LMFDB - Embedded newform 325.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("325.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
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			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} -1.17157 q^{6} +0.414214 q^{7} -1.58579 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q+0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} -1.17157 q^{6} +0.414214 q^{7} -1.58579 q^{8} +5.00000 q^{9} +3.58579 q^{11} +5.17157 q^{12} -1.00000 q^{13} +0.171573 q^{14} +3.00000 q^{16} -1.82843 q^{17} +2.07107 q^{18} +7.65685 q^{19} -1.17157 q^{21} +1.48528 q^{22} +8.82843 q^{23} +4.48528 q^{24} -0.414214 q^{26} -5.65685 q^{27} -0.757359 q^{28} -5.82843 q^{29} -7.24264 q^{31} +4.41421 q^{32} -10.1421 q^{33} -0.757359 q^{34} -9.14214 q^{36} +6.00000 q^{37} +3.17157 q^{38} +2.82843 q^{39} +5.65685 q^{41} -0.485281 q^{42} +4.82843 q^{43} -6.55635 q^{44} +3.65685 q^{46} -6.41421 q^{47} -8.48528 q^{48} -6.82843 q^{49} +5.17157 q^{51} +1.82843 q^{52} -3.00000 q^{53} -2.34315 q^{54} -0.656854 q^{56} -21.6569 q^{57} -2.41421 q^{58} +4.75736 q^{59} +1.00000 q^{61} -3.00000 q^{62} +2.07107 q^{63} -4.17157 q^{64} -4.20101 q^{66} +11.2426 q^{67} +3.34315 q^{68} -24.9706 q^{69} +13.3137 q^{71} -7.92893 q^{72} +6.00000 q^{73} +2.48528 q^{74} -14.0000 q^{76} +1.48528 q^{77} +1.17157 q^{78} -6.00000 q^{79} +1.00000 q^{81} +2.34315 q^{82} +12.8995 q^{83} +2.14214 q^{84} +2.00000 q^{86} +16.4853 q^{87} -5.68629 q^{88} +8.48528 q^{89} -0.414214 q^{91} -16.1421 q^{92} +20.4853 q^{93} -2.65685 q^{94} -12.4853 q^{96} -4.82843 q^{97} -2.82843 q^{98} +17.9289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^8 + 10 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{8} + 10 q^{9} + 10 q^{11} + 16 q^{12} - 2 q^{13} + 6 q^{14} + 6 q^{16} + 2 q^{17} - 10 q^{18} + 4 q^{19} - 8 q^{21} - 14 q^{22} + 12 q^{23} - 8 q^{24} + 2 q^{26} - 10 q^{28} - 6 q^{29} - 6 q^{31} + 6 q^{32} + 8 q^{33} - 10 q^{34} + 10 q^{36} + 12 q^{37} + 12 q^{38} + 16 q^{42} + 4 q^{43} + 18 q^{44} - 4 q^{46} - 10 q^{47} - 8 q^{49} + 16 q^{51} - 2 q^{52} - 6 q^{53} - 16 q^{54} + 10 q^{56} - 32 q^{57} - 2 q^{58} + 18 q^{59} + 2 q^{61} - 6 q^{62} - 10 q^{63} - 14 q^{64} - 48 q^{66} + 14 q^{67} + 18 q^{68} - 16 q^{69} + 4 q^{71} - 30 q^{72} + 12 q^{73} - 12 q^{74} - 28 q^{76} - 14 q^{77} + 8 q^{78} - 12 q^{79} + 2 q^{81} + 16 q^{82} + 6 q^{83} - 24 q^{84} + 4 q^{86} + 16 q^{87} - 34 q^{88} + 2 q^{91} - 4 q^{92} + 24 q^{93} + 6 q^{94} - 8 q^{96} - 4 q^{97} + 50 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^8 + 10 * q^9 + 10 * q^11 + 16 * q^12 - 2 * q^13 + 6 * q^14 + 6 * q^16 + 2 * q^17 - 10 * q^18 + 4 * q^19 - 8 * q^21 - 14 * q^22 + 12 * q^23 - 8 * q^24 + 2 * q^26 - 10 * q^28 - 6 * q^29 - 6 * q^31 + 6 * q^32 + 8 * q^33 - 10 * q^34 + 10 * q^36 + 12 * q^37 + 12 * q^38 + 16 * q^42 + 4 * q^43 + 18 * q^44 - 4 * q^46 - 10 * q^47 - 8 * q^49 + 16 * q^51 - 2 * q^52 - 6 * q^53 - 16 * q^54 + 10 * q^56 - 32 * q^57 - 2 * q^58 + 18 * q^59 + 2 * q^61 - 6 * q^62 - 10 * q^63 - 14 * q^64 - 48 * q^66 + 14 * q^67 + 18 * q^68 - 16 * q^69 + 4 * q^71 - 30 * q^72 + 12 * q^73 - 12 * q^74 - 28 * q^76 - 14 * q^77 + 8 * q^78 - 12 * q^79 + 2 * q^81 + 16 * q^82 + 6 * q^83 - 24 * q^84 + 4 * q^86 + 16 * q^87 - 34 * q^88 + 2 * q^91 - 4 * q^92 + 24 * q^93 + 6 * q^94 - 8 * q^96 - 4 * q^97 + 50 * 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 $

$2$	0.414214	0.292893	0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214	0.292893	0.146447	+	0.989219i	$0.453216\pi$
$3$	−2.82843	−1.63299	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−2.82843	−1.63299	−0.816497	+	0.577350i	$0.804087\pi$
$4$	−1.82843	−0.914214
$5$	0	0
$5$	0	0
$6$	−1.17157	−0.478293
$7$	0.414214	0.156558	0.0782790	−	0.996931i	$-0.475058\pi$
$7$	0.414214	0.156558	0.0782790	+	0.996931i	$0.475058\pi$
$8$	−1.58579	−0.560660
$9$	5.00000	1.66667
$10$	0	0
$11$	3.58579	1.08116	0.540578	−	0.841294i	$-0.318206\pi$
$11$	3.58579	1.08116	0.540578	+	0.841294i	$0.318206\pi$
$12$	5.17157	1.49290
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.171573	0.0458548
$15$	0	0
$16$	3.00000	0.750000
$17$	−1.82843	−0.443459	−0.221729	−	0.975108i	$-0.571170\pi$
$17$	−1.82843	−0.443459	−0.221729	+	0.975108i	$0.571170\pi$
$18$	2.07107	0.488155
$19$	7.65685	1.75660	0.878301	−	0.478107i	$-0.158677\pi$
$19$	7.65685	1.75660	0.878301	+	0.478107i	$0.158677\pi$
$20$	0	0
$21$	−1.17157	−0.255658
$22$	1.48528	0.316663
$23$	8.82843	1.84085	0.920427	−	0.390914i	$-0.127841\pi$
$23$	8.82843	1.84085	0.920427	+	0.390914i	$0.127841\pi$
$24$	4.48528	0.915554
$25$	0	0
$26$	−0.414214	−0.0812340
$27$	−5.65685	−1.08866
$28$	−0.757359	−0.143127
$29$	−5.82843	−1.08231	−0.541156	−	0.840922i	$-0.682013\pi$
$29$	−5.82843	−1.08231	−0.541156	+	0.840922i	$0.682013\pi$
$30$	0	0
$31$	−7.24264	−1.30082	−0.650408	−	0.759585i	$-0.725402\pi$
$31$	−7.24264	−1.30082	−0.650408	+	0.759585i	$0.725402\pi$
$32$	4.41421	0.780330
$33$	−10.1421	−1.76552
$34$	−0.757359	−0.129886
$35$	0	0
$36$	−9.14214	−1.52369
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	3.17157	0.514497
$39$	2.82843	0.452911
$40$	0	0
$41$	5.65685	0.883452	0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685	0.883452	0.441726	+	0.897150i	$0.354366\pi$
$42$	−0.485281	−0.0748805
$43$	4.82843	0.736328	0.368164	−	0.929761i	$-0.379986\pi$
$43$	4.82843	0.736328	0.368164	+	0.929761i	$0.379986\pi$
$44$	−6.55635	−0.988407
$45$	0	0
$46$	3.65685	0.539174
$47$	−6.41421	−0.935609	−0.467805	−	0.883832i	$-0.654955\pi$
$47$	−6.41421	−0.935609	−0.467805	+	0.883832i	$0.654955\pi$
$48$	−8.48528	−1.22474
$49$	−6.82843	−0.975490
$50$	0	0
$51$	5.17157	0.724165
$52$	1.82843	0.253557
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	−2.34315	−0.318862
$55$	0	0
$56$	−0.656854	−0.0877758
$57$	−21.6569	−2.86852
$58$	−2.41421	−0.317002
$59$	4.75736	0.619355	0.309678	−	0.950842i	$-0.399779\pi$
$59$	4.75736	0.619355	0.309678	+	0.950842i	$0.399779\pi$
$60$	0	0
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−3.00000	−0.381000
$63$	2.07107	0.260930
$64$	−4.17157	−0.521447
$65$	0	0
$66$	−4.20101	−0.517109
$67$	11.2426	1.37351	0.686754	−	0.726890i	$-0.259035\pi$
$67$	11.2426	1.37351	0.686754	+	0.726890i	$0.259035\pi$
$68$	3.34315	0.405416
$69$	−24.9706	−3.00610
$70$	0	0
$71$	13.3137	1.58005	0.790023	−	0.613077i	$-0.210068\pi$
$71$	13.3137	1.58005	0.790023	+	0.613077i	$0.210068\pi$
$72$	−7.92893	−0.934434
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	2.48528	0.288908
$75$	0	0
$76$	−14.0000	−1.60591
$77$	1.48528	0.169264
$78$	1.17157	0.132655
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.34315	0.258757
$83$	12.8995	1.41590	0.707952	−	0.706261i	$-0.249619\pi$
$83$	12.8995	1.41590	0.707952	+	0.706261i	$0.249619\pi$
$84$	2.14214	0.233726
$85$	0	0
$86$	2.00000	0.215666
$87$	16.4853	1.76741
$88$	−5.68629	−0.606161
$89$	8.48528	0.899438	0.449719	−	0.893170i	$-0.351524\pi$
$89$	8.48528	0.899438	0.449719	+	0.893170i	$0.351524\pi$
$90$	0	0
$91$	−0.414214	−0.0434214
$92$	−16.1421	−1.68293
$93$	20.4853	2.12422
$94$	−2.65685	−0.274034
$95$	0	0
$96$	−12.4853	−1.27427
$97$	−4.82843	−0.490252	−0.245126	−	0.969491i	$-0.578829\pi$
$97$	−4.82843	−0.490252	−0.245126	+	0.969491i	$0.578829\pi$
$98$	−2.82843	−0.285714
$99$	17.9289	1.80193
$100$	0	0
$101$	4.65685	0.463374	0.231687	−	0.972790i	$-0.425575\pi$
$101$	4.65685	0.463374	0.231687	+	0.972790i	$0.425575\pi$
$102$	2.14214	0.212103
$103$	−2.34315	−0.230877	−0.115439	−	0.993315i	$-0.536827\pi$
$103$	−2.34315	−0.230877	−0.115439	+	0.993315i	$0.536827\pi$
$104$	1.58579	0.155499
$105$	0	0
$106$	−1.24264	−0.120696
$107$	12.1421	1.17382	0.586912	−	0.809651i	$-0.300343\pi$
$107$	12.1421	1.17382	0.586912	+	0.809651i	$0.300343\pi$
$108$	10.3431	0.995270
$109$	0.485281	0.0464815	0.0232408	−	0.999730i	$-0.492602\pi$
$109$	0.485281	0.0464815	0.0232408	+	0.999730i	$0.492602\pi$
$110$	0	0
$111$	−16.9706	−1.61077
$112$	1.24264	0.117419
$113$	0.343146	0.0322804	0.0161402	−	0.999870i	$-0.494862\pi$
$113$	0.343146	0.0322804	0.0161402	+	0.999870i	$0.494862\pi$
$114$	−8.97056	−0.840170
$115$	0	0
$116$	10.6569	0.989464
$117$	−5.00000	−0.462250
$118$	1.97056	0.181405
$119$	−0.757359	−0.0694270
$120$	0	0
$121$	1.85786	0.168897
$122$	0.414214	0.0375011
$123$	−16.0000	−1.44267
$124$	13.2426	1.18922
$125$	0	0
$126$	0.857864	0.0764246
$127$	−7.65685	−0.679436	−0.339718	−	0.940527i	$-0.610332\pi$
$127$	−7.65685	−0.679436	−0.339718	+	0.940527i	$0.610332\pi$
$128$	−10.5563	−0.933058
$129$	−13.6569	−1.20242
$130$	0	0
$131$	−8.48528	−0.741362	−0.370681	−	0.928760i	$-0.620876\pi$
$131$	−8.48528	−0.741362	−0.370681	+	0.928760i	$0.620876\pi$
$132$	18.5442	1.61406
$133$	3.17157	0.275010
$134$	4.65685	0.402291
$135$	0	0
$136$	2.89949	0.248630
$137$	2.82843	0.241649	0.120824	−	0.992674i	$-0.461446\pi$
$137$	2.82843	0.241649	0.120824	+	0.992674i	$0.461446\pi$
$138$	−10.3431	−0.880467
$139$	−1.51472	−0.128477	−0.0642384	−	0.997935i	$-0.520462\pi$
$139$	−1.51472	−0.128477	−0.0642384	+	0.997935i	$0.520462\pi$
$140$	0	0
$141$	18.1421	1.52784
$142$	5.51472	0.462785
$143$	−3.58579	−0.299859
$144$	15.0000	1.25000
$145$	0	0
$146$	2.48528	0.205683
$147$	19.3137	1.59297
$148$	−10.9706	−0.901775
$149$	3.17157	0.259825	0.129913	−	0.991525i	$-0.458530\pi$
$149$	3.17157	0.259825	0.129913	+	0.991525i	$0.458530\pi$
$150$	0	0
$151$	−17.2426	−1.40319	−0.701593	−	0.712578i	$-0.747528\pi$
$151$	−17.2426	−1.40319	−0.701593	+	0.712578i	$0.747528\pi$
$152$	−12.1421	−0.984857
$153$	−9.14214	−0.739098
$154$	0.615224	0.0495761
$155$	0	0
$156$	−5.17157	−0.414057
$157$	−6.51472	−0.519931	−0.259966	−	0.965618i	$-0.583711\pi$
$157$	−6.51472	−0.519931	−0.259966	+	0.965618i	$0.583711\pi$
$158$	−2.48528	−0.197718
$159$	8.48528	0.672927
$160$	0	0
$161$	3.65685	0.288200
$162$	0.414214	0.0325437
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	−10.3431	−0.807664
$165$	0	0
$166$	5.34315	0.414709
$167$	−17.3137	−1.33977	−0.669887	−	0.742463i	$-0.733658\pi$
$167$	−17.3137	−1.33977	−0.669887	+	0.742463i	$0.733658\pi$
$168$	1.85786	0.143337
$169$	1.00000	0.0769231
$170$	0	0
$171$	38.2843	2.92767
$172$	−8.82843	−0.673161
$173$	−7.34315	−0.558289	−0.279145	−	0.960249i	$-0.590051\pi$
$173$	−7.34315	−0.558289	−0.279145	+	0.960249i	$0.590051\pi$
$174$	6.82843	0.517662
$175$	0	0
$176$	10.7574	0.810866
$177$	−13.4558	−1.01140
$178$	3.51472	0.263439
$179$	23.3137	1.74255	0.871274	−	0.490797i	$-0.163294\pi$
$179$	23.3137	1.74255	0.871274	+	0.490797i	$0.163294\pi$
$180$	0	0
$181$	−0.514719	−0.0382587	−0.0191294	−	0.999817i	$-0.506089\pi$
$181$	−0.514719	−0.0382587	−0.0191294	+	0.999817i	$0.506089\pi$
$182$	−0.171573	−0.0127178
$183$	−2.82843	−0.209083
$184$	−14.0000	−1.03209
$185$	0	0
$186$	8.48528	0.622171
$187$	−6.55635	−0.479448
$188$	11.7279	0.855347
$189$	−2.34315	−0.170439
$190$	0	0
$191$	2.68629	0.194373	0.0971866	−	0.995266i	$-0.469016\pi$
$191$	2.68629	0.194373	0.0971866	+	0.995266i	$0.469016\pi$
$192$	11.7990	0.851519
$193$	9.65685	0.695116	0.347558	−	0.937659i	$-0.387011\pi$
$193$	9.65685	0.695116	0.347558	+	0.937659i	$0.387011\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	12.4853	0.891806
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	7.42641	0.527772
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	0	0
$201$	−31.7990	−2.24293
$202$	1.92893	0.135719
$203$	−2.41421	−0.169445
$204$	−9.45584	−0.662042
$205$	0	0
$206$	−0.970563	−0.0676223
$207$	44.1421	3.06809
$208$	−3.00000	−0.208013
$209$	27.4558	1.89916
$210$	0	0
$211$	−21.7990	−1.50070	−0.750352	−	0.661038i	$-0.770116\pi$
$211$	−21.7990	−1.50070	−0.750352	+	0.661038i	$0.770116\pi$
$212$	5.48528	0.376731
$213$	−37.6569	−2.58021
$214$	5.02944	0.343805
$215$	0	0
$216$	8.97056	0.610369
$217$	−3.00000	−0.203653
$218$	0.201010	0.0136141
$219$	−16.9706	−1.14676
$220$	0	0
$221$	1.82843	0.122993
$222$	−7.02944	−0.471785
$223$	−22.9706	−1.53822	−0.769111	−	0.639115i	$-0.779301\pi$
$223$	−22.9706	−1.53822	−0.769111	+	0.639115i	$0.779301\pi$
$224$	1.82843	0.122167
$225$	0	0
$226$	0.142136	0.00945472
$227$	−10.8995	−0.723425	−0.361712	−	0.932290i	$-0.617808\pi$
$227$	−10.8995	−0.723425	−0.361712	+	0.932290i	$0.617808\pi$
$228$	39.5980	2.62244
$229$	0.828427	0.0547440	0.0273720	−	0.999625i	$-0.491286\pi$
$229$	0.828427	0.0547440	0.0273720	+	0.999625i	$0.491286\pi$
$230$	0	0
$231$	−4.20101	−0.276406
$232$	9.24264	0.606809
$233$	24.6274	1.61340	0.806698	−	0.590964i	$-0.201253\pi$
$233$	24.6274	1.61340	0.806698	+	0.590964i	$0.201253\pi$
$234$	−2.07107	−0.135390
$235$	0	0
$236$	−8.69848	−0.566223
$237$	16.9706	1.10236
$238$	−0.313708	−0.0203347
$239$	26.4142	1.70859	0.854297	−	0.519786i	$-0.173988\pi$
$239$	26.4142	1.70859	0.854297	+	0.519786i	$0.173988\pi$
$240$	0	0
$241$	−28.9706	−1.86616	−0.933079	−	0.359671i	$-0.882889\pi$
$241$	−28.9706	−1.86616	−0.933079	+	0.359671i	$0.882889\pi$
$242$	0.769553	0.0494687
$243$	14.1421	0.907218
$244$	−1.82843	−0.117053
$245$	0	0
$246$	−6.62742	−0.422549
$247$	−7.65685	−0.487194
$248$	11.4853	0.729316
$249$	−36.4853	−2.31216
$250$	0	0
$251$	5.65685	0.357057	0.178529	−	0.983935i	$-0.442866\pi$
$251$	5.65685	0.357057	0.178529	+	0.983935i	$0.442866\pi$
$252$	−3.78680	−0.238546
$253$	31.6569	1.99025
$254$	−3.17157	−0.199002
$255$	0	0
$256$	3.97056	0.248160
$257$	−4.65685	−0.290487	−0.145243	−	0.989396i	$-0.546396\pi$
$257$	−4.65685	−0.290487	−0.145243	+	0.989396i	$0.546396\pi$
$258$	−5.65685	−0.352180
$259$	2.48528	0.154428
$260$	0	0
$261$	−29.1421	−1.80385
$262$	−3.51472	−0.217140
$263$	−2.14214	−0.132090	−0.0660449	−	0.997817i	$-0.521038\pi$
$263$	−2.14214	−0.132090	−0.0660449	+	0.997817i	$0.521038\pi$
$264$	16.0833	0.989856
$265$	0	0
$266$	1.31371	0.0805486
$267$	−24.0000	−1.46878
$268$	−20.5563	−1.25568
$269$	−13.1421	−0.801290	−0.400645	−	0.916233i	$-0.631214\pi$
$269$	−13.1421	−0.801290	−0.400645	+	0.916233i	$0.631214\pi$
$270$	0	0
$271$	−0.272078	−0.0165276	−0.00826378	−	0.999966i	$-0.502630\pi$
$271$	−0.272078	−0.0165276	−0.00826378	+	0.999966i	$0.502630\pi$
$272$	−5.48528	−0.332594
$273$	1.17157	0.0709068
$274$	1.17157	0.0707773
$275$	0	0
$276$	45.6569	2.74822
$277$	13.3137	0.799943	0.399972	−	0.916528i	$-0.369020\pi$
$277$	13.3137	0.799943	0.399972	+	0.916528i	$0.369020\pi$
$278$	−0.627417	−0.0376300
$279$	−36.2132	−2.16803
$280$	0	0
$281$	−0.828427	−0.0494198	−0.0247099	−	0.999695i	$-0.507866\pi$
$281$	−0.828427	−0.0494198	−0.0247099	+	0.999695i	$0.507866\pi$
$282$	7.51472	0.447495
$283$	5.51472	0.327816	0.163908	−	0.986476i	$-0.447590\pi$
$283$	5.51472	0.327816	0.163908	+	0.986476i	$0.447590\pi$
$284$	−24.3431	−1.44450
$285$	0	0
$286$	−1.48528	−0.0878265
$287$	2.34315	0.138312
$288$	22.0711	1.30055
$289$	−13.6569	−0.803344
$290$	0	0
$291$	13.6569	0.800579
$292$	−10.9706	−0.642004
$293$	−3.17157	−0.185285	−0.0926426	−	0.995699i	$-0.529531\pi$
$293$	−3.17157	−0.185285	−0.0926426	+	0.995699i	$0.529531\pi$
$294$	8.00000	0.466569
$295$	0	0
$296$	−9.51472	−0.553032
$297$	−20.2843	−1.17701
$298$	1.31371	0.0761011
$299$	−8.82843	−0.510561
$300$	0	0
$301$	2.00000	0.115278
$302$	−7.14214	−0.410984
$303$	−13.1716	−0.756687
$304$	22.9706	1.31745
$305$	0	0
$306$	−3.78680	−0.216477
$307$	−13.3137	−0.759853	−0.379927	−	0.925017i	$-0.624051\pi$
$307$	−13.3137	−0.759853	−0.379927	+	0.925017i	$0.624051\pi$
$308$	−2.71573	−0.154743
$309$	6.62742	0.377021
$310$	0	0
$311$	26.4853	1.50184	0.750921	−	0.660392i	$-0.229610\pi$
$311$	26.4853	1.50184	0.750921	+	0.660392i	$0.229610\pi$
$312$	−4.48528	−0.253929
$313$	−31.1421	−1.76026	−0.880129	−	0.474735i	$-0.842544\pi$
$313$	−31.1421	−1.76026	−0.880129	+	0.474735i	$0.842544\pi$
$314$	−2.69848	−0.152284
$315$	0	0
$316$	10.9706	0.617142
$317$	8.14214	0.457308	0.228654	−	0.973508i	$-0.426568\pi$
$317$	8.14214	0.457308	0.228654	+	0.973508i	$0.426568\pi$
$318$	3.51472	0.197096
$319$	−20.8995	−1.17015
$320$	0	0
$321$	−34.3431	−1.91685
$322$	1.51472	0.0844120
$323$	−14.0000	−0.778981
$324$	−1.82843	−0.101579
$325$	0	0
$326$	−4.14214	−0.229412
$327$	−1.37258	−0.0759040
$328$	−8.97056	−0.495316
$329$	−2.65685	−0.146477
$330$	0	0
$331$	16.3431	0.898301	0.449150	−	0.893456i	$-0.351727\pi$
$331$	16.3431	0.898301	0.449150	+	0.893456i	$0.351727\pi$
$332$	−23.5858	−1.29444
$333$	30.0000	1.64399
$334$	−7.17157	−0.392411
$335$	0	0
$336$	−3.51472	−0.191744
$337$	−18.7990	−1.02405	−0.512023	−	0.858972i	$-0.671104\pi$
$337$	−18.7990	−1.02405	−0.512023	+	0.858972i	$0.671104\pi$
$338$	0.414214	0.0225302
$339$	−0.970563	−0.0527137
$340$	0	0
$341$	−25.9706	−1.40638
$342$	15.8579	0.857495
$343$	−5.72792	−0.309279
$344$	−7.65685	−0.412830
$345$	0	0
$346$	−3.04163	−0.163519
$347$	−31.4558	−1.68864	−0.844319	−	0.535841i	$-0.819995\pi$
$347$	−31.4558	−1.68864	−0.844319	+	0.535841i	$0.819995\pi$
$348$	−30.1421	−1.61579
$349$	−15.4558	−0.827332	−0.413666	−	0.910429i	$-0.635752\pi$
$349$	−15.4558	−0.827332	−0.413666	+	0.910429i	$0.635752\pi$
$350$	0	0
$351$	5.65685	0.301941
$352$	15.8284	0.843658
$353$	2.14214	0.114014	0.0570072	−	0.998374i	$-0.481844\pi$
$353$	2.14214	0.114014	0.0570072	+	0.998374i	$0.481844\pi$
$354$	−5.57359	−0.296233
$355$	0	0
$356$	−15.5147	−0.822278
$357$	2.14214	0.113374
$358$	9.65685	0.510381
$359$	−15.3848	−0.811977	−0.405989	−	0.913878i	$-0.633073\pi$
$359$	−15.3848	−0.811977	−0.405989	+	0.913878i	$0.633073\pi$
$360$	0	0
$361$	39.6274	2.08565
$362$	−0.213203	−0.0112057
$363$	−5.25483	−0.275807
$364$	0.757359	0.0396964
$365$	0	0
$366$	−1.17157	−0.0612391
$367$	29.1716	1.52274	0.761372	−	0.648315i	$-0.224526\pi$
$367$	29.1716	1.52274	0.761372	+	0.648315i	$0.224526\pi$
$368$	26.4853	1.38064
$369$	28.2843	1.47242
$370$	0	0
$371$	−1.24264	−0.0645147
$372$	−37.4558	−1.94200
$373$	27.1421	1.40537	0.702683	−	0.711503i	$-0.251985\pi$
$373$	27.1421	1.40537	0.702683	+	0.711503i	$0.251985\pi$
$374$	−2.71573	−0.140427
$375$	0	0
$376$	10.1716	0.524559
$377$	5.82843	0.300179
$378$	−0.970563	−0.0499204
$379$	21.8701	1.12339	0.561695	−	0.827345i	$-0.310150\pi$
$379$	21.8701	1.12339	0.561695	+	0.827345i	$0.310150\pi$
$380$	0	0
$381$	21.6569	1.10951
$382$	1.11270	0.0569306
$383$	−16.3431	−0.835096	−0.417548	−	0.908655i	$-0.637110\pi$
$383$	−16.3431	−0.835096	−0.417548	+	0.908655i	$0.637110\pi$
$384$	29.8579	1.52368
$385$	0	0
$386$	4.00000	0.203595
$387$	24.1421	1.22721
$388$	8.82843	0.448195
$389$	−16.6274	−0.843044	−0.421522	−	0.906818i	$-0.638504\pi$
$389$	−16.6274	−0.843044	−0.421522	+	0.906818i	$0.638504\pi$
$390$	0	0
$391$	−16.1421	−0.816343
$392$	10.8284	0.546918
$393$	24.0000	1.21064
$394$	4.97056	0.250413
$395$	0	0
$396$	−32.7817	−1.64734
$397$	3.65685	0.183532	0.0917661	−	0.995781i	$-0.470749\pi$
$397$	3.65685	0.183532	0.0917661	+	0.995781i	$0.470749\pi$
$398$	4.14214	0.207626
$399$	−8.97056	−0.449090
$400$	0	0
$401$	−32.1421	−1.60510	−0.802551	−	0.596584i	$-0.796524\pi$
$401$	−32.1421	−1.60510	−0.802551	+	0.596584i	$0.796524\pi$
$402$	−13.1716	−0.656938
$403$	7.24264	0.360782
$404$	−8.51472	−0.423623
$405$	0	0
$406$	−1.00000	−0.0496292
$407$	21.5147	1.06645
$408$	−8.20101	−0.406011
$409$	−5.17157	−0.255718	−0.127859	−	0.991792i	$-0.540810\pi$
$409$	−5.17157	−0.255718	−0.127859	+	0.991792i	$0.540810\pi$
$410$	0	0
$411$	−8.00000	−0.394611
$412$	4.28427	0.211071
$413$	1.97056	0.0969651
$414$	18.2843	0.898623
$415$	0	0
$416$	−4.41421	−0.216425
$417$	4.28427	0.209802
$418$	11.3726	0.556251
$419$	17.1716	0.838886	0.419443	−	0.907782i	$-0.362225\pi$
$419$	17.1716	0.838886	0.419443	+	0.907782i	$0.362225\pi$
$420$	0	0
$421$	16.9706	0.827095	0.413547	−	0.910483i	$-0.364290\pi$
$421$	16.9706	0.827095	0.413547	+	0.910483i	$0.364290\pi$
$422$	−9.02944	−0.439546
$423$	−32.0711	−1.55935
$424$	4.75736	0.231038
$425$	0	0
$426$	−15.5980	−0.755725
$427$	0.414214	0.0200452
$428$	−22.2010	−1.07313
$429$	10.1421	0.489667
$430$	0	0
$431$	−19.6569	−0.946837	−0.473419	−	0.880838i	$-0.656980\pi$
$431$	−19.6569	−0.946837	−0.473419	+	0.880838i	$0.656980\pi$
$432$	−16.9706	−0.816497
$433$	−27.6569	−1.32910	−0.664552	−	0.747242i	$-0.731377\pi$
$433$	−27.6569	−1.32910	−0.664552	+	0.747242i	$0.731377\pi$
$434$	−1.24264	−0.0596487
$435$	0	0
$436$	−0.887302	−0.0424940
$437$	67.5980	3.23365
$438$	−7.02944	−0.335880
$439$	14.0000	0.668184	0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000	0.668184	0.334092	+	0.942541i	$0.391570\pi$
$440$	0	0
$441$	−34.1421	−1.62582
$442$	0.757359	0.0360239
$443$	−9.79899	−0.465564	−0.232782	−	0.972529i	$-0.574783\pi$
$443$	−9.79899	−0.465564	−0.232782	+	0.972529i	$0.574783\pi$
$444$	31.0294	1.47259
$445$	0	0
$446$	−9.51472	−0.450535
$447$	−8.97056	−0.424293
$448$	−1.72792	−0.0816366
$449$	−10.8284	−0.511025	−0.255513	−	0.966806i	$-0.582244\pi$
$449$	−10.8284	−0.511025	−0.255513	+	0.966806i	$0.582244\pi$
$450$	0	0
$451$	20.2843	0.955149
$452$	−0.627417	−0.0295112
$453$	48.7696	2.29139
$454$	−4.51472	−0.211886
$455$	0	0
$456$	34.3431	1.60827
$457$	8.48528	0.396925	0.198462	−	0.980109i	$-0.436405\pi$
$457$	8.48528	0.396925	0.198462	+	0.980109i	$0.436405\pi$
$458$	0.343146	0.0160341
$459$	10.3431	0.482777
$460$	0	0
$461$	31.4558	1.46504	0.732522	−	0.680743i	$-0.238343\pi$
$461$	31.4558	1.46504	0.732522	+	0.680743i	$0.238343\pi$
$462$	−1.74012	−0.0809575
$463$	2.55635	0.118804	0.0594018	−	0.998234i	$-0.481081\pi$
$463$	2.55635	0.118804	0.0594018	+	0.998234i	$0.481081\pi$
$464$	−17.4853	−0.811734
$465$	0	0
$466$	10.2010	0.472553
$467$	31.1127	1.43972	0.719862	−	0.694117i	$-0.244205\pi$
$467$	31.1127	1.43972	0.719862	+	0.694117i	$0.244205\pi$
$468$	9.14214	0.422595
$469$	4.65685	0.215034
$470$	0	0
$471$	18.4264	0.849044
$472$	−7.54416	−0.347248
$473$	17.3137	0.796085
$474$	7.02944	0.322873
$475$	0	0
$476$	1.38478	0.0634711
$477$	−15.0000	−0.686803
$478$	10.9411	0.500435
$479$	39.7279	1.81522	0.907608	−	0.419820i	$-0.137907\pi$
$479$	39.7279	1.81522	0.907608	+	0.419820i	$0.137907\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	−12.0000	−0.546585
$483$	−10.3431	−0.470629
$484$	−3.39697	−0.154408
$485$	0	0
$486$	5.85786	0.265718
$487$	−0.213203	−0.00966117	−0.00483058	−	0.999988i	$-0.501538\pi$
$487$	−0.213203	−0.00966117	−0.00483058	+	0.999988i	$0.501538\pi$
$488$	−1.58579	−0.0717852
$489$	28.2843	1.27906
$490$	0	0
$491$	16.8284	0.759456	0.379728	−	0.925098i	$-0.376018\pi$
$491$	16.8284	0.759456	0.379728	+	0.925098i	$0.376018\pi$
$492$	29.2548	1.31891
$493$	10.6569	0.479961
$494$	−3.17157	−0.142696
$495$	0	0
$496$	−21.7279	−0.975613
$497$	5.51472	0.247369
$498$	−15.1127	−0.677216
$499$	−28.5563	−1.27836	−0.639179	−	0.769058i	$-0.720726\pi$
$499$	−28.5563	−1.27836	−0.639179	+	0.769058i	$0.720726\pi$
$500$	0	0
$501$	48.9706	2.18784
$502$	2.34315	0.104580
$503$	−30.6274	−1.36561	−0.682805	−	0.730601i	$-0.739240\pi$
$503$	−30.6274	−1.36561	−0.682805	+	0.730601i	$0.739240\pi$
$504$	−3.28427	−0.146293
$505$	0	0
$506$	13.1127	0.582931
$507$	−2.82843	−0.125615
$508$	14.0000	0.621150
$509$	−30.6274	−1.35754	−0.678768	−	0.734353i	$-0.737486\pi$
$509$	−30.6274	−1.35754	−0.678768	+	0.734353i	$0.737486\pi$
$510$	0	0
$511$	2.48528	0.109942
$512$	22.7574	1.00574
$513$	−43.3137	−1.91235
$514$	−1.92893	−0.0850816
$515$	0	0
$516$	24.9706	1.09927
$517$	−23.0000	−1.01154
$518$	1.02944	0.0452309
$519$	20.7696	0.911682
$520$	0	0
$521$	11.6569	0.510696	0.255348	−	0.966849i	$-0.417810\pi$
$521$	11.6569	0.510696	0.255348	+	0.966849i	$0.417810\pi$
$522$	−12.0711	−0.528336
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	15.5147	0.677764
$525$	0	0
$526$	−0.887302	−0.0386882
$527$	13.2426	0.576858
$528$	−30.4264	−1.32414
$529$	54.9411	2.38874
$530$	0	0
$531$	23.7868	1.03226
$532$	−5.79899	−0.251418
$533$	−5.65685	−0.245026
$534$	−9.94113	−0.430195
$535$	0	0
$536$	−17.8284	−0.770071
$537$	−65.9411	−2.84557
$538$	−5.44365	−0.234692
$539$	−24.4853	−1.05466
$540$	0	0
$541$	−5.79899	−0.249318	−0.124659	−	0.992200i	$-0.539784\pi$
$541$	−5.79899	−0.249318	−0.124659	+	0.992200i	$0.539784\pi$
$542$	−0.112698	−0.00484081
$543$	1.45584	0.0624763
$544$	−8.07107	−0.346044
$545$	0	0
$546$	0.485281	0.0207681
$547$	−11.5147	−0.492334	−0.246167	−	0.969227i	$-0.579171\pi$
$547$	−11.5147	−0.492334	−0.246167	+	0.969227i	$0.579171\pi$
$548$	−5.17157	−0.220919
$549$	5.00000	0.213395
$550$	0	0
$551$	−44.6274	−1.90119
$552$	39.5980	1.68540
$553$	−2.48528	−0.105685
$554$	5.51472	0.234298
$555$	0	0
$556$	2.76955	0.117455
$557$	−4.68629	−0.198565	−0.0992823	−	0.995059i	$-0.531655\pi$
$557$	−4.68629	−0.198565	−0.0992823	+	0.995059i	$0.531655\pi$
$558$	−15.0000	−0.635001
$559$	−4.82843	−0.204221
$560$	0	0
$561$	18.5442	0.782935
$562$	−0.343146	−0.0144747
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	−33.1716	−1.39678
$565$	0	0
$566$	2.28427	0.0960151
$567$	0.414214	0.0173953
$568$	−21.1127	−0.885869
$569$	21.2843	0.892283	0.446142	−	0.894962i	$-0.352798\pi$
$569$	21.2843	0.892283	0.446142	+	0.894962i	$0.352798\pi$
$570$	0	0
$571$	−2.00000	−0.0836974	−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000	−0.0836974	−0.0418487	+	0.999124i	$0.513325\pi$
$572$	6.55635	0.274135
$573$	−7.59798	−0.317410
$574$	0.970563	0.0405105
$575$	0	0
$576$	−20.8579	−0.869078
$577$	12.8284	0.534054	0.267027	−	0.963689i	$-0.413959\pi$
$577$	12.8284	0.534054	0.267027	+	0.963689i	$0.413959\pi$
$578$	−5.65685	−0.235294
$579$	−27.3137	−1.13512
$580$	0	0
$581$	5.34315	0.221671
$582$	5.65685	0.234484
$583$	−10.7574	−0.445524
$584$	−9.51472	−0.393722
$585$	0	0
$586$	−1.31371	−0.0542688
$587$	−11.5858	−0.478197	−0.239098	−	0.970995i	$-0.576852\pi$
$587$	−11.5858	−0.478197	−0.239098	+	0.970995i	$0.576852\pi$
$588$	−35.3137	−1.45631
$589$	−55.4558	−2.28502
$590$	0	0
$591$	−33.9411	−1.39615
$592$	18.0000	0.739795
$593$	−8.34315	−0.342612	−0.171306	−	0.985218i	$-0.554799\pi$
$593$	−8.34315	−0.342612	−0.171306	+	0.985218i	$0.554799\pi$
$594$	−8.40202	−0.344739
$595$	0	0
$596$	−5.79899	−0.237536
$597$	−28.2843	−1.15760
$598$	−3.65685	−0.149540
$599$	−20.4853	−0.837006	−0.418503	−	0.908215i	$-0.637445\pi$
$599$	−20.4853	−0.837006	−0.418503	+	0.908215i	$0.637445\pi$
$600$	0	0
$601$	8.17157	0.333325	0.166663	−	0.986014i	$-0.446701\pi$
$601$	8.17157	0.333325	0.166663	+	0.986014i	$0.446701\pi$
$602$	0.828427	0.0337642
$603$	56.2132	2.28918
$604$	31.5269	1.28281
$605$	0	0
$606$	−5.45584	−0.221629
$607$	38.4853	1.56207	0.781035	−	0.624488i	$-0.214692\pi$
$607$	38.4853	1.56207	0.781035	+	0.624488i	$0.214692\pi$
$608$	33.7990	1.37073
$609$	6.82843	0.276702
$610$	0	0
$611$	6.41421	0.259491
$612$	16.7157	0.675693
$613$	7.17157	0.289657	0.144829	−	0.989457i	$-0.453737\pi$
$613$	7.17157	0.289657	0.144829	+	0.989457i	$0.453737\pi$
$614$	−5.51472	−0.222556
$615$	0	0
$616$	−2.35534	−0.0948993
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	2.74517	0.110427
$619$	−10.9706	−0.440944	−0.220472	−	0.975393i	$-0.570760\pi$
$619$	−10.9706	−0.440944	−0.220472	+	0.975393i	$0.570760\pi$
$620$	0	0
$621$	−49.9411	−2.00407
$622$	10.9706	0.439879
$623$	3.51472	0.140814
$624$	8.48528	0.339683
$625$	0	0
$626$	−12.8995	−0.515568
$627$	−77.6569	−3.10132
$628$	11.9117	0.475328
$629$	−10.9706	−0.437425
$630$	0	0
$631$	34.0000	1.35352	0.676759	−	0.736204i	$-0.263384\pi$
$631$	34.0000	1.35352	0.676759	+	0.736204i	$0.263384\pi$
$632$	9.51472	0.378475
$633$	61.6569	2.45064
$634$	3.37258	0.133942
$635$	0	0
$636$	−15.5147	−0.615199
$637$	6.82843	0.270552
$638$	−8.65685	−0.342728
$639$	66.5685	2.63341
$640$	0	0
$641$	−34.1127	−1.34737	−0.673685	−	0.739018i	$-0.735290\pi$
$641$	−34.1127	−1.34737	−0.673685	+	0.739018i	$0.735290\pi$
$642$	−14.2254	−0.561432
$643$	34.9706	1.37910	0.689552	−	0.724236i	$-0.257807\pi$
$643$	34.9706	1.37910	0.689552	+	0.724236i	$0.257807\pi$
$644$	−6.68629	−0.263477
$645$	0	0
$646$	−5.79899	−0.228158
$647$	−13.1716	−0.517828	−0.258914	−	0.965900i	$-0.583365\pi$
$647$	−13.1716	−0.517828	−0.258914	+	0.965900i	$0.583365\pi$
$648$	−1.58579	−0.0622956
$649$	17.0589	0.669619
$650$	0	0
$651$	8.48528	0.332564
$652$	18.2843	0.716067
$653$	−28.4558	−1.11356	−0.556782	−	0.830659i	$-0.687964\pi$
$653$	−28.4558	−1.11356	−0.556782	+	0.830659i	$0.687964\pi$
$654$	−0.568542	−0.0222318
$655$	0	0
$656$	16.9706	0.662589
$657$	30.0000	1.17041
$658$	−1.10051	−0.0429022
$659$	36.6274	1.42680	0.713401	−	0.700756i	$-0.247154\pi$
$659$	36.6274	1.42680	0.713401	+	0.700756i	$0.247154\pi$
$660$	0	0
$661$	−1.17157	−0.0455689	−0.0227845	−	0.999740i	$-0.507253\pi$
$661$	−1.17157	−0.0455689	−0.0227845	+	0.999740i	$0.507253\pi$
$662$	6.76955	0.263106
$663$	−5.17157	−0.200847
$664$	−20.4558	−0.793841
$665$	0	0
$666$	12.4264	0.481513
$667$	−51.4558	−1.99238
$668$	31.6569	1.22484
$669$	64.9706	2.51191
$670$	0	0
$671$	3.58579	0.138428
$672$	−5.17157	−0.199498
$673$	26.4558	1.01980	0.509899	−	0.860234i	$-0.329683\pi$
$673$	26.4558	1.01980	0.509899	+	0.860234i	$0.329683\pi$
$674$	−7.78680	−0.299936
$675$	0	0
$676$	−1.82843	−0.0703241
$677$	18.6863	0.718173	0.359086	−	0.933304i	$-0.383088\pi$
$677$	18.6863	0.718173	0.359086	+	0.933304i	$0.383088\pi$
$678$	−0.402020	−0.0154395
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	30.8284	1.18135
$682$	−10.7574	−0.411921
$683$	−24.4142	−0.934184	−0.467092	−	0.884209i	$-0.654698\pi$
$683$	−24.4142	−0.934184	−0.467092	+	0.884209i	$0.654698\pi$
$684$	−70.0000	−2.67652
$685$	0	0
$686$	−2.37258	−0.0905856
$687$	−2.34315	−0.0893966
$688$	14.4853	0.552246
$689$	3.00000	0.114291
$690$	0	0
$691$	−10.8995	−0.414636	−0.207318	−	0.978274i	$-0.566474\pi$
$691$	−10.8995	−0.414636	−0.207318	+	0.978274i	$0.566474\pi$
$692$	13.4264	0.510395
$693$	7.42641	0.282106
$694$	−13.0294	−0.494591
$695$	0	0
$696$	−26.1421	−0.990915
$697$	−10.3431	−0.391775
$698$	−6.40202	−0.242320
$699$	−69.6569	−2.63466
$700$	0	0
$701$	−10.1716	−0.384175	−0.192088	−	0.981378i	$-0.561526\pi$
$701$	−10.1716	−0.384175	−0.192088	+	0.981378i	$0.561526\pi$
$702$	2.34315	0.0884363
$703$	45.9411	1.73270
$704$	−14.9584	−0.563765
$705$	0	0
$706$	0.887302	0.0333940
$707$	1.92893	0.0725450
$708$	24.6030	0.924639
$709$	41.2548	1.54936	0.774679	−	0.632355i	$-0.217911\pi$
$709$	41.2548	1.54936	0.774679	+	0.632355i	$0.217911\pi$
$710$	0	0
$711$	−30.0000	−1.12509
$712$	−13.4558	−0.504279
$713$	−63.9411	−2.39461
$714$	0.887302	0.0332064
$715$	0	0
$716$	−42.6274	−1.59306
$717$	−74.7107	−2.79012
$718$	−6.37258	−0.237823
$719$	1.45584	0.0542938	0.0271469	−	0.999631i	$-0.491358\pi$
$719$	1.45584	0.0542938	0.0271469	+	0.999631i	$0.491358\pi$
$720$	0	0
$721$	−0.970563	−0.0361456
$722$	16.4142	0.610874
$723$	81.9411	3.04742
$724$	0.941125	0.0349767
$725$	0	0
$726$	−2.17662	−0.0807821
$727$	−39.3137	−1.45806	−0.729032	−	0.684479i	$-0.760030\pi$
$727$	−39.3137	−1.45806	−0.729032	+	0.684479i	$0.760030\pi$
$728$	0.656854	0.0243446
$729$	−43.0000	−1.59259
$730$	0	0
$731$	−8.82843	−0.326531
$732$	5.17157	0.191147
$733$	−3.79899	−0.140319	−0.0701594	−	0.997536i	$-0.522351\pi$
$733$	−3.79899	−0.140319	−0.0701594	+	0.997536i	$0.522351\pi$
$734$	12.0833	0.446001
$735$	0	0
$736$	38.9706	1.43647
$737$	40.3137	1.48497
$738$	11.7157	0.431262
$739$	−2.27208	−0.0835797	−0.0417899	−	0.999126i	$-0.513306\pi$
$739$	−2.27208	−0.0835797	−0.0417899	+	0.999126i	$0.513306\pi$
$740$	0	0
$741$	21.6569	0.795584
$742$	−0.514719	−0.0188959
$743$	−44.6985	−1.63983	−0.819914	−	0.572486i	$-0.805979\pi$
$743$	−44.6985	−1.63983	−0.819914	+	0.572486i	$0.805979\pi$
$744$	−32.4853	−1.19097
$745$	0	0
$746$	11.2426	0.411622
$747$	64.4975	2.35984
$748$	11.9878	0.438318
$749$	5.02944	0.183772
$750$	0	0
$751$	−19.4558	−0.709954	−0.354977	−	0.934875i	$-0.615511\pi$
$751$	−19.4558	−0.709954	−0.354977	+	0.934875i	$0.615511\pi$
$752$	−19.2426	−0.701707
$753$	−16.0000	−0.583072
$754$	2.41421	0.0879205
$755$	0	0
$756$	4.28427	0.155817
$757$	−6.31371	−0.229476	−0.114738	−	0.993396i	$-0.536603\pi$
$757$	−6.31371	−0.229476	−0.114738	+	0.993396i	$0.536603\pi$
$758$	9.05887	0.329033
$759$	−89.5391	−3.25006
$760$	0	0
$761$	17.7990	0.645213	0.322606	−	0.946533i	$-0.395441\pi$
$761$	17.7990	0.645213	0.322606	+	0.946533i	$0.395441\pi$
$762$	8.97056	0.324969
$763$	0.201010	0.00727706
$764$	−4.91169	−0.177699
$765$	0	0
$766$	−6.76955	−0.244594
$767$	−4.75736	−0.171778
$768$	−11.2304	−0.405244
$769$	−28.9706	−1.04471	−0.522353	−	0.852730i	$-0.674946\pi$
$769$	−28.9706	−1.04471	−0.522353	+	0.852730i	$0.674946\pi$
$770$	0	0
$771$	13.1716	0.474363
$772$	−17.6569	−0.635484
$773$	−33.7990	−1.21567	−0.607833	−	0.794065i	$-0.707961\pi$
$773$	−33.7990	−1.21567	−0.607833	+	0.794065i	$0.707961\pi$
$774$	10.0000	0.359443
$775$	0	0
$776$	7.65685	0.274865
$777$	−7.02944	−0.252180
$778$	−6.88730	−0.246922
$779$	43.3137	1.55187
$780$	0	0
$781$	47.7401	1.70828
$782$	−6.68629	−0.239101
$783$	32.9706	1.17827
$784$	−20.4853	−0.731617
$785$	0	0
$786$	9.94113	0.354588
$787$	−47.2426	−1.68402	−0.842009	−	0.539463i	$-0.818627\pi$
$787$	−47.2426	−1.68402	−0.842009	+	0.539463i	$0.818627\pi$
$788$	−21.9411	−0.781620
$789$	6.05887	0.215702
$790$	0	0
$791$	0.142136	0.00505376
$792$	−28.4315	−1.01027
$793$	−1.00000	−0.0355110
$794$	1.51472	0.0537554
$795$	0	0
$796$	−18.2843	−0.648069
$797$	−5.48528	−0.194299	−0.0971493	−	0.995270i	$-0.530972\pi$
$797$	−5.48528	−0.194299	−0.0971493	+	0.995270i	$0.530972\pi$
$798$	−3.71573	−0.131535
$799$	11.7279	0.414904
$800$	0	0
$801$	42.4264	1.49906
$802$	−13.3137	−0.470123
$803$	21.5147	0.759238
$804$	58.1421	2.05052
$805$	0	0
$806$	3.00000	0.105670
$807$	37.1716	1.30850
$808$	−7.38478	−0.259796
$809$	−5.31371	−0.186820	−0.0934100	−	0.995628i	$-0.529777\pi$
$809$	−5.31371	−0.186820	−0.0934100	+	0.995628i	$0.529777\pi$
$810$	0	0
$811$	12.4142	0.435922	0.217961	−	0.975957i	$-0.430059\pi$
$811$	12.4142	0.435922	0.217961	+	0.975957i	$0.430059\pi$
$812$	4.41421	0.154909
$813$	0.769553	0.0269894
$814$	8.91169	0.312355
$815$	0	0
$816$	15.5147	0.543124
$817$	36.9706	1.29344
$818$	−2.14214	−0.0748980
$819$	−2.07107	−0.0723690
$820$	0	0
$821$	−15.1716	−0.529492	−0.264746	−	0.964318i	$-0.585288\pi$
$821$	−15.1716	−0.529492	−0.264746	+	0.964318i	$0.585288\pi$
$822$	−3.31371	−0.115579
$823$	−36.2843	−1.26479	−0.632395	−	0.774646i	$-0.717928\pi$
$823$	−36.2843	−1.26479	−0.632395	+	0.774646i	$0.717928\pi$
$824$	3.71573	0.129444
$825$	0	0
$826$	0.816234	0.0284004
$827$	−38.3553	−1.33375	−0.666873	−	0.745171i	$-0.732368\pi$
$827$	−38.3553	−1.33375	−0.666873	+	0.745171i	$0.732368\pi$
$828$	−80.7107	−2.80489
$829$	−25.9706	−0.901995	−0.450997	−	0.892525i	$-0.648932\pi$
$829$	−25.9706	−0.901995	−0.450997	+	0.892525i	$0.648932\pi$
$830$	0	0
$831$	−37.6569	−1.30630
$832$	4.17157	0.144623
$833$	12.4853	0.432589
$834$	1.77460	0.0614495
$835$	0	0
$836$	−50.2010	−1.73624
$837$	40.9706	1.41615
$838$	7.11270	0.245704
$839$	−34.9706	−1.20732	−0.603659	−	0.797243i	$-0.706291\pi$
$839$	−34.9706	−1.20732	−0.603659	+	0.797243i	$0.706291\pi$
$840$	0	0
$841$	4.97056	0.171399
$842$	7.02944	0.242250
$843$	2.34315	0.0807022
$844$	39.8579	1.37196
$845$	0	0
$846$	−13.2843	−0.456723
$847$	0.769553	0.0264421
$848$	−9.00000	−0.309061
$849$	−15.5980	−0.535321
$850$	0	0
$851$	52.9706	1.81581
$852$	68.8528	2.35886
$853$	−42.4264	−1.45265	−0.726326	−	0.687350i	$-0.758774\pi$
$853$	−42.4264	−1.45265	−0.726326	+	0.687350i	$0.758774\pi$
$854$	0.171573	0.00587110
$855$	0	0
$856$	−19.2548	−0.658117
$857$	−40.6274	−1.38781	−0.693903	−	0.720068i	$-0.744110\pi$
$857$	−40.6274	−1.38781	−0.693903	+	0.720068i	$0.744110\pi$
$858$	4.20101	0.143420
$859$	−4.14214	−0.141328	−0.0706639	−	0.997500i	$-0.522512\pi$
$859$	−4.14214	−0.141328	−0.0706639	+	0.997500i	$0.522512\pi$
$860$	0	0
$861$	−6.62742	−0.225862
$862$	−8.14214	−0.277322
$863$	47.1838	1.60615	0.803077	−	0.595875i	$-0.203195\pi$
$863$	47.1838	1.60615	0.803077	+	0.595875i	$0.203195\pi$
$864$	−24.9706	−0.849516
$865$	0	0
$866$	−11.4558	−0.389285
$867$	38.6274	1.31186
$868$	5.48528	0.186183
$869$	−21.5147	−0.729837
$870$	0	0
$871$	−11.2426	−0.380942
$872$	−0.769553	−0.0260603
$873$	−24.1421	−0.817087
$874$	28.0000	0.947114
$875$	0	0
$876$	31.0294	1.04839
$877$	−23.7990	−0.803635	−0.401817	−	0.915720i	$-0.631621\pi$
$877$	−23.7990	−0.803635	−0.401817	+	0.915720i	$0.631621\pi$
$878$	5.79899	0.195706
$879$	8.97056	0.302570
$880$	0	0
$881$	−15.0000	−0.505363	−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000	−0.505363	−0.252681	+	0.967550i	$0.581312\pi$
$882$	−14.1421	−0.476190
$883$	0.970563	0.0326620	0.0163310	−	0.999867i	$-0.494801\pi$
$883$	0.970563	0.0326620	0.0163310	+	0.999867i	$0.494801\pi$
$884$	−3.34315	−0.112442
$885$	0	0
$886$	−4.05887	−0.136361
$887$	36.6274	1.22983	0.614914	−	0.788594i	$-0.289191\pi$
$887$	36.6274	1.22983	0.614914	+	0.788594i	$0.289191\pi$
$888$	26.9117	0.903097
$889$	−3.17157	−0.106371
$890$	0	0
$891$	3.58579	0.120128
$892$	42.0000	1.40626
$893$	−49.1127	−1.64349
$894$	−3.71573	−0.124273
$895$	0	0
$896$	−4.37258	−0.146078
$897$	24.9706	0.833743
$898$	−4.48528	−0.149676
$899$	42.2132	1.40789
$900$	0	0
$901$	5.48528	0.182741
$902$	8.40202	0.279757
$903$	−5.65685	−0.188248
$904$	−0.544156	−0.0180984
$905$	0	0
$906$	20.2010	0.671134
$907$	24.0000	0.796907	0.398453	−	0.917189i	$-0.369547\pi$
$907$	24.0000	0.796907	0.398453	+	0.917189i	$0.369547\pi$
$908$	19.9289	0.661365
$909$	23.2843	0.772291
$910$	0	0
$911$	6.00000	0.198789	0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000	0.198789	0.0993944	+	0.995048i	$0.468309\pi$
$912$	−64.9706	−2.15139
$913$	46.2548	1.53081
$914$	3.51472	0.116257
$915$	0	0
$916$	−1.51472	−0.0500477
$917$	−3.51472	−0.116066
$918$	4.28427	0.141402
$919$	14.9706	0.493833	0.246917	−	0.969037i	$-0.420583\pi$
$919$	14.9706	0.493833	0.246917	+	0.969037i	$0.420583\pi$
$920$	0	0
$921$	37.6569	1.24084
$922$	13.0294	0.429102
$923$	−13.3137	−0.438226
$924$	7.68124	0.252694
$925$	0	0
$926$	1.05887	0.0347968
$927$	−11.7157	−0.384795
$928$	−25.7279	−0.844560
$929$	−26.2843	−0.862359	−0.431179	−	0.902266i	$-0.641902\pi$
$929$	−26.2843	−0.862359	−0.431179	+	0.902266i	$0.641902\pi$
$930$	0	0
$931$	−52.2843	−1.71355
$932$	−45.0294	−1.47499
$933$	−74.9117	−2.45250
$934$	12.8873	0.421685
$935$	0	0
$936$	7.92893	0.259165
$937$	31.9706	1.04443	0.522216	−	0.852813i	$-0.325105\pi$
$937$	31.9706	1.04443	0.522216	+	0.852813i	$0.325105\pi$
$938$	1.92893	0.0629819
$939$	88.0833	2.87449
$940$	0	0
$941$	−24.3431	−0.793564	−0.396782	−	0.917913i	$-0.629873\pi$
$941$	−24.3431	−0.793564	−0.396782	+	0.917913i	$0.629873\pi$
$942$	7.63247	0.248679
$943$	49.9411	1.62631
$944$	14.2721	0.464517
$945$	0	0
$946$	7.17157	0.233168
$947$	23.5858	0.766435	0.383218	−	0.923658i	$-0.374816\pi$
$947$	23.5858	0.766435	0.383218	+	0.923658i	$0.374816\pi$
$948$	−31.0294	−1.00779
$949$	−6.00000	−0.194768
$950$	0	0
$951$	−23.0294	−0.746781
$952$	1.20101	0.0389250
$953$	58.6569	1.90008	0.950041	−	0.312125i	$-0.101041\pi$
$953$	58.6569	1.90008	0.950041	+	0.312125i	$0.101041\pi$
$954$	−6.21320	−0.201160
$955$	0	0
$956$	−48.2965	−1.56202
$957$	59.1127	1.91084
$958$	16.4558	0.531664
$959$	1.17157	0.0378321
$960$	0	0
$961$	21.4558	0.692124
$962$	−2.48528	−0.0801287
$963$	60.7107	1.95637
$964$	52.9706	1.70607
$965$	0	0
$966$	−4.28427	−0.137844
$967$	−18.2721	−0.587590	−0.293795	−	0.955868i	$-0.594918\pi$
$967$	−18.2721	−0.587590	−0.293795	+	0.955868i	$0.594918\pi$
$968$	−2.94618	−0.0946937
$969$	39.5980	1.27207
$970$	0	0
$971$	31.1716	1.00034	0.500172	−	0.865926i	$-0.333270\pi$
$971$	31.1716	1.00034	0.500172	+	0.865926i	$0.333270\pi$
$972$	−25.8579	−0.829391
$973$	−0.627417	−0.0201141
$974$	−0.0883118	−0.00282969
$975$	0	0
$976$	3.00000	0.0960277
$977$	−8.48528	−0.271468	−0.135734	−	0.990745i	$-0.543339\pi$
$977$	−8.48528	−0.271468	−0.135734	+	0.990745i	$0.543339\pi$
$978$	11.7157	0.374628
$979$	30.4264	0.972432
$980$	0	0
$981$	2.42641	0.0774692
$982$	6.97056	0.222440
$983$	32.6985	1.04292	0.521460	−	0.853276i	$-0.325388\pi$
$983$	32.6985	1.04292	0.521460	+	0.853276i	$0.325388\pi$
$984$	25.3726	0.808848
$985$	0	0
$986$	4.41421	0.140577
$987$	7.51472	0.239196
$988$	14.0000	0.445399
$989$	42.6274	1.35547
$990$	0	0
$991$	−30.4853	−0.968397	−0.484198	−	0.874958i	$-0.660889\pi$
$991$	−30.4853	−0.968397	−0.484198	+	0.874958i	$0.660889\pi$
$992$	−31.9706	−1.01507
$993$	−46.2254	−1.46692
$994$	2.28427	0.0724527
$995$	0	0
$996$	66.7107	2.11381
$997$	−1.34315	−0.0425379	−0.0212689	−	0.999774i	$-0.506771\pi$
$997$	−1.34315	−0.0425379	−0.0212689	+	0.999774i	$0.506771\pi$
$998$	−11.8284	−0.374422
$999$	−33.9411	−1.07385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.a.f.1.2	✓	2
3.2	odd	2		2925.2.a.bd.1.1		2
4.3	odd	2		5200.2.a.bt.1.2		2
5.2	odd	4		325.2.b.d.274.3		4
5.3	odd	4		325.2.b.d.274.2		4
5.4	even	2		325.2.a.h.1.1	yes	2
13.12	even	2		4225.2.a.z.1.1		2
15.2	even	4		2925.2.c.q.2224.2		4
15.8	even	4		2925.2.c.q.2224.3		4
15.14	odd	2		2925.2.a.w.1.2		2
20.19	odd	2		5200.2.a.br.1.1		2
65.64	even	2		4225.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.a.f.1.2	✓	2	1.1	even	1	trivial
325.2.a.h.1.1	yes	2	5.4	even	2
325.2.b.d.274.2		4	5.3	odd	4
325.2.b.d.274.3		4	5.2	odd	4
2925.2.a.w.1.2		2	15.14	odd	2
2925.2.a.bd.1.1		2	3.2	odd	2
2925.2.c.q.2224.2		4	15.2	even	4
2925.2.c.q.2224.3		4	15.8	even	4
4225.2.a.s.1.2		2	65.64	even	2
4225.2.a.z.1.1		2	13.12	even	2
5200.2.a.br.1.1		2	20.19	odd	2
5200.2.a.bt.1.2		2	4.3	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} -1.17157 q^{6} +0.414214 q^{7} -1.58579 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} -1.17157 q^{6} +0.414214 q^{7} -1.58579 q^{8} +5.00000 q^{9} +3.58579 q^{11} +5.17157 q^{12} -1.00000 q^{13} +0.171573 q^{14} +3.00000 q^{16} -1.82843 q^{17} +2.07107 q^{18} +7.65685 q^{19} -1.17157 q^{21} +1.48528 q^{22} +8.82843 q^{23} +4.48528 q^{24} -0.414214 q^{26} -5.65685 q^{27} -0.757359 q^{28} -5.82843 q^{29} -7.24264 q^{31} +4.41421 q^{32} -10.1421 q^{33} -0.757359 q^{34} -9.14214 q^{36} +6.00000 q^{37} +3.17157 q^{38} +2.82843 q^{39} +5.65685 q^{41} -0.485281 q^{42} +4.82843 q^{43} -6.55635 q^{44} +3.65685 q^{46} -6.41421 q^{47} -8.48528 q^{48} -6.82843 q^{49} +5.17157 q^{51} +1.82843 q^{52} -3.00000 q^{53} -2.34315 q^{54} -0.656854 q^{56} -21.6569 q^{57} -2.41421 q^{58} +4.75736 q^{59} +1.00000 q^{61} -3.00000 q^{62} +2.07107 q^{63} -4.17157 q^{64} -4.20101 q^{66} +11.2426 q^{67} +3.34315 q^{68} -24.9706 q^{69} +13.3137 q^{71} -7.92893 q^{72} +6.00000 q^{73} +2.48528 q^{74} -14.0000 q^{76} +1.48528 q^{77} +1.17157 q^{78} -6.00000 q^{79} +1.00000 q^{81} +2.34315 q^{82} +12.8995 q^{83} +2.14214 q^{84} +2.00000 q^{86} +16.4853 q^{87} -5.68629 q^{88} +8.48528 q^{89} -0.414214 q^{91} -16.1421 q^{92} +20.4853 q^{93} -2.65685 q^{94} -12.4853 q^{96} -4.82843 q^{97} -2.82843 q^{98} +17.9289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^8 + 10 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{8} + 10 q^{9} + 10 q^{11} + 16 q^{12} - 2 q^{13} + 6 q^{14} + 6 q^{16} + 2 q^{17} - 10 q^{18} + 4 q^{19} - 8 q^{21} - 14 q^{22} + 12 q^{23} - 8 q^{24} + 2 q^{26} - 10 q^{28} - 6 q^{29} - 6 q^{31} + 6 q^{32} + 8 q^{33} - 10 q^{34} + 10 q^{36} + 12 q^{37} + 12 q^{38} + 16 q^{42} + 4 q^{43} + 18 q^{44} - 4 q^{46} - 10 q^{47} - 8 q^{49} + 16 q^{51} - 2 q^{52} - 6 q^{53} - 16 q^{54} + 10 q^{56} - 32 q^{57} - 2 q^{58} + 18 q^{59} + 2 q^{61} - 6 q^{62} - 10 q^{63} - 14 q^{64} - 48 q^{66} + 14 q^{67} + 18 q^{68} - 16 q^{69} + 4 q^{71} - 30 q^{72} + 12 q^{73} - 12 q^{74} - 28 q^{76} - 14 q^{77} + 8 q^{78} - 12 q^{79} + 2 q^{81} + 16 q^{82} + 6 q^{83} - 24 q^{84} + 4 q^{86} + 16 q^{87} - 34 q^{88} + 2 q^{91} - 4 q^{92} + 24 q^{93} + 6 q^{94} - 8 q^{96} - 4 q^{97} + 50 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^8 + 10 * q^9 + 10 * q^11 + 16 * q^12 - 2 * q^13 + 6 * q^14 + 6 * q^16 + 2 * q^17 - 10 * q^18 + 4 * q^19 - 8 * q^21 - 14 * q^22 + 12 * q^23 - 8 * q^24 + 2 * q^26 - 10 * q^28 - 6 * q^29 - 6 * q^31 + 6 * q^32 + 8 * q^33 - 10 * q^34 + 10 * q^36 + 12 * q^37 + 12 * q^38 + 16 * q^42 + 4 * q^43 + 18 * q^44 - 4 * q^46 - 10 * q^47 - 8 * q^49 + 16 * q^51 - 2 * q^52 - 6 * q^53 - 16 * q^54 + 10 * q^56 - 32 * q^57 - 2 * q^58 + 18 * q^59 + 2 * q^61 - 6 * q^62 - 10 * q^63 - 14 * q^64 - 48 * q^66 + 14 * q^67 + 18 * q^68 - 16 * q^69 + 4 * q^71 - 30 * q^72 + 12 * q^73 - 12 * q^74 - 28 * q^76 - 14 * q^77 + 8 * q^78 - 12 * q^79 + 2 * q^81 + 16 * q^82 + 6 * q^83 - 24 * q^84 + 4 * q^86 + 16 * q^87 - 34 * q^88 + 2 * q^91 - 4 * q^92 + 24 * q^93 + 6 * q^94 - 8 * q^96 - 4 * q^97 + 50 * q^99

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