LMFDB - Embedded newform 4650.2.a.ci.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4650,2,Mod(1,4650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4650, 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("4650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.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:	$37.1304369399$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1708.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 8x - 2 $ x^3 - x^2 - 8*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 930)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.260711$ of defining polynomial
Character	$\chi$	$=$	4650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.26071 q^{11} -1.00000 q^{12} -2.73929 q^{13} +2.00000 q^{14} +1.00000 q^{16} +4.93203 q^{17} -1.00000 q^{18} +4.93203 q^{19} +2.00000 q^{21} -3.26071 q^{22} +0.521423 q^{23} +1.00000 q^{24} +2.73929 q^{26} -1.00000 q^{27} -2.00000 q^{28} +0.521423 q^{29} -1.00000 q^{31} -1.00000 q^{32} -3.26071 q^{33} -4.93203 q^{34} +1.00000 q^{36} +10.8212 q^{37} -4.93203 q^{38} +2.73929 q^{39} +2.00000 q^{41} -2.00000 q^{42} -8.82121 q^{43} +3.26071 q^{44} -0.521423 q^{46} -4.93203 q^{47} -1.00000 q^{48} -3.00000 q^{49} -4.93203 q^{51} -2.73929 q^{52} -13.3426 q^{53} +1.00000 q^{54} +2.00000 q^{56} -4.93203 q^{57} -0.521423 q^{58} +9.34264 q^{59} -9.75324 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +3.26071 q^{66} +13.5605 q^{67} +4.93203 q^{68} -0.521423 q^{69} +5.56050 q^{71} -1.00000 q^{72} +3.04285 q^{73} -10.8212 q^{74} +4.93203 q^{76} -6.52142 q^{77} -2.73929 q^{78} -6.41061 q^{79} +1.00000 q^{81} -2.00000 q^{82} +1.36776 q^{83} +2.00000 q^{84} +8.82121 q^{86} -0.521423 q^{87} -3.26071 q^{88} -11.8641 q^{89} +5.47858 q^{91} +0.521423 q^{92} +1.00000 q^{93} +4.93203 q^{94} +1.00000 q^{96} +7.26071 q^{97} +3.00000 q^{98} +3.26071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{7} - 3 q^{8} + 3 q^{9} + 8 q^{11} - 3 q^{12} - 10 q^{13} + 6 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} + 6 q^{21} - 8 q^{22} - 2 q^{23} + 3 q^{24} + 10 q^{26} - 3 q^{27} - 6 q^{28} - 2 q^{29} - 3 q^{31} - 3 q^{32} - 8 q^{33} + 2 q^{34} + 3 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{41} - 6 q^{42} + 8 q^{44} + 2 q^{46} + 2 q^{47} - 3 q^{48} - 9 q^{49} + 2 q^{51} - 10 q^{52} - 10 q^{53} + 3 q^{54} + 6 q^{56} + 2 q^{57} + 2 q^{58} - 2 q^{59} + 14 q^{61} + 3 q^{62} - 6 q^{63} + 3 q^{64} + 8 q^{66} + 16 q^{67} - 2 q^{68} + 2 q^{69} - 8 q^{71} - 3 q^{72} + 2 q^{73} - 6 q^{74} - 2 q^{76} - 16 q^{77} - 10 q^{78} - 6 q^{79} + 3 q^{81} - 6 q^{82} - 2 q^{83} + 6 q^{84} + 2 q^{87} - 8 q^{88} - 2 q^{89} + 20 q^{91} - 2 q^{92} + 3 q^{93} - 2 q^{94} + 3 q^{96} + 20 q^{97} + 9 q^{98} + 8 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^7 - 3 * q^8 + 3 * q^9 + 8 * q^11 - 3 * q^12 - 10 * q^13 + 6 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 - 2 * q^19 + 6 * q^21 - 8 * q^22 - 2 * q^23 + 3 * q^24 + 10 * q^26 - 3 * q^27 - 6 * q^28 - 2 * q^29 - 3 * q^31 - 3 * q^32 - 8 * q^33 + 2 * q^34 + 3 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^41 - 6 * q^42 + 8 * q^44 + 2 * q^46 + 2 * q^47 - 3 * q^48 - 9 * q^49 + 2 * q^51 - 10 * q^52 - 10 * q^53 + 3 * q^54 + 6 * q^56 + 2 * q^57 + 2 * q^58 - 2 * q^59 + 14 * q^61 + 3 * q^62 - 6 * q^63 + 3 * q^64 + 8 * q^66 + 16 * q^67 - 2 * q^68 + 2 * q^69 - 8 * q^71 - 3 * q^72 + 2 * q^73 - 6 * q^74 - 2 * q^76 - 16 * q^77 - 10 * q^78 - 6 * q^79 + 3 * q^81 - 6 * q^82 - 2 * q^83 + 6 * q^84 + 2 * q^87 - 8 * q^88 - 2 * q^89 + 20 * q^91 - 2 * q^92 + 3 * q^93 - 2 * q^94 + 3 * q^96 + 20 * q^97 + 9 * q^98 + 8 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	3.26071	0.983141	0.491571	−	0.870838i	$-0.336423\pi$
$11$	3.26071	0.983141	0.491571	+	0.870838i	$0.336423\pi$
$12$	−1.00000	−0.288675
$13$	−2.73929	−0.759742	−0.379871	−	0.925039i	$-0.624032\pi$
$13$	−2.73929	−0.759742	−0.379871	+	0.925039i	$0.624032\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	4.93203	1.19619	0.598096	−	0.801424i	$-0.295924\pi$
$17$	4.93203	1.19619	0.598096	+	0.801424i	$0.295924\pi$
$18$	−1.00000	−0.235702
$19$	4.93203	1.13149	0.565743	−	0.824582i	$-0.308590\pi$
$19$	4.93203	1.13149	0.565743	+	0.824582i	$0.308590\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	−3.26071	−0.695186
$23$	0.521423	0.108724	0.0543621	−	0.998521i	$-0.482687\pi$
$23$	0.521423	0.108724	0.0543621	+	0.998521i	$0.482687\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	2.73929	0.537219
$27$	−1.00000	−0.192450
$28$	−2.00000	−0.377964
$29$	0.521423	0.0968258	0.0484129	−	0.998827i	$-0.484584\pi$
$29$	0.521423	0.0968258	0.0484129	+	0.998827i	$0.484584\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−3.26071	−0.567617
$34$	−4.93203	−0.845836
$35$	0	0
$36$	1.00000	0.166667
$37$	10.8212	1.77900	0.889498	−	0.456939i	$-0.151054\pi$
$37$	10.8212	1.77900	0.889498	+	0.456939i	$0.151054\pi$
$38$	−4.93203	−0.800081
$39$	2.73929	0.438637
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−2.00000	−0.308607
$43$	−8.82121	−1.34522	−0.672611	−	0.739996i	$-0.734827\pi$
$43$	−8.82121	−1.34522	−0.672611	+	0.739996i	$0.734827\pi$
$44$	3.26071	0.491571
$45$	0	0
$46$	−0.521423	−0.0768796
$47$	−4.93203	−0.719410	−0.359705	−	0.933066i	$-0.617123\pi$
$47$	−4.93203	−0.719410	−0.359705	+	0.933066i	$0.617123\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−4.93203	−0.690622
$52$	−2.73929	−0.379871
$53$	−13.3426	−1.83275	−0.916376	−	0.400319i	$-0.868899\pi$
$53$	−13.3426	−1.83275	−0.916376	+	0.400319i	$0.868899\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	2.00000	0.267261
$57$	−4.93203	−0.653263
$58$	−0.521423	−0.0684662
$59$	9.34264	1.21631	0.608154	−	0.793819i	$-0.291910\pi$
$59$	9.34264	1.21631	0.608154	+	0.793819i	$0.291910\pi$
$60$	0	0
$61$	−9.75324	−1.24877	−0.624387	−	0.781115i	$-0.714651\pi$
$61$	−9.75324	−1.24877	−0.624387	+	0.781115i	$0.714651\pi$
$62$	1.00000	0.127000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	3.26071	0.401366
$67$	13.5605	1.65668	0.828340	−	0.560226i	$-0.189286\pi$
$67$	13.5605	1.65668	0.828340	+	0.560226i	$0.189286\pi$
$68$	4.93203	0.598096
$69$	−0.521423	−0.0627719
$70$	0	0
$71$	5.56050	0.659910	0.329955	−	0.943997i	$-0.392966\pi$
$71$	5.56050	0.659910	0.329955	+	0.943997i	$0.392966\pi$
$72$	−1.00000	−0.117851
$73$	3.04285	0.356138	0.178069	−	0.984018i	$-0.443015\pi$
$73$	3.04285	0.356138	0.178069	+	0.984018i	$0.443015\pi$
$74$	−10.8212	−1.25794
$75$	0	0
$76$	4.93203	0.565743
$77$	−6.52142	−0.743185
$78$	−2.73929	−0.310163
$79$	−6.41061	−0.721250	−0.360625	−	0.932711i	$-0.617437\pi$
$79$	−6.41061	−0.721250	−0.360625	+	0.932711i	$0.617437\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	1.36776	0.150131	0.0750657	−	0.997179i	$-0.476083\pi$
$83$	1.36776	0.150131	0.0750657	+	0.997179i	$0.476083\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	8.82121	0.951216
$87$	−0.521423	−0.0559024
$88$	−3.26071	−0.347593
$89$	−11.8641	−1.25759	−0.628794	−	0.777572i	$-0.716451\pi$
$89$	−11.8641	−1.25759	−0.628794	+	0.777572i	$0.716451\pi$
$90$	0	0
$91$	5.47858	0.574311
$92$	0.521423	0.0543621
$93$	1.00000	0.103695
$94$	4.93203	0.508700
$95$	0	0
$96$	1.00000	0.102062
$97$	7.26071	0.737214	0.368607	−	0.929585i	$-0.379835\pi$
$97$	7.26071	0.737214	0.368607	+	0.929585i	$0.379835\pi$
$98$	3.00000	0.303046
$99$	3.26071	0.327714
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	4.93203	0.488344
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	2.73929	0.268609
$105$	0	0
$106$	13.3426	1.29595
$107$	−18.2998	−1.76911	−0.884554	−	0.466438i	$-0.845537\pi$
$107$	−18.2998	−1.76911	−0.884554	+	0.466438i	$0.845537\pi$
$108$	−1.00000	−0.0962250
$109$	5.34264	0.511732	0.255866	−	0.966712i	$-0.417639\pi$
$109$	5.34264	0.511732	0.255866	+	0.966712i	$0.417639\pi$
$110$	0	0
$111$	−10.8212	−1.02710
$112$	−2.00000	−0.188982
$113$	16.6853	1.56962	0.784809	−	0.619737i	$-0.212761\pi$
$113$	16.6853	1.56962	0.784809	+	0.619737i	$0.212761\pi$
$114$	4.93203	0.461927
$115$	0	0
$116$	0.521423	0.0484129
$117$	−2.73929	−0.253247
$118$	−9.34264	−0.860059
$119$	−9.86406	−0.904237
$120$	0	0
$121$	−0.367761	−0.0334328
$122$	9.75324	0.883017
$123$	−2.00000	−0.180334
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	2.00000	0.178174
$127$	6.52142	0.578683	0.289341	−	0.957226i	$-0.406564\pi$
$127$	6.52142	0.578683	0.289341	+	0.957226i	$0.406564\pi$
$128$	−1.00000	−0.0883883
$129$	8.82121	0.776665
$130$	0	0
$131$	13.3426	1.16575	0.582876	−	0.812561i	$-0.301927\pi$
$131$	13.3426	1.16575	0.582876	+	0.812561i	$0.301927\pi$
$132$	−3.26071	−0.283808
$133$	−9.86406	−0.855322
$134$	−13.5605	−1.17145
$135$	0	0
$136$	−4.93203	−0.422918
$137$	−3.77837	−0.322808	−0.161404	−	0.986888i	$-0.551602\pi$
$137$	−3.77837	−0.322808	−0.161404	+	0.986888i	$0.551602\pi$
$138$	0.521423	0.0443865
$139$	12.5214	1.06205	0.531027	−	0.847355i	$-0.321806\pi$
$139$	12.5214	1.06205	0.531027	+	0.847355i	$0.321806\pi$
$140$	0	0
$141$	4.93203	0.415352
$142$	−5.56050	−0.466627
$143$	−8.93203	−0.746934
$144$	1.00000	0.0833333
$145$	0	0
$146$	−3.04285	−0.251828
$147$	3.00000	0.247436
$148$	10.8212	0.889498
$149$	2.21787	0.181695	0.0908473	−	0.995865i	$-0.471042\pi$
$149$	2.21787	0.181695	0.0908473	+	0.995865i	$0.471042\pi$
$150$	0	0
$151$	18.1890	1.48020	0.740099	−	0.672498i	$-0.234779\pi$
$151$	18.1890	1.48020	0.740099	+	0.672498i	$0.234779\pi$
$152$	−4.93203	−0.400040
$153$	4.93203	0.398731
$154$	6.52142	0.525511
$155$	0	0
$156$	2.73929	0.219319
$157$	−19.2067	−1.53286	−0.766431	−	0.642327i	$-0.777969\pi$
$157$	−19.2067	−1.53286	−0.766431	+	0.642327i	$0.777969\pi$
$158$	6.41061	0.510000
$159$	13.3426	1.05814
$160$	0	0
$161$	−1.04285	−0.0821877
$162$	−1.00000	−0.0785674
$163$	9.56050	0.748836	0.374418	−	0.927260i	$-0.377842\pi$
$163$	9.56050	0.748836	0.374418	+	0.927260i	$0.377842\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−1.36776	−0.106159
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	−2.00000	−0.154303
$169$	−5.49630	−0.422792
$170$	0	0
$171$	4.93203	0.377162
$172$	−8.82121	−0.672611
$173$	1.45345	0.110504	0.0552520	−	0.998472i	$-0.482404\pi$
$173$	1.45345	0.110504	0.0552520	+	0.998472i	$0.482404\pi$
$174$	0.521423	0.0395290
$175$	0	0
$176$	3.26071	0.245785
$177$	−9.34264	−0.702236
$178$	11.8641	0.889249
$179$	−26.3817	−1.97186	−0.985931	−	0.167153i	$-0.946543\pi$
$179$	−26.3817	−1.97186	−0.985931	+	0.167153i	$0.946543\pi$
$180$	0	0
$181$	−7.77837	−0.578162	−0.289081	−	0.957305i	$-0.593350\pi$
$181$	−7.77837	−0.578162	−0.289081	+	0.957305i	$0.593350\pi$
$182$	−5.47858	−0.406099
$183$	9.75324	0.720980
$184$	−0.521423	−0.0384398
$185$	0	0
$186$	−1.00000	−0.0733236
$187$	16.0819	1.17603
$188$	−4.93203	−0.359705
$189$	2.00000	0.145479
$190$	0	0
$191$	7.56427	0.547331	0.273666	−	0.961825i	$-0.411764\pi$
$191$	7.56427	0.547331	0.273666	+	0.961825i	$0.411764\pi$
$192$	−1.00000	−0.0721688
$193$	22.3817	1.61107	0.805536	−	0.592547i	$-0.201878\pi$
$193$	22.3817	1.61107	0.805536	+	0.592547i	$0.201878\pi$
$194$	−7.26071	−0.521289
$195$	0	0
$196$	−3.00000	−0.214286
$197$	16.6853	1.18878	0.594388	−	0.804178i	$-0.297394\pi$
$197$	16.6853	1.18878	0.594388	+	0.804178i	$0.297394\pi$
$198$	−3.26071	−0.231729
$199$	15.4535	1.09547	0.547733	−	0.836653i	$-0.315491\pi$
$199$	15.4535	1.09547	0.547733	+	0.836653i	$0.315491\pi$
$200$	0	0
$201$	−13.5605	−0.956484
$202$	0	0
$203$	−1.04285	−0.0731934
$204$	−4.93203	−0.345311
$205$	0	0
$206$	−6.00000	−0.418040
$207$	0.521423	0.0362414
$208$	−2.73929	−0.189935
$209$	16.0819	1.11241
$210$	0	0
$211$	17.0428	1.17328	0.586639	−	0.809849i	$-0.300451\pi$
$211$	17.0428	1.17328	0.586639	+	0.809849i	$0.300451\pi$
$212$	−13.3426	−0.916376
$213$	−5.56050	−0.380999
$214$	18.2998	1.25095
$215$	0	0
$216$	1.00000	0.0680414
$217$	2.00000	0.135769
$218$	−5.34264	−0.361849
$219$	−3.04285	−0.205616
$220$	0	0
$221$	−13.5103	−0.908798
$222$	10.8212	0.726272
$223$	13.7821	0.922920	0.461460	−	0.887161i	$-0.347326\pi$
$223$	13.7821	0.922920	0.461460	+	0.887161i	$0.347326\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	−16.6853	−1.10989
$227$	2.52142	0.167353	0.0836764	−	0.996493i	$-0.473334\pi$
$227$	2.52142	0.167353	0.0836764	+	0.996493i	$0.473334\pi$
$228$	−4.93203	−0.326632
$229$	27.3957	1.81036	0.905178	−	0.425032i	$-0.139737\pi$
$229$	27.3957	1.81036	0.905178	+	0.425032i	$0.139737\pi$
$230$	0	0
$231$	6.52142	0.429078
$232$	−0.521423	−0.0342331
$233$	−22.8212	−1.49507	−0.747534	−	0.664224i	$-0.768762\pi$
$233$	−22.8212	−1.49507	−0.747534	+	0.664224i	$0.768762\pi$
$234$	2.73929	0.179073
$235$	0	0
$236$	9.34264	0.608154
$237$	6.41061	0.416414
$238$	9.86406	0.639392
$239$	−14.2998	−0.924977	−0.462488	−	0.886625i	$-0.653043\pi$
$239$	−14.2998	−0.924977	−0.462488	+	0.886625i	$0.653043\pi$
$240$	0	0
$241$	13.3426	0.859475	0.429737	−	0.902954i	$-0.358606\pi$
$241$	13.3426	0.859475	0.429737	+	0.902954i	$0.358606\pi$
$242$	0.367761	0.0236406
$243$	−1.00000	−0.0641500
$244$	−9.75324	−0.624387
$245$	0	0
$246$	2.00000	0.127515
$247$	−13.5103	−0.859637
$248$	1.00000	0.0635001
$249$	−1.36776	−0.0866783
$250$	0	0
$251$	10.5214	0.664106	0.332053	−	0.943261i	$-0.392259\pi$
$251$	10.5214	0.664106	0.332053	+	0.943261i	$0.392259\pi$
$252$	−2.00000	−0.125988
$253$	1.70021	0.106891
$254$	−6.52142	−0.409190
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.86406	−0.490547	−0.245273	−	0.969454i	$-0.578878\pi$
$257$	−7.86406	−0.490547	−0.245273	+	0.969454i	$0.578878\pi$
$258$	−8.82121	−0.549185
$259$	−21.6424	−1.34479
$260$	0	0
$261$	0.521423	0.0322753
$262$	−13.3426	−0.824311
$263$	−23.8641	−1.47152	−0.735760	−	0.677242i	$-0.763175\pi$
$263$	−23.8641	−1.47152	−0.735760	+	0.677242i	$0.763175\pi$
$264$	3.26071	0.200683
$265$	0	0
$266$	9.86406	0.604804
$267$	11.8641	0.726069
$268$	13.5605	0.828340
$269$	−8.95715	−0.546127	−0.273064	−	0.961996i	$-0.588037\pi$
$269$	−8.95715	−0.546127	−0.273064	+	0.961996i	$0.588037\pi$
$270$	0	0
$271$	−13.0959	−0.795518	−0.397759	−	0.917490i	$-0.630212\pi$
$271$	−13.0959	−0.795518	−0.397759	+	0.917490i	$0.630212\pi$
$272$	4.93203	0.299048
$273$	−5.47858	−0.331579
$274$	3.77837	0.228260
$275$	0	0
$276$	−0.521423	−0.0313860
$277$	3.78213	0.227246	0.113623	−	0.993524i	$-0.463754\pi$
$277$	3.78213	0.227246	0.113623	+	0.993524i	$0.463754\pi$
$278$	−12.5214	−0.750985
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	3.04285	0.181521	0.0907605	−	0.995873i	$-0.471070\pi$
$281$	3.04285	0.181521	0.0907605	+	0.995873i	$0.471070\pi$
$282$	−4.93203	−0.293698
$283$	−22.7672	−1.35337	−0.676685	−	0.736273i	$-0.736584\pi$
$283$	−22.7672	−1.35337	−0.676685	+	0.736273i	$0.736584\pi$
$284$	5.56050	0.329955
$285$	0	0
$286$	8.93203	0.528162
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	7.32492	0.430877
$290$	0	0
$291$	−7.26071	−0.425630
$292$	3.04285	0.178069
$293$	3.64243	0.212793	0.106396	−	0.994324i	$-0.466069\pi$
$293$	3.64243	0.212793	0.106396	+	0.994324i	$0.466069\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	−10.8212	−0.628970
$297$	−3.26071	−0.189206
$298$	−2.21787	−0.128478
$299$	−1.42833	−0.0826023
$300$	0	0
$301$	17.6424	1.01689
$302$	−18.1890	−1.04666
$303$	0	0
$304$	4.93203	0.282871
$305$	0	0
$306$	−4.93203	−0.281945
$307$	17.4786	0.997555	0.498778	−	0.866730i	$-0.333782\pi$
$307$	17.4786	0.997555	0.498778	+	0.866730i	$0.333782\pi$
$308$	−6.52142	−0.371593
$309$	−6.00000	−0.341328
$310$	0	0
$311$	18.1676	1.03019	0.515095	−	0.857133i	$-0.327756\pi$
$311$	18.1676	1.03019	0.515095	+	0.857133i	$0.327756\pi$
$312$	−2.73929	−0.155082
$313$	33.7281	1.90643	0.953213	−	0.302300i	$-0.0977543\pi$
$313$	33.7281	1.90643	0.953213	+	0.302300i	$0.0977543\pi$
$314$	19.2067	1.08390
$315$	0	0
$316$	−6.41061	−0.360625
$317$	2.54655	0.143028	0.0715142	−	0.997440i	$-0.477217\pi$
$317$	2.54655	0.143028	0.0715142	+	0.997440i	$0.477217\pi$
$318$	−13.3426	−0.748218
$319$	1.70021	0.0951934
$320$	0	0
$321$	18.2998	1.02139
$322$	1.04285	0.0581155
$323$	24.3249	1.35347
$324$	1.00000	0.0555556
$325$	0	0
$326$	−9.56050	−0.529507
$327$	−5.34264	−0.295448
$328$	−2.00000	−0.110432
$329$	9.86406	0.543823
$330$	0	0
$331$	10.1638	0.558656	0.279328	−	0.960196i	$-0.409888\pi$
$331$	10.1638	0.558656	0.279328	+	0.960196i	$0.409888\pi$
$332$	1.36776	0.0750657
$333$	10.8212	0.592999
$334$	2.00000	0.109435
$335$	0	0
$336$	2.00000	0.109109
$337$	24.9069	1.35677	0.678383	−	0.734709i	$-0.262681\pi$
$337$	24.9069	1.35677	0.678383	+	0.734709i	$0.262681\pi$
$338$	5.49630	0.298959
$339$	−16.6853	−0.906220
$340$	0	0
$341$	−3.26071	−0.176577
$342$	−4.93203	−0.266694
$343$	20.0000	1.07990
$344$	8.82121	0.475608
$345$	0	0
$346$	−1.45345	−0.0781381
$347$	7.67508	0.412020	0.206010	−	0.978550i	$-0.433952\pi$
$347$	7.67508	0.412020	0.206010	+	0.978550i	$0.433952\pi$
$348$	−0.521423	−0.0279512
$349$	−1.77837	−0.0951939	−0.0475969	−	0.998867i	$-0.515156\pi$
$349$	−1.77837	−0.0951939	−0.0475969	+	0.998867i	$0.515156\pi$
$350$	0	0
$351$	2.73929	0.146212
$352$	−3.26071	−0.173797
$353$	0.932030	0.0496069	0.0248035	−	0.999692i	$-0.492104\pi$
$353$	0.932030	0.0496069	0.0248035	+	0.999692i	$0.492104\pi$
$354$	9.34264	0.496556
$355$	0	0
$356$	−11.8641	−0.628794
$357$	9.86406	0.522061
$358$	26.3817	1.39432
$359$	17.2886	0.912458	0.456229	−	0.889862i	$-0.349200\pi$
$359$	17.2886	0.912458	0.456229	+	0.889862i	$0.349200\pi$
$360$	0	0
$361$	5.32492	0.280259
$362$	7.77837	0.408822
$363$	0.367761	0.0193025
$364$	5.47858	0.287155
$365$	0	0
$366$	−9.75324	−0.509810
$367$	6.82498	0.356261	0.178131	−	0.984007i	$-0.442995\pi$
$367$	6.82498	0.356261	0.178131	+	0.984007i	$0.442995\pi$
$368$	0.521423	0.0271810
$369$	2.00000	0.104116
$370$	0	0
$371$	26.6853	1.38543
$372$	1.00000	0.0518476
$373$	0.135941	0.00703875	0.00351938	−	0.999994i	$-0.498880\pi$
$373$	0.135941	0.00703875	0.00351938	+	0.999994i	$0.498880\pi$
$374$	−16.0819	−0.831577
$375$	0	0
$376$	4.93203	0.254350
$377$	−1.42833	−0.0735626
$378$	−2.00000	−0.102869
$379$	−10.7961	−0.554558	−0.277279	−	0.960789i	$-0.589433\pi$
$379$	−10.7961	−0.554558	−0.277279	+	0.960789i	$0.589433\pi$
$380$	0	0
$381$	−6.52142	−0.334103
$382$	−7.56427	−0.387022
$383$	23.4283	1.19713	0.598566	−	0.801074i	$-0.295738\pi$
$383$	23.4283	1.19713	0.598566	+	0.801074i	$0.295738\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−22.3817	−1.13920
$387$	−8.82121	−0.448407
$388$	7.26071	0.368607
$389$	10.3855	0.526565	0.263282	−	0.964719i	$-0.415195\pi$
$389$	10.3855	0.526565	0.263282	+	0.964719i	$0.415195\pi$
$390$	0	0
$391$	2.57167	0.130055
$392$	3.00000	0.151523
$393$	−13.3426	−0.673047
$394$	−16.6853	−0.840592
$395$	0	0
$396$	3.26071	0.163857
$397$	10.2141	0.512631	0.256315	−	0.966593i	$-0.417491\pi$
$397$	10.2141	0.512631	0.256315	+	0.966593i	$0.417491\pi$
$398$	−15.4535	−0.774612
$399$	9.86406	0.493821
$400$	0	0
$401$	6.30356	0.314785	0.157392	−	0.987536i	$-0.449691\pi$
$401$	6.30356	0.314785	0.157392	+	0.987536i	$0.449691\pi$
$402$	13.5605	0.676336
$403$	2.73929	0.136454
$404$	0	0
$405$	0	0
$406$	1.04285	0.0517556
$407$	35.2849	1.74901
$408$	4.93203	0.244172
$409$	−19.2569	−0.952195	−0.476097	−	0.879393i	$-0.657949\pi$
$409$	−19.2569	−0.952195	−0.476097	+	0.879393i	$0.657949\pi$
$410$	0	0
$411$	3.77837	0.186373
$412$	6.00000	0.295599
$413$	−18.6853	−0.919442
$414$	−0.521423	−0.0256265
$415$	0	0
$416$	2.73929	0.134305
$417$	−12.5214	−0.613177
$418$	−16.0819	−0.786593
$419$	3.47858	0.169940	0.0849698	−	0.996384i	$-0.472921\pi$
$419$	3.47858	0.169940	0.0849698	+	0.996384i	$0.472921\pi$
$420$	0	0
$421$	−4.35757	−0.212375	−0.106188	−	0.994346i	$-0.533864\pi$
$421$	−4.35757	−0.212375	−0.106188	+	0.994346i	$0.533864\pi$
$422$	−17.0428	−0.829633
$423$	−4.93203	−0.239803
$424$	13.3426	0.647976
$425$	0	0
$426$	5.56050	0.269407
$427$	19.5065	0.943985
$428$	−18.2998	−0.884554
$429$	8.93203	0.431242
$430$	0	0
$431$	−22.2495	−1.07172	−0.535861	−	0.844306i	$-0.680013\pi$
$431$	−22.2495	−1.07172	−0.535861	+	0.844306i	$0.680013\pi$
$432$	−1.00000	−0.0481125
$433$	18.8212	0.904490	0.452245	−	0.891894i	$-0.350623\pi$
$433$	18.8212	0.904490	0.452245	+	0.891894i	$0.350623\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	5.34264	0.255866
$437$	2.57167	0.123020
$438$	3.04285	0.145393
$439$	−9.25695	−0.441810	−0.220905	−	0.975295i	$-0.570901\pi$
$439$	−9.25695	−0.441810	−0.220905	+	0.975295i	$0.570901\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	13.5103	0.642617
$443$	8.82121	0.419109	0.209554	−	0.977797i	$-0.432799\pi$
$443$	8.82121	0.419109	0.209554	+	0.977797i	$0.432799\pi$
$444$	−10.8212	−0.513552
$445$	0	0
$446$	−13.7821	−0.652603
$447$	−2.21787	−0.104901
$448$	−2.00000	−0.0944911
$449$	−16.2179	−0.765368	−0.382684	−	0.923879i	$-0.625000\pi$
$449$	−16.2179	−0.765368	−0.382684	+	0.923879i	$0.625000\pi$
$450$	0	0
$451$	6.52142	0.307082
$452$	16.6853	0.784809
$453$	−18.1890	−0.854593
$454$	−2.52142	−0.118336
$455$	0	0
$456$	4.93203	0.230963
$457$	19.4283	0.908819	0.454409	−	0.890793i	$-0.349850\pi$
$457$	19.4283	0.908819	0.454409	+	0.890793i	$0.349850\pi$
$458$	−27.3957	−1.28012
$459$	−4.93203	−0.230207
$460$	0	0
$461$	−2.38548	−0.111103	−0.0555515	−	0.998456i	$-0.517692\pi$
$461$	−2.38548	−0.111103	−0.0555515	+	0.998456i	$0.517692\pi$
$462$	−6.52142	−0.303404
$463$	−4.90314	−0.227868	−0.113934	−	0.993488i	$-0.536345\pi$
$463$	−4.90314	−0.227868	−0.113934	+	0.993488i	$0.536345\pi$
$464$	0.521423	0.0242064
$465$	0	0
$466$	22.8212	1.05717
$467$	22.0857	1.02200	0.511002	−	0.859580i	$-0.329274\pi$
$467$	22.0857	1.02200	0.511002	+	0.859580i	$0.329274\pi$
$468$	−2.73929	−0.126624
$469$	−27.1210	−1.25233
$470$	0	0
$471$	19.2067	0.884998
$472$	−9.34264	−0.430030
$473$	−28.7634	−1.32254
$474$	−6.41061	−0.294449
$475$	0	0
$476$	−9.86406	−0.452118
$477$	−13.3426	−0.610917
$478$	14.2998	0.654057
$479$	−10.1676	−0.464570	−0.232285	−	0.972648i	$-0.574620\pi$
$479$	−10.1676	−0.464570	−0.232285	+	0.972648i	$0.574620\pi$
$480$	0	0
$481$	−29.6424	−1.35158
$482$	−13.3426	−0.607740
$483$	1.04285	0.0474511
$484$	−0.367761	−0.0167164
$485$	0	0
$486$	1.00000	0.0453609
$487$	38.5531	1.74701	0.873504	−	0.486817i	$-0.161842\pi$
$487$	38.5531	1.74701	0.873504	+	0.486817i	$0.161842\pi$
$488$	9.75324	0.441509
$489$	−9.56050	−0.432341
$490$	0	0
$491$	39.7206	1.79256	0.896282	−	0.443484i	$-0.146258\pi$
$491$	39.7206	1.79256	0.896282	+	0.443484i	$0.146258\pi$
$492$	−2.00000	−0.0901670
$493$	2.57167	0.115822
$494$	13.5103	0.607855
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	−11.1210	−0.498845
$498$	1.36776	0.0612908
$499$	31.8641	1.42643	0.713216	−	0.700945i	$-0.247238\pi$
$499$	31.8641	1.42643	0.713216	+	0.700945i	$0.247238\pi$
$500$	0	0
$501$	2.00000	0.0893534
$502$	−10.5214	−0.469594
$503$	26.7961	1.19478	0.597389	−	0.801951i	$-0.296205\pi$
$503$	26.7961	1.19478	0.597389	+	0.801951i	$0.296205\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	−1.70021	−0.0755835
$507$	5.49630	0.244099
$508$	6.52142	0.289341
$509$	−13.5065	−0.598664	−0.299332	−	0.954149i	$-0.596764\pi$
$509$	−13.5065	−0.598664	−0.299332	+	0.954149i	$0.596764\pi$
$510$	0	0
$511$	−6.08569	−0.269215
$512$	−1.00000	−0.0441942
$513$	−4.93203	−0.217754
$514$	7.86406	0.346869
$515$	0	0
$516$	8.82121	0.388332
$517$	−16.0819	−0.707282
$518$	21.6424	0.950914
$519$	−1.45345	−0.0637995
$520$	0	0
$521$	−2.16385	−0.0948000	−0.0474000	−	0.998876i	$-0.515094\pi$
$521$	−2.16385	−0.0948000	−0.0474000	+	0.998876i	$0.515094\pi$
$522$	−0.521423	−0.0228221
$523$	18.1359	0.793029	0.396515	−	0.918028i	$-0.370220\pi$
$523$	18.1359	0.793029	0.396515	+	0.918028i	$0.370220\pi$
$524$	13.3426	0.582876
$525$	0	0
$526$	23.8641	1.04052
$527$	−4.93203	−0.214843
$528$	−3.26071	−0.141904
$529$	−22.7281	−0.988179
$530$	0	0
$531$	9.34264	0.405436
$532$	−9.86406	−0.427661
$533$	−5.47858	−0.237304
$534$	−11.8641	−0.513408
$535$	0	0
$536$	−13.5605	−0.585724
$537$	26.3817	1.13846
$538$	8.95715	0.386170
$539$	−9.78213	−0.421346
$540$	0	0
$541$	7.64996	0.328897	0.164449	−	0.986386i	$-0.447415\pi$
$541$	7.64996	0.328897	0.164449	+	0.986386i	$0.447415\pi$
$542$	13.0959	0.562516
$543$	7.77837	0.333802
$544$	−4.93203	−0.211459
$545$	0	0
$546$	5.47858	0.234461
$547$	−15.1210	−0.646527	−0.323264	−	0.946309i	$-0.604780\pi$
$547$	−15.1210	−0.646527	−0.323264	+	0.946309i	$0.604780\pi$
$548$	−3.77837	−0.161404
$549$	−9.75324	−0.416258
$550$	0	0
$551$	2.57167	0.109557
$552$	0.521423	0.0221932
$553$	12.8212	0.545213
$554$	−3.78213	−0.160687
$555$	0	0
$556$	12.5214	0.531027
$557$	21.5065	0.911259	0.455630	−	0.890169i	$-0.349414\pi$
$557$	21.5065	0.911259	0.455630	+	0.890169i	$0.349414\pi$
$558$	1.00000	0.0423334
$559$	24.1638	1.02202
$560$	0	0
$561$	−16.0819	−0.678979
$562$	−3.04285	−0.128355
$563$	21.2569	0.895873	0.447937	−	0.894065i	$-0.352159\pi$
$563$	21.2569	0.895873	0.447937	+	0.894065i	$0.352159\pi$
$564$	4.93203	0.207676
$565$	0	0
$566$	22.7672	0.956977
$567$	−2.00000	−0.0839921
$568$	−5.56050	−0.233313
$569$	19.4208	0.814162	0.407081	−	0.913392i	$-0.366547\pi$
$569$	19.4208	0.814162	0.407081	+	0.913392i	$0.366547\pi$
$570$	0	0
$571$	23.8641	0.998680	0.499340	−	0.866406i	$-0.333576\pi$
$571$	23.8641	0.998680	0.499340	+	0.866406i	$0.333576\pi$
$572$	−8.93203	−0.373467
$573$	−7.56427	−0.316002
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−1.78213	−0.0741912	−0.0370956	−	0.999312i	$-0.511811\pi$
$577$	−1.78213	−0.0741912	−0.0370956	+	0.999312i	$0.511811\pi$
$578$	−7.32492	−0.304676
$579$	−22.3817	−0.930152
$580$	0	0
$581$	−2.73552	−0.113489
$582$	7.26071	0.300966
$583$	−43.5065	−1.80185
$584$	−3.04285	−0.125914
$585$	0	0
$586$	−3.64243	−0.150467
$587$	−10.1387	−0.418470	−0.209235	−	0.977865i	$-0.567097\pi$
$587$	−10.1387	−0.418470	−0.209235	+	0.977865i	$0.567097\pi$
$588$	3.00000	0.123718
$589$	−4.93203	−0.203221
$590$	0	0
$591$	−16.6853	−0.686340
$592$	10.8212	0.444749
$593$	−43.5846	−1.78981	−0.894903	−	0.446260i	$-0.852756\pi$
$593$	−43.5846	−1.78981	−0.894903	+	0.446260i	$0.852756\pi$
$594$	3.26071	0.133789
$595$	0	0
$596$	2.21787	0.0908473
$597$	−15.4535	−0.632468
$598$	1.42833	0.0584087
$599$	−16.6815	−0.681588	−0.340794	−	0.940138i	$-0.610696\pi$
$599$	−16.6815	−0.681588	−0.340794	+	0.940138i	$0.610696\pi$
$600$	0	0
$601$	−43.6424	−1.78021	−0.890106	−	0.455754i	$-0.849370\pi$
$601$	−43.6424	−1.78021	−0.890106	+	0.455754i	$0.849370\pi$
$602$	−17.6424	−0.719052
$603$	13.5605	0.552226
$604$	18.1890	0.740099
$605$	0	0
$606$	0	0
$607$	10.5996	0.430224	0.215112	−	0.976589i	$-0.430988\pi$
$607$	10.5996	0.430224	0.215112	+	0.976589i	$0.430988\pi$
$608$	−4.93203	−0.200020
$609$	1.04285	0.0422582
$610$	0	0
$611$	13.5103	0.546566
$612$	4.93203	0.199365
$613$	−44.5456	−1.79918	−0.899589	−	0.436737i	$-0.856134\pi$
$613$	−44.5456	−1.79918	−0.899589	+	0.436737i	$0.856134\pi$
$614$	−17.4786	−0.705378
$615$	0	0
$616$	6.52142	0.262756
$617$	40.6853	1.63793	0.818964	−	0.573845i	$-0.194549\pi$
$617$	40.6853	1.63793	0.818964	+	0.573845i	$0.194549\pi$
$618$	6.00000	0.241355
$619$	42.8212	1.72113	0.860565	−	0.509341i	$-0.170111\pi$
$619$	42.8212	1.72113	0.860565	+	0.509341i	$0.170111\pi$
$620$	0	0
$621$	−0.521423	−0.0209240
$622$	−18.1676	−0.728455
$623$	23.7281	0.950647
$624$	2.73929	0.109659
$625$	0	0
$626$	−33.7281	−1.34805
$627$	−16.0819	−0.642250
$628$	−19.2067	−0.766431
$629$	53.3705	2.12802
$630$	0	0
$631$	−1.31473	−0.0523385	−0.0261692	−	0.999658i	$-0.508331\pi$
$631$	−1.31473	−0.0523385	−0.0261692	+	0.999658i	$0.508331\pi$
$632$	6.41061	0.255000
$633$	−17.0428	−0.677392
$634$	−2.54655	−0.101136
$635$	0	0
$636$	13.3426	0.529070
$637$	8.21787	0.325604
$638$	−1.70021	−0.0673119
$639$	5.56050	0.219970
$640$	0	0
$641$	−25.4246	−1.00421	−0.502105	−	0.864807i	$-0.667441\pi$
$641$	−25.4246	−1.00421	−0.502105	+	0.864807i	$0.667441\pi$
$642$	−18.2998	−0.722235
$643$	44.3855	1.75039	0.875196	−	0.483768i	$-0.160732\pi$
$643$	44.3855	1.75039	0.875196	+	0.483768i	$0.160732\pi$
$644$	−1.04285	−0.0410939
$645$	0	0
$646$	−24.3249	−0.957051
$647$	17.5567	0.690227	0.345113	−	0.938561i	$-0.387841\pi$
$647$	17.5567	0.690227	0.345113	+	0.938561i	$0.387841\pi$
$648$	−1.00000	−0.0392837
$649$	30.4636	1.19580
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	9.56050	0.374418
$653$	18.0530	0.706470	0.353235	−	0.935535i	$-0.385082\pi$
$653$	18.0530	0.706470	0.353235	+	0.935535i	$0.385082\pi$
$654$	5.34264	0.208914
$655$	0	0
$656$	2.00000	0.0780869
$657$	3.04285	0.118713
$658$	−9.86406	−0.384541
$659$	−0.957154	−0.0372854	−0.0186427	−	0.999826i	$-0.505935\pi$
$659$	−0.957154	−0.0372854	−0.0186427	+	0.999826i	$0.505935\pi$
$660$	0	0
$661$	−9.56427	−0.372007	−0.186003	−	0.982549i	$-0.559554\pi$
$661$	−9.56427	−0.372007	−0.186003	+	0.982549i	$0.559554\pi$
$662$	−10.1638	−0.395029
$663$	13.5103	0.524695
$664$	−1.36776	−0.0530794
$665$	0	0
$666$	−10.8212	−0.419314
$667$	0.271882	0.0105273
$668$	−2.00000	−0.0773823
$669$	−13.7821	−0.532848
$670$	0	0
$671$	−31.8025	−1.22772
$672$	−2.00000	−0.0771517
$673$	41.7206	1.60821	0.804105	−	0.594487i	$-0.202645\pi$
$673$	41.7206	1.60821	0.804105	+	0.594487i	$0.202645\pi$
$674$	−24.9069	−0.959378
$675$	0	0
$676$	−5.49630	−0.211396
$677$	−21.7784	−0.837011	−0.418505	−	0.908214i	$-0.637446\pi$
$677$	−21.7784	−0.837011	−0.418505	+	0.908214i	$0.637446\pi$
$678$	16.6853	0.640794
$679$	−14.5214	−0.557281
$680$	0	0
$681$	−2.52142	−0.0966211
$682$	3.26071	0.124859
$683$	39.7281	1.52015	0.760077	−	0.649833i	$-0.225161\pi$
$683$	39.7281	1.52015	0.760077	+	0.649833i	$0.225161\pi$
$684$	4.93203	0.188581
$685$	0	0
$686$	−20.0000	−0.763604
$687$	−27.3957	−1.04521
$688$	−8.82121	−0.336306
$689$	36.5493	1.39242
$690$	0	0
$691$	37.5316	1.42777	0.713885	−	0.700263i	$-0.246934\pi$
$691$	37.5316	1.42777	0.713885	+	0.700263i	$0.246934\pi$
$692$	1.45345	0.0552520
$693$	−6.52142	−0.247728
$694$	−7.67508	−0.291342
$695$	0	0
$696$	0.521423	0.0197645
$697$	9.86406	0.373628
$698$	1.77837	0.0673122
$699$	22.8212	0.863178
$700$	0	0
$701$	−16.7393	−0.632234	−0.316117	−	0.948720i	$-0.602379\pi$
$701$	−16.7393	−0.632234	−0.316117	+	0.948720i	$0.602379\pi$
$702$	−2.73929	−0.103388
$703$	53.3705	2.01291
$704$	3.26071	0.122893
$705$	0	0
$706$	−0.932030	−0.0350774
$707$	0	0
$708$	−9.34264	−0.351118
$709$	−30.8463	−1.15846	−0.579229	−	0.815165i	$-0.696646\pi$
$709$	−30.8463	−1.15846	−0.579229	+	0.815165i	$0.696646\pi$
$710$	0	0
$711$	−6.41061	−0.240417
$712$	11.8641	0.444624
$713$	−0.521423	−0.0195274
$714$	−9.86406	−0.369153
$715$	0	0
$716$	−26.3817	−0.985931
$717$	14.2998	0.534035
$718$	−17.2886	−0.645206
$719$	−10.4712	−0.390509	−0.195254	−	0.980753i	$-0.562553\pi$
$719$	−10.4712	−0.390509	−0.195254	+	0.980753i	$0.562553\pi$
$720$	0	0
$721$	−12.0000	−0.446903
$722$	−5.32492	−0.198173
$723$	−13.3426	−0.496218
$724$	−7.77837	−0.289081
$725$	0	0
$726$	−0.367761	−0.0136489
$727$	−30.3779	−1.12666	−0.563328	−	0.826233i	$-0.690479\pi$
$727$	−30.3779	−1.12666	−0.563328	+	0.826233i	$0.690479\pi$
$728$	−5.47858	−0.203050
$729$	1.00000	0.0370370
$730$	0	0
$731$	−43.5065	−1.60915
$732$	9.75324	0.360490
$733$	−34.3855	−1.27006	−0.635028	−	0.772489i	$-0.719012\pi$
$733$	−34.3855	−1.27006	−0.635028	+	0.772489i	$0.719012\pi$
$734$	−6.82498	−0.251915
$735$	0	0
$736$	−0.521423	−0.0192199
$737$	44.2169	1.62875
$738$	−2.00000	−0.0736210
$739$	−17.1210	−0.629806	−0.314903	−	0.949124i	$-0.601972\pi$
$739$	−17.1210	−0.629806	−0.314903	+	0.949124i	$0.601972\pi$
$740$	0	0
$741$	13.5103	0.496312
$742$	−26.6853	−0.979647
$743$	−3.86406	−0.141759	−0.0708793	−	0.997485i	$-0.522581\pi$
$743$	−3.86406	−0.141759	−0.0708793	+	0.997485i	$0.522581\pi$
$744$	−1.00000	−0.0366618
$745$	0	0
$746$	−0.135941	−0.00497715
$747$	1.36776	0.0500438
$748$	16.0819	0.588013
$749$	36.5996	1.33732
$750$	0	0
$751$	−22.1359	−0.807752	−0.403876	−	0.914814i	$-0.632337\pi$
$751$	−22.1359	−0.807752	−0.403876	+	0.914814i	$0.632337\pi$
$752$	−4.93203	−0.179853
$753$	−10.5214	−0.383422
$754$	1.42833	0.0520166
$755$	0	0
$756$	2.00000	0.0727393
$757$	−43.5922	−1.58438	−0.792192	−	0.610272i	$-0.791060\pi$
$757$	−43.5922	−1.58438	−0.792192	+	0.610272i	$0.791060\pi$
$758$	10.7961	0.392132
$759$	−1.70021	−0.0617137
$760$	0	0
$761$	14.9107	0.540511	0.270256	−	0.962789i	$-0.412892\pi$
$761$	14.9107	0.540511	0.270256	+	0.962789i	$0.412892\pi$
$762$	6.52142	0.236246
$763$	−10.6853	−0.386833
$764$	7.56427	0.273666
$765$	0	0
$766$	−23.4283	−0.846500
$767$	−25.5922	−0.924080
$768$	−1.00000	−0.0360844
$769$	48.4134	1.74583	0.872916	−	0.487871i	$-0.162226\pi$
$769$	48.4134	1.74583	0.872916	+	0.487871i	$0.162226\pi$
$770$	0	0
$771$	7.86406	0.283217
$772$	22.3817	0.805536
$773$	6.54933	0.235563	0.117782	−	0.993040i	$-0.462422\pi$
$773$	6.54933	0.235563	0.117782	+	0.993040i	$0.462422\pi$
$774$	8.82121	0.317072
$775$	0	0
$776$	−7.26071	−0.260644
$777$	21.6424	0.776418
$778$	−10.3855	−0.372338
$779$	9.86406	0.353417
$780$	0	0
$781$	18.1312	0.648785
$782$	−2.57167	−0.0919628
$783$	−0.521423	−0.0186341
$784$	−3.00000	−0.107143
$785$	0	0
$786$	13.3426	0.475916
$787$	13.2569	0.472559	0.236280	−	0.971685i	$-0.424072\pi$
$787$	13.2569	0.472559	0.236280	+	0.971685i	$0.424072\pi$
$788$	16.6853	0.594388
$789$	23.8641	0.849583
$790$	0	0
$791$	−33.3705	−1.18652
$792$	−3.26071	−0.115864
$793$	26.7169	0.948747
$794$	−10.2141	−0.362485
$795$	0	0
$796$	15.4535	0.547733
$797$	−13.1210	−0.464770	−0.232385	−	0.972624i	$-0.574653\pi$
$797$	−13.1210	−0.464770	−0.232385	+	0.972624i	$0.574653\pi$
$798$	−9.86406	−0.349184
$799$	−24.3249	−0.860554
$800$	0	0
$801$	−11.8641	−0.419196
$802$	−6.30356	−0.222586
$803$	9.92184	0.350134
$804$	−13.5605	−0.478242
$805$	0	0
$806$	−2.73929	−0.0964873
$807$	8.95715	0.315307
$808$	0	0
$809$	−12.3892	−0.435583	−0.217791	−	0.975995i	$-0.569885\pi$
$809$	−12.3892	−0.435583	−0.217791	+	0.975995i	$0.569885\pi$
$810$	0	0
$811$	−25.6424	−0.900427	−0.450214	−	0.892921i	$-0.648652\pi$
$811$	−25.6424	−0.900427	−0.450214	+	0.892921i	$0.648652\pi$
$812$	−1.04285	−0.0365967
$813$	13.0959	0.459293
$814$	−35.2849	−1.23673
$815$	0	0
$816$	−4.93203	−0.172656
$817$	−43.5065	−1.52210
$818$	19.2569	0.673303
$819$	5.47858	0.191437
$820$	0	0
$821$	0.685273	0.0239162	0.0119581	−	0.999928i	$-0.496194\pi$
$821$	0.685273	0.0239162	0.0119581	+	0.999928i	$0.496194\pi$
$822$	−3.77837	−0.131786
$823$	−8.90314	−0.310344	−0.155172	−	0.987887i	$-0.549593\pi$
$823$	−8.90314	−0.310344	−0.155172	+	0.987887i	$0.549593\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	18.6853	0.650144
$827$	−36.0530	−1.25369	−0.626843	−	0.779145i	$-0.715653\pi$
$827$	−36.0530	−1.25369	−0.626843	+	0.779145i	$0.715653\pi$
$828$	0.521423	0.0181207
$829$	−21.5922	−0.749927	−0.374964	−	0.927040i	$-0.622345\pi$
$829$	−21.5922	−0.749927	−0.374964	+	0.927040i	$0.622345\pi$
$830$	0	0
$831$	−3.78213	−0.131201
$832$	−2.73929	−0.0949677
$833$	−14.7961	−0.512654
$834$	12.5214	0.433581
$835$	0	0
$836$	16.0819	0.556205
$837$	1.00000	0.0345651
$838$	−3.47858	−0.120165
$839$	55.4487	1.91430	0.957151	−	0.289590i	$-0.0935188\pi$
$839$	55.4487	1.91430	0.957151	+	0.289590i	$0.0935188\pi$
$840$	0	0
$841$	−28.7281	−0.990625
$842$	4.35757	0.150172
$843$	−3.04285	−0.104801
$844$	17.0428	0.586639
$845$	0	0
$846$	4.93203	0.169567
$847$	0.735523	0.0252729
$848$	−13.3426	−0.458188
$849$	22.7672	0.781368
$850$	0	0
$851$	5.64243	0.193420
$852$	−5.56050	−0.190500
$853$	34.1136	1.16803	0.584014	−	0.811744i	$-0.301481\pi$
$853$	34.1136	1.16803	0.584014	+	0.811744i	$0.301481\pi$
$854$	−19.5065	−0.667498
$855$	0	0
$856$	18.2998	0.625474
$857$	−37.5065	−1.28120	−0.640599	−	0.767876i	$-0.721314\pi$
$857$	−37.5065	−1.28120	−0.640599	+	0.767876i	$0.721314\pi$
$858$	−8.93203	−0.304934
$859$	−44.6853	−1.52464	−0.762321	−	0.647199i	$-0.775940\pi$
$859$	−44.6853	−1.52464	−0.762321	+	0.647199i	$0.775940\pi$
$860$	0	0
$861$	4.00000	0.136320
$862$	22.2495	0.757822
$863$	−16.7431	−0.569940	−0.284970	−	0.958536i	$-0.591984\pi$
$863$	−16.7431	−0.569940	−0.284970	+	0.958536i	$0.591984\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−18.8212	−0.639571
$867$	−7.32492	−0.248767
$868$	2.00000	0.0678844
$869$	−20.9031	−0.709090
$870$	0	0
$871$	−37.1461	−1.25865
$872$	−5.34264	−0.180924
$873$	7.26071	0.245738
$874$	−2.57167	−0.0869881
$875$	0	0
$876$	−3.04285	−0.102808
$877$	−44.5214	−1.50338	−0.751691	−	0.659516i	$-0.770761\pi$
$877$	−44.5214	−1.50338	−0.751691	+	0.659516i	$0.770761\pi$
$878$	9.25695	0.312407
$879$	−3.64243	−0.122856
$880$	0	0
$881$	52.2737	1.76115	0.880573	−	0.473911i	$-0.157158\pi$
$881$	52.2737	1.76115	0.880573	+	0.473911i	$0.157158\pi$
$882$	3.00000	0.101015
$883$	43.2924	1.45690	0.728452	−	0.685096i	$-0.240240\pi$
$883$	43.2924	1.45690	0.728452	+	0.685096i	$0.240240\pi$
$884$	−13.5103	−0.454399
$885$	0	0
$886$	−8.82121	−0.296354
$887$	29.3705	0.986166	0.493083	−	0.869982i	$-0.335870\pi$
$887$	29.3705	0.986166	0.493083	+	0.869982i	$0.335870\pi$
$888$	10.8212	0.363136
$889$	−13.0428	−0.437443
$890$	0	0
$891$	3.26071	0.109238
$892$	13.7821	0.461460
$893$	−24.3249	−0.814002
$894$	2.21787	0.0741765
$895$	0	0
$896$	2.00000	0.0668153
$897$	1.42833	0.0476905
$898$	16.2179	0.541197
$899$	−0.521423	−0.0173904
$900$	0	0
$901$	−65.8063	−2.19232
$902$	−6.52142	−0.217140
$903$	−17.6424	−0.587103
$904$	−16.6853	−0.554944
$905$	0	0
$906$	18.1890	0.604288
$907$	10.3315	0.343051	0.171525	−	0.985180i	$-0.445130\pi$
$907$	10.3315	0.343051	0.171525	+	0.985180i	$0.445130\pi$
$908$	2.52142	0.0836764
$909$	0	0
$910$	0	0
$911$	−34.9572	−1.15818	−0.579091	−	0.815263i	$-0.696592\pi$
$911$	−34.9572	−1.15818	−0.579091	+	0.815263i	$0.696592\pi$
$912$	−4.93203	−0.163316
$913$	4.45987	0.147600
$914$	−19.4283	−0.642632
$915$	0	0
$916$	27.3957	0.905178
$917$	−26.6853	−0.881225
$918$	4.93203	0.162781
$919$	7.17125	0.236558	0.118279	−	0.992980i	$-0.462262\pi$
$919$	7.17125	0.236558	0.118279	+	0.992980i	$0.462262\pi$
$920$	0	0
$921$	−17.4786	−0.575939
$922$	2.38548	0.0785617
$923$	−15.2318	−0.501361
$924$	6.52142	0.214539
$925$	0	0
$926$	4.90314	0.161127
$927$	6.00000	0.197066
$928$	−0.521423	−0.0171165
$929$	−51.1489	−1.67814	−0.839071	−	0.544022i	$-0.816901\pi$
$929$	−51.1489	−1.67814	−0.839071	+	0.544022i	$0.816901\pi$
$930$	0	0
$931$	−14.7961	−0.484922
$932$	−22.8212	−0.747534
$933$	−18.1676	−0.594781
$934$	−22.0857	−0.722666
$935$	0	0
$936$	2.73929	0.0895364
$937$	−21.5027	−0.702463	−0.351232	−	0.936289i	$-0.614237\pi$
$937$	−21.5027	−0.702463	−0.351232	+	0.936289i	$0.614237\pi$
$938$	27.1210	0.885532
$939$	−33.7281	−1.10068
$940$	0	0
$941$	4.79330	0.156257	0.0781286	−	0.996943i	$-0.475106\pi$
$941$	4.79330	0.156257	0.0781286	+	0.996943i	$0.475106\pi$
$942$	−19.2067	−0.625788
$943$	1.04285	0.0339597
$944$	9.34264	0.304077
$945$	0	0
$946$	28.7634	0.935180
$947$	−29.0959	−0.945489	−0.472745	−	0.881200i	$-0.656737\pi$
$947$	−29.0959	−0.945489	−0.472745	+	0.881200i	$0.656737\pi$
$948$	6.41061	0.208207
$949$	−8.33523	−0.270573
$950$	0	0
$951$	−2.54655	−0.0825775
$952$	9.86406	0.319696
$953$	−3.28960	−0.106561	−0.0532803	−	0.998580i	$-0.516968\pi$
$953$	−3.28960	−0.106561	−0.0532803	+	0.998580i	$0.516968\pi$
$954$	13.3426	0.431984
$955$	0	0
$956$	−14.2998	−0.462488
$957$	−1.70021	−0.0549600
$958$	10.1676	0.328501
$959$	7.55674	0.244020
$960$	0	0
$961$	1.00000	0.0322581
$962$	29.6424	0.955710
$963$	−18.2998	−0.589703
$964$	13.3426	0.429737
$965$	0	0
$966$	−1.04285	−0.0335530
$967$	12.2960	0.395413	0.197707	−	0.980261i	$-0.436651\pi$
$967$	12.2960	0.395413	0.197707	+	0.980261i	$0.436651\pi$
$968$	0.367761	0.0118203
$969$	−24.3249	−0.781429
$970$	0	0
$971$	53.4990	1.71686	0.858432	−	0.512928i	$-0.171439\pi$
$971$	53.4990	1.71686	0.858432	+	0.512928i	$0.171439\pi$
$972$	−1.00000	−0.0320750
$973$	−25.0428	−0.802837
$974$	−38.5531	−1.23532
$975$	0	0
$976$	−9.75324	−0.312194
$977$	40.2420	1.28746	0.643728	−	0.765254i	$-0.277387\pi$
$977$	40.2420	1.28746	0.643728	+	0.765254i	$0.277387\pi$
$978$	9.56050	0.305711
$979$	−38.6853	−1.23639
$980$	0	0
$981$	5.34264	0.170577
$982$	−39.7206	−1.26753
$983$	−6.87900	−0.219406	−0.109703	−	0.993964i	$-0.534990\pi$
$983$	−6.87900	−0.219406	−0.109703	+	0.993964i	$0.534990\pi$
$984$	2.00000	0.0637577
$985$	0	0
$986$	−2.57167	−0.0818987
$987$	−9.86406	−0.313976
$988$	−13.5103	−0.429818
$989$	−4.59958	−0.146258
$990$	0	0
$991$	8.44326	0.268209	0.134105	−	0.990967i	$-0.457184\pi$
$991$	8.44326	0.268209	0.134105	+	0.990967i	$0.457184\pi$
$992$	1.00000	0.0317500
$993$	−10.1638	−0.322540
$994$	11.1210	0.352737
$995$	0	0
$996$	−1.36776	−0.0433392
$997$	55.7560	1.76581	0.882906	−	0.469551i	$-0.155584\pi$
$997$	55.7560	1.76581	0.882906	+	0.469551i	$0.155584\pi$
$998$	−31.8641	−1.00864
$999$	−10.8212	−0.342368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.a.ci.1.2		3
5.2	odd	4		930.2.d.i.559.2	✓	6
5.3	odd	4		930.2.d.i.559.5	yes	6
5.4	even	2		4650.2.a.cp.1.2		3
15.2	even	4		2790.2.d.j.559.5		6
15.8	even	4		2790.2.d.j.559.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.i.559.2	✓	6	5.2	odd	4
930.2.d.i.559.5	yes	6	5.3	odd	4
2790.2.d.j.559.2		6	15.8	even	4
2790.2.d.j.559.5		6	15.2	even	4
4650.2.a.ci.1.2		3	1.1	even	1	trivial
4650.2.a.cp.1.2		3	5.4	even	2

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.26071 q^{11} -1.00000 q^{12} -2.73929 q^{13} +2.00000 q^{14} +1.00000 q^{16} +4.93203 q^{17} -1.00000 q^{18} +4.93203 q^{19} +2.00000 q^{21} -3.26071 q^{22} +0.521423 q^{23} +1.00000 q^{24} +2.73929 q^{26} -1.00000 q^{27} -2.00000 q^{28} +0.521423 q^{29} -1.00000 q^{31} -1.00000 q^{32} -3.26071 q^{33} -4.93203 q^{34} +1.00000 q^{36} +10.8212 q^{37} -4.93203 q^{38} +2.73929 q^{39} +2.00000 q^{41} -2.00000 q^{42} -8.82121 q^{43} +3.26071 q^{44} -0.521423 q^{46} -4.93203 q^{47} -1.00000 q^{48} -3.00000 q^{49} -4.93203 q^{51} -2.73929 q^{52} -13.3426 q^{53} +1.00000 q^{54} +2.00000 q^{56} -4.93203 q^{57} -0.521423 q^{58} +9.34264 q^{59} -9.75324 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +3.26071 q^{66} +13.5605 q^{67} +4.93203 q^{68} -0.521423 q^{69} +5.56050 q^{71} -1.00000 q^{72} +3.04285 q^{73} -10.8212 q^{74} +4.93203 q^{76} -6.52142 q^{77} -2.73929 q^{78} -6.41061 q^{79} +1.00000 q^{81} -2.00000 q^{82} +1.36776 q^{83} +2.00000 q^{84} +8.82121 q^{86} -0.521423 q^{87} -3.26071 q^{88} -11.8641 q^{89} +5.47858 q^{91} +0.521423 q^{92} +1.00000 q^{93} +4.93203 q^{94} +1.00000 q^{96} +7.26071 q^{97} +3.00000 q^{98} +3.26071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{7} - 3 q^{8} + 3 q^{9} + 8 q^{11} - 3 q^{12} - 10 q^{13} + 6 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} + 6 q^{21} - 8 q^{22} - 2 q^{23} + 3 q^{24} + 10 q^{26} - 3 q^{27} - 6 q^{28} - 2 q^{29} - 3 q^{31} - 3 q^{32} - 8 q^{33} + 2 q^{34} + 3 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{41} - 6 q^{42} + 8 q^{44} + 2 q^{46} + 2 q^{47} - 3 q^{48} - 9 q^{49} + 2 q^{51} - 10 q^{52} - 10 q^{53} + 3 q^{54} + 6 q^{56} + 2 q^{57} + 2 q^{58} - 2 q^{59} + 14 q^{61} + 3 q^{62} - 6 q^{63} + 3 q^{64} + 8 q^{66} + 16 q^{67} - 2 q^{68} + 2 q^{69} - 8 q^{71} - 3 q^{72} + 2 q^{73} - 6 q^{74} - 2 q^{76} - 16 q^{77} - 10 q^{78} - 6 q^{79} + 3 q^{81} - 6 q^{82} - 2 q^{83} + 6 q^{84} + 2 q^{87} - 8 q^{88} - 2 q^{89} + 20 q^{91} - 2 q^{92} + 3 q^{93} - 2 q^{94} + 3 q^{96} + 20 q^{97} + 9 q^{98} + 8 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^7 - 3 * q^8 + 3 * q^9 + 8 * q^11 - 3 * q^12 - 10 * q^13 + 6 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 - 2 * q^19 + 6 * q^21 - 8 * q^22 - 2 * q^23 + 3 * q^24 + 10 * q^26 - 3 * q^27 - 6 * q^28 - 2 * q^29 - 3 * q^31 - 3 * q^32 - 8 * q^33 + 2 * q^34 + 3 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^41 - 6 * q^42 + 8 * q^44 + 2 * q^46 + 2 * q^47 - 3 * q^48 - 9 * q^49 + 2 * q^51 - 10 * q^52 - 10 * q^53 + 3 * q^54 + 6 * q^56 + 2 * q^57 + 2 * q^58 - 2 * q^59 + 14 * q^61 + 3 * q^62 - 6 * q^63 + 3 * q^64 + 8 * q^66 + 16 * q^67 - 2 * q^68 + 2 * q^69 - 8 * q^71 - 3 * q^72 + 2 * q^73 - 6 * q^74 - 2 * q^76 - 16 * q^77 - 10 * q^78 - 6 * q^79 + 3 * q^81 - 6 * q^82 - 2 * q^83 + 6 * q^84 + 2 * q^87 - 8 * q^88 - 2 * q^89 + 20 * q^91 - 2 * q^92 + 3 * q^93 - 2 * q^94 + 3 * q^96 + 20 * q^97 + 9 * q^98 + 8 * q^99

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