LMFDB - Embedded newform 4025.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.255877.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 6x^{2} + 6x - 5 $ x^5 - x^4 - 6x^3 + 6x^2 + 6*x - 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.698160$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.698160 q^{2} +1.80045 q^{3} -1.51257 q^{4} +1.25700 q^{6} -1.00000 q^{7} -2.45234 q^{8} +0.241606 q^{9} +O(q^{10})$	\(q+0.698160 q^{2} +1.80045 q^{3} -1.51257 q^{4} +1.25700 q^{6} -1.00000 q^{7} -2.45234 q^{8} +0.241606 q^{9} +3.82559 q^{11} -2.72330 q^{12} +3.46630 q^{13} -0.698160 q^{14} +1.31302 q^{16} -6.82280 q^{17} +0.168680 q^{18} -4.61486 q^{19} -1.80045 q^{21} +2.67088 q^{22} -1.00000 q^{23} -4.41530 q^{24} +2.42004 q^{26} -4.96634 q^{27} +1.51257 q^{28} -0.951787 q^{29} -1.24161 q^{31} +5.82137 q^{32} +6.88777 q^{33} -4.76341 q^{34} -0.365447 q^{36} +2.82838 q^{37} -3.22191 q^{38} +6.24089 q^{39} -10.9298 q^{41} -1.25700 q^{42} -0.455126 q^{43} -5.78648 q^{44} -0.698160 q^{46} +5.75561 q^{47} +2.36402 q^{48} +1.00000 q^{49} -12.2841 q^{51} -5.24303 q^{52} +1.55382 q^{53} -3.46730 q^{54} +2.45234 q^{56} -8.30880 q^{57} -0.664500 q^{58} -10.1154 q^{59} -11.6603 q^{61} -0.866840 q^{62} -0.241606 q^{63} +1.43822 q^{64} +4.80877 q^{66} +1.38737 q^{67} +10.3200 q^{68} -1.80045 q^{69} +1.78354 q^{71} -0.592501 q^{72} -11.7493 q^{73} +1.97466 q^{74} +6.98030 q^{76} -3.82559 q^{77} +4.35715 q^{78} +0.0169084 q^{79} -9.66645 q^{81} -7.63077 q^{82} +8.11152 q^{83} +2.72330 q^{84} -0.317751 q^{86} -1.71364 q^{87} -9.38164 q^{88} -15.6434 q^{89} -3.46630 q^{91} +1.51257 q^{92} -2.23545 q^{93} +4.01834 q^{94} +10.4811 q^{96} -14.0621 q^{97} +0.698160 q^{98} +0.924287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	$ 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 7 q^{11} + 10 q^{12} + 5 q^{13} - q^{14} - 9 q^{16} + 7 q^{17} - 11 q^{18} - 10 q^{19} - 4 q^{21} - 4 q^{22} - 5 q^{23} - 4 q^{24} - 2 q^{26} + 7 q^{27} - 3 q^{28} - 14 q^{29} - 10 q^{31} - 4 q^{33} - 10 q^{34} + 20 q^{36} + 3 q^{37} + 15 q^{38} - 13 q^{39} - 15 q^{41} + 5 q^{42} - 8 q^{43} - 27 q^{44} - q^{46} + 10 q^{47} + 2 q^{48} + 5 q^{49} - 18 q^{51} - 18 q^{52} + 9 q^{53} - 39 q^{54} + 3 q^{56} - 23 q^{57} + 31 q^{58} - 19 q^{59} - 21 q^{61} + 10 q^{62} - 5 q^{63} - 7 q^{64} + 25 q^{66} - 5 q^{67} + 15 q^{68} - 4 q^{69} - 16 q^{71} - 26 q^{72} - q^{73} - 16 q^{74} + 7 q^{77} - 28 q^{78} + 20 q^{79} - 3 q^{81} - 11 q^{82} + 31 q^{83} - 10 q^{84} + 10 q^{86} - 38 q^{87} + 3 q^{88} - 21 q^{89} - 5 q^{91} - 3 q^{92} - 23 q^{93} + 28 q^{94} + 24 q^{96} - 19 q^{97} + q^{98} - 26 q^{99}+O(q^{100}) $ 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 7 * q^11 + 10 * q^12 + 5 * q^13 - q^14 - 9 * q^16 + 7 * q^17 - 11 * q^18 - 10 * q^19 - 4 * q^21 - 4 * q^22 - 5 * q^23 - 4 * q^24 - 2 * q^26 + 7 * q^27 - 3 * q^28 - 14 * q^29 - 10 * q^31 - 4 * q^33 - 10 * q^34 + 20 * q^36 + 3 * q^37 + 15 * q^38 - 13 * q^39 - 15 * q^41 + 5 * q^42 - 8 * q^43 - 27 * q^44 - q^46 + 10 * q^47 + 2 * q^48 + 5 * q^49 - 18 * q^51 - 18 * q^52 + 9 * q^53 - 39 * q^54 + 3 * q^56 - 23 * q^57 + 31 * q^58 - 19 * q^59 - 21 * q^61 + 10 * q^62 - 5 * q^63 - 7 * q^64 + 25 * q^66 - 5 * q^67 + 15 * q^68 - 4 * q^69 - 16 * q^71 - 26 * q^72 - q^73 - 16 * q^74 + 7 * q^77 - 28 * q^78 + 20 * q^79 - 3 * q^81 - 11 * q^82 + 31 * q^83 - 10 * q^84 + 10 * q^86 - 38 * q^87 + 3 * q^88 - 21 * q^89 - 5 * q^91 - 3 * q^92 - 23 * q^93 + 28 * q^94 + 24 * q^96 - 19 * q^97 + q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.698160	0.493674	0.246837	−	0.969057i	$-0.420609\pi$
$2$	0.698160	0.493674	0.246837	+	0.969057i	$0.420609\pi$
$3$	1.80045	1.03949	0.519744	−	0.854322i	$-0.326027\pi$
$3$	1.80045	1.03949	0.519744	+	0.854322i	$0.326027\pi$
$4$	−1.51257	−0.756286
$5$	0	0
$5$	0	0
$6$	1.25700	0.513168
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.45234	−0.867033
$9$	0.241606	0.0805354
$10$	0	0
$11$	3.82559	1.15346	0.576729	−	0.816935i	$-0.304329\pi$
$11$	3.82559	1.15346	0.576729	+	0.816935i	$0.304329\pi$
$12$	−2.72330	−0.786150
$13$	3.46630	0.961380	0.480690	−	0.876891i	$-0.340386\pi$
$13$	3.46630	0.961380	0.480690	+	0.876891i	$0.340386\pi$
$14$	−0.698160	−0.186591
$15$	0	0
$16$	1.31302	0.328255
$17$	−6.82280	−1.65477	−0.827386	−	0.561633i	$-0.810173\pi$
$17$	−6.82280	−1.65477	−0.827386	+	0.561633i	$0.810173\pi$
$18$	0.168680	0.0397583
$19$	−4.61486	−1.05872	−0.529360	−	0.848397i	$-0.677568\pi$
$19$	−4.61486	−1.05872	−0.529360	+	0.848397i	$0.677568\pi$
$20$	0	0
$21$	−1.80045	−0.392890
$22$	2.67088	0.569433
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−4.41530	−0.901270
$25$	0	0
$26$	2.42004	0.474608
$27$	−4.96634	−0.955772
$28$	1.51257	0.285849
$29$	−0.951787	−0.176742	−0.0883712	−	0.996088i	$-0.528166\pi$
$29$	−0.951787	−0.176742	−0.0883712	+	0.996088i	$0.528166\pi$
$30$	0	0
$31$	−1.24161	−0.222999	−0.111500	−	0.993764i	$-0.535565\pi$
$31$	−1.24161	−0.222999	−0.111500	+	0.993764i	$0.535565\pi$
$32$	5.82137	1.02908
$33$	6.88777	1.19901
$34$	−4.76341	−0.816918
$35$	0	0
$36$	−0.365447	−0.0609078
$37$	2.82838	0.464982	0.232491	−	0.972599i	$-0.425312\pi$
$37$	2.82838	0.464982	0.232491	+	0.972599i	$0.425312\pi$
$38$	−3.22191	−0.522663
$39$	6.24089	0.999343
$40$	0	0
$41$	−10.9298	−1.70695	−0.853476	−	0.521133i	$-0.825510\pi$
$41$	−10.9298	−1.70695	−0.853476	+	0.521133i	$0.825510\pi$
$42$	−1.25700	−0.193959
$43$	−0.455126	−0.0694060	−0.0347030	−	0.999398i	$-0.511049\pi$
$43$	−0.455126	−0.0694060	−0.0347030	+	0.999398i	$0.511049\pi$
$44$	−5.78648	−0.872345
$45$	0	0
$46$	−0.698160	−0.102938
$47$	5.75561	0.839542	0.419771	−	0.907630i	$-0.362110\pi$
$47$	5.75561	0.839542	0.419771	+	0.907630i	$0.362110\pi$
$48$	2.36402	0.341217
$49$	1.00000	0.142857
$50$	0	0
$51$	−12.2841	−1.72012
$52$	−5.24303	−0.727078
$53$	1.55382	0.213434	0.106717	−	0.994289i	$-0.465966\pi$
$53$	1.55382	0.213434	0.106717	+	0.994289i	$0.465966\pi$
$54$	−3.46730	−0.471840
$55$	0	0
$56$	2.45234	0.327708
$57$	−8.30880	−1.10053
$58$	−0.664500	−0.0872531
$59$	−10.1154	−1.31691	−0.658457	−	0.752618i	$-0.728791\pi$
$59$	−10.1154	−1.31691	−0.658457	+	0.752618i	$0.728791\pi$
$60$	0	0
$61$	−11.6603	−1.49295	−0.746473	−	0.665415i	$-0.768254\pi$
$61$	−11.6603	−1.49295	−0.746473	+	0.665415i	$0.768254\pi$
$62$	−0.866840	−0.110089
$63$	−0.241606	−0.0304395
$64$	1.43822	0.179777
$65$	0	0
$66$	4.80877	0.591918
$67$	1.38737	0.169495	0.0847473	−	0.996402i	$-0.472992\pi$
$67$	1.38737	0.169495	0.0847473	+	0.996402i	$0.472992\pi$
$68$	10.3200	1.25148
$69$	−1.80045	−0.216748
$70$	0	0
$71$	1.78354	0.211667	0.105833	−	0.994384i	$-0.466249\pi$
$71$	1.78354	0.211667	0.105833	+	0.994384i	$0.466249\pi$
$72$	−0.592501	−0.0698269
$73$	−11.7493	−1.37515	−0.687573	−	0.726115i	$-0.741324\pi$
$73$	−11.7493	−1.37515	−0.687573	+	0.726115i	$0.741324\pi$
$74$	1.97466	0.229550
$75$	0	0
$76$	6.98030	0.800696
$77$	−3.82559	−0.435966
$78$	4.35715	0.493350
$79$	0.0169084	0.00190235	0.000951173	−	1.00000i	$-0.499697\pi$
$79$	0.0169084	0.00190235	0.000951173		1.00000i	$0.499697\pi$
$80$	0	0
$81$	−9.66645	−1.07405
$82$	−7.63077	−0.842677
$83$	8.11152	0.890355	0.445177	−	0.895442i	$-0.353141\pi$
$83$	8.11152	0.890355	0.445177	+	0.895442i	$0.353141\pi$
$84$	2.72330	0.297137
$85$	0	0
$86$	−0.317751	−0.0342639
$87$	−1.71364	−0.183722
$88$	−9.38164	−1.00009
$89$	−15.6434	−1.65819	−0.829097	−	0.559104i	$-0.811145\pi$
$89$	−15.6434	−1.65819	−0.829097	+	0.559104i	$0.811145\pi$
$90$	0	0
$91$	−3.46630	−0.363367
$92$	1.51257	0.157697
$93$	−2.23545	−0.231805
$94$	4.01834	0.414460
$95$	0	0
$96$	10.4811	1.06972
$97$	−14.0621	−1.42779	−0.713897	−	0.700251i	$-0.753072\pi$
$97$	−14.0621	−1.42779	−0.713897	+	0.700251i	$0.753072\pi$
$98$	0.698160	0.0705249
$99$	0.924287	0.0928943
$100$	0	0
$101$	16.7716	1.66884	0.834419	−	0.551131i	$-0.185804\pi$
$101$	16.7716	1.66884	0.834419	+	0.551131i	$0.185804\pi$
$102$	−8.57627	−0.849177
$103$	−1.58061	−0.155742	−0.0778711	−	0.996963i	$-0.524812\pi$
$103$	−1.58061	−0.155742	−0.0778711	+	0.996963i	$0.524812\pi$
$104$	−8.50055	−0.833548
$105$	0	0
$106$	1.08482	0.105367
$107$	13.7835	1.33250	0.666251	−	0.745728i	$-0.267898\pi$
$107$	13.7835	1.33250	0.666251	+	0.745728i	$0.267898\pi$
$108$	7.51195	0.722837
$109$	13.5300	1.29594	0.647971	−	0.761665i	$-0.275618\pi$
$109$	13.5300	1.29594	0.647971	+	0.761665i	$0.275618\pi$
$110$	0	0
$111$	5.09234	0.483344
$112$	−1.31302	−0.124069
$113$	6.74718	0.634721	0.317360	−	0.948305i	$-0.397203\pi$
$113$	6.74718	0.634721	0.317360	+	0.948305i	$0.397203\pi$
$114$	−5.80088	−0.543302
$115$	0	0
$116$	1.43965	0.133668
$117$	0.837481	0.0774251
$118$	−7.06218	−0.650126
$119$	6.82280	0.625445
$120$	0	0
$121$	3.63514	0.330467
$122$	−8.14075	−0.737029
$123$	−19.6786	−1.77436
$124$	1.87802	0.168651
$125$	0	0
$126$	−0.168680	−0.0150272
$127$	−1.85372	−0.164491	−0.0822454	−	0.996612i	$-0.526209\pi$
$127$	−1.85372	−0.164491	−0.0822454	+	0.996612i	$0.526209\pi$
$128$	−10.6386	−0.940332
$129$	−0.819429	−0.0721467
$130$	0	0
$131$	−14.4630	−1.26364	−0.631819	−	0.775116i	$-0.717691\pi$
$131$	−14.4630	−1.26364	−0.631819	+	0.775116i	$0.717691\pi$
$132$	−10.4182	−0.906792
$133$	4.61486	0.400159
$134$	0.968609	0.0836751
$135$	0	0
$136$	16.7318	1.43474
$137$	−4.04432	−0.345530	−0.172765	−	0.984963i	$-0.555270\pi$
$137$	−4.04432	−0.345530	−0.172765	+	0.984963i	$0.555270\pi$
$138$	−1.25700	−0.107003
$139$	−12.6429	−1.07235	−0.536177	−	0.844106i	$-0.680132\pi$
$139$	−12.6429	−1.07235	−0.536177	+	0.844106i	$0.680132\pi$
$140$	0	0
$141$	10.3627	0.872693
$142$	1.24520	0.104494
$143$	13.2607	1.10891
$144$	0.317233	0.0264361
$145$	0	0
$146$	−8.20286	−0.678874
$147$	1.80045	0.148498
$148$	−4.27812	−0.351660
$149$	−10.7767	−0.882859	−0.441429	−	0.897296i	$-0.645528\pi$
$149$	−10.7767	−0.882859	−0.441429	+	0.897296i	$0.645528\pi$
$150$	0	0
$151$	−15.7786	−1.28405	−0.642024	−	0.766685i	$-0.721905\pi$
$151$	−15.7786	−1.28405	−0.642024	+	0.766685i	$0.721905\pi$
$152$	11.3172	0.917946
$153$	−1.64843	−0.133268
$154$	−2.67088	−0.215225
$155$	0	0
$156$	−9.43980	−0.755789
$157$	7.83884	0.625608	0.312804	−	0.949818i	$-0.398732\pi$
$157$	7.83884	0.625608	0.312804	+	0.949818i	$0.398732\pi$
$158$	0.0118048	0.000939139 0
$159$	2.79757	0.221862
$160$	0	0
$161$	1.00000	0.0788110
$162$	−6.74873	−0.530230
$163$	−13.2946	−1.04132	−0.520658	−	0.853765i	$-0.674313\pi$
$163$	−13.2946	−1.04132	−0.520658	+	0.853765i	$0.674313\pi$
$164$	16.5321	1.29094
$165$	0	0
$166$	5.66314	0.439545
$167$	−17.3688	−1.34404	−0.672018	−	0.740534i	$-0.734572\pi$
$167$	−17.3688	−1.34404	−0.672018	+	0.740534i	$0.734572\pi$
$168$	4.41530	0.340648
$169$	−0.984735	−0.0757488
$170$	0	0
$171$	−1.11498	−0.0852646
$172$	0.688410	0.0524908
$173$	−2.73027	−0.207578	−0.103789	−	0.994599i	$-0.533097\pi$
$173$	−2.73027	−0.207578	−0.103789	+	0.994599i	$0.533097\pi$
$174$	−1.19640	−0.0906985
$175$	0	0
$176$	5.02307	0.378628
$177$	−18.2123	−1.36892
$178$	−10.9216	−0.818607
$179$	−21.3148	−1.59314	−0.796570	−	0.604546i	$-0.793355\pi$
$179$	−21.3148	−1.59314	−0.796570	+	0.604546i	$0.793355\pi$
$180$	0	0
$181$	−15.4909	−1.15143	−0.575716	−	0.817650i	$-0.695277\pi$
$181$	−15.4909	−1.15143	−0.575716	+	0.817650i	$0.695277\pi$
$182$	−2.42004	−0.179385
$183$	−20.9937	−1.55190
$184$	2.45234	0.180789
$185$	0	0
$186$	−1.56070	−0.114436
$187$	−26.1012	−1.90871
$188$	−8.70577	−0.634934
$189$	4.96634	0.361248
$190$	0	0
$191$	4.11541	0.297781	0.148890	−	0.988854i	$-0.452430\pi$
$191$	4.11541	0.297781	0.148890	+	0.988854i	$0.452430\pi$
$192$	2.58943	0.186876
$193$	18.9732	1.36572	0.682862	−	0.730548i	$-0.260735\pi$
$193$	18.9732	1.36572	0.682862	+	0.730548i	$0.260735\pi$
$194$	−9.81763	−0.704865
$195$	0	0
$196$	−1.51257	−0.108041
$197$	−20.3550	−1.45023	−0.725117	−	0.688626i	$-0.758214\pi$
$197$	−20.3550	−1.45023	−0.725117	+	0.688626i	$0.758214\pi$
$198$	0.645300	0.0458595
$199$	−6.41122	−0.454479	−0.227240	−	0.973839i	$-0.572970\pi$
$199$	−6.41122	−0.454479	−0.227240	+	0.973839i	$0.572970\pi$
$200$	0	0
$201$	2.49789	0.176188
$202$	11.7093	0.823862
$203$	0.951787	0.0668023
$204$	18.5806	1.30090
$205$	0	0
$206$	−1.10352	−0.0768858
$207$	−0.241606	−0.0167928
$208$	4.55132	0.315577
$209$	−17.6546	−1.22119
$210$	0	0
$211$	6.30048	0.433743	0.216872	−	0.976200i	$-0.430415\pi$
$211$	6.30048	0.433743	0.216872	+	0.976200i	$0.430415\pi$
$212$	−2.35027	−0.161417
$213$	3.21116	0.220025
$214$	9.62309	0.657821
$215$	0	0
$216$	12.1791	0.828686
$217$	1.24161	0.0842857
$218$	9.44614	0.639773
$219$	−21.1539	−1.42945
$220$	0	0
$221$	−23.6499	−1.59087
$222$	3.55527	0.238614
$223$	27.3971	1.83465	0.917324	−	0.398142i	$-0.130345\pi$
$223$	27.3971	1.83465	0.917324	+	0.398142i	$0.130345\pi$
$224$	−5.82137	−0.388957
$225$	0	0
$226$	4.71061	0.313345
$227$	25.6001	1.69914	0.849571	−	0.527475i	$-0.176861\pi$
$227$	25.6001	1.69914	0.849571	+	0.527475i	$0.176861\pi$
$228$	12.5677	0.832314
$229$	7.44677	0.492096	0.246048	−	0.969258i	$-0.420868\pi$
$229$	7.44677	0.492096	0.246048	+	0.969258i	$0.420868\pi$
$230$	0	0
$231$	−6.88777	−0.453182
$232$	2.33410	0.153241
$233$	−9.51737	−0.623504	−0.311752	−	0.950164i	$-0.600916\pi$
$233$	−9.51737	−0.623504	−0.311752	+	0.950164i	$0.600916\pi$
$234$	0.584696	0.0382228
$235$	0	0
$236$	15.3003	0.995964
$237$	0.0304427	0.00197747
$238$	4.76341	0.308766
$239$	23.3175	1.50828	0.754142	−	0.656711i	$-0.228053\pi$
$239$	23.3175	1.50828	0.754142	+	0.656711i	$0.228053\pi$
$240$	0	0
$241$	2.83566	0.182661	0.0913306	−	0.995821i	$-0.470888\pi$
$241$	2.83566	0.182661	0.0913306	+	0.995821i	$0.470888\pi$
$242$	2.53791	0.163143
$243$	−2.50490	−0.160689
$244$	17.6370	1.12909
$245$	0	0
$246$	−13.7388	−0.875953
$247$	−15.9965	−1.01783
$248$	3.04484	0.193347
$249$	14.6044	0.925513
$250$	0	0
$251$	−23.6349	−1.49182	−0.745912	−	0.666044i	$-0.767986\pi$
$251$	−23.6349	−1.49182	−0.745912	+	0.666044i	$0.767986\pi$
$252$	0.365447	0.0230210
$253$	−3.82559	−0.240513
$254$	−1.29419	−0.0812048
$255$	0	0
$256$	−10.3039	−0.643995
$257$	23.3911	1.45909	0.729547	−	0.683930i	$-0.239731\pi$
$257$	23.3911	1.45909	0.729547	+	0.683930i	$0.239731\pi$
$258$	−0.572093	−0.0356170
$259$	−2.82838	−0.175747
$260$	0	0
$261$	−0.229958	−0.0142340
$262$	−10.0975	−0.623825
$263$	0.362073	0.0223264	0.0111632	−	0.999938i	$-0.496447\pi$
$263$	0.362073	0.0223264	0.0111632	+	0.999938i	$0.496447\pi$
$264$	−16.8911	−1.03958
$265$	0	0
$266$	3.22191	0.197548
$267$	−28.1651	−1.72367
$268$	−2.09850	−0.128186
$269$	28.5686	1.74186	0.870928	−	0.491411i	$-0.163519\pi$
$269$	28.5686	1.74186	0.870928	+	0.491411i	$0.163519\pi$
$270$	0	0
$271$	−5.67600	−0.344793	−0.172396	−	0.985028i	$-0.555151\pi$
$271$	−5.67600	−0.344793	−0.172396	+	0.985028i	$0.555151\pi$
$272$	−8.95846	−0.543187
$273$	−6.24089	−0.377716
$274$	−2.82359	−0.170579
$275$	0	0
$276$	2.72330	0.163924
$277$	−16.1998	−0.973351	−0.486676	−	0.873583i	$-0.661791\pi$
$277$	−16.1998	−0.973351	−0.486676	+	0.873583i	$0.661791\pi$
$278$	−8.82674	−0.529393
$279$	−0.299980	−0.0179593
$280$	0	0
$281$	8.93448	0.532986	0.266493	−	0.963837i	$-0.414135\pi$
$281$	8.93448	0.532986	0.266493	+	0.963837i	$0.414135\pi$
$282$	7.23480	0.430826
$283$	15.5909	0.926782	0.463391	−	0.886154i	$-0.346633\pi$
$283$	15.5909	0.926782	0.463391	+	0.886154i	$0.346633\pi$
$284$	−2.69773	−0.160081
$285$	0	0
$286$	9.25807	0.547441
$287$	10.9298	0.645167
$288$	1.40648	0.0828777
$289$	29.5506	1.73827
$290$	0	0
$291$	−25.3181	−1.48417
$292$	17.7716	1.04000
$293$	9.49384	0.554636	0.277318	−	0.960778i	$-0.410554\pi$
$293$	9.49384	0.554636	0.277318	+	0.960778i	$0.410554\pi$
$294$	1.25700	0.0733097
$295$	0	0
$296$	−6.93614	−0.403155
$297$	−18.9992	−1.10244
$298$	−7.52384	−0.435844
$299$	−3.46630	−0.200462
$300$	0	0
$301$	0.455126	0.0262330
$302$	−11.0160	−0.633901
$303$	30.1964	1.73474
$304$	−6.05939	−0.347530
$305$	0	0
$306$	−1.15087	−0.0657909
$307$	29.3902	1.67739	0.838694	−	0.544603i	$-0.183320\pi$
$307$	29.3902	1.67739	0.838694	+	0.544603i	$0.183320\pi$
$308$	5.78648	0.329715
$309$	−2.84580	−0.161892
$310$	0	0
$311$	0.189285	0.0107334	0.00536668	−	0.999986i	$-0.498292\pi$
$311$	0.189285	0.0107334	0.00536668	+	0.999986i	$0.498292\pi$
$312$	−15.3048	−0.866463
$313$	−22.4971	−1.27161	−0.635805	−	0.771849i	$-0.719332\pi$
$313$	−22.4971	−1.27161	−0.635805	+	0.771849i	$0.719332\pi$
$314$	5.47277	0.308846
$315$	0	0
$316$	−0.0255752	−0.00143872
$317$	5.63507	0.316497	0.158249	−	0.987399i	$-0.449415\pi$
$317$	5.63507	0.316497	0.158249	+	0.987399i	$0.449415\pi$
$318$	1.95315	0.109527
$319$	−3.64115	−0.203865
$320$	0	0
$321$	24.8164	1.38512
$322$	0.698160	0.0389070
$323$	31.4863	1.75194
$324$	14.6212	0.812289
$325$	0	0
$326$	−9.28179	−0.514071
$327$	24.3601	1.34712
$328$	26.8036	1.47998
$329$	−5.75561	−0.317317
$330$	0	0
$331$	16.6257	0.913832	0.456916	−	0.889510i	$-0.348954\pi$
$331$	16.6257	0.913832	0.456916	+	0.889510i	$0.348954\pi$
$332$	−12.2693	−0.673363
$333$	0.683354	0.0374476
$334$	−12.1262	−0.663516
$335$	0	0
$336$	−2.36402	−0.128968
$337$	5.10936	0.278324	0.139162	−	0.990270i	$-0.455559\pi$
$337$	5.10936	0.278324	0.139162	+	0.990270i	$0.455559\pi$
$338$	−0.687503	−0.0373952
$339$	12.1479	0.659785
$340$	0	0
$341$	−4.74988	−0.257220
$342$	−0.778434	−0.0420929
$343$	−1.00000	−0.0539949
$344$	1.11612	0.0601773
$345$	0	0
$346$	−1.90616	−0.102476
$347$	23.4040	1.25639	0.628196	−	0.778055i	$-0.283793\pi$
$347$	23.4040	1.25639	0.628196	+	0.778055i	$0.283793\pi$
$348$	2.59200	0.138946
$349$	13.9424	0.746318	0.373159	−	0.927767i	$-0.378275\pi$
$349$	13.9424	0.746318	0.373159	+	0.927767i	$0.378275\pi$
$350$	0	0
$351$	−17.2148	−0.918860
$352$	22.2702	1.18701
$353$	−0.0776861	−0.00413481	−0.00206741	−	0.999998i	$-0.500658\pi$
$353$	−0.0776861	−0.00413481	−0.00206741	+	0.999998i	$0.500658\pi$
$354$	−12.7151	−0.675798
$355$	0	0
$356$	23.6617	1.25407
$357$	12.2841	0.650143
$358$	−14.8811	−0.786492
$359$	−9.87277	−0.521065	−0.260532	−	0.965465i	$-0.583898\pi$
$359$	−9.87277	−0.521065	−0.260532	+	0.965465i	$0.583898\pi$
$360$	0	0
$361$	2.29691	0.120890
$362$	−10.8152	−0.568432
$363$	6.54487	0.343517
$364$	5.24303	0.274810
$365$	0	0
$366$	−14.6570	−0.766133
$367$	13.2274	0.690465	0.345233	−	0.938517i	$-0.387800\pi$
$367$	13.2274	0.690465	0.345233	+	0.938517i	$0.387800\pi$
$368$	−1.31302	−0.0684458
$369$	−2.64071	−0.137470
$370$	0	0
$371$	−1.55382	−0.0806704
$372$	3.38127	0.175311
$373$	−6.53334	−0.338284	−0.169142	−	0.985592i	$-0.554100\pi$
$373$	−6.53334	−0.338284	−0.169142	+	0.985592i	$0.554100\pi$
$374$	−18.2229	−0.942282
$375$	0	0
$376$	−14.1147	−0.727910
$377$	−3.29918	−0.169917
$378$	3.46730	0.178339
$379$	1.38180	0.0709783	0.0354891	−	0.999370i	$-0.488701\pi$
$379$	1.38180	0.0709783	0.0354891	+	0.999370i	$0.488701\pi$
$380$	0	0
$381$	−3.33752	−0.170986
$382$	2.87322	0.147007
$383$	11.5554	0.590452	0.295226	−	0.955427i	$-0.404605\pi$
$383$	11.5554	0.590452	0.295226	+	0.955427i	$0.404605\pi$
$384$	−19.1543	−0.977464
$385$	0	0
$386$	13.2464	0.674222
$387$	−0.109961	−0.00558964
$388$	21.2700	1.07982
$389$	−27.2015	−1.37917	−0.689586	−	0.724204i	$-0.742208\pi$
$389$	−27.2015	−1.37917	−0.689586	+	0.724204i	$0.742208\pi$
$390$	0	0
$391$	6.82280	0.345044
$392$	−2.45234	−0.123862
$393$	−26.0399	−1.31354
$394$	−14.2111	−0.715943
$395$	0	0
$396$	−1.39805	−0.0702547
$397$	−20.9405	−1.05097	−0.525487	−	0.850802i	$-0.676117\pi$
$397$	−20.9405	−1.05097	−0.525487	+	0.850802i	$0.676117\pi$
$398$	−4.47606	−0.224365
$399$	8.30880	0.415960
$400$	0	0
$401$	15.8494	0.791481	0.395741	−	0.918362i	$-0.370488\pi$
$401$	15.8494	0.791481	0.395741	+	0.918362i	$0.370488\pi$
$402$	1.74393	0.0869792
$403$	−4.30379	−0.214387
$404$	−25.3683	−1.26212
$405$	0	0
$406$	0.664500	0.0329786
$407$	10.8202	0.536338
$408$	30.1248	1.49140
$409$	−10.4646	−0.517439	−0.258719	−	0.965953i	$-0.583300\pi$
$409$	−10.4646	−0.517439	−0.258719	+	0.965953i	$0.583300\pi$
$410$	0	0
$411$	−7.28158	−0.359174
$412$	2.39079	0.117786
$413$	10.1154	0.497747
$414$	−0.168680	−0.00829017
$415$	0	0
$416$	20.1787	0.989340
$417$	−22.7628	−1.11470
$418$	−12.3257	−0.602870
$419$	−23.6726	−1.15648	−0.578241	−	0.815866i	$-0.696261\pi$
$419$	−23.6726	−1.15648	−0.578241	+	0.815866i	$0.696261\pi$
$420$	0	0
$421$	28.4711	1.38760	0.693799	−	0.720169i	$-0.255936\pi$
$421$	28.4711	1.38760	0.693799	+	0.720169i	$0.255936\pi$
$422$	4.39875	0.214128
$423$	1.39059	0.0676128
$424$	−3.81050	−0.185054
$425$	0	0
$426$	2.24191	0.108621
$427$	11.6603	0.564281
$428$	−20.8485	−1.00775
$429$	23.8751	1.15270
$430$	0	0
$431$	9.60035	0.462433	0.231216	−	0.972902i	$-0.425729\pi$
$431$	9.60035	0.462433	0.231216	+	0.972902i	$0.425729\pi$
$432$	−6.52089	−0.313737
$433$	−1.29845	−0.0623993	−0.0311997	−	0.999513i	$-0.509933\pi$
$433$	−1.29845	−0.0623993	−0.0311997	+	0.999513i	$0.509933\pi$
$434$	0.866840	0.0416097
$435$	0	0
$436$	−20.4652	−0.980103
$437$	4.61486	0.220759
$438$	−14.7688	−0.705681
$439$	24.7575	1.18161	0.590806	−	0.806814i	$-0.298810\pi$
$439$	24.7575	1.18161	0.590806	+	0.806814i	$0.298810\pi$
$440$	0	0
$441$	0.241606	0.0115051
$442$	−16.5114	−0.785369
$443$	26.0684	1.23855	0.619274	−	0.785175i	$-0.287427\pi$
$443$	26.0684	1.23855	0.619274	+	0.785175i	$0.287427\pi$
$444$	−7.70253	−0.365546
$445$	0	0
$446$	19.1276	0.905718
$447$	−19.4028	−0.917721
$448$	−1.43822	−0.0679494
$449$	−26.1656	−1.23483	−0.617415	−	0.786638i	$-0.711820\pi$
$449$	−26.1656	−1.23483	−0.617415	+	0.786638i	$0.711820\pi$
$450$	0	0
$451$	−41.8130	−1.96890
$452$	−10.2056	−0.480031
$453$	−28.4086	−1.33475
$454$	17.8730	0.838822
$455$	0	0
$456$	20.3760	0.954194
$457$	26.0882	1.22036	0.610178	−	0.792264i	$-0.291098\pi$
$457$	26.0882	1.22036	0.610178	+	0.792264i	$0.291098\pi$
$458$	5.19904	0.242935
$459$	33.8844	1.58159
$460$	0	0
$461$	−5.02471	−0.234024	−0.117012	−	0.993130i	$-0.537332\pi$
$461$	−5.02471	−0.234024	−0.117012	+	0.993130i	$0.537332\pi$
$462$	−4.80877	−0.223724
$463$	−17.2267	−0.800593	−0.400296	−	0.916386i	$-0.631093\pi$
$463$	−17.2267	−0.800593	−0.400296	+	0.916386i	$0.631093\pi$
$464$	−1.24971	−0.0580165
$465$	0	0
$466$	−6.64465	−0.307808
$467$	26.9639	1.24774	0.623871	−	0.781528i	$-0.285559\pi$
$467$	26.9639	1.24774	0.623871	+	0.781528i	$0.285559\pi$
$468$	−1.26675	−0.0585556
$469$	−1.38737	−0.0640629
$470$	0	0
$471$	14.1134	0.650312
$472$	24.8064	1.14181
$473$	−1.74112	−0.0800570
$474$	0.0212539	0.000976224 0
$475$	0	0
$476$	−10.3200	−0.473016
$477$	0.375413	0.0171890
$478$	16.2794	0.744601
$479$	−14.3097	−0.653827	−0.326914	−	0.945054i	$-0.606009\pi$
$479$	−14.3097	−0.653827	−0.326914	+	0.945054i	$0.606009\pi$
$480$	0	0
$481$	9.80402	0.447025
$482$	1.97975	0.0901751
$483$	1.80045	0.0819231
$484$	−5.49841	−0.249928
$485$	0	0
$486$	−1.74882	−0.0793281
$487$	−29.3984	−1.33217	−0.666083	−	0.745877i	$-0.732031\pi$
$487$	−29.3984	−1.33217	−0.666083	+	0.745877i	$0.732031\pi$
$488$	28.5950	1.29443
$489$	−23.9363	−1.08244
$490$	0	0
$491$	23.5841	1.06433	0.532167	−	0.846639i	$-0.321378\pi$
$491$	23.5841	1.06433	0.532167	+	0.846639i	$0.321378\pi$
$492$	29.7652	1.34192
$493$	6.49385	0.292468
$494$	−11.1681	−0.502478
$495$	0	0
$496$	−1.63025	−0.0732005
$497$	−1.78354	−0.0800026
$498$	10.1962	0.456902
$499$	11.1523	0.499246	0.249623	−	0.968343i	$-0.419693\pi$
$499$	11.1523	0.499246	0.249623	+	0.968343i	$0.419693\pi$
$500$	0	0
$501$	−31.2716	−1.39711
$502$	−16.5010	−0.736475
$503$	−15.3350	−0.683753	−0.341877	−	0.939745i	$-0.611063\pi$
$503$	−15.3350	−0.683753	−0.341877	+	0.939745i	$0.611063\pi$
$504$	0.592501	0.0263921
$505$	0	0
$506$	−2.67088	−0.118735
$507$	−1.77296	−0.0787400
$508$	2.80388	0.124402
$509$	−16.6869	−0.739635	−0.369817	−	0.929105i	$-0.620580\pi$
$509$	−16.6869	−0.739635	−0.369817	+	0.929105i	$0.620580\pi$
$510$	0	0
$511$	11.7493	0.519756
$512$	14.0835	0.622409
$513$	22.9189	1.01190
$514$	16.3307	0.720317
$515$	0	0
$516$	1.23945	0.0545636
$517$	22.0186	0.968377
$518$	−1.97466	−0.0867616
$519$	−4.91570	−0.215775
$520$	0	0
$521$	35.7832	1.56769	0.783846	−	0.620955i	$-0.213255\pi$
$521$	35.7832	1.56769	0.783846	+	0.620955i	$0.213255\pi$
$522$	−0.160547	−0.00702697
$523$	−25.9475	−1.13461	−0.567303	−	0.823509i	$-0.692013\pi$
$523$	−25.9475	−1.13461	−0.567303	+	0.823509i	$0.692013\pi$
$524$	21.8763	0.955672
$525$	0	0
$526$	0.252785	0.0110219
$527$	8.47124	0.369013
$528$	9.04377	0.393579
$529$	1.00000	0.0434783
$530$	0	0
$531$	−2.44395	−0.106058
$532$	−6.98030	−0.302635
$533$	−37.8861	−1.64103
$534$	−19.6637	−0.850933
$535$	0	0
$536$	−3.40231	−0.146957
$537$	−38.3761	−1.65605
$538$	19.9454	0.859909
$539$	3.82559	0.164780
$540$	0	0
$541$	−31.2551	−1.34376	−0.671881	−	0.740659i	$-0.734514\pi$
$541$	−31.2551	−1.34376	−0.671881	+	0.740659i	$0.734514\pi$
$542$	−3.96276	−0.170215
$543$	−27.8906	−1.19690
$544$	−39.7181	−1.70290
$545$	0	0
$546$	−4.35715	−0.186469
$547$	16.6314	0.711108	0.355554	−	0.934656i	$-0.384292\pi$
$547$	16.6314	0.711108	0.355554	+	0.934656i	$0.384292\pi$
$548$	6.11733	0.261319
$549$	−2.81720	−0.120235
$550$	0	0
$551$	4.39236	0.187121
$552$	4.41530	0.187928
$553$	−0.0169084	−0.000719019 0
$554$	−11.3101	−0.480518
$555$	0	0
$556$	19.1232	0.811006
$557$	38.2404	1.62030	0.810149	−	0.586224i	$-0.199386\pi$
$557$	38.2404	1.62030	0.810149	+	0.586224i	$0.199386\pi$
$558$	−0.209434	−0.00886605
$559$	−1.57760	−0.0667255
$560$	0	0
$561$	−46.9939	−1.98408
$562$	6.23770	0.263121
$563$	22.8271	0.962047	0.481023	−	0.876708i	$-0.340265\pi$
$563$	22.8271	0.962047	0.481023	+	0.876708i	$0.340265\pi$
$564$	−15.6743	−0.660006
$565$	0	0
$566$	10.8849	0.457528
$567$	9.66645	0.405953
$568$	−4.37384	−0.183522
$569$	14.4412	0.605407	0.302703	−	0.953085i	$-0.402111\pi$
$569$	14.4412	0.605407	0.302703	+	0.953085i	$0.402111\pi$
$570$	0	0
$571$	20.6134	0.862645	0.431323	−	0.902198i	$-0.358047\pi$
$571$	20.6134	0.862645	0.431323	+	0.902198i	$0.358047\pi$
$572$	−20.0577	−0.838655
$573$	7.40957	0.309539
$574$	7.63077	0.318502
$575$	0	0
$576$	0.347482	0.0144784
$577$	−7.40209	−0.308153	−0.154077	−	0.988059i	$-0.549240\pi$
$577$	−7.40209	−0.308153	−0.154077	+	0.988059i	$0.549240\pi$
$578$	20.6311	0.858140
$579$	34.1603	1.41965
$580$	0	0
$581$	−8.11152	−0.336522
$582$	−17.6761	−0.732698
$583$	5.94429	0.246187
$584$	28.8131	1.19230
$585$	0	0
$586$	6.62822	0.273809
$587$	−41.0523	−1.69441	−0.847204	−	0.531267i	$-0.821716\pi$
$587$	−41.0523	−1.69441	−0.847204	+	0.531267i	$0.821716\pi$
$588$	−2.72330	−0.112307
$589$	5.72984	0.236094
$590$	0	0
$591$	−36.6481	−1.50750
$592$	3.71371	0.152633
$593$	−35.0717	−1.44022	−0.720111	−	0.693859i	$-0.755909\pi$
$593$	−35.0717	−1.44022	−0.720111	+	0.693859i	$0.755909\pi$
$594$	−13.2645	−0.544248
$595$	0	0
$596$	16.3005	0.667694
$597$	−11.5431	−0.472426
$598$	−2.42004	−0.0989626
$599$	13.6332	0.557039	0.278519	−	0.960431i	$-0.410156\pi$
$599$	13.6332	0.557039	0.278519	+	0.960431i	$0.410156\pi$
$600$	0	0
$601$	32.8391	1.33954	0.669768	−	0.742570i	$-0.266394\pi$
$601$	32.8391	1.33954	0.669768	+	0.742570i	$0.266394\pi$
$602$	0.317751	0.0129506
$603$	0.335198	0.0136503
$604$	23.8663	0.971107
$605$	0	0
$606$	21.0819	0.856394
$607$	34.6656	1.40703	0.703516	−	0.710679i	$-0.251612\pi$
$607$	34.6656	1.40703	0.703516	+	0.710679i	$0.251612\pi$
$608$	−26.8648	−1.08951
$609$	1.71364	0.0694402
$610$	0	0
$611$	19.9507	0.807118
$612$	2.49337	0.100789
$613$	−10.4408	−0.421700	−0.210850	−	0.977518i	$-0.567623\pi$
$613$	−10.4408	−0.421700	−0.210850	+	0.977518i	$0.567623\pi$
$614$	20.5191	0.828082
$615$	0	0
$616$	9.38164	0.377997
$617$	−18.8347	−0.758257	−0.379128	−	0.925344i	$-0.623776\pi$
$617$	−18.8347	−0.758257	−0.379128	+	0.925344i	$0.623776\pi$
$618$	−1.98683	−0.0799219
$619$	17.1895	0.690906	0.345453	−	0.938436i	$-0.387725\pi$
$619$	17.1895	0.690906	0.345453	+	0.938436i	$0.387725\pi$
$620$	0	0
$621$	4.96634	0.199292
$622$	0.132151	0.00529878
$623$	15.6434	0.626739
$624$	8.19441	0.328039
$625$	0	0
$626$	−15.7066	−0.627761
$627$	−31.7861	−1.26941
$628$	−11.8568	−0.473138
$629$	−19.2975	−0.769440
$630$	0	0
$631$	−35.4654	−1.41185	−0.705927	−	0.708285i	$-0.749469\pi$
$631$	−35.4654	−1.41185	−0.705927	+	0.708285i	$0.749469\pi$
$632$	−0.0414652	−0.00164940
$633$	11.3437	0.450871
$634$	3.93418	0.156246
$635$	0	0
$636$	−4.23153	−0.167791
$637$	3.46630	0.137340
$638$	−2.54210	−0.100643
$639$	0.430914	0.0170467
$640$	0	0
$641$	17.3979	0.687176	0.343588	−	0.939120i	$-0.388358\pi$
$641$	17.3979	0.687176	0.343588	+	0.939120i	$0.388358\pi$
$642$	17.3259	0.683797
$643$	−27.8990	−1.10023	−0.550115	−	0.835089i	$-0.685416\pi$
$643$	−27.8990	−1.10023	−0.550115	+	0.835089i	$0.685416\pi$
$644$	−1.51257	−0.0596037
$645$	0	0
$646$	21.9825	0.864889
$647$	−28.7939	−1.13200	−0.566002	−	0.824404i	$-0.691511\pi$
$647$	−28.7939	−1.13200	−0.566002	+	0.824404i	$0.691511\pi$
$648$	23.7054	0.931236
$649$	−38.6974	−1.51901
$650$	0	0
$651$	2.23545	0.0876140
$652$	20.1091	0.787533
$653$	−47.5131	−1.85933	−0.929666	−	0.368403i	$-0.879905\pi$
$653$	−47.5131	−1.85933	−0.929666	+	0.368403i	$0.879905\pi$
$654$	17.0073	0.665037
$655$	0	0
$656$	−14.3511	−0.560315
$657$	−2.83869	−0.110748
$658$	−4.01834	−0.156651
$659$	−48.8739	−1.90386	−0.951928	−	0.306321i	$-0.900902\pi$
$659$	−48.8739	−1.90386	−0.951928	+	0.306321i	$0.900902\pi$
$660$	0	0
$661$	25.7144	1.00017	0.500087	−	0.865975i	$-0.333301\pi$
$661$	25.7144	1.00017	0.500087	+	0.865975i	$0.333301\pi$
$662$	11.6074	0.451135
$663$	−42.5804	−1.65369
$664$	−19.8922	−0.771967
$665$	0	0
$666$	0.477091	0.0184869
$667$	0.951787	0.0368533
$668$	26.2715	1.01648
$669$	49.3271	1.90709
$670$	0	0
$671$	−44.6075	−1.72205
$672$	−10.4811	−0.404316
$673$	7.87335	0.303495	0.151748	−	0.988419i	$-0.451510\pi$
$673$	7.87335	0.303495	0.151748	+	0.988419i	$0.451510\pi$
$674$	3.56715	0.137402
$675$	0	0
$676$	1.48948	0.0572878
$677$	28.2706	1.08653	0.543264	−	0.839562i	$-0.317188\pi$
$677$	28.2706	1.08653	0.543264	+	0.839562i	$0.317188\pi$
$678$	8.48120	0.325719
$679$	14.0621	0.539655
$680$	0	0
$681$	46.0917	1.76624
$682$	−3.31618	−0.126983
$683$	−12.4365	−0.475870	−0.237935	−	0.971281i	$-0.576471\pi$
$683$	−12.4365	−0.475870	−0.237935	+	0.971281i	$0.576471\pi$
$684$	1.68649	0.0644844
$685$	0	0
$686$	−0.698160	−0.0266559
$687$	13.4075	0.511528
$688$	−0.597588	−0.0227828
$689$	5.38602	0.205191
$690$	0	0
$691$	15.6767	0.596369	0.298184	−	0.954508i	$-0.403619\pi$
$691$	15.6767	0.596369	0.298184	+	0.954508i	$0.403619\pi$
$692$	4.12973	0.156989
$693$	−0.924287	−0.0351108
$694$	16.3397	0.620248
$695$	0	0
$696$	4.20243	0.159293
$697$	74.5720	2.82462
$698$	9.73401	0.368438
$699$	−17.1355	−0.648125
$700$	0	0
$701$	10.2955	0.388856	0.194428	−	0.980917i	$-0.437715\pi$
$701$	10.2955	0.388856	0.194428	+	0.980917i	$0.437715\pi$
$702$	−12.0187	−0.453617
$703$	−13.0526	−0.492287
$704$	5.50203	0.207366
$705$	0	0
$706$	−0.0542373	−0.00204125
$707$	−16.7716	−0.630761
$708$	27.5473	1.03529
$709$	29.0824	1.09221	0.546106	−	0.837716i	$-0.316109\pi$
$709$	29.0824	1.09221	0.546106	+	0.837716i	$0.316109\pi$
$710$	0	0
$711$	0.00408518	0.000153206 0
$712$	38.3629	1.43771
$713$	1.24161	0.0464985
$714$	8.57627	0.320959
$715$	0	0
$716$	32.2401	1.20487
$717$	41.9819	1.56784
$718$	−6.89278	−0.257236
$719$	−6.51114	−0.242825	−0.121412	−	0.992602i	$-0.538742\pi$
$719$	−6.51114	−0.242825	−0.121412	+	0.992602i	$0.538742\pi$
$720$	0	0
$721$	1.58061	0.0588650
$722$	1.60361	0.0596803
$723$	5.10546	0.189874
$724$	23.4311	0.870812
$725$	0	0
$726$	4.56937	0.169585
$727$	−31.0751	−1.15251	−0.576256	−	0.817269i	$-0.695487\pi$
$727$	−31.0751	−1.15251	−0.576256	+	0.817269i	$0.695487\pi$
$728$	8.50055	0.315051
$729$	24.4894	0.907015
$730$	0	0
$731$	3.10523	0.114851
$732$	31.7545	1.17368
$733$	−50.4895	−1.86487	−0.932436	−	0.361336i	$-0.882321\pi$
$733$	−50.4895	−1.86487	−0.932436	+	0.361336i	$0.882321\pi$
$734$	9.23485	0.340865
$735$	0	0
$736$	−5.82137	−0.214579
$737$	5.30752	0.195505
$738$	−1.84364	−0.0678654
$739$	−0.577002	−0.0212253	−0.0106127	−	0.999944i	$-0.503378\pi$
$739$	−0.577002	−0.0212253	−0.0106127	+	0.999944i	$0.503378\pi$
$740$	0	0
$741$	−28.8008	−1.05803
$742$	−1.08482	−0.0398249
$743$	44.3568	1.62729	0.813646	−	0.581361i	$-0.197480\pi$
$743$	44.3568	1.62729	0.813646	+	0.581361i	$0.197480\pi$
$744$	5.48207	0.200982
$745$	0	0
$746$	−4.56132	−0.167002
$747$	1.95979	0.0717051
$748$	39.4800	1.44353
$749$	−13.7835	−0.503638
$750$	0	0
$751$	−7.91511	−0.288827	−0.144413	−	0.989517i	$-0.546129\pi$
$751$	−7.91511	−0.288827	−0.144413	+	0.989517i	$0.546129\pi$
$752$	7.55722	0.275583
$753$	−42.5534	−1.55073
$754$	−2.30336	−0.0838834
$755$	0	0
$756$	−7.51195	−0.273207
$757$	46.1748	1.67825	0.839126	−	0.543936i	$-0.183067\pi$
$757$	46.1748	1.67825	0.839126	+	0.543936i	$0.183067\pi$
$758$	0.964718	0.0350401
$759$	−6.88777	−0.250010
$760$	0	0
$761$	−0.450155	−0.0163181	−0.00815906	−	0.999967i	$-0.502597\pi$
$761$	−0.450155	−0.0163181	−0.00815906	+	0.999967i	$0.502597\pi$
$762$	−2.33012	−0.0844114
$763$	−13.5300	−0.489820
$764$	−6.22485	−0.225207
$765$	0	0
$766$	8.06751	0.291491
$767$	−35.0631	−1.26605
$768$	−18.5516	−0.669425
$769$	20.3146	0.732564	0.366282	−	0.930504i	$-0.380631\pi$
$769$	20.3146	0.732564	0.366282	+	0.930504i	$0.380631\pi$
$770$	0	0
$771$	42.1144	1.51671
$772$	−28.6984	−1.03288
$773$	14.2601	0.512900	0.256450	−	0.966557i	$-0.417447\pi$
$773$	14.2601	0.512900	0.256450	+	0.966557i	$0.417447\pi$
$774$	−0.0767706	−0.00275946
$775$	0	0
$776$	34.4851	1.23794
$777$	−5.09234	−0.182687
$778$	−18.9910	−0.680862
$779$	50.4396	1.80719
$780$	0	0
$781$	6.82308	0.244149
$782$	4.76341	0.170339
$783$	4.72689	0.168925
$784$	1.31302	0.0468935
$785$	0	0
$786$	−18.1800	−0.648459
$787$	−2.27436	−0.0810722	−0.0405361	−	0.999178i	$-0.512907\pi$
$787$	−2.27436	−0.0810722	−0.0405361	+	0.999178i	$0.512907\pi$
$788$	30.7884	1.09679
$789$	0.651893	0.0232080
$790$	0	0
$791$	−6.74718	−0.239902
$792$	−2.26666	−0.0805424
$793$	−40.4181	−1.43529
$794$	−14.6198	−0.518839
$795$	0	0
$796$	9.69743	0.343716
$797$	−34.9507	−1.23802	−0.619008	−	0.785385i	$-0.712465\pi$
$797$	−34.9507	−1.23802	−0.619008	+	0.785385i	$0.712465\pi$
$798$	5.80088	0.205349
$799$	−39.2694	−1.38925
$800$	0	0
$801$	−3.77954	−0.133543
$802$	11.0654	0.390734
$803$	−44.9478	−1.58617
$804$	−3.77824	−0.133248
$805$	0	0
$806$	−3.00473	−0.105837
$807$	51.4361	1.81064
$808$	−41.1297	−1.44694
$809$	35.8469	1.26031	0.630155	−	0.776470i	$-0.282991\pi$
$809$	35.8469	1.26031	0.630155	+	0.776470i	$0.282991\pi$
$810$	0	0
$811$	2.84421	0.0998736	0.0499368	−	0.998752i	$-0.484098\pi$
$811$	2.84421	0.0998736	0.0499368	+	0.998752i	$0.484098\pi$
$812$	−1.43965	−0.0505217
$813$	−10.2193	−0.358408
$814$	7.55424	0.264776
$815$	0	0
$816$	−16.1292	−0.564636
$817$	2.10034	0.0734816
$818$	−7.30594	−0.255446
$819$	−0.837481	−0.0292640
$820$	0	0
$821$	−43.8864	−1.53165	−0.765823	−	0.643052i	$-0.777668\pi$
$821$	−43.8864	−1.53165	−0.765823	+	0.643052i	$0.777668\pi$
$822$	−5.08371	−0.177315
$823$	−7.47526	−0.260571	−0.130286	−	0.991477i	$-0.541589\pi$
$823$	−7.47526	−0.260571	−0.130286	+	0.991477i	$0.541589\pi$
$824$	3.87619	0.135033
$825$	0	0
$826$	7.06218	0.245725
$827$	−45.2598	−1.57384	−0.786919	−	0.617056i	$-0.788325\pi$
$827$	−45.2598	−1.57384	−0.786919	+	0.617056i	$0.788325\pi$
$828$	0.365447	0.0127002
$829$	−23.6631	−0.821852	−0.410926	−	0.911669i	$-0.634795\pi$
$829$	−23.6631	−0.821852	−0.410926	+	0.911669i	$0.634795\pi$
$830$	0	0
$831$	−29.1668	−1.01179
$832$	4.98530	0.172834
$833$	−6.82280	−0.236396
$834$	−15.8921	−0.550298
$835$	0	0
$836$	26.7038	0.923570
$837$	6.16624	0.213136
$838$	−16.5273	−0.570925
$839$	47.5354	1.64110	0.820552	−	0.571573i	$-0.193666\pi$
$839$	47.5354	1.64110	0.820552	+	0.571573i	$0.193666\pi$
$840$	0	0
$841$	−28.0941	−0.968762
$842$	19.8774	0.685021
$843$	16.0860	0.554033
$844$	−9.52993	−0.328034
$845$	0	0
$846$	0.970856	0.0333787
$847$	−3.63514	−0.124905
$848$	2.04020	0.0700606
$849$	28.0706	0.963379
$850$	0	0
$851$	−2.82838	−0.0969555
$852$	−4.85712	−0.166402
$853$	−30.4859	−1.04382	−0.521908	−	0.853002i	$-0.674780\pi$
$853$	−30.4859	−1.04382	−0.521908	+	0.853002i	$0.674780\pi$
$854$	8.14075	0.278571
$855$	0	0
$856$	−33.8018	−1.15532
$857$	26.9242	0.919714	0.459857	−	0.887993i	$-0.347901\pi$
$857$	26.9242	0.919714	0.459857	+	0.887993i	$0.347901\pi$
$858$	16.6687	0.569058
$859$	30.2649	1.03262	0.516312	−	0.856401i	$-0.327305\pi$
$859$	30.2649	1.03262	0.516312	+	0.856401i	$0.327305\pi$
$860$	0	0
$861$	19.6786	0.670643
$862$	6.70259	0.228291
$863$	5.68637	0.193566	0.0967831	−	0.995305i	$-0.469145\pi$
$863$	5.68637	0.193566	0.0967831	+	0.995305i	$0.469145\pi$
$864$	−28.9109	−0.983570
$865$	0	0
$866$	−0.906523	−0.0308049
$867$	53.2043	1.80691
$868$	−1.87802	−0.0637441
$869$	0.0646847	0.00219428
$870$	0	0
$871$	4.80906	0.162949
$872$	−33.1802	−1.12362
$873$	−3.39750	−0.114988
$874$	3.22191	0.108983
$875$	0	0
$876$	31.9968	1.08107
$877$	−19.0064	−0.641800	−0.320900	−	0.947113i	$-0.603985\pi$
$877$	−19.0064	−0.641800	−0.320900	+	0.947113i	$0.603985\pi$
$878$	17.2847	0.583331
$879$	17.0931	0.576537
$880$	0	0
$881$	−27.5900	−0.929530	−0.464765	−	0.885434i	$-0.653861\pi$
$881$	−27.5900	−0.929530	−0.464765	+	0.885434i	$0.653861\pi$
$882$	0.168680	0.00567975
$883$	−31.3980	−1.05663	−0.528314	−	0.849049i	$-0.677176\pi$
$883$	−31.3980	−1.05663	−0.528314	+	0.849049i	$0.677176\pi$
$884$	35.7722	1.20315
$885$	0	0
$886$	18.1999	0.611439
$887$	−11.5373	−0.387383	−0.193692	−	0.981062i	$-0.562046\pi$
$887$	−11.5373	−0.387383	−0.193692	+	0.981062i	$0.562046\pi$
$888$	−12.4881	−0.419075
$889$	1.85372	0.0621716
$890$	0	0
$891$	−36.9799	−1.23887
$892$	−41.4401	−1.38752
$893$	−26.5613	−0.888840
$894$	−13.5463	−0.453055
$895$	0	0
$896$	10.6386	0.355412
$897$	−6.24089	−0.208377
$898$	−18.2678	−0.609603
$899$	1.18174	0.0394134
$900$	0	0
$901$	−10.6014	−0.353185
$902$	−29.1922	−0.971994
$903$	0.819429	0.0272689
$904$	−16.5464	−0.550324
$905$	0	0
$906$	−19.8338	−0.658932
$907$	6.62633	0.220024	0.110012	−	0.993930i	$-0.464911\pi$
$907$	6.62633	0.220024	0.110012	+	0.993930i	$0.464911\pi$
$908$	−38.7221	−1.28504
$909$	4.05213	0.134401
$910$	0	0
$911$	8.39931	0.278282	0.139141	−	0.990273i	$-0.455566\pi$
$911$	8.39931	0.278282	0.139141	+	0.990273i	$0.455566\pi$
$912$	−10.9096	−0.361253
$913$	31.0313	1.02699
$914$	18.2138	0.602458
$915$	0	0
$916$	−11.2638	−0.372165
$917$	14.4630	0.477610
$918$	23.6567	0.780788
$919$	−6.55191	−0.216128	−0.108064	−	0.994144i	$-0.534465\pi$
$919$	−6.55191	−0.216128	−0.108064	+	0.994144i	$0.534465\pi$
$920$	0	0
$921$	52.9155	1.74362
$922$	−3.50806	−0.115532
$923$	6.18228	0.203492
$924$	10.4182	0.342735
$925$	0	0
$926$	−12.0270	−0.395232
$927$	−0.381885	−0.0125428
$928$	−5.54071	−0.181883
$929$	−28.4747	−0.934225	−0.467113	−	0.884198i	$-0.654706\pi$
$929$	−28.4747	−0.934225	−0.467113	+	0.884198i	$0.654706\pi$
$930$	0	0
$931$	−4.61486	−0.151246
$932$	14.3957	0.471547
$933$	0.340797	0.0111572
$934$	18.8251	0.615977
$935$	0	0
$936$	−2.05379	−0.0671301
$937$	−8.81303	−0.287909	−0.143955	−	0.989584i	$-0.545982\pi$
$937$	−8.81303	−0.287909	−0.143955	+	0.989584i	$0.545982\pi$
$938$	−0.968609	−0.0316262
$939$	−40.5048	−1.32182
$940$	0	0
$941$	28.6854	0.935118	0.467559	−	0.883962i	$-0.345133\pi$
$941$	28.6854	0.935118	0.467559	+	0.883962i	$0.345133\pi$
$942$	9.85343	0.321042
$943$	10.9298	0.355924
$944$	−13.2817	−0.432283
$945$	0	0
$946$	−1.21558	−0.0395220
$947$	6.58170	0.213876	0.106938	−	0.994266i	$-0.465895\pi$
$947$	6.58170	0.213876	0.106938	+	0.994266i	$0.465895\pi$
$948$	−0.0460468	−0.00149553
$949$	−40.7265	−1.32204
$950$	0	0
$951$	10.1456	0.328995
$952$	−16.7318	−0.542282
$953$	−18.7870	−0.608572	−0.304286	−	0.952581i	$-0.598418\pi$
$953$	−18.7870	−0.608572	−0.304286	+	0.952581i	$0.598418\pi$
$954$	0.262099	0.00848576
$955$	0	0
$956$	−35.2694	−1.14069
$957$	−6.55569	−0.211915
$958$	−9.99047	−0.322778
$959$	4.04432	0.130598
$960$	0	0
$961$	−29.4584	−0.950271
$962$	6.84478	0.220684
$963$	3.33018	0.107314
$964$	−4.28915	−0.138144
$965$	0	0
$966$	1.25700	0.0404433
$967$	20.6144	0.662913	0.331456	−	0.943471i	$-0.392460\pi$
$967$	20.6144	0.662913	0.331456	+	0.943471i	$0.392460\pi$
$968$	−8.91460	−0.286526
$969$	56.6893	1.82112
$970$	0	0
$971$	−17.1715	−0.551060	−0.275530	−	0.961293i	$-0.588853\pi$
$971$	−17.1715	−0.551060	−0.275530	+	0.961293i	$0.588853\pi$
$972$	3.78884	0.121527
$973$	12.6429	0.405311
$974$	−20.5248	−0.657656
$975$	0	0
$976$	−15.3102	−0.490066
$977$	10.9164	0.349246	0.174623	−	0.984635i	$-0.444129\pi$
$977$	10.9164	0.349246	0.174623	+	0.984635i	$0.444129\pi$
$978$	−16.7114	−0.534371
$979$	−59.8451	−1.91266
$980$	0	0
$981$	3.26894	0.104369
$982$	16.4655	0.525434
$983$	17.5384	0.559388	0.279694	−	0.960089i	$-0.409767\pi$
$983$	17.5384	0.559388	0.279694	+	0.960089i	$0.409767\pi$
$984$	48.2585	1.53842
$985$	0	0
$986$	4.53375	0.144384
$987$	−10.3627	−0.329847
$988$	24.1959	0.769773
$989$	0.455126	0.0144722
$990$	0	0
$991$	−12.4111	−0.394252	−0.197126	−	0.980378i	$-0.563161\pi$
$991$	−12.4111	−0.394252	−0.197126	+	0.980378i	$0.563161\pi$
$992$	−7.22786	−0.229485
$993$	29.9337	0.949917
$994$	−1.24520	−0.0394952
$995$	0	0
$996$	−22.0901	−0.699953
$997$	47.8065	1.51405	0.757024	−	0.653388i	$-0.226653\pi$
$997$	47.8065	1.51405	0.757024	+	0.653388i	$0.226653\pi$
$998$	7.78611	0.246465
$999$	−14.0467	−0.444417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.q.1.3		5
5.4	even	2		805.2.a.l.1.3	✓	5
15.14	odd	2		7245.2.a.bh.1.3		5
35.34	odd	2		5635.2.a.y.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.l.1.3	✓	5	5.4	even	2
4025.2.a.q.1.3		5	1.1	even	1	trivial
5635.2.a.y.1.3		5	35.34	odd	2
7245.2.a.bh.1.3		5	15.14	odd	2

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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.698160 q^{2} +1.80045 q^{3} -1.51257 q^{4} +1.25700 q^{6} -1.00000 q^{7} -2.45234 q^{8} +0.241606 q^{9} +O(q^{10})\)	\(q+0.698160 q^{2} +1.80045 q^{3} -1.51257 q^{4} +1.25700 q^{6} -1.00000 q^{7} -2.45234 q^{8} +0.241606 q^{9} +3.82559 q^{11} -2.72330 q^{12} +3.46630 q^{13} -0.698160 q^{14} +1.31302 q^{16} -6.82280 q^{17} +0.168680 q^{18} -4.61486 q^{19} -1.80045 q^{21} +2.67088 q^{22} -1.00000 q^{23} -4.41530 q^{24} +2.42004 q^{26} -4.96634 q^{27} +1.51257 q^{28} -0.951787 q^{29} -1.24161 q^{31} +5.82137 q^{32} +6.88777 q^{33} -4.76341 q^{34} -0.365447 q^{36} +2.82838 q^{37} -3.22191 q^{38} +6.24089 q^{39} -10.9298 q^{41} -1.25700 q^{42} -0.455126 q^{43} -5.78648 q^{44} -0.698160 q^{46} +5.75561 q^{47} +2.36402 q^{48} +1.00000 q^{49} -12.2841 q^{51} -5.24303 q^{52} +1.55382 q^{53} -3.46730 q^{54} +2.45234 q^{56} -8.30880 q^{57} -0.664500 q^{58} -10.1154 q^{59} -11.6603 q^{61} -0.866840 q^{62} -0.241606 q^{63} +1.43822 q^{64} +4.80877 q^{66} +1.38737 q^{67} +10.3200 q^{68} -1.80045 q^{69} +1.78354 q^{71} -0.592501 q^{72} -11.7493 q^{73} +1.97466 q^{74} +6.98030 q^{76} -3.82559 q^{77} +4.35715 q^{78} +0.0169084 q^{79} -9.66645 q^{81} -7.63077 q^{82} +8.11152 q^{83} +2.72330 q^{84} -0.317751 q^{86} -1.71364 q^{87} -9.38164 q^{88} -15.6434 q^{89} -3.46630 q^{91} +1.51257 q^{92} -2.23545 q^{93} +4.01834 q^{94} +10.4811 q^{96} -14.0621 q^{97} +0.698160 q^{98} +0.924287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 7 q^{11} + 10 q^{12} + 5 q^{13} - q^{14} - 9 q^{16} + 7 q^{17} - 11 q^{18} - 10 q^{19} - 4 q^{21} - 4 q^{22} - 5 q^{23} - 4 q^{24} - 2 q^{26} + 7 q^{27} - 3 q^{28} - 14 q^{29} - 10 q^{31} - 4 q^{33} - 10 q^{34} + 20 q^{36} + 3 q^{37} + 15 q^{38} - 13 q^{39} - 15 q^{41} + 5 q^{42} - 8 q^{43} - 27 q^{44} - q^{46} + 10 q^{47} + 2 q^{48} + 5 q^{49} - 18 q^{51} - 18 q^{52} + 9 q^{53} - 39 q^{54} + 3 q^{56} - 23 q^{57} + 31 q^{58} - 19 q^{59} - 21 q^{61} + 10 q^{62} - 5 q^{63} - 7 q^{64} + 25 q^{66} - 5 q^{67} + 15 q^{68} - 4 q^{69} - 16 q^{71} - 26 q^{72} - q^{73} - 16 q^{74} + 7 q^{77} - 28 q^{78} + 20 q^{79} - 3 q^{81} - 11 q^{82} + 31 q^{83} - 10 q^{84} + 10 q^{86} - 38 q^{87} + 3 q^{88} - 21 q^{89} - 5 q^{91} - 3 q^{92} - 23 q^{93} + 28 q^{94} + 24 q^{96} - 19 q^{97} + q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 7 * q^11 + 10 * q^12 + 5 * q^13 - q^14 - 9 * q^16 + 7 * q^17 - 11 * q^18 - 10 * q^19 - 4 * q^21 - 4 * q^22 - 5 * q^23 - 4 * q^24 - 2 * q^26 + 7 * q^27 - 3 * q^28 - 14 * q^29 - 10 * q^31 - 4 * q^33 - 10 * q^34 + 20 * q^36 + 3 * q^37 + 15 * q^38 - 13 * q^39 - 15 * q^41 + 5 * q^42 - 8 * q^43 - 27 * q^44 - q^46 + 10 * q^47 + 2 * q^48 + 5 * q^49 - 18 * q^51 - 18 * q^52 + 9 * q^53 - 39 * q^54 + 3 * q^56 - 23 * q^57 + 31 * q^58 - 19 * q^59 - 21 * q^61 + 10 * q^62 - 5 * q^63 - 7 * q^64 + 25 * q^66 - 5 * q^67 + 15 * q^68 - 4 * q^69 - 16 * q^71 - 26 * q^72 - q^73 - 16 * q^74 + 7 * q^77 - 28 * q^78 + 20 * q^79 - 3 * q^81 - 11 * q^82 + 31 * q^83 - 10 * q^84 + 10 * q^86 - 38 * q^87 + 3 * q^88 - 21 * q^89 - 5 * q^91 - 3 * q^92 - 23 * q^93 + 28 * q^94 + 24 * q^96 - 19 * q^97 + q^98 - 26 * q^99

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