LMFDB - Embedded newform 3850.2.a.bt.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} +3.10278 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.62721 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} +3.10278 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.62721 q^{9} +1.00000 q^{11} -3.10278 q^{12} +3.62721 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.20555 q^{17} -6.62721 q^{18} -8.15165 q^{19} -3.10278 q^{21} -1.00000 q^{22} -0.897225 q^{23} +3.10278 q^{24} -3.62721 q^{26} -11.2544 q^{27} +1.00000 q^{28} -7.30833 q^{29} -3.42166 q^{31} -1.00000 q^{32} -3.10278 q^{33} -4.20555 q^{34} +6.62721 q^{36} +1.10278 q^{37} +8.15165 q^{38} -11.2544 q^{39} +12.3572 q^{41} +3.10278 q^{42} -10.6761 q^{43} +1.00000 q^{44} +0.897225 q^{46} +1.15667 q^{47} -3.10278 q^{48} +1.00000 q^{49} -13.0489 q^{51} +3.62721 q^{52} -11.3083 q^{53} +11.2544 q^{54} -1.00000 q^{56} +25.2927 q^{57} +7.30833 q^{58} +7.25443 q^{59} -3.15667 q^{61} +3.42166 q^{62} +6.62721 q^{63} +1.00000 q^{64} +3.10278 q^{66} +8.41110 q^{67} +4.20555 q^{68} +2.78389 q^{69} -13.0489 q^{71} -6.62721 q^{72} -0.205550 q^{73} -1.10278 q^{74} -8.15165 q^{76} +1.00000 q^{77} +11.2544 q^{78} +12.1517 q^{79} +15.0383 q^{81} -12.3572 q^{82} -2.20555 q^{83} -3.10278 q^{84} +10.6761 q^{86} +22.6761 q^{87} -1.00000 q^{88} -7.45998 q^{89} +3.62721 q^{91} -0.897225 q^{92} +10.6167 q^{93} -1.15667 q^{94} +3.10278 q^{96} -2.25945 q^{97} -1.00000 q^{98} +6.62721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} + 3 q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} + 3 q^{16} - 2 q^{17} - 7 q^{18} - 6 q^{19} - 2 q^{21} - 3 q^{22} - 10 q^{23} + 2 q^{24} + 2 q^{26} - 8 q^{27} + 3 q^{28} - 12 q^{31} - 3 q^{32} - 2 q^{33} + 2 q^{34} + 7 q^{36} - 4 q^{37} + 6 q^{38} - 8 q^{39} + 4 q^{41} + 2 q^{42} - 8 q^{43} + 3 q^{44} + 10 q^{46} - 2 q^{48} + 3 q^{49} - 28 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} - 3 q^{56} + 8 q^{57} - 4 q^{59} - 6 q^{61} + 12 q^{62} + 7 q^{63} + 3 q^{64} + 2 q^{66} - 4 q^{67} - 2 q^{68} - 8 q^{69} - 28 q^{71} - 7 q^{72} + 14 q^{73} + 4 q^{74} - 6 q^{76} + 3 q^{77} + 8 q^{78} + 18 q^{79} + 3 q^{81} - 4 q^{82} + 8 q^{83} - 2 q^{84} + 8 q^{86} + 44 q^{87} - 3 q^{88} + 18 q^{89} - 2 q^{91} - 10 q^{92} - 12 q^{93} + 2 q^{96} + 4 q^{97} - 3 q^{98} + 7 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 + 3 * q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 + 3 * q^16 - 2 * q^17 - 7 * q^18 - 6 * q^19 - 2 * q^21 - 3 * q^22 - 10 * q^23 + 2 * q^24 + 2 * q^26 - 8 * q^27 + 3 * q^28 - 12 * q^31 - 3 * q^32 - 2 * q^33 + 2 * q^34 + 7 * q^36 - 4 * q^37 + 6 * q^38 - 8 * q^39 + 4 * q^41 + 2 * q^42 - 8 * q^43 + 3 * q^44 + 10 * q^46 - 2 * q^48 + 3 * q^49 - 28 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 - 3 * q^56 + 8 * q^57 - 4 * q^59 - 6 * q^61 + 12 * q^62 + 7 * q^63 + 3 * q^64 + 2 * q^66 - 4 * q^67 - 2 * q^68 - 8 * q^69 - 28 * q^71 - 7 * q^72 + 14 * q^73 + 4 * q^74 - 6 * q^76 + 3 * q^77 + 8 * q^78 + 18 * q^79 + 3 * q^81 - 4 * q^82 + 8 * q^83 - 2 * q^84 + 8 * q^86 + 44 * q^87 - 3 * q^88 + 18 * q^89 - 2 * q^91 - 10 * q^92 - 12 * q^93 + 2 * q^96 + 4 * q^97 - 3 * q^98 + 7 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.10278	−1.79139	−0.895694	−	0.444671i	$-0.853321\pi$
$3$	−3.10278	−1.79139	−0.895694	+	0.444671i	$0.853321\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	3.10278	1.26670
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	6.62721	2.20907
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.10278	−0.895694
$13$	3.62721	1.00601	0.503004	−	0.864284i	$-0.332228\pi$
$13$	3.62721	1.00601	0.503004	+	0.864284i	$0.332228\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	4.20555	1.02000	0.509998	−	0.860176i	$-0.329646\pi$
$17$	4.20555	1.02000	0.509998	+	0.860176i	$0.329646\pi$
$18$	−6.62721	−1.56205
$19$	−8.15165	−1.87012	−0.935058	−	0.354493i	$-0.884653\pi$
$19$	−8.15165	−1.87012	−0.935058	+	0.354493i	$0.884653\pi$
$20$	0	0
$21$	−3.10278	−0.677081
$22$	−1.00000	−0.213201
$23$	−0.897225	−0.187084	−0.0935422	−	0.995615i	$-0.529819\pi$
$23$	−0.897225	−0.187084	−0.0935422	+	0.995615i	$0.529819\pi$
$24$	3.10278	0.633351
$25$	0	0
$26$	−3.62721	−0.711355
$27$	−11.2544	−2.16592
$28$	1.00000	0.188982
$29$	−7.30833	−1.35712	−0.678561	−	0.734544i	$-0.737396\pi$
$29$	−7.30833	−1.35712	−0.678561	+	0.734544i	$0.737396\pi$
$30$	0	0
$31$	−3.42166	−0.614549	−0.307274	−	0.951621i	$-0.599417\pi$
$31$	−3.42166	−0.614549	−0.307274	+	0.951621i	$0.599417\pi$
$32$	−1.00000	−0.176777
$33$	−3.10278	−0.540124
$34$	−4.20555	−0.721246
$35$	0	0
$36$	6.62721	1.10454
$37$	1.10278	0.181295	0.0906476	−	0.995883i	$-0.471106\pi$
$37$	1.10278	0.181295	0.0906476	+	0.995883i	$0.471106\pi$
$38$	8.15165	1.32237
$39$	−11.2544	−1.80215
$40$	0	0
$41$	12.3572	1.92987	0.964935	−	0.262488i	$-0.0845430\pi$
$41$	12.3572	1.92987	0.964935	+	0.262488i	$0.0845430\pi$
$42$	3.10278	0.478769
$43$	−10.6761	−1.62809	−0.814044	−	0.580803i	$-0.802739\pi$
$43$	−10.6761	−1.62809	−0.814044	+	0.580803i	$0.802739\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	0.897225	0.132289
$47$	1.15667	0.168718	0.0843591	−	0.996435i	$-0.473116\pi$
$47$	1.15667	0.168718	0.0843591	+	0.996435i	$0.473116\pi$
$48$	−3.10278	−0.447847
$49$	1.00000	0.142857
$50$	0	0
$51$	−13.0489	−1.82721
$52$	3.62721	0.503004
$53$	−11.3083	−1.55332	−0.776659	−	0.629921i	$-0.783087\pi$
$53$	−11.3083	−1.55332	−0.776659	+	0.629921i	$0.783087\pi$
$54$	11.2544	1.53153
$55$	0	0
$56$	−1.00000	−0.133631
$57$	25.2927	3.35011
$58$	7.30833	0.959630
$59$	7.25443	0.944446	0.472223	−	0.881479i	$-0.343452\pi$
$59$	7.25443	0.944446	0.472223	+	0.881479i	$0.343452\pi$
$60$	0	0
$61$	−3.15667	−0.404171	−0.202085	−	0.979368i	$-0.564772\pi$
$61$	−3.15667	−0.404171	−0.202085	+	0.979368i	$0.564772\pi$
$62$	3.42166	0.434552
$63$	6.62721	0.834950
$64$	1.00000	0.125000
$65$	0	0
$66$	3.10278	0.381925
$67$	8.41110	1.02758	0.513790	−	0.857916i	$-0.328241\pi$
$67$	8.41110	1.02758	0.513790	+	0.857916i	$0.328241\pi$
$68$	4.20555	0.509998
$69$	2.78389	0.335141
$70$	0	0
$71$	−13.0489	−1.54862	−0.774308	−	0.632809i	$-0.781902\pi$
$71$	−13.0489	−1.54862	−0.774308	+	0.632809i	$0.781902\pi$
$72$	−6.62721	−0.781025
$73$	−0.205550	−0.0240578	−0.0120289	−	0.999928i	$-0.503829\pi$
$73$	−0.205550	−0.0240578	−0.0120289	+	0.999928i	$0.503829\pi$
$74$	−1.10278	−0.128195
$75$	0	0
$76$	−8.15165	−0.935058
$77$	1.00000	0.113961
$78$	11.2544	1.27431
$79$	12.1517	1.36717	0.683584	−	0.729872i	$-0.260420\pi$
$79$	12.1517	1.36717	0.683584	+	0.729872i	$0.260420\pi$
$80$	0	0
$81$	15.0383	1.67092
$82$	−12.3572	−1.36462
$83$	−2.20555	−0.242091	−0.121045	−	0.992647i	$-0.538625\pi$
$83$	−2.20555	−0.242091	−0.121045	+	0.992647i	$0.538625\pi$
$84$	−3.10278	−0.338541
$85$	0	0
$86$	10.6761	1.15123
$87$	22.6761	2.43113
$88$	−1.00000	−0.106600
$89$	−7.45998	−0.790756	−0.395378	−	0.918519i	$-0.629386\pi$
$89$	−7.45998	−0.790756	−0.395378	+	0.918519i	$0.629386\pi$
$90$	0	0
$91$	3.62721	0.380235
$92$	−0.897225	−0.0935422
$93$	10.6167	1.10090
$94$	−1.15667	−0.119302
$95$	0	0
$96$	3.10278	0.316676
$97$	−2.25945	−0.229412	−0.114706	−	0.993399i	$-0.536593\pi$
$97$	−2.25945	−0.229412	−0.114706	+	0.993399i	$0.536593\pi$
$98$	−1.00000	−0.101015
$99$	6.62721	0.666060
$100$	0	0
$101$	13.6655	1.35977	0.679885	−	0.733318i	$-0.262030\pi$
$101$	13.6655	1.35977	0.679885	+	0.733318i	$0.262030\pi$
$102$	13.0489	1.29203
$103$	5.04888	0.497481	0.248740	−	0.968570i	$-0.419983\pi$
$103$	5.04888	0.497481	0.248740	+	0.968570i	$0.419983\pi$
$104$	−3.62721	−0.355677
$105$	0	0
$106$	11.3083	1.09836
$107$	−12.9894	−1.25574	−0.627868	−	0.778320i	$-0.716072\pi$
$107$	−12.9894	−1.25574	−0.627868	+	0.778320i	$0.716072\pi$
$108$	−11.2544	−1.08296
$109$	5.10278	0.488757	0.244379	−	0.969680i	$-0.421416\pi$
$109$	5.10278	0.488757	0.244379	+	0.969680i	$0.421416\pi$
$110$	0	0
$111$	−3.42166	−0.324770
$112$	1.00000	0.0944911
$113$	10.4111	0.979394	0.489697	−	0.871893i	$-0.337107\pi$
$113$	10.4111	0.979394	0.489697	+	0.871893i	$0.337107\pi$
$114$	−25.2927	−2.36888
$115$	0	0
$116$	−7.30833	−0.678561
$117$	24.0383	2.22234
$118$	−7.25443	−0.667824
$119$	4.20555	0.385522
$120$	0	0
$121$	1.00000	0.0909091
$122$	3.15667	0.285792
$123$	−38.3416	−3.45715
$124$	−3.42166	−0.307274
$125$	0	0
$126$	−6.62721	−0.590399
$127$	−3.25443	−0.288784	−0.144392	−	0.989521i	$-0.546123\pi$
$127$	−3.25443	−0.288784	−0.144392	+	0.989521i	$0.546123\pi$
$128$	−1.00000	−0.0883883
$129$	33.1255	2.91654
$130$	0	0
$131$	−17.3083	−1.51224	−0.756118	−	0.654436i	$-0.772906\pi$
$131$	−17.3083	−1.51224	−0.756118	+	0.654436i	$0.772906\pi$
$132$	−3.10278	−0.270062
$133$	−8.15165	−0.706838
$134$	−8.41110	−0.726608
$135$	0	0
$136$	−4.20555	−0.360623
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	−2.78389	−0.236980
$139$	13.2005	1.11965	0.559827	−	0.828609i	$-0.310868\pi$
$139$	13.2005	1.11965	0.559827	+	0.828609i	$0.310868\pi$
$140$	0	0
$141$	−3.58890	−0.302240
$142$	13.0489	1.09504
$143$	3.62721	0.303323
$144$	6.62721	0.552268
$145$	0	0
$146$	0.205550	0.0170114
$147$	−3.10278	−0.255913
$148$	1.10278	0.0906476
$149$	−23.6116	−1.93434	−0.967170	−	0.254131i	$-0.918211\pi$
$149$	−23.6116	−1.93434	−0.967170	+	0.254131i	$0.918211\pi$
$150$	0	0
$151$	11.5139	0.936986	0.468493	−	0.883467i	$-0.344797\pi$
$151$	11.5139	0.936986	0.468493	+	0.883467i	$0.344797\pi$
$152$	8.15165	0.661186
$153$	27.8711	2.25324
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−11.2544	−0.901075
$157$	16.2056	1.29334	0.646672	−	0.762768i	$-0.276160\pi$
$157$	16.2056	1.29334	0.646672	+	0.762768i	$0.276160\pi$
$158$	−12.1517	−0.966733
$159$	35.0872	2.78260
$160$	0	0
$161$	−0.897225	−0.0707112
$162$	−15.0383	−1.18152
$163$	−6.31335	−0.494500	−0.247250	−	0.968952i	$-0.579527\pi$
$163$	−6.31335	−0.494500	−0.247250	+	0.968952i	$0.579527\pi$
$164$	12.3572	0.964935
$165$	0	0
$166$	2.20555	0.171184
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	3.10278	0.239384
$169$	0.156674	0.0120519
$170$	0	0
$171$	−54.0227	−4.13122
$172$	−10.6761	−0.814044
$173$	−9.25443	−0.703601	−0.351800	−	0.936075i	$-0.614430\pi$
$173$	−9.25443	−0.703601	−0.351800	+	0.936075i	$0.614430\pi$
$174$	−22.6761	−1.71907
$175$	0	0
$176$	1.00000	0.0753778
$177$	−22.5089	−1.69187
$178$	7.45998	0.559149
$179$	4.98944	0.372928	0.186464	−	0.982462i	$-0.440297\pi$
$179$	4.98944	0.372928	0.186464	+	0.982462i	$0.440297\pi$
$180$	0	0
$181$	−9.66553	−0.718433	−0.359216	−	0.933254i	$-0.616956\pi$
$181$	−9.66553	−0.718433	−0.359216	+	0.933254i	$0.616956\pi$
$182$	−3.62721	−0.268867
$183$	9.79445	0.724027
$184$	0.897225	0.0661443
$185$	0	0
$186$	−10.6167	−0.778451
$187$	4.20555	0.307540
$188$	1.15667	0.0843591
$189$	−11.2544	−0.818639
$190$	0	0
$191$	−9.15667	−0.662554	−0.331277	−	0.943534i	$-0.607479\pi$
$191$	−9.15667	−0.662554	−0.331277	+	0.943534i	$0.607479\pi$
$192$	−3.10278	−0.223924
$193$	−1.52946	−0.110093	−0.0550465	−	0.998484i	$-0.517531\pi$
$193$	−1.52946	−0.110093	−0.0550465	+	0.998484i	$0.517531\pi$
$194$	2.25945	0.162219
$195$	0	0
$196$	1.00000	0.0714286
$197$	−14.3033	−1.01907	−0.509534	−	0.860451i	$-0.670182\pi$
$197$	−14.3033	−1.01907	−0.509534	+	0.860451i	$0.670182\pi$
$198$	−6.62721	−0.470976
$199$	−10.0978	−0.715811	−0.357905	−	0.933758i	$-0.616509\pi$
$199$	−10.0978	−0.715811	−0.357905	+	0.933758i	$0.616509\pi$
$200$	0	0
$201$	−26.0978	−1.84079
$202$	−13.6655	−0.961503
$203$	−7.30833	−0.512944
$204$	−13.0489	−0.913604
$205$	0	0
$206$	−5.04888	−0.351772
$207$	−5.94610	−0.413283
$208$	3.62721	0.251502
$209$	−8.15165	−0.563861
$210$	0	0
$211$	10.8433	0.746485	0.373243	−	0.927734i	$-0.378246\pi$
$211$	10.8433	0.746485	0.373243	+	0.927734i	$0.378246\pi$
$212$	−11.3083	−0.776659
$213$	40.4877	2.77417
$214$	12.9894	0.887940
$215$	0	0
$216$	11.2544	0.765767
$217$	−3.42166	−0.232278
$218$	−5.10278	−0.345604
$219$	0.637776	0.0430969
$220$	0	0
$221$	15.2544	1.02612
$222$	3.42166	0.229647
$223$	9.45998	0.633487	0.316743	−	0.948511i	$-0.397411\pi$
$223$	9.45998	0.633487	0.316743	+	0.948511i	$0.397411\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−10.4111	−0.692536
$227$	17.5678	1.16601	0.583007	−	0.812467i	$-0.301876\pi$
$227$	17.5678	1.16601	0.583007	+	0.812467i	$0.301876\pi$
$228$	25.2927	1.67505
$229$	25.7250	1.69995	0.849977	−	0.526820i	$-0.176616\pi$
$229$	25.7250	1.69995	0.849977	+	0.526820i	$0.176616\pi$
$230$	0	0
$231$	−3.10278	−0.204148
$232$	7.30833	0.479815
$233$	−19.1567	−1.25500	−0.627498	−	0.778618i	$-0.715921\pi$
$233$	−19.1567	−1.25500	−0.627498	+	0.778618i	$0.715921\pi$
$234$	−24.0383	−1.57143
$235$	0	0
$236$	7.25443	0.472223
$237$	−37.7038	−2.44913
$238$	−4.20555	−0.272605
$239$	−18.0539	−1.16781	−0.583905	−	0.811822i	$-0.698476\pi$
$239$	−18.0539	−1.16781	−0.583905	+	0.811822i	$0.698476\pi$
$240$	0	0
$241$	6.15165	0.396263	0.198131	−	0.980175i	$-0.436513\pi$
$241$	6.15165	0.396263	0.198131	+	0.980175i	$0.436513\pi$
$242$	−1.00000	−0.0642824
$243$	−12.8972	−0.827357
$244$	−3.15667	−0.202085
$245$	0	0
$246$	38.3416	2.44457
$247$	−29.5678	−1.88135
$248$	3.42166	0.217276
$249$	6.84333	0.433678
$250$	0	0
$251$	−29.9789	−1.89225	−0.946125	−	0.323802i	$-0.895039\pi$
$251$	−29.9789	−1.89225	−0.946125	+	0.323802i	$0.895039\pi$
$252$	6.62721	0.417475
$253$	−0.897225	−0.0564080
$254$	3.25443	0.204201
$255$	0	0
$256$	1.00000	0.0625000
$257$	−4.05390	−0.252875	−0.126438	−	0.991975i	$-0.540354\pi$
$257$	−4.05390	−0.252875	−0.126438	+	0.991975i	$0.540354\pi$
$258$	−33.1255	−2.06230
$259$	1.10278	0.0685231
$260$	0	0
$261$	−48.4338	−2.99798
$262$	17.3083	1.06931
$263$	14.5089	0.894654	0.447327	−	0.894370i	$-0.352376\pi$
$263$	14.5089	0.894654	0.447327	+	0.894370i	$0.352376\pi$
$264$	3.10278	0.190963
$265$	0	0
$266$	8.15165	0.499810
$267$	23.1466	1.41655
$268$	8.41110	0.513790
$269$	4.37279	0.266614	0.133307	−	0.991075i	$-0.457440\pi$
$269$	4.37279	0.266614	0.133307	+	0.991075i	$0.457440\pi$
$270$	0	0
$271$	−10.6167	−0.644916	−0.322458	−	0.946584i	$-0.604509\pi$
$271$	−10.6167	−0.644916	−0.322458	+	0.946584i	$0.604509\pi$
$272$	4.20555	0.254999
$273$	−11.2544	−0.681149
$274$	10.0000	0.604122
$275$	0	0
$276$	2.78389	0.167570
$277$	19.7633	1.18746	0.593730	−	0.804664i	$-0.297655\pi$
$277$	19.7633	1.18746	0.593730	+	0.804664i	$0.297655\pi$
$278$	−13.2005	−0.791715
$279$	−22.6761	−1.35758
$280$	0	0
$281$	−27.0489	−1.61360	−0.806800	−	0.590824i	$-0.798803\pi$
$281$	−27.0489	−1.61360	−0.806800	+	0.590824i	$0.798803\pi$
$282$	3.58890	0.213716
$283$	−27.6655	−1.64454	−0.822272	−	0.569094i	$-0.807294\pi$
$283$	−27.6655	−1.64454	−0.822272	+	0.569094i	$0.807294\pi$
$284$	−13.0489	−0.774308
$285$	0	0
$286$	−3.62721	−0.214482
$287$	12.3572	0.729423
$288$	−6.62721	−0.390512
$289$	0.686652	0.0403913
$290$	0	0
$291$	7.01056	0.410966
$292$	−0.205550	−0.0120289
$293$	8.37279	0.489143	0.244572	−	0.969631i	$-0.421353\pi$
$293$	8.37279	0.489143	0.244572	+	0.969631i	$0.421353\pi$
$294$	3.10278	0.180958
$295$	0	0
$296$	−1.10278	−0.0640975
$297$	−11.2544	−0.653048
$298$	23.6116	1.36778
$299$	−3.25443	−0.188208
$300$	0	0
$301$	−10.6761	−0.615360
$302$	−11.5139	−0.662549
$303$	−42.4011	−2.43588
$304$	−8.15165	−0.467529
$305$	0	0
$306$	−27.8711	−1.59328
$307$	10.2056	0.582462	0.291231	−	0.956653i	$-0.405935\pi$
$307$	10.2056	0.582462	0.291231	+	0.956653i	$0.405935\pi$
$308$	1.00000	0.0569803
$309$	−15.6655	−0.891181
$310$	0	0
$311$	−8.16724	−0.463122	−0.231561	−	0.972820i	$-0.574383\pi$
$311$	−8.16724	−0.463122	−0.231561	+	0.972820i	$0.574383\pi$
$312$	11.2544	0.637156
$313$	−34.5628	−1.95360	−0.976801	−	0.214149i	$-0.931302\pi$
$313$	−34.5628	−1.95360	−0.976801	+	0.214149i	$0.931302\pi$
$314$	−16.2056	−0.914532
$315$	0	0
$316$	12.1517	0.683584
$317$	−9.21057	−0.517317	−0.258659	−	0.965969i	$-0.583280\pi$
$317$	−9.21057	−0.517317	−0.258659	+	0.965969i	$0.583280\pi$
$318$	−35.0872	−1.96759
$319$	−7.30833	−0.409188
$320$	0	0
$321$	40.3033	2.24951
$322$	0.897225	0.0500004
$323$	−34.2822	−1.90751
$324$	15.0383	0.835462
$325$	0	0
$326$	6.31335	0.349664
$327$	−15.8328	−0.875554
$328$	−12.3572	−0.682312
$329$	1.15667	0.0637695
$330$	0	0
$331$	16.2439	0.892843	0.446422	−	0.894823i	$-0.352698\pi$
$331$	16.2439	0.892843	0.446422	+	0.894823i	$0.352698\pi$
$332$	−2.20555	−0.121045
$333$	7.30833	0.400494
$334$	−8.00000	−0.437741
$335$	0	0
$336$	−3.10278	−0.169270
$337$	1.25443	0.0683329	0.0341665	−	0.999416i	$-0.489122\pi$
$337$	1.25443	0.0683329	0.0341665	+	0.999416i	$0.489122\pi$
$338$	−0.156674	−0.00852195
$339$	−32.3033	−1.75447
$340$	0	0
$341$	−3.42166	−0.185293
$342$	54.0227	2.92121
$343$	1.00000	0.0539949
$344$	10.6761	0.575616
$345$	0	0
$346$	9.25443	0.497521
$347$	−7.42166	−0.398416	−0.199208	−	0.979957i	$-0.563837\pi$
$347$	−7.42166	−0.398416	−0.199208	+	0.979957i	$0.563837\pi$
$348$	22.6761	1.21557
$349$	−18.3033	−0.979753	−0.489877	−	0.871792i	$-0.662958\pi$
$349$	−18.3033	−0.979753	−0.489877	+	0.871792i	$0.662958\pi$
$350$	0	0
$351$	−40.8222	−2.17893
$352$	−1.00000	−0.0533002
$353$	−28.8761	−1.53692	−0.768460	−	0.639898i	$-0.778977\pi$
$353$	−28.8761	−1.53692	−0.768460	+	0.639898i	$0.778977\pi$
$354$	22.5089	1.19633
$355$	0	0
$356$	−7.45998	−0.395378
$357$	−13.0489	−0.690620
$358$	−4.98944	−0.263700
$359$	4.15165	0.219116	0.109558	−	0.993980i	$-0.465057\pi$
$359$	4.15165	0.219116	0.109558	+	0.993980i	$0.465057\pi$
$360$	0	0
$361$	47.4494	2.49734
$362$	9.66553	0.508009
$363$	−3.10278	−0.162853
$364$	3.62721	0.190118
$365$	0	0
$366$	−9.79445	−0.511964
$367$	5.26447	0.274803	0.137402	−	0.990515i	$-0.456125\pi$
$367$	5.26447	0.274803	0.137402	+	0.990515i	$0.456125\pi$
$368$	−0.897225	−0.0467711
$369$	81.8938	4.26322
$370$	0	0
$371$	−11.3083	−0.587099
$372$	10.6167	0.550448
$373$	−35.8711	−1.85733	−0.928667	−	0.370915i	$-0.879044\pi$
$373$	−35.8711	−1.85733	−0.928667	+	0.370915i	$0.879044\pi$
$374$	−4.20555	−0.217464
$375$	0	0
$376$	−1.15667	−0.0596509
$377$	−26.5089	−1.36528
$378$	11.2544	0.578865
$379$	−33.0177	−1.69601	−0.848003	−	0.529992i	$-0.822195\pi$
$379$	−33.0177	−1.69601	−0.848003	+	0.529992i	$0.822195\pi$
$380$	0	0
$381$	10.0978	0.517323
$382$	9.15667	0.468496
$383$	−2.95112	−0.150795	−0.0753977	−	0.997154i	$-0.524023\pi$
$383$	−2.95112	−0.150795	−0.0753977	+	0.997154i	$0.524023\pi$
$384$	3.10278	0.158338
$385$	0	0
$386$	1.52946	0.0778475
$387$	−70.7527	−3.59656
$388$	−2.25945	−0.114706
$389$	1.89220	0.0959384	0.0479692	−	0.998849i	$-0.484725\pi$
$389$	1.89220	0.0959384	0.0479692	+	0.998849i	$0.484725\pi$
$390$	0	0
$391$	−3.77332	−0.190825
$392$	−1.00000	−0.0505076
$393$	53.7038	2.70900
$394$	14.3033	0.720590
$395$	0	0
$396$	6.62721	0.333030
$397$	−5.36222	−0.269122	−0.134561	−	0.990905i	$-0.542962\pi$
$397$	−5.36222	−0.269122	−0.134561	+	0.990905i	$0.542962\pi$
$398$	10.0978	0.506155
$399$	25.2927	1.26622
$400$	0	0
$401$	23.7038	1.18371	0.591857	−	0.806043i	$-0.298395\pi$
$401$	23.7038	1.18371	0.591857	+	0.806043i	$0.298395\pi$
$402$	26.0978	1.30164
$403$	−12.4111	−0.618241
$404$	13.6655	0.679885
$405$	0	0
$406$	7.30833	0.362706
$407$	1.10278	0.0546625
$408$	13.0489	0.646016
$409$	27.0816	1.33910	0.669551	−	0.742766i	$-0.266487\pi$
$409$	27.0816	1.33910	0.669551	+	0.742766i	$0.266487\pi$
$410$	0	0
$411$	31.0278	1.53049
$412$	5.04888	0.248740
$413$	7.25443	0.356967
$414$	5.94610	0.292235
$415$	0	0
$416$	−3.62721	−0.177839
$417$	−40.9583	−2.00573
$418$	8.15165	0.398710
$419$	−3.05892	−0.149438	−0.0747191	−	0.997205i	$-0.523806\pi$
$419$	−3.05892	−0.149438	−0.0747191	+	0.997205i	$0.523806\pi$
$420$	0	0
$421$	21.6655	1.05591	0.527957	−	0.849271i	$-0.322958\pi$
$421$	21.6655	1.05591	0.527957	+	0.849271i	$0.322958\pi$
$422$	−10.8433	−0.527845
$423$	7.66553	0.372711
$424$	11.3083	0.549181
$425$	0	0
$426$	−40.4877	−1.96164
$427$	−3.15667	−0.152762
$428$	−12.9894	−0.627868
$429$	−11.2544	−0.543369
$430$	0	0
$431$	−34.3260	−1.65343	−0.826713	−	0.562623i	$-0.809792\pi$
$431$	−34.3260	−1.65343	−0.826713	+	0.562623i	$0.809792\pi$
$432$	−11.2544	−0.541479
$433$	0.0538991	0.00259023	0.00129511	−	0.999999i	$-0.499588\pi$
$433$	0.0538991	0.00259023	0.00129511	+	0.999999i	$0.499588\pi$
$434$	3.42166	0.164245
$435$	0	0
$436$	5.10278	0.244379
$437$	7.31386	0.349870
$438$	−0.637776	−0.0304741
$439$	−7.14663	−0.341090	−0.170545	−	0.985350i	$-0.554553\pi$
$439$	−7.14663	−0.341090	−0.170545	+	0.985350i	$0.554553\pi$
$440$	0	0
$441$	6.62721	0.315582
$442$	−15.2544	−0.725579
$443$	−8.74557	−0.415515	−0.207757	−	0.978180i	$-0.566616\pi$
$443$	−8.74557	−0.415515	−0.207757	+	0.978180i	$0.566616\pi$
$444$	−3.42166	−0.162385
$445$	0	0
$446$	−9.45998	−0.447943
$447$	73.2616	3.46515
$448$	1.00000	0.0472456
$449$	39.7038	1.87374	0.936870	−	0.349678i	$-0.113709\pi$
$449$	39.7038	1.87374	0.936870	+	0.349678i	$0.113709\pi$
$450$	0	0
$451$	12.3572	0.581878
$452$	10.4111	0.489697
$453$	−35.7250	−1.67851
$454$	−17.5678	−0.824497
$455$	0	0
$456$	−25.2927	−1.18444
$457$	−12.3133	−0.575994	−0.287997	−	0.957631i	$-0.592989\pi$
$457$	−12.3133	−0.575994	−0.287997	+	0.957631i	$0.592989\pi$
$458$	−25.7250	−1.20205
$459$	−47.3311	−2.20922
$460$	0	0
$461$	−15.0489	−0.700896	−0.350448	−	0.936582i	$-0.613971\pi$
$461$	−15.0489	−0.700896	−0.350448	+	0.936582i	$0.613971\pi$
$462$	3.10278	0.144354
$463$	−31.4061	−1.45956	−0.729782	−	0.683680i	$-0.760378\pi$
$463$	−31.4061	−1.45956	−0.729782	+	0.683680i	$0.760378\pi$
$464$	−7.30833	−0.339280
$465$	0	0
$466$	19.1567	0.887416
$467$	19.0716	0.882529	0.441264	−	0.897377i	$-0.354530\pi$
$467$	19.0716	0.882529	0.441264	+	0.897377i	$0.354530\pi$
$468$	24.0383	1.11117
$469$	8.41110	0.388389
$470$	0	0
$471$	−50.2822	−2.31688
$472$	−7.25443	−0.333912
$473$	−10.6761	−0.490887
$474$	37.7038	1.73179
$475$	0	0
$476$	4.20555	0.192761
$477$	−74.9427	−3.43139
$478$	18.0539	0.825766
$479$	−9.49115	−0.433662	−0.216831	−	0.976209i	$-0.569572\pi$
$479$	−9.49115	−0.433662	−0.216831	+	0.976209i	$0.569572\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	−6.15165	−0.280200
$483$	2.78389	0.126671
$484$	1.00000	0.0454545
$485$	0	0
$486$	12.8972	0.585030
$487$	−0.0438527	−0.00198715	−0.000993577	−	1.00000i	$-0.500316\pi$
$487$	−0.0438527	−0.00198715	−0.000993577		1.00000i	$0.500316\pi$
$488$	3.15667	0.142896
$489$	19.5889	0.885841
$490$	0	0
$491$	1.56777	0.0707527	0.0353763	−	0.999374i	$-0.488737\pi$
$491$	1.56777	0.0707527	0.0353763	+	0.999374i	$0.488737\pi$
$492$	−38.3416	−1.72857
$493$	−30.7355	−1.38426
$494$	29.5678	1.33032
$495$	0	0
$496$	−3.42166	−0.153637
$497$	−13.0489	−0.585322
$498$	−6.84333	−0.306657
$499$	−42.3416	−1.89547	−0.947736	−	0.319057i	$-0.896634\pi$
$499$	−42.3416	−1.89547	−0.947736	+	0.319057i	$0.896634\pi$
$500$	0	0
$501$	−24.8222	−1.10897
$502$	29.9789	1.33802
$503$	36.4111	1.62349	0.811745	−	0.584012i	$-0.198518\pi$
$503$	36.4111	1.62349	0.811745	+	0.584012i	$0.198518\pi$
$504$	−6.62721	−0.295200
$505$	0	0
$506$	0.897225	0.0398865
$507$	−0.486125	−0.0215896
$508$	−3.25443	−0.144392
$509$	−30.0766	−1.33312	−0.666562	−	0.745450i	$-0.732235\pi$
$509$	−30.0766	−1.33312	−0.666562	+	0.745450i	$0.732235\pi$
$510$	0	0
$511$	−0.205550	−0.00909300
$512$	−1.00000	−0.0441942
$513$	91.7422	4.05051
$514$	4.05390	0.178810
$515$	0	0
$516$	33.1255	1.45827
$517$	1.15667	0.0508705
$518$	−1.10278	−0.0484532
$519$	28.7144	1.26042
$520$	0	0
$521$	−33.2233	−1.45554	−0.727769	−	0.685823i	$-0.759443\pi$
$521$	−33.2233	−1.45554	−0.727769	+	0.685823i	$0.759443\pi$
$522$	48.4338	2.11989
$523$	15.5577	0.680292	0.340146	−	0.940373i	$-0.389524\pi$
$523$	15.5577	0.680292	0.340146	+	0.940373i	$0.389524\pi$
$524$	−17.3083	−0.756118
$525$	0	0
$526$	−14.5089	−0.632616
$527$	−14.3900	−0.626837
$528$	−3.10278	−0.135031
$529$	−22.1950	−0.964999
$530$	0	0
$531$	48.0766	2.08635
$532$	−8.15165	−0.353419
$533$	44.8222	1.94147
$534$	−23.1466	−1.00165
$535$	0	0
$536$	−8.41110	−0.363304
$537$	−15.4811	−0.668059
$538$	−4.37279	−0.188524
$539$	1.00000	0.0430730
$540$	0	0
$541$	23.4161	1.00674	0.503369	−	0.864072i	$-0.332094\pi$
$541$	23.4161	1.00674	0.503369	+	0.864072i	$0.332094\pi$
$542$	10.6167	0.456024
$543$	29.9900	1.28699
$544$	−4.20555	−0.180311
$545$	0	0
$546$	11.2544	0.481645
$547$	8.41110	0.359633	0.179816	−	0.983700i	$-0.442450\pi$
$547$	8.41110	0.359633	0.179816	+	0.983700i	$0.442450\pi$
$548$	−10.0000	−0.427179
$549$	−20.9200	−0.892842
$550$	0	0
$551$	59.5749	2.53798
$552$	−2.78389	−0.118490
$553$	12.1517	0.516741
$554$	−19.7633	−0.839661
$555$	0	0
$556$	13.2005	0.559827
$557$	−37.0278	−1.56892	−0.784458	−	0.620182i	$-0.787059\pi$
$557$	−37.0278	−1.56892	−0.784458	+	0.620182i	$0.787059\pi$
$558$	22.6761	0.959955
$559$	−38.7244	−1.63787
$560$	0	0
$561$	−13.0489	−0.550924
$562$	27.0489	1.14099
$563$	−22.9200	−0.965961	−0.482980	−	0.875631i	$-0.660446\pi$
$563$	−22.9200	−0.965961	−0.482980	+	0.875631i	$0.660446\pi$
$564$	−3.58890	−0.151120
$565$	0	0
$566$	27.6655	1.16287
$567$	15.0383	0.631550
$568$	13.0489	0.547519
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	0	0
$571$	20.3033	0.849667	0.424833	−	0.905272i	$-0.360333\pi$
$571$	20.3033	0.849667	0.424833	+	0.905272i	$0.360333\pi$
$572$	3.62721	0.151661
$573$	28.4111	1.18689
$574$	−12.3572	−0.515780
$575$	0	0
$576$	6.62721	0.276134
$577$	−16.4650	−0.685447	−0.342723	−	0.939436i	$-0.611349\pi$
$577$	−16.4650	−0.685447	−0.342723	+	0.939436i	$0.611349\pi$
$578$	−0.686652	−0.0285609
$579$	4.74557	0.197219
$580$	0	0
$581$	−2.20555	−0.0915016
$582$	−7.01056	−0.290597
$583$	−11.3083	−0.468343
$584$	0.205550	0.00850572
$585$	0	0
$586$	−8.37279	−0.345877
$587$	30.6605	1.26549	0.632747	−	0.774358i	$-0.281927\pi$
$587$	30.6605	1.26549	0.632747	+	0.774358i	$0.281927\pi$
$588$	−3.10278	−0.127956
$589$	27.8922	1.14928
$590$	0	0
$591$	44.3799	1.82555
$592$	1.10278	0.0453238
$593$	−18.3033	−0.751627	−0.375813	−	0.926695i	$-0.622637\pi$
$593$	−18.3033	−0.751627	−0.375813	+	0.926695i	$0.622637\pi$
$594$	11.2544	0.461775
$595$	0	0
$596$	−23.6116	−0.967170
$597$	31.3311	1.28229
$598$	3.25443	0.133083
$599$	29.6555	1.21169	0.605845	−	0.795583i	$-0.292835\pi$
$599$	29.6555	1.21169	0.605845	+	0.795583i	$0.292835\pi$
$600$	0	0
$601$	18.7783	0.765985	0.382992	−	0.923751i	$-0.374894\pi$
$601$	18.7783	0.765985	0.382992	+	0.923751i	$0.374894\pi$
$602$	10.6761	0.435125
$603$	55.7422	2.27000
$604$	11.5139	0.468493
$605$	0	0
$606$	42.4011	1.72243
$607$	−14.6761	−0.595684	−0.297842	−	0.954615i	$-0.596267\pi$
$607$	−14.6761	−0.595684	−0.297842	+	0.954615i	$0.596267\pi$
$608$	8.15165	0.330593
$609$	22.6761	0.918881
$610$	0	0
$611$	4.19550	0.169732
$612$	27.8711	1.12662
$613$	5.28560	0.213483	0.106742	−	0.994287i	$-0.465958\pi$
$613$	5.28560	0.213483	0.106742	+	0.994287i	$0.465958\pi$
$614$	−10.2056	−0.411862
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	44.6933	1.79928	0.899642	−	0.436629i	$-0.143828\pi$
$617$	44.6933	1.79928	0.899642	+	0.436629i	$0.143828\pi$
$618$	15.6655	0.630160
$619$	−17.5678	−0.706108	−0.353054	−	0.935603i	$-0.614857\pi$
$619$	−17.5678	−0.706108	−0.353054	+	0.935603i	$0.614857\pi$
$620$	0	0
$621$	10.0978	0.405209
$622$	8.16724	0.327476
$623$	−7.45998	−0.298878
$624$	−11.2544	−0.450538
$625$	0	0
$626$	34.5628	1.38141
$627$	25.2927	1.01009
$628$	16.2056	0.646672
$629$	4.63778	0.184920
$630$	0	0
$631$	4.74557	0.188918	0.0944592	−	0.995529i	$-0.469888\pi$
$631$	4.74557	0.188918	0.0944592	+	0.995529i	$0.469888\pi$
$632$	−12.1517	−0.483367
$633$	−33.6444	−1.33724
$634$	9.21057	0.365799
$635$	0	0
$636$	35.0872	1.39130
$637$	3.62721	0.143715
$638$	7.30833	0.289339
$639$	−86.4777	−3.42100
$640$	0	0
$641$	−2.52998	−0.0999281	−0.0499641	−	0.998751i	$-0.515911\pi$
$641$	−2.52998	−0.0999281	−0.0499641	+	0.998751i	$0.515911\pi$
$642$	−40.3033	−1.59064
$643$	0.670549	0.0264439	0.0132219	−	0.999913i	$-0.495791\pi$
$643$	0.670549	0.0264439	0.0132219	+	0.999913i	$0.495791\pi$
$644$	−0.897225	−0.0353556
$645$	0	0
$646$	34.2822	1.34881
$647$	−11.8922	−0.467531	−0.233765	−	0.972293i	$-0.575105\pi$
$647$	−11.8922	−0.467531	−0.233765	+	0.972293i	$0.575105\pi$
$648$	−15.0383	−0.590761
$649$	7.25443	0.284761
$650$	0	0
$651$	10.6167	0.416099
$652$	−6.31335	−0.247250
$653$	11.4161	0.446747	0.223374	−	0.974733i	$-0.428293\pi$
$653$	11.4161	0.446747	0.223374	+	0.974733i	$0.428293\pi$
$654$	15.8328	0.619110
$655$	0	0
$656$	12.3572	0.482468
$657$	−1.36222	−0.0531454
$658$	−1.15667	−0.0450919
$659$	1.87108	0.0728868	0.0364434	−	0.999336i	$-0.488397\pi$
$659$	1.87108	0.0728868	0.0364434	+	0.999336i	$0.488397\pi$
$660$	0	0
$661$	33.1355	1.28882	0.644412	−	0.764679i	$-0.277102\pi$
$661$	33.1355	1.28882	0.644412	+	0.764679i	$0.277102\pi$
$662$	−16.2439	−0.631336
$663$	−47.3311	−1.83819
$664$	2.20555	0.0855919
$665$	0	0
$666$	−7.30833	−0.283192
$667$	6.55721	0.253896
$668$	8.00000	0.309529
$669$	−29.3522	−1.13482
$670$	0	0
$671$	−3.15667	−0.121862
$672$	3.10278	0.119692
$673$	18.1955	0.701385	0.350693	−	0.936491i	$-0.385946\pi$
$673$	18.1955	0.701385	0.350693	+	0.936491i	$0.385946\pi$
$674$	−1.25443	−0.0483187
$675$	0	0
$676$	0.156674	0.00602593
$677$	−15.9789	−0.614118	−0.307059	−	0.951690i	$-0.599345\pi$
$677$	−15.9789	−0.614118	−0.307059	+	0.951690i	$0.599345\pi$
$678$	32.3033	1.24060
$679$	−2.25945	−0.0867097
$680$	0	0
$681$	−54.5089	−2.08878
$682$	3.42166	0.131022
$683$	17.8711	0.683818	0.341909	−	0.939733i	$-0.388927\pi$
$683$	17.8711	0.683818	0.341909	+	0.939733i	$0.388927\pi$
$684$	−54.0227	−2.06561
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	−79.8188	−3.04528
$688$	−10.6761	−0.407022
$689$	−41.0177	−1.56265
$690$	0	0
$691$	−2.20555	−0.0839031	−0.0419515	−	0.999120i	$-0.513358\pi$
$691$	−2.20555	−0.0839031	−0.0419515	+	0.999120i	$0.513358\pi$
$692$	−9.25443	−0.351800
$693$	6.62721	0.251747
$694$	7.42166	0.281722
$695$	0	0
$696$	−22.6761	−0.859535
$697$	51.9688	1.96846
$698$	18.3033	0.692790
$699$	59.4389	2.24818
$700$	0	0
$701$	−25.6217	−0.967717	−0.483859	−	0.875146i	$-0.660765\pi$
$701$	−25.6217	−0.967717	−0.483859	+	0.875146i	$0.660765\pi$
$702$	40.8222	1.54073
$703$	−8.98944	−0.339043
$704$	1.00000	0.0376889
$705$	0	0
$706$	28.8761	1.08677
$707$	13.6655	0.513945
$708$	−22.5089	−0.845934
$709$	5.48110	0.205847	0.102924	−	0.994689i	$-0.467180\pi$
$709$	5.48110	0.205847	0.102924	+	0.994689i	$0.467180\pi$
$710$	0	0
$711$	80.5316	3.02017
$712$	7.45998	0.279574
$713$	3.07000	0.114972
$714$	13.0489	0.488342
$715$	0	0
$716$	4.98944	0.186464
$717$	56.0172	2.09200
$718$	−4.15165	−0.154938
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	0	0
$721$	5.04888	0.188030
$722$	−47.4494	−1.76588
$723$	−19.0872	−0.709860
$724$	−9.66553	−0.359216
$725$	0	0
$726$	3.10278	0.115155
$727$	−18.5855	−0.689297	−0.344649	−	0.938732i	$-0.612002\pi$
$727$	−18.5855	−0.689297	−0.344649	+	0.938732i	$0.612002\pi$
$728$	−3.62721	−0.134433
$729$	−5.09775	−0.188806
$730$	0	0
$731$	−44.8988	−1.66064
$732$	9.79445	0.362013
$733$	42.0000	1.55131	0.775653	−	0.631160i	$-0.217421\pi$
$733$	42.0000	1.55131	0.775653	+	0.631160i	$0.217421\pi$
$734$	−5.26447	−0.194315
$735$	0	0
$736$	0.897225	0.0330722
$737$	8.41110	0.309827
$738$	−81.8938	−3.01455
$739$	5.97887	0.219936	0.109968	−	0.993935i	$-0.464925\pi$
$739$	5.97887	0.219936	0.109968	+	0.993935i	$0.464925\pi$
$740$	0	0
$741$	91.7422	3.37023
$742$	11.3083	0.415142
$743$	50.0978	1.83791	0.918954	−	0.394364i	$-0.129035\pi$
$743$	50.0978	1.83791	0.918954	+	0.394364i	$0.129035\pi$
$744$	−10.6167	−0.389225
$745$	0	0
$746$	35.8711	1.31333
$747$	−14.6167	−0.534795
$748$	4.20555	0.153770
$749$	−12.9894	−0.474624
$750$	0	0
$751$	−8.63778	−0.315197	−0.157598	−	0.987503i	$-0.550375\pi$
$751$	−8.63778	−0.315197	−0.157598	+	0.987503i	$0.550375\pi$
$752$	1.15667	0.0421796
$753$	93.0177	3.38975
$754$	26.5089	0.965395
$755$	0	0
$756$	−11.2544	−0.409320
$757$	−25.5139	−0.927318	−0.463659	−	0.886014i	$-0.653464\pi$
$757$	−25.5139	−0.927318	−0.463659	+	0.886014i	$0.653464\pi$
$758$	33.0177	1.19926
$759$	2.78389	0.101049
$760$	0	0
$761$	−32.6605	−1.18394	−0.591971	−	0.805959i	$-0.701650\pi$
$761$	−32.6605	−1.18394	−0.591971	+	0.805959i	$0.701650\pi$
$762$	−10.0978	−0.365803
$763$	5.10278	0.184733
$764$	−9.15667	−0.331277
$765$	0	0
$766$	2.95112	0.106628
$767$	26.3133	0.950120
$768$	−3.10278	−0.111962
$769$	16.7683	0.604680	0.302340	−	0.953200i	$-0.402232\pi$
$769$	16.7683	0.604680	0.302340	+	0.953200i	$0.402232\pi$
$770$	0	0
$771$	12.5783	0.452998
$772$	−1.52946	−0.0550465
$773$	2.82220	0.101507	0.0507537	−	0.998711i	$-0.483838\pi$
$773$	2.82220	0.101507	0.0507537	+	0.998711i	$0.483838\pi$
$774$	70.7527	2.54315
$775$	0	0
$776$	2.25945	0.0811095
$777$	−3.42166	−0.122751
$778$	−1.89220	−0.0678387
$779$	−100.732	−3.60908
$780$	0	0
$781$	−13.0489	−0.466925
$782$	3.77332	0.134934
$783$	82.2510	2.93941
$784$	1.00000	0.0357143
$785$	0	0
$786$	−53.7038	−1.91555
$787$	4.82220	0.171893	0.0859464	−	0.996300i	$-0.472609\pi$
$787$	4.82220	0.171893	0.0859464	+	0.996300i	$0.472609\pi$
$788$	−14.3033	−0.509534
$789$	−45.0177	−1.60267
$790$	0	0
$791$	10.4111	0.370176
$792$	−6.62721	−0.235488
$793$	−11.4499	−0.406599
$794$	5.36222	0.190298
$795$	0	0
$796$	−10.0978	−0.357905
$797$	0.540024	0.0191286	0.00956431	−	0.999954i	$-0.496956\pi$
$797$	0.540024	0.0191286	0.00956431	+	0.999954i	$0.496956\pi$
$798$	−25.2927	−0.895353
$799$	4.86445	0.172092
$800$	0	0
$801$	−49.4389	−1.74684
$802$	−23.7038	−0.837012
$803$	−0.205550	−0.00725371
$804$	−26.0978	−0.920397
$805$	0	0
$806$	12.4111	0.437162
$807$	−13.5678	−0.477608
$808$	−13.6655	−0.480752
$809$	−17.8922	−0.629056	−0.314528	−	0.949248i	$-0.601846\pi$
$809$	−17.8922	−0.629056	−0.314528	+	0.949248i	$0.601846\pi$
$810$	0	0
$811$	−12.2283	−0.429393	−0.214696	−	0.976681i	$-0.568876\pi$
$811$	−12.2283	−0.429393	−0.214696	+	0.976681i	$0.568876\pi$
$812$	−7.30833	−0.256472
$813$	32.9411	1.15529
$814$	−1.10278	−0.0386522
$815$	0	0
$816$	−13.0489	−0.456802
$817$	87.0278	3.04472
$818$	−27.0816	−0.946888
$819$	24.0383	0.839967
$820$	0	0
$821$	38.5316	1.34476	0.672381	−	0.740206i	$-0.265272\pi$
$821$	38.5316	1.34476	0.672381	+	0.740206i	$0.265272\pi$
$822$	−31.0278	−1.08222
$823$	−21.9461	−0.764993	−0.382496	−	0.923957i	$-0.624936\pi$
$823$	−21.9461	−0.764993	−0.382496	+	0.923957i	$0.624936\pi$
$824$	−5.04888	−0.175886
$825$	0	0
$826$	−7.25443	−0.252414
$827$	−9.68665	−0.336838	−0.168419	−	0.985716i	$-0.553866\pi$
$827$	−9.68665	−0.336838	−0.168419	+	0.985716i	$0.553866\pi$
$828$	−5.94610	−0.206641
$829$	31.0771	1.07935	0.539677	−	0.841872i	$-0.318546\pi$
$829$	31.0771	1.07935	0.539677	+	0.841872i	$0.318546\pi$
$830$	0	0
$831$	−61.3210	−2.12720
$832$	3.62721	0.125751
$833$	4.20555	0.145714
$834$	40.9583	1.41827
$835$	0	0
$836$	−8.15165	−0.281931
$837$	38.5089	1.33106
$838$	3.05892	0.105669
$839$	−24.7738	−0.855288	−0.427644	−	0.903947i	$-0.640656\pi$
$839$	−24.7738	−0.855288	−0.427644	+	0.903947i	$0.640656\pi$
$840$	0	0
$841$	24.4116	0.841780
$842$	−21.6655	−0.746643
$843$	83.9266	2.89058
$844$	10.8433	0.373243
$845$	0	0
$846$	−7.66553	−0.263546
$847$	1.00000	0.0343604
$848$	−11.3083	−0.388329
$849$	85.8399	2.94602
$850$	0	0
$851$	−0.989437	−0.0339175
$852$	40.4877	1.38709
$853$	−1.58890	−0.0544029	−0.0272014	−	0.999630i	$-0.508660\pi$
$853$	−1.58890	−0.0544029	−0.0272014	+	0.999630i	$0.508660\pi$
$854$	3.15667	0.108019
$855$	0	0
$856$	12.9894	0.443970
$857$	−19.1255	−0.653315	−0.326657	−	0.945143i	$-0.605922\pi$
$857$	−19.1255	−0.653315	−0.326657	+	0.945143i	$0.605922\pi$
$858$	11.2544	0.384220
$859$	4.94108	0.168587	0.0842937	−	0.996441i	$-0.473137\pi$
$859$	4.94108	0.168587	0.0842937	+	0.996441i	$0.473137\pi$
$860$	0	0
$861$	−38.3416	−1.30668
$862$	34.3260	1.16915
$863$	19.3295	0.657982	0.328991	−	0.944333i	$-0.393291\pi$
$863$	19.3295	0.657982	0.328991	+	0.944333i	$0.393291\pi$
$864$	11.2544	0.382883
$865$	0	0
$866$	−0.0538991	−0.00183157
$867$	−2.13053	−0.0723564
$868$	−3.42166	−0.116139
$869$	12.1517	0.412217
$870$	0	0
$871$	30.5089	1.03375
$872$	−5.10278	−0.172802
$873$	−14.9739	−0.506788
$874$	−7.31386	−0.247395
$875$	0	0
$876$	0.637776	0.0215484
$877$	−16.4011	−0.553824	−0.276912	−	0.960895i	$-0.589311\pi$
$877$	−16.4011	−0.553824	−0.276912	+	0.960895i	$0.589311\pi$
$878$	7.14663	0.241187
$879$	−25.9789	−0.876246
$880$	0	0
$881$	39.5678	1.33307	0.666536	−	0.745473i	$-0.267776\pi$
$881$	39.5678	1.33307	0.666536	+	0.745473i	$0.267776\pi$
$882$	−6.62721	−0.223150
$883$	−55.4389	−1.86567	−0.932833	−	0.360309i	$-0.882671\pi$
$883$	−55.4389	−1.86567	−0.932833	+	0.360309i	$0.882671\pi$
$884$	15.2544	0.513062
$885$	0	0
$886$	8.74557	0.293813
$887$	−44.1955	−1.48394	−0.741970	−	0.670433i	$-0.766108\pi$
$887$	−44.1955	−1.48394	−0.741970	+	0.670433i	$0.766108\pi$
$888$	3.42166	0.114823
$889$	−3.25443	−0.109150
$890$	0	0
$891$	15.0383	0.503802
$892$	9.45998	0.316743
$893$	−9.42880	−0.315523
$894$	−73.2616	−2.45023
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	10.0978	0.337154
$898$	−39.7038	−1.32493
$899$	25.0066	0.834018
$900$	0	0
$901$	−47.5577	−1.58438
$902$	−12.3572	−0.411450
$903$	33.1255	1.10235
$904$	−10.4111	−0.346268
$905$	0	0
$906$	35.7250	1.18688
$907$	−9.26447	−0.307622	−0.153811	−	0.988100i	$-0.549155\pi$
$907$	−9.26447	−0.307622	−0.153811	+	0.988100i	$0.549155\pi$
$908$	17.5678	0.583007
$909$	90.5644	3.00383
$910$	0	0
$911$	−37.0489	−1.22748	−0.613742	−	0.789507i	$-0.710336\pi$
$911$	−37.0489	−1.22748	−0.613742	+	0.789507i	$0.710336\pi$
$912$	25.2927	0.837526
$913$	−2.20555	−0.0729931
$914$	12.3133	0.407289
$915$	0	0
$916$	25.7250	0.849977
$917$	−17.3083	−0.571571
$918$	47.3311	1.56216
$919$	−13.9149	−0.459011	−0.229506	−	0.973307i	$-0.573711\pi$
$919$	−13.9149	−0.459011	−0.229506	+	0.973307i	$0.573711\pi$
$920$	0	0
$921$	−31.6655	−1.04341
$922$	15.0489	0.495608
$923$	−47.3311	−1.55792
$924$	−3.10278	−0.102074
$925$	0	0
$926$	31.4061	1.03207
$927$	33.4600	1.09897
$928$	7.30833	0.239908
$929$	−32.0666	−1.05207	−0.526035	−	0.850463i	$-0.676322\pi$
$929$	−32.0666	−1.05207	−0.526035	+	0.850463i	$0.676322\pi$
$930$	0	0
$931$	−8.15165	−0.267160
$932$	−19.1567	−0.627498
$933$	25.3411	0.829630
$934$	−19.0716	−0.624042
$935$	0	0
$936$	−24.0383	−0.785717
$937$	−25.4499	−0.831413	−0.415706	−	0.909499i	$-0.636466\pi$
$937$	−25.4499	−0.831413	−0.415706	+	0.909499i	$0.636466\pi$
$938$	−8.41110	−0.274632
$939$	107.240	3.49966
$940$	0	0
$941$	−3.49115	−0.113808	−0.0569041	−	0.998380i	$-0.518123\pi$
$941$	−3.49115	−0.113808	−0.0569041	+	0.998380i	$0.518123\pi$
$942$	50.2822	1.63828
$943$	−11.0872	−0.361049
$944$	7.25443	0.236111
$945$	0	0
$946$	10.6761	0.347110
$947$	−30.6167	−0.994907	−0.497454	−	0.867491i	$-0.665732\pi$
$947$	−30.6167	−0.994907	−0.497454	+	0.867491i	$0.665732\pi$
$948$	−37.7038	−1.22456
$949$	−0.745574	−0.0242024
$950$	0	0
$951$	28.5783	0.926716
$952$	−4.20555	−0.136303
$953$	33.9406	1.09944	0.549721	−	0.835348i	$-0.314734\pi$
$953$	33.9406	1.09944	0.549721	+	0.835348i	$0.314734\pi$
$954$	74.9427	2.42636
$955$	0	0
$956$	−18.0539	−0.583905
$957$	22.6761	0.733014
$958$	9.49115	0.306645
$959$	−10.0000	−0.322917
$960$	0	0
$961$	−19.2922	−0.622330
$962$	−4.00000	−0.128965
$963$	−86.0838	−2.77401
$964$	6.15165	0.198131
$965$	0	0
$966$	−2.78389	−0.0895701
$967$	60.8021	1.95526	0.977632	−	0.210323i	$-0.0674515\pi$
$967$	60.8021	1.95526	0.977632	+	0.210323i	$0.0674515\pi$
$968$	−1.00000	−0.0321412
$969$	106.370	3.41709
$970$	0	0
$971$	50.2933	1.61399	0.806994	−	0.590560i	$-0.201093\pi$
$971$	50.2933	1.61399	0.806994	+	0.590560i	$0.201093\pi$
$972$	−12.8972	−0.413679
$973$	13.2005	0.423189
$974$	0.0438527	0.00140513
$975$	0	0
$976$	−3.15667	−0.101043
$977$	−28.0978	−0.898927	−0.449463	−	0.893299i	$-0.648385\pi$
$977$	−28.0978	−0.898927	−0.449463	+	0.893299i	$0.648385\pi$
$978$	−19.5889	−0.626384
$979$	−7.45998	−0.238422
$980$	0	0
$981$	33.8172	1.07970
$982$	−1.56777	−0.0500297
$983$	21.0489	0.671355	0.335677	−	0.941977i	$-0.391035\pi$
$983$	21.0489	0.671355	0.335677	+	0.941977i	$0.391035\pi$
$984$	38.3416	1.22229
$985$	0	0
$986$	30.7355	0.978819
$987$	−3.58890	−0.114236
$988$	−29.5678	−0.940676
$989$	9.57885	0.304590
$990$	0	0
$991$	−44.6832	−1.41941	−0.709705	−	0.704499i	$-0.751172\pi$
$991$	−44.6832	−1.41941	−0.709705	+	0.704499i	$0.751172\pi$
$992$	3.42166	0.108638
$993$	−50.4011	−1.59943
$994$	13.0489	0.413885
$995$	0	0
$996$	6.84333	0.216839
$997$	−9.47002	−0.299919	−0.149959	−	0.988692i	$-0.547914\pi$
$997$	−9.47002	−0.299919	−0.149959	+	0.988692i	$0.547914\pi$
$998$	42.3416	1.34030
$999$	−12.4111	−0.392670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.bt.1.1		3
5.2	odd	4		3850.2.c.ba.1849.3		6
5.3	odd	4		3850.2.c.ba.1849.4		6
5.4	even	2		770.2.a.m.1.3	✓	3
15.14	odd	2		6930.2.a.ce.1.1		3
20.19	odd	2		6160.2.a.bf.1.1		3
35.34	odd	2		5390.2.a.ca.1.1		3
55.54	odd	2		8470.2.a.ci.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.m.1.3	✓	3	5.4	even	2
3850.2.a.bt.1.1		3	1.1	even	1	trivial
3850.2.c.ba.1849.3		6	5.2	odd	4
3850.2.c.ba.1849.4		6	5.3	odd	4
5390.2.a.ca.1.1		3	35.34	odd	2
6160.2.a.bf.1.1		3	20.19	odd	2
6930.2.a.ce.1.1		3	15.14	odd	2
8470.2.a.ci.1.3		3	55.54	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} +3.10278 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.62721 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} +3.10278 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.62721 q^{9} +1.00000 q^{11} -3.10278 q^{12} +3.62721 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.20555 q^{17} -6.62721 q^{18} -8.15165 q^{19} -3.10278 q^{21} -1.00000 q^{22} -0.897225 q^{23} +3.10278 q^{24} -3.62721 q^{26} -11.2544 q^{27} +1.00000 q^{28} -7.30833 q^{29} -3.42166 q^{31} -1.00000 q^{32} -3.10278 q^{33} -4.20555 q^{34} +6.62721 q^{36} +1.10278 q^{37} +8.15165 q^{38} -11.2544 q^{39} +12.3572 q^{41} +3.10278 q^{42} -10.6761 q^{43} +1.00000 q^{44} +0.897225 q^{46} +1.15667 q^{47} -3.10278 q^{48} +1.00000 q^{49} -13.0489 q^{51} +3.62721 q^{52} -11.3083 q^{53} +11.2544 q^{54} -1.00000 q^{56} +25.2927 q^{57} +7.30833 q^{58} +7.25443 q^{59} -3.15667 q^{61} +3.42166 q^{62} +6.62721 q^{63} +1.00000 q^{64} +3.10278 q^{66} +8.41110 q^{67} +4.20555 q^{68} +2.78389 q^{69} -13.0489 q^{71} -6.62721 q^{72} -0.205550 q^{73} -1.10278 q^{74} -8.15165 q^{76} +1.00000 q^{77} +11.2544 q^{78} +12.1517 q^{79} +15.0383 q^{81} -12.3572 q^{82} -2.20555 q^{83} -3.10278 q^{84} +10.6761 q^{86} +22.6761 q^{87} -1.00000 q^{88} -7.45998 q^{89} +3.62721 q^{91} -0.897225 q^{92} +10.6167 q^{93} -1.15667 q^{94} +3.10278 q^{96} -2.25945 q^{97} -1.00000 q^{98} +6.62721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} + 3 q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} + 3 q^{16} - 2 q^{17} - 7 q^{18} - 6 q^{19} - 2 q^{21} - 3 q^{22} - 10 q^{23} + 2 q^{24} + 2 q^{26} - 8 q^{27} + 3 q^{28} - 12 q^{31} - 3 q^{32} - 2 q^{33} + 2 q^{34} + 7 q^{36} - 4 q^{37} + 6 q^{38} - 8 q^{39} + 4 q^{41} + 2 q^{42} - 8 q^{43} + 3 q^{44} + 10 q^{46} - 2 q^{48} + 3 q^{49} - 28 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} - 3 q^{56} + 8 q^{57} - 4 q^{59} - 6 q^{61} + 12 q^{62} + 7 q^{63} + 3 q^{64} + 2 q^{66} - 4 q^{67} - 2 q^{68} - 8 q^{69} - 28 q^{71} - 7 q^{72} + 14 q^{73} + 4 q^{74} - 6 q^{76} + 3 q^{77} + 8 q^{78} + 18 q^{79} + 3 q^{81} - 4 q^{82} + 8 q^{83} - 2 q^{84} + 8 q^{86} + 44 q^{87} - 3 q^{88} + 18 q^{89} - 2 q^{91} - 10 q^{92} - 12 q^{93} + 2 q^{96} + 4 q^{97} - 3 q^{98} + 7 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 + 3 * q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 + 3 * q^16 - 2 * q^17 - 7 * q^18 - 6 * q^19 - 2 * q^21 - 3 * q^22 - 10 * q^23 + 2 * q^24 + 2 * q^26 - 8 * q^27 + 3 * q^28 - 12 * q^31 - 3 * q^32 - 2 * q^33 + 2 * q^34 + 7 * q^36 - 4 * q^37 + 6 * q^38 - 8 * q^39 + 4 * q^41 + 2 * q^42 - 8 * q^43 + 3 * q^44 + 10 * q^46 - 2 * q^48 + 3 * q^49 - 28 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 - 3 * q^56 + 8 * q^57 - 4 * q^59 - 6 * q^61 + 12 * q^62 + 7 * q^63 + 3 * q^64 + 2 * q^66 - 4 * q^67 - 2 * q^68 - 8 * q^69 - 28 * q^71 - 7 * q^72 + 14 * q^73 + 4 * q^74 - 6 * q^76 + 3 * q^77 + 8 * q^78 + 18 * q^79 + 3 * q^81 - 4 * q^82 + 8 * q^83 - 2 * q^84 + 8 * q^86 + 44 * q^87 - 3 * q^88 + 18 * q^89 - 2 * q^91 - 10 * q^92 - 12 * q^93 + 2 * q^96 + 4 * q^97 - 3 * q^98 + 7 * q^99

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