LMFDB - Embedded newform 1.84.a.a.1.7

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			1.7
Root			$2.36930e11$ 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)

$f(q)$	$=$	$q+5.73595e12 q^{2} +4.63055e19 q^{3} +2.32297e25 q^{4} +7.41344e28 q^{5} +2.65606e32 q^{6} -1.39412e35 q^{7} +7.77697e37 q^{8} -1.84664e39 q^{9} +O(q^{10})$	\(q+5.73595e12 q^{2} +4.63055e19 q^{3} +2.32297e25 q^{4} +7.41344e28 q^{5} +2.65606e32 q^{6} -1.39412e35 q^{7} +7.77697e37 q^{8} -1.84664e39 q^{9} +4.25231e41 q^{10} +2.44551e43 q^{11} +1.07566e45 q^{12} +2.73761e46 q^{13} -7.99659e47 q^{14} +3.43283e48 q^{15} +2.21419e50 q^{16} -2.78560e50 q^{17} -1.05922e52 q^{18} -1.76437e52 q^{19} +1.72212e54 q^{20} -6.45554e54 q^{21} +1.40273e56 q^{22} +4.34531e56 q^{23} +3.60117e57 q^{24} -4.84385e57 q^{25} +1.57028e59 q^{26} -2.70307e59 q^{27} -3.23850e60 q^{28} -2.69391e60 q^{29} +1.96906e61 q^{30} -7.41160e61 q^{31} +5.17907e62 q^{32} +1.13241e63 q^{33} -1.59781e63 q^{34} -1.03352e64 q^{35} -4.28969e64 q^{36} +6.70212e64 q^{37} -1.01203e65 q^{38} +1.26767e66 q^{39} +5.76541e66 q^{40} -6.68086e65 q^{41} -3.70286e67 q^{42} -5.49204e67 q^{43} +5.68085e68 q^{44} -1.36899e68 q^{45} +2.49245e69 q^{46} -3.59297e68 q^{47} +1.02529e70 q^{48} +5.53174e69 q^{49} -2.77841e70 q^{50} -1.28989e70 q^{51} +6.35940e71 q^{52} -1.93291e71 q^{53} -1.55047e72 q^{54} +1.81296e72 q^{55} -1.08420e73 q^{56} -8.17000e71 q^{57} -1.54521e73 q^{58} +1.98325e73 q^{59} +7.97437e73 q^{60} -4.72939e73 q^{61} -4.25126e74 q^{62} +2.57443e74 q^{63} +8.29252e74 q^{64} +2.02951e75 q^{65} +6.49542e75 q^{66} -6.27987e75 q^{67} -6.47087e75 q^{68} +2.01212e76 q^{69} -5.92823e76 q^{70} -9.74042e76 q^{71} -1.43613e77 q^{72} +3.33031e77 q^{73} +3.84430e77 q^{74} -2.24297e77 q^{75} -4.09858e77 q^{76} -3.40933e78 q^{77} +7.27127e78 q^{78} +9.46449e77 q^{79} +1.64148e79 q^{80} -5.14709e78 q^{81} -3.83210e78 q^{82} +4.30384e78 q^{83} -1.49960e80 q^{84} -2.06509e79 q^{85} -3.15021e80 q^{86} -1.24743e80 q^{87} +1.90187e81 q^{88} -2.42561e80 q^{89} -7.85248e80 q^{90} -3.81656e81 q^{91} +1.00940e82 q^{92} -3.43198e81 q^{93} -2.06091e81 q^{94} -1.30801e81 q^{95} +2.39819e82 q^{96} -4.97028e82 q^{97} +3.17298e82 q^{98} -4.51597e82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.73595e12	1.84442	0.922211	−	0.386686i	$-0.126380\pi$
$2$	5.73595e12	1.84442	0.922211	+	0.386686i	$0.126380\pi$
$3$	4.63055e19	0.732994	0.366497	−	0.930419i	$-0.380557\pi$
$3$	4.63055e19	0.732994	0.366497	+	0.930419i	$0.380557\pi$
$4$	2.32297e25	2.40190
$5$	7.41344e28	0.729062	0.364531	−	0.931191i	$-0.381229\pi$
$5$	7.41344e28	0.729062	0.364531	+	0.931191i	$0.381229\pi$
$6$	2.65606e32	1.35195
$7$	−1.39412e35	−1.18231	−0.591154	−	0.806558i	$-0.701328\pi$
$7$	−1.39412e35	−1.18231	−0.591154	+	0.806558i	$0.701328\pi$
$8$	7.77697e37	2.58569
$9$	−1.84664e39	−0.462719
$10$	4.25231e41	1.34470
$11$	2.44551e43	1.48106	0.740531	−	0.672022i	$-0.234574\pi$
$11$	2.44551e43	1.48106	0.740531	+	0.672022i	$0.234574\pi$
$12$	1.07566e45	1.76058
$13$	2.73761e46	1.61705	0.808525	−	0.588462i	$-0.200267\pi$
$13$	2.73761e46	1.61705	0.808525	+	0.588462i	$0.200267\pi$
$14$	−7.99659e47	−2.18068
$15$	3.43283e48	0.534399
$16$	2.21419e50	2.36721
$17$	−2.78560e50	−0.240596	−0.120298	−	0.992738i	$-0.538385\pi$
$17$	−2.78560e50	−0.240596	−0.120298	+	0.992738i	$0.538385\pi$
$18$	−1.05922e52	−0.853450
$19$	−1.76437e52	−0.150770	−0.0753850	−	0.997154i	$-0.524019\pi$
$19$	−1.76437e52	−0.150770	−0.0753850	+	0.997154i	$0.524019\pi$
$20$	1.72212e54	1.75113
$21$	−6.45554e54	−0.866626
$22$	1.40273e56	2.73170
$23$	4.34531e56	1.33757	0.668784	−	0.743457i	$-0.266815\pi$
$23$	4.34531e56	1.33757	0.668784	+	0.743457i	$0.266815\pi$
$24$	3.60117e57	1.89529
$25$	−4.84385e57	−0.468468
$26$	1.57028e59	2.98252
$27$	−2.70307e59	−1.07216
$28$	−3.23850e60	−2.83978
$29$	−2.69391e60	−0.550638	−0.275319	−	0.961353i	$-0.588784\pi$
$29$	−2.69391e60	−0.550638	−0.275319	+	0.961353i	$0.588784\pi$
$30$	1.96906e61	0.985657
$31$	−7.41160e61	−0.951485	−0.475742	−	0.879585i	$-0.657820\pi$
$31$	−7.41160e61	−0.951485	−0.475742	+	0.879585i	$0.657820\pi$
$32$	5.17907e62	1.78044
$33$	1.13241e63	1.08561
$34$	−1.59781e63	−0.443761
$35$	−1.03352e64	−0.861977
$36$	−4.28969e64	−1.11140
$37$	6.70212e64	0.556981	0.278491	−	0.960439i	$-0.410166\pi$
$37$	6.70212e64	0.556981	0.278491	+	0.960439i	$0.410166\pi$
$38$	−1.01203e65	−0.278084
$39$	1.26767e66	1.18529
$40$	5.76541e66	1.88513
$41$	−6.68086e65	−0.0783975	−0.0391987	−	0.999231i	$-0.512481\pi$
$41$	−6.68086e65	−0.0783975	−0.0391987	+	0.999231i	$0.512481\pi$
$42$	−3.70286e67	−1.59842
$43$	−5.49204e67	−0.892879	−0.446440	−	0.894814i	$-0.647308\pi$
$43$	−5.49204e67	−0.892879	−0.446440	+	0.894814i	$0.647308\pi$
$44$	5.68085e68	3.55735
$45$	−1.36899e68	−0.337351
$46$	2.49245e69	2.46704
$47$	−3.59297e68	−0.145678	−0.0728388	−	0.997344i	$-0.523206\pi$
$47$	−3.59297e68	−0.145678	−0.0728388	+	0.997344i	$0.523206\pi$
$48$	1.02529e70	1.73515
$49$	5.53174e69	0.397854
$50$	−2.77841e70	−0.864053
$51$	−1.28989e70	−0.176356
$52$	6.35940e71	3.88398
$53$	−1.93291e71	−0.535504	−0.267752	−	0.963488i	$-0.586281\pi$
$53$	−1.93291e71	−0.535504	−0.267752	+	0.963488i	$0.586281\pi$
$54$	−1.55047e72	−1.97753
$55$	1.81296e72	1.07979
$56$	−1.08420e73	−3.05708
$57$	−8.17000e71	−0.110514
$58$	−1.54521e73	−1.01561
$59$	1.98325e73	0.641237	0.320619	−	0.947208i	$-0.396109\pi$
$59$	1.98325e73	0.641237	0.320619	+	0.947208i	$0.396109\pi$
$60$	7.97437e73	1.28357
$61$	−4.72939e73	−0.383369	−0.191684	−	0.981457i	$-0.561395\pi$
$61$	−4.72939e73	−0.383369	−0.191684	+	0.981457i	$0.561395\pi$
$62$	−4.25126e74	−1.75494
$63$	2.57443e74	0.547077
$64$	8.29252e74	0.916680
$65$	2.02951e75	1.17893
$66$	6.49542e75	2.00232
$67$	−6.27987e75	−1.03716	−0.518581	−	0.855029i	$-0.673540\pi$
$67$	−6.27987e75	−1.03716	−0.518581	+	0.855029i	$0.673540\pi$
$68$	−6.47087e75	−0.577887
$69$	2.01212e76	0.980430
$70$	−5.92823e76	−1.58985
$71$	−9.74042e76	−1.44996	−0.724980	−	0.688770i	$-0.758151\pi$
$71$	−9.74042e76	−1.44996	−0.724980	+	0.688770i	$0.758151\pi$
$72$	−1.43613e77	−1.19645
$73$	3.33031e77	1.56526	0.782630	−	0.622487i	$-0.213878\pi$
$73$	3.33031e77	1.56526	0.782630	+	0.622487i	$0.213878\pi$
$74$	3.84430e77	1.02731
$75$	−2.24297e77	−0.343384
$76$	−4.09858e77	−0.362134
$77$	−3.40933e78	−1.75107
$78$	7.27127e78	2.18617
$79$	9.46449e77	0.167715	0.0838577	−	0.996478i	$-0.473276\pi$
$79$	9.46449e77	0.167715	0.0838577	+	0.996478i	$0.473276\pi$
$80$	1.64148e79	1.72584
$81$	−5.14709e78	−0.323172
$82$	−3.83210e78	−0.144598
$83$	4.30384e78	0.0982009	0.0491004	−	0.998794i	$-0.484365\pi$
$83$	4.30384e78	0.0982009	0.0491004	+	0.998794i	$0.484365\pi$
$84$	−1.49960e80	−2.08154
$85$	−2.06509e79	−0.175410
$86$	−3.15021e80	−1.64685
$87$	−1.24743e80	−0.403615
$88$	1.90187e81	3.82956
$89$	−2.42561e80	−0.305588	−0.152794	−	0.988258i	$-0.548827\pi$
$89$	−2.42561e80	−0.305588	−0.152794	+	0.988258i	$0.548827\pi$
$90$	−7.85248e80	−0.622218
$91$	−3.81656e81	−1.91185
$92$	1.00940e82	3.21270
$93$	−3.43198e81	−0.697433
$94$	−2.06091e81	−0.268691
$95$	−1.30801e81	−0.109921
$96$	2.39819e82	1.30505
$97$	−4.97028e82	−1.75936	−0.879679	−	0.475568i	$-0.842242\pi$
$97$	−4.97028e82	−1.75936	−0.879679	+	0.475568i	$0.842242\pi$
$98$	3.17298e82	0.733812
$99$	−4.51597e82	−0.685316
$100$	−1.12521e83	−1.12521
$101$	−1.47861e83	−0.978400	−0.489200	−	0.872172i	$-0.662711\pi$
$101$	−1.47861e83	−0.978400	−0.489200	+	0.872172i	$0.662711\pi$
$102$	−7.39872e82	−0.325274
$103$	2.71333e83	0.795715	0.397858	−	0.917447i	$-0.369754\pi$
$103$	2.71333e83	0.795715	0.397858	+	0.917447i	$0.369754\pi$
$104$	2.12904e84	4.18118
$105$	−4.78577e83	−0.631824
$106$	−1.10871e84	−0.987695
$107$	1.89277e84	1.14201	0.571005	−	0.820947i	$-0.306554\pi$
$107$	1.89277e84	1.14201	0.571005	+	0.820947i	$0.306554\pi$
$108$	−6.27916e84	−2.57523
$109$	−2.49983e84	−0.699377	−0.349688	−	0.936866i	$-0.613713\pi$
$109$	−2.49983e84	−0.699377	−0.349688	+	0.936866i	$0.613713\pi$
$110$	1.03991e85	1.99158
$111$	3.10345e84	0.408264
$112$	−3.08685e85	−2.79877
$113$	2.10305e85	1.31854	0.659272	−	0.751905i	$-0.270865\pi$
$113$	2.10305e85	1.31854	0.659272	+	0.751905i	$0.270865\pi$
$114$	−4.68627e84	−0.203834
$115$	3.22137e85	0.975171
$116$	−6.25788e85	−1.32258
$117$	−5.05538e85	−0.748240
$118$	1.13758e86	1.18271
$119$	3.88346e85	0.284459
$120$	2.66970e86	1.38179
$121$	3.25410e86	1.19354
$122$	−2.71275e86	−0.707094
$123$	−3.09360e85	−0.0574649
$124$	−1.72169e87	−2.28537
$125$	−1.12563e87	−1.07060
$126$	1.47668e87	1.00904
$127$	−5.46713e86	−0.269095	−0.134547	−	0.990907i	$-0.542958\pi$
$127$	−5.46713e86	−0.269095	−0.134547	+	0.990907i	$0.542958\pi$
$128$	−2.52339e86	−0.0896956
$129$	−2.54312e87	−0.654475
$130$	1.16412e88	2.17444
$131$	−7.89651e87	−1.07319	−0.536595	−	0.843840i	$-0.680290\pi$
$131$	−7.89651e87	−1.07319	−0.536595	+	0.843840i	$0.680290\pi$
$132$	2.63055e88	2.60752
$133$	2.45974e87	0.178257
$134$	−3.60210e88	−1.91296
$135$	−2.00391e88	−0.781675
$136$	−2.16635e88	−0.622106
$137$	4.10421e88	0.869613	0.434807	−	0.900524i	$-0.356817\pi$
$137$	4.10421e88	0.869613	0.434807	+	0.900524i	$0.356817\pi$
$138$	1.15414e89	1.80833
$139$	3.76894e88	0.437628	0.218814	−	0.975767i	$-0.429781\pi$
$139$	3.76894e88	0.437628	0.218814	+	0.975767i	$0.429781\pi$
$140$	−2.40084e89	−2.07038
$141$	−1.66374e88	−0.106781
$142$	−5.58705e89	−2.67434
$143$	6.69487e89	2.39495
$144$	−4.08881e89	−1.09535
$145$	−1.99712e89	−0.401450
$146$	1.91025e90	2.88700
$147$	2.56150e89	0.291625
$148$	1.55688e90	1.33781
$149$	−2.40451e90	−1.56241	−0.781207	−	0.624273i	$-0.785395\pi$
$149$	−2.40451e90	−1.56241	−0.781207	+	0.624273i	$0.785395\pi$
$150$	−1.28655e90	−0.633346
$151$	1.93154e90	0.721705	0.360853	−	0.932623i	$-0.382486\pi$
$151$	1.93154e90	0.721705	0.360853	+	0.932623i	$0.382486\pi$
$152$	−1.37215e90	−0.389844
$153$	5.14399e89	0.111328
$154$	−1.95557e91	−3.22972
$155$	−5.49455e90	−0.693692
$156$	2.94475e91	2.84694
$157$	4.91816e90	0.364726	0.182363	−	0.983231i	$-0.441625\pi$
$157$	4.91816e90	0.364726	0.182363	+	0.983231i	$0.441625\pi$
$158$	5.42878e90	0.309338
$159$	−8.95042e90	−0.392521
$160$	3.83947e91	1.29805
$161$	−6.05788e91	−1.58142
$162$	−2.95234e91	−0.596065
$163$	8.76637e91	1.37099	0.685495	−	0.728077i	$-0.259586\pi$
$163$	8.76637e91	1.37099	0.685495	+	0.728077i	$0.259586\pi$
$164$	−1.55194e91	−0.188303
$165$	8.39503e91	0.791477
$166$	2.46866e91	0.181124
$167$	−3.72144e91	−0.212803	−0.106401	−	0.994323i	$-0.533933\pi$
$167$	−3.72144e91	−0.212803	−0.106401	+	0.994323i	$0.533933\pi$
$168$	−5.02045e92	−2.24082
$169$	4.62839e92	1.61485
$170$	−1.18452e92	−0.323529
$171$	3.25815e91	0.0697642
$172$	−1.27578e93	−2.14460
$173$	2.54744e92	0.336660	0.168330	−	0.985731i	$-0.446163\pi$
$173$	2.54744e92	0.336660	0.168330	+	0.985731i	$0.446163\pi$
$174$	−7.15519e92	−0.744436
$175$	6.75289e92	0.553874
$176$	5.41483e93	3.50598
$177$	9.18353e92	0.470023
$178$	−1.39132e93	−0.563633
$179$	3.35995e93	1.07878	0.539389	−	0.842056i	$-0.318655\pi$
$179$	3.35995e93	1.07878	0.539389	+	0.842056i	$0.318655\pi$
$180$	−3.18013e93	−0.810282
$181$	−5.06987e93	−1.02645	−0.513223	−	0.858255i	$-0.671549\pi$
$181$	−5.06987e93	−1.02645	−0.513223	+	0.858255i	$0.671549\pi$
$182$	−2.18916e94	−3.52626
$183$	−2.18997e93	−0.281007
$184$	3.37934e94	3.45853
$185$	4.96858e93	0.406074
$186$	−1.96857e94	−1.28636
$187$	−6.81221e93	−0.356338
$188$	−8.34636e93	−0.349902
$189$	3.76840e94	1.26763
$190$	−7.50265e93	−0.202740
$191$	−1.66015e94	−0.360798	−0.180399	−	0.983594i	$-0.557739\pi$
$191$	−1.66015e94	−0.360798	−0.180399	+	0.983594i	$0.557739\pi$
$192$	3.83990e94	0.671921
$193$	1.34346e95	1.89494	0.947470	−	0.319844i	$-0.103631\pi$
$193$	1.34346e95	1.89494	0.947470	+	0.319844i	$0.103631\pi$
$194$	−2.85093e95	−3.24500
$195$	9.39777e94	0.864149
$196$	1.28501e95	0.955605
$197$	1.16575e95	0.701871	0.350936	−	0.936400i	$-0.385864\pi$
$197$	1.16575e95	0.701871	0.350936	+	0.936400i	$0.385864\pi$
$198$	−2.59034e95	−1.26401
$199$	3.85030e95	1.52438	0.762188	−	0.647355i	$-0.224125\pi$
$199$	3.85030e95	1.52438	0.762188	+	0.647355i	$0.224125\pi$
$200$	−3.76705e95	−1.21131
$201$	−2.90793e95	−0.760234
$202$	−8.48122e95	−1.80458
$203$	3.75563e95	0.651025
$204$	−2.99637e95	−0.423588
$205$	−4.95281e94	−0.0571566
$206$	1.55635e96	1.46764
$207$	−8.02422e95	−0.618919
$208$	6.06161e96	3.82789
$209$	−4.31478e95	−0.223300
$210$	−2.74510e96	−1.16535
$211$	1.72216e95	0.0600277	0.0300138	−	0.999549i	$-0.490445\pi$
$211$	1.72216e95	0.0600277	0.0300138	+	0.999549i	$0.490445\pi$
$212$	−4.49009e96	−1.28622
$213$	−4.51035e96	−1.06281
$214$	1.08568e97	2.10635
$215$	−4.07149e96	−0.650965
$216$	−2.10217e97	−2.77228
$217$	1.03326e97	1.12495
$218$	−1.43389e97	−1.28995
$219$	1.54212e97	1.14733
$220$	4.21146e97	2.59353
$221$	−7.62590e96	−0.389056
$222$	1.78012e97	0.753012
$223$	−4.14911e97	−1.45648	−0.728238	−	0.685325i	$-0.759660\pi$
$223$	−4.14911e97	−1.45648	−0.728238	+	0.685325i	$0.759660\pi$
$224$	−7.22024e97	−2.10503
$225$	8.94483e96	0.216769
$226$	1.20630e98	2.43195
$227$	−3.76674e97	−0.632255	−0.316128	−	0.948717i	$-0.602383\pi$
$227$	−3.76674e97	−0.632255	−0.316128	+	0.948717i	$0.602383\pi$
$228$	−1.89787e97	−0.265442
$229$	1.20400e98	1.40429	0.702143	−	0.712036i	$-0.252227\pi$
$229$	1.20400e98	1.40429	0.702143	+	0.712036i	$0.252227\pi$
$230$	1.84776e98	1.79863
$231$	−1.57871e98	−1.28353
$232$	−2.09505e98	−1.42378
$233$	−2.11704e98	−1.20353	−0.601766	−	0.798672i	$-0.705536\pi$
$233$	−2.11704e98	−1.20353	−0.601766	+	0.798672i	$0.705536\pi$
$234$	−2.89974e98	−1.38007
$235$	−2.66363e97	−0.106208
$236$	4.60703e98	1.54018
$237$	4.38258e97	0.122934
$238$	2.22753e98	0.524662
$239$	−7.17206e98	−1.41949	−0.709743	−	0.704461i	$-0.751189\pi$
$239$	−7.17206e98	−1.41949	−0.709743	+	0.704461i	$0.751189\pi$
$240$	7.60095e98	1.26503
$241$	−3.29653e98	−0.461690	−0.230845	−	0.972991i	$-0.574149\pi$
$241$	−3.29653e98	−0.461690	−0.230845	+	0.972991i	$0.574149\pi$
$242$	1.86654e99	2.20140
$243$	8.40414e98	0.835282
$244$	−1.09862e99	−0.920811
$245$	4.10092e98	0.290061
$246$	−1.77448e98	−0.105990
$247$	−4.83016e98	−0.243803
$248$	−5.76398e99	−2.46024
$249$	1.99292e98	0.0719807
$250$	−6.45654e99	−1.97465
$251$	3.58601e99	0.929291	0.464645	−	0.885497i	$-0.346182\pi$
$251$	3.58601e99	0.929291	0.464645	+	0.885497i	$0.346182\pi$
$252$	5.98033e99	1.31402
$253$	1.06265e100	1.98102
$254$	−3.13592e99	−0.496325
$255$	−9.56250e98	−0.128574
$256$	−9.46744e99	−1.08212
$257$	9.31848e99	0.905984	0.452992	−	0.891515i	$-0.350357\pi$
$257$	9.31848e99	0.905984	0.452992	+	0.891515i	$0.350357\pi$
$258$	−1.45872e100	−1.20713
$259$	−9.34355e99	−0.658524
$260$	4.71450e100	2.83167
$261$	4.97468e99	0.254791
$262$	−4.52940e100	−1.97941
$263$	−2.18437e100	−0.815008	−0.407504	−	0.913203i	$-0.633601\pi$
$263$	−2.18437e100	−0.815008	−0.407504	+	0.913203i	$0.633601\pi$
$264$	8.80669e100	2.80705
$265$	−1.43295e100	−0.390416
$266$	1.41089e100	0.328781
$267$	−1.12319e100	−0.223994
$268$	−1.45880e101	−2.49115
$269$	7.31297e100	1.06998	0.534988	−	0.844860i	$-0.320316\pi$
$269$	7.31297e100	1.06998	0.534988	+	0.844860i	$0.320316\pi$
$270$	−1.14943e101	−1.44174
$271$	6.71403e100	0.722367	0.361184	−	0.932495i	$-0.382373\pi$
$271$	6.71403e100	0.722367	0.361184	+	0.932495i	$0.382373\pi$
$272$	−6.16785e100	−0.569540
$273$	−1.76728e101	−1.40138
$274$	2.35415e101	1.60393
$275$	−1.18457e101	−0.693830
$276$	4.67409e101	2.35489
$277$	3.25387e101	1.41088	0.705440	−	0.708770i	$-0.250750\pi$
$277$	3.25387e101	1.41088	0.705440	+	0.708770i	$0.250750\pi$
$278$	2.16185e101	0.807171
$279$	1.36865e101	0.440270
$280$	−8.03767e101	−2.22880
$281$	1.48861e101	0.356014	0.178007	−	0.984029i	$-0.443035\pi$
$281$	1.48861e101	0.356014	0.178007	+	0.984029i	$0.443035\pi$
$282$	−9.54315e100	−0.196949
$283$	−5.26335e101	−0.937832	−0.468916	−	0.883243i	$-0.655355\pi$
$283$	−5.26335e101	−0.937832	−0.468916	+	0.883243i	$0.655355\pi$
$284$	−2.26267e102	−3.48265
$285$	−6.05679e100	−0.0805713
$286$	3.84014e102	4.41730
$287$	9.31390e100	0.0926900
$288$	−9.56387e101	−0.823844
$289$	−1.26288e102	−0.942114
$290$	−1.14554e102	−0.740443
$291$	−2.30151e102	−1.28960
$292$	7.73622e102	3.75959
$293$	−2.57110e102	−1.08421	−0.542103	−	0.840312i	$-0.682372\pi$
$293$	−2.57110e102	−1.08421	−0.542103	+	0.840312i	$0.682372\pi$
$294$	1.46926e102	0.537880
$295$	1.47027e102	0.467502
$296$	5.21222e102	1.44018
$297$	−6.61039e102	−1.58794
$298$	−1.37921e103	−2.88175
$299$	1.18958e103	2.16291
$300$	−5.21035e102	−0.824773
$301$	7.65655e102	1.05566
$302$	1.10792e103	1.33113
$303$	−6.84677e102	−0.717161
$304$	−3.90665e102	−0.356904
$305$	−3.50610e102	−0.279500
$306$	2.95057e102	0.205337
$307$	1.34633e103	0.818291	0.409146	−	0.912469i	$-0.365827\pi$
$307$	1.34633e103	0.818291	0.409146	+	0.912469i	$0.365827\pi$
$308$	−7.91978e103	−4.20589
$309$	1.25642e103	0.583255
$310$	−3.15164e103	−1.27946
$311$	1.94060e103	0.689256	0.344628	−	0.938739i	$-0.388005\pi$
$311$	1.94060e103	0.689256	0.344628	+	0.938739i	$0.388005\pi$
$312$	9.85861e103	3.06478
$313$	2.42311e103	0.659603	0.329802	−	0.944050i	$-0.393018\pi$
$313$	2.42311e103	0.659603	0.329802	+	0.944050i	$0.393018\pi$
$314$	2.82103e103	0.672709
$315$	1.90854e103	0.398853
$316$	2.19857e103	0.402835
$317$	−3.70204e103	−0.594952	−0.297476	−	0.954729i	$-0.596145\pi$
$317$	−3.70204e103	−0.594952	−0.297476	+	0.954729i	$0.596145\pi$
$318$	−5.13392e103	−0.723975
$319$	−6.58799e103	−0.815529
$320$	6.14761e103	0.668317
$321$	8.76455e103	0.837087
$322$	−3.47477e104	−2.91680
$323$	4.91483e102	0.0362747
$324$	−1.19565e104	−0.776224
$325$	−1.32606e104	−0.757536
$326$	5.02835e104	2.52869
$327$	−1.15756e104	−0.512639
$328$	−5.19568e103	−0.202711
$329$	5.00903e103	0.172236
$330$	4.81534e104	1.45982
$331$	1.64352e104	0.439454	0.219727	−	0.975561i	$-0.429483\pi$
$331$	1.64352e104	0.439454	0.219727	+	0.975561i	$0.429483\pi$
$332$	9.99770e103	0.235868
$333$	−1.23764e104	−0.257726
$334$	−2.13460e104	−0.392498
$335$	−4.65555e104	−0.756156
$336$	−1.42938e105	−2.05148
$337$	1.61304e104	0.204647	0.102323	−	0.994751i	$-0.467372\pi$
$337$	1.61304e104	0.204647	0.102323	+	0.994751i	$0.467372\pi$
$338$	2.65482e105	2.97846
$339$	9.73829e104	0.966485
$340$	−4.79714e104	−0.421315
$341$	−1.81251e105	−1.40921
$342$	1.86886e104	0.128675
$343$	1.16718e105	0.711922
$344$	−4.27114e105	−2.30871
$345$	1.49167e105	0.714795
$346$	1.46120e105	0.620943
$347$	−4.27183e105	−1.61043	−0.805213	−	0.592986i	$-0.797949\pi$
$347$	−4.27183e105	−1.61043	−0.805213	+	0.592986i	$0.797949\pi$
$348$	−2.89774e105	−0.969441
$349$	3.66496e105	1.08846	0.544232	−	0.838935i	$-0.316821\pi$
$349$	3.66496e105	1.08846	0.544232	+	0.838935i	$0.316821\pi$
$350$	3.87343e105	1.02158
$351$	−7.39997e105	−1.73374
$352$	1.26655e106	2.63694
$353$	1.51235e105	0.279900	0.139950	−	0.990159i	$-0.455306\pi$
$353$	1.51235e105	0.279900	0.139950	+	0.990159i	$0.455306\pi$
$354$	5.26763e105	0.866922
$355$	−7.22100e105	−1.05711
$356$	−5.63462e105	−0.733990
$357$	1.79825e105	0.208507
$358$	1.92725e106	1.98972
$359$	1.09666e106	1.00845	0.504224	−	0.863573i	$-0.331779\pi$
$359$	1.09666e106	1.00845	0.504224	+	0.863573i	$0.331779\pi$
$360$	−1.06466e106	−0.872285
$361$	−1.33833e106	−0.977268
$362$	−2.90805e106	−1.89320
$363$	1.50683e106	0.874860
$364$	−8.86575e106	−4.59207
$365$	2.46891e106	1.14117
$366$	−1.25615e106	−0.518296
$367$	3.70532e106	1.36516	0.682581	−	0.730810i	$-0.260858\pi$
$367$	3.70532e106	1.36516	0.682581	+	0.730810i	$0.260858\pi$
$368$	9.62136e106	3.16630
$369$	1.23371e105	0.0362760
$370$	2.84995e106	0.748972
$371$	2.69470e106	0.633131
$372$	−7.97239e106	−1.67516
$373$	3.07328e106	0.577678	0.288839	−	0.957378i	$-0.406731\pi$
$373$	3.07328e106	0.577678	0.288839	+	0.957378i	$0.406731\pi$
$374$	−3.90745e106	−0.657237
$375$	−5.21228e106	−0.784747
$376$	−2.79424e106	−0.376677
$377$	−7.37489e106	−0.890409
$378$	2.16154e107	2.33805
$379$	5.47323e106	0.530538	0.265269	−	0.964174i	$-0.414539\pi$
$379$	5.47323e106	0.530538	0.265269	+	0.964174i	$0.414539\pi$
$380$	−3.03846e106	−0.264018
$381$	−2.53158e106	−0.197245
$382$	−9.52256e106	−0.665463
$383$	−9.71158e106	−0.608893	−0.304446	−	0.952529i	$-0.598471\pi$
$383$	−9.71158e106	−0.608893	−0.304446	+	0.952529i	$0.598471\pi$
$384$	−1.16847e106	−0.0657464
$385$	−2.52749e107	−1.27664
$386$	7.70600e107	3.49507
$387$	1.01418e107	0.413152
$388$	−1.15458e108	−4.22579
$389$	−1.42215e107	−0.467776	−0.233888	−	0.972264i	$-0.575145\pi$
$389$	−1.42215e107	−0.467776	−0.233888	+	0.972264i	$0.575145\pi$
$390$	5.39051e107	1.59386
$391$	−1.21043e107	−0.321814
$392$	4.30202e107	1.02873
$393$	−3.65652e107	−0.786641
$394$	6.68669e107	1.29455
$395$	7.01644e106	0.122275
$396$	−1.04905e108	−1.64606
$397$	1.14994e108	1.62506	0.812531	−	0.582918i	$-0.198089\pi$
$397$	1.14994e108	1.62506	0.812531	+	0.582918i	$0.198089\pi$
$398$	2.20851e108	2.81160
$399$	1.13900e107	0.130661
$400$	−1.07252e108	−1.10896
$401$	5.43350e107	0.506510	0.253255	−	0.967400i	$-0.418499\pi$
$401$	5.43350e107	0.506510	0.253255	+	0.967400i	$0.418499\pi$
$402$	−1.66797e108	−1.40219
$403$	−2.02901e108	−1.53860
$404$	−3.43476e108	−2.35001
$405$	−3.81576e107	−0.235612
$406$	2.15421e108	1.20076
$407$	1.63901e108	0.824923
$408$	−1.00314e108	−0.456000
$409$	1.39453e106	0.00572676	0.00286338	−	0.999996i	$-0.499089\pi$
$409$	1.39453e106	0.00572676	0.00286338	+	0.999996i	$0.499089\pi$
$410$	−2.84091e107	−0.105421
$411$	1.90048e108	0.637422
$412$	6.30298e108	1.91122
$413$	−2.76488e108	−0.758140
$414$	−4.60265e108	−1.14155
$415$	3.19063e107	0.0715946
$416$	1.41783e109	2.87906
$417$	1.74523e108	0.320779
$418$	−2.47494e108	−0.411859
$419$	−9.42224e108	−1.41995	−0.709974	−	0.704228i	$-0.751293\pi$
$419$	−9.42224e108	−1.41995	−0.709974	+	0.704228i	$0.751293\pi$
$420$	−1.11172e109	−1.51758
$421$	9.62089e108	1.18989	0.594947	−	0.803765i	$-0.297173\pi$
$421$	9.62089e108	1.18989	0.594947	+	0.803765i	$0.297173\pi$
$422$	9.87822e107	0.110716
$423$	6.63492e107	0.0674078
$424$	−1.50322e109	−1.38465
$425$	1.34930e108	0.112712
$426$	−2.58711e109	−1.96028
$427$	6.59332e108	0.453260
$428$	4.39684e109	2.74299
$429$	3.10009e109	1.75548
$430$	−2.33539e109	−1.20065
$431$	1.57176e109	0.733805	0.366902	−	0.930259i	$-0.380418\pi$
$431$	1.57176e109	0.733805	0.366902	+	0.930259i	$0.380418\pi$
$432$	−5.98512e109	−2.53804
$433$	−4.39836e109	−1.69450	−0.847252	−	0.531191i	$-0.821745\pi$
$433$	−4.39836e109	−1.69450	−0.847252	+	0.531191i	$0.821745\pi$
$434$	5.92675e109	2.07488
$435$	−9.24775e108	−0.294260
$436$	−5.80704e109	−1.67983
$437$	−7.66674e108	−0.201665
$438$	8.84551e109	2.11615
$439$	−3.99175e108	−0.0868731	−0.0434366	−	0.999056i	$-0.513831\pi$
$439$	−3.99175e108	−0.0868731	−0.0434366	+	0.999056i	$0.513831\pi$
$440$	1.40994e110	2.79199
$441$	−1.02151e109	−0.184095
$442$	−4.37418e109	−0.717583
$443$	6.39603e109	0.955335	0.477667	−	0.878541i	$-0.341482\pi$
$443$	6.39603e109	0.955335	0.477667	+	0.878541i	$0.341482\pi$
$444$	7.20922e109	0.980608
$445$	−1.79821e109	−0.222792
$446$	−2.37991e110	−2.68636
$447$	−1.11342e110	−1.14524
$448$	−1.15608e110	−1.08380
$449$	−1.42574e110	−1.21848	−0.609238	−	0.792988i	$-0.708524\pi$
$449$	−1.42574e110	−1.21848	−0.609238	+	0.792988i	$0.708524\pi$
$450$	5.13071e109	0.399814
$451$	−1.63381e109	−0.116111
$452$	4.88533e110	3.16700
$453$	8.94408e109	0.529006
$454$	−2.16058e110	−1.16615
$455$	−2.82938e110	−1.39386
$456$	−6.35379e109	−0.285754
$457$	−1.42495e110	−0.585164	−0.292582	−	0.956240i	$-0.594514\pi$
$457$	−1.42495e110	−0.585164	−0.292582	+	0.956240i	$0.594514\pi$
$458$	6.90611e110	2.59010
$459$	7.52968e109	0.257959
$460$	7.48315e110	2.34226
$461$	3.36333e110	0.962013	0.481006	−	0.876717i	$-0.340271\pi$
$461$	3.36333e110	0.962013	0.481006	+	0.876717i	$0.340271\pi$
$462$	−9.05539e110	−2.36736
$463$	5.37167e110	1.28380	0.641901	−	0.766788i	$-0.278146\pi$
$463$	5.37167e110	1.28380	0.641901	+	0.766788i	$0.278146\pi$
$464$	−5.96484e110	−1.30347
$465$	−2.54428e110	−0.508472
$466$	−1.21432e111	−2.21982
$467$	6.92656e110	1.15842	0.579212	−	0.815177i	$-0.303360\pi$
$467$	6.92656e110	1.15842	0.579212	+	0.815177i	$0.303360\pi$
$468$	−1.17435e111	−1.79719
$469$	8.75489e110	1.22625
$470$	−1.52784e110	−0.195892
$471$	2.27738e110	0.267342
$472$	1.54237e111	1.65804
$473$	−1.34308e111	−1.32241
$474$	2.51383e110	0.226743
$475$	8.54633e109	0.0706310
$476$	9.02115e110	0.683240
$477$	3.56938e110	0.247788
$478$	−4.11386e111	−2.61813
$479$	7.50347e110	0.437863	0.218932	−	0.975740i	$-0.429743\pi$
$479$	7.50347e110	0.437863	0.218932	+	0.975740i	$0.429743\pi$
$480$	1.77789e111	0.951465
$481$	1.83478e111	0.900666
$482$	−1.89088e111	−0.851551
$483$	−2.80513e111	−1.15917
$484$	7.55918e111	2.86677
$485$	−3.68469e111	−1.28268
$486$	4.82057e111	1.54061
$487$	−2.11122e111	−0.619557	−0.309779	−	0.950809i	$-0.600255\pi$
$487$	−2.11122e111	−0.619557	−0.309779	+	0.950809i	$0.600255\pi$
$488$	−3.67803e111	−0.991272
$489$	4.05931e111	1.00493
$490$	2.35227e111	0.534995
$491$	−2.18896e111	−0.457463	−0.228731	−	0.973490i	$-0.573458\pi$
$491$	−2.18896e111	−0.457463	−0.228731	+	0.973490i	$0.573458\pi$
$492$	−7.18635e110	−0.138025
$493$	7.50416e110	0.132481
$494$	−2.77056e111	−0.449675
$495$	−3.34789e111	−0.499638
$496$	−1.64107e112	−2.25236
$497$	1.35793e112	1.71430
$498$	1.14313e111	0.132763
$499$	−9.92007e111	−1.06009	−0.530044	−	0.847970i	$-0.677825\pi$
$499$	−9.92007e111	−1.06009	−0.530044	+	0.847970i	$0.677825\pi$
$500$	−2.61480e112	−2.57148
$501$	−1.72323e111	−0.155983
$502$	2.05692e112	1.71401
$503$	1.87927e112	1.44184	0.720922	−	0.693016i	$-0.243719\pi$
$503$	1.87927e112	1.44184	0.720922	+	0.693016i	$0.243719\pi$
$504$	2.00213e112	1.41457
$505$	−1.09616e112	−0.713314
$506$	6.09531e112	3.65384
$507$	2.14320e112	1.18367
$508$	−1.27000e112	−0.646338
$509$	−3.76115e112	−1.76414	−0.882070	−	0.471119i	$-0.843850\pi$
$509$	−3.76115e112	−1.76414	−0.882070	+	0.471119i	$0.843850\pi$
$510$	−5.48500e111	−0.237145
$511$	−4.64285e112	−1.85062
$512$	−5.18643e112	−1.90618
$513$	4.76922e111	0.161650
$514$	5.34504e112	1.67102
$515$	2.01151e112	0.580126
$516$	−5.90759e112	−1.57198
$517$	−8.78665e111	−0.215757
$518$	−5.35941e112	−1.21460
$519$	1.17961e112	0.246770
$520$	1.57835e113	3.04834
$521$	−3.51898e112	−0.627554	−0.313777	−	0.949497i	$-0.601594\pi$
$521$	−3.51898e112	−0.627554	−0.313777	+	0.949497i	$0.601594\pi$
$522$	2.85345e112	0.469942
$523$	5.35112e112	0.814001	0.407000	−	0.913428i	$-0.366575\pi$
$523$	5.35112e112	0.814001	0.407000	+	0.913428i	$0.366575\pi$
$524$	−1.83434e113	−2.57769
$525$	3.12696e112	0.405986
$526$	−1.25294e113	−1.50322
$527$	2.06458e112	0.228923
$528$	2.50737e113	2.56986
$529$	8.32791e112	0.789088
$530$	−8.21932e112	−0.720091
$531$	−3.66234e112	−0.296713
$532$	5.71390e112	0.428154
$533$	−1.82896e112	−0.126773
$534$	−6.44257e112	−0.413140
$535$	1.40319e113	0.832597
$536$	−4.88384e113	−2.68178
$537$	1.55584e113	0.790739
$538$	4.19468e113	1.97349
$539$	1.35279e113	0.589247
$540$	−4.65502e113	−1.87750
$541$	9.66777e112	0.361110	0.180555	−	0.983565i	$-0.442211\pi$
$541$	9.66777e112	0.361110	0.180555	+	0.983565i	$0.442211\pi$
$542$	3.85114e113	1.33235
$543$	−2.34763e113	−0.752379
$544$	−1.44268e113	−0.428367
$545$	−1.85324e113	−0.509889
$546$	−1.01370e114	−2.58473
$547$	−4.79012e113	−1.13207	−0.566034	−	0.824382i	$-0.691523\pi$
$547$	−4.79012e113	−1.13207	−0.566034	+	0.824382i	$0.691523\pi$
$548$	9.53396e113	2.08872
$549$	8.73346e112	0.177392
$550$	−6.79462e113	−1.27972
$551$	4.75306e112	0.0830198
$552$	1.56482e114	2.53509
$553$	−1.31946e113	−0.198291
$554$	1.86640e114	2.60226
$555$	2.30072e113	0.297650
$556$	8.75514e113	1.05114
$557$	−1.33380e114	−1.48628	−0.743139	−	0.669137i	$-0.766664\pi$
$557$	−1.33380e114	−1.48628	−0.743139	+	0.669137i	$0.766664\pi$
$558$	7.85053e113	0.812044
$559$	−1.50351e114	−1.44383
$560$	−2.28842e114	−2.04048
$561$	−3.15443e113	−0.261193
$562$	8.53856e113	0.656641
$563$	1.07366e114	0.766952	0.383476	−	0.923551i	$-0.374727\pi$
$563$	1.07366e114	0.766952	0.383476	+	0.923551i	$0.374727\pi$
$564$	−3.86483e113	−0.256476
$565$	1.55908e114	0.961300
$566$	−3.01903e114	−1.72976
$567$	7.17565e113	0.382089
$568$	−7.57510e114	−3.74914
$569$	6.91267e113	0.318043	0.159022	−	0.987275i	$-0.449166\pi$
$569$	6.91267e113	0.318043	0.159022	+	0.987275i	$0.449166\pi$
$570$	−3.47414e113	−0.148608
$571$	−1.12939e114	−0.449207	−0.224603	−	0.974450i	$-0.572109\pi$
$571$	−1.12939e114	−0.449207	−0.224603	+	0.974450i	$0.572109\pi$
$572$	1.55520e115	5.75242
$573$	−7.68743e113	−0.264463
$574$	5.34241e113	0.170960
$575$	−2.10480e114	−0.626608
$576$	−1.53133e114	−0.424166
$577$	5.69480e114	1.46785	0.733926	−	0.679229i	$-0.237686\pi$
$577$	5.69480e114	1.46785	0.733926	+	0.679229i	$0.237686\pi$
$578$	−7.24384e114	−1.73766
$579$	6.22095e114	1.38898
$580$	−4.63924e114	−0.964240
$581$	−6.00006e113	−0.116104
$582$	−1.32014e115	−2.37857
$583$	−4.72694e114	−0.793114
$584$	2.58998e115	4.04727
$585$	−3.74778e114	−0.545514
$586$	−1.47477e115	−1.99973
$587$	6.22626e114	0.786586	0.393293	−	0.919413i	$-0.371336\pi$
$587$	6.22626e114	0.786586	0.393293	+	0.919413i	$0.371336\pi$
$588$	5.95029e114	0.700453
$589$	1.30768e114	0.143455
$590$	8.43339e114	0.862271
$591$	5.39807e114	0.514468
$592$	1.48398e115	1.31849
$593$	−2.14520e115	−1.77704	−0.888521	−	0.458837i	$-0.848266\pi$
$593$	−2.14520e115	−1.77704	−0.888521	+	0.458837i	$0.848266\pi$
$594$	−3.79169e115	−2.92884
$595$	2.87898e114	0.207388
$596$	−5.58560e115	−3.75275
$597$	1.78290e115	1.11736
$598$	6.82337e115	3.98933
$599$	−6.65735e114	−0.363152	−0.181576	−	0.983377i	$-0.558120\pi$
$599$	−6.65735e114	−0.363152	−0.181576	+	0.983377i	$0.558120\pi$
$600$	−1.74435e115	−0.887885
$601$	−2.83273e115	−1.34559	−0.672797	−	0.739827i	$-0.734907\pi$
$601$	−2.83273e115	−1.34559	−0.672797	+	0.739827i	$0.734907\pi$
$602$	4.39176e115	1.94708
$603$	1.15967e115	0.479915
$604$	4.48690e115	1.73346
$605$	2.41241e115	0.870167
$606$	−3.92727e115	−1.32275
$607$	−1.19654e114	−0.0376354	−0.0188177	−	0.999823i	$-0.505990\pi$
$607$	−1.19654e114	−0.0376354	−0.0188177	+	0.999823i	$0.505990\pi$
$608$	−9.13779e114	−0.268437
$609$	1.73906e115	0.477197
$610$	−2.01108e115	−0.515515
$611$	−9.83617e114	−0.235568
$612$	1.19493e115	0.267399
$613$	1.22181e115	0.255503	0.127751	−	0.991806i	$-0.459224\pi$
$613$	1.22181e115	0.255503	0.127751	+	0.991806i	$0.459224\pi$
$614$	7.72246e115	1.50928
$615$	−2.29343e114	−0.0418955
$616$	−2.65143e116	−4.52773
$617$	−2.81178e115	−0.448898	−0.224449	−	0.974486i	$-0.572058\pi$
$617$	−2.81178e115	−0.448898	−0.224449	+	0.974486i	$0.572058\pi$
$618$	7.20677e115	1.07577
$619$	1.88468e115	0.263073	0.131537	−	0.991311i	$-0.458009\pi$
$619$	1.88468e115	0.263073	0.131537	+	0.991311i	$0.458009\pi$
$620$	−1.27637e116	−1.66617
$621$	−1.17457e116	−1.43409
$622$	1.11312e116	1.27128
$623$	3.38159e115	0.361299
$624$	2.80686e116	2.80582
$625$	−3.33636e115	−0.312070
$626$	1.38988e116	1.21659
$627$	−1.99798e115	−0.163677
$628$	1.14247e116	0.876034
$629$	−1.86694e115	−0.134007
$630$	1.09473e116	0.735654
$631$	−2.74123e116	−1.72475	−0.862377	−	0.506266i	$-0.831025\pi$
$631$	−2.74123e116	−1.72475	−0.862377	+	0.506266i	$0.831025\pi$
$632$	7.36051e115	0.433660
$633$	7.97455e114	0.0439999
$634$	−2.12347e116	−1.09734
$635$	−4.05303e115	−0.196187
$636$	−2.07916e116	−0.942795
$637$	1.51438e116	0.643350
$638$	−3.77884e116	−1.50418
$639$	1.79870e116	0.670925
$640$	−1.87070e115	−0.0653937
$641$	5.20673e116	1.70591	0.852957	−	0.521981i	$-0.174807\pi$
$641$	5.20673e116	1.70591	0.852957	+	0.521981i	$0.174807\pi$
$642$	5.02730e116	1.54394
$643$	4.71221e116	1.35666	0.678328	−	0.734759i	$-0.262705\pi$
$643$	4.71221e116	1.35666	0.678328	+	0.734759i	$0.262705\pi$
$644$	−1.40723e117	−3.79840
$645$	−1.88532e116	−0.477153
$646$	2.81912e115	0.0669059
$647$	−2.17791e115	−0.0484744	−0.0242372	−	0.999706i	$-0.507716\pi$
$647$	−2.17791e115	−0.0484744	−0.0242372	+	0.999706i	$0.507716\pi$
$648$	−4.00287e116	−0.835621
$649$	4.85006e116	0.949712
$650$	−7.60620e116	−1.39722
$651$	4.78459e116	0.824581
$652$	2.03640e117	3.29298
$653$	−8.05843e116	−1.22279	−0.611397	−	0.791324i	$-0.709392\pi$
$653$	−8.05843e116	−1.22279	−0.611397	+	0.791324i	$0.709392\pi$
$654$	−6.63971e116	−0.945524
$655$	−5.85403e116	−0.782422
$656$	−1.47927e116	−0.185583
$657$	−6.14988e116	−0.724276
$658$	2.87315e116	0.317676
$659$	1.59649e117	1.65737	0.828687	−	0.559712i	$-0.189088\pi$
$659$	1.59649e117	1.65737	0.828687	+	0.559712i	$0.189088\pi$
$660$	1.95014e117	1.90105
$661$	−3.70951e116	−0.339591	−0.169795	−	0.985479i	$-0.554311\pi$
$661$	−3.70951e116	−0.339591	−0.169795	+	0.985479i	$0.554311\pi$
$662$	9.42714e116	0.810538
$663$	−3.53121e116	−0.285176
$664$	3.34709e116	0.253917
$665$	1.82351e116	0.129960
$666$	−7.09903e116	−0.475356
$667$	−1.17059e117	−0.736516
$668$	−8.64479e116	−0.511130
$669$	−1.92127e117	−1.06759
$670$	−2.67040e117	−1.39467
$671$	−1.15658e117	−0.567792
$672$	−3.34337e117	−1.54298
$673$	−1.73647e117	−0.753428	−0.376714	−	0.926330i	$-0.622946\pi$
$673$	−1.73647e117	−0.753428	−0.376714	+	0.926330i	$0.622946\pi$
$674$	9.25232e116	0.377455
$675$	1.30933e117	0.502275
$676$	1.07516e118	3.87870
$677$	−3.55186e117	−1.20511	−0.602554	−	0.798078i	$-0.705850\pi$
$677$	−3.55186e117	−1.20511	−0.602554	+	0.798078i	$0.705850\pi$
$678$	5.58583e117	1.78261
$679$	6.92916e117	2.08010
$680$	−1.60601e117	−0.453554
$681$	−1.74421e117	−0.463439
$682$	−1.03965e118	−2.59917
$683$	1.29187e117	0.303919	0.151960	−	0.988387i	$-0.451442\pi$
$683$	1.29187e117	0.303919	0.151960	+	0.988387i	$0.451442\pi$
$684$	7.56859e116	0.167566
$685$	3.04263e117	0.634002
$686$	6.69489e117	1.31309
$687$	5.57520e117	1.02933
$688$	−1.21604e118	−2.11363
$689$	−5.29155e117	−0.865936
$690$	8.55616e117	1.31838
$691$	−9.45747e117	−1.37226	−0.686130	−	0.727479i	$-0.740692\pi$
$691$	−9.45747e117	−1.37226	−0.686130	+	0.727479i	$0.740692\pi$
$692$	5.91764e117	0.808622
$693$	6.29580e117	0.810255
$694$	−2.45030e118	−2.97031
$695$	2.79408e117	0.319058
$696$	−9.70123e117	−1.04362
$697$	1.86102e116	0.0188621
$698$	2.10220e118	2.00759
$699$	−9.80305e117	−0.882182
$700$	1.56868e118	1.33035
$701$	1.74599e118	1.39555	0.697773	−	0.716319i	$-0.254175\pi$
$701$	1.74599e118	1.39555	0.697773	+	0.716319i	$0.254175\pi$
$702$	−4.24459e118	−3.19776
$703$	−1.18250e117	−0.0839761
$704$	2.02795e118	1.35766
$705$	−1.23341e117	−0.0778499
$706$	8.67477e117	0.516253
$707$	2.06136e118	1.15677
$708$	2.13331e118	1.12895
$709$	−2.15519e118	−1.07564	−0.537820	−	0.843060i	$-0.680752\pi$
$709$	−2.15519e118	−1.07564	−0.537820	+	0.843060i	$0.680752\pi$
$710$	−4.14193e118	−1.94976
$711$	−1.74775e117	−0.0776051
$712$	−1.88639e118	−0.790154
$713$	−3.22057e118	−1.27268
$714$	1.03147e118	0.384575
$715$	4.96320e118	1.74607
$716$	7.80507e118	2.59111
$717$	−3.32106e118	−1.04048
$718$	6.29040e118	1.86000
$719$	5.23632e118	1.46143	0.730713	−	0.682684i	$-0.239188\pi$
$719$	5.23632e118	1.46143	0.730713	+	0.682684i	$0.239188\pi$
$720$	−3.03122e118	−0.798580
$721$	−3.78270e118	−0.940781
$722$	−7.67658e118	−1.80250
$723$	−1.52648e118	−0.338416
$724$	−1.17772e119	−2.46542
$725$	1.30489e118	0.257957
$726$	8.64309e118	1.61361
$727$	2.96822e118	0.523380	0.261690	−	0.965152i	$-0.415720\pi$
$727$	2.96822e118	0.523380	0.261690	+	0.965152i	$0.415720\pi$
$728$	−2.96813e119	−4.94345
$729$	5.94570e118	0.935429
$730$	1.41615e119	2.10480
$731$	1.52986e118	0.214823
$732$	−5.08723e118	−0.674949
$733$	−4.90635e118	−0.615097	−0.307548	−	0.951532i	$-0.599509\pi$
$733$	−4.90635e118	−0.615097	−0.307548	+	0.951532i	$0.599509\pi$
$734$	2.12535e119	2.51793
$735$	1.89895e118	0.212613
$736$	2.25047e119	2.38146
$737$	−1.53575e119	−1.53610
$738$	7.07651e117	0.0669083
$739$	−2.50614e118	−0.224006	−0.112003	−	0.993708i	$-0.535727\pi$
$739$	−2.50614e118	−0.224006	−0.112003	+	0.993708i	$0.535727\pi$
$740$	1.15419e119	0.975347
$741$	−2.23663e118	−0.178706
$742$	1.54567e119	1.16776
$743$	5.68434e118	0.406111	0.203055	−	0.979167i	$-0.434913\pi$
$743$	5.68434e118	0.406111	0.203055	+	0.979167i	$0.434913\pi$
$744$	−2.66904e119	−1.80334
$745$	−1.78257e119	−1.13910
$746$	1.76282e119	1.06548
$747$	−7.94764e117	−0.0454394
$748$	−1.58246e119	−0.855886
$749$	−2.63874e119	−1.35021
$750$	−2.98974e119	−1.44741
$751$	1.60839e119	0.736773	0.368386	−	0.929673i	$-0.379910\pi$
$751$	1.60839e119	0.736773	0.368386	+	0.929673i	$0.379910\pi$
$752$	−7.95553e118	−0.344849
$753$	1.66052e119	0.681165
$754$	−4.23020e119	−1.64229
$755$	1.43193e119	0.526168
$756$	8.75389e119	3.04472
$757$	−4.58990e119	−1.51121	−0.755603	−	0.655030i	$-0.772656\pi$
$757$	−4.58990e119	−1.51121	−0.755603	+	0.655030i	$0.772656\pi$
$758$	3.13942e119	0.978536
$759$	4.92066e119	1.45208
$760$	−1.01723e119	−0.284221
$761$	−1.69386e119	−0.448141	−0.224071	−	0.974573i	$-0.571935\pi$
$761$	−1.69386e119	−0.448141	−0.224071	+	0.974573i	$0.571935\pi$
$762$	−1.45210e119	−0.363803
$763$	3.48506e119	0.826880
$764$	−3.85649e119	−0.866598
$765$	3.81347e118	0.0811654
$766$	−5.57051e119	−1.12306
$767$	5.42937e119	1.03691
$768$	−4.38395e119	−0.793185
$769$	−3.51803e119	−0.603054	−0.301527	−	0.953458i	$-0.597496\pi$
$769$	−3.51803e119	−0.603054	−0.301527	+	0.953458i	$0.597496\pi$
$770$	−1.44975e120	−2.35467
$771$	4.31497e119	0.664081
$772$	3.12081e120	4.55145
$773$	1.30391e120	1.80218	0.901089	−	0.433635i	$-0.142769\pi$
$773$	1.30391e120	1.80218	0.901089	+	0.433635i	$0.142769\pi$
$774$	5.81729e119	0.762028
$775$	3.59007e119	0.445740
$776$	−3.86537e120	−4.54915
$777$	−4.32658e119	−0.482694
$778$	−8.15740e119	−0.862777
$779$	1.17875e118	0.0118200
$780$	2.18307e120	2.07560
$781$	−2.38203e120	−2.14748
$782$	−6.94297e119	−0.593560
$783$	7.28184e119	0.590375
$784$	1.22483e120	0.941804
$785$	3.64605e119	0.265908
$786$	−2.09736e120	−1.45090
$787$	1.71631e119	0.112627	0.0563137	−	0.998413i	$-0.482065\pi$
$787$	1.71631e119	0.112627	0.0563137	+	0.998413i	$0.482065\pi$
$788$	2.70801e120	1.68582
$789$	−1.01148e120	−0.597396
$790$	4.02460e119	0.225527
$791$	−2.93190e120	−1.55893
$792$	−3.51206e120	−1.77201
$793$	−1.29472e120	−0.619926
$794$	6.59601e120	2.99730
$795$	−6.63535e119	−0.286172
$796$	8.94414e120	3.66139
$797$	−8.26745e119	−0.321256	−0.160628	−	0.987015i	$-0.551352\pi$
$797$	−8.26745e119	−0.321256	−0.160628	+	0.987015i	$0.551352\pi$
$798$	6.53322e119	0.240995
$799$	1.00086e119	0.0350494
$800$	−2.50866e120	−0.834080
$801$	4.47923e119	0.141401
$802$	3.11663e120	0.934219
$803$	8.14432e120	2.31825
$804$	−6.75503e120	−1.82600
$805$	−4.49097e120	−1.15295
$806$	−1.16383e121	−2.83782
$807$	3.38631e120	0.784286
$808$	−1.14991e121	−2.52984
$809$	−4.09910e120	−0.856692	−0.428346	−	0.903615i	$-0.640904\pi$
$809$	−4.09910e120	−0.856692	−0.428346	+	0.903615i	$0.640904\pi$
$810$	−2.18870e120	−0.434569
$811$	−1.92720e120	−0.363548	−0.181774	−	0.983340i	$-0.558184\pi$
$811$	−1.92720e120	−0.363548	−0.181774	+	0.983340i	$0.558184\pi$
$812$	8.72422e120	1.56369
$813$	3.10897e120	0.529491
$814$	9.40128e120	1.52151
$815$	6.49890e120	0.999538
$816$	−2.85606e120	−0.417470
$817$	9.68999e119	0.134619
$818$	7.99893e118	0.0105626
$819$	7.04780e120	0.884651
$820$	−1.15052e120	−0.137284
$821$	−5.71778e120	−0.648614	−0.324307	−	0.945952i	$-0.605131\pi$
$821$	−5.71778e120	−0.648614	−0.324307	+	0.945952i	$0.605131\pi$
$822$	1.09010e121	1.17567
$823$	−1.02581e121	−1.05189	−0.525947	−	0.850517i	$-0.676289\pi$
$823$	−1.02581e121	−1.05189	−0.525947	+	0.850517i	$0.676289\pi$
$824$	2.11015e121	2.05747
$825$	−5.48520e120	−0.508573
$826$	−1.58592e121	−1.39833
$827$	4.70644e120	0.394652	0.197326	−	0.980338i	$-0.436774\pi$
$827$	4.70644e120	0.394652	0.197326	+	0.980338i	$0.436774\pi$
$828$	−1.86400e121	−1.48658
$829$	−1.39997e121	−1.06196	−0.530978	−	0.847386i	$-0.678175\pi$
$829$	−1.39997e121	−1.06196	−0.530978	+	0.847386i	$0.678175\pi$
$830$	1.83013e120	0.132051
$831$	1.50672e121	1.03417
$832$	2.27017e121	1.48232
$833$	−1.54092e120	−0.0957222
$834$	1.00105e121	0.591652
$835$	−2.75887e120	−0.155146
$836$	−1.00231e121	−0.536343
$837$	2.00341e121	1.02015
$838$	−5.40455e121	−2.61898
$839$	1.31175e121	0.604965	0.302482	−	0.953155i	$-0.402185\pi$
$839$	1.31175e121	0.604965	0.302482	+	0.953155i	$0.402185\pi$
$840$	−3.72188e121	−1.63370
$841$	−1.66779e121	−0.696797
$842$	5.51849e121	2.19467
$843$	6.89306e120	0.260956
$844$	4.00053e120	0.144180
$845$	3.43123e121	1.17732
$846$	3.80575e120	0.124328
$847$	−4.53660e121	−1.41114
$848$	−4.27983e121	−1.26765
$849$	−2.43722e121	−0.687426
$850$	7.73953e120	0.207888
$851$	2.91228e121	0.745000
$852$	−1.04774e122	−2.55276
$853$	7.58780e121	1.76089	0.880443	−	0.474152i	$-0.157245\pi$
$853$	7.58780e121	1.76089	0.880443	+	0.474152i	$0.157245\pi$
$854$	3.78190e121	0.836003
$855$	2.41541e120	0.0508625
$856$	1.47200e122	2.95288
$857$	−5.93254e121	−1.13380	−0.566900	−	0.823787i	$-0.691857\pi$
$857$	−5.93254e121	−1.13380	−0.566900	+	0.823787i	$0.691857\pi$
$858$	1.77820e122	3.23786
$859$	−3.20457e121	−0.555973	−0.277986	−	0.960585i	$-0.589667\pi$
$859$	−3.20457e121	−0.555973	−0.277986	+	0.960585i	$0.589667\pi$
$860$	−9.45796e121	−1.56355
$861$	4.31285e120	0.0679413
$862$	9.01556e121	1.35345
$863$	−3.79790e121	−0.543370	−0.271685	−	0.962386i	$-0.587581\pi$
$863$	−3.79790e121	−0.543370	−0.271685	+	0.962386i	$0.587581\pi$
$864$	−1.39994e122	−1.90893
$865$	1.88853e121	0.245446
$866$	−2.52287e122	−3.12538
$867$	−5.84785e121	−0.690564
$868$	2.40024e122	2.70201
$869$	2.31455e121	0.248397
$870$	−5.30446e121	−0.542741
$871$	−1.71919e122	−1.67714
$872$	−1.94411e122	−1.80837
$873$	9.17831e121	0.814089
$874$	−4.39760e121	−0.371956
$875$	1.56926e122	1.26579
$876$	3.58230e122	2.75576
$877$	−1.82343e122	−1.33784	−0.668921	−	0.743333i	$-0.733244\pi$
$877$	−1.82343e122	−1.33784	−0.668921	+	0.743333i	$0.733244\pi$
$878$	−2.28965e121	−0.160231
$879$	−1.19056e122	−0.794717
$880$	4.01425e122	2.55608
$881$	1.57188e122	0.954812	0.477406	−	0.878683i	$-0.341577\pi$
$881$	1.57188e122	0.954812	0.477406	+	0.878683i	$0.341577\pi$
$882$	−5.85934e121	−0.339549
$883$	−3.38304e122	−1.87042	−0.935208	−	0.354100i	$-0.884787\pi$
$883$	−3.38304e122	−1.87042	−0.935208	+	0.354100i	$0.884787\pi$
$884$	−1.77147e122	−0.934471
$885$	6.80816e121	0.342676
$886$	3.66873e122	1.76204
$887$	3.37751e122	1.54798	0.773992	−	0.633196i	$-0.218257\pi$
$887$	3.37751e122	1.54798	0.773992	+	0.633196i	$0.218257\pi$
$888$	2.41354e122	1.05564
$889$	7.62183e121	0.318153
$890$	−1.03145e122	−0.410924
$891$	−1.25873e122	−0.478637
$892$	−9.63826e122	−3.49830
$893$	6.33933e120	0.0219638
$894$	−6.38652e122	−2.11231
$895$	2.49088e122	0.786497
$896$	3.51791e121	0.106048
$897$	5.50841e122	1.58540
$898$	−8.17796e122	−2.24738
$899$	1.99662e122	0.523924
$900$	2.07786e122	0.520657
$901$	5.38431e121	0.128840
$902$	−9.37145e121	−0.214159
$903$	3.54541e122	0.773792
$904$	1.63554e123	3.40934
$905$	−3.75852e122	−0.748344
$906$	5.13028e122	0.975710
$907$	−6.71963e122	−1.22080	−0.610398	−	0.792095i	$-0.708991\pi$
$907$	−6.71963e122	−1.22080	−0.610398	+	0.792095i	$0.708991\pi$
$908$	−8.75002e122	−1.51861
$909$	2.73045e122	0.452724
$910$	−1.62292e123	−2.57087
$911$	−1.20667e122	−0.182631	−0.0913154	−	0.995822i	$-0.529107\pi$
$911$	−1.20667e122	−0.182631	−0.0913154	+	0.995822i	$0.529107\pi$
$912$	−1.80900e122	−0.261608
$913$	1.05251e122	0.145442
$914$	−8.17344e122	−1.07929
$915$	−1.62352e122	−0.204872
$916$	2.79687e123	3.37295
$917$	1.10087e123	1.26884
$918$	4.31899e122	0.475785
$919$	−1.44898e123	−1.52570	−0.762852	−	0.646573i	$-0.776201\pi$
$919$	−1.44898e123	−1.52570	−0.762852	+	0.646573i	$0.776201\pi$
$920$	2.50525e123	2.52149
$921$	6.23424e122	0.599803
$922$	1.92919e123	1.77436
$923$	−2.66655e123	−2.34466
$924$	−3.66729e123	−3.08290
$925$	−3.24640e122	−0.260928
$926$	3.08116e123	2.36787
$927$	−5.01054e122	−0.368193
$928$	−1.39520e123	−0.980379
$929$	9.61063e122	0.645802	0.322901	−	0.946433i	$-0.395342\pi$
$929$	9.61063e122	0.645802	0.322901	+	0.946433i	$0.395342\pi$
$930$	−1.45939e123	−0.937837
$931$	−9.76003e121	−0.0599846
$932$	−4.91781e123	−2.89076
$933$	8.98606e122	0.505221
$934$	3.97304e123	2.13662
$935$	−5.05019e122	−0.259792
$936$	−3.93156e123	−1.93471
$937$	−4.01216e123	−1.88880	−0.944398	−	0.328804i	$-0.893355\pi$
$937$	−4.01216e123	−1.88880	−0.944398	+	0.328804i	$0.893355\pi$
$938$	5.02176e123	2.26172
$939$	1.12203e123	0.483485
$940$	−6.18753e122	−0.255100
$941$	2.84096e123	1.12072	0.560359	−	0.828250i	$-0.310663\pi$
$941$	2.84096e123	1.12072	0.560359	+	0.828250i	$0.310663\pi$
$942$	1.30629e123	0.493092
$943$	−2.90304e122	−0.104862
$944$	4.39129e123	1.51794
$945$	2.79368e123	0.924182
$946$	−7.70386e123	−2.43908
$947$	2.06208e123	0.624859	0.312430	−	0.949941i	$-0.398857\pi$
$947$	2.06208e123	0.624859	0.312430	+	0.949941i	$0.398857\pi$
$948$	1.01806e123	0.295276
$949$	9.11711e123	2.53110
$950$	4.90213e122	0.130273
$951$	−1.71425e123	−0.436096
$952$	3.02015e123	0.735522
$953$	−7.70655e123	−1.79682	−0.898410	−	0.439159i	$-0.855277\pi$
$953$	−7.70655e123	−1.79682	−0.898410	+	0.439159i	$0.855277\pi$
$954$	2.04738e123	0.457026
$955$	−1.23075e123	−0.263044
$956$	−1.66605e124	−3.40946
$957$	−3.05060e123	−0.597778
$958$	4.30395e123	0.807605
$959$	−5.72176e123	−1.02815
$960$	2.84668e123	0.489873
$961$	−5.74468e122	−0.0946772
$962$	1.05242e124	1.66121
$963$	−3.49525e123	−0.528430
$964$	−7.65775e123	−1.10893
$965$	9.95964e123	1.38153
$966$	−1.60901e124	−2.13800
$967$	9.11804e123	1.16065	0.580327	−	0.814383i	$-0.302925\pi$
$967$	9.11804e123	1.16065	0.580327	+	0.814383i	$0.302925\pi$
$968$	2.53071e124	3.08613
$969$	2.27584e122	0.0265891
$970$	−2.11352e124	−2.36581
$971$	4.22485e123	0.453120	0.226560	−	0.973997i	$-0.427252\pi$
$971$	4.22485e123	0.453120	0.226560	+	0.973997i	$0.427252\pi$
$972$	1.95226e124	2.00626
$973$	−5.25435e123	−0.517412
$974$	−1.21098e124	−1.14273
$975$	−6.14038e123	−0.555269
$976$	−1.04718e124	−0.907513
$977$	−3.22951e123	−0.268233	−0.134117	−	0.990966i	$-0.542820\pi$
$977$	−3.22951e123	−0.268233	−0.134117	+	0.990966i	$0.542820\pi$
$978$	2.32840e124	1.85351
$979$	−5.93186e123	−0.452594
$980$	9.52632e123	0.696696
$981$	4.61629e123	0.323615
$982$	−1.25558e124	−0.843755
$983$	1.75024e124	1.12753	0.563764	−	0.825936i	$-0.309353\pi$
$983$	1.75024e124	1.12753	0.563764	+	0.825936i	$0.309353\pi$
$984$	−2.40589e123	−0.148586
$985$	8.64223e123	0.511708
$986$	4.30435e123	0.244352
$987$	2.31945e123	0.126248
$988$	−1.12203e124	−0.585588
$989$	−2.38646e124	−1.19429
$990$	−1.92033e124	−0.921544
$991$	5.75888e123	0.265022	0.132511	−	0.991182i	$-0.457696\pi$
$991$	5.75888e123	0.265022	0.132511	+	0.991182i	$0.457696\pi$
$992$	−3.83852e124	−1.69406
$993$	7.61040e123	0.322117
$994$	7.78901e124	3.16190
$995$	2.85440e124	1.11137
$996$	4.62948e123	0.172890
$997$	3.22059e124	1.15368	0.576841	−	0.816857i	$-0.304285\pi$
$997$	3.22059e124	1.15368	0.576841	+	0.816857i	$0.304285\pi$
$998$	−5.69010e124	−1.95525
$999$	−1.81163e124	−0.597176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.84.a.a.1.7	✓	7
3.2	odd	2		9.84.a.c.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.84.a.a.1.7	✓	7	1.1	even	1	trivial
9.84.a.c.1.1		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)

\(f(q)\)	\(=\)	\(q+5.73595e12 q^{2} +4.63055e19 q^{3} +2.32297e25 q^{4} +7.41344e28 q^{5} +2.65606e32 q^{6} -1.39412e35 q^{7} +7.77697e37 q^{8} -1.84664e39 q^{9} +O(q^{10})\)	\(q+5.73595e12 q^{2} +4.63055e19 q^{3} +2.32297e25 q^{4} +7.41344e28 q^{5} +2.65606e32 q^{6} -1.39412e35 q^{7} +7.77697e37 q^{8} -1.84664e39 q^{9} +4.25231e41 q^{10} +2.44551e43 q^{11} +1.07566e45 q^{12} +2.73761e46 q^{13} -7.99659e47 q^{14} +3.43283e48 q^{15} +2.21419e50 q^{16} -2.78560e50 q^{17} -1.05922e52 q^{18} -1.76437e52 q^{19} +1.72212e54 q^{20} -6.45554e54 q^{21} +1.40273e56 q^{22} +4.34531e56 q^{23} +3.60117e57 q^{24} -4.84385e57 q^{25} +1.57028e59 q^{26} -2.70307e59 q^{27} -3.23850e60 q^{28} -2.69391e60 q^{29} +1.96906e61 q^{30} -7.41160e61 q^{31} +5.17907e62 q^{32} +1.13241e63 q^{33} -1.59781e63 q^{34} -1.03352e64 q^{35} -4.28969e64 q^{36} +6.70212e64 q^{37} -1.01203e65 q^{38} +1.26767e66 q^{39} +5.76541e66 q^{40} -6.68086e65 q^{41} -3.70286e67 q^{42} -5.49204e67 q^{43} +5.68085e68 q^{44} -1.36899e68 q^{45} +2.49245e69 q^{46} -3.59297e68 q^{47} +1.02529e70 q^{48} +5.53174e69 q^{49} -2.77841e70 q^{50} -1.28989e70 q^{51} +6.35940e71 q^{52} -1.93291e71 q^{53} -1.55047e72 q^{54} +1.81296e72 q^{55} -1.08420e73 q^{56} -8.17000e71 q^{57} -1.54521e73 q^{58} +1.98325e73 q^{59} +7.97437e73 q^{60} -4.72939e73 q^{61} -4.25126e74 q^{62} +2.57443e74 q^{63} +8.29252e74 q^{64} +2.02951e75 q^{65} +6.49542e75 q^{66} -6.27987e75 q^{67} -6.47087e75 q^{68} +2.01212e76 q^{69} -5.92823e76 q^{70} -9.74042e76 q^{71} -1.43613e77 q^{72} +3.33031e77 q^{73} +3.84430e77 q^{74} -2.24297e77 q^{75} -4.09858e77 q^{76} -3.40933e78 q^{77} +7.27127e78 q^{78} +9.46449e77 q^{79} +1.64148e79 q^{80} -5.14709e78 q^{81} -3.83210e78 q^{82} +4.30384e78 q^{83} -1.49960e80 q^{84} -2.06509e79 q^{85} -3.15021e80 q^{86} -1.24743e80 q^{87} +1.90187e81 q^{88} -2.42561e80 q^{89} -7.85248e80 q^{90} -3.81656e81 q^{91} +1.00940e82 q^{92} -3.43198e81 q^{93} -2.06091e81 q^{94} -1.30801e81 q^{95} +2.39819e82 q^{96} -4.97028e82 q^{97} +3.17298e82 q^{98} -4.51597e82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) \) 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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