LMFDB - Embedded newform 1.84.a.a.1.4

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			1.4
Root			$2.25782e10$ 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)

$f(q)$	$=$	$q+5.91512e11 q^{2} +9.95960e19 q^{3} -9.32152e24 q^{4} +1.29632e29 q^{5} +5.89123e31 q^{6} +1.88228e35 q^{7} -1.12345e37 q^{8} +5.92853e39 q^{9} +O(q^{10})$	\(q+5.91512e11 q^{2} +9.95960e19 q^{3} -9.32152e24 q^{4} +1.29632e29 q^{5} +5.89123e31 q^{6} +1.88228e35 q^{7} -1.12345e37 q^{8} +5.92853e39 q^{9} +7.66792e40 q^{10} -1.53986e43 q^{11} -9.28386e44 q^{12} +2.07012e46 q^{13} +1.11339e47 q^{14} +1.29109e49 q^{15} +8.35068e49 q^{16} +6.28617e50 q^{17} +3.50680e51 q^{18} -1.57680e53 q^{19} -1.20837e54 q^{20} +1.87467e55 q^{21} -9.10848e54 q^{22} -6.31544e55 q^{23} -1.11892e57 q^{24} +6.46483e57 q^{25} +1.22450e58 q^{26} +1.92986e59 q^{27} -1.75457e60 q^{28} +1.01915e59 q^{29} +7.63694e60 q^{30} +2.53808e61 q^{31} +1.58049e62 q^{32} -1.53364e63 q^{33} +3.71835e62 q^{34} +2.44004e64 q^{35} -5.52629e64 q^{36} -3.48983e64 q^{37} -9.32694e64 q^{38} +2.06176e66 q^{39} -1.45636e66 q^{40} +2.65816e65 q^{41} +1.10889e67 q^{42} +1.23906e67 q^{43} +1.43539e68 q^{44} +7.68530e68 q^{45} -3.73566e67 q^{46} +1.13865e69 q^{47} +8.31695e69 q^{48} +2.15257e70 q^{49} +3.82402e69 q^{50} +6.26078e70 q^{51} -1.92967e71 q^{52} +4.75692e71 q^{53} +1.14154e71 q^{54} -1.99616e72 q^{55} -2.11465e72 q^{56} -1.57043e73 q^{57} +6.02841e70 q^{58} +5.56534e73 q^{59} -1.20349e74 q^{60} -5.06207e73 q^{61} +1.50131e73 q^{62} +1.11591e75 q^{63} -7.14141e74 q^{64} +2.68355e75 q^{65} -9.07168e74 q^{66} +4.03675e75 q^{67} -5.85967e75 q^{68} -6.28993e75 q^{69} +1.44331e76 q^{70} -9.07289e76 q^{71} -6.66043e76 q^{72} -1.82421e77 q^{73} -2.06427e76 q^{74} +6.43871e77 q^{75} +1.46981e78 q^{76} -2.89845e78 q^{77} +1.21955e78 q^{78} +6.07683e78 q^{79} +1.08252e79 q^{80} -4.43916e78 q^{81} +1.57233e77 q^{82} -1.68264e79 q^{83} -1.74748e80 q^{84} +8.14892e79 q^{85} +7.32918e78 q^{86} +1.01503e79 q^{87} +1.72997e80 q^{88} -1.03901e81 q^{89} +4.54595e80 q^{90} +3.89654e81 q^{91} +5.88695e80 q^{92} +2.52783e81 q^{93} +6.73526e80 q^{94} -2.04404e82 q^{95} +1.57411e82 q^{96} -1.40939e82 q^{97} +1.27327e82 q^{98} -9.12912e82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.91512e11	0.190204	0.0951018	−	0.995468i	$-0.469682\pi$
$2$	5.91512e11	0.190204	0.0951018	+	0.995468i	$0.469682\pi$
$3$	9.95960e19	1.57656	0.788279	−	0.615318i	$-0.210972\pi$
$3$	9.95960e19	1.57656	0.788279	+	0.615318i	$0.210972\pi$
$4$	−9.32152e24	−0.963823
$5$	1.29632e29	1.27485	0.637424	−	0.770513i	$-0.280000\pi$
$5$	1.29632e29	1.27485	0.637424	+	0.770513i	$0.280000\pi$
$6$	5.89123e31	0.299867
$7$	1.88228e35	1.59630	0.798150	−	0.602458i	$-0.205812\pi$
$7$	1.88228e35	1.59630	0.798150	+	0.602458i	$0.205812\pi$
$8$	−1.12345e37	−0.373526
$9$	5.92853e39	1.48553
$10$	7.66792e40	0.242481
$11$	−1.53986e43	−0.932579	−0.466289	−	0.884632i	$-0.654409\pi$
$11$	−1.53986e43	−0.932579	−0.466289	+	0.884632i	$0.654409\pi$
$12$	−9.28386e44	−1.51952
$13$	2.07012e46	1.22277	0.611387	−	0.791332i	$-0.290612\pi$
$13$	2.07012e46	1.22277	0.611387	+	0.791332i	$0.290612\pi$
$14$	1.11339e47	0.303622
$15$	1.29109e49	2.00987
$16$	8.35068e49	0.892776
$17$	6.28617e50	0.542945	0.271473	−	0.962446i	$-0.412489\pi$
$17$	6.28617e50	0.542945	0.271473	+	0.962446i	$0.412489\pi$
$18$	3.50680e51	0.282554
$19$	−1.57680e53	−1.34741	−0.673707	−	0.738998i	$-0.735299\pi$
$19$	−1.57680e53	−1.34741	−0.673707	+	0.738998i	$0.735299\pi$
$20$	−1.20837e54	−1.22873
$21$	1.87467e55	2.51666
$22$	−9.10848e54	−0.177380
$23$	−6.31544e55	−0.194401	−0.0972006	−	0.995265i	$-0.530989\pi$
$23$	−6.31544e55	−0.194401	−0.0972006	+	0.995265i	$0.530989\pi$
$24$	−1.11892e57	−0.588886
$25$	6.46483e57	0.625240
$26$	1.22450e58	0.232576
$27$	1.92986e59	0.765472
$28$	−1.75457e60	−1.53855
$29$	1.01915e59	0.0208316	0.0104158	−	0.999946i	$-0.496684\pi$
$29$	1.01915e59	0.0208316	0.0104158	+	0.999946i	$0.496684\pi$
$30$	7.63694e60	0.382285
$31$	2.53808e61	0.325833	0.162917	−	0.986640i	$-0.447910\pi$
$31$	2.53808e61	0.325833	0.162917	+	0.986640i	$0.447910\pi$
$32$	1.58049e62	0.543336
$33$	−1.53364e63	−1.47026
$34$	3.71835e62	0.103270
$35$	2.44004e64	2.03504
$36$	−5.52629e64	−1.43179
$37$	−3.48983e64	−0.290023	−0.145011	−	0.989430i	$-0.546322\pi$
$37$	−3.48983e64	−0.290023	−0.145011	+	0.989430i	$0.546322\pi$
$38$	−9.32694e64	−0.256283
$39$	2.06176e66	1.92777
$40$	−1.45636e66	−0.476190
$41$	2.65816e65	0.0311926	0.0155963	−	0.999878i	$-0.495035\pi$
$41$	2.65816e65	0.0311926	0.0155963	+	0.999878i	$0.495035\pi$
$42$	1.10889e67	0.478678
$43$	1.23906e67	0.201442	0.100721	−	0.994915i	$-0.467885\pi$
$43$	1.23906e67	0.201442	0.100721	+	0.994915i	$0.467885\pi$
$44$	1.43539e68	0.898840
$45$	7.68530e68	1.89383
$46$	−3.73566e67	−0.0369758
$47$	1.13865e69	0.461668	0.230834	−	0.972993i	$-0.425855\pi$
$47$	1.13865e69	0.461668	0.230834	+	0.972993i	$0.425855\pi$
$48$	8.31695e69	1.40751
$49$	2.15257e70	1.54818
$50$	3.82402e69	0.118923
$51$	6.26078e70	0.855985
$52$	−1.92967e71	−1.17854
$53$	4.75692e71	1.31789	0.658943	−	0.752193i	$-0.271004\pi$
$53$	4.75692e71	1.31789	0.658943	+	0.752193i	$0.271004\pi$
$54$	1.14154e71	0.145596
$55$	−1.99616e72	−1.18890
$56$	−2.11465e72	−0.596260
$57$	−1.57043e73	−2.12428
$58$	6.02841e70	0.00396224
$59$	5.56534e73	1.79942	0.899711	−	0.436486i	$-0.143777\pi$
$59$	5.56534e73	1.79942	0.899711	+	0.436486i	$0.143777\pi$
$60$	−1.20349e74	−1.93716
$61$	−5.06207e73	−0.410337	−0.205168	−	0.978727i	$-0.565774\pi$
$61$	−5.06207e73	−0.410337	−0.205168	+	0.978727i	$0.565774\pi$
$62$	1.50131e73	0.0619747
$63$	1.11591e75	2.37136
$64$	−7.14141e74	−0.789432
$65$	2.68355e75	1.55885
$66$	−9.07168e74	−0.279650
$67$	4.03675e75	0.666695	0.333348	−	0.942804i	$-0.391822\pi$
$67$	4.03675e75	0.666695	0.333348	+	0.942804i	$0.391822\pi$
$68$	−5.85967e75	−0.523303
$69$	−6.28993e75	−0.306485
$70$	1.44331e76	0.387073
$71$	−9.07289e76	−1.35059	−0.675296	−	0.737547i	$-0.735984\pi$
$71$	−9.07289e76	−1.35059	−0.675296	+	0.737547i	$0.735984\pi$
$72$	−6.66043e76	−0.554886
$73$	−1.82421e77	−0.857383	−0.428692	−	0.903451i	$-0.641025\pi$
$73$	−1.82421e77	−0.857383	−0.428692	+	0.903451i	$0.641025\pi$
$74$	−2.06427e76	−0.0551634
$75$	6.43871e77	0.985726
$76$	1.46981e78	1.29867
$77$	−2.89845e78	−1.48868
$78$	1.21955e78	0.366670
$79$	6.07683e78	1.07684	0.538422	−	0.842675i	$-0.319021\pi$
$79$	6.07683e78	1.07684	0.538422	+	0.842675i	$0.319021\pi$
$80$	1.08252e79	1.13816
$81$	−4.43916e78	−0.278723
$82$	1.57233e77	0.00593294
$83$	−1.68264e79	−0.383929	−0.191964	−	0.981402i	$-0.561486\pi$
$83$	−1.68264e79	−0.383929	−0.191964	+	0.981402i	$0.561486\pi$
$84$	−1.74748e80	−2.42561
$85$	8.14892e79	0.692173
$86$	7.32918e78	0.0383151
$87$	1.01503e79	0.0328422
$88$	1.72997e80	0.348343
$89$	−1.03901e81	−1.30898	−0.654489	−	0.756071i	$-0.727116\pi$
$89$	−1.03901e81	−1.30898	−0.654489	+	0.756071i	$0.727116\pi$
$90$	4.54595e80	0.360214
$91$	3.89654e81	1.95191
$92$	5.88695e80	0.187368
$93$	2.52783e81	0.513695
$94$	6.73526e80	0.0878109
$95$	−2.04404e82	−1.71775
$96$	1.57411e82	0.856600
$97$	−1.40939e82	−0.498891	−0.249446	−	0.968389i	$-0.580248\pi$
$97$	−1.40939e82	−0.498891	−0.249446	+	0.968389i	$0.580248\pi$
$98$	1.27327e82	0.294469
$99$	−9.12912e82	−1.38538
$100$	−6.02620e82	−0.602620
$101$	1.22890e83	0.813165	0.406582	−	0.913614i	$-0.366720\pi$
$101$	1.22890e83	0.813165	0.406582	+	0.913614i	$0.366720\pi$
$102$	3.70333e82	0.162811
$103$	−1.19195e83	−0.349554	−0.174777	−	0.984608i	$-0.555920\pi$
$103$	−1.19195e83	−0.349554	−0.174777	+	0.984608i	$0.555920\pi$
$104$	−2.32568e83	−0.456738
$105$	2.43018e84	3.20836
$106$	2.81378e83	0.250667
$107$	−1.87371e84	−1.13051	−0.565257	−	0.824915i	$-0.691223\pi$
$107$	−1.87371e84	−1.13051	−0.565257	+	0.824915i	$0.691223\pi$
$108$	−1.79892e84	−0.737779
$109$	1.18472e83	0.0331447	0.0165724	−	0.999863i	$-0.494725\pi$
$109$	1.18472e83	0.0331447	0.0165724	+	0.999863i	$0.494725\pi$
$110$	−1.18075e84	−0.226133
$111$	−3.47573e84	−0.457238
$112$	1.57183e85	1.42514
$113$	−2.95724e85	−1.85409	−0.927047	−	0.374944i	$-0.877662\pi$
$113$	−2.95724e85	−1.85409	−0.927047	+	0.374944i	$0.877662\pi$
$114$	−9.28926e84	−0.404045
$115$	−8.18687e84	−0.247832
$116$	−9.50004e83	−0.0200779
$117$	1.22728e86	1.81647
$118$	3.29196e85	0.342257
$119$	1.18323e86	0.866704
$120$	−1.45048e86	−0.750740
$121$	−3.55244e85	−0.130297
$122$	−2.99428e85	−0.0780476
$123$	2.64742e85	0.0491769
$124$	−2.36588e86	−0.314046
$125$	−5.02317e86	−0.477763
$126$	6.60076e86	0.451041
$127$	−2.69273e87	−1.32537	−0.662686	−	0.748898i	$-0.730584\pi$
$127$	−2.69273e87	−1.32537	−0.662686	+	0.748898i	$0.730584\pi$
$128$	−1.95098e87	−0.693489
$129$	1.23405e87	0.317585
$130$	1.58735e87	0.296499
$131$	1.39054e88	1.88984	0.944918	−	0.327308i	$-0.106142\pi$
$131$	1.39054e88	1.88984	0.944918	+	0.327308i	$0.106142\pi$
$132$	1.42959e88	1.41707
$133$	−2.96797e88	−2.15088
$134$	2.38779e87	0.126808
$135$	2.50173e88	0.975862
$136$	−7.06223e87	−0.202804
$137$	−3.48762e88	−0.738968	−0.369484	−	0.929237i	$-0.620466\pi$
$137$	−3.48762e88	−0.738968	−0.369484	+	0.929237i	$0.620466\pi$
$138$	−3.72057e87	−0.0582945
$139$	5.86430e88	0.680930	0.340465	−	0.940257i	$-0.389416\pi$
$139$	5.86430e88	0.680930	0.340465	+	0.940257i	$0.389416\pi$
$140$	−2.27449e89	−1.96142
$141$	1.13405e89	0.727846
$142$	−5.36673e88	−0.256888
$143$	−3.18770e89	−1.14033
$144$	4.95072e89	1.32625
$145$	1.32115e88	0.0265571
$146$	−1.07904e89	−0.163077
$147$	2.14388e90	2.44079
$148$	3.25305e89	0.279531
$149$	−1.84246e90	−1.19720	−0.598602	−	0.801047i	$-0.704277\pi$
$149$	−1.84246e90	−1.19720	−0.598602	+	0.801047i	$0.704277\pi$
$150$	3.80858e89	0.187489
$151$	−5.05977e90	−1.89055	−0.945274	−	0.326277i	$-0.894206\pi$
$151$	−5.05977e90	−1.89055	−0.945274	+	0.326277i	$0.894206\pi$
$152$	1.77146e90	0.503295
$153$	3.72677e90	0.806564
$154$	−1.71447e90	−0.283152
$155$	3.29018e90	0.415388
$156$	−1.92187e91	−1.85803
$157$	−1.24523e91	−0.923449	−0.461724	−	0.887023i	$-0.652769\pi$
$157$	−1.24523e91	−0.923449	−0.461724	+	0.887023i	$0.652769\pi$
$158$	3.59452e90	0.204820
$159$	4.73771e91	2.07772
$160$	2.04883e91	0.692671
$161$	−1.18874e91	−0.310323
$162$	−2.62582e90	−0.0530141
$163$	7.44217e91	1.16390	0.581948	−	0.813226i	$-0.302291\pi$
$163$	7.44217e91	1.16390	0.581948	+	0.813226i	$0.302291\pi$
$164$	−2.47781e90	−0.0300641
$165$	−1.98810e92	−1.87436
$166$	−9.95303e90	−0.0730247
$167$	1.95454e92	1.11766	0.558832	−	0.829281i	$-0.311249\pi$
$167$	1.95454e92	1.11766	0.558832	+	0.829281i	$0.311249\pi$
$168$	−2.10611e92	−0.940039
$169$	1.41925e92	0.495176
$170$	4.82019e91	0.131654
$171$	−9.34808e92	−2.00163
$172$	−1.15499e92	−0.194155
$173$	6.54546e92	0.865022	0.432511	−	0.901629i	$-0.357628\pi$
$173$	6.54546e92	0.865022	0.432511	+	0.901629i	$0.357628\pi$
$174$	6.00405e90	0.00624670
$175$	1.21686e93	0.998071
$176$	−1.28589e93	−0.832584
$177$	5.54285e93	2.83689
$178$	−6.14584e92	−0.248973
$179$	−7.33190e92	−0.235405	−0.117702	−	0.993049i	$-0.537553\pi$
$179$	−7.33190e92	−0.235405	−0.117702	+	0.993049i	$0.537553\pi$
$180$	−7.16386e93	−1.82532
$181$	1.13855e93	0.230511	0.115256	−	0.993336i	$-0.463231\pi$
$181$	1.13855e93	0.230511	0.115256	+	0.993336i	$0.463231\pi$
$182$	2.30485e93	0.371261
$183$	−5.04162e93	−0.646920
$184$	7.09512e92	0.0726139
$185$	−4.52395e93	−0.369735
$186$	1.49524e93	0.0977067
$187$	−9.67984e93	−0.506339
$188$	−1.06140e94	−0.444966
$189$	3.63253e94	1.22192
$190$	−1.20908e94	−0.326722
$191$	4.99940e94	1.08651	0.543254	−	0.839568i	$-0.317192\pi$
$191$	4.99940e94	1.08651	0.543254	+	0.839568i	$0.317192\pi$
$192$	−7.11255e94	−1.24459
$193$	9.30186e94	1.31202	0.656011	−	0.754751i	$-0.272242\pi$
$193$	9.30186e94	1.31202	0.656011	+	0.754751i	$0.272242\pi$
$194$	−8.33674e93	−0.0948909
$195$	2.67271e95	2.45762
$196$	−2.00652e95	−1.49217
$197$	−2.51456e95	−1.51396	−0.756978	−	0.653440i	$-0.773325\pi$
$197$	−2.51456e95	−1.51396	−0.756978	+	0.653440i	$0.773325\pi$
$198$	−5.39998e94	−0.263504
$199$	−1.93622e95	−0.766572	−0.383286	−	0.923630i	$-0.625208\pi$
$199$	−1.93622e95	−0.766572	−0.383286	+	0.923630i	$0.625208\pi$
$200$	−7.26294e94	−0.233543
$201$	4.02044e95	1.05108
$202$	7.26908e94	0.154667
$203$	1.91833e94	0.0332535
$204$	−5.83600e95	−0.825017
$205$	3.44584e94	0.0397658
$206$	−7.05054e94	−0.0664864
$207$	−3.74413e95	−0.288789
$208$	1.72869e96	1.09166
$209$	2.42805e96	1.25657
$210$	1.43748e96	0.610242
$211$	3.03696e96	1.05856	0.529282	−	0.848446i	$-0.322461\pi$
$211$	3.03696e96	1.05856	0.529282	+	0.848446i	$0.322461\pi$
$212$	−4.43418e96	−1.27021
$213$	−9.03624e96	−2.12929
$214$	−1.10832e96	−0.215028
$215$	1.60622e96	0.256809
$216$	−2.16811e96	−0.285924
$217$	4.77738e96	0.520128
$218$	7.00774e94	0.00630425
$219$	−1.81684e97	−1.35171
$220$	1.86073e97	1.14589
$221$	1.30131e97	0.663899
$222$	−2.05594e96	−0.0869683
$223$	−3.38548e97	−1.18842	−0.594208	−	0.804312i	$-0.702534\pi$
$223$	−3.38548e97	−1.18842	−0.594208	+	0.804312i	$0.702534\pi$
$224$	2.97492e97	0.867327
$225$	3.83269e97	0.928815
$226$	−1.74925e97	−0.352656
$227$	−9.76481e96	−0.163904	−0.0819522	−	0.996636i	$-0.526115\pi$
$227$	−9.76481e96	−0.163904	−0.0819522	+	0.996636i	$0.526115\pi$
$228$	1.46388e98	2.04743
$229$	−4.89770e97	−0.571241	−0.285621	−	0.958343i	$-0.592200\pi$
$229$	−4.89770e97	−0.571241	−0.285621	+	0.958343i	$0.592200\pi$
$230$	−4.84263e96	−0.0471386
$231$	−2.88674e98	−2.34698
$232$	−1.14497e96	−0.00778114
$233$	−7.65637e97	−0.435263	−0.217632	−	0.976031i	$-0.569833\pi$
$233$	−7.65637e97	−0.435263	−0.217632	+	0.976031i	$0.569833\pi$
$234$	7.25948e97	0.345500
$235$	1.47606e98	0.588557
$236$	−5.18774e98	−1.73432
$237$	6.05228e98	1.69771
$238$	6.99896e97	0.164850
$239$	−5.55817e98	−1.10007	−0.550034	−	0.835142i	$-0.685385\pi$
$239$	−5.55817e98	−1.10007	−0.550034	+	0.835142i	$0.685385\pi$
$240$	1.07815e99	1.79437
$241$	1.75262e98	0.245460	0.122730	−	0.992440i	$-0.460835\pi$
$241$	1.75262e98	0.245460	0.122730	+	0.992440i	$0.460835\pi$
$242$	−2.10131e97	−0.0247829
$243$	−1.21230e99	−1.20489
$244$	4.71862e98	0.395492
$245$	2.79043e99	1.97369
$246$	1.56598e97	0.00935362
$247$	−3.26416e99	−1.64758
$248$	−2.85142e98	−0.121707
$249$	−1.67584e99	−0.605286
$250$	−2.97127e98	−0.0908722
$251$	3.41610e99	0.885262	0.442631	−	0.896704i	$-0.354045\pi$
$251$	3.41610e99	0.885262	0.442631	+	0.896704i	$0.354045\pi$
$252$	−1.04020e100	−2.28557
$253$	9.72492e98	0.181294
$254$	−1.59278e99	−0.252091
$255$	8.11600e99	1.09125
$256$	5.75271e99	0.657528
$257$	1.76565e100	1.71664	0.858322	−	0.513112i	$-0.171507\pi$
$257$	1.76565e100	1.71664	0.858322	+	0.513112i	$0.171507\pi$
$258$	7.29957e98	0.0604059
$259$	−6.56882e99	−0.462964
$260$	−2.50147e100	−1.50246
$261$	6.04207e98	0.0309460
$262$	8.22520e99	0.359454
$263$	2.35912e99	0.0880210	0.0440105	−	0.999031i	$-0.485987\pi$
$263$	2.35912e99	0.0880210	0.0440105	+	0.999031i	$0.485987\pi$
$264$	1.72298e100	0.549182
$265$	6.16652e100	1.68010
$266$	−1.75559e100	−0.409105
$267$	−1.03481e101	−2.06368
$268$	−3.76286e100	−0.642576
$269$	−2.86460e100	−0.419126	−0.209563	−	0.977795i	$-0.567204\pi$
$269$	−2.86460e100	−0.419126	−0.209563	+	0.977795i	$0.567204\pi$
$270$	1.47980e100	0.185612
$271$	−1.69133e101	−1.81971	−0.909857	−	0.414923i	$-0.863809\pi$
$271$	−1.69133e101	−1.81971	−0.909857	+	0.414923i	$0.863809\pi$
$272$	5.24938e100	0.484729
$273$	3.88079e101	3.07731
$274$	−2.06297e100	−0.140554
$275$	−9.95494e100	−0.583085
$276$	5.86317e100	0.295397
$277$	1.29126e101	0.559891	0.279945	−	0.960016i	$-0.409684\pi$
$277$	1.29126e101	0.559891	0.279945	+	0.960016i	$0.409684\pi$
$278$	3.46881e100	0.129515
$279$	1.50471e101	0.484037
$280$	−2.74128e101	−0.760142
$281$	−3.30498e101	−0.790417	−0.395209	−	0.918591i	$-0.629328\pi$
$281$	−3.30498e101	−0.790417	−0.395209	+	0.918591i	$0.629328\pi$
$282$	6.70805e100	0.138439
$283$	3.27781e101	0.584046	0.292023	−	0.956411i	$-0.405672\pi$
$283$	3.27781e101	0.584046	0.292023	+	0.956411i	$0.405672\pi$
$284$	8.45732e101	1.30173
$285$	−2.03578e102	−2.70813
$286$	−1.88556e101	−0.216896
$287$	5.00339e100	0.0497927
$288$	9.36999e101	0.807144
$289$	−9.45321e101	−0.705210
$290$	7.81478e99	0.00505126
$291$	−1.40370e102	−0.786531
$292$	1.70044e102	0.826365
$293$	−3.08142e101	−0.129940	−0.0649702	−	0.997887i	$-0.520695\pi$
$293$	−3.08142e101	−0.129940	−0.0649702	+	0.997887i	$0.520695\pi$
$294$	1.26813e102	0.464247
$295$	7.21449e102	2.29399
$296$	3.92066e101	0.108331
$297$	−2.97172e102	−0.713863
$298$	−1.08984e102	−0.227713
$299$	−1.30737e102	−0.237709
$300$	−6.00186e102	−0.950065
$301$	2.33225e102	0.321563
$302$	−2.99292e102	−0.359589
$303$	1.22393e103	1.28200
$304$	−1.31673e103	−1.20294
$305$	−6.56209e102	−0.523117
$306$	2.20443e102	0.153411
$307$	−1.71163e103	−1.04032	−0.520160	−	0.854069i	$-0.674128\pi$
$307$	−1.71163e103	−1.04032	−0.520160	+	0.854069i	$0.674128\pi$
$308$	2.70179e103	1.43482
$309$	−1.18714e103	−0.551092
$310$	1.94618e102	0.0790084
$311$	−7.45964e101	−0.0264948	−0.0132474	−	0.999912i	$-0.504217\pi$
$311$	−7.45964e101	−0.0264948	−0.0132474	+	0.999912i	$0.504217\pi$
$312$	−2.31629e103	−0.720074
$313$	2.87040e103	0.781362	0.390681	−	0.920526i	$-0.372240\pi$
$313$	2.87040e103	0.781362	0.390681	+	0.920526i	$0.372240\pi$
$314$	−7.36567e102	−0.175643
$315$	1.44659e104	3.02312
$316$	−5.66453e103	−1.03789
$317$	2.03249e103	0.326640	0.163320	−	0.986573i	$-0.447780\pi$
$317$	2.03249e103	0.326640	0.163320	+	0.986573i	$0.447780\pi$
$318$	2.80241e103	0.395190
$319$	−1.56935e102	−0.0194271
$320$	−9.25758e103	−1.00641
$321$	−1.86614e104	−1.78232
$322$	−7.03155e102	−0.0590245
$323$	−9.91202e103	−0.731572
$324$	4.13797e103	0.268639
$325$	1.33830e104	0.764527
$326$	4.40213e103	0.221377
$327$	1.17993e103	0.0522546
$328$	−2.98632e102	−0.0116512
$329$	2.14326e104	0.736961
$330$	−1.17598e104	−0.356511
$331$	−3.59099e104	−0.960179	−0.480089	−	0.877220i	$-0.659396\pi$
$331$	−3.59099e104	−0.960179	−0.480089	+	0.877220i	$0.659396\pi$
$332$	1.56848e104	0.370039
$333$	−2.06895e104	−0.430839
$334$	1.15614e104	0.212584
$335$	5.23294e104	0.849936
$336$	1.56548e105	2.24682
$337$	5.50364e104	0.698247	0.349124	−	0.937077i	$-0.386479\pi$
$337$	5.50364e104	0.698247	0.349124	+	0.937077i	$0.386479\pi$
$338$	8.39501e103	0.0941842
$339$	−2.94530e105	−2.92309
$340$	−7.59604e104	−0.667132
$341$	−3.90830e104	−0.303865
$342$	−5.52950e104	−0.380717
$343$	1.43463e105	0.875054
$344$	−1.39203e104	−0.0752440
$345$	−8.15379e104	−0.390721
$346$	3.87172e104	0.164530
$347$	−1.48857e105	−0.561172	−0.280586	−	0.959829i	$-0.590529\pi$
$347$	−1.48857e105	−0.561172	−0.280586	+	0.959829i	$0.590529\pi$
$348$	−9.46166e103	−0.0316540
$349$	1.75725e105	0.521891	0.260945	−	0.965354i	$-0.415966\pi$
$349$	1.75725e105	0.521891	0.260945	+	0.965354i	$0.415966\pi$
$350$	7.19787e104	0.189837
$351$	3.99504e105	0.935999
$352$	−2.43374e105	−0.506703
$353$	2.58199e105	0.477863	0.238932	−	0.971036i	$-0.423203\pi$
$353$	2.58199e105	0.477863	0.238932	+	0.971036i	$0.423203\pi$
$354$	3.27867e105	0.539587
$355$	−1.17614e106	−1.72180
$356$	9.68511e105	1.26162
$357$	1.17845e106	1.36641
$358$	−4.33691e104	−0.0447749
$359$	−1.28249e106	−1.17932	−0.589662	−	0.807650i	$-0.700739\pi$
$359$	−1.28249e106	−1.17932	−0.589662	+	0.807650i	$0.700739\pi$
$360$	−8.63408e105	−0.707396
$361$	1.11683e106	0.815526
$362$	6.73468e104	0.0438441
$363$	−3.53809e105	−0.205420
$364$	−3.63216e106	−1.88130
$365$	−2.36476e106	−1.09303
$366$	−2.98218e105	−0.123046
$367$	4.64982e106	1.71315	0.856573	−	0.516026i	$-0.172589\pi$
$367$	4.64982e106	1.71315	0.856573	+	0.516026i	$0.172589\pi$
$368$	−5.27383e105	−0.173557
$369$	1.57590e105	0.0463376
$370$	−2.67597e105	−0.0703250
$371$	8.95384e106	2.10374
$372$	−2.35632e106	−0.495111
$373$	3.29206e106	0.618801	0.309401	−	0.950932i	$-0.399872\pi$
$373$	3.29206e106	0.618801	0.309401	+	0.950932i	$0.399872\pi$
$374$	−5.72575e105	−0.0963076
$375$	−5.00288e106	−0.753221
$376$	−1.27922e106	−0.172445
$377$	2.10977e105	0.0254723
$378$	2.14869e106	0.232414
$379$	−4.41184e106	−0.427654	−0.213827	−	0.976872i	$-0.568593\pi$
$379$	−4.41184e106	−0.427654	−0.213827	+	0.976872i	$0.568593\pi$
$380$	1.90536e107	1.65561
$381$	−2.68185e107	−2.08952
$382$	2.95720e106	0.206658
$383$	2.74930e107	1.72374	0.861872	−	0.507126i	$-0.169292\pi$
$383$	2.74930e107	1.72374	0.861872	+	0.507126i	$0.169292\pi$
$384$	−1.94310e107	−1.09332
$385$	−3.75733e107	−1.89784
$386$	5.50216e106	0.249551
$387$	7.34579e106	0.299249
$388$	1.31377e107	0.480842
$389$	−4.29523e107	−1.41279	−0.706395	−	0.707818i	$-0.749680\pi$
$389$	−4.29523e107	−1.41279	−0.706395	+	0.707818i	$0.749680\pi$
$390$	1.58094e107	0.467448
$391$	−3.97000e106	−0.105549
$392$	−2.41832e107	−0.578285
$393$	1.38492e108	2.97943
$394$	−1.48739e107	−0.287960
$395$	7.87754e107	1.37281
$396$	8.50972e107	1.33526
$397$	−1.11042e108	−1.56921	−0.784603	−	0.619998i	$-0.787133\pi$
$397$	−1.11042e108	−1.56921	−0.784603	+	0.619998i	$0.787133\pi$
$398$	−1.14530e107	−0.145805
$399$	−2.95598e108	−3.39098
$400$	5.39857e107	0.558199
$401$	1.54940e108	1.44434	0.722172	−	0.691713i	$-0.243144\pi$
$401$	1.54940e108	1.44434	0.722172	+	0.691713i	$0.243144\pi$
$402$	2.37814e107	0.199920
$403$	5.25413e107	0.398421
$404$	−1.14552e108	−0.783747
$405$	−5.75459e107	−0.355329
$406$	1.13471e106	0.00632493
$407$	5.37385e107	0.270469
$408$	−7.03370e107	−0.319733
$409$	−2.71809e108	−1.11621	−0.558106	−	0.829770i	$-0.688472\pi$
$409$	−2.71809e108	−1.11621	−0.558106	+	0.829770i	$0.688472\pi$
$410$	2.03826e106	0.00756360
$411$	−3.47353e108	−1.16503
$412$	1.11108e108	0.336908
$413$	1.04755e109	2.87242
$414$	−2.21470e107	−0.0549288
$415$	−2.18125e108	−0.489451
$416$	3.27181e108	0.664377
$417$	5.84061e108	1.07352
$418$	1.43622e108	0.239004
$419$	7.02063e108	1.05802	0.529011	−	0.848615i	$-0.322563\pi$
$419$	7.02063e108	1.05802	0.529011	+	0.848615i	$0.322563\pi$
$420$	−2.26530e109	−3.09229
$421$	−4.20986e108	−0.520667	−0.260334	−	0.965519i	$-0.583833\pi$
$421$	−4.20986e108	−0.520667	−0.260334	+	0.965519i	$0.583833\pi$
$422$	1.79640e108	0.201343
$423$	6.75052e108	0.685823
$424$	−5.34419e108	−0.492265
$425$	4.06390e108	0.339471
$426$	−5.34505e108	−0.404998
$427$	−9.52822e108	−0.655021
$428$	1.74658e109	1.08961
$429$	−3.17482e109	−1.79780
$430$	9.50100e107	0.0488459
$431$	1.06853e109	0.498862	0.249431	−	0.968393i	$-0.419756\pi$
$431$	1.06853e109	0.498862	0.249431	+	0.968393i	$0.419756\pi$
$432$	1.61156e109	0.683396
$433$	9.15441e107	0.0352681	0.0176341	−	0.999845i	$-0.494387\pi$
$433$	9.15441e107	0.0352681	0.0176341	+	0.999845i	$0.494387\pi$
$434$	2.82588e108	0.0989303
$435$	1.31581e108	0.0418688
$436$	−1.10433e108	−0.0319456
$437$	9.95817e108	0.261939
$438$	−1.07468e109	−0.257101
$439$	−2.39899e109	−0.522096	−0.261048	−	0.965326i	$-0.584068\pi$
$439$	−2.39899e109	−0.522096	−0.261048	+	0.965326i	$0.584068\pi$
$440$	2.24260e109	0.444084
$441$	1.27616e110	2.29987
$442$	7.69742e108	0.126276
$443$	−4.73471e108	−0.0707195	−0.0353597	−	0.999375i	$-0.511258\pi$
$443$	−4.73471e108	−0.0707195	−0.0353597	+	0.999375i	$0.511258\pi$
$444$	3.23991e109	0.440696
$445$	−1.34689e110	−1.66875
$446$	−2.00255e109	−0.226041
$447$	−1.83502e110	−1.88746
$448$	−1.34421e110	−1.26017
$449$	1.44275e110	1.23302	0.616509	−	0.787348i	$-0.288546\pi$
$449$	1.44275e110	1.23302	0.616509	+	0.787348i	$0.288546\pi$
$450$	2.26708e109	0.176664
$451$	−4.09320e108	−0.0290895
$452$	2.75660e110	1.78702
$453$	−5.03933e110	−2.98056
$454$	−5.77601e108	−0.0311752
$455$	5.05118e110	2.48840
$456$	1.76430e110	0.793473
$457$	−1.50937e110	−0.619830	−0.309915	−	0.950764i	$-0.600301\pi$
$457$	−1.50937e110	−0.619830	−0.309915	+	0.950764i	$0.600301\pi$
$458$	−2.89705e109	−0.108652
$459$	1.21314e110	0.415610
$460$	7.63141e109	0.238866
$461$	−4.40480e110	−1.25990	−0.629952	−	0.776634i	$-0.716926\pi$
$461$	−4.40480e110	−1.25990	−0.629952	+	0.776634i	$0.716926\pi$
$462$	−1.70754e110	−0.446405
$463$	7.22166e110	1.72594	0.862970	−	0.505255i	$-0.168602\pi$
$463$	7.22166e110	1.72594	0.862970	+	0.505255i	$0.168602\pi$
$464$	8.51061e108	0.0185979
$465$	3.27689e110	0.654884
$466$	−4.52884e109	−0.0827887
$467$	−2.33305e109	−0.0390188	−0.0195094	−	0.999810i	$-0.506210\pi$
$467$	−2.33305e109	−0.0390188	−0.0195094	+	0.999810i	$0.506210\pi$
$468$	−1.14401e111	−1.75076
$469$	7.59828e110	1.06425
$470$	8.73109e109	0.111946
$471$	−1.24020e111	−1.45587
$472$	−6.25240e110	−0.672131
$473$	−1.90798e110	−0.187861
$474$	3.58000e110	0.322910
$475$	−1.01937e111	−0.842457
$476$	−1.10295e111	−0.835349
$477$	2.82015e111	1.95776
$478$	−3.28773e110	−0.209237
$479$	2.49098e111	1.45361	0.726804	−	0.686845i	$-0.241005\pi$
$479$	2.49098e111	1.45361	0.726804	+	0.686845i	$0.241005\pi$
$480$	2.04055e111	1.09204
$481$	−7.22435e110	−0.354632
$482$	1.03670e110	0.0466874
$483$	−1.18394e111	−0.489242
$484$	3.31141e110	0.125583
$485$	−1.82703e111	−0.636011
$486$	−7.17089e110	−0.229175
$487$	−2.28307e111	−0.669989	−0.334994	−	0.942220i	$-0.608734\pi$
$487$	−2.28307e111	−0.669989	−0.334994	+	0.942220i	$0.608734\pi$
$488$	5.68701e110	0.153272
$489$	7.41210e111	1.83495
$490$	1.65058e111	0.375403
$491$	−2.47251e111	−0.516720	−0.258360	−	0.966049i	$-0.583182\pi$
$491$	−2.47251e111	−0.516720	−0.258360	+	0.966049i	$0.583182\pi$
$492$	−2.46780e110	−0.0473978
$493$	6.40657e109	0.0113104
$494$	−1.93079e111	−0.313376
$495$	−1.18343e112	−1.76615
$496$	2.11947e111	0.290896
$497$	−1.70777e112	−2.15595
$498$	−9.91282e110	−0.115128
$499$	9.13024e111	0.975685	0.487842	−	0.872932i	$-0.337784\pi$
$499$	9.13024e111	0.975685	0.487842	+	0.872932i	$0.337784\pi$
$500$	4.68236e111	0.460479
$501$	1.94665e112	1.76206
$502$	2.02067e111	0.168380
$503$	−3.05195e111	−0.234157	−0.117078	−	0.993123i	$-0.537353\pi$
$503$	−3.05195e111	−0.234157	−0.117078	+	0.993123i	$0.537353\pi$
$504$	−1.25368e112	−0.885765
$505$	1.59305e112	1.03666
$506$	5.75241e110	0.0344829
$507$	1.41351e112	0.780673
$508$	2.51003e112	1.27742
$509$	−2.28076e112	−1.06978	−0.534888	−	0.844923i	$-0.679646\pi$
$509$	−2.28076e112	−1.06978	−0.534888	+	0.844923i	$0.679646\pi$
$510$	4.80071e111	0.207560
$511$	−3.43366e112	−1.36864
$512$	2.22715e112	0.818553
$513$	−3.04300e112	−1.03141
$514$	1.04440e112	0.326512
$515$	−1.54516e112	−0.445628
$516$	−1.15032e112	−0.306096
$517$	−1.75337e112	−0.430542
$518$	−3.88554e111	−0.0880574
$519$	6.51902e112	1.36376
$520$	−3.01484e112	−0.582272
$521$	−7.42124e112	−1.32346	−0.661730	−	0.749742i	$-0.730177\pi$
$521$	−7.42124e112	−1.32346	−0.661730	+	0.749742i	$0.730177\pi$
$522$	3.57396e110	0.00588604
$523$	1.17499e113	1.78737	0.893684	−	0.448698i	$-0.148112\pi$
$523$	1.17499e113	1.78737	0.893684	+	0.448698i	$0.148112\pi$
$524$	−1.29619e113	−1.82147
$525$	1.21194e113	1.57352
$526$	1.39545e111	0.0167419
$527$	1.59548e112	0.176910
$528$	−1.28070e113	−1.31262
$529$	−1.01550e113	−0.962208
$530$	3.64757e112	0.319562
$531$	3.29942e113	2.67310
$532$	2.76660e113	2.07307
$533$	5.50271e111	0.0381415
$534$	−6.12102e112	−0.392520
$535$	−2.42894e113	−1.44123
$536$	−4.53510e112	−0.249028
$537$	−7.30228e112	−0.371129
$538$	−1.69445e112	−0.0797193
$539$	−3.31467e113	−1.44380
$540$	−2.33199e113	−0.940557
$541$	2.95004e113	1.10190	0.550948	−	0.834539i	$-0.314266\pi$
$541$	2.95004e113	1.10190	0.550948	+	0.834539i	$0.314266\pi$
$542$	−1.00044e113	−0.346116
$543$	1.13395e113	0.363414
$544$	9.93525e112	0.295002
$545$	1.53578e112	0.0422545
$546$	2.29554e113	0.585315
$547$	−4.88473e113	−1.15443	−0.577213	−	0.816594i	$-0.695860\pi$
$547$	−4.88473e113	−1.15443	−0.577213	+	0.816594i	$0.695860\pi$
$548$	3.25099e113	0.712234
$549$	−3.00106e113	−0.609569
$550$	−5.88847e112	−0.110905
$551$	−1.60700e112	−0.0280688
$552$	7.06645e112	0.114480
$553$	1.14383e114	1.71897
$554$	7.63796e112	0.106493
$555$	−4.50567e113	−0.582909
$556$	−5.46642e113	−0.656295
$557$	9.21576e113	1.02693	0.513465	−	0.858111i	$-0.328362\pi$
$557$	9.21576e113	1.02693	0.513465	+	0.858111i	$0.328362\pi$
$558$	8.90054e112	0.0920656
$559$	2.56500e113	0.246318
$560$	2.03760e114	1.81684
$561$	−9.64074e113	−0.798273
$562$	−1.95494e113	−0.150340
$563$	−9.50601e113	−0.679047	−0.339523	−	0.940598i	$-0.610266\pi$
$563$	−9.50601e113	−0.679047	−0.339523	+	0.940598i	$0.610266\pi$
$564$	−1.05711e114	−0.701514
$565$	−3.83355e114	−2.36369
$566$	1.93886e113	0.111088
$567$	−8.35572e113	−0.444925
$568$	1.01930e114	0.504482
$569$	1.68386e113	0.0774723	0.0387362	−	0.999249i	$-0.487667\pi$
$569$	1.68386e113	0.0774723	0.0387362	+	0.999249i	$0.487667\pi$
$570$	−1.20419e114	−0.515097
$571$	1.04563e114	0.415891	0.207946	−	0.978140i	$-0.433322\pi$
$571$	1.04563e114	0.415891	0.207946	+	0.978140i	$0.433322\pi$
$572$	2.97142e114	1.09908
$573$	4.97920e114	1.71294
$574$	2.95957e112	0.00947076
$575$	−4.08283e113	−0.121547
$576$	−4.23380e114	−1.17273
$577$	−2.49381e114	−0.642786	−0.321393	−	0.946946i	$-0.604151\pi$
$577$	−2.49381e114	−0.642786	−0.321393	+	0.946946i	$0.604151\pi$
$578$	−5.59169e113	−0.134134
$579$	9.26428e114	2.06848
$580$	−1.23151e113	−0.0255963
$581$	−3.16720e114	−0.612866
$582$	−8.30306e113	−0.149601
$583$	−7.32501e114	−1.22903
$584$	2.04941e114	0.320255
$585$	1.59095e115	2.31573
$586$	−1.82270e113	−0.0247152
$587$	1.19830e115	1.51386	0.756929	−	0.653497i	$-0.226699\pi$
$587$	1.19830e115	1.51386	0.756929	+	0.653497i	$0.226699\pi$
$588$	−1.99842e115	−2.35249
$589$	−4.00204e114	−0.439033
$590$	4.26746e114	0.436326
$591$	−2.50440e115	−2.38684
$592$	−2.91424e114	−0.258926
$593$	−3.02933e114	−0.250944	−0.125472	−	0.992097i	$-0.540044\pi$
$593$	−3.02933e114	−0.250944	−0.125472	+	0.992097i	$0.540044\pi$
$594$	−1.75781e114	−0.135779
$595$	1.53385e115	1.10492
$596$	1.71745e115	1.15389
$597$	−1.92840e115	−1.20854
$598$	−7.73326e113	−0.0452130
$599$	1.70444e115	0.929755	0.464877	−	0.885375i	$-0.346098\pi$
$599$	1.70444e115	0.929755	0.464877	+	0.885375i	$0.346098\pi$
$600$	−7.23360e114	−0.368195
$601$	−1.15940e115	−0.550736	−0.275368	−	0.961339i	$-0.588800\pi$
$601$	−1.15940e115	−0.550736	−0.275368	+	0.961339i	$0.588800\pi$
$602$	1.37955e114	0.0611624
$603$	2.39320e115	0.990398
$604$	4.71648e115	1.82215
$605$	−4.60511e114	−0.166109
$606$	7.23971e114	0.243841
$607$	−9.39775e114	−0.295592	−0.147796	−	0.989018i	$-0.547218\pi$
$607$	−9.39775e114	−0.295592	−0.147796	+	0.989018i	$0.547218\pi$
$608$	−2.49211e115	−0.732098
$609$	1.91058e114	0.0524260
$610$	−3.88156e114	−0.0994988
$611$	2.35714e115	0.564515
$612$	−3.47392e115	−0.777384
$613$	−5.94029e115	−1.24222	−0.621109	−	0.783724i	$-0.713318\pi$
$613$	−5.94029e115	−1.24222	−0.621109	+	0.783724i	$0.713318\pi$
$614$	−1.01245e115	−0.197873
$615$	3.43192e114	0.0626931
$616$	3.25627e115	0.556060
$617$	5.16421e115	0.824460	0.412230	−	0.911080i	$-0.364750\pi$
$617$	5.16421e115	0.824460	0.412230	+	0.911080i	$0.364750\pi$
$618$	−7.02206e114	−0.104820
$619$	−4.23803e115	−0.591564	−0.295782	−	0.955255i	$-0.595580\pi$
$619$	−4.23803e115	−0.591564	−0.295782	+	0.955255i	$0.595580\pi$
$620$	−3.06695e115	−0.400361
$621$	−1.21879e115	−0.148809
$622$	−4.41247e113	−0.00503942
$623$	−1.95570e116	−2.08952
$624$	1.72171e116	1.72107
$625$	−1.31961e116	−1.23432
$626$	1.69788e115	0.148618
$627$	2.41824e116	1.98106
$628$	1.16074e116	0.890041
$629$	−2.19377e115	−0.157467
$630$	8.55673e115	0.575009
$631$	7.05248e115	0.443735	0.221867	−	0.975077i	$-0.428785\pi$
$631$	7.05248e115	0.443735	0.221867	+	0.975077i	$0.428785\pi$
$632$	−6.82704e115	−0.402229
$633$	3.02469e116	1.66889
$634$	1.20224e115	0.0621281
$635$	−3.49065e116	−1.68965
$636$	−4.41626e116	−2.00256
$637$	4.45608e116	1.89307
$638$	−9.28292e113	−0.00369510
$639$	−5.37889e116	−2.00635
$640$	−2.52911e116	−0.884093
$641$	1.01008e116	0.330939	0.165470	−	0.986215i	$-0.447086\pi$
$641$	1.01008e116	0.330939	0.165470	+	0.986215i	$0.447086\pi$
$642$	−1.10384e116	−0.339004
$643$	6.25253e116	1.80012	0.900058	−	0.435771i	$-0.143524\pi$
$643$	6.25253e116	1.80012	0.900058	+	0.435771i	$0.143524\pi$
$644$	1.10809e116	0.299096
$645$	1.59973e116	0.404873
$646$	−5.86308e115	−0.139148
$647$	−3.41819e116	−0.760796	−0.380398	−	0.924823i	$-0.624213\pi$
$647$	−3.41819e116	−0.760796	−0.380398	+	0.924823i	$0.624213\pi$
$648$	4.98719e115	0.104110
$649$	−8.56985e116	−1.67810
$650$	7.91618e115	0.145416
$651$	4.75808e116	0.820012
$652$	−6.93723e116	−1.12179
$653$	5.33406e116	0.809395	0.404698	−	0.914451i	$-0.367377\pi$
$653$	5.33406e116	0.809395	0.404698	+	0.914451i	$0.367377\pi$
$654$	6.97943e114	0.00993901
$655$	1.80259e117	2.40925
$656$	2.21975e115	0.0278480
$657$	−1.08148e117	−1.27367
$658$	1.26776e116	0.140173
$659$	−3.76058e116	−0.390401	−0.195200	−	0.980763i	$-0.562536\pi$
$659$	−3.76058e116	−0.390401	−0.195200	+	0.980763i	$0.562536\pi$
$660$	1.85321e117	1.80655
$661$	3.94843e116	0.361463	0.180731	−	0.983532i	$-0.442154\pi$
$661$	3.94843e116	0.361463	0.180731	+	0.983532i	$0.442154\pi$
$662$	−2.12411e116	−0.182629
$663$	1.29606e117	1.04668
$664$	1.89037e116	0.143408
$665$	−3.84745e117	−2.74205
$666$	−1.22381e116	−0.0819471
$667$	−6.43640e114	−0.00404968
$668$	−1.82193e117	−1.07723
$669$	−3.37180e117	−1.87361
$670$	3.09535e116	0.161661
$671$	7.79490e116	0.382671
$672$	2.96290e117	1.36739
$673$	6.70569e116	0.290950	0.145475	−	0.989362i	$-0.453529\pi$
$673$	6.70569e116	0.290950	0.145475	+	0.989362i	$0.453529\pi$
$674$	3.25547e116	0.132809
$675$	1.24762e117	0.478604
$676$	−1.32295e117	−0.477261
$677$	3.62398e117	1.22958	0.614789	−	0.788692i	$-0.289241\pi$
$677$	3.62398e117	1.22958	0.614789	+	0.788692i	$0.289241\pi$
$678$	−1.74218e117	−0.555982
$679$	−2.65287e117	−0.796380
$680$	−9.15495e116	−0.258545
$681$	−9.72536e116	−0.258405
$682$	−2.31181e116	−0.0577963
$683$	5.22001e117	1.22804	0.614019	−	0.789291i	$-0.289552\pi$
$683$	5.22001e117	1.22804	0.614019	+	0.789291i	$0.289552\pi$
$684$	8.71383e117	1.92922
$685$	−4.52109e117	−0.942073
$686$	8.48603e116	0.166439
$687$	−4.87791e117	−0.900595
$688$	1.03470e117	0.179843
$689$	9.84739e117	1.61148
$690$	−4.82307e116	−0.0743167
$691$	−3.99891e116	−0.0580234	−0.0290117	−	0.999579i	$-0.509236\pi$
$691$	−3.99891e116	−0.0580234	−0.0290117	+	0.999579i	$0.509236\pi$
$692$	−6.10137e117	−0.833728
$693$	−1.71835e118	−2.21148
$694$	−8.80507e116	−0.106737
$695$	7.60204e117	0.868082
$696$	−1.14035e116	−0.0122674
$697$	1.67097e116	0.0169359
$698$	1.03944e117	0.0992655
$699$	−7.62544e117	−0.686218
$700$	−1.13430e118	−0.961963
$701$	−3.54961e117	−0.283715	−0.141858	−	0.989887i	$-0.545307\pi$
$701$	−3.54961e117	−0.283715	−0.141858	+	0.989887i	$0.545307\pi$
$702$	2.36311e117	0.178031
$703$	5.50275e117	0.390781
$704$	1.09968e118	0.736208
$705$	1.47010e118	0.927894
$706$	1.52728e117	0.0908914
$707$	2.31312e118	1.29806
$708$	−5.16678e118	−2.73426
$709$	2.71692e118	1.35599	0.677997	−	0.735065i	$-0.262848\pi$
$709$	2.71692e118	1.35599	0.677997	+	0.735065i	$0.262848\pi$
$710$	−6.95702e117	−0.327493
$711$	3.60266e118	1.59969
$712$	1.16728e118	0.488938
$713$	−1.60291e117	−0.0633424
$714$	6.97068e117	0.259896
$715$	−4.13229e118	−1.45375
$716$	6.83444e117	0.226889
$717$	−5.53572e118	−1.73432
$718$	−7.58607e117	−0.224312
$719$	1.50770e118	0.420792	0.210396	−	0.977616i	$-0.432525\pi$
$719$	1.50770e118	0.420792	0.210396	+	0.977616i	$0.432525\pi$
$720$	6.41775e118	1.69077
$721$	−2.24358e118	−0.557993
$722$	6.60618e117	0.155116
$723$	1.74554e118	0.386982
$724$	−1.06130e118	−0.222172
$725$	6.58864e116	0.0130247
$726$	−2.09282e117	−0.0390717
$727$	−7.57719e118	−1.33607	−0.668037	−	0.744128i	$-0.732865\pi$
$727$	−7.57719e118	−1.33607	−0.668037	+	0.744128i	$0.732865\pi$
$728$	−4.37758e118	−0.729091
$729$	−1.03024e119	−1.62086
$730$	−1.39879e118	−0.207899
$731$	7.78893e117	0.109372
$732$	4.69956e118	0.623516
$733$	5.66552e118	0.710272	0.355136	−	0.934815i	$-0.384435\pi$
$733$	5.66552e118	0.710272	0.355136	+	0.934815i	$0.384435\pi$
$734$	2.75042e118	0.325847
$735$	2.77916e119	3.11164
$736$	−9.98151e117	−0.105625
$737$	−6.21604e118	−0.621746
$738$	9.32163e116	0.00881359
$739$	1.67362e119	1.49593	0.747967	−	0.663736i	$-0.231030\pi$
$739$	1.67362e119	1.49593	0.747967	+	0.663736i	$0.231030\pi$
$740$	4.21701e118	0.356359
$741$	−3.25097e119	−2.59751
$742$	5.29631e118	0.400139
$743$	1.58886e119	1.13514	0.567571	−	0.823325i	$-0.307883\pi$
$743$	1.58886e119	1.13514	0.567571	+	0.823325i	$0.307883\pi$
$744$	−2.83990e118	−0.191879
$745$	−2.38843e119	−1.52625
$746$	1.94729e118	0.117698
$747$	−9.97558e118	−0.570339
$748$	9.02309e118	0.488021
$749$	−3.52684e119	−1.80464
$750$	−2.95926e118	−0.143265
$751$	3.41276e119	1.56332	0.781662	−	0.623703i	$-0.214372\pi$
$751$	3.41276e119	1.56332	0.781662	+	0.623703i	$0.214372\pi$
$752$	9.50852e118	0.412166
$753$	3.40230e119	1.39567
$754$	1.24795e117	0.00484492
$755$	−6.55911e119	−2.41016
$756$	−3.38607e119	−1.17772
$757$	1.90008e119	0.625596	0.312798	−	0.949820i	$-0.398734\pi$
$757$	1.90008e119	0.625596	0.312798	+	0.949820i	$0.398734\pi$
$758$	−2.60966e118	−0.0813414
$759$	9.68563e118	0.285821
$760$	2.29639e119	0.641625
$761$	8.92334e118	0.236083	0.118041	−	0.993009i	$-0.462338\pi$
$761$	8.92334e118	0.236083	0.118041	+	0.993009i	$0.462338\pi$
$762$	−1.58635e119	−0.397435
$763$	2.22996e118	0.0529090
$764$	−4.66020e119	−1.04720
$765$	4.83111e119	1.02825
$766$	1.62624e119	0.327862
$767$	1.15209e120	2.20029
$768$	5.72947e119	1.03663
$769$	−1.09409e120	−1.87547	−0.937734	−	0.347354i	$-0.887080\pi$
$769$	−1.09409e120	−1.87547	−0.937734	+	0.347354i	$0.887080\pi$
$770$	−2.22251e119	−0.360976
$771$	1.75852e120	2.70639
$772$	−8.67074e119	−1.26456
$773$	−1.21377e120	−1.67760	−0.838800	−	0.544440i	$-0.816742\pi$
$773$	−1.21377e120	−1.67760	−0.838800	+	0.544440i	$0.816742\pi$
$774$	4.34512e118	0.0569183
$775$	1.64083e119	0.203724
$776$	1.58339e119	0.186349
$777$	−6.54228e119	−0.729889
$778$	−2.54068e119	−0.268718
$779$	−4.19138e118	−0.0420293
$780$	−2.49137e120	−2.36871
$781$	1.39710e120	1.25953
$782$	−2.34830e118	−0.0200758
$783$	1.96682e118	0.0159460
$784$	1.79754e120	1.38218
$785$	−1.61422e120	−1.17726
$786$	8.19197e119	0.566699
$787$	−5.27952e119	−0.346452	−0.173226	−	0.984882i	$-0.555419\pi$
$787$	−5.27952e119	−0.346452	−0.173226	+	0.984882i	$0.555419\pi$
$788$	2.34395e120	1.45919
$789$	2.34959e119	0.138770
$790$	4.65966e119	0.261114
$791$	−5.56635e120	−2.95969
$792$	1.02561e120	0.517475
$793$	−1.04791e120	−0.501749
$794$	−6.56825e119	−0.298469
$795$	6.14161e120	2.64878
$796$	1.80486e120	0.738839
$797$	3.56779e120	1.38637	0.693185	−	0.720759i	$-0.256207\pi$
$797$	3.56779e120	1.38637	0.693185	+	0.720759i	$0.256207\pi$
$798$	−1.74850e120	−0.644978
$799$	7.15776e119	0.250660
$800$	1.02176e120	0.339715
$801$	−6.15977e120	−1.94453
$802$	9.16486e119	0.274720
$803$	2.80903e120	0.799577
$804$	−3.74766e120	−1.01306
$805$	−1.54099e120	−0.395614
$806$	3.10789e119	0.0757811
$807$	−2.85303e120	−0.660777
$808$	−1.38061e120	−0.303738
$809$	7.60349e120	1.58909	0.794546	−	0.607204i	$-0.207709\pi$
$809$	7.60349e120	1.58909	0.794546	+	0.607204i	$0.207709\pi$
$810$	−3.40391e119	−0.0675850
$811$	−7.88182e120	−1.48683	−0.743415	−	0.668831i	$-0.766795\pi$
$811$	−7.88182e120	−1.48683	−0.743415	+	0.668831i	$0.766795\pi$
$812$	−1.78817e119	−0.0320504
$813$	−1.68450e121	−2.86888
$814$	3.17870e119	0.0514442
$815$	9.64747e120	1.48379
$816$	5.22818e120	0.764203
$817$	−1.95374e120	−0.271426
$818$	−1.60778e120	−0.212307
$819$	2.31007e121	2.89964
$820$	−3.21205e119	−0.0383272
$821$	3.97486e118	0.00450900	0.00225450	−	0.999997i	$-0.499282\pi$
$821$	3.97486e118	0.00450900	0.00225450	+	0.999997i	$0.499282\pi$
$822$	−2.05464e120	−0.221592
$823$	3.80677e120	0.390358	0.195179	−	0.980768i	$-0.437471\pi$
$823$	3.80677e120	0.390358	0.195179	+	0.980768i	$0.437471\pi$
$824$	1.33910e120	0.130568
$825$	−9.91473e120	−0.919267
$826$	6.19639e120	0.546345
$827$	−2.39747e120	−0.201036	−0.100518	−	0.994935i	$-0.532050\pi$
$827$	−2.39747e120	−0.201036	−0.100518	+	0.994935i	$0.532050\pi$
$828$	3.49010e120	0.278342
$829$	−1.98319e121	−1.50436	−0.752178	−	0.658960i	$-0.770997\pi$
$829$	−1.98319e121	−1.50436	−0.752178	+	0.658960i	$0.770997\pi$
$830$	−1.29024e120	−0.0930954
$831$	1.28604e121	0.882700
$832$	−1.47836e121	−0.965297
$833$	1.35314e121	0.840575
$834$	3.45479e120	0.204188
$835$	2.53372e121	1.42485
$836$	−2.26331e121	−1.21111
$837$	4.89815e120	0.249417
$838$	4.15279e120	0.201240
$839$	6.17252e120	0.284669	0.142335	−	0.989819i	$-0.454539\pi$
$839$	6.17252e120	0.284669	0.142335	+	0.989819i	$0.454539\pi$
$840$	−2.73020e121	−1.19841
$841$	−2.39246e121	−0.999566
$842$	−2.49018e120	−0.0990328
$843$	−3.29163e121	−1.24614
$844$	−2.83091e121	−1.02027
$845$	1.83980e121	0.631274
$846$	3.99302e120	0.130446
$847$	−6.68667e120	−0.207993
$848$	3.97236e121	1.17658
$849$	3.26457e121	0.920781
$850$	2.40385e120	0.0645686
$851$	2.20398e120	0.0563808
$852$	8.42315e121	2.05226
$853$	6.46044e121	1.49926	0.749630	−	0.661857i	$-0.230231\pi$
$853$	6.46044e121	1.49926	0.749630	+	0.661857i	$0.230231\pi$
$854$	−5.63606e120	−0.124587
$855$	−1.21181e122	−2.55178
$856$	2.10503e121	0.422276
$857$	1.10370e121	0.210934	0.105467	−	0.994423i	$-0.466366\pi$
$857$	1.10370e121	0.210934	0.105467	+	0.994423i	$0.466366\pi$
$858$	−1.87794e121	−0.341948
$859$	−2.24938e121	−0.390253	−0.195127	−	0.980778i	$-0.562512\pi$
$859$	−2.24938e121	−0.390253	−0.195127	+	0.980778i	$0.562512\pi$
$860$	−1.49724e121	−0.247518
$861$	4.98318e120	0.0785011
$862$	6.32049e120	0.0948853
$863$	−3.01758e121	−0.431729	−0.215864	−	0.976423i	$-0.569257\pi$
$863$	−3.01758e121	−0.431729	−0.215864	+	0.976423i	$0.569257\pi$
$864$	3.05013e121	0.415908
$865$	8.48505e121	1.10277
$866$	5.41494e119	0.00670813
$867$	−9.41502e121	−1.11180
$868$	−4.45324e121	−0.501311
$869$	−9.35748e121	−1.00424
$870$	7.78320e119	0.00796360
$871$	8.35655e121	0.815217
$872$	−1.33097e120	−0.0123804
$873$	−8.35563e121	−0.741120
$874$	5.89038e120	0.0498217
$875$	−9.45499e121	−0.762653
$876$	1.69357e122	1.30281
$877$	−2.36614e121	−0.173603	−0.0868014	−	0.996226i	$-0.527665\pi$
$877$	−2.36614e121	−0.173603	−0.0868014	+	0.996226i	$0.527665\pi$
$878$	−1.41903e121	−0.0993045
$879$	−3.06897e121	−0.204859
$880$	−1.66693e122	−1.06142
$881$	3.87807e121	0.235568	0.117784	−	0.993039i	$-0.462421\pi$
$881$	3.87807e121	0.235568	0.117784	+	0.993039i	$0.462421\pi$
$882$	7.54863e121	0.437443
$883$	3.20084e122	1.76968	0.884840	−	0.465895i	$-0.154267\pi$
$883$	3.20084e122	1.76968	0.884840	+	0.465895i	$0.154267\pi$
$884$	−1.21302e122	−0.639881
$885$	7.18534e122	3.61661
$886$	−2.80064e120	−0.0134511
$887$	−1.80096e122	−0.825418	−0.412709	−	0.910863i	$-0.635417\pi$
$887$	−1.80096e122	−0.825418	−0.412709	+	0.910863i	$0.635417\pi$
$888$	3.90482e121	0.170790
$889$	−5.06845e122	−2.11569
$890$	−7.96701e121	−0.317402
$891$	6.83570e121	0.259931
$892$	3.15578e122	1.14542
$893$	−1.79542e122	−0.622058
$894$	−1.08544e122	−0.359002
$895$	−9.50452e121	−0.300106
$896$	−3.67229e122	−1.10702
$897$	−1.30209e122	−0.374761
$898$	8.53407e121	0.234525
$899$	2.58669e120	0.00678762
$900$	−3.57265e122	−0.895213
$901$	2.99028e122	0.715540
$902$	−2.42118e120	−0.00553294
$903$	2.32283e122	0.506962
$904$	3.32233e122	0.692553
$905$	1.47593e122	0.293867
$906$	−2.98083e122	−0.566913
$907$	−8.61403e122	−1.56496	−0.782481	−	0.622674i	$-0.786046\pi$
$907$	−8.61403e122	−1.56496	−0.782481	+	0.622674i	$0.786046\pi$
$908$	9.10229e121	0.157975
$909$	7.28555e122	1.20798
$910$	2.98783e122	0.473302
$911$	4.80408e122	0.727106	0.363553	−	0.931573i	$-0.381564\pi$
$911$	4.80408e122	0.727106	0.363553	+	0.931573i	$0.381564\pi$
$912$	−1.31141e123	−1.89650
$913$	2.59104e122	0.358044
$914$	−8.92809e121	−0.117894
$915$	−6.53558e122	−0.824725
$916$	4.56540e122	0.550575
$917$	2.61738e123	3.01675
$918$	7.17589e121	0.0790505
$919$	5.26540e122	0.554418	0.277209	−	0.960810i	$-0.410590\pi$
$919$	5.26540e122	0.554418	0.277209	+	0.960810i	$0.410590\pi$
$920$	9.19758e121	0.0925718
$921$	−1.70471e123	−1.64012
$922$	−2.60549e122	−0.239639
$923$	−1.87820e123	−1.65147
$924$	2.69088e123	2.26208
$925$	−2.25611e122	−0.181334
$926$	4.27170e122	0.328280
$927$	−7.06652e122	−0.519274
$928$	1.61076e121	0.0113185
$929$	−1.51288e123	−1.01661	−0.508303	−	0.861178i	$-0.669727\pi$
$929$	−1.51288e123	−1.01661	−0.508303	+	0.861178i	$0.669727\pi$
$930$	1.93832e122	0.124561
$931$	−3.39417e123	−2.08604
$932$	7.13690e122	0.419517
$933$	−7.42950e121	−0.0417707
$934$	−1.38003e121	−0.00742152
$935$	−1.25482e123	−0.645506
$936$	−1.37879e123	−0.678500
$937$	1.88293e123	0.886425	0.443212	−	0.896417i	$-0.353839\pi$
$937$	1.88293e123	0.886425	0.443212	+	0.896417i	$0.353839\pi$
$938$	4.49447e122	0.202424
$939$	2.85880e123	1.23186
$940$	−1.37591e123	−0.567264
$941$	3.80840e123	1.50236	0.751179	−	0.660098i	$-0.229485\pi$
$941$	3.80840e123	1.50236	0.751179	+	0.660098i	$0.229485\pi$
$942$	−7.33591e122	−0.276912
$943$	−1.67875e121	−0.00606387
$944$	4.64744e123	1.60648
$945$	4.70894e123	1.55777
$946$	−1.12859e122	−0.0357318
$947$	−5.36351e123	−1.62527	−0.812635	−	0.582774i	$-0.801967\pi$
$947$	−5.36351e123	−1.62527	−0.812635	+	0.582774i	$0.801967\pi$
$948$	−5.64164e123	−1.63629
$949$	−3.77632e123	−1.04839
$950$	−6.02971e122	−0.160238
$951$	2.02428e123	0.514966
$952$	−1.32931e123	−0.323737
$953$	4.22287e123	0.984582	0.492291	−	0.870431i	$-0.336159\pi$
$953$	4.22287e123	0.984582	0.492291	+	0.870431i	$0.336159\pi$
$954$	1.66816e123	0.372374
$955$	6.48084e123	1.38513
$956$	5.18106e123	1.06027
$957$	−1.56301e122	−0.0306279
$958$	1.47345e123	0.276482
$959$	−6.56467e123	−1.17962
$960$	−9.22018e123	−1.58666
$961$	−5.42346e123	−0.893833
$962$	−4.27329e122	−0.0674524
$963$	−1.11083e124	−1.67942
$964$	−1.63371e123	−0.236580
$965$	1.20582e124	1.67263
$966$	−7.00314e122	−0.0930555
$967$	−3.96913e123	−0.505239	−0.252619	−	0.967566i	$-0.581292\pi$
$967$	−3.96913e123	−0.505239	−0.252619	+	0.967566i	$0.581292\pi$
$968$	3.99100e122	0.0486693
$969$	−9.87197e123	−1.15337
$970$	−1.08071e123	−0.120972
$971$	1.03876e124	1.11408	0.557041	−	0.830485i	$-0.311937\pi$
$971$	1.03876e124	1.11408	0.557041	+	0.830485i	$0.311937\pi$
$972$	1.13005e124	1.16130
$973$	1.10382e124	1.08697
$974$	−1.35046e123	−0.127434
$975$	1.33289e124	1.20532
$976$	−4.22718e123	−0.366339
$977$	−3.73334e123	−0.310079	−0.155040	−	0.987908i	$-0.549551\pi$
$977$	−3.73334e123	−0.310079	−0.155040	+	0.987908i	$0.549551\pi$
$978$	4.38435e123	0.349014
$979$	1.59993e124	1.22073
$980$	−2.60111e124	−1.90229
$981$	7.02362e122	0.0492376
$982$	−1.46252e123	−0.0982821
$983$	3.54597e123	0.228436	0.114218	−	0.993456i	$-0.463564\pi$
$983$	3.54597e123	0.228436	0.114218	+	0.993456i	$0.463564\pi$
$984$	−2.97426e122	−0.0183689
$985$	−3.25969e124	−1.93007
$986$	3.78956e121	0.00215128
$987$	2.13460e124	1.16186
$988$	3.04269e124	1.58798
$989$	−7.82520e122	−0.0391606
$990$	−7.00013e123	−0.335928
$991$	−4.20643e123	−0.193579	−0.0967893	−	0.995305i	$-0.530857\pi$
$991$	−4.20643e123	−0.193579	−0.0967893	+	0.995305i	$0.530857\pi$
$992$	4.01142e123	0.177037
$993$	−3.57648e124	−1.51378
$994$	−1.01017e124	−0.410070
$995$	−2.50998e124	−0.977263
$996$	1.56214e124	0.583388
$997$	1.41892e124	0.508286	0.254143	−	0.967167i	$-0.418207\pi$
$997$	1.41892e124	0.508286	0.254143	+	0.967167i	$0.418207\pi$
$998$	5.40065e123	0.185579
$999$	−6.73487e123	−0.222004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.84.a.a.1.4	✓	7
3.2	odd	2		9.84.a.c.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.84.a.a.1.4	✓	7	1.1	even	1	trivial
9.84.a.c.1.4		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)

\(f(q)\)	\(=\)	\(q+5.91512e11 q^{2} +9.95960e19 q^{3} -9.32152e24 q^{4} +1.29632e29 q^{5} +5.89123e31 q^{6} +1.88228e35 q^{7} -1.12345e37 q^{8} +5.92853e39 q^{9} +O(q^{10})\)	\(q+5.91512e11 q^{2} +9.95960e19 q^{3} -9.32152e24 q^{4} +1.29632e29 q^{5} +5.89123e31 q^{6} +1.88228e35 q^{7} -1.12345e37 q^{8} +5.92853e39 q^{9} +7.66792e40 q^{10} -1.53986e43 q^{11} -9.28386e44 q^{12} +2.07012e46 q^{13} +1.11339e47 q^{14} +1.29109e49 q^{15} +8.35068e49 q^{16} +6.28617e50 q^{17} +3.50680e51 q^{18} -1.57680e53 q^{19} -1.20837e54 q^{20} +1.87467e55 q^{21} -9.10848e54 q^{22} -6.31544e55 q^{23} -1.11892e57 q^{24} +6.46483e57 q^{25} +1.22450e58 q^{26} +1.92986e59 q^{27} -1.75457e60 q^{28} +1.01915e59 q^{29} +7.63694e60 q^{30} +2.53808e61 q^{31} +1.58049e62 q^{32} -1.53364e63 q^{33} +3.71835e62 q^{34} +2.44004e64 q^{35} -5.52629e64 q^{36} -3.48983e64 q^{37} -9.32694e64 q^{38} +2.06176e66 q^{39} -1.45636e66 q^{40} +2.65816e65 q^{41} +1.10889e67 q^{42} +1.23906e67 q^{43} +1.43539e68 q^{44} +7.68530e68 q^{45} -3.73566e67 q^{46} +1.13865e69 q^{47} +8.31695e69 q^{48} +2.15257e70 q^{49} +3.82402e69 q^{50} +6.26078e70 q^{51} -1.92967e71 q^{52} +4.75692e71 q^{53} +1.14154e71 q^{54} -1.99616e72 q^{55} -2.11465e72 q^{56} -1.57043e73 q^{57} +6.02841e70 q^{58} +5.56534e73 q^{59} -1.20349e74 q^{60} -5.06207e73 q^{61} +1.50131e73 q^{62} +1.11591e75 q^{63} -7.14141e74 q^{64} +2.68355e75 q^{65} -9.07168e74 q^{66} +4.03675e75 q^{67} -5.85967e75 q^{68} -6.28993e75 q^{69} +1.44331e76 q^{70} -9.07289e76 q^{71} -6.66043e76 q^{72} -1.82421e77 q^{73} -2.06427e76 q^{74} +6.43871e77 q^{75} +1.46981e78 q^{76} -2.89845e78 q^{77} +1.21955e78 q^{78} +6.07683e78 q^{79} +1.08252e79 q^{80} -4.43916e78 q^{81} +1.57233e77 q^{82} -1.68264e79 q^{83} -1.74748e80 q^{84} +8.14892e79 q^{85} +7.32918e78 q^{86} +1.01503e79 q^{87} +1.72997e80 q^{88} -1.03901e81 q^{89} +4.54595e80 q^{90} +3.89654e81 q^{91} +5.88695e80 q^{92} +2.52783e81 q^{93} +6.73526e80 q^{94} -2.04404e82 q^{95} +1.57411e82 q^{96} -1.40939e82 q^{97} +1.27327e82 q^{98} -9.12912e82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) \) 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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