LMFDB - Embedded newform 2.76.a.a.1.1

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			1.1
Root			$1.02072e12$ 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)

$f(q)$	$=$	\(q-1.37439e11 q^{2} -3.89753e17 q^{3} +1.88895e22 q^{4} +7.75850e25 q^{5} +5.35672e28 q^{6} -4.72854e31 q^{7} -2.59615e33 q^{8} -4.56360e35 q^{9} -1.06632e37 q^{10} -5.11609e38 q^{11} -7.36222e39 q^{12} +4.50738e41 q^{13} +6.49886e42 q^{14} -3.02390e43 q^{15} +3.56812e44 q^{16} +5.70972e45 q^{17} +6.27216e46 q^{18} -3.51788e47 q^{19} +1.46554e48 q^{20} +1.84296e49 q^{21} +7.03151e49 q^{22} -1.50720e51 q^{23} +1.01186e51 q^{24} -2.04504e52 q^{25} -6.19490e52 q^{26} +4.14941e53 q^{27} -8.93196e53 q^{28} -4.96647e54 q^{29} +4.15601e54 q^{30} +4.96943e55 q^{31} -4.90399e55 q^{32} +1.99401e56 q^{33} -7.84737e56 q^{34} -3.66864e57 q^{35} -8.62039e57 q^{36} -9.67806e58 q^{37} +4.83494e58 q^{38} -1.75677e59 q^{39} -2.01422e59 q^{40} -1.27643e60 q^{41} -2.53295e60 q^{42} -2.20673e60 q^{43} -9.66403e60 q^{44} -3.54066e61 q^{45} +2.07148e62 q^{46} +4.95089e62 q^{47} -1.39068e62 q^{48} -1.75954e62 q^{49} +2.81067e63 q^{50} -2.22538e63 q^{51} +8.51421e63 q^{52} -4.82893e64 q^{53} -5.70291e64 q^{54} -3.96932e64 q^{55} +1.22760e65 q^{56} +1.37110e65 q^{57} +6.82586e65 q^{58} -1.51460e65 q^{59} -5.71198e65 q^{60} +6.05079e66 q^{61} -6.82993e66 q^{62} +2.15792e67 q^{63} +6.73999e66 q^{64} +3.49705e67 q^{65} -2.74055e67 q^{66} -2.23457e68 q^{67} +1.07853e68 q^{68} +5.87436e68 q^{69} +5.04214e68 q^{70} +2.32960e69 q^{71} +1.18478e69 q^{72} +1.23164e70 q^{73} +1.33014e70 q^{74} +7.97058e69 q^{75} -6.64509e69 q^{76} +2.41917e70 q^{77} +2.41448e70 q^{78} +2.33160e71 q^{79} +2.76832e70 q^{80} +1.15864e71 q^{81} +1.75432e71 q^{82} +1.73655e72 q^{83} +3.48126e71 q^{84} +4.42988e71 q^{85} +3.03290e71 q^{86} +1.93569e72 q^{87} +1.32821e72 q^{88} -1.75504e73 q^{89} +4.86625e72 q^{90} -2.13134e73 q^{91} -2.84702e73 q^{92} -1.93685e73 q^{93} -6.80445e73 q^{94} -2.72935e73 q^{95} +1.91134e73 q^{96} -4.85673e74 q^{97} +2.41830e73 q^{98} +2.33478e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.89753e17	−0.499738	−0.249869	−	0.968280i	$-0.580388\pi$
$3$	−3.89753e17	−0.499738	−0.249869	+	0.968280i	$0.580388\pi$
$4$	1.88895e22	0.500000
$5$	7.75850e25	0.476873	0.238436	−	0.971158i	$-0.423365\pi$
$5$	7.75850e25	0.476873	0.238436	+	0.971158i	$0.423365\pi$
$6$	5.35672e28	0.353368
$7$	−4.72854e31	−0.962833	−0.481416	−	0.876492i	$-0.659877\pi$
$7$	−4.72854e31	−0.962833	−0.481416	+	0.876492i	$0.659877\pi$
$8$	−2.59615e33	−0.353553
$9$	−4.56360e35	−0.750262
$10$	−1.06632e37	−0.337200
$11$	−5.11609e38	−0.453642	−0.226821	−	0.973937i	$-0.572833\pi$
$11$	−5.11609e38	−0.453642	−0.226821	+	0.973937i	$0.572833\pi$
$12$	−7.36222e39	−0.249869
$13$	4.50738e41	0.760412	0.380206	−	0.924902i	$-0.375853\pi$
$13$	4.50738e41	0.760412	0.380206	+	0.924902i	$0.375853\pi$
$14$	6.49886e42	0.680825
$15$	−3.02390e43	−0.238311
$16$	3.56812e44	0.250000
$17$	5.70972e45	0.411889	0.205944	−	0.978564i	$-0.433973\pi$
$17$	5.70972e45	0.411889	0.205944	+	0.978564i	$0.433973\pi$
$18$	6.27216e46	0.530515
$19$	−3.51788e47	−0.391761	−0.195881	−	0.980628i	$-0.562756\pi$
$19$	−3.51788e47	−0.391761	−0.195881	+	0.980628i	$0.562756\pi$
$20$	1.46554e48	0.238436
$21$	1.84296e49	0.481164
$22$	7.03151e49	0.320773
$23$	−1.50720e51	−1.29831	−0.649153	−	0.760658i	$-0.724877\pi$
$23$	−1.50720e51	−1.29831	−0.649153	+	0.760658i	$0.724877\pi$
$24$	1.01186e51	0.176684
$25$	−2.04504e52	−0.772592
$26$	−6.19490e52	−0.537692
$27$	4.14941e53	0.874672
$28$	−8.93196e53	−0.481416
$29$	−4.96647e54	−0.717997	−0.358999	−	0.933338i	$-0.616882\pi$
$29$	−4.96647e54	−0.717997	−0.358999	+	0.933338i	$0.616882\pi$
$30$	4.15601e54	0.168512
$31$	4.96943e55	0.589173	0.294587	−	0.955625i	$-0.404818\pi$
$31$	4.96943e55	0.589173	0.294587	+	0.955625i	$0.404818\pi$
$32$	−4.90399e55	−0.176777
$33$	1.99401e56	0.226702
$34$	−7.84737e56	−0.291249
$35$	−3.66864e57	−0.459149
$36$	−8.62039e57	−0.375131
$37$	−9.67806e58	−1.50738	−0.753691	−	0.657229i	$-0.771729\pi$
$37$	−9.67806e58	−1.50738	−0.753691	+	0.657229i	$0.771729\pi$
$38$	4.83494e58	0.277017
$39$	−1.75677e59	−0.380007
$40$	−2.01422e59	−0.168600
$41$	−1.27643e60	−0.423256	−0.211628	−	0.977350i	$-0.567877\pi$
$41$	−1.27643e60	−0.423256	−0.211628	+	0.977350i	$0.567877\pi$
$42$	−2.53295e60	−0.340234
$43$	−2.20673e60	−0.122654	−0.0613270	−	0.998118i	$-0.519533\pi$
$43$	−2.20673e60	−0.122654	−0.0613270	+	0.998118i	$0.519533\pi$
$44$	−9.66403e60	−0.226821
$45$	−3.54066e61	−0.357780
$46$	2.07148e62	0.918041
$47$	4.95089e62	0.979520	0.489760	−	0.871857i	$-0.337084\pi$
$47$	4.95089e62	0.979520	0.489760	+	0.871857i	$0.337084\pi$
$48$	−1.39068e62	−0.124934
$49$	−1.75954e62	−0.0729536
$50$	2.81067e63	0.546305
$51$	−2.22538e63	−0.205836
$52$	8.51421e63	0.380206
$53$	−4.82893e64	−1.05562	−0.527808	−	0.849364i	$-0.676986\pi$
$53$	−4.82893e64	−1.05562	−0.527808	+	0.849364i	$0.676986\pi$
$54$	−5.70291e64	−0.618487
$55$	−3.96932e64	−0.216329
$56$	1.22760e65	0.340413
$57$	1.37110e65	0.195778
$58$	6.82586e65	0.507701
$59$	−1.51460e65	−0.0593400	−0.0296700	−	0.999560i	$-0.509446\pi$
$59$	−1.51460e65	−0.0593400	−0.0296700	+	0.999560i	$0.509446\pi$
$60$	−5.71198e65	−0.119156
$61$	6.05079e66	0.679115	0.339558	−	0.940585i	$-0.389723\pi$
$61$	6.05079e66	0.679115	0.339558	+	0.940585i	$0.389723\pi$
$62$	−6.82993e66	−0.416608
$63$	2.15792e67	0.722377
$64$	6.73999e66	0.125000
$65$	3.49705e67	0.362620
$66$	−2.74055e67	−0.160302
$67$	−2.23457e68	−0.743683	−0.371842	−	0.928296i	$-0.621274\pi$
$67$	−2.23457e68	−0.743683	−0.371842	+	0.928296i	$0.621274\pi$
$68$	1.07853e68	0.205944
$69$	5.87436e68	0.648813
$70$	5.04214e68	0.324667
$71$	2.32960e69	0.881236	0.440618	−	0.897695i	$-0.354759\pi$
$71$	2.32960e69	0.881236	0.440618	+	0.897695i	$0.354759\pi$
$72$	1.18478e69	0.265258
$73$	1.23164e70	1.64390	0.821952	−	0.569556i	$-0.192885\pi$
$73$	1.23164e70	1.64390	0.821952	+	0.569556i	$0.192885\pi$
$74$	1.33014e70	1.06588
$75$	7.97058e69	0.386094
$76$	−6.64509e69	−0.195881
$77$	2.41917e70	0.436781
$78$	2.41448e70	0.268705
$79$	2.33160e71	1.60931	0.804653	−	0.593746i	$-0.202352\pi$
$79$	2.33160e71	1.60931	0.804653	+	0.593746i	$0.202352\pi$
$80$	2.76832e70	0.119218
$81$	1.15864e71	0.313155
$82$	1.75432e71	0.299287
$83$	1.73655e72	1.88044	0.940219	−	0.340570i	$-0.110620\pi$
$83$	1.73655e72	1.88044	0.940219	+	0.340570i	$0.110620\pi$
$84$	3.48126e71	0.240582
$85$	4.42988e71	0.196419
$86$	3.03290e71	0.0867294
$87$	1.93569e72	0.358810
$88$	1.32821e72	0.160386
$89$	−1.75504e73	−1.38727	−0.693635	−	0.720326i	$-0.743992\pi$
$89$	−1.75504e73	−1.38727	−0.693635	+	0.720326i	$0.743992\pi$
$90$	4.86625e72	0.252988
$91$	−2.13134e73	−0.732149
$92$	−2.84702e73	−0.649153
$93$	−1.93685e73	−0.294432
$94$	−6.80445e73	−0.692625
$95$	−2.72935e73	−0.186820
$96$	1.91134e73	0.0883420
$97$	−4.85673e74	−1.52196	−0.760981	−	0.648774i	$-0.775282\pi$
$97$	−4.85673e74	−1.52196	−0.760981	+	0.648774i	$0.775282\pi$
$98$	2.41830e73	0.0515860
$99$	2.33478e74	0.340350
$100$	−3.86296e74	−0.386296
$101$	9.92803e74	0.683615	0.341807	−	0.939770i	$-0.388961\pi$
$101$	9.92803e74	0.683615	0.341807	+	0.939770i	$0.388961\pi$
$102$	3.05854e74	0.145548
$103$	−3.85689e75	−1.27304	−0.636519	−	0.771261i	$-0.719626\pi$
$103$	−3.85689e75	−1.27304	−0.636519	+	0.771261i	$0.719626\pi$
$104$	−1.17018e75	−0.268846
$105$	1.42986e75	0.229454
$106$	6.63683e75	0.746433
$107$	1.72784e76	1.36651	0.683254	−	0.730181i	$-0.260564\pi$
$107$	1.72784e76	1.36651	0.683254	+	0.730181i	$0.260564\pi$
$108$	7.83802e75	0.437336
$109$	2.72466e76	1.07602	0.538008	−	0.842939i	$-0.319177\pi$
$109$	2.72466e76	1.07602	0.538008	+	0.842939i	$0.319177\pi$
$110$	5.45539e75	0.152968
$111$	3.77205e76	0.753296
$112$	−1.68720e76	−0.240708
$113$	3.85598e75	0.0394178	0.0197089	−	0.999806i	$-0.493726\pi$
$113$	3.85598e75	0.0394178	0.0197089	+	0.999806i	$0.493726\pi$
$114$	−1.88443e76	−0.138436
$115$	−1.16936e77	−0.619127
$116$	−9.38139e76	−0.358999
$117$	−2.05699e77	−0.570508
$118$	2.08165e76	0.0419597
$119$	−2.69986e77	−0.396580
$120$	7.85048e76	0.0842558
$121$	−1.01015e78	−0.794209
$122$	−8.31615e77	−0.480207
$123$	4.97493e77	0.211517
$124$	9.38699e77	0.294587
$125$	−3.64030e78	−0.845301
$126$	−2.96582e78	−0.510798
$127$	6.84492e78	0.876454	0.438227	−	0.898864i	$-0.355607\pi$
$127$	6.84492e78	0.876454	0.438227	+	0.898864i	$0.355607\pi$
$128$	−9.26337e77	−0.0883883
$129$	8.60078e77	0.0612948
$130$	−4.80631e78	−0.256411
$131$	2.83129e79	1.13321	0.566605	−	0.823990i	$-0.308257\pi$
$131$	2.83129e79	1.13321	0.566605	+	0.823990i	$0.308257\pi$
$132$	3.76658e78	0.113351
$133$	1.66345e79	0.377200
$134$	3.07116e79	0.525863
$135$	3.21932e79	0.417107
$136$	−1.48233e79	−0.145625
$137$	2.27615e80	1.69895	0.849474	−	0.527630i	$-0.176919\pi$
$137$	2.27615e80	1.69895	0.849474	+	0.527630i	$0.176919\pi$
$138$	−8.07365e79	−0.458780
$139$	−1.28554e80	−0.557225	−0.278612	−	0.960404i	$-0.589874\pi$
$139$	−1.28554e80	−0.557225	−0.278612	+	0.960404i	$0.589874\pi$
$140$	−6.92986e79	−0.229574
$141$	−1.92962e80	−0.489503
$142$	−3.20177e80	−0.623128
$143$	−2.30602e80	−0.344954
$144$	−1.62835e80	−0.187566
$145$	−3.85323e80	−0.342393
$146$	−1.69275e81	−1.16242
$147$	6.85786e79	0.0364577
$148$	−1.82813e81	−0.753691
$149$	3.20433e81	1.02625	0.513124	−	0.858314i	$-0.328488\pi$
$149$	3.20433e81	1.02625	0.513124	+	0.858314i	$0.328488\pi$
$150$	−1.09547e81	−0.273009
$151$	8.04403e81	1.56257	0.781283	−	0.624177i	$-0.214566\pi$
$151$	8.04403e81	1.56257	0.781283	+	0.624177i	$0.214566\pi$
$152$	9.13295e80	0.138508
$153$	−2.60568e81	−0.309025
$154$	−3.32488e81	−0.308851
$155$	3.85553e81	0.280961
$156$	−3.31844e81	−0.190003
$157$	3.25065e82	1.46465	0.732323	−	0.680957i	$-0.238436\pi$
$157$	3.25065e82	1.46465	0.732323	+	0.680957i	$0.238436\pi$
$158$	−3.20453e82	−1.13795
$159$	1.88209e82	0.527531
$160$	−3.80476e81	−0.0843000
$161$	7.12686e82	1.25005
$162$	−1.59242e82	−0.221434
$163$	8.08367e82	0.892428	0.446214	−	0.894926i	$-0.352772\pi$
$163$	8.08367e82	0.892428	0.446214	+	0.894926i	$0.352772\pi$
$164$	−2.41111e82	−0.211628
$165$	1.54705e82	0.108108
$166$	−2.38670e83	−1.32967
$167$	−2.51833e83	−1.12007	−0.560034	−	0.828470i	$-0.689212\pi$
$167$	−2.51833e83	−1.12007	−0.560034	+	0.828470i	$0.689212\pi$
$168$	−4.78460e82	−0.170117
$169$	−1.48194e83	−0.421774
$170$	−6.08838e82	−0.138889
$171$	1.60542e83	0.293924
$172$	−4.16839e82	−0.0613270
$173$	−8.78831e83	−1.04034	−0.520171	−	0.854062i	$-0.674132\pi$
$173$	−8.78831e83	−1.04034	−0.520171	+	0.854062i	$0.674132\pi$
$174$	−2.66040e83	−0.253717
$175$	9.67003e83	0.743877
$176$	−1.82548e83	−0.113410
$177$	5.90319e82	0.0296544
$178$	2.41210e84	0.980948
$179$	2.68321e84	0.884436	0.442218	−	0.896908i	$-0.354192\pi$
$179$	2.68321e84	0.884436	0.442218	+	0.896908i	$0.354192\pi$
$180$	−6.68813e83	−0.178890
$181$	3.64467e84	0.791976	0.395988	−	0.918256i	$-0.370402\pi$
$181$	3.64467e84	0.791976	0.395988	+	0.918256i	$0.370402\pi$
$182$	2.92929e84	0.517708
$183$	−2.35831e84	−0.339380
$184$	3.91292e84	0.459021
$185$	−7.50872e84	−0.718830
$186$	2.66199e84	0.208195
$187$	−2.92114e84	−0.186850
$188$	9.35196e84	0.489760
$189$	−1.96207e85	−0.842163
$190$	3.75119e84	0.132102
$191$	−4.54589e85	−1.31482	−0.657412	−	0.753531i	$-0.728349\pi$
$191$	−4.54589e85	−1.31482	−0.657412	+	0.753531i	$0.728349\pi$
$192$	−2.62693e84	−0.0624672
$193$	−2.04750e85	−0.400705	−0.200353	−	0.979724i	$-0.564209\pi$
$193$	−2.04750e85	−0.400705	−0.200353	+	0.979724i	$0.564209\pi$
$194$	6.67504e85	1.07619
$195$	−1.36299e85	−0.181215
$196$	−3.32368e84	−0.0364768
$197$	−8.43997e85	−0.765345	−0.382673	−	0.923884i	$-0.624996\pi$
$197$	−8.43997e85	−0.765345	−0.382673	+	0.923884i	$0.624996\pi$
$198$	−3.20889e85	−0.240664
$199$	−4.09126e85	−0.254020	−0.127010	−	0.991901i	$-0.540538\pi$
$199$	−4.09126e85	−0.254020	−0.127010	+	0.991901i	$0.540538\pi$
$200$	5.30921e85	0.273153
$201$	8.70928e85	0.371647
$202$	−1.36450e86	−0.483389
$203$	2.34842e86	0.691311
$204$	−4.20362e85	−0.102918
$205$	−9.90320e85	−0.201839
$206$	5.30087e86	0.900173
$207$	6.87825e86	0.974070
$208$	1.60829e86	0.190103
$209$	1.79978e86	0.177719
$210$	−1.96519e86	−0.162248
$211$	2.28400e87	1.57799	0.788996	−	0.614399i	$-0.210601\pi$
$211$	2.28400e87	1.57799	0.788996	+	0.614399i	$0.210601\pi$
$212$	−9.12159e86	−0.527808
$213$	−9.07966e86	−0.440387
$214$	−2.37473e87	−0.966267
$215$	−1.71209e86	−0.0584903
$216$	−1.07725e87	−0.309243
$217$	−2.34982e87	−0.567275
$218$	−3.74475e87	−0.760859
$219$	−4.80035e87	−0.821521
$220$	−7.49783e86	−0.108165
$221$	2.57359e87	0.313205
$222$	−5.18427e87	−0.532661
$223$	1.00347e88	0.871107	0.435553	−	0.900163i	$-0.356553\pi$
$223$	1.00347e88	0.871107	0.435553	+	0.900163i	$0.356553\pi$
$224$	2.31887e87	0.170206
$225$	9.33271e87	0.579647
$226$	−5.29961e86	−0.0278726
$227$	5.37085e87	0.239372	0.119686	−	0.992812i	$-0.461811\pi$
$227$	5.37085e87	0.239372	0.119686	+	0.992812i	$0.461811\pi$
$228$	2.58994e87	0.0978889
$229$	−9.36380e87	−0.300346	−0.150173	−	0.988660i	$-0.547983\pi$
$229$	−9.36380e87	−0.300346	−0.150173	+	0.988660i	$0.547983\pi$
$230$	1.60716e88	0.437789
$231$	−9.42877e87	−0.218276
$232$	1.28937e88	0.253850
$233$	4.53892e88	0.760511	0.380255	−	0.924882i	$-0.375836\pi$
$233$	4.53892e88	0.760511	0.380255	+	0.924882i	$0.375836\pi$
$234$	2.82710e88	0.403410
$235$	3.84114e88	0.467106
$236$	−2.86100e87	−0.0296700
$237$	−9.08748e88	−0.804231
$238$	3.71066e88	0.280424
$239$	−8.40871e88	−0.543010	−0.271505	−	0.962437i	$-0.587521\pi$
$239$	−8.40871e88	−0.543010	−0.271505	+	0.962437i	$0.587521\pi$
$240$	−1.07896e88	−0.0595778
$241$	−1.03827e89	−0.490535	−0.245267	−	0.969455i	$-0.578876\pi$
$241$	−1.03827e89	−0.490535	−0.245267	+	0.969455i	$0.578876\pi$
$242$	1.38834e89	0.561591
$243$	−2.97553e89	−1.03117
$244$	1.14296e89	0.339558
$245$	−1.36514e88	−0.0347896
$246$	−6.83749e88	−0.149565
$247$	−1.58564e89	−0.297900
$248$	−1.29014e89	−0.208304
$249$	−6.76826e89	−0.939726
$250$	5.00319e89	0.597718
$251$	−5.79300e89	−0.595853	−0.297926	−	0.954589i	$-0.596295\pi$
$251$	−5.79300e89	−0.595853	−0.297926	+	0.954589i	$0.596295\pi$
$252$	4.07619e89	0.361188
$253$	7.71098e89	0.588966
$254$	−9.40759e89	−0.619746
$255$	−1.72656e89	−0.0981578
$256$	1.27315e89	0.0625000
$257$	4.23811e90	1.79755	0.898773	−	0.438414i	$-0.144459\pi$
$257$	4.23811e90	1.79755	0.898773	+	0.438414i	$0.144459\pi$
$258$	−1.18208e89	−0.0433420
$259$	4.57631e90	1.45136
$260$	6.60575e89	0.181310
$261$	2.26650e90	0.538686
$262$	−3.89129e90	−0.801300
$263$	−1.51236e90	−0.269969	−0.134985	−	0.990848i	$-0.543098\pi$
$263$	−1.51236e90	−0.269969	−0.134985	+	0.990848i	$0.543098\pi$
$264$	−5.17675e89	−0.0801512
$265$	−3.74652e90	−0.503394
$266$	−2.28622e90	−0.266721
$267$	6.84031e90	0.693271
$268$	−4.22097e90	−0.371842
$269$	−1.37692e91	−1.05487	−0.527435	−	0.849595i	$-0.676846\pi$
$269$	−1.37692e91	−1.05487	−0.527435	+	0.849595i	$0.676846\pi$
$270$	−4.42460e90	−0.294939
$271$	−1.98752e91	−1.15335	−0.576677	−	0.816972i	$-0.695651\pi$
$271$	−1.98752e91	−1.15335	−0.576677	+	0.816972i	$0.695651\pi$
$272$	2.03729e90	0.102972
$273$	8.30694e90	0.365883
$274$	−3.12832e91	−1.20134
$275$	1.04626e91	0.350480
$276$	1.10963e91	0.324406
$277$	6.13709e91	1.56665	0.783323	−	0.621614i	$-0.213523\pi$
$277$	6.13709e91	1.56665	0.783323	+	0.621614i	$0.213523\pi$
$278$	1.76683e91	0.394017
$279$	−2.26785e91	−0.442034
$280$	9.52433e90	0.162334
$281$	−5.62078e91	−0.838126	−0.419063	−	0.907957i	$-0.637641\pi$
$281$	−5.62078e91	−0.838126	−0.419063	+	0.907957i	$0.637641\pi$
$282$	2.65205e91	0.346131
$283$	1.55575e91	0.177807	0.0889033	−	0.996040i	$-0.471664\pi$
$283$	1.55575e91	0.177807	0.0889033	+	0.996040i	$0.471664\pi$
$284$	4.40048e91	0.440618
$285$	1.06377e91	0.0933611
$286$	3.16937e91	0.243920
$287$	6.03566e91	0.407525
$288$	2.23798e91	0.132629
$289$	−1.59562e92	−0.830348
$290$	5.29584e91	0.242109
$291$	1.89292e92	0.760582
$292$	2.32650e92	0.821952
$293$	−3.98507e92	−1.23851	−0.619256	−	0.785189i	$-0.712566\pi$
$293$	−3.98507e92	−1.23851	−0.619256	+	0.785189i	$0.712566\pi$
$294$	−9.42538e90	−0.0257795
$295$	−1.17510e91	−0.0282976
$296$	2.51257e92	0.532940
$297$	−2.12288e92	−0.396788
$298$	−4.40400e92	−0.725667
$299$	−6.79353e92	−0.987247
$300$	1.50560e92	0.193047
$301$	1.04346e92	0.118095
$302$	−1.10556e93	−1.10490
$303$	−3.86948e92	−0.341628
$304$	−1.25522e92	−0.0979403
$305$	4.69451e92	0.323852
$306$	3.58122e92	0.218513
$307$	8.80496e92	0.475377	0.237689	−	0.971341i	$-0.423610\pi$
$307$	8.80496e92	0.475377	0.237689	+	0.971341i	$0.423610\pi$
$308$	4.56968e92	0.218390
$309$	1.50323e93	0.636185
$310$	−5.29900e92	−0.198669
$311$	5.52762e92	0.183664	0.0918318	−	0.995775i	$-0.470728\pi$
$311$	5.52762e92	0.183664	0.0918318	+	0.995775i	$0.470728\pi$
$312$	4.56082e92	0.134353
$313$	4.73425e93	1.23691	0.618455	−	0.785820i	$-0.287759\pi$
$313$	4.73425e93	1.23691	0.618455	+	0.785820i	$0.287759\pi$
$314$	−4.46766e93	−1.03566
$315$	1.67422e93	0.344482
$316$	4.40427e93	0.804653
$317$	5.20189e93	0.844187	0.422093	−	0.906552i	$-0.361295\pi$
$317$	5.20189e93	0.844187	0.422093	+	0.906552i	$0.361295\pi$
$318$	−2.58672e93	−0.373021
$319$	2.54089e93	0.325713
$320$	5.22922e92	0.0596091
$321$	−6.73431e93	−0.682896
$322$	−9.79508e93	−0.883920
$323$	−2.00861e93	−0.161362
$324$	2.18861e93	0.156578
$325$	−9.21776e93	−0.587488
$326$	−1.11101e94	−0.631042
$327$	−1.06195e94	−0.537726
$328$	3.31381e93	0.149644
$329$	−2.34105e94	−0.943114
$330$	−2.12625e93	−0.0764438
$331$	−1.35092e94	−0.433592	−0.216796	−	0.976217i	$-0.569561\pi$
$331$	−1.35092e94	−0.433592	−0.216796	+	0.976217i	$0.569561\pi$
$332$	3.28025e94	0.940219
$333$	4.41667e94	1.13093
$334$	3.46116e94	0.792007
$335$	−1.73369e94	−0.354642
$336$	6.57591e93	0.120291
$337$	−3.41665e94	−0.559087	−0.279543	−	0.960133i	$-0.590183\pi$
$337$	−3.41665e94	−0.559087	−0.279543	+	0.960133i	$0.590183\pi$
$338$	2.03677e94	0.298239
$339$	−1.50288e93	−0.0196986
$340$	8.36781e93	0.0982093
$341$	−2.54241e94	−0.267273
$342$	−2.20647e94	−0.207835
$343$	1.22366e95	1.03307
$344$	5.72899e93	0.0433647
$345$	4.55762e94	0.309401
$346$	1.20786e95	0.735633
$347$	−2.21303e95	−1.20957	−0.604786	−	0.796388i	$-0.706741\pi$
$347$	−2.21303e95	−1.20957	−0.604786	+	0.796388i	$0.706741\pi$
$348$	3.65642e94	0.179405
$349$	1.95961e95	0.863410	0.431705	−	0.902015i	$-0.357912\pi$
$349$	1.95961e95	0.863410	0.431705	+	0.902015i	$0.357912\pi$
$350$	−1.32904e95	−0.526001
$351$	1.87030e95	0.665111
$352$	2.50892e94	0.0801932
$353$	−4.64019e95	−1.33347	−0.666737	−	0.745293i	$-0.732309\pi$
$353$	−4.64019e95	−1.33347	−0.666737	+	0.745293i	$0.732309\pi$
$354$	−8.11329e93	−0.0209688
$355$	1.80742e95	0.420238
$356$	−3.31517e95	−0.693635
$357$	1.05228e95	0.198186
$358$	−3.68778e95	−0.625391
$359$	−3.89236e95	−0.594527	−0.297263	−	0.954796i	$-0.596074\pi$
$359$	−3.89236e95	−0.594527	−0.297263	+	0.954796i	$0.596074\pi$
$360$	9.19209e94	0.126494
$361$	−6.82588e95	−0.846523
$362$	−5.00920e95	−0.560012
$363$	3.93709e95	0.396896
$364$	−4.02598e95	−0.366075
$365$	9.55568e95	0.783933
$366$	3.24124e95	0.239978
$367$	8.17025e95	0.546082	0.273041	−	0.962002i	$-0.411971\pi$
$367$	8.17025e95	0.546082	0.273041	+	0.962002i	$0.411971\pi$
$368$	−5.37787e95	−0.324577
$369$	5.82512e95	0.317553
$370$	1.03199e96	0.508289
$371$	2.28338e96	1.01638
$372$	−3.65860e95	−0.147216
$373$	2.70613e96	0.984616	0.492308	−	0.870421i	$-0.336153\pi$
$373$	2.70613e96	0.984616	0.492308	+	0.870421i	$0.336153\pi$
$374$	4.01479e95	0.132123
$375$	1.41882e96	0.422429
$376$	−1.28532e96	−0.346313
$377$	−2.23858e96	−0.545974
$378$	2.69664e96	0.595499
$379$	−5.51206e96	−1.10241	−0.551205	−	0.834370i	$-0.685832\pi$
$379$	−5.51206e96	−1.10241	−0.551205	+	0.834370i	$0.685832\pi$
$380$	−5.15559e95	−0.0934101
$381$	−2.66783e96	−0.437997
$382$	6.24782e96	0.929721
$383$	−1.29342e97	−1.74496	−0.872480	−	0.488650i	$-0.837489\pi$
$383$	−1.29342e97	−1.74496	−0.872480	+	0.488650i	$0.837489\pi$
$384$	3.61042e95	0.0441710
$385$	1.87691e96	0.208289
$386$	2.81406e96	0.283341
$387$	1.00706e96	0.0920226
$388$	−9.17410e96	−0.760981
$389$	−7.85003e96	−0.591237	−0.295618	−	0.955306i	$-0.595526\pi$
$389$	−7.85003e96	−0.591237	−0.295618	+	0.955306i	$0.595526\pi$
$390$	1.87327e96	0.128138
$391$	−8.60569e96	−0.534758
$392$	4.56803e95	0.0257930
$393$	−1.10350e97	−0.566307
$394$	1.15998e97	0.541181
$395$	1.80897e97	0.767434
$396$	4.41027e96	0.170175
$397$	2.64884e97	0.929849	0.464925	−	0.885350i	$-0.346081\pi$
$397$	2.64884e97	0.929849	0.464925	+	0.885350i	$0.346081\pi$
$398$	5.62299e96	0.179619
$399$	−6.48333e96	−0.188501
$400$	−7.29693e96	−0.193148
$401$	6.46874e96	0.155921	0.0779607	−	0.996956i	$-0.475159\pi$
$401$	6.46874e96	0.155921	0.0779607	+	0.996956i	$0.475159\pi$
$402$	−1.19699e97	−0.262794
$403$	2.23991e97	0.448014
$404$	1.87535e97	0.341807
$405$	8.98930e96	0.149335
$406$	−3.22764e97	−0.488831
$407$	4.95138e97	0.683811
$408$	5.77741e96	0.0727742
$409$	3.65143e97	0.419603	0.209802	−	0.977744i	$-0.432718\pi$
$409$	3.65143e97	0.419603	0.209802	+	0.977744i	$0.432718\pi$
$410$	1.36109e97	0.142722
$411$	−8.87137e97	−0.849029
$412$	−7.28545e97	−0.636519
$413$	7.16184e96	0.0571344
$414$	−9.45340e97	−0.688772
$415$	1.34730e98	0.896730
$416$	−2.21041e97	−0.134423
$417$	5.01043e97	0.278466
$418$	−2.47360e97	−0.125666
$419$	1.49288e98	0.693425	0.346712	−	0.937971i	$-0.387298\pi$
$419$	1.49288e98	0.693425	0.346712	+	0.937971i	$0.387298\pi$
$420$	2.70093e97	0.114727
$421$	−4.35824e98	−1.69330	−0.846648	−	0.532153i	$-0.821383\pi$
$421$	−4.35824e98	−1.69330	−0.846648	+	0.532153i	$0.821383\pi$
$422$	−3.13911e98	−1.11581
$423$	−2.25938e98	−0.734897
$424$	1.25366e98	0.373216
$425$	−1.16766e98	−0.318222
$426$	1.24790e98	0.311401
$427$	−2.86114e98	−0.653874
$428$	3.26380e98	0.683254
$429$	8.98778e97	0.172387
$430$	2.35308e97	0.0413589
$431$	8.77835e98	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$431$	8.77835e98	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$432$	1.48056e98	0.218668
$433$	4.12665e98	0.558858	0.279429	−	0.960166i	$-0.409855\pi$
$433$	4.12665e98	0.558858	0.279429	+	0.960166i	$0.409855\pi$
$434$	3.22956e98	0.401124
$435$	1.50181e98	0.171107
$436$	5.14674e98	0.538008
$437$	5.30215e98	0.508626
$438$	6.59755e98	0.580903
$439$	−1.70016e99	−1.37426	−0.687130	−	0.726534i	$-0.741130\pi$
$439$	−1.70016e99	−1.37426	−0.687130	+	0.726534i	$0.741130\pi$
$440$	1.03049e98	0.0764839
$441$	8.02984e97	0.0547343
$442$	−3.53711e98	−0.221469
$443$	−5.82394e98	−0.335025	−0.167512	−	0.985870i	$-0.553573\pi$
$443$	−5.82394e98	−0.335025	−0.167512	+	0.985870i	$0.553573\pi$
$444$	7.12520e98	0.376648
$445$	−1.36165e99	−0.661551
$446$	−1.37916e99	−0.615966
$447$	−1.24890e99	−0.512855
$448$	−3.18703e98	−0.120354
$449$	6.48502e98	0.225254	0.112627	−	0.993637i	$-0.464073\pi$
$449$	6.48502e98	0.225254	0.112627	+	0.993637i	$0.464073\pi$
$450$	−1.28268e99	−0.409872
$451$	6.53035e98	0.192007
$452$	7.28373e97	0.0197089
$453$	−3.13518e99	−0.780873
$454$	−7.38164e98	−0.169262
$455$	−1.65360e99	−0.349142
$456$	−3.55959e98	−0.0692179
$457$	5.58847e99	1.00100	0.500502	−	0.865736i	$-0.333149\pi$
$457$	5.58847e99	1.00100	0.500502	+	0.865736i	$0.333149\pi$
$458$	1.28695e99	0.212377
$459$	2.36920e99	0.360268
$460$	−2.20886e99	−0.309563
$461$	−1.44878e99	−0.187162	−0.0935809	−	0.995612i	$-0.529831\pi$
$461$	−1.44878e99	−0.187162	−0.0935809	+	0.995612i	$0.529831\pi$
$462$	1.29588e99	0.154344
$463$	1.03262e100	1.13410	0.567052	−	0.823682i	$-0.308084\pi$
$463$	1.03262e100	1.13410	0.567052	+	0.823682i	$0.308084\pi$
$464$	−1.77210e99	−0.179499
$465$	−1.50270e99	−0.140407
$466$	−6.23824e99	−0.537762
$467$	1.62305e100	1.29106	0.645532	−	0.763733i	$-0.276636\pi$
$467$	1.62305e100	1.29106	0.645532	+	0.763733i	$0.276636\pi$
$468$	−3.88554e99	−0.285254
$469$	1.05662e100	0.716042
$470$	−5.27923e99	−0.330294
$471$	−1.26695e100	−0.731939
$472$	3.93212e98	0.0209798
$473$	1.12898e99	0.0556409
$474$	1.24897e100	0.568677
$475$	7.19419e99	0.302672
$476$	−5.09990e99	−0.198290
$477$	2.20373e100	0.791988
$478$	1.15568e100	0.383966
$479$	−3.86350e100	−1.18686	−0.593429	−	0.804886i	$-0.702226\pi$
$479$	−3.86350e100	−1.18686	−0.593429	+	0.804886i	$0.702226\pi$
$480$	1.48291e99	0.0421279
$481$	−4.36227e100	−1.14623
$482$	1.42698e100	0.346861
$483$	−2.77771e100	−0.624698
$484$	−1.90812e100	−0.397105
$485$	−3.76809e100	−0.725782
$486$	4.08954e100	0.729146
$487$	1.84468e100	0.304498	0.152249	−	0.988342i	$-0.451348\pi$
$487$	1.84468e100	0.304498	0.152249	+	0.988342i	$0.451348\pi$
$488$	−1.57088e100	−0.240104
$489$	−3.15063e100	−0.445980
$490$	1.87623e99	0.0245999
$491$	−1.37312e100	−0.166783	−0.0833914	−	0.996517i	$-0.526575\pi$
$491$	−1.37312e100	−0.166783	−0.0833914	+	0.996517i	$0.526575\pi$
$492$	9.39738e99	0.105759
$493$	−2.83571e100	−0.295735
$494$	2.17929e100	0.210647
$495$	1.81144e100	0.162304
$496$	1.77315e100	0.147293
$497$	−1.10156e101	−0.848483
$498$	9.30222e100	0.664487
$499$	2.41315e101	1.59887	0.799435	−	0.600753i	$-0.205132\pi$
$499$	2.41315e101	1.59887	0.799435	+	0.600753i	$0.205132\pi$
$500$	−6.87633e100	−0.422650
$501$	9.81524e100	0.559740
$502$	7.96184e100	0.421331
$503$	1.03234e101	0.507019	0.253510	−	0.967333i	$-0.418415\pi$
$503$	1.03234e101	0.507019	0.253510	+	0.967333i	$0.418415\pi$
$504$	−5.60227e100	−0.255399
$505$	7.70266e100	0.325997
$506$	−1.05979e101	−0.416462
$507$	5.77591e100	0.210776
$508$	1.29297e101	0.438227
$509$	3.98846e101	1.25571	0.627853	−	0.778332i	$-0.283934\pi$
$509$	3.98846e101	1.25571	0.627853	+	0.778332i	$0.283934\pi$
$510$	2.37296e100	0.0694080
$511$	−5.82386e101	−1.58280
$512$	−1.74980e100	−0.0441942
$513$	−1.45971e101	−0.342663
$514$	−5.82482e101	−1.27106
$515$	−2.99237e101	−0.607077
$516$	1.62464e100	0.0306474
$517$	−2.53292e101	−0.444351
$518$	−6.28963e101	−1.02626
$519$	3.42527e101	0.519899
$520$	−9.07887e100	−0.128205
$521$	4.52848e100	0.0595029	0.0297515	−	0.999557i	$-0.490528\pi$
$521$	4.52848e100	0.0595029	0.0297515	+	0.999557i	$0.490528\pi$
$522$	−3.11505e101	−0.380909
$523$	6.30144e101	0.717177	0.358589	−	0.933496i	$-0.383258\pi$
$523$	6.30144e101	0.717177	0.358589	+	0.933496i	$0.383258\pi$
$524$	5.34815e101	0.566605
$525$	−3.76892e101	−0.371743
$526$	2.07857e101	0.190897
$527$	2.83740e101	0.242674
$528$	7.11487e100	0.0566755
$529$	9.23971e101	0.685599
$530$	5.14918e101	0.355954
$531$	6.91202e100	0.0445205
$532$	3.14216e101	0.188600
$533$	−5.75337e101	−0.321849
$534$	−9.40125e101	−0.490217
$535$	1.34055e102	0.651650
$536$	5.80126e101	0.262932
$537$	−1.04579e102	−0.441986
$538$	1.89243e102	0.745906
$539$	9.00198e100	0.0330948
$540$	6.08112e101	0.208554
$541$	−3.92161e102	−1.25478	−0.627389	−	0.778706i	$-0.715877\pi$
$541$	−3.92161e102	−1.25478	−0.627389	+	0.778706i	$0.715877\pi$
$542$	2.73162e102	0.815544
$543$	−1.42052e102	−0.395780
$544$	−2.80004e101	−0.0728123
$545$	2.11393e102	0.513123
$546$	−1.14170e102	−0.258718
$547$	1.99372e102	0.421832	0.210916	−	0.977504i	$-0.432355\pi$
$547$	1.99372e102	0.421832	0.210916	+	0.977504i	$0.432355\pi$
$548$	4.29953e102	0.849474
$549$	−2.76134e102	−0.509515
$550$	−1.43797e102	−0.247827
$551$	1.74715e102	0.281283
$552$	−1.52507e102	−0.229390
$553$	−1.10251e103	−1.54949
$554$	−8.43475e102	−1.10779
$555$	2.92654e102	0.359226
$556$	−2.42832e102	−0.278612
$557$	−3.60184e102	−0.386326	−0.193163	−	0.981167i	$-0.561875\pi$
$557$	−3.60184e102	−0.386326	−0.193163	+	0.981167i	$0.561875\pi$
$558$	3.11690e102	0.312566
$559$	−9.94656e101	−0.0932675
$560$	−1.30901e102	−0.114787
$561$	1.13852e102	0.0933759
$562$	7.72514e102	0.592645
$563$	1.01126e103	0.725771	0.362886	−	0.931834i	$-0.381792\pi$
$563$	1.01126e103	0.725771	0.362886	+	0.931834i	$0.381792\pi$
$564$	−3.64495e102	−0.244752
$565$	2.99166e101	0.0187973
$566$	−2.13820e102	−0.125728
$567$	−5.47867e102	−0.301516
$568$	−6.04797e102	−0.311564
$569$	6.38228e102	0.307798	0.153899	−	0.988087i	$-0.450817\pi$
$569$	6.38228e102	0.307798	0.153899	+	0.988087i	$0.450817\pi$
$570$	−1.46204e102	−0.0660163
$571$	3.76270e103	1.59091	0.795455	−	0.606013i	$-0.207232\pi$
$571$	3.76270e103	1.59091	0.795455	+	0.606013i	$0.207232\pi$
$572$	−4.35595e102	−0.172477
$573$	1.77177e103	0.657067
$574$	−8.29535e102	−0.288163
$575$	3.08228e103	1.00306
$576$	−3.07586e102	−0.0937828
$577$	1.62562e103	0.464436	0.232218	−	0.972664i	$-0.425402\pi$
$577$	1.62562e103	0.464436	0.232218	+	0.972664i	$0.425402\pi$
$578$	2.19300e103	0.587144
$579$	7.98019e102	0.200248
$580$	−7.27855e102	−0.171197
$581$	−8.21135e103	−1.81055
$582$	−2.60161e103	−0.537813
$583$	2.47053e103	0.478871
$584$	−3.19752e103	−0.581208
$585$	−1.59591e103	−0.272060
$586$	5.47704e103	0.875760
$587$	−1.00463e104	−1.50688	−0.753439	−	0.657518i	$-0.771606\pi$
$587$	−1.00463e104	−1.50688	−0.753439	+	0.657518i	$0.771606\pi$
$588$	1.29541e102	0.0182288
$589$	−1.74819e103	−0.230815
$590$	1.61505e102	0.0200094
$591$	3.28950e103	0.382472
$592$	−3.45325e103	−0.376846
$593$	−1.75547e104	−1.79821	−0.899107	−	0.437729i	$-0.855783\pi$
$593$	−1.75547e104	−1.79821	−0.899107	+	0.437729i	$0.855783\pi$
$594$	2.91766e103	0.280571
$595$	−2.09469e103	−0.189118
$596$	6.05281e103	0.513124
$597$	1.59458e103	0.126943
$598$	9.33696e103	0.698089
$599$	1.55975e104	1.09534	0.547671	−	0.836694i	$-0.315515\pi$
$599$	1.55975e104	1.09534	0.547671	+	0.836694i	$0.315515\pi$
$600$	−2.06928e103	−0.136505
$601$	−1.18042e104	−0.731551	−0.365776	−	0.930703i	$-0.619196\pi$
$601$	−1.18042e104	−0.731551	−0.365776	+	0.930703i	$0.619196\pi$
$602$	−1.43412e103	−0.0835059
$603$	1.01977e104	0.557957
$604$	1.51947e104	0.781283
$605$	−7.83726e103	−0.378737
$606$	5.31817e103	0.241568
$607$	2.78350e104	1.18855	0.594273	−	0.804264i	$-0.297440\pi$
$607$	2.78350e104	1.18855	0.594273	+	0.804264i	$0.297440\pi$
$608$	1.72516e103	0.0692542
$609$	−9.15301e103	−0.345474
$610$	−6.45208e103	−0.228998
$611$	2.23155e104	0.744838
$612$	−4.92200e103	−0.154512
$613$	1.01264e104	0.299011	0.149505	−	0.988761i	$-0.452232\pi$
$613$	1.01264e104	0.299011	0.149505	+	0.988761i	$0.452232\pi$
$614$	−1.21014e104	−0.336143
$615$	3.85980e103	0.100867
$616$	−6.28051e103	−0.154425
$617$	−5.67734e104	−1.31356	−0.656782	−	0.754081i	$-0.728083\pi$
$617$	−5.67734e104	−1.31356	−0.656782	+	0.754081i	$0.728083\pi$
$618$	−2.06603e104	−0.449851
$619$	2.95196e104	0.604938	0.302469	−	0.953159i	$-0.402189\pi$
$619$	2.95196e104	0.604938	0.302469	+	0.953159i	$0.402189\pi$
$620$	7.28289e103	0.140480
$621$	−6.25399e104	−1.13559
$622$	−7.59710e103	−0.129870
$623$	8.29877e104	1.33571
$624$	−6.26835e103	−0.0950016
$625$	2.58884e104	0.369491
$626$	−6.50670e104	−0.874628
$627$	−7.01470e103	−0.0888130
$628$	6.14030e104	0.732323
$629$	−5.52590e104	−0.620874
$630$	−2.30103e104	−0.243585
$631$	5.81702e104	0.580229	0.290115	−	0.956992i	$-0.406307\pi$
$631$	5.81702e104	0.580229	0.290115	+	0.956992i	$0.406307\pi$
$632$	−6.05318e104	−0.568975
$633$	−8.90196e104	−0.788582
$634$	−7.14942e104	−0.596930
$635$	5.31063e104	0.417957
$636$	3.55517e104	0.263766
$637$	−7.93093e103	−0.0554748
$638$	−3.49217e104	−0.230314
$639$	−1.06313e105	−0.661158
$640$	−7.18698e103	−0.0421500
$641$	−6.02558e104	−0.333290	−0.166645	−	0.986017i	$-0.553293\pi$
$641$	−6.02558e104	−0.333290	−0.166645	+	0.986017i	$0.553293\pi$
$642$	9.25556e104	0.482880
$643$	3.75941e105	1.85016	0.925079	−	0.379776i	$-0.123999\pi$
$643$	3.75941e105	1.85016	0.925079	+	0.379776i	$0.123999\pi$
$644$	1.34623e105	0.625026
$645$	6.67291e103	0.0292298
$646$	2.76061e104	0.114100
$647$	1.67102e105	0.651737	0.325868	−	0.945415i	$-0.394343\pi$
$647$	1.67102e105	0.651737	0.325868	+	0.945415i	$0.394343\pi$
$648$	−3.00800e104	−0.110717
$649$	7.74883e103	0.0269191
$650$	1.26688e105	0.415417
$651$	9.15847e104	0.283489
$652$	1.52696e105	0.446214
$653$	−3.51917e105	−0.970949	−0.485474	−	0.874251i	$-0.661353\pi$
$653$	−3.51917e105	−0.970949	−0.485474	+	0.874251i	$0.661353\pi$
$654$	1.45953e105	0.380230
$655$	2.19665e105	0.540397
$656$	−4.55446e104	−0.105814
$657$	−5.62071e105	−1.23336
$658$	3.21751e105	0.666882
$659$	−4.70301e105	−0.920816	−0.460408	−	0.887707i	$-0.652297\pi$
$659$	−4.70301e105	−0.920816	−0.460408	+	0.887707i	$0.652297\pi$
$660$	2.92230e104	0.0540540
$661$	−8.54826e105	−1.49390	−0.746952	−	0.664878i	$-0.768484\pi$
$661$	−8.54826e105	−1.49390	−0.746952	+	0.664878i	$0.768484\pi$
$662$	1.85670e105	0.306596
$663$	−1.00306e105	−0.156520
$664$	−4.50834e105	−0.664835
$665$	1.29058e105	0.179877
$666$	−6.07023e105	−0.799690
$667$	7.48546e105	0.932180
$668$	−4.75698e105	−0.560034
$669$	−3.91105e105	−0.435325
$670$	2.38276e105	0.250770
$671$	−3.09564e105	−0.308075
$672$	−9.03786e104	−0.0850585
$673$	1.55076e106	1.38032	0.690158	−	0.723659i	$-0.257541\pi$
$673$	1.55076e106	1.38032	0.690158	+	0.723659i	$0.257541\pi$
$674$	4.69581e105	0.395334
$675$	−8.48569e105	−0.675765
$676$	−2.79931e105	−0.210887
$677$	−7.21673e105	−0.514358	−0.257179	−	0.966364i	$-0.582793\pi$
$677$	−7.21673e105	−0.514358	−0.257179	+	0.966364i	$0.582793\pi$
$678$	2.06554e104	0.0139290
$679$	2.29652e106	1.46539
$680$	−1.15006e105	−0.0694444
$681$	−2.09330e105	−0.119623
$682$	3.49426e105	0.188991
$683$	2.89170e106	1.48039	0.740196	−	0.672391i	$-0.234733\pi$
$683$	2.89170e106	1.48039	0.740196	+	0.672391i	$0.234733\pi$
$684$	3.03255e105	0.146962
$685$	1.76595e106	0.810182
$686$	−1.68179e106	−0.730494
$687$	3.64957e105	0.150094
$688$	−7.87386e104	−0.0306635
$689$	−2.17658e106	−0.802703
$690$	−6.26394e105	−0.218780
$691$	2.63690e106	0.872303	0.436152	−	0.899873i	$-0.356341\pi$
$691$	2.63690e106	0.872303	0.436152	+	0.899873i	$0.356341\pi$
$692$	−1.66006e106	−0.520171
$693$	−1.10401e106	−0.327700
$694$	3.04156e106	0.855297
$695$	−9.97386e105	−0.265725
$696$	−5.02535e105	−0.126859
$697$	−7.28807e105	−0.174334
$698$	−2.69327e106	−0.610523
$699$	−1.76906e106	−0.380056
$700$	1.82662e106	0.371939
$701$	−7.62304e106	−1.47130	−0.735652	−	0.677360i	$-0.763124\pi$
$701$	−7.62304e106	−1.47130	−0.735652	+	0.677360i	$0.763124\pi$
$702$	−2.57052e106	−0.470305
$703$	3.40463e106	0.590534
$704$	−3.44824e105	−0.0567052
$705$	−1.49710e106	−0.233431
$706$	6.37743e106	0.942908
$707$	−4.69451e106	−0.658207
$708$	1.11508e105	0.0148272
$709$	1.34186e107	1.69228	0.846142	−	0.532957i	$-0.178919\pi$
$709$	1.34186e107	1.69228	0.846142	+	0.532957i	$0.178919\pi$
$710$	−2.48409e106	−0.297153
$711$	−1.06405e107	−1.20740
$712$	4.55634e106	0.490474
$713$	−7.48993e106	−0.764927
$714$	−1.44624e106	−0.140139
$715$	−1.78913e106	−0.164499
$716$	5.06845e106	0.442218
$717$	3.27732e106	0.271363
$718$	5.34962e106	0.420394
$719$	−2.24405e107	−1.67378	−0.836890	−	0.547371i	$-0.815629\pi$
$719$	−2.24405e107	−1.67378	−0.836890	+	0.547371i	$0.815629\pi$
$720$	−1.26335e106	−0.0894449
$721$	1.82375e107	1.22572
$722$	9.38142e106	0.598582
$723$	4.04667e106	0.245139
$724$	6.88459e106	0.395988
$725$	1.01566e107	0.554719
$726$	−5.41110e106	−0.280648
$727$	1.32994e107	0.655077	0.327538	−	0.944838i	$-0.393781\pi$
$727$	1.32994e107	0.655077	0.327538	+	0.944838i	$0.393781\pi$
$728$	5.53326e106	0.258854
$729$	4.54960e106	0.202158
$730$	−1.31332e107	−0.554325
$731$	−1.25998e106	−0.0505198
$732$	−4.45473e106	−0.169690
$733$	1.18731e107	0.429701	0.214851	−	0.976647i	$-0.431074\pi$
$733$	1.18731e107	0.429701	0.214851	+	0.976647i	$0.431074\pi$
$734$	−1.12291e107	−0.386138
$735$	5.32067e105	0.0173857
$736$	7.39129e106	0.229510
$737$	1.14322e107	0.337366
$738$	−8.00599e106	−0.224544
$739$	−3.73411e106	−0.0995453	−0.0497726	−	0.998761i	$-0.515850\pi$
$739$	−3.73411e106	−0.0995453	−0.0497726	+	0.998761i	$0.515850\pi$
$740$	−1.41836e107	−0.359415
$741$	6.18010e106	0.148872
$742$	−3.13825e107	−0.718690
$743$	−3.36520e107	−0.732707	−0.366353	−	0.930476i	$-0.619394\pi$
$743$	−3.36520e107	−0.732707	−0.366353	+	0.930476i	$0.619394\pi$
$744$	5.02835e106	0.104097
$745$	2.48608e107	0.489390
$746$	−3.71927e107	−0.696229
$747$	−7.92492e107	−1.41082
$748$	−5.51789e106	−0.0934249
$749$	−8.17017e107	−1.31572
$750$	−1.95001e107	−0.298702
$751$	2.59910e107	0.378726	0.189363	−	0.981907i	$-0.439358\pi$
$751$	2.59910e107	0.378726	0.189363	+	0.981907i	$0.439358\pi$
$752$	1.76654e107	0.244880
$753$	2.25784e107	0.297770
$754$	3.07668e107	0.386062
$755$	6.24096e107	0.745145
$756$	−3.70624e107	−0.421081
$757$	1.54340e108	1.66872	0.834360	−	0.551220i	$-0.185837\pi$
$757$	1.54340e108	1.66872	0.834360	+	0.551220i	$0.185837\pi$
$758$	7.57571e107	0.779522
$759$	−3.00538e107	−0.294328
$760$	7.08579e106	0.0660509
$761$	1.52345e108	1.35177	0.675884	−	0.737008i	$-0.263762\pi$
$761$	1.52345e108	1.35177	0.675884	+	0.737008i	$0.263762\pi$
$762$	3.66663e107	0.309711
$763$	−1.28837e108	−1.03602
$764$	−8.58694e107	−0.657412
$765$	−2.02162e107	−0.147365
$766$	1.77766e108	1.23387
$767$	−6.82688e106	−0.0451228
$768$	−4.96213e106	−0.0312336
$769$	2.45626e108	1.47244	0.736220	−	0.676743i	$-0.236609\pi$
$769$	2.45626e108	1.47244	0.736220	+	0.676743i	$0.236609\pi$
$770$	−2.57961e107	−0.147282
$771$	−1.65182e108	−0.898302
$772$	−3.86762e107	−0.200353
$773$	−2.17522e108	−1.07343	−0.536713	−	0.843765i	$-0.680334\pi$
$773$	−2.17522e108	−1.07343	−0.536713	+	0.843765i	$0.680334\pi$
$774$	−1.38409e107	−0.0650698
$775$	−1.01627e108	−0.455191
$776$	1.26088e108	0.538095
$777$	−1.78363e108	−0.725298
$778$	1.07890e108	0.418068
$779$	4.49034e107	0.165815
$780$	−2.57461e107	−0.0906074
$781$	−1.19184e108	−0.399765
$782$	1.18276e108	0.378131
$783$	−2.06079e108	−0.628012
$784$	−6.27825e106	−0.0182384
$785$	2.52201e108	0.698450
$786$	1.51664e108	0.400440
$787$	−5.43232e108	−1.36752	−0.683759	−	0.729708i	$-0.739656\pi$
$787$	−5.43232e108	−1.36752	−0.683759	+	0.729708i	$0.739656\pi$
$788$	−1.59427e108	−0.382673
$789$	5.89446e107	0.134914
$790$	−2.48623e108	−0.542658
$791$	−1.82331e107	−0.0379528
$792$	−6.06143e107	−0.120332
$793$	2.72733e108	0.516407
$794$	−3.64054e108	−0.657503
$795$	1.46022e108	0.251565
$796$	−7.72818e107	−0.127010
$797$	3.98992e108	0.625572	0.312786	−	0.949824i	$-0.398738\pi$
$797$	3.98992e108	0.625572	0.312786	+	0.949824i	$0.398738\pi$
$798$	8.91062e107	0.133291
$799$	2.82682e108	0.403453
$800$	1.00288e108	0.136576
$801$	8.00928e108	1.04082
$802$	−8.89057e107	−0.110253
$803$	−6.30119e108	−0.745743
$804$	1.64514e108	0.185823
$805$	5.52937e108	0.596116
$806$	−3.07851e108	−0.316794
$807$	5.36659e108	0.527158
$808$	−2.57746e108	−0.241694
$809$	−3.48789e108	−0.312243	−0.156122	−	0.987738i	$-0.549899\pi$
$809$	−3.48789e108	−0.312243	−0.156122	+	0.987738i	$0.549899\pi$
$810$	−1.23548e108	−0.105596
$811$	6.33061e108	0.516610	0.258305	−	0.966063i	$-0.416836\pi$
$811$	6.33061e108	0.516610	0.258305	+	0.966063i	$0.416836\pi$
$812$	4.43603e108	0.345656
$813$	7.74640e108	0.576374
$814$	−6.80513e108	−0.483528
$815$	6.27171e108	0.425575
$816$	−7.94041e107	−0.0514591
$817$	7.76301e107	0.0480510
$818$	−5.01849e108	−0.296704
$819$	9.72655e108	0.549304
$820$	−1.87066e108	−0.100920
$821$	−2.74943e109	−1.41701	−0.708506	−	0.705704i	$-0.750631\pi$
$821$	−2.74943e109	−1.41701	−0.708506	+	0.705704i	$0.750631\pi$
$822$	1.21927e109	0.600354
$823$	−2.47134e109	−1.16262	−0.581311	−	0.813681i	$-0.697460\pi$
$823$	−2.47134e109	−1.16262	−0.581311	+	0.813681i	$0.697460\pi$
$824$	1.00131e109	0.450087
$825$	−4.07782e108	−0.175148
$826$	−9.84316e107	−0.0404001
$827$	2.19192e109	0.859742	0.429871	−	0.902890i	$-0.358559\pi$
$827$	2.19192e109	0.859742	0.429871	+	0.902890i	$0.358559\pi$
$828$	1.29927e109	0.487035
$829$	−4.49573e109	−1.61067	−0.805333	−	0.592822i	$-0.798014\pi$
$829$	−4.49573e109	−1.61067	−0.805333	+	0.592822i	$0.798014\pi$
$830$	−1.85172e109	−0.634084
$831$	−2.39195e109	−0.782913
$832$	3.03797e108	0.0950515
$833$	−1.00465e108	−0.0300488
$834$	−6.88628e108	−0.196905
$835$	−1.95384e109	−0.534130
$836$	3.39969e108	0.0888596
$837$	2.06202e109	0.515333
$838$	−2.05180e109	−0.490325
$839$	1.84537e109	0.421706	0.210853	−	0.977518i	$-0.432376\pi$
$839$	1.84537e109	0.421706	0.210853	+	0.977518i	$0.432376\pi$
$840$	−3.71213e108	−0.0811242
$841$	−2.31807e109	−0.484480
$842$	5.98992e109	1.19734
$843$	2.19071e109	0.418843
$844$	4.31436e109	0.788996
$845$	−1.14976e109	−0.201132
$846$	3.10527e109	0.519650
$847$	4.77654e109	0.764691
$848$	−1.72302e109	−0.263904
$849$	−6.06357e108	−0.0888566
$850$	1.60482e109	0.225017
$851$	1.45868e110	1.95704
$852$	−1.71510e109	−0.220194
$853$	−4.89137e109	−0.600955	−0.300478	−	0.953789i	$-0.597146\pi$
$853$	−4.89137e109	−0.600955	−0.300478	+	0.953789i	$0.597146\pi$
$854$	3.93233e109	0.462359
$855$	1.24556e109	0.140164
$856$	−4.48573e109	−0.483133
$857$	−1.75806e109	−0.181239	−0.0906197	−	0.995886i	$-0.528885\pi$
$857$	−1.75806e109	−0.181239	−0.0906197	+	0.995886i	$0.528885\pi$
$858$	−1.23527e109	−0.121896
$859$	−1.03510e110	−0.977773	−0.488887	−	0.872347i	$-0.662597\pi$
$859$	−1.03510e110	−0.977773	−0.488887	+	0.872347i	$0.662597\pi$
$860$	−3.23404e108	−0.0292452
$861$	−2.35242e109	−0.203655
$862$	−1.20649e110	−1.00000
$863$	1.08649e110	0.862226	0.431113	−	0.902298i	$-0.358121\pi$
$863$	1.08649e110	0.862226	0.431113	+	0.902298i	$0.358121\pi$
$864$	−2.03487e109	−0.154622
$865$	−6.81841e109	−0.496111
$866$	−5.67162e109	−0.395172
$867$	6.21897e109	0.414956
$868$	−4.43868e109	−0.283638
$869$	−1.19287e110	−0.730048
$870$	−2.06407e109	−0.120991
$871$	−1.00720e110	−0.565505
$872$	−7.07363e109	−0.380429
$873$	2.21641e110	1.14187
$874$	−7.28723e109	−0.359653
$875$	1.72133e110	0.813883
$876$	−9.06761e109	−0.410761
$877$	−3.02788e110	−1.31418	−0.657088	−	0.753814i	$-0.728212\pi$
$877$	−3.02788e110	−1.31418	−0.657088	+	0.753814i	$0.728212\pi$
$878$	2.33668e110	0.971749
$879$	1.55319e110	0.618931
$880$	−1.41630e109	−0.0540823
$881$	1.61834e110	0.592206	0.296103	−	0.955156i	$-0.404313\pi$
$881$	1.61834e110	0.592206	0.296103	+	0.955156i	$0.404313\pi$
$882$	−1.10361e109	−0.0387030
$883$	−1.15760e110	−0.389073	−0.194536	−	0.980895i	$-0.562320\pi$
$883$	−1.15760e110	−0.389073	−0.194536	+	0.980895i	$0.562320\pi$
$884$	4.86137e109	0.156603
$885$	4.57999e108	0.0141414
$886$	8.00436e109	0.236898
$887$	3.17666e110	0.901229	0.450615	−	0.892719i	$-0.351205\pi$
$887$	3.17666e110	0.901229	0.450615	+	0.892719i	$0.351205\pi$
$888$	−9.79280e109	−0.266330
$889$	−3.23665e110	−0.843878
$890$	1.87143e110	0.467787
$891$	−5.92771e109	−0.142060
$892$	1.89550e110	0.435553
$893$	−1.74166e110	−0.383738
$894$	1.71647e110	0.362643
$895$	2.08177e110	0.421763
$896$	4.38022e109	0.0851032
$897$	2.64780e110	0.493365
$898$	−8.91294e109	−0.159279
$899$	−2.46805e110	−0.423025
$900$	1.76290e110	0.289823
$901$	−2.75718e110	−0.434796
$902$	−8.97524e109	−0.135769
$903$	−4.06691e109	−0.0590166
$904$	−1.00107e109	−0.0139363
$905$	2.82772e110	0.377672
$906$	4.30896e110	0.552161
$907$	8.12073e110	0.998440	0.499220	−	0.866475i	$-0.333620\pi$
$907$	8.12073e110	0.998440	0.499220	+	0.866475i	$0.333620\pi$
$908$	1.01452e110	0.119686
$909$	−4.53075e110	−0.512890
$910$	2.27269e110	0.246881
$911$	−1.14284e111	−1.19137	−0.595686	−	0.803217i	$-0.703120\pi$
$911$	−1.14284e111	−1.19137	−0.595686	+	0.803217i	$0.703120\pi$
$912$	4.89227e109	0.0489445
$913$	−8.88436e110	−0.853045
$914$	−7.68074e110	−0.707816
$915$	−1.82970e110	−0.161841
$916$	−1.76877e110	−0.150173
$917$	−1.33879e111	−1.09109
$918$	−3.25620e110	−0.254748
$919$	−5.42637e110	−0.407547	−0.203774	−	0.979018i	$-0.565321\pi$
$919$	−5.42637e110	−0.407547	−0.203774	+	0.979018i	$0.565321\pi$
$920$	3.03584e110	0.218894
$921$	−3.43176e110	−0.237564
$922$	1.99118e110	0.132343
$923$	1.05004e111	0.670102
$924$	−1.78104e110	−0.109138
$925$	1.97920e111	1.16459
$926$	−1.41922e111	−0.801932
$927$	1.76013e111	0.955112
$928$	2.43555e110	0.126925
$929$	3.25795e110	0.163063	0.0815315	−	0.996671i	$-0.474019\pi$
$929$	3.25795e110	0.163063	0.0815315	+	0.996671i	$0.474019\pi$
$930$	2.06530e110	0.0992825
$931$	6.18986e109	0.0285804
$932$	8.57378e110	0.380255
$933$	−2.15440e110	−0.0917837
$934$	−2.23070e111	−0.912920
$935$	−2.26637e110	−0.0891036
$936$	5.34025e110	0.201705
$937$	4.45116e111	1.61525	0.807623	−	0.589699i	$-0.200754\pi$
$937$	4.45116e111	1.61525	0.807623	+	0.589699i	$0.200754\pi$
$938$	−1.45221e111	−0.506318
$939$	−1.84519e111	−0.618131
$940$	7.25572e110	0.233553
$941$	6.22369e111	1.92503	0.962515	−	0.271230i	$-0.0874303\pi$
$941$	6.22369e111	1.92503	0.962515	+	0.271230i	$0.0874303\pi$
$942$	1.74128e111	0.517559
$943$	1.92384e111	0.549516
$944$	−5.40427e109	−0.0148350
$945$	−1.52227e111	−0.401604
$946$	−1.55166e110	−0.0393441
$947$	−5.79575e111	−1.41249	−0.706245	−	0.707968i	$-0.749612\pi$
$947$	−5.79575e111	−1.41249	−0.706245	+	0.707968i	$0.749612\pi$
$948$	−1.71658e111	−0.402115
$949$	5.55148e111	1.25004
$950$	−9.88762e110	−0.214021
$951$	−2.02745e111	−0.421872
$952$	7.00925e110	0.140212
$953$	−2.84040e111	−0.546256	−0.273128	−	0.961978i	$-0.588058\pi$
$953$	−2.84040e111	−0.546256	−0.273128	+	0.961978i	$0.588058\pi$
$954$	−3.02878e111	−0.560020
$955$	−3.52693e111	−0.627004
$956$	−1.58836e111	−0.271505
$957$	−9.90320e110	−0.162771
$958$	5.30995e111	0.839236
$959$	−1.07629e112	−1.63580
$960$	−2.03810e110	−0.0297889
$961$	−4.64469e111	−0.652875
$962$	5.99546e111	0.810508
$963$	−7.88517e111	−1.02524
$964$	−1.96123e111	−0.245267
$965$	−1.58855e111	−0.191085
$966$	3.81766e111	0.441728
$967$	6.63866e111	0.738903	0.369451	−	0.929250i	$-0.379546\pi$
$967$	6.63866e111	0.738903	0.369451	+	0.929250i	$0.379546\pi$
$968$	2.62250e111	0.280795
$969$	7.82862e110	0.0806387
$970$	5.17883e111	0.513205
$971$	−8.71746e110	−0.0831130	−0.0415565	−	0.999136i	$-0.513232\pi$
$971$	−8.71746e110	−0.0831130	−0.0415565	+	0.999136i	$0.513232\pi$
$972$	−5.62062e111	−0.515584
$973$	6.07873e111	0.536514
$974$	−2.53531e111	−0.215313
$975$	3.59265e111	0.293590
$976$	2.15900e111	0.169779
$977$	2.35835e112	1.78469	0.892345	−	0.451355i	$-0.149059\pi$
$977$	2.35835e112	1.78469	0.892345	+	0.451355i	$0.149059\pi$
$978$	4.33019e111	0.315355
$979$	8.97894e111	0.629323
$980$	−2.57868e110	−0.0173948
$981$	−1.24343e112	−0.807295
$982$	1.88720e111	0.117933
$983$	−1.64466e112	−0.989282	−0.494641	−	0.869097i	$-0.664700\pi$
$983$	−1.64466e112	−0.989282	−0.494641	+	0.869097i	$0.664700\pi$
$984$	−1.29157e111	−0.0747826
$985$	−6.54815e111	−0.364972
$986$	3.89737e111	0.209116
$987$	9.12430e111	0.471309
$988$	−2.99520e111	−0.148950
$989$	3.32598e111	0.159242
$990$	−2.48962e111	−0.114766
$991$	−1.37374e111	−0.0609736	−0.0304868	−	0.999535i	$-0.509706\pi$
$991$	−1.37374e111	−0.0609736	−0.0304868	+	0.999535i	$0.509706\pi$
$992$	−2.43700e111	−0.104152
$993$	5.26526e111	0.216682
$994$	1.51397e112	0.599968
$995$	−3.17421e111	−0.121135
$996$	−1.27849e112	−0.469863
$997$	4.47235e112	1.58295	0.791475	−	0.611202i	$-0.209314\pi$
$997$	4.47235e112	1.58295	0.791475	+	0.611202i	$0.209314\pi$
$998$	−3.31660e112	−1.13057
$999$	−4.01582e112	−1.31847

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.76.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.37439e11 q^{2} -3.89753e17 q^{3} +1.88895e22 q^{4} +7.75850e25 q^{5} +5.35672e28 q^{6} -4.72854e31 q^{7} -2.59615e33 q^{8} -4.56360e35 q^{9} -1.06632e37 q^{10} -5.11609e38 q^{11} -7.36222e39 q^{12} +4.50738e41 q^{13} +6.49886e42 q^{14} -3.02390e43 q^{15} +3.56812e44 q^{16} +5.70972e45 q^{17} +6.27216e46 q^{18} -3.51788e47 q^{19} +1.46554e48 q^{20} +1.84296e49 q^{21} +7.03151e49 q^{22} -1.50720e51 q^{23} +1.01186e51 q^{24} -2.04504e52 q^{25} -6.19490e52 q^{26} +4.14941e53 q^{27} -8.93196e53 q^{28} -4.96647e54 q^{29} +4.15601e54 q^{30} +4.96943e55 q^{31} -4.90399e55 q^{32} +1.99401e56 q^{33} -7.84737e56 q^{34} -3.66864e57 q^{35} -8.62039e57 q^{36} -9.67806e58 q^{37} +4.83494e58 q^{38} -1.75677e59 q^{39} -2.01422e59 q^{40} -1.27643e60 q^{41} -2.53295e60 q^{42} -2.20673e60 q^{43} -9.66403e60 q^{44} -3.54066e61 q^{45} +2.07148e62 q^{46} +4.95089e62 q^{47} -1.39068e62 q^{48} -1.75954e62 q^{49} +2.81067e63 q^{50} -2.22538e63 q^{51} +8.51421e63 q^{52} -4.82893e64 q^{53} -5.70291e64 q^{54} -3.96932e64 q^{55} +1.22760e65 q^{56} +1.37110e65 q^{57} +6.82586e65 q^{58} -1.51460e65 q^{59} -5.71198e65 q^{60} +6.05079e66 q^{61} -6.82993e66 q^{62} +2.15792e67 q^{63} +6.73999e66 q^{64} +3.49705e67 q^{65} -2.74055e67 q^{66} -2.23457e68 q^{67} +1.07853e68 q^{68} +5.87436e68 q^{69} +5.04214e68 q^{70} +2.32960e69 q^{71} +1.18478e69 q^{72} +1.23164e70 q^{73} +1.33014e70 q^{74} +7.97058e69 q^{75} -6.64509e69 q^{76} +2.41917e70 q^{77} +2.41448e70 q^{78} +2.33160e71 q^{79} +2.76832e70 q^{80} +1.15864e71 q^{81} +1.75432e71 q^{82} +1.73655e72 q^{83} +3.48126e71 q^{84} +4.42988e71 q^{85} +3.03290e71 q^{86} +1.93569e72 q^{87} +1.32821e72 q^{88} -1.75504e73 q^{89} +4.86625e72 q^{90} -2.13134e73 q^{91} -2.84702e73 q^{92} -1.93685e73 q^{93} -6.80445e73 q^{94} -2.72935e73 q^{95} +1.91134e73 q^{96} -4.85673e74 q^{97} +2.41830e73 q^{98} +2.33478e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 412316860416 q^{2} + 12\!\cdots\!04 q^{3} + 56\!\cdots\!52 q^{4} + 16\!\cdots\!50 q^{5} - 17\!\cdots\!88 q^{6} + 49\!\cdots\!12 q^{7} - 77\!\cdots\!44 q^{8} + 35\!\cdots\!51 q^{9} - 22\!\cdots\!00 q^{10}+ \cdots - 11\!\cdots\!68 q^{99}+O(q^{100}) \) 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

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Groups

Database

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