LMFDB - Embedded newform 1.84.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,84,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, 84, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 84);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 84 $
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:	$43.6272128266$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots + 22\!\cdots\!00 $ x^7 - x^6 - 89641237459195851367368x^5 + 1490735848862859486144964924638452x^4 + 1930211822410210561241520455818961338113682960x^3 - 58721021531954131531332854115146412227388949851414322800x^2 - 9636367192739742930950668323030502132711885071308786705499042816000*x + 225425399226476103878513452100286122913961367345316581915847454103589416760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{82}\cdot 3^{30}\cdot 5^{8}\cdot 7^{4}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.16386e11$ 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)

$f(q)$	$=$	$q+2.84290e12 q^{2} +5.71915e17 q^{3} -1.58931e24 q^{4} -1.75639e29 q^{5} +1.62590e30 q^{6} +1.13550e35 q^{7} -3.20131e37 q^{8} -3.99051e39 q^{9} +O(q^{10})$	\(q+2.84290e12 q^{2} +5.71915e17 q^{3} -1.58931e24 q^{4} -1.75639e29 q^{5} +1.62590e30 q^{6} +1.13550e35 q^{7} -3.20131e37 q^{8} -3.99051e39 q^{9} -4.99324e41 q^{10} +1.77109e43 q^{11} -9.08948e41 q^{12} -1.59535e46 q^{13} +3.22810e47 q^{14} -1.00451e47 q^{15} -7.56394e49 q^{16} +1.35293e51 q^{17} -1.13446e52 q^{18} +6.45952e52 q^{19} +2.79144e53 q^{20} +6.49407e52 q^{21} +5.03503e55 q^{22} +3.19639e56 q^{23} -1.83088e55 q^{24} +2.05093e58 q^{25} -4.53542e58 q^{26} -4.56466e57 q^{27} -1.80465e59 q^{28} -6.07652e60 q^{29} -2.85571e59 q^{30} +5.47876e61 q^{31} +9.45764e61 q^{32} +1.01291e61 q^{33} +3.84624e63 q^{34} -1.99437e64 q^{35} +6.34214e63 q^{36} -1.27103e64 q^{37} +1.83638e65 q^{38} -9.12405e63 q^{39} +5.62275e66 q^{40} -8.21335e66 q^{41} +1.84620e65 q^{42} +6.38772e67 q^{43} -2.81480e67 q^{44} +7.00889e68 q^{45} +9.08704e68 q^{46} +4.62167e69 q^{47} -4.32593e67 q^{48} -1.01043e69 q^{49} +5.83059e70 q^{50} +7.73759e68 q^{51} +2.53550e70 q^{52} +3.46344e71 q^{53} -1.29769e70 q^{54} -3.11072e72 q^{55} -3.63507e72 q^{56} +3.69430e70 q^{57} -1.72750e73 q^{58} +5.67171e72 q^{59} +1.59647e71 q^{60} -8.36077e72 q^{61} +1.55756e74 q^{62} -4.53121e74 q^{63} +1.00041e75 q^{64} +2.80205e75 q^{65} +2.87961e73 q^{66} +3.21153e75 q^{67} -2.15021e75 q^{68} +1.82807e74 q^{69} -5.66981e76 q^{70} -9.46939e76 q^{71} +1.27749e77 q^{72} -1.03612e77 q^{73} -3.61341e76 q^{74} +1.17296e76 q^{75} -1.02661e77 q^{76} +2.01106e78 q^{77} -2.59388e76 q^{78} -1.09914e78 q^{79} +1.32852e79 q^{80} +1.59229e79 q^{81} -2.33498e79 q^{82} -4.49074e79 q^{83} -1.03211e77 q^{84} -2.37627e80 q^{85} +1.81597e80 q^{86} -3.47525e78 q^{87} -5.66980e80 q^{88} +1.11155e81 q^{89} +1.99256e81 q^{90} -1.81151e81 q^{91} -5.08004e80 q^{92} +3.13339e79 q^{93} +1.31390e82 q^{94} -1.13454e82 q^{95} +5.40897e79 q^{96} -1.32404e82 q^{97} -2.87255e81 q^{98} -7.06754e82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) $ 7 * q + 347450761416 * q^2 + 92768992732348371972 * q^3 + 35584105659089895299423296 * q^4 + 95882188896595936852480961970 * q^5 - 294670844093053176615850490328096 * q^6 + 41935337227745505345382734191463656 * q^7 - 53166432471809997748387310040100892160 * q^8 + 7173898769720313141925302496494258063219 * q^9	$ 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) $ 7 * q + 347450761416 * q^2 + 92768992732348371972 * q^3 + 35584105659089895299423296 * q^4 + 95882188896595936852480961970 * q^5 - 294670844093053176615850490328096 * q^6 + 41935337227745505345382734191463656 * q^7 - 53166432471809997748387310040100892160 * q^8 + 7173898769720313141925302496494258063219 * q^9 + 499744956856868951374871513628825303339120 * q^10 + 25877323689250927756216798585844787377793324 * q^11 + 2460442604910297198073551343877297856954713856 * q^12 + 17524422091988534325290637412825903296133795802 * q^13 - 667010599912297808117771255707130466716823613248 * q^14 + 495579388338965458292669248844531863255635208440 * q^15 + 417715742702857603748591276714238800242071723446272 * q^16 - 184492474792188340305787588512947709279311819300514 * q^17 - 28009030626032697117218836919123347961714662935963288 * q^18 + 70057685614612811247361635516613863476112345065711060 * q^19 - 57482583811152041858646735327362480085743726726490240 * q^20 + 1893373789164274184370249913565768587140340046764631904 * q^21 - 25459319566814701232336844310162548331034505268300277088 * q^22 + 824652389276591600045965278715869924572765810514596651832 * q^23 - 5108864246496902395549780448291862586480869954908681963520 * q^24 - 4561105897018180667341222610450479407531682079908284920975 * q^25 + 143121440625749988679618714232562854015797139977713783396144 * q^26 - 18306643512253151650162937588580319544032012511255116569240 * q^27 - 3306103780131881005943201423297958381438351892797060269926912 * q^28 + 6404767822227693446699906276316651921336727974067299509413290 * q^29 + 22115840914712862507238627077766882327252015550247576205746240 * q^30 - 37562467055768426209216291610175403000420584080976492348271456 * q^31 - 401973234215497826032118057547245647414044862108632758037479424 * q^32 + 2195918275671465028132881460796250927450387208449702006682532304 * q^33 - 3642106474236630222613516547778797986245715334909676776624068848 * q^34 - 2073208087472515985799712205841339482184218515995426084627529680 * q^35 + 57130418054952308452673267072095667495060459086592800380434471232 * q^36 + 11679830828485560240095590717771086910057022640967690418168414546 * q^37 - 100824829831783953690862886156130827794285762670109921453507515040 * q^38 + 1565953334461766292518881964176162886481814613037624778927724614488 * q^39 + 9486127421786581581058527875045788297835153320557141731458486656000 * q^40 + 17401669041790147490033877534513313327467761516699357985702287340054 * q^41 + 44973533593538917012168170148121446253249051280516070217105265222912 * q^42 + 155423693656840999526303865174514513948712784929597322758540542988492 * q^43 + 1348607485575405225144018262718175988997396446813103620526566114774272 * q^44 + 1880339750988019909779230148989197482912024900416496550280550343305690 * q^45 + 5506219190262487958701836671526521132048107774881360169694419306565184 * q^46 + 11104141751597135653133375816819520459474802577748272571942549885601776 * q^47 + 68535772806187659604752521040191262704244920099270422943498591509266432 * q^48 + 48858841649181147950169676419361972612175619458033829843989473166294751 * q^49 + 150128830200294018241623574757370340046061702636780234316678381973441400 * q^50 + 285323979437882241696128479102133404321665278074017384721958077373999304 * q^51 + 287156729453525056399055611675371787971339735611155780289523821420813696 * q^52 + 273161075599979193637636426681909962095058697602986681290913238279577122 * q^53 - 3035335179479589317975420635665461716944398657720830329060859634436191040 * q^54 - 5713148801806043865831522329085397613042534865163593217346624944021935960 * q^55 - 16548372571630294224019812720652384540821878073420179539137646605391810560 * q^56 - 34025570556802197911899195289016333635970214164767521145341412678086153680 * q^57 - 107856312851606062726720906610847944794517184506982834438591381099782874960 * q^58 - 23387662928216230581473943437005284343365902946251051301830585313805483620 * q^59 - 111426487760354848959531561221427047757146965306130391339788819029760724480 * q^60 + 174496853895103215296232800034629055024308568422892345549894754405198022474 * q^61 + 202911123959081503237789686733196890455024356155124318865846118460223535872 * q^62 + 1452472272578781819866280021221104701255297870249157972403070846844413328392 * q^63 + 6634340238508315566899158004225714692716612285250446595132287614710135914496 * q^64 + 7847697320266417932918441445560149353782900722209245969738521432028132712140 * q^65 + 5853477037889002409213418366788233179355537994202667769768656686338545312128 * q^66 + 4207870282072288819930283375229384131272485602664611977572129464006258765636 * q^67 - 2096504738666940955442779681368953687199581458034579489652465446528751795072 * q^68 - 20650746275200221772316139734189903533557652468456540358959577322030289931232 * q^69 - 145036588586277913982945740577079817793279246661749211931215600391874230481280 * q^70 - 255182116774353604409687783436303274428169526091219223291653972862797742675416 * q^71 - 870484407164078464103908172424456244246778900599455841998985045216713192261120 * q^72 - 305241553076526275791215297716487992856779743869787675846354786221090205747018 * q^73 + 519509459878782742271675046603917029597958567555546598174683109762008202679152 * q^74 - 108583349872086845300331949191600832920703338562329517576945108262256298985700 * q^75 + 3101616184715813078617408724804325452068973943873193050543089493292892226548480 * q^76 + 1968650017033252100145732463322846835178370212948913842977898825590858174818592 * q^77 + 21491900853406375307008391073223804676382414550199027500027607363780886431018304 * q^78 + 23447929932751548600263104762346056717107337920041167505701244565861009558020240 * q^79 + 17204514340446283418245025220202850902483487721576269901420959588660341138513920 * q^80 - 17753472117770960614378485370145730323852918650183577857034614500242589049352193 * q^81 - 31321993453816460140947801899215524216330716054375524262202008548706253113923248 * q^82 - 46082240797638648794744046457142731881250364210725285467604380362957138908759788 * q^83 - 396393323116531601318524278804366279023581302275903129719352432561583858694821888 * q^84 - 401284317909890185403267950222575247116869569644274198011711052575121501243134780 * q^85 - 845015265474066730430458068700259496114668382925856143568777375852322405810455136 * q^86 + 197750077894055178387517630023128464093882005300943753470627738978951228120838680 * q^87 + 324839816772448825066522872810525224209456499759931184227996411794156773784954880 * q^88 + 1029637925134517055127146751141931889566726599138062764000004109807115136117713670 * q^89 + 4141656580530762388567221011089632154433218135474509214945004172382456820926056240 * q^90 + 3803613049700949766857757374276498806030165436480764134599260004867484942314191344 * q^91 + 18037274986000955133271893922579105966324228705045824551878800657480298511213339136 * q^92 + 8685070641618931882536832652301281283748648395097048916956355973218904558772746624 * q^93 + 14309873718219401549749953357716417680483939380577663052969981365204963308304666752 * q^94 - 14391746226057476549769154981667785050800156202045812612412525445443768991871289000 * q^95 - 108145031724537483365505988938774635887900203900416762648300829840839318527629459456 * q^96 - 74638965785790533754670961742172384288953081898163477046944786055599953393772909074 * q^97 - 18956661788073492574129772794522396713191224901923159738123453486226051877064977912 * q^98 - 186867222990833548593390820999966230195685717791503334320194774977997201493521400292 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.84290e12	0.914150	0.457075	−	0.889428i	$-0.348897\pi$
$2$	2.84290e12	0.914150	0.457075	+	0.889428i	$0.348897\pi$
$3$	5.71915e17	0.00905315	0.00452657	−	0.999990i	$-0.498559\pi$
$3$	5.71915e17	0.00905315	0.00452657	+	0.999990i	$0.498559\pi$
$4$	−1.58931e24	−0.164330
$5$	−1.75639e29	−1.72729	−0.863646	−	0.504100i	$-0.831824\pi$
$5$	−1.75639e29	−1.72729	−0.863646	+	0.504100i	$0.831824\pi$
$6$	1.62590e30	0.00827593
$7$	1.13550e35	0.962979	0.481489	−	0.876452i	$-0.340096\pi$
$7$	1.13550e35	0.962979	0.481489	+	0.876452i	$0.340096\pi$
$8$	−3.20131e37	−1.06437
$9$	−3.99051e39	−0.999918
$10$	−4.99324e41	−1.57900
$11$	1.77109e43	1.07261	0.536307	−	0.844023i	$-0.319819\pi$
$11$	1.77109e43	1.07261	0.536307	+	0.844023i	$0.319819\pi$
$12$	−9.08948e41	−0.00148771
$13$	−1.59535e46	−0.942338	−0.471169	−	0.882043i	$-0.656168\pi$
$13$	−1.59535e46	−0.942338	−0.471169	+	0.882043i	$0.656168\pi$
$14$	3.22810e47	0.880307
$15$	−1.00451e47	−0.0156374
$16$	−7.56394e49	−0.808665
$17$	1.35293e51	1.16854	0.584271	−	0.811559i	$-0.301381\pi$
$17$	1.35293e51	1.16854	0.584271	+	0.811559i	$0.301381\pi$
$18$	−1.13446e52	−0.914075
$19$	6.45952e52	0.551983	0.275992	−	0.961160i	$-0.410994\pi$
$19$	6.45952e52	0.551983	0.275992	+	0.961160i	$0.410994\pi$
$20$	2.79144e53	0.283846
$21$	6.49407e52	0.00871799
$22$	5.03503e55	0.980530
$23$	3.19639e56	0.983909	0.491954	−	0.870621i	$-0.336283\pi$
$23$	3.19639e56	0.983909	0.491954	+	0.870621i	$0.336283\pi$
$24$	−1.83088e55	−0.00963592
$25$	2.05093e58	1.98353
$26$	−4.53542e58	−0.861438
$27$	−4.56466e57	−0.0181056
$28$	−1.80465e59	−0.158247
$29$	−6.07652e60	−1.24205	−0.621023	−	0.783792i	$-0.713283\pi$
$29$	−6.07652e60	−1.24205	−0.621023	+	0.783792i	$0.713283\pi$
$30$	−2.85571e59	−0.0142949
$31$	5.47876e61	0.703351	0.351675	−	0.936122i	$-0.385612\pi$
$31$	5.47876e61	0.703351	0.351675	+	0.936122i	$0.385612\pi$
$32$	9.45764e61	0.325131
$33$	1.01291e61	0.00971054
$34$	3.84624e63	1.06822
$35$	−1.99437e64	−1.66334
$36$	6.34214e63	0.164317
$37$	−1.27103e64	−0.105629	−0.0528146	−	0.998604i	$-0.516819\pi$
$37$	−1.27103e64	−0.105629	−0.0528146	+	0.998604i	$0.516819\pi$
$38$	1.83638e65	0.504595
$39$	−9.12405e63	−0.00853112
$40$	5.62275e66	1.83848
$41$	−8.21335e66	−0.963808	−0.481904	−	0.876224i	$-0.660055\pi$
$41$	−8.21335e66	−0.963808	−0.481904	+	0.876224i	$0.660055\pi$
$42$	1.84620e65	0.00796955
$43$	6.38772e67	1.03850	0.519248	−	0.854623i	$-0.326212\pi$
$43$	6.38772e67	1.03850	0.519248	+	0.854623i	$0.326212\pi$
$44$	−2.81480e67	−0.176263
$45$	7.00889e68	1.72715
$46$	9.08704e68	0.899440
$47$	4.62167e69	1.87386	0.936931	−	0.349515i	$-0.113654\pi$
$47$	4.62167e69	1.87386	0.936931	+	0.349515i	$0.113654\pi$
$48$	−4.32593e67	−0.00732097
$49$	−1.01043e69	−0.0726723
$50$	5.83059e70	1.81325
$51$	7.73759e68	0.0105790
$52$	2.53550e70	0.154855
$53$	3.46344e71	0.959531	0.479766	−	0.877397i	$-0.340722\pi$
$53$	3.46344e71	0.959531	0.479766	+	0.877397i	$0.340722\pi$
$54$	−1.29769e70	−0.0165512
$55$	−3.11072e72	−1.85272
$56$	−3.63507e72	−1.02497
$57$	3.69430e70	0.00499719
$58$	−1.72750e73	−1.13542
$59$	5.67171e72	0.183381	0.0916907	−	0.995788i	$-0.470773\pi$
$59$	5.67171e72	0.183381	0.0916907	+	0.995788i	$0.470773\pi$
$60$	1.59647e71	0.00256970
$61$	−8.36077e72	−0.0677732	−0.0338866	−	0.999426i	$-0.510789\pi$
$61$	−8.36077e72	−0.0677732	−0.0338866	+	0.999426i	$0.510789\pi$
$62$	1.55756e74	0.642968
$63$	−4.53121e74	−0.962900
$64$	1.00041e75	1.10588
$65$	2.80205e75	1.62769
$66$	2.87961e73	0.00887688
$67$	3.21153e75	0.530405	0.265203	−	0.964193i	$-0.414561\pi$
$67$	3.21153e75	0.530405	0.265203	+	0.964193i	$0.414561\pi$
$68$	−2.15021e75	−0.192027
$69$	1.82807e74	0.00890747
$70$	−5.66981e76	−1.52055
$71$	−9.46939e76	−1.40962	−0.704808	−	0.709398i	$-0.748967\pi$
$71$	−9.46939e76	−1.40962	−0.704808	+	0.709398i	$0.748967\pi$
$72$	1.27749e77	1.06428
$73$	−1.03612e77	−0.486979	−0.243490	−	0.969904i	$-0.578292\pi$
$73$	−1.03612e77	−0.486979	−0.243490	+	0.969904i	$0.578292\pi$
$74$	−3.61341e76	−0.0965609
$75$	1.17296e76	0.0179572
$76$	−1.02661e77	−0.0907076
$77$	2.01106e78	1.03290
$78$	−2.59388e76	−0.00779872
$79$	−1.09914e78	−0.194773	−0.0973867	−	0.995247i	$-0.531048\pi$
$79$	−1.09914e78	−0.194773	−0.0973867	+	0.995247i	$0.531048\pi$
$80$	1.32852e79	1.39680
$81$	1.59229e79	0.999754
$82$	−2.33498e79	−0.881065
$83$	−4.49074e79	−1.02465	−0.512327	−	0.858791i	$-0.671216\pi$
$83$	−4.49074e79	−1.02465	−0.512327	+	0.858791i	$0.671216\pi$
$84$	−1.03211e77	−0.00143263
$85$	−2.37627e80	−2.01841
$86$	1.81597e80	0.949341
$87$	−3.47525e78	−0.0112444
$88$	−5.66980e80	−1.14166
$89$	1.11155e81	1.40037	0.700186	−	0.713961i	$-0.253101\pi$
$89$	1.11155e81	1.40037	0.700186	+	0.713961i	$0.253101\pi$
$90$	1.99256e81	1.57887
$91$	−1.81151e81	−0.907451
$92$	−5.08004e80	−0.161686
$93$	3.13339e79	0.00636754
$94$	1.31390e82	1.71299
$95$	−1.13454e82	−0.953436
$96$	5.40897e79	0.00294346
$97$	−1.32404e82	−0.468676	−0.234338	−	0.972155i	$-0.575292\pi$
$97$	−1.32404e82	−0.468676	−0.234338	+	0.972155i	$0.575292\pi$
$98$	−2.87255e81	−0.0664333
$99$	−7.06754e82	−1.07253
$100$	−3.25955e82	−0.325955
$101$	−7.23496e82	−0.478739	−0.239370	−	0.970929i	$-0.576941\pi$
$101$	−7.23496e82	−0.478739	−0.239370	+	0.970929i	$0.576941\pi$
$102$	2.19972e81	0.00967077
$103$	4.61216e83	1.35257	0.676285	−	0.736640i	$-0.263589\pi$
$103$	4.61216e83	1.35257	0.676285	+	0.736640i	$0.263589\pi$
$104$	5.10721e83	1.00300
$105$	−1.14061e82	−0.0150585
$106$	9.84623e83	0.877155
$107$	−1.68897e84	−1.01905	−0.509525	−	0.860456i	$-0.670179\pi$
$107$	−1.68897e84	−1.01905	−0.509525	+	0.860456i	$0.670179\pi$
$108$	7.25463e81	0.00297529
$109$	2.45529e84	0.686915	0.343457	−	0.939168i	$-0.388402\pi$
$109$	2.45529e84	0.686915	0.343457	+	0.939168i	$0.388402\pi$
$110$	−8.84347e84	−1.69366
$111$	−7.26921e81	−0.000956277 0
$112$	−8.58882e84	−0.778727
$113$	2.25080e85	1.41118	0.705589	−	0.708622i	$-0.250683\pi$
$113$	2.25080e85	1.41118	0.705589	+	0.708622i	$0.250683\pi$
$114$	1.05025e83	0.00456818
$115$	−5.61411e85	−1.69950
$116$	9.65744e84	0.204106
$117$	6.36626e85	0.942260
$118$	1.61241e85	0.167638
$119$	1.53624e86	1.12528
$120$	3.21574e84	0.0166440
$121$	4.10329e85	0.150501
$122$	−2.37689e85	−0.0619548
$123$	−4.69734e84	−0.00872550
$124$	−8.70742e85	−0.115582
$125$	−1.78616e87	−1.69885
$126$	−1.28818e87	−0.880234
$127$	1.55410e86	0.0764935	0.0382468	−	0.999268i	$-0.487823\pi$
$127$	1.55410e86	0.0764935	0.0382468	+	0.999268i	$0.487823\pi$
$128$	1.92939e87	0.685812
$129$	3.65324e85	0.00940166
$130$	7.96597e87	1.48795
$131$	−4.02662e87	−0.547246	−0.273623	−	0.961837i	$-0.588222\pi$
$131$	−4.02662e87	−0.547246	−0.273623	+	0.961837i	$0.588222\pi$
$132$	−1.60983e85	−0.00159574
$133$	7.33475e87	0.531548
$134$	9.13007e87	0.484870
$135$	8.01731e86	0.0312736
$136$	−4.33114e88	−1.24376
$137$	2.67963e88	0.567768	0.283884	−	0.958859i	$-0.408377\pi$
$137$	2.67963e88	0.567768	0.283884	+	0.958859i	$0.408377\pi$
$138$	5.19702e86	0.00814276
$139$	−5.70178e88	−0.662059	−0.331029	−	0.943620i	$-0.607396\pi$
$139$	−5.70178e88	−0.662059	−0.331029	+	0.943620i	$0.607396\pi$
$140$	3.16966e88	0.273338
$141$	2.64320e87	0.0169643
$142$	−2.69206e89	−1.28860
$143$	−2.82550e89	−1.01076
$144$	3.01840e89	0.808599
$145$	1.06727e90	2.14538
$146$	−2.94558e89	−0.445172
$147$	−5.77880e86	−0.000657913 0
$148$	2.02005e88	0.0173581
$149$	2.68338e90	1.74362	0.871812	−	0.489841i	$-0.162945\pi$
$149$	2.68338e90	1.74362	0.871812	+	0.489841i	$0.162945\pi$
$150$	3.33460e88	0.0164156
$151$	−3.93547e90	−1.47046	−0.735231	−	0.677817i	$-0.762926\pi$
$151$	−3.93547e90	−1.47046	−0.735231	+	0.677817i	$0.762926\pi$
$152$	−2.06789e90	−0.587516
$153$	−5.39887e90	−1.16845
$154$	5.71725e90	0.944229
$155$	−9.62283e90	−1.21489
$156$	1.45009e88	0.00140192
$157$	2.00903e91	1.48988	0.744941	−	0.667131i	$-0.232478\pi$
$157$	2.00903e91	1.48988	0.744941	+	0.667131i	$0.232478\pi$
$158$	−3.12475e90	−0.178052
$159$	1.98079e89	0.00868678
$160$	−1.66113e91	−0.561596
$161$	3.62949e91	0.947483
$162$	4.52672e91	0.913925
$163$	−4.17694e91	−0.653240	−0.326620	−	0.945156i	$-0.605910\pi$
$163$	−4.17694e91	−0.653240	−0.326620	+	0.945156i	$0.605910\pi$
$164$	1.30535e91	0.158383
$165$	−1.77907e90	−0.0167729
$166$	−1.27667e92	−0.936687
$167$	1.93801e92	1.10821	0.554106	−	0.832446i	$-0.313060\pi$
$167$	1.93801e92	1.10821	0.554106	+	0.832446i	$0.313060\pi$
$168$	−2.07895e90	−0.00927919
$169$	−3.21007e91	−0.112000
$170$	−6.75549e92	−1.84513
$171$	−2.57768e92	−0.551938
$172$	−1.01520e92	−0.170656
$173$	6.97570e92	0.921880	0.460940	−	0.887431i	$-0.347512\pi$
$173$	6.97570e92	0.921880	0.460940	+	0.887431i	$0.347512\pi$
$174$	−9.87981e90	−0.0102791
$175$	2.32882e93	1.91010
$176$	−1.33964e93	−0.867386
$177$	3.24374e90	0.00166018
$178$	3.16003e93	1.28015
$179$	1.26905e93	0.407454	0.203727	−	0.979028i	$-0.434694\pi$
$179$	1.26905e93	0.407454	0.203727	+	0.979028i	$0.434694\pi$
$180$	−1.11393e93	−0.283823
$181$	−4.57871e93	−0.927006	−0.463503	−	0.886095i	$-0.653408\pi$
$181$	−4.57871e93	−0.927006	−0.463503	+	0.886095i	$0.653408\pi$
$182$	−5.14995e93	−0.829546
$183$	−4.78165e90	−0.000613561 0
$184$	−1.02326e94	−1.04725
$185$	2.23242e93	0.182452
$186$	8.90792e91	0.00582088
$187$	2.39615e94	1.25339
$188$	−7.34524e93	−0.307932
$189$	−5.18315e92	−0.0174353
$190$	−3.22540e94	−0.871583
$191$	5.73915e94	1.24728	0.623638	−	0.781713i	$-0.285654\pi$
$191$	5.73915e94	1.24728	0.623638	+	0.781713i	$0.285654\pi$
$192$	5.72150e92	0.0100117
$193$	5.52377e94	0.779126	0.389563	−	0.921000i	$-0.372626\pi$
$193$	5.52377e94	0.779126	0.389563	+	0.921000i	$0.372626\pi$
$194$	−3.76411e94	−0.428440
$195$	1.60254e93	0.0147357
$196$	1.60588e93	0.0119423
$197$	5.65768e94	0.340636	0.170318	−	0.985389i	$-0.445521\pi$
$197$	5.65768e94	0.340636	0.170318	+	0.985389i	$0.445521\pi$
$198$	−2.00923e95	−0.980450
$199$	4.18848e95	1.65826	0.829132	−	0.559053i	$-0.188835\pi$
$199$	4.18848e95	1.65826	0.829132	+	0.559053i	$0.188835\pi$
$200$	−6.56566e95	−2.11122
$201$	1.83672e93	0.00480184
$202$	−2.05683e95	−0.437639
$203$	−6.89986e95	−1.19606
$204$	−1.22974e93	−0.00173845
$205$	1.44258e96	1.66478
$206$	1.31119e96	1.23645
$207$	−1.27552e96	−0.983828
$208$	1.20671e96	0.762036
$209$	1.14404e96	0.592065
$210$	−3.24265e94	−0.0137657
$211$	6.51752e95	0.227175	0.113588	−	0.993528i	$-0.463766\pi$
$211$	6.51752e95	0.227175	0.113588	+	0.993528i	$0.463766\pi$
$212$	−5.50446e95	−0.157680
$213$	−5.41569e94	−0.0127615
$214$	−4.80158e96	−0.931563
$215$	−1.12193e97	−1.79379
$216$	1.46129e95	0.0192711
$217$	6.22111e96	0.677312
$218$	6.98015e96	0.627943
$219$	−5.92572e94	−0.00440870
$220$	4.94388e96	0.304458
$221$	−2.15839e97	−1.10116
$222$	−2.06657e94	−0.000874180 0
$223$	4.81716e97	1.69098	0.845492	−	0.533989i	$-0.179308\pi$
$223$	4.81716e97	1.69098	0.845492	+	0.533989i	$0.179308\pi$
$224$	1.07391e97	0.313094
$225$	−8.18425e97	−1.98337
$226$	6.39881e97	1.29003
$227$	6.38438e97	1.07163	0.535816	−	0.844335i	$-0.320004\pi$
$227$	6.38438e97	1.07163	0.535816	+	0.844335i	$0.320004\pi$
$228$	−5.87137e94	−0.000821189 0
$229$	−1.19088e97	−0.138898	−0.0694491	−	0.997585i	$-0.522124\pi$
$229$	−1.19088e97	−0.138898	−0.0694491	+	0.997585i	$0.522124\pi$
$230$	−1.59604e98	−1.55359
$231$	1.15016e96	0.00935104
$232$	1.94528e98	1.32200
$233$	−1.34913e98	−0.766980	−0.383490	−	0.923545i	$-0.625278\pi$
$233$	−1.34913e98	−0.766980	−0.383490	+	0.923545i	$0.625278\pi$
$234$	1.80987e98	0.861367
$235$	−8.11744e98	−3.23670
$236$	−9.01407e96	−0.0301351
$237$	−6.28616e95	−0.00176331
$238$	4.36739e98	1.02867
$239$	7.04617e98	1.39457	0.697285	−	0.716794i	$-0.254391\pi$
$239$	7.04617e98	1.39457	0.697285	+	0.716794i	$0.254391\pi$
$240$	7.59802e96	0.0126454
$241$	4.30858e98	0.603430	0.301715	−	0.953398i	$-0.402441\pi$
$241$	4.30858e98	0.603430	0.301715	+	0.953398i	$0.402441\pi$
$242$	1.16653e98	0.137580
$243$	2.73233e97	0.0271565
$244$	1.32878e97	0.0111372
$245$	1.77471e98	0.125526
$246$	−1.33541e97	−0.00797641
$247$	−1.03052e99	−0.520155
$248$	−1.75392e99	−0.748627
$249$	−2.56832e97	−0.00927634
$250$	−5.07789e99	−1.55300
$251$	1.24923e99	0.323729	0.161864	−	0.986813i	$-0.448249\pi$
$251$	1.24923e99	0.323729	0.161864	+	0.986813i	$0.448249\pi$
$252$	7.20147e98	0.158234
$253$	5.66109e99	1.05535
$254$	4.41816e98	0.0699265
$255$	−1.35902e98	−0.0182730
$256$	−4.19032e99	−0.478949
$257$	7.36546e99	0.716103	0.358051	−	0.933702i	$-0.383441\pi$
$257$	7.36546e99	0.716103	0.358051	+	0.933702i	$0.383441\pi$
$258$	1.03858e98	0.00859453
$259$	−1.44325e99	−0.101719
$260$	−4.45332e99	−0.267479
$261$	2.42484e100	1.24194
$262$	−1.14473e100	−0.500264
$263$	2.34631e100	0.875431	0.437716	−	0.899113i	$-0.355788\pi$
$263$	2.34631e100	0.875431	0.437716	+	0.899113i	$0.355788\pi$
$264$	−3.24265e98	−0.0103356
$265$	−6.08315e100	−1.65739
$266$	2.08520e100	0.485914
$267$	6.35712e98	0.0126778
$268$	−5.10410e99	−0.0871616
$269$	−4.77957e100	−0.699309	−0.349655	−	0.936879i	$-0.613701\pi$
$269$	−4.77957e100	−0.699309	−0.349655	+	0.936879i	$0.613701\pi$
$270$	2.27924e99	0.0285887
$271$	−5.04641e100	−0.542947	−0.271473	−	0.962446i	$-0.587511\pi$
$271$	−5.04641e100	−0.542947	−0.271473	+	0.962446i	$0.587511\pi$
$272$	−1.02335e101	−0.944959
$273$	−1.03603e99	−0.00821529
$274$	7.61793e100	0.519025
$275$	3.63237e101	2.12757
$276$	−2.90535e98	−0.00146377
$277$	2.61983e101	1.13596	0.567980	−	0.823042i	$-0.307725\pi$
$277$	2.61983e101	1.13596	0.567980	+	0.823042i	$0.307725\pi$
$278$	−1.62096e101	−0.605221
$279$	−2.18631e101	−0.703293
$280$	6.38460e101	1.77042
$281$	−6.89877e101	−1.64991	−0.824953	−	0.565201i	$-0.808798\pi$
$281$	−6.89877e101	−1.64991	−0.824953	+	0.565201i	$0.808798\pi$
$282$	7.51437e99	0.0155080
$283$	−3.55360e101	−0.633187	−0.316593	−	0.948561i	$-0.602539\pi$
$283$	−3.55360e101	−0.633187	−0.316593	+	0.948561i	$0.602539\pi$
$284$	1.50498e101	0.231643
$285$	−6.48863e99	−0.00863159
$286$	−8.03263e101	−0.923990
$287$	−9.32622e101	−0.928126
$288$	−3.77408e101	−0.325104
$289$	4.89930e101	0.365488
$290$	3.03415e102	1.96119
$291$	−7.57237e99	−0.00424300
$292$	1.64671e101	0.0800254
$293$	−5.97828e101	−0.252098	−0.126049	−	0.992024i	$-0.540230\pi$
$293$	−5.97828e101	−0.252098	−0.126049	+	0.992024i	$0.540230\pi$
$294$	−1.64286e99	−0.000601431 0
$295$	−9.96172e101	−0.316753
$296$	4.06896e101	0.112429
$297$	−8.08440e100	−0.0194203
$298$	7.62860e102	1.59393
$299$	−5.09936e102	−0.927174
$300$	−1.86419e100	−0.00295092
$301$	7.25323e102	1.00005
$302$	−1.11882e103	−1.34422
$303$	−4.13778e100	−0.00433410
$304$	−4.88594e102	−0.446370
$305$	1.46848e102	0.117064
$306$	−1.53485e103	−1.06813
$307$	8.35032e102	0.507529	0.253764	−	0.967266i	$-0.418331\pi$
$307$	8.35032e102	0.507529	0.253764	+	0.967266i	$0.418331\pi$
$308$	−3.19619e102	−0.169738
$309$	2.63777e101	0.0122450
$310$	−2.73568e103	−1.11059
$311$	3.81658e103	1.35556	0.677780	−	0.735265i	$-0.262942\pi$
$311$	3.81658e103	1.35556	0.677780	+	0.735265i	$0.262942\pi$
$312$	2.92089e101	0.00908029
$313$	−2.19904e103	−0.598607	−0.299304	−	0.954158i	$-0.596754\pi$
$313$	−2.19904e103	−0.598607	−0.299304	+	0.954158i	$0.596754\pi$
$314$	5.71149e103	1.36197
$315$	7.95856e103	1.66321
$316$	1.74687e102	0.0320072
$317$	2.08936e103	0.335779	0.167889	−	0.985806i	$-0.446305\pi$
$317$	2.08936e103	0.335779	0.167889	+	0.985806i	$0.446305\pi$
$318$	5.63121e101	0.00794102
$319$	−1.07620e104	−1.33224
$320$	−1.75711e104	−1.91018
$321$	−9.65948e101	−0.00922560
$322$	1.03183e104	0.866141
$323$	8.73926e103	0.645015
$324$	−2.53063e103	−0.164290
$325$	−3.27194e104	−1.86916
$326$	−1.18746e104	−0.597159
$327$	1.40422e102	0.00621874
$328$	2.62935e104	1.02585
$329$	5.24788e104	1.80449
$330$	−5.05772e102	−0.0153330
$331$	−2.71752e104	−0.726626	−0.363313	−	0.931667i	$-0.618354\pi$
$331$	−2.71752e104	−0.726626	−0.363313	+	0.931667i	$0.618354\pi$
$332$	7.13716e103	0.168382
$333$	5.07206e103	0.105621
$334$	5.50958e104	1.01307
$335$	−5.64070e104	−0.916164
$336$	−4.91208e102	−0.00704993
$337$	3.33179e103	0.0422704	0.0211352	−	0.999777i	$-0.493272\pi$
$337$	3.33179e103	0.0422704	0.0211352	+	0.999777i	$0.493272\pi$
$338$	−9.12593e103	−0.102384
$339$	1.28727e103	0.0127756
$340$	3.77661e104	0.331686
$341$	9.70336e104	0.754424
$342$	−7.32809e104	−0.504554
$343$	−1.69352e105	−1.03296
$344$	−2.04491e105	−1.10535
$345$	−3.21079e103	−0.0153858
$346$	1.98312e105	0.842737
$347$	−4.96054e104	−0.187006	−0.0935030	−	0.995619i	$-0.529806\pi$
$347$	−4.96054e104	−0.187006	−0.0935030	+	0.995619i	$0.529806\pi$
$348$	5.52324e102	0.00184780
$349$	−5.09510e105	−1.51320	−0.756602	−	0.653876i	$-0.773142\pi$
$349$	−5.09510e105	−1.51320	−0.756602	+	0.653876i	$0.773142\pi$
$350$	6.62060e105	1.74612
$351$	7.28222e103	0.0170615
$352$	1.67503e105	0.348740
$353$	−2.26069e105	−0.418399	−0.209200	−	0.977873i	$-0.567086\pi$
$353$	−2.26069e105	−0.418399	−0.209200	+	0.977873i	$0.567086\pi$
$354$	9.22163e102	0.00151765
$355$	1.66319e106	2.43482
$356$	−1.76659e105	−0.230123
$357$	8.78600e103	0.0101873
$358$	3.60779e105	0.372474
$359$	−1.56211e105	−0.143646	−0.0718229	−	0.997417i	$-0.522882\pi$
$359$	−1.56211e105	−0.143646	−0.0718229	+	0.997417i	$0.522882\pi$
$360$	−2.24376e106	−1.83833
$361$	−9.52205e105	−0.695315
$362$	−1.30168e106	−0.847422
$363$	2.34674e103	0.00136251
$364$	2.87904e105	0.149122
$365$	1.81983e106	0.841155
$366$	−1.35938e103	−0.000560886 0
$367$	−1.47997e106	−0.545269	−0.272634	−	0.962118i	$-0.587895\pi$
$367$	−1.47997e106	−0.545269	−0.272634	+	0.962118i	$0.587895\pi$
$368$	−2.41773e106	−0.795653
$369$	3.27755e106	0.963729
$370$	6.34656e105	0.166789
$371$	3.93272e106	0.924008
$372$	−4.97991e103	−0.00104638
$373$	1.47373e106	0.277014	0.138507	−	0.990361i	$-0.455770\pi$
$373$	1.47373e106	0.277014	0.138507	+	0.990361i	$0.455770\pi$
$374$	6.81203e106	1.14579
$375$	−1.02153e105	−0.0153800
$376$	−1.47954e107	−1.99449
$377$	9.69416e106	1.17043
$378$	−1.47352e105	−0.0159384
$379$	−1.44565e107	−1.40131	−0.700656	−	0.713499i	$-0.747109\pi$
$379$	−1.44565e107	−1.40131	−0.700656	+	0.713499i	$0.747109\pi$
$380$	1.80314e106	0.156678
$381$	8.88814e103	0.000692507 0
$382$	1.63158e107	1.14020
$383$	9.99134e105	0.0626433	0.0313217	−	0.999509i	$-0.490028\pi$
$383$	9.99134e105	0.0626433	0.0313217	+	0.999509i	$0.490028\pi$
$384$	1.10344e105	0.00620876
$385$	−3.53221e107	−1.78413
$386$	1.57036e107	0.712238
$387$	−2.54903e107	−1.03841
$388$	2.10430e106	0.0770178
$389$	−8.27221e106	−0.272090	−0.136045	−	0.990703i	$-0.543439\pi$
$389$	−8.27221e106	−0.272090	−0.136045	+	0.990703i	$0.543439\pi$
$390$	4.55586e105	0.0134707
$391$	4.32448e107	1.14974
$392$	3.23470e106	0.0773504
$393$	−2.30289e105	−0.00495430
$394$	1.60842e107	0.311392
$395$	1.93052e107	0.336430
$396$	1.12325e107	0.176249
$397$	−5.15842e106	−0.0728972	−0.0364486	−	0.999336i	$-0.511605\pi$
$397$	−5.15842e106	−0.0728972	−0.0364486	+	0.999336i	$0.511605\pi$
$398$	1.19074e108	1.51590
$399$	4.19486e105	0.00481218
$400$	−1.55131e108	−1.60402
$401$	7.54919e107	0.703734	0.351867	−	0.936050i	$-0.385547\pi$
$401$	7.54919e107	0.703734	0.351867	+	0.936050i	$0.385547\pi$
$402$	5.22163e105	0.00438960
$403$	−8.74053e107	−0.662794
$404$	1.14986e107	0.0786714
$405$	−2.79668e108	−1.72687
$406$	−1.96156e108	−1.09338
$407$	−2.25110e107	−0.113299
$408$	−2.47705e106	−0.0112600
$409$	2.49801e108	1.02583	0.512917	−	0.858438i	$-0.328565\pi$
$409$	2.49801e108	1.02583	0.512917	+	0.858438i	$0.328565\pi$
$410$	4.10113e108	1.52186
$411$	1.53252e106	0.00514009
$412$	−7.33013e107	−0.222268
$413$	6.44020e107	0.176592
$414$	−3.62619e108	−0.899366
$415$	7.88749e108	1.76988
$416$	−1.50882e108	−0.306383
$417$	−3.26094e106	−0.00599371
$418$	3.25239e108	0.541236
$419$	2.07976e108	0.313423	0.156711	−	0.987644i	$-0.449911\pi$
$419$	2.07976e108	0.313423	0.156711	+	0.987644i	$0.449911\pi$
$420$	1.81278e106	0.00247457
$421$	−7.85039e108	−0.970922	−0.485461	−	0.874258i	$-0.661348\pi$
$421$	−7.85039e108	−0.970922	−0.485461	+	0.874258i	$0.661348\pi$
$422$	1.85287e108	0.207672
$423$	−1.84428e109	−1.87371
$424$	−1.10876e109	−1.02130
$425$	2.77475e109	2.31784
$426$	−1.53963e107	−0.0116659
$427$	−9.49361e107	−0.0652641
$428$	2.68429e108	0.167461
$429$	−1.61595e107	−0.00915060
$430$	−3.18955e109	−1.63979
$431$	6.46767e108	0.301954	0.150977	−	0.988537i	$-0.451758\pi$
$431$	6.46767e108	0.301954	0.150977	+	0.988537i	$0.451758\pi$
$432$	3.45268e107	0.0146413
$433$	−9.91584e107	−0.0382016	−0.0191008	−	0.999818i	$-0.506080\pi$
$433$	−9.91584e107	−0.0382016	−0.0191008	+	0.999818i	$0.506080\pi$
$434$	1.76860e109	0.619164
$435$	6.10390e107	0.0194224
$436$	−3.90220e108	−0.112881
$437$	2.06472e109	0.543101
$438$	−1.68462e107	−0.00403021
$439$	−1.91995e108	−0.0417841	−0.0208921	−	0.999782i	$-0.506651\pi$
$439$	−1.91995e108	−0.0417841	−0.0208921	+	0.999782i	$0.506651\pi$
$440$	9.95838e109	1.97198
$441$	4.03213e108	0.0726663
$442$	−6.13609e109	−1.00663
$443$	2.65972e109	0.397266	0.198633	−	0.980074i	$-0.436350\pi$
$443$	2.65972e109	0.397266	0.198633	+	0.980074i	$0.436350\pi$
$444$	1.15530e106	0.000157145 0
$445$	−1.95231e110	−2.41885
$446$	1.36947e110	1.54581
$447$	1.53467e108	0.0157853
$448$	1.13596e110	1.06494
$449$	−1.41469e110	−1.20903	−0.604515	−	0.796594i	$-0.706633\pi$
$449$	−1.41469e110	−1.20903	−0.604515	+	0.796594i	$0.706633\pi$
$450$	−2.32670e110	−1.81310
$451$	−1.45466e110	−1.03379
$452$	−3.57721e109	−0.231899
$453$	−2.25076e108	−0.0133123
$454$	1.81502e110	0.979632
$455$	3.18172e110	1.56743
$456$	−1.18266e108	−0.00531887
$457$	2.33459e110	0.958711	0.479355	−	0.877621i	$-0.340870\pi$
$457$	2.33459e110	0.958711	0.479355	+	0.877621i	$0.340870\pi$
$458$	−3.38557e109	−0.126974
$459$	−6.17564e108	−0.0211571
$460$	8.92253e109	0.279279
$461$	2.71631e110	0.776946	0.388473	−	0.921460i	$-0.373003\pi$
$461$	2.71631e110	0.776946	0.388473	+	0.921460i	$0.373003\pi$
$462$	3.26978e108	0.00854825
$463$	−8.12192e110	−1.94110	−0.970550	−	0.240901i	$-0.922557\pi$
$463$	−8.12192e110	−1.94110	−0.970550	+	0.240901i	$0.922557\pi$
$464$	4.59624e110	1.00440
$465$	−5.50345e108	−0.0109986
$466$	−3.83546e110	−0.701135
$467$	5.14831e110	0.861022	0.430511	−	0.902585i	$-0.358333\pi$
$467$	5.14831e110	0.861022	0.430511	+	0.902585i	$0.358333\pi$
$468$	−1.01179e110	−0.154842
$469$	3.64668e110	0.510769
$470$	−2.30771e111	−2.95883
$471$	1.14900e109	0.0134881
$472$	−1.81569e110	−0.195186
$473$	1.13132e111	1.11391
$474$	−1.78710e108	−0.00161193
$475$	1.32480e111	1.09488
$476$	−2.44156e110	−0.184918
$477$	−1.38209e111	−0.959453
$478$	2.00316e111	1.27485
$479$	−2.02770e111	−1.18326	−0.591630	−	0.806209i	$-0.701515\pi$
$479$	−2.02770e111	−1.18326	−0.591630	+	0.806209i	$0.701515\pi$
$480$	−9.50025e108	−0.00508421
$481$	2.02774e110	0.0995384
$482$	1.22489e111	0.551626
$483$	2.07576e109	0.00857771
$484$	−6.52138e109	−0.0247319
$485$	2.32552e111	0.809541
$486$	7.76776e109	0.0248251
$487$	2.31196e111	0.678467	0.339233	−	0.940702i	$-0.389832\pi$
$487$	2.31196e111	0.678467	0.339233	+	0.940702i	$0.389832\pi$
$488$	2.67654e110	0.0721359
$489$	−2.38886e109	−0.00591388
$490$	5.04532e110	0.114750
$491$	−5.12356e111	−1.07075	−0.535377	−	0.844613i	$-0.679830\pi$
$491$	−5.12356e111	−1.07075	−0.535377	+	0.844613i	$0.679830\pi$
$492$	7.46551e108	0.00143386
$493$	−8.22108e111	−1.45138
$494$	−2.92967e111	−0.475499
$495$	1.24134e112	1.85257
$496$	−4.14410e111	−0.568775
$497$	−1.07525e112	−1.35743
$498$	−7.30150e109	−0.00847997
$499$	−2.98604e111	−0.319097	−0.159549	−	0.987190i	$-0.551004\pi$
$499$	−2.98604e111	−0.319097	−0.159549	+	0.987190i	$0.551004\pi$
$500$	2.83876e111	0.279173
$501$	1.10838e110	0.0100328
$502$	3.55143e111	0.295937
$503$	1.67219e111	0.128297	0.0641483	−	0.997940i	$-0.479567\pi$
$503$	1.67219e111	0.128297	0.0641483	+	0.997940i	$0.479567\pi$
$504$	1.45058e112	1.02488
$505$	1.27074e112	0.826922
$506$	1.60939e112	0.964752
$507$	−1.83589e109	−0.00101395
$508$	−2.46994e110	−0.0125702
$509$	−6.25610e110	−0.0293438	−0.0146719	−	0.999892i	$-0.504670\pi$
$509$	−6.25610e110	−0.0293438	−0.0146719	+	0.999892i	$0.504670\pi$
$510$	−3.86357e110	−0.0167042
$511$	−1.17651e112	−0.468951
$512$	−3.05726e112	−1.12364
$513$	−2.94855e110	−0.00999396
$514$	2.09393e112	0.654625
$515$	−8.10075e112	−2.33628
$516$	−5.80611e109	−0.00154498
$517$	8.18537e112	2.00993
$518$	−4.10301e111	−0.0929861
$519$	3.98951e110	0.00834592
$520$	−8.97025e112	−1.73247
$521$	−6.62789e112	−1.18198	−0.590989	−	0.806679i	$-0.701263\pi$
$521$	−6.62789e112	−1.18198	−0.590989	+	0.806679i	$0.701263\pi$
$522$	6.89359e112	1.13532
$523$	5.47854e112	0.833384	0.416692	−	0.909048i	$-0.363189\pi$
$523$	5.47854e112	0.833384	0.416692	+	0.909048i	$0.363189\pi$
$524$	6.39953e111	0.0899290
$525$	1.33189e111	0.0172924
$526$	6.67034e112	0.800275
$527$	7.41236e112	0.821894
$528$	−7.66160e110	−0.00785257
$529$	−3.36913e111	−0.0319233
$530$	−1.72938e113	−1.51510
$531$	−2.26330e112	−0.183366
$532$	−1.16572e112	−0.0873494
$533$	1.31032e113	0.908232
$534$	1.80727e111	0.0115894
$535$	2.96649e113	1.76019
$536$	−1.02811e113	−0.564548
$537$	7.25791e110	0.00368874
$538$	−1.35879e113	−0.639274
$539$	−1.78956e112	−0.0779493
$540$	−1.27420e111	−0.00513920
$541$	−2.36042e113	−0.881665	−0.440832	−	0.897589i	$-0.645317\pi$
$541$	−2.36042e113	−0.881665	−0.440832	+	0.897589i	$0.645317\pi$
$542$	−1.43465e113	−0.496335
$543$	−2.61864e111	−0.00839233
$544$	1.27955e113	0.379929
$545$	−4.31244e113	−1.18650
$546$	−2.94534e111	−0.00751000
$547$	−1.75852e112	−0.0415597	−0.0207799	−	0.999784i	$-0.506615\pi$
$547$	−1.75852e112	−0.0415597	−0.0207799	+	0.999784i	$0.506615\pi$
$548$	−4.25875e112	−0.0933016
$549$	3.33637e112	0.0677676
$550$	1.03265e114	1.94492
$551$	−3.92514e113	−0.685589
$552$	−5.85221e111	−0.00948087
$553$	−1.24807e113	−0.187563
$554$	7.44793e113	1.03844
$555$	1.27676e111	0.00165177
$556$	9.06187e112	0.108796
$557$	1.78462e114	1.98863	0.994316	−	0.106470i	$-0.0339547\pi$
$557$	1.78462e114	1.98863	0.994316	+	0.106470i	$0.0339547\pi$
$558$	−6.21546e113	−0.642915
$559$	−1.01906e114	−0.978614
$560$	1.50853e114	1.34509
$561$	1.37040e112	0.0113472
$562$	−1.96125e114	−1.50826
$563$	−1.28860e114	−0.920493	−0.460247	−	0.887791i	$-0.652239\pi$
$563$	−1.28860e114	−0.920493	−0.460247	+	0.887791i	$0.652239\pi$
$564$	−4.20085e111	−0.00278776
$565$	−3.95328e114	−2.43751
$566$	−1.01026e114	−0.578828
$567$	1.80803e114	0.962742
$568$	3.03145e114	1.50036
$569$	2.56608e114	1.18062	0.590310	−	0.807176i	$-0.299005\pi$
$569$	2.56608e114	1.18062	0.590310	+	0.807176i	$0.299005\pi$
$570$	−1.84465e112	−0.00789057
$571$	−3.99773e114	−1.59007	−0.795034	−	0.606565i	$-0.792547\pi$
$571$	−3.99773e114	−1.59007	−0.795034	+	0.606565i	$0.792547\pi$
$572$	4.49059e113	0.166099
$573$	3.28231e112	0.0112918
$574$	−2.65136e114	−0.848446
$575$	6.55557e114	1.95162
$576$	−3.99215e114	−1.10579
$577$	7.46950e114	1.92529	0.962644	−	0.270771i	$-0.0872787\pi$
$577$	7.46950e114	1.92529	0.962644	+	0.270771i	$0.0872787\pi$
$578$	1.39282e114	0.334111
$579$	3.15913e112	0.00705354
$580$	−1.69622e114	−0.352550
$581$	−5.09921e114	−0.986720
$582$	−2.15275e112	−0.00387874
$583$	6.13406e114	1.02921
$584$	3.31694e114	0.518327
$585$	−1.11816e115	−1.62756
$586$	−1.69957e114	−0.230456
$587$	2.67494e114	0.337935	0.168967	−	0.985622i	$-0.445957\pi$
$587$	2.67494e114	0.337935	0.168967	+	0.985622i	$0.445957\pi$
$588$	9.18428e110	0.000108115 0
$589$	3.53902e114	0.388238
$590$	−2.83202e114	−0.289560
$591$	3.23571e112	0.00308383
$592$	9.61399e113	0.0854187
$593$	2.44203e114	0.202293	0.101146	−	0.994872i	$-0.467749\pi$
$593$	2.44203e114	0.202293	0.101146	+	0.994872i	$0.467749\pi$
$594$	−2.29832e113	−0.0177530
$595$	−2.69824e115	−1.94369
$596$	−4.26472e114	−0.286530
$597$	2.39546e113	0.0150125
$598$	−1.44970e115	−0.847576
$599$	3.13804e115	1.71177	0.855884	−	0.517169i	$-0.173014\pi$
$599$	3.13804e115	1.71177	0.855884	+	0.517169i	$0.173014\pi$
$600$	−3.75500e113	−0.0191132
$601$	1.32290e115	0.628401	0.314201	−	0.949357i	$-0.398264\pi$
$601$	1.32290e115	0.628401	0.314201	+	0.949357i	$0.398264\pi$
$602$	2.06202e115	0.914195
$603$	−1.28156e115	−0.530362
$604$	6.25467e114	0.241641
$605$	−7.20698e114	−0.259959
$606$	−1.17633e113	−0.00396201
$607$	5.66673e115	1.78239	0.891193	−	0.453625i	$-0.149869\pi$
$607$	5.66673e115	1.78239	0.891193	+	0.453625i	$0.149869\pi$
$608$	6.10918e114	0.179467
$609$	−3.94613e113	−0.0108281
$610$	4.17474e114	0.107014
$611$	−7.37317e115	−1.76581
$612$	8.58045e114	0.192011
$613$	−6.68053e113	−0.0139702	−0.00698508	−	0.999976i	$-0.502223\pi$
$613$	−6.68053e113	−0.0139702	−0.00698508	+	0.999976i	$0.502223\pi$
$614$	2.37392e115	0.463957
$615$	8.25036e113	0.0150715
$616$	−6.43803e115	−1.09939
$617$	−8.04532e115	−1.28443	−0.642213	−	0.766526i	$-0.721983\pi$
$617$	−8.04532e115	−1.28443	−0.642213	+	0.766526i	$0.721983\pi$
$618$	7.49892e113	0.0111938
$619$	−1.06405e116	−1.48526	−0.742628	−	0.669704i	$-0.766421\pi$
$619$	−1.06405e116	−1.48526	−0.742628	+	0.669704i	$0.766421\pi$
$620$	1.52936e115	0.199644
$621$	−1.45904e114	−0.0178142
$622$	1.08502e116	1.23918
$623$	1.26216e116	1.34853
$624$	6.90137e113	0.00689882
$625$	1.01659e116	0.950875
$626$	−6.25164e115	−0.547217
$627$	6.54293e113	0.00536005
$628$	−3.19297e115	−0.244833
$629$	−1.71961e115	−0.123432
$630$	2.26254e116	1.52042
$631$	−1.48480e116	−0.934223	−0.467112	−	0.884198i	$-0.654705\pi$
$631$	−1.48480e116	−0.934223	−0.467112	+	0.884198i	$0.654705\pi$
$632$	3.51870e115	0.207311
$633$	3.72747e113	0.00205665
$634$	5.93984e115	0.306952
$635$	−2.72961e115	−0.132127
$636$	−3.14809e113	−0.00142750
$637$	1.61199e115	0.0684818
$638$	−3.05954e116	−1.21786
$639$	3.77877e116	1.40950
$640$	−3.38875e116	−1.18460
$641$	−4.44684e116	−1.45694	−0.728472	−	0.685075i	$-0.759769\pi$
$641$	−4.44684e116	−1.45694	−0.728472	+	0.685075i	$0.759769\pi$
$642$	−2.74610e114	−0.00843358
$643$	3.05679e116	0.880055	0.440028	−	0.897984i	$-0.354969\pi$
$643$	3.05679e116	0.880055	0.440028	+	0.897984i	$0.354969\pi$
$644$	−5.76836e115	−0.155700
$645$	−6.41650e114	−0.0162394
$646$	2.48449e116	0.589640
$647$	5.57523e116	1.24090	0.620448	−	0.784248i	$-0.286951\pi$
$647$	5.57523e116	1.24090	0.620448	+	0.784248i	$0.286951\pi$
$648$	−5.09741e116	−1.06411
$649$	1.00451e116	0.196697
$650$	−9.30182e116	−1.70869
$651$	3.55795e114	0.00613180
$652$	6.63843e115	0.107347
$653$	−7.87103e115	−0.119436	−0.0597179	−	0.998215i	$-0.519020\pi$
$653$	−7.87103e115	−0.119436	−0.0597179	+	0.998215i	$0.519020\pi$
$654$	3.99205e114	0.00568486
$655$	7.07232e116	0.945253
$656$	6.21253e116	0.779398
$657$	4.13464e116	0.486939
$658$	1.49192e117	1.64957
$659$	−1.10579e117	−1.14796	−0.573982	−	0.818868i	$-0.694602\pi$
$659$	−1.10579e117	−1.14796	−0.573982	+	0.818868i	$0.694602\pi$
$660$	2.82748e114	0.00275630
$661$	3.07841e116	0.281816	0.140908	−	0.990023i	$-0.454998\pi$
$661$	3.07841e116	0.281816	0.140908	+	0.990023i	$0.454998\pi$
$662$	−7.72565e116	−0.664245
$663$	−1.23442e115	−0.00996897
$664$	1.43763e117	1.09061
$665$	−1.28827e117	−0.918138
$666$	1.44194e116	0.0965530
$667$	−1.94229e117	−1.22206
$668$	−3.08009e116	−0.182113
$669$	2.75501e115	0.0153087
$670$	−1.60360e117	−0.837511
$671$	−1.48076e116	−0.0726945
$672$	6.14186e114	0.00283449
$673$	−7.72837e116	−0.335322	−0.167661	−	0.985845i	$-0.553621\pi$
$673$	−7.72837e116	−0.335322	−0.167661	+	0.985845i	$0.553621\pi$
$674$	9.47196e115	0.0386415
$675$	−9.36178e115	−0.0359130
$676$	5.10178e115	0.0184049
$677$	3.25149e116	0.110320	0.0551598	−	0.998478i	$-0.482433\pi$
$677$	3.25149e116	0.110320	0.0551598	+	0.998478i	$0.482433\pi$
$678$	3.65958e115	0.0116788
$679$	−1.50344e117	−0.451325
$680$	7.60717e117	2.14834
$681$	3.65133e115	0.00970164
$682$	2.75857e117	0.689657
$683$	8.11217e117	1.90844	0.954219	−	0.299109i	$-0.0966894\pi$
$683$	8.11217e117	1.90844	0.954219	+	0.299109i	$0.0966894\pi$
$684$	4.09672e116	0.0907001
$685$	−4.70647e117	−0.980701
$686$	−4.81451e117	−0.944280
$687$	−6.81085e114	−0.00125747
$688$	−4.83163e117	−0.839796
$689$	−5.52540e117	−0.904203
$690$	−9.12798e115	−0.0140649
$691$	1.05822e118	1.53546	0.767731	−	0.640772i	$-0.221386\pi$
$691$	1.05822e118	1.53546	0.767731	+	0.640772i	$0.221386\pi$
$692$	−1.10865e117	−0.151493
$693$	−8.02516e117	−1.03282
$694$	−1.41023e117	−0.170952
$695$	1.00145e118	1.14357
$696$	1.11254e116	0.0119683
$697$	−1.11121e118	−1.12625
$698$	−1.44849e118	−1.38329
$699$	−7.71590e115	−0.00694359
$700$	−3.70120e117	−0.313888
$701$	2.00349e118	1.60136	0.800682	−	0.599089i	$-0.204471\pi$
$701$	2.00349e118	1.60136	0.800682	+	0.599089i	$0.204471\pi$
$702$	2.07026e116	0.0155968
$703$	−8.21024e116	−0.0583055
$704$	1.77181e118	1.18619
$705$	−4.64249e116	−0.0293024
$706$	−6.42693e117	−0.382480
$707$	−8.21526e117	−0.461016
$708$	−5.15529e114	−0.000272818 0
$709$	−2.61333e118	−1.30429	−0.652147	−	0.758092i	$-0.726132\pi$
$709$	−2.61333e118	−1.30429	−0.652147	+	0.758092i	$0.726132\pi$
$710$	4.72830e118	2.22579
$711$	4.38614e117	0.194757
$712$	−3.55841e118	−1.49052
$713$	1.75123e118	0.692033
$714$	2.49778e116	0.00931274
$715$	4.96268e118	1.74589
$716$	−2.01691e117	−0.0669571
$717$	4.02981e116	0.0126252
$718$	−4.44094e117	−0.131314
$719$	−1.24902e118	−0.348595	−0.174297	−	0.984693i	$-0.555765\pi$
$719$	−1.24902e118	−0.348595	−0.174297	+	0.984693i	$0.555765\pi$
$720$	−5.30148e118	−1.39669
$721$	5.23709e118	1.30250
$722$	−2.70703e118	−0.635622
$723$	2.46414e116	0.00546295
$724$	7.27697e117	0.152335
$725$	−1.24625e119	−2.46364
$726$	6.67154e115	0.00124554
$727$	−2.35638e118	−0.415496	−0.207748	−	0.978182i	$-0.566613\pi$
$727$	−2.35638e118	−0.415496	−0.207748	+	0.978182i	$0.566613\pi$
$728$	5.79921e118	0.965866
$729$	−6.35300e118	−0.999508
$730$	5.17359e118	0.768941
$731$	8.64212e118	1.21353
$732$	7.59950e114	0.000100827 0
$733$	−3.47908e118	−0.436164	−0.218082	−	0.975930i	$-0.569980\pi$
$733$	−3.47908e118	−0.436164	−0.218082	+	0.975930i	$0.569980\pi$
$734$	−4.20741e118	−0.498457
$735$	1.01498e116	0.00113641
$736$	3.02303e118	0.319899
$737$	5.68790e118	0.568920
$738$	9.31775e118	0.880992
$739$	1.74800e119	1.56242	0.781208	−	0.624271i	$-0.214604\pi$
$739$	1.74800e119	1.56242	0.781208	+	0.624271i	$0.214604\pi$
$740$	−3.54800e117	−0.0299825
$741$	−5.89370e116	−0.00470904
$742$	1.11803e119	0.844682
$743$	−8.27979e118	−0.591539	−0.295770	−	0.955259i	$-0.595576\pi$
$743$	−8.27979e118	−0.591539	−0.295770	+	0.955259i	$0.595576\pi$
$744$	−1.00309e117	−0.00677743
$745$	−4.71307e119	−3.01174
$746$	4.18967e118	0.253232
$747$	1.79204e119	1.02457
$748$	−3.80822e118	−0.205971
$749$	−1.91782e119	−0.981322
$750$	−2.90412e117	−0.0140596
$751$	−9.64043e118	−0.441610	−0.220805	−	0.975318i	$-0.570868\pi$
$751$	−9.64043e118	−0.441610	−0.220805	+	0.975318i	$0.570868\pi$
$752$	−3.49580e119	−1.51533
$753$	7.14452e116	0.00293077
$754$	2.75596e119	1.06995
$755$	6.91222e119	2.53991
$756$	8.23760e116	0.00286514
$757$	−3.65676e119	−1.20397	−0.601987	−	0.798506i	$-0.705624\pi$
$757$	−3.65676e119	−1.20397	−0.601987	+	0.798506i	$0.705624\pi$
$758$	−4.10983e119	−1.28101
$759$	3.23766e117	0.00955428
$760$	3.63203e119	1.01481
$761$	−2.41198e119	−0.638131	−0.319065	−	0.947733i	$-0.603369\pi$
$761$	−2.41198e119	−0.638131	−0.319065	+	0.947733i	$0.603369\pi$
$762$	2.52681e116	0.000633055 0
$763$	2.78797e119	0.661484
$764$	−9.12126e118	−0.204965
$765$	9.48251e119	2.01825
$766$	2.84044e118	0.0572654
$767$	−9.04835e118	−0.172807
$768$	−2.39651e117	−0.00433599
$769$	1.02576e119	0.175835	0.0879173	−	0.996128i	$-0.471979\pi$
$769$	1.02576e119	0.175835	0.0879173	+	0.996128i	$0.471979\pi$
$770$	−1.00417e120	−1.63096
$771$	4.21242e117	0.00648299
$772$	−8.77896e118	−0.128034
$773$	4.24839e119	0.587186	0.293593	−	0.955931i	$-0.405149\pi$
$773$	4.24839e119	0.587186	0.293593	+	0.955931i	$0.405149\pi$
$774$	−7.24664e119	−0.949263
$775$	1.12365e120	1.39512
$776$	4.23866e119	0.498846
$777$	−8.25416e116	−0.000920874 0
$778$	−2.35171e119	−0.248731
$779$	−5.30543e119	−0.532006
$780$	−2.54692e117	−0.00242153
$781$	−1.67711e120	−1.51197
$782$	1.22941e120	1.05103
$783$	2.77372e118	0.0224879
$784$	7.64283e118	0.0587676
$785$	−3.52865e120	−2.57346
$786$	−6.54689e117	−0.00452897
$787$	7.24312e119	0.475307	0.237653	−	0.971350i	$-0.423622\pi$
$787$	7.24312e119	0.475307	0.237653	+	0.971350i	$0.423622\pi$
$788$	−8.99178e118	−0.0559768
$789$	1.34189e118	0.00792541
$790$	5.48828e119	0.307548
$791$	2.55577e120	1.35893
$792$	2.26254e120	1.14157
$793$	1.33383e119	0.0638652
$794$	−1.46649e119	−0.0666389
$795$	−3.47905e118	−0.0150046
$796$	−6.65677e119	−0.272503
$797$	−1.17327e120	−0.455907	−0.227953	−	0.973672i	$-0.573203\pi$
$797$	−1.17327e120	−0.455907	−0.227953	+	0.973672i	$0.573203\pi$
$798$	1.19256e118	0.00439906
$799$	6.25277e120	2.18968
$800$	1.93969e120	0.644909
$801$	−4.43565e120	−1.40026
$802$	2.14616e120	0.643319
$803$	−1.83505e120	−0.522341
$804$	−2.91911e117	−0.000789087 0
$805$	−6.37479e120	−1.63658
$806$	−2.48485e120	−0.605893
$807$	−2.73351e118	−0.00633095
$808$	2.31614e120	0.509557
$809$	3.84105e120	0.802760	0.401380	−	0.915912i	$-0.368531\pi$
$809$	3.84105e120	0.802760	0.401380	+	0.915912i	$0.368531\pi$
$810$	−7.95068e120	−1.57861
$811$	−8.55465e120	−1.61375	−0.806876	−	0.590721i	$-0.798844\pi$
$811$	−8.55465e120	−1.61375	−0.806876	+	0.590721i	$0.798844\pi$
$812$	1.09660e120	0.196550
$813$	−2.88612e118	−0.00491538
$814$	−6.39967e119	−0.103573
$815$	7.33633e120	1.12833
$816$	−5.85267e118	−0.00855485
$817$	4.12616e120	0.573232
$818$	7.10161e120	0.937766
$819$	7.22886e120	0.907377
$820$	−2.29271e120	−0.273573
$821$	3.26544e120	0.370426	0.185213	−	0.982698i	$-0.440703\pi$
$821$	3.26544e120	0.370426	0.185213	+	0.982698i	$0.440703\pi$
$822$	4.35681e118	0.00469881
$823$	−3.44213e120	−0.352967	−0.176484	−	0.984304i	$-0.556472\pi$
$823$	−3.44213e120	−0.352967	−0.176484	+	0.984304i	$0.556472\pi$
$824$	−1.47650e121	−1.43964
$825$	2.07741e119	0.0192612
$826$	1.83089e120	0.161432
$827$	1.90549e121	1.59782	0.798909	−	0.601452i	$-0.205411\pi$
$827$	1.90549e121	1.59782	0.798909	+	0.601452i	$0.205411\pi$
$828$	2.02720e120	0.161673
$829$	−1.36991e121	−1.03915	−0.519576	−	0.854424i	$-0.673910\pi$
$829$	−1.36991e121	−1.03915	−0.519576	+	0.854424i	$0.673910\pi$
$830$	2.24234e121	1.61793
$831$	1.49832e119	0.0102840
$832$	−1.59600e121	−1.04212
$833$	−1.36704e120	−0.0849205
$834$	−9.27053e118	−0.00547915
$835$	−3.40390e121	−1.91421
$836$	−1.81822e120	−0.0972942
$837$	−2.50087e119	−0.0127346
$838$	5.91255e120	0.286515
$839$	2.41826e121	1.11527	0.557636	−	0.830086i	$-0.311709\pi$
$839$	2.41826e121	1.11527	0.557636	+	0.830086i	$0.311709\pi$
$840$	3.65145e119	0.0160279
$841$	1.29890e121	0.542679
$842$	−2.23179e121	−0.887568
$843$	−3.94551e119	−0.0149368
$844$	−1.03583e120	−0.0373317
$845$	5.63814e120	0.193456
$846$	−5.24311e121	−1.71285
$847$	4.65927e120	0.144929
$848$	−2.61973e121	−0.775940
$849$	−2.03236e119	−0.00573234
$850$	7.88836e121	2.11885
$851$	−4.06271e120	−0.103930
$852$	8.60719e118	0.00209709
$853$	3.07435e120	0.0713459	0.0356730	−	0.999364i	$-0.488643\pi$
$853$	3.07435e120	0.0713459	0.0356730	+	0.999364i	$0.488643\pi$
$854$	−2.69894e120	−0.0596612
$855$	4.52741e121	0.953357
$856$	5.40692e121	1.08465
$857$	−8.75672e119	−0.0167355	−0.00836773	−	0.999965i	$-0.502664\pi$
$857$	−8.75672e119	−0.0167355	−0.00836773	+	0.999965i	$0.502664\pi$
$858$	−4.59398e119	−0.00836502
$859$	−1.97846e121	−0.343251	−0.171625	−	0.985162i	$-0.554902\pi$
$859$	−1.97846e121	−0.343251	−0.171625	+	0.985162i	$0.554902\pi$
$860$	1.78309e121	0.294773
$861$	−5.33381e119	−0.00840247
$862$	1.83870e121	0.276031
$863$	−3.76362e121	−0.538465	−0.269232	−	0.963075i	$-0.586770\pi$
$863$	−3.76362e121	−0.538465	−0.269232	+	0.963075i	$0.586770\pi$
$864$	−4.31709e119	−0.00588668
$865$	−1.22520e122	−1.59236
$866$	−2.81898e120	−0.0349220
$867$	2.80198e119	0.00330882
$868$	−9.88724e120	−0.111303
$869$	−1.94668e121	−0.208917
$870$	1.73528e120	0.0177550
$871$	−5.12351e121	−0.499821
$872$	−7.86014e121	−0.731133
$873$	5.28358e121	0.468638
$874$	5.86979e121	0.496476
$875$	−2.02818e122	−1.63596
$876$	9.41777e118	0.000724482 0
$877$	1.00737e122	0.739105	0.369552	−	0.929210i	$-0.379511\pi$
$877$	1.00737e122	0.739105	0.369552	+	0.929210i	$0.379511\pi$
$878$	−5.45822e120	−0.0381969
$879$	−3.41907e119	−0.00228228
$880$	2.35293e122	1.49823
$881$	2.51241e122	1.52612	0.763062	−	0.646325i	$-0.223695\pi$
$881$	2.51241e122	1.52612	0.763062	+	0.646325i	$0.223695\pi$
$882$	1.14630e121	0.0664279
$883$	9.72820e121	0.537853	0.268926	−	0.963161i	$-0.413331\pi$
$883$	9.72820e121	0.537853	0.268926	+	0.963161i	$0.413331\pi$
$884$	3.43034e121	0.180954
$885$	−5.69726e119	−0.00286761
$886$	7.56133e121	0.363161
$887$	−2.97595e122	−1.36394	−0.681970	−	0.731381i	$-0.738876\pi$
$887$	−2.97595e122	−1.36394	−0.681970	+	0.731381i	$0.738876\pi$
$888$	2.32710e119	0.00101783
$889$	1.76467e121	0.0736616
$890$	−5.55023e122	−2.21119
$891$	2.82008e122	1.07235
$892$	−7.65594e121	−0.277880
$893$	2.98537e122	1.03434
$894$	4.36291e120	0.0144301
$895$	−2.22895e122	−0.703792
$896$	2.19081e122	0.660422
$897$	−2.91640e120	−0.00839385
$898$	−4.02182e122	−1.10523
$899$	−3.32918e122	−0.873594
$900$	1.30073e122	0.325928
$901$	4.68578e122	1.12125
$902$	−4.13545e122	−0.945042
$903$	4.14823e120	0.00905360
$904$	−7.20551e122	−1.50202
$905$	8.04200e122	1.60121
$906$	−6.39869e120	−0.0121694
$907$	−8.58837e121	−0.156030	−0.0780150	−	0.996952i	$-0.524858\pi$
$907$	−8.58837e121	−0.156030	−0.0780150	+	0.996952i	$0.524858\pi$
$908$	−1.01467e122	−0.176102
$909$	2.88712e122	0.478700
$910$	9.04532e122	1.43287
$911$	−3.62747e122	−0.549023	−0.274512	−	0.961584i	$-0.588516\pi$
$911$	−3.62747e122	−0.549023	−0.274512	+	0.961584i	$0.588516\pi$
$912$	−2.79435e120	−0.00404105
$913$	−7.95349e122	−1.09906
$914$	6.63700e122	0.876405
$915$	8.39844e119	0.00105980
$916$	1.89268e121	0.0228252
$917$	−4.57221e122	−0.526986
$918$	−1.75568e121	−0.0193407
$919$	−3.38890e122	−0.356833	−0.178416	−	0.983955i	$-0.557097\pi$
$919$	−3.38890e122	−0.356833	−0.178416	+	0.983955i	$0.557097\pi$
$920$	1.79725e123	1.80890
$921$	4.77568e120	0.00459473
$922$	7.72220e122	0.710245
$923$	1.51070e123	1.32833
$924$	−1.82795e120	−0.00153666
$925$	−2.60679e122	−0.209519
$926$	−2.30898e123	−1.77446
$927$	−1.84049e123	−1.35246
$928$	−5.74695e122	−0.403828
$929$	−2.11304e122	−0.141989	−0.0709947	−	0.997477i	$-0.522617\pi$
$929$	−2.11304e122	−0.141989	−0.0709947	+	0.997477i	$0.522617\pi$
$930$	−1.56458e121	−0.0100544
$931$	−6.52689e121	−0.0401139
$932$	2.14419e122	0.126038
$933$	2.18276e121	0.0122721
$934$	1.46362e123	0.787103
$935$	−4.20857e123	−2.16498
$936$	−2.03804e123	−1.00292
$937$	1.71319e123	0.806513	0.403257	−	0.915087i	$-0.367878\pi$
$937$	1.71319e123	0.806513	0.403257	+	0.915087i	$0.367878\pi$
$938$	1.03672e123	0.466919
$939$	−1.25766e121	−0.00541928
$940$	1.29011e123	0.531889
$941$	4.90733e123	1.93587	0.967935	−	0.251201i	$-0.0808257\pi$
$941$	4.90733e123	1.93587	0.967935	+	0.251201i	$0.0808257\pi$
$942$	3.26649e121	0.0123302
$943$	−2.62531e123	−0.948299
$944$	−4.29004e122	−0.148294
$945$	9.10362e121	0.0301158
$946$	3.21624e123	1.01828
$947$	1.85840e123	0.563138	0.281569	−	0.959541i	$-0.409145\pi$
$947$	1.85840e123	0.563138	0.281569	+	0.959541i	$0.409145\pi$
$948$	9.99063e119	0.000289766 0
$949$	1.65297e123	0.458899
$950$	3.76628e123	1.00088
$951$	1.19494e121	0.00303986
$952$	−4.91799e123	−1.19772
$953$	6.53885e123	1.52456	0.762282	−	0.647245i	$-0.224079\pi$
$953$	6.53885e123	1.52456	0.762282	+	0.647245i	$0.224079\pi$
$954$	−3.92915e123	−0.877083
$955$	−1.00802e124	−2.15441
$956$	−1.11985e123	−0.229170
$957$	−6.15498e121	−0.0120609
$958$	−5.76456e123	−1.08168
$959$	3.04271e123	0.546749
$960$	−1.00492e122	−0.0172932
$961$	−3.06597e123	−0.505298
$962$	5.76466e122	0.0909930
$963$	6.73985e123	1.01897
$964$	−6.84765e122	−0.0991619
$965$	−9.70190e123	−1.34578
$966$	5.90119e121	0.00784131
$967$	1.22446e124	1.55864	0.779322	−	0.626623i	$-0.215563\pi$
$967$	1.22446e124	1.55864	0.779322	+	0.626623i	$0.215563\pi$
$968$	−1.31359e123	−0.160189
$969$	4.99811e121	0.00583942
$970$	6.61124e123	0.740041
$971$	−9.61810e123	−1.03155	−0.515776	−	0.856723i	$-0.672496\pi$
$971$	−9.61810e123	−1.03155	−0.515776	+	0.856723i	$0.672496\pi$
$972$	−4.34251e121	−0.00446263
$973$	−6.47435e123	−0.637548
$974$	6.57268e123	0.620220
$975$	−1.87128e122	−0.0169218
$976$	6.32403e122	0.0548058
$977$	1.28605e124	1.06815	0.534077	−	0.845436i	$-0.320659\pi$
$977$	1.28605e124	1.06815	0.534077	+	0.845436i	$0.320659\pi$
$978$	−6.79129e121	−0.00540617
$979$	1.96865e124	1.50206
$980$	−2.82055e122	−0.0206278
$981$	−9.79786e123	−0.686858
$982$	−1.45658e124	−0.978829
$983$	1.04024e124	0.670138	0.335069	−	0.942194i	$-0.391240\pi$
$983$	1.04024e124	0.670138	0.335069	+	0.942194i	$0.391240\pi$
$984$	1.50377e122	0.00928718
$985$	−9.93709e123	−0.588377
$986$	−2.33717e124	−1.32678
$987$	3.00134e122	0.0163363
$988$	1.63781e123	0.0854772
$989$	2.04177e124	1.02179
$990$	3.52900e124	1.69352
$991$	7.19139e123	0.330945	0.165473	−	0.986214i	$-0.447085\pi$
$991$	7.19139e123	0.330945	0.165473	+	0.986214i	$0.447085\pi$
$992$	5.18161e123	0.228681
$993$	−1.55419e122	−0.00657826
$994$	−3.05682e124	−1.24089
$995$	−7.35660e124	−2.86430
$996$	4.08185e121	0.00152438
$997$	−1.21141e124	−0.433953	−0.216976	−	0.976177i	$-0.569619\pi$
$997$	−1.21141e124	−0.433953	−0.216976	+	0.976177i	$0.569619\pi$
$998$	−8.48902e123	−0.291703
$999$	5.80181e121	0.00191248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.84.a.a.1.6	✓	7
3.2	odd	2		9.84.a.c.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.84.a.a.1.6	✓	7	1.1	even	1	trivial
9.84.a.c.1.2		7	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:	\( k \)	\(=\)	\( 84 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.84290e12 q^{2} +5.71915e17 q^{3} -1.58931e24 q^{4} -1.75639e29 q^{5} +1.62590e30 q^{6} +1.13550e35 q^{7} -3.20131e37 q^{8} -3.99051e39 q^{9} +O(q^{10})\)	\(q+2.84290e12 q^{2} +5.71915e17 q^{3} -1.58931e24 q^{4} -1.75639e29 q^{5} +1.62590e30 q^{6} +1.13550e35 q^{7} -3.20131e37 q^{8} -3.99051e39 q^{9} -4.99324e41 q^{10} +1.77109e43 q^{11} -9.08948e41 q^{12} -1.59535e46 q^{13} +3.22810e47 q^{14} -1.00451e47 q^{15} -7.56394e49 q^{16} +1.35293e51 q^{17} -1.13446e52 q^{18} +6.45952e52 q^{19} +2.79144e53 q^{20} +6.49407e52 q^{21} +5.03503e55 q^{22} +3.19639e56 q^{23} -1.83088e55 q^{24} +2.05093e58 q^{25} -4.53542e58 q^{26} -4.56466e57 q^{27} -1.80465e59 q^{28} -6.07652e60 q^{29} -2.85571e59 q^{30} +5.47876e61 q^{31} +9.45764e61 q^{32} +1.01291e61 q^{33} +3.84624e63 q^{34} -1.99437e64 q^{35} +6.34214e63 q^{36} -1.27103e64 q^{37} +1.83638e65 q^{38} -9.12405e63 q^{39} +5.62275e66 q^{40} -8.21335e66 q^{41} +1.84620e65 q^{42} +6.38772e67 q^{43} -2.81480e67 q^{44} +7.00889e68 q^{45} +9.08704e68 q^{46} +4.62167e69 q^{47} -4.32593e67 q^{48} -1.01043e69 q^{49} +5.83059e70 q^{50} +7.73759e68 q^{51} +2.53550e70 q^{52} +3.46344e71 q^{53} -1.29769e70 q^{54} -3.11072e72 q^{55} -3.63507e72 q^{56} +3.69430e70 q^{57} -1.72750e73 q^{58} +5.67171e72 q^{59} +1.59647e71 q^{60} -8.36077e72 q^{61} +1.55756e74 q^{62} -4.53121e74 q^{63} +1.00041e75 q^{64} +2.80205e75 q^{65} +2.87961e73 q^{66} +3.21153e75 q^{67} -2.15021e75 q^{68} +1.82807e74 q^{69} -5.66981e76 q^{70} -9.46939e76 q^{71} +1.27749e77 q^{72} -1.03612e77 q^{73} -3.61341e76 q^{74} +1.17296e76 q^{75} -1.02661e77 q^{76} +2.01106e78 q^{77} -2.59388e76 q^{78} -1.09914e78 q^{79} +1.32852e79 q^{80} +1.59229e79 q^{81} -2.33498e79 q^{82} -4.49074e79 q^{83} -1.03211e77 q^{84} -2.37627e80 q^{85} +1.81597e80 q^{86} -3.47525e78 q^{87} -5.66980e80 q^{88} +1.11155e81 q^{89} +1.99256e81 q^{90} -1.81151e81 q^{91} -5.08004e80 q^{92} +3.13339e79 q^{93} +1.31390e82 q^{94} -1.13454e82 q^{95} +5.40897e79 q^{96} -1.32404e82 q^{97} -2.87255e81 q^{98} -7.06754e82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) \) 7 * q + 347450761416 * q^2 + 92768992732348371972 * q^3 + 35584105659089895299423296 * q^4 + 95882188896595936852480961970 * q^5 - 294670844093053176615850490328096 * q^6 + 41935337227745505345382734191463656 * q^7 - 53166432471809997748387310040100892160 * q^8 + 7173898769720313141925302496494258063219 * q^9	\( 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) 7 * q + 347450761416 * q^2 + 92768992732348371972 * q^3 + 35584105659089895299423296 * q^4 + 95882188896595936852480961970 * q^5 - 294670844093053176615850490328096 * q^6 + 41935337227745505345382734191463656 * q^7 - 53166432471809997748387310040100892160 * q^8 + 7173898769720313141925302496494258063219 * q^9 + 499744956856868951374871513628825303339120 * q^10 + 25877323689250927756216798585844787377793324 * q^11 + 2460442604910297198073551343877297856954713856 * q^12 + 17524422091988534325290637412825903296133795802 * q^13 - 667010599912297808117771255707130466716823613248 * q^14 + 495579388338965458292669248844531863255635208440 * q^15 + 417715742702857603748591276714238800242071723446272 * q^16 - 184492474792188340305787588512947709279311819300514 * q^17 - 28009030626032697117218836919123347961714662935963288 * q^18 + 70057685614612811247361635516613863476112345065711060 * q^19 - 57482583811152041858646735327362480085743726726490240 * q^20 + 1893373789164274184370249913565768587140340046764631904 * q^21 - 25459319566814701232336844310162548331034505268300277088 * q^22 + 824652389276591600045965278715869924572765810514596651832 * q^23 - 5108864246496902395549780448291862586480869954908681963520 * q^24 - 4561105897018180667341222610450479407531682079908284920975 * q^25 + 143121440625749988679618714232562854015797139977713783396144 * q^26 - 18306643512253151650162937588580319544032012511255116569240 * q^27 - 3306103780131881005943201423297958381438351892797060269926912 * q^28 + 6404767822227693446699906276316651921336727974067299509413290 * q^29 + 22115840914712862507238627077766882327252015550247576205746240 * q^30 - 37562467055768426209216291610175403000420584080976492348271456 * q^31 - 401973234215497826032118057547245647414044862108632758037479424 * q^32 + 2195918275671465028132881460796250927450387208449702006682532304 * q^33 - 3642106474236630222613516547778797986245715334909676776624068848 * q^34 - 2073208087472515985799712205841339482184218515995426084627529680 * q^35 + 57130418054952308452673267072095667495060459086592800380434471232 * q^36 + 11679830828485560240095590717771086910057022640967690418168414546 * q^37 - 100824829831783953690862886156130827794285762670109921453507515040 * q^38 + 1565953334461766292518881964176162886481814613037624778927724614488 * q^39 + 9486127421786581581058527875045788297835153320557141731458486656000 * q^40 + 17401669041790147490033877534513313327467761516699357985702287340054 * q^41 + 44973533593538917012168170148121446253249051280516070217105265222912 * q^42 + 155423693656840999526303865174514513948712784929597322758540542988492 * q^43 + 1348607485575405225144018262718175988997396446813103620526566114774272 * q^44 + 1880339750988019909779230148989197482912024900416496550280550343305690 * q^45 + 5506219190262487958701836671526521132048107774881360169694419306565184 * q^46 + 11104141751597135653133375816819520459474802577748272571942549885601776 * q^47 + 68535772806187659604752521040191262704244920099270422943498591509266432 * q^48 + 48858841649181147950169676419361972612175619458033829843989473166294751 * q^49 + 150128830200294018241623574757370340046061702636780234316678381973441400 * q^50 + 285323979437882241696128479102133404321665278074017384721958077373999304 * q^51 + 287156729453525056399055611675371787971339735611155780289523821420813696 * q^52 + 273161075599979193637636426681909962095058697602986681290913238279577122 * q^53 - 3035335179479589317975420635665461716944398657720830329060859634436191040 * q^54 - 5713148801806043865831522329085397613042534865163593217346624944021935960 * q^55 - 16548372571630294224019812720652384540821878073420179539137646605391810560 * q^56 - 34025570556802197911899195289016333635970214164767521145341412678086153680 * q^57 - 107856312851606062726720906610847944794517184506982834438591381099782874960 * q^58 - 23387662928216230581473943437005284343365902946251051301830585313805483620 * q^59 - 111426487760354848959531561221427047757146965306130391339788819029760724480 * q^60 + 174496853895103215296232800034629055024308568422892345549894754405198022474 * q^61 + 202911123959081503237789686733196890455024356155124318865846118460223535872 * q^62 + 1452472272578781819866280021221104701255297870249157972403070846844413328392 * q^63 + 6634340238508315566899158004225714692716612285250446595132287614710135914496 * q^64 + 7847697320266417932918441445560149353782900722209245969738521432028132712140 * q^65 + 5853477037889002409213418366788233179355537994202667769768656686338545312128 * q^66 + 4207870282072288819930283375229384131272485602664611977572129464006258765636 * q^67 - 2096504738666940955442779681368953687199581458034579489652465446528751795072 * q^68 - 20650746275200221772316139734189903533557652468456540358959577322030289931232 * q^69 - 145036588586277913982945740577079817793279246661749211931215600391874230481280 * q^70 - 255182116774353604409687783436303274428169526091219223291653972862797742675416 * q^71 - 870484407164078464103908172424456244246778900599455841998985045216713192261120 * q^72 - 305241553076526275791215297716487992856779743869787675846354786221090205747018 * q^73 + 519509459878782742271675046603917029597958567555546598174683109762008202679152 * q^74 - 108583349872086845300331949191600832920703338562329517576945108262256298985700 * q^75 + 3101616184715813078617408724804325452068973943873193050543089493292892226548480 * q^76 + 1968650017033252100145732463322846835178370212948913842977898825590858174818592 * q^77 + 21491900853406375307008391073223804676382414550199027500027607363780886431018304 * q^78 + 23447929932751548600263104762346056717107337920041167505701244565861009558020240 * q^79 + 17204514340446283418245025220202850902483487721576269901420959588660341138513920 * q^80 - 17753472117770960614378485370145730323852918650183577857034614500242589049352193 * q^81 - 31321993453816460140947801899215524216330716054375524262202008548706253113923248 * q^82 - 46082240797638648794744046457142731881250364210725285467604380362957138908759788 * q^83 - 396393323116531601318524278804366279023581302275903129719352432561583858694821888 * q^84 - 401284317909890185403267950222575247116869569644274198011711052575121501243134780 * q^85 - 845015265474066730430458068700259496114668382925856143568777375852322405810455136 * q^86 + 197750077894055178387517630023128464093882005300943753470627738978951228120838680 * q^87 + 324839816772448825066522872810525224209456499759931184227996411794156773784954880 * q^88 + 1029637925134517055127146751141931889566726599138062764000004109807115136117713670 * q^89 + 4141656580530762388567221011089632154433218135474509214945004172382456820926056240 * q^90 + 3803613049700949766857757374276498806030165436480764134599260004867484942314191344 * q^91 + 18037274986000955133271893922579105966324228705045824551878800657480298511213339136 * q^92 + 8685070641618931882536832652301281283748648395097048916956355973218904558772746624 * q^93 + 14309873718219401549749953357716417680483939380577663052969981365204963308304666752 * q^94 - 14391746226057476549769154981667785050800156202045812612412525445443768991871289000 * q^95 - 108145031724537483365505988938774635887900203900416762648300829840839318527629459456 * q^96 - 74638965785790533754670961742172384288953081898163477046944786055599953393772909074 * q^97 - 18956661788073492574129772794522396713191224901923159738123453486226051877064977912 * q^98 - 186867222990833548593390820999966230195685717791503334320194774977997201493521400292 * q^99

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