LMFDB - Embedded newform 775.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, 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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.20308.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} + 4x + 12 $ x^4 - x^3 - 8x^2 + 4x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.15729$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.15729 q^{2} -3.02722 q^{3} -0.660672 q^{4} +3.50338 q^{6} +1.50338 q^{7} +3.07918 q^{8} +6.16405 q^{9} +O(q^{10})$	\(q-1.15729 q^{2} -3.02722 q^{3} -0.660672 q^{4} +3.50338 q^{6} +1.50338 q^{7} +3.07918 q^{8} +6.16405 q^{9} -5.81797 q^{11} +2.00000 q^{12} -5.50338 q^{13} -1.73985 q^{14} -2.24217 q^{16} +0.790747 q^{17} -7.13362 q^{18} -3.89714 q^{19} -4.55106 q^{21} +6.73309 q^{22} -5.24323 q^{23} -9.32134 q^{24} +6.36902 q^{26} -9.57828 q^{27} -0.993241 q^{28} +6.55106 q^{29} +1.00000 q^{31} -3.56351 q^{32} +17.6123 q^{33} -0.915126 q^{34} -4.07242 q^{36} -0.476161 q^{37} +4.51014 q^{38} +16.6599 q^{39} -3.40052 q^{41} +5.26691 q^{42} -2.79075 q^{43} +3.84377 q^{44} +6.06795 q^{46} +10.0544 q^{47} +6.78753 q^{48} -4.73985 q^{49} -2.39376 q^{51} +3.63593 q^{52} +10.0884 q^{53} +11.0849 q^{54} +4.62917 q^{56} +11.7975 q^{57} -7.58149 q^{58} -4.13362 q^{59} +12.0544 q^{61} -1.15729 q^{62} +9.26691 q^{63} +8.60836 q^{64} -20.3825 q^{66} -1.81797 q^{67} -0.522425 q^{68} +15.8724 q^{69} +5.16405 q^{71} +18.9802 q^{72} -6.45248 q^{73} +0.551058 q^{74} +2.57474 q^{76} -8.74661 q^{77} -19.2804 q^{78} +0.510138 q^{79} +10.5034 q^{81} +3.93540 q^{82} -3.53736 q^{83} +3.00676 q^{84} +3.22971 q^{86} -19.8315 q^{87} -17.9146 q^{88} +1.12579 q^{89} -8.27367 q^{91} +3.46406 q^{92} -3.02722 q^{93} -11.6359 q^{94} +10.7875 q^{96} -0.260149 q^{97} +5.48540 q^{98} -35.8622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9	$ 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9} - 6 q^{11} + 8 q^{12} - 16 q^{13} + 8 q^{14} + 11 q^{16} - q^{17} + q^{18} + 5 q^{19} + 2 q^{21} + 24 q^{22} - 14 q^{24} - 12 q^{26} - 5 q^{27} - 16 q^{28} + 6 q^{29} + 4 q^{31} + 29 q^{32} + 12 q^{33} - 18 q^{34} - 25 q^{36} - 9 q^{37} - 6 q^{39} + 13 q^{41} + 24 q^{42} - 7 q^{43} + 20 q^{44} - 26 q^{46} + 14 q^{47} - 2 q^{48} - 4 q^{49} + 5 q^{51} - 20 q^{52} - 11 q^{53} + 30 q^{54} - 4 q^{56} + 31 q^{57} - 22 q^{58} + 13 q^{59} + 22 q^{61} + q^{62} + 40 q^{63} + 47 q^{64} - 20 q^{66} + 10 q^{67} - 30 q^{68} + 20 q^{69} + 3 q^{71} - 19 q^{72} - 9 q^{73} - 18 q^{74} + 14 q^{76} - 8 q^{77} - 56 q^{78} - 16 q^{79} + 36 q^{81} - 6 q^{82} + 17 q^{83} + 16 q^{86} - 38 q^{87} + 44 q^{88} - 12 q^{89} - 24 q^{91} + 10 q^{92} + q^{93} - 12 q^{94} + 14 q^{96} - 16 q^{97} - 19 q^{98} - 52 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9 - 6 * q^11 + 8 * q^12 - 16 * q^13 + 8 * q^14 + 11 * q^16 - q^17 + q^18 + 5 * q^19 + 2 * q^21 + 24 * q^22 - 14 * q^24 - 12 * q^26 - 5 * q^27 - 16 * q^28 + 6 * q^29 + 4 * q^31 + 29 * q^32 + 12 * q^33 - 18 * q^34 - 25 * q^36 - 9 * q^37 - 6 * q^39 + 13 * q^41 + 24 * q^42 - 7 * q^43 + 20 * q^44 - 26 * q^46 + 14 * q^47 - 2 * q^48 - 4 * q^49 + 5 * q^51 - 20 * q^52 - 11 * q^53 + 30 * q^54 - 4 * q^56 + 31 * q^57 - 22 * q^58 + 13 * q^59 + 22 * q^61 + q^62 + 40 * q^63 + 47 * q^64 - 20 * q^66 + 10 * q^67 - 30 * q^68 + 20 * q^69 + 3 * q^71 - 19 * q^72 - 9 * q^73 - 18 * q^74 + 14 * q^76 - 8 * q^77 - 56 * q^78 - 16 * q^79 + 36 * q^81 - 6 * q^82 + 17 * q^83 + 16 * q^86 - 38 * q^87 + 44 * q^88 - 12 * q^89 - 24 * q^91 + 10 * q^92 + q^93 - 12 * q^94 + 14 * q^96 - 16 * q^97 - 19 * q^98 - 52 * 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 $

$2$	−1.15729	−0.818330	−0.409165	−	0.912460i	$-0.634180\pi$
$2$	−1.15729	−0.818330	−0.409165	+	0.912460i	$0.634180\pi$
$3$	−3.02722	−1.74777	−0.873883	−	0.486137i	$-0.838406\pi$
$3$	−3.02722	−1.74777	−0.873883	+	0.486137i	$0.838406\pi$
$4$	−0.660672	−0.330336
$5$	0	0
$5$	0	0
$6$	3.50338	1.43025
$7$	1.50338	0.568224	0.284112	−	0.958791i	$-0.408301\pi$
$7$	1.50338	0.568224	0.284112	+	0.958791i	$0.408301\pi$
$8$	3.07918	1.08865
$9$	6.16405	2.05468
$10$	0	0
$11$	−5.81797	−1.75418	−0.877091	−	0.480324i	$-0.840519\pi$
$11$	−5.81797	−1.75418	−0.877091	+	0.480324i	$0.840519\pi$
$12$	2.00000	0.577350
$13$	−5.50338	−1.52636	−0.763181	−	0.646184i	$-0.776364\pi$
$13$	−5.50338	−1.52636	−0.763181	+	0.646184i	$0.776364\pi$
$14$	−1.73985	−0.464995
$15$	0	0
$16$	−2.24217	−0.560542
$17$	0.790747	0.191784	0.0958922	−	0.995392i	$-0.469430\pi$
$17$	0.790747	0.191784	0.0958922	+	0.995392i	$0.469430\pi$
$18$	−7.13362	−1.68141
$19$	−3.89714	−0.894066	−0.447033	−	0.894517i	$-0.647519\pi$
$19$	−3.89714	−0.894066	−0.447033	+	0.894517i	$0.647519\pi$
$20$	0	0
$21$	−4.55106	−0.993122
$22$	6.73309	1.43550
$23$	−5.24323	−1.09329	−0.546645	−	0.837365i	$-0.684095\pi$
$23$	−5.24323	−1.09329	−0.546645	+	0.837365i	$0.684095\pi$
$24$	−9.32134	−1.90271
$25$	0	0
$26$	6.36902	1.24907
$27$	−9.57828	−1.84334
$28$	−0.993241	−0.187705
$29$	6.55106	1.21650	0.608250	−	0.793745i	$-0.291872\pi$
$29$	6.55106	1.21650	0.608250	+	0.793745i	$0.291872\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−3.56351	−0.629946
$33$	17.6123	3.06590
$34$	−0.915126	−0.156943
$35$	0	0
$36$	−4.07242	−0.678737
$37$	−0.476161	−0.0782804	−0.0391402	−	0.999234i	$-0.512462\pi$
$37$	−0.476161	−0.0782804	−0.0391402	+	0.999234i	$0.512462\pi$
$38$	4.51014	0.731641
$39$	16.6599	2.66772
$40$	0	0
$41$	−3.40052	−0.531072	−0.265536	−	0.964101i	$-0.585549\pi$
$41$	−3.40052	−0.531072	−0.265536	+	0.964101i	$0.585549\pi$
$42$	5.26691	0.812702
$43$	−2.79075	−0.425585	−0.212792	−	0.977097i	$-0.568256\pi$
$43$	−2.79075	−0.425585	−0.212792	+	0.977097i	$0.568256\pi$
$44$	3.84377	0.579470
$45$	0	0
$46$	6.06795	0.894671
$47$	10.0544	1.46659	0.733295	−	0.679910i	$-0.237981\pi$
$47$	10.0544	1.46659	0.733295	+	0.679910i	$0.237981\pi$
$48$	6.78753	0.979695
$49$	−4.73985	−0.677122
$50$	0	0
$51$	−2.39376	−0.335194
$52$	3.63593	0.504213
$53$	10.0884	1.38575	0.692875	−	0.721058i	$-0.256344\pi$
$53$	10.0884	1.38575	0.692875	+	0.721058i	$0.256344\pi$
$54$	11.0849	1.50846
$55$	0	0
$56$	4.62917	0.618599
$57$	11.7975	1.56262
$58$	−7.58149	−0.995499
$59$	−4.13362	−0.538151	−0.269075	−	0.963119i	$-0.586718\pi$
$59$	−4.13362	−0.538151	−0.269075	+	0.963119i	$0.586718\pi$
$60$	0	0
$61$	12.0544	1.54341	0.771706	−	0.635979i	$-0.219404\pi$
$61$	12.0544	1.54341	0.771706	+	0.635979i	$0.219404\pi$
$62$	−1.15729	−0.146976
$63$	9.26691	1.16752
$64$	8.60836	1.07605
$65$	0	0
$66$	−20.3825	−2.50892
$67$	−1.81797	−0.222100	−0.111050	−	0.993815i	$-0.535421\pi$
$67$	−1.81797	−0.222100	−0.111050	+	0.993815i	$0.535421\pi$
$68$	−0.522425	−0.0633533
$69$	15.8724	1.91081
$70$	0	0
$71$	5.16405	0.612860	0.306430	−	0.951893i	$-0.400865\pi$
$71$	5.16405	0.612860	0.306430	+	0.951893i	$0.400865\pi$
$72$	18.9802	2.23684
$73$	−6.45248	−0.755206	−0.377603	−	0.925968i	$-0.623252\pi$
$73$	−6.45248	−0.755206	−0.377603	+	0.925968i	$0.623252\pi$
$74$	0.551058	0.0640592
$75$	0	0
$76$	2.57474	0.295342
$77$	−8.74661	−0.996769
$78$	−19.2804	−2.18308
$79$	0.510138	0.0573950	0.0286975	−	0.999588i	$-0.490864\pi$
$79$	0.510138	0.0573950	0.0286975	+	0.999588i	$0.490864\pi$
$80$	0	0
$81$	10.5034	1.16704
$82$	3.93540	0.434592
$83$	−3.53736	−0.388275	−0.194138	−	0.980974i	$-0.562191\pi$
$83$	−3.53736	−0.388275	−0.194138	+	0.980974i	$0.562191\pi$
$84$	3.00676	0.328064
$85$	0	0
$86$	3.22971	0.348269
$87$	−19.8315	−2.12616
$88$	−17.9146	−1.90970
$89$	1.12579	0.119334	0.0596669	−	0.998218i	$-0.480996\pi$
$89$	1.12579	0.119334	0.0596669	+	0.998218i	$0.480996\pi$
$90$	0	0
$91$	−8.27367	−0.867316
$92$	3.46406	0.361153
$93$	−3.02722	−0.313908
$94$	−11.6359	−1.20015
$95$	0	0
$96$	10.7875	1.10100
$97$	−0.260149	−0.0264142	−0.0132071	−	0.999913i	$-0.504204\pi$
$97$	−0.260149	−0.0264142	−0.0132071	+	0.999913i	$0.504204\pi$
$98$	5.48540	0.554109
$99$	−35.8622	−3.60429
$100$	0	0
$101$	−0.630236	−0.0627108	−0.0313554	−	0.999508i	$-0.509982\pi$
$101$	−0.630236	−0.0627108	−0.0313554	+	0.999508i	$0.509982\pi$
$102$	2.77029	0.274299
$103$	10.7331	1.05756	0.528781	−	0.848758i	$-0.322649\pi$
$103$	10.7331	1.05756	0.528781	+	0.848758i	$0.322649\pi$
$104$	−16.9459	−1.66168
$105$	0	0
$106$	−11.6753	−1.13400
$107$	12.0680	1.16665	0.583327	−	0.812238i	$-0.301751\pi$
$107$	12.0680	1.16665	0.583327	+	0.812238i	$0.301751\pi$
$108$	6.32810	0.608922
$109$	6.89039	0.659979	0.329990	−	0.943985i	$-0.392955\pi$
$109$	6.89039	0.659979	0.329990	+	0.943985i	$0.392955\pi$
$110$	0	0
$111$	1.44144	0.136816
$112$	−3.37083	−0.318513
$113$	3.07136	0.288929	0.144464	−	0.989510i	$-0.453854\pi$
$113$	3.07136	0.288929	0.144464	+	0.989510i	$0.453854\pi$
$114$	−13.6532	−1.27874
$115$	0	0
$116$	−4.32810	−0.401854
$117$	−33.9231	−3.13619
$118$	4.78380	0.440385
$119$	1.18879	0.108976
$120$	0	0
$121$	22.8487	2.07716
$122$	−13.9505	−1.26302
$123$	10.2941	0.928190
$124$	−0.660672	−0.0593301
$125$	0	0
$126$	−10.7245	−0.955417
$127$	−7.97632	−0.707784	−0.353892	−	0.935286i	$-0.615142\pi$
$127$	−7.97632	−0.707784	−0.353892	+	0.935286i	$0.615142\pi$
$128$	−2.83537	−0.250614
$129$	8.44820	0.743823
$130$	0	0
$131$	19.3359	1.68939	0.844694	−	0.535250i	$-0.179783\pi$
$131$	19.3359	1.68939	0.844694	+	0.535250i	$0.179783\pi$
$132$	−11.6359	−1.01278
$133$	−5.85889	−0.508030
$134$	2.10392	0.181751
$135$	0	0
$136$	2.43485	0.208787
$137$	18.7671	1.60338	0.801689	−	0.597741i	$-0.203935\pi$
$137$	18.7671	1.60338	0.801689	+	0.597741i	$0.203935\pi$
$138$	−18.3690	−1.56368
$139$	−17.7685	−1.50710	−0.753552	−	0.657389i	$-0.771661\pi$
$139$	−17.7685	−1.50710	−0.753552	+	0.657389i	$0.771661\pi$
$140$	0	0
$141$	−30.4370	−2.56326
$142$	−5.97632	−0.501522
$143$	32.0185	2.67752
$144$	−13.8208	−1.15174
$145$	0	0
$146$	7.46741	0.618008
$147$	14.3486	1.18345
$148$	0.314586	0.0258588
$149$	6.81227	0.558083	0.279041	−	0.960279i	$-0.409983\pi$
$149$	6.81227	0.558083	0.279041	+	0.960279i	$0.409983\pi$
$150$	0	0
$151$	9.49482	0.772677	0.386339	−	0.922357i	$-0.373740\pi$
$151$	9.49482	0.772677	0.386339	+	0.922357i	$0.373740\pi$
$152$	−12.0000	−0.973329
$153$	4.87421	0.394056
$154$	10.1224	0.815686
$155$	0	0
$156$	−11.0068	−0.881246
$157$	−1.44894	−0.115638	−0.0578191	−	0.998327i	$-0.518415\pi$
$157$	−1.44894	−0.115638	−0.0578191	+	0.998327i	$0.518415\pi$
$158$	−0.590379	−0.0469680
$159$	−30.5398	−2.42197
$160$	0	0
$161$	−7.88256	−0.621233
$162$	−12.1555	−0.955025
$163$	−5.89608	−0.461817	−0.230908	−	0.972976i	$-0.574170\pi$
$163$	−5.89608	−0.461817	−0.230908	+	0.972976i	$0.574170\pi$
$164$	2.24663	0.175432
$165$	0	0
$166$	4.09376	0.317737
$167$	18.8587	1.45933	0.729665	−	0.683805i	$-0.239676\pi$
$167$	18.8587	1.45933	0.729665	+	0.683805i	$0.239676\pi$
$168$	−14.0135	−1.08117
$169$	17.2872	1.32978
$170$	0	0
$171$	−24.0222	−1.83702
$172$	1.84377	0.140586
$173$	4.17347	0.317303	0.158652	−	0.987335i	$-0.449285\pi$
$173$	4.17347	0.317303	0.158652	+	0.987335i	$0.449285\pi$
$174$	22.9508	1.73990
$175$	0	0
$176$	13.0448	0.983293
$177$	12.5134	0.940561
$178$	−1.30287	−0.0976545
$179$	−19.5578	−1.46182	−0.730910	−	0.682474i	$-0.760904\pi$
$179$	−19.5578	−1.46182	−0.730910	+	0.682474i	$0.760904\pi$
$180$	0	0
$181$	−14.8555	−1.10420	−0.552100	−	0.833778i	$-0.686173\pi$
$181$	−14.8555	−1.10420	−0.552100	+	0.833778i	$0.686173\pi$
$182$	9.57506	0.709751
$183$	−36.4914	−2.69752
$184$	−16.1448	−1.19021
$185$	0	0
$186$	3.50338	0.256880
$187$	−4.60054	−0.336425
$188$	−6.64269	−0.484468
$189$	−14.3998	−1.04743
$190$	0	0
$191$	20.3825	1.47483	0.737414	−	0.675441i	$-0.236047\pi$
$191$	20.3825	1.47483	0.737414	+	0.675441i	$0.236047\pi$
$192$	−26.0594	−1.88067
$193$	11.1021	0.799148	0.399574	−	0.916701i	$-0.369158\pi$
$193$	11.1021	0.799148	0.399574	+	0.916701i	$0.369158\pi$
$194$	0.301069	0.0216155
$195$	0	0
$196$	3.13149	0.223678
$197$	2.49662	0.177877	0.0889384	−	0.996037i	$-0.471653\pi$
$197$	2.49662	0.177877	0.0889384	+	0.996037i	$0.471653\pi$
$198$	41.5031	2.94950
$199$	−6.01724	−0.426551	−0.213275	−	0.976992i	$-0.568413\pi$
$199$	−6.01724	−0.426551	−0.213275	+	0.976992i	$0.568413\pi$
$200$	0	0
$201$	5.50338	0.388178
$202$	0.729368	0.0513181
$203$	9.84872	0.691245
$204$	1.58149	0.110727
$205$	0	0
$206$	−12.4213	−0.865435
$207$	−32.3195	−2.24636
$208$	12.3395	0.855590
$209$	22.6734	1.56836
$210$	0	0
$211$	−18.8420	−1.29713	−0.648567	−	0.761157i	$-0.724631\pi$
$211$	−18.8420	−1.29713	−0.648567	+	0.761157i	$0.724631\pi$
$212$	−6.66514	−0.457764
$213$	−15.6327	−1.07114
$214$	−13.9662	−0.954707
$215$	0	0
$216$	−29.4932	−2.00676
$217$	1.50338	0.102056
$218$	−7.97420	−0.540081
$219$	19.5331	1.31992
$220$	0	0
$221$	−4.35178	−0.292733
$222$	−1.66817	−0.111960
$223$	−18.3895	−1.23145	−0.615725	−	0.787961i	$-0.711137\pi$
$223$	−18.3895	−1.23145	−0.615725	+	0.787961i	$0.711137\pi$
$224$	−5.35731	−0.357950
$225$	0	0
$226$	−3.55446	−0.236439
$227$	−16.5781	−1.10033	−0.550163	−	0.835057i	$-0.685435\pi$
$227$	−16.5781	−1.10033	−0.550163	+	0.835057i	$0.685435\pi$
$228$	−7.79429	−0.516189
$229$	21.5105	1.42145	0.710726	−	0.703469i	$-0.248367\pi$
$229$	21.5105	1.42145	0.710726	+	0.703469i	$0.248367\pi$
$230$	0	0
$231$	26.4779	1.74212
$232$	20.1719	1.32435
$233$	20.2909	1.32930	0.664651	−	0.747154i	$-0.268580\pi$
$233$	20.2909	1.32930	0.664651	+	0.747154i	$0.268580\pi$
$234$	39.2590	2.56644
$235$	0	0
$236$	2.73097	0.177771
$237$	−1.54430	−0.100313
$238$	−1.37578	−0.0891787
$239$	−3.63806	−0.235326	−0.117663	−	0.993054i	$-0.537540\pi$
$239$	−3.63806	−0.235326	−0.117663	+	0.993054i	$0.537540\pi$
$240$	0	0
$241$	9.12579	0.587844	0.293922	−	0.955829i	$-0.405039\pi$
$241$	9.12579	0.587844	0.293922	+	0.955829i	$0.405039\pi$
$242$	−26.4427	−1.69980
$243$	−3.06120	−0.196376
$244$	−7.96403	−0.509845
$245$	0	0
$246$	−11.9133	−0.759566
$247$	21.4475	1.36467
$248$	3.07918	0.195528
$249$	10.7084	0.678614
$250$	0	0
$251$	0.205712	0.0129845	0.00649223	−	0.999979i	$-0.497933\pi$
$251$	0.205712	0.0129845	0.00649223	+	0.999979i	$0.497933\pi$
$252$	−6.12239	−0.385674
$253$	30.5049	1.91783
$254$	9.23094	0.579201
$255$	0	0
$256$	−13.9354	−0.870960
$257$	−18.0286	−1.12460	−0.562298	−	0.826935i	$-0.690082\pi$
$257$	−18.0286	−1.12460	−0.562298	+	0.826935i	$0.690082\pi$
$258$	−9.77705	−0.608692
$259$	−0.715850	−0.0444808
$260$	0	0
$261$	40.3811	2.49952
$262$	−22.3773	−1.38248
$263$	16.3621	1.00893	0.504465	−	0.863432i	$-0.331690\pi$
$263$	16.3621	1.00893	0.504465	+	0.863432i	$0.331690\pi$
$264$	54.2313	3.33770
$265$	0	0
$266$	6.78045	0.415736
$267$	−3.40802	−0.208568
$268$	1.20108	0.0733676
$269$	−13.4674	−0.821123	−0.410561	−	0.911833i	$-0.634667\pi$
$269$	−13.4674	−0.821123	−0.410561	+	0.911833i	$0.634667\pi$
$270$	0	0
$271$	3.76353	0.228618	0.114309	−	0.993445i	$-0.463535\pi$
$271$	3.76353	0.228618	0.114309	+	0.993445i	$0.463535\pi$
$272$	−1.77299	−0.107503
$273$	25.0462	1.51586
$274$	−21.7190	−1.31209
$275$	0	0
$276$	−10.4865	−0.631211
$277$	−12.0254	−0.722537	−0.361269	−	0.932462i	$-0.617656\pi$
$277$	−12.0254	−0.722537	−0.361269	+	0.932462i	$0.617656\pi$
$278$	20.5633	1.23331
$279$	6.16405	0.369032
$280$	0	0
$281$	20.1487	1.20197	0.600986	−	0.799259i	$-0.294775\pi$
$281$	20.1487	1.20197	0.600986	+	0.799259i	$0.294775\pi$
$282$	35.2245	2.09759
$283$	2.46586	0.146580	0.0732901	−	0.997311i	$-0.476650\pi$
$283$	2.46586	0.146580	0.0732901	+	0.997311i	$0.476650\pi$
$284$	−3.41175	−0.202450
$285$	0	0
$286$	−37.0548	−2.19109
$287$	−5.11228	−0.301768
$288$	−21.9657	−1.29434
$289$	−16.3747	−0.963219
$290$	0	0
$291$	0.787529	0.0461658
$292$	4.26298	0.249472
$293$	−21.5083	−1.25653	−0.628265	−	0.777999i	$-0.716235\pi$
$293$	−21.5083	−1.25653	−0.628265	+	0.777999i	$0.716235\pi$
$294$	−16.6055	−0.968452
$295$	0	0
$296$	−1.46618	−0.0852202
$297$	55.7261	3.23356
$298$	−7.88379	−0.456696
$299$	28.8555	1.66876
$300$	0	0
$301$	−4.19555	−0.241828
$302$	−10.9883	−0.632305
$303$	1.90786	0.109604
$304$	8.73805	0.501161
$305$	0	0
$306$	−5.64089	−0.322468
$307$	−6.96956	−0.397774	−0.198887	−	0.980022i	$-0.563733\pi$
$307$	−6.96956	−0.397774	−0.198887	+	0.980022i	$0.563733\pi$
$308$	5.77864	0.329269
$309$	−32.4914	−1.84837
$310$	0	0
$311$	−3.70159	−0.209898	−0.104949	−	0.994478i	$-0.533468\pi$
$311$	−3.70159	−0.209898	−0.104949	+	0.994478i	$0.533468\pi$
$312$	51.2989	2.90423
$313$	−30.3944	−1.71800	−0.858998	−	0.511980i	$-0.828912\pi$
$313$	−30.3944	−1.71800	−0.858998	+	0.511980i	$0.828912\pi$
$314$	1.67685	0.0946302
$315$	0	0
$316$	−0.337034	−0.0189597
$317$	14.5409	0.816698	0.408349	−	0.912826i	$-0.366105\pi$
$317$	14.5409	0.816698	0.408349	+	0.912826i	$0.366105\pi$
$318$	35.3435	1.98197
$319$	−38.1138	−2.13396
$320$	0	0
$321$	−36.5323	−2.03904
$322$	9.12244	0.508374
$323$	−3.08166	−0.171468
$324$	−6.93929	−0.385516
$325$	0	0
$326$	6.82349	0.377918
$327$	−20.8587	−1.15349
$328$	−10.4708	−0.578154
$329$	15.1156	0.833352
$330$	0	0
$331$	−8.11744	−0.446175	−0.223087	−	0.974798i	$-0.571614\pi$
$331$	−8.11744	−0.446175	−0.223087	+	0.974798i	$0.571614\pi$
$332$	2.33703	0.128261
$333$	−2.93508	−0.160841
$334$	−21.8250	−1.19421
$335$	0	0
$336$	10.2042	0.556686
$337$	8.04414	0.438192	0.219096	−	0.975703i	$-0.429689\pi$
$337$	8.04414	0.438192	0.219096	+	0.975703i	$0.429689\pi$
$338$	−20.0063	−1.08820
$339$	−9.29767	−0.504980
$340$	0	0
$341$	−5.81797	−0.315061
$342$	27.8007	1.50329
$343$	−17.6494	−0.952981
$344$	−8.59321	−0.463315
$345$	0	0
$346$	−4.82993	−0.259659
$347$	−3.77705	−0.202762	−0.101381	−	0.994848i	$-0.532326\pi$
$347$	−3.77705	−0.202762	−0.101381	+	0.994848i	$0.532326\pi$
$348$	13.1021	0.702347
$349$	31.1927	1.66971	0.834853	−	0.550473i	$-0.185553\pi$
$349$	31.1927	1.66971	0.834853	+	0.550473i	$0.185553\pi$
$350$	0	0
$351$	52.7129	2.81361
$352$	20.7324	1.10504
$353$	−9.13931	−0.486436	−0.243218	−	0.969972i	$-0.578203\pi$
$353$	−9.13931	−0.486436	−0.243218	+	0.969972i	$0.578203\pi$
$354$	−14.4816	−0.769690
$355$	0	0
$356$	−0.743781	−0.0394203
$357$	−3.59874	−0.190465
$358$	22.6341	1.19625
$359$	−14.2516	−0.752170	−0.376085	−	0.926585i	$-0.622730\pi$
$359$	−14.2516	−0.752170	−0.376085	+	0.926585i	$0.622730\pi$
$360$	0	0
$361$	−3.81227	−0.200646
$362$	17.1921	0.903599
$363$	−69.1681	−3.63038
$364$	5.46618	0.286506
$365$	0	0
$366$	42.2313	2.20746
$367$	19.8434	1.03582	0.517908	−	0.855436i	$-0.326711\pi$
$367$	19.8434	1.03582	0.517908	+	0.855436i	$0.326711\pi$
$368$	11.7562	0.612834
$369$	−20.9610	−1.09119
$370$	0	0
$371$	15.1667	0.787417
$372$	2.00000	0.103695
$373$	6.50158	0.336639	0.168319	−	0.985733i	$-0.446166\pi$
$373$	6.50158	0.336639	0.168319	+	0.985733i	$0.446166\pi$
$374$	5.32417	0.275306
$375$	0	0
$376$	30.9594	1.59661
$377$	−36.0530	−1.85682
$378$	16.6648	0.857143
$379$	8.17453	0.419898	0.209949	−	0.977712i	$-0.432670\pi$
$379$	8.17453	0.419898	0.209949	+	0.977712i	$0.432670\pi$
$380$	0	0
$381$	24.1461	1.23704
$382$	−23.5886	−1.20690
$383$	13.3144	0.680334	0.340167	−	0.940365i	$-0.389516\pi$
$383$	13.3144	0.680334	0.340167	+	0.940365i	$0.389516\pi$
$384$	8.58330	0.438015
$385$	0	0
$386$	−12.8484	−0.653966
$387$	−17.2023	−0.874443
$388$	0.171874	0.00872556
$389$	26.6993	1.35371	0.676853	−	0.736118i	$-0.263343\pi$
$389$	26.6993	1.35371	0.676853	+	0.736118i	$0.263343\pi$
$390$	0	0
$391$	−4.14607	−0.209676
$392$	−14.5948	−0.737151
$393$	−58.5341	−2.95265
$394$	−2.88932	−0.145562
$395$	0	0
$396$	23.6932	1.19063
$397$	32.9078	1.65159	0.825797	−	0.563967i	$-0.190725\pi$
$397$	32.9078	1.65159	0.825797	+	0.563967i	$0.190725\pi$
$398$	6.96371	0.349059
$399$	17.7361	0.887917
$400$	0	0
$401$	−14.3183	−0.715022	−0.357511	−	0.933909i	$-0.616375\pi$
$401$	−14.3183	−0.715022	−0.357511	+	0.933909i	$0.616375\pi$
$402$	−6.36902	−0.317658
$403$	−5.50338	−0.274143
$404$	0.416379	0.0207157
$405$	0	0
$406$	−11.3979	−0.565666
$407$	2.77029	0.137318
$408$	−7.37083	−0.364910
$409$	−0.564575	−0.0279164	−0.0139582	−	0.999903i	$-0.504443\pi$
$409$	−0.564575	−0.0279164	−0.0139582	+	0.999903i	$0.504443\pi$
$410$	0	0
$411$	−56.8120	−2.80233
$412$	−7.09106	−0.349351
$413$	−6.21439	−0.305790
$414$	37.4032	1.83827
$415$	0	0
$416$	19.6114	0.961526
$417$	53.7891	2.63406
$418$	−26.2398	−1.28343
$419$	33.7745	1.64999	0.824996	−	0.565138i	$-0.191177\pi$
$419$	33.7745	1.64999	0.824996	+	0.565138i	$0.191177\pi$
$420$	0	0
$421$	−7.87990	−0.384043	−0.192021	−	0.981391i	$-0.561504\pi$
$421$	−7.87990	−0.384043	−0.192021	+	0.981391i	$0.561504\pi$
$422$	21.8057	1.06148
$423$	61.9761	3.01338
$424$	31.0640	1.50860
$425$	0	0
$426$	18.0916	0.876542
$427$	18.1224	0.877004
$428$	−7.97297	−0.385388
$429$	−96.9269	−4.67968
$430$	0	0
$431$	20.7591	0.999929	0.499964	−	0.866046i	$-0.333346\pi$
$431$	20.7591	0.999929	0.499964	+	0.866046i	$0.333346\pi$
$432$	21.4761	1.03327
$433$	−16.3539	−0.785919	−0.392959	−	0.919556i	$-0.628549\pi$
$433$	−16.3539	−0.785919	−0.392959	+	0.919556i	$0.628549\pi$
$434$	−1.73985	−0.0835155
$435$	0	0
$436$	−4.55229	−0.218015
$437$	20.4336	0.977473
$438$	−22.6055	−1.08013
$439$	−13.6062	−0.649390	−0.324695	−	0.945819i	$-0.605262\pi$
$439$	−13.6062	−0.649390	−0.324695	+	0.945819i	$0.605262\pi$
$440$	0	0
$441$	−29.2167	−1.39127
$442$	5.03629	0.239552
$443$	8.90497	0.423088	0.211544	−	0.977369i	$-0.432151\pi$
$443$	8.90497	0.423088	0.211544	+	0.977369i	$0.432151\pi$
$444$	−0.952322	−0.0451952
$445$	0	0
$446$	21.2820	1.00773
$447$	−20.6222	−0.975398
$448$	12.9416	0.611435
$449$	29.6359	1.39861	0.699303	−	0.714825i	$-0.253494\pi$
$449$	29.6359	1.39861	0.699303	+	0.714825i	$0.253494\pi$
$450$	0	0
$451$	19.7841	0.931598
$452$	−2.02916	−0.0954437
$453$	−28.7429	−1.35046
$454$	19.1857	0.900430
$455$	0	0
$456$	36.3266	1.70115
$457$	−32.2076	−1.50661	−0.753304	−	0.657673i	$-0.771541\pi$
$457$	−32.2076	−1.50661	−0.753304	+	0.657673i	$0.771541\pi$
$458$	−24.8939	−1.16322
$459$	−7.57399	−0.353524
$460$	0	0
$461$	10.4197	0.485295	0.242648	−	0.970114i	$-0.421984\pi$
$461$	10.4197	0.485295	0.242648	+	0.970114i	$0.421984\pi$
$462$	−30.6427	−1.42563
$463$	−12.9265	−0.600746	−0.300373	−	0.953822i	$-0.597111\pi$
$463$	−12.9265	−0.600746	−0.300373	+	0.953822i	$0.597111\pi$
$464$	−14.6886	−0.681899
$465$	0	0
$466$	−23.4825	−1.08781
$467$	−31.3807	−1.45213	−0.726064	−	0.687627i	$-0.758652\pi$
$467$	−31.3807	−1.45213	−0.726064	+	0.687627i	$0.758652\pi$
$468$	22.4121	1.03600
$469$	−2.73309	−0.126202
$470$	0	0
$471$	4.38627	0.202108
$472$	−12.7281	−0.585860
$473$	16.2365	0.746554
$474$	1.78721	0.0820891
$475$	0	0
$476$	−0.785403	−0.0359989
$477$	62.1855	2.84728
$478$	4.21030	0.192575
$479$	−3.99144	−0.182373	−0.0911867	−	0.995834i	$-0.529066\pi$
$479$	−3.99144	−0.182373	−0.0911867	+	0.995834i	$0.529066\pi$
$480$	0	0
$481$	2.62049	0.119484
$482$	−10.5612	−0.481050
$483$	23.8622	1.08577
$484$	−15.0955	−0.686160
$485$	0	0
$486$	3.54270	0.160700
$487$	23.0457	1.04430	0.522150	−	0.852854i	$-0.325130\pi$
$487$	23.0457	1.04430	0.522150	+	0.852854i	$0.325130\pi$
$488$	37.1178	1.68024
$489$	17.8487	0.807147
$490$	0	0
$491$	43.3807	1.95775	0.978873	−	0.204471i	$-0.0655474\pi$
$491$	43.3807	1.95775	0.978873	+	0.204471i	$0.0655474\pi$
$492$	−6.80105	−0.306615
$493$	5.18023	0.233306
$494$	−24.8210	−1.11675
$495$	0	0
$496$	−2.24217	−0.100676
$497$	7.76353	0.348242
$498$	−12.3927	−0.555330
$499$	19.4695	0.871576	0.435788	−	0.900049i	$-0.356470\pi$
$499$	19.4695	0.871576	0.435788	+	0.900049i	$0.356470\pi$
$500$	0	0
$501$	−57.0894	−2.55057
$502$	−0.238070	−0.0106256
$503$	−6.18203	−0.275643	−0.137822	−	0.990457i	$-0.544010\pi$
$503$	−6.18203	−0.275643	−0.137822	+	0.990457i	$0.544010\pi$
$504$	28.5345	1.27103
$505$	0	0
$506$	−35.3031	−1.56942
$507$	−52.3321	−2.32415
$508$	5.26974	0.233807
$509$	2.18859	0.0970074	0.0485037	−	0.998823i	$-0.484555\pi$
$509$	2.18859	0.0970074	0.0485037	+	0.998823i	$0.484555\pi$
$510$	0	0
$511$	−9.70053	−0.429126
$512$	21.7981	0.963347
$513$	37.3279	1.64807
$514$	20.8644	0.920290
$515$	0	0
$516$	−5.58149	−0.245712
$517$	−58.4964	−2.57267
$518$	0.828449	0.0363999
$519$	−12.6340	−0.554572
$520$	0	0
$521$	−38.0309	−1.66617	−0.833083	−	0.553149i	$-0.813426\pi$
$521$	−38.0309	−1.66617	−0.833083	+	0.553149i	$0.813426\pi$
$522$	−46.7327	−2.04544
$523$	20.0921	0.878568	0.439284	−	0.898348i	$-0.355232\pi$
$523$	20.0921	0.878568	0.439284	+	0.898348i	$0.355232\pi$
$524$	−12.7747	−0.558066
$525$	0	0
$526$	−18.9357	−0.825637
$527$	0.790747	0.0344455
$528$	−39.4896	−1.71856
$529$	4.49146	0.195281
$530$	0	0
$531$	−25.4798	−1.10573
$532$	3.87080	0.167821
$533$	18.7144	0.810609
$534$	3.94408	0.170677
$535$	0	0
$536$	−5.59784	−0.241790
$537$	59.2058	2.55492
$538$	15.5857	0.671949
$539$	27.5763	1.18779
$540$	0	0
$541$	31.1291	1.33835	0.669173	−	0.743106i	$-0.266648\pi$
$541$	31.1291	1.33835	0.669173	+	0.743106i	$0.266648\pi$
$542$	−4.35551	−0.187085
$543$	44.9708	1.92988
$544$	−2.81784	−0.120814
$545$	0	0
$546$	−28.9858	−1.24048
$547$	−25.2955	−1.08156	−0.540780	−	0.841164i	$-0.681871\pi$
$547$	−25.2955	−1.08156	−0.540780	+	0.841164i	$0.681871\pi$
$548$	−12.3989	−0.529654
$549$	74.3042	3.17122
$550$	0	0
$551$	−25.5304	−1.08763
$552$	48.8740	2.08021
$553$	0.766931	0.0326132
$554$	13.9169	0.591274
$555$	0	0
$556$	11.7391	0.497851
$557$	−20.5016	−0.868680	−0.434340	−	0.900749i	$-0.643018\pi$
$557$	−20.5016	−0.868680	−0.434340	+	0.900749i	$0.643018\pi$
$558$	−7.13362	−0.301990
$559$	15.3585	0.649597
$560$	0	0
$561$	13.9268	0.587992
$562$	−23.3180	−0.983610
$563$	−31.1464	−1.31266	−0.656332	−	0.754472i	$-0.727893\pi$
$563$	−31.1464	−1.31266	−0.656332	+	0.754472i	$0.727893\pi$
$564$	20.1089	0.846736
$565$	0	0
$566$	−2.85372	−0.119951
$567$	15.7906	0.663141
$568$	15.9010	0.667193
$569$	−19.7722	−0.828894	−0.414447	−	0.910073i	$-0.636025\pi$
$569$	−19.7722	−0.828894	−0.414447	+	0.910073i	$0.636025\pi$
$570$	0	0
$571$	−47.2143	−1.97586	−0.987929	−	0.154905i	$-0.950493\pi$
$571$	−47.2143	−1.97586	−0.987929	+	0.154905i	$0.950493\pi$
$572$	−21.1537	−0.884482
$573$	−61.7024	−2.57765
$574$	5.91640	0.246946
$575$	0	0
$576$	53.0624	2.21093
$577$	3.65961	0.152352	0.0761758	−	0.997094i	$-0.475729\pi$
$577$	3.65961	0.152352	0.0761758	+	0.997094i	$0.475729\pi$
$578$	18.9504	0.788231
$579$	−33.6085	−1.39672
$580$	0	0
$581$	−5.31799	−0.220627
$582$	−0.911402	−0.0377788
$583$	−58.6940	−2.43086
$584$	−19.8683	−0.822158
$585$	0	0
$586$	24.8914	1.02826
$587$	−16.3318	−0.674087	−0.337043	−	0.941489i	$-0.609427\pi$
$587$	−16.3318	−0.674087	−0.337043	+	0.941489i	$0.609427\pi$
$588$	−9.47970	−0.390936
$589$	−3.89714	−0.160579
$590$	0	0
$591$	−7.55782	−0.310887
$592$	1.06763	0.0438794
$593$	−5.43022	−0.222992	−0.111496	−	0.993765i	$-0.535564\pi$
$593$	−5.43022	−0.222992	−0.111496	+	0.993765i	$0.535564\pi$
$594$	−64.4914	−2.64611
$595$	0	0
$596$	−4.50068	−0.184355
$597$	18.2155	0.745511
$598$	−33.3943	−1.36559
$599$	−2.10392	−0.0859638	−0.0429819	−	0.999076i	$-0.513686\pi$
$599$	−2.10392	−0.0859638	−0.0429819	+	0.999076i	$0.513686\pi$
$600$	0	0
$601$	−15.7383	−0.641977	−0.320988	−	0.947083i	$-0.604015\pi$
$601$	−15.7383	−0.641977	−0.320988	+	0.947083i	$0.604015\pi$
$602$	4.85548	0.197895
$603$	−11.2060	−0.456345
$604$	−6.27296	−0.255243
$605$	0	0
$606$	−2.20796	−0.0896920
$607$	21.1329	0.857757	0.428878	−	0.903362i	$-0.358909\pi$
$607$	21.1329	0.857757	0.428878	+	0.903362i	$0.358909\pi$
$608$	13.8875	0.563213
$609$	−29.8142	−1.20813
$610$	0	0
$611$	−55.3334	−2.23855
$612$	−3.22025	−0.130171
$613$	33.0764	1.33595	0.667973	−	0.744186i	$-0.267162\pi$
$613$	33.0764	1.33595	0.667973	+	0.744186i	$0.267162\pi$
$614$	8.06583	0.325510
$615$	0	0
$616$	−26.9324	−1.08514
$617$	37.2841	1.50100	0.750502	−	0.660869i	$-0.229812\pi$
$617$	37.2841	1.50100	0.750502	+	0.660869i	$0.229812\pi$
$618$	37.6021	1.51258
$619$	19.3149	0.776332	0.388166	−	0.921590i	$-0.373109\pi$
$619$	19.3149	0.776332	0.388166	+	0.921590i	$0.373109\pi$
$620$	0	0
$621$	50.2211	2.01530
$622$	4.28383	0.171766
$623$	1.69249	0.0678084
$624$	−37.3543	−1.49537
$625$	0	0
$626$	35.1753	1.40589
$627$	−68.6375	−2.74112
$628$	0.957276	0.0381995
$629$	−0.376523	−0.0150129
$630$	0	0
$631$	−2.35055	−0.0935740	−0.0467870	−	0.998905i	$-0.514898\pi$
$631$	−2.35055	−0.0935740	−0.0467870	+	0.998905i	$0.514898\pi$
$632$	1.57081	0.0624833
$633$	57.0387	2.26709
$634$	−16.8281	−0.668328
$635$	0	0
$636$	20.1768	0.800063
$637$	26.0852	1.03353
$638$	44.1089	1.74629
$639$	31.8315	1.25923
$640$	0	0
$641$	−24.4370	−0.965203	−0.482601	−	0.875840i	$-0.660308\pi$
$641$	−24.4370	−0.965203	−0.482601	+	0.875840i	$0.660308\pi$
$642$	42.2786	1.66860
$643$	43.0829	1.69902	0.849512	−	0.527570i	$-0.176897\pi$
$643$	43.0829	1.69902	0.849512	+	0.527570i	$0.176897\pi$
$644$	5.20779	0.205216
$645$	0	0
$646$	3.56638	0.140317
$647$	30.6530	1.20509	0.602547	−	0.798084i	$-0.294153\pi$
$647$	30.6530	1.20509	0.602547	+	0.798084i	$0.294153\pi$
$648$	32.3418	1.27050
$649$	24.0492	0.944015
$650$	0	0
$651$	−4.55106	−0.178370
$652$	3.89538	0.152555
$653$	−19.6245	−0.767968	−0.383984	−	0.923340i	$-0.625448\pi$
$653$	−19.6245	−0.767968	−0.383984	+	0.923340i	$0.625448\pi$
$654$	24.1396	0.943934
$655$	0	0
$656$	7.62454	0.297688
$657$	−39.7734	−1.55171
$658$	−17.4932	−0.681957
$659$	24.7031	0.962298	0.481149	−	0.876639i	$-0.340220\pi$
$659$	24.7031	0.962298	0.481149	+	0.876639i	$0.340220\pi$
$660$	0	0
$661$	39.1146	1.52138	0.760690	−	0.649115i	$-0.224861\pi$
$661$	39.1146	1.52138	0.760690	+	0.649115i	$0.224861\pi$
$662$	9.39425	0.365118
$663$	13.1738	0.511628
$664$	−10.8922	−0.422697
$665$	0	0
$666$	3.39675	0.131621
$667$	−34.3487	−1.32999
$668$	−12.4594	−0.482070
$669$	55.6690	2.15229
$670$	0	0
$671$	−70.1323	−2.70743
$672$	16.2177	0.625613
$673$	48.2825	1.86115	0.930576	−	0.366098i	$-0.119306\pi$
$673$	48.2825	1.86115	0.930576	+	0.366098i	$0.119306\pi$
$674$	−9.30943	−0.358586
$675$	0	0
$676$	−11.4212	−0.439276
$677$	−39.4519	−1.51626	−0.758130	−	0.652103i	$-0.773887\pi$
$677$	−39.4519	−1.51626	−0.758130	+	0.652103i	$0.773887\pi$
$678$	10.7601	0.413240
$679$	−0.391103	−0.0150092
$680$	0	0
$681$	50.1855	1.92311
$682$	6.73309	0.257823
$683$	−18.5667	−0.710435	−0.355218	−	0.934784i	$-0.615593\pi$
$683$	−18.5667	−0.710435	−0.355218	+	0.934784i	$0.615593\pi$
$684$	15.8708	0.606835
$685$	0	0
$686$	20.4256	0.779853
$687$	−65.1169	−2.48436
$688$	6.25732	0.238558
$689$	−55.5204	−2.11516
$690$	0	0
$691$	−22.5112	−0.856366	−0.428183	−	0.903692i	$-0.640846\pi$
$691$	−22.5112	−0.856366	−0.428183	+	0.903692i	$0.640846\pi$
$692$	−2.75730	−0.104817
$693$	−53.9146	−2.04804
$694$	4.37115	0.165927
$695$	0	0
$696$	−61.0647	−2.31465
$697$	−2.68895	−0.101851
$698$	−36.0991	−1.36637
$699$	−61.4250	−2.32331
$700$	0	0
$701$	−14.4256	−0.544847	−0.272423	−	0.962177i	$-0.587825\pi$
$701$	−14.4256	−0.544847	−0.272423	+	0.962177i	$0.587825\pi$
$702$	−61.0043	−2.30246
$703$	1.85567	0.0699878
$704$	−50.0832	−1.88758
$705$	0	0
$706$	10.5769	0.398065
$707$	−0.947483	−0.0356338
$708$	−8.26723	−0.310702
$709$	18.4914	0.694460	0.347230	−	0.937780i	$-0.387122\pi$
$709$	18.4914	0.694460	0.347230	+	0.937780i	$0.387122\pi$
$710$	0	0
$711$	3.14452	0.117929
$712$	3.46652	0.129913
$713$	−5.24323	−0.196361
$714$	4.16479	0.155863
$715$	0	0
$716$	12.9213	0.482892
$717$	11.0132	0.411295
$718$	16.4933	0.615523
$719$	−20.0185	−0.746563	−0.373282	−	0.927718i	$-0.621767\pi$
$719$	−20.0185	−0.746563	−0.373282	+	0.927718i	$0.621767\pi$
$720$	0	0
$721$	16.1359	0.600933
$722$	4.41191	0.164194
$723$	−27.6258	−1.02741
$724$	9.81461	0.364757
$725$	0	0
$726$	80.0477	2.97085
$727$	9.09355	0.337261	0.168631	−	0.985679i	$-0.446066\pi$
$727$	9.09355	0.337261	0.168631	+	0.985679i	$0.446066\pi$
$728$	−25.4761	−0.944207
$729$	−22.2432	−0.823823
$730$	0	0
$731$	−2.20678	−0.0816205
$732$	24.1089	0.891090
$733$	−31.8896	−1.17787	−0.588935	−	0.808180i	$-0.700453\pi$
$733$	−31.8896	−1.17787	−0.588935	+	0.808180i	$0.700453\pi$
$734$	−22.9646	−0.847639
$735$	0	0
$736$	18.6843	0.688713
$737$	10.5769	0.389604
$738$	24.2580	0.892950
$739$	9.44374	0.347393	0.173697	−	0.984799i	$-0.444429\pi$
$739$	9.44374	0.347393	0.173697	+	0.984799i	$0.444429\pi$
$740$	0	0
$741$	−64.9261	−2.38512
$742$	−17.5523	−0.644366
$743$	−0.105011	−0.00385249	−0.00192625	−	0.999998i	$-0.500613\pi$
$743$	−0.105011	−0.00385249	−0.00192625	+	0.999998i	$0.500613\pi$
$744$	−9.32134	−0.341737
$745$	0	0
$746$	−7.52423	−0.275482
$747$	−21.8044	−0.797783
$748$	3.03945	0.111133
$749$	18.1427	0.662920
$750$	0	0
$751$	−31.1156	−1.13543	−0.567713	−	0.823227i	$-0.692172\pi$
$751$	−31.1156	−1.13543	−0.567713	+	0.823227i	$0.692172\pi$
$752$	−22.5437	−0.822085
$753$	−0.622736	−0.0226938
$754$	41.7238	1.51949
$755$	0	0
$756$	9.51354	0.346004
$757$	−28.8485	−1.04852	−0.524259	−	0.851559i	$-0.675658\pi$
$757$	−28.8485	−1.04852	−0.524259	+	0.851559i	$0.675658\pi$
$758$	−9.46033	−0.343615
$759$	−92.3451	−3.35191
$760$	0	0
$761$	2.77897	0.100737	0.0503687	−	0.998731i	$-0.483960\pi$
$761$	2.77897	0.100737	0.0503687	+	0.998731i	$0.483960\pi$
$762$	−27.9441	−1.01231
$763$	10.3589	0.375016
$764$	−13.4662	−0.487189
$765$	0	0
$766$	−15.4087	−0.556738
$767$	22.7489	0.821413
$768$	42.1854	1.52223
$769$	−12.8258	−0.462510	−0.231255	−	0.972893i	$-0.574283\pi$
$769$	−12.8258	−0.462510	−0.231255	+	0.972893i	$0.574283\pi$
$770$	0	0
$771$	54.5766	1.96553
$772$	−7.33486	−0.263987
$773$	12.5760	0.452326	0.226163	−	0.974089i	$-0.427382\pi$
$773$	12.5760	0.452326	0.226163	+	0.974089i	$0.427382\pi$
$774$	19.9081	0.715582
$775$	0	0
$776$	−0.801046	−0.0287559
$777$	2.16704	0.0777420
$778$	−30.8989	−1.10778
$779$	13.2523	0.474814
$780$	0	0
$781$	−30.0443	−1.07507
$782$	4.79822	0.171584
$783$	−62.7478	−2.24242
$784$	10.6275	0.379555
$785$	0	0
$786$	67.7411	2.41624
$787$	−13.5599	−0.483360	−0.241680	−	0.970356i	$-0.577698\pi$
$787$	−13.5599	−0.483360	−0.241680	+	0.970356i	$0.577698\pi$
$788$	−1.64945	−0.0587592
$789$	−49.5316	−1.76337
$790$	0	0
$791$	4.61741	0.164176
$792$	−110.426	−3.92383
$793$	−66.3401	−2.35581
$794$	−38.0840	−1.35155
$795$	0	0
$796$	3.97543	0.140905
$797$	−11.4265	−0.404747	−0.202374	−	0.979308i	$-0.564866\pi$
$797$	−11.4265	−0.404747	−0.202374	+	0.979308i	$0.564866\pi$
$798$	−20.5259	−0.726609
$799$	7.95052	0.281269
$800$	0	0
$801$	6.93945	0.245193
$802$	16.5705	0.585124
$803$	37.5403	1.32477
$804$	−3.63593	−0.128229
$805$	0	0
$806$	6.36902	0.224339
$807$	40.7688	1.43513
$808$	−1.94061	−0.0682704
$809$	−14.5695	−0.512237	−0.256119	−	0.966645i	$-0.582444\pi$
$809$	−14.5695	−0.512237	−0.256119	+	0.966645i	$0.582444\pi$
$810$	0	0
$811$	34.0727	1.19646	0.598228	−	0.801326i	$-0.295872\pi$
$811$	34.0727	1.19646	0.598228	+	0.801326i	$0.295872\pi$
$812$	−6.50678	−0.228343
$813$	−11.3930	−0.399571
$814$	−3.20603	−0.112371
$815$	0	0
$816$	5.36722	0.187890
$817$	10.8759	0.380501
$818$	0.653379	0.0228449
$819$	−50.9993	−1.78206
$820$	0	0
$821$	9.41547	0.328602	0.164301	−	0.986410i	$-0.447463\pi$
$821$	9.41547	0.328602	0.164301	+	0.986410i	$0.447463\pi$
$822$	65.7482	2.29323
$823$	46.2247	1.61129	0.805646	−	0.592398i	$-0.201819\pi$
$823$	46.2247	1.61129	0.805646	+	0.592398i	$0.201819\pi$
$824$	33.0491	1.15132
$825$	0	0
$826$	7.19187	0.250237
$827$	27.9301	0.971223	0.485612	−	0.874175i	$-0.338597\pi$
$827$	27.9301	0.971223	0.485612	+	0.874175i	$0.338597\pi$
$828$	21.3526	0.742055
$829$	−27.8672	−0.967868	−0.483934	−	0.875105i	$-0.660792\pi$
$829$	−27.8672	−0.967868	−0.483934	+	0.875105i	$0.660792\pi$
$830$	0	0
$831$	36.4036	1.26283
$832$	−47.3751	−1.64244
$833$	−3.74802	−0.129861
$834$	−62.2497	−2.15553
$835$	0	0
$836$	−14.9797	−0.518085
$837$	−9.57828	−0.331074
$838$	−39.0870	−1.35024
$839$	−11.5007	−0.397049	−0.198524	−	0.980096i	$-0.563615\pi$
$839$	−11.5007	−0.397049	−0.198524	+	0.980096i	$0.563615\pi$
$840$	0	0
$841$	13.9164	0.479874
$842$	9.11936	0.314274
$843$	−60.9946	−2.10077
$844$	12.4484	0.428491
$845$	0	0
$846$	−71.7245	−2.46594
$847$	34.3503	1.18029
$848$	−22.6199	−0.776771
$849$	−7.46470	−0.256188
$850$	0	0
$851$	2.49662	0.0855831
$852$	10.3281	0.353835
$853$	18.6886	0.639884	0.319942	−	0.947437i	$-0.396337\pi$
$853$	18.6886	0.639884	0.319942	+	0.947437i	$0.396337\pi$
$854$	−20.9729	−0.717679
$855$	0	0
$856$	37.1594	1.27008
$857$	−13.0030	−0.444175	−0.222088	−	0.975027i	$-0.571287\pi$
$857$	−13.0030	−0.444175	−0.222088	+	0.975027i	$0.571287\pi$
$858$	112.173	3.82952
$859$	10.1649	0.346822	0.173411	−	0.984850i	$-0.444521\pi$
$859$	10.1649	0.346822	0.173411	+	0.984850i	$0.444521\pi$
$860$	0	0
$861$	15.4760	0.527420
$862$	−24.0243	−0.818272
$863$	19.5644	0.665980	0.332990	−	0.942930i	$-0.391943\pi$
$863$	19.5644	0.665980	0.332990	+	0.942930i	$0.391943\pi$
$864$	34.1323	1.16120
$865$	0	0
$866$	18.9263	0.643141
$867$	49.5699	1.68348
$868$	−0.993241	−0.0337128
$869$	−2.96797	−0.100681
$870$	0	0
$871$	10.0050	0.339005
$872$	21.2167	0.718489
$873$	−1.60357	−0.0542728
$874$	−23.6477	−0.799895
$875$	0	0
$876$	−12.9050	−0.436018
$877$	−4.01724	−0.135653	−0.0678263	−	0.997697i	$-0.521606\pi$
$877$	−4.01724	−0.135653	−0.0678263	+	0.997697i	$0.521606\pi$
$878$	15.7464	0.531415
$879$	65.1104	2.19612
$880$	0	0
$881$	37.5578	1.26535	0.632677	−	0.774415i	$-0.281956\pi$
$881$	37.5578	1.26535	0.632677	+	0.774415i	$0.281956\pi$
$882$	33.8123	1.13852
$883$	56.2567	1.89319	0.946594	−	0.322428i	$-0.104499\pi$
$883$	56.2567	1.89319	0.946594	+	0.322428i	$0.104499\pi$
$884$	2.87510	0.0967002
$885$	0	0
$886$	−10.3057	−0.346225
$887$	10.7208	0.359969	0.179985	−	0.983669i	$-0.442395\pi$
$887$	10.7208	0.359969	0.179985	+	0.983669i	$0.442395\pi$
$888$	4.43846	0.148945
$889$	−11.9914	−0.402180
$890$	0	0
$891$	−61.1083	−2.04721
$892$	12.1494	0.406793
$893$	−39.1836	−1.31123
$894$	23.8660	0.798197
$895$	0	0
$896$	−4.26264	−0.142405
$897$	−87.3519	−2.91659
$898$	−34.2975	−1.14452
$899$	6.55106	0.218490
$900$	0	0
$901$	7.97739	0.265765
$902$	−22.8960	−0.762355
$903$	12.7009	0.422658
$904$	9.45725	0.314544
$905$	0	0
$906$	33.2639	1.10512
$907$	29.1377	0.967502	0.483751	−	0.875206i	$-0.339274\pi$
$907$	29.1377	0.967502	0.483751	+	0.875206i	$0.339274\pi$
$908$	10.9527	0.363478
$909$	−3.88481	−0.128851
$910$	0	0
$911$	58.8642	1.95026	0.975128	−	0.221641i	$-0.0711413\pi$
$911$	58.8642	1.95026	0.975128	+	0.221641i	$0.0711413\pi$
$912$	−26.4520	−0.875912
$913$	20.5802	0.681106
$914$	37.2736	1.23290
$915$	0	0
$916$	−14.2114	−0.469557
$917$	29.0692	0.959951
$918$	8.76533	0.289299
$919$	−24.9174	−0.821950	−0.410975	−	0.911647i	$-0.634812\pi$
$919$	−24.9174	−0.821950	−0.410975	+	0.911647i	$0.634812\pi$
$920$	0	0
$921$	21.0984	0.695216
$922$	−12.0587	−0.397132
$923$	−28.4197	−0.935447
$924$	−17.4932	−0.575485
$925$	0	0
$926$	14.9598	0.491609
$927$	66.1593	2.17296
$928$	−23.3448	−0.766330
$929$	5.29431	0.173701	0.0868503	−	0.996221i	$-0.472320\pi$
$929$	5.29431	0.173701	0.0868503	+	0.996221i	$0.472320\pi$
$930$	0	0
$931$	18.4719	0.605391
$932$	−13.4056	−0.439117
$933$	11.2055	0.366853
$934$	36.3167	1.18832
$935$	0	0
$936$	−104.455	−3.41423
$937$	−34.3745	−1.12297	−0.561483	−	0.827488i	$-0.689769\pi$
$937$	−34.3745	−1.12297	−0.561483	+	0.827488i	$0.689769\pi$
$938$	3.16299	0.103275
$939$	92.0106	3.00265
$940$	0	0
$941$	−33.2159	−1.08281	−0.541404	−	0.840762i	$-0.682107\pi$
$941$	−33.2159	−1.08281	−0.541404	+	0.840762i	$0.682107\pi$
$942$	−5.07619	−0.165391
$943$	17.8297	0.580616
$944$	9.26825	0.301656
$945$	0	0
$946$	−18.7904	−0.610927
$947$	41.4168	1.34587	0.672933	−	0.739703i	$-0.265034\pi$
$947$	41.4168	1.34587	0.672933	+	0.739703i	$0.265034\pi$
$948$	1.02028	0.0331370
$949$	35.5105	1.15272
$950$	0	0
$951$	−44.0185	−1.42740
$952$	3.66051	0.118638
$953$	9.70375	0.314335	0.157168	−	0.987572i	$-0.449764\pi$
$953$	9.70375	0.314335	0.157168	+	0.987572i	$0.449764\pi$
$954$	−71.9669	−2.33001
$955$	0	0
$956$	2.40356	0.0777368
$957$	115.379	3.72967
$958$	4.61926	0.149242
$959$	28.2140	0.911078
$960$	0	0
$961$	1.00000	0.0322581
$962$	−3.03268	−0.0977775
$963$	74.3875	2.39710
$964$	−6.02916	−0.194186
$965$	0	0
$966$	−27.6156	−0.888518
$967$	49.4179	1.58917	0.794587	−	0.607151i	$-0.207688\pi$
$967$	49.4179	1.58917	0.794587	+	0.607151i	$0.207688\pi$
$968$	70.3553	2.26130
$969$	9.32884	0.299686
$970$	0	0
$971$	−20.3190	−0.652068	−0.326034	−	0.945358i	$-0.605712\pi$
$971$	−20.3190	−0.652068	−0.326034	+	0.945358i	$0.605712\pi$
$972$	2.02245	0.0648700
$973$	−26.7128	−0.856372
$974$	−26.6706	−0.854582
$975$	0	0
$976$	−27.0281	−0.865147
$977$	−39.9884	−1.27934	−0.639670	−	0.768649i	$-0.720929\pi$
$977$	−39.9884	−1.27934	−0.639670	+	0.768649i	$0.720929\pi$
$978$	−20.6562	−0.660513
$979$	−6.54983	−0.209333
$980$	0	0
$981$	42.4727	1.35605
$982$	−50.2042	−1.60208
$983$	−53.7432	−1.71414	−0.857071	−	0.515198i	$-0.827718\pi$
$983$	−53.7432	−1.71414	−0.857071	+	0.515198i	$0.827718\pi$
$984$	31.6974	1.01048
$985$	0	0
$986$	−5.99505	−0.190921
$987$	−45.7583	−1.45650
$988$	−14.1697	−0.450800
$989$	14.6325	0.465287
$990$	0	0
$991$	17.1169	0.543735	0.271868	−	0.962335i	$-0.412359\pi$
$991$	17.1169	0.543735	0.271868	+	0.962335i	$0.412359\pi$
$992$	−3.56351	−0.113142
$993$	24.5733	0.779809
$994$	−8.98468	−0.284977
$995$	0	0
$996$	−7.07471	−0.224171
$997$	56.2433	1.78124	0.890622	−	0.454745i	$-0.150270\pi$
$997$	56.2433	1.78124	0.890622	+	0.454745i	$0.150270\pi$
$998$	−22.5320	−0.713237
$999$	4.56080	0.144297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.g.1.2		4
3.2	odd	2		6975.2.a.bj.1.3		4
5.2	odd	4		775.2.b.e.249.4		8
5.3	odd	4		775.2.b.e.249.5		8
5.4	even	2		155.2.a.d.1.3	✓	4
15.14	odd	2		1395.2.a.m.1.2		4
20.19	odd	2		2480.2.a.z.1.1		4
35.34	odd	2		7595.2.a.q.1.3		4
40.19	odd	2		9920.2.a.cd.1.4		4
40.29	even	2		9920.2.a.ch.1.1		4
155.154	odd	2		4805.2.a.j.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.d.1.3	✓	4	5.4	even	2
775.2.a.g.1.2		4	1.1	even	1	trivial
775.2.b.e.249.4		8	5.2	odd	4
775.2.b.e.249.5		8	5.3	odd	4
1395.2.a.m.1.2		4	15.14	odd	2
2480.2.a.z.1.1		4	20.19	odd	2
4805.2.a.j.1.3		4	155.154	odd	2
6975.2.a.bj.1.3		4	3.2	odd	2
7595.2.a.q.1.3		4	35.34	odd	2
9920.2.a.cd.1.4		4	40.19	odd	2
9920.2.a.ch.1.1		4	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q-1.15729 q^{2} -3.02722 q^{3} -0.660672 q^{4} +3.50338 q^{6} +1.50338 q^{7} +3.07918 q^{8} +6.16405 q^{9} +O(q^{10})\)	\(q-1.15729 q^{2} -3.02722 q^{3} -0.660672 q^{4} +3.50338 q^{6} +1.50338 q^{7} +3.07918 q^{8} +6.16405 q^{9} -5.81797 q^{11} +2.00000 q^{12} -5.50338 q^{13} -1.73985 q^{14} -2.24217 q^{16} +0.790747 q^{17} -7.13362 q^{18} -3.89714 q^{19} -4.55106 q^{21} +6.73309 q^{22} -5.24323 q^{23} -9.32134 q^{24} +6.36902 q^{26} -9.57828 q^{27} -0.993241 q^{28} +6.55106 q^{29} +1.00000 q^{31} -3.56351 q^{32} +17.6123 q^{33} -0.915126 q^{34} -4.07242 q^{36} -0.476161 q^{37} +4.51014 q^{38} +16.6599 q^{39} -3.40052 q^{41} +5.26691 q^{42} -2.79075 q^{43} +3.84377 q^{44} +6.06795 q^{46} +10.0544 q^{47} +6.78753 q^{48} -4.73985 q^{49} -2.39376 q^{51} +3.63593 q^{52} +10.0884 q^{53} +11.0849 q^{54} +4.62917 q^{56} +11.7975 q^{57} -7.58149 q^{58} -4.13362 q^{59} +12.0544 q^{61} -1.15729 q^{62} +9.26691 q^{63} +8.60836 q^{64} -20.3825 q^{66} -1.81797 q^{67} -0.522425 q^{68} +15.8724 q^{69} +5.16405 q^{71} +18.9802 q^{72} -6.45248 q^{73} +0.551058 q^{74} +2.57474 q^{76} -8.74661 q^{77} -19.2804 q^{78} +0.510138 q^{79} +10.5034 q^{81} +3.93540 q^{82} -3.53736 q^{83} +3.00676 q^{84} +3.22971 q^{86} -19.8315 q^{87} -17.9146 q^{88} +1.12579 q^{89} -8.27367 q^{91} +3.46406 q^{92} -3.02722 q^{93} -11.6359 q^{94} +10.7875 q^{96} -0.260149 q^{97} +5.48540 q^{98} -35.8622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9	\( 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9} - 6 q^{11} + 8 q^{12} - 16 q^{13} + 8 q^{14} + 11 q^{16} - q^{17} + q^{18} + 5 q^{19} + 2 q^{21} + 24 q^{22} - 14 q^{24} - 12 q^{26} - 5 q^{27} - 16 q^{28} + 6 q^{29} + 4 q^{31} + 29 q^{32} + 12 q^{33} - 18 q^{34} - 25 q^{36} - 9 q^{37} - 6 q^{39} + 13 q^{41} + 24 q^{42} - 7 q^{43} + 20 q^{44} - 26 q^{46} + 14 q^{47} - 2 q^{48} - 4 q^{49} + 5 q^{51} - 20 q^{52} - 11 q^{53} + 30 q^{54} - 4 q^{56} + 31 q^{57} - 22 q^{58} + 13 q^{59} + 22 q^{61} + q^{62} + 40 q^{63} + 47 q^{64} - 20 q^{66} + 10 q^{67} - 30 q^{68} + 20 q^{69} + 3 q^{71} - 19 q^{72} - 9 q^{73} - 18 q^{74} + 14 q^{76} - 8 q^{77} - 56 q^{78} - 16 q^{79} + 36 q^{81} - 6 q^{82} + 17 q^{83} + 16 q^{86} - 38 q^{87} + 44 q^{88} - 12 q^{89} - 24 q^{91} + 10 q^{92} + q^{93} - 12 q^{94} + 14 q^{96} - 16 q^{97} - 19 q^{98} - 52 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9 - 6 * q^11 + 8 * q^12 - 16 * q^13 + 8 * q^14 + 11 * q^16 - q^17 + q^18 + 5 * q^19 + 2 * q^21 + 24 * q^22 - 14 * q^24 - 12 * q^26 - 5 * q^27 - 16 * q^28 + 6 * q^29 + 4 * q^31 + 29 * q^32 + 12 * q^33 - 18 * q^34 - 25 * q^36 - 9 * q^37 - 6 * q^39 + 13 * q^41 + 24 * q^42 - 7 * q^43 + 20 * q^44 - 26 * q^46 + 14 * q^47 - 2 * q^48 - 4 * q^49 + 5 * q^51 - 20 * q^52 - 11 * q^53 + 30 * q^54 - 4 * q^56 + 31 * q^57 - 22 * q^58 + 13 * q^59 + 22 * q^61 + q^62 + 40 * q^63 + 47 * q^64 - 20 * q^66 + 10 * q^67 - 30 * q^68 + 20 * q^69 + 3 * q^71 - 19 * q^72 - 9 * q^73 - 18 * q^74 + 14 * q^76 - 8 * q^77 - 56 * q^78 - 16 * q^79 + 36 * q^81 - 6 * q^82 + 17 * q^83 + 16 * q^86 - 38 * q^87 + 44 * q^88 - 12 * q^89 - 24 * q^91 + 10 * q^92 + q^93 - 12 * q^94 + 14 * q^96 - 16 * q^97 - 19 * q^98 - 52 * q^99

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