LMFDB - Embedded newform 3.18.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,18,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, 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("3.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	3.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:	$5.49666262034$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14569}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3642 $ x^2 - x - 3642
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-59.8511$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+659.106 q^{2} +6561.00 q^{3} +303349. q^{4} -1.08318e6 q^{5} +4.32440e6 q^{6} +1.59855e6 q^{7} +1.13549e8 q^{8} +4.30467e7 q^{9} +O(q^{10})$	\(q+659.106 q^{2} +6561.00 q^{3} +303349. q^{4} -1.08318e6 q^{5} +4.32440e6 q^{6} +1.59855e6 q^{7} +1.13549e8 q^{8} +4.30467e7 q^{9} -7.13934e8 q^{10} -4.47381e8 q^{11} +1.99027e9 q^{12} -2.48486e9 q^{13} +1.05361e9 q^{14} -7.10677e9 q^{15} +3.50803e10 q^{16} -2.48745e10 q^{17} +2.83724e10 q^{18} +8.23042e10 q^{19} -3.28583e11 q^{20} +1.04881e10 q^{21} -2.94872e11 q^{22} +6.43083e11 q^{23} +7.44995e11 q^{24} +4.10349e11 q^{25} -1.63779e12 q^{26} +2.82430e11 q^{27} +4.84918e11 q^{28} -9.82213e11 q^{29} -4.68412e12 q^{30} +3.28632e12 q^{31} +8.23853e12 q^{32} -2.93527e12 q^{33} -1.63949e13 q^{34} -1.73152e12 q^{35} +1.30582e13 q^{36} +2.63492e13 q^{37} +5.42472e13 q^{38} -1.63032e13 q^{39} -1.22994e14 q^{40} -3.33007e13 q^{41} +6.91276e12 q^{42} +9.83107e13 q^{43} -1.35713e14 q^{44} -4.66275e13 q^{45} +4.23860e14 q^{46} -1.62068e14 q^{47} +2.30162e14 q^{48} -2.30075e14 q^{49} +2.70463e14 q^{50} -1.63201e14 q^{51} -7.53780e14 q^{52} -1.40921e14 q^{53} +1.86151e14 q^{54} +4.84596e14 q^{55} +1.81514e14 q^{56} +5.39998e14 q^{57} -6.47383e14 q^{58} -9.80930e13 q^{59} -2.15583e15 q^{60} +1.37376e15 q^{61} +2.16603e15 q^{62} +6.88123e13 q^{63} +8.32030e14 q^{64} +2.69156e15 q^{65} -1.93465e15 q^{66} -1.85816e15 q^{67} -7.54565e15 q^{68} +4.21927e15 q^{69} -1.14126e15 q^{70} -6.17500e15 q^{71} +4.88791e15 q^{72} -1.30214e16 q^{73} +1.73670e16 q^{74} +2.69230e15 q^{75} +2.49669e16 q^{76} -7.15160e14 q^{77} -1.07455e16 q^{78} +1.27538e16 q^{79} -3.79984e16 q^{80} +1.85302e15 q^{81} -2.19487e16 q^{82} -1.42886e16 q^{83} +3.18155e15 q^{84} +2.69436e16 q^{85} +6.47972e16 q^{86} -6.44430e15 q^{87} -5.07996e16 q^{88} -3.77818e16 q^{89} -3.07325e16 q^{90} -3.97217e15 q^{91} +1.95079e17 q^{92} +2.15615e16 q^{93} -1.06820e17 q^{94} -8.91506e16 q^{95} +5.40530e16 q^{96} +1.09404e17 q^{97} -1.51644e17 q^{98} -1.92583e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 594 q^{2} + 13122 q^{3} + 176516 q^{4} + 382860 q^{5} + 3897234 q^{6} + 24471568 q^{7} + 130340232 q^{8} + 86093442 q^{9}+O(q^{10}) $ 2 * q + 594 * q^2 + 13122 * q^3 + 176516 * q^4 + 382860 * q^5 + 3897234 * q^6 + 24471568 * q^7 + 130340232 * q^8 + 86093442 * q^9	\( 2 q + 594 q^{2} + 13122 q^{3} + 176516 q^{4} + 382860 q^{5} + 3897234 q^{6} + 24471568 q^{7} + 130340232 q^{8} + 86093442 q^{9} - 809382420 q^{10} - 987553512 q^{11} + 1158121476 q^{12} - 2519398244 q^{13} - 435565296 q^{14} + 2511944460 q^{15} + 50611323920 q^{16} - 34313126364 q^{17} + 25569752274 q^{18} + 80053542184 q^{19} - 514526095080 q^{20} + 160557957648 q^{21} - 259702850088 q^{22} + 297228742704 q^{23} + 855162262152 q^{24} + 1796695260350 q^{25} - 1635537155076 q^{26} + 564859072962 q^{27} - 2416139220704 q^{28} - 470374069572 q^{29} - 5310358057620 q^{30} + 3400754454592 q^{31} + 5026499631648 q^{32} - 6479338592232 q^{33} - 15780403538748 q^{34} + 31801338154080 q^{35} + 7598435004036 q^{36} + 10652012180428 q^{37} + 54393717084264 q^{38} - 16529771878884 q^{39} - 98377731579600 q^{40} - 113376799448748 q^{41} - 2857743907056 q^{42} + 61637031489880 q^{43} - 67200775334352 q^{44} + 16480867602060 q^{45} + 446377123388592 q^{46} - 279645641926560 q^{47} + 332060896239120 q^{48} + 60469362475890 q^{49} + 180203550461550 q^{50} - 225128422074204 q^{51} - 749398920924104 q^{52} - 530964038611476 q^{53} + 167763144669714 q^{54} - 307321280077680 q^{55} + 565580346246720 q^{56} + 525231290269224 q^{57} - 680706445363812 q^{58} + 17\!\cdots\!56 q^{59}+ \cdots - 42\!\cdots\!52 q^{99}+O(q^{100}) \) 2 * q + 594 * q^2 + 13122 * q^3 + 176516 * q^4 + 382860 * q^5 + 3897234 * q^6 + 24471568 * q^7 + 130340232 * q^8 + 86093442 * q^9 - 809382420 * q^10 - 987553512 * q^11 + 1158121476 * q^12 - 2519398244 * q^13 - 435565296 * q^14 + 2511944460 * q^15 + 50611323920 * q^16 - 34313126364 * q^17 + 25569752274 * q^18 + 80053542184 * q^19 - 514526095080 * q^20 + 160557957648 * q^21 - 259702850088 * q^22 + 297228742704 * q^23 + 855162262152 * q^24 + 1796695260350 * q^25 - 1635537155076 * q^26 + 564859072962 * q^27 - 2416139220704 * q^28 - 470374069572 * q^29 - 5310358057620 * q^30 + 3400754454592 * q^31 + 5026499631648 * q^32 - 6479338592232 * q^33 - 15780403538748 * q^34 + 31801338154080 * q^35 + 7598435004036 * q^36 + 10652012180428 * q^37 + 54393717084264 * q^38 - 16529771878884 * q^39 - 98377731579600 * q^40 - 113376799448748 * q^41 - 2857743907056 * q^42 + 61637031489880 * q^43 - 67200775334352 * q^44 + 16480867602060 * q^45 + 446377123388592 * q^46 - 279645641926560 * q^47 + 332060896239120 * q^48 + 60469362475890 * q^49 + 180203550461550 * q^50 - 225128422074204 * q^51 - 749398920924104 * q^52 - 530964038611476 * q^53 + 167763144669714 * q^54 - 307321280077680 * q^55 + 565580346246720 * q^56 + 525231290269224 * q^57 - 680706445363812 * q^58 + 1727524231086456 * q^59 - 3375805709819880 * q^60 + 2784287656027900 * q^61 + 2158582756499136 * q^62 + 1053420760128528 * q^63 - 994533569423296 * q^64 + 2640922679811240 * q^65 - 1703910399427368 * q^66 - 3329301676696184 * q^67 - 6348514481766072 * q^68 + 1950117780880944 * q^69 - 3324459101139360 * q^70 - 13489402206504816 * q^71 + 5610719601979272 * q^72 + 436589918136724 * q^73 + 18388942762073004 * q^74 + 11788117603156350 * q^75 + 25252347669111376 * q^76 - 13070541011736384 * q^77 - 10730759274453636 * q^78 + 4376041565214880 * q^79 - 15229171694708640 * q^80 + 3706040377703682 * q^81 - 16735234653750924 * q^82 - 39886442265612888 * q^83 - 15852289427038944 * q^84 + 13106143850552280 * q^85 + 67184884152159768 * q^86 - 3086124270461892 * q^87 - 59869809989481888 * q^88 + 6972184096107444 * q^89 - 34841259216044820 * q^90 - 4762196572326688 * q^91 + 238944325336039008 * q^92 + 22312349976578112 * q^93 - 99165314702307744 * q^94 - 92450059415485200 * q^95 + 32978864083242528 * q^96 + 183569555712460996 * q^97 - 170560284296616126 * q^98 - 42510940503634152 * 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 $

$2$	659.106	1.82054	0.910271	−	0.414014i	$-0.135873\pi$
$2$	659.106	1.82054	0.910271	+	0.414014i	$0.135873\pi$
$3$	6561.00	0.577350
$3$	6561.00	0.577350
$4$	303349.	2.31437
$5$	−1.08318e6	−1.24010	−0.620051	−	0.784562i	$-0.712888\pi$
$5$	−1.08318e6	−1.24010	−0.620051	+	0.784562i	$0.712888\pi$
$6$	4.32440e6	1.05109
$7$	1.59855e6	0.104808	0.0524038	−	0.998626i	$-0.483312\pi$
$7$	1.59855e6	0.104808	0.0524038	+	0.998626i	$0.483312\pi$
$8$	1.13549e8	2.39287
$9$	4.30467e7	0.333333
$10$	−7.13934e8	−2.25766
$11$	−4.47381e8	−0.629274	−0.314637	−	0.949212i	$-0.601883\pi$
$11$	−4.47381e8	−0.629274	−0.314637	+	0.949212i	$0.601883\pi$
$12$	1.99027e9	1.33620
$13$	−2.48486e9	−0.844857	−0.422428	−	0.906396i	$-0.638822\pi$
$13$	−2.48486e9	−0.844857	−0.422428	+	0.906396i	$0.638822\pi$
$14$	1.05361e9	0.190806
$15$	−7.10677e9	−0.715973
$16$	3.50803e10	2.04194
$17$	−2.48745e10	−0.864844	−0.432422	−	0.901671i	$-0.642341\pi$
$17$	−2.48745e10	−0.864844	−0.432422	+	0.901671i	$0.642341\pi$
$18$	2.83724e10	0.606847
$19$	8.23042e10	1.11177	0.555887	−	0.831258i	$-0.312379\pi$
$19$	8.23042e10	1.11177	0.555887	+	0.831258i	$0.312379\pi$
$20$	−3.28583e11	−2.87005
$21$	1.04881e10	0.0605106
$22$	−2.94872e11	−1.14562
$23$	6.43083e11	1.71230	0.856151	−	0.516726i	$-0.172850\pi$
$23$	6.43083e11	1.71230	0.856151	+	0.516726i	$0.172850\pi$
$24$	7.44995e11	1.38152
$25$	4.10349e11	0.537852
$26$	−1.63779e12	−1.53810
$27$	2.82430e11	0.192450
$28$	4.84918e11	0.242563
$29$	−9.82213e11	−0.364605	−0.182302	−	0.983243i	$-0.558355\pi$
$29$	−9.82213e11	−0.364605	−0.182302	+	0.983243i	$0.558355\pi$
$30$	−4.68412e12	−1.30346
$31$	3.28632e12	0.692046	0.346023	−	0.938226i	$-0.387532\pi$
$31$	3.28632e12	0.692046	0.346023	+	0.938226i	$0.387532\pi$
$32$	8.23853e12	1.32457
$33$	−2.93527e12	−0.363311
$34$	−1.63949e13	−1.57448
$35$	−1.73152e12	−0.129972
$36$	1.30582e13	0.771457
$37$	2.63492e13	1.23326	0.616628	−	0.787254i	$-0.288498\pi$
$37$	2.63492e13	1.23326	0.616628	+	0.787254i	$0.288498\pi$
$38$	5.42472e13	2.02403
$39$	−1.63032e13	−0.487778
$40$	−1.22994e14	−2.96740
$41$	−3.33007e13	−0.651314	−0.325657	−	0.945488i	$-0.605585\pi$
$41$	−3.33007e13	−0.651314	−0.325657	+	0.945488i	$0.605585\pi$
$42$	6.91276e12	0.110162
$43$	9.83107e13	1.28268	0.641341	−	0.767256i	$-0.278378\pi$
$43$	9.83107e13	1.28268	0.641341	+	0.767256i	$0.278378\pi$
$44$	−1.35713e14	−1.45637
$45$	−4.66275e13	−0.413367
$46$	4.23860e14	3.11732
$47$	−1.62068e14	−0.992811	−0.496406	−	0.868091i	$-0.665347\pi$
$47$	−1.62068e14	−0.992811	−0.496406	+	0.868091i	$0.665347\pi$
$48$	2.30162e14	1.17891
$49$	−2.30075e14	−0.989015
$50$	2.70463e14	0.979182
$51$	−1.63201e14	−0.499318
$52$	−7.53780e14	−1.95531
$53$	−1.40921e14	−0.310907	−0.155453	−	0.987843i	$-0.549684\pi$
$53$	−1.40921e14	−0.310907	−0.155453	+	0.987843i	$0.549684\pi$
$54$	1.86151e14	0.350363
$55$	4.84596e14	0.780363
$56$	1.81514e14	0.250790
$57$	5.39998e14	0.641882
$58$	−6.47383e14	−0.663778
$59$	−9.80930e13	−0.0869753	−0.0434876	−	0.999054i	$-0.513847\pi$
$59$	−9.80930e13	−0.0869753	−0.0434876	+	0.999054i	$0.513847\pi$
$60$	−2.15583e15	−1.65703
$61$	1.37376e15	0.917503	0.458751	−	0.888565i	$-0.348297\pi$
$61$	1.37376e15	0.917503	0.458751	+	0.888565i	$0.348297\pi$
$62$	2.16603e15	1.25990
$63$	6.88123e13	0.0349358
$64$	8.32030e14	0.369495
$65$	2.69156e15	1.04771
$66$	−1.93465e15	−0.661423
$67$	−1.85816e15	−0.559046	−0.279523	−	0.960139i	$-0.590176\pi$
$67$	−1.85816e15	−0.559046	−0.279523	+	0.960139i	$0.590176\pi$
$68$	−7.54565e15	−2.00157
$69$	4.21927e15	0.988598
$70$	−1.14126e15	−0.236619
$71$	−6.17500e15	−1.13486	−0.567428	−	0.823423i	$-0.692061\pi$
$71$	−6.17500e15	−1.13486	−0.567428	+	0.823423i	$0.692061\pi$
$72$	4.88791e15	0.797622
$73$	−1.30214e16	−1.88979	−0.944896	−	0.327371i	$-0.893837\pi$
$73$	−1.30214e16	−1.88979	−0.944896	+	0.327371i	$0.893837\pi$
$74$	1.73670e16	2.24519
$75$	2.69230e15	0.310529
$76$	2.49669e16	2.57305
$77$	−7.15160e14	−0.0659526
$78$	−1.07455e16	−0.888021
$79$	1.27538e16	0.945824	0.472912	−	0.881110i	$-0.343203\pi$
$79$	1.27538e16	0.945824	0.472912	+	0.881110i	$0.343203\pi$
$80$	−3.79984e16	−2.53221
$81$	1.85302e15	0.111111
$82$	−2.19487e16	−1.18574
$83$	−1.42886e16	−0.696348	−0.348174	−	0.937430i	$-0.613198\pi$
$83$	−1.42886e16	−0.696348	−0.348174	+	0.937430i	$0.613198\pi$
$84$	3.18155e15	0.140044
$85$	2.69436e16	1.07250
$86$	6.47972e16	2.33517
$87$	−6.44430e15	−0.210505
$88$	−5.07996e16	−1.50577
$89$	−3.77818e16	−1.01734	−0.508672	−	0.860961i	$-0.669863\pi$
$89$	−3.77818e16	−1.01734	−0.508672	+	0.860961i	$0.669863\pi$
$90$	−3.07325e16	−0.752552
$91$	−3.97217e15	−0.0885473
$92$	1.95079e17	3.96290
$93$	2.15615e16	0.399553
$94$	−1.06820e17	−1.80745
$95$	−8.91506e16	−1.37871
$96$	5.40530e16	0.764741
$97$	1.09404e17	1.41733	0.708667	−	0.705543i	$-0.249297\pi$
$97$	1.09404e17	1.41733	0.708667	+	0.705543i	$0.249297\pi$
$98$	−1.51644e17	−1.80054
$99$	−1.92583e16	−0.209758
$100$	1.24479e17	1.24479
$101$	1.19047e17	1.09392	0.546962	−	0.837157i	$-0.315784\pi$
$101$	1.19047e17	1.09392	0.546962	+	0.837157i	$0.315784\pi$
$102$	−1.07567e17	−0.909029
$103$	−3.78871e16	−0.294697	−0.147348	−	0.989085i	$-0.547074\pi$
$103$	−3.78871e16	−0.294697	−0.147348	+	0.989085i	$0.547074\pi$
$104$	−2.82153e17	−2.02163
$105$	−1.13605e16	−0.0750394
$106$	−9.28817e16	−0.566018
$107$	−5.58893e16	−0.314461	−0.157230	−	0.987562i	$-0.550257\pi$
$107$	−5.58893e16	−0.314461	−0.157230	+	0.987562i	$0.550257\pi$
$108$	8.56748e16	0.445401
$109$	3.40417e17	1.63639	0.818193	−	0.574944i	$-0.194976\pi$
$109$	3.40417e17	1.63639	0.818193	+	0.574944i	$0.194976\pi$
$110$	3.19400e17	1.42068
$111$	1.72877e17	0.712021
$112$	5.60775e16	0.214011
$113$	−1.05411e16	−0.0373009	−0.0186505	−	0.999826i	$-0.505937\pi$
$113$	−1.05411e16	−0.0373009	−0.0186505	+	0.999826i	$0.505937\pi$
$114$	3.55916e17	1.16857
$115$	−6.96577e17	−2.12343
$116$	−2.97953e17	−0.843831
$117$	−1.06965e17	−0.281619
$118$	−6.46537e16	−0.158342
$119$	−3.97630e16	−0.0906422
$120$	−8.06967e17	−1.71323
$121$	−3.05297e17	−0.604015
$122$	9.05454e17	1.67035
$123$	−2.18486e17	−0.376036
$124$	9.96902e17	1.60165
$125$	3.81921e17	0.573110
$126$	4.53546e16	0.0636021
$127$	−7.32464e17	−0.960406	−0.480203	−	0.877157i	$-0.659437\pi$
$127$	−7.32464e17	−0.960406	−0.480203	+	0.877157i	$0.659437\pi$
$128$	−5.31445e17	−0.651889
$129$	6.45016e17	0.740557
$130$	1.77402e18	1.90740
$131$	−2.70892e17	−0.272891	−0.136446	−	0.990648i	$-0.543568\pi$
$131$	−2.70892e17	−0.272891	−0.136446	+	0.990648i	$0.543568\pi$
$132$	−8.90410e17	−0.840837
$133$	1.31567e17	0.116522
$134$	−1.22473e18	−1.01777
$135$	−3.05923e17	−0.238658
$136$	−2.82447e18	−2.06946
$137$	2.60762e18	1.79523	0.897614	−	0.440782i	$-0.145299\pi$
$137$	2.60762e18	1.79523	0.897614	+	0.440782i	$0.145299\pi$
$138$	2.78094e18	1.79978
$139$	1.06238e18	0.646628	0.323314	−	0.946292i	$-0.395203\pi$
$139$	1.06238e18	0.646628	0.323314	+	0.946292i	$0.395203\pi$
$140$	−5.25256e17	−0.300803
$141$	−1.06333e18	−0.573200
$142$	−4.06998e18	−2.06605
$143$	1.11168e18	0.531646
$144$	1.51009e18	0.680647
$145$	1.06392e18	0.452147
$146$	−8.58250e18	−3.44044
$147$	−1.50952e18	−0.571008
$148$	7.99302e18	2.85421
$149$	−1.93103e18	−0.651186	−0.325593	−	0.945510i	$-0.605564\pi$
$149$	−1.93103e18	−0.651186	−0.325593	+	0.945510i	$0.605564\pi$
$150$	1.77451e18	0.565331
$151$	2.89305e18	0.871067	0.435533	−	0.900173i	$-0.356560\pi$
$151$	2.89305e18	0.871067	0.435533	+	0.900173i	$0.356560\pi$
$152$	9.34555e18	2.66032
$153$	−1.07076e18	−0.288281
$154$	−4.71366e17	−0.120069
$155$	−3.55969e18	−0.858208
$156$	−4.94555e18	−1.12890
$157$	−3.49613e18	−0.755858	−0.377929	−	0.925835i	$-0.623364\pi$
$157$	−3.49613e18	−0.755858	−0.377929	+	0.925835i	$0.623364\pi$
$158$	8.40613e18	1.72191
$159$	−9.24581e17	−0.179502
$160$	−8.92385e18	−1.64260
$161$	1.02800e18	0.179462
$162$	1.22134e18	0.202282
$163$	−1.15214e18	−0.181096	−0.0905481	−	0.995892i	$-0.528862\pi$
$163$	−1.15214e18	−0.181096	−0.0905481	+	0.995892i	$0.528862\pi$
$164$	−1.01017e19	−1.50738
$165$	3.17943e18	0.450543
$166$	−9.41771e18	−1.26773
$167$	3.89891e18	0.498715	0.249358	−	0.968411i	$-0.419781\pi$
$167$	3.89891e18	0.498715	0.249358	+	0.968411i	$0.419781\pi$
$168$	1.19091e18	0.144794
$169$	−2.47589e18	−0.286217
$170$	1.77587e19	1.95252
$171$	3.54292e18	0.370591
$172$	2.98225e19	2.96860
$173$	−6.89759e17	−0.0653590	−0.0326795	−	0.999466i	$-0.510404\pi$
$173$	−6.89759e17	−0.0653590	−0.0326795	+	0.999466i	$0.510404\pi$
$174$	−4.24748e18	−0.383233
$175$	6.55962e17	0.0563710
$176$	−1.56942e19	−1.28494
$177$	−6.43588e17	−0.0502152
$178$	−2.49022e19	−1.85212
$179$	−1.57675e18	−0.111818	−0.0559092	−	0.998436i	$-0.517806\pi$
$179$	−1.57675e18	−0.111818	−0.0559092	+	0.998436i	$0.517806\pi$
$180$	−1.41444e19	−0.956685
$181$	−8.66463e18	−0.559091	−0.279545	−	0.960133i	$-0.590184\pi$
$181$	−8.66463e18	−0.559091	−0.279545	+	0.960133i	$0.590184\pi$
$182$	−2.61808e18	−0.161204
$183$	9.01324e18	0.529720
$184$	7.30214e19	4.09731
$185$	−2.85411e19	−1.52936
$186$	1.42113e19	0.727403
$187$	1.11284e19	0.544224
$188$	−4.91633e19	−2.29773
$189$	4.51477e17	0.0201702
$190$	−5.87597e19	−2.51000
$191$	3.05782e19	1.24919	0.624595	−	0.780949i	$-0.285264\pi$
$191$	3.05782e19	1.24919	0.624595	+	0.780949i	$0.285264\pi$
$192$	5.45895e18	0.213328
$193$	−8.47673e18	−0.316950	−0.158475	−	0.987363i	$-0.550658\pi$
$193$	−8.47673e18	−0.316950	−0.158475	+	0.987363i	$0.550658\pi$
$194$	7.21087e19	2.58032
$195$	1.76593e19	0.604895
$196$	−6.97931e19	−2.28895
$197$	−1.02174e18	−0.0320906	−0.0160453	−	0.999871i	$-0.505108\pi$
$197$	−1.02174e18	−0.0320906	−0.0160453	+	0.999871i	$0.505108\pi$
$198$	−1.26933e19	−0.381873
$199$	1.36420e19	0.393213	0.196606	−	0.980482i	$-0.437008\pi$
$199$	1.36420e19	0.393213	0.196606	+	0.980482i	$0.437008\pi$
$200$	4.65947e19	1.28701
$201$	−1.21914e19	−0.322765
$202$	7.84647e19	1.99153
$203$	−1.57011e18	−0.0382133
$204$	−4.95070e19	−1.15561
$205$	3.60708e19	0.807696
$206$	−2.49716e19	−0.536507
$207$	2.76826e19	0.570767
$208$	−8.71695e19	−1.72515
$209$	−3.68213e19	−0.699609
$210$	−7.48779e18	−0.136612
$211$	3.54105e19	0.620485	0.310242	−	0.950657i	$-0.399590\pi$
$211$	3.54105e19	0.620485	0.310242	+	0.950657i	$0.399590\pi$
$212$	−4.27482e19	−0.719553
$213$	−4.05142e19	−0.655209
$214$	−3.68370e19	−0.572489
$215$	−1.06489e20	−1.59066
$216$	3.20696e19	0.460507
$217$	5.25334e18	0.0725317
$218$	2.24371e20	2.97911
$219$	−8.54335e19	−1.09107
$220$	1.47002e20	1.80605
$221$	6.18095e19	0.730670
$222$	1.13945e20	1.29626
$223$	−1.07563e20	−1.17780	−0.588900	−	0.808206i	$-0.700439\pi$
$223$	−1.07563e20	−1.17780	−0.588900	+	0.808206i	$0.700439\pi$
$224$	1.31697e19	0.138825
$225$	1.76642e19	0.179284
$226$	−6.94771e18	−0.0679078
$227$	−3.19163e19	−0.300464	−0.150232	−	0.988651i	$-0.548002\pi$
$227$	−3.19163e19	−0.300464	−0.150232	+	0.988651i	$0.548002\pi$
$228$	1.63808e20	1.48555
$229$	−3.62295e19	−0.316564	−0.158282	−	0.987394i	$-0.550595\pi$
$229$	−3.62295e19	−0.316564	−0.158282	+	0.987394i	$0.550595\pi$
$230$	−4.59118e20	−3.86579
$231$	−4.69216e18	−0.0380778
$232$	−1.11529e20	−0.872451
$233$	1.40197e20	1.05734	0.528669	−	0.848828i	$-0.322691\pi$
$233$	1.40197e20	1.05734	0.528669	+	0.848828i	$0.322691\pi$
$234$	−7.05013e19	−0.512699
$235$	1.75550e20	1.23119
$236$	−2.97564e19	−0.201293
$237$	8.36779e19	0.546072
$238$	−2.62081e19	−0.165018
$239$	1.59138e20	0.966921	0.483461	−	0.875366i	$-0.339380\pi$
$239$	1.59138e20	0.966921	0.483461	+	0.875366i	$0.339380\pi$
$240$	−2.49307e20	−1.46197
$241$	−7.13132e19	−0.403669	−0.201834	−	0.979420i	$-0.564690\pi$
$241$	−7.13132e19	−0.403669	−0.201834	+	0.979420i	$0.564690\pi$
$242$	−2.01223e20	−1.09963
$243$	1.21577e19	0.0641500
$244$	4.16729e20	2.12344
$245$	2.49214e20	1.22648
$246$	−1.44005e20	−0.684590
$247$	−2.04514e20	−0.939289
$248$	3.73158e20	1.65597
$249$	−9.37476e19	−0.402037
$250$	2.51726e20	1.04337
$251$	−1.69237e20	−0.678063	−0.339031	−	0.940775i	$-0.610099\pi$
$251$	−1.69237e20	−0.678063	−0.339031	+	0.940775i	$0.610099\pi$
$252$	2.08741e19	0.0808545
$253$	−2.87703e20	−1.07751
$254$	−4.82772e20	−1.74846
$255$	1.76777e20	0.619205
$256$	−4.59335e20	−1.55629
$257$	4.63024e20	1.51765	0.758826	−	0.651293i	$-0.225773\pi$
$257$	4.63024e20	1.51765	0.758826	+	0.651293i	$0.225773\pi$
$258$	4.25134e20	1.34821
$259$	4.21205e19	0.129255
$260$	8.16482e20	2.42479
$261$	−4.22810e19	−0.121535
$262$	−1.78546e20	−0.496810
$263$	−5.31839e20	−1.43270	−0.716351	−	0.697740i	$-0.754189\pi$
$263$	−5.31839e20	−1.43270	−0.716351	+	0.697740i	$0.754189\pi$
$264$	−3.33296e20	−0.869355
$265$	1.52643e20	0.385556
$266$	8.67167e19	0.212133
$267$	−2.47886e20	−0.587363
$268$	−5.63672e20	−1.29384
$269$	−2.28606e20	−0.508386	−0.254193	−	0.967154i	$-0.581810\pi$
$269$	−2.28606e20	−0.508386	−0.254193	+	0.967154i	$0.581810\pi$
$270$	−2.01636e20	−0.434486
$271$	−3.88488e20	−0.811220	−0.405610	−	0.914046i	$-0.632941\pi$
$271$	−3.88488e20	−0.811220	−0.405610	+	0.914046i	$0.632941\pi$
$272$	−8.72603e20	−1.76596
$273$	−2.60614e19	−0.0511228
$274$	1.71870e21	3.26829
$275$	−1.83582e20	−0.338456
$276$	1.27991e21	2.28798
$277$	8.66031e20	1.50126	0.750629	−	0.660724i	$-0.229751\pi$
$277$	8.66031e20	1.50126	0.750629	+	0.660724i	$0.229751\pi$
$278$	7.00222e20	1.17721
$279$	1.41465e20	0.230682
$280$	−1.96613e20	−0.311005
$281$	1.08570e20	0.166612	0.0833059	−	0.996524i	$-0.473452\pi$
$281$	1.08570e20	0.166612	0.0833059	+	0.996524i	$0.473452\pi$
$282$	−7.00848e20	−1.04353
$283$	4.17569e20	0.603314	0.301657	−	0.953416i	$-0.402460\pi$
$283$	4.17569e20	0.603314	0.301657	+	0.953416i	$0.402460\pi$
$284$	−1.87318e21	−2.62648
$285$	−5.84917e20	−0.796000
$286$	7.32714e20	0.967884
$287$	−5.32328e19	−0.0682626
$288$	3.54642e20	0.441524
$289$	−2.08501e20	−0.252044
$290$	7.01235e20	0.823153
$291$	7.17798e20	0.818299
$292$	−3.95004e21	−4.37368
$293$	2.71816e20	0.292348	0.146174	−	0.989259i	$-0.453304\pi$
$293$	2.71816e20	0.292348	0.146174	+	0.989259i	$0.453304\pi$
$294$	−9.94936e20	−1.03954
$295$	1.06253e20	0.107858
$296$	2.99193e21	2.95102
$297$	−1.26354e20	−0.121104
$298$	−1.27275e21	−1.18551
$299$	−1.59797e21	−1.44665
$300$	8.16706e20	0.718680
$301$	1.57154e20	0.134435
$302$	1.90683e21	1.58581
$303$	7.81068e20	0.631577
$304$	2.88725e21	2.27017
$305$	−1.48804e21	−1.13780
$306$	−7.05748e20	−0.524828
$307$	2.41849e21	1.74932	0.874659	−	0.484739i	$-0.161085\pi$
$307$	2.41849e21	1.74932	0.874659	+	0.484739i	$0.161085\pi$
$308$	−2.16943e20	−0.152639
$309$	−2.48577e20	−0.170143
$310$	−2.34621e21	−1.56240
$311$	9.44749e20	0.612144	0.306072	−	0.952008i	$-0.400985\pi$
$311$	9.44749e20	0.612144	0.306072	+	0.952008i	$0.400985\pi$
$312$	−1.85121e21	−1.16719
$313$	−2.44821e21	−1.50218	−0.751089	−	0.660201i	$-0.770471\pi$
$313$	−2.44821e21	−1.50218	−0.751089	+	0.660201i	$0.770471\pi$
$314$	−2.30432e21	−1.37607
$315$	−7.45364e19	−0.0433240
$316$	3.86886e21	2.18899
$317$	3.49751e21	1.92644	0.963219	−	0.268718i	$-0.0866001\pi$
$317$	3.49751e21	1.92644	0.963219	+	0.268718i	$0.0866001\pi$
$318$	−6.09397e20	−0.326791
$319$	4.39423e20	0.229436
$320$	−9.01241e20	−0.458212
$321$	−3.66690e20	−0.181554
$322$	6.77560e20	0.326718
$323$	−2.04727e21	−0.961511
$324$	5.62112e20	0.257152
$325$	−1.01966e21	−0.454408
$326$	−7.59381e20	−0.329693
$327$	2.23347e21	0.944768
$328$	−3.78126e21	−1.55851
$329$	−2.59074e20	−0.104054
$330$	2.09558e21	0.820232
$331$	−1.98378e20	−0.0756754	−0.0378377	−	0.999284i	$-0.512047\pi$
$331$	−1.98378e20	−0.0756754	−0.0378377	+	0.999284i	$0.512047\pi$
$332$	−4.33444e21	−1.61161
$333$	1.13425e21	0.411086
$334$	2.56979e21	0.907932
$335$	2.01273e21	0.693274
$336$	3.67924e20	0.123559
$337$	−4.38592e21	−1.43617	−0.718087	−	0.695954i	$-0.754982\pi$
$337$	−4.38592e21	−1.43617	−0.718087	+	0.695954i	$0.754982\pi$
$338$	−1.63188e21	−0.521070
$339$	−6.91602e19	−0.0215357
$340$	8.17333e21	2.48215
$341$	−1.47024e21	−0.435487
$342$	2.33516e21	0.674676
$343$	−7.39657e20	−0.208464
$344$	1.11631e22	3.06928
$345$	−4.57024e21	−1.22596
$346$	−4.54625e20	−0.118989
$347$	−1.91053e20	−0.0487926	−0.0243963	−	0.999702i	$-0.507766\pi$
$347$	−1.91053e20	−0.0487926	−0.0243963	+	0.999702i	$0.507766\pi$
$348$	−1.95487e21	−0.487186
$349$	−3.63772e21	−0.884735	−0.442368	−	0.896834i	$-0.645861\pi$
$349$	−3.63772e21	−0.884735	−0.442368	+	0.896834i	$0.645861\pi$
$350$	4.32349e20	0.102626
$351$	−7.01797e20	−0.162593
$352$	−3.68576e21	−0.833517
$353$	3.41663e21	0.754245	0.377123	−	0.926163i	$-0.376913\pi$
$353$	3.41663e21	0.754245	0.377123	+	0.926163i	$0.376913\pi$
$354$	−4.24193e20	−0.0914189
$355$	6.68866e21	1.40734
$356$	−1.14611e22	−2.35451
$357$	−2.60885e20	−0.0523323
$358$	−1.03925e21	−0.203570
$359$	−1.00013e22	−1.91317	−0.956587	−	0.291447i	$-0.905863\pi$
$359$	−1.00013e22	−1.91317	−0.956587	+	0.291447i	$0.905863\pi$
$360$	−5.29451e21	−0.989132
$361$	1.29359e21	0.236039
$362$	−5.71091e21	−1.01785
$363$	−2.00306e21	−0.348728
$364$	−1.20495e21	−0.204931
$365$	1.41046e22	2.34353
$366$	5.94068e21	0.964378
$367$	1.19598e22	1.89698	0.948490	−	0.316807i	$-0.102611\pi$
$367$	1.19598e22	1.89698	0.948490	+	0.316807i	$0.102611\pi$
$368$	2.25595e22	3.49642
$369$	−1.43349e21	−0.217105
$370$	−1.88116e22	−2.78427
$371$	−2.25269e20	−0.0325853
$372$	6.54067e21	0.924714
$373$	6.67362e21	0.922224	0.461112	−	0.887342i	$-0.347451\pi$
$373$	6.67362e21	0.922224	0.461112	+	0.887342i	$0.347451\pi$
$374$	7.33477e21	0.990782
$375$	2.50578e21	0.330885
$376$	−1.84027e22	−2.37566
$377$	2.44066e21	0.308039
$378$	2.97572e20	0.0367207
$379$	−1.30692e22	−1.57694	−0.788470	−	0.615073i	$-0.789127\pi$
$379$	−1.30692e22	−1.57694	−0.788470	+	0.615073i	$0.789127\pi$
$380$	−2.70437e22	−3.19085
$381$	−4.80570e21	−0.554491
$382$	2.01543e22	2.27420
$383$	7.55282e19	0.00833527	0.00416763	−	0.999991i	$-0.498673\pi$
$383$	7.55282e19	0.00833527	0.00416763	+	0.999991i	$0.498673\pi$
$384$	−3.48681e21	−0.376368
$385$	7.74650e20	0.0817879
$386$	−5.58706e21	−0.577021
$387$	4.23195e21	0.427561
$388$	3.31875e22	3.28024
$389$	3.90337e21	0.377457	0.188729	−	0.982029i	$-0.439563\pi$
$389$	3.90337e21	0.377457	0.188729	+	0.982029i	$0.439563\pi$
$390$	1.16394e22	1.10124
$391$	−1.59963e22	−1.48087
$392$	−2.61248e22	−2.36658
$393$	−1.77732e21	−0.157554
$394$	−6.73437e20	−0.0584224
$395$	−1.38147e22	−1.17292
$396$	−5.84198e21	−0.485457
$397$	6.50366e21	0.528979	0.264489	−	0.964389i	$-0.414797\pi$
$397$	6.50366e21	0.528979	0.264489	+	0.964389i	$0.414797\pi$
$398$	8.99155e21	0.715860
$399$	8.63212e20	0.0672741
$400$	1.43951e22	1.09826
$401$	2.12436e21	0.158672	0.0793361	−	0.996848i	$-0.474720\pi$
$401$	2.12436e21	0.158672	0.0793361	+	0.996848i	$0.474720\pi$
$402$	−8.03543e21	−0.587608
$403$	−8.16604e21	−0.584680
$404$	3.61128e22	2.53175
$405$	−2.00716e21	−0.137789
$406$	−1.03487e21	−0.0695689
$407$	−1.17881e22	−0.776056
$408$	−1.85313e22	−1.19480
$409$	−1.66641e22	−1.05229	−0.526143	−	0.850396i	$-0.676362\pi$
$409$	−1.66641e22	−1.05229	−0.526143	+	0.850396i	$0.676362\pi$
$410$	2.37745e22	1.47044
$411$	1.71086e22	1.03648
$412$	−1.14930e22	−0.682037
$413$	−1.56806e20	−0.00911566
$414$	1.82458e22	1.03911
$415$	1.54772e22	0.863542
$416$	−2.04716e22	−1.11907
$417$	6.97028e21	0.373331
$418$	−2.42692e22	−1.27367
$419$	2.00258e22	1.02984	0.514920	−	0.857238i	$-0.327822\pi$
$419$	2.00258e22	1.02984	0.514920	+	0.857238i	$0.327822\pi$
$420$	−3.44620e21	−0.173669
$421$	1.39887e22	0.690846	0.345423	−	0.938447i	$-0.387736\pi$
$421$	1.39887e22	0.690846	0.345423	+	0.938447i	$0.387736\pi$
$422$	2.33393e22	1.12962
$423$	−6.97651e21	−0.330937
$424$	−1.60014e22	−0.743958
$425$	−1.02072e22	−0.465159
$426$	−2.67031e22	−1.19284
$427$	2.19602e21	0.0961612
$428$	−1.69540e22	−0.727779
$429$	7.29372e21	0.306946
$430$	−7.01873e22	−2.89585
$431$	−3.18029e22	−1.28650	−0.643250	−	0.765656i	$-0.722414\pi$
$431$	−3.18029e22	−1.28650	−0.643250	+	0.765656i	$0.722414\pi$
$432$	9.90770e21	0.392972
$433$	−1.40201e22	−0.545259	−0.272630	−	0.962119i	$-0.587893\pi$
$433$	−1.40201e22	−0.545259	−0.272630	+	0.962119i	$0.587893\pi$
$434$	3.46251e21	0.132047
$435$	6.98036e21	0.261047
$436$	1.03265e23	3.78720
$437$	5.29284e22	1.90369
$438$	−5.63098e22	−1.98634
$439$	6.28127e21	0.217320	0.108660	−	0.994079i	$-0.465344\pi$
$439$	6.28127e21	0.217320	0.108660	+	0.994079i	$0.465344\pi$
$440$	5.50254e22	1.86730
$441$	−9.90398e21	−0.329672
$442$	4.07391e22	1.33021
$443$	−2.96942e22	−0.951131	−0.475566	−	0.879680i	$-0.657757\pi$
$443$	−2.96942e22	−0.951131	−0.475566	+	0.879680i	$0.657757\pi$
$444$	5.24422e22	1.64788
$445$	4.09246e22	1.26161
$446$	−7.08955e22	−2.14423
$447$	−1.26695e22	−0.375962
$448$	1.33004e21	0.0387259
$449$	−6.58706e22	−1.88190	−0.940952	−	0.338540i	$-0.890067\pi$
$449$	−6.58706e22	−1.88190	−0.940952	+	0.338540i	$0.890067\pi$
$450$	1.16426e22	0.326394
$451$	1.48981e22	0.409855
$452$	−3.19764e21	−0.0863281
$453$	1.89813e22	0.502911
$454$	−2.10362e22	−0.547007
$455$	4.30259e21	0.109808
$456$	6.13162e22	1.53594
$457$	−4.15015e22	−1.02041	−0.510207	−	0.860052i	$-0.670431\pi$
$457$	−4.15015e22	−1.02041	−0.510207	+	0.860052i	$0.670431\pi$
$458$	−2.38791e22	−0.576317
$459$	−7.02528e21	−0.166439
$460$	−2.11306e23	−4.91440
$461$	5.89682e22	1.34636	0.673178	−	0.739480i	$-0.264929\pi$
$461$	5.89682e22	1.34636	0.673178	+	0.739480i	$0.264929\pi$
$462$	−3.09263e21	−0.0693221
$463$	5.09403e22	1.12104	0.560522	−	0.828139i	$-0.310600\pi$
$463$	5.09403e22	1.12104	0.560522	+	0.828139i	$0.310600\pi$
$464$	−3.44563e22	−0.744501
$465$	−2.33551e22	−0.495487
$466$	9.24049e22	1.92493
$467$	3.80032e22	0.777369	0.388684	−	0.921371i	$-0.372930\pi$
$467$	3.80032e22	0.777369	0.388684	+	0.921371i	$0.372930\pi$
$468$	−3.24477e22	−0.651771
$469$	−2.97036e21	−0.0585922
$470$	1.15706e23	2.24143
$471$	−2.29381e22	−0.436395
$472$	−1.11384e22	−0.208120
$473$	−4.39823e22	−0.807158
$474$	5.51526e22	0.994146
$475$	3.37734e22	0.597970
$476$	−1.20621e22	−0.209780
$477$	−6.06617e21	−0.103636
$478$	1.04889e23	1.76032
$479$	2.68315e22	0.442378	0.221189	−	0.975231i	$-0.429006\pi$
$479$	2.68315e22	0.442378	0.221189	+	0.975231i	$0.429006\pi$
$480$	−5.85494e22	−0.948357
$481$	−6.54741e22	−1.04193
$482$	−4.70030e22	−0.734895
$483$	6.74470e21	0.103612
$484$	−9.26117e22	−1.39791
$485$	−1.18504e23	−1.75764
$486$	8.01319e21	0.116788
$487$	−1.42499e22	−0.204088	−0.102044	−	0.994780i	$-0.532538\pi$
$487$	−1.42499e22	−0.204088	−0.102044	+	0.994780i	$0.532538\pi$
$488$	1.55989e23	2.19546
$489$	−7.55917e21	−0.104556
$490$	1.64258e23	2.23286
$491$	8.22531e22	1.09890	0.549452	−	0.835525i	$-0.314837\pi$
$491$	8.22531e22	1.09890	0.549452	+	0.835525i	$0.314837\pi$
$492$	−6.62775e22	−0.870287
$493$	2.44320e22	0.315327
$494$	−1.34797e23	−1.71001
$495$	2.08603e22	0.260121
$496$	1.15285e23	1.41312
$497$	−9.87103e21	−0.118941
$498$	−6.17896e22	−0.731924
$499$	−1.57611e23	−1.83541	−0.917703	−	0.397267i	$-0.869959\pi$
$499$	−1.57611e23	−1.83541	−0.917703	+	0.397267i	$0.869959\pi$
$500$	1.15855e23	1.32639
$501$	2.55807e22	0.287933
$502$	−1.11545e23	−1.23444
$503$	1.64035e23	1.78488	0.892439	−	0.451169i	$-0.148993\pi$
$503$	1.64035e23	1.78488	0.892439	+	0.451169i	$0.148993\pi$
$504$	7.81356e21	0.0835968
$505$	−1.28950e23	−1.35658
$506$	−1.89627e23	−1.96164
$507$	−1.62443e22	−0.165247
$508$	−2.22192e23	−2.22274
$509$	6.26797e22	0.616632	0.308316	−	0.951284i	$-0.400235\pi$
$509$	6.26797e22	0.616632	0.308316	+	0.951284i	$0.400235\pi$
$510$	1.16515e23	1.12729
$511$	−2.08154e22	−0.198064
$512$	−2.33093e23	−2.18139
$513$	2.32451e22	0.213961
$514$	3.05182e23	2.76295
$515$	4.10387e22	0.365454
$516$	1.95665e23	1.71392
$517$	7.25063e22	0.624750
$518$	2.77619e22	0.235313
$519$	−4.52551e21	−0.0377351
$520$	3.05624e23	2.50703
$521$	2.67297e21	0.0215712	0.0107856	−	0.999942i	$-0.496567\pi$
$521$	2.67297e21	0.0215712	0.0107856	+	0.999942i	$0.496567\pi$
$522$	−2.78677e22	−0.221259
$523$	−1.11499e22	−0.0870975	−0.0435487	−	0.999051i	$-0.513866\pi$
$523$	−1.11499e22	−0.0870975	−0.0435487	+	0.999051i	$0.513866\pi$
$524$	−8.21748e22	−0.631572
$525$	4.30377e21	0.0325458
$526$	−3.50538e23	−2.60829
$527$	−8.17454e22	−0.598512
$528$	−1.02970e23	−0.741860
$529$	2.72505e23	1.93198
$530$	1.00608e23	0.701920
$531$	−4.22258e21	−0.0289918
$532$	3.99108e22	0.269675
$533$	8.27475e22	0.550267
$534$	−1.63383e23	−1.06932
$535$	6.05384e22	0.389963
$536$	−2.10992e23	−1.33772
$537$	−1.03451e22	−0.0645584
$538$	−1.50676e23	−0.925537
$539$	1.02931e23	0.622361
$540$	−9.28016e22	−0.552342
$541$	1.32087e23	0.773895	0.386948	−	0.922102i	$-0.373529\pi$
$541$	1.32087e23	0.773895	0.386948	+	0.922102i	$0.373529\pi$
$542$	−2.56055e23	−1.47686
$543$	−5.68486e22	−0.322791
$544$	−2.04929e23	−1.14555
$545$	−3.68734e23	−2.02929
$546$	−1.71772e22	−0.0930712
$547$	−1.49221e23	−0.796044	−0.398022	−	0.917376i	$-0.630303\pi$
$547$	−1.49221e23	−0.796044	−0.398022	+	0.917376i	$0.630303\pi$
$548$	7.91020e23	4.15482
$549$	5.91359e22	0.305834
$550$	−1.21000e23	−0.616174
$551$	−8.08402e22	−0.405358
$552$	4.79093e23	2.36558
$553$	2.03876e22	0.0991295
$554$	5.70806e23	2.73310
$555$	−1.87258e23	−0.882979
$556$	3.22272e23	1.49654
$557$	−1.16177e23	−0.531314	−0.265657	−	0.964068i	$-0.585589\pi$
$557$	−1.16177e23	−0.531314	−0.265657	+	0.964068i	$0.585589\pi$
$558$	9.32406e22	0.419966
$559$	−2.44288e23	−1.08368
$560$	−6.07423e22	−0.265395
$561$	7.30132e22	0.314208
$562$	7.15591e22	0.303324
$563$	−1.98226e23	−0.827635	−0.413818	−	0.910360i	$-0.635805\pi$
$563$	−1.98226e23	−0.827635	−0.413818	+	0.910360i	$0.635805\pi$
$564$	−3.22561e23	−1.32660
$565$	1.14180e22	0.0462569
$566$	2.75222e23	1.09836
$567$	2.96214e21	0.0116453
$568$	−7.01164e23	−2.71556
$569$	−1.75181e23	−0.668393	−0.334196	−	0.942504i	$-0.608465\pi$
$569$	−1.75181e23	−0.668393	−0.334196	+	0.942504i	$0.608465\pi$
$570$	−3.85522e23	−1.44915
$571$	2.24895e23	0.832862	0.416431	−	0.909167i	$-0.363281\pi$
$571$	2.24895e23	0.832862	0.416431	+	0.909167i	$0.363281\pi$
$572$	3.37227e23	1.23043
$573$	2.00624e23	0.721220
$574$	−3.50861e22	−0.124275
$575$	2.63888e23	0.920965
$576$	3.58161e22	0.123165
$577$	1.19606e23	0.405282	0.202641	−	0.979253i	$-0.435048\pi$
$577$	1.19606e23	0.405282	0.202641	+	0.979253i	$0.435048\pi$
$578$	−1.37424e23	−0.458857
$579$	−5.56158e22	−0.182991
$580$	3.22738e23	1.04644
$581$	−2.28410e22	−0.0729825
$582$	4.73105e23	1.48975
$583$	6.30452e22	0.195645
$584$	−1.47857e24	−4.52202
$585$	1.15863e23	0.349236
$586$	1.79155e23	0.532231
$587$	−3.75879e23	−1.10059	−0.550294	−	0.834971i	$-0.685484\pi$
$587$	−3.75879e23	−1.10059	−0.550294	+	0.834971i	$0.685484\pi$
$588$	−4.57913e23	−1.32152
$589$	2.70478e23	0.769399
$590$	7.00319e22	0.196360
$591$	−6.70365e21	−0.0185275
$592$	9.24338e23	2.51824
$593$	5.09614e23	1.36860	0.684299	−	0.729201i	$-0.260108\pi$
$593$	5.09614e23	1.36860	0.684299	+	0.729201i	$0.260108\pi$
$594$	−8.32804e22	−0.220474
$595$	4.30707e22	0.112406
$596$	−5.85775e23	−1.50709
$597$	8.95053e22	0.227022
$598$	−1.05323e24	−2.63369
$599$	1.79949e23	0.443631	0.221816	−	0.975089i	$-0.428802\pi$
$599$	1.79949e23	0.443631	0.221816	+	0.975089i	$0.428802\pi$
$600$	3.05708e23	0.743055
$601$	−2.48454e23	−0.595406	−0.297703	−	0.954659i	$-0.596220\pi$
$601$	−2.48454e23	−0.595406	−0.297703	+	0.954659i	$0.596220\pi$
$602$	1.03581e23	0.244744
$603$	−7.99878e22	−0.186349
$604$	8.77603e23	2.01597
$605$	3.30693e23	0.749040
$606$	5.14807e23	1.14981
$607$	−6.42239e23	−1.41447	−0.707233	−	0.706980i	$-0.750057\pi$
$607$	−6.42239e23	−1.41447	−0.707233	+	0.706980i	$0.750057\pi$
$608$	6.78066e23	1.47262
$609$	−1.03015e22	−0.0220625
$610$	−9.80774e23	−2.07141
$611$	4.02717e23	0.838783
$612$	−3.24815e23	−0.667190
$613$	−1.05608e23	−0.213936	−0.106968	−	0.994262i	$-0.534114\pi$
$613$	−1.05608e23	−0.213936	−0.106968	+	0.994262i	$0.534114\pi$
$614$	1.59404e24	3.18470
$615$	2.36660e23	0.466323
$616$	−8.12057e22	−0.157816
$617$	−7.88025e23	−1.51048	−0.755242	−	0.655446i	$-0.772481\pi$
$617$	−7.88025e23	−1.51048	−0.755242	+	0.655446i	$0.772481\pi$
$618$	−1.63839e23	−0.309753
$619$	5.08064e23	0.947432	0.473716	−	0.880678i	$-0.342912\pi$
$619$	5.08064e23	0.947432	0.473716	+	0.880678i	$0.342912\pi$
$620$	−1.07983e24	−1.98621
$621$	1.81626e23	0.329533
$622$	6.22690e23	1.11443
$623$	−6.03960e22	−0.106625
$624$	−5.71919e23	−0.996014
$625$	−7.26762e23	−1.24857
$626$	−1.61363e24	−2.73478
$627$	−2.41585e23	−0.403920
$628$	−1.06055e24	−1.74934
$629$	−6.55423e23	−1.06658
$630$	−4.91274e22	−0.0788731
$631$	−6.58521e23	−1.04309	−0.521543	−	0.853225i	$-0.674643\pi$
$631$	−6.58521e23	−1.04309	−0.521543	+	0.853225i	$0.674643\pi$
$632$	1.44818e24	2.26323
$633$	2.32328e23	0.358237
$634$	2.30523e24	3.50716
$635$	7.93394e23	1.19100
$636$	−2.80471e23	−0.415434
$637$	5.71704e23	0.835576
$638$	2.89627e23	0.417698
$639$	−2.65813e23	−0.378285
$640$	5.75653e23	0.808409
$641$	8.38263e23	1.16168	0.580841	−	0.814017i	$-0.302724\pi$
$641$	8.38263e23	1.16168	0.580841	+	0.814017i	$0.302724\pi$
$642$	−2.41687e23	−0.330527
$643$	4.04743e23	0.546243	0.273122	−	0.961980i	$-0.411944\pi$
$643$	4.04743e23	0.546243	0.273122	+	0.961980i	$0.411944\pi$
$644$	3.11843e23	0.415342
$645$	−6.98672e23	−0.918365
$646$	−1.34937e24	−1.75047
$647$	1.11703e24	1.43014	0.715068	−	0.699055i	$-0.246396\pi$
$647$	1.11703e24	1.43014	0.715068	+	0.699055i	$0.246396\pi$
$648$	2.10409e23	0.265874
$649$	4.38849e22	0.0547313
$650$	−6.72063e23	−0.827269
$651$	3.44672e22	0.0418762
$652$	−3.49500e23	−0.419124
$653$	−7.44989e23	−0.881836	−0.440918	−	0.897547i	$-0.645347\pi$
$653$	−7.44989e23	−0.881836	−0.440918	+	0.897547i	$0.645347\pi$
$654$	1.47210e24	1.71999
$655$	2.93426e23	0.338413
$656$	−1.16820e24	−1.32994
$657$	−5.60529e23	−0.629931
$658$	−1.70757e23	−0.189435
$659$	−1.19920e24	−1.31331	−0.656653	−	0.754192i	$-0.728029\pi$
$659$	−1.19920e24	−1.31331	−0.656653	+	0.754192i	$0.728029\pi$
$660$	9.64478e23	1.04272
$661$	−8.62286e22	−0.0920320	−0.0460160	−	0.998941i	$-0.514653\pi$
$661$	−8.62286e22	−0.0920320	−0.0460160	+	0.998941i	$0.514653\pi$
$662$	−1.30752e23	−0.137770
$663$	4.05532e23	0.421852
$664$	−1.62246e24	−1.66627
$665$	−1.42511e23	−0.144499
$666$	7.47590e23	0.748398
$667$	−6.31644e23	−0.624313
$668$	1.18273e24	1.15421
$669$	−7.05721e23	−0.680003
$670$	1.32660e24	1.26213
$671$	−6.14594e23	−0.577360
$672$	8.64064e22	0.0801506
$673$	1.93031e24	1.76807	0.884033	−	0.467425i	$-0.154818\pi$
$673$	1.93031e24	1.76807	0.884033	+	0.467425i	$0.154818\pi$
$674$	−2.89079e24	−2.61461
$675$	1.15895e23	0.103510
$676$	−7.51061e23	−0.662412
$677$	−9.44660e22	−0.0822757	−0.0411379	−	0.999153i	$-0.513098\pi$
$677$	−9.44660e22	−0.0822757	−0.0411379	+	0.999153i	$0.513098\pi$
$678$	−4.55839e22	−0.0392066
$679$	1.74887e23	0.148547
$680$	3.05942e24	2.56634
$681$	−2.09403e23	−0.173473
$682$	−9.69042e23	−0.792821
$683$	1.90689e24	1.54081	0.770404	−	0.637556i	$-0.220055\pi$
$683$	1.90689e24	1.54081	0.770404	+	0.637556i	$0.220055\pi$
$684$	1.07474e24	0.857685
$685$	−2.82453e24	−2.22627
$686$	−4.87513e23	−0.379517
$687$	−2.37702e23	−0.182768
$688$	3.44876e24	2.61916
$689$	3.50168e23	0.262672
$690$	−3.01228e24	−2.23191
$691$	1.44684e24	1.05890	0.529451	−	0.848341i	$-0.322398\pi$
$691$	1.44684e24	1.05890	0.529451	+	0.848341i	$0.322398\pi$
$692$	−2.09238e23	−0.151265
$693$	−3.07853e22	−0.0219842
$694$	−1.25924e23	−0.0888289
$695$	−1.15075e24	−0.801884
$696$	−7.31743e23	−0.503710
$697$	8.28337e23	0.563285
$698$	−2.39765e24	−1.61070
$699$	9.19834e23	0.610455
$700$	1.98986e23	0.130463
$701$	3.28966e23	0.213083	0.106541	−	0.994308i	$-0.466022\pi$
$701$	3.28966e23	0.213083	0.106541	+	0.994308i	$0.466022\pi$
$702$	−4.62559e23	−0.296007
$703$	2.16865e24	1.37110
$704$	−3.72234e23	−0.232514
$705$	1.15178e24	0.710826
$706$	2.25192e24	1.37313
$707$	1.90303e23	0.114651
$708$	−1.95232e23	−0.116217
$709$	−3.08015e24	−1.81167	−0.905833	−	0.423634i	$-0.860754\pi$
$709$	−3.08015e24	−1.81167	−0.905833	+	0.423634i	$0.860754\pi$
$710$	4.40854e24	2.56211
$711$	5.49011e23	0.315275
$712$	−4.29008e24	−2.43437
$713$	2.11337e24	1.18499
$714$	−1.71951e23	−0.0952731
$715$	−1.20415e24	−0.659295
$716$	−4.78307e23	−0.258789
$717$	1.04410e24	0.558252
$718$	−6.59193e24	−3.48301
$719$	−1.08990e24	−0.569103	−0.284551	−	0.958661i	$-0.591845\pi$
$719$	−1.08990e24	−0.569103	−0.284551	+	0.958661i	$0.591845\pi$
$720$	−1.63571e24	−0.844071
$721$	−6.05644e22	−0.0308864
$722$	8.52611e23	0.429719
$723$	−4.67886e23	−0.233058
$724$	−2.62841e24	−1.29394
$725$	−4.03050e23	−0.196104
$726$	−1.32023e24	−0.634874
$727$	1.49760e24	0.711795	0.355897	−	0.934525i	$-0.384175\pi$
$727$	1.49760e24	0.711795	0.355897	+	0.934525i	$0.384175\pi$
$728$	−4.51035e23	−0.211882
$729$	7.97664e22	0.0370370
$730$	9.29643e24	4.26650
$731$	−2.44543e24	−1.10932
$732$	2.73416e24	1.22597
$733$	−9.64969e23	−0.427691	−0.213845	−	0.976868i	$-0.568599\pi$
$733$	−9.64969e23	−0.427691	−0.213845	+	0.976868i	$0.568599\pi$
$734$	7.88279e24	3.45353
$735$	1.63509e24	0.708108
$736$	5.29806e24	2.26806
$737$	8.31306e23	0.351793
$738$	−9.44819e23	−0.395248
$739$	−3.37306e24	−1.39491	−0.697456	−	0.716627i	$-0.745685\pi$
$739$	−3.37306e24	−1.39491	−0.697456	+	0.716627i	$0.745685\pi$
$740$	−8.65791e24	−3.53951
$741$	−1.34182e24	−0.542299
$742$	−1.48476e23	−0.0593230
$743$	−4.24164e24	−1.67544	−0.837719	−	0.546101i	$-0.816111\pi$
$743$	−4.24164e24	−1.67544	−0.837719	+	0.546101i	$0.816111\pi$
$744$	2.44829e24	0.956077
$745$	2.09166e24	0.807537
$746$	4.39862e24	1.67895
$747$	−6.15078e23	−0.232116
$748$	3.37578e24	1.25954
$749$	−8.93417e22	−0.0329578
$750$	1.65158e24	0.602390
$751$	−8.44312e23	−0.304483	−0.152242	−	0.988343i	$-0.548649\pi$
$751$	−8.44312e23	−0.304483	−0.152242	+	0.988343i	$0.548649\pi$
$752$	−5.68540e24	−2.02726
$753$	−1.11037e24	−0.391480
$754$	1.60865e24	0.560798
$755$	−3.13370e24	−1.08021
$756$	1.36955e23	0.0466813
$757$	3.10995e24	1.04819	0.524093	−	0.851661i	$-0.324404\pi$
$757$	3.10995e24	1.04819	0.524093	+	0.851661i	$0.324404\pi$
$758$	−8.61398e24	−2.87089
$759$	−1.88762e24	−0.622098
$760$	−1.01230e25	−3.29907
$761$	5.22689e24	1.68451	0.842256	−	0.539078i	$-0.181227\pi$
$761$	5.22689e24	1.68451	0.842256	+	0.539078i	$0.181227\pi$
$762$	−3.16747e24	−1.00947
$763$	5.44173e23	0.171506
$764$	9.27588e24	2.89109
$765$	1.15984e24	0.357498
$766$	4.97811e22	0.0151747
$767$	2.43747e23	0.0734817
$768$	−3.01369e24	−0.898522
$769$	−5.37000e23	−0.158343	−0.0791717	−	0.996861i	$-0.525228\pi$
$769$	−5.37000e23	−0.158343	−0.0791717	+	0.996861i	$0.525228\pi$
$770$	5.10577e23	0.148898
$771$	3.03790e24	0.876217
$772$	−2.57141e24	−0.733540
$773$	−1.13193e23	−0.0319370	−0.0159685	−	0.999872i	$-0.505083\pi$
$773$	−1.13193e23	−0.0319370	−0.0159685	+	0.999872i	$0.505083\pi$
$774$	2.78931e24	0.778392
$775$	1.34854e24	0.372219
$776$	1.24227e25	3.39149
$777$	2.76353e23	0.0746252
$778$	2.57274e24	0.687177
$779$	−2.74079e24	−0.724113
$780$	5.35694e24	1.39995
$781$	2.76257e24	0.714135
$782$	−1.05433e25	−2.69599
$783$	−2.77406e23	−0.0701682
$784$	−8.07110e24	−2.01951
$785$	3.78695e24	0.937341
$786$	−1.17144e24	−0.286833
$787$	4.40987e24	1.06817	0.534085	−	0.845431i	$-0.320656\pi$
$787$	4.40987e24	1.06817	0.534085	+	0.845431i	$0.320656\pi$
$788$	−3.09945e23	−0.0742696
$789$	−3.48939e24	−0.827171
$790$	−9.10539e24	−2.13535
$791$	−1.68505e22	−0.00390942
$792$	−2.18676e24	−0.501922
$793$	−3.41360e24	−0.775158
$794$	4.28660e24	0.963028
$795$	1.00149e24	0.222601
$796$	4.13830e24	0.910040
$797$	1.93825e24	0.421710	0.210855	−	0.977517i	$-0.432375\pi$
$797$	1.93825e24	0.421710	0.210855	+	0.977517i	$0.432375\pi$
$798$	5.68949e23	0.122475
$799$	4.03137e24	0.858627
$800$	3.38067e24	0.712423
$801$	−1.62638e24	−0.339114
$802$	1.40018e24	0.288869
$803$	5.82553e24	1.18920
$804$	−3.69825e24	−0.746999
$805$	−1.11351e24	−0.222551
$806$	−5.38229e24	−1.06443
$807$	−1.49988e24	−0.293517
$808$	1.35177e25	2.61761
$809$	−5.28909e24	−1.01349	−0.506744	−	0.862096i	$-0.669151\pi$
$809$	−5.28909e24	−1.01349	−0.506744	+	0.862096i	$0.669151\pi$
$810$	−1.32293e24	−0.250851
$811$	−9.67847e24	−1.81606	−0.908028	−	0.418909i	$-0.862413\pi$
$811$	−9.67847e24	−1.81606	−0.908028	+	0.418909i	$0.862413\pi$
$812$	−4.76293e23	−0.0884398
$813$	−2.54887e24	−0.468358
$814$	−7.76964e24	−1.41284
$815$	1.24798e24	0.224578
$816$	−5.72515e24	−1.01958
$817$	8.09138e24	1.42605
$818$	−1.09834e25	−1.91573
$819$	−1.70989e23	−0.0295158
$820$	1.09420e25	1.86931
$821$	−1.86577e24	−0.315458	−0.157729	−	0.987482i	$-0.550417\pi$
$821$	−1.86577e24	−0.315458	−0.157729	+	0.987482i	$0.550417\pi$
$822$	1.12764e25	1.88695
$823$	−5.64893e23	−0.0935552	−0.0467776	−	0.998905i	$-0.514895\pi$
$823$	−5.64893e23	−0.0935552	−0.0467776	+	0.998905i	$0.514895\pi$
$824$	−4.30204e24	−0.705169
$825$	−1.20448e24	−0.195408
$826$	−1.03352e23	−0.0165954
$827$	−3.63429e24	−0.577595	−0.288797	−	0.957390i	$-0.593255\pi$
$827$	−3.63429e24	−0.577595	−0.288797	+	0.957390i	$0.593255\pi$
$828$	8.39749e24	1.32097
$829$	−1.24734e25	−1.94210	−0.971052	−	0.238870i	$-0.923223\pi$
$829$	−1.24734e25	−1.94210	−0.971052	+	0.238870i	$0.923223\pi$
$830$	1.02011e25	1.57211
$831$	5.68203e24	0.866751
$832$	−2.06748e24	−0.312171
$833$	5.72300e24	0.855344
$834$	4.59416e24	0.679664
$835$	−4.22323e24	−0.618458
$836$	−1.11697e25	−1.61916
$837$	9.28153e23	0.133184
$838$	1.31991e25	1.87487
$839$	−1.32854e24	−0.186809	−0.0934045	−	0.995628i	$-0.529775\pi$
$839$	−1.32854e24	−0.186809	−0.0934045	+	0.995628i	$0.529775\pi$
$840$	−1.28998e24	−0.179559
$841$	−6.29241e24	−0.867063
$842$	9.22007e24	1.25771
$843$	7.12327e23	0.0961934
$844$	1.07417e25	1.43603
$845$	2.68185e24	0.354938
$846$	−4.59827e24	−0.602485
$847$	−4.88033e23	−0.0633053
$848$	−4.94353e24	−0.634853
$849$	2.73967e24	0.348324
$850$	−6.72764e24	−0.846840
$851$	1.69447e25	2.11171
$852$	−1.22899e25	−1.51640
$853$	−5.83602e23	−0.0712935	−0.0356468	−	0.999364i	$-0.511349\pi$
$853$	−5.83602e23	−0.0712935	−0.0356468	+	0.999364i	$0.511349\pi$
$854$	1.44741e24	0.175065
$855$	−3.83764e24	−0.459571
$856$	−6.34617e24	−0.752462
$857$	5.11451e24	0.600437	0.300218	−	0.953871i	$-0.402940\pi$
$857$	5.11451e24	0.600437	0.300218	+	0.953871i	$0.402940\pi$
$858$	4.80734e24	0.558808
$859$	2.96778e24	0.341578	0.170789	−	0.985308i	$-0.445368\pi$
$859$	2.96778e24	0.341578	0.170789	+	0.985308i	$0.445368\pi$
$860$	−3.23032e25	−3.68137
$861$	−3.49260e23	−0.0394114
$862$	−2.09615e25	−2.34213
$863$	−8.25654e24	−0.913495	−0.456748	−	0.889596i	$-0.650986\pi$
$863$	−8.25654e24	−0.913495	−0.456748	+	0.889596i	$0.650986\pi$
$864$	2.32681e24	0.254914
$865$	7.47136e23	0.0810519
$866$	−9.24071e24	−0.992667
$867$	−1.36798e24	−0.145518
$868$	1.59360e24	0.167865
$869$	−5.70582e24	−0.595182
$870$	4.60080e24	0.475247
$871$	4.61727e24	0.472314
$872$	3.86540e25	3.91565
$873$	4.70947e24	0.472445
$874$	3.48854e25	3.46575
$875$	6.10519e23	0.0600662
$876$	−2.59162e25	−2.52514
$877$	−2.48925e24	−0.240199	−0.120100	−	0.992762i	$-0.538321\pi$
$877$	−2.48925e24	−0.240199	−0.120100	+	0.992762i	$0.538321\pi$
$878$	4.14002e24	0.395639
$879$	1.78338e24	0.168787
$880$	1.69998e25	1.59346
$881$	−1.53069e25	−1.42099	−0.710495	−	0.703702i	$-0.751529\pi$
$881$	−1.53069e25	−1.42099	−0.710495	+	0.703702i	$0.751529\pi$
$882$	−6.52778e24	−0.600181
$883$	1.37054e25	1.24803	0.624014	−	0.781413i	$-0.285501\pi$
$883$	1.37054e25	1.24803	0.624014	+	0.781413i	$0.285501\pi$
$884$	1.87499e25	1.69104
$885$	6.97125e23	0.0622720
$886$	−1.95717e25	−1.73157
$887$	−1.43271e24	−0.125548	−0.0627739	−	0.998028i	$-0.519995\pi$
$887$	−1.43271e24	−0.125548	−0.0627739	+	0.998028i	$0.519995\pi$
$888$	1.96300e25	1.70377
$889$	−1.17088e24	−0.100658
$890$	2.69737e25	2.29681
$891$	−8.29006e23	−0.0699193
$892$	−3.26292e25	−2.72587
$893$	−1.33389e25	−1.10378
$894$	−8.35052e24	−0.684455
$895$	1.70792e24	0.138666
$896$	−8.49541e23	−0.0683229
$897$	−1.04843e25	−0.835223
$898$	−4.34157e25	−3.42608
$899$	−3.22786e24	−0.252324
$900$	5.35841e24	0.414930
$901$	3.50533e24	0.268886
$902$	9.81943e24	0.746157
$903$	1.03109e24	0.0776159
$904$	−1.19693e24	−0.0892561
$905$	9.38539e24	0.693329
$906$	1.25107e25	0.915569
$907$	2.00624e25	1.45453	0.727263	−	0.686359i	$-0.240792\pi$
$907$	2.00624e25	1.45453	0.727263	+	0.686359i	$0.240792\pi$
$908$	−9.68177e24	−0.695385
$909$	5.12459e24	0.364641
$910$	2.83586e24	0.199909
$911$	7.29637e24	0.509566	0.254783	−	0.966998i	$-0.417996\pi$
$911$	7.29637e24	0.509566	0.254783	+	0.966998i	$0.417996\pi$
$912$	1.89433e25	1.31069
$913$	6.39245e24	0.438193
$914$	−2.73539e25	−1.85771
$915$	−9.76300e24	−0.656907
$916$	−1.09902e25	−0.732645
$917$	−4.33034e23	−0.0286011
$918$	−4.63041e24	−0.303010
$919$	4.06033e24	0.263257	0.131628	−	0.991299i	$-0.457979\pi$
$919$	4.06033e24	0.263257	0.131628	+	0.991299i	$0.457979\pi$
$920$	−7.90956e25	−5.08108
$921$	1.58677e25	1.00997
$922$	3.88663e25	2.45110
$923$	1.53440e25	0.958791
$924$	−1.42336e24	−0.0881260
$925$	1.08124e25	0.663310
$926$	3.35751e25	2.04091
$927$	−1.63092e24	−0.0982322
$928$	−8.09199e24	−0.482945
$929$	−2.87442e25	−1.69987	−0.849936	−	0.526886i	$-0.823359\pi$
$929$	−2.87442e25	−1.69987	−0.849936	+	0.526886i	$0.823359\pi$
$930$	−1.53935e25	−0.902054
$931$	−1.89361e25	−1.09956
$932$	4.25287e25	2.44707
$933$	6.19850e24	0.353421
$934$	2.50482e25	1.41523
$935$	−1.20541e25	−0.674893
$936$	−1.21458e25	−0.673876
$937$	−9.52788e24	−0.523853	−0.261927	−	0.965088i	$-0.584358\pi$
$937$	−9.52788e24	−0.523853	−0.261927	+	0.965088i	$0.584358\pi$
$938$	−1.95778e24	−0.106670
$939$	−1.60627e25	−0.867283
$940$	5.32529e25	2.84942
$941$	4.74128e24	0.251411	0.125705	−	0.992068i	$-0.459881\pi$
$941$	4.74128e24	0.251411	0.125705	+	0.992068i	$0.459881\pi$
$942$	−1.51186e25	−0.794475
$943$	−2.14151e25	−1.11525
$944$	−3.44113e24	−0.177598
$945$	−4.89033e23	−0.0250131
$946$	−2.89890e25	−1.46946
$947$	−1.05058e25	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$947$	−1.05058e25	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$948$	2.53836e25	1.26381
$949$	3.23564e25	1.59660
$950$	2.22603e25	1.08863
$951$	2.29471e25	1.11223
$952$	−4.51505e24	−0.216895
$953$	−2.86764e24	−0.136532	−0.0682660	−	0.997667i	$-0.521747\pi$
$953$	−2.86764e24	−0.136532	−0.0682660	+	0.997667i	$0.521747\pi$
$954$	−3.99825e24	−0.188673
$955$	−3.31218e25	−1.54912
$956$	4.82743e25	2.23781
$957$	2.88305e24	0.132465
$958$	1.76848e25	0.805367
$959$	4.16841e24	0.188153
$960$	−5.91304e24	−0.264549
$961$	−1.17502e25	−0.521072
$962$	−4.31544e25	−1.89687
$963$	−2.40585e24	−0.104820
$964$	−2.16328e25	−0.934239
$965$	9.18186e24	0.393050
$966$	4.44547e24	0.188631
$967$	−3.11121e25	−1.30859	−0.654297	−	0.756238i	$-0.727035\pi$
$967$	−3.11121e25	−1.30859	−0.654297	+	0.756238i	$0.727035\pi$
$968$	−3.46662e25	−1.44533
$969$	−1.34322e25	−0.555128
$970$	−7.81070e25	−3.19985
$971$	1.46309e25	0.594165	0.297083	−	0.954852i	$-0.403986\pi$
$971$	1.46309e25	0.594165	0.297083	+	0.954852i	$0.403986\pi$
$972$	3.68802e24	0.148467
$973$	1.69827e24	0.0677715
$974$	−9.39223e24	−0.371550
$975$	−6.68998e24	−0.262353
$976$	4.81919e25	1.87349
$977$	−3.44513e25	−1.32771	−0.663853	−	0.747863i	$-0.731080\pi$
$977$	−3.44513e25	−1.32771	−0.663853	+	0.747863i	$0.731080\pi$
$978$	−4.98230e24	−0.190348
$979$	1.69028e25	0.640187
$980$	7.55988e25	2.83853
$981$	1.46538e25	0.545462
$982$	5.42135e25	2.00060
$983$	4.21774e25	1.54303	0.771515	−	0.636211i	$-0.219499\pi$
$983$	4.21774e25	1.54303	0.771515	+	0.636211i	$0.219499\pi$
$984$	−2.48088e25	−0.899804
$985$	1.10674e24	0.0397957
$986$	1.61033e25	0.574065
$987$	−1.69979e24	−0.0600756
$988$	−6.20392e25	−2.17386
$989$	6.32219e25	2.19634
$990$	1.37491e25	0.473561
$991$	−2.46032e25	−0.840169	−0.420084	−	0.907485i	$-0.637999\pi$
$991$	−2.46032e25	−0.840169	−0.420084	+	0.907485i	$0.637999\pi$
$992$	2.70744e25	0.916664
$993$	−1.30156e24	−0.0436912
$994$	−6.50606e24	−0.216538
$995$	−1.47768e25	−0.487624
$996$	−2.84382e25	−0.930462
$997$	5.58760e25	1.81266	0.906330	−	0.422571i	$-0.138872\pi$
$997$	5.58760e25	1.81266	0.906330	+	0.422571i	$0.138872\pi$
$998$	−1.03883e26	−3.34143
$999$	7.44180e24	0.237340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.18.a.b.1.2	✓	2
3.2	odd	2		9.18.a.c.1.1		2
4.3	odd	2		48.18.a.h.1.1		2
5.2	odd	4		75.18.b.c.49.4		4
5.3	odd	4		75.18.b.c.49.1		4
5.4	even	2		75.18.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.18.a.b.1.2	✓	2	1.1	even	1	trivial
9.18.a.c.1.1		2	3.2	odd	2
48.18.a.h.1.1		2	4.3	odd	2
75.18.a.b.1.1		2	5.4	even	2
75.18.b.c.49.1		4	5.3	odd	4
75.18.b.c.49.4		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+659.106 q^{2} +6561.00 q^{3} +303349. q^{4} -1.08318e6 q^{5} +4.32440e6 q^{6} +1.59855e6 q^{7} +1.13549e8 q^{8} +4.30467e7 q^{9} +O(q^{10})\)	\(q+659.106 q^{2} +6561.00 q^{3} +303349. q^{4} -1.08318e6 q^{5} +4.32440e6 q^{6} +1.59855e6 q^{7} +1.13549e8 q^{8} +4.30467e7 q^{9} -7.13934e8 q^{10} -4.47381e8 q^{11} +1.99027e9 q^{12} -2.48486e9 q^{13} +1.05361e9 q^{14} -7.10677e9 q^{15} +3.50803e10 q^{16} -2.48745e10 q^{17} +2.83724e10 q^{18} +8.23042e10 q^{19} -3.28583e11 q^{20} +1.04881e10 q^{21} -2.94872e11 q^{22} +6.43083e11 q^{23} +7.44995e11 q^{24} +4.10349e11 q^{25} -1.63779e12 q^{26} +2.82430e11 q^{27} +4.84918e11 q^{28} -9.82213e11 q^{29} -4.68412e12 q^{30} +3.28632e12 q^{31} +8.23853e12 q^{32} -2.93527e12 q^{33} -1.63949e13 q^{34} -1.73152e12 q^{35} +1.30582e13 q^{36} +2.63492e13 q^{37} +5.42472e13 q^{38} -1.63032e13 q^{39} -1.22994e14 q^{40} -3.33007e13 q^{41} +6.91276e12 q^{42} +9.83107e13 q^{43} -1.35713e14 q^{44} -4.66275e13 q^{45} +4.23860e14 q^{46} -1.62068e14 q^{47} +2.30162e14 q^{48} -2.30075e14 q^{49} +2.70463e14 q^{50} -1.63201e14 q^{51} -7.53780e14 q^{52} -1.40921e14 q^{53} +1.86151e14 q^{54} +4.84596e14 q^{55} +1.81514e14 q^{56} +5.39998e14 q^{57} -6.47383e14 q^{58} -9.80930e13 q^{59} -2.15583e15 q^{60} +1.37376e15 q^{61} +2.16603e15 q^{62} +6.88123e13 q^{63} +8.32030e14 q^{64} +2.69156e15 q^{65} -1.93465e15 q^{66} -1.85816e15 q^{67} -7.54565e15 q^{68} +4.21927e15 q^{69} -1.14126e15 q^{70} -6.17500e15 q^{71} +4.88791e15 q^{72} -1.30214e16 q^{73} +1.73670e16 q^{74} +2.69230e15 q^{75} +2.49669e16 q^{76} -7.15160e14 q^{77} -1.07455e16 q^{78} +1.27538e16 q^{79} -3.79984e16 q^{80} +1.85302e15 q^{81} -2.19487e16 q^{82} -1.42886e16 q^{83} +3.18155e15 q^{84} +2.69436e16 q^{85} +6.47972e16 q^{86} -6.44430e15 q^{87} -5.07996e16 q^{88} -3.77818e16 q^{89} -3.07325e16 q^{90} -3.97217e15 q^{91} +1.95079e17 q^{92} +2.15615e16 q^{93} -1.06820e17 q^{94} -8.91506e16 q^{95} +5.40530e16 q^{96} +1.09404e17 q^{97} -1.51644e17 q^{98} -1.92583e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 594 q^{2} + 13122 q^{3} + 176516 q^{4} + 382860 q^{5} + 3897234 q^{6} + 24471568 q^{7} + 130340232 q^{8} + 86093442 q^{9}+O(q^{10}) \) 2 * q + 594 * q^2 + 13122 * q^3 + 176516 * q^4 + 382860 * q^5 + 3897234 * q^6 + 24471568 * q^7 + 130340232 * q^8 + 86093442 * q^9	\( 2 q + 594 q^{2} + 13122 q^{3} + 176516 q^{4} + 382860 q^{5} + 3897234 q^{6} + 24471568 q^{7} + 130340232 q^{8} + 86093442 q^{9} - 809382420 q^{10} - 987553512 q^{11} + 1158121476 q^{12} - 2519398244 q^{13} - 435565296 q^{14} + 2511944460 q^{15} + 50611323920 q^{16} - 34313126364 q^{17} + 25569752274 q^{18} + 80053542184 q^{19} - 514526095080 q^{20} + 160557957648 q^{21} - 259702850088 q^{22} + 297228742704 q^{23} + 855162262152 q^{24} + 1796695260350 q^{25} - 1635537155076 q^{26} + 564859072962 q^{27} - 2416139220704 q^{28} - 470374069572 q^{29} - 5310358057620 q^{30} + 3400754454592 q^{31} + 5026499631648 q^{32} - 6479338592232 q^{33} - 15780403538748 q^{34} + 31801338154080 q^{35} + 7598435004036 q^{36} + 10652012180428 q^{37} + 54393717084264 q^{38} - 16529771878884 q^{39} - 98377731579600 q^{40} - 113376799448748 q^{41} - 2857743907056 q^{42} + 61637031489880 q^{43} - 67200775334352 q^{44} + 16480867602060 q^{45} + 446377123388592 q^{46} - 279645641926560 q^{47} + 332060896239120 q^{48} + 60469362475890 q^{49} + 180203550461550 q^{50} - 225128422074204 q^{51} - 749398920924104 q^{52} - 530964038611476 q^{53} + 167763144669714 q^{54} - 307321280077680 q^{55} + 565580346246720 q^{56} + 525231290269224 q^{57} - 680706445363812 q^{58} + 17\!\cdots\!56 q^{59}+ \cdots - 42\!\cdots\!52 q^{99}+O(q^{100}) \) 2 * q + 594 * q^2 + 13122 * q^3 + 176516 * q^4 + 382860 * q^5 + 3897234 * q^6 + 24471568 * q^7 + 130340232 * q^8 + 86093442 * q^9 - 809382420 * q^10 - 987553512 * q^11 + 1158121476 * q^12 - 2519398244 * q^13 - 435565296 * q^14 + 2511944460 * q^15 + 50611323920 * q^16 - 34313126364 * q^17 + 25569752274 * q^18 + 80053542184 * q^19 - 514526095080 * q^20 + 160557957648 * q^21 - 259702850088 * q^22 + 297228742704 * q^23 + 855162262152 * q^24 + 1796695260350 * q^25 - 1635537155076 * q^26 + 564859072962 * q^27 - 2416139220704 * q^28 - 470374069572 * q^29 - 5310358057620 * q^30 + 3400754454592 * q^31 + 5026499631648 * q^32 - 6479338592232 * q^33 - 15780403538748 * q^34 + 31801338154080 * q^35 + 7598435004036 * q^36 + 10652012180428 * q^37 + 54393717084264 * q^38 - 16529771878884 * q^39 - 98377731579600 * q^40 - 113376799448748 * q^41 - 2857743907056 * q^42 + 61637031489880 * q^43 - 67200775334352 * q^44 + 16480867602060 * q^45 + 446377123388592 * q^46 - 279645641926560 * q^47 + 332060896239120 * q^48 + 60469362475890 * q^49 + 180203550461550 * q^50 - 225128422074204 * q^51 - 749398920924104 * q^52 - 530964038611476 * q^53 + 167763144669714 * q^54 - 307321280077680 * q^55 + 565580346246720 * q^56 + 525231290269224 * q^57 - 680706445363812 * q^58 + 1727524231086456 * q^59 - 3375805709819880 * q^60 + 2784287656027900 * q^61 + 2158582756499136 * q^62 + 1053420760128528 * q^63 - 994533569423296 * q^64 + 2640922679811240 * q^65 - 1703910399427368 * q^66 - 3329301676696184 * q^67 - 6348514481766072 * q^68 + 1950117780880944 * q^69 - 3324459101139360 * q^70 - 13489402206504816 * q^71 + 5610719601979272 * q^72 + 436589918136724 * q^73 + 18388942762073004 * q^74 + 11788117603156350 * q^75 + 25252347669111376 * q^76 - 13070541011736384 * q^77 - 10730759274453636 * q^78 + 4376041565214880 * q^79 - 15229171694708640 * q^80 + 3706040377703682 * q^81 - 16735234653750924 * q^82 - 39886442265612888 * q^83 - 15852289427038944 * q^84 + 13106143850552280 * q^85 + 67184884152159768 * q^86 - 3086124270461892 * q^87 - 59869809989481888 * q^88 + 6972184096107444 * q^89 - 34841259216044820 * q^90 - 4762196572326688 * q^91 + 238944325336039008 * q^92 + 22312349976578112 * q^93 - 99165314702307744 * q^94 - 92450059415485200 * q^95 + 32978864083242528 * q^96 + 183569555712460996 * q^97 - 170560284296616126 * q^98 - 42510940503634152 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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