LMFDB - Embedded newform 2.76.a.a.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,76,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 76); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 76, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 76 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-412316860416] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$71.2456785644$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2545113646097216346229262x + 1534393340960420283457013132957235840 $ x^3 - x^2 - 2545113646097216346229262*x + 1534393340960420283457013132957235840
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{7}\cdot 5^{4}\cdot 7\cdot 11\cdot 19 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$8.17691e11$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.37439e11 q^{2} +2.34098e17 q^{3} +1.88895e22 q^{4} -1.81463e26 q^{5} -3.21742e28 q^{6} +7.29430e31 q^{7} -2.59615e33 q^{8} -5.53465e35 q^{9} +2.49400e37 q^{10} +1.36663e39 q^{11} +4.42199e39 q^{12} -4.52800e41 q^{13} -1.00252e43 q^{14} -4.24800e43 q^{15} +3.56812e44 q^{16} -1.82603e46 q^{17} +7.60676e46 q^{18} +1.73367e48 q^{19} -3.42773e48 q^{20} +1.70758e49 q^{21} -1.87828e50 q^{22} +6.67720e50 q^{23} -6.07753e50 q^{24} +6.45888e51 q^{25} +6.22323e52 q^{26} -2.71959e53 q^{27} +1.37785e54 q^{28} +6.83281e53 q^{29} +5.83841e54 q^{30} -1.23578e56 q^{31} -4.90399e55 q^{32} +3.19924e56 q^{33} +2.50968e57 q^{34} -1.32364e58 q^{35} -1.04547e58 q^{36} +4.21056e58 q^{37} -2.38273e59 q^{38} -1.06000e59 q^{39} +4.71104e59 q^{40} -4.88352e60 q^{41} -2.34688e60 q^{42} -3.39926e60 q^{43} +2.58148e61 q^{44} +1.00433e62 q^{45} -9.17707e61 q^{46} -1.52499e61 q^{47} +8.35290e61 q^{48} +2.90882e63 q^{49} -8.87702e62 q^{50} -4.27471e63 q^{51} -8.55315e63 q^{52} +1.24483e64 q^{53} +3.73778e64 q^{54} -2.47991e65 q^{55} -1.89371e65 q^{56} +4.05848e65 q^{57} -9.39094e64 q^{58} +2.54281e66 q^{59} -8.02425e65 q^{60} +4.43205e66 q^{61} +1.69844e67 q^{62} -4.03714e67 q^{63} +6.73999e66 q^{64} +8.21662e67 q^{65} -4.39701e67 q^{66} +5.52549e67 q^{67} -3.44928e68 q^{68} +1.56312e68 q^{69} +1.81920e69 q^{70} +3.08813e69 q^{71} +1.43688e69 q^{72} +1.19428e70 q^{73} -5.78695e69 q^{74} +1.51201e69 q^{75} +3.27480e70 q^{76} +9.96858e70 q^{77} +1.45685e70 q^{78} +4.69829e70 q^{79} -6.47480e70 q^{80} +2.72989e71 q^{81} +6.71186e71 q^{82} +4.36337e71 q^{83} +3.22553e71 q^{84} +3.31357e72 q^{85} +4.67191e71 q^{86} +1.59955e71 q^{87} -3.54796e72 q^{88} -4.75704e72 q^{89} -1.38034e73 q^{90} -3.30286e73 q^{91} +1.26129e73 q^{92} -2.89293e73 q^{93} +2.09593e72 q^{94} -3.14596e74 q^{95} -1.14801e73 q^{96} +5.91346e74 q^{97} -3.99785e74 q^{98} -7.56379e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 412316860416 q^{2} + 12\!\cdots\!04 q^{3} + 56\!\cdots\!52 q^{4} + 16\!\cdots\!50 q^{5} - 17\!\cdots\!88 q^{6} + 49\!\cdots\!12 q^{7} - 77\!\cdots\!44 q^{8} + 35\!\cdots\!51 q^{9} - 22\!\cdots\!00 q^{10}+ \cdots - 11\!\cdots\!68 q^{99}+O(q^{100}) $ 3 * q - 412316860416 * q^2 + 1247256736634198004 * q^3 + 56668397794435742564352 * q^4 + 164841037010073038656676250 * q^5 - 171421660593906097355791269888 * q^6 + 49188484889350831330680498887112 * q^7 - 7788445287802241442795744493830144 * q^8 + 350069357182276058179837291235129151 * q^9 - 22655579615903658355256584505917440000 * q^10 + 376028144461193866320847155952833356796 * q^11 + 23560013634458836001219698571880626651136 * q^12 - 925070104562370942171863215664607476425566 * q^13 - 6760413886065663975541916932643533948452864 * q^14 + 304269429637489871036834079247530526228335000 * q^15 + 1070435769529469910793714477087121352287059968 * q^16 + 11105717807078079560338878984556957971267357462 * q^17 - 48113166093747788183238222478595428796199862272 * q^18 + 1226070865667475560419994296781687078098256026500 * q^19 + 3113759152711374531922693764530423144833351680000 * q^20 + 68517185882331308774796793377188076110575410338016 * q^21 - 51680914650764518302842700090624991551255018995712 * q^22 + 271328792137896997383389612251048821761834150147544 * q^23 - 3238063617706073577070912687270566293843683879944192 * q^24 + 31748451106721345935032757125860501117730610058203125 * q^25 + 127140667059285874843163511125276288509596702345265152 * q^26 + 1197448038136873386430122156284924279903233737117284040 * q^27 + 929144209538441500271292067291283620303065621681143808 * q^28 - 2192192441744294863307671608209094010102596849162475470 * q^29 - 41818471982898948212302719415885308765195809713029120000 * q^30 - 84475319706390463018423912220261407196388754491533828064 * q^31 - 147119571923125330402401314606429681627398955729625808896 * q^32 - 152651908525049572295389965461339076489002087512241778672 * q^33 - 1526358232960166048964529405311162353146873855092210008064 * q^34 - 10581882005980808610246098771932820539289975861854133370000 * q^35 + 6612623196149210250218989469527661654232801841214216208384 * q^36 - 66467156559661428016435329175985053243116052098537071406918 * q^37 - 168509896659846935772260720933883649668409840270477099008000 * q^38 - 1576575655050891506325267408432832107424195089029358618993288 * q^39 - 427951799312512746938088887004201350531222938741333032960000 * q^40 - 4931831025653402196557722046034935103637243072704239197865874 * q^41 - 9416930322514108013588161811222149738754568548593888816791552 * q^42 - 20756681407708278323173156546593085322222288647517659582599396 * q^43 + 7102970824076827760252890263090258397213331658958137735512064 * q^44 + 430455289229109660667382851976501730627013861372014944449721250 * q^45 - 37291145238254384831304190663820020197325144827508961751072768 * q^46 + 51571462381763314515108804623667311044662303402547877540507952 * q^47 + 445036074893281041730857774870353847534673548816726238244634624 * q^48 + 874703066390889543299993126070490968782377105753545374031866619 * q^49 - 4363473894464741970434183441417017861082381310019554508800000000 * q^50 + 26687643671570090614605289380399353628646518403234111773363733416 * q^51 - 17474080224360234418116365102835002179615309399115530505231007744 * q^52 + 6373650417776797701672439632011840936956406793203656616477981514 * q^53 - 164576005198631422925124635216920020480663646258003080580568186880 * q^54 - 416397474908805676143485768937466126874738084681826965490191835000 * q^55 - 127700607783532079951179985813769422561988750517197478247452901376 * q^56 + 324374862297075653278748857063883477999874298820902947102578684400 * q^57 + 301292635002564212239591678181305084901764706298415268289671331840 * q^58 + 5164661149603341451990328866011056430426032323285413754497779833260 * q^59 + 5747487025127784123028411031778931969068100664118374895861104640000 * q^60 + 6112904160012928128712528481475458535407529031872677635552463254866 * q^61 + 11610199534658923547853700750412719759341719994985948813202143838208 * q^62 + 13207243195255893358298630339555911394008670199338112701744595846504 * q^63 + 20219960000362979846000261315264723005227858316905429360827707686912 * q^64 - 130892903197384045097570057369266929060996843870951145661159667802500 * q^65 + 20980318553186288313199601703136668348387407025305870049315529949184 * q^66 - 136137738816805460535298375335076702172786722063275309182255486993868 * q^67 + 209781078161416398433030030714936672336391228552271521567960840798208 * q^68 + 2302114699257823143259687991707123968073297464808491488252678944581792 * q^69 + 1454362788666190380308550551585191261609200940393373335890312560640000 * q^70 + 10384877370088278005014559441463902818134695856776063874032337197444616 * q^71 - 908832011783419237149393171513270251913060604110836593449036832309248 * q^72 + 23960042075251086966999537195044028280663199284717397149070565023693454 * q^73 + 9135176437819446597223932457915213832448069788667164516362544580919296 * q^74 + 73651649014806681647280357044768244600220326928118781461607720567187500 * q^75 + 23159823846604231216245513612685211315038128265161053905802049355776000 * q^76 + 112606444794187449919020541060114371108822468615691116879839101242785184 * q^77 + 216682908099627399529958421045558032449461654608156916877820684912295936 * q^78 + 207600583714452906248332854115664313358280271635394763063638195459831120 * q^79 + 58817247433971121013830909005570694884180311960929176960246082437120000 * q^80 + 1040997430154496315690711192050972807021466062787523736282834877959617563 * q^81 + 677825694866543982891199358847304087795338548635752244332646458382614528 * q^82 + 1167639752536908153859168711897497594398247447354194893620746224951064004 * q^83 + 1294253048445082445343125714942568285400506101977630056114555247650668544 * q^84 + 10113448117368406780812318911043868851473369769419767324525240781711092500 * q^85 + 2852776570227145526607821642006579253717835257067533423671213327659302912 * q^86 + 5029129967375119029953943778547857750798463238735644189412390040078806840 * q^87 - 976224876603268627894754955822383862791060384333652064226810006190686208 * q^88 - 39521664848491905275031652813807887505386797709550908292289684142644361570 * q^89 - 59161324468135905400450140260809084592973635479407420033113903522119680000 * q^90 - 76061144334143564334879783774020507949888992229194116049886624616643162064 * q^91 + 5125255975318038751329599229723376549682270838803665659768717807238250496 * q^92 - 63157470235075274925966093148023612999965331967498255414086440472939495552 * q^93 - 7087927818770166484958541239689750032674694031295125027542226210174009344 * q^94 - 383757279880654476069446138229405811984616709991648142174485235232603525000 * q^95 - 61165292390619160459867052067056013283494179782531158113465925041576214528 * q^96 - 394916692348392721348110030097230776686065428055487460723991200429722029978 * q^97 - 120218274043513194906299084591922038450677331531219546160606553294050951168 * q^98 - 1174273799576543370476209530112641026492928709676247191346470741033657155668 * q^99

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 $

$2$	−1.37439e11	−0.707107
$2$	−1.37439e11	−0.707107
$3$	2.34098e17	0.300159	0.150079	−	0.988674i	$-0.452047\pi$
$3$	2.34098e17	0.300159	0.150079	+	0.988674i	$0.452047\pi$
$4$	1.88895e22	0.500000
$5$	−1.81463e26	−1.11535	−0.557676	−	0.830059i	$-0.688307\pi$
$5$	−1.81463e26	−1.11535	−0.557676	+	0.830059i	$0.688307\pi$
$6$	−3.21742e28	−0.212244
$7$	7.29430e31	1.48528	0.742638	−	0.669693i	$-0.233574\pi$
$7$	7.29430e31	1.48528	0.742638	+	0.669693i	$0.233574\pi$
$8$	−2.59615e33	−0.353553
$9$	−5.53465e35	−0.909905
$10$	2.49400e37	0.788673
$11$	1.36663e39	1.21178	0.605890	−	0.795548i	$-0.292817\pi$
$11$	1.36663e39	1.21178	0.605890	+	0.795548i	$0.292817\pi$
$12$	4.42199e39	0.150079
$13$	−4.52800e41	−0.763889	−0.381945	−	0.924185i	$-0.624746\pi$
$13$	−4.52800e41	−0.763889	−0.381945	+	0.924185i	$0.624746\pi$
$14$	−1.00252e43	−1.05025
$15$	−4.24800e43	−0.334782
$16$	3.56812e44	0.250000
$17$	−1.82603e46	−1.31727	−0.658634	−	0.752464i	$-0.728865\pi$
$17$	−1.82603e46	−1.31727	−0.658634	+	0.752464i	$0.728865\pi$
$18$	7.60676e46	0.643400
$19$	1.73367e48	1.93066	0.965329	−	0.261035i	$-0.0840639\pi$
$19$	1.73367e48	1.93066	0.965329	+	0.261035i	$0.0840639\pi$
$20$	−3.42773e48	−0.557676
$21$	1.70758e49	0.445819
$22$	−1.87828e50	−0.856858
$23$	6.67720e50	0.575176	0.287588	−	0.957754i	$-0.407147\pi$
$23$	6.67720e50	0.575176	0.287588	+	0.957754i	$0.407147\pi$
$24$	−6.07753e50	−0.106122
$25$	6.45888e51	0.244010
$26$	6.22323e52	0.540151
$27$	−2.71959e53	−0.573274
$28$	1.37785e54	0.742638
$29$	6.83281e53	0.0987812	0.0493906	−	0.998780i	$-0.484272\pi$
$29$	6.83281e53	0.0987812	0.0493906	+	0.998780i	$0.484272\pi$
$30$	5.83841e54	0.236727
$31$	−1.23578e56	−1.46513	−0.732565	−	0.680697i	$-0.761677\pi$
$31$	−1.23578e56	−1.46513	−0.732565	+	0.680697i	$0.761677\pi$
$32$	−4.90399e55	−0.176777
$33$	3.19924e56	0.363726
$34$	2.50968e57	0.931449
$35$	−1.32364e58	−1.65661
$36$	−1.04547e58	−0.454952
$37$	4.21056e58	0.655806	0.327903	−	0.944711i	$-0.393658\pi$
$37$	4.21056e58	0.655806	0.327903	+	0.944711i	$0.393658\pi$
$38$	−2.38273e59	−1.36518
$39$	−1.06000e59	−0.229288
$40$	4.71104e59	0.394336
$41$	−4.88352e60	−1.61934	−0.809670	−	0.586885i	$-0.800354\pi$
$41$	−4.88352e60	−1.61934	−0.809670	+	0.586885i	$0.800354\pi$
$42$	−2.34688e60	−0.315241
$43$	−3.39926e60	−0.188937	−0.0944687	−	0.995528i	$-0.530115\pi$
$43$	−3.39926e60	−0.188937	−0.0944687	+	0.995528i	$0.530115\pi$
$44$	2.58148e61	0.605890
$45$	1.00433e62	1.01486
$46$	−9.17707e61	−0.406711
$47$	−1.52499e61	−0.0301716	−0.0150858	−	0.999886i	$-0.504802\pi$
$47$	−1.52499e61	−0.0301716	−0.0150858	+	0.999886i	$0.504802\pi$
$48$	8.35290e61	0.0750397
$49$	2.90882e63	1.20605
$50$	−8.87702e62	−0.172541
$51$	−4.27471e63	−0.395389
$52$	−8.55315e63	−0.381945
$53$	1.24483e64	0.272124	0.136062	−	0.990700i	$-0.456555\pi$
$53$	1.24483e64	0.272124	0.136062	+	0.990700i	$0.456555\pi$
$54$	3.73778e64	0.405366
$55$	−2.47991e65	−1.35156
$56$	−1.89371e65	−0.525125
$57$	4.05848e65	0.579504
$58$	−9.39094e64	−0.0698489
$59$	2.54281e66	0.996240	0.498120	−	0.867108i	$-0.334024\pi$
$59$	2.54281e66	0.996240	0.498120	+	0.867108i	$0.334024\pi$
$60$	−8.02425e65	−0.167391
$61$	4.43205e66	0.497434	0.248717	−	0.968576i	$-0.419991\pi$
$61$	4.43205e66	0.497434	0.248717	+	0.968576i	$0.419991\pi$
$62$	1.69844e67	1.03600
$63$	−4.03714e67	−1.35146
$64$	6.73999e66	0.125000
$65$	8.21662e67	0.852005
$66$	−4.39701e67	−0.257193
$67$	5.52549e67	0.183893	0.0919467	−	0.995764i	$-0.470691\pi$
$67$	5.52549e67	0.183893	0.0919467	+	0.995764i	$0.470691\pi$
$68$	−3.44928e68	−0.658634
$69$	1.56312e68	0.172644
$70$	1.81920e69	1.17140
$71$	3.08813e69	1.16817	0.584087	−	0.811691i	$-0.301453\pi$
$71$	3.08813e69	1.16817	0.584087	+	0.811691i	$0.301453\pi$
$72$	1.43688e69	0.321700
$73$	1.19428e70	1.59404	0.797021	−	0.603952i	$-0.206408\pi$
$73$	1.19428e70	1.59404	0.797021	+	0.603952i	$0.206408\pi$
$74$	−5.78695e69	−0.463725
$75$	1.51201e69	0.0732416
$76$	3.27480e70	0.965329
$77$	9.96858e70	1.79983
$78$	1.45685e70	0.162131
$79$	4.69829e70	0.324283	0.162141	−	0.986768i	$-0.448160\pi$
$79$	4.69829e70	0.324283	0.162141	+	0.986768i	$0.448160\pi$
$80$	−6.47480e70	−0.278838
$81$	2.72989e71	0.737832
$82$	6.71186e71	1.14505
$83$	4.36337e71	0.472492	0.236246	−	0.971693i	$-0.424083\pi$
$83$	4.36337e71	0.472492	0.236246	+	0.971693i	$0.424083\pi$
$84$	3.22553e71	0.222909
$85$	3.31357e72	1.46922
$86$	4.67191e71	0.133599
$87$	1.59955e71	0.0296500
$88$	−3.54796e72	−0.428429
$89$	−4.75704e72	−0.376020	−0.188010	−	0.982167i	$-0.560204\pi$
$89$	−4.75704e72	−0.376020	−0.188010	+	0.982167i	$0.560204\pi$
$90$	−1.38034e73	−0.717617
$91$	−3.30286e73	−1.13459
$92$	1.26129e73	0.287588
$93$	−2.89293e73	−0.439771
$94$	2.09593e72	0.0213345
$95$	−3.14596e74	−2.15336
$96$	−1.14801e73	−0.0530610
$97$	5.91346e74	1.85311	0.926555	−	0.376159i	$-0.122755\pi$
$97$	5.91346e74	1.85311	0.926555	+	0.376159i	$0.122755\pi$
$98$	−3.99785e74	−0.852803
$99$	−7.56379e74	−1.10260
$100$	1.22005e74	0.122005
$101$	−1.86083e75	−1.28131	−0.640657	−	0.767827i	$-0.721338\pi$
$101$	−1.86083e75	−1.28131	−0.640657	+	0.767827i	$0.721338\pi$
$102$	5.87511e74	0.279582
$103$	3.72830e75	1.23059	0.615297	−	0.788296i	$-0.289036\pi$
$103$	3.72830e75	1.23059	0.615297	+	0.788296i	$0.289036\pi$
$104$	1.17554e75	0.270076
$105$	−3.09862e75	−0.497244
$106$	−1.71089e75	−0.192420
$107$	2.06879e76	1.63616	0.818079	−	0.575106i	$-0.195039\pi$
$107$	2.06879e76	1.63616	0.818079	+	0.575106i	$0.195039\pi$
$108$	−5.13716e75	−0.286637
$109$	3.38196e76	1.33560	0.667798	−	0.744343i	$-0.267237\pi$
$109$	3.38196e76	1.33560	0.667798	+	0.744343i	$0.267237\pi$
$110$	3.40837e76	0.955698
$111$	9.85684e75	0.196846
$112$	2.60269e76	0.371319
$113$	−4.31570e76	−0.441174	−0.220587	−	0.975367i	$-0.570797\pi$
$113$	−4.31570e76	−0.441174	−0.220587	+	0.975367i	$0.570797\pi$
$114$	−5.57793e76	−0.409771
$115$	−1.21166e77	−0.641523
$116$	1.29068e76	0.0493906
$117$	2.50609e77	0.695067
$118$	−3.49482e77	−0.704448
$119$	−1.33196e78	−1.95651
$120$	1.10284e77	0.118363
$121$	5.95769e77	0.468411
$122$	−6.09136e77	−0.351739
$123$	−1.14322e78	−0.486059
$124$	−2.33431e78	−0.732565
$125$	3.63123e78	0.843195
$126$	5.54860e78	0.955627
$127$	−7.45672e78	−0.954791	−0.477395	−	0.878689i	$-0.658419\pi$
$127$	−7.45672e78	−0.954791	−0.477395	+	0.878689i	$0.658419\pi$
$128$	−9.26337e77	−0.0883883
$129$	−7.95761e77	−0.0567112
$130$	−1.12928e79	−0.602459
$131$	6.47145e78	0.259017	0.129508	−	0.991578i	$-0.458660\pi$
$131$	6.47145e78	0.259017	0.129508	+	0.991578i	$0.458660\pi$
$132$	6.04320e78	0.181863
$133$	1.26459e80	2.86756
$134$	−7.59418e78	−0.130032
$135$	4.93504e79	0.639403
$136$	4.74065e79	0.465724
$137$	−1.76499e80	−1.31741	−0.658704	−	0.752402i	$-0.728895\pi$
$137$	−1.76499e80	−1.31741	−0.658704	+	0.752402i	$0.728895\pi$
$138$	−2.14834e79	−0.122078
$139$	2.84598e80	1.23361	0.616804	−	0.787117i	$-0.288427\pi$
$139$	2.84598e80	1.23361	0.616804	+	0.787117i	$0.288427\pi$
$140$	−2.50029e80	−0.828303
$141$	−3.56998e78	−0.00905626
$142$	−4.24430e80	−0.826024
$143$	−6.18808e80	−0.925666
$144$	−1.97483e80	−0.227476
$145$	−1.23990e80	−0.110176
$146$	−1.64141e81	−1.12716
$147$	6.80949e80	0.362005
$148$	7.95352e80	0.327903
$149$	−7.06704e80	−0.226335	−0.113168	−	0.993576i	$-0.536100\pi$
$149$	−7.06704e80	−0.226335	−0.113168	+	0.993576i	$0.536100\pi$
$150$	−2.07809e80	−0.0517896
$151$	4.33963e81	0.842980	0.421490	−	0.906833i	$-0.361507\pi$
$151$	4.33963e81	0.842980	0.421490	+	0.906833i	$0.361507\pi$
$152$	−4.50085e81	−0.682591
$153$	1.01064e82	1.19859
$154$	−1.37007e82	−1.27267
$155$	2.24247e82	1.63414
$156$	−2.00228e81	−0.114644
$157$	9.71286e81	0.437633	0.218817	−	0.975766i	$-0.429780\pi$
$157$	9.71286e81	0.437633	0.218817	+	0.975766i	$0.429780\pi$
$158$	−6.45728e81	−0.229303
$159$	2.91413e81	0.0816803
$160$	8.89890e81	0.197168
$161$	4.87055e82	0.854295
$162$	−3.75193e82	−0.521726
$163$	9.22323e82	1.01823	0.509117	−	0.860697i	$-0.329972\pi$
$163$	9.22323e82	1.01823	0.509117	+	0.860697i	$0.329972\pi$
$164$	−9.22471e82	−0.809670
$165$	−5.80543e82	−0.405683
$166$	−5.99698e82	−0.334102
$167$	9.81886e82	0.436710	0.218355	−	0.975869i	$-0.429931\pi$
$167$	9.81886e82	0.436710	0.218355	+	0.975869i	$0.429931\pi$
$168$	−4.43314e82	−0.157621
$169$	−1.46332e83	−0.416473
$170$	−4.55413e83	−1.03889
$171$	−9.59523e83	−1.75672
$172$	−6.42103e82	−0.0944687
$173$	7.25502e83	0.858835	0.429418	−	0.903106i	$-0.358719\pi$
$173$	7.25502e83	0.858835	0.429418	+	0.903106i	$0.358719\pi$
$174$	−2.19840e82	−0.0209657
$175$	4.71130e83	0.362422
$176$	4.87628e83	0.302945
$177$	5.95268e83	0.299030
$178$	6.53802e83	0.265886
$179$	−1.10428e84	−0.363992	−0.181996	−	0.983299i	$-0.558256\pi$
$179$	−1.10428e84	−0.363992	−0.181996	+	0.983299i	$0.558256\pi$
$180$	1.89713e84	0.507432
$181$	6.94718e84	1.50960	0.754800	−	0.655954i	$-0.227734\pi$
$181$	6.94718e84	1.50960	0.754800	+	0.655954i	$0.227734\pi$
$182$	4.53941e84	0.802274
$183$	1.03753e84	0.149309
$184$	−1.73350e84	−0.203355
$185$	−7.64059e84	−0.731454
$186$	3.97601e84	0.310965
$187$	−2.49550e85	−1.59624
$188$	−2.88063e83	−0.0150858
$189$	−1.98375e85	−0.851471
$190$	4.32377e85	1.52266
$191$	2.67106e85	0.772561	0.386280	−	0.922381i	$-0.373760\pi$
$191$	2.67106e85	0.772561	0.386280	+	0.922381i	$0.373760\pi$
$192$	1.57782e84	0.0375198
$193$	−6.51856e85	−1.27571	−0.637855	−	0.770156i	$-0.720178\pi$
$193$	−6.51856e85	−1.27571	−0.637855	+	0.770156i	$0.720178\pi$
$194$	−8.12739e85	−1.31035
$195$	1.92350e85	0.255737
$196$	5.49461e85	0.603023
$197$	−1.46610e86	−1.32947	−0.664736	−	0.747078i	$-0.731456\pi$
$197$	−1.46610e86	−1.32947	−0.664736	+	0.747078i	$0.731456\pi$
$198$	1.03956e86	0.779659
$199$	−9.55828e85	−0.593457	−0.296729	−	0.954962i	$-0.595896\pi$
$199$	−9.55828e85	−0.593457	−0.296729	+	0.954962i	$0.595896\pi$
$200$	−1.67682e85	−0.0862705
$201$	1.29351e85	0.0551972
$202$	2.55751e86	0.906026
$203$	4.98406e85	0.146717
$204$	−8.07469e85	−0.197695
$205$	8.86176e86	1.80613
$206$	−5.12413e86	−0.870161
$207$	−3.69560e86	−0.523355
$208$	−1.61564e86	−0.190972
$209$	2.36927e87	2.33953
$210$	4.25871e86	0.351605
$211$	−9.01151e86	−0.622595	−0.311298	−	0.950312i	$-0.600764\pi$
$211$	−9.01151e86	−0.622595	−0.311298	+	0.950312i	$0.600764\pi$
$212$	2.35142e86	0.136062
$213$	7.22926e86	0.350638
$214$	−2.84333e87	−1.15694
$215$	6.16839e86	0.210732
$216$	7.06046e86	0.202683
$217$	−9.01412e87	−2.17612
$218$	−4.64813e87	−0.944409
$219$	2.79579e87	0.478465
$220$	−4.68442e87	−0.675780
$221$	8.26827e87	1.00625
$222$	−1.35471e87	−0.139191
$223$	1.00986e87	0.0876656	0.0438328	−	0.999039i	$-0.486043\pi$
$223$	1.00986e87	0.0876656	0.0438328	+	0.999039i	$0.486043\pi$
$224$	−3.57712e87	−0.262562
$225$	−3.57476e87	−0.222026
$226$	5.93146e87	0.311957
$227$	5.18295e86	0.0230998	0.0115499	−	0.999933i	$-0.496323\pi$
$227$	5.18295e86	0.0230998	0.0115499	+	0.999933i	$0.496323\pi$
$228$	7.66625e87	0.289752
$229$	4.55134e88	1.45985	0.729925	−	0.683527i	$-0.239555\pi$
$229$	4.55134e88	1.45985	0.729925	+	0.683527i	$0.239555\pi$
$230$	1.66530e88	0.453625
$231$	2.33363e88	0.540234
$232$	−1.77390e87	−0.0349244
$233$	−6.25167e88	−1.04749	−0.523744	−	0.851876i	$-0.675465\pi$
$233$	−6.25167e88	−1.04749	−0.523744	+	0.851876i	$0.675465\pi$
$234$	−3.44434e88	−0.491486
$235$	2.76729e87	0.0336519
$236$	4.80324e88	0.498120
$237$	1.09986e88	0.0973363
$238$	1.83064e89	1.38346
$239$	−1.69479e89	−1.09445	−0.547224	−	0.836986i	$-0.684315\pi$
$239$	−1.69479e89	−1.09445	−0.547224	+	0.836986i	$0.684315\pi$
$240$	−1.51574e88	−0.0836956
$241$	−1.44127e89	−0.680935	−0.340468	−	0.940256i	$-0.610585\pi$
$241$	−1.44127e89	−0.680935	−0.340468	+	0.940256i	$0.610585\pi$
$242$	−8.18819e88	−0.331216
$243$	2.29330e89	0.794741
$244$	8.37190e88	0.248717
$245$	−5.27842e89	−1.34517
$246$	1.57123e89	0.343696
$247$	−7.85004e89	−1.47481
$248$	3.20826e89	0.518002
$249$	1.02146e89	0.141822
$250$	−4.99072e89	−0.596229
$251$	−6.87796e88	−0.0707449	−0.0353724	−	0.999374i	$-0.511262\pi$
$251$	−6.87796e88	−0.0707449	−0.0353724	+	0.999374i	$0.511262\pi$
$252$	−7.62594e89	−0.675730
$253$	9.12523e89	0.696986
$254$	1.02484e90	0.675139
$255$	7.75699e89	0.440998
$256$	1.27315e89	0.0625000
$257$	1.75243e90	0.743274	0.371637	−	0.928378i	$-0.378797\pi$
$257$	1.75243e90	0.743274	0.371637	+	0.928378i	$0.378797\pi$
$258$	1.09369e89	0.0401009
$259$	3.07131e90	0.974053
$260$	1.55208e90	0.426003
$261$	−3.78172e89	−0.0898815
$262$	−8.89429e89	−0.183153
$263$	3.94345e90	0.703940	0.351970	−	0.936011i	$-0.385512\pi$
$263$	3.94345e90	0.703940	0.351970	+	0.936011i	$0.385512\pi$
$264$	−8.30571e89	−0.128597
$265$	−2.25891e90	−0.303514
$266$	−1.73804e91	−2.02767
$267$	−1.11361e90	−0.112866
$268$	1.04374e90	0.0919467
$269$	9.52494e90	0.729713	0.364856	−	0.931064i	$-0.381118\pi$
$269$	9.52494e90	0.729713	0.364856	+	0.931064i	$0.381118\pi$
$270$	−6.78267e90	−0.452126
$271$	−1.59222e91	−0.923964	−0.461982	−	0.886889i	$-0.652862\pi$
$271$	−1.59222e91	−0.923964	−0.461982	+	0.886889i	$0.652862\pi$
$272$	−6.51550e90	−0.329317
$273$	−7.73193e90	−0.340556
$274$	2.42578e91	0.931548
$275$	8.82687e90	0.295686
$276$	2.95265e90	0.0863220
$277$	−7.34227e91	−1.87430	−0.937150	−	0.348927i	$-0.886546\pi$
$277$	−7.34227e91	−1.87430	−0.937150	+	0.348927i	$0.886546\pi$
$278$	−3.91149e91	−0.872293
$279$	6.83958e91	1.33313
$280$	3.43637e91	0.585699
$281$	1.16590e92	1.73850	0.869250	−	0.494372i	$-0.164602\pi$
$281$	1.16590e92	1.73850	0.869250	+	0.494372i	$0.164602\pi$
$282$	4.90654e89	0.00640374
$283$	3.13780e91	0.358620	0.179310	−	0.983793i	$-0.442614\pi$
$283$	3.13780e91	0.358620	0.179310	+	0.983793i	$0.442614\pi$
$284$	5.83332e91	0.584087
$285$	−7.36462e91	−0.646351
$286$	8.50483e91	0.654545
$287$	−3.56219e92	−2.40517
$288$	2.71418e91	0.160850
$289$	1.41277e92	0.735193
$290$	1.70410e91	0.0779061
$291$	1.38433e92	0.556227
$292$	2.25594e92	0.797021
$293$	2.09635e92	0.651521	0.325761	−	0.945452i	$-0.394380\pi$
$293$	2.09635e92	0.651521	0.325761	+	0.945452i	$0.394380\pi$
$294$	−9.35889e91	−0.255976
$295$	−4.61425e92	−1.11116
$296$	−1.09312e92	−0.231862
$297$	−3.71666e92	−0.694682
$298$	9.71287e91	0.160043
$299$	−3.02343e92	−0.439371
$300$	2.85611e91	0.0366208
$301$	−2.47953e92	−0.280624
$302$	−5.96435e92	−0.596077
$303$	−4.35617e92	−0.384597
$304$	6.18593e92	0.482665
$305$	−8.04251e92	−0.554814
$306$	−1.38902e93	−0.847530
$307$	1.65941e93	0.895909	0.447954	−	0.894056i	$-0.352153\pi$
$307$	1.65941e93	0.895909	0.447954	+	0.894056i	$0.352153\pi$
$308$	1.88301e93	0.899914
$309$	8.72787e92	0.369373
$310$	−3.08203e93	−1.15551
$311$	4.98043e93	1.65482	0.827412	−	0.561595i	$-0.189812\pi$
$311$	4.98043e93	1.65482	0.827412	+	0.561595i	$0.189812\pi$
$312$	2.75191e92	0.0810655
$313$	2.02107e93	0.528042	0.264021	−	0.964517i	$-0.414951\pi$
$313$	2.02107e93	0.528042	0.264021	+	0.964517i	$0.414951\pi$
$314$	−1.33493e93	−0.309453
$315$	7.32590e93	1.50735
$316$	8.87482e92	0.162141
$317$	−2.28903e93	−0.371474	−0.185737	−	0.982599i	$-0.559467\pi$
$317$	−2.28903e93	−0.371474	−0.185737	+	0.982599i	$0.559467\pi$
$318$	−4.00515e92	−0.0577567
$319$	9.33789e92	0.119701
$320$	−1.22306e93	−0.139419
$321$	4.84300e93	0.491107
$322$	−6.69404e93	−0.604078
$323$	−3.16573e94	−2.54319
$324$	5.15662e93	0.368916
$325$	−2.92458e93	−0.186396
$326$	−1.26763e94	−0.720000
$327$	7.91711e93	0.400891
$328$	1.26783e94	0.572523
$329$	−1.11238e93	−0.0448131
$330$	7.97892e93	0.286861
$331$	−1.52726e94	−0.490189	−0.245095	−	0.969499i	$-0.578819\pi$
$331$	−1.52726e94	−0.490189	−0.245095	+	0.969499i	$0.578819\pi$
$332$	8.24218e93	0.236246
$333$	−2.33040e94	−0.596721
$334$	−1.34949e94	−0.308801
$335$	−1.00267e94	−0.205106
$336$	6.09286e93	0.111455
$337$	9.97951e94	1.63301	0.816504	−	0.577340i	$-0.195909\pi$
$337$	9.97951e94	1.63301	0.816504	+	0.577340i	$0.195909\pi$
$338$	2.01117e94	0.294491
$339$	−1.01030e94	−0.132422
$340$	6.25915e94	0.734608
$341$	−1.68884e95	−1.77542
$342$	1.31876e95	1.24219
$343$	3.62494e94	0.306035
$344$	8.82499e93	0.0667994
$345$	−2.83648e94	−0.192559
$346$	−9.97123e94	−0.607288
$347$	2.32770e95	1.27225	0.636124	−	0.771587i	$-0.280537\pi$
$347$	2.32770e95	1.27225	0.636124	+	0.771587i	$0.280537\pi$
$348$	3.02146e93	0.0148250
$349$	−2.33241e94	−0.102766	−0.0513832	−	0.998679i	$-0.516363\pi$
$349$	−2.33241e94	−0.102766	−0.0513832	+	0.998679i	$0.516363\pi$
$350$	−6.47517e94	−0.256271
$351$	1.23143e95	0.437918
$352$	−6.70191e94	−0.214214
$353$	7.44966e94	0.214084	0.107042	−	0.994254i	$-0.465862\pi$
$353$	7.44966e94	0.214084	0.107042	+	0.994254i	$0.465862\pi$
$354$	−8.18130e94	−0.211446
$355$	−5.60380e95	−1.30293
$356$	−8.98579e94	−0.188010
$357$	−3.11810e95	−0.587262
$358$	1.51771e95	0.257381
$359$	−7.48180e95	−1.14278	−0.571392	−	0.820677i	$-0.693596\pi$
$359$	−7.48180e95	−1.14278	−0.571392	+	0.820677i	$0.693596\pi$
$360$	−2.60739e95	−0.358809
$361$	2.19926e96	2.72744
$362$	−9.54814e95	−1.06745
$363$	1.39468e95	0.140597
$364$	−6.23892e95	−0.567293
$365$	−2.16717e96	−1.77792
$366$	−1.42598e95	−0.105577
$367$	1.67474e96	1.11936	0.559679	−	0.828709i	$-0.310924\pi$
$367$	1.67474e96	1.11936	0.559679	+	0.828709i	$0.310924\pi$
$368$	2.38250e95	0.143794
$369$	2.70286e96	1.47345
$370$	1.05011e96	0.517216
$371$	9.08020e95	0.404179
$372$	−5.46459e95	−0.219886
$373$	−2.86578e95	−0.104271	−0.0521353	−	0.998640i	$-0.516603\pi$
$373$	−2.86578e95	−0.104271	−0.0521353	+	0.998640i	$0.516603\pi$
$374$	3.42979e96	1.12871
$375$	8.50064e95	0.253092
$376$	3.95911e94	0.0106673
$377$	−3.09389e95	−0.0754579
$378$	2.72645e96	0.602081
$379$	7.13865e95	0.142773	0.0713864	−	0.997449i	$-0.477258\pi$
$379$	7.13865e95	0.142773	0.0713864	+	0.997449i	$0.477258\pi$
$380$	−5.94254e96	−1.07668
$381$	−1.74560e96	−0.286589
$382$	−3.67108e96	−0.546283
$383$	−8.66283e96	−1.16871	−0.584354	−	0.811499i	$-0.698652\pi$
$383$	−8.66283e96	−1.16871	−0.584354	+	0.811499i	$0.698652\pi$
$384$	−2.16854e95	−0.0265305
$385$	−1.80892e97	−2.00744
$386$	8.95903e96	0.902064
$387$	1.88137e96	0.171915
$388$	1.11702e97	0.926555
$389$	8.40472e96	0.633014	0.316507	−	0.948590i	$-0.397490\pi$
$389$	8.40472e96	0.633014	0.316507	+	0.948590i	$0.397490\pi$
$390$	−2.64363e96	−0.180833
$391$	−1.21928e97	−0.757660
$392$	−7.55173e96	−0.426402
$393$	1.51495e96	0.0777461
$394$	2.01499e97	0.940079
$395$	−8.52564e96	−0.361690
$396$	−1.42876e97	−0.551302
$397$	−1.13061e97	−0.396888	−0.198444	−	0.980112i	$-0.563589\pi$
$397$	−1.13061e97	−0.396888	−0.198444	+	0.980112i	$0.563589\pi$
$398$	1.31368e97	0.419638
$399$	2.96038e97	0.860723
$400$	2.30461e96	0.0610024
$401$	3.77325e97	0.909497	0.454748	−	0.890620i	$-0.349729\pi$
$401$	3.77325e97	0.909497	0.454748	+	0.890620i	$0.349729\pi$
$402$	−1.77778e96	−0.0390303
$403$	5.59559e97	1.11920
$404$	−3.51501e97	−0.640657
$405$	−4.95373e97	−0.822942
$406$	−6.85004e96	−0.103745
$407$	5.75426e97	0.794692
$408$	1.10978e97	0.139791
$409$	6.54095e96	0.0751652	0.0375826	−	0.999294i	$-0.488034\pi$
$409$	6.54095e96	0.0751652	0.0375826	+	0.999294i	$0.488034\pi$
$410$	−1.21795e98	−1.27713
$411$	−4.13180e97	−0.395431
$412$	7.04255e97	0.615297
$413$	1.85481e98	1.47969
$414$	5.07919e97	0.370068
$415$	−7.91789e97	−0.526994
$416$	2.22052e97	0.135038
$417$	6.66239e97	0.370278
$418$	−3.25630e98	−1.65430
$419$	−4.13523e98	−1.92076	−0.960381	−	0.278691i	$-0.910100\pi$
$419$	−4.13523e98	−1.92076	−0.960381	+	0.278691i	$0.910100\pi$
$420$	−5.85313e97	−0.248622
$421$	−1.03586e97	−0.0402459	−0.0201230	−	0.999798i	$-0.506406\pi$
$421$	−1.03586e97	−0.0402459	−0.0201230	+	0.999798i	$0.506406\pi$
$422$	1.23853e98	0.440241
$423$	8.44030e96	0.0274533
$424$	−3.23177e97	−0.0962102
$425$	−1.17941e98	−0.321426
$426$	−9.93581e97	−0.247938
$427$	3.23287e98	0.738827
$428$	3.90784e98	0.818079
$429$	−1.44862e98	−0.277847
$430$	−8.47777e97	−0.149010
$431$	5.93011e98	0.955356	0.477678	−	0.878535i	$-0.341478\pi$
$431$	5.93011e98	0.955356	0.477678	+	0.878535i	$0.341478\pi$
$432$	−9.70383e97	−0.143319
$433$	−7.12665e98	−0.965138	−0.482569	−	0.875858i	$-0.660296\pi$
$433$	−7.12665e98	−0.965138	−0.482569	+	0.875858i	$0.660296\pi$
$434$	1.23889e99	1.53875
$435$	−2.90258e97	−0.0330702
$436$	6.38835e98	0.667798
$437$	1.15760e99	1.11047
$438$	−3.84251e98	−0.338326
$439$	3.83531e98	0.310013	0.155007	−	0.987913i	$-0.450460\pi$
$439$	3.83531e98	0.310013	0.155007	+	0.987913i	$0.450460\pi$
$440$	6.43822e98	0.477849
$441$	−1.60993e99	−1.09739
$442$	−1.13638e99	−0.711524
$443$	−5.22470e98	−0.300554	−0.150277	−	0.988644i	$-0.548016\pi$
$443$	−5.22470e98	−0.300554	−0.150277	+	0.988644i	$0.548016\pi$
$444$	1.86190e98	0.0984229
$445$	8.63224e98	0.419395
$446$	−1.38794e98	−0.0619889
$447$	−1.65438e98	−0.0679365
$448$	4.91635e98	0.185660
$449$	−4.57980e99	−1.59077	−0.795387	−	0.606102i	$-0.792732\pi$
$449$	−4.57980e99	−1.59077	−0.795387	+	0.606102i	$0.792732\pi$
$450$	4.91312e98	0.156996
$451$	−6.67394e99	−1.96228
$452$	−8.15213e98	−0.220587
$453$	1.01590e99	0.253028
$454$	−7.12339e97	−0.0163340
$455$	5.99345e99	1.26546
$456$	−1.05364e99	−0.204886
$457$	6.91435e99	1.23849	0.619247	−	0.785196i	$-0.287438\pi$
$457$	6.91435e99	1.23849	0.619247	+	0.785196i	$0.287438\pi$
$458$	−6.25531e99	−1.03227
$459$	4.96606e99	0.755156
$460$	−2.28876e99	−0.320762
$461$	3.33907e99	0.431361	0.215681	−	0.976464i	$-0.430803\pi$
$461$	3.33907e99	0.431361	0.215681	+	0.976464i	$0.430803\pi$
$462$	−3.20731e99	−0.382003
$463$	1.14582e99	0.125843	0.0629216	−	0.998018i	$-0.479958\pi$
$463$	1.14582e99	0.125843	0.0629216	+	0.998018i	$0.479958\pi$
$464$	2.43803e98	0.0246953
$465$	5.24958e99	0.490500
$466$	8.59223e99	0.740686
$467$	−5.20506e99	−0.414040	−0.207020	−	0.978337i	$-0.566377\pi$
$467$	−5.20506e99	−0.414040	−0.207020	+	0.978337i	$0.566377\pi$
$468$	4.73387e99	0.347533
$469$	4.03046e99	0.273132
$470$	−3.80334e98	−0.0237955
$471$	2.27376e99	0.131359
$472$	−6.60152e99	−0.352224
$473$	−4.64552e99	−0.228950
$474$	−1.51164e99	−0.0688272
$475$	1.11975e100	0.471099
$476$	−2.51601e100	−0.978253
$477$	−6.88972e99	−0.247607
$478$	2.32930e100	0.773892
$479$	2.12255e100	0.652044	0.326022	−	0.945362i	$-0.394292\pi$
$479$	2.12255e100	0.652044	0.326022	+	0.945362i	$0.394292\pi$
$480$	2.08322e99	0.0591817
$481$	−1.90654e100	−0.500963
$482$	1.98086e100	0.481494
$483$	1.14019e100	0.256424
$484$	1.12538e100	0.234205
$485$	−1.07307e101	−2.06687
$486$	−3.15189e100	−0.561967
$487$	−7.08629e100	−1.16972	−0.584862	−	0.811133i	$-0.698851\pi$
$487$	−7.08629e100	−1.16972	−0.584862	+	0.811133i	$0.698851\pi$
$488$	−1.15063e100	−0.175869
$489$	2.15914e100	0.305632
$490$	7.25460e100	0.951176
$491$	−1.05933e101	−1.28669	−0.643345	−	0.765576i	$-0.722454\pi$
$491$	−1.05933e101	−1.28669	−0.643345	+	0.765576i	$0.722454\pi$
$492$	−2.15949e100	−0.243030
$493$	−1.24769e100	−0.130121
$494$	1.07890e101	1.04285
$495$	1.37254e101	1.22979
$496$	−4.40940e100	−0.366282
$497$	2.25258e101	1.73506
$498$	−1.40388e100	−0.100284
$499$	−2.03829e101	−1.35050	−0.675251	−	0.737588i	$-0.735965\pi$
$499$	−2.03829e101	−1.35050	−0.675251	+	0.737588i	$0.735965\pi$
$500$	6.85920e100	0.421598
$501$	2.29858e100	0.131082
$502$	9.45299e99	0.0500242
$503$	1.51580e101	0.744461	0.372230	−	0.928140i	$-0.378593\pi$
$503$	1.51580e101	0.744461	0.372230	+	0.928140i	$0.378593\pi$
$504$	1.04810e101	0.477813
$505$	3.37671e101	1.42912
$506$	−1.25416e101	−0.492844
$507$	−3.42560e100	−0.125008
$508$	−1.40853e101	−0.477395
$509$	−4.29845e101	−1.35330	−0.676651	−	0.736304i	$-0.736569\pi$
$509$	−4.29845e101	−1.35330	−0.676651	+	0.736304i	$0.736569\pi$
$510$	−1.06611e101	−0.311833
$511$	8.71145e101	2.36759
$512$	−1.74980e100	−0.0441942
$513$	−4.71486e101	−1.10680
$514$	−2.40852e101	−0.525574
$515$	−6.76546e101	−1.37254
$516$	−1.50315e100	−0.0283556
$517$	−2.08409e100	−0.0365613
$518$	−4.22118e101	−0.688759
$519$	1.69839e101	0.257787
$520$	−2.13316e101	−0.301229
$521$	−6.15408e101	−0.808627	−0.404314	−	0.914620i	$-0.632490\pi$
$521$	−6.15408e101	−0.808627	−0.404314	+	0.914620i	$0.632490\pi$
$522$	5.19756e100	0.0635558
$523$	6.23640e101	0.709774	0.354887	−	0.934909i	$-0.384519\pi$
$523$	6.23640e101	0.709774	0.354887	+	0.934909i	$0.384519\pi$
$524$	1.22242e101	0.129508
$525$	1.10291e101	0.108784
$526$	−5.41984e101	−0.497761
$527$	2.25657e102	1.92997
$528$	1.14153e101	0.0909315
$529$	−9.01833e101	−0.669173
$530$	3.10462e101	0.214617
$531$	−1.40736e102	−0.906484
$532$	2.38874e102	1.43378
$533$	2.21126e102	1.23700
$534$	1.53054e101	0.0798081
$535$	−3.75408e102	−1.82489
$536$	−1.43450e101	−0.0650161
$537$	−2.58510e101	−0.109255
$538$	−1.30910e102	−0.515985
$539$	3.97527e102	1.46146
$540$	9.32203e101	0.319701
$541$	1.38899e102	0.444429	0.222215	−	0.974998i	$-0.428671\pi$
$541$	1.38899e102	0.444429	0.222215	+	0.974998i	$0.428671\pi$
$542$	2.18833e102	0.653342
$543$	1.62632e102	0.453120
$544$	8.95484e101	0.232862
$545$	−6.13700e102	−1.48966
$546$	1.06267e102	0.240809
$547$	−5.66887e102	−1.19942	−0.599710	−	0.800217i	$-0.704718\pi$
$547$	−5.66887e102	−1.19942	−0.599710	+	0.800217i	$0.704718\pi$
$548$	−3.33397e102	−0.658704
$549$	−2.45298e102	−0.452618
$550$	−1.21316e102	−0.209082
$551$	1.18458e102	0.190713
$552$	−4.05809e101	−0.0610389
$553$	3.42708e102	0.481650
$554$	1.00911e103	1.32533
$555$	−1.78865e102	−0.219552
$556$	5.37591e102	0.616804
$557$	−1.16837e103	−1.25317	−0.626584	−	0.779354i	$-0.715547\pi$
$557$	−1.16837e103	−1.25317	−0.626584	+	0.779354i	$0.715547\pi$
$558$	−9.40025e102	−0.942664
$559$	1.53919e102	0.144327
$560$	−4.72292e102	−0.414151
$561$	−5.84192e102	−0.479125
$562$	−1.60240e103	−1.22931
$563$	1.54821e103	1.11113	0.555564	−	0.831474i	$-0.312502\pi$
$563$	1.54821e103	1.11113	0.555564	+	0.831474i	$0.312502\pi$
$564$	−6.74350e100	−0.00452813
$565$	7.83139e102	0.492064
$566$	−4.31256e102	−0.253582
$567$	1.99127e103	1.09588
$568$	−8.01725e102	−0.413012
$569$	−5.94072e102	−0.286503	−0.143251	−	0.989686i	$-0.545756\pi$
$569$	−5.94072e102	−0.286503	−0.143251	+	0.989686i	$0.545756\pi$
$570$	1.01219e103	0.457039
$571$	3.83869e103	1.62304	0.811520	−	0.584325i	$-0.198641\pi$
$571$	3.83869e103	1.62304	0.811520	+	0.584325i	$0.198641\pi$
$572$	−1.16889e103	−0.462833
$573$	6.25290e102	0.231891
$574$	4.89583e103	1.70071
$575$	4.31273e102	0.140348
$576$	−3.73035e102	−0.113738
$577$	−1.06097e103	−0.303118	−0.151559	−	0.988448i	$-0.548429\pi$
$577$	−1.06097e103	−0.303118	−0.151559	+	0.988448i	$0.548429\pi$
$578$	−1.94169e103	−0.519860
$579$	−1.52598e103	−0.382916
$580$	−2.34210e102	−0.0550879
$581$	3.18278e103	0.701781
$582$	−1.90261e103	−0.393312
$583$	1.70122e103	0.329754
$584$	−3.10053e103	−0.563579
$585$	−4.54761e103	−0.775244
$586$	−2.88121e103	−0.460695
$587$	1.36349e103	0.204514	0.102257	−	0.994758i	$-0.467394\pi$
$587$	1.36349e103	0.204514	0.102257	+	0.994758i	$0.467394\pi$
$588$	1.28628e103	0.181003
$589$	−2.14242e104	−2.82867
$590$	6.34178e103	0.785708
$591$	−3.43211e103	−0.399053
$592$	1.50238e103	0.163951
$593$	−1.19973e104	−1.22894	−0.614472	−	0.788939i	$-0.710631\pi$
$593$	−1.19973e104	−1.22894	−0.614472	+	0.788939i	$0.710631\pi$
$594$	5.10814e103	0.491215
$595$	2.41701e104	2.18219
$596$	−1.33493e103	−0.113168
$597$	−2.23758e103	−0.178131
$598$	4.15538e103	0.310682
$599$	−1.21229e104	−0.851336	−0.425668	−	0.904879i	$-0.639961\pi$
$599$	−1.21229e104	−0.851336	−0.425668	+	0.904879i	$0.639961\pi$
$600$	−3.92541e102	−0.0258948
$601$	1.83221e104	1.13549	0.567743	−	0.823206i	$-0.307817\pi$
$601$	1.83221e104	1.13549	0.567743	+	0.823206i	$0.307817\pi$
$602$	3.40783e103	0.198431
$603$	−3.05817e103	−0.167325
$604$	8.19733e103	0.421490
$605$	−1.08110e104	−0.522443
$606$	5.98708e103	0.271951
$607$	2.48994e104	1.06319	0.531597	−	0.846997i	$-0.321592\pi$
$607$	2.48994e104	1.06319	0.531597	+	0.846997i	$0.321592\pi$
$608$	−8.50187e103	−0.341295
$609$	1.16676e103	0.0440385
$610$	1.10535e104	0.392313
$611$	6.90516e102	0.0230478
$612$	1.90905e104	0.599294
$613$	−2.47190e104	−0.729900	−0.364950	−	0.931027i	$-0.618914\pi$
$613$	−2.47190e104	−0.729900	−0.364950	+	0.931027i	$0.618914\pi$
$614$	−2.28067e104	−0.633503
$615$	2.07452e104	0.542127
$616$	−2.58799e104	−0.636335
$617$	−1.26589e104	−0.292888	−0.146444	−	0.989219i	$-0.546783\pi$
$617$	−1.26589e104	−0.292888	−0.146444	+	0.989219i	$0.546783\pi$
$618$	−1.19955e104	−0.261186
$619$	8.28090e104	1.69699	0.848493	−	0.529207i	$-0.177510\pi$
$619$	8.28090e104	1.69699	0.848493	+	0.529207i	$0.177510\pi$
$620$	4.23591e104	0.817068
$621$	−1.81593e104	−0.329734
$622$	−6.84504e104	−1.17014
$623$	−3.46993e104	−0.558494
$624$	−3.78219e103	−0.0573220
$625$	−8.29897e104	−1.18447
$626$	−2.77774e104	−0.373382
$627$	5.54642e104	0.702231
$628$	1.83471e104	0.218817
$629$	−7.68862e104	−0.863872
$630$	−1.00686e105	−1.06586
$631$	1.72661e105	1.72224	0.861121	−	0.508400i	$-0.169763\pi$
$631$	1.72661e105	1.72224	0.861121	+	0.508400i	$0.169763\pi$
$632$	−1.21975e104	−0.114651
$633$	−2.10958e104	−0.186877
$634$	3.14602e104	0.262672
$635$	1.35312e105	1.06493
$636$	5.50464e103	0.0408401
$637$	−1.31711e105	−0.921286
$638$	−1.28339e104	−0.0846415
$639$	−1.70917e105	−1.06293
$640$	1.68095e104	0.0985841
$641$	−8.09929e104	−0.447993	−0.223996	−	0.974590i	$-0.571910\pi$
$641$	−8.09929e104	−0.447993	−0.223996	+	0.974590i	$0.571910\pi$
$642$	−6.65617e104	−0.347265
$643$	1.88945e105	0.929871	0.464936	−	0.885344i	$-0.346077\pi$
$643$	1.88945e105	0.929871	0.464936	+	0.885344i	$0.346077\pi$
$644$	9.20021e104	0.427147
$645$	1.44401e104	0.0632529
$646$	4.35095e105	1.79831
$647$	1.45945e105	0.569218	0.284609	−	0.958644i	$-0.408136\pi$
$647$	1.45945e105	0.569218	0.284609	+	0.958644i	$0.408136\pi$
$648$	−7.08720e104	−0.260863
$649$	3.47507e105	1.20722
$650$	4.01951e104	0.131802
$651$	−2.11019e105	−0.653182
$652$	1.74222e105	0.509117
$653$	−2.34661e104	−0.0647434	−0.0323717	−	0.999476i	$-0.510306\pi$
$653$	−2.34661e104	−0.0647434	−0.0323717	+	0.999476i	$0.510306\pi$
$654$	−1.08812e105	−0.283472
$655$	−1.17433e105	−0.288895
$656$	−1.74250e105	−0.404835
$657$	−6.60993e105	−1.45043
$658$	1.52884e104	0.0316877
$659$	6.84889e105	1.34096	0.670482	−	0.741926i	$-0.266088\pi$
$659$	6.84889e105	1.34096	0.670482	+	0.741926i	$0.266088\pi$
$660$	−1.09661e105	−0.202841
$661$	−4.21542e105	−0.736692	−0.368346	−	0.929689i	$-0.620076\pi$
$661$	−4.21542e105	−0.736692	−0.368346	+	0.929689i	$0.620076\pi$
$662$	2.09905e105	0.346616
$663$	1.93559e105	0.302034
$664$	−1.13280e105	−0.167051
$665$	−2.29475e106	−3.19834
$666$	3.20287e105	0.421945
$667$	4.56240e104	0.0568166
$668$	1.85473e105	0.218355
$669$	2.36406e104	0.0263136
$670$	1.37806e105	0.145032
$671$	6.05695e105	0.602781
$672$	−8.37396e104	−0.0788103
$673$	−4.29679e105	−0.382454	−0.191227	−	0.981546i	$-0.561247\pi$
$673$	−4.29679e105	−0.382454	−0.191227	+	0.981546i	$0.561247\pi$
$674$	−1.37157e106	−1.15471
$675$	−1.75655e105	−0.139885
$676$	−2.76413e105	−0.208237
$677$	1.94401e106	1.38556	0.692778	−	0.721151i	$-0.256387\pi$
$677$	1.94401e106	1.38556	0.692778	+	0.721151i	$0.256387\pi$
$678$	1.38854e105	0.0936366
$679$	4.31345e106	2.75238
$680$	−8.60251e105	−0.519446
$681$	1.21332e104	0.00693359
$682$	2.32113e106	1.25541
$683$	−1.98673e106	−1.01710	−0.508549	−	0.861033i	$-0.669818\pi$
$683$	−1.98673e106	−1.01710	−0.508549	+	0.861033i	$0.669818\pi$
$684$	−1.81249e106	−0.878358
$685$	3.20279e106	1.46937
$686$	−4.98208e105	−0.216400
$687$	1.06546e106	0.438187
$688$	−1.21290e105	−0.0472343
$689$	−5.63661e105	−0.207872
$690$	3.89842e105	0.136160
$691$	3.84764e104	0.0127282	0.00636411	−	0.999980i	$-0.497974\pi$
$691$	3.84764e104	0.0127282	0.00636411	+	0.999980i	$0.497974\pi$
$692$	1.37043e106	0.429418
$693$	−5.51726e106	−1.63767
$694$	−3.19917e106	−0.899615
$695$	−5.16439e106	−1.37591
$696$	−4.15266e104	−0.0104829
$697$	8.91746e106	2.13310
$698$	3.20564e105	0.0726668
$699$	−1.46350e106	−0.314413
$700$	8.89940e105	0.181211
$701$	−2.49842e106	−0.482215	−0.241107	−	0.970498i	$-0.577511\pi$
$701$	−2.49842e106	−0.482215	−0.241107	+	0.970498i	$0.577511\pi$
$702$	−1.69247e106	−0.309655
$703$	7.29971e106	1.26614
$704$	9.21104e105	0.151472
$705$	6.47818e104	0.0101009
$706$	−1.02387e106	−0.151380
$707$	−1.35735e107	−1.90311
$708$	1.12443e106	0.149515
$709$	−1.00825e107	−1.27155	−0.635775	−	0.771874i	$-0.719319\pi$
$709$	−1.00825e107	−1.27155	−0.635775	+	0.771874i	$0.719319\pi$
$710$	7.70181e106	0.921307
$711$	−2.60034e106	−0.295067
$712$	1.23500e106	0.132943
$713$	−8.25152e106	−0.842707
$714$	4.28548e106	0.415257
$715$	1.12290e107	1.03244
$716$	−2.08593e106	−0.181996
$717$	−3.96748e106	−0.328508
$718$	1.02829e107	0.808070
$719$	1.87927e106	0.140170	0.0700852	−	0.997541i	$-0.477673\pi$
$719$	1.87927e106	0.140170	0.0700852	+	0.997541i	$0.477673\pi$
$720$	3.58357e106	0.253716
$721$	2.71953e107	1.82777
$722$	−3.02263e107	−1.92859
$723$	−3.37398e106	−0.204389
$724$	1.31229e107	0.754800
$725$	4.41323e105	0.0241036
$726$	−1.91684e106	−0.0994174
$727$	1.10710e106	0.0545313	0.0272656	−	0.999628i	$-0.491320\pi$
$727$	1.10710e106	0.0545313	0.0272656	+	0.999628i	$0.491320\pi$
$728$	8.57471e106	0.401137
$729$	−1.12365e107	−0.499283
$730$	2.97854e107	1.25718
$731$	6.20717e106	0.248881
$732$	1.95985e106	0.0746546
$733$	3.73162e107	1.35051	0.675256	−	0.737584i	$-0.264033\pi$
$733$	3.73162e107	1.35051	0.675256	+	0.737584i	$0.264033\pi$
$734$	−2.30174e107	−0.791506
$735$	−1.23567e107	−0.403763
$736$	−3.27449e106	−0.101678
$737$	7.55128e106	0.222838
$738$	−3.71478e107	−1.04188
$739$	−8.06051e106	−0.214880	−0.107440	−	0.994212i	$-0.534265\pi$
$739$	−8.06051e106	−0.214880	−0.107440	+	0.994212i	$0.534265\pi$
$740$	−1.44327e107	−0.365727
$741$	−1.83768e107	−0.442677
$742$	−1.24797e107	−0.285798
$743$	−6.15321e107	−1.33974	−0.669871	−	0.742478i	$-0.733651\pi$
$743$	−6.15321e107	−1.33974	−0.669871	+	0.742478i	$0.733651\pi$
$744$	7.51047e106	0.155483
$745$	1.28240e107	0.252444
$746$	3.93870e106	0.0737304
$747$	−2.41497e107	−0.429922
$748$	−4.71387e107	−0.798119
$749$	1.50904e108	2.43015
$750$	−1.16832e107	−0.178963
$751$	−9.45611e107	−1.37789	−0.688945	−	0.724813i	$-0.741926\pi$
$751$	−9.45611e107	−1.37789	−0.688945	+	0.724813i	$0.741926\pi$
$752$	−5.44136e105	−0.00754290
$753$	−1.61012e106	−0.0212347
$754$	4.25222e106	0.0533568
$755$	−7.87481e107	−0.940220
$756$	−3.74720e107	−0.425735
$757$	1.13470e108	1.22683	0.613417	−	0.789759i	$-0.289795\pi$
$757$	1.13470e108	1.22683	0.613417	+	0.789759i	$0.289795\pi$
$758$	−9.81128e106	−0.100956
$759$	2.13620e107	0.209206
$760$	8.16737e107	0.761329
$761$	1.13592e108	1.00791	0.503957	−	0.863729i	$-0.331877\pi$
$761$	1.13592e108	1.00791	0.503957	+	0.863729i	$0.331877\pi$
$762$	2.39914e107	0.202649
$763$	2.46691e108	1.98373
$764$	5.04549e107	0.386280
$765$	−1.83394e108	−1.33685
$766$	1.19061e108	0.826401
$767$	−1.15139e108	−0.761017
$768$	2.98041e106	0.0187599
$769$	−2.13399e108	−1.27925	−0.639623	−	0.768689i	$-0.720909\pi$
$769$	−2.13399e108	−1.27925	−0.639623	+	0.768689i	$0.720909\pi$
$770$	2.48617e108	1.41948
$771$	4.10241e107	0.223100
$772$	−1.23132e108	−0.637855
$773$	1.55049e108	0.765134	0.382567	−	0.923928i	$-0.375040\pi$
$773$	1.55049e108	0.765134	0.382567	+	0.923928i	$0.375040\pi$
$774$	−2.58574e107	−0.121562
$775$	−7.98173e107	−0.357506
$776$	−1.53522e108	−0.655173
$777$	7.18988e107	0.292370
$778$	−1.15514e108	−0.447609
$779$	−8.46639e108	−3.12639
$780$	3.63338e107	0.127868
$781$	4.22032e108	1.41557
$782$	1.67576e108	0.535747
$783$	−1.85825e107	−0.0566287
$784$	1.03790e108	0.301511
$785$	−1.76252e108	−0.488115
$786$	−2.08214e107	−0.0549748
$787$	8.85011e107	0.222790	0.111395	−	0.993776i	$-0.464468\pi$
$787$	8.85011e107	0.222790	0.111395	+	0.993776i	$0.464468\pi$
$788$	−2.76938e108	−0.664736
$789$	9.23154e107	0.211294
$790$	1.17176e108	0.255753
$791$	−3.14800e108	−0.655265
$792$	1.96367e108	0.389830
$793$	−2.00683e108	−0.379985
$794$	1.55389e108	0.280642
$795$	−5.28806e107	−0.0911022
$796$	−1.80551e108	−0.296729
$797$	7.03968e108	1.10374	0.551869	−	0.833931i	$-0.313915\pi$
$797$	7.03968e108	1.10374	0.551869	+	0.833931i	$0.313915\pi$
$798$	−4.06871e108	−0.608623
$799$	2.78469e107	0.0397440
$800$	−3.16743e107	−0.0431352
$801$	2.63285e108	0.342143
$802$	−5.18591e108	−0.643111
$803$	1.63214e109	1.93163
$804$	2.44337e107	0.0275986
$805$	−8.83823e108	−0.952839
$806$	−7.69052e108	−0.791392
$807$	2.22977e108	0.219030
$808$	4.83099e108	0.453013
$809$	2.01497e109	1.80384	0.901922	−	0.431898i	$-0.142156\pi$
$809$	2.01497e109	1.80384	0.901922	+	0.431898i	$0.142156\pi$
$810$	6.80836e108	0.581908
$811$	−1.40522e108	−0.114673	−0.0573367	−	0.998355i	$-0.518261\pi$
$811$	−1.40522e108	−0.114673	−0.0573367	+	0.998355i	$0.518261\pi$
$812$	9.41462e107	0.0733587
$813$	−3.72736e108	−0.277336
$814$	−7.90859e108	−0.561932
$815$	−1.67367e109	−1.13569
$816$	−1.52527e108	−0.0988473
$817$	−5.89319e108	−0.364773
$818$	−8.98982e107	−0.0531499
$819$	1.82802e109	1.03237
$820$	1.67394e109	0.903067
$821$	2.78665e108	0.143620	0.0718099	−	0.997418i	$-0.477123\pi$
$821$	2.78665e108	0.143620	0.0718099	+	0.997418i	$0.477123\pi$
$822$	5.67870e108	0.279612
$823$	1.38696e109	0.652484	0.326242	−	0.945286i	$-0.394217\pi$
$823$	1.38696e109	0.652484	0.326242	+	0.945286i	$0.394217\pi$
$824$	−9.67921e108	−0.435080
$825$	2.06635e108	0.0887527
$826$	−2.54922e109	−1.04630
$827$	−3.84504e109	−1.50815	−0.754074	−	0.656789i	$-0.771914\pi$
$827$	−3.84504e109	−1.50815	−0.754074	+	0.656789i	$0.771914\pi$
$828$	−6.98078e108	−0.261678
$829$	−3.47676e109	−1.24560	−0.622802	−	0.782380i	$-0.714006\pi$
$829$	−3.47676e109	−1.24560	−0.622802	+	0.782380i	$0.714006\pi$
$830$	1.08823e109	0.372641
$831$	−1.71881e109	−0.562587
$832$	−3.05186e108	−0.0954862
$833$	−5.31160e109	−1.58868
$834$	−9.15672e108	−0.261826
$835$	−1.78175e109	−0.487085
$836$	4.47543e109	1.16977
$837$	3.36081e109	0.839921
$838$	5.68341e109	1.35818
$839$	5.66847e109	1.29536	0.647682	−	0.761911i	$-0.275738\pi$
$839$	5.66847e109	1.29536	0.647682	+	0.761911i	$0.275738\pi$
$840$	8.04448e108	0.175802
$841$	−4.73796e109	−0.990242
$842$	1.42367e108	0.0284582
$843$	2.72935e109	0.521826
$844$	−1.70223e109	−0.311298
$845$	2.65537e109	0.464514
$846$	−1.16003e108	−0.0194124
$847$	4.34572e109	0.695719
$848$	4.44172e108	0.0680309
$849$	7.34553e108	0.107643
$850$	1.62097e109	0.227283
$851$	2.81148e109	0.377204
$852$	1.36557e109	0.175319
$853$	−8.91072e109	−1.09477	−0.547387	−	0.836880i	$-0.684377\pi$
$853$	−8.91072e109	−1.09477	−0.547387	+	0.836880i	$0.684377\pi$
$854$	−4.44322e109	−0.522430
$855$	1.74118e110	1.95936
$856$	−5.37089e109	−0.578469
$857$	1.18796e110	1.22468	0.612339	−	0.790595i	$-0.290229\pi$
$857$	1.18796e110	1.22468	0.612339	+	0.790595i	$0.290229\pi$
$858$	1.99096e109	0.196467
$859$	−1.68692e110	−1.59349	−0.796746	−	0.604315i	$-0.793447\pi$
$859$	−1.68692e110	−1.59349	−0.796746	+	0.604315i	$0.793447\pi$
$860$	1.16518e109	0.105366
$861$	−8.33901e109	−0.721932
$862$	−8.15029e109	−0.675539
$863$	3.33632e109	0.264766	0.132383	−	0.991199i	$-0.457737\pi$
$863$	3.33632e109	0.264766	0.132383	+	0.991199i	$0.457737\pi$
$864$	1.33368e109	0.101342
$865$	−1.31651e110	−0.957904
$866$	9.79480e109	0.682456
$867$	3.30726e109	0.220675
$868$	−1.70272e110	−1.08806
$869$	6.42081e109	0.392960
$870$	3.98928e108	0.0233842
$871$	−2.50194e109	−0.140474
$872$	−8.78008e109	−0.472204
$873$	−3.27289e110	−1.68615
$874$	−1.59100e110	−0.785219
$875$	2.64873e110	1.25238
$876$	5.28110e109	0.239233
$877$	1.31977e110	0.572812	0.286406	−	0.958108i	$-0.407539\pi$
$877$	1.31977e110	0.572812	0.286406	+	0.958108i	$0.407539\pi$
$878$	−5.27120e109	−0.219213
$879$	4.90752e109	0.195560
$880$	−8.84863e109	−0.337890
$881$	1.61344e110	0.590414	0.295207	−	0.955433i	$-0.404611\pi$
$881$	1.61344e110	0.590414	0.295207	+	0.955433i	$0.404611\pi$
$882$	2.21267e110	0.775970
$883$	1.17397e110	0.394575	0.197287	−	0.980346i	$-0.436787\pi$
$883$	1.17397e110	0.394575	0.197287	+	0.980346i	$0.436787\pi$
$884$	1.56183e110	0.503123
$885$	−1.08019e110	−0.333524
$886$	7.18078e109	0.212523
$887$	1.78691e110	0.506953	0.253476	−	0.967342i	$-0.418426\pi$
$887$	1.78691e110	0.506953	0.253476	+	0.967342i	$0.418426\pi$
$888$	−2.55898e109	−0.0695955
$889$	−5.43916e110	−1.41813
$890$	−1.18641e110	−0.296557
$891$	3.73074e110	0.894089
$892$	1.90757e109	0.0438328
$893$	−2.64383e109	−0.0582510
$894$	2.27376e109	0.0480384
$895$	2.00386e110	0.405979
$896$	−6.75698e109	−0.131281
$897$	−7.07780e109	−0.131881
$898$	6.29442e110	1.12485
$899$	−8.44382e109	−0.144727
$900$	−6.75254e109	−0.111013
$901$	−2.27311e110	−0.358460
$902$	9.17259e110	1.38754
$903$	−5.80452e109	−0.0842318
$904$	1.12042e110	0.155979
$905$	−1.26065e111	−1.68374
$906$	−1.39624e110	−0.178918
$907$	−2.41470e110	−0.296886	−0.148443	−	0.988921i	$-0.547426\pi$
$907$	−2.41470e110	−0.296886	−0.148443	+	0.988921i	$0.547426\pi$
$908$	9.79031e108	0.0115499
$909$	1.02990e111	1.16587
$910$	−8.23734e110	−0.894818
$911$	−5.30089e110	−0.552598	−0.276299	−	0.961072i	$-0.589108\pi$
$911$	−5.30089e110	−0.552598	−0.276299	+	0.961072i	$0.589108\pi$
$912$	1.44811e110	0.144876
$913$	5.96310e110	0.572556
$914$	−9.50302e110	−0.875748
$915$	−1.88274e110	−0.166532
$916$	8.59723e110	0.729925
$917$	4.72047e110	0.384711
$918$	−6.82530e110	−0.533976
$919$	−2.05092e111	−1.54034	−0.770169	−	0.637840i	$-0.779828\pi$
$919$	−2.05092e111	−1.54034	−0.770169	+	0.637840i	$0.779828\pi$
$920$	3.14565e110	0.226813
$921$	3.88464e110	0.268915
$922$	−4.58919e110	−0.305019
$923$	−1.39831e111	−0.892356
$924$	4.40809e110	0.270117
$925$	2.71955e110	0.160023
$926$	−1.57480e110	−0.0889845
$927$	−2.06348e111	−1.11972
$928$	−3.35080e109	−0.0174622
$929$	6.67135e110	0.333906	0.166953	−	0.985965i	$-0.446607\pi$
$929$	6.67135e110	0.333906	0.166953	+	0.985965i	$0.446607\pi$
$930$	−7.21497e110	−0.346836
$931$	5.04292e111	2.32846
$932$	−1.18091e111	−0.523744
$933$	1.16591e111	0.496710
$934$	7.15378e110	0.292771
$935$	4.52840e111	1.78037
$936$	−6.50618e110	−0.245743
$937$	5.11270e111	1.85531	0.927654	−	0.373441i	$-0.121822\pi$
$937$	5.11270e111	1.85531	0.927654	+	0.373441i	$0.121822\pi$
$938$	−5.53943e110	−0.193134
$939$	4.73128e110	0.158496
$940$	5.22727e109	0.0168260
$941$	−5.68722e111	−1.75909	−0.879547	−	0.475812i	$-0.842154\pi$
$941$	−5.68722e111	−1.75909	−0.879547	+	0.475812i	$0.842154\pi$
$942$	−3.12504e110	−0.0928851
$943$	−3.26082e111	−0.931406
$944$	9.07306e110	0.249060
$945$	3.59977e111	0.949690
$946$	6.38475e110	0.161892
$947$	3.57908e111	0.872262	0.436131	−	0.899883i	$-0.356348\pi$
$947$	3.57908e111	0.872262	0.436131	+	0.899883i	$0.356348\pi$
$948$	2.07758e110	0.0486682
$949$	−5.40771e111	−1.21767
$950$	−1.53898e111	−0.333118
$951$	−5.35857e110	−0.111501
$952$	3.45797e111	0.691729
$953$	−2.60532e111	−0.501045	−0.250523	−	0.968111i	$-0.580602\pi$
$953$	−2.60532e111	−0.501045	−0.250523	+	0.968111i	$0.580602\pi$
$954$	9.46916e110	0.175084
$955$	−4.84698e111	−0.861677
$956$	−3.20137e111	−0.547224
$957$	2.18598e110	0.0359293
$958$	−2.91722e111	−0.461065
$959$	−1.28743e112	−1.95671
$960$	−2.86315e110	−0.0418478
$961$	8.15720e111	1.14661
$962$	2.62033e111	0.354234
$963$	−1.14500e112	−1.48875
$964$	−2.72248e111	−0.340468
$965$	1.18287e112	1.42287
$966$	−1.56706e111	−0.181319
$967$	5.71776e111	0.636404	0.318202	−	0.948023i	$-0.396921\pi$
$967$	5.71776e111	0.636404	0.318202	+	0.948023i	$0.396921\pi$
$968$	−1.54671e111	−0.165608
$969$	−7.41091e111	−0.763361
$970$	1.47482e112	1.46150
$971$	−1.56929e112	−1.49618	−0.748088	−	0.663600i	$-0.769028\pi$
$971$	−1.56929e112	−1.49618	−0.748088	+	0.663600i	$0.769028\pi$
$972$	4.33192e111	0.397370
$973$	2.07595e112	1.83225
$974$	9.73933e111	0.827119
$975$	−6.84639e110	−0.0559485
$976$	1.58141e111	0.124359
$977$	7.19391e110	0.0544401	0.0272200	−	0.999629i	$-0.491335\pi$
$977$	7.19391e110	0.0544401	0.0272200	+	0.999629i	$0.491335\pi$
$978$	−2.96750e111	−0.216114
$979$	−6.50109e111	−0.455654
$980$	−9.97065e111	−0.672583
$981$	−1.87180e112	−1.21527
$982$	1.45593e112	0.909827
$983$	1.26480e112	0.760790	0.380395	−	0.924824i	$-0.375788\pi$
$983$	1.26480e112	0.760790	0.380395	+	0.924824i	$0.375788\pi$
$984$	2.96798e111	0.171848
$985$	2.66042e112	1.48283
$986$	1.71482e111	0.0920096
$987$	−2.60405e110	−0.0134511
$988$	−1.48283e112	−0.737405
$989$	−2.26976e111	−0.108672
$990$	−1.88641e112	−0.869594
$991$	5.98993e111	0.265864	0.132932	−	0.991125i	$-0.457561\pi$
$991$	5.98993e111	0.265864	0.132932	+	0.991125i	$0.457561\pi$
$992$	6.06023e111	0.259001
$993$	−3.57529e111	−0.147135
$994$	−3.09592e112	−1.22687
$995$	1.73447e112	0.661914
$996$	1.92948e111	0.0709112
$997$	4.88137e112	1.72772	0.863860	−	0.503733i	$-0.168040\pi$
$997$	4.88137e112	1.72772	0.863860	+	0.503733i	$0.168040\pi$
$998$	2.80140e112	0.954949
$999$	−1.14510e112	−0.375957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.76.a.a.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.76.a.a.1.2	✓	3	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-1.37439e11 q^{2} +2.34098e17 q^{3} +1.88895e22 q^{4} -1.81463e26 q^{5} -3.21742e28 q^{6} +7.29430e31 q^{7} -2.59615e33 q^{8} -5.53465e35 q^{9} +2.49400e37 q^{10} +1.36663e39 q^{11} +4.42199e39 q^{12} -4.52800e41 q^{13} -1.00252e43 q^{14} -4.24800e43 q^{15} +3.56812e44 q^{16} -1.82603e46 q^{17} +7.60676e46 q^{18} +1.73367e48 q^{19} -3.42773e48 q^{20} +1.70758e49 q^{21} -1.87828e50 q^{22} +6.67720e50 q^{23} -6.07753e50 q^{24} +6.45888e51 q^{25} +6.22323e52 q^{26} -2.71959e53 q^{27} +1.37785e54 q^{28} +6.83281e53 q^{29} +5.83841e54 q^{30} -1.23578e56 q^{31} -4.90399e55 q^{32} +3.19924e56 q^{33} +2.50968e57 q^{34} -1.32364e58 q^{35} -1.04547e58 q^{36} +4.21056e58 q^{37} -2.38273e59 q^{38} -1.06000e59 q^{39} +4.71104e59 q^{40} -4.88352e60 q^{41} -2.34688e60 q^{42} -3.39926e60 q^{43} +2.58148e61 q^{44} +1.00433e62 q^{45} -9.17707e61 q^{46} -1.52499e61 q^{47} +8.35290e61 q^{48} +2.90882e63 q^{49} -8.87702e62 q^{50} -4.27471e63 q^{51} -8.55315e63 q^{52} +1.24483e64 q^{53} +3.73778e64 q^{54} -2.47991e65 q^{55} -1.89371e65 q^{56} +4.05848e65 q^{57} -9.39094e64 q^{58} +2.54281e66 q^{59} -8.02425e65 q^{60} +4.43205e66 q^{61} +1.69844e67 q^{62} -4.03714e67 q^{63} +6.73999e66 q^{64} +8.21662e67 q^{65} -4.39701e67 q^{66} +5.52549e67 q^{67} -3.44928e68 q^{68} +1.56312e68 q^{69} +1.81920e69 q^{70} +3.08813e69 q^{71} +1.43688e69 q^{72} +1.19428e70 q^{73} -5.78695e69 q^{74} +1.51201e69 q^{75} +3.27480e70 q^{76} +9.96858e70 q^{77} +1.45685e70 q^{78} +4.69829e70 q^{79} -6.47480e70 q^{80} +2.72989e71 q^{81} +6.71186e71 q^{82} +4.36337e71 q^{83} +3.22553e71 q^{84} +3.31357e72 q^{85} +4.67191e71 q^{86} +1.59955e71 q^{87} -3.54796e72 q^{88} -4.75704e72 q^{89} -1.38034e73 q^{90} -3.30286e73 q^{91} +1.26129e73 q^{92} -2.89293e73 q^{93} +2.09593e72 q^{94} -3.14596e74 q^{95} -1.14801e73 q^{96} +5.91346e74 q^{97} -3.99785e74 q^{98} -7.56379e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 412316860416 q^{2} + 12\!\cdots\!04 q^{3} + 56\!\cdots\!52 q^{4} + 16\!\cdots\!50 q^{5} - 17\!\cdots\!88 q^{6} + 49\!\cdots\!12 q^{7} - 77\!\cdots\!44 q^{8} + 35\!\cdots\!51 q^{9} - 22\!\cdots\!00 q^{10}+ \cdots - 11\!\cdots\!68 q^{99}+O(q^{100}) \) 3 * q - 412316860416 * q^2 + 1247256736634198004 * q^3 + 56668397794435742564352 * q^4 + 164841037010073038656676250 * q^5 - 171421660593906097355791269888 * q^6 + 49188484889350831330680498887112 * q^7 - 7788445287802241442795744493830144 * q^8 + 350069357182276058179837291235129151 * q^9 - 22655579615903658355256584505917440000 * q^10 + 376028144461193866320847155952833356796 * q^11 + 23560013634458836001219698571880626651136 * q^12 - 925070104562370942171863215664607476425566 * q^13 - 6760413886065663975541916932643533948452864 * q^14 + 304269429637489871036834079247530526228335000 * q^15 + 1070435769529469910793714477087121352287059968 * q^16 + 11105717807078079560338878984556957971267357462 * q^17 - 48113166093747788183238222478595428796199862272 * q^18 + 1226070865667475560419994296781687078098256026500 * q^19 + 3113759152711374531922693764530423144833351680000 * q^20 + 68517185882331308774796793377188076110575410338016 * q^21 - 51680914650764518302842700090624991551255018995712 * q^22 + 271328792137896997383389612251048821761834150147544 * q^23 - 3238063617706073577070912687270566293843683879944192 * q^24 + 31748451106721345935032757125860501117730610058203125 * q^25 + 127140667059285874843163511125276288509596702345265152 * q^26 + 1197448038136873386430122156284924279903233737117284040 * q^27 + 929144209538441500271292067291283620303065621681143808 * q^28 - 2192192441744294863307671608209094010102596849162475470 * q^29 - 41818471982898948212302719415885308765195809713029120000 * q^30 - 84475319706390463018423912220261407196388754491533828064 * q^31 - 147119571923125330402401314606429681627398955729625808896 * q^32 - 152651908525049572295389965461339076489002087512241778672 * q^33 - 1526358232960166048964529405311162353146873855092210008064 * q^34 - 10581882005980808610246098771932820539289975861854133370000 * q^35 + 6612623196149210250218989469527661654232801841214216208384 * q^36 - 66467156559661428016435329175985053243116052098537071406918 * q^37 - 168509896659846935772260720933883649668409840270477099008000 * q^38 - 1576575655050891506325267408432832107424195089029358618993288 * q^39 - 427951799312512746938088887004201350531222938741333032960000 * q^40 - 4931831025653402196557722046034935103637243072704239197865874 * q^41 - 9416930322514108013588161811222149738754568548593888816791552 * q^42 - 20756681407708278323173156546593085322222288647517659582599396 * q^43 + 7102970824076827760252890263090258397213331658958137735512064 * q^44 + 430455289229109660667382851976501730627013861372014944449721250 * q^45 - 37291145238254384831304190663820020197325144827508961751072768 * q^46 + 51571462381763314515108804623667311044662303402547877540507952 * q^47 + 445036074893281041730857774870353847534673548816726238244634624 * q^48 + 874703066390889543299993126070490968782377105753545374031866619 * q^49 - 4363473894464741970434183441417017861082381310019554508800000000 * q^50 + 26687643671570090614605289380399353628646518403234111773363733416 * q^51 - 17474080224360234418116365102835002179615309399115530505231007744 * q^52 + 6373650417776797701672439632011840936956406793203656616477981514 * q^53 - 164576005198631422925124635216920020480663646258003080580568186880 * q^54 - 416397474908805676143485768937466126874738084681826965490191835000 * q^55 - 127700607783532079951179985813769422561988750517197478247452901376 * q^56 + 324374862297075653278748857063883477999874298820902947102578684400 * q^57 + 301292635002564212239591678181305084901764706298415268289671331840 * q^58 + 5164661149603341451990328866011056430426032323285413754497779833260 * q^59 + 5747487025127784123028411031778931969068100664118374895861104640000 * q^60 + 6112904160012928128712528481475458535407529031872677635552463254866 * q^61 + 11610199534658923547853700750412719759341719994985948813202143838208 * q^62 + 13207243195255893358298630339555911394008670199338112701744595846504 * q^63 + 20219960000362979846000261315264723005227858316905429360827707686912 * q^64 - 130892903197384045097570057369266929060996843870951145661159667802500 * q^65 + 20980318553186288313199601703136668348387407025305870049315529949184 * q^66 - 136137738816805460535298375335076702172786722063275309182255486993868 * q^67 + 209781078161416398433030030714936672336391228552271521567960840798208 * q^68 + 2302114699257823143259687991707123968073297464808491488252678944581792 * q^69 + 1454362788666190380308550551585191261609200940393373335890312560640000 * q^70 + 10384877370088278005014559441463902818134695856776063874032337197444616 * q^71 - 908832011783419237149393171513270251913060604110836593449036832309248 * q^72 + 23960042075251086966999537195044028280663199284717397149070565023693454 * q^73 + 9135176437819446597223932457915213832448069788667164516362544580919296 * q^74 + 73651649014806681647280357044768244600220326928118781461607720567187500 * q^75 + 23159823846604231216245513612685211315038128265161053905802049355776000 * q^76 + 112606444794187449919020541060114371108822468615691116879839101242785184 * q^77 + 216682908099627399529958421045558032449461654608156916877820684912295936 * q^78 + 207600583714452906248332854115664313358280271635394763063638195459831120 * q^79 + 58817247433971121013830909005570694884180311960929176960246082437120000 * q^80 + 1040997430154496315690711192050972807021466062787523736282834877959617563 * q^81 + 677825694866543982891199358847304087795338548635752244332646458382614528 * q^82 + 1167639752536908153859168711897497594398247447354194893620746224951064004 * q^83 + 1294253048445082445343125714942568285400506101977630056114555247650668544 * q^84 + 10113448117368406780812318911043868851473369769419767324525240781711092500 * q^85 + 2852776570227145526607821642006579253717835257067533423671213327659302912 * q^86 + 5029129967375119029953943778547857750798463238735644189412390040078806840 * q^87 - 976224876603268627894754955822383862791060384333652064226810006190686208 * q^88 - 39521664848491905275031652813807887505386797709550908292289684142644361570 * q^89 - 59161324468135905400450140260809084592973635479407420033113903522119680000 * q^90 - 76061144334143564334879783774020507949888992229194116049886624616643162064 * q^91 + 5125255975318038751329599229723376549682270838803665659768717807238250496 * q^92 - 63157470235075274925966093148023612999965331967498255414086440472939495552 * q^93 - 7087927818770166484958541239689750032674694031295125027542226210174009344 * q^94 - 383757279880654476069446138229405811984616709991648142174485235232603525000 * q^95 - 61165292390619160459867052067056013283494179782531158113465925041576214528 * q^96 - 394916692348392721348110030097230776686065428055487460723991200429722029978 * q^97 - 120218274043513194906299084591922038450677331531219546160606553294050951168 * q^98 - 1174273799576543370476209530112641026492928709676247191346470741033657155668 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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