LMFDB - Embedded newform 3.28.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,28,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, 28, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 28 $
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:	$13.8556672451$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{30001}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 7500 $ x^2 - x - 7500
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$87.1040$ 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)

$f(q)$	$=$	$q-121.102 q^{2} -1.59432e6 q^{3} -1.34203e8 q^{4} -1.07803e9 q^{5} +1.93076e8 q^{6} -1.13904e10 q^{7} +3.25063e10 q^{8} +2.54187e12 q^{9} +O(q^{10})$	\(q-121.102 q^{2} -1.59432e6 q^{3} -1.34203e8 q^{4} -1.07803e9 q^{5} +1.93076e8 q^{6} -1.13904e10 q^{7} +3.25063e10 q^{8} +2.54187e12 q^{9} +1.30551e11 q^{10} -5.05749e13 q^{11} +2.13963e14 q^{12} +1.21304e15 q^{13} +1.37940e12 q^{14} +1.71872e15 q^{15} +1.80085e16 q^{16} +7.00452e16 q^{17} -3.07825e14 q^{18} +2.51027e16 q^{19} +1.44674e17 q^{20} +1.81600e16 q^{21} +6.12472e15 q^{22} -3.40370e18 q^{23} -5.18255e16 q^{24} -6.28844e18 q^{25} -1.46901e17 q^{26} -4.05256e18 q^{27} +1.52863e18 q^{28} +5.74556e19 q^{29} -2.08141e17 q^{30} +1.08167e20 q^{31} -6.54378e18 q^{32} +8.06328e19 q^{33} -8.48261e18 q^{34} +1.22791e19 q^{35} -3.41126e20 q^{36} -1.90073e21 q^{37} -3.03999e18 q^{38} -1.93398e21 q^{39} -3.50426e19 q^{40} +6.66148e21 q^{41} -2.19921e18 q^{42} +1.03265e21 q^{43} +6.78731e21 q^{44} -2.74020e21 q^{45} +4.12194e20 q^{46} +6.43133e22 q^{47} -2.87114e22 q^{48} -6.55826e22 q^{49} +7.61542e20 q^{50} -1.11675e23 q^{51} -1.62794e23 q^{52} +2.13714e23 q^{53} +4.90772e20 q^{54} +5.45211e22 q^{55} -3.70259e20 q^{56} -4.00218e22 q^{57} -6.95799e21 q^{58} +1.07026e24 q^{59} -2.30658e23 q^{60} +8.16628e23 q^{61} -1.30992e22 q^{62} -2.89528e22 q^{63} -2.41627e24 q^{64} -1.30769e24 q^{65} -9.76479e21 q^{66} +1.68630e24 q^{67} -9.40028e24 q^{68} +5.42659e24 q^{69} -1.48703e21 q^{70} -3.18547e24 q^{71} +8.26266e22 q^{72} +2.09853e25 q^{73} +2.30183e23 q^{74} +1.00258e25 q^{75} -3.36886e24 q^{76} +5.76068e23 q^{77} +2.34208e23 q^{78} -8.88148e22 q^{79} -1.94136e25 q^{80} +6.46108e24 q^{81} -8.06718e23 q^{82} -6.50402e25 q^{83} -2.43712e24 q^{84} -7.55105e25 q^{85} -1.25056e23 q^{86} -9.16028e25 q^{87} -1.64400e24 q^{88} +3.38617e26 q^{89} +3.31843e23 q^{90} -1.38170e25 q^{91} +4.56787e26 q^{92} -1.72453e26 q^{93} -7.78847e24 q^{94} -2.70614e25 q^{95} +1.04329e25 q^{96} -4.16124e26 q^{97} +7.94218e24 q^{98} -1.28555e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9}+O(q^{10}) $ 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9	$ 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9} - 14929666656300 q^{10} + 75762335668248 q^{11} - 323015968377612 q^{12} - 103021079177588 q^{13} + 82\!\cdots\!36 q^{14}+ \cdots + 19\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9 - 14929666656300 * q^10 + 75762335668248 * q^11 - 323015968377612 * q^12 - 103021079177588 * q^13 + 8271467686583136 * q^14 + 2825054421990300 * q^15 + 68227529433700880 * q^16 + 34691611579147908 * q^17 + 54858548306996478 * q^18 + 111620476558642216 * q^19 - 89042670767082600 * q^20 - 589365730506544992 * q^21 + 2748035308851015336 * q^22 - 2892743075819387952 * q^23 - 7061766547600378152 * q^24 - 13257495997920171250 * q^25 - 28709486590882989996 * q^26 - 8105110306037952534 * q^27 + 129870778968981827392 * q^28 + 29959552473322806972 * q^29 + 23802710932472184900 * q^30 + 10367463257055494032 * q^31 + 493234742263884106464 * q^32 - 120789634289608156104 * q^33 - 775764702062031404772 * q^34 - 252142979584030920000 * q^35 + 514991787751699496676 * q^36 - 3703660908819524869316 * q^37 + 1874664150379356981528 * q^38 + 164248876017649632924 * q^39 - 3086079750063749300400 * q^40 + 1481814928479478034772 * q^41 - 13187391176476285136928 * q^42 + 9778778623457380249240 * q^43 + 49338574711945832880432 * q^44 - 4504049241230841066900 * q^45 + 11501496706538201034672 * q^46 + 89494998518809740323520 * q^47 - 108776719409326288104240 * q^48 + 13908377820361409575890 * q^49 - 150488580768890263638750 * q^50 - 55309634247701830126284 * q^51 - 606051653487262224622952 * q^52 + 425671275824601813476748 * q^53 - 87462245312455545794394 * q^54 - 33146870181194328159600 * q^55 + 1675060131754321848708480 * q^56 - 177959093048404133739768 * q^57 - 603708195922408484547804 * q^58 + 369418769643380130292824 * q^59 + 141962777985387432079800 * q^60 + 925133397428892745249420 * q^61 - 2135654804561872705821072 * q^62 + 939639339558386331280416 * q^63 + 1690192763441891790257216 * q^64 - 394447136075147294825400 * q^65 - 4381255897713277323537528 * q^66 + 4151706674555213948132968 * q^67 - 21307603540300350668680824 * q^68 + 4611966818869594057796496 * q^69 - 5740267152557252353752000 * q^70 + 9760455855870867537668784 * q^71 + 11258736827469877696431096 * q^72 + 28449956347640075157409588 * q^73 - 38898941191404112127623644 * q^74 + 21136730791892081187813750 * q^75 + 25770925690602426011538256 * q^76 + 48717589762471785388668288 * q^77 + 45772194790036341259392708 * q^78 - 49553221898675501744231120 * q^79 - 54261621238075868678378400 * q^80 + 12922163778453346597864482 * q^81 - 113221448313178537381548852 * q^82 - 120473408203228735926347736 * q^83 - 207055969938164013993095616 * q^84 - 50977978054175038499879400 * q^85 + 189693121470759531169760808 * q^86 - 47765203577925437580019956 * q^87 + 553837409674913803181095584 * q^88 + 205644052209697133056985556 * q^89 - 37949209501991851246322700 * q^90 - 515309018103795393250147648 * q^91 + 628879743331458256476717984 * q^92 - 16529085122378486411580336 * q^93 + 538732610344725656813388864 * q^94 - 87097784513216888583651600 * q^95 - 786375493990382500270003872 * q^96 - 1478339006400409594836427772 * q^97 + 1733143443943237696043598078 * q^98 + 192577692109510944264197592 * 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 $

$2$	−121.102	−0.0104531	−0.00522656	−	0.999986i	$-0.501664\pi$
$2$	−121.102	−0.0104531	−0.00522656	+	0.999986i	$0.501664\pi$
$3$	−1.59432e6	−0.577350
$3$	−1.59432e6	−0.577350
$4$	−1.34203e8	−0.999891
$5$	−1.07803e9	−0.394943	−0.197471	−	0.980309i	$-0.563273\pi$
$5$	−1.07803e9	−0.394943	−0.197471	+	0.980309i	$0.563273\pi$
$6$	1.93076e8	0.00603512
$7$	−1.13904e10	−0.0444340	−0.0222170	−	0.999753i	$-0.507072\pi$
$7$	−1.13904e10	−0.0444340	−0.0222170	+	0.999753i	$0.507072\pi$
$8$	3.25063e10	0.0209051
$9$	2.54187e12	0.333333
$10$	1.30551e11	0.00412839
$11$	−5.05749e13	−0.441707	−0.220853	−	0.975307i	$-0.570884\pi$
$11$	−5.05749e13	−0.441707	−0.220853	+	0.975307i	$0.570884\pi$
$12$	2.13963e14	0.577287
$13$	1.21304e15	1.11081	0.555405	−	0.831580i	$-0.312563\pi$
$13$	1.21304e15	1.11081	0.555405	+	0.831580i	$0.312563\pi$
$14$	1.37940e12	0.000464474 0
$15$	1.71872e15	0.228020
$16$	1.80085e16	0.999672
$17$	7.00452e16	1.71521	0.857606	−	0.514307i	$-0.171951\pi$
$17$	7.00452e16	1.71521	0.857606	+	0.514307i	$0.171951\pi$
$18$	−3.07825e14	−0.00348438
$19$	2.51027e16	0.136945	0.0684726	−	0.997653i	$-0.478187\pi$
$19$	2.51027e16	0.136945	0.0684726	+	0.997653i	$0.478187\pi$
$20$	1.44674e17	0.394900
$21$	1.81600e16	0.0256540
$22$	6.12472e15	0.00461722
$23$	−3.40370e18	−1.40807	−0.704037	−	0.710164i	$-0.748621\pi$
$23$	−3.40370e18	−1.40807	−0.704037	+	0.710164i	$0.748621\pi$
$24$	−5.18255e16	−0.0120696
$25$	−6.28844e18	−0.844020
$26$	−1.46901e17	−0.0116114
$27$	−4.05256e18	−0.192450
$28$	1.52863e18	0.0444291
$29$	5.74556e19	1.03982	0.519912	−	0.854220i	$-0.325965\pi$
$29$	5.74556e19	1.03982	0.519912	+	0.854220i	$0.325965\pi$
$30$	−2.08141e17	−0.00238353
$31$	1.08167e20	0.795632	0.397816	−	0.917465i	$-0.369768\pi$
$31$	1.08167e20	0.795632	0.397816	+	0.917465i	$0.369768\pi$
$32$	−6.54378e18	−0.0313548
$33$	8.06328e19	0.255020
$34$	−8.48261e18	−0.0179293
$35$	1.22791e19	0.0175489
$36$	−3.41126e20	−0.333297
$37$	−1.90073e21	−1.28292	−0.641458	−	0.767159i	$-0.721670\pi$
$37$	−1.90073e21	−1.28292	−0.641458	+	0.767159i	$0.721670\pi$
$38$	−3.03999e18	−0.00143151
$39$	−1.93398e21	−0.641326
$40$	−3.50426e19	−0.00825632
$41$	6.66148e21	1.12458	0.562288	−	0.826942i	$-0.309921\pi$
$41$	6.66148e21	1.12458	0.562288	+	0.826942i	$0.309921\pi$
$42$	−2.19921e18	−0.000268164 0
$43$	1.03265e21	0.0916490	0.0458245	−	0.998950i	$-0.485408\pi$
$43$	1.03265e21	0.0916490	0.0458245	+	0.998950i	$0.485408\pi$
$44$	6.78731e21	0.441659
$45$	−2.74020e21	−0.131648
$46$	4.12194e20	0.0147188
$47$	6.43133e22	1.71783	0.858914	−	0.512120i	$-0.171140\pi$
$47$	6.43133e22	1.71783	0.858914	+	0.512120i	$0.171140\pi$
$48$	−2.87114e22	−0.577161
$49$	−6.55826e22	−0.998026
$50$	7.61542e20	0.00882265
$51$	−1.11675e23	−0.990278
$52$	−1.62794e23	−1.11069
$53$	2.13714e23	1.12748	0.563740	−	0.825953i	$-0.309362\pi$
$53$	2.13714e23	1.12748	0.563740	+	0.825953i	$0.309362\pi$
$54$	4.90772e20	0.00201171
$55$	5.45211e22	0.174449
$56$	−3.70259e20	−0.000928897 0
$57$	−4.00218e22	−0.0790653
$58$	−6.95799e21	−0.0108694
$59$	1.07026e24	1.32736	0.663679	−	0.748017i	$-0.268994\pi$
$59$	1.07026e24	1.32736	0.663679	+	0.748017i	$0.268994\pi$
$60$	−2.30658e23	−0.227995
$61$	8.16628e23	0.645761	0.322880	−	0.946440i	$-0.395349\pi$
$61$	8.16628e23	0.645761	0.322880	+	0.946440i	$0.395349\pi$
$62$	−1.30992e22	−0.00831684
$63$	−2.89528e22	−0.0148113
$64$	−2.41627e24	−0.999344
$65$	−1.30769e24	−0.438706
$66$	−9.76479e21	−0.00266575
$67$	1.68630e24	0.375773	0.187886	−	0.982191i	$-0.439836\pi$
$67$	1.68630e24	0.375773	0.187886	+	0.982191i	$0.439836\pi$
$68$	−9.40028e24	−1.71502
$69$	5.42659e24	0.812951
$70$	−1.48703e21	−0.000183441 0
$71$	−3.18547e24	−0.324478	−0.162239	−	0.986751i	$-0.551872\pi$
$71$	−3.18547e24	−0.324478	−0.162239	+	0.986751i	$0.551872\pi$
$72$	8.26266e22	0.00696837
$73$	2.09853e25	1.46912	0.734559	−	0.678545i	$-0.237389\pi$
$73$	2.09853e25	1.46912	0.734559	+	0.678545i	$0.237389\pi$
$74$	2.30183e23	0.0134105
$75$	1.00258e25	0.487295
$76$	−3.36886e24	−0.136930
$77$	5.76068e23	0.0196268
$78$	2.34208e23	0.00670386
$79$	−8.88148e22	−0.00214052	−0.00107026	−	0.999999i	$-0.500341\pi$
$79$	−8.88148e22	−0.00214052	−0.00107026	+	0.999999i	$0.500341\pi$
$80$	−1.94136e25	−0.394813
$81$	6.46108e24	0.111111
$82$	−8.06718e23	−0.0117553
$83$	−6.50402e25	−0.804689	−0.402344	−	0.915488i	$-0.631805\pi$
$83$	−6.50402e25	−0.804689	−0.402344	+	0.915488i	$0.631805\pi$
$84$	−2.43712e24	−0.0256512
$85$	−7.55105e25	−0.677411
$86$	−1.25056e23	−0.000958019 0
$87$	−9.16028e25	−0.600342
$88$	−1.64400e24	−0.00923393
$89$	3.38617e26	1.63284	0.816420	−	0.577459i	$-0.195956\pi$
$89$	3.38617e26	1.63284	0.816420	+	0.577459i	$0.195956\pi$
$90$	3.31843e23	0.00137613
$91$	−1.38170e25	−0.0493577
$92$	4.56787e26	1.40792
$93$	−1.72453e26	−0.459358
$94$	−7.78847e24	−0.0179567
$95$	−2.70614e25	−0.0540855
$96$	1.04329e25	0.0181027
$97$	−4.16124e26	−0.627775	−0.313888	−	0.949460i	$-0.601632\pi$
$97$	−4.16124e26	−0.627775	−0.313888	+	0.949460i	$0.601632\pi$
$98$	7.94218e24	0.0104325
$99$	−1.28555e26	−0.147236
$100$	8.43928e26	0.843928
$101$	−9.90798e26	−0.866256	−0.433128	−	0.901332i	$-0.642590\pi$
$101$	−9.90798e26	−0.866256	−0.433128	+	0.901332i	$0.642590\pi$
$102$	1.35240e25	0.0103515
$103$	−2.01221e27	−1.35012	−0.675059	−	0.737764i	$-0.735882\pi$
$103$	−2.01221e27	−1.35012	−0.675059	+	0.737764i	$0.735882\pi$
$104$	3.94314e25	0.0232216
$105$	−1.95769e25	−0.0101318
$106$	−2.58812e25	−0.0117857
$107$	2.23219e25	0.00895470	0.00447735	−	0.999990i	$-0.498575\pi$
$107$	2.23219e25	0.00895470	0.00447735	+	0.999990i	$0.498575\pi$
$108$	5.43865e26	0.192429
$109$	5.40319e27	1.68808	0.844039	−	0.536281i	$-0.180171\pi$
$109$	5.40319e27	1.68808	0.844039	+	0.536281i	$0.180171\pi$
$110$	−6.60261e24	−0.00182354
$111$	3.03038e27	0.740691
$112$	−2.05124e26	−0.0444194
$113$	−3.71413e27	−0.713342	−0.356671	−	0.934230i	$-0.616088\pi$
$113$	−3.71413e27	−0.713342	−0.356671	+	0.934230i	$0.616088\pi$
$114$	4.84672e24	0.000826480 0
$115$	3.66927e27	0.556108
$116$	−7.71072e27	−1.03971
$117$	3.08338e27	0.370270
$118$	−1.29611e26	−0.0138750
$119$	−7.97842e26	−0.0762137
$120$	5.58693e25	0.00476679
$121$	−1.05522e28	−0.804895
$122$	−9.88953e25	−0.00675022
$123$	−1.06205e28	−0.649274
$124$	−1.45164e28	−0.795545
$125$	1.48110e28	0.728282
$126$	3.50625e24	0.000154825 0
$127$	2.13925e28	0.849007	0.424503	−	0.905426i	$-0.360449\pi$
$127$	2.13925e28	0.849007	0.424503	+	0.905426i	$0.360449\pi$
$128$	1.17091e27	0.0418011
$129$	−1.64637e27	−0.0529136
$130$	1.58364e26	0.00458585
$131$	5.14435e28	1.34328	0.671642	−	0.740876i	$-0.265589\pi$
$131$	5.14435e28	1.34328	0.671642	+	0.740876i	$0.265589\pi$
$132$	−1.08212e28	−0.254992
$133$	−2.85930e26	−0.00608502
$134$	−2.04214e26	−0.00392800
$135$	4.36876e27	0.0760068
$136$	2.27691e27	0.0358567
$137$	3.71968e28	0.530612	0.265306	−	0.964164i	$-0.414527\pi$
$137$	3.71968e28	0.530612	0.265306	+	0.964164i	$0.414527\pi$
$138$	−6.57171e26	−0.00849788
$139$	−1.00529e29	−1.17921	−0.589605	−	0.807692i	$-0.700717\pi$
$139$	−1.00529e29	−1.17921	−0.589605	+	0.807692i	$0.700717\pi$
$140$	−1.64790e27	−0.0175470
$141$	−1.02536e29	−0.991788
$142$	3.85766e26	0.00339181
$143$	−6.13494e28	−0.490652
$144$	4.57752e28	0.333224
$145$	−6.19387e28	−0.410671
$146$	−2.54136e27	−0.0153569
$147$	1.04560e29	0.576210
$148$	2.55084e29	1.28277
$149$	−2.06193e29	−0.946801	−0.473400	−	0.880847i	$-0.656974\pi$
$149$	−2.06193e29	−0.946801	−0.473400	+	0.880847i	$0.656974\pi$
$150$	−1.21414e27	−0.00509376
$151$	8.73857e28	0.335160	0.167580	−	0.985859i	$-0.446405\pi$
$151$	8.73857e28	0.335160	0.167580	+	0.985859i	$0.446405\pi$
$152$	8.15995e26	0.00286285
$153$	1.78045e29	0.571737
$154$	−6.97630e25	−0.000205161 0
$155$	−1.16607e29	−0.314229
$156$	2.59545e29	0.641256
$157$	3.66647e29	0.831004	0.415502	−	0.909592i	$-0.363606\pi$
$157$	3.66647e29	0.831004	0.415502	+	0.909592i	$0.363606\pi$
$158$	1.07556e25	2.23751e−5 0
$159$	−3.40729e29	−0.650950
$160$	7.05437e27	0.0123834
$161$	3.87694e28	0.0625663
$162$	−7.82450e26	−0.00116146
$163$	−9.33235e29	−1.27485	−0.637424	−	0.770513i	$-0.720000\pi$
$163$	−9.33235e29	−1.27485	−0.637424	+	0.770513i	$0.720000\pi$
$164$	−8.93991e29	−1.12445
$165$	−8.69242e28	−0.100718
$166$	7.87650e27	0.00841151
$167$	3.46815e29	0.341527	0.170764	−	0.985312i	$-0.445377\pi$
$167$	3.46815e29	0.341527	0.170764	+	0.985312i	$0.445377\pi$
$168$	5.90313e26	0.000536299 0
$169$	2.78930e29	0.233897
$170$	9.14447e27	0.00708106
$171$	6.38077e28	0.0456484
$172$	−1.38584e29	−0.0916390
$173$	2.65803e30	1.62532	0.812659	−	0.582740i	$-0.198019\pi$
$173$	2.65803e30	1.62532	0.812659	+	0.582740i	$0.198019\pi$
$174$	1.10933e28	0.00627545
$175$	7.16278e28	0.0375032
$176$	−9.10778e29	−0.441562
$177$	−1.70634e30	−0.766351
$178$	−4.10072e28	−0.0170683
$179$	4.30907e30	1.66291	0.831454	−	0.555594i	$-0.187509\pi$
$179$	4.30907e30	1.66291	0.831454	+	0.555594i	$0.187509\pi$
$180$	3.67743e29	0.131633
$181$	−5.56401e29	−0.184811	−0.0924053	−	0.995721i	$-0.529456\pi$
$181$	−5.56401e29	−0.184811	−0.0924053	+	0.995721i	$0.529456\pi$
$182$	1.67326e27	0.000515942 0
$183$	−1.30197e30	−0.372830
$184$	−1.10642e29	−0.0294359
$185$	2.04904e30	0.506678
$186$	2.08844e28	0.00480173
$187$	−3.54253e30	−0.757621
$188$	−8.63104e30	−1.71764
$189$	4.61602e28	0.00855132
$190$	3.27718e27	0.000565363 0
$191$	−4.19469e30	−0.674139	−0.337070	−	0.941480i	$-0.609436\pi$
$191$	−4.19469e30	−0.674139	−0.337070	+	0.941480i	$0.609436\pi$
$192$	3.85231e30	0.576972
$193$	4.85628e28	0.00678078	0.00339039	−	0.999994i	$-0.498921\pi$
$193$	4.85628e28	0.00678078	0.00339039	+	0.999994i	$0.498921\pi$
$194$	5.03934e28	0.00656221
$195$	2.08488e30	0.253287
$196$	8.80139e30	0.997917
$197$	−2.40097e29	−0.0254151	−0.0127075	−	0.999919i	$-0.504045\pi$
$197$	−2.40097e29	−0.0254151	−0.0127075	+	0.999919i	$0.504045\pi$
$198$	1.55682e28	0.00153907
$199$	7.40632e30	0.684047	0.342024	−	0.939691i	$-0.388888\pi$
$199$	7.40632e30	0.684047	0.342024	+	0.939691i	$0.388888\pi$
$200$	−2.04414e29	−0.0176443
$201$	−2.68851e30	−0.216953
$202$	1.19988e29	0.00905509
$203$	−6.54442e29	−0.0462035
$204$	1.49871e31	0.990170
$205$	−7.18125e30	−0.444143
$206$	2.43683e29	0.0141129
$207$	−8.65174e30	−0.469358
$208$	2.18450e31	1.11045
$209$	−1.26957e30	−0.0604896
$210$	2.37080e27	0.000105909 0
$211$	−3.11843e31	−1.30654	−0.653271	−	0.757124i	$-0.726604\pi$
$211$	−3.11843e31	−1.30654	−0.653271	+	0.757124i	$0.726604\pi$
$212$	−2.86811e31	−1.12736
$213$	5.07866e30	0.187337
$214$	−2.70323e27	−9.36046e−5 0
$215$	−1.11322e30	−0.0361961
$216$	−1.31733e29	−0.00402319
$217$	−1.23207e30	−0.0353531
$218$	−6.54337e29	−0.0176457
$219$	−3.34574e31	−0.848196
$220$	−7.31690e30	−0.174430
$221$	8.49675e31	1.90527
$222$	−3.66985e29	−0.00774254
$223$	−2.26940e31	−0.450605	−0.225302	−	0.974289i	$-0.572337\pi$
$223$	−2.26940e31	−0.450605	−0.225302	+	0.974289i	$0.572337\pi$
$224$	7.45362e28	0.00139322
$225$	−1.59844e31	−0.281340
$226$	4.49788e29	0.00745665
$227$	8.41908e31	1.31497	0.657484	−	0.753468i	$-0.271621\pi$
$227$	8.41908e31	1.31497	0.657484	+	0.753468i	$0.271621\pi$
$228$	5.37105e30	0.0790567
$229$	4.09888e31	0.568703	0.284352	−	0.958720i	$-0.408222\pi$
$229$	4.09888e31	0.568703	0.284352	+	0.958720i	$0.408222\pi$
$230$	−4.44356e29	−0.00581307
$231$	−9.18439e29	−0.0113315
$232$	1.86767e30	0.0217376
$233$	6.99046e31	0.767717	0.383858	−	0.923392i	$-0.374595\pi$
$233$	6.99046e31	0.767717	0.383858	+	0.923392i	$0.374595\pi$
$234$	−3.73404e29	−0.00387048
$235$	−6.93314e31	−0.678444
$236$	−1.43633e32	−1.32721
$237$	1.41599e29	0.00123583
$238$	9.66202e28	0.000796671 0
$239$	−1.89074e32	−1.47320	−0.736598	−	0.676330i	$-0.763569\pi$
$239$	−1.89074e32	−1.47320	−0.736598	+	0.676330i	$0.763569\pi$
$240$	3.09516e31	0.227946
$241$	1.01767e32	0.708563	0.354281	−	0.935139i	$-0.384725\pi$
$241$	1.01767e32	0.708563	0.354281	+	0.935139i	$0.384725\pi$
$242$	1.27789e30	0.00841367
$243$	−1.03011e31	−0.0641500
$244$	−1.09594e32	−0.645690
$245$	7.06998e31	0.394163
$246$	1.28617e30	0.00678694
$247$	3.04506e31	0.152120
$248$	3.51611e30	0.0166328
$249$	1.03695e32	0.464587
$250$	−1.79364e30	−0.00761283
$251$	−2.25120e32	−0.905356	−0.452678	−	0.891674i	$-0.649531\pi$
$251$	−2.25120e32	−0.905356	−0.452678	+	0.891674i	$0.649531\pi$
$252$	3.88556e30	0.0148097
$253$	1.72142e32	0.621955
$254$	−2.59067e30	−0.00887478
$255$	1.20388e32	0.391103
$256$	3.24164e32	0.998908
$257$	1.28310e32	0.375113	0.187557	−	0.982254i	$-0.439943\pi$
$257$	1.28310e32	0.375113	0.187557	+	0.982254i	$0.439943\pi$
$258$	1.99379e29	0.000553113 0
$259$	2.16501e31	0.0570050
$260$	1.75496e32	0.438658
$261$	1.46045e32	0.346608
$262$	−6.22990e30	−0.0140415
$263$	−6.17345e32	−1.32168	−0.660838	−	0.750528i	$-0.729799\pi$
$263$	−6.17345e32	−1.32168	−0.660838	+	0.750528i	$0.729799\pi$
$264$	2.62107e30	0.00533121
$265$	−2.30389e32	−0.445290
$266$	3.46266e28	6.36075e−5 0
$267$	−5.39865e32	−0.942720
$268$	−2.26307e32	−0.375732
$269$	−1.70730e31	−0.0269559	−0.0134779	−	0.999909i	$-0.504290\pi$
$269$	−1.70730e31	−0.0269559	−0.0134779	+	0.999909i	$0.504290\pi$
$270$	−5.29065e29	−0.000794508 0
$271$	−1.06709e33	−1.52446	−0.762229	−	0.647307i	$-0.775895\pi$
$271$	−1.06709e33	−1.52446	−0.762229	+	0.647307i	$0.775895\pi$
$272$	1.26141e33	1.71465
$273$	2.20287e31	0.0284967
$274$	−4.50460e30	−0.00554656
$275$	3.18037e32	0.372809
$276$	−7.28265e32	−0.812863
$277$	5.90772e32	0.627976	0.313988	−	0.949427i	$-0.398335\pi$
$277$	5.90772e32	0.627976	0.313988	+	0.949427i	$0.398335\pi$
$278$	1.21742e31	0.0123264
$279$	2.74946e32	0.265211
$280$	3.99149e29	0.000366861 0
$281$	3.49531e32	0.306161	0.153081	−	0.988214i	$-0.451081\pi$
$281$	3.49531e32	0.306161	0.153081	+	0.988214i	$0.451081\pi$
$282$	1.24173e31	0.0103673
$283$	−1.04098e32	−0.0828565	−0.0414282	−	0.999141i	$-0.513191\pi$
$283$	−1.04098e32	−0.0828565	−0.0414282	+	0.999141i	$0.513191\pi$
$284$	4.27499e32	0.324443
$285$	4.31446e31	0.0312263
$286$	7.42953e30	0.00512885
$287$	−7.58768e31	−0.0499693
$288$	−1.66334e31	−0.0104516
$289$	3.23862e33	1.94195
$290$	7.50089e30	0.00429279
$291$	6.63436e32	0.362446
$292$	−2.81629e33	−1.46896
$293$	−4.57358e32	−0.227794	−0.113897	−	0.993493i	$-0.536333\pi$
$293$	−4.57358e32	−0.227794	−0.113897	+	0.993493i	$0.536333\pi$
$294$	−1.26624e31	−0.00602320
$295$	−1.15377e33	−0.524231
$296$	−6.17858e31	−0.0268195
$297$	2.04958e32	0.0850065
$298$	2.49703e31	0.00989703
$299$	−4.12882e33	−1.56410
$300$	−1.34549e33	−0.487242
$301$	−1.17623e31	−0.00407233
$302$	−1.05826e31	−0.00350346
$303$	1.57965e33	0.500133
$304$	4.52062e32	0.136900
$305$	−8.80347e32	−0.255039
$306$	−2.15617e31	−0.00597644
$307$	2.50586e33	0.664642	0.332321	−	0.943166i	$-0.392168\pi$
$307$	2.50586e33	0.664642	0.332321	+	0.943166i	$0.392168\pi$
$308$	−7.73101e31	−0.0196246
$309$	3.20812e33	0.779491
$310$	1.41213e31	0.00328468
$311$	−4.09104e33	−0.911104	−0.455552	−	0.890209i	$-0.650558\pi$
$311$	−4.09104e33	−0.911104	−0.455552	+	0.890209i	$0.650558\pi$
$312$	−6.28664e31	−0.0134070
$313$	5.57324e33	1.13831	0.569154	−	0.822231i	$-0.307271\pi$
$313$	5.57324e33	1.13831	0.569154	+	0.822231i	$0.307271\pi$
$314$	−4.44017e31	−0.00868659
$315$	3.12119e31	0.00584962
$316$	1.19192e31	0.00214029
$317$	6.22580e33	1.07126	0.535631	−	0.844452i	$-0.320074\pi$
$317$	6.22580e33	1.07126	0.535631	+	0.844452i	$0.320074\pi$
$318$	4.12629e31	0.00680447
$319$	−2.90581e33	−0.459297
$320$	2.60480e33	0.394684
$321$	−3.55884e31	−0.00517000
$322$	−4.69505e30	−0.000654013 0
$323$	1.75832e33	0.234890
$324$	−8.67097e32	−0.111099
$325$	−7.62812e33	−0.937545
$326$	1.13017e32	0.0133261
$327$	−8.61443e33	−0.974613
$328$	2.16540e32	0.0235094
$329$	−7.32553e32	−0.0763299
$330$	1.05267e31	0.00105282
$331$	−6.69049e33	−0.642363	−0.321181	−	0.947018i	$-0.604080\pi$
$331$	−6.69049e33	−0.642363	−0.321181	+	0.947018i	$0.604080\pi$
$332$	8.72860e33	0.804601
$333$	−4.83141e33	−0.427638
$334$	−4.20000e31	−0.00357003
$335$	−1.81788e33	−0.148409
$336$	3.27033e32	0.0256455
$337$	−8.45330e33	−0.636829	−0.318414	−	0.947952i	$-0.603150\pi$
$337$	−8.45330e33	−0.636829	−0.318414	+	0.947952i	$0.603150\pi$
$338$	−3.37790e31	−0.00244496
$339$	5.92152e33	0.411848
$340$	1.01337e34	0.677337
$341$	−5.47054e33	−0.351436
$342$	−7.72724e30	−0.000477168 0
$343$	1.49550e33	0.0887802
$344$	3.35675e31	0.00191593
$345$	−5.85001e33	−0.321069
$346$	−3.21893e32	−0.0169896
$347$	3.54455e34	1.79934	0.899671	−	0.436568i	$-0.143806\pi$
$347$	3.54455e34	1.79934	0.899671	+	0.436568i	$0.143806\pi$
$348$	1.22934e34	0.600277
$349$	1.62742e34	0.764462	0.382231	−	0.924067i	$-0.375156\pi$
$349$	1.62742e34	0.764462	0.382231	+	0.924067i	$0.375156\pi$
$350$	−8.67426e30	−0.000392025 0
$351$	−4.91591e33	−0.213775
$352$	3.30951e32	0.0138496
$353$	−6.68547e33	−0.269261	−0.134630	−	0.990896i	$-0.542985\pi$
$353$	−6.68547e33	−0.269261	−0.134630	+	0.990896i	$0.542985\pi$
$354$	2.06642e32	0.00801076
$355$	3.43402e33	0.128150
$356$	−4.54434e34	−1.63266
$357$	1.27202e33	0.0440020
$358$	−5.21837e32	−0.0173826
$359$	−7.80470e33	−0.250369	−0.125185	−	0.992133i	$-0.539952\pi$
$359$	−7.80470e33	−0.250369	−0.125185	+	0.992133i	$0.539952\pi$
$360$	−8.90736e31	−0.00275211
$361$	−3.29705e34	−0.981246
$362$	6.73812e31	0.00193185
$363$	1.68236e34	0.464706
$364$	1.85428e33	0.0493523
$365$	−2.26227e34	−0.580218
$366$	1.57671e32	0.00389724
$367$	6.61615e34	1.57621	0.788104	−	0.615542i	$-0.211063\pi$
$367$	6.61615e34	1.57621	0.788104	+	0.615542i	$0.211063\pi$
$368$	−6.12955e34	−1.40761
$369$	1.69326e34	0.374858
$370$	−2.48143e32	−0.00529637
$371$	−2.43428e33	−0.0500984
$372$	2.31438e34	0.459308
$373$	−6.79473e34	−1.30048	−0.650239	−	0.759729i	$-0.725331\pi$
$373$	−6.79473e34	−1.30048	−0.650239	+	0.759729i	$0.725331\pi$
$374$	4.29007e32	0.00791951
$375$	−2.36136e34	−0.420474
$376$	2.09059e33	0.0359114
$377$	6.96959e34	1.15505
$378$	−5.59009e30	−8.93880e−5 0
$379$	7.98595e34	1.23224	0.616122	−	0.787650i	$-0.288703\pi$
$379$	7.98595e34	1.23224	0.616122	+	0.787650i	$0.288703\pi$
$380$	3.63172e33	0.0540796
$381$	−3.41065e34	−0.490174
$382$	5.07985e32	0.00704686
$383$	1.19033e35	1.59399	0.796994	−	0.603987i	$-0.206422\pi$
$383$	1.19033e35	1.59399	0.796994	+	0.603987i	$0.206422\pi$
$384$	−1.86680e33	−0.0241339
$385$	−6.21016e32	−0.00775146
$386$	−5.88105e30	−7.08804e−5 0
$387$	2.62485e33	0.0305497
$388$	5.58451e34	0.627707
$389$	1.48935e34	0.161688	0.0808441	−	0.996727i	$-0.474238\pi$
$389$	1.48935e34	0.161688	0.0808441	+	0.996727i	$0.474238\pi$
$390$	−2.52483e32	−0.00264764
$391$	−2.38413e35	−2.41514
$392$	−2.13185e33	−0.0208638
$393$	−8.20175e34	−0.775545
$394$	2.90762e31	0.000265667 0
$395$	9.57447e31	0.000845384 0
$396$	1.72524e34	0.147220
$397$	4.07374e34	0.335986	0.167993	−	0.985788i	$-0.446271\pi$
$397$	4.07374e34	0.335986	0.167993	+	0.985788i	$0.446271\pi$
$398$	−8.96920e32	−0.00715043
$399$	4.55864e32	0.00351319
$400$	−1.13245e35	−0.843744
$401$	−1.64933e35	−1.18812	−0.594058	−	0.804422i	$-0.702475\pi$
$401$	−1.64933e35	−1.18812	−0.594058	+	0.804422i	$0.702475\pi$
$402$	3.25584e32	0.00226783
$403$	1.31211e35	0.883796
$404$	1.32968e35	0.866162
$405$	−6.96521e33	−0.0438825
$406$	7.92542e31	0.000482971 0
$407$	9.61295e34	0.566672
$408$	−3.63013e33	−0.0207019
$409$	−2.13655e35	−1.17882	−0.589411	−	0.807833i	$-0.700640\pi$
$409$	−2.13655e35	−1.17882	−0.589411	+	0.807833i	$0.700640\pi$
$410$	8.69663e32	0.00464268
$411$	−5.93036e34	−0.306349
$412$	2.70045e35	1.34997
$413$	−1.21907e34	−0.0589798
$414$	1.04774e33	0.00490626
$415$	7.01151e34	0.317806
$416$	−7.93786e33	−0.0348292
$417$	1.60276e35	0.680817
$418$	1.53747e32	0.000632306 0
$419$	6.25908e34	0.249242	0.124621	−	0.992204i	$-0.460228\pi$
$419$	6.25908e34	0.249242	0.124621	+	0.992204i	$0.460228\pi$
$420$	2.62728e33	0.0101307
$421$	1.62873e35	0.608191	0.304096	−	0.952641i	$-0.401646\pi$
$421$	1.62873e35	0.608191	0.304096	+	0.952641i	$0.401646\pi$
$422$	3.77648e33	0.0136574
$423$	1.63476e35	0.572609
$424$	6.94704e33	0.0235701
$425$	−4.40475e35	−1.44767
$426$	−6.15036e32	−0.00195826
$427$	−9.30171e33	−0.0286937
$428$	−2.99567e33	−0.00895372
$429$	9.78107e34	0.283278
$430$	1.34813e32	0.000378363 0
$431$	−6.21025e35	−1.68914	−0.844571	−	0.535444i	$-0.820144\pi$
$431$	−6.21025e35	−1.68914	−0.844571	+	0.535444i	$0.820144\pi$
$432$	−7.29804e34	−0.192387
$433$	1.04792e35	0.267757	0.133878	−	0.990998i	$-0.457257\pi$
$433$	1.04792e35	0.267757	0.133878	+	0.990998i	$0.457257\pi$
$434$	1.49206e32	0.000369550 0
$435$	9.87502e34	0.237101
$436$	−7.25125e35	−1.68789
$437$	−8.54420e34	−0.192829
$438$	4.05175e33	0.00886630
$439$	6.93788e35	1.47216	0.736081	−	0.676893i	$-0.236674\pi$
$439$	6.93788e35	1.47216	0.736081	+	0.676893i	$0.236674\pi$
$440$	1.77228e33	0.00364687
$441$	−1.66702e35	−0.332675
$442$	−1.02897e34	−0.0199161
$443$	5.15844e35	0.968430	0.484215	−	0.874949i	$-0.339105\pi$
$443$	5.15844e35	0.968430	0.484215	+	0.874949i	$0.339105\pi$
$444$	−4.06687e35	−0.740610
$445$	−3.65038e35	−0.644878
$446$	2.74829e33	0.00471023
$447$	3.28738e35	0.546636
$448$	2.75222e34	0.0444048
$449$	9.16926e35	1.43552	0.717759	−	0.696292i	$-0.245168\pi$
$449$	9.16926e35	1.43552	0.717759	+	0.696292i	$0.245168\pi$
$450$	1.93574e33	0.00294088
$451$	−3.36904e35	−0.496732
$452$	4.98447e35	0.713264
$453$	−1.39321e35	−0.193504
$454$	−1.01957e34	−0.0137455
$455$	1.48951e34	0.0194934
$456$	−1.30096e33	−0.00165287
$457$	1.55254e36	1.91502	0.957510	−	0.288400i	$-0.0931232\pi$
$457$	1.55254e36	1.91502	0.957510	+	0.288400i	$0.0931232\pi$
$458$	−4.96382e33	−0.00594473
$459$	−2.83862e35	−0.330093
$460$	−4.92428e35	−0.556048
$461$	−5.06840e35	−0.555787	−0.277893	−	0.960612i	$-0.589636\pi$
$461$	−5.06840e35	−0.555787	−0.277893	+	0.960612i	$0.589636\pi$
$462$	1.11225e32	0.000118450 0
$463$	−1.45476e36	−1.50469	−0.752347	−	0.658767i	$-0.771078\pi$
$463$	−1.45476e36	−1.50469	−0.752347	+	0.658767i	$0.771078\pi$
$464$	1.03469e36	1.03948
$465$	1.85909e35	0.181420
$466$	−8.46559e33	−0.00802504
$467$	−6.89399e35	−0.634881	−0.317441	−	0.948278i	$-0.602823\pi$
$467$	−6.89399e35	−0.634881	−0.317441	+	0.948278i	$0.602823\pi$
$468$	−4.13799e35	−0.370229
$469$	−1.92076e34	−0.0166971
$470$	8.39617e33	0.00709186
$471$	−5.84554e35	−0.479780
$472$	3.47903e34	0.0277486
$473$	−5.22261e34	−0.0404820
$474$	−1.71480e31	−1.29183e−5 0
$475$	−1.57857e35	−0.115585
$476$	1.07073e35	0.0762053
$477$	5.43232e35	0.375826
$478$	2.28973e34	0.0153995
$479$	−6.34595e35	−0.414923	−0.207461	−	0.978243i	$-0.566520\pi$
$479$	−6.34595e35	−0.414923	−0.207461	+	0.978243i	$0.566520\pi$
$480$	−1.12469e34	−0.00714953
$481$	−2.30566e36	−1.42507
$482$	−1.23242e34	−0.00740670
$483$	−6.18110e34	−0.0361226
$484$	1.41613e36	0.804807
$485$	4.48592e35	0.247935
$486$	1.24748e33	0.000670568 0
$487$	2.48287e36	1.29812	0.649058	−	0.760739i	$-0.275163\pi$
$487$	2.48287e36	1.29812	0.649058	+	0.760739i	$0.275163\pi$
$488$	2.65456e34	0.0134997
$489$	1.48788e36	0.736034
$490$	−8.56188e33	−0.00412024
$491$	−2.37415e36	−1.11150	−0.555748	−	0.831351i	$-0.687568\pi$
$491$	−2.37415e36	−1.11150	−0.555748	+	0.831351i	$0.687568\pi$
$492$	1.42531e36	0.649203
$493$	4.02449e36	1.78352
$494$	−3.68762e33	−0.00159013
$495$	1.38585e35	0.0581496
$496$	1.94793e36	0.795371
$497$	3.62837e34	0.0144178
$498$	−1.25577e34	−0.00485639
$499$	−5.00732e36	−1.88472	−0.942362	−	0.334595i	$-0.891400\pi$
$499$	−5.00732e36	−1.88472	−0.942362	+	0.334595i	$0.891400\pi$
$500$	−1.98768e36	−0.728203
$501$	−5.52935e35	−0.197181
$502$	2.72625e34	0.00946380
$503$	−1.61560e36	−0.545966	−0.272983	−	0.962019i	$-0.588010\pi$
$503$	−1.61560e36	−0.545966	−0.272983	+	0.962019i	$0.588010\pi$
$504$	−9.41149e32	−0.000309632 0
$505$	1.06811e36	0.342122
$506$	−2.08467e34	−0.00650138
$507$	−4.44705e35	−0.135041
$508$	−2.87094e36	−0.848914
$509$	1.80638e36	0.520139	0.260069	−	0.965590i	$-0.416255\pi$
$509$	1.80638e36	0.520139	0.260069	+	0.965590i	$0.416255\pi$
$510$	−1.45792e34	−0.00408825
$511$	−2.39031e35	−0.0652787
$512$	−1.96413e35	−0.0522428
$513$	−1.01730e35	−0.0263551
$514$	−1.55386e34	−0.00392111
$515$	2.16922e36	0.533219
$516$	2.20948e35	0.0529078
$517$	−3.25264e36	−0.758776
$518$	−2.62187e33	−0.000595880 0
$519$	−4.23776e36	−0.938377
$520$	−4.25081e34	−0.00917120
$521$	4.59028e36	0.965006	0.482503	−	0.875894i	$-0.339728\pi$
$521$	4.59028e36	0.965006	0.482503	+	0.875894i	$0.339728\pi$
$522$	−1.76863e34	−0.00362314
$523$	5.82915e35	0.116368	0.0581838	−	0.998306i	$-0.481469\pi$
$523$	5.82915e35	0.116368	0.0581838	+	0.998306i	$0.481469\pi$
$524$	−6.90387e36	−1.34314
$525$	−1.14198e35	−0.0216525
$526$	7.47617e34	0.0138157
$527$	7.57658e36	1.36468
$528$	1.45207e36	0.254936
$529$	5.74195e36	0.982670
$530$	2.79006e34	0.00465467
$531$	2.72046e36	0.442453
$532$	3.83726e34	0.00608435
$533$	8.08063e36	1.24919
$534$	6.53787e34	0.00985437
$535$	−2.40636e34	−0.00353659
$536$	5.48154e34	0.00785558
$537$	−6.87006e36	−0.960080
$538$	2.06757e33	0.000281773 0
$539$	3.31684e36	0.440835
$540$	−5.86301e35	−0.0759985
$541$	−6.32438e36	−0.799567	−0.399783	−	0.916610i	$-0.630915\pi$
$541$	−6.32438e36	−0.799567	−0.399783	+	0.916610i	$0.630915\pi$
$542$	1.29227e35	0.0159354
$543$	8.87082e35	0.106700
$544$	−4.58360e35	−0.0537801
$545$	−5.82478e36	−0.666695
$546$	−2.66772e33	−0.000297879 0
$547$	−9.05384e36	−0.986289	−0.493144	−	0.869948i	$-0.664153\pi$
$547$	−9.05384e36	−0.986289	−0.493144	+	0.869948i	$0.664153\pi$
$548$	−4.99192e36	−0.530554
$549$	2.07576e36	0.215254
$550$	−3.85150e34	−0.00389702
$551$	1.44229e36	0.142399
$552$	1.76398e35	0.0169948
$553$	1.01164e33	9.51118e−5 0
$554$	−7.15436e34	−0.00656431
$555$	−3.26683e36	−0.292531
$556$	1.34913e37	1.17908
$557$	−1.74285e37	−1.48668	−0.743338	−	0.668917i	$-0.766758\pi$
$557$	−1.74285e37	−1.48668	−0.743338	+	0.668917i	$0.766758\pi$
$558$	−3.32965e34	−0.00277228
$559$	1.25264e36	0.101805
$560$	2.21129e35	0.0175431
$561$	5.64794e36	0.437413
$562$	−4.23289e34	−0.00320034
$563$	−7.81650e36	−0.576964	−0.288482	−	0.957485i	$-0.593151\pi$
$563$	−7.81650e36	−0.576964	−0.288482	+	0.957485i	$0.593151\pi$
$564$	1.37607e37	0.991680
$565$	4.00393e36	0.281729
$566$	1.26065e34	0.000866109 0
$567$	−7.35942e34	−0.00493711
$568$	−1.03548e35	−0.00678325
$569$	−1.42845e37	−0.913797	−0.456899	−	0.889519i	$-0.651040\pi$
$569$	−1.42845e37	−0.913797	−0.456899	+	0.889519i	$0.651040\pi$
$570$	−5.22489e33	−0.000326412 0
$571$	2.26975e37	1.38481	0.692406	−	0.721508i	$-0.256551\pi$
$571$	2.26975e37	1.38481	0.692406	+	0.721508i	$0.256551\pi$
$572$	8.23327e36	0.490598
$573$	6.68769e36	0.389214
$574$	9.18883e33	0.000522336 0
$575$	2.14040e37	1.18844
$576$	−6.14183e36	−0.333115
$577$	−1.49672e37	−0.792987	−0.396494	−	0.918038i	$-0.629773\pi$
$577$	−1.49672e37	−0.792987	−0.396494	+	0.918038i	$0.629773\pi$
$578$	−3.92203e35	−0.0202995
$579$	−7.74247e34	−0.00391489
$580$	8.31236e36	0.410626
$581$	7.40834e35	0.0357555
$582$	−8.03434e34	−0.00378870
$583$	−1.08086e37	−0.498015
$584$	6.82154e35	0.0307121
$585$	−3.32397e36	−0.146235
$586$	5.53869e34	0.00238116
$587$	−7.65028e36	−0.321413	−0.160706	−	0.987002i	$-0.551377\pi$
$587$	−7.65028e36	−0.321413	−0.160706	+	0.987002i	$0.551377\pi$
$588$	−1.40323e37	−0.576147
$589$	2.71529e36	0.108958
$590$	1.39724e35	0.00547985
$591$	3.82791e35	0.0146734
$592$	−3.42293e37	−1.28249
$593$	−1.64866e37	−0.603799	−0.301900	−	0.953340i	$-0.597621\pi$
$593$	−1.64866e37	−0.603799	−0.301900	+	0.953340i	$0.597621\pi$
$594$	−2.48208e34	−0.000888584 0
$595$	8.60094e35	0.0301000
$596$	2.76717e37	0.946698
$597$	−1.18081e37	−0.394935
$598$	5.00008e35	0.0163497
$599$	−5.74500e36	−0.183665	−0.0918327	−	0.995774i	$-0.529273\pi$
$599$	−5.74500e36	−0.183665	−0.0918327	+	0.995774i	$0.529273\pi$
$600$	3.25902e35	0.0101870
$601$	−5.09841e36	−0.155822	−0.0779112	−	0.996960i	$-0.524825\pi$
$601$	−5.09841e36	−0.155822	−0.0779112	+	0.996960i	$0.524825\pi$
$602$	1.42443e33	4.25686e−5 0
$603$	4.28635e36	0.125258
$604$	−1.17274e37	−0.335123
$605$	1.13755e37	0.317888
$606$	−1.91299e35	−0.00522796
$607$	1.21769e37	0.325453	0.162727	−	0.986671i	$-0.447971\pi$
$607$	1.21769e37	0.325453	0.162727	+	0.986671i	$0.447971\pi$
$608$	−1.64267e35	−0.00429389
$609$	1.04339e36	0.0266756
$610$	1.06612e35	0.00266595
$611$	7.80145e37	1.90818
$612$	−2.38942e37	−0.571675
$613$	2.55443e37	0.597829	0.298915	−	0.954280i	$-0.403375\pi$
$613$	2.55443e37	0.597829	0.298915	+	0.954280i	$0.403375\pi$
$614$	−3.03464e35	−0.00694759
$615$	1.14492e37	0.256426
$616$	1.87258e34	0.000410300 0
$617$	1.30077e37	0.278838	0.139419	−	0.990234i	$-0.455477\pi$
$617$	1.30077e37	0.278838	0.139419	+	0.990234i	$0.455477\pi$
$618$	−3.88509e35	−0.00814812
$619$	−2.04833e37	−0.420316	−0.210158	−	0.977667i	$-0.567398\pi$
$619$	−2.04833e37	−0.420316	−0.210158	+	0.977667i	$0.567398\pi$
$620$	1.56490e37	0.314195
$621$	1.37937e37	0.270984
$622$	4.95433e35	0.00952389
$623$	−3.85698e36	−0.0725535
$624$	−3.48280e37	−0.641116
$625$	3.08859e37	0.556390
$626$	−6.74931e35	−0.0118989
$627$	2.02410e36	0.0349237
$628$	−4.92052e37	−0.830913
$629$	−1.33137e38	−2.20047
$630$	−3.77982e33	−6.11469e−5 0
$631$	7.16988e37	1.13531	0.567656	−	0.823266i	$-0.307850\pi$
$631$	7.16988e37	1.13531	0.567656	+	0.823266i	$0.307850\pi$
$632$	−2.88704e33	−4.47478e−5 0
$633$	4.97179e37	0.754332
$634$	−7.53957e35	−0.0111980
$635$	−2.30617e37	−0.335309
$636$	4.57269e37	0.650879
$637$	−7.95543e37	−1.10862
$638$	3.51900e35	0.00480109
$639$	−8.09703e36	−0.108159
$640$	−1.26227e36	−0.0165090
$641$	−1.00079e38	−1.28161	−0.640807	−	0.767702i	$-0.721400\pi$
$641$	−1.00079e38	−1.28161	−0.640807	+	0.767702i	$0.721400\pi$
$642$	4.30982e33	5.40426e−5 0
$643$	7.58172e37	0.930936	0.465468	−	0.885065i	$-0.345886\pi$
$643$	7.58172e37	0.930936	0.465468	+	0.885065i	$0.345886\pi$
$644$	−5.20298e36	−0.0625594
$645$	1.77483e36	0.0208978
$646$	−2.12936e35	−0.00245534
$647$	−7.13094e37	−0.805265	−0.402632	−	0.915362i	$-0.631905\pi$
$647$	−7.13094e37	−0.805265	−0.402632	+	0.915362i	$0.631905\pi$
$648$	2.10026e35	0.00232279
$649$	−5.41285e37	−0.586303
$650$	9.23781e35	0.00980028
$651$	1.96431e36	0.0204111
$652$	1.25243e38	1.27471
$653$	2.47590e37	0.246835	0.123417	−	0.992355i	$-0.460615\pi$
$653$	2.47590e37	0.246835	0.123417	+	0.992355i	$0.460615\pi$
$654$	1.04322e36	0.0101878
$655$	−5.54574e37	−0.530520
$656$	1.19963e38	1.12421
$657$	5.33418e37	0.489706
$658$	8.87136e34	0.000797886 0
$659$	1.51836e38	1.33789	0.668946	−	0.743311i	$-0.266746\pi$
$659$	1.51836e38	1.33789	0.668946	+	0.743311i	$0.266746\pi$
$660$	1.16655e37	0.100707
$661$	1.92148e38	1.62523	0.812617	−	0.582798i	$-0.198042\pi$
$661$	1.92148e38	1.62523	0.812617	+	0.582798i	$0.198042\pi$
$662$	8.10232e35	0.00671470
$663$	−1.35466e38	−1.10001
$664$	−2.11422e36	−0.0168221
$665$	3.08239e35	0.00240323
$666$	5.85093e35	0.00447016
$667$	−1.95562e38	−1.46415
$668$	−4.65436e37	−0.341490
$669$	3.61816e37	0.260157
$670$	2.20149e35	0.00155134
$671$	−4.13009e37	−0.285237
$672$	−1.18835e35	−0.000804375 0
$673$	−9.37859e37	−0.622206	−0.311103	−	0.950376i	$-0.600698\pi$
$673$	−9.37859e37	−0.622206	−0.311103	+	0.950376i	$0.600698\pi$
$674$	1.02371e36	0.00665685
$675$	2.54843e37	0.162432
$676$	−3.74333e37	−0.233872
$677$	−2.93781e37	−0.179919	−0.0899595	−	0.995945i	$-0.528674\pi$
$677$	−2.93781e37	−0.179919	−0.0899595	+	0.995945i	$0.528674\pi$
$678$	−7.17107e35	−0.00430510
$679$	4.73981e36	0.0278945
$680$	−2.45457e36	−0.0141613
$681$	−1.34227e38	−0.759197
$682$	6.62494e35	0.00367361
$683$	1.68599e38	0.916591	0.458295	−	0.888800i	$-0.348460\pi$
$683$	1.68599e38	0.916591	0.458295	+	0.888800i	$0.348460\pi$
$684$	−8.56319e36	−0.0456434
$685$	−4.00991e37	−0.209562
$686$	−1.81108e35	−0.000928031 0
$687$	−6.53493e37	−0.328341
$688$	1.85964e37	0.0916190
$689$	2.59243e38	1.25241
$690$	7.08448e35	0.00335618
$691$	−3.72820e38	−1.73199	−0.865996	−	0.500051i	$-0.833314\pi$
$691$	−3.72820e38	−1.73199	−0.865996	+	0.500051i	$0.833314\pi$
$692$	−3.56716e38	−1.62514
$693$	1.46429e36	0.00654226
$694$	−4.29252e36	−0.0188088
$695$	1.08373e38	0.465720
$696$	−2.97767e36	−0.0125502
$697$	4.66604e38	1.92888
$698$	−1.97084e36	−0.00799102
$699$	−1.11451e38	−0.443241
$700$	−9.61267e36	−0.0374991
$701$	3.38534e38	1.29541	0.647707	−	0.761890i	$-0.275728\pi$
$701$	3.38534e38	1.29541	0.647707	+	0.761890i	$0.275728\pi$
$702$	5.95326e35	0.00223462
$703$	−4.77135e37	−0.175689
$704$	1.22203e38	0.441417
$705$	1.10537e38	0.391700
$706$	8.09623e35	0.00281462
$707$	1.12856e37	0.0384912
$708$	2.28997e38	0.766267
$709$	2.34891e38	0.771155	0.385578	−	0.922675i	$-0.374002\pi$
$709$	2.34891e38	0.771155	0.385578	+	0.922675i	$0.374002\pi$
$710$	−4.15866e35	−0.00133957
$711$	−2.25755e35	−0.000713507 0
$712$	1.10072e37	0.0341347
$713$	−3.68168e38	−1.12031
$714$	−1.54044e35	−0.000459958 0
$715$	6.61362e37	0.193779
$716$	−5.78291e38	−1.66273
$717$	3.01445e38	0.850551
$718$	9.45165e35	0.00261714
$719$	−1.57531e38	−0.428082	−0.214041	−	0.976825i	$-0.568663\pi$
$719$	−1.57531e38	−0.428082	−0.214041	+	0.976825i	$0.568663\pi$
$720$	−4.93468e37	−0.131604
$721$	2.29199e37	0.0599911
$722$	3.99279e36	0.0102571
$723$	−1.62250e38	−0.409089
$724$	7.46707e37	0.184790
$725$	−3.61306e38	−0.877632
$726$	−2.03737e36	−0.00485763
$727$	−2.38862e38	−0.559027	−0.279513	−	0.960142i	$-0.590173\pi$
$727$	−2.38862e38	−0.559027	−0.279513	+	0.960142i	$0.590173\pi$
$728$	−4.49139e35	−0.00103183
$729$	1.64232e37	0.0370370
$730$	2.73965e36	0.00606509
$731$	7.23320e37	0.157198
$732$	1.74728e38	0.372789
$733$	−1.39015e38	−0.291177	−0.145589	−	0.989345i	$-0.546508\pi$
$733$	−1.39015e38	−0.291177	−0.145589	+	0.989345i	$0.546508\pi$
$734$	−8.01229e36	−0.0164763
$735$	−1.12718e38	−0.227570
$736$	2.22731e37	0.0441499
$737$	−8.52846e37	−0.165981
$738$	−2.05057e36	−0.00391844
$739$	3.01753e37	0.0566176	0.0283088	−	0.999599i	$-0.490988\pi$
$739$	3.01753e37	0.0566176	0.0283088	+	0.999599i	$0.490988\pi$
$740$	−2.74987e38	−0.506623
$741$	−4.85480e37	−0.0878265
$742$	2.94797e35	0.000523685 0
$743$	8.48049e38	1.47935	0.739677	−	0.672962i	$-0.234978\pi$
$743$	8.48049e38	1.47935	0.739677	+	0.672962i	$0.234978\pi$
$744$	−5.60582e36	−0.00960294
$745$	2.22281e38	0.373932
$746$	8.22856e36	0.0135941
$747$	−1.65324e38	−0.268230
$748$	4.75418e38	0.757538
$749$	−2.54256e35	−0.000397893 0
$750$	2.85965e36	0.00439527
$751$	−1.00379e39	−1.51532	−0.757658	−	0.652651i	$-0.773657\pi$
$751$	−1.00379e39	−1.51532	−0.757658	+	0.652651i	$0.773657\pi$
$752$	1.15819e39	1.71726
$753$	3.58914e38	0.522707
$754$	−8.44031e36	−0.0120738
$755$	−9.42041e37	−0.132369
$756$	−6.19484e36	−0.00855038
$757$	1.01436e39	1.37530	0.687652	−	0.726040i	$-0.258641\pi$
$757$	1.01436e39	1.37530	0.687652	+	0.726040i	$0.258641\pi$
$758$	−9.67114e36	−0.0128808
$759$	−2.74450e38	−0.359086
$760$	−8.79664e35	−0.00113066
$761$	−1.18512e39	−1.49648	−0.748240	−	0.663428i	$-0.769101\pi$
$761$	−1.18512e39	−1.49648	−0.748240	+	0.663428i	$0.769101\pi$
$762$	4.13037e36	0.00512385
$763$	−6.15445e37	−0.0750080
$764$	5.62940e38	0.674065
$765$	−1.91938e38	−0.225804
$766$	−1.44152e37	−0.0166622
$767$	1.29827e39	1.47444
$768$	−5.16822e38	−0.576720
$769$	−1.38650e39	−1.52024	−0.760122	−	0.649780i	$-0.774861\pi$
$769$	−1.38650e39	−1.52024	−0.760122	+	0.649780i	$0.774861\pi$
$770$	7.52063e34	8.10269e−5 0
$771$	−2.04567e38	−0.216572
$772$	−6.51727e36	−0.00678004
$773$	−3.84501e38	−0.393074	−0.196537	−	0.980496i	$-0.562970\pi$
$773$	−3.84501e38	−0.393074	−0.196537	+	0.980496i	$0.562970\pi$
$774$	−3.17875e35	−0.000319340 0
$775$	−6.80202e38	−0.671530
$776$	−1.35266e37	−0.0131237
$777$	−3.45172e37	−0.0329118
$778$	−1.80364e36	−0.00169015
$779$	1.67221e38	0.154005
$780$	−2.79797e38	−0.253259
$781$	1.61105e38	0.143324
$782$	2.88722e37	0.0252458
$783$	−2.32842e38	−0.200114
$784$	−1.18104e39	−0.997698
$785$	−3.95255e38	−0.328199
$786$	9.93248e36	0.00810687
$787$	8.31177e38	0.666860	0.333430	−	0.942775i	$-0.391794\pi$
$787$	8.31177e38	0.666860	0.333430	+	0.942775i	$0.391794\pi$
$788$	3.22217e37	0.0254123
$789$	9.84247e38	0.763070
$790$	−1.15949e34	−8.83690e−6 0
$791$	4.23054e37	0.0316966
$792$	−4.17883e36	−0.00307798
$793$	9.90602e38	0.717317
$794$	−4.93337e36	−0.00351210
$795$	3.67315e38	0.257088
$796$	−9.93951e38	−0.683973
$797$	−5.86889e38	−0.397071	−0.198536	−	0.980094i	$-0.563619\pi$
$797$	−5.86889e38	−0.397071	−0.198536	+	0.980094i	$0.563619\pi$
$798$	−5.52060e34	−3.67238e−5 0
$799$	4.50484e39	2.94644
$800$	4.11502e37	0.0264641
$801$	8.60719e38	0.544280
$802$	1.99737e37	0.0124195
$803$	−1.06133e39	−0.648919
$804$	3.60806e38	0.216929
$805$	−4.17945e37	−0.0247101
$806$	−1.58899e37	−0.00923843
$807$	2.72198e37	0.0155630
$808$	−3.22072e37	−0.0181092
$809$	−2.02827e39	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$809$	−2.02827e39	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$810$	8.43501e35	0.000458710 0
$811$	−1.61063e39	−0.861421	−0.430710	−	0.902490i	$-0.641737\pi$
$811$	−1.61063e39	−0.861421	−0.430710	+	0.902490i	$0.641737\pi$
$812$	8.78281e37	0.0461984
$813$	1.70129e39	0.880147
$814$	−1.16415e37	−0.00592350
$815$	1.00605e39	0.503492
$816$	−2.01109e39	−0.989954
$817$	2.59222e37	0.0125509
$818$	2.58740e37	0.0123224
$819$	−3.51209e37	−0.0164526
$820$	9.63745e38	0.444094
$821$	−2.30031e39	−1.04268	−0.521342	−	0.853348i	$-0.674569\pi$
$821$	−2.30031e39	−1.04268	−0.521342	+	0.853348i	$0.674569\pi$
$822$	7.18179e36	0.00320231
$823$	−2.08776e39	−0.915764	−0.457882	−	0.889013i	$-0.651392\pi$
$823$	−2.08776e39	−0.915764	−0.457882	+	0.889013i	$0.651392\pi$
$824$	−6.54096e37	−0.0282244
$825$	−5.07054e38	−0.215242
$826$	1.47632e36	0.000616523 0
$827$	3.43290e39	1.41038	0.705192	−	0.709017i	$-0.250861\pi$
$827$	3.43290e39	1.41038	0.705192	+	0.709017i	$0.250861\pi$
$828$	1.16109e39	0.469306
$829$	8.03456e38	0.319504	0.159752	−	0.987157i	$-0.448931\pi$
$829$	8.03456e38	0.319504	0.159752	+	0.987157i	$0.448931\pi$
$830$	−8.49107e36	−0.00332207
$831$	−9.41881e38	−0.362562
$832$	−2.93103e39	−1.11008
$833$	−4.59375e39	−1.71183
$834$	−1.94097e37	−0.00711667
$835$	−3.73875e38	−0.134884
$836$	1.70380e38	0.0604830
$837$	−4.38353e38	−0.153119
$838$	−7.57987e36	−0.00260536
$839$	2.54669e39	0.861369	0.430685	−	0.902502i	$-0.358272\pi$
$839$	2.54669e39	0.861369	0.430685	+	0.902502i	$0.358272\pi$
$840$	−6.36372e35	−0.000211807 0
$841$	2.48015e38	0.0812329
$842$	−1.97242e37	−0.00635750
$843$	−5.57266e38	−0.176762
$844$	4.18503e39	1.30640
$845$	−3.00694e38	−0.0923760
$846$	−1.97972e37	−0.00598556
$847$	1.20193e38	0.0357647
$848$	3.84867e39	1.12711
$849$	1.65966e38	0.0478372
$850$	5.33424e37	0.0151327
$851$	6.46952e39	1.80644
$852$	−6.81572e38	−0.187317
$853$	1.61849e39	0.437823	0.218912	−	0.975745i	$-0.429749\pi$
$853$	1.61849e39	0.437823	0.218912	+	0.975745i	$0.429749\pi$
$854$	1.12646e36	0.000299939 0
$855$	−6.87864e37	−0.0180285
$856$	7.25603e35	0.000187199 0
$857$	1.79678e38	0.0456304	0.0228152	−	0.999740i	$-0.492737\pi$
$857$	1.79678e38	0.0456304	0.0228152	+	0.999740i	$0.492737\pi$
$858$	−1.18451e37	−0.00296114
$859$	−6.83644e39	−1.68237	−0.841187	−	0.540744i	$-0.818143\pi$
$859$	−6.83644e39	−1.68237	−0.841187	+	0.540744i	$0.818143\pi$
$860$	1.49398e38	0.0361922
$861$	1.20972e38	0.0288498
$862$	7.52074e37	0.0176568
$863$	−8.93182e37	−0.0206440	−0.0103220	−	0.999947i	$-0.503286\pi$
$863$	−8.93182e37	−0.0206440	−0.0103220	+	0.999947i	$0.503286\pi$
$864$	2.65190e37	0.00603424
$865$	−2.86543e39	−0.641907
$866$	−1.26905e37	−0.00279890
$867$	−5.16340e39	−1.12119
$868$	1.65347e38	0.0353492
$869$	4.49180e36	0.000945483 0
$870$	−1.19588e37	−0.00247845
$871$	2.04555e39	0.417412
$872$	1.75638e38	0.0352895
$873$	−1.05773e39	−0.209258
$874$	1.03472e37	0.00201566
$875$	−1.68703e38	−0.0323605
$876$	4.49008e39	0.848103
$877$	−4.74244e39	−0.882078	−0.441039	−	0.897488i	$-0.645390\pi$
$877$	−4.74244e39	−0.882078	−0.441039	+	0.897488i	$0.645390\pi$
$878$	−8.40191e37	−0.0153887
$879$	7.29176e38	0.131517
$880$	9.81843e38	0.174392
$881$	−4.04555e39	−0.707624	−0.353812	−	0.935317i	$-0.615115\pi$
$881$	−4.04555e39	−0.707624	−0.353812	+	0.935317i	$0.615115\pi$
$882$	2.01880e37	0.00347750
$883$	7.15911e39	1.21448	0.607239	−	0.794519i	$-0.292277\pi$
$883$	7.15911e39	1.21448	0.607239	+	0.794519i	$0.292277\pi$
$884$	−1.14029e40	−1.90507
$885$	1.83948e39	0.302665
$886$	−6.24697e37	−0.0101231
$887$	−3.43934e39	−0.548916	−0.274458	−	0.961599i	$-0.588498\pi$
$887$	−3.43934e39	−0.548916	−0.274458	+	0.961599i	$0.588498\pi$
$888$	9.85065e37	0.0154842
$889$	−2.43669e38	−0.0377247
$890$	4.42068e37	0.00674099
$891$	−3.26769e38	−0.0490785
$892$	3.04561e39	0.450556
$893$	1.61444e39	0.235248
$894$	−3.98108e37	−0.00571405
$895$	−4.64529e39	−0.656753
$896$	−1.33371e37	−0.00185739
$897$	6.58267e39	0.903034
$898$	−1.11041e38	−0.0150056
$899$	6.21481e39	0.827317
$900$	2.14515e39	0.281309
$901$	1.49696e40	1.93387
$902$	4.07997e37	0.00519241
$903$	1.87528e37	0.00235116
$904$	−1.20732e38	−0.0149125
$905$	5.99814e38	0.0729896
$906$	1.68720e37	0.00202273
$907$	2.71200e38	0.0320325	0.0160163	−	0.999872i	$-0.494902\pi$
$907$	2.71200e38	0.0320325	0.0160163	+	0.999872i	$0.494902\pi$
$908$	−1.12987e40	−1.31482
$909$	−2.51848e39	−0.288752
$910$	−1.80382e36	−0.000203767 0
$911$	1.18591e40	1.31994	0.659970	−	0.751292i	$-0.270569\pi$
$911$	1.18591e40	1.31994	0.659970	+	0.751292i	$0.270569\pi$
$912$	−7.20733e38	−0.0790394
$913$	3.28941e39	0.355436
$914$	−1.88015e38	−0.0200179
$915$	1.40356e39	0.147247
$916$	−5.50082e39	−0.568641
$917$	−5.85961e38	−0.0596874
$918$	3.43762e37	0.00345050
$919$	−1.70613e40	−1.68753	−0.843766	−	0.536711i	$-0.819667\pi$
$919$	−1.70613e40	−1.68753	−0.843766	+	0.536711i	$0.819667\pi$
$920$	1.19274e38	0.0116255
$921$	−3.99514e39	−0.383731
$922$	6.13793e37	0.00580971
$923$	−3.86409e39	−0.360433
$924$	1.23257e38	0.0113303
$925$	1.19526e40	1.08281
$926$	1.76174e38	0.0157287
$927$	−5.11478e39	−0.450039
$928$	−3.75977e38	−0.0326035
$929$	−8.89239e39	−0.759987	−0.379994	−	0.924989i	$-0.624074\pi$
$929$	−8.89239e39	−0.759987	−0.379994	+	0.924989i	$0.624074\pi$
$930$	−2.25140e37	−0.00189641
$931$	−1.64630e39	−0.136675
$932$	−9.38141e39	−0.767633
$933$	6.52243e39	0.526026
$934$	8.34875e37	0.00663649
$935$	3.81894e39	0.299217
$936$	1.00229e38	0.00774053
$937$	−1.80674e40	−1.37534	−0.687670	−	0.726023i	$-0.741367\pi$
$937$	−1.80674e40	−1.37534	−0.687670	+	0.726023i	$0.741367\pi$
$938$	2.32608e36	0.000174537 0
$939$	−8.88555e39	−0.657202
$940$	9.30449e39	0.678370
$941$	2.62451e40	1.88620	0.943101	−	0.332507i	$-0.107895\pi$
$941$	2.62451e40	1.88620	0.943101	+	0.332507i	$0.107895\pi$
$942$	7.07906e37	0.00501520
$943$	−2.26737e40	−1.58348
$944$	1.92738e40	1.32692
$945$	−4.97619e37	−0.00337728
$946$	6.32468e36	0.000423163 0
$947$	−6.71744e39	−0.443077	−0.221539	−	0.975152i	$-0.571108\pi$
$947$	−6.71744e39	−0.443077	−0.221539	+	0.975152i	$0.571108\pi$
$948$	−1.90031e37	−0.00123570
$949$	2.54560e40	1.63191
$950$	1.91168e37	0.00120822
$951$	−9.92594e39	−0.618493
$952$	−2.59349e37	−0.00159325
$953$	1.95322e39	0.118303	0.0591516	−	0.998249i	$-0.481160\pi$
$953$	1.95322e39	0.118303	0.0591516	+	0.998249i	$0.481160\pi$
$954$	−6.57865e37	−0.00392856
$955$	4.52199e39	0.266246
$956$	2.53743e40	1.47304
$957$	4.63281e39	0.265175
$958$	7.68507e37	0.00433724
$959$	−4.23686e38	−0.0235772
$960$	−4.15289e39	−0.227871
$961$	−6.78259e39	−0.366969
$962$	2.79220e38	0.0148965
$963$	5.67394e37	0.00298490
$964$	−1.36575e40	−0.708486
$965$	−5.23519e37	−0.00267802
$966$	7.48543e36	0.000377595 0
$967$	1.48699e40	0.739690	0.369845	−	0.929093i	$-0.379411\pi$
$967$	1.48699e40	0.739690	0.369845	+	0.929093i	$0.379411\pi$
$968$	−3.43012e38	−0.0168264
$969$	−2.80333e39	−0.135614
$970$	−5.43254e37	−0.00259170
$971$	−1.17711e40	−0.553804	−0.276902	−	0.960898i	$-0.589308\pi$
$971$	−1.17711e40	−0.553804	−0.276902	+	0.960898i	$0.589308\pi$
$972$	1.38243e39	0.0641430
$973$	1.14506e39	0.0523970
$974$	−3.00681e38	−0.0135694
$975$	1.21617e40	0.541292
$976$	1.47062e40	0.645549
$977$	−3.52154e40	−1.52460	−0.762300	−	0.647224i	$-0.775930\pi$
$977$	−3.52154e40	−1.52460	−0.762300	+	0.647224i	$0.775930\pi$
$978$	−1.80185e38	−0.00769385
$979$	−1.71255e40	−0.721236
$980$	−9.48813e39	−0.394120
$981$	1.37342e40	0.562693
$982$	2.87514e38	0.0116186
$983$	−3.23914e40	−1.29109	−0.645547	−	0.763721i	$-0.723371\pi$
$983$	−3.23914e40	−1.29109	−0.645547	+	0.763721i	$0.723371\pi$
$984$	−3.45234e38	−0.0135731
$985$	2.58830e38	0.0100375
$986$	−4.87374e38	−0.0186433
$987$	1.16793e39	0.0440691
$988$	−4.08656e39	−0.152103
$989$	−3.51482e39	−0.129049
$990$	−1.67830e37	−0.000607845 0
$991$	5.97175e38	0.0213357	0.0106679	−	0.999943i	$-0.496604\pi$
$991$	5.97175e38	0.0213357	0.0106679	+	0.999943i	$0.496604\pi$
$992$	−7.07822e38	−0.0249469
$993$	1.06668e40	0.370868
$994$	−4.39403e36	−0.000150712 0
$995$	−7.98421e39	−0.270160
$996$	−1.39162e40	−0.464536
$997$	−1.51823e40	−0.499980	−0.249990	−	0.968248i	$-0.580427\pi$
$997$	−1.51823e40	−0.499980	−0.249990	+	0.968248i	$0.580427\pi$
$998$	6.06396e38	0.0197013
$999$	7.70283e39	0.246897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.28.a.b.1.1	✓	2
3.2	odd	2		9.28.a.b.1.2		2
4.3	odd	2		48.28.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.28.a.b.1.1	✓	2	1.1	even	1	trivial
9.28.a.b.1.2		2	3.2	odd	2
48.28.a.e.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-121.102 q^{2} -1.59432e6 q^{3} -1.34203e8 q^{4} -1.07803e9 q^{5} +1.93076e8 q^{6} -1.13904e10 q^{7} +3.25063e10 q^{8} +2.54187e12 q^{9} +O(q^{10})\)	\(q-121.102 q^{2} -1.59432e6 q^{3} -1.34203e8 q^{4} -1.07803e9 q^{5} +1.93076e8 q^{6} -1.13904e10 q^{7} +3.25063e10 q^{8} +2.54187e12 q^{9} +1.30551e11 q^{10} -5.05749e13 q^{11} +2.13963e14 q^{12} +1.21304e15 q^{13} +1.37940e12 q^{14} +1.71872e15 q^{15} +1.80085e16 q^{16} +7.00452e16 q^{17} -3.07825e14 q^{18} +2.51027e16 q^{19} +1.44674e17 q^{20} +1.81600e16 q^{21} +6.12472e15 q^{22} -3.40370e18 q^{23} -5.18255e16 q^{24} -6.28844e18 q^{25} -1.46901e17 q^{26} -4.05256e18 q^{27} +1.52863e18 q^{28} +5.74556e19 q^{29} -2.08141e17 q^{30} +1.08167e20 q^{31} -6.54378e18 q^{32} +8.06328e19 q^{33} -8.48261e18 q^{34} +1.22791e19 q^{35} -3.41126e20 q^{36} -1.90073e21 q^{37} -3.03999e18 q^{38} -1.93398e21 q^{39} -3.50426e19 q^{40} +6.66148e21 q^{41} -2.19921e18 q^{42} +1.03265e21 q^{43} +6.78731e21 q^{44} -2.74020e21 q^{45} +4.12194e20 q^{46} +6.43133e22 q^{47} -2.87114e22 q^{48} -6.55826e22 q^{49} +7.61542e20 q^{50} -1.11675e23 q^{51} -1.62794e23 q^{52} +2.13714e23 q^{53} +4.90772e20 q^{54} +5.45211e22 q^{55} -3.70259e20 q^{56} -4.00218e22 q^{57} -6.95799e21 q^{58} +1.07026e24 q^{59} -2.30658e23 q^{60} +8.16628e23 q^{61} -1.30992e22 q^{62} -2.89528e22 q^{63} -2.41627e24 q^{64} -1.30769e24 q^{65} -9.76479e21 q^{66} +1.68630e24 q^{67} -9.40028e24 q^{68} +5.42659e24 q^{69} -1.48703e21 q^{70} -3.18547e24 q^{71} +8.26266e22 q^{72} +2.09853e25 q^{73} +2.30183e23 q^{74} +1.00258e25 q^{75} -3.36886e24 q^{76} +5.76068e23 q^{77} +2.34208e23 q^{78} -8.88148e22 q^{79} -1.94136e25 q^{80} +6.46108e24 q^{81} -8.06718e23 q^{82} -6.50402e25 q^{83} -2.43712e24 q^{84} -7.55105e25 q^{85} -1.25056e23 q^{86} -9.16028e25 q^{87} -1.64400e24 q^{88} +3.38617e26 q^{89} +3.31843e23 q^{90} -1.38170e25 q^{91} +4.56787e26 q^{92} -1.72453e26 q^{93} -7.78847e24 q^{94} -2.70614e25 q^{95} +1.04329e25 q^{96} -4.16124e26 q^{97} +7.94218e24 q^{98} -1.28555e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9}+O(q^{10}) \) 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9	\( 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9} - 14929666656300 q^{10} + 75762335668248 q^{11} - 323015968377612 q^{12} - 103021079177588 q^{13} + 82\!\cdots\!36 q^{14}+ \cdots + 19\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9 - 14929666656300 * q^10 + 75762335668248 * q^11 - 323015968377612 * q^12 - 103021079177588 * q^13 + 8271467686583136 * q^14 + 2825054421990300 * q^15 + 68227529433700880 * q^16 + 34691611579147908 * q^17 + 54858548306996478 * q^18 + 111620476558642216 * q^19 - 89042670767082600 * q^20 - 589365730506544992 * q^21 + 2748035308851015336 * q^22 - 2892743075819387952 * q^23 - 7061766547600378152 * q^24 - 13257495997920171250 * q^25 - 28709486590882989996 * q^26 - 8105110306037952534 * q^27 + 129870778968981827392 * q^28 + 29959552473322806972 * q^29 + 23802710932472184900 * q^30 + 10367463257055494032 * q^31 + 493234742263884106464 * q^32 - 120789634289608156104 * q^33 - 775764702062031404772 * q^34 - 252142979584030920000 * q^35 + 514991787751699496676 * q^36 - 3703660908819524869316 * q^37 + 1874664150379356981528 * q^38 + 164248876017649632924 * q^39 - 3086079750063749300400 * q^40 + 1481814928479478034772 * q^41 - 13187391176476285136928 * q^42 + 9778778623457380249240 * q^43 + 49338574711945832880432 * q^44 - 4504049241230841066900 * q^45 + 11501496706538201034672 * q^46 + 89494998518809740323520 * q^47 - 108776719409326288104240 * q^48 + 13908377820361409575890 * q^49 - 150488580768890263638750 * q^50 - 55309634247701830126284 * q^51 - 606051653487262224622952 * q^52 + 425671275824601813476748 * q^53 - 87462245312455545794394 * q^54 - 33146870181194328159600 * q^55 + 1675060131754321848708480 * q^56 - 177959093048404133739768 * q^57 - 603708195922408484547804 * q^58 + 369418769643380130292824 * q^59 + 141962777985387432079800 * q^60 + 925133397428892745249420 * q^61 - 2135654804561872705821072 * q^62 + 939639339558386331280416 * q^63 + 1690192763441891790257216 * q^64 - 394447136075147294825400 * q^65 - 4381255897713277323537528 * q^66 + 4151706674555213948132968 * q^67 - 21307603540300350668680824 * q^68 + 4611966818869594057796496 * q^69 - 5740267152557252353752000 * q^70 + 9760455855870867537668784 * q^71 + 11258736827469877696431096 * q^72 + 28449956347640075157409588 * q^73 - 38898941191404112127623644 * q^74 + 21136730791892081187813750 * q^75 + 25770925690602426011538256 * q^76 + 48717589762471785388668288 * q^77 + 45772194790036341259392708 * q^78 - 49553221898675501744231120 * q^79 - 54261621238075868678378400 * q^80 + 12922163778453346597864482 * q^81 - 113221448313178537381548852 * q^82 - 120473408203228735926347736 * q^83 - 207055969938164013993095616 * q^84 - 50977978054175038499879400 * q^85 + 189693121470759531169760808 * q^86 - 47765203577925437580019956 * q^87 + 553837409674913803181095584 * q^88 + 205644052209697133056985556 * q^89 - 37949209501991851246322700 * q^90 - 515309018103795393250147648 * q^91 + 628879743331458256476717984 * q^92 - 16529085122378486411580336 * q^93 + 538732610344725656813388864 * q^94 - 87097784513216888583651600 * q^95 - 786375493990382500270003872 * q^96 - 1478339006400409594836427772 * q^97 + 1733143443943237696043598078 * q^98 + 192577692109510944264197592 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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