LMFDB - Embedded newform 7595.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
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} - 14x^{9} + 67x^{7} - 130x^{5} - 2x^{4} + 90x^{3} + 4x^{2} - 14x + 2 $ x^11 - 14x^9 + 67x^7 - 130x^5 - 2x^4 + 90x^3 + 4x^2 - 14*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.88741$ of defining polynomial
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88741 q^{2} -0.286056 q^{3} +1.56230 q^{4} +1.00000 q^{5} +0.539905 q^{6} +0.826115 q^{8} -2.91817 q^{9} +O(q^{10})$	\(q-1.88741 q^{2} -0.286056 q^{3} +1.56230 q^{4} +1.00000 q^{5} +0.539905 q^{6} +0.826115 q^{8} -2.91817 q^{9} -1.88741 q^{10} -2.22180 q^{11} -0.446906 q^{12} -0.483853 q^{13} -0.286056 q^{15} -4.68382 q^{16} +3.67006 q^{17} +5.50777 q^{18} -0.596602 q^{19} +1.56230 q^{20} +4.19345 q^{22} -3.14490 q^{23} -0.236316 q^{24} +1.00000 q^{25} +0.913226 q^{26} +1.69293 q^{27} +3.67812 q^{29} +0.539905 q^{30} -1.00000 q^{31} +7.18803 q^{32} +0.635562 q^{33} -6.92689 q^{34} -4.55906 q^{36} +3.13982 q^{37} +1.12603 q^{38} +0.138409 q^{39} +0.826115 q^{40} -8.10222 q^{41} +1.67103 q^{43} -3.47113 q^{44} -2.91817 q^{45} +5.93570 q^{46} -5.67943 q^{47} +1.33984 q^{48} -1.88741 q^{50} -1.04984 q^{51} -0.755924 q^{52} +6.68608 q^{53} -3.19525 q^{54} -2.22180 q^{55} +0.170662 q^{57} -6.94211 q^{58} -2.09427 q^{59} -0.446906 q^{60} +3.07032 q^{61} +1.88741 q^{62} -4.19910 q^{64} -0.483853 q^{65} -1.19956 q^{66} +2.59775 q^{67} +5.73374 q^{68} +0.899619 q^{69} +15.3455 q^{71} -2.41075 q^{72} +14.2465 q^{73} -5.92612 q^{74} -0.286056 q^{75} -0.932073 q^{76} -0.261234 q^{78} -2.92083 q^{79} -4.68382 q^{80} +8.27024 q^{81} +15.2922 q^{82} +6.42898 q^{83} +3.67006 q^{85} -3.15392 q^{86} -1.05215 q^{87} -1.83547 q^{88} +0.308587 q^{89} +5.50777 q^{90} -4.91328 q^{92} +0.286056 q^{93} +10.7194 q^{94} -0.596602 q^{95} -2.05618 q^{96} -9.93610 q^{97} +6.48361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9}+O(q^{10}) $ 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9	$ 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9} - 3 q^{11} + 16 q^{12} - 5 q^{13} - q^{15} - 15 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} - 10 q^{22} - 6 q^{23} - 16 q^{24} + 11 q^{25} + 14 q^{26} - 13 q^{27} - 15 q^{29} - 8 q^{30} - 11 q^{31} - 5 q^{33} - 16 q^{34} - 12 q^{36} - 24 q^{37} - 18 q^{38} - q^{39} - 30 q^{43} - 26 q^{44} - 2 q^{45} - 12 q^{46} - q^{47} + 4 q^{48} - 7 q^{51} - 14 q^{52} - 4 q^{53} + 2 q^{54} - 3 q^{55} - 30 q^{57} - 14 q^{58} - 2 q^{59} + 16 q^{60} + 10 q^{61} - 16 q^{64} - 5 q^{65} + 4 q^{66} + 8 q^{67} - 42 q^{68} + 24 q^{69} - 8 q^{71} - 34 q^{72} - 14 q^{73} + 24 q^{74} - q^{75} + 2 q^{76} + 2 q^{78} - 21 q^{79} + 3 q^{81} + 26 q^{82} + 12 q^{83} - 15 q^{85} - 40 q^{86} - 9 q^{87} - 4 q^{88} - 8 q^{89} - 4 q^{90} - 6 q^{92} + q^{93} + 24 q^{94} + 14 q^{95} + 28 q^{96} - 13 q^{97} - 26 q^{99}+O(q^{100}) $ 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9 - 3 * q^11 + 16 * q^12 - 5 * q^13 - q^15 - 15 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 - 10 * q^22 - 6 * q^23 - 16 * q^24 + 11 * q^25 + 14 * q^26 - 13 * q^27 - 15 * q^29 - 8 * q^30 - 11 * q^31 - 5 * q^33 - 16 * q^34 - 12 * q^36 - 24 * q^37 - 18 * q^38 - q^39 - 30 * q^43 - 26 * q^44 - 2 * q^45 - 12 * q^46 - q^47 + 4 * q^48 - 7 * q^51 - 14 * q^52 - 4 * q^53 + 2 * q^54 - 3 * q^55 - 30 * q^57 - 14 * q^58 - 2 * q^59 + 16 * q^60 + 10 * q^61 - 16 * q^64 - 5 * q^65 + 4 * q^66 + 8 * q^67 - 42 * q^68 + 24 * q^69 - 8 * q^71 - 34 * q^72 - 14 * q^73 + 24 * q^74 - q^75 + 2 * q^76 + 2 * q^78 - 21 * q^79 + 3 * q^81 + 26 * q^82 + 12 * q^83 - 15 * q^85 - 40 * q^86 - 9 * q^87 - 4 * q^88 - 8 * q^89 - 4 * q^90 - 6 * q^92 + q^93 + 24 * q^94 + 14 * q^95 + 28 * q^96 - 13 * q^97 - 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.88741	−1.33460	−0.667299	−	0.744790i	$-0.732550\pi$
$2$	−1.88741	−1.33460	−0.667299	+	0.744790i	$0.732550\pi$
$3$	−0.286056	−0.165155	−0.0825774	−	0.996585i	$-0.526315\pi$
$3$	−0.286056	−0.165155	−0.0825774	+	0.996585i	$0.526315\pi$
$4$	1.56230	0.781151
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.539905	0.220415
$7$	0	0
$7$	0	0
$8$	0.826115	0.292076
$9$	−2.91817	−0.972724
$10$	−1.88741	−0.596850
$11$	−2.22180	−0.669899	−0.334950	−	0.942236i	$-0.608719\pi$
$11$	−2.22180	−0.669899	−0.334950	+	0.942236i	$0.608719\pi$
$12$	−0.446906	−0.129011
$13$	−0.483853	−0.134197	−0.0670983	−	0.997746i	$-0.521374\pi$
$13$	−0.483853	−0.134197	−0.0670983	+	0.997746i	$0.521374\pi$
$14$	0	0
$15$	−0.286056	−0.0738595
$16$	−4.68382	−1.17095
$17$	3.67006	0.890120	0.445060	−	0.895501i	$-0.353182\pi$
$17$	3.67006	0.890120	0.445060	+	0.895501i	$0.353182\pi$
$18$	5.50777	1.29819
$19$	−0.596602	−0.136870	−0.0684350	−	0.997656i	$-0.521801\pi$
$19$	−0.596602	−0.136870	−0.0684350	+	0.997656i	$0.521801\pi$
$20$	1.56230	0.349341
$21$	0	0
$22$	4.19345	0.894046
$23$	−3.14490	−0.655757	−0.327878	−	0.944720i	$-0.606334\pi$
$23$	−3.14490	−0.655757	−0.327878	+	0.944720i	$0.606334\pi$
$24$	−0.236316	−0.0482377
$25$	1.00000	0.200000
$26$	0.913226	0.179098
$27$	1.69293	0.325805
$28$	0	0
$29$	3.67812	0.683010	0.341505	−	0.939880i	$-0.389063\pi$
$29$	3.67812	0.683010	0.341505	+	0.939880i	$0.389063\pi$
$30$	0.539905	0.0985726
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	7.18803	1.27068
$33$	0.635562	0.110637
$34$	−6.92689	−1.18795
$35$	0	0
$36$	−4.55906	−0.759844
$37$	3.13982	0.516184	0.258092	−	0.966120i	$-0.416906\pi$
$37$	3.13982	0.516184	0.258092	+	0.966120i	$0.416906\pi$
$38$	1.12603	0.182666
$39$	0.138409	0.0221632
$40$	0.826115	0.130620
$41$	−8.10222	−1.26535	−0.632677	−	0.774416i	$-0.718044\pi$
$41$	−8.10222	−1.26535	−0.632677	+	0.774416i	$0.718044\pi$
$42$	0	0
$43$	1.67103	0.254830	0.127415	−	0.991849i	$-0.459332\pi$
$43$	1.67103	0.254830	0.127415	+	0.991849i	$0.459332\pi$
$44$	−3.47113	−0.523292
$45$	−2.91817	−0.435015
$46$	5.93570	0.875171
$47$	−5.67943	−0.828430	−0.414215	−	0.910179i	$-0.635944\pi$
$47$	−5.67943	−0.828430	−0.414215	+	0.910179i	$0.635944\pi$
$48$	1.33984	0.193389
$49$	0	0
$50$	−1.88741	−0.266920
$51$	−1.04984	−0.147008
$52$	−0.755924	−0.104828
$53$	6.68608	0.918403	0.459202	−	0.888332i	$-0.348136\pi$
$53$	6.68608	0.918403	0.459202	+	0.888332i	$0.348136\pi$
$54$	−3.19525	−0.434818
$55$	−2.22180	−0.299588
$56$	0	0
$57$	0.170662	0.0226047
$58$	−6.94211	−0.911544
$59$	−2.09427	−0.272651	−0.136325	−	0.990664i	$-0.543529\pi$
$59$	−2.09427	−0.272651	−0.136325	+	0.990664i	$0.543529\pi$
$60$	−0.446906	−0.0576954
$61$	3.07032	0.393114	0.196557	−	0.980492i	$-0.437024\pi$
$61$	3.07032	0.393114	0.196557	+	0.980492i	$0.437024\pi$
$62$	1.88741	0.239701
$63$	0	0
$64$	−4.19910	−0.524888
$65$	−0.483853	−0.0600145
$66$	−1.19956	−0.147656
$67$	2.59775	0.317366	0.158683	−	0.987330i	$-0.449275\pi$
$67$	2.59775	0.317366	0.158683	+	0.987330i	$0.449275\pi$
$68$	5.73374	0.695318
$69$	0.899619	0.108301
$70$	0	0
$71$	15.3455	1.82117	0.910586	−	0.413320i	$-0.135631\pi$
$71$	15.3455	1.82117	0.910586	+	0.413320i	$0.135631\pi$
$72$	−2.41075	−0.284109
$73$	14.2465	1.66742	0.833711	−	0.552202i	$-0.186212\pi$
$73$	14.2465	1.66742	0.833711	+	0.552202i	$0.186212\pi$
$74$	−5.92612	−0.688897
$75$	−0.286056	−0.0330310
$76$	−0.932073	−0.106916
$77$	0	0
$78$	−0.261234	−0.0295790
$79$	−2.92083	−0.328619	−0.164310	−	0.986409i	$-0.552540\pi$
$79$	−2.92083	−0.328619	−0.164310	+	0.986409i	$0.552540\pi$
$80$	−4.68382	−0.523667
$81$	8.27024	0.918916
$82$	15.2922	1.68874
$83$	6.42898	0.705672	0.352836	−	0.935685i	$-0.385217\pi$
$83$	6.42898	0.705672	0.352836	+	0.935685i	$0.385217\pi$
$84$	0	0
$85$	3.67006	0.398074
$86$	−3.15392	−0.340095
$87$	−1.05215	−0.112802
$88$	−1.83547	−0.195661
$89$	0.308587	0.0327102	0.0163551	−	0.999866i	$-0.494794\pi$
$89$	0.308587	0.0327102	0.0163551	+	0.999866i	$0.494794\pi$
$90$	5.50777	0.580570
$91$	0	0
$92$	−4.91328	−0.512245
$93$	0.286056	0.0296627
$94$	10.7194	1.10562
$95$	−0.596602	−0.0612101
$96$	−2.05618	−0.209858
$97$	−9.93610	−1.00886	−0.504429	−	0.863453i	$-0.668297\pi$
$97$	−9.93610	−1.00886	−0.504429	+	0.863453i	$0.668297\pi$
$98$	0	0
$99$	6.48361	0.651627
$100$	1.56230	0.156230
$101$	−11.7046	−1.16465	−0.582327	−	0.812954i	$-0.697858\pi$
$101$	−11.7046	−1.16465	−0.582327	+	0.812954i	$0.697858\pi$
$102$	1.98148	0.196196
$103$	−3.37034	−0.332090	−0.166045	−	0.986118i	$-0.553100\pi$
$103$	−3.37034	−0.332090	−0.166045	+	0.986118i	$0.553100\pi$
$104$	−0.399718	−0.0391956
$105$	0	0
$106$	−12.6193	−1.22570
$107$	−1.26646	−0.122434	−0.0612168	−	0.998124i	$-0.519498\pi$
$107$	−1.26646	−0.122434	−0.0612168	+	0.998124i	$0.519498\pi$
$108$	2.64487	0.254503
$109$	−14.6313	−1.40143	−0.700714	−	0.713442i	$-0.747135\pi$
$109$	−14.6313	−1.40143	−0.700714	+	0.713442i	$0.747135\pi$
$110$	4.19345	0.399830
$111$	−0.898166	−0.0852502
$112$	0	0
$113$	−5.98361	−0.562891	−0.281445	−	0.959577i	$-0.590814\pi$
$113$	−5.98361	−0.562891	−0.281445	+	0.959577i	$0.590814\pi$
$114$	−0.322108	−0.0301682
$115$	−3.14490	−0.293263
$116$	5.74634	0.533534
$117$	1.41197	0.130536
$118$	3.95274	0.363879
$119$	0	0
$120$	−0.236316	−0.0215726
$121$	−6.06358	−0.551235
$122$	−5.79493	−0.524649
$123$	2.31769	0.208979
$124$	−1.56230	−0.140299
$125$	1.00000	0.0894427
$126$	0	0
$127$	4.40812	0.391158	0.195579	−	0.980688i	$-0.437341\pi$
$127$	4.40812	0.391158	0.195579	+	0.980688i	$0.437341\pi$
$128$	−6.45066	−0.570163
$129$	−0.478009	−0.0420864
$130$	0.913226	0.0800953
$131$	5.20809	0.455033	0.227517	−	0.973774i	$-0.426939\pi$
$131$	5.20809	0.455033	0.227517	+	0.973774i	$0.426939\pi$
$132$	0.992939	0.0864242
$133$	0	0
$134$	−4.90302	−0.423556
$135$	1.69293	0.145704
$136$	3.03189	0.259983
$137$	−10.3304	−0.882582	−0.441291	−	0.897364i	$-0.645479\pi$
$137$	−10.3304	−0.882582	−0.441291	+	0.897364i	$0.645479\pi$
$138$	−1.69795	−0.144539
$139$	20.3012	1.72193	0.860963	−	0.508668i	$-0.169862\pi$
$139$	20.3012	1.72193	0.860963	+	0.508668i	$0.169862\pi$
$140$	0	0
$141$	1.62464	0.136819
$142$	−28.9631	−2.43053
$143$	1.07503	0.0898982
$144$	13.6682	1.13902
$145$	3.67812	0.305452
$146$	−26.8888	−2.22534
$147$	0	0
$148$	4.90535	0.403217
$149$	−5.05369	−0.414015	−0.207007	−	0.978339i	$-0.566372\pi$
$149$	−5.05369	−0.414015	−0.207007	+	0.978339i	$0.566372\pi$
$150$	0.539905	0.0440830
$151$	6.43053	0.523309	0.261654	−	0.965162i	$-0.415732\pi$
$151$	6.43053	0.523309	0.261654	+	0.965162i	$0.415732\pi$
$152$	−0.492863	−0.0399764
$153$	−10.7099	−0.865841
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	0.216237	0.0173128
$157$	−12.2140	−0.974784	−0.487392	−	0.873183i	$-0.662052\pi$
$157$	−12.2140	−0.974784	−0.487392	+	0.873183i	$0.662052\pi$
$158$	5.51280	0.438575
$159$	−1.91260	−0.151679
$160$	7.18803	0.568264
$161$	0	0
$162$	−15.6093	−1.22638
$163$	−10.5288	−0.824681	−0.412341	−	0.911030i	$-0.635289\pi$
$163$	−10.5288	−0.824681	−0.412341	+	0.911030i	$0.635289\pi$
$164$	−12.6581	−0.988432
$165$	0.635562	0.0494784
$166$	−12.1341	−0.941789
$167$	−11.1346	−0.861618	−0.430809	−	0.902443i	$-0.641772\pi$
$167$	−11.1346	−0.861618	−0.430809	+	0.902443i	$0.641772\pi$
$168$	0	0
$169$	−12.7659	−0.981991
$170$	−6.92689	−0.531268
$171$	1.74099	0.133137
$172$	2.61065	0.199061
$173$	−22.1675	−1.68536	−0.842681	−	0.538414i	$-0.819024\pi$
$173$	−22.1675	−1.68536	−0.842681	+	0.538414i	$0.819024\pi$
$174$	1.98584	0.150546
$175$	0	0
$176$	10.4065	0.784422
$177$	0.599079	0.0450296
$178$	−0.582429	−0.0436549
$179$	23.4363	1.75171	0.875855	−	0.482575i	$-0.160298\pi$
$179$	23.4363	1.75171	0.875855	+	0.482575i	$0.160298\pi$
$180$	−4.55906	−0.339812
$181$	−7.13929	−0.530659	−0.265330	−	0.964158i	$-0.585481\pi$
$181$	−7.13929	−0.530659	−0.265330	+	0.964158i	$0.585481\pi$
$182$	0	0
$183$	−0.878284	−0.0649246
$184$	−2.59805	−0.191531
$185$	3.13982	0.230844
$186$	−0.539905	−0.0395877
$187$	−8.15415	−0.596291
$188$	−8.87298	−0.647129
$189$	0	0
$190$	1.12603	0.0816909
$191$	−9.86064	−0.713491	−0.356745	−	0.934202i	$-0.616114\pi$
$191$	−9.86064	−0.713491	−0.356745	+	0.934202i	$0.616114\pi$
$192$	1.20118	0.0866877
$193$	−4.11702	−0.296349	−0.148175	−	0.988961i	$-0.547340\pi$
$193$	−4.11702	−0.296349	−0.148175	+	0.988961i	$0.547340\pi$
$194$	18.7535	1.34642
$195$	0.138409	0.00991169
$196$	0	0
$197$	9.01587	0.642354	0.321177	−	0.947019i	$-0.395922\pi$
$197$	9.01587	0.642354	0.321177	+	0.947019i	$0.395922\pi$
$198$	−12.2372	−0.869660
$199$	19.8115	1.40440	0.702201	−	0.711979i	$-0.252201\pi$
$199$	19.8115	1.40440	0.702201	+	0.711979i	$0.252201\pi$
$200$	0.826115	0.0584152
$201$	−0.743104	−0.0524145
$202$	22.0914	1.55434
$203$	0	0
$204$	−1.64017	−0.114835
$205$	−8.10222	−0.565884
$206$	6.36120	0.443206
$207$	9.17736	0.637870
$208$	2.26628	0.157138
$209$	1.32553	0.0916891
$210$	0	0
$211$	−3.90745	−0.269000	−0.134500	−	0.990914i	$-0.542943\pi$
$211$	−3.90745	−0.269000	−0.134500	+	0.990914i	$0.542943\pi$
$212$	10.4457	0.717411
$213$	−4.38967	−0.300775
$214$	2.39033	0.163399
$215$	1.67103	0.113963
$216$	1.39856	0.0951597
$217$	0	0
$218$	27.6153	1.87034
$219$	−4.07529	−0.275383
$220$	−3.47113	−0.234023
$221$	−1.77577	−0.119451
$222$	1.69520	0.113775
$223$	11.8706	0.794915	0.397458	−	0.917621i	$-0.369893\pi$
$223$	11.8706	0.794915	0.397458	+	0.917621i	$0.369893\pi$
$224$	0	0
$225$	−2.91817	−0.194545
$226$	11.2935	0.751233
$227$	12.9406	0.858897	0.429449	−	0.903091i	$-0.358708\pi$
$227$	12.9406	0.858897	0.429449	+	0.903091i	$0.358708\pi$
$228$	0.266625	0.0176577
$229$	−13.4238	−0.887072	−0.443536	−	0.896257i	$-0.646276\pi$
$229$	−13.4238	−0.887072	−0.443536	+	0.896257i	$0.646276\pi$
$230$	5.93570	0.391389
$231$	0	0
$232$	3.03855	0.199491
$233$	−12.8090	−0.839142	−0.419571	−	0.907722i	$-0.637820\pi$
$233$	−12.8090	−0.839142	−0.419571	+	0.907722i	$0.637820\pi$
$234$	−2.66495	−0.174213
$235$	−5.67943	−0.370485
$236$	−3.27188	−0.212981
$237$	0.835523	0.0542731
$238$	0	0
$239$	−14.3148	−0.925949	−0.462975	−	0.886372i	$-0.653218\pi$
$239$	−14.3148	−0.925949	−0.462975	+	0.886372i	$0.653218\pi$
$240$	1.33984	0.0864860
$241$	10.5921	0.682298	0.341149	−	0.940009i	$-0.389184\pi$
$241$	10.5921	0.682298	0.341149	+	0.940009i	$0.389184\pi$
$242$	11.4444	0.735677
$243$	−7.44455	−0.477568
$244$	4.79676	0.307081
$245$	0	0
$246$	−4.37443	−0.278903
$247$	0.288668	0.0183675
$248$	−0.826115	−0.0524584
$249$	−1.83905	−0.116545
$250$	−1.88741	−0.119370
$251$	7.24753	0.457460	0.228730	−	0.973490i	$-0.426543\pi$
$251$	7.24753	0.457460	0.228730	+	0.973490i	$0.426543\pi$
$252$	0	0
$253$	6.98735	0.439291
$254$	−8.31992	−0.522038
$255$	−1.04984	−0.0657438
$256$	20.5732	1.28583
$257$	29.1017	1.81532	0.907658	−	0.419710i	$-0.137868\pi$
$257$	29.1017	1.81532	0.907658	+	0.419710i	$0.137868\pi$
$258$	0.902198	0.0561684
$259$	0	0
$260$	−0.755924	−0.0468804
$261$	−10.7334	−0.664381
$262$	−9.82978	−0.607286
$263$	4.27174	0.263407	0.131703	−	0.991289i	$-0.457955\pi$
$263$	4.27174	0.263407	0.131703	+	0.991289i	$0.457955\pi$
$264$	0.525047	0.0323144
$265$	6.68608	0.410723
$266$	0	0
$267$	−0.0882734	−0.00540224
$268$	4.05848	0.247911
$269$	−0.111018	−0.00676886	−0.00338443	−	0.999994i	$-0.501077\pi$
$269$	−0.111018	−0.00676886	−0.00338443	+	0.999994i	$0.501077\pi$
$270$	−3.19525	−0.194457
$271$	3.39000	0.205928	0.102964	−	0.994685i	$-0.467167\pi$
$271$	3.39000	0.205928	0.102964	+	0.994685i	$0.467167\pi$
$272$	−17.1899	−1.04229
$273$	0	0
$274$	19.4976	1.17789
$275$	−2.22180	−0.133980
$276$	1.40548	0.0845997
$277$	−1.90397	−0.114398	−0.0571992	−	0.998363i	$-0.518217\pi$
$277$	−1.90397	−0.114398	−0.0571992	+	0.998363i	$0.518217\pi$
$278$	−38.3166	−2.29808
$279$	2.91817	0.174706
$280$	0	0
$281$	−14.6491	−0.873891	−0.436946	−	0.899488i	$-0.643940\pi$
$281$	−14.6491	−0.873891	−0.436946	+	0.899488i	$0.643940\pi$
$282$	−3.06635	−0.182599
$283$	−17.6440	−1.04883	−0.524415	−	0.851463i	$-0.675716\pi$
$283$	−17.6440	−1.04883	−0.524415	+	0.851463i	$0.675716\pi$
$284$	23.9742	1.42261
$285$	0.170662	0.0101091
$286$	−2.02901	−0.119978
$287$	0	0
$288$	−20.9759	−1.23602
$289$	−3.53067	−0.207687
$290$	−6.94211	−0.407655
$291$	2.84229	0.166618
$292$	22.2572	1.30251
$293$	9.75563	0.569930	0.284965	−	0.958538i	$-0.408018\pi$
$293$	9.75563	0.569930	0.284965	+	0.958538i	$0.408018\pi$
$294$	0	0
$295$	−2.09427	−0.121933
$296$	2.59386	0.150765
$297$	−3.76136	−0.218256
$298$	9.53837	0.552543
$299$	1.52167	0.0880003
$300$	−0.446906	−0.0258021
$301$	0	0
$302$	−12.1370	−0.698407
$303$	3.34819	0.192348
$304$	2.79438	0.160269
$305$	3.07032	0.175806
$306$	20.2139	1.15555
$307$	−8.68459	−0.495656	−0.247828	−	0.968804i	$-0.579717\pi$
$307$	−8.68459	−0.495656	−0.247828	+	0.968804i	$0.579717\pi$
$308$	0	0
$309$	0.964108	0.0548462
$310$	1.88741	0.107197
$311$	−13.9804	−0.792757	−0.396379	−	0.918087i	$-0.629733\pi$
$311$	−13.9804	−0.792757	−0.396379	+	0.918087i	$0.629733\pi$
$312$	0.114342	0.00647334
$313$	−28.4753	−1.60952	−0.804759	−	0.593602i	$-0.797705\pi$
$313$	−28.4753	−1.60952	−0.804759	+	0.593602i	$0.797705\pi$
$314$	23.0528	1.30094
$315$	0	0
$316$	−4.56322	−0.256701
$317$	−4.57460	−0.256935	−0.128468	−	0.991714i	$-0.541006\pi$
$317$	−4.57460	−0.256935	−0.128468	+	0.991714i	$0.541006\pi$
$318$	3.60984	0.202430
$319$	−8.17207	−0.457548
$320$	−4.19910	−0.234737
$321$	0.362280	0.0202205
$322$	0	0
$323$	−2.18957	−0.121831
$324$	12.9206	0.717812
$325$	−0.483853	−0.0268393
$326$	19.8722	1.10062
$327$	4.18539	0.231452
$328$	−6.69337	−0.369579
$329$	0	0
$330$	−1.19956	−0.0660338
$331$	6.18943	0.340202	0.170101	−	0.985427i	$-0.445591\pi$
$331$	6.18943	0.340202	0.170101	+	0.985427i	$0.445591\pi$
$332$	10.0440	0.551236
$333$	−9.16254	−0.502104
$334$	21.0154	1.14991
$335$	2.59775	0.141931
$336$	0	0
$337$	5.38400	0.293285	0.146643	−	0.989190i	$-0.453153\pi$
$337$	5.38400	0.293285	0.146643	+	0.989190i	$0.453153\pi$
$338$	24.0944	1.31056
$339$	1.71165	0.0929641
$340$	5.73374	0.310955
$341$	2.22180	0.120317
$342$	−3.28595	−0.177684
$343$	0	0
$344$	1.38046	0.0744297
$345$	0.899619	0.0484338
$346$	41.8390	2.24928
$347$	9.90790	0.531884	0.265942	−	0.963989i	$-0.414317\pi$
$347$	9.90790	0.531884	0.265942	+	0.963989i	$0.414317\pi$
$348$	−1.64378	−0.0881157
$349$	29.0616	1.55563	0.777817	−	0.628491i	$-0.216327\pi$
$349$	29.0616	1.55563	0.777817	+	0.628491i	$0.216327\pi$
$350$	0	0
$351$	−0.819129	−0.0437219
$352$	−15.9704	−0.851226
$353$	−2.15591	−0.114748	−0.0573738	−	0.998353i	$-0.518273\pi$
$353$	−2.15591	−0.114748	−0.0573738	+	0.998353i	$0.518273\pi$
$354$	−1.13071	−0.0600964
$355$	15.3455	0.814453
$356$	0.482106	0.0255516
$357$	0	0
$358$	−44.2338	−2.33783
$359$	27.7029	1.46210	0.731051	−	0.682323i	$-0.239030\pi$
$359$	27.7029	1.46210	0.731051	+	0.682323i	$0.239030\pi$
$360$	−2.41075	−0.127058
$361$	−18.6441	−0.981267
$362$	13.4747	0.708217
$363$	1.73453	0.0910391
$364$	0	0
$365$	14.2465	0.745693
$366$	1.65768	0.0866482
$367$	−21.7052	−1.13300	−0.566501	−	0.824061i	$-0.691703\pi$
$367$	−21.7052	−1.13300	−0.566501	+	0.824061i	$0.691703\pi$
$368$	14.7301	0.767861
$369$	23.6437	1.23084
$370$	−5.92612	−0.308084
$371$	0	0
$372$	0.446906	0.0231710
$373$	−2.47263	−0.128028	−0.0640141	−	0.997949i	$-0.520390\pi$
$373$	−2.47263	−0.128028	−0.0640141	+	0.997949i	$0.520390\pi$
$374$	15.3902	0.795808
$375$	−0.286056	−0.0147719
$376$	−4.69186	−0.241964
$377$	−1.77967	−0.0916577
$378$	0	0
$379$	−13.9538	−0.716761	−0.358380	−	0.933576i	$-0.616671\pi$
$379$	−13.9538	−0.716761	−0.358380	+	0.933576i	$0.616671\pi$
$380$	−0.932073	−0.0478143
$381$	−1.26097	−0.0646015
$382$	18.6110	0.952223
$383$	−25.5448	−1.30528	−0.652640	−	0.757668i	$-0.726339\pi$
$383$	−25.5448	−1.30528	−0.652640	+	0.757668i	$0.726339\pi$
$384$	1.84525	0.0941651
$385$	0	0
$386$	7.77048	0.395507
$387$	−4.87636	−0.247879
$388$	−15.5232	−0.788070
$389$	18.3689	0.931341	0.465670	−	0.884958i	$-0.345813\pi$
$389$	18.3689	0.931341	0.465670	+	0.884958i	$0.345813\pi$
$390$	−0.261234	−0.0132281
$391$	−11.5420	−0.583702
$392$	0	0
$393$	−1.48981	−0.0751509
$394$	−17.0166	−0.857284
$395$	−2.92083	−0.146963
$396$	10.1293	0.509019
$397$	14.1743	0.711388	0.355694	−	0.934602i	$-0.384244\pi$
$397$	14.1743	0.711388	0.355694	+	0.934602i	$0.384244\pi$
$398$	−37.3924	−1.87431
$399$	0	0
$400$	−4.68382	−0.234191
$401$	−0.987243	−0.0493005	−0.0246503	−	0.999696i	$-0.507847\pi$
$401$	−0.987243	−0.0493005	−0.0246503	+	0.999696i	$0.507847\pi$
$402$	1.40254	0.0699523
$403$	0.483853	0.0241024
$404$	−18.2862	−0.909770
$405$	8.27024	0.410952
$406$	0	0
$407$	−6.97607	−0.345791
$408$	−0.867292	−0.0429374
$409$	20.1658	0.997137	0.498568	−	0.866850i	$-0.333859\pi$
$409$	20.1658	0.997137	0.498568	+	0.866850i	$0.333859\pi$
$410$	15.2922	0.755227
$411$	2.95507	0.145763
$412$	−5.26549	−0.259412
$413$	0	0
$414$	−17.3214	−0.851300
$415$	6.42898	0.315586
$416$	−3.47795	−0.170521
$417$	−5.80729	−0.284384
$418$	−2.50182	−0.122368
$419$	26.9311	1.31567	0.657835	−	0.753162i	$-0.271472\pi$
$419$	26.9311	1.31567	0.657835	+	0.753162i	$0.271472\pi$
$420$	0	0
$421$	−18.0489	−0.879652	−0.439826	−	0.898083i	$-0.644960\pi$
$421$	−18.0489	−0.879652	−0.439826	+	0.898083i	$0.644960\pi$
$422$	7.37494	0.359006
$423$	16.5736	0.805834
$424$	5.52347	0.268244
$425$	3.67006	0.178024
$426$	8.28509	0.401414
$427$	0	0
$428$	−1.97860	−0.0956390
$429$	−0.307518	−0.0148471
$430$	−3.15392	−0.152095
$431$	−6.74014	−0.324661	−0.162331	−	0.986736i	$-0.551901\pi$
$431$	−6.74014	−0.324661	−0.162331	+	0.986736i	$0.551901\pi$
$432$	−7.92938	−0.381502
$433$	−28.0389	−1.34746	−0.673732	−	0.738975i	$-0.735310\pi$
$433$	−28.0389	−1.34746	−0.673732	+	0.738975i	$0.735310\pi$
$434$	0	0
$435$	−1.05215	−0.0504468
$436$	−22.8586	−1.09473
$437$	1.87625	0.0897534
$438$	7.69172	0.367525
$439$	16.2526	0.775694	0.387847	−	0.921724i	$-0.373219\pi$
$439$	16.2526	0.775694	0.387847	+	0.921724i	$0.373219\pi$
$440$	−1.83547	−0.0875025
$441$	0	0
$442$	3.35159	0.159419
$443$	−25.1500	−1.19491	−0.597456	−	0.801902i	$-0.703822\pi$
$443$	−25.1500	−1.19491	−0.597456	+	0.801902i	$0.703822\pi$
$444$	−1.40321	−0.0665932
$445$	0.308587	0.0146284
$446$	−22.4047	−1.06089
$447$	1.44564	0.0683765
$448$	0	0
$449$	16.1945	0.764264	0.382132	−	0.924108i	$-0.375190\pi$
$449$	16.1945	0.764264	0.382132	+	0.924108i	$0.375190\pi$
$450$	5.50777	0.259639
$451$	18.0016	0.847660
$452$	−9.34820	−0.439703
$453$	−1.83949	−0.0864270
$454$	−24.4241	−1.14628
$455$	0	0
$456$	0.140986	0.00660230
$457$	16.0110	0.748963	0.374481	−	0.927234i	$-0.377821\pi$
$457$	16.0110	0.748963	0.374481	+	0.927234i	$0.377821\pi$
$458$	25.3362	1.18388
$459$	6.21316	0.290005
$460$	−4.91328	−0.229083
$461$	7.06703	0.329144	0.164572	−	0.986365i	$-0.447376\pi$
$461$	7.06703	0.329144	0.164572	+	0.986365i	$0.447376\pi$
$462$	0	0
$463$	−42.1162	−1.95730	−0.978652	−	0.205522i	$-0.934111\pi$
$463$	−42.1162	−1.95730	−0.978652	+	0.205522i	$0.934111\pi$
$464$	−17.2277	−0.799774
$465$	0.286056	0.0132655
$466$	24.1757	1.11992
$467$	7.54135	0.348972	0.174486	−	0.984660i	$-0.444174\pi$
$467$	7.54135	0.348972	0.174486	+	0.984660i	$0.444174\pi$
$468$	2.20591	0.101968
$469$	0	0
$470$	10.7194	0.494449
$471$	3.49390	0.160990
$472$	−1.73011	−0.0796347
$473$	−3.71271	−0.170710
$474$	−1.57697	−0.0724327
$475$	−0.596602	−0.0273740
$476$	0	0
$477$	−19.5111	−0.893353
$478$	27.0179	1.23577
$479$	2.62640	0.120003	0.0600016	−	0.998198i	$-0.480889\pi$
$479$	2.62640	0.120003	0.0600016	+	0.998198i	$0.480889\pi$
$480$	−2.05618	−0.0938515
$481$	−1.51921	−0.0692701
$482$	−19.9916	−0.910594
$483$	0	0
$484$	−9.47314	−0.430597
$485$	−9.93610	−0.451175
$486$	14.0509	0.637361
$487$	−9.44038	−0.427784	−0.213892	−	0.976857i	$-0.568614\pi$
$487$	−9.44038	−0.427784	−0.213892	+	0.976857i	$0.568614\pi$
$488$	2.53644	0.114819
$489$	3.01184	0.136200
$490$	0	0
$491$	−10.0566	−0.453850	−0.226925	−	0.973912i	$-0.572867\pi$
$491$	−10.0566	−0.453850	−0.226925	+	0.973912i	$0.572867\pi$
$492$	3.62093	0.163244
$493$	13.4989	0.607961
$494$	−0.544833	−0.0245132
$495$	6.48361	0.291417
$496$	4.68382	0.210310
$497$	0	0
$498$	3.47104	0.155541
$499$	−4.69637	−0.210238	−0.105119	−	0.994460i	$-0.533522\pi$
$499$	−4.69637	−0.210238	−0.105119	+	0.994460i	$0.533522\pi$
$500$	1.56230	0.0698682
$501$	3.18511	0.142300
$502$	−13.6790	−0.610525
$503$	−10.4286	−0.464989	−0.232495	−	0.972598i	$-0.574689\pi$
$503$	−10.4286	−0.464989	−0.232495	+	0.972598i	$0.574689\pi$
$504$	0	0
$505$	−11.7046	−0.520849
$506$	−13.1880	−0.586277
$507$	3.65176	0.162181
$508$	6.88681	0.305553
$509$	15.3085	0.678536	0.339268	−	0.940690i	$-0.389821\pi$
$509$	15.3085	0.678536	0.339268	+	0.940690i	$0.389821\pi$
$510$	1.98148	0.0877415
$511$	0	0
$512$	−25.9287	−1.14590
$513$	−1.01001	−0.0445929
$514$	−54.9268	−2.42272
$515$	−3.37034	−0.148515
$516$	−0.746795	−0.0328758
$517$	12.6186	0.554965
$518$	0	0
$519$	6.34115	0.278345
$520$	−0.399718	−0.0175288
$521$	−23.7893	−1.04223	−0.521115	−	0.853486i	$-0.674484\pi$
$521$	−23.7893	−1.04223	−0.521115	+	0.853486i	$0.674484\pi$
$522$	20.2583	0.886681
$523$	−9.18193	−0.401498	−0.200749	−	0.979643i	$-0.564338\pi$
$523$	−9.18193	−0.401498	−0.200749	+	0.979643i	$0.564338\pi$
$524$	8.13661	0.355449
$525$	0	0
$526$	−8.06251	−0.351542
$527$	−3.67006	−0.159870
$528$	−2.97685	−0.129551
$529$	−13.1096	−0.569983
$530$	−12.6193	−0.548149
$531$	6.11144	0.265214
$532$	0	0
$533$	3.92028	0.169806
$534$	0.166608	0.00720982
$535$	−1.26646	−0.0547539
$536$	2.14605	0.0926950
$537$	−6.70410	−0.289303
$538$	0.209535	0.00903371
$539$	0	0
$540$	2.64487	0.113817
$541$	−11.4713	−0.493191	−0.246596	−	0.969118i	$-0.579312\pi$
$541$	−11.4713	−0.493191	−0.246596	+	0.969118i	$0.579312\pi$
$542$	−6.39831	−0.274831
$543$	2.04224	0.0876409
$544$	26.3805	1.13105
$545$	−14.6313	−0.626738
$546$	0	0
$547$	−33.8402	−1.44690	−0.723451	−	0.690376i	$-0.757445\pi$
$547$	−33.8402	−1.44690	−0.723451	+	0.690376i	$0.757445\pi$
$548$	−16.1391	−0.689429
$549$	−8.95971	−0.382391
$550$	4.19345	0.178809
$551$	−2.19438	−0.0934836
$552$	0.743189	0.0316322
$553$	0	0
$554$	3.59356	0.152676
$555$	−0.898166	−0.0381250
$556$	31.7166	1.34508
$557$	2.83337	0.120054	0.0600268	−	0.998197i	$-0.480881\pi$
$557$	2.83337	0.120054	0.0600268	+	0.998197i	$0.480881\pi$
$558$	−5.50777	−0.233163
$559$	−0.808533	−0.0341973
$560$	0	0
$561$	2.33255	0.0984803
$562$	27.6488	1.16629
$563$	−9.13883	−0.385156	−0.192578	−	0.981282i	$-0.561685\pi$
$563$	−9.13883	−0.385156	−0.192578	+	0.981282i	$0.561685\pi$
$564$	2.53817	0.106876
$565$	−5.98361	−0.251732
$566$	33.3015	1.39976
$567$	0	0
$568$	12.6771	0.531920
$569$	6.64027	0.278375	0.139187	−	0.990266i	$-0.455551\pi$
$569$	6.64027	0.278375	0.139187	+	0.990266i	$0.455551\pi$
$570$	−0.322108	−0.0134916
$571$	−15.4478	−0.646471	−0.323236	−	0.946319i	$-0.604771\pi$
$571$	−15.4478	−0.646471	−0.323236	+	0.946319i	$0.604771\pi$
$572$	1.67951	0.0702240
$573$	2.82070	0.117836
$574$	0	0
$575$	−3.14490	−0.131151
$576$	12.2537	0.510571
$577$	−37.2477	−1.55064	−0.775320	−	0.631568i	$-0.782412\pi$
$577$	−37.2477	−1.55064	−0.775320	+	0.631568i	$0.782412\pi$
$578$	6.66381	0.277178
$579$	1.17770	0.0489435
$580$	5.74634	0.238604
$581$	0	0
$582$	−5.36455	−0.222368
$583$	−14.8552	−0.615238
$584$	11.7692	0.487013
$585$	1.41197	0.0583776
$586$	−18.4128	−0.760627
$587$	−7.11927	−0.293844	−0.146922	−	0.989148i	$-0.546937\pi$
$587$	−7.11927	−0.293844	−0.146922	+	0.989148i	$0.546937\pi$
$588$	0	0
$589$	0.596602	0.0245826
$590$	3.95274	0.162732
$591$	−2.57905	−0.106088
$592$	−14.7064	−0.604427
$593$	−8.35959	−0.343287	−0.171644	−	0.985159i	$-0.554908\pi$
$593$	−8.35959	−0.343287	−0.171644	+	0.985159i	$0.554908\pi$
$594$	7.09922	0.291284
$595$	0	0
$596$	−7.89539	−0.323408
$597$	−5.66721	−0.231944
$598$	−2.87200	−0.117445
$599$	−24.9148	−1.01799	−0.508996	−	0.860769i	$-0.669983\pi$
$599$	−24.9148	−1.01799	−0.508996	+	0.860769i	$0.669983\pi$
$600$	−0.236316	−0.00964755
$601$	−20.7367	−0.845868	−0.422934	−	0.906160i	$-0.639000\pi$
$601$	−20.7367	−0.845868	−0.422934	+	0.906160i	$0.639000\pi$
$602$	0	0
$603$	−7.58069	−0.308710
$604$	10.0464	0.408783
$605$	−6.06358	−0.246520
$606$	−6.31938	−0.256707
$607$	−20.5727	−0.835019	−0.417510	−	0.908673i	$-0.637097\pi$
$607$	−20.5727	−0.835019	−0.417510	+	0.908673i	$0.637097\pi$
$608$	−4.28840	−0.173918
$609$	0	0
$610$	−5.79493	−0.234630
$611$	2.74801	0.111172
$612$	−16.7320	−0.676352
$613$	−46.3605	−1.87248	−0.936242	−	0.351357i	$-0.885720\pi$
$613$	−46.3605	−1.87248	−0.936242	+	0.351357i	$0.885720\pi$
$614$	16.3913	0.661501
$615$	2.31769	0.0934584
$616$	0	0
$617$	−8.12187	−0.326974	−0.163487	−	0.986545i	$-0.552274\pi$
$617$	−8.12187	−0.326974	−0.163487	+	0.986545i	$0.552274\pi$
$618$	−1.81966	−0.0731976
$619$	0.0425806	0.00171146	0.000855729	−	1.00000i	$-0.499728\pi$
$619$	0.0425806	0.00171146	0.000855729		1.00000i	$0.499728\pi$
$620$	−1.56230	−0.0627435
$621$	−5.32410	−0.213649
$622$	26.3867	1.05801
$623$	0	0
$624$	−0.648283	−0.0259521
$625$	1.00000	0.0400000
$626$	53.7444	2.14806
$627$	−0.379178	−0.0151429
$628$	−19.0820	−0.761453
$629$	11.5233	0.459465
$630$	0	0
$631$	2.33612	0.0929994	0.0464997	−	0.998918i	$-0.485193\pi$
$631$	2.33612	0.0929994	0.0464997	+	0.998918i	$0.485193\pi$
$632$	−2.41295	−0.0959818
$633$	1.11775	0.0444266
$634$	8.63412	0.342905
$635$	4.40812	0.174931
$636$	−2.98805	−0.118484
$637$	0	0
$638$	15.4240	0.610643
$639$	−44.7807	−1.77150
$640$	−6.45066	−0.254985
$641$	−49.4883	−1.95467	−0.977335	−	0.211701i	$-0.932100\pi$
$641$	−49.4883	−1.95467	−0.977335	+	0.211701i	$0.932100\pi$
$642$	−0.683769	−0.0269862
$643$	−4.00533	−0.157955	−0.0789774	−	0.996876i	$-0.525166\pi$
$643$	−4.00533	−0.157955	−0.0789774	+	0.996876i	$0.525166\pi$
$644$	0	0
$645$	−0.478009	−0.0188216
$646$	4.13260	0.162595
$647$	−13.9998	−0.550387	−0.275194	−	0.961389i	$-0.588742\pi$
$647$	−13.9998	−0.550387	−0.275194	+	0.961389i	$0.588742\pi$
$648$	6.83217	0.268393
$649$	4.65306	0.182649
$650$	0.913226	0.0358197
$651$	0	0
$652$	−16.4492	−0.644200
$653$	25.2007	0.986180	0.493090	−	0.869978i	$-0.335867\pi$
$653$	25.2007	0.986180	0.493090	+	0.869978i	$0.335867\pi$
$654$	−7.89953	−0.308896
$655$	5.20809	0.203497
$656$	37.9493	1.48167
$657$	−41.5736	−1.62194
$658$	0	0
$659$	1.12253	0.0437277	0.0218639	−	0.999761i	$-0.493040\pi$
$659$	1.12253	0.0437277	0.0218639	+	0.999761i	$0.493040\pi$
$660$	0.992939	0.0386501
$661$	−16.7994	−0.653419	−0.326710	−	0.945125i	$-0.605940\pi$
$661$	−16.7994	−0.653419	−0.326710	+	0.945125i	$0.605940\pi$
$662$	−11.6820	−0.454033
$663$	0.507970	0.0197279
$664$	5.31108	0.206110
$665$	0	0
$666$	17.2934	0.670107
$667$	−11.5673	−0.447889
$668$	−17.3955	−0.673053
$669$	−3.39567	−0.131284
$670$	−4.90302	−0.189420
$671$	−6.82164	−0.263347
$672$	0	0
$673$	31.7885	1.22535	0.612677	−	0.790333i	$-0.290092\pi$
$673$	31.7885	1.22535	0.612677	+	0.790333i	$0.290092\pi$
$674$	−10.1618	−0.391418
$675$	1.69293	0.0651609
$676$	−19.9442	−0.767083
$677$	6.32198	0.242974	0.121487	−	0.992593i	$-0.461234\pi$
$677$	6.32198	0.242974	0.121487	+	0.992593i	$0.461234\pi$
$678$	−3.23058	−0.124070
$679$	0	0
$680$	3.03189	0.116268
$681$	−3.70174	−0.141851
$682$	−4.19345	−0.160575
$683$	−18.9991	−0.726979	−0.363489	−	0.931598i	$-0.618415\pi$
$683$	−18.9991	−0.726979	−0.363489	+	0.931598i	$0.618415\pi$
$684$	2.71995	0.104000
$685$	−10.3304	−0.394703
$686$	0	0
$687$	3.83997	0.146504
$688$	−7.82681	−0.298394
$689$	−3.23508	−0.123247
$690$	−1.69795	−0.0646397
$691$	2.19880	0.0836463	0.0418231	−	0.999125i	$-0.486683\pi$
$691$	2.19880	0.0836463	0.0418231	+	0.999125i	$0.486683\pi$
$692$	−34.6323	−1.31652
$693$	0	0
$694$	−18.7002	−0.709851
$695$	20.3012	0.770068
$696$	−0.869198	−0.0329469
$697$	−29.7356	−1.12632
$698$	−54.8511	−2.07615
$699$	3.66408	0.138588
$700$	0	0
$701$	7.07842	0.267348	0.133674	−	0.991025i	$-0.457322\pi$
$701$	7.07842	0.267348	0.133674	+	0.991025i	$0.457322\pi$
$702$	1.54603	0.0583511
$703$	−1.87323	−0.0706500
$704$	9.32959	0.351622
$705$	1.62464	0.0611874
$706$	4.06908	0.153142
$707$	0	0
$708$	0.935943	0.0351749
$709$	−5.99399	−0.225109	−0.112554	−	0.993646i	$-0.535903\pi$
$709$	−5.99399	−0.225109	−0.112554	+	0.993646i	$0.535903\pi$
$710$	−28.9631	−1.08697
$711$	8.52349	0.319656
$712$	0.254929	0.00955386
$713$	3.14490	0.117777
$714$	0	0
$715$	1.07503	0.0402037
$716$	36.6145	1.36835
$717$	4.09485	0.152925
$718$	−52.2866	−1.95132
$719$	37.0065	1.38011	0.690055	−	0.723757i	$-0.257586\pi$
$719$	37.0065	1.38011	0.690055	+	0.723757i	$0.257586\pi$
$720$	13.6682	0.509383
$721$	0	0
$722$	35.1889	1.30960
$723$	−3.02994	−0.112685
$724$	−11.1537	−0.414525
$725$	3.67812	0.136602
$726$	−3.27376	−0.121500
$727$	11.6101	0.430596	0.215298	−	0.976548i	$-0.430928\pi$
$727$	11.6101	0.430596	0.215298	+	0.976548i	$0.430928\pi$
$728$	0	0
$729$	−22.6812	−0.840043
$730$	−26.8888	−0.995200
$731$	6.13278	0.226829
$732$	−1.37214	−0.0507159
$733$	−43.9975	−1.62508	−0.812542	−	0.582903i	$-0.801917\pi$
$733$	−43.9975	−1.62508	−0.812542	+	0.582903i	$0.801917\pi$
$734$	40.9665	1.51210
$735$	0	0
$736$	−22.6056	−0.833255
$737$	−5.77170	−0.212603
$738$	−44.6252	−1.64268
$739$	−29.4937	−1.08495	−0.542473	−	0.840074i	$-0.682512\pi$
$739$	−29.4937	−1.08495	−0.542473	+	0.840074i	$0.682512\pi$
$740$	4.90535	0.180324
$741$	−0.0825753	−0.00303348
$742$	0	0
$743$	−6.50514	−0.238651	−0.119325	−	0.992855i	$-0.538073\pi$
$743$	−6.50514	−0.238651	−0.119325	+	0.992855i	$0.538073\pi$
$744$	0.236316	0.00866375
$745$	−5.05369	−0.185153
$746$	4.66686	0.170866
$747$	−18.7609	−0.686424
$748$	−12.7392	−0.465793
$749$	0	0
$750$	0.539905	0.0197145
$751$	−39.8854	−1.45544	−0.727720	−	0.685874i	$-0.759420\pi$
$751$	−39.8854	−1.45544	−0.727720	+	0.685874i	$0.759420\pi$
$752$	26.6014	0.970054
$753$	−2.07320	−0.0755517
$754$	3.35896	0.122326
$755$	6.43053	0.234031
$756$	0	0
$757$	−12.2321	−0.444582	−0.222291	−	0.974980i	$-0.571353\pi$
$757$	−12.2321	−0.444582	−0.222291	+	0.974980i	$0.571353\pi$
$758$	26.3366	0.956587
$759$	−1.99878	−0.0725510
$760$	−0.492863	−0.0178780
$761$	−1.52268	−0.0551972	−0.0275986	−	0.999619i	$-0.508786\pi$
$761$	−1.52268	−0.0551972	−0.0275986	+	0.999619i	$0.508786\pi$
$762$	2.37997	0.0862171
$763$	0	0
$764$	−15.4053	−0.557344
$765$	−10.7099	−0.387216
$766$	48.2135	1.74202
$767$	1.01332	0.0365888
$768$	−5.88510	−0.212360
$769$	47.6180	1.71715	0.858575	−	0.512689i	$-0.171350\pi$
$769$	47.6180	1.71715	0.858575	+	0.512689i	$0.171350\pi$
$770$	0	0
$771$	−8.32474	−0.299808
$772$	−6.43202	−0.231493
$773$	29.4641	1.05975	0.529874	−	0.848076i	$-0.322239\pi$
$773$	29.4641	1.05975	0.529874	+	0.848076i	$0.322239\pi$
$774$	9.20367	0.330819
$775$	−1.00000	−0.0359211
$776$	−8.20837	−0.294663
$777$	0	0
$778$	−34.6696	−1.24297
$779$	4.83380	0.173189
$780$	0.216237	0.00774252
$781$	−34.0946	−1.22000
$782$	21.7844	0.779007
$783$	6.22681	0.222528
$784$	0	0
$785$	−12.2140	−0.435937
$786$	2.81187	0.100296
$787$	27.5787	0.983074	0.491537	−	0.870857i	$-0.336435\pi$
$787$	27.5787	0.983074	0.491537	+	0.870857i	$0.336435\pi$
$788$	14.0855	0.501775
$789$	−1.22196	−0.0435029
$790$	5.51280	0.196137
$791$	0	0
$792$	5.35621	0.190325
$793$	−1.48558	−0.0527545
$794$	−26.7527	−0.949417
$795$	−1.91260	−0.0678328
$796$	30.9516	1.09705
$797$	−42.8673	−1.51844	−0.759219	−	0.650835i	$-0.774419\pi$
$797$	−42.8673	−1.51844	−0.759219	+	0.650835i	$0.774419\pi$
$798$	0	0
$799$	−20.8438	−0.737402
$800$	7.18803	0.254135
$801$	−0.900511	−0.0318180
$802$	1.86333	0.0657964
$803$	−31.6528	−1.11700
$804$	−1.16095	−0.0409437
$805$	0	0
$806$	−0.913226	−0.0321670
$807$	0.0317573	0.00111791
$808$	−9.66938	−0.340167
$809$	−34.1344	−1.20010	−0.600051	−	0.799962i	$-0.704853\pi$
$809$	−34.1344	−1.20010	−0.600051	+	0.799962i	$0.704853\pi$
$810$	−15.6093	−0.548455
$811$	−24.9243	−0.875211	−0.437606	−	0.899167i	$-0.644173\pi$
$811$	−24.9243	−0.875211	−0.437606	+	0.899167i	$0.644173\pi$
$812$	0	0
$813$	−0.969731	−0.0340100
$814$	13.1667	0.461492
$815$	−10.5288	−0.368809
$816$	4.91728	0.172139
$817$	−0.996942	−0.0348786
$818$	−38.0611	−1.33078
$819$	0	0
$820$	−12.6581	−0.442040
$821$	14.5995	0.509525	0.254763	−	0.967004i	$-0.418003\pi$
$821$	14.5995	0.509525	0.254763	+	0.967004i	$0.418003\pi$
$822$	−5.57741	−0.194534
$823$	−14.1610	−0.493623	−0.246811	−	0.969064i	$-0.579383\pi$
$823$	−14.1610	−0.493623	−0.246811	+	0.969064i	$0.579383\pi$
$824$	−2.78429	−0.0969953
$825$	0.635562	0.0221274
$826$	0	0
$827$	38.4718	1.33780	0.668898	−	0.743354i	$-0.266766\pi$
$827$	38.4718	1.33780	0.668898	+	0.743354i	$0.266766\pi$
$828$	14.3378	0.498273
$829$	−35.9256	−1.24775	−0.623874	−	0.781525i	$-0.714442\pi$
$829$	−35.9256	−1.24775	−0.623874	+	0.781525i	$0.714442\pi$
$830$	−12.1341	−0.421181
$831$	0.544643	0.0188934
$832$	2.03175	0.0704382
$833$	0	0
$834$	10.9607	0.379538
$835$	−11.1346	−0.385327
$836$	2.07088	0.0716230
$837$	−1.69293	−0.0585163
$838$	−50.8299	−1.75589
$839$	33.9515	1.17214	0.586068	−	0.810262i	$-0.300675\pi$
$839$	33.9515	1.17214	0.586068	+	0.810262i	$0.300675\pi$
$840$	0	0
$841$	−15.4714	−0.533497
$842$	34.0657	1.17398
$843$	4.19047	0.144327
$844$	−6.10461	−0.210129
$845$	−12.7659	−0.439160
$846$	−31.2810	−1.07546
$847$	0	0
$848$	−31.3164	−1.07541
$849$	5.04719	0.173219
$850$	−6.92689	−0.237590
$851$	−9.87442	−0.338491
$852$	−6.85798	−0.234951
$853$	6.82696	0.233751	0.116875	−	0.993147i	$-0.462712\pi$
$853$	6.82696	0.233751	0.116875	+	0.993147i	$0.462712\pi$
$854$	0	0
$855$	1.74099	0.0595406
$856$	−1.04624	−0.0357599
$857$	39.3984	1.34582	0.672912	−	0.739723i	$-0.265043\pi$
$857$	39.3984	1.34582	0.672912	+	0.739723i	$0.265043\pi$
$858$	0.580412	0.0198149
$859$	29.5058	1.00672	0.503362	−	0.864075i	$-0.332096\pi$
$859$	29.5058	1.00672	0.503362	+	0.864075i	$0.332096\pi$
$860$	2.61065	0.0890226
$861$	0	0
$862$	12.7214	0.433292
$863$	29.0801	0.989897	0.494948	−	0.868922i	$-0.335187\pi$
$863$	29.0801	0.989897	0.494948	+	0.868922i	$0.335187\pi$
$864$	12.1688	0.413993
$865$	−22.1675	−0.753717
$866$	52.9208	1.79832
$867$	1.00997	0.0343004
$868$	0	0
$869$	6.48952	0.220142
$870$	1.98584	0.0673261
$871$	−1.25693	−0.0425895
$872$	−12.0872	−0.409323
$873$	28.9952	0.981340
$874$	−3.54125	−0.119785
$875$	0	0
$876$	−6.36683	−0.215115
$877$	1.16102	0.0392049	0.0196025	−	0.999808i	$-0.493760\pi$
$877$	1.16102	0.0392049	0.0196025	+	0.999808i	$0.493760\pi$
$878$	−30.6752	−1.03524
$879$	−2.79066	−0.0941266
$880$	10.4065	0.350804
$881$	5.13058	0.172854	0.0864268	−	0.996258i	$-0.472455\pi$
$881$	5.13058	0.172854	0.0864268	+	0.996258i	$0.472455\pi$
$882$	0	0
$883$	1.41527	0.0476276	0.0238138	−	0.999716i	$-0.492419\pi$
$883$	1.41527	0.0476276	0.0238138	+	0.999716i	$0.492419\pi$
$884$	−2.77428	−0.0933093
$885$	0.599079	0.0201378
$886$	47.4682	1.59473
$887$	−14.9613	−0.502351	−0.251176	−	0.967942i	$-0.580817\pi$
$887$	−14.9613	−0.502351	−0.251176	+	0.967942i	$0.580817\pi$
$888$	−0.741989	−0.0248995
$889$	0	0
$890$	−0.582429	−0.0195231
$891$	−18.3749	−0.615581
$892$	18.5455	0.620948
$893$	3.38836	0.113387
$894$	−2.72851	−0.0912551
$895$	23.4363	0.783388
$896$	0	0
$897$	−0.435283	−0.0145337
$898$	−30.5655	−1.01999
$899$	−3.67812	−0.122672
$900$	−4.55906	−0.151969
$901$	24.5383	0.817489
$902$	−33.9762	−1.13128
$903$	0	0
$904$	−4.94315	−0.164407
$905$	−7.13929	−0.237318
$906$	3.47187	0.115345
$907$	−9.46730	−0.314357	−0.157178	−	0.987570i	$-0.550240\pi$
$907$	−9.46730	−0.314357	−0.157178	+	0.987570i	$0.550240\pi$
$908$	20.2171	0.670928
$909$	34.1561	1.13289
$910$	0	0
$911$	−28.4892	−0.943889	−0.471945	−	0.881628i	$-0.656448\pi$
$911$	−28.4892	−0.943889	−0.471945	+	0.881628i	$0.656448\pi$
$912$	−0.799350	−0.0264691
$913$	−14.2839	−0.472730
$914$	−30.2193	−0.999564
$915$	−0.878284	−0.0290352
$916$	−20.9721	−0.692937
$917$	0	0
$918$	−11.7267	−0.387040
$919$	27.4320	0.904897	0.452448	−	0.891791i	$-0.350551\pi$
$919$	27.4320	0.904897	0.452448	+	0.891791i	$0.350551\pi$
$920$	−2.59805	−0.0856552
$921$	2.48428	0.0818599
$922$	−13.3384	−0.439275
$923$	−7.42494	−0.244395
$924$	0	0
$925$	3.13982	0.103237
$926$	79.4903	2.61221
$927$	9.83523	0.323031
$928$	26.4385	0.867886
$929$	−15.9816	−0.524338	−0.262169	−	0.965022i	$-0.584438\pi$
$929$	−15.9816	−0.524338	−0.262169	+	0.965022i	$0.584438\pi$
$930$	−0.539905	−0.0177042
$931$	0	0
$932$	−20.0114	−0.655497
$933$	3.99919	0.130928
$934$	−14.2336	−0.465737
$935$	−8.15415	−0.266669
$936$	1.16645	0.0381265
$937$	−25.1584	−0.821889	−0.410944	−	0.911660i	$-0.634801\pi$
$937$	−25.1584	−0.821889	−0.410944	+	0.911660i	$0.634801\pi$
$938$	0	0
$939$	8.14554	0.265820
$940$	−8.87298	−0.289405
$941$	4.42736	0.144328	0.0721640	−	0.997393i	$-0.477010\pi$
$941$	4.42736	0.144328	0.0721640	+	0.997393i	$0.477010\pi$
$942$	−6.59440	−0.214857
$943$	25.4807	0.829764
$944$	9.80918	0.319262
$945$	0	0
$946$	7.00738	0.227830
$947$	9.07122	0.294775	0.147387	−	0.989079i	$-0.452914\pi$
$947$	9.07122	0.294775	0.147387	+	0.989079i	$0.452914\pi$
$948$	1.30534	0.0423954
$949$	−6.89318	−0.223762
$950$	1.12603	0.0365333
$951$	1.30859	0.0424340
$952$	0	0
$953$	14.5941	0.472749	0.236374	−	0.971662i	$-0.424041\pi$
$953$	14.5941	0.472749	0.236374	+	0.971662i	$0.424041\pi$
$954$	36.8254	1.19227
$955$	−9.86064	−0.319083
$956$	−22.3641	−0.723306
$957$	2.33767	0.0755663
$958$	−4.95708	−0.160156
$959$	0	0
$960$	1.20118	0.0387679
$961$	1.00000	0.0322581
$962$	2.86737	0.0924477
$963$	3.69575	0.119094
$964$	16.5481	0.532978
$965$	−4.11702	−0.132531
$966$	0	0
$967$	−34.0836	−1.09605	−0.548027	−	0.836461i	$-0.684621\pi$
$967$	−34.0836	−1.09605	−0.548027	+	0.836461i	$0.684621\pi$
$968$	−5.00922	−0.161002
$969$	0.626339	0.0201209
$970$	18.7535	0.602137
$971$	38.8925	1.24812	0.624060	−	0.781376i	$-0.285482\pi$
$971$	38.8925	1.24812	0.624060	+	0.781376i	$0.285482\pi$
$972$	−11.6306	−0.373053
$973$	0	0
$974$	17.8178	0.570920
$975$	0.138409	0.00443264
$976$	−14.3808	−0.460318
$977$	−45.4167	−1.45301	−0.726504	−	0.687162i	$-0.758856\pi$
$977$	−45.4167	−1.45301	−0.726504	+	0.687162i	$0.758856\pi$
$978$	−5.68456	−0.181772
$979$	−0.685621	−0.0219125
$980$	0	0
$981$	42.6968	1.36320
$982$	18.9810	0.605707
$983$	25.8529	0.824581	0.412290	−	0.911053i	$-0.364729\pi$
$983$	25.8529	0.824581	0.412290	+	0.911053i	$0.364729\pi$
$984$	1.91468	0.0610378
$985$	9.01587	0.287270
$986$	−25.4780	−0.811383
$987$	0	0
$988$	0.450986	0.0143478
$989$	−5.25523	−0.167106
$990$	−12.2372	−0.388924
$991$	−0.683293	−0.0217055	−0.0108528	−	0.999941i	$-0.503455\pi$
$991$	−0.683293	−0.0217055	−0.0108528	+	0.999941i	$0.503455\pi$
$992$	−7.18803	−0.228220
$993$	−1.77053	−0.0561860
$994$	0	0
$995$	19.8115	0.628067
$996$	−2.87315	−0.0910393
$997$	27.7300	0.878217	0.439108	−	0.898434i	$-0.355294\pi$
$997$	27.7300	0.878217	0.439108	+	0.898434i	$0.355294\pi$
$998$	8.86396	0.280584
$999$	5.31550	0.168175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.w.1.2	✓	11
7.6	odd	2		7595.2.a.x.1.2	yes	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7595.2.a.w.1.2	✓	11	1.1	even	1	trivial
7595.2.a.x.1.2	yes	11	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88741 q^{2} -0.286056 q^{3} +1.56230 q^{4} +1.00000 q^{5} +0.539905 q^{6} +0.826115 q^{8} -2.91817 q^{9} +O(q^{10})\)	\(q-1.88741 q^{2} -0.286056 q^{3} +1.56230 q^{4} +1.00000 q^{5} +0.539905 q^{6} +0.826115 q^{8} -2.91817 q^{9} -1.88741 q^{10} -2.22180 q^{11} -0.446906 q^{12} -0.483853 q^{13} -0.286056 q^{15} -4.68382 q^{16} +3.67006 q^{17} +5.50777 q^{18} -0.596602 q^{19} +1.56230 q^{20} +4.19345 q^{22} -3.14490 q^{23} -0.236316 q^{24} +1.00000 q^{25} +0.913226 q^{26} +1.69293 q^{27} +3.67812 q^{29} +0.539905 q^{30} -1.00000 q^{31} +7.18803 q^{32} +0.635562 q^{33} -6.92689 q^{34} -4.55906 q^{36} +3.13982 q^{37} +1.12603 q^{38} +0.138409 q^{39} +0.826115 q^{40} -8.10222 q^{41} +1.67103 q^{43} -3.47113 q^{44} -2.91817 q^{45} +5.93570 q^{46} -5.67943 q^{47} +1.33984 q^{48} -1.88741 q^{50} -1.04984 q^{51} -0.755924 q^{52} +6.68608 q^{53} -3.19525 q^{54} -2.22180 q^{55} +0.170662 q^{57} -6.94211 q^{58} -2.09427 q^{59} -0.446906 q^{60} +3.07032 q^{61} +1.88741 q^{62} -4.19910 q^{64} -0.483853 q^{65} -1.19956 q^{66} +2.59775 q^{67} +5.73374 q^{68} +0.899619 q^{69} +15.3455 q^{71} -2.41075 q^{72} +14.2465 q^{73} -5.92612 q^{74} -0.286056 q^{75} -0.932073 q^{76} -0.261234 q^{78} -2.92083 q^{79} -4.68382 q^{80} +8.27024 q^{81} +15.2922 q^{82} +6.42898 q^{83} +3.67006 q^{85} -3.15392 q^{86} -1.05215 q^{87} -1.83547 q^{88} +0.308587 q^{89} +5.50777 q^{90} -4.91328 q^{92} +0.286056 q^{93} +10.7194 q^{94} -0.596602 q^{95} -2.05618 q^{96} -9.93610 q^{97} +6.48361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9}+O(q^{10}) \) 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9	\( 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9} - 3 q^{11} + 16 q^{12} - 5 q^{13} - q^{15} - 15 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} - 10 q^{22} - 6 q^{23} - 16 q^{24} + 11 q^{25} + 14 q^{26} - 13 q^{27} - 15 q^{29} - 8 q^{30} - 11 q^{31} - 5 q^{33} - 16 q^{34} - 12 q^{36} - 24 q^{37} - 18 q^{38} - q^{39} - 30 q^{43} - 26 q^{44} - 2 q^{45} - 12 q^{46} - q^{47} + 4 q^{48} - 7 q^{51} - 14 q^{52} - 4 q^{53} + 2 q^{54} - 3 q^{55} - 30 q^{57} - 14 q^{58} - 2 q^{59} + 16 q^{60} + 10 q^{61} - 16 q^{64} - 5 q^{65} + 4 q^{66} + 8 q^{67} - 42 q^{68} + 24 q^{69} - 8 q^{71} - 34 q^{72} - 14 q^{73} + 24 q^{74} - q^{75} + 2 q^{76} + 2 q^{78} - 21 q^{79} + 3 q^{81} + 26 q^{82} + 12 q^{83} - 15 q^{85} - 40 q^{86} - 9 q^{87} - 4 q^{88} - 8 q^{89} - 4 q^{90} - 6 q^{92} + q^{93} + 24 q^{94} + 14 q^{95} + 28 q^{96} - 13 q^{97} - 26 q^{99}+O(q^{100}) \) 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9 - 3 * q^11 + 16 * q^12 - 5 * q^13 - q^15 - 15 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 - 10 * q^22 - 6 * q^23 - 16 * q^24 + 11 * q^25 + 14 * q^26 - 13 * q^27 - 15 * q^29 - 8 * q^30 - 11 * q^31 - 5 * q^33 - 16 * q^34 - 12 * q^36 - 24 * q^37 - 18 * q^38 - q^39 - 30 * q^43 - 26 * q^44 - 2 * q^45 - 12 * q^46 - q^47 + 4 * q^48 - 7 * q^51 - 14 * q^52 - 4 * q^53 + 2 * q^54 - 3 * q^55 - 30 * q^57 - 14 * q^58 - 2 * q^59 + 16 * q^60 + 10 * q^61 - 16 * q^64 - 5 * q^65 + 4 * q^66 + 8 * q^67 - 42 * q^68 + 24 * q^69 - 8 * q^71 - 34 * q^72 - 14 * q^73 + 24 * q^74 - q^75 + 2 * q^76 + 2 * q^78 - 21 * q^79 + 3 * q^81 + 26 * q^82 + 12 * q^83 - 15 * q^85 - 40 * q^86 - 9 * q^87 - 4 * q^88 - 8 * q^89 - 4 * q^90 - 6 * q^92 + q^93 + 24 * q^94 + 14 * q^95 + 28 * q^96 - 13 * q^97 - 26 * q^99

Introduction

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