LMFDB - Embedded newform 1.70.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1,70,Mod(1,1)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1.1"); S:= CuspForms(chi, 70); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 70, names="a")

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 70 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$30.1514953292$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots - 94\!\cdots\!36 $ x^5 - x^4 - 24985894640345560x^3 - 309075533549354721261224x^2 + 93046016582444120336711740360848*x - 941262570723617919770907675844106102736
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{43}\cdot 3^{17}\cdot 5^{5}\cdot 7^{2}\cdot 17\cdot 23 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.52577e8$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.75433e10 q^{2} -9.70523e15 q^{3} +1.67007e21 q^{4} -1.40726e24 q^{5} +4.61419e26 q^{6} -1.18429e27 q^{7} -5.13361e31 q^{8} -7.40194e32 q^{9} +6.69057e34 q^{10} +2.72474e34 q^{11} -1.62084e37 q^{12} +4.14237e38 q^{13} +5.63052e37 q^{14} +1.36578e40 q^{15} +1.45485e42 q^{16} -7.81618e41 q^{17} +3.51913e43 q^{18} +6.36441e43 q^{19} -2.35022e45 q^{20} +1.14938e43 q^{21} -1.29543e45 q^{22} +8.76109e46 q^{23} +4.98228e47 q^{24} +2.86308e47 q^{25} -1.96942e49 q^{26} +1.52816e49 q^{27} -1.97785e48 q^{28} +5.98090e49 q^{29} -6.49335e50 q^{30} +1.30933e51 q^{31} -3.88650e52 q^{32} -2.64442e50 q^{33} +3.71607e52 q^{34} +1.66661e51 q^{35} -1.23618e54 q^{36} +1.23271e54 q^{37} -3.02585e54 q^{38} -4.02026e54 q^{39} +7.22431e55 q^{40} +1.03929e55 q^{41} -5.46455e53 q^{42} -2.30147e56 q^{43} +4.55051e55 q^{44} +1.04164e57 q^{45} -4.16531e57 q^{46} +5.31802e57 q^{47} -1.41197e58 q^{48} -2.04991e58 q^{49} -1.36120e58 q^{50} +7.58578e57 q^{51} +6.91804e59 q^{52} -2.46445e59 q^{53} -7.26540e59 q^{54} -3.83441e58 q^{55} +6.07970e58 q^{56} -6.17680e59 q^{57} -2.84352e60 q^{58} -7.33567e60 q^{59} +2.28094e61 q^{60} -4.55049e61 q^{61} -6.22497e61 q^{62} +8.76606e59 q^{63} +9.88976e62 q^{64} -5.82938e62 q^{65} +1.25725e61 q^{66} -9.77457e62 q^{67} -1.30536e63 q^{68} -8.50284e62 q^{69} -7.92359e61 q^{70} -1.10646e64 q^{71} +3.79986e64 q^{72} +3.21128e63 q^{73} -5.86072e64 q^{74} -2.77868e63 q^{75} +1.06290e65 q^{76} -3.22689e61 q^{77} +1.91137e65 q^{78} +3.60745e65 q^{79} -2.04735e66 q^{80} +4.69295e65 q^{81} -4.94112e65 q^{82} +1.23807e66 q^{83} +1.91955e64 q^{84} +1.09994e66 q^{85} +1.09419e67 q^{86} -5.80460e65 q^{87} -1.39877e66 q^{88} -1.50302e67 q^{89} -4.95232e67 q^{90} -4.90578e65 q^{91} +1.46316e68 q^{92} -1.27073e67 q^{93} -2.52836e68 q^{94} -8.95636e67 q^{95} +3.77193e68 q^{96} -4.11315e68 q^{97} +9.74596e68 q^{98} -2.01684e67 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3} + 12\!\cdots\!60 q^{4} - 18\!\cdots\!50 q^{5} + 65\!\cdots\!60 q^{6} + 76\!\cdots\!92 q^{7} - 45\!\cdots\!00 q^{8} - 31\!\cdots\!35 q^{9} + 44\!\cdots\!00 q^{10}+ \cdots + 58\!\cdots\!80 q^{99}+O(q^{100}) $ 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9 + 44330196388334747724288536990904000 * q^10 - 60667038452283127772973811588820340 * q^11 - 11483075252723727688688753994339790848 * q^12 + 241757308976474000869098277194908009686 * q^13 + 354251192093531665156722201608564593920 * q^14 - 22070061029664005246083216762166031993000 * q^15 + 959158246463054504693505368032717942292480 * q^16 - 3406116484103989032025799295223462139713638 * q^17 + 24028760578245796491398335690330074428977056 * q^18 + 50409644862695734347948203723209710229820500 * q^19 - 1423124021474831957749573329409407107348736000 * q^20 + 3013464004165585730133470747616333350946636960 * q^21 - 11532803895526133094453480299474752792963837056 * q^22 + 49597077165419749499080141147449313474867772376 * q^23 - 3758573903021835292505270073849755869023436800 * q^24 + 464109230075747674561453215791202707168413296875 * q^25 - 16366243363702391437841515238911258759405955787840 * q^26 - 4656668144254073384201536267744600116223141335000 * q^27 - 145657936238300983941227399236934030905596038045696 * q^28 - 623609331535478016897341347681349171717970694417050 * q^29 - 3363430262026080628144709187077082169492181498016000 * q^30 - 7773979811443490840377264327630961134705736859811040 * q^31 - 59446525385187765185716890552455969166501734680363008 * q^32 - 114056291760419605293140369499335251414708842916007568 * q^33 - 257146382902997900108453969123952433606251002004626880 * q^34 - 746713702965644817139124842748848714607056852166946000 * q^35 - 2051949564713522439077005513759167028086223411246648320 * q^36 + 1173349927804932358065167442366744839628119054724224302 * q^37 + 118225357325580676139934406348110667239400005459024000 * q^38 + 14057637047001351842470294363781888979755467326981836280 * q^39 + 113448309945374158392264311043353386142011790732943360000 * q^40 + 126046983235211396249316718220813524712126370275682679410 * q^41 + 293618058653079520265272756273690037096976372387400909824 * q^42 + 182990795236310295463906097926157021228111368794869386156 * q^43 - 207861964397629572369029141530074424104092312018072801280 * q^44 - 1643209216033810606361059101690783215624601629799145190250 * q^45 - 10254004636983168196931301388746633342901210187441053098240 * q^46 - 10227620449924872974485942387482033943920758356350760046928 * q^47 - 32395077603800850016659260748043884333789001078303069569024 * q^48 - 18333133463047872956569862100374253860638045246565546349315 * q^49 + 36528582075561740316450944849185458926809558787823115500000 * q^50 + 118668467511484226348705374365583184000267089107653013314760 * q^51 + 942523544779067327174672695236090488789159958525129397368832 * q^52 + 632699876044410239466855544904774161379655010323706866957246 * q^53 + 180558070990413352422035814551902697653880540863671629472000 * q^54 + 908306905388987301982805388456202130484984202488366374469000 * q^55 - 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 10204523476105540193819201045109650965597050176490899356681200 * q^57 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 - 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 4120988224178099264267892216282931461935581678787045796864000 * q^60 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 + 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 328016742630707922691415372382087941549150107260006661759940136 * q^63 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 + 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 338570852359916448113902185281844117937336911423509879777978880 * q^66 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 - 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 6814317814451425604632002110369996993863432815743912687188684320 * q^69 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 - 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33340305480431860824635017027459448788044465030309454443456921600 * q^72 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 + 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 133279503236831559979066107911998455423803652698542098545072437500 * q^75 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 - 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 57072566318401512231072936702879380800620122459787990692269387008 * q^78 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 - 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 1101671322957552996191157562976784281568686466036132881049220065795 * q^81 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 + 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 2982792317318014581404535874546389828859810656181796104246410117120 * q^84 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 + 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 12567354207673775260644045622671132292173268168085315900596903577400 * q^87 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 - 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 85191607767474905371023384802405560846731062106202026396755774248000 * q^90 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 - 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 112906043990099714252090302813260364787306717550744493130306572821888 * q^93 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 + 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 782790419970794266899143250915194035456012168622622133055202797813760 * q^96 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 + 1783735577381778172290937711296356094085482547558896852990197505179424 * q^98 + 586262466890180722819447934223042169763434625676688596008715148885980 * q^99

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 $

$2$	−4.75433e10	−1.95684	−0.978418	−	0.206634i	$-0.933749\pi$
$2$	−4.75433e10	−1.95684	−0.978418	+	0.206634i	$0.933749\pi$
$3$	−9.70523e15	−0.335987	−0.167994	−	0.985788i	$-0.553729\pi$
$3$	−9.70523e15	−0.335987	−0.167994	+	0.985788i	$0.553729\pi$
$4$	1.67007e21	2.82921
$5$	−1.40726e24	−1.08121	−0.540603	−	0.841278i	$-0.681804\pi$
$5$	−1.40726e24	−1.08121	−0.540603	+	0.841278i	$0.681804\pi$
$6$	4.61419e26	0.657472
$7$	−1.18429e27	−0.00827136	−0.00413568	−	0.999991i	$-0.501316\pi$
$7$	−1.18429e27	−0.00827136	−0.00413568	+	0.999991i	$0.501316\pi$
$8$	−5.13361e31	−3.57946
$9$	−7.40194e32	−0.887113
$10$	6.69057e34	2.11574
$11$	2.72474e34	0.0321572	0.0160786	−	0.999871i	$-0.494882\pi$
$11$	2.72474e34	0.0321572	0.0160786	+	0.999871i	$0.494882\pi$
$12$	−1.62084e37	−0.950578
$13$	4.14237e38	1.53533	0.767667	−	0.640849i	$-0.221418\pi$
$13$	4.14237e38	1.53533	0.767667	+	0.640849i	$0.221418\pi$
$14$	5.63052e37	0.0161857
$15$	1.36578e40	0.363271
$16$	1.45485e42	4.17522
$17$	−7.81618e41	−0.277017	−0.138509	−	0.990361i	$-0.544231\pi$
$17$	−7.81618e41	−0.277017	−0.138509	+	0.990361i	$0.544231\pi$
$18$	3.51913e43	1.73593
$19$	6.36441e43	0.486137	0.243069	−	0.970009i	$-0.421846\pi$
$19$	6.36441e43	0.486137	0.243069	+	0.970009i	$0.421846\pi$
$20$	−2.35022e45	−3.05896
$21$	1.14938e43	0.00277907
$22$	−1.29543e45	−0.0629263
$23$	8.76109e46	0.918222	0.459111	−	0.888379i	$-0.348168\pi$
$23$	8.76109e46	0.918222	0.459111	+	0.888379i	$0.348168\pi$
$24$	4.98228e47	1.20265
$25$	2.86308e47	0.169006
$26$	−1.96942e49	−3.00440
$27$	1.52816e49	0.634045
$28$	−1.97785e48	−0.0234014
$29$	5.98090e49	0.210880	0.105440	−	0.994426i	$-0.466375\pi$
$29$	5.98090e49	0.210880	0.105440	+	0.994426i	$0.466375\pi$
$30$	−6.49335e50	−0.710862
$31$	1.30933e51	0.462455	0.231228	−	0.972900i	$-0.425726\pi$
$31$	1.30933e51	0.462455	0.231228	+	0.972900i	$0.425726\pi$
$32$	−3.88650e52	−4.59075
$33$	−2.64442e50	−0.0108044
$34$	3.71607e52	0.542077
$35$	1.66661e51	0.00894304
$36$	−1.23618e54	−2.50983
$37$	1.23271e54	0.972528	0.486264	−	0.873812i	$-0.338359\pi$
$37$	1.23271e54	0.972528	0.486264	+	0.873812i	$0.338359\pi$
$38$	−3.02585e54	−0.951291
$39$	−4.02026e54	−0.515852
$40$	7.22431e55	3.87014
$41$	1.03929e55	0.237516	0.118758	−	0.992923i	$-0.462109\pi$
$41$	1.03929e55	0.237516	0.118758	+	0.992923i	$0.462109\pi$
$42$	−5.46455e53	−0.00543819
$43$	−2.30147e56	−1.01705	−0.508525	−	0.861047i	$-0.669809\pi$
$43$	−2.30147e56	−1.01705	−0.508525	+	0.861047i	$0.669809\pi$
$44$	4.55051e55	0.0909793
$45$	1.04164e57	0.959152
$46$	−4.16531e57	−1.79681
$47$	5.31802e57	1.09238	0.546190	−	0.837662i	$-0.316078\pi$
$47$	5.31802e57	1.09238	0.546190	+	0.837662i	$0.316078\pi$
$48$	−1.41197e58	−1.40282
$49$	−2.04991e58	−0.999932
$50$	−1.36120e58	−0.330718
$51$	7.58578e57	0.0930742
$52$	6.91804e59	4.34378
$53$	−2.46445e59	−0.802051	−0.401026	−	0.916067i	$-0.631346\pi$
$53$	−2.46445e59	−0.802051	−0.401026	+	0.916067i	$0.631346\pi$
$54$	−7.26540e59	−1.24072
$55$	−3.83441e58	−0.0347685
$56$	6.07970e58	0.0296070
$57$	−6.17680e59	−0.163336
$58$	−2.84352e60	−0.412658
$59$	−7.33567e60	−0.590263	−0.295132	−	0.955457i	$-0.595363\pi$
$59$	−7.33567e60	−0.590263	−0.295132	+	0.955457i	$0.595363\pi$
$60$	2.28094e61	1.02777
$61$	−4.55049e61	−1.15926	−0.579628	−	0.814881i	$-0.696802\pi$
$61$	−4.55049e61	−1.15926	−0.579628	+	0.814881i	$0.696802\pi$
$62$	−6.22497e61	−0.904949
$63$	8.76606e59	0.00733763
$64$	9.88976e62	4.80814
$65$	−5.82938e62	−1.66001
$66$	1.25725e61	0.0211424
$67$	−9.77457e62	−0.978401	−0.489201	−	0.872171i	$-0.662711\pi$
$67$	−9.77457e62	−0.978401	−0.489201	+	0.872171i	$0.662711\pi$
$68$	−1.30536e63	−0.783740
$69$	−8.50284e62	−0.308511
$70$	−7.92359e61	−0.0175001
$71$	−1.10646e64	−1.49804	−0.749018	−	0.662550i	$-0.769474\pi$
$71$	−1.10646e64	−1.49804	−0.749018	+	0.662550i	$0.769474\pi$
$72$	3.79986e64	3.17539
$73$	3.21128e63	0.166740	0.0833699	−	0.996519i	$-0.473432\pi$
$73$	3.21128e63	0.166740	0.0833699	+	0.996519i	$0.473432\pi$
$74$	−5.86072e64	−1.90308
$75$	−2.77868e63	−0.0567839
$76$	1.06290e65	1.37538
$77$	−3.22689e61	−0.000265983 0
$78$	1.91137e65	1.00944
$79$	3.60745e65	1.22762	0.613812	−	0.789453i	$-0.289635\pi$
$79$	3.60745e65	1.22762	0.613812	+	0.789453i	$0.289635\pi$
$80$	−2.04735e66	−4.51427
$81$	4.69295e65	0.674082
$82$	−4.94112e65	−0.464780
$83$	1.23807e66	0.766569	0.383285	−	0.923630i	$-0.374793\pi$
$83$	1.23807e66	0.766569	0.383285	+	0.923630i	$0.374793\pi$
$84$	1.91955e64	0.00786257
$85$	1.09994e66	0.299513
$86$	1.09419e67	1.99020
$87$	−5.80460e65	−0.0708530
$88$	−1.39877e66	−0.115105
$89$	−1.50302e67	−0.837545	−0.418773	−	0.908091i	$-0.637540\pi$
$89$	−1.50302e67	−0.837545	−0.418773	+	0.908091i	$0.637540\pi$
$90$	−4.95232e67	−1.87690
$91$	−4.90578e65	−0.0126993
$92$	1.46316e68	2.59784
$93$	−1.27073e67	−0.155379
$94$	−2.52836e68	−2.13761
$95$	−8.95636e67	−0.525614
$96$	3.77193e68	1.54243
$97$	−4.11315e68	−1.17639	−0.588194	−	0.808720i	$-0.700161\pi$
$97$	−4.11315e68	−1.17639	−0.588194	+	0.808720i	$0.700161\pi$
$98$	9.74596e68	1.95670
$99$	−2.01684e67	−0.0285270
$100$	4.78154e68	0.478154
$101$	−1.18761e68	−0.0842530	−0.0421265	−	0.999112i	$-0.513413\pi$
$101$	−1.18761e68	−0.0842530	−0.0421265	+	0.999112i	$0.513413\pi$
$102$	−3.60653e68	−0.182131
$103$	4.66232e69	1.68158	0.840791	−	0.541360i	$-0.182090\pi$
$103$	4.66232e69	1.68158	0.840791	+	0.541360i	$0.182090\pi$
$104$	−2.12653e70	−5.49567
$105$	−1.61748e67	−0.00300475
$106$	1.17168e70	1.56948
$107$	1.24749e70	1.20864	0.604318	−	0.796743i	$-0.293446\pi$
$107$	1.24749e70	1.20864	0.604318	+	0.796743i	$0.293446\pi$
$108$	2.55214e70	1.79385
$109$	−2.39650e70	−1.22564	−0.612820	−	0.790222i	$-0.709965\pi$
$109$	−2.39650e70	−1.22564	−0.612820	+	0.790222i	$0.709965\pi$
$110$	1.82301e69	0.0680363
$111$	−1.19637e70	−0.326757
$112$	−1.72297e69	−0.0345347
$113$	1.93197e70	0.284966	0.142483	−	0.989797i	$-0.454491\pi$
$113$	1.93197e70	0.284966	0.142483	+	0.989797i	$0.454491\pi$
$114$	2.93666e70	0.319621
$115$	−1.23291e71	−0.992787
$116$	9.98852e70	0.596624
$117$	−3.06615e71	−1.36201
$118$	3.48762e71	1.15505
$119$	9.25665e68	0.00229131
$120$	−7.01135e71	−1.30032
$121$	−7.17209e71	−0.998966
$122$	2.16346e72	2.26847
$123$	−1.00865e71	−0.0798023
$124$	2.18667e72	1.30838
$125$	1.98108e72	0.898475
$126$	−4.16768e70	−0.0143585
$127$	−1.49058e72	−0.390956	−0.195478	−	0.980708i	$-0.562626\pi$
$127$	−1.49058e72	−0.390956	−0.195478	+	0.980708i	$0.562626\pi$
$128$	−2.40774e73	−4.81799
$129$	2.23362e72	0.341716
$130$	2.77148e73	3.24837
$131$	−1.53034e73	−1.37698	−0.688492	−	0.725244i	$-0.741727\pi$
$131$	−1.53034e73	−1.37698	−0.688492	+	0.725244i	$0.741727\pi$
$132$	−4.41637e71	−0.0305679
$133$	−7.53733e70	−0.00402102
$134$	4.64716e73	1.91457
$135$	−2.15052e73	−0.685534
$136$	4.01252e73	0.991573
$137$	−6.90072e73	−1.32445	−0.662223	−	0.749306i	$-0.730387\pi$
$137$	−6.90072e73	−1.32445	−0.662223	+	0.749306i	$0.730387\pi$
$138$	4.04253e73	0.603705
$139$	−1.02770e74	−1.19634	−0.598169	−	0.801370i	$-0.704105\pi$
$139$	−1.02770e74	−1.19634	−0.598169	+	0.801370i	$0.704105\pi$
$140$	2.78335e72	0.0253017
$141$	−5.16126e73	−0.367025
$142$	5.26047e74	2.93141
$143$	1.12869e73	0.0493720
$144$	−1.07687e75	−3.70389
$145$	−8.41667e73	−0.228005
$146$	−1.52675e74	−0.326283
$147$	1.98949e74	0.335964
$148$	2.05871e75	2.75148
$149$	−1.83242e74	−0.194133	−0.0970663	−	0.995278i	$-0.530946\pi$
$149$	−1.83242e74	−0.194133	−0.0970663	+	0.995278i	$0.530946\pi$
$150$	1.32108e74	0.111117
$151$	1.98978e75	1.33076	0.665382	−	0.746503i	$-0.268269\pi$
$151$	1.98978e75	1.33076	0.665382	+	0.746503i	$0.268269\pi$
$152$	−3.26724e75	−1.74011
$153$	5.78549e74	0.245746
$154$	1.53417e72	0.000520486 0
$155$	−1.84256e75	−0.500009
$156$	−6.71412e75	−1.45945
$157$	3.13434e75	0.546523	0.273261	−	0.961940i	$-0.411898\pi$
$157$	3.13434e75	0.546523	0.273261	+	0.961940i	$0.411898\pi$
$158$	−1.71510e76	−2.40226
$159$	2.39180e75	0.269479
$160$	5.46930e76	4.96355
$161$	−1.03757e74	−0.00759495
$162$	−2.23118e76	−1.31907
$163$	−2.16359e76	−1.03444	−0.517218	−	0.855854i	$-0.673032\pi$
$163$	−2.16359e76	−1.03444	−0.517218	+	0.855854i	$0.673032\pi$
$164$	1.73568e76	0.671983
$165$	3.72139e74	0.0116818
$166$	−5.88620e76	−1.50005
$167$	5.73499e76	1.18799	0.593997	−	0.804467i	$-0.297549\pi$
$167$	5.73499e76	1.18799	0.593997	+	0.804467i	$0.297549\pi$
$168$	−5.90048e74	−0.00994758
$169$	9.87987e76	1.35725
$170$	−5.22947e76	−0.586097
$171$	−4.71090e76	−0.431258
$172$	−3.84361e77	−2.87745
$173$	2.41165e77	1.47817	0.739085	−	0.673613i	$-0.235258\pi$
$173$	2.41165e77	1.47817	0.739085	+	0.673613i	$0.235258\pi$
$174$	2.75970e76	0.138648
$175$	−3.39072e74	−0.00139791
$176$	3.96409e76	0.134263
$177$	7.11944e76	0.198321
$178$	7.14584e77	1.63894
$179$	−5.78963e77	−1.09451	−0.547257	−	0.836965i	$-0.684328\pi$
$179$	−5.78963e77	−1.09451	−0.547257	+	0.836965i	$0.684328\pi$
$180$	1.73962e78	2.71364
$181$	−1.16858e78	−1.50573	−0.752863	−	0.658177i	$-0.771328\pi$
$181$	−1.16858e78	−1.50573	−0.752863	+	0.658177i	$0.771328\pi$
$182$	2.33237e76	0.0248505
$183$	4.41636e77	0.389495
$184$	−4.49760e78	−3.28674
$185$	−1.73474e78	−1.05150
$186$	6.04148e77	0.304051
$187$	−2.12971e76	−0.00890809
$188$	8.88146e78	3.09057
$189$	−1.80980e76	−0.00524442
$190$	4.25815e78	1.02854
$191$	−5.94585e78	−1.19829	−0.599146	−	0.800640i	$-0.704493\pi$
$191$	−5.94585e78	−1.19829	−0.599146	+	0.800640i	$0.704493\pi$
$192$	−9.59824e78	−1.61547
$193$	1.93367e78	0.272055	0.136027	−	0.990705i	$-0.456567\pi$
$193$	1.93367e78	0.272055	0.136027	+	0.990705i	$0.456567\pi$
$194$	1.95553e79	2.30200
$195$	5.65754e78	0.557742
$196$	−3.42350e79	−2.82902
$197$	9.34495e78	0.647877	0.323938	−	0.946078i	$-0.394993\pi$
$197$	9.34495e78	0.647877	0.323938	+	0.946078i	$0.394993\pi$
$198$	9.58871e77	0.0558227
$199$	2.69839e78	0.132030	0.0660152	−	0.997819i	$-0.478971\pi$
$199$	2.69839e78	0.132030	0.0660152	+	0.997819i	$0.478971\pi$
$200$	−1.46979e79	−0.604952
$201$	9.48645e78	0.328730
$202$	5.64627e78	0.164869
$203$	−7.08314e76	−0.00174427
$204$	1.26688e79	0.263326
$205$	−1.46255e79	−0.256804
$206$	−2.21662e80	−3.29058
$207$	−6.48490e79	−0.814567
$208$	6.02652e80	6.41035
$209$	1.73414e78	0.0156328
$210$	7.69003e77	0.00587980
$211$	7.71421e79	0.500665	0.250332	−	0.968160i	$-0.419460\pi$
$211$	7.71421e79	0.500665	0.250332	+	0.968160i	$0.419460\pi$
$212$	−4.11580e80	−2.26917
$213$	1.07384e80	0.503321
$214$	−5.93096e80	−2.36510
$215$	3.23875e80	1.09964
$216$	−7.84500e80	−2.26954
$217$	−1.55063e78	−0.00382513
$218$	1.13937e81	2.39838
$219$	−3.11662e79	−0.0560224
$220$	−6.40374e79	−0.0983674
$221$	−3.23775e80	−0.425314
$222$	5.68796e80	0.639409
$223$	1.62026e81	1.55980	0.779898	−	0.625907i	$-0.215271\pi$
$223$	1.62026e81	1.55980	0.779898	+	0.625907i	$0.215271\pi$
$224$	4.60275e79	0.0379718
$225$	−2.11923e80	−0.149928
$226$	−9.18520e80	−0.557632
$227$	−2.43804e81	−1.27101	−0.635505	−	0.772097i	$-0.719208\pi$
$227$	−2.43804e81	−1.27101	−0.635505	+	0.772097i	$0.719208\pi$
$228$	−1.03157e81	−0.462111
$229$	−1.14930e81	−0.442701	−0.221351	−	0.975194i	$-0.571047\pi$
$229$	−1.14930e81	−0.442701	−0.221351	+	0.975194i	$0.571047\pi$
$230$	5.86167e81	1.94272
$231$	3.13177e77	8.93670e−5 0
$232$	−3.07036e81	−0.754838
$233$	−4.64743e81	−0.984994	−0.492497	−	0.870314i	$-0.663916\pi$
$233$	−4.64743e81	−0.984994	−0.492497	+	0.870314i	$0.663916\pi$
$234$	1.45775e82	2.66524
$235$	−7.48382e81	−1.18109
$236$	−1.22511e82	−1.66998
$237$	−3.50111e81	−0.412465
$238$	−4.40092e79	−0.00448372
$239$	1.79106e81	0.157900	0.0789500	−	0.996879i	$-0.474843\pi$
$239$	1.79106e81	0.157900	0.0789500	+	0.996879i	$0.474843\pi$
$240$	1.98700e82	1.51674
$241$	2.19407e82	1.45098	0.725490	−	0.688232i	$-0.241613\pi$
$241$	2.19407e82	1.45098	0.725490	+	0.688232i	$0.241613\pi$
$242$	3.40985e82	1.95481
$243$	−1.73054e82	−0.860528
$244$	−7.59965e82	−3.27978
$245$	2.88475e82	1.08113
$246$	4.79547e81	0.156160
$247$	2.63637e82	0.746383
$248$	−6.72157e82	−1.65534
$249$	−1.20158e82	−0.257557
$250$	−9.41870e82	−1.75817
$251$	5.39936e82	0.878211	0.439105	−	0.898436i	$-0.355295\pi$
$251$	5.39936e82	0.878211	0.439105	+	0.898436i	$0.355295\pi$
$252$	1.46399e81	0.0207597
$253$	2.38717e81	0.0295274
$254$	7.08673e82	0.765038
$255$	−1.06751e82	−0.100632
$256$	5.60930e83	4.61987
$257$	−1.14417e83	−0.823752	−0.411876	−	0.911240i	$-0.635126\pi$
$257$	−1.14417e83	−0.823752	−0.411876	+	0.911240i	$0.635126\pi$
$258$	−1.06194e83	−0.668682
$259$	−1.45989e81	−0.00804413
$260$	−9.73547e83	−4.69652
$261$	−4.42702e82	−0.187074
$262$	7.27575e83	2.69453
$263$	−7.65214e82	−0.248490	−0.124245	−	0.992252i	$-0.539651\pi$
$263$	−7.65214e82	−0.248490	−0.124245	+	0.992252i	$0.539651\pi$
$264$	1.35754e82	0.0386739
$265$	3.46811e83	0.867182
$266$	3.58349e81	0.00786847
$267$	1.45871e83	0.281404
$268$	−1.63242e84	−2.76810
$269$	2.43965e83	0.363810	0.181905	−	0.983316i	$-0.441774\pi$
$269$	2.43965e83	0.363810	0.181905	+	0.983316i	$0.441774\pi$
$270$	1.02243e84	1.34148
$271$	−9.89400e82	−0.114270	−0.0571349	−	0.998366i	$-0.518197\pi$
$271$	−9.89400e82	−0.114270	−0.0571349	+	0.998366i	$0.518197\pi$
$272$	−1.13714e84	−1.15661
$273$	4.76117e81	0.00426680
$274$	3.28083e84	2.59173
$275$	7.80114e81	0.00543476
$276$	−1.42003e84	−0.872842
$277$	−2.18243e84	−1.18410	−0.592050	−	0.805901i	$-0.701681\pi$
$277$	−2.18243e84	−1.18410	−0.592050	+	0.805901i	$0.701681\pi$
$278$	4.88600e84	2.34104
$279$	−9.69155e83	−0.410250
$280$	−8.55570e82	−0.0320113
$281$	2.98947e81	0.000989067 0	0.000494533	−	1.00000i	$-0.499843\pi$
$281$	2.98947e81	0.000989067 0	0.000494533		1.00000i	$0.499843\pi$
$282$	2.45383e84	0.718209
$283$	−2.71964e84	−0.704498	−0.352249	−	0.935906i	$-0.614583\pi$
$283$	−2.71964e84	−0.704498	−0.352249	+	0.935906i	$0.614583\pi$
$284$	−1.84786e85	−4.23826
$285$	8.69235e83	0.176600
$286$	−5.36615e83	−0.0966129
$287$	−1.23082e82	−0.00196458
$288$	2.87676e85	4.07252
$289$	−7.35022e84	−0.923261
$290$	4.00156e84	0.446168
$291$	3.99191e84	0.395251
$292$	5.36306e84	0.471742
$293$	9.86994e84	0.771581	0.385791	−	0.922586i	$-0.373929\pi$
$293$	9.86994e84	0.771581	0.385791	+	0.922586i	$0.373929\pi$
$294$	−9.45867e84	−0.657427
$295$	1.03232e85	0.638196
$296$	−6.32825e85	−3.48113
$297$	4.16385e83	0.0203891
$298$	8.71193e84	0.379886
$299$	3.62916e85	1.40978
$300$	−4.64060e84	−0.160654
$301$	2.72561e83	0.00841239
$302$	−9.46008e85	−2.60409
$303$	1.15260e84	0.0283079
$304$	9.25927e85	2.02973
$305$	6.40372e85	1.25339
$306$	−2.75061e85	−0.480884
$307$	−3.27318e85	−0.511324	−0.255662	−	0.966766i	$-0.582293\pi$
$307$	−3.27318e85	−0.511324	−0.255662	+	0.966766i	$0.582293\pi$
$308$	−5.38914e82	−0.000752523 0
$309$	−4.52489e85	−0.564990
$310$	8.76014e85	0.978436
$311$	−1.76892e86	−1.76797	−0.883986	−	0.467513i	$-0.845150\pi$
$311$	−1.76892e86	−1.76797	−0.883986	+	0.467513i	$0.845150\pi$
$312$	2.06384e86	1.84647
$313$	−3.41545e85	−0.273633	−0.136816	−	0.990596i	$-0.543687\pi$
$313$	−3.41545e85	−0.273633	−0.136816	+	0.990596i	$0.543687\pi$
$314$	−1.49017e86	−1.06946
$315$	−1.23361e84	−0.00793349
$316$	6.02469e86	3.47320
$317$	7.71691e85	0.398932	0.199466	−	0.979905i	$-0.436079\pi$
$317$	7.71691e85	0.398932	0.199466	+	0.979905i	$0.436079\pi$
$318$	−1.13714e86	−0.527326
$319$	1.62964e84	0.00678130
$320$	−1.39174e87	−5.19859
$321$	−1.21071e86	−0.406086
$322$	4.93295e84	0.0148621
$323$	−4.97454e85	−0.134668
$324$	7.83755e86	1.90712
$325$	1.18599e86	0.259481
$326$	1.02864e87	2.02422
$327$	2.32586e86	0.411799
$328$	−5.33530e86	−0.850180
$329$	−6.29809e84	−0.00903546
$330$	−1.76927e85	−0.0228593
$331$	−1.76756e83	−0.000205735 0	−0.000102867	−	1.00000i	$-0.500033\pi$
$331$	−1.76756e83	−0.000205735 0	−0.000102867		1.00000i	$0.500033\pi$
$332$	2.06767e87	2.16879
$333$	−9.12445e86	−0.862742
$334$	−2.72660e87	−2.32471
$335$	1.37553e87	1.05785
$336$	1.67218e85	0.0116032
$337$	−5.65069e86	−0.353891	−0.176946	−	0.984221i	$-0.556622\pi$
$337$	−5.65069e86	−0.353891	−0.176946	+	0.984221i	$0.556622\pi$
$338$	−4.69722e87	−2.65592
$339$	−1.87502e86	−0.0957449
$340$	1.83697e87	0.847384
$341$	3.56758e85	0.0148712
$342$	2.23972e87	0.843902
$343$	4.85556e85	0.0165422
$344$	1.18148e88	3.64050
$345$	1.19657e87	0.333564
$346$	−1.14658e88	−2.89254
$347$	−6.30525e87	−1.43991	−0.719955	−	0.694021i	$-0.755838\pi$
$347$	−6.30525e87	−1.43991	−0.719955	+	0.694021i	$0.755838\pi$
$348$	−9.69409e86	−0.200458
$349$	4.26563e87	0.798925	0.399463	−	0.916750i	$-0.369197\pi$
$349$	4.26563e87	0.798925	0.399463	+	0.916750i	$0.369197\pi$
$350$	1.61206e85	0.00273548
$351$	6.33022e87	0.973471
$352$	−1.05897e87	−0.147626
$353$	5.91830e87	0.748117	0.374058	−	0.927405i	$-0.377966\pi$
$353$	5.91830e87	0.748117	0.374058	+	0.927405i	$0.377966\pi$
$354$	−3.38482e87	−0.388081
$355$	1.55707e88	1.61968
$356$	−2.51014e88	−2.36959
$357$	−8.98379e84	−0.000769850 0
$358$	2.75258e88	2.14179
$359$	−1.96053e88	−1.38553	−0.692764	−	0.721164i	$-0.743607\pi$
$359$	−1.96053e88	−1.38553	−0.692764	+	0.721164i	$0.743607\pi$
$360$	−5.34739e88	−3.43325
$361$	−1.30889e88	−0.763671
$362$	5.55580e88	2.94646
$363$	6.96068e87	0.335640
$364$	−8.19299e86	−0.0359290
$365$	−4.51910e87	−0.180280
$366$	−2.09968e88	−0.762178
$367$	−4.95070e88	−1.63564	−0.817819	−	0.575475i	$-0.804817\pi$
$367$	−4.95070e88	−1.63564	−0.817819	+	0.575475i	$0.804817\pi$
$368$	1.27461e89	3.83378
$369$	−7.69275e87	−0.210703
$370$	8.24754e88	2.05762
$371$	2.91863e86	0.00663405
$372$	−2.12221e88	−0.439599
$373$	−3.78408e88	−0.714505	−0.357253	−	0.934008i	$-0.616286\pi$
$373$	−3.78408e88	−0.714505	−0.357253	+	0.934008i	$0.616286\pi$
$374$	1.01253e87	0.0174317
$375$	−1.92268e88	−0.301876
$376$	−2.73006e89	−3.91013
$377$	2.47751e88	0.323771
$378$	8.60437e86	0.0102625
$379$	1.13681e89	1.23776	0.618880	−	0.785485i	$-0.287587\pi$
$379$	1.13681e89	1.23776	0.618880	+	0.785485i	$0.287587\pi$
$380$	−1.49578e89	−1.48707
$381$	1.44665e88	0.131356
$382$	2.82685e89	2.34486
$383$	−8.73915e87	−0.0662387	−0.0331193	−	0.999451i	$-0.510544\pi$
$383$	−8.73915e87	−0.0662387	−0.0331193	+	0.999451i	$0.510544\pi$
$384$	2.33677e89	1.61878
$385$	4.54107e85	0.000287583 0
$386$	−9.19332e88	−0.532366
$387$	1.70353e89	0.902239
$388$	−6.86926e89	−3.32825
$389$	2.58092e89	1.14423	0.572115	−	0.820173i	$-0.306123\pi$
$389$	2.58092e89	1.14423	0.572115	+	0.820173i	$0.306123\pi$
$390$	−2.68978e89	−1.09141
$391$	−6.84783e88	−0.254363
$392$	1.05234e90	3.57922
$393$	1.48523e89	0.462649
$394$	−4.44290e89	−1.26779
$395$	−5.07660e89	−1.32731
$396$	−3.36826e88	−0.0807089
$397$	−4.90688e88	−0.107779	−0.0538893	−	0.998547i	$-0.517162\pi$
$397$	−4.90688e88	−0.107779	−0.0538893	+	0.998547i	$0.517162\pi$
$398$	−1.28290e89	−0.258362
$399$	7.31515e86	0.00135101
$400$	4.16535e89	0.705638
$401$	−1.24261e89	−0.193132	−0.0965662	−	0.995327i	$-0.530786\pi$
$401$	−1.24261e89	−0.193132	−0.0965662	+	0.995327i	$0.530786\pi$
$402$	−4.51017e89	−0.643271
$403$	5.42371e89	0.710023
$404$	−1.98339e89	−0.238369
$405$	−6.60419e89	−0.728821
$406$	3.36756e87	0.00341324
$407$	3.35882e88	0.0312737
$408$	−3.89424e89	−0.333156
$409$	−6.64009e89	−0.522060	−0.261030	−	0.965331i	$-0.584062\pi$
$409$	−6.64009e89	−0.522060	−0.261030	+	0.965331i	$0.584062\pi$
$410$	6.95343e89	0.502523
$411$	6.69730e89	0.444997
$412$	7.78641e90	4.75755
$413$	8.68759e87	0.00488228
$414$	3.08314e90	1.59397
$415$	−1.74229e90	−0.828819
$416$	−1.60993e91	−7.04834
$417$	9.97402e89	0.401954
$418$	−8.24466e88	−0.0305908
$419$	2.42519e90	0.828633	0.414317	−	0.910133i	$-0.364021\pi$
$419$	2.42519e90	0.828633	0.414317	+	0.910133i	$0.364021\pi$
$420$	−2.70130e88	−0.00850106
$421$	8.45515e89	0.245126	0.122563	−	0.992461i	$-0.460889\pi$
$421$	8.45515e89	0.245126	0.122563	+	0.992461i	$0.460889\pi$
$422$	−3.66759e90	−0.979719
$423$	−3.93636e90	−0.969064
$424$	1.26515e91	2.87091
$425$	−2.23783e89	−0.0468176
$426$	−5.10541e90	−0.984916
$427$	5.38912e88	0.00958862
$428$	2.08339e91	3.41948
$429$	−1.09542e89	−0.0165883
$430$	−1.53981e91	−2.15182
$431$	−1.00762e91	−1.29966	−0.649832	−	0.760078i	$-0.725161\pi$
$431$	−1.00762e91	−1.29966	−0.649832	+	0.760078i	$0.725161\pi$
$432$	2.22325e91	2.64728
$433$	2.48563e90	0.273278	0.136639	−	0.990621i	$-0.456370\pi$
$433$	2.48563e90	0.273278	0.136639	+	0.990621i	$0.456370\pi$
$434$	7.37219e88	0.00748516
$435$	8.16857e89	0.0766067
$436$	−4.00232e91	−3.46759
$437$	5.57592e90	0.446382
$438$	1.48174e90	0.109627
$439$	−7.87845e90	−0.538784	−0.269392	−	0.963031i	$-0.586823\pi$
$439$	−7.87845e90	−0.538784	−0.269392	+	0.963031i	$0.586823\pi$
$440$	1.96844e90	0.124453
$441$	1.51733e91	0.887052
$442$	1.53933e91	0.832270
$443$	2.92208e91	1.46138	0.730692	−	0.682708i	$-0.239198\pi$
$443$	2.92208e91	1.46138	0.730692	+	0.682708i	$0.239198\pi$
$444$	−1.99803e91	−0.924463
$445$	2.11513e91	0.905559
$446$	−7.70327e91	−3.05227
$447$	1.77840e90	0.0652260
$448$	−1.17124e90	−0.0397698
$449$	−1.09047e91	−0.342858	−0.171429	−	0.985196i	$-0.554838\pi$
$449$	−1.09047e91	−0.342858	−0.171429	+	0.985196i	$0.554838\pi$
$450$	1.00755e91	0.293384
$451$	2.83179e89	0.00763784
$452$	3.22652e91	0.806228
$453$	−1.93113e91	−0.447119
$454$	1.15913e92	2.48716
$455$	6.90369e89	0.0137306
$456$	3.17093e91	0.584655
$457$	−1.22143e91	−0.208813	−0.104407	−	0.994535i	$-0.533294\pi$
$457$	−1.22143e91	−0.208813	−0.104407	+	0.994535i	$0.533294\pi$
$458$	5.46417e91	0.866294
$459$	−1.19444e91	−0.175642
$460$	−2.05905e92	−2.80880
$461$	−2.42324e91	−0.306700	−0.153350	−	0.988172i	$-0.549006\pi$
$461$	−2.42324e91	−0.306700	−0.153350	+	0.988172i	$0.549006\pi$
$462$	−1.48895e88	−0.000174877 0
$463$	−1.70450e92	−1.85803	−0.929015	−	0.370042i	$-0.879343\pi$
$463$	−1.70450e92	−1.85803	−0.929015	+	0.370042i	$0.879343\pi$
$464$	8.70132e91	0.880470
$465$	1.78825e91	0.167997
$466$	2.20954e92	1.92747
$467$	−1.90134e91	−0.154038	−0.0770188	−	0.997030i	$-0.524540\pi$
$467$	−1.90134e91	−0.154038	−0.0770188	+	0.997030i	$0.524540\pi$
$468$	−5.12069e92	−3.85342
$469$	1.15760e90	0.00809271
$470$	3.55805e92	2.31119
$471$	−3.04195e91	−0.183625
$472$	3.76585e92	2.11283
$473$	−6.27090e90	−0.0327055
$474$	1.66454e92	0.807128
$475$	1.82218e91	0.0821602
$476$	1.54593e90	0.00648259
$477$	1.82417e92	0.711510
$478$	−8.51528e91	−0.308984
$479$	−1.43905e92	−0.485847	−0.242923	−	0.970045i	$-0.578106\pi$
$479$	−1.43905e92	−0.485847	−0.242923	+	0.970045i	$0.578106\pi$
$480$	−5.30808e92	−1.66769
$481$	5.10634e92	1.49315
$482$	−1.04313e93	−2.83933
$483$	1.00699e90	0.00255180
$484$	−1.19779e93	−2.82628
$485$	5.78827e92	1.27192
$486$	8.22756e92	1.68391
$487$	−5.62055e91	−0.107159	−0.0535796	−	0.998564i	$-0.517063\pi$
$487$	−5.62055e91	−0.107159	−0.0535796	+	0.998564i	$0.517063\pi$
$488$	2.33604e93	4.14951
$489$	2.09982e92	0.347557
$490$	−1.37151e93	−2.11560
$491$	−9.59231e92	−1.37915	−0.689576	−	0.724214i	$-0.742203\pi$
$491$	−9.59231e92	−1.37915	−0.689576	+	0.724214i	$0.742203\pi$
$492$	−1.68452e92	−0.225777
$493$	−4.67478e91	−0.0584174
$494$	−1.25342e93	−1.46055
$495$	2.83821e91	0.0308436
$496$	1.90487e93	1.93085
$497$	1.31037e91	0.0123908
$498$	5.71269e92	0.503998
$499$	−8.50645e92	−0.700293	−0.350146	−	0.936695i	$-0.613868\pi$
$499$	−8.50645e92	−0.700293	−0.350146	+	0.936695i	$0.613868\pi$
$500$	3.30854e93	2.54198
$501$	−5.56594e92	−0.399151
$502$	−2.56703e93	−1.71852
$503$	9.92271e92	0.620204	0.310102	−	0.950703i	$-0.399637\pi$
$503$	9.92271e92	0.620204	0.310102	+	0.950703i	$0.399637\pi$
$504$	−4.50015e91	−0.0262648
$505$	1.67127e92	0.0910948
$506$	−1.13494e92	−0.0577803
$507$	−9.58864e92	−0.456018
$508$	−2.48938e93	−1.10610
$509$	4.21070e93	1.74820	0.874099	−	0.485747i	$-0.161452\pi$
$509$	4.21070e93	1.74820	0.874099	+	0.485747i	$0.161452\pi$
$510$	5.07532e92	0.196921
$511$	−3.80310e90	−0.00137916
$512$	−1.24557e94	−4.22235
$513$	9.72587e92	0.308233
$514$	5.43974e93	1.61195
$515$	−6.56109e93	−1.81814
$516$	3.73031e93	0.966786
$517$	1.44902e92	0.0351278
$518$	6.94081e91	0.0157410
$519$	−2.34056e93	−0.496646
$520$	2.99257e94	5.94195
$521$	7.50601e93	1.39479	0.697393	−	0.716689i	$-0.254343\pi$
$521$	7.50601e93	1.39479	0.697393	+	0.716689i	$0.254343\pi$
$522$	2.10475e93	0.366074
$523$	−9.56209e93	−1.55684	−0.778421	−	0.627742i	$-0.783979\pi$
$523$	−9.56209e93	−1.55684	−0.778421	+	0.627742i	$0.783979\pi$
$524$	−2.55578e94	−3.89578
$525$	3.29078e90	0.000469680 0
$526$	3.63808e93	0.486255
$527$	−1.02339e93	−0.128108
$528$	−3.84724e92	−0.0451107
$529$	−1.42809e93	−0.156868
$530$	−1.64886e94	−1.69693
$531$	5.42982e93	0.523630
$532$	−1.25879e92	−0.0113763
$533$	4.30511e93	0.364666
$534$	−6.93520e93	−0.550662
$535$	−1.75553e94	−1.30678
$536$	5.01788e94	3.50215
$537$	5.61897e93	0.367743
$538$	−1.15989e94	−0.711917
$539$	−5.58548e92	−0.0321550
$540$	−3.59152e94	−1.93952
$541$	1.58147e94	0.801226	0.400613	−	0.916247i	$-0.368797\pi$
$541$	1.58147e94	0.801226	0.400613	+	0.916247i	$0.368797\pi$
$542$	4.70393e93	0.223607
$543$	1.13413e94	0.505905
$544$	3.03776e94	1.27172
$545$	3.37249e94	1.32517
$546$	−2.26362e92	−0.00834943
$547$	−2.71305e94	−0.939495	−0.469748	−	0.882801i	$-0.655655\pi$
$547$	−2.71305e94	−0.939495	−0.469748	+	0.882801i	$0.655655\pi$
$548$	−1.15247e95	−3.74714
$549$	3.36825e94	1.02839
$550$	−3.70892e92	−0.0106349
$551$	3.80649e93	0.102517
$552$	4.36502e94	1.10430
$553$	−4.27227e92	−0.0101541
$554$	1.03760e95	2.31709
$555$	1.68361e94	0.353291
$556$	−1.71632e95	−3.38469
$557$	3.94686e94	0.731555	0.365777	−	0.930702i	$-0.380803\pi$
$557$	3.94686e94	0.731555	0.365777	+	0.930702i	$0.380803\pi$
$558$	4.60768e94	0.802792
$559$	−9.53351e94	−1.56151
$560$	2.42466e93	0.0373391
$561$	2.06693e92	0.00299300
$562$	−1.42129e92	−0.00193544
$563$	−1.43702e95	−1.84044	−0.920222	−	0.391396i	$-0.871992\pi$
$563$	−1.43702e95	−1.84044	−0.920222	+	0.391396i	$0.871992\pi$
$564$	−8.61966e94	−1.03839
$565$	−2.71877e94	−0.308107
$566$	1.29301e95	1.37859
$567$	−5.55783e92	−0.00557557
$568$	5.68012e95	5.36216
$569$	6.44138e94	0.572276	0.286138	−	0.958188i	$-0.407628\pi$
$569$	6.44138e94	0.572276	0.286138	+	0.958188i	$0.407628\pi$
$570$	−4.13263e94	−0.345577
$571$	−1.65144e95	−1.29992	−0.649959	−	0.759969i	$-0.725214\pi$
$571$	−1.65144e95	−1.29992	−0.649959	+	0.759969i	$0.725214\pi$
$572$	1.88499e94	0.139684
$573$	5.77058e94	0.402611
$574$	5.85174e92	0.00384436
$575$	2.50837e94	0.155185
$576$	−7.32034e95	−4.26536
$577$	−3.57373e94	−0.196136	−0.0980678	−	0.995180i	$-0.531266\pi$
$577$	−3.57373e94	−0.196136	−0.0980678	+	0.995180i	$0.531266\pi$
$578$	3.49454e95	1.80667
$579$	−1.87667e94	−0.0914068
$580$	−1.40564e95	−0.645073
$581$	−1.46624e93	−0.00634057
$582$	−1.89789e95	−0.773441
$583$	−6.71498e93	−0.0257917
$584$	−1.64854e95	−0.596839
$585$	4.31487e95	1.47262
$586$	−4.69250e95	−1.50986
$587$	5.28696e95	1.60395	0.801976	−	0.597356i	$-0.203782\pi$
$587$	5.28696e95	1.60395	0.801976	+	0.597356i	$0.203782\pi$
$588$	3.32258e95	0.950513
$589$	8.33309e94	0.224817
$590$	−4.90798e95	−1.24885
$591$	−9.06949e94	−0.217678
$592$	1.79341e96	4.06051
$593$	−4.37868e95	−0.935312	−0.467656	−	0.883910i	$-0.654901\pi$
$593$	−4.37868e95	−0.935312	−0.467656	+	0.883910i	$0.654901\pi$
$594$	−1.97963e94	−0.0398981
$595$	−1.30265e93	−0.00247738
$596$	−3.06027e95	−0.549242
$597$	−2.61885e94	−0.0443605
$598$	−1.72542e96	−2.75870
$599$	−3.20966e95	−0.484433	−0.242217	−	0.970222i	$-0.577875\pi$
$599$	−3.20966e95	−0.484433	−0.242217	+	0.970222i	$0.577875\pi$
$600$	1.42647e95	0.203256
$601$	−5.87229e95	−0.790020	−0.395010	−	0.918677i	$-0.629259\pi$
$601$	−5.87229e95	−0.790020	−0.395010	+	0.918677i	$0.629259\pi$
$602$	−1.29585e94	−0.0164617
$603$	7.23508e95	0.867952
$604$	3.32308e96	3.76501
$605$	1.00930e96	1.08009
$606$	−5.47984e94	−0.0553939
$607$	−1.99576e96	−1.90589	−0.952944	−	0.303145i	$-0.901963\pi$
$607$	−1.99576e96	−1.90589	−0.952944	+	0.303145i	$0.901963\pi$
$608$	−2.47352e96	−2.23174
$609$	6.87435e92	0.000586050 0
$610$	−3.04454e96	−2.45269
$611$	2.20292e96	1.67717
$612$	9.66217e95	0.695266
$613$	−1.69286e96	−1.15142	−0.575711	−	0.817653i	$-0.695275\pi$
$613$	−1.69286e96	−1.15142	−0.575711	+	0.817653i	$0.695275\pi$
$614$	1.55618e96	1.00058
$615$	1.41943e95	0.0862827
$616$	1.65656e93	0.000952078 0
$617$	2.01970e96	1.09761	0.548807	−	0.835949i	$-0.315082\pi$
$617$	2.01970e96	1.09761	0.548807	+	0.835949i	$0.315082\pi$
$618$	2.15128e96	1.10559
$619$	−1.55484e96	−0.755713	−0.377857	−	0.925864i	$-0.623339\pi$
$619$	−1.55484e96	−0.755713	−0.377857	+	0.925864i	$0.623339\pi$
$620$	−3.07720e96	−1.41463
$621$	1.33884e96	0.582195
$622$	8.41005e96	3.45963
$623$	1.78001e94	0.00692764
$624$	−5.84888e96	−2.15379
$625$	−3.27291e96	−1.14044
$626$	1.62382e96	0.535454
$627$	−1.68302e94	−0.00525241
$628$	5.23457e96	1.54623
$629$	−9.63509e95	−0.269407
$630$	5.86499e94	0.0155245
$631$	1.41840e96	0.355456	0.177728	−	0.984080i	$-0.443125\pi$
$631$	1.41840e96	0.355456	0.177728	+	0.984080i	$0.443125\pi$
$632$	−1.85192e97	−4.39423
$633$	−7.48682e95	−0.168217
$634$	−3.66887e96	−0.780645
$635$	2.09764e96	0.422704
$636$	3.99448e96	0.762412
$637$	−8.49148e96	−1.53523
$638$	−7.74785e94	−0.0132699
$639$	8.18994e96	1.32893
$640$	3.38831e97	5.20923
$641$	−1.09579e97	−1.59635	−0.798173	−	0.602429i	$-0.794200\pi$
$641$	−1.09579e97	−1.59635	−0.798173	+	0.602429i	$0.794200\pi$
$642$	5.75614e96	0.794644
$643$	1.16589e96	0.152539	0.0762693	−	0.997087i	$-0.475699\pi$
$643$	1.16589e96	0.152539	0.0762693	+	0.997087i	$0.475699\pi$
$644$	−1.73282e95	−0.0214877
$645$	−3.14329e96	−0.369465
$646$	2.36506e96	0.263524
$647$	7.27773e96	0.768773	0.384387	−	0.923172i	$-0.374413\pi$
$647$	7.27773e96	0.768773	0.384387	+	0.923172i	$0.374413\pi$
$648$	−2.40917e97	−2.41285
$649$	−1.99878e95	−0.0189812
$650$	−5.63860e96	−0.507762
$651$	1.50492e94	0.00128519
$652$	−3.61336e97	−2.92664
$653$	2.36544e97	1.81722	0.908611	−	0.417644i	$-0.137144\pi$
$653$	2.36544e97	1.81722	0.908611	+	0.417644i	$0.137144\pi$
$654$	−1.10579e97	−0.805824
$655$	2.15359e97	1.48880
$656$	1.51201e97	0.991681
$657$	−2.37697e96	−0.147917
$658$	2.99432e95	0.0176809
$659$	4.12773e96	0.231294	0.115647	−	0.993290i	$-0.463106\pi$
$659$	4.12773e96	0.231294	0.115647	+	0.993290i	$0.463106\pi$
$660$	6.21498e95	0.0330502
$661$	−1.44124e97	−0.727422	−0.363711	−	0.931512i	$-0.618490\pi$
$661$	−1.44124e97	−0.727422	−0.363711	+	0.931512i	$0.618490\pi$
$662$	8.40356e93	0.000402590 0
$663$	3.14231e96	0.142900
$664$	−6.35577e97	−2.74391
$665$	1.06070e95	0.00434755
$666$	4.33807e97	1.68824
$667$	5.23992e96	0.193635
$668$	9.57784e97	3.36109
$669$	−1.57250e97	−0.524071
$670$	−6.53974e97	−2.07005
$671$	−1.23989e96	−0.0372784
$672$	−4.46708e95	−0.0127580
$673$	−5.38065e97	−1.45987	−0.729936	−	0.683516i	$-0.760450\pi$
$673$	−5.38065e97	−1.45987	−0.729936	+	0.683516i	$0.760450\pi$
$674$	2.68652e97	0.692507
$675$	4.37525e96	0.107158
$676$	1.65001e98	3.83994
$677$	−7.23414e97	−1.59984	−0.799922	−	0.600104i	$-0.795126\pi$
$677$	−7.23414e97	−1.59984	−0.799922	+	0.600104i	$0.795126\pi$
$678$	8.91445e96	0.187357
$679$	4.87118e95	0.00973032
$680$	−5.64665e97	−1.07209
$681$	2.36617e97	0.427043
$682$	−1.69614e96	−0.0291006
$683$	−2.87542e97	−0.469015	−0.234507	−	0.972114i	$-0.575348\pi$
$683$	−2.87542e97	−0.469015	−0.234507	+	0.972114i	$0.575348\pi$
$684$	−7.86753e97	−1.22012
$685$	9.71108e97	1.43200
$686$	−2.30849e96	−0.0323703
$687$	1.11543e97	0.148742
$688$	−3.34829e98	−4.24641
$689$	−1.02086e98	−1.23142
$690$	−5.68888e97	−0.652730
$691$	−2.09622e97	−0.228794	−0.114397	−	0.993435i	$-0.536494\pi$
$691$	−2.09622e97	−0.228794	−0.114397	+	0.993435i	$0.536494\pi$
$692$	4.02763e98	4.18205
$693$	2.38853e94	0.000235957 0
$694$	2.99772e98	2.81767
$695$	1.44623e98	1.29349
$696$	2.97985e97	0.253616
$697$	−8.12326e96	−0.0657960
$698$	−2.02802e98	−1.56337
$699$	4.51044e97	0.330945
$700$	−5.66275e95	−0.00395498
$701$	1.95600e97	0.130046	0.0650231	−	0.997884i	$-0.479288\pi$
$701$	1.95600e97	0.130046	0.0650231	+	0.997884i	$0.479288\pi$
$702$	−3.00960e98	−1.90492
$703$	7.84548e97	0.472782
$704$	2.69470e97	0.154616
$705$	7.26322e97	0.396830
$706$	−2.81375e98	−1.46394
$707$	1.40647e95	0.000696887 0
$708$	1.18900e98	0.561091
$709$	1.46385e98	0.657962	0.328981	−	0.944337i	$-0.393295\pi$
$709$	1.46385e98	0.657962	0.328981	+	0.944337i	$0.393295\pi$
$710$	−7.40284e98	−3.16946
$711$	−2.67021e98	−1.08904
$712$	7.71589e98	2.99796
$713$	1.14711e98	0.424636
$714$	4.27119e95	0.00150647
$715$	−1.58835e97	−0.0533813
$716$	−9.66909e98	−3.09661
$717$	−1.73826e97	−0.0530523
$718$	9.32102e98	2.71125
$719$	−2.66577e98	−0.739054	−0.369527	−	0.929220i	$-0.620480\pi$
$719$	−2.66577e98	−0.739054	−0.369527	+	0.929220i	$0.620480\pi$
$720$	1.51544e99	4.00467
$721$	−5.52156e96	−0.0139090
$722$	6.22292e98	1.49438
$723$	−2.12939e98	−0.487511
$724$	−1.95160e99	−4.26002
$725$	1.71238e97	0.0356401
$726$	−3.30934e98	−0.656792
$727$	−9.09844e97	−0.172199	−0.0860993	−	0.996287i	$-0.527440\pi$
$727$	−9.09844e97	−0.172199	−0.0860993	+	0.996287i	$0.527440\pi$
$728$	2.51843e97	0.0454567
$729$	−2.23620e98	−0.384955
$730$	2.14853e98	0.352779
$731$	1.79887e98	0.281741
$732$	7.37563e98	1.10196
$733$	1.09199e99	1.55644	0.778222	−	0.627989i	$-0.216122\pi$
$733$	1.09199e99	1.55644	0.778222	+	0.627989i	$0.216122\pi$
$734$	2.35373e99	3.20068
$735$	−2.79972e98	−0.363246
$736$	−3.40499e99	−4.21533
$737$	−2.66332e97	−0.0314626
$738$	3.65739e98	0.412312
$739$	1.00500e99	1.08127	0.540634	−	0.841258i	$-0.318185\pi$
$739$	1.00500e99	1.08127	0.540634	+	0.841258i	$0.318185\pi$
$740$	−2.89714e99	−2.97492
$741$	−2.55866e98	−0.250775
$742$	−1.38761e97	−0.0129818
$743$	−1.61438e99	−1.44175	−0.720876	−	0.693064i	$-0.756260\pi$
$743$	−1.61438e99	−1.44175	−0.720876	+	0.693064i	$0.756260\pi$
$744$	6.52343e98	0.556173
$745$	2.57869e98	0.209897
$746$	1.79908e99	1.39817
$747$	−9.16413e98	−0.680034
$748$	−3.55676e97	−0.0252028
$749$	−1.47739e97	−0.00999706
$750$	9.14107e98	0.590722
$751$	−1.42488e98	−0.0879427	−0.0439714	−	0.999033i	$-0.514001\pi$
$751$	−1.42488e98	−0.0879427	−0.0439714	+	0.999033i	$0.514001\pi$
$752$	7.73692e99	4.56092
$753$	−5.24020e98	−0.295067
$754$	−1.17789e99	−0.633568
$755$	−2.80014e99	−1.43883
$756$	−3.02249e97	−0.0148376
$757$	2.24957e99	1.05510	0.527548	−	0.849525i	$-0.323112\pi$
$757$	2.24957e99	1.05510	0.527548	+	0.849525i	$0.323112\pi$
$758$	−5.40479e99	−2.42209
$759$	−2.31680e97	−0.00992083
$760$	4.59784e99	1.88142
$761$	2.11733e99	0.827977	0.413989	−	0.910282i	$-0.364135\pi$
$761$	2.11733e99	0.827977	0.413989	+	0.910282i	$0.364135\pi$
$762$	−6.87784e98	−0.257043
$763$	2.83816e97	0.0101377
$764$	−9.92999e99	−3.39022
$765$	−8.14167e98	−0.265701
$766$	4.15488e98	0.129618
$767$	−3.03870e99	−0.906251
$768$	−5.44396e99	−1.55222
$769$	5.07951e99	1.38472	0.692362	−	0.721550i	$-0.256570\pi$
$769$	5.07951e99	1.38472	0.692362	+	0.721550i	$0.256570\pi$
$770$	−2.15897e96	−0.000562753 0
$771$	1.11044e99	0.276770
$772$	3.22937e99	0.769699
$773$	7.19171e99	1.63923	0.819614	−	0.572916i	$-0.194188\pi$
$773$	7.19171e99	1.63923	0.819614	+	0.572916i	$0.194188\pi$
$774$	−8.09915e99	−1.76553
$775$	3.74870e98	0.0781578
$776$	2.11153e100	4.21084
$777$	1.41686e97	0.00270272
$778$	−1.22705e100	−2.23907
$779$	6.61445e98	0.115465
$780$	9.44850e99	1.57797
$781$	−3.01481e98	−0.0481726
$782$	3.25568e99	0.497748
$783$	9.13980e98	0.133708
$784$	−2.98231e100	−4.17493
$785$	−4.41083e99	−0.590904
$786$	−7.06128e99	−0.905328
$787$	2.21935e99	0.272331	0.136166	−	0.990686i	$-0.456522\pi$
$787$	2.21935e99	0.272331	0.136166	+	0.990686i	$0.456522\pi$
$788$	1.56067e100	1.83298
$789$	7.42657e98	0.0834895
$790$	2.41359e100	2.59734
$791$	−2.28801e97	−0.00235706
$792$	1.03536e99	0.102111
$793$	−1.88498e100	−1.77984
$794$	2.33289e99	0.210905
$795$	−3.36588e99	−0.291362
$796$	4.50650e99	0.373542
$797$	−1.80947e100	−1.43628	−0.718139	−	0.695899i	$-0.755006\pi$
$797$	−1.80947e100	−1.43628	−0.718139	+	0.695899i	$0.755006\pi$
$798$	−3.47786e97	−0.00264370
$799$	−4.15666e99	−0.302608
$800$	−1.11273e100	−0.775866
$801$	1.11252e100	0.742997
$802$	5.90779e99	0.377928
$803$	8.74990e97	0.00536188
$804$	1.58430e100	0.930047
$805$	1.46013e98	0.00821170
$806$	−2.57861e100	−1.38940
$807$	−2.36774e99	−0.122235
$808$	6.09670e99	0.301580
$809$	1.24685e100	0.591004	0.295502	−	0.955342i	$-0.404513\pi$
$809$	1.24685e100	0.591004	0.295502	+	0.955342i	$0.404513\pi$
$810$	3.13985e100	1.42618
$811$	−9.08873e99	−0.395625	−0.197813	−	0.980240i	$-0.563384\pi$
$811$	−9.08873e99	−0.395625	−0.197813	+	0.980240i	$0.563384\pi$
$812$	−1.18293e98	−0.00493489
$813$	9.60235e98	0.0383932
$814$	−1.59689e99	−0.0611976
$815$	3.04473e100	1.11844
$816$	1.10362e100	0.388605
$817$	−1.46475e100	−0.494426
$818$	3.15692e100	1.02159
$819$	3.63122e98	0.0112657
$820$	−2.44255e100	−0.726552
$821$	1.37155e100	0.391176	0.195588	−	0.980686i	$-0.437338\pi$
$821$	1.37155e100	0.391176	0.195588	+	0.980686i	$0.437338\pi$
$822$	−3.18412e100	−0.870786
$823$	5.47295e100	1.43525	0.717624	−	0.696430i	$-0.245229\pi$
$823$	5.47295e100	1.43525	0.717624	+	0.696430i	$0.245229\pi$
$824$	−2.39345e101	−6.01916
$825$	−7.57119e97	−0.00182601
$826$	−4.13037e98	−0.00955382
$827$	1.68367e100	0.373523	0.186761	−	0.982405i	$-0.440201\pi$
$827$	1.68367e100	0.373523	0.186761	+	0.982405i	$0.440201\pi$
$828$	−1.08302e101	−2.30458
$829$	−3.72126e100	−0.759554	−0.379777	−	0.925078i	$-0.623999\pi$
$829$	−3.72126e100	−0.759554	−0.379777	+	0.925078i	$0.623999\pi$
$830$	8.28340e100	1.62186
$831$	2.11810e100	0.397842
$832$	4.09670e101	7.38209
$833$	1.60225e100	0.276998
$834$	−4.74198e100	−0.786558
$835$	−8.07061e100	−1.28447
$836$	2.89613e99	0.0442284
$837$	2.00087e100	0.293217
$838$	−1.15302e101	−1.62150
$839$	6.67827e100	0.901314	0.450657	−	0.892697i	$-0.351190\pi$
$839$	6.67827e100	0.901314	0.450657	+	0.892697i	$0.351190\pi$
$840$	8.30350e98	0.0107554
$841$	−7.68610e100	−0.955530
$842$	−4.01986e100	−0.479671
$843$	−2.90135e97	−0.000332314 0
$844$	1.28833e101	1.41648
$845$	−1.39035e101	−1.46747
$846$	1.87148e101	1.89630
$847$	8.49386e98	0.00826281
$848$	−3.58540e101	−3.34874
$849$	2.63947e100	0.236702
$850$	1.06394e100	0.0916145
$851$	1.07999e101	0.892996
$852$	1.79339e101	1.42400
$853$	−6.96534e100	−0.531130	−0.265565	−	0.964093i	$-0.585558\pi$
$853$	−6.96534e100	−0.531130	−0.265565	+	0.964093i	$0.585558\pi$
$854$	−2.56217e99	−0.0187634
$855$	6.62944e100	0.466279
$856$	−6.40410e101	−4.32627
$857$	−7.62224e99	−0.0494589	−0.0247294	−	0.999694i	$-0.507872\pi$
$857$	−7.62224e99	−0.0494589	−0.0247294	+	0.999694i	$0.507872\pi$
$858$	5.20798e99	0.0324607
$859$	2.50764e101	1.50142	0.750708	−	0.660634i	$-0.229713\pi$
$859$	2.50764e101	1.50142	0.750708	+	0.660634i	$0.229713\pi$
$860$	5.40895e101	3.11112
$861$	1.19454e98	0.000660074 0
$862$	4.79056e101	2.54323
$863$	−6.09184e100	−0.310725	−0.155362	−	0.987858i	$-0.549655\pi$
$863$	−6.09184e100	−0.310725	−0.155362	+	0.987858i	$0.549655\pi$
$864$	−5.93921e101	−2.91075
$865$	−3.39382e101	−1.59821
$866$	−1.18175e101	−0.534760
$867$	7.13356e100	0.310204
$868$	−2.58966e99	−0.0108221
$869$	9.82935e99	0.0394769
$870$	−3.88361e100	−0.149907
$871$	−4.04899e101	−1.50217
$872$	1.23027e102	4.38714
$873$	3.04453e101	1.04359
$874$	−2.65097e101	−0.873497
$875$	−2.34618e99	−0.00743161
$876$	−5.20497e100	−0.158499
$877$	−2.02770e101	−0.593633	−0.296817	−	0.954934i	$-0.595925\pi$
$877$	−2.02770e101	−0.593633	−0.296817	+	0.954934i	$0.595925\pi$
$878$	3.74567e101	1.05431
$879$	−9.57900e100	−0.259241
$880$	−5.57850e100	−0.145166
$881$	2.95221e101	0.738717	0.369359	−	0.929287i	$-0.379577\pi$
$881$	2.95221e101	0.738717	0.369359	+	0.929287i	$0.379577\pi$
$882$	−7.21390e101	−1.73582
$883$	3.63350e101	0.840778	0.420389	−	0.907344i	$-0.361894\pi$
$883$	3.63350e101	0.840778	0.420389	+	0.907344i	$0.361894\pi$
$884$	−5.40727e101	−1.20330
$885$	−1.00189e101	−0.214426
$886$	−1.38926e102	−2.85969
$887$	−5.78176e101	−1.14471	−0.572355	−	0.820006i	$-0.693970\pi$
$887$	−5.78176e101	−1.14471	−0.572355	+	0.820006i	$0.693970\pi$
$888$	6.14172e101	1.16961
$889$	1.76529e99	0.00323374
$890$	−1.00560e102	−1.77203
$891$	1.27871e100	0.0216765
$892$	2.70595e102	4.41299
$893$	3.38460e101	0.531046
$894$	−8.45513e100	−0.127637
$895$	8.14750e101	1.18340
$896$	2.85147e100	0.0398513
$897$	−3.52219e101	−0.473667
$898$	5.18445e101	0.670917
$899$	7.83095e100	0.0975226
$900$	−3.53927e101	−0.424177
$901$	1.92626e101	0.222182
$902$	−1.34633e100	−0.0149460
$903$	−2.64527e99	−0.00282646
$904$	−9.91795e101	−1.02003
$905$	1.64449e102	1.62800
$906$	9.18123e101	0.874939
$907$	−8.87640e100	−0.0814302	−0.0407151	−	0.999171i	$-0.512964\pi$
$907$	−8.87640e100	−0.0814302	−0.0407151	+	0.999171i	$0.512964\pi$
$908$	−4.07170e102	−3.59595
$909$	8.79059e100	0.0747419
$910$	−3.28224e100	−0.0268685
$911$	−4.55318e101	−0.358864	−0.179432	−	0.983770i	$-0.557426\pi$
$911$	−4.55318e101	−0.358864	−0.179432	+	0.983770i	$0.557426\pi$
$912$	−8.98633e101	−0.681962
$913$	3.37342e100	0.0246507
$914$	5.80707e101	0.408614
$915$	−6.21495e101	−0.421124
$916$	−1.91942e102	−1.25249
$917$	1.81237e100	0.0113895
$918$	5.67877e101	0.343702
$919$	8.86482e101	0.516755	0.258378	−	0.966044i	$-0.416812\pi$
$919$	8.86482e101	0.516755	0.258378	+	0.966044i	$0.416812\pi$
$920$	6.32928e102	3.55365
$921$	3.17670e101	0.171798
$922$	1.15209e102	0.600163
$923$	−4.58336e102	−2.29998
$924$	5.23028e98	0.000252838 0
$925$	3.52935e101	0.164363
$926$	8.10375e102	3.63586
$927$	−3.45102e102	−1.49175
$928$	−2.32447e102	−0.968098
$929$	−3.08187e102	−1.23672	−0.618362	−	0.785894i	$-0.712203\pi$
$929$	−3.08187e102	−1.23672	−0.618362	+	0.785894i	$0.712203\pi$
$930$	−8.50191e101	−0.328742
$931$	−1.30465e102	−0.486104
$932$	−7.76153e102	−2.78675
$933$	1.71678e102	0.594016
$934$	9.03959e101	0.301427
$935$	2.99705e100	0.00963148
$936$	1.57404e103	4.87528
$937$	5.42024e102	1.61809	0.809044	−	0.587748i	$-0.199985\pi$
$937$	5.42024e102	1.61809	0.809044	+	0.587748i	$0.199985\pi$
$938$	−5.50360e100	−0.0158361
$939$	3.31477e101	0.0919370
$940$	−1.24985e103	−3.34154
$941$	1.40089e102	0.361045	0.180522	−	0.983571i	$-0.442221\pi$
$941$	1.40089e102	0.361045	0.180522	+	0.983571i	$0.442221\pi$
$942$	1.44624e102	0.359323
$943$	9.10530e101	0.218092
$944$	−1.06723e103	−2.46448
$945$	2.54685e100	0.00567030
$946$	2.98139e101	0.0639992
$947$	1.40868e102	0.291566	0.145783	−	0.989317i	$-0.453430\pi$
$947$	1.40868e102	0.291566	0.145783	+	0.989317i	$0.453430\pi$
$948$	−5.84710e102	−1.16695
$949$	1.33023e102	0.256001
$950$	−8.66324e101	−0.160774
$951$	−7.48944e101	−0.134036
$952$	−4.75200e100	−0.00820166
$953$	5.24667e102	0.873331	0.436666	−	0.899624i	$-0.356159\pi$
$953$	5.24667e102	0.873331	0.436666	+	0.899624i	$0.356159\pi$
$954$	−8.67270e102	−1.39231
$955$	8.36734e102	1.29560
$956$	2.99119e102	0.446732
$957$	−1.58160e100	−0.00227843
$958$	6.84170e102	0.950723
$959$	8.17247e100	0.0109550
$960$	1.35072e103	1.74666
$961$	−6.30165e102	−0.786135
$962$	−2.42772e103	−2.92186
$963$	−9.23381e102	−1.07220
$964$	3.66424e103	4.10513
$965$	−2.72118e102	−0.294147
$966$	−4.78754e100	−0.00499346
$967$	7.85802e102	0.790860	0.395430	−	0.918496i	$-0.370596\pi$
$967$	7.85802e102	0.790860	0.395430	+	0.918496i	$0.370596\pi$
$968$	3.68187e103	3.57576
$969$	4.82790e101	0.0452468
$970$	−2.75193e103	−2.48893
$971$	−8.53716e102	−0.745161	−0.372580	−	0.928000i	$-0.621527\pi$
$971$	−8.53716e102	−0.745161	−0.372580	+	0.928000i	$0.621527\pi$
$972$	−2.89012e103	−2.43461
$973$	1.21709e101	0.00989534
$974$	2.67220e102	0.209693
$975$	−1.15103e102	−0.0871823
$976$	−6.62029e103	−4.84014
$977$	−1.72478e102	−0.121722	−0.0608611	−	0.998146i	$-0.519385\pi$
$977$	−1.72478e102	−0.121722	−0.0608611	+	0.998146i	$0.519385\pi$
$978$	−9.98323e102	−0.680112
$979$	−4.09533e101	−0.0269331
$980$	4.81774e103	3.05875
$981$	1.77387e103	1.08728
$982$	4.56050e103	2.69877
$983$	−1.14304e103	−0.653078	−0.326539	−	0.945184i	$-0.605882\pi$
$983$	−1.14304e103	−0.653078	−0.326539	+	0.945184i	$0.605882\pi$
$984$	5.17803e102	0.285649
$985$	−1.31508e103	−0.700488
$986$	2.22254e102	0.114313
$987$	6.11244e100	0.00303580
$988$	4.40293e103	2.11167
$989$	−2.01633e103	−0.933879
$990$	−1.34938e102	−0.0603559
$991$	2.50288e103	1.08118	0.540591	−	0.841286i	$-0.318201\pi$
$991$	2.50288e103	1.08118	0.540591	+	0.841286i	$0.318201\pi$
$992$	−5.08869e103	−2.12302
$993$	1.71546e99	6.91243e−5 0
$994$	−6.22994e101	−0.0242468
$995$	−3.79733e102	−0.142752
$996$	−2.00672e103	−0.728684
$997$	1.06606e103	0.373937	0.186969	−	0.982366i	$-0.440134\pi$
$997$	1.06606e103	0.373937	0.186969	+	0.982366i	$0.440134\pi$
$998$	4.04425e103	1.37036
$999$	1.88379e103	0.616627

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.70.a.a.1.1	✓	5
3.2	odd	2		9.70.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.70.a.a.1.1	✓	5	1.1	even	1	trivial
9.70.a.b.1.5		5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-4.75433e10 q^{2} -9.70523e15 q^{3} +1.67007e21 q^{4} -1.40726e24 q^{5} +4.61419e26 q^{6} -1.18429e27 q^{7} -5.13361e31 q^{8} -7.40194e32 q^{9} +6.69057e34 q^{10} +2.72474e34 q^{11} -1.62084e37 q^{12} +4.14237e38 q^{13} +5.63052e37 q^{14} +1.36578e40 q^{15} +1.45485e42 q^{16} -7.81618e41 q^{17} +3.51913e43 q^{18} +6.36441e43 q^{19} -2.35022e45 q^{20} +1.14938e43 q^{21} -1.29543e45 q^{22} +8.76109e46 q^{23} +4.98228e47 q^{24} +2.86308e47 q^{25} -1.96942e49 q^{26} +1.52816e49 q^{27} -1.97785e48 q^{28} +5.98090e49 q^{29} -6.49335e50 q^{30} +1.30933e51 q^{31} -3.88650e52 q^{32} -2.64442e50 q^{33} +3.71607e52 q^{34} +1.66661e51 q^{35} -1.23618e54 q^{36} +1.23271e54 q^{37} -3.02585e54 q^{38} -4.02026e54 q^{39} +7.22431e55 q^{40} +1.03929e55 q^{41} -5.46455e53 q^{42} -2.30147e56 q^{43} +4.55051e55 q^{44} +1.04164e57 q^{45} -4.16531e57 q^{46} +5.31802e57 q^{47} -1.41197e58 q^{48} -2.04991e58 q^{49} -1.36120e58 q^{50} +7.58578e57 q^{51} +6.91804e59 q^{52} -2.46445e59 q^{53} -7.26540e59 q^{54} -3.83441e58 q^{55} +6.07970e58 q^{56} -6.17680e59 q^{57} -2.84352e60 q^{58} -7.33567e60 q^{59} +2.28094e61 q^{60} -4.55049e61 q^{61} -6.22497e61 q^{62} +8.76606e59 q^{63} +9.88976e62 q^{64} -5.82938e62 q^{65} +1.25725e61 q^{66} -9.77457e62 q^{67} -1.30536e63 q^{68} -8.50284e62 q^{69} -7.92359e61 q^{70} -1.10646e64 q^{71} +3.79986e64 q^{72} +3.21128e63 q^{73} -5.86072e64 q^{74} -2.77868e63 q^{75} +1.06290e65 q^{76} -3.22689e61 q^{77} +1.91137e65 q^{78} +3.60745e65 q^{79} -2.04735e66 q^{80} +4.69295e65 q^{81} -4.94112e65 q^{82} +1.23807e66 q^{83} +1.91955e64 q^{84} +1.09994e66 q^{85} +1.09419e67 q^{86} -5.80460e65 q^{87} -1.39877e66 q^{88} -1.50302e67 q^{89} -4.95232e67 q^{90} -4.90578e65 q^{91} +1.46316e68 q^{92} -1.27073e67 q^{93} -2.52836e68 q^{94} -8.95636e67 q^{95} +3.77193e68 q^{96} -4.11315e68 q^{97} +9.74596e68 q^{98} -2.01684e67 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3} + 12\!\cdots\!60 q^{4} - 18\!\cdots\!50 q^{5} + 65\!\cdots\!60 q^{6} + 76\!\cdots\!92 q^{7} - 45\!\cdots\!00 q^{8} - 31\!\cdots\!35 q^{9} + 44\!\cdots\!00 q^{10}+ \cdots + 58\!\cdots\!80 q^{99}+O(q^{100}) \) 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9 + 44330196388334747724288536990904000 * q^10 - 60667038452283127772973811588820340 * q^11 - 11483075252723727688688753994339790848 * q^12 + 241757308976474000869098277194908009686 * q^13 + 354251192093531665156722201608564593920 * q^14 - 22070061029664005246083216762166031993000 * q^15 + 959158246463054504693505368032717942292480 * q^16 - 3406116484103989032025799295223462139713638 * q^17 + 24028760578245796491398335690330074428977056 * q^18 + 50409644862695734347948203723209710229820500 * q^19 - 1423124021474831957749573329409407107348736000 * q^20 + 3013464004165585730133470747616333350946636960 * q^21 - 11532803895526133094453480299474752792963837056 * q^22 + 49597077165419749499080141147449313474867772376 * q^23 - 3758573903021835292505270073849755869023436800 * q^24 + 464109230075747674561453215791202707168413296875 * q^25 - 16366243363702391437841515238911258759405955787840 * q^26 - 4656668144254073384201536267744600116223141335000 * q^27 - 145657936238300983941227399236934030905596038045696 * q^28 - 623609331535478016897341347681349171717970694417050 * q^29 - 3363430262026080628144709187077082169492181498016000 * q^30 - 7773979811443490840377264327630961134705736859811040 * q^31 - 59446525385187765185716890552455969166501734680363008 * q^32 - 114056291760419605293140369499335251414708842916007568 * q^33 - 257146382902997900108453969123952433606251002004626880 * q^34 - 746713702965644817139124842748848714607056852166946000 * q^35 - 2051949564713522439077005513759167028086223411246648320 * q^36 + 1173349927804932358065167442366744839628119054724224302 * q^37 + 118225357325580676139934406348110667239400005459024000 * q^38 + 14057637047001351842470294363781888979755467326981836280 * q^39 + 113448309945374158392264311043353386142011790732943360000 * q^40 + 126046983235211396249316718220813524712126370275682679410 * q^41 + 293618058653079520265272756273690037096976372387400909824 * q^42 + 182990795236310295463906097926157021228111368794869386156 * q^43 - 207861964397629572369029141530074424104092312018072801280 * q^44 - 1643209216033810606361059101690783215624601629799145190250 * q^45 - 10254004636983168196931301388746633342901210187441053098240 * q^46 - 10227620449924872974485942387482033943920758356350760046928 * q^47 - 32395077603800850016659260748043884333789001078303069569024 * q^48 - 18333133463047872956569862100374253860638045246565546349315 * q^49 + 36528582075561740316450944849185458926809558787823115500000 * q^50 + 118668467511484226348705374365583184000267089107653013314760 * q^51 + 942523544779067327174672695236090488789159958525129397368832 * q^52 + 632699876044410239466855544904774161379655010323706866957246 * q^53 + 180558070990413352422035814551902697653880540863671629472000 * q^54 + 908306905388987301982805388456202130484984202488366374469000 * q^55 - 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 10204523476105540193819201045109650965597050176490899356681200 * q^57 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 - 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 4120988224178099264267892216282931461935581678787045796864000 * q^60 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 + 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 328016742630707922691415372382087941549150107260006661759940136 * q^63 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 + 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 338570852359916448113902185281844117937336911423509879777978880 * q^66 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 - 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 6814317814451425604632002110369996993863432815743912687188684320 * q^69 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 - 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33340305480431860824635017027459448788044465030309454443456921600 * q^72 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 + 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 133279503236831559979066107911998455423803652698542098545072437500 * q^75 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 - 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 57072566318401512231072936702879380800620122459787990692269387008 * q^78 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 - 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 1101671322957552996191157562976784281568686466036132881049220065795 * q^81 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 + 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 2982792317318014581404535874546389828859810656181796104246410117120 * q^84 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 + 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 12567354207673775260644045622671132292173268168085315900596903577400 * q^87 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 - 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 85191607767474905371023384802405560846731062106202026396755774248000 * q^90 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 - 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 112906043990099714252090302813260364787306717550744493130306572821888 * q^93 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 + 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 782790419970794266899143250915194035456012168622622133055202797813760 * q^96 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 + 1783735577381778172290937711296356094085482547558896852990197505179424 * q^98 + 586262466890180722819447934223042169763434625676688596008715148885980 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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