LMFDB - Embedded newform 5.26.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,26,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	5.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:	$19.7998389976$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1769856x^{2} + 106836475x + 628040620025 $ x^4 - x^3 - 1769856x^2 + 106836475x + 628040620025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$785.715$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6133.72 q^{2} -1.60154e6 q^{3} +4.06809e6 q^{4} -2.44141e8 q^{5} +9.82339e9 q^{6} -2.17553e9 q^{7} +1.80861e11 q^{8} +1.71764e12 q^{9} +O(q^{10})$	\(q-6133.72 q^{2} -1.60154e6 q^{3} +4.06809e6 q^{4} -2.44141e8 q^{5} +9.82339e9 q^{6} -2.17553e9 q^{7} +1.80861e11 q^{8} +1.71764e12 q^{9} +1.49749e12 q^{10} -8.98635e12 q^{11} -6.51521e12 q^{12} +1.16354e14 q^{13} +1.33441e13 q^{14} +3.91001e14 q^{15} -1.24585e15 q^{16} +2.27335e15 q^{17} -1.05355e16 q^{18} -1.75942e16 q^{19} -9.93187e14 q^{20} +3.48419e15 q^{21} +5.51198e16 q^{22} +1.45315e15 q^{23} -2.89656e17 q^{24} +5.96046e16 q^{25} -7.13685e17 q^{26} -1.39390e18 q^{27} -8.85025e15 q^{28} +1.07238e18 q^{29} -2.39829e18 q^{30} +5.76804e18 q^{31} +1.57303e18 q^{32} +1.43920e19 q^{33} -1.39441e19 q^{34} +5.31135e17 q^{35} +6.98751e18 q^{36} +6.50051e19 q^{37} +1.07918e20 q^{38} -1.86346e20 q^{39} -4.41555e19 q^{40} +5.23898e19 q^{41} -2.13711e19 q^{42} -1.34400e20 q^{43} -3.65573e19 q^{44} -4.19345e20 q^{45} -8.91324e18 q^{46} -1.15282e20 q^{47} +1.99528e21 q^{48} -1.33634e21 q^{49} -3.65598e20 q^{50} -3.64085e21 q^{51} +4.73340e20 q^{52} -4.60571e21 q^{53} +8.54977e21 q^{54} +2.19393e21 q^{55} -3.93468e20 q^{56} +2.81778e22 q^{57} -6.57765e21 q^{58} +1.73561e22 q^{59} +1.59063e21 q^{60} -3.93060e22 q^{61} -3.53795e22 q^{62} -3.73677e21 q^{63} +3.21554e22 q^{64} -2.84068e22 q^{65} -8.82765e22 q^{66} +5.12843e21 q^{67} +9.24819e21 q^{68} -2.32728e21 q^{69} -3.25783e21 q^{70} +1.37350e23 q^{71} +3.10653e23 q^{72} -1.15989e23 q^{73} -3.98723e23 q^{74} -9.54591e22 q^{75} -7.15750e22 q^{76} +1.95501e22 q^{77} +1.14299e24 q^{78} -4.01895e23 q^{79} +3.04163e23 q^{80} +7.77044e23 q^{81} -3.21344e23 q^{82} -6.71311e23 q^{83} +1.41740e22 q^{84} -5.55017e23 q^{85} +8.24373e23 q^{86} -1.71745e24 q^{87} -1.62528e24 q^{88} +3.91519e23 q^{89} +2.57214e24 q^{90} -2.53132e23 q^{91} +5.91157e21 q^{92} -9.23774e24 q^{93} +7.07107e23 q^{94} +4.29547e24 q^{95} -2.51927e24 q^{96} +4.07158e24 q^{97} +8.19671e24 q^{98} -1.54353e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9}+O(q^{10}) $ 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9	$ 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9} - 146484375000 q^{10} - 23641453790592 q^{11} - 42051883516800 q^{12} + 109063914225800 q^{13} + 109980501036336 q^{14} + 194970703125000 q^{15} - 28\!\cdots\!76 q^{16}+ \cdots - 19\!\cdots\!16 q^{99}+O(q^{100}) $ 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9 - 146484375000 * q^10 - 23641453790592 * q^11 - 42051883516800 * q^12 + 109063914225800 * q^13 + 109980501036336 * q^14 + 194970703125000 * q^15 - 2811357146648576 * q^16 - 337440158866200 * q^17 - 8986517054418600 * q^18 - 5765957235759760 * q^19 - 22561984375000000 * q^20 - 76777748650758672 * q^21 - 247170171892300800 * q^22 - 84289919171581800 * q^23 - 750163283268986880 * q^24 + 238418579101562500 * q^25 - 2172668626545951312 * q^26 - 2324539610168425200 * q^27 + 715367314323708800 * q^28 - 1530771705074446440 * q^29 + 968060261718750000 * q^30 - 3405335632352491792 * q^31 + 8794451084429721600 * q^32 + 38579776790129836800 * q^33 + 12360736169963080176 * q^34 + 11947780029296875000 * q^35 + 29754645353627097024 * q^36 + 54849661150838347400 * q^37 + 167830012254298039200 * q^38 + 26980019582506147824 * q^39 - 54793331250000000000 * q^40 + 294765092997163901208 * q^41 - 275649307903658959200 * q^42 - 1266847513533640537000 * q^43 - 739285598894744039424 * q^44 - 509659620969726562500 * q^45 - 669486761007570298992 * q^46 + 826481836956124900200 * q^47 - 389112939053996236800 * q^48 - 2497667097456123567372 * q^49 + 35762786865234375000 * q^50 - 732051781800631123152 * q^51 - 3824820275638519888000 * q^52 + 7304325845439007895400 * q^53 + 15784899184389947603040 * q^54 + 5771839304343750000000 * q^55 + 14029366421126577776640 * q^56 + 15974193201590955213600 * q^57 + 11714010248956820950800 * q^58 - 2217164203172823251280 * q^59 + 10266573124218750000000 * q^60 - 50917697960481835727992 * q^61 - 24701477049499711624800 * q^62 + 2223612189174803070600 * q^63 - 20457521683182533476352 * q^64 - 26626932184033203125000 * q^65 - 16106812566256687908864 * q^66 - 76670956029519070862200 * q^67 - 318284068848532686249600 * q^68 - 211835176227690988743216 * q^69 - 26850708260824218750000 * q^70 + 150298050225701362285008 * q^71 + 399372518437664399078400 * q^72 - 106773821938777386935800 * q^73 + 286932321536483813083056 * q^74 - 47600269317626953125000 * q^75 + 793491830268069721114880 * q^76 - 215630079777610746336000 * q^77 + 1847661803543761572804000 * q^78 - 151978174282543555164640 * q^79 + 686366490881000000000000 * q^80 - 1579018732178689012033836 * q^81 + 3094333027045954774045200 * q^82 + 117573693202171400616600 * q^83 - 1614703102161158475120384 * q^84 + 82382851285693359375000 * q^85 - 1608810179612708665216752 * q^86 - 2896477998479054993943600 * q^87 - 4936697892190706144870400 * q^88 - 6860971673379749077360920 * q^89 + 2193973890238916015625000 * q^90 - 5097829330173411603898352 * q^91 + 6577026773676031203676800 * q^92 - 13171898336704209119455200 * q^93 + 1406225817996660389994096 * q^94 + 1407704403261660156250000 * q^95 + 13005904207859351375904768 * q^96 + 8538350425643241402216200 * q^97 + 10780561809722171059198200 * q^98 - 19223568526197742048146816 * 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 $

$2$	−6133.72	−1.05889	−0.529443	−	0.848346i	$-0.677599\pi$
$2$	−6133.72	−1.05889	−0.529443	+	0.848346i	$0.677599\pi$
$3$	−1.60154e6	−1.73989	−0.869945	−	0.493149i	$-0.835846\pi$
$3$	−1.60154e6	−1.73989	−0.869945	+	0.493149i	$0.835846\pi$
$4$	4.06809e6	0.121239
$5$	−2.44141e8	−0.447214
$5$	−2.44141e8	−0.447214
$6$	9.82339e9	1.84234
$7$	−2.17553e9	−0.0594072	−0.0297036	−	0.999559i	$-0.509456\pi$
$7$	−2.17553e9	−0.0594072	−0.0297036	+	0.999559i	$0.509456\pi$
$8$	1.80861e11	0.930508
$9$	1.71764e12	2.02722
$10$	1.49749e12	0.473548
$11$	−8.98635e12	−0.863326	−0.431663	−	0.902035i	$-0.642073\pi$
$11$	−8.98635e12	−0.863326	−0.431663	+	0.902035i	$0.642073\pi$
$12$	−6.51521e12	−0.210942
$13$	1.16354e14	1.38513	0.692565	−	0.721355i	$-0.256481\pi$
$13$	1.16354e14	1.38513	0.692565	+	0.721355i	$0.256481\pi$
$14$	1.33441e13	0.0629054
$15$	3.91001e14	0.778102
$16$	−1.24585e15	−1.10654
$17$	2.27335e15	0.946356	0.473178	−	0.880967i	$-0.343107\pi$
$17$	2.27335e15	0.946356	0.473178	+	0.880967i	$0.343107\pi$
$18$	−1.05355e16	−2.14659
$19$	−1.75942e16	−1.82369	−0.911844	−	0.410538i	$-0.865341\pi$
$19$	−1.75942e16	−1.82369	−0.911844	+	0.410538i	$0.865341\pi$
$20$	−9.93187e14	−0.0542196
$21$	3.48419e15	0.103362
$22$	5.51198e16	0.914164
$23$	1.45315e15	0.0138266	0.00691328	−	0.999976i	$-0.497799\pi$
$23$	1.45315e15	0.0138266	0.00691328	+	0.999976i	$0.497799\pi$
$24$	−2.89656e17	−1.61898
$25$	5.96046e16	0.200000
$26$	−7.13685e17	−1.46669
$27$	−1.39390e18	−1.78724
$28$	−8.85025e15	−0.00720245
$29$	1.07238e18	0.562823	0.281411	−	0.959587i	$-0.409197\pi$
$29$	1.07238e18	0.562823	0.281411	+	0.959587i	$0.409197\pi$
$30$	−2.39829e18	−0.823921
$31$	5.76804e18	1.31525	0.657623	−	0.753347i	$-0.271562\pi$
$31$	5.76804e18	1.31525	0.657623	+	0.753347i	$0.271562\pi$
$32$	1.57303e18	0.241191
$33$	1.43920e19	1.50209
$34$	−1.39441e19	−1.00208
$35$	5.31135e17	0.0265677
$36$	6.98751e18	0.245777
$37$	6.50051e19	1.62340	0.811701	−	0.584073i	$-0.198542\pi$
$37$	6.50051e19	1.62340	0.811701	+	0.584073i	$0.198542\pi$
$38$	1.07918e20	1.93108
$39$	−1.86346e20	−2.40997
$40$	−4.41555e19	−0.416136
$41$	5.23898e19	0.362617	0.181309	−	0.983426i	$-0.441967\pi$
$41$	5.23898e19	0.362617	0.181309	+	0.983426i	$0.441967\pi$
$42$	−2.13711e19	−0.109448
$43$	−1.34400e20	−0.512913	−0.256457	−	0.966556i	$-0.582555\pi$
$43$	−1.34400e20	−0.512913	−0.256457	+	0.966556i	$0.582555\pi$
$44$	−3.65573e19	−0.104669
$45$	−4.19345e20	−0.906598
$46$	−8.91324e18	−0.0146407
$47$	−1.15282e20	−0.144723	−0.0723615	−	0.997378i	$-0.523054\pi$
$47$	−1.15282e20	−0.144723	−0.0723615	+	0.997378i	$0.523054\pi$
$48$	1.99528e21	1.92526
$49$	−1.33634e21	−0.996471
$50$	−3.65598e20	−0.211777
$51$	−3.64085e21	−1.64655
$52$	4.73340e20	0.167931
$53$	−4.60571e21	−1.28780	−0.643900	−	0.765110i	$-0.722685\pi$
$53$	−4.60571e21	−1.28780	−0.643900	+	0.765110i	$0.722685\pi$
$54$	8.54977e21	1.89248
$55$	2.19393e21	0.386091
$56$	−3.93468e20	−0.0552789
$57$	2.81778e22	3.17301
$58$	−6.57765e21	−0.595965
$59$	1.73561e22	1.27000	0.634998	−	0.772513i	$-0.281001\pi$
$59$	1.73561e22	1.27000	0.634998	+	0.772513i	$0.281001\pi$
$60$	1.59063e21	0.0943361
$61$	−3.93060e22	−1.89599	−0.947995	−	0.318286i	$-0.896893\pi$
$61$	−3.93060e22	−1.89599	−0.947995	+	0.318286i	$0.896893\pi$
$62$	−3.53795e22	−1.39270
$63$	−3.73677e21	−0.120431
$64$	3.21554e22	0.851146
$65$	−2.84068e22	−0.619449
$66$	−8.82765e22	−1.59054
$67$	5.12843e21	0.0765683	0.0382842	−	0.999267i	$-0.487811\pi$
$67$	5.12843e21	0.0765683	0.0382842	+	0.999267i	$0.487811\pi$
$68$	9.24819e21	0.114735
$69$	−2.32728e21	−0.0240567
$70$	−3.25783e21	−0.0281322
$71$	1.37350e23	0.993344	0.496672	−	0.867938i	$-0.334555\pi$
$71$	1.37350e23	0.993344	0.496672	+	0.867938i	$0.334555\pi$
$72$	3.10653e23	1.88634
$73$	−1.15989e23	−0.592765	−0.296382	−	0.955069i	$-0.595780\pi$
$73$	−1.15989e23	−0.592765	−0.296382	+	0.955069i	$0.595780\pi$
$74$	−3.98723e23	−1.71900
$75$	−9.54591e22	−0.347978
$76$	−7.15750e22	−0.221101
$77$	1.95501e22	0.0512878
$78$	1.14299e24	2.55189
$79$	−4.01895e23	−0.765198	−0.382599	−	0.923915i	$-0.624971\pi$
$79$	−4.01895e23	−0.765198	−0.382599	+	0.923915i	$0.624971\pi$
$80$	3.04163e23	0.494860
$81$	7.77044e23	1.08239
$82$	−3.21344e23	−0.383970
$83$	−6.71311e23	−0.689363	−0.344681	−	0.938720i	$-0.612013\pi$
$83$	−6.71311e23	−0.689363	−0.344681	+	0.938720i	$0.612013\pi$
$84$	1.41740e22	0.0125315
$85$	−5.55017e23	−0.423223
$86$	8.24373e23	0.543116
$87$	−1.71745e24	−0.979250
$88$	−1.62528e24	−0.803332
$89$	3.91519e23	0.168026	0.0840132	−	0.996465i	$-0.473226\pi$
$89$	3.91519e23	0.168026	0.0840132	+	0.996465i	$0.473226\pi$
$90$	2.57214e24	0.959984
$91$	−2.53132e23	−0.0822867
$92$	5.91157e21	0.00167631
$93$	−9.23774e24	−2.28838
$94$	7.07107e23	0.153245
$95$	4.29547e24	0.815578
$96$	−2.51927e24	−0.419646
$97$	4.07158e24	0.595822	0.297911	−	0.954594i	$-0.403710\pi$
$97$	4.07158e24	0.595822	0.297911	+	0.954594i	$0.403710\pi$
$98$	8.19671e24	1.05515
$99$	−1.54353e25	−1.75015
$100$	2.42477e23	0.0242477
$101$	3.11692e24	0.275238	0.137619	−	0.990485i	$-0.456055\pi$
$101$	3.11692e24	0.275238	0.137619	+	0.990485i	$0.456055\pi$
$102$	2.23320e25	1.74351
$103$	−5.35436e24	−0.370035	−0.185017	−	0.982735i	$-0.559234\pi$
$103$	−5.35436e24	−0.370035	−0.185017	+	0.982735i	$0.559234\pi$
$104$	2.10439e25	1.28887
$105$	−8.50633e23	−0.0462249
$106$	2.82501e25	1.36363
$107$	1.28079e25	0.549772	0.274886	−	0.961477i	$-0.411360\pi$
$107$	1.28079e25	0.549772	0.274886	+	0.961477i	$0.411360\pi$
$108$	−5.67050e24	−0.216683
$109$	−2.77995e25	−0.946684	−0.473342	−	0.880879i	$-0.656953\pi$
$109$	−2.77995e25	−0.946684	−0.473342	+	0.880879i	$0.656953\pi$
$110$	−1.34570e25	−0.408826
$111$	−1.04108e26	−2.82454
$112$	2.71039e24	0.0657364
$113$	7.32888e25	1.59059	0.795293	−	0.606225i	$-0.207317\pi$
$113$	7.32888e25	1.59059	0.795293	+	0.606225i	$0.207317\pi$
$114$	−1.72835e26	−3.35986
$115$	−3.54774e23	−0.00618342
$116$	4.36252e24	0.0682359
$117$	1.99854e26	2.80796
$118$	−1.06458e26	−1.34478
$119$	−4.94573e24	−0.0562203
$120$	7.07167e25	0.724030
$121$	−2.75925e25	−0.254668
$122$	2.41092e26	2.00764
$123$	−8.39043e25	−0.630914
$124$	2.34649e25	0.159459
$125$	−1.45519e25	−0.0894427
$126$	2.29203e25	0.127523
$127$	−1.56254e26	−0.787562	−0.393781	−	0.919204i	$-0.628833\pi$
$127$	−1.56254e26	−0.787562	−0.393781	+	0.919204i	$0.628833\pi$
$128$	−2.50014e26	−1.14246
$129$	2.15247e26	0.892412
$130$	1.74239e26	0.655926
$131$	−1.68244e26	−0.575503	−0.287751	−	0.957705i	$-0.592908\pi$
$131$	−1.68244e26	−0.575503	−0.287751	+	0.957705i	$0.592908\pi$
$132$	5.85480e25	0.182112
$133$	3.82767e25	0.108340
$134$	−3.14563e25	−0.0810771
$135$	3.40307e26	0.799279
$136$	4.11160e26	0.880591
$137$	4.68654e26	0.915893	0.457947	−	0.888980i	$-0.348585\pi$
$137$	4.68654e26	0.915893	0.457947	+	0.888980i	$0.348585\pi$
$138$	1.42749e25	0.0254733
$139$	−7.98365e26	−1.30172	−0.650858	−	0.759199i	$-0.725591\pi$
$139$	−7.98365e26	−1.30172	−0.650858	+	0.759199i	$0.725591\pi$
$140$	2.16071e24	0.00322103
$141$	1.84628e26	0.251802
$142$	−8.42467e26	−1.05184
$143$	−1.04560e27	−1.19582
$144$	−2.13992e27	−2.24319
$145$	−2.61810e26	−0.251702
$146$	7.11446e26	0.627670
$147$	2.14019e27	1.73375
$148$	2.64447e26	0.196819
$149$	−4.03414e26	−0.276009	−0.138004	−	0.990432i	$-0.544069\pi$
$149$	−4.03414e26	−0.276009	−0.138004	+	0.990432i	$0.544069\pi$
$150$	5.85520e26	0.368469
$151$	1.67851e26	0.0972103	0.0486051	−	0.998818i	$-0.484522\pi$
$151$	1.67851e26	0.0972103	0.0486051	+	0.998818i	$0.484522\pi$
$152$	−3.18211e27	−1.69696
$153$	3.90479e27	1.91847
$154$	−1.19915e26	−0.0543079
$155$	−1.40821e27	−0.588196
$156$	−7.58073e26	−0.292182
$157$	2.80218e27	0.997126	0.498563	−	0.866854i	$-0.333861\pi$
$157$	2.80218e27	0.997126	0.498563	+	0.866854i	$0.333861\pi$
$158$	2.46511e27	0.810257
$159$	7.37622e27	2.24063
$160$	−3.84040e26	−0.107864
$161$	−3.16138e24	−0.000821397 0
$162$	−4.76617e27	−1.14612
$163$	−5.93323e27	−1.32113	−0.660566	−	0.750768i	$-0.729684\pi$
$163$	−5.93323e27	−1.32113	−0.660566	+	0.750768i	$0.729684\pi$
$164$	2.13127e26	0.0439632
$165$	−3.51367e27	−0.671756
$166$	4.11763e27	0.729956
$167$	5.03281e27	0.827665	0.413832	−	0.910353i	$-0.364190\pi$
$167$	5.03281e27	0.827665	0.413832	+	0.910353i	$0.364190\pi$
$168$	6.30154e26	0.0961791
$169$	6.48191e27	0.918585
$170$	3.40432e27	0.448145
$171$	−3.02205e28	−3.69701
$172$	−5.46752e26	−0.0621849
$173$	−1.22991e28	−1.30106	−0.650530	−	0.759480i	$-0.725453\pi$
$173$	−1.22991e28	−1.30106	−0.650530	+	0.759480i	$0.725453\pi$
$174$	1.05344e28	1.03691
$175$	−1.29672e26	−0.0118814
$176$	1.11957e28	0.955305
$177$	−2.77965e28	−2.20965
$178$	−2.40147e27	−0.177921
$179$	1.11967e28	0.773442	0.386721	−	0.922197i	$-0.373608\pi$
$179$	1.11967e28	0.773442	0.386721	+	0.922197i	$0.373608\pi$
$180$	−1.70593e27	−0.109915
$181$	−3.30295e27	−0.198573	−0.0992864	−	0.995059i	$-0.531656\pi$
$181$	−3.30295e27	−0.198573	−0.0992864	+	0.995059i	$0.531656\pi$
$182$	1.55264e27	0.0871322
$183$	6.29501e28	3.29881
$184$	2.62819e26	0.0128657
$185$	−1.58704e28	−0.726007
$186$	5.66617e28	2.42314
$187$	−2.04291e28	−0.817014
$188$	−4.68978e26	−0.0175460
$189$	3.03246e27	0.106175
$190$	−2.63472e28	−0.863603
$191$	1.98666e28	0.609825	0.304913	−	0.952380i	$-0.401373\pi$
$191$	1.98666e28	0.609825	0.304913	+	0.952380i	$0.401373\pi$
$192$	−5.14981e28	−1.48090
$193$	−5.55158e28	−1.49606	−0.748032	−	0.663663i	$-0.769001\pi$
$193$	−5.55158e28	−1.49606	−0.748032	+	0.663663i	$0.769001\pi$
$194$	−2.49740e28	−0.630907
$195$	4.54946e28	1.07777
$196$	−5.43634e27	−0.120811
$197$	4.62899e28	0.965292	0.482646	−	0.875816i	$-0.339676\pi$
$197$	4.62899e28	0.965292	0.482646	+	0.875816i	$0.339676\pi$
$198$	9.46758e28	1.85321
$199$	−6.98123e28	−1.28312	−0.641562	−	0.767071i	$-0.721713\pi$
$199$	−6.98123e28	−1.28312	−0.641562	+	0.767071i	$0.721713\pi$
$200$	1.07802e28	0.186102
$201$	−8.21337e27	−0.133220
$202$	−1.91183e28	−0.291446
$203$	−2.33298e27	−0.0334357
$204$	−1.48113e28	−0.199626
$205$	−1.27905e28	−0.162167
$206$	3.28422e28	0.391824
$207$	2.49599e27	0.0280294
$208$	−1.44960e29	−1.53270
$209$	1.58108e29	1.57444
$210$	5.21754e27	0.0489469
$211$	−5.77611e28	−0.510628	−0.255314	−	0.966858i	$-0.582179\pi$
$211$	−5.77611e28	−0.510628	−0.255314	+	0.966858i	$0.582179\pi$
$212$	−1.87365e28	−0.156131
$213$	−2.19971e29	−1.72831
$214$	−7.85604e28	−0.582145
$215$	3.28125e28	0.229382
$216$	−2.52101e29	−1.66304
$217$	−1.25485e28	−0.0781351
$218$	1.70514e29	1.00243
$219$	1.85761e29	1.03135
$220$	8.92513e27	0.0468092
$221$	2.64514e29	1.31083
$222$	6.38571e29	2.99086
$223$	8.62394e28	0.381852	0.190926	−	0.981604i	$-0.438851\pi$
$223$	8.62394e28	0.381852	0.190926	+	0.981604i	$0.438851\pi$
$224$	−3.42217e27	−0.0143285
$225$	1.02379e29	0.405443
$226$	−4.49533e29	−1.68425
$227$	1.40627e29	0.498594	0.249297	−	0.968427i	$-0.419801\pi$
$227$	1.40627e29	0.498594	0.249297	+	0.968427i	$0.419801\pi$
$228$	1.14630e29	0.384692
$229$	−7.75165e28	−0.246292	−0.123146	−	0.992389i	$-0.539298\pi$
$229$	−7.75165e28	−0.246292	−0.123146	+	0.992389i	$0.539298\pi$
$230$	2.17608e27	0.00654754
$231$	−3.13102e28	−0.0892351
$232$	1.93951e29	0.523711
$233$	−4.23387e29	−1.08340	−0.541700	−	0.840572i	$-0.682219\pi$
$233$	−4.23387e29	−1.08340	−0.541700	+	0.840572i	$0.682219\pi$
$234$	−1.22585e30	−2.97331
$235$	2.81450e28	0.0647221
$236$	7.06064e28	0.153973
$237$	6.43650e29	1.33136
$238$	3.03357e28	0.0595309
$239$	−6.99856e29	−1.30327	−0.651636	−	0.758532i	$-0.725917\pi$
$239$	−6.99856e29	−1.30327	−0.651636	+	0.758532i	$0.725917\pi$
$240$	−4.87129e29	−0.861001
$241$	4.16386e29	0.698688	0.349344	−	0.936995i	$-0.386404\pi$
$241$	4.16386e29	0.698688	0.349344	+	0.936995i	$0.386404\pi$
$242$	1.69245e29	0.269664
$243$	−6.34337e28	−0.0959935
$244$	−1.59901e29	−0.229867
$245$	3.26254e29	0.445635
$246$	5.14646e29	0.668066
$247$	−2.04716e30	−2.52604
$248$	1.04321e30	1.22385
$249$	1.07513e30	1.19941
$250$	8.92574e28	0.0947096
$251$	−6.78513e29	−0.684915	−0.342458	−	0.939533i	$-0.611259\pi$
$251$	−6.78513e29	−0.684915	−0.342458	+	0.939533i	$0.611259\pi$
$252$	−1.52015e28	−0.0146009
$253$	−1.30586e28	−0.0119368
$254$	9.58418e29	0.833938
$255$	8.88880e29	0.736362
$256$	4.54562e29	0.358586
$257$	−1.39562e29	−0.104858	−0.0524290	−	0.998625i	$-0.516696\pi$
$257$	−1.39562e29	−0.104858	−0.0524290	+	0.998625i	$0.516696\pi$
$258$	−1.32026e30	−0.944963
$259$	−1.41420e29	−0.0964417
$260$	−1.15562e29	−0.0751012
$261$	1.84195e30	1.14096
$262$	1.03196e30	0.609391
$263$	−1.75699e30	−0.989287	−0.494644	−	0.869096i	$-0.664701\pi$
$263$	−1.75699e30	−0.989287	−0.494644	+	0.869096i	$0.664701\pi$
$264$	2.60295e30	1.39771
$265$	1.12444e30	0.575922
$266$	−2.34779e29	−0.114720
$267$	−6.27032e29	−0.292347
$268$	2.08629e28	0.00928304
$269$	−9.84406e29	−0.418091	−0.209045	−	0.977906i	$-0.567036\pi$
$269$	−9.84406e29	−0.418091	−0.209045	+	0.977906i	$0.567036\pi$
$270$	−2.08735e30	−0.846345
$271$	−1.20481e30	−0.466449	−0.233224	−	0.972423i	$-0.574928\pi$
$271$	−1.20481e30	−0.466449	−0.233224	+	0.972423i	$0.574928\pi$
$272$	−2.83226e30	−1.04718
$273$	4.05401e29	0.143170
$274$	−2.87459e30	−0.969826
$275$	−5.35628e29	−0.172665
$276$	−9.46761e27	−0.00291660
$277$	−4.15693e30	−1.22398	−0.611992	−	0.790864i	$-0.709632\pi$
$277$	−4.15693e30	−1.22398	−0.611992	+	0.790864i	$0.709632\pi$
$278$	4.89695e30	1.37837
$279$	9.90740e30	2.66629
$280$	9.60615e28	0.0247215
$281$	−6.64698e30	−1.63604	−0.818022	−	0.575187i	$-0.804929\pi$
$281$	−6.64698e30	−1.63604	−0.818022	+	0.575187i	$0.804929\pi$
$282$	−1.13246e30	−0.266630
$283$	1.97527e30	0.444935	0.222467	−	0.974940i	$-0.428589\pi$
$283$	1.97527e30	0.444935	0.222467	+	0.974940i	$0.428589\pi$
$284$	5.58753e29	0.120432
$285$	−6.87936e30	−1.41902
$286$	6.41342e30	1.26624
$287$	−1.13975e29	−0.0215421
$288$	2.70189e30	0.488947
$289$	−6.02516e29	−0.104411
$290$	1.60587e30	0.266524
$291$	−6.52080e30	−1.03666
$292$	−4.71856e29	−0.0718660
$293$	2.33764e30	0.341140	0.170570	−	0.985346i	$-0.445439\pi$
$293$	2.33764e30	0.341140	0.170570	+	0.985346i	$0.445439\pi$
$294$	−1.31273e31	−1.83584
$295$	−4.23734e30	−0.567960
$296$	1.17569e31	1.51059
$297$	1.25260e31	1.54297
$298$	2.47443e30	0.292262
$299$	1.69081e29	0.0191516
$300$	−3.88337e29	−0.0421884
$301$	2.92391e29	0.0304707
$302$	−1.02955e30	−0.102935
$303$	−4.99187e30	−0.478884
$304$	2.19198e31	2.01798
$305$	9.59619e30	0.847912
$306$	−2.39509e31	−2.03144
$307$	9.47546e30	0.771562	0.385781	−	0.922590i	$-0.373932\pi$
$307$	9.47546e30	0.771562	0.385781	+	0.922590i	$0.373932\pi$
$308$	7.95315e28	0.00621806
$309$	8.57522e30	0.643820
$310$	8.63758e30	0.622832
$311$	2.12987e31	1.47519	0.737595	−	0.675243i	$-0.235961\pi$
$311$	2.12987e31	1.47519	0.737595	+	0.675243i	$0.235961\pi$
$312$	−3.37027e31	−2.24250
$313$	5.59893e30	0.357933	0.178966	−	0.983855i	$-0.442725\pi$
$313$	5.59893e30	0.357933	0.178966	+	0.983855i	$0.442725\pi$
$314$	−1.71878e31	−1.05584
$315$	9.12296e29	0.0538585
$316$	−1.63495e30	−0.0927715
$317$	−9.31662e30	−0.508180	−0.254090	−	0.967181i	$-0.581776\pi$
$317$	−9.31662e30	−0.508180	−0.254090	+	0.967181i	$0.581776\pi$
$318$	−4.52437e31	−2.37257
$319$	−9.63674e30	−0.485900
$320$	−7.85043e30	−0.380644
$321$	−2.05124e31	−0.956542
$322$	1.93910e28	0.000869765 0
$323$	−3.99978e31	−1.72586
$324$	3.16109e30	0.131227
$325$	6.93526e30	0.277026
$326$	3.63928e31	1.39893
$327$	4.45219e31	1.64713
$328$	9.47527e30	0.337418
$329$	2.50799e29	0.00859759
$330$	2.15519e31	0.711313
$331$	3.03797e31	0.965459	0.482729	−	0.875770i	$-0.339645\pi$
$331$	3.03797e31	0.965459	0.482729	+	0.875770i	$0.339645\pi$
$332$	−2.73096e30	−0.0835774
$333$	1.11655e32	3.29099
$334$	−3.08698e31	−0.876402
$335$	−1.25206e30	−0.0342424
$336$	−4.34079e30	−0.114374
$337$	1.31855e31	0.334751	0.167375	−	0.985893i	$-0.446471\pi$
$337$	1.31855e31	0.334751	0.167375	+	0.985893i	$0.446471\pi$
$338$	−3.97582e31	−0.972677
$339$	−1.17375e32	−2.76744
$340$	−2.25786e30	−0.0513110
$341$	−5.18336e31	−1.13549
$342$	1.85364e32	3.91471
$343$	5.82477e30	0.118605
$344$	−2.43077e31	−0.477270
$345$	5.68184e29	0.0107585
$346$	7.54393e31	1.37767
$347$	−9.98531e31	−1.75891	−0.879454	−	0.475984i	$-0.842092\pi$
$347$	−9.98531e31	−1.75891	−0.879454	+	0.475984i	$0.842092\pi$
$348$	−6.98675e30	−0.118723
$349$	1.53371e30	0.0251434	0.0125717	−	0.999921i	$-0.495998\pi$
$349$	1.53371e30	0.0251434	0.0125717	+	0.999921i	$0.495998\pi$
$350$	7.95369e29	0.0125811
$351$	−1.62186e32	−2.47556
$352$	−1.41358e31	−0.208227
$353$	2.81875e30	0.0400749	0.0200375	−	0.999799i	$-0.493621\pi$
$353$	2.81875e30	0.0400749	0.0200375	+	0.999799i	$0.493621\pi$
$354$	1.70496e32	2.33977
$355$	−3.35327e31	−0.444237
$356$	1.59273e30	0.0203713
$357$	7.92078e30	0.0978172
$358$	−6.86775e31	−0.818986
$359$	−4.01523e31	−0.462413	−0.231206	−	0.972905i	$-0.574267\pi$
$359$	−4.01523e31	−0.462413	−0.231206	+	0.972905i	$0.574267\pi$
$360$	−7.58431e31	−0.843597
$361$	2.16481e32	2.32584
$362$	2.02594e31	0.210266
$363$	4.41904e31	0.443094
$364$	−1.02976e30	−0.00997633
$365$	2.83177e31	0.265092
$366$	−3.86118e32	−3.49307
$367$	−8.30488e31	−0.726119	−0.363059	−	0.931766i	$-0.618268\pi$
$367$	−8.30488e31	−0.726119	−0.363059	+	0.931766i	$0.618268\pi$
$368$	−1.81042e30	−0.0152996
$369$	8.99867e31	0.735104
$370$	9.73445e31	0.768759
$371$	1.00199e31	0.0765046
$372$	−3.75800e31	−0.277440
$373$	−7.48815e31	−0.534582	−0.267291	−	0.963616i	$-0.586128\pi$
$373$	−7.48815e31	−0.534582	−0.267291	+	0.963616i	$0.586128\pi$
$374$	1.25306e32	0.865124
$375$	2.33055e31	0.155620
$376$	−2.08500e31	−0.134666
$377$	1.24775e32	0.779583
$378$	−1.86003e31	−0.112427
$379$	−4.62012e31	−0.270186	−0.135093	−	0.990833i	$-0.543133\pi$
$379$	−4.62012e31	−0.270186	−0.135093	+	0.990833i	$0.543133\pi$
$380$	1.74744e31	0.0988795
$381$	2.50247e32	1.37027
$382$	−1.21856e32	−0.645735
$383$	−5.46634e31	−0.280357	−0.140179	−	0.990126i	$-0.544768\pi$
$383$	−5.46634e31	−0.280357	−0.140179	+	0.990126i	$0.544768\pi$
$384$	4.00407e32	1.98775
$385$	−4.77296e30	−0.0229366
$386$	3.40518e32	1.58416
$387$	−2.30851e32	−1.03979
$388$	1.65636e31	0.0722367
$389$	−9.38326e31	−0.396263	−0.198132	−	0.980175i	$-0.563487\pi$
$389$	−9.38326e31	−0.396263	−0.198132	+	0.980175i	$0.563487\pi$
$390$	−2.79051e32	−1.14124
$391$	3.30353e30	0.0130848
$392$	−2.41691e32	−0.927224
$393$	2.69449e32	1.00131
$394$	−2.83929e32	−1.02213
$395$	9.81188e31	0.342207
$396$	−6.27922e31	−0.212186
$397$	−4.77324e32	−1.56290	−0.781451	−	0.623967i	$-0.785520\pi$
$397$	−4.77324e32	−1.56290	−0.781451	+	0.623967i	$0.785520\pi$
$398$	4.28209e32	1.35868
$399$	−6.13017e31	−0.188500
$400$	−7.42586e31	−0.221308
$401$	4.48268e32	1.29489	0.647445	−	0.762112i	$-0.275837\pi$
$401$	4.48268e32	1.29489	0.647445	+	0.762112i	$0.275837\pi$
$402$	5.03785e31	0.141065
$403$	6.71136e32	1.82179
$404$	1.26799e31	0.0333695
$405$	−1.89708e32	−0.484059
$406$	1.43099e31	0.0354046
$407$	−5.84159e32	−1.40153
$408$	−6.58488e32	−1.53213
$409$	−5.09007e32	−1.14864	−0.574318	−	0.818633i	$-0.694733\pi$
$409$	−5.09007e32	−1.14864	−0.574318	+	0.818633i	$0.694733\pi$
$410$	7.84532e31	0.171717
$411$	−7.50567e32	−1.59355
$412$	−2.17821e31	−0.0448625
$413$	−3.77587e31	−0.0754470
$414$	−1.53097e31	−0.0296799
$415$	1.63894e32	0.308292
$416$	1.83029e32	0.334081
$417$	1.27861e33	2.26484
$418$	−9.69790e32	−1.66715
$419$	1.01319e33	1.69051	0.845254	−	0.534365i	$-0.179449\pi$
$419$	1.01319e33	1.69051	0.845254	+	0.534365i	$0.179449\pi$
$420$	−3.46045e30	−0.00560424
$421$	−7.06000e32	−1.10989	−0.554943	−	0.831889i	$-0.687260\pi$
$421$	−7.06000e32	−1.10989	−0.554943	+	0.831889i	$0.687260\pi$
$422$	3.54290e32	0.540696
$423$	−1.98012e32	−0.293385
$424$	−8.32993e32	−1.19831
$425$	1.35502e32	0.189271
$426$	1.34924e33	1.83008
$427$	8.55113e31	0.112635
$428$	5.21039e31	0.0666536
$429$	1.67457e33	2.08059
$430$	−2.01263e32	−0.242889
$431$	−1.05189e33	−1.23311	−0.616556	−	0.787311i	$-0.711473\pi$
$431$	−1.05189e33	−1.23311	−0.616556	+	0.787311i	$0.711473\pi$
$432$	1.73659e33	1.97765
$433$	1.47607e33	1.63309	0.816543	−	0.577285i	$-0.195888\pi$
$433$	1.47607e33	1.63309	0.816543	+	0.577285i	$0.195888\pi$
$434$	7.69692e31	0.0827361
$435$	4.19299e32	0.437934
$436$	−1.13091e32	−0.114775
$437$	−2.55671e31	−0.0252153
$438$	−1.13941e33	−1.09208
$439$	1.87165e32	0.174349	0.0871743	−	0.996193i	$-0.472216\pi$
$439$	1.87165e32	0.174349	0.0871743	+	0.996193i	$0.472216\pi$
$440$	3.96797e32	0.359261
$441$	−2.29534e33	−2.02006
$442$	−1.62245e33	−1.38801
$443$	−9.42921e32	−0.784203	−0.392102	−	0.919922i	$-0.628252\pi$
$443$	−9.42921e32	−0.784203	−0.392102	+	0.919922i	$0.628252\pi$
$444$	−4.23522e32	−0.342443
$445$	−9.55856e31	−0.0751437
$446$	−5.28968e32	−0.404337
$447$	6.46084e32	0.480225
$448$	−6.99549e31	−0.0505642
$449$	−2.15505e33	−1.51488	−0.757439	−	0.652906i	$-0.773550\pi$
$449$	−2.15505e33	−1.51488	−0.757439	+	0.652906i	$0.773550\pi$
$450$	−6.27965e32	−0.429318
$451$	−4.70793e32	−0.313057
$452$	2.98146e32	0.192841
$453$	−2.68820e32	−0.169135
$454$	−8.62569e32	−0.527953
$455$	6.17998e31	0.0367997
$456$	5.09627e33	2.95251
$457$	2.76872e33	1.56072	0.780362	−	0.625328i	$-0.215035\pi$
$457$	2.76872e33	1.56072	0.780362	+	0.625328i	$0.215035\pi$
$458$	4.75464e32	0.260795
$459$	−3.16881e33	−1.69137
$460$	−1.44325e30	−0.000749670 0
$461$	−2.11177e32	−0.106754	−0.0533770	−	0.998574i	$-0.516999\pi$
$461$	−2.11177e32	−0.106754	−0.0533770	+	0.998574i	$0.516999\pi$
$462$	1.92048e32	0.0944898
$463$	−6.48868e32	−0.310737	−0.155369	−	0.987857i	$-0.549657\pi$
$463$	−6.48868e32	−0.310737	−0.155369	+	0.987857i	$0.549657\pi$
$464$	−1.33602e33	−0.622786
$465$	2.25531e33	1.02340
$466$	2.59694e33	1.14720
$467$	4.56722e32	0.196422	0.0982111	−	0.995166i	$-0.468688\pi$
$467$	4.56722e32	0.196422	0.0982111	+	0.995166i	$0.468688\pi$
$468$	8.13027e32	0.340433
$469$	−1.11570e31	−0.00454871
$470$	−1.72634e32	−0.0685333
$471$	−4.48779e33	−1.73489
$472$	3.13905e33	1.18174
$473$	1.20777e33	0.442811
$474$	−3.94797e33	−1.40976
$475$	−1.04870e33	−0.364737
$476$	−2.01197e31	−0.00681608
$477$	−7.91094e33	−2.61065
$478$	4.29272e33	1.38002
$479$	4.00561e33	1.25451	0.627255	−	0.778814i	$-0.284178\pi$
$479$	4.00561e33	1.25451	0.627255	+	0.778814i	$0.284178\pi$
$480$	6.15055e32	0.187672
$481$	7.56362e33	2.24862
$482$	−2.55400e33	−0.739831
$483$	5.06307e30	0.00142914
$484$	−1.12249e32	−0.0308756
$485$	−9.94039e32	−0.266460
$486$	3.89085e32	0.101646
$487$	−1.13862e33	−0.289912	−0.144956	−	0.989438i	$-0.546304\pi$
$487$	−1.13862e33	−0.289912	−0.144956	+	0.989438i	$0.546304\pi$
$488$	−7.10892e33	−1.76423
$489$	9.50229e33	2.29862
$490$	−2.00115e33	−0.471877
$491$	3.66622e32	0.0842752	0.0421376	−	0.999112i	$-0.486583\pi$
$491$	3.66622e32	0.0842752	0.0421376	+	0.999112i	$0.486583\pi$
$492$	−3.41331e32	−0.0764912
$493$	2.43788e33	0.532631
$494$	1.25567e34	2.67479
$495$	3.76838e33	0.782690
$496$	−7.18613e33	−1.45537
$497$	−2.98809e32	−0.0590118
$498$	−6.59455e33	−1.27004
$499$	−4.31964e33	−0.811318	−0.405659	−	0.914024i	$-0.632958\pi$
$499$	−4.31964e33	−0.811318	−0.405659	+	0.914024i	$0.632958\pi$
$500$	−5.91986e31	−0.0108439
$501$	−8.06024e33	−1.44005
$502$	4.16181e33	0.725247
$503$	−6.71880e33	−1.14207	−0.571034	−	0.820926i	$-0.693458\pi$
$503$	−6.71880e33	−1.14207	−0.571034	+	0.820926i	$0.693458\pi$
$504$	−6.75835e32	−0.112062
$505$	−7.60968e32	−0.123090
$506$	8.00976e31	0.0126397
$507$	−1.03810e34	−1.59824
$508$	−6.35656e32	−0.0954829
$509$	−1.09454e34	−1.60420	−0.802101	−	0.597189i	$-0.796284\pi$
$509$	−1.09454e34	−1.60420	−0.802101	+	0.597189i	$0.796284\pi$
$510$	−5.45214e33	−0.779723
$511$	2.52338e32	0.0352145
$512$	5.60093e33	0.762756
$513$	2.45245e34	3.25937
$514$	8.56032e32	0.111033
$515$	1.30722e33	0.165485
$516$	8.75645e32	0.108195
$517$	1.03596e33	0.124943
$518$	8.67433e32	0.102121
$519$	1.96975e34	2.26370
$520$	−5.13768e33	−0.576402
$521$	−1.56140e34	−1.71018	−0.855089	−	0.518481i	$-0.826498\pi$
$521$	−1.56140e34	−1.71018	−0.855089	+	0.518481i	$0.826498\pi$
$522$	−1.12980e34	−1.20815
$523$	1.31380e34	1.37170	0.685848	−	0.727745i	$-0.259431\pi$
$523$	1.31380e34	1.37170	0.685848	+	0.727745i	$0.259431\pi$
$524$	−6.84431e32	−0.0697732
$525$	2.07674e32	0.0206724
$526$	1.07769e34	1.04754
$527$	1.31128e34	1.24469
$528$	−1.79303e34	−1.66213
$529$	−1.10437e34	−0.999809
$530$	−6.89701e33	−0.609835
$531$	2.98115e34	2.57456
$532$	1.55713e32	0.0131350
$533$	6.09578e33	0.502272
$534$	3.84604e33	0.309562
$535$	−3.12694e33	−0.245865
$536$	9.27532e32	0.0712474
$537$	−1.79320e34	−1.34570
$538$	6.03807e33	0.442710
$539$	1.20088e34	0.860279
$540$	1.38440e33	0.0969035
$541$	−5.93385e33	−0.405855	−0.202928	−	0.979194i	$-0.565046\pi$
$541$	−5.93385e33	−0.405855	−0.202928	+	0.979194i	$0.565046\pi$
$542$	7.39000e33	0.493916
$543$	5.28980e33	0.345495
$544$	3.57604e33	0.228253
$545$	6.78698e33	0.423370
$546$	−2.48661e33	−0.151600
$547$	−3.72801e33	−0.222144	−0.111072	−	0.993812i	$-0.535428\pi$
$547$	−3.72801e33	−0.222144	−0.111072	+	0.993812i	$0.535428\pi$
$548$	1.90653e33	0.111042
$549$	−6.75134e34	−3.84358
$550$	3.28540e33	0.182833
$551$	−1.88676e34	−1.02641
$552$	−4.20915e32	−0.0223849
$553$	8.74333e32	0.0454582
$554$	2.54975e34	1.29606
$555$	2.54170e34	1.26317
$556$	−3.24782e33	−0.157818
$557$	−1.57367e34	−0.747694	−0.373847	−	0.927490i	$-0.621961\pi$
$557$	−1.57367e34	−0.747694	−0.373847	+	0.927490i	$0.621961\pi$
$558$	−6.07692e34	−2.82329
$559$	−1.56380e34	−0.710452
$560$	−6.61716e32	−0.0293982
$561$	3.27180e34	1.42151
$562$	4.07707e34	1.73238
$563$	−2.49818e34	−1.03817	−0.519086	−	0.854722i	$-0.673728\pi$
$563$	−2.49818e34	−1.03817	−0.519086	+	0.854722i	$0.673728\pi$
$564$	7.51086e32	0.0305282
$565$	−1.78928e34	−0.711332
$566$	−1.21158e34	−0.471135
$567$	−1.69048e33	−0.0643016
$568$	2.48413e34	0.924314
$569$	9.68155e33	0.352405	0.176202	−	0.984354i	$-0.443619\pi$
$569$	9.68155e33	0.352405	0.176202	+	0.984354i	$0.443619\pi$
$570$	4.21960e34	1.50257
$571$	−2.72119e34	−0.947997	−0.473999	−	0.880526i	$-0.657190\pi$
$571$	−2.72119e34	−0.947997	−0.473999	+	0.880526i	$0.657190\pi$
$572$	−4.25360e33	−0.144980
$573$	−3.18170e34	−1.06103
$574$	6.99094e32	0.0228106
$575$	8.66148e31	0.00276531
$576$	5.52313e34	1.72546
$577$	2.75821e34	0.843197	0.421599	−	0.906783i	$-0.361469\pi$
$577$	2.75821e34	0.843197	0.421599	+	0.906783i	$0.361469\pi$
$578$	3.69566e33	0.110559
$579$	8.89107e34	2.60299
$580$	−1.06507e33	−0.0305160
$581$	1.46046e33	0.0409531
$582$	3.99967e34	1.09771
$583$	4.13886e34	1.11179
$584$	−2.09779e34	−0.551572
$585$	−4.87926e34	−1.25576
$586$	−1.43384e34	−0.361228
$587$	2.77293e33	0.0683853	0.0341927	−	0.999415i	$-0.489114\pi$
$587$	2.77293e33	0.0683853	0.0341927	+	0.999415i	$0.489114\pi$
$588$	8.70651e33	0.210197
$589$	−1.01484e35	−2.39860
$590$	2.59906e34	0.601405
$591$	−7.41351e34	−1.67950
$592$	−8.09868e34	−1.79636
$593$	4.17859e34	0.907498	0.453749	−	0.891130i	$-0.350086\pi$
$593$	4.17859e34	0.907498	0.453749	+	0.891130i	$0.350086\pi$
$594$	−7.68313e34	−1.63383
$595$	1.20745e33	0.0251425
$596$	−1.64113e33	−0.0334629
$597$	1.11807e35	2.23249
$598$	−1.03709e33	−0.0202793
$599$	1.92057e34	0.367785	0.183893	−	0.982946i	$-0.441130\pi$
$599$	1.92057e34	0.367785	0.183893	+	0.982946i	$0.441130\pi$
$600$	−1.72648e34	−0.323796
$601$	−3.10144e33	−0.0569682	−0.0284841	−	0.999594i	$-0.509068\pi$
$601$	−3.10144e33	−0.0569682	−0.0284841	+	0.999594i	$0.509068\pi$
$602$	−1.79345e33	−0.0322650
$603$	8.80878e33	0.155221
$604$	6.82834e32	0.0117856
$605$	6.73645e33	0.113891
$606$	3.06187e34	0.507084
$607$	1.07465e35	1.74345	0.871726	−	0.489993i	$-0.163001\pi$
$607$	1.07465e35	1.74345	0.871726	+	0.489993i	$0.163001\pi$
$608$	−2.76762e34	−0.439858
$609$	3.73636e33	0.0581745
$610$	−5.88604e34	−0.897842
$611$	−1.34135e34	−0.200460
$612$	1.58850e34	0.232592
$613$	2.89344e32	0.00415106	0.00207553	−	0.999998i	$-0.499339\pi$
$613$	2.89344e32	0.00415106	0.00207553	+	0.999998i	$0.499339\pi$
$614$	−5.81198e34	−0.816996
$615$	2.04844e34	0.282153
$616$	3.53584e33	0.0477237
$617$	6.33284e33	0.0837595	0.0418798	−	0.999123i	$-0.486665\pi$
$617$	6.33284e33	0.0837595	0.0418798	+	0.999123i	$0.486665\pi$
$618$	−5.25980e34	−0.681731
$619$	−6.70910e34	−0.852180	−0.426090	−	0.904681i	$-0.640109\pi$
$619$	−6.70910e34	−0.852180	−0.426090	+	0.904681i	$0.640109\pi$
$620$	−5.72874e33	−0.0713121
$621$	−2.02555e33	−0.0247114
$622$	−1.30640e35	−1.56206
$623$	−8.51760e32	−0.00998197
$624$	2.32160e35	2.66673
$625$	3.55271e33	0.0400000
$626$	−3.43423e34	−0.379010
$627$	−2.53216e35	−2.73935
$628$	1.13995e34	0.120890
$629$	1.47779e35	1.53632
$630$	−5.59577e33	−0.0570300
$631$	−6.74457e34	−0.673887	−0.336944	−	0.941525i	$-0.609393\pi$
$631$	−6.74457e34	−0.673887	−0.336944	+	0.941525i	$0.609393\pi$
$632$	−7.26870e34	−0.712022
$633$	9.25066e34	0.888436
$634$	5.71456e34	0.538105
$635$	3.81479e34	0.352208
$636$	3.00072e34	0.271651
$637$	−1.55488e35	−1.38024
$638$	5.91091e34	0.514512
$639$	2.35918e35	2.01372
$640$	6.10386e34	0.510922
$641$	1.20658e35	0.990443	0.495222	−	0.868767i	$-0.335087\pi$
$641$	1.20658e35	0.990443	0.495222	+	0.868767i	$0.335087\pi$
$642$	1.25817e35	1.01287
$643$	−1.46466e35	−1.15638	−0.578190	−	0.815902i	$-0.696241\pi$
$643$	−1.46466e35	−1.15638	−0.578190	+	0.815902i	$0.696241\pi$
$644$	−1.28608e31	−9.95850e−5 0
$645$	−5.25505e34	−0.399099
$646$	2.45335e35	1.82748
$647$	1.45885e35	1.06587	0.532937	−	0.846155i	$-0.321088\pi$
$647$	1.45885e35	1.06587	0.532937	+	0.846155i	$0.321088\pi$
$648$	1.40537e35	1.00717
$649$	−1.55968e35	−1.09642
$650$	−4.25389e34	−0.293339
$651$	2.00970e34	0.135946
$652$	−2.41369e34	−0.160172
$653$	−5.67831e34	−0.369661	−0.184831	−	0.982770i	$-0.559174\pi$
$653$	−5.67831e34	−0.369661	−0.184831	+	0.982770i	$0.559174\pi$
$654$	−2.73085e35	−1.74412
$655$	4.10751e34	0.257373
$656$	−6.52700e34	−0.401251
$657$	−1.99228e35	−1.20166
$658$	−1.53833e33	−0.00910387
$659$	2.87507e35	1.66948	0.834739	−	0.550646i	$-0.185619\pi$
$659$	2.87507e35	1.66948	0.834739	+	0.550646i	$0.185619\pi$
$660$	−1.42939e34	−0.0814428
$661$	2.48620e35	1.39001	0.695005	−	0.719005i	$-0.255402\pi$
$661$	2.48620e35	1.39001	0.695005	+	0.719005i	$0.255402\pi$
$662$	−1.86341e35	−1.02231
$663$	−4.23629e35	−2.28069
$664$	−1.21414e35	−0.641457
$665$	−9.34491e33	−0.0484512
$666$	−6.84862e35	−3.48478
$667$	1.55833e33	0.00778190
$668$	2.04739e34	0.100345
$669$	−1.38116e35	−0.664380
$670$	7.67977e33	0.0362588
$671$	3.53218e35	1.63686
$672$	5.48073e33	0.0249300
$673$	4.05223e35	1.80928	0.904640	−	0.426176i	$-0.140140\pi$
$673$	4.05223e35	1.80928	0.904640	+	0.426176i	$0.140140\pi$
$674$	−8.08759e34	−0.354463
$675$	−8.30827e34	−0.357448
$676$	2.63690e34	0.111368
$677$	1.50367e34	0.0623441	0.0311721	−	0.999514i	$-0.490076\pi$
$677$	1.50367e34	0.0623441	0.0311721	+	0.999514i	$0.490076\pi$
$678$	7.19945e35	2.93041
$679$	−8.85784e33	−0.0353961
$680$	−1.00381e35	−0.393812
$681$	−2.25220e35	−0.867498
$682$	3.17933e35	1.20235
$683$	−3.52715e35	−1.30968	−0.654840	−	0.755767i	$-0.727264\pi$
$683$	−3.52715e35	−1.30968	−0.654840	+	0.755767i	$0.727264\pi$
$684$	−1.22940e35	−0.448220
$685$	−1.14417e35	−0.409600
$686$	−3.57275e34	−0.125589
$687$	1.24146e35	0.428521
$688$	1.67443e35	0.567559
$689$	−5.35894e35	−1.78377
$690$	−3.48508e33	−0.0113920
$691$	4.06863e35	1.30609	0.653045	−	0.757319i	$-0.273491\pi$
$691$	4.06863e35	1.30609	0.653045	+	0.757319i	$0.273491\pi$
$692$	−5.00340e34	−0.157739
$693$	3.35799e34	0.103971
$694$	6.12471e35	1.86248
$695$	1.94913e35	0.582145
$696$	−3.10620e35	−0.911199
$697$	1.19100e35	0.343165
$698$	−9.40733e33	−0.0266240
$699$	6.78071e35	1.88500
$700$	−5.27516e32	−0.00144049
$701$	−1.14794e35	−0.307924	−0.153962	−	0.988077i	$-0.549203\pi$
$701$	−1.14794e35	−0.307924	−0.153962	+	0.988077i	$0.549203\pi$
$702$	9.94802e35	2.62134
$703$	−1.14372e36	−2.96058
$704$	−2.88960e35	−0.734817
$705$	−4.50753e34	−0.112609
$706$	−1.72894e34	−0.0424347
$707$	−6.78095e33	−0.0163511
$708$	−1.13079e35	−0.267896
$709$	−4.02226e34	−0.0936251	−0.0468125	−	0.998904i	$-0.514906\pi$
$709$	−4.02226e34	−0.0936251	−0.0468125	+	0.998904i	$0.514906\pi$
$710$	2.05680e35	0.470396
$711$	−6.90309e35	−1.55122
$712$	7.08104e34	0.156350
$713$	8.38185e33	0.0181853
$714$	−4.85838e34	−0.103577
$715$	2.55274e35	0.534787
$716$	4.55493e34	0.0937710
$717$	1.12085e36	2.26755
$718$	2.46283e35	0.489642
$719$	−7.81509e35	−1.52694	−0.763472	−	0.645841i	$-0.776507\pi$
$719$	−7.81509e35	−1.52694	−0.763472	+	0.645841i	$0.776507\pi$
$720$	5.22442e35	1.00319
$721$	1.16486e34	0.0219827
$722$	−1.32783e36	−2.46279
$723$	−6.66859e35	−1.21564
$724$	−1.34367e34	−0.0240747
$725$	6.39185e34	0.112565
$726$	−2.71052e35	−0.469185
$727$	−3.01317e35	−0.512677	−0.256338	−	0.966587i	$-0.582516\pi$
$727$	−3.01317e35	−0.512677	−0.256338	+	0.966587i	$0.582516\pi$
$728$	−4.57817e34	−0.0765684
$729$	−5.56789e35	−0.915370
$730$	−1.73693e35	−0.280703
$731$	−3.05538e35	−0.485398
$732$	2.56087e35	0.399944
$733$	1.38923e35	0.213292	0.106646	−	0.994297i	$-0.465989\pi$
$733$	1.38923e35	0.213292	0.106646	+	0.994297i	$0.465989\pi$
$734$	5.09398e35	0.768877
$735$	−5.22508e35	−0.775356
$736$	2.28585e33	0.00333484
$737$	−4.60859e34	−0.0661035
$738$	−5.51953e35	−0.778391
$739$	1.13245e36	1.57023	0.785116	−	0.619349i	$-0.212603\pi$
$739$	1.13245e36	1.57023	0.785116	+	0.619349i	$0.212603\pi$
$740$	−6.45622e34	−0.0880201
$741$	3.27861e36	4.39504
$742$	−6.14590e34	−0.0810096
$743$	1.15896e36	1.50214	0.751068	−	0.660225i	$-0.229539\pi$
$743$	1.15896e36	1.50214	0.751068	+	0.660225i	$0.229539\pi$
$744$	−1.67075e36	−2.12936
$745$	9.84898e34	0.123435
$746$	4.59302e35	0.566061
$747$	−1.15307e36	−1.39749
$748$	−8.31076e34	−0.0990537
$749$	−2.78640e34	−0.0326604
$750$	−1.42949e35	−0.164784
$751$	−1.02473e36	−1.16175	−0.580874	−	0.813993i	$-0.697289\pi$
$751$	−1.02473e36	−1.16175	−0.580874	+	0.813993i	$0.697289\pi$
$752$	1.43624e35	0.160142
$753$	1.08667e36	1.19168
$754$	−7.65338e35	−0.825489
$755$	−4.09793e34	−0.0434738
$756$	1.23363e34	0.0128725
$757$	4.76233e35	0.488789	0.244394	−	0.969676i	$-0.421411\pi$
$757$	4.76233e35	0.488789	0.244394	+	0.969676i	$0.421411\pi$
$758$	2.83385e35	0.286096
$759$	2.09138e34	0.0207688
$760$	7.76882e35	0.758901
$761$	−8.07207e35	−0.775670	−0.387835	−	0.921729i	$-0.626777\pi$
$761$	−8.07207e35	−0.775670	−0.387835	+	0.921729i	$0.626777\pi$
$762$	−1.53494e36	−1.45096
$763$	6.04785e34	0.0562398
$764$	8.08190e34	0.0739344
$765$	−9.53317e35	−0.857965
$766$	3.35290e35	0.296866
$767$	2.01946e36	1.75911
$768$	−7.27998e35	−0.623900
$769$	4.64514e34	0.0391669	0.0195835	−	0.999808i	$-0.493766\pi$
$769$	4.64514e34	0.0391669	0.0195835	+	0.999808i	$0.493766\pi$
$770$	2.92760e34	0.0242872
$771$	2.23513e35	0.182441
$772$	−2.25843e35	−0.181381
$773$	1.89997e36	1.50143	0.750713	−	0.660628i	$-0.229710\pi$
$773$	1.89997e36	1.50143	0.750713	+	0.660628i	$0.229710\pi$
$774$	1.41597e36	1.10101
$775$	3.43802e35	0.263049
$776$	7.36390e35	0.554417
$777$	2.26490e35	0.167798
$778$	5.75543e35	0.419597
$779$	−9.21759e35	−0.661301
$780$	1.85076e35	0.130668
$781$	−1.23428e36	−0.857580
$782$	−2.02629e34	−0.0138553
$783$	−1.49478e36	−1.00590
$784$	1.66488e36	1.10263
$785$	−6.84125e35	−0.445928
$786$	−1.65272e36	−1.06027
$787$	−2.20885e36	−1.39471	−0.697353	−	0.716728i	$-0.745639\pi$
$787$	−2.20885e36	−1.39471	−0.697353	+	0.716728i	$0.745639\pi$
$788$	1.88312e35	0.117031
$789$	2.81389e36	1.72125
$790$	−6.01833e35	−0.362358
$791$	−1.59442e35	−0.0944923
$792$	−2.79164e36	−1.62853
$793$	−4.57342e36	−2.62619
$794$	2.92777e36	1.65493
$795$	−1.80084e36	−1.00204
$796$	−2.84003e35	−0.155564
$797$	9.75567e35	0.526051	0.263026	−	0.964789i	$-0.415280\pi$
$797$	9.75567e35	0.526051	0.263026	+	0.964789i	$0.415280\pi$
$798$	3.76007e35	0.199600
$799$	−2.62076e35	−0.136960
$800$	9.37598e34	0.0482383
$801$	6.72487e35	0.340626
$802$	−2.74955e36	−1.37114
$803$	1.04232e36	0.511749
$804$	−3.34128e34	−0.0161515
$805$	7.71821e32	0.000367340 0
$806$	−4.11656e36	−1.92906
$807$	1.57656e36	0.727432
$808$	5.63730e35	0.256111
$809$	−5.11743e35	−0.228926	−0.114463	−	0.993428i	$-0.536515\pi$
$809$	−5.11743e35	−0.228926	−0.114463	+	0.993428i	$0.536515\pi$
$810$	1.16362e36	0.512563
$811$	−2.14970e36	−0.932432	−0.466216	−	0.884671i	$-0.654383\pi$
$811$	−2.14970e36	−0.932432	−0.466216	+	0.884671i	$0.654383\pi$
$812$	−9.49079e33	−0.00405370
$813$	1.92956e36	0.811570
$814$	3.58307e36	1.48406
$815$	1.44854e36	0.590828
$816$	4.53597e36	1.82198
$817$	2.36467e36	0.935393
$818$	3.12210e36	1.21627
$819$	−4.34789e35	−0.166813
$820$	−5.20329e34	−0.0196610
$821$	7.29782e35	0.271584	0.135792	−	0.990737i	$-0.456642\pi$
$821$	7.29782e35	0.271584	0.135792	+	0.990737i	$0.456642\pi$
$822$	4.60377e36	1.68739
$823$	−6.42218e33	−0.00231838	−0.00115919	−	0.999999i	$-0.500369\pi$
$823$	−6.42218e33	−0.00231838	−0.00115919	+	0.999999i	$0.500369\pi$
$824$	−9.68395e35	−0.344320
$825$	8.57830e35	0.300418
$826$	2.31601e35	0.0798897
$827$	−1.96287e36	−0.666919	−0.333459	−	0.942764i	$-0.608216\pi$
$827$	−1.96287e36	−0.666919	−0.333459	+	0.942764i	$0.608216\pi$
$828$	1.01539e34	0.00339825
$829$	−2.55181e36	−0.841233	−0.420617	−	0.907239i	$-0.638186\pi$
$829$	−2.55181e36	−0.841233	−0.420617	+	0.907239i	$0.638186\pi$
$830$	−1.00528e36	−0.326446
$831$	6.65749e36	2.12960
$832$	3.74142e36	1.17895
$833$	−3.03796e36	−0.943016
$834$	−7.84265e36	−2.39821
$835$	−1.22871e36	−0.370143
$836$	6.43198e35	0.190883
$837$	−8.04005e36	−2.35066
$838$	−6.21464e36	−1.79005
$839$	−6.18617e36	−1.75549	−0.877743	−	0.479133i	$-0.840951\pi$
$839$	−6.18617e36	−1.75549	−0.877743	+	0.479133i	$0.840951\pi$
$840$	−1.53846e35	−0.0430126
$841$	−2.48037e36	−0.683230
$842$	4.33040e36	1.17524
$843$	1.06454e37	2.84654
$844$	−2.34977e35	−0.0619078
$845$	−1.58250e36	−0.410804
$846$	1.21455e36	0.310661
$847$	6.00282e34	0.0151291
$848$	5.73804e36	1.42500
$849$	−3.16347e36	−0.774137
$850$	−8.31132e35	−0.200416
$851$	9.44625e34	0.0224460
$852$	−8.94865e35	−0.209538
$853$	−6.16915e36	−1.42352	−0.711758	−	0.702425i	$-0.752101\pi$
$853$	−6.16915e36	−1.42352	−0.711758	+	0.702425i	$0.752101\pi$
$854$	−5.24502e35	−0.119268
$855$	7.37805e36	1.65335
$856$	2.31646e36	0.511567
$857$	−6.40813e36	−1.39467	−0.697334	−	0.716746i	$-0.745631\pi$
$857$	−6.40813e36	−1.39467	−0.697334	+	0.716746i	$0.745631\pi$
$858$	−1.02713e37	−2.20311
$859$	8.32936e36	1.76075	0.880374	−	0.474280i	$-0.157292\pi$
$859$	8.32936e36	1.76075	0.880374	+	0.474280i	$0.157292\pi$
$860$	1.33484e35	0.0278099
$861$	1.82536e35	0.0374808
$862$	6.45197e36	1.30572
$863$	−8.62697e35	−0.172077	−0.0860386	−	0.996292i	$-0.527421\pi$
$863$	−8.62697e35	−0.172077	−0.0860386	+	0.996292i	$0.527421\pi$
$864$	−2.19264e36	−0.431067
$865$	3.00271e36	0.581852
$866$	−9.05382e36	−1.72925
$867$	9.64952e35	0.181663
$868$	−5.10486e34	−0.00947299
$869$	3.61157e36	0.660615
$870$	−2.57186e36	−0.463722
$871$	5.96715e35	0.106057
$872$	−5.02784e36	−0.880897
$873$	6.99350e36	1.20786
$874$	1.56822e35	0.0267001
$875$	3.16581e34	0.00531354
$876$	7.55695e35	0.125039
$877$	3.48132e36	0.567870	0.283935	−	0.958844i	$-0.408360\pi$
$877$	3.48132e36	0.567870	0.283935	+	0.958844i	$0.408360\pi$
$878$	−1.14802e36	−0.184615
$879$	−3.74382e36	−0.593546
$880$	−2.73332e36	−0.427225
$881$	−8.96949e35	−0.138219	−0.0691097	−	0.997609i	$-0.522016\pi$
$881$	−8.96949e35	−0.138219	−0.0691097	+	0.997609i	$0.522016\pi$
$882$	1.40790e37	2.13901
$883$	−5.38739e36	−0.806993	−0.403497	−	0.914981i	$-0.632205\pi$
$883$	−5.38739e36	−0.806993	−0.403497	+	0.914981i	$0.632205\pi$
$884$	1.07607e36	0.158923
$885$	6.78626e36	0.988187
$886$	5.78361e36	0.830382
$887$	1.30520e37	1.84771	0.923853	−	0.382748i	$-0.125022\pi$
$887$	1.30520e37	1.84771	0.923853	+	0.382748i	$0.125022\pi$
$888$	−1.88291e37	−2.62826
$889$	3.39935e35	0.0467868
$890$	5.86295e35	0.0795685
$891$	−6.98279e36	−0.934454
$892$	3.50830e35	0.0462952
$893$	2.02830e36	0.263930
$894$	−3.96290e36	−0.508503
$895$	−2.73357e36	−0.345894
$896$	5.43913e35	0.0678702
$897$	−2.70789e35	−0.0333216
$898$	1.32185e37	1.60408
$899$	6.18550e36	0.740251
$900$	4.16488e35	0.0491554
$901$	−1.04704e37	−1.21872
$902$	2.88772e36	0.331492
$903$	−4.68276e35	−0.0530157
$904$	1.32551e37	1.48005
$905$	8.06385e35	0.0888045
$906$	1.64887e36	0.179095
$907$	3.71116e36	0.397574	0.198787	−	0.980043i	$-0.436300\pi$
$907$	3.71116e36	0.397574	0.198787	+	0.980043i	$0.436300\pi$
$908$	5.72085e35	0.0604488
$909$	5.35374e36	0.557967
$910$	−3.79063e35	−0.0389667
$911$	−2.44970e36	−0.248390	−0.124195	−	0.992258i	$-0.539635\pi$
$911$	−2.44970e36	−0.248390	−0.124195	+	0.992258i	$0.539635\pi$
$912$	−3.51055e37	−3.51107
$913$	6.03264e36	0.595145
$914$	−1.69825e37	−1.65263
$915$	−1.53687e37	−1.47527
$916$	−3.15344e35	−0.0298601
$917$	3.66018e35	0.0341890
$918$	1.94366e37	1.79096
$919$	−9.34263e36	−0.849230	−0.424615	−	0.905374i	$-0.639590\pi$
$919$	−9.34263e36	−0.849230	−0.424615	+	0.905374i	$0.639590\pi$
$920$	−6.41648e34	−0.00575372
$921$	−1.51753e37	−1.34243
$922$	1.29530e36	0.113040
$923$	1.59813e37	1.37591
$924$	−1.27373e35	−0.0108187
$925$	3.87461e36	0.324680
$926$	3.97997e36	0.329035
$927$	−9.19685e36	−0.750140
$928$	1.68688e36	0.135748
$929$	2.25641e37	1.79152	0.895760	−	0.444538i	$-0.146632\pi$
$929$	2.25641e37	1.79152	0.895760	+	0.444538i	$0.146632\pi$
$930$	−1.38334e37	−1.08366
$931$	2.35118e37	1.81725
$932$	−1.72238e36	−0.131350
$933$	−3.41107e37	−2.56667
$934$	−2.80140e36	−0.207989
$935$	4.98758e36	0.365380
$936$	3.61459e37	2.61283
$937$	−1.41017e37	−1.00584	−0.502918	−	0.864334i	$-0.667740\pi$
$937$	−1.41017e37	−1.00584	−0.502918	+	0.864334i	$0.667740\pi$
$938$	6.84341e34	0.00481656
$939$	−8.96691e36	−0.622763
$940$	1.14496e35	0.00784682
$941$	−2.34181e37	−1.58373	−0.791866	−	0.610695i	$-0.790890\pi$
$941$	−2.34181e37	−1.58373	−0.791866	+	0.610695i	$0.790890\pi$
$942$	2.75269e37	1.83705
$943$	7.61305e34	0.00501375
$944$	−2.16232e37	−1.40530
$945$	−7.40346e35	−0.0474829
$946$	−7.40810e36	−0.468887
$947$	−2.63624e37	−1.64668	−0.823342	−	0.567545i	$-0.807893\pi$
$947$	−2.63624e37	−1.64668	−0.823342	+	0.567545i	$0.807893\pi$
$948$	2.61843e36	0.161412
$949$	−1.34959e37	−0.821056
$950$	6.43242e36	0.386215
$951$	1.49209e37	0.884177
$952$	−8.94490e35	−0.0523135
$953$	2.87957e37	1.66213	0.831067	−	0.556173i	$-0.187731\pi$
$953$	2.87957e37	1.66213	0.831067	+	0.556173i	$0.187731\pi$
$954$	4.85235e37	2.76438
$955$	−4.85023e36	−0.272722
$956$	−2.84708e36	−0.158007
$957$	1.54336e37	0.845412
$958$	−2.45693e37	−1.32838
$959$	−1.01957e36	−0.0544107
$960$	1.25728e37	0.662278
$961$	1.40375e37	0.729872
$962$	−4.63932e37	−2.38103
$963$	2.19994e37	1.11451
$964$	1.69390e36	0.0847080
$965$	1.35537e37	0.669060
$966$	−3.10554e34	−0.00151330
$967$	9.70177e36	0.466681	0.233341	−	0.972395i	$-0.425034\pi$
$967$	9.70177e36	0.466681	0.233341	+	0.972395i	$0.425034\pi$
$968$	−4.99040e36	−0.236970
$969$	6.40580e37	3.00280
$970$	6.09716e36	0.282150
$971$	−1.57467e37	−0.719364	−0.359682	−	0.933075i	$-0.617115\pi$
$971$	−1.57467e37	−0.719364	−0.359682	+	0.933075i	$0.617115\pi$
$972$	−2.58054e35	−0.0116381
$973$	1.73686e36	0.0773313
$974$	6.98398e36	0.306984
$975$	−1.11071e37	−0.481995
$976$	4.89695e37	2.09799
$977$	−2.28996e37	−0.968604	−0.484302	−	0.874901i	$-0.660926\pi$
$977$	−2.28996e37	−0.968604	−0.484302	+	0.874901i	$0.660926\pi$
$978$	−5.82844e37	−2.43398
$979$	−3.51833e36	−0.145062
$980$	1.32723e36	0.0540282
$981$	−4.77494e37	−1.91913
$982$	−2.24876e36	−0.0892378
$983$	2.40011e37	0.940401	0.470200	−	0.882560i	$-0.344182\pi$
$983$	2.40011e37	0.940401	0.470200	+	0.882560i	$0.344182\pi$
$984$	−1.51750e37	−0.587071
$985$	−1.13012e37	−0.431692
$986$	−1.49533e37	−0.563995
$987$	−4.01664e35	−0.0149589
$988$	−8.32806e36	−0.306254
$989$	−1.95304e35	−0.00709182
$990$	−2.31142e37	−0.828779
$991$	−3.24340e37	−1.14837	−0.574183	−	0.818727i	$-0.694680\pi$
$991$	−3.24340e37	−1.14837	−0.574183	+	0.818727i	$0.694680\pi$
$992$	9.07329e36	0.317226
$993$	−4.86543e37	−1.67979
$994$	1.83281e36	0.0624867
$995$	1.70440e37	0.573831
$996$	4.37373e36	0.145415
$997$	−2.68614e37	−0.881941	−0.440971	−	0.897522i	$-0.645366\pi$
$997$	−2.68614e37	−0.881941	−0.440971	+	0.897522i	$0.645366\pi$
$998$	2.64955e37	0.859093
$999$	−9.06104e37	−2.90141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.a.a.1.2	✓	4
3.2	odd	2		45.26.a.c.1.3		4
5.2	odd	4		25.26.b.b.24.3		8
5.3	odd	4		25.26.b.b.24.6		8
5.4	even	2		25.26.a.b.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.a.a.1.2	✓	4	1.1	even	1	trivial
25.26.a.b.1.3		4	5.4	even	2
25.26.b.b.24.3		8	5.2	odd	4
25.26.b.b.24.6		8	5.3	odd	4
45.26.a.c.1.3		4	3.2	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-6133.72 q^{2} -1.60154e6 q^{3} +4.06809e6 q^{4} -2.44141e8 q^{5} +9.82339e9 q^{6} -2.17553e9 q^{7} +1.80861e11 q^{8} +1.71764e12 q^{9} +O(q^{10})\)	\(q-6133.72 q^{2} -1.60154e6 q^{3} +4.06809e6 q^{4} -2.44141e8 q^{5} +9.82339e9 q^{6} -2.17553e9 q^{7} +1.80861e11 q^{8} +1.71764e12 q^{9} +1.49749e12 q^{10} -8.98635e12 q^{11} -6.51521e12 q^{12} +1.16354e14 q^{13} +1.33441e13 q^{14} +3.91001e14 q^{15} -1.24585e15 q^{16} +2.27335e15 q^{17} -1.05355e16 q^{18} -1.75942e16 q^{19} -9.93187e14 q^{20} +3.48419e15 q^{21} +5.51198e16 q^{22} +1.45315e15 q^{23} -2.89656e17 q^{24} +5.96046e16 q^{25} -7.13685e17 q^{26} -1.39390e18 q^{27} -8.85025e15 q^{28} +1.07238e18 q^{29} -2.39829e18 q^{30} +5.76804e18 q^{31} +1.57303e18 q^{32} +1.43920e19 q^{33} -1.39441e19 q^{34} +5.31135e17 q^{35} +6.98751e18 q^{36} +6.50051e19 q^{37} +1.07918e20 q^{38} -1.86346e20 q^{39} -4.41555e19 q^{40} +5.23898e19 q^{41} -2.13711e19 q^{42} -1.34400e20 q^{43} -3.65573e19 q^{44} -4.19345e20 q^{45} -8.91324e18 q^{46} -1.15282e20 q^{47} +1.99528e21 q^{48} -1.33634e21 q^{49} -3.65598e20 q^{50} -3.64085e21 q^{51} +4.73340e20 q^{52} -4.60571e21 q^{53} +8.54977e21 q^{54} +2.19393e21 q^{55} -3.93468e20 q^{56} +2.81778e22 q^{57} -6.57765e21 q^{58} +1.73561e22 q^{59} +1.59063e21 q^{60} -3.93060e22 q^{61} -3.53795e22 q^{62} -3.73677e21 q^{63} +3.21554e22 q^{64} -2.84068e22 q^{65} -8.82765e22 q^{66} +5.12843e21 q^{67} +9.24819e21 q^{68} -2.32728e21 q^{69} -3.25783e21 q^{70} +1.37350e23 q^{71} +3.10653e23 q^{72} -1.15989e23 q^{73} -3.98723e23 q^{74} -9.54591e22 q^{75} -7.15750e22 q^{76} +1.95501e22 q^{77} +1.14299e24 q^{78} -4.01895e23 q^{79} +3.04163e23 q^{80} +7.77044e23 q^{81} -3.21344e23 q^{82} -6.71311e23 q^{83} +1.41740e22 q^{84} -5.55017e23 q^{85} +8.24373e23 q^{86} -1.71745e24 q^{87} -1.62528e24 q^{88} +3.91519e23 q^{89} +2.57214e24 q^{90} -2.53132e23 q^{91} +5.91157e21 q^{92} -9.23774e24 q^{93} +7.07107e23 q^{94} +4.29547e24 q^{95} -2.51927e24 q^{96} +4.07158e24 q^{97} +8.19671e24 q^{98} -1.54353e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9}+O(q^{10}) \) 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9	\( 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9} - 146484375000 q^{10} - 23641453790592 q^{11} - 42051883516800 q^{12} + 109063914225800 q^{13} + 109980501036336 q^{14} + 194970703125000 q^{15} - 28\!\cdots\!76 q^{16}+ \cdots - 19\!\cdots\!16 q^{99}+O(q^{100}) \) 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9 - 146484375000 * q^10 - 23641453790592 * q^11 - 42051883516800 * q^12 + 109063914225800 * q^13 + 109980501036336 * q^14 + 194970703125000 * q^15 - 2811357146648576 * q^16 - 337440158866200 * q^17 - 8986517054418600 * q^18 - 5765957235759760 * q^19 - 22561984375000000 * q^20 - 76777748650758672 * q^21 - 247170171892300800 * q^22 - 84289919171581800 * q^23 - 750163283268986880 * q^24 + 238418579101562500 * q^25 - 2172668626545951312 * q^26 - 2324539610168425200 * q^27 + 715367314323708800 * q^28 - 1530771705074446440 * q^29 + 968060261718750000 * q^30 - 3405335632352491792 * q^31 + 8794451084429721600 * q^32 + 38579776790129836800 * q^33 + 12360736169963080176 * q^34 + 11947780029296875000 * q^35 + 29754645353627097024 * q^36 + 54849661150838347400 * q^37 + 167830012254298039200 * q^38 + 26980019582506147824 * q^39 - 54793331250000000000 * q^40 + 294765092997163901208 * q^41 - 275649307903658959200 * q^42 - 1266847513533640537000 * q^43 - 739285598894744039424 * q^44 - 509659620969726562500 * q^45 - 669486761007570298992 * q^46 + 826481836956124900200 * q^47 - 389112939053996236800 * q^48 - 2497667097456123567372 * q^49 + 35762786865234375000 * q^50 - 732051781800631123152 * q^51 - 3824820275638519888000 * q^52 + 7304325845439007895400 * q^53 + 15784899184389947603040 * q^54 + 5771839304343750000000 * q^55 + 14029366421126577776640 * q^56 + 15974193201590955213600 * q^57 + 11714010248956820950800 * q^58 - 2217164203172823251280 * q^59 + 10266573124218750000000 * q^60 - 50917697960481835727992 * q^61 - 24701477049499711624800 * q^62 + 2223612189174803070600 * q^63 - 20457521683182533476352 * q^64 - 26626932184033203125000 * q^65 - 16106812566256687908864 * q^66 - 76670956029519070862200 * q^67 - 318284068848532686249600 * q^68 - 211835176227690988743216 * q^69 - 26850708260824218750000 * q^70 + 150298050225701362285008 * q^71 + 399372518437664399078400 * q^72 - 106773821938777386935800 * q^73 + 286932321536483813083056 * q^74 - 47600269317626953125000 * q^75 + 793491830268069721114880 * q^76 - 215630079777610746336000 * q^77 + 1847661803543761572804000 * q^78 - 151978174282543555164640 * q^79 + 686366490881000000000000 * q^80 - 1579018732178689012033836 * q^81 + 3094333027045954774045200 * q^82 + 117573693202171400616600 * q^83 - 1614703102161158475120384 * q^84 + 82382851285693359375000 * q^85 - 1608810179612708665216752 * q^86 - 2896477998479054993943600 * q^87 - 4936697892190706144870400 * q^88 - 6860971673379749077360920 * q^89 + 2193973890238916015625000 * q^90 - 5097829330173411603898352 * q^91 + 6577026773676031203676800 * q^92 - 13171898336704209119455200 * q^93 + 1406225817996660389994096 * q^94 + 1407704403261660156250000 * q^95 + 13005904207859351375904768 * q^96 + 8538350425643241402216200 * q^97 + 10780561809722171059198200 * q^98 - 19223568526197742048146816 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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