LMFDB - Embedded newform 25.40.b.a.24.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,40,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 40, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 40 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$240.848878474$
Analytic rank:	$0$
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} + 351260054x^{4} + 30845906384020729x^{2} + 20234842822783221799716 $ x^6 + 351260054x^4 + 30845906384020729x^2 + 20234842822783221799716
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{10}\cdot 5^{8}\cdot 13^{2} $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.6
Root			$12827.3i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.40.b.a.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.10652e6i q^{2} -2.98790e9i q^{3} -6.74631e11 q^{4} +3.30617e15 q^{6} -5.05826e16i q^{7} -1.38177e17i q^{8} -4.87501e18 q^{9} +O(q^{10})$	\(q+1.10652e6i q^{2} -2.98790e9i q^{3} -6.74631e11 q^{4} +3.30617e15 q^{6} -5.05826e16i q^{7} -1.38177e17i q^{8} -4.87501e18 q^{9} +7.53597e19 q^{11} +2.01573e21i q^{12} -3.07373e21i q^{13} +5.59707e22 q^{14} -2.17987e23 q^{16} -4.56106e23i q^{17} -5.39430e24i q^{18} +1.63031e24 q^{19} -1.51136e26 q^{21} +8.33870e25i q^{22} -2.17009e26i q^{23} -4.12858e26 q^{24} +3.40114e27 q^{26} +2.45742e27i q^{27} +3.41246e28i q^{28} +6.88782e27 q^{29} +1.62636e29 q^{31} -3.17170e29i q^{32} -2.25168e29i q^{33} +5.04690e29 q^{34} +3.28883e30 q^{36} -1.23773e30i q^{37} +1.80397e30i q^{38} -9.18399e30 q^{39} +1.60595e31 q^{41} -1.67235e32i q^{42} -1.28211e32i q^{43} -5.08400e31 q^{44} +2.40125e32 q^{46} -6.09258e32i q^{47} +6.51324e32i q^{48} -1.64906e33 q^{49} -1.36280e33 q^{51} +2.07363e33i q^{52} -1.51248e33i q^{53} -2.71918e33 q^{54} -6.98933e33 q^{56} -4.87122e33i q^{57} +7.62152e33i q^{58} +4.73479e34 q^{59} +7.02166e34 q^{61} +1.79960e35i q^{62} +2.46591e35i q^{63} +2.31116e35 q^{64} +2.49152e35 q^{66} -9.34963e34i q^{67} +3.07703e35i q^{68} -6.48402e35 q^{69} +2.40247e36 q^{71} +6.73613e35i q^{72} +7.72964e35i q^{73} +1.36958e36 q^{74} -1.09986e36 q^{76} -3.81189e36i q^{77} -1.01623e37i q^{78} -1.44777e37 q^{79} -1.24137e37 q^{81} +1.77702e37i q^{82} -1.12684e37i q^{83} +1.01961e38 q^{84} +1.41868e38 q^{86} -2.05802e37i q^{87} -1.04129e37i q^{88} +1.09111e38 q^{89} -1.55477e38 q^{91} +1.46401e38i q^{92} -4.85940e38i q^{93} +6.74156e38 q^{94} -9.47674e38 q^{96} +7.84026e37i q^{97} -1.82471e39i q^{98} -3.67379e38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 544157962368 q^{4} + 30\!\cdots\!92 q^{6}+ \cdots - 16\!\cdots\!82 q^{9}+O(q^{10}) $ 6 * q - 544157962368 * q^4 + 3059455695734592 * q^6 - 16611759804157354782 * q^9	$ 6 q - 544157962368 q^{4} + 30\!\cdots\!92 q^{6}+ \cdots - 21\!\cdots\!44 q^{99}+O(q^{100}) $ 6 * q - 544157962368 * q^4 + 3059455695734592 * q^6 - 16611759804157354782 * q^9 + 1335629936531503072152 * q^11 + 126127449131778606927744 * q^14 - 703461881120738114002944 * q^16 - 18455224370015395147037160 * q^19 - 380417317145185862942503488 * q^21 - 3345920537272389120092590080 * q^24 + 567557211609191164338405792 * q^26 + 4985364438517296554592888060 * q^29 + 612215343495645408819109492032 * q^31 + 3366785739059531738207598491424 * q^34 + 377368646146534808816114733696 * q^36 - 44504167036690804030291840119984 * q^39 + 4783848412475539012464959980572 * q^41 + 91155294598227820726749797113344 * q^44 - 48593082291062060955954043041408 * q^46 - 736475363444998124770546403282358 * q^49 + 1571302207630868682506432323828752 * q^51 - 15861629703958117392304207114335360 * q^54 - 12544233406497214477800860233359360 * q^56 + 112165362771242560634218577339274120 * q^59 + 79155351364252856663797379953667652 * q^61 + 338729813927122879167425723330199552 * q^64 - 574243521945218186753137588470510336 * q^66 - 3168350097391405603579685370419006784 * q^69 + 7698106421748136293400590482832435792 * q^71 + 10141414083395714373064024083405506784 * q^74 - 14725183421980568378050368272542302720 * q^76 - 27615544402432458579791347713389118240 * q^79 - 37596046292353241924597531317677774474 * q^81 + 144305151797281626583582527674355953664 * q^84 + 340024195160570221708545563575832966592 * q^86 - 410100079820219714273123706444152449020 * q^89 - 331050209996663685142398339776733965088 * q^91 + 2255945337070303769176521619142573278464 * q^94 - 2902189048981286701184128274058776936448 * q^96 - 2114036316237136283540072069426181873144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	1.10652e6i	1.49236i	0.665743	+	0.746181i	$0.268115\pi$
$2$	1.10652e6i	1.49236i	−0.665743	+	0.746181i	$0.731885\pi$
$3$	− 2.98790e9i	− 1.48423i	−0.670271	−	0.742116i	$-0.733822\pi$
$3$	− 2.98790e9i	− 1.48423i	0.670271	−	0.742116i	$-0.266178\pi$
$4$	−6.74631e11	−1.22715
$5$	0	0
$5$	0	0
$6$	3.30617e15	2.21501
$7$	− 5.05826e16i	− 1.67722i	−0.544734	−	0.838609i	$-0.683369\pi$
$7$	− 5.05826e16i	− 1.67722i	0.544734	−	0.838609i	$-0.316631\pi$
$8$	− 1.38177e17i	− 0.338984i
$9$	−4.87501e18	−1.20295
$10$	0	0
$11$	7.53597e19	0.371520	0.185760	−	0.982595i	$-0.440525\pi$
$11$	7.53597e19	0.371520	0.185760	+	0.982595i	$0.440525\pi$
$12$	2.01573e21i	1.82137i
$13$	− 3.07373e21i	− 0.583136i	−0.956550	−	0.291568i	$-0.905823\pi$
$13$	− 3.07373e21i	− 0.583136i	0.956550	−	0.291568i	$-0.0941769\pi$
$14$	5.59707e22	2.50302
$15$	0	0
$16$	−2.17987e23	−0.721258
$17$	− 4.56106e23i	− 0.462713i	−0.972869	−	0.231357i	$-0.925684\pi$
$17$	− 4.56106e23i	− 0.462713i	0.972869	−	0.231357i	$-0.0743164\pi$
$18$	− 5.39430e24i	− 1.79523i
$19$	1.63031e24	0.189050	0.0945248	−	0.995523i	$-0.469867\pi$
$19$	1.63031e24	0.189050	0.0945248	+	0.995523i	$0.469867\pi$
$20$	0	0
$21$	−1.51136e26	−2.48938
$22$	8.33870e25i	0.554442i
$23$	− 2.17009e26i	− 0.606436i	−0.952921	−	0.303218i	$-0.901939\pi$
$23$	− 2.17009e26i	− 0.606436i	0.952921	−	0.303218i	$-0.0980610\pi$
$24$	−4.12858e26	−0.503132
$25$	0	0
$26$	3.40114e27	0.870250
$27$	2.45742e27i	0.301222i
$28$	3.41246e28i	2.05819i
$29$	6.88782e27	0.209566	0.104783	−	0.994495i	$-0.466585\pi$
$29$	6.88782e27	0.209566	0.104783	+	0.994495i	$0.466585\pi$
$30$	0	0
$31$	1.62636e29	1.34792	0.673959	−	0.738769i	$-0.264593\pi$
$31$	1.62636e29	1.34792	0.673959	+	0.738769i	$0.264593\pi$
$32$	− 3.17170e29i	− 1.41536i
$33$	− 2.25168e29i	− 0.551422i
$34$	5.04690e29	0.690536
$35$	0	0
$36$	3.28883e30	1.47619
$37$	− 1.23773e30i	− 0.325606i	−0.986659	−	0.162803i	$-0.947946\pi$
$37$	− 1.23773e30i	− 0.325606i	0.986659	−	0.162803i	$-0.0520536\pi$
$38$	1.80397e30i	0.282130i
$39$	−9.18399e30	−0.865509
$40$	0	0
$41$	1.60595e31	0.570751	0.285375	−	0.958416i	$-0.407882\pi$
$41$	1.60595e31	0.570751	0.285375	+	0.958416i	$0.407882\pi$
$42$	− 1.67235e32i	− 3.71506i
$43$	− 1.28211e32i	− 1.80007i	−0.435815	−	0.900036i	$-0.643540\pi$
$43$	− 1.28211e32i	− 1.80007i	0.435815	−	0.900036i	$-0.356460\pi$
$44$	−5.08400e31	−0.455909
$45$	0	0
$46$	2.40125e32	0.905022
$47$	− 6.09258e32i	− 1.50971i	−0.655893	−	0.754854i	$-0.727708\pi$
$47$	− 6.09258e32i	− 1.50971i	0.655893	−	0.754854i	$-0.272292\pi$
$48$	6.51324e32i	1.07052i
$49$	−1.64906e33	−1.81306
$50$	0	0
$51$	−1.36280e33	−0.686774
$52$	2.07363e33i	0.715593i
$53$	− 1.51248e33i	− 0.360006i	−0.983666	−	0.180003i	$-0.942389\pi$
$53$	− 1.51248e33i	− 0.360006i	0.983666	−	0.180003i	$-0.0576108\pi$
$54$	−2.71918e33	−0.449532
$55$	0	0
$56$	−6.98933e33	−0.568551
$57$	− 4.87122e33i	− 0.280594i
$58$	7.62152e33i	0.312749i
$59$	4.73479e34	1.39215	0.696076	−	0.717969i	$-0.254928\pi$
$59$	4.73479e34	1.39215	0.696076	+	0.717969i	$0.254928\pi$
$60$	0	0
$61$	7.02166e34	1.07772	0.538862	−	0.842394i	$-0.318854\pi$
$61$	7.02166e34	1.07772	0.538862	+	0.842394i	$0.318854\pi$
$62$	1.79960e35i	2.01158i
$63$	2.46591e35i	2.01760i
$64$	2.31116e35	1.39098
$65$	0	0
$66$	2.49152e35	0.822921
$67$	− 9.34963e34i	− 0.230322i	−0.993347	−	0.115161i	$-0.963262\pi$
$67$	− 9.34963e34i	− 0.230322i	0.993347	−	0.115161i	$-0.0367384\pi$
$68$	3.07703e35i	0.567817i
$69$	−6.48402e35	−0.900092
$70$	0	0
$71$	2.40247e36	1.91038	0.955190	−	0.295994i	$-0.0956509\pi$
$71$	2.40247e36	1.91038	0.955190	+	0.295994i	$0.0956509\pi$
$72$	6.73613e35i	0.407781i
$73$	7.72964e35i	0.357572i	0.983888	+	0.178786i	$0.0572170\pi$
$73$	7.72964e35i	0.357572i	−0.983888	+	0.178786i	$0.942783\pi$
$74$	1.36958e36	0.485923
$75$	0	0
$76$	−1.09986e36	−0.231991
$77$	− 3.81189e36i	− 0.623119i
$78$	− 1.01623e37i	− 1.29165i
$79$	−1.44777e37	−1.43540	−0.717699	−	0.696353i	$-0.754805\pi$
$79$	−1.44777e37	−1.43540	−0.717699	+	0.696353i	$0.754805\pi$
$80$	0	0
$81$	−1.24137e37	−0.755865
$82$	1.77702e37i	0.851767i
$83$	− 1.12684e37i	− 0.426423i	−0.977006	−	0.213212i	$-0.931608\pi$
$83$	− 1.12684e37i	− 0.426423i	0.977006	−	0.213212i	$-0.0683924\pi$
$84$	1.01961e38	3.05483
$85$	0	0
$86$	1.41868e38	2.68636
$87$	− 2.05802e37i	− 0.311045i
$88$	− 1.04129e37i	− 0.125939i
$89$	1.09111e38	1.05868	0.529338	−	0.848411i	$-0.322440\pi$
$89$	1.09111e38	1.05868	0.529338	+	0.848411i	$0.322440\pi$
$90$	0	0
$91$	−1.55477e38	−0.978045
$92$	1.46401e38i	0.744185i
$93$	− 4.85940e38i	− 2.00062i
$94$	6.74156e38	2.25303
$95$	0	0
$96$	−9.47674e38	−2.10073
$97$	7.84026e37i	0.141998i	0.997476	+	0.0709989i	$0.0226187\pi$
$97$	7.84026e37i	0.141998i	−0.997476	+	0.0709989i	$0.977381\pi$
$98$	− 1.82471e39i	− 2.70574i
$99$	−3.67379e38	−0.446919
$100$	0	0
$101$	1.53402e39	1.26347	0.631734	−	0.775185i	$-0.282344\pi$
$101$	1.53402e39	1.26347	0.631734	+	0.775185i	$0.282344\pi$
$102$	− 1.50797e39i	− 1.02492i
$103$	1.10618e39i	0.621586i	0.950478	+	0.310793i	$0.100595\pi$
$103$	1.10618e39i	0.621586i	−0.950478	+	0.310793i	$0.899405\pi$
$104$	−4.24717e38	−0.197674
$105$	0	0
$106$	1.67359e39	0.537260
$107$	2.25314e39i	0.602288i	0.953579	+	0.301144i	$0.0973685\pi$
$107$	2.25314e39i	0.602288i	−0.953579	+	0.301144i	$0.902631\pi$
$108$	− 1.65785e39i	− 0.369643i
$109$	3.29726e38	0.0614239	0.0307119	−	0.999528i	$-0.490223\pi$
$109$	3.29726e38	0.0614239	0.0307119	+	0.999528i	$0.490223\pi$
$110$	0	0
$111$	−3.69822e39	−0.483276
$112$	1.10263e40i	1.20971i
$113$	9.62984e39i	0.888361i	0.895937	+	0.444181i	$0.146505\pi$
$113$	9.62984e39i	0.888361i	−0.895937	+	0.444181i	$0.853495\pi$
$114$	5.39010e39	0.418747
$115$	0	0
$116$	−4.64674e39	−0.257168
$117$	1.49844e40i	0.701482i
$118$	5.23914e40i	2.07759i
$119$	−2.30710e40	−0.776070
$120$	0	0
$121$	−3.54657e40	−0.861973
$122$	7.76961e40i	1.60836i
$123$	− 4.79842e40i	− 0.847127i
$124$	−1.09719e41	−1.65409
$125$	0	0
$126$	−2.72858e41	−3.01100
$127$	− 7.59694e40i	− 0.718565i	−0.933229	−	0.359282i	$-0.883022\pi$
$127$	− 7.59694e40i	− 0.718565i	0.933229	−	0.359282i	$-0.116978\pi$
$128$	8.13679e40i	0.660479i
$129$	−3.83082e41	−2.67173
$130$	0	0
$131$	−2.08014e41	−1.07474	−0.537368	−	0.843348i	$-0.680581\pi$
$131$	−2.08014e41	−1.07474	−0.537368	+	0.843348i	$0.680581\pi$
$132$	1.51905e41i	0.676675i
$133$	− 8.24654e40i	− 0.317077i
$134$	1.03456e41	0.343724
$135$	0	0
$136$	−6.30232e40	−0.156853
$137$	− 3.53926e41i	− 0.763592i	−0.924247	−	0.381796i	$-0.875306\pi$
$137$	− 3.53926e41i	− 0.763592i	0.924247	−	0.381796i	$-0.124694\pi$
$138$	− 7.17470e41i	− 1.34326i
$139$	5.01395e39	0.00815438	0.00407719	−	0.999992i	$-0.498702\pi$
$139$	5.01395e39	0.00815438	0.00407719	+	0.999992i	$0.498702\pi$
$140$	0	0
$141$	−1.82040e42	−2.24076
$142$	2.65838e42i	2.85098i
$143$	− 2.31635e41i	− 0.216646i
$144$	1.06269e42	0.867636
$145$	0	0
$146$	−8.55300e41	−0.533627
$147$	4.92722e42i	2.69100i
$148$	8.35012e41i	0.399567i
$149$	−1.36965e42	−0.574749	−0.287374	−	0.957818i	$-0.592782\pi$
$149$	−1.36965e42	−0.574749	−0.287374	+	0.957818i	$0.592782\pi$
$150$	0	0
$151$	−2.28466e42	−0.739214	−0.369607	−	0.929188i	$-0.620508\pi$
$151$	−2.28466e42	−0.739214	−0.369607	+	0.929188i	$0.620508\pi$
$152$	− 2.25271e41i	− 0.0640848i
$153$	2.22352e42i	0.556620i
$154$	4.21793e42	0.929920
$155$	0	0
$156$	6.19580e42	1.06211
$157$	− 3.22622e42i	− 0.488260i	−0.969743	−	0.244130i	$-0.921498\pi$
$157$	− 3.22622e42i	− 0.488260i	0.969743	−	0.244130i	$-0.0785024\pi$
$158$	− 1.60199e43i	− 2.14213i
$159$	−4.51914e42	−0.534333
$160$	0	0
$161$	−1.09769e43	−1.01712
$162$	− 1.37360e43i	− 1.12802i
$163$	4.44788e42i	0.323963i	0.986794	+	0.161981i	$0.0517884\pi$
$163$	4.44788e42i	0.323963i	−0.986794	+	0.161981i	$0.948212\pi$
$164$	−1.08342e43	−0.700395
$165$	0	0
$166$	1.24688e43	0.636378
$167$	4.33425e42i	0.196762i	0.995149	+	0.0983812i	$0.0313665\pi$
$167$	4.33425e42i	0.196762i	−0.995149	+	0.0983812i	$0.968634\pi$
$168$	2.08834e43i	0.843862i
$169$	1.83360e43	0.659953
$170$	0	0
$171$	−7.94779e42	−0.227417
$172$	8.64950e43i	2.20895i
$173$	− 2.21391e43i	− 0.504965i	−0.967601	−	0.252482i	$-0.918753\pi$
$173$	− 2.21391e43i	− 0.504965i	0.967601	−	0.252482i	$-0.0812470\pi$
$174$	2.27724e43	0.464192
$175$	0	0
$176$	−1.64274e43	−0.267962
$177$	− 1.41471e44i	− 2.06628i
$178$	1.20733e44i	1.57993i
$179$	−1.32994e44	−1.56026	−0.780130	−	0.625618i	$-0.784847\pi$
$179$	−1.32994e44	−1.56026	−0.780130	+	0.625618i	$0.784847\pi$
$180$	0	0
$181$	−1.07254e44	−1.01317	−0.506584	−	0.862191i	$-0.669092\pi$
$181$	−1.07254e44	−1.01317	−0.506584	+	0.862191i	$0.669092\pi$
$182$	− 1.72038e44i	− 1.45960i
$183$	− 2.09800e44i	− 1.59959i
$184$	−2.99856e43	−0.205572
$185$	0	0
$186$	5.37703e44	2.98566
$187$	− 3.43720e43i	− 0.171907i
$188$	4.11024e44i	1.85263i
$189$	1.24303e44	0.505214
$190$	0	0
$191$	2.71109e44	0.897414	0.448707	−	0.893679i	$-0.351885\pi$
$191$	2.71109e44	0.897414	0.448707	+	0.893679i	$0.351885\pi$
$192$	− 6.90551e44i	− 2.06453i
$193$	8.26925e43i	0.223408i	0.993742	+	0.111704i	$0.0356309\pi$
$193$	8.26925e43i	0.223408i	−0.993742	+	0.111704i	$0.964369\pi$
$194$	−8.67541e43	−0.211912
$195$	0	0
$196$	1.11250e45	2.22489
$197$	− 5.36056e44i	− 0.970776i	−0.874299	−	0.485388i	$-0.838678\pi$
$197$	− 5.36056e44i	− 0.970776i	0.874299	−	0.485388i	$-0.161322\pi$
$198$	− 4.06513e44i	− 0.666965i
$199$	1.00046e45	1.48787	0.743935	−	0.668252i	$-0.232957\pi$
$199$	1.00046e45	1.48787	0.743935	+	0.668252i	$0.232957\pi$
$200$	0	0
$201$	−2.79358e44	−0.341852
$202$	1.69742e45i	1.88555i
$203$	− 3.48404e44i	− 0.351488i
$204$	9.19387e44	0.842772
$205$	0	0
$206$	−1.22401e45	−0.927631
$207$	1.05792e45i	0.729511i
$208$	6.70032e44i	0.420592i
$209$	1.22860e44	0.0702356
$210$	0	0
$211$	−1.34673e45	−0.639402	−0.319701	−	0.947518i	$-0.603582\pi$
$211$	−1.34673e45	−0.639402	−0.319701	+	0.947518i	$0.603582\pi$
$212$	1.02037e45i	0.441780i
$213$	− 7.17834e45i	− 2.83545i
$214$	−2.49314e45	−0.898832
$215$	0	0
$216$	3.39558e44	0.102109
$217$	− 8.22655e45i	− 2.26075i
$218$	3.64849e44i	0.0916667i
$219$	2.30954e45	0.530720
$220$	0	0
$221$	−1.40194e45	−0.269825
$222$	− 4.09216e45i	− 0.721223i
$223$	4.53007e45i	0.731409i	0.930731	+	0.365705i	$0.119172\pi$
$223$	4.53007e45i	0.731409i	−0.930731	+	0.365705i	$0.880828\pi$
$224$	−1.60433e46	−2.37387
$225$	0	0
$226$	−1.06556e46	−1.32576
$227$	1.08195e46i	1.23510i	0.786532	+	0.617550i	$0.211875\pi$
$227$	1.08195e46i	1.23510i	−0.786532	+	0.617550i	$0.788125\pi$
$228$	3.28627e45i	0.344329i
$229$	−1.83988e46	−1.77010	−0.885051	−	0.465494i	$-0.845877\pi$
$229$	−1.83988e46	−1.77010	−0.885051	+	0.465494i	$0.845877\pi$
$230$	0	0
$231$	−1.13896e46	−0.924854
$232$	− 9.51736e44i	− 0.0710397i
$233$	1.58389e46i	1.08714i	0.839364	+	0.543570i	$0.182928\pi$
$233$	1.58389e46i	1.08714i	−0.839364	+	0.543570i	$0.817072\pi$
$234$	−1.65806e46	−1.04687
$235$	0	0
$236$	−3.19423e46	−1.70837
$237$	4.32581e46i	2.13047i
$238$	− 2.55285e46i	− 1.15818i
$239$	2.86406e46	1.19736	0.598678	−	0.800990i	$-0.295693\pi$
$239$	2.86406e46	1.19736	0.598678	+	0.800990i	$0.295693\pi$
$240$	0	0
$241$	1.94777e46	0.692159	0.346080	−	0.938205i	$-0.387513\pi$
$241$	1.94777e46	0.692159	0.346080	+	0.938205i	$0.387513\pi$
$242$	− 3.92435e46i	− 1.28638i
$243$	4.70498e46i	1.42310i
$244$	−4.73703e46	−1.32253
$245$	0	0
$246$	5.30955e46	1.26422
$247$	− 5.01113e45i	− 0.110242i
$248$	− 2.24725e46i	− 0.456923i
$249$	−3.36690e46	−0.632911
$250$	0	0
$251$	6.63788e46	1.06756	0.533779	−	0.845624i	$-0.320771\pi$
$251$	6.63788e46	1.06756	0.533779	+	0.845624i	$0.320771\pi$
$252$	− 1.66358e47i	− 2.47590i
$253$	− 1.63537e46i	− 0.225303i
$254$	8.40616e46	1.07236
$255$	0	0
$256$	3.70220e46	0.405303
$257$	− 1.60889e47i	− 1.63241i	−0.577761	−	0.816206i	$-0.696073\pi$
$257$	− 1.60889e47i	− 1.63241i	0.577761	−	0.816206i	$-0.303927\pi$
$258$	− 4.23888e47i	− 3.98719i
$259$	−6.26077e46	−0.546113
$260$	0	0
$261$	−3.35782e46	−0.252097
$262$	− 2.30171e47i	− 1.60390i
$263$	− 3.82398e46i	− 0.247388i	−0.992320	−	0.123694i	$-0.960526\pi$
$263$	− 3.82398e46i	− 0.247388i	0.992320	−	0.123694i	$-0.0394742\pi$
$264$	−3.11129e46	−0.186923
$265$	0	0
$266$	9.12497e46	0.473194
$267$	− 3.26013e47i	− 1.57132i
$268$	6.30755e46i	0.282639i
$269$	−7.76998e46	−0.323780	−0.161890	−	0.986809i	$-0.551759\pi$
$269$	−7.76998e46	−0.323780	−0.161890	+	0.986809i	$0.551759\pi$
$270$	0	0
$271$	2.35011e47	0.847591	0.423796	−	0.905758i	$-0.360697\pi$
$271$	2.35011e47	0.847591	0.423796	+	0.905758i	$0.360697\pi$
$272$	9.94252e46i	0.333736i
$273$	4.64550e47i	1.45165i
$274$	3.91626e47	1.13956
$275$	0	0
$276$	4.37432e47	1.10454
$277$	4.19090e47i	0.986170i	0.869981	+	0.493085i	$0.164131\pi$
$277$	4.19090e47i	0.986170i	−0.869981	+	0.493085i	$0.835869\pi$
$278$	5.54803e45i	0.0121693i
$279$	−7.92852e47	−1.62147
$280$	0	0
$281$	2.30674e46	0.0410417	0.0205209	−	0.999789i	$-0.493468\pi$
$281$	2.30674e46	0.0410417	0.0205209	+	0.999789i	$0.493468\pi$
$282$	− 2.01431e48i	− 3.34402i
$283$	− 6.25956e47i	− 0.969858i	−0.874554	−	0.484929i	$-0.838846\pi$
$283$	− 6.25956e47i	− 0.969858i	0.874554	−	0.484929i	$-0.161154\pi$
$284$	−1.62078e48	−2.34431
$285$	0	0
$286$	2.56309e47	0.323315
$287$	− 8.12331e47i	− 0.957273i
$288$	1.54621e48i	1.70261i
$289$	7.63613e47	0.785897
$290$	0	0
$291$	2.34259e47	0.210758
$292$	− 5.21465e47i	− 0.438793i
$293$	− 4.49093e47i	− 0.353523i	−0.984254	−	0.176762i	$-0.943438\pi$
$293$	− 4.49093e47i	− 0.353523i	0.984254	−	0.176762i	$-0.0565621\pi$
$294$	−5.45207e48	−4.01595
$295$	0	0
$296$	−1.71026e47	−0.110376
$297$	1.85190e47i	0.111910i
$298$	− 1.51555e48i	− 0.857733i
$299$	−6.67026e47	−0.353634
$300$	0	0
$301$	−6.48524e48	−3.01911
$302$	− 2.52802e48i	− 1.10318i
$303$	− 4.58350e48i	− 1.87528i
$304$	−3.55387e47	−0.136354
$305$	0	0
$306$	−2.46037e48	−0.830678
$307$	5.77022e48i	1.82808i	0.405628	+	0.914038i	$0.367053\pi$
$307$	5.77022e48i	1.82808i	−0.405628	+	0.914038i	$0.632947\pi$
$308$	2.57162e48i	0.764659i
$309$	3.30517e48	0.922578
$310$	0	0
$311$	−3.50073e48	−0.861651	−0.430826	−	0.902435i	$-0.641778\pi$
$311$	−3.50073e48	−0.861651	−0.430826	+	0.902435i	$0.641778\pi$
$312$	1.26901e48i	0.293394i
$313$	− 4.32088e48i	− 0.938551i	−0.883052	−	0.469276i	$-0.844515\pi$
$313$	− 4.32088e48i	− 0.938551i	0.883052	−	0.469276i	$-0.155485\pi$
$314$	3.56988e48	0.728661
$315$	0	0
$316$	9.76713e48	1.76144
$317$	− 3.38834e47i	− 0.0574554i	−0.999587	−	0.0287277i	$-0.990854\pi$
$317$	− 3.38834e47i	− 0.0574554i	0.999587	−	0.0287277i	$-0.00914557\pi$
$318$	− 5.00052e48i	− 0.797419i
$319$	5.19065e47	0.0778580
$320$	0	0
$321$	6.73216e48	0.893936
$322$	− 1.21461e49i	− 1.51792i
$323$	− 7.43595e47i	− 0.0874757i
$324$	8.37468e48	0.927556
$325$	0	0
$326$	−4.92167e48	−0.483470
$327$	− 9.85191e47i	− 0.0911673i
$328$	− 2.21905e48i	− 0.193476i
$329$	−3.08178e49	−2.53211
$330$	0	0
$331$	−1.23716e49	−0.903189	−0.451595	−	0.892223i	$-0.649145\pi$
$331$	−1.23716e49	−0.903189	−0.451595	+	0.892223i	$0.649145\pi$
$332$	7.60203e48i	0.523284i
$333$	6.03396e48i	0.391688i
$334$	−4.79593e48	−0.293641
$335$	0	0
$336$	3.29457e49	1.79549
$337$	− 1.65140e49i	− 0.849316i	−0.905354	−	0.424658i	$-0.860394\pi$
$337$	− 1.65140e49i	− 0.849316i	0.905354	−	0.424658i	$-0.139606\pi$
$338$	2.02891e49i	0.984889i
$339$	2.87730e49	1.31853
$340$	0	0
$341$	1.22562e49	0.500778
$342$	− 8.79439e48i	− 0.339388i
$343$	3.74064e49i	1.36368i
$344$	−1.77157e49	−0.610197
$345$	0	0
$346$	2.44974e49	0.753591
$347$	3.18063e49i	0.924885i	0.886649	+	0.462443i	$0.153027\pi$
$347$	3.18063e49i	0.924885i	−0.886649	+	0.462443i	$0.846973\pi$
$348$	1.38840e49i	0.381698i
$349$	−1.04623e49	−0.271976	−0.135988	−	0.990711i	$-0.543421\pi$
$349$	−1.04623e49	−0.271976	−0.135988	+	0.990711i	$0.543421\pi$
$350$	0	0
$351$	7.55343e48	0.175653
$352$	− 2.39019e49i	− 0.525835i
$353$	3.28850e49i	0.684527i	0.939604	+	0.342263i	$0.111194\pi$
$353$	3.28850e49i	0.684527i	−0.939604	+	0.342263i	$0.888806\pi$
$354$	1.56540e50	3.08363
$355$	0	0
$356$	−7.36096e49	−1.29915
$357$	6.89340e49i	1.15187i
$358$	− 1.47160e50i	− 2.32847i
$359$	−4.88065e49	−0.731367	−0.365684	−	0.930739i	$-0.619165\pi$
$359$	−4.88065e49	−0.731367	−0.365684	+	0.930739i	$0.619165\pi$
$360$	0	0
$361$	−7.17108e49	−0.964260
$362$	− 1.18679e50i	− 1.51201i
$363$	1.05968e50i	1.27937i
$364$	1.04890e50	1.20020
$365$	0	0
$366$	2.32148e50	2.38718
$367$	7.14273e49i	0.696428i	0.937415	+	0.348214i	$0.113212\pi$
$367$	7.14273e49i	0.696428i	−0.937415	+	0.348214i	$0.886788\pi$
$368$	4.73051e49i	0.437397i
$369$	−7.82902e49	−0.686583
$370$	0	0
$371$	−7.65051e49	−0.603809
$372$	3.27830e50i	2.45506i
$373$	− 1.05915e50i	− 0.752724i	−0.926473	−	0.376362i	$-0.877175\pi$
$373$	− 1.05915e50i	− 0.752724i	0.926473	−	0.376362i	$-0.122825\pi$
$374$	3.80333e49	0.256548
$375$	0	0
$376$	−8.41852e49	−0.511767
$377$	− 2.11713e49i	− 0.122206i
$378$	1.37543e50i	0.753962i
$379$	1.87195e50	0.974605	0.487302	−	0.873233i	$-0.337981\pi$
$379$	1.87195e50	0.974605	0.487302	+	0.873233i	$0.337981\pi$
$380$	0	0
$381$	−2.26989e50	−1.06652
$382$	2.99987e50i	1.33927i
$383$	− 3.66531e50i	− 1.55502i	−0.628873	−	0.777508i	$-0.716484\pi$
$383$	− 3.66531e50i	− 1.55502i	0.628873	−	0.777508i	$-0.283516\pi$
$384$	2.43120e50	0.980305
$385$	0	0
$386$	−9.15009e49	−0.333406
$387$	6.25030e50i	2.16539i
$388$	− 5.28928e49i	− 0.174252i
$389$	4.12272e49	0.129171	0.0645857	−	0.997912i	$-0.479427\pi$
$389$	4.12272e49	0.129171	0.0645857	+	0.997912i	$0.479427\pi$
$390$	0	0
$391$	−9.89791e49	−0.280606
$392$	2.27861e50i	0.614598i
$393$	6.21525e50i	1.59516i
$394$	5.93157e50	1.44875
$395$	0	0
$396$	2.47845e50	0.548435
$397$	4.25670e50i	0.896723i	0.893852	+	0.448361i	$0.147992\pi$
$397$	4.25670e50i	0.896723i	−0.893852	+	0.448361i	$0.852008\pi$
$398$	1.10703e51i	2.22044i
$399$	−2.46399e50	−0.470616
$400$	0	0
$401$	−6.90511e50	−1.19634	−0.598171	−	0.801368i	$-0.704106\pi$
$401$	−6.90511e50	−1.19634	−0.598171	+	0.801368i	$0.704106\pi$
$402$	− 3.09115e50i	− 0.510167i
$403$	− 4.99898e50i	− 0.786019i
$404$	−1.03490e51	−1.55046
$405$	0	0
$406$	3.85516e50	0.524548
$407$	− 9.32751e49i	− 0.120969i
$408$	1.88307e50i	0.232806i
$409$	5.24800e50	0.618571	0.309286	−	0.950969i	$-0.399910\pi$
$409$	5.24800e50	0.618571	0.309286	+	0.950969i	$0.399910\pi$
$410$	0	0
$411$	−1.05750e51	−1.13335
$412$	− 7.46265e50i	− 0.762776i
$413$	− 2.39498e51i	− 2.33494i
$414$	−1.17061e51	−1.08869
$415$	0	0
$416$	−9.74895e50	−0.825349
$417$	− 1.49812e49i	− 0.0121030i
$418$	1.35947e50i	0.104817i
$419$	−1.54729e51	−1.13867	−0.569334	−	0.822106i	$-0.692799\pi$
$419$	−1.54729e51	−1.13867	−0.569334	+	0.822106i	$0.692799\pi$
$420$	0	0
$421$	−1.69195e51	−1.13472	−0.567359	−	0.823471i	$-0.692035\pi$
$421$	−1.69195e51	−1.13472	−0.567359	+	0.823471i	$0.692035\pi$
$422$	− 1.49019e51i	− 0.954220i
$423$	2.97014e51i	1.81610i
$424$	−2.08989e50	−0.122037
$425$	0	0
$426$	7.94298e51	4.23152
$427$	− 3.55174e51i	− 1.80758i
$428$	− 1.52004e51i	− 0.739096i
$429$	−6.92103e50	−0.321554
$430$	0	0
$431$	2.11949e51	0.899341	0.449670	−	0.893195i	$-0.351541\pi$
$431$	2.11949e51	0.899341	0.449670	+	0.893195i	$0.351541\pi$
$432$	− 5.35686e50i	− 0.217259i
$433$	− 1.57391e51i	− 0.610193i	−0.952321	−	0.305097i	$-0.901311\pi$
$433$	− 1.57391e51i	− 0.610193i	0.952321	−	0.305097i	$-0.0986887\pi$
$434$	9.10284e51	3.37386
$435$	0	0
$436$	−2.22444e50	−0.0753761
$437$	− 3.53792e50i	− 0.114646i
$438$	2.55555e51i	0.792027i
$439$	−7.36309e50	−0.218274	−0.109137	−	0.994027i	$-0.534809\pi$
$439$	−7.36309e50	−0.218274	−0.109137	+	0.994027i	$0.534809\pi$
$440$	0	0
$441$	8.03916e51	2.18101
$442$	− 1.55128e51i	− 0.402676i
$443$	3.79349e51i	0.942251i	0.882066	+	0.471125i	$0.156152\pi$
$443$	3.79349e51i	0.942251i	−0.882066	+	0.471125i	$0.843848\pi$
$444$	2.49494e51	0.593050
$445$	0	0
$446$	−5.01262e51	−1.09153
$447$	4.09239e51i	0.853061i
$448$	− 1.16904e52i	− 2.33297i
$449$	−7.69430e51	−1.47016	−0.735081	−	0.677979i	$-0.762856\pi$
$449$	−7.69430e51	−1.47016	−0.735081	+	0.677979i	$0.762856\pi$
$450$	0	0
$451$	1.21024e51	0.212045
$452$	− 6.49659e51i	− 1.09015i
$453$	6.82633e51i	1.09717i
$454$	−1.19720e52	−1.84322
$455$	0	0
$456$	−6.73088e50	−0.0951168
$457$	− 9.48171e51i	− 1.28387i	−0.766759	−	0.641935i	$-0.778132\pi$
$457$	− 9.48171e51i	− 1.28387i	0.766759	−	0.641935i	$-0.221868\pi$
$458$	− 2.03587e52i	− 2.64163i
$459$	1.12084e51	0.139379
$460$	0	0
$461$	−1.00315e52	−1.14604	−0.573018	−	0.819543i	$-0.694227\pi$
$461$	−1.00315e52	−1.14604	−0.573018	+	0.819543i	$0.694227\pi$
$462$	− 1.26028e52i	− 1.38022i
$463$	6.38266e51i	0.670151i	0.942191	+	0.335075i	$0.108762\pi$
$463$	6.38266e51i	0.670151i	−0.942191	+	0.335075i	$0.891238\pi$
$464$	−1.50146e51	−0.151151
$465$	0	0
$466$	−1.75261e52	−1.62241
$467$	8.44728e51i	0.749960i	0.927033	+	0.374980i	$0.122350\pi$
$467$	8.44728e51i	0.749960i	−0.927033	+	0.374980i	$0.877650\pi$
$468$	− 1.01090e52i	− 0.860821i
$469$	−4.72929e51	−0.386300
$470$	0	0
$471$	−9.63964e51	−0.724692
$472$	− 6.54237e51i	− 0.471918i
$473$	− 9.66194e51i	− 0.668762i
$474$	−4.78659e52	−3.17943
$475$	0	0
$476$	1.55644e52	0.952352
$477$	7.37335e51i	0.433069i
$478$	3.16914e52i	1.78689i
$479$	−3.34415e51	−0.181027	−0.0905134	−	0.995895i	$-0.528851\pi$
$479$	−3.34415e51	−0.181027	−0.0905134	+	0.995895i	$0.528851\pi$
$480$	0	0
$481$	−3.80445e51	−0.189873
$482$	2.15525e52i	1.03295i
$483$	3.27978e52i	1.50965i
$484$	2.39262e52	1.05777
$485$	0	0
$486$	−5.20616e52	−2.12378
$487$	3.02586e52i	1.18586i	0.805254	+	0.592931i	$0.202029\pi$
$487$	3.02586e52i	1.18586i	−0.805254	+	0.592931i	$0.797971\pi$
$488$	− 9.70229e51i	− 0.365332i
$489$	1.32898e52	0.480836
$490$	0	0
$491$	5.39058e52	1.80114	0.900568	−	0.434715i	$-0.143151\pi$
$491$	5.39058e52	1.80114	0.900568	+	0.434715i	$0.143151\pi$
$492$	3.23716e52i	1.03955i
$493$	− 3.14158e51i	− 0.0969690i
$494$	5.54492e51	0.164520
$495$	0	0
$496$	−3.54525e52	−0.972197
$497$	− 1.21523e53i	− 3.20412i
$498$	− 3.72554e52i	− 0.944533i
$499$	−4.77343e52	−1.16378	−0.581888	−	0.813269i	$-0.697686\pi$
$499$	−4.77343e52	−1.16378	−0.581888	+	0.813269i	$0.697686\pi$
$500$	0	0
$501$	1.29503e52	0.292041
$502$	7.34494e52i	1.59318i
$503$	− 4.55769e51i	− 0.0950974i	−0.998869	−	0.0475487i	$-0.984859\pi$
$503$	− 4.55769e51i	− 0.0950974i	0.998869	−	0.0475487i	$-0.0151409\pi$
$504$	3.40731e52	0.683937
$505$	0	0
$506$	1.80957e52	0.336234
$507$	− 5.47861e52i	− 0.979524i
$508$	5.12513e52i	0.881784i
$509$	4.13304e52	0.684341	0.342170	−	0.939638i	$-0.388838\pi$
$509$	4.13304e52	0.684341	0.342170	+	0.939638i	$0.388838\pi$
$510$	0	0
$511$	3.90985e52	0.599726
$512$	8.56980e52i	1.26534i
$513$	4.00636e51i	0.0569458i
$514$	1.78027e53	2.43615
$515$	0	0
$516$	2.58439e53	3.27860
$517$	− 4.59135e52i	− 0.560886i
$518$	− 6.92767e52i	− 0.814998i
$519$	−6.61495e52	−0.749486
$520$	0	0
$521$	−4.81863e52	−0.506510	−0.253255	−	0.967400i	$-0.581501\pi$
$521$	−4.81863e52	−0.506510	−0.253255	+	0.967400i	$0.581501\pi$
$522$	− 3.71550e52i	− 0.376220i
$523$	− 1.41580e52i	− 0.138108i	−0.997613	−	0.0690541i	$-0.978002\pi$
$523$	− 1.41580e52i	− 0.138108i	0.997613	−	0.0690541i	$-0.0219981\pi$
$524$	1.40333e53	1.31886
$525$	0	0
$526$	4.23131e52	0.369193
$527$	− 7.41792e52i	− 0.623699i
$528$	4.90836e52i	0.397718i
$529$	8.09589e52	0.632236
$530$	0	0
$531$	−2.30821e53	−1.67468
$532$	5.56337e52i	0.389100i
$533$	− 4.93625e52i	− 0.332825i
$534$	3.60740e53	2.34498
$535$	0	0
$536$	−1.29190e52	−0.0780756
$537$	3.97372e53i	2.31579i
$538$	− 8.59763e52i	− 0.483197i
$539$	−1.24272e53	−0.673587
$540$	0	0
$541$	1.61080e53	0.812258	0.406129	−	0.913816i	$-0.366878\pi$
$541$	1.61080e53	0.812258	0.406129	+	0.913816i	$0.366878\pi$
$542$	2.60044e53i	1.26491i
$543$	3.20465e53i	1.50378i
$544$	−1.44663e53	−0.654907
$545$	0	0
$546$	−5.14034e53	−2.16638
$547$	− 2.03359e52i	− 0.0827010i	−0.999145	−	0.0413505i	$-0.986834\pi$
$547$	− 2.03359e52i	− 0.0827010i	0.999145	−	0.0413505i	$-0.0131660\pi$
$548$	2.38769e53i	0.937039i
$549$	−3.42307e53	−1.29645
$550$	0	0
$551$	1.12293e52	0.0396184
$552$	8.95940e52i	0.305117i
$553$	7.32322e53i	2.40747i
$554$	−4.63731e53	−1.47172
$555$	0	0
$556$	−3.38256e51	−0.0100066
$557$	− 4.33061e53i	− 1.23701i	−0.785781	−	0.618505i	$-0.787739\pi$
$557$	− 4.33061e53i	− 1.23701i	0.785781	−	0.618505i	$-0.212261\pi$
$558$	− 8.77306e53i	− 2.41983i
$559$	−3.94085e53	−1.04969
$560$	0	0
$561$	−1.02700e53	−0.255150
$562$	2.55246e52i	0.0612491i
$563$	6.67730e53i	1.54770i	0.633368	+	0.773851i	$0.281672\pi$
$563$	6.67730e53i	1.54770i	−0.633368	+	0.773851i	$0.718328\pi$
$564$	1.22810e54	2.74974
$565$	0	0
$566$	6.92632e53	1.44738
$567$	6.27918e53i	1.26775i
$568$	− 3.31965e53i	− 0.647589i
$569$	−9.32793e53	−1.75831	−0.879156	−	0.476534i	$-0.841893\pi$
$569$	−9.32793e53	−1.75831	−0.879156	+	0.476534i	$0.841893\pi$
$570$	0	0
$571$	−2.47736e53	−0.436099	−0.218049	−	0.975938i	$-0.569969\pi$
$571$	−2.47736e53	−0.436099	−0.218049	+	0.975938i	$0.569969\pi$
$572$	1.56268e53i	0.265857i
$573$	− 8.10046e53i	− 1.33197i
$574$	8.98860e53	1.42860
$575$	0	0
$576$	−1.12669e54	−1.67327
$577$	4.60066e53i	0.660528i	0.943889	+	0.330264i	$0.107138\pi$
$577$	4.60066e53i	0.660528i	−0.943889	+	0.330264i	$0.892862\pi$
$578$	8.44953e53i	1.17284i
$579$	2.47077e53	0.331590
$580$	0	0
$581$	−5.69987e53	−0.715204
$582$	2.59213e53i	0.314527i
$583$	− 1.13980e53i	− 0.133749i
$584$	1.06806e53	0.121211
$585$	0	0
$586$	4.96930e53	0.527585
$587$	1.03979e54i	1.06783i	0.845537	+	0.533916i	$0.179280\pi$
$587$	1.03979e54i	1.06783i	−0.845537	+	0.533916i	$0.820720\pi$
$588$	− 3.32405e54i	− 3.30225i
$589$	2.65147e53	0.254823
$590$	0	0
$591$	−1.60168e54	−1.44086
$592$	2.69809e53i	0.234846i
$593$	4.68001e53i	0.394167i	0.980387	+	0.197084i	$0.0631471\pi$
$593$	4.68001e53i	0.394167i	−0.980387	+	0.197084i	$0.936853\pi$
$594$	−2.04917e53	−0.167010
$595$	0	0
$596$	9.24009e53	0.705301
$597$	− 2.98928e54i	− 2.20835i
$598$	− 7.38078e53i	− 0.527751i
$599$	−1.95085e54	−1.35021	−0.675106	−	0.737721i	$-0.735902\pi$
$599$	−1.95085e54	−1.35021	−0.675106	+	0.737721i	$0.735902\pi$
$600$	0	0
$601$	2.02439e54	1.31293	0.656467	−	0.754355i	$-0.272050\pi$
$601$	2.02439e54	1.31293	0.656467	+	0.754355i	$0.272050\pi$
$602$	− 7.17605e54i	− 4.50561i
$603$	4.55796e53i	0.277066i
$604$	1.54130e54	0.907124
$605$	0	0
$606$	5.07174e54	2.79860
$607$	2.12357e54i	1.13472i	0.823471	+	0.567359i	$0.192035\pi$
$607$	2.12357e54i	1.13472i	−0.823471	+	0.567359i	$0.807965\pi$
$608$	− 5.17087e53i	− 0.267574i
$609$	−1.04100e54	−0.521690
$610$	0	0
$611$	−1.87269e54	−0.880364
$612$	− 1.50006e54i	− 0.683054i
$613$	3.14022e54i	1.38510i	0.721371	+	0.692549i	$0.243512\pi$
$613$	3.14022e54i	1.38510i	−0.721371	+	0.692549i	$0.756488\pi$
$614$	−6.38487e54	−2.72815
$615$	0	0
$616$	−5.26714e53	−0.211228
$617$	− 2.88947e54i	− 1.12268i	−0.827585	−	0.561341i	$-0.810286\pi$
$617$	− 2.88947e54i	− 1.12268i	0.827585	−	0.561341i	$-0.189714\pi$
$618$	3.65723e54i	1.37682i
$619$	8.69334e53	0.317116	0.158558	−	0.987350i	$-0.449315\pi$
$619$	8.69334e53	0.317116	0.158558	+	0.987350i	$0.449315\pi$
$620$	0	0
$621$	5.33282e53	0.182672
$622$	− 3.87363e54i	− 1.28590i
$623$	− 5.51912e54i	− 1.77563i
$624$	2.00199e54	0.624256
$625$	0	0
$626$	4.78114e54	1.40066
$627$	− 3.67093e53i	− 0.104246i
$628$	2.17651e54i	0.599166i
$629$	−5.64537e53	−0.150662
$630$	0	0
$631$	−2.40764e54	−0.603976	−0.301988	−	0.953312i	$-0.597650\pi$
$631$	−2.40764e54	−0.603976	−0.301988	+	0.953312i	$0.597650\pi$
$632$	2.00048e54i	0.486578i
$633$	4.02391e54i	0.949022i
$634$	3.74926e53	0.0857443
$635$	0	0
$636$	3.04875e54	0.655705
$637$	5.06874e54i	1.05726i
$638$	5.74355e53i	0.116192i
$639$	−1.17121e55	−2.29809
$640$	0	0
$641$	−2.69211e53	−0.0497005	−0.0248503	−	0.999691i	$-0.507911\pi$
$641$	−2.69211e53	−0.0497005	−0.0248503	+	0.999691i	$0.507911\pi$
$642$	7.44927e54i	1.33408i
$643$	3.09318e54i	0.537393i	0.963225	+	0.268696i	$0.0865928\pi$
$643$	3.09318e54i	0.537393i	−0.963225	+	0.268696i	$0.913407\pi$
$644$	7.40534e54	1.24816
$645$	0	0
$646$	8.22803e53	0.130545
$647$	− 1.66944e54i	− 0.257003i	−0.991709	−	0.128501i	$-0.958983\pi$
$647$	− 1.66944e54i	− 0.257003i	0.991709	−	0.128501i	$-0.0410167\pi$
$648$	1.71529e54i	0.256226i
$649$	3.56812e54	0.517212
$650$	0	0
$651$	−2.45801e55	−3.35548
$652$	− 3.00068e54i	− 0.397549i
$653$	− 1.05739e55i	− 1.35965i	−0.733375	−	0.679824i	$-0.762056\pi$
$653$	− 1.05739e55i	− 1.35965i	0.733375	−	0.679824i	$-0.237944\pi$
$654$	1.09013e54	0.136055
$655$	0	0
$656$	−3.50076e54	−0.411659
$657$	− 3.76821e54i	− 0.430140i
$658$	− 3.41006e55i	− 3.77882i
$659$	−3.28150e54	−0.353026	−0.176513	−	0.984298i	$-0.556482\pi$
$659$	−3.28150e54	−0.353026	−0.176513	+	0.984298i	$0.556482\pi$
$660$	0	0
$661$	1.10445e55	1.12000	0.560001	−	0.828492i	$-0.310801\pi$
$661$	1.10445e55	1.12000	0.560001	+	0.828492i	$0.310801\pi$
$662$	− 1.36894e55i	− 1.34789i
$663$	4.18887e54i	0.400482i
$664$	−1.55703e54	−0.144551
$665$	0	0
$666$	−6.67670e54	−0.584540
$667$	− 1.49472e54i	− 0.127088i
$668$	− 2.92402e54i	− 0.241456i
$669$	1.35354e55	1.08558
$670$	0	0
$671$	5.29150e54	0.400396
$672$	4.79358e55i	3.52338i
$673$	1.32277e55i	0.944478i	0.881471	+	0.472239i	$0.156554\pi$
$673$	1.32277e55i	0.944478i	−0.881471	+	0.472239i	$0.843446\pi$
$674$	1.82731e55	1.26749
$675$	0	0
$676$	−1.23700e55	−0.809858
$677$	1.10632e54i	0.0703723i	0.999381	+	0.0351861i	$0.0112024\pi$
$677$	1.10632e54i	0.0703723i	−0.999381	+	0.0351861i	$0.988798\pi$
$678$	3.18379e55i	1.96773i
$679$	3.96581e54	0.238161
$680$	0	0
$681$	3.23276e55	1.83318
$682$	1.35617e55i	0.747342i
$683$	− 1.00248e55i	− 0.536873i	−0.963297	−	0.268437i	$-0.913493\pi$
$683$	− 1.00248e55i	− 0.536873i	0.963297	−	0.268437i	$-0.0865070\pi$
$684$	5.36182e54	0.279073
$685$	0	0
$686$	−4.13910e55	−2.03510
$687$	5.49739e55i	2.62724i
$688$	2.79483e55i	1.29832i
$689$	−4.64895e54	−0.209933
$690$	0	0
$691$	−1.51432e55	−0.646242	−0.323121	−	0.946358i	$-0.604732\pi$
$691$	−1.51432e55	−0.646242	−0.323121	+	0.946358i	$0.604732\pi$
$692$	1.49357e55i	0.619666i
$693$	1.85830e55i	0.749580i
$694$	−3.51943e55	−1.38026
$695$	0	0
$696$	−2.84370e54	−0.105439
$697$	− 7.32483e54i	− 0.264094i
$698$	− 1.15767e55i	− 0.405886i
$699$	4.73252e55	1.61357
$700$	0	0
$701$	4.82172e55	1.55489	0.777447	−	0.628948i	$-0.216514\pi$
$701$	4.82172e55	1.55489	0.777447	+	0.628948i	$0.216514\pi$
$702$	8.35803e54i	0.262138i
$703$	− 2.01789e54i	− 0.0615557i
$704$	1.74168e55	0.516775
$705$	0	0
$706$	−3.63879e55	−1.02156
$707$	− 7.75947e55i	− 2.11911i
$708$	9.54406e55i	2.53562i
$709$	−6.05445e53	−0.0156485	−0.00782426	−	0.999969i	$-0.502491\pi$
$709$	−6.05445e53	−0.0156485	−0.00782426	+	0.999969i	$0.502491\pi$
$710$	0	0
$711$	7.05791e55	1.72671
$712$	− 1.50766e55i	− 0.358875i
$713$	− 3.52934e55i	− 0.817425i
$714$	−7.62768e55	−1.71901
$715$	0	0
$716$	8.97216e55	1.91467
$717$	− 8.55754e55i	− 1.77716i
$718$	− 5.40053e55i	− 1.09147i
$719$	7.05056e54	0.138679	0.0693394	−	0.997593i	$-0.477911\pi$
$719$	7.05056e54	0.138679	0.0693394	+	0.997593i	$0.477911\pi$
$720$	0	0
$721$	5.59536e55	1.04253
$722$	− 7.93495e55i	− 1.43903i
$723$	− 5.81976e55i	− 1.02733i
$724$	7.23568e55	1.24330
$725$	0	0
$726$	−1.17256e56	−1.90928
$727$	7.92077e55i	1.25559i	0.778380	+	0.627793i	$0.216042\pi$
$727$	7.92077e55i	1.25559i	−0.778380	+	0.627793i	$0.783958\pi$
$728$	2.14833e55i	0.331542i
$729$	9.02730e55	1.35635
$730$	0	0
$731$	−5.84777e55	−0.832917
$732$	1.41538e56i	1.96294i
$733$	6.30225e55i	0.851076i	0.904941	+	0.425538i	$0.139915\pi$
$733$	6.30225e55i	0.851076i	−0.904941	+	0.425538i	$0.860085\pi$
$734$	−7.90358e55	−1.03932
$735$	0	0
$736$	−6.88288e55	−0.858327
$737$	− 7.04586e54i	− 0.0855692i
$738$	− 8.66297e55i	− 1.02463i
$739$	1.14548e56	1.31954	0.659768	−	0.751469i	$-0.270655\pi$
$739$	1.14548e56	1.31954	0.659768	+	0.751469i	$0.270655\pi$
$740$	0	0
$741$	−1.49728e55	−0.163624
$742$	− 8.46545e55i	− 0.901101i
$743$	− 3.14628e55i	− 0.326224i	−0.986608	−	0.163112i	$-0.947847\pi$
$743$	− 3.14628e55i	− 0.326224i	0.986608	−	0.163112i	$-0.0521532\pi$
$744$	−6.71456e55	−0.678180
$745$	0	0
$746$	1.17197e56	1.12334
$747$	5.49338e55i	0.512965i
$748$	2.31884e55i	0.210955i
$749$	1.13970e56	1.01017
$750$	0	0
$751$	1.74710e56	1.47007	0.735036	−	0.678028i	$-0.237165\pi$
$751$	1.74710e56	1.47007	0.735036	+	0.678028i	$0.237165\pi$
$752$	1.32810e56i	1.08889i
$753$	− 1.98333e56i	− 1.58451i
$754$	2.34264e55	0.182375
$755$	0	0
$756$	−8.38584e55	−0.619971
$757$	2.77438e55i	0.199893i	0.994993	+	0.0999463i	$0.0318671\pi$
$757$	2.77438e55i	0.199893i	−0.994993	+	0.0999463i	$0.968133\pi$
$758$	2.07134e56i	1.45446i
$759$	−4.88634e55	−0.334402
$760$	0	0
$761$	−2.40584e56	−1.56411	−0.782053	−	0.623212i	$-0.785827\pi$
$761$	−2.40584e56	−1.56411	−0.782053	+	0.623212i	$0.785827\pi$
$762$	− 2.51168e56i	− 1.59163i
$763$	− 1.66784e55i	− 0.103021i
$764$	−1.82898e56	−1.10126
$765$	0	0
$766$	4.05574e56	2.32065
$767$	− 1.45534e56i	− 0.811813i
$768$	− 1.10618e56i	− 0.601565i
$769$	−3.04973e56	−1.61695	−0.808477	−	0.588528i	$-0.799708\pi$
$769$	−3.04973e56	−1.61695	−0.808477	+	0.588528i	$0.799708\pi$
$770$	0	0
$771$	−4.80720e56	−2.42288
$772$	− 5.57869e55i	− 0.274154i
$773$	− 4.36657e55i	− 0.209238i	−0.994512	−	0.104619i	$-0.966638\pi$
$773$	− 4.36657e55i	− 0.209238i	0.994512	−	0.104619i	$-0.0333623\pi$
$774$	−6.91608e56	−3.23155
$775$	0	0
$776$	1.08334e55	0.0481351
$777$	1.87066e56i	0.810559i
$778$	4.56187e55i	0.192771i
$779$	2.61820e55	0.107900
$780$	0	0
$781$	1.81049e56	0.709744
$782$	− 1.09522e56i	− 0.418766i
$783$	1.69263e55i	0.0631258i
$784$	3.59473e56	1.30768
$785$	0	0
$786$	−6.87730e56	−2.38056
$787$	− 4.86747e56i	− 1.64360i	−0.569777	−	0.821800i	$-0.692970\pi$
$787$	− 4.86747e56i	− 1.64360i	0.569777	−	0.821800i	$-0.307030\pi$
$788$	3.61640e56i	1.19128i
$789$	−1.14257e56	−0.367182
$790$	0	0
$791$	4.87102e56	1.48997
$792$	5.07632e55i	0.151499i
$793$	− 2.15827e56i	− 0.628460i
$794$	−4.71012e56	−1.33824
$795$	0	0
$796$	−6.74942e56	−1.82583
$797$	5.82796e56i	1.53844i	0.638986	+	0.769218i	$0.279354\pi$
$797$	5.82796e56i	1.53844i	−0.638986	+	0.769218i	$0.720646\pi$
$798$	− 2.72645e56i	− 0.702330i
$799$	−2.77886e56	−0.698561
$800$	0	0
$801$	−5.31917e56	−1.27353
$802$	− 7.64064e56i	− 1.78538i
$803$	5.82503e55i	0.132845i
$804$	1.88463e56	0.419502
$805$	0	0
$806$	5.53147e56	1.17303
$807$	2.32159e56i	0.480565i
$808$	− 2.11966e56i	− 0.428296i
$809$	7.85718e56	1.54978	0.774891	−	0.632095i	$-0.217805\pi$
$809$	7.85718e56	1.54978	0.774891	+	0.632095i	$0.217805\pi$
$810$	0	0
$811$	4.57812e56	0.860558	0.430279	−	0.902696i	$-0.358415\pi$
$811$	4.57812e56	0.860558	0.430279	+	0.902696i	$0.358415\pi$
$812$	2.35044e56i	0.431327i
$813$	− 7.02189e56i	− 1.25802i
$814$	1.03211e56	0.180530
$815$	0	0
$816$	2.97073e56	0.495342
$817$	− 2.09024e56i	− 0.340303i
$818$	5.80702e56i	0.923132i
$819$	7.57952e56	1.17654
$820$	0	0
$821$	5.79486e56	0.857731	0.428866	−	0.903368i	$-0.358913\pi$
$821$	5.79486e56	0.857731	0.428866	+	0.903368i	$0.358913\pi$
$822$	− 1.17014e57i	− 1.69137i
$823$	1.26890e57i	1.79114i	0.444916	+	0.895572i	$0.353233\pi$
$823$	1.26890e57i	1.79114i	−0.444916	+	0.895572i	$0.646767\pi$
$824$	1.52849e56	0.210708
$825$	0	0
$826$	2.65009e57	3.48458
$827$	3.04410e56i	0.390932i	0.980710	+	0.195466i	$0.0626219\pi$
$827$	3.04410e56i	0.390932i	−0.980710	+	0.195466i	$0.937378\pi$
$828$	− 7.13706e56i	− 0.895216i
$829$	4.36698e56	0.535017	0.267509	−	0.963555i	$-0.413800\pi$
$829$	4.36698e56	0.535017	0.267509	+	0.963555i	$0.413800\pi$
$830$	0	0
$831$	1.25220e57	1.46371
$832$	− 7.10386e56i	− 0.811129i
$833$	7.52144e56i	0.838926i
$834$	1.65770e55	0.0180621
$835$	0	0
$836$	−8.28850e55	−0.0861894
$837$	3.99665e56i	0.406022i
$838$	− 1.71210e57i	− 1.69931i
$839$	−1.05819e56	−0.102614	−0.0513070	−	0.998683i	$-0.516339\pi$
$839$	−1.05819e56	−0.102614	−0.0513070	+	0.998683i	$0.516339\pi$
$840$	0	0
$841$	−1.03280e57	−0.956082
$842$	− 1.87218e57i	− 1.69341i
$843$	− 6.89232e55i	− 0.0609155i
$844$	9.08549e56	0.784640
$845$	0	0
$846$	−3.28652e57	−2.71028
$847$	1.79395e57i	1.44572i
$848$	3.29701e56i	0.259658i
$849$	−1.87029e57	−1.43949
$850$	0	0
$851$	−2.68599e56	−0.197459
$852$	4.84273e57i	3.47951i
$853$	1.08758e57i	0.763756i	0.924213	+	0.381878i	$0.124723\pi$
$853$	1.08758e57i	0.763756i	−0.924213	+	0.381878i	$0.875277\pi$
$854$	3.93007e57	2.69756
$855$	0	0
$856$	3.11331e56	0.204166
$857$	1.97964e57i	1.26900i	0.772925	+	0.634498i	$0.218793\pi$
$857$	1.97964e57i	1.26900i	−0.772925	+	0.634498i	$0.781207\pi$
$858$	− 7.65826e56i	− 0.479875i
$859$	−5.66557e56	−0.347038	−0.173519	−	0.984831i	$-0.555514\pi$
$859$	−5.66557e56	−0.347038	−0.173519	+	0.984831i	$0.555514\pi$
$860$	0	0
$861$	−2.42717e57	−1.42082
$862$	2.34526e57i	1.34214i
$863$	5.59601e56i	0.313089i	0.987671	+	0.156545i	$0.0500355\pi$
$863$	5.59601e56i	0.313089i	−0.987671	+	0.156545i	$0.949964\pi$
$864$	7.79421e56	0.426338
$865$	0	0
$866$	1.74157e57	0.910629
$867$	− 2.28160e57i	− 1.16645i
$868$	5.54988e57i	2.77427i
$869$	−1.09104e57	−0.533279
$870$	0	0
$871$	−2.87382e56	−0.134309
$872$	− 4.55605e55i	− 0.0208217i
$873$	− 3.82214e56i	− 0.170816i
$874$	3.91478e56	0.171094
$875$	0	0
$876$	−1.55809e57	−0.651271
$877$	− 3.51912e57i	− 1.43861i	−0.694695	−	0.719304i	$-0.744461\pi$
$877$	− 3.51912e57i	− 1.43861i	0.694695	−	0.719304i	$-0.255539\pi$
$878$	− 8.14740e56i	− 0.325744i
$879$	−1.34185e57	−0.524711
$880$	0	0
$881$	−2.67197e57	−0.999542	−0.499771	−	0.866158i	$-0.666583\pi$
$881$	−2.67197e57	−0.999542	−0.499771	+	0.866158i	$0.666583\pi$
$882$	8.89550e57i	3.25486i
$883$	− 3.97981e57i	− 1.42439i	−0.701982	−	0.712194i	$-0.747701\pi$
$883$	− 3.97981e57i	− 1.42439i	0.701982	−	0.712194i	$-0.252299\pi$
$884$	9.45795e56	0.331114
$885$	0	0
$886$	−4.19757e57	−1.40618
$887$	− 2.01262e57i	− 0.659555i	−0.944059	−	0.329778i	$-0.893026\pi$
$887$	− 2.01262e57i	− 0.659555i	0.944059	−	0.329778i	$-0.106974\pi$
$888$	5.11008e56i	0.163823i
$889$	−3.84273e57	−1.20519
$890$	0	0
$891$	−9.35494e56	−0.280819
$892$	− 3.05613e57i	− 0.897546i
$893$	− 9.93280e56i	− 0.285409i
$894$	−4.52831e57	−1.27308
$895$	0	0
$896$	4.11580e57	1.10777
$897$	1.99301e57i	0.524876i
$898$	− 8.51389e57i	− 2.19401i
$899$	1.12021e57	0.282478
$900$	0	0
$901$	−6.89851e56	−0.166580
$902$	1.33915e57i	0.316448i
$903$	1.93773e58i	4.48107i
$904$	1.33062e57	0.301141
$905$	0	0
$906$	−7.55347e57	−1.63737
$907$	− 1.92035e57i	− 0.407416i	−0.979032	−	0.203708i	$-0.934701\pi$
$907$	− 1.92035e57i	− 0.407416i	0.979032	−	0.203708i	$-0.0652994\pi$
$908$	− 7.29915e57i	− 1.51565i
$909$	−7.47836e57	−1.51989
$910$	0	0
$911$	5.42803e57	1.05690	0.528450	−	0.848964i	$-0.322773\pi$
$911$	5.42803e57	1.05690	0.528450	+	0.848964i	$0.322773\pi$
$912$	1.06186e57i	0.202380i
$913$	− 8.49186e56i	− 0.158425i
$914$	1.04917e58	1.91600
$915$	0	0
$916$	1.24124e58	2.17217
$917$	1.05219e58i	1.80257i
$918$	1.24024e57i	0.208004i
$919$	1.06801e58	1.75357	0.876785	−	0.480883i	$-0.159684\pi$
$919$	1.06801e58	1.75357	0.876785	+	0.480883i	$0.159684\pi$
$920$	0	0
$921$	1.72409e58	2.71329
$922$	− 1.11001e58i	− 1.71030i
$923$	− 7.38452e57i	− 1.11401i
$924$	7.68375e57	1.13493
$925$	0	0
$926$	−7.06255e57	−1.00011
$927$	− 5.39265e57i	− 0.747735i
$928$	− 2.18461e57i	− 0.296612i
$929$	9.61260e57	1.27801	0.639005	−	0.769202i	$-0.279346\pi$
$929$	9.61260e57	1.27801	0.639005	+	0.769202i	$0.279346\pi$
$930$	0	0
$931$	−2.68848e57	−0.342758
$932$	− 1.06854e58i	− 1.33408i
$933$	1.04599e58i	1.27889i
$934$	−9.34709e57	−1.11921
$935$	0	0
$936$	2.07050e57	0.237791
$937$	− 6.32461e57i	− 0.711396i	−0.934601	−	0.355698i	$-0.884243\pi$
$937$	− 6.32461e57i	− 0.711396i	0.934601	−	0.355698i	$-0.115757\pi$
$938$	− 5.23305e57i	− 0.576500i
$939$	−1.29104e58	−1.39303
$940$	0	0
$941$	4.44546e57	0.460171	0.230085	−	0.973170i	$-0.426099\pi$
$941$	4.44546e57	0.460171	0.230085	+	0.973170i	$0.426099\pi$
$942$	− 1.06665e58i	− 1.08150i
$943$	− 3.48505e57i	− 0.346124i
$944$	−1.03212e58	−1.00410
$945$	0	0
$946$	1.06911e58	0.998036
$947$	− 2.02681e58i	− 1.85348i	−0.375705	−	0.926739i	$-0.622599\pi$
$947$	− 2.02681e58i	− 1.85348i	0.375705	−	0.926739i	$-0.377401\pi$
$948$	− 2.91832e58i	− 2.61439i
$949$	2.37588e57	0.208513
$950$	0	0
$951$	−1.01240e57	−0.0852772
$952$	3.18788e57i	0.263076i
$953$	2.18717e58i	1.76837i	0.467141	+	0.884183i	$0.345284\pi$
$953$	2.18717e58i	1.76837i	−0.467141	+	0.884183i	$0.654716\pi$
$954$	−8.15876e57	−0.646295
$955$	0	0
$956$	−1.93218e58	−1.46933
$957$	− 1.55091e57i	− 0.115559i
$958$	− 3.70037e57i	− 0.270158i
$959$	−1.79025e58	−1.28071
$960$	0	0
$961$	1.18923e58	0.816882
$962$	− 4.20970e57i	− 0.283359i
$963$	− 1.09841e58i	− 0.724521i
$964$	−1.31403e58	−0.849381
$965$	0	0
$966$	−3.62915e58	−2.25295
$967$	− 8.40382e57i	− 0.511282i	−0.966772	−	0.255641i	$-0.917713\pi$
$967$	− 8.40382e57i	− 0.511282i	0.966772	−	0.255641i	$-0.0822865\pi$
$968$	4.90053e57i	0.292195i
$969$	−2.22179e57	−0.129834
$970$	0	0
$971$	2.19465e58	1.23194	0.615972	−	0.787768i	$-0.288763\pi$
$971$	2.19465e58	1.23194	0.615972	+	0.787768i	$0.288763\pi$
$972$	− 3.17413e58i	− 1.74635i
$973$	− 2.53618e56i	− 0.0136767i
$974$	−3.34817e58	−1.76974
$975$	0	0
$976$	−1.53063e58	−0.777318
$977$	4.53213e57i	0.225610i	0.993617	+	0.112805i	$0.0359835\pi$
$977$	4.53213e57i	0.225610i	−0.993617	+	0.112805i	$0.964016\pi$
$978$	1.47055e58i	0.717581i
$979$	8.22257e57	0.393319
$980$	0	0
$981$	−1.60742e57	−0.0738897
$982$	5.96479e58i	2.68795i
$983$	3.96363e58i	1.75105i	0.483169	+	0.875527i	$0.339486\pi$
$983$	3.96363e58i	1.75105i	−0.483169	+	0.875527i	$0.660514\pi$
$984$	−6.63030e57	−0.287163
$985$	0	0
$986$	3.47622e57	0.144713
$987$	9.20807e58i	3.75824i
$988$	3.38066e57i	0.135282i
$989$	−2.78229e58	−1.09163
$990$	0	0
$991$	−1.58403e58	−0.597486	−0.298743	−	0.954334i	$-0.596567\pi$
$991$	−1.58403e58	−0.597486	−0.298743	+	0.954334i	$0.596567\pi$
$992$	− 5.15833e58i	− 1.90779i
$993$	3.69650e58i	1.34054i
$994$	1.34468e59	4.78171
$995$	0	0
$996$	2.27141e58	0.776675
$997$	6.66270e57i	0.223406i	0.993742	+	0.111703i	$0.0356305\pi$
$997$	6.66270e57i	0.223406i	−0.993742	+	0.111703i	$0.964369\pi$
$998$	− 5.28189e58i	− 1.73678i
$999$	3.04163e57	0.0980797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.40.b.a.24.6		6
5.2	odd	4		25.40.a.a.1.1		3
5.3	odd	4		1.40.a.a.1.3	✓	3
5.4	even	2	inner	25.40.b.a.24.1		6
15.8	even	4		9.40.a.b.1.1		3
20.3	even	4		16.40.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.40.a.a.1.3	✓	3	5.3	odd	4
9.40.a.b.1.1		3	15.8	even	4
16.40.a.c.1.1		3	20.3	even	4
25.40.a.a.1.1		3	5.2	odd	4
25.40.b.a.24.1		6	5.4	even	2	inner
25.40.b.a.24.6		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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.10652e6i q^{2} -2.98790e9i q^{3} -6.74631e11 q^{4} +3.30617e15 q^{6} -5.05826e16i q^{7} -1.38177e17i q^{8} -4.87501e18 q^{9} +O(q^{10})\)	\(q+1.10652e6i q^{2} -2.98790e9i q^{3} -6.74631e11 q^{4} +3.30617e15 q^{6} -5.05826e16i q^{7} -1.38177e17i q^{8} -4.87501e18 q^{9} +7.53597e19 q^{11} +2.01573e21i q^{12} -3.07373e21i q^{13} +5.59707e22 q^{14} -2.17987e23 q^{16} -4.56106e23i q^{17} -5.39430e24i q^{18} +1.63031e24 q^{19} -1.51136e26 q^{21} +8.33870e25i q^{22} -2.17009e26i q^{23} -4.12858e26 q^{24} +3.40114e27 q^{26} +2.45742e27i q^{27} +3.41246e28i q^{28} +6.88782e27 q^{29} +1.62636e29 q^{31} -3.17170e29i q^{32} -2.25168e29i q^{33} +5.04690e29 q^{34} +3.28883e30 q^{36} -1.23773e30i q^{37} +1.80397e30i q^{38} -9.18399e30 q^{39} +1.60595e31 q^{41} -1.67235e32i q^{42} -1.28211e32i q^{43} -5.08400e31 q^{44} +2.40125e32 q^{46} -6.09258e32i q^{47} +6.51324e32i q^{48} -1.64906e33 q^{49} -1.36280e33 q^{51} +2.07363e33i q^{52} -1.51248e33i q^{53} -2.71918e33 q^{54} -6.98933e33 q^{56} -4.87122e33i q^{57} +7.62152e33i q^{58} +4.73479e34 q^{59} +7.02166e34 q^{61} +1.79960e35i q^{62} +2.46591e35i q^{63} +2.31116e35 q^{64} +2.49152e35 q^{66} -9.34963e34i q^{67} +3.07703e35i q^{68} -6.48402e35 q^{69} +2.40247e36 q^{71} +6.73613e35i q^{72} +7.72964e35i q^{73} +1.36958e36 q^{74} -1.09986e36 q^{76} -3.81189e36i q^{77} -1.01623e37i q^{78} -1.44777e37 q^{79} -1.24137e37 q^{81} +1.77702e37i q^{82} -1.12684e37i q^{83} +1.01961e38 q^{84} +1.41868e38 q^{86} -2.05802e37i q^{87} -1.04129e37i q^{88} +1.09111e38 q^{89} -1.55477e38 q^{91} +1.46401e38i q^{92} -4.85940e38i q^{93} +6.74156e38 q^{94} -9.47674e38 q^{96} +7.84026e37i q^{97} -1.82471e39i q^{98} -3.67379e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 544157962368 q^{4} + 30\!\cdots\!92 q^{6}+ \cdots - 16\!\cdots\!82 q^{9}+O(q^{10}) \) 6 * q - 544157962368 * q^4 + 3059455695734592 * q^6 - 16611759804157354782 * q^9	\( 6 q - 544157962368 q^{4} + 30\!\cdots\!92 q^{6}+ \cdots - 21\!\cdots\!44 q^{99}+O(q^{100}) \) 6 * q - 544157962368 * q^4 + 3059455695734592 * q^6 - 16611759804157354782 * q^9 + 1335629936531503072152 * q^11 + 126127449131778606927744 * q^14 - 703461881120738114002944 * q^16 - 18455224370015395147037160 * q^19 - 380417317145185862942503488 * q^21 - 3345920537272389120092590080 * q^24 + 567557211609191164338405792 * q^26 + 4985364438517296554592888060 * q^29 + 612215343495645408819109492032 * q^31 + 3366785739059531738207598491424 * q^34 + 377368646146534808816114733696 * q^36 - 44504167036690804030291840119984 * q^39 + 4783848412475539012464959980572 * q^41 + 91155294598227820726749797113344 * q^44 - 48593082291062060955954043041408 * q^46 - 736475363444998124770546403282358 * q^49 + 1571302207630868682506432323828752 * q^51 - 15861629703958117392304207114335360 * q^54 - 12544233406497214477800860233359360 * q^56 + 112165362771242560634218577339274120 * q^59 + 79155351364252856663797379953667652 * q^61 + 338729813927122879167425723330199552 * q^64 - 574243521945218186753137588470510336 * q^66 - 3168350097391405603579685370419006784 * q^69 + 7698106421748136293400590482832435792 * q^71 + 10141414083395714373064024083405506784 * q^74 - 14725183421980568378050368272542302720 * q^76 - 27615544402432458579791347713389118240 * q^79 - 37596046292353241924597531317677774474 * q^81 + 144305151797281626583582527674355953664 * q^84 + 340024195160570221708545563575832966592 * q^86 - 410100079820219714273123706444152449020 * q^89 - 331050209996663685142398339776733965088 * q^91 + 2255945337070303769176521619142573278464 * q^94 - 2902189048981286701184128274058776936448 * q^96 - 2114036316237136283540072069426181873144 * q^99

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