LMFDB - Embedded newform 3.36.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,36,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, 36, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 36 $
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:	$23.2785391901$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 1847580440x + 20051963761200 $ x^3 - x^2 - 1847580440*x + 20051963761200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$35904.5$ 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)

$f(q)$	$=$	$q+186315. q^{2} -1.29140e8 q^{3} +3.53648e8 q^{4} -2.21366e12 q^{5} -2.40608e13 q^{6} +5.41817e14 q^{7} -6.33585e15 q^{8} +1.66772e16 q^{9} +O(q^{10})$	\(q+186315. q^{2} -1.29140e8 q^{3} +3.53648e8 q^{4} -2.21366e12 q^{5} -2.40608e13 q^{6} +5.41817e14 q^{7} -6.33585e15 q^{8} +1.66772e16 q^{9} -4.12439e17 q^{10} +3.21813e18 q^{11} -4.56702e16 q^{12} +2.69641e19 q^{13} +1.00949e20 q^{14} +2.85873e20 q^{15} -1.19262e21 q^{16} +7.92043e20 q^{17} +3.10721e21 q^{18} -1.88201e22 q^{19} -7.82858e20 q^{20} -6.99703e22 q^{21} +5.99587e23 q^{22} +4.62681e23 q^{23} +8.18213e23 q^{24} +1.98991e24 q^{25} +5.02382e24 q^{26} -2.15369e24 q^{27} +1.91613e23 q^{28} +3.40984e25 q^{29} +5.32624e25 q^{30} +2.21957e26 q^{31} -4.50463e24 q^{32} -4.15590e26 q^{33} +1.47570e26 q^{34} -1.19940e27 q^{35} +5.89786e24 q^{36} -2.96148e27 q^{37} -3.50648e27 q^{38} -3.48215e27 q^{39} +1.40254e28 q^{40} -6.83917e27 q^{41} -1.30365e28 q^{42} +5.22591e28 q^{43} +1.13809e27 q^{44} -3.69176e28 q^{45} +8.62045e28 q^{46} +3.56414e28 q^{47} +1.54015e29 q^{48} -8.52530e28 q^{49} +3.70751e29 q^{50} -1.02285e29 q^{51} +9.53581e27 q^{52} -5.00298e29 q^{53} -4.01266e29 q^{54} -7.12385e30 q^{55} -3.43287e30 q^{56} +2.43043e30 q^{57} +6.35306e30 q^{58} +1.24787e31 q^{59} +1.01098e29 q^{60} -2.00076e31 q^{61} +4.13540e31 q^{62} +9.03598e30 q^{63} +4.01388e31 q^{64} -5.96894e31 q^{65} -7.74307e31 q^{66} +1.01341e32 q^{67} +2.80105e29 q^{68} -5.97507e31 q^{69} -2.23466e32 q^{70} +3.89186e32 q^{71} -1.05664e32 q^{72} -2.91523e32 q^{73} -5.51770e32 q^{74} -2.56978e32 q^{75} -6.65571e30 q^{76} +1.74364e33 q^{77} -6.48778e32 q^{78} -1.06599e33 q^{79} +2.64005e33 q^{80} +2.78128e32 q^{81} -1.27424e33 q^{82} +6.15561e33 q^{83} -2.47449e31 q^{84} -1.75332e33 q^{85} +9.73666e33 q^{86} -4.40348e33 q^{87} -2.03896e34 q^{88} -1.61775e34 q^{89} -6.87832e33 q^{90} +1.46096e34 q^{91} +1.63626e32 q^{92} -2.86636e34 q^{93} +6.64054e33 q^{94} +4.16614e34 q^{95} +5.81729e32 q^{96} +5.66621e34 q^{97} -1.58839e34 q^{98} +5.36693e34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 50\!\cdots\!07 q^{9}+O(q^{10}) $ 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9	$ 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 57\!\cdots\!76 q^{99}+O(q^{100}) $ 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9 - 1127779626928867020 * q^10 + 3426356175124224804 * q^11 - 4195602845172722700 * q^12 + 50087718431258539506 * q^13 - 217880362960444050144 * q^14 - 357547300335073771830 * q^15 + 606906765664363747344 * q^16 + 2730709287864549111942 * q^17 - 1456418277831881470770 * q^18 + 28794251065778257727292 * q^19 + 88477655809138293889560 * q^20 - 63051115342974896664432 * q^21 - 122741766765729403865496 * q^22 + 1806983834691084779311608 * q^23 + 2412744607366739676625176 * q^24 + 8598840806404444672708725 * q^25 + 12462234191474761114326516 * q^26 - 6461081889226673298932241 * q^27 + 88582873604432535904569792 * q^28 + 78927943791269118086922714 * q^29 + 145641644849673076368124260 * q^30 - 1597007179004406242679048 * q^31 + 212133152341134442715841504 * q^32 - 442480194951598936437203052 * q^33 - 1031323232079473133177847620 * q^34 - 1159830211565676145196532000 * q^35 + 541820835308869172631800100 * q^36 - 5102549932092597658956094086 * q^37 - 8724219045726720381610922664 * q^38 - 6468336122510832086946779478 * q^39 - 17377992868876213570860774960 * q^40 - 20208748955896036456754429058 * q^41 + 28137105587210907187976333472 * q^42 + 46721962642013867129638134372 * q^43 + 194349428414233101115805936688 * q^44 + 46173716645481381511151008290 * q^45 + 52087178478532028950981302192 * q^46 + 293197746513164578153478190816 * q^47 - 78376038643698737623294977072 * q^48 + 836105627836985614440420595707 * q^49 - 701125828082122697797800571950 * q^50 - 352644242540441794237695126546 * q^51 - 2520178249741268871517789030248 * q^52 - 108875909240521237104294715182 * q^53 + 188082093795388459731917535510 * q^54 - 6237008697722857733231584966440 * q^55 - 9347630291312236144016149603200 * q^56 - 3718494276097527924758498428596 * q^57 + 11382186268398399744329433517572 * q^58 + 11320340569522247618095325505348 * q^59 - 11426018893050016162439682398280 * q^60 + 12771547929195071355310409383218 * q^61 + 101447293741849863418951127675568 * q^62 + 8142431312723579060152904782416 * q^63 - 41280658033851993168324127190976 * q^64 - 7709579158673152743776325663060 * q^65 + 15850891767034278029082983515848 * q^66 + 175757710780078940305499908875612 * q^67 + 281442880096236379198382763169800 * q^68 - 233354186950371743047120084912104 * q^69 - 1040498682940112273466514884936000 * q^70 - 27474747461715252213775775690424 * q^71 - 311582231872711762617942518543688 * q^72 - 585184619829428568163757555870322 * q^73 + 134392541523566959843290841608516 * q^74 - 1110455703350121428958086398022175 * q^75 + 403477747366730076622590548780112 * q^76 + 5306726056931811905707525354511808 * q^77 - 1609374954831223860690187911462108 * q^78 - 2667396066634861458375845391576600 * q^79 + 7102490190805235743681469824979040 * q^80 + 834385168331080533771857328695283 * q^81 + 917242845604400818117266629806188 * q^82 + 6578360642441675208543593208203580 * q^83 - 11439606736284815209219495383756096 * q^84 + 3560960065600250795485268792239140 * q^85 + 18773659018851120901851911340565224 * q^86 - 10192767526459331886611447454362382 * q^87 - 34961215155916125706150543997131872 * q^88 + 11419551912179244059325275346141822 * q^89 - 18808185755474891578891014940654380 * q^90 - 40541093249602611010364470781007648 * q^91 - 19232540048657476273178638696239456 * q^92 + 206237767408799199897789815404824 * q^93 - 101336598951909608865466201817694528 * q^94 + 159588702835640097495158571410457960 * q^95 - 27394909871037933537237934508725152 * q^96 + 211792260572805448951439211684683142 * q^97 - 124471288129025507609829835395708786 * q^98 + 57141964500321263762127041399377476 * 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 $

$2$	186315.	1.00513	0.502567	−	0.864539i	$-0.332389\pi$
$2$	186315.	1.00513	0.502567	+	0.864539i	$0.332389\pi$
$3$	−1.29140e8	−0.577350
$3$	−1.29140e8	−0.577350
$4$	3.53648e8	0.0102925
$5$	−2.21366e12	−1.29759	−0.648793	−	0.760965i	$-0.724726\pi$
$5$	−2.21366e12	−1.29759	−0.648793	+	0.760965i	$0.724726\pi$
$6$	−2.40608e13	−0.580314
$7$	5.41817e14	0.880313	0.440156	−	0.897921i	$-0.354923\pi$
$7$	5.41817e14	0.880313	0.440156	+	0.897921i	$0.354923\pi$
$8$	−6.33585e15	−0.994788
$9$	1.66772e16	0.333333
$10$	−4.12439e17	−1.30425
$11$	3.21813e18	1.91969	0.959846	−	0.280527i	$-0.0905092\pi$
$11$	3.21813e18	1.91969	0.959846	+	0.280527i	$0.0905092\pi$
$12$	−4.56702e16	−0.00594239
$13$	2.69641e19	0.864525	0.432262	−	0.901748i	$-0.357715\pi$
$13$	2.69641e19	0.864525	0.432262	+	0.901748i	$0.357715\pi$
$14$	1.00949e20	0.884831
$15$	2.85873e20	0.749162
$16$	−1.19262e21	−1.01019
$17$	7.92043e20	0.232216	0.116108	−	0.993237i	$-0.462958\pi$
$17$	7.92043e20	0.232216	0.116108	+	0.993237i	$0.462958\pi$
$18$	3.10721e21	0.335044
$19$	−1.88201e22	−0.787833	−0.393917	−	0.919146i	$-0.628880\pi$
$19$	−1.88201e22	−0.787833	−0.393917	+	0.919146i	$0.628880\pi$
$20$	−7.82858e20	−0.0133554
$21$	−6.99703e22	−0.508249
$22$	5.99587e23	1.92955
$23$	4.62681e23	0.683982	0.341991	−	0.939703i	$-0.388899\pi$
$23$	4.62681e23	0.683982	0.341991	+	0.939703i	$0.388899\pi$
$24$	8.18213e23	0.574341
$25$	1.98991e24	0.683729
$26$	5.02382e24	0.868962
$27$	−2.15369e24	−0.192450
$28$	1.91613e23	0.00906064
$29$	3.40984e25	0.872508	0.436254	−	0.899824i	$-0.356305\pi$
$29$	3.40984e25	0.872508	0.436254	+	0.899824i	$0.356305\pi$
$30$	5.32624e25	0.753007
$31$	2.21957e26	1.76783	0.883914	−	0.467650i	$-0.154899\pi$
$31$	2.21957e26	1.76783	0.883914	+	0.467650i	$0.154899\pi$
$32$	−4.50463e24	−0.0205842
$33$	−4.15590e26	−1.10833
$34$	1.47570e26	0.233408
$35$	−1.19940e27	−1.14228
$36$	5.89786e24	0.00343084
$37$	−2.96148e27	−1.06655	−0.533273	−	0.845943i	$-0.679038\pi$
$37$	−2.96148e27	−1.06655	−0.533273	+	0.845943i	$0.679038\pi$
$38$	−3.50648e27	−0.791877
$39$	−3.48215e27	−0.499133
$40$	1.40254e28	1.29082
$41$	−6.83917e27	−0.408588	−0.204294	−	0.978910i	$-0.565490\pi$
$41$	−6.83917e27	−0.408588	−0.204294	+	0.978910i	$0.565490\pi$
$42$	−1.30365e28	−0.510858
$43$	5.22591e28	1.35664	0.678319	−	0.734768i	$-0.262709\pi$
$43$	5.22591e28	1.35664	0.678319	+	0.734768i	$0.262709\pi$
$44$	1.13809e27	0.0197585
$45$	−3.69176e28	−0.432529
$46$	8.62045e28	0.687493
$47$	3.56414e28	0.195093	0.0975466	−	0.995231i	$-0.468900\pi$
$47$	3.56414e28	0.195093	0.0975466	+	0.995231i	$0.468900\pi$
$48$	1.54015e29	0.583231
$49$	−8.52530e28	−0.225050
$50$	3.70751e29	0.687239
$51$	−1.02285e29	−0.134070
$52$	9.53581e27	0.00889814
$53$	−5.00298e29	−0.334504	−0.167252	−	0.985914i	$-0.553489\pi$
$53$	−5.00298e29	−0.334504	−0.167252	+	0.985914i	$0.553489\pi$
$54$	−4.01266e29	−0.193438
$55$	−7.12385e30	−2.49097
$56$	−3.43287e30	−0.875724
$57$	2.43043e30	0.454856
$58$	6.35306e30	0.876987
$59$	1.24787e31	1.27720	0.638600	−	0.769539i	$-0.279514\pi$
$59$	1.24787e31	1.27720	0.638600	+	0.769539i	$0.279514\pi$
$60$	1.01098e29	0.00771076
$61$	−2.00076e31	−1.14268	−0.571338	−	0.820715i	$-0.693576\pi$
$61$	−2.00076e31	−1.14268	−0.571338	+	0.820715i	$0.693576\pi$
$62$	4.13540e31	1.77690
$63$	9.03598e30	0.293438
$64$	4.01388e31	0.989497
$65$	−5.96894e31	−1.12179
$66$	−7.74307e31	−1.11402
$67$	1.01341e32	1.12067	0.560335	−	0.828266i	$-0.310672\pi$
$67$	1.01341e32	1.12067	0.560335	+	0.828266i	$0.310672\pi$
$68$	2.80105e29	0.00239009
$69$	−5.97507e31	−0.394897
$70$	−2.23466e32	−1.14814
$71$	3.89186e32	1.56004	0.780021	−	0.625753i	$-0.215208\pi$
$71$	3.89186e32	1.56004	0.780021	+	0.625753i	$0.215208\pi$
$72$	−1.05664e32	−0.331596
$73$	−2.91523e32	−0.718660	−0.359330	−	0.933211i	$-0.616995\pi$
$73$	−2.91523e32	−0.718660	−0.359330	+	0.933211i	$0.616995\pi$
$74$	−5.51770e32	−1.07202
$75$	−2.56978e32	−0.394751
$76$	−6.65571e30	−0.00810879
$77$	1.74364e33	1.68993
$78$	−6.48778e32	−0.501696
$79$	−1.06599e33	−0.659596	−0.329798	−	0.944052i	$-0.606981\pi$
$79$	−1.06599e33	−0.659596	−0.329798	+	0.944052i	$0.606981\pi$
$80$	2.64005e33	1.31080
$81$	2.78128e32	0.111111
$82$	−1.27424e33	−0.410686
$83$	6.15561e33	1.60474	0.802370	−	0.596827i	$-0.203572\pi$
$83$	6.15561e33	1.60474	0.802370	+	0.596827i	$0.203572\pi$
$84$	−2.47449e31	−0.00523116
$85$	−1.75332e33	−0.301321
$86$	9.73666e33	1.36360
$87$	−4.40348e33	−0.503743
$88$	−2.03896e34	−1.90969
$89$	−1.61775e34	−1.24333	−0.621666	−	0.783283i	$-0.713544\pi$
$89$	−1.61775e34	−1.24333	−0.621666	+	0.783283i	$0.713544\pi$
$90$	−6.87832e33	−0.434749
$91$	1.46096e34	0.761052
$92$	1.63626e32	0.00703990
$93$	−2.86636e34	−1.02066
$94$	6.64054e33	0.196095
$95$	4.16614e34	1.02228
$96$	5.81729e32	0.0118843
$97$	5.66621e34	0.965578	0.482789	−	0.875737i	$-0.339624\pi$
$97$	5.66621e34	0.965578	0.482789	+	0.875737i	$0.339624\pi$
$98$	−1.58839e34	−0.226205
$99$	5.36693e34	0.639897
$100$	7.03730e32	0.00703730
$101$	2.17021e34	0.182338	0.0911692	−	0.995835i	$-0.470940\pi$
$101$	2.17021e34	0.182338	0.0911692	+	0.995835i	$0.470940\pi$
$102$	−1.90572e34	−0.134758
$103$	−5.84326e34	−0.348340	−0.174170	−	0.984716i	$-0.555724\pi$
$103$	−5.84326e34	−0.348340	−0.174170	+	0.984716i	$0.555724\pi$
$104$	−1.70841e35	−0.860018
$105$	1.54891e35	0.659496
$106$	−9.32132e34	−0.336221
$107$	3.01655e35	0.923199	0.461599	−	0.887089i	$-0.347276\pi$
$107$	3.01655e35	0.923199	0.461599	+	0.887089i	$0.347276\pi$
$108$	−7.61650e32	−0.00198080
$109$	4.64351e35	1.02774	0.513869	−	0.857869i	$-0.328212\pi$
$109$	4.64351e35	1.02774	0.513869	+	0.857869i	$0.328212\pi$
$110$	−1.32728e36	−2.50375
$111$	3.82447e35	0.615770
$112$	−6.46181e35	−0.889280
$113$	−3.68588e35	−0.434179	−0.217089	−	0.976152i	$-0.569656\pi$
$113$	−3.68588e35	−0.434179	−0.217089	+	0.976152i	$0.569656\pi$
$114$	4.52827e35	0.457191
$115$	−1.02422e36	−0.887525
$116$	1.20589e34	0.00898031
$117$	4.49685e35	0.288175
$118$	2.32497e36	1.28376
$119$	4.29142e35	0.204423
$120$	−1.81125e36	−0.745257
$121$	7.54612e36	2.68522
$122$	−3.72773e36	−1.14854
$123$	8.83212e35	0.235899
$124$	7.84949e34	0.0181954
$125$	2.03761e36	0.410389
$126$	1.68354e36	0.294944
$127$	−8.21692e36	−1.25356	−0.626778	−	0.779198i	$-0.715627\pi$
$127$	−8.21692e36	−1.25356	−0.626778	+	0.779198i	$0.715627\pi$
$128$	7.63324e36	1.01516
$129$	−6.74875e36	−0.783255
$130$	−1.11210e37	−1.12755
$131$	−1.34012e37	−1.18822	−0.594109	−	0.804384i	$-0.702495\pi$
$131$	−1.34012e37	−1.18822	−0.594109	+	0.804384i	$0.702495\pi$
$132$	−1.46973e35	−0.0114076
$133$	−1.01971e37	−0.693540
$134$	1.88815e37	1.12642
$135$	4.76755e36	0.249721
$136$	−5.01827e36	−0.231006
$137$	3.38081e37	1.36902	0.684511	−	0.729003i	$-0.260016\pi$
$137$	3.38081e37	1.36902	0.684511	+	0.729003i	$0.260016\pi$
$138$	−1.11325e37	−0.396924
$139$	−1.79051e37	−0.562622	−0.281311	−	0.959617i	$-0.590769\pi$
$139$	−1.79051e37	−0.562622	−0.281311	+	0.959617i	$0.590769\pi$
$140$	−4.24166e35	−0.0117570
$141$	−4.60274e36	−0.112637
$142$	7.25113e37	1.56805
$143$	8.67740e37	1.65962
$144$	−1.98895e37	−0.336729
$145$	−7.54824e37	−1.13215
$146$	−5.43152e37	−0.722349
$147$	1.10096e37	0.129932
$148$	−1.04732e36	−0.0109774
$149$	−5.17633e37	−0.482239	−0.241119	−	0.970495i	$-0.577515\pi$
$149$	−5.17633e37	−0.482239	−0.241119	+	0.970495i	$0.577515\pi$
$150$	−4.78789e37	−0.396777
$151$	2.62205e37	0.193439	0.0967195	−	0.995312i	$-0.469165\pi$
$151$	2.62205e37	0.193439	0.0967195	+	0.995312i	$0.469165\pi$
$152$	1.19242e38	0.783727
$153$	1.32090e37	0.0774054
$154$	3.24866e38	1.69860
$155$	−4.91338e38	−2.29391
$156$	−1.23146e36	−0.00513734
$157$	−2.50259e38	−0.933567	−0.466783	−	0.884372i	$-0.654587\pi$
$157$	−2.50259e38	−0.933567	−0.466783	+	0.884372i	$0.654587\pi$
$158$	−1.98610e38	−0.662981
$159$	6.46086e37	0.193126
$160$	9.97173e36	0.0267098
$161$	2.50688e38	0.602118
$162$	5.18196e37	0.111681
$163$	−5.07630e38	−0.982346	−0.491173	−	0.871062i	$-0.663432\pi$
$163$	−5.07630e38	−0.982346	−0.491173	+	0.871062i	$0.663432\pi$
$164$	−2.41866e36	−0.00420541
$165$	9.19975e38	1.43816
$166$	1.14688e39	1.61298
$167$	5.54564e37	0.0702123	0.0351061	−	0.999384i	$-0.488823\pi$
$167$	5.54564e37	0.0702123	0.0351061	+	0.999384i	$0.488823\pi$
$168$	4.43322e38	0.505600
$169$	−2.45723e38	−0.252597
$170$	−3.26669e38	−0.302867
$171$	−3.13867e38	−0.262611
$172$	1.84813e37	0.0139632
$173$	1.01253e39	0.691195	0.345597	−	0.938383i	$-0.387676\pi$
$173$	1.01253e39	0.691195	0.345597	+	0.938383i	$0.387676\pi$
$174$	−8.20435e38	−0.506329
$175$	1.07817e39	0.601895
$176$	−3.83800e39	−1.93925
$177$	−1.61150e39	−0.737392
$178$	−3.01412e39	−1.24971
$179$	−6.06404e38	−0.227947	−0.113974	−	0.993484i	$-0.536358\pi$
$179$	−6.06404e38	−0.227947	−0.113974	+	0.993484i	$0.536358\pi$
$180$	−1.30559e37	−0.00445181
$181$	1.91654e39	0.593121	0.296561	−	0.955014i	$-0.404160\pi$
$181$	1.91654e39	0.593121	0.296561	+	0.955014i	$0.404160\pi$
$182$	2.72199e39	0.764958
$183$	2.58379e39	0.659725
$184$	−2.93148e39	−0.680417
$185$	6.55572e39	1.38393
$186$	−5.34047e39	−1.02589
$187$	2.54890e39	0.445784
$188$	1.26045e37	0.00200800
$189$	−1.16691e39	−0.169416
$190$	7.76215e39	1.02753
$191$	7.10703e39	0.858231	0.429115	−	0.903250i	$-0.358825\pi$
$191$	7.10703e39	0.858231	0.429115	+	0.903250i	$0.358825\pi$
$192$	−5.18353e39	−0.571286
$193$	−1.28681e40	−1.29498	−0.647489	−	0.762075i	$-0.724181\pi$
$193$	−1.28681e40	−1.29498	−0.647489	+	0.762075i	$0.724181\pi$
$194$	1.05570e40	0.970535
$195$	7.70830e39	0.647669
$196$	−3.01496e37	−0.00231633
$197$	−3.41138e39	−0.239757	−0.119879	−	0.992789i	$-0.538251\pi$
$197$	−3.41138e39	−0.239757	−0.119879	+	0.992789i	$0.538251\pi$
$198$	9.99942e39	0.643182
$199$	−2.57301e40	−1.51535	−0.757675	−	0.652632i	$-0.773665\pi$
$199$	−2.57301e40	−1.51535	−0.757675	+	0.652632i	$0.773665\pi$
$200$	−1.26078e40	−0.680165
$201$	−1.30872e40	−0.647019
$202$	4.04344e39	0.183274
$203$	1.84751e40	0.768080
$204$	−3.61728e37	−0.00137992
$205$	1.51396e40	0.530179
$206$	−1.08869e40	−0.350128
$207$	7.71621e39	0.227994
$208$	−3.21579e40	−0.873331
$209$	−6.05656e40	−1.51240
$210$	2.88585e40	0.662882
$211$	6.29150e40	1.32988	0.664938	−	0.746898i	$-0.268458\pi$
$211$	6.29150e40	1.32988	0.664938	+	0.746898i	$0.268458\pi$
$212$	−1.76930e38	−0.00344289
$213$	−5.02596e40	−0.900691
$214$	5.62030e40	0.927937
$215$	−1.15684e41	−1.76035
$216$	1.36455e40	0.191447
$217$	1.20260e41	1.55624
$218$	8.65156e40	1.03301
$219$	3.76474e40	0.414918
$220$	−2.51934e39	−0.0256383
$221$	2.13567e40	0.200757
$222$	7.12556e40	0.618931
$223$	−9.46477e40	−0.759933	−0.379966	−	0.925000i	$-0.624064\pi$
$223$	−9.46477e40	−0.759933	−0.379966	+	0.925000i	$0.624064\pi$
$224$	−2.44069e39	−0.0181206
$225$	3.31861e40	0.227910
$226$	−6.86736e40	−0.436408
$227$	1.57603e40	0.0927071	0.0463536	−	0.998925i	$-0.485240\pi$
$227$	1.57603e40	0.0927071	0.0463536	+	0.998925i	$0.485240\pi$
$228$	8.59519e38	0.00468161
$229$	−1.16145e41	−0.585974	−0.292987	−	0.956116i	$-0.594649\pi$
$229$	−1.16145e41	−0.585974	−0.292987	+	0.956116i	$0.594649\pi$
$230$	−1.90828e41	−0.892081
$231$	−2.25174e41	−0.975681
$232$	−2.16043e41	−0.867961
$233$	2.69972e39	0.0100598	0.00502990	−	0.999987i	$-0.498399\pi$
$233$	2.69972e39	0.0100598	0.00502990	+	0.999987i	$0.498399\pi$
$234$	8.37832e40	0.289654
$235$	−7.88980e40	−0.253150
$236$	4.41307e39	0.0131456
$237$	1.37662e41	0.380818
$238$	7.99558e40	0.205472
$239$	3.54936e41	0.847592	0.423796	−	0.905758i	$-0.360697\pi$
$239$	3.54936e41	0.847592	0.423796	+	0.905758i	$0.360697\pi$
$240$	−3.40937e41	−0.756793
$241$	2.65481e41	0.547943	0.273971	−	0.961738i	$-0.411663\pi$
$241$	2.65481e41	0.547943	0.273971	+	0.961738i	$0.411663\pi$
$242$	1.40596e42	2.69900
$243$	−3.59175e40	−0.0641500
$244$	−7.07566e39	−0.0117610
$245$	1.88721e41	0.292021
$246$	1.64556e41	0.237110
$247$	−5.07468e41	−0.681101
$248$	−1.40629e42	−1.75861
$249$	−7.94936e41	−0.926497
$250$	3.79638e41	0.412495
$251$	9.57100e41	0.969767	0.484883	−	0.874579i	$-0.338862\pi$
$251$	9.57100e41	0.969767	0.484883	+	0.874579i	$0.338862\pi$
$252$	3.19556e39	0.00302021
$253$	1.48897e42	1.31303
$254$	−1.53094e42	−1.25999
$255$	2.26423e41	0.173968
$256$	4.30325e40	0.0308743
$257$	2.62723e41	0.176063	0.0880317	−	0.996118i	$-0.471942\pi$
$257$	2.62723e41	0.176063	0.0880317	+	0.996118i	$0.471942\pi$
$258$	−1.25739e42	−0.787275
$259$	−1.60458e42	−0.938893
$260$	−2.11091e40	−0.0115461
$261$	5.68666e41	0.290836
$262$	−2.49685e42	−1.19432
$263$	8.84289e41	0.395703	0.197851	−	0.980232i	$-0.436604\pi$
$263$	8.84289e41	0.395703	0.197851	+	0.980232i	$0.436604\pi$
$264$	2.63312e42	1.10256
$265$	1.10749e42	0.434048
$266$	−1.89987e42	−0.697100
$267$	2.08917e42	0.717838
$268$	3.58392e40	0.0115345
$269$	−3.53617e42	−1.06627	−0.533137	−	0.846029i	$-0.678987\pi$
$269$	−3.53617e42	−1.06627	−0.533137	+	0.846029i	$0.678987\pi$
$270$	8.88267e41	0.251002
$271$	−1.22213e42	−0.323709	−0.161855	−	0.986815i	$-0.551748\pi$
$271$	−1.22213e42	−0.323709	−0.161855	+	0.986815i	$0.551748\pi$
$272$	−9.44605e41	−0.234582
$273$	−1.88669e42	−0.439394
$274$	6.29896e42	1.37605
$275$	6.40380e42	1.31255
$276$	−2.11307e40	−0.00406449
$277$	2.13004e42	0.384584	0.192292	−	0.981338i	$-0.438408\pi$
$277$	2.13004e42	0.384584	0.192292	+	0.981338i	$0.438408\pi$
$278$	−3.33599e42	−0.565510
$279$	3.70162e42	0.589276
$280$	7.59922e42	1.13633
$281$	−3.16863e42	−0.445155	−0.222577	−	0.974915i	$-0.571447\pi$
$281$	−3.16863e42	−0.445155	−0.222577	+	0.974915i	$0.571447\pi$
$282$	−8.57560e41	−0.113215
$283$	−1.40318e43	−1.74120	−0.870602	−	0.491988i	$-0.836271\pi$
$283$	−1.40318e43	−1.74120	−0.870602	+	0.491988i	$0.836271\pi$
$284$	1.37635e41	0.0160568
$285$	−5.38016e42	−0.590215
$286$	1.61673e43	1.66814
$287$	−3.70558e42	−0.359686
$288$	−7.51246e40	−0.00686141
$289$	−1.10062e43	−0.946076
$290$	−1.40635e43	−1.13797
$291$	−7.31736e42	−0.557477
$292$	−1.03097e41	−0.00739682
$293$	1.22499e43	0.827845	0.413923	−	0.910312i	$-0.364158\pi$
$293$	1.22499e43	0.827845	0.413923	+	0.910312i	$0.364158\pi$
$294$	2.05125e42	0.130599
$295$	−2.76236e43	−1.65728
$296$	1.87635e43	1.06099
$297$	−6.93087e42	−0.369445
$298$	−9.64429e42	−0.484714
$299$	1.24758e43	0.591319
$300$	−9.08798e40	−0.00406299
$301$	2.83149e43	1.19426
$302$	4.88527e42	0.194432
$303$	−2.80261e42	−0.105273
$304$	2.24452e43	0.795859
$305$	4.42901e43	1.48272
$306$	2.46105e42	0.0778028
$307$	2.75983e43	0.824065	0.412032	−	0.911169i	$-0.364819\pi$
$307$	2.75983e43	0.824065	0.412032	+	0.911169i	$0.364819\pi$
$308$	6.16635e41	0.0173936
$309$	7.54599e42	0.201114
$310$	−9.15439e43	−2.30568
$311$	3.11548e43	0.741682	0.370841	−	0.928696i	$-0.379069\pi$
$311$	3.11548e43	0.741682	0.370841	+	0.928696i	$0.379069\pi$
$312$	2.20624e43	0.496532
$313$	−7.70434e43	−1.63949	−0.819747	−	0.572726i	$-0.805886\pi$
$313$	−7.70434e43	−1.63949	−0.819747	+	0.572726i	$0.805886\pi$
$314$	−4.66270e43	−0.938359
$315$	−2.00026e43	−0.380760
$316$	−3.76985e41	−0.00678890
$317$	−1.12503e43	−0.191702	−0.0958508	−	0.995396i	$-0.530557\pi$
$317$	−1.12503e43	−0.191702	−0.0958508	+	0.995396i	$0.530557\pi$
$318$	1.20376e43	0.194117
$319$	1.09733e44	1.67495
$320$	−8.88536e43	−1.28396
$321$	−3.89558e43	−0.533009
$322$	4.67071e43	0.605208
$323$	−1.49063e43	−0.182948
$324$	9.83597e40	0.00114361
$325$	5.36562e43	0.591101
$326$	−9.45793e43	−0.987388
$327$	−5.99663e43	−0.593365
$328$	4.33320e43	0.406459
$329$	1.93111e43	0.171743
$330$	1.71405e44	1.44554
$331$	3.78227e43	0.302526	0.151263	−	0.988494i	$-0.451666\pi$
$331$	3.78227e43	0.302526	0.151263	+	0.988494i	$0.451666\pi$
$332$	2.17692e42	0.0165168
$333$	−4.93892e43	−0.355515
$334$	1.03324e43	0.0705727
$335$	−2.24336e44	−1.45417
$336$	8.34479e43	0.513426
$337$	−2.71690e43	−0.158690	−0.0793451	−	0.996847i	$-0.525283\pi$
$337$	−2.71690e43	−0.158690	−0.0793451	+	0.996847i	$0.525283\pi$
$338$	−4.57820e43	−0.253894
$339$	4.75995e43	0.250673
$340$	−6.20057e41	−0.00310135
$341$	7.14288e44	3.39368
$342$	−5.84781e43	−0.263959
$343$	−2.51442e44	−1.07843
$344$	−3.31106e44	−1.34957
$345$	1.32268e44	0.512413
$346$	1.88650e44	0.694743
$347$	−1.63684e43	−0.0573114	−0.0286557	−	0.999589i	$-0.509123\pi$
$347$	−1.63684e43	−0.0573114	−0.0286557	+	0.999589i	$0.509123\pi$
$348$	−1.55728e42	−0.00518479
$349$	1.12736e44	0.356959	0.178480	−	0.983944i	$-0.442882\pi$
$349$	1.12736e44	0.356959	0.178480	+	0.983944i	$0.442882\pi$
$350$	2.00879e44	0.604985
$351$	−5.80724e43	−0.166378
$352$	−1.44965e43	−0.0395154
$353$	−5.95732e44	−1.54523	−0.772616	−	0.634873i	$-0.781052\pi$
$353$	−5.95732e44	−1.54523	−0.772616	+	0.634873i	$0.781052\pi$
$354$	−3.00247e44	−0.741177
$355$	−8.61526e44	−2.02429
$356$	−5.72115e42	−0.0127970
$357$	−5.54195e43	−0.118024
$358$	−1.12982e44	−0.229117
$359$	7.88657e44	1.52313	0.761563	−	0.648091i	$-0.224433\pi$
$359$	7.88657e44	1.52313	0.761563	+	0.648091i	$0.224433\pi$
$360$	2.33905e44	0.430274
$361$	−2.16461e44	−0.379318
$362$	3.57081e44	0.596166
$363$	−9.74507e44	−1.55031
$364$	5.16667e42	0.00783314
$365$	6.45334e44	0.932523
$366$	4.81399e44	0.663111
$367$	8.47379e44	1.11281	0.556405	−	0.830911i	$-0.312180\pi$
$367$	8.47379e44	1.11281	0.556405	+	0.830911i	$0.312180\pi$
$368$	−5.51801e44	−0.690949
$369$	−1.14058e44	−0.136196
$370$	1.22143e45	1.39104
$371$	−2.71070e44	−0.294468
$372$	−1.01368e43	−0.0105051
$373$	4.61628e44	0.456444	0.228222	−	0.973609i	$-0.426709\pi$
$373$	4.61628e44	0.456444	0.228222	+	0.973609i	$0.426709\pi$
$374$	4.74899e44	0.448072
$375$	−2.63137e44	−0.236938
$376$	−2.25819e44	−0.194076
$377$	9.19434e44	0.754305
$378$	−2.17413e44	−0.170286
$379$	−1.20577e45	−0.901734	−0.450867	−	0.892591i	$-0.648885\pi$
$379$	−1.20577e45	−0.901734	−0.450867	+	0.892591i	$0.648885\pi$
$380$	1.47335e43	0.0105219
$381$	1.06113e45	0.723741
$382$	1.32415e45	0.862636
$383$	−1.20477e45	−0.749763	−0.374881	−	0.927073i	$-0.622317\pi$
$383$	−1.20477e45	−0.749763	−0.374881	+	0.927073i	$0.622317\pi$
$384$	−9.85758e44	−0.586103
$385$	−3.85982e45	−2.19283
$386$	−2.39753e45	−1.30162
$387$	8.71534e44	0.452212
$388$	2.00385e43	0.00993824
$389$	−1.66678e45	−0.790244	−0.395122	−	0.918629i	$-0.629298\pi$
$389$	−1.66678e45	−0.790244	−0.395122	+	0.918629i	$0.629298\pi$
$390$	1.43617e45	0.650993
$391$	3.66463e44	0.158832
$392$	5.40151e44	0.223877
$393$	1.73063e45	0.686018
$394$	−6.35593e44	−0.240988
$395$	2.35973e45	0.855882
$396$	1.89801e43	0.00658616
$397$	2.62127e45	0.870319	0.435159	−	0.900353i	$-0.356692\pi$
$397$	2.62127e45	0.870319	0.435159	+	0.900353i	$0.356692\pi$
$398$	−4.79391e45	−1.52313
$399$	1.31685e45	0.400415
$400$	−2.37321e45	−0.690694
$401$	4.49477e45	1.25222	0.626111	−	0.779734i	$-0.284646\pi$
$401$	4.49477e45	1.25222	0.626111	+	0.779734i	$0.284646\pi$
$402$	−2.43835e45	−0.650341
$403$	5.98488e45	1.52833
$404$	7.67492e42	0.00187672
$405$	−6.15682e44	−0.144176
$406$	3.44220e45	0.772023
$407$	−9.53044e45	−2.04744
$408$	6.48060e44	0.133371
$409$	6.81652e45	1.34402	0.672009	−	0.740543i	$-0.265432\pi$
$409$	6.81652e45	1.34402	0.672009	+	0.740543i	$0.265432\pi$
$410$	2.82074e45	0.532900
$411$	−4.36598e45	−0.790405
$412$	−2.06646e43	−0.00358530
$413$	6.76117e45	1.12434
$414$	1.43765e45	0.229164
$415$	−1.36264e46	−2.08229
$416$	−1.21463e44	−0.0177956
$417$	2.31226e45	0.324830
$418$	−1.12843e46	−1.52016
$419$	−3.07203e45	−0.396899	−0.198450	−	0.980111i	$-0.563591\pi$
$419$	−3.07203e45	−0.396899	−0.198450	+	0.980111i	$0.563591\pi$
$420$	5.47768e43	0.00678788
$421$	1.61078e46	1.91470	0.957350	−	0.288930i	$-0.0932994\pi$
$421$	1.61078e46	1.91470	0.957350	+	0.288930i	$0.0932994\pi$
$422$	1.17220e46	1.33670
$423$	5.94398e44	0.0650311
$424$	3.16982e45	0.332760
$425$	1.57610e45	0.158773
$426$	−9.36413e45	−0.905314
$427$	−1.08405e46	−1.00591
$428$	1.06680e44	0.00950204
$429$	−1.12060e46	−0.958183
$430$	−2.15537e46	−1.76939
$431$	−1.78158e46	−1.40428	−0.702140	−	0.712039i	$-0.747772\pi$
$431$	−1.78158e46	−1.40428	−0.702140	+	0.712039i	$0.747772\pi$
$432$	2.56853e45	0.194410
$433$	5.01344e45	0.364416	0.182208	−	0.983260i	$-0.441676\pi$
$433$	5.01344e45	0.364416	0.182208	+	0.983260i	$0.441676\pi$
$434$	2.24063e46	1.56423
$435$	9.74781e45	0.653650
$436$	1.64217e44	0.0105780
$437$	−8.70771e45	−0.538864
$438$	7.01428e45	0.417048
$439$	−1.60746e46	−0.918356	−0.459178	−	0.888344i	$-0.651856\pi$
$439$	−1.60746e46	−0.918356	−0.459178	+	0.888344i	$0.651856\pi$
$440$	4.51357e46	2.47798
$441$	−1.42178e45	−0.0750166
$442$	3.97909e45	0.201787
$443$	2.65183e45	0.129265	0.0646325	−	0.997909i	$-0.479413\pi$
$443$	2.65183e45	0.129265	0.0646325	+	0.997909i	$0.479413\pi$
$444$	1.35252e44	0.00633783
$445$	3.58115e46	1.61333
$446$	−1.76343e46	−0.763834
$447$	6.68472e45	0.278421
$448$	2.17479e46	0.871066
$449$	−1.18933e46	−0.458134	−0.229067	−	0.973411i	$-0.573567\pi$
$449$	−1.18933e46	−0.458134	−0.229067	+	0.973411i	$0.573567\pi$
$450$	6.18309e45	0.229080
$451$	−2.20093e46	−0.784364
$452$	−1.30351e44	−0.00446880
$453$	−3.38612e45	−0.111682
$454$	2.93639e45	0.0931830
$455$	−3.23407e46	−0.987530
$456$	−1.53989e46	−0.452485
$457$	1.09145e46	0.308652	0.154326	−	0.988020i	$-0.450679\pi$
$457$	1.09145e46	0.308652	0.154326	+	0.988020i	$0.450679\pi$
$458$	−2.16395e46	−0.588981
$459$	−1.70582e45	−0.0446900
$460$	−3.62213e44	−0.00913487
$461$	−4.32908e46	−1.05107	−0.525533	−	0.850773i	$-0.676134\pi$
$461$	−4.32908e46	−1.05107	−0.525533	+	0.850773i	$0.676134\pi$
$462$	−4.19533e46	−0.980689
$463$	2.67615e46	0.602343	0.301171	−	0.953570i	$-0.402622\pi$
$463$	2.67615e46	0.602343	0.301171	+	0.953570i	$0.402622\pi$
$464$	−4.06664e46	−0.881396
$465$	6.34515e46	1.32439
$466$	5.02998e44	0.0101114
$467$	−6.16584e46	−1.19384	−0.596921	−	0.802300i	$-0.703609\pi$
$467$	−6.16584e46	−1.19384	−0.596921	+	0.802300i	$0.703609\pi$
$468$	1.59030e44	0.00296605
$469$	5.49085e46	0.986541
$470$	−1.46999e46	−0.254450
$471$	3.23185e46	0.538995
$472$	−7.90632e46	−1.27054
$473$	1.68177e47	2.60433
$474$	2.56485e46	0.382773
$475$	−3.74504e46	−0.538665
$476$	1.51766e44	0.00210403
$477$	−8.34356e45	−0.111501
$478$	6.61300e46	0.851942
$479$	6.22522e46	0.773184	0.386592	−	0.922251i	$-0.373652\pi$
$479$	6.22522e46	0.773184	0.386592	+	0.922251i	$0.373652\pi$
$480$	−1.28775e45	−0.0154209
$481$	−7.98538e46	−0.922055
$482$	4.94632e46	0.550755
$483$	−3.23739e46	−0.347633
$484$	2.66867e45	0.0276377
$485$	−1.25431e47	−1.25292
$486$	−6.69199e45	−0.0644793
$487$	1.72346e46	0.160193	0.0800967	−	0.996787i	$-0.474477\pi$
$487$	1.72346e46	0.160193	0.0800967	+	0.996787i	$0.474477\pi$
$488$	1.26765e47	1.13672
$489$	6.55555e46	0.567158
$490$	3.51617e46	0.293520
$491$	−1.71814e46	−0.138399	−0.0691994	−	0.997603i	$-0.522044\pi$
$491$	−1.71814e46	−0.138399	−0.0691994	+	0.997603i	$0.522044\pi$
$492$	3.12346e44	0.00242799
$493$	2.70074e46	0.202611
$494$	−9.45490e46	−0.684598
$495$	−1.18806e47	−0.830322
$496$	−2.64710e47	−1.78584
$497$	2.10868e47	1.37332
$498$	−1.48109e47	−0.931252
$499$	−9.41743e45	−0.0571706	−0.0285853	−	0.999591i	$-0.509100\pi$
$499$	−9.41743e45	−0.0571706	−0.0285853	+	0.999591i	$0.509100\pi$
$500$	7.20597e44	0.00422394
$501$	−7.16164e45	−0.0405371
$502$	1.78322e47	0.974745
$503$	−1.34141e47	−0.708144	−0.354072	−	0.935218i	$-0.615203\pi$
$503$	−1.34141e47	−0.708144	−0.354072	+	0.935218i	$0.615203\pi$
$504$	−5.72507e46	−0.291908
$505$	−4.80411e46	−0.236600
$506$	2.77417e47	1.31977
$507$	3.17327e46	0.145837
$508$	−2.90590e45	−0.0129023
$509$	−4.69861e46	−0.201562	−0.100781	−	0.994909i	$-0.532134\pi$
$509$	−4.69861e46	−0.201562	−0.100781	+	0.994909i	$0.532134\pi$
$510$	4.21861e46	0.174861
$511$	−1.57952e47	−0.632645
$512$	−2.54259e47	−0.984127
$513$	4.05328e46	0.151619
$514$	4.89494e46	0.176967
$515$	1.29350e47	0.452001
$516$	−2.38668e45	−0.00806167
$517$	1.14699e47	0.374519
$518$	−2.98958e47	−0.943713
$519$	−1.30758e47	−0.399061
$520$	3.78183e47	1.11595
$521$	2.15709e47	0.615473	0.307736	−	0.951472i	$-0.400429\pi$
$521$	2.15709e47	0.615473	0.307736	+	0.951472i	$0.400429\pi$
$522$	1.05951e47	0.292329
$523$	1.87650e47	0.500690	0.250345	−	0.968157i	$-0.419456\pi$
$523$	1.87650e47	0.500690	0.250345	+	0.968157i	$0.419456\pi$
$524$	−4.73932e45	−0.0122298
$525$	−1.39235e47	−0.347504
$526$	1.64757e47	0.397734
$527$	1.75800e47	0.410518
$528$	4.95640e47	1.11962
$529$	−2.43514e47	−0.532169
$530$	2.06342e47	0.436276
$531$	2.08109e47	0.425733
$532$	−3.60617e45	−0.00713827
$533$	−1.84412e47	−0.353235
$534$	3.89244e47	0.721522
$535$	−6.67763e47	−1.19793
$536$	−6.42085e47	−1.11483
$537$	7.83111e46	0.131605
$538$	−6.58843e47	−1.07175
$539$	−2.74355e47	−0.432026
$540$	1.68604e45	0.00257025
$541$	−2.17182e47	−0.320532	−0.160266	−	0.987074i	$-0.551235\pi$
$541$	−2.17182e47	−0.320532	−0.160266	+	0.987074i	$0.551235\pi$
$542$	−2.27702e47	−0.325371
$543$	−2.47503e47	−0.342439
$544$	−3.56786e45	−0.00477999
$545$	−1.02791e48	−1.33358
$546$	−3.51519e47	−0.441649
$547$	1.35111e48	1.64404	0.822019	−	0.569461i	$-0.192848\pi$
$547$	1.35111e48	1.64404	0.822019	+	0.569461i	$0.192848\pi$
$548$	1.19562e46	0.0140907
$549$	−3.33671e47	−0.380892
$550$	1.19313e48	1.31929
$551$	−6.41737e47	−0.687391
$552$	3.78572e47	0.392839
$553$	−5.77570e47	−0.580650
$554$	3.96859e47	0.386558
$555$	−8.46607e47	−0.799015
$556$	−6.33210e45	−0.00579080
$557$	1.73957e48	1.54162	0.770809	−	0.637066i	$-0.219852\pi$
$557$	1.73957e48	1.54162	0.770809	+	0.637066i	$0.219852\pi$
$558$	6.89669e47	0.592301
$559$	1.40912e48	1.17285
$560$	1.43043e48	1.15392
$561$	−3.29165e47	−0.257373
$562$	−5.90364e47	−0.447440
$563$	1.83208e48	1.34601	0.673003	−	0.739640i	$-0.265004\pi$
$563$	1.83208e48	1.34601	0.673003	+	0.739640i	$0.265004\pi$
$564$	−1.62775e45	−0.00115932
$565$	8.15930e47	0.563384
$566$	−2.61433e48	−1.75014
$567$	1.50695e47	0.0978125
$568$	−2.46583e48	−1.55191
$569$	1.02267e48	0.624124	0.312062	−	0.950062i	$-0.398980\pi$
$569$	1.02267e48	0.624124	0.312062	+	0.950062i	$0.398980\pi$
$570$	−1.00241e48	−0.593244
$571$	3.05894e47	0.175565	0.0877827	−	0.996140i	$-0.472022\pi$
$571$	3.05894e47	0.175565	0.0877827	+	0.996140i	$0.472022\pi$
$572$	3.06875e46	0.0170817
$573$	−9.17803e47	−0.495500
$574$	−6.90406e47	−0.361532
$575$	9.20695e47	0.467658
$576$	6.69401e47	0.329832
$577$	−2.64351e48	−1.26359	−0.631793	−	0.775137i	$-0.717681\pi$
$577$	−2.64351e48	−1.26359	−0.631793	+	0.775137i	$0.717681\pi$
$578$	−2.05063e48	−0.950932
$579$	1.66179e48	0.747656
$580$	−2.66942e46	−0.0116527
$581$	3.33521e48	1.41267
$582$	−1.36334e48	−0.560338
$583$	−1.61002e48	−0.642145
$584$	1.84705e48	0.714914
$585$	−9.95451e47	−0.373932
$586$	2.28234e48	0.832095
$587$	1.85836e48	0.657601	0.328801	−	0.944399i	$-0.393356\pi$
$587$	1.85836e48	0.657601	0.328801	+	0.944399i	$0.393356\pi$
$588$	3.89352e45	0.00133733
$589$	−4.17726e48	−1.39275
$590$	−5.14670e48	−1.66578
$591$	4.40546e47	0.138424
$592$	3.53192e48	1.07741
$593$	−3.98184e48	−1.17931	−0.589654	−	0.807656i	$-0.700736\pi$
$593$	−3.98184e48	−1.17931	−0.589654	+	0.807656i	$0.700736\pi$
$594$	−1.29133e48	−0.371341
$595$	−9.49976e47	−0.265256
$596$	−1.83060e46	−0.00496346
$597$	3.32279e48	0.874888
$598$	2.32443e48	0.594354
$599$	6.12940e48	1.52212	0.761059	−	0.648683i	$-0.224680\pi$
$599$	6.12940e48	1.52212	0.761059	+	0.648683i	$0.224680\pi$
$600$	1.62817e48	0.392694
$601$	1.03591e48	0.242671	0.121336	−	0.992612i	$-0.461282\pi$
$601$	1.03591e48	0.242671	0.121336	+	0.992612i	$0.461282\pi$
$602$	5.27549e48	1.20040
$603$	1.69009e48	0.373557
$604$	9.27283e45	0.00199097
$605$	−1.67045e49	−3.48430
$606$	−5.22170e47	−0.105813
$607$	1.00192e48	0.197256	0.0986279	−	0.995124i	$-0.468555\pi$
$607$	1.00192e48	0.197256	0.0986279	+	0.995124i	$0.468555\pi$
$608$	8.47777e46	0.0162169
$609$	−2.38588e48	−0.443451
$610$	8.25192e48	1.49033
$611$	9.61039e47	0.168663
$612$	4.67136e45	0.000796697 0
$613$	1.02022e49	1.69096	0.845482	−	0.534003i	$-0.179313\pi$
$613$	1.02022e49	1.69096	0.845482	+	0.534003i	$0.179313\pi$
$614$	5.14199e48	0.828295
$615$	−1.95513e48	−0.306099
$616$	−1.10474e49	−1.68112
$617$	−3.23493e48	−0.478492	−0.239246	−	0.970959i	$-0.576900\pi$
$617$	−3.23493e48	−0.478492	−0.239246	+	0.970959i	$0.576900\pi$
$618$	1.40593e48	0.202147
$619$	6.00308e48	0.839050	0.419525	−	0.907744i	$-0.362197\pi$
$619$	6.00308e48	0.839050	0.419525	+	0.907744i	$0.362197\pi$
$620$	−1.73761e47	−0.0236101
$621$	−9.96473e47	−0.131632
$622$	5.80461e48	0.745489
$623$	−8.76525e48	−1.09452
$624$	4.15287e48	0.504218
$625$	−1.03020e49	−1.21624
$626$	−1.43544e49	−1.64791
$627$	7.82145e48	0.873183
$628$	−8.85036e46	−0.00960876
$629$	−2.34562e48	−0.247669
$630$	−3.72679e48	−0.382715
$631$	−1.83897e49	−1.83680	−0.918400	−	0.395653i	$-0.870518\pi$
$631$	−1.83897e49	−1.83680	−0.918400	+	0.395653i	$0.870518\pi$
$632$	6.75394e48	0.656158
$633$	−8.12485e48	−0.767804
$634$	−2.09610e48	−0.192686
$635$	1.81895e49	1.62660
$636$	2.28487e46	0.00198775
$637$	−2.29877e48	−0.194561
$638$	2.04450e49	1.68354
$639$	6.49053e48	0.520014
$640$	−1.68974e49	−1.31726
$641$	−6.37358e48	−0.483468	−0.241734	−	0.970343i	$-0.577716\pi$
$641$	−6.37358e48	−0.483468	−0.241734	+	0.970343i	$0.577716\pi$
$642$	−7.25807e48	−0.535745
$643$	1.61413e48	0.115944	0.0579718	−	0.998318i	$-0.481537\pi$
$643$	1.61413e48	0.115944	0.0579718	+	0.998318i	$0.481537\pi$
$644$	8.86555e46	0.00619731
$645$	1.49394e49	1.01634
$646$	−2.77728e48	−0.183887
$647$	7.44259e48	0.479622	0.239811	−	0.970820i	$-0.422915\pi$
$647$	7.44259e48	0.479622	0.239811	+	0.970820i	$0.422915\pi$
$648$	−1.76218e48	−0.110532
$649$	4.01581e49	2.45183
$650$	9.99698e48	0.594135
$651$	−1.55304e49	−0.898496
$652$	−1.79523e47	−0.0101108
$653$	1.47940e49	0.811158	0.405579	−	0.914060i	$-0.367070\pi$
$653$	1.47940e49	0.811158	0.405579	+	0.914060i	$0.367070\pi$
$654$	−1.11726e49	−0.596410
$655$	2.96657e49	1.54182
$656$	8.15652e48	0.412751
$657$	−4.86179e48	−0.239553
$658$	3.59796e48	0.172625
$659$	−3.54287e49	−1.65524	−0.827618	−	0.561291i	$-0.810305\pi$
$659$	−3.54287e49	−1.65524	−0.827618	+	0.561291i	$0.810305\pi$
$660$	3.25348e47	0.0148023
$661$	−3.65119e49	−1.61774	−0.808870	−	0.587988i	$-0.799920\pi$
$661$	−3.65119e49	−1.61774	−0.808870	+	0.587988i	$0.799920\pi$
$662$	7.04695e48	0.304079
$663$	−2.75801e48	−0.115907
$664$	−3.90010e49	−1.59637
$665$	2.25728e49	0.899927
$666$	−9.20197e48	−0.357340
$667$	1.57767e49	0.596780
$668$	1.96121e46	0.000722662 0
$669$	1.22228e49	0.438747
$670$	−4.17972e49	−1.46163
$671$	−6.43871e49	−2.19359
$672$	3.15191e47	0.0104619
$673$	1.97492e49	0.638684	0.319342	−	0.947639i	$-0.396538\pi$
$673$	1.97492e49	0.638684	0.319342	+	0.947639i	$0.396538\pi$
$674$	−5.06200e48	−0.159505
$675$	−4.28566e48	−0.131584
$676$	−8.68996e46	−0.00259986
$677$	1.66421e49	0.485184	0.242592	−	0.970128i	$-0.422002\pi$
$677$	1.66421e49	0.485184	0.242592	+	0.970128i	$0.422002\pi$
$678$	8.86852e48	0.251960
$679$	3.07005e49	0.850011
$680$	1.11087e49	0.299750
$681$	−2.03529e48	−0.0535245
$682$	1.33083e50	3.41110
$683$	4.56106e48	0.113947	0.0569736	−	0.998376i	$-0.481855\pi$
$683$	4.56106e48	0.113947	0.0569736	+	0.998376i	$0.481855\pi$
$684$	−1.10998e47	−0.00270293
$685$	−7.48396e49	−1.77642
$686$	−4.68475e49	−1.08396
$687$	1.49989e49	0.338312
$688$	−6.23251e49	−1.37046
$689$	−1.34901e49	−0.289187
$690$	2.46435e49	0.515043
$691$	2.05671e49	0.419090	0.209545	−	0.977799i	$-0.432802\pi$
$691$	2.05671e49	0.419090	0.209545	+	0.977799i	$0.432802\pi$
$692$	3.58079e47	0.00711414
$693$	2.90790e49	0.563310
$694$	−3.04969e48	−0.0576056
$695$	3.96358e49	0.730051
$696$	2.78998e49	0.501117
$697$	−5.41692e48	−0.0948809
$698$	2.10045e49	0.358791
$699$	−3.48642e47	−0.00580803
$700$	3.81293e47	0.00619502
$701$	−1.20795e50	−1.91419	−0.957093	−	0.289781i	$-0.906418\pi$
$701$	−1.20795e50	−1.91419	−0.957093	+	0.289781i	$0.906418\pi$
$702$	−1.08198e49	−0.167232
$703$	5.57355e49	0.840260
$704$	1.29172e50	1.89953
$705$	1.01889e49	0.146156
$706$	−1.10994e50	−1.55316
$707$	1.17586e49	0.160515
$708$	−5.69905e47	−0.00758962
$709$	8.57440e49	1.11402	0.557012	−	0.830504i	$-0.311948\pi$
$709$	8.57440e49	1.11402	0.557012	+	0.830504i	$0.311948\pi$
$710$	−1.60516e50	−2.03468
$711$	−1.77777e49	−0.219865
$712$	1.02498e50	1.23685
$713$	1.02695e50	1.20916
$714$	−1.03255e49	−0.118629
$715$	−1.92088e50	−2.15350
$716$	−2.14454e47	−0.00234615
$717$	−4.58365e49	−0.489357
$718$	1.46939e50	1.53094
$719$	−9.30158e49	−0.945804	−0.472902	−	0.881115i	$-0.656794\pi$
$719$	−9.30158e49	−0.945804	−0.472902	+	0.881115i	$0.656794\pi$
$720$	4.40286e49	0.436935
$721$	−3.16598e49	−0.306648
$722$	−4.03300e49	−0.381266
$723$	−3.42843e49	−0.316355
$724$	6.77782e47	0.00610471
$725$	6.78529e49	0.596559
$726$	−1.81566e50	−1.55827
$727$	−1.51517e50	−1.26943	−0.634714	−	0.772747i	$-0.718882\pi$
$727$	−1.51517e50	−1.26943	−0.634714	+	0.772747i	$0.718882\pi$
$728$	−9.25644e49	−0.757085
$729$	4.63840e48	0.0370370
$730$	1.20236e50	0.937309
$731$	4.13914e49	0.315033
$732$	9.13752e47	0.00679023
$733$	3.71679e49	0.269680	0.134840	−	0.990867i	$-0.456948\pi$
$733$	3.71679e49	0.269680	0.134840	+	0.990867i	$0.456948\pi$
$734$	1.57880e50	1.11852
$735$	−2.43715e49	−0.168599
$736$	−2.08421e48	−0.0140792
$737$	3.26130e50	2.15134
$738$	−2.12508e49	−0.136895
$739$	−1.41482e50	−0.890068	−0.445034	−	0.895514i	$-0.646808\pi$
$739$	−1.41482e50	−0.890068	−0.445034	+	0.895514i	$0.646808\pi$
$740$	2.31842e48	0.0142442
$741$	6.55345e49	0.393234
$742$	−5.05045e49	−0.295980
$743$	−1.32718e49	−0.0759671	−0.0379836	−	0.999278i	$-0.512093\pi$
$743$	−1.32718e49	−0.0759671	−0.0379836	+	0.999278i	$0.512093\pi$
$744$	1.81608e50	1.01534
$745$	1.14586e50	0.625746
$746$	8.60083e49	0.458787
$747$	1.02658e50	0.534913
$748$	9.01414e47	0.00458824
$749$	1.63442e50	0.812703
$750$	−4.90265e49	−0.238154
$751$	−3.46826e50	−1.64593	−0.822966	−	0.568090i	$-0.807683\pi$
$751$	−3.46826e50	−1.64593	−0.822966	+	0.568090i	$0.807683\pi$
$752$	−4.25066e49	−0.197081
$753$	−1.23600e50	−0.559895
$754$	1.71305e50	0.758177
$755$	−5.80432e49	−0.251004
$756$	−4.12675e47	−0.00174372
$757$	1.74431e50	0.720190	0.360095	−	0.932916i	$-0.382744\pi$
$757$	1.74431e50	0.720190	0.360095	+	0.932916i	$0.382744\pi$
$758$	−2.24653e50	−0.906362
$759$	−1.92285e50	−0.758081
$760$	−2.63960e50	−1.01695
$761$	−2.34679e50	−0.883573	−0.441787	−	0.897120i	$-0.645655\pi$
$761$	−2.34679e50	−0.883573	−0.441787	+	0.897120i	$0.645655\pi$
$762$	1.97706e50	0.727456
$763$	2.51593e50	0.904730
$764$	2.51339e48	0.00883336
$765$	−2.92404e49	−0.100440
$766$	−2.24466e50	−0.753611
$767$	3.36477e50	1.10417
$768$	−5.55723e48	−0.0178253
$769$	−2.43660e50	−0.763965	−0.381983	−	0.924170i	$-0.624759\pi$
$769$	−2.43660e50	−0.763965	−0.381983	+	0.924170i	$0.624759\pi$
$770$	−7.19144e50	−2.20408
$771$	−3.39282e49	−0.101650
$772$	−4.55079e48	−0.0133286
$773$	−2.84978e50	−0.815961	−0.407981	−	0.912991i	$-0.633767\pi$
$773$	−2.84978e50	−0.815961	−0.407981	+	0.912991i	$0.633767\pi$
$774$	1.62380e50	0.454534
$775$	4.41676e50	1.20871
$776$	−3.59003e50	−0.960545
$777$	2.07216e50	0.542070
$778$	−3.10547e50	−0.794300
$779$	1.28714e50	0.321900
$780$	2.72603e48	0.00666614
$781$	1.25245e51	2.99480
$782$	6.82777e49	0.159647
$783$	−7.34376e49	−0.167914
$784$	1.01674e50	0.227342
$785$	5.53988e50	1.21138
$786$	3.22444e50	0.689540
$787$	−1.97882e50	−0.413855	−0.206927	−	0.978356i	$-0.566346\pi$
$787$	−1.97882e50	−0.413855	−0.206927	+	0.978356i	$0.566346\pi$
$788$	−1.20643e48	−0.00246771
$789$	−1.14197e50	−0.228459
$790$	4.39655e50	0.860275
$791$	−1.99707e50	−0.382213
$792$	−3.40041e50	−0.636562
$793$	−5.39488e50	−0.987872
$794$	4.88383e50	0.874786
$795$	−1.43022e50	−0.250597
$796$	−9.09942e48	−0.0155968
$797$	−7.01990e50	−1.17709	−0.588545	−	0.808464i	$-0.700299\pi$
$797$	−7.01990e50	−1.17709	−0.588545	+	0.808464i	$0.700299\pi$
$798$	2.45349e50	0.402471
$799$	2.82295e49	0.0453038
$800$	−8.96383e48	−0.0140740
$801$	−2.69795e50	−0.414444
$802$	8.37445e50	1.25865
$803$	−9.38160e50	−1.37961
$804$	−4.62828e48	−0.00665946
$805$	−5.54939e50	−0.781299
$806$	1.11507e51	1.53618
$807$	4.56662e50	0.615613
$808$	−1.37501e50	−0.181388
$809$	5.73388e49	0.0740201	0.0370100	−	0.999315i	$-0.488217\pi$
$809$	5.73388e49	0.0740201	0.0370100	+	0.999315i	$0.488217\pi$
$810$	−1.14711e50	−0.144916
$811$	−9.21150e50	−1.13885	−0.569424	−	0.822044i	$-0.692834\pi$
$811$	−9.21150e50	−1.13885	−0.569424	+	0.822044i	$0.692834\pi$
$812$	6.53369e48	0.00790548
$813$	1.57826e50	0.186894
$814$	−1.77567e51	−2.05795
$815$	1.12372e51	1.27468
$816$	1.21986e50	0.135436
$817$	−9.83522e50	−1.06880
$818$	1.27002e51	1.35092
$819$	2.43647e50	0.253684
$820$	5.35410e48	0.00545688
$821$	−1.46860e50	−0.146520	−0.0732601	−	0.997313i	$-0.523340\pi$
$821$	−1.46860e50	−0.146520	−0.0732601	+	0.997313i	$0.523340\pi$
$822$	−8.13448e50	−0.794462
$823$	−1.56888e50	−0.150000	−0.0750001	−	0.997184i	$-0.523896\pi$
$823$	−1.56888e50	−0.150000	−0.0750001	+	0.997184i	$0.523896\pi$
$824$	3.70220e50	0.346525
$825$	−8.26988e50	−0.757801
$826$	1.25971e51	1.13011
$827$	4.83402e50	0.424582	0.212291	−	0.977206i	$-0.431907\pi$
$827$	4.83402e50	0.424582	0.212291	+	0.977206i	$0.431907\pi$
$828$	2.72883e48	0.00234663
$829$	6.20934e50	0.522807	0.261404	−	0.965230i	$-0.415815\pi$
$829$	6.20934e50	0.522807	0.261404	+	0.965230i	$0.415815\pi$
$830$	−2.53881e51	−2.09298
$831$	−2.75074e50	−0.222040
$832$	1.08231e51	0.855444
$833$	−6.75241e49	−0.0522602
$834$	4.30810e50	0.326498
$835$	−1.22762e50	−0.0911065
$836$	−2.14189e49	−0.0155664
$837$	−4.78028e50	−0.340219
$838$	−5.72367e50	−0.398937
$839$	1.99533e49	0.0136201	0.00681004	−	0.999977i	$-0.497832\pi$
$839$	1.99533e49	0.0136201	0.00681004	+	0.999977i	$0.497832\pi$
$840$	−9.81364e50	−0.656059
$841$	−3.64616e50	−0.238729
$842$	3.00114e51	1.92453
$843$	4.09197e50	0.257010
$844$	2.22498e49	0.0136878
$845$	5.43948e50	0.327767
$846$	1.10745e50	0.0653649
$847$	4.08862e51	2.36383
$848$	5.96665e50	0.337911
$849$	1.81206e51	1.00528
$850$	2.93651e50	0.159588
$851$	−1.37022e51	−0.729497
$852$	−1.77742e49	−0.00927038
$853$	1.93386e51	0.988138	0.494069	−	0.869423i	$-0.335509\pi$
$853$	1.93386e51	0.988138	0.494069	+	0.869423i	$0.335509\pi$
$854$	−2.01975e51	−1.01108
$855$	6.94794e50	0.340761
$856$	−1.91125e51	−0.918387
$857$	−2.82879e51	−1.33179	−0.665897	−	0.746044i	$-0.731951\pi$
$857$	−2.82879e51	−1.33179	−0.665897	+	0.746044i	$0.731951\pi$
$858$	−2.08785e51	−0.963101
$859$	−8.03822e50	−0.363312	−0.181656	−	0.983362i	$-0.558146\pi$
$859$	−8.03822e50	−0.363312	−0.181656	+	0.983362i	$0.558146\pi$
$860$	−4.09114e49	−0.0181185
$861$	4.78539e50	0.207665
$862$	−3.31936e51	−1.41149
$863$	3.76230e50	0.156771	0.0783853	−	0.996923i	$-0.475024\pi$
$863$	3.76230e50	0.156771	0.0783853	+	0.996923i	$0.475024\pi$
$864$	9.70160e48	0.00396144
$865$	−2.24139e51	−0.896884
$866$	9.34080e50	0.366287
$867$	1.42134e51	0.546217
$868$	4.25299e49	0.0160176
$869$	−3.43049e51	−1.26622
$870$	1.81617e51	0.657005
$871$	2.73258e51	0.968847
$872$	−2.94206e51	−1.02238
$873$	9.44964e50	0.321859
$874$	−1.62238e51	−0.541630
$875$	1.10401e51	0.361270
$876$	1.33139e49	0.00427056
$877$	−6.05168e51	−1.90276	−0.951378	−	0.308026i	$-0.900332\pi$
$877$	−6.05168e51	−1.90276	−0.951378	+	0.308026i	$0.900332\pi$
$878$	−2.99494e51	−0.923070
$879$	−1.58195e51	−0.477957
$880$	8.49603e51	2.51634
$881$	4.30414e51	1.24971	0.624853	−	0.780743i	$-0.285159\pi$
$881$	4.30414e51	1.24971	0.624853	+	0.780743i	$0.285159\pi$
$882$	−2.64899e50	−0.0754016
$883$	4.92037e51	1.37305	0.686523	−	0.727108i	$-0.259136\pi$
$883$	4.92037e51	1.37305	0.686523	+	0.727108i	$0.259136\pi$
$884$	7.55277e48	0.00206629
$885$	3.56732e51	0.956829
$886$	4.94077e50	0.129928
$887$	−2.14319e51	−0.552583	−0.276291	−	0.961074i	$-0.589106\pi$
$887$	−2.14319e51	−0.552583	−0.276291	+	0.961074i	$0.589106\pi$
$888$	−2.42313e51	−0.612561
$889$	−4.45207e51	−1.10352
$890$	6.67224e51	1.62161
$891$	8.95053e50	0.213299
$892$	−3.34720e49	−0.00782163
$893$	−6.70776e50	−0.153701
$894$	1.24547e51	0.279850
$895$	1.34237e51	0.295781
$896$	4.13582e51	0.893658
$897$	−1.61112e51	−0.341398
$898$	−2.21591e51	−0.460485
$899$	7.56840e51	1.54244
$900$	1.17362e49	0.00234577
$901$	−3.96258e50	−0.0776773
$902$	−4.10068e51	−0.788390
$903$	−3.65659e51	−0.689509
$904$	2.33532e51	0.431916
$905$	−4.24258e51	−0.769626
$906$	−6.30885e50	−0.112255
$907$	−4.87052e51	−0.850056	−0.425028	−	0.905180i	$-0.639736\pi$
$907$	−4.87052e51	−0.850056	−0.425028	+	0.905180i	$0.639736\pi$
$908$	5.57362e48	0.000954190 0
$909$	3.61930e50	0.0607794
$910$	−6.02557e51	−0.992599
$911$	−6.77380e51	−1.09461	−0.547306	−	0.836932i	$-0.684347\pi$
$911$	−6.77380e51	−1.09461	−0.547306	+	0.836932i	$0.684347\pi$
$912$	−2.89858e51	−0.459489
$913$	1.98096e52	3.08061
$914$	2.03353e51	0.310236
$915$	−5.71963e51	−0.856049
$916$	−4.10743e49	−0.00603115
$917$	−7.26100e51	−1.04600
$918$	−3.17820e50	−0.0449194
$919$	−5.35641e51	−0.742766	−0.371383	−	0.928480i	$-0.621116\pi$
$919$	−5.35641e51	−0.742766	−0.371383	+	0.928480i	$0.621116\pi$
$920$	6.48930e51	0.882899
$921$	−3.56405e51	−0.475774
$922$	−8.06575e51	−1.05646
$923$	1.04941e52	1.34869
$924$	−7.96323e49	−0.0100422
$925$	−5.89310e51	−0.729228
$926$	4.98609e51	0.605435
$927$	−9.74491e50	−0.116113
$928$	−1.53601e50	−0.0179599
$929$	1.90228e51	0.218273	0.109137	−	0.994027i	$-0.465191\pi$
$929$	1.90228e51	0.218273	0.109137	+	0.994027i	$0.465191\pi$
$930$	1.18220e52	1.33119
$931$	1.60447e51	0.177302
$932$	9.54751e47	0.000103541 0
$933$	−4.02333e51	−0.428210
$934$	−1.14879e52	−1.19997
$935$	−5.64240e51	−0.578443
$936$	−2.84914e51	−0.286673
$937$	−1.91815e51	−0.189426	−0.0947131	−	0.995505i	$-0.530193\pi$
$937$	−1.91815e51	−0.189426	−0.0947131	+	0.995505i	$0.530193\pi$
$938$	1.02303e52	0.991605
$939$	9.94940e51	0.946562
$940$	−2.79022e49	−0.00260556
$941$	3.93099e51	0.360316	0.180158	−	0.983638i	$-0.442339\pi$
$941$	3.93099e51	0.360316	0.180158	+	0.983638i	$0.442339\pi$
$942$	6.02142e51	0.541762
$943$	−3.16435e51	−0.279467
$944$	−1.48823e52	−1.29021
$945$	2.58314e51	0.219832
$946$	3.13339e52	2.61769
$947$	8.55914e51	0.701949	0.350975	−	0.936385i	$-0.385850\pi$
$947$	8.55914e51	0.701949	0.350975	+	0.936385i	$0.385850\pi$
$948$	4.86839e49	0.00391958
$949$	−7.86066e51	−0.621299
$950$	−6.97758e51	−0.541430
$951$	1.45286e51	0.110679
$952$	−2.71898e51	−0.203357
$953$	−1.86653e52	−1.37059	−0.685296	−	0.728265i	$-0.740327\pi$
$953$	−1.86653e52	−1.37059	−0.685296	+	0.728265i	$0.740327\pi$
$954$	−1.55453e51	−0.112074
$955$	−1.57325e52	−1.11363
$956$	1.25523e50	0.00872386
$957$	−1.41710e52	−0.967031
$958$	1.15985e52	0.777153
$959$	1.83178e52	1.20517
$960$	1.14746e52	0.741293
$961$	3.35013e52	2.12521
$962$	−1.48780e52	−0.926788
$963$	5.03076e51	0.307733
$964$	9.38869e49	0.00563971
$965$	2.84857e52	1.68034
$966$	−6.03176e51	−0.349417
$967$	2.01895e52	1.14858	0.574291	−	0.818651i	$-0.305278\pi$
$967$	2.01895e52	1.14858	0.574291	+	0.818651i	$0.305278\pi$
$968$	−4.78111e52	−2.67122
$969$	1.92501e51	0.105625
$970$	−2.33697e52	−1.25935
$971$	−2.52832e52	−1.33812	−0.669062	−	0.743207i	$-0.733304\pi$
$971$	−2.52832e52	−1.33812	−0.669062	+	0.743207i	$0.733304\pi$
$972$	−1.27022e49	−0.000660266 0
$973$	−9.70127e51	−0.495284
$974$	3.21107e51	0.161016
$975$	−6.92917e51	−0.341272
$976$	2.38614e52	1.15432
$977$	−1.01954e52	−0.484449	−0.242224	−	0.970220i	$-0.577877\pi$
$977$	−1.01954e52	−0.484449	−0.242224	+	0.970220i	$0.577877\pi$
$978$	1.22140e52	0.570069
$979$	−5.20614e52	−2.38681
$980$	6.67410e49	0.00300564
$981$	7.74406e51	0.342579
$982$	−3.20116e51	−0.139109
$983$	−1.83516e52	−0.783409	−0.391704	−	0.920091i	$-0.628114\pi$
$983$	−1.83516e52	−0.783409	−0.391704	+	0.920091i	$0.628114\pi$
$984$	−5.59590e51	−0.234669
$985$	7.55164e51	0.311105
$986$	5.03190e51	0.203651
$987$	−2.49384e51	−0.0991559
$988$	−1.79465e50	−0.00701025
$989$	2.41793e52	0.927915
$990$	−2.21353e52	−0.834584
$991$	1.14097e52	0.422653	0.211326	−	0.977416i	$-0.432222\pi$
$991$	1.14097e52	0.422653	0.211326	+	0.977416i	$0.432222\pi$
$992$	−9.99836e50	−0.0363894
$993$	−4.88443e51	−0.174664
$994$	3.92879e52	1.38037
$995$	5.69578e52	1.96630
$996$	−2.81128e50	−0.00953599
$997$	1.40660e52	0.468819	0.234409	−	0.972138i	$-0.424684\pi$
$997$	1.40660e52	0.468819	0.234409	+	0.972138i	$0.424684\pi$
$998$	−1.75461e51	−0.0574641
$999$	6.37813e51	0.205257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.36.a.b.1.3	✓	3
3.2	odd	2		9.36.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.36.a.b.1.3	✓	3	1.1	even	1	trivial
9.36.a.c.1.1		3	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+186315. q^{2} -1.29140e8 q^{3} +3.53648e8 q^{4} -2.21366e12 q^{5} -2.40608e13 q^{6} +5.41817e14 q^{7} -6.33585e15 q^{8} +1.66772e16 q^{9} +O(q^{10})\)	\(q+186315. q^{2} -1.29140e8 q^{3} +3.53648e8 q^{4} -2.21366e12 q^{5} -2.40608e13 q^{6} +5.41817e14 q^{7} -6.33585e15 q^{8} +1.66772e16 q^{9} -4.12439e17 q^{10} +3.21813e18 q^{11} -4.56702e16 q^{12} +2.69641e19 q^{13} +1.00949e20 q^{14} +2.85873e20 q^{15} -1.19262e21 q^{16} +7.92043e20 q^{17} +3.10721e21 q^{18} -1.88201e22 q^{19} -7.82858e20 q^{20} -6.99703e22 q^{21} +5.99587e23 q^{22} +4.62681e23 q^{23} +8.18213e23 q^{24} +1.98991e24 q^{25} +5.02382e24 q^{26} -2.15369e24 q^{27} +1.91613e23 q^{28} +3.40984e25 q^{29} +5.32624e25 q^{30} +2.21957e26 q^{31} -4.50463e24 q^{32} -4.15590e26 q^{33} +1.47570e26 q^{34} -1.19940e27 q^{35} +5.89786e24 q^{36} -2.96148e27 q^{37} -3.50648e27 q^{38} -3.48215e27 q^{39} +1.40254e28 q^{40} -6.83917e27 q^{41} -1.30365e28 q^{42} +5.22591e28 q^{43} +1.13809e27 q^{44} -3.69176e28 q^{45} +8.62045e28 q^{46} +3.56414e28 q^{47} +1.54015e29 q^{48} -8.52530e28 q^{49} +3.70751e29 q^{50} -1.02285e29 q^{51} +9.53581e27 q^{52} -5.00298e29 q^{53} -4.01266e29 q^{54} -7.12385e30 q^{55} -3.43287e30 q^{56} +2.43043e30 q^{57} +6.35306e30 q^{58} +1.24787e31 q^{59} +1.01098e29 q^{60} -2.00076e31 q^{61} +4.13540e31 q^{62} +9.03598e30 q^{63} +4.01388e31 q^{64} -5.96894e31 q^{65} -7.74307e31 q^{66} +1.01341e32 q^{67} +2.80105e29 q^{68} -5.97507e31 q^{69} -2.23466e32 q^{70} +3.89186e32 q^{71} -1.05664e32 q^{72} -2.91523e32 q^{73} -5.51770e32 q^{74} -2.56978e32 q^{75} -6.65571e30 q^{76} +1.74364e33 q^{77} -6.48778e32 q^{78} -1.06599e33 q^{79} +2.64005e33 q^{80} +2.78128e32 q^{81} -1.27424e33 q^{82} +6.15561e33 q^{83} -2.47449e31 q^{84} -1.75332e33 q^{85} +9.73666e33 q^{86} -4.40348e33 q^{87} -2.03896e34 q^{88} -1.61775e34 q^{89} -6.87832e33 q^{90} +1.46096e34 q^{91} +1.63626e32 q^{92} -2.86636e34 q^{93} +6.64054e33 q^{94} +4.16614e34 q^{95} +5.81729e32 q^{96} +5.66621e34 q^{97} -1.58839e34 q^{98} +5.36693e34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 50\!\cdots\!07 q^{9}+O(q^{10}) \) 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9	\( 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 57\!\cdots\!76 q^{99}+O(q^{100}) \) 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9 - 1127779626928867020 * q^10 + 3426356175124224804 * q^11 - 4195602845172722700 * q^12 + 50087718431258539506 * q^13 - 217880362960444050144 * q^14 - 357547300335073771830 * q^15 + 606906765664363747344 * q^16 + 2730709287864549111942 * q^17 - 1456418277831881470770 * q^18 + 28794251065778257727292 * q^19 + 88477655809138293889560 * q^20 - 63051115342974896664432 * q^21 - 122741766765729403865496 * q^22 + 1806983834691084779311608 * q^23 + 2412744607366739676625176 * q^24 + 8598840806404444672708725 * q^25 + 12462234191474761114326516 * q^26 - 6461081889226673298932241 * q^27 + 88582873604432535904569792 * q^28 + 78927943791269118086922714 * q^29 + 145641644849673076368124260 * q^30 - 1597007179004406242679048 * q^31 + 212133152341134442715841504 * q^32 - 442480194951598936437203052 * q^33 - 1031323232079473133177847620 * q^34 - 1159830211565676145196532000 * q^35 + 541820835308869172631800100 * q^36 - 5102549932092597658956094086 * q^37 - 8724219045726720381610922664 * q^38 - 6468336122510832086946779478 * q^39 - 17377992868876213570860774960 * q^40 - 20208748955896036456754429058 * q^41 + 28137105587210907187976333472 * q^42 + 46721962642013867129638134372 * q^43 + 194349428414233101115805936688 * q^44 + 46173716645481381511151008290 * q^45 + 52087178478532028950981302192 * q^46 + 293197746513164578153478190816 * q^47 - 78376038643698737623294977072 * q^48 + 836105627836985614440420595707 * q^49 - 701125828082122697797800571950 * q^50 - 352644242540441794237695126546 * q^51 - 2520178249741268871517789030248 * q^52 - 108875909240521237104294715182 * q^53 + 188082093795388459731917535510 * q^54 - 6237008697722857733231584966440 * q^55 - 9347630291312236144016149603200 * q^56 - 3718494276097527924758498428596 * q^57 + 11382186268398399744329433517572 * q^58 + 11320340569522247618095325505348 * q^59 - 11426018893050016162439682398280 * q^60 + 12771547929195071355310409383218 * q^61 + 101447293741849863418951127675568 * q^62 + 8142431312723579060152904782416 * q^63 - 41280658033851993168324127190976 * q^64 - 7709579158673152743776325663060 * q^65 + 15850891767034278029082983515848 * q^66 + 175757710780078940305499908875612 * q^67 + 281442880096236379198382763169800 * q^68 - 233354186950371743047120084912104 * q^69 - 1040498682940112273466514884936000 * q^70 - 27474747461715252213775775690424 * q^71 - 311582231872711762617942518543688 * q^72 - 585184619829428568163757555870322 * q^73 + 134392541523566959843290841608516 * q^74 - 1110455703350121428958086398022175 * q^75 + 403477747366730076622590548780112 * q^76 + 5306726056931811905707525354511808 * q^77 - 1609374954831223860690187911462108 * q^78 - 2667396066634861458375845391576600 * q^79 + 7102490190805235743681469824979040 * q^80 + 834385168331080533771857328695283 * q^81 + 917242845604400818117266629806188 * q^82 + 6578360642441675208543593208203580 * q^83 - 11439606736284815209219495383756096 * q^84 + 3560960065600250795485268792239140 * q^85 + 18773659018851120901851911340565224 * q^86 - 10192767526459331886611447454362382 * q^87 - 34961215155916125706150543997131872 * q^88 + 11419551912179244059325275346141822 * q^89 - 18808185755474891578891014940654380 * q^90 - 40541093249602611010364470781007648 * q^91 - 19232540048657476273178638696239456 * q^92 + 206237767408799199897789815404824 * q^93 - 101336598951909608865466201817694528 * q^94 + 159588702835640097495158571410457960 * q^95 - 27394909871037933537237934508725152 * q^96 + 211792260572805448951439211684683142 * q^97 - 124471288129025507609829835395708786 * q^98 + 57141964500321263762127041399377476 * q^99

Introduction

L-functions

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