LMFDB - Embedded newform 21.30.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(1,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 30, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$111.883889004$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 110200839 x^{4} - 84515300136 x^{3} + \cdots - 12\!\cdots\!00 $ x^6 - 110200839x^4 - 84515300136x^3 + 2909822349515976x^2 + 3144706297269234912x - 12496546686906381337200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{8}\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-5362.48$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20705.9 q^{2} +4.78297e6 q^{3} -1.08136e8 q^{4} +1.18612e10 q^{5} -9.90357e10 q^{6} +6.78223e11 q^{7} +1.33555e13 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q-20705.9 q^{2} +4.78297e6 q^{3} -1.08136e8 q^{4} +1.18612e10 q^{5} -9.90357e10 q^{6} +6.78223e11 q^{7} +1.33555e13 q^{8} +2.28768e13 q^{9} -2.45596e14 q^{10} +5.61873e14 q^{11} -5.17212e14 q^{12} -5.01240e15 q^{13} -1.40432e16 q^{14} +5.67316e16 q^{15} -2.18482e17 q^{16} -6.41669e17 q^{17} -4.73685e17 q^{18} +4.30377e17 q^{19} -1.28262e18 q^{20} +3.24392e18 q^{21} -1.16341e19 q^{22} +9.94615e18 q^{23} +6.38787e19 q^{24} -4.55772e19 q^{25} +1.03786e20 q^{26} +1.09419e20 q^{27} -7.33404e19 q^{28} -2.76102e21 q^{29} -1.17468e21 q^{30} -1.03438e21 q^{31} -2.64629e21 q^{32} +2.68742e21 q^{33} +1.32863e22 q^{34} +8.04452e21 q^{35} -2.47381e21 q^{36} +1.16676e22 q^{37} -8.91134e21 q^{38} -2.39742e22 q^{39} +1.58411e23 q^{40} -1.68160e23 q^{41} -6.71683e22 q^{42} -6.59027e22 q^{43} -6.07588e22 q^{44} +2.71345e23 q^{45} -2.05944e23 q^{46} -2.45224e24 q^{47} -1.04499e24 q^{48} +4.59987e23 q^{49} +9.43718e23 q^{50} -3.06908e24 q^{51} +5.42022e23 q^{52} +3.48184e24 q^{53} -2.26562e24 q^{54} +6.66447e24 q^{55} +9.05798e24 q^{56} +2.05848e24 q^{57} +5.71694e25 q^{58} +7.73601e25 q^{59} -6.13474e24 q^{60} -3.73143e25 q^{61} +2.14179e25 q^{62} +1.55156e25 q^{63} +1.72090e26 q^{64} -5.94529e25 q^{65} -5.56455e25 q^{66} +2.24582e26 q^{67} +6.93876e25 q^{68} +4.75721e25 q^{69} -1.66569e26 q^{70} +4.49599e26 q^{71} +3.05530e26 q^{72} +3.72244e26 q^{73} -2.41589e26 q^{74} -2.17995e26 q^{75} -4.65393e25 q^{76} +3.81075e26 q^{77} +4.96407e26 q^{78} +2.90538e27 q^{79} -2.59145e27 q^{80} +5.23348e26 q^{81} +3.48190e27 q^{82} -2.68756e27 q^{83} -3.50785e26 q^{84} -7.61094e27 q^{85} +1.36457e27 q^{86} -1.32059e28 q^{87} +7.50407e27 q^{88} -3.21549e28 q^{89} -5.61845e27 q^{90} -3.39953e27 q^{91} -1.07554e27 q^{92} -4.94743e27 q^{93} +5.07758e28 q^{94} +5.10477e27 q^{95} -1.26571e28 q^{96} -5.82099e28 q^{97} -9.52444e27 q^{98} +1.28539e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4464 q^{2} + 28697814 q^{3} + 308522592 q^{4} - 34057000980 q^{5} + 21351173616 q^{6} + 4069338437094 q^{7} + 19307209833216 q^{8} + 137260754729766 q^{9}+O(q^{10}) $ 6 * q + 4464 * q^2 + 28697814 * q^3 + 308522592 * q^4 - 34057000980 * q^5 + 21351173616 * q^6 + 4069338437094 * q^7 + 19307209833216 * q^8 + 137260754729766 * q^9	$ 6 q + 4464 q^{2} + 28697814 q^{3} + 308522592 q^{4} - 34057000980 q^{5} + 21351173616 q^{6} + 4069338437094 q^{7} + 19307209833216 q^{8} + 137260754729766 q^{9} - 27416413415040 q^{10} - 19\!\cdots\!00 q^{11}+ \cdots - 44\!\cdots\!00 q^{99}+O(q^{100}) $ 6 * q + 4464 * q^2 + 28697814 * q^3 + 308522592 * q^4 - 34057000980 * q^5 + 21351173616 * q^6 + 4069338437094 * q^7 + 19307209833216 * q^8 + 137260754729766 * q^9 - 27416413415040 * q^10 - 1943661000024000 * q^11 + 1475653993335648 * q^12 - 13450748854074012 * q^13 + 3027587797197936 * q^14 - 162893579920309620 * q^15 - 657484628537888256 * q^16 - 891734887537201404 * q^17 + 102122001518945904 * q^18 - 6787214411699759016 * q^19 - 4606719795227370240 * q^20 + 19463519595129052086 * q^21 + 58706820582380556000 * q^22 + 4141068849861725304 * q^23 + 92345786108767298304 * q^24 + 272136706732123231050 * q^25 - 341440176492089614368 * q^26 + 656513934789074155254 * q^27 + 209247140389578304608 * q^28 + 2585597660188970274612 * q^29 - 131131855455320453760 * q^30 - 1204878539299247831904 * q^31 - 4159797202844651556864 * q^32 - 9296470309623791256000 * q^33 - 21195441540025996469376 * q^34 - 23098243856677004392020 * q^35 + 7058007304850610978912 * q^36 - 132254788220404822298508 * q^37 - 220889407221302869969344 * q^38 - 64334514795821523101628 * q^39 - 437212759571392303349760 * q^40 - 26110030054236268409244 * q^41 + 14480858578776014751984 * q^42 + 141767508828723725476008 * q^43 - 188729676402659111433024 * q^44 - 779114943057863382861780 * q^45 - 2085553124450449717109280 * q^46 - 2578234389089045150723184 * q^47 - 3144728596273234853912064 * q^48 + 2759919219268439765860806 * q^49 + 941455479402850770594000 * q^50 - 4265140323308920662088476 * q^51 - 3374918204913260684537664 * q^52 - 2752352962631124928912908 * q^53 + 488446367483071171508976 * q^54 - 96873810309318198174960 * q^55 + 13094595181224184307952384 * q^56 - 32463036127513184680998504 * q^57 + 5390021975912281392317856 * q^58 + 29783273333457762702531576 * q^59 - 22033797972258859809442560 * q^60 - 95449739708469802905230316 * q^61 + 237026204448598888591992192 * q^62 + 93093410854394807126723334 * q^63 - 32040206007864683612381184 * q^64 + 269913485905060559518443240 * q^65 + 280792902934088145550764000 * q^66 - 238913035844993441877771960 * q^67 + 981842221641787438830499584 * q^68 + 19806603935754286415547576 * q^69 - 18594444152846974792248960 * q^70 - 115682196667471827012154872 * q^71 + 441687032238864616001784576 * q^72 + 458603587013811635903661420 * q^73 - 446904060615029827280849184 * q^74 + 1301621432061836718291987450 * q^75 - 6092111550972759049305091968 * q^76 - 1318235736013037542748376000 * q^77 - 1633097779516193370744098592 * q^78 - 10034906777945539831743009648 * q^79 - 5997340528902652488008601600 * q^80 + 3140085798164163223281069126 * q^81 - 8752939790814405210267639360 * q^82 - 19309516074459975169018955016 * q^83 + 1000822585822000954012621152 * q^84 - 4150151002407090538173069480 * q^85 - 4621430320291243191543788736 * q^86 + 12366833455156378965390683028 * q^87 + 25799589562519757129329307136 * q^88 + 29301646004663462420780732292 * q^89 - 627199599555278615400013440 * q^90 - 9122608219930241911113700188 * q^91 + 14620997740278659176227485376 * q^92 - 5762896702233584103314042976 * q^93 - 78217476468449813455052050368 * q^94 + 99722018112699072468995806320 * q^95 - 19896181067492680212282249216 * q^96 - 7806999688449057487843013988 * q^97 + 2053379899135719185800439664 * q^98 - 44464729300350995239919064000 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−20705.9	−0.893633	−0.446817	−	0.894626i	$-0.647442\pi$
$2$	−20705.9	−0.893633	−0.446817	+	0.894626i	$0.647442\pi$
$3$	4.78297e6	0.577350
$3$	4.78297e6	0.577350
$4$	−1.08136e8	−0.201419
$5$	1.18612e10	0.869085	0.434543	−	0.900651i	$-0.356910\pi$
$5$	1.18612e10	0.869085	0.434543	+	0.900651i	$0.356910\pi$
$6$	−9.90357e10	−0.515940
$7$	6.78223e11	0.377964
$7$	6.78223e11	0.377964
$8$	1.33555e13	1.07363
$9$	2.28768e13	0.333333
$10$	−2.45596e14	−0.776644
$11$	5.61873e14	0.446112	0.223056	−	0.974806i	$-0.428397\pi$
$11$	5.61873e14	0.446112	0.223056	+	0.974806i	$0.428397\pi$
$12$	−5.17212e14	−0.116289
$13$	−5.01240e15	−0.353075	−0.176538	−	0.984294i	$-0.556490\pi$
$13$	−5.01240e15	−0.353075	−0.176538	+	0.984294i	$0.556490\pi$
$14$	−1.40432e16	−0.337762
$15$	5.67316e16	0.501767
$16$	−2.18482e17	−0.758011
$17$	−6.41669e17	−0.924276	−0.462138	−	0.886808i	$-0.652918\pi$
$17$	−6.41669e17	−0.924276	−0.462138	+	0.886808i	$0.652918\pi$
$18$	−4.73685e17	−0.297878
$19$	4.30377e17	0.123572	0.0617862	−	0.998089i	$-0.480320\pi$
$19$	4.30377e17	0.123572	0.0617862	+	0.998089i	$0.480320\pi$
$20$	−1.28262e18	−0.175050
$21$	3.24392e18	0.218218
$22$	−1.16341e19	−0.398661
$23$	9.94615e18	0.178896	0.0894481	−	0.995991i	$-0.471490\pi$
$23$	9.94615e18	0.178896	0.0894481	+	0.995991i	$0.471490\pi$
$24$	6.38787e19	0.619860
$25$	−4.55772e19	−0.244691
$26$	1.03786e20	0.315520
$27$	1.09419e20	0.192450
$28$	−7.33404e19	−0.0761293
$29$	−2.76102e21	−1.72305	−0.861526	−	0.507713i	$-0.830491\pi$
$29$	−2.76102e21	−1.72305	−0.861526	+	0.507713i	$0.830491\pi$
$30$	−1.17468e21	−0.448395
$31$	−1.03438e21	−0.245436	−0.122718	−	0.992442i	$-0.539161\pi$
$31$	−1.03438e21	−0.245436	−0.122718	+	0.992442i	$0.539161\pi$
$32$	−2.64629e21	−0.396244
$33$	2.68742e21	0.257563
$34$	1.32863e22	0.825964
$35$	8.04452e21	0.328483
$36$	−2.47381e21	−0.0671398
$37$	1.16676e22	0.212842	0.106421	−	0.994321i	$-0.466061\pi$
$37$	1.16676e22	0.212842	0.106421	+	0.994321i	$0.466061\pi$
$38$	−8.91134e21	−0.110428
$39$	−2.39742e22	−0.203848
$40$	1.58411e23	0.933075
$41$	−1.68160e23	−0.692398	−0.346199	−	0.938161i	$-0.612528\pi$
$41$	−1.68160e23	−0.692398	−0.346199	+	0.938161i	$0.612528\pi$
$42$	−6.71683e22	−0.195007
$43$	−6.59027e22	−0.136022	−0.0680112	−	0.997685i	$-0.521665\pi$
$43$	−6.59027e22	−0.136022	−0.0680112	+	0.997685i	$0.521665\pi$
$44$	−6.07588e22	−0.0898556
$45$	2.71345e23	0.289695
$46$	−2.05944e23	−0.159868
$47$	−2.45224e24	−1.39362	−0.696808	−	0.717257i	$-0.745397\pi$
$47$	−2.45224e24	−1.39362	−0.696808	+	0.717257i	$0.745397\pi$
$48$	−1.04499e24	−0.437638
$49$	4.59987e23	0.142857
$50$	9.43718e23	0.218664
$51$	−3.06908e24	−0.533631
$52$	5.42022e23	0.0711162
$53$	3.48184e24	0.346584	0.173292	−	0.984870i	$-0.444560\pi$
$53$	3.48184e24	0.346584	0.173292	+	0.984870i	$0.444560\pi$
$54$	−2.26562e24	−0.171980
$55$	6.66447e24	0.387710
$56$	9.05798e24	0.405793
$57$	2.05848e24	0.0713446
$58$	5.71694e25	1.53978
$59$	7.73601e25	1.62616	0.813079	−	0.582153i	$-0.197790\pi$
$59$	7.73601e25	1.62616	0.813079	+	0.582153i	$0.197790\pi$
$60$	−6.13474e24	−0.101065
$61$	−3.73143e25	−0.483719	−0.241859	−	0.970311i	$-0.577757\pi$
$61$	−3.73143e25	−0.483719	−0.241859	+	0.970311i	$0.577757\pi$
$62$	2.14179e25	0.219329
$63$	1.55156e25	0.125988
$64$	1.72090e26	1.11211
$65$	−5.94529e25	−0.306852
$66$	−5.56455e25	−0.230167
$67$	2.24582e26	0.746947	0.373474	−	0.927641i	$-0.378167\pi$
$67$	2.24582e26	0.746947	0.373474	+	0.927641i	$0.378167\pi$
$68$	6.93876e25	0.186167
$69$	4.75721e25	0.103286
$70$	−1.66569e26	−0.293544
$71$	4.49599e26	0.645030	0.322515	−	0.946564i	$-0.395472\pi$
$71$	4.49599e26	0.645030	0.322515	+	0.946564i	$0.395472\pi$
$72$	3.05530e26	0.357876
$73$	3.72244e26	0.356982	0.178491	−	0.983942i	$-0.442879\pi$
$73$	3.72244e26	0.356982	0.178491	+	0.983942i	$0.442879\pi$
$74$	−2.41589e26	−0.190203
$75$	−2.17995e26	−0.141272
$76$	−4.65393e25	−0.0248899
$77$	3.81075e26	0.168615
$78$	4.96407e26	0.182165
$79$	2.90538e27	0.886360	0.443180	−	0.896433i	$-0.353850\pi$
$79$	2.90538e27	0.886360	0.443180	+	0.896433i	$0.353850\pi$
$80$	−2.59145e27	−0.658776
$81$	5.23348e26	0.111111
$82$	3.48190e27	0.618750
$83$	−2.68756e27	−0.400614	−0.200307	−	0.979733i	$-0.564194\pi$
$83$	−2.68756e27	−0.400614	−0.200307	+	0.979733i	$0.564194\pi$
$84$	−3.50785e26	−0.0439533
$85$	−7.61094e27	−0.803275
$86$	1.36457e27	0.121554
$87$	−1.32059e28	−0.994805
$88$	7.50407e27	0.478959
$89$	−3.21549e28	−1.74218	−0.871089	−	0.491125i	$-0.836586\pi$
$89$	−3.21549e28	−1.74218	−0.871089	+	0.491125i	$0.836586\pi$
$90$	−5.61845e27	−0.258881
$91$	−3.39953e27	−0.133450
$92$	−1.07554e27	−0.0360331
$93$	−4.94743e27	−0.141702
$94$	5.07758e28	1.24538
$95$	5.10477e27	0.107395
$96$	−1.26571e28	−0.228772
$97$	−5.82099e28	−0.905330	−0.452665	−	0.891681i	$-0.649527\pi$
$97$	−5.82099e28	−0.905330	−0.452665	+	0.891681i	$0.649527\pi$
$98$	−9.52444e27	−0.127662
$99$	1.28539e28	0.148704
$100$	4.92855e27	0.0492855
$101$	−4.64193e28	−0.401827	−0.200913	−	0.979609i	$-0.564391\pi$
$101$	−4.64193e28	−0.401827	−0.200913	+	0.979609i	$0.564391\pi$
$102$	6.35482e28	0.476871
$103$	−2.25982e29	−1.47209	−0.736044	−	0.676934i	$-0.763308\pi$
$103$	−2.25982e29	−1.47209	−0.736044	+	0.676934i	$0.763308\pi$
$104$	−6.69429e28	−0.379072
$105$	3.84767e28	0.189650
$106$	−7.20947e28	−0.309719
$107$	−1.16616e29	−0.437212	−0.218606	−	0.975813i	$-0.570151\pi$
$107$	−1.16616e29	−0.437212	−0.218606	+	0.975813i	$0.570151\pi$
$108$	−1.18321e28	−0.0387632
$109$	−1.69332e29	−0.485349	−0.242674	−	0.970108i	$-0.578025\pi$
$109$	−1.69332e29	−0.485349	−0.242674	+	0.970108i	$0.578025\pi$
$110$	−1.37994e29	−0.346470
$111$	5.58059e28	0.122884
$112$	−1.48179e29	−0.286501
$113$	3.07421e29	0.522512	0.261256	−	0.965270i	$-0.415863\pi$
$113$	3.07421e29	0.522512	0.261256	+	0.965270i	$0.415863\pi$
$114$	−4.26227e28	−0.0637559
$115$	1.17973e29	0.155476
$116$	2.98566e29	0.347056
$117$	−1.14668e29	−0.117692
$118$	−1.60181e30	−1.45319
$119$	−4.35195e29	−0.349344
$120$	7.57676e29	0.538711
$121$	−1.27061e30	−0.800984
$122$	7.72627e29	0.432267
$123$	−8.04303e29	−0.399756
$124$	1.11854e29	0.0494355
$125$	−2.74991e30	−1.08174
$126$	−3.21264e29	−0.112587
$127$	3.23790e30	1.01184	0.505918	−	0.862582i	$-0.331154\pi$
$127$	3.23790e30	1.01184	0.505918	+	0.862582i	$0.331154\pi$
$128$	−2.14257e30	−0.597573
$129$	−3.15210e29	−0.0785325
$130$	1.23103e30	0.274214
$131$	2.13467e30	0.425498	0.212749	−	0.977107i	$-0.431758\pi$
$131$	2.13467e30	0.425498	0.212749	+	0.977107i	$0.431758\pi$
$132$	−2.90607e29	−0.0518782
$133$	2.91891e29	0.0467060
$134$	−4.65017e30	−0.667497
$135$	1.29784e30	0.167256
$136$	−8.56979e30	−0.992329
$137$	−1.58268e31	−1.64795	−0.823977	−	0.566623i	$-0.808249\pi$
$137$	−1.58268e31	−1.64795	−0.823977	+	0.566623i	$0.808249\pi$
$138$	−9.85024e29	−0.0922996
$139$	−1.07016e31	−0.903097	−0.451548	−	0.892247i	$-0.649128\pi$
$139$	−1.07016e31	−0.903097	−0.451548	+	0.892247i	$0.649128\pi$
$140$	−8.69903e29	−0.0661629
$141$	−1.17290e31	−0.804605
$142$	−9.30937e30	−0.576420
$143$	−2.81633e30	−0.157511
$144$	−4.99816e30	−0.252670
$145$	−3.27489e31	−1.49748
$146$	−7.70765e30	−0.319011
$147$	2.20010e30	0.0824786
$148$	−1.26169e30	−0.0428705
$149$	4.30979e30	0.132817	0.0664087	−	0.997793i	$-0.478846\pi$
$149$	4.30979e30	0.132817	0.0664087	+	0.997793i	$0.478846\pi$
$150$	4.51377e30	0.126246
$151$	−4.14677e31	−1.05328	−0.526640	−	0.850088i	$-0.676548\pi$
$151$	−4.14677e31	−1.05328	−0.526640	+	0.850088i	$0.676548\pi$
$152$	5.74788e30	0.132671
$153$	−1.46793e31	−0.308092
$154$	−7.89051e30	−0.150680
$155$	−1.22690e31	−0.213304
$156$	2.59247e30	0.0410589
$157$	9.86360e30	0.142394	0.0711968	−	0.997462i	$-0.477318\pi$
$157$	9.86360e30	0.142394	0.0711968	+	0.997462i	$0.477318\pi$
$158$	−6.01586e31	−0.792081
$159$	1.66535e31	0.200100
$160$	−3.13881e31	−0.344370
$161$	6.74571e30	0.0676164
$162$	−1.08364e31	−0.0992926
$163$	9.44955e31	0.791937	0.395969	−	0.918264i	$-0.370409\pi$
$163$	9.44955e31	0.791937	0.395969	+	0.918264i	$0.370409\pi$
$164$	1.81841e31	0.139462
$165$	3.18760e31	0.223844
$166$	5.56484e31	0.358002
$167$	−1.80762e30	−0.0106591	−0.00532953	−	0.999986i	$-0.501696\pi$
$167$	−1.80762e30	−0.0106591	−0.00532953	+	0.999986i	$0.501696\pi$
$168$	4.33240e31	0.234285
$169$	−1.76414e32	−0.875338
$170$	1.57592e32	0.717833
$171$	9.84564e30	0.0411908
$172$	7.12646e30	0.0273975
$173$	4.84813e32	1.71359	0.856793	−	0.515660i	$-0.172453\pi$
$173$	4.84813e32	1.71359	0.856793	+	0.515660i	$0.172453\pi$
$174$	2.73440e32	0.888991
$175$	−3.09115e31	−0.0924845
$176$	−1.22759e32	−0.338158
$177$	3.70011e32	0.938863
$178$	6.65797e32	1.55687
$179$	3.70827e32	0.799470	0.399735	−	0.916631i	$-0.369102\pi$
$179$	3.70827e32	0.799470	0.399735	+	0.916631i	$0.369102\pi$
$180$	−2.93422e31	−0.0583502
$181$	−8.49469e32	−1.55886	−0.779432	−	0.626487i	$-0.784492\pi$
$181$	−8.49469e32	−1.55886	−0.779432	+	0.626487i	$0.784492\pi$
$182$	7.03903e31	0.119255
$183$	−1.78473e32	−0.279275
$184$	1.32835e32	0.192068
$185$	1.38392e32	0.184978
$186$	1.02441e32	0.126630
$187$	−3.60537e32	−0.412331
$188$	2.65175e32	0.280701
$189$	7.42105e31	0.0727393
$190$	−1.05699e32	−0.0959717
$191$	2.04793e32	0.172318	0.0861591	−	0.996281i	$-0.472541\pi$
$191$	2.04793e32	0.172318	0.0861591	+	0.996281i	$0.472541\pi$
$192$	8.23103e32	0.642076
$193$	−1.41870e33	−1.02638	−0.513191	−	0.858274i	$-0.671537\pi$
$193$	−1.41870e33	−1.02638	−0.513191	+	0.858274i	$0.671537\pi$
$194$	1.20529e33	0.809033
$195$	−2.84362e32	−0.177161
$196$	−4.97412e31	−0.0287742
$197$	7.77731e32	0.417897	0.208948	−	0.977927i	$-0.432996\pi$
$197$	7.77731e32	0.417897	0.208948	+	0.977927i	$0.432996\pi$
$198$	−2.66151e32	−0.132887
$199$	−1.75798e32	−0.0815915	−0.0407958	−	0.999168i	$-0.512989\pi$
$199$	−1.75798e32	−0.0815915	−0.0407958	+	0.999168i	$0.512989\pi$
$200$	−6.08705e32	−0.262707
$201$	1.07417e33	0.431250
$202$	9.61154e32	0.359086
$203$	−1.87259e33	−0.651253
$204$	3.31879e32	0.107484
$205$	−1.99457e33	−0.601753
$206$	4.67916e33	1.31551
$207$	2.27536e32	0.0596321
$208$	1.09512e33	0.267635
$209$	2.41817e32	0.0551272
$210$	−7.96695e32	−0.169478
$211$	3.24396e33	0.644139	0.322070	−	0.946716i	$-0.395621\pi$
$211$	3.24396e33	0.644139	0.322070	+	0.946716i	$0.395621\pi$
$212$	−3.76513e32	−0.0698087
$213$	2.15042e33	0.372408
$214$	2.41463e33	0.390707
$215$	−7.81682e32	−0.118215
$216$	1.46134e33	0.206620
$217$	−7.01544e32	−0.0927659
$218$	3.50617e33	0.433724
$219$	1.78043e33	0.206103
$220$	−7.20670e32	−0.0780922
$221$	3.21630e33	0.326339
$222$	−1.15551e33	−0.109814
$223$	−4.56635e33	−0.406582	−0.203291	−	0.979118i	$-0.565164\pi$
$223$	−4.56635e33	−0.406582	−0.203291	+	0.979118i	$0.565164\pi$
$224$	−1.79478e33	−0.149766
$225$	−1.04266e33	−0.0815636
$226$	−6.36544e33	−0.466934
$227$	7.02309e33	0.483229	0.241615	−	0.970372i	$-0.422323\pi$
$227$	7.02309e33	0.483229	0.241615	+	0.970372i	$0.422323\pi$
$228$	−2.22596e32	−0.0143702
$229$	−1.11859e34	−0.677730	−0.338865	−	0.940835i	$-0.610043\pi$
$229$	−1.11859e34	−0.677730	−0.338865	+	0.940835i	$0.610043\pi$
$230$	−2.44274e33	−0.138939
$231$	1.82267e33	0.0973497
$232$	−3.68747e34	−1.84992
$233$	−4.93640e33	−0.232675	−0.116338	−	0.993210i	$-0.537115\pi$
$233$	−4.93640e33	−0.232675	−0.116338	+	0.993210i	$0.537115\pi$
$234$	2.37430e33	0.105173
$235$	−2.90864e34	−1.21117
$236$	−8.36542e33	−0.327540
$237$	1.38964e34	0.511740
$238$	9.01110e33	0.312185
$239$	−6.55250e33	−0.213618	−0.106809	−	0.994280i	$-0.534063\pi$
$239$	−6.55250e33	−0.213618	−0.106809	+	0.994280i	$0.534063\pi$
$240$	−1.23948e34	−0.380345
$241$	−4.27635e34	−1.23545	−0.617727	−	0.786393i	$-0.711946\pi$
$241$	−4.27635e34	−1.23545	−0.617727	+	0.786393i	$0.711946\pi$
$242$	2.63091e34	0.715786
$243$	2.50316e33	0.0641500
$244$	4.03503e33	0.0974303
$245$	5.45598e33	0.124155
$246$	1.66538e34	0.357236
$247$	−2.15722e33	−0.0436304
$248$	−1.38147e34	−0.263507
$249$	−1.28545e34	−0.231295
$250$	5.69395e34	0.966681
$251$	−4.79256e34	−0.767890	−0.383945	−	0.923356i	$-0.625435\pi$
$251$	−4.79256e34	−0.767890	−0.383945	+	0.923356i	$0.625435\pi$
$252$	−1.67779e33	−0.0253764
$253$	5.58847e33	0.0798078
$254$	−6.70437e34	−0.904210
$255$	−3.64029e34	−0.463771
$256$	−4.80264e34	−0.578097
$257$	−6.08822e34	−0.692565	−0.346282	−	0.938130i	$-0.612556\pi$
$257$	−6.08822e34	−0.692565	−0.346282	+	0.938130i	$0.612556\pi$
$258$	6.52672e33	0.0701793
$259$	7.91325e33	0.0804467
$260$	6.42901e33	0.0618060
$261$	−6.31633e34	−0.574351
$262$	−4.42003e34	−0.380239
$263$	−8.08793e33	−0.0658384	−0.0329192	−	0.999458i	$-0.510480\pi$
$263$	−8.08793e33	−0.0658384	−0.0329192	+	0.999458i	$0.510480\pi$
$264$	3.58917e34	0.276527
$265$	4.12987e34	0.301211
$266$	−6.04388e33	−0.0417380
$267$	−1.53796e35	−1.00585
$268$	−2.42854e34	−0.150450
$269$	−1.33904e35	−0.785931	−0.392966	−	0.919553i	$-0.628551\pi$
$269$	−1.33904e35	−0.785931	−0.392966	+	0.919553i	$0.628551\pi$
$270$	−2.68729e34	−0.149465
$271$	2.62504e35	1.38382	0.691912	−	0.721982i	$-0.256769\pi$
$271$	2.62504e35	1.38382	0.691912	+	0.721982i	$0.256769\pi$
$272$	1.40193e35	0.700612
$273$	−1.62598e34	−0.0770473
$274$	3.27708e35	1.47267
$275$	−2.56086e34	−0.109160
$276$	−5.14426e33	−0.0208037
$277$	3.52930e35	1.35435	0.677177	−	0.735820i	$-0.263203\pi$
$277$	3.52930e35	1.35435	0.677177	+	0.735820i	$0.263203\pi$
$278$	2.21587e35	0.807038
$279$	−2.36634e34	−0.0818119
$280$	1.07438e35	0.352669
$281$	4.45996e35	1.39024	0.695119	−	0.718895i	$-0.255352\pi$
$281$	4.45996e35	1.39024	0.695119	+	0.718895i	$0.255352\pi$
$282$	2.42859e35	0.719022
$283$	−3.26330e35	−0.917811	−0.458905	−	0.888485i	$-0.651758\pi$
$283$	−3.26330e35	−0.917811	−0.458905	+	0.888485i	$0.651758\pi$
$284$	−4.86179e34	−0.129921
$285$	2.44160e34	0.0620045
$286$	5.83148e34	0.140757
$287$	−1.14050e35	−0.261702
$288$	−6.05387e34	−0.132081
$289$	−7.02294e34	−0.145714
$290$	6.78096e35	1.33820
$291$	−2.78416e35	−0.522693
$292$	−4.02530e34	−0.0719030
$293$	−3.10975e34	−0.0528621	−0.0264310	−	0.999651i	$-0.508414\pi$
$293$	−3.10975e34	−0.0528621	−0.0264310	+	0.999651i	$0.508414\pi$
$294$	−4.55551e34	−0.0737056
$295$	9.17581e35	1.41327
$296$	1.55826e35	0.228513
$297$	6.14796e34	0.0858544
$298$	−8.92381e34	−0.118690
$299$	−4.98541e34	−0.0631638
$300$	2.35731e34	0.0284550
$301$	−4.46967e34	−0.0514116
$302$	8.58626e35	0.941247
$303$	−2.22022e35	−0.231995
$304$	−9.40295e34	−0.0936693
$305$	−4.42592e35	−0.420393
$306$	3.03949e35	0.275321
$307$	7.72996e35	0.667838	0.333919	−	0.942602i	$-0.391629\pi$
$307$	7.72996e35	0.667838	0.333919	+	0.942602i	$0.391629\pi$
$308$	−4.12080e34	−0.0339622
$309$	−1.08086e36	−0.849911
$310$	2.54041e35	0.190616
$311$	6.06121e35	0.434044	0.217022	−	0.976167i	$-0.430366\pi$
$311$	6.06121e35	0.434044	0.217022	+	0.976167i	$0.430366\pi$
$312$	−3.20186e35	−0.218857
$313$	−6.26542e35	−0.408844	−0.204422	−	0.978883i	$-0.565531\pi$
$313$	−6.26542e35	−0.408844	−0.204422	+	0.978883i	$0.565531\pi$
$314$	−2.04235e35	−0.127248
$315$	1.84033e35	0.109494
$316$	−3.14177e35	−0.178530
$317$	−1.35490e36	−0.735443	−0.367722	−	0.929936i	$-0.619862\pi$
$317$	−1.35490e36	−0.735443	−0.367722	+	0.929936i	$0.619862\pi$
$318$	−3.44827e35	−0.178816
$319$	−1.55134e36	−0.768675
$320$	2.04119e36	0.966517
$321$	−5.57769e35	−0.252424
$322$	−1.39676e35	−0.0604243
$323$	−2.76159e35	−0.114215
$324$	−5.65928e34	−0.0223799
$325$	2.28451e35	0.0863943
$326$	−1.95661e36	−0.707702
$327$	−8.09908e35	−0.280216
$328$	−2.24585e36	−0.743378
$329$	−1.66316e36	−0.526738
$330$	−6.60021e35	−0.200035
$331$	−4.35481e36	−1.26317	−0.631587	−	0.775305i	$-0.717596\pi$
$331$	−4.35481e36	−1.26317	−0.631587	+	0.775305i	$0.717596\pi$
$332$	2.90622e35	0.0806914
$333$	2.66918e35	0.0709473
$334$	3.74285e34	0.00952529
$335$	2.66380e36	0.649161
$336$	−7.08737e35	−0.165412
$337$	−3.65085e36	−0.816131	−0.408066	−	0.912953i	$-0.633797\pi$
$337$	−3.65085e36	−0.816131	−0.408066	+	0.912953i	$0.633797\pi$
$338$	3.65281e36	0.782231
$339$	1.47039e36	0.301673
$340$	8.23018e35	0.161795
$341$	−5.81193e35	−0.109492
$342$	−2.03863e35	−0.0368095
$343$	3.11973e35	0.0539949
$344$	−8.80160e35	−0.146037
$345$	5.64261e35	0.0897641
$346$	−1.00385e37	−1.53132
$347$	−4.55717e36	−0.666681	−0.333340	−	0.942807i	$-0.608176\pi$
$347$	−4.55717e36	−0.666681	−0.333340	+	0.942807i	$0.608176\pi$
$348$	1.42803e36	0.200373
$349$	1.11095e37	1.49529	0.747644	−	0.664100i	$-0.231185\pi$
$349$	1.11095e37	1.49529	0.747644	+	0.664100i	$0.231185\pi$
$350$	6.40051e35	0.0826472
$351$	−5.48452e35	−0.0679494
$352$	−1.48688e36	−0.176770
$353$	1.32035e37	1.50646	0.753228	−	0.657759i	$-0.228496\pi$
$353$	1.32035e37	1.50646	0.753228	+	0.657759i	$0.228496\pi$
$354$	−7.66141e36	−0.838999
$355$	5.33277e36	0.560586
$356$	3.47711e36	0.350908
$357$	−2.08152e36	−0.201694
$358$	−7.67831e36	−0.714433
$359$	9.20920e36	0.822910	0.411455	−	0.911430i	$-0.365021\pi$
$359$	9.20920e36	0.822910	0.411455	+	0.911430i	$0.365021\pi$
$360$	3.62394e36	0.311025
$361$	−1.19446e37	−0.984730
$362$	1.75890e37	1.39305
$363$	−6.07728e36	−0.462448
$364$	3.67612e35	0.0268794
$365$	4.41525e36	0.310248
$366$	3.69545e36	0.249570
$367$	−2.18661e37	−1.41943	−0.709713	−	0.704491i	$-0.751176\pi$
$367$	−2.18661e37	−1.41943	−0.709713	+	0.704491i	$0.751176\pi$
$368$	−2.17305e36	−0.135605
$369$	−3.84695e36	−0.230799
$370$	−2.86552e36	−0.165302
$371$	2.36146e36	0.130997
$372$	5.34996e35	0.0285416
$373$	−3.38463e37	−1.73673	−0.868367	−	0.495922i	$-0.834830\pi$
$373$	−3.38463e37	−1.73673	−0.868367	+	0.495922i	$0.834830\pi$
$374$	7.46524e36	0.368473
$375$	−1.31528e37	−0.624544
$376$	−3.27507e37	−1.49623
$377$	1.38393e37	0.608367
$378$	−1.53660e36	−0.0650023
$379$	4.07203e37	1.65784	0.828919	−	0.559369i	$-0.188956\pi$
$379$	4.07203e37	1.65784	0.828919	+	0.559369i	$0.188956\pi$
$380$	−5.52010e35	−0.0216314
$381$	1.54868e37	0.584183
$382$	−4.24043e36	−0.153989
$383$	−7.03919e36	−0.246116	−0.123058	−	0.992399i	$-0.539270\pi$
$383$	−7.03919e36	−0.246116	−0.123058	+	0.992399i	$0.539270\pi$
$384$	−1.02479e37	−0.345009
$385$	4.52000e36	0.146540
$386$	2.93754e37	0.917210
$387$	−1.50764e36	−0.0453408
$388$	6.29460e36	0.182351
$389$	3.57221e37	0.996936	0.498468	−	0.866908i	$-0.333896\pi$
$389$	3.57221e37	0.996936	0.498468	+	0.866908i	$0.333896\pi$
$390$	5.88797e36	0.158317
$391$	−6.38213e36	−0.165350
$392$	6.14333e36	0.153375
$393$	1.02101e37	0.245661
$394$	−1.61036e37	−0.373447
$395$	3.44612e37	0.770323
$396$	−1.38997e36	−0.0299519
$397$	−2.46288e37	−0.511660	−0.255830	−	0.966722i	$-0.582349\pi$
$397$	−2.46288e37	−0.511660	−0.255830	+	0.966722i	$0.582349\pi$
$398$	3.64006e36	0.0729129
$399$	1.39611e36	0.0269657
$400$	9.95780e36	0.185478
$401$	1.04392e38	1.87531	0.937653	−	0.347573i	$-0.112994\pi$
$401$	1.04392e38	1.87531	0.937653	+	0.347573i	$0.112994\pi$
$402$	−2.22416e37	−0.385380
$403$	5.18475e36	0.0866572
$404$	5.01960e36	0.0809356
$405$	6.20751e36	0.0965650
$406$	3.87736e37	0.581981
$407$	6.55572e36	0.0949514
$408$	−4.09890e37	−0.572922
$409$	6.95031e37	0.937597	0.468799	−	0.883305i	$-0.344687\pi$
$409$	6.95031e37	0.937597	0.468799	+	0.883305i	$0.344687\pi$
$410$	4.12994e37	0.537747
$411$	−7.56991e37	−0.951447
$412$	2.44368e37	0.296507
$413$	5.24674e37	0.614630
$414$	−4.71134e36	−0.0532892
$415$	−3.18776e37	−0.348168
$416$	1.32643e37	0.139904
$417$	−5.11855e37	−0.521403
$418$	−5.00704e36	−0.0492635
$419$	1.73564e38	1.64952	0.824758	−	0.565485i	$-0.191311\pi$
$419$	1.73564e38	1.64952	0.824758	+	0.565485i	$0.191311\pi$
$420$	−4.16072e36	−0.0381991
$421$	1.10055e38	0.976161	0.488080	−	0.872799i	$-0.337697\pi$
$421$	1.10055e38	0.976161	0.488080	+	0.872799i	$0.337697\pi$
$422$	−6.71691e37	−0.575624
$423$	−5.60993e37	−0.464539
$424$	4.65016e37	0.372103
$425$	2.92455e37	0.226162
$426$	−4.45264e37	−0.332796
$427$	−2.53074e37	−0.182829
$428$	1.26104e37	0.0880629
$429$	−1.34704e37	−0.0909392
$430$	1.61854e37	0.105641
$431$	−2.97181e38	−1.87543	−0.937714	−	0.347409i	$-0.887062\pi$
$431$	−2.97181e38	−1.87543	−0.937714	+	0.347409i	$0.887062\pi$
$432$	−2.39061e37	−0.145879
$433$	−6.55193e36	−0.0386630	−0.0193315	−	0.999813i	$-0.506154\pi$
$433$	−6.55193e36	−0.0386630	−0.0193315	+	0.999813i	$0.506154\pi$
$434$	1.45261e37	0.0828987
$435$	−1.56637e38	−0.864570
$436$	1.83109e37	0.0977586
$437$	4.28059e36	0.0221066
$438$	−3.68654e37	−0.184181
$439$	−2.19329e38	−1.06013	−0.530066	−	0.847957i	$-0.677833\pi$
$439$	−2.19329e38	−1.06013	−0.530066	+	0.847957i	$0.677833\pi$
$440$	8.90071e37	0.416256
$441$	1.05230e37	0.0476190
$442$	−6.65965e37	−0.291627
$443$	−1.02399e38	−0.433952	−0.216976	−	0.976177i	$-0.569619\pi$
$443$	−1.02399e38	−0.433952	−0.216976	+	0.976177i	$0.569619\pi$
$444$	−6.03463e36	−0.0247513
$445$	−3.81395e38	−1.51410
$446$	9.45504e37	0.363336
$447$	2.06136e37	0.0766822
$448$	1.16716e38	0.420337
$449$	−2.14119e38	−0.746594	−0.373297	−	0.927712i	$-0.621773\pi$
$449$	−2.14119e38	−0.746594	−0.373297	+	0.927712i	$0.621773\pi$
$450$	2.15892e37	0.0728880
$451$	−9.44844e37	−0.308887
$452$	−3.32433e37	−0.105244
$453$	−1.98339e38	−0.608112
$454$	−1.45419e38	−0.431830
$455$	−4.03224e37	−0.115979
$456$	2.74919e37	0.0765976
$457$	−4.10913e38	−1.10909	−0.554543	−	0.832155i	$-0.687107\pi$
$457$	−4.10913e38	−1.10909	−0.554543	+	0.832155i	$0.687107\pi$
$458$	2.31615e38	0.605643
$459$	−7.02108e37	−0.177877
$460$	−1.27571e37	−0.0313159
$461$	1.07349e38	0.255348	0.127674	−	0.991816i	$-0.459249\pi$
$461$	1.07349e38	0.255348	0.127674	+	0.991816i	$0.459249\pi$
$462$	−3.77401e37	−0.0869949
$463$	−7.13107e38	−1.59305	−0.796526	−	0.604604i	$-0.793331\pi$
$463$	−7.13107e38	−1.59305	−0.796526	+	0.604604i	$0.793331\pi$
$464$	6.03233e38	1.30609
$465$	−5.86823e37	−0.123151
$466$	1.02213e38	0.207926
$467$	−8.76401e38	−1.72826	−0.864128	−	0.503272i	$-0.832129\pi$
$467$	−8.76401e38	−1.72826	−0.864128	+	0.503272i	$0.832129\pi$
$468$	1.23997e37	0.0237054
$469$	1.52317e38	0.282320
$470$	6.02260e38	1.08234
$471$	4.71773e37	0.0822110
$472$	1.03318e39	1.74589
$473$	−3.70289e37	−0.0606813
$474$	−2.87737e38	−0.457308
$475$	−1.96154e37	−0.0302371
$476$	4.70603e37	0.0703645
$477$	7.96533e37	0.115528
$478$	1.35676e38	0.190896
$479$	8.19556e38	1.11870	0.559350	−	0.828932i	$-0.311051\pi$
$479$	8.19556e38	1.11870	0.559350	+	0.828932i	$0.311051\pi$
$480$	−1.50128e38	−0.198822
$481$	−5.84828e37	−0.0751492
$482$	8.85458e38	1.10404
$483$	3.22645e37	0.0390384
$484$	1.37399e38	0.161334
$485$	−6.90438e38	−0.786809
$486$	−5.18301e37	−0.0573266
$487$	−1.56187e39	−1.67678	−0.838388	−	0.545074i	$-0.816502\pi$
$487$	−1.56187e39	−1.67678	−0.838388	+	0.545074i	$0.816502\pi$
$488$	−4.98350e38	−0.519334
$489$	4.51969e38	0.457225
$490$	−1.12971e38	−0.110949
$491$	1.07366e39	1.02373	0.511865	−	0.859066i	$-0.328955\pi$
$491$	1.07366e39	1.02373	0.511865	+	0.859066i	$0.328955\pi$
$492$	8.69742e37	0.0805186
$493$	1.77166e39	1.59258
$494$	4.46672e37	0.0389896
$495$	1.52462e38	0.129237
$496$	2.25994e38	0.186043
$497$	3.04929e38	0.243798
$498$	2.66165e38	0.206693
$499$	8.56182e38	0.645815	0.322908	−	0.946430i	$-0.395340\pi$
$499$	8.56182e38	0.645815	0.322908	+	0.946430i	$0.395340\pi$
$500$	2.97365e38	0.217884
$501$	−8.64580e36	−0.00615401
$502$	9.92344e38	0.686212
$503$	3.24492e38	0.218006	0.109003	−	0.994041i	$-0.465234\pi$
$503$	3.24492e38	0.218006	0.109003	+	0.994041i	$0.465234\pi$
$504$	2.07218e38	0.135264
$505$	−5.50587e38	−0.349221
$506$	−1.15714e38	−0.0713189
$507$	−8.43782e38	−0.505377
$508$	−3.50134e38	−0.203803
$509$	−9.47448e38	−0.535979	−0.267989	−	0.963422i	$-0.586359\pi$
$509$	−9.47448e38	−0.535979	−0.267989	+	0.963422i	$0.586359\pi$
$510$	7.53755e38	0.414441
$511$	2.52464e38	0.134926
$512$	2.14472e39	1.11418
$513$	4.70914e37	0.0237815
$514$	1.26062e39	0.618899
$515$	−2.68041e39	−1.27937
$516$	3.40856e37	0.0158180
$517$	−1.37785e39	−0.621710
$518$	−1.63851e38	−0.0718899
$519$	2.31885e39	0.989340
$520$	−7.94021e38	−0.329446
$521$	−3.35732e38	−0.135471	−0.0677354	−	0.997703i	$-0.521577\pi$
$521$	−3.35732e38	−0.135471	−0.0677354	+	0.997703i	$0.521577\pi$
$522$	1.30785e39	0.513259
$523$	2.45793e38	0.0938198	0.0469099	−	0.998899i	$-0.485063\pi$
$523$	2.45793e38	0.0938198	0.0469099	+	0.998899i	$0.485063\pi$
$524$	−2.30835e38	−0.0857035
$525$	−1.47849e38	−0.0533959
$526$	1.67468e38	0.0588354
$527$	6.63733e38	0.226850
$528$	−5.87153e38	−0.195236
$529$	−2.99213e39	−0.967996
$530$	−8.55127e38	−0.269172
$531$	1.76975e39	0.542053
$532$	−3.15640e37	−0.00940749
$533$	8.42884e38	0.244469
$534$	3.18449e39	0.898859
$535$	−1.38320e39	−0.379974
$536$	2.99939e39	0.801944
$537$	1.77365e39	0.461574
$538$	2.77260e39	0.702335
$539$	2.58454e38	0.0637303
$540$	−1.40343e38	−0.0336885
$541$	−7.04045e39	−1.64528	−0.822640	−	0.568562i	$-0.807500\pi$
$541$	−7.04045e39	−1.64528	−0.822640	+	0.568562i	$0.807500\pi$
$542$	−5.43538e39	−1.23663
$543$	−4.06298e39	−0.900011
$544$	1.69804e39	0.366239
$545$	−2.00847e39	−0.421809
$546$	3.36675e38	0.0688521
$547$	1.57742e39	0.314145	0.157073	−	0.987587i	$-0.449794\pi$
$547$	1.57742e39	0.314145	0.157073	+	0.987587i	$0.449794\pi$
$548$	1.71145e39	0.331930
$549$	−8.53632e38	−0.161240
$550$	5.30250e38	0.0975487
$551$	−1.18828e39	−0.212922
$552$	6.35347e38	0.110891
$553$	1.97050e39	0.335013
$554$	−7.30774e39	−1.21030
$555$	6.61923e38	0.106797
$556$	1.15723e39	0.181901
$557$	−1.30168e40	−1.99345	−0.996723	−	0.0808894i	$-0.974224\pi$
$557$	−1.30168e40	−1.99345	−0.996723	+	0.0808894i	$0.974224\pi$
$558$	4.89972e38	0.0731098
$559$	3.30331e38	0.0480261
$560$	−1.75758e39	−0.248994
$561$	−1.72444e39	−0.238059
$562$	−9.23474e39	−1.24236
$563$	−1.02276e40	−1.34092	−0.670461	−	0.741945i	$-0.733904\pi$
$563$	−1.02276e40	−1.34092	−0.670461	+	0.741945i	$0.733904\pi$
$564$	1.26833e39	0.162063
$565$	3.64637e39	0.454108
$566$	6.75695e39	0.820186
$567$	3.54946e38	0.0419961
$568$	6.00461e39	0.692522
$569$	−6.61531e39	−0.743742	−0.371871	−	0.928284i	$-0.621284\pi$
$569$	−6.61531e39	−0.743742	−0.371871	+	0.928284i	$0.621284\pi$
$570$	−5.05555e38	−0.0554093
$571$	1.32974e40	1.42083	0.710417	−	0.703781i	$-0.248506\pi$
$571$	1.32974e40	1.42083	0.710417	+	0.703781i	$0.248506\pi$
$572$	3.04547e38	0.0317258
$573$	9.79519e38	0.0994880
$574$	2.36150e39	0.233866
$575$	−4.53318e38	−0.0437743
$576$	3.93688e39	0.370703
$577$	1.20274e40	1.10439	0.552194	−	0.833716i	$-0.313791\pi$
$577$	1.20274e40	1.10439	0.552194	+	0.833716i	$0.313791\pi$
$578$	1.45416e39	0.130215
$579$	−6.78559e39	−0.592582
$580$	3.54134e39	0.301621
$581$	−1.82277e39	−0.151418
$582$	5.76486e39	0.467096
$583$	1.95635e39	0.154615
$584$	4.97149e39	0.383266
$585$	−1.36009e39	−0.102284
$586$	6.43901e38	0.0472393
$587$	−8.42140e39	−0.602742	−0.301371	−	0.953507i	$-0.597444\pi$
$587$	−8.42140e39	−0.602742	−0.301371	+	0.953507i	$0.597444\pi$
$588$	−2.37910e38	−0.0166128
$589$	−4.45175e38	−0.0303291
$590$	−1.89994e40	−1.26295
$591$	3.71986e39	0.241273
$592$	−2.54916e39	−0.161337
$593$	−6.28685e39	−0.388275	−0.194138	−	0.980974i	$-0.562191\pi$
$593$	−6.28685e39	−0.388275	−0.194138	+	0.980974i	$0.562191\pi$
$594$	−1.27299e39	−0.0767223
$595$	−5.16192e39	−0.303609
$596$	−4.66044e38	−0.0267520
$597$	−8.40838e38	−0.0471069
$598$	1.03227e39	0.0564453
$599$	−7.52662e39	−0.401709	−0.200854	−	0.979621i	$-0.564372\pi$
$599$	−7.52662e39	−0.401709	−0.200854	+	0.979621i	$0.564372\pi$
$600$	−2.91142e39	−0.151674
$601$	−1.48353e40	−0.754427	−0.377213	−	0.926126i	$-0.623118\pi$
$601$	−1.48353e40	−0.754427	−0.377213	+	0.926126i	$0.623118\pi$
$602$	9.25486e38	0.0459431
$603$	5.13771e39	0.248982
$604$	4.48415e39	0.212151
$605$	−1.50709e40	−0.696123
$606$	4.59717e39	0.207318
$607$	2.14861e40	0.946065	0.473032	−	0.881045i	$-0.343159\pi$
$607$	2.14861e40	0.946065	0.473032	+	0.881045i	$0.343159\pi$
$608$	−1.13890e39	−0.0489649
$609$	−8.95653e39	−0.376001
$610$	9.16426e39	0.375677
$611$	1.22916e40	0.492052
$612$	1.58737e39	0.0620557
$613$	3.35797e40	1.28203	0.641017	−	0.767526i	$-0.278513\pi$
$613$	3.35797e40	1.28203	0.641017	+	0.767526i	$0.278513\pi$
$614$	−1.60056e40	−0.596802
$615$	−9.53997e39	−0.347422
$616$	5.08944e39	0.181029
$617$	−2.95462e40	−1.02652	−0.513259	−	0.858234i	$-0.671562\pi$
$617$	−2.95462e40	−1.02652	−0.513259	+	0.858234i	$0.671562\pi$
$618$	2.23803e40	0.759509
$619$	2.46082e40	0.815767	0.407884	−	0.913034i	$-0.366267\pi$
$619$	2.46082e40	0.815767	0.407884	+	0.913034i	$0.366267\pi$
$620$	1.32672e39	0.0429636
$621$	1.08830e39	0.0344286
$622$	−1.25503e40	−0.387876
$623$	−2.18082e40	−0.658482
$624$	5.23792e39	0.154519
$625$	−2.41278e40	−0.695435
$626$	1.29731e40	0.365356
$627$	1.15660e39	0.0318277
$628$	−1.06661e39	−0.0286808
$629$	−7.48675e39	−0.196725
$630$	−3.81057e39	−0.0978479
$631$	1.76083e40	0.441868	0.220934	−	0.975289i	$-0.429089\pi$
$631$	1.76083e40	0.441868	0.220934	+	0.975289i	$0.429089\pi$
$632$	3.88027e40	0.951622
$633$	1.55158e40	0.371894
$634$	2.80545e40	0.657217
$635$	3.84053e40	0.879371
$636$	−1.80085e39	−0.0403041
$637$	−2.30564e39	−0.0504393
$638$	3.21220e40	0.686914
$639$	1.02854e40	0.215010
$640$	−2.54134e40	−0.519342
$641$	7.95820e39	0.158991	0.0794957	−	0.996835i	$-0.474669\pi$
$641$	7.95820e39	0.158991	0.0794957	+	0.996835i	$0.474669\pi$
$642$	1.15491e40	0.225575
$643$	−1.18021e40	−0.225371	−0.112686	−	0.993631i	$-0.535945\pi$
$643$	−1.18021e40	−0.225371	−0.112686	+	0.993631i	$0.535945\pi$
$644$	−7.29455e38	−0.0136192
$645$	−3.73876e39	−0.0682515
$646$	5.71813e39	0.102066
$647$	5.57719e40	0.973427	0.486714	−	0.873562i	$-0.338195\pi$
$647$	5.57719e40	0.973427	0.486714	+	0.873562i	$0.338195\pi$
$648$	6.98955e39	0.119292
$649$	4.34666e40	0.725449
$650$	−4.73029e39	−0.0772048
$651$	−3.35546e39	−0.0535584
$652$	−1.02184e40	−0.159511
$653$	4.70831e40	0.718826	0.359413	−	0.933179i	$-0.382977\pi$
$653$	4.70831e40	0.718826	0.359413	+	0.933179i	$0.382977\pi$
$654$	1.67699e40	0.250411
$655$	2.53197e40	0.369794
$656$	3.67398e40	0.524846
$657$	8.51574e39	0.118994
$658$	3.44373e40	0.470710
$659$	−5.40824e40	−0.723132	−0.361566	−	0.932347i	$-0.617758\pi$
$659$	−5.40824e40	−0.723132	−0.361566	+	0.932347i	$0.617758\pi$
$660$	−3.44694e39	−0.0450865
$661$	−1.50268e41	−1.92285	−0.961426	−	0.275065i	$-0.911300\pi$
$661$	−1.50268e41	−1.92285	−0.961426	+	0.275065i	$0.911300\pi$
$662$	9.01702e40	1.12881
$663$	1.53835e40	0.188412
$664$	−3.58936e40	−0.430110
$665$	3.46217e39	0.0405915
$666$	−5.52677e39	−0.0634009
$667$	−2.74615e40	−0.308248
$668$	1.95469e38	0.00214694
$669$	−2.18407e40	−0.234741
$670$	−5.51565e40	−0.580112
$671$	−2.09659e40	−0.215793
$672$	−8.58436e39	−0.0864676
$673$	−7.68141e40	−0.757221	−0.378611	−	0.925556i	$-0.623598\pi$
$673$	−7.68141e40	−0.757221	−0.378611	+	0.925556i	$0.623598\pi$
$674$	7.55941e40	0.729322
$675$	−4.98702e39	−0.0470908
$676$	1.90767e40	0.176310
$677$	−1.13388e41	−1.02573	−0.512863	−	0.858471i	$-0.671415\pi$
$677$	−1.13388e41	−1.02573	−0.512863	+	0.858471i	$0.671415\pi$
$678$	−3.04457e40	−0.269585
$679$	−3.94793e40	−0.342183
$680$	−1.01648e41	−0.862419
$681$	3.35912e40	0.278992
$682$	1.20341e40	0.0978456
$683$	1.54566e41	1.23031	0.615154	−	0.788407i	$-0.289094\pi$
$683$	1.54566e41	1.23031	0.615154	+	0.788407i	$0.289094\pi$
$684$	−1.06467e39	−0.00829662
$685$	−1.87724e41	−1.43221
$686$	−6.45970e39	−0.0482517
$687$	−5.35019e40	−0.391288
$688$	1.43985e40	0.103106
$689$	−1.74524e40	−0.122370
$690$	−1.16835e40	−0.0802162
$691$	−5.24297e40	−0.352489	−0.176244	−	0.984346i	$-0.556395\pi$
$691$	−5.24297e40	−0.352489	−0.176244	+	0.984346i	$0.556395\pi$
$692$	−5.24258e40	−0.345149
$693$	8.71778e39	0.0562049
$694$	9.43604e40	0.595768
$695$	−1.26934e41	−0.784868
$696$	−1.76371e41	−1.06805
$697$	1.07903e41	0.639967
$698$	−2.30032e41	−1.33624
$699$	−2.36107e40	−0.134335
$700$	3.34265e39	0.0186282
$701$	2.86740e41	1.56523	0.782614	−	0.622507i	$-0.213886\pi$
$701$	2.86740e41	1.56523	0.782614	+	0.622507i	$0.213886\pi$
$702$	1.13562e40	0.0607218
$703$	5.02147e39	0.0263014
$704$	9.66930e40	0.496125
$705$	−1.39119e41	−0.699270
$706$	−2.73391e41	−1.34622
$707$	−3.14826e40	−0.151876
$708$	−4.00116e40	−0.189105
$709$	−6.23313e40	−0.288626	−0.144313	−	0.989532i	$-0.546097\pi$
$709$	−6.23313e40	−0.288626	−0.144313	+	0.989532i	$0.546097\pi$
$710$	−1.10420e41	−0.500958
$711$	6.64658e40	0.295453
$712$	−4.29444e41	−1.87045
$713$	−1.02881e40	−0.0439075
$714$	4.30998e40	0.180240
$715$	−3.34050e40	−0.136891
$716$	−4.00998e40	−0.161029
$717$	−3.13404e40	−0.123332
$718$	−1.90685e41	−0.735380
$719$	3.57363e41	1.35064	0.675322	−	0.737523i	$-0.264005\pi$
$719$	3.57363e41	1.35064	0.675322	+	0.737523i	$0.264005\pi$
$720$	−5.92840e40	−0.219592
$721$	−1.53266e41	−0.556397
$722$	2.47324e41	0.879988
$723$	−2.04537e41	−0.713290
$724$	9.18583e40	0.313985
$725$	1.25840e41	0.421615
$726$	1.25836e41	0.413259
$727$	3.58738e41	1.15486	0.577430	−	0.816440i	$-0.304056\pi$
$727$	3.58738e41	1.15486	0.577430	+	0.816440i	$0.304056\pi$
$728$	−4.54022e40	−0.143276
$729$	1.19725e40	0.0370370
$730$	−9.14217e40	−0.277248
$731$	4.22877e40	0.125722
$732$	1.92994e40	0.0562514
$733$	4.59031e41	1.31170	0.655850	−	0.754891i	$-0.272310\pi$
$733$	4.59031e41	1.31170	0.655850	+	0.754891i	$0.272310\pi$
$734$	4.52757e41	1.26845
$735$	2.60958e40	0.0716809
$736$	−2.63204e40	−0.0708866
$737$	1.26186e41	0.333222
$738$	7.96547e40	0.206250
$739$	9.04744e40	0.229711	0.114855	−	0.993382i	$-0.463360\pi$
$739$	9.04744e40	0.229711	0.114855	+	0.993382i	$0.463360\pi$
$740$	−1.49651e40	−0.0372581
$741$	−1.03179e40	−0.0251900
$742$	−4.88963e40	−0.117063
$743$	6.27690e41	1.47369	0.736847	−	0.676059i	$-0.236314\pi$
$743$	6.27690e41	1.47369	0.736847	+	0.676059i	$0.236314\pi$
$744$	−6.60752e40	−0.152136
$745$	5.11191e40	0.115430
$746$	7.00819e41	1.55200
$747$	−6.14828e40	−0.133538
$748$	3.89870e40	0.0830514
$749$	−7.90914e40	−0.165251
$750$	2.72340e41	0.558114
$751$	6.24267e41	1.25485	0.627424	−	0.778678i	$-0.284109\pi$
$751$	6.24267e41	1.25485	0.627424	+	0.778678i	$0.284109\pi$
$752$	5.35769e41	1.05638
$753$	−2.29227e41	−0.443341
$754$	−2.86556e41	−0.543657
$755$	−4.91855e41	−0.915390
$756$	−8.02484e39	−0.0146511
$757$	7.05183e41	1.26302	0.631512	−	0.775366i	$-0.282435\pi$
$757$	7.05183e41	1.26302	0.631512	+	0.775366i	$0.282435\pi$
$758$	−8.43150e41	−1.48150
$759$	2.67295e40	0.0460771
$760$	6.81766e40	0.115302
$761$	3.41943e40	0.0567383	0.0283692	−	0.999598i	$-0.490969\pi$
$761$	3.41943e40	0.0567383	0.0283692	+	0.999598i	$0.490969\pi$
$762$	−3.20668e41	−0.522046
$763$	−1.14845e41	−0.183445
$764$	−2.21455e40	−0.0347082
$765$	−1.74114e41	−0.267758
$766$	1.45753e41	0.219938
$767$	−3.87760e41	−0.574156
$768$	−2.29709e41	−0.333765
$769$	4.73266e41	0.674798	0.337399	−	0.941362i	$-0.390453\pi$
$769$	4.73266e41	0.674798	0.337399	+	0.941362i	$0.390453\pi$
$770$	−9.35907e40	−0.130953
$771$	−2.91198e41	−0.399852
$772$	1.53413e41	0.206733
$773$	1.91548e41	0.253323	0.126662	−	0.991946i	$-0.459574\pi$
$773$	1.91548e41	0.253323	0.126662	+	0.991946i	$0.459574\pi$
$774$	3.12171e40	0.0405180
$775$	4.71444e40	0.0600559
$776$	−7.77420e41	−0.971988
$777$	3.78488e40	0.0464459
$778$	−7.39658e41	−0.890895
$779$	−7.23720e40	−0.0855613
$780$	3.07498e40	0.0356837
$781$	2.52618e41	0.287756
$782$	1.32148e41	0.147762
$783$	−3.02108e41	−0.331602
$784$	−1.00499e41	−0.108287
$785$	1.16994e41	0.123752
$786$	−2.11409e41	−0.219531
$787$	1.36721e42	1.39380	0.696901	−	0.717167i	$-0.254562\pi$
$787$	1.36721e42	1.39380	0.696901	+	0.717167i	$0.254562\pi$
$788$	−8.41008e40	−0.0841725
$789$	−3.86843e40	−0.0380118
$790$	−7.13551e41	−0.688386
$791$	2.08500e41	0.197491
$792$	1.71669e41	0.159653
$793$	1.87034e41	0.170789
$794$	5.09963e41	0.457237
$795$	1.97530e41	0.173904
$796$	1.90101e40	0.0164341
$797$	1.47789e42	1.25457	0.627287	−	0.778789i	$-0.284165\pi$
$797$	1.47789e42	1.25457	0.627287	+	0.778789i	$0.284165\pi$
$798$	−2.89077e40	−0.0240975
$799$	1.57352e42	1.28809
$800$	1.20611e41	0.0969574
$801$	−7.35602e41	−0.580726
$802$	−2.16152e42	−1.67584
$803$	2.09154e41	0.159254
$804$	−1.16156e41	−0.0868621
$805$	8.00119e40	0.0587644
$806$	−1.07355e41	−0.0774398
$807$	−6.40457e41	−0.453758
$808$	−6.19951e41	−0.431412
$809$	−2.55305e42	−1.74504	−0.872522	−	0.488575i	$-0.837517\pi$
$809$	−2.55305e42	−1.74504	−0.872522	+	0.488575i	$0.837517\pi$
$810$	−1.28532e41	−0.0862937
$811$	−3.30393e41	−0.217885	−0.108943	−	0.994048i	$-0.534746\pi$
$811$	−3.30393e41	−0.217885	−0.108943	+	0.994048i	$0.534746\pi$
$812$	2.02494e41	0.131175
$813$	1.25555e42	0.798951
$814$	−1.35742e41	−0.0848518
$815$	1.12083e42	0.688261
$816$	6.70539e41	0.404498
$817$	−2.83630e40	−0.0168086
$818$	−1.43913e42	−0.837868
$819$	−7.77703e40	−0.0444833
$820$	2.15685e41	0.121205
$821$	−1.57355e42	−0.868771	−0.434386	−	0.900727i	$-0.643035\pi$
$821$	−1.57355e42	−0.868771	−0.434386	+	0.900727i	$0.643035\pi$
$822$	1.56742e42	0.850244
$823$	−3.06756e42	−1.63491	−0.817457	−	0.575989i	$-0.804617\pi$
$823$	−3.06756e42	−1.63491	−0.817457	+	0.575989i	$0.804617\pi$
$824$	−3.01809e42	−1.58048
$825$	−1.22485e41	−0.0630234
$826$	−1.08639e42	−0.549254
$827$	1.96614e42	0.976754	0.488377	−	0.872633i	$-0.337589\pi$
$827$	1.96614e42	0.976754	0.488377	+	0.872633i	$0.337589\pi$
$828$	−2.46049e40	−0.0120110
$829$	1.11086e42	0.532867	0.266433	−	0.963853i	$-0.414155\pi$
$829$	1.11086e42	0.532867	0.266433	+	0.963853i	$0.414155\pi$
$830$	6.60055e41	0.311134
$831$	1.68805e42	0.781936
$832$	−8.62586e41	−0.392658
$833$	−2.95159e41	−0.132039
$834$	1.05984e42	0.465943
$835$	−2.14405e40	−0.00926363
$836$	−2.61492e40	−0.0111037
$837$	−1.13181e41	−0.0472341
$838$	−3.59380e42	−1.47406
$839$	5.19459e41	0.209412	0.104706	−	0.994503i	$-0.466610\pi$
$839$	5.19459e41	0.209412	0.104706	+	0.994503i	$0.466610\pi$
$840$	5.13874e41	0.203614
$841$	5.05555e42	1.96891
$842$	−2.27880e42	−0.872330
$843$	2.13318e42	0.802654
$844$	−3.50789e41	−0.129742
$845$	−2.09248e42	−0.760743
$846$	1.16159e42	0.415128
$847$	−8.61756e41	−0.302743
$848$	−7.60719e41	−0.262715
$849$	−1.56082e42	−0.529898
$850$	−6.05555e41	−0.202106
$851$	1.16048e41	0.0380766
$852$	−2.32538e41	−0.0750102
$853$	−1.51737e41	−0.0481207	−0.0240603	−	0.999711i	$-0.507659\pi$
$853$	−1.51737e41	−0.0481207	−0.0240603	+	0.999711i	$0.507659\pi$
$854$	5.24014e41	0.163382
$855$	1.16781e41	0.0357983
$856$	−1.55745e42	−0.469403
$857$	−1.10780e42	−0.328275	−0.164137	−	0.986437i	$-0.552484\pi$
$857$	−1.10780e42	−0.328275	−0.164137	+	0.986437i	$0.552484\pi$
$858$	2.78918e41	0.0812663
$859$	−4.77574e42	−1.36817	−0.684084	−	0.729403i	$-0.739798\pi$
$859$	−4.77574e42	−1.36817	−0.684084	+	0.729403i	$0.739798\pi$
$860$	8.45281e40	0.0238108
$861$	−5.45497e41	−0.151094
$862$	6.15340e42	1.67594
$863$	−1.75286e42	−0.469452	−0.234726	−	0.972062i	$-0.575419\pi$
$863$	−1.75286e42	−0.469452	−0.234726	+	0.972062i	$0.575419\pi$
$864$	−2.89555e41	−0.0762573
$865$	5.75045e42	1.48925
$866$	1.35664e41	0.0345505
$867$	−3.35905e41	−0.0841278
$868$	7.58622e40	0.0186848
$869$	1.63246e42	0.395416
$870$	3.24331e42	0.772609
$871$	−1.12569e42	−0.263729
$872$	−2.26150e42	−0.521084
$873$	−1.33166e42	−0.301777
$874$	−8.86335e40	−0.0197552
$875$	−1.86505e42	−0.408860
$876$	−1.92529e41	−0.0415132
$877$	−5.97902e42	−1.26805	−0.634024	−	0.773313i	$-0.718598\pi$
$877$	−5.97902e42	−1.26805	−0.634024	+	0.773313i	$0.718598\pi$
$878$	4.54140e42	0.947369
$879$	−1.48738e41	−0.0305199
$880$	−1.45607e42	−0.293888
$881$	−7.26843e42	−1.44308	−0.721539	−	0.692374i	$-0.756565\pi$
$881$	−7.26843e42	−1.44308	−0.721539	+	0.692374i	$0.756565\pi$
$882$	−2.17889e41	−0.0425540
$883$	6.93245e42	1.33185	0.665927	−	0.746017i	$-0.268036\pi$
$883$	6.93245e42	1.33185	0.665927	+	0.746017i	$0.268036\pi$
$884$	−3.47799e41	−0.0657310
$885$	4.38876e42	0.815952
$886$	2.12026e42	0.387794
$887$	−6.88083e42	−1.23808	−0.619040	−	0.785360i	$-0.712478\pi$
$887$	−6.88083e42	−1.23808	−0.619040	+	0.785360i	$0.712478\pi$
$888$	7.45313e41	0.131932
$889$	2.19602e42	0.382438
$890$	7.89713e42	1.35305
$891$	2.94055e41	0.0495680
$892$	4.93787e41	0.0818935
$893$	−1.05539e42	−0.172213
$894$	−4.26823e41	−0.0685257
$895$	4.39844e42	0.694808
$896$	−1.45314e42	−0.225861
$897$	−2.38451e41	−0.0364677
$898$	4.43354e42	0.667181
$899$	2.85596e42	0.422898
$900$	1.12749e41	0.0164285
$901$	−2.23419e42	−0.320339
$902$	1.95639e42	0.276032
$903$	−2.13783e41	−0.0296825
$904$	4.10575e42	0.560984
$905$	−1.00757e43	−1.35479
$906$	4.10678e42	0.543429
$907$	1.98466e42	0.258453	0.129226	−	0.991615i	$-0.458751\pi$
$907$	1.98466e42	0.258453	0.129226	+	0.991615i	$0.458751\pi$
$908$	−7.59450e41	−0.0973317
$909$	−1.06192e42	−0.133942
$910$	8.34911e41	0.103643
$911$	2.16582e42	0.264609	0.132305	−	0.991209i	$-0.457762\pi$
$911$	2.16582e42	0.264609	0.132305	+	0.991209i	$0.457762\pi$
$912$	−4.49740e41	−0.0540800
$913$	−1.51007e42	−0.178719
$914$	8.50833e42	0.991116
$915$	−2.11690e42	−0.242714
$916$	1.20960e42	0.136508
$917$	1.44778e42	0.160823
$918$	1.45378e42	0.158957
$919$	9.72847e41	0.104706	0.0523528	−	0.998629i	$-0.483328\pi$
$919$	9.72847e41	0.104706	0.0523528	+	0.998629i	$0.483328\pi$
$920$	1.57558e42	0.166924
$921$	3.69722e42	0.385576
$922$	−2.22275e42	−0.228188
$923$	−2.25357e42	−0.227744
$924$	−1.97097e41	−0.0196081
$925$	−5.31778e41	−0.0520805
$926$	1.47655e43	1.42360
$927$	−5.16974e42	−0.490696
$928$	7.30647e42	0.682750
$929$	−1.42961e43	−1.31519	−0.657597	−	0.753370i	$-0.728427\pi$
$929$	−1.42961e43	−1.31519	−0.657597	+	0.753370i	$0.728427\pi$
$930$	1.21507e42	0.110052
$931$	1.97968e41	0.0176532
$932$	5.33804e41	0.0468652
$933$	2.89906e42	0.250595
$934$	1.81467e43	1.54443
$935$	−4.27638e42	−0.358351
$936$	−1.53144e42	−0.126357
$937$	−7.31236e41	−0.0594064	−0.0297032	−	0.999559i	$-0.509456\pi$
$937$	−7.31236e41	−0.0594064	−0.0297032	+	0.999559i	$0.509456\pi$
$938$	−3.15385e42	−0.252290
$939$	−2.99673e42	−0.236046
$940$	3.14529e42	0.243953
$941$	7.96209e42	0.608104	0.304052	−	0.952656i	$-0.401660\pi$
$941$	7.96209e42	0.608104	0.304052	+	0.952656i	$0.401660\pi$
$942$	−9.76849e41	−0.0734665
$943$	−1.67254e42	−0.123867
$944$	−1.69018e43	−1.23265
$945$	8.80223e41	0.0632166
$946$	7.66718e41	0.0542268
$947$	4.94394e42	0.344349	0.172174	−	0.985067i	$-0.444921\pi$
$947$	4.94394e42	0.344349	0.172174	+	0.985067i	$0.444921\pi$
$948$	−1.50270e42	−0.103074
$949$	−1.86584e42	−0.126041
$950$	4.06154e41	0.0270208
$951$	−6.48046e42	−0.424608
$952$	−5.81223e42	−0.375065
$953$	1.71181e43	1.08795	0.543973	−	0.839103i	$-0.316919\pi$
$953$	1.71181e43	1.08795	0.543973	+	0.839103i	$0.316919\pi$
$954$	−1.64929e42	−0.103240
$955$	2.42908e42	0.149759
$956$	7.08562e41	0.0430268
$957$	−7.42002e42	−0.443795
$958$	−1.69696e43	−0.999707
$959$	−1.07341e43	−0.622868
$960$	9.76296e42	0.558019
$961$	−1.66919e43	−0.939761
$962$	1.21094e42	0.0671559
$963$	−2.66779e42	−0.145737
$964$	4.62429e42	0.248844
$965$	−1.68274e43	−0.892014
$966$	−6.68066e41	−0.0348860
$967$	1.01041e43	0.519772	0.259886	−	0.965639i	$-0.416315\pi$
$967$	1.01041e43	0.519772	0.259886	+	0.965639i	$0.416315\pi$
$968$	−1.69696e43	−0.859959
$969$	−1.32086e42	−0.0659421
$970$	1.42961e43	0.703119
$971$	−1.80759e43	−0.875834	−0.437917	−	0.899015i	$-0.644284\pi$
$971$	−1.80759e43	−0.875834	−0.437917	+	0.899015i	$0.644284\pi$
$972$	−2.70682e41	−0.0129211
$973$	−7.25808e42	−0.341339
$974$	3.23399e43	1.49842
$975$	1.09268e42	0.0498798
$976$	8.15250e42	0.366664
$977$	2.95155e43	1.30792	0.653958	−	0.756531i	$-0.273107\pi$
$977$	2.95155e43	1.30792	0.653958	+	0.756531i	$0.273107\pi$
$978$	−9.35843e42	−0.408592
$979$	−1.80670e43	−0.777207
$980$	−5.89988e41	−0.0250072
$981$	−3.87377e42	−0.161783
$982$	−2.22311e43	−0.914838
$983$	7.42642e42	0.301130	0.150565	−	0.988600i	$-0.451891\pi$
$983$	7.42642e42	0.301130	0.150565	+	0.988600i	$0.451891\pi$
$984$	−1.07418e43	−0.429190
$985$	9.22480e42	0.363188
$986$	−3.66839e43	−1.42318
$987$	−7.95486e42	−0.304112
$988$	2.33274e41	0.00878800
$989$	−6.55477e41	−0.0243339
$990$	−3.15686e42	−0.115490
$991$	−1.36141e43	−0.490820	−0.245410	−	0.969419i	$-0.578923\pi$
$991$	−1.36141e43	−0.490820	−0.245410	+	0.969419i	$0.578923\pi$
$992$	2.73728e42	0.0972525
$993$	−2.08289e43	−0.729293
$994$	−6.31383e42	−0.217866
$995$	−2.08517e42	−0.0709100
$996$	1.39004e42	0.0465872
$997$	2.57708e41	0.00851233	0.00425616	−	0.999991i	$-0.498645\pi$
$997$	2.57708e41	0.00851233	0.00425616	+	0.999991i	$0.498645\pi$
$998$	−1.77280e43	−0.577122
$999$	1.27666e42	0.0409614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.a.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.a.1.2	✓	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q-20705.9 q^{2} +4.78297e6 q^{3} -1.08136e8 q^{4} +1.18612e10 q^{5} -9.90357e10 q^{6} +6.78223e11 q^{7} +1.33555e13 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q-20705.9 q^{2} +4.78297e6 q^{3} -1.08136e8 q^{4} +1.18612e10 q^{5} -9.90357e10 q^{6} +6.78223e11 q^{7} +1.33555e13 q^{8} +2.28768e13 q^{9} -2.45596e14 q^{10} +5.61873e14 q^{11} -5.17212e14 q^{12} -5.01240e15 q^{13} -1.40432e16 q^{14} +5.67316e16 q^{15} -2.18482e17 q^{16} -6.41669e17 q^{17} -4.73685e17 q^{18} +4.30377e17 q^{19} -1.28262e18 q^{20} +3.24392e18 q^{21} -1.16341e19 q^{22} +9.94615e18 q^{23} +6.38787e19 q^{24} -4.55772e19 q^{25} +1.03786e20 q^{26} +1.09419e20 q^{27} -7.33404e19 q^{28} -2.76102e21 q^{29} -1.17468e21 q^{30} -1.03438e21 q^{31} -2.64629e21 q^{32} +2.68742e21 q^{33} +1.32863e22 q^{34} +8.04452e21 q^{35} -2.47381e21 q^{36} +1.16676e22 q^{37} -8.91134e21 q^{38} -2.39742e22 q^{39} +1.58411e23 q^{40} -1.68160e23 q^{41} -6.71683e22 q^{42} -6.59027e22 q^{43} -6.07588e22 q^{44} +2.71345e23 q^{45} -2.05944e23 q^{46} -2.45224e24 q^{47} -1.04499e24 q^{48} +4.59987e23 q^{49} +9.43718e23 q^{50} -3.06908e24 q^{51} +5.42022e23 q^{52} +3.48184e24 q^{53} -2.26562e24 q^{54} +6.66447e24 q^{55} +9.05798e24 q^{56} +2.05848e24 q^{57} +5.71694e25 q^{58} +7.73601e25 q^{59} -6.13474e24 q^{60} -3.73143e25 q^{61} +2.14179e25 q^{62} +1.55156e25 q^{63} +1.72090e26 q^{64} -5.94529e25 q^{65} -5.56455e25 q^{66} +2.24582e26 q^{67} +6.93876e25 q^{68} +4.75721e25 q^{69} -1.66569e26 q^{70} +4.49599e26 q^{71} +3.05530e26 q^{72} +3.72244e26 q^{73} -2.41589e26 q^{74} -2.17995e26 q^{75} -4.65393e25 q^{76} +3.81075e26 q^{77} +4.96407e26 q^{78} +2.90538e27 q^{79} -2.59145e27 q^{80} +5.23348e26 q^{81} +3.48190e27 q^{82} -2.68756e27 q^{83} -3.50785e26 q^{84} -7.61094e27 q^{85} +1.36457e27 q^{86} -1.32059e28 q^{87} +7.50407e27 q^{88} -3.21549e28 q^{89} -5.61845e27 q^{90} -3.39953e27 q^{91} -1.07554e27 q^{92} -4.94743e27 q^{93} +5.07758e28 q^{94} +5.10477e27 q^{95} -1.26571e28 q^{96} -5.82099e28 q^{97} -9.52444e27 q^{98} +1.28539e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4464 q^{2} + 28697814 q^{3} + 308522592 q^{4} - 34057000980 q^{5} + 21351173616 q^{6} + 4069338437094 q^{7} + 19307209833216 q^{8} + 137260754729766 q^{9}+O(q^{10}) \) 6 * q + 4464 * q^2 + 28697814 * q^3 + 308522592 * q^4 - 34057000980 * q^5 + 21351173616 * q^6 + 4069338437094 * q^7 + 19307209833216 * q^8 + 137260754729766 * q^9	\( 6 q + 4464 q^{2} + 28697814 q^{3} + 308522592 q^{4} - 34057000980 q^{5} + 21351173616 q^{6} + 4069338437094 q^{7} + 19307209833216 q^{8} + 137260754729766 q^{9} - 27416413415040 q^{10} - 19\!\cdots\!00 q^{11}+ \cdots - 44\!\cdots\!00 q^{99}+O(q^{100}) \) 6 * q + 4464 * q^2 + 28697814 * q^3 + 308522592 * q^4 - 34057000980 * q^5 + 21351173616 * q^6 + 4069338437094 * q^7 + 19307209833216 * q^8 + 137260754729766 * q^9 - 27416413415040 * q^10 - 1943661000024000 * q^11 + 1475653993335648 * q^12 - 13450748854074012 * q^13 + 3027587797197936 * q^14 - 162893579920309620 * q^15 - 657484628537888256 * q^16 - 891734887537201404 * q^17 + 102122001518945904 * q^18 - 6787214411699759016 * q^19 - 4606719795227370240 * q^20 + 19463519595129052086 * q^21 + 58706820582380556000 * q^22 + 4141068849861725304 * q^23 + 92345786108767298304 * q^24 + 272136706732123231050 * q^25 - 341440176492089614368 * q^26 + 656513934789074155254 * q^27 + 209247140389578304608 * q^28 + 2585597660188970274612 * q^29 - 131131855455320453760 * q^30 - 1204878539299247831904 * q^31 - 4159797202844651556864 * q^32 - 9296470309623791256000 * q^33 - 21195441540025996469376 * q^34 - 23098243856677004392020 * q^35 + 7058007304850610978912 * q^36 - 132254788220404822298508 * q^37 - 220889407221302869969344 * q^38 - 64334514795821523101628 * q^39 - 437212759571392303349760 * q^40 - 26110030054236268409244 * q^41 + 14480858578776014751984 * q^42 + 141767508828723725476008 * q^43 - 188729676402659111433024 * q^44 - 779114943057863382861780 * q^45 - 2085553124450449717109280 * q^46 - 2578234389089045150723184 * q^47 - 3144728596273234853912064 * q^48 + 2759919219268439765860806 * q^49 + 941455479402850770594000 * q^50 - 4265140323308920662088476 * q^51 - 3374918204913260684537664 * q^52 - 2752352962631124928912908 * q^53 + 488446367483071171508976 * q^54 - 96873810309318198174960 * q^55 + 13094595181224184307952384 * q^56 - 32463036127513184680998504 * q^57 + 5390021975912281392317856 * q^58 + 29783273333457762702531576 * q^59 - 22033797972258859809442560 * q^60 - 95449739708469802905230316 * q^61 + 237026204448598888591992192 * q^62 + 93093410854394807126723334 * q^63 - 32040206007864683612381184 * q^64 + 269913485905060559518443240 * q^65 + 280792902934088145550764000 * q^66 - 238913035844993441877771960 * q^67 + 981842221641787438830499584 * q^68 + 19806603935754286415547576 * q^69 - 18594444152846974792248960 * q^70 - 115682196667471827012154872 * q^71 + 441687032238864616001784576 * q^72 + 458603587013811635903661420 * q^73 - 446904060615029827280849184 * q^74 + 1301621432061836718291987450 * q^75 - 6092111550972759049305091968 * q^76 - 1318235736013037542748376000 * q^77 - 1633097779516193370744098592 * q^78 - 10034906777945539831743009648 * q^79 - 5997340528902652488008601600 * q^80 + 3140085798164163223281069126 * q^81 - 8752939790814405210267639360 * q^82 - 19309516074459975169018955016 * q^83 + 1000822585822000954012621152 * q^84 - 4150151002407090538173069480 * q^85 - 4621430320291243191543788736 * q^86 + 12366833455156378965390683028 * q^87 + 25799589562519757129329307136 * q^88 + 29301646004663462420780732292 * q^89 - 627199599555278615400013440 * q^90 - 9122608219930241911113700188 * q^91 + 14620997740278659176227485376 * q^92 - 5762896702233584103314042976 * q^93 - 78217476468449813455052050368 * q^94 + 99722018112699072468995806320 * q^95 - 19896181067492680212282249216 * q^96 - 7806999688449057487843013988 * q^97 + 2053379899135719185800439664 * q^98 - 44464729300350995239919064000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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