LMFDB - Embedded newform 21.30.a.c.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:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 678740466 x^{5} - 2954969748680 x^{4} + \cdots - 14\!\cdots\!64 $ x^7 - x^6 - 678740466x^5 - 2954969748680x^4 + 92148363808982720x^3 + 418126965823508980224x^2 - 2978683903673490966301184*x - 14143029174281721602229028864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{12}\cdot 5^{3}\cdot 7^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$10372.4$ 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)

$f(q)$	$=$	$q-12048.8 q^{2} -4.78297e6 q^{3} -3.91697e8 q^{4} -3.60173e9 q^{5} +5.76290e10 q^{6} +6.78223e11 q^{7} +1.11881e13 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q-12048.8 q^{2} -4.78297e6 q^{3} -3.91697e8 q^{4} -3.60173e9 q^{5} +5.76290e10 q^{6} +6.78223e11 q^{7} +1.11881e13 q^{8} +2.28768e13 q^{9} +4.33965e13 q^{10} +2.47063e15 q^{11} +1.87348e15 q^{12} +1.86546e16 q^{13} -8.17177e15 q^{14} +1.72270e16 q^{15} +7.54875e16 q^{16} -1.63789e17 q^{17} -2.75638e17 q^{18} +4.78889e18 q^{19} +1.41079e18 q^{20} -3.24392e18 q^{21} -2.97681e19 q^{22} +8.72928e19 q^{23} -5.35125e19 q^{24} -1.73292e20 q^{25} -2.24766e20 q^{26} -1.09419e20 q^{27} -2.65658e20 q^{28} +4.12318e20 q^{29} -2.07564e20 q^{30} +2.72422e21 q^{31} -6.91611e21 q^{32} -1.18170e22 q^{33} +1.97346e21 q^{34} -2.44278e21 q^{35} -8.96078e21 q^{36} +8.47570e21 q^{37} -5.77004e22 q^{38} -8.92245e22 q^{39} -4.02967e22 q^{40} +1.03801e23 q^{41} +3.90853e22 q^{42} +9.09244e23 q^{43} -9.67741e23 q^{44} -8.23961e22 q^{45} -1.05177e24 q^{46} -1.23824e24 q^{47} -3.61054e23 q^{48} +4.59987e23 q^{49} +2.08796e24 q^{50} +7.83397e23 q^{51} -7.30697e24 q^{52} +9.35713e24 q^{53} +1.31837e24 q^{54} -8.89856e24 q^{55} +7.58805e24 q^{56} -2.29051e25 q^{57} -4.96794e24 q^{58} -4.11703e25 q^{59} -6.74776e24 q^{60} +6.20050e25 q^{61} -3.28235e25 q^{62} +1.55156e25 q^{63} +4.28038e25 q^{64} -6.71890e25 q^{65} +1.42380e26 q^{66} -3.26694e26 q^{67} +6.41556e25 q^{68} -4.17519e26 q^{69} +2.94325e25 q^{70} -1.43733e26 q^{71} +2.55949e26 q^{72} +7.74062e26 q^{73} -1.02122e26 q^{74} +8.28850e26 q^{75} -1.87580e27 q^{76} +1.67564e27 q^{77} +1.07505e27 q^{78} -4.94593e27 q^{79} -2.71886e26 q^{80} +5.23348e26 q^{81} -1.25068e27 q^{82} -6.81874e27 q^{83} +1.27064e27 q^{84} +5.89923e26 q^{85} -1.09553e28 q^{86} -1.97211e27 q^{87} +2.76418e28 q^{88} +2.47771e28 q^{89} +9.92774e26 q^{90} +1.26520e28 q^{91} -3.41924e28 q^{92} -1.30299e28 q^{93} +1.49193e28 q^{94} -1.72483e28 q^{95} +3.30796e28 q^{96} +8.17497e28 q^{97} -5.54228e27 q^{98} +5.65202e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9}+O(q^{10}) $ 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9	$ 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9} - 472777770164028 q^{10} + 135879674344284 q^{11} - 10\!\cdots\!44 q^{12}+ \cdots + 31\!\cdots\!24 q^{99}+O(q^{100}) $ 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9 - 472777770164028 * q^10 + 135879674344284 * q^11 - 10527962746508244 * q^12 + 12138994948536170 * q^13 + 41283438444318630 * q^14 + 13687032584892438 * q^15 + 1300607396354614288 * q^16 - 385869676567281066 * q^17 + 1392510356733476070 * q^18 + 726075641163594644 * q^19 + 8133031378709443032 * q^20 - 22707439527650560767 * q^21 - 40013549861901162600 * q^22 + 81623233895572110192 * q^23 - 47659100600287417320 * q^24 - 344687932818137236151 * q^25 + 557803893676418715300 * q^26 - 765932923920586514463 * q^27 + 1492860866289666291124 * q^28 + 2523262928009462965506 * q^29 + 2261281418583670839132 * q^30 + 3097457398331417166752 * q^31 + 3797011810352053176480 * q^32 - 649908270118805699196 * q^33 + 63335711497801752433500 * q^34 - 1940815693747992252198 * q^35 + 50354919449703789296436 * q^36 + 12145140799949814343466 * q^37 - 108697233906951781953720 * q^38 - 58060436530005096488730 * q^39 - 475320691810097154363216 * q^40 - 262433505631892547251154 * q^41 - 197457406292584233412470 * q^42 - 193139951479227114687580 * q^43 - 2430431685366465708769488 * q^44 - 65464652555530399288422 * q^45 - 6981072827049021325022880 * q^46 - 1146871717647137318395248 * q^47 - 6220764857934833146461072 * q^48 + 3219905755813179726837607 * q^49 + 4481749443828030876391386 * q^50 + 1845602701061331752964954 * q^51 + 1236271786388417967514040 * q^52 - 6665695659633633475901814 * q^53 - 6660333868435157305051830 * q^54 + 5317495916141118544489032 * q^55 + 6758041220494331589303720 * q^56 - 3472797283340597110818036 * q^57 - 19887500189096257342540140 * q^58 + 252077122803863627555062380 * q^59 - 38900036960394526029322008 * q^60 + 286844596551467198960110586 * q^61 + 655482484647841866799404480 * q^62 + 108608979330127274981177223 * q^63 + 523821984648801603783498304 * q^64 + 677830247031279033073631964 * q^65 + 191383568569427541779759400 * q^66 - 21966489249761249366283412 * q^67 - 230093364489444117467612568 * q^68 - 390401397402270640312920048 * q^69 - 320648792055345340923275772 * q^70 + 236873286033551829517504320 * q^71 + 227952000739056108131623080 * q^72 + 1436061741885259500381870806 * q^73 - 3275022628978202210175964380 * q^74 + 1648631697343233038255912319 * q^75 - 4562877250128321487477927888 * q^76 + 92156730271501723638745116 * q^77 - 2667958731533606746299725700 * q^78 + 442695609959843509130102048 * q^79 + 7254106132718389061591220192 * q^80 + 3663433431191523760494580647 * q^81 + 4421292535141977509208500940 * q^82 + 4700059828307966195559697476 * q^83 - 7140307244776618890791067156 * q^84 - 13424791113423208631620606908 * q^85 + 12752722226530676548320081000 * q^86 - 12068688363518493070663267314 * q^87 + 4553745967919270581660489440 * q^88 + 52994579350095331884835317486 * q^89 - 10815638925361721529772342908 * q^90 + 8232946455294689831821448330 * q^91 + 54926079962260892072539429536 * q^92 - 14815042715039820034642646688 * q^93 - 26892181494551465508576501600 * q^94 - 74456487258213633048885368328 * q^95 - 18160989781547749429455369120 * q^96 + 74985775395694126905639860942 * q^97 + 27999380479478321424657876870 * q^98 + 3108491108821873976277792924 * 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 $

$2$	−12048.8	−0.520006	−0.260003	−	0.965608i	$-0.583724\pi$
$2$	−12048.8	−0.520006	−0.260003	+	0.965608i	$0.583724\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	−3.91697e8	−0.729593
$5$	−3.60173e9	−0.263904	−0.131952	−	0.991256i	$-0.542125\pi$
$5$	−3.60173e9	−0.263904	−0.131952	+	0.991256i	$0.542125\pi$
$6$	5.76290e10	0.300226
$7$	6.78223e11	0.377964
$7$	6.78223e11	0.377964
$8$	1.11881e13	0.899400
$9$	2.28768e13	0.333333
$10$	4.33965e13	0.137232
$11$	2.47063e15	1.96162	0.980809	−	0.194973i	$-0.0624618\pi$
$11$	2.47063e15	1.96162	0.980809	+	0.194973i	$0.0624618\pi$
$12$	1.87348e15	0.421231
$13$	1.86546e16	1.31404	0.657019	−	0.753874i	$-0.271817\pi$
$13$	1.86546e16	1.31404	0.657019	+	0.753874i	$0.271817\pi$
$14$	−8.17177e15	−0.196544
$15$	1.72270e16	0.152365
$16$	7.54875e16	0.261900
$17$	−1.63789e17	−0.235925	−0.117963	−	0.993018i	$-0.537636\pi$
$17$	−1.63789e17	−0.235925	−0.117963	+	0.993018i	$0.537636\pi$
$18$	−2.75638e17	−0.173335
$19$	4.78889e18	1.37502	0.687508	−	0.726177i	$-0.258705\pi$
$19$	4.78889e18	1.37502	0.687508	+	0.726177i	$0.258705\pi$
$20$	1.41079e18	0.192543
$21$	−3.24392e18	−0.218218
$22$	−2.97681e19	−1.02005
$23$	8.72928e19	1.57009	0.785046	−	0.619438i	$-0.212639\pi$
$23$	8.72928e19	1.57009	0.785046	+	0.619438i	$0.212639\pi$
$24$	−5.35125e19	−0.519269
$25$	−1.73292e20	−0.930355
$26$	−2.24766e20	−0.683308
$27$	−1.09419e20	−0.192450
$28$	−2.65658e20	−0.275760
$29$	4.12318e20	0.257313	0.128656	−	0.991689i	$-0.458934\pi$
$29$	4.12318e20	0.257313	0.128656	+	0.991689i	$0.458934\pi$
$30$	−2.07564e20	−0.0792309
$31$	2.72422e21	0.646394	0.323197	−	0.946332i	$-0.395242\pi$
$31$	2.72422e21	0.646394	0.323197	+	0.946332i	$0.395242\pi$
$32$	−6.91611e21	−1.03559
$33$	−1.18170e22	−1.13254
$34$	1.97346e21	0.122683
$35$	−2.44278e21	−0.0997465
$36$	−8.96078e21	−0.243198
$37$	8.47570e21	0.154615	0.0773073	−	0.997007i	$-0.475368\pi$
$37$	8.47570e21	0.154615	0.0773073	+	0.997007i	$0.475368\pi$
$38$	−5.77004e22	−0.715017
$39$	−8.92245e22	−0.758660
$40$	−4.02967e22	−0.237355
$41$	1.03801e23	0.427402	0.213701	−	0.976899i	$-0.431448\pi$
$41$	1.03801e23	0.427402	0.213701	+	0.976899i	$0.431448\pi$
$42$	3.90853e22	0.113475
$43$	9.09244e23	1.87667	0.938335	−	0.345728i	$-0.112368\pi$
$43$	9.09244e23	1.87667	0.938335	+	0.345728i	$0.112368\pi$
$44$	−9.67741e23	−1.43118
$45$	−8.23961e22	−0.0879681
$46$	−1.05177e24	−0.816458
$47$	−1.23824e24	−0.703696	−0.351848	−	0.936057i	$-0.614447\pi$
$47$	−1.23824e24	−0.703696	−0.351848	+	0.936057i	$0.614447\pi$
$48$	−3.61054e23	−0.151208
$49$	4.59987e23	0.142857
$50$	2.08796e24	0.483790
$51$	7.83397e23	0.136212
$52$	−7.30697e24	−0.958713
$53$	9.35713e24	0.931413	0.465707	−	0.884939i	$-0.345800\pi$
$53$	9.35713e24	0.931413	0.465707	+	0.884939i	$0.345800\pi$
$54$	1.31837e24	0.100075
$55$	−8.89856e24	−0.517679
$56$	7.58805e24	0.339941
$57$	−2.29051e25	−0.793866
$58$	−4.96794e24	−0.133804
$59$	−4.11703e25	−0.865426	−0.432713	−	0.901532i	$-0.642444\pi$
$59$	−4.11703e25	−0.865426	−0.432713	+	0.901532i	$0.642444\pi$
$60$	−6.74776e24	−0.111165
$61$	6.20050e25	0.803793	0.401896	−	0.915685i	$-0.368351\pi$
$61$	6.20050e25	0.803793	0.401896	+	0.915685i	$0.368351\pi$
$62$	−3.28235e25	−0.336129
$63$	1.55156e25	0.125988
$64$	4.28038e25	0.276613
$65$	−6.71890e25	−0.346780
$66$	1.42380e26	0.588928
$67$	−3.26694e26	−1.08657	−0.543283	−	0.839550i	$-0.682819\pi$
$67$	−3.26694e26	−1.08657	−0.543283	+	0.839550i	$0.682819\pi$
$68$	6.41556e25	0.172130
$69$	−4.17519e26	−0.906493
$70$	2.94325e25	0.0518688
$71$	−1.43733e26	−0.206211	−0.103105	−	0.994670i	$-0.532878\pi$
$71$	−1.43733e26	−0.206211	−0.103105	+	0.994670i	$0.532878\pi$
$72$	2.55949e26	0.299800
$73$	7.74062e26	0.742325	0.371163	−	0.928568i	$-0.378959\pi$
$73$	7.74062e26	0.742325	0.371163	+	0.928568i	$0.378959\pi$
$74$	−1.02122e26	−0.0804006
$75$	8.28850e26	0.537140
$76$	−1.87580e27	−1.00320
$77$	1.67564e27	0.741422
$78$	1.07505e27	0.394508
$79$	−4.94593e27	−1.50888	−0.754441	−	0.656368i	$-0.772092\pi$
$79$	−4.94593e27	−1.50888	−0.754441	+	0.656368i	$0.772092\pi$
$80$	−2.71886e26	−0.0691165
$81$	5.23348e26	0.111111
$82$	−1.25068e27	−0.222252
$83$	−6.81874e27	−1.01642	−0.508208	−	0.861234i	$-0.669692\pi$
$83$	−6.81874e27	−1.01642	−0.508208	+	0.861234i	$0.669692\pi$
$84$	1.27064e27	0.159210
$85$	5.89923e26	0.0622617
$86$	−1.09553e28	−0.975880
$87$	−1.97211e27	−0.148560
$88$	2.76418e28	1.76428
$89$	2.47771e28	1.34244	0.671220	−	0.741258i	$-0.265770\pi$
$89$	2.47771e28	1.34244	0.671220	+	0.741258i	$0.265770\pi$
$90$	9.92774e26	0.0457440
$91$	1.26520e28	0.496660
$92$	−3.41924e28	−1.14553
$93$	−1.30299e28	−0.373196
$94$	1.49193e28	0.365927
$95$	−1.72483e28	−0.362873
$96$	3.30796e28	0.597898
$97$	8.17497e28	1.27144	0.635720	−	0.771920i	$-0.280703\pi$
$97$	8.17497e28	1.27144	0.635720	+	0.771920i	$0.280703\pi$
$98$	−5.54228e27	−0.0742866
$99$	5.65202e28	0.653872
$100$	6.78781e28	0.678781
$101$	1.71668e29	1.48604	0.743020	−	0.669269i	$-0.233393\pi$
$101$	1.71668e29	1.48604	0.743020	+	0.669269i	$0.233393\pi$
$102$	−9.43898e27	−0.0708309
$103$	−5.80243e28	−0.377981	−0.188991	−	0.981979i	$-0.560522\pi$
$103$	−5.80243e28	−0.377981	−0.188991	+	0.981979i	$0.560522\pi$
$104$	2.08710e29	1.18184
$105$	1.16837e28	0.0575886
$106$	−1.12742e29	−0.484341
$107$	−1.78168e29	−0.667981	−0.333990	−	0.942577i	$-0.608395\pi$
$107$	−1.78168e29	−0.667981	−0.333990	+	0.942577i	$0.608395\pi$
$108$	4.28591e28	0.140410
$109$	−1.22694e29	−0.351673	−0.175836	−	0.984419i	$-0.556263\pi$
$109$	−1.22694e29	−0.351673	−0.175836	+	0.984419i	$0.556263\pi$
$110$	1.07217e29	0.269196
$111$	−4.05390e28	−0.0892668
$112$	5.11974e28	0.0989889
$113$	−5.98484e29	−1.01722	−0.508610	−	0.860997i	$-0.669841\pi$
$113$	−5.98484e29	−1.01722	−0.508610	+	0.860997i	$0.669841\pi$
$114$	2.75979e29	0.412815
$115$	−3.14405e29	−0.414354
$116$	−1.61504e29	−0.187734
$117$	4.26758e29	0.438013
$118$	4.96053e29	0.450027
$119$	−1.11085e29	−0.0891714
$120$	1.92738e29	0.137037
$121$	4.51772e30	2.84794
$122$	−7.47086e29	−0.417977
$123$	−4.96479e29	−0.246761
$124$	−1.06707e30	−0.471605
$125$	1.29503e30	0.509429
$126$	−1.86944e29	−0.0655146
$127$	2.56451e30	0.801402	0.400701	−	0.916209i	$-0.368767\pi$
$127$	2.56451e30	0.801402	0.400701	+	0.916209i	$0.368767\pi$
$128$	3.19733e30	0.891749
$129$	−4.34889e30	−1.08350
$130$	8.09546e29	0.180328
$131$	7.66046e30	1.52694	0.763468	−	0.645845i	$-0.223495\pi$
$131$	7.66046e30	1.52694	0.763468	+	0.645845i	$0.223495\pi$
$132$	4.62867e30	0.826294
$133$	3.24794e30	0.519707
$134$	3.93626e30	0.565021
$135$	3.94098e29	0.0507884
$136$	−1.83249e30	−0.212191
$137$	1.74131e30	0.181313	0.0906565	−	0.995882i	$-0.471103\pi$
$137$	1.74131e30	0.181313	0.0906565	+	0.995882i	$0.471103\pi$
$138$	5.03060e30	0.471382
$139$	−3.09341e30	−0.261050	−0.130525	−	0.991445i	$-0.541666\pi$
$139$	−3.09341e30	−0.261050	−0.130525	+	0.991445i	$0.541666\pi$
$140$	9.56830e29	0.0727744
$141$	5.92246e30	0.406279
$142$	1.73181e30	0.107231
$143$	4.60887e31	2.57764
$144$	1.72691e30	0.0873000
$145$	−1.48506e30	−0.0679060
$146$	−9.32651e30	−0.386014
$147$	−2.20010e30	−0.0824786
$148$	−3.31991e30	−0.112806
$149$	−1.93287e31	−0.595666	−0.297833	−	0.954618i	$-0.596264\pi$
$149$	−1.93287e31	−0.595666	−0.297833	+	0.954618i	$0.596264\pi$
$150$	−9.98665e30	−0.279316
$151$	3.41440e31	0.867259	0.433630	−	0.901091i	$-0.357233\pi$
$151$	3.41440e31	0.867259	0.433630	+	0.901091i	$0.357233\pi$
$152$	5.35787e31	1.23669
$153$	−3.74696e30	−0.0786418
$154$	−2.01894e31	−0.385544
$155$	−9.81191e30	−0.170586
$156$	3.49490e31	0.553513
$157$	3.88711e31	0.561153	0.280577	−	0.959832i	$-0.409474\pi$
$157$	3.88711e31	0.561153	0.280577	+	0.959832i	$0.409474\pi$
$158$	5.95925e31	0.784628
$159$	−4.47548e31	−0.537752
$160$	2.49100e31	0.273296
$161$	5.92040e31	0.593439
$162$	−6.30571e30	−0.0577785
$163$	−9.97555e31	−0.836020	−0.418010	−	0.908443i	$-0.637272\pi$
$163$	−9.97555e31	−0.836020	−0.418010	+	0.908443i	$0.637272\pi$
$164$	−4.06587e31	−0.311830
$165$	4.25615e31	0.298882
$166$	8.21575e31	0.528543
$167$	−1.01531e32	−0.598699	−0.299349	−	0.954144i	$-0.596770\pi$
$167$	−1.01531e32	−0.598699	−0.299349	+	0.954144i	$0.596770\pi$
$168$	−3.62934e31	−0.196265
$169$	1.46457e32	0.726695
$170$	−7.10787e30	−0.0323765
$171$	1.09554e32	0.458339
$172$	−3.56149e32	−1.36921
$173$	−4.88170e32	−1.72545	−0.862726	−	0.505672i	$-0.831245\pi$
$173$	−4.88170e32	−1.72545	−0.862726	+	0.505672i	$0.831245\pi$
$174$	2.37615e31	0.0772520
$175$	−1.17531e32	−0.351641
$176$	1.86502e32	0.513748
$177$	1.96916e32	0.499654
$178$	−2.98534e32	−0.698078
$179$	−5.56686e32	−1.20017	−0.600083	−	0.799937i	$-0.704866\pi$
$179$	−5.56686e32	−1.20017	−0.600083	+	0.799937i	$0.704866\pi$
$180$	3.22743e31	0.0641809
$181$	−8.16285e32	−1.49797	−0.748984	−	0.662588i	$-0.769458\pi$
$181$	−8.16285e32	−1.49797	−0.748984	+	0.662588i	$0.769458\pi$
$182$	−1.52441e32	−0.258266
$183$	−2.96568e32	−0.464070
$184$	9.76643e32	1.41214
$185$	−3.05272e31	−0.0408035
$186$	1.56994e32	0.194064
$187$	−4.04662e32	−0.462795
$188$	4.85015e32	0.513412
$189$	−7.42105e31	−0.0727393
$190$	2.07821e32	0.188696
$191$	7.50694e32	0.631654	0.315827	−	0.948817i	$-0.397718\pi$
$191$	7.50694e32	0.631654	0.315827	+	0.948817i	$0.397718\pi$
$192$	−2.04729e32	−0.159703
$193$	−1.12022e33	−0.810443	−0.405222	−	0.914218i	$-0.632806\pi$
$193$	−1.12022e33	−0.810443	−0.405222	+	0.914218i	$0.632806\pi$
$194$	−9.84985e32	−0.661157
$195$	3.21363e32	0.200214
$196$	−1.80176e32	−0.104228
$197$	−8.81790e32	−0.473811	−0.236905	−	0.971533i	$-0.576133\pi$
$197$	−8.81790e32	−0.473811	−0.236905	+	0.971533i	$0.576133\pi$
$198$	−6.81000e32	−0.340018
$199$	−3.18513e33	−1.47828	−0.739142	−	0.673550i	$-0.764769\pi$
$199$	−3.18513e33	−1.47828	−0.739142	+	0.673550i	$0.764769\pi$
$200$	−1.93881e33	−0.836760
$201$	1.56257e33	0.627329
$202$	−2.06840e33	−0.772750
$203$	2.79644e32	0.0972551
$204$	−3.06854e32	−0.0993791
$205$	−3.73865e32	−0.112793
$206$	6.99123e32	0.196553
$207$	1.99698e33	0.523364
$208$	1.40819e33	0.344146
$209$	1.18316e34	2.69726
$210$	−1.40775e32	−0.0299465
$211$	−5.78570e33	−1.14884	−0.574421	−	0.818560i	$-0.694773\pi$
$211$	−5.78570e33	−1.14884	−0.574421	+	0.818560i	$0.694773\pi$
$212$	−3.66516e33	−0.679553
$213$	6.87473e32	0.119056
$214$	2.14670e33	0.347354
$215$	−3.27485e33	−0.495261
$216$	−1.22419e33	−0.173090
$217$	1.84763e33	0.244314
$218$	1.47831e33	0.182872
$219$	−3.70232e33	−0.428582
$220$	3.48554e33	0.377695
$221$	−3.05542e33	−0.310015
$222$	4.88446e32	0.0464193
$223$	−1.16334e34	−1.03583	−0.517913	−	0.855433i	$-0.673291\pi$
$223$	−1.16334e34	−1.03583	−0.517913	+	0.855433i	$0.673291\pi$
$224$	−4.69067e33	−0.391416
$225$	−3.96437e33	−0.310118
$226$	7.21101e33	0.528961
$227$	5.87231e33	0.404049	0.202024	−	0.979380i	$-0.435248\pi$
$227$	5.87231e33	0.404049	0.202024	+	0.979380i	$0.435248\pi$
$228$	8.97188e33	0.579199
$229$	5.05899e33	0.306513	0.153257	−	0.988186i	$-0.451024\pi$
$229$	5.05899e33	0.306513	0.153257	+	0.988186i	$0.451024\pi$
$230$	3.78821e33	0.215467
$231$	−8.01454e33	−0.428060
$232$	4.61307e33	0.231427
$233$	3.45133e34	1.62677	0.813384	−	0.581727i	$-0.197623\pi$
$233$	3.45133e34	1.62677	0.813384	+	0.581727i	$0.197623\pi$
$234$	−5.14192e33	−0.227769
$235$	4.45980e33	0.185708
$236$	1.61263e34	0.631409
$237$	2.36562e34	0.871153
$238$	1.33844e33	0.0463697
$239$	1.54557e34	0.503869	0.251935	−	0.967744i	$-0.418933\pi$
$239$	1.54557e34	0.503869	0.251935	+	0.967744i	$0.418933\pi$
$240$	1.30042e33	0.0399044
$241$	−4.82322e34	−1.39345	−0.696723	−	0.717340i	$-0.745359\pi$
$241$	−4.82322e34	−1.39345	−0.696723	+	0.717340i	$0.745359\pi$
$242$	−5.44330e34	−1.48095
$243$	−2.50316e33	−0.0641500
$244$	−2.42872e34	−0.586442
$245$	−1.65675e33	−0.0377006
$246$	5.98197e33	0.128317
$247$	8.93350e34	1.80682
$248$	3.04789e34	0.581366
$249$	3.26138e34	0.586828
$250$	−1.56035e34	−0.264906
$251$	9.71104e34	1.55595	0.777977	−	0.628293i	$-0.216246\pi$
$251$	9.71104e34	1.55595	0.777977	+	0.628293i	$0.216246\pi$
$252$	−6.07741e33	−0.0919201
$253$	2.15669e35	3.07992
$254$	−3.08993e34	−0.416734
$255$	−2.82159e33	−0.0359468
$256$	−6.15040e34	−0.740328
$257$	−8.66459e34	−0.985639	−0.492819	−	0.870132i	$-0.664034\pi$
$257$	−8.66459e34	−0.985639	−0.492819	+	0.870132i	$0.664034\pi$
$258$	5.23988e34	0.563425
$259$	5.74842e33	0.0584389
$260$	2.63177e34	0.253009
$261$	9.43252e33	0.0857710
$262$	−9.22993e34	−0.794017
$263$	1.57485e35	1.28198	0.640990	−	0.767549i	$-0.278524\pi$
$263$	1.57485e35	1.28198	0.640990	+	0.767549i	$0.278524\pi$
$264$	−1.32210e35	−1.01861
$265$	−3.37019e34	−0.245804
$266$	−3.91337e34	−0.270251
$267$	−1.18508e35	−0.775058
$268$	1.27965e35	0.792751
$269$	−1.07619e35	−0.631657	−0.315828	−	0.948816i	$-0.602282\pi$
$269$	−1.07619e35	−0.631657	−0.315828	+	0.948816i	$0.602282\pi$
$270$	−4.74841e33	−0.0264103
$271$	3.36198e35	1.77231	0.886157	−	0.463385i	$-0.153365\pi$
$271$	3.36198e35	1.77231	0.886157	+	0.463385i	$0.153365\pi$
$272$	−1.23640e34	−0.0617889
$273$	−6.05141e34	−0.286747
$274$	−2.09807e34	−0.0942839
$275$	−4.28141e35	−1.82500
$276$	1.63541e35	0.661371
$277$	−4.25512e35	−1.63288	−0.816441	−	0.577429i	$-0.804056\pi$
$277$	−4.25512e35	−1.63288	−0.816441	+	0.577429i	$0.804056\pi$
$278$	3.72719e34	0.135748
$279$	6.23214e34	0.215465
$280$	−2.73301e34	−0.0897119
$281$	−2.51616e35	−0.784327	−0.392164	−	0.919895i	$-0.628273\pi$
$281$	−2.51616e35	−0.784327	−0.392164	+	0.919895i	$0.628273\pi$
$282$	−7.13584e34	−0.211268
$283$	−3.33719e35	−0.938593	−0.469297	−	0.883041i	$-0.655493\pi$
$283$	−3.33719e35	−0.938593	−0.469297	+	0.883041i	$0.655493\pi$
$284$	5.63000e34	0.150450
$285$	8.24981e34	0.209505
$286$	−5.55313e35	−1.34039
$287$	7.04005e34	0.161543
$288$	−1.58219e35	−0.345196
$289$	−4.55142e35	−0.944339
$290$	1.78932e34	0.0353115
$291$	−3.91006e35	−0.734066
$292$	−3.03198e35	−0.541596
$293$	1.23585e35	0.210081	0.105040	−	0.994468i	$-0.466503\pi$
$293$	1.23585e35	0.210081	0.105040	+	0.994468i	$0.466503\pi$
$294$	2.65086e34	0.0428894
$295$	1.48285e35	0.228390
$296$	9.48273e34	0.139060
$297$	−2.70334e35	−0.377513
$298$	2.32888e35	0.309750
$299$	1.62841e36	2.06316
$300$	−3.24659e35	−0.391894
$301$	6.16670e35	0.709314
$302$	−4.11394e35	−0.450980
$303$	−8.21085e35	−0.857966
$304$	3.61502e35	0.360117
$305$	−2.23326e35	−0.212124
$306$	4.51464e34	0.0408942
$307$	2.35055e35	0.203078	0.101539	−	0.994832i	$-0.467623\pi$
$307$	2.35055e35	0.203078	0.101539	+	0.994832i	$0.467623\pi$
$308$	−6.56344e35	−0.540936
$309$	2.77528e35	0.218228
$310$	1.18222e35	0.0887059
$311$	−8.18335e35	−0.586011	−0.293005	−	0.956111i	$-0.594655\pi$
$311$	−8.18335e35	−0.586011	−0.293005	+	0.956111i	$0.594655\pi$
$312$	−9.98255e35	−0.682338
$313$	3.55765e35	0.232151	0.116075	−	0.993240i	$-0.462969\pi$
$313$	3.55765e35	0.232151	0.116075	+	0.993240i	$0.462969\pi$
$314$	−4.68349e35	−0.291803
$315$	−5.58829e34	−0.0332488
$316$	1.93731e36	1.10087
$317$	3.27798e36	1.77929	0.889645	−	0.456652i	$-0.150952\pi$
$317$	3.27798e36	1.77929	0.889645	+	0.456652i	$0.150952\pi$
$318$	5.39242e35	0.279634
$319$	1.01869e36	0.504750
$320$	−1.54168e35	−0.0729994
$321$	8.52170e35	0.385659
$322$	−7.13337e35	−0.308592
$323$	−7.84367e35	−0.324401
$324$	−2.04994e35	−0.0810659
$325$	−3.23270e36	−1.22252
$326$	1.20193e36	0.434735
$327$	5.86841e35	0.203038
$328$	1.16134e36	0.384406
$329$	−8.39802e35	−0.265972
$330$	−5.12815e35	−0.155421
$331$	−4.91200e36	−1.42480	−0.712398	−	0.701776i	$-0.752391\pi$
$331$	−4.91200e36	−1.42480	−0.712398	+	0.701776i	$0.752391\pi$
$332$	2.67088e36	0.741571
$333$	1.93897e35	0.0515382
$334$	1.22332e36	0.311327
$335$	1.17666e36	0.286749
$336$	−2.44875e35	−0.0571513
$337$	−4.10313e36	−0.917237	−0.458619	−	0.888633i	$-0.651656\pi$
$337$	−4.10313e36	−0.917237	−0.458619	+	0.888633i	$0.651656\pi$
$338$	−1.76463e36	−0.377886
$339$	2.86253e36	0.587292
$340$	−2.31072e35	−0.0454258
$341$	6.73054e36	1.26798
$342$	−1.32000e36	−0.238339
$343$	3.11973e35	0.0539949
$344$	1.01727e37	1.68788
$345$	1.50379e36	0.239227
$346$	5.88186e36	0.897246
$347$	1.55461e36	0.227428	0.113714	−	0.993514i	$-0.463725\pi$
$347$	1.55461e36	0.227428	0.113714	+	0.993514i	$0.463725\pi$
$348$	7.72469e35	0.108388
$349$	1.05174e37	1.41560	0.707799	−	0.706414i	$-0.249688\pi$
$349$	1.05174e37	1.41560	0.707799	+	0.706414i	$0.249688\pi$
$350$	1.41610e36	0.182856
$351$	−2.04117e36	−0.252887
$352$	−1.70872e37	−2.03143
$353$	1.40166e37	1.59923	0.799613	−	0.600516i	$-0.205038\pi$
$353$	1.40166e37	1.59923	0.799613	+	0.600516i	$0.205038\pi$
$354$	−2.37261e36	−0.259823
$355$	5.17689e35	0.0544200
$356$	−9.70512e36	−0.979436
$357$	5.31318e35	0.0514831
$358$	6.70740e36	0.624094
$359$	−7.34419e35	−0.0656257	−0.0328129	−	0.999462i	$-0.510447\pi$
$359$	−7.34419e35	−0.0656257	−0.0328129	+	0.999462i	$0.510447\pi$
$360$	−9.21858e35	−0.0791185
$361$	1.08037e37	0.890669
$362$	9.83525e36	0.778953
$363$	−2.16081e37	−1.64426
$364$	−4.95575e36	−0.362360
$365$	−2.78797e36	−0.195903
$366$	3.57329e36	0.241319
$367$	−2.52332e37	−1.63800	−0.819002	−	0.573791i	$-0.805472\pi$
$367$	−2.52332e37	−1.63800	−0.819002	+	0.573791i	$0.805472\pi$
$368$	6.58952e36	0.411207
$369$	2.37464e36	0.142467
$370$	3.67816e35	0.0212181
$371$	6.34622e36	0.352041
$372$	5.10376e36	0.272281
$373$	−1.74513e36	−0.0895466	−0.0447733	−	0.998997i	$-0.514257\pi$
$373$	−1.74513e36	−0.0895466	−0.0447733	+	0.998997i	$0.514257\pi$
$374$	4.87569e36	0.240657
$375$	−6.19407e36	−0.294119
$376$	−1.38536e37	−0.632904
$377$	7.69164e36	0.338119
$378$	8.94147e35	0.0378249
$379$	−3.55362e37	−1.44678	−0.723389	−	0.690441i	$-0.757417\pi$
$379$	−3.55362e37	−1.44678	−0.723389	+	0.690441i	$0.757417\pi$
$380$	6.75612e36	0.264750
$381$	−1.22660e37	−0.462690
$382$	−9.04495e36	−0.328464
$383$	3.52705e37	1.23319	0.616594	−	0.787281i	$-0.288512\pi$
$383$	3.52705e37	1.23319	0.616594	+	0.787281i	$0.288512\pi$
$384$	−1.52927e37	−0.514851
$385$	−6.03521e36	−0.195664
$386$	1.34973e37	0.421436
$387$	2.08006e37	0.625557
$388$	−3.20211e37	−0.927634
$389$	−1.39514e37	−0.389357	−0.194678	−	0.980867i	$-0.562366\pi$
$389$	−1.39514e37	−0.389357	−0.194678	+	0.980867i	$0.562366\pi$
$390$	−3.87203e36	−0.104112
$391$	−1.42976e37	−0.370425
$392$	5.14639e36	0.128486
$393$	−3.66397e37	−0.881577
$394$	1.06245e37	0.246385
$395$	1.78139e37	0.398200
$396$	−2.21388e37	−0.477061
$397$	−1.82168e37	−0.378452	−0.189226	−	0.981934i	$-0.560598\pi$
$397$	−1.82168e37	−0.378452	−0.189226	+	0.981934i	$0.560598\pi$
$398$	3.83770e37	0.768717
$399$	−1.55348e37	−0.300053
$400$	−1.30814e37	−0.243660
$401$	6.00144e37	1.07811	0.539054	−	0.842271i	$-0.318782\pi$
$401$	6.00144e37	1.07811	0.539054	+	0.842271i	$0.318782\pi$
$402$	−1.88270e37	−0.326215
$403$	5.08193e37	0.849386
$404$	−6.72421e37	−1.08421
$405$	−1.88496e36	−0.0293227
$406$	−3.36937e36	−0.0505733
$407$	2.09404e37	0.303295
$408$	8.76474e36	0.122509
$409$	−1.05039e38	−1.41698	−0.708490	−	0.705721i	$-0.750623\pi$
$409$	−1.05039e38	−1.41698	−0.708490	+	0.705721i	$0.750623\pi$
$410$	4.50462e36	0.0586533
$411$	−8.32865e36	−0.104681
$412$	2.27280e37	0.275773
$413$	−2.79227e37	−0.327100
$414$	−2.40612e37	−0.272153
$415$	2.45593e37	0.268237
$416$	−1.29017e38	−1.36080
$417$	1.47957e37	0.150717
$418$	−1.42556e38	−1.40259
$419$	3.21424e37	0.305475	0.152737	−	0.988267i	$-0.451191\pi$
$419$	3.21424e37	0.305475	0.152737	+	0.988267i	$0.451191\pi$
$420$	−4.57649e36	−0.0420163
$421$	8.07296e36	0.0716048	0.0358024	−	0.999359i	$-0.488601\pi$
$421$	8.07296e36	0.0716048	0.0358024	+	0.999359i	$0.488601\pi$
$422$	6.97107e37	0.597405
$423$	−2.83269e37	−0.234565
$424$	1.04689e38	0.837713
$425$	2.83833e37	0.219494
$426$	−8.28322e36	−0.0619098
$427$	4.20532e37	0.303805
$428$	6.97878e37	0.487354
$429$	−2.20441e38	−1.48820
$430$	3.94580e37	0.257539
$431$	1.61061e38	1.01641	0.508207	−	0.861235i	$-0.330308\pi$
$431$	1.61061e38	1.01641	0.508207	+	0.861235i	$0.330308\pi$
$432$	−8.25977e36	−0.0504027
$433$	−2.43722e38	−1.43820	−0.719102	−	0.694905i	$-0.755447\pi$
$433$	−2.43722e38	−1.43820	−0.719102	+	0.694905i	$0.755447\pi$
$434$	−2.22617e37	−0.127045
$435$	7.10300e36	0.0392055
$436$	4.80589e37	0.256578
$437$	4.18036e38	2.15890
$438$	4.46084e37	0.222865
$439$	2.27047e38	1.09744	0.548719	−	0.836007i	$-0.315116\pi$
$439$	2.27047e38	1.09744	0.548719	+	0.836007i	$0.315116\pi$
$440$	−9.95582e37	−0.465600
$441$	1.05230e37	0.0476190
$442$	3.68141e37	0.161210
$443$	2.33984e38	0.991590	0.495795	−	0.868439i	$-0.334877\pi$
$443$	2.33984e38	0.991590	0.495795	+	0.868439i	$0.334877\pi$
$444$	1.58790e37	0.0651285
$445$	−8.92404e37	−0.354276
$446$	1.40169e38	0.538636
$447$	9.24488e37	0.343908
$448$	2.90305e37	0.104550
$449$	−1.89136e38	−0.659481	−0.329741	−	0.944072i	$-0.606961\pi$
$449$	−1.89136e38	−0.659481	−0.329741	+	0.944072i	$0.606961\pi$
$450$	4.77658e37	0.161263
$451$	2.56455e38	0.838400
$452$	2.34425e38	0.742157
$453$	−1.63310e38	−0.500712
$454$	−7.07542e37	−0.210108
$455$	−4.55691e37	−0.131071
$456$	−2.56265e38	−0.714003
$457$	5.18294e38	1.39892	0.699458	−	0.714674i	$-0.253425\pi$
$457$	5.18294e38	1.39892	0.699458	+	0.714674i	$0.253425\pi$
$458$	−6.09547e37	−0.159389
$459$	1.79216e37	0.0454039
$460$	1.23152e38	0.302310
$461$	3.03734e38	0.722487	0.361244	−	0.932471i	$-0.382352\pi$
$461$	3.03734e38	0.722487	0.361244	+	0.932471i	$0.382352\pi$
$462$	9.65655e37	0.222594
$463$	6.70271e38	1.49736	0.748680	−	0.662931i	$-0.230688\pi$
$463$	6.70271e38	1.49736	0.748680	+	0.662931i	$0.230688\pi$
$464$	3.11249e37	0.0673902
$465$	4.69300e37	0.0984880
$466$	−4.15844e38	−0.845930
$467$	−3.61190e38	−0.712264	−0.356132	−	0.934436i	$-0.615905\pi$
$467$	−3.61190e38	−0.712264	−0.356132	+	0.934436i	$0.615905\pi$
$468$	−1.67160e38	−0.319571
$469$	−2.21571e38	−0.410683
$470$	−5.37353e37	−0.0965696
$471$	−1.85919e38	−0.323982
$472$	−4.60619e38	−0.778364
$473$	2.24641e39	3.68131
$474$	−2.85029e38	−0.453005
$475$	−8.29877e38	−1.27925
$476$	4.35118e37	0.0650589
$477$	2.14061e38	0.310471
$478$	−1.86222e38	−0.262015
$479$	−8.75677e38	−1.19531	−0.597653	−	0.801755i	$-0.703900\pi$
$479$	−8.75677e38	−1.19531	−0.597653	+	0.801755i	$0.703900\pi$
$480$	−1.19144e38	−0.157788
$481$	1.58111e38	0.203170
$482$	5.81140e38	0.724601
$483$	−2.83171e38	−0.342622
$484$	−1.76958e39	−2.07784
$485$	−2.94441e38	−0.335539
$486$	3.01600e37	0.0333584
$487$	−4.47843e37	−0.0480790	−0.0240395	−	0.999711i	$-0.507653\pi$
$487$	−4.47843e37	−0.0480790	−0.0240395	+	0.999711i	$0.507653\pi$
$488$	6.93720e38	0.722931
$489$	4.77127e38	0.482676
$490$	1.99618e37	0.0196046
$491$	−8.86479e38	−0.845253	−0.422626	−	0.906304i	$-0.638892\pi$
$491$	−8.86479e38	−0.845253	−0.422626	+	0.906304i	$0.638892\pi$
$492$	1.94469e38	0.180035
$493$	−6.75331e37	−0.0607067
$494$	−1.07638e39	−0.939559
$495$	−2.03571e38	−0.172560
$496$	2.05644e38	0.169291
$497$	−9.74833e37	−0.0779404
$498$	−3.92957e38	−0.305154
$499$	1.72257e39	1.29933	0.649666	−	0.760220i	$-0.274909\pi$
$499$	1.72257e39	1.29933	0.649666	+	0.760220i	$0.274909\pi$
$500$	−5.07259e38	−0.371676
$501$	4.85618e38	0.345659
$502$	−1.17006e39	−0.809106
$503$	−1.37688e39	−0.925039	−0.462520	−	0.886609i	$-0.653055\pi$
$503$	−1.37688e39	−0.925039	−0.462520	+	0.886609i	$0.653055\pi$
$504$	1.73590e38	0.113314
$505$	−6.18304e38	−0.392172
$506$	−2.59855e39	−1.60158
$507$	−7.00498e38	−0.419558
$508$	−1.00451e39	−0.584698
$509$	1.06295e39	0.601321	0.300660	−	0.953731i	$-0.402793\pi$
$509$	1.06295e39	0.601321	0.300660	+	0.953731i	$0.402793\pi$
$510$	3.39967e37	0.0186926
$511$	5.24987e38	0.280573
$512$	−9.75502e38	−0.506773
$513$	−5.23996e38	−0.264622
$514$	1.04398e39	0.512538
$515$	2.08988e38	0.0997509
$516$	1.70345e39	0.790511
$517$	−3.05923e39	−1.38038
$518$	−6.92615e37	−0.0303886
$519$	2.33490e39	0.996190
$520$	−7.51719e38	−0.311894
$521$	2.34458e39	0.946060	0.473030	−	0.881046i	$-0.343160\pi$
$521$	2.34458e39	0.946060	0.473030	+	0.881046i	$0.343160\pi$
$522$	−1.13650e38	−0.0446015
$523$	2.41202e39	0.920677	0.460338	−	0.887744i	$-0.347728\pi$
$523$	2.41202e39	0.920677	0.460338	+	0.887744i	$0.347728\pi$
$524$	−3.00058e39	−1.11404
$525$	5.62145e38	0.203020
$526$	−1.89751e39	−0.666638
$527$	−4.46196e38	−0.152501
$528$	−8.92033e38	−0.296612
$529$	4.52898e39	1.46519
$530$	4.06067e38	0.127820
$531$	−9.41845e38	−0.288475
$532$	−1.27221e39	−0.379175
$533$	1.93637e39	0.561623
$534$	1.42788e39	0.403035
$535$	6.41712e38	0.176283
$536$	−3.65509e39	−0.977257
$537$	2.66261e39	0.692917
$538$	1.29668e39	0.328466
$539$	1.13646e39	0.280231
$540$	−1.54367e38	−0.0370549
$541$	−5.95969e39	−1.39272	−0.696359	−	0.717693i	$-0.745198\pi$
$541$	−5.95969e39	−1.39272	−0.696359	+	0.717693i	$0.745198\pi$
$542$	−4.05078e39	−0.921615
$543$	3.90426e39	0.864852
$544$	1.13278e39	0.244322
$545$	4.41911e38	0.0928080
$546$	7.29122e38	0.149110
$547$	4.94919e39	0.985639	0.492819	−	0.870132i	$-0.335966\pi$
$547$	4.94919e39	0.985639	0.492819	+	0.870132i	$0.335966\pi$
$548$	−6.82068e38	−0.132285
$549$	1.41848e39	0.267931
$550$	5.15858e39	0.949011
$551$	1.97455e39	0.353809
$552$	−4.67126e39	−0.815299
$553$	−3.35444e39	−0.570304
$554$	5.12690e39	0.849109
$555$	1.46011e38	0.0235579
$556$	1.21168e39	0.190460
$557$	−5.11826e39	−0.783830	−0.391915	−	0.920001i	$-0.628187\pi$
$557$	−5.11826e39	−0.783830	−0.391915	+	0.920001i	$0.628187\pi$
$558$	−7.50897e38	−0.112043
$559$	1.69616e40	2.46601
$560$	−1.84399e38	−0.0261236
$561$	1.93549e39	0.267195
$562$	3.03167e39	0.407855
$563$	−6.42430e39	−0.842275	−0.421138	−	0.906997i	$-0.638369\pi$
$563$	−6.42430e39	−0.842275	−0.421138	+	0.906997i	$0.638369\pi$
$564$	−2.31981e39	−0.296419
$565$	2.15558e39	0.268449
$566$	4.02091e39	0.488074
$567$	3.54946e38	0.0419961
$568$	−1.60811e39	−0.185466
$569$	3.24452e39	0.364773	0.182387	−	0.983227i	$-0.441618\pi$
$569$	3.24452e39	0.364773	0.182387	+	0.983227i	$0.441618\pi$
$570$	−9.94003e38	−0.108944
$571$	−6.87756e39	−0.734871	−0.367435	−	0.930049i	$-0.619764\pi$
$571$	−6.87756e39	−0.734871	−0.367435	+	0.930049i	$0.619764\pi$
$572$	−1.80528e40	−1.88063
$573$	−3.59055e39	−0.364685
$574$	−8.48241e38	−0.0840034
$575$	−1.51272e40	−1.46074
$576$	9.79213e38	0.0922043
$577$	−4.56568e39	−0.419234	−0.209617	−	0.977784i	$-0.567222\pi$
$577$	−4.56568e39	−0.419234	−0.209617	+	0.977784i	$0.567222\pi$
$578$	5.48391e39	0.491062
$579$	5.35798e39	0.467910
$580$	5.81694e38	0.0495438
$581$	−4.62462e39	−0.384169
$582$	4.71115e39	0.381719
$583$	2.31180e40	1.82708
$584$	8.66031e39	0.667647
$585$	−1.53707e39	−0.115593
$586$	−1.48905e39	−0.109243
$587$	2.20352e40	1.57712	0.788560	−	0.614958i	$-0.210827\pi$
$587$	2.20352e40	1.57712	0.788560	+	0.614958i	$0.210827\pi$
$588$	8.61774e38	0.0601759
$589$	1.30460e40	0.888802
$590$	−1.78665e39	−0.118764
$591$	4.21758e39	0.273555
$592$	6.39810e38	0.0404936
$593$	7.89228e39	0.487427	0.243713	−	0.969847i	$-0.421634\pi$
$593$	7.89228e39	0.487427	0.243713	+	0.969847i	$0.421634\pi$
$594$	3.25720e39	0.196309
$595$	4.00100e38	0.0235327
$596$	7.57102e39	0.434594
$597$	1.52344e40	0.853487
$598$	−1.96204e40	−1.07286
$599$	−1.12876e40	−0.602436	−0.301218	−	0.953555i	$-0.597393\pi$
$599$	−1.12876e40	−0.602436	−0.301218	+	0.953555i	$0.597393\pi$
$600$	9.27329e39	0.483104
$601$	−1.89834e39	−0.0965370	−0.0482685	−	0.998834i	$-0.515370\pi$
$601$	−1.89834e39	−0.0965370	−0.0482685	+	0.998834i	$0.515370\pi$
$602$	−7.43013e39	−0.368848
$603$	−7.47370e39	−0.362189
$604$	−1.33741e40	−0.632747
$605$	−1.62716e40	−0.751584
$606$	9.89308e39	0.446148
$607$	2.60286e40	1.14608	0.573040	−	0.819527i	$-0.305764\pi$
$607$	2.60286e40	1.14608	0.573040	+	0.819527i	$0.305764\pi$
$608$	−3.31205e40	−1.42395
$609$	−1.33753e39	−0.0561503
$610$	2.69080e39	0.110306
$611$	−2.30989e40	−0.924684
$612$	1.46768e39	0.0573765
$613$	−5.66181e39	−0.216162	−0.108081	−	0.994142i	$-0.534471\pi$
$613$	−5.66181e39	−0.216162	−0.108081	+	0.994142i	$0.534471\pi$
$614$	−2.83212e39	−0.105602
$615$	1.78818e39	0.0651213
$616$	1.87473e40	0.666834
$617$	−5.32242e40	−1.84916	−0.924579	−	0.380990i	$-0.875583\pi$
$617$	−5.32242e40	−1.84916	−0.924579	+	0.380990i	$0.875583\pi$
$618$	−3.34388e39	−0.113480
$619$	1.43031e40	0.474150	0.237075	−	0.971491i	$-0.423811\pi$
$619$	1.43031e40	0.474150	0.237075	+	0.971491i	$0.423811\pi$
$620$	3.84330e39	0.124459
$621$	−9.55149e39	−0.302164
$622$	9.85996e39	0.304729
$623$	1.68044e40	0.507395
$624$	−6.73533e39	−0.198693
$625$	2.76138e40	0.795914
$626$	−4.28654e39	−0.120720
$627$	−5.65901e40	−1.55726
$628$	−1.52257e40	−0.409414
$629$	−1.38822e39	−0.0364775
$630$	6.73322e38	0.0172896
$631$	−9.97726e39	−0.250372	−0.125186	−	0.992133i	$-0.539953\pi$
$631$	−9.97726e39	−0.250372	−0.125186	+	0.992133i	$0.539953\pi$
$632$	−5.53357e40	−1.35709
$633$	2.76728e40	0.663285
$634$	−3.94957e40	−0.925242
$635$	−9.23668e39	−0.211493
$636$	1.75304e40	0.392340
$637$	8.58087e39	0.187720
$638$	−1.22740e40	−0.262473
$639$	−3.28816e39	−0.0687370
$640$	−1.15159e40	−0.235336
$641$	−7.49472e39	−0.149732	−0.0748659	−	0.997194i	$-0.523853\pi$
$641$	−7.49472e39	−0.149732	−0.0748659	+	0.997194i	$0.523853\pi$
$642$	−1.02676e40	−0.200545
$643$	−3.12537e40	−0.596819	−0.298410	−	0.954438i	$-0.596456\pi$
$643$	−3.12537e40	−0.596819	−0.298410	+	0.954438i	$0.596456\pi$
$644$	−2.31901e40	−0.432969
$645$	1.56635e40	0.285939
$646$	9.45067e39	0.168691
$647$	6.52066e40	1.13810	0.569049	−	0.822304i	$-0.307311\pi$
$647$	6.52066e40	1.13810	0.569049	+	0.822304i	$0.307311\pi$
$648$	5.85528e39	0.0999333
$649$	−1.01717e41	−1.69764
$650$	3.89501e40	0.635719
$651$	−8.83715e39	−0.141055
$652$	3.90740e40	0.609954
$653$	2.66449e40	0.406793	0.203396	−	0.979096i	$-0.434802\pi$
$653$	2.66449e40	0.406793	0.203396	+	0.979096i	$0.434802\pi$
$654$	−7.07073e39	−0.105581
$655$	−2.75909e40	−0.402965
$656$	7.83571e39	0.111937
$657$	1.77081e40	0.247442
$658$	1.01186e40	0.138307
$659$	−3.71085e40	−0.496174	−0.248087	−	0.968738i	$-0.579802\pi$
$659$	−3.71085e40	−0.496174	−0.248087	+	0.968738i	$0.579802\pi$
$660$	−1.66712e40	−0.218063
$661$	−4.76897e40	−0.610244	−0.305122	−	0.952313i	$-0.598697\pi$
$661$	−4.76897e40	−0.610244	−0.305122	+	0.952313i	$0.598697\pi$
$662$	5.91837e40	0.740903
$663$	1.46140e40	0.178987
$664$	−7.62889e40	−0.914164
$665$	−1.16982e40	−0.137153
$666$	−2.33622e39	−0.0268002
$667$	3.59924e40	0.404005
$668$	3.97693e40	0.436807
$669$	5.56423e40	0.598034
$670$	−1.41774e40	−0.149112
$671$	1.53192e41	1.57673
$672$	2.24353e40	0.225984
$673$	7.02173e40	0.692191	0.346095	−	0.938199i	$-0.387507\pi$
$673$	7.02173e40	0.692191	0.346095	+	0.938199i	$0.387507\pi$
$674$	4.94378e40	0.476969
$675$	1.89614e40	0.179047
$676$	−5.73667e40	−0.530192
$677$	−9.65506e39	−0.0873412	−0.0436706	−	0.999046i	$-0.513905\pi$
$677$	−9.65506e39	−0.0873412	−0.0436706	+	0.999046i	$0.513905\pi$
$678$	−3.44900e40	−0.305396
$679$	5.54445e40	0.480559
$680$	6.60014e39	0.0559982
$681$	−2.80871e40	−0.233278
$682$	−8.10949e40	−0.659356
$683$	3.19366e40	0.254207	0.127104	−	0.991889i	$-0.459432\pi$
$683$	3.19366e40	0.254207	0.127104	+	0.991889i	$0.459432\pi$
$684$	−4.29122e40	−0.334401
$685$	−6.27175e39	−0.0478493
$686$	−3.75890e39	−0.0280777
$687$	−2.41970e40	−0.176965
$688$	6.86366e40	0.491500
$689$	1.74554e41	1.22391
$690$	−1.81189e40	−0.124400
$691$	1.74579e41	1.17371	0.586853	−	0.809693i	$-0.300367\pi$
$691$	1.74579e41	1.17371	0.586853	+	0.809693i	$0.300367\pi$
$692$	1.91215e41	1.25888
$693$	3.83333e40	0.247141
$694$	−1.87311e40	−0.118264
$695$	1.11416e40	0.0688922
$696$	−2.20642e40	−0.133615
$697$	−1.70015e40	−0.100835
$698$	−1.26722e41	−0.736120
$699$	−1.65076e41	−0.939215
$700$	4.60365e40	0.256555
$701$	5.50524e39	0.0300514	0.0150257	−	0.999887i	$-0.495217\pi$
$701$	5.50524e39	0.0300514	0.0150257	+	0.999887i	$0.495217\pi$
$702$	2.45936e40	0.131503
$703$	4.05892e40	0.212598
$704$	1.05752e41	0.542609
$705$	−2.13311e40	−0.107219
$706$	−1.68883e41	−0.831607
$707$	1.16429e41	0.561670
$708$	−7.71317e40	−0.364544
$709$	−3.09401e41	−1.43269	−0.716343	−	0.697748i	$-0.754186\pi$
$709$	−3.09401e41	−1.43269	−0.716343	+	0.697748i	$0.754186\pi$
$710$	−6.23753e39	−0.0282987
$711$	−1.13147e41	−0.502961
$712$	2.77209e41	1.20739
$713$	2.37805e41	1.01490
$714$	−6.40174e39	−0.0267716
$715$	−1.65999e41	−0.680250
$716$	2.18053e41	0.875634
$717$	−7.39239e40	−0.290909
$718$	8.84886e39	0.0341258
$719$	2.16416e41	0.817937	0.408968	−	0.912549i	$-0.365889\pi$
$719$	2.16416e41	0.817937	0.408968	+	0.912549i	$0.365889\pi$
$720$	−6.21988e39	−0.0230388
$721$	−3.93534e40	−0.142863
$722$	−1.30171e41	−0.463154
$723$	2.30693e41	0.804506
$724$	3.19737e41	1.09291
$725$	−7.14515e40	−0.239392
$726$	2.60352e41	0.855026
$727$	2.10955e41	0.679112	0.339556	−	0.940586i	$-0.389723\pi$
$727$	2.10955e41	0.679112	0.339556	+	0.940586i	$0.389723\pi$
$728$	1.41552e41	0.446695
$729$	1.19725e40	0.0370370
$730$	3.35916e40	0.101871
$731$	−1.48924e41	−0.442754
$732$	1.16165e41	0.338582
$733$	−2.75205e41	−0.786409	−0.393204	−	0.919451i	$-0.628634\pi$
$733$	−2.75205e41	−0.786409	−0.393204	+	0.919451i	$0.628634\pi$
$734$	3.04030e41	0.851772
$735$	7.92418e39	0.0217665
$736$	−6.03727e41	−1.62597
$737$	−8.07140e41	−2.13143
$738$	−2.86116e40	−0.0740840
$739$	6.06488e40	0.153985	0.0769924	−	0.997032i	$-0.475468\pi$
$739$	6.06488e40	0.153985	0.0769924	+	0.997032i	$0.475468\pi$
$740$	1.19574e40	0.0297699
$741$	−4.27286e41	−1.04317
$742$	−7.64643e40	−0.183064
$743$	1.60466e40	0.0376743	0.0188372	−	0.999823i	$-0.494004\pi$
$743$	1.60466e40	0.0376743	0.0188372	+	0.999823i	$0.494004\pi$
$744$	−1.45780e41	−0.335652
$745$	6.96170e40	0.157199
$746$	2.10267e40	0.0465648
$747$	−1.55991e41	−0.338805
$748$	1.58505e41	0.337652
$749$	−1.20837e41	−0.252473
$750$	7.46311e40	0.152944
$751$	1.38995e40	0.0279395	0.0139698	−	0.999902i	$-0.495553\pi$
$751$	1.38995e40	0.0279395	0.0139698	+	0.999902i	$0.495553\pi$
$752$	−9.34715e40	−0.184298
$753$	−4.64476e41	−0.898330
$754$	−9.26750e40	−0.175824
$755$	−1.22978e41	−0.228873
$756$	2.90681e40	0.0530701
$757$	−7.39461e41	−1.32442	−0.662209	−	0.749319i	$-0.730381\pi$
$757$	−7.39461e41	−1.32442	−0.662209	+	0.749319i	$0.730381\pi$
$758$	4.28168e41	0.752334
$759$	−1.03154e42	−1.77819
$760$	−1.92976e41	−0.326368
$761$	7.61561e40	0.126365	0.0631825	−	0.998002i	$-0.479875\pi$
$761$	7.61561e40	0.126365	0.0631825	+	0.998002i	$0.479875\pi$
$762$	1.47790e41	0.240602
$763$	−8.32139e40	−0.132920
$764$	−2.94045e41	−0.460850
$765$	1.34956e40	0.0207539
$766$	−4.24967e41	−0.641265
$767$	−7.68017e41	−1.13720
$768$	2.94172e41	0.427429
$769$	1.10504e42	1.57560	0.787802	−	0.615928i	$-0.211219\pi$
$769$	1.10504e42	1.57560	0.787802	+	0.615928i	$0.211219\pi$
$770$	7.27170e40	0.101747
$771$	4.14425e41	0.569059
$772$	4.38788e41	0.591294
$773$	−6.99984e41	−0.925732	−0.462866	−	0.886428i	$-0.653179\pi$
$773$	−6.99984e41	−0.925732	−0.462866	+	0.886428i	$0.653179\pi$
$774$	−2.50622e41	−0.325293
$775$	−4.72085e41	−0.601376
$776$	9.14626e41	1.14353
$777$	−2.74945e40	−0.0337397
$778$	1.68097e41	0.202468
$779$	4.97093e41	0.587685
$780$	−1.25877e41	−0.146075
$781$	−3.55113e41	−0.404507
$782$	1.72269e41	0.192623
$783$	−4.51154e40	−0.0495199
$784$	3.47232e40	0.0374143
$785$	−1.40003e41	−0.148091
$786$	4.41465e41	0.458426
$787$	−1.33300e42	−1.35893	−0.679466	−	0.733707i	$-0.737789\pi$
$787$	−1.33300e42	−1.35893	−0.679466	+	0.733707i	$0.737789\pi$
$788$	3.45395e41	0.345689
$789$	−7.53247e41	−0.740152
$790$	−2.14636e41	−0.207067
$791$	−4.05906e41	−0.384473
$792$	6.32355e41	0.588093
$793$	1.15668e42	1.05621
$794$	2.19491e41	0.196797
$795$	1.61195e41	0.141915
$796$	1.24761e42	1.07855
$797$	−9.88533e41	−0.839161	−0.419581	−	0.907718i	$-0.637823\pi$
$797$	−9.88533e41	−0.839161	−0.419581	+	0.907718i	$0.637823\pi$
$798$	1.87175e41	0.156030
$799$	2.02810e41	0.166020
$800$	1.19851e42	0.963465
$801$	5.66820e41	0.447480
$802$	−7.23101e41	−0.560623
$803$	1.91242e42	1.45616
$804$	−6.12053e41	−0.457695
$805$	−2.13237e41	−0.156611
$806$	−6.12311e41	−0.441686
$807$	5.14739e41	0.364687
$808$	1.92065e42	1.33654
$809$	2.05427e42	1.40412	0.702059	−	0.712119i	$-0.252264\pi$
$809$	2.05427e42	1.40412	0.702059	+	0.712119i	$0.252264\pi$
$810$	2.27115e40	0.0152480
$811$	−2.79922e42	−1.84601	−0.923006	−	0.384785i	$-0.874276\pi$
$811$	−2.79922e42	−1.84601	−0.923006	+	0.384785i	$0.874276\pi$
$812$	−1.09536e41	−0.0709567
$813$	−1.60803e42	−1.02325
$814$	−2.52306e41	−0.157715
$815$	3.59293e41	0.220629
$816$	5.91367e40	0.0356738
$817$	4.35427e42	2.58045
$818$	1.26560e42	0.736838
$819$	2.89437e41	0.165553
$820$	1.46442e41	0.0822933
$821$	−1.38819e42	−0.766431	−0.383216	−	0.923659i	$-0.625183\pi$
$821$	−1.38819e42	−0.766431	−0.383216	+	0.923659i	$0.625183\pi$
$822$	1.00350e41	0.0544348
$823$	−1.19435e42	−0.636551	−0.318276	−	0.947998i	$-0.603104\pi$
$823$	−1.19435e42	−0.636551	−0.318276	+	0.947998i	$0.603104\pi$
$824$	−6.49183e41	−0.339956
$825$	2.04779e42	1.05366
$826$	3.36434e41	0.170094
$827$	−3.72137e42	−1.84873	−0.924365	−	0.381509i	$-0.875404\pi$
$827$	−3.72137e42	−1.84873	−0.924365	+	0.381509i	$0.875404\pi$
$828$	−7.82212e41	−0.381843
$829$	−1.70400e42	−0.817387	−0.408693	−	0.912672i	$-0.634015\pi$
$829$	−1.70400e42	−0.817387	−0.408693	+	0.912672i	$0.634015\pi$
$830$	−2.95910e41	−0.139485
$831$	2.03521e42	0.942745
$832$	7.98488e41	0.363480
$833$	−7.53406e40	−0.0337036
$834$	−1.78270e41	−0.0783739
$835$	3.65686e41	0.157999
$836$	−4.63441e42	−1.96790
$837$	−2.98081e41	−0.124399
$838$	−3.87277e41	−0.158849
$839$	1.88179e42	0.758617	0.379308	−	0.925270i	$-0.376162\pi$
$839$	1.88179e42	0.758617	0.379308	+	0.925270i	$0.376162\pi$
$840$	1.30719e41	0.0517952
$841$	−2.39768e42	−0.933790
$842$	−9.72694e40	−0.0372350
$843$	1.20347e42	0.452832
$844$	2.26625e42	0.838188
$845$	−5.27498e41	−0.191778
$846$	3.41305e41	0.121976
$847$	3.06402e42	1.07642
$848$	7.06346e41	0.243937
$849$	1.59617e42	0.541897
$850$	−3.41984e41	−0.114138
$851$	7.39868e41	0.242759
$852$	−2.69281e41	−0.0868624
$853$	4.37736e42	1.38820	0.694098	−	0.719880i	$-0.255803\pi$
$853$	4.37736e42	1.38820	0.694098	+	0.719880i	$0.255803\pi$
$854$	−5.06691e41	−0.157981
$855$	−3.94586e41	−0.120958
$856$	−1.99336e42	−0.600781
$857$	−9.12026e41	−0.270262	−0.135131	−	0.990828i	$-0.543146\pi$
$857$	−9.12026e41	−0.270262	−0.135131	+	0.990828i	$0.543146\pi$
$858$	2.65605e42	0.773874
$859$	4.97414e42	1.42501	0.712504	−	0.701668i	$-0.247561\pi$
$859$	4.97414e42	1.42501	0.712504	+	0.701668i	$0.247561\pi$
$860$	1.28275e42	0.361339
$861$	−3.36723e41	−0.0932669
$862$	−1.94059e42	−0.528542
$863$	3.43677e41	0.0920438	0.0460219	−	0.998940i	$-0.485346\pi$
$863$	3.43677e41	0.0920438	0.0460219	+	0.998940i	$0.485346\pi$
$864$	7.56754e41	0.199299
$865$	1.75826e42	0.455354
$866$	2.93656e42	0.747875
$867$	2.17693e42	0.545214
$868$	−7.23711e41	−0.178250
$869$	−1.22196e43	−2.95985
$870$	−8.55826e40	−0.0203871
$871$	−6.09435e42	−1.42779
$872$	−1.37272e42	−0.316294
$873$	1.87017e42	0.423813
$874$	−5.03683e42	−1.12264
$875$	8.78317e41	0.192546
$876$	1.45019e42	0.312690
$877$	5.62458e42	1.19288	0.596439	−	0.802658i	$-0.296582\pi$
$877$	5.62458e42	1.19288	0.596439	+	0.802658i	$0.296582\pi$
$878$	−2.73564e42	−0.570675
$879$	−5.91104e41	−0.121290
$880$	−6.71730e41	−0.135580
$881$	−1.16065e41	−0.0230436	−0.0115218	−	0.999934i	$-0.503668\pi$
$881$	−1.16065e41	−0.0230436	−0.0115218	+	0.999934i	$0.503668\pi$
$882$	−1.26790e41	−0.0247622
$883$	−9.03859e41	−0.173648	−0.0868241	−	0.996224i	$-0.527672\pi$
$883$	−9.03859e41	−0.173648	−0.0868241	+	0.996224i	$0.527672\pi$
$884$	1.19680e42	0.226185
$885$	−7.09240e41	−0.131861
$886$	−2.81923e42	−0.515633
$887$	7.32328e41	0.131769	0.0658845	−	0.997827i	$-0.479013\pi$
$887$	7.32328e41	0.131769	0.0658845	+	0.997827i	$0.479013\pi$
$888$	−4.53556e41	−0.0802865
$889$	1.73931e42	0.302902
$890$	1.07524e42	0.184226
$891$	1.29300e42	0.217957
$892$	4.55678e42	0.755732
$893$	−5.92979e42	−0.967594
$894$	−1.11390e42	−0.178834
$895$	2.00504e42	0.316729
$896$	2.16850e42	0.337049
$897$	−7.78866e42	−1.19117
$898$	2.27886e42	0.342934
$899$	1.12324e42	0.166326
$900$	1.55283e42	0.226260
$901$	−1.53259e42	−0.219744
$902$	−3.08997e42	−0.435973
$903$	−2.94951e42	−0.409523
$904$	−6.69591e42	−0.914887
$905$	2.94004e42	0.395320
$906$	1.96769e42	0.260374
$907$	6.24210e42	0.812877	0.406438	−	0.913678i	$-0.366771\pi$
$907$	6.24210e42	0.812877	0.406438	+	0.913678i	$0.366771\pi$
$908$	−2.30017e42	−0.294791
$909$	3.92722e42	0.495347
$910$	5.49053e41	0.0681575
$911$	−3.51059e42	−0.428908	−0.214454	−	0.976734i	$-0.568797\pi$
$911$	−3.51059e42	−0.428908	−0.214454	+	0.976734i	$0.568797\pi$
$912$	−1.72905e42	−0.207913
$913$	−1.68466e43	−1.99382
$914$	−6.24482e42	−0.727445
$915$	1.06816e42	0.122470
$916$	−1.98159e42	−0.223630
$917$	5.19550e42	0.577128
$918$	−2.15934e41	−0.0236103
$919$	1.34954e42	0.145248	0.0726242	−	0.997359i	$-0.476863\pi$
$919$	1.34954e42	0.145248	0.0726242	+	0.997359i	$0.476863\pi$
$920$	−3.51761e42	−0.372670
$921$	−1.12426e42	−0.117247
$922$	−3.65963e42	−0.375698
$923$	−2.68129e42	−0.270969
$924$	3.13927e42	0.312310
$925$	−1.46877e42	−0.143846
$926$	−8.07596e42	−0.778637
$927$	−1.32741e42	−0.125994
$928$	−2.85164e42	−0.266470
$929$	8.66408e41	0.0797067	0.0398533	−	0.999206i	$-0.487311\pi$
$929$	8.66408e41	0.0797067	0.0398533	+	0.999206i	$0.487311\pi$
$930$	−5.65450e41	−0.0512144
$931$	2.20283e42	0.196431
$932$	−1.35188e43	−1.18688
$933$	3.91407e42	0.338334
$934$	4.35191e42	0.370382
$935$	1.45748e42	0.122134
$936$	4.77462e42	0.393948
$937$	2.34837e43	1.90784	0.953921	−	0.300059i	$-0.0970065\pi$
$937$	2.34837e43	1.90784	0.953921	+	0.300059i	$0.0970065\pi$
$938$	2.66967e42	0.213558
$939$	−1.70161e42	−0.134032
$940$	−1.74689e42	−0.135492
$941$	1.97799e43	1.51069	0.755343	−	0.655330i	$-0.227470\pi$
$941$	1.97799e43	1.51069	0.755343	+	0.655330i	$0.227470\pi$
$942$	2.24010e42	0.168473
$943$	9.06111e42	0.671061
$944$	−3.10785e42	−0.226655
$945$	2.67286e41	0.0191962
$946$	−2.70665e43	−1.91430
$947$	−1.15620e43	−0.805304	−0.402652	−	0.915353i	$-0.631911\pi$
$947$	−1.15620e43	−0.805304	−0.402652	+	0.915353i	$0.631911\pi$
$948$	−9.26609e42	−0.635588
$949$	1.44398e43	0.975444
$950$	9.99901e42	0.665219
$951$	−1.56785e43	−1.02727
$952$	−1.24284e42	−0.0802007
$953$	−1.23543e43	−0.785186	−0.392593	−	0.919712i	$-0.628422\pi$
$953$	−1.23543e43	−0.785186	−0.392593	+	0.919712i	$0.628422\pi$
$954$	−2.57918e42	−0.161447
$955$	−2.70380e42	−0.166696
$956$	−6.05394e42	−0.367620
$957$	−4.87235e42	−0.291417
$958$	1.05508e43	0.621566
$959$	1.18100e42	0.0685299
$960$	7.37380e41	0.0421462
$961$	−1.03405e43	−0.582175
$962$	−1.90505e42	−0.105649
$963$	−4.07590e42	−0.222660
$964$	1.88924e43	1.01665
$965$	4.03474e42	0.213880
$966$	3.41187e42	0.178166
$967$	9.15452e42	0.470925	0.235463	−	0.971883i	$-0.424339\pi$
$967$	9.15452e42	0.470925	0.235463	+	0.971883i	$0.424339\pi$
$968$	5.05448e43	2.56144
$969$	3.75160e42	0.187293
$970$	3.54765e42	0.174482
$971$	2.65526e43	1.28655	0.643277	−	0.765634i	$-0.277574\pi$
$971$	2.65526e43	1.28655	0.643277	+	0.765634i	$0.277574\pi$
$972$	9.80480e41	0.0468034
$973$	−2.09802e42	−0.0986675
$974$	5.39597e41	0.0250014
$975$	1.54619e43	0.705823
$976$	4.68061e42	0.210513
$977$	−8.08639e42	−0.358330	−0.179165	−	0.983819i	$-0.557340\pi$
$977$	−8.08639e42	−0.358330	−0.179165	+	0.983819i	$0.557340\pi$
$978$	−5.74881e42	−0.250995
$979$	6.12151e43	2.63335
$980$	6.48944e41	0.0275061
$981$	−2.80684e42	−0.117224
$982$	1.06810e43	0.439537
$983$	−4.35834e43	−1.76724	−0.883619	−	0.468206i	$-0.844901\pi$
$983$	−4.35834e43	−1.76724	−0.883619	+	0.468206i	$0.844901\pi$
$984$	−5.55467e42	−0.221937
$985$	3.17597e42	0.125041
$986$	8.13692e41	0.0315678
$987$	4.01675e42	0.153559
$988$	−3.49923e43	−1.31825
$989$	7.93705e43	2.94654
$990$	2.45278e42	0.0897322
$991$	−4.27571e43	−1.54149	−0.770744	−	0.637145i	$-0.780115\pi$
$991$	−4.27571e43	−1.54149	−0.770744	+	0.637145i	$0.780115\pi$
$992$	−1.88410e43	−0.669399
$993$	2.34940e43	0.822606
$994$	1.17456e42	0.0405295
$995$	1.14720e43	0.390125
$996$	−1.27747e43	−0.428146
$997$	2.85631e42	0.0943463	0.0471731	−	0.998887i	$-0.484979\pi$
$997$	2.85631e42	0.0943463	0.0471731	+	0.998887i	$0.484979\pi$
$998$	−2.07549e43	−0.675660
$999$	−9.27403e41	−0.0297556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.c.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.c.1.2	✓	7	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)

\(f(q)\)	\(=\)	\(q-12048.8 q^{2} -4.78297e6 q^{3} -3.91697e8 q^{4} -3.60173e9 q^{5} +5.76290e10 q^{6} +6.78223e11 q^{7} +1.11881e13 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q-12048.8 q^{2} -4.78297e6 q^{3} -3.91697e8 q^{4} -3.60173e9 q^{5} +5.76290e10 q^{6} +6.78223e11 q^{7} +1.11881e13 q^{8} +2.28768e13 q^{9} +4.33965e13 q^{10} +2.47063e15 q^{11} +1.87348e15 q^{12} +1.86546e16 q^{13} -8.17177e15 q^{14} +1.72270e16 q^{15} +7.54875e16 q^{16} -1.63789e17 q^{17} -2.75638e17 q^{18} +4.78889e18 q^{19} +1.41079e18 q^{20} -3.24392e18 q^{21} -2.97681e19 q^{22} +8.72928e19 q^{23} -5.35125e19 q^{24} -1.73292e20 q^{25} -2.24766e20 q^{26} -1.09419e20 q^{27} -2.65658e20 q^{28} +4.12318e20 q^{29} -2.07564e20 q^{30} +2.72422e21 q^{31} -6.91611e21 q^{32} -1.18170e22 q^{33} +1.97346e21 q^{34} -2.44278e21 q^{35} -8.96078e21 q^{36} +8.47570e21 q^{37} -5.77004e22 q^{38} -8.92245e22 q^{39} -4.02967e22 q^{40} +1.03801e23 q^{41} +3.90853e22 q^{42} +9.09244e23 q^{43} -9.67741e23 q^{44} -8.23961e22 q^{45} -1.05177e24 q^{46} -1.23824e24 q^{47} -3.61054e23 q^{48} +4.59987e23 q^{49} +2.08796e24 q^{50} +7.83397e23 q^{51} -7.30697e24 q^{52} +9.35713e24 q^{53} +1.31837e24 q^{54} -8.89856e24 q^{55} +7.58805e24 q^{56} -2.29051e25 q^{57} -4.96794e24 q^{58} -4.11703e25 q^{59} -6.74776e24 q^{60} +6.20050e25 q^{61} -3.28235e25 q^{62} +1.55156e25 q^{63} +4.28038e25 q^{64} -6.71890e25 q^{65} +1.42380e26 q^{66} -3.26694e26 q^{67} +6.41556e25 q^{68} -4.17519e26 q^{69} +2.94325e25 q^{70} -1.43733e26 q^{71} +2.55949e26 q^{72} +7.74062e26 q^{73} -1.02122e26 q^{74} +8.28850e26 q^{75} -1.87580e27 q^{76} +1.67564e27 q^{77} +1.07505e27 q^{78} -4.94593e27 q^{79} -2.71886e26 q^{80} +5.23348e26 q^{81} -1.25068e27 q^{82} -6.81874e27 q^{83} +1.27064e27 q^{84} +5.89923e26 q^{85} -1.09553e28 q^{86} -1.97211e27 q^{87} +2.76418e28 q^{88} +2.47771e28 q^{89} +9.92774e26 q^{90} +1.26520e28 q^{91} -3.41924e28 q^{92} -1.30299e28 q^{93} +1.49193e28 q^{94} -1.72483e28 q^{95} +3.30796e28 q^{96} +8.17497e28 q^{97} -5.54228e27 q^{98} +5.65202e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9	\( 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9} - 472777770164028 q^{10} + 135879674344284 q^{11} - 10\!\cdots\!44 q^{12}+ \cdots + 31\!\cdots\!24 q^{99}+O(q^{100}) \) 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9 - 472777770164028 * q^10 + 135879674344284 * q^11 - 10527962746508244 * q^12 + 12138994948536170 * q^13 + 41283438444318630 * q^14 + 13687032584892438 * q^15 + 1300607396354614288 * q^16 - 385869676567281066 * q^17 + 1392510356733476070 * q^18 + 726075641163594644 * q^19 + 8133031378709443032 * q^20 - 22707439527650560767 * q^21 - 40013549861901162600 * q^22 + 81623233895572110192 * q^23 - 47659100600287417320 * q^24 - 344687932818137236151 * q^25 + 557803893676418715300 * q^26 - 765932923920586514463 * q^27 + 1492860866289666291124 * q^28 + 2523262928009462965506 * q^29 + 2261281418583670839132 * q^30 + 3097457398331417166752 * q^31 + 3797011810352053176480 * q^32 - 649908270118805699196 * q^33 + 63335711497801752433500 * q^34 - 1940815693747992252198 * q^35 + 50354919449703789296436 * q^36 + 12145140799949814343466 * q^37 - 108697233906951781953720 * q^38 - 58060436530005096488730 * q^39 - 475320691810097154363216 * q^40 - 262433505631892547251154 * q^41 - 197457406292584233412470 * q^42 - 193139951479227114687580 * q^43 - 2430431685366465708769488 * q^44 - 65464652555530399288422 * q^45 - 6981072827049021325022880 * q^46 - 1146871717647137318395248 * q^47 - 6220764857934833146461072 * q^48 + 3219905755813179726837607 * q^49 + 4481749443828030876391386 * q^50 + 1845602701061331752964954 * q^51 + 1236271786388417967514040 * q^52 - 6665695659633633475901814 * q^53 - 6660333868435157305051830 * q^54 + 5317495916141118544489032 * q^55 + 6758041220494331589303720 * q^56 - 3472797283340597110818036 * q^57 - 19887500189096257342540140 * q^58 + 252077122803863627555062380 * q^59 - 38900036960394526029322008 * q^60 + 286844596551467198960110586 * q^61 + 655482484647841866799404480 * q^62 + 108608979330127274981177223 * q^63 + 523821984648801603783498304 * q^64 + 677830247031279033073631964 * q^65 + 191383568569427541779759400 * q^66 - 21966489249761249366283412 * q^67 - 230093364489444117467612568 * q^68 - 390401397402270640312920048 * q^69 - 320648792055345340923275772 * q^70 + 236873286033551829517504320 * q^71 + 227952000739056108131623080 * q^72 + 1436061741885259500381870806 * q^73 - 3275022628978202210175964380 * q^74 + 1648631697343233038255912319 * q^75 - 4562877250128321487477927888 * q^76 + 92156730271501723638745116 * q^77 - 2667958731533606746299725700 * q^78 + 442695609959843509130102048 * q^79 + 7254106132718389061591220192 * q^80 + 3663433431191523760494580647 * q^81 + 4421292535141977509208500940 * q^82 + 4700059828307966195559697476 * q^83 - 7140307244776618890791067156 * q^84 - 13424791113423208631620606908 * q^85 + 12752722226530676548320081000 * q^86 - 12068688363518493070663267314 * q^87 + 4553745967919270581660489440 * q^88 + 52994579350095331884835317486 * q^89 - 10815638925361721529772342908 * q^90 + 8232946455294689831821448330 * q^91 + 54926079962260892072539429536 * q^92 - 14815042715039820034642646688 * q^93 - 26892181494551465508576501600 * q^94 - 74456487258213633048885368328 * q^95 - 18160989781547749429455369120 * q^96 + 74985775395694126905639860942 * q^97 + 27999380479478321424657876870 * q^98 + 3108491108821873976277792924 * q^99

Introduction

L-functions

Modular forms

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