LMFDB - Embedded newform 1.84.a.a.1.2

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			1.2
Root			$-1.58823e11$ 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)

$f(q)$	$=$	$q-3.76211e12 q^{2} -6.68720e19 q^{3} +4.48205e24 q^{4} +1.95538e28 q^{5} +2.51580e32 q^{6} +1.66208e35 q^{7} +1.95229e37 q^{8} +4.81025e38 q^{9} +O(q^{10})$	\(q-3.76211e12 q^{2} -6.68720e19 q^{3} +4.48205e24 q^{4} +1.95538e28 q^{5} +2.51580e32 q^{6} +1.66208e35 q^{7} +1.95229e37 q^{8} +4.81025e38 q^{9} -7.35637e40 q^{10} +1.57715e43 q^{11} -2.99724e44 q^{12} +1.54355e46 q^{13} -6.25291e47 q^{14} -1.30760e48 q^{15} -1.16795e50 q^{16} -2.86818e50 q^{17} -1.80967e51 q^{18} +1.03565e53 q^{19} +8.76414e52 q^{20} -1.11146e55 q^{21} -5.93342e55 q^{22} -2.08646e56 q^{23} -1.30554e57 q^{24} -9.95741e57 q^{25} -5.80700e58 q^{26} +2.34708e59 q^{27} +7.44952e59 q^{28} +6.67410e60 q^{29} +4.91935e60 q^{30} -1.54744e62 q^{31} +2.50582e62 q^{32} -1.05467e63 q^{33} +1.07904e63 q^{34} +3.25000e63 q^{35} +2.15598e63 q^{36} +2.28009e65 q^{37} -3.89622e65 q^{38} -1.03220e66 q^{39} +3.81748e65 q^{40} +3.48018e66 q^{41} +4.18145e67 q^{42} +4.05016e67 q^{43} +7.06889e67 q^{44} +9.40588e66 q^{45} +7.84950e68 q^{46} +2.43131e69 q^{47} +7.81032e69 q^{48} +1.37211e70 q^{49} +3.74608e70 q^{50} +1.91801e70 q^{51} +6.91827e70 q^{52} -3.24750e71 q^{53} -8.82998e71 q^{54} +3.08394e71 q^{55} +3.24486e72 q^{56} -6.92558e72 q^{57} -2.51087e73 q^{58} -3.03695e73 q^{59} -5.86075e72 q^{60} -6.07893e73 q^{61} +5.82164e74 q^{62} +7.99500e73 q^{63} +1.86857e74 q^{64} +3.01823e74 q^{65} +3.96780e75 q^{66} -5.36442e75 q^{67} -1.28553e75 q^{68} +1.39526e76 q^{69} -1.22268e76 q^{70} -8.80285e76 q^{71} +9.39100e75 q^{72} -1.58272e76 q^{73} -8.57795e77 q^{74} +6.65872e77 q^{75} +4.64183e77 q^{76} +2.62135e78 q^{77} +3.88325e78 q^{78} +9.61180e77 q^{79} -2.28379e78 q^{80} -1.76151e79 q^{81} -1.30928e79 q^{82} +6.23836e79 q^{83} -4.98164e79 q^{84} -5.60839e78 q^{85} -1.52371e80 q^{86} -4.46310e80 q^{87} +3.07906e80 q^{88} +3.80332e80 q^{89} -3.53859e79 q^{90} +2.56550e81 q^{91} -9.35165e80 q^{92} +1.03480e82 q^{93} -9.14684e81 q^{94} +2.02509e81 q^{95} -1.67569e82 q^{96} -8.03314e81 q^{97} -5.16202e82 q^{98} +7.58650e81 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.76211e12	−1.20972	−0.604862	−	0.796330i	$-0.706772\pi$
$2$	−3.76211e12	−1.20972	−0.604862	+	0.796330i	$0.706772\pi$
$3$	−6.68720e19	−1.05855	−0.529276	−	0.848450i	$-0.677536\pi$
$3$	−6.68720e19	−1.05855	−0.529276	+	0.848450i	$0.677536\pi$
$4$	4.48205e24	0.463434
$5$	1.95538e28	0.192299	0.0961494	−	0.995367i	$-0.469347\pi$
$5$	1.95538e28	0.192299	0.0961494	+	0.995367i	$0.469347\pi$
$6$	2.51580e32	1.28056
$7$	1.66208e35	1.40956	0.704778	−	0.709428i	$-0.251047\pi$
$7$	1.66208e35	1.40956	0.704778	+	0.709428i	$0.251047\pi$
$8$	1.95229e37	0.649098
$9$	4.81025e38	0.120532
$10$	−7.35637e40	−0.232629
$11$	1.57715e43	0.955163	0.477582	−	0.878587i	$-0.341514\pi$
$11$	1.57715e43	0.955163	0.477582	+	0.878587i	$0.341514\pi$
$12$	−2.99724e44	−0.490569
$13$	1.54355e46	0.911740	0.455870	−	0.890046i	$-0.349328\pi$
$13$	1.54355e46	0.911740	0.455870	+	0.890046i	$0.349328\pi$
$14$	−6.25291e47	−1.70518
$15$	−1.30760e48	−0.203558
$16$	−1.16795e50	−1.24866
$17$	−2.86818e50	−0.247728	−0.123864	−	0.992299i	$-0.539529\pi$
$17$	−2.86818e50	−0.247728	−0.123864	+	0.992299i	$0.539529\pi$
$18$	−1.80967e51	−0.145811
$19$	1.03565e53	0.884988	0.442494	−	0.896771i	$-0.354094\pi$
$19$	1.03565e53	0.884988	0.442494	+	0.896771i	$0.354094\pi$
$20$	8.76414e52	0.0891178
$21$	−1.11146e55	−1.49209
$22$	−5.93342e55	−1.15548
$23$	−2.08646e56	−0.642252	−0.321126	−	0.947036i	$-0.604061\pi$
$23$	−2.08646e56	−0.642252	−0.321126	+	0.947036i	$0.604061\pi$
$24$	−1.30554e57	−0.687104
$25$	−9.95741e57	−0.963021
$26$	−5.80700e58	−1.10295
$27$	2.34708e59	0.930962
$28$	7.44952e59	0.653236
$29$	6.67410e60	1.36419	0.682096	−	0.731262i	$-0.261069\pi$
$29$	6.67410e60	1.36419	0.682096	+	0.731262i	$0.261069\pi$
$30$	4.91935e60	0.246250
$31$	−1.54744e62	−1.98657	−0.993284	−	0.115701i	$-0.963089\pi$
$31$	−1.54744e62	−1.98657	−0.993284	+	0.115701i	$0.963089\pi$
$32$	2.50582e62	0.861441
$33$	−1.05467e63	−1.01109
$34$	1.07904e63	0.299683
$35$	3.25000e63	0.271056
$36$	2.15598e63	0.0558587
$37$	2.28009e65	1.89488	0.947438	−	0.319941i	$-0.103663\pi$
$37$	2.28009e65	1.89488	0.947438	+	0.319941i	$0.103663\pi$
$38$	−3.89622e65	−1.07059
$39$	−1.03220e66	−0.965125
$40$	3.81748e65	0.124821
$41$	3.48018e66	0.408387	0.204193	−	0.978931i	$-0.434543\pi$
$41$	3.48018e66	0.408387	0.204193	+	0.978931i	$0.434543\pi$
$42$	4.18145e67	1.80502
$43$	4.05016e67	0.658462	0.329231	−	0.944249i	$-0.393210\pi$
$43$	4.05016e67	0.658462	0.329231	+	0.944249i	$0.393210\pi$
$44$	7.06889e67	0.442655
$45$	9.40588e66	0.0231782
$46$	7.84950e68	0.776949
$47$	2.43131e69	0.985777	0.492889	−	0.870092i	$-0.335941\pi$
$47$	2.43131e69	0.985777	0.492889	+	0.870092i	$0.335941\pi$
$48$	7.81032e69	1.32177
$49$	1.37211e70	0.986849
$50$	3.74608e70	1.16499
$51$	1.91801e70	0.262233
$52$	6.91827e70	0.422531
$53$	−3.24750e71	−0.899706	−0.449853	−	0.893103i	$-0.648524\pi$
$53$	−3.24750e71	−0.899706	−0.449853	+	0.893103i	$0.648524\pi$
$54$	−8.82998e71	−1.12621
$55$	3.08394e71	0.183677
$56$	3.24486e72	0.914940
$57$	−6.92558e72	−0.936806
$58$	−2.51087e73	−1.65030
$59$	−3.03695e73	−0.981929	−0.490964	−	0.871180i	$-0.663355\pi$
$59$	−3.03695e73	−0.981929	−0.490964	+	0.871180i	$0.663355\pi$
$60$	−5.86075e72	−0.0943358
$61$	−6.07893e73	−0.492764	−0.246382	−	0.969173i	$-0.579242\pi$
$61$	−6.07893e73	−0.492764	−0.246382	+	0.969173i	$0.579242\pi$
$62$	5.82164e74	2.40320
$63$	7.99500e73	0.169897
$64$	1.86857e74	0.206557
$65$	3.01823e74	0.175327
$66$	3.96780e75	1.22314
$67$	−5.36442e75	−0.885969	−0.442984	−	0.896529i	$-0.646080\pi$
$67$	−5.36442e75	−0.885969	−0.442984	+	0.896529i	$0.646080\pi$
$68$	−1.28553e75	−0.114806
$69$	1.39526e76	0.679858
$70$	−1.22268e76	−0.327903
$71$	−8.80285e76	−1.31039	−0.655197	−	0.755458i	$-0.727414\pi$
$71$	−8.80285e76	−1.31039	−0.655197	+	0.755458i	$0.727414\pi$
$72$	9.39100e75	0.0782372
$73$	−1.58272e76	−0.0743887	−0.0371943	−	0.999308i	$-0.511842\pi$
$73$	−1.58272e76	−0.0743887	−0.0371943	+	0.999308i	$0.511842\pi$
$74$	−8.57795e77	−2.29228
$75$	6.65872e77	1.01941
$76$	4.64183e77	0.410133
$77$	2.62135e78	1.34636
$78$	3.88325e78	1.16753
$79$	9.61180e77	0.170326	0.0851629	−	0.996367i	$-0.472859\pi$
$79$	9.61180e77	0.170326	0.0851629	+	0.996367i	$0.472859\pi$
$80$	−2.28379e78	−0.240116
$81$	−1.76151e79	−1.10600
$82$	−1.30928e79	−0.494035
$83$	6.23836e79	1.42341	0.711704	−	0.702479i	$-0.247924\pi$
$83$	6.23836e79	1.42341	0.711704	+	0.702479i	$0.247924\pi$
$84$	−4.98164e79	−0.691484
$85$	−5.60839e78	−0.0476379
$86$	−1.52371e80	−0.796558
$87$	−4.46310e80	−1.44407
$88$	3.07906e80	0.619994
$89$	3.80332e80	0.479157	0.239578	−	0.970877i	$-0.422991\pi$
$89$	3.80332e80	0.479157	0.239578	+	0.970877i	$0.422991\pi$
$90$	−3.53859e79	−0.0280393
$91$	2.56550e81	1.28515
$92$	−9.35165e80	−0.297641
$93$	1.03480e82	2.10289
$94$	−9.14684e81	−1.19252
$95$	2.02509e81	0.170182
$96$	−1.67569e82	−0.911880
$97$	−8.03314e81	−0.284353	−0.142177	−	0.989841i	$-0.545410\pi$
$97$	−8.03314e81	−0.284353	−0.142177	+	0.989841i	$0.545410\pi$
$98$	−5.16202e82	−1.19382
$99$	7.58650e81	0.115128
$100$	−4.46296e82	−0.446296
$101$	2.79563e83	1.84988	0.924939	−	0.380116i	$-0.124116\pi$
$101$	2.79563e83	1.84988	0.924939	+	0.380116i	$0.124116\pi$
$102$	−7.21575e82	−0.317230
$103$	−2.74147e83	−0.803969	−0.401984	−	0.915646i	$-0.631679\pi$
$103$	−2.74147e83	−0.803969	−0.401984	+	0.915646i	$0.631679\pi$
$104$	3.01346e83	0.591809
$105$	−2.17334e83	−0.286927
$106$	1.22174e84	1.08840
$107$	4.90933e82	0.0296207	0.0148103	−	0.999890i	$-0.495286\pi$
$107$	4.90933e82	0.0296207	0.0148103	+	0.999890i	$0.495286\pi$
$108$	1.05198e84	0.431439
$109$	2.89032e84	0.808624	0.404312	−	0.914621i	$-0.367511\pi$
$109$	2.89032e84	0.808624	0.404312	+	0.914621i	$0.367511\pi$
$110$	−1.16021e84	−0.222198
$111$	−1.52474e85	−2.00582
$112$	−1.94122e85	−1.76006
$113$	3.23999e84	0.203136	0.101568	−	0.994829i	$-0.467614\pi$
$113$	3.23999e84	0.203136	0.101568	+	0.994829i	$0.467614\pi$
$114$	2.60548e85	1.13328
$115$	−4.07984e84	−0.123504
$116$	2.99137e85	0.632213
$117$	7.42485e84	0.109894
$118$	1.14254e86	1.18786
$119$	−4.76713e85	−0.349187
$120$	−2.55282e85	−0.132129
$121$	−2.39007e85	−0.0876634
$122$	2.28696e86	0.596109
$123$	−2.32727e86	−0.432299
$124$	−6.93571e86	−0.920642
$125$	−3.96887e86	−0.377487
$126$	−3.00781e86	−0.205529
$127$	2.95189e87	1.45293	0.726467	−	0.687201i	$-0.241161\pi$
$127$	2.95189e87	1.45293	0.726467	+	0.687201i	$0.241161\pi$
$128$	−3.12645e87	−1.11132
$129$	−2.70842e87	−0.697017
$130$	−1.13549e87	−0.212097
$131$	8.76943e87	1.19183	0.595913	−	0.803049i	$-0.296790\pi$
$131$	8.76943e87	1.19183	0.595913	+	0.803049i	$0.296790\pi$
$132$	−4.72711e87	−0.468573
$133$	1.72133e88	1.24744
$134$	2.01815e88	1.07178
$135$	4.58945e87	0.179023
$136$	−5.59951e87	−0.160800
$137$	−3.81478e88	−0.808287	−0.404144	−	0.914696i	$-0.632430\pi$
$137$	−3.81478e88	−0.808287	−0.404144	+	0.914696i	$0.632430\pi$
$138$	−5.24912e88	−0.822440
$139$	−1.12530e89	−1.30663	−0.653315	−	0.757086i	$-0.726622\pi$
$139$	−1.12530e89	−1.30663	−0.653315	+	0.757086i	$0.726622\pi$
$140$	1.45667e88	0.125617
$141$	−1.62586e89	−1.04350
$142$	3.31173e89	1.58522
$143$	2.43441e89	0.870861
$144$	−5.61813e88	−0.150504
$145$	1.30504e89	0.262333
$146$	5.95438e88	0.0899898
$147$	−9.17556e89	−1.04463
$148$	1.02195e90	0.878149
$149$	1.73231e90	1.12563	0.562815	−	0.826583i	$-0.309718\pi$
$149$	1.73231e90	1.12563	0.562815	+	0.826583i	$0.309718\pi$
$150$	−2.50508e90	−1.23320
$151$	8.38919e89	0.313456	0.156728	−	0.987642i	$-0.449905\pi$
$151$	8.38919e89	0.313456	0.156728	+	0.987642i	$0.449905\pi$
$152$	2.02189e90	0.574444
$153$	−1.37966e89	−0.0298593
$154$	−9.86181e90	−1.62872
$155$	−3.02584e90	−0.382015
$156$	−4.62638e90	−0.447271
$157$	6.87875e90	0.510122	0.255061	−	0.966925i	$-0.417904\pi$
$157$	6.87875e90	0.510122	0.255061	+	0.966925i	$0.417904\pi$
$158$	−3.61606e90	−0.206047
$159$	2.17167e91	0.952386
$160$	4.89983e90	0.165654
$161$	−3.46786e91	−0.905291
$162$	6.62699e91	1.33796
$163$	9.29918e91	1.45432	0.727158	−	0.686470i	$-0.240841\pi$
$163$	9.29918e91	1.45432	0.727158	+	0.686470i	$0.240841\pi$
$164$	1.55984e91	0.189260
$165$	−2.06229e91	−0.194431
$166$	−2.34694e92	−1.72193
$167$	−4.16853e91	−0.238369	−0.119184	−	0.992872i	$-0.538028\pi$
$167$	−4.16853e91	−0.238369	−0.119184	+	0.992872i	$0.538028\pi$
$168$	−2.16990e92	−0.968511
$169$	−4.83603e91	−0.168729
$170$	2.10994e91	0.0576287
$171$	4.98172e91	0.106670
$172$	1.81530e92	0.305154
$173$	4.60190e92	0.608169	0.304084	−	0.952645i	$-0.401650\pi$
$173$	4.60190e92	0.608169	0.304084	+	0.952645i	$0.401650\pi$
$174$	1.67907e93	1.74693
$175$	−1.65500e93	−1.35743
$176$	−1.84204e93	−1.19268
$177$	2.03087e93	1.03942
$178$	−1.43085e93	−0.579647
$179$	4.63689e93	1.48876	0.744382	−	0.667754i	$-0.232744\pi$
$179$	4.63689e93	1.48876	0.744382	+	0.667754i	$0.232744\pi$
$180$	4.21577e91	0.0107416
$181$	3.06896e93	0.621341	0.310671	−	0.950518i	$-0.399446\pi$
$181$	3.06896e93	0.621341	0.310671	+	0.950518i	$0.399446\pi$
$182$	−9.65168e93	−1.55468
$183$	4.06510e93	0.521617
$184$	−4.07338e93	−0.416885
$185$	4.45845e93	0.364382
$186$	−3.89304e94	−2.54391
$187$	−4.52355e93	−0.236621
$188$	1.08973e94	0.456842
$189$	3.90103e94	1.31224
$190$	−7.61860e93	−0.205874
$191$	8.40728e94	1.82714	0.913568	−	0.406686i	$-0.133316\pi$
$191$	8.40728e94	1.82714	0.913568	+	0.406686i	$0.133316\pi$
$192$	−1.24955e94	−0.218651
$193$	−9.56818e93	−0.134959	−0.0674794	−	0.997721i	$-0.521496\pi$
$193$	−9.56818e93	−0.134959	−0.0674794	+	0.997721i	$0.521496\pi$
$194$	3.02215e94	0.343989
$195$	−2.01835e94	−0.185592
$196$	6.14986e94	0.457339
$197$	−2.10092e95	−1.26491	−0.632456	−	0.774596i	$-0.717953\pi$
$197$	−2.10092e95	−1.26491	−0.632456	+	0.774596i	$0.717953\pi$
$198$	−2.85412e94	−0.139273
$199$	−1.13664e95	−0.450010	−0.225005	−	0.974358i	$-0.572240\pi$
$199$	−1.13664e95	−0.450010	−0.225005	+	0.974358i	$0.572240\pi$
$200$	−1.94397e95	−0.625095
$201$	3.58729e95	0.937844
$202$	−1.05175e96	−2.23784
$203$	1.10929e96	1.92291
$204$	8.59661e94	0.121528
$205$	6.80509e94	0.0785323
$206$	1.03137e96	0.972581
$207$	−1.00364e95	−0.0774121
$208$	−1.80279e96	−1.13846
$209$	1.63338e96	0.845308
$210$	8.17633e95	0.347103
$211$	−1.71697e96	−0.598468	−0.299234	−	0.954180i	$-0.596731\pi$
$211$	−1.71697e96	−0.598468	−0.299234	+	0.954180i	$0.596731\pi$
$212$	−1.45555e96	−0.416954
$213$	5.88664e96	1.38712
$214$	−1.84694e95	−0.0358329
$215$	7.91961e95	0.126622
$216$	4.58219e96	0.604285
$217$	−2.57196e97	−2.80018
$218$	−1.08737e97	−0.978213
$219$	1.05840e96	0.0787443
$220$	1.38224e96	0.0851220
$221$	−4.42717e96	−0.225864
$222$	5.73625e97	2.42649
$223$	−1.09963e97	−0.386008	−0.193004	−	0.981198i	$-0.561823\pi$
$223$	−1.09963e97	−0.386008	−0.193004	+	0.981198i	$0.561823\pi$
$224$	4.16486e97	1.21425
$225$	−4.78976e96	−0.116075
$226$	−1.21892e97	−0.245739
$227$	7.81227e97	1.31131	0.655653	−	0.755062i	$-0.272393\pi$
$227$	7.81227e97	1.31131	0.655653	+	0.755062i	$0.272393\pi$
$228$	−3.10408e97	−0.434147
$229$	−1.50776e98	−1.75858	−0.879288	−	0.476291i	$-0.841981\pi$
$229$	−1.50776e98	−1.75858	−0.879288	+	0.476291i	$0.841981\pi$
$230$	1.53488e97	0.149406
$231$	−1.75295e98	−1.42519
$232$	1.30298e98	0.885494
$233$	9.20166e96	0.0523113	0.0261557	−	0.999658i	$-0.491673\pi$
$233$	9.20166e96	0.0523113	0.0261557	+	0.999658i	$0.491673\pi$
$234$	−2.79331e97	−0.132942
$235$	4.75414e97	0.189564
$236$	−1.36118e98	−0.455059
$237$	−6.42760e97	−0.180299
$238$	1.79345e98	0.422420
$239$	2.98788e98	0.591357	0.295679	−	0.955287i	$-0.404454\pi$
$239$	2.98788e98	0.591357	0.295679	+	0.955287i	$0.404454\pi$
$240$	1.52722e98	0.254176
$241$	−9.04678e97	−0.126703	−0.0633515	−	0.997991i	$-0.520179\pi$
$241$	−9.04678e97	−0.126703	−0.0633515	+	0.997991i	$0.520179\pi$
$242$	8.99172e97	0.106049
$243$	2.41274e98	0.239801
$244$	−2.72461e98	−0.228364
$245$	2.68300e98	0.189770
$246$	8.75542e98	0.522962
$247$	1.59857e99	0.806880
$248$	−3.02105e99	−1.28948
$249$	−4.17172e99	−1.50675
$250$	1.49313e99	0.456655
$251$	2.57941e99	0.668437	0.334219	−	0.942496i	$-0.391528\pi$
$251$	2.57941e99	0.668437	0.334219	+	0.942496i	$0.391528\pi$
$252$	3.58340e98	0.0787360
$253$	−3.29067e99	−0.613456
$254$	−1.11053e100	−1.75765
$255$	3.75044e98	0.0504272
$256$	9.95489e99	1.13783
$257$	−4.68226e99	−0.455230	−0.227615	−	0.973751i	$-0.573093\pi$
$257$	−4.68226e99	−0.455230	−0.227615	+	0.973751i	$0.573093\pi$
$258$	1.01894e100	0.843198
$259$	3.78969e100	2.67093
$260$	1.35279e99	0.0812523
$261$	3.21041e99	0.164429
$262$	−3.29915e100	−1.44178
$263$	1.03753e100	0.387114	0.193557	−	0.981089i	$-0.437998\pi$
$263$	1.03753e100	0.387114	0.193557	+	0.981089i	$0.437998\pi$
$264$	−2.05903e100	−0.656296
$265$	−6.35011e99	−0.173012
$266$	−6.47582e100	−1.50906
$267$	−2.54335e100	−0.507212
$268$	−2.40436e100	−0.410588
$269$	9.23197e100	1.35075	0.675375	−	0.737475i	$-0.263982\pi$
$269$	9.23197e100	1.35075	0.675375	+	0.737475i	$0.263982\pi$
$270$	−1.72660e100	−0.216569
$271$	1.13749e101	1.22383	0.611917	−	0.790922i	$-0.290399\pi$
$271$	1.13749e101	1.22383	0.611917	+	0.790922i	$0.290399\pi$
$272$	3.34989e100	0.309329
$273$	−1.71560e101	−1.36040
$274$	1.43516e101	0.977805
$275$	−1.57044e101	−0.919842
$276$	6.25363e100	0.315069
$277$	−9.66258e100	−0.418970	−0.209485	−	0.977812i	$-0.567179\pi$
$277$	−9.66258e100	−0.418970	−0.209485	+	0.977812i	$0.567179\pi$
$278$	4.23349e101	1.58066
$279$	−7.44357e100	−0.239446
$280$	6.34494e100	0.175942
$281$	−1.19538e101	−0.285885	−0.142943	−	0.989731i	$-0.545656\pi$
$281$	−1.19538e101	−0.285885	−0.142943	+	0.989731i	$0.545656\pi$
$282$	6.11668e101	1.26234
$283$	−5.03803e101	−0.897684	−0.448842	−	0.893611i	$-0.648163\pi$
$283$	−5.03803e101	−0.897684	−0.448842	+	0.893611i	$0.648163\pi$
$284$	−3.94548e101	−0.607280
$285$	−1.35422e101	−0.180147
$286$	−9.15853e101	−1.05350
$287$	5.78433e101	0.575644
$288$	1.20536e101	0.103831
$289$	−1.25822e102	−0.938631
$290$	−4.90971e101	−0.317350
$291$	5.37192e101	0.301003
$292$	−7.09386e100	−0.0344742
$293$	9.31769e101	0.392918	0.196459	−	0.980512i	$-0.437056\pi$
$293$	9.31769e101	0.392918	0.196459	+	0.980512i	$0.437056\pi$
$294$	3.45194e102	1.26372
$295$	−5.93841e101	−0.188824
$296$	4.45140e102	1.22996
$297$	3.70171e102	0.889221
$298$	−6.51714e102	−1.36170
$299$	−3.22056e102	−0.585567
$300$	2.98447e102	0.472428
$301$	6.73167e102	0.928140
$302$	−3.15611e102	−0.379196
$303$	−1.86949e103	−1.95819
$304$	−1.20959e103	−1.10505
$305$	−1.18866e102	−0.0947580
$306$	5.19045e101	0.0361215
$307$	2.81336e102	0.170995	0.0854973	−	0.996338i	$-0.472752\pi$
$307$	2.81336e102	0.170995	0.0854973	+	0.996338i	$0.472752\pi$
$308$	1.17490e103	0.623947
$309$	1.83328e103	0.851043
$310$	1.13835e103	0.462133
$311$	7.00646e102	0.248853	0.124426	−	0.992229i	$-0.460291\pi$
$311$	7.00646e102	0.248853	0.124426	+	0.992229i	$0.460291\pi$
$312$	−2.01516e103	−0.626460
$313$	3.43919e103	0.936194	0.468097	−	0.883677i	$-0.344940\pi$
$313$	3.43919e103	0.936194	0.468097	+	0.883677i	$0.344940\pi$
$314$	−2.58786e103	−0.617107
$315$	1.56333e102	0.0326710
$316$	4.30806e102	0.0789347
$317$	−8.71226e102	−0.140014	−0.0700070	−	0.997547i	$-0.522302\pi$
$317$	−8.71226e102	−0.140014	−0.0700070	+	0.997547i	$0.522302\pi$
$318$	−8.17005e103	−1.15212
$319$	1.05261e104	1.30303
$320$	3.65377e102	0.0397207
$321$	−3.28296e102	−0.0313550
$322$	1.30465e104	1.09515
$323$	−2.97042e103	−0.219237
$324$	−7.89518e103	−0.512559
$325$	−1.53697e104	−0.878025
$326$	−3.49845e104	−1.75932
$327$	−1.93282e104	−0.855971
$328$	6.79432e103	0.265083
$329$	4.04102e104	1.38951
$330$	7.75857e103	0.235209
$331$	1.74091e104	0.465495	0.232747	−	0.972537i	$-0.425228\pi$
$331$	1.74091e104	0.465495	0.232747	+	0.972537i	$0.425228\pi$
$332$	2.79607e104	0.659655
$333$	1.09678e104	0.228394
$334$	1.56825e104	0.288360
$335$	−1.04895e104	−0.170371
$336$	1.29813e105	1.86312
$337$	−1.17971e105	−1.49670	−0.748350	−	0.663304i	$-0.769154\pi$
$337$	−1.17971e105	−1.49670	−0.748350	+	0.663304i	$0.769154\pi$
$338$	1.81937e104	0.204116
$339$	−2.16664e104	−0.215030
$340$	−2.51371e103	−0.0220770
$341$	−2.44055e105	−1.89750
$342$	−1.87418e104	−0.129041
$343$	−3.03907e103	−0.0185368
$344$	7.90708e104	0.427406
$345$	2.72827e104	0.130736
$346$	−1.73129e105	−0.735717
$347$	9.62166e104	0.362725	0.181362	−	0.983416i	$-0.441949\pi$
$347$	9.62166e104	0.362725	0.181362	+	0.983416i	$0.441949\pi$
$348$	−2.00039e105	−0.669230
$349$	−8.73629e104	−0.259461	−0.129730	−	0.991549i	$-0.541411\pi$
$349$	−8.73629e104	−0.259461	−0.129730	+	0.991549i	$0.541411\pi$
$350$	6.22628e105	1.64212
$351$	3.62284e105	0.848796
$352$	3.95206e105	0.822816
$353$	1.21464e105	0.224801	0.112401	−	0.993663i	$-0.464146\pi$
$353$	1.21464e105	0.224801	0.112401	+	0.993663i	$0.464146\pi$
$354$	−7.64036e105	−1.25741
$355$	−1.72129e105	−0.251987
$356$	1.70467e105	0.222057
$357$	3.18787e105	0.369633
$358$	−1.74445e106	−1.80099
$359$	1.68929e106	1.55340	0.776702	−	0.629869i	$-0.216891\pi$
$359$	1.68929e106	1.55340	0.776702	+	0.629869i	$0.216891\pi$
$360$	1.83630e104	0.0150449
$361$	−2.96893e105	−0.216796
$362$	−1.15458e106	−0.751652
$363$	1.59829e105	0.0927963
$364$	1.14987e106	0.595581
$365$	−3.09483e104	−0.0143049
$366$	−1.52934e106	−0.631013
$367$	−3.04040e106	−1.12018	−0.560092	−	0.828430i	$-0.689234\pi$
$367$	−3.04040e106	−1.12018	−0.560092	+	0.828430i	$0.689234\pi$
$368$	2.43689e106	0.801957
$369$	1.67405e105	0.0492238
$370$	−1.67732e106	−0.440802
$371$	−5.39759e106	−1.26819
$372$	4.63805e106	0.974548
$373$	7.73158e106	1.45329	0.726644	−	0.687014i	$-0.241079\pi$
$373$	7.73158e106	1.45329	0.726644	+	0.687014i	$0.241079\pi$
$374$	1.70181e106	0.286246
$375$	2.65407e106	0.399589
$376$	4.74662e106	0.639866
$377$	1.03018e107	1.24379
$378$	−1.46761e107	−1.58745
$379$	1.33873e107	1.29767	0.648836	−	0.760929i	$-0.275256\pi$
$379$	1.33873e107	1.29767	0.648836	+	0.760929i	$0.275256\pi$
$380$	9.07656e105	0.0788682
$381$	−1.97399e107	−1.53801
$382$	−3.16291e107	−2.21033
$383$	−2.43713e107	−1.52802	−0.764010	−	0.645204i	$-0.776772\pi$
$383$	−2.43713e107	−1.52802	−0.764010	+	0.645204i	$0.776772\pi$
$384$	2.09072e107	1.17639
$385$	5.12575e106	0.258903
$386$	3.59965e106	0.163263
$387$	1.94823e106	0.0793660
$388$	−3.60049e106	−0.131779
$389$	2.96841e107	0.976371	0.488186	−	0.872740i	$-0.337659\pi$
$389$	2.96841e107	0.976371	0.488186	+	0.872740i	$0.337659\pi$
$390$	7.59325e106	0.224516
$391$	5.98435e106	0.159104
$392$	2.67875e107	0.640561
$393$	−5.86429e107	−1.26161
$394$	7.90388e107	1.53020
$395$	1.87948e106	0.0327535
$396$	3.40031e106	0.0533542
$397$	−7.61528e107	−1.07617	−0.538084	−	0.842891i	$-0.680852\pi$
$397$	−7.61528e107	−1.07617	−0.538084	+	0.842891i	$0.680852\pi$
$398$	4.27618e107	0.544388
$399$	−1.15108e108	−1.32048
$400$	1.16298e108	1.20249
$401$	1.83663e108	1.71210	0.856051	−	0.516891i	$-0.172911\pi$
$401$	1.83663e108	1.71210	0.856051	+	0.516891i	$0.172911\pi$
$402$	−1.34958e108	−1.13453
$403$	−2.38855e108	−1.81123
$404$	1.25302e108	0.857295
$405$	−3.44443e107	−0.212683
$406$	−4.17326e108	−2.32619
$407$	3.59605e108	1.80991
$408$	3.74451e107	0.170215
$409$	2.54069e107	0.104336	0.0521680	−	0.998638i	$-0.483387\pi$
$409$	2.54069e107	0.104336	0.0521680	+	0.998638i	$0.483387\pi$
$410$	−2.56015e107	−0.0950025
$411$	2.55102e108	0.855614
$412$	−1.22874e108	−0.372586
$413$	−5.04765e108	−1.38408
$414$	3.77581e107	0.0936474
$415$	1.21984e108	0.273720
$416$	3.86785e108	0.785410
$417$	7.52508e108	1.38314
$418$	−6.14494e108	−1.02259
$419$	1.24138e109	1.87079	0.935393	−	0.353609i	$-0.115046\pi$
$419$	1.24138e109	1.87079	0.935393	+	0.353609i	$0.115046\pi$
$420$	−9.74102e107	−0.132972
$421$	−1.01700e109	−1.25781	−0.628904	−	0.777483i	$-0.716496\pi$
$421$	−1.01700e109	−1.25781	−0.628904	+	0.777483i	$0.716496\pi$
$422$	6.45943e108	0.723981
$423$	1.16952e108	0.118818
$424$	−6.34006e108	−0.583997
$425$	2.85596e108	0.238568
$426$	−2.21462e109	−1.67803
$427$	−1.01037e109	−0.694579
$428$	2.20039e107	0.0137272
$429$	−1.62794e109	−0.921851
$430$	−2.97944e108	−0.153177
$431$	1.04249e109	0.486703	0.243352	−	0.969938i	$-0.421753\pi$
$431$	1.04249e109	0.486703	0.243352	+	0.969938i	$0.421753\pi$
$432$	−2.74128e109	−1.16246
$433$	3.20495e109	1.23474	0.617368	−	0.786674i	$-0.288199\pi$
$433$	3.20495e109	1.23474	0.617368	+	0.786674i	$0.288199\pi$
$434$	9.67601e109	3.38745
$435$	−8.72708e108	−0.277693
$436$	1.29546e109	0.374744
$437$	−2.16084e109	−0.568386
$438$	−3.98181e108	−0.0952589
$439$	−1.87780e109	−0.408669	−0.204335	−	0.978901i	$-0.565503\pi$
$439$	−1.87780e109	−0.408669	−0.204335	+	0.978901i	$0.565503\pi$
$440$	6.02075e108	0.119224
$441$	6.60018e108	0.118947
$442$	1.66555e109	0.273233
$443$	−5.14989e109	−0.769207	−0.384604	−	0.923082i	$-0.625662\pi$
$443$	−5.14989e109	−0.769207	−0.384604	+	0.923082i	$0.625662\pi$
$444$	−6.83398e109	−0.929566
$445$	7.43695e108	0.0921413
$446$	4.13694e109	0.466964
$447$	−1.15843e110	−1.19154
$448$	3.10570e109	0.291154
$449$	8.93975e109	0.764016	0.382008	−	0.924159i	$-0.375233\pi$
$449$	8.93975e109	0.764016	0.382008	+	0.924159i	$0.375233\pi$
$450$	1.80196e109	0.140419
$451$	5.48878e109	0.390076
$452$	1.45218e109	0.0941402
$453$	−5.61002e109	−0.331810
$454$	−2.93906e110	−1.58632
$455$	5.01653e109	0.247133
$456$	−1.35207e110	−0.608079
$457$	−5.58235e109	−0.229242	−0.114621	−	0.993409i	$-0.536565\pi$
$457$	−5.58235e109	−0.229242	−0.114621	+	0.993409i	$0.536565\pi$
$458$	5.67237e110	2.12739
$459$	−6.73185e109	−0.230626
$460$	−1.82861e109	−0.0572361
$461$	2.21966e110	0.634891	0.317445	−	0.948277i	$-0.397175\pi$
$461$	2.21966e110	0.634891	0.317445	+	0.948277i	$0.397175\pi$
$462$	6.59479e110	1.72409
$463$	−6.75566e109	−0.161457	−0.0807285	−	0.996736i	$-0.525725\pi$
$463$	−6.75566e109	−0.161457	−0.0807285	+	0.996736i	$0.525725\pi$
$464$	−7.79502e110	−1.70342
$465$	2.02344e110	0.404383
$466$	−3.46177e109	−0.0632823
$467$	3.66494e110	0.612937	0.306469	−	0.951881i	$-0.400853\pi$
$467$	3.66494e110	0.612937	0.306469	+	0.951881i	$0.400853\pi$
$468$	3.32786e109	0.0509286
$469$	−8.91608e110	−1.24882
$470$	−1.78856e110	−0.229320
$471$	−4.59996e110	−0.539990
$472$	−5.92902e110	−0.637367
$473$	6.38772e110	0.628939
$474$	2.41813e110	0.218112
$475$	−1.03124e111	−0.852263
$476$	−2.13665e110	−0.161825
$477$	−1.56213e110	−0.108444
$478$	−1.12407e111	−0.715380
$479$	2.39386e111	1.39693	0.698465	−	0.715644i	$-0.253867\pi$
$479$	2.39386e111	1.39693	0.698465	+	0.715644i	$0.253867\pi$
$480$	−3.27662e110	−0.175353
$481$	3.51943e111	1.72763
$482$	3.40350e110	0.153276
$483$	2.31903e111	0.958298
$484$	−1.07124e110	−0.0406262
$485$	−1.57079e110	−0.0546808
$486$	−9.07700e110	−0.290093
$487$	2.38100e111	0.698726	0.349363	−	0.936988i	$-0.386398\pi$
$487$	2.38100e111	0.698726	0.349363	+	0.936988i	$0.386398\pi$
$488$	−1.18678e111	−0.319852
$489$	−6.21855e111	−1.53947
$490$	−1.00937e111	−0.229569
$491$	−2.91833e111	−0.609891	−0.304945	−	0.952370i	$-0.598638\pi$
$491$	−2.91833e111	−0.609891	−0.304945	+	0.952370i	$0.598638\pi$
$492$	−1.04309e111	−0.200342
$493$	−1.91425e111	−0.337949
$494$	−6.01400e111	−0.976102
$495$	1.48345e110	0.0221390
$496$	1.80733e112	2.48055
$497$	−1.46310e112	−1.84707
$498$	1.56944e112	1.82275
$499$	2.64463e111	0.282613	0.141307	−	0.989966i	$-0.454870\pi$
$499$	2.64463e111	0.282613	0.141307	+	0.989966i	$0.454870\pi$
$500$	−1.77887e111	−0.174940
$501$	2.78758e111	0.252326
$502$	−9.70401e111	−0.808625
$503$	−1.45072e112	−1.11304	−0.556520	−	0.830834i	$-0.687864\pi$
$503$	−1.45072e112	−1.11304	−0.556520	+	0.830834i	$0.687864\pi$
$504$	1.56086e111	0.110280
$505$	5.46653e111	0.355729
$506$	1.23799e112	0.742113
$507$	3.23395e111	0.178609
$508$	1.32305e112	0.673339
$509$	−2.78815e111	−0.130776	−0.0653880	−	0.997860i	$-0.520829\pi$
$509$	−2.78815e111	−0.130776	−0.0653880	+	0.997860i	$0.520829\pi$
$510$	−1.41096e111	−0.0610030
$511$	−2.63061e111	−0.104855
$512$	−7.21417e111	−0.265145
$513$	2.43075e112	0.823891
$514$	1.76152e112	0.550703
$515$	−5.36063e111	−0.154602
$516$	−1.21393e112	−0.323021
$517$	3.83455e112	0.941578
$518$	−1.42572e113	−3.23109
$519$	−3.07738e112	−0.643778
$520$	5.89246e111	0.113804
$521$	−2.73888e112	−0.488436	−0.244218	−	0.969720i	$-0.578531\pi$
$521$	−2.73888e112	−0.488436	−0.244218	+	0.969720i	$0.578531\pi$
$522$	−1.20779e112	−0.198914
$523$	1.03362e112	0.157232	0.0786159	−	0.996905i	$-0.474950\pi$
$523$	1.03362e112	0.157232	0.0786159	+	0.996905i	$0.474950\pi$
$524$	3.93051e112	0.552332
$525$	1.10673e113	1.43691
$526$	−3.90331e112	−0.468301
$527$	4.43833e112	0.492129
$528$	1.23181e113	1.26251
$529$	−6.20050e112	−0.587512
$530$	2.38898e112	0.209297
$531$	−1.46085e112	−0.118354
$532$	7.71508e112	0.578106
$533$	5.37183e112	0.372343
$534$	9.56838e112	0.613587
$535$	9.59962e110	0.00569603
$536$	−1.04729e113	−0.575080
$537$	−3.10078e113	−1.57593
$538$	−3.47317e113	−1.63403
$539$	2.16402e113	0.942602
$540$	2.05701e112	0.0829653
$541$	3.60651e113	1.34710	0.673551	−	0.739141i	$-0.264768\pi$
$541$	3.60651e113	1.34710	0.673551	+	0.739141i	$0.264768\pi$
$542$	−4.27937e113	−1.48050
$543$	−2.05227e113	−0.657722
$544$	−7.18713e112	−0.213403
$545$	5.65169e112	0.155498
$546$	6.45427e113	1.64571
$547$	−5.93233e113	−1.40201	−0.701006	−	0.713156i	$-0.747265\pi$
$547$	−5.93233e113	−1.40201	−0.701006	+	0.713156i	$0.747265\pi$
$548$	−1.70980e113	−0.374587
$549$	−2.92412e112	−0.0593940
$550$	5.90815e113	1.11276
$551$	6.91201e113	1.20729
$552$	2.72395e113	0.441294
$553$	1.59755e113	0.240084
$554$	3.63517e113	0.506838
$555$	−2.98146e113	−0.385718
$556$	−5.04364e113	−0.605536
$557$	−1.60497e114	−1.78845	−0.894226	−	0.447615i	$-0.852273\pi$
$557$	−1.60497e114	−1.78845	−0.894226	+	0.447615i	$0.852273\pi$
$558$	2.80035e113	0.289663
$559$	6.25161e113	0.600347
$560$	−3.79584e113	−0.338458
$561$	3.02499e113	0.250476
$562$	4.49713e113	0.345843
$563$	1.36019e114	0.971632	0.485816	−	0.874061i	$-0.338522\pi$
$563$	1.36019e114	0.971632	0.485816	+	0.874061i	$0.338522\pi$
$564$	−7.28721e113	−0.483591
$565$	6.33541e112	0.0390629
$566$	1.89536e114	1.08595
$567$	−2.92776e114	−1.55898
$568$	−1.71857e114	−0.850573
$569$	−2.49280e114	−1.14691	−0.573454	−	0.819238i	$-0.694397\pi$
$569$	−2.49280e114	−1.14691	−0.573454	+	0.819238i	$0.694397\pi$
$570$	5.09471e113	0.217928
$571$	2.45827e114	0.977758	0.488879	−	0.872352i	$-0.337406\pi$
$571$	2.45827e114	0.977758	0.488879	+	0.872352i	$0.337406\pi$
$572$	1.09112e114	0.403586
$573$	−5.62212e114	−1.93412
$574$	−2.17613e114	−0.696371
$575$	2.07758e114	0.618503
$576$	8.98828e112	0.0248968
$577$	6.41691e114	1.65398	0.826990	−	0.562217i	$-0.190052\pi$
$577$	6.41691e114	1.65398	0.826990	+	0.562217i	$0.190052\pi$
$578$	4.73355e114	1.13548
$579$	6.39843e113	0.142861
$580$	5.84927e113	0.121574
$581$	1.03686e115	2.00637
$582$	−2.02097e114	−0.364130
$583$	−5.12181e114	−0.859366
$584$	−3.08994e113	−0.0482855
$585$	1.45184e113	0.0211325
$586$	−3.50541e114	−0.475322
$587$	−5.70812e114	−0.721127	−0.360563	−	0.932735i	$-0.617416\pi$
$587$	−5.70812e114	−0.721127	−0.360563	+	0.932735i	$0.617416\pi$
$588$	−4.11253e114	−0.484117
$589$	−1.60260e115	−1.75809
$590$	2.23410e114	0.228425
$591$	1.40493e115	1.33898
$592$	−2.66303e115	−2.36606
$593$	2.38483e115	1.97555	0.987775	−	0.155885i	$-0.0498229\pi$
$593$	2.38483e115	1.97555	0.987775	+	0.155885i	$0.0498229\pi$
$594$	−1.39262e115	−1.07571
$595$	−9.32157e113	−0.0671483
$596$	7.76431e114	0.521654
$597$	7.60097e114	0.476359
$598$	1.21161e115	0.708375
$599$	−8.39829e114	−0.458118	−0.229059	−	0.973412i	$-0.573565\pi$
$599$	−8.39829e114	−0.458118	−0.229059	+	0.973412i	$0.573565\pi$
$600$	1.29997e115	0.661695
$601$	1.94245e115	0.922698	0.461349	−	0.887219i	$-0.347366\pi$
$601$	1.94245e115	0.922698	0.461349	+	0.887219i	$0.347366\pi$
$602$	−2.53253e115	−1.12279
$603$	−2.58042e114	−0.106788
$604$	3.76008e114	0.145266
$605$	−4.67351e113	−0.0168576
$606$	7.03324e115	2.36887
$607$	−5.08563e115	−1.59961	−0.799805	−	0.600260i	$-0.795064\pi$
$607$	−5.08563e115	−1.59961	−0.799805	+	0.600260i	$0.795064\pi$
$608$	2.59514e115	0.762365
$609$	−7.41802e115	−2.03550
$610$	4.47189e114	0.114631
$611$	3.75284e115	0.898773
$612$	−6.18373e113	−0.0138378
$613$	−8.90445e114	−0.186208	−0.0931039	−	0.995656i	$-0.529679\pi$
$613$	−8.90445e114	−0.186208	−0.0931039	+	0.995656i	$0.529679\pi$
$614$	−1.05842e115	−0.206856
$615$	−4.55070e114	−0.0831305
$616$	5.11764e115	0.873917
$617$	−6.82203e115	−1.08913	−0.544565	−	0.838719i	$-0.683305\pi$
$617$	−6.82203e115	−1.08913	−0.544565	+	0.838719i	$0.683305\pi$
$618$	−6.89699e115	−1.02953
$619$	3.57057e115	0.498398	0.249199	−	0.968452i	$-0.419833\pi$
$619$	3.57057e115	0.498398	0.249199	+	0.968452i	$0.419833\pi$
$620$	−1.35620e115	−0.177039
$621$	−4.89710e115	−0.597913
$622$	−2.63591e115	−0.301043
$623$	6.32141e115	0.675398
$624$	1.20556e116	1.20512
$625$	9.51965e115	0.890431
$626$	−1.29386e116	−1.13254
$627$	−1.09227e116	−0.894803
$628$	3.08309e115	0.236408
$629$	−6.53970e115	−0.469414
$630$	−5.88142e114	−0.0395229
$631$	2.68414e116	1.68883	0.844416	−	0.535687i	$-0.179947\pi$
$631$	2.68414e116	1.68883	0.844416	+	0.535687i	$0.179947\pi$
$632$	1.87650e115	0.110558
$633$	1.14817e116	0.633509
$634$	3.27765e115	0.169378
$635$	5.77208e115	0.279398
$636$	9.73353e115	0.441367
$637$	2.11791e116	0.899750
$638$	−3.96002e116	−1.57630
$639$	−4.23439e115	−0.157945
$640$	−6.11342e115	−0.213705
$641$	−4.40590e116	−1.44353	−0.721766	−	0.692137i	$-0.756669\pi$
$641$	−4.40590e116	−1.44353	−0.721766	+	0.692137i	$0.756669\pi$
$642$	1.23509e115	0.0379310
$643$	−1.91871e116	−0.552400	−0.276200	−	0.961100i	$-0.589075\pi$
$643$	−1.91871e116	−0.552400	−0.276200	+	0.961100i	$0.589075\pi$
$644$	−1.55432e116	−0.419542
$645$	−5.29600e115	−0.134036
$646$	1.11750e116	0.265216
$647$	−4.37850e116	−0.974536	−0.487268	−	0.873253i	$-0.662006\pi$
$647$	−4.37850e116	−0.974536	−0.487268	+	0.873253i	$0.662006\pi$
$648$	−3.43898e116	−0.717905
$649$	−4.78974e116	−0.937902
$650$	5.78226e116	1.06217
$651$	1.71992e117	2.96414
$652$	4.16794e116	0.673979
$653$	3.03451e116	0.460459	0.230230	−	0.973136i	$-0.426052\pi$
$653$	3.03451e116	0.460459	0.230230	+	0.973136i	$0.426052\pi$
$654$	7.27147e116	1.03549
$655$	1.71476e116	0.229187
$656$	−4.06468e116	−0.509937
$657$	−7.61330e114	−0.00896623
$658$	−1.52028e117	−1.68092
$659$	−1.18132e116	−0.122637	−0.0613186	−	0.998118i	$-0.519531\pi$
$659$	−1.18132e116	−0.122637	−0.0613186	+	0.998118i	$0.519531\pi$
$660$	−9.24331e115	−0.0901061
$661$	−1.93365e116	−0.177018	−0.0885092	−	0.996075i	$-0.528210\pi$
$661$	−1.93365e116	−0.177018	−0.0885092	+	0.996075i	$0.528210\pi$
$662$	−6.54950e116	−0.563120
$663$	2.96054e116	0.239089
$664$	1.21791e117	0.923931
$665$	3.36585e116	0.239882
$666$	−4.12621e116	−0.276293
$667$	−1.39253e117	−0.876156
$668$	−1.86836e116	−0.110468
$669$	7.35347e116	0.408610
$670$	3.94626e116	0.206102
$671$	−9.58741e116	−0.470670
$672$	−2.78513e117	−1.28535
$673$	6.98440e116	0.303043	0.151521	−	0.988454i	$-0.451583\pi$
$673$	6.98440e116	0.303043	0.151521	+	0.988454i	$0.451583\pi$
$674$	4.43820e117	1.81059
$675$	−2.33708e117	−0.896536
$676$	−2.16754e116	−0.0781949
$677$	−9.10436e116	−0.308901	−0.154451	−	0.988001i	$-0.549361\pi$
$677$	−9.10436e116	−0.308901	−0.154451	+	0.988001i	$0.549361\pi$
$678$	8.15114e116	0.260128
$679$	−1.33517e117	−0.400812
$680$	−1.09492e116	−0.0309216
$681$	−5.22422e117	−1.38809
$682$	9.18161e117	2.29545
$683$	3.36570e117	0.791800	0.395900	−	0.918294i	$-0.370433\pi$
$683$	3.36570e117	0.791800	0.395900	+	0.918294i	$0.370433\pi$
$684$	2.23284e116	0.0494343
$685$	−7.45935e116	−0.155433
$686$	1.14333e116	0.0224244
$687$	1.00827e118	1.86154
$688$	−4.73038e117	−0.822197
$689$	−5.01267e117	−0.820298
$690$	−1.02640e117	−0.158154
$691$	−1.14140e117	−0.165614	−0.0828071	−	0.996566i	$-0.526389\pi$
$691$	−1.14140e117	−0.165614	−0.0828071	+	0.996566i	$0.526389\pi$
$692$	2.06260e117	0.281846
$693$	1.26093e117	0.162279
$694$	−3.61977e117	−0.438797
$695$	−2.20039e117	−0.251264
$696$	−8.71327e117	−0.937341
$697$	−9.98177e116	−0.101169
$698$	3.28669e117	0.313876
$699$	−6.15334e116	−0.0553742
$700$	−7.41779e117	−0.629080
$701$	−1.37335e118	−1.09770	−0.548851	−	0.835920i	$-0.684935\pi$
$701$	−1.37335e118	−1.09770	−0.548851	+	0.835920i	$0.684935\pi$
$702$	−1.36295e118	−1.02681
$703$	2.36137e118	1.67694
$704$	2.94702e117	0.197296
$705$	−3.17919e117	−0.200663
$706$	−4.56962e117	−0.271947
$707$	4.64656e118	2.60751
$708$	9.10248e117	0.481703
$709$	−1.80564e118	−0.901181	−0.450591	−	0.892731i	$-0.648787\pi$
$709$	−1.80564e118	−0.901181	−0.450591	+	0.892731i	$0.648787\pi$
$710$	6.47570e117	0.304835
$711$	4.62351e116	0.0205298
$712$	7.42518e117	0.311019
$713$	3.22868e118	1.27588
$714$	−1.19931e118	−0.447154
$715$	4.76021e117	0.167466
$716$	2.07828e118	0.689943
$717$	−1.99805e118	−0.625982
$718$	−6.35529e118	−1.87919
$719$	−1.93376e118	−0.539703	−0.269851	−	0.962902i	$-0.586975\pi$
$719$	−1.93376e118	−0.539703	−0.269851	+	0.962902i	$0.586975\pi$
$720$	−1.09856e117	−0.0289418
$721$	−4.55654e118	−1.13324
$722$	1.11694e118	0.262263
$723$	6.04976e117	0.134122
$724$	1.37552e118	0.287950
$725$	−6.64567e118	−1.31375
$726$	−6.01294e117	−0.112258
$727$	5.50038e118	0.969873	0.484937	−	0.874549i	$-0.338843\pi$
$727$	5.50038e118	0.969873	0.484937	+	0.874549i	$0.338843\pi$
$728$	5.00859e118	0.834187
$729$	5.41645e118	0.852163
$730$	1.16431e117	0.0173049
$731$	−1.16166e118	−0.163120
$732$	1.82200e118	0.241735
$733$	−7.49231e118	−0.939292	−0.469646	−	0.882855i	$-0.655618\pi$
$733$	−7.49231e118	−0.939292	−0.469646	+	0.882855i	$0.655618\pi$
$734$	1.14383e119	1.35511
$735$	−1.79417e118	−0.200881
$736$	−5.22830e118	−0.553262
$737$	−8.46051e118	−0.846245
$738$	−6.29797e117	−0.0595472
$739$	−8.09019e117	−0.0723127	−0.0361564	−	0.999346i	$-0.511511\pi$
$739$	−8.09019e117	−0.0723127	−0.0361564	+	0.999346i	$0.511511\pi$
$740$	1.99830e118	0.168867
$741$	−1.06900e119	−0.854124
$742$	2.03063e119	1.53416
$743$	1.54577e119	1.10435	0.552177	−	0.833727i	$-0.313797\pi$
$743$	1.54577e119	1.10435	0.552177	+	0.833727i	$0.313797\pi$
$744$	2.02024e119	1.36498
$745$	3.38733e118	0.216457
$746$	−2.90870e119	−1.75808
$747$	3.00081e118	0.171567
$748$	−2.02748e118	−0.109658
$749$	8.15968e117	0.0417520
$750$	−9.98488e118	−0.483393
$751$	1.41537e119	0.648354	0.324177	−	0.945997i	$-0.394913\pi$
$751$	1.41537e119	0.648354	0.324177	+	0.945997i	$0.394913\pi$
$752$	−2.83965e119	−1.23090
$753$	−1.72490e119	−0.707576
$754$	−3.87565e119	−1.50464
$755$	1.64041e118	0.0602773
$756$	1.74846e119	0.608138
$757$	2.40708e119	0.792521	0.396261	−	0.918138i	$-0.370308\pi$
$757$	2.40708e119	0.792521	0.396261	+	0.918138i	$0.370308\pi$
$758$	−5.03643e119	−1.56982
$759$	2.20054e119	0.649375
$760$	3.95356e118	0.110465
$761$	−5.04788e119	−1.33550	−0.667752	−	0.744383i	$-0.732744\pi$
$761$	−5.04788e119	−1.33550	−0.667752	+	0.744383i	$0.732744\pi$
$762$	7.42636e119	1.86056
$763$	4.80394e119	1.13980
$764$	3.76819e119	0.846756
$765$	−2.69777e117	−0.00574190
$766$	9.16874e119	1.84848
$767$	−4.68769e119	−0.895264
$768$	−6.65703e119	−1.20445
$769$	−1.69583e118	−0.0290697	−0.0145348	−	0.999894i	$-0.504627\pi$
$769$	−1.69583e118	−0.0290697	−0.0145348	+	0.999894i	$0.504627\pi$
$770$	−1.92836e119	−0.313201
$771$	3.13112e119	0.481885
$772$	−4.28851e118	−0.0625444
$773$	2.48383e119	0.343299	0.171650	−	0.985158i	$-0.445090\pi$
$773$	2.48383e119	0.343299	0.171650	+	0.985158i	$0.445090\pi$
$774$	−7.32944e118	−0.0960110
$775$	1.54085e120	1.91311
$776$	−1.56830e119	−0.184573
$777$	−2.53424e120	−2.82732
$778$	−1.11675e120	−1.18114
$779$	3.60424e119	0.361417
$780$	−9.04636e118	−0.0860097
$781$	−1.38834e120	−1.25164
$782$	−2.25138e119	−0.192472
$783$	1.56647e120	1.27001
$784$	−1.60255e120	−1.23224
$785$	1.34506e119	0.0980958
$786$	2.20621e120	1.52620
$787$	2.35369e120	1.54454	0.772269	−	0.635296i	$-0.219122\pi$
$787$	2.35369e120	1.54454	0.772269	+	0.635296i	$0.219122\pi$
$788$	−9.41643e119	−0.586203
$789$	−6.93819e119	−0.409780
$790$	−7.07079e118	−0.0396227
$791$	5.38510e119	0.286332
$792$	1.48111e119	0.0747293
$793$	−9.38313e119	−0.449273
$794$	2.86495e120	1.30187
$795$	4.24644e119	0.183143
$796$	−5.09450e119	−0.208550
$797$	−1.42809e120	−0.554927	−0.277463	−	0.960736i	$-0.589494\pi$
$797$	−1.42809e120	−0.554927	−0.277463	+	0.960736i	$0.589494\pi$
$798$	4.33051e120	1.59742
$799$	−6.97342e119	−0.244205
$800$	−2.49514e120	−0.829585
$801$	1.82949e119	0.0577538
$802$	−6.90959e120	−2.07117
$803$	−2.49620e119	−0.0710533
$804$	1.60784e120	0.434628
$805$	−6.78100e119	−0.174086
$806$	8.98598e120	2.19109
$807$	−6.17360e120	−1.42984
$808$	5.45789e120	1.20075
$809$	−3.58829e120	−0.749935	−0.374967	−	0.927038i	$-0.622346\pi$
$809$	−3.58829e120	−0.749935	−0.374967	+	0.927038i	$0.622346\pi$
$810$	1.29583e120	0.257288
$811$	4.55375e119	0.0859021	0.0429510	−	0.999077i	$-0.486324\pi$
$811$	4.55375e119	0.0859021	0.0429510	+	0.999077i	$0.486324\pi$
$812$	4.97188e120	0.891139
$813$	−7.60664e120	−1.29549
$814$	−1.35287e121	−2.18950
$815$	1.81835e120	0.279664
$816$	−2.24014e120	−0.327441
$817$	4.19454e120	0.582732
$818$	−9.55835e119	−0.126218
$819$	1.23407e120	0.154902
$820$	3.05008e119	0.0363945
$821$	6.38182e120	0.723941	0.361971	−	0.932189i	$-0.382104\pi$
$821$	6.38182e120	0.723941	0.361971	+	0.932189i	$0.382104\pi$
$822$	−9.59720e120	−1.03506
$823$	1.21516e121	1.24607	0.623034	−	0.782195i	$-0.285900\pi$
$823$	1.21516e121	1.24607	0.623034	+	0.782195i	$0.285900\pi$
$824$	−5.35215e120	−0.521854
$825$	1.05018e121	0.973701
$826$	1.89898e121	1.67436
$827$	7.06562e120	0.592477	0.296239	−	0.955114i	$-0.404268\pi$
$827$	7.06562e120	0.592477	0.296239	+	0.955114i	$0.404268\pi$
$828$	−4.49837e119	−0.0358754
$829$	3.78118e119	0.0286823	0.0143412	−	0.999897i	$-0.495435\pi$
$829$	3.78118e119	0.0286823	0.0143412	+	0.999897i	$0.495435\pi$
$830$	−4.58917e120	−0.331126
$831$	6.46156e120	0.443501
$832$	2.88423e120	0.188326
$833$	−3.93545e120	−0.244470
$834$	−2.83102e121	−1.67321
$835$	−8.15107e119	−0.0458380
$836$	7.32088e120	0.391744
$837$	−3.63197e121	−1.84942
$838$	−4.67022e121	−2.26314
$839$	1.95436e120	0.0901329	0.0450664	−	0.998984i	$-0.485650\pi$
$839$	1.95436e120	0.0901329	0.0450664	+	0.998984i	$0.485650\pi$
$840$	−4.24299e120	−0.186244
$841$	2.06086e121	0.861021
$842$	3.82606e121	1.52160
$843$	7.99371e120	0.302625
$844$	−7.69555e120	−0.277350
$845$	−9.45630e119	−0.0324465
$846$	−4.39986e120	−0.143737
$847$	−3.97249e120	−0.123567
$848$	3.79292e121	1.12343
$849$	3.36903e121	0.950246
$850$	−1.07444e121	−0.288601
$851$	−4.75733e121	−1.21699
$852$	2.63842e121	0.642838
$853$	5.99716e120	0.139175	0.0695874	−	0.997576i	$-0.477832\pi$
$853$	5.99716e120	0.139175	0.0695874	+	0.997576i	$0.477832\pi$
$854$	3.80111e121	0.840249
$855$	9.74118e119	0.0205125
$856$	9.58443e119	0.0192267
$857$	−6.42993e121	−1.22886	−0.614429	−	0.788972i	$-0.710614\pi$
$857$	−6.42993e121	−1.22886	−0.614429	+	0.788972i	$0.710614\pi$
$858$	6.12449e121	1.11519
$859$	2.36235e121	0.409852	0.204926	−	0.978777i	$-0.434305\pi$
$859$	2.36235e121	0.409852	0.204926	+	0.978777i	$0.434305\pi$
$860$	3.54961e120	0.0586807
$861$	−3.86809e121	−0.609349
$862$	−3.92195e121	−0.588777
$863$	−3.26016e121	−0.466435	−0.233218	−	0.972425i	$-0.574925\pi$
$863$	−3.26016e121	−0.466435	−0.233218	+	0.972425i	$0.574925\pi$
$864$	5.88136e121	0.801969
$865$	8.99848e120	0.116950
$866$	−1.20574e122	−1.49369
$867$	8.41394e121	0.993589
$868$	−1.15277e122	−1.29770
$869$	1.51593e121	0.162689
$870$	3.28322e121	0.335932
$871$	−8.28024e121	−0.807773
$872$	5.64275e121	0.524876
$873$	−3.86414e120	−0.0342737
$874$	8.12932e121	0.687590
$875$	−6.59657e121	−0.532089
$876$	4.74380e120	0.0364927
$877$	5.81721e121	0.426807	0.213404	−	0.976964i	$-0.431545\pi$
$877$	5.81721e121	0.426807	0.213404	+	0.976964i	$0.431545\pi$
$878$	7.06450e121	0.494378
$879$	−6.23092e121	−0.415924
$880$	−3.60189e121	−0.229350
$881$	−8.70995e121	−0.529073	−0.264536	−	0.964376i	$-0.585219\pi$
$881$	−8.70995e121	−0.529073	−0.264536	+	0.964376i	$0.585219\pi$
$882$	−2.48306e121	−0.143893
$883$	1.15838e122	0.640442	0.320221	−	0.947343i	$-0.396243\pi$
$883$	1.15838e122	0.640442	0.320221	+	0.947343i	$0.396243\pi$
$884$	−1.98428e121	−0.104673
$885$	3.97113e121	0.199880
$886$	1.93744e122	0.930529
$887$	8.70278e121	0.398867	0.199433	−	0.979911i	$-0.436090\pi$
$887$	8.70278e121	0.398867	0.199433	+	0.979911i	$0.436090\pi$
$888$	−2.97674e122	−1.30198
$889$	4.90627e122	2.04799
$890$	−2.79786e121	−0.111466
$891$	−2.77817e122	−1.05641
$892$	−4.92862e121	−0.178889
$893$	2.51798e122	0.872402
$894$	4.35814e122	1.44143
$895$	9.06690e121	0.286288
$896$	−5.19641e122	−1.56646
$897$	2.15365e122	0.619854
$898$	−3.36323e122	−0.924249
$899$	−1.03278e123	−2.71006
$900$	−2.14680e121	−0.0537931
$901$	9.31440e121	0.222883
$902$	−2.06494e122	−0.471884
$903$	−4.50160e122	−0.982484
$904$	6.32539e121	0.131855
$905$	6.00099e121	0.119483
$906$	2.11055e122	0.401398
$907$	4.66008e122	0.846625	0.423313	−	0.905984i	$-0.360867\pi$
$907$	4.66008e122	0.846625	0.423313	+	0.905984i	$0.360867\pi$
$908$	3.50150e122	0.607703
$909$	1.34477e122	0.222970
$910$	−1.88727e122	−0.298963
$911$	−2.69220e122	−0.407469	−0.203735	−	0.979026i	$-0.565308\pi$
$911$	−2.69220e122	−0.407469	−0.203735	+	0.979026i	$0.565308\pi$
$912$	8.08874e122	1.16976
$913$	9.83885e122	1.35959
$914$	2.10014e122	0.277320
$915$	7.94884e121	0.100306
$916$	−6.75788e122	−0.814983
$917$	1.45755e123	1.67994
$918$	2.53259e122	0.278994
$919$	−4.70853e122	−0.495783	−0.247891	−	0.968788i	$-0.579738\pi$
$919$	−4.70853e122	−0.495783	−0.247891	+	0.968788i	$0.579738\pi$
$920$	−7.96503e121	−0.0801664
$921$	−1.88135e122	−0.181007
$922$	−8.35062e122	−0.768043
$923$	−1.35876e123	−1.19474
$924$	−7.85681e122	−0.660480
$925$	−2.27038e123	−1.82480
$926$	2.54155e122	0.195319
$927$	−1.31872e122	−0.0969042
$928$	1.67241e123	1.17517
$929$	2.03493e123	1.36740	0.683702	−	0.729761i	$-0.260369\pi$
$929$	2.03493e123	1.36740	0.683702	+	0.729761i	$0.260369\pi$
$930$	−7.61240e122	−0.489192
$931$	1.42102e123	0.873350
$932$	4.12424e121	0.0242428
$933$	−4.68536e122	−0.263424
$934$	−1.37879e123	−0.741486
$935$	−8.84529e121	−0.0455019
$936$	1.44955e122	0.0713320
$937$	−3.17058e123	−1.49261	−0.746305	−	0.665605i	$-0.768174\pi$
$937$	−3.17058e123	−1.49261	−0.746305	+	0.665605i	$0.768174\pi$
$938$	3.35433e123	1.51073
$939$	−2.29985e123	−0.991010
$940$	2.13083e122	0.0878503
$941$	6.89910e122	0.272159	0.136080	−	0.990698i	$-0.456550\pi$
$941$	6.89910e122	0.272159	0.136080	+	0.990698i	$0.456550\pi$
$942$	1.73055e123	0.653240
$943$	−7.26127e122	−0.262287
$944$	3.54701e123	1.22610
$945$	7.62801e122	0.252343
$946$	−2.40313e123	−0.760843
$947$	−1.35585e123	−0.410855	−0.205428	−	0.978672i	$-0.565859\pi$
$947$	−1.35585e123	−0.410855	−0.205428	+	0.978672i	$0.565859\pi$
$948$	−2.88089e122	−0.0835565
$949$	−2.44301e122	−0.0678231
$950$	3.87962e123	1.03100
$951$	5.82606e122	0.148212
$952$	−9.30682e122	−0.226656
$953$	6.10390e123	1.42315	0.711577	−	0.702608i	$-0.247981\pi$
$953$	6.10390e123	1.42315	0.711577	+	0.702608i	$0.247981\pi$
$954$	5.87690e122	0.131187
$955$	1.64395e123	0.351356
$956$	1.33918e123	0.274055
$957$	−7.03900e123	−1.37932
$958$	−9.00595e123	−1.68990
$959$	−6.34045e123	−1.13933
$960$	−2.44335e122	−0.0420464
$961$	1.78780e124	2.94645
$962$	−1.32405e124	−2.08996
$963$	2.36151e121	0.00357025
$964$	−4.05482e122	−0.0587184
$965$	−1.87095e122	−0.0259524
$966$	−8.72444e123	−1.15928
$967$	6.41485e123	0.816559	0.408280	−	0.912857i	$-0.366129\pi$
$967$	6.41485e123	0.816559	0.408280	+	0.912857i	$0.366129\pi$
$968$	−4.66612e122	−0.0569021
$969$	1.98638e123	0.232073
$970$	5.90947e122	0.0661487
$971$	3.86744e123	0.414787	0.207394	−	0.978258i	$-0.433502\pi$
$971$	3.86744e123	0.414787	0.207394	+	0.978258i	$0.433502\pi$
$972$	1.08140e123	0.111132
$973$	−1.87033e124	−1.84177
$974$	−8.95756e123	−0.845266
$975$	1.02781e124	0.929435
$976$	7.09990e123	0.615297
$977$	1.43586e124	1.19258	0.596292	−	0.802768i	$-0.296640\pi$
$977$	1.43586e124	1.19258	0.596292	+	0.802768i	$0.296640\pi$
$978$	2.33948e124	1.86233
$979$	5.99842e123	0.457673
$980$	1.20253e123	0.0879458
$981$	1.39032e123	0.0974653
$982$	1.09791e124	0.737800
$983$	−1.00422e124	−0.646933	−0.323466	−	0.946240i	$-0.604848\pi$
$983$	−1.00422e124	−0.646933	−0.323466	+	0.946240i	$0.604848\pi$
$984$	−4.54350e123	−0.280604
$985$	−4.10810e123	−0.243241
$986$	7.20161e123	0.408825
$987$	−2.70231e124	−1.47087
$988$	7.16489e123	0.373935
$989$	−8.45051e123	−0.422899
$990$	−5.58091e122	−0.0267821
$991$	−3.50545e124	−1.61319	−0.806597	−	0.591102i	$-0.798693\pi$
$991$	−3.50545e124	−1.61319	−0.806597	+	0.591102i	$0.798693\pi$
$992$	−3.87760e124	−1.71131
$993$	−1.16418e124	−0.492750
$994$	5.50435e124	2.23445
$995$	−2.22258e123	−0.0865364
$996$	−1.86979e124	−0.698279
$997$	−1.71517e124	−0.614410	−0.307205	−	0.951643i	$-0.599394\pi$
$997$	−1.71517e124	−0.614410	−0.307205	+	0.951643i	$0.599394\pi$
$998$	−9.94939e123	−0.341884
$999$	5.35156e124	1.76406

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.84.a.a.1.2	✓	7	1.1	even	1	trivial
9.84.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q-3.76211e12 q^{2} -6.68720e19 q^{3} +4.48205e24 q^{4} +1.95538e28 q^{5} +2.51580e32 q^{6} +1.66208e35 q^{7} +1.95229e37 q^{8} +4.81025e38 q^{9} +O(q^{10})\)	\(q-3.76211e12 q^{2} -6.68720e19 q^{3} +4.48205e24 q^{4} +1.95538e28 q^{5} +2.51580e32 q^{6} +1.66208e35 q^{7} +1.95229e37 q^{8} +4.81025e38 q^{9} -7.35637e40 q^{10} +1.57715e43 q^{11} -2.99724e44 q^{12} +1.54355e46 q^{13} -6.25291e47 q^{14} -1.30760e48 q^{15} -1.16795e50 q^{16} -2.86818e50 q^{17} -1.80967e51 q^{18} +1.03565e53 q^{19} +8.76414e52 q^{20} -1.11146e55 q^{21} -5.93342e55 q^{22} -2.08646e56 q^{23} -1.30554e57 q^{24} -9.95741e57 q^{25} -5.80700e58 q^{26} +2.34708e59 q^{27} +7.44952e59 q^{28} +6.67410e60 q^{29} +4.91935e60 q^{30} -1.54744e62 q^{31} +2.50582e62 q^{32} -1.05467e63 q^{33} +1.07904e63 q^{34} +3.25000e63 q^{35} +2.15598e63 q^{36} +2.28009e65 q^{37} -3.89622e65 q^{38} -1.03220e66 q^{39} +3.81748e65 q^{40} +3.48018e66 q^{41} +4.18145e67 q^{42} +4.05016e67 q^{43} +7.06889e67 q^{44} +9.40588e66 q^{45} +7.84950e68 q^{46} +2.43131e69 q^{47} +7.81032e69 q^{48} +1.37211e70 q^{49} +3.74608e70 q^{50} +1.91801e70 q^{51} +6.91827e70 q^{52} -3.24750e71 q^{53} -8.82998e71 q^{54} +3.08394e71 q^{55} +3.24486e72 q^{56} -6.92558e72 q^{57} -2.51087e73 q^{58} -3.03695e73 q^{59} -5.86075e72 q^{60} -6.07893e73 q^{61} +5.82164e74 q^{62} +7.99500e73 q^{63} +1.86857e74 q^{64} +3.01823e74 q^{65} +3.96780e75 q^{66} -5.36442e75 q^{67} -1.28553e75 q^{68} +1.39526e76 q^{69} -1.22268e76 q^{70} -8.80285e76 q^{71} +9.39100e75 q^{72} -1.58272e76 q^{73} -8.57795e77 q^{74} +6.65872e77 q^{75} +4.64183e77 q^{76} +2.62135e78 q^{77} +3.88325e78 q^{78} +9.61180e77 q^{79} -2.28379e78 q^{80} -1.76151e79 q^{81} -1.30928e79 q^{82} +6.23836e79 q^{83} -4.98164e79 q^{84} -5.60839e78 q^{85} -1.52371e80 q^{86} -4.46310e80 q^{87} +3.07906e80 q^{88} +3.80332e80 q^{89} -3.53859e79 q^{90} +2.56550e81 q^{91} -9.35165e80 q^{92} +1.03480e82 q^{93} -9.14684e81 q^{94} +2.02509e81 q^{95} -1.67569e82 q^{96} -8.03314e81 q^{97} -5.16202e82 q^{98} +7.58650e81 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) \) 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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