LMFDB - Embedded newform 2225.2.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2225,2,Mod(1,2225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2225, 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("2225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2225 = 5^{2} \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2225.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:	$17.7667144497$
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} - 8x^{5} + 6x^{4} + 19x^{3} - 10x^{2} - 12x + 6 $ x^7 - x^6 - 8x^5 + 6x^4 + 19x^3 - 10x^2 - 12*x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 445)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.49803$ of defining polynomial
Character	$\chi$	$=$	2225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.755898 q^{2} +2.82660 q^{3} -1.42862 q^{4} +2.13662 q^{6} -0.0498231 q^{7} -2.59169 q^{8} +4.98967 q^{9} +O(q^{10})$	\(q+0.755898 q^{2} +2.82660 q^{3} -1.42862 q^{4} +2.13662 q^{6} -0.0498231 q^{7} -2.59169 q^{8} +4.98967 q^{9} +4.45116 q^{11} -4.03813 q^{12} +2.43229 q^{13} -0.0376612 q^{14} +0.898186 q^{16} +2.48065 q^{17} +3.77168 q^{18} -5.16842 q^{19} -0.140830 q^{21} +3.36463 q^{22} +4.99050 q^{23} -7.32566 q^{24} +1.83856 q^{26} +5.62400 q^{27} +0.0711781 q^{28} +2.59152 q^{29} -7.31064 q^{31} +5.86231 q^{32} +12.5817 q^{33} +1.87512 q^{34} -7.12833 q^{36} -5.13825 q^{37} -3.90680 q^{38} +6.87512 q^{39} +9.11073 q^{41} -0.106453 q^{42} +0.543007 q^{43} -6.35901 q^{44} +3.77231 q^{46} +9.63395 q^{47} +2.53881 q^{48} -6.99752 q^{49} +7.01180 q^{51} -3.47482 q^{52} +10.7093 q^{53} +4.25117 q^{54} +0.129126 q^{56} -14.6091 q^{57} +1.95893 q^{58} -12.6337 q^{59} -2.47399 q^{61} -5.52610 q^{62} -0.248601 q^{63} +2.63494 q^{64} +9.51045 q^{66} +5.36128 q^{67} -3.54390 q^{68} +14.1061 q^{69} +9.58146 q^{71} -12.9317 q^{72} -2.86369 q^{73} -3.88400 q^{74} +7.38370 q^{76} -0.221771 q^{77} +5.19689 q^{78} +6.62473 q^{79} +0.927782 q^{81} +6.88678 q^{82} +12.0061 q^{83} +0.201192 q^{84} +0.410458 q^{86} +7.32520 q^{87} -11.5360 q^{88} +1.00000 q^{89} -0.121184 q^{91} -7.12952 q^{92} -20.6643 q^{93} +7.28229 q^{94} +16.5704 q^{96} -4.82051 q^{97} -5.28941 q^{98} +22.2098 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9	$ 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9} - 10 q^{11} + 11 q^{12} + 7 q^{13} + 3 q^{14} + 10 q^{16} + 13 q^{17} - 4 q^{18} - 7 q^{19} + 16 q^{21} - 2 q^{22} + 13 q^{23} + 4 q^{24} + q^{26} + 23 q^{27} + 21 q^{28} - 4 q^{29} + q^{31} + 13 q^{32} + 6 q^{33} + 10 q^{34} + 20 q^{36} + 5 q^{37} + 40 q^{38} - 13 q^{39} + 5 q^{41} - 30 q^{42} + 31 q^{43} - 21 q^{44} + 16 q^{46} + 14 q^{47} + 7 q^{48} + 19 q^{49} - q^{51} + 13 q^{53} - 17 q^{54} - q^{56} - 21 q^{57} - 17 q^{58} - 14 q^{59} + 3 q^{61} - 26 q^{62} + 54 q^{63} + 14 q^{64} + 36 q^{66} - q^{67} + 35 q^{68} + 31 q^{69} - 8 q^{71} - 53 q^{72} - 9 q^{73} - 35 q^{74} + 40 q^{76} - 42 q^{77} - 46 q^{78} + 9 q^{79} + 35 q^{81} - 29 q^{82} + 42 q^{83} + 55 q^{84} + 35 q^{86} - 6 q^{87} - 30 q^{88} + 7 q^{89} + 31 q^{91} - 19 q^{92} - 24 q^{93} + 37 q^{94} + 44 q^{96} + 7 q^{97} - 9 q^{98} + 5 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9 - 10 * q^11 + 11 * q^12 + 7 * q^13 + 3 * q^14 + 10 * q^16 + 13 * q^17 - 4 * q^18 - 7 * q^19 + 16 * q^21 - 2 * q^22 + 13 * q^23 + 4 * q^24 + q^26 + 23 * q^27 + 21 * q^28 - 4 * q^29 + q^31 + 13 * q^32 + 6 * q^33 + 10 * q^34 + 20 * q^36 + 5 * q^37 + 40 * q^38 - 13 * q^39 + 5 * q^41 - 30 * q^42 + 31 * q^43 - 21 * q^44 + 16 * q^46 + 14 * q^47 + 7 * q^48 + 19 * q^49 - q^51 + 13 * q^53 - 17 * q^54 - q^56 - 21 * q^57 - 17 * q^58 - 14 * q^59 + 3 * q^61 - 26 * q^62 + 54 * q^63 + 14 * q^64 + 36 * q^66 - q^67 + 35 * q^68 + 31 * q^69 - 8 * q^71 - 53 * q^72 - 9 * q^73 - 35 * q^74 + 40 * q^76 - 42 * q^77 - 46 * q^78 + 9 * q^79 + 35 * q^81 - 29 * q^82 + 42 * q^83 + 55 * q^84 + 35 * q^86 - 6 * q^87 - 30 * q^88 + 7 * q^89 + 31 * q^91 - 19 * q^92 - 24 * q^93 + 37 * q^94 + 44 * q^96 + 7 * q^97 - 9 * q^98 + 5 * 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 $

$2$	0.755898	0.534501	0.267250	−	0.963627i	$-0.413885\pi$
$2$	0.755898	0.534501	0.267250	+	0.963627i	$0.413885\pi$
$3$	2.82660	1.63194	0.815969	−	0.578095i	$-0.196204\pi$
$3$	2.82660	1.63194	0.815969	+	0.578095i	$0.196204\pi$
$4$	−1.42862	−0.714309
$5$	0	0
$5$	0	0
$6$	2.13662	0.872272
$7$	−0.0498231	−0.0188314	−0.00941568	−	0.999956i	$-0.502997\pi$
$7$	−0.0498231	−0.0188314	−0.00941568	+	0.999956i	$0.502997\pi$
$8$	−2.59169	−0.916299
$9$	4.98967	1.66322
$10$	0	0
$11$	4.45116	1.34208	0.671038	−	0.741423i	$-0.265849\pi$
$11$	4.45116	1.34208	0.671038	+	0.741423i	$0.265849\pi$
$12$	−4.03813	−1.16571
$13$	2.43229	0.674596	0.337298	−	0.941398i	$-0.390487\pi$
$13$	2.43229	0.674596	0.337298	+	0.941398i	$0.390487\pi$
$14$	−0.0376612	−0.0100654
$15$	0	0
$16$	0.898186	0.224546
$17$	2.48065	0.601646	0.300823	−	0.953680i	$-0.402739\pi$
$17$	2.48065	0.601646	0.300823	+	0.953680i	$0.402739\pi$
$18$	3.77168	0.888994
$19$	−5.16842	−1.18572	−0.592858	−	0.805307i	$-0.702001\pi$
$19$	−5.16842	−1.18572	−0.592858	+	0.805307i	$0.702001\pi$
$20$	0	0
$21$	−0.140830	−0.0307316
$22$	3.36463	0.717341
$23$	4.99050	1.04059	0.520295	−	0.853986i	$-0.325822\pi$
$23$	4.99050	1.04059	0.520295	+	0.853986i	$0.325822\pi$
$24$	−7.32566	−1.49534
$25$	0	0
$26$	1.83856	0.360572
$27$	5.62400	1.08234
$28$	0.0711781	0.0134514
$29$	2.59152	0.481234	0.240617	−	0.970620i	$-0.422650\pi$
$29$	2.59152	0.481234	0.240617	+	0.970620i	$0.422650\pi$
$30$	0	0
$31$	−7.31064	−1.31303	−0.656515	−	0.754313i	$-0.727970\pi$
$31$	−7.31064	−1.31303	−0.656515	+	0.754313i	$0.727970\pi$
$32$	5.86231	1.03632
$33$	12.5817	2.19019
$34$	1.87512	0.321580
$35$	0	0
$36$	−7.12833	−1.18805
$37$	−5.13825	−0.844724	−0.422362	−	0.906427i	$-0.638799\pi$
$37$	−5.13825	−0.844724	−0.422362	+	0.906427i	$0.638799\pi$
$38$	−3.90680	−0.633766
$39$	6.87512	1.10090
$40$	0	0
$41$	9.11073	1.42286	0.711428	−	0.702759i	$-0.248049\pi$
$41$	9.11073	1.42286	0.711428	+	0.702759i	$0.248049\pi$
$42$	−0.106453	−0.0164261
$43$	0.543007	0.0828078	0.0414039	−	0.999142i	$-0.486817\pi$
$43$	0.543007	0.0828078	0.0414039	+	0.999142i	$0.486817\pi$
$44$	−6.35901	−0.958657
$45$	0	0
$46$	3.77231	0.556196
$47$	9.63395	1.40526	0.702628	−	0.711557i	$-0.252010\pi$
$47$	9.63395	1.40526	0.702628	+	0.711557i	$0.252010\pi$
$48$	2.53881	0.366446
$49$	−6.99752	−0.999645
$50$	0	0
$51$	7.01180	0.981849
$52$	−3.47482	−0.481870
$53$	10.7093	1.47104	0.735519	−	0.677504i	$-0.236938\pi$
$53$	10.7093	1.47104	0.735519	+	0.677504i	$0.236938\pi$
$54$	4.25117	0.578511
$55$	0	0
$56$	0.129126	0.0172552
$57$	−14.6091	−1.93502
$58$	1.95893	0.257220
$59$	−12.6337	−1.64477	−0.822383	−	0.568934i	$-0.807356\pi$
$59$	−12.6337	−1.64477	−0.822383	+	0.568934i	$0.807356\pi$
$60$	0	0
$61$	−2.47399	−0.316762	−0.158381	−	0.987378i	$-0.550627\pi$
$61$	−2.47399	−0.316762	−0.158381	+	0.987378i	$0.550627\pi$
$62$	−5.52610	−0.701816
$63$	−0.248601	−0.0313207
$64$	2.63494	0.329367
$65$	0	0
$66$	9.51045	1.17066
$67$	5.36128	0.654984	0.327492	−	0.944854i	$-0.393797\pi$
$67$	5.36128	0.654984	0.327492	+	0.944854i	$0.393797\pi$
$68$	−3.54390	−0.429761
$69$	14.1061	1.69818
$70$	0	0
$71$	9.58146	1.13711	0.568555	−	0.822645i	$-0.307503\pi$
$71$	9.58146	1.13711	0.568555	+	0.822645i	$0.307503\pi$
$72$	−12.9317	−1.52401
$73$	−2.86369	−0.335169	−0.167585	−	0.985858i	$-0.553597\pi$
$73$	−2.86369	−0.335169	−0.167585	+	0.985858i	$0.553597\pi$
$74$	−3.88400	−0.451505
$75$	0	0
$76$	7.38370	0.846968
$77$	−0.221771	−0.0252731
$78$	5.19689	0.588432
$79$	6.62473	0.745340	0.372670	−	0.927964i	$-0.378442\pi$
$79$	6.62473	0.745340	0.372670	+	0.927964i	$0.378442\pi$
$80$	0	0
$81$	0.927782	0.103087
$82$	6.88678	0.760518
$83$	12.0061	1.31784	0.658919	−	0.752214i	$-0.271014\pi$
$83$	12.0061	1.31784	0.658919	+	0.752214i	$0.271014\pi$
$84$	0.201192	0.0219519
$85$	0	0
$86$	0.410458	0.0442608
$87$	7.32520	0.785344
$88$	−11.5360	−1.22974
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	0	0
$91$	−0.121184	−0.0127036
$92$	−7.12952	−0.743303
$93$	−20.6643	−2.14278
$94$	7.28229	0.751111
$95$	0	0
$96$	16.5704	1.69121
$97$	−4.82051	−0.489449	−0.244724	−	0.969593i	$-0.578697\pi$
$97$	−4.82051	−0.489449	−0.244724	+	0.969593i	$0.578697\pi$
$98$	−5.28941	−0.534311
$99$	22.2098	2.23217
$100$	0	0
$101$	−11.5561	−1.14988	−0.574938	−	0.818197i	$-0.694974\pi$
$101$	−11.5561	−1.14988	−0.574938	+	0.818197i	$0.694974\pi$
$102$	5.30021	0.524799
$103$	2.92606	0.288314	0.144157	−	0.989555i	$-0.453953\pi$
$103$	2.92606	0.288314	0.144157	+	0.989555i	$0.453953\pi$
$104$	−6.30374	−0.618132
$105$	0	0
$106$	8.09516	0.786271
$107$	3.97982	0.384744	0.192372	−	0.981322i	$-0.438382\pi$
$107$	3.97982	0.384744	0.192372	+	0.981322i	$0.438382\pi$
$108$	−8.03454	−0.773124
$109$	5.30200	0.507840	0.253920	−	0.967225i	$-0.418280\pi$
$109$	5.30200	0.507840	0.253920	+	0.967225i	$0.418280\pi$
$110$	0	0
$111$	−14.5238	−1.37854
$112$	−0.0447504	−0.00422851
$113$	10.3888	0.977296	0.488648	−	0.872481i	$-0.337490\pi$
$113$	10.3888	0.977296	0.488648	+	0.872481i	$0.337490\pi$
$114$	−11.0430	−1.03427
$115$	0	0
$116$	−3.70230	−0.343750
$117$	12.1363	1.12200
$118$	−9.54978	−0.879129
$119$	−0.123594	−0.0113298
$120$	0	0
$121$	8.81287	0.801170
$122$	−1.87008	−0.169310
$123$	25.7524	2.32201
$124$	10.4441	0.937909
$125$	0	0
$126$	−0.187917	−0.0167410
$127$	−5.31244	−0.471403	−0.235701	−	0.971826i	$-0.575739\pi$
$127$	−5.31244	−0.471403	−0.235701	+	0.971826i	$0.575739\pi$
$128$	−9.73287	−0.860273
$129$	1.53486	0.135137
$130$	0	0
$131$	−22.2268	−1.94197	−0.970984	−	0.239145i	$-0.923133\pi$
$131$	−22.2268	−1.94197	−0.970984	+	0.239145i	$0.923133\pi$
$132$	−17.9744	−1.56447
$133$	0.257507	0.0223287
$134$	4.05258	0.350089
$135$	0	0
$136$	−6.42906	−0.551288
$137$	−8.08077	−0.690387	−0.345193	−	0.938532i	$-0.612187\pi$
$137$	−8.08077	−0.690387	−0.345193	+	0.938532i	$0.612187\pi$
$138$	10.6628	0.907678
$139$	0.763404	0.0647511	0.0323755	−	0.999476i	$-0.489693\pi$
$139$	0.763404	0.0647511	0.0323755	+	0.999476i	$0.489693\pi$
$140$	0	0
$141$	27.2313	2.29329
$142$	7.24261	0.607786
$143$	10.8265	0.905360
$144$	4.48165	0.373471
$145$	0	0
$146$	−2.16466	−0.179148
$147$	−19.7792	−1.63136
$148$	7.34060	0.603394
$149$	−0.645836	−0.0529089	−0.0264545	−	0.999650i	$-0.508422\pi$
$149$	−0.645836	−0.0529089	−0.0264545	+	0.999650i	$0.508422\pi$
$150$	0	0
$151$	−16.4449	−1.33827	−0.669134	−	0.743142i	$-0.733335\pi$
$151$	−16.4449	−1.33827	−0.669134	+	0.743142i	$0.733335\pi$
$152$	13.3949	1.08647
$153$	12.3776	1.00067
$154$	−0.167636	−0.0135085
$155$	0	0
$156$	−9.82192	−0.786383
$157$	−8.23439	−0.657176	−0.328588	−	0.944473i	$-0.606573\pi$
$157$	−8.23439	−0.657176	−0.328588	+	0.944473i	$0.606573\pi$
$158$	5.00762	0.398385
$159$	30.2710	2.40064
$160$	0	0
$161$	−0.248642	−0.0195957
$162$	0.701308	0.0551000
$163$	−1.57747	−0.123557	−0.0617786	−	0.998090i	$-0.519677\pi$
$163$	−1.57747	−0.123557	−0.0617786	+	0.998090i	$0.519677\pi$
$164$	−13.0157	−1.01636
$165$	0	0
$166$	9.07537	0.704385
$167$	−1.78625	−0.138224	−0.0691121	−	0.997609i	$-0.522017\pi$
$167$	−1.78625	−0.138224	−0.0691121	+	0.997609i	$0.522017\pi$
$168$	0.364987	0.0281594
$169$	−7.08396	−0.544920
$170$	0	0
$171$	−25.7887	−1.97211
$172$	−0.775750	−0.0591504
$173$	−23.0808	−1.75480	−0.877399	−	0.479761i	$-0.840723\pi$
$173$	−23.0808	−1.75480	−0.877399	+	0.479761i	$0.840723\pi$
$174$	5.53711	0.419767
$175$	0	0
$176$	3.99797	0.301359
$177$	−35.7104	−2.68416
$178$	0.755898	0.0566570
$179$	−9.63601	−0.720229	−0.360115	−	0.932908i	$-0.617262\pi$
$179$	−9.63601	−0.720229	−0.360115	+	0.932908i	$0.617262\pi$
$180$	0	0
$181$	−7.10071	−0.527792	−0.263896	−	0.964551i	$-0.585008\pi$
$181$	−7.10071	−0.527792	−0.263896	+	0.964551i	$0.585008\pi$
$182$	−0.0916030	−0.00679006
$183$	−6.99298	−0.516936
$184$	−12.9338	−0.953493
$185$	0	0
$186$	−15.6201	−1.14532
$187$	11.0418	0.807455
$188$	−13.7632	−1.00379
$189$	−0.280205	−0.0203819
$190$	0	0
$191$	9.47202	0.685371	0.342686	−	0.939450i	$-0.388663\pi$
$191$	9.47202	0.685371	0.342686	+	0.939450i	$0.388663\pi$
$192$	7.44791	0.537507
$193$	−11.7250	−0.843985	−0.421992	−	0.906599i	$-0.638669\pi$
$193$	−11.7250	−0.843985	−0.421992	+	0.906599i	$0.638669\pi$
$194$	−3.64382	−0.261611
$195$	0	0
$196$	9.99678	0.714056
$197$	18.2857	1.30280	0.651402	−	0.758733i	$-0.274181\pi$
$197$	18.2857	1.30280	0.651402	+	0.758733i	$0.274181\pi$
$198$	16.7884	1.19310
$199$	25.0469	1.77553	0.887763	−	0.460302i	$-0.152259\pi$
$199$	25.0469	1.77553	0.887763	+	0.460302i	$0.152259\pi$
$200$	0	0
$201$	15.1542	1.06889
$202$	−8.73524	−0.614609
$203$	−0.129118	−0.00906229
$204$	−10.0172	−0.701343
$205$	0	0
$206$	2.21181	0.154104
$207$	24.9009	1.73073
$208$	2.18465	0.151478
$209$	−23.0055	−1.59132
$210$	0	0
$211$	−17.6282	−1.21358	−0.606789	−	0.794863i	$-0.707543\pi$
$211$	−17.6282	−1.21358	−0.606789	+	0.794863i	$0.707543\pi$
$212$	−15.2995	−1.05078
$213$	27.0830	1.85569
$214$	3.00834	0.205646
$215$	0	0
$216$	−14.5756	−0.991746
$217$	0.364239	0.0247261
$218$	4.00777	0.271441
$219$	−8.09450	−0.546976
$220$	0	0
$221$	6.03366	0.405868
$222$	−10.9785	−0.736829
$223$	−27.8359	−1.86403	−0.932014	−	0.362421i	$-0.881950\pi$
$223$	−27.8359	−1.86403	−0.932014	+	0.362421i	$0.881950\pi$
$224$	−0.292078	−0.0195153
$225$	0	0
$226$	7.85288	0.522366
$227$	−10.7150	−0.711181	−0.355591	−	0.934642i	$-0.615720\pi$
$227$	−10.7150	−0.711181	−0.355591	+	0.934642i	$0.615720\pi$
$228$	20.8708	1.38220
$229$	−20.0837	−1.32717	−0.663584	−	0.748102i	$-0.730966\pi$
$229$	−20.0837	−1.32717	−0.663584	+	0.748102i	$0.730966\pi$
$230$	0	0
$231$	−0.626857	−0.0412442
$232$	−6.71642	−0.440954
$233$	−1.64318	−0.107648	−0.0538242	−	0.998550i	$-0.517141\pi$
$233$	−1.64318	−0.107648	−0.0538242	+	0.998550i	$0.517141\pi$
$234$	9.17383	0.599712
$235$	0	0
$236$	18.0487	1.17487
$237$	18.7255	1.21635
$238$	−0.0934241	−0.00605579
$239$	−12.3117	−0.796379	−0.398189	−	0.917303i	$-0.630361\pi$
$239$	−12.3117	−0.796379	−0.398189	+	0.917303i	$0.630361\pi$
$240$	0	0
$241$	−10.7917	−0.695152	−0.347576	−	0.937652i	$-0.612995\pi$
$241$	−10.7917	−0.695152	−0.347576	+	0.937652i	$0.612995\pi$
$242$	6.66163	0.428226
$243$	−14.2495	−0.914107
$244$	3.53439	0.226266
$245$	0	0
$246$	19.4662	1.24112
$247$	−12.5711	−0.799880
$248$	18.9469	1.20313
$249$	33.9364	2.15063
$250$	0	0
$251$	−31.0270	−1.95840	−0.979202	−	0.202888i	$-0.934967\pi$
$251$	−31.0270	−1.95840	−0.979202	+	0.202888i	$0.934967\pi$
$252$	0.355155	0.0223727
$253$	22.2135	1.39655
$254$	−4.01566	−0.251965
$255$	0	0
$256$	−12.6269	−0.789183
$257$	−16.5586	−1.03290	−0.516449	−	0.856318i	$-0.672747\pi$
$257$	−16.5586	−1.03290	−0.516449	+	0.856318i	$0.672747\pi$
$258$	1.16020	0.0722310
$259$	0.256004	0.0159073
$260$	0	0
$261$	12.9308	0.800399
$262$	−16.8012	−1.03798
$263$	12.0270	0.741619	0.370810	−	0.928709i	$-0.379080\pi$
$263$	12.0270	0.741619	0.370810	+	0.928709i	$0.379080\pi$
$264$	−32.6077	−2.00687
$265$	0	0
$266$	0.194649	0.0119347
$267$	2.82660	0.172985
$268$	−7.65922	−0.467861
$269$	−22.0871	−1.34667	−0.673336	−	0.739336i	$-0.735139\pi$
$269$	−22.0871	−1.34667	−0.673336	+	0.739336i	$0.735139\pi$
$270$	0	0
$271$	13.8002	0.838302	0.419151	−	0.907917i	$-0.362328\pi$
$271$	13.8002	0.838302	0.419151	+	0.907917i	$0.362328\pi$
$272$	2.22808	0.135097
$273$	−0.342539	−0.0207314
$274$	−6.10824	−0.369012
$275$	0	0
$276$	−20.1523	−1.21303
$277$	−3.04290	−0.182830	−0.0914151	−	0.995813i	$-0.529139\pi$
$277$	−3.04290	−0.182830	−0.0914151	+	0.995813i	$0.529139\pi$
$278$	0.577056	0.0346095
$279$	−36.4777	−2.18386
$280$	0	0
$281$	21.1218	1.26002	0.630011	−	0.776586i	$-0.283050\pi$
$281$	21.1218	1.26002	0.630011	+	0.776586i	$0.283050\pi$
$282$	20.5841	1.22577
$283$	−32.4871	−1.93116	−0.965579	−	0.260111i	$-0.916241\pi$
$283$	−32.4871	−1.93116	−0.965579	+	0.260111i	$0.916241\pi$
$284$	−13.6882	−0.812248
$285$	0	0
$286$	8.18376	0.483916
$287$	−0.453924	−0.0267943
$288$	29.2510	1.72363
$289$	−10.8464	−0.638022
$290$	0	0
$291$	−13.6257	−0.798750
$292$	4.09112	0.239414
$293$	−32.0101	−1.87005	−0.935026	−	0.354578i	$-0.884624\pi$
$293$	−32.0101	−1.87005	−0.935026	+	0.354578i	$0.884624\pi$
$294$	−14.9510	−0.871963
$295$	0	0
$296$	13.3167	0.774020
$297$	25.0333	1.45258
$298$	−0.488186	−0.0282798
$299$	12.1383	0.701979
$300$	0	0
$301$	−0.0270543	−0.00155938
$302$	−12.4307	−0.715305
$303$	−32.6645	−1.87653
$304$	−4.64220	−0.266248
$305$	0	0
$306$	9.35621	0.534859
$307$	19.6188	1.11970	0.559852	−	0.828593i	$-0.310858\pi$
$307$	19.6188	1.11970	0.559852	+	0.828593i	$0.310858\pi$
$308$	0.316826	0.0180528
$309$	8.27081	0.470510
$310$	0	0
$311$	24.8863	1.41117	0.705586	−	0.708625i	$-0.250684\pi$
$311$	24.8863	1.41117	0.705586	+	0.708625i	$0.250684\pi$
$312$	−17.8181	−1.00875
$313$	6.17328	0.348934	0.174467	−	0.984663i	$-0.444180\pi$
$313$	6.17328	0.348934	0.174467	+	0.984663i	$0.444180\pi$
$314$	−6.22436	−0.351261
$315$	0	0
$316$	−9.46420	−0.532403
$317$	32.9455	1.85041	0.925203	−	0.379473i	$-0.123895\pi$
$317$	32.9455	1.85041	0.925203	+	0.379473i	$0.123895\pi$
$318$	22.8818	1.28315
$319$	11.5353	0.645853
$320$	0	0
$321$	11.2494	0.627878
$322$	−0.187948	−0.0104739
$323$	−12.8210	−0.713381
$324$	−1.32545	−0.0736359
$325$	0	0
$326$	−1.19241	−0.0660414
$327$	14.9866	0.828763
$328$	−23.6121	−1.30376
$329$	−0.479993	−0.0264629
$330$	0	0
$331$	30.9785	1.70273	0.851367	−	0.524570i	$-0.175774\pi$
$331$	30.9785	1.70273	0.851367	+	0.524570i	$0.175774\pi$
$332$	−17.1521	−0.941343
$333$	−25.6382	−1.40496
$334$	−1.35022	−0.0738809
$335$	0	0
$336$	−0.126491	−0.00690067
$337$	3.53709	0.192678	0.0963389	−	0.995349i	$-0.469287\pi$
$337$	3.53709	0.192678	0.0963389	+	0.995349i	$0.469287\pi$
$338$	−5.35475	−0.291260
$339$	29.3650	1.59489
$340$	0	0
$341$	−32.5409	−1.76219
$342$	−19.4936	−1.05409
$343$	0.697399	0.0376560
$344$	−1.40730	−0.0758768
$345$	0	0
$346$	−17.4467	−0.937941
$347$	13.0198	0.698939	0.349470	−	0.936948i	$-0.386362\pi$
$347$	13.0198	0.698939	0.349470	+	0.936948i	$0.386362\pi$
$348$	−10.4649	−0.560978
$349$	27.6562	1.48040	0.740201	−	0.672385i	$-0.234730\pi$
$349$	27.6562	1.48040	0.740201	+	0.672385i	$0.234730\pi$
$350$	0	0
$351$	13.6792	0.730142
$352$	26.0941	1.39082
$353$	26.3090	1.40029	0.700144	−	0.714002i	$-0.253119\pi$
$353$	26.3090	1.40029	0.700144	+	0.714002i	$0.253119\pi$
$354$	−26.9934	−1.43468
$355$	0	0
$356$	−1.42862	−0.0757166
$357$	−0.349350	−0.0184895
$358$	−7.28384	−0.384963
$359$	14.0008	0.738934	0.369467	−	0.929244i	$-0.379540\pi$
$359$	14.0008	0.738934	0.369467	+	0.929244i	$0.379540\pi$
$360$	0	0
$361$	7.71256	0.405924
$362$	−5.36741	−0.282105
$363$	24.9105	1.30746
$364$	0.173126	0.00907427
$365$	0	0
$366$	−5.28598	−0.276303
$367$	−22.0304	−1.14998	−0.574989	−	0.818161i	$-0.694994\pi$
$367$	−22.0304	−1.14998	−0.574989	+	0.818161i	$0.694994\pi$
$368$	4.48239	0.233661
$369$	45.4595	2.36653
$370$	0	0
$371$	−0.533571	−0.0277016
$372$	29.5213	1.53061
$373$	−13.6705	−0.707830	−0.353915	−	0.935278i	$-0.615150\pi$
$373$	−13.6705	−0.707830	−0.353915	+	0.935278i	$0.615150\pi$
$374$	8.34646	0.431585
$375$	0	0
$376$	−24.9682	−1.28764
$377$	6.30334	0.324639
$378$	−0.211806	−0.0108941
$379$	−15.1907	−0.780292	−0.390146	−	0.920753i	$-0.627575\pi$
$379$	−15.1907	−0.780292	−0.390146	+	0.920753i	$0.627575\pi$
$380$	0	0
$381$	−15.0161	−0.769300
$382$	7.15988	0.366331
$383$	0.297784	0.0152160	0.00760802	−	0.999971i	$-0.497578\pi$
$383$	0.297784	0.0152160	0.00760802	+	0.999971i	$0.497578\pi$
$384$	−27.5109	−1.40391
$385$	0	0
$386$	−8.86291	−0.451110
$387$	2.70943	0.137728
$388$	6.88667	0.349618
$389$	−2.25933	−0.114553	−0.0572763	−	0.998358i	$-0.518242\pi$
$389$	−2.25933	−0.114553	−0.0572763	+	0.998358i	$0.518242\pi$
$390$	0	0
$391$	12.3797	0.626067
$392$	18.1354	0.915974
$393$	−62.8264	−3.16917
$394$	13.8221	0.696349
$395$	0	0
$396$	−31.7294	−1.59446
$397$	23.8373	1.19636	0.598180	−	0.801361i	$-0.295891\pi$
$397$	23.8373	1.19636	0.598180	+	0.801361i	$0.295891\pi$
$398$	18.9329	0.949019
$399$	0.727868	0.0364390
$400$	0	0
$401$	26.1681	1.30677	0.653386	−	0.757025i	$-0.273348\pi$
$401$	26.1681	1.30677	0.653386	+	0.757025i	$0.273348\pi$
$402$	11.4550	0.571324
$403$	−17.7816	−0.885766
$404$	16.5093	0.821366
$405$	0	0
$406$	−0.0975998	−0.00484380
$407$	−22.8712	−1.13368
$408$	−18.1724	−0.899667
$409$	−22.9348	−1.13406	−0.567028	−	0.823699i	$-0.691907\pi$
$409$	−22.9348	−1.13406	−0.567028	+	0.823699i	$0.691907\pi$
$410$	0	0
$411$	−22.8411	−1.12667
$412$	−4.18023	−0.205945
$413$	0.629449	0.0309732
$414$	18.8226	0.925079
$415$	0	0
$416$	14.2588	0.699097
$417$	2.15784	0.105670
$418$	−17.3898	−0.850563
$419$	5.25412	0.256681	0.128340	−	0.991730i	$-0.459035\pi$
$419$	5.25412	0.256681	0.128340	+	0.991730i	$0.459035\pi$
$420$	0	0
$421$	18.0800	0.881166	0.440583	−	0.897712i	$-0.354772\pi$
$421$	18.0800	0.881166	0.440583	+	0.897712i	$0.354772\pi$
$422$	−13.3251	−0.648658
$423$	48.0702	2.33725
$424$	−27.7552	−1.34791
$425$	0	0
$426$	20.4720	0.991870
$427$	0.123262	0.00596506
$428$	−5.68564	−0.274826
$429$	30.6023	1.47749
$430$	0	0
$431$	5.55910	0.267773	0.133886	−	0.990997i	$-0.457254\pi$
$431$	5.55910	0.267773	0.133886	+	0.990997i	$0.457254\pi$
$432$	5.05139	0.243035
$433$	−20.5795	−0.988986	−0.494493	−	0.869182i	$-0.664646\pi$
$433$	−20.5795	−0.988986	−0.494493	+	0.869182i	$0.664646\pi$
$434$	0.275327	0.0132161
$435$	0	0
$436$	−7.57454	−0.362755
$437$	−25.7930	−1.23385
$438$	−6.11862	−0.292359
$439$	26.6104	1.27004	0.635022	−	0.772494i	$-0.280991\pi$
$439$	26.6104	1.27004	0.635022	+	0.772494i	$0.280991\pi$
$440$	0	0
$441$	−34.9153	−1.66263
$442$	4.56083	0.216937
$443$	−20.4411	−0.971188	−0.485594	−	0.874185i	$-0.661397\pi$
$443$	−20.4411	−0.971188	−0.485594	+	0.874185i	$0.661397\pi$
$444$	20.7489	0.984702
$445$	0	0
$446$	−21.0411	−0.996325
$447$	−1.82552	−0.0863441
$448$	−0.131281	−0.00620243
$449$	5.61381	0.264932	0.132466	−	0.991188i	$-0.457710\pi$
$449$	5.61381	0.264932	0.132466	+	0.991188i	$0.457710\pi$
$450$	0	0
$451$	40.5533	1.90958
$452$	−14.8416	−0.698092
$453$	−46.4832	−2.18397
$454$	−8.09947	−0.380127
$455$	0	0
$456$	37.8621	1.77305
$457$	7.13528	0.333774	0.166887	−	0.985976i	$-0.446628\pi$
$457$	7.13528	0.333774	0.166887	+	0.985976i	$0.446628\pi$
$458$	−15.1812	−0.709372
$459$	13.9512	0.651184
$460$	0	0
$461$	−24.0844	−1.12172	−0.560860	−	0.827911i	$-0.689529\pi$
$461$	−24.0844	−1.12172	−0.560860	+	0.827911i	$0.689529\pi$
$462$	−0.473840	−0.0220450
$463$	22.2301	1.03312	0.516561	−	0.856250i	$-0.327212\pi$
$463$	22.2301	1.03312	0.516561	+	0.856250i	$0.327212\pi$
$464$	2.32767	0.108059
$465$	0	0
$466$	−1.24208	−0.0575382
$467$	−10.4176	−0.482069	−0.241034	−	0.970517i	$-0.577487\pi$
$467$	−10.4176	−0.482069	−0.241034	+	0.970517i	$0.577487\pi$
$468$	−17.3382	−0.801458
$469$	−0.267115	−0.0123342
$470$	0	0
$471$	−23.2753	−1.07247
$472$	32.7426	1.50710
$473$	2.41701	0.111134
$474$	14.1545	0.650139
$475$	0	0
$476$	0.176568	0.00809298
$477$	53.4360	2.44666
$478$	−9.30640	−0.425665
$479$	−20.6366	−0.942912	−0.471456	−	0.881889i	$-0.656271\pi$
$479$	−20.6366	−0.942912	−0.471456	+	0.881889i	$0.656271\pi$
$480$	0	0
$481$	−12.4977	−0.569848
$482$	−8.15740	−0.371559
$483$	−0.702811	−0.0319790
$484$	−12.5902	−0.572283
$485$	0	0
$486$	−10.7712	−0.488591
$487$	29.5496	1.33902	0.669510	−	0.742803i	$-0.266504\pi$
$487$	29.5496	1.33902	0.669510	+	0.742803i	$0.266504\pi$
$488$	6.41181	0.290249
$489$	−4.45888	−0.201638
$490$	0	0
$491$	37.8108	1.70638	0.853189	−	0.521602i	$-0.174665\pi$
$491$	37.8108	1.70638	0.853189	+	0.521602i	$0.174665\pi$
$492$	−36.7903	−1.65864
$493$	6.42866	0.289532
$494$	−9.50247	−0.427537
$495$	0	0
$496$	−6.56632	−0.294836
$497$	−0.477378	−0.0214133
$498$	25.6524	1.14951
$499$	7.09756	0.317730	0.158865	−	0.987300i	$-0.449217\pi$
$499$	7.09756	0.317730	0.158865	+	0.987300i	$0.449217\pi$
$500$	0	0
$501$	−5.04902	−0.225573
$502$	−23.4532	−1.04677
$503$	25.0615	1.11744	0.558718	−	0.829358i	$-0.311294\pi$
$503$	25.0615	1.11744	0.558718	+	0.829358i	$0.311294\pi$
$504$	0.644295	0.0286992
$505$	0	0
$506$	16.7912	0.746458
$507$	−20.0235	−0.889275
$508$	7.58945	0.336727
$509$	−1.59934	−0.0708895	−0.0354447	−	0.999372i	$-0.511285\pi$
$509$	−1.59934	−0.0708895	−0.0354447	+	0.999372i	$0.511285\pi$
$510$	0	0
$511$	0.142678	0.00631169
$512$	9.92107	0.438454
$513$	−29.0672	−1.28335
$514$	−12.5166	−0.552085
$515$	0	0
$516$	−2.19273	−0.0965298
$517$	42.8823	1.88596
$518$	0.193513	0.00850246
$519$	−65.2401	−2.86372
$520$	0	0
$521$	25.2660	1.10693	0.553463	−	0.832874i	$-0.313306\pi$
$521$	25.2660	1.10693	0.553463	+	0.832874i	$0.313306\pi$
$522$	9.77440	0.427814
$523$	1.75283	0.0766458	0.0383229	−	0.999265i	$-0.487798\pi$
$523$	1.75283	0.0766458	0.0383229	+	0.999265i	$0.487798\pi$
$524$	31.7537	1.38717
$525$	0	0
$526$	9.09122	0.396396
$527$	−18.1351	−0.789979
$528$	11.3007	0.491799
$529$	1.90507	0.0828292
$530$	0	0
$531$	−63.0379	−2.73561
$532$	−0.367879	−0.0159496
$533$	22.1599	0.959854
$534$	2.13662	0.0924607
$535$	0	0
$536$	−13.8947	−0.600161
$537$	−27.2372	−1.17537
$538$	−16.6956	−0.719797
$539$	−31.1471	−1.34160
$540$	0	0
$541$	5.15589	0.221669	0.110835	−	0.993839i	$-0.464648\pi$
$541$	5.15589	0.221669	0.110835	+	0.993839i	$0.464648\pi$
$542$	10.4315	0.448073
$543$	−20.0709	−0.861323
$544$	14.5423	0.623497
$545$	0	0
$546$	−0.258925	−0.0110810
$547$	−13.3060	−0.568925	−0.284462	−	0.958687i	$-0.591815\pi$
$547$	−13.3060	−0.568925	−0.284462	+	0.958687i	$0.591815\pi$
$548$	11.5443	0.493149
$549$	−12.3444	−0.526846
$550$	0	0
$551$	−13.3941	−0.570607
$552$	−36.5587	−1.55604
$553$	−0.330064	−0.0140358
$554$	−2.30012	−0.0977229
$555$	0	0
$556$	−1.09061	−0.0462523
$557$	32.2911	1.36822	0.684109	−	0.729380i	$-0.260191\pi$
$557$	32.2911	1.36822	0.684109	+	0.729380i	$0.260191\pi$
$558$	−27.5734	−1.16728
$559$	1.32075	0.0558619
$560$	0	0
$561$	31.2107	1.31772
$562$	15.9659	0.673482
$563$	1.17102	0.0493525	0.0246762	−	0.999695i	$-0.492145\pi$
$563$	1.17102	0.0493525	0.0246762	+	0.999695i	$0.492145\pi$
$564$	−38.9032	−1.63812
$565$	0	0
$566$	−24.5569	−1.03221
$567$	−0.0462249	−0.00194126
$568$	−24.8321	−1.04193
$569$	20.9355	0.877662	0.438831	−	0.898570i	$-0.355393\pi$
$569$	20.9355	0.877662	0.438831	+	0.898570i	$0.355393\pi$
$570$	0	0
$571$	−44.5105	−1.86271	−0.931354	−	0.364116i	$-0.881371\pi$
$571$	−44.5105	−1.86271	−0.931354	+	0.364116i	$0.881371\pi$
$572$	−15.4670	−0.646707
$573$	26.7736	1.11848
$574$	−0.343121	−0.0143216
$575$	0	0
$576$	13.1475	0.547811
$577$	44.7453	1.86277	0.931386	−	0.364034i	$-0.118601\pi$
$577$	44.7453	1.86277	0.931386	+	0.364034i	$0.118601\pi$
$578$	−8.19876	−0.341023
$579$	−33.1419	−1.37733
$580$	0	0
$581$	−0.598180	−0.0248167
$582$	−10.2996	−0.426933
$583$	47.6690	1.97425
$584$	7.42178	0.307115
$585$	0	0
$586$	−24.1964	−0.999544
$587$	−14.8194	−0.611663	−0.305832	−	0.952086i	$-0.598934\pi$
$587$	−14.8194	−0.611663	−0.305832	+	0.952086i	$0.598934\pi$
$588$	28.2569	1.16529
$589$	37.7845	1.55688
$590$	0	0
$591$	51.6864	2.12609
$592$	−4.61511	−0.189680
$593$	23.3625	0.959384	0.479692	−	0.877437i	$-0.340748\pi$
$593$	23.3625	0.959384	0.479692	+	0.877437i	$0.340748\pi$
$594$	18.9226	0.776406
$595$	0	0
$596$	0.922652	0.0377933
$597$	70.7975	2.89755
$598$	9.17535	0.375208
$599$	−2.73683	−0.111824	−0.0559120	−	0.998436i	$-0.517807\pi$
$599$	−2.73683	−0.111824	−0.0559120	+	0.998436i	$0.517807\pi$
$600$	0	0
$601$	−14.7244	−0.600622	−0.300311	−	0.953841i	$-0.597090\pi$
$601$	−14.7244	−0.600622	−0.300311	+	0.953841i	$0.597090\pi$
$602$	−0.0204503	−0.000833491 0
$603$	26.7510	1.08938
$604$	23.4935	0.955937
$605$	0	0
$606$	−24.6910	−1.00300
$607$	7.93966	0.322261	0.161131	−	0.986933i	$-0.448486\pi$
$607$	7.93966	0.322261	0.161131	+	0.986933i	$0.448486\pi$
$608$	−30.2989	−1.22878
$609$	−0.364964	−0.0147891
$610$	0	0
$611$	23.4326	0.947981
$612$	−17.6829	−0.714788
$613$	5.63827	0.227728	0.113864	−	0.993496i	$-0.463677\pi$
$613$	5.63827	0.227728	0.113864	+	0.993496i	$0.463677\pi$
$614$	14.8298	0.598483
$615$	0	0
$616$	0.574760	0.0231577
$617$	−24.0408	−0.967848	−0.483924	−	0.875110i	$-0.660789\pi$
$617$	−24.0408	−0.967848	−0.483924	+	0.875110i	$0.660789\pi$
$618$	6.25189	0.251488
$619$	18.0743	0.726469	0.363234	−	0.931698i	$-0.381672\pi$
$619$	18.0743	0.726469	0.363234	+	0.931698i	$0.381672\pi$
$620$	0	0
$621$	28.0665	1.12627
$622$	18.8115	0.754272
$623$	−0.0498231	−0.00199612
$624$	6.17513	0.247203
$625$	0	0
$626$	4.66637	0.186506
$627$	−65.0273	−2.59694
$628$	11.7638	0.469427
$629$	−12.7462	−0.508224
$630$	0	0
$631$	−3.58541	−0.142733	−0.0713665	−	0.997450i	$-0.522736\pi$
$631$	−3.58541	−0.142733	−0.0713665	+	0.997450i	$0.522736\pi$
$632$	−17.1692	−0.682955
$633$	−49.8279	−1.98048
$634$	24.9035	0.989043
$635$	0	0
$636$	−43.2457	−1.71480
$637$	−17.0200	−0.674357
$638$	8.71951	0.345209
$639$	47.8083	1.89127
$640$	0	0
$641$	−19.3761	−0.765311	−0.382656	−	0.923891i	$-0.624990\pi$
$641$	−19.3761	−0.765311	−0.382656	+	0.923891i	$0.624990\pi$
$642$	8.50337	0.335601
$643$	−26.7275	−1.05403	−0.527015	−	0.849856i	$-0.676689\pi$
$643$	−26.7275	−1.05403	−0.527015	+	0.849856i	$0.676689\pi$
$644$	0.355214	0.0139974
$645$	0	0
$646$	−9.69139	−0.381303
$647$	−20.6868	−0.813281	−0.406641	−	0.913588i	$-0.633300\pi$
$647$	−20.6868	−0.813281	−0.406641	+	0.913588i	$0.633300\pi$
$648$	−2.40452	−0.0944584
$649$	−56.2346	−2.20740
$650$	0	0
$651$	1.02956	0.0403515
$652$	2.25361	0.0882580
$653$	33.7364	1.32021	0.660104	−	0.751174i	$-0.270512\pi$
$653$	33.7364	1.32021	0.660104	+	0.751174i	$0.270512\pi$
$654$	11.3284	0.442975
$655$	0	0
$656$	8.18313	0.319497
$657$	−14.2888	−0.557461
$658$	−0.362826	−0.0141444
$659$	−9.44930	−0.368092	−0.184046	−	0.982918i	$-0.558920\pi$
$659$	−9.44930	−0.368092	−0.184046	+	0.982918i	$0.558920\pi$
$660$	0	0
$661$	−36.6486	−1.42547	−0.712733	−	0.701435i	$-0.752543\pi$
$661$	−36.6486	−1.42547	−0.712733	+	0.701435i	$0.752543\pi$
$662$	23.4166	0.910113
$663$	17.0547	0.662352
$664$	−31.1160	−1.20753
$665$	0	0
$666$	−19.3799	−0.750954
$667$	12.9330	0.500768
$668$	2.55187	0.0987348
$669$	−78.6809	−3.04198
$670$	0	0
$671$	−11.0121	−0.425119
$672$	−0.825588	−0.0318478
$673$	−42.5711	−1.64099	−0.820497	−	0.571651i	$-0.806303\pi$
$673$	−42.5711	−1.64099	−0.820497	+	0.571651i	$0.806303\pi$
$674$	2.67368	0.102986
$675$	0	0
$676$	10.1203	0.389241
$677$	29.6301	1.13878	0.569389	−	0.822068i	$-0.307180\pi$
$677$	29.6301	1.13878	0.569389	+	0.822068i	$0.307180\pi$
$678$	22.1969	0.852468
$679$	0.240173	0.00921698
$680$	0	0
$681$	−30.2871	−1.16060
$682$	−24.5976	−0.941890
$683$	−18.4389	−0.705545	−0.352772	−	0.935709i	$-0.614761\pi$
$683$	−18.4389	−0.705545	−0.352772	+	0.935709i	$0.614761\pi$
$684$	36.8422	1.40870
$685$	0	0
$686$	0.527163	0.0201272
$687$	−56.7686	−2.16586
$688$	0.487721	0.0185942
$689$	26.0482	0.992357
$690$	0	0
$691$	−39.7294	−1.51138	−0.755689	−	0.654930i	$-0.772698\pi$
$691$	−39.7294	−1.51138	−0.755689	+	0.654930i	$0.772698\pi$
$692$	32.9736	1.25347
$693$	−1.10656	−0.0420348
$694$	9.84164	0.373584
$695$	0	0
$696$	−18.9846	−0.719610
$697$	22.6005	0.856056
$698$	20.9053	0.791276
$699$	−4.64462	−0.175676
$700$	0	0
$701$	−8.13101	−0.307104	−0.153552	−	0.988141i	$-0.549071\pi$
$701$	−8.13101	−0.307104	−0.153552	+	0.988141i	$0.549071\pi$
$702$	10.3401	0.390261
$703$	26.5567	1.00160
$704$	11.7285	0.442036
$705$	0	0
$706$	19.8869	0.748455
$707$	0.575761	0.0216537
$708$	51.0165	1.91732
$709$	24.2930	0.912343	0.456171	−	0.889892i	$-0.349220\pi$
$709$	24.2930	0.912343	0.456171	+	0.889892i	$0.349220\pi$
$710$	0	0
$711$	33.0552	1.23967
$712$	−2.59169	−0.0971275
$713$	−36.4838	−1.36633
$714$	−0.264073	−0.00988267
$715$	0	0
$716$	13.7662	0.514466
$717$	−34.8003	−1.29964
$718$	10.5832	0.394961
$719$	35.3355	1.31779	0.658896	−	0.752234i	$-0.271024\pi$
$719$	35.3355	1.31779	0.658896	+	0.752234i	$0.271024\pi$
$720$	0	0
$721$	−0.145785	−0.00542933
$722$	5.82991	0.216967
$723$	−30.5037	−1.13445
$724$	10.1442	0.377006
$725$	0	0
$726$	18.8298	0.698838
$727$	27.6135	1.02413	0.512065	−	0.858947i	$-0.328881\pi$
$727$	27.6135	1.02413	0.512065	+	0.858947i	$0.328881\pi$
$728$	0.314072	0.0116403
$729$	−43.0610	−1.59485
$730$	0	0
$731$	1.34701	0.0498210
$732$	9.99030	0.369252
$733$	19.3580	0.715005	0.357503	−	0.933912i	$-0.383628\pi$
$733$	19.3580	0.715005	0.357503	+	0.933912i	$0.383628\pi$
$734$	−16.6527	−0.614664
$735$	0	0
$736$	29.2558	1.07838
$737$	23.8639	0.879039
$738$	34.3628	1.26491
$739$	28.8545	1.06143	0.530715	−	0.847550i	$-0.321923\pi$
$739$	28.8545	1.06143	0.530715	+	0.847550i	$0.321923\pi$
$740$	0	0
$741$	−35.5335	−1.30536
$742$	−0.403326	−0.0148065
$743$	−25.5760	−0.938292	−0.469146	−	0.883121i	$-0.655438\pi$
$743$	−25.5760	−0.938292	−0.469146	+	0.883121i	$0.655438\pi$
$744$	53.5553	1.96343
$745$	0	0
$746$	−10.3335	−0.378336
$747$	59.9063	2.19186
$748$	−15.7745	−0.576772
$749$	−0.198287	−0.00724525
$750$	0	0
$751$	−26.6217	−0.971440	−0.485720	−	0.874114i	$-0.661443\pi$
$751$	−26.6217	−0.971440	−0.485720	+	0.874114i	$0.661443\pi$
$752$	8.65308	0.315545
$753$	−87.7008	−3.19599
$754$	4.76468	0.173520
$755$	0	0
$756$	0.400306	0.0145590
$757$	−16.8066	−0.610848	−0.305424	−	0.952216i	$-0.598798\pi$
$757$	−16.8066	−0.610848	−0.305424	+	0.952216i	$0.598798\pi$
$758$	−11.4826	−0.417067
$759$	62.7888	2.27909
$760$	0	0
$761$	−23.6421	−0.857026	−0.428513	−	0.903536i	$-0.640962\pi$
$761$	−23.6421	−0.857026	−0.428513	+	0.903536i	$0.640962\pi$
$762$	−11.3507	−0.411191
$763$	−0.264162	−0.00956331
$764$	−13.5319	−0.489567
$765$	0	0
$766$	0.225094	0.00813299
$767$	−30.7288	−1.10955
$768$	−35.6913	−1.28790
$769$	20.1859	0.727921	0.363960	−	0.931414i	$-0.381424\pi$
$769$	20.1859	0.727921	0.363960	+	0.931414i	$0.381424\pi$
$770$	0	0
$771$	−46.8046	−1.68563
$772$	16.7506	0.602866
$773$	14.8504	0.534132	0.267066	−	0.963678i	$-0.413946\pi$
$773$	14.8504	0.534132	0.267066	+	0.963678i	$0.413946\pi$
$774$	2.04805	0.0736156
$775$	0	0
$776$	12.4933	0.448482
$777$	0.723620	0.0259597
$778$	−1.70782	−0.0612285
$779$	−47.0881	−1.68710
$780$	0	0
$781$	42.6487	1.52609
$782$	9.35777	0.334633
$783$	14.5747	0.520858
$784$	−6.28507	−0.224467
$785$	0	0
$786$	−47.4903	−1.69392
$787$	−22.9126	−0.816746	−0.408373	−	0.912815i	$-0.633904\pi$
$787$	−22.9126	−0.816746	−0.408373	+	0.912815i	$0.633904\pi$
$788$	−26.1233	−0.930604
$789$	33.9956	1.21028
$790$	0	0
$791$	−0.517602	−0.0184038
$792$	−57.5609	−2.04534
$793$	−6.01747	−0.213687
$794$	18.0186	0.639456
$795$	0	0
$796$	−35.7824	−1.26827
$797$	−32.7951	−1.16166	−0.580831	−	0.814024i	$-0.697272\pi$
$797$	−32.7951	−1.16166	−0.580831	+	0.814024i	$0.697272\pi$
$798$	0.550194	0.0194767
$799$	23.8985	0.845467
$800$	0	0
$801$	4.98967	0.176301
$802$	19.7804	0.698470
$803$	−12.7467	−0.449823
$804$	−21.6495	−0.763520
$805$	0	0
$806$	−13.4411	−0.473442
$807$	−62.4313	−2.19769
$808$	29.9498	1.05363
$809$	−25.8540	−0.908978	−0.454489	−	0.890752i	$-0.650178\pi$
$809$	−25.8540	−0.908978	−0.454489	+	0.890752i	$0.650178\pi$
$810$	0	0
$811$	−5.12583	−0.179992	−0.0899962	−	0.995942i	$-0.528685\pi$
$811$	−5.12583	−0.179992	−0.0899962	+	0.995942i	$0.528685\pi$
$812$	0.184460	0.00647327
$813$	39.0076	1.36806
$814$	−17.2883	−0.605955
$815$	0	0
$816$	6.29790	0.220471
$817$	−2.80649	−0.0981866
$818$	−17.3364	−0.606153
$819$	−0.604669	−0.0211289
$820$	0	0
$821$	−15.9798	−0.557701	−0.278850	−	0.960335i	$-0.589953\pi$
$821$	−15.9798	−0.557701	−0.278850	+	0.960335i	$0.589953\pi$
$822$	−17.2655	−0.602205
$823$	−37.5936	−1.31043	−0.655216	−	0.755442i	$-0.727422\pi$
$823$	−37.5936	−1.31043	−0.655216	+	0.755442i	$0.727422\pi$
$824$	−7.58344	−0.264182
$825$	0	0
$826$	0.475799	0.0165552
$827$	53.0600	1.84508	0.922538	−	0.385906i	$-0.126111\pi$
$827$	53.0600	1.84508	0.922538	+	0.385906i	$0.126111\pi$
$828$	−35.5739	−1.23628
$829$	7.43536	0.258241	0.129120	−	0.991629i	$-0.458785\pi$
$829$	7.43536	0.258241	0.129120	+	0.991629i	$0.458785\pi$
$830$	0	0
$831$	−8.60106	−0.298368
$832$	6.40893	0.222190
$833$	−17.3584	−0.601432
$834$	1.63111	0.0564806
$835$	0	0
$836$	32.8661	1.13670
$837$	−41.1150	−1.42114
$838$	3.97158	0.137196
$839$	−38.6435	−1.33412	−0.667061	−	0.745003i	$-0.732448\pi$
$839$	−38.6435	−1.33412	−0.667061	+	0.745003i	$0.732448\pi$
$840$	0	0
$841$	−22.2840	−0.768414
$842$	13.6667	0.470984
$843$	59.7029	2.05628
$844$	25.1840	0.866869
$845$	0	0
$846$	36.3362	1.24926
$847$	−0.439084	−0.0150871
$848$	9.61896	0.330316
$849$	−91.8280	−3.15153
$850$	0	0
$851$	−25.6424	−0.879012
$852$	−38.6912	−1.32554
$853$	−34.8883	−1.19455	−0.597277	−	0.802035i	$-0.703751\pi$
$853$	−34.8883	−1.19455	−0.597277	+	0.802035i	$0.703751\pi$
$854$	0.0931734	0.00318833
$855$	0	0
$856$	−10.3144	−0.352540
$857$	5.99133	0.204660	0.102330	−	0.994751i	$-0.467370\pi$
$857$	5.99133	0.204660	0.102330	+	0.994751i	$0.467370\pi$
$858$	23.1322	0.789720
$859$	36.8422	1.25704	0.628519	−	0.777794i	$-0.283661\pi$
$859$	36.8422	1.25704	0.628519	+	0.777794i	$0.283661\pi$
$860$	0	0
$861$	−1.28306	−0.0437267
$862$	4.20212	0.143125
$863$	−51.2726	−1.74534	−0.872669	−	0.488312i	$-0.837613\pi$
$863$	−51.2726	−1.74534	−0.872669	+	0.488312i	$0.837613\pi$
$864$	32.9696	1.12165
$865$	0	0
$866$	−15.5560	−0.528614
$867$	−30.6584	−1.04121
$868$	−0.520358	−0.0176621
$869$	29.4877	1.00030
$870$	0	0
$871$	13.0402	0.441850
$872$	−13.7411	−0.465333
$873$	−24.0528	−0.814062
$874$	−19.4969	−0.659491
$875$	0	0
$876$	11.5639	0.390710
$877$	5.47506	0.184880	0.0924399	−	0.995718i	$-0.470533\pi$
$877$	5.47506	0.184880	0.0924399	+	0.995718i	$0.470533\pi$
$878$	20.1147	0.678840
$879$	−90.4799	−3.05181
$880$	0	0
$881$	−16.6965	−0.562521	−0.281260	−	0.959632i	$-0.590752\pi$
$881$	−16.6965	−0.562521	−0.281260	+	0.959632i	$0.590752\pi$
$882$	−26.3924	−0.888678
$883$	20.7620	0.698696	0.349348	−	0.936993i	$-0.386403\pi$
$883$	20.7620	0.698696	0.349348	+	0.936993i	$0.386403\pi$
$884$	−8.61980	−0.289915
$885$	0	0
$886$	−15.4514	−0.519100
$887$	30.8479	1.03577	0.517886	−	0.855450i	$-0.326719\pi$
$887$	30.8479	1.03577	0.517886	+	0.855450i	$0.326719\pi$
$888$	37.6411	1.26315
$889$	0.264682	0.00887715
$890$	0	0
$891$	4.12971	0.138350
$892$	39.7669	1.33149
$893$	−49.7923	−1.66624
$894$	−1.37991	−0.0461510
$895$	0	0
$896$	0.484922	0.0162001
$897$	34.3103	1.14559
$898$	4.24347	0.141606
$899$	−18.9457	−0.631875
$900$	0	0
$901$	26.5661	0.885044
$902$	30.6542	1.02067
$903$	−0.0764717	−0.00254482
$904$	−26.9245	−0.895496
$905$	0	0
$906$	−35.1365	−1.16733
$907$	−30.8544	−1.02450	−0.512251	−	0.858836i	$-0.671188\pi$
$907$	−30.8544	−1.02450	−0.512251	+	0.858836i	$0.671188\pi$
$908$	15.3077	0.508003
$909$	−57.6611	−1.91250
$910$	0	0
$911$	34.6247	1.14717	0.573584	−	0.819147i	$-0.305553\pi$
$911$	34.6247	1.14717	0.573584	+	0.819147i	$0.305553\pi$
$912$	−13.1216	−0.434501
$913$	53.4410	1.76864
$914$	5.39354	0.178403
$915$	0	0
$916$	28.6919	0.948008
$917$	1.10741	0.0365699
$918$	10.5457	0.348058
$919$	−3.03636	−0.100160	−0.0500802	−	0.998745i	$-0.515948\pi$
$919$	−3.03636	−0.100160	−0.0500802	+	0.998745i	$0.515948\pi$
$920$	0	0
$921$	55.4545	1.82729
$922$	−18.2053	−0.599560
$923$	23.3049	0.767090
$924$	0.895539	0.0294611
$925$	0	0
$926$	16.8037	0.552204
$927$	14.6001	0.479530
$928$	15.1923	0.498712
$929$	−17.2687	−0.566568	−0.283284	−	0.959036i	$-0.591424\pi$
$929$	−17.2687	−0.566568	−0.283284	+	0.959036i	$0.591424\pi$
$930$	0	0
$931$	36.1661	1.18530
$932$	2.34748	0.0768943
$933$	70.3435	2.30294
$934$	−7.87464	−0.257666
$935$	0	0
$936$	−31.4536	−1.02809
$937$	−41.8282	−1.36647	−0.683234	−	0.730199i	$-0.739427\pi$
$937$	−41.8282	−1.36647	−0.683234	+	0.730199i	$0.739427\pi$
$938$	−0.201912	−0.00659266
$939$	17.4494	0.569439
$940$	0	0
$941$	55.0411	1.79429	0.897145	−	0.441736i	$-0.145637\pi$
$941$	55.0411	1.79429	0.897145	+	0.441736i	$0.145637\pi$
$942$	−17.5938	−0.573236
$943$	45.4671	1.48061
$944$	−11.3474	−0.369326
$945$	0	0
$946$	1.82702	0.0594014
$947$	−5.20266	−0.169064	−0.0845318	−	0.996421i	$-0.526939\pi$
$947$	−5.20266	−0.169064	−0.0845318	+	0.996421i	$0.526939\pi$
$948$	−26.7515	−0.868849
$949$	−6.96532	−0.226104
$950$	0	0
$951$	93.1238	3.01975
$952$	0.320316	0.0103815
$953$	−23.9232	−0.774950	−0.387475	−	0.921880i	$-0.626653\pi$
$953$	−23.9232	−0.774950	−0.387475	+	0.921880i	$0.626653\pi$
$954$	40.3921	1.30774
$955$	0	0
$956$	17.5887	0.568860
$957$	32.6057	1.05399
$958$	−15.5992	−0.503987
$959$	0.402609	0.0130009
$960$	0	0
$961$	22.4455	0.724049
$962$	−9.44701	−0.304584
$963$	19.8580	0.639915
$964$	15.4172	0.496553
$965$	0	0
$966$	−0.531254	−0.0170928
$967$	−47.9852	−1.54310	−0.771550	−	0.636168i	$-0.780518\pi$
$967$	−47.9852	−1.54310	−0.771550	+	0.636168i	$0.780518\pi$
$968$	−22.8402	−0.734111
$969$	−36.2399	−1.16419
$970$	0	0
$971$	4.06546	0.130467	0.0652334	−	0.997870i	$-0.479221\pi$
$971$	4.06546	0.130467	0.0652334	+	0.997870i	$0.479221\pi$
$972$	20.3571	0.652955
$973$	−0.0380351	−0.00121935
$974$	22.3365	0.715707
$975$	0	0
$976$	−2.22210	−0.0711278
$977$	−4.40304	−0.140866	−0.0704328	−	0.997517i	$-0.522438\pi$
$977$	−4.40304	−0.140866	−0.0704328	+	0.997517i	$0.522438\pi$
$978$	−3.37046	−0.107775
$979$	4.45116	0.142260
$980$	0	0
$981$	26.4552	0.844651
$982$	28.5811	0.912060
$983$	8.02508	0.255960	0.127980	−	0.991777i	$-0.459151\pi$
$983$	8.02508	0.255960	0.127980	+	0.991777i	$0.459151\pi$
$984$	−66.7421	−2.12766
$985$	0	0
$986$	4.85941	0.154755
$987$	−1.35675	−0.0431858
$988$	17.9593	0.571362
$989$	2.70988	0.0861691
$990$	0	0
$991$	28.4040	0.902282	0.451141	−	0.892453i	$-0.351017\pi$
$991$	28.4040	0.902282	0.451141	+	0.892453i	$0.351017\pi$
$992$	−42.8572	−1.36072
$993$	87.5639	2.77876
$994$	−0.360849	−0.0114454
$995$	0	0
$996$	−48.4821	−1.53621
$997$	6.03403	0.191100	0.0955499	−	0.995425i	$-0.469539\pi$
$997$	6.03403	0.191100	0.0955499	+	0.995425i	$0.469539\pi$
$998$	5.36503	0.169827
$999$	−28.8975	−0.914277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2225.2.a.k.1.4		7
5.4	even	2		445.2.a.f.1.4	✓	7
15.14	odd	2		4005.2.a.o.1.4		7
20.19	odd	2		7120.2.a.bj.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.a.f.1.4	✓	7	5.4	even	2
2225.2.a.k.1.4		7	1.1	even	1	trivial
4005.2.a.o.1.4		7	15.14	odd	2
7120.2.a.bj.1.6		7	20.19	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2225 = 5^{2} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2225.a (trivial)

\(f(q)\)	\(=\)	\(q+0.755898 q^{2} +2.82660 q^{3} -1.42862 q^{4} +2.13662 q^{6} -0.0498231 q^{7} -2.59169 q^{8} +4.98967 q^{9} +O(q^{10})\)	\(q+0.755898 q^{2} +2.82660 q^{3} -1.42862 q^{4} +2.13662 q^{6} -0.0498231 q^{7} -2.59169 q^{8} +4.98967 q^{9} +4.45116 q^{11} -4.03813 q^{12} +2.43229 q^{13} -0.0376612 q^{14} +0.898186 q^{16} +2.48065 q^{17} +3.77168 q^{18} -5.16842 q^{19} -0.140830 q^{21} +3.36463 q^{22} +4.99050 q^{23} -7.32566 q^{24} +1.83856 q^{26} +5.62400 q^{27} +0.0711781 q^{28} +2.59152 q^{29} -7.31064 q^{31} +5.86231 q^{32} +12.5817 q^{33} +1.87512 q^{34} -7.12833 q^{36} -5.13825 q^{37} -3.90680 q^{38} +6.87512 q^{39} +9.11073 q^{41} -0.106453 q^{42} +0.543007 q^{43} -6.35901 q^{44} +3.77231 q^{46} +9.63395 q^{47} +2.53881 q^{48} -6.99752 q^{49} +7.01180 q^{51} -3.47482 q^{52} +10.7093 q^{53} +4.25117 q^{54} +0.129126 q^{56} -14.6091 q^{57} +1.95893 q^{58} -12.6337 q^{59} -2.47399 q^{61} -5.52610 q^{62} -0.248601 q^{63} +2.63494 q^{64} +9.51045 q^{66} +5.36128 q^{67} -3.54390 q^{68} +14.1061 q^{69} +9.58146 q^{71} -12.9317 q^{72} -2.86369 q^{73} -3.88400 q^{74} +7.38370 q^{76} -0.221771 q^{77} +5.19689 q^{78} +6.62473 q^{79} +0.927782 q^{81} +6.88678 q^{82} +12.0061 q^{83} +0.201192 q^{84} +0.410458 q^{86} +7.32520 q^{87} -11.5360 q^{88} +1.00000 q^{89} -0.121184 q^{91} -7.12952 q^{92} -20.6643 q^{93} +7.28229 q^{94} +16.5704 q^{96} -4.82051 q^{97} -5.28941 q^{98} +22.2098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9	\( 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9} - 10 q^{11} + 11 q^{12} + 7 q^{13} + 3 q^{14} + 10 q^{16} + 13 q^{17} - 4 q^{18} - 7 q^{19} + 16 q^{21} - 2 q^{22} + 13 q^{23} + 4 q^{24} + q^{26} + 23 q^{27} + 21 q^{28} - 4 q^{29} + q^{31} + 13 q^{32} + 6 q^{33} + 10 q^{34} + 20 q^{36} + 5 q^{37} + 40 q^{38} - 13 q^{39} + 5 q^{41} - 30 q^{42} + 31 q^{43} - 21 q^{44} + 16 q^{46} + 14 q^{47} + 7 q^{48} + 19 q^{49} - q^{51} + 13 q^{53} - 17 q^{54} - q^{56} - 21 q^{57} - 17 q^{58} - 14 q^{59} + 3 q^{61} - 26 q^{62} + 54 q^{63} + 14 q^{64} + 36 q^{66} - q^{67} + 35 q^{68} + 31 q^{69} - 8 q^{71} - 53 q^{72} - 9 q^{73} - 35 q^{74} + 40 q^{76} - 42 q^{77} - 46 q^{78} + 9 q^{79} + 35 q^{81} - 29 q^{82} + 42 q^{83} + 55 q^{84} + 35 q^{86} - 6 q^{87} - 30 q^{88} + 7 q^{89} + 31 q^{91} - 19 q^{92} - 24 q^{93} + 37 q^{94} + 44 q^{96} + 7 q^{97} - 9 q^{98} + 5 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9 - 10 * q^11 + 11 * q^12 + 7 * q^13 + 3 * q^14 + 10 * q^16 + 13 * q^17 - 4 * q^18 - 7 * q^19 + 16 * q^21 - 2 * q^22 + 13 * q^23 + 4 * q^24 + q^26 + 23 * q^27 + 21 * q^28 - 4 * q^29 + q^31 + 13 * q^32 + 6 * q^33 + 10 * q^34 + 20 * q^36 + 5 * q^37 + 40 * q^38 - 13 * q^39 + 5 * q^41 - 30 * q^42 + 31 * q^43 - 21 * q^44 + 16 * q^46 + 14 * q^47 + 7 * q^48 + 19 * q^49 - q^51 + 13 * q^53 - 17 * q^54 - q^56 - 21 * q^57 - 17 * q^58 - 14 * q^59 + 3 * q^61 - 26 * q^62 + 54 * q^63 + 14 * q^64 + 36 * q^66 - q^67 + 35 * q^68 + 31 * q^69 - 8 * q^71 - 53 * q^72 - 9 * q^73 - 35 * q^74 + 40 * q^76 - 42 * q^77 - 46 * q^78 + 9 * q^79 + 35 * q^81 - 29 * q^82 + 42 * q^83 + 55 * q^84 + 35 * q^86 - 6 * q^87 - 30 * q^88 + 7 * q^89 + 31 * q^91 - 19 * q^92 - 24 * q^93 + 37 * q^94 + 44 * q^96 + 7 * q^97 - 9 * q^98 + 5 * q^99

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