LMFDB - Embedded newform 4025.2.a.w.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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 19x^{5} + 12x^{4} - 34x^{3} - 12x^{2} + 17x + 7 $ x^8 - 3x^7 - 6x^6 + 19x^5 + 12x^4 - 34x^3 - 12x^2 + 17*x + 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.673262$ 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)

$f(q)$	$=$	$q-0.673262 q^{2} +0.897707 q^{3} -1.54672 q^{4} -0.604392 q^{6} -1.00000 q^{7} +2.38787 q^{8} -2.19412 q^{9} +O(q^{10})$	\(q-0.673262 q^{2} +0.897707 q^{3} -1.54672 q^{4} -0.604392 q^{6} -1.00000 q^{7} +2.38787 q^{8} -2.19412 q^{9} -1.69202 q^{11} -1.38850 q^{12} -0.185572 q^{13} +0.673262 q^{14} +1.48577 q^{16} -6.58168 q^{17} +1.47722 q^{18} -0.983713 q^{19} -0.897707 q^{21} +1.13918 q^{22} -1.00000 q^{23} +2.14361 q^{24} +0.124939 q^{26} -4.66280 q^{27} +1.54672 q^{28} +7.11115 q^{29} -4.91782 q^{31} -5.77606 q^{32} -1.51894 q^{33} +4.43120 q^{34} +3.39369 q^{36} -1.58366 q^{37} +0.662297 q^{38} -0.166589 q^{39} +0.327612 q^{41} +0.604392 q^{42} +6.87084 q^{43} +2.61708 q^{44} +0.673262 q^{46} +10.1894 q^{47} +1.33379 q^{48} +1.00000 q^{49} -5.90842 q^{51} +0.287027 q^{52} -5.51100 q^{53} +3.13929 q^{54} -2.38787 q^{56} -0.883086 q^{57} -4.78767 q^{58} -7.65443 q^{59} +11.8573 q^{61} +3.31098 q^{62} +2.19412 q^{63} +0.917260 q^{64} +1.02265 q^{66} -3.44265 q^{67} +10.1800 q^{68} -0.897707 q^{69} -11.3114 q^{71} -5.23928 q^{72} +10.6009 q^{73} +1.06622 q^{74} +1.52153 q^{76} +1.69202 q^{77} +0.112158 q^{78} -0.255570 q^{79} +2.39654 q^{81} -0.220569 q^{82} +17.4343 q^{83} +1.38850 q^{84} -4.62588 q^{86} +6.38373 q^{87} -4.04034 q^{88} -0.304653 q^{89} +0.185572 q^{91} +1.54672 q^{92} -4.41476 q^{93} -6.86016 q^{94} -5.18520 q^{96} -5.81373 q^{97} -0.673262 q^{98} +3.71251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8}+O(q^{10}) $ 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8	$ 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8} - 5 q^{11} + 3 q^{12} + 9 q^{13} - 3 q^{14} - q^{16} - q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{21} - 5 q^{22} - 8 q^{23} + 16 q^{24} + 22 q^{26} - q^{27} - 5 q^{28} - 5 q^{29} - q^{31} + 2 q^{32} + 12 q^{33} - 2 q^{34} + 16 q^{36} + 18 q^{37} + 14 q^{38} + 14 q^{39} - q^{41} + q^{42} + 20 q^{43} - 3 q^{46} + 10 q^{47} + 31 q^{48} + 8 q^{49} - 4 q^{51} + 11 q^{52} + 11 q^{53} + 29 q^{54} - 12 q^{56} + 8 q^{57} + 24 q^{58} + 20 q^{59} - 6 q^{61} + 2 q^{62} + 8 q^{64} - 37 q^{66} + 23 q^{67} + 9 q^{68} - 2 q^{69} + 3 q^{71} + 29 q^{72} - 8 q^{73} + 35 q^{74} - 29 q^{76} + 5 q^{77} + 31 q^{78} + 4 q^{79} - 44 q^{81} + 27 q^{82} + 4 q^{83} - 3 q^{84} - 18 q^{86} + 27 q^{87} - 4 q^{88} - 17 q^{89} - 9 q^{91} - 5 q^{92} - 7 q^{93} + 13 q^{94} + 22 q^{96} + 41 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8 - 5 * q^11 + 3 * q^12 + 9 * q^13 - 3 * q^14 - q^16 - q^17 + 6 * q^18 - 4 * q^19 - 2 * q^21 - 5 * q^22 - 8 * q^23 + 16 * q^24 + 22 * q^26 - q^27 - 5 * q^28 - 5 * q^29 - q^31 + 2 * q^32 + 12 * q^33 - 2 * q^34 + 16 * q^36 + 18 * q^37 + 14 * q^38 + 14 * q^39 - q^41 + q^42 + 20 * q^43 - 3 * q^46 + 10 * q^47 + 31 * q^48 + 8 * q^49 - 4 * q^51 + 11 * q^52 + 11 * q^53 + 29 * q^54 - 12 * q^56 + 8 * q^57 + 24 * q^58 + 20 * q^59 - 6 * q^61 + 2 * q^62 + 8 * q^64 - 37 * q^66 + 23 * q^67 + 9 * q^68 - 2 * q^69 + 3 * q^71 + 29 * q^72 - 8 * q^73 + 35 * q^74 - 29 * q^76 + 5 * q^77 + 31 * q^78 + 4 * q^79 - 44 * q^81 + 27 * q^82 + 4 * q^83 - 3 * q^84 - 18 * q^86 + 27 * q^87 - 4 * q^88 - 17 * q^89 - 9 * q^91 - 5 * q^92 - 7 * q^93 + 13 * q^94 + 22 * q^96 + 41 * q^97 + 3 * q^98 + 7 * 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 $

$2$	−0.673262	−0.476068	−0.238034	−	0.971257i	$-0.576503\pi$
$2$	−0.673262	−0.476068	−0.238034	+	0.971257i	$0.576503\pi$
$3$	0.897707	0.518291	0.259146	−	0.965838i	$-0.416559\pi$
$3$	0.897707	0.518291	0.259146	+	0.965838i	$0.416559\pi$
$4$	−1.54672	−0.773359
$5$	0	0
$5$	0	0
$6$	−0.604392	−0.246742
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.38787	0.844240
$9$	−2.19412	−0.731374
$10$	0	0
$11$	−1.69202	−0.510164	−0.255082	−	0.966919i	$-0.582103\pi$
$11$	−1.69202	−0.510164	−0.255082	+	0.966919i	$0.582103\pi$
$12$	−1.38850	−0.400825
$13$	−0.185572	−0.0514684	−0.0257342	−	0.999669i	$-0.508192\pi$
$13$	−0.185572	−0.0514684	−0.0257342	+	0.999669i	$0.508192\pi$
$14$	0.673262	0.179937
$15$	0	0
$16$	1.48577	0.371443
$17$	−6.58168	−1.59629	−0.798146	−	0.602464i	$-0.794186\pi$
$17$	−6.58168	−1.59629	−0.798146	+	0.602464i	$0.794186\pi$
$18$	1.47722	0.348184
$19$	−0.983713	−0.225679	−0.112840	−	0.993613i	$-0.535995\pi$
$19$	−0.983713	−0.225679	−0.112840	+	0.993613i	$0.535995\pi$
$20$	0	0
$21$	−0.897707	−0.195896
$22$	1.13918	0.242873
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.14361	0.437562
$25$	0	0
$26$	0.124939	0.0245025
$27$	−4.66280	−0.897356
$28$	1.54672	0.292302
$29$	7.11115	1.32051	0.660254	−	0.751042i	$-0.270449\pi$
$29$	7.11115	1.32051	0.660254	+	0.751042i	$0.270449\pi$
$30$	0	0
$31$	−4.91782	−0.883267	−0.441633	−	0.897196i	$-0.645601\pi$
$31$	−4.91782	−0.883267	−0.441633	+	0.897196i	$0.645601\pi$
$32$	−5.77606	−1.02107
$33$	−1.51894	−0.264414
$34$	4.43120	0.759944
$35$	0	0
$36$	3.39369	0.565615
$37$	−1.58366	−0.260352	−0.130176	−	0.991491i	$-0.541554\pi$
$37$	−1.58366	−0.260352	−0.130176	+	0.991491i	$0.541554\pi$
$38$	0.662297	0.107439
$39$	−0.166589	−0.0266756
$40$	0	0
$41$	0.327612	0.0511644	0.0255822	−	0.999673i	$-0.491856\pi$
$41$	0.327612	0.0511644	0.0255822	+	0.999673i	$0.491856\pi$
$42$	0.604392	0.0932597
$43$	6.87084	1.04779	0.523897	−	0.851782i	$-0.324478\pi$
$43$	6.87084	1.04779	0.523897	+	0.851782i	$0.324478\pi$
$44$	2.61708	0.394540
$45$	0	0
$46$	0.673262	0.0992671
$47$	10.1894	1.48628	0.743140	−	0.669136i	$-0.233336\pi$
$47$	10.1894	1.48628	0.743140	+	0.669136i	$0.233336\pi$
$48$	1.33379	0.192516
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.90842	−0.827344
$52$	0.287027	0.0398035
$53$	−5.51100	−0.756994	−0.378497	−	0.925603i	$-0.623559\pi$
$53$	−5.51100	−0.756994	−0.378497	+	0.925603i	$0.623559\pi$
$54$	3.13929	0.427203
$55$	0	0
$56$	−2.38787	−0.319093
$57$	−0.883086	−0.116968
$58$	−4.78767	−0.628652
$59$	−7.65443	−0.996522	−0.498261	−	0.867027i	$-0.666028\pi$
$59$	−7.65443	−0.996522	−0.498261	+	0.867027i	$0.666028\pi$
$60$	0	0
$61$	11.8573	1.51817	0.759087	−	0.650989i	$-0.225645\pi$
$61$	11.8573	1.51817	0.759087	+	0.650989i	$0.225645\pi$
$62$	3.31098	0.420495
$63$	2.19412	0.276433
$64$	0.917260	0.114657
$65$	0	0
$66$	1.02265	0.125879
$67$	−3.44265	−0.420587	−0.210294	−	0.977638i	$-0.567442\pi$
$67$	−3.44265	−0.420587	−0.210294	+	0.977638i	$0.567442\pi$
$68$	10.1800	1.23451
$69$	−0.897707	−0.108071
$70$	0	0
$71$	−11.3114	−1.34241	−0.671206	−	0.741271i	$-0.734223\pi$
$71$	−11.3114	−1.34241	−0.671206	+	0.741271i	$0.734223\pi$
$72$	−5.23928	−0.617456
$73$	10.6009	1.24075	0.620373	−	0.784307i	$-0.286981\pi$
$73$	10.6009	1.24075	0.620373	+	0.784307i	$0.286981\pi$
$74$	1.06622	0.123945
$75$	0	0
$76$	1.52153	0.174531
$77$	1.69202	0.192824
$78$	0.112158	0.0126994
$79$	−0.255570	−0.0287539	−0.0143769	−	0.999897i	$-0.504576\pi$
$79$	−0.255570	−0.0287539	−0.0143769	+	0.999897i	$0.504576\pi$
$80$	0	0
$81$	2.39654	0.266283
$82$	−0.220569	−0.0243578
$83$	17.4343	1.91366	0.956831	−	0.290644i	$-0.0938695\pi$
$83$	17.4343	1.91366	0.956831	+	0.290644i	$0.0938695\pi$
$84$	1.38850	0.151498
$85$	0	0
$86$	−4.62588	−0.498821
$87$	6.38373	0.684408
$88$	−4.04034	−0.430701
$89$	−0.304653	−0.0322932	−0.0161466	−	0.999870i	$-0.505140\pi$
$89$	−0.304653	−0.0322932	−0.0161466	+	0.999870i	$0.505140\pi$
$90$	0	0
$91$	0.185572	0.0194532
$92$	1.54672	0.161256
$93$	−4.41476	−0.457789
$94$	−6.86016	−0.707571
$95$	0	0
$96$	−5.18520	−0.529213
$97$	−5.81373	−0.590294	−0.295147	−	0.955452i	$-0.595369\pi$
$97$	−5.81373	−0.590294	−0.295147	+	0.955452i	$0.595369\pi$
$98$	−0.673262	−0.0680098
$99$	3.71251	0.373121
$100$	0	0
$101$	−8.93529	−0.889095	−0.444547	−	0.895755i	$-0.646635\pi$
$101$	−8.93529	−0.889095	−0.444547	+	0.895755i	$0.646635\pi$
$102$	3.97792	0.393872
$103$	5.54561	0.546426	0.273213	−	0.961954i	$-0.411914\pi$
$103$	5.54561	0.546426	0.273213	+	0.961954i	$0.411914\pi$
$104$	−0.443122	−0.0434517
$105$	0	0
$106$	3.71035	0.360381
$107$	15.8426	1.53156	0.765782	−	0.643100i	$-0.222352\pi$
$107$	15.8426	1.53156	0.765782	+	0.643100i	$0.222352\pi$
$108$	7.21203	0.693978
$109$	−0.933297	−0.0893936	−0.0446968	−	0.999001i	$-0.514232\pi$
$109$	−0.933297	−0.0893936	−0.0446968	+	0.999001i	$0.514232\pi$
$110$	0	0
$111$	−1.42166	−0.134938
$112$	−1.48577	−0.140392
$113$	−12.3410	−1.16094	−0.580471	−	0.814281i	$-0.697132\pi$
$113$	−12.3410	−1.16094	−0.580471	+	0.814281i	$0.697132\pi$
$114$	0.594548	0.0556846
$115$	0	0
$116$	−10.9989	−1.02123
$117$	0.407168	0.0376427
$118$	5.15344	0.474413
$119$	6.58168	0.603342
$120$	0	0
$121$	−8.13705	−0.739732
$122$	−7.98309	−0.722755
$123$	0.294100	0.0265181
$124$	7.60648	0.683082
$125$	0	0
$126$	−1.47722	−0.131601
$127$	−4.46797	−0.396468	−0.198234	−	0.980155i	$-0.563521\pi$
$127$	−4.46797	−0.396468	−0.198234	+	0.980155i	$0.563521\pi$
$128$	10.9346	0.966488
$129$	6.16800	0.543062
$130$	0	0
$131$	7.14313	0.624098	0.312049	−	0.950066i	$-0.398985\pi$
$131$	7.14313	0.624098	0.312049	+	0.950066i	$0.398985\pi$
$132$	2.34937	0.204487
$133$	0.983713	0.0852987
$134$	2.31781	0.200228
$135$	0	0
$136$	−15.7162	−1.34765
$137$	11.3048	0.965837	0.482918	−	0.875665i	$-0.339577\pi$
$137$	11.3048	0.965837	0.482918	+	0.875665i	$0.339577\pi$
$138$	0.604392	0.0514493
$139$	4.32929	0.367205	0.183603	−	0.983001i	$-0.441224\pi$
$139$	4.32929	0.367205	0.183603	+	0.983001i	$0.441224\pi$
$140$	0	0
$141$	9.14711	0.770326
$142$	7.61552	0.639080
$143$	0.313992	0.0262573
$144$	−3.25996	−0.271664
$145$	0	0
$146$	−7.13722	−0.590680
$147$	0.897707	0.0740416
$148$	2.44948	0.201346
$149$	−0.747538	−0.0612407	−0.0306203	−	0.999531i	$-0.509748\pi$
$149$	−0.747538	−0.0612407	−0.0306203	+	0.999531i	$0.509748\pi$
$150$	0	0
$151$	21.5525	1.75392	0.876961	−	0.480562i	$-0.159567\pi$
$151$	21.5525	1.75392	0.876961	+	0.480562i	$0.159567\pi$
$152$	−2.34898	−0.190527
$153$	14.4410	1.16749
$154$	−1.13918	−0.0917974
$155$	0	0
$156$	0.257666	0.0206298
$157$	8.30072	0.662470	0.331235	−	0.943548i	$-0.392535\pi$
$157$	8.30072	0.662470	0.331235	+	0.943548i	$0.392535\pi$
$158$	0.172066	0.0136888
$159$	−4.94726	−0.392343
$160$	0	0
$161$	1.00000	0.0788110
$162$	−1.61350	−0.126769
$163$	11.7280	0.918607	0.459304	−	0.888279i	$-0.348099\pi$
$163$	11.7280	0.918607	0.459304	+	0.888279i	$0.348099\pi$
$164$	−0.506724	−0.0395685
$165$	0	0
$166$	−11.7379	−0.911034
$167$	−7.63000	−0.590427	−0.295213	−	0.955431i	$-0.595391\pi$
$167$	−7.63000	−0.590427	−0.295213	+	0.955431i	$0.595391\pi$
$168$	−2.14361	−0.165383
$169$	−12.9656	−0.997351
$170$	0	0
$171$	2.15839	0.165056
$172$	−10.6272	−0.810320
$173$	16.2018	1.23180	0.615901	−	0.787823i	$-0.288792\pi$
$173$	16.2018	1.23180	0.615901	+	0.787823i	$0.288792\pi$
$174$	−4.29792	−0.325825
$175$	0	0
$176$	−2.51396	−0.189497
$177$	−6.87143	−0.516488
$178$	0.205112	0.0153738
$179$	3.34297	0.249866	0.124933	−	0.992165i	$-0.460128\pi$
$179$	3.34297	0.249866	0.124933	+	0.992165i	$0.460128\pi$
$180$	0	0
$181$	−1.54023	−0.114484	−0.0572421	−	0.998360i	$-0.518231\pi$
$181$	−1.54023	−0.114484	−0.0572421	+	0.998360i	$0.518231\pi$
$182$	−0.124939	−0.00926107
$183$	10.6444	0.786857
$184$	−2.38787	−0.176036
$185$	0	0
$186$	2.97229	0.217939
$187$	11.1364	0.814372
$188$	−15.7602	−1.14943
$189$	4.66280	0.339169
$190$	0	0
$191$	−16.5772	−1.19949	−0.599743	−	0.800192i	$-0.704731\pi$
$191$	−16.5772	−1.19949	−0.599743	+	0.800192i	$0.704731\pi$
$192$	0.823430	0.0594259
$193$	14.5264	1.04563	0.522815	−	0.852446i	$-0.324882\pi$
$193$	14.5264	1.04563	0.522815	+	0.852446i	$0.324882\pi$
$194$	3.91416	0.281021
$195$	0	0
$196$	−1.54672	−0.110480
$197$	18.8325	1.34176	0.670879	−	0.741567i	$-0.265917\pi$
$197$	18.8325	1.34176	0.670879	+	0.741567i	$0.265917\pi$
$198$	−2.49949	−0.177631
$199$	−7.46638	−0.529277	−0.264639	−	0.964348i	$-0.585253\pi$
$199$	−7.46638	−0.529277	−0.264639	+	0.964348i	$0.585253\pi$
$200$	0	0
$201$	−3.09049	−0.217987
$202$	6.01580	0.423270
$203$	−7.11115	−0.499105
$204$	9.13866	0.639834
$205$	0	0
$206$	−3.73365	−0.260136
$207$	2.19412	0.152502
$208$	−0.275717	−0.0191176
$209$	1.66447	0.115134
$210$	0	0
$211$	−0.739167	−0.0508863	−0.0254432	−	0.999676i	$-0.508100\pi$
$211$	−0.739167	−0.0508863	−0.0254432	+	0.999676i	$0.508100\pi$
$212$	8.52396	0.585428
$213$	−10.1543	−0.695760
$214$	−10.6662	−0.729130
$215$	0	0
$216$	−11.1342	−0.757584
$217$	4.91782	0.333843
$218$	0.628353	0.0425575
$219$	9.51654	0.643068
$220$	0	0
$221$	1.22138	0.0821586
$222$	0.957152	0.0642398
$223$	−18.7449	−1.25525	−0.627626	−	0.778515i	$-0.715973\pi$
$223$	−18.7449	−1.25525	−0.627626	+	0.778515i	$0.715973\pi$
$224$	5.77606	0.385929
$225$	0	0
$226$	8.30872	0.552688
$227$	−15.6818	−1.04083	−0.520417	−	0.853912i	$-0.674224\pi$
$227$	−15.6818	−1.04083	−0.520417	+	0.853912i	$0.674224\pi$
$228$	1.36588	0.0904579
$229$	−18.8546	−1.24595	−0.622975	−	0.782242i	$-0.714076\pi$
$229$	−18.8546	−1.24595	−0.622975	+	0.782242i	$0.714076\pi$
$230$	0	0
$231$	1.51894	0.0999390
$232$	16.9805	1.11483
$233$	18.4240	1.20699	0.603497	−	0.797365i	$-0.293774\pi$
$233$	18.4240	1.20699	0.603497	+	0.797365i	$0.293774\pi$
$234$	−0.274131	−0.0179205
$235$	0	0
$236$	11.8392	0.770669
$237$	−0.229427	−0.0149029
$238$	−4.43120	−0.287232
$239$	21.8282	1.41195	0.705975	−	0.708237i	$-0.250509\pi$
$239$	21.8282	1.41195	0.705975	+	0.708237i	$0.250509\pi$
$240$	0	0
$241$	11.0783	0.713613	0.356807	−	0.934178i	$-0.383866\pi$
$241$	11.0783	0.713613	0.356807	+	0.934178i	$0.383866\pi$
$242$	5.47837	0.352163
$243$	16.1398	1.03537
$244$	−18.3399	−1.17409
$245$	0	0
$246$	−0.198006	−0.0126244
$247$	0.182550	0.0116153
$248$	−11.7431	−0.745689
$249$	15.6509	0.991834
$250$	0	0
$251$	7.81310	0.493158	0.246579	−	0.969123i	$-0.420693\pi$
$251$	7.81310	0.493158	0.246579	+	0.969123i	$0.420693\pi$
$252$	−3.39369	−0.213782
$253$	1.69202	0.106377
$254$	3.00812	0.188746
$255$	0	0
$256$	−9.19635	−0.574772
$257$	−1.83449	−0.114433	−0.0572163	−	0.998362i	$-0.518222\pi$
$257$	−1.83449	−0.114433	−0.0572163	+	0.998362i	$0.518222\pi$
$258$	−4.15268	−0.258535
$259$	1.58366	0.0984039
$260$	0	0
$261$	−15.6027	−0.965786
$262$	−4.80920	−0.297113
$263$	−5.25860	−0.324259	−0.162130	−	0.986769i	$-0.551836\pi$
$263$	−5.25860	−0.324259	−0.162130	+	0.986769i	$0.551836\pi$
$264$	−3.62704	−0.223229
$265$	0	0
$266$	−0.662297	−0.0406080
$267$	−0.273489	−0.0167373
$268$	5.32481	0.325265
$269$	17.8643	1.08920	0.544602	−	0.838694i	$-0.316681\pi$
$269$	17.8643	1.08920	0.544602	+	0.838694i	$0.316681\pi$
$270$	0	0
$271$	23.1830	1.40827	0.704135	−	0.710066i	$-0.251335\pi$
$271$	23.1830	1.40827	0.704135	+	0.710066i	$0.251335\pi$
$272$	−9.77887	−0.592931
$273$	0.166589	0.0100824
$274$	−7.61112	−0.459804
$275$	0	0
$276$	1.38850	0.0835778
$277$	24.5024	1.47221	0.736104	−	0.676869i	$-0.236664\pi$
$277$	24.5024	1.47221	0.736104	+	0.676869i	$0.236664\pi$
$278$	−2.91475	−0.174815
$279$	10.7903	0.645999
$280$	0	0
$281$	19.1223	1.14074	0.570370	−	0.821388i	$-0.306800\pi$
$281$	19.1223	1.14074	0.570370	+	0.821388i	$0.306800\pi$
$282$	−6.15841	−0.366728
$283$	10.7414	0.638509	0.319254	−	0.947669i	$-0.396568\pi$
$283$	10.7414	0.638509	0.319254	+	0.947669i	$0.396568\pi$
$284$	17.4955	1.03817
$285$	0	0
$286$	−0.211399	−0.0125003
$287$	−0.327612	−0.0193383
$288$	12.6734	0.746786
$289$	26.3185	1.54815
$290$	0	0
$291$	−5.21902	−0.305944
$292$	−16.3967	−0.959543
$293$	−8.19049	−0.478493	−0.239247	−	0.970959i	$-0.576900\pi$
$293$	−8.19049	−0.478493	−0.239247	+	0.970959i	$0.576900\pi$
$294$	−0.604392	−0.0352489
$295$	0	0
$296$	−3.78158	−0.219800
$297$	7.88957	0.457799
$298$	0.503289	0.0291548
$299$	0.185572	0.0107319
$300$	0	0
$301$	−6.87084	−0.396029
$302$	−14.5105	−0.834986
$303$	−8.02127	−0.460810
$304$	−1.46157	−0.0838269
$305$	0	0
$306$	−9.72259	−0.555804
$307$	19.7764	1.12870	0.564348	−	0.825537i	$-0.309127\pi$
$307$	19.7764	1.12870	0.564348	+	0.825537i	$0.309127\pi$
$308$	−2.61708	−0.149122
$309$	4.97833	0.283208
$310$	0	0
$311$	−23.7011	−1.34397	−0.671984	−	0.740566i	$-0.734558\pi$
$311$	−23.7011	−1.34397	−0.671984	+	0.740566i	$0.734558\pi$
$312$	−0.397794	−0.0225206
$313$	26.5075	1.49829	0.749147	−	0.662404i	$-0.230464\pi$
$313$	26.5075	1.49829	0.749147	+	0.662404i	$0.230464\pi$
$314$	−5.58856	−0.315381
$315$	0	0
$316$	0.395295	0.0222371
$317$	6.96360	0.391114	0.195557	−	0.980692i	$-0.437348\pi$
$317$	6.96360	0.391114	0.195557	+	0.980692i	$0.437348\pi$
$318$	3.33080	0.186782
$319$	−12.0322	−0.673676
$320$	0	0
$321$	14.2220	0.793797
$322$	−0.673262	−0.0375194
$323$	6.47449	0.360250
$324$	−3.70678	−0.205932
$325$	0	0
$326$	−7.89602	−0.437320
$327$	−0.837826	−0.0463319
$328$	0.782296	0.0431951
$329$	−10.1894	−0.561761
$330$	0	0
$331$	−33.5450	−1.84380	−0.921899	−	0.387431i	$-0.873362\pi$
$331$	−33.5450	−1.84380	−0.921899	+	0.387431i	$0.873362\pi$
$332$	−26.9659	−1.47995
$333$	3.47475	0.190415
$334$	5.13699	0.281084
$335$	0	0
$336$	−1.33379	−0.0727640
$337$	−9.97975	−0.543631	−0.271816	−	0.962349i	$-0.587624\pi$
$337$	−9.97975	−0.543631	−0.271816	+	0.962349i	$0.587624\pi$
$338$	8.72923	0.474807
$339$	−11.0786	−0.601706
$340$	0	0
$341$	8.32107	0.450611
$342$	−1.45316	−0.0785779
$343$	−1.00000	−0.0539949
$344$	16.4067	0.884589
$345$	0	0
$346$	−10.9081	−0.586422
$347$	16.3979	0.880287	0.440143	−	0.897928i	$-0.354928\pi$
$347$	16.3979	0.880287	0.440143	+	0.897928i	$0.354928\pi$
$348$	−9.87383	−0.529293
$349$	−6.65180	−0.356063	−0.178031	−	0.984025i	$-0.556973\pi$
$349$	−6.65180	−0.356063	−0.178031	+	0.984025i	$0.556973\pi$
$350$	0	0
$351$	0.865285	0.0461855
$352$	9.77323	0.520915
$353$	−0.0257102	−0.00136842	−0.000684208	−	1.00000i	$-0.500218\pi$
$353$	−0.0257102	−0.00136842	−0.000684208		1.00000i	$0.500218\pi$
$354$	4.62628	0.245884
$355$	0	0
$356$	0.471212	0.0249742
$357$	5.90842	0.312707
$358$	−2.25070	−0.118953
$359$	−34.0059	−1.79476	−0.897382	−	0.441255i	$-0.854533\pi$
$359$	−34.0059	−1.79476	−0.897382	+	0.441255i	$0.854533\pi$
$360$	0	0
$361$	−18.0323	−0.949069
$362$	1.03698	0.0545023
$363$	−7.30469	−0.383397
$364$	−0.287027	−0.0150443
$365$	0	0
$366$	−7.16647	−0.374598
$367$	14.5191	0.757890	0.378945	−	0.925419i	$-0.376287\pi$
$367$	14.5191	0.757890	0.378945	+	0.925419i	$0.376287\pi$
$368$	−1.48577	−0.0774512
$369$	−0.718822	−0.0374204
$370$	0	0
$371$	5.51100	0.286117
$372$	6.82839	0.354035
$373$	−18.2429	−0.944582	−0.472291	−	0.881443i	$-0.656573\pi$
$373$	−18.2429	−0.944582	−0.472291	+	0.881443i	$0.656573\pi$
$374$	−7.49769	−0.387697
$375$	0	0
$376$	24.3310	1.25478
$377$	−1.31963	−0.0679644
$378$	−3.13929	−0.161467
$379$	31.3989	1.61285	0.806427	−	0.591333i	$-0.201398\pi$
$379$	31.3989	1.61285	0.806427	+	0.591333i	$0.201398\pi$
$380$	0	0
$381$	−4.01093	−0.205486
$382$	11.1608	0.571038
$383$	14.8060	0.756554	0.378277	−	0.925693i	$-0.376517\pi$
$383$	14.8060	0.756554	0.378277	+	0.925693i	$0.376517\pi$
$384$	9.81603	0.500922
$385$	0	0
$386$	−9.78005	−0.497792
$387$	−15.0755	−0.766329
$388$	8.99219	0.456509
$389$	−16.5420	−0.838715	−0.419358	−	0.907821i	$-0.637745\pi$
$389$	−16.5420	−0.838715	−0.419358	+	0.907821i	$0.637745\pi$
$390$	0	0
$391$	6.58168	0.332850
$392$	2.38787	0.120606
$393$	6.41244	0.323465
$394$	−12.6792	−0.638769
$395$	0	0
$396$	−5.74220	−0.288557
$397$	8.82107	0.442717	0.221358	−	0.975193i	$-0.428951\pi$
$397$	8.82107	0.442717	0.221358	+	0.975193i	$0.428951\pi$
$398$	5.02683	0.251972
$399$	0.883086	0.0442096
$400$	0	0
$401$	19.5136	0.974465	0.487232	−	0.873272i	$-0.338006\pi$
$401$	19.5136	0.974465	0.487232	+	0.873272i	$0.338006\pi$
$402$	2.08071	0.103777
$403$	0.912610	0.0454603
$404$	13.8204	0.687589
$405$	0	0
$406$	4.78767	0.237608
$407$	2.67959	0.132822
$408$	−14.1085	−0.698477
$409$	−34.4654	−1.70421	−0.852103	−	0.523374i	$-0.824673\pi$
$409$	−34.4654	−1.70421	−0.852103	+	0.523374i	$0.824673\pi$
$410$	0	0
$411$	10.1484	0.500585
$412$	−8.57750	−0.422583
$413$	7.65443	0.376650
$414$	−1.47722	−0.0726014
$415$	0	0
$416$	1.07187	0.0525530
$417$	3.88643	0.190319
$418$	−1.12062	−0.0548114
$419$	5.98534	0.292403	0.146201	−	0.989255i	$-0.453295\pi$
$419$	5.98534	0.292403	0.146201	+	0.989255i	$0.453295\pi$
$420$	0	0
$421$	11.4583	0.558444	0.279222	−	0.960227i	$-0.409923\pi$
$421$	11.4583	0.558444	0.279222	+	0.960227i	$0.409923\pi$
$422$	0.497653	0.0242254
$423$	−22.3568	−1.08703
$424$	−13.1596	−0.639084
$425$	0	0
$426$	6.83650	0.331229
$427$	−11.8573	−0.573816
$428$	−24.5041	−1.18445
$429$	0.281873	0.0136090
$430$	0	0
$431$	−21.7995	−1.05004	−0.525022	−	0.851089i	$-0.675943\pi$
$431$	−21.7995	−1.05004	−0.525022	+	0.851089i	$0.675943\pi$
$432$	−6.92785	−0.333316
$433$	−23.7948	−1.14350	−0.571752	−	0.820427i	$-0.693736\pi$
$433$	−23.7948	−1.14350	−0.571752	+	0.820427i	$0.693736\pi$
$434$	−3.31098	−0.158932
$435$	0	0
$436$	1.44355	0.0691333
$437$	0.983713	0.0470574
$438$	−6.40713	−0.306144
$439$	6.18613	0.295248	0.147624	−	0.989044i	$-0.452837\pi$
$439$	6.18613	0.295248	0.147624	+	0.989044i	$0.452837\pi$
$440$	0	0
$441$	−2.19412	−0.104482
$442$	−0.822306	−0.0391131
$443$	20.6876	0.982899	0.491450	−	0.870906i	$-0.336467\pi$
$443$	20.6876	0.982899	0.491450	+	0.870906i	$0.336467\pi$
$444$	2.19891	0.104356
$445$	0	0
$446$	12.6202	0.597586
$447$	−0.671070	−0.0317405
$448$	−0.917260	−0.0433364
$449$	−24.5335	−1.15781	−0.578904	−	0.815396i	$-0.696519\pi$
$449$	−24.5335	−1.15781	−0.578904	+	0.815396i	$0.696519\pi$
$450$	0	0
$451$	−0.554328	−0.0261023
$452$	19.0880	0.897825
$453$	19.3479	0.909042
$454$	10.5579	0.495509
$455$	0	0
$456$	−2.10870	−0.0987487
$457$	17.2274	0.805864	0.402932	−	0.915230i	$-0.367991\pi$
$457$	17.2274	0.805864	0.402932	+	0.915230i	$0.367991\pi$
$458$	12.6941	0.593157
$459$	30.6891	1.43244
$460$	0	0
$461$	33.6532	1.56739	0.783693	−	0.621149i	$-0.213334\pi$
$461$	33.6532	1.56739	0.783693	+	0.621149i	$0.213334\pi$
$462$	−1.02265	−0.0475778
$463$	15.2664	0.709490	0.354745	−	0.934963i	$-0.384568\pi$
$463$	15.2664	0.709490	0.354745	+	0.934963i	$0.384568\pi$
$464$	10.5655	0.490493
$465$	0	0
$466$	−12.4042	−0.574612
$467$	−8.84431	−0.409266	−0.204633	−	0.978839i	$-0.565600\pi$
$467$	−8.84431	−0.409266	−0.204633	+	0.978839i	$0.565600\pi$
$468$	−0.629773	−0.0291113
$469$	3.44265	0.158967
$470$	0	0
$471$	7.45161	0.343352
$472$	−18.2778	−0.841304
$473$	−11.6256	−0.534547
$474$	0.154465	0.00709479
$475$	0	0
$476$	−10.1800	−0.466600
$477$	12.0918	0.553646
$478$	−14.6961	−0.672185
$479$	16.0456	0.733142	0.366571	−	0.930390i	$-0.380532\pi$
$479$	16.0456	0.733142	0.366571	+	0.930390i	$0.380532\pi$
$480$	0	0
$481$	0.293883	0.0133999
$482$	−7.45857	−0.339729
$483$	0.897707	0.0408471
$484$	12.5857	0.572078
$485$	0	0
$486$	−10.8663	−0.492906
$487$	32.9780	1.49437	0.747187	−	0.664614i	$-0.231404\pi$
$487$	32.9780	1.49437	0.747187	+	0.664614i	$0.231404\pi$
$488$	28.3138	1.28170
$489$	10.5283	0.476106
$490$	0	0
$491$	−31.8599	−1.43782	−0.718908	−	0.695105i	$-0.755358\pi$
$491$	−31.8599	−1.43782	−0.718908	+	0.695105i	$0.755358\pi$
$492$	−0.454889	−0.0205080
$493$	−46.8033	−2.10792
$494$	−0.122904	−0.00552970
$495$	0	0
$496$	−7.30676	−0.328083
$497$	11.3114	0.507384
$498$	−10.5372	−0.472181
$499$	−6.35777	−0.284613	−0.142306	−	0.989823i	$-0.545452\pi$
$499$	−6.35777	−0.284613	−0.142306	+	0.989823i	$0.545452\pi$
$500$	0	0
$501$	−6.84950	−0.306013
$502$	−5.26027	−0.234777
$503$	−35.7623	−1.59456	−0.797282	−	0.603607i	$-0.793729\pi$
$503$	−35.7623	−1.59456	−0.797282	+	0.603607i	$0.793729\pi$
$504$	5.23928	0.233376
$505$	0	0
$506$	−1.13918	−0.0506426
$507$	−11.6393	−0.516918
$508$	6.91069	0.306612
$509$	26.6211	1.17996	0.589980	−	0.807418i	$-0.299135\pi$
$509$	26.6211	1.17996	0.589980	+	0.807418i	$0.299135\pi$
$510$	0	0
$511$	−10.6009	−0.468958
$512$	−15.6776	−0.692857
$513$	4.58686	0.202515
$514$	1.23510	0.0544778
$515$	0	0
$516$	−9.54015	−0.419982
$517$	−17.2407	−0.758247
$518$	−1.06622	−0.0468470
$519$	14.5445	0.638432
$520$	0	0
$521$	28.5811	1.25216	0.626081	−	0.779758i	$-0.284658\pi$
$521$	28.5811	1.25216	0.626081	+	0.779758i	$0.284658\pi$
$522$	10.5047	0.459780
$523$	−14.3746	−0.628559	−0.314279	−	0.949331i	$-0.601763\pi$
$523$	−14.3746	−0.628559	−0.314279	+	0.949331i	$0.601763\pi$
$524$	−11.0484	−0.482652
$525$	0	0
$526$	3.54042	0.154369
$527$	32.3675	1.40995
$528$	−2.25680	−0.0982146
$529$	1.00000	0.0434783
$530$	0	0
$531$	16.7948	0.728830
$532$	−1.52153	−0.0659665
$533$	−0.0607956	−0.00263335
$534$	0.184130	0.00796808
$535$	0	0
$536$	−8.22062	−0.355077
$537$	3.00101	0.129503
$538$	−12.0274	−0.518536
$539$	−1.69202	−0.0728806
$540$	0	0
$541$	3.91888	0.168486	0.0842429	−	0.996445i	$-0.473153\pi$
$541$	3.91888	0.168486	0.0842429	+	0.996445i	$0.473153\pi$
$542$	−15.6083	−0.670433
$543$	−1.38267	−0.0593362
$544$	38.0162	1.62993
$545$	0	0
$546$	−0.112158	−0.00479993
$547$	−0.246732	−0.0105495	−0.00527475	−	0.999986i	$-0.501679\pi$
$547$	−0.246732	−0.0105495	−0.00527475	+	0.999986i	$0.501679\pi$
$548$	−17.4854	−0.746938
$549$	−26.0164	−1.11035
$550$	0	0
$551$	−6.99533	−0.298011
$552$	−2.14361	−0.0912380
$553$	0.255570	0.0108679
$554$	−16.4966	−0.700871
$555$	0	0
$556$	−6.69619	−0.283982
$557$	−21.8070	−0.923991	−0.461996	−	0.886882i	$-0.652866\pi$
$557$	−21.8070	−0.923991	−0.461996	+	0.886882i	$0.652866\pi$
$558$	−7.26471	−0.307540
$559$	−1.27503	−0.0539282
$560$	0	0
$561$	9.99719	0.422082
$562$	−12.8743	−0.543070
$563$	24.9633	1.05208	0.526039	−	0.850460i	$-0.323677\pi$
$563$	24.9633	1.05208	0.526039	+	0.850460i	$0.323677\pi$
$564$	−14.1480	−0.595738
$565$	0	0
$566$	−7.23177	−0.303974
$567$	−2.39654	−0.100645
$568$	−27.0101	−1.13332
$569$	−9.09620	−0.381333	−0.190666	−	0.981655i	$-0.561065\pi$
$569$	−9.09620	−0.381333	−0.190666	+	0.981655i	$0.561065\pi$
$570$	0	0
$571$	30.1265	1.26075	0.630377	−	0.776289i	$-0.282900\pi$
$571$	30.1265	1.26075	0.630377	+	0.776289i	$0.282900\pi$
$572$	−0.485657	−0.0203064
$573$	−14.8815	−0.621683
$574$	0.220569	0.00920637
$575$	0	0
$576$	−2.01258	−0.0838575
$577$	−0.0967699	−0.00402858	−0.00201429	−	0.999998i	$-0.500641\pi$
$577$	−0.0967699	−0.00402858	−0.00201429	+	0.999998i	$0.500641\pi$
$578$	−17.7193	−0.737025
$579$	13.0404	0.541941
$580$	0	0
$581$	−17.4343	−0.723296
$582$	3.51377	0.145650
$583$	9.32474	0.386191
$584$	25.3137	1.04749
$585$	0	0
$586$	5.51435	0.227796
$587$	−1.92530	−0.0794657	−0.0397329	−	0.999210i	$-0.512651\pi$
$587$	−1.92530	−0.0794657	−0.0397329	+	0.999210i	$0.512651\pi$
$588$	−1.38850	−0.0572607
$589$	4.83772	0.199335
$590$	0	0
$591$	16.9060	0.695421
$592$	−2.35296	−0.0967060
$593$	−28.1804	−1.15723	−0.578616	−	0.815600i	$-0.696407\pi$
$593$	−28.1804	−1.15723	−0.578616	+	0.815600i	$0.696407\pi$
$594$	−5.31175	−0.217944
$595$	0	0
$596$	1.15623	0.0473610
$597$	−6.70262	−0.274320
$598$	−0.124939	−0.00510912
$599$	−18.2993	−0.747687	−0.373844	−	0.927492i	$-0.621960\pi$
$599$	−18.2993	−0.747687	−0.373844	+	0.927492i	$0.621960\pi$
$600$	0	0
$601$	0.259626	0.0105904	0.00529519	−	0.999986i	$-0.498314\pi$
$601$	0.259626	0.0105904	0.00529519	+	0.999986i	$0.498314\pi$
$602$	4.62588	0.188537
$603$	7.55361	0.307607
$604$	−33.3357	−1.35641
$605$	0	0
$606$	5.40042	0.219377
$607$	−17.4695	−0.709066	−0.354533	−	0.935044i	$-0.615360\pi$
$607$	−17.4695	−0.709066	−0.354533	+	0.935044i	$0.615360\pi$
$608$	5.68198	0.230435
$609$	−6.38373	−0.258682
$610$	0	0
$611$	−1.89087	−0.0764964
$612$	−22.3362	−0.902886
$613$	−36.5523	−1.47634	−0.738168	−	0.674617i	$-0.764309\pi$
$613$	−36.5523	−1.47634	−0.738168	+	0.674617i	$0.764309\pi$
$614$	−13.3147	−0.537337
$615$	0	0
$616$	4.04034	0.162790
$617$	−35.4102	−1.42556	−0.712781	−	0.701386i	$-0.752565\pi$
$617$	−35.4102	−1.42556	−0.712781	+	0.701386i	$0.752565\pi$
$618$	−3.35173	−0.134826
$619$	−23.5207	−0.945378	−0.472689	−	0.881229i	$-0.656717\pi$
$619$	−23.5207	−0.945378	−0.472689	+	0.881229i	$0.656717\pi$
$620$	0	0
$621$	4.66280	0.187112
$622$	15.9571	0.639821
$623$	0.304653	0.0122057
$624$	−0.247513	−0.00990847
$625$	0	0
$626$	−17.8465	−0.713291
$627$	1.49420	0.0596727
$628$	−12.8389	−0.512327
$629$	10.4231	0.415598
$630$	0	0
$631$	19.5582	0.778600	0.389300	−	0.921111i	$-0.372717\pi$
$631$	19.5582	0.778600	0.389300	+	0.921111i	$0.372717\pi$
$632$	−0.610268	−0.0242752
$633$	−0.663555	−0.0263739
$634$	−4.68833	−0.186197
$635$	0	0
$636$	7.65201	0.303422
$637$	−0.185572	−0.00735263
$638$	8.10086	0.320716
$639$	24.8185	0.981806
$640$	0	0
$641$	24.2626	0.958313	0.479157	−	0.877729i	$-0.340943\pi$
$641$	24.2626	0.958313	0.479157	+	0.877729i	$0.340943\pi$
$642$	−9.57516	−0.377901
$643$	6.48547	0.255762	0.127881	−	0.991790i	$-0.459182\pi$
$643$	6.48547	0.255762	0.127881	+	0.991790i	$0.459182\pi$
$644$	−1.54672	−0.0609492
$645$	0	0
$646$	−4.35903	−0.171504
$647$	29.4251	1.15682	0.578411	−	0.815746i	$-0.303673\pi$
$647$	29.4251	1.15682	0.578411	+	0.815746i	$0.303673\pi$
$648$	5.72264	0.224806
$649$	12.9515	0.508390
$650$	0	0
$651$	4.41476	0.173028
$652$	−18.1399	−0.710413
$653$	8.81454	0.344940	0.172470	−	0.985015i	$-0.444825\pi$
$653$	8.81454	0.344940	0.172470	+	0.985015i	$0.444825\pi$
$654$	0.564077	0.0220572
$655$	0	0
$656$	0.486757	0.0190047
$657$	−23.2598	−0.907450
$658$	6.86016	0.267437
$659$	43.1867	1.68232	0.841158	−	0.540789i	$-0.181874\pi$
$659$	43.1867	1.68232	0.841158	+	0.540789i	$0.181874\pi$
$660$	0	0
$661$	38.3922	1.49328	0.746641	−	0.665227i	$-0.231665\pi$
$661$	38.3922	1.49328	0.746641	+	0.665227i	$0.231665\pi$
$662$	22.5846	0.877774
$663$	1.09644	0.0425821
$664$	41.6309	1.61559
$665$	0	0
$666$	−2.33942	−0.0906505
$667$	−7.11115	−0.275345
$668$	11.8014	0.456612
$669$	−16.8274	−0.650586
$670$	0	0
$671$	−20.0629	−0.774519
$672$	5.18520	0.200024
$673$	26.0874	1.00560	0.502798	−	0.864404i	$-0.332304\pi$
$673$	26.0874	1.00560	0.502798	+	0.864404i	$0.332304\pi$
$674$	6.71899	0.258806
$675$	0	0
$676$	20.0541	0.771310
$677$	−34.8989	−1.34127	−0.670637	−	0.741785i	$-0.733979\pi$
$677$	−34.8989	−1.34127	−0.670637	+	0.741785i	$0.733979\pi$
$678$	7.45880	0.286453
$679$	5.81373	0.223110
$680$	0	0
$681$	−14.0776	−0.539455
$682$	−5.60226	−0.214522
$683$	−35.3964	−1.35440	−0.677202	−	0.735797i	$-0.736808\pi$
$683$	−35.3964	−1.35440	−0.677202	+	0.735797i	$0.736808\pi$
$684$	−3.33842	−0.127648
$685$	0	0
$686$	0.673262	0.0257053
$687$	−16.9259	−0.645765
$688$	10.2085	0.389195
$689$	1.02269	0.0389612
$690$	0	0
$691$	19.3991	0.737976	0.368988	−	0.929434i	$-0.379704\pi$
$691$	19.3991	0.737976	0.368988	+	0.929434i	$0.379704\pi$
$692$	−25.0597	−0.952625
$693$	−3.71251	−0.141027
$694$	−11.0401	−0.419077
$695$	0	0
$696$	15.2435	0.577804
$697$	−2.15624	−0.0816734
$698$	4.47840	0.169510
$699$	16.5393	0.625574
$700$	0	0
$701$	18.4835	0.698113	0.349057	−	0.937102i	$-0.386502\pi$
$701$	18.4835	0.698113	0.349057	+	0.937102i	$0.386502\pi$
$702$	−0.582564	−0.0219874
$703$	1.55787	0.0587561
$704$	−1.55203	−0.0584942
$705$	0	0
$706$	0.0173097	0.000651459 0
$707$	8.93529	0.336046
$708$	10.6282	0.399431
$709$	−41.7180	−1.56675	−0.783376	−	0.621548i	$-0.786504\pi$
$709$	−41.7180	−1.56675	−0.783376	+	0.621548i	$0.786504\pi$
$710$	0	0
$711$	0.560752	0.0210298
$712$	−0.727473	−0.0272632
$713$	4.91782	0.184174
$714$	−3.97792	−0.148870
$715$	0	0
$716$	−5.17064	−0.193236
$717$	19.5953	0.731801
$718$	22.8949	0.854430
$719$	−43.6520	−1.62794	−0.813972	−	0.580904i	$-0.802699\pi$
$719$	−43.6520	−1.62794	−0.813972	+	0.580904i	$0.802699\pi$
$720$	0	0
$721$	−5.54561	−0.206529
$722$	12.1405	0.451822
$723$	9.94502	0.369859
$724$	2.38230	0.0885374
$725$	0	0
$726$	4.91797	0.182523
$727$	−23.3402	−0.865639	−0.432819	−	0.901481i	$-0.642481\pi$
$727$	−23.3402	−0.865639	−0.432819	+	0.901481i	$0.642481\pi$
$728$	0.443122	0.0164232
$729$	7.29916	0.270339
$730$	0	0
$731$	−45.2217	−1.67258
$732$	−16.4639	−0.608523
$733$	49.9971	1.84669	0.923343	−	0.383977i	$-0.125446\pi$
$733$	49.9971	1.84669	0.923343	+	0.383977i	$0.125446\pi$
$734$	−9.77516	−0.360808
$735$	0	0
$736$	5.77606	0.212908
$737$	5.82505	0.214569
$738$	0.483956	0.0178147
$739$	−15.1016	−0.555523	−0.277761	−	0.960650i	$-0.589592\pi$
$739$	−15.1016	−0.555523	−0.277761	+	0.960650i	$0.589592\pi$
$740$	0	0
$741$	0.163876	0.00602013
$742$	−3.71035	−0.136211
$743$	6.11587	0.224370	0.112185	−	0.993687i	$-0.464215\pi$
$743$	6.11587	0.224370	0.112185	+	0.993687i	$0.464215\pi$
$744$	−10.5419	−0.386484
$745$	0	0
$746$	12.2823	0.449686
$747$	−38.2530	−1.39960
$748$	−17.2248	−0.629801
$749$	−15.8426	−0.578877
$750$	0	0
$751$	13.9815	0.510191	0.255095	−	0.966916i	$-0.417893\pi$
$751$	13.9815	0.510191	0.255095	+	0.966916i	$0.417893\pi$
$752$	15.1392	0.552068
$753$	7.01387	0.255600
$754$	0.888458	0.0323557
$755$	0	0
$756$	−7.21203	−0.262299
$757$	−35.6189	−1.29459	−0.647295	−	0.762240i	$-0.724100\pi$
$757$	−35.6189	−1.29459	−0.647295	+	0.762240i	$0.724100\pi$
$758$	−21.1397	−0.767829
$759$	1.51894	0.0551341
$760$	0	0
$761$	13.1855	0.477973	0.238987	−	0.971023i	$-0.423185\pi$
$761$	13.1855	0.477973	0.238987	+	0.971023i	$0.423185\pi$
$762$	2.70041	0.0978254
$763$	0.933297	0.0337876
$764$	25.6403	0.927634
$765$	0	0
$766$	−9.96836	−0.360171
$767$	1.42045	0.0512894
$768$	−8.25562	−0.297899
$769$	−26.4252	−0.952917	−0.476458	−	0.879197i	$-0.658080\pi$
$769$	−26.4252	−0.952917	−0.476458	+	0.879197i	$0.658080\pi$
$770$	0	0
$771$	−1.64684	−0.0593094
$772$	−22.4682	−0.808648
$773$	0.234245	0.00842521	0.00421261	−	0.999991i	$-0.498659\pi$
$773$	0.234245	0.00842521	0.00421261	+	0.999991i	$0.498659\pi$
$774$	10.1497	0.364825
$775$	0	0
$776$	−13.8824	−0.498350
$777$	1.42166	0.0510019
$778$	11.1371	0.399286
$779$	−0.322276	−0.0115468
$780$	0	0
$781$	19.1391	0.684851
$782$	−4.43120	−0.158459
$783$	−33.1579	−1.18497
$784$	1.48577	0.0530633
$785$	0	0
$786$	−4.31725	−0.153991
$787$	38.5928	1.37569	0.687843	−	0.725860i	$-0.258558\pi$
$787$	38.5928	1.37569	0.687843	+	0.725860i	$0.258558\pi$
$788$	−29.1285	−1.03766
$789$	−4.72068	−0.168061
$790$	0	0
$791$	12.3410	0.438795
$792$	8.86499	0.315004
$793$	−2.20039	−0.0781380
$794$	−5.93889	−0.210763
$795$	0	0
$796$	11.5484	0.409321
$797$	−7.22601	−0.255958	−0.127979	−	0.991777i	$-0.540849\pi$
$797$	−7.22601	−0.255958	−0.127979	+	0.991777i	$0.540849\pi$
$798$	−0.594548	−0.0210468
$799$	−67.0635	−2.37254
$800$	0	0
$801$	0.668446	0.0236184
$802$	−13.1378	−0.463912
$803$	−17.9371	−0.632985
$804$	4.78012	0.168582
$805$	0	0
$806$	−0.614426	−0.0216422
$807$	16.0369	0.564525
$808$	−21.3363	−0.750610
$809$	−31.9538	−1.12343	−0.561717	−	0.827329i	$-0.689859\pi$
$809$	−31.9538	−1.12343	−0.561717	+	0.827329i	$0.689859\pi$
$810$	0	0
$811$	7.73231	0.271518	0.135759	−	0.990742i	$-0.456653\pi$
$811$	7.73231	0.271518	0.135759	+	0.990742i	$0.456653\pi$
$812$	10.9989	0.385987
$813$	20.8116	0.729894
$814$	−1.80407	−0.0632326
$815$	0	0
$816$	−8.77856	−0.307311
$817$	−6.75893	−0.236465
$818$	23.2043	0.811319
$819$	−0.407168	−0.0142276
$820$	0	0
$821$	−5.16446	−0.180241	−0.0901204	−	0.995931i	$-0.528725\pi$
$821$	−5.16446	−0.180241	−0.0901204	+	0.995931i	$0.528725\pi$
$822$	−6.83255	−0.238313
$823$	−19.4937	−0.679506	−0.339753	−	0.940515i	$-0.610344\pi$
$823$	−19.4937	−0.679506	−0.339753	+	0.940515i	$0.610344\pi$
$824$	13.2422	0.461314
$825$	0	0
$826$	−5.15344	−0.179311
$827$	−0.588072	−0.0204493	−0.0102246	−	0.999948i	$-0.503255\pi$
$827$	−0.588072	−0.0204493	−0.0102246	+	0.999948i	$0.503255\pi$
$828$	−3.39369	−0.117939
$829$	32.2322	1.11947	0.559736	−	0.828671i	$-0.310903\pi$
$829$	32.2322	1.11947	0.559736	+	0.828671i	$0.310903\pi$
$830$	0	0
$831$	21.9960	0.763032
$832$	−0.170218	−0.00590124
$833$	−6.58168	−0.228042
$834$	−2.61659	−0.0906050
$835$	0	0
$836$	−2.57446	−0.0890395
$837$	22.9308	0.792605
$838$	−4.02970	−0.139204
$839$	−15.4985	−0.535069	−0.267535	−	0.963548i	$-0.586209\pi$
$839$	−15.4985	−0.535069	−0.267535	+	0.963548i	$0.586209\pi$
$840$	0	0
$841$	21.5685	0.743741
$842$	−7.71445	−0.265858
$843$	17.1662	0.591235
$844$	1.14328	0.0393534
$845$	0	0
$846$	15.0520	0.517499
$847$	8.13705	0.279593
$848$	−8.18808	−0.281180
$849$	9.64261	0.330934
$850$	0	0
$851$	1.58366	0.0542872
$852$	15.7058	0.538072
$853$	27.8822	0.954668	0.477334	−	0.878722i	$-0.341603\pi$
$853$	27.8822	0.954668	0.477334	+	0.878722i	$0.341603\pi$
$854$	7.98309	0.273176
$855$	0	0
$856$	37.8302	1.29301
$857$	10.8271	0.369846	0.184923	−	0.982753i	$-0.440796\pi$
$857$	10.8271	0.369846	0.184923	+	0.982753i	$0.440796\pi$
$858$	−0.189774	−0.00647879
$859$	31.2974	1.06785	0.533927	−	0.845531i	$-0.320716\pi$
$859$	31.2974	1.06785	0.533927	+	0.845531i	$0.320716\pi$
$860$	0	0
$861$	−0.294100	−0.0100229
$862$	14.6768	0.499893
$863$	−11.3308	−0.385705	−0.192853	−	0.981228i	$-0.561774\pi$
$863$	−11.3308	−0.385705	−0.192853	+	0.981228i	$0.561774\pi$
$864$	26.9326	0.916265
$865$	0	0
$866$	16.0201	0.544386
$867$	23.6263	0.802392
$868$	−7.60648	−0.258181
$869$	0.432431	0.0146692
$870$	0	0
$871$	0.638860	0.0216469
$872$	−2.22859	−0.0754697
$873$	12.7560	0.431726
$874$	−0.662297	−0.0224025
$875$	0	0
$876$	−14.7194	−0.497322
$877$	20.6628	0.697732	0.348866	−	0.937173i	$-0.386567\pi$
$877$	20.6628	0.697732	0.348866	+	0.937173i	$0.386567\pi$
$878$	−4.16489	−0.140558
$879$	−7.35266	−0.247999
$880$	0	0
$881$	22.3389	0.752616	0.376308	−	0.926495i	$-0.377193\pi$
$881$	22.3389	0.752616	0.376308	+	0.926495i	$0.377193\pi$
$882$	1.47722	0.0497406
$883$	33.3114	1.12102	0.560509	−	0.828148i	$-0.310606\pi$
$883$	33.3114	1.12102	0.560509	+	0.828148i	$0.310606\pi$
$884$	−1.88912	−0.0635381
$885$	0	0
$886$	−13.9282	−0.467927
$887$	−57.5639	−1.93281	−0.966403	−	0.257033i	$-0.917255\pi$
$887$	−57.5639	−1.93281	−0.966403	+	0.257033i	$0.917255\pi$
$888$	−3.39475	−0.113920
$889$	4.46797	0.149851
$890$	0	0
$891$	−4.05501	−0.135848
$892$	28.9931	0.970760
$893$	−10.0235	−0.335423
$894$	0.451806	0.0151107
$895$	0	0
$896$	−10.9346	−0.365298
$897$	0.166589	0.00556225
$898$	16.5175	0.551196
$899$	−34.9714	−1.16636
$900$	0	0
$901$	36.2716	1.20838
$902$	0.373208	0.0124265
$903$	−6.16800	−0.205258
$904$	−29.4687	−0.980114
$905$	0	0
$906$	−13.0262	−0.432766
$907$	30.3439	1.00755	0.503776	−	0.863834i	$-0.331944\pi$
$907$	30.3439	1.00755	0.503776	+	0.863834i	$0.331944\pi$
$908$	24.2553	0.804939
$909$	19.6051	0.650261
$910$	0	0
$911$	−33.5083	−1.11018	−0.555090	−	0.831790i	$-0.687316\pi$
$911$	−33.5083	−1.11018	−0.555090	+	0.831790i	$0.687316\pi$
$912$	−1.31206	−0.0434468
$913$	−29.4992	−0.976283
$914$	−11.5986	−0.383647
$915$	0	0
$916$	29.1628	0.963566
$917$	−7.14313	−0.235887
$918$	−20.6618	−0.681941
$919$	−35.0642	−1.15666	−0.578331	−	0.815802i	$-0.696296\pi$
$919$	−35.0642	−1.15666	−0.578331	+	0.815802i	$0.696296\pi$
$920$	0	0
$921$	17.7534	0.584994
$922$	−22.6574	−0.746183
$923$	2.09907	0.0690918
$924$	−2.34937	−0.0772887
$925$	0	0
$926$	−10.2783	−0.337766
$927$	−12.1678	−0.399642
$928$	−41.0744	−1.34833
$929$	−48.2938	−1.58447	−0.792235	−	0.610216i	$-0.791083\pi$
$929$	−48.2938	−1.58447	−0.792235	+	0.610216i	$0.791083\pi$
$930$	0	0
$931$	−0.983713	−0.0322399
$932$	−28.4967	−0.933439
$933$	−21.2767	−0.696567
$934$	5.95454	0.194839
$935$	0	0
$936$	0.972264	0.0317794
$937$	46.6428	1.52375	0.761877	−	0.647721i	$-0.224278\pi$
$937$	46.6428	1.52375	0.761877	+	0.647721i	$0.224278\pi$
$938$	−2.31781	−0.0756792
$939$	23.7960	0.776553
$940$	0	0
$941$	−8.10506	−0.264217	−0.132109	−	0.991235i	$-0.542175\pi$
$941$	−8.10506	−0.264217	−0.132109	+	0.991235i	$0.542175\pi$
$942$	−5.01689	−0.163459
$943$	−0.327612	−0.0106685
$944$	−11.3727	−0.370151
$945$	0	0
$946$	7.82710	0.254481
$947$	13.0916	0.425418	0.212709	−	0.977116i	$-0.431771\pi$
$947$	13.0916	0.425418	0.212709	+	0.977116i	$0.431771\pi$
$948$	0.354859	0.0115253
$949$	−1.96724	−0.0638593
$950$	0	0
$951$	6.25127	0.202711
$952$	15.7162	0.509365
$953$	−35.4105	−1.14706	−0.573530	−	0.819185i	$-0.694426\pi$
$953$	−35.4105	−1.14706	−0.573530	+	0.819185i	$0.694426\pi$
$954$	−8.14096	−0.263573
$955$	0	0
$956$	−33.7621	−1.09194
$957$	−10.8014	−0.349160
$958$	−10.8029	−0.349026
$959$	−11.3048	−0.365052
$960$	0	0
$961$	−6.81503	−0.219840
$962$	−0.197860	−0.00637927
$963$	−34.7607	−1.12015
$964$	−17.1349	−0.551879
$965$	0	0
$966$	−0.604392	−0.0194460
$967$	56.6361	1.82129	0.910647	−	0.413186i	$-0.135584\pi$
$967$	56.6361	1.82129	0.910647	+	0.413186i	$0.135584\pi$
$968$	−19.4302	−0.624512
$969$	5.81219	0.186714
$970$	0	0
$971$	30.8663	0.990546	0.495273	−	0.868737i	$-0.335068\pi$
$971$	30.8663	0.990546	0.495273	+	0.868737i	$0.335068\pi$
$972$	−24.9637	−0.800711
$973$	−4.32929	−0.138791
$974$	−22.2028	−0.711424
$975$	0	0
$976$	17.6173	0.563915
$977$	−32.9245	−1.05335	−0.526674	−	0.850067i	$-0.676561\pi$
$977$	−32.9245	−1.05335	−0.526674	+	0.850067i	$0.676561\pi$
$978$	−7.08831	−0.226659
$979$	0.515480	0.0164748
$980$	0	0
$981$	2.04777	0.0653802
$982$	21.4501	0.684499
$983$	5.90690	0.188401	0.0942004	−	0.995553i	$-0.469971\pi$
$983$	5.90690	0.188401	0.0942004	+	0.995553i	$0.469971\pi$
$984$	0.702272	0.0223876
$985$	0	0
$986$	31.5109	1.00351
$987$	−9.14711	−0.291156
$988$	−0.282353	−0.00898283
$989$	−6.87084	−0.218480
$990$	0	0
$991$	−12.4365	−0.395058	−0.197529	−	0.980297i	$-0.563292\pi$
$991$	−12.4365	−0.395058	−0.197529	+	0.980297i	$0.563292\pi$
$992$	28.4056	0.901879
$993$	−30.1135	−0.955624
$994$	−7.61552	−0.241550
$995$	0	0
$996$	−24.2075	−0.767044
$997$	−36.8819	−1.16806	−0.584030	−	0.811732i	$-0.698525\pi$
$997$	−36.8819	−1.16806	−0.584030	+	0.811732i	$0.698525\pi$
$998$	4.28045	0.135495
$999$	7.38429	0.233629

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.w.1.3	yes	8
5.4	even	2		4025.2.a.s.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.s.1.6	✓	8	5.4	even	2
4025.2.a.w.1.3	yes	8	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.673262 q^{2} +0.897707 q^{3} -1.54672 q^{4} -0.604392 q^{6} -1.00000 q^{7} +2.38787 q^{8} -2.19412 q^{9} +O(q^{10})\)	\(q-0.673262 q^{2} +0.897707 q^{3} -1.54672 q^{4} -0.604392 q^{6} -1.00000 q^{7} +2.38787 q^{8} -2.19412 q^{9} -1.69202 q^{11} -1.38850 q^{12} -0.185572 q^{13} +0.673262 q^{14} +1.48577 q^{16} -6.58168 q^{17} +1.47722 q^{18} -0.983713 q^{19} -0.897707 q^{21} +1.13918 q^{22} -1.00000 q^{23} +2.14361 q^{24} +0.124939 q^{26} -4.66280 q^{27} +1.54672 q^{28} +7.11115 q^{29} -4.91782 q^{31} -5.77606 q^{32} -1.51894 q^{33} +4.43120 q^{34} +3.39369 q^{36} -1.58366 q^{37} +0.662297 q^{38} -0.166589 q^{39} +0.327612 q^{41} +0.604392 q^{42} +6.87084 q^{43} +2.61708 q^{44} +0.673262 q^{46} +10.1894 q^{47} +1.33379 q^{48} +1.00000 q^{49} -5.90842 q^{51} +0.287027 q^{52} -5.51100 q^{53} +3.13929 q^{54} -2.38787 q^{56} -0.883086 q^{57} -4.78767 q^{58} -7.65443 q^{59} +11.8573 q^{61} +3.31098 q^{62} +2.19412 q^{63} +0.917260 q^{64} +1.02265 q^{66} -3.44265 q^{67} +10.1800 q^{68} -0.897707 q^{69} -11.3114 q^{71} -5.23928 q^{72} +10.6009 q^{73} +1.06622 q^{74} +1.52153 q^{76} +1.69202 q^{77} +0.112158 q^{78} -0.255570 q^{79} +2.39654 q^{81} -0.220569 q^{82} +17.4343 q^{83} +1.38850 q^{84} -4.62588 q^{86} +6.38373 q^{87} -4.04034 q^{88} -0.304653 q^{89} +0.185572 q^{91} +1.54672 q^{92} -4.41476 q^{93} -6.86016 q^{94} -5.18520 q^{96} -5.81373 q^{97} -0.673262 q^{98} +3.71251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8	\( 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8} - 5 q^{11} + 3 q^{12} + 9 q^{13} - 3 q^{14} - q^{16} - q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{21} - 5 q^{22} - 8 q^{23} + 16 q^{24} + 22 q^{26} - q^{27} - 5 q^{28} - 5 q^{29} - q^{31} + 2 q^{32} + 12 q^{33} - 2 q^{34} + 16 q^{36} + 18 q^{37} + 14 q^{38} + 14 q^{39} - q^{41} + q^{42} + 20 q^{43} - 3 q^{46} + 10 q^{47} + 31 q^{48} + 8 q^{49} - 4 q^{51} + 11 q^{52} + 11 q^{53} + 29 q^{54} - 12 q^{56} + 8 q^{57} + 24 q^{58} + 20 q^{59} - 6 q^{61} + 2 q^{62} + 8 q^{64} - 37 q^{66} + 23 q^{67} + 9 q^{68} - 2 q^{69} + 3 q^{71} + 29 q^{72} - 8 q^{73} + 35 q^{74} - 29 q^{76} + 5 q^{77} + 31 q^{78} + 4 q^{79} - 44 q^{81} + 27 q^{82} + 4 q^{83} - 3 q^{84} - 18 q^{86} + 27 q^{87} - 4 q^{88} - 17 q^{89} - 9 q^{91} - 5 q^{92} - 7 q^{93} + 13 q^{94} + 22 q^{96} + 41 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8 - 5 * q^11 + 3 * q^12 + 9 * q^13 - 3 * q^14 - q^16 - q^17 + 6 * q^18 - 4 * q^19 - 2 * q^21 - 5 * q^22 - 8 * q^23 + 16 * q^24 + 22 * q^26 - q^27 - 5 * q^28 - 5 * q^29 - q^31 + 2 * q^32 + 12 * q^33 - 2 * q^34 + 16 * q^36 + 18 * q^37 + 14 * q^38 + 14 * q^39 - q^41 + q^42 + 20 * q^43 - 3 * q^46 + 10 * q^47 + 31 * q^48 + 8 * q^49 - 4 * q^51 + 11 * q^52 + 11 * q^53 + 29 * q^54 - 12 * q^56 + 8 * q^57 + 24 * q^58 + 20 * q^59 - 6 * q^61 + 2 * q^62 + 8 * q^64 - 37 * q^66 + 23 * q^67 + 9 * q^68 - 2 * q^69 + 3 * q^71 + 29 * q^72 - 8 * q^73 + 35 * q^74 - 29 * q^76 + 5 * q^77 + 31 * q^78 + 4 * q^79 - 44 * q^81 + 27 * q^82 + 4 * q^83 - 3 * q^84 - 18 * q^86 + 27 * q^87 - 4 * q^88 - 17 * q^89 - 9 * q^91 - 5 * q^92 - 7 * q^93 + 13 * q^94 + 22 * q^96 + 41 * q^97 + 3 * q^98 + 7 * q^99

Introduction

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