+	0.950904i	$0.399843\pi$
$6$	5.89843e6	1.43368
$7$	1.54300e7	1.01165	0.505827	−	0.862635i	$-0.331187\pi$
$7$	1.54300e7	1.01165	0.505827	+	0.862635i	$0.331187\pi$
$8$	−7.14501e7	−1.50570
$9$	−3.71746e7	−0.287862
$10$	−3.32536e8	−1.05157
$11$	4.98361e7	0.0700980	0.0350490	−	0.999386i	$-0.488841\pi$
$11$	4.98361e7	0.0700980	0.0350490	+	0.999386i	$0.488841\pi$
$12$	−2.37098e9	−1.59180
$13$	−1.90169e9	−0.646577	−0.323288	−	0.946300i	$-0.604788\pi$
$13$	−1.90169e9	−0.646577	−0.323288	+	0.946300i	$0.604788\pi$
$14$	−9.49051e9	−1.71870
$15$	−5.18475e9	−0.522338
$16$	1.15408e10	0.671762
$17$	−9.27691e9	−0.322543	−0.161272	−	0.986910i	$-0.551559\pi$
$17$	−9.27691e9	−0.322543	−0.161272	+	0.986910i	$0.551559\pi$
$18$	2.28649e10	0.489051
$19$	1.60351e10	0.216604	0.108302	−	0.994118i	$-0.465459\pi$
$19$	1.60351e10	0.216604	0.108302	+	0.994118i	$0.465459\pi$
$20$	1.33669e11	1.16755
$21$	−1.47972e11	−0.853717
$22$	−3.06526e10	−0.119090
$23$	1.02479e11	0.272867	0.136433	−	0.990649i	$-0.456436\pi$
$23$	1.02479e11	0.272867	0.136433	+	0.990649i	$0.456436\pi$
$24$	6.85197e11	1.27063
$25$	−4.70639e11	−0.616876
$26$	1.16967e12	1.09847
$27$	1.59494e12	1.08680
$28$	3.81488e12	1.90826
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	3.18898e12	0.887403
$31$	6.11884e12	1.28853	0.644265	−	0.764802i	$-0.277163\pi$
$31$	6.11884e12	1.28853	0.644265	+	0.764802i	$0.277163\pi$
$32$	2.26673e12	0.364439
$33$	−4.77921e11	−0.0591545
$34$	5.70594e12	0.547970
$35$	8.34220e12	0.626184
$36$	−9.19097e12	−0.542988
$37$	−2.81110e13	−1.31572	−0.657858	−	0.753142i	$-0.728537\pi$
$37$	−2.81110e13	−1.31572	−0.657858	+	0.753142i	$0.728537\pi$
$38$	−9.86269e12	−0.367989
$39$	1.82369e13	0.545635
$40$	−3.86294e13	−0.931983
$41$	1.19930e13	0.234566	0.117283	−	0.993099i	$-0.462581\pi$
$41$	1.19930e13	0.234566	0.117283	+	0.993099i	$0.462581\pi$
$42$	9.10127e13	1.45038
$43$	4.35110e12	0.0567697	0.0283849	−	0.999597i	$-0.490964\pi$
$43$	4.35110e12	0.0567697	0.0283849	+	0.999597i	$0.490964\pi$
$44$	1.23214e13	0.132224
$45$	−2.00984e13	−0.178178
$46$	−6.30320e13	−0.463574
$47$	1.36005e14	0.833150	0.416575	−	0.909101i	$-0.363230\pi$
$47$	1.36005e14	0.833150	0.416575	+	0.909101i	$0.363230\pi$
$48$	−1.10675e14	−0.566888
$49$	5.45393e12	0.0234446
$50$	2.89475e14	1.04801
$51$	8.89644e13	0.272188
$52$	−4.70169e14	−1.21962
$53$	−1.75625e14	−0.387473	−0.193736	−	0.981054i	$-0.562061\pi$
$53$	−1.75625e14	−0.387473	−0.193736	+	0.981054i	$0.562061\pi$
$54$	−9.80996e14	−1.84638
$55$	2.69438e13	0.0433886
$56$	−1.10247e15	−1.52325
$57$	−1.53774e14	−0.182788
$58$	3.07686e14	0.315479
$59$	−7.83735e14	−0.694907	−0.347454	−	0.937697i	$-0.612954\pi$
$59$	−7.83735e14	−0.694907	−0.347454	+	0.937697i	$0.612954\pi$
$60$	−1.28187e15	−0.985274
$61$	−5.56644e13	−0.0371770	−0.0185885	−	0.999827i	$-0.505917\pi$
$61$	−5.56644e13	−0.0371770	−0.0185885	+	0.999827i	$0.505917\pi$
$62$	−3.76351e15	−2.18909
$63$	−5.73603e14	−0.291217
$64$	−2.90687e15	−1.29091
$65$	−1.02814e15	−0.400212
$66$	2.93955e14	0.100498
$67$	−1.15479e15	−0.347431	−0.173715	−	0.984796i	$-0.555577\pi$
$67$	−1.15479e15	−0.347431	−0.173715	+	0.984796i	$0.555577\pi$
$68$	−2.29361e15	−0.608405
$69$	−9.82765e14	−0.230267
$70$	−5.13103e15	−1.06383
$71$	5.64491e15	1.03744	0.518718	−	0.854946i	$-0.326410\pi$
$71$	5.64491e15	1.03744	0.518718	+	0.854946i	$0.326410\pi$
$72$	2.65613e15	0.433434
$73$	6.92692e15	1.00530	0.502650	−	0.864490i	$-0.332358\pi$
$73$	6.92692e15	1.00530	0.502650	+	0.864490i	$0.332358\pi$
$74$	1.72902e16	2.23528
$75$	4.51336e15	0.520571
$76$	3.96448e15	0.408574
$77$	7.68970e14	0.0709150
$78$	−1.12170e16	−0.926981
$79$	−7.04213e15	−0.522244	−0.261122	−	0.965306i	$-0.584093\pi$
$79$	−7.04213e15	−0.522244	−0.261122	+	0.965306i	$0.584093\pi$
$80$	6.23951e15	0.415801
$81$	−1.04945e16	−0.629273
$82$	−7.37654e15	−0.398506
$83$	6.03501e15	0.294113	0.147057	−	0.989128i	$-0.453020\pi$
$83$	6.03501e15	0.294113	0.147057	+	0.989128i	$0.453020\pi$
$84$	−3.65842e16	−1.61035
$85$	−5.01555e15	−0.199645
$86$	−2.67623e15	−0.0964464
$87$	4.79730e15	0.156705
$88$	−3.56079e15	−0.105547
$89$	3.99565e16	1.07590	0.537951	−	0.842976i	$-0.319199\pi$
$89$	3.99565e16	1.07590	0.537951	+	0.842976i	$0.319199\pi$
$90$	1.23619e16	0.302708
$91$	−2.93430e16	−0.654112
$92$	2.53368e16	0.514702
$93$	−5.86789e16	−1.08737
$94$	−8.36525e16	−1.41544
$95$	8.66935e15	0.134071
$96$	−2.17377e16	−0.307544
$97$	−2.91975e16	−0.378256	−0.189128	−	0.981952i	$-0.560566\pi$
$97$	−2.91975e16	−0.378256	−0.189128	+	0.981952i	$0.560566\pi$
$98$	−3.35455e15	−0.0398302
$99$	−1.85264e15	−0.0201786
$100$	−1.16360e17	−1.16360
$101$	6.84313e16	0.628815	0.314408	−	0.949288i	$-0.398194\pi$
$101$	6.84313e16	0.628815	0.314408	+	0.949288i	$0.398194\pi$
$102$	−5.47192e16	−0.462422
$103$	9.83207e16	0.764766	0.382383	−	0.924004i	$-0.375103\pi$
$103$	9.83207e16	0.764766	0.382383	+	0.924004i	$0.375103\pi$
$104$	1.35876e17	0.973550
$105$	−8.00006e16	−0.528426
$106$	1.08021e17	0.658279
$107$	−2.75342e16	−0.154921	−0.0774606	−	0.996995i	$-0.524681\pi$
$107$	−2.75342e16	−0.154921	−0.0774606	+	0.996995i	$0.524681\pi$
$108$	3.94329e17	2.05001
$109$	−1.51396e17	−0.727760	−0.363880	−	0.931446i	$-0.618548\pi$
$109$	−1.51396e17	−0.727760	−0.363880	+	0.931446i	$0.618548\pi$
$110$	−1.65723e16	−0.0737131
$111$	2.69581e17	1.11031
$112$	1.78074e17	0.679591
$113$	1.64692e17	0.582780	0.291390	−	0.956604i	$-0.405882\pi$
$113$	1.64692e17	0.582780	0.291390	+	0.956604i	$0.405882\pi$
$114$	9.45819e16	0.310539
$115$	5.54054e16	0.168896
$116$	−1.23680e17	−0.350273
$117$	7.06944e16	0.186125
$118$	4.82051e17	1.18058
$119$	−1.43143e17	−0.326302
$120$	3.70451e17	0.786484
$121$	−5.02963e17	−0.995086
$122$	3.42375e16	0.0631602
$123$	−1.15012e17	−0.197947
$124$	1.51281e18	2.43053
$125$	−6.66932e17	−1.00080
$126$	3.52806e17	0.494750
$127$	−6.45307e17	−0.846125	−0.423062	−	0.906101i	$-0.639045\pi$
$127$	−6.45307e17	−0.846125	−0.423062	+	0.906101i	$0.639045\pi$
$128$	1.49082e18	1.82869
$129$	−4.17264e16	−0.0479070
$130$	6.32379e17	0.679922
$131$	−9.51591e17	−0.958615	−0.479307	−	0.877647i	$-0.659112\pi$
$131$	−9.51591e17	−0.958615	−0.479307	+	0.877647i	$0.659112\pi$
$132$	−1.18160e17	−0.111582
$133$	2.47421e17	0.219128
$134$	7.10278e17	0.590252
$135$	8.62300e17	0.672700
$136$	6.62837e17	0.485653
$137$	−2.44967e18	−1.68649	−0.843244	−	0.537532i	$-0.819357\pi$
$137$	−2.44967e18	−1.68649	−0.843244	+	0.537532i	$0.819357\pi$
$138$	6.04468e17	0.391202
$139$	−1.74796e18	−1.06391	−0.531955	−	0.846772i	$-0.678543\pi$
$139$	−1.74796e18	−1.06391	−0.531955	+	0.846772i	$0.678543\pi$
$140$	2.06251e18	1.18116
$141$	−1.30427e18	−0.703081
$142$	−3.47201e18	−1.76250
$143$	−9.47725e16	−0.0453238
$144$	−4.29024e17	−0.193375
$145$	−2.70457e17	−0.114940
$146$	−4.26053e18	−1.70791
$147$	−5.23025e16	−0.0197845
$148$	−6.95012e18	−2.48181
$149$	−5.10022e18	−1.71991	−0.859955	−	0.510371i	$-0.829508\pi$
$149$	−5.10022e18	−1.71991	−0.859955	+	0.510371i	$0.829508\pi$
$150$	−2.77603e18	−0.884400
$151$	−5.35179e18	−1.61137	−0.805685	−	0.592345i	$-0.798202\pi$
$151$	−5.35179e18	−1.61137	−0.805685	+	0.592345i	$0.798202\pi$
$152$	−1.14571e18	−0.326140
$153$	3.44865e17	0.0928480
$154$	−4.72970e17	−0.120478
$155$	3.30814e18	0.797562
$156$	4.50886e18	1.02922
$157$	4.18341e18	0.904449	0.452224	−	0.891904i	$-0.350631\pi$
$157$	4.18341e18	0.904449	0.452224	+	0.891904i	$0.350631\pi$
$158$	4.33139e18	0.887243
$159$	1.68422e18	0.326981
$160$	1.22550e18	0.225577
$161$	1.58126e18	0.276047
$162$	6.45484e18	1.06907
$163$	−1.66157e18	−0.261171	−0.130585	−	0.991437i	$-0.541686\pi$
$163$	−1.66157e18	−0.261171	−0.130585	+	0.991437i	$0.541686\pi$
$164$	2.96513e18	0.442457
$165$	−2.58387e17	−0.0366149
$166$	−3.71195e18	−0.499670
$167$	5.91344e18	0.756397	0.378199	−	0.925724i	$-0.376544\pi$
$167$	5.91344e18	0.756397	0.378199	+	0.925724i	$0.376544\pi$
$168$	1.05726e19	1.28544
$169$	−5.03401e18	−0.581938
$170$	3.08491e18	0.339177
$171$	−5.96098e17	−0.0623520
$172$	1.07576e18	0.107083
$173$	8.89120e18	0.842497	0.421249	−	0.906945i	$-0.361592\pi$
$173$	8.89120e18	0.842497	0.421249	+	0.906945i	$0.361592\pi$
$174$	−2.95067e18	−0.266227
$175$	−7.26195e18	−0.624065
$176$	5.75147e17	0.0470892
$177$	7.51591e18	0.586420
$178$	−2.45760e19	−1.82785
$179$	−2.33730e18	−0.165754	−0.0828771	−	0.996560i	$-0.526411\pi$
$179$	−2.33730e18	−0.165754	−0.0828771	+	0.996560i	$0.526411\pi$
$180$	−4.96908e18	−0.336093
$181$	−2.63456e19	−1.69997	−0.849984	−	0.526808i	$-0.823389\pi$
$181$	−2.63456e19	−1.69997	−0.849984	+	0.526808i	$0.823389\pi$
$182$	1.80480e19	1.11127
$183$	5.33815e17	0.0313730
$184$	−7.32217e18	−0.410855
$185$	−1.51982e19	−0.814390
$186$	3.60916e19	1.84734
$187$	−4.62325e17	−0.0226096
$188$	3.36256e19	1.57155
$189$	2.46098e19	1.09947
$190$	−5.33225e18	−0.227774
$191$	−2.69587e19	−1.10132	−0.550662	−	0.834728i	$-0.685625\pi$
$191$	−2.69587e19	−1.10132	−0.550662	+	0.834728i	$0.685625\pi$
$192$	2.78765e19	1.08938
$193$	−3.84897e19	−1.43916	−0.719578	−	0.694412i	$-0.755665\pi$
$193$	−3.84897e19	−1.43916	−0.719578	+	0.694412i	$0.755665\pi$
$194$	1.79585e19	0.642621
$195$	9.85976e18	0.337732
$196$	1.34842e18	0.0442230
$197$	2.17611e19	0.683468	0.341734	−	0.939797i	$-0.388986\pi$
$197$	2.17611e19	0.683468	0.341734	+	0.939797i	$0.388986\pi$
$198$	1.13950e18	0.0342815
$199$	3.14148e19	0.905488	0.452744	−	0.891641i	$-0.350445\pi$
$199$	3.14148e19	0.905488	0.452744	+	0.891641i	$0.350445\pi$
$200$	3.36272e19	0.928829
$201$	1.10743e19	0.293191
$202$	−4.20900e19	−1.06830
$203$	−7.71879e18	−0.187860
$204$	2.19954e19	0.513423
$205$	6.48401e18	0.145190
$206$	−6.04740e19	−1.29926
$207$	−3.80963e18	−0.0785480
$208$	−2.19469e19	−0.434346
$209$	7.99126e17	0.0151835
$210$	4.92059e19	0.897745
$211$	2.85039e19	0.499463	0.249731	−	0.968315i	$-0.419658\pi$
$211$	2.85039e19	0.499463	0.249731	+	0.968315i	$0.419658\pi$
$212$	−4.34211e19	−0.730881
$213$	−5.41340e19	−0.875474
$214$	1.69355e19	0.263196
$215$	2.35241e18	0.0351388
$216$	−1.13958e20	−1.63640
$217$	9.44136e19	1.30355
$218$	9.31188e19	1.23639
$219$	−6.64283e19	−0.848355
$220$	6.66153e18	0.0818429
$221$	1.76418e19	0.208549
$222$	−1.65811e20	−1.88631
$223$	−7.73971e18	−0.0847487	−0.0423744	−	0.999102i	$-0.513492\pi$
$223$	−7.73971e18	−0.0847487	−0.0423744	+	0.999102i	$0.513492\pi$
$224$	3.49756e19	0.368687
$225$	1.74958e19	0.177575
$226$	−1.01297e20	−0.990087
$227$	5.60701e18	0.0527851	0.0263926	−	0.999652i	$-0.491598\pi$
$227$	5.60701e18	0.0527851	0.0263926	+	0.999652i	$0.491598\pi$
$228$	−3.80189e19	−0.344789
$229$	1.97456e20	1.72531	0.862656	−	0.505790i	$-0.168799\pi$
$229$	1.97456e20	1.72531	0.862656	+	0.505790i	$0.168799\pi$
$230$	−3.40781e19	−0.286939
$231$	−7.37432e18	−0.0598439
$232$	3.57427e19	0.279601
$233$	2.34268e20	1.76680	0.883401	−	0.468617i	$-0.155248\pi$
$233$	2.34268e20	1.76680	0.883401	+	0.468617i	$0.155248\pi$
$234$	−4.34819e19	−0.316209
$235$	7.35309e19	0.515695
$236$	−1.93769e20	−1.31079
$237$	6.75331e19	0.440713
$238$	8.80426e19	0.554356
$239$	4.75665e18	0.0289014	0.0144507	−	0.999896i	$-0.495400\pi$
$239$	4.75665e18	0.0289014	0.0144507	+	0.999896i	$0.495400\pi$
$240$	−5.98360e19	−0.350887
$241$	−1.50174e20	−0.850062	−0.425031	−	0.905179i	$-0.639737\pi$
$241$	−1.50174e20	−0.850062	−0.425031	+	0.905179i	$0.639737\pi$
$242$	3.09357e20	1.69056
$243$	−1.05330e20	−0.555772
$244$	−1.37624e19	−0.0701261
$245$	2.94866e18	0.0145115
$246$	7.07400e19	0.336292
$247$	−3.04937e19	−0.140051
$248$	−4.37192e20	−1.94014
$249$	−5.78750e19	−0.248197
$250$	4.10209e20	1.70026
$251$	−3.50093e20	−1.40267	−0.701337	−	0.712830i	$-0.747413\pi$
$251$	−3.50093e20	−1.40267	−0.701337	+	0.712830i	$0.747413\pi$
$252$	−1.41817e20	−0.549316
$253$	5.10717e18	0.0191274
$254$	3.96908e20	1.43749
$255$	4.80985e19	0.168477
$256$	−5.35949e20	−1.81586
$257$	−3.27368e20	−1.07301	−0.536505	−	0.843897i	$-0.680256\pi$
$257$	−3.27368e20	−1.07301	−0.536505	+	0.843897i	$0.680256\pi$
$258$	2.56646e19	0.0813894
$259$	−4.33753e20	−1.33105
$260$	−2.54196e20	−0.754910
$261$	1.85965e19	0.0534547
$262$	5.85294e20	1.62859
$263$	−1.46387e20	−0.394348	−0.197174	−	0.980368i	$-0.563176\pi$
$263$	−1.46387e20	−0.394348	−0.197174	+	0.980368i	$0.563176\pi$
$264$	3.41475e19	0.0890689
$265$	−9.49513e19	−0.239834
$266$	−1.52181e20	−0.372278
$267$	−3.83178e20	−0.907935
$268$	−2.85509e20	−0.655351
$269$	1.38578e20	0.308176	0.154088	−	0.988057i	$-0.450756\pi$
$269$	1.38578e20	0.308176	0.154088	+	0.988057i	$0.450756\pi$
$270$	−5.30374e20	−1.14285
$271$	−6.73002e20	−1.40533	−0.702663	−	0.711522i	$-0.748006\pi$
$271$	−6.73002e20	−1.40533	−0.702663	+	0.711522i	$0.748006\pi$
$272$	−1.07063e20	−0.216672
$273$	2.81395e20	0.551994
$274$	1.50672e21	2.86518
$275$	−2.34548e19	−0.0432418
$276$	−2.42977e20	−0.434348
$277$	−1.05504e21	−1.82891	−0.914455	−	0.404687i	$-0.867381\pi$
$277$	−1.05504e21	−1.82891	−0.914455	+	0.404687i	$0.867381\pi$
$278$	1.07511e21	1.80748
$279$	−2.27465e20	−0.370920
$280$	−5.96051e20	−0.942845
$281$	2.50089e20	0.383787	0.191894	−	0.981416i	$-0.438537\pi$
$281$	2.50089e20	0.383787	0.191894	+	0.981416i	$0.438537\pi$
$282$	8.02217e20	1.19447
$283$	−1.04682e20	−0.151248	−0.0756238	−	0.997136i	$-0.524095\pi$
$283$	−1.04682e20	−0.151248	−0.0756238	+	0.997136i	$0.524095\pi$
$284$	1.39564e21	1.95689
$285$	−8.31379e19	−0.113140
$286$	5.82916e19	0.0770008
$287$	1.85052e20	0.237300
$288$	−8.42648e19	−0.104908
$289$	−7.41179e20	−0.895966
$290$	1.66350e20	0.195272
$291$	2.80000e20	0.319204
$292$	1.71260e21	1.89627
$293$	1.65112e21	1.77584	0.887918	−	0.460002i	$-0.152151\pi$
$293$	1.65112e21	1.77584	0.887918	+	0.460002i	$0.152151\pi$
$294$	3.21696e19	0.0336120
$295$	−4.23725e20	−0.430127
$296$	2.00854e21	1.98107
$297$	7.94854e19	0.0761829
$298$	3.13699e21	2.92196
$299$	−1.94884e20	−0.176429
$300$	1.11588e21	0.981940
$301$	6.71374e19	0.0574314
$302$	3.29172e21	2.73756
$303$	−6.56247e20	−0.530646
$304$	1.85058e20	0.145506
$305$	−3.00949e19	−0.0230115
$306$	−2.12116e20	−0.157740
$307$	−1.18238e21	−0.855230	−0.427615	−	0.903961i	$-0.640646\pi$
$307$	−1.18238e21	−0.855230	−0.427615	+	0.903961i	$0.640646\pi$
$308$	1.90119e20	0.133765
$309$	−9.42883e20	−0.645373
$310$	−2.03474e21	−1.35498
$311$	1.19237e21	0.772585	0.386292	−	0.922376i	$-0.373756\pi$
$311$	1.19237e21	0.772585	0.386292	+	0.922376i	$0.373756\pi$
$312$	−1.30303e21	−0.821562
$313$	−2.41544e21	−1.48207	−0.741037	−	0.671464i	$-0.765666\pi$
$313$	−2.41544e21	−1.48207	−0.741037	+	0.671464i	$0.765666\pi$
$314$	−2.57309e21	−1.53657
$315$	−3.10118e20	−0.180255
$316$	−1.74108e21	−0.985097
$317$	−2.37445e21	−1.30786	−0.653928	−	0.756556i	$-0.726880\pi$
$317$	−2.37445e21	−1.30786	−0.653928	+	0.756556i	$0.726880\pi$
$318$	−1.03591e21	−0.555510
$319$	−2.49303e19	−0.0130169
$320$	−1.57159e21	−0.799035
$321$	2.64050e20	0.130735
$322$	−9.72582e20	−0.468977
$323$	−1.48756e20	−0.0698640
$324$	−2.59464e21	−1.18698
$325$	8.95007e20	0.398857
$326$	1.02198e21	0.443704
$327$	1.45186e21	0.614144
$328$	−8.56903e20	−0.353186
$329$	2.09856e21	0.842860
$330$	1.58926e20	0.0622052
$331$	−4.40280e20	−0.167954	−0.0839771	−	0.996468i	$-0.526762\pi$
$331$	−4.40280e20	−0.167954	−0.0839771	+	0.996468i	$0.526762\pi$
$332$	1.49208e21	0.554778
$333$	1.04502e21	0.378745
$334$	−3.63717e21	−1.28505
$335$	−6.24337e20	−0.215049
$336$	−1.70771e21	−0.573495
$337$	4.31562e20	0.141315	0.0706576	−	0.997501i	$-0.477490\pi$
$337$	4.31562e20	0.141315	0.0706576	+	0.997501i	$0.477490\pi$
$338$	3.09626e21	0.988658
$339$	−1.57937e21	−0.491798
$340$	−1.24003e21	−0.376585
$341$	3.04939e20	0.0903235
$342$	3.66641e20	0.105930
$343$	−3.50533e21	−0.987937
$344$	−3.10886e20	−0.0854781
$345$	−5.31330e20	−0.142529
$346$	−5.46870e21	−1.43132
$347$	9.08787e20	0.232093	0.116046	−	0.993244i	$-0.462978\pi$
$347$	9.08787e20	0.232093	0.116046	+	0.993244i	$0.462978\pi$
$348$	1.18607e21	0.295589
$349$	−6.50327e21	−1.58167	−0.790834	−	0.612031i	$-0.790353\pi$
$349$	−6.50327e21	−1.58167	−0.790834	+	0.612031i	$0.790353\pi$
$350$	4.46660e21	1.06023
$351$	−3.03307e21	−0.702703
$352$	1.12965e20	0.0255465
$353$	1.64783e21	0.363770	0.181885	−	0.983320i	$-0.441780\pi$
$353$	1.64783e21	0.363770	0.181885	+	0.983320i	$0.441780\pi$
$354$	−4.62281e21	−0.996272
$355$	3.05191e21	0.642142
$356$	9.87877e21	2.02945
$357$	1.37272e21	0.275361
$358$	1.43760e21	0.281600
$359$	−7.87421e21	−1.50627	−0.753137	−	0.657864i	$-0.771460\pi$
$359$	−7.87421e21	−1.50627	−0.753137	+	0.657864i	$0.771460\pi$
$360$	1.43603e21	0.268283
$361$	−5.22326e21	−0.953083
$362$	1.62044e22	2.88808
$363$	4.82335e21	0.839736
$364$	−7.25470e21	−1.23384
$365$	3.74503e21	0.622251
$366$	−3.28333e20	−0.0532997
$367$	1.23118e20	0.0195281	0.00976403	−	0.999952i	$-0.496892\pi$
$367$	1.23118e20	0.0195281	0.00976403	+	0.999952i	$0.496892\pi$
$368$	1.18269e21	0.183301
$369$	−4.45836e20	−0.0675229
$370$	9.34794e21	1.38357
$371$	−2.70989e21	−0.391988
$372$	−1.45077e22	−2.05108
$373$	3.86144e21	0.533611	0.266805	−	0.963750i	$-0.414032\pi$
$373$	3.86144e21	0.533611	0.266805	+	0.963750i	$0.414032\pi$
$374$	2.84362e20	0.0384116
$375$	6.39579e21	0.844556
$376$	−9.71758e21	−1.25447
$377$	9.51311e20	0.120066
$378$	−1.51368e22	−1.86790
$379$	3.26550e21	0.394018	0.197009	−	0.980402i	$-0.436877\pi$
$379$	3.26550e21	0.394018	0.197009	+	0.980402i	$0.436877\pi$
$380$	2.14339e21	0.252895
$381$	6.18841e21	0.714030
$382$	1.65815e22	1.87105
$383$	1.64152e22	1.81158	0.905788	−	0.423731i	$-0.139280\pi$
$383$	1.64152e22	1.81158	0.905788	+	0.423731i	$0.139280\pi$
$384$	−1.42968e22	−1.54320
$385$	4.15742e20	0.0438943
$386$	2.36739e22	2.44499
$387$	−1.61750e20	−0.0163419
$388$	−7.21873e21	−0.713495
$389$	1.20478e22	1.16502	0.582512	−	0.812822i	$-0.302070\pi$
$389$	1.20478e22	1.16502	0.582512	+	0.812822i	$0.302070\pi$
$390$	−6.06443e21	−0.573774
$391$	−9.50693e20	−0.0880112
$392$	−3.89684e20	−0.0353005
$393$	9.12563e21	0.808958
$394$	−1.33846e22	−1.16115
$395$	−3.80731e21	−0.323254
$396$	−4.58042e20	−0.0380624
$397$	9.84960e21	0.801123	0.400562	−	0.916270i	$-0.368815\pi$
$397$	9.84960e21	0.801123	0.400562	+	0.916270i	$0.368815\pi$
$398$	−1.93222e22	−1.53834
$399$	−2.37274e21	−0.184918
$400$	−5.43154e21	−0.414394
$401$	−5.18497e21	−0.387275	−0.193637	−	0.981073i	$-0.562029\pi$
$401$	−5.18497e21	−0.387275	−0.193637	+	0.981073i	$0.562029\pi$
$402$	−6.81147e21	−0.498103
$403$	−1.16361e22	−0.833134
$404$	1.69188e22	1.18612
$405$	−5.67383e21	−0.389501
$406$	4.74759e21	0.319155
$407$	−1.40094e21	−0.0922292
$408$	−6.35652e21	−0.409834
$409$	1.30469e22	0.823872	0.411936	−	0.911213i	$-0.364853\pi$
$409$	1.30469e22	0.823872	0.411936	+	0.911213i	$0.364853\pi$
$410$	−3.98811e21	−0.246663
$411$	2.34920e22	1.42320
$412$	2.43086e22	1.44256
$413$	−1.20930e22	−0.703006
$414$	2.34319e21	0.133446
$415$	3.26282e21	0.182047
$416$	−4.31061e21	−0.235638
$417$	1.67627e22	0.897815
$418$	−4.91518e20	−0.0257953
$419$	−3.12850e22	−1.60885	−0.804427	−	0.594052i	$-0.797527\pi$
$419$	−3.12850e22	−1.60885	−0.804427	+	0.594052i	$0.797527\pi$
$420$	−1.97792e22	−0.996757
$421$	−1.20558e22	−0.595383	−0.297692	−	0.954662i	$-0.596217\pi$
$421$	−1.20558e22	−0.595383	−0.297692	+	0.954662i	$0.596217\pi$
$422$	−1.75319e22	−0.848539
$423$	−5.05593e21	−0.239833
$424$	1.25484e22	0.583417
$425$	4.36608e21	0.198969
$426$	3.32961e22	1.48735
$427$	−8.58901e20	−0.0376103
$428$	−6.80751e21	−0.292224
$429$	9.08856e20	0.0382479
$430$	−1.44690e21	−0.0596974
$431$	−1.56992e22	−0.635070	−0.317535	−	0.948247i	$-0.602855\pi$
$431$	−1.56992e22	−0.635070	−0.317535	+	0.948247i	$0.602855\pi$
$432$	1.84068e22	0.730074
$433$	9.59245e21	0.373063	0.186532	−	0.982449i	$-0.440275\pi$
$433$	9.59245e21	0.373063	0.186532	+	0.982449i	$0.440275\pi$
$434$	−5.80709e22	−2.21460
$435$	2.59365e21	0.0969958
$436$	−3.74308e22	−1.37276
$437$	1.64327e21	0.0591039
$438$	4.08580e22	1.44127
$439$	4.08302e22	1.41264	0.706322	−	0.707890i	$-0.250353\pi$
$439$	4.08302e22	1.41264	0.706322	+	0.707890i	$0.250353\pi$
$440$	−1.92514e21	−0.0653302
$441$	−2.02748e20	−0.00674882
$442$	−1.08509e22	−0.354305
$443$	−1.01541e22	−0.325243	−0.162622	−	0.986689i	$-0.551995\pi$
$443$	−1.01541e22	−0.325243	−0.162622	+	0.986689i	$0.551995\pi$
$444$	6.66507e22	2.09435
$445$	2.16024e22	0.665952
$446$	4.76046e21	0.143980
$447$	4.89104e22	1.45140
$448$	−4.48530e22	−1.30595
$449$	−1.12789e22	−0.322235	−0.161117	−	0.986935i	$-0.551510\pi$
$449$	−1.12789e22	−0.322235	−0.161117	+	0.986935i	$0.551510\pi$
$450$	−1.07611e22	−0.301683
$451$	5.97685e20	0.0164427
$452$	4.07180e22	1.09928
$453$	5.13230e22	1.35981
$454$	−3.44870e21	−0.0896769
$455$	−1.58642e22	−0.404876
$456$	1.09872e22	0.275224
$457$	6.97161e22	1.71414	0.857068	−	0.515203i	$-0.172284\pi$
$457$	6.97161e22	1.71414	0.857068	+	0.515203i	$0.172284\pi$
$458$	−1.21449e23	−2.93114
$459$	−1.47961e22	−0.350541
$460$	1.36983e22	0.318585
$461$	−3.79642e22	−0.866796	−0.433398	−	0.901203i	$-0.642686\pi$
$461$	−3.79642e22	−0.866796	−0.433398	+	0.901203i	$0.642686\pi$
$462$	4.53572e21	0.101669
$463$	−2.87562e22	−0.632839	−0.316419	−	0.948619i	$-0.602481\pi$
$463$	−2.87562e22	−0.632839	−0.316419	+	0.948619i	$0.602481\pi$
$464$	−5.77324e21	−0.124743
$465$	−3.17246e22	−0.673049
$466$	−1.44091e23	−3.00163
$467$	8.30427e22	1.69867	0.849333	−	0.527857i	$-0.177004\pi$
$467$	8.30427e22	1.69867	0.849333	+	0.527857i	$0.177004\pi$
$468$	1.74783e22	0.351083
$469$	−1.78184e22	−0.351480
$470$	−4.52266e22	−0.876117
$471$	−4.01184e22	−0.763248
$472$	5.59979e22	1.04632
$473$	2.16842e20	0.00397945
$474$	−4.15375e22	−0.748729
$475$	−7.54674e21	−0.133618
$476$	−3.53903e22	−0.615496
$477$	6.52878e21	0.111539
$478$	−2.92567e21	−0.0491007
$479$	−1.03904e23	−1.71309	−0.856547	−	0.516070i	$-0.827395\pi$
$479$	−1.03904e23	−1.71309	−0.856547	+	0.516070i	$0.827395\pi$
$480$	−1.17524e22	−0.190361
$481$	5.34584e22	0.850712
$482$	9.23676e22	1.44417
$483$	−1.51640e22	−0.232951
$484$	−1.24352e23	−1.87701
$485$	−1.57856e22	−0.234129
$486$	6.47849e22	0.944204
$487$	−6.63237e22	−0.949889	−0.474944	−	0.880016i	$-0.657532\pi$
$487$	−6.63237e22	−0.949889	−0.474944	+	0.880016i	$0.657532\pi$
$488$	3.97723e21	0.0559773
$489$	1.59343e22	0.220397
$490$	−1.81363e21	−0.0246537
$491$	−3.74498e22	−0.500331	−0.250165	−	0.968203i	$-0.580485\pi$
$491$	−3.74498e22	−0.500331	−0.250165	+	0.968203i	$0.580485\pi$
$492$	−2.84352e22	−0.373382
$493$	4.64074e21	0.0598947
$494$	1.87557e22	0.237933
$495$	−1.00162e21	−0.0124899
$496$	7.06162e22	0.865586
$497$	8.71009e22	1.04953
$498$	3.55971e22	0.421663
$499$	−1.10674e23	−1.28881	−0.644407	−	0.764683i	$-0.722896\pi$
$499$	−1.10674e23	−1.28881	−0.644407	+	0.764683i	$0.722896\pi$
$500$	−1.64891e23	−1.88778
$501$	−5.67091e22	−0.638311
$502$	2.15331e23	2.38301
$503$	6.69273e22	0.728241	0.364121	−	0.931352i	$-0.381370\pi$
$503$	6.69273e22	0.728241	0.364121	+	0.931352i	$0.381370\pi$
$504$	4.09840e22	0.438485
$505$	3.69973e22	0.389218
$506$	−3.14127e21	−0.0324956
$507$	4.82755e22	0.491088
$508$	−1.59544e23	−1.59603
$509$	−8.62929e22	−0.848934	−0.424467	−	0.905443i	$-0.639539\pi$
$509$	−8.62929e22	−0.848934	−0.424467	+	0.905443i	$0.639539\pi$
$510$	−2.95839e22	−0.286226
$511$	1.06882e23	1.01702
$512$	1.34241e23	1.25629
$513$	2.55750e22	0.235406
$514$	2.01354e23	1.82294
$515$	5.31569e22	0.473368
$516$	−1.03164e22	−0.0903658
$517$	6.77796e21	0.0584022
$518$	2.66788e23	2.26133
$519$	−8.52654e22	−0.710969
$520$	7.34609e22	0.602599
$521$	8.70557e22	0.702549	0.351275	−	0.936272i	$-0.385748\pi$
$521$	8.70557e22	0.702549	0.351275	+	0.936272i	$0.385748\pi$
$522$	−1.14381e22	−0.0908144
$523$	−1.15210e23	−0.899962	−0.449981	−	0.893038i	$-0.648569\pi$
$523$	−1.15210e23	−0.899962	−0.449981	+	0.893038i	$0.648569\pi$
$524$	−2.35269e23	−1.80821
$525$	6.96411e22	0.526637
$526$	9.00384e22	0.669960
$527$	−5.67640e22	−0.415607
$528$	−5.51559e21	−0.0397378
$529$	−1.30548e23	−0.925544
$530$	5.84016e22	0.407455
$531$	2.91350e22	0.200038
$532$	6.11719e22	0.413336
$533$	−2.28070e22	−0.151665
$534$	2.35681e23	1.54249
$535$	−1.48863e22	−0.0958916
$536$	8.25101e22	0.523126
$537$	2.24144e22	0.139877
$538$	−8.52349e22	−0.523562
$539$	2.71803e20	0.00164342
$540$	2.13193e23	1.26890
$541$	−2.79565e23	−1.63797	−0.818984	−	0.573816i	$-0.805462\pi$
$541$	−2.79565e23	−1.63797	−0.818984	+	0.573816i	$0.805462\pi$
$542$	4.13943e23	2.38752
$543$	2.52651e23	1.43457
$544$	−2.10283e22	−0.117547
$545$	−8.18518e22	−0.450462
$546$	−1.73078e23	−0.937785
$547$	1.39135e23	0.742241	0.371120	−	0.928585i	$-0.378974\pi$
$547$	1.39135e23	0.742241	0.371120	+	0.928585i	$0.378974\pi$
$548$	−6.05652e23	−3.18118
$549$	2.06930e21	0.0107019
$550$	1.44263e22	0.0734636
$551$	−8.02150e21	−0.0402223
$552$	7.02187e22	0.346713
$553$	−1.08660e23	−0.528331
$554$	6.48925e23	3.10714
$555$	1.45749e23	0.687249
$556$	−4.32162e23	−2.00683
$557$	−2.90994e23	−1.33081	−0.665404	−	0.746484i	$-0.731741\pi$
$557$	−2.90994e23	−1.33081	−0.665404	+	0.746484i	$0.731741\pi$
$558$	1.39907e23	0.630157
$559$	−8.27442e21	−0.0367060
$560$	9.62755e22	0.420647
$561$	4.43363e21	0.0190799
$562$	−1.53822e23	−0.652018
$563$	1.04139e23	0.434804	0.217402	−	0.976082i	$-0.430242\pi$
$563$	1.04139e23	0.434804	0.217402	+	0.976082i	$0.430242\pi$
$564$	−3.22465e23	−1.32620
$565$	8.90402e22	0.360724
$566$	6.43869e22	0.256955
$567$	−1.61930e23	−0.636607
$568$	−4.03330e23	−1.56207
$569$	−2.79385e22	−0.106598	−0.0532990	−	0.998579i	$-0.516974\pi$
$569$	−2.79385e22	−0.106598	−0.0532990	+	0.998579i	$0.516974\pi$
$570$	5.11356e22	0.192215
$571$	4.38844e23	1.62519	0.812593	−	0.582832i	$-0.198055\pi$
$571$	4.38844e23	1.62519	0.812593	+	0.582832i	$0.198055\pi$
$572$	−2.34314e22	−0.0854931
$573$	2.58530e23	0.929389
$574$	−1.13820e23	−0.403150
$575$	−4.82308e22	−0.168325
$576$	1.08062e23	0.371604
$577$	−1.37109e23	−0.464592	−0.232296	−	0.972645i	$-0.574624\pi$
$577$	−1.37109e23	−0.464592	−0.232296	+	0.972645i	$0.574624\pi$
$578$	4.55876e23	1.52216
$579$	3.69112e23	1.21448
$580$	−6.68674e22	−0.216808
$581$	9.31201e22	0.297541
$582$	−1.72219e23	−0.542296
$583$	−8.75245e21	−0.0271611
$584$	−4.94929e23	−1.51368
$585$	3.82208e22	0.115206
$586$	−1.01555e24	−3.01698
$587$	−5.63934e22	−0.165122	−0.0825609	−	0.996586i	$-0.526310\pi$
$587$	−5.63934e22	−0.165122	−0.0825609	+	0.996586i	$0.526310\pi$
$588$	−1.29312e22	−0.0373190
$589$	9.81162e22	0.279101
$590$	2.60620e23	0.730745
$591$	−2.08686e23	−0.576766
$592$	−3.24424e23	−0.883848
$593$	−2.30654e23	−0.619437	−0.309718	−	0.950828i	$-0.600235\pi$
$593$	−2.30654e23	−0.619437	−0.309718	+	0.950828i	$0.600235\pi$
$594$	−4.88890e22	−0.129427
$595$	−7.73898e22	−0.201971
$596$	−1.26097e24	−3.24422
$597$	−3.01263e23	−0.764125
$598$	1.19867e23	0.299736
$599$	−1.97437e23	−0.486745	−0.243372	−	0.969933i	$-0.578254\pi$
$599$	−1.97437e23	−0.486745	−0.243372	+	0.969933i	$0.578254\pi$
$600$	−3.22480e23	−0.783822
$601$	−1.04940e23	−0.251483	−0.125742	−	0.992063i	$-0.540131\pi$
$601$	−1.04940e23	−0.251483	−0.125742	+	0.992063i	$0.540131\pi$
$602$	−4.12941e22	−0.0975704
$603$	4.29290e22	0.100012
$604$	−1.32317e24	−3.03949
$605$	−2.71926e23	−0.615929
$606$	4.03637e23	0.901517
$607$	−6.71255e22	−0.147837	−0.0739186	−	0.997264i	$-0.523550\pi$
$607$	−6.71255e22	−0.147837	−0.0739186	+	0.997264i	$0.523550\pi$
$608$	3.63472e22	0.0789389
$609$	7.40222e22	0.158531
$610$	1.85104e22	0.0390943
$611$	−2.58639e23	−0.538696
$612$	8.52639e22	0.175137
$613$	2.49422e22	0.0505266	0.0252633	−	0.999681i	$-0.491958\pi$
$613$	2.49422e22	0.0505266	0.0252633	+	0.999681i	$0.491958\pi$
$614$	7.27248e23	1.45295
$615$	−6.21808e22	−0.122523
$616$	−5.49430e22	−0.106777
$617$	1.63542e23	0.313477	0.156738	−	0.987640i	$-0.449902\pi$
$617$	1.63542e23	0.313477	0.156738	+	0.987640i	$0.449902\pi$
$618$	5.79938e23	1.09643
$619$	3.29303e23	0.614080	0.307040	−	0.951697i	$-0.400661\pi$
$619$	3.29303e23	0.614080	0.307040	+	0.951697i	$0.400661\pi$
$620$	8.17898e23	1.50442
$621$	1.63448e23	0.296553
$622$	−7.33387e23	−1.31255
$623$	6.16529e23	1.08844
$624$	2.10468e23	0.366537
$625$	−1.50689e21	−0.00258882
$626$	1.48566e24	2.51790
$627$	−7.66351e21	−0.0128131
$628$	1.03430e24	1.70604
$629$	2.60784e23	0.424375
$630$	1.90744e23	0.306236
$631$	5.67786e23	0.899363	0.449681	−	0.893189i	$-0.351538\pi$
$631$	5.67786e23	0.899363	0.449681	+	0.893189i	$0.351538\pi$
$632$	5.03161e23	0.786342
$633$	−2.73348e23	−0.421488
$634$	1.46045e24	2.22192
$635$	−3.48884e23	−0.523726
$636$	4.16403e23	0.616777
$637$	−1.03717e22	−0.0151587
$638$	1.53339e22	0.0221144
$639$	−2.09847e23	−0.298639
$640$	8.06010e23	1.13191
$641$	9.37622e23	1.29937	0.649687	−	0.760201i	$-0.274900\pi$
$641$	9.37622e23	1.29937	0.649687	+	0.760201i	$0.274900\pi$
$642$	−1.62409e23	−0.222107
$643$	9.78928e23	1.32117	0.660583	−	0.750753i	$-0.270309\pi$
$643$	9.78928e23	1.32117	0.660583	+	0.750753i	$0.270309\pi$
$644$	3.90947e23	0.520700
$645$	−2.25593e22	−0.0296530
$646$	9.14953e22	0.118692
$647$	−7.73122e23	−0.989833	−0.494916	−	0.868941i	$-0.664801\pi$
$647$	−7.73122e23	−0.989833	−0.494916	+	0.868941i	$0.664801\pi$
$648$	7.49833e23	0.947495
$649$	−3.90583e22	−0.0487117
$650$	−5.50491e23	−0.677621
$651$	−9.05414e23	−1.10004
$652$	−4.10804e23	−0.492640
$653$	−1.32297e24	−1.56598	−0.782992	−	0.622031i	$-0.786308\pi$
$653$	−1.32297e24	−1.56598	−0.782992	+	0.622031i	$0.786308\pi$
$654$	−8.92997e23	−1.04337
$655$	−5.14476e23	−0.593354
$656$	1.38409e23	0.157573
$657$	−2.57505e23	−0.289388
$658$	−1.29076e24	−1.43194
$659$	−1.15928e23	−0.126959	−0.0634793	−	0.997983i	$-0.520220\pi$
$659$	−1.15928e23	−0.126959	−0.0634793	+	0.997983i	$0.520220\pi$
$660$	−6.38832e22	−0.0690658
$661$	−3.96246e23	−0.422914	−0.211457	−	0.977387i	$-0.567821\pi$
$661$	−3.96246e23	−0.422914	−0.211457	+	0.977387i	$0.567821\pi$
$662$	2.70803e23	0.285338
$663$	−1.69182e23	−0.175991
$664$	−4.31202e23	−0.442846
$665$	1.33768e23	0.135634
$666$	−6.42758e23	−0.643452
$667$	−5.12650e22	−0.0506700
$668$	1.46203e24	1.42677
$669$	7.42228e22	0.0715180
$670$	3.84010e23	0.365348
$671$	−2.77410e21	−0.00260603
$672$	−3.35412e23	−0.311128
$673$	8.72088e23	0.798789	0.399395	−	0.916779i	$-0.369220\pi$
$673$	8.72088e23	0.798789	0.399395	+	0.916779i	$0.369220\pi$
$674$	−2.65440e23	−0.240081
$675$	−7.50639e23	−0.670423
$676$	−1.24460e24	−1.09770
$677$	−1.89607e24	−1.65139	−0.825695	−	0.564117i	$-0.809217\pi$
$677$	−1.89607e24	−1.65139	−0.825695	+	0.564117i	$0.809217\pi$
$678$	9.71422e23	0.835517
$679$	−4.50517e23	−0.382664
$680$	3.58362e23	0.300605
$681$	−5.37705e22	−0.0445444
$682$	−1.87559e23	−0.153451
$683$	2.18867e24	1.76850	0.884248	−	0.467017i	$-0.154671\pi$
$683$	2.18867e24	1.76850	0.884248	+	0.467017i	$0.154671\pi$
$684$	−1.47378e23	−0.117613
$685$	−1.32441e24	−1.04389
$686$	2.15602e24	1.67841
$687$	−1.89357e24	−1.45596
$688$	5.02151e22	0.0381358
$689$	3.33983e23	0.250531
$690$	3.26805e23	0.242143
$691$	−1.50485e24	−1.10136	−0.550679	−	0.834717i	$-0.685631\pi$
$691$	−1.50485e24	−1.10136	−0.550679	+	0.834717i	$0.685631\pi$
$692$	2.19824e24	1.58918
$693$	−2.85861e22	−0.0204138
$694$	−5.58967e23	−0.394303
$695$	−9.45031e23	−0.658529
$696$	−3.42767e23	−0.235951
$697$	−1.11258e23	−0.0756578
$698$	3.99996e24	2.68710
$699$	−2.24660e24	−1.49097
$700$	−1.79543e24	−1.17716
$701$	7.97446e23	0.516533	0.258267	−	0.966074i	$-0.416849\pi$
$701$	7.97446e23	0.516533	0.258267	+	0.966074i	$0.416849\pi$
$702$	1.86555e24	1.19382
$703$	−4.50763e23	−0.284989
$704$	−1.44867e23	−0.0904902
$705$	−7.05152e23	−0.435186
$706$	−1.01353e24	−0.618010
$707$	1.05589e24	0.636144
$708$	1.85822e24	1.10615
$709$	1.33820e24	0.787099	0.393550	−	0.919303i	$-0.371247\pi$
$709$	1.33820e24	0.787099	0.393550	+	0.919303i	$0.371247\pi$
$710$	−1.87714e24	−1.09094
$711$	2.61788e23	0.150334
$712$	−2.85490e24	−1.61998
$713$	6.27056e23	0.351597
$714$	−8.44317e23	−0.467811
$715$	−5.12386e22	−0.0280541
$716$	−5.77870e23	−0.312658
$717$	−4.56156e22	−0.0243894
$718$	4.84318e24	2.55902
$719$	1.72077e24	0.898517	0.449259	−	0.893402i	$-0.351688\pi$
$719$	1.72077e24	0.898517	0.449259	+	0.893402i	$0.351688\pi$
$720$	−2.31951e23	−0.119693
$721$	1.51709e24	0.773679
$722$	3.21267e24	1.61920
$723$	1.44015e24	0.717353
$724$	−6.51364e24	−3.20661
$725$	2.35435e23	0.114551
$726$	−2.96670e24	−1.42663
$727$	2.28924e24	1.08805	0.544026	−	0.839068i	$-0.316899\pi$
$727$	2.28924e24	1.08805	0.544026	+	0.839068i	$0.316899\pi$
$728$	2.09656e24	0.984896
$729$	2.36536e24	1.09828
$730$	−2.30345e24	−1.05715
$731$	−4.03648e22	−0.0183107
$732$	1.31979e23	0.0591782
$733$	−1.16697e24	−0.517222	−0.258611	−	0.965981i	$-0.583265\pi$
$733$	−1.16697e24	−0.517222	−0.258611	+	0.965981i	$0.583265\pi$
$734$	−7.57259e22	−0.0331763
$735$	−2.82773e22	−0.0122460
$736$	2.32293e23	0.0994433
$737$	−5.75503e22	−0.0243542
$738$	2.74220e23	0.114715
$739$	−3.54493e24	−1.46599	−0.732994	−	0.680235i	$-0.761878\pi$
$739$	−3.54493e24	−1.46599	−0.732994	+	0.680235i	$0.761878\pi$
$740$	−3.75757e24	−1.53616
$741$	2.92431e23	0.118187
$742$	1.66677e24	0.665951
$743$	−2.25058e24	−0.888975	−0.444487	−	0.895785i	$-0.646614\pi$
$743$	−2.25058e24	−0.888975	−0.444487	+	0.895785i	$0.646614\pi$
$744$	4.19261e24	1.63725
$745$	−2.75742e24	−1.06457
$746$	−2.37505e24	−0.906553
$747$	−2.24349e23	−0.0846641
$748$	−1.14304e23	−0.0426480
$749$	−4.24853e23	−0.156727
$750$	−3.93385e24	−1.43482
$751$	5.30377e24	1.91269	0.956346	−	0.292237i	$-0.0943995\pi$
$751$	5.30377e24	1.91269	0.956346	+	0.292237i	$0.0943995\pi$
$752$	1.56960e24	0.559679
$753$	3.35735e24	1.18369
$754$	−5.85122e23	−0.203981
$755$	−2.89344e24	−0.997390
$756$	6.08449e24	2.07391
$757$	−3.27234e23	−0.110292	−0.0551460	−	0.998478i	$-0.517562\pi$
$757$	−3.27234e23	−0.110292	−0.0551460	+	0.998478i	$0.517562\pi$
$758$	−2.00851e24	−0.669399
$759$	−4.89771e22	−0.0161413
$760$	−6.19426e23	−0.201871
$761$	1.63197e24	0.525947	0.262974	−	0.964803i	$-0.415297\pi$
$761$	1.63197e24	0.525947	0.262974	+	0.964803i	$0.415297\pi$
$762$	−3.80630e24	−1.21307
$763$	−2.33603e24	−0.736242
$764$	−6.66522e24	−2.07740
$765$	1.86451e23	0.0574702
$766$	−1.00965e25	−3.07769
$767$	1.49042e24	0.449311
$768$	5.13968e24	1.53238
$769$	1.07464e24	0.316877	0.158438	−	0.987369i	$-0.449354\pi$
$769$	1.07464e24	0.316877	0.158438	+	0.987369i	$0.449354\pi$
$770$	−2.55710e23	−0.0745722
$771$	3.13941e24	0.905495
$772$	−9.51613e24	−2.71465
$773$	2.34697e24	0.662189	0.331094	−	0.943598i	$-0.392582\pi$
$773$	2.34697e24	0.662189	0.331094	+	0.943598i	$0.392582\pi$
$774$	9.94876e22	0.0277633
$775$	−2.87976e24	−0.794863
$776$	2.08616e24	0.569540
$777$	4.15963e24	1.12325
$778$	−7.41021e24	−1.97926
$779$	1.92309e23	0.0508080
$780$	2.43771e24	0.637055
$781$	2.81320e23	0.0727222
$782$	5.84742e23	0.149523
$783$	−7.97861e23	−0.201815
$784$	6.29427e22	0.0157492
$785$	2.26176e24	0.559827
$786$	−5.61289e24	−1.37434
$787$	−7.91665e23	−0.191759	−0.0958796	−	0.995393i	$-0.530566\pi$
$787$	−7.91665e23	−0.191759	−0.0958796	+	0.995393i	$0.530566\pi$
$788$	5.38017e24	1.28921
$789$	1.40384e24	0.332784
$790$	2.34176e24	0.549177
$791$	2.54119e24	0.589572
$792$	1.32371e23	0.0303829
$793$	1.05856e23	0.0240378
$794$	−6.05819e24	−1.36103
$795$	9.10570e23	0.202392
$796$	7.76692e24	1.70800
$797$	6.43432e24	1.39993	0.699966	−	0.714176i	$-0.253198\pi$
$797$	6.43432e24	1.39993	0.699966	+	0.714176i	$0.253198\pi$
$798$	1.45940e24	0.314159
$799$	−1.26171e24	−0.268727
$800$	−1.06681e24	−0.224814
$801$	−1.48537e24	−0.309712
$802$	3.18912e24	0.657943
$803$	3.45210e23	0.0704696
$804$	2.73799e24	0.553039
$805$	8.54904e23	0.170865
$806$	7.15701e24	1.41542
$807$	−1.32894e24	−0.260065
$808$	−4.88943e24	−0.946807
$809$	7.33098e24	1.40475	0.702376	−	0.711806i	$-0.252122\pi$
$809$	7.33098e24	1.40475	0.702376	+	0.711806i	$0.252122\pi$
$810$	3.48980e24	0.661726
$811$	4.36945e24	0.819879	0.409939	−	0.912113i	$-0.365550\pi$
$811$	4.36945e24	0.819879	0.409939	+	0.912113i	$0.365550\pi$
$812$	−1.90838e24	−0.354355
$813$	6.45400e24	1.18593
$814$	8.61677e23	0.156689
$815$	−8.98326e23	−0.161657
$816$	1.02672e24	0.182846
$817$	6.97702e22	0.0122965
$818$	−8.02475e24	−1.39968
$819$	1.09081e24	0.188294
$820$	1.60309e24	0.273868
$821$	−5.43345e23	−0.0918669	−0.0459334	−	0.998945i	$-0.514626\pi$
$821$	−5.43345e23	−0.0918669	−0.0459334	+	0.998945i	$0.514626\pi$
$822$	−1.44492e25	−2.41788
$823$	−4.80808e24	−0.796294	−0.398147	−	0.917322i	$-0.630347\pi$
$823$	−4.80808e24	−0.796294	−0.398147	+	0.917322i	$0.630347\pi$
$824$	−7.02503e24	−1.15151
$825$	2.24928e23	0.0364910
$826$	7.43804e24	1.19434
$827$	−3.91173e24	−0.621687	−0.310843	−	0.950461i	$-0.600611\pi$
$827$	−3.91173e24	−0.621687	−0.310843	+	0.950461i	$0.600611\pi$
$828$	−9.41886e23	−0.148163
$829$	−3.93248e24	−0.612285	−0.306142	−	0.951986i	$-0.599038\pi$
$829$	−3.93248e24	−0.612285	−0.306142	+	0.951986i	$0.599038\pi$
$830$	−2.00686e24	−0.309281
$831$	1.01177e25	1.54339
$832$	5.52795e24	0.834672
$833$	−5.05957e22	−0.00756190
$834$	−1.03102e25	−1.52530
$835$	3.19709e24	0.468188
$836$	1.97574e23	0.0286403
$837$	9.75916e24	1.40038
$838$	1.92424e25	2.73329
$839$	5.95644e24	0.837549	0.418774	−	0.908090i	$-0.362460\pi$
$839$	5.95644e24	0.837549	0.418774	+	0.908090i	$0.362460\pi$
$840$	5.71605e24	0.795650
$841$	2.50246e23	0.0344828
$842$	7.41512e24	1.01150
$843$	−2.39832e24	−0.323871
$844$	7.04724e24	0.942125
$845$	−2.72163e24	−0.360203
$846$	3.10975e24	0.407453
$847$	−7.76072e24	−1.00668
$848$	−2.02685e24	−0.260289
$849$	1.00389e24	0.127635
$850$	−2.68544e24	−0.338029
$851$	−2.88081e24	−0.359015
$852$	−1.33840e25	−1.65139
$853$	4.48798e24	0.548257	0.274128	−	0.961693i	$-0.411611\pi$
$853$	4.48798e24	0.548257	0.274128	+	0.961693i	$0.411611\pi$
$854$	5.28284e23	0.0638962
$855$	−3.22279e23	−0.0385941
$856$	1.96732e24	0.233265
$857$	−6.75654e24	−0.793209	−0.396604	−	0.917990i	$-0.629811\pi$
$857$	−6.75654e24	−0.793209	−0.396604	+	0.917990i	$0.629811\pi$
$858$	−5.59009e23	−0.0649796
$859$	−2.02323e24	−0.232864	−0.116432	−	0.993199i	$-0.537146\pi$
$859$	−2.02323e24	−0.232864	−0.116432	+	0.993199i	$0.537146\pi$
$860$	5.81606e23	0.0662815
$861$	−1.77463e24	−0.200253
$862$	9.65611e24	1.07892
$863$	−1.61172e25	−1.78320	−0.891598	−	0.452828i	$-0.850415\pi$
$863$	−1.61172e25	−1.78320	−0.891598	+	0.452828i	$0.850415\pi$
$864$	3.61529e24	0.396074
$865$	4.80701e24	0.521481
$866$	−5.90002e24	−0.633799
$867$	7.10781e24	0.756090
$868$	2.33426e25	2.45885
$869$	−3.50952e23	−0.0366083
$870$	−1.59527e24	−0.164787
$871$	2.19605e24	0.224641
$872$	1.08172e25	1.09579
$873$	1.08540e24	0.108886
$874$	−1.01072e24	−0.100412
$875$	−1.02908e25	−1.01246
$876$	−1.64236e25	−1.60023
$877$	7.43928e22	0.00717851	0.00358925	−	0.999994i	$-0.498858\pi$
$877$	7.43928e22	0.00717851	0.00358925	+	0.999994i	$0.498858\pi$
$878$	−2.51134e25	−2.39995
$879$	−1.58340e25	−1.49860
$880$	3.10952e23	0.0291468
$881$	−1.13164e24	−0.105054	−0.0525271	−	0.998619i	$-0.516728\pi$
$881$	−1.13164e24	−0.105054	−0.0525271	+	0.998619i	$0.516728\pi$
$882$	1.24704e23	0.0114656
$883$	2.09000e25	1.90318	0.951592	−	0.307365i	$-0.0994472\pi$
$883$	2.09000e25	1.90318	0.951592	+	0.307365i	$0.0994472\pi$
$884$	4.36172e24	0.393381
$885$	4.06347e24	0.362977
$886$	6.24545e24	0.552557
$887$	−1.65382e25	−1.44923	−0.724614	−	0.689155i	$-0.757982\pi$
$887$	−1.65382e25	−1.44923	−0.724614	+	0.689155i	$0.757982\pi$
$888$	−1.92616e25	−1.67179
$889$	−9.95707e24	−0.855986
$890$	−1.32870e25	−1.13139
$891$	−5.23005e23	−0.0441108
$892$	−1.91355e24	−0.159860
$893$	2.18085e24	0.180463
$894$	−3.00833e25	−2.46579
$895$	−1.26366e24	−0.102597
$896$	2.30033e25	1.85000
$897$	1.86891e24	0.148885
$898$	6.93730e24	0.547446
$899$	−3.06093e24	−0.239274
$900$	4.32563e24	0.334956
$901$	1.62926e24	0.124977
$902$	−3.67618e23	−0.0279345
$903$	−6.43838e23	−0.0484653
$904$	−1.17672e25	−0.877491
$905$	−1.42437e25	−1.05223
$906$	−3.15672e25	−2.31018
$907$	−1.02246e25	−0.741281	−0.370640	−	0.928776i	$-0.620862\pi$
$907$	−1.02246e25	−0.741281	−0.370640	+	0.928776i	$0.620862\pi$
$908$	1.38627e24	0.0995673
$909$	−2.54391e24	−0.181012
$910$	9.75760e24	0.687846
$911$	−1.72219e25	−1.20275	−0.601375	−	0.798967i	$-0.705380\pi$
$911$	−1.72219e25	−1.20275	−0.601375	+	0.798967i	$0.705380\pi$
$912$	−1.77468e24	−0.122790
$913$	3.00761e23	0.0206167
$914$	−4.28802e25	−2.91215
$915$	2.88606e23	0.0194190
$916$	4.88185e25	3.25442
$917$	−1.46830e25	−0.969787
$918$	9.10062e24	0.595536
$919$	−2.65675e25	−1.72254	−0.861269	−	0.508149i	$-0.830330\pi$
$919$	−2.65675e25	−1.72254	−0.861269	+	0.508149i	$0.830330\pi$
$920$	−3.95872e24	−0.254307
$921$	1.13389e25	0.721713
$922$	2.33506e25	1.47260
$923$	−1.07348e25	−0.670782
$924$	−1.82321e24	−0.112882
$925$	1.32301e25	0.811634
$926$	1.76870e25	1.07513
$927$	−3.65503e24	−0.220147
$928$	−1.13392e24	−0.0676747
$929$	−1.22681e25	−0.725510	−0.362755	−	0.931885i	$-0.618164\pi$
$929$	−1.22681e25	−0.725510	−0.362755	+	0.931885i	$0.618164\pi$
$930$	1.95129e25	1.14345
$931$	8.74543e22	0.00507819
$932$	5.79200e25	3.33268
$933$	−1.14346e25	−0.651971
$934$	−5.10770e25	−2.88587
$935$	−2.49955e23	−0.0139947
$936$	−5.05112e24	−0.280248
$937$	2.19680e25	1.20782	0.603911	−	0.797051i	$-0.293608\pi$
$937$	2.19680e25	1.20782	0.603911	+	0.797051i	$0.293608\pi$
$938$	1.09596e25	0.597131
$939$	2.31638e25	1.25070
$940$	1.81796e25	0.972744
$941$	1.78235e25	0.945106	0.472553	−	0.881302i	$-0.343332\pi$
$941$	1.78235e25	0.945106	0.472553	+	0.881302i	$0.343332\pi$
$942$	2.46756e25	1.29669
$943$	1.22904e24	0.0640053
$944$	−9.04491e24	−0.466812
$945$	1.33053e25	0.680540
$946$	−1.33373e23	−0.00676070
$947$	−1.42523e25	−0.715997	−0.357998	−	0.933722i	$-0.616541\pi$
$947$	−1.42523e25	−0.715997	−0.357998	+	0.933722i	$0.616541\pi$
$948$	1.66967e25	0.831306
$949$	−1.31728e25	−0.650004
$950$	4.64176e24	0.227003
$951$	2.27707e25	1.10368
$952$	1.02276e25	0.491313
$953$	2.86905e25	1.36599	0.682996	−	0.730422i	$-0.260677\pi$
$953$	2.86905e25	1.36599	0.682996	+	0.730422i	$0.260677\pi$
$954$	−4.01565e24	−0.189494
$955$	−1.45752e25	−0.681687
$956$	1.17602e24	0.0545160
$957$	2.39078e23	0.0109847
$958$	6.39082e25	2.91038
$959$	−3.77984e25	−1.70614
$960$	1.50714e25	0.674291
$961$	1.48901e25	0.660312
$962$	−3.28806e25	−1.44528
$963$	1.02357e24	0.0445960
$964$	−3.71288e25	−1.60345
$965$	−2.08094e25	−0.890795
$966$	9.32694e24	0.395761
$967$	1.51733e25	0.638197	0.319099	−	0.947721i	$-0.396620\pi$
$967$	1.51733e25	0.638197	0.319099	+	0.947721i	$0.396620\pi$
$968$	3.59368e25	1.49830
$969$	1.42655e24	0.0589570
$970$	9.70922e24	0.397763
$971$	−2.37156e24	−0.0963097	−0.0481549	−	0.998840i	$-0.515334\pi$
$971$	−2.37156e24	−0.0963097	−0.0481549	+	0.998840i	$0.515334\pi$
$972$	−2.60415e25	−1.04834
$973$	−2.69710e25	−1.07631
$974$	4.07937e25	1.61377
$975$	−8.58300e24	−0.336589
$976$	−6.42411e23	−0.0249741
$977$	−3.97426e25	−1.53162	−0.765812	−	0.643064i	$-0.777663\pi$
$977$	−3.97426e25	−1.53162	−0.765812	+	0.643064i	$0.777663\pi$
$978$	−9.80067e24	−0.374434
$979$	1.99128e24	0.0754186
$980$	7.29021e23	0.0273727
$981$	5.62807e24	0.209495
$982$	2.30342e25	0.850014
$983$	5.62205e24	0.205679	0.102839	−	0.994698i	$-0.467207\pi$
$983$	5.62205e24	0.205679	0.102839	+	0.994698i	$0.467207\pi$
$984$	8.21759e24	0.298048
$985$	1.17651e25	0.423046
$986$	−2.85438e24	−0.101755
$987$	−2.01249e25	−0.711275
$988$	−7.53920e24	−0.264175
$989$	4.45898e23	0.0154906
$990$	6.16068e23	0.0212192
$991$	2.23677e25	0.763829	0.381914	−	0.924198i	$-0.375265\pi$
$991$	2.23677e25	0.763829	0.381914	+	0.924198i	$0.375265\pi$
$992$	1.38698e25	0.469591
$993$	4.22223e24	0.141734
$994$	−5.35731e25	−1.78304
$995$	1.69843e25	0.560470
$996$	−1.43089e25	−0.468168
$997$	1.65891e25	0.538163	0.269081	−	0.963117i	$-0.413280\pi$
$997$	1.65891e25	0.538163	0.269081	+	0.963117i	$0.413280\pi$
$998$	6.80720e25	2.18957
$999$	−4.48353e25	−1.42993

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-615.069 q^{2} -9589.87 q^{3} +247238. q^{4} +540648. q^{5} +5.89843e6 q^{6} +1.54300e7 q^{7} -7.14501e7 q^{8} -3.71746e7 q^{9} +O(q^{10})\)	\(q-615.069 q^{2} -9589.87 q^{3} +247238. q^{4} +540648. q^{5} +5.89843e6 q^{6} +1.54300e7 q^{7} -7.14501e7 q^{8} -3.71746e7 q^{9} -3.32536e8 q^{10} +4.98361e7 q^{11} -2.37098e9 q^{12} -1.90169e9 q^{13} -9.49051e9 q^{14} -5.18475e9 q^{15} +1.15408e10 q^{16} -9.27691e9 q^{17} +2.28649e10 q^{18} +1.60351e10 q^{19} +1.33669e11 q^{20} -1.47972e11 q^{21} -3.06526e10 q^{22} +1.02479e11 q^{23} +6.85197e11 q^{24} -4.70639e11 q^{25} +1.16967e12 q^{26} +1.59494e12 q^{27} +3.81488e12 q^{28} -5.00246e11 q^{29} +3.18898e12 q^{30} +6.11884e12 q^{31} +2.26673e12 q^{32} -4.77921e11 q^{33} +5.70594e12 q^{34} +8.34220e12 q^{35} -9.19097e12 q^{36} -2.81110e13 q^{37} -9.86269e12 q^{38} +1.82369e13 q^{39} -3.86294e13 q^{40} +1.19930e13 q^{41} +9.10127e13 q^{42} +4.35110e12 q^{43} +1.23214e13 q^{44} -2.00984e13 q^{45} -6.30320e13 q^{46} +1.36005e14 q^{47} -1.10675e14 q^{48} +5.45393e12 q^{49} +2.89475e14 q^{50} +8.89644e13 q^{51} -4.70169e14 q^{52} -1.75625e14 q^{53} -9.80996e14 q^{54} +2.69438e13 q^{55} -1.10247e15 q^{56} -1.53774e14 q^{57} +3.07686e14 q^{58} -7.83735e14 q^{59} -1.28187e15 q^{60} -5.56644e13 q^{61} -3.76351e15 q^{62} -5.73603e14 q^{63} -2.90687e15 q^{64} -1.02814e15 q^{65} +2.93955e14 q^{66} -1.15479e15 q^{67} -2.29361e15 q^{68} -9.82765e14 q^{69} -5.13103e15 q^{70} +5.64491e15 q^{71} +2.65613e15 q^{72} +6.92692e15 q^{73} +1.72902e16 q^{74} +4.51336e15 q^{75} +3.96448e15 q^{76} +7.68970e14 q^{77} -1.12170e16 q^{78} -7.04213e15 q^{79} +6.23951e15 q^{80} -1.04945e16 q^{81} -7.37654e15 q^{82} +6.03501e15 q^{83} -3.65842e16 q^{84} -5.01555e15 q^{85} -2.67623e15 q^{86} +4.79730e15 q^{87} -3.56079e15 q^{88} +3.99565e16 q^{89} +1.23619e16 q^{90} -2.93430e16 q^{91} +2.53368e16 q^{92} -5.86789e16 q^{93} -8.36525e16 q^{94} +8.66935e15 q^{95} -2.17377e16 q^{96} -2.91975e16 q^{97} -3.35455e15 q^{98} -1.85264e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 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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