LMFDB - Embedded newform 1175.2.a.k.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 23 x^{11} - x^{10} + 200 x^{9} + 11 x^{8} - 816 x^{7} - 19 x^{6} + 1581 x^{5} - 102 x^{4} + \cdots - 117 $ x^13 - 23x^11 - x^10 + 200x^9 + 11x^8 - 816x^7 - 19x^6 + 1581x^5 - 102x^4 - 1309x^3 + 300x^2 + 341x - 117
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			1.11
Root			$-2.30741$ 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)

$f(q)$	$=$	$q+2.30741 q^{2} -2.74069 q^{3} +3.32413 q^{4} -6.32389 q^{6} +4.14817 q^{7} +3.05531 q^{8} +4.51138 q^{9} +O(q^{10})$	\(q+2.30741 q^{2} -2.74069 q^{3} +3.32413 q^{4} -6.32389 q^{6} +4.14817 q^{7} +3.05531 q^{8} +4.51138 q^{9} +3.63735 q^{11} -9.11042 q^{12} -4.90370 q^{13} +9.57153 q^{14} +0.401591 q^{16} -1.12222 q^{17} +10.4096 q^{18} +1.01823 q^{19} -11.3689 q^{21} +8.39285 q^{22} +5.59658 q^{23} -8.37367 q^{24} -11.3148 q^{26} -4.14223 q^{27} +13.7891 q^{28} +1.09219 q^{29} +7.84984 q^{31} -5.18399 q^{32} -9.96885 q^{33} -2.58942 q^{34} +14.9964 q^{36} +6.04278 q^{37} +2.34948 q^{38} +13.4395 q^{39} +10.0759 q^{41} -26.2326 q^{42} -3.65158 q^{43} +12.0910 q^{44} +12.9136 q^{46} -1.00000 q^{47} -1.10064 q^{48} +10.2073 q^{49} +3.07566 q^{51} -16.3006 q^{52} +8.70197 q^{53} -9.55782 q^{54} +12.6740 q^{56} -2.79067 q^{57} +2.52014 q^{58} -14.2060 q^{59} +9.09993 q^{61} +18.1128 q^{62} +18.7140 q^{63} -12.7648 q^{64} -23.0022 q^{66} -12.1935 q^{67} -3.73041 q^{68} -15.3385 q^{69} +4.30626 q^{71} +13.7837 q^{72} -15.3463 q^{73} +13.9432 q^{74} +3.38475 q^{76} +15.0884 q^{77} +31.0105 q^{78} +9.20884 q^{79} -2.18157 q^{81} +23.2492 q^{82} -8.44147 q^{83} -37.7916 q^{84} -8.42568 q^{86} -2.99337 q^{87} +11.1132 q^{88} +1.62424 q^{89} -20.3414 q^{91} +18.6038 q^{92} -21.5140 q^{93} -2.30741 q^{94} +14.2077 q^{96} -18.1628 q^{97} +23.5525 q^{98} +16.4095 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9}+O(q^{10}) $ 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9	$ 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9} + 9 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 34 q^{16} - 5 q^{17} + 7 q^{18} + 16 q^{19} + 26 q^{21} - 15 q^{22} + 10 q^{23} - 8 q^{24} + 3 q^{26} - 15 q^{27} + 30 q^{28} + 10 q^{29} + 15 q^{31} - 36 q^{32} + 22 q^{33} + q^{34} + 57 q^{36} - 5 q^{37} + 42 q^{38} - 2 q^{39} + 24 q^{41} - 62 q^{42} + 2 q^{43} - 6 q^{44} + 50 q^{46} - 13 q^{47} + 67 q^{48} + 39 q^{49} + 9 q^{51} - 36 q^{52} - 4 q^{53} - 34 q^{54} - 9 q^{56} + 5 q^{57} + 27 q^{58} - 25 q^{59} + 22 q^{61} - 2 q^{62} + 7 q^{63} + 53 q^{64} + 2 q^{66} + 4 q^{67} - 5 q^{68} + 5 q^{69} - 6 q^{71} - 66 q^{72} + 3 q^{73} - 49 q^{74} + 63 q^{76} + 8 q^{77} + 59 q^{78} + 37 q^{79} + 49 q^{81} - 48 q^{82} - 27 q^{83} - 2 q^{84} + 3 q^{86} + 35 q^{87} + 44 q^{88} + 32 q^{89} + 12 q^{91} - 29 q^{92} - 56 q^{93} - 11 q^{96} - 25 q^{97} + 61 q^{98} + 36 q^{99}+O(q^{100}) $ 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9 + 9 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 34 * q^16 - 5 * q^17 + 7 * q^18 + 16 * q^19 + 26 * q^21 - 15 * q^22 + 10 * q^23 - 8 * q^24 + 3 * q^26 - 15 * q^27 + 30 * q^28 + 10 * q^29 + 15 * q^31 - 36 * q^32 + 22 * q^33 + q^34 + 57 * q^36 - 5 * q^37 + 42 * q^38 - 2 * q^39 + 24 * q^41 - 62 * q^42 + 2 * q^43 - 6 * q^44 + 50 * q^46 - 13 * q^47 + 67 * q^48 + 39 * q^49 + 9 * q^51 - 36 * q^52 - 4 * q^53 - 34 * q^54 - 9 * q^56 + 5 * q^57 + 27 * q^58 - 25 * q^59 + 22 * q^61 - 2 * q^62 + 7 * q^63 + 53 * q^64 + 2 * q^66 + 4 * q^67 - 5 * q^68 + 5 * q^69 - 6 * q^71 - 66 * q^72 + 3 * q^73 - 49 * q^74 + 63 * q^76 + 8 * q^77 + 59 * q^78 + 37 * q^79 + 49 * q^81 - 48 * q^82 - 27 * q^83 - 2 * q^84 + 3 * q^86 + 35 * q^87 + 44 * q^88 + 32 * q^89 + 12 * q^91 - 29 * q^92 - 56 * q^93 - 11 * q^96 - 25 * q^97 + 61 * q^98 + 36 * 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 $

$2$	2.30741	1.63158	0.815792	−	0.578345i	$-0.196301\pi$
$2$	2.30741	1.63158	0.815792	+	0.578345i	$0.196301\pi$
$3$	−2.74069	−1.58234	−0.791169	−	0.611597i	$-0.790527\pi$
$3$	−2.74069	−1.58234	−0.791169	+	0.611597i	$0.790527\pi$
$4$	3.32413	1.66207
$5$	0	0
$5$	0	0
$6$	−6.32389	−2.58172
$7$	4.14817	1.56786	0.783931	−	0.620848i	$-0.213212\pi$
$7$	4.14817	1.56786	0.783931	+	0.620848i	$0.213212\pi$
$8$	3.05531	1.08022
$9$	4.51138	1.50379
$10$	0	0
$11$	3.63735	1.09670	0.548351	−	0.836248i	$-0.315256\pi$
$11$	3.63735	1.09670	0.548351	+	0.836248i	$0.315256\pi$
$12$	−9.11042	−2.62995
$13$	−4.90370	−1.36004	−0.680021	−	0.733192i	$-0.738030\pi$
$13$	−4.90370	−1.36004	−0.680021	+	0.733192i	$0.738030\pi$
$14$	9.57153	2.55810
$15$	0	0
$16$	0.401591	0.100398
$17$	−1.12222	−0.272178	−0.136089	−	0.990697i	$-0.543453\pi$
$17$	−1.12222	−0.272178	−0.136089	+	0.990697i	$0.543453\pi$
$18$	10.4096	2.45357
$19$	1.01823	0.233599	0.116800	−	0.993156i	$-0.462736\pi$
$19$	1.01823	0.233599	0.116800	+	0.993156i	$0.462736\pi$
$20$	0	0
$21$	−11.3689	−2.48089
$22$	8.39285	1.78936
$23$	5.59658	1.16697	0.583484	−	0.812125i	$-0.301689\pi$
$23$	5.59658	1.16697	0.583484	+	0.812125i	$0.301689\pi$
$24$	−8.37367	−1.70927
$25$	0	0
$26$	−11.3148	−2.21902
$27$	−4.14223	−0.797173
$28$	13.7891	2.60589
$29$	1.09219	0.202815	0.101408	−	0.994845i	$-0.467665\pi$
$29$	1.09219	0.202815	0.101408	+	0.994845i	$0.467665\pi$
$30$	0	0
$31$	7.84984	1.40987	0.704937	−	0.709270i	$-0.250975\pi$
$31$	7.84984	1.40987	0.704937	+	0.709270i	$0.250975\pi$
$32$	−5.18399	−0.916409
$33$	−9.96885	−1.73535
$34$	−2.58942	−0.444081
$35$	0	0
$36$	14.9964	2.49941
$37$	6.04278	0.993427	0.496713	−	0.867915i	$-0.334540\pi$
$37$	6.04278	0.993427	0.496713	+	0.867915i	$0.334540\pi$
$38$	2.34948	0.381137
$39$	13.4395	2.15205
$40$	0	0
$41$	10.0759	1.57359	0.786795	−	0.617215i	$-0.211739\pi$
$41$	10.0759	1.57359	0.786795	+	0.617215i	$0.211739\pi$
$42$	−26.2326	−4.04778
$43$	−3.65158	−0.556861	−0.278430	−	0.960456i	$-0.589814\pi$
$43$	−3.65158	−0.556861	−0.278430	+	0.960456i	$0.589814\pi$
$44$	12.0910	1.82279
$45$	0	0
$46$	12.9136	1.90401
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−1.10064	−0.158863
$49$	10.2073	1.45819
$50$	0	0
$51$	3.07566	0.430678
$52$	−16.3006	−2.26048
$53$	8.70197	1.19531	0.597654	−	0.801754i	$-0.296100\pi$
$53$	8.70197	1.19531	0.597654	+	0.801754i	$0.296100\pi$
$54$	−9.55782	−1.30065
$55$	0	0
$56$	12.6740	1.69363
$57$	−2.79067	−0.369633
$58$	2.52014	0.330910
$59$	−14.2060	−1.84947	−0.924734	−	0.380613i	$-0.875713\pi$
$59$	−14.2060	−1.84947	−0.924734	+	0.380613i	$0.875713\pi$
$60$	0	0
$61$	9.09993	1.16513	0.582564	−	0.812785i	$-0.302050\pi$
$61$	9.09993	1.16513	0.582564	+	0.812785i	$0.302050\pi$
$62$	18.1128	2.30033
$63$	18.7140	2.35774
$64$	−12.7648	−1.59560
$65$	0	0
$66$	−23.0022	−2.83138
$67$	−12.1935	−1.48967	−0.744834	−	0.667250i	$-0.767471\pi$
$67$	−12.1935	−1.48967	−0.744834	+	0.667250i	$0.767471\pi$
$68$	−3.73041	−0.452378
$69$	−15.3385	−1.84654
$70$	0	0
$71$	4.30626	0.511059	0.255530	−	0.966801i	$-0.417750\pi$
$71$	4.30626	0.511059	0.255530	+	0.966801i	$0.417750\pi$
$72$	13.7837	1.62442
$73$	−15.3463	−1.79615	−0.898074	−	0.439845i	$-0.855033\pi$
$73$	−15.3463	−1.79615	−0.898074	+	0.439845i	$0.855033\pi$
$74$	13.9432	1.62086
$75$	0	0
$76$	3.38475	0.388257
$77$	15.0884	1.71948
$78$	31.0105	3.51125
$79$	9.20884	1.03608	0.518038	−	0.855358i	$-0.326663\pi$
$79$	9.20884	1.03608	0.518038	+	0.855358i	$0.326663\pi$
$80$	0	0
$81$	−2.18157	−0.242397
$82$	23.2492	2.56744
$83$	−8.44147	−0.926571	−0.463286	−	0.886209i	$-0.653330\pi$
$83$	−8.44147	−0.926571	−0.463286	+	0.886209i	$0.653330\pi$
$84$	−37.7916	−4.12340
$85$	0	0
$86$	−8.42568	−0.908565
$87$	−2.99337	−0.320923
$88$	11.1132	1.18468
$89$	1.62424	0.172169	0.0860844	−	0.996288i	$-0.472565\pi$
$89$	1.62424	0.172169	0.0860844	+	0.996288i	$0.472565\pi$
$90$	0	0
$91$	−20.3414	−2.13236
$92$	18.6038	1.93958
$93$	−21.5140	−2.23090
$94$	−2.30741	−0.237991
$95$	0	0
$96$	14.2077	1.45007
$97$	−18.1628	−1.84416	−0.922078	−	0.387004i	$-0.873510\pi$
$97$	−18.1628	−1.84416	−0.922078	+	0.387004i	$0.873510\pi$
$98$	23.5525	2.37916
$99$	16.4095	1.64921
$100$	0	0
$101$	−3.75642	−0.373778	−0.186889	−	0.982381i	$-0.559840\pi$
$101$	−3.75642	−0.373778	−0.186889	+	0.982381i	$0.559840\pi$
$102$	7.09679	0.702687
$103$	16.2929	1.60538	0.802691	−	0.596395i	$-0.203401\pi$
$103$	16.2929	1.60538	0.802691	+	0.596395i	$0.203401\pi$
$104$	−14.9824	−1.46914
$105$	0	0
$106$	20.0790	1.95025
$107$	8.26883	0.799378	0.399689	−	0.916651i	$-0.369118\pi$
$107$	8.26883	0.799378	0.399689	+	0.916651i	$0.369118\pi$
$108$	−13.7693	−1.32495
$109$	−0.0474670	−0.00454651	−0.00227325	−	0.999997i	$-0.500724\pi$
$109$	−0.0474670	−0.00454651	−0.00227325	+	0.999997i	$0.500724\pi$
$110$	0	0
$111$	−16.5614	−1.57194
$112$	1.66587	0.157410
$113$	−9.42181	−0.886330	−0.443165	−	0.896440i	$-0.646144\pi$
$113$	−9.42181	−0.886330	−0.443165	+	0.896440i	$0.646144\pi$
$114$	−6.43921	−0.603087
$115$	0	0
$116$	3.63060	0.337093
$117$	−22.1225	−2.04522
$118$	−32.7791	−3.01756
$119$	−4.65516	−0.426738
$120$	0	0
$121$	2.23031	0.202756
$122$	20.9973	1.90100
$123$	−27.6149	−2.48995
$124$	26.0939	2.34330
$125$	0	0
$126$	43.1808	3.84685
$127$	−0.0565931	−0.00502182	−0.00251091	−	0.999997i	$-0.500799\pi$
$127$	−0.0565931	−0.00502182	−0.00251091	+	0.999997i	$0.500799\pi$
$128$	−19.0855	−1.68694
$129$	10.0078	0.881142
$130$	0	0
$131$	−17.6183	−1.53932	−0.769659	−	0.638455i	$-0.779574\pi$
$131$	−17.6183	−1.53932	−0.769659	+	0.638455i	$0.779574\pi$
$132$	−33.1378	−2.88427
$133$	4.22381	0.366251
$134$	−28.1353	−2.43052
$135$	0	0
$136$	−3.42873	−0.294011
$137$	−0.0514978	−0.00439975	−0.00219988	−	0.999998i	$-0.500700\pi$
$137$	−0.0514978	−0.00439975	−0.00219988	+	0.999998i	$0.500700\pi$
$138$	−35.3922	−3.01278
$139$	−7.51849	−0.637710	−0.318855	−	0.947803i	$-0.603298\pi$
$139$	−7.51849	−0.637710	−0.318855	+	0.947803i	$0.603298\pi$
$140$	0	0
$141$	2.74069	0.230808
$142$	9.93630	0.833836
$143$	−17.8365	−1.49156
$144$	1.81173	0.150977
$145$	0	0
$146$	−35.4102	−2.93057
$147$	−27.9751	−2.30735
$148$	20.0870	1.65114
$149$	−12.4439	−1.01944	−0.509720	−	0.860340i	$-0.670251\pi$
$149$	−12.4439	−1.01944	−0.509720	+	0.860340i	$0.670251\pi$
$150$	0	0
$151$	1.41165	0.114878	0.0574392	−	0.998349i	$-0.481706\pi$
$151$	1.41165	0.114878	0.0574392	+	0.998349i	$0.481706\pi$
$152$	3.11103	0.252338
$153$	−5.06276	−0.409300
$154$	34.8150	2.80547
$155$	0	0
$156$	44.6748	3.57685
$157$	−3.84814	−0.307115	−0.153557	−	0.988140i	$-0.549073\pi$
$157$	−3.84814	−0.307115	−0.153557	+	0.988140i	$0.549073\pi$
$158$	21.2485	1.69044
$159$	−23.8494	−1.89138
$160$	0	0
$161$	23.2156	1.82964
$162$	−5.03378	−0.395491
$163$	−0.644766	−0.0505020	−0.0252510	−	0.999681i	$-0.508038\pi$
$163$	−0.644766	−0.0505020	−0.0252510	+	0.999681i	$0.508038\pi$
$164$	33.4936	2.61541
$165$	0	0
$166$	−19.4779	−1.51178
$167$	−23.5337	−1.82110	−0.910548	−	0.413403i	$-0.864340\pi$
$167$	−23.5337	−1.82110	−0.910548	+	0.413403i	$0.864340\pi$
$168$	−34.7354	−2.67990
$169$	11.0463	0.849716
$170$	0	0
$171$	4.59365	0.351285
$172$	−12.1383	−0.925539
$173$	7.87985	0.599094	0.299547	−	0.954082i	$-0.403164\pi$
$173$	7.87985	0.599094	0.299547	+	0.954082i	$0.403164\pi$
$174$	−6.90692	−0.523612
$175$	0	0
$176$	1.46073	0.110106
$177$	38.9343	2.92648
$178$	3.74778	0.280908
$179$	8.63061	0.645082	0.322541	−	0.946556i	$-0.395463\pi$
$179$	8.63061	0.645082	0.322541	+	0.946556i	$0.395463\pi$
$180$	0	0
$181$	12.4146	0.922771	0.461385	−	0.887200i	$-0.347353\pi$
$181$	12.4146	0.922771	0.461385	+	0.887200i	$0.347353\pi$
$182$	−46.9359	−3.47912
$183$	−24.9401	−1.84363
$184$	17.0993	1.26058
$185$	0	0
$186$	−49.6415	−3.63989
$187$	−4.08190	−0.298498
$188$	−3.32413	−0.242437
$189$	−17.1827	−1.24986
$190$	0	0
$191$	−13.1920	−0.954537	−0.477268	−	0.878758i	$-0.658373\pi$
$191$	−13.1920	−0.954537	−0.477268	+	0.878758i	$0.658373\pi$
$192$	34.9843	2.52477
$193$	15.5822	1.12163	0.560817	−	0.827940i	$-0.310487\pi$
$193$	15.5822	1.12163	0.560817	+	0.827940i	$0.310487\pi$
$194$	−41.9091	−3.00890
$195$	0	0
$196$	33.9305	2.42361
$197$	4.45192	0.317186	0.158593	−	0.987344i	$-0.449304\pi$
$197$	4.45192	0.317186	0.158593	+	0.987344i	$0.449304\pi$
$198$	37.8634	2.69083
$199$	11.2382	0.796656	0.398328	−	0.917243i	$-0.369591\pi$
$199$	11.2382	0.796656	0.398328	+	0.917243i	$0.369591\pi$
$200$	0	0
$201$	33.4185	2.35716
$202$	−8.66759	−0.609849
$203$	4.53061	0.317986
$204$	10.2239	0.715815
$205$	0	0
$206$	37.5943	2.61932
$207$	25.2483	1.75488
$208$	−1.96928	−0.136545
$209$	3.70368	0.256189
$210$	0	0
$211$	−22.4877	−1.54812	−0.774059	−	0.633114i	$-0.781777\pi$
$211$	−22.4877	−1.54812	−0.774059	+	0.633114i	$0.781777\pi$
$212$	28.9265	1.98668
$213$	−11.8021	−0.808668
$214$	19.0796	1.30425
$215$	0	0
$216$	−12.6558	−0.861119
$217$	32.5625	2.21049
$218$	−0.109526	−0.00741801
$219$	42.0594	2.84211
$220$	0	0
$221$	5.50303	0.370174
$222$	−38.2139	−2.56475
$223$	14.1680	0.948757	0.474378	−	0.880321i	$-0.342673\pi$
$223$	14.1680	0.948757	0.474378	+	0.880321i	$0.342673\pi$
$224$	−21.5041	−1.43680
$225$	0	0
$226$	−21.7400	−1.44612
$227$	−0.791874	−0.0525586	−0.0262793	−	0.999655i	$-0.508366\pi$
$227$	−0.791874	−0.0525586	−0.0262793	+	0.999655i	$0.508366\pi$
$228$	−9.27654	−0.614354
$229$	15.9283	1.05257	0.526286	−	0.850308i	$-0.323584\pi$
$229$	15.9283	1.05257	0.526286	+	0.850308i	$0.323584\pi$
$230$	0	0
$231$	−41.3525	−2.72079
$232$	3.33700	0.219084
$233$	−3.26114	−0.213644	−0.106822	−	0.994278i	$-0.534068\pi$
$233$	−3.26114	−0.213644	−0.106822	+	0.994278i	$0.534068\pi$
$234$	−51.0456	−3.33696
$235$	0	0
$236$	−47.2227	−3.07394
$237$	−25.2386	−1.63942
$238$	−10.7413	−0.696258
$239$	−21.8290	−1.41200	−0.705999	−	0.708212i	$-0.749502\pi$
$239$	−21.8290	−1.41200	−0.705999	+	0.708212i	$0.749502\pi$
$240$	0	0
$241$	15.5054	0.998788	0.499394	−	0.866375i	$-0.333556\pi$
$241$	15.5054	0.998788	0.499394	+	0.866375i	$0.333556\pi$
$242$	5.14625	0.330813
$243$	18.4057	1.18073
$244$	30.2494	1.93652
$245$	0	0
$246$	−63.7188	−4.06256
$247$	−4.99312	−0.317705
$248$	23.9837	1.52297
$249$	23.1354	1.46615
$250$	0	0
$251$	−25.0890	−1.58361	−0.791803	−	0.610777i	$-0.790857\pi$
$251$	−25.0890	−1.58361	−0.791803	+	0.610777i	$0.790857\pi$
$252$	62.2078	3.91872
$253$	20.3567	1.27982
$254$	−0.130583	−0.00819353
$255$	0	0
$256$	−18.5086	−1.15679
$257$	−7.29672	−0.455157	−0.227578	−	0.973760i	$-0.573081\pi$
$257$	−7.29672	−0.455157	−0.227578	+	0.973760i	$0.573081\pi$
$258$	23.0922	1.43766
$259$	25.0665	1.55756
$260$	0	0
$261$	4.92731	0.304993
$262$	−40.6526	−2.51153
$263$	−6.07454	−0.374572	−0.187286	−	0.982305i	$-0.559969\pi$
$263$	−6.07454	−0.374572	−0.187286	+	0.982305i	$0.559969\pi$
$264$	−30.4580	−1.87456
$265$	0	0
$266$	9.74606	0.597569
$267$	−4.45153	−0.272429
$268$	−40.5327	−2.47593
$269$	−6.99342	−0.426397	−0.213198	−	0.977009i	$-0.568388\pi$
$269$	−6.99342	−0.426397	−0.213198	+	0.977009i	$0.568388\pi$
$270$	0	0
$271$	−14.0415	−0.852962	−0.426481	−	0.904496i	$-0.640247\pi$
$271$	−14.0415	−0.852962	−0.426481	+	0.904496i	$0.640247\pi$
$272$	−0.450673	−0.0273261
$273$	55.7495	3.37411
$274$	−0.118826	−0.00717857
$275$	0	0
$276$	−50.9872	−3.06907
$277$	−8.83202	−0.530665	−0.265332	−	0.964157i	$-0.585482\pi$
$277$	−8.83202	−0.530665	−0.265332	+	0.964157i	$0.585482\pi$
$278$	−17.3482	−1.04048
$279$	35.4136	2.12016
$280$	0	0
$281$	−6.97536	−0.416115	−0.208057	−	0.978117i	$-0.566714\pi$
$281$	−6.97536	−0.416115	−0.208057	+	0.978117i	$0.566714\pi$
$282$	6.32389	0.376582
$283$	−30.2034	−1.79541	−0.897704	−	0.440598i	$-0.854766\pi$
$283$	−30.2034	−1.79541	−0.897704	+	0.440598i	$0.854766\pi$
$284$	14.3146	0.849414
$285$	0	0
$286$	−41.1561	−2.43361
$287$	41.7965	2.46717
$288$	−23.3870	−1.37809
$289$	−15.7406	−0.925919
$290$	0	0
$291$	49.7787	2.91808
$292$	−51.0131	−2.98532
$293$	0.933709	0.0545479	0.0272739	−	0.999628i	$-0.491317\pi$
$293$	0.933709	0.0545479	0.0272739	+	0.999628i	$0.491317\pi$
$294$	−64.5500	−3.76463
$295$	0	0
$296$	18.4626	1.07312
$297$	−15.0668	−0.874262
$298$	−28.7130	−1.66330
$299$	−27.4440	−1.58713
$300$	0	0
$301$	−15.1474	−0.873080
$302$	3.25725	0.187434
$303$	10.2952	0.591443
$304$	0.408914	0.0234528
$305$	0	0
$306$	−11.6819	−0.667807
$307$	6.25292	0.356873	0.178437	−	0.983951i	$-0.442896\pi$
$307$	6.25292	0.356873	0.178437	+	0.983951i	$0.442896\pi$
$308$	50.1557	2.85789
$309$	−44.6537	−2.54026
$310$	0	0
$311$	−3.97824	−0.225585	−0.112793	−	0.993619i	$-0.535980\pi$
$311$	−3.97824	−0.225585	−0.112793	+	0.993619i	$0.535980\pi$
$312$	41.0620	2.32468
$313$	4.63841	0.262179	0.131089	−	0.991371i	$-0.458153\pi$
$313$	4.63841	0.262179	0.131089	+	0.991371i	$0.458153\pi$
$314$	−8.87923	−0.501084
$315$	0	0
$316$	30.6114	1.72203
$317$	25.7607	1.44686	0.723432	−	0.690396i	$-0.242563\pi$
$317$	25.7607	1.44686	0.723432	+	0.690396i	$0.242563\pi$
$318$	−55.0303	−3.08595
$319$	3.97269	0.222428
$320$	0	0
$321$	−22.6623	−1.26489
$322$	53.5678	2.98522
$323$	−1.14268	−0.0635806
$324$	−7.25183	−0.402880
$325$	0	0
$326$	−1.48774	−0.0823982
$327$	0.130092	0.00719412
$328$	30.7850	1.69982
$329$	−4.14817	−0.228696
$330$	0	0
$331$	−11.1073	−0.610512	−0.305256	−	0.952270i	$-0.598742\pi$
$331$	−11.1073	−0.610512	−0.305256	+	0.952270i	$0.598742\pi$
$332$	−28.0606	−1.54002
$333$	27.2613	1.49391
$334$	−54.3020	−2.97127
$335$	0	0
$336$	−4.56563	−0.249075
$337$	25.6919	1.39953	0.699764	−	0.714374i	$-0.253289\pi$
$337$	25.6919	1.39953	0.699764	+	0.714374i	$0.253289\pi$
$338$	25.4884	1.38638
$339$	25.8223	1.40247
$340$	0	0
$341$	28.5526	1.54621
$342$	10.5994	0.573151
$343$	13.3046	0.718378
$344$	−11.1567	−0.601530
$345$	0	0
$346$	18.1820	0.977472
$347$	−2.47897	−0.133078	−0.0665389	−	0.997784i	$-0.521196\pi$
$347$	−2.47897	−0.133078	−0.0665389	+	0.997784i	$0.521196\pi$
$348$	−9.95034	−0.533394
$349$	27.2398	1.45811	0.729057	−	0.684454i	$-0.239959\pi$
$349$	27.2398	1.45811	0.729057	+	0.684454i	$0.239959\pi$
$350$	0	0
$351$	20.3123	1.08419
$352$	−18.8560	−1.00503
$353$	31.2197	1.66165	0.830827	−	0.556530i	$-0.187868\pi$
$353$	31.2197	1.66165	0.830827	+	0.556530i	$0.187868\pi$
$354$	89.8374	4.77481
$355$	0	0
$356$	5.39918	0.286156
$357$	12.7583	0.675243
$358$	19.9143	1.05251
$359$	−0.666343	−0.0351682	−0.0175841	−	0.999845i	$-0.505597\pi$
$359$	−0.666343	−0.0351682	−0.0175841	+	0.999845i	$0.505597\pi$
$360$	0	0
$361$	−17.9632	−0.945431
$362$	28.6456	1.50558
$363$	−6.11260	−0.320828
$364$	−67.6175	−3.54412
$365$	0	0
$366$	−57.5470	−3.00803
$367$	−3.35215	−0.174981	−0.0874905	−	0.996165i	$-0.527885\pi$
$367$	−3.35215	−0.174981	−0.0874905	+	0.996165i	$0.527885\pi$
$368$	2.24754	0.117161
$369$	45.4562	2.36635
$370$	0	0
$371$	36.0973	1.87408
$372$	−71.5153	−3.70790
$373$	18.5591	0.960953	0.480476	−	0.877008i	$-0.340464\pi$
$373$	18.5591	0.960953	0.480476	+	0.877008i	$0.340464\pi$
$374$	−9.41862	−0.487025
$375$	0	0
$376$	−3.05531	−0.157566
$377$	−5.35580	−0.275838
$378$	−39.6475	−2.03925
$379$	−21.3963	−1.09905	−0.549527	−	0.835476i	$-0.685192\pi$
$379$	−21.3963	−1.09905	−0.549527	+	0.835476i	$0.685192\pi$
$380$	0	0
$381$	0.155104	0.00794622
$382$	−30.4392	−1.55741
$383$	−7.59001	−0.387831	−0.193916	−	0.981018i	$-0.562119\pi$
$383$	−7.59001	−0.387831	−0.193916	+	0.981018i	$0.562119\pi$
$384$	52.3076	2.66931
$385$	0	0
$386$	35.9546	1.83004
$387$	−16.4737	−0.837404
$388$	−60.3757	−3.06511
$389$	−17.1577	−0.869932	−0.434966	−	0.900447i	$-0.643240\pi$
$389$	−17.1577	−0.869932	−0.434966	+	0.900447i	$0.643240\pi$
$390$	0	0
$391$	−6.28059	−0.317623
$392$	31.1866	1.57516
$393$	48.2863	2.43572
$394$	10.2724	0.517515
$395$	0	0
$396$	54.5473	2.74110
$397$	15.8855	0.797268	0.398634	−	0.917110i	$-0.369484\pi$
$397$	15.8855	0.797268	0.398634	+	0.917110i	$0.369484\pi$
$398$	25.9311	1.29981
$399$	−11.5762	−0.579533
$400$	0	0
$401$	6.35371	0.317289	0.158645	−	0.987336i	$-0.449288\pi$
$401$	6.35371	0.317289	0.158645	+	0.987336i	$0.449288\pi$
$402$	77.1101	3.84590
$403$	−38.4933	−1.91749
$404$	−12.4868	−0.621243
$405$	0	0
$406$	10.4540	0.518822
$407$	21.9797	1.08949
$408$	9.39709	0.465225
$409$	6.68456	0.330530	0.165265	−	0.986249i	$-0.447152\pi$
$409$	6.68456	0.330530	0.165265	+	0.986249i	$0.447152\pi$
$410$	0	0
$411$	0.141139	0.00696190
$412$	54.1596	2.66825
$413$	−58.9291	−2.89971
$414$	58.2582	2.86323
$415$	0	0
$416$	25.4208	1.24636
$417$	20.6059	1.00907
$418$	8.54589	0.417993
$419$	22.4836	1.09839	0.549197	−	0.835693i	$-0.314934\pi$
$419$	22.4836	1.09839	0.549197	+	0.835693i	$0.314934\pi$
$420$	0	0
$421$	−4.63180	−0.225740	−0.112870	−	0.993610i	$-0.536004\pi$
$421$	−4.63180	−0.225740	−0.112870	+	0.993610i	$0.536004\pi$
$422$	−51.8883	−2.52588
$423$	−4.51138	−0.219351
$424$	26.5873	1.29119
$425$	0	0
$426$	−27.2323	−1.31941
$427$	37.7481	1.82676
$428$	27.4867	1.32862
$429$	48.8843	2.36016
$430$	0	0
$431$	−0.702404	−0.0338336	−0.0169168	−	0.999857i	$-0.505385\pi$
$431$	−0.702404	−0.0338336	−0.0169168	+	0.999857i	$0.505385\pi$
$432$	−1.66348	−0.0800343
$433$	−21.0383	−1.01104	−0.505518	−	0.862816i	$-0.668699\pi$
$433$	−21.0383	−1.01104	−0.505518	+	0.862816i	$0.668699\pi$
$434$	75.1350	3.60659
$435$	0	0
$436$	−0.157786	−0.00755660
$437$	5.69863	0.272603
$438$	97.0483	4.63715
$439$	12.9037	0.615862	0.307931	−	0.951409i	$-0.400363\pi$
$439$	12.9037	0.615862	0.307931	+	0.951409i	$0.400363\pi$
$440$	0	0
$441$	46.0492	2.19282
$442$	12.6977	0.603970
$443$	−7.98715	−0.379481	−0.189740	−	0.981834i	$-0.560765\pi$
$443$	−7.98715	−0.379481	−0.189740	+	0.981834i	$0.560765\pi$
$444$	−55.0522	−2.61266
$445$	0	0
$446$	32.6913	1.54798
$447$	34.1047	1.61310
$448$	−52.9505	−2.50167
$449$	−32.7915	−1.54753	−0.773763	−	0.633475i	$-0.781628\pi$
$449$	−32.7915	−1.54753	−0.773763	+	0.633475i	$0.781628\pi$
$450$	0	0
$451$	36.6495	1.72576
$452$	−31.3194	−1.47314
$453$	−3.86889	−0.181776
$454$	−1.82718	−0.0857537
$455$	0	0
$456$	−8.52636	−0.399283
$457$	−8.39138	−0.392532	−0.196266	−	0.980551i	$-0.562882\pi$
$457$	−8.39138	−0.392532	−0.196266	+	0.980551i	$0.562882\pi$
$458$	36.7531	1.71736
$459$	4.64849	0.216973
$460$	0	0
$461$	7.45329	0.347134	0.173567	−	0.984822i	$-0.444471\pi$
$461$	7.45329	0.347134	0.173567	+	0.984822i	$0.444471\pi$
$462$	−95.4171	−4.43921
$463$	39.0484	1.81473	0.907365	−	0.420343i	$-0.138090\pi$
$463$	39.0484	1.81473	0.907365	+	0.420343i	$0.138090\pi$
$464$	0.438615	0.0203622
$465$	0	0
$466$	−7.52478	−0.348579
$467$	−23.2236	−1.07466	−0.537330	−	0.843372i	$-0.680567\pi$
$467$	−23.2236	−1.07466	−0.537330	+	0.843372i	$0.680567\pi$
$468$	−73.5381	−3.39930
$469$	−50.5806	−2.33559
$470$	0	0
$471$	10.5466	0.485960
$472$	−43.4039	−1.99783
$473$	−13.2821	−0.610710
$474$	−58.2357	−2.67485
$475$	0	0
$476$	−15.4744	−0.709266
$477$	39.2579	1.79750
$478$	−50.3683	−2.30379
$479$	−17.7562	−0.811299	−0.405650	−	0.914029i	$-0.632955\pi$
$479$	−17.7562	−0.811299	−0.405650	+	0.914029i	$0.632955\pi$
$480$	0	0
$481$	−29.6320	−1.35110
$482$	35.7772	1.62961
$483$	−63.6267	−2.89512
$484$	7.41386	0.336994
$485$	0	0
$486$	42.4695	1.92646
$487$	15.7253	0.712582	0.356291	−	0.934375i	$-0.384041\pi$
$487$	15.7253	0.712582	0.356291	+	0.934375i	$0.384041\pi$
$488$	27.8032	1.25859
$489$	1.76710	0.0799112
$490$	0	0
$491$	5.38308	0.242935	0.121467	−	0.992595i	$-0.461240\pi$
$491$	5.38308	0.242935	0.121467	+	0.992595i	$0.461240\pi$
$492$	−91.7955	−4.13846
$493$	−1.22568	−0.0552019
$494$	−11.5212	−0.518362
$495$	0	0
$496$	3.15242	0.141548
$497$	17.8631	0.801270
$498$	53.3829	2.39215
$499$	−8.24783	−0.369223	−0.184612	−	0.982812i	$-0.559103\pi$
$499$	−8.24783	−0.369223	−0.184612	+	0.982812i	$0.559103\pi$
$500$	0	0
$501$	64.4987	2.88159
$502$	−57.8906	−2.58379
$503$	−16.6480	−0.742296	−0.371148	−	0.928574i	$-0.621036\pi$
$503$	−16.6480	−0.742296	−0.371148	+	0.928574i	$0.621036\pi$
$504$	57.1771	2.54687
$505$	0	0
$506$	46.9713	2.08813
$507$	−30.2745	−1.34454
$508$	−0.188123	−0.00834660
$509$	−34.0868	−1.51087	−0.755435	−	0.655224i	$-0.772574\pi$
$509$	−34.0868	−1.51087	−0.755435	+	0.655224i	$0.772574\pi$
$510$	0	0
$511$	−63.6590	−2.81611
$512$	−4.53582	−0.200457
$513$	−4.21777	−0.186219
$514$	−16.8365	−0.742627
$515$	0	0
$516$	33.2674	1.46452
$517$	−3.63735	−0.159970
$518$	57.8386	2.54128
$519$	−21.5962	−0.947969
$520$	0	0
$521$	−2.13861	−0.0936943	−0.0468472	−	0.998902i	$-0.514917\pi$
$521$	−2.13861	−0.0936943	−0.0468472	+	0.998902i	$0.514917\pi$
$522$	11.3693	0.497621
$523$	24.2515	1.06045	0.530223	−	0.847858i	$-0.322108\pi$
$523$	24.2515	1.06045	0.530223	+	0.847858i	$0.322108\pi$
$524$	−58.5656	−2.55845
$525$	0	0
$526$	−14.0164	−0.611146
$527$	−8.80924	−0.383737
$528$	−4.00340	−0.174226
$529$	8.32172	0.361814
$530$	0	0
$531$	−64.0889	−2.78122
$532$	14.0405	0.608734
$533$	−49.4092	−2.14015
$534$	−10.2715	−0.444491
$535$	0	0
$536$	−37.2548	−1.60916
$537$	−23.6538	−1.02074
$538$	−16.1367	−0.695702
$539$	37.1276	1.59920
$540$	0	0
$541$	−27.2085	−1.16978	−0.584891	−	0.811112i	$-0.698863\pi$
$541$	−27.2085	−1.16978	−0.584891	+	0.811112i	$0.698863\pi$
$542$	−32.3995	−1.39168
$543$	−34.0246	−1.46014
$544$	5.81758	0.249427
$545$	0	0
$546$	128.637	5.50515
$547$	15.5281	0.663934	0.331967	−	0.943291i	$-0.392288\pi$
$547$	15.5281	0.663934	0.331967	+	0.943291i	$0.392288\pi$
$548$	−0.171185	−0.00731268
$549$	41.0533	1.75211
$550$	0	0
$551$	1.11211	0.0473775
$552$	−46.8639	−1.99466
$553$	38.1998	1.62442
$554$	−20.3791	−0.865824
$555$	0	0
$556$	−24.9925	−1.05992
$557$	20.2928	0.859834	0.429917	−	0.902868i	$-0.358543\pi$
$557$	20.2928	0.859834	0.429917	+	0.902868i	$0.358543\pi$
$558$	81.7137	3.45922
$559$	17.9063	0.757354
$560$	0	0
$561$	11.1872	0.472325
$562$	−16.0950	−0.678926
$563$	22.9800	0.968490	0.484245	−	0.874933i	$-0.339094\pi$
$563$	22.9800	0.968490	0.484245	+	0.874933i	$0.339094\pi$
$564$	9.11042	0.383618
$565$	0	0
$566$	−69.6917	−2.92936
$567$	−9.04954	−0.380045
$568$	13.1570	0.552054
$569$	29.5533	1.23894	0.619469	−	0.785021i	$-0.287348\pi$
$569$	29.5533	1.23894	0.619469	+	0.785021i	$0.287348\pi$
$570$	0	0
$571$	18.9981	0.795045	0.397523	−	0.917592i	$-0.369870\pi$
$571$	18.9981	0.795045	0.397523	+	0.917592i	$0.369870\pi$
$572$	−59.2908	−2.47907
$573$	36.1551	1.51040
$574$	96.4416	4.02540
$575$	0	0
$576$	−57.5868	−2.39945
$577$	20.9406	0.871770	0.435885	−	0.900002i	$-0.356435\pi$
$577$	20.9406	0.871770	0.435885	+	0.900002i	$0.356435\pi$
$578$	−36.3200	−1.51071
$579$	−42.7061	−1.77480
$580$	0	0
$581$	−35.0167	−1.45274
$582$	114.860	4.76109
$583$	31.6521	1.31090
$584$	−46.8877	−1.94023
$585$	0	0
$586$	2.15445	0.0889994
$587$	13.4997	0.557194	0.278597	−	0.960408i	$-0.410131\pi$
$587$	13.4997	0.557194	0.278597	+	0.960408i	$0.410131\pi$
$588$	−92.9930	−3.83497
$589$	7.99298	0.329345
$590$	0	0
$591$	−12.2013	−0.501895
$592$	2.42672	0.0997378
$593$	−12.9952	−0.533650	−0.266825	−	0.963745i	$-0.585975\pi$
$593$	−12.9952	−0.533650	−0.266825	+	0.963745i	$0.585975\pi$
$594$	−34.7651	−1.42643
$595$	0	0
$596$	−41.3650	−1.69438
$597$	−30.8005	−1.26058
$598$	−63.3245	−2.58953
$599$	−21.3477	−0.872244	−0.436122	−	0.899888i	$-0.643648\pi$
$599$	−21.3477	−0.872244	−0.436122	+	0.899888i	$0.643648\pi$
$600$	0	0
$601$	18.6395	0.760323	0.380161	−	0.924920i	$-0.375868\pi$
$601$	18.6395	0.760323	0.380161	+	0.924920i	$0.375868\pi$
$602$	−34.9512	−1.42450
$603$	−55.0094	−2.24015
$604$	4.69251	0.190935
$605$	0	0
$606$	23.7552	0.964988
$607$	48.7253	1.97770	0.988849	−	0.148920i	$-0.0475798\pi$
$607$	48.7253	1.97770	0.988849	+	0.148920i	$0.0475798\pi$
$608$	−5.27852	−0.214072
$609$	−12.4170	−0.503162
$610$	0	0
$611$	4.90370	0.198383
$612$	−16.8293	−0.680284
$613$	−8.45532	−0.341507	−0.170754	−	0.985314i	$-0.554620\pi$
$613$	−8.45532	−0.341507	−0.170754	+	0.985314i	$0.554620\pi$
$614$	14.4280	0.582269
$615$	0	0
$616$	46.0996	1.85741
$617$	−20.7293	−0.834529	−0.417265	−	0.908785i	$-0.637011\pi$
$617$	−20.7293	−0.834529	−0.417265	+	0.908785i	$0.637011\pi$
$618$	−103.034	−4.14464
$619$	−39.5237	−1.58859	−0.794295	−	0.607532i	$-0.792160\pi$
$619$	−39.5237	−1.58859	−0.794295	+	0.607532i	$0.792160\pi$
$620$	0	0
$621$	−23.1823	−0.930275
$622$	−9.17943	−0.368061
$623$	6.73762	0.269937
$624$	5.39719	0.216061
$625$	0	0
$626$	10.7027	0.427766
$627$	−10.1506	−0.405377
$628$	−12.7917	−0.510445
$629$	−6.78132	−0.270389
$630$	0	0
$631$	21.0527	0.838096	0.419048	−	0.907964i	$-0.362364\pi$
$631$	21.0527	0.838096	0.419048	+	0.907964i	$0.362364\pi$
$632$	28.1359	1.11919
$633$	61.6318	2.44965
$634$	59.4404	2.36068
$635$	0	0
$636$	−79.2786	−3.14360
$637$	−50.0537	−1.98320
$638$	9.16662	0.362910
$639$	19.4272	0.768528
$640$	0	0
$641$	42.2327	1.66809	0.834045	−	0.551696i	$-0.186019\pi$
$641$	42.2327	1.66809	0.834045	+	0.551696i	$0.186019\pi$
$642$	−52.2912	−2.06377
$643$	−4.91357	−0.193772	−0.0968862	−	0.995295i	$-0.530888\pi$
$643$	−4.91357	−0.193772	−0.0968862	+	0.995295i	$0.530888\pi$
$644$	77.1717	3.04099
$645$	0	0
$646$	−2.63664	−0.103737
$647$	−50.1112	−1.97007	−0.985036	−	0.172346i	$-0.944865\pi$
$647$	−50.1112	−1.97007	−0.985036	+	0.172346i	$0.944865\pi$
$648$	−6.66539	−0.261841
$649$	−51.6723	−2.02832
$650$	0	0
$651$	−89.2437	−3.49774
$652$	−2.14329	−0.0839377
$653$	8.69387	0.340217	0.170109	−	0.985425i	$-0.445588\pi$
$653$	8.69387	0.340217	0.170109	+	0.985425i	$0.445588\pi$
$654$	0.300176	0.0117378
$655$	0	0
$656$	4.04638	0.157985
$657$	−69.2330	−2.70104
$658$	−9.57153	−0.373137
$659$	9.14103	0.356084	0.178042	−	0.984023i	$-0.443024\pi$
$659$	9.14103	0.356084	0.178042	+	0.984023i	$0.443024\pi$
$660$	0	0
$661$	20.1094	0.782165	0.391083	−	0.920356i	$-0.372101\pi$
$661$	20.1094	0.782165	0.391083	+	0.920356i	$0.372101\pi$
$662$	−25.6291	−0.996101
$663$	−15.0821	−0.585740
$664$	−25.7913	−1.00090
$665$	0	0
$666$	62.9029	2.43744
$667$	6.11255	0.236679
$668$	−78.2293	−3.02678
$669$	−38.8300	−1.50125
$670$	0	0
$671$	33.0996	1.27780
$672$	58.9361	2.27351
$673$	−29.4716	−1.13605	−0.568024	−	0.823012i	$-0.692292\pi$
$673$	−29.4716	−1.13605	−0.568024	+	0.823012i	$0.692292\pi$
$674$	59.2817	2.28345
$675$	0	0
$676$	36.7194	1.41228
$677$	11.6677	0.448428	0.224214	−	0.974540i	$-0.428019\pi$
$677$	11.6677	0.448428	0.224214	+	0.974540i	$0.428019\pi$
$678$	59.5825	2.28825
$679$	−75.3426	−2.89138
$680$	0	0
$681$	2.17028	0.0831654
$682$	65.8825	2.52277
$683$	−20.4743	−0.783427	−0.391713	−	0.920087i	$-0.628118\pi$
$683$	−20.4743	−0.783427	−0.391713	+	0.920087i	$0.628118\pi$
$684$	15.2699	0.583859
$685$	0	0
$686$	30.6990	1.17209
$687$	−43.6545	−1.66552
$688$	−1.46644	−0.0559075
$689$	−42.6719	−1.62567
$690$	0	0
$691$	29.1487	1.10887	0.554434	−	0.832228i	$-0.312935\pi$
$691$	29.1487	1.10887	0.554434	+	0.832228i	$0.312935\pi$
$692$	26.1937	0.995734
$693$	68.0693	2.58574
$694$	−5.71999	−0.217128
$695$	0	0
$696$	−9.14567	−0.346666
$697$	−11.3074	−0.428297
$698$	62.8533	2.37903
$699$	8.93778	0.338058
$700$	0	0
$701$	−38.7260	−1.46266	−0.731330	−	0.682024i	$-0.761100\pi$
$701$	−38.7260	−1.46266	−0.731330	+	0.682024i	$0.761100\pi$
$702$	46.8687	1.76895
$703$	6.15297	0.232064
$704$	−46.4299	−1.74989
$705$	0	0
$706$	72.0365	2.71113
$707$	−15.5823	−0.586031
$708$	129.423	4.86401
$709$	−7.76792	−0.291730	−0.145865	−	0.989304i	$-0.546597\pi$
$709$	−7.76792	−0.291730	−0.145865	+	0.989304i	$0.546597\pi$
$710$	0	0
$711$	41.5446	1.55804
$712$	4.96255	0.185980
$713$	43.9323	1.64528
$714$	29.4387	1.10172
$715$	0	0
$716$	28.6893	1.07217
$717$	59.8264	2.23426
$718$	−1.53753	−0.0573799
$719$	41.0130	1.52953	0.764764	−	0.644310i	$-0.222855\pi$
$719$	41.0130	1.52953	0.764764	+	0.644310i	$0.222855\pi$
$720$	0	0
$721$	67.5856	2.51702
$722$	−41.4484	−1.54255
$723$	−42.4954	−1.58042
$724$	41.2678	1.53371
$725$	0	0
$726$	−14.1043	−0.523458
$727$	−33.4003	−1.23875	−0.619374	−	0.785096i	$-0.712614\pi$
$727$	−33.4003	−1.23875	−0.619374	+	0.785096i	$0.712614\pi$
$728$	−62.1494	−2.30341
$729$	−43.8996	−1.62591
$730$	0	0
$731$	4.09787	0.151565
$732$	−82.9042	−3.06423
$733$	−14.4254	−0.532816	−0.266408	−	0.963860i	$-0.585837\pi$
$733$	−14.4254	−0.532816	−0.266408	+	0.963860i	$0.585837\pi$
$734$	−7.73478	−0.285496
$735$	0	0
$736$	−29.0126	−1.06942
$737$	−44.3519	−1.63372
$738$	104.886	3.86091
$739$	1.13145	0.0416209	0.0208104	−	0.999783i	$-0.493375\pi$
$739$	1.13145	0.0416209	0.0208104	+	0.999783i	$0.493375\pi$
$740$	0	0
$741$	13.6846	0.502716
$742$	83.2912	3.05772
$743$	36.9602	1.35594	0.677970	−	0.735090i	$-0.262860\pi$
$743$	36.9602	1.35594	0.677970	+	0.735090i	$0.262860\pi$
$744$	−65.7320	−2.40985
$745$	0	0
$746$	42.8234	1.56788
$747$	−38.0827	−1.39337
$748$	−13.5688	−0.496124
$749$	34.3005	1.25331
$750$	0	0
$751$	9.37338	0.342040	0.171020	−	0.985268i	$-0.445294\pi$
$751$	9.37338	0.342040	0.171020	+	0.985268i	$0.445294\pi$
$752$	−0.401591	−0.0146445
$753$	68.7613	2.50580
$754$	−12.3580	−0.450052
$755$	0	0
$756$	−57.1175	−2.07735
$757$	−20.1991	−0.734147	−0.367074	−	0.930192i	$-0.619640\pi$
$757$	−20.1991	−0.734147	−0.367074	+	0.930192i	$0.619640\pi$
$758$	−49.3700	−1.79320
$759$	−55.7915	−2.02510
$760$	0	0
$761$	−30.4885	−1.10521	−0.552603	−	0.833444i	$-0.686365\pi$
$761$	−30.4885	−1.10521	−0.552603	+	0.833444i	$0.686365\pi$
$762$	0.357888	0.0129649
$763$	−0.196901	−0.00712830
$764$	−43.8518	−1.58650
$765$	0	0
$766$	−17.5132	−0.632779
$767$	69.6622	2.51536
$768$	50.7264	1.83043
$769$	49.2872	1.77734	0.888671	−	0.458545i	$-0.151629\pi$
$769$	49.2872	1.77734	0.888671	+	0.458545i	$0.151629\pi$
$770$	0	0
$771$	19.9980	0.720212
$772$	51.7974	1.86423
$773$	14.4435	0.519495	0.259748	−	0.965677i	$-0.416361\pi$
$773$	14.4435	0.519495	0.259748	+	0.965677i	$0.416361\pi$
$774$	−38.0115	−1.36629
$775$	0	0
$776$	−55.4932	−1.99209
$777$	−68.6995	−2.46458
$778$	−39.5899	−1.41937
$779$	10.2596	0.367589
$780$	0	0
$781$	15.6634	0.560480
$782$	−14.4919	−0.518229
$783$	−4.52412	−0.161679
$784$	4.09917	0.146399
$785$	0	0
$786$	111.416	3.97409
$787$	33.2453	1.18507	0.592534	−	0.805545i	$-0.298128\pi$
$787$	33.2453	1.18507	0.592534	+	0.805545i	$0.298128\pi$
$788$	14.7988	0.527184
$789$	16.6484	0.592700
$790$	0	0
$791$	−39.0833	−1.38964
$792$	50.1361	1.78151
$793$	−44.6234	−1.58462
$794$	36.6542	1.30081
$795$	0	0
$796$	37.3573	1.32409
$797$	−18.5517	−0.657133	−0.328567	−	0.944481i	$-0.606566\pi$
$797$	−18.5517	−0.657133	−0.328567	+	0.944481i	$0.606566\pi$
$798$	−26.7109	−0.945557
$799$	1.12222	0.0397013
$800$	0	0
$801$	7.32756	0.258907
$802$	14.6606	0.517684
$803$	−55.8198	−1.96984
$804$	111.088	3.91775
$805$	0	0
$806$	−88.8197	−3.12854
$807$	19.1668	0.674704
$808$	−11.4770	−0.403761
$809$	−10.9979	−0.386665	−0.193333	−	0.981133i	$-0.561930\pi$
$809$	−10.9979	−0.386665	−0.193333	+	0.981133i	$0.561930\pi$
$810$	0	0
$811$	−5.86752	−0.206037	−0.103018	−	0.994679i	$-0.532850\pi$
$811$	−5.86752	−0.206037	−0.103018	+	0.994679i	$0.532850\pi$
$812$	15.0603	0.528514
$813$	38.4835	1.34967
$814$	50.7162	1.77760
$815$	0	0
$816$	1.23515	0.0432391
$817$	−3.71817	−0.130082
$818$	15.4240	0.539288
$819$	−91.7679	−3.20663
$820$	0	0
$821$	47.4158	1.65482	0.827411	−	0.561597i	$-0.189813\pi$
$821$	47.4158	1.65482	0.827411	+	0.561597i	$0.189813\pi$
$822$	0.325666	0.0113589
$823$	49.9832	1.74230	0.871152	−	0.491013i	$-0.163373\pi$
$823$	49.9832	1.74230	0.871152	+	0.491013i	$0.163373\pi$
$824$	49.7798	1.73416
$825$	0	0
$826$	−135.973	−4.73112
$827$	18.1280	0.630373	0.315186	−	0.949030i	$-0.397933\pi$
$827$	18.1280	0.630373	0.315186	+	0.949030i	$0.397933\pi$
$828$	83.9288	2.91673
$829$	9.19312	0.319290	0.159645	−	0.987174i	$-0.448965\pi$
$829$	9.19312	0.319290	0.159645	+	0.987174i	$0.448965\pi$
$830$	0	0
$831$	24.2058	0.839691
$832$	62.5947	2.17008
$833$	−11.4549	−0.396887
$834$	47.5461	1.64639
$835$	0	0
$836$	12.3115	0.425803
$837$	−32.5159	−1.12391
$838$	51.8787	1.79212
$839$	19.3873	0.669323	0.334662	−	0.942338i	$-0.391378\pi$
$839$	19.3873	0.669323	0.334662	+	0.942338i	$0.391378\pi$
$840$	0	0
$841$	−27.8071	−0.958866
$842$	−10.6874	−0.368314
$843$	19.1173	0.658434
$844$	−74.7521	−2.57307
$845$	0	0
$846$	−10.4096	−0.357889
$847$	9.25173	0.317893
$848$	3.49463	0.120006
$849$	82.7783	2.84094
$850$	0	0
$851$	33.8189	1.15930
$852$	−39.2318	−1.34406
$853$	2.04243	0.0699314	0.0349657	−	0.999389i	$-0.488868\pi$
$853$	2.04243	0.0699314	0.0349657	+	0.999389i	$0.488868\pi$
$854$	87.1003	2.98051
$855$	0	0
$856$	25.2639	0.863502
$857$	38.1640	1.30366	0.651828	−	0.758366i	$-0.274002\pi$
$857$	38.1640	1.30366	0.651828	+	0.758366i	$0.274002\pi$
$858$	112.796	3.85079
$859$	−24.4831	−0.835354	−0.417677	−	0.908596i	$-0.637156\pi$
$859$	−24.4831	−0.835354	−0.417677	+	0.908596i	$0.637156\pi$
$860$	0	0
$861$	−114.551	−3.90390
$862$	−1.62073	−0.0552024
$863$	−10.0283	−0.341366	−0.170683	−	0.985326i	$-0.554597\pi$
$863$	−10.0283	−0.341366	−0.170683	+	0.985326i	$0.554597\pi$
$864$	21.4733	0.730537
$865$	0	0
$866$	−48.5440	−1.64959
$867$	43.1402	1.46512
$868$	108.242	3.67397
$869$	33.4958	1.13627
$870$	0	0
$871$	59.7931	2.02601
$872$	−0.145026	−0.00491121
$873$	−81.9395	−2.77323
$874$	13.1491	0.444774
$875$	0	0
$876$	139.811	4.72378
$877$	−28.4525	−0.960773	−0.480387	−	0.877057i	$-0.659504\pi$
$877$	−28.4525	−0.960773	−0.480387	+	0.877057i	$0.659504\pi$
$878$	29.7742	1.00483
$879$	−2.55901	−0.0863132
$880$	0	0
$881$	42.8739	1.44446	0.722229	−	0.691654i	$-0.243118\pi$
$881$	42.8739	1.44446	0.722229	+	0.691654i	$0.243118\pi$
$882$	106.254	3.57777
$883$	21.4216	0.720895	0.360448	−	0.932779i	$-0.382624\pi$
$883$	21.4216	0.720895	0.360448	+	0.932779i	$0.382624\pi$
$884$	18.2928	0.615254
$885$	0	0
$886$	−18.4296	−0.619155
$887$	10.6953	0.359112	0.179556	−	0.983748i	$-0.442534\pi$
$887$	10.6953	0.359112	0.179556	+	0.983748i	$0.442534\pi$
$888$	−50.6002	−1.69803
$889$	−0.234758	−0.00787352
$890$	0	0
$891$	−7.93514	−0.265837
$892$	47.0962	1.57690
$893$	−1.01823	−0.0340739
$894$	78.6936	2.63191
$895$	0	0
$896$	−79.1701	−2.64489
$897$	75.2154	2.51137
$898$	−75.6634	−2.52492
$899$	8.57355	0.285944
$900$	0	0
$901$	−9.76552	−0.325337
$902$	84.5654	2.81572
$903$	41.5143	1.38151
$904$	−28.7866	−0.957428
$905$	0	0
$906$	−8.92711	−0.296584
$907$	−2.67040	−0.0886691	−0.0443346	−	0.999017i	$-0.514117\pi$
$907$	−2.67040	−0.0886691	−0.0443346	+	0.999017i	$0.514117\pi$
$908$	−2.63230	−0.0873558
$909$	−16.9466	−0.562085
$910$	0	0
$911$	−28.8928	−0.957261	−0.478631	−	0.878016i	$-0.658867\pi$
$911$	−28.8928	−0.957261	−0.478631	+	0.878016i	$0.658867\pi$
$912$	−1.12071	−0.0371103
$913$	−30.7046	−1.01617
$914$	−19.3623	−0.640449
$915$	0	0
$916$	52.9478	1.74944
$917$	−73.0838	−2.41344
$918$	10.7260	0.354010
$919$	0.392638	0.0129519	0.00647597	−	0.999979i	$-0.497939\pi$
$919$	0.392638	0.0129519	0.00647597	+	0.999979i	$0.497939\pi$
$920$	0	0
$921$	−17.1373	−0.564694
$922$	17.1978	0.566379
$923$	−21.1166	−0.695062
$924$	−137.461	−4.52214
$925$	0	0
$926$	90.1005	2.96089
$927$	73.5033	2.41417
$928$	−5.66193	−0.185862
$929$	−11.5634	−0.379383	−0.189692	−	0.981844i	$-0.560749\pi$
$929$	−11.5634	−0.379383	−0.189692	+	0.981844i	$0.560749\pi$
$930$	0	0
$931$	10.3935	0.340632
$932$	−10.8405	−0.355091
$933$	10.9031	0.356952
$934$	−53.5863	−1.75340
$935$	0	0
$936$	−67.5911	−2.20929
$937$	−23.3760	−0.763661	−0.381831	−	0.924232i	$-0.624706\pi$
$937$	−23.3760	−0.763661	−0.381831	+	0.924232i	$0.624706\pi$
$938$	−116.710	−3.81072
$939$	−12.7124	−0.414855
$940$	0	0
$941$	−12.1103	−0.394783	−0.197392	−	0.980325i	$-0.563247\pi$
$941$	−12.1103	−0.394783	−0.197392	+	0.980325i	$0.563247\pi$
$942$	24.3352	0.792884
$943$	56.3905	1.83633
$944$	−5.70501	−0.185682
$945$	0	0
$946$	−30.6472	−0.996425
$947$	17.4726	0.567782	0.283891	−	0.958857i	$-0.408375\pi$
$947$	17.4726	0.567782	0.283891	+	0.958857i	$0.408375\pi$
$948$	−83.8963	−2.72483
$949$	75.2537	2.44284
$950$	0	0
$951$	−70.6021	−2.28943
$952$	−14.2230	−0.460969
$953$	−6.45394	−0.209064	−0.104532	−	0.994522i	$-0.533334\pi$
$953$	−6.45394	−0.209064	−0.104532	+	0.994522i	$0.533334\pi$
$954$	90.5841	2.93277
$955$	0	0
$956$	−72.5624	−2.34684
$957$	−10.8879	−0.351956
$958$	−40.9707	−1.32370
$959$	−0.213622	−0.00689820
$960$	0	0
$961$	30.6200	0.987742
$962$	−68.3731	−2.20444
$963$	37.3039	1.20210
$964$	51.5418	1.66005
$965$	0	0
$966$	−146.813	−4.72362
$967$	−15.9328	−0.512365	−0.256183	−	0.966628i	$-0.582465\pi$
$967$	−15.9328	−0.512365	−0.256183	+	0.966628i	$0.582465\pi$
$968$	6.81431	0.219020
$969$	3.13174	0.100606
$970$	0	0
$971$	−23.2070	−0.744747	−0.372374	−	0.928083i	$-0.621456\pi$
$971$	−23.2070	−0.744747	−0.372374	+	0.928083i	$0.621456\pi$
$972$	61.1830	1.96245
$973$	−31.1880	−0.999841
$974$	36.2847	1.16264
$975$	0	0
$976$	3.65445	0.116976
$977$	17.8955	0.572528	0.286264	−	0.958151i	$-0.407586\pi$
$977$	17.8955	0.572528	0.286264	+	0.958151i	$0.407586\pi$
$978$	4.07743	0.130382
$979$	5.90792	0.188818
$980$	0	0
$981$	−0.214142	−0.00683702
$982$	12.4210	0.396369
$983$	−29.2720	−0.933631	−0.466815	−	0.884355i	$-0.654599\pi$
$983$	−29.2720	−0.933631	−0.466815	+	0.884355i	$0.654599\pi$
$984$	−84.3721	−2.68969
$985$	0	0
$986$	−2.82815	−0.0900666
$987$	11.3689	0.361875
$988$	−16.5978	−0.528046
$989$	−20.4364	−0.649838
$990$	0	0
$991$	−22.1622	−0.704004	−0.352002	−	0.935999i	$-0.614499\pi$
$991$	−22.1622	−0.704004	−0.352002	+	0.935999i	$0.614499\pi$
$992$	−40.6935	−1.29202
$993$	30.4416	0.966036
$994$	41.2175	1.30734
$995$	0	0
$996$	76.9053	2.43684
$997$	42.1490	1.33487	0.667436	−	0.744667i	$-0.267392\pi$
$997$	42.1490	1.33487	0.667436	+	0.744667i	$0.267392\pi$
$998$	−19.0311	−0.602419
$999$	−25.0306	−0.791933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.k.1.11	✓	13
5.2	odd	4		1175.2.c.h.424.22		26
5.3	odd	4		1175.2.c.h.424.5		26
5.4	even	2		1175.2.a.l.1.3	yes	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1175.2.a.k.1.11	✓	13	1.1	even	1	trivial
1175.2.a.l.1.3	yes	13	5.4	even	2
1175.2.c.h.424.5		26	5.3	odd	4
1175.2.c.h.424.22		26	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+2.30741 q^{2} -2.74069 q^{3} +3.32413 q^{4} -6.32389 q^{6} +4.14817 q^{7} +3.05531 q^{8} +4.51138 q^{9} +O(q^{10})\)	\(q+2.30741 q^{2} -2.74069 q^{3} +3.32413 q^{4} -6.32389 q^{6} +4.14817 q^{7} +3.05531 q^{8} +4.51138 q^{9} +3.63735 q^{11} -9.11042 q^{12} -4.90370 q^{13} +9.57153 q^{14} +0.401591 q^{16} -1.12222 q^{17} +10.4096 q^{18} +1.01823 q^{19} -11.3689 q^{21} +8.39285 q^{22} +5.59658 q^{23} -8.37367 q^{24} -11.3148 q^{26} -4.14223 q^{27} +13.7891 q^{28} +1.09219 q^{29} +7.84984 q^{31} -5.18399 q^{32} -9.96885 q^{33} -2.58942 q^{34} +14.9964 q^{36} +6.04278 q^{37} +2.34948 q^{38} +13.4395 q^{39} +10.0759 q^{41} -26.2326 q^{42} -3.65158 q^{43} +12.0910 q^{44} +12.9136 q^{46} -1.00000 q^{47} -1.10064 q^{48} +10.2073 q^{49} +3.07566 q^{51} -16.3006 q^{52} +8.70197 q^{53} -9.55782 q^{54} +12.6740 q^{56} -2.79067 q^{57} +2.52014 q^{58} -14.2060 q^{59} +9.09993 q^{61} +18.1128 q^{62} +18.7140 q^{63} -12.7648 q^{64} -23.0022 q^{66} -12.1935 q^{67} -3.73041 q^{68} -15.3385 q^{69} +4.30626 q^{71} +13.7837 q^{72} -15.3463 q^{73} +13.9432 q^{74} +3.38475 q^{76} +15.0884 q^{77} +31.0105 q^{78} +9.20884 q^{79} -2.18157 q^{81} +23.2492 q^{82} -8.44147 q^{83} -37.7916 q^{84} -8.42568 q^{86} -2.99337 q^{87} +11.1132 q^{88} +1.62424 q^{89} -20.3414 q^{91} +18.6038 q^{92} -21.5140 q^{93} -2.30741 q^{94} +14.2077 q^{96} -18.1628 q^{97} +23.5525 q^{98} +16.4095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9}+O(q^{10}) \) 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9	\( 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9} + 9 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 34 q^{16} - 5 q^{17} + 7 q^{18} + 16 q^{19} + 26 q^{21} - 15 q^{22} + 10 q^{23} - 8 q^{24} + 3 q^{26} - 15 q^{27} + 30 q^{28} + 10 q^{29} + 15 q^{31} - 36 q^{32} + 22 q^{33} + q^{34} + 57 q^{36} - 5 q^{37} + 42 q^{38} - 2 q^{39} + 24 q^{41} - 62 q^{42} + 2 q^{43} - 6 q^{44} + 50 q^{46} - 13 q^{47} + 67 q^{48} + 39 q^{49} + 9 q^{51} - 36 q^{52} - 4 q^{53} - 34 q^{54} - 9 q^{56} + 5 q^{57} + 27 q^{58} - 25 q^{59} + 22 q^{61} - 2 q^{62} + 7 q^{63} + 53 q^{64} + 2 q^{66} + 4 q^{67} - 5 q^{68} + 5 q^{69} - 6 q^{71} - 66 q^{72} + 3 q^{73} - 49 q^{74} + 63 q^{76} + 8 q^{77} + 59 q^{78} + 37 q^{79} + 49 q^{81} - 48 q^{82} - 27 q^{83} - 2 q^{84} + 3 q^{86} + 35 q^{87} + 44 q^{88} + 32 q^{89} + 12 q^{91} - 29 q^{92} - 56 q^{93} - 11 q^{96} - 25 q^{97} + 61 q^{98} + 36 q^{99}+O(q^{100}) \) 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9 + 9 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 34 * q^16 - 5 * q^17 + 7 * q^18 + 16 * q^19 + 26 * q^21 - 15 * q^22 + 10 * q^23 - 8 * q^24 + 3 * q^26 - 15 * q^27 + 30 * q^28 + 10 * q^29 + 15 * q^31 - 36 * q^32 + 22 * q^33 + q^34 + 57 * q^36 - 5 * q^37 + 42 * q^38 - 2 * q^39 + 24 * q^41 - 62 * q^42 + 2 * q^43 - 6 * q^44 + 50 * q^46 - 13 * q^47 + 67 * q^48 + 39 * q^49 + 9 * q^51 - 36 * q^52 - 4 * q^53 - 34 * q^54 - 9 * q^56 + 5 * q^57 + 27 * q^58 - 25 * q^59 + 22 * q^61 - 2 * q^62 + 7 * q^63 + 53 * q^64 + 2 * q^66 + 4 * q^67 - 5 * q^68 + 5 * q^69 - 6 * q^71 - 66 * q^72 + 3 * q^73 - 49 * q^74 + 63 * q^76 + 8 * q^77 + 59 * q^78 + 37 * q^79 + 49 * q^81 - 48 * q^82 - 27 * q^83 - 2 * q^84 + 3 * q^86 + 35 * q^87 + 44 * q^88 + 32 * q^89 + 12 * q^91 - 29 * q^92 - 56 * q^93 - 11 * q^96 - 25 * q^97 + 61 * q^98 + 36 * q^99

Introduction

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Database

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