LMFDB - Embedded newform 1175.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, 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("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 8x^{4} + 28x^{3} - 17x^{2} - 19x + 2 $ x^7 - x^6 - 10x^5 + 8x^4 + 28x^3 - 17x^2 - 19*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.49903$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.49903 q^{2} -2.14267 q^{3} +0.247101 q^{4} +3.21194 q^{6} -0.914748 q^{7} +2.62765 q^{8} +1.59105 q^{9} +O(q^{10})$	\(q-1.49903 q^{2} -2.14267 q^{3} +0.247101 q^{4} +3.21194 q^{6} -0.914748 q^{7} +2.62765 q^{8} +1.59105 q^{9} -5.69180 q^{11} -0.529457 q^{12} +5.13117 q^{13} +1.37124 q^{14} -4.43314 q^{16} -5.54912 q^{17} -2.38504 q^{18} +4.24685 q^{19} +1.96001 q^{21} +8.53219 q^{22} -7.15053 q^{23} -5.63020 q^{24} -7.69180 q^{26} +3.01892 q^{27} -0.226035 q^{28} +1.00193 q^{29} -6.52323 q^{31} +1.39012 q^{32} +12.1957 q^{33} +8.31832 q^{34} +0.393150 q^{36} -10.0620 q^{37} -6.36616 q^{38} -10.9944 q^{39} -4.42388 q^{41} -2.93812 q^{42} -0.310136 q^{43} -1.40645 q^{44} +10.7189 q^{46} +1.00000 q^{47} +9.49878 q^{48} -6.16324 q^{49} +11.8900 q^{51} +1.26792 q^{52} +6.38803 q^{53} -4.52546 q^{54} -2.40364 q^{56} -9.09960 q^{57} -1.50193 q^{58} +1.42791 q^{59} +12.9582 q^{61} +9.77853 q^{62} -1.45541 q^{63} +6.78245 q^{64} -18.2817 q^{66} -4.25337 q^{67} -1.37119 q^{68} +15.3213 q^{69} +3.83337 q^{71} +4.18073 q^{72} +9.86340 q^{73} +15.0832 q^{74} +1.04940 q^{76} +5.20656 q^{77} +16.4810 q^{78} -6.00906 q^{79} -11.2417 q^{81} +6.63154 q^{82} -2.43649 q^{83} +0.484320 q^{84} +0.464904 q^{86} -2.14682 q^{87} -14.9561 q^{88} +11.8146 q^{89} -4.69373 q^{91} -1.76690 q^{92} +13.9771 q^{93} -1.49903 q^{94} -2.97858 q^{96} +18.0420 q^{97} +9.23890 q^{98} -9.05593 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9	$ 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9} + q^{11} + 4 q^{12} - 2 q^{13} + 10 q^{14} - q^{16} - 12 q^{17} + 17 q^{18} + 3 q^{19} + 7 q^{21} + 5 q^{22} - q^{23} + 8 q^{24} - 13 q^{26} - q^{27} + 27 q^{28} + 26 q^{29} - 5 q^{31} - 12 q^{32} + 15 q^{33} + 6 q^{34} - 34 q^{36} + 7 q^{38} + q^{39} + 12 q^{41} + 18 q^{42} + 33 q^{43} + 3 q^{44} - 36 q^{46} + 7 q^{47} + 25 q^{48} + 6 q^{49} - 14 q^{51} + 11 q^{52} - 4 q^{53} - 2 q^{54} - 27 q^{56} + 21 q^{57} + 38 q^{58} + 13 q^{59} + 20 q^{61} - 15 q^{62} + 10 q^{63} - 9 q^{64} - 41 q^{66} + 32 q^{67} - 15 q^{68} + 16 q^{69} + 11 q^{71} + 8 q^{72} + 8 q^{73} + 48 q^{74} + 11 q^{76} - 29 q^{77} + 17 q^{78} + 17 q^{79} + 15 q^{81} - 6 q^{82} - 19 q^{83} + 46 q^{84} - 30 q^{86} - 2 q^{87} - 7 q^{88} + 13 q^{89} - 11 q^{91} - 16 q^{92} + 29 q^{93} - q^{94} - 29 q^{96} + 12 q^{97} - 6 q^{98} - 32 q^{99}+O(q^{100}) $ 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9 + q^11 + 4 * q^12 - 2 * q^13 + 10 * q^14 - q^16 - 12 * q^17 + 17 * q^18 + 3 * q^19 + 7 * q^21 + 5 * q^22 - q^23 + 8 * q^24 - 13 * q^26 - q^27 + 27 * q^28 + 26 * q^29 - 5 * q^31 - 12 * q^32 + 15 * q^33 + 6 * q^34 - 34 * q^36 + 7 * q^38 + q^39 + 12 * q^41 + 18 * q^42 + 33 * q^43 + 3 * q^44 - 36 * q^46 + 7 * q^47 + 25 * q^48 + 6 * q^49 - 14 * q^51 + 11 * q^52 - 4 * q^53 - 2 * q^54 - 27 * q^56 + 21 * q^57 + 38 * q^58 + 13 * q^59 + 20 * q^61 - 15 * q^62 + 10 * q^63 - 9 * q^64 - 41 * q^66 + 32 * q^67 - 15 * q^68 + 16 * q^69 + 11 * q^71 + 8 * q^72 + 8 * q^73 + 48 * q^74 + 11 * q^76 - 29 * q^77 + 17 * q^78 + 17 * q^79 + 15 * q^81 - 6 * q^82 - 19 * q^83 + 46 * q^84 - 30 * q^86 - 2 * q^87 - 7 * q^88 + 13 * q^89 - 11 * q^91 - 16 * q^92 + 29 * q^93 - q^94 - 29 * q^96 + 12 * q^97 - 6 * q^98 - 32 * 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 $

$2$	−1.49903	−1.05998	−0.529988	−	0.848005i	$-0.677804\pi$
$2$	−1.49903	−1.05998	−0.529988	+	0.848005i	$0.677804\pi$
$3$	−2.14267	−1.23707	−0.618537	−	0.785756i	$-0.712274\pi$
$3$	−2.14267	−1.23707	−0.618537	+	0.785756i	$0.712274\pi$
$4$	0.247101	0.123551
$5$	0	0
$5$	0	0
$6$	3.21194	1.31127
$7$	−0.914748	−0.345742	−0.172871	−	0.984944i	$-0.555304\pi$
$7$	−0.914748	−0.345742	−0.172871	+	0.984944i	$0.555304\pi$
$8$	2.62765	0.929016
$9$	1.59105	0.530350
$10$	0	0
$11$	−5.69180	−1.71614	−0.858071	−	0.513532i	$-0.828337\pi$
$11$	−5.69180	−1.71614	−0.858071	+	0.513532i	$0.828337\pi$
$12$	−0.529457	−0.152841
$13$	5.13117	1.42313	0.711565	−	0.702620i	$-0.247987\pi$
$13$	5.13117	1.42313	0.711565	+	0.702620i	$0.247987\pi$
$14$	1.37124	0.366479
$15$	0	0
$16$	−4.43314	−1.10829
$17$	−5.54912	−1.34586	−0.672930	−	0.739706i	$-0.734964\pi$
$17$	−5.54912	−1.34586	−0.672930	+	0.739706i	$0.734964\pi$
$18$	−2.38504	−0.562158
$19$	4.24685	0.974293	0.487147	−	0.873320i	$-0.338038\pi$
$19$	4.24685	0.974293	0.487147	+	0.873320i	$0.338038\pi$
$20$	0	0
$21$	1.96001	0.427709
$22$	8.53219	1.81907
$23$	−7.15053	−1.49099	−0.745495	−	0.666512i	$-0.767787\pi$
$23$	−7.15053	−1.49099	−0.745495	+	0.666512i	$0.767787\pi$
$24$	−5.63020	−1.14926
$25$	0	0
$26$	−7.69180	−1.50849
$27$	3.01892	0.580992
$28$	−0.226035	−0.0427167
$29$	1.00193	0.186054	0.0930272	−	0.995664i	$-0.470346\pi$
$29$	1.00193	0.186054	0.0930272	+	0.995664i	$0.470346\pi$
$30$	0	0
$31$	−6.52323	−1.17161	−0.585803	−	0.810453i	$-0.699221\pi$
$31$	−6.52323	−1.17161	−0.585803	+	0.810453i	$0.699221\pi$
$32$	1.39012	0.245741
$33$	12.1957	2.12299
$34$	8.31832	1.42658
$35$	0	0
$36$	0.393150	0.0655250
$37$	−10.0620	−1.65418	−0.827088	−	0.562073i	$-0.810004\pi$
$37$	−10.0620	−1.65418	−0.827088	+	0.562073i	$0.810004\pi$
$38$	−6.36616	−1.03273
$39$	−10.9944	−1.76052
$40$	0	0
$41$	−4.42388	−0.690894	−0.345447	−	0.938438i	$-0.612273\pi$
$41$	−4.42388	−0.690894	−0.345447	+	0.938438i	$0.612273\pi$
$42$	−2.93812	−0.453361
$43$	−0.310136	−0.0472953	−0.0236476	−	0.999720i	$-0.507528\pi$
$43$	−0.310136	−0.0472953	−0.0236476	+	0.999720i	$0.507528\pi$
$44$	−1.40645	−0.212030
$45$	0	0
$46$	10.7189	1.58041
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	9.49878	1.37103
$49$	−6.16324	−0.880462
$50$	0	0
$51$	11.8900	1.66493
$52$	1.26792	0.175829
$53$	6.38803	0.877463	0.438731	−	0.898618i	$-0.355428\pi$
$53$	6.38803	0.877463	0.438731	+	0.898618i	$0.355428\pi$
$54$	−4.52546	−0.615838
$55$	0	0
$56$	−2.40364	−0.321200
$57$	−9.09960	−1.20527
$58$	−1.50193	−0.197213
$59$	1.42791	0.185898	0.0929488	−	0.995671i	$-0.470371\pi$
$59$	1.42791	0.185898	0.0929488	+	0.995671i	$0.470371\pi$
$60$	0	0
$61$	12.9582	1.65912	0.829562	−	0.558415i	$-0.188590\pi$
$61$	12.9582	1.65912	0.829562	+	0.558415i	$0.188590\pi$
$62$	9.77853	1.24188
$63$	−1.45541	−0.183364
$64$	6.78245	0.847806
$65$	0	0
$66$	−18.2817	−2.25032
$67$	−4.25337	−0.519632	−0.259816	−	0.965658i	$-0.583662\pi$
$67$	−4.25337	−0.519632	−0.259816	+	0.965658i	$0.583662\pi$
$68$	−1.37119	−0.166282
$69$	15.3213	1.84446
$70$	0	0
$71$	3.83337	0.454937	0.227469	−	0.973785i	$-0.426955\pi$
$71$	3.83337	0.454937	0.227469	+	0.973785i	$0.426955\pi$
$72$	4.18073	0.492703
$73$	9.86340	1.15442	0.577212	−	0.816594i	$-0.304141\pi$
$73$	9.86340	1.15442	0.577212	+	0.816594i	$0.304141\pi$
$74$	15.0832	1.75339
$75$	0	0
$76$	1.04940	0.120375
$77$	5.20656	0.593343
$78$	16.4810	1.86611
$79$	−6.00906	−0.676072	−0.338036	−	0.941133i	$-0.609763\pi$
$79$	−6.00906	−0.676072	−0.338036	+	0.941133i	$0.609763\pi$
$80$	0	0
$81$	−11.2417	−1.24908
$82$	6.63154	0.732331
$83$	−2.43649	−0.267439	−0.133720	−	0.991019i	$-0.542692\pi$
$83$	−2.43649	−0.267439	−0.133720	+	0.991019i	$0.542692\pi$
$84$	0.484320	0.0528436
$85$	0	0
$86$	0.464904	0.0501319
$87$	−2.14682	−0.230163
$88$	−14.9561	−1.59432
$89$	11.8146	1.25234	0.626171	−	0.779686i	$-0.284621\pi$
$89$	11.8146	1.25234	0.626171	+	0.779686i	$0.284621\pi$
$90$	0	0
$91$	−4.69373	−0.492037
$92$	−1.76690	−0.184213
$93$	13.9771	1.44936
$94$	−1.49903	−0.154613
$95$	0	0
$96$	−2.97858	−0.304000
$97$	18.0420	1.83189	0.915945	−	0.401305i	$-0.131443\pi$
$97$	18.0420	1.83189	0.915945	+	0.401305i	$0.131443\pi$
$98$	9.23890	0.933269
$99$	−9.05593	−0.910155
$100$	0	0
$101$	14.4809	1.44090	0.720452	−	0.693504i	$-0.243934\pi$
$101$	14.4809	1.44090	0.720452	+	0.693504i	$0.243934\pi$
$102$	−17.8234	−1.76478
$103$	13.7890	1.35867	0.679334	−	0.733829i	$-0.262269\pi$
$103$	13.7890	1.35867	0.679334	+	0.733829i	$0.262269\pi$
$104$	13.4829	1.32211
$105$	0	0
$106$	−9.57587	−0.930090
$107$	−8.57925	−0.829388	−0.414694	−	0.909961i	$-0.636111\pi$
$107$	−8.57925	−0.829388	−0.414694	+	0.909961i	$0.636111\pi$
$108$	0.745979	0.0717819
$109$	1.93915	0.185737	0.0928686	−	0.995678i	$-0.470396\pi$
$109$	1.93915	0.185737	0.0928686	+	0.995678i	$0.470396\pi$
$110$	0	0
$111$	21.5595	2.04634
$112$	4.05521	0.383181
$113$	−4.62487	−0.435071	−0.217535	−	0.976052i	$-0.569802\pi$
$113$	−4.62487	−0.435071	−0.217535	+	0.976052i	$0.569802\pi$
$114$	13.6406	1.27756
$115$	0	0
$116$	0.247579	0.0229871
$117$	8.16395	0.754757
$118$	−2.14048	−0.197047
$119$	5.07605	0.465321
$120$	0	0
$121$	21.3965	1.94514
$122$	−19.4247	−1.75863
$123$	9.47893	0.854686
$124$	−1.61190	−0.144753
$125$	0	0
$126$	2.18171	0.194362
$127$	6.48137	0.575129	0.287564	−	0.957761i	$-0.407155\pi$
$127$	6.48137	0.575129	0.287564	+	0.957761i	$0.407155\pi$
$128$	−12.9474	−1.14440
$129$	0.664520	0.0585077
$130$	0	0
$131$	−6.01653	−0.525667	−0.262834	−	0.964841i	$-0.584657\pi$
$131$	−6.01653	−0.525667	−0.262834	+	0.964841i	$0.584657\pi$
$132$	3.01356	0.262297
$133$	−3.88480	−0.336854
$134$	6.37595	0.550798
$135$	0	0
$136$	−14.5812	−1.25033
$137$	8.71965	0.744970	0.372485	−	0.928038i	$-0.378506\pi$
$137$	8.71965	0.744970	0.372485	+	0.928038i	$0.378506\pi$
$138$	−22.9671	−1.95509
$139$	0.522531	0.0443205	0.0221602	−	0.999754i	$-0.492946\pi$
$139$	0.522531	0.0443205	0.0221602	+	0.999754i	$0.492946\pi$
$140$	0	0
$141$	−2.14267	−0.180446
$142$	−5.74635	−0.482223
$143$	−29.2056	−2.44229
$144$	−7.05335	−0.587779
$145$	0	0
$146$	−14.7856	−1.22366
$147$	13.2058	1.08920
$148$	−2.48632	−0.204374
$149$	0.888318	0.0727739	0.0363869	−	0.999338i	$-0.488415\pi$
$149$	0.888318	0.0727739	0.0363869	+	0.999338i	$0.488415\pi$
$150$	0	0
$151$	−12.0150	−0.977766	−0.488883	−	0.872349i	$-0.662595\pi$
$151$	−12.0150	−0.977766	−0.488883	+	0.872349i	$0.662595\pi$
$152$	11.1592	0.905134
$153$	−8.82893	−0.713777
$154$	−7.80481	−0.628929
$155$	0	0
$156$	−2.71673	−0.217513
$157$	−11.4503	−0.913836	−0.456918	−	0.889509i	$-0.651047\pi$
$157$	−11.4503	−0.913836	−0.456918	+	0.889509i	$0.651047\pi$
$158$	9.00778	0.716621
$159$	−13.6875	−1.08549
$160$	0	0
$161$	6.54094	0.515498
$162$	16.8517	1.32399
$163$	17.8166	1.39550	0.697750	−	0.716341i	$-0.254185\pi$
$163$	17.8166	1.39550	0.697750	+	0.716341i	$0.254185\pi$
$164$	−1.09315	−0.0853603
$165$	0	0
$166$	3.65238	0.283479
$167$	−1.75297	−0.135649	−0.0678245	−	0.997697i	$-0.521606\pi$
$167$	−1.75297	−0.135649	−0.0678245	+	0.997697i	$0.521606\pi$
$168$	5.15022	0.397348
$169$	13.3289	1.02530
$170$	0	0
$171$	6.75694	0.516716
$172$	−0.0766349	−0.00584336
$173$	−15.9130	−1.20985	−0.604923	−	0.796284i	$-0.706796\pi$
$173$	−15.9130	−1.20985	−0.604923	+	0.796284i	$0.706796\pi$
$174$	3.21815	0.243967
$175$	0	0
$176$	25.2325	1.90197
$177$	−3.05954	−0.229969
$178$	−17.7104	−1.32745
$179$	0.538350	0.0402382	0.0201191	−	0.999798i	$-0.493595\pi$
$179$	0.538350	0.0402382	0.0201191	+	0.999798i	$0.493595\pi$
$180$	0	0
$181$	20.4723	1.52169	0.760846	−	0.648933i	$-0.224784\pi$
$181$	20.4723	1.52169	0.760846	+	0.648933i	$0.224784\pi$
$182$	7.03606	0.521547
$183$	−27.7651	−2.05246
$184$	−18.7891	−1.38515
$185$	0	0
$186$	−20.9522	−1.53629
$187$	31.5845	2.30969
$188$	0.247101	0.0180217
$189$	−2.76155	−0.200873
$190$	0	0
$191$	4.26056	0.308283	0.154142	−	0.988049i	$-0.450739\pi$
$191$	4.26056	0.308283	0.154142	+	0.988049i	$0.450739\pi$
$192$	−14.5326	−1.04880
$193$	−0.793909	−0.0571468	−0.0285734	−	0.999592i	$-0.509096\pi$
$193$	−0.793909	−0.0571468	−0.0285734	+	0.999592i	$0.509096\pi$
$194$	−27.0456	−1.94176
$195$	0	0
$196$	−1.52294	−0.108782
$197$	8.47189	0.603597	0.301799	−	0.953372i	$-0.402413\pi$
$197$	8.47189	0.603597	0.301799	+	0.953372i	$0.402413\pi$
$198$	13.5751	0.964743
$199$	−11.8930	−0.843076	−0.421538	−	0.906811i	$-0.638510\pi$
$199$	−11.8930	−0.843076	−0.421538	+	0.906811i	$0.638510\pi$
$200$	0	0
$201$	9.11359	0.642823
$202$	−21.7074	−1.52733
$203$	−0.916517	−0.0643269
$204$	2.93802	0.205703
$205$	0	0
$206$	−20.6701	−1.44016
$207$	−11.3769	−0.790746
$208$	−22.7472	−1.57724
$209$	−24.1722	−1.67202
$210$	0	0
$211$	−8.76285	−0.603259	−0.301630	−	0.953425i	$-0.597531\pi$
$211$	−8.76285	−0.603259	−0.301630	+	0.953425i	$0.597531\pi$
$212$	1.57849	0.108411
$213$	−8.21366	−0.562791
$214$	12.8606	0.879132
$215$	0	0
$216$	7.93268	0.539750
$217$	5.96711	0.405074
$218$	−2.90685	−0.196877
$219$	−21.1340	−1.42811
$220$	0	0
$221$	−28.4735	−1.91533
$222$	−32.3184	−2.16907
$223$	20.0879	1.34518	0.672591	−	0.740014i	$-0.265181\pi$
$223$	20.0879	1.34518	0.672591	+	0.740014i	$0.265181\pi$
$224$	−1.27161	−0.0849631
$225$	0	0
$226$	6.93283	0.461165
$227$	12.8123	0.850383	0.425192	−	0.905103i	$-0.360207\pi$
$227$	12.8123	0.850383	0.425192	+	0.905103i	$0.360207\pi$
$228$	−2.24852	−0.148912
$229$	−10.6840	−0.706021	−0.353010	−	0.935619i	$-0.614842\pi$
$229$	−10.6840	−0.706021	−0.353010	+	0.935619i	$0.614842\pi$
$230$	0	0
$231$	−11.1560	−0.734008
$232$	2.63273	0.172847
$233$	−9.98275	−0.653992	−0.326996	−	0.945026i	$-0.606036\pi$
$233$	−9.98275	−0.653992	−0.326996	+	0.945026i	$0.606036\pi$
$234$	−12.2380	−0.800025
$235$	0	0
$236$	0.352837	0.0229678
$237$	12.8755	0.836350
$238$	−7.60917	−0.493229
$239$	−3.29765	−0.213307	−0.106654	−	0.994296i	$-0.534014\pi$
$239$	−3.29765	−0.213307	−0.106654	+	0.994296i	$0.534014\pi$
$240$	0	0
$241$	7.85843	0.506206	0.253103	−	0.967439i	$-0.418549\pi$
$241$	7.85843	0.506206	0.253103	+	0.967439i	$0.418549\pi$
$242$	−32.0741	−2.06180
$243$	15.0306	0.964210
$244$	3.20198	0.204986
$245$	0	0
$246$	−14.2092	−0.905947
$247$	21.7913	1.38655
$248$	−17.1408	−1.08844
$249$	5.22060	0.330842
$250$	0	0
$251$	−6.38314	−0.402900	−0.201450	−	0.979499i	$-0.564565\pi$
$251$	−6.38314	−0.402900	−0.201450	+	0.979499i	$0.564565\pi$
$252$	−0.359633	−0.0226548
$253$	40.6994	2.55875
$254$	−9.71579	−0.609623
$255$	0	0
$256$	5.84363	0.365227
$257$	−5.57138	−0.347533	−0.173766	−	0.984787i	$-0.555594\pi$
$257$	−5.57138	−0.347533	−0.173766	+	0.984787i	$0.555594\pi$
$258$	−0.996137	−0.0620168
$259$	9.20416	0.571918
$260$	0	0
$261$	1.59413	0.0986739
$262$	9.01899	0.557195
$263$	15.3933	0.949192	0.474596	−	0.880204i	$-0.342594\pi$
$263$	15.3933	0.949192	0.474596	+	0.880204i	$0.342594\pi$
$264$	32.0460	1.97229
$265$	0	0
$266$	5.82344	0.357058
$267$	−25.3148	−1.54924
$268$	−1.05101	−0.0642009
$269$	22.5153	1.37278	0.686390	−	0.727233i	$-0.259194\pi$
$269$	22.5153	1.37278	0.686390	+	0.727233i	$0.259194\pi$
$270$	0	0
$271$	13.0934	0.795366	0.397683	−	0.917523i	$-0.369814\pi$
$271$	13.0934	0.795366	0.397683	+	0.917523i	$0.369814\pi$
$272$	24.6001	1.49160
$273$	10.0571	0.608685
$274$	−13.0711	−0.789651
$275$	0	0
$276$	3.78590	0.227884
$277$	−4.31244	−0.259110	−0.129555	−	0.991572i	$-0.541355\pi$
$277$	−4.31244	−0.259110	−0.129555	+	0.991572i	$0.541355\pi$
$278$	−0.783291	−0.0469787
$279$	−10.3788	−0.621361
$280$	0	0
$281$	2.58062	0.153947	0.0769733	−	0.997033i	$-0.475474\pi$
$281$	2.58062	0.153947	0.0769733	+	0.997033i	$0.475474\pi$
$282$	3.21194	0.191268
$283$	22.2786	1.32433	0.662163	−	0.749360i	$-0.269639\pi$
$283$	22.2786	1.32433	0.662163	+	0.749360i	$0.269639\pi$
$284$	0.947230	0.0562078
$285$	0	0
$286$	43.7801	2.58877
$287$	4.04673	0.238871
$288$	2.21175	0.130329
$289$	13.7928	0.811339
$290$	0	0
$291$	−38.6582	−2.26618
$292$	2.43726	0.142630
$293$	−24.5481	−1.43412	−0.717058	−	0.697013i	$-0.754512\pi$
$293$	−24.5481	−1.43412	−0.717058	+	0.697013i	$0.754512\pi$
$294$	−19.7959	−1.15452
$295$	0	0
$296$	−26.4393	−1.53676
$297$	−17.1831	−0.997064
$298$	−1.33162	−0.0771386
$299$	−36.6906	−2.12187
$300$	0	0
$301$	0.283696	0.0163520
$302$	18.0109	1.03641
$303$	−31.0279	−1.78250
$304$	−18.8269	−1.07980
$305$	0	0
$306$	13.2349	0.756587
$307$	−20.7591	−1.18478	−0.592392	−	0.805650i	$-0.701816\pi$
$307$	−20.7591	−1.18478	−0.592392	+	0.805650i	$0.701816\pi$
$308$	1.28655	0.0733078
$309$	−29.5453	−1.68077
$310$	0	0
$311$	−0.860082	−0.0487708	−0.0243854	−	0.999703i	$-0.507763\pi$
$311$	−0.860082	−0.0487708	−0.0243854	+	0.999703i	$0.507763\pi$
$312$	−28.8895	−1.63555
$313$	19.7368	1.11559	0.557796	−	0.829978i	$-0.311647\pi$
$313$	19.7368	1.11559	0.557796	+	0.829978i	$0.311647\pi$
$314$	17.1644	0.968645
$315$	0	0
$316$	−1.48485	−0.0835291
$317$	−18.0973	−1.01644	−0.508222	−	0.861226i	$-0.669697\pi$
$317$	−18.0973	−1.01644	−0.508222	+	0.861226i	$0.669697\pi$
$318$	20.5180	1.15059
$319$	−5.70280	−0.319295
$320$	0	0
$321$	18.3825	1.02601
$322$	−9.80508	−0.546416
$323$	−23.5663	−1.31126
$324$	−2.77784	−0.154324
$325$	0	0
$326$	−26.7076	−1.47920
$327$	−4.15497	−0.229770
$328$	−11.6244	−0.641851
$329$	−0.914748	−0.0504317
$330$	0	0
$331$	−17.9305	−0.985548	−0.492774	−	0.870157i	$-0.664017\pi$
$331$	−17.9305	−0.985548	−0.492774	+	0.870157i	$0.664017\pi$
$332$	−0.602059	−0.0330423
$333$	−16.0091	−0.877291
$334$	2.62776	0.143785
$335$	0	0
$336$	−8.68899	−0.474023
$337$	15.4323	0.840650	0.420325	−	0.907374i	$-0.361916\pi$
$337$	15.4323	0.840650	0.420325	+	0.907374i	$0.361916\pi$
$338$	−19.9805	−1.08680
$339$	9.90958	0.538215
$340$	0	0
$341$	37.1289	2.01064
$342$	−10.1289	−0.547707
$343$	12.0410	0.650155
$344$	−0.814930	−0.0439381
$345$	0	0
$346$	23.8542	1.28241
$347$	−18.4047	−0.988014	−0.494007	−	0.869458i	$-0.664468\pi$
$347$	−18.4047	−0.988014	−0.494007	+	0.869458i	$0.664468\pi$
$348$	−0.530481	−0.0284367
$349$	−4.62286	−0.247456	−0.123728	−	0.992316i	$-0.539485\pi$
$349$	−4.62286	−0.247456	−0.123728	+	0.992316i	$0.539485\pi$
$350$	0	0
$351$	15.4906	0.826827
$352$	−7.91229	−0.421727
$353$	26.2365	1.39643	0.698215	−	0.715888i	$-0.253978\pi$
$353$	26.2365	1.39643	0.698215	+	0.715888i	$0.253978\pi$
$354$	4.58635	0.243762
$355$	0	0
$356$	2.91939	0.154728
$357$	−10.8763	−0.575636
$358$	−0.807005	−0.0426515
$359$	24.3933	1.28743	0.643714	−	0.765266i	$-0.277393\pi$
$359$	24.3933	1.28743	0.643714	+	0.765266i	$0.277393\pi$
$360$	0	0
$361$	−0.964297	−0.0507525
$362$	−30.6886	−1.61296
$363$	−45.8458	−2.40628
$364$	−1.15983	−0.0607914
$365$	0	0
$366$	41.6208	2.17556
$367$	19.3648	1.01084	0.505418	−	0.862875i	$-0.331338\pi$
$367$	19.3648	1.01084	0.505418	+	0.862875i	$0.331338\pi$
$368$	31.6993	1.65244
$369$	−7.03861	−0.366415
$370$	0	0
$371$	−5.84344	−0.303376
$372$	3.45377	0.179070
$373$	−28.1998	−1.46013	−0.730065	−	0.683378i	$-0.760510\pi$
$373$	−28.1998	−1.46013	−0.730065	+	0.683378i	$0.760510\pi$
$374$	−47.3462	−2.44821
$375$	0	0
$376$	2.62765	0.135511
$377$	5.14109	0.264780
$378$	4.13966	0.212921
$379$	2.86556	0.147194	0.0735970	−	0.997288i	$-0.476552\pi$
$379$	2.86556	0.147194	0.0735970	+	0.997288i	$0.476552\pi$
$380$	0	0
$381$	−13.8875	−0.711476
$382$	−6.38672	−0.326773
$383$	−21.2620	−1.08644	−0.543218	−	0.839592i	$-0.682794\pi$
$383$	−21.2620	−1.08644	−0.543218	+	0.839592i	$0.682794\pi$
$384$	27.7420	1.41570
$385$	0	0
$386$	1.19010	0.0605743
$387$	−0.493441	−0.0250830
$388$	4.45820	0.226331
$389$	32.1800	1.63159	0.815795	−	0.578341i	$-0.196300\pi$
$389$	32.1800	1.63159	0.815795	+	0.578341i	$0.196300\pi$
$390$	0	0
$391$	39.6792	2.00666
$392$	−16.1949	−0.817963
$393$	12.8915	0.650288
$394$	−12.6996	−0.639799
$395$	0	0
$396$	−2.23773	−0.112450
$397$	18.3473	0.920825	0.460412	−	0.887705i	$-0.347702\pi$
$397$	18.3473	0.920825	0.460412	+	0.887705i	$0.347702\pi$
$398$	17.8281	0.893640
$399$	8.32385	0.416714
$400$	0	0
$401$	−25.8262	−1.28970	−0.644850	−	0.764309i	$-0.723080\pi$
$401$	−25.8262	−1.28970	−0.644850	+	0.764309i	$0.723080\pi$
$402$	−13.6616	−0.681378
$403$	−33.4718	−1.66735
$404$	3.57825	0.178025
$405$	0	0
$406$	1.37389	0.0681850
$407$	57.2706	2.83880
$408$	31.2427	1.54674
$409$	2.90723	0.143753	0.0718765	−	0.997414i	$-0.477101\pi$
$409$	2.90723	0.143753	0.0718765	+	0.997414i	$0.477101\pi$
$410$	0	0
$411$	−18.6834	−0.921583
$412$	3.40727	0.167864
$413$	−1.30617	−0.0642727
$414$	17.0543	0.838172
$415$	0	0
$416$	7.13295	0.349722
$417$	−1.11961	−0.0548277
$418$	36.2349	1.77231
$419$	−27.5597	−1.34638	−0.673191	−	0.739469i	$-0.735077\pi$
$419$	−27.5597	−1.34638	−0.673191	+	0.739469i	$0.735077\pi$
$420$	0	0
$421$	17.5508	0.855372	0.427686	−	0.903927i	$-0.359329\pi$
$421$	17.5508	0.855372	0.427686	+	0.903927i	$0.359329\pi$
$422$	13.1358	0.639441
$423$	1.59105	0.0773595
$424$	16.7855	0.815177
$425$	0	0
$426$	12.3125	0.596545
$427$	−11.8535	−0.573629
$428$	−2.11994	−0.102471
$429$	62.5780	3.02130
$430$	0	0
$431$	16.4810	0.793863	0.396931	−	0.917848i	$-0.370075\pi$
$431$	16.4810	0.793863	0.396931	+	0.917848i	$0.370075\pi$
$432$	−13.3833	−0.643905
$433$	−11.0784	−0.532393	−0.266196	−	0.963919i	$-0.585767\pi$
$433$	−11.0784	−0.532393	−0.266196	+	0.963919i	$0.585767\pi$
$434$	−8.94490	−0.429369
$435$	0	0
$436$	0.479167	0.0229479
$437$	−30.3672	−1.45266
$438$	31.6806	1.51376
$439$	20.5578	0.981168	0.490584	−	0.871394i	$-0.336783\pi$
$439$	20.5578	0.981168	0.490584	+	0.871394i	$0.336783\pi$
$440$	0	0
$441$	−9.80601	−0.466953
$442$	42.6827	2.03021
$443$	40.4857	1.92353	0.961767	−	0.273868i	$-0.0883031\pi$
$443$	40.4857	1.92353	0.961767	+	0.273868i	$0.0883031\pi$
$444$	5.32737	0.252826
$445$	0	0
$446$	−30.1124	−1.42586
$447$	−1.90338	−0.0900266
$448$	−6.20423	−0.293122
$449$	−27.5326	−1.29934	−0.649672	−	0.760214i	$-0.725094\pi$
$449$	−27.5326	−1.29934	−0.649672	+	0.760214i	$0.725094\pi$
$450$	0	0
$451$	25.1798	1.18567
$452$	−1.14281	−0.0537533
$453$	25.7442	1.20957
$454$	−19.2061	−0.901386
$455$	0	0
$456$	−23.9106	−1.11972
$457$	2.23304	0.104457	0.0522286	−	0.998635i	$-0.483368\pi$
$457$	2.23304	0.104457	0.0522286	+	0.998635i	$0.483368\pi$
$458$	16.0157	0.748365
$459$	−16.7524	−0.781933
$460$	0	0
$461$	21.1869	0.986771	0.493386	−	0.869811i	$-0.335759\pi$
$461$	21.1869	0.986771	0.493386	+	0.869811i	$0.335759\pi$
$462$	16.7232	0.778032
$463$	−12.6056	−0.585831	−0.292916	−	0.956138i	$-0.594626\pi$
$463$	−12.6056	−0.585831	−0.292916	+	0.956138i	$0.594626\pi$
$464$	−4.44171	−0.206201
$465$	0	0
$466$	14.9645	0.693216
$467$	18.3306	0.848238	0.424119	−	0.905606i	$-0.360584\pi$
$467$	18.3306	0.848238	0.424119	+	0.905606i	$0.360584\pi$
$468$	2.01732	0.0932507
$469$	3.89077	0.179659
$470$	0	0
$471$	24.5343	1.13048
$472$	3.75204	0.172702
$473$	1.76523	0.0811654
$474$	−19.3007	−0.886512
$475$	0	0
$476$	1.25430	0.0574907
$477$	10.1637	0.465362
$478$	4.94329	0.226101
$479$	−0.302465	−0.0138200	−0.00690998	−	0.999976i	$-0.502200\pi$
$479$	−0.302465	−0.0138200	−0.00690998	+	0.999976i	$0.502200\pi$
$480$	0	0
$481$	−51.6296	−2.35411
$482$	−11.7800	−0.536566
$483$	−14.0151	−0.637709
$484$	5.28711	0.240323
$485$	0	0
$486$	−22.5313	−1.02204
$487$	20.7010	0.938053	0.469027	−	0.883184i	$-0.344605\pi$
$487$	20.7010	0.938053	0.469027	+	0.883184i	$0.344605\pi$
$488$	34.0496	1.54135
$489$	−38.1751	−1.72634
$490$	0	0
$491$	−15.4089	−0.695394	−0.347697	−	0.937607i	$-0.613036\pi$
$491$	−15.4089	−0.695394	−0.347697	+	0.937607i	$0.613036\pi$
$492$	2.34225	0.105597
$493$	−5.55985	−0.250403
$494$	−32.6659	−1.46971
$495$	0	0
$496$	28.9184	1.29847
$497$	−3.50657	−0.157291
$498$	−7.82585	−0.350685
$499$	−24.0667	−1.07737	−0.538687	−	0.842506i	$-0.681079\pi$
$499$	−24.0667	−1.07737	−0.538687	+	0.842506i	$0.681079\pi$
$500$	0	0
$501$	3.75604	0.167808
$502$	9.56854	0.427065
$503$	18.3245	0.817049	0.408524	−	0.912747i	$-0.366043\pi$
$503$	18.3245	0.817049	0.408524	+	0.912747i	$0.366043\pi$
$504$	−3.82431	−0.170348
$505$	0	0
$506$	−61.0097	−2.71221
$507$	−28.5595	−1.26837
$508$	1.60155	0.0710575
$509$	26.5321	1.17602	0.588008	−	0.808855i	$-0.299912\pi$
$509$	26.5321	1.17602	0.588008	+	0.808855i	$0.299912\pi$
$510$	0	0
$511$	−9.02253	−0.399133
$512$	17.1349	0.757264
$513$	12.8209	0.566056
$514$	8.35168	0.368377
$515$	0	0
$516$	0.164204	0.00722866
$517$	−5.69180	−0.250325
$518$	−13.7973	−0.606220
$519$	34.0964	1.49667
$520$	0	0
$521$	12.6192	0.552857	0.276428	−	0.961035i	$-0.410849\pi$
$521$	12.6192	0.552857	0.276428	+	0.961035i	$0.410849\pi$
$522$	−2.38965	−0.104592
$523$	−13.1556	−0.575253	−0.287626	−	0.957743i	$-0.592866\pi$
$523$	−13.1556	−0.575253	−0.287626	+	0.957743i	$0.592866\pi$
$524$	−1.48669	−0.0649465
$525$	0	0
$526$	−23.0751	−1.00612
$527$	36.1982	1.57682
$528$	−54.0651	−2.35288
$529$	28.1301	1.22305
$530$	0	0
$531$	2.27187	0.0985907
$532$	−0.959937	−0.0416186
$533$	−22.6997	−0.983232
$534$	37.9477	1.64216
$535$	0	0
$536$	−11.1764	−0.482747
$537$	−1.15351	−0.0497776
$538$	−33.7511	−1.45512
$539$	35.0799	1.51100
$540$	0	0
$541$	−42.7170	−1.83655	−0.918273	−	0.395948i	$-0.870416\pi$
$541$	−42.7170	−1.83655	−0.918273	+	0.395948i	$0.870416\pi$
$542$	−19.6274	−0.843069
$543$	−43.8654	−1.88244
$544$	−7.71396	−0.330733
$545$	0	0
$546$	−15.0760	−0.645192
$547$	−16.8228	−0.719291	−0.359645	−	0.933089i	$-0.617102\pi$
$547$	−16.8228	−0.719291	−0.359645	+	0.933089i	$0.617102\pi$
$548$	2.15464	0.0920415
$549$	20.6171	0.879916
$550$	0	0
$551$	4.25506	0.181271
$552$	40.2590	1.71354
$553$	5.49678	0.233747
$554$	6.46450	0.274650
$555$	0	0
$556$	0.129118	0.00547582
$557$	7.63018	0.323301	0.161651	−	0.986848i	$-0.448318\pi$
$557$	7.63018	0.323301	0.161651	+	0.986848i	$0.448318\pi$
$558$	15.5581	0.658628
$559$	−1.59136	−0.0673074
$560$	0	0
$561$	−67.6752	−2.85725
$562$	−3.86843	−0.163180
$563$	21.6737	0.913438	0.456719	−	0.889611i	$-0.349024\pi$
$563$	21.6737	0.913438	0.456719	+	0.889611i	$0.349024\pi$
$564$	−0.529457	−0.0222942
$565$	0	0
$566$	−33.3964	−1.40376
$567$	10.2833	0.431859
$568$	10.0728	0.422644
$569$	3.20280	0.134268	0.0671342	−	0.997744i	$-0.478614\pi$
$569$	3.20280	0.134268	0.0671342	+	0.997744i	$0.478614\pi$
$570$	0	0
$571$	30.3925	1.27189	0.635943	−	0.771736i	$-0.280612\pi$
$571$	30.3925	1.27189	0.635943	+	0.771736i	$0.280612\pi$
$572$	−7.21673	−0.301747
$573$	−9.12898	−0.381369
$574$	−6.06619	−0.253198
$575$	0	0
$576$	10.7912	0.449634
$577$	−30.9617	−1.28895	−0.644475	−	0.764625i	$-0.722924\pi$
$577$	−30.9617	−1.28895	−0.644475	+	0.764625i	$0.722924\pi$
$578$	−20.6758	−0.860001
$579$	1.70109	0.0706948
$580$	0	0
$581$	2.22877	0.0924651
$582$	57.9499	2.40210
$583$	−36.3593	−1.50585
$584$	25.9176	1.07248
$585$	0	0
$586$	36.7984	1.52013
$587$	−37.2804	−1.53873	−0.769364	−	0.638811i	$-0.779427\pi$
$587$	−37.2804	−1.53873	−0.769364	+	0.638811i	$0.779427\pi$
$588$	3.26317	0.134571
$589$	−27.7031	−1.14149
$590$	0	0
$591$	−18.1525	−0.746694
$592$	44.6061	1.83330
$593$	−32.2520	−1.32443	−0.662215	−	0.749314i	$-0.730384\pi$
$593$	−32.2520	−1.32443	−0.662215	+	0.749314i	$0.730384\pi$
$594$	25.7580	1.05686
$595$	0	0
$596$	0.219504	0.00899125
$597$	25.4829	1.04295
$598$	55.0004	2.24914
$599$	40.0161	1.63501	0.817507	−	0.575918i	$-0.195355\pi$
$599$	40.0161	1.63501	0.817507	+	0.575918i	$0.195355\pi$
$600$	0	0
$601$	39.5989	1.61527	0.807636	−	0.589681i	$-0.200746\pi$
$601$	39.5989	1.61527	0.807636	+	0.589681i	$0.200746\pi$
$602$	−0.425270	−0.0173327
$603$	−6.76733	−0.275587
$604$	−2.96892	−0.120804
$605$	0	0
$606$	46.5118	1.88941
$607$	16.9508	0.688012	0.344006	−	0.938967i	$-0.388216\pi$
$607$	16.9508	0.688012	0.344006	+	0.938967i	$0.388216\pi$
$608$	5.90364	0.239424
$609$	1.96380	0.0795770
$610$	0	0
$611$	5.13117	0.207585
$612$	−2.18164	−0.0881875
$613$	21.3450	0.862118	0.431059	−	0.902324i	$-0.358140\pi$
$613$	21.3450	0.862118	0.431059	+	0.902324i	$0.358140\pi$
$614$	31.1186	1.25584
$615$	0	0
$616$	13.6810	0.551225
$617$	41.4104	1.66712	0.833560	−	0.552429i	$-0.186299\pi$
$617$	41.4104	1.66712	0.833560	+	0.552429i	$0.186299\pi$
$618$	44.2893	1.78158
$619$	13.7564	0.552915	0.276458	−	0.961026i	$-0.410839\pi$
$619$	13.7564	0.552915	0.276458	+	0.961026i	$0.410839\pi$
$620$	0	0
$621$	−21.5869	−0.866252
$622$	1.28929	0.0516959
$623$	−10.8074	−0.432988
$624$	48.7399	1.95116
$625$	0	0
$626$	−29.5862	−1.18250
$627$	51.7931	2.06842
$628$	−2.82939	−0.112905
$629$	55.8350	2.22629
$630$	0	0
$631$	−3.13298	−0.124722	−0.0623610	−	0.998054i	$-0.519863\pi$
$631$	−3.13298	−0.124722	−0.0623610	+	0.998054i	$0.519863\pi$
$632$	−15.7897	−0.628082
$633$	18.7759	0.746276
$634$	27.1284	1.07741
$635$	0	0
$636$	−3.38219	−0.134112
$637$	−31.6246	−1.25301
$638$	8.54869	0.338446
$639$	6.09908	0.241276
$640$	0	0
$641$	−1.00566	−0.0397210	−0.0198605	−	0.999803i	$-0.506322\pi$
$641$	−1.00566	−0.0397210	−0.0198605	+	0.999803i	$0.506322\pi$
$642$	−27.5560	−1.08755
$643$	−8.71791	−0.343801	−0.171900	−	0.985114i	$-0.554991\pi$
$643$	−8.71791	−0.343801	−0.171900	+	0.985114i	$0.554991\pi$
$644$	1.61627	0.0636901
$645$	0	0
$646$	35.3266	1.38991
$647$	−33.6352	−1.32233	−0.661167	−	0.750239i	$-0.729939\pi$
$647$	−33.6352	−1.32233	−0.661167	+	0.750239i	$0.729939\pi$
$648$	−29.5393	−1.16041
$649$	−8.12735	−0.319026
$650$	0	0
$651$	−12.7856	−0.501106
$652$	4.40249	0.172415
$653$	25.1445	0.983979	0.491990	−	0.870601i	$-0.336270\pi$
$653$	25.1445	0.983979	0.491990	+	0.870601i	$0.336270\pi$
$654$	6.22844	0.243551
$655$	0	0
$656$	19.6117	0.765708
$657$	15.6932	0.612248
$658$	1.37124	0.0534564
$659$	−40.1903	−1.56559	−0.782797	−	0.622278i	$-0.786207\pi$
$659$	−40.1903	−1.56559	−0.782797	+	0.622278i	$0.786207\pi$
$660$	0	0
$661$	23.9156	0.930208	0.465104	−	0.885256i	$-0.346017\pi$
$661$	23.9156	0.930208	0.465104	+	0.885256i	$0.346017\pi$
$662$	26.8784	1.04466
$663$	61.0094	2.36941
$664$	−6.40225	−0.248455
$665$	0	0
$666$	23.9981	0.929908
$667$	−7.16436	−0.277405
$668$	−0.433161	−0.0167595
$669$	−43.0417	−1.66409
$670$	0	0
$671$	−73.7552	−2.84729
$672$	2.72465	0.105106
$673$	1.35488	0.0522269	0.0261135	−	0.999659i	$-0.491687\pi$
$673$	1.35488	0.0522269	0.0261135	+	0.999659i	$0.491687\pi$
$674$	−23.1335	−0.891069
$675$	0	0
$676$	3.29359	0.126677
$677$	−47.7017	−1.83333	−0.916663	−	0.399661i	$-0.869128\pi$
$677$	−47.7017	−1.83333	−0.916663	+	0.399661i	$0.869128\pi$
$678$	−14.8548	−0.570495
$679$	−16.5039	−0.633362
$680$	0	0
$681$	−27.4526	−1.05199
$682$	−55.6574	−2.13123
$683$	6.42735	0.245936	0.122968	−	0.992411i	$-0.460759\pi$
$683$	6.42735	0.245936	0.122968	+	0.992411i	$0.460759\pi$
$684$	1.66965	0.0638406
$685$	0	0
$686$	−18.0499	−0.689150
$687$	22.8924	0.873399
$688$	1.37488	0.0524167
$689$	32.7781	1.24874
$690$	0	0
$691$	5.95096	0.226385	0.113193	−	0.993573i	$-0.463892\pi$
$691$	5.95096	0.226385	0.113193	+	0.993573i	$0.463892\pi$
$692$	−3.93213	−0.149477
$693$	8.28390	0.314679
$694$	27.5892	1.04727
$695$	0	0
$696$	−5.64109	−0.213825
$697$	24.5486	0.929846
$698$	6.92982	0.262298
$699$	21.3898	0.809036
$700$	0	0
$701$	−9.40590	−0.355256	−0.177628	−	0.984098i	$-0.556842\pi$
$701$	−9.40590	−0.355256	−0.177628	+	0.984098i	$0.556842\pi$
$702$	−23.2209	−0.876417
$703$	−42.7316	−1.61165
$704$	−38.6043	−1.45495
$705$	0	0
$706$	−39.3294	−1.48018
$707$	−13.2464	−0.498182
$708$	−0.756015	−0.0284128
$709$	−35.6599	−1.33923	−0.669617	−	0.742706i	$-0.733542\pi$
$709$	−35.6599	−1.33923	−0.669617	+	0.742706i	$0.733542\pi$
$710$	0	0
$711$	−9.56071	−0.358555
$712$	31.0446	1.16345
$713$	46.6445	1.74685
$714$	16.3040	0.610161
$715$	0	0
$716$	0.133027	0.00497145
$717$	7.06579	0.263877
$718$	−36.5664	−1.36464
$719$	13.1364	0.489907	0.244953	−	0.969535i	$-0.421227\pi$
$719$	13.1364	0.489907	0.244953	+	0.969535i	$0.421227\pi$
$720$	0	0
$721$	−12.6134	−0.469749
$722$	1.44551	0.0537965
$723$	−16.8380	−0.626214
$724$	5.05872	0.188006
$725$	0	0
$726$	68.7244	2.55060
$727$	−41.4898	−1.53877	−0.769386	−	0.638785i	$-0.779437\pi$
$727$	−41.4898	−1.53877	−0.769386	+	0.638785i	$0.779437\pi$
$728$	−12.3335	−0.457110
$729$	1.51957	0.0562804
$730$	0	0
$731$	1.72098	0.0636528
$732$	−6.86079	−0.253582
$733$	40.0603	1.47966	0.739830	−	0.672794i	$-0.234906\pi$
$733$	40.0603	1.47966	0.739830	+	0.672794i	$0.234906\pi$
$734$	−29.0285	−1.07146
$735$	0	0
$736$	−9.94011	−0.366397
$737$	24.2093	0.891763
$738$	10.5511	0.388392
$739$	50.3020	1.85039	0.925195	−	0.379492i	$-0.123901\pi$
$739$	50.3020	1.85039	0.925195	+	0.379492i	$0.123901\pi$
$740$	0	0
$741$	−46.6916	−1.71526
$742$	8.75951	0.321572
$743$	−2.49914	−0.0916844	−0.0458422	−	0.998949i	$-0.514597\pi$
$743$	−2.49914	−0.0916844	−0.0458422	+	0.998949i	$0.514597\pi$
$744$	36.7271	1.34648
$745$	0	0
$746$	42.2724	1.54770
$747$	−3.87657	−0.141836
$748$	7.80456	0.285363
$749$	7.84786	0.286755
$750$	0	0
$751$	39.6375	1.44639	0.723196	−	0.690643i	$-0.242672\pi$
$751$	39.6375	1.44639	0.723196	+	0.690643i	$0.242672\pi$
$752$	−4.43314	−0.161660
$753$	13.6770	0.498417
$754$	−7.70667	−0.280660
$755$	0	0
$756$	−0.682383	−0.0248180
$757$	−2.61228	−0.0949449	−0.0474724	−	0.998873i	$-0.515117\pi$
$757$	−2.61228	−0.0949449	−0.0474724	+	0.998873i	$0.515117\pi$
$758$	−4.29557	−0.156022
$759$	−87.2055	−3.16536
$760$	0	0
$761$	14.3538	0.520326	0.260163	−	0.965565i	$-0.416224\pi$
$761$	14.3538	0.520326	0.260163	+	0.965565i	$0.416224\pi$
$762$	20.8178	0.754148
$763$	−1.77384	−0.0642172
$764$	1.05279	0.0380886
$765$	0	0
$766$	31.8724	1.15160
$767$	7.32683	0.264557
$768$	−12.5210	−0.451812
$769$	−32.0536	−1.15588	−0.577941	−	0.816079i	$-0.696144\pi$
$769$	−32.0536	−1.15588	−0.577941	+	0.816079i	$0.696144\pi$
$770$	0	0
$771$	11.9376	0.429924
$772$	−0.196176	−0.00706052
$773$	8.76144	0.315127	0.157564	−	0.987509i	$-0.449636\pi$
$773$	8.76144	0.315127	0.157564	+	0.987509i	$0.449636\pi$
$774$	0.739685	0.0265874
$775$	0	0
$776$	47.4082	1.70185
$777$	−19.7215	−0.707505
$778$	−48.2389	−1.72945
$779$	−18.7875	−0.673133
$780$	0	0
$781$	−21.8188	−0.780736
$782$	−59.4804	−2.12702
$783$	3.02476	0.108096
$784$	27.3225	0.975804
$785$	0	0
$786$	−19.3247	−0.689291
$787$	−42.0114	−1.49755	−0.748773	−	0.662826i	$-0.769357\pi$
$787$	−42.0114	−1.49755	−0.748773	+	0.662826i	$0.769357\pi$
$788$	2.09341	0.0745748
$789$	−32.9828	−1.17422
$790$	0	0
$791$	4.23059	0.150422
$792$	−23.7958	−0.845549
$793$	66.4906	2.36115
$794$	−27.5032	−0.976053
$795$	0	0
$796$	−2.93879	−0.104162
$797$	38.3695	1.35912	0.679559	−	0.733621i	$-0.262171\pi$
$797$	38.3695	1.35912	0.679559	+	0.733621i	$0.262171\pi$
$798$	−12.4777	−0.441707
$799$	−5.54912	−0.196314
$800$	0	0
$801$	18.7976	0.664179
$802$	38.7144	1.36705
$803$	−56.1405	−1.98115
$804$	2.25198	0.0794212
$805$	0	0
$806$	50.1753	1.76735
$807$	−48.2429	−1.69823
$808$	38.0508	1.33862
$809$	−36.0104	−1.26606	−0.633030	−	0.774127i	$-0.718189\pi$
$809$	−36.0104	−1.26606	−0.633030	+	0.774127i	$0.718189\pi$
$810$	0	0
$811$	−3.94278	−0.138450	−0.0692249	−	0.997601i	$-0.522053\pi$
$811$	−3.94278	−0.138450	−0.0692249	+	0.997601i	$0.522053\pi$
$812$	−0.226472	−0.00794762
$813$	−28.0548	−0.983925
$814$	−85.8505	−3.00906
$815$	0	0
$816$	−52.7099	−1.84522
$817$	−1.31710	−0.0460795
$818$	−4.35803	−0.152375
$819$	−7.46796	−0.260951
$820$	0	0
$821$	15.7830	0.550830	0.275415	−	0.961325i	$-0.411185\pi$
$821$	15.7830	0.550830	0.275415	+	0.961325i	$0.411185\pi$
$822$	28.0070	0.976856
$823$	−10.5342	−0.367198	−0.183599	−	0.983001i	$-0.558775\pi$
$823$	−10.5342	−0.367198	−0.183599	+	0.983001i	$0.558775\pi$
$824$	36.2326	1.26222
$825$	0	0
$826$	1.95800	0.0681275
$827$	−50.3101	−1.74945	−0.874726	−	0.484618i	$-0.838959\pi$
$827$	−50.3101	−1.74945	−0.874726	+	0.484618i	$0.838959\pi$
$828$	−2.81123	−0.0976971
$829$	49.0211	1.70257	0.851287	−	0.524701i	$-0.175823\pi$
$829$	49.0211	1.70257	0.851287	+	0.524701i	$0.175823\pi$
$830$	0	0
$831$	9.24016	0.320538
$832$	34.8019	1.20654
$833$	34.2006	1.18498
$834$	1.67834	0.0581161
$835$	0	0
$836$	−5.97298	−0.206580
$837$	−19.6931	−0.680693
$838$	41.3130	1.42713
$839$	11.9588	0.412864	0.206432	−	0.978461i	$-0.433815\pi$
$839$	11.9588	0.412864	0.206432	+	0.978461i	$0.433815\pi$
$840$	0	0
$841$	−27.9961	−0.965384
$842$	−26.3092	−0.906674
$843$	−5.52942	−0.190443
$844$	−2.16531	−0.0745331
$845$	0	0
$846$	−2.38504	−0.0819992
$847$	−19.5725	−0.672517
$848$	−28.3190	−0.972480
$849$	−47.7358	−1.63829
$850$	0	0
$851$	71.9483	2.46636
$852$	−2.02960	−0.0695331
$853$	14.7352	0.504524	0.252262	−	0.967659i	$-0.418826\pi$
$853$	14.7352	0.504524	0.252262	+	0.967659i	$0.418826\pi$
$854$	17.7687	0.608034
$855$	0	0
$856$	−22.5433	−0.770515
$857$	6.24918	0.213468	0.106734	−	0.994288i	$-0.465961\pi$
$857$	6.24918	0.213468	0.106734	+	0.994288i	$0.465961\pi$
$858$	−93.8065	−3.20250
$859$	−55.8303	−1.90490	−0.952452	−	0.304689i	$-0.901447\pi$
$859$	−55.8303	−1.90490	−0.952452	+	0.304689i	$0.901447\pi$
$860$	0	0
$861$	−8.67083	−0.295501
$862$	−24.7056	−0.841476
$863$	24.3426	0.828631	0.414315	−	0.910133i	$-0.364021\pi$
$863$	24.3426	0.828631	0.414315	+	0.910133i	$0.364021\pi$
$864$	4.19667	0.142774
$865$	0	0
$866$	16.6069	0.564324
$867$	−29.5534	−1.00369
$868$	1.47448	0.0500471
$869$	34.2023	1.16024
$870$	0	0
$871$	−21.8248	−0.739505
$872$	5.09542	0.172553
$873$	28.7057	0.971542
$874$	45.5215	1.53979
$875$	0	0
$876$	−5.22225	−0.176443
$877$	−30.7416	−1.03807	−0.519036	−	0.854753i	$-0.673709\pi$
$877$	−30.7416	−1.03807	−0.519036	+	0.854753i	$0.673709\pi$
$878$	−30.8168	−1.04002
$879$	52.5986	1.77411
$880$	0	0
$881$	8.91329	0.300297	0.150148	−	0.988663i	$-0.452025\pi$
$881$	8.91329	0.300297	0.150148	+	0.988663i	$0.452025\pi$
$882$	14.6995	0.494959
$883$	−24.7273	−0.832141	−0.416071	−	0.909332i	$-0.636593\pi$
$883$	−24.7273	−0.832141	−0.416071	+	0.909332i	$0.636593\pi$
$884$	−7.03583	−0.236641
$885$	0	0
$886$	−60.6894	−2.03890
$887$	1.29105	0.0433494	0.0216747	−	0.999765i	$-0.493100\pi$
$887$	1.29105	0.0433494	0.0216747	+	0.999765i	$0.493100\pi$
$888$	56.6509	1.90108
$889$	−5.92882	−0.198846
$890$	0	0
$891$	63.9855	2.14360
$892$	4.96373	0.166198
$893$	4.24685	0.142115
$894$	2.85322	0.0954261
$895$	0	0
$896$	11.8436	0.395666
$897$	78.6160	2.62491
$898$	41.2723	1.37728
$899$	−6.53584	−0.217982
$900$	0	0
$901$	−35.4479	−1.18094
$902$	−37.7454	−1.25678
$903$	−0.607868	−0.0202286
$904$	−12.1526	−0.404188
$905$	0	0
$906$	−38.5914	−1.28211
$907$	−39.2886	−1.30456	−0.652279	−	0.757979i	$-0.726187\pi$
$907$	−39.2886	−1.30456	−0.652279	+	0.757979i	$0.726187\pi$
$908$	3.16594	0.105065
$909$	23.0399	0.764184
$910$	0	0
$911$	−32.2801	−1.06949	−0.534743	−	0.845015i	$-0.679592\pi$
$911$	−32.2801	−1.06949	−0.534743	+	0.845015i	$0.679592\pi$
$912$	40.3399	1.33579
$913$	13.8680	0.458964
$914$	−3.34740	−0.110722
$915$	0	0
$916$	−2.64004	−0.0872293
$917$	5.50361	0.181745
$918$	25.1124	0.828831
$919$	−36.8825	−1.21664	−0.608322	−	0.793691i	$-0.708157\pi$
$919$	−36.8825	−1.21664	−0.608322	+	0.793691i	$0.708157\pi$
$920$	0	0
$921$	44.4799	1.46566
$922$	−31.7598	−1.04595
$923$	19.6697	0.647435
$924$	−2.75665	−0.0906872
$925$	0	0
$926$	18.8962	0.620967
$927$	21.9389	0.720569
$928$	1.39281	0.0457212
$929$	−33.5762	−1.10160	−0.550800	−	0.834637i	$-0.685677\pi$
$929$	−33.5762	−1.10160	−0.550800	+	0.834637i	$0.685677\pi$
$930$	0	0
$931$	−26.1743	−0.857828
$932$	−2.46675	−0.0808011
$933$	1.84288	0.0603330
$934$	−27.4782	−0.899113
$935$	0	0
$936$	21.4520	0.701181
$937$	16.9155	0.552605	0.276302	−	0.961071i	$-0.410891\pi$
$937$	16.9155	0.552605	0.276302	+	0.961071i	$0.410891\pi$
$938$	−5.83239	−0.190434
$939$	−42.2896	−1.38007
$940$	0	0
$941$	−22.6918	−0.739730	−0.369865	−	0.929086i	$-0.620596\pi$
$941$	−22.6918	−0.739730	−0.369865	+	0.929086i	$0.620596\pi$
$942$	−36.7778	−1.19828
$943$	31.6331	1.03011
$944$	−6.33011	−0.206028
$945$	0	0
$946$	−2.64614	−0.0860334
$947$	33.1654	1.07773	0.538865	−	0.842392i	$-0.318853\pi$
$947$	33.1654	1.07773	0.538865	+	0.842392i	$0.318853\pi$
$948$	3.18154	0.103332
$949$	50.6108	1.64290
$950$	0	0
$951$	38.7765	1.25742
$952$	13.3381	0.432290
$953$	−7.14211	−0.231355	−0.115678	−	0.993287i	$-0.536904\pi$
$953$	−7.14211	−0.231355	−0.115678	+	0.993287i	$0.536904\pi$
$954$	−15.2357	−0.493273
$955$	0	0
$956$	−0.814854	−0.0263543
$957$	12.2192	0.394992
$958$	0.453405	0.0146488
$959$	−7.97629	−0.257568
$960$	0	0
$961$	11.5525	0.372661
$962$	77.3945	2.49530
$963$	−13.6500	−0.439866
$964$	1.94183	0.0625420
$965$	0	0
$966$	21.0091	0.675956
$967$	7.31994	0.235393	0.117697	−	0.993050i	$-0.462449\pi$
$967$	7.31994	0.235393	0.117697	+	0.993050i	$0.462449\pi$
$968$	56.2227	1.80707
$969$	50.4948	1.62213
$970$	0	0
$971$	−28.9075	−0.927687	−0.463844	−	0.885917i	$-0.653530\pi$
$971$	−28.9075	−0.927687	−0.463844	+	0.885917i	$0.653530\pi$
$972$	3.71407	0.119129
$973$	−0.477984	−0.0153235
$974$	−31.0315	−0.994315
$975$	0	0
$976$	−57.4454	−1.83878
$977$	−25.5796	−0.818364	−0.409182	−	0.912453i	$-0.634186\pi$
$977$	−25.5796	−0.818364	−0.409182	+	0.912453i	$0.634186\pi$
$978$	57.2257	1.82988
$979$	−67.2461	−2.14920
$980$	0	0
$981$	3.08529	0.0985056
$982$	23.0985	0.737101
$983$	−2.01618	−0.0643060	−0.0321530	−	0.999483i	$-0.510236\pi$
$983$	−2.01618	−0.0643060	−0.0321530	+	0.999483i	$0.510236\pi$
$984$	24.9073	0.794017
$985$	0	0
$986$	8.33440	0.265421
$987$	1.96001	0.0623877
$988$	5.38465	0.171309
$989$	2.21764	0.0705167
$990$	0	0
$991$	−16.5524	−0.525804	−0.262902	−	0.964823i	$-0.584680\pi$
$991$	−16.5524	−0.525804	−0.262902	+	0.964823i	$0.584680\pi$
$992$	−9.06808	−0.287912
$993$	38.4191	1.21919
$994$	5.25646	0.166725
$995$	0	0
$996$	1.29002	0.0408757
$997$	−37.7331	−1.19502	−0.597510	−	0.801861i	$-0.703843\pi$
$997$	−37.7331	−1.19502	−0.597510	+	0.801861i	$0.703843\pi$
$998$	36.0768	1.14199
$999$	−30.3762	−0.961062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.h.1.3		7
5.2	odd	4		1175.2.c.g.424.5		14
5.3	odd	4		1175.2.c.g.424.10		14
5.4	even	2		235.2.a.e.1.5	✓	7
15.14	odd	2		2115.2.a.v.1.3		7
20.19	odd	2		3760.2.a.bi.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.a.e.1.5	✓	7	5.4	even	2
1175.2.a.h.1.3		7	1.1	even	1	trivial
1175.2.c.g.424.5		14	5.2	odd	4
1175.2.c.g.424.10		14	5.3	odd	4
2115.2.a.v.1.3		7	15.14	odd	2
3760.2.a.bi.1.2		7	20.19	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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-1.49903 q^{2} -2.14267 q^{3} +0.247101 q^{4} +3.21194 q^{6} -0.914748 q^{7} +2.62765 q^{8} +1.59105 q^{9} +O(q^{10})\)	\(q-1.49903 q^{2} -2.14267 q^{3} +0.247101 q^{4} +3.21194 q^{6} -0.914748 q^{7} +2.62765 q^{8} +1.59105 q^{9} -5.69180 q^{11} -0.529457 q^{12} +5.13117 q^{13} +1.37124 q^{14} -4.43314 q^{16} -5.54912 q^{17} -2.38504 q^{18} +4.24685 q^{19} +1.96001 q^{21} +8.53219 q^{22} -7.15053 q^{23} -5.63020 q^{24} -7.69180 q^{26} +3.01892 q^{27} -0.226035 q^{28} +1.00193 q^{29} -6.52323 q^{31} +1.39012 q^{32} +12.1957 q^{33} +8.31832 q^{34} +0.393150 q^{36} -10.0620 q^{37} -6.36616 q^{38} -10.9944 q^{39} -4.42388 q^{41} -2.93812 q^{42} -0.310136 q^{43} -1.40645 q^{44} +10.7189 q^{46} +1.00000 q^{47} +9.49878 q^{48} -6.16324 q^{49} +11.8900 q^{51} +1.26792 q^{52} +6.38803 q^{53} -4.52546 q^{54} -2.40364 q^{56} -9.09960 q^{57} -1.50193 q^{58} +1.42791 q^{59} +12.9582 q^{61} +9.77853 q^{62} -1.45541 q^{63} +6.78245 q^{64} -18.2817 q^{66} -4.25337 q^{67} -1.37119 q^{68} +15.3213 q^{69} +3.83337 q^{71} +4.18073 q^{72} +9.86340 q^{73} +15.0832 q^{74} +1.04940 q^{76} +5.20656 q^{77} +16.4810 q^{78} -6.00906 q^{79} -11.2417 q^{81} +6.63154 q^{82} -2.43649 q^{83} +0.484320 q^{84} +0.464904 q^{86} -2.14682 q^{87} -14.9561 q^{88} +11.8146 q^{89} -4.69373 q^{91} -1.76690 q^{92} +13.9771 q^{93} -1.49903 q^{94} -2.97858 q^{96} +18.0420 q^{97} +9.23890 q^{98} -9.05593 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9	\( 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9} + q^{11} + 4 q^{12} - 2 q^{13} + 10 q^{14} - q^{16} - 12 q^{17} + 17 q^{18} + 3 q^{19} + 7 q^{21} + 5 q^{22} - q^{23} + 8 q^{24} - 13 q^{26} - q^{27} + 27 q^{28} + 26 q^{29} - 5 q^{31} - 12 q^{32} + 15 q^{33} + 6 q^{34} - 34 q^{36} + 7 q^{38} + q^{39} + 12 q^{41} + 18 q^{42} + 33 q^{43} + 3 q^{44} - 36 q^{46} + 7 q^{47} + 25 q^{48} + 6 q^{49} - 14 q^{51} + 11 q^{52} - 4 q^{53} - 2 q^{54} - 27 q^{56} + 21 q^{57} + 38 q^{58} + 13 q^{59} + 20 q^{61} - 15 q^{62} + 10 q^{63} - 9 q^{64} - 41 q^{66} + 32 q^{67} - 15 q^{68} + 16 q^{69} + 11 q^{71} + 8 q^{72} + 8 q^{73} + 48 q^{74} + 11 q^{76} - 29 q^{77} + 17 q^{78} + 17 q^{79} + 15 q^{81} - 6 q^{82} - 19 q^{83} + 46 q^{84} - 30 q^{86} - 2 q^{87} - 7 q^{88} + 13 q^{89} - 11 q^{91} - 16 q^{92} + 29 q^{93} - q^{94} - 29 q^{96} + 12 q^{97} - 6 q^{98} - 32 q^{99}+O(q^{100}) \) 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9 + q^11 + 4 * q^12 - 2 * q^13 + 10 * q^14 - q^16 - 12 * q^17 + 17 * q^18 + 3 * q^19 + 7 * q^21 + 5 * q^22 - q^23 + 8 * q^24 - 13 * q^26 - q^27 + 27 * q^28 + 26 * q^29 - 5 * q^31 - 12 * q^32 + 15 * q^33 + 6 * q^34 - 34 * q^36 + 7 * q^38 + q^39 + 12 * q^41 + 18 * q^42 + 33 * q^43 + 3 * q^44 - 36 * q^46 + 7 * q^47 + 25 * q^48 + 6 * q^49 - 14 * q^51 + 11 * q^52 - 4 * q^53 - 2 * q^54 - 27 * q^56 + 21 * q^57 + 38 * q^58 + 13 * q^59 + 20 * q^61 - 15 * q^62 + 10 * q^63 - 9 * q^64 - 41 * q^66 + 32 * q^67 - 15 * q^68 + 16 * q^69 + 11 * q^71 + 8 * q^72 + 8 * q^73 + 48 * q^74 + 11 * q^76 - 29 * q^77 + 17 * q^78 + 17 * q^79 + 15 * q^81 - 6 * q^82 - 19 * q^83 + 46 * q^84 - 30 * q^86 - 2 * q^87 - 7 * q^88 + 13 * q^89 - 11 * q^91 - 16 * q^92 + 29 * q^93 - q^94 - 29 * q^96 + 12 * q^97 - 6 * q^98 - 32 * q^99

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