LMFDB - Embedded newform 1175.2.a.i.1.2

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:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 8x^{9} + 44x^{8} + 8x^{7} - 156x^{6} + 48x^{5} + 208x^{4} - 96x^{3} - 86x^{2} + 41x + 4 $ x^11 - 4x^10 - 8x^9 + 44x^8 + 8x^7 - 156x^6 + 48x^5 + 208x^4 - 96x^3 - 86x^2 + 41x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.47667$ 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)

$f(q)$	$=$	$q-2.47667 q^{2} -1.85547 q^{3} +4.13392 q^{4} +4.59540 q^{6} +1.40219 q^{7} -5.28501 q^{8} +0.442781 q^{9} +O(q^{10})$	\(q-2.47667 q^{2} -1.85547 q^{3} +4.13392 q^{4} +4.59540 q^{6} +1.40219 q^{7} -5.28501 q^{8} +0.442781 q^{9} +3.06964 q^{11} -7.67037 q^{12} -2.69103 q^{13} -3.47277 q^{14} +4.82143 q^{16} +1.05796 q^{17} -1.09662 q^{18} -4.73653 q^{19} -2.60173 q^{21} -7.60250 q^{22} -0.726082 q^{23} +9.80620 q^{24} +6.66481 q^{26} +4.74485 q^{27} +5.79654 q^{28} +2.95300 q^{29} -10.8816 q^{31} -1.37107 q^{32} -5.69564 q^{33} -2.62023 q^{34} +1.83042 q^{36} -6.90900 q^{37} +11.7308 q^{38} +4.99314 q^{39} +11.4500 q^{41} +6.44363 q^{42} +11.6517 q^{43} +12.6896 q^{44} +1.79827 q^{46} +1.00000 q^{47} -8.94602 q^{48} -5.03386 q^{49} -1.96302 q^{51} -11.1245 q^{52} +0.891935 q^{53} -11.7515 q^{54} -7.41060 q^{56} +8.78850 q^{57} -7.31361 q^{58} +2.05322 q^{59} +8.90252 q^{61} +26.9503 q^{62} +0.620863 q^{63} -6.24715 q^{64} +14.1062 q^{66} -11.0344 q^{67} +4.37353 q^{68} +1.34723 q^{69} -0.815886 q^{71} -2.34010 q^{72} +0.153009 q^{73} +17.1113 q^{74} -19.5804 q^{76} +4.30423 q^{77} -12.3664 q^{78} +1.63022 q^{79} -10.1323 q^{81} -28.3580 q^{82} -4.45266 q^{83} -10.7553 q^{84} -28.8575 q^{86} -5.47921 q^{87} -16.2231 q^{88} -13.5273 q^{89} -3.77334 q^{91} -3.00156 q^{92} +20.1906 q^{93} -2.47667 q^{94} +2.54399 q^{96} +3.02569 q^{97} +12.4672 q^{98} +1.35918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9	$ 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9} - 12 q^{12} - 19 q^{13} + 12 q^{16} - 16 q^{17} + 10 q^{18} - 6 q^{21} - 22 q^{22} - 3 q^{23} - 12 q^{24} + 6 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 2 q^{31} - 28 q^{32} - 18 q^{33} - 16 q^{34} - 8 q^{36} - 40 q^{37} + 14 q^{38} - 10 q^{39} + 4 q^{41} - 16 q^{42} - 23 q^{43} + 24 q^{44} - 16 q^{46} + 11 q^{47} + 18 q^{48} + 5 q^{49} + 12 q^{51} - 46 q^{52} - 16 q^{53} + 26 q^{56} - 42 q^{57} - 16 q^{58} + 7 q^{59} - 7 q^{61} - 14 q^{63} + 24 q^{64} + 12 q^{66} - 32 q^{67} + 58 q^{68} - 2 q^{69} - 17 q^{71} - 57 q^{73} - 16 q^{74} - 10 q^{76} - 8 q^{77} + 22 q^{78} - 13 q^{79} - 25 q^{81} - 12 q^{82} - 8 q^{83} - 4 q^{84} - 6 q^{86} + 10 q^{87} - 26 q^{88} - 37 q^{89} + 32 q^{91} - 4 q^{92} + 10 q^{93} - 4 q^{94} - 6 q^{96} - 32 q^{97} + 20 q^{98} - 8 q^{99}+O(q^{100}) $ 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9 - 12 * q^12 - 19 * q^13 + 12 * q^16 - 16 * q^17 + 10 * q^18 - 6 * q^21 - 22 * q^22 - 3 * q^23 - 12 * q^24 + 6 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 2 * q^31 - 28 * q^32 - 18 * q^33 - 16 * q^34 - 8 * q^36 - 40 * q^37 + 14 * q^38 - 10 * q^39 + 4 * q^41 - 16 * q^42 - 23 * q^43 + 24 * q^44 - 16 * q^46 + 11 * q^47 + 18 * q^48 + 5 * q^49 + 12 * q^51 - 46 * q^52 - 16 * q^53 + 26 * q^56 - 42 * q^57 - 16 * q^58 + 7 * q^59 - 7 * q^61 - 14 * q^63 + 24 * q^64 + 12 * q^66 - 32 * q^67 + 58 * q^68 - 2 * q^69 - 17 * q^71 - 57 * q^73 - 16 * q^74 - 10 * q^76 - 8 * q^77 + 22 * q^78 - 13 * q^79 - 25 * q^81 - 12 * q^82 - 8 * q^83 - 4 * q^84 - 6 * q^86 + 10 * q^87 - 26 * q^88 - 37 * q^89 + 32 * q^91 - 4 * q^92 + 10 * q^93 - 4 * q^94 - 6 * q^96 - 32 * q^97 + 20 * q^98 - 8 * 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 $

$2$	−2.47667	−1.75127	−0.875637	−	0.482971i	$-0.839558\pi$
$2$	−2.47667	−1.75127	−0.875637	+	0.482971i	$0.839558\pi$
$3$	−1.85547	−1.07126	−0.535629	−	0.844453i	$-0.679925\pi$
$3$	−1.85547	−1.07126	−0.535629	+	0.844453i	$0.679925\pi$
$4$	4.13392	2.06696
$5$	0	0
$5$	0	0
$6$	4.59540	1.87607
$7$	1.40219	0.529978	0.264989	−	0.964251i	$-0.414632\pi$
$7$	1.40219	0.529978	0.264989	+	0.964251i	$0.414632\pi$
$8$	−5.28501	−1.86853
$9$	0.442781	0.147594
$10$	0	0
$11$	3.06964	0.925532	0.462766	−	0.886481i	$-0.346857\pi$
$11$	3.06964	0.925532	0.462766	+	0.886481i	$0.346857\pi$
$12$	−7.67037	−2.21424
$13$	−2.69103	−0.746358	−0.373179	−	0.927759i	$-0.621732\pi$
$13$	−2.69103	−0.746358	−0.373179	+	0.927759i	$0.621732\pi$
$14$	−3.47277	−0.928137
$15$	0	0
$16$	4.82143	1.20536
$17$	1.05796	0.256594	0.128297	−	0.991736i	$-0.459049\pi$
$17$	1.05796	0.256594	0.128297	+	0.991736i	$0.459049\pi$
$18$	−1.09662	−0.258477
$19$	−4.73653	−1.08663	−0.543317	−	0.839528i	$-0.682832\pi$
$19$	−4.73653	−1.08663	−0.543317	+	0.839528i	$0.682832\pi$
$20$	0	0
$21$	−2.60173	−0.567744
$22$	−7.60250	−1.62086
$23$	−0.726082	−0.151399	−0.0756993	−	0.997131i	$-0.524119\pi$
$23$	−0.726082	−0.151399	−0.0756993	+	0.997131i	$0.524119\pi$
$24$	9.80620	2.00168
$25$	0	0
$26$	6.66481	1.30708
$27$	4.74485	0.913147
$28$	5.79654	1.09544
$29$	2.95300	0.548358	0.274179	−	0.961679i	$-0.411594\pi$
$29$	2.95300	0.548358	0.274179	+	0.961679i	$0.411594\pi$
$30$	0	0
$31$	−10.8816	−1.95440	−0.977200	−	0.212322i	$-0.931898\pi$
$31$	−10.8816	−1.95440	−0.977200	+	0.212322i	$0.931898\pi$
$32$	−1.37107	−0.242374
$33$	−5.69564	−0.991483
$34$	−2.62023	−0.449366
$35$	0	0
$36$	1.83042	0.305070
$37$	−6.90900	−1.13583	−0.567916	−	0.823086i	$-0.692250\pi$
$37$	−6.90900	−1.13583	−0.567916	+	0.823086i	$0.692250\pi$
$38$	11.7308	1.90299
$39$	4.99314	0.799542
$40$	0	0
$41$	11.4500	1.78820	0.894098	−	0.447871i	$-0.147817\pi$
$41$	11.4500	1.78820	0.894098	+	0.447871i	$0.147817\pi$
$42$	6.44363	0.994274
$43$	11.6517	1.77687	0.888435	−	0.459003i	$-0.151793\pi$
$43$	11.6517	1.77687	0.888435	+	0.459003i	$0.151793\pi$
$44$	12.6896	1.91304
$45$	0	0
$46$	1.79827	0.265140
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−8.94602	−1.29125
$49$	−5.03386	−0.719123
$50$	0	0
$51$	−1.96302	−0.274878
$52$	−11.1245	−1.54269
$53$	0.891935	0.122517	0.0612583	−	0.998122i	$-0.480489\pi$
$53$	0.891935	0.122517	0.0612583	+	0.998122i	$0.480489\pi$
$54$	−11.7515	−1.59917
$55$	0	0
$56$	−7.41060	−0.990283
$57$	8.78850	1.16407
$58$	−7.31361	−0.960324
$59$	2.05322	0.267307	0.133654	−	0.991028i	$-0.457329\pi$
$59$	2.05322	0.267307	0.133654	+	0.991028i	$0.457329\pi$
$60$	0	0
$61$	8.90252	1.13985	0.569925	−	0.821696i	$-0.306972\pi$
$61$	8.90252	1.13985	0.569925	+	0.821696i	$0.306972\pi$
$62$	26.9503	3.42269
$63$	0.620863	0.0782214
$64$	−6.24715	−0.780894
$65$	0	0
$66$	14.1062	1.73636
$67$	−11.0344	−1.34806	−0.674032	−	0.738702i	$-0.735439\pi$
$67$	−11.0344	−1.34806	−0.674032	+	0.738702i	$0.735439\pi$
$68$	4.37353	0.530368
$69$	1.34723	0.162187
$70$	0	0
$71$	−0.815886	−0.0968279	−0.0484139	−	0.998827i	$-0.515417\pi$
$71$	−0.815886	−0.0968279	−0.0484139	+	0.998827i	$0.515417\pi$
$72$	−2.34010	−0.275784
$73$	0.153009	0.0179083	0.00895416	−	0.999960i	$-0.497150\pi$
$73$	0.153009	0.0179083	0.00895416	+	0.999960i	$0.497150\pi$
$74$	17.1113	1.98915
$75$	0	0
$76$	−19.5804	−2.24603
$77$	4.30423	0.490512
$78$	−12.3664	−1.40022
$79$	1.63022	0.183414	0.0917068	−	0.995786i	$-0.470768\pi$
$79$	1.63022	0.183414	0.0917068	+	0.995786i	$0.470768\pi$
$80$	0	0
$81$	−10.1323	−1.12581
$82$	−28.3580	−3.13162
$83$	−4.45266	−0.488743	−0.244371	−	0.969682i	$-0.578582\pi$
$83$	−4.45266	−0.488743	−0.244371	+	0.969682i	$0.578582\pi$
$84$	−10.7553	−1.17350
$85$	0	0
$86$	−28.8575	−3.11178
$87$	−5.47921	−0.587432
$88$	−16.2231	−1.72939
$89$	−13.5273	−1.43389	−0.716943	−	0.697132i	$-0.754459\pi$
$89$	−13.5273	−1.43389	−0.716943	+	0.697132i	$0.754459\pi$
$90$	0	0
$91$	−3.77334	−0.395554
$92$	−3.00156	−0.312935
$93$	20.1906	2.09367
$94$	−2.47667	−0.255449
$95$	0	0
$96$	2.54399	0.259645
$97$	3.02569	0.307212	0.153606	−	0.988132i	$-0.450911\pi$
$97$	3.02569	0.307212	0.153606	+	0.988132i	$0.450911\pi$
$98$	12.4672	1.25938
$99$	1.35918	0.136603
$100$	0	0
$101$	−8.29080	−0.824965	−0.412483	−	0.910966i	$-0.635338\pi$
$101$	−8.29080	−0.824965	−0.412483	+	0.910966i	$0.635338\pi$
$102$	4.86176	0.481386
$103$	17.0127	1.67631	0.838156	−	0.545431i	$-0.183634\pi$
$103$	17.0127	1.67631	0.838156	+	0.545431i	$0.183634\pi$
$104$	14.2221	1.39460
$105$	0	0
$106$	−2.20903	−0.214560
$107$	−5.77895	−0.558672	−0.279336	−	0.960193i	$-0.590114\pi$
$107$	−5.77895	−0.558672	−0.279336	+	0.960193i	$0.590114\pi$
$108$	19.6148	1.88744
$109$	−12.5370	−1.20083	−0.600413	−	0.799690i	$-0.704997\pi$
$109$	−12.5370	−1.20083	−0.600413	+	0.799690i	$0.704997\pi$
$110$	0	0
$111$	12.8195	1.21677
$112$	6.76056	0.638813
$113$	−17.9069	−1.68454	−0.842269	−	0.539058i	$-0.818780\pi$
$113$	−17.9069	−1.68454	−0.842269	+	0.539058i	$0.818780\pi$
$114$	−21.7663	−2.03860
$115$	0	0
$116$	12.2074	1.13343
$117$	−1.19154	−0.110158
$118$	−5.08517	−0.468128
$119$	1.48347	0.135989
$120$	0	0
$121$	−1.57730	−0.143391
$122$	−22.0486	−1.99619
$123$	−21.2453	−1.91562
$124$	−44.9838	−4.03966
$125$	0	0
$126$	−1.53768	−0.136987
$127$	−12.1892	−1.08162	−0.540809	−	0.841145i	$-0.681882\pi$
$127$	−12.1892	−1.08162	−0.540809	+	0.841145i	$0.681882\pi$
$128$	18.2143	1.60993
$129$	−21.6194	−1.90349
$130$	0	0
$131$	−14.4486	−1.26238	−0.631192	−	0.775627i	$-0.717434\pi$
$131$	−14.4486	−1.26238	−0.631192	+	0.775627i	$0.717434\pi$
$132$	−23.5453	−2.04935
$133$	−6.64152	−0.575893
$134$	27.3286	2.36083
$135$	0	0
$136$	−5.59135	−0.479454
$137$	−9.57683	−0.818204	−0.409102	−	0.912489i	$-0.634158\pi$
$137$	−9.57683	−0.818204	−0.409102	+	0.912489i	$0.634158\pi$
$138$	−3.33664	−0.284034
$139$	10.9284	0.926939	0.463469	−	0.886113i	$-0.346604\pi$
$139$	10.9284	0.926939	0.463469	+	0.886113i	$0.346604\pi$
$140$	0	0
$141$	−1.85547	−0.156259
$142$	2.02068	0.169572
$143$	−8.26050	−0.690778
$144$	2.13483	0.177903
$145$	0	0
$146$	−0.378953	−0.0313624
$147$	9.34019	0.770366
$148$	−28.5612	−2.34772
$149$	−7.31777	−0.599495	−0.299748	−	0.954019i	$-0.596902\pi$
$149$	−7.31777	−0.599495	−0.299748	+	0.954019i	$0.596902\pi$
$150$	0	0
$151$	−6.93732	−0.564551	−0.282276	−	0.959333i	$-0.591089\pi$
$151$	−6.93732	−0.564551	−0.282276	+	0.959333i	$0.591089\pi$
$152$	25.0326	2.03041
$153$	0.468445	0.0378716
$154$	−10.6602	−0.859020
$155$	0	0
$156$	20.6412	1.65262
$157$	−10.6419	−0.849319	−0.424660	−	0.905353i	$-0.639606\pi$
$157$	−10.6419	−0.849319	−0.424660	+	0.905353i	$0.639606\pi$
$158$	−4.03751	−0.321207
$159$	−1.65496	−0.131247
$160$	0	0
$161$	−1.01811	−0.0802380
$162$	25.0944	1.97160
$163$	−16.5816	−1.29877	−0.649387	−	0.760458i	$-0.724974\pi$
$163$	−16.5816	−1.29877	−0.649387	+	0.760458i	$0.724974\pi$
$164$	47.3335	3.69613
$165$	0	0
$166$	11.0278	0.855922
$167$	15.7506	1.21881	0.609407	−	0.792857i	$-0.291407\pi$
$167$	15.7506	1.21881	0.609407	+	0.792857i	$0.291407\pi$
$168$	13.7502	1.06085
$169$	−5.75835	−0.442950
$170$	0	0
$171$	−2.09724	−0.160380
$172$	48.1672	3.67271
$173$	−13.0275	−0.990460	−0.495230	−	0.868762i	$-0.664916\pi$
$173$	−13.0275	−0.990460	−0.495230	+	0.868762i	$0.664916\pi$
$174$	13.5702	1.02875
$175$	0	0
$176$	14.8000	1.11560
$177$	−3.80970	−0.286355
$178$	33.5026	2.51113
$179$	5.92354	0.442746	0.221373	−	0.975189i	$-0.428946\pi$
$179$	5.92354	0.442746	0.221373	+	0.975189i	$0.428946\pi$
$180$	0	0
$181$	11.6964	0.869385	0.434692	−	0.900579i	$-0.356857\pi$
$181$	11.6964	0.869385	0.434692	+	0.900579i	$0.356857\pi$
$182$	9.34534	0.692722
$183$	−16.5184	−1.22107
$184$	3.83735	0.282894
$185$	0	0
$186$	−50.0055	−3.66658
$187$	3.24757	0.237486
$188$	4.13392	0.301497
$189$	6.65319	0.483948
$190$	0	0
$191$	21.5366	1.55833	0.779167	−	0.626817i	$-0.215643\pi$
$191$	21.5366	1.55833	0.779167	+	0.626817i	$0.215643\pi$
$192$	11.5914	0.836538
$193$	−20.7244	−1.49178	−0.745888	−	0.666071i	$-0.767975\pi$
$193$	−20.7244	−1.49178	−0.745888	+	0.666071i	$0.767975\pi$
$194$	−7.49364	−0.538012
$195$	0	0
$196$	−20.8095	−1.48640
$197$	5.64002	0.401835	0.200917	−	0.979608i	$-0.435608\pi$
$197$	5.64002	0.401835	0.200917	+	0.979608i	$0.435608\pi$
$198$	−3.36624	−0.239228
$199$	7.61257	0.539641	0.269821	−	0.962911i	$-0.413036\pi$
$199$	7.61257	0.539641	0.269821	+	0.962911i	$0.413036\pi$
$200$	0	0
$201$	20.4740	1.44412
$202$	20.5336	1.44474
$203$	4.14067	0.290618
$204$	−8.11496	−0.568161
$205$	0	0
$206$	−42.1349	−2.93568
$207$	−0.321495	−0.0223455
$208$	−12.9746	−0.899627
$209$	−14.5394	−1.00571
$210$	0	0
$211$	−11.7370	−0.808010	−0.404005	−	0.914757i	$-0.632382\pi$
$211$	−11.7370	−0.808010	−0.404005	+	0.914757i	$0.632382\pi$
$212$	3.68718	0.253237
$213$	1.51386	0.103728
$214$	14.3126	0.978387
$215$	0	0
$216$	−25.0766	−1.70625
$217$	−15.2581	−1.03579
$218$	31.0500	2.10297
$219$	−0.283904	−0.0191844
$220$	0	0
$221$	−2.84701	−0.191511
$222$	−31.7496	−2.13090
$223$	−0.0576246	−0.00385883	−0.00192941	−	0.999998i	$-0.500614\pi$
$223$	−0.0576246	−0.00385883	−0.00192941	+	0.999998i	$0.500614\pi$
$224$	−1.92251	−0.128453
$225$	0	0
$226$	44.3495	2.95009
$227$	−11.2182	−0.744577	−0.372288	−	0.928117i	$-0.621427\pi$
$227$	−11.2182	−0.744577	−0.372288	+	0.928117i	$0.621427\pi$
$228$	36.3309	2.40607
$229$	23.4306	1.54833	0.774167	−	0.632981i	$-0.218169\pi$
$229$	23.4306	1.54833	0.774167	+	0.632981i	$0.218169\pi$
$230$	0	0
$231$	−7.98637	−0.525465
$232$	−15.6066	−1.02463
$233$	1.24374	0.0814801	0.0407400	−	0.999170i	$-0.487028\pi$
$233$	1.24374	0.0814801	0.0407400	+	0.999170i	$0.487028\pi$
$234$	2.95105	0.192916
$235$	0	0
$236$	8.48786	0.552512
$237$	−3.02482	−0.196483
$238$	−3.67406	−0.238154
$239$	−15.6947	−1.01521	−0.507604	−	0.861590i	$-0.669469\pi$
$239$	−15.6947	−1.01521	−0.507604	+	0.861590i	$0.669469\pi$
$240$	0	0
$241$	1.27081	0.0818601	0.0409300	−	0.999162i	$-0.486968\pi$
$241$	1.27081	0.0818601	0.0409300	+	0.999162i	$0.486968\pi$
$242$	3.90646	0.251116
$243$	4.56563	0.292885
$244$	36.8023	2.35602
$245$	0	0
$246$	52.6176	3.35477
$247$	12.7461	0.811018
$248$	57.5096	3.65186
$249$	8.26179	0.523570
$250$	0	0
$251$	29.7673	1.87890	0.939448	−	0.342692i	$-0.111339\pi$
$251$	29.7673	1.87890	0.939448	+	0.342692i	$0.111339\pi$
$252$	2.56660	0.161680
$253$	−2.22881	−0.140124
$254$	30.1887	1.89421
$255$	0	0
$256$	−32.6166	−2.03854
$257$	−19.9953	−1.24727	−0.623637	−	0.781714i	$-0.714346\pi$
$257$	−19.9953	−1.24727	−0.623637	+	0.781714i	$0.714346\pi$
$258$	53.5443	3.33352
$259$	−9.68774	−0.601967
$260$	0	0
$261$	1.30753	0.0809341
$262$	35.7846	2.21078
$263$	−19.0192	−1.17277	−0.586386	−	0.810032i	$-0.699450\pi$
$263$	−19.0192	−1.17277	−0.586386	+	0.810032i	$0.699450\pi$
$264$	30.1015	1.85262
$265$	0	0
$266$	16.4489	1.00855
$267$	25.0995	1.53606
$268$	−45.6152	−2.78639
$269$	−13.3102	−0.811540	−0.405770	−	0.913975i	$-0.632997\pi$
$269$	−13.3102	−0.811540	−0.405770	+	0.913975i	$0.632997\pi$
$270$	0	0
$271$	−20.5726	−1.24970	−0.624849	−	0.780746i	$-0.714839\pi$
$271$	−20.5726	−1.24970	−0.624849	+	0.780746i	$0.714839\pi$
$272$	5.10089	0.309287
$273$	7.00133	0.423740
$274$	23.7187	1.43290
$275$	0	0
$276$	5.56932	0.335234
$277$	−4.01696	−0.241355	−0.120678	−	0.992692i	$-0.538507\pi$
$277$	−4.01696	−0.241355	−0.120678	+	0.992692i	$0.538507\pi$
$278$	−27.0662	−1.62332
$279$	−4.81818	−0.288457
$280$	0	0
$281$	−5.04550	−0.300989	−0.150495	−	0.988611i	$-0.548087\pi$
$281$	−5.04550	−0.300989	−0.150495	+	0.988611i	$0.548087\pi$
$282$	4.59540	0.273652
$283$	16.9301	1.00639	0.503194	−	0.864173i	$-0.332158\pi$
$283$	16.9301	1.00639	0.503194	+	0.864173i	$0.332158\pi$
$284$	−3.37281	−0.200139
$285$	0	0
$286$	20.4586	1.20974
$287$	16.0552	0.947706
$288$	−0.607085	−0.0357728
$289$	−15.8807	−0.934160
$290$	0	0
$291$	−5.61408	−0.329103
$292$	0.632525	0.0370157
$293$	25.5161	1.49067	0.745334	−	0.666691i	$-0.232290\pi$
$293$	25.5161	1.49067	0.745334	+	0.666691i	$0.232290\pi$
$294$	−23.1326	−1.34912
$295$	0	0
$296$	36.5141	2.12234
$297$	14.5650	0.845147
$298$	18.1237	1.04988
$299$	1.95391	0.112998
$300$	0	0
$301$	16.3379	0.941703
$302$	17.1815	0.988683
$303$	15.3834	0.883750
$304$	−22.8368	−1.30978
$305$	0	0
$306$	−1.16019	−0.0663235
$307$	−20.0659	−1.14522	−0.572612	−	0.819827i	$-0.694070\pi$
$307$	−20.0659	−1.14522	−0.572612	+	0.819827i	$0.694070\pi$
$308$	17.7933	1.01387
$309$	−31.5666	−1.79576
$310$	0	0
$311$	−20.4150	−1.15763	−0.578815	−	0.815459i	$-0.696485\pi$
$311$	−20.4150	−1.15763	−0.578815	+	0.815459i	$0.696485\pi$
$312$	−26.3888	−1.49397
$313$	−9.51931	−0.538063	−0.269032	−	0.963131i	$-0.586704\pi$
$313$	−9.51931	−0.538063	−0.269032	+	0.963131i	$0.586704\pi$
$314$	26.3566	1.48739
$315$	0	0
$316$	6.73917	0.379108
$317$	−8.07209	−0.453374	−0.226687	−	0.973968i	$-0.572789\pi$
$317$	−8.07209	−0.453374	−0.226687	+	0.973968i	$0.572789\pi$
$318$	4.09880	0.229849
$319$	9.06464	0.507522
$320$	0	0
$321$	10.7227	0.598482
$322$	2.52152	0.140519
$323$	−5.01107	−0.278823
$324$	−41.8860	−2.32700
$325$	0	0
$326$	41.0673	2.27451
$327$	23.2620	1.28639
$328$	−60.5136	−3.34131
$329$	1.40219	0.0773053
$330$	0	0
$331$	6.46615	0.355412	0.177706	−	0.984084i	$-0.443132\pi$
$331$	6.46615	0.355412	0.177706	+	0.984084i	$0.443132\pi$
$332$	−18.4069	−1.01021
$333$	−3.05917	−0.167641
$334$	−39.0090	−2.13448
$335$	0	0
$336$	−12.5440	−0.684333
$337$	−28.4771	−1.55125	−0.775624	−	0.631195i	$-0.782565\pi$
$337$	−28.4771	−1.55125	−0.775624	+	0.631195i	$0.782565\pi$
$338$	14.2616	0.775727
$339$	33.2257	1.80457
$340$	0	0
$341$	−33.4027	−1.80886
$342$	5.19419	0.280870
$343$	−16.8738	−0.911098
$344$	−61.5795	−3.32014
$345$	0	0
$346$	32.2648	1.73457
$347$	15.6868	0.842112	0.421056	−	0.907035i	$-0.361660\pi$
$347$	15.6868	0.842112	0.421056	+	0.907035i	$0.361660\pi$
$348$	−22.6506	−1.21420
$349$	15.2408	0.815821	0.407910	−	0.913022i	$-0.366258\pi$
$349$	15.2408	0.815821	0.407910	+	0.913022i	$0.366258\pi$
$350$	0	0
$351$	−12.7685	−0.681534
$352$	−4.20870	−0.224325
$353$	−2.10431	−0.112001	−0.0560004	−	0.998431i	$-0.517835\pi$
$353$	−2.10431	−0.112001	−0.0560004	+	0.998431i	$0.517835\pi$
$354$	9.43539	0.501485
$355$	0	0
$356$	−55.9205	−2.96378
$357$	−2.75253	−0.145679
$358$	−14.6707	−0.775369
$359$	7.75806	0.409455	0.204727	−	0.978819i	$-0.434369\pi$
$359$	7.75806	0.409455	0.204727	+	0.978819i	$0.434369\pi$
$360$	0	0
$361$	3.43470	0.180774
$362$	−28.9681	−1.52253
$363$	2.92664	0.153609
$364$	−15.5987	−0.817592
$365$	0	0
$366$	40.9107	2.13843
$367$	25.9920	1.35677	0.678384	−	0.734707i	$-0.262680\pi$
$367$	25.9920	1.35677	0.678384	+	0.734707i	$0.262680\pi$
$368$	−3.50075	−0.182489
$369$	5.06986	0.263926
$370$	0	0
$371$	1.25066	0.0649312
$372$	83.4662	4.32752
$373$	−21.1460	−1.09490	−0.547450	−	0.836839i	$-0.684401\pi$
$373$	−21.1460	−1.09490	−0.547450	+	0.836839i	$0.684401\pi$
$374$	−8.04316	−0.415902
$375$	0	0
$376$	−5.28501	−0.272554
$377$	−7.94661	−0.409271
$378$	−16.4778	−0.847526
$379$	32.1426	1.65106	0.825528	−	0.564362i	$-0.190878\pi$
$379$	32.1426	1.65106	0.825528	+	0.564362i	$0.190878\pi$
$380$	0	0
$381$	22.6168	1.15869
$382$	−53.3391	−2.72907
$383$	5.95055	0.304059	0.152029	−	0.988376i	$-0.451419\pi$
$383$	5.95055	0.304059	0.152029	+	0.988376i	$0.451419\pi$
$384$	−33.7961	−1.72465
$385$	0	0
$386$	51.3276	2.61251
$387$	5.15915	0.262255
$388$	12.5079	0.634994
$389$	−3.17070	−0.160761	−0.0803805	−	0.996764i	$-0.525614\pi$
$389$	−3.17070	−0.160761	−0.0803805	+	0.996764i	$0.525614\pi$
$390$	0	0
$391$	−0.768168	−0.0388479
$392$	26.6040	1.34371
$393$	26.8091	1.35234
$394$	−13.9685	−0.703723
$395$	0	0
$396$	5.61873	0.282352
$397$	−15.6582	−0.785865	−0.392932	−	0.919567i	$-0.628539\pi$
$397$	−15.6582	−0.785865	−0.392932	+	0.919567i	$0.628539\pi$
$398$	−18.8539	−0.945059
$399$	12.3232	0.616930
$400$	0	0
$401$	−15.4468	−0.771376	−0.385688	−	0.922629i	$-0.626036\pi$
$401$	−15.4468	−0.771376	−0.385688	+	0.922629i	$0.626036\pi$
$402$	−50.7074	−2.52906
$403$	29.2828	1.45868
$404$	−34.2734	−1.70517
$405$	0	0
$406$	−10.2551	−0.508951
$407$	−21.2081	−1.05125
$408$	10.3746	0.513619
$409$	−12.6851	−0.627240	−0.313620	−	0.949549i	$-0.601542\pi$
$409$	−12.6851	−0.627240	−0.313620	+	0.949549i	$0.601542\pi$
$410$	0	0
$411$	17.7696	0.876507
$412$	70.3291	3.46487
$413$	2.87901	0.141667
$414$	0.796239	0.0391330
$415$	0	0
$416$	3.68960	0.180898
$417$	−20.2774	−0.992991
$418$	36.0095	1.76128
$419$	26.2002	1.27996	0.639981	−	0.768390i	$-0.278942\pi$
$419$	26.2002	1.27996	0.639981	+	0.768390i	$0.278942\pi$
$420$	0	0
$421$	−30.5531	−1.48907	−0.744535	−	0.667584i	$-0.767329\pi$
$421$	−30.5531	−1.48907	−0.744535	+	0.667584i	$0.767329\pi$
$422$	29.0688	1.41505
$423$	0.442781	0.0215287
$424$	−4.71389	−0.228927
$425$	0	0
$426$	−3.74933	−0.181655
$427$	12.4830	0.604096
$428$	−23.8897	−1.15475
$429$	15.3271	0.740001
$430$	0	0
$431$	−17.8313	−0.858903	−0.429451	−	0.903090i	$-0.641293\pi$
$431$	−17.8313	−0.858903	−0.429451	+	0.903090i	$0.641293\pi$
$432$	22.8769	1.10067
$433$	−22.5509	−1.08372	−0.541862	−	0.840467i	$-0.682281\pi$
$433$	−22.5509	−1.08372	−0.541862	+	0.840467i	$0.682281\pi$
$434$	37.7894	1.81395
$435$	0	0
$436$	−51.8269	−2.48206
$437$	3.43911	0.164515
$438$	0.703137	0.0335972
$439$	−13.6499	−0.651476	−0.325738	−	0.945460i	$-0.605613\pi$
$439$	−13.6499	−0.651476	−0.325738	+	0.945460i	$0.605613\pi$
$440$	0	0
$441$	−2.22890	−0.106138
$442$	7.05112	0.335387
$443$	−5.40787	−0.256936	−0.128468	−	0.991714i	$-0.541006\pi$
$443$	−5.40787	−0.256936	−0.128468	+	0.991714i	$0.541006\pi$
$444$	52.9946	2.51501
$445$	0	0
$446$	0.142717	0.00675786
$447$	13.5779	0.642214
$448$	−8.75970	−0.413857
$449$	−3.85520	−0.181938	−0.0909691	−	0.995854i	$-0.528996\pi$
$449$	−3.85520	−0.181938	−0.0909691	+	0.995854i	$0.528996\pi$
$450$	0	0
$451$	35.1475	1.65503
$452$	−74.0255	−3.48187
$453$	12.8720	0.604780
$454$	27.7838	1.30396
$455$	0	0
$456$	−46.4473	−2.17510
$457$	1.95505	0.0914534	0.0457267	−	0.998954i	$-0.485440\pi$
$457$	1.95505	0.0914534	0.0457267	+	0.998954i	$0.485440\pi$
$458$	−58.0299	−2.71156
$459$	5.01988	0.234308
$460$	0	0
$461$	−33.0560	−1.53957	−0.769785	−	0.638303i	$-0.779637\pi$
$461$	−33.0560	−1.53957	−0.769785	+	0.638303i	$0.779637\pi$
$462$	19.7796	0.920232
$463$	14.7632	0.686106	0.343053	−	0.939316i	$-0.388539\pi$
$463$	14.7632	0.686106	0.343053	+	0.939316i	$0.388539\pi$
$464$	14.2377	0.660966
$465$	0	0
$466$	−3.08034	−0.142694
$467$	−3.64794	−0.168807	−0.0844033	−	0.996432i	$-0.526898\pi$
$467$	−3.64794	−0.168807	−0.0844033	+	0.996432i	$0.526898\pi$
$468$	−4.92571	−0.227691
$469$	−15.4723	−0.714445
$470$	0	0
$471$	19.7458	0.909840
$472$	−10.8513	−0.499472
$473$	35.7666	1.64455
$474$	7.49149	0.344096
$475$	0	0
$476$	6.13252	0.281084
$477$	0.394932	0.0180827
$478$	38.8708	1.77791
$479$	−8.90528	−0.406893	−0.203446	−	0.979086i	$-0.565214\pi$
$479$	−8.90528	−0.406893	−0.203446	+	0.979086i	$0.565214\pi$
$480$	0	0
$481$	18.5923	0.847737
$482$	−3.14738	−0.143359
$483$	1.88907	0.0859556
$484$	−6.52042	−0.296383
$485$	0	0
$486$	−11.3076	−0.512922
$487$	1.05430	0.0477748	0.0238874	−	0.999715i	$-0.492396\pi$
$487$	1.05430	0.0477748	0.0238874	+	0.999715i	$0.492396\pi$
$488$	−47.0499	−2.12985
$489$	30.7668	1.39132
$490$	0	0
$491$	29.3923	1.32645	0.663227	−	0.748418i	$-0.269186\pi$
$491$	29.3923	1.32645	0.663227	+	0.748418i	$0.269186\pi$
$492$	−87.8261	−3.95951
$493$	3.12416	0.140705
$494$	−31.5681	−1.42031
$495$	0	0
$496$	−52.4650	−2.35575
$497$	−1.14403	−0.0513167
$498$	−20.4618	−0.916914
$499$	−9.08368	−0.406641	−0.203321	−	0.979112i	$-0.565173\pi$
$499$	−9.08368	−0.406641	−0.203321	+	0.979112i	$0.565173\pi$
$500$	0	0
$501$	−29.2247	−1.30566
$502$	−73.7239	−3.29046
$503$	19.9433	0.889226	0.444613	−	0.895723i	$-0.353341\pi$
$503$	19.9433	0.889226	0.444613	+	0.895723i	$0.353341\pi$
$504$	−3.28127	−0.146159
$505$	0	0
$506$	5.52004	0.245396
$507$	10.6845	0.474514
$508$	−50.3892	−2.23566
$509$	39.6875	1.75912	0.879558	−	0.475792i	$-0.157838\pi$
$509$	39.6875	1.75912	0.879558	+	0.475792i	$0.157838\pi$
$510$	0	0
$511$	0.214547	0.00949102
$512$	44.3521	1.96010
$513$	−22.4741	−0.992257
$514$	49.5219	2.18432
$515$	0	0
$516$	−89.3729	−3.93442
$517$	3.06964	0.135003
$518$	23.9934	1.05421
$519$	24.1721	1.06104
$520$	0	0
$521$	10.3357	0.452815	0.226408	−	0.974033i	$-0.427302\pi$
$521$	10.3357	0.452815	0.226408	+	0.974033i	$0.427302\pi$
$522$	−3.23833	−0.141738
$523$	4.99975	0.218624	0.109312	−	0.994007i	$-0.465135\pi$
$523$	4.99975	0.218624	0.109312	+	0.994007i	$0.465135\pi$
$524$	−59.7295	−2.60929
$525$	0	0
$526$	47.1043	2.05384
$527$	−11.5124	−0.501486
$528$	−27.4611	−1.19509
$529$	−22.4728	−0.977078
$530$	0	0
$531$	0.909128	0.0394528
$532$	−27.4555	−1.19035
$533$	−30.8124	−1.33463
$534$	−62.1632	−2.69006
$535$	0	0
$536$	58.3168	2.51890
$537$	−10.9910	−0.474295
$538$	32.9651	1.42123
$539$	−15.4521	−0.665571
$540$	0	0
$541$	−8.57782	−0.368789	−0.184395	−	0.982852i	$-0.559032\pi$
$541$	−8.57782	−0.368789	−0.184395	+	0.982852i	$0.559032\pi$
$542$	50.9517	2.18856
$543$	−21.7023	−0.931335
$544$	−1.45054	−0.0621916
$545$	0	0
$546$	−17.3400	−0.742084
$547$	−41.2890	−1.76539	−0.882695	−	0.469947i	$-0.844273\pi$
$547$	−41.2890	−1.76539	−0.882695	+	0.469947i	$0.844273\pi$
$548$	−39.5898	−1.69119
$549$	3.94186	0.168235
$550$	0	0
$551$	−13.9870	−0.595864
$552$	−7.12011	−0.303052
$553$	2.28587	0.0972052
$554$	9.94869	0.422679
$555$	0	0
$556$	45.1773	1.91594
$557$	9.65844	0.409241	0.204621	−	0.978841i	$-0.434404\pi$
$557$	9.65844	0.409241	0.204621	+	0.978841i	$0.434404\pi$
$558$	11.9331	0.505167
$559$	−31.3551	−1.32618
$560$	0	0
$561$	−6.02577	−0.254408
$562$	12.4961	0.527115
$563$	−1.14676	−0.0483303	−0.0241652	−	0.999708i	$-0.507693\pi$
$563$	−1.14676	−0.0483303	−0.0241652	+	0.999708i	$0.507693\pi$
$564$	−7.67037	−0.322981
$565$	0	0
$566$	−41.9303	−1.76246
$567$	−14.2074	−0.596655
$568$	4.31197	0.180926
$569$	4.12160	0.172787	0.0863933	−	0.996261i	$-0.472466\pi$
$569$	4.12160	0.172787	0.0863933	+	0.996261i	$0.472466\pi$
$570$	0	0
$571$	−0.414219	−0.0173345	−0.00866726	−	0.999962i	$-0.502759\pi$
$571$	−0.414219	−0.0173345	−0.00866726	+	0.999962i	$0.502759\pi$
$572$	−34.1482	−1.42781
$573$	−39.9606	−1.66938
$574$	−39.7634	−1.65969
$575$	0	0
$576$	−2.76612	−0.115255
$577$	34.0247	1.41647	0.708234	−	0.705978i	$-0.249492\pi$
$577$	34.0247	1.41647	0.708234	+	0.705978i	$0.249492\pi$
$578$	39.3314	1.63597
$579$	38.4536	1.59808
$580$	0	0
$581$	−6.24348	−0.259023
$582$	13.9042	0.576349
$583$	2.73792	0.113393
$584$	−0.808653	−0.0334623
$585$	0	0
$586$	−63.1951	−2.61057
$587$	1.76540	0.0728657	0.0364328	−	0.999336i	$-0.488401\pi$
$587$	1.76540	0.0728657	0.0364328	+	0.999336i	$0.488401\pi$
$588$	38.6116	1.59231
$589$	51.5412	2.12372
$590$	0	0
$591$	−10.4649	−0.430469
$592$	−33.3112	−1.36908
$593$	−15.3831	−0.631707	−0.315853	−	0.948808i	$-0.602291\pi$
$593$	−15.3831	−0.631707	−0.315853	+	0.948808i	$0.602291\pi$
$594$	−36.0727	−1.48008
$595$	0	0
$596$	−30.2511	−1.23913
$597$	−14.1249	−0.578095
$598$	−4.83920	−0.197890
$599$	9.00558	0.367958	0.183979	−	0.982930i	$-0.441102\pi$
$599$	9.00558	0.367958	0.183979	+	0.982930i	$0.441102\pi$
$600$	0	0
$601$	−38.5394	−1.57205	−0.786027	−	0.618193i	$-0.787865\pi$
$601$	−38.5394	−1.57205	−0.786027	+	0.618193i	$0.787865\pi$
$602$	−40.4637	−1.64918
$603$	−4.88581	−0.198966
$604$	−28.6783	−1.16690
$605$	0	0
$606$	−38.0995	−1.54769
$607$	22.1976	0.900972	0.450486	−	0.892783i	$-0.351251\pi$
$607$	22.1976	0.900972	0.450486	+	0.892783i	$0.351251\pi$
$608$	6.49413	0.263372
$609$	−7.68289	−0.311327
$610$	0	0
$611$	−2.69103	−0.108867
$612$	1.93651	0.0782789
$613$	12.8695	0.519793	0.259896	−	0.965637i	$-0.416312\pi$
$613$	12.8695	0.519793	0.259896	+	0.965637i	$0.416312\pi$
$614$	49.6968	2.00560
$615$	0	0
$616$	−22.7479	−0.916538
$617$	−13.4733	−0.542413	−0.271206	−	0.962521i	$-0.587423\pi$
$617$	−13.4733	−0.542413	−0.271206	+	0.962521i	$0.587423\pi$
$618$	78.1802	3.14487
$619$	−13.5251	−0.543620	−0.271810	−	0.962351i	$-0.587622\pi$
$619$	−13.5251	−0.543620	−0.271810	+	0.962351i	$0.587622\pi$
$620$	0	0
$621$	−3.44515	−0.138249
$622$	50.5614	2.02733
$623$	−18.9678	−0.759929
$624$	24.0740	0.963733
$625$	0	0
$626$	23.5762	0.942296
$627$	26.9776	1.07738
$628$	−43.9929	−1.75551
$629$	−7.30946	−0.291447
$630$	0	0
$631$	−15.4363	−0.614509	−0.307254	−	0.951627i	$-0.599410\pi$
$631$	−15.4363	−0.614509	−0.307254	+	0.951627i	$0.599410\pi$
$632$	−8.61571	−0.342714
$633$	21.7777	0.865587
$634$	19.9919	0.793981
$635$	0	0
$636$	−6.84147	−0.271282
$637$	13.5463	0.536723
$638$	−22.4502	−0.888810
$639$	−0.361259	−0.0142912
$640$	0	0
$641$	−24.7302	−0.976785	−0.488392	−	0.872624i	$-0.662416\pi$
$641$	−24.7302	−0.976785	−0.488392	+	0.872624i	$0.662416\pi$
$642$	−26.5566	−1.04810
$643$	21.7423	0.857431	0.428716	−	0.903440i	$-0.358966\pi$
$643$	21.7423	0.857431	0.428716	+	0.903440i	$0.358966\pi$
$644$	−4.20877	−0.165849
$645$	0	0
$646$	12.4108	0.488296
$647$	21.5657	0.847836	0.423918	−	0.905701i	$-0.360655\pi$
$647$	21.5657	0.847836	0.423918	+	0.905701i	$0.360655\pi$
$648$	53.5493	2.10361
$649$	6.30266	0.247401
$650$	0	0
$651$	28.3111	1.10960
$652$	−68.5471	−2.68451
$653$	−5.15466	−0.201718	−0.100859	−	0.994901i	$-0.532159\pi$
$653$	−5.15466	−0.201718	−0.100859	+	0.994901i	$0.532159\pi$
$654$	−57.6125	−2.25283
$655$	0	0
$656$	55.2055	2.15541
$657$	0.0677493	0.00264315
$658$	−3.47277	−0.135383
$659$	3.32417	0.129491	0.0647457	−	0.997902i	$-0.479376\pi$
$659$	3.32417	0.129491	0.0647457	+	0.997902i	$0.479376\pi$
$660$	0	0
$661$	44.8493	1.74444	0.872219	−	0.489116i	$-0.162681\pi$
$661$	44.8493	1.74444	0.872219	+	0.489116i	$0.162681\pi$
$662$	−16.0146	−0.622423
$663$	5.28255	0.205157
$664$	23.5324	0.913233
$665$	0	0
$666$	7.57657	0.293586
$667$	−2.14412	−0.0830206
$668$	65.1115	2.51924
$669$	0.106921	0.00413380
$670$	0	0
$671$	27.3275	1.05497
$672$	3.56716	0.137606
$673$	7.76034	0.299139	0.149570	−	0.988751i	$-0.452211\pi$
$673$	7.76034	0.299139	0.149570	+	0.988751i	$0.452211\pi$
$674$	70.5286	2.71666
$675$	0	0
$676$	−23.8045	−0.915559
$677$	4.97199	0.191089	0.0955446	−	0.995425i	$-0.469541\pi$
$677$	4.97199	0.191089	0.0955446	+	0.995425i	$0.469541\pi$
$678$	−82.2893	−3.16030
$679$	4.24259	0.162816
$680$	0	0
$681$	20.8150	0.797634
$682$	82.7277	3.16781
$683$	21.0449	0.805259	0.402630	−	0.915363i	$-0.368096\pi$
$683$	21.0449	0.805259	0.402630	+	0.915363i	$0.368096\pi$
$684$	−8.66983	−0.331499
$685$	0	0
$686$	41.7908	1.59558
$687$	−43.4748	−1.65867
$688$	56.1779	2.14176
$689$	−2.40022	−0.0914413
$690$	0	0
$691$	8.08445	0.307547	0.153773	−	0.988106i	$-0.450857\pi$
$691$	8.08445	0.307547	0.153773	+	0.988106i	$0.450857\pi$
$692$	−53.8544	−2.04724
$693$	1.90583	0.0723964
$694$	−38.8511	−1.47477
$695$	0	0
$696$	28.9577	1.09764
$697$	12.1137	0.458840
$698$	−37.7465	−1.42873
$699$	−2.30773	−0.0872862
$700$	0	0
$701$	38.0011	1.43528	0.717641	−	0.696414i	$-0.245222\pi$
$701$	38.0011	1.43528	0.717641	+	0.696414i	$0.245222\pi$
$702$	31.6235	1.19355
$703$	32.7247	1.23423
$704$	−19.1765	−0.722742
$705$	0	0
$706$	5.21168	0.196144
$707$	−11.6253	−0.437214
$708$	−15.7490	−0.591883
$709$	12.4496	0.467553	0.233777	−	0.972290i	$-0.424892\pi$
$709$	12.4496	0.467553	0.233777	+	0.972290i	$0.424892\pi$
$710$	0	0
$711$	0.721828	0.0270707
$712$	71.4917	2.67927
$713$	7.90096	0.295893
$714$	6.81712	0.255124
$715$	0	0
$716$	24.4874	0.915137
$717$	29.1212	1.08755
$718$	−19.2142	−0.717067
$719$	−37.7050	−1.40616	−0.703079	−	0.711112i	$-0.748192\pi$
$719$	−37.7050	−1.40616	−0.703079	+	0.711112i	$0.748192\pi$
$720$	0	0
$721$	23.8551	0.888409
$722$	−8.50664	−0.316584
$723$	−2.35795	−0.0876933
$724$	48.3518	1.79698
$725$	0	0
$726$	−7.24832	−0.269011
$727$	25.5939	0.949224	0.474612	−	0.880195i	$-0.342588\pi$
$727$	25.5939	0.949224	0.474612	+	0.880195i	$0.342588\pi$
$728$	19.9422	0.739105
$729$	21.9255	0.812054
$730$	0	0
$731$	12.3271	0.455933
$732$	−68.2856	−2.52391
$733$	−25.3158	−0.935062	−0.467531	−	0.883977i	$-0.654856\pi$
$733$	−25.3158	−0.935062	−0.467531	+	0.883977i	$0.654856\pi$
$734$	−64.3736	−2.37607
$735$	0	0
$736$	0.995512	0.0366951
$737$	−33.8716	−1.24768
$738$	−12.5564	−0.462207
$739$	45.2392	1.66415	0.832075	−	0.554664i	$-0.187153\pi$
$739$	45.2392	1.66415	0.832075	+	0.554664i	$0.187153\pi$
$740$	0	0
$741$	−23.6501	−0.868809
$742$	−3.09749	−0.113712
$743$	22.9116	0.840544	0.420272	−	0.907398i	$-0.361935\pi$
$743$	22.9116	0.840544	0.420272	+	0.907398i	$0.361935\pi$
$744$	−106.708	−3.91209
$745$	0	0
$746$	52.3718	1.91747
$747$	−1.97155	−0.0721353
$748$	13.4252	0.490873
$749$	−8.10319	−0.296084
$750$	0	0
$751$	−1.16437	−0.0424884	−0.0212442	−	0.999774i	$-0.506763\pi$
$751$	−1.16437	−0.0424884	−0.0212442	+	0.999774i	$0.506763\pi$
$752$	4.82143	0.175819
$753$	−55.2324	−2.01278
$754$	19.6812	0.716745
$755$	0	0
$756$	27.5037	1.00030
$757$	19.8664	0.722058	0.361029	−	0.932555i	$-0.382426\pi$
$757$	19.8664	0.722058	0.361029	+	0.932555i	$0.382426\pi$
$758$	−79.6068	−2.89145
$759$	4.13550	0.150109
$760$	0	0
$761$	31.2822	1.13398	0.566990	−	0.823725i	$-0.308108\pi$
$761$	31.2822	1.13398	0.566990	+	0.823725i	$0.308108\pi$
$762$	−56.0144	−2.02919
$763$	−17.5793	−0.636412
$764$	89.0305	3.22101
$765$	0	0
$766$	−14.7376	−0.532490
$767$	−5.52529	−0.199507
$768$	60.5192	2.18380
$769$	−7.57136	−0.273030	−0.136515	−	0.990638i	$-0.543590\pi$
$769$	−7.57136	−0.273030	−0.136515	+	0.990638i	$0.543590\pi$
$770$	0	0
$771$	37.1008	1.33615
$772$	−85.6730	−3.08344
$773$	27.3139	0.982413	0.491206	−	0.871043i	$-0.336556\pi$
$773$	27.3139	0.982413	0.491206	+	0.871043i	$0.336556\pi$
$774$	−12.7775	−0.459279
$775$	0	0
$776$	−15.9908	−0.574036
$777$	17.9753	0.644861
$778$	7.85280	0.281536
$779$	−54.2335	−1.94312
$780$	0	0
$781$	−2.50448	−0.0896173
$782$	1.90250	0.0680333
$783$	14.0115	0.500731
$784$	−24.2704	−0.866799
$785$	0	0
$786$	−66.3973	−2.36831
$787$	26.9158	0.959444	0.479722	−	0.877421i	$-0.340738\pi$
$787$	26.9158	0.959444	0.479722	+	0.877421i	$0.340738\pi$
$788$	23.3154	0.830576
$789$	35.2895	1.25634
$790$	0	0
$791$	−25.1089	−0.892769
$792$	−7.18327	−0.255247
$793$	−23.9570	−0.850737
$794$	38.7804	1.37626
$795$	0	0
$796$	31.4697	1.11542
$797$	46.4241	1.64442	0.822212	−	0.569181i	$-0.192740\pi$
$797$	46.4241	1.64442	0.822212	+	0.569181i	$0.192740\pi$
$798$	−30.5205	−1.08041
$799$	1.05796	0.0374280
$800$	0	0
$801$	−5.98961	−0.211632
$802$	38.2567	1.35089
$803$	0.469682	0.0165747
$804$	84.6378	2.98494
$805$	0	0
$806$	−72.5240	−2.55455
$807$	24.6968	0.869368
$808$	43.8170	1.54148
$809$	16.2963	0.572947	0.286474	−	0.958088i	$-0.407517\pi$
$809$	16.2963	0.572947	0.286474	+	0.958088i	$0.407517\pi$
$810$	0	0
$811$	−32.1329	−1.12834	−0.564170	−	0.825659i	$-0.690804\pi$
$811$	−32.1329	−1.12834	−0.564170	+	0.825659i	$0.690804\pi$
$812$	17.1172	0.600695
$813$	38.1720	1.33875
$814$	52.5257	1.84102
$815$	0	0
$816$	−9.46456	−0.331326
$817$	−55.1887	−1.93081
$818$	31.4170	1.09847
$819$	−1.67076	−0.0583812
$820$	0	0
$821$	32.7769	1.14392	0.571961	−	0.820281i	$-0.306183\pi$
$821$	32.7769	1.14392	0.571961	+	0.820281i	$0.306183\pi$
$822$	−44.0094	−1.53500
$823$	−20.0067	−0.697388	−0.348694	−	0.937237i	$-0.613375\pi$
$823$	−20.0067	−0.697388	−0.348694	+	0.937237i	$0.613375\pi$
$824$	−89.9124	−3.13225
$825$	0	0
$826$	−7.13038	−0.248098
$827$	−42.5465	−1.47949	−0.739743	−	0.672889i	$-0.765053\pi$
$827$	−42.5465	−1.47949	−0.739743	+	0.672889i	$0.765053\pi$
$828$	−1.32903	−0.0461871
$829$	24.3299	0.845011	0.422505	−	0.906360i	$-0.361151\pi$
$829$	24.3299	0.845011	0.422505	+	0.906360i	$0.361151\pi$
$830$	0	0
$831$	7.45335	0.258554
$832$	16.8113	0.582826
$833$	−5.32564	−0.184522
$834$	50.2206	1.73900
$835$	0	0
$836$	−60.1048	−2.07877
$837$	−51.6318	−1.78465
$838$	−64.8893	−2.24156
$839$	−33.0360	−1.14053	−0.570265	−	0.821461i	$-0.693159\pi$
$839$	−33.0360	−1.14053	−0.570265	+	0.821461i	$0.693159\pi$
$840$	0	0
$841$	−20.2798	−0.699304
$842$	75.6702	2.60777
$843$	9.36179	0.322437
$844$	−48.5198	−1.67012
$845$	0	0
$846$	−1.09662	−0.0377027
$847$	−2.21167	−0.0759940
$848$	4.30040	0.147676
$849$	−31.4133	−1.07810
$850$	0	0
$851$	5.01650	0.171963
$852$	6.25815	0.214401
$853$	−53.4749	−1.83095	−0.915473	−	0.402379i	$-0.868183\pi$
$853$	−53.4749	−1.83095	−0.915473	+	0.402379i	$0.868183\pi$
$854$	−30.9164	−1.05794
$855$	0	0
$856$	30.5418	1.04390
$857$	10.3887	0.354872	0.177436	−	0.984132i	$-0.443220\pi$
$857$	10.3887	0.354872	0.177436	+	0.984132i	$0.443220\pi$
$858$	−37.9603	−1.29594
$859$	−28.8659	−0.984891	−0.492445	−	0.870343i	$-0.663897\pi$
$859$	−28.8659	−0.984891	−0.492445	+	0.870343i	$0.663897\pi$
$860$	0	0
$861$	−29.7899	−1.01524
$862$	44.1623	1.50417
$863$	30.6732	1.04413	0.522063	−	0.852907i	$-0.325163\pi$
$863$	30.6732	1.04413	0.522063	+	0.852907i	$0.325163\pi$
$864$	−6.50554	−0.221323
$865$	0	0
$866$	55.8511	1.89790
$867$	29.4662	1.00073
$868$	−63.0758	−2.14093
$869$	5.00418	0.169755
$870$	0	0
$871$	29.6939	1.00614
$872$	66.2582	2.24378
$873$	1.33971	0.0453425
$874$	−8.51756	−0.288111
$875$	0	0
$876$	−1.17363	−0.0396534
$877$	−14.8895	−0.502781	−0.251391	−	0.967886i	$-0.580888\pi$
$877$	−14.8895	−0.502781	−0.251391	+	0.967886i	$0.580888\pi$
$878$	33.8065	1.14091
$879$	−47.3445	−1.59689
$880$	0	0
$881$	−27.5696	−0.928842	−0.464421	−	0.885615i	$-0.653738\pi$
$881$	−27.5696	−0.928842	−0.464421	+	0.885615i	$0.653738\pi$
$882$	5.52025	0.185876
$883$	−30.0505	−1.01128	−0.505640	−	0.862744i	$-0.668744\pi$
$883$	−30.0505	−1.01128	−0.505640	+	0.862744i	$0.668744\pi$
$884$	−11.7693	−0.395844
$885$	0	0
$886$	13.3935	0.449965
$887$	33.2673	1.11701	0.558503	−	0.829503i	$-0.311376\pi$
$887$	33.2673	1.11701	0.558503	+	0.829503i	$0.311376\pi$
$888$	−67.7510	−2.27357
$889$	−17.0916	−0.573234
$890$	0	0
$891$	−31.1025	−1.04197
$892$	−0.238215	−0.00797604
$893$	−4.73653	−0.158502
$894$	−33.6281	−1.12469
$895$	0	0
$896$	25.5399	0.853229
$897$	−3.62543	−0.121050
$898$	9.54808	0.318623
$899$	−32.1334	−1.07171
$900$	0	0
$901$	0.943634	0.0314370
$902$	−87.0490	−2.89842
$903$	−30.3146	−1.00881
$904$	94.6381	3.14762
$905$	0	0
$906$	−31.8798	−1.05913
$907$	19.4534	0.645939	0.322969	−	0.946409i	$-0.395319\pi$
$907$	19.4534	0.645939	0.322969	+	0.946409i	$0.395319\pi$
$908$	−46.3750	−1.53901
$909$	−3.67100	−0.121760
$910$	0	0
$911$	24.8070	0.821894	0.410947	−	0.911659i	$-0.365198\pi$
$911$	24.8070	0.821894	0.410947	+	0.911659i	$0.365198\pi$
$912$	42.3731	1.40311
$913$	−13.6681	−0.452347
$914$	−4.84202	−0.160160
$915$	0	0
$916$	96.8599	3.20034
$917$	−20.2598	−0.669036
$918$	−12.4326	−0.410337
$919$	43.3148	1.42882	0.714411	−	0.699726i	$-0.246695\pi$
$919$	43.3148	1.42882	0.714411	+	0.699726i	$0.246695\pi$
$920$	0	0
$921$	37.2318	1.22683
$922$	81.8689	2.69621
$923$	2.19558	0.0722683
$924$	−33.0150	−1.08611
$925$	0	0
$926$	−36.5637	−1.20156
$927$	7.53290	0.247413
$928$	−4.04877	−0.132908
$929$	9.73512	0.319399	0.159699	−	0.987166i	$-0.448948\pi$
$929$	9.73512	0.319399	0.159699	+	0.987166i	$0.448948\pi$
$930$	0	0
$931$	23.8430	0.781423
$932$	5.14151	0.168416
$933$	37.8796	1.24012
$934$	9.03476	0.295626
$935$	0	0
$936$	6.29729	0.205833
$937$	−43.5630	−1.42314	−0.711571	−	0.702614i	$-0.752016\pi$
$937$	−43.5630	−1.42314	−0.711571	+	0.702614i	$0.752016\pi$
$938$	38.3199	1.25119
$939$	17.6628	0.576404
$940$	0	0
$941$	−15.8644	−0.517165	−0.258582	−	0.965989i	$-0.583255\pi$
$941$	−15.8644	−0.517165	−0.258582	+	0.965989i	$0.583255\pi$
$942$	−48.9040	−1.59338
$943$	−8.31368	−0.270731
$944$	9.89947	0.322200
$945$	0	0
$946$	−88.5822	−2.88006
$947$	30.9741	1.00652	0.503261	−	0.864134i	$-0.332133\pi$
$947$	30.9741	1.00652	0.503261	+	0.864134i	$0.332133\pi$
$948$	−12.5044	−0.406122
$949$	−0.411751	−0.0133660
$950$	0	0
$951$	14.9775	0.485680
$952$	−7.84014	−0.254100
$953$	20.3290	0.658522	0.329261	−	0.944239i	$-0.393200\pi$
$953$	20.3290	0.658522	0.329261	+	0.944239i	$0.393200\pi$
$954$	−0.978117	−0.0316677
$955$	0	0
$956$	−64.8808	−2.09839
$957$	−16.8192	−0.543687
$958$	22.0555	0.712580
$959$	−13.4285	−0.433630
$960$	0	0
$961$	87.4100	2.81968
$962$	−46.0471	−1.48462
$963$	−2.55881	−0.0824563
$964$	5.25342	0.169201
$965$	0	0
$966$	−4.67861	−0.150532
$967$	−41.6758	−1.34020	−0.670101	−	0.742270i	$-0.733749\pi$
$967$	−41.6758	−1.34020	−0.670101	+	0.742270i	$0.733749\pi$
$968$	8.33605	0.267931
$969$	9.29791	0.298692
$970$	0	0
$971$	−4.19468	−0.134614	−0.0673068	−	0.997732i	$-0.521441\pi$
$971$	−4.19468	−0.134614	−0.0673068	+	0.997732i	$0.521441\pi$
$972$	18.8739	0.605382
$973$	15.3238	0.491258
$974$	−2.61115	−0.0836667
$975$	0	0
$976$	42.9228	1.37393
$977$	49.0170	1.56819	0.784096	−	0.620640i	$-0.213127\pi$
$977$	49.0170	1.56819	0.784096	+	0.620640i	$0.213127\pi$
$978$	−76.1993	−2.43658
$979$	−41.5238	−1.32711
$980$	0	0
$981$	−5.55114	−0.177234
$982$	−72.7951	−2.32298
$983$	24.5079	0.781680	0.390840	−	0.920459i	$-0.372185\pi$
$983$	24.5079	0.781680	0.390840	+	0.920459i	$0.372185\pi$
$984$	112.281	3.57940
$985$	0	0
$986$	−7.73753	−0.246413
$987$	−2.60173	−0.0828139
$988$	52.6915	1.67634
$989$	−8.46010	−0.269016
$990$	0	0
$991$	1.57065	0.0498935	0.0249467	−	0.999689i	$-0.492058\pi$
$991$	1.57065	0.0498935	0.0249467	+	0.999689i	$0.492058\pi$
$992$	14.9195	0.473695
$993$	−11.9978	−0.380738
$994$	2.83339	0.0898696
$995$	0	0
$996$	34.1535	1.08220
$997$	−17.8645	−0.565774	−0.282887	−	0.959153i	$-0.591292\pi$
$997$	−17.8645	−0.565774	−0.282887	+	0.959153i	$0.591292\pi$
$998$	22.4973	0.712140
$999$	−32.7822	−1.03718

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.i.1.2		11
5.2	odd	4		235.2.c.a.189.2	✓	22
5.3	odd	4		235.2.c.a.189.21	yes	22
5.4	even	2		1175.2.a.j.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.c.a.189.2	✓	22	5.2	odd	4
235.2.c.a.189.21	yes	22	5.3	odd	4
1175.2.a.i.1.2		11	1.1	even	1	trivial
1175.2.a.j.1.10		11	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47667 q^{2} -1.85547 q^{3} +4.13392 q^{4} +4.59540 q^{6} +1.40219 q^{7} -5.28501 q^{8} +0.442781 q^{9} +O(q^{10})\)	\(q-2.47667 q^{2} -1.85547 q^{3} +4.13392 q^{4} +4.59540 q^{6} +1.40219 q^{7} -5.28501 q^{8} +0.442781 q^{9} +3.06964 q^{11} -7.67037 q^{12} -2.69103 q^{13} -3.47277 q^{14} +4.82143 q^{16} +1.05796 q^{17} -1.09662 q^{18} -4.73653 q^{19} -2.60173 q^{21} -7.60250 q^{22} -0.726082 q^{23} +9.80620 q^{24} +6.66481 q^{26} +4.74485 q^{27} +5.79654 q^{28} +2.95300 q^{29} -10.8816 q^{31} -1.37107 q^{32} -5.69564 q^{33} -2.62023 q^{34} +1.83042 q^{36} -6.90900 q^{37} +11.7308 q^{38} +4.99314 q^{39} +11.4500 q^{41} +6.44363 q^{42} +11.6517 q^{43} +12.6896 q^{44} +1.79827 q^{46} +1.00000 q^{47} -8.94602 q^{48} -5.03386 q^{49} -1.96302 q^{51} -11.1245 q^{52} +0.891935 q^{53} -11.7515 q^{54} -7.41060 q^{56} +8.78850 q^{57} -7.31361 q^{58} +2.05322 q^{59} +8.90252 q^{61} +26.9503 q^{62} +0.620863 q^{63} -6.24715 q^{64} +14.1062 q^{66} -11.0344 q^{67} +4.37353 q^{68} +1.34723 q^{69} -0.815886 q^{71} -2.34010 q^{72} +0.153009 q^{73} +17.1113 q^{74} -19.5804 q^{76} +4.30423 q^{77} -12.3664 q^{78} +1.63022 q^{79} -10.1323 q^{81} -28.3580 q^{82} -4.45266 q^{83} -10.7553 q^{84} -28.8575 q^{86} -5.47921 q^{87} -16.2231 q^{88} -13.5273 q^{89} -3.77334 q^{91} -3.00156 q^{92} +20.1906 q^{93} -2.47667 q^{94} +2.54399 q^{96} +3.02569 q^{97} +12.4672 q^{98} +1.35918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9	\( 11 q - 4 q^{2} - 4 q^{3} + 10 q^{4} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 9 q^{9} - 12 q^{12} - 19 q^{13} + 12 q^{16} - 16 q^{17} + 10 q^{18} - 6 q^{21} - 22 q^{22} - 3 q^{23} - 12 q^{24} + 6 q^{26} - 16 q^{27} - 18 q^{28} + 4 q^{29} + 2 q^{31} - 28 q^{32} - 18 q^{33} - 16 q^{34} - 8 q^{36} - 40 q^{37} + 14 q^{38} - 10 q^{39} + 4 q^{41} - 16 q^{42} - 23 q^{43} + 24 q^{44} - 16 q^{46} + 11 q^{47} + 18 q^{48} + 5 q^{49} + 12 q^{51} - 46 q^{52} - 16 q^{53} + 26 q^{56} - 42 q^{57} - 16 q^{58} + 7 q^{59} - 7 q^{61} - 14 q^{63} + 24 q^{64} + 12 q^{66} - 32 q^{67} + 58 q^{68} - 2 q^{69} - 17 q^{71} - 57 q^{73} - 16 q^{74} - 10 q^{76} - 8 q^{77} + 22 q^{78} - 13 q^{79} - 25 q^{81} - 12 q^{82} - 8 q^{83} - 4 q^{84} - 6 q^{86} + 10 q^{87} - 26 q^{88} - 37 q^{89} + 32 q^{91} - 4 q^{92} + 10 q^{93} - 4 q^{94} - 6 q^{96} - 32 q^{97} + 20 q^{98} - 8 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 - 4 * q^3 + 10 * q^4 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 9 * q^9 - 12 * q^12 - 19 * q^13 + 12 * q^16 - 16 * q^17 + 10 * q^18 - 6 * q^21 - 22 * q^22 - 3 * q^23 - 12 * q^24 + 6 * q^26 - 16 * q^27 - 18 * q^28 + 4 * q^29 + 2 * q^31 - 28 * q^32 - 18 * q^33 - 16 * q^34 - 8 * q^36 - 40 * q^37 + 14 * q^38 - 10 * q^39 + 4 * q^41 - 16 * q^42 - 23 * q^43 + 24 * q^44 - 16 * q^46 + 11 * q^47 + 18 * q^48 + 5 * q^49 + 12 * q^51 - 46 * q^52 - 16 * q^53 + 26 * q^56 - 42 * q^57 - 16 * q^58 + 7 * q^59 - 7 * q^61 - 14 * q^63 + 24 * q^64 + 12 * q^66 - 32 * q^67 + 58 * q^68 - 2 * q^69 - 17 * q^71 - 57 * q^73 - 16 * q^74 - 10 * q^76 - 8 * q^77 + 22 * q^78 - 13 * q^79 - 25 * q^81 - 12 * q^82 - 8 * q^83 - 4 * q^84 - 6 * q^86 + 10 * q^87 - 26 * q^88 - 37 * q^89 + 32 * q^91 - 4 * q^92 + 10 * q^93 - 4 * q^94 - 6 * q^96 - 32 * q^97 + 20 * q^98 - 8 * q^99

Introduction

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