LMFDB - Embedded newform 1875.2.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.46840000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 8x^{3} + 31x^{2} - 15x - 9 $ x^6 - x^5 - 11x^4 + 8x^3 + 31x^2 - 15x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.13324$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.13324 q^{2} -1.00000 q^{3} +2.55073 q^{4} -2.13324 q^{6} -2.16876 q^{7} +1.17484 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.13324 q^{2} -1.00000 q^{3} +2.55073 q^{4} -2.13324 q^{6} -2.16876 q^{7} +1.17484 q^{8} +1.00000 q^{9} -2.50913 q^{11} -2.55073 q^{12} +4.33379 q^{13} -4.62650 q^{14} -2.59524 q^{16} +6.77562 q^{17} +2.13324 q^{18} +6.83602 q^{19} +2.16876 q^{21} -5.35259 q^{22} +1.67843 q^{23} -1.17484 q^{24} +9.24504 q^{26} -1.00000 q^{27} -5.53193 q^{28} +4.44927 q^{29} +6.56295 q^{31} -7.88596 q^{32} +2.50913 q^{33} +14.4541 q^{34} +2.55073 q^{36} -7.97720 q^{37} +14.5829 q^{38} -4.33379 q^{39} +11.2249 q^{41} +4.62650 q^{42} +4.25487 q^{43} -6.40012 q^{44} +3.58050 q^{46} -4.98652 q^{47} +2.59524 q^{48} -2.29646 q^{49} -6.77562 q^{51} +11.0543 q^{52} +8.21338 q^{53} -2.13324 q^{54} -2.54795 q^{56} -6.83602 q^{57} +9.49138 q^{58} +3.67416 q^{59} +4.93960 q^{61} +14.0004 q^{62} -2.16876 q^{63} -11.6322 q^{64} +5.35259 q^{66} -11.5812 q^{67} +17.2828 q^{68} -1.67843 q^{69} -2.30251 q^{71} +1.17484 q^{72} +1.11599 q^{73} -17.0173 q^{74} +17.4368 q^{76} +5.44172 q^{77} -9.24504 q^{78} +7.78306 q^{79} +1.00000 q^{81} +23.9454 q^{82} -9.87708 q^{83} +5.53193 q^{84} +9.07667 q^{86} -4.44927 q^{87} -2.94783 q^{88} -1.24025 q^{89} -9.39897 q^{91} +4.28122 q^{92} -6.56295 q^{93} -10.6375 q^{94} +7.88596 q^{96} -15.0488 q^{97} -4.89892 q^{98} -2.50913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 11 q^{12} - 4 q^{14} + 17 q^{16} + 2 q^{17} + q^{18} - 2 q^{19} + 2 q^{21} + 9 q^{22} - q^{23} - 6 q^{24} + 37 q^{26} - 6 q^{27} - 44 q^{28} + 31 q^{29} - 2 q^{31} + 33 q^{32} + 37 q^{34} + 11 q^{36} - 22 q^{37} + 27 q^{38} + 33 q^{41} + 4 q^{42} - 3 q^{43} - 11 q^{44} - 12 q^{46} - 6 q^{47} - 17 q^{48} + 4 q^{49} - 2 q^{51} - 33 q^{52} + 14 q^{53} - q^{54} - 30 q^{56} + 2 q^{57} - q^{58} - 8 q^{59} + 34 q^{61} + 31 q^{62} - 2 q^{63} + 12 q^{64} - 9 q^{66} + 2 q^{67} + 27 q^{68} + q^{69} - 3 q^{71} + 6 q^{72} - 36 q^{73} + 36 q^{74} + 27 q^{76} + 16 q^{77} - 37 q^{78} + 25 q^{79} + 6 q^{81} + 36 q^{82} - 12 q^{83} + 44 q^{84} - 30 q^{86} - 31 q^{87} + 56 q^{88} + 18 q^{89} + 28 q^{91} + 3 q^{92} + 2 q^{93} - 50 q^{94} - 33 q^{96} + 7 q^{97} + 15 q^{98}+O(q^{100}) $ 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 11 * q^12 - 4 * q^14 + 17 * q^16 + 2 * q^17 + q^18 - 2 * q^19 + 2 * q^21 + 9 * q^22 - q^23 - 6 * q^24 + 37 * q^26 - 6 * q^27 - 44 * q^28 + 31 * q^29 - 2 * q^31 + 33 * q^32 + 37 * q^34 + 11 * q^36 - 22 * q^37 + 27 * q^38 + 33 * q^41 + 4 * q^42 - 3 * q^43 - 11 * q^44 - 12 * q^46 - 6 * q^47 - 17 * q^48 + 4 * q^49 - 2 * q^51 - 33 * q^52 + 14 * q^53 - q^54 - 30 * q^56 + 2 * q^57 - q^58 - 8 * q^59 + 34 * q^61 + 31 * q^62 - 2 * q^63 + 12 * q^64 - 9 * q^66 + 2 * q^67 + 27 * q^68 + q^69 - 3 * q^71 + 6 * q^72 - 36 * q^73 + 36 * q^74 + 27 * q^76 + 16 * q^77 - 37 * q^78 + 25 * q^79 + 6 * q^81 + 36 * q^82 - 12 * q^83 + 44 * q^84 - 30 * q^86 - 31 * q^87 + 56 * q^88 + 18 * q^89 + 28 * q^91 + 3 * q^92 + 2 * q^93 - 50 * q^94 - 33 * q^96 + 7 * q^97 + 15 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.13324	1.50843	0.754216	−	0.656627i	$-0.228017\pi$
$2$	2.13324	1.50843	0.754216	+	0.656627i	$0.228017\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.55073	1.27536
$5$	0	0
$5$	0	0
$6$	−2.13324	−0.870893
$7$	−2.16876	−0.819716	−0.409858	−	0.912149i	$-0.634422\pi$
$7$	−2.16876	−0.819716	−0.409858	+	0.912149i	$0.634422\pi$
$8$	1.17484	0.415369
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.50913	−0.756532	−0.378266	−	0.925697i	$-0.623480\pi$
$11$	−2.50913	−0.756532	−0.378266	+	0.925697i	$0.623480\pi$
$12$	−2.55073	−0.736332
$13$	4.33379	1.20198	0.600989	−	0.799257i	$-0.294774\pi$
$13$	4.33379	1.20198	0.600989	+	0.799257i	$0.294774\pi$
$14$	−4.62650	−1.23648
$15$	0	0
$16$	−2.59524	−0.648810
$17$	6.77562	1.64333	0.821665	−	0.569971i	$-0.193046\pi$
$17$	6.77562	1.64333	0.821665	+	0.569971i	$0.193046\pi$
$18$	2.13324	0.502810
$19$	6.83602	1.56829	0.784145	−	0.620578i	$-0.213102\pi$
$19$	6.83602	1.56829	0.784145	+	0.620578i	$0.213102\pi$
$20$	0	0
$21$	2.16876	0.473263
$22$	−5.35259	−1.14118
$23$	1.67843	0.349977	0.174989	−	0.984570i	$-0.444011\pi$
$23$	1.67843	0.349977	0.174989	+	0.984570i	$0.444011\pi$
$24$	−1.17484	−0.239813
$25$	0	0
$26$	9.24504	1.81310
$27$	−1.00000	−0.192450
$28$	−5.53193	−1.04544
$29$	4.44927	0.826209	0.413104	−	0.910684i	$-0.364444\pi$
$29$	4.44927	0.826209	0.413104	+	0.910684i	$0.364444\pi$
$30$	0	0
$31$	6.56295	1.17874	0.589371	−	0.807863i	$-0.299376\pi$
$31$	6.56295	1.17874	0.589371	+	0.807863i	$0.299376\pi$
$32$	−7.88596	−1.39405
$33$	2.50913	0.436784
$34$	14.4541	2.47885
$35$	0	0
$36$	2.55073	0.425122
$37$	−7.97720	−1.31144	−0.655722	−	0.755002i	$-0.727636\pi$
$37$	−7.97720	−1.31144	−0.655722	+	0.755002i	$0.727636\pi$
$38$	14.5829	2.36566
$39$	−4.33379	−0.693962
$40$	0	0
$41$	11.2249	1.75303	0.876517	−	0.481371i	$-0.159861\pi$
$41$	11.2249	1.75303	0.876517	+	0.481371i	$0.159861\pi$
$42$	4.62650	0.713885
$43$	4.25487	0.648861	0.324431	−	0.945909i	$-0.394827\pi$
$43$	4.25487	0.648861	0.324431	+	0.945909i	$0.394827\pi$
$44$	−6.40012	−0.964854
$45$	0	0
$46$	3.58050	0.527916
$47$	−4.98652	−0.727358	−0.363679	−	0.931524i	$-0.618479\pi$
$47$	−4.98652	−0.727358	−0.363679	+	0.931524i	$0.618479\pi$
$48$	2.59524	0.374590
$49$	−2.29646	−0.328066
$50$	0	0
$51$	−6.77562	−0.948777
$52$	11.0543	1.53296
$53$	8.21338	1.12820	0.564098	−	0.825708i	$-0.309224\pi$
$53$	8.21338	1.12820	0.564098	+	0.825708i	$0.309224\pi$
$54$	−2.13324	−0.290298
$55$	0	0
$56$	−2.54795	−0.340484
$57$	−6.83602	−0.905453
$58$	9.49138	1.24628
$59$	3.67416	0.478335	0.239168	−	0.970978i	$-0.423125\pi$
$59$	3.67416	0.478335	0.239168	+	0.970978i	$0.423125\pi$
$60$	0	0
$61$	4.93960	0.632451	0.316226	−	0.948684i	$-0.397584\pi$
$61$	4.93960	0.632451	0.316226	+	0.948684i	$0.397584\pi$
$62$	14.0004	1.77805
$63$	−2.16876	−0.273239
$64$	−11.6322	−1.45402
$65$	0	0
$66$	5.35259	0.658859
$67$	−11.5812	−1.41487	−0.707436	−	0.706778i	$-0.750148\pi$
$67$	−11.5812	−1.41487	−0.707436	+	0.706778i	$0.750148\pi$
$68$	17.2828	2.09584
$69$	−1.67843	−0.202059
$70$	0	0
$71$	−2.30251	−0.273257	−0.136629	−	0.990622i	$-0.543627\pi$
$71$	−2.30251	−0.273257	−0.136629	+	0.990622i	$0.543627\pi$
$72$	1.17484	0.138456
$73$	1.11599	0.130617	0.0653084	−	0.997865i	$-0.479197\pi$
$73$	1.11599	0.130617	0.0653084	+	0.997865i	$0.479197\pi$
$74$	−17.0173	−1.97822
$75$	0	0
$76$	17.4368	2.00014
$77$	5.44172	0.620141
$78$	−9.24504	−1.04679
$79$	7.78306	0.875663	0.437831	−	0.899057i	$-0.355747\pi$
$79$	7.78306	0.875663	0.437831	+	0.899057i	$0.355747\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	23.9454	2.64433
$83$	−9.87708	−1.08415	−0.542075	−	0.840330i	$-0.682361\pi$
$83$	−9.87708	−1.08415	−0.542075	+	0.840330i	$0.682361\pi$
$84$	5.53193	0.603583
$85$	0	0
$86$	9.07667	0.978763
$87$	−4.44927	−0.477012
$88$	−2.94783	−0.314240
$89$	−1.24025	−0.131466	−0.0657329	−	0.997837i	$-0.520939\pi$
$89$	−1.24025	−0.131466	−0.0657329	+	0.997837i	$0.520939\pi$
$90$	0	0
$91$	−9.39897	−0.985280
$92$	4.28122	0.446348
$93$	−6.56295	−0.680546
$94$	−10.6375	−1.09717
$95$	0	0
$96$	7.88596	0.804857
$97$	−15.0488	−1.52797	−0.763985	−	0.645234i	$-0.776760\pi$
$97$	−15.0488	−1.52797	−0.763985	+	0.645234i	$0.776760\pi$
$98$	−4.89892	−0.494866
$99$	−2.50913	−0.252177
$100$	0	0
$101$	−17.0211	−1.69366	−0.846830	−	0.531864i	$-0.821492\pi$
$101$	−17.0211	−1.69366	−0.846830	+	0.531864i	$0.821492\pi$
$102$	−14.4541	−1.43116
$103$	−10.0859	−0.993793	−0.496897	−	0.867810i	$-0.665527\pi$
$103$	−10.0859	−0.993793	−0.496897	+	0.867810i	$0.665527\pi$
$104$	5.09151	0.499264
$105$	0	0
$106$	17.5212	1.70180
$107$	−5.67218	−0.548351	−0.274175	−	0.961680i	$-0.588405\pi$
$107$	−5.67218	−0.548351	−0.274175	+	0.961680i	$0.588405\pi$
$108$	−2.55073	−0.245444
$109$	8.34557	0.799361	0.399680	−	0.916655i	$-0.369121\pi$
$109$	8.34557	0.799361	0.399680	+	0.916655i	$0.369121\pi$
$110$	0	0
$111$	7.97720	0.757163
$112$	5.62846	0.531839
$113$	14.8224	1.39438	0.697188	−	0.716888i	$-0.254434\pi$
$113$	14.8224	1.39438	0.697188	+	0.716888i	$0.254434\pi$
$114$	−14.5829	−1.36581
$115$	0	0
$116$	11.3489	1.05372
$117$	4.33379	0.400659
$118$	7.83788	0.721536
$119$	−14.6947	−1.34706
$120$	0	0
$121$	−4.70425	−0.427659
$122$	10.5374	0.954009
$123$	−11.2249	−1.01211
$124$	16.7403	1.50332
$125$	0	0
$126$	−4.62650	−0.412162
$127$	0.502113	0.0445553	0.0222777	−	0.999752i	$-0.492908\pi$
$127$	0.502113	0.0445553	0.0222777	+	0.999752i	$0.492908\pi$
$128$	−9.04239	−0.799242
$129$	−4.25487	−0.374620
$130$	0	0
$131$	6.05788	0.529280	0.264640	−	0.964347i	$-0.414747\pi$
$131$	6.05788	0.529280	0.264640	+	0.964347i	$0.414747\pi$
$132$	6.40012	0.557059
$133$	−14.8257	−1.28555
$134$	−24.7056	−2.13424
$135$	0	0
$136$	7.96027	0.682588
$137$	1.94014	0.165757	0.0828786	−	0.996560i	$-0.473589\pi$
$137$	1.94014	0.165757	0.0828786	+	0.996560i	$0.473589\pi$
$138$	−3.58050	−0.304793
$139$	19.2023	1.62872	0.814358	−	0.580363i	$-0.197089\pi$
$139$	19.2023	1.62872	0.814358	+	0.580363i	$0.197089\pi$
$140$	0	0
$141$	4.98652	0.419940
$142$	−4.91181	−0.412190
$143$	−10.8741	−0.909335
$144$	−2.59524	−0.216270
$145$	0	0
$146$	2.38068	0.197026
$147$	2.29646	0.189409
$148$	−20.3477	−1.67257
$149$	9.49138	0.777564	0.388782	−	0.921330i	$-0.372896\pi$
$149$	9.49138	0.777564	0.388782	+	0.921330i	$0.372896\pi$
$150$	0	0
$151$	−12.5747	−1.02332	−0.511659	−	0.859189i	$-0.670969\pi$
$151$	−12.5747	−1.02332	−0.511659	+	0.859189i	$0.670969\pi$
$152$	8.03123	0.651419
$153$	6.77562	0.547776
$154$	11.6085	0.935440
$155$	0	0
$156$	−11.0543	−0.885055
$157$	18.7991	1.50033	0.750165	−	0.661250i	$-0.229974\pi$
$157$	18.7991	1.50033	0.750165	+	0.661250i	$0.229974\pi$
$158$	16.6032	1.32088
$159$	−8.21338	−0.651364
$160$	0	0
$161$	−3.64012	−0.286882
$162$	2.13324	0.167603
$163$	7.29949	0.571740	0.285870	−	0.958268i	$-0.407717\pi$
$163$	7.29949	0.571740	0.285870	+	0.958268i	$0.407717\pi$
$164$	28.6317	2.23576
$165$	0	0
$166$	−21.0702	−1.63537
$167$	−14.7991	−1.14519	−0.572594	−	0.819839i	$-0.694063\pi$
$167$	−14.7991	−1.14519	−0.572594	+	0.819839i	$0.694063\pi$
$168$	2.54795	0.196579
$169$	5.78176	0.444750
$170$	0	0
$171$	6.83602	0.522763
$172$	10.8530	0.827535
$173$	−2.29460	−0.174455	−0.0872276	−	0.996188i	$-0.527801\pi$
$173$	−2.29460	−0.174455	−0.0872276	+	0.996188i	$0.527801\pi$
$174$	−9.49138	−0.719540
$175$	0	0
$176$	6.51180	0.490845
$177$	−3.67416	−0.276167
$178$	−2.64575	−0.198307
$179$	13.6637	1.02127	0.510636	−	0.859797i	$-0.329410\pi$
$179$	13.6637	1.02127	0.510636	+	0.859797i	$0.329410\pi$
$180$	0	0
$181$	8.71878	0.648062	0.324031	−	0.946046i	$-0.394962\pi$
$181$	8.71878	0.648062	0.324031	+	0.946046i	$0.394962\pi$
$182$	−20.0503	−1.48623
$183$	−4.93960	−0.365146
$184$	1.97189	0.145370
$185$	0	0
$186$	−14.0004	−1.02656
$187$	−17.0009	−1.24323
$188$	−12.7193	−0.927647
$189$	2.16876	0.157754
$190$	0	0
$191$	11.6080	0.839925	0.419963	−	0.907541i	$-0.362043\pi$
$191$	11.6080	0.839925	0.419963	+	0.907541i	$0.362043\pi$
$192$	11.6322	0.839481
$193$	−14.8653	−1.07002	−0.535012	−	0.844844i	$-0.679693\pi$
$193$	−14.8653	−1.07002	−0.535012	+	0.844844i	$0.679693\pi$
$194$	−32.1027	−2.30484
$195$	0	0
$196$	−5.85766	−0.418404
$197$	22.8292	1.62651	0.813256	−	0.581906i	$-0.197693\pi$
$197$	22.8292	1.62651	0.813256	+	0.581906i	$0.197693\pi$
$198$	−5.35259	−0.380392
$199$	5.87697	0.416607	0.208304	−	0.978064i	$-0.433206\pi$
$199$	5.87697	0.416607	0.208304	+	0.978064i	$0.433206\pi$
$200$	0	0
$201$	11.5812	0.816876
$202$	−36.3101	−2.55477
$203$	−9.64942	−0.677256
$204$	−17.2828	−1.21004
$205$	0	0
$206$	−21.5157	−1.49907
$207$	1.67843	0.116659
$208$	−11.2472	−0.779855
$209$	−17.1525	−1.18646
$210$	0	0
$211$	−24.6884	−1.69962	−0.849810	−	0.527090i	$-0.823283\pi$
$211$	−24.6884	−1.69962	−0.849810	+	0.527090i	$0.823283\pi$
$212$	20.9501	1.43886
$213$	2.30251	0.157765
$214$	−12.1002	−0.827149
$215$	0	0
$216$	−1.17484	−0.0799378
$217$	−14.2335	−0.966232
$218$	17.8031	1.20578
$219$	−1.11599	−0.0754116
$220$	0	0
$221$	29.3641	1.97525
$222$	17.0173	1.14213
$223$	−3.31060	−0.221694	−0.110847	−	0.993837i	$-0.535356\pi$
$223$	−3.31060	−0.221694	−0.110847	+	0.993837i	$0.535356\pi$
$224$	17.1028	1.14273
$225$	0	0
$226$	31.6198	2.10332
$227$	−2.70185	−0.179328	−0.0896641	−	0.995972i	$-0.528579\pi$
$227$	−2.70185	−0.179328	−0.0896641	+	0.995972i	$0.528579\pi$
$228$	−17.4368	−1.15478
$229$	−9.33473	−0.616856	−0.308428	−	0.951248i	$-0.599803\pi$
$229$	−9.33473	−0.616856	−0.308428	+	0.951248i	$0.599803\pi$
$230$	0	0
$231$	−5.44172	−0.358039
$232$	5.22718	0.343181
$233$	9.52491	0.623998	0.311999	−	0.950083i	$-0.399002\pi$
$233$	9.52491	0.623998	0.311999	+	0.950083i	$0.399002\pi$
$234$	9.24504	0.604367
$235$	0	0
$236$	9.37179	0.610052
$237$	−7.78306	−0.505564
$238$	−31.3474	−2.03195
$239$	7.84648	0.507546	0.253773	−	0.967264i	$-0.418328\pi$
$239$	7.84648	0.507546	0.253773	+	0.967264i	$0.418328\pi$
$240$	0	0
$241$	1.42783	0.0919747	0.0459874	−	0.998942i	$-0.485357\pi$
$241$	1.42783	0.0919747	0.0459874	+	0.998942i	$0.485357\pi$
$242$	−10.0353	−0.645095
$243$	−1.00000	−0.0641500
$244$	12.5996	0.806606
$245$	0	0
$246$	−23.9454	−1.52670
$247$	29.6259	1.88505
$248$	7.71042	0.489612
$249$	9.87708	0.625935
$250$	0	0
$251$	−17.5762	−1.10940	−0.554701	−	0.832050i	$-0.687167\pi$
$251$	−17.5762	−1.10940	−0.554701	+	0.832050i	$0.687167\pi$
$252$	−5.53193	−0.348479
$253$	−4.21141	−0.264769
$254$	1.07113	0.0672087
$255$	0	0
$256$	3.97476	0.248423
$257$	−19.2890	−1.20322	−0.601608	−	0.798791i	$-0.705473\pi$
$257$	−19.2890	−1.20322	−0.601608	+	0.798791i	$0.705473\pi$
$258$	−9.07667	−0.565089
$259$	17.3007	1.07501
$260$	0	0
$261$	4.44927	0.275403
$262$	12.9229	0.798382
$263$	−22.2432	−1.37157	−0.685786	−	0.727803i	$-0.740541\pi$
$263$	−22.2432	−1.37157	−0.685786	+	0.727803i	$0.740541\pi$
$264$	2.94783	0.181426
$265$	0	0
$266$	−31.6268	−1.93917
$267$	1.24025	0.0759018
$268$	−29.5406	−1.80448
$269$	25.1785	1.53516	0.767581	−	0.640951i	$-0.221460\pi$
$269$	25.1785	1.53516	0.767581	+	0.640951i	$0.221460\pi$
$270$	0	0
$271$	−5.70091	−0.346306	−0.173153	−	0.984895i	$-0.555395\pi$
$271$	−5.70091	−0.346306	−0.173153	+	0.984895i	$0.555395\pi$
$272$	−17.5843	−1.06621
$273$	9.39897	0.568852
$274$	4.13879	0.250033
$275$	0	0
$276$	−4.28122	−0.257699
$277$	19.1611	1.15128	0.575638	−	0.817704i	$-0.304754\pi$
$277$	19.1611	1.15128	0.575638	+	0.817704i	$0.304754\pi$
$278$	40.9631	2.45681
$279$	6.56295	0.392914
$280$	0	0
$281$	4.36015	0.260105	0.130052	−	0.991507i	$-0.458485\pi$
$281$	4.36015	0.260105	0.130052	+	0.991507i	$0.458485\pi$
$282$	10.6375	0.633451
$283$	−24.9081	−1.48063	−0.740317	−	0.672258i	$-0.765324\pi$
$283$	−24.9081	−1.48063	−0.740317	+	0.672258i	$0.765324\pi$
$284$	−5.87307	−0.348503
$285$	0	0
$286$	−23.1970	−1.37167
$287$	−24.3441	−1.43699
$288$	−7.88596	−0.464684
$289$	28.9090	1.70053
$290$	0	0
$291$	15.0488	0.882174
$292$	2.84659	0.166584
$293$	−13.5651	−0.792484	−0.396242	−	0.918146i	$-0.629686\pi$
$293$	−13.5651	−0.792484	−0.396242	+	0.918146i	$0.629686\pi$
$294$	4.89892	0.285711
$295$	0	0
$296$	−9.37194	−0.544733
$297$	2.50913	0.145595
$298$	20.2474	1.17290
$299$	7.27397	0.420665
$300$	0	0
$301$	−9.22780	−0.531882
$302$	−26.8250	−1.54360
$303$	17.0211	0.977835
$304$	−17.7411	−1.01752
$305$	0	0
$306$	14.4541	0.826283
$307$	−11.9672	−0.683007	−0.341504	−	0.939880i	$-0.610936\pi$
$307$	−11.9672	−0.683007	−0.341504	+	0.939880i	$0.610936\pi$
$308$	13.8803	0.790906
$309$	10.0859	0.573767
$310$	0	0
$311$	7.66452	0.434615	0.217308	−	0.976103i	$-0.430273\pi$
$311$	7.66452	0.434615	0.217308	+	0.976103i	$0.430273\pi$
$312$	−5.09151	−0.288250
$313$	26.3840	1.49131	0.745655	−	0.666332i	$-0.232137\pi$
$313$	26.3840	1.49131	0.745655	+	0.666332i	$0.232137\pi$
$314$	40.1030	2.26315
$315$	0	0
$316$	19.8525	1.11679
$317$	−10.8880	−0.611529	−0.305765	−	0.952107i	$-0.598912\pi$
$317$	−10.8880	−0.611529	−0.305765	+	0.952107i	$0.598912\pi$
$318$	−17.5212	−0.982537
$319$	−11.1638	−0.625053
$320$	0	0
$321$	5.67218	0.316590
$322$	−7.76526	−0.432741
$323$	46.3183	2.57722
$324$	2.55073	0.141707
$325$	0	0
$326$	15.5716	0.862431
$327$	−8.34557	−0.461511
$328$	13.1875	0.728155
$329$	10.8146	0.596227
$330$	0	0
$331$	−32.2137	−1.77062	−0.885312	−	0.464998i	$-0.846055\pi$
$331$	−32.2137	−1.77062	−0.885312	+	0.464998i	$0.846055\pi$
$332$	−25.1938	−1.38269
$333$	−7.97720	−0.437148
$334$	−31.5701	−1.72744
$335$	0	0
$336$	−5.62846	−0.307058
$337$	−3.47169	−0.189115	−0.0945576	−	0.995519i	$-0.530144\pi$
$337$	−3.47169	−0.189115	−0.0945576	+	0.995519i	$0.530144\pi$
$338$	12.3339	0.670875
$339$	−14.8224	−0.805043
$340$	0	0
$341$	−16.4673	−0.891755
$342$	14.5829	0.788553
$343$	20.1618	1.08864
$344$	4.99879	0.269517
$345$	0	0
$346$	−4.89494	−0.263154
$347$	−10.9805	−0.589465	−0.294733	−	0.955580i	$-0.595231\pi$
$347$	−10.9805	−0.589465	−0.294733	+	0.955580i	$0.595231\pi$
$348$	−11.3489	−0.608364
$349$	−26.3158	−1.40865	−0.704325	−	0.709878i	$-0.748750\pi$
$349$	−26.3158	−1.40865	−0.704325	+	0.709878i	$0.748750\pi$
$350$	0	0
$351$	−4.33379	−0.231321
$352$	19.7869	1.05465
$353$	−16.3668	−0.871119	−0.435559	−	0.900160i	$-0.643449\pi$
$353$	−16.3668	−0.871119	−0.435559	+	0.900160i	$0.643449\pi$
$354$	−7.83788	−0.416579
$355$	0	0
$356$	−3.16353	−0.167667
$357$	14.6947	0.777727
$358$	29.1480	1.54052
$359$	−17.4871	−0.922934	−0.461467	−	0.887157i	$-0.652677\pi$
$359$	−17.4871	−0.922934	−0.461467	+	0.887157i	$0.652677\pi$
$360$	0	0
$361$	27.7311	1.45953
$362$	18.5993	0.977557
$363$	4.70425	0.246909
$364$	−23.9742	−1.25659
$365$	0	0
$366$	−10.5374	−0.550798
$367$	8.29594	0.433044	0.216522	−	0.976278i	$-0.430529\pi$
$367$	8.29594	0.433044	0.216522	+	0.976278i	$0.430529\pi$
$368$	−4.35593	−0.227068
$369$	11.2249	0.584345
$370$	0	0
$371$	−17.8129	−0.924799
$372$	−16.7403	−0.867945
$373$	−19.1295	−0.990486	−0.495243	−	0.868755i	$-0.664921\pi$
$373$	−19.1295	−0.990486	−0.495243	+	0.868755i	$0.664921\pi$
$374$	−36.2671	−1.87533
$375$	0	0
$376$	−5.85836	−0.302122
$377$	19.2822	0.993085
$378$	4.62650	0.237962
$379$	−27.0952	−1.39179	−0.695894	−	0.718145i	$-0.744992\pi$
$379$	−27.0952	−1.39179	−0.695894	+	0.718145i	$0.744992\pi$
$380$	0	0
$381$	−0.502113	−0.0257240
$382$	24.7627	1.26697
$383$	19.8026	1.01187	0.505933	−	0.862573i	$-0.331148\pi$
$383$	19.8026	1.01187	0.505933	+	0.862573i	$0.331148\pi$
$384$	9.04239	0.461443
$385$	0	0
$386$	−31.7112	−1.61406
$387$	4.25487	0.216287
$388$	−38.3853	−1.94872
$389$	−23.0130	−1.16680	−0.583402	−	0.812183i	$-0.698279\pi$
$389$	−23.0130	−1.16680	−0.583402	+	0.812183i	$0.698279\pi$
$390$	0	0
$391$	11.3724	0.575128
$392$	−2.69798	−0.136269
$393$	−6.05788	−0.305580
$394$	48.7002	2.45348
$395$	0	0
$396$	−6.40012	−0.321618
$397$	−20.5745	−1.03260	−0.516301	−	0.856407i	$-0.672691\pi$
$397$	−20.5745	−1.03260	−0.516301	+	0.856407i	$0.672691\pi$
$398$	12.5370	0.628423
$399$	14.8257	0.742214
$400$	0	0
$401$	−13.1542	−0.656889	−0.328444	−	0.944523i	$-0.606524\pi$
$401$	−13.1542	−0.656889	−0.328444	+	0.944523i	$0.606524\pi$
$402$	24.7056	1.23220
$403$	28.4425	1.41682
$404$	−43.4161	−2.16003
$405$	0	0
$406$	−20.5846	−1.02159
$407$	20.0159	0.992150
$408$	−7.96027	−0.394092
$409$	2.76531	0.136736	0.0683679	−	0.997660i	$-0.478221\pi$
$409$	2.76531	0.136736	0.0683679	+	0.997660i	$0.478221\pi$
$410$	0	0
$411$	−1.94014	−0.0956999
$412$	−25.7264	−1.26745
$413$	−7.96839	−0.392099
$414$	3.58050	0.175972
$415$	0	0
$416$	−34.1761	−1.67562
$417$	−19.2023	−0.940340
$418$	−36.5904	−1.78970
$419$	−9.70852	−0.474292	−0.237146	−	0.971474i	$-0.576212\pi$
$419$	−9.70852	−0.474292	−0.237146	+	0.971474i	$0.576212\pi$
$420$	0	0
$421$	−4.21745	−0.205546	−0.102773	−	0.994705i	$-0.532772\pi$
$421$	−4.21745	−0.205546	−0.102773	+	0.994705i	$0.532772\pi$
$422$	−52.6664	−2.56376
$423$	−4.98652	−0.242453
$424$	9.64942	0.468617
$425$	0	0
$426$	4.91181	0.237978
$427$	−10.7128	−0.518430
$428$	−14.4682	−0.699347
$429$	10.8741	0.525005
$430$	0	0
$431$	18.9785	0.914164	0.457082	−	0.889425i	$-0.348895\pi$
$431$	18.9785	0.914164	0.457082	+	0.889425i	$0.348895\pi$
$432$	2.59524	0.124863
$433$	13.7054	0.658640	0.329320	−	0.944218i	$-0.393181\pi$
$433$	13.7054	0.658640	0.329320	+	0.944218i	$0.393181\pi$
$434$	−30.3635	−1.45750
$435$	0	0
$436$	21.2873	1.01948
$437$	11.4738	0.548866
$438$	−2.38068	−0.113753
$439$	−33.3843	−1.59335	−0.796673	−	0.604410i	$-0.793409\pi$
$439$	−33.3843	−1.59335	−0.796673	+	0.604410i	$0.793409\pi$
$440$	0	0
$441$	−2.29646	−0.109355
$442$	62.6409	2.97952
$443$	11.6290	0.552512	0.276256	−	0.961084i	$-0.410906\pi$
$443$	11.6290	0.552512	0.276256	+	0.961084i	$0.410906\pi$
$444$	20.3477	0.965659
$445$	0	0
$446$	−7.06231	−0.334410
$447$	−9.49138	−0.448927
$448$	25.2275	1.19189
$449$	−13.3509	−0.630069	−0.315034	−	0.949080i	$-0.602016\pi$
$449$	−13.3509	−0.630069	−0.315034	+	0.949080i	$0.602016\pi$
$450$	0	0
$451$	−28.1647	−1.32623
$452$	37.8080	1.77834
$453$	12.5747	0.590813
$454$	−5.76371	−0.270504
$455$	0	0
$456$	−8.03123	−0.376097
$457$	−23.3042	−1.09013	−0.545063	−	0.838395i	$-0.683494\pi$
$457$	−23.3042	−1.09013	−0.545063	+	0.838395i	$0.683494\pi$
$458$	−19.9132	−0.930485
$459$	−6.77562	−0.316259
$460$	0	0
$461$	5.03269	0.234396	0.117198	−	0.993109i	$-0.462609\pi$
$461$	5.03269	0.234396	0.117198	+	0.993109i	$0.462609\pi$
$462$	−11.6085	−0.540077
$463$	−12.7759	−0.593746	−0.296873	−	0.954917i	$-0.595944\pi$
$463$	−12.7759	−0.593746	−0.296873	+	0.954917i	$0.595944\pi$
$464$	−11.5469	−0.536052
$465$	0	0
$466$	20.3190	0.941257
$467$	4.86284	0.225025	0.112513	−	0.993650i	$-0.464110\pi$
$467$	4.86284	0.225025	0.112513	+	0.993650i	$0.464110\pi$
$468$	11.0543	0.510987
$469$	25.1169	1.15979
$470$	0	0
$471$	−18.7991	−0.866216
$472$	4.31655	0.198685
$473$	−10.6760	−0.490884
$474$	−16.6032	−0.762609
$475$	0	0
$476$	−37.4823	−1.71800
$477$	8.21338	0.376065
$478$	16.7385	0.765599
$479$	4.79202	0.218953	0.109476	−	0.993989i	$-0.465083\pi$
$479$	4.79202	0.218953	0.109476	+	0.993989i	$0.465083\pi$
$480$	0	0
$481$	−34.5715	−1.57633
$482$	3.04591	0.138738
$483$	3.64012	0.165631
$484$	−11.9993	−0.545421
$485$	0	0
$486$	−2.13324	−0.0967659
$487$	9.16949	0.415509	0.207755	−	0.978181i	$-0.433384\pi$
$487$	9.16949	0.415509	0.207755	+	0.978181i	$0.433384\pi$
$488$	5.80325	0.262701
$489$	−7.29949	−0.330094
$490$	0	0
$491$	31.9054	1.43987	0.719935	−	0.694042i	$-0.244172\pi$
$491$	31.9054	1.43987	0.719935	+	0.694042i	$0.244172\pi$
$492$	−28.6317	−1.29081
$493$	30.1466	1.35773
$494$	63.1992	2.84347
$495$	0	0
$496$	−17.0324	−0.764778
$497$	4.99359	0.223993
$498$	21.0702	0.944179
$499$	9.07297	0.406162	0.203081	−	0.979162i	$-0.434905\pi$
$499$	9.07297	0.406162	0.203081	+	0.979162i	$0.434905\pi$
$500$	0	0
$501$	14.7991	0.661175
$502$	−37.4944	−1.67346
$503$	38.7485	1.72771	0.863856	−	0.503739i	$-0.168043\pi$
$503$	38.7485	1.72771	0.863856	+	0.503739i	$0.168043\pi$
$504$	−2.54795	−0.113495
$505$	0	0
$506$	−8.98396	−0.399386
$507$	−5.78176	−0.256777
$508$	1.28075	0.0568243
$509$	32.9367	1.45989	0.729947	−	0.683503i	$-0.239545\pi$
$509$	32.9367	1.45989	0.729947	+	0.683503i	$0.239545\pi$
$510$	0	0
$511$	−2.42032	−0.107069
$512$	26.5639	1.17397
$513$	−6.83602	−0.301818
$514$	−41.1482	−1.81497
$515$	0	0
$516$	−10.8530	−0.477777
$517$	12.5118	0.550270
$518$	36.9065	1.62158
$519$	2.29460	0.100722
$520$	0	0
$521$	−17.7521	−0.777735	−0.388867	−	0.921294i	$-0.627134\pi$
$521$	−17.7521	−0.777735	−0.388867	+	0.921294i	$0.627134\pi$
$522$	9.49138	0.415426
$523$	−4.98678	−0.218056	−0.109028	−	0.994039i	$-0.534774\pi$
$523$	−4.98678	−0.218056	−0.109028	+	0.994039i	$0.534774\pi$
$524$	15.4520	0.675025
$525$	0	0
$526$	−47.4501	−2.06892
$527$	44.4681	1.93706
$528$	−6.51180	−0.283390
$529$	−20.1829	−0.877516
$530$	0	0
$531$	3.67416	0.159445
$532$	−37.8164	−1.63955
$533$	48.6463	2.10711
$534$	2.64575	0.114493
$535$	0	0
$536$	−13.6061	−0.587693
$537$	−13.6637	−0.589632
$538$	53.7120	2.31569
$539$	5.76214	0.248193
$540$	0	0
$541$	−3.49960	−0.150460	−0.0752298	−	0.997166i	$-0.523969\pi$
$541$	−3.49960	−0.150460	−0.0752298	+	0.997166i	$0.523969\pi$
$542$	−12.1614	−0.522378
$543$	−8.71878	−0.374159
$544$	−53.4322	−2.29089
$545$	0	0
$546$	20.0503	0.858073
$547$	−17.4640	−0.746709	−0.373354	−	0.927689i	$-0.621792\pi$
$547$	−17.4640	−0.746709	−0.373354	+	0.927689i	$0.621792\pi$
$548$	4.94877	0.211401
$549$	4.93960	0.210817
$550$	0	0
$551$	30.4153	1.29574
$552$	−1.97189	−0.0839291
$553$	−16.8796	−0.717795
$554$	40.8752	1.73662
$555$	0	0
$556$	48.9798	2.07721
$557$	6.02774	0.255403	0.127702	−	0.991813i	$-0.459240\pi$
$557$	6.02774	0.255403	0.127702	+	0.991813i	$0.459240\pi$
$558$	14.0004	0.592683
$559$	18.4397	0.779917
$560$	0	0
$561$	17.0009	0.717780
$562$	9.30126	0.392350
$563$	9.19823	0.387659	0.193830	−	0.981035i	$-0.437909\pi$
$563$	9.19823	0.387659	0.193830	+	0.981035i	$0.437909\pi$
$564$	12.7193	0.535577
$565$	0	0
$566$	−53.1351	−2.23343
$567$	−2.16876	−0.0910795
$568$	−2.70508	−0.113503
$569$	9.06517	0.380032	0.190016	−	0.981781i	$-0.439146\pi$
$569$	9.06517	0.380032	0.190016	+	0.981781i	$0.439146\pi$
$570$	0	0
$571$	−6.34688	−0.265609	−0.132804	−	0.991142i	$-0.542398\pi$
$571$	−6.34688	−0.265609	−0.132804	+	0.991142i	$0.542398\pi$
$572$	−27.7368	−1.15973
$573$	−11.6080	−0.484931
$574$	−51.9320	−2.16760
$575$	0	0
$576$	−11.6322	−0.484675
$577$	2.41418	0.100504	0.0502519	−	0.998737i	$-0.483998\pi$
$577$	2.41418	0.100504	0.0502519	+	0.998737i	$0.483998\pi$
$578$	61.6700	2.56513
$579$	14.8653	0.617779
$580$	0	0
$581$	21.4211	0.888695
$582$	32.1027	1.33070
$583$	−20.6085	−0.853516
$584$	1.31111	0.0542541
$585$	0	0
$586$	−28.9378	−1.19541
$587$	4.50976	0.186138	0.0930689	−	0.995660i	$-0.470332\pi$
$587$	4.50976	0.186138	0.0930689	+	0.995660i	$0.470332\pi$
$588$	5.85766	0.241566
$589$	44.8645	1.84861
$590$	0	0
$591$	−22.8292	−0.939067
$592$	20.7027	0.850877
$593$	−33.2824	−1.36674	−0.683371	−	0.730071i	$-0.739487\pi$
$593$	−33.2824	−1.36674	−0.683371	+	0.730071i	$0.739487\pi$
$594$	5.35259	0.219620
$595$	0	0
$596$	24.2099	0.991678
$597$	−5.87697	−0.240528
$598$	15.5172	0.634544
$599$	39.1061	1.59783	0.798915	−	0.601444i	$-0.205408\pi$
$599$	39.1061	1.59783	0.798915	+	0.601444i	$0.205408\pi$
$600$	0	0
$601$	−28.8076	−1.17509	−0.587543	−	0.809193i	$-0.699905\pi$
$601$	−28.8076	−1.17509	−0.587543	+	0.809193i	$0.699905\pi$
$602$	−19.6852	−0.802307
$603$	−11.5812	−0.471624
$604$	−32.0747	−1.30510
$605$	0	0
$606$	36.3101	1.47500
$607$	−23.0933	−0.937327	−0.468663	−	0.883377i	$-0.655264\pi$
$607$	−23.0933	−0.937327	−0.468663	+	0.883377i	$0.655264\pi$
$608$	−53.9085	−2.18628
$609$	9.64942	0.391014
$610$	0	0
$611$	−21.6105	−0.874268
$612$	17.2828	0.698615
$613$	−18.2228	−0.736013	−0.368007	−	0.929823i	$-0.619960\pi$
$613$	−18.2228	−0.736013	−0.368007	+	0.929823i	$0.619960\pi$
$614$	−25.5291	−1.03027
$615$	0	0
$616$	6.39315	0.257587
$617$	15.4484	0.621930	0.310965	−	0.950421i	$-0.399348\pi$
$617$	15.4484	0.621930	0.310965	+	0.950421i	$0.399348\pi$
$618$	21.5157	0.865488
$619$	16.5042	0.663359	0.331680	−	0.943392i	$-0.392385\pi$
$619$	16.5042	0.663359	0.331680	+	0.943392i	$0.392385\pi$
$620$	0	0
$621$	−1.67843	−0.0673531
$622$	16.3503	0.655587
$623$	2.68980	0.107765
$624$	11.2472	0.450249
$625$	0	0
$626$	56.2835	2.24954
$627$	17.1525	0.685004
$628$	47.9514	1.91347
$629$	−54.0505	−2.15513
$630$	0	0
$631$	−38.1237	−1.51768	−0.758841	−	0.651276i	$-0.774234\pi$
$631$	−38.1237	−1.51768	−0.758841	+	0.651276i	$0.774234\pi$
$632$	9.14386	0.363723
$633$	24.6884	0.981276
$634$	−23.2267	−0.922450
$635$	0	0
$636$	−20.9501	−0.830726
$637$	−9.95240	−0.394329
$638$	−23.8151	−0.942850
$639$	−2.30251	−0.0910858
$640$	0	0
$641$	38.9299	1.53764	0.768819	−	0.639466i	$-0.220845\pi$
$641$	38.9299	1.53764	0.768819	+	0.639466i	$0.220845\pi$
$642$	12.1002	0.477555
$643$	40.5346	1.59853	0.799265	−	0.600979i	$-0.205222\pi$
$643$	40.5346	1.59853	0.799265	+	0.600979i	$0.205222\pi$
$644$	−9.28496	−0.365879
$645$	0	0
$646$	98.8082	3.88755
$647$	31.8752	1.25315	0.626573	−	0.779363i	$-0.284457\pi$
$647$	31.8752	1.25315	0.626573	+	0.779363i	$0.284457\pi$
$648$	1.17484	0.0461521
$649$	−9.21896	−0.361876
$650$	0	0
$651$	14.2335	0.557855
$652$	18.6190	0.729177
$653$	−19.5285	−0.764210	−0.382105	−	0.924119i	$-0.624801\pi$
$653$	−19.5285	−0.764210	−0.382105	+	0.924119i	$0.624801\pi$
$654$	−17.8031	−0.696158
$655$	0	0
$656$	−29.1313	−1.13738
$657$	1.11599	0.0435389
$658$	23.0701	0.899367
$659$	47.6562	1.85642	0.928211	−	0.372055i	$-0.121347\pi$
$659$	47.6562	1.85642	0.928211	+	0.372055i	$0.121347\pi$
$660$	0	0
$661$	3.91738	0.152368	0.0761842	−	0.997094i	$-0.475726\pi$
$661$	3.91738	0.152368	0.0761842	+	0.997094i	$0.475726\pi$
$662$	−68.7196	−2.67086
$663$	−29.3641	−1.14041
$664$	−11.6040	−0.450322
$665$	0	0
$666$	−17.0173	−0.659408
$667$	7.46779	0.289154
$668$	−37.7485	−1.46053
$669$	3.31060	0.127995
$670$	0	0
$671$	−12.3941	−0.478470
$672$	−17.1028	−0.659754
$673$	28.1866	1.08651	0.543257	−	0.839566i	$-0.317191\pi$
$673$	28.1866	1.08651	0.543257	+	0.839566i	$0.317191\pi$
$674$	−7.40597	−0.285267
$675$	0	0
$676$	14.7477	0.567219
$677$	−9.50611	−0.365350	−0.182675	−	0.983173i	$-0.558476\pi$
$677$	−9.50611	−0.365350	−0.182675	+	0.983173i	$0.558476\pi$
$678$	−31.6198	−1.21435
$679$	32.6372	1.25250
$680$	0	0
$681$	2.70185	0.103535
$682$	−35.1288	−1.34515
$683$	7.49565	0.286813	0.143407	−	0.989664i	$-0.454194\pi$
$683$	7.49565	0.286813	0.143407	+	0.989664i	$0.454194\pi$
$684$	17.4368	0.666714
$685$	0	0
$686$	43.0101	1.64213
$687$	9.33473	0.356142
$688$	−11.0424	−0.420987
$689$	35.5951	1.35607
$690$	0	0
$691$	−0.745188	−0.0283483	−0.0141741	−	0.999900i	$-0.504512\pi$
$691$	−0.745188	−0.0283483	−0.0141741	+	0.999900i	$0.504512\pi$
$692$	−5.85290	−0.222494
$693$	5.44172	0.206714
$694$	−23.4241	−0.889167
$695$	0	0
$696$	−5.22718	−0.198136
$697$	76.0556	2.88081
$698$	−56.1379	−2.12485
$699$	−9.52491	−0.360265
$700$	0	0
$701$	31.6488	1.19536	0.597679	−	0.801735i	$-0.296090\pi$
$701$	31.6488	1.19536	0.597679	+	0.801735i	$0.296090\pi$
$702$	−9.24504	−0.348931
$703$	−54.5323	−2.05672
$704$	29.1867	1.10002
$705$	0	0
$706$	−34.9145	−1.31402
$707$	36.9147	1.38832
$708$	−9.37179	−0.352214
$709$	−16.0181	−0.601571	−0.300785	−	0.953692i	$-0.597249\pi$
$709$	−16.0181	−0.601571	−0.300785	+	0.953692i	$0.597249\pi$
$710$	0	0
$711$	7.78306	0.291888
$712$	−1.45709	−0.0546068
$713$	11.0155	0.412532
$714$	31.3474	1.17315
$715$	0	0
$716$	34.8524	1.30250
$717$	−7.84648	−0.293032
$718$	−37.3043	−1.39218
$719$	14.3316	0.534478	0.267239	−	0.963630i	$-0.413889\pi$
$719$	14.3316	0.534478	0.267239	+	0.963630i	$0.413889\pi$
$720$	0	0
$721$	21.8739	0.814628
$722$	59.1573	2.20161
$723$	−1.42783	−0.0531016
$724$	22.2393	0.826515
$725$	0	0
$726$	10.0353	0.372445
$727$	−18.3551	−0.680755	−0.340377	−	0.940289i	$-0.610555\pi$
$727$	−18.3551	−0.680755	−0.340377	+	0.940289i	$0.610555\pi$
$728$	−11.0423	−0.409254
$729$	1.00000	0.0370370
$730$	0	0
$731$	28.8294	1.06629
$732$	−12.5996	−0.465694
$733$	−0.665145	−0.0245677	−0.0122838	−	0.999925i	$-0.503910\pi$
$733$	−0.665145	−0.0245677	−0.0122838	+	0.999925i	$0.503910\pi$
$734$	17.6973	0.653218
$735$	0	0
$736$	−13.2360	−0.487887
$737$	29.0588	1.07040
$738$	23.9454	0.881443
$739$	−32.8332	−1.20779	−0.603895	−	0.797064i	$-0.706385\pi$
$739$	−32.8332	−1.20779	−0.603895	+	0.797064i	$0.706385\pi$
$740$	0	0
$741$	−29.6259	−1.08833
$742$	−37.9992	−1.39500
$743$	29.6004	1.08593	0.542967	−	0.839754i	$-0.317301\pi$
$743$	29.6004	1.08593	0.542967	+	0.839754i	$0.317301\pi$
$744$	−7.71042	−0.282678
$745$	0	0
$746$	−40.8078	−1.49408
$747$	−9.87708	−0.361383
$748$	−43.3648	−1.58557
$749$	12.3016	0.449492
$750$	0	0
$751$	24.9709	0.911199	0.455600	−	0.890185i	$-0.349425\pi$
$751$	24.9709	0.911199	0.455600	+	0.890185i	$0.349425\pi$
$752$	12.9412	0.471917
$753$	17.5762	0.640514
$754$	41.1337	1.49800
$755$	0	0
$756$	5.53193	0.201194
$757$	11.2173	0.407700	0.203850	−	0.979002i	$-0.434655\pi$
$757$	11.2173	0.407700	0.203850	+	0.979002i	$0.434655\pi$
$758$	−57.8007	−2.09942
$759$	4.21141	0.152864
$760$	0	0
$761$	19.3105	0.700004	0.350002	−	0.936749i	$-0.386181\pi$
$761$	19.3105	0.700004	0.350002	+	0.936749i	$0.386181\pi$
$762$	−1.07113	−0.0388029
$763$	−18.0996	−0.655249
$764$	29.6089	1.07121
$765$	0	0
$766$	42.2438	1.52633
$767$	15.9231	0.574948
$768$	−3.97476	−0.143427
$769$	−19.3372	−0.697318	−0.348659	−	0.937250i	$-0.613363\pi$
$769$	−19.3372	−0.697318	−0.348659	+	0.937250i	$0.613363\pi$
$770$	0	0
$771$	19.2890	0.694677
$772$	−37.9172	−1.36467
$773$	−7.79217	−0.280265	−0.140132	−	0.990133i	$-0.544753\pi$
$773$	−7.79217	−0.280265	−0.140132	+	0.990133i	$0.544753\pi$
$774$	9.07667	0.326254
$775$	0	0
$776$	−17.6799	−0.634671
$777$	−17.3007	−0.620658
$778$	−49.0923	−1.76004
$779$	76.7336	2.74926
$780$	0	0
$781$	5.77730	0.206728
$782$	24.2601	0.867540
$783$	−4.44927	−0.159004
$784$	5.95987	0.212853
$785$	0	0
$786$	−12.9229	−0.460946
$787$	9.07666	0.323548	0.161774	−	0.986828i	$-0.448278\pi$
$787$	9.07666	0.323548	0.161774	+	0.986828i	$0.448278\pi$
$788$	58.2311	2.07440
$789$	22.2432	0.791877
$790$	0	0
$791$	−32.1463	−1.14299
$792$	−2.94783	−0.104747
$793$	21.4072	0.760192
$794$	−43.8903	−1.55761
$795$	0	0
$796$	14.9906	0.531326
$797$	22.9954	0.814541	0.407270	−	0.913308i	$-0.366481\pi$
$797$	22.9954	0.814541	0.407270	+	0.913308i	$0.366481\pi$
$798$	31.6268	1.11958
$799$	−33.7867	−1.19529
$800$	0	0
$801$	−1.24025	−0.0438219
$802$	−28.0611	−0.990872
$803$	−2.80017	−0.0988158
$804$	29.5406	1.04182
$805$	0	0
$806$	60.6747	2.13718
$807$	−25.1785	−0.886327
$808$	−19.9970	−0.703493
$809$	−50.6773	−1.78172	−0.890860	−	0.454278i	$-0.849897\pi$
$809$	−50.6773	−1.78172	−0.890860	+	0.454278i	$0.849897\pi$
$810$	0	0
$811$	26.7614	0.939720	0.469860	−	0.882741i	$-0.344304\pi$
$811$	26.7614	0.939720	0.469860	+	0.882741i	$0.344304\pi$
$812$	−24.6130	−0.863749
$813$	5.70091	0.199940
$814$	42.6987	1.49659
$815$	0	0
$816$	17.5843	0.615575
$817$	29.0864	1.01760
$818$	5.89908	0.206256
$819$	−9.39897	−0.328427
$820$	0	0
$821$	−0.832947	−0.0290700	−0.0145350	−	0.999894i	$-0.504627\pi$
$821$	−0.832947	−0.0290700	−0.0145350	+	0.999894i	$0.504627\pi$
$822$	−4.13879	−0.144357
$823$	6.67034	0.232514	0.116257	−	0.993219i	$-0.462910\pi$
$823$	6.67034	0.232514	0.116257	+	0.993219i	$0.462910\pi$
$824$	−11.8493	−0.412791
$825$	0	0
$826$	−16.9985	−0.591454
$827$	−1.34470	−0.0467599	−0.0233799	−	0.999727i	$-0.507443\pi$
$827$	−1.34470	−0.0467599	−0.0233799	+	0.999727i	$0.507443\pi$
$828$	4.28122	0.148783
$829$	−24.7770	−0.860541	−0.430270	−	0.902700i	$-0.641582\pi$
$829$	−24.7770	−0.860541	−0.430270	+	0.902700i	$0.641582\pi$
$830$	0	0
$831$	−19.1611	−0.664690
$832$	−50.4115	−1.74770
$833$	−15.5600	−0.539121
$834$	−40.9631	−1.41844
$835$	0	0
$836$	−43.7513	−1.51317
$837$	−6.56295	−0.226849
$838$	−20.7106	−0.715437
$839$	−6.72534	−0.232184	−0.116092	−	0.993238i	$-0.537037\pi$
$839$	−6.72534	−0.232184	−0.116092	+	0.993238i	$0.537037\pi$
$840$	0	0
$841$	−9.20399	−0.317379
$842$	−8.99685	−0.310052
$843$	−4.36015	−0.150171
$844$	−62.9734	−2.16763
$845$	0	0
$846$	−10.6375	−0.365723
$847$	10.2024	0.350559
$848$	−21.3157	−0.731984
$849$	24.9081	0.854844
$850$	0	0
$851$	−13.3892	−0.458975
$852$	5.87307	0.201208
$853$	−16.7244	−0.572632	−0.286316	−	0.958135i	$-0.592431\pi$
$853$	−16.7244	−0.572632	−0.286316	+	0.958135i	$0.592431\pi$
$854$	−22.8531	−0.782016
$855$	0	0
$856$	−6.66391	−0.227768
$857$	12.9930	0.443831	0.221915	−	0.975066i	$-0.428769\pi$
$857$	12.9930	0.443831	0.221915	+	0.975066i	$0.428769\pi$
$858$	23.1970	0.791933
$859$	−36.5682	−1.24769	−0.623845	−	0.781548i	$-0.714430\pi$
$859$	−36.5682	−1.24769	−0.623845	+	0.781548i	$0.714430\pi$
$860$	0	0
$861$	24.3441	0.829646
$862$	40.4859	1.37895
$863$	−46.3384	−1.57738	−0.788688	−	0.614794i	$-0.789239\pi$
$863$	−46.3384	−1.57738	−0.788688	+	0.614794i	$0.789239\pi$
$864$	7.88596	0.268286
$865$	0	0
$866$	29.2370	0.993513
$867$	−28.9090	−0.981802
$868$	−36.3058	−1.23230
$869$	−19.5287	−0.662467
$870$	0	0
$871$	−50.1906	−1.70064
$872$	9.80472	0.332030
$873$	−15.0488	−0.509323
$874$	24.4764	0.827926
$875$	0	0
$876$	−2.84659	−0.0961773
$877$	−44.2548	−1.49438	−0.747190	−	0.664611i	$-0.768597\pi$
$877$	−44.2548	−1.49438	−0.747190	+	0.664611i	$0.768597\pi$
$878$	−71.2169	−2.40345
$879$	13.5651	0.457541
$880$	0	0
$881$	−42.2495	−1.42342	−0.711712	−	0.702472i	$-0.752080\pi$
$881$	−42.2495	−1.42342	−0.711712	+	0.702472i	$0.752080\pi$
$882$	−4.89892	−0.164955
$883$	3.49289	0.117545	0.0587726	−	0.998271i	$-0.481281\pi$
$883$	3.49289	0.117545	0.0587726	+	0.998271i	$0.481281\pi$
$884$	74.9000	2.51916
$885$	0	0
$886$	24.8076	0.833427
$887$	14.7275	0.494501	0.247250	−	0.968952i	$-0.420473\pi$
$887$	14.7275	0.494501	0.247250	+	0.968952i	$0.420473\pi$
$888$	9.37194	0.314502
$889$	−1.08896	−0.0365227
$890$	0	0
$891$	−2.50913	−0.0840591
$892$	−8.44444	−0.282741
$893$	−34.0879	−1.14071
$894$	−20.2474	−0.677175
$895$	0	0
$896$	19.6108	0.655151
$897$	−7.27397	−0.242871
$898$	−28.4808	−0.950416
$899$	29.2004	0.973886
$900$	0	0
$901$	55.6508	1.85400
$902$	−60.0823	−2.00052
$903$	9.22780	0.307082
$904$	17.4140	0.579180
$905$	0	0
$906$	26.8250	0.891200
$907$	7.33785	0.243649	0.121825	−	0.992552i	$-0.461125\pi$
$907$	7.33785	0.243649	0.121825	+	0.992552i	$0.461125\pi$
$908$	−6.89169	−0.228709
$909$	−17.0211	−0.564553
$910$	0	0
$911$	−53.5731	−1.77496	−0.887479	−	0.460849i	$-0.847545\pi$
$911$	−53.5731	−1.77496	−0.887479	+	0.460849i	$0.847545\pi$
$912$	17.7411	0.587466
$913$	24.7829	0.820195
$914$	−49.7136	−1.64438
$915$	0	0
$916$	−23.8104	−0.786717
$917$	−13.1381	−0.433859
$918$	−14.4541	−0.477055
$919$	−43.2016	−1.42509	−0.712545	−	0.701627i	$-0.752458\pi$
$919$	−43.2016	−1.42509	−0.712545	+	0.701627i	$0.752458\pi$
$920$	0	0
$921$	11.9672	0.394334
$922$	10.7359	0.353570
$923$	−9.97859	−0.328449
$924$	−13.8803	−0.456630
$925$	0	0
$926$	−27.2541	−0.895625
$927$	−10.0859	−0.331264
$928$	−35.0868	−1.15178
$929$	−14.8420	−0.486951	−0.243476	−	0.969907i	$-0.578288\pi$
$929$	−14.8420	−0.486951	−0.243476	+	0.969907i	$0.578288\pi$
$930$	0	0
$931$	−15.6987	−0.514503
$932$	24.2955	0.795824
$933$	−7.66452	−0.250925
$934$	10.3736	0.339435
$935$	0	0
$936$	5.09151	0.166421
$937$	−3.75611	−0.122707	−0.0613534	−	0.998116i	$-0.519542\pi$
$937$	−3.75611	−0.122707	−0.0613534	+	0.998116i	$0.519542\pi$
$938$	53.5805	1.74947
$939$	−26.3840	−0.861008
$940$	0	0
$941$	59.9208	1.95336	0.976682	−	0.214692i	$-0.0688747\pi$
$941$	59.9208	1.95336	0.976682	+	0.214692i	$0.0688747\pi$
$942$	−40.1030	−1.30663
$943$	18.8402	0.613521
$944$	−9.53532	−0.310348
$945$	0	0
$946$	−22.7746	−0.740465
$947$	−24.4212	−0.793581	−0.396791	−	0.917909i	$-0.629876\pi$
$947$	−24.4212	−0.793581	−0.396791	+	0.917909i	$0.629876\pi$
$948$	−19.8525	−0.644779
$949$	4.83647	0.156998
$950$	0	0
$951$	10.8880	0.353067
$952$	−17.2639	−0.559528
$953$	−36.6466	−1.18710	−0.593550	−	0.804797i	$-0.702274\pi$
$953$	−36.6466	−1.18710	−0.593550	+	0.804797i	$0.702274\pi$
$954$	17.5212	0.567268
$955$	0	0
$956$	20.0142	0.647307
$957$	11.1638	0.360875
$958$	10.2225	0.330275
$959$	−4.20770	−0.135874
$960$	0	0
$961$	12.0723	0.389431
$962$	−73.7495	−2.37778
$963$	−5.67218	−0.182784
$964$	3.64201	0.117301
$965$	0	0
$966$	7.76526	0.249843
$967$	−47.4395	−1.52555	−0.762776	−	0.646663i	$-0.776164\pi$
$967$	−47.4395	−1.52555	−0.762776	+	0.646663i	$0.776164\pi$
$968$	−5.52674	−0.177636
$969$	−46.3183	−1.48796
$970$	0	0
$971$	−5.68782	−0.182531	−0.0912655	−	0.995827i	$-0.529091\pi$
$971$	−5.68782	−0.182531	−0.0912655	+	0.995827i	$0.529091\pi$
$972$	−2.55073	−0.0818147
$973$	−41.6452	−1.33508
$974$	19.5608	0.626767
$975$	0	0
$976$	−12.8194	−0.410340
$977$	2.29901	0.0735518	0.0367759	−	0.999324i	$-0.488291\pi$
$977$	2.29901	0.0735518	0.0367759	+	0.999324i	$0.488291\pi$
$978$	−15.5716	−0.497925
$979$	3.11194	0.0994581
$980$	0	0
$981$	8.34557	0.266454
$982$	68.0620	2.17194
$983$	2.35879	0.0752336	0.0376168	−	0.999292i	$-0.488023\pi$
$983$	2.35879	0.0752336	0.0376168	+	0.999292i	$0.488023\pi$
$984$	−13.1875	−0.420401
$985$	0	0
$986$	64.3100	2.04805
$987$	−10.8146	−0.344232
$988$	75.5676	2.40413
$989$	7.14150	0.227087
$990$	0	0
$991$	−7.76677	−0.246720	−0.123360	−	0.992362i	$-0.539367\pi$
$991$	−7.76677	−0.246720	−0.123360	+	0.992362i	$0.539367\pi$
$992$	−51.7552	−1.64323
$993$	32.2137	1.02227
$994$	10.6526	0.337879
$995$	0	0
$996$	25.1938	0.798295
$997$	−8.35947	−0.264747	−0.132374	−	0.991200i	$-0.542260\pi$
$997$	−8.35947	−0.264747	−0.132374	+	0.991200i	$0.542260\pi$
$998$	19.3549	0.612668
$999$	7.97720	0.252388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.l.1.5	yes	6
3.2	odd	2		5625.2.a.o.1.2		6
5.2	odd	4		1875.2.b.e.1249.10		12
5.3	odd	4		1875.2.b.e.1249.3		12
5.4	even	2		1875.2.a.i.1.2	✓	6
15.14	odd	2		5625.2.a.r.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.i.1.2	✓	6	5.4	even	2
1875.2.a.l.1.5	yes	6	1.1	even	1	trivial
1875.2.b.e.1249.3		12	5.3	odd	4
1875.2.b.e.1249.10		12	5.2	odd	4
5625.2.a.o.1.2		6	3.2	odd	2
5625.2.a.r.1.5		6	15.14	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+2.13324 q^{2} -1.00000 q^{3} +2.55073 q^{4} -2.13324 q^{6} -2.16876 q^{7} +1.17484 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.13324 q^{2} -1.00000 q^{3} +2.55073 q^{4} -2.13324 q^{6} -2.16876 q^{7} +1.17484 q^{8} +1.00000 q^{9} -2.50913 q^{11} -2.55073 q^{12} +4.33379 q^{13} -4.62650 q^{14} -2.59524 q^{16} +6.77562 q^{17} +2.13324 q^{18} +6.83602 q^{19} +2.16876 q^{21} -5.35259 q^{22} +1.67843 q^{23} -1.17484 q^{24} +9.24504 q^{26} -1.00000 q^{27} -5.53193 q^{28} +4.44927 q^{29} +6.56295 q^{31} -7.88596 q^{32} +2.50913 q^{33} +14.4541 q^{34} +2.55073 q^{36} -7.97720 q^{37} +14.5829 q^{38} -4.33379 q^{39} +11.2249 q^{41} +4.62650 q^{42} +4.25487 q^{43} -6.40012 q^{44} +3.58050 q^{46} -4.98652 q^{47} +2.59524 q^{48} -2.29646 q^{49} -6.77562 q^{51} +11.0543 q^{52} +8.21338 q^{53} -2.13324 q^{54} -2.54795 q^{56} -6.83602 q^{57} +9.49138 q^{58} +3.67416 q^{59} +4.93960 q^{61} +14.0004 q^{62} -2.16876 q^{63} -11.6322 q^{64} +5.35259 q^{66} -11.5812 q^{67} +17.2828 q^{68} -1.67843 q^{69} -2.30251 q^{71} +1.17484 q^{72} +1.11599 q^{73} -17.0173 q^{74} +17.4368 q^{76} +5.44172 q^{77} -9.24504 q^{78} +7.78306 q^{79} +1.00000 q^{81} +23.9454 q^{82} -9.87708 q^{83} +5.53193 q^{84} +9.07667 q^{86} -4.44927 q^{87} -2.94783 q^{88} -1.24025 q^{89} -9.39897 q^{91} +4.28122 q^{92} -6.56295 q^{93} -10.6375 q^{94} +7.88596 q^{96} -15.0488 q^{97} -4.89892 q^{98} -2.50913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 11 q^{12} - 4 q^{14} + 17 q^{16} + 2 q^{17} + q^{18} - 2 q^{19} + 2 q^{21} + 9 q^{22} - q^{23} - 6 q^{24} + 37 q^{26} - 6 q^{27} - 44 q^{28} + 31 q^{29} - 2 q^{31} + 33 q^{32} + 37 q^{34} + 11 q^{36} - 22 q^{37} + 27 q^{38} + 33 q^{41} + 4 q^{42} - 3 q^{43} - 11 q^{44} - 12 q^{46} - 6 q^{47} - 17 q^{48} + 4 q^{49} - 2 q^{51} - 33 q^{52} + 14 q^{53} - q^{54} - 30 q^{56} + 2 q^{57} - q^{58} - 8 q^{59} + 34 q^{61} + 31 q^{62} - 2 q^{63} + 12 q^{64} - 9 q^{66} + 2 q^{67} + 27 q^{68} + q^{69} - 3 q^{71} + 6 q^{72} - 36 q^{73} + 36 q^{74} + 27 q^{76} + 16 q^{77} - 37 q^{78} + 25 q^{79} + 6 q^{81} + 36 q^{82} - 12 q^{83} + 44 q^{84} - 30 q^{86} - 31 q^{87} + 56 q^{88} + 18 q^{89} + 28 q^{91} + 3 q^{92} + 2 q^{93} - 50 q^{94} - 33 q^{96} + 7 q^{97} + 15 q^{98}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 11 * q^12 - 4 * q^14 + 17 * q^16 + 2 * q^17 + q^18 - 2 * q^19 + 2 * q^21 + 9 * q^22 - q^23 - 6 * q^24 + 37 * q^26 - 6 * q^27 - 44 * q^28 + 31 * q^29 - 2 * q^31 + 33 * q^32 + 37 * q^34 + 11 * q^36 - 22 * q^37 + 27 * q^38 + 33 * q^41 + 4 * q^42 - 3 * q^43 - 11 * q^44 - 12 * q^46 - 6 * q^47 - 17 * q^48 + 4 * q^49 - 2 * q^51 - 33 * q^52 + 14 * q^53 - q^54 - 30 * q^56 + 2 * q^57 - q^58 - 8 * q^59 + 34 * q^61 + 31 * q^62 - 2 * q^63 + 12 * q^64 - 9 * q^66 + 2 * q^67 + 27 * q^68 + q^69 - 3 * q^71 + 6 * q^72 - 36 * q^73 + 36 * q^74 + 27 * q^76 + 16 * q^77 - 37 * q^78 + 25 * q^79 + 6 * q^81 + 36 * q^82 - 12 * q^83 + 44 * q^84 - 30 * q^86 - 31 * q^87 + 56 * q^88 + 18 * q^89 + 28 * q^91 + 3 * q^92 + 2 * q^93 - 50 * q^94 - 33 * q^96 + 7 * q^97 + 15 * q^98

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