LMFDB - Embedded newform 3475.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3475,2,Mod(1,3475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3475, 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("3475.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3475 = 5^{2} \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3475.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:	$27.7480147024$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11x^{5} + 8x^{4} + 35x^{3} - 10x^{2} - 32x - 8 $ x^7 - x^6 - 11x^5 + 8x^4 + 35x^3 - 10x^2 - 32*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 139)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.47985$ of defining polynomial
Character	$\chi$	$=$	3475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47985 q^{2} +0.245836 q^{3} +4.14965 q^{4} -0.609636 q^{6} +0.326651 q^{7} -5.33082 q^{8} -2.93956 q^{9} +O(q^{10})$	\(q-2.47985 q^{2} +0.245836 q^{3} +4.14965 q^{4} -0.609636 q^{6} +0.326651 q^{7} -5.33082 q^{8} -2.93956 q^{9} +0.570671 q^{11} +1.02013 q^{12} -0.655030 q^{13} -0.810045 q^{14} +4.92032 q^{16} -1.14453 q^{17} +7.28968 q^{18} -2.77067 q^{19} +0.0803026 q^{21} -1.41518 q^{22} -7.23464 q^{23} -1.31051 q^{24} +1.62438 q^{26} -1.46016 q^{27} +1.35549 q^{28} +7.86393 q^{29} -8.91763 q^{31} -1.54002 q^{32} +0.140292 q^{33} +2.83826 q^{34} -12.1982 q^{36} +4.69099 q^{37} +6.87084 q^{38} -0.161030 q^{39} +9.63165 q^{41} -0.199138 q^{42} -11.2545 q^{43} +2.36809 q^{44} +17.9408 q^{46} +8.96119 q^{47} +1.20959 q^{48} -6.89330 q^{49} -0.281366 q^{51} -2.71815 q^{52} -7.21477 q^{53} +3.62098 q^{54} -1.74132 q^{56} -0.681130 q^{57} -19.5014 q^{58} -5.58094 q^{59} +10.8663 q^{61} +22.1144 q^{62} -0.960211 q^{63} -6.02163 q^{64} -0.347902 q^{66} +3.89682 q^{67} -4.74939 q^{68} -1.77853 q^{69} -4.74151 q^{71} +15.6703 q^{72} +5.98781 q^{73} -11.6329 q^{74} -11.4973 q^{76} +0.186410 q^{77} +0.399330 q^{78} +6.17739 q^{79} +8.45973 q^{81} -23.8850 q^{82} +14.5135 q^{83} +0.333228 q^{84} +27.9095 q^{86} +1.93324 q^{87} -3.04214 q^{88} +11.5467 q^{89} -0.213966 q^{91} -30.0212 q^{92} -2.19228 q^{93} -22.2224 q^{94} -0.378592 q^{96} +5.82160 q^{97} +17.0943 q^{98} -1.67752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 2 q^{3} + 9 q^{4} - 7 q^{6} + 5 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q - q^2 + 2 * q^3 + 9 * q^4 - 7 * q^6 + 5 * q^7 - 6 * q^8 + 13 * q^9	$ 7 q - q^{2} + 2 q^{3} + 9 q^{4} - 7 q^{6} + 5 q^{7} - 6 q^{8} + 13 q^{9} + 2 q^{11} + 8 q^{12} - 6 q^{13} + 7 q^{14} + 5 q^{16} - 5 q^{17} + 10 q^{18} - 10 q^{19} - 5 q^{21} + 18 q^{22} + q^{23} - 21 q^{24} - 8 q^{26} + 11 q^{27} + 28 q^{28} + 30 q^{29} - 20 q^{31} + 12 q^{32} + 20 q^{33} - 17 q^{34} + 2 q^{36} - 6 q^{37} - 6 q^{38} + 11 q^{39} + 19 q^{41} - 6 q^{42} + 12 q^{43} + 25 q^{44} + 22 q^{46} + 3 q^{47} - 15 q^{48} - 8 q^{49} + 23 q^{51} + 8 q^{52} - 38 q^{53} - 7 q^{54} + 21 q^{56} + 19 q^{57} + 21 q^{58} - 14 q^{59} + 4 q^{61} + q^{62} + 18 q^{63} - 16 q^{64} + 18 q^{66} - 9 q^{67} + 25 q^{68} + 9 q^{69} + 24 q^{71} - 41 q^{72} + 5 q^{73} + 9 q^{74} + 3 q^{76} + 13 q^{77} - 20 q^{78} + 8 q^{79} + 39 q^{81} - 56 q^{82} + 9 q^{83} - q^{84} + 39 q^{86} + 25 q^{87} + 29 q^{88} + 10 q^{89} + 7 q^{91} - 29 q^{92} + 15 q^{93} - 36 q^{94} - 11 q^{96} + 5 q^{97} + 49 q^{98} - 31 q^{99}+O(q^{100}) $ 7 * q - q^2 + 2 * q^3 + 9 * q^4 - 7 * q^6 + 5 * q^7 - 6 * q^8 + 13 * q^9 + 2 * q^11 + 8 * q^12 - 6 * q^13 + 7 * q^14 + 5 * q^16 - 5 * q^17 + 10 * q^18 - 10 * q^19 - 5 * q^21 + 18 * q^22 + q^23 - 21 * q^24 - 8 * q^26 + 11 * q^27 + 28 * q^28 + 30 * q^29 - 20 * q^31 + 12 * q^32 + 20 * q^33 - 17 * q^34 + 2 * q^36 - 6 * q^37 - 6 * q^38 + 11 * q^39 + 19 * q^41 - 6 * q^42 + 12 * q^43 + 25 * q^44 + 22 * q^46 + 3 * q^47 - 15 * q^48 - 8 * q^49 + 23 * q^51 + 8 * q^52 - 38 * q^53 - 7 * q^54 + 21 * q^56 + 19 * q^57 + 21 * q^58 - 14 * q^59 + 4 * q^61 + q^62 + 18 * q^63 - 16 * q^64 + 18 * q^66 - 9 * q^67 + 25 * q^68 + 9 * q^69 + 24 * q^71 - 41 * q^72 + 5 * q^73 + 9 * q^74 + 3 * q^76 + 13 * q^77 - 20 * q^78 + 8 * q^79 + 39 * q^81 - 56 * q^82 + 9 * q^83 - q^84 + 39 * q^86 + 25 * q^87 + 29 * q^88 + 10 * q^89 + 7 * q^91 - 29 * q^92 + 15 * q^93 - 36 * q^94 - 11 * q^96 + 5 * q^97 + 49 * q^98 - 31 * 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 $

$2$	−2.47985	−1.75352	−0.876759	−	0.480930i	$-0.840299\pi$
$2$	−2.47985	−1.75352	−0.876759	+	0.480930i	$0.840299\pi$
$3$	0.245836	0.141934	0.0709668	−	0.997479i	$-0.477392\pi$
$3$	0.245836	0.141934	0.0709668	+	0.997479i	$0.477392\pi$
$4$	4.14965	2.07483
$5$	0	0
$5$	0	0
$6$	−0.609636	−0.248883
$7$	0.326651	0.123462	0.0617312	−	0.998093i	$-0.480338\pi$
$7$	0.326651	0.123462	0.0617312	+	0.998093i	$0.480338\pi$
$8$	−5.33082	−1.88473
$9$	−2.93956	−0.979855
$10$	0	0
$11$	0.570671	0.172064	0.0860319	−	0.996292i	$-0.472581\pi$
$11$	0.570671	0.172064	0.0860319	+	0.996292i	$0.472581\pi$
$12$	1.02013	0.294487
$13$	−0.655030	−0.181673	−0.0908364	−	0.995866i	$-0.528954\pi$
$13$	−0.655030	−0.181673	−0.0908364	+	0.995866i	$0.528954\pi$
$14$	−0.810045	−0.216494
$15$	0	0
$16$	4.92032	1.23008
$17$	−1.14453	−0.277589	−0.138794	−	0.990321i	$-0.544323\pi$
$17$	−1.14453	−0.277589	−0.138794	+	0.990321i	$0.544323\pi$
$18$	7.28968	1.71819
$19$	−2.77067	−0.635634	−0.317817	−	0.948152i	$-0.602950\pi$
$19$	−2.77067	−0.635634	−0.317817	+	0.948152i	$0.602950\pi$
$20$	0	0
$21$	0.0803026	0.0175235
$22$	−1.41518	−0.301717
$23$	−7.23464	−1.50853	−0.754263	−	0.656572i	$-0.772006\pi$
$23$	−7.23464	−1.50853	−0.754263	+	0.656572i	$0.772006\pi$
$24$	−1.31051	−0.267506
$25$	0	0
$26$	1.62438	0.318567
$27$	−1.46016	−0.281008
$28$	1.35549	0.256163
$29$	7.86393	1.46029	0.730147	−	0.683290i	$-0.239451\pi$
$29$	7.86393	1.46029	0.730147	+	0.683290i	$0.239451\pi$
$30$	0	0
$31$	−8.91763	−1.60165	−0.800827	−	0.598896i	$-0.795606\pi$
$31$	−8.91763	−1.60165	−0.800827	+	0.598896i	$0.795606\pi$
$32$	−1.54002	−0.272239
$33$	0.140292	0.0244216
$34$	2.83826	0.486757
$35$	0	0
$36$	−12.1982	−2.03303
$37$	4.69099	0.771194	0.385597	−	0.922667i	$-0.373996\pi$
$37$	4.69099	0.771194	0.385597	+	0.922667i	$0.373996\pi$
$38$	6.87084	1.11460
$39$	−0.161030	−0.0257855
$40$	0	0
$41$	9.63165	1.50421	0.752105	−	0.659043i	$-0.229039\pi$
$41$	9.63165	1.50421	0.752105	+	0.659043i	$0.229039\pi$
$42$	−0.199138	−0.0307277
$43$	−11.2545	−1.71630	−0.858148	−	0.513403i	$-0.828385\pi$
$43$	−11.2545	−1.71630	−0.858148	+	0.513403i	$0.828385\pi$
$44$	2.36809	0.357003
$45$	0	0
$46$	17.9408	2.64523
$47$	8.96119	1.30712	0.653562	−	0.756873i	$-0.273274\pi$
$47$	8.96119	1.30712	0.653562	+	0.756873i	$0.273274\pi$
$48$	1.20959	0.174590
$49$	−6.89330	−0.984757
$50$	0	0
$51$	−0.281366	−0.0393991
$52$	−2.71815	−0.376940
$53$	−7.21477	−0.991025	−0.495512	−	0.868601i	$-0.665020\pi$
$53$	−7.21477	−0.991025	−0.495512	+	0.868601i	$0.665020\pi$
$54$	3.62098	0.492752
$55$	0	0
$56$	−1.74132	−0.232693
$57$	−0.681130	−0.0902178
$58$	−19.5014	−2.56065
$59$	−5.58094	−0.726577	−0.363288	−	0.931677i	$-0.618346\pi$
$59$	−5.58094	−0.726577	−0.363288	+	0.931677i	$0.618346\pi$
$60$	0	0
$61$	10.8663	1.39129	0.695646	−	0.718385i	$-0.255118\pi$
$61$	10.8663	1.39129	0.695646	+	0.718385i	$0.255118\pi$
$62$	22.1144	2.80853
$63$	−0.960211	−0.120975
$64$	−6.02163	−0.752704
$65$	0	0
$66$	−0.347902	−0.0428238
$67$	3.89682	0.476073	0.238036	−	0.971256i	$-0.423496\pi$
$67$	3.89682	0.476073	0.238036	+	0.971256i	$0.423496\pi$
$68$	−4.74939	−0.575949
$69$	−1.77853	−0.214110
$70$	0	0
$71$	−4.74151	−0.562713	−0.281357	−	0.959603i	$-0.590784\pi$
$71$	−4.74151	−0.562713	−0.281357	+	0.959603i	$0.590784\pi$
$72$	15.6703	1.84676
$73$	5.98781	0.700820	0.350410	−	0.936596i	$-0.386042\pi$
$73$	5.98781	0.700820	0.350410	+	0.936596i	$0.386042\pi$
$74$	−11.6329	−1.35230
$75$	0	0
$76$	−11.4973	−1.31883
$77$	0.186410	0.0212434
$78$	0.399330	0.0452153
$79$	6.17739	0.695010	0.347505	−	0.937678i	$-0.387029\pi$
$79$	6.17739	0.695010	0.347505	+	0.937678i	$0.387029\pi$
$80$	0	0
$81$	8.45973	0.939970
$82$	−23.8850	−2.63766
$83$	14.5135	1.59306	0.796529	−	0.604600i	$-0.206667\pi$
$83$	14.5135	1.59306	0.796529	+	0.604600i	$0.206667\pi$
$84$	0.333228	0.0363581
$85$	0	0
$86$	27.9095	3.00956
$87$	1.93324	0.207265
$88$	−3.04214	−0.324294
$89$	11.5467	1.22395	0.611975	−	0.790877i	$-0.290375\pi$
$89$	11.5467	1.22395	0.611975	+	0.790877i	$0.290375\pi$
$90$	0	0
$91$	−0.213966	−0.0224298
$92$	−30.0212	−3.12993
$93$	−2.19228	−0.227328
$94$	−22.2224	−2.29207
$95$	0	0
$96$	−0.378592	−0.0386399
$97$	5.82160	0.591094	0.295547	−	0.955328i	$-0.404498\pi$
$97$	5.82160	0.591094	0.295547	+	0.955328i	$0.404498\pi$
$98$	17.0943	1.72679
$99$	−1.67752	−0.168598
$100$	0	0
$101$	10.2902	1.02392	0.511958	−	0.859011i	$-0.328920\pi$
$101$	10.2902	1.02392	0.511958	+	0.859011i	$0.328920\pi$
$102$	0.697746	0.0690871
$103$	0.0520725	0.00513086	0.00256543	−	0.999997i	$-0.499183\pi$
$103$	0.0520725	0.00513086	0.00256543	+	0.999997i	$0.499183\pi$
$104$	3.49185	0.342404
$105$	0	0
$106$	17.8915	1.73778
$107$	8.26648	0.799151	0.399575	−	0.916700i	$-0.369158\pi$
$107$	8.26648	0.799151	0.399575	+	0.916700i	$0.369158\pi$
$108$	−6.05916	−0.583042
$109$	−0.971231	−0.0930270	−0.0465135	−	0.998918i	$-0.514811\pi$
$109$	−0.971231	−0.0930270	−0.0465135	+	0.998918i	$0.514811\pi$
$110$	0	0
$111$	1.15321	0.109458
$112$	1.60723	0.151869
$113$	−0.0781957	−0.00735603	−0.00367802	−	0.999993i	$-0.501171\pi$
$113$	−0.0781957	−0.00735603	−0.00367802	+	0.999993i	$0.501171\pi$
$114$	1.68910	0.158199
$115$	0	0
$116$	32.6326	3.02986
$117$	1.92550	0.178013
$118$	13.8399	1.27407
$119$	−0.373861	−0.0342718
$120$	0	0
$121$	−10.6743	−0.970394
$122$	−26.9469	−2.43966
$123$	2.36781	0.213498
$124$	−37.0051	−3.32316
$125$	0	0
$126$	2.38118	0.212132
$127$	3.90704	0.346693	0.173347	−	0.984861i	$-0.444542\pi$
$127$	3.90704	0.346693	0.173347	+	0.984861i	$0.444542\pi$
$128$	18.0128	1.59212
$129$	−2.76676	−0.243600
$130$	0	0
$131$	−3.91653	−0.342189	−0.171095	−	0.985255i	$-0.554730\pi$
$131$	−3.91653	−0.342189	−0.171095	+	0.985255i	$0.554730\pi$
$132$	0.582161	0.0506706
$133$	−0.905041	−0.0784770
$134$	−9.66354	−0.834803
$135$	0	0
$136$	6.10127	0.523179
$137$	19.5648	1.67153	0.835766	−	0.549086i	$-0.185024\pi$
$137$	19.5648	1.67153	0.835766	+	0.549086i	$0.185024\pi$
$138$	4.41050	0.375447
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	0	0
$141$	2.20298	0.185525
$142$	11.7582	0.986728
$143$	−0.373807	−0.0312593
$144$	−14.4636	−1.20530
$145$	0	0
$146$	−14.8489	−1.22890
$147$	−1.69462	−0.139770
$148$	19.4660	1.60009
$149$	4.30582	0.352747	0.176373	−	0.984323i	$-0.443563\pi$
$149$	4.30582	0.352747	0.176373	+	0.984323i	$0.443563\pi$
$150$	0	0
$151$	−15.8273	−1.28801	−0.644003	−	0.765023i	$-0.722728\pi$
$151$	−15.8273	−1.28801	−0.644003	+	0.765023i	$0.722728\pi$
$152$	14.7699	1.19800
$153$	3.36441	0.271997
$154$	−0.462269	−0.0372507
$155$	0	0
$156$	−0.668219	−0.0535004
$157$	−1.14090	−0.0910534	−0.0455267	−	0.998963i	$-0.514497\pi$
$157$	−1.14090	−0.0910534	−0.0455267	+	0.998963i	$0.514497\pi$
$158$	−15.3190	−1.21871
$159$	−1.77365	−0.140660
$160$	0	0
$161$	−2.36320	−0.186246
$162$	−20.9789	−1.64826
$163$	2.94076	0.230338	0.115169	−	0.993346i	$-0.463259\pi$
$163$	2.94076	0.230338	0.115169	+	0.993346i	$0.463259\pi$
$164$	39.9680	3.12098
$165$	0	0
$166$	−35.9912	−2.79346
$167$	−4.64987	−0.359818	−0.179909	−	0.983683i	$-0.557580\pi$
$167$	−4.64987	−0.359818	−0.179909	+	0.983683i	$0.557580\pi$
$168$	−0.428078	−0.0330270
$169$	−12.5709	−0.966995
$170$	0	0
$171$	8.14455	0.622830
$172$	−46.7023	−3.56102
$173$	−2.04281	−0.155312	−0.0776559	−	0.996980i	$-0.524744\pi$
$173$	−2.04281	−0.155312	−0.0776559	+	0.996980i	$0.524744\pi$
$174$	−4.79414	−0.363443
$175$	0	0
$176$	2.80788	0.211652
$177$	−1.37200	−0.103126
$178$	−28.6341	−2.14622
$179$	−18.4289	−1.37744	−0.688719	−	0.725029i	$-0.741827\pi$
$179$	−18.4289	−1.37744	−0.688719	+	0.725029i	$0.741827\pi$
$180$	0	0
$181$	1.48337	0.110258	0.0551290	−	0.998479i	$-0.482443\pi$
$181$	1.48337	0.110258	0.0551290	+	0.998479i	$0.482443\pi$
$182$	0.530604	0.0393310
$183$	2.67134	0.197471
$184$	38.5665	2.84316
$185$	0	0
$186$	5.43651	0.398625
$187$	−0.653149	−0.0477630
$188$	37.1859	2.71206
$189$	−0.476962	−0.0346939
$190$	0	0
$191$	15.1176	1.09387	0.546937	−	0.837174i	$-0.315794\pi$
$191$	15.1176	1.09387	0.546937	+	0.837174i	$0.315794\pi$
$192$	−1.48033	−0.106834
$193$	−12.6498	−0.910553	−0.455276	−	0.890350i	$-0.650460\pi$
$193$	−12.6498	−0.910553	−0.455276	+	0.890350i	$0.650460\pi$
$194$	−14.4367	−1.03649
$195$	0	0
$196$	−28.6048	−2.04320
$197$	−20.0054	−1.42532	−0.712662	−	0.701508i	$-0.752511\pi$
$197$	−20.0054	−1.42532	−0.712662	+	0.701508i	$0.752511\pi$
$198$	4.16001	0.295639
$199$	−11.0064	−0.780220	−0.390110	−	0.920768i	$-0.627563\pi$
$199$	−11.0064	−0.780220	−0.390110	+	0.920768i	$0.627563\pi$
$200$	0	0
$201$	0.957980	0.0675707
$202$	−25.5182	−1.79546
$203$	2.56876	0.180292
$204$	−1.16757	−0.0817464
$205$	0	0
$206$	−0.129132	−0.00899705
$207$	21.2667	1.47814
$208$	−3.22296	−0.223472
$209$	−1.58114	−0.109370
$210$	0	0
$211$	9.89782	0.681394	0.340697	−	0.940173i	$-0.389337\pi$
$211$	9.89782	0.681394	0.340697	+	0.940173i	$0.389337\pi$
$212$	−29.9388	−2.05621
$213$	−1.16563	−0.0798679
$214$	−20.4996	−1.40133
$215$	0	0
$216$	7.78384	0.529623
$217$	−2.91295	−0.197744
$218$	2.40851	0.163125
$219$	1.47202	0.0994698
$220$	0	0
$221$	0.749700	0.0504303
$222$	−2.85980	−0.191937
$223$	−6.88052	−0.460753	−0.230377	−	0.973102i	$-0.573996\pi$
$223$	−6.88052	−0.460753	−0.230377	+	0.973102i	$0.573996\pi$
$224$	−0.503048	−0.0336113
$225$	0	0
$226$	0.193914	0.0128989
$227$	−28.2205	−1.87306	−0.936529	−	0.350591i	$-0.885981\pi$
$227$	−28.2205	−1.87306	−0.936529	+	0.350591i	$0.885981\pi$
$228$	−2.82645	−0.187186
$229$	24.7429	1.63505	0.817527	−	0.575890i	$-0.195344\pi$
$229$	24.7429	1.63505	0.817527	+	0.575890i	$0.195344\pi$
$230$	0	0
$231$	0.0458263	0.00301515
$232$	−41.9212	−2.75226
$233$	18.1608	1.18975	0.594877	−	0.803817i	$-0.297201\pi$
$233$	18.1608	1.18975	0.594877	+	0.803817i	$0.297201\pi$
$234$	−4.77496	−0.312149
$235$	0	0
$236$	−23.1590	−1.50752
$237$	1.51862	0.0986452
$238$	0.927119	0.0600962
$239$	22.9960	1.48748	0.743742	−	0.668466i	$-0.233049\pi$
$239$	22.9960	1.48748	0.743742	+	0.668466i	$0.233049\pi$
$240$	0	0
$241$	29.9171	1.92713	0.963564	−	0.267477i	$-0.0861900\pi$
$241$	29.9171	1.92713	0.963564	+	0.267477i	$0.0861900\pi$
$242$	26.4707	1.70160
$243$	6.46019	0.414421
$244$	45.0915	2.88669
$245$	0	0
$246$	−5.87180	−0.374372
$247$	1.81487	0.115477
$248$	47.5383	3.01868
$249$	3.56793	0.226108
$250$	0	0
$251$	14.5346	0.917416	0.458708	−	0.888587i	$-0.348312\pi$
$251$	14.5346	0.917416	0.458708	+	0.888587i	$0.348312\pi$
$252$	−3.98455	−0.251003
$253$	−4.12860	−0.259563
$254$	−9.68886	−0.607933
$255$	0	0
$256$	−32.6257	−2.03911
$257$	−0.986686	−0.0615478	−0.0307739	−	0.999526i	$-0.509797\pi$
$257$	−0.986686	−0.0615478	−0.0307739	+	0.999526i	$0.509797\pi$
$258$	6.86116	0.427157
$259$	1.53232	0.0952134
$260$	0	0
$261$	−23.1165	−1.43088
$262$	9.71241	0.600035
$263$	9.74159	0.600692	0.300346	−	0.953830i	$-0.402898\pi$
$263$	9.74159	0.600692	0.300346	+	0.953830i	$0.402898\pi$
$264$	−0.747869	−0.0460281
$265$	0	0
$266$	2.24437	0.137611
$267$	2.83860	0.173720
$268$	16.1705	0.987769
$269$	2.53822	0.154758	0.0773791	−	0.997002i	$-0.475345\pi$
$269$	2.53822	0.154758	0.0773791	+	0.997002i	$0.475345\pi$
$270$	0	0
$271$	13.1783	0.800527	0.400263	−	0.916400i	$-0.368919\pi$
$271$	13.1783	0.800527	0.400263	+	0.916400i	$0.368919\pi$
$272$	−5.63144	−0.341456
$273$	−0.0526006	−0.00318354
$274$	−48.5177	−2.93106
$275$	0	0
$276$	−7.38030	−0.444242
$277$	−14.6123	−0.877967	−0.438983	−	0.898495i	$-0.644661\pi$
$277$	−14.6123	−0.877967	−0.438983	+	0.898495i	$0.644661\pi$
$278$	−2.47985	−0.148731
$279$	26.2140	1.56939
$280$	0	0
$281$	3.35534	0.200163	0.100081	−	0.994979i	$-0.468090\pi$
$281$	3.35534	0.200163	0.100081	+	0.994979i	$0.468090\pi$
$282$	−5.46307	−0.325321
$283$	−11.8499	−0.704403	−0.352202	−	0.935924i	$-0.614567\pi$
$283$	−11.8499	−0.704403	−0.352202	+	0.935924i	$0.614567\pi$
$284$	−19.6756	−1.16753
$285$	0	0
$286$	0.926985	0.0548138
$287$	3.14619	0.185713
$288$	4.52698	0.266755
$289$	−15.6901	−0.922945
$290$	0	0
$291$	1.43116	0.0838960
$292$	24.8473	1.45408
$293$	−13.7232	−0.801717	−0.400859	−	0.916140i	$-0.631288\pi$
$293$	−13.7232	−0.801717	−0.400859	+	0.916140i	$0.631288\pi$
$294$	4.20241	0.245089
$295$	0	0
$296$	−25.0068	−1.45349
$297$	−0.833270	−0.0483513
$298$	−10.6778	−0.618548
$299$	4.73891	0.274058
$300$	0	0
$301$	−3.67629	−0.211898
$302$	39.2493	2.25854
$303$	2.52971	0.145328
$304$	−13.6326	−0.781881
$305$	0	0
$306$	−8.34324	−0.476951
$307$	19.3132	1.10226	0.551131	−	0.834419i	$-0.314197\pi$
$307$	19.3132	1.10226	0.551131	+	0.834419i	$0.314197\pi$
$308$	0.773538	0.0440764
$309$	0.0128013	0.000728241 0
$310$	0	0
$311$	20.7756	1.17807	0.589037	−	0.808106i	$-0.299507\pi$
$311$	20.7756	1.17807	0.589037	+	0.808106i	$0.299507\pi$
$312$	0.858422	0.0485986
$313$	27.5648	1.55805	0.779026	−	0.626991i	$-0.215714\pi$
$313$	27.5648	1.55805	0.779026	+	0.626991i	$0.215714\pi$
$314$	2.82925	0.159664
$315$	0	0
$316$	25.6340	1.44203
$317$	18.7677	1.05410	0.527049	−	0.849835i	$-0.323298\pi$
$317$	18.7677	1.05410	0.527049	+	0.849835i	$0.323298\pi$
$318$	4.39839	0.246649
$319$	4.48772	0.251264
$320$	0	0
$321$	2.03220	0.113426
$322$	5.86038	0.326586
$323$	3.17110	0.176445
$324$	35.1050	1.95028
$325$	0	0
$326$	−7.29264	−0.403902
$327$	−0.238764	−0.0132037
$328$	−51.3446	−2.83503
$329$	2.92718	0.161381
$330$	0	0
$331$	−0.0825219	−0.00453581	−0.00226791	−	0.999997i	$-0.500722\pi$
$331$	−0.0825219	−0.00453581	−0.00226791	+	0.999997i	$0.500722\pi$
$332$	60.2258	3.30532
$333$	−13.7895	−0.755658
$334$	11.5310	0.630947
$335$	0	0
$336$	0.395114	0.0215553
$337$	−13.5611	−0.738718	−0.369359	−	0.929287i	$-0.620423\pi$
$337$	−13.5611	−0.738718	−0.369359	+	0.929287i	$0.620423\pi$
$338$	31.1740	1.69564
$339$	−0.0192233	−0.00104407
$340$	0	0
$341$	−5.08903	−0.275587
$342$	−20.1973	−1.09214
$343$	−4.53826	−0.245043
$344$	59.9957	3.23475
$345$	0	0
$346$	5.06586	0.272342
$347$	14.0479	0.754130	0.377065	−	0.926187i	$-0.376933\pi$
$347$	14.0479	0.754130	0.377065	+	0.926187i	$0.376933\pi$
$348$	8.02226	0.430038
$349$	29.7905	1.59465	0.797323	−	0.603553i	$-0.206249\pi$
$349$	29.7905	1.59465	0.797323	+	0.603553i	$0.206249\pi$
$350$	0	0
$351$	0.956449	0.0510515
$352$	−0.878843	−0.0468425
$353$	−1.66236	−0.0884787	−0.0442394	−	0.999021i	$-0.514086\pi$
$353$	−1.66236	−0.0884787	−0.0442394	+	0.999021i	$0.514086\pi$
$354$	3.40235	0.180833
$355$	0	0
$356$	47.9149	2.53949
$357$	−0.0919085	−0.00486431
$358$	45.7008	2.41536
$359$	−19.7653	−1.04317	−0.521586	−	0.853198i	$-0.674660\pi$
$359$	−19.7653	−1.04317	−0.521586	+	0.853198i	$0.674660\pi$
$360$	0	0
$361$	−11.3234	−0.595969
$362$	−3.67854	−0.193340
$363$	−2.62414	−0.137731
$364$	−0.887886	−0.0465379
$365$	0	0
$366$	−6.62451	−0.346269
$367$	20.9268	1.09237	0.546185	−	0.837665i	$-0.316080\pi$
$367$	20.9268	1.09237	0.546185	+	0.837665i	$0.316080\pi$
$368$	−35.5967	−1.85561
$369$	−28.3128	−1.47391
$370$	0	0
$371$	−2.35671	−0.122354
$372$	−9.09719	−0.471667
$373$	−11.5715	−0.599147	−0.299574	−	0.954073i	$-0.596844\pi$
$373$	−11.5715	−0.599147	−0.299574	+	0.954073i	$0.596844\pi$
$374$	1.61971	0.0837532
$375$	0	0
$376$	−47.7705	−2.46358
$377$	−5.15111	−0.265296
$378$	1.18279	0.0608364
$379$	20.9839	1.07787	0.538935	−	0.842347i	$-0.318827\pi$
$379$	20.9839	1.07787	0.538935	+	0.842347i	$0.318827\pi$
$380$	0	0
$381$	0.960490	0.0492074
$382$	−37.4895	−1.91813
$383$	15.1795	0.775639	0.387819	−	0.921735i	$-0.373228\pi$
$383$	15.1795	0.775639	0.387819	+	0.921735i	$0.373228\pi$
$384$	4.42819	0.225975
$385$	0	0
$386$	31.3696	1.59667
$387$	33.0833	1.68172
$388$	24.1576	1.22642
$389$	2.64861	0.134290	0.0671450	−	0.997743i	$-0.478611\pi$
$389$	2.64861	0.134290	0.0671450	+	0.997743i	$0.478611\pi$
$390$	0	0
$391$	8.28024	0.418750
$392$	36.7469	1.85600
$393$	−0.962825	−0.0485681
$394$	49.6103	2.49933
$395$	0	0
$396$	−6.96115	−0.349811
$397$	24.5634	1.23280	0.616400	−	0.787433i	$-0.288590\pi$
$397$	24.5634	1.23280	0.616400	+	0.787433i	$0.288590\pi$
$398$	27.2941	1.36813
$399$	−0.222492	−0.0111385
$400$	0	0
$401$	36.8459	1.84000	0.919998	−	0.391923i	$-0.128190\pi$
$401$	36.8459	1.84000	0.919998	+	0.391923i	$0.128190\pi$
$402$	−2.37565	−0.118486
$403$	5.84132	0.290977
$404$	42.7009	2.12445
$405$	0	0
$406$	−6.37014	−0.316145
$407$	2.67701	0.132694
$408$	1.49991	0.0742567
$409$	−6.96504	−0.344399	−0.172199	−	0.985062i	$-0.555087\pi$
$409$	−6.96504	−0.344399	−0.172199	+	0.985062i	$0.555087\pi$
$410$	0	0
$411$	4.80973	0.237246
$412$	0.216083	0.0106456
$413$	−1.82302	−0.0897049
$414$	−52.7382	−2.59194
$415$	0	0
$416$	1.00876	0.0494585
$417$	0.245836	0.0120386
$418$	3.92099	0.191782
$419$	−1.96945	−0.0962140	−0.0481070	−	0.998842i	$-0.515319\pi$
$419$	−1.96945	−0.0962140	−0.0481070	+	0.998842i	$0.515319\pi$
$420$	0	0
$421$	−35.7362	−1.74168	−0.870838	−	0.491570i	$-0.836423\pi$
$421$	−35.7362	−1.74168	−0.870838	+	0.491570i	$0.836423\pi$
$422$	−24.5451	−1.19484
$423$	−26.3420	−1.28079
$424$	38.4606	1.86781
$425$	0	0
$426$	2.89060	0.140050
$427$	3.54950	0.171772
$428$	34.3030	1.65810
$429$	−0.0918952	−0.00443674
$430$	0	0
$431$	−28.8284	−1.38862	−0.694308	−	0.719678i	$-0.744289\pi$
$431$	−28.8284	−1.38862	−0.694308	+	0.719678i	$0.744289\pi$
$432$	−7.18445	−0.345662
$433$	28.0446	1.34774	0.673869	−	0.738851i	$-0.264631\pi$
$433$	28.0446	1.34774	0.673869	+	0.738851i	$0.264631\pi$
$434$	7.22369	0.346748
$435$	0	0
$436$	−4.03027	−0.193015
$437$	20.0448	0.958871
$438$	−3.65039	−0.174422
$439$	27.0360	1.29036	0.645180	−	0.764031i	$-0.276782\pi$
$439$	27.0360	1.29036	0.645180	+	0.764031i	$0.276782\pi$
$440$	0	0
$441$	20.2633	0.964919
$442$	−1.85914	−0.0884305
$443$	8.67760	0.412285	0.206143	−	0.978522i	$-0.433909\pi$
$443$	8.67760	0.412285	0.206143	+	0.978522i	$0.433909\pi$
$444$	4.78544	0.227107
$445$	0	0
$446$	17.0626	0.807940
$447$	1.05853	0.0500666
$448$	−1.96697	−0.0929306
$449$	−14.6027	−0.689142	−0.344571	−	0.938760i	$-0.611976\pi$
$449$	−14.6027	−0.689142	−0.344571	+	0.938760i	$0.611976\pi$
$450$	0	0
$451$	5.49650	0.258820
$452$	−0.324485	−0.0152625
$453$	−3.89092	−0.182811
$454$	69.9825	3.28444
$455$	0	0
$456$	3.63098	0.170036
$457$	−13.1688	−0.616010	−0.308005	−	0.951385i	$-0.599661\pi$
$457$	−13.1688	−0.616010	−0.308005	+	0.951385i	$0.599661\pi$
$458$	−61.3586	−2.86710
$459$	1.67119	0.0780046
$460$	0	0
$461$	−4.68827	−0.218354	−0.109177	−	0.994022i	$-0.534822\pi$
$461$	−4.68827	−0.218354	−0.109177	+	0.994022i	$0.534822\pi$
$462$	−0.113642	−0.00528713
$463$	−25.1950	−1.17091	−0.585454	−	0.810705i	$-0.699084\pi$
$463$	−25.1950	−1.17091	−0.585454	+	0.810705i	$0.699084\pi$
$464$	38.6930	1.79628
$465$	0	0
$466$	−45.0360	−2.08625
$467$	24.2118	1.12039	0.560193	−	0.828362i	$-0.310727\pi$
$467$	24.2118	1.12039	0.560193	+	0.828362i	$0.310727\pi$
$468$	7.99018	0.369346
$469$	1.27290	0.0587771
$470$	0	0
$471$	−0.280473	−0.0129235
$472$	29.7510	1.36940
$473$	−6.42262	−0.295312
$474$	−3.76596	−0.172976
$475$	0	0
$476$	−1.55139	−0.0711080
$477$	21.2083	0.971060
$478$	−57.0265	−2.60833
$479$	−22.0171	−1.00599	−0.502994	−	0.864290i	$-0.667768\pi$
$479$	−22.0171	−1.00599	−0.502994	+	0.864290i	$0.667768\pi$
$480$	0	0
$481$	−3.07274	−0.140105
$482$	−74.1899	−3.37926
$483$	−0.580960	−0.0264346
$484$	−44.2948	−2.01340
$485$	0	0
$486$	−16.0203	−0.726695
$487$	35.4094	1.60455	0.802276	−	0.596953i	$-0.203622\pi$
$487$	35.4094	1.60455	0.802276	+	0.596953i	$0.203622\pi$
$488$	−57.9265	−2.62221
$489$	0.722944	0.0326927
$490$	0	0
$491$	43.9214	1.98214	0.991072	−	0.133328i	$-0.0425663\pi$
$491$	43.9214	1.98214	0.991072	+	0.133328i	$0.0425663\pi$
$492$	9.82557	0.442971
$493$	−9.00048	−0.405361
$494$	−4.50061	−0.202492
$495$	0	0
$496$	−43.8776	−1.97016
$497$	−1.54882	−0.0694740
$498$	−8.84793	−0.396485
$499$	6.73789	0.301630	0.150815	−	0.988562i	$-0.451810\pi$
$499$	6.73789	0.301630	0.150815	+	0.988562i	$0.451810\pi$
$500$	0	0
$501$	−1.14311	−0.0510702
$502$	−36.0436	−1.60871
$503$	0.982907	0.0438257	0.0219128	−	0.999760i	$-0.493024\pi$
$503$	0.982907	0.0438257	0.0219128	+	0.999760i	$0.493024\pi$
$504$	5.11871	0.228006
$505$	0	0
$506$	10.2383	0.455148
$507$	−3.09039	−0.137249
$508$	16.2129	0.719329
$509$	−32.6107	−1.44544	−0.722721	−	0.691140i	$-0.757109\pi$
$509$	−32.6107	−1.44544	−0.722721	+	0.691140i	$0.757109\pi$
$510$	0	0
$511$	1.95592	0.0865249
$512$	44.8813	1.98349
$513$	4.04561	0.178618
$514$	2.44683	0.107925
$515$	0	0
$516$	−11.4811	−0.505428
$517$	5.11389	0.224909
$518$	−3.79991	−0.166959
$519$	−0.502196	−0.0220440
$520$	0	0
$521$	8.76803	0.384134	0.192067	−	0.981382i	$-0.438481\pi$
$521$	8.76803	0.384134	0.192067	+	0.981382i	$0.438481\pi$
$522$	57.3255	2.50907
$523$	28.4574	1.24436	0.622178	−	0.782876i	$-0.286248\pi$
$523$	28.4574	1.24436	0.622178	+	0.782876i	$0.286248\pi$
$524$	−16.2523	−0.709983
$525$	0	0
$526$	−24.1577	−1.05332
$527$	10.2065	0.444601
$528$	0.690279	0.0300405
$529$	29.3400	1.27565
$530$	0	0
$531$	16.4055	0.711940
$532$	−3.75561	−0.162826
$533$	−6.30902	−0.273274
$534$	−7.03930	−0.304620
$535$	0	0
$536$	−20.7733	−0.897268
$537$	−4.53048	−0.195505
$538$	−6.29441	−0.271371
$539$	−3.93381	−0.169441
$540$	0	0
$541$	25.4795	1.09545	0.547725	−	0.836658i	$-0.315494\pi$
$541$	25.4795	1.09545	0.547725	+	0.836658i	$0.315494\pi$
$542$	−32.6803	−1.40374
$543$	0.364666	0.0156493
$544$	1.76259	0.0755705
$545$	0	0
$546$	0.130442	0.00558239
$547$	10.7278	0.458689	0.229344	−	0.973345i	$-0.426342\pi$
$547$	10.7278	0.458689	0.229344	+	0.973345i	$0.426342\pi$
$548$	81.1870	3.46814
$549$	−31.9423	−1.36326
$550$	0	0
$551$	−21.7883	−0.928214
$552$	9.48105	0.403540
$553$	2.01785	0.0858077
$554$	36.2363	1.53953
$555$	0	0
$556$	4.14965	0.175985
$557$	−31.2761	−1.32521	−0.662606	−	0.748968i	$-0.730550\pi$
$557$	−31.2761	−1.32521	−0.662606	+	0.748968i	$0.730550\pi$
$558$	−65.0067	−2.75195
$559$	7.37204	0.311804
$560$	0	0
$561$	−0.160567	−0.00677916
$562$	−8.32074	−0.350989
$563$	−18.9842	−0.800090	−0.400045	−	0.916496i	$-0.631005\pi$
$563$	−18.9842	−0.800090	−0.400045	+	0.916496i	$0.631005\pi$
$564$	9.14162	0.384932
$565$	0	0
$566$	29.3860	1.23518
$567$	2.76338	0.116051
$568$	25.2761	1.06056
$569$	20.9669	0.878978	0.439489	−	0.898248i	$-0.355159\pi$
$569$	20.9669	0.878978	0.439489	+	0.898248i	$0.355159\pi$
$570$	0	0
$571$	−10.2145	−0.427464	−0.213732	−	0.976892i	$-0.568562\pi$
$571$	−10.2145	−0.427464	−0.213732	+	0.976892i	$0.568562\pi$
$572$	−1.55117	−0.0648576
$573$	3.71646	0.155257
$574$	−7.80207	−0.325652
$575$	0	0
$576$	17.7010	0.737540
$577$	3.73780	0.155607	0.0778033	−	0.996969i	$-0.475209\pi$
$577$	3.73780	0.155607	0.0778033	+	0.996969i	$0.475209\pi$
$578$	38.9090	1.61840
$579$	−3.10978	−0.129238
$580$	0	0
$581$	4.74083	0.196683
$582$	−3.54906	−0.147113
$583$	−4.11726	−0.170519
$584$	−31.9199	−1.32086
$585$	0	0
$586$	34.0315	1.40583
$587$	15.3677	0.634293	0.317147	−	0.948377i	$-0.397275\pi$
$587$	15.3677	0.634293	0.317147	+	0.948377i	$0.397275\pi$
$588$	−7.03209	−0.289999
$589$	24.7078	1.01807
$590$	0	0
$591$	−4.91804	−0.202301
$592$	23.0812	0.948630
$593$	34.5495	1.41878	0.709389	−	0.704817i	$-0.248971\pi$
$593$	34.5495	1.41878	0.709389	+	0.704817i	$0.248971\pi$
$594$	2.06639	0.0847848
$595$	0	0
$596$	17.8677	0.731889
$597$	−2.70576	−0.110739
$598$	−11.7518	−0.480566
$599$	46.5366	1.90143	0.950717	−	0.310060i	$-0.100349\pi$
$599$	46.5366	1.90143	0.950717	+	0.310060i	$0.100349\pi$
$600$	0	0
$601$	−30.4861	−1.24356	−0.621778	−	0.783194i	$-0.713589\pi$
$601$	−30.4861	−1.24356	−0.621778	+	0.783194i	$0.713589\pi$
$602$	9.11666	0.371567
$603$	−11.4550	−0.466482
$604$	−65.6778	−2.67239
$605$	0	0
$606$	−6.27330	−0.254835
$607$	13.2182	0.536511	0.268256	−	0.963348i	$-0.413553\pi$
$607$	13.2182	0.536511	0.268256	+	0.963348i	$0.413553\pi$
$608$	4.26688	0.173045
$609$	0.631494	0.0255894
$610$	0	0
$611$	−5.86986	−0.237469
$612$	13.9611	0.564346
$613$	16.8823	0.681869	0.340935	−	0.940087i	$-0.389257\pi$
$613$	16.8823	0.681869	0.340935	+	0.940087i	$0.389257\pi$
$614$	−47.8938	−1.93284
$615$	0	0
$616$	−0.993719	−0.0400381
$617$	16.5346	0.665659	0.332829	−	0.942987i	$-0.391997\pi$
$617$	16.5346	0.665659	0.332829	+	0.942987i	$0.391997\pi$
$618$	−0.0317453	−0.00127698
$619$	19.1064	0.767952	0.383976	−	0.923343i	$-0.374555\pi$
$619$	19.1064	0.767952	0.383976	+	0.923343i	$0.374555\pi$
$620$	0	0
$621$	10.5637	0.423908
$622$	−51.5202	−2.06577
$623$	3.77175	0.151112
$624$	−0.792320	−0.0317182
$625$	0	0
$626$	−68.3565	−2.73207
$627$	−0.388701	−0.0155232
$628$	−4.73432	−0.188920
$629$	−5.36896	−0.214075
$630$	0	0
$631$	−20.1170	−0.800844	−0.400422	−	0.916331i	$-0.631136\pi$
$631$	−20.1170	−0.800844	−0.400422	+	0.916331i	$0.631136\pi$
$632$	−32.9305	−1.30991
$633$	2.43324	0.0967127
$634$	−46.5410	−1.84838
$635$	0	0
$636$	−7.36004	−0.291844
$637$	4.51532	0.178904
$638$	−11.1289	−0.440596
$639$	13.9380	0.551378
$640$	0	0
$641$	−19.2938	−0.762061	−0.381031	−	0.924562i	$-0.624431\pi$
$641$	−19.2938	−0.762061	−0.381031	+	0.924562i	$0.624431\pi$
$642$	−5.03955	−0.198895
$643$	−29.2745	−1.15447	−0.577237	−	0.816577i	$-0.695869\pi$
$643$	−29.2745	−1.15447	−0.577237	+	0.816577i	$0.695869\pi$
$644$	−9.80647	−0.386429
$645$	0	0
$646$	−7.86386	−0.309399
$647$	−19.8266	−0.779466	−0.389733	−	0.920928i	$-0.627433\pi$
$647$	−19.8266	−0.779466	−0.389733	+	0.920928i	$0.627433\pi$
$648$	−45.0973	−1.77159
$649$	−3.18488	−0.125018
$650$	0	0
$651$	−0.716109	−0.0280665
$652$	12.2031	0.477911
$653$	35.7848	1.40037	0.700183	−	0.713963i	$-0.253102\pi$
$653$	35.7848	1.40037	0.700183	+	0.713963i	$0.253102\pi$
$654$	0.592098	0.0231529
$655$	0	0
$656$	47.3908	1.85030
$657$	−17.6015	−0.686702
$658$	−7.25897	−0.282984
$659$	−21.1886	−0.825389	−0.412695	−	0.910869i	$-0.635412\pi$
$659$	−21.1886	−0.825389	−0.412695	+	0.910869i	$0.635412\pi$
$660$	0	0
$661$	8.67722	0.337505	0.168752	−	0.985658i	$-0.446026\pi$
$661$	8.67722	0.337505	0.168752	+	0.985658i	$0.446026\pi$
$662$	0.204642	0.00795363
$663$	0.184303	0.00715775
$664$	−77.3686	−3.00248
$665$	0	0
$666$	34.1958	1.32506
$667$	−56.8927	−2.20289
$668$	−19.2953	−0.746559
$669$	−1.69148	−0.0653964
$670$	0	0
$671$	6.20110	0.239391
$672$	−0.123667	−0.00477057
$673$	7.11219	0.274155	0.137077	−	0.990560i	$-0.456229\pi$
$673$	7.11219	0.274155	0.137077	+	0.990560i	$0.456229\pi$
$674$	33.6294	1.29536
$675$	0	0
$676$	−52.1650	−2.00635
$677$	16.7747	0.644704	0.322352	−	0.946620i	$-0.395527\pi$
$677$	16.7747	0.644704	0.322352	+	0.946620i	$0.395527\pi$
$678$	0.0476709	0.00183079
$679$	1.90163	0.0729779
$680$	0	0
$681$	−6.93760	−0.265850
$682$	12.6200	0.483246
$683$	−47.7431	−1.82684	−0.913419	−	0.407020i	$-0.866568\pi$
$683$	−47.7431	−1.82684	−0.913419	+	0.407020i	$0.866568\pi$
$684$	33.7971	1.29226
$685$	0	0
$686$	11.2542	0.429687
$687$	6.08269	0.232069
$688$	−55.3758	−2.11118
$689$	4.72589	0.180042
$690$	0	0
$691$	−30.4574	−1.15865	−0.579327	−	0.815095i	$-0.696685\pi$
$691$	−30.4574	−1.15865	−0.579327	+	0.815095i	$0.696685\pi$
$692$	−8.47695	−0.322245
$693$	−0.547965	−0.0208155
$694$	−34.8367	−1.32238
$695$	0	0
$696$	−10.3057	−0.390638
$697$	−11.0237	−0.417552
$698$	−73.8758	−2.79624
$699$	4.46458	0.168866
$700$	0	0
$701$	−19.6196	−0.741020	−0.370510	−	0.928828i	$-0.620817\pi$
$701$	−19.6196	−0.741020	−0.370510	+	0.928828i	$0.620817\pi$
$702$	−2.37185	−0.0895197
$703$	−12.9972	−0.490197
$704$	−3.43637	−0.129513
$705$	0	0
$706$	4.12241	0.155149
$707$	3.36131	0.126415
$708$	−5.69331	−0.213968
$709$	11.6038	0.435790	0.217895	−	0.975972i	$-0.430081\pi$
$709$	11.6038	0.435790	0.217895	+	0.975972i	$0.430081\pi$
$710$	0	0
$711$	−18.1588	−0.681009
$712$	−61.5535	−2.30681
$713$	64.5158	2.41614
$714$	0.227919	0.00852966
$715$	0	0
$716$	−76.4734	−2.85794
$717$	5.65323	0.211124
$718$	49.0150	1.82922
$719$	26.2649	0.979514	0.489757	−	0.871859i	$-0.337085\pi$
$719$	26.2649	0.979514	0.489757	+	0.871859i	$0.337085\pi$
$720$	0	0
$721$	0.0170095	0.000633468 0
$722$	28.0803	1.04504
$723$	7.35470	0.273524
$724$	6.15548	0.228766
$725$	0	0
$726$	6.50746	0.241515
$727$	−0.451096	−0.0167302	−0.00836512	−	0.999965i	$-0.502663\pi$
$727$	−0.451096	−0.0167302	−0.00836512	+	0.999965i	$0.502663\pi$
$728$	1.14062	0.0422740
$729$	−23.7911	−0.881150
$730$	0	0
$731$	12.8811	0.476424
$732$	11.0851	0.409718
$733$	−36.4971	−1.34805	−0.674025	−	0.738708i	$-0.735436\pi$
$733$	−36.4971	−1.34805	−0.674025	+	0.738708i	$0.735436\pi$
$734$	−51.8953	−1.91549
$735$	0	0
$736$	11.1415	0.410680
$737$	2.22380	0.0819149
$738$	70.2116	2.58452
$739$	−15.0007	−0.551811	−0.275905	−	0.961185i	$-0.588978\pi$
$739$	−15.0007	−0.551811	−0.275905	+	0.961185i	$0.588978\pi$
$740$	0	0
$741$	0.446161	0.0163901
$742$	5.84429	0.214551
$743$	28.6822	1.05225	0.526125	−	0.850407i	$-0.323644\pi$
$743$	28.6822	1.05225	0.526125	+	0.850407i	$0.323644\pi$
$744$	11.6866	0.428452
$745$	0	0
$746$	28.6955	1.05062
$747$	−42.6632	−1.56097
$748$	−2.71034	−0.0990999
$749$	2.70025	0.0986651
$750$	0	0
$751$	30.4351	1.11059	0.555297	−	0.831652i	$-0.312605\pi$
$751$	30.4351	1.11059	0.555297	+	0.831652i	$0.312605\pi$
$752$	44.0919	1.60787
$753$	3.57313	0.130212
$754$	12.7740	0.465201
$755$	0	0
$756$	−1.97923	−0.0719838
$757$	−51.7252	−1.87998	−0.939992	−	0.341197i	$-0.889168\pi$
$757$	−51.7252	−1.87998	−0.939992	+	0.341197i	$0.889168\pi$
$758$	−52.0369	−1.89007
$759$	−1.01496	−0.0368406
$760$	0	0
$761$	29.6807	1.07593	0.537963	−	0.842969i	$-0.319194\pi$
$761$	29.6807	1.07593	0.537963	+	0.842969i	$0.319194\pi$
$762$	−2.38187	−0.0862861
$763$	−0.317253	−0.0114853
$764$	62.7330	2.26960
$765$	0	0
$766$	−37.6430	−1.36010
$767$	3.65569	0.131999
$768$	−8.02057	−0.289418
$769$	−3.68318	−0.132819	−0.0664095	−	0.997792i	$-0.521154\pi$
$769$	−3.68318	−0.132819	−0.0664095	+	0.997792i	$0.521154\pi$
$770$	0	0
$771$	−0.242563	−0.00873570
$772$	−52.4923	−1.88924
$773$	−24.8227	−0.892809	−0.446405	−	0.894831i	$-0.647296\pi$
$773$	−24.8227	−0.892809	−0.446405	+	0.894831i	$0.647296\pi$
$774$	−82.0417	−2.94893
$775$	0	0
$776$	−31.0339	−1.11405
$777$	0.376698	0.0135140
$778$	−6.56816	−0.235480
$779$	−26.6861	−0.956128
$780$	0	0
$781$	−2.70584	−0.0968226
$782$	−20.5338	−0.734285
$783$	−11.4826	−0.410354
$784$	−33.9172	−1.21133
$785$	0	0
$786$	2.38766	0.0851650
$787$	21.0833	0.751538	0.375769	−	0.926713i	$-0.377379\pi$
$787$	21.0833	0.751538	0.375769	+	0.926713i	$0.377379\pi$
$788$	−83.0154	−2.95730
$789$	2.39483	0.0852583
$790$	0	0
$791$	−0.0255427	−0.000908194 0
$792$	8.94258	0.317761
$793$	−7.11778	−0.252760
$794$	−60.9135	−2.16174
$795$	0	0
$796$	−45.6726	−1.61882
$797$	24.3975	0.864204	0.432102	−	0.901825i	$-0.357772\pi$
$797$	24.3975	0.864204	0.432102	+	0.901825i	$0.357772\pi$
$798$	0.551746	0.0195316
$799$	−10.2563	−0.362843
$800$	0	0
$801$	−33.9423	−1.19929
$802$	−91.3723	−3.22647
$803$	3.41707	0.120586
$804$	3.97529	0.140198
$805$	0	0
$806$	−14.4856	−0.510233
$807$	0.623987	0.0219654
$808$	−54.8553	−1.92980
$809$	9.84260	0.346048	0.173024	−	0.984918i	$-0.444646\pi$
$809$	9.84260	0.346048	0.173024	+	0.984918i	$0.444646\pi$
$810$	0	0
$811$	−46.1782	−1.62154	−0.810769	−	0.585367i	$-0.800951\pi$
$811$	−46.1782	−1.62154	−0.810769	+	0.585367i	$0.800951\pi$
$812$	10.6595	0.374074
$813$	3.23971	0.113622
$814$	−6.63858	−0.232682
$815$	0	0
$816$	−1.38441	−0.0484641
$817$	31.1825	1.09094
$818$	17.2722	0.603910
$819$	0.628968	0.0219779
$820$	0	0
$821$	−3.25038	−0.113439	−0.0567195	−	0.998390i	$-0.518064\pi$
$821$	−3.25038	−0.113439	−0.0567195	+	0.998390i	$0.518064\pi$
$822$	−11.9274	−0.416016
$823$	1.80449	0.0629005	0.0314503	−	0.999505i	$-0.489987\pi$
$823$	1.80449	0.0629005	0.0314503	+	0.999505i	$0.489987\pi$
$824$	−0.277589	−0.00967028
$825$	0	0
$826$	4.52081	0.157299
$827$	8.40455	0.292255	0.146127	−	0.989266i	$-0.453319\pi$
$827$	8.40455	0.292255	0.146127	+	0.989266i	$0.453319\pi$
$828$	88.2494	3.06688
$829$	−11.0909	−0.385205	−0.192602	−	0.981277i	$-0.561693\pi$
$829$	−11.0909	−0.385205	−0.192602	+	0.981277i	$0.561693\pi$
$830$	0	0
$831$	−3.59223	−0.124613
$832$	3.94435	0.136746
$833$	7.88957	0.273357
$834$	−0.609636	−0.0211100
$835$	0	0
$836$	−6.56118	−0.226923
$837$	13.0212	0.450077
$838$	4.88394	0.168713
$839$	−49.3189	−1.70268	−0.851339	−	0.524617i	$-0.824209\pi$
$839$	−49.3189	−1.70268	−0.851339	+	0.524617i	$0.824209\pi$
$840$	0	0
$841$	32.8413	1.13246
$842$	88.6204	3.05406
$843$	0.824864	0.0284098
$844$	41.0725	1.41378
$845$	0	0
$846$	65.3242	2.24589
$847$	−3.48678	−0.119807
$848$	−35.4990	−1.21904
$849$	−2.91313	−0.0999784
$850$	0	0
$851$	−33.9376	−1.16337
$852$	−4.83698	−0.165712
$853$	7.86042	0.269136	0.134568	−	0.990904i	$-0.457035\pi$
$853$	7.86042	0.269136	0.134568	+	0.990904i	$0.457035\pi$
$854$	−8.80222	−0.301206
$855$	0	0
$856$	−44.0671	−1.50618
$857$	−3.23243	−0.110418	−0.0552088	−	0.998475i	$-0.517582\pi$
$857$	−3.23243	−0.110418	−0.0552088	+	0.998475i	$0.517582\pi$
$858$	0.227886	0.00777991
$859$	−3.07827	−0.105029	−0.0525146	−	0.998620i	$-0.516724\pi$
$859$	−3.07827	−0.105029	−0.0525146	+	0.998620i	$0.516724\pi$
$860$	0	0
$861$	0.773446	0.0263590
$862$	71.4901	2.43496
$863$	50.4748	1.71818	0.859091	−	0.511822i	$-0.171029\pi$
$863$	50.4748	1.71818	0.859091	+	0.511822i	$0.171029\pi$
$864$	2.24867	0.0765013
$865$	0	0
$866$	−69.5464	−2.36328
$867$	−3.85718	−0.130997
$868$	−12.0877	−0.410285
$869$	3.52525	0.119586
$870$	0	0
$871$	−2.55254	−0.0864895
$872$	5.17746	0.175331
$873$	−17.1130	−0.579186
$874$	−49.7080	−1.68140
$875$	0	0
$876$	6.10837	0.206383
$877$	21.1020	0.712563	0.356281	−	0.934379i	$-0.384044\pi$
$877$	21.1020	0.712563	0.356281	+	0.934379i	$0.384044\pi$
$878$	−67.0453	−2.26267
$879$	−3.37366	−0.113791
$880$	0	0
$881$	27.3881	0.922730	0.461365	−	0.887210i	$-0.347360\pi$
$881$	27.3881	0.922730	0.461365	+	0.887210i	$0.347360\pi$
$882$	−50.2499	−1.69200
$883$	−23.3136	−0.784567	−0.392283	−	0.919844i	$-0.628315\pi$
$883$	−23.3136	−0.784567	−0.392283	+	0.919844i	$0.628315\pi$
$884$	3.11100	0.104634
$885$	0	0
$886$	−21.5191	−0.722950
$887$	−30.1658	−1.01287	−0.506435	−	0.862278i	$-0.669037\pi$
$887$	−30.1658	−1.01287	−0.506435	+	0.862278i	$0.669037\pi$
$888$	−6.14757	−0.206299
$889$	1.27624	0.0428036
$890$	0	0
$891$	4.82772	0.161735
$892$	−28.5518	−0.955984
$893$	−24.8285	−0.830853
$894$	−2.62499	−0.0877927
$895$	0	0
$896$	5.88389	0.196567
$897$	1.16499	0.0388980
$898$	36.2124	1.20842
$899$	−70.1276	−2.33889
$900$	0	0
$901$	8.25750	0.275097
$902$	−13.6305	−0.453846
$903$	−0.903766	−0.0300754
$904$	0.416847	0.0138641
$905$	0	0
$906$	9.64889	0.320563
$907$	26.8143	0.890353	0.445176	−	0.895443i	$-0.353141\pi$
$907$	26.8143	0.890353	0.445176	+	0.895443i	$0.353141\pi$
$908$	−117.105	−3.88627
$909$	−30.2488	−1.00329
$910$	0	0
$911$	24.7438	0.819798	0.409899	−	0.912131i	$-0.365564\pi$
$911$	24.7438	0.819798	0.409899	+	0.912131i	$0.365564\pi$
$912$	−3.35138	−0.110975
$913$	8.28241	0.274108
$914$	32.6566	1.08018
$915$	0	0
$916$	102.674	3.39246
$917$	−1.27934	−0.0422475
$918$	−4.14431	−0.136782
$919$	−27.2810	−0.899916	−0.449958	−	0.893050i	$-0.648561\pi$
$919$	−27.2810	−0.899916	−0.449958	+	0.893050i	$0.648561\pi$
$920$	0	0
$921$	4.74788	0.156448
$922$	11.6262	0.382888
$923$	3.10583	0.102230
$924$	0.190163	0.00625592
$925$	0	0
$926$	62.4797	2.05321
$927$	−0.153071	−0.00502750
$928$	−12.1106	−0.397549
$929$	31.6186	1.03737	0.518687	−	0.854964i	$-0.326421\pi$
$929$	31.6186	1.03737	0.518687	+	0.854964i	$0.326421\pi$
$930$	0	0
$931$	19.0990	0.625946
$932$	75.3610	2.46853
$933$	5.10738	0.167208
$934$	−60.0415	−1.96462
$935$	0	0
$936$	−10.2645	−0.335506
$937$	−35.8451	−1.17101	−0.585504	−	0.810670i	$-0.699103\pi$
$937$	−35.8451	−1.17101	−0.585504	+	0.810670i	$0.699103\pi$
$938$	−3.15660	−0.103067
$939$	6.77641	0.221140
$940$	0	0
$941$	49.3069	1.60736	0.803679	−	0.595063i	$-0.202873\pi$
$941$	49.3069	1.60736	0.803679	+	0.595063i	$0.202873\pi$
$942$	0.695531	0.0226616
$943$	−69.6815	−2.26914
$944$	−27.4600	−0.893748
$945$	0	0
$946$	15.9271	0.517836
$947$	43.3960	1.41018	0.705090	−	0.709118i	$-0.250907\pi$
$947$	43.3960	1.41018	0.705090	+	0.709118i	$0.250907\pi$
$948$	6.30176	0.204672
$949$	−3.92220	−0.127320
$950$	0	0
$951$	4.61377	0.149612
$952$	1.99299	0.0645930
$953$	−46.8528	−1.51771	−0.758856	−	0.651259i	$-0.774241\pi$
$953$	−46.8528	−1.51771	−0.758856	+	0.651259i	$0.774241\pi$
$954$	−52.5933	−1.70277
$955$	0	0
$956$	95.4253	3.08627
$957$	1.10324	0.0356628
$958$	54.5991	1.76402
$959$	6.39085	0.206371
$960$	0	0
$961$	48.5242	1.56530
$962$	7.61993	0.245676
$963$	−24.2999	−0.783052
$964$	124.146	3.99846
$965$	0	0
$966$	1.44069	0.0463535
$967$	9.07659	0.291884	0.145942	−	0.989293i	$-0.453379\pi$
$967$	9.07659	0.291884	0.145942	+	0.989293i	$0.453379\pi$
$968$	56.9029	1.82893
$969$	0.779572	0.0250435
$970$	0	0
$971$	−40.2761	−1.29252	−0.646260	−	0.763117i	$-0.723668\pi$
$971$	−40.2761	−1.29252	−0.646260	+	0.763117i	$0.723668\pi$
$972$	26.8075	0.859852
$973$	0.326651	0.0104719
$974$	−87.8099	−2.81361
$975$	0	0
$976$	53.4658	1.71140
$977$	22.5984	0.722987	0.361493	−	0.932375i	$-0.382267\pi$
$977$	22.5984	0.722987	0.361493	+	0.932375i	$0.382267\pi$
$978$	−1.79279	−0.0573272
$979$	6.58938	0.210598
$980$	0	0
$981$	2.85500	0.0911530
$982$	−108.918	−3.47573
$983$	−36.5906	−1.16706	−0.583530	−	0.812092i	$-0.698329\pi$
$983$	−36.5906	−1.16706	−0.583530	+	0.812092i	$0.698329\pi$
$984$	−12.6223	−0.402386
$985$	0	0
$986$	22.3198	0.710808
$987$	0.719607	0.0229053
$988$	7.53109	0.239596
$989$	81.4222	2.58908
$990$	0	0
$991$	−3.42163	−0.108692	−0.0543458	−	0.998522i	$-0.517307\pi$
$991$	−3.42163	−0.108692	−0.0543458	+	0.998522i	$0.517307\pi$
$992$	13.7333	0.436033
$993$	−0.0202868	−0.000643784 0
$994$	3.84084	0.121824
$995$	0	0
$996$	14.8057	0.469136
$997$	−57.7784	−1.82986	−0.914930	−	0.403613i	$-0.867754\pi$
$997$	−57.7784	−1.82986	−0.914930	+	0.403613i	$0.867754\pi$
$998$	−16.7090	−0.528913
$999$	−6.84959	−0.216711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3475.2.a.e.1.1		7
5.4	even	2		139.2.a.c.1.7	✓	7
15.14	odd	2		1251.2.a.k.1.1		7
20.19	odd	2		2224.2.a.o.1.4		7
35.34	odd	2		6811.2.a.p.1.7		7
40.19	odd	2		8896.2.a.bd.1.4		7
40.29	even	2		8896.2.a.be.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
139.2.a.c.1.7	✓	7	5.4	even	2
1251.2.a.k.1.1		7	15.14	odd	2
2224.2.a.o.1.4		7	20.19	odd	2
3475.2.a.e.1.1		7	1.1	even	1	trivial
6811.2.a.p.1.7		7	35.34	odd	2
8896.2.a.bd.1.4		7	40.19	odd	2
8896.2.a.be.1.4		7	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3475 = 5^{2} \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3475.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47985 q^{2} +0.245836 q^{3} +4.14965 q^{4} -0.609636 q^{6} +0.326651 q^{7} -5.33082 q^{8} -2.93956 q^{9} +O(q^{10})\)	\(q-2.47985 q^{2} +0.245836 q^{3} +4.14965 q^{4} -0.609636 q^{6} +0.326651 q^{7} -5.33082 q^{8} -2.93956 q^{9} +0.570671 q^{11} +1.02013 q^{12} -0.655030 q^{13} -0.810045 q^{14} +4.92032 q^{16} -1.14453 q^{17} +7.28968 q^{18} -2.77067 q^{19} +0.0803026 q^{21} -1.41518 q^{22} -7.23464 q^{23} -1.31051 q^{24} +1.62438 q^{26} -1.46016 q^{27} +1.35549 q^{28} +7.86393 q^{29} -8.91763 q^{31} -1.54002 q^{32} +0.140292 q^{33} +2.83826 q^{34} -12.1982 q^{36} +4.69099 q^{37} +6.87084 q^{38} -0.161030 q^{39} +9.63165 q^{41} -0.199138 q^{42} -11.2545 q^{43} +2.36809 q^{44} +17.9408 q^{46} +8.96119 q^{47} +1.20959 q^{48} -6.89330 q^{49} -0.281366 q^{51} -2.71815 q^{52} -7.21477 q^{53} +3.62098 q^{54} -1.74132 q^{56} -0.681130 q^{57} -19.5014 q^{58} -5.58094 q^{59} +10.8663 q^{61} +22.1144 q^{62} -0.960211 q^{63} -6.02163 q^{64} -0.347902 q^{66} +3.89682 q^{67} -4.74939 q^{68} -1.77853 q^{69} -4.74151 q^{71} +15.6703 q^{72} +5.98781 q^{73} -11.6329 q^{74} -11.4973 q^{76} +0.186410 q^{77} +0.399330 q^{78} +6.17739 q^{79} +8.45973 q^{81} -23.8850 q^{82} +14.5135 q^{83} +0.333228 q^{84} +27.9095 q^{86} +1.93324 q^{87} -3.04214 q^{88} +11.5467 q^{89} -0.213966 q^{91} -30.0212 q^{92} -2.19228 q^{93} -22.2224 q^{94} -0.378592 q^{96} +5.82160 q^{97} +17.0943 q^{98} -1.67752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 2 q^{3} + 9 q^{4} - 7 q^{6} + 5 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q - q^2 + 2 * q^3 + 9 * q^4 - 7 * q^6 + 5 * q^7 - 6 * q^8 + 13 * q^9	\( 7 q - q^{2} + 2 q^{3} + 9 q^{4} - 7 q^{6} + 5 q^{7} - 6 q^{8} + 13 q^{9} + 2 q^{11} + 8 q^{12} - 6 q^{13} + 7 q^{14} + 5 q^{16} - 5 q^{17} + 10 q^{18} - 10 q^{19} - 5 q^{21} + 18 q^{22} + q^{23} - 21 q^{24} - 8 q^{26} + 11 q^{27} + 28 q^{28} + 30 q^{29} - 20 q^{31} + 12 q^{32} + 20 q^{33} - 17 q^{34} + 2 q^{36} - 6 q^{37} - 6 q^{38} + 11 q^{39} + 19 q^{41} - 6 q^{42} + 12 q^{43} + 25 q^{44} + 22 q^{46} + 3 q^{47} - 15 q^{48} - 8 q^{49} + 23 q^{51} + 8 q^{52} - 38 q^{53} - 7 q^{54} + 21 q^{56} + 19 q^{57} + 21 q^{58} - 14 q^{59} + 4 q^{61} + q^{62} + 18 q^{63} - 16 q^{64} + 18 q^{66} - 9 q^{67} + 25 q^{68} + 9 q^{69} + 24 q^{71} - 41 q^{72} + 5 q^{73} + 9 q^{74} + 3 q^{76} + 13 q^{77} - 20 q^{78} + 8 q^{79} + 39 q^{81} - 56 q^{82} + 9 q^{83} - q^{84} + 39 q^{86} + 25 q^{87} + 29 q^{88} + 10 q^{89} + 7 q^{91} - 29 q^{92} + 15 q^{93} - 36 q^{94} - 11 q^{96} + 5 q^{97} + 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q - q^2 + 2 * q^3 + 9 * q^4 - 7 * q^6 + 5 * q^7 - 6 * q^8 + 13 * q^9 + 2 * q^11 + 8 * q^12 - 6 * q^13 + 7 * q^14 + 5 * q^16 - 5 * q^17 + 10 * q^18 - 10 * q^19 - 5 * q^21 + 18 * q^22 + q^23 - 21 * q^24 - 8 * q^26 + 11 * q^27 + 28 * q^28 + 30 * q^29 - 20 * q^31 + 12 * q^32 + 20 * q^33 - 17 * q^34 + 2 * q^36 - 6 * q^37 - 6 * q^38 + 11 * q^39 + 19 * q^41 - 6 * q^42 + 12 * q^43 + 25 * q^44 + 22 * q^46 + 3 * q^47 - 15 * q^48 - 8 * q^49 + 23 * q^51 + 8 * q^52 - 38 * q^53 - 7 * q^54 + 21 * q^56 + 19 * q^57 + 21 * q^58 - 14 * q^59 + 4 * q^61 + q^62 + 18 * q^63 - 16 * q^64 + 18 * q^66 - 9 * q^67 + 25 * q^68 + 9 * q^69 + 24 * q^71 - 41 * q^72 + 5 * q^73 + 9 * q^74 + 3 * q^76 + 13 * q^77 - 20 * q^78 + 8 * q^79 + 39 * q^81 - 56 * q^82 + 9 * q^83 - q^84 + 39 * q^86 + 25 * q^87 + 29 * q^88 + 10 * q^89 + 7 * q^91 - 29 * q^92 + 15 * q^93 - 36 * q^94 - 11 * q^96 + 5 * q^97 + 49 * q^98 - 31 * q^99

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