LMFDB - Embedded newform 3.34.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,34,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, 34, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 34 $
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:	$20.6948486643$
Analytic rank:	$1$
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} - 5357605x + 842871622 $ x^3 - x^2 - 5357605*x + 842871622
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{6}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$158.055$ 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)

$f(q)$	$=$	$q-92260.3 q^{2} -4.30467e7 q^{3} -7.79766e7 q^{4} -3.77234e10 q^{5} +3.97150e12 q^{6} -2.13696e13 q^{7} +7.99704e14 q^{8} +1.85302e15 q^{9} +O(q^{10})$	\(q-92260.3 q^{2} -4.30467e7 q^{3} -7.79766e7 q^{4} -3.77234e10 q^{5} +3.97150e12 q^{6} -2.13696e13 q^{7} +7.99704e14 q^{8} +1.85302e15 q^{9} +3.48037e15 q^{10} +1.25789e17 q^{11} +3.35664e15 q^{12} +2.98845e18 q^{13} +1.97157e18 q^{14} +1.62387e18 q^{15} -7.31111e19 q^{16} -1.73339e20 q^{17} -1.70960e20 q^{18} -4.45630e19 q^{19} +2.94154e18 q^{20} +9.19892e20 q^{21} -1.16054e22 q^{22} -3.44187e22 q^{23} -3.44246e22 q^{24} -1.14992e23 q^{25} -2.75715e23 q^{26} -7.97664e22 q^{27} +1.66633e21 q^{28} +3.07199e23 q^{29} -1.49818e23 q^{30} +5.39368e24 q^{31} -1.24155e23 q^{32} -5.41482e24 q^{33} +1.59923e25 q^{34} +8.06134e23 q^{35} -1.44492e23 q^{36} +1.27563e26 q^{37} +4.11139e24 q^{38} -1.28643e26 q^{39} -3.01675e25 q^{40} -6.60365e26 q^{41} -8.48695e25 q^{42} -9.67926e26 q^{43} -9.80863e24 q^{44} -6.99022e25 q^{45} +3.17548e27 q^{46} +1.84223e27 q^{47} +3.14719e27 q^{48} -7.27433e27 q^{49} +1.06092e28 q^{50} +7.46168e27 q^{51} -2.33029e26 q^{52} -1.46833e28 q^{53} +7.35927e27 q^{54} -4.74520e27 q^{55} -1.70894e28 q^{56} +1.91829e27 q^{57} -2.83423e28 q^{58} -1.77909e29 q^{59} -1.26624e26 q^{60} +2.00566e29 q^{61} -4.97622e29 q^{62} -3.95983e28 q^{63} +6.39474e29 q^{64} -1.12734e29 q^{65} +4.99573e29 q^{66} +2.10593e30 q^{67} +1.35164e28 q^{68} +1.48161e30 q^{69} -7.43742e28 q^{70} -4.12649e30 q^{71} +1.48187e30 q^{72} -5.52960e30 q^{73} -1.17690e31 q^{74} +4.95004e30 q^{75} +3.47487e27 q^{76} -2.68807e30 q^{77} +1.18686e31 q^{78} -9.45950e29 q^{79} +2.75800e30 q^{80} +3.43368e30 q^{81} +6.09254e31 q^{82} -7.81636e31 q^{83} -7.17300e28 q^{84} +6.53894e30 q^{85} +8.93012e31 q^{86} -1.32239e31 q^{87} +1.00594e32 q^{88} -7.99293e31 q^{89} +6.44920e30 q^{90} -6.38620e31 q^{91} +2.68385e30 q^{92} -2.32180e32 q^{93} -1.69965e32 q^{94} +1.68107e30 q^{95} +5.34448e30 q^{96} -1.07590e33 q^{97} +6.71132e32 q^{98} +2.33090e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 136620 q^{2} - 129140163 q^{3} + 14589555600 q^{4} - 260488036134 q^{5} - 5881043023020 q^{6} + 10760698892832 q^{7} + 18\!\cdots\!76 q^{8}+ \cdots + 55\!\cdots\!23 q^{9}+O(q^{10}) $ 3 * q + 136620 * q^2 - 129140163 * q^3 + 14589555600 * q^4 - 260488036134 * q^5 - 5881043023020 * q^6 + 10760698892832 * q^7 + 1806352049808576 * q^8 + 5559060566555523 * q^9	$ 3 q + 136620 q^{2} - 129140163 q^{3} + 14589555600 q^{4} - 260488036134 q^{5} - 5881043023020 q^{6} + 10760698892832 q^{7} + 18\!\cdots\!76 q^{8}+ \cdots - 64\!\cdots\!96 q^{99}+O(q^{100}) $ 3 * q + 136620 * q^2 - 129140163 * q^3 + 14589555600 * q^4 - 260488036134 * q^5 - 5881043023020 * q^6 + 10760698892832 * q^7 + 1806352049808576 * q^8 + 5559060566555523 * q^9 - 56442714195076056 * q^10 - 345482369200786356 * q^11 - 628032529427187600 * q^12 + 730047702981793722 * q^13 - 9466648738386811776 * q^14 + 11213155815298216614 * q^15 + 57097856385199812864 * q^16 - 241702143352594866234 * q^17 + 253159618200938517420 * q^18 - 302063201058090006732 * q^19 - 9511079529660801113376 * q^20 - 463212803004748003872 * q^21 - 62637844423105026039888 * q^22 - 62177828305895870808024 * q^23 - 77757532715887874479296 * q^24 - 113362765411196109398019 * q^25 - 274958228188114840257624 * q^26 - 239299329230617529590083 * q^27 - 3222271636207020516112896 * q^28 - 1259920260916004318716494 * q^29 + 2429673770438178556412376 * q^30 + 11135125624283076100487352 * q^31 + 13995317245307766511168512 * q^32 + 14871883157405243247338676 * q^33 + 2693352737405664780350040 * q^34 + 89265959101072598849081280 * q^35 + 27034741073176434431859600 * q^36 - 47470694780535466043761518 * q^37 + 15348541159835774116798032 * q^38 - 31426159786948142430485562 * q^39 - 1000865216529547256276226432 * q^40 - 510043583286993345182539218 * q^41 + 407508187046339076600986496 * q^42 - 241949512345382263987418676 * q^43 - 2802266702859033871786911168 * q^44 - 482689589910669862380422694 * q^45 + 1894559041786498078265576352 * q^46 + 1921077201868476933761742528 * q^47 - 2457875493511764873608818944 * q^48 + 18186134741403006655682598123 * q^49 + 18465455874376386239717829204 * q^50 + 10404484730001155832807318714 * q^51 + 42532175939901401243990183136 * q^52 + 8039908215852241665398717466 * q^53 - 10897691453162322297532379820 * q^54 + 30088015095001838816140788456 * q^55 - 377844291996686623593396172800 * q^56 + 13002830340314505312680525772 * q^57 - 308504983868142890433522752376 * q^58 - 247660094389221812820609454068 * q^59 + 409420786922119730163986040096 * q^60 + 37736108183042272792017479418 * q^61 + 302392999582755025784699411424 * q^62 + 19939792294573348997984903712 * q^63 + 1193868512245765263646771286016 * q^64 - 1439546196636635959290593941812 * q^65 + 2696353812922808009636793607248 * q^66 + 1000778046108011502274286558196 * q^67 - 1741077115261984900728913356000 * q^68 + 2676551627469802205725053689304 * q^69 + 11179426654384923501066012952320 * q^70 - 13161136343851691507425619260584 * q^71 + 3347206816469197599993275188416 * q^72 - 2102232382664339647381735290594 * q^73 - 36192879788033917171536014449656 * q^74 + 4879895334444209197542001845699 * q^75 + 7431716486141494636076085792192 * q^76 - 18011309120068715154396356501376 * q^77 + 11836050135468115044529508450904 * q^78 + 2220668017769877386018864526600 * q^79 - 59638374077820540688333624951296 * q^80 + 10301051460877537453973547267843 * q^81 + 128405842979035073898453989818104 * q^82 - 36455583004258570245309903891660 * q^83 + 138708228110017110398387838614016 * q^84 + 47494471216195568447991651883572 * q^85 + 249696091044323323817104420734384 * q^86 + 54235435953898442342583995316174 * q^87 - 64292534102628440519093096373504 * q^88 - 301000215018751428734710041573522 * q^89 - 104589488917070320066066310619096 * q^90 - 793065761375571553941370782547008 * q^91 + 233024630810116195988192414904192 * q^92 - 479330646048464401919447005572792 * q^93 + 134856701076698355695283792200448 * q^94 - 217499295515701461216485225187816 * q^95 - 602452516765251984139414320049152 * q^96 - 876561469773784134737853121199994 * q^97 + 3099174773064755865455550107098188 * q^98 - 640185805021422590005321978281396 * 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 $

$2$	−92260.3	−0.995451	−0.497725	−	0.867335i	$-0.665831\pi$
$2$	−92260.3	−0.995451	−0.497725	+	0.867335i	$0.665831\pi$
$3$	−4.30467e7	−0.577350
$3$	−4.30467e7	−0.577350
$4$	−7.79766e7	−0.00907767
$5$	−3.77234e10	−0.110562	−0.0552810	−	0.998471i	$-0.517605\pi$
$5$	−3.77234e10	−0.110562	−0.0552810	+	0.998471i	$0.517605\pi$
$6$	3.97150e12	0.574724
$7$	−2.13696e13	−0.243041	−0.121520	−	0.992589i	$-0.538777\pi$
$7$	−2.13696e13	−0.243041	−0.121520	+	0.992589i	$0.538777\pi$
$8$	7.99704e14	1.00449
$9$	1.85302e15	0.333333
$10$	3.48037e15	0.110059
$11$	1.25789e17	0.825401	0.412701	−	0.910867i	$-0.364586\pi$
$11$	1.25789e17	0.825401	0.412701	+	0.910867i	$0.364586\pi$
$12$	3.35664e15	0.00524099
$13$	2.98845e18	1.24561	0.622803	−	0.782379i	$-0.285994\pi$
$13$	2.98845e18	1.24561	0.622803	+	0.782379i	$0.285994\pi$
$14$	1.97157e18	0.241935
$15$	1.62387e18	0.0638330
$16$	−7.31111e19	−0.990840
$17$	−1.73339e20	−0.863952	−0.431976	−	0.901885i	$-0.642183\pi$
$17$	−1.73339e20	−0.863952	−0.431976	+	0.901885i	$0.642183\pi$
$18$	−1.70960e20	−0.331817
$19$	−4.45630e19	−0.0354438	−0.0177219	−	0.999843i	$-0.505641\pi$
$19$	−4.45630e19	−0.0354438	−0.0177219	+	0.999843i	$0.505641\pi$
$20$	2.94154e18	0.00100364
$21$	9.19892e20	0.140320
$22$	−1.16054e22	−0.821646
$23$	−3.44187e22	−1.17027	−0.585134	−	0.810937i	$-0.698958\pi$
$23$	−3.44187e22	−1.17027	−0.585134	+	0.810937i	$0.698958\pi$
$24$	−3.44246e22	−0.579941
$25$	−1.14992e23	−0.987776
$26$	−2.75715e23	−1.23994
$27$	−7.97664e22	−0.192450
$28$	1.66633e21	0.00220624
$29$	3.07199e23	0.227957	0.113979	−	0.993483i	$-0.463640\pi$
$29$	3.07199e23	0.227957	0.113979	+	0.993483i	$0.463640\pi$
$30$	−1.49818e23	−0.0635426
$31$	5.39368e24	1.33173	0.665867	−	0.746071i	$-0.268062\pi$
$31$	5.39368e24	1.33173	0.665867	+	0.746071i	$0.268062\pi$
$32$	−1.24155e23	−0.0181548
$33$	−5.41482e24	−0.476546
$34$	1.59923e25	0.860022
$35$	8.06134e23	0.0268711
$36$	−1.44492e23	−0.00302589
$37$	1.27563e26	1.69980	0.849898	−	0.526947i	$-0.176663\pi$
$37$	1.27563e26	1.69980	0.849898	+	0.526947i	$0.176663\pi$
$38$	4.11139e24	0.0352825
$39$	−1.28643e26	−0.719151
$40$	−3.01675e25	−0.111058
$41$	−6.60365e26	−1.61752	−0.808761	−	0.588137i	$-0.799862\pi$
$41$	−6.60365e26	−1.61752	−0.808761	+	0.588137i	$0.799862\pi$
$42$	−8.48695e25	−0.139681
$43$	−9.67926e26	−1.08047	−0.540235	−	0.841514i	$-0.681665\pi$
$43$	−9.67926e26	−1.08047	−0.540235	+	0.841514i	$0.681665\pi$
$44$	−9.80863e24	−0.00749272
$45$	−6.99022e25	−0.0368540
$46$	3.17548e27	1.16494
$47$	1.84223e27	0.473946	0.236973	−	0.971516i	$-0.423845\pi$
$47$	1.84223e27	0.473946	0.236973	+	0.971516i	$0.423845\pi$
$48$	3.14719e27	0.572062
$49$	−7.27433e27	−0.940931
$50$	1.06092e28	0.983282
$51$	7.46168e27	0.498803
$52$	−2.33029e26	−0.0113072
$53$	−1.46833e28	−0.520320	−0.260160	−	0.965565i	$-0.583775\pi$
$53$	−1.46833e28	−0.520320	−0.260160	+	0.965565i	$0.583775\pi$
$54$	7.35927e27	0.191575
$55$	−4.74520e27	−0.0912579
$56$	−1.70894e28	−0.244131
$57$	1.91829e27	0.0204635
$58$	−2.83423e28	−0.226920
$59$	−1.77909e29	−1.07433	−0.537167	−	0.843476i	$-0.680506\pi$
$59$	−1.77909e29	−1.07433	−0.537167	+	0.843476i	$0.680506\pi$
$60$	−1.26624e26	−0.000579454 0
$61$	2.00566e29	0.698738	0.349369	−	0.936985i	$-0.386396\pi$
$61$	2.00566e29	0.698738	0.349369	+	0.936985i	$0.386396\pi$
$62$	−4.97622e29	−1.32567
$63$	−3.95983e28	−0.0810136
$64$	6.39474e29	1.00891
$65$	−1.12734e29	−0.137717
$66$	4.99573e29	0.474378
$67$	2.10593e30	1.56030	0.780151	−	0.625591i	$-0.215142\pi$
$67$	2.10593e30	1.56030	0.780151	+	0.625591i	$0.215142\pi$
$68$	1.35164e28	0.00784267
$69$	1.48161e30	0.675654
$70$	−7.43742e28	−0.0267488
$71$	−4.12649e30	−1.17441	−0.587203	−	0.809440i	$-0.699771\pi$
$71$	−4.12649e30	−1.17441	−0.587203	+	0.809440i	$0.699771\pi$
$72$	1.48187e30	0.334829
$73$	−5.52960e30	−0.995099	−0.497550	−	0.867436i	$-0.665767\pi$
$73$	−5.52960e30	−0.995099	−0.497550	+	0.867436i	$0.665767\pi$
$74$	−1.17690e31	−1.69206
$75$	4.95004e30	0.570293
$76$	3.47487e27	0.000321747 0
$77$	−2.68807e30	−0.200606
$78$	1.18686e31	0.715879
$79$	−9.45950e29	−0.0462404	−0.0231202	−	0.999733i	$-0.507360\pi$
$79$	−9.45950e29	−0.0462404	−0.0231202	+	0.999733i	$0.507360\pi$
$80$	2.75800e30	0.109549
$81$	3.43368e30	0.111111
$82$	6.09254e31	1.61016
$83$	−7.81636e31	−1.69128	−0.845641	−	0.533752i	$-0.820782\pi$
$83$	−7.81636e31	−1.69128	−0.845641	+	0.533752i	$0.820782\pi$
$84$	−7.17300e28	−0.00127378
$85$	6.53894e30	0.0955202
$86$	8.93012e31	1.07556
$87$	−1.32239e31	−0.131611
$88$	1.00594e32	0.829105
$89$	−7.99293e31	−0.546727	−0.273364	−	0.961911i	$-0.588136\pi$
$89$	−7.99293e31	−0.546727	−0.273364	+	0.961911i	$0.588136\pi$
$90$	6.44920e30	0.0366863
$91$	−6.38620e31	−0.302733
$92$	2.68385e30	0.0106233
$93$	−2.32180e32	−0.768876
$94$	−1.69965e32	−0.471790
$95$	1.68107e30	0.00391873
$96$	5.34448e30	0.0104817
$97$	−1.07590e33	−1.77843	−0.889217	−	0.457485i	$-0.848750\pi$
$97$	−1.07590e33	−1.77843	−0.889217	+	0.457485i	$0.848750\pi$
$98$	6.71132e32	0.936651
$99$	2.33090e32	0.275134
$100$	8.96670e30	0.00896670
$101$	1.80351e33	1.53044	0.765221	−	0.643767i	$-0.222630\pi$
$101$	1.80351e33	1.53044	0.765221	+	0.643767i	$0.222630\pi$
$102$	−6.88417e32	−0.496534
$103$	1.45712e32	0.0894708	0.0447354	−	0.998999i	$-0.485756\pi$
$103$	1.45712e32	0.0894708	0.0447354	+	0.998999i	$0.485756\pi$
$104$	2.38988e33	1.25120
$105$	−3.47014e31	−0.0155140
$106$	1.35468e33	0.517953
$107$	−6.51635e32	−0.213389	−0.106695	−	0.994292i	$-0.534027\pi$
$107$	−6.51635e32	−0.213389	−0.106695	+	0.994292i	$0.534027\pi$
$108$	6.21991e30	0.00174700
$109$	−3.95159e33	−0.953311	−0.476656	−	0.879090i	$-0.658151\pi$
$109$	−3.95159e33	−0.953311	−0.476656	+	0.879090i	$0.658151\pi$
$110$	4.37794e32	0.0908428
$111$	−5.49118e33	−0.981378
$112$	1.56236e33	0.240814
$113$	−1.07508e34	−1.43102	−0.715509	−	0.698603i	$-0.753805\pi$
$113$	−1.07508e34	−1.43102	−0.715509	+	0.698603i	$0.753805\pi$
$114$	−1.76982e32	−0.0203704
$115$	1.29839e33	0.129387
$116$	−2.39543e31	−0.00206932
$117$	5.53766e33	0.415202
$118$	1.64139e34	1.06945
$119$	3.70419e33	0.209976
$120$	1.29861e33	0.0641194
$121$	−7.40216e33	−0.318713
$122$	−1.85042e34	−0.695559
$123$	2.84265e34	0.933877
$124$	−4.20581e32	−0.0120890
$125$	8.72948e33	0.219772
$126$	3.65335e33	0.0806450
$127$	1.23866e34	0.239988	0.119994	−	0.992775i	$-0.461712\pi$
$127$	1.23866e34	0.239988	0.119994	+	0.992775i	$0.461712\pi$
$128$	−5.79316e34	−0.986168
$129$	4.16661e34	0.623810
$130$	1.04009e34	0.137090
$131$	6.83061e34	0.793383	0.396692	−	0.917952i	$-0.370158\pi$
$131$	6.83061e34	0.793383	0.396692	+	0.917952i	$0.370158\pi$
$132$	4.22229e32	0.00432592
$133$	9.52294e32	0.00861428
$134$	−1.94293e35	−1.55320
$135$	3.00906e33	0.0212777
$136$	−1.38620e35	−0.867829
$137$	−5.81782e34	−0.322753	−0.161377	−	0.986893i	$-0.551593\pi$
$137$	−5.81782e34	−0.322753	−0.161377	+	0.986893i	$0.551593\pi$
$138$	−1.36694e35	−0.672581
$139$	9.69084e34	0.423270	0.211635	−	0.977349i	$-0.432121\pi$
$139$	9.69084e34	0.423270	0.211635	+	0.977349i	$0.432121\pi$
$140$	−6.28596e31	−0.000243926 0
$141$	−7.93020e34	−0.273633
$142$	3.80711e35	1.16906
$143$	3.75916e35	1.02812
$144$	−1.35476e35	−0.330280
$145$	−1.15886e34	−0.0252034
$146$	5.10162e35	0.990572
$147$	3.13136e35	0.543247
$148$	−9.94694e33	−0.0154302
$149$	7.41694e35	1.02956	0.514779	−	0.857323i	$-0.327874\pi$
$149$	7.41694e35	1.02956	0.514779	+	0.857323i	$0.327874\pi$
$150$	−4.56692e35	−0.567698
$151$	−1.45390e36	−1.61963	−0.809815	−	0.586685i	$-0.800433\pi$
$151$	−1.45390e36	−1.61963	−0.809815	+	0.586685i	$0.800433\pi$
$152$	−3.56372e34	−0.0356028
$153$	−3.21201e35	−0.287984
$154$	2.48002e35	0.199693
$155$	−2.03468e35	−0.147239
$156$	1.00311e34	0.00652821
$157$	−2.71605e36	−1.59072	−0.795359	−	0.606138i	$-0.792718\pi$
$157$	−2.71605e36	−1.59072	−0.795359	+	0.606138i	$0.792718\pi$
$158$	8.72736e34	0.0460300
$159$	6.32067e35	0.300407
$160$	4.68356e33	0.00200723
$161$	7.35515e35	0.284423
$162$	−3.16793e35	−0.110606
$163$	1.01732e36	0.320896	0.160448	−	0.987044i	$-0.448706\pi$
$163$	1.01732e36	0.320896	0.160448	+	0.987044i	$0.448706\pi$
$164$	5.14930e34	0.0146833
$165$	2.04265e35	0.0526878
$166$	7.21139e36	1.68359
$167$	−4.29054e36	−0.907174	−0.453587	−	0.891212i	$-0.649856\pi$
$167$	−4.29054e36	−0.907174	−0.453587	+	0.891212i	$0.649856\pi$
$168$	7.35641e35	0.140949
$169$	3.17470e36	0.551534
$170$	−6.03285e35	−0.0950857
$171$	−8.25761e34	−0.0118146
$172$	7.54756e34	0.00980815
$173$	−4.22361e36	−0.498796	−0.249398	−	0.968401i	$-0.580233\pi$
$173$	−4.22361e36	−0.498796	−0.249398	+	0.968401i	$0.580233\pi$
$174$	1.22004e36	0.131012
$175$	2.45734e36	0.240070
$176$	−9.19660e36	−0.817840
$177$	7.65840e36	0.620268
$178$	7.37430e36	0.544240
$179$	−8.40549e36	−0.565572	−0.282786	−	0.959183i	$-0.591259\pi$
$179$	−8.40549e36	−0.565572	−0.282786	+	0.959183i	$0.591259\pi$
$180$	5.45073e33	0.000334548 0
$181$	−7.47568e36	−0.418750	−0.209375	−	0.977835i	$-0.567143\pi$
$181$	−7.47568e36	−0.418750	−0.209375	+	0.977835i	$0.567143\pi$
$182$	5.89193e36	0.301356
$183$	−8.63369e36	−0.403416
$184$	−2.75248e37	−1.17552
$185$	−4.81211e36	−0.187933
$186$	2.14210e37	0.765379
$187$	−2.18042e37	−0.713107
$188$	−1.43651e35	−0.00430233
$189$	1.70458e36	0.0467732
$190$	−1.55096e35	−0.00390090
$191$	1.90473e37	0.439321	0.219661	−	0.975576i	$-0.429505\pi$
$191$	1.90473e37	0.439321	0.219661	+	0.975576i	$0.429505\pi$
$192$	−2.75273e37	−0.582496
$193$	5.72679e37	1.11228	0.556142	−	0.831087i	$-0.312281\pi$
$193$	5.72679e37	1.11228	0.556142	+	0.831087i	$0.312281\pi$
$194$	9.92627e37	1.77034
$195$	4.85285e36	0.0795107
$196$	5.67228e35	0.00854146
$197$	6.43397e37	0.890813	0.445406	−	0.895329i	$-0.353059\pi$
$197$	6.43397e37	0.890813	0.445406	+	0.895329i	$0.353059\pi$
$198$	−2.15050e37	−0.273882
$199$	7.65606e37	0.897283	0.448641	−	0.893712i	$-0.351908\pi$
$199$	7.65606e37	0.897283	0.448641	+	0.893712i	$0.351908\pi$
$200$	−9.19598e37	−0.992208
$201$	−9.06532e37	−0.900841
$202$	−1.66393e38	−1.52348
$203$	−6.56473e36	−0.0554028
$204$	−5.81837e35	−0.00452797
$205$	2.49112e37	0.178836
$206$	−1.34434e37	−0.0890637
$207$	−6.37786e37	−0.390089
$208$	−2.18489e38	−1.23420
$209$	−5.60555e36	−0.0292553
$210$	3.20156e36	0.0154434
$211$	2.52695e38	1.12703	0.563515	−	0.826106i	$-0.309449\pi$
$211$	2.52695e38	1.12703	0.563515	+	0.826106i	$0.309449\pi$
$212$	1.14495e36	0.00472330
$213$	1.77632e38	0.678043
$214$	6.01201e37	0.212418
$215$	3.65135e37	0.119459
$216$	−6.37895e37	−0.193314
$217$	−1.15261e38	−0.323665
$218$	3.64575e38	0.948975
$219$	2.38031e38	0.574521
$220$	3.70015e35	0.000828409 0
$221$	−5.18016e38	−1.07614
$222$	5.06617e38	0.976913
$223$	−2.97099e38	−0.531951	−0.265975	−	0.963980i	$-0.585694\pi$
$223$	−2.97099e38	−0.531951	−0.265975	+	0.963980i	$0.585694\pi$
$224$	2.65315e36	0.00441235
$225$	−2.13083e38	−0.329259
$226$	9.91869e38	1.42451
$227$	−7.81708e38	−1.04380	−0.521900	−	0.853006i	$-0.674777\pi$
$227$	−7.81708e38	−1.04380	−0.521900	+	0.853006i	$0.674777\pi$
$228$	−1.49582e35	−0.000185761 0
$229$	−4.74694e37	−0.0548439	−0.0274220	−	0.999624i	$-0.508730\pi$
$229$	−4.74694e37	−0.0548439	−0.0274220	+	0.999624i	$0.508730\pi$
$230$	−1.19790e38	−0.128798
$231$	1.15713e38	0.115820
$232$	2.45668e38	0.228980
$233$	−1.12103e39	−0.973297	−0.486649	−	0.873598i	$-0.661781\pi$
$233$	−1.12103e39	−0.973297	−0.486649	+	0.873598i	$0.661781\pi$
$234$	−5.10906e38	−0.413313
$235$	−6.94951e37	−0.0524004
$236$	1.38727e37	0.00975245
$237$	4.07201e37	0.0266969
$238$	−3.41750e38	−0.209020
$239$	−2.63507e38	−0.150392	−0.0751962	−	0.997169i	$-0.523958\pi$
$239$	−2.63507e38	−0.150392	−0.0751962	+	0.997169i	$0.523958\pi$
$240$	−1.18723e38	−0.0632482
$241$	6.81432e38	0.338954	0.169477	−	0.985534i	$-0.445792\pi$
$241$	6.81432e38	0.338954	0.169477	+	0.985534i	$0.445792\pi$
$242$	6.82925e38	0.317263
$243$	−1.47809e38	−0.0641500
$244$	−1.56394e37	−0.00634291
$245$	2.74412e38	0.104031
$246$	−2.62264e39	−0.929629
$247$	−1.33174e38	−0.0441490
$248$	4.31335e39	1.33771
$249$	3.36469e39	0.976462
$250$	−8.05384e38	−0.218773
$251$	7.04962e39	1.79287	0.896436	−	0.443173i	$-0.146147\pi$
$251$	7.04962e39	1.79287	0.896436	+	0.443173i	$0.146147\pi$
$252$	3.08774e36	0.000735414 0
$253$	−4.32951e39	−0.965940
$254$	−1.14279e39	−0.238896
$255$	−2.81480e38	−0.0551486
$256$	−1.48258e38	−0.0272308
$257$	2.30926e39	0.397720	0.198860	−	0.980028i	$-0.436276\pi$
$257$	2.30926e39	0.397720	0.198860	+	0.980028i	$0.436276\pi$
$258$	−3.84412e39	−0.620972
$259$	−2.72598e39	−0.413120
$260$	8.79065e36	0.00125015
$261$	5.69246e38	0.0759857
$262$	−6.30194e39	−0.789774
$263$	−1.49820e40	−1.76319	−0.881596	−	0.472006i	$-0.843530\pi$
$263$	−1.49820e40	−1.76319	−0.881596	+	0.472006i	$0.843530\pi$
$264$	−4.33026e39	−0.478684
$265$	5.53902e38	0.0575276
$266$	−8.78589e37	−0.00857509
$267$	3.44069e39	0.315653
$268$	−1.64213e38	−0.0141639
$269$	2.49184e39	0.202119	0.101060	−	0.994880i	$-0.467777\pi$
$269$	2.49184e39	0.202119	0.101060	+	0.994880i	$0.467777\pi$
$270$	−2.77617e38	−0.0211809
$271$	2.46289e40	1.76787	0.883937	−	0.467605i	$-0.154883\pi$
$271$	2.46289e40	1.76787	0.883937	+	0.467605i	$0.154883\pi$
$272$	1.26730e40	0.856038
$273$	2.74905e39	0.174783
$274$	5.36754e39	0.321285
$275$	−1.44648e40	−0.815311
$276$	−1.15531e38	−0.00613337
$277$	2.44039e40	1.22051	0.610256	−	0.792204i	$-0.291066\pi$
$277$	2.44039e40	1.22051	0.610256	+	0.792204i	$0.291066\pi$
$278$	−8.94080e39	−0.421344
$279$	9.99460e39	0.443911
$280$	6.44669e38	0.0269916
$281$	−2.82759e40	−1.11625	−0.558126	−	0.829757i	$-0.688479\pi$
$281$	−2.82759e40	−1.11625	−0.558126	+	0.829757i	$0.688479\pi$
$282$	7.31642e39	0.272388
$283$	−1.11840e40	−0.392753	−0.196376	−	0.980529i	$-0.562917\pi$
$283$	−1.11840e40	−0.392753	−0.196376	+	0.980529i	$0.562917\pi$
$284$	3.21769e38	0.0106609
$285$	−7.23644e37	−0.00226248
$286$	−3.46821e40	−1.02345
$287$	1.41117e40	0.393124
$288$	−2.30062e38	−0.00605159
$289$	−1.02080e40	−0.253587
$290$	1.06917e39	0.0250887
$291$	4.63139e40	1.02678
$292$	4.31179e38	0.00903318
$293$	−6.02718e40	−1.19343	−0.596717	−	0.802452i	$-0.703528\pi$
$293$	−6.02718e40	−1.19343	−0.596717	+	0.802452i	$0.703528\pi$
$294$	−2.88900e40	−0.540776
$295$	6.71133e39	0.118781
$296$	1.02013e41	1.70742
$297$	−1.00338e40	−0.158849
$298$	−6.84289e40	−1.02488
$299$	−1.02859e41	−1.45769
$300$	−3.85987e38	−0.00517693
$301$	2.06842e40	0.262598
$302$	1.34137e41	1.61226
$303$	−7.76354e40	−0.883601
$304$	3.25805e39	0.0351191
$305$	−7.56601e39	−0.0772538
$306$	2.96341e40	0.286674
$307$	1.15345e41	1.05734	0.528670	−	0.848827i	$-0.322691\pi$
$307$	1.15345e41	1.05734	0.528670	+	0.848827i	$0.322691\pi$
$308$	2.09607e38	0.00182104
$309$	−6.27242e39	−0.0516560
$310$	1.87720e40	0.146569
$311$	1.70109e41	1.25945	0.629724	−	0.776819i	$-0.283168\pi$
$311$	1.70109e41	1.25945	0.629724	+	0.776819i	$0.283168\pi$
$312$	−1.02876e41	−0.722378
$313$	−2.77862e40	−0.185075	−0.0925376	−	0.995709i	$-0.529498\pi$
$313$	−2.77862e40	−0.185075	−0.0925376	+	0.995709i	$0.529498\pi$
$314$	2.50583e41	1.58348
$315$	1.49378e39	0.00895702
$316$	7.37620e37	0.000419755 0
$317$	−3.46754e41	−1.87303	−0.936513	−	0.350633i	$-0.885966\pi$
$317$	−3.46754e41	−1.87303	−0.936513	+	0.350633i	$0.885966\pi$
$318$	−5.83146e40	−0.299041
$319$	3.86424e40	0.188156
$320$	−2.41231e40	−0.111547
$321$	2.80508e40	0.123200
$322$	−6.78588e40	−0.283129
$323$	7.72451e39	0.0306217
$324$	−2.67747e38	−0.00100863
$325$	−3.43649e41	−1.23038
$326$	−9.38586e40	−0.319436
$327$	1.70103e41	0.550395
$328$	−5.28096e41	−1.62478
$329$	−3.93678e40	−0.115188
$330$	−1.88456e40	−0.0524481
$331$	3.20078e41	0.847409	0.423705	−	0.905800i	$-0.360729\pi$
$331$	3.20078e41	0.847409	0.423705	+	0.905800i	$0.360729\pi$
$332$	6.09493e39	0.0153529
$333$	2.36377e41	0.566599
$334$	3.95847e41	0.903047
$335$	−7.94426e40	−0.172510
$336$	−6.72543e40	−0.139034
$337$	5.53082e41	1.08867	0.544335	−	0.838868i	$-0.316782\pi$
$337$	5.53082e41	1.08867	0.544335	+	0.838868i	$0.316782\pi$
$338$	−2.92899e41	−0.549025
$339$	4.62786e41	0.826199
$340$	−5.09884e38	−0.000867101 0
$341$	6.78468e41	1.09921
$342$	7.61849e39	0.0117608
$343$	3.20658e41	0.471725
$344$	−7.74055e41	−1.08532
$345$	−5.58914e40	−0.0747017
$346$	3.89671e41	0.496527
$347$	−9.80513e40	−0.119129	−0.0595644	−	0.998224i	$-0.518971\pi$
$347$	−9.80513e40	−0.119129	−0.0595644	+	0.998224i	$0.518971\pi$
$348$	1.03116e39	0.00119472
$349$	−4.83491e41	−0.534280	−0.267140	−	0.963658i	$-0.586079\pi$
$349$	−4.83491e41	−0.534280	−0.267140	+	0.963658i	$0.586079\pi$
$350$	−2.26715e41	−0.238978
$351$	−2.38378e41	−0.239717
$352$	−1.56174e40	−0.0149850
$353$	−2.02531e42	−1.85442	−0.927212	−	0.374537i	$-0.877802\pi$
$353$	−2.02531e42	−1.85442	−0.927212	+	0.374537i	$0.877802\pi$
$354$	−7.06566e41	−0.617446
$355$	1.55665e41	0.129844
$356$	6.23261e39	0.00496301
$357$	−1.59453e41	−0.121229
$358$	7.75493e41	0.562999
$359$	2.04265e42	1.41624	0.708118	−	0.706094i	$-0.249544\pi$
$359$	2.04265e42	1.41624	0.708118	+	0.706094i	$0.249544\pi$
$360$	−5.59010e40	−0.0370193
$361$	−1.57878e42	−0.998744
$362$	6.89709e41	0.416845
$363$	3.18639e41	0.184009
$364$	4.97974e39	0.00274811
$365$	2.08595e41	0.110020
$366$	7.96547e41	0.401581
$367$	−2.12244e42	−1.02293	−0.511465	−	0.859304i	$-0.670897\pi$
$367$	−2.12244e42	−1.02293	−0.511465	+	0.859304i	$0.670897\pi$
$368$	2.51639e42	1.15955
$369$	−1.22367e42	−0.539174
$370$	4.43967e41	0.187078
$371$	3.13776e41	0.126459
$372$	1.81046e40	0.00697960
$373$	−2.66743e42	−0.983779	−0.491889	−	0.870658i	$-0.663694\pi$
$373$	−2.66743e42	−0.983779	−0.491889	+	0.870658i	$0.663694\pi$
$374$	2.01167e42	0.709863
$375$	−3.75775e41	−0.126886
$376$	1.47324e42	0.476073
$377$	9.18049e41	0.283945
$378$	−1.57265e41	−0.0465604
$379$	2.17364e42	0.616085	0.308042	−	0.951373i	$-0.400326\pi$
$379$	2.17364e42	0.616085	0.308042	+	0.951373i	$0.400326\pi$
$380$	−1.31084e38	−3.55729e−5 0
$381$	−5.33201e41	−0.138557
$382$	−1.75731e42	−0.437323
$383$	5.66908e42	1.35124	0.675621	−	0.737249i	$-0.263876\pi$
$383$	5.66908e42	1.35124	0.675621	+	0.737249i	$0.263876\pi$
$384$	2.49376e42	0.569364
$385$	1.01403e41	0.0221794
$386$	−5.28355e42	−1.10722
$387$	−1.79359e42	−0.360157
$388$	8.38949e40	0.0161440
$389$	−5.88684e42	−1.08571	−0.542855	−	0.839826i	$-0.682657\pi$
$389$	−5.88684e42	−1.08571	−0.542855	+	0.839826i	$0.682657\pi$
$390$	−4.47725e41	−0.0791490
$391$	5.96611e42	1.01106
$392$	−5.81731e42	−0.945153
$393$	−2.94035e42	−0.458060
$394$	−5.93600e42	−0.886760
$395$	3.56844e40	0.00511242
$396$	−1.81756e40	−0.00249757
$397$	−3.84265e42	−0.506509	−0.253254	−	0.967400i	$-0.581501\pi$
$397$	−3.84265e42	−0.506509	−0.253254	+	0.967400i	$0.581501\pi$
$398$	−7.06350e42	−0.893201
$399$	−4.09931e40	−0.00497346
$400$	8.40721e42	0.978728
$401$	−6.27125e42	−0.700603	−0.350301	−	0.936637i	$-0.613921\pi$
$401$	−6.27125e42	−0.700603	−0.350301	+	0.936637i	$0.613921\pi$
$402$	8.36369e42	0.896743
$403$	1.61187e43	1.65881
$404$	−1.40632e41	−0.0138928
$405$	−1.29530e41	−0.0122847
$406$	6.05664e41	0.0551508
$407$	1.60461e43	1.40301
$408$	5.96714e42	0.501041
$409$	−9.22665e42	−0.744062	−0.372031	−	0.928220i	$-0.621339\pi$
$409$	−9.22665e42	−0.744062	−0.372031	+	0.928220i	$0.621339\pi$
$410$	−2.29831e42	−0.178023
$411$	2.50438e42	0.186342
$412$	−1.13621e40	−0.000812186 0
$413$	3.80185e42	0.261107
$414$	5.88423e42	0.388315
$415$	2.94860e42	0.186991
$416$	−3.71032e41	−0.0226137
$417$	−4.17159e42	−0.244375
$418$	5.17170e41	0.0291222
$419$	−1.23133e42	−0.0666566	−0.0333283	−	0.999444i	$-0.510611\pi$
$419$	−1.23133e42	−0.0666566	−0.0333283	+	0.999444i	$0.510611\pi$
$420$	2.70590e39	0.000140831 0
$421$	−2.56902e43	−1.28562	−0.642811	−	0.766025i	$-0.722232\pi$
$421$	−2.56902e43	−1.28562	−0.642811	+	0.766025i	$0.722232\pi$
$422$	−2.33137e43	−1.12190
$423$	3.41369e42	0.157982
$424$	−1.17423e43	−0.522655
$425$	1.99327e43	0.853391
$426$	−1.63884e43	−0.674959
$427$	−4.28601e42	−0.169822
$428$	5.08123e40	0.00193708
$429$	−1.61819e43	−0.593588
$430$	−3.36874e42	−0.118915
$431$	9.38763e42	0.318919	0.159460	−	0.987204i	$-0.449025\pi$
$431$	9.38763e42	0.318919	0.159460	+	0.987204i	$0.449025\pi$
$432$	5.83181e42	0.190687
$433$	1.13296e43	0.356587	0.178293	−	0.983977i	$-0.442942\pi$
$433$	1.13296e43	0.356587	0.178293	+	0.983977i	$0.442942\pi$
$434$	1.06340e43	0.322193
$435$	4.98851e41	0.0145512
$436$	3.08132e41	0.00865384
$437$	1.53380e42	0.0414787
$438$	−2.19608e43	−0.571907
$439$	1.68236e43	0.421944	0.210972	−	0.977492i	$-0.432337\pi$
$439$	1.68236e43	0.421944	0.210972	+	0.977492i	$0.432337\pi$
$440$	−3.79476e42	−0.0916674
$441$	−1.34795e43	−0.313644
$442$	4.77923e43	1.07125
$443$	7.64453e43	1.65078	0.825391	−	0.564562i	$-0.190955\pi$
$443$	7.64453e43	1.65078	0.825391	+	0.564562i	$0.190955\pi$
$444$	4.28183e41	0.00890862
$445$	3.01520e42	0.0604472
$446$	2.74105e43	0.529531
$447$	−3.19275e43	−0.594416
$448$	−1.36653e43	−0.245207
$449$	−6.56001e43	−1.13459	−0.567296	−	0.823514i	$-0.692011\pi$
$449$	−6.56001e43	−1.13459	−0.567296	+	0.823514i	$0.692011\pi$
$450$	1.96591e43	0.327761
$451$	−8.30670e43	−1.33510
$452$	8.38308e41	0.0129903
$453$	6.25858e43	0.935094
$454$	7.21206e43	1.03905
$455$	2.40909e42	0.0334707
$456$	1.53406e42	0.0205553
$457$	−7.95912e43	−1.02860	−0.514301	−	0.857609i	$-0.671949\pi$
$457$	−7.95912e43	−1.02860	−0.514301	+	0.857609i	$0.671949\pi$
$458$	4.37954e42	0.0545944
$459$	1.38267e43	0.166268
$460$	−1.01244e41	−0.00117453
$461$	2.88214e42	0.0322589	0.0161295	−	0.999870i	$-0.494866\pi$
$461$	2.88214e42	0.0322589	0.0161295	+	0.999870i	$0.494866\pi$
$462$	−1.06757e43	−0.115293
$463$	−1.45473e43	−0.151599	−0.0757995	−	0.997123i	$-0.524151\pi$
$463$	−1.45473e43	−0.151599	−0.0757995	+	0.997123i	$0.524151\pi$
$464$	−2.24597e43	−0.225869
$465$	8.75862e42	0.0850085
$466$	1.03427e44	0.968870
$467$	−1.72406e44	−1.55892	−0.779462	−	0.626449i	$-0.784507\pi$
$467$	−1.72406e44	−1.55892	−0.779462	+	0.626449i	$0.784507\pi$
$468$	−4.31808e41	−0.00376907
$469$	−4.50028e43	−0.379217
$470$	6.41164e42	0.0521620
$471$	1.16917e44	0.918402
$472$	−1.42274e44	−1.07916
$473$	−1.21755e44	−0.891821
$474$	−3.75684e42	−0.0265754
$475$	5.12440e42	0.0350105
$476$	−2.88840e41	−0.00190609
$477$	−2.72084e43	−0.173440
$478$	2.43112e43	0.149708
$479$	5.40050e43	0.321291	0.160645	−	0.987012i	$-0.448642\pi$
$479$	5.40050e43	0.321291	0.160645	+	0.987012i	$0.448642\pi$
$480$	−2.01612e41	−0.00115887
$481$	3.81216e44	2.11728
$482$	−6.28691e43	−0.337412
$483$	−3.16615e43	−0.164212
$484$	5.77195e41	0.00289317
$485$	4.05865e43	0.196627
$486$	1.36369e43	0.0638582
$487$	3.80065e44	1.72040	0.860202	−	0.509954i	$-0.170338\pi$
$487$	3.80065e44	1.72040	0.860202	+	0.509954i	$0.170338\pi$
$488$	1.60393e44	0.701873
$489$	−4.37925e43	−0.185269
$490$	−2.53174e43	−0.103558
$491$	3.30135e43	0.130571	0.0652856	−	0.997867i	$-0.479204\pi$
$491$	3.30135e43	0.130571	0.0652856	+	0.997867i	$0.479204\pi$
$492$	−2.21660e42	−0.00847743
$493$	−5.32496e43	−0.196944
$494$	1.22867e43	0.0439481
$495$	−8.79296e42	−0.0304193
$496$	−3.94338e44	−1.31953
$497$	8.81815e43	0.285428
$498$	−3.10427e44	−0.972020
$499$	−1.52769e44	−0.462783	−0.231391	−	0.972861i	$-0.574328\pi$
$499$	−1.52769e44	−0.462783	−0.231391	+	0.972861i	$0.574328\pi$
$500$	−6.80695e41	−0.00199502
$501$	1.84694e44	0.523757
$502$	−6.50400e44	−1.78472
$503$	−4.41483e44	−1.17231	−0.586155	−	0.810199i	$-0.699359\pi$
$503$	−4.41483e44	−1.17231	−0.586155	+	0.810199i	$0.699359\pi$
$504$	−3.16669e43	−0.0813771
$505$	−6.80347e43	−0.169209
$506$	3.99442e44	0.961546
$507$	−1.36661e44	−0.318429
$508$	−9.65862e41	−0.00217853
$509$	2.78843e44	0.608859	0.304429	−	0.952535i	$-0.401534\pi$
$509$	2.78843e44	0.608859	0.304429	+	0.952535i	$0.401534\pi$
$510$	2.59694e43	0.0548977
$511$	1.18165e44	0.241850
$512$	5.11307e44	1.01327
$513$	3.55463e42	0.00682116
$514$	−2.13053e44	−0.395910
$515$	−5.49675e42	−0.00989206
$516$	−3.24898e42	−0.00566274
$517$	2.31733e44	0.391196
$518$	2.51499e44	0.411240
$519$	1.81813e44	0.287980
$520$	−9.01542e43	−0.138335
$521$	5.79541e44	0.861513	0.430757	−	0.902468i	$-0.358247\pi$
$521$	5.79541e44	0.861513	0.430757	+	0.902468i	$0.358247\pi$
$522$	−5.25188e43	−0.0756400
$523$	−4.08667e44	−0.570284	−0.285142	−	0.958485i	$-0.592041\pi$
$523$	−4.08667e44	−0.570284	−0.285142	+	0.958485i	$0.592041\pi$
$524$	−5.32627e42	−0.00720207
$525$	−1.05780e44	−0.138604
$526$	1.38224e45	1.75517
$527$	−9.34936e44	−1.15055
$528$	3.95884e44	0.472180
$529$	3.19643e44	0.369527
$530$	−5.11032e43	−0.0572659
$531$	−3.29669e44	−0.358112
$532$	−7.42566e40	−7.81976e−5 0
$533$	−1.97347e45	−2.01480
$534$	−3.17439e44	−0.314217
$535$	2.45819e43	0.0235927
$536$	1.68412e45	1.56730
$537$	3.61829e44	0.326533
$538$	−2.29898e44	−0.201200
$539$	−9.15035e44	−0.776646
$540$	−2.34636e41	−0.000193151 0
$541$	1.75859e45	1.40414	0.702068	−	0.712110i	$-0.252260\pi$
$541$	1.75859e45	1.40414	0.702068	+	0.712110i	$0.252260\pi$
$542$	−2.27227e45	−1.75983
$543$	3.21804e44	0.241765
$544$	2.15210e43	0.0156849
$545$	1.49067e44	0.105400
$546$	−2.53628e44	−0.173988
$547$	−2.66887e45	−1.77638	−0.888191	−	0.459474i	$-0.848038\pi$
$547$	−2.66887e45	−1.77638	−0.888191	+	0.459474i	$0.848038\pi$
$548$	4.53654e42	0.00292985
$549$	3.71652e44	0.232913
$550$	1.33453e45	0.811602
$551$	−1.36897e43	−0.00807965
$552$	1.18485e45	0.678686
$553$	2.02146e43	0.0112383
$554$	−2.25151e45	−1.21496
$555$	2.07146e44	0.108503
$556$	−7.55659e42	−0.00384230
$557$	3.50542e45	1.73033	0.865165	−	0.501488i	$-0.167214\pi$
$557$	3.50542e45	1.73033	0.865165	+	0.501488i	$0.167214\pi$
$558$	−9.22104e44	−0.441892
$559$	−2.89260e45	−1.34584
$560$	−5.89374e43	−0.0266249
$561$	9.38601e44	0.411712
$562$	2.60874e45	1.11117
$563$	−1.57933e43	−0.00653258	−0.00326629	−	0.999995i	$-0.501040\pi$
$563$	−1.57933e43	−0.00653258	−0.00326629	+	0.999995i	$0.501040\pi$
$564$	6.18370e42	0.00248395
$565$	4.05556e44	0.158216
$566$	1.03183e45	0.390966
$567$	−7.33765e43	−0.0270045
$568$	−3.29997e45	−1.17967
$569$	2.64742e45	0.919327	0.459664	−	0.888093i	$-0.347970\pi$
$569$	2.64742e45	0.919327	0.459664	+	0.888093i	$0.347970\pi$
$570$	6.67636e42	0.00225219
$571$	4.25145e45	1.39329	0.696644	−	0.717417i	$-0.254676\pi$
$571$	4.25145e45	1.39329	0.696644	+	0.717417i	$0.254676\pi$
$572$	−2.93126e43	−0.00933297
$573$	−8.19922e44	−0.253642
$574$	−1.30195e45	−0.391336
$575$	3.95789e45	1.15596
$576$	1.18496e45	0.336304
$577$	−2.88842e45	−0.796636	−0.398318	−	0.917247i	$-0.630406\pi$
$577$	−2.88842e45	−0.796636	−0.398318	+	0.917247i	$0.630406\pi$
$578$	9.41794e44	0.252433
$579$	−2.46519e45	−0.642177
$580$	9.03638e41	0.000228788 0
$581$	1.67033e45	0.411050
$582$	−4.27294e45	−1.02211
$583$	−1.84700e45	−0.429473
$584$	−4.42204e45	−0.999564
$585$	−2.08899e44	−0.0459055
$586$	5.56069e45	1.18800
$587$	−8.80280e45	−1.82849	−0.914244	−	0.405165i	$-0.867214\pi$
$587$	−8.80280e45	−1.82849	−0.914244	+	0.405165i	$0.867214\pi$
$588$	−2.44173e43	−0.00493141
$589$	−2.40358e44	−0.0472016
$590$	−6.19189e44	−0.118240
$591$	−2.76961e45	−0.514311
$592$	−9.32628e45	−1.68423
$593$	4.96539e45	0.872070	0.436035	−	0.899930i	$-0.356382\pi$
$593$	4.96539e45	0.872070	0.436035	+	0.899930i	$0.356382\pi$
$594$	9.25719e44	0.158126
$595$	−1.39735e44	−0.0232153
$596$	−5.78347e43	−0.00934599
$597$	−3.29568e45	−0.518046
$598$	9.48976e45	1.45106
$599$	1.01916e46	1.51600	0.758000	−	0.652255i	$-0.226177\pi$
$599$	1.01916e46	1.51600	0.758000	+	0.652255i	$0.226177\pi$
$600$	3.95857e45	0.572852
$601$	−3.45962e45	−0.487079	−0.243539	−	0.969891i	$-0.578309\pi$
$601$	−3.45962e45	−0.487079	−0.243539	+	0.969891i	$0.578309\pi$
$602$	−1.90833e45	−0.261404
$603$	3.90232e45	0.520101
$604$	1.13370e44	0.0147025
$605$	2.79235e44	0.0352375
$606$	7.16266e45	0.879582
$607$	7.98381e45	0.954106	0.477053	−	0.878874i	$-0.341705\pi$
$607$	7.98381e45	0.954106	0.477053	+	0.878874i	$0.341705\pi$
$608$	5.53273e42	0.000643473 0
$609$	2.82590e44	0.0319868
$610$	6.98042e44	0.0769023
$611$	5.50541e45	0.590350
$612$	2.50462e43	0.00261422
$613$	5.30348e45	0.538844	0.269422	−	0.963022i	$-0.413167\pi$
$613$	5.30348e45	0.538844	0.269422	+	0.963022i	$0.413167\pi$
$614$	−1.06417e46	−1.05253
$615$	−1.07235e45	−0.103251
$616$	−2.14966e45	−0.201506
$617$	−1.50495e46	−1.37346	−0.686732	−	0.726910i	$-0.740956\pi$
$617$	−1.50495e46	−1.37346	−0.686732	+	0.726910i	$0.740956\pi$
$618$	5.78696e44	0.0514210
$619$	−1.42194e46	−1.23023	−0.615113	−	0.788439i	$-0.710890\pi$
$619$	−1.42194e46	−1.23023	−0.615113	+	0.788439i	$0.710890\pi$
$620$	1.58657e43	0.00133659
$621$	2.74546e45	0.225218
$622$	−1.56943e46	−1.25372
$623$	1.70806e45	0.132877
$624$	9.40523e45	0.712564
$625$	1.30576e46	0.963478
$626$	2.56357e45	0.184233
$627$	2.41301e44	0.0168906
$628$	2.11788e44	0.0144400
$629$	−2.21117e46	−1.46854
$630$	−1.37817e44	−0.00891627
$631$	1.93787e45	0.122135	0.0610677	−	0.998134i	$-0.480549\pi$
$631$	1.93787e45	0.122135	0.0610677	+	0.998134i	$0.480549\pi$
$632$	−7.56480e44	−0.0464479
$633$	−1.08777e46	−0.650691
$634$	3.19916e46	1.86450
$635$	−4.67263e44	−0.0265335
$636$	−4.92864e43	−0.00272700
$637$	−2.17390e46	−1.17203
$638$	−3.56516e45	−0.187300
$639$	−7.64647e45	−0.391468
$640$	2.18537e45	0.109033
$641$	1.96421e46	0.955058	0.477529	−	0.878616i	$-0.341533\pi$
$641$	1.96421e46	0.955058	0.477529	+	0.878616i	$0.341533\pi$
$642$	−2.58797e45	−0.122640
$643$	2.49133e46	1.15067	0.575335	−	0.817918i	$-0.304872\pi$
$643$	2.49133e46	1.15067	0.575335	+	0.817918i	$0.304872\pi$
$644$	−5.73529e43	−0.00258190
$645$	−1.57178e45	−0.0689696
$646$	−7.12666e44	−0.0304824
$647$	−2.68219e46	−1.11833	−0.559163	−	0.829057i	$-0.688878\pi$
$647$	−2.68219e46	−1.11833	−0.559163	+	0.829057i	$0.688878\pi$
$648$	2.74593e45	0.111610
$649$	−2.23791e46	−0.886757
$650$	3.17051e46	1.22478
$651$	4.96160e45	0.186868
$652$	−7.93274e43	−0.00291298
$653$	3.87771e45	0.138838	0.0694188	−	0.997588i	$-0.477886\pi$
$653$	3.87771e45	0.138838	0.0694188	+	0.997588i	$0.477886\pi$
$654$	−1.56938e46	−0.547891
$655$	−2.57674e45	−0.0877179
$656$	4.82800e46	1.60271
$657$	−1.02465e46	−0.331700
$658$	3.63208e45	0.114664
$659$	4.87066e46	1.49961	0.749806	−	0.661658i	$-0.230147\pi$
$659$	4.87066e46	1.49961	0.749806	+	0.661658i	$0.230147\pi$
$660$	−1.59279e43	−0.000478282 0
$661$	2.72529e46	0.798157	0.399079	−	0.916917i	$-0.369330\pi$
$661$	2.72529e46	0.798157	0.399079	+	0.916917i	$0.369330\pi$
$662$	−2.95304e46	−0.843554
$663$	2.22989e46	0.621312
$664$	−6.25077e46	−1.69887
$665$	−3.59237e43	−0.000952411 0
$666$	−2.18082e46	−0.564021
$667$	−1.05734e46	−0.266771
$668$	3.34562e44	0.00823503
$669$	1.27892e46	0.307122
$670$	7.32940e45	0.171725
$671$	2.52290e46	0.576739
$672$	−1.14210e44	−0.00254747
$673$	−7.15864e46	−1.55805	−0.779026	−	0.626991i	$-0.784286\pi$
$673$	−7.15864e46	−1.55805	−0.779026	+	0.626991i	$0.784286\pi$
$674$	−5.10275e46	−1.08372
$675$	9.17252e45	0.190098
$676$	−2.47553e44	−0.00500665
$677$	1.32670e46	0.261853	0.130927	−	0.991392i	$-0.458205\pi$
$677$	1.32670e46	0.261853	0.130927	+	0.991392i	$0.458205\pi$
$678$	−4.26967e46	−0.822441
$679$	2.29916e46	0.432232
$680$	5.22922e45	0.0959488
$681$	3.36499e46	0.602639
$682$	−6.25957e46	−1.09421
$683$	−2.30832e46	−0.393871	−0.196935	−	0.980416i	$-0.563099\pi$
$683$	−2.30832e46	−0.393871	−0.196935	+	0.980416i	$0.563099\pi$
$684$	6.43900e42	0.000107249 0
$685$	2.19468e45	0.0356842
$686$	−2.95840e46	−0.469579
$687$	2.04340e45	0.0316642
$688$	7.07662e46	1.07057
$689$	−4.38802e46	−0.648114
$690$	5.15656e45	0.0743618
$691$	1.19649e47	1.68469	0.842344	−	0.538940i	$-0.181175\pi$
$691$	1.19649e47	1.68469	0.842344	+	0.538940i	$0.181175\pi$
$692$	3.29343e44	0.00452790
$693$	−4.98105e45	−0.0668687
$694$	9.04624e45	0.118587
$695$	−3.65571e45	−0.0467975
$696$	−1.05752e46	−0.132202
$697$	1.14467e47	1.39746
$698$	4.46071e46	0.531850
$699$	4.82568e46	0.561934
$700$	−1.91615e44	−0.00217927
$701$	−1.03662e47	−1.15152	−0.575762	−	0.817618i	$-0.695294\pi$
$701$	−1.03662e47	−1.15152	−0.575762	+	0.817618i	$0.695294\pi$
$702$	2.19928e46	0.238626
$703$	−5.68459e45	−0.0602472
$704$	8.04391e46	0.832757
$705$	2.99154e45	0.0302534
$706$	1.86856e47	1.84599
$707$	−3.85404e46	−0.371960
$708$	−5.97176e44	−0.00563058
$709$	−1.80394e47	−1.66172	−0.830862	−	0.556479i	$-0.812152\pi$
$709$	−1.80394e47	−1.66172	−0.830862	+	0.556479i	$0.812152\pi$
$710$	−1.43617e46	−0.129254
$711$	−1.75287e45	−0.0154135
$712$	−6.39197e46	−0.549181
$713$	−1.85643e47	−1.55848
$714$	1.47112e46	0.120678
$715$	−1.41808e46	−0.113671
$716$	6.55431e44	0.00513408
$717$	1.13431e46	0.0868291
$718$	−1.88456e47	−1.40979
$719$	−3.54435e46	−0.259125	−0.129563	−	0.991571i	$-0.541357\pi$
$719$	−3.54435e46	−0.259125	−0.129563	+	0.991571i	$0.541357\pi$
$720$	5.11062e45	0.0365164
$721$	−3.11381e45	−0.0217450
$722$	1.45659e47	0.994200
$723$	−2.93334e46	−0.195695
$724$	5.82928e44	0.00380127
$725$	−3.53255e46	−0.225170
$726$	−2.93977e46	−0.183172
$727$	−7.03180e46	−0.428301	−0.214150	−	0.976801i	$-0.568698\pi$
$727$	−7.03180e46	−0.428301	−0.214150	+	0.976801i	$0.568698\pi$
$728$	−5.10707e46	−0.304091
$729$	6.36269e45	0.0370370
$730$	−1.92450e46	−0.109520
$731$	1.67780e47	0.933475
$732$	6.73226e44	0.00366208
$733$	8.23511e46	0.437980	0.218990	−	0.975727i	$-0.429724\pi$
$733$	8.23511e46	0.437980	0.218990	+	0.975727i	$0.429724\pi$
$734$	1.95817e47	1.01828
$735$	−1.18126e46	−0.0600624
$736$	4.27327e45	0.0212459
$737$	2.64903e47	1.28788
$738$	1.12896e47	0.536721
$739$	−6.83604e46	−0.317813	−0.158906	−	0.987294i	$-0.550797\pi$
$739$	−6.83604e46	−0.317813	−0.158906	+	0.987294i	$0.550797\pi$
$740$	3.75232e44	0.00170599
$741$	5.73271e45	0.0254894
$742$	−2.89490e46	−0.125884
$743$	−1.46985e47	−0.625110	−0.312555	−	0.949900i	$-0.601185\pi$
$743$	−1.46985e47	−0.625110	−0.312555	+	0.949900i	$0.601185\pi$
$744$	−1.85675e47	−0.772327
$745$	−2.79792e46	−0.113830
$746$	2.46098e47	0.979303
$747$	−1.44839e47	−0.563761
$748$	1.70022e45	0.00647335
$749$	1.39252e46	0.0518623
$750$	3.46691e46	0.126308
$751$	2.34140e47	0.834481	0.417241	−	0.908796i	$-0.362997\pi$
$751$	2.34140e47	0.834481	0.417241	+	0.908796i	$0.362997\pi$
$752$	−1.34687e47	−0.469605
$753$	−3.03463e47	−1.03512
$754$	−8.46995e46	−0.282653
$755$	5.48461e46	0.179069
$756$	−1.32917e44	−0.000424592 0
$757$	3.94734e47	1.23374	0.616868	−	0.787066i	$-0.288401\pi$
$757$	3.94734e47	1.23374	0.616868	+	0.787066i	$0.288401\pi$
$758$	−2.00540e47	−0.613282
$759$	1.86371e47	0.557686
$760$	1.34436e45	0.00393631
$761$	2.33575e47	0.669235	0.334618	−	0.942354i	$-0.391393\pi$
$761$	2.33575e47	0.669235	0.334618	+	0.942354i	$0.391393\pi$
$762$	4.91933e46	0.137927
$763$	8.44440e46	0.231694
$764$	−1.48524e45	−0.00398801
$765$	1.21168e46	0.0318401
$766$	−5.23031e47	−1.34509
$767$	−5.31672e47	−1.33820
$768$	6.38203e45	0.0157217
$769$	9.99578e46	0.241008	0.120504	−	0.992713i	$-0.461549\pi$
$769$	9.99578e46	0.241008	0.120504	+	0.992713i	$0.461549\pi$
$770$	−9.35549e45	−0.0220785
$771$	−9.94063e46	−0.229624
$772$	−4.46555e45	−0.0100969
$773$	4.81242e47	1.06513	0.532564	−	0.846390i	$-0.321229\pi$
$773$	4.81242e47	1.06513	0.532564	+	0.846390i	$0.321229\pi$
$774$	1.65477e47	0.358518
$775$	−6.20231e47	−1.31545
$776$	−8.60401e47	−1.78641
$777$	1.17344e47	0.238515
$778$	5.43122e47	1.08077
$779$	2.94278e46	0.0573311
$780$	−3.78408e44	−0.000721772 0
$781$	−5.19069e47	−0.969355
$782$	−5.50435e47	−1.00646
$783$	−2.45042e46	−0.0438703
$784$	5.31834e47	0.932312
$785$	1.02459e47	0.175873
$786$	2.71278e47	0.455976
$787$	−4.46790e46	−0.0735394	−0.0367697	−	0.999324i	$-0.511707\pi$
$787$	−4.46790e46	−0.0735394	−0.0367697	+	0.999324i	$0.511707\pi$
$788$	−5.01699e45	−0.00808650
$789$	6.44925e47	1.01798
$790$	−3.29226e45	−0.00508917
$791$	2.29740e47	0.347796
$792$	1.86403e47	0.276368
$793$	5.99380e47	0.870352
$794$	3.54524e47	0.504205
$795$	−2.38437e46	−0.0332136
$796$	−5.96993e45	−0.00814524
$797$	1.03387e48	1.38167	0.690836	−	0.723011i	$-0.257242\pi$
$797$	1.03387e48	1.38167	0.690836	+	0.723011i	$0.257242\pi$
$798$	3.78204e45	0.00495083
$799$	−3.19331e47	−0.409467
$800$	1.42769e46	0.0179329
$801$	−1.48111e47	−0.182242
$802$	5.78587e47	0.697415
$803$	−6.95565e47	−0.821356
$804$	7.06883e45	0.00817754
$805$	−2.77461e46	−0.0314463
$806$	−1.48712e48	−1.65127
$807$	−1.07265e47	−0.116693
$808$	1.44228e48	1.53731
$809$	1.35583e47	0.141597	0.0707983	−	0.997491i	$-0.477445\pi$
$809$	1.35583e47	0.141597	0.0707983	+	0.997491i	$0.477445\pi$
$810$	1.19505e46	0.0122288
$811$	−6.99700e47	−0.701564	−0.350782	−	0.936457i	$-0.614084\pi$
$811$	−6.99700e47	−0.701564	−0.350782	+	0.936457i	$0.614084\pi$
$812$	5.11895e44	0.000502929 0
$813$	−1.06019e48	−1.02068
$814$	−1.48042e48	−1.39663
$815$	−3.83769e46	−0.0354788
$816$	−5.45532e47	−0.494234
$817$	4.31337e46	0.0382959
$818$	8.51253e47	0.740678
$819$	−1.18338e47	−0.100911
$820$	−1.94249e45	−0.00162342
$821$	−7.84721e47	−0.642766	−0.321383	−	0.946949i	$-0.604148\pi$
$821$	−7.84721e47	−0.642766	−0.321383	+	0.946949i	$0.604148\pi$
$822$	−2.31055e47	−0.185494
$823$	−7.53505e47	−0.592910	−0.296455	−	0.955047i	$-0.595805\pi$
$823$	−7.53505e47	−0.592910	−0.296455	+	0.955047i	$0.595805\pi$
$824$	1.16526e47	0.0898722
$825$	6.22663e47	0.470720
$826$	−3.50759e47	−0.259919
$827$	9.63068e47	0.699546	0.349773	−	0.936835i	$-0.386259\pi$
$827$	9.63068e47	0.699546	0.349773	+	0.936835i	$0.386259\pi$
$828$	4.97323e45	0.00354110
$829$	−4.69747e47	−0.327879	−0.163940	−	0.986470i	$-0.552420\pi$
$829$	−4.69747e47	−0.327879	−0.163940	+	0.986470i	$0.552420\pi$
$830$	−2.72038e47	−0.186141
$831$	−1.05051e48	−0.704663
$832$	1.91104e48	1.25671
$833$	1.26093e48	0.812919
$834$	3.84872e47	0.243263
$835$	1.61854e47	0.100299
$836$	4.37102e44	0.000265570 0
$837$	−4.30235e47	−0.256292
$838$	1.13603e47	0.0663534
$839$	2.58972e48	1.48314	0.741568	−	0.670878i	$-0.234082\pi$
$839$	2.58972e48	1.48314	0.741568	+	0.670878i	$0.234082\pi$
$840$	−2.77509e46	−0.0155836
$841$	−1.72170e48	−0.948036
$842$	2.37019e48	1.27977
$843$	1.21718e48	0.644468
$844$	−1.97043e46	−0.0102308
$845$	−1.19761e47	−0.0609787
$846$	−3.14948e47	−0.157263
$847$	1.58181e47	0.0774603
$848$	1.07351e48	0.515554
$849$	4.81433e47	0.226756
$850$	−1.83899e48	−0.849509
$851$	−4.39056e48	−1.98922
$852$	−1.38511e46	−0.00615505
$853$	2.34006e48	1.01993	0.509963	−	0.860196i	$-0.329659\pi$
$853$	2.34006e48	1.01993	0.509963	+	0.860196i	$0.329659\pi$
$854$	3.95429e47	0.169049
$855$	3.11505e45	0.00130624
$856$	−5.21115e47	−0.214347
$857$	8.42927e47	0.340100	0.170050	−	0.985435i	$-0.445607\pi$
$857$	8.42927e47	0.340100	0.170050	+	0.985435i	$0.445607\pi$
$858$	1.49295e48	0.590888
$859$	−2.44961e48	−0.951064	−0.475532	−	0.879698i	$-0.657744\pi$
$859$	−2.44961e48	−0.951064	−0.475532	+	0.879698i	$0.657744\pi$
$860$	−2.84719e45	−0.00108441
$861$	−6.07464e47	−0.226970
$862$	−8.66105e47	−0.317469
$863$	−3.37661e48	−1.21423	−0.607117	−	0.794613i	$-0.707674\pi$
$863$	−3.37661e48	−1.21423	−0.607117	+	0.794613i	$0.707674\pi$
$864$	9.90343e45	0.00349389
$865$	1.59329e47	0.0551478
$866$	−1.04527e48	−0.354965
$867$	4.39421e47	0.146408
$868$	8.98765e45	0.00293813
$869$	−1.18991e47	−0.0381669
$870$	−4.60241e46	−0.0144850
$871$	6.29345e48	1.94352
$872$	−3.16010e48	−0.957589
$873$	−1.99366e48	−0.592812
$874$	−1.41509e47	−0.0412900
$875$	−1.86546e47	−0.0534136
$876$	−1.85608e46	−0.00521531
$877$	2.11474e48	0.583128	0.291564	−	0.956551i	$-0.405824\pi$
$877$	2.11474e48	0.583128	0.291564	+	0.956551i	$0.405824\pi$
$878$	−1.55215e48	−0.420024
$879$	2.59450e48	0.689029
$880$	3.46927e47	0.0904220
$881$	−4.14561e48	−1.06044	−0.530220	−	0.847860i	$-0.677891\pi$
$881$	−4.14561e48	−1.06044	−0.530220	+	0.847860i	$0.677891\pi$
$882$	1.24362e48	0.312217
$883$	5.74012e48	1.41439	0.707195	−	0.707018i	$-0.249960\pi$
$883$	5.74012e48	1.41439	0.707195	+	0.707018i	$0.249960\pi$
$884$	4.03931e46	0.00976888
$885$	−2.88901e47	−0.0685780
$886$	−7.05287e48	−1.64327
$887$	1.36174e48	0.311426	0.155713	−	0.987802i	$-0.450232\pi$
$887$	1.36174e48	0.311426	0.155713	+	0.987802i	$0.450232\pi$
$888$	−4.39131e48	−0.985781
$889$	−2.64696e47	−0.0583269
$890$	−2.78183e47	−0.0601722
$891$	4.31921e47	0.0917112
$892$	2.31668e46	0.00482887
$893$	−8.20953e46	−0.0167984
$894$	2.94564e48	0.591712
$895$	3.17084e47	0.0625307
$896$	1.23798e48	0.239679
$897$	4.42773e48	0.841599
$898$	6.05228e48	1.12943
$899$	1.65693e48	0.303578
$900$	1.66155e46	0.00298890
$901$	2.54519e48	0.449532
$902$	7.66378e48	1.32903
$903$	−8.90388e47	−0.151611
$904$	−8.59743e48	−1.43744
$905$	2.82008e47	0.0462978
$906$	−5.77418e48	−0.930840
$907$	4.20513e48	0.665670	0.332835	−	0.942985i	$-0.391995\pi$
$907$	4.20513e48	0.665670	0.332835	+	0.942985i	$0.391995\pi$
$908$	6.09549e46	0.00947528
$909$	3.34195e48	0.510147
$910$	−2.22263e47	−0.0333185
$911$	2.88442e48	0.424625	0.212312	−	0.977202i	$-0.431901\pi$
$911$	2.88442e48	0.424625	0.212312	+	0.977202i	$0.431901\pi$
$912$	−1.40248e47	−0.0202760
$913$	−9.83216e48	−1.39599
$914$	7.34311e48	1.02392
$915$	3.25692e47	0.0446025
$916$	3.70150e45	0.000497855 0
$917$	−1.45967e48	−0.192824
$918$	−1.27565e48	−0.165511
$919$	−1.09479e49	−1.39516	−0.697580	−	0.716507i	$-0.745740\pi$
$919$	−1.09479e49	−1.39516	−0.697580	+	0.716507i	$0.745740\pi$
$920$	1.03833e48	0.129968
$921$	−4.96522e48	−0.610456
$922$	−2.65907e47	−0.0321122
$923$	−1.23318e49	−1.46285
$924$	−9.02288e45	−0.00105138
$925$	−1.46688e49	−1.67902
$926$	1.34214e48	0.150909
$927$	2.70007e47	0.0298236
$928$	−3.81404e46	−0.00413851
$929$	5.11995e48	0.545766	0.272883	−	0.962047i	$-0.412023\pi$
$929$	5.11995e48	0.545766	0.272883	+	0.962047i	$0.412023\pi$
$930$	−8.08073e47	−0.0846217
$931$	3.24166e47	0.0333501
$932$	8.74143e46	0.00883527
$933$	−7.32263e48	−0.727143
$934$	1.59063e49	1.55183
$935$	8.22530e47	0.0788425
$936$	4.42849e48	0.417065
$937$	4.80086e48	0.444238	0.222119	−	0.975020i	$-0.428703\pi$
$937$	4.80086e48	0.444238	0.222119	+	0.975020i	$0.428703\pi$
$938$	4.15197e48	0.377492
$939$	1.19611e48	0.106853
$940$	5.41899e45	0.000475674 0
$941$	−2.24044e48	−0.193243	−0.0966217	−	0.995321i	$-0.530804\pi$
$941$	−2.24044e48	−0.193243	−0.0966217	+	0.995321i	$0.530804\pi$
$942$	−1.07868e49	−0.914224
$943$	2.27289e49	1.89293
$944$	1.30071e49	1.06449
$945$	−6.43025e46	−0.00517134
$946$	1.12331e49	0.887764
$947$	3.90014e48	0.302905	0.151452	−	0.988465i	$-0.451605\pi$
$947$	3.90014e48	0.302905	0.151452	+	0.988465i	$0.451605\pi$
$948$	−3.17521e45	−0.000242346 0
$949$	−1.65249e49	−1.23950
$950$	−4.72778e47	−0.0348512
$951$	1.49266e49	1.08139
$952$	2.96226e48	0.210918
$953$	−1.21941e49	−0.853330	−0.426665	−	0.904410i	$-0.640312\pi$
$953$	−1.21941e49	−0.853330	−0.426665	+	0.904410i	$0.640312\pi$
$954$	2.51025e48	0.172651
$955$	−7.18527e47	−0.0485722
$956$	2.05473e46	0.00136521
$957$	−1.66343e48	−0.108632
$958$	−4.98252e48	−0.319829
$959$	1.24325e48	0.0784422
$960$	1.03842e48	0.0644018
$961$	1.26883e49	0.773513
$962$	−3.51711e49	−2.10764
$963$	−1.20749e48	−0.0711297
$964$	−5.31357e46	−0.00307692
$965$	−2.16034e48	−0.122976
$966$	2.92110e48	0.163465
$967$	−6.90419e48	−0.379818	−0.189909	−	0.981802i	$-0.560819\pi$
$967$	−6.90419e48	−0.379818	−0.189909	+	0.981802i	$0.560819\pi$
$968$	−5.91954e48	−0.320143
$969$	−3.32515e47	−0.0176795
$970$	−3.74453e48	−0.195733
$971$	2.14347e49	1.10154	0.550770	−	0.834657i	$-0.314334\pi$
$971$	2.14347e49	1.10154	0.550770	+	0.834657i	$0.314334\pi$
$972$	1.15256e46	0.000582333 0
$973$	−2.07090e48	−0.102872
$974$	−3.50649e49	−1.71258
$975$	1.47929e49	0.710360
$976$	−1.46636e49	−0.692337
$977$	1.44315e49	0.669965	0.334983	−	0.942224i	$-0.391270\pi$
$977$	1.44315e49	0.669965	0.334983	+	0.942224i	$0.391270\pi$
$978$	4.04030e48	0.184426
$979$	−1.00543e49	−0.451269
$980$	−2.13977e46	−0.000944360 0
$981$	−7.32238e48	−0.317770
$982$	−3.04584e48	−0.129977
$983$	−2.69042e49	−1.12898	−0.564490	−	0.825440i	$-0.690927\pi$
$983$	−2.69042e49	−1.12898	−0.564490	+	0.825440i	$0.690927\pi$
$984$	2.27328e49	0.938068
$985$	−2.42711e48	−0.0984899
$986$	4.91283e48	0.196048
$987$	1.69465e48	0.0665040
$988$	1.03845e46	0.000400770 0
$989$	3.33148e49	1.26444
$990$	8.11241e47	0.0302809
$991$	2.49558e49	0.916129	0.458065	−	0.888919i	$-0.348543\pi$
$991$	2.49558e49	0.916129	0.458065	+	0.888919i	$0.348543\pi$
$992$	−6.69654e47	−0.0241773
$993$	−1.37783e49	−0.489252
$994$	−8.13565e48	−0.284130
$995$	−2.88812e48	−0.0992053
$996$	−2.62367e47	−0.00886400
$997$	−4.18470e48	−0.139057	−0.0695287	−	0.997580i	$-0.522150\pi$
$997$	−4.18470e48	−0.139057	−0.0695287	+	0.997580i	$0.522150\pi$
$998$	1.40945e49	0.460677
$999$	−1.01753e49	−0.327126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.34.a.b.1.1	✓	3
3.2	odd	2		9.34.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.34.a.b.1.1	✓	3	1.1	even	1	trivial
9.34.a.c.1.3		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:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-92260.3 q^{2} -4.30467e7 q^{3} -7.79766e7 q^{4} -3.77234e10 q^{5} +3.97150e12 q^{6} -2.13696e13 q^{7} +7.99704e14 q^{8} +1.85302e15 q^{9} +O(q^{10})\)	\(q-92260.3 q^{2} -4.30467e7 q^{3} -7.79766e7 q^{4} -3.77234e10 q^{5} +3.97150e12 q^{6} -2.13696e13 q^{7} +7.99704e14 q^{8} +1.85302e15 q^{9} +3.48037e15 q^{10} +1.25789e17 q^{11} +3.35664e15 q^{12} +2.98845e18 q^{13} +1.97157e18 q^{14} +1.62387e18 q^{15} -7.31111e19 q^{16} -1.73339e20 q^{17} -1.70960e20 q^{18} -4.45630e19 q^{19} +2.94154e18 q^{20} +9.19892e20 q^{21} -1.16054e22 q^{22} -3.44187e22 q^{23} -3.44246e22 q^{24} -1.14992e23 q^{25} -2.75715e23 q^{26} -7.97664e22 q^{27} +1.66633e21 q^{28} +3.07199e23 q^{29} -1.49818e23 q^{30} +5.39368e24 q^{31} -1.24155e23 q^{32} -5.41482e24 q^{33} +1.59923e25 q^{34} +8.06134e23 q^{35} -1.44492e23 q^{36} +1.27563e26 q^{37} +4.11139e24 q^{38} -1.28643e26 q^{39} -3.01675e25 q^{40} -6.60365e26 q^{41} -8.48695e25 q^{42} -9.67926e26 q^{43} -9.80863e24 q^{44} -6.99022e25 q^{45} +3.17548e27 q^{46} +1.84223e27 q^{47} +3.14719e27 q^{48} -7.27433e27 q^{49} +1.06092e28 q^{50} +7.46168e27 q^{51} -2.33029e26 q^{52} -1.46833e28 q^{53} +7.35927e27 q^{54} -4.74520e27 q^{55} -1.70894e28 q^{56} +1.91829e27 q^{57} -2.83423e28 q^{58} -1.77909e29 q^{59} -1.26624e26 q^{60} +2.00566e29 q^{61} -4.97622e29 q^{62} -3.95983e28 q^{63} +6.39474e29 q^{64} -1.12734e29 q^{65} +4.99573e29 q^{66} +2.10593e30 q^{67} +1.35164e28 q^{68} +1.48161e30 q^{69} -7.43742e28 q^{70} -4.12649e30 q^{71} +1.48187e30 q^{72} -5.52960e30 q^{73} -1.17690e31 q^{74} +4.95004e30 q^{75} +3.47487e27 q^{76} -2.68807e30 q^{77} +1.18686e31 q^{78} -9.45950e29 q^{79} +2.75800e30 q^{80} +3.43368e30 q^{81} +6.09254e31 q^{82} -7.81636e31 q^{83} -7.17300e28 q^{84} +6.53894e30 q^{85} +8.93012e31 q^{86} -1.32239e31 q^{87} +1.00594e32 q^{88} -7.99293e31 q^{89} +6.44920e30 q^{90} -6.38620e31 q^{91} +2.68385e30 q^{92} -2.32180e32 q^{93} -1.69965e32 q^{94} +1.68107e30 q^{95} +5.34448e30 q^{96} -1.07590e33 q^{97} +6.71132e32 q^{98} +2.33090e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 136620 q^{2} - 129140163 q^{3} + 14589555600 q^{4} - 260488036134 q^{5} - 5881043023020 q^{6} + 10760698892832 q^{7} + 18\!\cdots\!76 q^{8}+ \cdots + 55\!\cdots\!23 q^{9}+O(q^{10}) \) 3 * q + 136620 * q^2 - 129140163 * q^3 + 14589555600 * q^4 - 260488036134 * q^5 - 5881043023020 * q^6 + 10760698892832 * q^7 + 1806352049808576 * q^8 + 5559060566555523 * q^9	\( 3 q + 136620 q^{2} - 129140163 q^{3} + 14589555600 q^{4} - 260488036134 q^{5} - 5881043023020 q^{6} + 10760698892832 q^{7} + 18\!\cdots\!76 q^{8}+ \cdots - 64\!\cdots\!96 q^{99}+O(q^{100}) \) 3 * q + 136620 * q^2 - 129140163 * q^3 + 14589555600 * q^4 - 260488036134 * q^5 - 5881043023020 * q^6 + 10760698892832 * q^7 + 1806352049808576 * q^8 + 5559060566555523 * q^9 - 56442714195076056 * q^10 - 345482369200786356 * q^11 - 628032529427187600 * q^12 + 730047702981793722 * q^13 - 9466648738386811776 * q^14 + 11213155815298216614 * q^15 + 57097856385199812864 * q^16 - 241702143352594866234 * q^17 + 253159618200938517420 * q^18 - 302063201058090006732 * q^19 - 9511079529660801113376 * q^20 - 463212803004748003872 * q^21 - 62637844423105026039888 * q^22 - 62177828305895870808024 * q^23 - 77757532715887874479296 * q^24 - 113362765411196109398019 * q^25 - 274958228188114840257624 * q^26 - 239299329230617529590083 * q^27 - 3222271636207020516112896 * q^28 - 1259920260916004318716494 * q^29 + 2429673770438178556412376 * q^30 + 11135125624283076100487352 * q^31 + 13995317245307766511168512 * q^32 + 14871883157405243247338676 * q^33 + 2693352737405664780350040 * q^34 + 89265959101072598849081280 * q^35 + 27034741073176434431859600 * q^36 - 47470694780535466043761518 * q^37 + 15348541159835774116798032 * q^38 - 31426159786948142430485562 * q^39 - 1000865216529547256276226432 * q^40 - 510043583286993345182539218 * q^41 + 407508187046339076600986496 * q^42 - 241949512345382263987418676 * q^43 - 2802266702859033871786911168 * q^44 - 482689589910669862380422694 * q^45 + 1894559041786498078265576352 * q^46 + 1921077201868476933761742528 * q^47 - 2457875493511764873608818944 * q^48 + 18186134741403006655682598123 * q^49 + 18465455874376386239717829204 * q^50 + 10404484730001155832807318714 * q^51 + 42532175939901401243990183136 * q^52 + 8039908215852241665398717466 * q^53 - 10897691453162322297532379820 * q^54 + 30088015095001838816140788456 * q^55 - 377844291996686623593396172800 * q^56 + 13002830340314505312680525772 * q^57 - 308504983868142890433522752376 * q^58 - 247660094389221812820609454068 * q^59 + 409420786922119730163986040096 * q^60 + 37736108183042272792017479418 * q^61 + 302392999582755025784699411424 * q^62 + 19939792294573348997984903712 * q^63 + 1193868512245765263646771286016 * q^64 - 1439546196636635959290593941812 * q^65 + 2696353812922808009636793607248 * q^66 + 1000778046108011502274286558196 * q^67 - 1741077115261984900728913356000 * q^68 + 2676551627469802205725053689304 * q^69 + 11179426654384923501066012952320 * q^70 - 13161136343851691507425619260584 * q^71 + 3347206816469197599993275188416 * q^72 - 2102232382664339647381735290594 * q^73 - 36192879788033917171536014449656 * q^74 + 4879895334444209197542001845699 * q^75 + 7431716486141494636076085792192 * q^76 - 18011309120068715154396356501376 * q^77 + 11836050135468115044529508450904 * q^78 + 2220668017769877386018864526600 * q^79 - 59638374077820540688333624951296 * q^80 + 10301051460877537453973547267843 * q^81 + 128405842979035073898453989818104 * q^82 - 36455583004258570245309903891660 * q^83 + 138708228110017110398387838614016 * q^84 + 47494471216195568447991651883572 * q^85 + 249696091044323323817104420734384 * q^86 + 54235435953898442342583995316174 * q^87 - 64292534102628440519093096373504 * q^88 - 301000215018751428734710041573522 * q^89 - 104589488917070320066066310619096 * q^90 - 793065761375571553941370782547008 * q^91 + 233024630810116195988192414904192 * q^92 - 479330646048464401919447005572792 * q^93 + 134856701076698355695283792200448 * q^94 - 217499295515701461216485225187816 * q^95 - 602452516765251984139414320049152 * q^96 - 876561469773784134737853121199994 * q^97 + 3099174773064755865455550107098188 * q^98 - 640185805021422590005321978281396 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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