LMFDB - Embedded newform 1.84.a.a.1.5

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			1.5
Root			$1.15014e11$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.80997e12 q^{2} -9.69898e19 q^{3} -1.77546e24 q^{4} +1.10914e29 q^{5} -2.72539e32 q^{6} -5.50994e34 q^{7} -3.21654e37 q^{8} +5.41619e39 q^{9} +O(q^{10})$	\(q+2.80997e12 q^{2} -9.69898e19 q^{3} -1.77546e24 q^{4} +1.10914e29 q^{5} -2.72539e32 q^{6} -5.50994e34 q^{7} -3.21654e37 q^{8} +5.41619e39 q^{9} +3.11666e41 q^{10} -2.22342e43 q^{11} +1.72201e44 q^{12} -6.42697e45 q^{13} -1.54828e47 q^{14} -1.07576e49 q^{15} -7.32127e49 q^{16} -1.88220e51 q^{17} +1.52193e52 q^{18} +1.37355e53 q^{19} -1.96924e53 q^{20} +5.34408e54 q^{21} -6.24776e55 q^{22} +6.47368e56 q^{23} +3.11971e57 q^{24} +1.96223e57 q^{25} -1.80596e58 q^{26} -1.38244e59 q^{27} +9.78266e58 q^{28} +6.73588e59 q^{29} -3.02285e61 q^{30} +4.12876e61 q^{31} +1.05359e62 q^{32} +2.15650e63 q^{33} -5.28894e63 q^{34} -6.11131e63 q^{35} -9.61621e63 q^{36} -4.23854e63 q^{37} +3.85965e65 q^{38} +6.23351e65 q^{39} -3.56760e66 q^{40} +1.30264e67 q^{41} +1.50167e67 q^{42} -3.87111e67 q^{43} +3.94759e67 q^{44} +6.00733e68 q^{45} +1.81909e69 q^{46} +2.21707e69 q^{47} +7.10089e69 q^{48} -1.08680e70 q^{49} +5.51381e69 q^{50} +1.82554e71 q^{51} +1.14108e70 q^{52} -3.92695e70 q^{53} -3.88463e71 q^{54} -2.46610e72 q^{55} +1.77229e72 q^{56} -1.33221e73 q^{57} +1.89277e72 q^{58} -3.16234e73 q^{59} +1.90996e73 q^{60} +5.48024e73 q^{61} +1.16017e74 q^{62} -2.98429e74 q^{63} +1.00413e75 q^{64} -7.12843e74 q^{65} +6.05970e75 q^{66} +6.60851e75 q^{67} +3.34177e75 q^{68} -6.27881e76 q^{69} -1.71726e76 q^{70} +7.10431e76 q^{71} -1.74214e77 q^{72} +9.86952e76 q^{73} -1.19102e76 q^{74} -1.90316e77 q^{75} -2.43869e77 q^{76} +1.22509e78 q^{77} +1.75160e78 q^{78} +1.00412e79 q^{79} -8.12034e78 q^{80} -8.20683e78 q^{81} +3.66038e79 q^{82} -4.07093e79 q^{83} -9.48818e78 q^{84} -2.08763e80 q^{85} -1.08777e80 q^{86} -6.53312e79 q^{87} +7.15173e80 q^{88} -2.55096e80 q^{89} +1.68804e81 q^{90} +3.54122e80 q^{91} -1.14937e81 q^{92} -4.00448e81 q^{93} +6.22992e81 q^{94} +1.52347e82 q^{95} -1.02187e82 q^{96} -7.47161e81 q^{97} -3.05387e82 q^{98} -1.20425e83 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) $ 7 * q + 347450761416 * q^2 + 92768992732348371972 * q^3 + 35584105659089895299423296 * q^4 + 95882188896595936852480961970 * q^5 - 294670844093053176615850490328096 * q^6 + 41935337227745505345382734191463656 * q^7 - 53166432471809997748387310040100892160 * q^8 + 7173898769720313141925302496494258063219 * q^9	$ 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) $ 7 * q + 347450761416 * q^2 + 92768992732348371972 * q^3 + 35584105659089895299423296 * q^4 + 95882188896595936852480961970 * q^5 - 294670844093053176615850490328096 * q^6 + 41935337227745505345382734191463656 * q^7 - 53166432471809997748387310040100892160 * q^8 + 7173898769720313141925302496494258063219 * q^9 + 499744956856868951374871513628825303339120 * q^10 + 25877323689250927756216798585844787377793324 * q^11 + 2460442604910297198073551343877297856954713856 * q^12 + 17524422091988534325290637412825903296133795802 * q^13 - 667010599912297808117771255707130466716823613248 * q^14 + 495579388338965458292669248844531863255635208440 * q^15 + 417715742702857603748591276714238800242071723446272 * q^16 - 184492474792188340305787588512947709279311819300514 * q^17 - 28009030626032697117218836919123347961714662935963288 * q^18 + 70057685614612811247361635516613863476112345065711060 * q^19 - 57482583811152041858646735327362480085743726726490240 * q^20 + 1893373789164274184370249913565768587140340046764631904 * q^21 - 25459319566814701232336844310162548331034505268300277088 * q^22 + 824652389276591600045965278715869924572765810514596651832 * q^23 - 5108864246496902395549780448291862586480869954908681963520 * q^24 - 4561105897018180667341222610450479407531682079908284920975 * q^25 + 143121440625749988679618714232562854015797139977713783396144 * q^26 - 18306643512253151650162937588580319544032012511255116569240 * q^27 - 3306103780131881005943201423297958381438351892797060269926912 * q^28 + 6404767822227693446699906276316651921336727974067299509413290 * q^29 + 22115840914712862507238627077766882327252015550247576205746240 * q^30 - 37562467055768426209216291610175403000420584080976492348271456 * q^31 - 401973234215497826032118057547245647414044862108632758037479424 * q^32 + 2195918275671465028132881460796250927450387208449702006682532304 * q^33 - 3642106474236630222613516547778797986245715334909676776624068848 * q^34 - 2073208087472515985799712205841339482184218515995426084627529680 * q^35 + 57130418054952308452673267072095667495060459086592800380434471232 * q^36 + 11679830828485560240095590717771086910057022640967690418168414546 * q^37 - 100824829831783953690862886156130827794285762670109921453507515040 * q^38 + 1565953334461766292518881964176162886481814613037624778927724614488 * q^39 + 9486127421786581581058527875045788297835153320557141731458486656000 * q^40 + 17401669041790147490033877534513313327467761516699357985702287340054 * q^41 + 44973533593538917012168170148121446253249051280516070217105265222912 * q^42 + 155423693656840999526303865174514513948712784929597322758540542988492 * q^43 + 1348607485575405225144018262718175988997396446813103620526566114774272 * q^44 + 1880339750988019909779230148989197482912024900416496550280550343305690 * q^45 + 5506219190262487958701836671526521132048107774881360169694419306565184 * q^46 + 11104141751597135653133375816819520459474802577748272571942549885601776 * q^47 + 68535772806187659604752521040191262704244920099270422943498591509266432 * q^48 + 48858841649181147950169676419361972612175619458033829843989473166294751 * q^49 + 150128830200294018241623574757370340046061702636780234316678381973441400 * q^50 + 285323979437882241696128479102133404321665278074017384721958077373999304 * q^51 + 287156729453525056399055611675371787971339735611155780289523821420813696 * q^52 + 273161075599979193637636426681909962095058697602986681290913238279577122 * q^53 - 3035335179479589317975420635665461716944398657720830329060859634436191040 * q^54 - 5713148801806043865831522329085397613042534865163593217346624944021935960 * q^55 - 16548372571630294224019812720652384540821878073420179539137646605391810560 * q^56 - 34025570556802197911899195289016333635970214164767521145341412678086153680 * q^57 - 107856312851606062726720906610847944794517184506982834438591381099782874960 * q^58 - 23387662928216230581473943437005284343365902946251051301830585313805483620 * q^59 - 111426487760354848959531561221427047757146965306130391339788819029760724480 * q^60 + 174496853895103215296232800034629055024308568422892345549894754405198022474 * q^61 + 202911123959081503237789686733196890455024356155124318865846118460223535872 * q^62 + 1452472272578781819866280021221104701255297870249157972403070846844413328392 * q^63 + 6634340238508315566899158004225714692716612285250446595132287614710135914496 * q^64 + 7847697320266417932918441445560149353782900722209245969738521432028132712140 * q^65 + 5853477037889002409213418366788233179355537994202667769768656686338545312128 * q^66 + 4207870282072288819930283375229384131272485602664611977572129464006258765636 * q^67 - 2096504738666940955442779681368953687199581458034579489652465446528751795072 * q^68 - 20650746275200221772316139734189903533557652468456540358959577322030289931232 * q^69 - 145036588586277913982945740577079817793279246661749211931215600391874230481280 * q^70 - 255182116774353604409687783436303274428169526091219223291653972862797742675416 * q^71 - 870484407164078464103908172424456244246778900599455841998985045216713192261120 * q^72 - 305241553076526275791215297716487992856779743869787675846354786221090205747018 * q^73 + 519509459878782742271675046603917029597958567555546598174683109762008202679152 * q^74 - 108583349872086845300331949191600832920703338562329517576945108262256298985700 * q^75 + 3101616184715813078617408724804325452068973943873193050543089493292892226548480 * q^76 + 1968650017033252100145732463322846835178370212948913842977898825590858174818592 * q^77 + 21491900853406375307008391073223804676382414550199027500027607363780886431018304 * q^78 + 23447929932751548600263104762346056717107337920041167505701244565861009558020240 * q^79 + 17204514340446283418245025220202850902483487721576269901420959588660341138513920 * q^80 - 17753472117770960614378485370145730323852918650183577857034614500242589049352193 * q^81 - 31321993453816460140947801899215524216330716054375524262202008548706253113923248 * q^82 - 46082240797638648794744046457142731881250364210725285467604380362957138908759788 * q^83 - 396393323116531601318524278804366279023581302275903129719352432561583858694821888 * q^84 - 401284317909890185403267950222575247116869569644274198011711052575121501243134780 * q^85 - 845015265474066730430458068700259496114668382925856143568777375852322405810455136 * q^86 + 197750077894055178387517630023128464093882005300943753470627738978951228120838680 * q^87 + 324839816772448825066522872810525224209456499759931184227996411794156773784954880 * q^88 + 1029637925134517055127146751141931889566726599138062764000004109807115136117713670 * q^89 + 4141656580530762388567221011089632154433218135474509214945004172382456820926056240 * q^90 + 3803613049700949766857757374276498806030165436480764134599260004867484942314191344 * q^91 + 18037274986000955133271893922579105966324228705045824551878800657480298511213339136 * q^92 + 8685070641618931882536832652301281283748648395097048916956355973218904558772746624 * q^93 + 14309873718219401549749953357716417680483939380577663052969981365204963308304666752 * q^94 - 14391746226057476549769154981667785050800156202045812612412525445443768991871289000 * q^95 - 108145031724537483365505988938774635887900203900416762648300829840839318527629459456 * q^96 - 74638965785790533754670961742172384288953081898163477046944786055599953393772909074 * q^97 - 18956661788073492574129772794522396713191224901923159738123453486226051877064977912 * q^98 - 186867222990833548593390820999966230195685717791503334320194774977997201493521400292 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.80997e12	0.903561	0.451780	−	0.892129i	$-0.350789\pi$
$2$	2.80997e12	0.903561	0.451780	+	0.892129i	$0.350789\pi$
$3$	−9.69898e19	−1.53530	−0.767652	−	0.640867i	$-0.778575\pi$
$3$	−9.69898e19	−1.53530	−0.767652	+	0.640867i	$0.778575\pi$
$4$	−1.77546e24	−0.183578
$5$	1.10914e29	1.09077	0.545384	−	0.838186i	$-0.316384\pi$
$5$	1.10914e29	1.09077	0.545384	+	0.838186i	$0.316384\pi$
$6$	−2.72539e32	−1.38724
$7$	−5.50994e34	−0.467281	−0.233641	−	0.972323i	$-0.575064\pi$
$7$	−5.50994e34	−0.467281	−0.233641	+	0.972323i	$0.575064\pi$
$8$	−3.21654e37	−1.06943
$9$	5.41619e39	1.35716
$10$	3.11666e41	0.985575
$11$	−2.22342e43	−1.34656	−0.673280	−	0.739387i	$-0.735115\pi$
$11$	−2.22342e43	−1.34656	−0.673280	+	0.739387i	$0.735115\pi$
$12$	1.72201e44	0.281848
$13$	−6.42697e45	−0.379627	−0.189814	−	0.981820i	$-0.560788\pi$
$13$	−6.42697e45	−0.379627	−0.189814	+	0.981820i	$0.560788\pi$
$14$	−1.54828e47	−0.422217
$15$	−1.07576e49	−1.67466
$16$	−7.32127e49	−0.782721
$17$	−1.88220e51	−1.62568	−0.812841	−	0.582485i	$-0.802080\pi$
$17$	−1.88220e51	−1.62568	−0.812841	+	0.582485i	$0.802080\pi$
$18$	1.52193e52	1.22627
$19$	1.37355e53	1.17374	0.586869	−	0.809682i	$-0.300360\pi$
$19$	1.37355e53	1.17374	0.586869	+	0.809682i	$0.300360\pi$
$20$	−1.96924e53	−0.200241
$21$	5.34408e54	0.717418
$22$	−6.24776e55	−1.21670
$23$	6.47368e56	1.99272	0.996359	−	0.0852535i	$-0.0271700\pi$
$23$	6.47368e56	1.99272	0.996359	+	0.0852535i	$0.0271700\pi$
$24$	3.11971e57	1.64191
$25$	1.96223e57	0.189775
$26$	−1.80596e58	−0.343016
$27$	−1.38244e59	−0.548342
$28$	9.78266e58	0.0857825
$29$	6.73588e59	0.137682	0.0688411	−	0.997628i	$-0.478070\pi$
$29$	6.73588e59	0.137682	0.0688411	+	0.997628i	$0.478070\pi$
$30$	−3.02285e61	−1.51316
$31$	4.12876e61	0.530041	0.265021	−	0.964243i	$-0.414621\pi$
$31$	4.12876e61	0.530041	0.265021	+	0.964243i	$0.414621\pi$
$32$	1.05359e62	0.362198
$33$	2.15650e63	2.06738
$34$	−5.28894e63	−1.46890
$35$	−6.11131e63	−0.509695
$36$	−9.61621e63	−0.249144
$37$	−4.23854e63	−0.0352245	−0.0176122	−	0.999845i	$-0.505606\pi$
$37$	−4.23854e63	−0.0352245	−0.0176122	+	0.999845i	$0.505606\pi$
$38$	3.85965e65	1.06054
$39$	6.23351e65	0.582843
$40$	−3.56760e66	−1.16651
$41$	1.30264e67	1.52860	0.764300	−	0.644861i	$-0.223085\pi$
$41$	1.30264e67	1.52860	0.764300	+	0.644861i	$0.223085\pi$
$42$	1.50167e67	0.648231
$43$	−3.87111e67	−0.629354	−0.314677	−	0.949199i	$-0.601896\pi$
$43$	−3.87111e67	−0.629354	−0.314677	+	0.949199i	$0.601896\pi$
$44$	3.94759e67	0.247199
$45$	6.00733e68	1.48034
$46$	1.81909e69	1.80054
$47$	2.21707e69	0.898916	0.449458	−	0.893301i	$-0.351617\pi$
$47$	2.21707e69	0.898916	0.449458	+	0.893301i	$0.351617\pi$
$48$	7.10089e69	1.20171
$49$	−1.08680e70	−0.781648
$50$	5.51381e69	0.171473
$51$	1.82554e71	2.49592
$52$	1.14108e70	0.0696912
$53$	−3.92695e70	−0.108795	−0.0543973	−	0.998519i	$-0.517324\pi$
$53$	−3.92695e70	−0.108795	−0.0543973	+	0.998519i	$0.517324\pi$
$54$	−3.88463e71	−0.495460
$55$	−2.46610e72	−1.46879
$56$	1.77229e72	0.499726
$57$	−1.33221e73	−1.80204
$58$	1.89277e72	0.124404
$59$	−3.16234e73	−1.02247	−0.511234	−	0.859442i	$-0.670811\pi$
$59$	−3.16234e73	−1.02247	−0.511234	+	0.859442i	$0.670811\pi$
$60$	1.90996e73	0.307430
$61$	5.48024e73	0.444234	0.222117	−	0.975020i	$-0.428703\pi$
$61$	5.48024e73	0.444234	0.222117	+	0.975020i	$0.428703\pi$
$62$	1.16017e74	0.478925
$63$	−2.98429e74	−0.634173
$64$	1.00413e75	1.10999
$65$	−7.12843e74	−0.414085
$66$	6.05970e75	1.86800
$67$	6.60851e75	1.09144	0.545719	−	0.837968i	$-0.316257\pi$
$67$	6.60851e75	1.09144	0.545719	+	0.837968i	$0.316257\pi$
$68$	3.34177e75	0.298439
$69$	−6.27881e76	−3.05943
$70$	−1.71726e76	−0.460541
$71$	7.10431e76	1.05755	0.528775	−	0.848762i	$-0.322652\pi$
$71$	7.10431e76	1.05755	0.528775	+	0.848762i	$0.322652\pi$
$72$	−1.74214e77	−1.45139
$73$	9.86952e76	0.463871	0.231936	−	0.972731i	$-0.425494\pi$
$73$	9.86952e76	0.463871	0.231936	+	0.972731i	$0.425494\pi$
$74$	−1.19102e76	−0.0318275
$75$	−1.90316e77	−0.291362
$76$	−2.43869e77	−0.215472
$77$	1.22509e78	0.629222
$78$	1.75160e78	0.526634
$79$	1.00412e79	1.77934	0.889671	−	0.456602i	$-0.150934\pi$
$79$	1.00412e79	1.77934	0.889671	+	0.456602i	$0.150934\pi$
$80$	−8.12034e78	−0.853767
$81$	−8.20683e78	−0.515285
$82$	3.66038e79	1.38118
$83$	−4.07093e79	−0.928865	−0.464432	−	0.885609i	$-0.653742\pi$
$83$	−4.07093e79	−0.928865	−0.464432	+	0.885609i	$0.653742\pi$
$84$	−9.48818e78	−0.131702
$85$	−2.08763e80	−1.77324
$86$	−1.08777e80	−0.568659
$87$	−6.53312e79	−0.211384
$88$	7.15173e80	1.44006
$89$	−2.55096e80	−0.321379	−0.160690	−	0.987005i	$-0.551372\pi$
$89$	−2.55096e80	−0.321379	−0.160690	+	0.987005i	$0.551372\pi$
$90$	1.68804e81	1.33758
$91$	3.54122e80	0.177393
$92$	−1.14937e81	−0.365819
$93$	−4.00448e81	−0.813774
$94$	6.22992e81	0.812225
$95$	1.52347e82	1.28028
$96$	−1.02187e82	−0.556084
$97$	−7.47161e81	−0.264477	−0.132238	−	0.991218i	$-0.542216\pi$
$97$	−7.47161e81	−0.264477	−0.132238	+	0.991218i	$0.542216\pi$
$98$	−3.05387e82	−0.706267
$99$	−1.20425e83	−1.82749
$100$	−3.48385e81	−0.0348385
$101$	−2.35199e82	−0.155632	−0.0778158	−	0.996968i	$-0.524795\pi$
$101$	−2.35199e82	−0.155632	−0.0778158	+	0.996968i	$0.524795\pi$
$102$	5.12973e83	2.25521
$103$	−2.96486e83	−0.869479	−0.434739	−	0.900556i	$-0.643159\pi$
$103$	−2.96486e83	−0.869479	−0.434739	+	0.900556i	$0.643159\pi$
$104$	2.06726e83	0.405986
$105$	5.92735e83	0.782537
$106$	−1.10346e83	−0.0983025
$107$	1.23142e84	0.742982	0.371491	−	0.928436i	$-0.378847\pi$
$107$	1.23142e84	0.742982	0.371491	+	0.928436i	$0.378847\pi$
$108$	2.45447e83	0.100663
$109$	−2.68366e84	−0.750806	−0.375403	−	0.926862i	$-0.622496\pi$
$109$	−2.68366e84	−0.750806	−0.375403	+	0.926862i	$0.622496\pi$
$110$	−6.92966e84	−1.32714
$111$	4.11095e83	0.0540802
$112$	4.03398e84	0.365751
$113$	−2.38078e84	−0.149267	−0.0746334	−	0.997211i	$-0.523779\pi$
$113$	−2.38078e84	−0.149267	−0.0746334	+	0.997211i	$0.523779\pi$
$114$	−3.74347e85	−1.62826
$115$	7.18024e85	2.17359
$116$	−1.19593e84	−0.0252754
$117$	−3.48097e85	−0.515213
$118$	−8.88608e85	−0.923862
$119$	1.03708e86	0.759651
$120$	3.46021e86	1.79094
$121$	2.21720e86	0.813226
$122$	1.53993e86	0.401392
$123$	−1.26343e87	−2.34686
$124$	−7.33044e85	−0.0973039
$125$	−9.29188e86	−0.883768
$126$	−8.38577e86	−0.573014
$127$	−3.71870e86	−0.183036	−0.0915179	−	0.995803i	$-0.529172\pi$
$127$	−3.71870e86	−0.183036	−0.0915179	+	0.995803i	$0.529172\pi$
$128$	1.80260e87	0.640745
$129$	3.75459e87	0.966249
$130$	−2.00307e87	−0.374151
$131$	7.73181e87	1.05081	0.525403	−	0.850854i	$-0.323915\pi$
$131$	7.73181e87	1.05081	0.525403	+	0.850854i	$0.323915\pi$
$132$	−3.82876e87	−0.379525
$133$	−7.56820e87	−0.548466
$134$	1.85697e88	0.986181
$135$	−1.53333e88	−0.598114
$136$	6.05417e88	1.73856
$137$	−1.50305e88	−0.318472	−0.159236	−	0.987241i	$-0.550903\pi$
$137$	−1.50305e88	−0.318472	−0.159236	+	0.987241i	$0.550903\pi$
$138$	−1.76433e89	−2.76438
$139$	8.51634e88	0.988869	0.494434	−	0.869215i	$-0.335375\pi$
$139$	8.51634e88	0.988869	0.494434	+	0.869215i	$0.335375\pi$
$140$	1.08504e88	0.0935688
$141$	−2.15034e89	−1.38011
$142$	1.99629e89	0.955560
$143$	1.42899e89	0.511191
$144$	−3.96534e89	−1.06227
$145$	7.47106e88	0.150179
$146$	2.77331e89	0.419136
$147$	1.05408e90	1.20007
$148$	7.52534e87	0.00646643
$149$	1.91000e90	1.24109	0.620545	−	0.784171i	$-0.286911\pi$
$149$	1.91000e90	1.24109	0.620545	+	0.784171i	$0.286911\pi$
$150$	−5.34783e89	−0.263263
$151$	−1.73413e89	−0.0647944	−0.0323972	−	0.999475i	$-0.510314\pi$
$151$	−1.73413e89	−0.0647944	−0.0323972	+	0.999475i	$0.510314\pi$
$152$	−4.41809e90	−1.25524
$153$	−1.01944e91	−2.20630
$154$	3.44248e90	0.568541
$155$	4.57939e90	0.578152
$156$	−1.10673e90	−0.106997
$157$	−7.34137e90	−0.544430	−0.272215	−	0.962236i	$-0.587756\pi$
$157$	−7.34137e90	−0.544430	−0.272215	+	0.962236i	$0.587756\pi$
$158$	2.82154e91	1.60774
$159$	3.80875e90	0.167033
$160$	1.16858e91	0.395074
$161$	−3.56696e91	−0.931160
$162$	−2.30610e91	−0.465591
$163$	4.95193e91	0.774442	0.387221	−	0.921987i	$-0.373435\pi$
$163$	4.95193e91	0.774442	0.387221	+	0.921987i	$0.373435\pi$
$164$	−2.31278e91	−0.280617
$165$	2.39186e92	2.25503
$166$	−1.14392e92	−0.839286
$167$	−6.79461e91	−0.388536	−0.194268	−	0.980949i	$-0.562233\pi$
$167$	−6.79461e91	−0.388536	−0.194268	+	0.980949i	$0.562233\pi$
$168$	−1.71894e92	−0.767232
$169$	−2.45309e92	−0.855883
$170$	−5.86619e92	−1.60223
$171$	7.43943e92	1.59295
$172$	6.87299e91	0.115535
$173$	−4.20084e90	−0.00555166	−0.00277583	−	0.999996i	$-0.500884\pi$
$173$	−4.20084e90	−0.00555166	−0.00277583	+	0.999996i	$0.500884\pi$
$174$	−1.83579e92	−0.190998
$175$	−1.08118e92	−0.0886783
$176$	1.62783e93	1.05398
$177$	3.06714e93	1.56980
$178$	−7.16812e92	−0.290386
$179$	−2.93908e93	−0.943649	−0.471825	−	0.881692i	$-0.656404\pi$
$179$	−2.93908e93	−0.943649	−0.471825	+	0.881692i	$0.656404\pi$
$180$	−1.06657e93	−0.271758
$181$	4.16514e93	0.843274	0.421637	−	0.906765i	$-0.361456\pi$
$181$	4.16514e93	0.843274	0.421637	+	0.906765i	$0.361456\pi$
$182$	9.95074e92	0.160285
$183$	−5.31528e93	−0.682033
$184$	−2.08228e94	−2.13108
$185$	−4.70114e92	−0.0384217
$186$	−1.12525e94	−0.735294
$187$	4.18493e94	2.18908
$188$	−3.93632e93	−0.165021
$189$	7.61718e93	0.256230
$190$	4.28091e94	1.15681
$191$	−1.29323e94	−0.281055	−0.140527	−	0.990077i	$-0.544880\pi$
$191$	−1.29323e94	−0.281055	−0.140527	+	0.990077i	$0.544880\pi$
$192$	−9.73899e94	−1.70417
$193$	6.89445e94	0.972460	0.486230	−	0.873831i	$-0.338372\pi$
$193$	6.89445e94	0.972460	0.486230	+	0.873831i	$0.338372\pi$
$194$	−2.09950e94	−0.238971
$195$	6.91386e94	0.635746
$196$	1.92956e94	0.143493
$197$	2.68133e95	1.61437	0.807183	−	0.590302i	$-0.200991\pi$
$197$	2.68133e95	1.61437	0.807183	+	0.590302i	$0.200991\pi$
$198$	−3.38391e95	−1.65125
$199$	−1.99179e94	−0.0788573	−0.0394287	−	0.999222i	$-0.512554\pi$
$199$	−1.99179e94	−0.0788573	−0.0394287	+	0.999222i	$0.512554\pi$
$200$	−6.31158e94	−0.202952
$201$	−6.40958e95	−1.67569
$202$	−6.60902e94	−0.140623
$203$	−3.71143e94	−0.0643362
$204$	−3.24117e95	−0.458195
$205$	1.44481e96	1.66735
$206$	−8.33117e95	−0.785627
$207$	3.50627e96	2.70443
$208$	4.70536e95	0.297142
$209$	−3.05400e96	−1.58051
$210$	1.66557e96	0.707069
$211$	4.19396e95	0.146185	0.0730923	−	0.997325i	$-0.476713\pi$
$211$	4.19396e95	0.146185	0.0730923	+	0.997325i	$0.476713\pi$
$212$	6.97213e94	0.0199723
$213$	−6.89046e96	−1.62366
$214$	3.46025e96	0.671330
$215$	−4.29362e96	−0.686479
$216$	4.44668e96	0.586416
$217$	−2.27492e96	−0.247678
$218$	−7.54101e96	−0.678399
$219$	−9.57243e96	−0.712183
$220$	4.37845e96	0.269637
$221$	1.20969e97	0.617153
$222$	1.15517e96	0.0488648
$223$	4.43026e97	1.55517	0.777584	−	0.628779i	$-0.216445\pi$
$223$	4.43026e97	1.55517	0.777584	+	0.628779i	$0.216445\pi$
$224$	−5.80520e96	−0.169248
$225$	1.06278e97	0.257554
$226$	−6.68992e96	−0.134872
$227$	−7.99852e97	−1.34257	−0.671285	−	0.741200i	$-0.734257\pi$
$227$	−7.99852e97	−1.34257	−0.671285	+	0.741200i	$0.734257\pi$
$228$	2.36528e97	0.330816
$229$	3.85175e96	0.0449247	0.0224624	−	0.999748i	$-0.492849\pi$
$229$	3.85175e96	0.0449247	0.0224624	+	0.999748i	$0.492849\pi$
$230$	2.01763e98	1.96397
$231$	−1.18822e98	−0.966047
$232$	−2.16662e97	−0.147242
$233$	−2.61038e98	−1.48399	−0.741997	−	0.670403i	$-0.766121\pi$
$233$	−2.61038e98	−1.48399	−0.741997	+	0.670403i	$0.766121\pi$
$234$	−9.78143e97	−0.465526
$235$	2.45905e98	0.980509
$236$	5.61459e97	0.187702
$237$	−9.73890e98	−2.73183
$238$	2.91417e98	0.686391
$239$	4.16456e98	0.824244	0.412122	−	0.911129i	$-0.364788\pi$
$239$	4.16456e98	0.824244	0.412122	+	0.911129i	$0.364788\pi$
$240$	7.87590e98	1.31079
$241$	3.07755e98	0.431020	0.215510	−	0.976502i	$-0.430859\pi$
$241$	3.07755e98	0.431020	0.215510	+	0.976502i	$0.430859\pi$
$242$	6.23026e98	0.734799
$243$	1.34769e99	1.33946
$244$	−9.72993e97	−0.0815515
$245$	−1.20541e99	−0.852597
$246$	−3.55020e99	−2.12053
$247$	−8.82780e98	−0.445583
$248$	−1.32803e99	−0.566845
$249$	3.94838e99	1.42609
$250$	−2.61099e99	−0.798538
$251$	5.69031e99	1.47461	0.737303	−	0.675562i	$-0.236099\pi$
$251$	5.69031e99	1.47461	0.737303	+	0.675562i	$0.236099\pi$
$252$	5.29847e98	0.116420
$253$	−1.43937e100	−2.68332
$254$	−1.04494e99	−0.165384
$255$	2.02479e100	2.72247
$256$	−4.64605e99	−0.531038
$257$	−8.59709e99	−0.835847	−0.417923	−	0.908482i	$-0.637242\pi$
$257$	−8.59709e99	−0.835847	−0.417923	+	0.908482i	$0.637242\pi$
$258$	1.05503e100	0.873065
$259$	2.33541e98	0.0164597
$260$	1.26562e99	0.0760169
$261$	3.64828e99	0.186856
$262$	2.17262e100	0.949467
$263$	2.92430e100	1.09109	0.545543	−	0.838083i	$-0.316324\pi$
$263$	2.92430e100	1.09109	0.545543	+	0.838083i	$0.316324\pi$
$264$	−6.93645e100	−2.21093
$265$	−4.35555e99	−0.118670
$266$	−2.12664e100	−0.495572
$267$	2.47417e100	0.493415
$268$	−1.17331e100	−0.200364
$269$	−3.41166e100	−0.499167	−0.249584	−	0.968353i	$-0.580294\pi$
$269$	−3.41166e100	−0.499167	−0.249584	+	0.968353i	$0.580294\pi$
$270$	−4.30861e100	−0.540432
$271$	−3.78368e100	−0.407088	−0.203544	−	0.979066i	$-0.565246\pi$
$271$	−3.78368e100	−0.407088	−0.203544	+	0.979066i	$0.565246\pi$
$272$	1.37801e101	1.27246
$273$	−3.43463e100	−0.272351
$274$	−4.22354e100	−0.287759
$275$	−4.36286e100	−0.255544
$276$	1.11478e101	0.561643
$277$	1.63415e101	0.708566	0.354283	−	0.935138i	$-0.384725\pi$
$277$	1.63415e101	0.708566	0.354283	+	0.935138i	$0.384725\pi$
$278$	2.39307e101	0.893503
$279$	2.23622e101	0.719349
$280$	1.96573e101	0.545086
$281$	−1.46792e101	−0.351067	−0.175533	−	0.984474i	$-0.556165\pi$
$281$	−1.46792e101	−0.351067	−0.175533	+	0.984474i	$0.556165\pi$
$282$	−6.04239e101	−1.24701
$283$	−2.44671e101	−0.435959	−0.217980	−	0.975953i	$-0.569947\pi$
$283$	−2.44671e101	−0.435959	−0.217980	+	0.975953i	$0.569947\pi$
$284$	−1.26134e101	−0.194143
$285$	−1.47761e102	−1.96561
$286$	4.01542e101	0.461892
$287$	−7.17746e101	−0.714286
$288$	5.70643e101	0.491559
$289$	2.20220e102	1.64284
$290$	2.09935e101	0.135696
$291$	7.24670e101	0.406052
$292$	−1.75229e101	−0.0851565
$293$	−2.44827e102	−1.03241	−0.516205	−	0.856465i	$-0.672656\pi$
$293$	−2.44827e102	−1.03241	−0.516205	+	0.856465i	$0.672656\pi$
$294$	2.96195e102	1.08433
$295$	−3.50748e102	−1.11528
$296$	1.36334e101	0.0376703
$297$	3.07376e102	0.738376
$298$	5.36705e102	1.12140
$299$	−4.16062e102	−0.756490
$300$	3.37898e101	0.0534876
$301$	2.13296e102	0.294085
$302$	−4.87285e101	−0.0585457
$303$	2.28119e102	0.238942
$304$	−1.00562e103	−0.918710
$305$	6.07837e102	0.484556
$306$	−2.86459e103	−1.99353
$307$	−1.88449e103	−1.14539	−0.572693	−	0.819770i	$-0.694101\pi$
$307$	−1.88449e103	−1.14539	−0.572693	+	0.819770i	$0.694101\pi$
$308$	−2.17510e102	−0.115511
$309$	2.87561e103	1.33491
$310$	1.28680e103	0.522396
$311$	3.09287e103	1.09851	0.549257	−	0.835654i	$-0.314911\pi$
$311$	3.09287e103	1.09851	0.549257	+	0.835654i	$0.314911\pi$
$312$	−2.00503e103	−0.623312
$313$	5.92290e103	1.61229	0.806147	−	0.591716i	$-0.201549\pi$
$313$	5.92290e103	1.61229	0.806147	+	0.591716i	$0.201549\pi$
$314$	−2.06291e103	−0.491925
$315$	−3.31000e103	−0.691736
$316$	−1.78276e103	−0.326648
$317$	7.22268e103	1.16075	0.580375	−	0.814349i	$-0.302906\pi$
$317$	7.22268e103	1.16075	0.580375	+	0.814349i	$0.302906\pi$
$318$	1.07025e103	0.150924
$319$	−1.49767e103	−0.185397
$320$	1.11372e104	1.21074
$321$	−1.19435e104	−1.14070
$322$	−1.00231e104	−0.841359
$323$	−2.58531e104	−1.90813
$324$	1.45709e103	0.0945948
$325$	−1.26112e103	−0.0720438
$326$	1.39148e104	0.699756
$327$	2.60288e104	1.15271
$328$	−4.18999e104	−1.63474
$329$	−1.22159e104	−0.420046
$330$	6.72107e104	2.03756
$331$	1.88004e104	0.502697	0.251348	−	0.967897i	$-0.419126\pi$
$331$	1.88004e104	0.502697	0.251348	+	0.967897i	$0.419126\pi$
$332$	7.22775e103	0.170519
$333$	−2.29567e103	−0.0478051
$334$	−1.90927e104	−0.351066
$335$	7.32978e104	1.19051
$336$	−3.91255e104	−0.561538
$337$	−6.47074e104	−0.820944	−0.410472	−	0.911873i	$-0.634636\pi$
$337$	−6.47074e104	−0.820944	−0.410472	+	0.911873i	$0.634636\pi$
$338$	−6.89311e104	−0.773342
$339$	2.30911e104	0.229170
$340$	3.70650e104	0.325528
$341$	−9.18000e104	−0.713733
$342$	2.09046e105	1.43932
$343$	1.36492e105	0.832531
$344$	1.24516e105	0.673053
$345$	−6.96410e105	−3.33713
$346$	−1.18042e103	−0.00501626
$347$	−3.02604e105	−1.14078	−0.570389	−	0.821375i	$-0.693208\pi$
$347$	−3.02604e105	−1.14078	−0.570389	+	0.821375i	$0.693208\pi$
$348$	1.15993e104	0.0388054
$349$	4.36981e105	1.29780	0.648899	−	0.760874i	$-0.275230\pi$
$349$	4.36981e105	1.29780	0.648899	+	0.760874i	$0.275230\pi$
$350$	−3.03807e104	−0.0801262
$351$	8.88493e104	0.208166
$352$	−2.34257e105	−0.487722
$353$	7.49254e105	1.38669	0.693344	−	0.720606i	$-0.256136\pi$
$353$	7.49254e105	1.38669	0.693344	+	0.720606i	$0.256136\pi$
$354$	8.61859e105	1.41841
$355$	7.87970e105	1.15354
$356$	4.52911e104	0.0589981
$357$	−1.00586e106	−1.16629
$358$	−8.25873e105	−0.852644
$359$	−6.56581e104	−0.0603766	−0.0301883	−	0.999544i	$-0.509611\pi$
$359$	−6.56581e104	−0.0603766	−0.0301883	+	0.999544i	$0.509611\pi$
$360$	−1.93228e106	−1.58313
$361$	5.17194e105	0.377663
$362$	1.17039e106	0.761949
$363$	−2.15046e106	−1.24855
$364$	−6.28729e104	−0.0325654
$365$	1.09467e106	0.505976
$366$	−1.49358e106	−0.616259
$367$	1.92196e106	0.708112	0.354056	−	0.935224i	$-0.384802\pi$
$367$	1.92196e106	0.708112	0.354056	+	0.935224i	$0.384802\pi$
$368$	−4.73956e106	−1.55974
$369$	7.05533e106	2.07455
$370$	−1.32101e105	−0.0347164
$371$	2.16373e105	0.0508376
$372$	7.10978e105	0.149391
$373$	−8.19946e106	−1.54123	−0.770617	−	0.637299i	$-0.780052\pi$
$373$	−8.19946e106	−1.54123	−0.770617	+	0.637299i	$0.780052\pi$
$374$	1.17595e107	1.97797
$375$	9.01218e106	1.35685
$376$	−7.13130e106	−0.961332
$377$	−4.32913e105	−0.0522679
$378$	2.14041e106	0.231519
$379$	−8.97801e106	−0.870268	−0.435134	−	0.900366i	$-0.643299\pi$
$379$	−8.97801e106	−0.870268	−0.435134	+	0.900366i	$0.643299\pi$
$380$	−2.70485e106	−0.235031
$381$	3.60676e106	0.281015
$382$	−3.63394e106	−0.253950
$383$	−1.19512e107	−0.749310	−0.374655	−	0.927164i	$-0.622239\pi$
$383$	−1.19512e107	−0.749310	−0.374655	+	0.927164i	$0.622239\pi$
$384$	−1.74834e107	−0.983737
$385$	1.35880e107	0.686336
$386$	1.93732e107	0.878676
$387$	−2.09667e107	−0.854131
$388$	1.32655e106	0.0485520
$389$	4.92917e107	1.62131	0.810653	−	0.585526i	$-0.199112\pi$
$389$	4.92917e107	1.62131	0.810653	+	0.585526i	$0.199112\pi$
$390$	1.94277e107	0.574436
$391$	−1.21848e108	−3.23953
$392$	3.49573e107	0.835922
$393$	−7.49907e107	−1.61331
$394$	7.53446e107	1.45868
$395$	1.11371e108	1.94085
$396$	2.13809e107	0.335487
$397$	3.68616e107	0.520916	0.260458	−	0.965485i	$-0.416126\pi$
$397$	3.68616e107	0.520916	0.260458	+	0.965485i	$0.416126\pi$
$398$	−5.59689e106	−0.0712524
$399$	7.34039e107	0.842061
$400$	−1.43660e107	−0.148541
$401$	−9.25710e107	−0.862946	−0.431473	−	0.902126i	$-0.642006\pi$
$401$	−9.25710e107	−0.862946	−0.431473	+	0.902126i	$0.642006\pi$
$402$	−1.80107e108	−1.51409
$403$	−2.65355e107	−0.201218
$404$	4.17585e106	0.0285705
$405$	−9.10255e107	−0.562056
$406$	−1.04290e107	−0.0581317
$407$	9.42407e106	0.0474319
$408$	−5.87193e108	−2.66922
$409$	2.88225e108	1.18363	0.591814	−	0.806075i	$-0.298412\pi$
$409$	2.88225e108	1.18363	0.591814	+	0.806075i	$0.298412\pi$
$410$	4.05988e108	1.50655
$411$	1.45781e108	0.488951
$412$	5.26397e107	0.159617
$413$	1.74243e108	0.477780
$414$	9.85252e108	2.44362
$415$	−4.51524e108	−1.01318
$416$	−6.77138e107	−0.137500
$417$	−8.25998e108	−1.51821
$418$	−8.58164e108	−1.42809
$419$	1.24808e109	1.88088	0.940440	−	0.339961i	$-0.110414\pi$
$419$	1.24808e109	1.88088	0.940440	+	0.339961i	$0.110414\pi$
$420$	−1.05238e108	−0.143656
$421$	−3.52905e108	−0.436466	−0.218233	−	0.975897i	$-0.570029\pi$
$421$	−3.52905e108	−0.436466	−0.218233	+	0.975897i	$0.570029\pi$
$422$	1.17849e108	0.132087
$423$	1.20081e109	1.21997
$424$	1.26312e108	0.116349
$425$	−3.69331e108	−0.308514
$426$	−1.93620e109	−1.46707
$427$	−3.01958e108	−0.207582
$428$	−2.18633e108	−0.136395
$429$	−1.38597e109	−0.784833
$430$	−1.20650e109	−0.620276
$431$	3.06629e109	1.43155	0.715774	−	0.698332i	$-0.246074\pi$
$431$	3.06629e109	1.43155	0.715774	+	0.698332i	$0.246074\pi$
$432$	1.01212e109	0.429199
$433$	−3.52234e108	−0.135701	−0.0678506	−	0.997695i	$-0.521614\pi$
$433$	−3.52234e108	−0.135701	−0.0678506	+	0.997695i	$0.521614\pi$
$434$	−6.39248e108	−0.223792
$435$	−7.24617e108	−0.230571
$436$	4.76472e108	0.137831
$437$	8.89195e109	2.33893
$438$	−2.68983e109	−0.643500
$439$	−5.01954e109	−1.09241	−0.546205	−	0.837651i	$-0.683928\pi$
$439$	−5.01954e109	−1.09241	−0.546205	+	0.837651i	$0.683928\pi$
$440$	7.93229e109	1.57077
$441$	−5.88630e109	−1.06082
$442$	3.39918e109	0.557636
$443$	−9.95067e108	−0.148627	−0.0743135	−	0.997235i	$-0.523677\pi$
$443$	−9.95067e108	−0.148627	−0.0743135	+	0.997235i	$0.523677\pi$
$444$	−7.29881e107	−0.00992794
$445$	−2.82938e109	−0.350550
$446$	1.24489e110	1.40519
$447$	−1.85251e110	−1.90545
$448$	−5.53267e109	−0.518677
$449$	8.27680e109	0.707358	0.353679	−	0.935367i	$-0.384930\pi$
$449$	8.27680e109	0.707358	0.353679	+	0.935367i	$0.384930\pi$
$450$	2.98638e109	0.232716
$451$	−2.89632e110	−2.05835
$452$	4.22696e108	0.0274021
$453$	1.68193e109	0.0994790
$454$	−2.24756e110	−1.21309
$455$	3.92772e109	0.193494
$456$	4.28510e110	1.92717
$457$	2.90214e110	1.19178	0.595889	−	0.803067i	$-0.296800\pi$
$457$	2.90214e110	1.19178	0.595889	+	0.803067i	$0.296800\pi$
$458$	1.08233e109	0.0405922
$459$	2.60204e110	0.891430
$460$	−1.27482e110	−0.399024
$461$	1.65611e110	0.473697	0.236849	−	0.971547i	$-0.423885\pi$
$461$	1.65611e110	0.473697	0.236849	+	0.971547i	$0.423885\pi$
$462$	−3.33886e110	−0.872882
$463$	7.80467e110	1.86528	0.932639	−	0.360812i	$-0.117500\pi$
$463$	7.80467e110	1.86528	0.932639	+	0.360812i	$0.117500\pi$
$464$	−4.93152e109	−0.107767
$465$	−4.44154e110	−0.887639
$466$	−7.33509e110	−1.34088
$467$	−1.05840e111	−1.77010	−0.885051	−	0.465494i	$-0.845877\pi$
$467$	−1.05840e111	−1.77010	−0.885051	+	0.465494i	$0.845877\pi$
$468$	6.18031e109	0.0945817
$469$	−3.64125e110	−0.510008
$470$	6.90987e110	0.885950
$471$	7.12039e110	0.835865
$472$	1.01718e111	1.09346
$473$	8.60713e110	0.847463
$474$	−2.73660e111	−2.46837
$475$	2.69523e110	0.222746
$476$	−1.84129e110	−0.139455
$477$	−2.12691e110	−0.147651
$478$	1.17023e111	0.744754
$479$	−7.31994e110	−0.427154	−0.213577	−	0.976926i	$-0.568511\pi$
$479$	−7.31994e110	−0.427154	−0.213577	+	0.976926i	$0.568511\pi$
$480$	−1.13340e111	−0.606559
$481$	2.72410e109	0.0133722
$482$	8.64782e110	0.389453
$483$	3.45959e111	1.42961
$484$	−3.93654e110	−0.149290
$485$	−8.28708e110	−0.288483
$486$	3.78697e111	1.21028
$487$	3.45843e111	1.01491	0.507454	−	0.861679i	$-0.330587\pi$
$487$	3.45843e111	1.01491	0.507454	+	0.861679i	$0.330587\pi$
$488$	−1.76274e111	−0.475079
$489$	−4.80287e111	−1.18900
$490$	−3.38718e111	−0.770373
$491$	2.31117e111	0.483004	0.241502	−	0.970400i	$-0.422360\pi$
$491$	2.31117e111	0.483004	0.241502	+	0.970400i	$0.422360\pi$
$492$	2.24316e111	0.430832
$493$	−1.26783e111	−0.223827
$494$	−2.48059e111	−0.402612
$495$	−1.33568e112	−1.99337
$496$	−3.02278e111	−0.414875
$497$	−3.91443e111	−0.494173
$498$	1.10949e112	1.28856
$499$	−1.57598e110	−0.0168414	−0.00842070	−	0.999965i	$-0.502680\pi$
$499$	−1.57598e110	−0.0168414	−0.00842070	+	0.999965i	$0.502680\pi$
$500$	1.64973e111	0.162240
$501$	6.59008e111	0.596520
$502$	1.59896e112	1.33240
$503$	−6.31998e111	−0.484892	−0.242446	−	0.970165i	$-0.577950\pi$
$503$	−6.31998e111	−0.484892	−0.242446	+	0.970165i	$0.577950\pi$
$504$	9.59907e111	0.678207
$505$	−2.60869e111	−0.169758
$506$	−4.04460e112	−2.42454
$507$	2.37924e112	1.31404
$508$	6.60238e110	0.0336013
$509$	2.23632e112	1.04893	0.524464	−	0.851433i	$-0.324266\pi$
$509$	2.23632e112	1.04893	0.524464	+	0.851433i	$0.324266\pi$
$510$	5.68960e112	2.45991
$511$	−5.43805e111	−0.216758
$512$	−3.04889e112	−1.12057
$513$	−1.89886e112	−0.643610
$514$	−2.41576e112	−0.755238
$515$	−3.28845e112	−0.948399
$516$	−6.66610e111	−0.177382
$517$	−4.92950e112	−1.21045
$518$	6.56244e110	0.0148724
$519$	4.07439e110	0.00852348
$520$	2.29289e112	0.442837
$521$	1.79230e112	0.319628	0.159814	−	0.987147i	$-0.448911\pi$
$521$	1.79230e112	0.319628	0.159814	+	0.987147i	$0.448911\pi$
$522$	1.02516e112	0.168836
$523$	6.39631e112	0.972992	0.486496	−	0.873683i	$-0.338275\pi$
$523$	6.39631e112	0.972992	0.486496	+	0.873683i	$0.338275\pi$
$524$	−1.37275e112	−0.192905
$525$	1.04863e112	0.136148
$526$	8.21721e112	0.985862
$527$	−7.77117e112	−0.861679
$528$	−1.57883e113	−1.61818
$529$	3.13547e113	2.97093
$530$	−1.22390e112	−0.107225
$531$	−1.71278e113	−1.38765
$532$	1.34370e112	0.100686
$533$	−8.37202e112	−0.580298
$534$	6.95235e112	0.445830
$535$	1.36582e113	0.810421
$536$	−2.12565e113	−1.16722
$537$	2.85061e113	1.44879
$538$	−9.58667e112	−0.451028
$539$	2.41641e113	1.05254
$540$	2.72236e112	0.109800
$541$	−1.93124e113	−0.721356	−0.360678	−	0.932690i	$-0.617455\pi$
$541$	−1.93124e113	−0.721356	−0.360678	+	0.932690i	$0.617455\pi$
$542$	−1.06320e113	−0.367829
$543$	−4.03976e113	−1.29468
$544$	−1.98306e113	−0.588820
$545$	−2.97656e113	−0.818955
$546$	−9.65121e112	−0.246086
$547$	6.65668e112	0.157320	0.0786600	−	0.996902i	$-0.474936\pi$
$547$	6.65668e112	0.157320	0.0786600	+	0.996902i	$0.474936\pi$
$548$	2.66861e112	0.0584644
$549$	2.96820e113	0.602894
$550$	−1.22595e113	−0.230899
$551$	9.25210e112	0.161603
$552$	2.01960e114	3.27186
$553$	−5.53261e113	−0.831453
$554$	4.59190e113	0.640232
$555$	4.55963e112	0.0589890
$556$	−1.51204e113	−0.181534
$557$	−3.65020e113	−0.406748	−0.203374	−	0.979101i	$-0.565191\pi$
$557$	−3.65020e113	−0.406748	−0.203374	+	0.979101i	$0.565191\pi$
$558$	6.28371e113	0.649975
$559$	2.48795e113	0.238920
$560$	4.47426e113	0.398949
$561$	−4.05896e114	−3.36090
$562$	−4.12481e113	−0.317210
$563$	1.57629e114	1.12600	0.562999	−	0.826458i	$-0.309648\pi$
$563$	1.57629e114	1.12600	0.562999	+	0.826458i	$0.309648\pi$
$564$	3.81783e113	0.253357
$565$	−2.64062e113	−0.162815
$566$	−6.87520e113	−0.393916
$567$	4.52191e113	0.240783
$568$	−2.28513e114	−1.13098
$569$	3.55450e114	1.63538	0.817691	−	0.575657i	$-0.195254\pi$
$569$	3.55450e114	1.63538	0.817691	+	0.575657i	$0.195254\pi$
$570$	−4.15204e114	−1.77605
$571$	1.11770e114	0.444557	0.222279	−	0.974983i	$-0.428651\pi$
$571$	1.11770e114	0.444557	0.222279	+	0.974983i	$0.428651\pi$
$572$	−2.53711e113	−0.0938434
$573$	1.25430e114	0.431504
$574$	−2.01685e114	−0.645401
$575$	1.27028e114	0.378168
$576$	5.43853e114	1.50643
$577$	−5.86198e111	−0.00151094	−0.000755471	−	1.00000i	$-0.500240\pi$
$577$	−5.86198e111	−0.00151094	−0.000755471		1.00000i	$0.500240\pi$
$578$	6.18813e114	1.48441
$579$	−6.68692e114	−1.49302
$580$	−1.32645e113	−0.0275696
$581$	2.24306e114	0.434041
$582$	2.03630e114	0.366892
$583$	8.73128e113	0.146498
$584$	−3.17457e114	−0.496080
$585$	−3.86089e114	−0.561978
$586$	−6.87956e114	−0.932846
$587$	1.10984e115	1.40210	0.701050	−	0.713112i	$-0.252715\pi$
$587$	1.10984e115	1.40210	0.701050	+	0.713112i	$0.252715\pi$
$588$	−1.87148e114	−0.220306
$589$	5.67108e114	0.622130
$590$	−9.85594e114	−1.00772
$591$	−2.60062e115	−2.47854
$592$	3.10315e113	0.0275709
$593$	1.82797e115	1.51426	0.757128	−	0.653266i	$-0.226602\pi$
$593$	1.82797e115	1.51426	0.757128	+	0.653266i	$0.226602\pi$
$594$	8.63719e114	0.667167
$595$	1.15027e115	0.828603
$596$	−3.39112e114	−0.227837
$597$	1.93184e114	0.121070
$598$	−1.16912e115	−0.683535
$599$	−3.38658e115	−1.84735	−0.923674	−	0.383180i	$-0.874829\pi$
$599$	−3.38658e115	−1.84735	−0.923674	+	0.383180i	$0.874829\pi$
$600$	6.12159e114	0.311593
$601$	−1.29143e115	−0.613450	−0.306725	−	0.951798i	$-0.599233\pi$
$601$	−1.29143e115	−0.613450	−0.306725	+	0.951798i	$0.599233\pi$
$602$	5.99356e114	0.265724
$603$	3.57929e115	1.48125
$604$	3.07887e113	0.0118948
$605$	2.45919e115	0.887041
$606$	6.41007e114	0.215898
$607$	3.68241e115	1.15825	0.579124	−	0.815239i	$-0.303395\pi$
$607$	3.68241e115	1.15825	0.579124	+	0.815239i	$0.303395\pi$
$608$	1.44716e115	0.425126
$609$	3.59971e114	0.0987756
$610$	1.70801e115	0.437826
$611$	−1.42491e115	−0.341253
$612$	1.80996e115	0.405029
$613$	−8.36996e115	−1.75030	−0.875152	−	0.483848i	$-0.839239\pi$
$613$	−8.36996e115	−1.75030	−0.875152	+	0.483848i	$0.839239\pi$
$614$	−5.29537e115	−1.03493
$615$	−1.40132e116	−2.55988
$616$	−3.94056e115	−0.672912
$617$	4.22168e115	0.673987	0.336993	−	0.941507i	$-0.390590\pi$
$617$	4.22168e115	0.673987	0.336993	+	0.941507i	$0.390590\pi$
$618$	8.08039e115	1.20618
$619$	6.08631e115	0.849557	0.424778	−	0.905297i	$-0.360352\pi$
$619$	6.08631e115	0.849557	0.424778	+	0.905297i	$0.360352\pi$
$620$	−8.13051e114	−0.106136
$621$	−8.94950e115	−1.09269
$622$	8.69088e115	0.992574
$623$	1.40556e115	0.150174
$624$	−4.56372e115	−0.456204
$625$	−1.23349e116	−1.15376
$626$	1.66432e116	1.45681
$627$	2.96206e116	2.42656
$628$	1.30343e115	0.0999452
$629$	7.97778e114	0.0572638
$630$	−9.30101e115	−0.625025
$631$	1.27998e115	0.0805353	0.0402677	−	0.999189i	$-0.487179\pi$
$631$	1.27998e115	0.0805353	0.0402677	+	0.999189i	$0.487179\pi$
$632$	−3.22978e116	−1.90289
$633$	−4.06771e115	−0.224438
$634$	2.02955e116	1.04881
$635$	−4.12457e115	−0.199650
$636$	−6.76226e114	−0.0306635
$637$	6.98482e115	0.296735
$638$	−4.20842e115	−0.167518
$639$	3.84783e116	1.43526
$640$	1.99934e116	0.698904
$641$	−4.97777e116	−1.63090	−0.815449	−	0.578829i	$-0.803510\pi$
$641$	−4.97777e116	−1.63090	−0.815449	+	0.578829i	$0.803510\pi$
$642$	−3.35609e116	−1.03069
$643$	−2.96461e116	−0.853516	−0.426758	−	0.904366i	$-0.640344\pi$
$643$	−2.96461e116	−0.853516	−0.426758	+	0.904366i	$0.640344\pi$
$644$	6.33298e115	0.170940
$645$	4.16437e116	1.05395
$646$	−7.26464e116	−1.72411
$647$	−3.24219e116	−0.721623	−0.360812	−	0.932639i	$-0.617500\pi$
$647$	−3.24219e116	−0.721623	−0.360812	+	0.932639i	$0.617500\pi$
$648$	2.63976e116	0.551063
$649$	7.03122e116	1.37681
$650$	−3.54371e115	−0.0650959
$651$	2.20644e116	0.380261
$652$	−8.79194e115	−0.142170
$653$	−4.29160e116	−0.651212	−0.325606	−	0.945506i	$-0.605568\pi$
$653$	−4.29160e116	−0.651212	−0.325606	+	0.945506i	$0.605568\pi$
$654$	7.31401e116	1.04155
$655$	8.57569e116	1.14619
$656$	−9.53697e116	−1.19647
$657$	5.34552e116	0.629545
$658$	−3.43265e116	−0.379538
$659$	4.77469e116	0.495679	0.247839	−	0.968801i	$-0.420279\pi$
$659$	4.77469e116	0.495679	0.247839	+	0.968801i	$0.420279\pi$
$660$	−4.24665e116	−0.413974
$661$	6.21890e116	0.569315	0.284658	−	0.958629i	$-0.408120\pi$
$661$	6.21890e116	0.569315	0.284658	+	0.958629i	$0.408120\pi$
$662$	5.28287e116	0.454217
$663$	−1.17327e117	−0.947518
$664$	1.30943e117	0.993360
$665$	−8.39422e116	−0.598249
$666$	−6.45078e115	−0.0431948
$667$	4.36059e116	0.274362
$668$	1.20635e116	0.0713266
$669$	−4.29690e117	−2.38765
$670$	2.05965e117	1.07569
$671$	−1.21849e117	−0.598188
$672$	5.63046e116	0.259848
$673$	−2.47087e117	−1.07207	−0.536037	−	0.844194i	$-0.680079\pi$
$673$	−2.47087e117	−1.07207	−0.536037	+	0.844194i	$0.680079\pi$
$674$	−1.81826e117	−0.741772
$675$	−2.71267e116	−0.104062
$676$	4.35535e116	0.157121
$677$	9.32188e116	0.316282	0.158141	−	0.987417i	$-0.449450\pi$
$677$	9.32188e116	0.316282	0.158141	+	0.987417i	$0.449450\pi$
$678$	6.48854e116	0.207069
$679$	4.11681e116	0.123585
$680$	6.71494e117	1.89637
$681$	7.75775e117	2.06125
$682$	−2.57955e117	−0.644901
$683$	1.36200e116	0.0320419	0.0160210	−	0.999872i	$-0.494900\pi$
$683$	1.36200e116	0.0320419	0.0160210	+	0.999872i	$0.494900\pi$
$684$	−1.32084e117	−0.292430
$685$	−1.66710e117	−0.347379
$686$	3.83538e117	0.752242
$687$	−3.73580e116	−0.0689730
$688$	2.83415e117	0.492609
$689$	2.52384e116	0.0413014
$690$	−1.95689e118	−3.01530
$691$	−3.67543e117	−0.533297	−0.266648	−	0.963794i	$-0.585916\pi$
$691$	−3.67543e117	−0.533297	−0.266648	+	0.963794i	$0.585916\pi$
$692$	7.45841e114	0.00101916
$693$	6.63534e117	0.853953
$694$	−8.50308e117	−1.03076
$695$	9.44584e117	1.07863
$696$	2.10140e117	0.226061
$697$	−2.45183e118	−2.48502
$698$	1.22791e118	1.17264
$699$	2.53180e118	2.27838
$700$	1.91958e116	0.0162794
$701$	−3.65225e117	−0.291920	−0.145960	−	0.989291i	$-0.546627\pi$
$701$	−3.65225e117	−0.291920	−0.145960	+	0.989291i	$0.546627\pi$
$702$	2.49664e117	0.188090
$703$	−5.82186e116	−0.0413443
$704$	−2.23260e118	−1.49467
$705$	−2.38503e118	−1.50538
$706$	2.10539e118	1.25296
$707$	1.29593e117	0.0727237
$708$	−5.44558e117	−0.288180
$709$	−2.19372e118	−1.09487	−0.547434	−	0.836849i	$-0.684395\pi$
$709$	−2.19372e118	−1.09487	−0.547434	+	0.836849i	$0.684395\pi$
$710$	2.21417e118	1.04229
$711$	5.43848e118	2.41484
$712$	8.20525e117	0.343694
$713$	2.67283e118	1.05622
$714$	−2.82645e118	−1.05382
$715$	1.58495e118	0.557591
$716$	5.21821e117	0.173233
$717$	−4.03920e118	−1.26546
$718$	−1.84498e117	−0.0545539
$719$	−2.53004e117	−0.0706119	−0.0353059	−	0.999377i	$-0.511241\pi$
$719$	−2.53004e117	−0.0706119	−0.0353059	+	0.999377i	$0.511241\pi$
$720$	−4.39813e118	−1.15870
$721$	1.63362e118	0.406291
$722$	1.45330e118	0.341241
$723$	−2.98491e118	−0.661746
$724$	−7.39502e117	−0.154806
$725$	1.32173e117	0.0261286
$726$	−6.04272e118	−1.12814
$727$	4.33246e118	0.763935	0.381968	−	0.924176i	$-0.375247\pi$
$727$	4.33246e118	0.763935	0.381968	+	0.924176i	$0.375247\pi$
$728$	−1.13905e118	−0.189710
$729$	−9.79601e118	−1.54119
$730$	3.07600e118	0.457180
$731$	7.28621e118	1.02313
$732$	9.43704e117	0.125206
$733$	−3.62367e118	−0.454291	−0.227145	−	0.973861i	$-0.572939\pi$
$733$	−3.62367e118	−0.454291	−0.227145	+	0.973861i	$0.572939\pi$
$734$	5.40065e118	0.639822
$735$	1.16913e119	1.30900
$736$	6.82059e118	0.721759
$737$	−1.46935e119	−1.46969
$738$	1.98253e119	1.87448
$739$	−1.70314e119	−1.52232	−0.761159	−	0.648565i	$-0.775370\pi$
$739$	−1.70314e119	−1.52232	−0.761159	+	0.648565i	$0.775370\pi$
$740$	8.34668e116	0.00705338
$741$	8.56207e118	0.684105
$742$	6.08002e117	0.0459349
$743$	−1.59451e118	−0.113918	−0.0569588	−	0.998377i	$-0.518140\pi$
$743$	−1.59451e118	−0.113918	−0.0569588	+	0.998377i	$0.518140\pi$
$744$	1.28806e119	0.870278
$745$	2.11846e119	1.35374
$746$	−2.30403e119	−1.39260
$747$	−2.20489e119	−1.26061
$748$	−7.43017e118	−0.401867
$749$	−6.78503e118	−0.347182
$750$	2.53240e119	1.22600
$751$	−1.53587e119	−0.703552	−0.351776	−	0.936084i	$-0.614422\pi$
$751$	−1.53587e119	−0.703552	−0.351776	+	0.936084i	$0.614422\pi$
$752$	−1.62318e119	−0.703601
$753$	−5.51902e119	−2.26397
$754$	−1.21648e118	−0.0472272
$755$	−1.92339e118	−0.0706757
$756$	−1.35240e118	−0.0470381
$757$	4.62877e119	1.52401	0.762003	−	0.647573i	$-0.224216\pi$
$757$	4.62877e119	1.52401	0.762003	+	0.647573i	$0.224216\pi$
$758$	−2.52280e119	−0.786340
$759$	1.39605e120	4.11970
$760$	−4.90029e119	−1.36917
$761$	2.08782e119	0.552370	0.276185	−	0.961104i	$-0.410930\pi$
$761$	2.08782e119	0.552370	0.276185	+	0.961104i	$0.410930\pi$
$762$	1.01349e119	0.253915
$763$	1.47868e119	0.350837
$764$	2.29607e118	0.0515955
$765$	−1.13070e120	−2.40657
$766$	−3.35825e119	−0.677047
$767$	2.03243e119	0.388157
$768$	4.50620e119	0.815304
$769$	1.64843e119	0.282571	0.141286	−	0.989969i	$-0.454876\pi$
$769$	1.64843e119	0.282571	0.141286	+	0.989969i	$0.454876\pi$
$770$	3.81820e119	0.620146
$771$	8.33830e119	1.28328
$772$	−1.22408e119	−0.178522
$773$	−1.29235e120	−1.78621	−0.893104	−	0.449850i	$-0.851478\pi$
$773$	−1.29235e120	−1.78621	−0.893104	+	0.449850i	$0.851478\pi$
$774$	−5.89158e119	−0.771759
$775$	8.10157e118	0.100589
$776$	2.40327e119	0.282840
$777$	−2.26511e118	−0.0252707
$778$	1.38508e120	1.46495
$779$	1.78924e120	1.79418
$780$	−1.22752e119	−0.116709
$781$	−1.57959e120	−1.42405
$782$	−3.42389e120	−2.92711
$783$	−9.31198e118	−0.0754969
$784$	7.95674e119	0.611813
$785$	−8.14264e119	−0.593847
$786$	−2.10722e120	−1.45772
$787$	2.56771e120	1.68498	0.842490	−	0.538712i	$-0.181089\pi$
$787$	2.56771e120	1.68498	0.842490	+	0.538712i	$0.181089\pi$
$788$	−4.76058e119	−0.296362
$789$	−2.83628e120	−1.67515
$790$	3.12949e120	1.75368
$791$	1.31179e119	0.0697495
$792$	3.87351e120	1.95438
$793$	−3.52214e119	−0.168643
$794$	1.03580e120	0.470680
$795$	4.22444e119	0.182194
$796$	3.53634e118	0.0144765
$797$	4.16334e120	1.61779	0.808893	−	0.587956i	$-0.200067\pi$
$797$	4.16334e120	1.61779	0.808893	+	0.587956i	$0.200067\pi$
$798$	2.06263e120	0.760854
$799$	−4.17298e120	−1.46135
$800$	2.06738e119	0.0687362
$801$	−1.38165e120	−0.436162
$802$	−2.60122e120	−0.779724
$803$	−2.19441e120	−0.624631
$804$	1.13799e120	0.307619
$805$	−3.95627e120	−1.01568
$806$	−7.45639e119	−0.181813
$807$	3.30896e120	0.766373
$808$	7.56525e119	0.166438
$809$	−6.06645e120	−1.26786	−0.633929	−	0.773391i	$-0.718559\pi$
$809$	−6.06645e120	−1.26786	−0.633929	+	0.773391i	$0.718559\pi$
$810$	−2.55779e120	−0.507852
$811$	3.21152e120	0.605822	0.302911	−	0.953019i	$-0.402041\pi$
$811$	3.21152e120	0.605822	0.302911	+	0.953019i	$0.402041\pi$
$812$	6.58948e118	0.0118107
$813$	3.66978e120	0.625004
$814$	2.64814e119	0.0428576
$815$	5.49240e120	0.844737
$816$	−1.33653e121	−1.95361
$817$	−5.31718e120	−0.738697
$818$	8.09906e120	1.06948
$819$	1.91799e120	0.240749
$820$	−2.56520e120	−0.306088
$821$	9.84262e120	1.11653	0.558264	−	0.829663i	$-0.311468\pi$
$821$	9.84262e120	1.11653	0.558264	+	0.829663i	$0.311468\pi$
$822$	4.09640e120	0.441797
$823$	−5.22581e120	−0.535871	−0.267936	−	0.963437i	$-0.586341\pi$
$823$	−5.22581e120	−0.535871	−0.267936	+	0.963437i	$0.586341\pi$
$824$	9.53657e120	0.929850
$825$	4.23154e120	0.392337
$826$	4.89618e120	0.431703
$827$	1.47320e121	1.23533	0.617663	−	0.786443i	$-0.288079\pi$
$827$	1.47320e121	1.23533	0.617663	+	0.786443i	$0.288079\pi$
$828$	−6.22522e120	−0.496473
$829$	−5.62232e120	−0.426484	−0.213242	−	0.976999i	$-0.568402\pi$
$829$	−5.62232e120	−0.426484	−0.213242	+	0.976999i	$0.568402\pi$
$830$	−1.26877e121	−0.915466
$831$	−1.58495e121	−1.08786
$832$	−6.45348e120	−0.421382
$833$	2.04557e121	1.27071
$834$	−2.32103e121	−1.37180
$835$	−7.53620e120	−0.423802
$836$	5.42223e120	0.290147
$837$	−5.70779e120	−0.290644
$838$	3.50707e121	1.69949
$839$	9.83590e120	0.453620	0.226810	−	0.973939i	$-0.427170\pi$
$839$	9.83590e120	0.453620	0.226810	+	0.973939i	$0.427170\pi$
$840$	−1.90655e121	−0.836872
$841$	−2.34813e121	−0.981044
$842$	−9.91653e120	−0.394374
$843$	1.42373e121	0.538993
$844$	−7.44618e119	−0.0268363
$845$	−2.72082e121	−0.933570
$846$	3.37424e121	1.10232
$847$	−1.22166e121	−0.380005
$848$	2.87503e120	0.0851558
$849$	2.37306e121	0.669330
$850$	−1.03781e121	−0.278761
$851$	−2.74389e120	−0.0701925
$852$	1.22337e121	0.298068
$853$	−4.21166e121	−0.977391	−0.488696	−	0.872454i	$-0.662527\pi$
$853$	−4.21166e121	−0.977391	−0.488696	+	0.872454i	$0.662527\pi$
$854$	−8.48494e120	−0.187563
$855$	8.25139e121	1.73753
$856$	−3.96090e121	−0.794571
$857$	4.77037e121	0.911692	0.455846	−	0.890059i	$-0.349337\pi$
$857$	4.77037e121	0.911692	0.455846	+	0.890059i	$0.349337\pi$
$858$	−3.89455e121	−0.709145
$859$	9.31345e121	1.61582	0.807912	−	0.589303i	$-0.200598\pi$
$859$	9.31345e121	1.61582	0.807912	+	0.589303i	$0.200598\pi$
$860$	7.62313e120	0.126022
$861$	6.96140e121	1.09665
$862$	8.61618e121	1.29349
$863$	−1.20871e122	−1.72931	−0.864657	−	0.502362i	$-0.832464\pi$
$863$	−1.20871e122	−1.72931	−0.864657	+	0.502362i	$0.832464\pi$
$864$	−1.45653e121	−0.198608
$865$	−4.65933e119	−0.00605557
$866$	−9.89769e120	−0.122614
$867$	−2.13591e122	−2.52226
$868$	4.03903e120	0.0454683
$869$	−2.23258e122	−2.39599
$870$	−2.03615e121	−0.208335
$871$	−4.24727e121	−0.414340
$872$	8.63209e121	0.802938
$873$	−4.04676e121	−0.358936
$874$	2.49861e122	2.11337
$875$	5.11977e121	0.412968
$876$	1.69954e121	0.130741
$877$	−1.30082e121	−0.0954410	−0.0477205	−	0.998861i	$-0.515196\pi$
$877$	−1.30082e121	−0.0954410	−0.0477205	+	0.998861i	$0.515196\pi$
$878$	−1.41048e122	−0.987059
$879$	2.37457e122	1.58506
$880$	1.80550e122	1.14965
$881$	1.41162e122	0.857470	0.428735	−	0.903430i	$-0.358959\pi$
$881$	1.41162e122	0.857470	0.428735	+	0.903430i	$0.358959\pi$
$882$	−1.65404e122	−0.958514
$883$	−1.81033e122	−1.00089	−0.500447	−	0.865767i	$-0.666831\pi$
$883$	−1.81033e122	−1.00089	−0.500447	+	0.865767i	$0.666831\pi$
$884$	−2.14774e121	−0.113296
$885$	3.40190e122	1.71229
$886$	−2.79611e121	−0.134294
$887$	−2.16370e122	−0.991667	−0.495833	−	0.868418i	$-0.665137\pi$
$887$	−2.16370e122	−0.991667	−0.495833	+	0.868418i	$0.665137\pi$
$888$	−1.32230e121	−0.0578353
$889$	2.04898e121	0.0855292
$890$	−7.95048e121	−0.316744
$891$	1.82473e122	0.693862
$892$	−7.86573e121	−0.285494
$893$	3.04527e122	1.05509
$894$	−5.20549e122	−1.72169
$895$	−3.25986e122	−1.02930
$896$	−9.93220e121	−0.299408
$897$	4.03537e122	1.16144
$898$	2.32576e122	0.639141
$899$	2.78109e121	0.0729772
$900$	−1.88692e121	−0.0472812
$901$	7.39132e121	0.176865
$902$	−8.13858e122	−1.85985
$903$	−2.06875e122	−0.451510
$904$	7.65785e121	0.159631
$905$	4.61973e122	0.919816
$906$	4.72617e121	0.0898854
$907$	−7.55951e122	−1.37338	−0.686690	−	0.726950i	$-0.740937\pi$
$907$	−7.55951e122	−1.37338	−0.686690	+	0.726950i	$0.740937\pi$
$908$	1.42010e122	0.246466
$909$	−1.27388e122	−0.211216
$910$	1.10368e122	0.174834
$911$	6.62684e121	0.100298	0.0501492	−	0.998742i	$-0.484030\pi$
$911$	6.62684e121	0.100298	0.0501492	+	0.998742i	$0.484030\pi$
$912$	9.75346e122	1.41050
$913$	9.05140e122	1.25077
$914$	8.15492e122	1.07684
$915$	−5.89540e122	−0.743940
$916$	−6.83861e120	−0.00824718
$917$	−4.26018e122	−0.491022
$918$	7.31166e122	0.805461
$919$	−9.46858e122	−0.996991	−0.498496	−	0.866892i	$-0.666114\pi$
$919$	−9.46858e122	−0.996991	−0.498496	+	0.866892i	$0.666114\pi$
$920$	−2.30955e123	−2.32452
$921$	1.82777e123	1.75851
$922$	4.65363e122	0.428014
$923$	−4.56592e122	−0.401474
$924$	2.10963e122	0.177345
$925$	−8.31697e120	−0.00668472
$926$	2.19309e123	1.68539
$927$	−1.60582e123	−1.18002
$928$	7.09684e121	0.0498682
$929$	4.68321e122	0.314696	0.157348	−	0.987543i	$-0.449706\pi$
$929$	4.68321e122	0.314696	0.157348	+	0.987543i	$0.449706\pi$
$930$	−1.24806e123	−0.802036
$931$	−1.49278e123	−0.917451
$932$	4.63461e122	0.272429
$933$	−2.99977e123	−1.68655
$934$	−2.97407e123	−1.59939
$935$	4.64169e123	2.38778
$936$	1.11967e123	0.550987
$937$	1.63823e123	0.771226	0.385613	−	0.922661i	$-0.373990\pi$
$937$	1.63823e123	0.771226	0.385613	+	0.922661i	$0.373990\pi$
$938$	−1.02318e123	−0.460824
$939$	−5.74461e123	−2.47536
$940$	−4.36594e122	−0.180000
$941$	−3.08725e123	−1.21787	−0.608937	−	0.793219i	$-0.708404\pi$
$941$	−3.08725e123	−1.21787	−0.608937	+	0.793219i	$0.708404\pi$
$942$	2.00081e123	0.755254
$943$	8.43286e123	3.04607
$944$	2.31523e123	0.800307
$945$	8.44855e122	0.279487
$946$	2.41858e123	0.765735
$947$	4.16237e123	1.26129	0.630647	−	0.776070i	$-0.282789\pi$
$947$	4.16237e123	1.26129	0.630647	+	0.776070i	$0.282789\pi$
$948$	1.72910e123	0.501503
$949$	−6.34311e122	−0.176098
$950$	7.57351e122	0.201265
$951$	−7.00526e123	−1.78210
$952$	−3.33581e123	−0.812397
$953$	−3.77194e122	−0.0879447	−0.0439724	−	0.999033i	$-0.514001\pi$
$953$	−3.77194e122	−0.0879447	−0.0439724	+	0.999033i	$0.514001\pi$
$954$	−5.97657e122	−0.133412
$955$	−1.43438e123	−0.306566
$956$	−7.39399e122	−0.151313
$957$	1.45259e123	0.284641
$958$	−2.05688e123	−0.385959
$959$	8.28173e122	0.148816
$960$	−1.08019e124	−1.85885
$961$	−4.36298e123	−0.719056
$962$	7.65464e121	0.0120826
$963$	6.66959e123	1.00834
$964$	−5.46405e122	−0.0791257
$965$	7.64694e123	1.06073
$966$	9.72134e123	1.29174
$967$	−1.51746e124	−1.93161	−0.965805	−	0.259270i	$-0.916518\pi$
$967$	−1.51746e124	−1.93161	−0.965805	+	0.259270i	$0.916518\pi$
$968$	−7.13170e123	−0.869692
$969$	2.50748e124	2.92955
$970$	−2.32865e123	−0.260662
$971$	−6.47354e123	−0.694295	−0.347147	−	0.937811i	$-0.612850\pi$
$971$	−6.47354e123	−0.694295	−0.347147	+	0.937811i	$0.612850\pi$
$972$	−2.39276e123	−0.245895
$973$	−4.69245e123	−0.462080
$974$	9.71808e123	0.917031
$975$	1.22316e123	0.110609
$976$	−4.01223e123	−0.347711
$977$	5.17252e123	0.429613	0.214807	−	0.976657i	$-0.431088\pi$
$977$	5.17252e123	0.429613	0.214807	+	0.976657i	$0.431088\pi$
$978$	−1.34959e124	−1.07434
$979$	5.67186e123	0.432757
$980$	2.14016e123	0.156518
$981$	−1.45352e124	−1.01896
$982$	6.49434e123	0.436423
$983$	−1.22964e124	−0.792147	−0.396074	−	0.918219i	$-0.629628\pi$
$983$	−1.22964e124	−0.792147	−0.396074	+	0.918219i	$0.629628\pi$
$984$	4.06386e124	2.50982
$985$	2.97398e124	1.76090
$986$	−3.56256e123	−0.202242
$987$	1.18482e124	0.644899
$988$	1.56734e123	0.0817992
$989$	−2.50603e124	−1.25413
$990$	−3.75324e124	−1.80113
$991$	−1.35315e124	−0.622715	−0.311357	−	0.950293i	$-0.600784\pi$
$991$	−1.35315e124	−0.622715	−0.311357	+	0.950293i	$0.600784\pi$
$992$	4.35001e123	0.191980
$993$	−1.82345e124	−0.771792
$994$	−1.09995e124	−0.446515
$995$	−2.20919e123	−0.0860150
$996$	−7.01018e123	−0.261798
$997$	−6.51967e123	−0.233548	−0.116774	−	0.993159i	$-0.537255\pi$
$997$	−6.51967e123	−0.233548	−0.116774	+	0.993159i	$0.537255\pi$
$998$	−4.42846e122	−0.0152172
$999$	5.85954e122	0.0193151

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 84 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.80997e12 q^{2} -9.69898e19 q^{3} -1.77546e24 q^{4} +1.10914e29 q^{5} -2.72539e32 q^{6} -5.50994e34 q^{7} -3.21654e37 q^{8} +5.41619e39 q^{9} +O(q^{10})\)	\(q+2.80997e12 q^{2} -9.69898e19 q^{3} -1.77546e24 q^{4} +1.10914e29 q^{5} -2.72539e32 q^{6} -5.50994e34 q^{7} -3.21654e37 q^{8} +5.41619e39 q^{9} +3.11666e41 q^{10} -2.22342e43 q^{11} +1.72201e44 q^{12} -6.42697e45 q^{13} -1.54828e47 q^{14} -1.07576e49 q^{15} -7.32127e49 q^{16} -1.88220e51 q^{17} +1.52193e52 q^{18} +1.37355e53 q^{19} -1.96924e53 q^{20} +5.34408e54 q^{21} -6.24776e55 q^{22} +6.47368e56 q^{23} +3.11971e57 q^{24} +1.96223e57 q^{25} -1.80596e58 q^{26} -1.38244e59 q^{27} +9.78266e58 q^{28} +6.73588e59 q^{29} -3.02285e61 q^{30} +4.12876e61 q^{31} +1.05359e62 q^{32} +2.15650e63 q^{33} -5.28894e63 q^{34} -6.11131e63 q^{35} -9.61621e63 q^{36} -4.23854e63 q^{37} +3.85965e65 q^{38} +6.23351e65 q^{39} -3.56760e66 q^{40} +1.30264e67 q^{41} +1.50167e67 q^{42} -3.87111e67 q^{43} +3.94759e67 q^{44} +6.00733e68 q^{45} +1.81909e69 q^{46} +2.21707e69 q^{47} +7.10089e69 q^{48} -1.08680e70 q^{49} +5.51381e69 q^{50} +1.82554e71 q^{51} +1.14108e70 q^{52} -3.92695e70 q^{53} -3.88463e71 q^{54} -2.46610e72 q^{55} +1.77229e72 q^{56} -1.33221e73 q^{57} +1.89277e72 q^{58} -3.16234e73 q^{59} +1.90996e73 q^{60} +5.48024e73 q^{61} +1.16017e74 q^{62} -2.98429e74 q^{63} +1.00413e75 q^{64} -7.12843e74 q^{65} +6.05970e75 q^{66} +6.60851e75 q^{67} +3.34177e75 q^{68} -6.27881e76 q^{69} -1.71726e76 q^{70} +7.10431e76 q^{71} -1.74214e77 q^{72} +9.86952e76 q^{73} -1.19102e76 q^{74} -1.90316e77 q^{75} -2.43869e77 q^{76} +1.22509e78 q^{77} +1.75160e78 q^{78} +1.00412e79 q^{79} -8.12034e78 q^{80} -8.20683e78 q^{81} +3.66038e79 q^{82} -4.07093e79 q^{83} -9.48818e78 q^{84} -2.08763e80 q^{85} -1.08777e80 q^{86} -6.53312e79 q^{87} +7.15173e80 q^{88} -2.55096e80 q^{89} +1.68804e81 q^{90} +3.54122e80 q^{91} -1.14937e81 q^{92} -4.00448e81 q^{93} +6.22992e81 q^{94} +1.52347e82 q^{95} -1.02187e82 q^{96} -7.47161e81 q^{97} -3.05387e82 q^{98} -1.20425e83 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 347450761416 q^{2} + 92\!\cdots\!72 q^{3}+ \cdots + 71\!\cdots\!19 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more