LMFDB - Embedded newform 1.70.a.a.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			1.4
Root			$-8.63045e7$ 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)

$f(q)$	$=$	\(q+2.12545e10 q^{2} +3.67245e16 q^{3} -1.38540e20 q^{4} -2.01597e24 q^{5} +7.80563e26 q^{6} +2.05778e29 q^{7} -1.54911e31 q^{8} +5.14307e32 q^{9} -4.28486e34 q^{10} -1.09142e36 q^{11} -5.08782e36 q^{12} -2.46650e37 q^{13} +4.37373e39 q^{14} -7.40358e40 q^{15} -2.47476e41 q^{16} -2.55025e42 q^{17} +1.09314e43 q^{18} -1.09623e44 q^{19} +2.79293e44 q^{20} +7.55712e45 q^{21} -2.31976e46 q^{22} -8.34028e45 q^{23} -5.68903e47 q^{24} +2.37009e48 q^{25} -5.24243e47 q^{26} -1.17547e49 q^{27} -2.85086e49 q^{28} -4.43119e49 q^{29} -1.57360e51 q^{30} -2.07006e51 q^{31} +3.88433e51 q^{32} -4.00818e52 q^{33} -5.42044e52 q^{34} -4.14844e53 q^{35} -7.12521e52 q^{36} +2.01350e54 q^{37} -2.32999e54 q^{38} -9.05809e53 q^{39} +3.12296e55 q^{40} -1.70767e55 q^{41} +1.60623e56 q^{42} -1.46418e55 q^{43} +1.51205e56 q^{44} -1.03683e57 q^{45} -1.77269e56 q^{46} -7.82219e57 q^{47} -9.08845e57 q^{48} +2.18442e58 q^{49} +5.03751e58 q^{50} -9.36567e58 q^{51} +3.41709e57 q^{52} +4.83946e59 q^{53} -2.49841e59 q^{54} +2.20027e60 q^{55} -3.18773e60 q^{56} -4.02587e60 q^{57} -9.41829e59 q^{58} -1.34248e61 q^{59} +1.02569e61 q^{60} +3.06698e61 q^{61} -4.39982e61 q^{62} +1.05833e62 q^{63} +2.28644e62 q^{64} +4.97239e61 q^{65} -8.51920e62 q^{66} +5.79237e62 q^{67} +3.53312e62 q^{68} -3.06293e62 q^{69} -8.81732e63 q^{70} +5.96461e63 q^{71} -7.96717e63 q^{72} -2.58846e63 q^{73} +4.27961e64 q^{74} +8.70404e64 q^{75} +1.51872e64 q^{76} -2.24590e65 q^{77} -1.92526e64 q^{78} -1.36419e65 q^{79} +4.98906e65 q^{80} -8.60817e65 q^{81} -3.62958e65 q^{82} +4.54701e65 q^{83} -1.04696e66 q^{84} +5.14124e66 q^{85} -3.11206e65 q^{86} -1.62733e66 q^{87} +1.69072e67 q^{88} -6.95403e66 q^{89} -2.20373e67 q^{90} -5.07552e66 q^{91} +1.15546e66 q^{92} -7.60220e67 q^{93} -1.66257e68 q^{94} +2.20998e68 q^{95} +1.42650e68 q^{96} +3.36085e68 q^{97} +4.64289e68 q^{98} -5.61323e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3} + 12\!\cdots\!60 q^{4} - 18\!\cdots\!50 q^{5} + 65\!\cdots\!60 q^{6} + 76\!\cdots\!92 q^{7} - 45\!\cdots\!00 q^{8} - 31\!\cdots\!35 q^{9} + 44\!\cdots\!00 q^{10}+ \cdots + 58\!\cdots\!80 q^{99}+O(q^{100}) $ 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9 + 44330196388334747724288536990904000 * q^10 - 60667038452283127772973811588820340 * q^11 - 11483075252723727688688753994339790848 * q^12 + 241757308976474000869098277194908009686 * q^13 + 354251192093531665156722201608564593920 * q^14 - 22070061029664005246083216762166031993000 * q^15 + 959158246463054504693505368032717942292480 * q^16 - 3406116484103989032025799295223462139713638 * q^17 + 24028760578245796491398335690330074428977056 * q^18 + 50409644862695734347948203723209710229820500 * q^19 - 1423124021474831957749573329409407107348736000 * q^20 + 3013464004165585730133470747616333350946636960 * q^21 - 11532803895526133094453480299474752792963837056 * q^22 + 49597077165419749499080141147449313474867772376 * q^23 - 3758573903021835292505270073849755869023436800 * q^24 + 464109230075747674561453215791202707168413296875 * q^25 - 16366243363702391437841515238911258759405955787840 * q^26 - 4656668144254073384201536267744600116223141335000 * q^27 - 145657936238300983941227399236934030905596038045696 * q^28 - 623609331535478016897341347681349171717970694417050 * q^29 - 3363430262026080628144709187077082169492181498016000 * q^30 - 7773979811443490840377264327630961134705736859811040 * q^31 - 59446525385187765185716890552455969166501734680363008 * q^32 - 114056291760419605293140369499335251414708842916007568 * q^33 - 257146382902997900108453969123952433606251002004626880 * q^34 - 746713702965644817139124842748848714607056852166946000 * q^35 - 2051949564713522439077005513759167028086223411246648320 * q^36 + 1173349927804932358065167442366744839628119054724224302 * q^37 + 118225357325580676139934406348110667239400005459024000 * q^38 + 14057637047001351842470294363781888979755467326981836280 * q^39 + 113448309945374158392264311043353386142011790732943360000 * q^40 + 126046983235211396249316718220813524712126370275682679410 * q^41 + 293618058653079520265272756273690037096976372387400909824 * q^42 + 182990795236310295463906097926157021228111368794869386156 * q^43 - 207861964397629572369029141530074424104092312018072801280 * q^44 - 1643209216033810606361059101690783215624601629799145190250 * q^45 - 10254004636983168196931301388746633342901210187441053098240 * q^46 - 10227620449924872974485942387482033943920758356350760046928 * q^47 - 32395077603800850016659260748043884333789001078303069569024 * q^48 - 18333133463047872956569862100374253860638045246565546349315 * q^49 + 36528582075561740316450944849185458926809558787823115500000 * q^50 + 118668467511484226348705374365583184000267089107653013314760 * q^51 + 942523544779067327174672695236090488789159958525129397368832 * q^52 + 632699876044410239466855544904774161379655010323706866957246 * q^53 + 180558070990413352422035814551902697653880540863671629472000 * q^54 + 908306905388987301982805388456202130484984202488366374469000 * q^55 - 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 10204523476105540193819201045109650965597050176490899356681200 * q^57 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 - 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 4120988224178099264267892216282931461935581678787045796864000 * q^60 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 + 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 328016742630707922691415372382087941549150107260006661759940136 * q^63 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 + 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 338570852359916448113902185281844117937336911423509879777978880 * q^66 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 - 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 6814317814451425604632002110369996993863432815743912687188684320 * q^69 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 - 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33340305480431860824635017027459448788044465030309454443456921600 * q^72 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 + 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 133279503236831559979066107911998455423803652698542098545072437500 * q^75 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 - 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 57072566318401512231072936702879380800620122459787990692269387008 * q^78 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 - 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 1101671322957552996191157562976784281568686466036132881049220065795 * q^81 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 + 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 2982792317318014581404535874546389828859810656181796104246410117120 * q^84 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 + 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 12567354207673775260644045622671132292173268168085315900596903577400 * q^87 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 - 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 85191607767474905371023384802405560846731062106202026396755774248000 * q^90 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 - 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 112906043990099714252090302813260364787306717550744493130306572821888 * q^93 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 + 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 782790419970794266899143250915194035456012168622622133055202797813760 * q^96 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 + 1783735577381778172290937711296356094085482547558896852990197505179424 * q^98 + 586262466890180722819447934223042169763434625676688596008715148885980 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.12545e10	0.874816	0.437408	−	0.899263i	$-0.355896\pi$
$2$	2.12545e10	0.874816	0.437408	+	0.899263i	$0.355896\pi$
$3$	3.67245e16	1.27137	0.635687	−	0.771947i	$-0.280717\pi$
$3$	3.67245e16	1.27137	0.635687	+	0.771947i	$0.280717\pi$
$4$	−1.38540e20	−0.234696
$5$	−2.01597e24	−1.54889	−0.774444	−	0.632643i	$-0.781970\pi$
$5$	−2.01597e24	−1.54889	−0.774444	+	0.632643i	$0.781970\pi$
$6$	7.80563e26	1.11222
$7$	2.05778e29	1.43720	0.718600	−	0.695423i	$-0.244783\pi$
$7$	2.05778e29	1.43720	0.718600	+	0.695423i	$0.244783\pi$
$8$	−1.54911e31	−1.08013
$9$	5.14307e32	0.616390
$10$	−4.28486e34	−1.35499
$11$	−1.09142e36	−1.28808	−0.644040	−	0.764991i	$-0.722743\pi$
$11$	−1.09142e36	−1.28808	−0.644040	+	0.764991i	$0.722743\pi$
$12$	−5.08782e36	−0.298386
$13$	−2.46650e37	−0.0914186	−0.0457093	−	0.998955i	$-0.514555\pi$
$13$	−2.46650e37	−0.0914186	−0.0457093	+	0.998955i	$0.514555\pi$
$14$	4.37373e39	1.25729
$15$	−7.40358e40	−1.96921
$16$	−2.47476e41	−0.710222
$17$	−2.55025e42	−0.903846	−0.451923	−	0.892057i	$-0.649262\pi$
$17$	−2.55025e42	−0.903846	−0.451923	+	0.892057i	$0.649262\pi$
$18$	1.09314e43	0.539228
$19$	−1.09623e44	−0.837344	−0.418672	−	0.908138i	$-0.637504\pi$
$19$	−1.09623e44	−0.837344	−0.418672	+	0.908138i	$0.637504\pi$
$20$	2.79293e44	0.363518
$21$	7.55712e45	1.82722
$22$	−2.31976e46	−1.12683
$23$	−8.34028e45	−0.0874118	−0.0437059	−	0.999044i	$-0.513916\pi$
$23$	−8.34028e45	−0.0874118	−0.0437059	+	0.999044i	$0.513916\pi$
$24$	−5.68903e47	−1.37325
$25$	2.37009e48	1.39905
$26$	−5.24243e47	−0.0799745
$27$	−1.17547e49	−0.487711
$28$	−2.85086e49	−0.337305
$29$	−4.43119e49	−0.156239	−0.0781195	−	0.996944i	$-0.524892\pi$
$29$	−4.43119e49	−0.156239	−0.0781195	+	0.996944i	$0.524892\pi$
$30$	−1.57360e51	−1.72270
$31$	−2.07006e51	−0.731147	−0.365573	−	0.930783i	$-0.619127\pi$
$31$	−2.07006e51	−0.731147	−0.365573	+	0.930783i	$0.619127\pi$
$32$	3.88433e51	0.458819
$33$	−4.00818e52	−1.63763
$34$	−5.42044e52	−0.790700
$35$	−4.14844e53	−2.22606
$36$	−7.12521e52	−0.144664
$37$	2.01350e54	1.58852	0.794261	−	0.607577i	$-0.207858\pi$
$37$	2.01350e54	1.58852	0.794261	+	0.607577i	$0.207858\pi$
$38$	−2.32999e54	−0.732522
$39$	−9.05809e53	−0.116227
$40$	3.12296e55	1.67300
$41$	−1.70767e55	−0.390266	−0.195133	−	0.980777i	$-0.562514\pi$
$41$	−1.70767e55	−0.390266	−0.195133	+	0.980777i	$0.562514\pi$
$42$	1.60623e56	1.59848
$43$	−1.46418e55	−0.0647044	−0.0323522	−	0.999477i	$-0.510300\pi$
$43$	−1.46418e55	−0.0647044	−0.0323522	+	0.999477i	$0.510300\pi$
$44$	1.51205e56	0.302308
$45$	−1.03683e57	−0.954719
$46$	−1.77269e56	−0.0764693
$47$	−7.82219e57	−1.60676	−0.803382	−	0.595464i	$-0.796968\pi$
$47$	−7.82219e57	−1.60676	−0.803382	+	0.595464i	$0.796968\pi$
$48$	−9.08845e57	−0.902957
$49$	2.18442e58	1.06555
$50$	5.03751e58	1.22391
$51$	−9.36567e58	−1.14913
$52$	3.41709e57	0.0214556
$53$	4.83946e59	1.57500	0.787498	−	0.616317i	$-0.211376\pi$
$53$	4.83946e59	1.57500	0.787498	+	0.616317i	$0.211376\pi$
$54$	−2.49841e59	−0.426658
$55$	2.20027e60	1.99509
$56$	−3.18773e60	−1.55237
$57$	−4.02587e60	−1.06458
$58$	−9.41829e59	−0.136680
$59$	−1.34248e61	−1.08023	−0.540113	−	0.841592i	$-0.681619\pi$
$59$	−1.34248e61	−1.08023	−0.540113	+	0.841592i	$0.681619\pi$
$60$	1.02569e61	0.462167
$61$	3.06698e61	0.781326	0.390663	−	0.920534i	$-0.372246\pi$
$61$	3.06698e61	0.781326	0.390663	+	0.920534i	$0.372246\pi$
$62$	−4.39982e61	−0.639619
$63$	1.05833e62	0.885876
$64$	2.28644e62	1.11160
$65$	4.97239e61	0.141597
$66$	−8.51920e62	−1.43263
$67$	5.79237e62	0.579796	0.289898	−	0.957057i	$-0.406379\pi$
$67$	5.79237e62	0.579796	0.289898	+	0.957057i	$0.406379\pi$
$68$	3.53312e62	0.212129
$69$	−3.06293e62	−0.111133
$70$	−8.81732e63	−1.94740
$71$	5.96461e63	0.807549	0.403775	−	0.914859i	$-0.367698\pi$
$71$	5.96461e63	0.807549	0.403775	+	0.914859i	$0.367698\pi$
$72$	−7.96717e63	−0.665783
$73$	−2.58846e63	−0.134401	−0.0672004	−	0.997739i	$-0.521407\pi$
$73$	−2.58846e63	−0.134401	−0.0672004	+	0.997739i	$0.521407\pi$
$74$	4.27961e64	1.38966
$75$	8.70404e64	1.77872
$76$	1.51872e64	0.196521
$77$	−2.24590e65	−1.85123
$78$	−1.92526e64	−0.101677
$79$	−1.36419e65	−0.464237	−0.232118	−	0.972688i	$-0.574566\pi$
$79$	−1.36419e65	−0.464237	−0.232118	+	0.972688i	$0.574566\pi$
$80$	4.98906e65	1.10005
$81$	−8.60817e65	−1.23645
$82$	−3.62958e65	−0.341411
$83$	4.54701e65	0.281534	0.140767	−	0.990043i	$-0.455043\pi$
$83$	4.54701e65	0.281534	0.140767	+	0.990043i	$0.455043\pi$
$84$	−1.04696e66	−0.428841
$85$	5.14124e66	1.39996
$86$	−3.11206e65	−0.0566045
$87$	−1.62733e66	−0.198638
$88$	1.69072e67	1.39130
$89$	−6.95403e66	−0.387509	−0.193754	−	0.981050i	$-0.562066\pi$
$89$	−6.95403e66	−0.387509	−0.193754	+	0.981050i	$0.562066\pi$
$90$	−2.20373e67	−0.835204
$91$	−5.07552e66	−0.131387
$92$	1.15546e66	0.0205152
$93$	−7.60220e67	−0.929560
$94$	−1.66257e68	−1.40562
$95$	2.20998e68	1.29695
$96$	1.42650e68	0.583330
$97$	3.36085e68	0.961224	0.480612	−	0.876933i	$-0.340414\pi$
$97$	3.36085e68	0.961224	0.480612	+	0.876933i	$0.340414\pi$
$98$	4.64289e68	0.932156
$99$	−5.61323e68	−0.793960
$100$	−3.28352e68	−0.328352
$101$	−4.26999e68	−0.302928	−0.151464	−	0.988463i	$-0.548399\pi$
$101$	−4.26999e68	−0.302928	−0.151464	+	0.988463i	$0.548399\pi$
$102$	−1.99063e69	−1.00527
$103$	4.89975e69	1.76721	0.883607	−	0.468229i	$-0.155108\pi$
$103$	4.89975e69	1.76721	0.883607	+	0.468229i	$0.155108\pi$
$104$	3.82087e68	0.0987442
$105$	−1.52350e70	−2.83016
$106$	1.02861e70	1.37783
$107$	−2.44106e69	−0.236504	−0.118252	−	0.992984i	$-0.537729\pi$
$107$	−2.44106e69	−0.236504	−0.118252	+	0.992984i	$0.537729\pi$
$108$	1.62850e69	0.114464
$109$	−1.65662e70	−0.847245	−0.423623	−	0.905839i	$-0.639242\pi$
$109$	−1.65662e70	−0.847245	−0.423623	+	0.905839i	$0.639242\pi$
$110$	4.67657e70	1.74534
$111$	7.39450e70	2.01960
$112$	−5.09252e70	−1.02073
$113$	−4.32535e70	−0.637992	−0.318996	−	0.947756i	$-0.603346\pi$
$113$	−4.32535e70	−0.637992	−0.318996	+	0.947756i	$0.603346\pi$
$114$	−8.55679e70	−0.931309
$115$	1.68138e70	0.135391
$116$	6.13897e69	0.0366687
$117$	−1.26854e70	−0.0563496
$118$	−2.85339e71	−0.945000
$119$	−5.24786e71	−1.29901
$120$	1.14689e72	2.12701
$121$	4.73239e71	0.659152
$122$	6.51873e71	0.683517
$123$	−6.27134e71	−0.496174
$124$	2.86786e71	0.171597
$125$	−1.36284e72	−0.618089
$126$	2.24944e72	0.774979
$127$	−5.32946e72	−1.39783	−0.698916	−	0.715204i	$-0.746334\pi$
$127$	−5.32946e72	−1.39783	−0.698916	+	0.715204i	$0.746334\pi$
$128$	2.56682e72	0.513631
$129$	−5.37715e71	−0.0822635
$130$	1.05686e72	0.123872
$131$	−9.29599e72	−0.836442	−0.418221	−	0.908345i	$-0.637346\pi$
$131$	−9.29599e72	−0.836442	−0.418221	+	0.908345i	$0.637346\pi$
$132$	5.55294e72	0.384346
$133$	−2.25581e73	−1.20343
$134$	1.23114e73	0.507215
$135$	2.36972e73	0.755410
$136$	3.95061e73	0.976274
$137$	7.89544e73	1.51536	0.757681	−	0.652625i	$-0.226332\pi$
$137$	7.89544e73	1.51536	0.757681	+	0.652625i	$0.226332\pi$
$138$	−6.51012e72	−0.0972210
$139$	−1.62132e74	−1.88737	−0.943686	−	0.330842i	$-0.892667\pi$
$139$	−1.62132e74	−1.88737	−0.943686	+	0.330842i	$0.892667\pi$
$140$	5.74725e73	0.522448
$141$	−2.87266e74	−2.04280
$142$	1.26775e74	0.706457
$143$	2.69198e73	0.117755
$144$	−1.27279e74	−0.437774
$145$	8.93316e73	0.241997
$146$	−5.50164e73	−0.117576
$147$	8.02219e74	1.35471
$148$	−2.78951e74	−0.372820
$149$	−4.94682e74	−0.524083	−0.262041	−	0.965057i	$-0.584396\pi$
$149$	−4.94682e74	−0.524083	−0.262041	+	0.965057i	$0.584396\pi$
$150$	1.85000e75	1.55605
$151$	−1.17268e75	−0.784287	−0.392144	−	0.919904i	$-0.628266\pi$
$151$	−1.17268e75	−0.784287	−0.392144	+	0.919904i	$0.628266\pi$
$152$	1.69818e75	0.904442
$153$	−1.31161e75	−0.557122
$154$	−4.77356e75	−1.61949
$155$	4.17319e75	1.13246
$156$	1.25491e74	0.0272781
$157$	−8.35431e75	−1.45671	−0.728354	−	0.685201i	$-0.759715\pi$
$157$	−8.35431e75	−1.45671	−0.728354	+	0.685201i	$0.759715\pi$
$158$	−2.89952e75	−0.406122
$159$	1.77727e76	2.00241
$160$	−7.83070e75	−0.710659
$161$	−1.71625e75	−0.125628
$162$	−1.82963e76	−1.08167
$163$	2.80579e76	1.34148	0.670738	−	0.741695i	$-0.265978\pi$
$163$	2.80579e76	1.34148	0.670738	+	0.741695i	$0.265978\pi$
$164$	2.36581e75	0.0915940
$165$	8.08039e76	2.53651
$166$	9.66446e75	0.246291
$167$	−6.66449e76	−1.38054	−0.690269	−	0.723553i	$-0.742508\pi$
$167$	−6.66449e76	−1.38054	−0.690269	+	0.723553i	$0.742508\pi$
$168$	−1.17068e77	−1.97364
$169$	−7.21849e76	−0.991643
$170$	1.09275e77	1.22471
$171$	−5.63800e76	−0.516130
$172$	2.02848e75	0.0151859
$173$	−4.02628e76	−0.246782	−0.123391	−	0.992358i	$-0.539377\pi$
$173$	−4.02628e76	−0.246782	−0.123391	+	0.992358i	$0.539377\pi$
$174$	−3.45882e76	−0.173772
$175$	4.87713e77	2.01072
$176$	2.70100e77	0.914823
$177$	−4.93021e77	−1.37337
$178$	−1.47805e77	−0.338999
$179$	1.65322e77	0.312537	0.156268	−	0.987715i	$-0.450054\pi$
$179$	1.65322e77	0.312537	0.156268	+	0.987715i	$0.450054\pi$
$180$	1.43643e77	0.224069
$181$	−7.58549e76	−0.0977401	−0.0488700	−	0.998805i	$-0.515562\pi$
$181$	−7.58549e76	−0.0977401	−0.0488700	+	0.998805i	$0.515562\pi$
$182$	−1.07878e77	−0.114939
$183$	1.12634e78	0.993357
$184$	1.29200e77	0.0944164
$185$	−4.05917e78	−2.46044
$186$	−1.61581e78	−0.813195
$187$	2.78338e78	1.16423
$188$	1.08369e78	0.377101
$189$	−2.41887e78	−0.700939
$190$	4.69721e78	1.13459
$191$	−2.53179e78	−0.510243	−0.255121	−	0.966909i	$-0.582115\pi$
$191$	−2.53179e78	−0.510243	−0.255121	+	0.966909i	$0.582115\pi$
$192$	8.39683e78	1.41326
$193$	−6.20489e78	−0.872985	−0.436492	−	0.899708i	$-0.643779\pi$
$193$	−6.20489e78	−0.872985	−0.436492	+	0.899708i	$0.643779\pi$
$194$	7.14334e78	0.840895
$195$	1.82609e78	0.180023
$196$	−3.02630e78	−0.250079
$197$	7.90415e78	0.547987	0.273994	−	0.961732i	$-0.411655\pi$
$197$	7.90415e78	0.547987	0.273994	+	0.961732i	$0.411655\pi$
$198$	−1.19307e79	−0.694570
$199$	−1.63250e79	−0.798769	−0.399385	−	0.916783i	$-0.630776\pi$
$199$	−1.63250e79	−0.798769	−0.399385	+	0.916783i	$0.630776\pi$
$200$	−3.67152e79	−1.51116
$201$	2.12722e79	0.737138
$202$	−9.07567e78	−0.265006
$203$	−9.11843e78	−0.224547
$204$	1.29752e79	0.269695
$205$	3.44262e79	0.604479
$206$	1.04142e80	1.54599
$207$	−4.28946e78	−0.0538798
$208$	6.10399e78	0.0649275
$209$	1.19645e80	1.07857
$210$	−3.23812e80	−2.47587
$211$	1.14615e79	0.0743866	0.0371933	−	0.999308i	$-0.488158\pi$
$211$	1.14615e79	0.0743866	0.0371933	+	0.999308i	$0.488158\pi$
$212$	−6.70460e79	−0.369645
$213$	2.19048e80	1.02670
$214$	−5.18837e79	−0.206898
$215$	2.95176e79	0.100220
$216$	1.82093e80	0.526793
$217$	−4.25974e80	−1.05080
$218$	−3.52107e80	−0.741184
$219$	−9.50599e79	−0.170874
$220$	−3.04826e80	−0.468240
$221$	6.29018e79	0.0826284
$222$	1.57167e81	1.76678
$223$	7.96925e79	0.0767184	0.0383592	−	0.999264i	$-0.487787\pi$
$223$	7.96925e79	0.0767184	0.0383592	+	0.999264i	$0.487787\pi$
$224$	7.99310e80	0.659415
$225$	1.21895e81	0.862363
$226$	−9.19334e80	−0.558126
$227$	−2.05085e81	−1.06916	−0.534578	−	0.845119i	$-0.679529\pi$
$227$	−2.05085e81	−1.06916	−0.534578	+	0.845119i	$0.679529\pi$
$228$	5.57744e80	0.249852
$229$	1.65307e81	0.636747	0.318374	−	0.947965i	$-0.396863\pi$
$229$	1.65307e81	0.636747	0.318374	+	0.947965i	$0.396863\pi$
$230$	3.57370e80	0.118442
$231$	−8.24797e81	−2.35360
$232$	6.86439e80	0.168759
$233$	−5.09024e81	−1.07884	−0.539422	−	0.842035i	$-0.681357\pi$
$233$	−5.09024e81	−1.07884	−0.539422	+	0.842035i	$0.681357\pi$
$234$	−2.69622e80	−0.0492955
$235$	1.57693e82	2.48870
$236$	1.85988e81	0.253525
$237$	−5.00991e81	−0.590218
$238$	−1.11541e82	−1.13639
$239$	2.60321e81	0.229500	0.114750	−	0.993394i	$-0.463393\pi$
$239$	2.60321e81	0.229500	0.114750	+	0.993394i	$0.463393\pi$
$240$	1.83221e82	1.39858
$241$	1.75774e82	1.16243	0.581214	−	0.813751i	$-0.302578\pi$
$241$	1.75774e82	1.16243	0.581214	+	0.813751i	$0.302578\pi$
$242$	1.00585e82	0.576637
$243$	−2.18051e82	−1.08428
$244$	−4.24900e81	−0.183374
$245$	−4.40374e82	−1.65041
$246$	−1.33295e82	−0.434061
$247$	2.70385e81	0.0765488
$248$	3.20675e82	0.789735
$249$	1.66987e82	0.357935
$250$	−2.89666e82	−0.540714
$251$	1.40922e82	0.229212	0.114606	−	0.993411i	$-0.463440\pi$
$251$	1.40922e82	0.229212	0.114606	+	0.993411i	$0.463440\pi$
$252$	−1.46621e82	−0.207912
$253$	9.10272e81	0.112594
$254$	−1.13275e83	−1.22285
$255$	1.88810e83	1.77987
$256$	−8.04109e82	−0.662272
$257$	−1.05298e81	−0.00758099	−0.00379050	−	0.999993i	$-0.501207\pi$
$257$	−1.05298e81	−0.00758099	−0.00379050	+	0.999993i	$0.501207\pi$
$258$	−1.14289e82	−0.0719654
$259$	4.14336e83	2.28302
$260$	−6.88876e81	−0.0332323
$261$	−2.27899e82	−0.0963041
$262$	−1.97582e83	−0.731733
$263$	−3.38100e83	−1.09792	−0.548962	−	0.835847i	$-0.684977\pi$
$263$	−3.38100e83	−1.09792	−0.548962	+	0.835847i	$0.684977\pi$
$264$	6.20910e83	1.76886
$265$	−9.75623e83	−2.43949
$266$	−4.79462e83	−1.05278
$267$	−2.55384e83	−0.492668
$268$	−8.02476e82	−0.136076
$269$	1.30658e84	1.94841	0.974206	−	0.225661i	$-0.0724541\pi$
$269$	1.30658e84	1.94841	0.974206	+	0.225661i	$0.0724541\pi$
$270$	5.03674e83	0.660845
$271$	−1.19681e83	−0.138225	−0.0691124	−	0.997609i	$-0.522017\pi$
$271$	−1.19681e83	−0.138225	−0.0691124	+	0.997609i	$0.522017\pi$
$272$	6.31125e83	0.641931
$273$	−1.86396e83	−0.167042
$274$	1.67814e84	1.32566
$275$	−2.58675e84	−1.80209
$276$	4.24339e82	0.0260825
$277$	2.91614e84	1.58218	0.791090	−	0.611700i	$-0.209514\pi$
$277$	2.91614e84	1.58218	0.791090	+	0.611700i	$0.209514\pi$
$278$	−3.44604e84	−1.65110
$279$	−1.06465e84	−0.450672
$280$	6.42638e84	2.40444
$281$	−2.47628e84	−0.819279	−0.409639	−	0.912248i	$-0.634345\pi$
$281$	−2.47628e84	−0.819279	−0.409639	+	0.912248i	$0.634345\pi$
$282$	−6.10571e84	−1.78707
$283$	−3.68218e84	−0.953833	−0.476917	−	0.878949i	$-0.658246\pi$
$283$	−3.68218e84	−0.953833	−0.476917	+	0.878949i	$0.658246\pi$
$284$	−8.26338e83	−0.189529
$285$	8.11604e84	1.64891
$286$	5.72167e83	0.103014
$287$	−3.51402e84	−0.560891
$288$	1.99774e84	0.282811
$289$	−1.45738e84	−0.183062
$290$	1.89870e84	0.211703
$291$	1.23426e85	1.22207
$292$	3.58605e83	0.0315434
$293$	−2.21476e85	−1.73139	−0.865694	−	0.500573i	$-0.833123\pi$
$293$	−2.21476e85	−1.73139	−0.865694	+	0.500573i	$0.833123\pi$
$294$	1.70508e85	1.18512
$295$	2.70642e85	1.67315
$296$	−3.11913e85	−1.71581
$297$	1.28293e85	0.628212
$298$	−1.05142e85	−0.458476
$299$	2.05713e83	0.00799107
$300$	−1.20586e85	−0.417458
$301$	−3.01297e84	−0.0929932
$302$	−2.49248e85	−0.686107
$303$	−1.56813e85	−0.385135
$304$	2.71291e85	0.594699
$305$	−6.18296e85	−1.21019
$306$	−2.78777e85	−0.487380
$307$	3.33336e85	0.520725	0.260363	−	0.965511i	$-0.416158\pi$
$307$	3.33336e85	0.520725	0.260363	+	0.965511i	$0.416158\pi$
$308$	3.11147e85	0.434477
$309$	1.79941e86	2.24679
$310$	8.86992e85	0.990698
$311$	5.41154e85	0.540863	0.270432	−	0.962739i	$-0.412834\pi$
$311$	5.41154e85	0.540863	0.270432	+	0.962739i	$0.412834\pi$
$312$	1.40320e85	0.125541
$313$	−1.40450e86	−1.12523	−0.562615	−	0.826719i	$-0.690205\pi$
$313$	−1.40450e86	−1.12523	−0.562615	+	0.826719i	$0.690205\pi$
$314$	−1.77567e86	−1.27435
$315$	−2.13357e86	−1.37212
$316$	1.88995e85	0.108955
$317$	−1.70168e85	−0.0879699	−0.0439849	−	0.999032i	$-0.514005\pi$
$317$	−1.70168e85	−0.0879699	−0.0439849	+	0.999032i	$0.514005\pi$
$318$	3.77751e86	1.75174
$319$	4.83627e85	0.201248
$320$	−4.60940e86	−1.72175
$321$	−8.96469e85	−0.300685
$322$	−3.64781e85	−0.109902
$323$	2.79567e86	0.756830
$324$	1.19258e86	0.290191
$325$	−5.84581e85	−0.127900
$326$	5.96358e86	1.17354
$327$	−6.08387e86	−1.07716
$328$	2.64537e86	0.421539
$329$	−1.60964e87	−2.30924
$330$	1.71745e87	2.21898
$331$	1.21390e87	1.41292	0.706462	−	0.707751i	$-0.250290\pi$
$331$	1.21390e87	1.41292	0.706462	+	0.707751i	$0.250290\pi$
$332$	−6.29943e85	−0.0660750
$333$	1.03556e87	0.979149
$334$	−1.41651e87	−1.20772
$335$	−1.16773e87	−0.898040
$336$	−1.87021e87	−1.29773
$337$	2.61386e87	1.63701	0.818505	−	0.574499i	$-0.194803\pi$
$337$	2.61386e87	1.63701	0.818505	+	0.574499i	$0.194803\pi$
$338$	−1.53426e87	−0.867505
$339$	−1.58847e87	−0.811126
$340$	−7.12267e86	−0.328564
$341$	2.25930e87	0.941776
$342$	−1.19833e87	−0.451519
$343$	2.76506e86	0.0942013
$344$	2.26818e86	0.0698893
$345$	6.17479e86	0.172133
$346$	−8.55768e86	−0.215889
$347$	2.58424e87	0.590155	0.295078	−	0.955473i	$-0.404655\pi$
$347$	2.58424e87	0.590155	0.295078	+	0.955473i	$0.404655\pi$
$348$	2.25451e86	0.0466196
$349$	1.39983e87	0.262180	0.131090	−	0.991370i	$-0.458152\pi$
$349$	1.39983e87	0.262180	0.131090	+	0.991370i	$0.458152\pi$
$350$	1.03661e88	1.75901
$351$	2.89930e86	0.0445859
$352$	−4.23942e87	−0.590996
$353$	7.18553e87	0.908304	0.454152	−	0.890924i	$-0.349942\pi$
$353$	7.18553e87	0.908304	0.454152	+	0.890924i	$0.349942\pi$
$354$	−1.04789e88	−1.20145
$355$	−1.20245e88	−1.25080
$356$	9.63412e86	0.0909467
$357$	−1.92725e88	−1.65152
$358$	3.51384e87	0.273412
$359$	−2.70510e87	−0.191172	−0.0955860	−	0.995421i	$-0.530472\pi$
$359$	−2.70510e87	−0.191172	−0.0955860	+	0.995421i	$0.530472\pi$
$360$	1.60616e88	1.03122
$361$	−5.12224e87	−0.298856
$362$	−1.61226e87	−0.0855046
$363$	1.73795e88	0.838028
$364$	7.03163e86	0.0308360
$365$	5.21826e87	0.208172
$366$	2.39398e88	0.869005
$367$	−6.88002e86	−0.0227306	−0.0113653	−	0.999935i	$-0.503618\pi$
$367$	−6.88002e86	−0.0227306	−0.0113653	+	0.999935i	$0.503618\pi$
$368$	2.06402e87	0.0620818
$369$	−8.78267e87	−0.240556
$370$	−8.62759e88	−2.15243
$371$	9.95856e88	2.26359
$372$	1.05321e88	0.218164
$373$	−8.56864e88	−1.61792	−0.808960	−	0.587864i	$-0.799969\pi$
$373$	−8.56864e88	−1.61792	−0.808960	+	0.587864i	$0.799969\pi$
$374$	5.91596e88	1.01849
$375$	−5.00498e88	−0.785821
$376$	1.21174e89	1.73552
$377$	1.09295e87	0.0142831
$378$	−5.14120e88	−0.613193
$379$	−8.36126e88	−0.910373	−0.455186	−	0.890396i	$-0.650427\pi$
$379$	−8.36126e88	−0.910373	−0.455186	+	0.890396i	$0.650427\pi$
$380$	−3.06171e88	−0.304389
$381$	−1.95722e89	−1.77717
$382$	−5.38121e88	−0.446369
$383$	2.17691e88	0.164999	0.0824997	−	0.996591i	$-0.473710\pi$
$383$	2.17691e88	0.164999	0.0824997	+	0.996591i	$0.473710\pi$
$384$	9.42652e88	0.653016
$385$	4.52768e89	2.86735
$386$	−1.31882e89	−0.763702
$387$	−7.53040e87	−0.0398832
$388$	−4.65613e88	−0.225596
$389$	3.57077e89	1.58307	0.791537	−	0.611122i	$-0.209281\pi$
$389$	3.57077e89	1.58307	0.791537	+	0.611122i	$0.209281\pi$
$390$	3.88127e88	0.157487
$391$	2.12698e88	0.0790069
$392$	−3.38390e89	−1.15093
$393$	−3.41391e89	−1.06343
$394$	1.67999e89	0.479388
$395$	2.75017e89	0.719050
$396$	7.77658e88	0.186339
$397$	−1.10958e89	−0.243717	−0.121859	−	0.992547i	$-0.538885\pi$
$397$	−1.10958e89	−0.243717	−0.121859	+	0.992547i	$0.538885\pi$
$398$	−3.46980e89	−0.698777
$399$	−8.28436e89	−1.53001
$400$	−5.86540e89	−0.993638
$401$	4.75128e89	0.738465	0.369233	−	0.929337i	$-0.379621\pi$
$401$	4.75128e89	0.738465	0.369233	+	0.929337i	$0.379621\pi$
$402$	4.52131e89	0.644860
$403$	5.10580e88	0.0668404
$404$	5.91565e88	0.0710960
$405$	1.73539e90	1.91513
$406$	−1.93808e89	−0.196437
$407$	−2.19757e90	−2.04614
$408$	1.45084e90	1.24121
$409$	2.42528e89	0.190681	0.0953406	−	0.995445i	$-0.469606\pi$
$409$	2.42528e89	0.190681	0.0953406	+	0.995445i	$0.469606\pi$
$410$	7.31713e89	0.528808
$411$	2.89956e90	1.92659
$412$	−6.78811e89	−0.414758
$413$	−2.76254e90	−1.55250
$414$	−9.11706e88	−0.0471349
$415$	−9.16665e89	−0.436065
$416$	−9.58067e88	−0.0419446
$417$	−5.95422e90	−2.39955
$418$	2.54299e90	0.943547
$419$	1.70435e90	0.582338	0.291169	−	0.956672i	$-0.405956\pi$
$419$	1.70435e90	0.582338	0.291169	+	0.956672i	$0.405956\pi$
$420$	2.11065e90	0.664227
$421$	4.90128e90	1.42094	0.710472	−	0.703725i	$-0.248481\pi$
$421$	4.90128e90	1.42094	0.710472	+	0.703725i	$0.248481\pi$
$422$	2.43608e89	0.0650747
$423$	−4.02300e90	−0.990393
$424$	−7.49685e90	−1.70120
$425$	−6.04431e90	−1.26453
$426$	4.65576e90	0.898171
$427$	6.31119e90	1.12292
$428$	3.38185e89	0.0555066
$429$	9.88616e89	0.149710
$430$	6.27383e89	0.0876740
$431$	3.44401e90	0.444221	0.222111	−	0.975021i	$-0.428705\pi$
$431$	3.44401e90	0.444221	0.222111	+	0.975021i	$0.428705\pi$
$432$	2.90901e90	0.346383
$433$	1.42290e91	1.56438	0.782189	−	0.623041i	$-0.214103\pi$
$433$	1.42290e91	1.56438	0.782189	+	0.623041i	$0.214103\pi$
$434$	−9.05388e90	−0.919261
$435$	3.28066e90	0.307668
$436$	2.29509e90	0.198845
$437$	9.14289e89	0.0731937
$438$	−2.02045e90	−0.149483
$439$	−2.33620e91	−1.59766	−0.798828	−	0.601559i	$-0.794546\pi$
$439$	−2.33620e91	−1.59766	−0.798828	+	0.601559i	$0.794546\pi$
$440$	−3.40845e91	−2.15496
$441$	1.12346e91	0.656791
$442$	1.33695e90	0.0722847
$443$	3.82184e90	0.191136	0.0955682	−	0.995423i	$-0.469533\pi$
$443$	3.82184e90	0.191136	0.0955682	+	0.995423i	$0.469533\pi$
$444$	−1.02444e91	−0.473993
$445$	1.40191e91	0.600207
$446$	1.69383e90	0.0671145
$447$	−1.81670e91	−0.666305
$448$	4.70499e91	1.59760
$449$	1.14776e91	0.360871	0.180436	−	0.983587i	$-0.442249\pi$
$449$	1.14776e91	0.360871	0.180436	+	0.983587i	$0.442249\pi$
$450$	2.59083e91	0.754409
$451$	1.86378e91	0.502695
$452$	5.99235e90	0.149734
$453$	−4.30662e91	−0.997122
$454$	−4.35898e91	−0.935315
$455$	1.02321e91	0.203504
$456$	6.23650e91	1.14988
$457$	−7.31030e91	−1.24976	−0.624880	−	0.780721i	$-0.714852\pi$
$457$	−7.31030e91	−1.24976	−0.624880	+	0.780721i	$0.714852\pi$
$458$	3.51352e91	0.557037
$459$	2.99775e91	0.440816
$460$	−2.32939e90	−0.0317758
$461$	7.71415e91	0.976351	0.488176	−	0.872745i	$-0.337663\pi$
$461$	7.71415e91	0.976351	0.488176	+	0.872745i	$0.337663\pi$
$462$	−1.75307e92	−2.05897
$463$	−1.44206e92	−1.57195	−0.785974	−	0.618260i	$-0.787838\pi$
$463$	−1.44206e92	−1.57195	−0.785974	+	0.618260i	$0.787838\pi$
$464$	1.09661e91	0.110964
$465$	1.53258e92	1.43978
$466$	−1.08191e92	−0.943791
$467$	−4.34642e91	−0.352127	−0.176063	−	0.984379i	$-0.556336\pi$
$467$	−4.34642e91	−0.352127	−0.176063	+	0.984379i	$0.556336\pi$
$468$	1.75743e90	0.0132250
$469$	1.19194e92	0.833284
$470$	3.35170e92	2.17715
$471$	−3.06808e92	−1.85202
$472$	2.07965e92	1.16679
$473$	1.59803e91	0.0833445
$474$	−1.06483e92	−0.516332
$475$	−2.59817e92	−1.17149
$476$	7.27039e91	0.304872
$477$	2.48897e92	0.970812
$478$	5.53301e91	0.200770
$479$	2.77463e92	0.936764	0.468382	−	0.883526i	$-0.344837\pi$
$479$	2.77463e92	0.936764	0.468382	+	0.883526i	$0.344837\pi$
$480$	−2.87579e92	−0.903513
$481$	−4.96630e91	−0.145220
$482$	3.73599e92	1.01691
$483$	−6.30285e91	−0.159721
$484$	−6.55627e91	−0.154700
$485$	−6.77540e92	−1.48883
$486$	−4.63458e92	−0.948548
$487$	3.06757e91	0.0584851	0.0292426	−	0.999572i	$-0.490690\pi$
$487$	3.06757e91	0.0584851	0.0292426	+	0.999572i	$0.490690\pi$
$488$	−4.75109e92	−0.843935
$489$	1.03041e93	1.70552
$490$	−9.35995e92	−1.44381
$491$	6.50375e91	0.0935088	0.0467544	−	0.998906i	$-0.485112\pi$
$491$	6.50375e91	0.0935088	0.0467544	+	0.998906i	$0.485112\pi$
$492$	8.68833e91	0.116450
$493$	1.13006e92	0.141216
$494$	5.74692e91	0.0669662
$495$	1.13161e93	1.22976
$496$	5.12290e92	0.519276
$497$	1.22739e93	1.16061
$498$	3.54923e92	0.313128
$499$	1.05364e93	0.867412	0.433706	−	0.901054i	$-0.357206\pi$
$499$	1.05364e93	0.867412	0.433706	+	0.901054i	$0.357206\pi$
$500$	1.88809e92	0.145063
$501$	−2.44750e93	−1.75518
$502$	2.99524e92	0.200518
$503$	−2.42087e93	−1.51313	−0.756564	−	0.653919i	$-0.773124\pi$
$503$	−2.42087e93	−1.51313	−0.756564	+	0.653919i	$0.773124\pi$
$504$	−1.63947e93	−0.956864
$505$	8.60819e92	0.469201
$506$	1.93474e92	0.0984987
$507$	−2.65096e93	−1.26075
$508$	7.38344e92	0.328066
$509$	1.96613e93	0.816298	0.408149	−	0.912915i	$-0.366174\pi$
$509$	1.96613e93	0.816298	0.408149	+	0.912915i	$0.366174\pi$
$510$	4.01306e93	1.55706
$511$	−5.32648e92	−0.193161
$512$	−3.22428e93	−1.09300
$513$	1.28859e93	0.408382
$514$	−2.23805e91	−0.00663198
$515$	−9.87776e93	−2.73722
$516$	7.44951e91	0.0193069
$517$	8.53727e93	2.06964
$518$	8.80651e93	1.99723
$519$	−1.47863e93	−0.313752
$520$	−7.70277e92	−0.152944
$521$	1.44982e92	0.0269409	0.0134704	−	0.999909i	$-0.495712\pi$
$521$	1.44982e92	0.0269409	0.0134704	+	0.999909i	$0.495712\pi$
$522$	−4.84389e92	−0.0842484
$523$	−1.14702e94	−1.86750	−0.933751	−	0.357923i	$-0.883485\pi$
$523$	−1.14702e94	−1.86750	−0.933751	+	0.357923i	$0.883485\pi$
$524$	1.28787e93	0.196310
$525$	1.79110e94	2.55638
$526$	−7.18617e93	−0.960482
$527$	5.27917e93	0.660844
$528$	9.91929e93	1.16308
$529$	−9.03420e93	−0.992359
$530$	−2.07364e94	−2.13411
$531$	−6.90449e93	−0.665841
$532$	3.12520e93	0.282440
$533$	4.21196e92	0.0356776
$534$	−5.42806e93	−0.430994
$535$	4.92112e93	0.366318
$536$	−8.97300e93	−0.626257
$537$	6.07137e93	0.397351
$538$	2.77707e94	1.70450
$539$	−2.38412e94	−1.37251
$540$	−3.28302e93	−0.177292
$541$	1.83776e94	0.931072	0.465536	−	0.885029i	$-0.345862\pi$
$541$	1.83776e94	0.931072	0.465536	+	0.885029i	$0.345862\pi$
$542$	−2.54377e93	−0.120921
$543$	−2.78574e93	−0.124264
$544$	−9.90599e93	−0.414702
$545$	3.33971e94	1.31229
$546$	−3.96176e93	−0.146131
$547$	5.34702e94	1.85161	0.925805	−	0.378002i	$-0.123389\pi$
$547$	5.34702e94	1.85161	0.925805	+	0.378002i	$0.123389\pi$
$548$	−1.09383e94	−0.355650
$549$	1.57737e94	0.481602
$550$	−5.49803e94	−1.57650
$551$	4.85761e93	0.130826
$552$	4.74481e93	0.120038
$553$	−2.80720e94	−0.667201
$554$	6.19811e94	1.38412
$555$	−1.49071e95	−3.12814
$556$	2.24618e94	0.442959
$557$	−9.92032e94	−1.83874	−0.919372	−	0.393389i	$-0.871302\pi$
$557$	−9.92032e94	−1.83874	−0.919372	+	0.393389i	$0.871302\pi$
$558$	−2.26286e94	−0.394255
$559$	3.61140e92	0.00591519
$560$	1.02664e95	1.58100
$561$	1.02219e95	1.48017
$562$	−5.26322e94	−0.716718
$563$	1.16398e95	1.49076	0.745379	−	0.666641i	$-0.232268\pi$
$563$	1.16398e95	1.49076	0.745379	+	0.666641i	$0.232268\pi$
$564$	3.97979e94	0.479436
$565$	8.71980e94	0.988178
$566$	−7.82630e94	−0.834429
$567$	−1.77138e95	−1.77703
$568$	−9.23982e94	−0.872260
$569$	1.17606e95	1.04485	0.522426	−	0.852685i	$-0.325027\pi$
$569$	1.17606e95	1.04485	0.522426	+	0.852685i	$0.325027\pi$
$570$	1.72503e95	1.44249
$571$	−1.80537e94	−0.142108	−0.0710542	−	0.997472i	$-0.522636\pi$
$571$	−1.80537e94	−0.142108	−0.0710542	+	0.997472i	$0.522636\pi$
$572$	−3.72947e93	−0.0276365
$573$	−9.29789e94	−0.648709
$574$	−7.46888e94	−0.490677
$575$	−1.97672e94	−0.122294
$576$	1.17593e95	0.685182
$577$	1.06348e95	0.583667	0.291834	−	0.956469i	$-0.405735\pi$
$577$	1.06348e95	0.583667	0.291834	+	0.956469i	$0.405735\pi$
$578$	−3.09760e94	−0.160145
$579$	−2.27872e95	−1.10989
$580$	−1.23760e94	−0.0567957
$581$	9.35676e94	0.404621
$582$	2.62336e95	1.06909
$583$	−5.28187e95	−2.02872
$584$	4.00980e94	0.145171
$585$	2.55734e94	0.0872791
$586$	−4.70738e95	−1.51465
$587$	7.48046e94	0.226941	0.113471	−	0.993541i	$-0.463803\pi$
$587$	7.48046e94	0.226941	0.113471	+	0.993541i	$0.463803\pi$
$588$	−1.11140e95	−0.317944
$589$	2.26927e95	0.612221
$590$	5.75236e95	1.46370
$591$	2.90276e95	0.696696
$592$	−4.98294e95	−1.12820
$593$	3.74120e95	0.799142	0.399571	−	0.916702i	$-0.369159\pi$
$593$	3.74120e95	0.799142	0.399571	+	0.916702i	$0.369159\pi$
$594$	2.72681e95	0.549570
$595$	1.05796e96	2.01202
$596$	6.85333e94	0.123000
$597$	−5.99527e95	−1.01553
$598$	4.37233e93	0.00699072
$599$	−9.07159e95	−1.36917	−0.684586	−	0.728932i	$-0.740017\pi$
$599$	−9.07159e95	−1.36917	−0.684586	+	0.728932i	$0.740017\pi$
$600$	−1.34835e96	−1.92125
$601$	1.14169e96	1.53596	0.767979	−	0.640475i	$-0.221262\pi$
$601$	1.14169e96	1.53596	0.767979	+	0.640475i	$0.221262\pi$
$602$	−6.40394e94	−0.0813520
$603$	2.97905e95	0.357381
$604$	1.62463e95	0.184069
$605$	−9.54039e95	−1.02095
$606$	−3.33300e95	−0.336922
$607$	4.17459e95	0.398661	0.199330	−	0.979932i	$-0.436123\pi$
$607$	4.17459e95	0.398661	0.199330	+	0.979932i	$0.436123\pi$
$608$	−4.25813e95	−0.384189
$609$	−3.34870e95	−0.285483
$610$	−1.31416e96	−1.05869
$611$	1.92934e95	0.146888
$612$	1.81711e95	0.130754
$613$	6.32712e95	0.430348	0.215174	−	0.976576i	$-0.430968\pi$
$613$	6.32712e95	0.430348	0.215174	+	0.976576i	$0.430968\pi$
$614$	7.08491e95	0.455539
$615$	1.26429e96	0.768518
$616$	3.47914e96	1.99957
$617$	−2.85759e96	−1.55297	−0.776483	−	0.630138i	$-0.782998\pi$
$617$	−2.85759e96	−1.55297	−0.776483	+	0.630138i	$0.782998\pi$
$618$	3.82456e96	1.96553
$619$	−2.33642e96	−1.13560	−0.567798	−	0.823168i	$-0.692205\pi$
$619$	−2.33642e96	−1.13560	−0.567798	+	0.823168i	$0.692205\pi$
$620$	−5.78154e95	−0.265785
$621$	9.80377e94	0.0426317
$622$	1.15020e96	0.473156
$623$	−1.43099e96	−0.556927
$624$	2.24166e95	0.0825471
$625$	−1.26763e96	−0.441703
$626$	−2.98520e96	−0.984370
$627$	4.39390e96	1.37126
$628$	1.15741e96	0.341884
$629$	−5.13493e96	−1.43578
$630$	−4.53481e96	−1.20036
$631$	−1.91201e96	−0.479157	−0.239578	−	0.970877i	$-0.577009\pi$
$631$	−1.91201e96	−0.479157	−0.239578	+	0.970877i	$0.577009\pi$
$632$	2.11327e96	0.501437
$633$	4.20917e95	0.0945732
$634$	−3.61685e95	−0.0769575
$635$	1.07441e97	2.16508
$636$	−2.46223e96	−0.469957
$637$	−5.38787e95	−0.0974107
$638$	1.02793e96	0.176055
$639$	3.06764e96	0.497765
$640$	−5.17464e96	−0.795556
$641$	−6.94117e96	−1.01119	−0.505593	−	0.862772i	$-0.668726\pi$
$641$	−6.94117e96	−1.01119	−0.505593	+	0.862772i	$0.668726\pi$
$642$	−1.90540e96	−0.263044
$643$	−1.73392e96	−0.226856	−0.113428	−	0.993546i	$-0.536183\pi$
$643$	−1.73392e96	−0.226856	−0.113428	+	0.993546i	$0.536183\pi$
$644$	2.37769e95	0.0294845
$645$	1.08402e96	0.127417
$646$	5.94206e96	0.662087
$647$	1.35608e97	1.43248	0.716241	−	0.697853i	$-0.245861\pi$
$647$	1.35608e97	1.43248	0.716241	+	0.697853i	$0.245861\pi$
$648$	1.33350e97	1.33553
$649$	1.46521e97	1.39142
$650$	−1.24250e96	−0.111889
$651$	−1.56437e97	−1.33596
$652$	−3.88714e96	−0.314839
$653$	−2.52462e97	−1.93950	−0.969752	−	0.244090i	$-0.921511\pi$
$653$	−2.52462e97	−1.93950	−0.969752	+	0.244090i	$0.921511\pi$
$654$	−1.29310e97	−0.942322
$655$	1.87405e97	1.29555
$656$	4.22608e96	0.277176
$657$	−1.33126e96	−0.0828434
$658$	−3.42121e97	−2.02016
$659$	−1.64922e95	−0.00924128	−0.00462064	−	0.999989i	$-0.501471\pi$
$659$	−1.64922e95	−0.00924128	−0.00462064	+	0.999989i	$0.501471\pi$
$660$	−1.11946e97	−0.595308
$661$	−1.36393e97	−0.688403	−0.344202	−	0.938896i	$-0.611850\pi$
$661$	−1.36393e97	−0.688403	−0.344202	+	0.938896i	$0.611850\pi$
$662$	2.58010e97	1.23605
$663$	2.31004e96	0.105052
$664$	−7.04380e96	−0.304094
$665$	4.54766e97	1.86398
$666$	2.20103e97	0.856576
$667$	3.69573e95	0.0136571
$668$	9.23299e96	0.324007
$669$	2.92667e96	0.0975377
$670$	−2.48195e97	−0.785620
$671$	−3.34736e97	−1.00641
$672$	2.93543e97	0.838362
$673$	2.24509e97	0.609135	0.304567	−	0.952491i	$-0.401488\pi$
$673$	2.24509e97	0.609135	0.304567	+	0.952491i	$0.401488\pi$
$674$	5.55565e97	1.43208
$675$	−2.78597e97	−0.682334
$676$	1.00005e97	0.232735
$677$	−6.81276e97	−1.50666	−0.753328	−	0.657645i	$-0.771553\pi$
$677$	−6.81276e97	−1.50666	−0.753328	+	0.657645i	$0.771553\pi$
$678$	−3.37621e97	−0.709587
$679$	6.91591e97	1.38147
$680$	−7.96433e97	−1.51214
$681$	−7.53164e97	−1.35930
$682$	4.80204e97	0.823881
$683$	1.00743e98	1.64324	0.821618	−	0.570039i	$-0.193072\pi$
$683$	1.00743e98	1.64324	0.821618	+	0.570039i	$0.193072\pi$
$684$	7.81089e96	0.121134
$685$	−1.59170e98	−2.34713
$686$	5.87700e96	0.0824089
$687$	6.07082e97	0.809544
$688$	3.62350e96	0.0459545
$689$	−1.19365e97	−0.143984
$690$	1.31242e97	0.150584
$691$	−2.94162e97	−0.321066	−0.160533	−	0.987030i	$-0.551321\pi$
$691$	−2.94162e97	−0.321066	−0.160533	+	0.987030i	$0.551321\pi$
$692$	5.57802e96	0.0579188
$693$	−1.15508e98	−1.14108
$694$	5.49269e97	0.516277
$695$	3.26854e98	2.92333
$696$	2.52091e97	0.214555
$697$	4.35498e97	0.352741
$698$	2.97528e97	0.229359
$699$	−1.86937e98	−1.37161
$700$	−6.75678e97	−0.471908
$701$	1.33034e97	0.0884485	0.0442243	−	0.999022i	$-0.485918\pi$
$701$	1.33034e97	0.0884485	0.0442243	+	0.999022i	$0.485918\pi$
$702$	6.16233e96	0.0390045
$703$	−2.20727e98	−1.33014
$704$	−2.49546e98	−1.43184
$705$	5.79121e98	3.16406
$706$	1.52725e98	0.794599
$707$	−8.78671e97	−0.435368
$708$	6.83032e97	0.322325
$709$	−1.39958e98	−0.629075	−0.314537	−	0.949245i	$-0.601849\pi$
$709$	−1.39958e98	−0.629075	−0.314537	+	0.949245i	$0.601849\pi$
$710$	−2.55575e98	−1.09422
$711$	−7.01611e97	−0.286151
$712$	1.07725e98	0.418561
$713$	1.72649e97	0.0639109
$714$	−4.09629e98	−1.44478
$715$	−5.42696e97	−0.182389
$716$	−2.29037e97	−0.0733511
$717$	9.56019e97	0.291780
$718$	−5.74956e97	−0.167240
$719$	−6.02544e98	−1.67048	−0.835241	−	0.549884i	$-0.814672\pi$
$719$	−6.02544e98	−1.67048	−0.835241	+	0.549884i	$0.814672\pi$
$720$	2.56591e98	0.678062
$721$	1.00826e99	2.53984
$722$	−1.08871e98	−0.261444
$723$	6.45521e98	1.47788
$724$	1.05089e97	0.0229392
$725$	−1.05023e98	−0.218587
$726$	3.69393e98	0.733121
$727$	−9.25498e97	−0.175161	−0.0875807	−	0.996157i	$-0.527914\pi$
$727$	−9.25498e97	−0.175161	−0.0875807	+	0.996157i	$0.527914\pi$
$728$	7.86252e97	0.141915
$729$	−8.25308e97	−0.142075
$730$	1.10912e98	0.182112
$731$	3.73403e97	0.0584828
$732$	−1.56043e98	−0.233137
$733$	−4.12420e98	−0.587831	−0.293916	−	0.955831i	$-0.594959\pi$
$733$	−4.12420e98	−0.587831	−0.293916	+	0.955831i	$0.594959\pi$
$734$	−1.46232e97	−0.0198851
$735$	−1.61725e99	−2.09829
$736$	−3.23964e97	−0.0401062
$737$	−6.32189e98	−0.746825
$738$	−1.86672e98	−0.210443
$739$	−6.23242e98	−0.670539	−0.335269	−	0.942122i	$-0.608827\pi$
$739$	−6.23242e98	−0.670539	−0.335269	+	0.942122i	$0.608827\pi$
$740$	5.62358e98	0.577456
$741$	9.92978e97	0.0973221
$742$	2.11665e99	1.98022
$743$	−9.37642e97	−0.0837381	−0.0418690	−	0.999123i	$-0.513331\pi$
$743$	−9.37642e97	−0.0837381	−0.0418690	+	0.999123i	$0.513331\pi$
$744$	1.17766e99	1.00405
$745$	9.97267e98	0.811745
$746$	−1.82122e99	−1.41538
$747$	2.33856e98	0.173535
$748$	−3.85610e98	−0.273240
$749$	−5.02318e98	−0.339904
$750$	−1.06379e99	−0.687450
$751$	−8.97025e98	−0.553639	−0.276819	−	0.960922i	$-0.589280\pi$
$751$	−8.97025e98	−0.553639	−0.276819	+	0.960922i	$0.589280\pi$
$752$	1.93580e99	1.14116
$753$	5.17531e98	0.291413
$754$	2.32302e97	0.0124951
$755$	2.36409e99	1.21477
$756$	3.35110e98	0.164508
$757$	2.27469e99	1.06688	0.533439	−	0.845839i	$-0.320899\pi$
$757$	2.27469e99	1.06688	0.533439	+	0.845839i	$0.320899\pi$
$758$	−1.77715e99	−0.796409
$759$	3.34293e98	0.143148
$760$	−3.42349e99	−1.40088
$761$	3.10760e99	1.21522	0.607608	−	0.794237i	$-0.292129\pi$
$761$	3.10760e99	1.21522	0.607608	+	0.794237i	$0.292129\pi$
$762$	−4.15998e99	−1.55469
$763$	−3.40897e99	−1.21766
$764$	3.50755e98	0.119752
$765$	2.64417e99	0.862919
$766$	4.62692e98	0.144344
$767$	3.31123e98	0.0987529
$768$	−2.95305e99	−0.841994
$769$	−6.21896e99	−1.69535	−0.847674	−	0.530517i	$-0.821998\pi$
$769$	−6.21896e99	−1.69535	−0.847674	+	0.530517i	$0.821998\pi$
$770$	9.62337e99	2.50840
$771$	−3.86701e97	−0.00963827
$772$	8.59626e98	0.204886
$773$	−5.78018e99	−1.31749	−0.658747	−	0.752364i	$-0.728913\pi$
$773$	−5.78018e99	−1.31749	−0.658747	+	0.752364i	$0.728913\pi$
$774$	−1.60055e98	−0.0348904
$775$	−4.90623e99	−1.02291
$776$	−5.20632e99	−1.03825
$777$	1.52163e100	2.90258
$778$	7.58952e99	1.38490
$779$	1.87200e99	0.326787
$780$	−2.52987e98	−0.0422507
$781$	−6.50988e99	−1.04019
$782$	4.52079e98	0.0691165
$783$	5.20874e98	0.0761995
$784$	−5.40592e99	−0.756773
$785$	1.68421e100	2.25628
$786$	−7.25611e99	−0.930306
$787$	8.49135e99	1.04195	0.520977	−	0.853571i	$-0.325568\pi$
$787$	8.49135e99	1.04195	0.520977	+	0.853571i	$0.325568\pi$
$788$	−1.09504e99	−0.128610
$789$	−1.24166e100	−1.39587
$790$	5.84535e99	0.629037
$791$	−8.90064e99	−0.916923
$792$	8.69550e99	0.857582
$793$	−7.56470e98	−0.0714278
$794$	−2.35836e99	−0.213208
$795$	−3.58293e100	−3.10151
$796$	2.26166e99	0.187468
$797$	6.54680e98	0.0519657	0.0259829	−	0.999662i	$-0.491728\pi$
$797$	6.54680e98	0.0519657	0.0259829	+	0.999662i	$0.491728\pi$
$798$	−1.76080e100	−1.33848
$799$	1.99485e100	1.45227
$800$	9.20619e99	0.641912
$801$	−3.57650e99	−0.238856
$802$	1.00986e100	0.646021
$803$	2.82508e99	0.173119
$804$	−2.94705e99	−0.173003
$805$	3.45991e99	0.194584
$806$	1.08521e99	0.0584731
$807$	4.79834e100	2.47716
$808$	6.61467e99	0.327202
$809$	−1.91402e100	−0.907239	−0.453620	−	0.891195i	$-0.649868\pi$
$809$	−1.91402e100	−0.907239	−0.453620	+	0.891195i	$0.649868\pi$
$810$	3.68848e100	1.67539
$811$	−1.81091e100	−0.788275	−0.394138	−	0.919051i	$-0.628957\pi$
$811$	−1.81091e100	−0.788275	−0.394138	+	0.919051i	$0.628957\pi$
$812$	1.26327e99	0.0527002
$813$	−4.39524e99	−0.175735
$814$	−4.67084e100	−1.79000
$815$	−5.65640e100	−2.07779
$816$	2.31778e100	0.816134
$817$	1.60509e99	0.0541798
$818$	5.15482e99	0.166811
$819$	−2.61037e99	−0.0809856
$820$	−4.76941e99	−0.141869
$821$	4.37394e100	1.24748	0.623740	−	0.781632i	$-0.285612\pi$
$821$	4.37394e100	1.24748	0.623740	+	0.781632i	$0.285612\pi$
$822$	6.16289e100	1.68541
$823$	4.69012e100	1.22996	0.614978	−	0.788544i	$-0.289165\pi$
$823$	4.69012e100	1.22996	0.614978	+	0.788544i	$0.289165\pi$
$824$	−7.59023e100	−1.90883
$825$	−9.49974e100	−2.29113
$826$	−5.87166e100	−1.35815
$827$	4.85405e100	1.07687	0.538436	−	0.842666i	$-0.319015\pi$
$827$	4.85405e100	1.07687	0.538436	+	0.842666i	$0.319015\pi$
$828$	5.94263e98	0.0126454
$829$	1.00919e100	0.205988	0.102994	−	0.994682i	$-0.467158\pi$
$829$	1.00919e100	0.205988	0.102994	+	0.994682i	$0.467158\pi$
$830$	−1.94833e100	−0.381477
$831$	1.07094e101	2.01154
$832$	−5.63949e99	−0.101621
$833$	−5.57082e100	−0.963089
$834$	−1.26554e101	−2.09917
$835$	1.34354e101	2.13830
$836$	−1.65756e100	−0.253135
$837$	2.43330e100	0.356589
$838$	3.62252e100	0.509439
$839$	−9.55850e100	−1.29004	−0.645019	−	0.764167i	$-0.723150\pi$
$839$	−9.55850e100	−1.29004	−0.645019	+	0.764167i	$0.723150\pi$
$840$	2.36006e101	3.05694
$841$	−7.84746e100	−0.975589
$842$	1.04174e101	1.24307
$843$	−9.09402e100	−1.04161
$844$	−1.58787e99	−0.0174583
$845$	1.45523e101	1.53594
$846$	−8.55071e100	−0.866413
$847$	9.73824e100	0.947334
$848$	−1.19765e101	−1.11860
$849$	−1.35226e101	−1.21268
$850$	−1.28469e101	−1.10623
$851$	−1.67932e100	−0.138856
$852$	−3.03469e100	−0.240962
$853$	−1.93739e101	−1.47732	−0.738662	−	0.674076i	$-0.764542\pi$
$853$	−1.93739e101	−1.47732	−0.738662	+	0.674076i	$0.764542\pi$
$854$	1.34141e101	0.982351
$855$	1.13661e101	0.799428
$856$	3.78147e100	0.255456
$857$	−1.15045e101	−0.746500	−0.373250	−	0.927731i	$-0.621757\pi$
$857$	−1.15045e101	−0.746500	−0.373250	+	0.927731i	$0.621757\pi$
$858$	2.10126e100	0.130969
$859$	1.59766e101	0.956578	0.478289	−	0.878203i	$-0.341257\pi$
$859$	1.59766e101	0.956578	0.478289	+	0.878203i	$0.341257\pi$
$860$	−4.08937e99	−0.0235212
$861$	−1.29051e101	−0.713102
$862$	7.32010e100	0.388612
$863$	−1.27110e101	−0.648345	−0.324172	−	0.945998i	$-0.605086\pi$
$863$	−1.27110e101	−0.648345	−0.324172	+	0.945998i	$0.605086\pi$
$864$	−4.56592e100	−0.223771
$865$	8.11688e100	0.382238
$866$	3.02431e101	1.36854
$867$	−5.35217e100	−0.232740
$868$	5.90144e100	0.246620
$869$	1.48890e101	0.597974
$870$	6.97290e100	0.269153
$871$	−1.42869e100	−0.0530042
$872$	2.56628e101	0.915137
$873$	1.72851e101	0.592489
$874$	1.94328e100	0.0640311
$875$	−2.80444e101	−0.888317
$876$	1.31696e100	0.0401034
$877$	9.97885e100	0.292142	0.146071	−	0.989274i	$-0.453337\pi$
$877$	9.97885e100	0.292142	0.146071	+	0.989274i	$0.453337\pi$
$878$	−4.96548e101	−1.39766
$879$	−8.13362e101	−2.20124
$880$	−5.44514e101	−1.41696
$881$	7.47754e100	0.187107	0.0935535	−	0.995614i	$-0.470177\pi$
$881$	7.47754e100	0.187107	0.0935535	+	0.995614i	$0.470177\pi$
$882$	2.38787e101	0.574572
$883$	1.70719e101	0.395036	0.197518	−	0.980299i	$-0.436712\pi$
$883$	1.70719e101	0.395036	0.197518	+	0.980299i	$0.436712\pi$
$884$	−8.71442e99	−0.0193926
$885$	9.93919e101	2.12720
$886$	8.12314e100	0.167209
$887$	5.22741e101	1.03496	0.517478	−	0.855697i	$-0.326871\pi$
$887$	5.22741e101	1.03496	0.517478	+	0.855697i	$0.326871\pi$
$888$	−1.14549e102	−2.18144
$889$	−1.09669e102	−2.00896
$890$	2.97971e101	0.525071
$891$	9.39510e101	1.59265
$892$	−1.10406e100	−0.0180055
$893$	8.57494e101	1.34541
$894$	−3.86131e101	−0.582895
$895$	−3.33285e101	−0.484084
$896$	5.28195e101	0.738190
$897$	7.55470e99	0.0101596
$898$	2.43951e101	0.315696
$899$	9.17283e100	0.114234
$900$	−1.68874e101	−0.202393
$901$	−1.23418e102	−1.42355
$902$	3.96138e101	0.439765
$903$	−1.10650e101	−0.118229
$904$	6.70044e101	0.689116
$905$	1.52922e101	0.151388
$906$	−9.15352e101	−0.872298
$907$	1.78006e102	1.63299	0.816497	−	0.577350i	$-0.195913\pi$
$907$	1.78006e102	1.63299	0.816497	+	0.577350i	$0.195913\pi$
$908$	2.84125e101	0.250927
$909$	−2.19608e101	−0.186722
$910$	2.17479e101	0.178028
$911$	−5.06510e101	−0.399213	−0.199606	−	0.979876i	$-0.563966\pi$
$911$	−5.06510e101	−0.399213	−0.199606	+	0.979876i	$0.563966\pi$
$912$	9.96306e101	0.756085
$913$	−4.96268e101	−0.362639
$914$	−1.55377e102	−1.09331
$915$	−2.27066e102	−1.53860
$916$	−2.29017e101	−0.149442
$917$	−1.91291e102	−1.20213
$918$	6.37158e101	0.385633
$919$	−1.40587e102	−0.819523	−0.409762	−	0.912193i	$-0.634388\pi$
$919$	−1.40587e102	−0.819523	−0.409762	+	0.912193i	$0.634388\pi$
$920$	−2.60464e101	−0.146240
$921$	1.22416e102	0.662037
$922$	1.63961e102	0.854128
$923$	−1.47117e101	−0.0738250
$924$	1.14267e102	0.552382
$925$	4.77218e102	2.22243
$926$	−3.06502e102	−1.37517
$927$	2.51997e102	1.08929
$928$	−1.72122e101	−0.0716854
$929$	6.77380e101	0.271826	0.135913	−	0.990721i	$-0.456603\pi$
$929$	6.77380e101	0.271826	0.135913	+	0.990721i	$0.456603\pi$
$930$	3.25744e102	1.25955
$931$	−2.39464e102	−0.892227
$932$	7.05202e101	0.253201
$933$	1.98736e102	0.687639
$934$	−9.23811e101	−0.308046
$935$	−5.61123e102	−1.80326
$936$	1.96510e101	0.0608650
$937$	1.41794e102	0.423295	0.211647	−	0.977346i	$-0.432117\pi$
$937$	1.41794e102	0.423295	0.211647	+	0.977346i	$0.432117\pi$
$938$	2.53342e102	0.728970
$939$	−5.15795e102	−1.43059
$940$	−2.18469e102	−0.584087
$941$	2.70724e102	0.697726	0.348863	−	0.937174i	$-0.386568\pi$
$941$	2.70724e102	0.697726	0.348863	+	0.937174i	$0.386568\pi$
$942$	−6.52107e102	−1.62018
$943$	1.42424e101	0.0341139
$944$	3.32233e102	0.767200
$945$	4.87638e102	1.08568
$946$	3.39655e101	0.0729111
$947$	−8.25080e102	−1.70774	−0.853870	−	0.520487i	$-0.825750\pi$
$947$	−8.25080e102	−1.70774	−0.853870	+	0.520487i	$0.825750\pi$
$948$	6.94074e101	0.138522
$949$	6.38442e100	0.0122867
$950$	−5.52229e102	−1.02484
$951$	−6.24935e101	−0.111843
$952$	8.12950e102	1.40310
$953$	−5.79812e102	−0.965122	−0.482561	−	0.875862i	$-0.660293\pi$
$953$	−5.79812e102	−0.965122	−0.482561	+	0.875862i	$0.660293\pi$
$954$	5.29019e102	0.849282
$955$	5.10403e102	0.790309
$956$	−3.60650e101	−0.0538627
$957$	1.77610e102	0.255862
$958$	5.89735e102	0.819496
$959$	1.62471e103	2.17788
$960$	−1.69278e103	−2.18899
$961$	−3.73084e102	−0.465424
$962$	−1.05556e102	−0.127041
$963$	−1.25546e102	−0.145779
$964$	−2.43517e102	−0.272817
$965$	1.25089e103	1.35216
$966$	−1.33964e102	−0.139726
$967$	4.01425e102	0.404009	0.202004	−	0.979385i	$-0.435254\pi$
$967$	4.01425e102	0.404009	0.202004	+	0.979385i	$0.435254\pi$
$968$	−7.33099e102	−0.711972
$969$	1.02670e103	0.962213
$970$	−1.44008e103	−1.30245
$971$	5.69960e102	0.497486	0.248743	−	0.968570i	$-0.419983\pi$
$971$	5.69960e102	0.497486	0.248743	+	0.968570i	$0.419983\pi$
$972$	3.02089e102	0.254477
$973$	−3.33632e103	−2.71253
$974$	6.51998e101	0.0511638
$975$	−2.14685e102	−0.162608
$976$	−7.59005e102	−0.554915
$977$	8.26703e102	0.583428	0.291714	−	0.956506i	$-0.405774\pi$
$977$	8.26703e102	0.583428	0.291714	+	0.956506i	$0.405774\pi$
$978$	2.19010e103	1.49201
$979$	7.58975e102	0.499142
$980$	6.10095e102	0.387345
$981$	−8.52012e102	−0.522234
$982$	1.38234e102	0.0818030
$983$	−6.43048e102	−0.367407	−0.183703	−	0.982982i	$-0.558809\pi$
$983$	−6.43048e102	−0.367407	−0.183703	+	0.982982i	$0.558809\pi$
$984$	9.71498e102	0.535934
$985$	−1.59346e103	−0.848770
$986$	2.40190e102	0.123538
$987$	−5.91132e103	−2.93591
$988$	−3.74592e101	−0.0179657
$989$	1.22117e101	0.00565593
$990$	2.40519e103	1.07581
$991$	3.91036e103	1.68918	0.844590	−	0.535413i	$-0.179844\pi$
$991$	3.91036e103	1.68918	0.844590	+	0.535413i	$0.179844\pi$
$992$	−8.04079e102	−0.335464
$993$	4.45801e103	1.79635
$994$	2.60876e103	1.01532
$995$	3.29107e103	1.23720
$996$	−2.31344e102	−0.0840060
$997$	−5.45024e103	−1.91176	−0.955878	−	0.293763i	$-0.905092\pi$
$997$	−5.45024e103	−1.91176	−0.955878	+	0.293763i	$0.905092\pi$
$998$	2.23947e103	0.758826
$999$	−2.36682e103	−0.774740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.70.a.a.1.4	✓	5
3.2	odd	2		9.70.a.b.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.70.a.a.1.4	✓	5	1.1	even	1	trivial
9.70.a.b.1.2		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.12545e10 q^{2} +3.67245e16 q^{3} -1.38540e20 q^{4} -2.01597e24 q^{5} +7.80563e26 q^{6} +2.05778e29 q^{7} -1.54911e31 q^{8} +5.14307e32 q^{9} -4.28486e34 q^{10} -1.09142e36 q^{11} -5.08782e36 q^{12} -2.46650e37 q^{13} +4.37373e39 q^{14} -7.40358e40 q^{15} -2.47476e41 q^{16} -2.55025e42 q^{17} +1.09314e43 q^{18} -1.09623e44 q^{19} +2.79293e44 q^{20} +7.55712e45 q^{21} -2.31976e46 q^{22} -8.34028e45 q^{23} -5.68903e47 q^{24} +2.37009e48 q^{25} -5.24243e47 q^{26} -1.17547e49 q^{27} -2.85086e49 q^{28} -4.43119e49 q^{29} -1.57360e51 q^{30} -2.07006e51 q^{31} +3.88433e51 q^{32} -4.00818e52 q^{33} -5.42044e52 q^{34} -4.14844e53 q^{35} -7.12521e52 q^{36} +2.01350e54 q^{37} -2.32999e54 q^{38} -9.05809e53 q^{39} +3.12296e55 q^{40} -1.70767e55 q^{41} +1.60623e56 q^{42} -1.46418e55 q^{43} +1.51205e56 q^{44} -1.03683e57 q^{45} -1.77269e56 q^{46} -7.82219e57 q^{47} -9.08845e57 q^{48} +2.18442e58 q^{49} +5.03751e58 q^{50} -9.36567e58 q^{51} +3.41709e57 q^{52} +4.83946e59 q^{53} -2.49841e59 q^{54} +2.20027e60 q^{55} -3.18773e60 q^{56} -4.02587e60 q^{57} -9.41829e59 q^{58} -1.34248e61 q^{59} +1.02569e61 q^{60} +3.06698e61 q^{61} -4.39982e61 q^{62} +1.05833e62 q^{63} +2.28644e62 q^{64} +4.97239e61 q^{65} -8.51920e62 q^{66} +5.79237e62 q^{67} +3.53312e62 q^{68} -3.06293e62 q^{69} -8.81732e63 q^{70} +5.96461e63 q^{71} -7.96717e63 q^{72} -2.58846e63 q^{73} +4.27961e64 q^{74} +8.70404e64 q^{75} +1.51872e64 q^{76} -2.24590e65 q^{77} -1.92526e64 q^{78} -1.36419e65 q^{79} +4.98906e65 q^{80} -8.60817e65 q^{81} -3.62958e65 q^{82} +4.54701e65 q^{83} -1.04696e66 q^{84} +5.14124e66 q^{85} -3.11206e65 q^{86} -1.62733e66 q^{87} +1.69072e67 q^{88} -6.95403e66 q^{89} -2.20373e67 q^{90} -5.07552e66 q^{91} +1.15546e66 q^{92} -7.60220e67 q^{93} -1.66257e68 q^{94} +2.20998e68 q^{95} +1.42650e68 q^{96} +3.36085e68 q^{97} +4.64289e68 q^{98} -5.61323e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3} + 12\!\cdots\!60 q^{4} - 18\!\cdots\!50 q^{5} + 65\!\cdots\!60 q^{6} + 76\!\cdots\!92 q^{7} - 45\!\cdots\!00 q^{8} - 31\!\cdots\!35 q^{9} + 44\!\cdots\!00 q^{10}+ \cdots + 58\!\cdots\!80 q^{99}+O(q^{100}) \) 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9 + 44330196388334747724288536990904000 * q^10 - 60667038452283127772973811588820340 * q^11 - 11483075252723727688688753994339790848 * q^12 + 241757308976474000869098277194908009686 * q^13 + 354251192093531665156722201608564593920 * q^14 - 22070061029664005246083216762166031993000 * q^15 + 959158246463054504693505368032717942292480 * q^16 - 3406116484103989032025799295223462139713638 * q^17 + 24028760578245796491398335690330074428977056 * q^18 + 50409644862695734347948203723209710229820500 * q^19 - 1423124021474831957749573329409407107348736000 * q^20 + 3013464004165585730133470747616333350946636960 * q^21 - 11532803895526133094453480299474752792963837056 * q^22 + 49597077165419749499080141147449313474867772376 * q^23 - 3758573903021835292505270073849755869023436800 * q^24 + 464109230075747674561453215791202707168413296875 * q^25 - 16366243363702391437841515238911258759405955787840 * q^26 - 4656668144254073384201536267744600116223141335000 * q^27 - 145657936238300983941227399236934030905596038045696 * q^28 - 623609331535478016897341347681349171717970694417050 * q^29 - 3363430262026080628144709187077082169492181498016000 * q^30 - 7773979811443490840377264327630961134705736859811040 * q^31 - 59446525385187765185716890552455969166501734680363008 * q^32 - 114056291760419605293140369499335251414708842916007568 * q^33 - 257146382902997900108453969123952433606251002004626880 * q^34 - 746713702965644817139124842748848714607056852166946000 * q^35 - 2051949564713522439077005513759167028086223411246648320 * q^36 + 1173349927804932358065167442366744839628119054724224302 * q^37 + 118225357325580676139934406348110667239400005459024000 * q^38 + 14057637047001351842470294363781888979755467326981836280 * q^39 + 113448309945374158392264311043353386142011790732943360000 * q^40 + 126046983235211396249316718220813524712126370275682679410 * q^41 + 293618058653079520265272756273690037096976372387400909824 * q^42 + 182990795236310295463906097926157021228111368794869386156 * q^43 - 207861964397629572369029141530074424104092312018072801280 * q^44 - 1643209216033810606361059101690783215624601629799145190250 * q^45 - 10254004636983168196931301388746633342901210187441053098240 * q^46 - 10227620449924872974485942387482033943920758356350760046928 * q^47 - 32395077603800850016659260748043884333789001078303069569024 * q^48 - 18333133463047872956569862100374253860638045246565546349315 * q^49 + 36528582075561740316450944849185458926809558787823115500000 * q^50 + 118668467511484226348705374365583184000267089107653013314760 * q^51 + 942523544779067327174672695236090488789159958525129397368832 * q^52 + 632699876044410239466855544904774161379655010323706866957246 * q^53 + 180558070990413352422035814551902697653880540863671629472000 * q^54 + 908306905388987301982805388456202130484984202488366374469000 * q^55 - 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 10204523476105540193819201045109650965597050176490899356681200 * q^57 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 - 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 4120988224178099264267892216282931461935581678787045796864000 * q^60 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 + 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 328016742630707922691415372382087941549150107260006661759940136 * q^63 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 + 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 338570852359916448113902185281844117937336911423509879777978880 * q^66 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 - 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 6814317814451425604632002110369996993863432815743912687188684320 * q^69 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 - 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33340305480431860824635017027459448788044465030309454443456921600 * q^72 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 + 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 133279503236831559979066107911998455423803652698542098545072437500 * q^75 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 - 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 57072566318401512231072936702879380800620122459787990692269387008 * q^78 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 - 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 1101671322957552996191157562976784281568686466036132881049220065795 * q^81 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 + 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 2982792317318014581404535874546389828859810656181796104246410117120 * q^84 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 + 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 12567354207673775260644045622671132292173268168085315900596903577400 * q^87 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 - 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 85191607767474905371023384802405560846731062106202026396755774248000 * q^90 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 - 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 112906043990099714252090302813260364787306717550744493130306572821888 * q^93 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 + 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 782790419970794266899143250915194035456012168622622133055202797813760 * q^96 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 + 1783735577381778172290937711296356094085482547558896852990197505179424 * q^98 + 586262466890180722819447934223042169763434625676688596008715148885980 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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