LMFDB - Embedded newform 1.84.a.a.1.3

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			1.3
Root			$-7.80143e10$ 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)

$f(q)$	$=$	$q-1.82271e12 q^{2} +1.57108e19 q^{3} -6.34915e24 q^{4} -2.84572e28 q^{5} -2.86362e31 q^{6} -2.18145e35 q^{7} +2.92008e37 q^{8} -3.74401e39 q^{9} +O(q^{10})$	\(q-1.82271e12 q^{2} +1.57108e19 q^{3} -6.34915e24 q^{4} -2.84572e28 q^{5} -2.86362e31 q^{6} -2.18145e35 q^{7} +2.92008e37 q^{8} -3.74401e39 q^{9} +5.18692e40 q^{10} -1.21785e43 q^{11} -9.97501e43 q^{12} -1.12299e46 q^{13} +3.97614e47 q^{14} -4.47086e47 q^{15} +8.18073e48 q^{16} -8.27596e49 q^{17} +6.82423e51 q^{18} -1.06507e53 q^{19} +1.80679e53 q^{20} -3.42723e54 q^{21} +2.21978e55 q^{22} -5.45939e56 q^{23} +4.58767e56 q^{24} -9.52994e57 q^{25} +2.04688e58 q^{26} -1.21521e59 q^{27} +1.38503e60 q^{28} -1.24217e60 q^{29} +8.14906e59 q^{30} +4.29532e61 q^{31} -2.97324e62 q^{32} -1.91334e62 q^{33} +1.50846e62 q^{34} +6.20780e63 q^{35} +2.37713e64 q^{36} -8.01321e64 q^{37} +1.94131e65 q^{38} -1.76431e65 q^{39} -8.30973e65 q^{40} +7.03211e66 q^{41} +6.24683e66 q^{42} +8.10113e67 q^{43} +7.73229e67 q^{44} +1.06544e68 q^{45} +9.95087e68 q^{46} +2.80552e69 q^{47} +1.28526e68 q^{48} +3.36833e70 q^{49} +1.73703e70 q^{50} -1.30022e69 q^{51} +7.13003e70 q^{52} -3.32565e71 q^{53} +2.21496e71 q^{54} +3.46566e71 q^{55} -6.37000e72 q^{56} -1.67331e72 q^{57} +2.26411e72 q^{58} -5.84063e73 q^{59} +2.83861e72 q^{60} +6.63109e73 q^{61} -7.82911e73 q^{62} +8.16736e74 q^{63} +4.62815e74 q^{64} +3.19572e74 q^{65} +3.48745e74 q^{66} +2.26563e75 q^{67} +5.25453e74 q^{68} -8.57714e75 q^{69} -1.13150e76 q^{70} -8.10885e75 q^{71} -1.09328e77 q^{72} -2.53640e77 q^{73} +1.46057e77 q^{74} -1.49723e77 q^{75} +6.76228e77 q^{76} +2.65667e78 q^{77} +3.21581e77 q^{78} +1.36742e78 q^{79} -2.32801e77 q^{80} +1.30326e79 q^{81} -1.28175e79 q^{82} -5.99046e79 q^{83} +2.17600e79 q^{84} +2.35511e78 q^{85} -1.47660e80 q^{86} -1.95155e79 q^{87} -3.55621e80 q^{88} +5.14206e80 q^{89} -1.94199e80 q^{90} +2.44974e81 q^{91} +3.46625e81 q^{92} +6.74829e80 q^{93} -5.11365e81 q^{94} +3.03089e81 q^{95} -4.67119e81 q^{96} -2.08996e82 q^{97} -6.13947e82 q^{98} +4.55963e82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.82271e12	−0.586100	−0.293050	−	0.956097i	$-0.594670\pi$
$2$	−1.82271e12	−0.586100	−0.293050	+	0.956097i	$0.594670\pi$
$3$	1.57108e19	0.248694	0.124347	−	0.992239i	$-0.460316\pi$
$3$	1.57108e19	0.248694	0.124347	+	0.992239i	$0.460316\pi$
$4$	−6.34915e24	−0.656486
$5$	−2.84572e28	−0.279858	−0.139929	−	0.990162i	$-0.544687\pi$
$5$	−2.84572e28	−0.279858	−0.139929	+	0.990162i	$0.544687\pi$
$6$	−2.86362e31	−0.145760
$7$	−2.18145e35	−1.85002	−0.925010	−	0.379943i	$-0.875943\pi$
$7$	−2.18145e35	−1.85002	−0.925010	+	0.379943i	$0.875943\pi$
$8$	2.92008e37	0.970867
$9$	−3.74401e39	−0.938151
$10$	5.18692e40	0.164025
$11$	−1.21785e43	−0.737559	−0.368779	−	0.929517i	$-0.620224\pi$
$11$	−1.21785e43	−0.737559	−0.368779	+	0.929517i	$0.620224\pi$
$12$	−9.97501e43	−0.163265
$13$	−1.12299e46	−0.663326	−0.331663	−	0.943398i	$-0.607610\pi$
$13$	−1.12299e46	−0.663326	−0.331663	+	0.943398i	$0.607610\pi$
$14$	3.97614e47	1.08430
$15$	−4.47086e47	−0.0695991
$16$	8.18073e48	0.0874607
$17$	−8.27596e49	−0.0714806	−0.0357403	−	0.999361i	$-0.511379\pi$
$17$	−8.27596e49	−0.0714806	−0.0357403	+	0.999361i	$0.511379\pi$
$18$	6.82423e51	0.549851
$19$	−1.06507e53	−0.910129	−0.455065	−	0.890458i	$-0.650384\pi$
$19$	−1.06507e53	−0.910129	−0.455065	+	0.890458i	$0.650384\pi$
$20$	1.80679e53	0.183723
$21$	−3.42723e54	−0.460090
$22$	2.21978e55	0.432283
$23$	−5.45939e56	−1.68050	−0.840251	−	0.542198i	$-0.817592\pi$
$23$	−5.45939e56	−1.68050	−0.840251	+	0.542198i	$0.817592\pi$
$24$	4.58767e56	0.241449
$25$	−9.52994e57	−0.921680
$26$	2.04688e58	0.388775
$27$	−1.21521e59	−0.482007
$28$	1.38503e60	1.21451
$29$	−1.24217e60	−0.253901	−0.126950	−	0.991909i	$-0.540519\pi$
$29$	−1.24217e60	−0.253901	−0.126950	+	0.991909i	$0.540519\pi$
$30$	8.14906e59	0.0407921
$31$	4.29532e61	0.551424	0.275712	−	0.961240i	$-0.411086\pi$
$31$	4.29532e61	0.551424	0.275712	+	0.961240i	$0.411086\pi$
$32$	−2.97324e62	−1.02213
$33$	−1.91334e62	−0.183427
$34$	1.50846e62	0.0418948
$35$	6.20780e63	0.517743
$36$	2.37713e64	0.615883
$37$	−8.01321e64	−0.665940	−0.332970	−	0.942937i	$-0.608051\pi$
$37$	−8.01321e64	−0.665940	−0.332970	+	0.942937i	$0.608051\pi$
$38$	1.94131e65	0.533427
$39$	−1.76431e65	−0.164965
$40$	−8.30973e65	−0.271705
$41$	7.03211e66	0.825194	0.412597	−	0.910914i	$-0.364622\pi$
$41$	7.03211e66	0.825194	0.412597	+	0.910914i	$0.364622\pi$
$42$	6.24683e66	0.269659
$43$	8.10113e67	1.31706	0.658529	−	0.752555i	$-0.271179\pi$
$43$	8.10113e67	1.31706	0.658529	+	0.752555i	$0.271179\pi$
$44$	7.73229e67	0.484197
$45$	1.06544e68	0.262549
$46$	9.95087e68	0.984943
$47$	2.80552e69	1.13750	0.568752	−	0.822509i	$-0.307426\pi$
$47$	2.80552e69	1.13750	0.568752	+	0.822509i	$0.307426\pi$
$48$	1.28526e68	0.0217510
$49$	3.36833e70	2.42257
$50$	1.73703e70	0.540197
$51$	−1.30022e69	−0.0177768
$52$	7.13003e70	0.435464
$53$	−3.32565e71	−0.921356	−0.460678	−	0.887567i	$-0.652394\pi$
$53$	−3.32565e71	−0.921356	−0.460678	+	0.887567i	$0.652394\pi$
$54$	2.21496e71	0.282505
$55$	3.46566e71	0.206412
$56$	−6.37000e72	−1.79612
$57$	−1.67331e72	−0.226344
$58$	2.26411e72	0.148811
$59$	−5.84063e73	−1.88843	−0.944216	−	0.329328i	$-0.893178\pi$
$59$	−5.84063e73	−1.88843	−0.944216	+	0.329328i	$0.893178\pi$
$60$	2.83861e72	0.0456909
$61$	6.63109e73	0.537523	0.268761	−	0.963207i	$-0.413386\pi$
$61$	6.63109e73	0.537523	0.268761	+	0.963207i	$0.413386\pi$
$62$	−7.82911e73	−0.323190
$63$	8.16736e74	1.73560
$64$	4.62815e74	0.511609
$65$	3.19572e74	0.185637
$66$	3.48745e74	0.107506
$67$	2.26563e75	0.374184	0.187092	−	0.982342i	$-0.440094\pi$
$67$	2.26563e75	0.374184	0.187092	+	0.982342i	$0.440094\pi$
$68$	5.25453e74	0.0469260
$69$	−8.57714e75	−0.417931
$70$	−1.13150e76	−0.303449
$71$	−8.10885e75	−0.120709	−0.0603543	−	0.998177i	$-0.519223\pi$
$71$	−8.10885e75	−0.120709	−0.0603543	+	0.998177i	$0.519223\pi$
$72$	−1.09328e77	−0.910820
$73$	−2.53640e77	−1.19212	−0.596059	−	0.802941i	$-0.703267\pi$
$73$	−2.53640e77	−1.19212	−0.596059	+	0.802941i	$0.703267\pi$
$74$	1.46057e77	0.390308
$75$	−1.49723e77	−0.229217
$76$	6.76228e77	0.597487
$77$	2.65667e78	1.36450
$78$	3.21581e77	0.0966863
$79$	1.36742e78	0.242313	0.121157	−	0.992633i	$-0.461340\pi$
$79$	1.36742e78	0.242313	0.121157	+	0.992633i	$0.461340\pi$
$80$	−2.32801e77	−0.0244766
$81$	1.30326e79	0.818278
$82$	−1.28175e79	−0.483646
$83$	−5.99046e79	−1.36685	−0.683423	−	0.730023i	$-0.739509\pi$
$83$	−5.99046e79	−1.36685	−0.683423	+	0.730023i	$0.739509\pi$
$84$	2.17600e79	0.302043
$85$	2.35511e78	0.0200044
$86$	−1.47660e80	−0.771928
$87$	−1.95155e79	−0.0631437
$88$	−3.55621e80	−0.716072
$89$	5.14206e80	0.647816	0.323908	−	0.946089i	$-0.395003\pi$
$89$	5.14206e80	0.647816	0.323908	+	0.946089i	$0.395003\pi$
$90$	−1.94199e80	−0.153880
$91$	2.44974e81	1.22717
$92$	3.46625e81	1.10323
$93$	6.74829e80	0.137136
$94$	−5.11365e81	−0.666692
$95$	3.03089e81	0.254707
$96$	−4.67119e81	−0.254198
$97$	−2.08996e82	−0.739795	−0.369898	−	0.929073i	$-0.620607\pi$
$97$	−2.08996e82	−0.739795	−0.369898	+	0.929073i	$0.620607\pi$
$98$	−6.13947e82	−1.41987
$99$	4.55963e82	0.691941
$100$	6.05070e82	0.605070
$101$	−1.74403e83	−1.15403	−0.577015	−	0.816733i	$-0.695783\pi$
$101$	−1.74403e83	−1.15403	−0.577015	+	0.816733i	$0.695783\pi$
$102$	2.36992e81	0.0104190
$103$	5.58842e83	1.63887	0.819435	−	0.573172i	$-0.194287\pi$
$103$	5.58842e83	1.63887	0.819435	+	0.573172i	$0.194287\pi$
$104$	−3.27922e83	−0.644001
$105$	9.75295e82	0.128760
$106$	6.06168e83	0.540007
$107$	1.68204e84	1.01487	0.507434	−	0.861690i	$-0.330594\pi$
$107$	1.68204e84	1.01487	0.507434	+	0.861690i	$0.330594\pi$
$108$	7.71552e83	0.316431
$109$	−5.14475e84	−1.43934	−0.719671	−	0.694315i	$-0.755708\pi$
$109$	−5.14475e84	−1.43934	−0.719671	+	0.694315i	$0.755708\pi$
$110$	−6.31688e83	−0.120978
$111$	−1.25894e84	−0.165616
$112$	−1.78458e84	−0.161804
$113$	−2.28598e85	−1.43324	−0.716618	−	0.697466i	$-0.754311\pi$
$113$	−2.28598e85	−1.43324	−0.716618	+	0.697466i	$0.754311\pi$
$114$	3.04995e84	0.132660
$115$	1.55359e85	0.470302
$116$	7.88672e84	0.166682
$117$	4.20448e85	0.622300
$118$	1.06458e86	1.10681
$119$	1.80536e85	0.132240
$120$	−1.30553e85	−0.0675715
$121$	−1.24327e86	−0.456007
$122$	−1.20865e86	−0.315042
$123$	1.10480e86	0.205221
$124$	−2.72716e86	−0.362002
$125$	5.65437e86	0.537797
$126$	−1.48867e87	−1.01723
$127$	−2.49879e87	−1.22991	−0.614957	−	0.788561i	$-0.710827\pi$
$127$	−2.49879e87	−1.22991	−0.614957	+	0.788561i	$0.710827\pi$
$128$	2.03196e87	0.722274
$129$	1.27275e87	0.327545
$130$	−5.82486e86	−0.108802
$131$	1.42809e87	0.194087	0.0970437	−	0.995280i	$-0.469061\pi$
$131$	1.42809e87	0.194087	0.0970437	+	0.995280i	$0.469061\pi$
$132$	1.21480e87	0.120417
$133$	2.32339e88	1.68376
$134$	−4.12959e87	−0.219310
$135$	3.45814e87	0.134894
$136$	−2.41664e87	−0.0693981
$137$	−3.57426e88	−0.757325	−0.378663	−	0.925535i	$-0.623616\pi$
$137$	−3.57426e88	−0.757325	−0.378663	+	0.925535i	$0.623616\pi$
$138$	1.56336e88	0.244950
$139$	−1.34520e89	−1.56197	−0.780987	−	0.624547i	$-0.785284\pi$
$139$	−1.34520e89	−1.56197	−0.780987	+	0.624547i	$0.785284\pi$
$140$	−3.94142e88	−0.339891
$141$	4.40770e88	0.282891
$142$	1.47801e88	0.0707473
$143$	1.36763e89	0.489241
$144$	−3.06287e88	−0.0820513
$145$	3.53487e88	0.0710562
$146$	4.62311e89	0.698700
$147$	5.29191e89	0.602480
$148$	5.08771e89	0.437181
$149$	−1.76647e90	−1.14783	−0.573914	−	0.818916i	$-0.694576\pi$
$149$	−1.76647e90	−1.14783	−0.573914	+	0.818916i	$0.694576\pi$
$150$	2.72901e89	0.134344
$151$	2.24432e90	0.838573	0.419286	−	0.907854i	$-0.362280\pi$
$151$	2.24432e90	0.838573	0.419286	+	0.907854i	$0.362280\pi$
$152$	−3.11008e90	−0.883615
$153$	3.09853e89	0.0670596
$154$	−4.84233e90	−0.799733
$155$	−1.22233e90	−0.154320
$156$	1.12018e90	0.108298
$157$	−7.28513e90	−0.540259	−0.270129	−	0.962824i	$-0.587066\pi$
$157$	−7.28513e90	−0.540259	−0.270129	+	0.962824i	$0.587066\pi$
$158$	−2.49240e90	−0.142020
$159$	−5.22486e90	−0.229136
$160$	8.46101e90	0.286051
$161$	1.19094e92	3.10896
$162$	−2.37545e91	−0.479593
$163$	−2.77205e91	−0.433526	−0.216763	−	0.976224i	$-0.569550\pi$
$163$	−2.77205e91	−0.433526	−0.216763	+	0.976224i	$0.569550\pi$
$164$	−4.46479e91	−0.541728
$165$	5.44482e90	0.0513334
$166$	1.09189e92	0.801109
$167$	−2.40750e92	−1.37668	−0.688339	−	0.725389i	$-0.741660\pi$
$167$	−2.40750e92	−1.37668	−0.688339	+	0.725389i	$0.741660\pi$
$168$	−1.00078e92	−0.446686
$169$	−1.60504e92	−0.559999
$170$	−4.29267e90	−0.0117246
$171$	3.98763e92	0.853839
$172$	−5.14353e92	−0.864630
$173$	1.11682e92	0.147595	0.0737973	−	0.997273i	$-0.476488\pi$
$173$	1.11682e92	0.147595	0.0737973	+	0.997273i	$0.476488\pi$
$174$	3.55710e91	0.0370086
$175$	2.07891e93	1.70513
$176$	−9.96288e91	−0.0645074
$177$	−9.17609e92	−0.469642
$178$	−9.37247e92	−0.379685
$179$	2.87807e93	0.924062	0.462031	−	0.886864i	$-0.347121\pi$
$179$	2.87807e93	0.924062	0.462031	+	0.886864i	$0.347121\pi$
$180$	−6.76464e92	−0.172360
$181$	2.94830e93	0.596912	0.298456	−	0.954423i	$-0.403528\pi$
$181$	2.94830e93	0.596912	0.298456	+	0.954423i	$0.403528\pi$
$182$	−4.46517e93	−0.719242
$183$	1.04180e93	0.133679
$184$	−1.59418e94	−1.63154
$185$	2.28034e93	0.186369
$186$	−1.23002e93	−0.0803755
$187$	1.00789e93	0.0527211
$188$	−1.78127e94	−0.746756
$189$	2.65091e94	0.891723
$190$	−5.52442e93	−0.149284
$191$	4.73638e94	1.02935	0.514673	−	0.857386i	$-0.327913\pi$
$191$	4.73638e94	1.02935	0.514673	+	0.857386i	$0.327913\pi$
$192$	7.27119e93	0.127234
$193$	5.66633e94	0.799233	0.399616	−	0.916682i	$-0.369143\pi$
$193$	5.66633e94	0.799233	0.399616	+	0.916682i	$0.369143\pi$
$194$	3.80939e94	0.433594
$195$	5.02073e93	0.0461669
$196$	−2.13860e95	−1.59039
$197$	1.13926e95	0.685923	0.342962	−	0.939349i	$-0.388570\pi$
$197$	1.13926e95	0.685923	0.342962	+	0.939349i	$0.388570\pi$
$198$	−8.31087e94	−0.405547
$199$	−2.05176e95	−0.812314	−0.406157	−	0.913803i	$-0.633131\pi$
$199$	−2.05176e95	−0.812314	−0.406157	+	0.913803i	$0.633131\pi$
$200$	−2.78282e95	−0.894829
$201$	3.55949e94	0.0930576
$202$	3.17886e95	0.676378
$203$	2.70973e95	0.469722
$204$	8.25528e93	0.0116702
$205$	−2.00114e95	−0.230937
$206$	−1.01861e96	−0.960542
$207$	2.04400e96	1.57656
$208$	−9.18688e94	−0.0580149
$209$	1.29709e96	0.671274
$210$	−1.77768e95	−0.0754661
$211$	−8.44924e95	−0.294507	−0.147253	−	0.989099i	$-0.547043\pi$
$211$	−8.44924e95	−0.294507	−0.147253	+	0.989099i	$0.547043\pi$
$212$	2.11150e96	0.604858
$213$	−1.27397e95	−0.0300196
$214$	−3.06587e96	−0.594815
$215$	−2.30536e96	−0.368589
$216$	−3.54850e96	−0.467965
$217$	−9.37002e96	−1.02014
$218$	9.37736e96	0.843599
$219$	−3.98489e96	−0.296473
$220$	−2.20040e96	−0.135506
$221$	9.29381e95	0.0474149
$222$	2.29468e96	0.0970674
$223$	−1.45905e97	−0.512175	−0.256088	−	0.966654i	$-0.582434\pi$
$223$	−1.45905e97	−0.512175	−0.256088	+	0.966654i	$0.582434\pi$
$224$	6.48596e97	1.89096
$225$	3.56802e97	0.864675
$226$	4.16668e97	0.840020
$227$	−8.22573e97	−1.38071	−0.690354	−	0.723472i	$-0.742545\pi$
$227$	−8.22573e97	−1.38071	−0.690354	+	0.723472i	$0.742545\pi$
$228$	1.06241e97	0.148592
$229$	−6.70977e97	−0.782592	−0.391296	−	0.920265i	$-0.627973\pi$
$229$	−6.70977e97	−0.782592	−0.391296	+	0.920265i	$0.627973\pi$
$230$	−2.83174e97	−0.275644
$231$	4.17384e97	0.339343
$232$	−3.62723e97	−0.246504
$233$	−1.63287e98	−0.928286	−0.464143	−	0.885760i	$-0.653638\pi$
$233$	−1.63287e98	−0.928286	−0.464143	+	0.885760i	$0.653638\pi$
$234$	−7.66354e97	−0.364730
$235$	−7.98375e97	−0.318339
$236$	3.70830e98	1.23973
$237$	2.14832e97	0.0602619
$238$	−3.29064e97	−0.0775062
$239$	−5.05717e97	−0.100091	−0.0500455	−	0.998747i	$-0.515937\pi$
$239$	−5.05717e97	−0.100091	−0.0500455	+	0.998747i	$0.515937\pi$
$240$	−3.65749e96	−0.00608719
$241$	4.99364e98	0.699375	0.349688	−	0.936866i	$-0.386288\pi$
$241$	4.99364e98	0.699375	0.349688	+	0.936866i	$0.386288\pi$
$242$	2.26611e98	0.267266
$243$	6.89721e98	0.685509
$244$	−4.21018e98	−0.352876
$245$	−9.58532e98	−0.677976
$246$	−2.01373e98	−0.120280
$247$	1.19606e99	0.603712
$248$	1.25427e99	0.535359
$249$	−9.41149e98	−0.339927
$250$	−1.03063e99	−0.315203
$251$	−7.40324e99	−1.91850	−0.959251	−	0.282555i	$-0.908818\pi$
$251$	−7.40324e99	−1.91850	−0.959251	+	0.282555i	$0.908818\pi$
$252$	−5.18558e99	−1.13940
$253$	6.64871e99	1.23947
$254$	4.55455e99	0.720853
$255$	3.70006e97	0.00497498
$256$	−8.17974e99	−0.934934
$257$	1.66764e100	1.62135	0.810674	−	0.585497i	$-0.199101\pi$
$257$	1.66764e100	1.62135	0.810674	+	0.585497i	$0.199101\pi$
$258$	−2.31985e99	−0.191974
$259$	1.74804e100	1.23200
$260$	−2.02901e99	−0.121868
$261$	4.65070e99	0.238197
$262$	−2.60299e99	−0.113755
$263$	−1.57683e100	−0.588332	−0.294166	−	0.955754i	$-0.595042\pi$
$263$	−1.57683e100	−0.588332	−0.294166	+	0.955754i	$0.595042\pi$
$264$	−5.58709e99	−0.178083
$265$	9.46387e99	0.257849
$266$	−4.23486e100	−0.986851
$267$	8.07859e99	0.161108
$268$	−1.43848e100	−0.245647
$269$	−6.96825e100	−1.01954	−0.509770	−	0.860311i	$-0.670269\pi$
$269$	−6.96825e100	−1.01954	−0.509770	+	0.860311i	$0.670269\pi$
$270$	−6.30318e99	−0.0790612
$271$	6.17580e100	0.664458	0.332229	−	0.943199i	$-0.392199\pi$
$271$	6.17580e100	0.664458	0.332229	+	0.943199i	$0.392199\pi$
$272$	−6.77034e98	−0.00625174
$273$	3.84874e100	0.305189
$274$	6.51482e100	0.443868
$275$	1.16060e101	0.679793
$276$	5.44575e100	0.274366
$277$	−2.76207e101	−1.19763	−0.598817	−	0.800886i	$-0.704362\pi$
$277$	−2.76207e101	−1.19763	−0.598817	+	0.800886i	$0.704362\pi$
$278$	2.45191e101	0.915474
$279$	−1.60817e101	−0.517319
$280$	1.81273e101	0.502659
$281$	2.81938e101	0.674281	0.337140	−	0.941454i	$-0.390540\pi$
$281$	2.81938e101	0.674281	0.337140	+	0.941454i	$0.390540\pi$
$282$	−8.03395e100	−0.165803
$283$	−4.58502e101	−0.816967	−0.408484	−	0.912766i	$-0.633942\pi$
$283$	−4.58502e101	−0.816967	−0.408484	+	0.912766i	$0.633942\pi$
$284$	5.14843e100	0.0792435
$285$	4.76177e100	0.0633442
$286$	−2.49279e101	−0.286745
$287$	−1.53402e102	−1.52662
$288$	1.11318e102	0.958910
$289$	−1.33363e102	−0.994891
$290$	−6.44304e100	−0.0416460
$291$	−3.28350e101	−0.183983
$292$	1.61040e102	0.782609
$293$	3.50789e102	1.47924	0.739621	−	0.673023i	$-0.235005\pi$
$293$	3.50789e102	1.47924	0.739621	+	0.673023i	$0.235005\pi$
$294$	−9.64560e101	−0.353114
$295$	1.66208e102	0.528492
$296$	−2.33992e102	−0.646540
$297$	1.47994e102	0.355509
$298$	3.21976e102	0.672742
$299$	6.13084e102	1.11472
$300$	9.50613e101	0.150478
$301$	−1.76722e103	−2.43658
$302$	−4.09073e102	−0.491488
$303$	−2.74001e102	−0.287001
$304$	−8.71304e101	−0.0796005
$305$	−1.88703e102	−0.150430
$306$	−5.64770e101	−0.0393036
$307$	1.52289e103	0.925603	0.462801	−	0.886462i	$-0.346844\pi$
$307$	1.52289e103	0.925603	0.462801	+	0.886462i	$0.346844\pi$
$308$	−1.68676e103	−0.895774
$309$	8.77986e102	0.407578
$310$	2.22795e102	0.0904472
$311$	5.70689e102	0.202695	0.101348	−	0.994851i	$-0.467685\pi$
$311$	5.70689e102	0.202695	0.101348	+	0.994851i	$0.467685\pi$
$312$	−5.15191e102	−0.160160
$313$	3.84710e103	1.04723	0.523616	−	0.851954i	$-0.324583\pi$
$313$	3.84710e103	1.04723	0.523616	+	0.851954i	$0.324583\pi$
$314$	1.32787e103	0.316646
$315$	−2.32421e103	−0.485721
$316$	−8.68193e102	−0.159075
$317$	3.21533e103	0.516733	0.258366	−	0.966047i	$-0.416816\pi$
$317$	3.21533e103	0.516733	0.258366	+	0.966047i	$0.416816\pi$
$318$	9.52338e102	0.134297
$319$	1.51277e103	0.187267
$320$	−1.31704e103	−0.143178
$321$	2.64262e103	0.252392
$322$	−2.17073e104	−1.82216
$323$	8.81446e102	0.0650566
$324$	−8.27456e103	−0.537189
$325$	1.07020e104	0.611374
$326$	5.05263e103	0.254090
$327$	−8.08281e103	−0.357957
$328$	2.05343e104	0.801153
$329$	−6.12011e104	−2.10440
$330$	−9.92432e102	−0.0300865
$331$	3.63909e104	0.973042	0.486521	−	0.873669i	$-0.338266\pi$
$331$	3.63909e104	0.973042	0.486521	+	0.873669i	$0.338266\pi$
$332$	3.80343e104	0.897315
$333$	3.00016e104	0.624753
$334$	4.38816e104	0.806872
$335$	−6.44737e103	−0.104718
$336$	−2.80372e103	−0.0402398
$337$	−1.76087e104	−0.223401	−0.111701	−	0.993742i	$-0.535630\pi$
$337$	−1.76087e104	−0.223401	−0.111701	+	0.993742i	$0.535630\pi$
$338$	2.92552e104	0.328216
$339$	−3.59146e104	−0.356438
$340$	−1.49529e103	−0.0131326
$341$	−5.23105e104	−0.406707
$342$	−7.26827e104	−0.500435
$343$	−4.31476e105	−2.63179
$344$	2.36559e105	1.27869
$345$	2.44082e104	0.116961
$346$	−2.03564e104	−0.0865052
$347$	2.98798e105	1.12643	0.563215	−	0.826310i	$-0.309564\pi$
$347$	2.98798e105	1.12643	0.563215	+	0.826310i	$0.309564\pi$
$348$	1.23907e104	0.0414530
$349$	3.83775e104	0.113978	0.0569890	−	0.998375i	$-0.481850\pi$
$349$	3.83775e104	0.113978	0.0569890	+	0.998375i	$0.481850\pi$
$350$	−3.78924e105	−0.999375
$351$	1.36466e105	0.319728
$352$	3.62095e105	0.753879
$353$	4.09153e105	0.757244	0.378622	−	0.925551i	$-0.376398\pi$
$353$	4.09153e105	0.757244	0.378622	+	0.925551i	$0.376398\pi$
$354$	1.67253e105	0.275258
$355$	2.30756e104	0.0337812
$356$	−3.26477e105	−0.425283
$357$	2.83636e104	0.0328875
$358$	−5.24588e105	−0.541593
$359$	1.54352e105	0.141936	0.0709681	−	0.997479i	$-0.477391\pi$
$359$	1.54352e105	0.141936	0.0709681	+	0.997479i	$0.477391\pi$
$360$	3.11117e105	0.254900
$361$	−2.35088e105	−0.171665
$362$	−5.37388e105	−0.349850
$363$	−1.95327e105	−0.113406
$364$	−1.55538e106	−0.805617
$365$	7.21789e105	0.333623
$366$	−1.89889e105	−0.0783493
$367$	−3.97957e105	−0.146620	−0.0733102	−	0.997309i	$-0.523356\pi$
$367$	−3.97957e105	−0.146620	−0.0733102	+	0.997309i	$0.523356\pi$
$368$	−4.46618e105	−0.146978
$369$	−2.63283e106	−0.774156
$370$	−4.15639e105	−0.109231
$371$	7.25473e106	1.70453
$372$	−4.28459e105	−0.0900279
$373$	3.39452e106	0.638061	0.319031	−	0.947744i	$-0.396643\pi$
$373$	3.39452e106	0.638061	0.319031	+	0.947744i	$0.396643\pi$
$374$	−1.83708e105	−0.0308999
$375$	8.88346e105	0.133747
$376$	8.19235e106	1.10437
$377$	1.39494e106	0.168419
$378$	−4.83183e106	−0.522639
$379$	−6.93001e106	−0.671749	−0.335874	−	0.941907i	$-0.609032\pi$
$379$	−6.93001e106	−0.671749	−0.335874	+	0.941907i	$0.609032\pi$
$380$	−1.92436e106	−0.167212
$381$	−3.92579e106	−0.305873
$382$	−8.63303e106	−0.603300
$383$	2.48582e106	0.155855	0.0779275	−	0.996959i	$-0.475170\pi$
$383$	2.48582e106	0.155855	0.0779275	+	0.996959i	$0.475170\pi$
$384$	3.19237e106	0.179626
$385$	−7.56015e106	−0.381865
$386$	−1.03281e107	−0.468431
$387$	−3.03307e107	−1.23560
$388$	1.32695e107	0.485665
$389$	1.58550e107	0.521503	0.260751	−	0.965406i	$-0.416030\pi$
$389$	1.58550e107	0.521503	0.260751	+	0.965406i	$0.416030\pi$
$390$	−9.15132e105	−0.0270584
$391$	4.51817e106	0.120123
$392$	9.83577e107	2.35200
$393$	2.24365e106	0.0482685
$394$	−2.07654e107	−0.402020
$395$	−3.89129e106	−0.0678132
$396$	−2.89498e107	−0.454250
$397$	−7.95370e106	−0.112399	−0.0561996	−	0.998420i	$-0.517898\pi$
$397$	−7.95370e106	−0.112399	−0.0561996	+	0.998420i	$0.517898\pi$
$398$	3.73976e107	0.476097
$399$	3.65023e107	0.418741
$400$	−7.79619e106	−0.0806107
$401$	−1.42712e108	−1.33036	−0.665178	−	0.746685i	$-0.731644\pi$
$401$	−1.42712e108	−1.33036	−0.665178	+	0.746685i	$0.731644\pi$
$402$	−6.48791e106	−0.0545411
$403$	−4.82360e107	−0.365773
$404$	1.10731e108	0.757605
$405$	−3.70870e107	−0.229002
$406$	−4.93904e107	−0.275304
$407$	9.75888e107	0.491170
$408$	−3.79674e106	−0.0172589
$409$	−3.81328e108	−1.56596	−0.782982	−	0.622044i	$-0.786302\pi$
$409$	−3.81328e108	−1.56596	−0.782982	+	0.622044i	$0.786302\pi$
$410$	3.64750e107	0.135352
$411$	−5.61544e107	−0.188343
$412$	−3.54817e108	−1.07590
$413$	1.27410e109	3.49363
$414$	−3.72561e108	−0.924025
$415$	1.70472e108	0.382522
$416$	3.33891e108	0.678004
$417$	−2.11342e108	−0.388455
$418$	−2.36422e108	−0.393434
$419$	5.20008e108	0.783661	0.391831	−	0.920037i	$-0.371842\pi$
$419$	5.20008e108	0.783661	0.391831	+	0.920037i	$0.371842\pi$
$420$	−6.19229e107	−0.0845290
$421$	5.66657e108	0.700831	0.350416	−	0.936594i	$-0.386040\pi$
$421$	5.66657e108	0.700831	0.350416	+	0.936594i	$0.386040\pi$
$422$	1.54005e108	0.172611
$423$	−1.05039e109	−1.06715
$424$	−9.71114e108	−0.894515
$425$	7.88694e107	0.0658822
$426$	2.32207e107	0.0175945
$427$	−1.44654e109	−0.994428
$428$	−1.06795e109	−0.666247
$429$	2.14866e108	0.121672
$430$	4.20199e108	0.216030
$431$	2.02602e109	0.945884	0.472942	−	0.881094i	$-0.343192\pi$
$431$	2.02602e109	0.945884	0.472942	+	0.881094i	$0.343192\pi$
$432$	−9.94128e107	−0.0421567
$433$	−2.56197e109	−0.987022	−0.493511	−	0.869740i	$-0.664287\pi$
$433$	−2.56197e109	−0.987022	−0.493511	+	0.869740i	$0.664287\pi$
$434$	1.70788e109	0.597907
$435$	5.55357e107	0.0176713
$436$	3.26647e109	0.944909
$437$	5.81462e109	1.52947
$438$	7.26328e108	0.173763
$439$	−5.41020e108	−0.117743	−0.0588716	−	0.998266i	$-0.518750\pi$
$439$	−5.41020e108	−0.117743	−0.0588716	+	0.998266i	$0.518750\pi$
$440$	1.01200e109	0.200398
$441$	−1.26110e110	−2.27274
$442$	−1.69399e108	−0.0277899
$443$	6.34373e109	0.947524	0.473762	−	0.880653i	$-0.342896\pi$
$443$	6.34373e109	0.947524	0.473762	+	0.880653i	$0.342896\pi$
$444$	7.99319e108	0.108724
$445$	−1.46329e109	−0.181297
$446$	2.65942e109	0.300186
$447$	−2.77527e109	−0.285459
$448$	−1.00961e110	−0.946487
$449$	−3.21235e109	−0.274536	−0.137268	−	0.990534i	$-0.543832\pi$
$449$	−3.21235e109	−0.274536	−0.137268	+	0.990534i	$0.543832\pi$
$450$	−6.50345e109	−0.506786
$451$	−8.56404e109	−0.608629
$452$	1.45140e110	0.940900
$453$	3.52600e109	0.208548
$454$	1.49931e110	0.809233
$455$	−6.97130e109	−0.343432
$456$	−4.88619e109	−0.219750
$457$	−3.93387e109	−0.161546	−0.0807732	−	0.996733i	$-0.525739\pi$
$457$	−3.93387e109	−0.161546	−0.0807732	+	0.996733i	$0.525739\pi$
$458$	1.22299e110	0.458677
$459$	1.00570e109	0.0344542
$460$	−9.86398e109	−0.308747
$461$	5.78331e110	1.65420	0.827100	−	0.562055i	$-0.189989\pi$
$461$	5.78331e110	1.65420	0.827100	+	0.562055i	$0.189989\pi$
$462$	−7.60769e109	−0.198889
$463$	−1.42859e110	−0.341427	−0.170713	−	0.985321i	$-0.554607\pi$
$463$	−1.42859e110	−0.341427	−0.170713	+	0.985321i	$0.554607\pi$
$464$	−1.01619e109	−0.0222063
$465$	−1.92038e109	−0.0383786
$466$	2.97625e110	0.544069
$467$	2.20866e110	0.369385	0.184692	−	0.982796i	$-0.440871\pi$
$467$	2.20866e110	0.369385	0.184692	+	0.982796i	$0.440871\pi$
$468$	−2.66949e110	−0.408531
$469$	−4.94237e110	−0.692248
$470$	1.45520e110	0.186579
$471$	−1.14455e110	−0.134359
$472$	−1.70551e111	−1.83342
$473$	−9.86594e110	−0.971407
$474$	−3.91576e109	−0.0353195
$475$	1.01500e111	0.838848
$476$	−1.14625e110	−0.0868140
$477$	1.24513e111	0.864371
$478$	9.21774e109	0.0586634
$479$	1.24974e111	0.729280	0.364640	−	0.931149i	$-0.381192\pi$
$479$	1.24974e111	0.729280	0.364640	+	0.931149i	$0.381192\pi$
$480$	1.32929e110	0.0711392
$481$	8.99876e110	0.441735
$482$	−9.10195e110	−0.409904
$483$	1.87106e111	0.773181
$484$	7.89369e110	0.299363
$485$	5.94746e110	0.207038
$486$	−1.25716e111	−0.401777
$487$	−1.79854e111	−0.527799	−0.263900	−	0.964550i	$-0.585009\pi$
$487$	−1.79854e111	−0.527799	−0.263900	+	0.964550i	$0.585009\pi$
$488$	1.93633e111	0.521863
$489$	−4.35511e110	−0.107815
$490$	1.74712e111	0.397362
$491$	−7.90487e111	−1.65201	−0.826006	−	0.563662i	$-0.809392\pi$
$491$	−7.90487e111	−1.65201	−0.826006	+	0.563662i	$0.809392\pi$
$492$	−7.01454e110	−0.134725
$493$	1.02801e110	0.0181490
$494$	−2.18007e111	−0.353836
$495$	−1.29755e111	−0.193645
$496$	3.51389e110	0.0482279
$497$	1.76890e111	0.223313
$498$	1.71544e111	0.199231
$499$	−4.83195e110	−0.0516357	−0.0258178	−	0.999667i	$-0.508219\pi$
$499$	−4.83195e110	−0.0516357	−0.0258178	+	0.999667i	$0.508219\pi$
$500$	−3.59004e111	−0.353056
$501$	−3.78237e111	−0.342372
$502$	1.34939e112	1.12443
$503$	−9.53165e111	−0.731302	−0.365651	−	0.930752i	$-0.619154\pi$
$503$	−9.53165e111	−0.731302	−0.365651	+	0.930752i	$0.619154\pi$
$504$	2.38493e112	1.68504
$505$	4.96303e111	0.322964
$506$	−1.21186e112	−0.726453
$507$	−2.52164e111	−0.139269
$508$	1.58652e112	0.807421
$509$	−3.37431e112	−1.58269	−0.791346	−	0.611368i	$-0.790619\pi$
$509$	−3.37431e112	−1.58269	−0.791346	+	0.611368i	$0.790619\pi$
$510$	−6.74413e109	−0.00291584
$511$	5.53302e112	2.20544
$512$	−4.74267e111	−0.174309
$513$	1.29428e112	0.438689
$514$	−3.03961e112	−0.950273
$515$	−1.59031e112	−0.458651
$516$	−8.08089e111	−0.215029
$517$	−3.41670e112	−0.838976
$518$	−3.18617e112	−0.722077
$519$	1.75461e111	0.0367060
$520$	9.33174e111	0.180229
$521$	2.84354e112	0.507100	0.253550	−	0.967322i	$-0.418402\pi$
$521$	2.84354e112	0.507100	0.253550	+	0.967322i	$0.418402\pi$
$522$	−8.47686e111	−0.139608
$523$	−5.04023e112	−0.766709	−0.383354	−	0.923601i	$-0.625231\pi$
$523$	−5.04023e112	−0.766709	−0.383354	+	0.923601i	$0.625231\pi$
$524$	−9.06717e111	−0.127416
$525$	3.26613e112	0.424055
$526$	2.87410e112	0.344821
$527$	−3.55479e111	−0.0394161
$528$	−1.56525e111	−0.0160426
$529$	1.92511e113	1.82409
$530$	−1.72499e112	−0.151125
$531$	2.18674e113	1.77163
$532$	−1.47516e113	−1.10536
$533$	−7.89699e112	−0.547372
$534$	−1.47249e112	−0.0944257
$535$	−4.78662e112	−0.284019
$536$	6.61583e112	0.363283
$537$	4.52168e112	0.229809
$538$	1.27011e113	0.597552
$539$	−4.10211e113	−1.78679
$540$	−2.19562e112	−0.0885558
$541$	−3.59523e113	−1.34289	−0.671445	−	0.741054i	$-0.734326\pi$
$541$	−3.59523e113	−1.34289	−0.671445	+	0.741054i	$0.734326\pi$
$542$	−1.12567e113	−0.389439
$543$	4.63201e112	0.148449
$544$	2.46064e112	0.0730623
$545$	1.46405e113	0.402811
$546$	−7.01513e112	−0.178872
$547$	6.81717e113	1.61113	0.805564	−	0.592509i	$-0.201863\pi$
$547$	6.81717e113	1.61113	0.805564	+	0.592509i	$0.201863\pi$
$548$	2.26935e113	0.497174
$549$	−2.48269e113	−0.504278
$550$	−2.11544e113	−0.398427
$551$	1.32300e113	0.231083
$552$	−2.50459e113	−0.405756
$553$	−2.98295e113	−0.448284
$554$	5.03444e113	0.701933
$555$	3.58259e112	0.0463488
$556$	8.54090e113	1.02542
$557$	4.08803e113	0.455537	0.227769	−	0.973715i	$-0.426857\pi$
$557$	4.08803e113	0.455537	0.227769	+	0.973715i	$0.426857\pi$
$558$	2.93123e113	0.303201
$559$	−9.09749e113	−0.873638
$560$	5.07843e112	0.0452821
$561$	1.58347e112	0.0131114
$562$	−5.13890e113	−0.395196
$563$	−6.73729e113	−0.481268	−0.240634	−	0.970616i	$-0.577355\pi$
$563$	−6.73729e113	−0.481268	−0.240634	+	0.970616i	$0.577355\pi$
$564$	−2.79851e113	−0.185714
$565$	6.50528e113	0.401102
$566$	8.35715e113	0.478825
$567$	−2.84298e114	−1.51383
$568$	−2.36785e113	−0.117192
$569$	−4.43352e113	−0.203981	−0.101991	−	0.994785i	$-0.532521\pi$
$569$	−4.43352e113	−0.203981	−0.101991	+	0.994785i	$0.532521\pi$
$570$	−8.67931e112	−0.0371261
$571$	−6.29044e113	−0.250197	−0.125099	−	0.992144i	$-0.539925\pi$
$571$	−6.29044e113	−0.250197	−0.125099	+	0.992144i	$0.539925\pi$
$572$	−8.68329e113	−0.321180
$573$	7.44123e113	0.255993
$574$	2.79607e114	0.894755
$575$	5.20277e114	1.54888
$576$	−1.73278e114	−0.479966
$577$	−6.67499e114	−1.72050	−0.860249	−	0.509873i	$-0.829692\pi$
$577$	−6.67499e114	−1.72050	−0.860249	+	0.509873i	$0.829692\pi$
$578$	2.43082e114	0.583106
$579$	8.90225e113	0.198765
$580$	−2.24434e113	−0.0466474
$581$	1.30679e115	2.52869
$582$	5.98485e113	0.107832
$583$	4.05013e114	0.679554
$584$	−7.40648e114	−1.15739
$585$	−1.19648e114	−0.174155
$586$	−6.39385e114	−0.866985
$587$	−1.38775e114	−0.175319	−0.0876596	−	0.996150i	$-0.527939\pi$
$587$	−1.38775e114	−0.175319	−0.0876596	+	0.996150i	$0.527939\pi$
$588$	−3.35991e114	−0.395520
$589$	−4.57481e114	−0.501867
$590$	−3.02949e114	−0.309750
$591$	1.78987e114	0.170585
$592$	−6.55540e113	−0.0582436
$593$	−8.39619e114	−0.695524	−0.347762	−	0.937583i	$-0.613058\pi$
$593$	−8.39619e114	−0.695524	−0.347762	+	0.937583i	$0.613058\pi$
$594$	−2.69749e114	−0.208364
$595$	−5.13755e113	−0.0370085
$596$	1.12156e115	0.753533
$597$	−3.22348e114	−0.202018
$598$	−1.11747e115	−0.653338
$599$	2.82400e115	1.54046	0.770232	−	0.637763i	$-0.220140\pi$
$599$	2.82400e115	1.54046	0.770232	+	0.637763i	$0.220140\pi$
$600$	−4.37203e114	−0.222539
$601$	6.29824e114	0.299178	0.149589	−	0.988748i	$-0.452205\pi$
$601$	6.29824e114	0.299178	0.149589	+	0.988748i	$0.452205\pi$
$602$	3.22112e115	1.42808
$603$	−8.48256e114	−0.351041
$604$	−1.42495e115	−0.550512
$605$	3.53800e114	0.127617
$606$	4.99424e114	0.168211
$607$	−1.98354e115	−0.623893	−0.311946	−	0.950100i	$-0.600981\pi$
$607$	−1.98354e115	−0.623893	−0.311946	+	0.950100i	$0.600981\pi$
$608$	3.16670e115	0.930269
$609$	4.25720e114	0.116817
$610$	3.43949e114	0.0881671
$611$	−3.15058e115	−0.754536
$612$	−1.96730e114	−0.0440237
$613$	−1.57908e115	−0.330213	−0.165106	−	0.986276i	$-0.552797\pi$
$613$	−1.57908e115	−0.330213	−0.165106	+	0.986276i	$0.552797\pi$
$614$	−2.77577e115	−0.542496
$615$	−3.14396e114	−0.0574327
$616$	7.75769e115	1.32475
$617$	−9.51904e115	−1.51970	−0.759852	−	0.650096i	$-0.774729\pi$
$617$	−9.51904e115	−1.51970	−0.759852	+	0.650096i	$0.774729\pi$
$618$	−1.60031e115	−0.238882
$619$	−2.38140e114	−0.0332408	−0.0166204	−	0.999862i	$-0.505291\pi$
$619$	−2.38140e114	−0.0332408	−0.0166204	+	0.999862i	$0.505291\pi$
$620$	7.76075e114	0.101309
$621$	6.63428e115	0.810014
$622$	−1.04020e115	−0.118800
$623$	−1.12171e116	−1.19847
$624$	−1.44333e114	−0.0144280
$625$	8.24465e115	0.771173
$626$	−7.01213e115	−0.613783
$627$	2.03783e115	0.166942
$628$	4.62544e115	0.354672
$629$	6.63170e114	0.0476018
$630$	4.23635e115	0.284681
$631$	3.12356e116	1.96531	0.982656	−	0.185440i	$-0.0593709\pi$
$631$	3.12356e116	1.96531	0.982656	+	0.185440i	$0.0593709\pi$
$632$	3.99296e115	0.235254
$633$	−1.32744e115	−0.0732423
$634$	−5.86060e115	−0.302857
$635$	7.11085e115	0.344201
$636$	3.31734e115	0.150425
$637$	−3.78260e116	−1.60695
$638$	−2.75734e115	−0.109757
$639$	3.03596e115	0.113243
$640$	−5.78240e115	−0.202134
$641$	−3.15757e115	−0.103453	−0.0517266	−	0.998661i	$-0.516472\pi$
$641$	−3.15757e115	−0.103453	−0.0517266	+	0.998661i	$0.516472\pi$
$642$	−4.81672e115	−0.147927
$643$	9.42601e115	0.271377	0.135688	−	0.990752i	$-0.456675\pi$
$643$	9.42601e115	0.271377	0.135688	+	0.990752i	$0.456675\pi$
$644$	−7.56144e116	−2.04099
$645$	−3.62190e115	−0.0916660
$646$	−1.60662e115	−0.0381297
$647$	−2.99922e115	−0.0667545	−0.0333772	−	0.999443i	$-0.510626\pi$
$647$	−2.99922e115	−0.0667545	−0.0333772	+	0.999443i	$0.510626\pi$
$648$	3.80561e116	0.794440
$649$	7.11300e116	1.39283
$650$	−1.95067e116	−0.358326
$651$	−1.47211e116	−0.253704
$652$	1.76001e116	0.284604
$653$	−2.42814e116	−0.368448	−0.184224	−	0.982884i	$-0.558977\pi$
$653$	−2.42814e116	−0.368448	−0.184224	+	0.982884i	$0.558977\pi$
$654$	1.47326e116	0.209799
$655$	−4.06396e115	−0.0543169
$656$	5.75278e115	0.0721720
$657$	9.49630e116	1.11839
$658$	1.11552e117	1.23339
$659$	4.48090e116	0.465180	0.232590	−	0.972575i	$-0.425280\pi$
$659$	4.48090e116	0.465180	0.232590	+	0.972575i	$0.425280\pi$
$660$	−3.45700e115	−0.0336997
$661$	−1.04880e117	−0.960134	−0.480067	−	0.877232i	$-0.659388\pi$
$661$	−1.04880e117	−0.960134	−0.480067	+	0.877232i	$0.659388\pi$
$662$	−6.63300e116	−0.570300
$663$	1.46013e115	0.0117918
$664$	−1.74926e117	−1.32703
$665$	−6.61173e116	−0.471213
$666$	−5.46840e116	−0.366168
$667$	6.78149e116	0.426681
$668$	1.52856e117	0.903771
$669$	−2.29229e116	−0.127375
$670$	1.17517e116	0.0613755
$671$	−8.07566e116	−0.396455
$672$	1.01900e117	0.470271
$673$	−3.58253e117	−1.55441	−0.777204	−	0.629249i	$-0.783363\pi$
$673$	−3.58253e117	−1.55441	−0.777204	+	0.629249i	$0.783363\pi$
$674$	3.20954e116	0.130936
$675$	1.15808e117	0.444256
$676$	1.01906e117	0.367632
$677$	−2.59860e117	−0.881679	−0.440839	−	0.897586i	$-0.645319\pi$
$677$	−2.59860e117	−0.881679	−0.440839	+	0.897586i	$0.645319\pi$
$678$	6.54618e116	0.208908
$679$	4.55915e117	1.36864
$680$	6.87710e115	0.0194216
$681$	−1.29233e117	−0.343374
$682$	9.53467e116	0.238371
$683$	3.27710e116	0.0770958	0.0385479	−	0.999257i	$-0.487727\pi$
$683$	3.27710e116	0.0770958	0.0385479	+	0.999257i	$0.487727\pi$
$684$	−2.53180e117	−0.560534
$685$	1.01713e117	0.211943
$686$	7.86454e117	1.54249
$687$	−1.05416e117	−0.194626
$688$	6.62732e116	0.115191
$689$	3.73467e117	0.611159
$690$	−4.44889e116	−0.0685511
$691$	−3.61023e117	−0.523837	−0.261919	−	0.965090i	$-0.584355\pi$
$691$	−3.61023e117	−0.523837	−0.261919	+	0.965090i	$0.584355\pi$
$692$	−7.09086e116	−0.0968938
$693$	−9.94660e117	−1.28011
$694$	−5.44621e117	−0.660201
$695$	3.82808e117	0.437131
$696$	−5.69867e116	−0.0613042
$697$	−5.81975e116	−0.0589853
$698$	−6.99509e116	−0.0668026
$699$	−2.56538e117	−0.230860
$700$	−1.31993e118	−1.11939
$701$	3.35747e117	0.268358	0.134179	−	0.990957i	$-0.457160\pi$
$701$	3.35747e117	0.268358	0.134179	+	0.990957i	$0.457160\pi$
$702$	−2.48738e117	−0.187393
$703$	8.53462e117	0.606092
$704$	−5.63638e117	−0.377342
$705$	−1.25431e117	−0.0791693
$706$	−7.45766e117	−0.443821
$707$	3.80451e118	2.13498
$708$	5.82604e117	0.308314
$709$	2.46427e118	1.22990	0.614949	−	0.788567i	$-0.289176\pi$
$709$	2.46427e118	1.22990	0.614949	+	0.788567i	$0.289176\pi$
$710$	−4.20600e116	−0.0197992
$711$	−5.11962e117	−0.227326
$712$	1.50152e118	0.628944
$713$	−2.34498e118	−0.926668
$714$	−5.16985e116	−0.0192754
$715$	−3.89190e117	−0.136918
$716$	−1.82733e118	−0.606634
$717$	−7.94522e116	−0.0248921
$718$	−2.81339e117	−0.0831889
$719$	5.63671e118	1.57317	0.786586	−	0.617480i	$-0.211846\pi$
$719$	5.63671e118	1.57317	0.786586	+	0.617480i	$0.211846\pi$
$720$	8.71609e116	0.0229627
$721$	−1.21909e119	−3.03194
$722$	4.28496e117	0.100613
$723$	7.84541e117	0.173931
$724$	−1.87192e118	−0.391865
$725$	1.18378e118	0.234015
$726$	3.56024e117	0.0664676
$727$	4.63772e117	0.0817761	0.0408881	−	0.999164i	$-0.486981\pi$
$727$	4.63772e117	0.0817761	0.0408881	+	0.999164i	$0.486981\pi$
$728$	7.15344e118	1.19141
$729$	−4.11747e118	−0.647796
$730$	−1.31561e118	−0.195537
$731$	−6.70446e117	−0.0941440
$732$	−6.61452e117	−0.0877584
$733$	−3.04688e118	−0.381980	−0.190990	−	0.981592i	$-0.561170\pi$
$733$	−3.04688e118	−0.381980	−0.190990	+	0.981592i	$0.561170\pi$
$734$	7.25359e117	0.0859343
$735$	−1.50593e118	−0.168609
$736$	1.62321e119	1.71769
$737$	−2.75920e118	−0.275983
$738$	4.79888e118	0.453733
$739$	1.13803e119	1.01720	0.508602	−	0.861002i	$-0.330162\pi$
$739$	1.13803e119	1.01720	0.508602	+	0.861002i	$0.330162\pi$
$740$	−1.44782e118	−0.122348
$741$	1.87911e118	0.150140
$742$	−1.32232e119	−0.999024
$743$	−8.16429e118	−0.583287	−0.291644	−	0.956527i	$-0.594202\pi$
$743$	−8.16429e118	−0.583287	−0.291644	+	0.956527i	$0.594202\pi$
$744$	1.97055e118	0.133141
$745$	5.02689e118	0.321229
$746$	−6.18722e118	−0.373968
$747$	2.24283e119	1.28231
$748$	−6.39921e117	−0.0346107
$749$	−3.66929e119	−1.87753
$750$	−1.61919e118	−0.0783893
$751$	1.50012e119	0.687177	0.343589	−	0.939120i	$-0.388357\pi$
$751$	1.50012e119	0.687177	0.343589	+	0.939120i	$0.388357\pi$
$752$	2.29512e118	0.0994869
$753$	−1.16311e119	−0.477121
$754$	−2.54257e118	−0.0987104
$755$	−6.38671e118	−0.234681
$756$	−1.68310e119	−0.585404
$757$	−3.12193e119	−1.02789	−0.513943	−	0.857825i	$-0.671816\pi$
$757$	−3.12193e119	−1.02789	−0.513943	+	0.857825i	$0.671816\pi$
$758$	1.26314e119	0.393712
$759$	1.04456e119	0.308249
$760$	8.85043e118	0.247287
$761$	−3.11801e119	−0.824924	−0.412462	−	0.910975i	$-0.635331\pi$
$761$	−3.11801e119	−0.824924	−0.412462	+	0.910975i	$0.635331\pi$
$762$	7.15557e118	0.179272
$763$	1.12230e120	2.66281
$764$	−3.00720e119	−0.675752
$765$	−8.81755e117	−0.0187671
$766$	−4.53092e118	−0.0913466
$767$	6.55897e119	1.25264
$768$	−1.28510e119	−0.232513
$769$	5.40298e119	0.926170	0.463085	−	0.886314i	$-0.346742\pi$
$769$	5.40298e119	0.926170	0.463085	+	0.886314i	$0.346742\pi$
$770$	1.37799e119	0.223811
$771$	2.61999e119	0.403220
$772$	−3.59763e119	−0.524686
$773$	−1.34907e120	−1.86460	−0.932300	−	0.361686i	$-0.882201\pi$
$773$	−1.34907e120	−1.86460	−0.932300	+	0.361686i	$0.882201\pi$
$774$	5.52840e119	0.724185
$775$	−4.09342e119	−0.508236
$776$	−6.10285e119	−0.718243
$777$	2.74631e119	0.306392
$778$	−2.88989e119	−0.305653
$779$	−7.48968e119	−0.751033
$780$	−3.18773e118	−0.0303079
$781$	9.87535e118	0.0890296
$782$	−8.23529e118	−0.0704043
$783$	1.50949e119	0.122382
$784$	2.75554e119	0.211880
$785$	2.07315e119	0.151196
$786$	−4.08951e118	−0.0282902
$787$	−1.09404e120	−0.717932	−0.358966	−	0.933351i	$-0.616871\pi$
$787$	−1.09404e120	−0.717932	−0.358966	+	0.933351i	$0.616871\pi$
$788$	−7.23334e119	−0.450299
$789$	−2.47733e119	−0.146315
$790$	7.09268e118	0.0397453
$791$	4.98675e120	2.65151
$792$	1.33145e120	0.671783
$793$	−7.44665e119	−0.356553
$794$	1.44973e119	0.0658772
$795$	1.48685e119	0.0641256
$796$	1.30269e120	0.533273
$797$	−4.56632e120	−1.77438	−0.887190	−	0.461405i	$-0.847346\pi$
$797$	−4.56632e120	−1.77438	−0.887190	+	0.461405i	$0.847346\pi$
$798$	−6.65331e119	−0.245424
$799$	−2.32184e119	−0.0813094
$800$	2.83348e120	0.942075
$801$	−1.92519e120	−0.607750
$802$	2.60121e120	0.779722
$803$	3.08895e120	0.879256
$804$	−2.25997e119	−0.0610910
$805$	−3.38908e120	−0.870067
$806$	8.79201e119	0.214380
$807$	−1.09477e120	−0.253554
$808$	−5.09270e120	−1.12041
$809$	−4.71174e120	−0.984731	−0.492365	−	0.870389i	$-0.663868\pi$
$809$	−4.71174e120	−0.984731	−0.492365	+	0.870389i	$0.663868\pi$
$810$	6.75988e119	0.134218
$811$	4.99532e120	0.942318	0.471159	−	0.882048i	$-0.343836\pi$
$811$	4.99532e120	0.942318	0.471159	+	0.882048i	$0.343836\pi$
$812$	−1.72045e120	−0.308366
$813$	9.70268e119	0.165247
$814$	−1.77876e120	−0.287875
$815$	7.88848e119	0.121326
$816$	−1.06367e118	−0.00155477
$817$	−8.62826e120	−1.19869
$818$	6.95050e120	0.917812
$819$	−9.17187e120	−1.15127
$820$	1.27056e120	0.151607
$821$	9.17687e120	1.04101	0.520503	−	0.853860i	$-0.325744\pi$
$821$	9.17687e120	1.04101	0.520503	+	0.853860i	$0.325744\pi$
$822$	1.02353e120	0.110388
$823$	1.44040e121	1.47703	0.738515	−	0.674238i	$-0.235528\pi$
$823$	1.44040e121	1.47703	0.738515	+	0.674238i	$0.235528\pi$
$824$	1.63186e121	1.59113
$825$	1.82340e120	0.169061
$826$	−2.32232e121	−2.04762
$827$	9.82056e120	0.823489	0.411745	−	0.911299i	$-0.364920\pi$
$827$	9.82056e120	0.823489	0.411745	+	0.911299i	$0.364920\pi$
$828$	−1.29777e121	−1.03499
$829$	1.86562e121	1.41517	0.707587	−	0.706626i	$-0.249784\pi$
$829$	1.86562e121	1.41517	0.707587	+	0.706626i	$0.249784\pi$
$830$	−3.10720e120	−0.224197
$831$	−4.33943e120	−0.297845
$832$	−5.19736e120	−0.339363
$833$	−2.78761e120	−0.173167
$834$	3.85215e120	0.227673
$835$	6.85108e120	0.385274
$836$	−8.23542e120	−0.440682
$837$	−5.21970e120	−0.265790
$838$	−9.47823e120	−0.459304
$839$	−2.30098e121	−1.06118	−0.530592	−	0.847627i	$-0.678030\pi$
$839$	−2.30098e121	−1.06118	−0.530592	+	0.847627i	$0.678030\pi$
$840$	2.84794e120	0.125009
$841$	−2.23920e121	−0.935534
$842$	−1.03285e121	−0.410758
$843$	4.42947e120	0.167690
$844$	5.36454e120	0.193340
$845$	4.56750e120	0.156720
$846$	1.91455e121	0.625457
$847$	2.71212e121	0.843622
$848$	−2.72062e120	−0.0805824
$849$	−7.20344e120	−0.203175
$850$	−1.43756e120	−0.0386136
$851$	4.37473e121	1.11911
$852$	8.08859e119	0.0197074
$853$	−1.09508e120	−0.0254133	−0.0127066	−	0.999919i	$-0.504045\pi$
$853$	−1.09508e120	−0.0254133	−0.0127066	+	0.999919i	$0.504045\pi$
$854$	2.63662e121	0.582834
$855$	−1.13477e121	−0.238954
$856$	4.91169e121	0.985303
$857$	1.24805e121	0.238522	0.119261	−	0.992863i	$-0.461947\pi$
$857$	1.24805e121	0.238522	0.119261	+	0.992863i	$0.461947\pi$
$858$	−3.91637e120	−0.0713118
$859$	−8.39956e121	−1.45727	−0.728636	−	0.684902i	$-0.759845\pi$
$859$	−8.39956e121	−1.45727	−0.728636	+	0.684902i	$0.759845\pi$
$860$	1.46371e121	0.241974
$861$	−2.41007e121	−0.379663
$862$	−3.69285e121	−0.554383
$863$	−5.00811e121	−0.716516	−0.358258	−	0.933623i	$-0.616629\pi$
$863$	−5.00811e121	−0.716516	−0.358258	+	0.933623i	$0.616629\pi$
$864$	3.61309e121	0.492673
$865$	−3.17816e120	−0.0413055
$866$	4.66972e121	0.578494
$867$	−2.09524e121	−0.247424
$868$	5.94916e121	0.669711
$869$	−1.66531e121	−0.178720
$870$	−1.01225e120	−0.0103571
$871$	−2.54429e121	−0.248206
$872$	−1.50231e122	−1.39741
$873$	7.82484e121	0.694040
$874$	−1.05984e122	−0.896425
$875$	−1.23347e122	−0.994935
$876$	2.53006e121	0.194630
$877$	1.97820e122	1.45140	0.725699	−	0.688012i	$-0.241516\pi$
$877$	1.97820e122	1.45140	0.725699	+	0.688012i	$0.241516\pi$
$878$	9.86121e120	0.0690093
$879$	5.51117e121	0.367880
$880$	2.83516e120	0.0180529
$881$	−8.64195e121	−0.524942	−0.262471	−	0.964940i	$-0.584537\pi$
$881$	−8.64195e121	−0.524942	−0.262471	+	0.964940i	$0.584537\pi$
$882$	2.29862e122	1.33205
$883$	1.23976e121	0.0685438	0.0342719	−	0.999413i	$-0.489089\pi$
$883$	1.23976e121	0.0685438	0.0342719	+	0.999413i	$0.489089\pi$
$884$	−5.90078e120	−0.0311272
$885$	2.61126e121	0.131433
$886$	−1.15628e122	−0.555344
$887$	−1.31284e121	−0.0601703	−0.0300852	−	0.999547i	$-0.509578\pi$
$887$	−1.31284e121	−0.0601703	−0.0300852	+	0.999547i	$0.509578\pi$
$888$	−3.67620e121	−0.160791
$889$	5.45097e122	2.27536
$890$	2.66715e121	0.106258
$891$	−1.58717e122	−0.603528
$892$	9.26373e121	0.336236
$893$	−2.98808e122	−1.03528
$894$	5.05850e121	0.167307
$895$	−8.19020e121	−0.258606
$896$	−4.43262e122	−1.33622
$897$	9.63204e121	0.277225
$898$	5.85517e121	0.160906
$899$	−5.33552e121	−0.140007
$900$	−2.26539e122	−0.567647
$901$	2.75229e121	0.0658591
$902$	1.56097e122	0.356717
$903$	−2.77644e122	−0.605965
$904$	−6.67525e122	−1.39148
$905$	−8.39004e121	−0.167051
$906$	−6.42687e121	−0.122230
$907$	2.00864e122	0.364921	0.182460	−	0.983213i	$-0.441594\pi$
$907$	2.00864e122	0.364921	0.182460	+	0.983213i	$0.441594\pi$
$908$	5.22264e122	0.906415
$909$	6.52967e122	1.08265
$910$	1.27066e122	0.201286
$911$	4.07730e121	0.0617106	0.0308553	−	0.999524i	$-0.490177\pi$
$911$	4.07730e121	0.0617106	0.0308553	+	0.999524i	$0.490177\pi$
$912$	−1.36889e121	−0.0197962
$913$	7.29547e122	1.00813
$914$	7.17029e121	0.0946824
$915$	−2.96467e121	−0.0374111
$916$	4.26013e122	0.513761
$917$	−3.11531e122	−0.359066
$918$	−1.83310e121	−0.0201936
$919$	−4.12126e122	−0.433946	−0.216973	−	0.976178i	$-0.569618\pi$
$919$	−4.12126e122	−0.433946	−0.216973	+	0.976178i	$0.569618\pi$
$920$	4.53661e122	0.456600
$921$	2.39257e122	0.230192
$922$	−1.05413e123	−0.969527
$923$	9.10616e121	0.0800691
$924$	−2.65003e122	−0.222774
$925$	7.63655e122	0.613783
$926$	2.60391e122	0.200110
$927$	−2.09231e123	−1.53751
$928$	3.69327e122	0.259519
$929$	3.90309e122	0.262275	0.131137	−	0.991364i	$-0.458137\pi$
$929$	3.90309e122	0.262275	0.131137	+	0.991364i	$0.458137\pi$
$930$	3.50029e121	0.0224937
$931$	−3.58750e123	−2.20485
$932$	1.03674e123	0.609407
$933$	8.96598e121	0.0504092
$934$	−4.02575e122	−0.216497
$935$	−2.86816e121	−0.0147544
$936$	1.22774e123	0.604170
$937$	2.02902e122	0.0955196	0.0477598	−	0.998859i	$-0.484792\pi$
$937$	2.02902e122	0.0955196	0.0477598	+	0.998859i	$0.484792\pi$
$938$	9.00848e122	0.405727
$939$	6.04410e122	0.260441
$940$	5.06900e122	0.208986
$941$	2.04926e123	0.808401	0.404200	−	0.914670i	$-0.367550\pi$
$941$	2.04926e123	0.808401	0.404200	+	0.914670i	$0.367550\pi$
$942$	2.08618e122	0.0787481
$943$	−3.83911e123	−1.38674
$944$	−4.77806e122	−0.165163
$945$	−7.54376e122	−0.249556
$946$	1.79827e123	0.569342
$947$	3.61266e123	1.09472	0.547360	−	0.836897i	$-0.315633\pi$
$947$	3.61266e123	1.09472	0.547360	+	0.836897i	$0.315633\pi$
$948$	−1.36400e122	−0.0395611
$949$	2.84835e123	0.790762
$950$	−1.85006e123	−0.491649
$951$	5.05154e122	0.128509
$952$	5.27178e122	0.128388
$953$	−1.94058e122	−0.0452457	−0.0226228	−	0.999744i	$-0.507202\pi$
$953$	−1.94058e122	−0.0452457	−0.0226228	+	0.999744i	$0.507202\pi$
$954$	−2.26950e123	−0.506608
$955$	−1.34784e123	−0.288071
$956$	3.21087e122	0.0657084
$957$	2.37669e122	0.0465722
$958$	−2.27790e123	−0.427431
$959$	7.79706e123	1.40107
$960$	−2.06918e122	−0.0356075
$961$	−4.22267e123	−0.695932
$962$	−1.64021e123	−0.258901
$963$	−6.29758e123	−0.952100
$964$	−3.17054e123	−0.459130
$965$	−1.61248e123	−0.223672
$966$	−3.41039e123	−0.453162
$967$	−4.86734e123	−0.619574	−0.309787	−	0.950806i	$-0.600258\pi$
$967$	−4.86734e123	−0.619574	−0.309787	+	0.950806i	$0.600258\pi$
$968$	−3.63044e123	−0.442723
$969$	1.38482e122	0.0161792
$970$	−1.08405e123	−0.121345
$971$	1.16473e124	1.24918	0.624590	−	0.780952i	$-0.285266\pi$
$971$	1.16473e124	1.24918	0.624590	+	0.780952i	$0.285266\pi$
$972$	−4.37914e123	−0.450027
$973$	2.93449e124	2.88968
$974$	3.27821e123	0.309343
$975$	1.68137e123	0.152045
$976$	5.42472e122	0.0470121
$977$	−1.61888e124	−1.34459	−0.672297	−	0.740282i	$-0.734692\pi$
$977$	−1.61888e124	−1.34459	−0.672297	+	0.740282i	$0.734692\pi$
$978$	7.93808e122	0.0631907
$979$	−6.26225e123	−0.477803
$980$	6.08586e123	0.445082
$981$	1.92620e124	1.35032
$982$	1.44083e124	0.968244
$983$	−9.53292e123	−0.614122	−0.307061	−	0.951690i	$-0.599346\pi$
$983$	−9.53292e123	−0.614122	−0.307061	+	0.951690i	$0.599346\pi$
$984$	3.22610e123	0.199242
$985$	−3.24203e123	−0.191961
$986$	−1.87377e122	−0.0106371
$987$	−9.61518e123	−0.523354
$988$	−7.59397e123	−0.396329
$989$	−4.42272e124	−2.21332
$990$	2.36505e123	0.113496
$991$	2.51558e124	1.15766	0.578829	−	0.815449i	$-0.303510\pi$
$991$	2.51558e124	1.15766	0.578829	+	0.815449i	$0.303510\pi$
$992$	−1.27710e124	−0.563626
$993$	5.71731e123	0.241990
$994$	−3.22420e123	−0.130884
$995$	5.83874e123	0.227332
$996$	5.97549e123	0.223157
$997$	−4.85494e124	−1.73914	−0.869571	−	0.493808i	$-0.835605\pi$
$997$	−4.85494e124	−1.73914	−0.869571	+	0.493808i	$0.835605\pi$
$998$	8.80723e122	0.0302637
$999$	9.73771e123	0.320988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.84.a.a.1.3	✓	7
3.2	odd	2		9.84.a.c.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.84.a.a.1.3	✓	7	1.1	even	1	trivial
9.84.a.c.1.5		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)

\(f(q)\)	\(=\)	\(q-1.82271e12 q^{2} +1.57108e19 q^{3} -6.34915e24 q^{4} -2.84572e28 q^{5} -2.86362e31 q^{6} -2.18145e35 q^{7} +2.92008e37 q^{8} -3.74401e39 q^{9} +O(q^{10})\)	\(q-1.82271e12 q^{2} +1.57108e19 q^{3} -6.34915e24 q^{4} -2.84572e28 q^{5} -2.86362e31 q^{6} -2.18145e35 q^{7} +2.92008e37 q^{8} -3.74401e39 q^{9} +5.18692e40 q^{10} -1.21785e43 q^{11} -9.97501e43 q^{12} -1.12299e46 q^{13} +3.97614e47 q^{14} -4.47086e47 q^{15} +8.18073e48 q^{16} -8.27596e49 q^{17} +6.82423e51 q^{18} -1.06507e53 q^{19} +1.80679e53 q^{20} -3.42723e54 q^{21} +2.21978e55 q^{22} -5.45939e56 q^{23} +4.58767e56 q^{24} -9.52994e57 q^{25} +2.04688e58 q^{26} -1.21521e59 q^{27} +1.38503e60 q^{28} -1.24217e60 q^{29} +8.14906e59 q^{30} +4.29532e61 q^{31} -2.97324e62 q^{32} -1.91334e62 q^{33} +1.50846e62 q^{34} +6.20780e63 q^{35} +2.37713e64 q^{36} -8.01321e64 q^{37} +1.94131e65 q^{38} -1.76431e65 q^{39} -8.30973e65 q^{40} +7.03211e66 q^{41} +6.24683e66 q^{42} +8.10113e67 q^{43} +7.73229e67 q^{44} +1.06544e68 q^{45} +9.95087e68 q^{46} +2.80552e69 q^{47} +1.28526e68 q^{48} +3.36833e70 q^{49} +1.73703e70 q^{50} -1.30022e69 q^{51} +7.13003e70 q^{52} -3.32565e71 q^{53} +2.21496e71 q^{54} +3.46566e71 q^{55} -6.37000e72 q^{56} -1.67331e72 q^{57} +2.26411e72 q^{58} -5.84063e73 q^{59} +2.83861e72 q^{60} +6.63109e73 q^{61} -7.82911e73 q^{62} +8.16736e74 q^{63} +4.62815e74 q^{64} +3.19572e74 q^{65} +3.48745e74 q^{66} +2.26563e75 q^{67} +5.25453e74 q^{68} -8.57714e75 q^{69} -1.13150e76 q^{70} -8.10885e75 q^{71} -1.09328e77 q^{72} -2.53640e77 q^{73} +1.46057e77 q^{74} -1.49723e77 q^{75} +6.76228e77 q^{76} +2.65667e78 q^{77} +3.21581e77 q^{78} +1.36742e78 q^{79} -2.32801e77 q^{80} +1.30326e79 q^{81} -1.28175e79 q^{82} -5.99046e79 q^{83} +2.17600e79 q^{84} +2.35511e78 q^{85} -1.47660e80 q^{86} -1.95155e79 q^{87} -3.55621e80 q^{88} +5.14206e80 q^{89} -1.94199e80 q^{90} +2.44974e81 q^{91} +3.46625e81 q^{92} +6.74829e80 q^{93} -5.11365e81 q^{94} +3.03089e81 q^{95} -4.67119e81 q^{96} -2.08996e82 q^{97} -6.13947e82 q^{98} +4.55963e82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) \) 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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