LMFDB - Embedded newform 25.36.b.a.24.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,36,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, 36, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 36 $
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:	$193.987826584$
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} + 24844388x^{4} + 154310903773636x^{2} + 6999547445919666225 $ x^6 + 24844388x^4 + 154310903773636x^2 + 6999547445919666225
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.5
Root			$-213.765i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.36.b.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+165109. i q^{2} -3.45913e8i q^{3} +7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14i q^{7} +6.84517e15i q^{8} -6.96245e16 q^{9} +O(q^{10})$	\(q+165109. i q^{2} -3.45913e8i q^{3} +7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14i q^{7} +6.84517e15i q^{8} -6.96245e16 q^{9} -1.70842e18 q^{11} -2.45554e18i q^{12} -4.94986e19i q^{13} -2.06651e19 q^{14} -8.86291e20 q^{16} -1.32045e21i q^{17} -1.14956e22i q^{18} -3.94388e21 q^{19} +4.32945e22 q^{21} -2.82076e23i q^{22} -3.48881e23i q^{23} +2.36784e24 q^{24} +8.17268e24 q^{26} +6.77748e24i q^{27} +8.88473e23i q^{28} -3.21628e25 q^{29} +3.41044e25 q^{31} +8.88635e25i q^{32} +5.90965e26i q^{33} +2.18018e26 q^{34} -4.94244e26 q^{36} +4.03624e27i q^{37} -6.51171e26i q^{38} -1.71222e28 q^{39} +8.65857e27 q^{41} +7.14832e27i q^{42} +9.89389e26i q^{43} -1.21276e28 q^{44} +5.76034e28 q^{46} -1.95852e29i q^{47} +3.06580e29i q^{48} +3.63154e29 q^{49} -4.56760e29 q^{51} -3.51376e29i q^{52} -9.96909e29i q^{53} -1.11902e30 q^{54} -8.56741e29 q^{56} +1.36424e30i q^{57} -5.31037e30i q^{58} -3.91953e30 q^{59} +7.64909e29 q^{61} +5.63096e30i q^{62} -8.71420e30i q^{63} -4.51249e31 q^{64} -9.75738e31 q^{66} +1.64301e32i q^{67} -9.37346e30i q^{68} -1.20682e32 q^{69} +7.65930e31 q^{71} -4.76592e32i q^{72} -7.08063e32i q^{73} -6.66421e32 q^{74} -2.79964e31 q^{76} -2.13826e32i q^{77} -2.82704e33i q^{78} -2.34599e33 q^{79} -1.13900e33 q^{81} +1.42961e33i q^{82} +5.18971e33i q^{83} +3.07335e32 q^{84} -1.63357e32 q^{86} +1.11255e34i q^{87} -1.16944e34i q^{88} -1.44578e34 q^{89} +6.19525e33 q^{91} -2.47660e33i q^{92} -1.17972e34i q^{93} +3.23369e34 q^{94} +3.07391e34 q^{96} +2.87399e34i q^{97} +5.99600e34i q^{98} +1.18948e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 69682524288 q^{4} - 9573061128768 q^{6} - 30\!\cdots\!02 q^{9}+O(q^{10}) $ 6 * q - 69682524288 * q^4 - 9573061128768 * q^6 - 300183957752487102 * q^9	$ 6 q - 69682524288 q^{4} - 9573061128768 q^{6} - 30\!\cdots\!02 q^{9}+ \cdots - 60\!\cdots\!04 q^{99}+O(q^{100}) $ 6 * q - 69682524288 * q^4 - 9573061128768 * q^6 - 300183957752487102 * q^9 - 2315890857099974088 * q^11 - 271818686510142877056 * q^14 + 4311388034571636842496 * q^16 + 64606792485869241101880 * q^19 + 444244917507334797615552 * q^21 + 7521458029847229416509440 * q^24 + 8568963719869816338936672 * q^26 + 76920798287968875196496220 * q^29 + 207463189127449379460059712 * q^31 + 1108273470697007566053414624 * q^34 - 12104409432261180621062968704 * q^36 - 37223963908125755485412775024 * q^39 + 47045973169065536258074174812 * q^41 + 161909641397410604027847796224 * q^44 + 620243394040769877901011779712 * q^46 + 1190178076169851463244074901642 * q^49 - 3606088149701589454704519855408 * q^51 - 8848462809538007800988211803520 * q^54 + 11341840434826113134505180487680 * q^56 - 8741057166185293399690487262360 * q^59 + 47074156553032057894438160976612 * q^61 - 187020561473268641262186528768 * q^64 - 151280835682131675595281896084736 * q^66 + 651966424792548500617306631868096 * q^69 + 697549204590716421077242324013712 * q^71 - 4212674766353133731580090791579616 * q^74 - 5458148575336648395699070897789440 * q^76 + 852425725182123323803473261748320 * q^79 + 3734442301593956911190817869446326 * q^81 + 26049577017381684485650485151739904 * q^84 + 296981501312941625080810196380992 * q^86 - 61167181692387502670411984836068540 * q^89 + 2006783405038974725132244313994592 * q^91 - 38152386540837025150844554284001536 * q^94 - 64784055731908851933994586445447168 * q^96 - 60577372683195463856883721504068504 * 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 $

$2$	165109.i	0.890730i	0.895349	+	0.445365i	$0.146926\pi$
$2$	165109.i	0.890730i	−0.895349	+	0.445365i	$0.853074\pi$
$3$	− 3.45913e8i	− 1.54648i	−0.634111	−	0.773242i	$-0.718634\pi$
$3$	− 3.45913e8i	− 1.54648i	0.634111	−	0.773242i	$-0.281366\pi$
$4$	7.09870e9	0.206599
$5$	0	0
$5$	0	0
$6$	5.71135e13	1.37750
$7$	1.25160e14i	0.203353i	0.994818	+	0.101676i	$0.0324206\pi$
$7$	1.25160e14i	0.203353i	−0.994818	+	0.101676i	$0.967579\pi$
$8$	6.84517e15i	1.07475i
$9$	−6.96245e16	−1.39161
$10$	0	0
$11$	−1.70842e18	−1.01911	−0.509557	−	0.860437i	$-0.670191\pi$
$11$	−1.70842e18	−1.01911	−0.509557	+	0.860437i	$0.670191\pi$
$12$	− 2.45554e18i	− 0.319503i
$13$	− 4.94986e19i	− 1.58703i	−0.608552	−	0.793514i	$-0.708249\pi$
$13$	− 4.94986e19i	− 1.58703i	0.608552	−	0.793514i	$-0.291751\pi$
$14$	−2.06651e19	−0.181132
$15$	0	0
$16$	−8.86291e20	−0.750717
$17$	− 1.32045e21i	− 0.387137i	−0.981087	−	0.193569i	$-0.937994\pi$
$17$	− 1.32045e21i	− 0.387137i	0.981087	−	0.193569i	$-0.0620062\pi$
$18$	− 1.14956e22i	− 1.23955i
$19$	−3.94388e21	−0.165096	−0.0825479	−	0.996587i	$-0.526306\pi$
$19$	−3.94388e21	−0.165096	−0.0825479	+	0.996587i	$0.526306\pi$
$20$	0	0
$21$	4.32945e22	0.314482
$22$	− 2.82076e23i	− 0.907756i
$23$	− 3.48881e23i	− 0.515750i	−0.966178	−	0.257875i	$-0.916978\pi$
$23$	− 3.48881e23i	− 0.515750i	0.966178	−	0.257875i	$-0.0830224\pi$
$24$	2.36784e24	1.66209
$25$	0	0
$26$	8.17268e24	1.41361
$27$	6.77748e24i	0.605623i
$28$	8.88473e23i	0.0420125i
$29$	−3.21628e25	−0.822979	−0.411489	−	0.911415i	$-0.634991\pi$
$29$	−3.21628e25	−0.822979	−0.411489	+	0.911415i	$0.634991\pi$
$30$	0	0
$31$	3.41044e25	0.271632	0.135816	−	0.990734i	$-0.456634\pi$
$31$	3.41044e25	0.271632	0.135816	+	0.990734i	$0.456634\pi$
$32$	8.88635e25i	0.406068i
$33$	5.90965e26i	1.57604i
$34$	2.18018e26	0.344835
$35$	0	0
$36$	−4.94244e26	−0.287506
$37$	4.03624e27i	1.45361i	0.686845	+	0.726804i	$0.258995\pi$
$37$	4.03624e27i	1.45361i	−0.686845	+	0.726804i	$0.741005\pi$
$38$	− 6.51171e26i	− 0.147056i
$39$	−1.71222e28	−2.45431
$40$	0	0
$41$	8.65857e27	0.517283	0.258642	−	0.965973i	$-0.416725\pi$
$41$	8.65857e27	0.517283	0.258642	+	0.965973i	$0.416725\pi$
$42$	7.14832e27i	0.280118i
$43$	9.89389e26i	0.0256844i	0.999918	+	0.0128422i	$0.00408791\pi$
$43$	9.89389e26i	0.0256844i	−0.999918	+	0.0128422i	$0.995912\pi$
$44$	−1.21276e28	−0.210548
$45$	0	0
$46$	5.76034e28	0.459395
$47$	− 1.95852e29i	− 1.07205i	−0.844202	−	0.536025i	$-0.819925\pi$
$47$	− 1.95852e29i	− 1.07205i	0.844202	−	0.536025i	$-0.180075\pi$
$48$	3.06580e29i	1.16097i
$49$	3.63154e29	0.958648
$50$	0	0
$51$	−4.56760e29	−0.598702
$52$	− 3.51376e29i	− 0.327879i
$53$	− 9.96909e29i	− 0.666543i	−0.942831	−	0.333271i	$-0.891847\pi$
$53$	− 9.96909e29i	− 0.666543i	0.942831	−	0.333271i	$-0.108153\pi$
$54$	−1.11902e30	−0.539447
$55$	0	0
$56$	−8.56741e29	−0.218554
$57$	1.36424e30i	0.255318i
$58$	− 5.31037e30i	− 0.733052i
$59$	−3.91953e30	−0.401166	−0.200583	−	0.979677i	$-0.564284\pi$
$59$	−3.91953e30	−0.401166	−0.200583	+	0.979677i	$0.564284\pi$
$60$	0	0
$61$	7.64909e29	0.0436855	0.0218428	−	0.999761i	$-0.493047\pi$
$61$	7.64909e29	0.0436855	0.0218428	+	0.999761i	$0.493047\pi$
$62$	5.63096e30i	0.241951i
$63$	− 8.71420e30i	− 0.282988i
$64$	−4.51249e31	−1.11241
$65$	0	0
$66$	−9.75738e31	−1.40383
$67$	1.64301e32i	1.81690i	0.417992	+	0.908451i	$0.362734\pi$
$67$	1.64301e32i	1.81690i	−0.417992	+	0.908451i	$0.637266\pi$
$68$	− 9.37346e30i	− 0.0799823i
$69$	−1.20682e32	−0.797600
$70$	0	0
$71$	7.65930e31	0.307021	0.153510	−	0.988147i	$-0.450942\pi$
$71$	7.65930e31	0.307021	0.153510	+	0.988147i	$0.450942\pi$
$72$	− 4.76592e32i	− 1.49564i
$73$	− 7.08063e32i	− 1.74551i	−0.488160	−	0.872754i	$-0.662332\pi$
$73$	− 7.08063e32i	− 1.74551i	0.488160	−	0.872754i	$-0.337668\pi$
$74$	−6.66421e32	−1.29477
$75$	0	0
$76$	−2.79964e31	−0.0341087
$77$	− 2.13826e32i	− 0.207239i
$78$	− 2.82704e33i	− 2.18613i
$79$	−2.34599e33	−1.45162	−0.725809	−	0.687896i	$-0.758534\pi$
$79$	−2.34599e33	−1.45162	−0.725809	+	0.687896i	$0.758534\pi$
$80$	0	0
$81$	−1.13900e33	−0.455027
$82$	1.42961e33i	0.460760i
$83$	5.18971e33i	1.35293i	0.736473	+	0.676467i	$0.236490\pi$
$83$	5.18971e33i	1.35293i	−0.736473	+	0.676467i	$0.763510\pi$
$84$	3.07335e32	0.0649717
$85$	0	0
$86$	−1.63357e32	−0.0228779
$87$	1.11255e34i	1.27272i
$88$	− 1.16944e34i	− 1.09530i
$89$	−1.44578e34	−1.11116	−0.555582	−	0.831461i	$-0.687505\pi$
$89$	−1.44578e34	−1.11116	−0.555582	+	0.831461i	$0.687505\pi$
$90$	0	0
$91$	6.19525e33	0.322726
$92$	− 2.47660e33i	− 0.106554i
$93$	− 1.17972e34i	− 0.420075i
$94$	3.23369e34	0.954907
$95$	0	0
$96$	3.07391e34	0.627978
$97$	2.87399e34i	0.489756i	0.969554	+	0.244878i	$0.0787479\pi$
$97$	2.87399e34i	0.489756i	−0.969554	+	0.244878i	$0.921252\pi$
$98$	5.99600e34i	0.853897i
$99$	1.18948e35	1.41821
$100$	0	0
$101$	1.13198e35	0.951079	0.475539	−	0.879694i	$-0.342253\pi$
$101$	1.13198e35	0.951079	0.475539	+	0.879694i	$0.342253\pi$
$102$	− 7.54153e34i	− 0.533282i
$103$	2.53635e35i	1.51202i	0.654559	+	0.756011i	$0.272855\pi$
$103$	2.53635e35i	1.51202i	−0.654559	+	0.756011i	$0.727145\pi$
$104$	3.38826e35	1.70567
$105$	0	0
$106$	1.64599e35	0.593710
$107$	3.63939e35i	1.11381i	0.830575	+	0.556907i	$0.188012\pi$
$107$	3.63939e35i	1.11381i	−0.830575	+	0.556907i	$0.811988\pi$
$108$	4.81113e34i	0.125121i
$109$	4.65371e34	0.103000	0.0514998	−	0.998673i	$-0.483600\pi$
$109$	4.65371e34	0.103000	0.0514998	+	0.998673i	$0.483600\pi$
$110$	0	0
$111$	1.39619e36	2.24798
$112$	− 1.10928e35i	− 0.152660i
$113$	− 2.18346e35i	− 0.257201i	−0.991696	−	0.128601i	$-0.958951\pi$
$113$	− 2.18346e35i	− 0.257201i	0.991696	−	0.128601i	$-0.0410485\pi$
$114$	−2.25249e35	−0.227419
$115$	0	0
$116$	−2.28314e35	−0.170027
$117$	3.44632e36i	2.20853i
$118$	− 6.47150e35i	− 0.357330i
$119$	1.65267e35	0.0787254
$120$	0	0
$121$	1.08456e35	0.0385932
$122$	1.26293e35i	0.0389120i
$123$	− 2.99511e36i	− 0.799970i
$124$	2.42097e35	0.0561191
$125$	0	0
$126$	1.43880e36	0.252066
$127$	− 4.19558e36i	− 0.640070i	−0.947406	−	0.320035i	$-0.896305\pi$
$127$	− 4.19558e36i	− 0.640070i	0.947406	−	0.320035i	$-0.103695\pi$
$128$	− 4.39721e36i	− 0.584793i
$129$	3.42243e35	0.0397205
$130$	0	0
$131$	2.40631e36	0.213355	0.106678	−	0.994294i	$-0.465979\pi$
$131$	2.40631e36	0.213355	0.106678	+	0.994294i	$0.465979\pi$
$132$	4.19509e36i	0.325610i
$133$	− 4.93616e35i	− 0.0335727i
$134$	−2.71276e37	−1.61837
$135$	0	0
$136$	9.03869e36	0.416078
$137$	2.14718e37i	0.869477i	0.900557	+	0.434739i	$0.143159\pi$
$137$	2.14718e37i	0.869477i	−0.900557	+	0.434739i	$0.856841\pi$
$138$	− 1.99258e37i	− 0.710446i
$139$	−2.63209e37	−0.827068	−0.413534	−	0.910489i	$-0.635706\pi$
$139$	−2.63209e37	−0.827068	−0.413534	+	0.910489i	$0.635706\pi$
$140$	0	0
$141$	−6.77477e37	−1.65791
$142$	1.26462e37i	0.273473i
$143$	8.45645e37i	1.61736i
$144$	6.17076e37	1.04471
$145$	0	0
$146$	1.16908e38	1.55478
$147$	− 1.25620e38i	− 1.48253i
$148$	2.86521e37i	0.300314i
$149$	1.74389e38	1.62465	0.812324	−	0.583206i	$-0.198202\pi$
$149$	1.74389e38	1.62465	0.812324	+	0.583206i	$0.198202\pi$
$150$	0	0
$151$	−1.40947e38	−1.03982	−0.519912	−	0.854220i	$-0.674035\pi$
$151$	−1.40947e38	−1.03982	−0.519912	+	0.854220i	$0.674035\pi$
$152$	− 2.69965e37i	− 0.177437i
$153$	9.19355e37i	0.538745i
$154$	3.53046e37	0.184595
$155$	0	0
$156$	−1.21546e38	−0.507059
$157$	− 1.49924e38i	− 0.559277i	−0.960105	−	0.279639i	$-0.909785\pi$
$157$	− 1.49924e38i	− 0.559277i	0.960105	−	0.279639i	$-0.0902147\pi$
$158$	− 3.87345e38i	− 1.29300i
$159$	−3.44844e38	−1.03080
$160$	0	0
$161$	4.36659e37	0.104879
$162$	− 1.88060e38i	− 0.405306i
$163$	8.60787e38i	1.66576i	0.553453	+	0.832880i	$0.313310\pi$
$163$	8.60787e38i	1.66576i	−0.553453	+	0.832880i	$0.686690\pi$
$164$	6.14646e37	0.106870
$165$	0	0
$166$	−8.56869e38	−1.20510
$167$	9.23344e38i	1.16903i	0.811383	+	0.584515i	$0.198715\pi$
$167$	9.23344e38i	1.16903i	−0.811383	+	0.584515i	$0.801285\pi$
$168$	2.96358e38i	0.337991i
$169$	−1.47733e39	−1.51866
$170$	0	0
$171$	2.74591e38	0.229749
$172$	7.02337e36i	0.00530638i
$173$	− 1.33161e39i	− 0.909012i	−0.890744	−	0.454506i	$-0.849816\pi$
$173$	− 1.33161e39i	− 0.909012i	0.890744	−	0.454506i	$-0.150184\pi$
$174$	−1.83693e39	−1.13365
$175$	0	0
$176$	1.51416e39	0.765066
$177$	1.35582e39i	0.620396i
$178$	− 2.38712e39i	− 0.989748i
$179$	−6.27202e38	−0.235765	−0.117883	−	0.993028i	$-0.537611\pi$
$179$	−6.27202e38	−0.235765	−0.117883	+	0.993028i	$0.537611\pi$
$180$	0	0
$181$	−2.39965e39	−0.742629	−0.371315	−	0.928507i	$-0.621093\pi$
$181$	−2.39965e39	−0.742629	−0.371315	+	0.928507i	$0.621093\pi$
$182$	1.02289e39i	0.287462i
$183$	− 2.64592e38i	− 0.0675590i
$184$	2.38815e39	0.554305
$185$	0	0
$186$	1.94782e39	0.374174
$187$	2.25588e39i	0.394537i
$188$	− 1.39029e39i	− 0.221485i
$189$	−8.48269e38	−0.123155
$190$	0	0
$191$	8.14518e39	0.983596	0.491798	−	0.870709i	$-0.336340\pi$
$191$	8.14518e39	0.983596	0.491798	+	0.870709i	$0.336340\pi$
$192$	1.56093e40i	1.72033i
$193$	1.38549e40i	1.39428i	0.716936	+	0.697139i	$0.245544\pi$
$193$	1.38549e40i	1.39428i	−0.716936	+	0.697139i	$0.754456\pi$
$194$	−4.74522e39	−0.436240
$195$	0	0
$196$	2.57792e39	0.198056
$197$	1.15539e40i	0.812026i	0.913867	+	0.406013i	$0.133081\pi$
$197$	1.15539e40i	0.812026i	−0.913867	+	0.406013i	$0.866919\pi$
$198$	1.96394e40i	1.26324i
$199$	4.76691e39	0.280742	0.140371	−	0.990099i	$-0.455170\pi$
$199$	4.76691e39	0.280742	0.140371	+	0.990099i	$0.455170\pi$
$200$	0	0
$201$	5.68340e40	2.80981
$202$	1.86901e40i	0.847155i
$203$	− 4.02549e39i	− 0.167355i
$204$	−3.24241e39	−0.123691
$205$	0	0
$206$	−4.18775e40	−1.34680
$207$	2.42906e40i	0.717725i
$208$	4.38702e40i	1.19141i
$209$	6.73781e39	0.168251
$210$	0	0
$211$	−1.87354e40	−0.396022	−0.198011	−	0.980200i	$-0.563448\pi$
$211$	−1.87354e40	−0.396022	−0.198011	+	0.980200i	$0.563448\pi$
$212$	− 7.07676e39i	− 0.137707i
$213$	− 2.64945e40i	− 0.474803i
$214$	−6.00896e40	−0.992107
$215$	0	0
$216$	−4.63930e40	−0.650896
$217$	4.26851e39i	0.0552371i
$218$	7.68370e39i	0.0917448i
$219$	−2.44929e41	−2.69940
$220$	0	0
$221$	−6.53603e40	−0.614398
$222$	2.30524e41i	2.00234i
$223$	− 7.12100e40i	− 0.571750i	−0.958267	−	0.285875i	$-0.907716\pi$
$223$	− 7.12100e40i	− 0.571750i	0.958267	−	0.285875i	$-0.0922841\pi$
$224$	−1.11222e40	−0.0825750
$225$	0	0
$226$	3.60510e40	0.229097
$227$	1.04005e41i	0.611787i	0.952066	+	0.305893i	$0.0989551\pi$
$227$	1.04005e41i	0.611787i	−0.952066	+	0.305893i	$0.901045\pi$
$228$	9.68434e39i	0.0527485i
$229$	−1.82859e41	−0.922564	−0.461282	−	0.887254i	$-0.652610\pi$
$229$	−1.82859e41	−0.922564	−0.461282	+	0.887254i	$0.652610\pi$
$230$	0	0
$231$	−7.39652e40	−0.320493
$232$	− 2.20160e41i	− 0.884501i
$233$	1.57847e41i	0.588177i	0.955778	+	0.294088i	$0.0950160\pi$
$233$	1.57847e41i	0.588177i	−0.955778	+	0.294088i	$0.904984\pi$
$234$	−5.69019e41	−1.96720
$235$	0	0
$236$	−2.78236e40	−0.0828806
$237$	8.11510e41i	2.24490i
$238$	2.72871e40i	0.0701231i
$239$	−5.00984e41	−1.19636	−0.598178	−	0.801363i	$-0.704108\pi$
$239$	−5.00984e41	−1.19636	−0.598178	+	0.801363i	$0.704108\pi$
$240$	0	0
$241$	−3.33164e41	−0.687638	−0.343819	−	0.939036i	$-0.611721\pi$
$241$	−3.33164e41	−0.687638	−0.343819	+	0.939036i	$0.611721\pi$
$242$	1.79072e40i	0.0343762i
$243$	7.33084e41i	1.30931i
$244$	5.42986e39	0.00902540
$245$	0	0
$246$	4.94521e41	0.712558
$247$	1.95217e41i	0.262011i
$248$	2.33451e41i	0.291938i
$249$	1.79519e42	2.09229
$250$	0	0
$251$	1.52760e42	1.54782	0.773909	−	0.633297i	$-0.218299\pi$
$251$	1.52760e42	1.54782	0.773909	+	0.633297i	$0.218299\pi$
$252$	− 6.18595e40i	− 0.0584652i
$253$	5.96035e41i	0.525608i
$254$	6.92730e41	0.570130
$255$	0	0
$256$	−8.24460e41	−0.591521
$257$	2.72482e42i	1.82603i	0.407925	+	0.913016i	$0.366253\pi$
$257$	2.72482e42i	1.82603i	−0.407925	+	0.913016i	$0.633747\pi$
$258$	5.65074e40i	0.0353802i
$259$	−5.05176e41	−0.295595
$260$	0	0
$261$	2.23932e42	1.14527
$262$	3.97303e41i	0.190042i
$263$	4.22055e40i	0.0188861i	0.999955	+	0.00944307i	$0.00300587\pi$
$263$	4.22055e40i	0.0188861i	−0.999955	+	0.00944307i	$0.996994\pi$
$264$	−4.04526e42	−1.69386
$265$	0	0
$266$	8.15005e40	0.0299042
$267$	5.00116e42i	1.71840i
$268$	1.16632e42i	0.375371i
$269$	1.30618e42	0.393858	0.196929	−	0.980418i	$-0.436903\pi$
$269$	1.30618e42	0.393858	0.196929	+	0.980418i	$0.436903\pi$
$270$	0	0
$271$	−4.11918e41	−0.109106	−0.0545529	−	0.998511i	$-0.517373\pi$
$271$	−4.11918e41	−0.109106	−0.0545529	+	0.998511i	$0.517373\pi$
$272$	1.17030e42i	0.290631i
$273$	− 2.14302e42i	− 0.499091i
$274$	−3.54519e42	−0.774470
$275$	0	0
$276$	−8.56689e41	−0.164784
$277$	− 7.38232e42i	− 1.33290i	−0.745551	−	0.666449i	$-0.767813\pi$
$277$	− 7.38232e42i	− 1.33290i	0.745551	−	0.666449i	$-0.232187\pi$
$278$	− 4.34582e42i	− 0.736694i
$279$	−2.37451e42	−0.378007
$280$	0	0
$281$	4.08223e42	0.573505	0.286752	−	0.958005i	$-0.407424\pi$
$281$	4.08223e42	0.573505	0.286752	+	0.958005i	$0.407424\pi$
$282$	− 1.11858e43i	− 1.47675i
$283$	− 1.06503e43i	− 1.32159i	−0.750565	−	0.660796i	$-0.770219\pi$
$283$	− 1.06503e43i	− 1.32159i	0.750565	−	0.660796i	$-0.229781\pi$
$284$	5.43711e41	0.0634303
$285$	0	0
$286$	−1.39624e43	−1.44063
$287$	1.08371e42i	0.105191i
$288$	− 6.18708e42i	− 0.565089i
$289$	9.88997e42	0.850125
$290$	0	0
$291$	9.94151e42	0.757399
$292$	− 5.02633e42i	− 0.360621i
$293$	1.90474e43i	1.28722i	0.765353	+	0.643610i	$0.222564\pi$
$293$	1.90474e43i	1.28722i	−0.765353	+	0.643610i	$0.777436\pi$
$294$	2.07410e43	1.32054
$295$	0	0
$296$	−2.76288e43	−1.56227
$297$	− 1.15788e43i	− 0.617199i
$298$	2.87932e43i	1.44712i
$299$	−1.72691e43	−0.818510
$300$	0	0
$301$	−1.23832e41	−0.00522298
$302$	− 2.32717e43i	− 0.926203i
$303$	− 3.91569e43i	− 1.47083i
$304$	3.49543e42	0.123940
$305$	0	0
$306$	−1.51794e43	−0.479877
$307$	1.39752e43i	0.417288i	0.977992	+	0.208644i	$0.0669050\pi$
$307$	1.39752e43i	0.417288i	−0.977992	+	0.208644i	$0.933095\pi$
$308$	− 1.51789e42i	− 0.0428156i
$309$	8.77359e43	2.33832
$310$	0	0
$311$	2.22377e43	0.529399	0.264700	−	0.964331i	$-0.414727\pi$
$311$	2.22377e43	0.529399	0.264700	+	0.964331i	$0.414727\pi$
$312$	− 1.17205e44i	− 2.63778i
$313$	3.63171e43i	0.772833i	0.922324	+	0.386417i	$0.126287\pi$
$313$	3.63171e43i	0.772833i	−0.922324	+	0.386417i	$0.873713\pi$
$314$	2.47538e43	0.498165
$315$	0	0
$316$	−1.66535e43	−0.299903
$317$	− 5.29385e43i	− 0.902058i	−0.892509	−	0.451029i	$-0.851057\pi$
$317$	− 5.29385e43i	− 0.902058i	0.892509	−	0.451029i	$-0.148943\pi$
$318$	− 5.69370e43i	− 0.918163i
$319$	5.49476e43	0.838709
$320$	0	0
$321$	1.25891e44	1.72249
$322$	7.20964e42i	0.0934191i
$323$	5.20769e42i	0.0639147i
$324$	−8.08544e42	−0.0940083
$325$	0	0
$326$	−1.42124e44	−1.48374
$327$	− 1.60978e43i	− 0.159287i
$328$	5.92693e43i	0.555953i
$329$	2.45128e43	0.218004
$330$	0	0
$331$	6.25551e43	0.500349	0.250174	−	0.968201i	$-0.419512\pi$
$331$	6.25551e43	0.500349	0.250174	+	0.968201i	$0.419512\pi$
$332$	3.68402e43i	0.279515i
$333$	− 2.81022e44i	− 2.02286i
$334$	−1.52453e44	−1.04129
$335$	0	0
$336$	−3.83715e43	−0.236087
$337$	1.04185e44i	0.608529i	0.952588	+	0.304264i	$0.0984106\pi$
$337$	1.04185e44i	0.608529i	−0.952588	+	0.304264i	$0.901589\pi$
$338$	− 2.43920e44i	− 1.35271i
$339$	−7.55289e43	−0.397757
$340$	0	0
$341$	−5.82647e43	−0.276824
$342$	4.53375e43i	0.204645i
$343$	9.28652e43i	0.398296i
$344$	−6.77253e42	−0.0276044
$345$	0	0
$346$	2.19861e44	0.809685
$347$	3.07657e44i	1.07721i	0.842557	+	0.538606i	$0.181049\pi$
$347$	3.07657e44i	1.07721i	−0.842557	+	0.538606i	$0.818951\pi$
$348$	7.89769e43i	0.262944i
$349$	2.62767e44	0.832005	0.416003	−	0.909363i	$-0.363431\pi$
$349$	2.62767e44	0.832005	0.416003	+	0.909363i	$0.363431\pi$
$350$	0	0
$351$	3.35476e44	0.961140
$352$	− 1.51816e44i	− 0.413830i
$353$	7.06671e44i	1.83299i	0.400048	+	0.916494i	$0.368994\pi$
$353$	7.06671e44i	1.83299i	−0.400048	+	0.916494i	$0.631006\pi$
$354$	−2.23858e44	−0.552606
$355$	0	0
$356$	−1.02632e44	−0.229566
$357$	− 5.71681e43i	− 0.121748i
$358$	− 1.03557e44i	− 0.210003i
$359$	5.35788e44	1.03476	0.517380	−	0.855756i	$-0.326907\pi$
$359$	5.35788e44	1.03476	0.517380	+	0.855756i	$0.326907\pi$
$360$	0	0
$361$	−5.55104e44	−0.972743
$362$	− 3.96204e44i	− 0.661483i
$363$	− 3.75165e43i	− 0.0596838i
$364$	4.39782e43	0.0666750
$365$	0	0
$366$	4.36866e43	0.0601768
$367$	3.00056e44i	0.394045i	0.980399	+	0.197022i	$0.0631272\pi$
$367$	3.00056e44i	0.394045i	−0.980399	+	0.197022i	$0.936873\pi$
$368$	3.09210e44i	0.387183i
$369$	−6.02849e44	−0.719858
$370$	0	0
$371$	1.24773e44	0.135543
$372$	− 8.37447e43i	− 0.0867872i
$373$	1.08201e45i	1.06986i	0.844895	+	0.534932i	$0.179663\pi$
$373$	1.08201e45i	1.06986i	−0.844895	+	0.534932i	$0.820337\pi$
$374$	−3.72466e44	−0.351426
$375$	0	0
$376$	1.34064e45	1.15219
$377$	1.59201e45i	1.30609i
$378$	− 1.40057e44i	− 0.109698i
$379$	−1.21847e45	−0.911229	−0.455614	−	0.890177i	$-0.650580\pi$
$379$	−1.21847e45	−0.911229	−0.455614	+	0.890177i	$0.650580\pi$
$380$	0	0
$381$	−1.45131e45	−0.989858
$382$	1.34484e45i	0.876119i
$383$	− 9.53201e43i	− 0.0593207i	−0.999560	−	0.0296603i	$-0.990557\pi$
$383$	− 9.53201e43i	− 0.0593207i	0.999560	−	0.0296603i	$-0.00944256\pi$
$384$	−1.52105e45	−0.904373
$385$	0	0
$386$	−2.28757e45	−1.24193
$387$	− 6.88857e43i	− 0.0357427i
$388$	2.04016e44i	0.101183i
$389$	−1.90493e45	−0.903152	−0.451576	−	0.892233i	$-0.649138\pi$
$389$	−1.90493e45	−0.903152	−0.451576	+	0.892233i	$0.649138\pi$
$390$	0	0
$391$	−4.60678e44	−0.199666
$392$	2.48585e45i	1.03031i
$393$	− 8.32373e44i	− 0.329950i
$394$	−1.90766e45	−0.723296
$395$	0	0
$396$	8.44376e44	0.293002
$397$	− 3.96399e45i	− 1.31613i	−0.752961	−	0.658065i	$-0.771375\pi$
$397$	− 3.96399e45i	− 1.31613i	0.752961	−	0.658065i	$-0.228625\pi$
$398$	7.87060e44i	0.250066i
$399$	−1.70748e44	−0.0519196
$400$	0	0
$401$	−5.53039e44	−0.154074	−0.0770369	−	0.997028i	$-0.524546\pi$
$401$	−5.53039e44	−0.154074	−0.0770369	+	0.997028i	$0.524546\pi$
$402$	9.38381e45i	2.50278i
$403$	− 1.68812e45i	− 0.431088i
$404$	8.03562e44	0.196492
$405$	0	0
$406$	6.64646e44	0.149068
$407$	− 6.89560e45i	− 1.48139i
$408$	− 3.12660e45i	− 0.643457i
$409$	−3.35495e45	−0.661498	−0.330749	−	0.943719i	$-0.607301\pi$
$409$	−3.35495e45	−0.661498	−0.330749	+	0.943719i	$0.607301\pi$
$410$	0	0
$411$	7.42738e45	1.34463
$412$	1.80048e45i	0.312383i
$413$	− 4.90568e44i	− 0.0815781i
$414$	−4.01061e45	−0.639299
$415$	0	0
$416$	4.39862e45	0.644441
$417$	9.10474e45i	1.27905i
$418$	1.11247e45i	0.149867i
$419$	7.69138e45	0.993708	0.496854	−	0.867834i	$-0.334488\pi$
$419$	7.69138e45	0.993708	0.496854	+	0.867834i	$0.334488\pi$
$420$	0	0
$421$	−2.77229e45	−0.329535	−0.164767	−	0.986332i	$-0.552687\pi$
$421$	−2.77229e45	−0.329535	−0.164767	+	0.986332i	$0.552687\pi$
$422$	− 3.09338e45i	− 0.352749i
$423$	1.36361e46i	1.49188i
$424$	6.82401e45	0.716370
$425$	0	0
$426$	4.37449e45	0.422921
$427$	9.57360e43i	0.00888357i
$428$	2.58349e45i	0.230113i
$429$	2.92520e46	2.50122
$430$	0	0
$431$	6.18484e45	0.487502	0.243751	−	0.969838i	$-0.421622\pi$
$431$	6.18484e45	0.487502	0.243751	+	0.969838i	$0.421622\pi$
$432$	− 6.00681e45i	− 0.454651i
$433$	2.21783e46i	1.61209i	0.591852	+	0.806047i	$0.298397\pi$
$433$	2.21783e46i	1.61209i	−0.591852	+	0.806047i	$0.701603\pi$
$434$	−7.04770e44	−0.0492014
$435$	0	0
$436$	3.30353e44	0.0212796
$437$	1.37594e45i	0.0851482i
$438$	− 4.04399e46i	− 2.40444i
$439$	−1.91766e45	−0.109557	−0.0547787	−	0.998499i	$-0.517445\pi$
$439$	−1.91766e45	−0.109557	−0.0547787	+	0.998499i	$0.517445\pi$
$440$	0	0
$441$	−2.52844e46	−1.33407
$442$	− 1.07916e46i	− 0.547263i
$443$	− 3.00864e46i	− 1.46658i	−0.679916	−	0.733290i	$-0.737984\pi$
$443$	− 3.00864e46i	− 1.46658i	0.679916	−	0.733290i	$-0.262016\pi$
$444$	9.91114e45	0.464431
$445$	0	0
$446$	1.17574e46	0.509275
$447$	− 6.03235e46i	− 2.51249i
$448$	− 5.64783e45i	− 0.226212i
$449$	−5.68788e45	−0.219099	−0.109549	−	0.993981i	$-0.534941\pi$
$449$	−5.68788e45	−0.219099	−0.109549	+	0.993981i	$0.534941\pi$
$450$	0	0
$451$	−1.47925e46	−0.527171
$452$	− 1.54997e45i	− 0.0531376i
$453$	4.87555e46i	1.60807i
$454$	−1.71721e46	−0.544937
$455$	0	0
$456$	−9.33846e45	−0.274404
$457$	− 4.67626e46i	− 1.32241i	−0.750206	−	0.661204i	$-0.770046\pi$
$457$	− 4.67626e46i	− 1.32241i	0.750206	−	0.661204i	$-0.229954\pi$
$458$	− 3.01918e46i	− 0.821755i
$459$	8.94930e45	0.234459
$460$	0	0
$461$	−3.72978e46	−0.905560	−0.452780	−	0.891622i	$-0.649568\pi$
$461$	−3.72978e46	−0.905560	−0.452780	+	0.891622i	$0.649568\pi$
$462$	− 1.22123e46i	− 0.285472i
$463$	− 3.67649e46i	− 0.827497i	−0.910391	−	0.413748i	$-0.864219\pi$
$463$	− 3.67649e46i	− 0.827497i	0.910391	−	0.413748i	$-0.135781\pi$
$464$	2.85056e46	0.617825
$465$	0	0
$466$	−2.60620e46	−0.523907
$467$	2.37743e46i	0.460323i	0.973152	+	0.230161i	$0.0739254\pi$
$467$	2.37743e46i	0.460323i	−0.973152	+	0.230161i	$0.926075\pi$
$468$	2.44644e46i	0.456280i
$469$	−2.05639e46	−0.369472
$470$	0	0
$471$	−5.18607e46	−0.864914
$472$	− 2.68298e46i	− 0.431155i
$473$	− 1.69029e45i	− 0.0261753i
$474$	−1.33988e47	−1.99960
$475$	0	0
$476$	1.17318e45	0.0162646
$477$	6.94094e46i	0.927569i
$478$	− 8.27170e46i	− 1.06563i
$479$	8.80315e46	1.09337	0.546684	−	0.837339i	$-0.315890\pi$
$479$	8.80315e46	1.09337	0.546684	+	0.837339i	$0.315890\pi$
$480$	0	0
$481$	1.99788e47	2.30691
$482$	− 5.50084e46i	− 0.612500i
$483$	− 1.51046e46i	− 0.162194i
$484$	7.69900e44	0.00797334
$485$	0	0
$486$	−1.21039e47	−1.16625
$487$	− 7.13443e46i	− 0.663136i	−0.943431	−	0.331568i	$-0.892422\pi$
$487$	− 7.13443e46i	− 0.663136i	0.943431	−	0.331568i	$-0.107578\pi$
$488$	5.23593e45i	0.0469512i
$489$	2.97758e47	2.57607
$490$	0	0
$491$	8.49115e46	0.683975	0.341988	−	0.939704i	$-0.388900\pi$
$491$	8.49115e46	0.683975	0.341988	+	0.939704i	$0.388900\pi$
$492$	− 2.12614e46i	− 0.165273i
$493$	4.24693e46i	0.318606i
$494$	−3.22321e46	−0.233382
$495$	0	0
$496$	−3.02265e46	−0.203919
$497$	9.58638e45i	0.0624335i
$498$	2.96402e47i	1.86367i
$499$	1.75876e47	1.06770	0.533848	−	0.845581i	$-0.320745\pi$
$499$	1.75876e47	1.06770	0.533848	+	0.845581i	$0.320745\pi$
$500$	0	0
$501$	3.19397e47	1.80789
$502$	2.52221e47i	1.37869i
$503$	1.24051e47i	0.654880i	0.944872	+	0.327440i	$0.106186\pi$
$503$	1.24051e47i	0.654880i	−0.944872	+	0.327440i	$0.893814\pi$
$504$	5.96502e46	0.304143
$505$	0	0
$506$	−9.84108e46	−0.468175
$507$	5.11027e47i	2.34858i
$508$	− 2.97832e46i	− 0.132238i
$509$	−3.71512e47	−1.59372	−0.796859	−	0.604166i	$-0.793507\pi$
$509$	−3.71512e47	−1.59372	−0.796859	+	0.604166i	$0.793507\pi$
$510$	0	0
$511$	8.86212e46	0.354954
$512$	− 2.87213e47i	− 1.11168i
$513$	− 2.67296e46i	− 0.0999857i
$514$	−4.49893e47	−1.62650
$515$	0	0
$516$	2.42948e45	0.00820623
$517$	3.34597e47i	1.09254i
$518$	− 8.34092e46i	− 0.263295i
$519$	−4.60621e47	−1.40577
$520$	0	0
$521$	7.89659e45	0.0225309	0.0112655	−	0.999937i	$-0.496414\pi$
$521$	7.89659e45	0.0225309	0.0112655	+	0.999937i	$0.496414\pi$
$522$	3.69732e47i	1.02012i
$523$	1.18122e47i	0.315175i	0.987505	+	0.157588i	$0.0503717\pi$
$523$	1.18122e47i	0.315175i	−0.987505	+	0.157588i	$0.949628\pi$
$524$	1.70816e46	0.0440790
$525$	0	0
$526$	−6.96851e45	−0.0168225
$527$	− 4.50331e46i	− 0.105159i
$528$	− 5.23767e47i	− 1.18316i
$529$	3.35870e47	0.734001
$530$	0	0
$531$	2.72895e47	0.558267
$532$	− 3.50403e45i	− 0.00693609i
$533$	− 4.28587e47i	− 0.820943i
$534$	−8.25738e47	−1.53063
$535$	0	0
$536$	−1.12467e48	−1.95272
$537$	2.16958e47i	0.364607i
$538$	2.15663e47i	0.350821i
$539$	−6.20419e47	−0.976971
$540$	0	0
$541$	−6.62658e47	−0.977997	−0.488998	−	0.872285i	$-0.662638\pi$
$541$	−6.62658e47	−0.977997	−0.488998	+	0.872285i	$0.662638\pi$
$542$	− 6.80114e46i	− 0.0971839i
$543$	8.30070e47i	1.14846i
$544$	1.17340e47	0.157204
$545$	0	0
$546$	3.53832e47	0.444555
$547$	1.12424e47i	0.136798i	0.997658	+	0.0683990i	$0.0217891\pi$
$547$	1.12424e47i	0.136798i	−0.997658	+	0.0683990i	$0.978211\pi$
$548$	1.52422e47i	0.179633i
$549$	−5.32564e46	−0.0607933
$550$	0	0
$551$	1.26846e47	0.135870
$552$	− 8.26092e47i	− 0.857224i
$553$	− 2.93624e47i	− 0.295190i
$554$	1.21889e48	1.18725
$555$	0	0
$556$	−1.86844e47	−0.170872
$557$	− 6.68090e47i	− 0.592064i	−0.955178	−	0.296032i	$-0.904336\pi$
$557$	− 6.68090e47i	− 0.592064i	0.955178	−	0.296032i	$-0.0956636\pi$
$558$	− 3.92053e47i	− 0.336702i
$559$	4.89734e46	0.0407618
$560$	0	0
$561$	7.80339e47	0.610145
$562$	6.74014e47i	0.510838i
$563$	2.47733e48i	1.82007i	0.414536	+	0.910033i	$0.363944\pi$
$563$	2.47733e48i	1.82007i	−0.414536	+	0.910033i	$0.636056\pi$
$564$	−4.80921e47	−0.342523
$565$	0	0
$566$	1.75846e48	1.17718
$567$	− 1.42558e47i	− 0.0925309i
$568$	5.24292e47i	0.329972i
$569$	−8.59661e47	−0.524641	−0.262321	−	0.964981i	$-0.584488\pi$
$569$	−8.59661e47	−0.524641	−0.262321	+	0.964981i	$0.584488\pi$
$570$	0	0
$571$	−3.39185e48	−1.94673	−0.973364	−	0.229266i	$-0.926367\pi$
$571$	−3.39185e48	−1.94673	−0.973364	+	0.229266i	$0.926367\pi$
$572$	6.00298e47i	0.334146i
$573$	− 2.81753e48i	− 1.52112i
$574$	−1.78930e47	−0.0936968
$575$	0	0
$576$	3.14180e48	1.54805
$577$	− 2.12534e48i	− 1.01590i	−0.861386	−	0.507951i	$-0.830403\pi$
$577$	− 2.12534e48i	− 1.01590i	0.861386	−	0.507951i	$-0.169597\pi$
$578$	1.63292e48i	0.757232i
$579$	4.79258e48	2.15623
$580$	0	0
$581$	−6.49544e47	−0.275123
$582$	1.64143e48i	0.674639i
$583$	1.70314e48i	0.679283i
$584$	4.84681e48	1.87599
$585$	0	0
$586$	−3.14491e48	−1.14657
$587$	− 1.06269e48i	− 0.376044i	−0.982165	−	0.188022i	$-0.939792\pi$
$587$	− 1.06269e48i	− 0.376044i	0.982165	−	0.188022i	$-0.0602076\pi$
$588$	− 8.91737e47i	− 0.306290i
$589$	−1.34504e47	−0.0448453
$590$	0	0
$591$	3.99665e48	1.25578
$592$	− 3.57728e48i	− 1.09125i
$593$	− 3.98260e48i	− 1.17953i	−0.807574	−	0.589766i	$-0.799220\pi$
$593$	− 3.98260e48i	− 1.17953i	0.807574	−	0.589766i	$-0.200780\pi$
$594$	1.91176e48	0.549758
$595$	0	0
$596$	1.23794e48	0.335651
$597$	− 1.64894e48i	− 0.434163i
$598$	− 2.85129e48i	− 0.729072i
$599$	−5.14535e48	−1.27775	−0.638874	−	0.769311i	$-0.720599\pi$
$599$	−5.14535e48	−1.27775	−0.638874	+	0.769311i	$0.720599\pi$
$600$	0	0
$601$	−1.83878e48	−0.430751	−0.215375	−	0.976531i	$-0.569098\pi$
$601$	−1.83878e48	−0.430751	−0.215375	+	0.976531i	$0.569098\pi$
$602$	− 2.04458e46i	− 0.00465227i
$603$	− 1.14394e49i	− 2.52842i
$604$	−1.00054e48	−0.214827
$605$	0	0
$606$	6.46516e48	1.31011
$607$	− 2.06846e48i	− 0.407236i	−0.979050	−	0.203618i	$-0.934730\pi$
$607$	− 2.06846e48i	− 0.407236i	0.979050	−	0.203618i	$-0.0652700\pi$
$608$	− 3.50467e47i	− 0.0670401i
$609$	−1.39247e48	−0.258812
$610$	0	0
$611$	−9.69439e48	−1.70137
$612$	6.52623e47i	0.111304i
$613$	1.02050e48i	0.169143i	0.996417	+	0.0845717i	$0.0269522\pi$
$613$	1.02050e48i	0.169143i	−0.996417	+	0.0845717i	$0.973048\pi$
$614$	−2.30743e48	−0.371691
$615$	0	0
$616$	1.46367e48	0.222732
$617$	3.46313e48i	0.512246i	0.966644	+	0.256123i	$0.0824452\pi$
$617$	3.46313e48i	0.512246i	−0.966644	+	0.256123i	$0.917555\pi$
$618$	1.44860e49i	2.08281i
$619$	−6.56428e48	−0.917488	−0.458744	−	0.888568i	$-0.651701\pi$
$619$	−6.56428e48	−0.917488	−0.458744	+	0.888568i	$0.651701\pi$
$620$	0	0
$621$	2.36453e48	0.312350
$622$	3.67165e48i	0.471552i
$623$	− 1.80954e48i	− 0.225958i
$624$	1.51753e49	1.84249
$625$	0	0
$626$	−5.99629e48	−0.688386
$627$	− 2.33070e48i	− 0.260198i
$628$	− 1.06427e48i	− 0.115546i
$629$	5.32965e48	0.562746
$630$	0	0
$631$	5.18692e48	0.518079	0.259039	−	0.965867i	$-0.416594\pi$
$631$	5.18692e48	0.518079	0.259039	+	0.965867i	$0.416594\pi$
$632$	− 1.60587e49i	− 1.56013i
$633$	6.48082e48i	0.612442i
$634$	8.74063e48	0.803490
$635$	0	0
$636$	−2.44795e48	−0.212962
$637$	− 1.79756e49i	− 1.52140i
$638$	9.07235e48i	0.747064i
$639$	−5.33275e48	−0.427254
$640$	0	0
$641$	−6.15569e48	−0.466940	−0.233470	−	0.972364i	$-0.575008\pi$
$641$	−6.15569e48	−0.466940	−0.233470	+	0.972364i	$0.575008\pi$
$642$	2.07858e49i	1.53428i
$643$	− 6.50853e48i	− 0.467510i	−0.972296	−	0.233755i	$-0.924899\pi$
$643$	− 6.50853e48i	− 0.467510i	0.972296	−	0.233755i	$-0.0751013\pi$
$644$	3.09971e47	0.0216680
$645$	0	0
$646$	−8.59837e47	−0.0569308
$647$	− 2.43533e49i	− 1.56940i	−0.619878	−	0.784698i	$-0.712818\pi$
$647$	− 2.43533e49i	− 1.56940i	0.619878	−	0.784698i	$-0.287182\pi$
$648$	− 7.79667e48i	− 0.489042i
$649$	6.69620e48	0.408833
$650$	0	0
$651$	1.47654e48	0.0854233
$652$	6.11047e48i	0.344145i
$653$	4.33343e48i	0.237602i	0.992918	+	0.118801i	$0.0379051\pi$
$653$	4.33343e48i	0.237602i	−0.992918	+	0.118801i	$0.962095\pi$
$654$	2.65789e48	0.141882
$655$	0	0
$656$	−7.67401e48	−0.388334
$657$	4.92986e49i	2.42907i
$658$	4.04729e48i	0.194183i
$659$	−2.26798e49	−1.05960	−0.529802	−	0.848121i	$-0.677734\pi$
$659$	−2.26798e49	−1.05960	−0.529802	+	0.848121i	$0.677734\pi$
$660$	0	0
$661$	−2.84364e49	−1.25994	−0.629969	−	0.776620i	$-0.716932\pi$
$661$	−2.84364e49	−1.25994	−0.629969	+	0.776620i	$0.716932\pi$
$662$	1.03284e49i	0.445676i
$663$	2.26090e49i	0.950156i
$664$	−3.55245e49	−1.45407
$665$	0	0
$666$	4.63992e49	1.80182
$667$	1.12210e49i	0.424452i
$668$	6.55455e48i	0.241521i
$669$	−2.46325e49	−0.884202
$670$	0	0
$671$	−1.30679e48	−0.0445205
$672$	3.84730e48i	0.127701i
$673$	1.14434e49i	0.370077i	0.982731	+	0.185039i	$0.0592410\pi$
$673$	1.14434e49i	0.370077i	−0.982731	+	0.185039i	$0.940759\pi$
$674$	−1.72019e49	−0.542035
$675$	0	0
$676$	−1.04871e49	−0.313753
$677$	3.00594e49i	0.876351i	0.898890	+	0.438175i	$0.144375\pi$
$677$	3.00594e49i	0.876351i	−0.898890	+	0.438175i	$0.855625\pi$
$678$	− 1.24705e49i	− 0.354295i
$679$	−3.59708e48	−0.0995931
$680$	0	0
$681$	3.59766e49	0.946119
$682$	− 9.62004e48i	− 0.246576i
$683$	− 7.78736e49i	− 1.94549i	−0.231885	−	0.972743i	$-0.574489\pi$
$683$	− 7.78736e49i	− 1.94549i	0.231885	−	0.972743i	$-0.425511\pi$
$684$	1.94924e48	0.0474661
$685$	0	0
$686$	−1.53329e49	−0.354774
$687$	6.32535e49i	1.42673i
$688$	− 8.76886e47i	− 0.0192817i
$689$	−4.93456e49	−1.05782
$690$	0	0
$691$	9.61614e49	1.95945	0.979726	−	0.200340i	$-0.0642046\pi$
$691$	9.61614e49	1.95945	0.979726	+	0.200340i	$0.0642046\pi$
$692$	− 9.45269e48i	− 0.187801i
$693$	1.48875e49i	0.288397i
$694$	−5.07971e49	−0.959506
$695$	0	0
$696$	−7.61562e49	−1.36787
$697$	− 1.14332e49i	− 0.200260i
$698$	4.33853e49i	0.741093i
$699$	5.46014e49	0.909606
$700$	0	0
$701$	1.19741e49	0.189748	0.0948742	−	0.995489i	$-0.469755\pi$
$701$	1.19741e49	0.189748	0.0948742	+	0.995489i	$0.469755\pi$
$702$	5.53901e49i	0.856116i
$703$	− 1.59185e49i	− 0.239984i
$704$	7.70923e49	1.13368
$705$	0	0
$706$	−1.16678e50	−1.63270
$707$	1.41679e49i	0.193404i
$708$	9.62454e48i	0.128173i
$709$	4.80032e49	0.623680	0.311840	−	0.950135i	$-0.399055\pi$
$709$	4.80032e49	0.623680	0.311840	+	0.950135i	$0.399055\pi$
$710$	0	0
$711$	1.63339e50	2.02009
$712$	− 9.89664e49i	− 1.19423i
$713$	− 1.18984e49i	− 0.140094i
$714$	9.43898e48	0.108444
$715$	0	0
$716$	−4.45232e48	−0.0487089
$717$	1.73297e50i	1.85015i
$718$	8.84635e49i	0.921693i
$719$	1.45387e49	0.147832	0.0739162	−	0.997264i	$-0.476450\pi$
$719$	1.45387e49	0.147832	0.0739162	+	0.997264i	$0.476450\pi$
$720$	0	0
$721$	−3.17450e49	−0.307474
$722$	− 9.16528e49i	− 0.866452i
$723$	1.15246e50i	1.06342i
$724$	−1.70344e49	−0.153427
$725$	0	0
$726$	6.19432e48	0.0531622
$727$	− 1.25503e50i	− 1.05148i	−0.850644	−	0.525742i	$-0.823788\pi$
$727$	− 1.25503e50i	− 1.05148i	0.850644	−	0.525742i	$-0.176212\pi$
$728$	4.24075e49i	0.346851i
$729$	1.96598e50	1.56981
$730$	0	0
$731$	1.30644e48	0.00994338
$732$	− 1.87826e48i	− 0.0139576i
$733$	− 1.40440e50i	− 1.01899i	−0.860473	−	0.509495i	$-0.829832\pi$
$733$	− 1.40440e50i	− 1.01899i	0.860473	−	0.509495i	$-0.170168\pi$
$734$	−4.95419e49	−0.350988
$735$	0	0
$736$	3.10027e49	0.209430
$737$	− 2.80695e50i	− 1.85163i
$738$	− 9.95358e49i	− 0.641199i
$739$	−2.93572e49	−0.184687	−0.0923435	−	0.995727i	$-0.529436\pi$
$739$	−2.93572e49	−0.184687	−0.0923435	+	0.995727i	$0.529436\pi$
$740$	0	0
$741$	6.75281e49	0.405197
$742$	2.06012e49i	0.120732i
$743$	1.10795e50i	0.634185i	0.948395	+	0.317093i	$0.102707\pi$
$743$	1.10795e50i	0.634185i	−0.948395	+	0.317093i	$0.897293\pi$
$744$	8.07537e49	0.451478
$745$	0	0
$746$	−1.78650e50	−0.952960
$747$	− 3.61331e50i	− 1.88276i
$748$	1.60138e49i	0.0815111i
$749$	−4.55506e49	−0.226497
$750$	0	0
$751$	−4.13601e50	−1.96283	−0.981416	−	0.191892i	$-0.938538\pi$
$751$	−4.13601e50	−1.96283	−0.981416	+	0.191892i	$0.938538\pi$
$752$	1.73582e50i	0.804806i
$753$	− 5.28418e50i	− 2.39368i
$754$	−2.62856e50	−1.16337
$755$	0	0
$756$	−6.02161e48	−0.0254437
$757$	− 3.15399e50i	− 1.30221i	−0.758987	−	0.651106i	$-0.774305\pi$
$757$	− 3.15399e50i	− 1.30221i	0.758987	−	0.651106i	$-0.225695\pi$
$758$	− 2.01180e50i	− 0.811659i
$759$	2.06176e50	0.812845
$760$	0	0
$761$	−3.65841e50	−1.37740	−0.688702	−	0.725045i	$-0.741819\pi$
$761$	−3.65841e50	−1.37740	−0.688702	+	0.725045i	$0.741819\pi$
$762$	− 2.39624e50i	− 0.881696i
$763$	5.82458e48i	0.0209452i
$764$	5.78202e49	0.203210
$765$	0	0
$766$	1.57382e49	0.0528387
$767$	1.94011e50i	0.636661i
$768$	2.85192e50i	0.914778i
$769$	2.07264e50	0.649849	0.324925	−	0.945740i	$-0.394661\pi$
$769$	2.07264e50	0.649849	0.324925	+	0.945740i	$0.394661\pi$
$770$	0	0
$771$	9.42552e50	2.82393
$772$	9.83516e49i	0.288057i
$773$	2.04692e50i	0.586084i	0.956100	+	0.293042i	$0.0946675\pi$
$773$	2.04692e50i	0.586084i	−0.956100	+	0.293042i	$0.905332\pi$
$774$	1.13737e49	0.0318371
$775$	0	0
$776$	−1.96729e50	−0.526367
$777$	1.74747e50i	0.457133i
$778$	− 3.14521e50i	− 0.804465i
$779$	−3.41484e49	−0.0854013
$780$	0	0
$781$	−1.30853e50	−0.312889
$782$	− 7.60622e49i	− 0.177849i
$783$	− 2.17983e50i	− 0.498415i
$784$	−3.21860e50	−0.719673
$785$	0	0
$786$	1.37432e50	0.293897
$787$	2.74398e50i	0.573882i	0.957948	+	0.286941i	$0.0926383\pi$
$787$	2.74398e50i	0.573882i	−0.957948	+	0.286941i	$0.907362\pi$
$788$	8.20177e49i	0.167764i
$789$	1.45994e49	0.0292071
$790$	0	0
$791$	2.73282e49	0.0523025
$792$	8.14219e50i	1.52423i
$793$	− 3.78619e49i	− 0.0693301i
$794$	6.54491e50	1.17232
$795$	0	0
$796$	3.38388e49	0.0580012
$797$	− 3.73868e50i	− 0.626899i	−0.949605	−	0.313450i	$-0.898515\pi$
$797$	− 3.73868e50i	− 0.626899i	0.949605	−	0.313450i	$-0.101485\pi$
$798$	− 2.81921e49i	− 0.0462463i
$799$	−2.58612e50	−0.415030
$800$	0	0
$801$	1.00662e51	1.54631
$802$	− 9.13117e49i	− 0.137238i
$803$	1.20967e51i	1.77887i
$804$	4.03447e50	0.580505
$805$	0	0
$806$	2.78725e50	0.383983
$807$	− 4.51827e50i	− 0.609095i
$808$	7.74862e50i	1.02218i
$809$	3.87407e50	0.500114	0.250057	−	0.968231i	$-0.419551\pi$
$809$	3.87407e50	0.500114	0.250057	+	0.968231i	$0.419551\pi$
$810$	0	0
$811$	−9.21816e50	−1.13967	−0.569835	−	0.821759i	$-0.692993\pi$
$811$	−9.21816e50	−1.13967	−0.569835	+	0.821759i	$0.692993\pi$
$812$	− 2.85758e49i	− 0.0345754i
$813$	1.42488e50i	0.168730i
$814$	1.13853e51	1.31952
$815$	0	0
$816$	4.04823e50	0.449456
$817$	− 3.90203e48i	− 0.00424038i
$818$	− 5.53933e50i	− 0.589216i
$819$	−4.31341e50	−0.449110
$820$	0	0
$821$	1.64737e51	1.64357	0.821783	−	0.569801i	$-0.192980\pi$
$821$	1.64737e51	1.64357	0.821783	+	0.569801i	$0.192980\pi$
$822$	1.22633e51i	1.19771i
$823$	− 6.02163e50i	− 0.575727i	−0.957671	−	0.287864i	$-0.907055\pi$
$823$	− 6.02163e50i	− 0.575727i	0.957671	−	0.287864i	$-0.0929449\pi$
$824$	−1.73618e51	−1.62505
$825$	0	0
$826$	8.09973e49	0.0726641
$827$	4.30476e50i	0.378097i	0.981968	+	0.189048i	$0.0605403\pi$
$827$	4.30476e50i	0.378097i	−0.981968	+	0.189048i	$0.939460\pi$
$828$	1.72432e50i	0.148282i
$829$	−8.88751e50	−0.748300	−0.374150	−	0.927368i	$-0.622065\pi$
$829$	−8.88751e50	−0.748300	−0.374150	+	0.927368i	$0.622065\pi$
$830$	0	0
$831$	−2.55364e51	−2.06131
$832$	2.23362e51i	1.76543i
$833$	− 4.79525e50i	− 0.371128i
$834$	−1.50328e51	−1.13929
$835$	0	0
$836$	4.78297e49	0.0347606
$837$	2.31142e50i	0.164507i
$838$	1.26992e51i	0.885126i
$839$	−3.76912e50	−0.257280	−0.128640	−	0.991691i	$-0.541061\pi$
$839$	−3.76912e50	−0.257280	−0.128640	+	0.991691i	$0.541061\pi$
$840$	0	0
$841$	−4.92875e50	−0.322706
$842$	− 4.57730e50i	− 0.293527i
$843$	− 1.41210e51i	− 0.886916i
$844$	−1.32997e50	−0.0818179
$845$	0	0
$846$	−2.25144e51	−1.32886
$847$	1.35744e49i	0.00784804i
$848$	8.83551e50i	0.500385i
$849$	−3.68407e51	−2.04382
$850$	0	0
$851$	1.40817e51	0.749699
$852$	− 1.88077e50i	− 0.0980940i
$853$	− 3.00248e51i	− 1.53417i	−0.641547	−	0.767083i	$-0.721707\pi$
$853$	− 3.00248e51i	− 1.53417i	0.641547	−	0.767083i	$-0.278293\pi$
$854$	−1.58069e49	−0.00791286
$855$	0	0
$856$	−2.49122e51	−1.19708
$857$	2.46088e50i	0.115858i	0.998321	+	0.0579291i	$0.0184497\pi$
$857$	2.46088e50i	0.115858i	−0.998321	+	0.0579291i	$0.981550\pi$
$858$	4.82977e51i	2.22792i
$859$	−2.64506e51	−1.19551	−0.597757	−	0.801677i	$-0.703941\pi$
$859$	−2.64506e51	−1.19551	−0.597757	+	0.801677i	$0.703941\pi$
$860$	0	0
$861$	3.74868e50	0.162676
$862$	1.02117e51i	0.434233i
$863$	− 9.93861e50i	− 0.414130i	−0.978327	−	0.207065i	$-0.933609\pi$
$863$	− 9.93861e50i	− 0.414130i	0.978327	−	0.207065i	$-0.0663911\pi$
$864$	−6.02270e50	−0.245924
$865$	0	0
$866$	−3.66184e51	−1.43594
$867$	− 3.42107e51i	− 1.31470i
$868$	3.03009e49i	0.0114120i
$869$	4.00794e51	1.47936
$870$	0	0
$871$	8.13268e51	2.88347
$872$	3.18554e50i	0.110699i
$873$	− 2.00100e51i	− 0.681550i
$874$	−2.27181e50	−0.0758441
$875$	0	0
$876$	−1.73867e51	−0.557695
$877$	2.79832e50i	0.0879842i	0.999032	+	0.0439921i	$0.0140076\pi$
$877$	2.79832e50i	0.0879842i	−0.999032	+	0.0439921i	$0.985992\pi$
$878$	− 3.16623e50i	− 0.0975861i
$879$	6.58876e51	1.99067
$880$	0	0
$881$	−5.95050e50	−0.172773	−0.0863863	−	0.996262i	$-0.527532\pi$
$881$	−5.95050e50	−0.172773	−0.0863863	+	0.996262i	$0.527532\pi$
$882$	− 4.17469e51i	− 1.18829i
$883$	− 3.85350e51i	− 1.07533i	−0.843157	−	0.537667i	$-0.819306\pi$
$883$	− 3.85350e51i	− 1.07533i	0.843157	−	0.537667i	$-0.180694\pi$
$884$	−4.63973e50	−0.126934
$885$	0	0
$886$	4.96755e51	1.30633
$887$	4.56338e50i	0.117658i	0.998268	+	0.0588292i	$0.0187367\pi$
$887$	4.56338e50i	0.117658i	−0.998268	+	0.0588292i	$0.981263\pi$
$888$	9.55716e51i	2.41603i
$889$	5.25119e50	0.130160
$890$	0	0
$891$	1.94590e51	0.463724
$892$	− 5.05498e50i	− 0.118123i
$893$	7.72416e50i	0.176991i
$894$	9.95996e51	2.23795
$895$	0	0
$896$	5.50354e50	0.118919
$897$	5.97362e51i	1.26581i
$898$	− 9.39122e50i	− 0.195158i
$899$	−1.09689e51	−0.223548
$900$	0	0
$901$	−1.31637e51	−0.258044
$902$	− 2.44237e51i	− 0.469567i
$903$	4.28351e49i	0.00807726i
$904$	1.49462e51	0.276428
$905$	0	0
$906$	−8.04998e51	−1.43236
$907$	4.12286e51i	0.719566i	0.933036	+	0.359783i	$0.117149\pi$
$907$	4.12286e51i	0.719566i	−0.933036	+	0.359783i	$0.882851\pi$
$908$	7.38298e50i	0.126395i
$909$	−7.88139e51	−1.32353
$910$	0	0
$911$	6.95561e51	1.12399	0.561996	−	0.827140i	$-0.310034\pi$
$911$	6.95561e51	1.12399	0.561996	+	0.827140i	$0.310034\pi$
$912$	− 1.20911e51i	− 0.191672i
$913$	− 8.86621e51i	− 1.37879i
$914$	7.72094e51	1.17791
$915$	0	0
$916$	−1.29806e51	−0.190601
$917$	3.01173e50i	0.0433863i
$918$	1.47761e51i	0.208840i
$919$	−1.23335e51	−0.171027	−0.0855136	−	0.996337i	$-0.527253\pi$
$919$	−1.23335e51	−0.171027	−0.0855136	+	0.996337i	$0.527253\pi$
$920$	0	0
$921$	4.83420e51	0.645329
$922$	− 6.15821e51i	− 0.806610i
$923$	− 3.79125e51i	− 0.487251i
$924$	−5.25057e50	−0.0662136
$925$	0	0
$926$	6.07023e51	0.737076
$927$	− 1.76592e52i	− 2.10415i
$928$	− 2.85810e51i	− 0.334185i
$929$	9.97208e51	1.14422	0.572112	−	0.820176i	$-0.306124\pi$
$929$	9.97208e51	1.14422	0.572112	+	0.820176i	$0.306124\pi$
$930$	0	0
$931$	−1.43224e51	−0.158269
$932$	1.12051e51i	0.121517i
$933$	− 7.69232e51i	− 0.818707i
$934$	−3.92536e51	−0.410024
$935$	0	0
$936$	−2.35906e52	−2.37363
$937$	− 6.01334e51i	− 0.593844i	−0.954902	−	0.296922i	$-0.904040\pi$
$937$	− 6.01334e51i	− 0.593844i	0.954902	−	0.296922i	$-0.0959602\pi$
$938$	− 3.39529e51i	− 0.329100i
$939$	1.25626e52	1.19517
$940$	0	0
$941$	1.38035e52	1.26523	0.632617	−	0.774465i	$-0.281981\pi$
$941$	1.38035e52	1.26523	0.632617	+	0.774465i	$0.281981\pi$
$942$	− 8.56268e51i	− 0.770405i
$943$	− 3.02081e51i	− 0.266789i
$944$	3.47384e51	0.301162
$945$	0	0
$946$	2.79083e50	0.0233151
$947$	9.01648e51i	0.739456i	0.929140	+	0.369728i	$0.120549\pi$
$947$	9.01648e51i	0.739456i	−0.929140	+	0.369728i	$0.879451\pi$
$948$	5.76067e51i	0.463796i
$949$	−3.50482e52	−2.77017
$950$	0	0
$951$	−1.83121e52	−1.39502
$952$	1.13128e51i	0.0846105i
$953$	4.32450e51i	0.317549i	0.987315	+	0.158774i	$0.0507542\pi$
$953$	4.32450e51i	0.317549i	−0.987315	+	0.158774i	$0.949246\pi$
$954$	−1.14601e52	−0.826214
$955$	0	0
$956$	−3.55633e51	−0.247166
$957$	− 1.90071e52i	− 1.29705i
$958$	1.45348e52i	0.973897i
$959$	−2.68741e51	−0.176810
$960$	0	0
$961$	−1.46006e52	−0.926216
$962$	3.29869e52i	2.05484i
$963$	− 2.53391e52i	− 1.55000i
$964$	−2.36503e51	−0.142066
$965$	0	0
$966$	2.49391e51	0.144471
$967$	1.91085e51i	0.108709i	0.998522	+	0.0543543i	$0.0173101\pi$
$967$	1.91085e51i	0.108709i	−0.998522	+	0.0543543i	$0.982690\pi$
$968$	7.42403e50i	0.0414783i
$969$	1.80141e51	0.0988431
$970$	0	0
$971$	2.54698e52	1.34800	0.674000	−	0.738732i	$-0.264575\pi$
$971$	2.54698e52	1.34800	0.674000	+	0.738732i	$0.264575\pi$
$972$	5.20394e51i	0.270504i
$973$	− 3.29432e51i	− 0.168186i
$974$	1.17796e52	0.590675
$975$	0	0
$976$	−6.77932e50	−0.0327955
$977$	− 2.34465e52i	− 1.11410i	−0.830480	−	0.557048i	$-0.811934\pi$
$977$	− 2.34465e52i	− 1.11410i	0.830480	−	0.557048i	$-0.188066\pi$
$978$	4.91625e52i	2.29459i
$979$	2.47001e52	1.13240
$980$	0	0
$981$	−3.24012e51	−0.143335
$982$	1.40197e52i	0.609238i
$983$	1.06892e52i	0.456308i	0.973625	+	0.228154i	$0.0732690\pi$
$983$	1.06892e52i	0.456308i	−0.973625	+	0.228154i	$0.926731\pi$
$984$	2.05021e52	0.859772
$985$	0	0
$986$	−7.01207e51	−0.283792
$987$	− 8.47931e51i	− 0.337140i
$988$	1.38579e51i	0.0541314i
$989$	3.45178e50	0.0132467
$990$	0	0
$991$	1.97227e52	0.730597	0.365298	−	0.930891i	$-0.380967\pi$
$991$	1.97227e52	0.730597	0.365298	+	0.930891i	$0.380967\pi$
$992$	3.03064e51i	0.110301i
$993$	− 2.16387e52i	− 0.773782i
$994$	−1.58280e51	−0.0556114
$995$	0	0
$996$	1.27435e52	0.432266
$997$	1.44359e52i	0.481149i	0.970631	+	0.240575i	$0.0773358\pi$
$997$	1.44359e52i	0.481149i	−0.970631	+	0.240575i	$0.922664\pi$
$998$	2.90388e52i	0.951029i
$999$	−2.73555e52	−0.880338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.36.b.a.24.5		6
5.2	odd	4		1.36.a.a.1.1	✓	3
5.3	odd	4		25.36.a.a.1.3		3
5.4	even	2	inner	25.36.b.a.24.2		6
15.2	even	4		9.36.a.b.1.3		3
20.7	even	4		16.36.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.36.a.a.1.1	✓	3	5.2	odd	4
9.36.a.b.1.3		3	15.2	even	4
16.36.a.d.1.3		3	20.7	even	4
25.36.a.a.1.3		3	5.3	odd	4
25.36.b.a.24.2		6	5.4	even	2	inner
25.36.b.a.24.5		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:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+165109. i q^{2} -3.45913e8i q^{3} +7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14i q^{7} +6.84517e15i q^{8} -6.96245e16 q^{9} +O(q^{10})\)	\(q+165109. i q^{2} -3.45913e8i q^{3} +7.09870e9 q^{4} +5.71135e13 q^{6} +1.25160e14i q^{7} +6.84517e15i q^{8} -6.96245e16 q^{9} -1.70842e18 q^{11} -2.45554e18i q^{12} -4.94986e19i q^{13} -2.06651e19 q^{14} -8.86291e20 q^{16} -1.32045e21i q^{17} -1.14956e22i q^{18} -3.94388e21 q^{19} +4.32945e22 q^{21} -2.82076e23i q^{22} -3.48881e23i q^{23} +2.36784e24 q^{24} +8.17268e24 q^{26} +6.77748e24i q^{27} +8.88473e23i q^{28} -3.21628e25 q^{29} +3.41044e25 q^{31} +8.88635e25i q^{32} +5.90965e26i q^{33} +2.18018e26 q^{34} -4.94244e26 q^{36} +4.03624e27i q^{37} -6.51171e26i q^{38} -1.71222e28 q^{39} +8.65857e27 q^{41} +7.14832e27i q^{42} +9.89389e26i q^{43} -1.21276e28 q^{44} +5.76034e28 q^{46} -1.95852e29i q^{47} +3.06580e29i q^{48} +3.63154e29 q^{49} -4.56760e29 q^{51} -3.51376e29i q^{52} -9.96909e29i q^{53} -1.11902e30 q^{54} -8.56741e29 q^{56} +1.36424e30i q^{57} -5.31037e30i q^{58} -3.91953e30 q^{59} +7.64909e29 q^{61} +5.63096e30i q^{62} -8.71420e30i q^{63} -4.51249e31 q^{64} -9.75738e31 q^{66} +1.64301e32i q^{67} -9.37346e30i q^{68} -1.20682e32 q^{69} +7.65930e31 q^{71} -4.76592e32i q^{72} -7.08063e32i q^{73} -6.66421e32 q^{74} -2.79964e31 q^{76} -2.13826e32i q^{77} -2.82704e33i q^{78} -2.34599e33 q^{79} -1.13900e33 q^{81} +1.42961e33i q^{82} +5.18971e33i q^{83} +3.07335e32 q^{84} -1.63357e32 q^{86} +1.11255e34i q^{87} -1.16944e34i q^{88} -1.44578e34 q^{89} +6.19525e33 q^{91} -2.47660e33i q^{92} -1.17972e34i q^{93} +3.23369e34 q^{94} +3.07391e34 q^{96} +2.87399e34i q^{97} +5.99600e34i q^{98} +1.18948e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 69682524288 q^{4} - 9573061128768 q^{6} - 30\!\cdots\!02 q^{9}+O(q^{10}) \) 6 * q - 69682524288 * q^4 - 9573061128768 * q^6 - 300183957752487102 * q^9	\( 6 q - 69682524288 q^{4} - 9573061128768 q^{6} - 30\!\cdots\!02 q^{9}+ \cdots - 60\!\cdots\!04 q^{99}+O(q^{100}) \) 6 * q - 69682524288 * q^4 - 9573061128768 * q^6 - 300183957752487102 * q^9 - 2315890857099974088 * q^11 - 271818686510142877056 * q^14 + 4311388034571636842496 * q^16 + 64606792485869241101880 * q^19 + 444244917507334797615552 * q^21 + 7521458029847229416509440 * q^24 + 8568963719869816338936672 * q^26 + 76920798287968875196496220 * q^29 + 207463189127449379460059712 * q^31 + 1108273470697007566053414624 * q^34 - 12104409432261180621062968704 * q^36 - 37223963908125755485412775024 * q^39 + 47045973169065536258074174812 * q^41 + 161909641397410604027847796224 * q^44 + 620243394040769877901011779712 * q^46 + 1190178076169851463244074901642 * q^49 - 3606088149701589454704519855408 * q^51 - 8848462809538007800988211803520 * q^54 + 11341840434826113134505180487680 * q^56 - 8741057166185293399690487262360 * q^59 + 47074156553032057894438160976612 * q^61 - 187020561473268641262186528768 * q^64 - 151280835682131675595281896084736 * q^66 + 651966424792548500617306631868096 * q^69 + 697549204590716421077242324013712 * q^71 - 4212674766353133731580090791579616 * q^74 - 5458148575336648395699070897789440 * q^76 + 852425725182123323803473261748320 * q^79 + 3734442301593956911190817869446326 * q^81 + 26049577017381684485650485151739904 * q^84 + 296981501312941625080810196380992 * q^86 - 61167181692387502670411984836068540 * q^89 + 2006783405038974725132244313994592 * q^91 - 38152386540837025150844554284001536 * q^94 - 64784055731908851933994586445447168 * q^96 - 60577372683195463856883721504068504 * q^99

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