LMFDB - Embedded newform 1.70.a.a.1.3

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			1.3
Root			$1.08482e7$ 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)

$f(q)$	$=$	$q-6.72544e9 q^{2} -4.13926e16 q^{3} -5.45064e20 q^{4} -6.57446e23 q^{5} +2.78383e26 q^{6} +1.09182e29 q^{7} +7.63579e30 q^{8} +8.78961e32 q^{9} +O(q^{10})$	\(q-6.72544e9 q^{2} -4.13926e16 q^{3} -5.45064e20 q^{4} -6.57446e23 q^{5} +2.78383e26 q^{6} +1.09182e29 q^{7} +7.63579e30 q^{8} +8.78961e32 q^{9} +4.42161e33 q^{10} +1.33172e36 q^{11} +2.25616e37 q^{12} -4.12780e38 q^{13} -7.34294e38 q^{14} +2.72134e40 q^{15} +2.70395e41 q^{16} -6.74158e41 q^{17} -5.91140e42 q^{18} +4.81748e43 q^{19} +3.58350e44 q^{20} -4.51931e45 q^{21} -8.95643e45 q^{22} +1.69186e47 q^{23} -3.16065e47 q^{24} -1.26183e48 q^{25} +2.77612e48 q^{26} -1.84511e48 q^{27} -5.95110e49 q^{28} -1.58578e50 q^{29} -1.83022e50 q^{30} -2.69817e51 q^{31} -6.32590e51 q^{32} -5.51235e52 q^{33} +4.53401e51 q^{34} -7.17810e52 q^{35} -4.79090e53 q^{36} -8.15325e53 q^{37} -3.23996e53 q^{38} +1.70860e55 q^{39} -5.02012e54 q^{40} +2.61880e55 q^{41} +3.03943e55 q^{42} +4.10933e56 q^{43} -7.25876e56 q^{44} -5.77869e56 q^{45} -1.13785e57 q^{46} +9.62235e56 q^{47} -1.11924e58 q^{48} -8.57990e57 q^{49} +8.48636e57 q^{50} +2.79051e58 q^{51} +2.24991e59 q^{52} +1.75042e59 q^{53} +1.24092e58 q^{54} -8.75537e59 q^{55} +8.33688e59 q^{56} -1.99408e60 q^{57} +1.06651e60 q^{58} -1.91926e61 q^{59} -1.48330e61 q^{60} +5.14748e61 q^{61} +1.81464e61 q^{62} +9.59664e61 q^{63} -1.17069e62 q^{64} +2.71380e62 q^{65} +3.70730e62 q^{66} -5.82869e62 q^{67} +3.67459e62 q^{68} -7.00305e63 q^{69} +4.82758e62 q^{70} +6.68198e63 q^{71} +6.71156e63 q^{72} -1.20455e64 q^{73} +5.48341e63 q^{74} +5.22304e64 q^{75} -2.62583e64 q^{76} +1.45400e65 q^{77} -1.14911e65 q^{78} -1.97073e65 q^{79} -1.77770e65 q^{80} -6.57018e65 q^{81} -1.76126e65 q^{82} +5.46209e65 q^{83} +2.46331e66 q^{84} +4.43222e65 q^{85} -2.76370e66 q^{86} +6.56395e66 q^{87} +1.01688e67 q^{88} -8.41635e66 q^{89} +3.88642e66 q^{90} -4.50679e67 q^{91} -9.22174e67 q^{92} +1.11684e68 q^{93} -6.47145e66 q^{94} -3.16723e67 q^{95} +2.61845e68 q^{96} -3.94984e68 q^{97} +5.77035e67 q^{98} +1.17053e69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.72544e9	−0.276812	−0.138406	−	0.990376i	$-0.544198\pi$
$2$	−6.72544e9	−0.276812	−0.138406	+	0.990376i	$0.544198\pi$
$3$	−4.13926e16	−1.43298	−0.716489	−	0.697599i	$-0.754252\pi$
$3$	−4.13926e16	−1.43298	−0.716489	+	0.697599i	$0.754252\pi$
$4$	−5.45064e20	−0.923375
$5$	−6.57446e23	−0.505120	−0.252560	−	0.967581i	$-0.581273\pi$
$5$	−6.57446e23	−0.505120	−0.252560	+	0.967581i	$0.581273\pi$
$6$	2.78383e26	0.396666
$7$	1.09182e29	0.762548	0.381274	−	0.924462i	$-0.375485\pi$
$7$	1.09182e29	0.762548	0.381274	+	0.924462i	$0.375485\pi$
$8$	7.63579e30	0.532414
$9$	8.78961e32	1.05342
$10$	4.42161e33	0.139824
$11$	1.33172e36	1.57169	0.785845	−	0.618424i	$-0.212228\pi$
$11$	1.33172e36	1.57169	0.785845	+	0.618424i	$0.212228\pi$
$12$	2.25616e37	1.32318
$13$	−4.12780e38	−1.52993	−0.764967	−	0.644069i	$-0.777245\pi$
$13$	−4.12780e38	−1.52993	−0.764967	+	0.644069i	$0.777245\pi$
$14$	−7.34294e38	−0.211083
$15$	2.72134e40	0.723826
$16$	2.70395e41	0.775996
$17$	−6.74158e41	−0.238932	−0.119466	−	0.992838i	$-0.538118\pi$
$17$	−6.74158e41	−0.238932	−0.119466	+	0.992838i	$0.538118\pi$
$18$	−5.91140e42	−0.291601
$19$	4.81748e43	0.367977	0.183988	−	0.982928i	$-0.441099\pi$
$19$	4.81748e43	0.367977	0.183988	+	0.982928i	$0.441099\pi$
$20$	3.58350e44	0.466416
$21$	−4.51931e45	−1.09271
$22$	−8.95643e45	−0.435063
$23$	1.69186e47	1.77319	0.886594	−	0.462549i	$-0.153065\pi$
$23$	1.69186e47	1.77319	0.886594	+	0.462549i	$0.153065\pi$
$24$	−3.16065e47	−0.762937
$25$	−1.26183e48	−0.744853
$26$	2.77612e48	0.423505
$27$	−1.84511e48	−0.0765548
$28$	−5.95110e49	−0.704117
$29$	−1.58578e50	−0.559128	−0.279564	−	0.960127i	$-0.590190\pi$
$29$	−1.58578e50	−0.559128	−0.279564	+	0.960127i	$0.590190\pi$
$30$	−1.83022e50	−0.200364
$31$	−2.69817e51	−0.952996	−0.476498	−	0.879176i	$-0.658094\pi$
$31$	−2.69817e51	−0.952996	−0.476498	+	0.879176i	$0.658094\pi$
$32$	−6.32590e51	−0.747219
$33$	−5.51235e52	−2.25220
$34$	4.53401e51	0.0661393
$35$	−7.17810e52	−0.385178
$36$	−4.79090e53	−0.972705
$37$	−8.15325e53	−0.643237	−0.321619	−	0.946869i	$-0.604227\pi$
$37$	−8.15325e53	−0.643237	−0.321619	+	0.946869i	$0.604227\pi$
$38$	−3.23996e53	−0.101861
$39$	1.70860e55	2.19236
$40$	−5.02012e54	−0.268933
$41$	2.61880e55	0.598493	0.299246	−	0.954176i	$-0.403265\pi$
$41$	2.61880e55	0.598493	0.299246	+	0.954176i	$0.403265\pi$
$42$	3.03943e55	0.302477
$43$	4.10933e56	1.81597	0.907986	−	0.419001i	$-0.137620\pi$
$43$	4.10933e56	1.81597	0.907986	+	0.419001i	$0.137620\pi$
$44$	−7.25876e56	−1.45126
$45$	−5.77869e56	−0.532106
$46$	−1.13785e57	−0.490840
$47$	9.62235e56	0.197654	0.0988269	−	0.995105i	$-0.468491\pi$
$47$	9.62235e56	0.197654	0.0988269	+	0.995105i	$0.468491\pi$
$48$	−1.11924e58	−1.11198
$49$	−8.57990e57	−0.418521
$50$	8.48636e57	0.206185
$51$	2.79051e58	0.342384
$52$	2.24991e59	1.41270
$53$	1.75042e59	0.569672	0.284836	−	0.958576i	$-0.408061\pi$
$53$	1.75042e59	0.569672	0.284836	+	0.958576i	$0.408061\pi$
$54$	1.24092e58	0.0211913
$55$	−8.75537e59	−0.793893
$56$	8.33688e59	0.405991
$57$	−1.99408e60	−0.527302
$58$	1.06651e60	0.154774
$59$	−1.91926e61	−1.54433	−0.772163	−	0.635425i	$-0.780825\pi$
$59$	−1.91926e61	−1.54433	−0.772163	+	0.635425i	$0.780825\pi$
$60$	−1.48330e61	−0.668363
$61$	5.14748e61	1.31134	0.655670	−	0.755048i	$-0.272386\pi$
$61$	5.14748e61	1.31134	0.655670	+	0.755048i	$0.272386\pi$
$62$	1.81464e61	0.263801
$63$	9.59664e61	0.803286
$64$	−1.17069e62	−0.569156
$65$	2.71380e62	0.772801
$66$	3.70730e62	0.623436
$67$	−5.82869e62	−0.583432	−0.291716	−	0.956505i	$-0.594226\pi$
$67$	−5.82869e62	−0.583432	−0.291716	+	0.956505i	$0.594226\pi$
$68$	3.67459e62	0.220624
$69$	−7.00305e63	−2.54094
$70$	4.82758e62	0.106622
$71$	6.68198e63	0.904675	0.452337	−	0.891847i	$-0.350590\pi$
$71$	6.68198e63	0.904675	0.452337	+	0.891847i	$0.350590\pi$
$72$	6.71156e63	0.560858
$73$	−1.20455e64	−0.625441	−0.312720	−	0.949845i	$-0.601240\pi$
$73$	−1.20455e64	−0.625441	−0.312720	+	0.949845i	$0.601240\pi$
$74$	5.48341e63	0.178056
$75$	5.22304e64	1.06736
$76$	−2.62583e64	−0.339780
$77$	1.45400e65	1.19849
$78$	−1.14911e65	−0.606873
$79$	−1.97073e65	−0.670643	−0.335322	−	0.942104i	$-0.608845\pi$
$79$	−1.97073e65	−0.670643	−0.335322	+	0.942104i	$0.608845\pi$
$80$	−1.77770e65	−0.391971
$81$	−6.57018e65	−0.943722
$82$	−1.76126e65	−0.165670
$83$	5.46209e65	0.338193	0.169097	−	0.985599i	$-0.445915\pi$
$83$	5.46209e65	0.338193	0.169097	+	0.985599i	$0.445915\pi$
$84$	2.46331e66	1.00898
$85$	4.43222e65	0.120689
$86$	−2.76370e66	−0.502684
$87$	6.56395e66	0.801218
$88$	1.01688e67	0.836790
$89$	−8.41635e66	−0.468995	−0.234498	−	0.972117i	$-0.575345\pi$
$89$	−8.41635e66	−0.468995	−0.234498	+	0.972117i	$0.575345\pi$
$90$	3.88642e66	0.147293
$91$	−4.50679e67	−1.16665
$92$	−9.22174e67	−1.63732
$93$	1.11684e68	1.36562
$94$	−6.47145e66	−0.0547130
$95$	−3.16723e67	−0.185873
$96$	2.61845e68	1.07075
$97$	−3.94984e68	−1.12968	−0.564840	−	0.825201i	$-0.691062\pi$
$97$	−3.94984e68	−1.12968	−0.564840	+	0.825201i	$0.691062\pi$
$98$	5.77035e67	0.115852
$99$	1.17053e69	1.65565
$100$	6.87779e68	0.687779
$101$	−1.06893e69	−0.758338	−0.379169	−	0.925327i	$-0.623790\pi$
$101$	−1.06893e69	−0.758338	−0.379169	+	0.925327i	$0.623790\pi$
$102$	−1.87674e68	−0.0947761
$103$	−3.99860e69	−1.44219	−0.721097	−	0.692834i	$-0.756362\pi$
$103$	−3.99860e69	−1.44219	−0.721097	+	0.692834i	$0.756362\pi$
$104$	−3.15190e69	−0.814558
$105$	2.97120e69	0.551952
$106$	−1.17723e69	−0.157692
$107$	9.26493e69	0.897639	0.448820	−	0.893622i	$-0.351845\pi$
$107$	9.26493e69	0.897639	0.448820	+	0.893622i	$0.351845\pi$
$108$	1.00570e69	0.0706888
$109$	−6.11339e69	−0.312657	−0.156328	−	0.987705i	$-0.549966\pi$
$109$	−6.11339e69	−0.312657	−0.156328	+	0.987705i	$0.549966\pi$
$110$	5.88837e69	0.219759
$111$	3.37484e70	0.921744
$112$	2.95222e70	0.591734
$113$	−6.06342e70	−0.894358	−0.447179	−	0.894444i	$-0.647571\pi$
$113$	−6.06342e70	−0.894358	−0.447179	+	0.894444i	$0.647571\pi$
$114$	1.34110e70	0.145964
$115$	−1.11231e71	−0.895673
$116$	8.64351e70	0.516285
$117$	−3.62817e71	−1.61167
$118$	1.29078e71	0.427488
$119$	−7.36056e70	−0.182197
$120$	2.07796e71	0.385375
$121$	1.05554e72	1.47021
$122$	−3.46190e71	−0.362995
$123$	−1.08399e72	−0.857627
$124$	1.47068e72	0.879972
$125$	1.94334e72	0.881361
$126$	−6.45416e71	−0.222359
$127$	−2.77881e72	−0.728836	−0.364418	−	0.931235i	$-0.618732\pi$
$127$	−2.77881e72	−0.728836	−0.364418	+	0.931235i	$0.618732\pi$
$128$	4.52149e72	0.904769
$129$	−1.70096e73	−2.60225
$130$	−1.82515e72	−0.213921
$131$	−6.62064e72	−0.595718	−0.297859	−	0.954610i	$-0.596272\pi$
$131$	−6.62064e72	−0.595718	−0.297859	+	0.954610i	$0.596272\pi$
$132$	3.00459e73	2.07962
$133$	5.25980e72	0.280600
$134$	3.92005e72	0.161501
$135$	1.21306e72	0.0386694
$136$	−5.14773e72	−0.127211
$137$	−1.46579e73	−0.281327	−0.140663	−	0.990057i	$-0.544924\pi$
$137$	−1.46579e73	−0.281327	−0.140663	+	0.990057i	$0.544924\pi$
$138$	4.70986e73	0.703363
$139$	−1.11987e73	−0.130364	−0.0651818	−	0.997873i	$-0.520763\pi$
$139$	−1.11987e73	−0.130364	−0.0651818	+	0.997873i	$0.520763\pi$
$140$	3.91253e73	0.355664
$141$	−3.98294e73	−0.283233
$142$	−4.49393e73	−0.250425
$143$	−5.49709e74	−2.40458
$144$	2.37667e74	0.817453
$145$	1.04256e74	0.282427
$146$	8.10112e73	0.173130
$147$	3.55144e74	0.599731
$148$	4.44404e74	0.593949
$149$	1.93136e74	0.204615	0.102308	−	0.994753i	$-0.467377\pi$
$149$	1.93136e74	0.204615	0.102308	+	0.994753i	$0.467377\pi$
$150$	−3.51272e74	−0.295458
$151$	4.68967e74	0.313644	0.156822	−	0.987627i	$-0.449875\pi$
$151$	4.68967e74	0.313644	0.156822	+	0.987627i	$0.449875\pi$
$152$	3.67852e74	0.195916
$153$	−5.92559e74	−0.251696
$154$	−9.77877e74	−0.331756
$155$	1.77390e75	0.481378
$156$	−9.31298e75	−2.02437
$157$	2.27330e75	0.396387	0.198193	−	0.980163i	$-0.436493\pi$
$157$	2.27330e75	0.396387	0.198193	+	0.980163i	$0.436493\pi$
$158$	1.32540e75	0.185642
$159$	−7.24544e75	−0.816327
$160$	4.15894e75	0.377436
$161$	1.84720e76	1.35214
$162$	4.41873e75	0.261234
$163$	7.08855e75	0.338911	0.169455	−	0.985538i	$-0.445799\pi$
$163$	7.08855e75	0.338911	0.169455	+	0.985538i	$0.445799\pi$
$164$	−1.42741e76	−0.552633
$165$	3.62407e76	1.13763
$166$	−3.67349e75	−0.0936160
$167$	−8.63978e76	−1.78972	−0.894859	−	0.446349i	$-0.852724\pi$
$167$	−8.63978e76	−1.78972	−0.894859	+	0.446349i	$0.852724\pi$
$168$	−3.45085e76	−0.581776
$169$	9.75938e76	1.34070
$170$	−2.98086e75	−0.0334083
$171$	4.23437e76	0.387635
$172$	−2.23985e77	−1.67682
$173$	−7.56106e75	−0.0463439	−0.0231719	−	0.999731i	$-0.507377\pi$
$173$	−7.56106e75	−0.0463439	−0.0231719	+	0.999731i	$0.507377\pi$
$174$	−4.41454e76	−0.221787
$175$	−1.37769e77	−0.567986
$176$	3.60092e77	1.21963
$177$	7.94430e77	2.21298
$178$	5.66036e76	0.129824
$179$	−4.74532e77	−0.897091	−0.448545	−	0.893760i	$-0.648058\pi$
$179$	−4.74532e77	−0.897091	−0.448545	+	0.893760i	$0.648058\pi$
$180$	3.14976e77	0.491333
$181$	−7.62895e77	−0.983000	−0.491500	−	0.870877i	$-0.663551\pi$
$181$	−7.62895e77	−0.983000	−0.491500	+	0.870877i	$0.663551\pi$
$182$	3.03102e77	0.322943
$183$	−2.13067e78	−1.87912
$184$	1.29187e78	0.944070
$185$	5.36032e77	0.324912
$186$	−7.51125e77	−0.378021
$187$	−8.97793e77	−0.375527
$188$	−5.24480e77	−0.182508
$189$	−2.01452e77	−0.0583767
$190$	2.13010e77	0.0514518
$191$	3.26226e78	0.657458	0.328729	−	0.944424i	$-0.393380\pi$
$191$	3.26226e78	0.657458	0.328729	+	0.944424i	$0.393380\pi$
$192$	4.84578e78	0.815588
$193$	5.00103e78	0.703611	0.351805	−	0.936073i	$-0.385568\pi$
$193$	5.00103e78	0.703611	0.351805	+	0.936073i	$0.385568\pi$
$194$	2.65644e78	0.312709
$195$	−1.12331e79	−1.10741
$196$	4.67659e78	0.386452
$197$	−6.39535e78	−0.443383	−0.221692	−	0.975117i	$-0.571158\pi$
$197$	−6.39535e78	−0.443383	−0.221692	+	0.975117i	$0.571158\pi$
$198$	−7.87235e78	−0.458306
$199$	−1.38753e79	−0.678909	−0.339455	−	0.940622i	$-0.610242\pi$
$199$	−1.38753e79	−0.678909	−0.339455	+	0.940622i	$0.610242\pi$
$200$	−9.63508e78	−0.396570
$201$	2.41264e79	0.836044
$202$	7.18904e78	0.209917
$203$	−1.73138e79	−0.426362
$204$	−1.52101e79	−0.316149
$205$	−1.72172e79	−0.302311
$206$	2.68923e79	0.399217
$207$	1.48708e80	1.86792
$208$	−1.11614e80	−1.18722
$209$	6.41555e79	0.578345
$210$	−1.99826e79	−0.152787
$211$	2.63566e80	1.71059	0.855294	−	0.518143i	$-0.173376\pi$
$211$	2.63566e80	1.71059	0.855294	+	0.518143i	$0.173376\pi$
$212$	−9.54091e79	−0.526021
$213$	−2.76585e80	−1.29638
$214$	−6.23107e79	−0.248478
$215$	−2.70166e80	−0.917284
$216$	−1.40889e79	−0.0407588
$217$	−2.94591e80	−0.726705
$218$	4.11152e79	0.0865473
$219$	4.98594e80	0.896242
$220$	4.77224e80	0.733060
$221$	2.78279e80	0.365550
$222$	−2.26973e80	−0.255150
$223$	8.25684e80	0.794870	0.397435	−	0.917630i	$-0.369900\pi$
$223$	8.25684e80	0.794870	0.397435	+	0.917630i	$0.369900\pi$
$224$	−6.90672e80	−0.569790
$225$	−1.10910e81	−0.784646
$226$	4.07792e80	0.247569
$227$	2.13570e81	1.11339	0.556696	−	0.830716i	$-0.312069\pi$
$227$	2.13570e81	1.11339	0.556696	+	0.830716i	$0.312069\pi$
$228$	1.08690e81	0.486898
$229$	−1.45659e81	−0.561064	−0.280532	−	0.959845i	$-0.590511\pi$
$229$	−1.45659e81	−0.561064	−0.280532	+	0.959845i	$0.590511\pi$
$230$	7.48075e80	0.247933
$231$	−6.01847e81	−1.71741
$232$	−1.21087e81	−0.297688
$233$	−4.98509e81	−1.05656	−0.528279	−	0.849071i	$-0.677163\pi$
$233$	−4.98509e81	−1.05656	−0.528279	+	0.849071i	$0.677163\pi$
$234$	2.44010e81	0.446130
$235$	−6.32617e80	−0.0998389
$236$	1.04612e82	1.42599
$237$	8.15734e81	0.961016
$238$	4.95030e80	0.0504344
$239$	−1.52673e82	−1.34597	−0.672984	−	0.739657i	$-0.734988\pi$
$239$	−1.52673e82	−1.34597	−0.672984	+	0.739657i	$0.734988\pi$
$240$	7.35837e81	0.561686
$241$	7.65570e81	0.506287	0.253144	−	0.967429i	$-0.418535\pi$
$241$	7.65570e81	0.506287	0.253144	+	0.967429i	$0.418535\pi$
$242$	−7.09896e81	−0.406972
$243$	2.87352e82	1.42889
$244$	−2.80571e82	−1.21086
$245$	5.64082e81	0.211403
$246$	7.29029e81	0.237402
$247$	−1.98856e82	−0.562980
$248$	−2.06027e82	−0.507388
$249$	−2.26090e82	−0.484623
$250$	−1.30698e82	−0.243972
$251$	−5.91288e82	−0.961735	−0.480868	−	0.876793i	$-0.659678\pi$
$251$	−5.91288e82	−0.961735	−0.480868	+	0.876793i	$0.659678\pi$
$252$	−5.23078e82	−0.741734
$253$	2.25309e83	2.78690
$254$	1.86887e82	0.201751
$255$	−1.83461e82	−0.172945
$256$	3.86962e82	0.318705
$257$	5.81357e82	0.418552	0.209276	−	0.977857i	$-0.432889\pi$
$257$	5.81357e82	0.418552	0.209276	+	0.977857i	$0.432889\pi$
$258$	1.14397e83	0.720334
$259$	−8.90184e82	−0.490499
$260$	−1.47920e83	−0.713585
$261$	−1.39384e83	−0.588999
$262$	4.45267e82	0.164902
$263$	2.53167e83	0.822117	0.411058	−	0.911609i	$-0.365159\pi$
$263$	2.53167e83	0.822117	0.411058	+	0.911609i	$0.365159\pi$
$264$	−4.20912e83	−1.19910
$265$	−1.15081e83	−0.287753
$266$	−3.53744e82	−0.0776735
$267$	3.48374e83	0.672060
$268$	3.17701e83	0.538726
$269$	−1.26960e84	−1.89327	−0.946635	−	0.322307i	$-0.895542\pi$
$269$	−1.26960e84	−1.89327	−0.946635	+	0.322307i	$0.895542\pi$
$270$	−8.15836e81	−0.0107042
$271$	5.66289e83	0.654029	0.327015	−	0.945019i	$-0.393957\pi$
$271$	5.66289e83	0.654029	0.327015	+	0.945019i	$0.393957\pi$
$272$	−1.82289e83	−0.185410
$273$	1.86548e84	1.67178
$274$	9.85805e82	0.0778747
$275$	−1.68041e84	−1.17068
$276$	3.81711e84	2.34624
$277$	−5.54041e83	−0.300601	−0.150300	−	0.988640i	$-0.548024\pi$
$277$	−5.54041e83	−0.300601	−0.150300	+	0.988640i	$0.548024\pi$
$278$	7.53161e82	0.0360863
$279$	−2.37159e84	−1.00391
$280$	−5.48105e83	−0.205074
$281$	−5.34120e84	−1.76714	−0.883570	−	0.468299i	$-0.844867\pi$
$281$	−5.34120e84	−1.76714	−0.883570	+	0.468299i	$0.844867\pi$
$282$	2.67870e83	0.0784025
$283$	3.82595e84	0.991076	0.495538	−	0.868586i	$-0.334971\pi$
$283$	3.82595e84	0.991076	0.495538	+	0.868586i	$0.334971\pi$
$284$	−3.64211e84	−0.835354
$285$	1.31100e84	0.266351
$286$	3.69703e84	0.665618
$287$	2.85925e84	0.456379
$288$	−5.56022e84	−0.787139
$289$	−7.50666e84	−0.942912
$290$	−7.01170e83	−0.0781794
$291$	1.63494e85	1.61880
$292$	6.56557e84	0.577516
$293$	5.88808e84	0.460300	0.230150	−	0.973155i	$-0.426078\pi$
$293$	5.88808e84	0.460300	0.230150	+	0.973155i	$0.426078\pi$
$294$	−2.38850e84	−0.166013
$295$	1.26181e85	0.780070
$296$	−6.22565e84	−0.342468
$297$	−2.45718e84	−0.120320
$298$	−1.29893e84	−0.0566400
$299$	−6.98366e85	−2.71286
$300$	−2.84689e85	−0.985571
$301$	4.48663e85	1.38477
$302$	−3.15401e84	−0.0868207
$303$	4.42459e85	1.08668
$304$	1.30262e85	0.285549
$305$	−3.38419e85	−0.662384
$306$	3.98521e84	0.0696727
$307$	7.32850e84	0.114483	0.0572415	−	0.998360i	$-0.481770\pi$
$307$	7.32850e84	0.114483	0.0572415	+	0.998360i	$0.481770\pi$
$308$	−7.92523e85	−1.10665
$309$	1.65512e86	2.06663
$310$	−1.19303e85	−0.133251
$311$	−1.15607e86	−1.15545	−0.577727	−	0.816230i	$-0.696060\pi$
$311$	−1.15607e86	−1.15545	−0.577727	+	0.816230i	$0.696060\pi$
$312$	1.30465e86	1.16724
$313$	8.69860e85	0.696899	0.348449	−	0.937328i	$-0.386708\pi$
$313$	8.69860e85	0.696899	0.348449	+	0.937328i	$0.386708\pi$
$314$	−1.52889e85	−0.109725
$315$	−6.30927e85	−0.405756
$316$	1.07417e86	0.619255
$317$	−2.43097e86	−1.25671	−0.628356	−	0.777926i	$-0.716272\pi$
$317$	−2.43097e86	−1.25671	−0.628356	+	0.777926i	$0.716272\pi$
$318$	4.87287e85	0.225969
$319$	−2.11182e86	−0.878776
$320$	7.69663e85	0.287493
$321$	−3.83499e86	−1.28630
$322$	−1.24232e86	−0.374289
$323$	−3.24774e85	−0.0879213
$324$	3.58117e86	0.871410
$325$	5.20858e86	1.13958
$326$	−4.76736e85	−0.0938146
$327$	2.53049e86	0.448030
$328$	1.99966e86	0.318646
$329$	1.05058e86	0.150720
$330$	−2.43735e86	−0.314910
$331$	5.07358e86	0.590539	0.295269	−	0.955414i	$-0.404591\pi$
$331$	5.07358e86	0.590539	0.295269	+	0.955414i	$0.404591\pi$
$332$	−2.97719e86	−0.312279
$333$	−7.16638e86	−0.677601
$334$	5.81063e86	0.495416
$335$	3.83205e86	0.294703
$336$	−1.22200e87	−0.847941
$337$	−9.67112e86	−0.605683	−0.302841	−	0.953041i	$-0.597935\pi$
$337$	−9.67112e86	−0.605683	−0.302841	+	0.953041i	$0.597935\pi$
$338$	−6.56361e86	−0.371122
$339$	2.50981e87	1.28159
$340$	−2.41585e86	−0.111441
$341$	−3.59322e87	−1.49781
$342$	−2.84780e86	−0.107302
$343$	−3.17505e87	−1.08169
$344$	3.13780e87	0.966849
$345$	4.60413e87	1.28348
$346$	5.08514e85	0.0128286
$347$	6.61082e87	1.50969	0.754847	−	0.655901i	$-0.227711\pi$
$347$	6.61082e87	1.50969	0.754847	+	0.655901i	$0.227711\pi$
$348$	−3.57777e87	−0.739825
$349$	3.04467e87	0.570247	0.285123	−	0.958491i	$-0.407965\pi$
$349$	3.04467e87	0.570247	0.285123	+	0.958491i	$0.407965\pi$
$350$	9.26554e86	0.157226
$351$	7.61624e86	0.117124
$352$	−8.42436e87	−1.17440
$353$	7.37095e86	0.0931742	0.0465871	−	0.998914i	$-0.485165\pi$
$353$	7.37095e86	0.0931742	0.0465871	+	0.998914i	$0.485165\pi$
$354$	−5.34289e87	−0.612581
$355$	−4.39304e87	−0.456970
$356$	4.58745e87	0.433058
$357$	3.04673e87	0.261084
$358$	3.19144e87	0.248326
$359$	1.32606e87	0.0937143	0.0468572	−	0.998902i	$-0.485079\pi$
$359$	1.32606e87	0.0937143	0.0468572	+	0.998902i	$0.485079\pi$
$360$	−4.41249e87	−0.283301
$361$	−1.48187e88	−0.864593
$362$	5.13080e87	0.272107
$363$	−4.36915e88	−2.10678
$364$	2.45649e88	1.07725
$365$	7.91926e87	0.315923
$366$	1.43297e88	0.520164
$367$	1.96257e88	0.648403	0.324201	−	0.945988i	$-0.394904\pi$
$367$	1.96257e88	0.648403	0.324201	+	0.945988i	$0.394904\pi$
$368$	4.57471e88	1.37599
$369$	2.30182e88	0.630466
$370$	−3.60505e87	−0.0899397
$371$	1.91114e88	0.434402
$372$	−6.08751e88	−1.26098
$373$	−4.03852e88	−0.762548	−0.381274	−	0.924462i	$-0.624515\pi$
$373$	−4.03852e88	−0.762548	−0.381274	+	0.924462i	$0.624515\pi$
$374$	6.03805e87	0.103950
$375$	−8.04400e88	−1.26297
$376$	7.34742e87	0.105234
$377$	6.54577e88	0.855430
$378$	1.35485e87	0.0161594
$379$	−1.57713e89	−1.71717	−0.858586	−	0.512669i	$-0.828657\pi$
$379$	−1.57713e89	−1.71717	−0.858586	+	0.512669i	$0.828657\pi$
$380$	1.72634e88	0.171630
$381$	1.15022e89	1.04441
$382$	−2.19401e88	−0.181993
$383$	1.65255e89	1.25256	0.626278	−	0.779599i	$-0.284577\pi$
$383$	1.65255e89	1.25256	0.626278	+	0.779599i	$0.284577\pi$
$384$	−1.87156e89	−1.29651
$385$	−9.55925e88	−0.605381
$386$	−3.36341e88	−0.194768
$387$	3.61194e89	1.91299
$388$	2.15292e89	1.04312
$389$	−2.04536e89	−0.906794	−0.453397	−	0.891309i	$-0.649788\pi$
$389$	−2.04536e89	−0.906794	−0.453397	+	0.891309i	$0.649788\pi$
$390$	7.55477e88	0.306544
$391$	−1.14058e89	−0.423671
$392$	−6.55143e88	−0.222826
$393$	2.74046e89	0.853650
$394$	4.30115e88	0.122734
$395$	1.29565e89	0.338756
$396$	−6.38016e89	−1.52879
$397$	−2.28353e89	−0.501574	−0.250787	−	0.968042i	$-0.580689\pi$
$397$	−2.28353e89	−0.501574	−0.250787	+	0.968042i	$0.580689\pi$
$398$	9.33175e88	0.187930
$399$	−2.17717e89	−0.402093
$400$	−3.41193e89	−0.578003
$401$	−4.35274e89	−0.676522	−0.338261	−	0.941052i	$-0.609839\pi$
$401$	−4.35274e89	−0.676522	−0.338261	+	0.941052i	$0.609839\pi$
$402$	−1.62261e89	−0.231427
$403$	1.11375e90	1.45802
$404$	5.82637e89	0.700230
$405$	4.31954e89	0.476693
$406$	1.16443e89	0.118022
$407$	−1.08579e90	−1.01097
$408$	2.13078e89	0.182290
$409$	4.28319e89	0.336754	0.168377	−	0.985723i	$-0.446147\pi$
$409$	4.28319e89	0.336754	0.168377	+	0.985723i	$0.446147\pi$
$410$	1.15793e89	0.0836834
$411$	6.06727e89	0.403135
$412$	2.17949e90	1.33169
$413$	−2.09548e90	−1.17762
$414$	−1.00013e90	−0.517063
$415$	−3.59103e89	−0.170828
$416$	2.61120e90	1.14320
$417$	4.63543e89	0.186808
$418$	−4.31474e89	−0.160093
$419$	−4.72781e90	−1.61538	−0.807692	−	0.589605i	$-0.799284\pi$
$419$	−4.72781e90	−1.61538	−0.807692	+	0.589605i	$0.799284\pi$
$420$	−1.61950e90	−0.509659
$421$	−2.27950e90	−0.660856	−0.330428	−	0.943831i	$-0.607193\pi$
$421$	−2.27950e90	−0.660856	−0.330428	+	0.943831i	$0.607193\pi$
$422$	−1.77260e90	−0.473512
$423$	8.45767e89	0.208213
$424$	1.33658e90	0.303301
$425$	8.50673e89	0.177969
$426$	1.86015e90	0.358854
$427$	5.62010e90	0.999959
$428$	−5.04998e90	−0.828858
$429$	2.27539e91	3.44571
$430$	1.81698e90	0.253916
$431$	−1.51932e91	−1.95967	−0.979837	−	0.199798i	$-0.935971\pi$
$431$	−1.51932e91	−1.95967	−0.979837	+	0.199798i	$0.935971\pi$
$432$	−4.98909e89	−0.0594062
$433$	−9.57091e90	−1.05225	−0.526127	−	0.850406i	$-0.676356\pi$
$433$	−9.57091e90	−1.05225	−0.526127	+	0.850406i	$0.676356\pi$
$434$	1.98125e90	0.201161
$435$	−4.31544e90	−0.404712
$436$	3.33219e90	0.288699
$437$	8.15051e90	0.652492
$438$	−3.35326e90	−0.248091
$439$	7.99929e90	0.547048	0.273524	−	0.961865i	$-0.411811\pi$
$439$	7.99929e90	0.547048	0.273524	+	0.961865i	$0.411811\pi$
$440$	−6.68542e90	−0.422680
$441$	−7.54139e90	−0.440880
$442$	−1.87155e90	−0.101189
$443$	−8.18200e90	−0.409196	−0.204598	−	0.978846i	$-0.565589\pi$
$443$	−8.18200e90	−0.409196	−0.204598	+	0.978846i	$0.565589\pi$
$444$	−1.83950e91	−0.851115
$445$	5.53329e90	0.236899
$446$	−5.55308e90	−0.220030
$447$	−7.99441e90	−0.293209
$448$	−1.27817e91	−0.434009
$449$	5.69186e91	1.78960	0.894799	−	0.446468i	$-0.147319\pi$
$449$	5.69186e91	1.78960	0.894799	+	0.446468i	$0.147319\pi$
$450$	7.45918e90	0.217200
$451$	3.48752e91	0.940645
$452$	3.30495e91	0.825828
$453$	−1.94118e91	−0.449445
$454$	−1.43635e91	−0.308201
$455$	2.96297e91	0.589298
$456$	−1.52264e91	−0.280743
$457$	−7.50198e91	−1.28253	−0.641264	−	0.767320i	$-0.721590\pi$
$457$	−7.50198e91	−1.28253	−0.641264	+	0.767320i	$0.721590\pi$
$458$	9.79619e90	0.155310
$459$	1.24390e90	0.0182914
$460$	6.06279e91	0.827042
$461$	−9.01739e91	−1.14130	−0.570649	−	0.821194i	$-0.693308\pi$
$461$	−9.01739e91	−1.14130	−0.570649	+	0.821194i	$0.693308\pi$
$462$	4.04769e91	0.475399
$463$	−6.50698e91	−0.709309	−0.354655	−	0.934997i	$-0.615402\pi$
$463$	−6.50698e91	−0.709309	−0.354655	+	0.934997i	$0.615402\pi$
$464$	−4.28787e91	−0.433882
$465$	−7.34264e91	−0.689803
$466$	3.35269e91	0.292469
$467$	−2.91848e91	−0.236442	−0.118221	−	0.992987i	$-0.537719\pi$
$467$	−2.91848e91	−0.236442	−0.118221	+	0.992987i	$0.537719\pi$
$468$	1.97759e92	1.48817
$469$	−6.36385e91	−0.444894
$470$	4.25463e90	0.0276367
$471$	−9.40978e91	−0.568013
$472$	−1.46550e92	−0.822220
$473$	5.47249e92	2.85414
$474$	−5.48617e91	−0.266021
$475$	−6.07884e91	−0.274089
$476$	4.01198e91	0.168236
$477$	1.53855e92	0.600106
$478$	1.02679e92	0.372581
$479$	−1.18268e92	−0.399293	−0.199647	−	0.979868i	$-0.563979\pi$
$479$	−1.18268e92	−0.399293	−0.199647	+	0.979868i	$0.563979\pi$
$480$	−1.72149e92	−0.540857
$481$	3.36549e92	0.984110
$482$	−5.14879e91	−0.140147
$483$	−7.64605e92	−1.93759
$484$	−5.75337e92	−1.35755
$485$	2.59681e92	0.570624
$486$	−1.93257e92	−0.395534
$487$	1.07235e92	0.204451	0.102225	−	0.994761i	$-0.467404\pi$
$487$	1.07235e92	0.204451	0.102225	+	0.994761i	$0.467404\pi$
$488$	3.93051e92	0.698176
$489$	−2.93413e92	−0.485651
$490$	−3.79370e91	−0.0585191
$491$	6.08028e92	0.874202	0.437101	−	0.899412i	$-0.356005\pi$
$491$	6.08028e92	0.874202	0.437101	+	0.899412i	$0.356005\pi$
$492$	5.90843e92	0.791911
$493$	1.06907e92	0.133594
$494$	1.33739e92	0.155840
$495$	−7.69563e92	−0.836305
$496$	−7.29572e92	−0.739521
$497$	7.29550e92	0.689858
$498$	1.52055e92	0.134150
$499$	3.14472e91	0.0258889	0.0129444	−	0.999916i	$-0.495880\pi$
$499$	3.14472e91	0.0258889	0.0129444	+	0.999916i	$0.495880\pi$
$500$	−1.05925e93	−0.813827
$501$	3.57623e93	2.56462
$502$	3.97667e92	0.266220
$503$	−1.72824e93	−1.08021	−0.540105	−	0.841598i	$-0.681616\pi$
$503$	−1.72824e93	−1.08021	−0.540105	+	0.841598i	$0.681616\pi$
$504$	7.32779e92	0.427681
$505$	7.02765e92	0.383052
$506$	−1.51530e93	−0.771449
$507$	−4.03966e93	−1.92119
$508$	1.51463e93	0.672989
$509$	−1.42010e93	−0.589596	−0.294798	−	0.955560i	$-0.595252\pi$
$509$	−1.42010e93	−0.589596	−0.294798	+	0.955560i	$0.595252\pi$
$510$	1.23386e92	0.0478733
$511$	−1.31515e93	−0.476928
$512$	−2.92927e93	−0.992991
$513$	−8.88877e91	−0.0281704
$514$	−3.90988e92	−0.115861
$515$	2.62886e93	0.728482
$516$	9.27131e93	2.40285
$517$	1.28143e93	0.310650
$518$	5.98688e92	0.135776
$519$	3.12972e92	0.0664097
$520$	2.07220e93	0.411450
$521$	−8.81177e93	−1.63743	−0.818713	−	0.574204i	$-0.805312\pi$
$521$	−8.81177e93	−1.63743	−0.818713	+	0.574204i	$0.805312\pi$
$522$	9.37416e92	0.163042
$523$	−2.80331e93	−0.456418	−0.228209	−	0.973612i	$-0.573287\pi$
$523$	−2.80331e93	−0.456418	−0.228209	+	0.973612i	$0.573287\pi$
$524$	3.60868e93	0.550071
$525$	5.70260e93	0.813911
$526$	−1.70266e93	−0.227572
$527$	1.81899e93	0.227701
$528$	−1.49051e94	−1.74769
$529$	1.95202e94	2.14419
$530$	7.73967e92	0.0796535
$531$	−1.68695e94	−1.62683
$532$	−2.86693e93	−0.259099
$533$	−1.08099e94	−0.915655
$534$	−2.34297e93	−0.186034
$535$	−6.09119e93	−0.453416
$536$	−4.45066e93	−0.310627
$537$	1.96421e94	1.28551
$538$	8.53860e93	0.524081
$539$	−1.14261e94	−0.657785
$540$	−6.61196e92	−0.0357063
$541$	2.30494e94	1.16776	0.583880	−	0.811840i	$-0.301534\pi$
$541$	2.30494e94	1.16776	0.583880	+	0.811840i	$0.301534\pi$
$542$	−3.80854e93	−0.181043
$543$	3.15782e94	1.40862
$544$	4.26466e93	0.178534
$545$	4.01922e93	0.157929
$546$	−1.25462e94	−0.462769
$547$	−4.73577e94	−1.63994	−0.819970	−	0.572406i	$-0.806010\pi$
$547$	−4.73577e94	−1.63994	−0.819970	+	0.572406i	$0.806010\pi$
$548$	7.98947e93	0.259770
$549$	4.52443e94	1.38140
$550$	1.13015e94	0.324058
$551$	−7.63945e93	−0.205746
$552$	−5.34739e94	−1.35283
$553$	−2.15167e94	−0.511397
$554$	3.72617e93	0.0832100
$555$	−2.21877e94	−0.465592
$556$	6.10401e93	0.120375
$557$	9.22074e94	1.70908	0.854538	−	0.519389i	$-0.173840\pi$
$557$	9.22074e94	1.70908	0.854538	+	0.519389i	$0.173840\pi$
$558$	1.59500e94	0.277894
$559$	−1.69625e95	−2.77832
$560$	−1.94092e94	−0.298897
$561$	3.71620e94	0.538121
$562$	3.59219e94	0.489166
$563$	7.88231e93	0.100952	0.0504759	−	0.998725i	$-0.483926\pi$
$563$	7.88231e93	0.100952	0.0504759	+	0.998725i	$0.483926\pi$
$564$	2.17096e94	0.261530
$565$	3.98637e94	0.451759
$566$	−2.57312e94	−0.274342
$567$	−7.17343e94	−0.719633
$568$	5.10222e94	0.481661
$569$	9.17833e94	0.815437	0.407718	−	0.913108i	$-0.366324\pi$
$569$	9.17833e94	0.815437	0.407718	+	0.913108i	$0.366324\pi$
$570$	−8.81704e93	−0.0737293
$571$	1.43436e95	1.12905	0.564526	−	0.825416i	$-0.309059\pi$
$571$	1.43436e95	1.12905	0.564526	+	0.825416i	$0.309059\pi$
$572$	2.99627e95	2.22033
$573$	−1.35034e95	−0.942122
$574$	−1.92297e94	−0.126331
$575$	−2.13484e95	−1.32076
$576$	−1.02899e95	−0.599563
$577$	−2.02368e95	−1.11065	−0.555323	−	0.831635i	$-0.687405\pi$
$577$	−2.02368e95	−1.11065	−0.555323	+	0.831635i	$0.687405\pi$
$578$	5.04855e94	0.261010
$579$	−2.07006e95	−1.00826
$580$	−5.68264e94	−0.260786
$581$	5.96360e94	0.257888
$582$	−1.09957e95	−0.448105
$583$	2.33108e95	0.895347
$584$	−9.19769e94	−0.332993
$585$	2.38533e95	0.814087
$586$	−3.95999e94	−0.127417
$587$	3.87261e95	1.17487	0.587434	−	0.809272i	$-0.300138\pi$
$587$	3.87261e95	1.17487	0.587434	+	0.809272i	$0.300138\pi$
$588$	−1.93576e95	−0.553777
$589$	−1.29984e95	−0.350680
$590$	−8.48621e94	−0.215933
$591$	2.64720e95	0.635358
$592$	−2.20460e95	−0.499149
$593$	1.94348e95	0.415139	0.207569	−	0.978220i	$-0.433445\pi$
$593$	1.94348e95	0.415139	0.207569	+	0.978220i	$0.433445\pi$
$594$	1.65256e94	0.0333062
$595$	4.83917e94	0.0920314
$596$	−1.05272e95	−0.188936
$597$	5.74335e95	0.972861
$598$	4.69682e95	0.750953
$599$	2.48951e94	0.0375741	0.0187871	−	0.999824i	$-0.494020\pi$
$599$	2.48951e94	0.0375741	0.0187871	+	0.999824i	$0.494020\pi$
$600$	3.98821e95	0.568276
$601$	−9.88491e95	−1.32985	−0.664926	−	0.746909i	$-0.731537\pi$
$601$	−9.88491e95	−1.32985	−0.664926	+	0.746909i	$0.731537\pi$
$602$	−3.01745e95	−0.383320
$603$	−5.12319e95	−0.614601
$604$	−2.55617e95	−0.289611
$605$	−6.93960e95	−0.742632
$606$	−2.97573e95	−0.300807
$607$	−2.30873e95	−0.220477	−0.110239	−	0.993905i	$-0.535162\pi$
$607$	−2.30873e95	−0.220477	−0.110239	+	0.993905i	$0.535162\pi$
$608$	−3.04749e95	−0.274959
$609$	7.16662e95	0.610967
$610$	2.27601e95	0.183356
$611$	−3.97191e95	−0.302397
$612$	3.22983e95	0.232410
$613$	1.67994e96	1.14263	0.571317	−	0.820729i	$-0.306433\pi$
$613$	1.67994e96	1.14263	0.571317	+	0.820729i	$0.306433\pi$
$614$	−4.92873e94	−0.0316903
$615$	7.12664e95	0.433205
$616$	1.11024e96	0.638092
$617$	−1.01648e96	−0.552407	−0.276204	−	0.961099i	$-0.589076\pi$
$617$	−1.01648e96	−0.552407	−0.276204	+	0.961099i	$0.589076\pi$
$618$	−1.11314e96	−0.572069
$619$	1.08493e96	0.527318	0.263659	−	0.964616i	$-0.415071\pi$
$619$	1.08493e96	0.527318	0.263659	+	0.964616i	$0.415071\pi$
$620$	−9.66891e95	−0.444492
$621$	−3.12167e95	−0.135746
$622$	7.77511e95	0.319844
$623$	−9.18910e95	−0.357631
$624$	4.61998e96	1.70126
$625$	8.59982e95	0.299660
$626$	−5.85019e95	−0.192910
$627$	−2.65556e96	−0.828756
$628$	−1.23910e96	−0.366013
$629$	5.49658e95	0.153690
$630$	4.24326e95	0.112318
$631$	−3.61793e96	−0.906667	−0.453333	−	0.891341i	$-0.649765\pi$
$631$	−3.61793e96	−0.906667	−0.453333	+	0.891341i	$0.649765\pi$
$632$	−1.50480e96	−0.357060
$633$	−1.09097e97	−2.45123
$634$	1.63494e96	0.347874
$635$	1.82692e96	0.368150
$636$	3.94923e96	0.753775
$637$	3.54161e96	0.640309
$638$	1.42029e96	0.243256
$639$	5.87320e96	0.953006
$640$	−2.97264e96	−0.457017
$641$	−5.93103e96	−0.864028	−0.432014	−	0.901867i	$-0.642197\pi$
$641$	−5.93103e96	−0.864028	−0.432014	+	0.901867i	$0.642197\pi$
$642$	2.57920e96	0.356063
$643$	1.51768e97	1.98565	0.992825	−	0.119580i	$-0.0381550\pi$
$643$	1.51768e97	1.98565	0.992825	+	0.119580i	$0.0381550\pi$
$644$	−1.00684e97	−1.24853
$645$	1.11829e97	1.31445
$646$	2.18425e95	0.0243377
$647$	1.33789e97	1.41326	0.706630	−	0.707584i	$-0.250215\pi$
$647$	1.33789e97	1.41326	0.706630	+	0.707584i	$0.250215\pi$
$648$	−5.01685e96	−0.502451
$649$	−2.55592e97	−2.42720
$650$	−3.50300e96	−0.315449
$651$	1.21939e97	1.04135
$652$	−3.86372e96	−0.312941
$653$	−1.19882e97	−0.920978	−0.460489	−	0.887665i	$-0.652326\pi$
$653$	−1.19882e97	−0.920978	−0.460489	+	0.887665i	$0.652326\pi$
$654$	−1.70186e96	−0.124020
$655$	4.35272e96	0.300909
$656$	7.08110e96	0.464428
$657$	−1.05875e97	−0.658854
$658$	−7.06563e95	−0.0417213
$659$	1.08314e97	0.606929	0.303465	−	0.952843i	$-0.401857\pi$
$659$	1.08314e97	0.606929	0.303465	+	0.952843i	$0.401857\pi$
$660$	−1.97535e97	−1.05046
$661$	1.68218e97	0.849028	0.424514	−	0.905421i	$-0.360445\pi$
$661$	1.68218e97	0.849028	0.424514	+	0.905421i	$0.360445\pi$
$662$	−3.41220e96	−0.163469
$663$	−1.15187e97	−0.523825
$664$	4.17074e96	0.180059
$665$	−3.45803e96	−0.141737
$666$	4.81971e96	0.187568
$667$	−2.68292e97	−0.991439
$668$	4.70924e97	1.65258
$669$	−3.41772e97	−1.13903
$670$	−2.57722e96	−0.0815775
$671$	6.85502e97	2.06102
$672$	2.85887e97	0.816497
$673$	1.90781e97	0.517624	0.258812	−	0.965928i	$-0.416669\pi$
$673$	1.90781e97	0.517624	0.258812	+	0.965928i	$0.416669\pi$
$674$	6.50425e96	0.167661
$675$	2.32822e96	0.0570221
$676$	−5.31949e97	−1.23797
$677$	1.40207e97	0.310070	0.155035	−	0.987909i	$-0.450451\pi$
$677$	1.40207e97	0.310070	0.155035	+	0.987909i	$0.450451\pi$
$678$	−1.68795e97	−0.354761
$679$	−4.31250e97	−0.861434
$680$	3.38435e96	0.0642567
$681$	−8.84021e97	−1.59547
$682$	2.41660e97	0.414613
$683$	−2.55619e97	−0.416945	−0.208472	−	0.978028i	$-0.566849\pi$
$683$	−2.55619e97	−0.416945	−0.208472	+	0.978028i	$0.566849\pi$
$684$	−2.30801e97	−0.357933
$685$	9.63675e96	0.142104
$686$	2.13536e97	0.299425
$687$	6.02920e97	0.803993
$688$	1.11114e98	1.40919
$689$	−7.22538e97	−0.871560
$690$	−3.09648e97	−0.355283
$691$	−1.18804e98	−1.29669	−0.648346	−	0.761346i	$-0.724539\pi$
$691$	−1.18804e98	−1.29669	−0.648346	+	0.761346i	$0.724539\pi$
$692$	4.12127e96	0.0427928
$693$	1.27801e98	1.26252
$694$	−4.44607e97	−0.417902
$695$	7.36253e96	0.0658494
$696$	5.01209e97	0.426580
$697$	−1.76548e97	−0.142999
$698$	−2.04767e97	−0.157851
$699$	2.06346e98	1.51402
$700$	7.50928e97	0.524464
$701$	9.38181e97	0.623756	0.311878	−	0.950122i	$-0.399042\pi$
$701$	9.38181e97	0.623756	0.311878	+	0.950122i	$0.399042\pi$
$702$	−5.12225e96	−0.0324213
$703$	−3.92781e97	−0.236696
$704$	−1.55903e98	−0.894537
$705$	2.61857e97	0.143067
$706$	−4.95728e96	−0.0257918
$707$	−1.16708e98	−0.578269
$708$	−4.33016e98	−2.04341
$709$	2.22016e98	0.997903	0.498951	−	0.866630i	$-0.333719\pi$
$709$	2.22016e98	0.997903	0.498951	+	0.866630i	$0.333719\pi$
$710$	2.95451e97	0.126495
$711$	−1.73219e98	−0.706471
$712$	−6.42655e97	−0.249700
$713$	−4.56493e98	−1.68984
$714$	−2.04906e97	−0.0722713
$715$	3.61404e98	1.21460
$716$	2.58651e98	0.828351
$717$	6.31953e98	1.92874
$718$	−8.91836e96	−0.0259413
$719$	5.69180e97	0.157799	0.0788993	−	0.996883i	$-0.474859\pi$
$719$	5.69180e97	0.157799	0.0788993	+	0.996883i	$0.474859\pi$
$720$	−1.56253e98	−0.412912
$721$	−4.36574e98	−1.09974
$722$	9.96622e97	0.239330
$723$	−3.16889e98	−0.725498
$724$	4.15827e98	0.907678
$725$	2.00098e98	0.416469
$726$	2.93844e98	0.583182
$727$	3.64329e98	0.689535	0.344767	−	0.938688i	$-0.387958\pi$
$727$	3.64329e98	0.689535	0.344767	+	0.938688i	$0.387958\pi$
$728$	−3.44129e98	−0.621140
$729$	−6.41219e98	−1.10384
$730$	−5.32605e97	−0.0874514
$731$	−2.77034e98	−0.433893
$732$	1.16135e99	1.73513
$733$	6.80586e98	0.970053	0.485027	−	0.874499i	$-0.338810\pi$
$733$	6.80586e98	0.970053	0.485027	+	0.874499i	$0.338810\pi$
$734$	−1.31991e98	−0.179486
$735$	−2.33488e98	−0.302936
$736$	−1.07026e99	−1.32496
$737$	−7.76220e98	−0.916973
$738$	−1.54808e98	−0.174521
$739$	−4.51663e98	−0.485939	−0.242969	−	0.970034i	$-0.578121\pi$
$739$	−4.51663e98	−0.485939	−0.242969	+	0.970034i	$0.578121\pi$
$740$	−2.92172e98	−0.300016
$741$	8.23115e98	0.806738
$742$	−1.28532e98	−0.120248
$743$	−1.36718e99	−1.22099	−0.610493	−	0.792022i	$-0.709029\pi$
$743$	−1.36718e99	−1.22099	−0.610493	+	0.792022i	$0.709029\pi$
$744$	8.52798e98	0.727076
$745$	−1.26977e98	−0.103355
$746$	2.71608e98	0.211083
$747$	4.80096e98	0.356260
$748$	4.89355e98	0.346752
$749$	1.01156e99	0.684493
$750$	5.40994e98	0.349606
$751$	−5.82039e98	−0.359232	−0.179616	−	0.983737i	$-0.557485\pi$
$751$	−5.82039e98	−0.359232	−0.179616	+	0.983737i	$0.557485\pi$
$752$	2.60184e98	0.153379
$753$	2.44749e99	1.37814
$754$	−4.40232e98	−0.236794
$755$	−3.08320e98	−0.158428
$756$	1.09804e98	0.0539035
$757$	3.20631e99	1.50383	0.751913	−	0.659262i	$-0.229131\pi$
$757$	3.20631e99	1.50383	0.751913	+	0.659262i	$0.229131\pi$
$758$	1.06069e99	0.475335
$759$	−9.32614e99	−3.99356
$760$	−2.41843e98	−0.0989612
$761$	2.29653e99	0.898053	0.449026	−	0.893519i	$-0.351771\pi$
$761$	2.29653e99	0.898053	0.449026	+	0.893519i	$0.351771\pi$
$762$	−7.73573e98	−0.289105
$763$	−6.67469e98	−0.238416
$764$	−1.77814e99	−0.607080
$765$	3.89575e98	0.127137
$766$	−1.11141e99	−0.346723
$767$	7.92230e99	2.36272
$768$	−1.60173e99	−0.456697
$769$	−4.43332e99	−1.20856	−0.604282	−	0.796770i	$-0.706540\pi$
$769$	−4.43332e99	−1.20856	−0.604282	+	0.796770i	$0.706540\pi$
$770$	6.42901e98	0.167577
$771$	−2.40639e99	−0.599776
$772$	−2.72588e99	−0.649696
$773$	2.18161e99	0.497260	0.248630	−	0.968598i	$-0.420020\pi$
$773$	2.18161e99	0.497260	0.248630	+	0.968598i	$0.420020\pi$
$774$	−2.42919e99	−0.529539
$775$	3.40463e99	0.709842
$776$	−3.01602e99	−0.601457
$777$	3.68470e99	0.702874
$778$	1.37559e99	0.251012
$779$	1.26160e99	0.220231
$780$	6.12278e99	1.02255
$781$	8.89856e99	1.42187
$782$	7.67091e98	0.117277
$783$	2.92593e98	0.0428040
$784$	−2.31996e99	−0.324771
$785$	−1.49457e99	−0.200223
$786$	−1.84308e99	−0.236301
$787$	−5.72016e99	−0.701908	−0.350954	−	0.936393i	$-0.614143\pi$
$787$	−5.72016e99	−0.701908	−0.350954	+	0.936393i	$0.614143\pi$
$788$	3.48587e99	0.409409
$789$	−1.04792e100	−1.17807
$790$	−8.71378e98	−0.0937717
$791$	−6.62014e99	−0.681991
$792$	8.93795e99	0.881494
$793$	−2.12477e100	−2.00626
$794$	1.53578e99	0.138842
$795$	4.76348e99	0.412343
$796$	7.56294e99	0.626888
$797$	8.36136e99	0.663690	0.331845	−	0.943334i	$-0.392329\pi$
$797$	8.36136e99	0.663690	0.331845	+	0.943334i	$0.392329\pi$
$798$	1.46424e99	0.111304
$799$	−6.48698e98	−0.0472258
$800$	7.98222e99	0.556569
$801$	−7.39764e99	−0.494051
$802$	2.92741e99	0.187270
$803$	−1.60413e100	−0.982999
$804$	−1.31505e100	−0.771982
$805$	−1.21444e100	−0.682993
$806$	−7.49046e99	−0.403598
$807$	5.25520e100	2.71301
$808$	−8.16215e99	−0.403750
$809$	1.17927e100	0.558969	0.279484	−	0.960150i	$-0.409836\pi$
$809$	1.17927e100	0.558969	0.279484	+	0.960150i	$0.409836\pi$
$810$	−2.90508e99	−0.131955
$811$	3.58173e100	1.55910	0.779550	−	0.626340i	$-0.215448\pi$
$811$	3.58173e100	1.55910	0.779550	+	0.626340i	$0.215448\pi$
$812$	9.43713e99	0.393692
$813$	−2.34401e100	−0.937209
$814$	7.30240e99	0.279849
$815$	−4.66034e99	−0.171191
$816$	7.54542e99	0.265688
$817$	1.97966e100	0.668235
$818$	−2.88063e99	−0.0932178
$819$	−3.96130e100	−1.22897
$820$	9.38447e99	0.279146
$821$	−6.03679e100	−1.72174	−0.860869	−	0.508826i	$-0.830080\pi$
$821$	−6.03679e100	−1.72174	−0.860869	+	0.508826i	$0.830080\pi$
$822$	−4.08050e99	−0.111593
$823$	−5.26932e100	−1.38185	−0.690924	−	0.722928i	$-0.742796\pi$
$823$	−5.26932e100	−1.38185	−0.690924	+	0.722928i	$0.742796\pi$
$824$	−3.05325e100	−0.767844
$825$	6.95566e100	1.67756
$826$	1.40930e100	0.325980
$827$	9.11018e99	0.202110	0.101055	−	0.994881i	$-0.467778\pi$
$827$	9.11018e99	0.202110	0.101055	+	0.994881i	$0.467778\pi$
$828$	−8.10555e100	−1.72479
$829$	4.86693e100	0.993399	0.496700	−	0.867923i	$-0.334545\pi$
$829$	4.86693e100	0.993399	0.496700	+	0.867923i	$0.334545\pi$
$830$	2.41512e99	0.0472874
$831$	2.29332e100	0.430754
$832$	4.83236e100	0.870772
$833$	5.78420e99	0.0999980
$834$	−3.11753e99	−0.0517108
$835$	5.68019e100	0.904023
$836$	−3.49689e100	−0.534029
$837$	4.97842e99	0.0729564
$838$	3.17966e100	0.447158
$839$	−4.85563e100	−0.655327	−0.327664	−	0.944794i	$-0.606261\pi$
$839$	−4.85563e100	−0.655327	−0.327664	+	0.944794i	$0.606261\pi$
$840$	2.26875e100	0.293867
$841$	−5.52912e100	−0.687375
$842$	1.53306e100	0.182933
$843$	2.21086e101	2.53227
$844$	−1.43661e101	−1.57951
$845$	−6.41627e100	−0.677214
$846$	−5.68815e99	−0.0576360
$847$	1.15245e101	1.12110
$848$	4.73305e100	0.442063
$849$	−1.58366e101	−1.42019
$850$	−5.72115e99	−0.0492641
$851$	−1.37942e101	−1.14058
$852$	1.50756e101	1.19704
$853$	−1.95295e101	−1.48919	−0.744594	−	0.667518i	$-0.767357\pi$
$853$	−1.95295e101	−1.48919	−0.744594	+	0.667518i	$0.767357\pi$
$854$	−3.77976e100	−0.276801
$855$	−2.78387e100	−0.195803
$856$	7.07451e100	0.477916
$857$	2.23074e101	1.44747	0.723737	−	0.690076i	$-0.242423\pi$
$857$	2.23074e101	1.44747	0.723737	+	0.690076i	$0.242423\pi$
$858$	−1.53030e101	−0.953815
$859$	−2.74712e101	−1.64480	−0.822401	−	0.568908i	$-0.807366\pi$
$859$	−2.74712e101	−1.64480	−0.822401	+	0.568908i	$0.807366\pi$
$860$	1.47258e101	0.846997
$861$	−1.18352e101	−0.653981
$862$	1.02181e101	0.542462
$863$	2.09690e101	1.06956	0.534781	−	0.844991i	$-0.320394\pi$
$863$	2.09690e101	1.06956	0.534781	+	0.844991i	$0.320394\pi$
$864$	1.16720e100	0.0572032
$865$	4.97099e99	0.0234092
$866$	6.43685e100	0.291277
$867$	3.10720e101	1.35117
$868$	1.60571e101	0.671021
$869$	−2.62446e101	−1.05404
$870$	2.90232e100	0.112029
$871$	2.40596e101	0.892612
$872$	−4.66806e100	−0.166463
$873$	−3.47176e101	−1.19003
$874$	−5.48157e100	−0.180618
$875$	2.12177e101	0.672080
$876$	−2.71766e101	−0.827567
$877$	−5.73845e99	−0.0168000	−0.00839999	−	0.999965i	$-0.502674\pi$
$877$	−5.73845e99	−0.0168000	−0.00839999	+	0.999965i	$0.502674\pi$
$878$	−5.37987e100	−0.151430
$879$	−2.43723e101	−0.659599
$880$	−2.36741e101	−0.616057
$881$	6.61154e101	1.65437	0.827187	−	0.561926i	$-0.189939\pi$
$881$	6.61154e101	1.65437	0.827187	+	0.561926i	$0.189939\pi$
$882$	5.07192e100	0.122041
$883$	−3.07268e100	−0.0711005	−0.0355503	−	0.999368i	$-0.511318\pi$
$883$	−3.07268e100	−0.0711005	−0.0355503	+	0.999368i	$0.511318\pi$
$884$	−1.51680e101	−0.337540
$885$	−5.22295e101	−1.11782
$886$	5.50275e100	0.113270
$887$	1.95143e101	0.386357	0.193179	−	0.981164i	$-0.438120\pi$
$887$	1.95143e101	0.386357	0.193179	+	0.981164i	$0.438120\pi$
$888$	2.57696e101	0.490749
$889$	−3.03395e101	−0.555773
$890$	−3.72138e100	−0.0655766
$891$	−8.74967e101	−1.48324
$892$	−4.50051e101	−0.733963
$893$	4.63554e100	0.0727320
$894$	5.37659e100	0.0811638
$895$	3.11979e101	0.453139
$896$	4.93664e101	0.689930
$897$	2.89072e102	3.88747
$898$	−3.82803e101	−0.495383
$899$	4.27870e101	0.532847
$900$	6.04531e101	0.724522
$901$	−1.18006e101	−0.136113
$902$	−2.34551e101	−0.260382
$903$	−1.85713e102	−1.98434
$904$	−4.62990e101	−0.476169
$905$	5.01562e101	0.496534
$906$	1.30552e101	0.124412
$907$	6.03137e101	0.553305	0.276653	−	0.960970i	$-0.410775\pi$
$907$	6.03137e101	0.553305	0.276653	+	0.960970i	$0.410775\pi$
$908$	−1.16409e102	−1.02808
$909$	−9.39550e101	−0.798851
$910$	−1.99273e101	−0.163125
$911$	−1.49378e102	−1.17734	−0.588671	−	0.808373i	$-0.700348\pi$
$911$	−1.49378e102	−1.17734	−0.588671	+	0.808373i	$0.700348\pi$
$912$	−5.39189e101	−0.409184
$913$	7.27400e101	0.531534
$914$	5.04541e101	0.355020
$915$	1.40080e102	0.949182
$916$	7.93934e101	0.518073
$917$	−7.22852e101	−0.454263
$918$	−8.36574e99	−0.00506328
$919$	6.29052e100	0.0366692	0.0183346	−	0.999832i	$-0.494164\pi$
$919$	6.29052e100	0.0366692	0.0183346	+	0.999832i	$0.494164\pi$
$920$	−8.49335e101	−0.476869
$921$	−3.03345e101	−0.164052
$922$	6.06459e101	0.315925
$923$	−2.75819e102	−1.38409
$924$	3.28046e102	1.58581
$925$	1.02880e102	0.479117
$926$	4.37623e101	0.196346
$927$	−3.51461e102	−1.51924
$928$	1.00315e102	0.417792
$929$	1.38011e102	0.553824	0.276912	−	0.960895i	$-0.410689\pi$
$929$	1.38011e102	0.553824	0.276912	+	0.960895i	$0.410689\pi$
$930$	4.93824e101	0.190946
$931$	−4.13334e101	−0.154006
$932$	2.71719e102	0.975600
$933$	4.78529e102	1.65574
$934$	1.96280e101	0.0654500
$935$	5.90250e101	0.189686
$936$	−2.77040e102	−0.858075
$937$	−3.52270e102	−1.05162	−0.525812	−	0.850601i	$-0.676238\pi$
$937$	−3.52270e102	−1.05162	−0.525812	+	0.850601i	$0.676238\pi$
$938$	4.27997e101	0.123152
$939$	−3.60058e102	−0.998640
$940$	3.44817e101	0.0921888
$941$	−1.93126e102	−0.497735	−0.248868	−	0.968537i	$-0.580058\pi$
$941$	−1.93126e102	−0.497735	−0.248868	+	0.968537i	$0.580058\pi$
$942$	6.32849e101	0.157233
$943$	4.43065e102	1.06124
$944$	−5.18958e102	−1.19839
$945$	1.32444e101	0.0294872
$946$	−3.68049e102	−0.790063
$947$	−2.99511e102	−0.619925	−0.309962	−	0.950749i	$-0.600316\pi$
$947$	−2.99511e102	−0.619925	−0.309962	+	0.950749i	$0.600316\pi$
$948$	−4.44628e102	−0.887378
$949$	4.97214e102	0.956883
$950$	4.08828e101	0.0758712
$951$	1.00624e103	1.80084
$952$	−5.62037e101	−0.0970042
$953$	−6.44143e102	−1.07220	−0.536102	−	0.844154i	$-0.680104\pi$
$953$	−6.44143e102	−1.07220	−0.536102	+	0.844154i	$0.680104\pi$
$954$	−1.03474e102	−0.166117
$955$	−2.14476e102	−0.332095
$956$	8.32166e102	1.24283
$957$	8.74137e102	1.25927
$958$	7.95404e101	0.110529
$959$	−1.60037e102	−0.214525
$960$	−3.18584e102	−0.411970
$961$	−7.35858e101	−0.0917988
$962$	−2.26344e102	−0.272414
$963$	8.14351e102	0.945594
$964$	−4.17285e102	−0.467493
$965$	−3.28791e102	−0.355408
$966$	5.14230e102	0.536348
$967$	1.87413e102	0.188619	0.0943096	−	0.995543i	$-0.469936\pi$
$967$	1.87413e102	0.188619	0.0943096	+	0.995543i	$0.469936\pi$
$968$	8.05987e102	0.782760
$969$	1.34432e102	0.125989
$970$	−1.74647e102	−0.157956
$971$	−1.78043e102	−0.155404	−0.0777020	−	0.996977i	$-0.524758\pi$
$971$	−1.78043e102	−0.155404	−0.0777020	+	0.996977i	$0.524758\pi$
$972$	−1.56625e103	−1.31940
$973$	−1.22269e102	−0.0994085
$974$	−7.21204e101	−0.0565945
$975$	−2.15597e103	−1.63299
$976$	1.39185e103	1.01759
$977$	−1.73120e102	−0.122175	−0.0610877	−	0.998132i	$-0.519457\pi$
$977$	−1.73120e102	−0.122175	−0.0610877	+	0.998132i	$0.519457\pi$
$978$	1.97333e102	0.134434
$979$	−1.12083e103	−0.737115
$980$	−3.07461e102	−0.195205
$981$	−5.37343e102	−0.329360
$982$	−4.08925e102	−0.241990
$983$	1.37363e103	0.784825	0.392413	−	0.919789i	$-0.371641\pi$
$983$	1.37363e103	0.784825	0.392413	+	0.919789i	$0.371641\pi$
$984$	−8.27711e102	−0.456612
$985$	4.20459e102	0.223962
$986$	−7.18993e101	−0.0369804
$987$	−4.34864e102	−0.215979
$988$	1.08389e103	0.519842
$989$	6.95242e103	3.22006
$990$	5.17565e102	0.231500
$991$	−1.81342e103	−0.783354	−0.391677	−	0.920103i	$-0.628105\pi$
$991$	−1.81342e103	−0.783354	−0.391677	+	0.920103i	$0.628105\pi$
$992$	1.70684e103	0.712097
$993$	−2.10009e103	−0.846229
$994$	−4.90654e102	−0.190961
$995$	9.12227e102	0.342931
$996$	1.23234e103	0.447489
$997$	−3.65689e103	−1.28271	−0.641356	−	0.767243i	$-0.721628\pi$
$997$	−3.65689e103	−1.28271	−0.641356	+	0.767243i	$0.721628\pi$
$998$	−2.11496e101	−0.00716636
$999$	1.50436e102	0.0492429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.70.a.a.1.3	✓	5
3.2	odd	2		9.70.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.70.a.a.1.3	✓	5	1.1	even	1	trivial
9.70.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q-6.72544e9 q^{2} -4.13926e16 q^{3} -5.45064e20 q^{4} -6.57446e23 q^{5} +2.78383e26 q^{6} +1.09182e29 q^{7} +7.63579e30 q^{8} +8.78961e32 q^{9} +O(q^{10})\)	\(q-6.72544e9 q^{2} -4.13926e16 q^{3} -5.45064e20 q^{4} -6.57446e23 q^{5} +2.78383e26 q^{6} +1.09182e29 q^{7} +7.63579e30 q^{8} +8.78961e32 q^{9} +4.42161e33 q^{10} +1.33172e36 q^{11} +2.25616e37 q^{12} -4.12780e38 q^{13} -7.34294e38 q^{14} +2.72134e40 q^{15} +2.70395e41 q^{16} -6.74158e41 q^{17} -5.91140e42 q^{18} +4.81748e43 q^{19} +3.58350e44 q^{20} -4.51931e45 q^{21} -8.95643e45 q^{22} +1.69186e47 q^{23} -3.16065e47 q^{24} -1.26183e48 q^{25} +2.77612e48 q^{26} -1.84511e48 q^{27} -5.95110e49 q^{28} -1.58578e50 q^{29} -1.83022e50 q^{30} -2.69817e51 q^{31} -6.32590e51 q^{32} -5.51235e52 q^{33} +4.53401e51 q^{34} -7.17810e52 q^{35} -4.79090e53 q^{36} -8.15325e53 q^{37} -3.23996e53 q^{38} +1.70860e55 q^{39} -5.02012e54 q^{40} +2.61880e55 q^{41} +3.03943e55 q^{42} +4.10933e56 q^{43} -7.25876e56 q^{44} -5.77869e56 q^{45} -1.13785e57 q^{46} +9.62235e56 q^{47} -1.11924e58 q^{48} -8.57990e57 q^{49} +8.48636e57 q^{50} +2.79051e58 q^{51} +2.24991e59 q^{52} +1.75042e59 q^{53} +1.24092e58 q^{54} -8.75537e59 q^{55} +8.33688e59 q^{56} -1.99408e60 q^{57} +1.06651e60 q^{58} -1.91926e61 q^{59} -1.48330e61 q^{60} +5.14748e61 q^{61} +1.81464e61 q^{62} +9.59664e61 q^{63} -1.17069e62 q^{64} +2.71380e62 q^{65} +3.70730e62 q^{66} -5.82869e62 q^{67} +3.67459e62 q^{68} -7.00305e63 q^{69} +4.82758e62 q^{70} +6.68198e63 q^{71} +6.71156e63 q^{72} -1.20455e64 q^{73} +5.48341e63 q^{74} +5.22304e64 q^{75} -2.62583e64 q^{76} +1.45400e65 q^{77} -1.14911e65 q^{78} -1.97073e65 q^{79} -1.77770e65 q^{80} -6.57018e65 q^{81} -1.76126e65 q^{82} +5.46209e65 q^{83} +2.46331e66 q^{84} +4.43222e65 q^{85} -2.76370e66 q^{86} +6.56395e66 q^{87} +1.01688e67 q^{88} -8.41635e66 q^{89} +3.88642e66 q^{90} -4.50679e67 q^{91} -9.22174e67 q^{92} +1.11684e68 q^{93} -6.47145e66 q^{94} -3.16723e67 q^{95} +2.61845e68 q^{96} -3.94984e68 q^{97} +5.77035e67 q^{98} +1.17053e69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots - 31\!\cdots\!35 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more