LMFDB - Embedded newform 3.42.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,42,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, 42, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 42 $
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:	$31.9415011369$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 196497525461x^{2} + 10360343667016365x + 6095744045744274504000 $ x^4 - x^3 - 196497525461x^2 + 10360343667016365x + 6095744045744274504000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{10}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-433547.$ 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)

$f(q)$	$=$	$q+2.58383e6 q^{2} +3.48678e9 q^{3} +4.47715e12 q^{4} +2.55548e14 q^{5} +9.00926e15 q^{6} +1.98945e17 q^{7} +5.88630e18 q^{8} +1.21577e19 q^{9} +O(q^{10})$	\(q+2.58383e6 q^{2} +3.48678e9 q^{3} +4.47715e12 q^{4} +2.55548e14 q^{5} +9.00926e15 q^{6} +1.98945e17 q^{7} +5.88630e18 q^{8} +1.21577e19 q^{9} +6.60294e20 q^{10} -2.76444e21 q^{11} +1.56109e22 q^{12} -8.56075e22 q^{13} +5.14041e23 q^{14} +8.91042e23 q^{15} +5.36384e24 q^{16} -3.38977e24 q^{17} +3.14133e25 q^{18} +2.99407e26 q^{19} +1.14413e27 q^{20} +6.93680e26 q^{21} -7.14285e27 q^{22} -1.40889e28 q^{23} +2.05243e28 q^{24} +1.98303e28 q^{25} -2.21195e29 q^{26} +4.23912e28 q^{27} +8.90709e29 q^{28} -4.94074e28 q^{29} +2.30230e30 q^{30} +5.76050e30 q^{31} +9.15126e29 q^{32} -9.63902e30 q^{33} -8.75860e30 q^{34} +5.08402e31 q^{35} +5.44317e31 q^{36} -1.16818e32 q^{37} +7.73616e32 q^{38} -2.98495e32 q^{39} +1.50424e33 q^{40} +1.48580e32 q^{41} +1.79235e33 q^{42} +2.64197e32 q^{43} -1.23768e34 q^{44} +3.10687e33 q^{45} -3.64032e34 q^{46} +2.16318e34 q^{47} +1.87025e34 q^{48} -4.98839e33 q^{49} +5.12381e34 q^{50} -1.18194e34 q^{51} -3.83278e35 q^{52} +5.57170e34 q^{53} +1.09532e35 q^{54} -7.06449e35 q^{55} +1.17105e36 q^{56} +1.04397e36 q^{57} -1.27660e35 q^{58} -2.05748e36 q^{59} +3.98933e36 q^{60} +1.01936e36 q^{61} +1.48842e37 q^{62} +2.41871e36 q^{63} -9.43067e36 q^{64} -2.18769e37 q^{65} -2.49056e37 q^{66} -2.42878e37 q^{67} -1.51765e37 q^{68} -4.91248e37 q^{69} +1.31362e38 q^{70} +5.77043e36 q^{71} +7.15637e37 q^{72} -1.22382e38 q^{73} -3.01839e38 q^{74} +6.91439e37 q^{75} +1.34049e39 q^{76} -5.49973e38 q^{77} -7.71260e38 q^{78} -7.70707e38 q^{79} +1.37072e39 q^{80} +1.47809e38 q^{81} +3.83906e38 q^{82} +1.70727e39 q^{83} +3.10571e39 q^{84} -8.66251e38 q^{85} +6.82641e38 q^{86} -1.72273e38 q^{87} -1.62723e40 q^{88} -4.08353e39 q^{89} +8.02763e39 q^{90} -1.70312e40 q^{91} -6.30780e40 q^{92} +2.00856e40 q^{93} +5.58928e40 q^{94} +7.65129e40 q^{95} +3.19085e39 q^{96} +1.60920e40 q^{97} -1.28891e40 q^{98} -3.36092e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 48\!\cdots\!04 q^{9}+O(q^{10}) $ 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9	$ 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 88\!\cdots\!56 q^{99}+O(q^{100}) $ 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9 + 725751018728422700940 * q^10 + 724810647231440683056 * q^11 + 18664574152458657849732 * q^12 - 8843977274373065537608 * q^13 + 493449664223337937919568 * q^14 + 413312836237035157808280 * q^15 - 5962194966280197033033200 * q^16 - 38231582029295844707285688 * q^17 - 848872517682272882743422 * q^18 + 261842746845948075837831248 * q^19 + 785441926018305471679038360 * q^20 + 523911200567235135430405536 * q^21 - 6322149663566345845522943976 * q^22 - 15395573913207335266380880032 * q^23 + 21895702846052864805196365384 * q^24 + 117350921958371528604086683900 * q^25 - 62942545095927728709970694052 * q^26 + 169564633100864814057177732804 * q^27 + 684437536459146482218511575712 * q^28 - 1036098964520685524199931325064 * q^29 + 2530537331112123128971880036940 * q^30 + 9280613209905247622577480610304 * q^31 + 19645397922916950127447685511456 * q^32 + 2527258458445301210436445809456 * q^33 + 92420157643501864091330064020004 * q^34 + 207436667553525639419383641992640 * q^35 + 65079346006100643987841739630532 * q^36 + 200754880510048713109452091192856 * q^37 + 1146938682238729575315585266559528 * q^38 - 30837042003082501971082253252808 * q^39 + 2565083222429486590317315499815600 * q^40 + 2357905268481965433001096926030504 * q^41 + 1720552591892622502089456095058768 * q^42 + 3943358618915609696106480688157360 * q^43 - 18494278585991583572852191821764304 * q^44 + 1441132750124361726734484052640280 * q^45 - 44252120640849956767942988241684816 * q^46 - 8890000412230234893665157147040320 * q^47 - 20788888404146512009986643475113200 * q^48 - 33104900387055220681685954563991580 * q^49 - 216323679312314207800001999371642050 * q^50 - 133305283845300676339482147968952888 * q^51 - 596234086188669794371774262733483208 * q^52 + 95704753827317216756019399314791128 * q^53 - 2959835453092145761775065914960222 * q^54 + 1291057043675253444545805475556816160 * q^55 + 1940580325939766339139469085046208320 * q^56 + 912989205217443700887315001196762448 * q^57 + 3859053206955865617315425524661917116 * q^58 - 1809289331104083090977131835906657808 * q^59 + 2738666655532023559103418232328622360 * q^60 + 5381027332088000515346282395501157240 * q^61 + 14109494547714507002913033009898657152 * q^62 + 1826765401647017821917860444028843936 * q^63 - 389844533130084697385386794140537792 * q^64 - 9754648834359651370261564655441346480 * q^65 - 22043972827710532722740556743113718376 * q^66 - 73273159367285254897696664016673247728 * q^67 - 89019363361032581039655795923994746424 * q^68 - 53681046965013864485594032220229980832 * q^69 - 127374089191018487217525315519713602080 * q^70 - 84396091414708989106237239330896374752 * q^71 + 76345595132548433424120590562827574984 * q^72 - 44706579271813174655854382994714255832 * q^73 - 299692406925616462116506150539738813812 * q^74 + 409177364127418217299254754274337843900 * q^75 + 1128262001217587654782588548338718696272 * q^76 + 833312137190144115784050615522845895552 * q^77 - 219467084399719853089285669187657082852 * q^78 + 1416534390331633014953369475707893311680 * q^79 + 1539903590051088861086709486592809053280 * q^80 + 591235317657383693264332840825533190404 * q^81 + 613971248288365719286532695984150451412 * q^82 + 1526205590962076227407755639349783073104 * q^83 + 2386486125584620727973530035630532068512 * q^84 - 285377453319367852617718519171747770960 * q^85 - 12934468921257599734617599325958640634024 * q^86 - 3612653707382978727606828549504415526664 * q^87 - 13219976774504188013705589441700285953696 * q^88 - 39593715237961905051969833281675978558872 * q^89 + 8823438092269922908090462480445695772940 * q^90 - 8845052344004724172694600210873108791616 * q^91 - 65206363053810587386463980322833360400544 * q^92 + 32359497372012156098445494805887947067904 * q^93 + 98582759073905793403791649187553312740832 * q^94 + 7880313586718908134850457997267850706400 * q^95 + 68499267029064622122879551784898487597856 * q^96 + 36750128325858234547252025624989137001352 * q^97 - 68350119771260167200829379908744318383822 * q^98 + 8812005370202382972296217650292999095856 * 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 $

$2$	2.58383e6	1.74240	0.871202	−	0.490924i	$-0.163341\pi$
$2$	2.58383e6	1.74240	0.871202	+	0.490924i	$0.163341\pi$
$3$	3.48678e9	0.577350
$3$	3.48678e9	0.577350
$4$	4.47715e12	2.03597
$5$	2.55548e14	1.19836	0.599181	−	0.800613i	$-0.295493\pi$
$5$	2.55548e14	1.19836	0.599181	+	0.800613i	$0.295493\pi$
$6$	9.00926e15	1.00598
$7$	1.98945e17	0.942375	0.471188	−	0.882033i	$-0.343825\pi$
$7$	1.98945e17	0.942375	0.471188	+	0.882033i	$0.343825\pi$
$8$	5.88630e18	1.80509
$9$	1.21577e19	0.333333
$10$	6.60294e20	2.08803
$11$	−2.76444e21	−1.23896	−0.619480	−	0.785012i	$-0.712657\pi$
$11$	−2.76444e21	−1.23896	−0.619480	+	0.785012i	$0.712657\pi$
$12$	1.56109e22	1.17547
$13$	−8.56075e22	−1.24932	−0.624659	−	0.780898i	$-0.714762\pi$
$13$	−8.56075e22	−1.24932	−0.624659	+	0.780898i	$0.714762\pi$
$14$	5.14041e23	1.64200
$15$	8.91042e23	0.691875
$16$	5.36384e24	1.10922
$17$	−3.38977e24	−0.202287	−0.101143	−	0.994872i	$-0.532250\pi$
$17$	−3.38977e24	−0.202287	−0.101143	+	0.994872i	$0.532250\pi$
$18$	3.14133e25	0.580802
$19$	2.99407e26	1.82731	0.913656	−	0.406488i	$-0.133247\pi$
$19$	2.99407e26	1.82731	0.913656	+	0.406488i	$0.133247\pi$
$20$	1.14413e27	2.43983
$21$	6.93680e26	0.544081
$22$	−7.14285e27	−2.15877
$23$	−1.40889e28	−1.71181	−0.855904	−	0.517134i	$-0.826999\pi$
$23$	−1.40889e28	−1.71181	−0.855904	+	0.517134i	$0.826999\pi$
$24$	2.05243e28	1.04217
$25$	1.98303e28	0.436072
$26$	−2.21195e29	−2.17682
$27$	4.23912e28	0.192450
$28$	8.90709e29	1.91865
$29$	−4.94074e28	−0.0518361	−0.0259181	−	0.999664i	$-0.508251\pi$
$29$	−4.94074e28	−0.0518361	−0.0259181	+	0.999664i	$0.508251\pi$
$30$	2.30230e30	1.20553
$31$	5.76050e30	1.54009	0.770044	−	0.637991i	$-0.220234\pi$
$31$	5.76050e30	1.54009	0.770044	+	0.637991i	$0.220234\pi$
$32$	9.15126e29	0.127616
$33$	−9.63902e30	−0.715314
$34$	−8.75860e30	−0.352466
$35$	5.08402e31	1.12931
$36$	5.44317e31	0.678658
$37$	−1.16818e32	−0.830569	−0.415284	−	0.909692i	$-0.636318\pi$
$37$	−1.16818e32	−0.830569	−0.415284	+	0.909692i	$0.636318\pi$
$38$	7.73616e32	3.18392
$39$	−2.98495e32	−0.721294
$40$	1.50424e33	2.16315
$41$	1.48580e32	0.128793	0.0643964	−	0.997924i	$-0.479488\pi$
$41$	1.48580e32	0.128793	0.0643964	+	0.997924i	$0.479488\pi$
$42$	1.79235e33	0.948009
$43$	2.64197e32	0.0862631	0.0431315	−	0.999069i	$-0.486267\pi$
$43$	2.64197e32	0.0862631	0.0431315	+	0.999069i	$0.486267\pi$
$44$	−1.23768e34	−2.52249
$45$	3.10687e33	0.399454
$46$	−3.64032e34	−2.98266
$47$	2.16318e34	1.14048	0.570238	−	0.821480i	$-0.306851\pi$
$47$	2.16318e34	1.14048	0.570238	+	0.821480i	$0.306851\pi$
$48$	1.87025e34	0.640406
$49$	−4.98839e33	−0.111928
$50$	5.12381e34	0.759814
$51$	−1.18194e34	−0.116790
$52$	−3.83278e35	−2.54358
$53$	5.57170e34	0.250226	0.125113	−	0.992142i	$-0.460071\pi$
$53$	5.57170e34	0.250226	0.125113	+	0.992142i	$0.460071\pi$
$54$	1.09532e35	0.335326
$55$	−7.06449e35	−1.48472
$56$	1.17105e36	1.70107
$57$	1.04397e36	1.05500
$58$	−1.27660e35	−0.0903195
$59$	−2.05748e36	−1.02534	−0.512672	−	0.858584i	$-0.671344\pi$
$59$	−2.05748e36	−1.02534	−0.512672	+	0.858584i	$0.671344\pi$
$60$	3.98933e36	1.40864
$61$	1.01936e36	0.256489	0.128244	−	0.991743i	$-0.459066\pi$
$61$	1.01936e36	0.256489	0.128244	+	0.991743i	$0.459066\pi$
$62$	1.48842e37	2.68346
$63$	2.41871e36	0.314125
$64$	−9.43067e36	−0.886856
$65$	−2.18769e37	−1.49714
$66$	−2.49056e37	−1.24637
$67$	−2.42878e37	−0.893006	−0.446503	−	0.894782i	$-0.647331\pi$
$67$	−2.42878e37	−0.893006	−0.446503	+	0.894782i	$0.647331\pi$
$68$	−1.51765e37	−0.411851
$69$	−4.91248e37	−0.988313
$70$	1.31362e38	1.96771
$71$	5.77043e36	0.0646268	0.0323134	−	0.999478i	$-0.489713\pi$
$71$	5.77043e36	0.0646268	0.0323134	+	0.999478i	$0.489713\pi$
$72$	7.15637e37	0.601695
$73$	−1.22382e38	−0.775532	−0.387766	−	0.921758i	$-0.626753\pi$
$73$	−1.22382e38	−0.775532	−0.387766	+	0.921758i	$0.626753\pi$
$74$	−3.01839e38	−1.44719
$75$	6.91439e37	0.251766
$76$	1.34049e39	3.72036
$77$	−5.49973e38	−1.16757
$78$	−7.71260e38	−1.25679
$79$	−7.70707e38	−0.967240	−0.483620	−	0.875278i	$-0.660678\pi$
$79$	−7.70707e38	−0.967240	−0.483620	+	0.875278i	$0.660678\pi$
$80$	1.37072e39	1.32924
$81$	1.47809e38	0.111111
$82$	3.83906e38	0.224409
$83$	1.70727e39	0.778397	0.389198	−	0.921154i	$-0.372752\pi$
$83$	1.70727e39	0.778397	0.389198	+	0.921154i	$0.372752\pi$
$84$	3.10571e39	1.10773
$85$	−8.66251e38	−0.242413
$86$	6.82641e38	0.150305
$87$	−1.72273e38	−0.0299276
$88$	−1.62723e40	−2.23643
$89$	−4.08353e39	−0.445185	−0.222592	−	0.974912i	$-0.571452\pi$
$89$	−4.08353e39	−0.445185	−0.222592	+	0.974912i	$0.571452\pi$
$90$	8.02763e39	0.696011
$91$	−1.70312e40	−1.17733
$92$	−6.30780e40	−3.48520
$93$	2.00856e40	0.889170
$94$	5.58928e40	1.98717
$95$	7.65129e40	2.18978
$96$	3.19085e39	0.0736793
$97$	1.60920e40	0.300462	0.150231	−	0.988651i	$-0.451998\pi$
$97$	1.60920e40	0.300462	0.150231	+	0.988651i	$0.451998\pi$
$98$	−1.28891e40	−0.195025
$99$	−3.36092e40	−0.412987
$100$	8.87832e40	0.887832
$101$	8.47485e39	0.0691105	0.0345552	−	0.999403i	$-0.488999\pi$
$101$	8.47485e39	0.0691105	0.0345552	+	0.999403i	$0.488999\pi$
$102$	−3.05393e40	−0.203496
$103$	2.25909e41	1.23246	0.616228	−	0.787568i	$-0.288660\pi$
$103$	2.25909e41	1.23246	0.616228	+	0.787568i	$0.288660\pi$
$104$	−5.03911e41	−2.25513
$105$	1.77269e41	0.652006
$106$	1.43963e41	0.435995
$107$	−6.78077e41	−1.69399	−0.846996	−	0.531599i	$-0.821591\pi$
$107$	−6.78077e41	−1.69399	−0.846996	+	0.531599i	$0.821591\pi$
$108$	1.89792e41	0.391823
$109$	7.17358e41	1.22601	0.613003	−	0.790080i	$-0.289961\pi$
$109$	7.17358e41	1.22601	0.613003	+	0.790080i	$0.289961\pi$
$110$	−1.82534e42	−2.58699
$111$	−4.07320e41	−0.479529
$112$	1.06711e42	1.04530
$113$	1.60519e42	1.31045	0.655223	−	0.755435i	$-0.272575\pi$
$113$	1.60519e42	1.31045	0.655223	+	0.755435i	$0.272575\pi$
$114$	2.69743e42	1.83824
$115$	−3.60039e42	−2.05137
$116$	−2.21204e41	−0.105537
$117$	−1.04079e42	−0.416439
$118$	−5.31619e42	−1.78657
$119$	−6.74380e41	−0.190630
$120$	5.24494e42	1.24889
$121$	2.66363e42	0.535024
$122$	2.63386e42	0.446907
$123$	5.18067e41	0.0743586
$124$	2.57906e43	3.13558
$125$	−6.55340e42	−0.675790
$126$	6.24954e42	0.547333
$127$	2.84948e42	0.212222	0.106111	−	0.994354i	$-0.466160\pi$
$127$	2.84948e42	0.212222	0.106111	+	0.994354i	$0.466160\pi$
$128$	−2.63796e43	−1.67288
$129$	9.21199e41	0.0498040
$130$	−5.65261e43	−2.60862
$131$	2.19486e43	0.865656	0.432828	−	0.901477i	$-0.357516\pi$
$131$	2.19486e43	0.865656	0.432828	+	0.901477i	$0.357516\pi$
$132$	−4.31554e43	−1.45636
$133$	5.95656e43	1.72201
$134$	−6.27555e43	−1.55598
$135$	1.08330e43	0.230625
$136$	−1.99532e43	−0.365145
$137$	3.35892e43	0.528966	0.264483	−	0.964390i	$-0.414799\pi$
$137$	3.35892e43	0.528966	0.264483	+	0.964390i	$0.414799\pi$
$138$	−1.26930e44	−1.72204
$139$	4.50230e43	0.526782	0.263391	−	0.964689i	$-0.415159\pi$
$139$	4.50230e43	0.526782	0.263391	+	0.964689i	$0.415159\pi$
$140$	2.27619e44	2.29924
$141$	7.54253e43	0.658454
$142$	1.49098e43	0.112606
$143$	2.36657e44	1.54786
$144$	6.52117e43	0.369738
$145$	−1.26260e43	−0.0621185
$146$	−3.16215e44	−1.35129
$147$	−1.73934e43	−0.0646219
$148$	−5.23013e44	−1.69102
$149$	−2.36545e44	−0.666186	−0.333093	−	0.942894i	$-0.608092\pi$
$149$	−2.36545e44	−0.666186	−0.333093	+	0.942894i	$0.608092\pi$
$150$	1.78656e44	0.438679
$151$	−4.16293e44	−0.892015	−0.446007	−	0.895029i	$-0.647154\pi$
$151$	−4.16293e44	−0.892015	−0.446007	+	0.895029i	$0.647154\pi$
$152$	1.76240e45	3.29845
$153$	−4.12117e43	−0.0674290
$154$	−1.42104e45	−2.03437
$155$	1.47209e45	1.84558
$156$	−1.33641e45	−1.46854
$157$	1.20032e45	1.15706	0.578528	−	0.815663i	$-0.303627\pi$
$157$	1.20032e45	1.15706	0.578528	+	0.815663i	$0.303627\pi$
$158$	−1.99138e45	−1.68532
$159$	1.94273e44	0.144468
$160$	2.33859e44	0.152931
$161$	−2.80291e45	−1.61317
$162$	3.81913e44	0.193601
$163$	2.08406e45	0.931246	0.465623	−	0.884983i	$-0.345830\pi$
$163$	2.08406e45	0.931246	0.465623	+	0.884983i	$0.345830\pi$
$164$	6.65216e44	0.262219
$165$	−2.46324e45	−0.857206
$166$	4.41129e45	1.35628
$167$	−3.55110e45	−0.965328	−0.482664	−	0.875806i	$-0.660331\pi$
$167$	−3.55110e45	−0.965328	−0.482664	+	0.875806i	$0.660331\pi$
$168$	4.08321e45	0.982112
$169$	2.63319e45	0.560795
$170$	−2.23825e45	−0.422382
$171$	3.64009e45	0.609104
$172$	1.18285e45	0.175629
$173$	1.13689e46	1.49890	0.749449	−	0.662062i	$-0.230319\pi$
$173$	1.13689e46	1.49890	0.749449	+	0.662062i	$0.230319\pi$
$174$	−4.45124e44	−0.0521460
$175$	3.94514e45	0.410944
$176$	−1.48280e46	−1.37427
$177$	−7.17400e45	−0.591983
$178$	−1.05511e46	−0.775692
$179$	7.48686e45	0.490696	0.245348	−	0.969435i	$-0.421098\pi$
$179$	7.48686e45	0.490696	0.245348	+	0.969435i	$0.421098\pi$
$180$	1.39099e46	0.813278
$181$	−5.11394e45	−0.266898	−0.133449	−	0.991056i	$-0.542605\pi$
$181$	−5.11394e45	−0.266898	−0.133449	+	0.991056i	$0.542605\pi$
$182$	−4.40057e46	−2.05138
$183$	3.55430e45	0.148084
$184$	−8.29313e46	−3.08996
$185$	−2.98527e46	−0.995322
$186$	5.18978e46	1.54929
$187$	9.37084e45	0.250626
$188$	9.68487e46	2.32198
$189$	8.43352e45	0.181360
$190$	1.97696e47	3.81549
$191$	−6.00314e46	−1.04039	−0.520193	−	0.854049i	$-0.674140\pi$
$191$	−6.00314e46	−1.04039	−0.520193	+	0.854049i	$0.674140\pi$
$192$	−3.28827e46	−0.512026
$193$	−9.10745e45	−0.127489	−0.0637444	−	0.997966i	$-0.520304\pi$
$193$	−9.10745e45	−0.127489	−0.0637444	+	0.997966i	$0.520304\pi$
$194$	4.15790e46	0.523526
$195$	−7.62799e46	−0.864372
$196$	−2.23338e46	−0.227883
$197$	−3.20025e46	−0.294189	−0.147094	−	0.989122i	$-0.546992\pi$
$197$	−3.20025e46	−0.294189	−0.147094	+	0.989122i	$0.546992\pi$
$198$	−8.68404e46	−0.719590
$199$	−4.23622e46	−0.316585	−0.158293	−	0.987392i	$-0.550599\pi$
$199$	−4.23622e46	−0.316585	−0.158293	+	0.987392i	$0.550599\pi$
$200$	1.16727e47	0.787148
$201$	−8.46863e46	−0.515577
$202$	2.18976e46	0.120418
$203$	−9.82936e45	−0.0488491
$204$	−5.29173e46	−0.237782
$205$	3.79694e46	0.154340
$206$	5.83712e47	2.14744
$207$	−1.71288e47	−0.570603
$208$	−4.59184e47	−1.38576
$209$	−8.27693e47	−2.26397
$210$	4.58032e47	1.13606
$211$	5.34998e47	1.20382	0.601911	−	0.798563i	$-0.294406\pi$
$211$	5.34998e47	1.20382	0.601911	+	0.798563i	$0.294406\pi$
$212$	2.49454e47	0.509454
$213$	2.01203e46	0.0373123
$214$	−1.75204e48	−2.95162
$215$	6.75152e46	0.103374
$216$	2.49527e47	0.347389
$217$	1.14602e48	1.45134
$218$	1.85353e48	2.13620
$219$	−4.26721e47	−0.447754
$220$	−3.16288e48	−3.02286
$221$	2.90190e47	0.252721
$222$	−1.05245e48	−0.835533
$223$	2.57714e48	1.86590	0.932950	−	0.360006i	$-0.117225\pi$
$223$	2.57714e48	1.86590	0.932950	+	0.360006i	$0.117225\pi$
$224$	1.82060e47	0.120263
$225$	2.41090e47	0.145357
$226$	4.14755e48	2.28333
$227$	2.96815e48	1.49264	0.746320	−	0.665587i	$-0.231819\pi$
$227$	2.96815e48	1.49264	0.746320	+	0.665587i	$0.231819\pi$
$228$	4.67400e48	2.14795
$229$	−2.39386e48	−1.00571	−0.502854	−	0.864371i	$-0.667717\pi$
$229$	−2.39386e48	−1.00571	−0.502854	+	0.864371i	$0.667717\pi$
$230$	−9.30279e48	−3.57431
$231$	−1.91764e48	−0.674095
$232$	−2.90827e47	−0.0935686
$233$	−2.35236e48	−0.692960	−0.346480	−	0.938057i	$-0.612623\pi$
$233$	−2.35236e48	−0.692960	−0.346480	+	0.938057i	$0.612623\pi$
$234$	−2.68922e48	−0.725606
$235$	5.52796e48	1.36670
$236$	−9.21167e48	−2.08758
$237$	−2.68729e48	−0.558436
$238$	−1.74248e48	−0.332155
$239$	−5.65009e48	−0.988322	−0.494161	−	0.869370i	$-0.664525\pi$
$239$	−5.65009e48	−0.988322	−0.494161	+	0.869370i	$0.664525\pi$
$240$	4.77940e48	0.767438
$241$	1.15148e49	1.69788	0.848940	−	0.528490i	$-0.177241\pi$
$241$	1.15148e49	1.69788	0.848940	+	0.528490i	$0.177241\pi$
$242$	6.88236e48	0.932229
$243$	5.15378e47	0.0641500
$244$	4.56385e48	0.522204
$245$	−1.27477e48	−0.134131
$246$	1.33860e48	0.129563
$247$	−2.56315e49	−2.28289
$248$	3.39080e49	2.77999
$249$	5.95288e48	0.449407
$250$	−1.69329e49	−1.17750
$251$	1.49455e48	0.0957634	0.0478817	−	0.998853i	$-0.484753\pi$
$251$	1.49455e48	0.0957634	0.0478817	+	0.998853i	$0.484753\pi$
$252$	1.08289e49	0.639551
$253$	3.89479e49	2.12086
$254$	7.36258e48	0.369776
$255$	−3.02043e48	−0.139957
$256$	−4.74222e49	−2.02797
$257$	−5.98105e48	−0.236129	−0.118064	−	0.993006i	$-0.537669\pi$
$257$	−5.98105e48	−0.236129	−0.118064	+	0.993006i	$0.537669\pi$
$258$	2.38022e48	0.0867787
$259$	−2.32405e49	−0.782707
$260$	−9.79460e49	−3.04813
$261$	−6.00678e47	−0.0172787
$262$	5.67115e49	1.50832
$263$	3.57534e49	0.879476	0.439738	−	0.898126i	$-0.355071\pi$
$263$	3.57534e49	0.879476	0.439738	+	0.898126i	$0.355071\pi$
$264$	−5.67382e49	−1.29120
$265$	1.42384e49	0.299861
$266$	1.53907e50	3.00045
$267$	−1.42384e49	−0.257028
$268$	−1.08740e50	−1.81814
$269$	2.52785e48	0.0391589	0.0195794	−	0.999808i	$-0.493767\pi$
$269$	2.52785e48	0.0391589	0.0195794	+	0.999808i	$0.493767\pi$
$270$	2.79906e49	0.401842
$271$	5.81899e49	0.774421	0.387211	−	0.921991i	$-0.373439\pi$
$271$	5.81899e49	0.774421	0.387211	+	0.921991i	$0.373439\pi$
$272$	−1.81822e49	−0.224380
$273$	−5.93842e49	−0.679730
$274$	8.67887e49	0.921673
$275$	−5.48197e49	−0.540277
$276$	−2.19939e50	−2.01218
$277$	−1.51629e50	−1.28810	−0.644048	−	0.764985i	$-0.722746\pi$
$277$	−1.51629e50	−1.28810	−0.644048	+	0.764985i	$0.722746\pi$
$278$	1.16332e50	0.917867
$279$	7.00342e49	0.513363
$280$	2.99261e50	2.03850
$281$	−1.12012e50	−0.709226	−0.354613	−	0.935013i	$-0.615387\pi$
$281$	−1.12012e50	−0.709226	−0.354613	+	0.935013i	$0.615387\pi$
$282$	1.94886e50	1.14729
$283$	−2.86308e50	−1.56752	−0.783758	−	0.621066i	$-0.786700\pi$
$283$	−2.86308e50	−1.56752	−0.783758	+	0.621066i	$0.786700\pi$
$284$	2.58351e49	0.131578
$285$	2.66784e50	1.26427
$286$	6.11481e50	2.69699
$287$	2.95593e49	0.121371
$288$	1.11258e49	0.0425388
$289$	−2.69315e50	−0.959080
$290$	−3.26234e49	−0.108236
$291$	5.61093e49	0.173472
$292$	−5.47924e50	−1.57896
$293$	−1.89439e50	−0.508960	−0.254480	−	0.967078i	$-0.581904\pi$
$293$	−1.89439e50	−0.508960	−0.254480	+	0.967078i	$0.581904\pi$
$294$	−4.49417e49	−0.112598
$295$	−5.25787e50	−1.22873
$296$	−6.87628e50	−1.49925
$297$	−1.17188e50	−0.238438
$298$	−6.11193e50	−1.16077
$299$	1.20611e51	2.13859
$300$	3.09568e50	0.512590
$301$	5.25608e49	0.0812922
$302$	−1.07563e51	−1.55425
$303$	2.95500e49	0.0399009
$304$	1.60597e51	2.02688
$305$	2.60497e50	0.307366
$306$	−1.06484e50	−0.117489
$307$	4.49477e50	0.463843	0.231921	−	0.972735i	$-0.425499\pi$
$307$	4.49477e50	0.463843	0.231921	+	0.972735i	$0.425499\pi$
$308$	−2.46231e51	−2.37713
$309$	7.87698e50	0.711559
$310$	3.80362e51	3.21575
$311$	−4.89729e50	−0.387586	−0.193793	−	0.981042i	$-0.562079\pi$
$311$	−4.89729e50	−0.387586	−0.193793	+	0.981042i	$0.562079\pi$
$312$	−1.75703e51	−1.30200
$313$	1.99055e51	1.38139	0.690693	−	0.723148i	$-0.257306\pi$
$313$	1.99055e51	1.38139	0.690693	+	0.723148i	$0.257306\pi$
$314$	3.10142e51	2.01606
$315$	6.18098e50	0.376436
$316$	−3.45057e51	−1.96927
$317$	8.77183e50	0.469219	0.234609	−	0.972090i	$-0.424619\pi$
$317$	8.77183e50	0.469219	0.234609	+	0.972090i	$0.424619\pi$
$318$	5.01969e50	0.251722
$319$	1.36584e50	0.0642230
$320$	−2.40999e51	−1.06277
$321$	−2.36431e51	−0.978027
$322$	−7.24225e51	−2.81079
$323$	−1.01492e51	−0.369641
$324$	6.61763e50	0.226219
$325$	−1.69762e51	−0.544793
$326$	5.38486e51	1.62261
$327$	2.50127e51	0.707835
$328$	8.74587e50	0.232482
$329$	4.30354e51	1.07476
$330$	−6.36458e51	−1.49360
$331$	2.35505e51	0.519429	0.259715	−	0.965685i	$-0.416372\pi$
$331$	2.35505e51	0.519429	0.259715	+	0.965685i	$0.416372\pi$
$332$	7.64370e51	1.58479
$333$	−1.42024e51	−0.276856
$334$	−9.17543e51	−1.68199
$335$	−6.20670e51	−1.07014
$336$	3.72078e51	0.603503
$337$	2.75468e51	0.420396	0.210198	−	0.977659i	$-0.432589\pi$
$337$	2.75468e51	0.420396	0.210198	+	0.977659i	$0.432589\pi$
$338$	6.80371e51	0.977132
$339$	5.59696e51	0.756587
$340$	−3.87834e51	−0.493547
$341$	−1.59246e52	−1.90811
$342$	9.40537e51	1.06131
$343$	−9.85894e51	−1.04785
$344$	1.55514e51	0.155712
$345$	−1.25538e52	−1.18436
$346$	2.93752e52	2.61169
$347$	8.25043e51	0.691389	0.345695	−	0.938347i	$-0.387643\pi$
$347$	8.25043e51	0.691389	0.345695	+	0.938347i	$0.387643\pi$
$348$	−7.71292e50	−0.0609318
$349$	8.65779e51	0.644891	0.322445	−	0.946588i	$-0.395495\pi$
$349$	8.65779e51	0.644891	0.322445	+	0.946588i	$0.395495\pi$
$350$	1.01936e52	0.716031
$351$	−3.62900e51	−0.240431
$352$	−2.52981e51	−0.158112
$353$	−6.01269e51	−0.354558	−0.177279	−	0.984161i	$-0.556730\pi$
$353$	−6.01269e51	−0.354558	−0.177279	+	0.984161i	$0.556730\pi$
$354$	−1.85364e52	−1.03147
$355$	1.47463e51	0.0774463
$356$	−1.82826e52	−0.906385
$357$	−2.35142e51	−0.110060
$358$	1.93448e52	0.854991
$359$	−1.54293e52	−0.644035	−0.322017	−	0.946734i	$-0.604361\pi$
$359$	−1.54293e52	−0.644035	−0.322017	+	0.946734i	$0.604361\pi$
$360$	1.82880e52	0.721049
$361$	6.27973e52	2.33907
$362$	−1.32136e52	−0.465044
$363$	9.28750e51	0.308896
$364$	−7.62513e52	−2.39701
$365$	−3.12746e52	−0.929369
$366$	9.18372e51	0.258022
$367$	−3.80556e52	−1.01103	−0.505515	−	0.862818i	$-0.668698\pi$
$367$	−3.80556e52	−1.01103	−0.505515	+	0.862818i	$0.668698\pi$
$368$	−7.55703e52	−1.89876
$369$	1.80639e51	0.0429309
$370$	−7.71344e52	−1.73425
$371$	1.10846e52	0.235807
$372$	8.99264e52	1.81033
$373$	4.94905e52	0.942955	0.471478	−	0.881878i	$-0.343721\pi$
$373$	4.94905e52	0.942955	0.471478	+	0.881878i	$0.343721\pi$
$374$	2.42126e52	0.436691
$375$	−2.28503e52	−0.390167
$376$	1.27331e53	2.05865
$377$	4.22964e51	0.0647598
$378$	2.17908e52	0.316003
$379$	4.34671e52	0.597113	0.298557	−	0.954392i	$-0.403495\pi$
$379$	4.34671e52	0.597113	0.298557	+	0.954392i	$0.403495\pi$
$380$	3.42560e53	4.45834
$381$	9.93553e51	0.122526
$382$	−1.55111e53	−1.81277
$383$	−2.09548e52	−0.232118	−0.116059	−	0.993242i	$-0.537026\pi$
$383$	−2.09548e52	−0.232118	−0.116059	+	0.993242i	$0.537026\pi$
$384$	−9.19801e52	−0.965837
$385$	−1.40545e53	−1.39917
$386$	−2.35321e52	−0.222137
$387$	3.21202e51	0.0287544
$388$	7.20463e52	0.611732
$389$	−1.49021e53	−1.20028	−0.600139	−	0.799896i	$-0.704888\pi$
$389$	−1.49021e53	−1.20028	−0.600139	+	0.799896i	$0.704888\pi$
$390$	−1.97094e53	−1.50608
$391$	4.77581e52	0.346277
$392$	−2.93631e52	−0.202040
$393$	7.65300e52	0.499787
$394$	−8.26890e52	−0.512596
$395$	−1.96953e53	−1.15910
$396$	−1.50473e53	−0.840831
$397$	3.46598e53	1.83916	0.919582	−	0.392898i	$-0.128528\pi$
$397$	3.46598e53	1.83916	0.919582	+	0.392898i	$0.128528\pi$
$398$	−1.09457e53	−0.551620
$399$	2.07692e53	0.994205
$400$	1.06366e53	0.483698
$401$	3.81967e53	1.65031	0.825157	−	0.564904i	$-0.191087\pi$
$401$	3.81967e53	1.65031	0.825157	+	0.564904i	$0.191087\pi$
$402$	−2.18815e53	−0.898344
$403$	−4.93142e53	−1.92406
$404$	3.79432e52	0.140707
$405$	3.77723e52	0.133151
$406$	−2.53974e52	−0.0851149
$407$	3.22938e53	1.02904
$408$	−6.95726e52	−0.210817
$409$	−1.49738e53	−0.431523	−0.215761	−	0.976446i	$-0.569223\pi$
$409$	−1.49738e53	−0.431523	−0.215761	+	0.976446i	$0.569223\pi$
$410$	9.81065e52	0.268923
$411$	1.17118e53	0.305399
$412$	1.01143e54	2.50925
$413$	−4.09327e53	−0.966260
$414$	−4.42578e53	−0.994221
$415$	4.36290e53	0.932801
$416$	−7.83416e52	−0.159433
$417$	1.56985e53	0.304138
$418$	−2.13862e54	−3.94475
$419$	5.57082e53	0.978434	0.489217	−	0.872162i	$-0.337283\pi$
$419$	5.57082e53	0.978434	0.489217	+	0.872162i	$0.337283\pi$
$420$	7.93659e53	1.32747
$421$	−4.02757e53	−0.641593	−0.320797	−	0.947148i	$-0.603951\pi$
$421$	−4.02757e53	−0.641593	−0.320797	+	0.947148i	$0.603951\pi$
$422$	1.38234e54	2.09754
$423$	2.62992e53	0.380158
$424$	3.27967e53	0.451679
$425$	−6.72201e52	−0.0882117
$426$	5.19873e52	0.0650131
$427$	2.02798e53	0.241708
$428$	−3.03585e54	−3.44892
$429$	8.25172e53	0.893655
$430$	1.74448e53	0.180120
$431$	−1.10307e54	−1.08597	−0.542986	−	0.839742i	$-0.682706\pi$
$431$	−1.10307e54	−1.08597	−0.542986	+	0.839742i	$0.682706\pi$
$432$	2.27379e53	0.213469
$433$	2.59468e53	0.232317	0.116159	−	0.993231i	$-0.462942\pi$
$433$	2.59468e53	0.232317	0.116159	+	0.993231i	$0.462942\pi$
$434$	2.96113e54	2.52882
$435$	−4.40240e52	−0.0358641
$436$	3.21172e54	2.49612
$437$	−4.21830e54	−3.12801
$438$	−1.10257e54	−0.780168
$439$	−6.51584e53	−0.439995	−0.219997	−	0.975500i	$-0.570605\pi$
$439$	−6.51584e53	−0.439995	−0.219997	+	0.975500i	$0.570605\pi$
$440$	−4.15837e54	−2.68005
$441$	−6.06471e52	−0.0373095
$442$	7.49801e53	0.440342
$443$	−8.31973e53	−0.466480	−0.233240	−	0.972419i	$-0.574933\pi$
$443$	−8.31973e53	−0.466480	−0.233240	+	0.972419i	$0.574933\pi$
$444$	−1.82363e54	−0.976308
$445$	−1.04354e54	−0.533493
$446$	6.65889e54	3.25115
$447$	−8.24782e53	−0.384623
$448$	−1.87619e54	−0.835751
$449$	1.75134e54	0.745280	0.372640	−	0.927976i	$-0.378453\pi$
$449$	1.75134e54	0.745280	0.372640	+	0.927976i	$0.378453\pi$
$450$	6.22935e53	0.253271
$451$	−4.10741e53	−0.159569
$452$	7.18670e54	2.66803
$453$	−1.45153e54	−0.515005
$454$	7.66919e54	2.60078
$455$	−4.35230e54	−1.41086
$456$	6.14510e54	1.90436
$457$	5.74991e54	1.70364	0.851822	−	0.523831i	$-0.175498\pi$
$457$	5.74991e54	1.70364	0.851822	+	0.523831i	$0.175498\pi$
$458$	−6.18534e54	−1.75235
$459$	−1.43696e53	−0.0389301
$460$	−1.61195e55	−4.17653
$461$	7.61685e54	1.88758	0.943792	−	0.330540i	$-0.107231\pi$
$461$	7.61685e54	1.88758	0.943792	+	0.330540i	$0.107231\pi$
$462$	−4.95485e54	−1.17455
$463$	4.82618e54	1.09444	0.547221	−	0.836988i	$-0.315686\pi$
$463$	4.82618e54	1.09444	0.547221	+	0.836988i	$0.315686\pi$
$464$	−2.65013e53	−0.0574974
$465$	5.13285e54	1.06555
$466$	−6.07811e54	−1.20742
$467$	−8.48997e54	−1.61402	−0.807012	−	0.590535i	$-0.798917\pi$
$467$	−8.48997e54	−1.61402	−0.807012	+	0.590535i	$0.798917\pi$
$468$	−4.65976e54	−0.847859
$469$	−4.83194e54	−0.841547
$470$	1.42833e55	2.38135
$471$	4.18526e54	0.668026
$472$	−1.21110e55	−1.85084
$473$	−7.30358e53	−0.106877
$474$	−6.94350e54	−0.973022
$475$	5.93732e54	0.796840
$476$	−3.01930e54	−0.388118
$477$	6.77389e53	0.0834087
$478$	−1.45989e55	−1.72206
$479$	−7.54248e54	−0.852385	−0.426193	−	0.904632i	$-0.640145\pi$
$479$	−7.54248e54	−0.852385	−0.426193	+	0.904632i	$0.640145\pi$
$480$	8.15416e53	0.0882945
$481$	1.00005e55	1.03764
$482$	2.97523e55	2.95839
$483$	−9.77315e54	−0.931362
$484$	1.19255e55	1.08930
$485$	4.11228e54	0.360062
$486$	1.33165e54	0.111775
$487$	2.26646e55	1.82392	0.911958	−	0.410283i	$-0.134570\pi$
$487$	2.26646e55	1.82392	0.911958	+	0.410283i	$0.134570\pi$
$488$	6.00029e54	0.462984
$489$	7.26667e54	0.537655
$490$	−3.29380e54	−0.233710
$491$	−9.02019e54	−0.613826	−0.306913	−	0.951738i	$-0.599296\pi$
$491$	−9.02019e54	−0.613826	−0.306913	+	0.951738i	$0.599296\pi$
$492$	2.31946e54	0.151392
$493$	1.67480e53	0.0104858
$494$	−6.62273e55	−3.97772
$495$	−8.58877e54	−0.494908
$496$	3.08984e55	1.70829
$497$	1.14800e54	0.0609027
$498$	1.53812e55	0.783050
$499$	−4.11207e54	−0.200909	−0.100454	−	0.994942i	$-0.532030\pi$
$499$	−4.11207e54	−0.200909	−0.100454	+	0.994942i	$0.532030\pi$
$500$	−2.93406e55	−1.37589
$501$	−1.23819e55	−0.557332
$502$	3.86167e54	0.166859
$503$	−3.08721e55	−1.28063	−0.640313	−	0.768114i	$-0.721195\pi$
$503$	−3.08721e55	−1.28063	−0.640313	+	0.768114i	$0.721195\pi$
$504$	1.42373e55	0.567023
$505$	2.16573e54	0.0828194
$506$	1.00635e56	3.69540
$507$	9.18135e54	0.323775
$508$	1.27576e55	0.432078
$509$	2.73650e54	0.0890185	0.0445092	−	0.999009i	$-0.485828\pi$
$509$	2.73650e54	0.0890185	0.0445092	+	0.999009i	$0.485828\pi$
$510$	−7.80428e54	−0.243862
$511$	−2.43474e55	−0.730843
$512$	−6.45215e55	−1.86067
$513$	1.26922e55	0.351666
$514$	−1.54540e55	−0.411432
$515$	5.77308e55	1.47693
$516$	4.12435e54	0.101400
$517$	−5.97998e55	−1.41300
$518$	−6.00494e55	−1.36379
$519$	3.96408e55	0.865389
$520$	−1.28774e56	−2.70246
$521$	−7.68480e54	−0.155046	−0.0775228	−	0.996991i	$-0.524701\pi$
$521$	−7.68480e54	−0.155046	−0.0775228	+	0.996991i	$0.524701\pi$
$522$	−1.55205e54	−0.0301065
$523$	−5.42535e55	−1.01191	−0.505957	−	0.862559i	$-0.668860\pi$
$523$	−5.42535e55	−1.01191	−0.505957	+	0.862559i	$0.668860\pi$
$524$	9.82673e55	1.76245
$525$	1.37559e55	0.237259
$526$	9.23806e55	1.53240
$527$	−1.95268e55	−0.311540
$528$	−5.17021e55	−0.793438
$529$	1.30757e56	1.93029
$530$	3.67896e55	0.522480
$531$	−2.50142e55	−0.341782
$532$	2.66684e56	3.50598
$533$	−1.27196e55	−0.160903
$534$	−3.67896e55	−0.447846
$535$	−1.73282e56	−2.03002
$536$	−1.42965e56	−1.61195
$537$	2.61051e55	0.283303
$538$	6.53154e54	0.0682306
$539$	1.37901e55	0.138675
$540$	4.85010e55	0.469546
$541$	1.06824e56	0.995687	0.497844	−	0.867267i	$-0.334125\pi$
$541$	1.06824e56	0.995687	0.497844	+	0.867267i	$0.334125\pi$
$542$	1.50353e56	1.34936
$543$	−1.78312e55	−0.154094
$544$	−3.10207e54	−0.0258151
$545$	1.83320e56	1.46920
$546$	−1.53439e56	−1.18436
$547$	−2.25958e56	−1.67991	−0.839956	−	0.542654i	$-0.817419\pi$
$547$	−2.25958e56	−1.67991	−0.839956	+	0.542654i	$0.817419\pi$
$548$	1.50384e56	1.07696
$549$	1.23931e55	0.0854962
$550$	−1.41645e56	−0.941381
$551$	−1.47929e55	−0.0947208
$552$	−2.89163e56	−1.78399
$553$	−1.53329e56	−0.911503
$554$	−3.91785e56	−2.24438
$555$	−1.04090e56	−0.574649
$556$	2.01575e56	1.07251
$557$	−9.26630e55	−0.475198	−0.237599	−	0.971363i	$-0.576360\pi$
$557$	−9.26630e55	−0.475198	−0.237599	+	0.971363i	$0.576360\pi$
$558$	1.80957e56	0.894485
$559$	−2.26173e55	−0.107770
$560$	2.72698e56	1.25264
$561$	3.26741e55	0.144699
$562$	−2.89420e56	−1.23576
$563$	1.20733e56	0.497053	0.248526	−	0.968625i	$-0.420054\pi$
$563$	1.20733e56	0.497053	0.248526	+	0.968625i	$0.420054\pi$
$564$	3.37691e56	1.34059
$565$	4.10205e56	1.57039
$566$	−7.39772e56	−2.73125
$567$	2.94059e55	0.104708
$568$	3.39665e55	0.116657
$569$	2.31976e56	0.768495	0.384248	−	0.923230i	$-0.374461\pi$
$569$	2.31976e56	0.768495	0.384248	+	0.923230i	$0.374461\pi$
$570$	6.89325e56	2.20287
$571$	2.57033e55	0.0792409	0.0396204	−	0.999215i	$-0.487385\pi$
$571$	2.57033e55	0.0792409	0.0396204	+	0.999215i	$0.487385\pi$
$572$	1.05955e57	3.15139
$573$	−2.09316e56	−0.600667
$574$	7.63763e55	0.211478
$575$	−2.79386e56	−0.746472
$576$	−1.14655e56	−0.295619
$577$	−2.83608e56	−0.705690	−0.352845	−	0.935682i	$-0.614786\pi$
$577$	−2.83608e56	−0.705690	−0.352845	+	0.935682i	$0.614786\pi$
$578$	−6.95864e56	−1.67111
$579$	−3.17557e55	−0.0736057
$580$	−5.65284e55	−0.126472
$581$	3.39653e56	0.733542
$582$	1.44977e56	0.302258
$583$	−1.54027e56	−0.310020
$584$	−7.20379e56	−1.39990
$585$	−2.65971e56	−0.499045
$586$	−4.89479e56	−0.886814
$587$	3.96279e56	0.693298	0.346649	−	0.937995i	$-0.387319\pi$
$587$	3.96279e56	0.693298	0.346649	+	0.937995i	$0.387319\pi$
$588$	−7.78730e55	−0.131569
$589$	1.72473e57	2.81422
$590$	−1.35854e57	−2.14095
$591$	−1.11586e56	−0.169850
$592$	−6.26594e56	−0.921279
$593$	1.25467e57	1.78200	0.891001	−	0.454001i	$-0.150004\pi$
$593$	1.25467e57	1.78200	0.891001	+	0.454001i	$0.150004\pi$
$594$	−3.02794e56	−0.415456
$595$	−1.72337e56	−0.228444
$596$	−1.05905e57	−1.35634
$597$	−1.47708e56	−0.182781
$598$	3.11639e57	3.72629
$599$	−1.06361e57	−1.22895	−0.614475	−	0.788936i	$-0.710632\pi$
$599$	−1.06361e57	−1.22895	−0.614475	+	0.788936i	$0.710632\pi$
$600$	4.07002e56	0.454460
$601$	−4.74011e56	−0.511519	−0.255759	−	0.966740i	$-0.582325\pi$
$601$	−4.74011e56	−0.511519	−0.255759	+	0.966740i	$0.582325\pi$
$602$	1.35808e56	0.141644
$603$	−2.95283e56	−0.297669
$604$	−1.86381e57	−1.81612
$605$	6.80686e56	0.641153
$606$	7.63521e55	0.0695236
$607$	−3.75437e56	−0.330498	−0.165249	−	0.986252i	$-0.552843\pi$
$607$	−3.75437e56	−0.330498	−0.165249	+	0.986252i	$0.552843\pi$
$608$	2.73995e56	0.233195
$609$	−3.42729e55	−0.0282030
$610$	6.73080e56	0.535556
$611$	−1.85184e57	−1.42482
$612$	−1.84511e56	−0.137284
$613$	1.97052e57	1.41788	0.708941	−	0.705267i	$-0.249173\pi$
$613$	1.97052e57	1.41788	0.708941	+	0.705267i	$0.249173\pi$
$614$	1.16137e57	0.808202
$615$	1.32391e56	0.0891085
$616$	−3.23731e57	−2.10756
$617$	1.04592e57	0.658649	0.329325	−	0.944217i	$-0.393179\pi$
$617$	1.04592e57	0.658649	0.329325	+	0.944217i	$0.393179\pi$
$618$	2.03528e57	1.23982
$619$	−3.26806e57	−1.92589	−0.962947	−	0.269692i	$-0.913078\pi$
$619$	−3.26806e57	−1.92589	−0.962947	+	0.269692i	$0.913078\pi$
$620$	6.59076e57	3.75756
$621$	−5.97243e56	−0.329438
$622$	−1.26538e57	−0.675332
$623$	−8.12399e56	−0.419531
$624$	−1.60108e57	−0.800070
$625$	−2.57649e57	−1.24591
$626$	5.14325e57	2.40693
$627$	−2.88599e57	−1.30710
$628$	5.37402e57	2.35574
$629$	3.95988e56	0.168013
$630$	1.59706e57	0.655903
$631$	7.88492e54	0.00313470	0.00156735	−	0.999999i	$-0.499501\pi$
$631$	7.88492e54	0.00313470	0.00156735	+	0.999999i	$0.499501\pi$
$632$	−4.53662e57	−1.74595
$633$	1.86542e57	0.695027
$634$	2.26649e57	0.817569
$635$	7.28181e56	0.254318
$636$	8.69791e56	0.294133
$637$	4.27043e56	0.139834
$638$	3.52909e56	0.111902
$639$	7.01550e55	0.0215423
$640$	−6.74127e57	−2.00471
$641$	−5.60781e57	−1.61511	−0.807557	−	0.589789i	$-0.799211\pi$
$641$	−5.60781e57	−1.61511	−0.807557	+	0.589789i	$0.799211\pi$
$642$	−6.10897e57	−1.70412
$643$	−2.39387e57	−0.646810	−0.323405	−	0.946261i	$-0.604828\pi$
$643$	−2.39387e57	−0.646810	−0.323405	+	0.946261i	$0.604828\pi$
$644$	−1.25491e58	−3.28436
$645$	2.35411e56	0.0596832
$646$	−2.62238e57	−0.644065
$647$	5.56725e57	1.32466	0.662328	−	0.749214i	$-0.269569\pi$
$647$	5.56725e57	1.32466	0.662328	+	0.749214i	$0.269569\pi$
$648$	8.70047e56	0.200565
$649$	5.68779e57	1.27036
$650$	−4.38636e57	−0.949250
$651$	3.99594e57	0.837932
$652$	9.33066e57	1.89599
$653$	6.52017e57	1.28392	0.641961	−	0.766737i	$-0.278121\pi$
$653$	6.52017e57	1.28392	0.641961	+	0.766737i	$0.278121\pi$
$654$	6.46286e57	1.23334
$655$	5.60893e57	1.03737
$656$	7.96959e56	0.142859
$657$	−1.48788e57	−0.258511
$658$	1.11196e58	1.87266
$659$	−7.55343e57	−1.23309	−0.616543	−	0.787321i	$-0.711467\pi$
$659$	−7.55343e57	−1.23309	−0.616543	+	0.787321i	$0.711467\pi$
$660$	−1.10283e58	−1.74525
$661$	−7.41557e57	−1.13767	−0.568833	−	0.822453i	$-0.692605\pi$
$661$	−7.41557e57	−1.13767	−0.568833	+	0.822453i	$0.692605\pi$
$662$	6.08505e57	0.905056
$663$	1.01183e57	0.145908
$664$	1.00495e58	1.40507
$665$	1.52219e58	2.06360
$666$	−3.66965e57	−0.482395
$667$	6.96093e56	0.0887336
$668$	−1.58988e58	−1.96538
$669$	8.98593e57	1.07728
$670$	−1.60371e58	−1.86463
$671$	−2.81798e57	−0.317779
$672$	6.34804e56	0.0694336
$673$	−1.69942e58	−1.80298	−0.901490	−	0.432800i	$-0.857526\pi$
$673$	−1.69942e58	−1.80298	−0.901490	+	0.432800i	$0.857526\pi$
$674$	7.11763e57	0.732500
$675$	8.40628e56	0.0839222
$676$	1.17892e58	1.14176
$677$	−1.85953e57	−0.174717	−0.0873585	−	0.996177i	$-0.527843\pi$
$677$	−1.85953e57	−0.174717	−0.0873585	+	0.996177i	$0.527843\pi$
$678$	1.44616e58	1.31828
$679$	3.20143e57	0.283148
$680$	−5.09902e57	−0.437576
$681$	1.03493e58	0.861776
$682$	−4.11464e58	−3.32470
$683$	−1.28888e58	−1.01062	−0.505312	−	0.862937i	$-0.668623\pi$
$683$	−1.28888e58	−1.01062	−0.505312	+	0.862937i	$0.668623\pi$
$684$	1.62972e58	1.24012
$685$	8.58366e57	0.633893
$686$	−2.54738e58	−1.82579
$687$	−8.34689e57	−0.580646
$688$	1.41711e57	0.0956843
$689$	−4.76979e57	−0.312612
$690$	−3.24368e58	−2.06363
$691$	5.69871e57	0.351947	0.175973	−	0.984395i	$-0.443693\pi$
$691$	5.69871e57	0.351947	0.175973	+	0.984395i	$0.443693\pi$
$692$	5.09001e58	3.05172
$693$	−6.68639e57	−0.389189
$694$	2.13177e58	1.20468
$695$	1.15056e58	0.631276
$696$	−1.01405e57	−0.0540219
$697$	−5.03653e56	−0.0260531
$698$	2.23703e58	1.12366
$699$	−8.20218e57	−0.400080
$700$	1.76630e58	0.836671
$701$	−8.78499e57	−0.404131	−0.202065	−	0.979372i	$-0.564765\pi$
$701$	−8.78499e57	−0.404131	−0.202065	+	0.979372i	$0.564765\pi$
$702$	−9.37672e57	−0.418929
$703$	−3.49762e58	−1.51771
$704$	2.60706e58	1.09878
$705$	1.92748e58	0.789066
$706$	−1.55358e58	−0.617784
$707$	1.68603e57	0.0651280
$708$	−3.21191e58	−1.20526
$709$	4.95487e58	1.80628	0.903139	−	0.429347i	$-0.141256\pi$
$709$	4.95487e58	1.80628	0.903139	+	0.429347i	$0.141256\pi$
$710$	3.81018e57	0.134943
$711$	−9.37000e57	−0.322413
$712$	−2.40369e58	−0.803597
$713$	−8.11589e58	−2.63634
$714$	−6.07566e57	−0.191770
$715$	6.04773e58	1.85489
$716$	3.35198e58	0.999044
$717$	−1.97007e58	−0.570608
$718$	−3.98666e58	−1.12217
$719$	−4.51451e58	−1.23500	−0.617501	−	0.786570i	$-0.711855\pi$
$719$	−4.51451e58	−1.23500	−0.617501	+	0.786570i	$0.711855\pi$
$720$	1.66648e58	0.443081
$721$	4.49436e58	1.16144
$722$	1.62258e59	4.07561
$723$	4.01496e58	0.980271
$724$	−2.28959e58	−0.543397
$725$	−9.79761e56	−0.0226043
$726$	2.39973e58	0.538223
$727$	1.85132e58	0.403669	0.201834	−	0.979420i	$-0.435310\pi$
$727$	1.85132e58	0.403669	0.201834	+	0.979420i	$0.435310\pi$
$728$	−1.00251e59	−2.12517
$729$	1.79701e57	0.0370370
$730$	−8.08083e58	−1.61934
$731$	−8.95569e56	−0.0174499
$732$	1.59132e58	0.301495
$733$	−7.75891e57	−0.142945	−0.0714725	−	0.997443i	$-0.522770\pi$
$733$	−7.75891e57	−0.142945	−0.0714725	+	0.997443i	$0.522770\pi$
$734$	−9.83292e58	−1.76162
$735$	−4.44486e57	−0.0774405
$736$	−1.28931e58	−0.218455
$737$	6.71422e58	1.10640
$738$	4.66740e57	0.0748030
$739$	−1.13939e59	−1.77608	−0.888041	−	0.459764i	$-0.847934\pi$
$739$	−1.13939e59	−1.77608	−0.888041	+	0.459764i	$0.847934\pi$
$740$	−1.33655e59	−2.02645
$741$	−8.93714e58	−1.31803
$742$	2.86408e58	0.410871
$743$	9.08942e58	1.26843	0.634213	−	0.773158i	$-0.281324\pi$
$743$	9.08942e58	1.26843	0.634213	+	0.773158i	$0.281324\pi$
$744$	1.18230e59	1.60503
$745$	−6.04488e58	−0.798333
$746$	1.27875e59	1.64301
$747$	2.07564e58	0.259466
$748$	4.19547e58	0.510267
$749$	−1.34900e59	−1.59638
$750$	−5.90413e58	−0.679829
$751$	1.09322e59	1.22487	0.612433	−	0.790522i	$-0.290191\pi$
$751$	1.09322e59	1.22487	0.612433	+	0.790522i	$0.290191\pi$
$752$	1.16029e59	1.26503
$753$	5.21118e57	0.0552890
$754$	1.09287e58	0.112838
$755$	−1.06383e59	−1.06896
$756$	3.77582e58	0.369245
$757$	−1.50195e59	−1.42951	−0.714757	−	0.699372i	$-0.753463\pi$
$757$	−1.50195e59	−1.42951	−0.714757	+	0.699372i	$0.753463\pi$
$758$	1.12312e59	1.04041
$759$	1.35803e59	1.22448
$760$	4.50378e59	3.95274
$761$	−1.91836e58	−0.163887	−0.0819436	−	0.996637i	$-0.526113\pi$
$761$	−1.91836e58	−0.163887	−0.0819436	+	0.996637i	$0.526113\pi$
$762$	2.56717e58	0.213490
$763$	1.42715e59	1.15536
$764$	−2.68770e59	−2.11820
$765$	−1.05316e58	−0.0808043
$766$	−5.41438e58	−0.404444
$767$	1.76136e59	1.28098
$768$	−1.65351e59	−1.17085
$769$	8.09865e58	0.558371	0.279185	−	0.960237i	$-0.409936\pi$
$769$	8.09865e58	0.558371	0.279185	+	0.960237i	$0.409936\pi$
$770$	−3.63144e59	−2.43792
$771$	−2.08546e58	−0.136329
$772$	−4.07755e58	−0.259564
$773$	−1.75935e59	−1.09062	−0.545310	−	0.838234i	$-0.683588\pi$
$773$	−1.75935e59	−1.09062	−0.545310	+	0.838234i	$0.683588\pi$
$774$	8.29932e57	0.0501017
$775$	1.14232e59	0.671590
$776$	9.47223e58	0.542359
$777$	−8.10345e58	−0.451896
$778$	−3.85046e59	−2.09137
$779$	4.44859e58	0.235345
$780$	−3.41517e59	−1.75984
$781$	−1.59520e58	−0.0800700
$782$	1.23399e59	0.603354
$783$	−2.09443e57	−0.00997587
$784$	−2.67569e58	−0.124153
$785$	3.06740e59	1.38657
$786$	1.97741e59	0.870831
$787$	−1.42029e59	−0.609390	−0.304695	−	0.952450i	$-0.598555\pi$
$787$	−1.42029e59	−0.609390	−0.304695	+	0.952450i	$0.598555\pi$
$788$	−1.43280e59	−0.598961
$789$	1.24664e59	0.507766
$790$	−5.08893e59	−2.01963
$791$	3.19346e59	1.23493
$792$	−1.97834e59	−0.745477
$793$	−8.72652e58	−0.320436
$794$	8.95550e59	3.20457
$795$	4.96462e58	0.173125
$796$	−1.89662e59	−0.644559
$797$	1.77809e59	0.588922	0.294461	−	0.955664i	$-0.404860\pi$
$797$	1.77809e59	0.588922	0.294461	+	0.955664i	$0.404860\pi$
$798$	5.36642e59	1.73231
$799$	−7.33268e58	−0.230703
$800$	1.81472e58	0.0556500
$801$	−4.96462e58	−0.148395
$802$	9.86938e59	2.87551
$803$	3.38319e59	0.960854
$804$	−3.79153e59	−1.04970
$805$	−7.16280e59	−1.93316
$806$	−1.27419e60	−3.35249
$807$	8.81408e57	0.0226084
$808$	4.98855e58	0.124750
$809$	−4.67029e59	−1.13867	−0.569336	−	0.822105i	$-0.692800\pi$
$809$	−4.67029e59	−1.13867	−0.569336	+	0.822105i	$0.692800\pi$
$810$	9.75972e58	0.232004
$811$	−1.45390e59	−0.336983	−0.168492	−	0.985703i	$-0.553890\pi$
$811$	−1.45390e59	−0.336983	−0.168492	+	0.985703i	$0.553890\pi$
$812$	−4.40076e58	−0.0994555
$813$	2.02896e59	0.447112
$814$	8.34416e59	1.79301
$815$	5.32578e59	1.11597
$816$	−6.33974e58	−0.129546
$817$	7.91024e58	0.157630
$818$	−3.86897e59	−0.751887
$819$	−2.07060e59	−0.392442
$820$	1.69995e59	0.314233
$821$	−1.07845e59	−0.194432	−0.0972158	−	0.995263i	$-0.530994\pi$
$821$	−1.07845e59	−0.194432	−0.0972158	+	0.995263i	$0.530994\pi$
$822$	3.02614e59	0.532128
$823$	2.28591e59	0.392069	0.196035	−	0.980597i	$-0.437193\pi$
$823$	2.28591e59	0.392069	0.196035	+	0.980597i	$0.437193\pi$
$824$	1.32977e60	2.22469
$825$	−1.91144e59	−0.311929
$826$	−1.05763e60	−1.68362
$827$	−5.76088e59	−0.894594	−0.447297	−	0.894385i	$-0.647613\pi$
$827$	−5.76088e59	−0.894594	−0.447297	+	0.894385i	$0.647613\pi$
$828$	−7.66881e59	−1.16173
$829$	2.25613e59	0.333424	0.166712	−	0.986006i	$-0.446685\pi$
$829$	2.25613e59	0.333424	0.166712	+	0.986006i	$0.446685\pi$
$830$	1.12730e60	1.62532
$831$	−5.28699e59	−0.743682
$832$	8.07336e59	1.10796
$833$	1.69095e58	0.0226417
$834$	4.05624e59	0.529931
$835$	−9.07477e59	−1.15681
$836$	−3.70571e60	−4.60938
$837$	2.44194e59	0.296390
$838$	1.43940e60	1.70483
$839$	−1.01240e60	−1.17012	−0.585060	−	0.810990i	$-0.698929\pi$
$839$	−1.01240e60	−1.17012	−0.585060	+	0.810990i	$0.698929\pi$
$840$	1.04346e60	1.17693
$841$	−9.06044e59	−0.997313
$842$	−1.04065e60	−1.11791
$843$	−3.90561e59	−0.409472
$844$	2.39527e60	2.45095
$845$	6.72907e59	0.672036
$846$	6.79526e59	0.662390
$847$	5.29916e59	0.504194
$848$	2.98857e59	0.277555
$849$	−9.98295e59	−0.905006
$850$	−1.73685e59	−0.153701
$851$	1.64584e60	1.42177
$852$	9.00815e58	0.0759668
$853$	−1.19199e60	−0.981337	−0.490669	−	0.871346i	$-0.663247\pi$
$853$	−1.19199e60	−0.981337	−0.490669	+	0.871346i	$0.663247\pi$
$854$	5.23995e59	0.421154
$855$	9.30219e59	0.729927
$856$	−3.99136e60	−3.05780
$857$	−1.98782e60	−1.48686	−0.743431	−	0.668813i	$-0.766803\pi$
$857$	−1.98782e60	−1.48686	−0.743431	+	0.668813i	$0.766803\pi$
$858$	2.13210e60	1.55711
$859$	1.93547e60	1.38015	0.690076	−	0.723737i	$-0.257577\pi$
$859$	1.93547e60	1.38015	0.690076	+	0.723737i	$0.257577\pi$
$860$	3.02276e59	0.210468
$861$	1.03067e59	0.0700737
$862$	−2.85014e60	−1.89220
$863$	1.93131e60	1.25208	0.626038	−	0.779793i	$-0.284675\pi$
$863$	1.93131e60	1.25208	0.626038	+	0.779793i	$0.284675\pi$
$864$	3.87932e58	0.0245598
$865$	2.90530e60	1.79622
$866$	6.70421e59	0.404791
$867$	−9.39043e59	−0.553725
$868$	5.13093e60	2.95489
$869$	2.13058e60	1.19837
$870$	−1.13751e59	−0.0624898
$871$	2.07922e60	1.11565
$872$	4.22258e60	2.21305
$873$	1.95641e59	0.100154
$874$	−1.08994e61	−5.45026
$875$	−1.30377e60	−0.636848
$876$	−1.91049e60	−0.911615
$877$	4.31437e59	0.201106	0.100553	−	0.994932i	$-0.467939\pi$
$877$	4.31437e59	0.201106	0.100553	+	0.994932i	$0.467939\pi$
$878$	−1.68358e60	−0.766649
$879$	−6.60534e59	−0.293848
$880$	−3.78928e60	−1.64688
$881$	−1.33549e60	−0.567066	−0.283533	−	0.958962i	$-0.591507\pi$
$881$	−1.33549e60	−0.567066	−0.283533	+	0.958962i	$0.591507\pi$
$882$	−1.56702e59	−0.0650082
$883$	−9.62321e59	−0.390055	−0.195027	−	0.980798i	$-0.562480\pi$
$883$	−9.62321e59	−0.390055	−0.195027	+	0.980798i	$0.562480\pi$
$884$	1.29922e60	0.514533
$885$	−1.83330e60	−0.709410
$886$	−2.14968e60	−0.812796
$887$	−3.90527e60	−1.44283	−0.721417	−	0.692500i	$-0.756509\pi$
$887$	−3.90527e60	−1.44283	−0.721417	+	0.692500i	$0.756509\pi$
$888$	−2.39761e60	−0.865591
$889$	5.66891e59	0.199993
$890$	−2.69633e60	−0.929560
$891$	−4.08609e59	−0.137662
$892$	1.15383e61	3.79892
$893$	6.47670e60	2.08400
$894$	−2.13110e60	−0.670169
$895$	1.91325e60	0.588031
$896$	−5.24810e60	−1.57648
$897$	4.20545e60	1.23472
$898$	4.52515e60	1.29858
$899$	−2.84611e59	−0.0798322
$900$	1.07940e60	0.295944
$901$	−1.88868e59	−0.0506175
$902$	−1.06129e60	−0.278034
$903$	1.83268e59	0.0469341
$904$	9.44865e60	2.36547
$905$	−1.30686e60	−0.319840
$906$	−3.75049e60	−0.897347
$907$	−2.96464e60	−0.693462	−0.346731	−	0.937965i	$-0.612708\pi$
$907$	−2.96464e60	−0.693462	−0.346731	+	0.937965i	$0.612708\pi$
$908$	1.32888e61	3.03898
$909$	1.03034e59	0.0230368
$910$	−1.12456e61	−2.45830
$911$	−7.01681e60	−1.49973	−0.749865	−	0.661591i	$-0.769882\pi$
$911$	−7.01681e60	−1.49973	−0.749865	+	0.661591i	$0.769882\pi$
$912$	5.59967e60	1.17022
$913$	−4.71965e60	−0.964403
$914$	1.48568e61	2.96844
$915$	9.08297e59	0.177458
$916$	−1.07177e61	−2.04760
$917$	4.36657e60	0.815773
$918$	−3.71287e59	−0.0678321
$919$	−6.52121e60	−1.16509	−0.582546	−	0.812798i	$-0.697943\pi$
$919$	−6.52121e60	−1.16509	−0.582546	+	0.812798i	$0.697943\pi$
$920$	−2.11930e61	−3.70289
$921$	1.56723e60	0.267800
$922$	1.96806e61	3.28893
$923$	−4.93992e59	−0.0807394
$924$	−8.58556e60	−1.37244
$925$	−2.31654e60	−0.362188
$926$	1.24700e61	1.90696
$927$	2.74653e60	0.410819
$928$	−4.52140e58	−0.00661514
$929$	−4.97882e60	−0.712532	−0.356266	−	0.934385i	$-0.615950\pi$
$929$	−4.97882e60	−0.712532	−0.356266	+	0.934385i	$0.615950\pi$
$930$	1.32624e61	1.85662
$931$	−1.49356e60	−0.204528
$932$	−1.05319e61	−1.41085
$933$	−1.70758e60	−0.223773
$934$	−2.19366e61	−2.81228
$935$	2.39470e60	0.300340
$936$	−6.12639e60	−0.751708
$937$	9.62681e60	1.15564	0.577818	−	0.816166i	$-0.303904\pi$
$937$	9.62681e60	1.15564	0.577818	+	0.816166i	$0.303904\pi$
$938$	−1.24849e61	−1.46632
$939$	6.94063e60	0.797544
$940$	2.47495e61	2.78257
$941$	−3.82719e60	−0.421010	−0.210505	−	0.977593i	$-0.567511\pi$
$941$	−3.82719e60	−0.421010	−0.210505	+	0.977593i	$0.567511\pi$
$942$	1.08140e61	1.16397
$943$	−2.09332e60	−0.220469
$944$	−1.10360e61	−1.13733
$945$	2.15517e60	0.217335
$946$	−1.88712e60	−0.186222
$947$	8.12706e59	0.0784800	0.0392400	−	0.999230i	$-0.487506\pi$
$947$	8.12706e59	0.0784800	0.0392400	+	0.999230i	$0.487506\pi$
$948$	−1.20314e61	−1.13696
$949$	1.04768e61	0.968886
$950$	1.53410e61	1.38842
$951$	3.05855e60	0.270904
$952$	−3.96960e60	−0.344104
$953$	−3.41043e60	−0.289337	−0.144669	−	0.989480i	$-0.546212\pi$
$953$	−3.41043e60	−0.289337	−0.144669	+	0.989480i	$0.546212\pi$
$954$	1.75026e60	0.145332
$955$	−1.53409e61	−1.24676
$956$	−2.52963e61	−2.01220
$957$	4.76238e59	0.0370791
$958$	−1.94885e61	−1.48520
$959$	6.68241e60	0.498485
$960$	−8.40313e60	−0.613593
$961$	1.91930e61	1.37187
$962$	2.58396e61	1.80800
$963$	−8.24383e60	−0.564664
$964$	5.15535e61	3.45684
$965$	−2.32740e60	−0.152778
$966$	−2.52522e61	−1.62281
$967$	−2.57180e61	−1.61806	−0.809030	−	0.587767i	$-0.800007\pi$
$967$	−2.57180e61	−1.61806	−0.809030	+	0.587767i	$0.800007\pi$
$968$	1.56789e61	0.965765
$969$	−3.53881e60	−0.213413
$970$	1.06254e61	0.627374
$971$	−1.55166e61	−0.897019	−0.448509	−	0.893778i	$-0.648045\pi$
$971$	−1.55166e61	−0.897019	−0.448509	+	0.893778i	$0.648045\pi$
$972$	2.30742e60	0.130608
$973$	8.95711e60	0.496426
$974$	5.85616e61	3.17800
$975$	−5.91923e60	−0.314536
$976$	5.46770e60	0.284501
$977$	4.45394e60	0.226937	0.113469	−	0.993542i	$-0.463804\pi$
$977$	4.45394e60	0.226937	0.113469	+	0.993542i	$0.463804\pi$
$978$	1.87758e61	0.936812
$979$	1.12887e61	0.551567
$980$	−5.70736e60	−0.273087
$981$	8.72140e60	0.408669
$982$	−2.33066e61	−1.06953
$983$	−3.36188e61	−1.51090	−0.755450	−	0.655207i	$-0.772582\pi$
$983$	−3.36188e61	−1.51090	−0.755450	+	0.655207i	$0.772582\pi$
$984$	3.04950e60	0.134224
$985$	−8.17819e60	−0.352545
$986$	4.32739e59	0.0182705
$987$	1.50055e61	0.620510
$988$	−1.14756e62	−4.64791
$989$	−3.72224e60	−0.147666
$990$	−2.21919e61	−0.862330
$991$	5.79150e60	0.220435	0.110218	−	0.993907i	$-0.464845\pi$
$991$	5.79150e60	0.220435	0.110218	+	0.993907i	$0.464845\pi$
$992$	5.27158e60	0.196540
$993$	8.21155e60	0.299893
$994$	2.96624e60	0.106117
$995$	−1.08256e61	−0.379384
$996$	2.66519e61	0.914982
$997$	1.75910e61	0.591615	0.295808	−	0.955248i	$-0.404411\pi$
$997$	1.75910e61	0.591615	0.295808	+	0.955248i	$0.404411\pi$
$998$	−1.06249e61	−0.350065
$999$	−4.95206e60	−0.159843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.42.a.b.1.4	✓	4
3.2	odd	2		9.42.a.c.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.b.1.4	✓	4	1.1	even	1	trivial
9.42.a.c.1.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+2.58383e6 q^{2} +3.48678e9 q^{3} +4.47715e12 q^{4} +2.55548e14 q^{5} +9.00926e15 q^{6} +1.98945e17 q^{7} +5.88630e18 q^{8} +1.21577e19 q^{9} +O(q^{10})\)	\(q+2.58383e6 q^{2} +3.48678e9 q^{3} +4.47715e12 q^{4} +2.55548e14 q^{5} +9.00926e15 q^{6} +1.98945e17 q^{7} +5.88630e18 q^{8} +1.21577e19 q^{9} +6.60294e20 q^{10} -2.76444e21 q^{11} +1.56109e22 q^{12} -8.56075e22 q^{13} +5.14041e23 q^{14} +8.91042e23 q^{15} +5.36384e24 q^{16} -3.38977e24 q^{17} +3.14133e25 q^{18} +2.99407e26 q^{19} +1.14413e27 q^{20} +6.93680e26 q^{21} -7.14285e27 q^{22} -1.40889e28 q^{23} +2.05243e28 q^{24} +1.98303e28 q^{25} -2.21195e29 q^{26} +4.23912e28 q^{27} +8.90709e29 q^{28} -4.94074e28 q^{29} +2.30230e30 q^{30} +5.76050e30 q^{31} +9.15126e29 q^{32} -9.63902e30 q^{33} -8.75860e30 q^{34} +5.08402e31 q^{35} +5.44317e31 q^{36} -1.16818e32 q^{37} +7.73616e32 q^{38} -2.98495e32 q^{39} +1.50424e33 q^{40} +1.48580e32 q^{41} +1.79235e33 q^{42} +2.64197e32 q^{43} -1.23768e34 q^{44} +3.10687e33 q^{45} -3.64032e34 q^{46} +2.16318e34 q^{47} +1.87025e34 q^{48} -4.98839e33 q^{49} +5.12381e34 q^{50} -1.18194e34 q^{51} -3.83278e35 q^{52} +5.57170e34 q^{53} +1.09532e35 q^{54} -7.06449e35 q^{55} +1.17105e36 q^{56} +1.04397e36 q^{57} -1.27660e35 q^{58} -2.05748e36 q^{59} +3.98933e36 q^{60} +1.01936e36 q^{61} +1.48842e37 q^{62} +2.41871e36 q^{63} -9.43067e36 q^{64} -2.18769e37 q^{65} -2.49056e37 q^{66} -2.42878e37 q^{67} -1.51765e37 q^{68} -4.91248e37 q^{69} +1.31362e38 q^{70} +5.77043e36 q^{71} +7.15637e37 q^{72} -1.22382e38 q^{73} -3.01839e38 q^{74} +6.91439e37 q^{75} +1.34049e39 q^{76} -5.49973e38 q^{77} -7.71260e38 q^{78} -7.70707e38 q^{79} +1.37072e39 q^{80} +1.47809e38 q^{81} +3.83906e38 q^{82} +1.70727e39 q^{83} +3.10571e39 q^{84} -8.66251e38 q^{85} +6.82641e38 q^{86} -1.72273e38 q^{87} -1.62723e40 q^{88} -4.08353e39 q^{89} +8.02763e39 q^{90} -1.70312e40 q^{91} -6.30780e40 q^{92} +2.00856e40 q^{93} +5.58928e40 q^{94} +7.65129e40 q^{95} +3.19085e39 q^{96} +1.60920e40 q^{97} -1.28891e40 q^{98} -3.36092e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 48\!\cdots\!04 q^{9}+O(q^{10}) \) 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9	\( 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 88\!\cdots\!56 q^{99}+O(q^{100}) \) 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9 + 725751018728422700940 * q^10 + 724810647231440683056 * q^11 + 18664574152458657849732 * q^12 - 8843977274373065537608 * q^13 + 493449664223337937919568 * q^14 + 413312836237035157808280 * q^15 - 5962194966280197033033200 * q^16 - 38231582029295844707285688 * q^17 - 848872517682272882743422 * q^18 + 261842746845948075837831248 * q^19 + 785441926018305471679038360 * q^20 + 523911200567235135430405536 * q^21 - 6322149663566345845522943976 * q^22 - 15395573913207335266380880032 * q^23 + 21895702846052864805196365384 * q^24 + 117350921958371528604086683900 * q^25 - 62942545095927728709970694052 * q^26 + 169564633100864814057177732804 * q^27 + 684437536459146482218511575712 * q^28 - 1036098964520685524199931325064 * q^29 + 2530537331112123128971880036940 * q^30 + 9280613209905247622577480610304 * q^31 + 19645397922916950127447685511456 * q^32 + 2527258458445301210436445809456 * q^33 + 92420157643501864091330064020004 * q^34 + 207436667553525639419383641992640 * q^35 + 65079346006100643987841739630532 * q^36 + 200754880510048713109452091192856 * q^37 + 1146938682238729575315585266559528 * q^38 - 30837042003082501971082253252808 * q^39 + 2565083222429486590317315499815600 * q^40 + 2357905268481965433001096926030504 * q^41 + 1720552591892622502089456095058768 * q^42 + 3943358618915609696106480688157360 * q^43 - 18494278585991583572852191821764304 * q^44 + 1441132750124361726734484052640280 * q^45 - 44252120640849956767942988241684816 * q^46 - 8890000412230234893665157147040320 * q^47 - 20788888404146512009986643475113200 * q^48 - 33104900387055220681685954563991580 * q^49 - 216323679312314207800001999371642050 * q^50 - 133305283845300676339482147968952888 * q^51 - 596234086188669794371774262733483208 * q^52 + 95704753827317216756019399314791128 * q^53 - 2959835453092145761775065914960222 * q^54 + 1291057043675253444545805475556816160 * q^55 + 1940580325939766339139469085046208320 * q^56 + 912989205217443700887315001196762448 * q^57 + 3859053206955865617315425524661917116 * q^58 - 1809289331104083090977131835906657808 * q^59 + 2738666655532023559103418232328622360 * q^60 + 5381027332088000515346282395501157240 * q^61 + 14109494547714507002913033009898657152 * q^62 + 1826765401647017821917860444028843936 * q^63 - 389844533130084697385386794140537792 * q^64 - 9754648834359651370261564655441346480 * q^65 - 22043972827710532722740556743113718376 * q^66 - 73273159367285254897696664016673247728 * q^67 - 89019363361032581039655795923994746424 * q^68 - 53681046965013864485594032220229980832 * q^69 - 127374089191018487217525315519713602080 * q^70 - 84396091414708989106237239330896374752 * q^71 + 76345595132548433424120590562827574984 * q^72 - 44706579271813174655854382994714255832 * q^73 - 299692406925616462116506150539738813812 * q^74 + 409177364127418217299254754274337843900 * q^75 + 1128262001217587654782588548338718696272 * q^76 + 833312137190144115784050615522845895552 * q^77 - 219467084399719853089285669187657082852 * q^78 + 1416534390331633014953369475707893311680 * q^79 + 1539903590051088861086709486592809053280 * q^80 + 591235317657383693264332840825533190404 * q^81 + 613971248288365719286532695984150451412 * q^82 + 1526205590962076227407755639349783073104 * q^83 + 2386486125584620727973530035630532068512 * q^84 - 285377453319367852617718519171747770960 * q^85 - 12934468921257599734617599325958640634024 * q^86 - 3612653707382978727606828549504415526664 * q^87 - 13219976774504188013705589441700285953696 * q^88 - 39593715237961905051969833281675978558872 * q^89 + 8823438092269922908090462480445695772940 * q^90 - 8845052344004724172694600210873108791616 * q^91 - 65206363053810587386463980322833360400544 * q^92 + 32359497372012156098445494805887947067904 * q^93 + 98582759073905793403791649187553312740832 * q^94 + 7880313586718908134850457997267850706400 * q^95 + 68499267029064622122879551784898487597856 * q^96 + 36750128325858234547252025624989137001352 * q^97 - 68350119771260167200829379908744318383822 * q^98 + 8812005370202382972296217650292999095856 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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