LMFDB - Embedded newform 1075.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.32503921.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 11x - 7 $ x^6 - 3x^5 - 5x^4 + 13x^3 + 9x^2 - 11*x - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.673596$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67360 q^{2} -2.56351 q^{3} +0.800923 q^{4} +4.29028 q^{6} +0.173417 q^{7} +2.00677 q^{8} +3.57157 q^{9} +O(q^{10})$	\(q-1.67360 q^{2} -2.56351 q^{3} +0.800923 q^{4} +4.29028 q^{6} +0.173417 q^{7} +2.00677 q^{8} +3.57157 q^{9} -5.84327 q^{11} -2.05317 q^{12} +1.34719 q^{13} -0.290230 q^{14} -4.96037 q^{16} -6.45318 q^{17} -5.97737 q^{18} +7.23336 q^{19} -0.444556 q^{21} +9.77927 q^{22} +6.87236 q^{23} -5.14437 q^{24} -2.25465 q^{26} -1.46523 q^{27} +0.138894 q^{28} +1.48801 q^{29} +7.78880 q^{31} +4.28811 q^{32} +14.9793 q^{33} +10.8000 q^{34} +2.86055 q^{36} -1.12190 q^{37} -12.1057 q^{38} -3.45354 q^{39} +5.63502 q^{41} +0.744007 q^{42} -1.00000 q^{43} -4.68001 q^{44} -11.5016 q^{46} -2.12737 q^{47} +12.7159 q^{48} -6.96993 q^{49} +16.5428 q^{51} +1.07900 q^{52} +0.601488 q^{53} +2.45220 q^{54} +0.348008 q^{56} -18.5428 q^{57} -2.49033 q^{58} -4.54248 q^{59} -14.4877 q^{61} -13.0353 q^{62} +0.619371 q^{63} +2.74417 q^{64} -25.0692 q^{66} +4.96258 q^{67} -5.16850 q^{68} -17.6173 q^{69} -7.96222 q^{71} +7.16732 q^{72} -3.03834 q^{73} +1.87760 q^{74} +5.79336 q^{76} -1.01332 q^{77} +5.77982 q^{78} +9.33396 q^{79} -6.95859 q^{81} -9.43074 q^{82} -2.90684 q^{83} -0.356055 q^{84} +1.67360 q^{86} -3.81453 q^{87} -11.7261 q^{88} +4.81418 q^{89} +0.233626 q^{91} +5.50423 q^{92} -19.9667 q^{93} +3.56036 q^{94} -10.9926 q^{96} -12.6150 q^{97} +11.6648 q^{98} -20.8697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9	$ 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} + 11 q^{18} + 6 q^{19} - 12 q^{21} + q^{22} - 32 q^{26} - 10 q^{27} + 10 q^{28} - 10 q^{29} - 11 q^{32} - 6 q^{33} + 14 q^{34} - 41 q^{36} - 28 q^{37} + 6 q^{38} + 8 q^{39} - 6 q^{41} - 5 q^{42} - 6 q^{43} + 4 q^{44} - 8 q^{46} + 6 q^{47} + 32 q^{48} + 20 q^{49} - 8 q^{51} + 16 q^{52} + 4 q^{53} - 5 q^{54} - 35 q^{56} - 4 q^{57} + 26 q^{58} - 20 q^{59} - 8 q^{61} - 2 q^{62} + 2 q^{63} + 17 q^{64} - 35 q^{66} - 22 q^{67} - 22 q^{68} - 42 q^{69} + 8 q^{71} + 2 q^{72} - 34 q^{73} + 45 q^{74} - 16 q^{76} - 8 q^{77} + 26 q^{78} - 16 q^{79} + 46 q^{81} - 22 q^{82} + 14 q^{83} + 37 q^{84} + 3 q^{86} + 2 q^{87} - 20 q^{88} + 24 q^{91} - 46 q^{92} - 30 q^{93} + 12 q^{94} - 23 q^{96} - 34 q^{97} - 32 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 + 11 * q^18 + 6 * q^19 - 12 * q^21 + q^22 - 32 * q^26 - 10 * q^27 + 10 * q^28 - 10 * q^29 - 11 * q^32 - 6 * q^33 + 14 * q^34 - 41 * q^36 - 28 * q^37 + 6 * q^38 + 8 * q^39 - 6 * q^41 - 5 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^46 + 6 * q^47 + 32 * q^48 + 20 * q^49 - 8 * q^51 + 16 * q^52 + 4 * q^53 - 5 * q^54 - 35 * q^56 - 4 * q^57 + 26 * q^58 - 20 * q^59 - 8 * q^61 - 2 * q^62 + 2 * q^63 + 17 * q^64 - 35 * q^66 - 22 * q^67 - 22 * q^68 - 42 * q^69 + 8 * q^71 + 2 * q^72 - 34 * q^73 + 45 * q^74 - 16 * q^76 - 8 * q^77 + 26 * q^78 - 16 * q^79 + 46 * q^81 - 22 * q^82 + 14 * q^83 + 37 * q^84 + 3 * q^86 + 2 * q^87 - 20 * q^88 + 24 * q^91 - 46 * q^92 - 30 * q^93 + 12 * q^94 - 23 * q^96 - 34 * q^97 - 32 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.67360	−1.18341	−0.591705	−	0.806154i	$-0.701545\pi$
$2$	−1.67360	−1.18341	−0.591705	+	0.806154i	$0.701545\pi$
$3$	−2.56351	−1.48004	−0.740021	−	0.672584i	$-0.765184\pi$
$3$	−2.56351	−1.48004	−0.740021	+	0.672584i	$0.765184\pi$
$4$	0.800923	0.400462
$5$	0	0
$5$	0	0
$6$	4.29028	1.75150
$7$	0.173417	0.0655455	0.0327727	−	0.999463i	$-0.489566\pi$
$7$	0.173417	0.0655455	0.0327727	+	0.999463i	$0.489566\pi$
$8$	2.00677	0.709500
$9$	3.57157	1.19052
$10$	0	0
$11$	−5.84327	−1.76181	−0.880906	−	0.473291i	$-0.843066\pi$
$11$	−5.84327	−1.76181	−0.880906	+	0.473291i	$0.843066\pi$
$12$	−2.05317	−0.592700
$13$	1.34719	0.373644	0.186822	−	0.982394i	$-0.440181\pi$
$13$	1.34719	0.373644	0.186822	+	0.982394i	$0.440181\pi$
$14$	−0.290230	−0.0775672
$15$	0	0
$16$	−4.96037	−1.24009
$17$	−6.45318	−1.56513	−0.782563	−	0.622572i	$-0.786088\pi$
$17$	−6.45318	−1.56513	−0.782563	+	0.622572i	$0.786088\pi$
$18$	−5.97737	−1.40888
$19$	7.23336	1.65945	0.829723	−	0.558175i	$-0.188498\pi$
$19$	7.23336	1.65945	0.829723	+	0.558175i	$0.188498\pi$
$20$	0	0
$21$	−0.444556	−0.0970101
$22$	9.77927	2.08495
$23$	6.87236	1.43299	0.716493	−	0.697594i	$-0.245746\pi$
$23$	6.87236	1.43299	0.716493	+	0.697594i	$0.245746\pi$
$24$	−5.14437	−1.05009
$25$	0	0
$26$	−2.25465	−0.442174
$27$	−1.46523	−0.281983
$28$	0.138894	0.0262484
$29$	1.48801	0.276317	0.138159	−	0.990410i	$-0.455882\pi$
$29$	1.48801	0.276317	0.138159	+	0.990410i	$0.455882\pi$
$30$	0	0
$31$	7.78880	1.39891	0.699455	−	0.714676i	$-0.253426\pi$
$31$	7.78880	1.39891	0.699455	+	0.714676i	$0.253426\pi$
$32$	4.28811	0.758038
$33$	14.9793	2.60756
$34$	10.8000	1.85219
$35$	0	0
$36$	2.86055	0.476759
$37$	−1.12190	−0.184439	−0.0922193	−	0.995739i	$-0.529396\pi$
$37$	−1.12190	−0.184439	−0.0922193	+	0.995739i	$0.529396\pi$
$38$	−12.1057	−1.96381
$39$	−3.45354	−0.553008
$40$	0	0
$41$	5.63502	0.880042	0.440021	−	0.897988i	$-0.354971\pi$
$41$	5.63502	0.880042	0.440021	+	0.897988i	$0.354971\pi$
$42$	0.744007	0.114803
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.68001	−0.705538
$45$	0	0
$46$	−11.5016	−1.69581
$47$	−2.12737	−0.310309	−0.155155	−	0.987890i	$-0.549588\pi$
$47$	−2.12737	−0.310309	−0.155155	+	0.987890i	$0.549588\pi$
$48$	12.7159	1.83539
$49$	−6.96993	−0.995704
$50$	0	0
$51$	16.5428	2.31645
$52$	1.07900	0.149630
$53$	0.601488	0.0826208	0.0413104	−	0.999146i	$-0.486847\pi$
$53$	0.601488	0.0826208	0.0413104	+	0.999146i	$0.486847\pi$
$54$	2.45220	0.333702
$55$	0	0
$56$	0.348008	0.0465045
$57$	−18.5428	−2.45605
$58$	−2.49033	−0.326997
$59$	−4.54248	−0.591380	−0.295690	−	0.955284i	$-0.595550\pi$
$59$	−4.54248	−0.591380	−0.295690	+	0.955284i	$0.595550\pi$
$60$	0	0
$61$	−14.4877	−1.85497	−0.927483	−	0.373865i	$-0.878032\pi$
$61$	−14.4877	−1.85497	−0.927483	+	0.373865i	$0.878032\pi$
$62$	−13.0353	−1.65549
$63$	0.619371	0.0780334
$64$	2.74417	0.343021
$65$	0	0
$66$	−25.0692	−3.08581
$67$	4.96258	0.606275	0.303138	−	0.952947i	$-0.401966\pi$
$67$	4.96258	0.606275	0.303138	+	0.952947i	$0.401966\pi$
$68$	−5.16850	−0.626773
$69$	−17.6173	−2.12088
$70$	0	0
$71$	−7.96222	−0.944942	−0.472471	−	0.881346i	$-0.656638\pi$
$71$	−7.96222	−0.944942	−0.472471	+	0.881346i	$0.656638\pi$
$72$	7.16732	0.844677
$73$	−3.03834	−0.355611	−0.177805	−	0.984066i	$-0.556900\pi$
$73$	−3.03834	−0.355611	−0.177805	+	0.984066i	$0.556900\pi$
$74$	1.87760	0.218267
$75$	0	0
$76$	5.79336	0.664544
$77$	−1.01332	−0.115479
$78$	5.77982	0.654436
$79$	9.33396	1.05015	0.525076	−	0.851055i	$-0.324037\pi$
$79$	9.33396	1.05015	0.525076	+	0.851055i	$0.324037\pi$
$80$	0	0
$81$	−6.95859	−0.773177
$82$	−9.43074	−1.04145
$83$	−2.90684	−0.319067	−0.159533	−	0.987193i	$-0.550999\pi$
$83$	−2.90684	−0.319067	−0.159533	+	0.987193i	$0.550999\pi$
$84$	−0.356055	−0.0388488
$85$	0	0
$86$	1.67360	0.180468
$87$	−3.81453	−0.408961
$88$	−11.7261	−1.25001
$89$	4.81418	0.510302	0.255151	−	0.966901i	$-0.417875\pi$
$89$	4.81418	0.510302	0.255151	+	0.966901i	$0.417875\pi$
$90$	0	0
$91$	0.233626	0.0244907
$92$	5.50423	0.573856
$93$	−19.9667	−2.07045
$94$	3.56036	0.367223
$95$	0	0
$96$	−10.9926	−1.12193
$97$	−12.6150	−1.28086	−0.640431	−	0.768016i	$-0.721244\pi$
$97$	−12.6150	−1.28086	−0.640431	+	0.768016i	$0.721244\pi$
$98$	11.6648	1.17833
$99$	−20.8697	−2.09748
$100$	0	0
$101$	−10.9191	−1.08649	−0.543247	−	0.839573i	$-0.682805\pi$
$101$	−10.9191	−1.08649	−0.543247	+	0.839573i	$0.682805\pi$
$102$	−27.6859	−2.74131
$103$	5.37677	0.529789	0.264894	−	0.964277i	$-0.414663\pi$
$103$	5.37677	0.529789	0.264894	+	0.964277i	$0.414663\pi$
$104$	2.70350	0.265100
$105$	0	0
$106$	−1.00665	−0.0977743
$107$	−0.296229	−0.0286376	−0.0143188	−	0.999897i	$-0.504558\pi$
$107$	−0.296229	−0.0286376	−0.0143188	+	0.999897i	$0.504558\pi$
$108$	−1.17353	−0.112923
$109$	4.57157	0.437877	0.218939	−	0.975739i	$-0.429741\pi$
$109$	4.57157	0.437877	0.218939	+	0.975739i	$0.429741\pi$
$110$	0	0
$111$	2.87599	0.272977
$112$	−0.860212	−0.0812824
$113$	−1.72024	−0.161826	−0.0809132	−	0.996721i	$-0.525784\pi$
$113$	−1.72024	−0.161826	−0.0809132	+	0.996721i	$0.525784\pi$
$114$	31.0331	2.90652
$115$	0	0
$116$	1.19178	0.110654
$117$	4.81159	0.444832
$118$	7.60227	0.699846
$119$	−1.11909	−0.102587
$120$	0	0
$121$	23.1438	2.10398
$122$	24.2466	2.19519
$123$	−14.4454	−1.30250
$124$	6.23823	0.560210
$125$	0	0
$126$	−1.03658	−0.0923456
$127$	9.21652	0.817834	0.408917	−	0.912572i	$-0.365907\pi$
$127$	9.21652	0.817834	0.408917	+	0.912572i	$0.365907\pi$
$128$	−13.1689	−1.16397
$129$	2.56351	0.225704
$130$	0	0
$131$	−2.46067	−0.214989	−0.107495	−	0.994206i	$-0.534283\pi$
$131$	−2.46067	−0.214989	−0.107495	+	0.994206i	$0.534283\pi$
$132$	11.9972	1.04423
$133$	1.25439	0.108769
$134$	−8.30535	−0.717473
$135$	0	0
$136$	−12.9500	−1.11046
$137$	−13.2924	−1.13564	−0.567822	−	0.823151i	$-0.692214\pi$
$137$	−13.2924	−1.13564	−0.567822	+	0.823151i	$0.692214\pi$
$138$	29.4843	2.50987
$139$	−1.84810	−0.156753	−0.0783767	−	0.996924i	$-0.524974\pi$
$139$	−1.84810	−0.156753	−0.0783767	+	0.996924i	$0.524974\pi$
$140$	0	0
$141$	5.45354	0.459271
$142$	13.3255	1.11825
$143$	−7.87200	−0.658290
$144$	−17.7163	−1.47636
$145$	0	0
$146$	5.08495	0.420834
$147$	17.8675	1.47368
$148$	−0.898552	−0.0738605
$149$	−11.2334	−0.920273	−0.460136	−	0.887848i	$-0.652199\pi$
$149$	−11.2334	−0.920273	−0.460136	+	0.887848i	$0.652199\pi$
$150$	0	0
$151$	−4.74240	−0.385931	−0.192966	−	0.981206i	$-0.561811\pi$
$151$	−4.74240	−0.385931	−0.192966	+	0.981206i	$0.561811\pi$
$152$	14.5157	1.17738
$153$	−23.0480	−1.86332
$154$	1.69589	0.136659
$155$	0	0
$156$	−2.76602	−0.221459
$157$	−16.3007	−1.30093	−0.650467	−	0.759535i	$-0.725427\pi$
$157$	−16.3007	−1.30093	−0.650467	+	0.759535i	$0.725427\pi$
$158$	−15.6213	−1.24276
$159$	−1.54192	−0.122282
$160$	0	0
$161$	1.19178	0.0939258
$162$	11.6459	0.914986
$163$	−21.6302	−1.69421	−0.847104	−	0.531428i	$-0.821656\pi$
$163$	−21.6302	−1.69421	−0.847104	+	0.531428i	$0.821656\pi$
$164$	4.51321	0.352423
$165$	0	0
$166$	4.86487	0.377587
$167$	3.25697	0.252032	0.126016	−	0.992028i	$-0.459781\pi$
$167$	3.25697	0.252032	0.126016	+	0.992028i	$0.459781\pi$
$168$	−0.892122	−0.0688287
$169$	−11.1851	−0.860390
$170$	0	0
$171$	25.8345	1.97561
$172$	−0.800923	−0.0610698
$173$	−0.923590	−0.0702192	−0.0351096	−	0.999383i	$-0.511178\pi$
$173$	−0.923590	−0.0702192	−0.0351096	+	0.999383i	$0.511178\pi$
$174$	6.38399	0.483969
$175$	0	0
$176$	28.9848	2.18481
$177$	11.6447	0.875268
$178$	−8.05699	−0.603897
$179$	−26.5083	−1.98132	−0.990661	−	0.136345i	$-0.956465\pi$
$179$	−26.5083	−1.98132	−0.990661	+	0.136345i	$0.956465\pi$
$180$	0	0
$181$	23.7104	1.76238	0.881192	−	0.472759i	$-0.156742\pi$
$181$	23.7104	1.76238	0.881192	+	0.472759i	$0.156742\pi$
$182$	−0.390995	−0.0289825
$183$	37.1394	2.74543
$184$	13.7912	1.01670
$185$	0	0
$186$	33.4161	2.45019
$187$	37.7077	2.75746
$188$	−1.70386	−0.124267
$189$	−0.254095	−0.0184827
$190$	0	0
$191$	−17.6513	−1.27721	−0.638603	−	0.769536i	$-0.720487\pi$
$191$	−17.6513	−1.27721	−0.638603	+	0.769536i	$0.720487\pi$
$192$	−7.03470	−0.507686
$193$	−13.2544	−0.954072	−0.477036	−	0.878884i	$-0.658289\pi$
$193$	−13.2544	−0.954072	−0.477036	+	0.878884i	$0.658289\pi$
$194$	21.1125	1.51579
$195$	0	0
$196$	−5.58237	−0.398741
$197$	−8.73750	−0.622521	−0.311261	−	0.950325i	$-0.600751\pi$
$197$	−8.73750	−0.622521	−0.311261	+	0.950325i	$0.600751\pi$
$198$	34.9274	2.48218
$199$	21.8478	1.54875	0.774373	−	0.632729i	$-0.218065\pi$
$199$	21.8478	1.54875	0.774373	+	0.632729i	$0.218065\pi$
$200$	0	0
$201$	−12.7216	−0.897313
$202$	18.2742	1.28577
$203$	0.258047	0.0181113
$204$	13.2495	0.927650
$205$	0	0
$206$	−8.99854	−0.626958
$207$	24.5451	1.70600
$208$	−6.68257	−0.463353
$209$	−42.2665	−2.92363
$210$	0	0
$211$	−9.06225	−0.623871	−0.311935	−	0.950103i	$-0.600977\pi$
$211$	−9.06225	−0.623871	−0.311935	+	0.950103i	$0.600977\pi$
$212$	0.481746	0.0330864
$213$	20.4112	1.39855
$214$	0.495768	0.0338900
$215$	0	0
$216$	−2.94037	−0.200067
$217$	1.35071	0.0916923
$218$	−7.65096	−0.518189
$219$	7.78880	0.526319
$220$	0	0
$221$	−8.69367	−0.584799
$222$	−4.81324	−0.323044
$223$	25.3738	1.69915	0.849577	−	0.527464i	$-0.176857\pi$
$223$	25.3738	1.69915	0.849577	+	0.527464i	$0.176857\pi$
$224$	0.743632	0.0496860
$225$	0	0
$226$	2.87898	0.191507
$227$	−0.205671	−0.0136509	−0.00682543	−	0.999977i	$-0.502173\pi$
$227$	−0.205671	−0.0136509	−0.00682543	+	0.999977i	$0.502173\pi$
$228$	−14.8513	−0.983554
$229$	4.21372	0.278450	0.139225	−	0.990261i	$-0.455539\pi$
$229$	4.21372	0.278450	0.139225	+	0.990261i	$0.455539\pi$
$230$	0	0
$231$	2.59766	0.170913
$232$	2.98610	0.196047
$233$	14.2691	0.934801	0.467400	−	0.884046i	$-0.345191\pi$
$233$	14.2691	0.934801	0.467400	+	0.884046i	$0.345191\pi$
$234$	−8.05266	−0.526419
$235$	0	0
$236$	−3.63818	−0.236825
$237$	−23.9277	−1.55427
$238$	1.87291	0.121402
$239$	−13.9559	−0.902733	−0.451367	−	0.892339i	$-0.649063\pi$
$239$	−13.9559	−0.902733	−0.451367	+	0.892339i	$0.649063\pi$
$240$	0	0
$241$	−18.2189	−1.17358	−0.586792	−	0.809738i	$-0.699609\pi$
$241$	−18.2189	−1.17358	−0.586792	+	0.809738i	$0.699609\pi$
$242$	−38.7334	−2.48987
$243$	22.2341	1.42632
$244$	−11.6036	−0.742842
$245$	0	0
$246$	24.1758	1.54139
$247$	9.74472	0.620042
$248$	15.6303	0.992528
$249$	7.45170	0.472232
$250$	0	0
$251$	−20.1371	−1.27104	−0.635522	−	0.772083i	$-0.719215\pi$
$251$	−20.1371	−1.27104	−0.635522	+	0.772083i	$0.719215\pi$
$252$	0.496069	0.0312494
$253$	−40.1571	−2.52465
$254$	−15.4247	−0.967833
$255$	0	0
$256$	16.5510	1.03444
$257$	−14.0128	−0.874097	−0.437048	−	0.899438i	$-0.643976\pi$
$257$	−14.0128	−0.874097	−0.437048	+	0.899438i	$0.643976\pi$
$258$	−4.29028	−0.267101
$259$	−0.194556	−0.0120891
$260$	0	0
$261$	5.31455	0.328962
$262$	4.11816	0.254421
$263$	11.4168	0.703989	0.351995	−	0.936002i	$-0.385504\pi$
$263$	11.4168	0.703989	0.351995	+	0.936002i	$0.385504\pi$
$264$	30.0599	1.85006
$265$	0	0
$266$	−2.09934	−0.128719
$267$	−12.3412	−0.755268
$268$	3.97464	0.242790
$269$	−6.22592	−0.379601	−0.189801	−	0.981823i	$-0.560784\pi$
$269$	−6.22592	−0.379601	−0.189801	+	0.981823i	$0.560784\pi$
$270$	0	0
$271$	−8.94750	−0.543522	−0.271761	−	0.962365i	$-0.587606\pi$
$271$	−8.94750	−0.543522	−0.271761	+	0.962365i	$0.587606\pi$
$272$	32.0101	1.94090
$273$	−0.598902	−0.0362472
$274$	22.2461	1.34393
$275$	0	0
$276$	−14.1101	−0.849331
$277$	17.6961	1.06326	0.531629	−	0.846977i	$-0.321580\pi$
$277$	17.6961	1.06326	0.531629	+	0.846977i	$0.321580\pi$
$278$	3.09297	0.185504
$279$	27.8183	1.66544
$280$	0	0
$281$	13.2059	0.787796	0.393898	−	0.919154i	$-0.371126\pi$
$281$	13.2059	0.787796	0.393898	+	0.919154i	$0.371126\pi$
$282$	−9.12702	−0.543506
$283$	−17.0844	−1.01556	−0.507782	−	0.861486i	$-0.669534\pi$
$283$	−17.0844	−1.01556	−0.507782	+	0.861486i	$0.669534\pi$
$284$	−6.37713	−0.378413
$285$	0	0
$286$	13.1746	0.779028
$287$	0.977208	0.0576828
$288$	15.3153	0.902462
$289$	24.6435	1.44962
$290$	0	0
$291$	32.3387	1.89573
$292$	−2.43348	−0.142408
$293$	21.8350	1.27562	0.637808	−	0.770195i	$-0.279841\pi$
$293$	21.8350	1.27562	0.637808	+	0.770195i	$0.279841\pi$
$294$	−29.9029	−1.74397
$295$	0	0
$296$	−2.25139	−0.130859
$297$	8.56171	0.496801
$298$	18.8001	1.08906
$299$	9.25839	0.535426
$300$	0	0
$301$	−0.173417	−0.00999559
$302$	7.93686	0.456715
$303$	27.9912	1.60806
$304$	−35.8801	−2.05787
$305$	0	0
$306$	38.5730	2.20507
$307$	−11.9693	−0.683125	−0.341563	−	0.939859i	$-0.610956\pi$
$307$	−11.9693	−0.683125	−0.341563	+	0.939859i	$0.610956\pi$
$308$	−0.811593	−0.0462448
$309$	−13.7834	−0.784109
$310$	0	0
$311$	27.9646	1.58573	0.792864	−	0.609399i	$-0.208589\pi$
$311$	27.9646	1.58573	0.792864	+	0.609399i	$0.208589\pi$
$312$	−6.93045	−0.392360
$313$	−5.48345	−0.309943	−0.154972	−	0.987919i	$-0.549529\pi$
$313$	−5.48345	−0.309943	−0.154972	+	0.987919i	$0.549529\pi$
$314$	27.2807	1.53954
$315$	0	0
$316$	7.47578	0.420546
$317$	−10.5810	−0.594290	−0.297145	−	0.954832i	$-0.596034\pi$
$317$	−10.5810	−0.594290	−0.297145	+	0.954832i	$0.596034\pi$
$318$	2.58055	0.144710
$319$	−8.69487	−0.486819
$320$	0	0
$321$	0.759386	0.0423848
$322$	−1.99457	−0.111153
$323$	−46.6782	−2.59724
$324$	−5.57330	−0.309628
$325$	0	0
$326$	36.2002	2.00494
$327$	−11.7193	−0.648076
$328$	11.3082	0.624390
$329$	−0.368923	−0.0203394
$330$	0	0
$331$	8.91174	0.489834	0.244917	−	0.969544i	$-0.421239\pi$
$331$	8.91174	0.489834	0.244917	+	0.969544i	$0.421239\pi$
$332$	−2.32815	−0.127774
$333$	−4.00693	−0.219578
$334$	−5.45086	−0.298258
$335$	0	0
$336$	2.20516	0.120301
$337$	3.17982	0.173216	0.0866078	−	0.996242i	$-0.472397\pi$
$337$	3.17982	0.173216	0.0866078	+	0.996242i	$0.472397\pi$
$338$	18.7193	1.01820
$339$	4.40984	0.239510
$340$	0	0
$341$	−45.5121	−2.46462
$342$	−43.2364	−2.33796
$343$	−2.42262	−0.130809
$344$	−2.00677	−0.108198
$345$	0	0
$346$	1.54572	0.0830982
$347$	−2.73996	−0.147089	−0.0735444	−	0.997292i	$-0.523431\pi$
$347$	−2.73996	−0.147089	−0.0735444	+	0.997292i	$0.523431\pi$
$348$	−3.05515	−0.163773
$349$	−2.74499	−0.146936	−0.0734679	−	0.997298i	$-0.523407\pi$
$349$	−2.74499	−0.146936	−0.0734679	+	0.997298i	$0.523407\pi$
$350$	0	0
$351$	−1.97394	−0.105361
$352$	−25.0566	−1.33552
$353$	−10.2379	−0.544909	−0.272454	−	0.962169i	$-0.587835\pi$
$353$	−10.2379	−0.544909	−0.272454	+	0.962169i	$0.587835\pi$
$354$	−19.4885	−1.03580
$355$	0	0
$356$	3.85579	0.204356
$357$	2.86880	0.151833
$358$	44.3642	2.34472
$359$	−0.536390	−0.0283096	−0.0141548	−	0.999900i	$-0.504506\pi$
$359$	−0.536390	−0.0283096	−0.0141548	+	0.999900i	$0.504506\pi$
$360$	0	0
$361$	33.3215	1.75376
$362$	−39.6817	−2.08562
$363$	−59.3293	−3.11398
$364$	0.187116	0.00980757
$365$	0	0
$366$	−62.1564	−3.24897
$367$	30.1820	1.57549	0.787744	−	0.616003i	$-0.211249\pi$
$367$	30.1820	1.57549	0.787744	+	0.616003i	$0.211249\pi$
$368$	−34.0894	−1.77703
$369$	20.1259	1.04771
$370$	0	0
$371$	0.104308	0.00541542
$372$	−15.9918	−0.829134
$373$	15.5841	0.806916	0.403458	−	0.914998i	$-0.367808\pi$
$373$	15.5841	0.806916	0.403458	+	0.914998i	$0.367808\pi$
$374$	−63.1074	−3.26320
$375$	0	0
$376$	−4.26915	−0.220165
$377$	2.00464	0.103244
$378$	0.425253	0.0218726
$379$	−23.1476	−1.18901	−0.594507	−	0.804090i	$-0.702653\pi$
$379$	−23.1476	−1.18901	−0.594507	+	0.804090i	$0.702653\pi$
$380$	0	0
$381$	−23.6266	−1.21043
$382$	29.5412	1.51146
$383$	−30.2673	−1.54659	−0.773293	−	0.634049i	$-0.781392\pi$
$383$	−30.2673	−1.54659	−0.773293	+	0.634049i	$0.781392\pi$
$384$	33.7585	1.72273
$385$	0	0
$386$	22.1825	1.12906
$387$	−3.57157	−0.181553
$388$	−10.1037	−0.512936
$389$	26.7568	1.35662	0.678312	−	0.734774i	$-0.262712\pi$
$389$	26.7568	1.35662	0.678312	+	0.734774i	$0.262712\pi$
$390$	0	0
$391$	−44.3486	−2.24280
$392$	−13.9870	−0.706452
$393$	6.30794	0.318193
$394$	14.6230	0.736698
$395$	0	0
$396$	−16.7150	−0.839959
$397$	−23.0057	−1.15462	−0.577311	−	0.816524i	$-0.695898\pi$
$397$	−23.0057	−1.15462	−0.577311	+	0.816524i	$0.695898\pi$
$398$	−36.5643	−1.83280
$399$	−3.21563	−0.160983
$400$	0	0
$401$	26.4736	1.32203	0.661014	−	0.750373i	$-0.270126\pi$
$401$	26.4736	1.32203	0.661014	+	0.750373i	$0.270126\pi$
$402$	21.2908	1.06189
$403$	10.4930	0.522694
$404$	−8.74537	−0.435099
$405$	0	0
$406$	−0.431866	−0.0214332
$407$	6.55554	0.324946
$408$	33.1975	1.64352
$409$	1.99404	0.0985989	0.0492994	−	0.998784i	$-0.484301\pi$
$409$	1.99404	0.0985989	0.0492994	+	0.998784i	$0.484301\pi$
$410$	0	0
$411$	34.0751	1.68080
$412$	4.30638	0.212160
$413$	−0.787743	−0.0387623
$414$	−41.0786	−2.01890
$415$	0	0
$416$	5.77691	0.283236
$417$	4.73761	0.232002
$418$	70.7370	3.45986
$419$	−21.5701	−1.05377	−0.526885	−	0.849937i	$-0.676640\pi$
$419$	−21.5701	−1.05377	−0.526885	+	0.849937i	$0.676640\pi$
$420$	0	0
$421$	19.3761	0.944335	0.472168	−	0.881509i	$-0.343472\pi$
$421$	19.3761	0.944335	0.472168	+	0.881509i	$0.343472\pi$
$422$	15.1665	0.738295
$423$	−7.59806	−0.369430
$424$	1.20705	0.0586195
$425$	0	0
$426$	−34.1601	−1.65506
$427$	−2.51242	−0.121585
$428$	−0.237257	−0.0114682
$429$	20.1799	0.974297
$430$	0	0
$431$	25.9246	1.24875	0.624373	−	0.781126i	$-0.285355\pi$
$431$	25.9246	1.24875	0.624373	+	0.781126i	$0.285355\pi$
$432$	7.26806	0.349685
$433$	2.52355	0.121274	0.0606370	−	0.998160i	$-0.480687\pi$
$433$	2.52355	0.121274	0.0606370	+	0.998160i	$0.480687\pi$
$434$	−2.26054	−0.108510
$435$	0	0
$436$	3.66148	0.175353
$437$	49.7103	2.37796
$438$	−13.0353	−0.622851
$439$	−35.0146	−1.67116	−0.835578	−	0.549372i	$-0.814867\pi$
$439$	−35.0146	−1.67116	−0.835578	+	0.549372i	$0.814867\pi$
$440$	0	0
$441$	−24.8936	−1.18541
$442$	14.5497	0.692058
$443$	−1.12393	−0.0533997	−0.0266999	−	0.999643i	$-0.508500\pi$
$443$	−1.12393	−0.0533997	−0.0266999	+	0.999643i	$0.508500\pi$
$444$	2.30344	0.109317
$445$	0	0
$446$	−42.4655	−2.01080
$447$	28.7968	1.36204
$448$	0.475886	0.0224835
$449$	−35.6349	−1.68172	−0.840858	−	0.541256i	$-0.817949\pi$
$449$	−35.6349	−1.68172	−0.840858	+	0.541256i	$0.817949\pi$
$450$	0	0
$451$	−32.9269	−1.55047
$452$	−1.37778	−0.0648053
$453$	12.1572	0.571194
$454$	0.344210	0.0161546
$455$	0	0
$456$	−37.2111	−1.74257
$457$	−27.6564	−1.29371	−0.646857	−	0.762611i	$-0.723917\pi$
$457$	−27.6564	−1.29371	−0.646857	+	0.762611i	$0.723917\pi$
$458$	−7.05206	−0.329521
$459$	9.45537	0.441339
$460$	0	0
$461$	2.55498	0.118997	0.0594985	−	0.998228i	$-0.481050\pi$
$461$	2.55498	0.118997	0.0594985	+	0.998228i	$0.481050\pi$
$462$	−4.34743	−0.202261
$463$	1.25213	0.0581916	0.0290958	−	0.999577i	$-0.490737\pi$
$463$	1.25213	0.0581916	0.0290958	+	0.999577i	$0.490737\pi$
$464$	−7.38110	−0.342659
$465$	0	0
$466$	−23.8807	−1.10625
$467$	−31.3408	−1.45028	−0.725140	−	0.688601i	$-0.758225\pi$
$467$	−31.3408	−1.45028	−0.725140	+	0.688601i	$0.758225\pi$
$468$	3.85371	0.178138
$469$	0.860596	0.0397386
$470$	0	0
$471$	41.7868	1.92544
$472$	−9.11571	−0.419585
$473$	5.84327	0.268674
$474$	40.0453	1.83934
$475$	0	0
$476$	−0.896306	−0.0410821
$477$	2.14826	0.0983620
$478$	23.3566	1.06830
$479$	23.9963	1.09642	0.548209	−	0.836341i	$-0.315310\pi$
$479$	23.9963	1.09642	0.548209	+	0.836341i	$0.315310\pi$
$480$	0	0
$481$	−1.51141	−0.0689143
$482$	30.4911	1.38883
$483$	−3.05515	−0.139014
$484$	18.5364	0.842563
$485$	0	0
$486$	−37.2109	−1.68792
$487$	−9.99622	−0.452972	−0.226486	−	0.974014i	$-0.572724\pi$
$487$	−9.99622	−0.452972	−0.226486	+	0.974014i	$0.572724\pi$
$488$	−29.0736	−1.31610
$489$	55.4492	2.50750
$490$	0	0
$491$	−29.2530	−1.32017	−0.660086	−	0.751190i	$-0.729480\pi$
$491$	−29.2530	−1.32017	−0.660086	+	0.751190i	$0.729480\pi$
$492$	−11.5697	−0.521601
$493$	−9.60242	−0.432471
$494$	−16.3087	−0.733764
$495$	0	0
$496$	−38.6353	−1.73478
$497$	−1.38078	−0.0619367
$498$	−12.4711	−0.558845
$499$	34.5976	1.54880	0.774400	−	0.632697i	$-0.218052\pi$
$499$	34.5976	1.54880	0.774400	+	0.632697i	$0.218052\pi$
$500$	0	0
$501$	−8.34928	−0.373018
$502$	33.7014	1.50417
$503$	3.56666	0.159030	0.0795149	−	0.996834i	$-0.474663\pi$
$503$	3.56666	0.159030	0.0795149	+	0.996834i	$0.474663\pi$
$504$	1.24294	0.0553648
$505$	0	0
$506$	67.2067	2.98770
$507$	28.6730	1.27341
$508$	7.38172	0.327511
$509$	13.8848	0.615432	0.307716	−	0.951478i	$-0.400435\pi$
$509$	13.8848	0.615432	0.307716	+	0.951478i	$0.400435\pi$
$510$	0	0
$511$	−0.526900	−0.0233087
$512$	−1.36197	−0.0601912
$513$	−10.5985	−0.467936
$514$	23.4518	1.03442
$515$	0	0
$516$	2.05317	0.0903859
$517$	12.4308	0.546706
$518$	0.325608	0.0143064
$519$	2.36763	0.103927
$520$	0	0
$521$	18.4939	0.810232	0.405116	−	0.914265i	$-0.367231\pi$
$521$	18.4939	0.810232	0.405116	+	0.914265i	$0.367231\pi$
$522$	−8.89440	−0.389297
$523$	−31.2838	−1.36794	−0.683972	−	0.729509i	$-0.739749\pi$
$523$	−31.2838	−1.36794	−0.683972	+	0.729509i	$0.739749\pi$
$524$	−1.97080	−0.0860950
$525$	0	0
$526$	−19.1071	−0.833108
$527$	−50.2625	−2.18947
$528$	−74.3027	−3.23361
$529$	24.2293	1.05345
$530$	0	0
$531$	−16.2238	−0.704052
$532$	1.00467	0.0435579
$533$	7.59145	0.328822
$534$	20.6541	0.893792
$535$	0	0
$536$	9.95875	0.430153
$537$	67.9542	2.93244
$538$	10.4197	0.449224
$539$	40.7272	1.75424
$540$	0	0
$541$	−19.6586	−0.845190	−0.422595	−	0.906319i	$-0.638881\pi$
$541$	−19.6586	−0.845190	−0.422595	+	0.906319i	$0.638881\pi$
$542$	14.9745	0.643210
$543$	−60.7819	−2.60840
$544$	−27.6719	−1.18642
$545$	0	0
$546$	1.00232	0.0428953
$547$	−28.7866	−1.23083	−0.615413	−	0.788205i	$-0.711011\pi$
$547$	−28.7866	−1.23083	−0.615413	+	0.788205i	$0.711011\pi$
$548$	−10.6462	−0.454782
$549$	−51.7440	−2.20838
$550$	0	0
$551$	10.7633	0.458534
$552$	−35.3540	−1.50476
$553$	1.61867	0.0688328
$554$	−29.6162	−1.25827
$555$	0	0
$556$	−1.48018	−0.0627737
$557$	−21.5860	−0.914629	−0.457314	−	0.889305i	$-0.651189\pi$
$557$	−21.5860	−0.914629	−0.457314	+	0.889305i	$0.651189\pi$
$558$	−46.5565	−1.97090
$559$	−1.34719	−0.0569801
$560$	0	0
$561$	−96.6639	−4.08115
$562$	−22.1013	−0.932287
$563$	27.1386	1.14376	0.571879	−	0.820338i	$-0.306215\pi$
$563$	27.1386	1.14376	0.571879	+	0.820338i	$0.306215\pi$
$564$	4.36786	0.183920
$565$	0	0
$566$	28.5924	1.20183
$567$	−1.20674	−0.0506783
$568$	−15.9783	−0.670437
$569$	11.7280	0.491665	0.245832	−	0.969312i	$-0.420939\pi$
$569$	11.7280	0.491665	0.245832	+	0.969312i	$0.420939\pi$
$570$	0	0
$571$	−28.9019	−1.20951	−0.604754	−	0.796412i	$-0.706729\pi$
$571$	−28.9019	−1.20951	−0.604754	+	0.796412i	$0.706729\pi$
$572$	−6.30487	−0.263620
$573$	45.2494	1.89032
$574$	−1.63545	−0.0682624
$575$	0	0
$576$	9.80100	0.408375
$577$	4.65233	0.193679	0.0968394	−	0.995300i	$-0.469127\pi$
$577$	4.65233	0.193679	0.0968394	+	0.995300i	$0.469127\pi$
$578$	−41.2433	−1.71549
$579$	33.9777	1.41207
$580$	0	0
$581$	−0.504095	−0.0209134
$582$	−54.1220	−2.24343
$583$	−3.51466	−0.145562
$584$	−6.09725	−0.252306
$585$	0	0
$586$	−36.5430	−1.50958
$587$	36.4014	1.50245	0.751223	−	0.660048i	$-0.229464\pi$
$587$	36.4014	1.50245	0.751223	+	0.660048i	$0.229464\pi$
$588$	14.3105	0.590153
$589$	56.3392	2.32142
$590$	0	0
$591$	22.3986	0.921357
$592$	5.56502	0.228721
$593$	−44.1817	−1.81432	−0.907162	−	0.420781i	$-0.861756\pi$
$593$	−44.1817	−1.81432	−0.907162	+	0.420781i	$0.861756\pi$
$594$	−14.3288	−0.587920
$595$	0	0
$596$	−8.99706	−0.368534
$597$	−56.0069	−2.29221
$598$	−15.4948	−0.633629
$599$	−12.7193	−0.519695	−0.259847	−	0.965650i	$-0.583672\pi$
$599$	−12.7193	−0.519695	−0.259847	+	0.965650i	$0.583672\pi$
$600$	0	0
$601$	−19.6360	−0.800970	−0.400485	−	0.916303i	$-0.631158\pi$
$601$	−19.6360	−0.800970	−0.400485	+	0.916303i	$0.631158\pi$
$602$	0.290230	0.0118289
$603$	17.7242	0.721785
$604$	−3.79830	−0.154551
$605$	0	0
$606$	−46.8460	−1.90299
$607$	19.2983	0.783293	0.391646	−	0.920116i	$-0.371906\pi$
$607$	19.2983	0.783293	0.391646	+	0.920116i	$0.371906\pi$
$608$	31.0175	1.25792
$609$	−0.661505	−0.0268055
$610$	0	0
$611$	−2.86598	−0.115945
$612$	−18.4597	−0.746188
$613$	40.1886	1.62320	0.811602	−	0.584211i	$-0.198596\pi$
$613$	40.1886	1.62320	0.811602	+	0.584211i	$0.198596\pi$
$614$	20.0318	0.808418
$615$	0	0
$616$	−2.03351	−0.0819323
$617$	−8.76941	−0.353043	−0.176522	−	0.984297i	$-0.556485\pi$
$617$	−8.76941	−0.353043	−0.176522	+	0.984297i	$0.556485\pi$
$618$	23.0678	0.927924
$619$	−48.0938	−1.93305	−0.966526	−	0.256570i	$-0.917408\pi$
$619$	−48.0938	−1.93305	−0.966526	+	0.256570i	$0.917408\pi$
$620$	0	0
$621$	−10.0696	−0.404078
$622$	−46.8015	−1.87657
$623$	0.834860	0.0334480
$624$	17.1308	0.685781
$625$	0	0
$626$	9.17708	0.366790
$627$	108.350	4.32710
$628$	−13.0556	−0.520974
$629$	7.23979	0.288669
$630$	0	0
$631$	35.8860	1.42860	0.714300	−	0.699839i	$-0.246745\pi$
$631$	35.8860	1.42860	0.714300	+	0.699839i	$0.246745\pi$
$632$	18.7311	0.745084
$633$	23.2311	0.923355
$634$	17.7084	0.703289
$635$	0	0
$636$	−1.23496	−0.0489693
$637$	−9.38983	−0.372038
$638$	14.5517	0.576107
$639$	−28.4376	−1.12498
$640$	0	0
$641$	8.50718	0.336013	0.168007	−	0.985786i	$-0.446267\pi$
$641$	8.50718	0.336013	0.168007	+	0.985786i	$0.446267\pi$
$642$	−1.27091	−0.0501586
$643$	−5.21723	−0.205748	−0.102874	−	0.994694i	$-0.532804\pi$
$643$	−5.21723	−0.205748	−0.102874	+	0.994694i	$0.532804\pi$
$644$	0.954528	0.0376137
$645$	0	0
$646$	78.1204	3.07360
$647$	−7.69101	−0.302365	−0.151182	−	0.988506i	$-0.548308\pi$
$647$	−7.69101	−0.302365	−0.151182	+	0.988506i	$0.548308\pi$
$648$	−13.9643	−0.548569
$649$	26.5429	1.04190
$650$	0	0
$651$	−3.46256	−0.135708
$652$	−17.3241	−0.678465
$653$	−4.38169	−0.171469	−0.0857343	−	0.996318i	$-0.527324\pi$
$653$	−4.38169	−0.171469	−0.0857343	+	0.996318i	$0.527324\pi$
$654$	19.6133	0.766941
$655$	0	0
$656$	−27.9518	−1.09133
$657$	−10.8516	−0.423363
$658$	0.617427	0.0240698
$659$	20.9340	0.815471	0.407735	−	0.913100i	$-0.366319\pi$
$659$	20.9340	0.815471	0.407735	+	0.913100i	$0.366319\pi$
$660$	0	0
$661$	−41.5269	−1.61521	−0.807605	−	0.589724i	$-0.799237\pi$
$661$	−41.5269	−1.61521	−0.807605	+	0.589724i	$0.799237\pi$
$662$	−14.9147	−0.579674
$663$	22.2863	0.865528
$664$	−5.83336	−0.226378
$665$	0	0
$666$	6.70598	0.259851
$667$	10.2262	0.395959
$668$	2.60859	0.100929
$669$	−65.0459	−2.51482
$670$	0	0
$671$	84.6558	3.26810
$672$	−1.90631	−0.0735373
$673$	−5.77002	−0.222418	−0.111209	−	0.993797i	$-0.535472\pi$
$673$	−5.77002	−0.222418	−0.111209	+	0.993797i	$0.535472\pi$
$674$	−5.32173	−0.204985
$675$	0	0
$676$	−8.95838	−0.344553
$677$	−36.8492	−1.41623	−0.708116	−	0.706096i	$-0.750455\pi$
$677$	−36.8492	−1.41623	−0.708116	+	0.706096i	$0.750455\pi$
$678$	−7.38030	−0.283439
$679$	−2.18766	−0.0839547
$680$	0	0
$681$	0.527239	0.0202038
$682$	76.1688	2.91665
$683$	29.2430	1.11895	0.559476	−	0.828847i	$-0.311003\pi$
$683$	29.2430	1.11895	0.559476	+	0.828847i	$0.311003\pi$
$684$	20.6914	0.791156
$685$	0	0
$686$	4.05449	0.154801
$687$	−10.8019	−0.412118
$688$	4.96037	0.189112
$689$	0.810320	0.0308707
$690$	0	0
$691$	8.42066	0.320337	0.160169	−	0.987090i	$-0.448796\pi$
$691$	8.42066	0.320337	0.160169	+	0.987090i	$0.448796\pi$
$692$	−0.739724	−0.0281201
$693$	−3.61915	−0.137480
$694$	4.58559	0.174066
$695$	0	0
$696$	−7.65489	−0.290158
$697$	−36.3638	−1.37738
$698$	4.59400	0.173885
$699$	−36.5790	−1.38354
$700$	0	0
$701$	−26.6765	−1.00756	−0.503779	−	0.863833i	$-0.668057\pi$
$701$	−26.6765	−1.00756	−0.503779	+	0.863833i	$0.668057\pi$
$702$	3.30358	0.124686
$703$	−8.11507	−0.306066
$704$	−16.0349	−0.604339
$705$	0	0
$706$	17.1341	0.644851
$707$	−1.89356	−0.0712147
$708$	9.32649	0.350511
$709$	−19.2771	−0.723967	−0.361983	−	0.932185i	$-0.617900\pi$
$709$	−19.2771	−0.723967	−0.361983	+	0.932185i	$0.617900\pi$
$710$	0	0
$711$	33.3369	1.25023
$712$	9.66095	0.362059
$713$	53.5275	2.00462
$714$	−4.80121	−0.179681
$715$	0	0
$716$	−21.2311	−0.793444
$717$	35.7761	1.33608
$718$	0.897700	0.0335019
$719$	12.2238	0.455869	0.227935	−	0.973676i	$-0.426803\pi$
$719$	12.2238	0.455869	0.227935	+	0.973676i	$0.426803\pi$
$720$	0	0
$721$	0.932423	0.0347253
$722$	−55.7667	−2.07542
$723$	46.7044	1.73695
$724$	18.9902	0.705767
$725$	0	0
$726$	99.2932	3.68512
$727$	−20.0656	−0.744193	−0.372096	−	0.928194i	$-0.621361\pi$
$727$	−20.0656	−0.744193	−0.372096	+	0.928194i	$0.621361\pi$
$728$	0.468834	0.0173761
$729$	−36.1215	−1.33783
$730$	0	0
$731$	6.45318	0.238679
$732$	29.7458	1.09944
$733$	−26.9741	−0.996310	−0.498155	−	0.867088i	$-0.665989\pi$
$733$	−26.9741	−0.996310	−0.498155	+	0.867088i	$0.665989\pi$
$734$	−50.5125	−1.86445
$735$	0	0
$736$	29.4694	1.08626
$737$	−28.9977	−1.06814
$738$	−33.6826	−1.23987
$739$	−20.0370	−0.737074	−0.368537	−	0.929613i	$-0.620141\pi$
$739$	−20.0370	−0.737074	−0.368537	+	0.929613i	$0.620141\pi$
$740$	0	0
$741$	−24.9807	−0.917688
$742$	−0.174570	−0.00640867
$743$	−1.38743	−0.0508999	−0.0254499	−	0.999676i	$-0.508102\pi$
$743$	−1.38743	−0.0508999	−0.0254499	+	0.999676i	$0.508102\pi$
$744$	−40.0685	−1.46898
$745$	0	0
$746$	−26.0815	−0.954913
$747$	−10.3820	−0.379857
$748$	30.2009	1.10426
$749$	−0.0513712	−0.00187706
$750$	0	0
$751$	10.0017	0.364969	0.182484	−	0.983209i	$-0.441586\pi$
$751$	10.0017	0.364969	0.182484	+	0.983209i	$0.441586\pi$
$752$	10.5526	0.384812
$753$	51.6217	1.88120
$754$	−3.35496	−0.122180
$755$	0	0
$756$	−0.203511	−0.00740161
$757$	−0.0394586	−0.00143415	−0.000717074	−	1.00000i	$-0.500228\pi$
$757$	−0.0394586	−0.00143415	−0.000717074		1.00000i	$0.500228\pi$
$758$	38.7398	1.40709
$759$	102.943	3.73659
$760$	0	0
$761$	−28.0745	−1.01770	−0.508850	−	0.860855i	$-0.669929\pi$
$761$	−28.0745	−1.01770	−0.508850	+	0.860855i	$0.669929\pi$
$762$	39.5414	1.43243
$763$	0.792788	0.0287009
$764$	−14.1374	−0.511472
$765$	0	0
$766$	50.6552	1.83025
$767$	−6.11959	−0.220966
$768$	−42.4286	−1.53101
$769$	−29.9862	−1.08133	−0.540664	−	0.841238i	$-0.681827\pi$
$769$	−29.9862	−1.08133	−0.540664	+	0.841238i	$0.681827\pi$
$770$	0	0
$771$	35.9220	1.29370
$772$	−10.6157	−0.382069
$773$	−29.9405	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$773$	−29.9405	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$774$	5.97737	0.214852
$775$	0	0
$776$	−25.3155	−0.908772
$777$	0.498745	0.0178924
$778$	−44.7801	−1.60544
$779$	40.7601	1.46038
$780$	0	0
$781$	46.5254	1.66481
$782$	74.2216	2.65416
$783$	−2.18028	−0.0779168
$784$	34.5734	1.23476
$785$	0	0
$786$	−10.5569	−0.376553
$787$	−45.1568	−1.60967	−0.804833	−	0.593502i	$-0.797745\pi$
$787$	−45.1568	−1.60967	−0.804833	+	0.593502i	$0.797745\pi$
$788$	−6.99806	−0.249296
$789$	−29.2670	−1.04193
$790$	0	0
$791$	−0.298319	−0.0106070
$792$	−41.8806	−1.48816
$793$	−19.5178	−0.693096
$794$	38.5022	1.36639
$795$	0	0
$796$	17.4984	0.620214
$797$	−12.5608	−0.444925	−0.222463	−	0.974941i	$-0.571410\pi$
$797$	−12.5608	−0.444925	−0.222463	+	0.974941i	$0.571410\pi$
$798$	5.38167	0.190509
$799$	13.7283	0.485673
$800$	0	0
$801$	17.1942	0.607526
$802$	−44.3061	−1.56450
$803$	17.7538	0.626519
$804$	−10.1890	−0.359339
$805$	0	0
$806$	−17.5611	−0.618562
$807$	15.9602	0.561825
$808$	−21.9122	−0.770867
$809$	12.6800	0.445805	0.222903	−	0.974841i	$-0.428447\pi$
$809$	12.6800	0.445805	0.222903	+	0.974841i	$0.428447\pi$
$810$	0	0
$811$	11.2790	0.396058	0.198029	−	0.980196i	$-0.436546\pi$
$811$	11.2790	0.396058	0.198029	+	0.980196i	$0.436546\pi$
$812$	0.206676	0.00725290
$813$	22.9370	0.804435
$814$	−10.9713	−0.384545
$815$	0	0
$816$	−82.0582	−2.87261
$817$	−7.23336	−0.253063
$818$	−3.33721	−0.116683
$819$	0.834412	0.0291567
$820$	0	0
$821$	22.3558	0.780222	0.390111	−	0.920768i	$-0.372437\pi$
$821$	22.3558	0.780222	0.390111	+	0.920768i	$0.372437\pi$
$822$	−57.0279	−1.98908
$823$	15.2105	0.530203	0.265102	−	0.964220i	$-0.414594\pi$
$823$	15.2105	0.530203	0.265102	+	0.964220i	$0.414594\pi$
$824$	10.7899	0.375885
$825$	0	0
$826$	1.31836	0.0458717
$827$	55.1205	1.91673	0.958363	−	0.285552i	$-0.0921768\pi$
$827$	55.1205	1.91673	0.958363	+	0.285552i	$0.0921768\pi$
$828$	19.6588	0.683189
$829$	−28.0866	−0.975487	−0.487743	−	0.872987i	$-0.662180\pi$
$829$	−28.0866	−0.975487	−0.487743	+	0.872987i	$0.662180\pi$
$830$	0	0
$831$	−45.3642	−1.57367
$832$	3.69693	0.128168
$833$	44.9782	1.55840
$834$	−7.92884	−0.274553
$835$	0	0
$836$	−33.8522	−1.17080
$837$	−11.4124	−0.394469
$838$	36.0997	1.24704
$839$	−32.3898	−1.11822	−0.559110	−	0.829093i	$-0.688857\pi$
$839$	−32.3898	−1.11822	−0.559110	+	0.829093i	$0.688857\pi$
$840$	0	0
$841$	−26.7858	−0.923649
$842$	−32.4278	−1.11754
$843$	−33.8534	−1.16597
$844$	−7.25816	−0.249836
$845$	0	0
$846$	12.7161	0.437188
$847$	4.01353	0.137906
$848$	−2.98360	−0.102457
$849$	43.7961	1.50308
$850$	0	0
$851$	−7.71007	−0.264298
$852$	16.3478	0.560067
$853$	24.1669	0.827459	0.413729	−	0.910400i	$-0.364226\pi$
$853$	24.1669	0.827459	0.413729	+	0.910400i	$0.364226\pi$
$854$	4.20478	0.143885
$855$	0	0
$856$	−0.594464	−0.0203184
$857$	−4.35077	−0.148620	−0.0743098	−	0.997235i	$-0.523675\pi$
$857$	−4.35077	−0.148620	−0.0743098	+	0.997235i	$0.523675\pi$
$858$	−33.7731	−1.15299
$859$	−15.1737	−0.517720	−0.258860	−	0.965915i	$-0.583347\pi$
$859$	−15.1737	−0.517720	−0.258860	+	0.965915i	$0.583347\pi$
$860$	0	0
$861$	−2.50508	−0.0853729
$862$	−43.3874	−1.47778
$863$	5.50092	0.187253	0.0936267	−	0.995607i	$-0.470154\pi$
$863$	5.50092	0.187253	0.0936267	+	0.995607i	$0.470154\pi$
$864$	−6.28306	−0.213754
$865$	0	0
$866$	−4.22340	−0.143517
$867$	−63.1738	−2.14550
$868$	1.08182	0.0367192
$869$	−54.5408	−1.85017
$870$	0	0
$871$	6.68554	0.226531
$872$	9.17409	0.310674
$873$	−45.0555	−1.52490
$874$	−83.1949	−2.81411
$875$	0	0
$876$	6.23823	0.210770
$877$	53.2530	1.79823	0.899114	−	0.437715i	$-0.144212\pi$
$877$	53.2530	1.79823	0.899114	+	0.437715i	$0.144212\pi$
$878$	58.6003	1.97766
$879$	−55.9743	−1.88797
$880$	0	0
$881$	4.41286	0.148673	0.0743366	−	0.997233i	$-0.476316\pi$
$881$	4.41286	0.148673	0.0743366	+	0.997233i	$0.476316\pi$
$882$	41.6618	1.40283
$883$	59.0412	1.98689	0.993447	−	0.114290i	$-0.0364592\pi$
$883$	59.0412	1.98689	0.993447	+	0.114290i	$0.0364592\pi$
$884$	−6.96296	−0.234190
$885$	0	0
$886$	1.88101	0.0631938
$887$	−18.3381	−0.615735	−0.307867	−	0.951429i	$-0.599615\pi$
$887$	−18.3381	−0.615735	−0.307867	+	0.951429i	$0.599615\pi$
$888$	5.77145	0.193677
$889$	1.59830	0.0536053
$890$	0	0
$891$	40.6609	1.36219
$892$	20.3225	0.680446
$893$	−15.3881	−0.514942
$894$	−48.1942	−1.61186
$895$	0	0
$896$	−2.28370	−0.0762932
$897$	−23.7339	−0.792453
$898$	59.6385	1.99016
$899$	11.5898	0.386543
$900$	0	0
$901$	−3.88151	−0.129312
$902$	55.1064	1.83484
$903$	0.444556	0.0147939
$904$	−3.45212	−0.114816
$905$	0	0
$906$	−20.3462	−0.675958
$907$	−30.9833	−1.02878	−0.514391	−	0.857556i	$-0.671982\pi$
$907$	−30.9833	−1.02878	−0.514391	+	0.857556i	$0.671982\pi$
$908$	−0.164727	−0.00546664
$909$	−38.9984	−1.29350
$910$	0	0
$911$	6.44648	0.213582	0.106791	−	0.994282i	$-0.465942\pi$
$911$	6.44648	0.213582	0.106791	+	0.994282i	$0.465942\pi$
$912$	91.9790	3.04573
$913$	16.9854	0.562136
$914$	46.2857	1.53100
$915$	0	0
$916$	3.37486	0.111509
$917$	−0.426721	−0.0140916
$918$	−15.8245	−0.522285
$919$	52.4439	1.72997	0.864983	−	0.501801i	$-0.167329\pi$
$919$	52.4439	1.72997	0.864983	+	0.501801i	$0.167329\pi$
$920$	0	0
$921$	30.6834	1.01105
$922$	−4.27600	−0.140822
$923$	−10.7266	−0.353072
$924$	2.08053	0.0684443
$925$	0	0
$926$	−2.09556	−0.0688645
$927$	19.2035	0.630726
$928$	6.38077	0.209459
$929$	25.3884	0.832966	0.416483	−	0.909144i	$-0.363263\pi$
$929$	25.3884	0.832966	0.416483	+	0.909144i	$0.363263\pi$
$930$	0	0
$931$	−50.4160	−1.65232
$932$	11.4285	0.374352
$933$	−71.6875	−2.34694
$934$	52.4519	1.71628
$935$	0	0
$936$	9.65576	0.315608
$937$	−6.93234	−0.226470	−0.113235	−	0.993568i	$-0.536121\pi$
$937$	−6.93234	−0.226470	−0.113235	+	0.993568i	$0.536121\pi$
$938$	−1.44029	−0.0470271
$939$	14.0569	0.458729
$940$	0	0
$941$	29.8415	0.972804	0.486402	−	0.873735i	$-0.338309\pi$
$941$	29.8415	0.972804	0.486402	+	0.873735i	$0.338309\pi$
$942$	−69.9343	−2.27858
$943$	38.7259	1.26109
$944$	22.5324	0.733366
$945$	0	0
$946$	−9.77927	−0.317952
$947$	−3.31609	−0.107758	−0.0538792	−	0.998547i	$-0.517159\pi$
$947$	−3.31609	−0.107758	−0.0538792	+	0.998547i	$0.517159\pi$
$948$	−19.1642	−0.622425
$949$	−4.09322	−0.132872
$950$	0	0
$951$	27.1246	0.879574
$952$	−2.24576	−0.0727855
$953$	34.9712	1.13283	0.566414	−	0.824121i	$-0.308330\pi$
$953$	34.9712	1.13283	0.566414	+	0.824121i	$0.308330\pi$
$954$	−3.59532	−0.116403
$955$	0	0
$956$	−11.1776	−0.361510
$957$	22.2894	0.720512
$958$	−40.1601	−1.29751
$959$	−2.30512	−0.0744363
$960$	0	0
$961$	29.6655	0.956950
$962$	2.52949	0.0815539
$963$	−1.05800	−0.0340937
$964$	−14.5920	−0.469975
$965$	0	0
$966$	5.11308	0.164511
$967$	−18.0690	−0.581060	−0.290530	−	0.956866i	$-0.593832\pi$
$967$	−18.0690	−0.581060	−0.290530	+	0.956866i	$0.593832\pi$
$968$	46.4443	1.49278
$969$	119.660	3.84403
$970$	0	0
$971$	−26.0239	−0.835147	−0.417574	−	0.908643i	$-0.637119\pi$
$971$	−26.0239	−0.835147	−0.417574	+	0.908643i	$0.637119\pi$
$972$	17.8078	0.571185
$973$	−0.320491	−0.0102745
$974$	16.7296	0.536052
$975$	0	0
$976$	71.8646	2.30033
$977$	44.7227	1.43081	0.715403	−	0.698712i	$-0.246243\pi$
$977$	44.7227	1.43081	0.715403	+	0.698712i	$0.246243\pi$
$978$	−92.7995	−2.96740
$979$	−28.1305	−0.899056
$980$	0	0
$981$	16.3277	0.521303
$982$	48.9578	1.56231
$983$	36.7639	1.17259	0.586294	−	0.810099i	$-0.300586\pi$
$983$	36.7639	1.17259	0.586294	+	0.810099i	$0.300586\pi$
$984$	−28.9886	−0.924123
$985$	0	0
$986$	16.0706	0.511791
$987$	0.945736	0.0301031
$988$	7.80477	0.248303
$989$	−6.87236	−0.218528
$990$	0	0
$991$	41.2812	1.31134	0.655670	−	0.755047i	$-0.272386\pi$
$991$	41.2812	1.31134	0.655670	+	0.755047i	$0.272386\pi$
$992$	33.3993	1.06043
$993$	−22.8453	−0.724974
$994$	2.31088	0.0732965
$995$	0	0
$996$	5.96824	0.189111
$997$	−34.2074	−1.08336	−0.541680	−	0.840585i	$-0.682212\pi$
$997$	−34.2074	−1.08336	−0.541680	+	0.840585i	$0.682212\pi$
$998$	−57.9023	−1.83287
$999$	1.64383	0.0520085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.p.1.3		6
3.2	odd	2		9675.2.a.cl.1.4		6
5.2	odd	4		1075.2.b.k.474.4		12
5.3	odd	4		1075.2.b.k.474.9		12
5.4	even	2		215.2.a.d.1.4	✓	6
15.14	odd	2		1935.2.a.z.1.3		6
20.19	odd	2		3440.2.a.x.1.2		6
215.214	odd	2		9245.2.a.n.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.d.1.4	✓	6	5.4	even	2
1075.2.a.p.1.3		6	1.1	even	1	trivial
1075.2.b.k.474.4		12	5.2	odd	4
1075.2.b.k.474.9		12	5.3	odd	4
1935.2.a.z.1.3		6	15.14	odd	2
3440.2.a.x.1.2		6	20.19	odd	2
9245.2.a.n.1.3		6	215.214	odd	2
9675.2.a.cl.1.4		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67360 q^{2} -2.56351 q^{3} +0.800923 q^{4} +4.29028 q^{6} +0.173417 q^{7} +2.00677 q^{8} +3.57157 q^{9} +O(q^{10})\)	\(q-1.67360 q^{2} -2.56351 q^{3} +0.800923 q^{4} +4.29028 q^{6} +0.173417 q^{7} +2.00677 q^{8} +3.57157 q^{9} -5.84327 q^{11} -2.05317 q^{12} +1.34719 q^{13} -0.290230 q^{14} -4.96037 q^{16} -6.45318 q^{17} -5.97737 q^{18} +7.23336 q^{19} -0.444556 q^{21} +9.77927 q^{22} +6.87236 q^{23} -5.14437 q^{24} -2.25465 q^{26} -1.46523 q^{27} +0.138894 q^{28} +1.48801 q^{29} +7.78880 q^{31} +4.28811 q^{32} +14.9793 q^{33} +10.8000 q^{34} +2.86055 q^{36} -1.12190 q^{37} -12.1057 q^{38} -3.45354 q^{39} +5.63502 q^{41} +0.744007 q^{42} -1.00000 q^{43} -4.68001 q^{44} -11.5016 q^{46} -2.12737 q^{47} +12.7159 q^{48} -6.96993 q^{49} +16.5428 q^{51} +1.07900 q^{52} +0.601488 q^{53} +2.45220 q^{54} +0.348008 q^{56} -18.5428 q^{57} -2.49033 q^{58} -4.54248 q^{59} -14.4877 q^{61} -13.0353 q^{62} +0.619371 q^{63} +2.74417 q^{64} -25.0692 q^{66} +4.96258 q^{67} -5.16850 q^{68} -17.6173 q^{69} -7.96222 q^{71} +7.16732 q^{72} -3.03834 q^{73} +1.87760 q^{74} +5.79336 q^{76} -1.01332 q^{77} +5.77982 q^{78} +9.33396 q^{79} -6.95859 q^{81} -9.43074 q^{82} -2.90684 q^{83} -0.356055 q^{84} +1.67360 q^{86} -3.81453 q^{87} -11.7261 q^{88} +4.81418 q^{89} +0.233626 q^{91} +5.50423 q^{92} -19.9667 q^{93} +3.56036 q^{94} -10.9926 q^{96} -12.6150 q^{97} +11.6648 q^{98} -20.8697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9	\( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} + 11 q^{18} + 6 q^{19} - 12 q^{21} + q^{22} - 32 q^{26} - 10 q^{27} + 10 q^{28} - 10 q^{29} - 11 q^{32} - 6 q^{33} + 14 q^{34} - 41 q^{36} - 28 q^{37} + 6 q^{38} + 8 q^{39} - 6 q^{41} - 5 q^{42} - 6 q^{43} + 4 q^{44} - 8 q^{46} + 6 q^{47} + 32 q^{48} + 20 q^{49} - 8 q^{51} + 16 q^{52} + 4 q^{53} - 5 q^{54} - 35 q^{56} - 4 q^{57} + 26 q^{58} - 20 q^{59} - 8 q^{61} - 2 q^{62} + 2 q^{63} + 17 q^{64} - 35 q^{66} - 22 q^{67} - 22 q^{68} - 42 q^{69} + 8 q^{71} + 2 q^{72} - 34 q^{73} + 45 q^{74} - 16 q^{76} - 8 q^{77} + 26 q^{78} - 16 q^{79} + 46 q^{81} - 22 q^{82} + 14 q^{83} + 37 q^{84} + 3 q^{86} + 2 q^{87} - 20 q^{88} + 24 q^{91} - 46 q^{92} - 30 q^{93} + 12 q^{94} - 23 q^{96} - 34 q^{97} - 32 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 + 11 * q^18 + 6 * q^19 - 12 * q^21 + q^22 - 32 * q^26 - 10 * q^27 + 10 * q^28 - 10 * q^29 - 11 * q^32 - 6 * q^33 + 14 * q^34 - 41 * q^36 - 28 * q^37 + 6 * q^38 + 8 * q^39 - 6 * q^41 - 5 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^46 + 6 * q^47 + 32 * q^48 + 20 * q^49 - 8 * q^51 + 16 * q^52 + 4 * q^53 - 5 * q^54 - 35 * q^56 - 4 * q^57 + 26 * q^58 - 20 * q^59 - 8 * q^61 - 2 * q^62 + 2 * q^63 + 17 * q^64 - 35 * q^66 - 22 * q^67 - 22 * q^68 - 42 * q^69 + 8 * q^71 + 2 * q^72 - 34 * q^73 + 45 * q^74 - 16 * q^76 - 8 * q^77 + 26 * q^78 - 16 * q^79 + 46 * q^81 - 22 * q^82 + 14 * q^83 + 37 * q^84 + 3 * q^86 + 2 * q^87 - 20 * q^88 + 24 * q^91 - 46 * q^92 - 30 * q^93 + 12 * q^94 - 23 * q^96 - 34 * q^97 - 32 * q^98 - 16 * q^99

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