LMFDB - Embedded newform 1.70.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,70,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 70, names="a")

//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);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 70 $
Character orbit:	$[\chi]$	$=$	1.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:	$30.1514953292$
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			1.5
Root			$-1.28427e8$ 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)

$f(q)$	$=$	$q+3.33859e10 q^{2} -1.33163e16 q^{3} +5.24322e20 q^{4} +1.09328e24 q^{5} -4.44575e26 q^{6} -1.48686e29 q^{7} -2.20259e30 q^{8} -6.57062e32 q^{9} +O(q^{10})$	\(q+3.33859e10 q^{2} -1.33163e16 q^{3} +5.24322e20 q^{4} +1.09328e24 q^{5} -4.44575e26 q^{6} -1.48686e29 q^{7} -2.20259e30 q^{8} -6.57062e32 q^{9} +3.65000e34 q^{10} +3.06873e35 q^{11} -6.98201e36 q^{12} +1.14858e38 q^{13} -4.96402e39 q^{14} -1.45583e40 q^{15} -3.83041e41 q^{16} -4.51308e42 q^{17} -2.19366e43 q^{18} +1.29128e44 q^{19} +5.73229e44 q^{20} +1.97994e45 q^{21} +1.02452e46 q^{22} -1.62820e47 q^{23} +2.93302e46 q^{24} -4.98815e47 q^{25} +3.83464e48 q^{26} +1.98605e49 q^{27} -7.79595e49 q^{28} -5.30666e50 q^{29} -4.86043e50 q^{30} +1.03303e51 q^{31} -1.14880e52 q^{32} -4.08640e51 q^{33} -1.50673e53 q^{34} -1.62555e53 q^{35} -3.44512e53 q^{36} +3.96132e53 q^{37} +4.31107e54 q^{38} -1.52948e54 q^{39} -2.40804e54 q^{40} +3.97903e55 q^{41} +6.61022e55 q^{42} +2.19103e56 q^{43} +1.60900e56 q^{44} -7.18350e56 q^{45} -5.43589e57 q^{46} -1.05065e57 q^{47} +5.10067e57 q^{48} +1.60709e57 q^{49} -1.66534e58 q^{50} +6.00973e58 q^{51} +6.02226e58 q^{52} -7.74716e58 q^{53} +6.63061e59 q^{54} +3.35496e59 q^{55} +3.27495e59 q^{56} -1.71951e60 q^{57} -1.77168e61 q^{58} +4.93714e60 q^{59} -7.63326e60 q^{60} +4.27197e61 q^{61} +3.44885e61 q^{62} +9.76962e61 q^{63} -1.57429e62 q^{64} +1.25572e62 q^{65} -1.36428e62 q^{66} +1.10432e63 q^{67} -2.36631e63 q^{68} +2.16815e63 q^{69} -5.42705e63 q^{70} -1.05763e64 q^{71} +1.44724e63 q^{72} +3.43414e64 q^{73} +1.32252e64 q^{74} +6.64234e63 q^{75} +6.77049e64 q^{76} -4.56278e64 q^{77} -5.10631e64 q^{78} -3.22940e65 q^{79} -4.18769e65 q^{80} +2.83776e65 q^{81} +1.32843e66 q^{82} -1.44619e66 q^{83} +1.03813e66 q^{84} -4.93404e66 q^{85} +7.31495e66 q^{86} +7.06649e66 q^{87} -6.75914e65 q^{88} +1.81631e67 q^{89} -2.39828e67 q^{90} -1.70778e67 q^{91} -8.53701e67 q^{92} -1.37561e67 q^{93} -3.50770e67 q^{94} +1.41173e68 q^{95} +1.52977e68 q^{96} +3.55540e68 q^{97} +5.36542e67 q^{98} -2.01635e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots - 31\!\cdots\!35 q^{9}+O(q^{10}) $ 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	$ 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \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

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 $

$2$	3.33859e10	1.37413	0.687066	−	0.726595i	$-0.258899\pi$
$2$	3.33859e10	1.37413	0.687066	+	0.726595i	$0.258899\pi$
$3$	−1.33163e16	−0.460998	−0.230499	−	0.973073i	$-0.574036\pi$
$3$	−1.33163e16	−0.460998	−0.230499	+	0.973073i	$0.574036\pi$
$4$	5.24322e20	0.888236
$5$	1.09328e24	0.839971	0.419986	−	0.907531i	$-0.362035\pi$
$5$	1.09328e24	0.839971	0.419986	+	0.907531i	$0.362035\pi$
$6$	−4.44575e26	−0.633472
$7$	−1.48686e29	−1.03846	−0.519228	−	0.854635i	$-0.673781\pi$
$7$	−1.48686e29	−1.03846	−0.519228	+	0.854635i	$0.673781\pi$
$8$	−2.20259e30	−0.153578
$9$	−6.57062e32	−0.787481
$10$	3.65000e34	1.15423
$11$	3.06873e35	0.362168	0.181084	−	0.983468i	$-0.442039\pi$
$11$	3.06873e35	0.362168	0.181084	+	0.983468i	$0.442039\pi$
$12$	−6.98201e36	−0.409475
$13$	1.14858e38	0.425712	0.212856	−	0.977084i	$-0.431723\pi$
$13$	1.14858e38	0.425712	0.212856	+	0.977084i	$0.431723\pi$
$14$	−4.96402e39	−1.42698
$15$	−1.45583e40	−0.387225
$16$	−3.83041e41	−1.09927
$17$	−4.51308e42	−1.59950	−0.799752	−	0.600331i	$-0.795036\pi$
$17$	−4.51308e42	−1.59950	−0.799752	+	0.600331i	$0.795036\pi$
$18$	−2.19366e43	−1.08210
$19$	1.29128e44	0.986331	0.493165	−	0.869936i	$-0.335840\pi$
$19$	1.29128e44	0.986331	0.493165	+	0.869936i	$0.335840\pi$
$20$	5.73229e44	0.746093
$21$	1.97994e45	0.478726
$22$	1.02452e46	0.497667
$23$	−1.62820e47	−1.70646	−0.853232	−	0.521531i	$-0.825361\pi$
$23$	−1.62820e47	−1.70646	−0.853232	+	0.521531i	$0.825361\pi$
$24$	2.93302e46	0.0707991
$25$	−4.98815e47	−0.294448
$26$	3.83464e48	0.584984
$27$	1.98605e49	0.824025
$28$	−7.79595e49	−0.922395
$29$	−5.30666e50	−1.87107	−0.935536	−	0.353232i	$-0.885083\pi$
$29$	−5.30666e50	−1.87107	−0.935536	+	0.353232i	$0.885083\pi$
$30$	−4.86043e50	−0.532098
$31$	1.03303e51	0.364866	0.182433	−	0.983218i	$-0.441603\pi$
$31$	1.03303e51	0.364866	0.182433	+	0.983218i	$0.441603\pi$
$32$	−1.14880e52	−1.35697
$33$	−4.08640e51	−0.166959
$34$	−1.50673e53	−2.19793
$35$	−1.62555e53	−0.872274
$36$	−3.44512e53	−0.699469
$37$	3.96132e53	0.312522	0.156261	−	0.987716i	$-0.450056\pi$
$37$	3.96132e53	0.312522	0.156261	+	0.987716i	$0.450056\pi$
$38$	4.31107e54	1.35535
$39$	−1.52948e54	−0.196252
$40$	−2.40804e54	−0.129001
$41$	3.97903e55	0.909355	0.454678	−	0.890656i	$-0.349754\pi$
$41$	3.97903e55	0.909355	0.454678	+	0.890656i	$0.349754\pi$
$42$	6.61022e55	0.657833
$43$	2.19103e56	0.968248	0.484124	−	0.874999i	$-0.339138\pi$
$43$	2.19103e56	0.968248	0.484124	+	0.874999i	$0.339138\pi$
$44$	1.60900e56	0.321691
$45$	−7.18350e56	−0.661461
$46$	−5.43589e57	−2.34491
$47$	−1.05065e57	−0.215816	−0.107908	−	0.994161i	$-0.534415\pi$
$47$	−1.05065e57	−0.215816	−0.107908	+	0.994161i	$0.534415\pi$
$48$	5.10067e57	0.506762
$49$	1.60709e57	0.0783927
$50$	−1.66534e58	−0.404610
$51$	6.00973e58	0.737368
$52$	6.02226e58	0.378133
$53$	−7.74716e58	−0.252130	−0.126065	−	0.992022i	$-0.540235\pi$
$53$	−7.74716e58	−0.252130	−0.126065	+	0.992022i	$0.540235\pi$
$54$	6.63061e59	1.13232
$55$	3.35496e59	0.304211
$56$	3.27495e59	0.159484
$57$	−1.71951e60	−0.454696
$58$	−1.77168e61	−2.57110
$59$	4.93714e60	0.397266	0.198633	−	0.980074i	$-0.436350\pi$
$59$	4.93714e60	0.397266	0.198633	+	0.980074i	$0.436350\pi$
$60$	−7.63326e60	−0.343947
$61$	4.27197e61	1.08830	0.544150	−	0.838988i	$-0.316852\pi$
$61$	4.27197e61	1.08830	0.544150	+	0.838988i	$0.316852\pi$
$62$	3.44885e61	0.501374
$63$	9.76962e61	0.817765
$64$	−1.57429e62	−0.765378
$65$	1.25572e62	0.357586
$66$	−1.36428e62	−0.229423
$67$	1.10432e63	1.10539	0.552695	−	0.833384i	$-0.313599\pi$
$67$	1.10432e63	1.10539	0.552695	+	0.833384i	$0.313599\pi$
$68$	−2.36631e63	−1.42074
$69$	2.16815e63	0.786677
$70$	−5.42705e63	−1.19862
$71$	−1.05763e64	−1.43192	−0.715962	−	0.698139i	$-0.754012\pi$
$71$	−1.05763e64	−1.43192	−0.715962	+	0.698139i	$0.754012\pi$
$72$	1.44724e63	0.120940
$73$	3.43414e64	1.78311	0.891556	−	0.452910i	$-0.149614\pi$
$73$	3.43414e64	1.78311	0.891556	+	0.452910i	$0.149614\pi$
$74$	1.32252e64	0.429446
$75$	6.64234e63	0.135740
$76$	6.77049e64	0.876095
$77$	−4.56278e64	−0.376096
$78$	−5.10631e64	−0.269676
$79$	−3.22940e65	−1.09897	−0.549487	−	0.835502i	$-0.685177\pi$
$79$	−3.22940e65	−1.09897	−0.549487	+	0.835502i	$0.685177\pi$
$80$	−4.18769e65	−0.923357
$81$	2.83776e65	0.407607
$82$	1.32843e66	1.24957
$83$	−1.44619e66	−0.895427	−0.447714	−	0.894177i	$-0.647762\pi$
$83$	−1.44619e66	−0.895427	−0.447714	+	0.894177i	$0.647762\pi$
$84$	1.03813e66	0.425222
$85$	−4.93404e66	−1.34354
$86$	7.31495e66	1.33050
$87$	7.06649e66	0.862560
$88$	−6.75914e65	−0.0556211
$89$	1.81631e67	1.01213	0.506064	−	0.862496i	$-0.331100\pi$
$89$	1.81631e67	1.01213	0.506064	+	0.862496i	$0.331100\pi$
$90$	−2.39828e67	−0.908935
$91$	−1.70778e67	−0.442084
$92$	−8.53701e67	−1.51574
$93$	−1.37561e67	−0.168202
$94$	−3.50770e67	−0.296560
$95$	1.41173e68	0.828490
$96$	1.52977e68	0.625559
$97$	3.55540e68	1.01687	0.508433	−	0.861102i	$-0.330225\pi$
$97$	3.55540e68	1.01687	0.508433	+	0.861102i	$0.330225\pi$
$98$	5.36542e67	0.107722
$99$	−2.01635e68	−0.285201
$100$	−2.61540e68	−0.261540
$101$	−9.36000e68	−0.664031	−0.332016	−	0.943274i	$-0.607729\pi$
$101$	−9.36000e68	−0.664031	−0.332016	+	0.943274i	$0.607729\pi$
$102$	2.00640e69	1.01324
$103$	−3.11841e69	−1.12473	−0.562366	−	0.826888i	$-0.690109\pi$
$103$	−3.11841e69	−1.12473	−0.562366	+	0.826888i	$0.690109\pi$
$104$	−2.52985e68	−0.0653800
$105$	2.16463e69	0.402116
$106$	−2.58646e69	−0.346460
$107$	−1.12774e70	−1.09262	−0.546311	−	0.837583i	$-0.683968\pi$
$107$	−1.12774e70	−1.09262	−0.546311	+	0.837583i	$0.683968\pi$
$108$	1.04133e70	0.731929
$109$	9.74708e69	0.498495	0.249247	−	0.968440i	$-0.419817\pi$
$109$	9.74708e69	0.498495	0.249247	+	0.968440i	$0.419817\pi$
$110$	1.12008e70	0.418026
$111$	−5.27500e69	−0.144072
$112$	5.69529e70	1.14155
$113$	5.90939e70	0.871639	0.435819	−	0.900034i	$-0.356459\pi$
$113$	5.90939e70	0.871639	0.435819	+	0.900034i	$0.356459\pi$
$114$	−5.74073e70	−0.624813
$115$	−1.78007e71	−1.43338
$116$	−2.78240e71	−1.66195
$117$	−7.54689e70	−0.335240
$118$	1.64831e71	0.545895
$119$	6.71033e71	1.66102
$120$	3.20660e70	0.0594692
$121$	−6.23781e71	−0.868834
$122$	1.42624e72	1.49547
$123$	−5.29857e71	−0.419211
$124$	5.41639e71	0.324087
$125$	−2.39742e72	−1.08730
$126$	3.26167e72	1.12372
$127$	−3.53335e72	−0.926740	−0.463370	−	0.886165i	$-0.653360\pi$
$127$	−3.53335e72	−0.926740	−0.463370	+	0.886165i	$0.653360\pi$
$128$	1.52539e72	0.305237
$129$	−2.91763e72	−0.446360
$130$	4.19232e72	0.491370
$131$	−1.16166e73	−1.04525	−0.522624	−	0.852563i	$-0.675047\pi$
$131$	−1.16166e73	−1.04525	−0.522624	+	0.852563i	$0.675047\pi$
$132$	−2.14259e72	−0.148299
$133$	−1.91996e73	−1.02426
$134$	3.68688e73	1.51895
$135$	2.17130e73	0.692157
$136$	9.94045e72	0.245648
$137$	2.02412e73	0.388486	0.194243	−	0.980953i	$-0.437775\pi$
$137$	2.02412e73	0.388486	0.194243	+	0.980953i	$0.437775\pi$
$138$	7.23857e73	1.08100
$139$	−7.74542e73	−0.901643	−0.450821	−	0.892614i	$-0.648869\pi$
$139$	−7.74542e73	−0.901643	−0.450821	+	0.892614i	$0.648869\pi$
$140$	−8.52312e73	−0.774785
$141$	1.39908e73	0.0994908
$142$	−3.53099e74	−1.96765
$143$	3.52468e73	0.154179
$144$	2.51682e74	0.865656
$145$	−5.80164e74	−1.57165
$146$	1.14652e75	2.45023
$147$	−2.14004e73	−0.0361389
$148$	2.07701e74	0.277594
$149$	3.21877e74	0.341007	0.170504	−	0.985357i	$-0.445461\pi$
$149$	3.21877e74	0.341007	0.170504	+	0.985357i	$0.445461\pi$
$150$	2.21761e74	0.186525
$151$	−2.24095e75	−1.49874	−0.749371	−	0.662150i	$-0.769644\pi$
$151$	−2.24095e75	−1.49874	−0.749371	+	0.662150i	$0.769644\pi$
$152$	−2.84417e74	−0.151479
$153$	2.96537e75	1.25958
$154$	−1.52332e75	−0.516806
$155$	1.12938e75	0.306477
$156$	−8.01940e74	−0.174318
$157$	−3.05508e74	−0.0532703	−0.0266351	−	0.999645i	$-0.508479\pi$
$157$	−3.05508e74	−0.0532703	−0.0266351	+	0.999645i	$0.508479\pi$
$158$	−1.07817e76	−1.51013
$159$	1.03163e75	0.116231
$160$	−1.25595e76	−1.13981
$161$	2.42091e76	1.77209
$162$	9.47410e75	0.560106
$163$	1.23091e76	0.588510	0.294255	−	0.955727i	$-0.404929\pi$
$163$	1.23091e76	0.588510	0.294255	+	0.955727i	$0.404929\pi$
$164$	2.08629e76	0.807722
$165$	−4.46756e75	−0.140241
$166$	−4.82822e76	−1.23043
$167$	5.42598e76	1.12398	0.561992	−	0.827143i	$-0.310035\pi$
$167$	5.42598e76	1.12398	0.561992	+	0.827143i	$0.310035\pi$
$168$	−4.36100e75	−0.0735218
$169$	−5.96009e76	−0.818769
$170$	−1.64727e77	−1.84620
$171$	−8.48454e76	−0.776717
$172$	1.14881e77	0.860033
$173$	8.73350e76	0.535301	0.267650	−	0.963516i	$-0.413753\pi$
$173$	8.73350e76	0.535301	0.267650	+	0.963516i	$0.413753\pi$
$174$	2.35921e77	1.18527
$175$	7.41669e76	0.305772
$176$	−1.17545e77	−0.398122
$177$	−6.57442e76	−0.183139
$178$	6.06392e77	1.39080
$179$	−5.63287e77	−1.06488	−0.532439	−	0.846468i	$-0.678725\pi$
$179$	−5.63287e77	−1.06488	−0.532439	+	0.846468i	$0.678725\pi$
$180$	−3.76647e77	−0.587534
$181$	8.30874e77	1.07059	0.535296	−	0.844664i	$-0.320200\pi$
$181$	8.30874e77	1.07059	0.535296	+	0.844664i	$0.320200\pi$
$182$	−5.70158e77	−0.607481
$183$	−5.68867e77	−0.501704
$184$	3.58625e77	0.262075
$185$	4.33082e77	0.262510
$186$	−4.59258e77	−0.231132
$187$	−1.38494e78	−0.579290
$188$	−5.50882e77	−0.191696
$189$	−2.95298e78	−0.855714
$190$	4.71319e78	1.13845
$191$	−2.30079e78	−0.463688	−0.231844	−	0.972753i	$-0.574476\pi$
$191$	−2.30079e78	−0.463688	−0.231844	+	0.972753i	$0.574476\pi$
$192$	2.09637e78	0.352837
$193$	8.58446e78	1.20777	0.603887	−	0.797070i	$-0.293618\pi$
$193$	8.58446e78	1.20777	0.603887	+	0.797070i	$0.293618\pi$
$194$	1.18700e79	1.39731
$195$	−1.67214e78	−0.164846
$196$	8.42633e77	0.0696312
$197$	−2.11212e79	−1.46431	−0.732156	−	0.681137i	$-0.761486\pi$
$197$	−2.11212e79	−1.46431	−0.732156	+	0.681137i	$0.761486\pi$
$198$	−6.73175e78	−0.391903
$199$	−2.19954e79	−1.07622	−0.538111	−	0.842874i	$-0.680862\pi$
$199$	−2.19954e79	−1.07622	−0.538111	+	0.842874i	$0.680862\pi$
$200$	1.09868e78	0.0452207
$201$	−1.47055e79	−0.509583
$202$	−3.12492e79	−0.912466
$203$	7.89028e79	1.94303
$204$	3.15104e79	0.654957
$205$	4.35017e79	0.763832
$206$	−1.04111e80	−1.54553
$207$	1.06983e80	1.34381
$208$	−4.39953e79	−0.467974
$209$	3.96260e79	0.357218
$210$	7.22679e79	0.552561
$211$	−1.54836e80	−1.00491	−0.502455	−	0.864603i	$-0.667570\pi$
$211$	−1.54836e80	−1.00491	−0.502455	+	0.864603i	$0.667570\pi$
$212$	−4.06201e79	−0.223951
$213$	1.40837e80	0.660114
$214$	−3.76507e80	−1.50141
$215$	2.39540e80	0.813301
$216$	−4.37445e79	−0.126552
$217$	−1.53597e80	−0.378898
$218$	3.25415e80	0.684997
$219$	−4.57298e80	−0.822011
$220$	1.75908e80	0.270211
$221$	−5.18364e80	−0.680928
$222$	−1.76111e80	−0.197974
$223$	5.11766e80	0.492667	0.246333	−	0.969185i	$-0.420774\pi$
$223$	5.11766e80	0.492667	0.246333	+	0.969185i	$0.420774\pi$
$224$	1.70810e81	1.40915
$225$	3.27752e80	0.231872
$226$	1.97290e81	1.19775
$227$	−3.41994e80	−0.178290	−0.0891450	−	0.996019i	$-0.528413\pi$
$227$	−3.41994e80	−0.178290	−0.0891450	+	0.996019i	$0.528413\pi$
$228$	−9.01576e80	−0.403878
$229$	−1.35567e81	−0.522192	−0.261096	−	0.965313i	$-0.584084\pi$
$229$	−1.35567e81	−0.522192	−0.261096	+	0.965313i	$0.584084\pi$
$230$	−5.94293e81	−1.96965
$231$	6.07591e80	0.173380
$232$	1.16884e81	0.287355
$233$	−2.21214e81	−0.468849	−0.234425	−	0.972134i	$-0.575321\pi$
$233$	−2.21214e81	−0.468849	−0.234425	+	0.972134i	$0.575321\pi$
$234$	−2.51960e81	−0.460664
$235$	−1.14865e81	−0.181279
$236$	2.58865e81	0.352866
$237$	4.30036e81	0.506625
$238$	2.24030e82	2.28245
$239$	−1.28714e81	−0.113474	−0.0567371	−	0.998389i	$-0.518070\pi$
$239$	−1.28714e81	−0.113474	−0.0567371	+	0.998389i	$0.518070\pi$
$240$	5.57643e81	0.425666
$241$	−5.65464e81	−0.373953	−0.186976	−	0.982364i	$-0.559869\pi$
$241$	−5.65464e81	−0.373953	−0.186976	+	0.982364i	$0.559869\pi$
$242$	−2.08255e82	−1.19389
$243$	−2.03501e82	−1.01193
$244$	2.23989e82	0.966668
$245$	1.75699e81	0.0658476
$246$	−1.76898e82	−0.576051
$247$	1.48314e82	0.419893
$248$	−2.27533e81	−0.0560354
$249$	1.92578e82	0.412790
$250$	−8.00401e82	−1.49409
$251$	2.72558e82	0.443319	0.221659	−	0.975124i	$-0.428853\pi$
$251$	2.72558e82	0.443319	0.221659	+	0.975124i	$0.428853\pi$
$252$	5.12243e82	0.726369
$253$	−4.99650e82	−0.618028
$254$	−1.17964e83	−1.27346
$255$	6.57029e82	0.619368
$256$	1.43856e83	1.18481
$257$	1.85886e83	1.33830	0.669151	−	0.743126i	$-0.266658\pi$
$257$	1.85886e83	1.33830	0.669151	+	0.743126i	$0.266658\pi$
$258$	−9.74078e82	−0.613358
$259$	−5.88994e82	−0.324541
$260$	6.58399e82	0.317621
$261$	3.48681e83	1.47343
$262$	−3.87830e83	−1.43631
$263$	−1.49982e83	−0.487040	−0.243520	−	0.969896i	$-0.578302\pi$
$263$	−1.49982e83	−0.487040	−0.243520	+	0.969896i	$0.578302\pi$
$264$	9.00065e81	0.0256412
$265$	−8.46978e82	−0.211782
$266$	−6.40997e83	−1.40747
$267$	−2.41865e83	−0.466589
$268$	5.79021e83	0.981848
$269$	−1.02493e84	−1.52842	−0.764210	−	0.644968i	$-0.776871\pi$
$269$	−1.02493e84	−1.52842	−0.764210	+	0.644968i	$0.776871\pi$
$270$	7.24908e83	0.951115
$271$	3.51588e83	0.406063	0.203031	−	0.979172i	$-0.434921\pi$
$271$	3.51588e83	0.406063	0.203031	+	0.979172i	$0.434921\pi$
$272$	1.72869e84	1.75829
$273$	2.27413e83	0.203800
$274$	6.75769e83	0.533831
$275$	−1.53073e83	−0.106640
$276$	1.13681e84	0.698755
$277$	−2.11779e84	−1.14903	−0.574516	−	0.818494i	$-0.694810\pi$
$277$	−2.11779e84	−1.14903	−0.574516	+	0.818494i	$0.694810\pi$
$278$	−2.58588e84	−1.23898
$279$	−6.78763e83	−0.287325
$280$	3.58042e83	0.133962
$281$	−1.81711e84	−0.601192	−0.300596	−	0.953752i	$-0.597186\pi$
$281$	−1.81711e84	−0.601192	−0.300596	+	0.953752i	$0.597186\pi$
$282$	4.67095e83	0.136713
$283$	7.40610e84	1.91848	0.959240	−	0.282591i	$-0.0911940\pi$
$283$	7.40610e84	1.91848	0.959240	+	0.282591i	$0.0911940\pi$
$284$	−5.54538e84	−1.27189
$285$	−1.87990e84	−0.381932
$286$	1.17675e84	0.211863
$287$	−5.91626e84	−0.944326
$288$	7.54832e84	1.06859
$289$	1.24067e85	1.55841
$290$	−1.93693e85	−2.15965
$291$	−4.73446e84	−0.468773
$292$	1.80059e85	1.58383
$293$	4.21629e84	0.329608	0.164804	−	0.986326i	$-0.447301\pi$
$293$	4.21629e84	0.329608	0.164804	+	0.986326i	$0.447301\pi$
$294$	−7.14473e83	−0.0496595
$295$	5.39765e84	0.333692
$296$	−8.72516e83	−0.0479965
$297$	6.09465e84	0.298436
$298$	1.07462e85	0.468589
$299$	−1.87012e85	−0.726463
$300$	3.48273e84	0.120569
$301$	−3.25776e85	−1.00548
$302$	−7.48161e85	−2.05947
$303$	1.24640e85	0.306117
$304$	−4.94614e85	−1.08425
$305$	4.67044e85	0.914141
$306$	9.90017e85	1.73083
$307$	4.27730e85	0.668183	0.334092	−	0.942541i	$-0.391571\pi$
$307$	4.27730e85	0.668183	0.334092	+	0.942541i	$0.391571\pi$
$308$	−2.39236e85	−0.334062
$309$	4.15256e85	0.518499
$310$	3.77055e85	0.421140
$311$	−9.59066e83	−0.00958550	−0.00479275	−	0.999989i	$-0.501526\pi$
$311$	−9.59066e83	−0.00958550	−0.00479275	+	0.999989i	$0.501526\pi$
$312$	3.36881e84	0.0301400
$313$	−9.21743e84	−0.0738465	−0.0369233	−	0.999318i	$-0.511756\pi$
$313$	−9.21743e84	−0.0738465	−0.0369233	+	0.999318i	$0.511756\pi$
$314$	−1.01997e85	−0.0732003
$315$	1.06809e86	0.686899
$316$	−1.69325e86	−0.976149
$317$	−2.74826e86	−1.42074	−0.710368	−	0.703831i	$-0.751471\pi$
$317$	−2.74826e86	−1.42074	−0.710368	+	0.703831i	$0.751471\pi$
$318$	3.44419e85	0.159717
$319$	−1.62847e86	−0.677643
$320$	−1.72113e86	−0.642895
$321$	1.50173e86	0.503696
$322$	8.08242e86	2.43508
$323$	−5.82767e86	−1.57764
$324$	1.48790e86	0.362052
$325$	−5.72929e85	−0.125350
$326$	4.10950e86	0.808690
$327$	−1.29795e86	−0.229805
$328$	−8.76415e85	−0.139657
$329$	1.56218e86	0.224116
$330$	−1.49153e86	−0.192709
$331$	2.93761e86	0.341924	0.170962	−	0.985278i	$-0.445313\pi$
$331$	2.93761e86	0.341924	0.170962	+	0.985278i	$0.445313\pi$
$332$	−7.58268e86	−0.795351
$333$	−2.60284e86	−0.246105
$334$	1.81151e87	1.54450
$335$	1.20733e87	0.928496
$336$	−7.58399e86	−0.526251
$337$	−9.85960e85	−0.0617487	−0.0308743	−	0.999523i	$-0.509829\pi$
$337$	−9.85960e85	−0.0617487	−0.0308743	+	0.999523i	$0.509829\pi$
$338$	−1.98983e87	−1.12510
$339$	−7.86910e86	−0.401824
$340$	−2.58703e87	−1.19338
$341$	3.17008e86	0.132143
$342$	−2.83264e87	−1.06731
$343$	2.80919e87	0.957049
$344$	−4.82594e86	−0.148702
$345$	2.37039e87	0.660786
$346$	2.91576e87	0.735573
$347$	2.16749e87	0.494984	0.247492	−	0.968890i	$-0.420394\pi$
$347$	2.16749e87	0.494984	0.247492	+	0.968890i	$0.420394\pi$
$348$	3.70512e87	0.766157
$349$	5.35272e86	0.100253	0.0501265	−	0.998743i	$-0.484038\pi$
$349$	5.35272e86	0.100253	0.0501265	+	0.998743i	$0.484038\pi$
$350$	2.47613e87	0.420170
$351$	2.28114e87	0.350797
$352$	−3.52535e87	−0.491451
$353$	−5.11860e87	−0.647029	−0.323515	−	0.946223i	$-0.604864\pi$
$353$	−5.11860e87	−0.647029	−0.323515	+	0.946223i	$0.604864\pi$
$354$	−2.19493e87	−0.251656
$355$	−1.15628e88	−1.20278
$356$	9.52333e87	0.899009
$357$	−8.93565e87	−0.765725
$358$	−1.88058e88	−1.46328
$359$	4.89613e87	0.346015	0.173007	−	0.984921i	$-0.444652\pi$
$359$	4.89613e87	0.346015	0.173007	+	0.984921i	$0.444652\pi$
$360$	1.58223e87	0.101586
$361$	−4.65361e86	−0.0271513
$362$	2.77395e88	1.47113
$363$	8.30643e87	0.400531
$364$	−8.95428e87	−0.392675
$365$	3.75446e88	1.49776
$366$	−1.89921e88	−0.689407
$367$	−5.99403e88	−1.98034	−0.990170	−	0.139870i	$-0.955332\pi$
$367$	−5.99403e88	−1.98034	−0.990170	+	0.139870i	$0.955332\pi$
$368$	6.23667e88	1.87587
$369$	−2.61447e88	−0.716100
$370$	1.44588e88	0.360723
$371$	1.15190e88	0.261826
$372$	−7.21261e87	−0.149404
$373$	3.54730e88	0.669798	0.334899	−	0.942254i	$-0.391298\pi$
$373$	3.54730e88	0.669798	0.334899	+	0.942254i	$0.391298\pi$
$374$	−4.62375e88	−0.796020
$375$	3.19247e88	0.501243
$376$	2.31416e87	0.0331446
$377$	−6.09513e88	−0.796538
$378$	−9.85880e88	−1.17586
$379$	2.22937e88	0.242733	0.121367	−	0.992608i	$-0.461272\pi$
$379$	2.22937e88	0.242733	0.121367	+	0.992608i	$0.461272\pi$
$380$	7.40201e88	0.735895
$381$	4.70510e88	0.427225
$382$	−7.68140e88	−0.637168
$383$	−1.24464e89	−0.943377	−0.471688	−	0.881765i	$-0.656355\pi$
$383$	−1.24464e89	−0.943377	−0.471688	+	0.881765i	$0.656355\pi$
$384$	−2.03125e88	−0.140714
$385$	−4.98837e88	−0.315910
$386$	2.86600e89	1.65964
$387$	−1.43964e89	−0.762477
$388$	1.86418e89	0.903217
$389$	5.53987e88	0.245606	0.122803	−	0.992431i	$-0.460812\pi$
$389$	5.53987e88	0.245606	0.122803	+	0.992431i	$0.460812\pi$
$390$	−5.58260e88	−0.226521
$391$	7.34819e89	2.72950
$392$	−3.53976e87	−0.0120394
$393$	1.54690e89	0.481857
$394$	−7.05150e89	−2.01216
$395$	−3.53063e89	−0.923107
$396$	−1.05721e89	−0.253326
$397$	−4.52792e89	−0.994549	−0.497275	−	0.867593i	$-0.665666\pi$
$397$	−4.52792e89	−0.994549	−0.497275	+	0.867593i	$0.665666\pi$
$398$	−7.34338e89	−1.47887
$399$	2.55667e89	0.472183
$400$	1.91066e89	0.323679
$401$	8.61105e89	1.33837	0.669184	−	0.743097i	$-0.266644\pi$
$401$	8.61105e89	1.33837	0.669184	+	0.743097i	$0.266644\pi$
$402$	−4.90955e89	−0.700233
$403$	1.18652e89	0.155328
$404$	−4.90766e89	−0.589817
$405$	3.10245e89	0.342378
$406$	2.63424e90	2.66997
$407$	1.21562e89	0.113186
$408$	−1.32370e89	−0.113243
$409$	−2.16606e90	−1.70301	−0.851503	−	0.524349i	$-0.824309\pi$
$409$	−2.16606e90	−1.70301	−0.851503	+	0.524349i	$0.824309\pi$
$410$	1.45234e90	1.04961
$411$	−2.69537e89	−0.179091
$412$	−1.63505e90	−0.999028
$413$	−7.34085e89	−0.412543
$414$	3.57172e90	1.84657
$415$	−1.58108e90	−0.752133
$416$	−1.31949e90	−0.577677
$417$	1.03140e90	0.415656
$418$	1.32295e90	0.490864
$419$	−4.26463e90	−1.45713	−0.728564	−	0.684978i	$-0.759812\pi$
$419$	−4.26463e90	−1.45713	−0.728564	+	0.684978i	$0.759812\pi$
$420$	1.13496e90	0.357174
$421$	2.14948e90	0.623161	0.311580	−	0.950220i	$-0.399142\pi$
$421$	2.14948e90	0.623161	0.311580	+	0.950220i	$0.399142\pi$
$422$	−5.16934e90	−1.38088
$423$	6.90346e89	0.169951
$424$	1.70638e89	0.0387216
$425$	2.25119e90	0.470971
$426$	4.70195e90	0.907083
$427$	−6.35183e90	−1.13015
$428$	−5.91301e90	−0.970506
$429$	−4.69356e89	−0.0710764
$430$	7.99726e90	1.11758
$431$	1.33305e91	1.71942	0.859709	−	0.510784i	$-0.170645\pi$
$431$	1.33305e91	1.71942	0.859709	+	0.510784i	$0.170645\pi$
$432$	−7.60738e90	−0.905828
$433$	1.51128e91	1.66155	0.830775	−	0.556609i	$-0.187898\pi$
$433$	1.51128e91	1.66155	0.830775	+	0.556609i	$0.187898\pi$
$434$	−5.12797e90	−0.520655
$435$	7.72562e90	0.724526
$436$	5.11061e90	0.442781
$437$	−2.10247e91	−1.68314
$438$	−1.52673e91	−1.12955
$439$	2.64868e90	0.181135	0.0905676	−	0.995890i	$-0.471132\pi$
$439$	2.64868e90	0.181135	0.0905676	+	0.995890i	$0.471132\pi$
$440$	−7.38960e89	−0.0467201
$441$	−1.05596e90	−0.0617327
$442$	−1.73060e91	−0.935684
$443$	−2.29504e91	−1.14779	−0.573895	−	0.818929i	$-0.694568\pi$
$443$	−2.29504e91	−1.14779	−0.573895	+	0.818929i	$0.694568\pi$
$444$	−2.76580e90	−0.127970
$445$	1.98573e91	0.850158
$446$	1.70858e91	0.676989
$447$	−4.28620e90	−0.157204
$448$	2.34075e91	0.794812
$449$	2.43709e90	0.0766254	0.0383127	−	0.999266i	$-0.487802\pi$
$449$	2.43709e90	0.0766254	0.0383127	+	0.999266i	$0.487802\pi$
$450$	1.09423e91	0.318623
$451$	1.22105e91	0.329340
$452$	3.09842e91	0.774221
$453$	2.98410e91	0.690917
$454$	−1.14178e91	−0.244994
$455$	−1.86708e91	−0.371338
$456$	3.78737e90	0.0698313
$457$	−1.52668e91	−0.260999	−0.130499	−	0.991448i	$-0.541658\pi$
$457$	−1.52668e91	−0.260999	−0.130499	+	0.991448i	$0.541658\pi$
$458$	−4.52603e91	−0.717560
$459$	−8.96320e91	−1.31803
$460$	−9.33331e91	−1.27318
$461$	8.38473e91	1.06122	0.530612	−	0.847615i	$-0.321962\pi$
$461$	8.38473e91	1.06122	0.530612	+	0.847615i	$0.321962\pi$
$462$	2.02850e91	0.238246
$463$	−4.55428e91	−0.496450	−0.248225	−	0.968702i	$-0.579847\pi$
$463$	−4.55428e91	−0.496450	−0.248225	+	0.968702i	$0.579847\pi$
$464$	2.03267e92	2.05682
$465$	−1.50392e91	−0.141285
$466$	−7.38542e91	−0.644260
$467$	8.33552e91	0.675306	0.337653	−	0.941271i	$-0.390367\pi$
$467$	8.33552e91	0.675306	0.337653	+	0.941271i	$0.390367\pi$
$468$	−3.95700e91	−0.297772
$469$	−1.64198e92	−1.14790
$470$	−3.83489e91	−0.249102
$471$	4.06823e90	0.0245575
$472$	−1.08745e91	−0.0610112
$473$	6.72367e91	0.350669
$474$	1.43571e92	0.696169
$475$	−6.44111e91	−0.290423
$476$	3.51837e92	1.47537
$477$	5.09037e91	0.198548
$478$	−4.29722e91	−0.155928
$479$	−3.70416e91	−0.125059	−0.0625294	−	0.998043i	$-0.519917\pi$
$479$	−3.70416e91	−0.125059	−0.0625294	+	0.998043i	$0.519917\pi$
$480$	1.67246e92	0.525451
$481$	4.54990e91	0.133044
$482$	−1.88785e92	−0.513860
$483$	−3.22375e92	−0.816930
$484$	−3.27062e92	−0.771730
$485$	3.88703e92	0.854138
$486$	−6.79408e92	−1.39053
$487$	2.37954e91	0.0453674	0.0226837	−	0.999743i	$-0.492779\pi$
$487$	2.37954e91	0.0453674	0.0226837	+	0.999743i	$0.492779\pi$
$488$	−9.40939e91	−0.167139
$489$	−1.63911e92	−0.271302
$490$	5.86588e91	0.0904833
$491$	−9.67144e92	−1.39053	−0.695264	−	0.718755i	$-0.744712\pi$
$491$	−9.67144e92	−1.39053	−0.695264	+	0.718755i	$0.744712\pi$
$492$	−2.77816e92	−0.372358
$493$	2.39494e93	2.99279
$494$	4.95161e92	0.576988
$495$	−2.20442e92	−0.239560
$496$	−3.95691e92	−0.401087
$497$	1.57255e93	1.48699
$498$	6.42939e92	0.567228
$499$	4.76253e92	0.392075	0.196038	−	0.980596i	$-0.437193\pi$
$499$	4.76253e92	0.392075	0.196038	+	0.980596i	$0.437193\pi$
$500$	−1.25702e93	−0.965779
$501$	−7.22538e92	−0.518154
$502$	9.09961e92	0.609178
$503$	−1.36831e93	−0.855241	−0.427621	−	0.903958i	$-0.640648\pi$
$503$	−1.36831e93	−0.855241	−0.427621	+	0.903958i	$0.640648\pi$
$504$	−2.15184e92	−0.125591
$505$	−1.02331e93	−0.557767
$506$	−1.66813e93	−0.849251
$507$	7.93661e92	0.377451
$508$	−1.85261e93	−0.823164
$509$	−1.95379e92	−0.0811174	−0.0405587	−	0.999177i	$-0.512914\pi$
$509$	−1.95379e92	−0.0811174	−0.0405587	+	0.999177i	$0.512914\pi$
$510$	2.19355e93	0.851092
$511$	−5.10609e93	−1.85169
$512$	3.90234e93	1.32285
$513$	2.56456e93	0.812761
$514$	6.20598e93	1.83900
$515$	−3.40928e93	−0.944743
$516$	−1.52978e93	−0.396473
$517$	−3.22417e92	−0.0781618
$518$	−1.96641e93	−0.445962
$519$	−1.16298e93	−0.246773
$520$	−2.76582e92	−0.0549173
$521$	−5.63899e92	−0.104785	−0.0523926	−	0.998627i	$-0.516685\pi$
$521$	−5.63899e92	−0.104785	−0.0523926	+	0.998627i	$0.516685\pi$
$522$	1.16410e94	2.02469
$523$	3.06121e93	0.498408	0.249204	−	0.968451i	$-0.419831\pi$
$523$	3.06121e93	0.498408	0.249204	+	0.968451i	$0.419831\pi$
$524$	−6.09084e93	−0.928427
$525$	−9.87625e92	−0.140960
$526$	−5.00727e93	−0.669257
$527$	−4.66213e93	−0.583604
$528$	1.56526e93	0.183533
$529$	1.74066e94	1.91202
$530$	−2.82771e93	−0.291016
$531$	−3.24401e93	−0.312839
$532$	−1.00668e94	−0.909787
$533$	4.57023e93	0.387124
$534$	−8.07487e93	−0.641154
$535$	−1.23293e94	−0.917771
$536$	−2.43237e93	−0.169764
$537$	7.50087e93	0.490907
$538$	−3.42184e94	−2.10025
$539$	4.93172e92	0.0283914
$540$	1.13846e94	0.614799
$541$	3.42402e94	1.73473	0.867363	−	0.497676i	$-0.165813\pi$
$541$	3.42402e94	1.73473	0.867363	+	0.497676i	$0.165813\pi$
$542$	1.17381e94	0.557983
$543$	−1.10641e94	−0.493541
$544$	5.18461e94	2.17047
$545$	1.06562e94	0.418721
$546$	7.59238e93	0.280047
$547$	−9.21148e93	−0.318982	−0.159491	−	0.987199i	$-0.550985\pi$
$547$	−9.21148e93	−0.318982	−0.159491	+	0.987199i	$0.550985\pi$
$548$	1.06129e94	0.345068
$549$	−2.80695e94	−0.857016
$550$	−5.11047e93	−0.146537
$551$	−6.85241e94	−1.84550
$552$	−4.77555e93	−0.120816
$553$	4.80168e94	1.14124
$554$	−7.07045e94	−1.57892
$555$	−5.76703e93	−0.121016
$556$	−4.06110e94	−0.800872
$557$	4.57947e94	0.848810	0.424405	−	0.905472i	$-0.360483\pi$
$557$	4.57947e94	0.848810	0.424405	+	0.905472i	$0.360483\pi$
$558$	−2.26611e94	−0.394822
$559$	2.51658e94	0.412195
$560$	6.22652e94	0.958867
$561$	1.84422e94	0.267051
$562$	−6.06659e94	−0.826117
$563$	−7.69524e94	−0.985558	−0.492779	−	0.870154i	$-0.664019\pi$
$563$	−7.69524e94	−0.985558	−0.492779	+	0.870154i	$0.664019\pi$
$564$	7.33568e93	0.0883713
$565$	6.46059e94	0.732151
$566$	2.47259e95	2.63624
$567$	−4.21935e94	−0.423282
$568$	2.32952e94	0.219912
$569$	−2.74215e94	−0.243623	−0.121811	−	0.992553i	$-0.538870\pi$
$569$	−2.74215e94	−0.243623	−0.121811	+	0.992553i	$0.538870\pi$
$570$	−6.27620e94	−0.524825
$571$	−8.73385e94	−0.687480	−0.343740	−	0.939065i	$-0.611694\pi$
$571$	−8.73385e94	−0.687480	−0.343740	+	0.939065i	$0.611694\pi$
$572$	1.84807e94	0.136948
$573$	3.06379e94	0.213759
$574$	−1.97520e95	−1.29763
$575$	8.12170e94	0.502465
$576$	1.03441e95	0.602720
$577$	−1.84195e95	−1.01091	−0.505456	−	0.862852i	$-0.668676\pi$
$577$	−1.84195e95	−1.01091	−0.505456	+	0.862852i	$0.668676\pi$
$578$	4.14210e95	2.14146
$579$	−1.14313e95	−0.556781
$580$	−3.04193e95	−1.39599
$581$	2.15028e95	0.929862
$582$	−1.58064e95	−0.644156
$583$	−2.37739e94	−0.0913136
$584$	−7.56399e94	−0.273847
$585$	−8.25083e94	−0.281592
$586$	1.40764e95	0.452924
$587$	−4.28656e95	−1.30045	−0.650226	−	0.759741i	$-0.725326\pi$
$587$	−4.28656e95	−1.30045	−0.650226	+	0.759741i	$0.725326\pi$
$588$	−1.12207e94	−0.0320999
$589$	1.33393e95	0.359879
$590$	1.80206e95	0.458536
$591$	2.81255e95	0.675045
$592$	−1.51735e95	−0.343547
$593$	1.24823e95	0.266629	0.133314	−	0.991074i	$-0.457438\pi$
$593$	1.24823e95	0.266629	0.133314	+	0.991074i	$0.457438\pi$
$594$	2.03475e95	0.410090
$595$	7.33624e95	1.39521
$596$	1.68767e95	0.302895
$597$	2.92897e95	0.496136
$598$	−6.24356e95	−0.998255
$599$	1.05846e95	0.159752	0.0798761	−	0.996805i	$-0.474548\pi$
$599$	1.05846e95	0.159752	0.0798761	+	0.996805i	$0.474548\pi$
$600$	−1.46303e94	−0.0208467
$601$	8.57967e95	1.15425	0.577127	−	0.816654i	$-0.304174\pi$
$601$	8.57967e95	1.15425	0.577127	+	0.816654i	$0.304174\pi$
$602$	−1.08763e96	−1.38167
$603$	−7.25609e95	−0.870474
$604$	−1.17498e96	−1.33124
$605$	−6.81964e95	−0.729796
$606$	4.16123e95	0.420645
$607$	4.90330e95	0.468250	0.234125	−	0.972206i	$-0.424777\pi$
$607$	4.90330e95	0.468250	0.234125	+	0.972206i	$0.424777\pi$
$608$	−1.48342e96	−1.33842
$609$	−1.05069e96	−0.895732
$610$	1.55927e96	1.25615
$611$	−1.20676e95	−0.0918755
$612$	1.55481e96	1.11880
$613$	1.07997e96	0.734556	0.367278	−	0.930111i	$-0.380290\pi$
$613$	1.07997e96	0.734556	0.367278	+	0.930111i	$0.380290\pi$
$614$	1.42801e96	0.918171
$615$	−5.79280e95	−0.352125
$616$	1.00499e95	0.0577601
$617$	−6.04192e95	−0.328350	−0.164175	−	0.986431i	$-0.552496\pi$
$617$	−6.04192e95	−0.328350	−0.164175	+	0.986431i	$0.552496\pi$
$618$	1.38637e96	0.712486
$619$	2.55704e96	1.24283	0.621413	−	0.783483i	$-0.286559\pi$
$619$	2.55704e96	1.24283	0.621413	+	0.783483i	$0.286559\pi$
$620$	5.92161e95	0.272224
$621$	−3.23369e96	−1.40617
$622$	−3.20193e94	−0.0131717
$623$	−2.70061e96	−1.05105
$624$	5.85853e95	0.215735
$625$	−1.77602e96	−0.618852
$626$	−3.07732e95	−0.101475
$627$	−5.27670e95	−0.164677
$628$	−1.60185e95	−0.0473166
$629$	−1.78778e96	−0.499880
$630$	3.56591e96	0.943890
$631$	4.61934e96	1.15762	0.578812	−	0.815461i	$-0.303517\pi$
$631$	4.61934e96	1.15762	0.578812	+	0.815461i	$0.303517\pi$
$632$	7.11304e95	0.168778
$633$	2.06184e96	0.463261
$634$	−9.17531e96	−1.95228
$635$	−3.86292e96	−0.778435
$636$	5.40907e95	0.103241
$637$	1.84587e95	0.0333727
$638$	−5.43679e96	−0.931171
$639$	6.94928e96	1.12761
$640$	1.66767e96	0.256391
$641$	−4.05240e96	−0.590351	−0.295176	−	0.955443i	$-0.595378\pi$
$641$	−4.05240e96	−0.590351	−0.295176	+	0.955443i	$0.595378\pi$
$642$	5.01367e96	0.692145
$643$	6.21130e96	0.812650	0.406325	−	0.913729i	$-0.366810\pi$
$643$	6.21130e96	0.812650	0.406325	+	0.913729i	$0.366810\pi$
$644$	1.26934e97	1.57403
$645$	−3.18978e96	−0.374930
$646$	−1.94562e97	−2.16788
$647$	1.26722e97	1.33861	0.669305	−	0.742988i	$-0.266592\pi$
$647$	1.26722e97	1.33861	0.669305	+	0.742988i	$0.266592\pi$
$648$	−6.25041e95	−0.0625995
$649$	1.51507e96	0.143877
$650$	−1.91277e96	−0.172248
$651$	2.04534e96	0.174671
$652$	6.45393e96	0.522736
$653$	1.30200e97	1.00024	0.500121	−	0.865956i	$-0.333289\pi$
$653$	1.30200e97	1.00024	0.500121	+	0.865956i	$0.333289\pi$
$654$	−4.33331e96	−0.315782
$655$	−1.27001e97	−0.877978
$656$	−1.52413e97	−0.999629
$657$	−2.25644e97	−1.40417
$658$	5.21547e96	0.307964
$659$	2.36954e96	0.132776	0.0663878	−	0.997794i	$-0.478853\pi$
$659$	2.36954e96	0.132776	0.0663878	+	0.997794i	$0.478853\pi$
$660$	−2.34244e96	−0.124567
$661$	−3.01280e97	−1.52062	−0.760309	−	0.649561i	$-0.774953\pi$
$661$	−3.01280e97	−1.52062	−0.760309	+	0.649561i	$0.774953\pi$
$662$	9.80749e96	0.469848
$663$	6.90267e96	0.313906
$664$	3.18535e96	0.137518
$665$	−2.09905e97	−0.860351
$666$	−8.68980e96	−0.338181
$667$	8.64030e97	3.19292
$668$	2.84496e97	0.998364
$669$	−6.81481e96	−0.227118
$670$	4.03078e97	1.27588
$671$	1.31095e97	0.394148
$672$	−2.27456e97	−0.649616
$673$	−2.89421e97	−0.785255	−0.392628	−	0.919698i	$-0.628434\pi$
$673$	−2.89421e97	−0.785255	−0.392628	+	0.919698i	$0.628434\pi$
$674$	−3.29172e96	−0.0848508
$675$	−9.90671e96	−0.242633
$676$	−3.12501e97	−0.727261
$677$	2.23424e97	0.494106	0.247053	−	0.969002i	$-0.420538\pi$
$677$	2.23424e97	0.494106	0.247053	+	0.969002i	$0.420538\pi$
$678$	−2.62717e97	−0.552158
$679$	−5.28639e97	−1.05597
$680$	1.08677e97	0.206338
$681$	4.55409e96	0.0821913
$682$	1.05836e97	0.181582
$683$	−4.84431e97	−0.790165	−0.395083	−	0.918646i	$-0.629284\pi$
$683$	−4.84431e97	−0.790165	−0.395083	+	0.918646i	$0.629284\pi$
$684$	−4.44863e97	−0.689908
$685$	2.21292e97	0.326318
$686$	9.37874e97	1.31511
$687$	1.80525e97	0.240729
$688$	−8.39253e97	−1.06437
$689$	−8.89824e96	−0.107335
$690$	7.91375e97	0.908006
$691$	−6.77284e96	−0.0739227	−0.0369614	−	0.999317i	$-0.511768\pi$
$691$	−6.77284e96	−0.0739227	−0.0369614	+	0.999317i	$0.511768\pi$
$692$	4.57917e97	0.475474
$693$	2.99803e97	0.296169
$694$	7.23637e97	0.680173
$695$	−8.46788e97	−0.757354
$696$	−1.55646e97	−0.132470
$697$	−1.79577e98	−1.45452
$698$	1.78705e97	0.137761
$699$	2.94574e97	0.216138
$700$	3.88873e97	0.271598
$701$	1.99785e98	1.32829	0.664144	−	0.747605i	$-0.268796\pi$
$701$	1.99785e98	1.32829	0.664144	+	0.747605i	$0.268796\pi$
$702$	7.61579e97	0.482042
$703$	5.11519e97	0.308250
$704$	−4.83107e97	−0.277196
$705$	1.52958e97	0.0835694
$706$	−1.70889e98	−0.889103
$707$	1.39170e98	0.689568
$708$	−3.44712e97	−0.162670
$709$	−2.67263e97	−0.120128	−0.0600640	−	0.998195i	$-0.519130\pi$
$709$	−2.67263e97	−0.120128	−0.0600640	+	0.998195i	$0.519130\pi$
$710$	−3.86034e98	−1.65277
$711$	2.12192e98	0.865421
$712$	−4.00059e97	−0.155440
$713$	−1.68197e98	−0.622631
$714$	−2.98325e98	−1.05221
$715$	3.85345e97	0.129506
$716$	−2.95344e98	−0.945864
$717$	1.71398e97	0.0523113
$718$	1.63462e98	0.475470
$719$	7.00234e97	0.194132	0.0970659	−	0.995278i	$-0.469054\pi$
$719$	7.00234e97	0.194132	0.0970659	+	0.995278i	$0.469054\pi$
$720$	2.75157e98	0.727126
$721$	4.63665e98	1.16799
$722$	−1.55365e97	−0.0373095
$723$	7.52986e97	0.172391
$724$	4.35646e98	0.950939
$725$	2.64704e98	0.550934
$726$	2.77318e98	0.550382
$727$	−6.73415e98	−1.27452	−0.637259	−	0.770650i	$-0.719932\pi$
$727$	−6.73415e98	−1.27452	−0.637259	+	0.770650i	$0.719932\pi$
$728$	3.76154e97	0.0678943
$729$	3.42096e97	0.0588909
$730$	1.25346e99	2.05812
$731$	−9.88829e98	−1.54872
$732$	−2.98269e98	−0.445632
$733$	−2.73438e98	−0.389737	−0.194868	−	0.980829i	$-0.562428\pi$
$733$	−2.73438e98	−0.389737	−0.194868	+	0.980829i	$0.562428\pi$
$734$	−2.00116e99	−2.72125
$735$	−2.33966e97	−0.0303556
$736$	1.87047e99	2.31562
$737$	3.38887e98	0.400338
$738$	−8.72863e98	−0.984015
$739$	−1.70145e99	−1.83057	−0.915286	−	0.402804i	$-0.868036\pi$
$739$	−1.70145e99	−1.83057	−0.915286	+	0.402804i	$0.868036\pi$
$740$	2.27074e98	0.233171
$741$	−1.97499e98	−0.193570
$742$	3.84571e98	0.359784
$743$	1.16332e98	0.103893	0.0519465	−	0.998650i	$-0.483457\pi$
$743$	1.16332e98	0.103893	0.0519465	+	0.998650i	$0.483457\pi$
$744$	3.02989e97	0.0258322
$745$	3.51900e98	0.286436
$746$	1.18430e99	0.920390
$747$	9.50235e98	0.705132
$748$	−7.26155e98	−0.514546
$749$	1.67680e99	1.13464
$750$	1.06583e99	0.688773
$751$	1.48592e98	0.0917099	0.0458550	−	0.998948i	$-0.485399\pi$
$751$	1.48592e98	0.0917099	0.0458550	+	0.998948i	$0.485399\pi$
$752$	4.02443e98	0.237241
$753$	−3.62946e98	−0.204369
$754$	−2.03491e99	−1.09455
$755$	−2.44997e99	−1.25890
$756$	−1.54831e99	−0.760077
$757$	7.78263e98	0.365021	0.182511	−	0.983204i	$-0.441578\pi$
$757$	7.78263e98	0.365021	0.182511	+	0.983204i	$0.441578\pi$
$758$	7.44295e98	0.333548
$759$	6.65347e98	0.284910
$760$	−3.10946e98	−0.127238
$761$	3.37753e99	1.32077	0.660387	−	0.750926i	$-0.270392\pi$
$761$	3.37753e99	1.32077	0.660387	+	0.750926i	$0.270392\pi$
$762$	1.57084e99	0.587064
$763$	−1.44926e99	−0.517665
$764$	−1.20636e99	−0.411865
$765$	3.24197e99	1.05801
$766$	−4.15533e99	−1.29632
$767$	5.67070e98	0.169121
$768$	−1.91563e99	−0.546197
$769$	−4.43773e99	−1.20977	−0.604884	−	0.796313i	$-0.706781\pi$
$769$	−4.43773e99	−1.20977	−0.604884	+	0.796313i	$0.706781\pi$
$770$	−1.66541e99	−0.434102
$771$	−2.47531e99	−0.616955
$772$	4.50102e99	1.07279
$773$	4.82208e99	1.09911	0.549556	−	0.835457i	$-0.314797\pi$
$773$	4.82208e99	1.09911	0.549556	+	0.835457i	$0.314797\pi$
$774$	−4.80638e99	−1.04774
$775$	−5.15289e98	−0.107434
$776$	−7.83108e98	−0.156168
$777$	7.84320e98	0.149613
$778$	1.84954e99	0.337494
$779$	5.13805e99	0.896925
$780$	−8.76742e98	−0.146423
$781$	−3.24557e99	−0.518598
$782$	2.45326e100	3.75069
$783$	−1.05393e100	−1.54181
$784$	−6.15581e98	−0.0861749
$785$	−3.34005e98	−0.0447455
$786$	5.16445e99	0.662134
$787$	7.88562e99	0.967626	0.483813	−	0.875171i	$-0.339252\pi$
$787$	7.88562e99	0.967626	0.483813	+	0.875171i	$0.339252\pi$
$788$	−1.10743e100	−1.30066
$789$	1.99719e99	0.224524
$790$	−1.17873e100	−1.26847
$791$	−8.78645e99	−0.905159
$792$	4.44118e98	0.0438005
$793$	4.90670e99	0.463303
$794$	−1.51169e100	−1.36664
$795$	1.12786e99	0.0976311
$796$	−1.15327e100	−0.955939
$797$	−1.25803e100	−0.998568	−0.499284	−	0.866439i	$-0.666403\pi$
$797$	−1.25803e100	−0.998568	−0.499284	+	0.866439i	$0.666403\pi$
$798$	8.53568e99	0.648841
$799$	4.74169e99	0.345199
$800$	5.73037e99	0.399556
$801$	−1.19343e100	−0.797031
$802$	2.87488e100	1.83909
$803$	1.05384e100	0.645787
$804$	−7.71040e99	−0.452630
$805$	2.64672e100	1.48850
$806$	3.96129e99	0.213441
$807$	1.36483e100	0.704598
$808$	2.06162e99	0.101981
$809$	−3.84669e100	−1.82332	−0.911660	−	0.410945i	$-0.865199\pi$
$809$	−3.84669e100	−1.82332	−0.911660	+	0.410945i	$0.865199\pi$
$810$	1.03578e100	0.470473
$811$	−3.67612e100	−1.60018	−0.800092	−	0.599877i	$-0.795216\pi$
$811$	−3.67612e100	−1.60018	−0.800092	+	0.599877i	$0.795216\pi$
$812$	4.13705e100	1.72587
$813$	−4.68183e99	−0.187194
$814$	4.05846e99	0.155532
$815$	1.34572e100	0.494332
$816$	−2.30197e100	−0.810568
$817$	2.82924e100	0.955013
$818$	−7.23159e100	−2.34015
$819$	1.12212e100	0.348132
$820$	2.28089e100	0.678464
$821$	−2.26554e100	−0.646150	−0.323075	−	0.946373i	$-0.604717\pi$
$821$	−2.26554e100	−0.646150	−0.323075	+	0.946373i	$0.604717\pi$
$822$	−8.99872e99	−0.246095
$823$	−9.10937e99	−0.238888	−0.119444	−	0.992841i	$-0.538111\pi$
$823$	−9.10937e99	−0.238888	−0.119444	+	0.992841i	$0.538111\pi$
$824$	6.86858e99	0.172734
$825$	2.03835e99	0.0491607
$826$	−2.45081e100	−0.566889
$827$	6.95998e100	1.54407	0.772036	−	0.635579i	$-0.219238\pi$
$827$	6.95998e100	1.54407	0.772036	+	0.635579i	$0.219238\pi$
$828$	5.60935e100	1.19362
$829$	−8.75117e100	−1.78622	−0.893110	−	0.449839i	$-0.851481\pi$
$829$	−8.75117e100	−1.78622	−0.893110	+	0.449839i	$0.851481\pi$
$830$	−5.27858e100	−1.03353
$831$	2.82011e100	0.529701
$832$	−1.80820e100	−0.325830
$833$	−7.25293e99	−0.125389
$834$	3.44342e100	0.571165
$835$	5.93210e100	0.944115
$836$	2.07768e100	0.317294
$837$	2.05164e100	0.300659
$838$	−1.42379e101	−2.00228
$839$	−2.45769e100	−0.331695	−0.165848	−	0.986151i	$-0.553036\pi$
$839$	−2.45769e100	−0.331695	−0.165848	+	0.986151i	$0.553036\pi$
$840$	−4.76778e99	−0.0617562
$841$	2.01168e101	2.50091
$842$	7.17621e100	0.856305
$843$	2.41971e100	0.277148
$844$	−8.11839e100	−0.892598
$845$	−6.51602e100	−0.687743
$846$	2.30478e100	0.233535
$847$	9.27477e100	0.902247
$848$	2.96748e100	0.277160
$849$	−9.86215e100	−0.884416
$850$	7.51580e100	0.647176
$851$	−6.44983e100	−0.533308
$852$	7.38437e100	0.586337
$853$	−2.04726e101	−1.56110	−0.780552	−	0.625090i	$-0.785062\pi$
$853$	−2.04726e101	−1.56110	−0.780552	+	0.625090i	$0.785062\pi$
$854$	−2.12062e101	−1.55298
$855$	−9.27594e100	−0.652420
$856$	2.48395e100	0.167803
$857$	−2.37001e101	−1.53784	−0.768922	−	0.639342i	$-0.779207\pi$
$857$	−2.37001e101	−1.53784	−0.768922	+	0.639342i	$0.779207\pi$
$858$	−1.56699e100	−0.0976683
$859$	4.04034e99	0.0241910	0.0120955	−	0.999927i	$-0.496150\pi$
$859$	4.04034e99	0.0241910	0.0120955	+	0.999927i	$0.496150\pi$
$860$	1.25596e101	0.722403
$861$	7.87825e100	0.435332
$862$	4.45051e101	2.36271
$863$	1.44294e101	0.735998	0.367999	−	0.929826i	$-0.380043\pi$
$863$	1.44294e101	0.735998	0.367999	+	0.929826i	$0.380043\pi$
$864$	−2.28157e101	−1.11817
$865$	9.54812e100	0.449637
$866$	5.04555e101	2.28319
$867$	−1.65211e101	−0.718424
$868$	−8.05343e100	−0.336551
$869$	−9.91016e100	−0.398014
$870$	2.57927e101	0.995593
$871$	1.26840e101	0.470578
$872$	−2.14688e100	−0.0765577
$873$	−2.33612e101	−0.800763
$874$	−7.01928e101	−2.31285
$875$	3.56464e101	1.12911
$876$	−2.39772e101	−0.730140
$877$	1.03367e101	0.302618	0.151309	−	0.988486i	$-0.451651\pi$
$877$	1.03367e101	0.302618	0.151309	+	0.988486i	$0.451651\pi$
$878$	8.84284e100	0.248904
$879$	−5.61452e100	−0.151948
$880$	−1.28509e101	−0.334411
$881$	−1.84554e100	−0.0461801	−0.0230900	−	0.999733i	$-0.507350\pi$
$881$	−1.84554e100	−0.0461801	−0.0230900	+	0.999733i	$0.507350\pi$
$882$	−3.52541e100	−0.0848289
$883$	2.67901e100	0.0619911	0.0309956	−	0.999520i	$-0.490132\pi$
$883$	2.67901e100	0.0619911	0.0309956	+	0.999520i	$0.490132\pi$
$884$	−2.71790e101	−0.604825
$885$	−7.18766e100	−0.153831
$886$	−7.66221e101	−1.57721
$887$	5.27008e101	1.04340	0.521701	−	0.853128i	$-0.325297\pi$
$887$	5.27008e101	1.04340	0.521701	+	0.853128i	$0.325297\pi$
$888$	1.16187e100	0.0221263
$889$	5.25360e101	0.962380
$890$	6.62954e101	1.16823
$891$	8.70830e100	0.147622
$892$	2.68330e101	0.437605
$893$	−1.35669e101	−0.212866
$894$	−1.43099e101	−0.216019
$895$	−6.15828e101	−0.894467
$896$	−2.26805e101	−0.316976
$897$	2.49030e101	0.334898
$898$	8.13644e100	0.105293
$899$	−5.48193e101	−0.682690
$900$	1.71848e101	0.205957
$901$	3.49635e101	0.403283
$902$	4.07660e101	0.452556
$903$	4.33812e101	0.463526
$904$	−1.30160e101	−0.133864
$905$	9.08374e101	0.899267
$906$	9.96270e101	0.949411
$907$	−1.42836e102	−1.31035	−0.655173	−	0.755479i	$-0.727404\pi$
$907$	−1.42836e102	−1.31035	−0.655173	+	0.755479i	$0.727404\pi$
$908$	−1.79315e101	−0.158364
$909$	6.15011e101	0.522912
$910$	−6.23340e101	−0.510267
$911$	−1.37535e102	−1.08400	−0.542000	−	0.840378i	$-0.682333\pi$
$911$	−1.37535e102	−1.08400	−0.542000	+	0.840378i	$0.682333\pi$
$912$	6.58641e101	0.499835
$913$	−4.43795e101	−0.324295
$914$	−5.09695e101	−0.358646
$915$	−6.21928e101	−0.421417
$916$	−7.10809e101	−0.463830
$917$	1.72723e102	1.08544
$918$	−2.99245e102	−1.81115
$919$	−2.81280e101	−0.163966	−0.0819829	−	0.996634i	$-0.526125\pi$
$919$	−2.81280e101	−0.163966	−0.0819829	+	0.996634i	$0.526125\pi$
$920$	3.92076e101	0.220136
$921$	−5.69576e101	−0.308031
$922$	2.79932e102	1.45826
$923$	−1.21477e102	−0.609587
$924$	3.18573e101	0.154002
$925$	−1.97597e101	−0.0920216
$926$	−1.52049e102	−0.682188
$927$	2.04899e102	0.885705
$928$	6.09628e102	2.53898
$929$	6.85921e101	0.275253	0.137626	−	0.990484i	$-0.456053\pi$
$929$	6.85921e101	0.275253	0.137626	+	0.990484i	$0.456053\pi$
$930$	−5.02096e101	−0.194144
$931$	2.07521e101	0.0773211
$932$	−1.15987e102	−0.416449
$933$	1.27712e100	0.00441890
$934$	2.78289e102	0.927958
$935$	−1.51412e102	−0.486587
$936$	1.66227e101	0.0514855
$937$	4.17633e102	1.24675	0.623375	−	0.781923i	$-0.285761\pi$
$937$	4.17633e102	1.24675	0.623375	+	0.781923i	$0.285761\pi$
$938$	−5.48189e102	−1.57737
$939$	1.22742e101	0.0340431
$940$	−6.02265e101	−0.161019
$941$	−6.90927e102	−1.78070	−0.890349	−	0.455280i	$-0.849539\pi$
$941$	−6.90927e102	−1.78070	−0.890349	+	0.455280i	$0.849539\pi$
$942$	1.35821e101	0.0337452
$943$	−6.47865e102	−1.55178
$944$	−1.89112e102	−0.436703
$945$	−3.22842e102	−0.718776
$946$	2.24476e102	0.481865
$947$	2.68653e102	0.556055	0.278028	−	0.960573i	$-0.410319\pi$
$947$	2.68653e102	0.556055	0.278028	+	0.960573i	$0.410319\pi$
$948$	2.25477e102	0.450003
$949$	3.94438e102	0.759093
$950$	−2.15042e102	−0.399080
$951$	3.65965e102	0.654956
$952$	−1.47801e102	−0.255095
$953$	1.09155e103	1.81694	0.908470	−	0.417950i	$-0.137251\pi$
$953$	1.09155e103	1.81694	0.908470	+	0.417950i	$0.137251\pi$
$954$	1.69946e102	0.272831
$955$	−2.51540e102	−0.389485
$956$	−6.74874e101	−0.100792
$957$	2.16851e102	0.312392
$958$	−1.23667e102	−0.171847
$959$	−3.00958e102	−0.403426
$960$	2.29191e102	0.296373
$961$	−6.94884e102	−0.866873
$962$	1.51902e102	0.182821
$963$	7.40998e102	0.860419
$964$	−2.96485e102	−0.332158
$965$	9.38518e102	1.01450
$966$	−1.07628e103	−1.12257
$967$	−1.75819e103	−1.76950	−0.884751	−	0.466063i	$-0.845672\pi$
$967$	−1.75819e103	−1.76950	−0.884751	+	0.466063i	$0.845672\pi$
$968$	1.37393e102	0.133434
$969$	7.76027e102	0.727289
$970$	1.29772e103	1.17370
$971$	6.68592e102	0.583576	0.291788	−	0.956483i	$-0.405750\pi$
$971$	6.68592e102	0.583576	0.291788	+	0.956483i	$0.405750\pi$
$972$	−1.06700e103	−0.898834
$973$	1.15164e103	0.936317
$974$	7.94430e101	0.0623407
$975$	7.62927e101	0.0577862
$976$	−1.63634e103	−1.19634
$977$	−9.63413e102	−0.679908	−0.339954	−	0.940442i	$-0.610411\pi$
$977$	−9.63413e102	−0.679908	−0.339954	+	0.940442i	$0.610411\pi$
$978$	−5.47232e102	−0.372804
$979$	5.57377e102	0.366561
$980$	9.21230e101	0.0584882
$981$	−6.40444e102	−0.392555
$982$	−3.22890e103	−1.91077
$983$	5.82748e102	0.332954	0.166477	−	0.986045i	$-0.446761\pi$
$983$	5.82748e102	0.332954	0.166477	+	0.986045i	$0.446761\pi$
$984$	1.16706e102	0.0643815
$985$	−2.30913e103	−1.22998
$986$	7.99572e103	4.11248
$987$	−2.08024e102	−0.103317
$988$	7.77646e102	0.372964
$989$	−3.56743e103	−1.65228
$990$	−7.35966e102	−0.329187
$991$	2.95358e103	1.27587	0.637936	−	0.770090i	$-0.279789\pi$
$991$	2.95358e103	1.27587	0.637936	+	0.770090i	$0.279789\pi$
$992$	−1.18674e103	−0.495111
$993$	−3.91180e102	−0.157626
$994$	5.25009e103	2.04332
$995$	−2.40471e103	−0.903995
$996$	1.00973e103	0.366655
$997$	1.27987e103	0.448933	0.224467	−	0.974482i	$-0.427936\pi$
$997$	1.27987e103	0.448933	0.224467	+	0.974482i	$0.427936\pi$
$998$	1.59001e103	0.538763
$999$	7.86739e102	0.257526

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+3.33859e10 q^{2} -1.33163e16 q^{3} +5.24322e20 q^{4} +1.09328e24 q^{5} -4.44575e26 q^{6} -1.48686e29 q^{7} -2.20259e30 q^{8} -6.57062e32 q^{9} +O(q^{10})\)	\(q+3.33859e10 q^{2} -1.33163e16 q^{3} +5.24322e20 q^{4} +1.09328e24 q^{5} -4.44575e26 q^{6} -1.48686e29 q^{7} -2.20259e30 q^{8} -6.57062e32 q^{9} +3.65000e34 q^{10} +3.06873e35 q^{11} -6.98201e36 q^{12} +1.14858e38 q^{13} -4.96402e39 q^{14} -1.45583e40 q^{15} -3.83041e41 q^{16} -4.51308e42 q^{17} -2.19366e43 q^{18} +1.29128e44 q^{19} +5.73229e44 q^{20} +1.97994e45 q^{21} +1.02452e46 q^{22} -1.62820e47 q^{23} +2.93302e46 q^{24} -4.98815e47 q^{25} +3.83464e48 q^{26} +1.98605e49 q^{27} -7.79595e49 q^{28} -5.30666e50 q^{29} -4.86043e50 q^{30} +1.03303e51 q^{31} -1.14880e52 q^{32} -4.08640e51 q^{33} -1.50673e53 q^{34} -1.62555e53 q^{35} -3.44512e53 q^{36} +3.96132e53 q^{37} +4.31107e54 q^{38} -1.52948e54 q^{39} -2.40804e54 q^{40} +3.97903e55 q^{41} +6.61022e55 q^{42} +2.19103e56 q^{43} +1.60900e56 q^{44} -7.18350e56 q^{45} -5.43589e57 q^{46} -1.05065e57 q^{47} +5.10067e57 q^{48} +1.60709e57 q^{49} -1.66534e58 q^{50} +6.00973e58 q^{51} +6.02226e58 q^{52} -7.74716e58 q^{53} +6.63061e59 q^{54} +3.35496e59 q^{55} +3.27495e59 q^{56} -1.71951e60 q^{57} -1.77168e61 q^{58} +4.93714e60 q^{59} -7.63326e60 q^{60} +4.27197e61 q^{61} +3.44885e61 q^{62} +9.76962e61 q^{63} -1.57429e62 q^{64} +1.25572e62 q^{65} -1.36428e62 q^{66} +1.10432e63 q^{67} -2.36631e63 q^{68} +2.16815e63 q^{69} -5.42705e63 q^{70} -1.05763e64 q^{71} +1.44724e63 q^{72} +3.43414e64 q^{73} +1.32252e64 q^{74} +6.64234e63 q^{75} +6.77049e64 q^{76} -4.56278e64 q^{77} -5.10631e64 q^{78} -3.22940e65 q^{79} -4.18769e65 q^{80} +2.83776e65 q^{81} +1.32843e66 q^{82} -1.44619e66 q^{83} +1.03813e66 q^{84} -4.93404e66 q^{85} +7.31495e66 q^{86} +7.06649e66 q^{87} -6.75914e65 q^{88} +1.81631e67 q^{89} -2.39828e67 q^{90} -1.70778e67 q^{91} -8.53701e67 q^{92} -1.37561e67 q^{93} -3.50770e67 q^{94} +1.41173e68 q^{95} +1.52977e68 q^{96} +3.55540e68 q^{97} +5.36542e67 q^{98} -2.01635e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots - 31\!\cdots\!35 q^{9}+O(q^{10}) \) 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	\( 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots + 58\!\cdots\!80 q^{99}+O(q^{100}) \) 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

Representations

Groups

Database

Properties

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