LMFDB - Embedded newform 1550.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1550,2,Mod(1,1550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1550, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1550 = 2 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1550.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:	$12.3768123133$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.6224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 2x + 5 $ x^4 - 6x^2 - 2x + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 310)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.37033$ of defining polynomial
Character	$\chi$	$=$	1550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.370326 q^{3} +1.00000 q^{4} +0.370326 q^{6} +4.27844 q^{7} -1.00000 q^{8} -2.86286 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.370326 q^{3} +1.00000 q^{4} +0.370326 q^{6} +4.27844 q^{7} -1.00000 q^{8} -2.86286 q^{9} +2.81252 q^{11} -0.370326 q^{12} +4.53408 q^{13} -4.27844 q^{14} +1.00000 q^{16} -0.197785 q^{17} +2.86286 q^{18} +2.66000 q^{19} -1.58442 q^{21} -2.81252 q^{22} +0.877793 q^{23} +0.370326 q^{24} -4.53408 q^{26} +2.17117 q^{27} +4.27844 q^{28} -7.47252 q^{29} -1.00000 q^{31} -1.00000 q^{32} -1.04155 q^{33} +0.197785 q^{34} -2.86286 q^{36} +5.87409 q^{37} -2.66000 q^{38} -1.67909 q^{39} -8.99908 q^{41} +1.58442 q^{42} +5.71033 q^{43} +2.81252 q^{44} -0.877793 q^{46} +10.0873 q^{47} -0.370326 q^{48} +11.3051 q^{49} +0.0732449 q^{51} +4.53408 q^{52} -0.206568 q^{53} -2.17117 q^{54} -4.27844 q^{56} -0.985065 q^{57} +7.47252 q^{58} +4.55688 q^{59} -5.96876 q^{61} +1.00000 q^{62} -12.2486 q^{63} +1.00000 q^{64} +1.04155 q^{66} -5.70571 q^{67} -0.197785 q^{68} -0.325070 q^{69} -8.06064 q^{71} +2.86286 q^{72} -14.8079 q^{73} -5.87409 q^{74} +2.66000 q^{76} +12.0332 q^{77} +1.67909 q^{78} +1.97754 q^{79} +7.78454 q^{81} +8.99908 q^{82} -0.554096 q^{83} -1.58442 q^{84} -5.71033 q^{86} +2.76727 q^{87} -2.81252 q^{88} +12.0532 q^{89} +19.3988 q^{91} +0.877793 q^{92} +0.370326 q^{93} -10.0873 q^{94} +0.370326 q^{96} +1.88287 q^{97} -11.3051 q^{98} -8.05186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{11} + 4 q^{12} + 10 q^{13} - 6 q^{14} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{21} + 8 q^{22} + 8 q^{23} - 4 q^{24} - 10 q^{26} + 22 q^{27} + 6 q^{28} - 6 q^{29} - 4 q^{31} - 4 q^{32} - 6 q^{33} - 4 q^{34} + 4 q^{36} + 20 q^{37} - 6 q^{38} + 20 q^{39} + 2 q^{42} + 22 q^{43} - 8 q^{44} - 8 q^{46} + 2 q^{47} + 4 q^{48} + 16 q^{49} - 22 q^{51} + 10 q^{52} + 2 q^{53} - 22 q^{54} - 6 q^{56} + 16 q^{57} + 6 q^{58} - 4 q^{59} + 2 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 6 q^{66} + 22 q^{67} + 4 q^{68} + 14 q^{69} - 12 q^{71} - 4 q^{72} + 4 q^{73} - 20 q^{74} + 6 q^{76} - 2 q^{77} - 20 q^{78} - 16 q^{79} + 44 q^{81} - 8 q^{83} - 2 q^{84} - 22 q^{86} - 18 q^{87} + 8 q^{88} + 12 q^{89} - 10 q^{91} + 8 q^{92} - 4 q^{93} - 2 q^{94} - 4 q^{96} + 6 q^{97} - 16 q^{98} - 10 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^11 + 4 * q^12 + 10 * q^13 - 6 * q^14 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 6 * q^19 - 2 * q^21 + 8 * q^22 + 8 * q^23 - 4 * q^24 - 10 * q^26 + 22 * q^27 + 6 * q^28 - 6 * q^29 - 4 * q^31 - 4 * q^32 - 6 * q^33 - 4 * q^34 + 4 * q^36 + 20 * q^37 - 6 * q^38 + 20 * q^39 + 2 * q^42 + 22 * q^43 - 8 * q^44 - 8 * q^46 + 2 * q^47 + 4 * q^48 + 16 * q^49 - 22 * q^51 + 10 * q^52 + 2 * q^53 - 22 * q^54 - 6 * q^56 + 16 * q^57 + 6 * q^58 - 4 * q^59 + 2 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 + 6 * q^66 + 22 * q^67 + 4 * q^68 + 14 * q^69 - 12 * q^71 - 4 * q^72 + 4 * q^73 - 20 * q^74 + 6 * q^76 - 2 * q^77 - 20 * q^78 - 16 * q^79 + 44 * q^81 - 8 * q^83 - 2 * q^84 - 22 * q^86 - 18 * q^87 + 8 * q^88 + 12 * q^89 - 10 * q^91 + 8 * q^92 - 4 * q^93 - 2 * q^94 - 4 * q^96 + 6 * q^97 - 16 * q^98 - 10 * 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
$3$	−0.370326	−0.213808	−0.106904	−	0.994269i	$-0.534094\pi$
$3$	−0.370326	−0.213808	−0.106904	+	0.994269i	$0.534094\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.370326	0.151185
$7$	4.27844	1.61710	0.808549	−	0.588428i	$-0.200253\pi$
$7$	4.27844	1.61710	0.808549	+	0.588428i	$0.200253\pi$
$8$	−1.00000	−0.353553
$9$	−2.86286	−0.954286
$10$	0	0
$11$	2.81252	0.848008	0.424004	−	0.905660i	$-0.360624\pi$
$11$	2.81252	0.848008	0.424004	+	0.905660i	$0.360624\pi$
$12$	−0.370326	−0.106904
$13$	4.53408	1.25753	0.628764	−	0.777596i	$-0.283561\pi$
$13$	4.53408	1.25753	0.628764	+	0.777596i	$0.283561\pi$
$14$	−4.27844	−1.14346
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.197785	−0.0479699	−0.0239850	−	0.999712i	$-0.507635\pi$
$17$	−0.197785	−0.0479699	−0.0239850	+	0.999712i	$0.507635\pi$
$18$	2.86286	0.674782
$19$	2.66000	0.610245	0.305122	−	0.952313i	$-0.401303\pi$
$19$	2.66000	0.610245	0.305122	+	0.952313i	$0.401303\pi$
$20$	0	0
$21$	−1.58442	−0.345748
$22$	−2.81252	−0.599632
$23$	0.877793	0.183033	0.0915163	−	0.995804i	$-0.470829\pi$
$23$	0.877793	0.183033	0.0915163	+	0.995804i	$0.470829\pi$
$24$	0.370326	0.0755925
$25$	0	0
$26$	−4.53408	−0.889207
$27$	2.17117	0.417842
$28$	4.27844	0.808549
$29$	−7.47252	−1.38761	−0.693806	−	0.720162i	$-0.744068\pi$
$29$	−7.47252	−1.38761	−0.693806	+	0.720162i	$0.744068\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−1.04155	−0.181311
$34$	0.197785	0.0339198
$35$	0	0
$36$	−2.86286	−0.477143
$37$	5.87409	0.965694	0.482847	−	0.875705i	$-0.339603\pi$
$37$	5.87409	0.965694	0.482847	+	0.875705i	$0.339603\pi$
$38$	−2.66000	−0.431508
$39$	−1.67909	−0.268869
$40$	0	0
$41$	−8.99908	−1.40542	−0.702710	−	0.711476i	$-0.748027\pi$
$41$	−8.99908	−1.40542	−0.702710	+	0.711476i	$0.748027\pi$
$42$	1.58442	0.244481
$43$	5.71033	0.870817	0.435409	−	0.900233i	$-0.356604\pi$
$43$	5.71033	0.870817	0.435409	+	0.900233i	$0.356604\pi$
$44$	2.81252	0.424004
$45$	0	0
$46$	−0.877793	−0.129424
$47$	10.0873	1.47138	0.735689	−	0.677319i	$-0.236858\pi$
$47$	10.0873	1.47138	0.735689	+	0.677319i	$0.236858\pi$
$48$	−0.370326	−0.0534519
$49$	11.3051	1.61501
$50$	0	0
$51$	0.0732449	0.0102563
$52$	4.53408	0.628764
$53$	−0.206568	−0.0283743	−0.0141872	−	0.999899i	$-0.504516\pi$
$53$	−0.206568	−0.0283743	−0.0141872	+	0.999899i	$0.504516\pi$
$54$	−2.17117	−0.295459
$55$	0	0
$56$	−4.27844	−0.571731
$57$	−0.985065	−0.130475
$58$	7.47252	0.981190
$59$	4.55688	0.593256	0.296628	−	0.954993i	$-0.404138\pi$
$59$	4.55688	0.593256	0.296628	+	0.954993i	$0.404138\pi$
$60$	0	0
$61$	−5.96876	−0.764221	−0.382111	−	0.924117i	$-0.624803\pi$
$61$	−5.96876	−0.764221	−0.382111	+	0.924117i	$0.624803\pi$
$62$	1.00000	0.127000
$63$	−12.2486	−1.54318
$64$	1.00000	0.125000
$65$	0	0
$66$	1.04155	0.128206
$67$	−5.70571	−0.697063	−0.348531	−	0.937297i	$-0.613320\pi$
$67$	−5.70571	−0.697063	−0.348531	+	0.937297i	$0.613320\pi$
$68$	−0.197785	−0.0239850
$69$	−0.325070	−0.0391338
$70$	0	0
$71$	−8.06064	−0.956622	−0.478311	−	0.878190i	$-0.658751\pi$
$71$	−8.06064	−0.956622	−0.478311	+	0.878190i	$0.658751\pi$
$72$	2.86286	0.337391
$73$	−14.8079	−1.73313	−0.866567	−	0.499061i	$-0.833678\pi$
$73$	−14.8079	−1.73313	−0.866567	+	0.499061i	$0.833678\pi$
$74$	−5.87409	−0.682849
$75$	0	0
$76$	2.66000	0.305122
$77$	12.0332	1.37131
$78$	1.67909	0.190119
$79$	1.97754	0.222491	0.111245	−	0.993793i	$-0.464516\pi$
$79$	1.97754	0.222491	0.111245	+	0.993793i	$0.464516\pi$
$80$	0	0
$81$	7.78454	0.864948
$82$	8.99908	0.993782
$83$	−0.554096	−0.0608199	−0.0304100	−	0.999538i	$-0.509681\pi$
$83$	−0.554096	−0.0608199	−0.0304100	+	0.999538i	$0.509681\pi$
$84$	−1.58442	−0.172874
$85$	0	0
$86$	−5.71033	−0.615761
$87$	2.76727	0.296682
$88$	−2.81252	−0.299816
$89$	12.0532	1.27764	0.638820	−	0.769356i	$-0.279423\pi$
$89$	12.0532	1.27764	0.638820	+	0.769356i	$0.279423\pi$
$90$	0	0
$91$	19.3988	2.03355
$92$	0.877793	0.0915163
$93$	0.370326	0.0384010
$94$	−10.0873	−1.04042
$95$	0	0
$96$	0.370326	0.0377962
$97$	1.88287	0.191177	0.0955883	−	0.995421i	$-0.469527\pi$
$97$	1.88287	0.191177	0.0955883	+	0.995421i	$0.469527\pi$
$98$	−11.3051	−1.14198
$99$	−8.05186	−0.809242
$100$	0	0
$101$	14.8820	1.48081	0.740405	−	0.672161i	$-0.234634\pi$
$101$	14.8820	1.48081	0.740405	+	0.672161i	$0.234634\pi$
$102$	−0.0732449	−0.00725233
$103$	13.0457	1.28543	0.642716	−	0.766105i	$-0.277808\pi$
$103$	13.0457	1.28543	0.642716	+	0.766105i	$0.277808\pi$
$104$	−4.53408	−0.444603
$105$	0	0
$106$	0.206568	0.0200637
$107$	0.103114	0.00996840	0.00498420	−	0.999988i	$-0.498413\pi$
$107$	0.103114	0.00996840	0.00498420	+	0.999988i	$0.498413\pi$
$108$	2.17117	0.208921
$109$	10.1413	0.971360	0.485680	−	0.874137i	$-0.338572\pi$
$109$	10.1413	0.971360	0.485680	+	0.874137i	$0.338572\pi$
$110$	0	0
$111$	−2.17533	−0.206473
$112$	4.27844	0.404275
$113$	8.91842	0.838975	0.419487	−	0.907761i	$-0.362210\pi$
$113$	8.91842	0.838975	0.419487	+	0.907761i	$0.362210\pi$
$114$	0.985065	0.0922598
$115$	0	0
$116$	−7.47252	−0.693806
$117$	−12.9804	−1.20004
$118$	−4.55688	−0.419495
$119$	−0.846211	−0.0775721
$120$	0	0
$121$	−3.08971	−0.280882
$122$	5.96876	0.540386
$123$	3.33259	0.300490
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	12.2486	1.09119
$127$	−2.56349	−0.227473	−0.113736	−	0.993511i	$-0.536282\pi$
$127$	−2.56349	−0.227473	−0.113736	+	0.993511i	$0.536282\pi$
$128$	−1.00000	−0.0883883
$129$	−2.11468	−0.186187
$130$	0	0
$131$	−8.72064	−0.761926	−0.380963	−	0.924590i	$-0.624407\pi$
$131$	−8.72064	−0.761926	−0.380963	+	0.924590i	$0.624407\pi$
$132$	−1.04155	−0.0906554
$133$	11.3806	0.986826
$134$	5.70571	0.492898
$135$	0	0
$136$	0.197785	0.0169599
$137$	−9.12221	−0.779363	−0.389681	−	0.920950i	$-0.627415\pi$
$137$	−9.12221	−0.779363	−0.389681	+	0.920950i	$0.627415\pi$
$138$	0.325070	0.0276718
$139$	16.5407	1.40296	0.701481	−	0.712688i	$-0.252522\pi$
$139$	16.5407	1.40296	0.701481	+	0.712688i	$0.252522\pi$
$140$	0	0
$141$	−3.73557	−0.314592
$142$	8.06064	0.676434
$143$	12.7522	1.06639
$144$	−2.86286	−0.238572
$145$	0	0
$146$	14.8079	1.22551
$147$	−4.18656	−0.345301
$148$	5.87409	0.482847
$149$	14.2426	1.16680	0.583399	−	0.812186i	$-0.301723\pi$
$149$	14.2426	1.16680	0.583399	+	0.812186i	$0.301723\pi$
$150$	0	0
$151$	23.6632	1.92569	0.962843	−	0.270060i	$-0.0870437\pi$
$151$	23.6632	1.92569	0.962843	+	0.270060i	$0.0870437\pi$
$152$	−2.66000	−0.215754
$153$	0.566231	0.0457770
$154$	−12.0332	−0.969665
$155$	0	0
$156$	−1.67909	−0.134435
$157$	−14.1970	−1.13304	−0.566521	−	0.824047i	$-0.691711\pi$
$157$	−14.1970	−1.13304	−0.566521	+	0.824047i	$0.691711\pi$
$158$	−1.97754	−0.157325
$159$	0.0764976	0.00606666
$160$	0	0
$161$	3.75559	0.295982
$162$	−7.78454	−0.611611
$163$	1.83128	0.143437	0.0717183	−	0.997425i	$-0.477152\pi$
$163$	1.83128	0.143437	0.0717183	+	0.997425i	$0.477152\pi$
$164$	−8.99908	−0.702710
$165$	0	0
$166$	0.554096	0.0430062
$167$	18.6417	1.44254	0.721269	−	0.692655i	$-0.243559\pi$
$167$	18.6417	1.44254	0.721269	+	0.692655i	$0.243559\pi$
$168$	1.58442	0.122240
$169$	7.55791	0.581378
$170$	0	0
$171$	−7.61519	−0.582348
$172$	5.71033	0.435409
$173$	−12.1139	−0.921001	−0.460500	−	0.887659i	$-0.652330\pi$
$173$	−12.1139	−0.921001	−0.460500	+	0.887659i	$0.652330\pi$
$174$	−2.76727	−0.209786
$175$	0	0
$176$	2.81252	0.212002
$177$	−1.68753	−0.126843
$178$	−12.0532	−0.903428
$179$	−21.6720	−1.61984	−0.809921	−	0.586539i	$-0.800490\pi$
$179$	−21.6720	−1.61984	−0.809921	+	0.586539i	$0.800490\pi$
$180$	0	0
$181$	24.4151	1.81476	0.907381	−	0.420310i	$-0.138079\pi$
$181$	24.4151	1.81476	0.907381	+	0.420310i	$0.138079\pi$
$182$	−19.3988	−1.43794
$183$	2.21039	0.163396
$184$	−0.877793	−0.0647118
$185$	0	0
$186$	−0.370326	−0.0271536
$187$	−0.556275	−0.0406789
$188$	10.0873	0.735689
$189$	9.28922	0.675691
$190$	0	0
$191$	−14.6035	−1.05667	−0.528336	−	0.849035i	$-0.677184\pi$
$191$	−14.6035	−1.05667	−0.528336	+	0.849035i	$0.677184\pi$
$192$	−0.370326	−0.0267260
$193$	25.0839	1.80558	0.902789	−	0.430083i	$-0.141516\pi$
$193$	25.0839	1.80558	0.902789	+	0.430083i	$0.141516\pi$
$194$	−1.88287	−0.135182
$195$	0	0
$196$	11.3051	0.807504
$197$	11.5672	0.824128	0.412064	−	0.911155i	$-0.364808\pi$
$197$	11.5672	0.824128	0.412064	+	0.911155i	$0.364808\pi$
$198$	8.05186	0.572221
$199$	0.518696	0.0367694	0.0183847	−	0.999831i	$-0.494148\pi$
$199$	0.518696	0.0367694	0.0183847	+	0.999831i	$0.494148\pi$
$200$	0	0
$201$	2.11297	0.149037
$202$	−14.8820	−1.04709
$203$	−31.9707	−2.24391
$204$	0.0732449	0.00512817
$205$	0	0
$206$	−13.0457	−0.908938
$207$	−2.51300	−0.174665
$208$	4.53408	0.314382
$209$	7.48130	0.517493
$210$	0	0
$211$	−20.2626	−1.39493	−0.697467	−	0.716617i	$-0.745690\pi$
$211$	−20.2626	−1.39493	−0.697467	+	0.716617i	$0.745690\pi$
$212$	−0.206568	−0.0141872
$213$	2.98507	0.204533
$214$	−0.103114	−0.00704872
$215$	0	0
$216$	−2.17117	−0.147729
$217$	−4.27844	−0.290439
$218$	−10.1413	−0.686855
$219$	5.48375	0.370557
$220$	0	0
$221$	−0.896774	−0.0603235
$222$	2.17533	0.145998
$223$	19.6166	1.31363	0.656813	−	0.754054i	$-0.271904\pi$
$223$	19.6166	1.31363	0.656813	+	0.754054i	$0.271904\pi$
$224$	−4.27844	−0.285865
$225$	0	0
$226$	−8.91842	−0.593245
$227$	19.2501	1.27767	0.638837	−	0.769342i	$-0.279416\pi$
$227$	19.2501	1.27767	0.638837	+	0.769342i	$0.279416\pi$
$228$	−0.985065	−0.0652376
$229$	−23.1807	−1.53182	−0.765911	−	0.642947i	$-0.777712\pi$
$229$	−23.1807	−1.53182	−0.765911	+	0.642947i	$0.777712\pi$
$230$	0	0
$231$	−4.45621	−0.293197
$232$	7.47252	0.490595
$233$	−7.04155	−0.461307	−0.230654	−	0.973036i	$-0.574086\pi$
$233$	−7.04155	−0.461307	−0.230654	+	0.973036i	$0.574086\pi$
$234$	12.9804	0.848558
$235$	0	0
$236$	4.55688	0.296628
$237$	−0.732335	−0.0475703
$238$	0.846211	0.0548517
$239$	−19.9908	−1.29309	−0.646547	−	0.762874i	$-0.723788\pi$
$239$	−19.9908	−1.29309	−0.646547	+	0.762874i	$0.723788\pi$
$240$	0	0
$241$	−22.7788	−1.46731	−0.733657	−	0.679520i	$-0.762188\pi$
$241$	−22.7788	−1.46731	−0.733657	+	0.679520i	$0.762188\pi$
$242$	3.08971	0.198614
$243$	−9.39632	−0.602774
$244$	−5.96876	−0.382111
$245$	0	0
$246$	−3.33259	−0.212478
$247$	12.0606	0.767400
$248$	1.00000	0.0635001
$249$	0.205196	0.0130038
$250$	0	0
$251$	19.8050	1.25008	0.625040	−	0.780592i	$-0.285083\pi$
$251$	19.8050	1.25008	0.625040	+	0.780592i	$0.285083\pi$
$252$	−12.2486	−0.771588
$253$	2.46881	0.155213
$254$	2.56349	0.160847
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.8826	−1.17786	−0.588931	−	0.808183i	$-0.700451\pi$
$257$	−18.8826	−1.17786	−0.588931	+	0.808183i	$0.700451\pi$
$258$	2.11468	0.131654
$259$	25.1319	1.56162
$260$	0	0
$261$	21.3928	1.32418
$262$	8.72064	0.538763
$263$	−23.5411	−1.45161	−0.725804	−	0.687901i	$-0.758532\pi$
$263$	−23.5411	−1.45161	−0.725804	+	0.687901i	$0.758532\pi$
$264$	1.04155	0.0641030
$265$	0	0
$266$	−11.3806	−0.697792
$267$	−4.46362	−0.273169
$268$	−5.70571	−0.348531
$269$	−0.0792837	−0.00483401	−0.00241701	−	0.999997i	$-0.500769\pi$
$269$	−0.0792837	−0.00483401	−0.00241701	+	0.999997i	$0.500769\pi$
$270$	0	0
$271$	−21.3508	−1.29697	−0.648483	−	0.761229i	$-0.724596\pi$
$271$	−21.3508	−1.29697	−0.648483	+	0.761229i	$0.724596\pi$
$272$	−0.197785	−0.0119925
$273$	−7.18388	−0.434788
$274$	9.12221	0.551093
$275$	0	0
$276$	−0.325070	−0.0195669
$277$	−1.24396	−0.0747424	−0.0373712	−	0.999301i	$-0.511898\pi$
$277$	−1.24396	−0.0747424	−0.0373712	+	0.999301i	$0.511898\pi$
$278$	−16.5407	−0.992045
$279$	2.86286	0.171395
$280$	0	0
$281$	23.1818	1.38291	0.691456	−	0.722419i	$-0.256970\pi$
$281$	23.1818	1.38291	0.691456	+	0.722419i	$0.256970\pi$
$282$	3.73557	0.222450
$283$	−19.3182	−1.14834	−0.574172	−	0.818734i	$-0.694676\pi$
$283$	−19.3182	−1.14834	−0.574172	+	0.818734i	$0.694676\pi$
$284$	−8.06064	−0.478311
$285$	0	0
$286$	−12.7522	−0.754055
$287$	−38.5020	−2.27270
$288$	2.86286	0.168696
$289$	−16.9609	−0.997699
$290$	0	0
$291$	−0.697276	−0.0408750
$292$	−14.8079	−0.866567
$293$	9.55455	0.558183	0.279091	−	0.960265i	$-0.409967\pi$
$293$	9.55455	0.558183	0.279091	+	0.960265i	$0.409967\pi$
$294$	4.18656	0.244165
$295$	0	0
$296$	−5.87409	−0.341424
$297$	6.10647	0.354333
$298$	−14.2426	−0.825050
$299$	3.97999	0.230169
$300$	0	0
$301$	24.4313	1.40820
$302$	−23.6632	−1.36167
$303$	−5.51117	−0.316609
$304$	2.66000	0.152561
$305$	0	0
$306$	−0.566231	−0.0323692
$307$	−16.8669	−0.962645	−0.481323	−	0.876544i	$-0.659843\pi$
$307$	−16.8669	−0.962645	−0.481323	+	0.876544i	$0.659843\pi$
$308$	12.0332	0.685656
$309$	−4.83116	−0.274835
$310$	0	0
$311$	−8.12870	−0.460936	−0.230468	−	0.973080i	$-0.574026\pi$
$311$	−8.12870	−0.460936	−0.230468	+	0.973080i	$0.574026\pi$
$312$	1.67909	0.0950597
$313$	−8.53362	−0.482349	−0.241174	−	0.970482i	$-0.577533\pi$
$313$	−8.53362	−0.482349	−0.241174	+	0.970482i	$0.577533\pi$
$314$	14.1970	0.801182
$315$	0	0
$316$	1.97754	0.111245
$317$	22.0588	1.23895	0.619473	−	0.785018i	$-0.287346\pi$
$317$	22.0588	1.23895	0.619473	+	0.785018i	$0.287346\pi$
$318$	−0.0764976	−0.00428977
$319$	−21.0166	−1.17671
$320$	0	0
$321$	−0.0381858	−0.00213132
$322$	−3.75559	−0.209291
$323$	−0.526107	−0.0292734
$324$	7.78454	0.432474
$325$	0	0
$326$	−1.83128	−0.101425
$327$	−3.75559	−0.207684
$328$	8.99908	0.496891
$329$	43.1577	2.37936
$330$	0	0
$331$	−35.4100	−1.94631	−0.973156	−	0.230147i	$-0.926079\pi$
$331$	−35.4100	−1.94631	−0.973156	+	0.230147i	$0.926079\pi$
$332$	−0.554096	−0.0304100
$333$	−16.8167	−0.921549
$334$	−18.6417	−1.02003
$335$	0	0
$336$	−1.58442	−0.0864371
$337$	12.1827	0.663636	0.331818	−	0.943343i	$-0.392338\pi$
$337$	12.1827	0.663636	0.331818	+	0.943343i	$0.392338\pi$
$338$	−7.55791	−0.411096
$339$	−3.30272	−0.179379
$340$	0	0
$341$	−2.81252	−0.152307
$342$	7.61519	0.411782
$343$	18.4189	0.994529
$344$	−5.71033	−0.307880
$345$	0	0
$346$	12.1139	0.651246
$347$	−29.0561	−1.55981	−0.779907	−	0.625895i	$-0.784734\pi$
$347$	−29.0561	−1.55981	−0.779907	+	0.625895i	$0.784734\pi$
$348$	2.76727	0.148341
$349$	6.65014	0.355974	0.177987	−	0.984033i	$-0.443042\pi$
$349$	6.65014	0.355974	0.177987	+	0.984033i	$0.443042\pi$
$350$	0	0
$351$	9.84426	0.525448
$352$	−2.81252	−0.149908
$353$	−4.37414	−0.232812	−0.116406	−	0.993202i	$-0.537137\pi$
$353$	−4.37414	−0.232812	−0.116406	+	0.993202i	$0.537137\pi$
$354$	1.68753	0.0896913
$355$	0	0
$356$	12.0532	0.638820
$357$	0.313374	0.0165855
$358$	21.6720	1.14540
$359$	−8.42463	−0.444635	−0.222318	−	0.974974i	$-0.571362\pi$
$359$	−8.42463	−0.444635	−0.222318	+	0.974974i	$0.571362\pi$
$360$	0	0
$361$	−11.9244	−0.627601
$362$	−24.4151	−1.28323
$363$	1.14420	0.0600548
$364$	19.3988	1.01677
$365$	0	0
$366$	−2.21039	−0.115539
$367$	23.0748	1.20449	0.602247	−	0.798310i	$-0.294272\pi$
$367$	23.0748	1.20449	0.602247	+	0.798310i	$0.294272\pi$
$368$	0.877793	0.0457581
$369$	25.7631	1.34117
$370$	0	0
$371$	−0.883790	−0.0458841
$372$	0.370326	0.0192005
$373$	−29.9809	−1.55235	−0.776176	−	0.630516i	$-0.782843\pi$
$373$	−29.9809	−1.55235	−0.776176	+	0.630516i	$0.782843\pi$
$374$	0.556275	0.0287643
$375$	0	0
$376$	−10.0873	−0.520211
$377$	−33.8810	−1.74496
$378$	−9.28922	−0.477786
$379$	−1.67990	−0.0862905	−0.0431452	−	0.999069i	$-0.513738\pi$
$379$	−1.67990	−0.0862905	−0.0431452	+	0.999069i	$0.513738\pi$
$380$	0	0
$381$	0.949325	0.0486354
$382$	14.6035	0.747181
$383$	11.1130	0.567846	0.283923	−	0.958847i	$-0.408364\pi$
$383$	11.1130	0.567846	0.283923	+	0.958847i	$0.408364\pi$
$384$	0.370326	0.0188981
$385$	0	0
$386$	−25.0839	−1.27674
$387$	−16.3479	−0.831009
$388$	1.88287	0.0955883
$389$	−22.1026	−1.12065	−0.560324	−	0.828273i	$-0.689324\pi$
$389$	−22.1026	−1.12065	−0.560324	+	0.828273i	$0.689324\pi$
$390$	0	0
$391$	−0.173614	−0.00878005
$392$	−11.3051	−0.570992
$393$	3.22948	0.162906
$394$	−11.5672	−0.582747
$395$	0	0
$396$	−8.05186	−0.404621
$397$	9.80141	0.491919	0.245959	−	0.969280i	$-0.420897\pi$
$397$	9.80141	0.491919	0.245959	+	0.969280i	$0.420897\pi$
$398$	−0.518696	−0.0259999
$399$	−4.21454	−0.210991
$400$	0	0
$401$	14.1389	0.706061	0.353030	−	0.935612i	$-0.385151\pi$
$401$	14.1389	0.706061	0.353030	+	0.935612i	$0.385151\pi$
$402$	−2.11297	−0.105385
$403$	−4.53408	−0.225859
$404$	14.8820	0.740405
$405$	0	0
$406$	31.9707	1.58668
$407$	16.5210	0.818916
$408$	−0.0732449	−0.00362616
$409$	9.05312	0.447648	0.223824	−	0.974630i	$-0.428146\pi$
$409$	9.05312	0.447648	0.223824	+	0.974630i	$0.428146\pi$
$410$	0	0
$411$	3.37819	0.166634
$412$	13.0457	0.642716
$413$	19.4964	0.959353
$414$	2.51300	0.123507
$415$	0	0
$416$	−4.53408	−0.222302
$417$	−6.12545	−0.299964
$418$	−7.48130	−0.365923
$419$	−24.5652	−1.20009	−0.600044	−	0.799967i	$-0.704850\pi$
$419$	−24.5652	−1.20009	−0.600044	+	0.799967i	$0.704850\pi$
$420$	0	0
$421$	−1.92431	−0.0937851	−0.0468926	−	0.998900i	$-0.514932\pi$
$421$	−1.92431	−0.0937851	−0.0468926	+	0.998900i	$0.514932\pi$
$422$	20.2626	0.986367
$423$	−28.8784	−1.40412
$424$	0.206568	0.0100318
$425$	0	0
$426$	−2.98507	−0.144627
$427$	−25.5370	−1.23582
$428$	0.103114	0.00498420
$429$	−4.72248	−0.228003
$430$	0	0
$431$	22.4711	1.08240	0.541198	−	0.840895i	$-0.317971\pi$
$431$	22.4711	1.08240	0.541198	+	0.840895i	$0.317971\pi$
$432$	2.17117	0.104460
$433$	28.8079	1.38442	0.692210	−	0.721696i	$-0.256637\pi$
$433$	28.8079	1.38442	0.692210	+	0.721696i	$0.256637\pi$
$434$	4.27844	0.205372
$435$	0	0
$436$	10.1413	0.485680
$437$	2.33493	0.111695
$438$	−5.48375	−0.262024
$439$	−11.3814	−0.543207	−0.271603	−	0.962409i	$-0.587554\pi$
$439$	−11.3814	−0.543207	−0.271603	+	0.962409i	$0.587554\pi$
$440$	0	0
$441$	−32.3648	−1.54118
$442$	0.896774	0.0426552
$443$	5.48894	0.260787	0.130394	−	0.991462i	$-0.458376\pi$
$443$	5.48894	0.260787	0.130394	+	0.991462i	$0.458376\pi$
$444$	−2.17533	−0.103236
$445$	0	0
$446$	−19.6166	−0.928873
$447$	−5.27439	−0.249470
$448$	4.27844	0.202137
$449$	−11.7183	−0.553021	−0.276511	−	0.961011i	$-0.589178\pi$
$449$	−11.7183	−0.553021	−0.276511	+	0.961011i	$0.589178\pi$
$450$	0	0
$451$	−25.3101	−1.19181
$452$	8.91842	0.419487
$453$	−8.76311	−0.411727
$454$	−19.2501	−0.903452
$455$	0	0
$456$	0.985065	0.0461299
$457$	19.6698	0.920116	0.460058	−	0.887889i	$-0.347829\pi$
$457$	19.6698	0.920116	0.460058	+	0.887889i	$0.347829\pi$
$458$	23.1807	1.08316
$459$	−0.429425	−0.0200438
$460$	0	0
$461$	34.0577	1.58623	0.793113	−	0.609074i	$-0.208459\pi$
$461$	34.0577	1.58623	0.793113	+	0.609074i	$0.208459\pi$
$462$	4.45621	0.207322
$463$	16.0140	0.744234	0.372117	−	0.928186i	$-0.378632\pi$
$463$	16.0140	0.744234	0.372117	+	0.928186i	$0.378632\pi$
$464$	−7.47252	−0.346903
$465$	0	0
$466$	7.04155	0.326194
$467$	−31.6506	−1.46462	−0.732308	−	0.680973i	$-0.761557\pi$
$467$	−31.6506	−1.46462	−0.732308	+	0.680973i	$0.761557\pi$
$468$	−12.9804	−0.600021
$469$	−24.4115	−1.12722
$470$	0	0
$471$	5.25751	0.242253
$472$	−4.55688	−0.209747
$473$	16.0604	0.738460
$474$	0.732335	0.0336373
$475$	0	0
$476$	−0.846211	−0.0387860
$477$	0.591376	0.0270772
$478$	19.9908	0.914356
$479$	3.25751	0.148839	0.0744197	−	0.997227i	$-0.476290\pi$
$479$	3.25751	0.148839	0.0744197	+	0.997227i	$0.476290\pi$
$480$	0	0
$481$	26.6336	1.21439
$482$	22.7788	1.03755
$483$	−1.39079	−0.0632832
$484$	−3.08971	−0.140441
$485$	0	0
$486$	9.39632	0.426226
$487$	−40.0906	−1.81668	−0.908340	−	0.418234i	$-0.862649\pi$
$487$	−40.0906	−1.81668	−0.908340	+	0.418234i	$0.862649\pi$
$488$	5.96876	0.270193
$489$	−0.678169	−0.0306679
$490$	0	0
$491$	−28.6488	−1.29290	−0.646450	−	0.762956i	$-0.723747\pi$
$491$	−28.6488	−1.29290	−0.646450	+	0.762956i	$0.723747\pi$
$492$	3.33259	0.150245
$493$	1.47795	0.0665636
$494$	−12.0606	−0.542634
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	−34.4870	−1.54695
$498$	−0.205196	−0.00919506
$499$	−18.5438	−0.830135	−0.415068	−	0.909791i	$-0.636242\pi$
$499$	−18.5438	−0.830135	−0.415068	+	0.909791i	$0.636242\pi$
$500$	0	0
$501$	−6.90350	−0.308426
$502$	−19.8050	−0.883940
$503$	−38.4488	−1.71435	−0.857174	−	0.515027i	$-0.827782\pi$
$503$	−38.4488	−1.71435	−0.857174	+	0.515027i	$0.827782\pi$
$504$	12.2486	0.545595
$505$	0	0
$506$	−2.46881	−0.109752
$507$	−2.79889	−0.124303
$508$	−2.56349	−0.113736
$509$	−38.6820	−1.71455	−0.857274	−	0.514860i	$-0.827844\pi$
$509$	−38.6820	−1.71455	−0.857274	+	0.514860i	$0.827844\pi$
$510$	0	0
$511$	−63.3547	−2.80265
$512$	−1.00000	−0.0441942
$513$	5.77530	0.254986
$514$	18.8826	0.832874
$515$	0	0
$516$	−2.11468	−0.0930937
$517$	28.3707	1.24774
$518$	−25.1319	−1.10423
$519$	4.48608	0.196917
$520$	0	0
$521$	−11.4945	−0.503584	−0.251792	−	0.967781i	$-0.581020\pi$
$521$	−11.4945	−0.503584	−0.251792	+	0.967781i	$0.581020\pi$
$522$	−21.3928	−0.936336
$523$	7.48837	0.327444	0.163722	−	0.986507i	$-0.447650\pi$
$523$	7.48837	0.327444	0.163722	+	0.986507i	$0.447650\pi$
$524$	−8.72064	−0.380963
$525$	0	0
$526$	23.5411	1.02644
$527$	0.197785	0.00861565
$528$	−1.04155	−0.0453277
$529$	−22.2295	−0.966499
$530$	0	0
$531$	−13.0457	−0.566136
$532$	11.3806	0.493413
$533$	−40.8026	−1.76736
$534$	4.46362	0.193160
$535$	0	0
$536$	5.70571	0.246449
$537$	8.02571	0.346335
$538$	0.0792837	0.00341816
$539$	31.7958	1.36954
$540$	0	0
$541$	14.3075	0.615128	0.307564	−	0.951527i	$-0.400486\pi$
$541$	14.3075	0.615128	0.307564	+	0.951527i	$0.400486\pi$
$542$	21.3508	0.917094
$543$	−9.04155	−0.388010
$544$	0.197785	0.00847996
$545$	0	0
$546$	7.18388	0.307442
$547$	11.8919	0.508462	0.254231	−	0.967144i	$-0.418178\pi$
$547$	11.8919	0.508462	0.254231	+	0.967144i	$0.418178\pi$
$548$	−9.12221	−0.389681
$549$	17.0877	0.729286
$550$	0	0
$551$	−19.8769	−0.846783
$552$	0.325070	0.0138359
$553$	8.46080	0.359790
$554$	1.24396	0.0528508
$555$	0	0
$556$	16.5407	0.701481
$557$	−10.9703	−0.464826	−0.232413	−	0.972617i	$-0.574662\pi$
$557$	−10.9703	−0.464826	−0.232413	+	0.972617i	$0.574662\pi$
$558$	−2.86286	−0.121194
$559$	25.8911	1.09508
$560$	0	0
$561$	0.206003	0.00869746
$562$	−23.1818	−0.977866
$563$	−3.76635	−0.158733	−0.0793663	−	0.996846i	$-0.525290\pi$
$563$	−3.76635	−0.158733	−0.0793663	+	0.996846i	$0.525290\pi$
$564$	−3.73557	−0.157296
$565$	0	0
$566$	19.3182	0.812003
$567$	33.3057	1.39871
$568$	8.06064	0.338217
$569$	−13.3107	−0.558015	−0.279008	−	0.960289i	$-0.590005\pi$
$569$	−13.3107	−0.558015	−0.279008	+	0.960289i	$0.590005\pi$
$570$	0	0
$571$	−14.6540	−0.613249	−0.306625	−	0.951831i	$-0.599200\pi$
$571$	−14.6540	−0.613249	−0.306625	+	0.951831i	$0.599200\pi$
$572$	12.7522	0.533197
$573$	5.40806	0.225925
$574$	38.5020	1.60704
$575$	0	0
$576$	−2.86286	−0.119286
$577$	1.56856	0.0653002	0.0326501	−	0.999467i	$-0.489605\pi$
$577$	1.56856	0.0653002	0.0326501	+	0.999467i	$0.489605\pi$
$578$	16.9609	0.705480
$579$	−9.28922	−0.386047
$580$	0	0
$581$	−2.37067	−0.0983518
$582$	0.697276	0.0289030
$583$	−0.580978	−0.0240617
$584$	14.8079	0.612755
$585$	0	0
$586$	−9.55455	−0.394695
$587$	−27.8374	−1.14897	−0.574487	−	0.818514i	$-0.694798\pi$
$587$	−27.8374	−1.14897	−0.574487	+	0.818514i	$0.694798\pi$
$588$	−4.18656	−0.172651
$589$	−2.66000	−0.109603
$590$	0	0
$591$	−4.28363	−0.176205
$592$	5.87409	0.241424
$593$	7.78777	0.319806	0.159903	−	0.987133i	$-0.448882\pi$
$593$	7.78777	0.319806	0.159903	+	0.987133i	$0.448882\pi$
$594$	−6.10647	−0.250551
$595$	0	0
$596$	14.2426	0.583399
$597$	−0.192087	−0.00786158
$598$	−3.97999	−0.162754
$599$	20.4329	0.834868	0.417434	−	0.908707i	$-0.362930\pi$
$599$	20.4329	0.834868	0.417434	+	0.908707i	$0.362930\pi$
$600$	0	0
$601$	2.23121	0.0910128	0.0455064	−	0.998964i	$-0.485510\pi$
$601$	2.23121	0.0910128	0.0455064	+	0.998964i	$0.485510\pi$
$602$	−24.4313	−0.995746
$603$	16.3346	0.665197
$604$	23.6632	0.962843
$605$	0	0
$606$	5.51117	0.223876
$607$	−21.3582	−0.866902	−0.433451	−	0.901177i	$-0.642704\pi$
$607$	−21.3582	−0.866902	−0.433451	+	0.901177i	$0.642704\pi$
$608$	−2.66000	−0.107877
$609$	11.8396	0.479765
$610$	0	0
$611$	45.7365	1.85030
$612$	0.566231	0.0228885
$613$	25.5373	1.03144	0.515721	−	0.856756i	$-0.327524\pi$
$613$	25.5373	1.03144	0.515721	+	0.856756i	$0.327524\pi$
$614$	16.8669	0.680693
$615$	0	0
$616$	−12.0332	−0.484832
$617$	7.64751	0.307877	0.153939	−	0.988080i	$-0.450804\pi$
$617$	7.64751	0.307877	0.153939	+	0.988080i	$0.450804\pi$
$618$	4.83116	0.194338
$619$	19.5972	0.787676	0.393838	−	0.919180i	$-0.371147\pi$
$619$	19.5972	0.787676	0.393838	+	0.919180i	$0.371147\pi$
$620$	0	0
$621$	1.90584	0.0764786
$622$	8.12870	0.325931
$623$	51.5690	2.06607
$624$	−1.67909	−0.0672173
$625$	0	0
$626$	8.53362	0.341072
$627$	−2.77052	−0.110644
$628$	−14.1970	−0.566521
$629$	−1.16181	−0.0463243
$630$	0	0
$631$	17.5038	0.696814	0.348407	−	0.937343i	$-0.386723\pi$
$631$	17.5038	0.696814	0.348407	+	0.937343i	$0.386723\pi$
$632$	−1.97754	−0.0786624
$633$	7.50376	0.298248
$634$	−22.0588	−0.876067
$635$	0	0
$636$	0.0764976	0.00303333
$637$	51.2581	2.03092
$638$	21.0166	0.832057
$639$	23.0765	0.912892
$640$	0	0
$641$	18.9832	0.749792	0.374896	−	0.927067i	$-0.377678\pi$
$641$	18.9832	0.749792	0.374896	+	0.927067i	$0.377678\pi$
$642$	0.0381858	0.00150707
$643$	7.85904	0.309930	0.154965	−	0.987920i	$-0.450473\pi$
$643$	7.85904	0.309930	0.154965	+	0.987920i	$0.450473\pi$
$644$	3.75559	0.147991
$645$	0	0
$646$	0.526107	0.0206994
$647$	42.4505	1.66890	0.834451	−	0.551082i	$-0.185785\pi$
$647$	42.4505	1.66890	0.834451	+	0.551082i	$0.185785\pi$
$648$	−7.78454	−0.305805
$649$	12.8163	0.503085
$650$	0	0
$651$	1.58442	0.0620982
$652$	1.83128	0.0717183
$653$	−20.0881	−0.786107	−0.393053	−	0.919516i	$-0.628581\pi$
$653$	−20.0881	−0.786107	−0.393053	+	0.919516i	$0.628581\pi$
$654$	3.75559	0.146855
$655$	0	0
$656$	−8.99908	−0.351355
$657$	42.3929	1.65391
$658$	−43.1577	−1.68246
$659$	−43.1928	−1.68255	−0.841276	−	0.540605i	$-0.818195\pi$
$659$	−43.1928	−1.68255	−0.841276	+	0.540605i	$0.818195\pi$
$660$	0	0
$661$	10.7458	0.417965	0.208982	−	0.977919i	$-0.432985\pi$
$661$	10.7458	0.417965	0.208982	+	0.977919i	$0.432985\pi$
$662$	35.4100	1.37625
$663$	0.332099	0.0128976
$664$	0.554096	0.0215031
$665$	0	0
$666$	16.8167	0.651633
$667$	−6.55933	−0.253978
$668$	18.6417	0.721269
$669$	−7.26454	−0.280863
$670$	0	0
$671$	−16.7873	−0.648066
$672$	1.58442	0.0611202
$673$	48.3880	1.86522	0.932611	−	0.360884i	$-0.117525\pi$
$673$	48.3880	1.86522	0.932611	+	0.360884i	$0.117525\pi$
$674$	−12.1827	−0.469262
$675$	0	0
$676$	7.55791	0.290689
$677$	17.4893	0.672168	0.336084	−	0.941832i	$-0.390897\pi$
$677$	17.4893	0.672168	0.336084	+	0.941832i	$0.390897\pi$
$678$	3.30272	0.126840
$679$	8.05575	0.309151
$680$	0	0
$681$	−7.12881	−0.273177
$682$	2.81252	0.107697
$683$	10.4920	0.401463	0.200732	−	0.979646i	$-0.435668\pi$
$683$	10.4920	0.401463	0.200732	+	0.979646i	$0.435668\pi$
$684$	−7.61519	−0.291174
$685$	0	0
$686$	−18.4189	−0.703238
$687$	8.58440	0.327515
$688$	5.71033	0.217704
$689$	−0.936598	−0.0356815
$690$	0	0
$691$	2.24999	0.0855935	0.0427967	−	0.999084i	$-0.486373\pi$
$691$	2.24999	0.0855935	0.0427967	+	0.999084i	$0.486373\pi$
$692$	−12.1139	−0.460500
$693$	−34.4494	−1.30862
$694$	29.0561	1.10296
$695$	0	0
$696$	−2.76727	−0.104893
$697$	1.77988	0.0674179
$698$	−6.65014	−0.251711
$699$	2.60767	0.0986311
$700$	0	0
$701$	−12.1951	−0.460604	−0.230302	−	0.973119i	$-0.573971\pi$
$701$	−12.1951	−0.460604	−0.230302	+	0.973119i	$0.573971\pi$
$702$	−9.84426	−0.371548
$703$	15.6250	0.589310
$704$	2.81252	0.106001
$705$	0	0
$706$	4.37414	0.164623
$707$	63.6716	2.39462
$708$	−1.68753	−0.0634213
$709$	−10.6764	−0.400961	−0.200481	−	0.979698i	$-0.564250\pi$
$709$	−10.6764	−0.400961	−0.200481	+	0.979698i	$0.564250\pi$
$710$	0	0
$711$	−5.66142	−0.212320
$712$	−12.0532	−0.451714
$713$	−0.877793	−0.0328736
$714$	−0.313374	−0.0117277
$715$	0	0
$716$	−21.6720	−0.809921
$717$	7.40309	0.276474
$718$	8.42463	0.314404
$719$	−5.49146	−0.204797	−0.102398	−	0.994743i	$-0.532652\pi$
$719$	−5.49146	−0.204797	−0.102398	+	0.994743i	$0.532652\pi$
$720$	0	0
$721$	55.8153	2.07867
$722$	11.9244	0.443781
$723$	8.43559	0.313723
$724$	24.4151	0.907381
$725$	0	0
$726$	−1.14420	−0.0424652
$727$	27.0989	1.00504	0.502522	−	0.864564i	$-0.332406\pi$
$727$	27.0989	1.00504	0.502522	+	0.864564i	$0.332406\pi$
$728$	−19.3988	−0.718968
$729$	−19.8739	−0.736071
$730$	0	0
$731$	−1.12942	−0.0417730
$732$	2.21039	0.0816982
$733$	−42.3891	−1.56568	−0.782838	−	0.622226i	$-0.786229\pi$
$733$	−42.3891	−1.56568	−0.782838	+	0.622226i	$0.786229\pi$
$734$	−23.0748	−0.851705
$735$	0	0
$736$	−0.877793	−0.0323559
$737$	−16.0474	−0.591115
$738$	−25.7631	−0.948353
$739$	−2.05370	−0.0755465	−0.0377733	−	0.999286i	$-0.512026\pi$
$739$	−2.05370	−0.0755465	−0.0377733	+	0.999286i	$0.512026\pi$
$740$	0	0
$741$	−4.46637	−0.164076
$742$	0.883790	0.0324450
$743$	39.0597	1.43296	0.716481	−	0.697606i	$-0.245752\pi$
$743$	39.0597	1.43296	0.716481	+	0.697606i	$0.245752\pi$
$744$	−0.370326	−0.0135768
$745$	0	0
$746$	29.9809	1.09768
$747$	1.58630	0.0580396
$748$	−0.556275	−0.0203394
$749$	0.441167	0.0161199
$750$	0	0
$751$	−6.86549	−0.250525	−0.125263	−	0.992124i	$-0.539977\pi$
$751$	−6.86549	−0.250525	−0.125263	+	0.992124i	$0.539977\pi$
$752$	10.0873	0.367845
$753$	−7.33431	−0.267277
$754$	33.8810	1.23387
$755$	0	0
$756$	9.28922	0.337846
$757$	−11.3406	−0.412180	−0.206090	−	0.978533i	$-0.566074\pi$
$757$	−11.3406	−0.412180	−0.206090	+	0.978533i	$0.566074\pi$
$758$	1.67990	0.0610166
$759$	−0.914266	−0.0331858
$760$	0	0
$761$	4.58423	0.166178	0.0830891	−	0.996542i	$-0.473521\pi$
$761$	4.58423	0.166178	0.0830891	+	0.996542i	$0.473521\pi$
$762$	−0.949325	−0.0343904
$763$	43.3890	1.57079
$764$	−14.6035	−0.528336
$765$	0	0
$766$	−11.1130	−0.401527
$767$	20.6613	0.746036
$768$	−0.370326	−0.0133630
$769$	11.5710	0.417261	0.208631	−	0.977995i	$-0.433099\pi$
$769$	11.5710	0.417261	0.208631	+	0.977995i	$0.433099\pi$
$770$	0	0
$771$	6.99270	0.251836
$772$	25.0839	0.902789
$773$	−30.6711	−1.10316	−0.551581	−	0.834121i	$-0.685975\pi$
$773$	−30.6711	−1.10316	−0.551581	+	0.834121i	$0.685975\pi$
$774$	16.3479	0.587612
$775$	0	0
$776$	−1.88287	−0.0675911
$777$	−9.30701	−0.333887
$778$	22.1026	0.792418
$779$	−23.9375	−0.857651
$780$	0	0
$781$	−22.6708	−0.811224
$782$	0.173614	0.00620844
$783$	−16.2241	−0.579802
$784$	11.3051	0.403752
$785$	0	0
$786$	−3.22948	−0.115192
$787$	10.4710	0.373251	0.186625	−	0.982431i	$-0.440245\pi$
$787$	10.4710	0.373251	0.186625	+	0.982431i	$0.440245\pi$
$788$	11.5672	0.412064
$789$	8.71790	0.310365
$790$	0	0
$791$	38.1570	1.35671
$792$	8.05186	0.286110
$793$	−27.0629	−0.961030
$794$	−9.80141	−0.347839
$795$	0	0
$796$	0.518696	0.0183847
$797$	−32.9860	−1.16842	−0.584212	−	0.811601i	$-0.698596\pi$
$797$	−32.9860	−1.16842	−0.584212	+	0.811601i	$0.698596\pi$
$798$	4.21454	0.149193
$799$	−1.99511	−0.0705819
$800$	0	0
$801$	−34.5067	−1.21923
$802$	−14.1389	−0.499260
$803$	−41.6476	−1.46971
$804$	2.11297	0.0745187
$805$	0	0
$806$	4.53408	0.159706
$807$	0.0293608	0.00103355
$808$	−14.8820	−0.523545
$809$	36.6076	1.28705	0.643527	−	0.765423i	$-0.277470\pi$
$809$	36.6076	1.28705	0.643527	+	0.765423i	$0.277470\pi$
$810$	0	0
$811$	−41.2334	−1.44790	−0.723951	−	0.689851i	$-0.757676\pi$
$811$	−41.2334	−1.44790	−0.723951	+	0.689851i	$0.757676\pi$
$812$	−31.9707	−1.12195
$813$	7.90674	0.277302
$814$	−16.5210	−0.579061
$815$	0	0
$816$	0.0732449	0.00256408
$817$	15.1895	0.531412
$818$	−9.05312	−0.316535
$819$	−55.5360	−1.94059
$820$	0	0
$821$	1.51560	0.0528947	0.0264474	−	0.999650i	$-0.491581\pi$
$821$	1.51560	0.0528947	0.0264474	+	0.999650i	$0.491581\pi$
$822$	−3.37819	−0.117828
$823$	9.48975	0.330792	0.165396	−	0.986227i	$-0.447110\pi$
$823$	9.48975	0.330792	0.165396	+	0.986227i	$0.447110\pi$
$824$	−13.0457	−0.454469
$825$	0	0
$826$	−19.4964	−0.678365
$827$	20.3371	0.707190	0.353595	−	0.935399i	$-0.384959\pi$
$827$	20.3371	0.707190	0.353595	+	0.935399i	$0.384959\pi$
$828$	−2.51300	−0.0873327
$829$	−8.76509	−0.304424	−0.152212	−	0.988348i	$-0.548640\pi$
$829$	−8.76509	−0.304424	−0.152212	+	0.988348i	$0.548640\pi$
$830$	0	0
$831$	0.460671	0.0159805
$832$	4.53408	0.157191
$833$	−2.23597	−0.0774718
$834$	6.12545	0.212107
$835$	0	0
$836$	7.48130	0.258746
$837$	−2.17117	−0.0750466
$838$	24.5652	0.848591
$839$	−1.47196	−0.0508175	−0.0254088	−	0.999677i	$-0.508089\pi$
$839$	−1.47196	−0.0508175	−0.0254088	+	0.999677i	$0.508089\pi$
$840$	0	0
$841$	26.8386	0.925468
$842$	1.92431	0.0663161
$843$	−8.58483	−0.295677
$844$	−20.2626	−0.697467
$845$	0	0
$846$	28.8784	0.992860
$847$	−13.2191	−0.454214
$848$	−0.206568	−0.00709359
$849$	7.15401	0.245525
$850$	0	0
$851$	5.15623	0.176753
$852$	2.98507	0.102267
$853$	−32.0816	−1.09845	−0.549226	−	0.835674i	$-0.685077\pi$
$853$	−32.0816	−1.09845	−0.549226	+	0.835674i	$0.685077\pi$
$854$	25.5370	0.873858
$855$	0	0
$856$	−0.103114	−0.00352436
$857$	−37.1503	−1.26903	−0.634516	−	0.772910i	$-0.718800\pi$
$857$	−37.1503	−1.26903	−0.634516	+	0.772910i	$0.718800\pi$
$858$	4.72248	0.161223
$859$	8.95811	0.305647	0.152823	−	0.988254i	$-0.451163\pi$
$859$	8.95811	0.305647	0.152823	+	0.988254i	$0.451163\pi$
$860$	0	0
$861$	14.2583	0.485922
$862$	−22.4711	−0.765370
$863$	−5.40970	−0.184148	−0.0920741	−	0.995752i	$-0.529350\pi$
$863$	−5.40970	−0.184148	−0.0920741	+	0.995752i	$0.529350\pi$
$864$	−2.17117	−0.0738647
$865$	0	0
$866$	−28.8079	−0.978932
$867$	6.28105	0.213316
$868$	−4.27844	−0.145220
$869$	5.56189	0.188674
$870$	0	0
$871$	−25.8701	−0.876576
$872$	−10.1413	−0.343428
$873$	−5.39039	−0.182437
$874$	−2.33493	−0.0789801
$875$	0	0
$876$	5.48375	0.185279
$877$	17.6725	0.596757	0.298379	−	0.954448i	$-0.403554\pi$
$877$	17.6725	0.596757	0.298379	+	0.954448i	$0.403554\pi$
$878$	11.3814	0.384105
$879$	−3.53830	−0.119344
$880$	0	0
$881$	2.64487	0.0891081	0.0445540	−	0.999007i	$-0.485813\pi$
$881$	2.64487	0.0891081	0.0445540	+	0.999007i	$0.485813\pi$
$882$	32.3648	1.08978
$883$	36.2706	1.22060	0.610301	−	0.792170i	$-0.291049\pi$
$883$	36.2706	1.22060	0.610301	+	0.792170i	$0.291049\pi$
$884$	−0.896774	−0.0301618
$885$	0	0
$886$	−5.48894	−0.184405
$887$	26.9316	0.904276	0.452138	−	0.891948i	$-0.350662\pi$
$887$	26.9316	0.904276	0.452138	+	0.891948i	$0.350662\pi$
$888$	2.17533	0.0729992
$889$	−10.9677	−0.367846
$890$	0	0
$891$	21.8942	0.733483
$892$	19.6166	0.656813
$893$	26.8321	0.897901
$894$	5.27439	0.176402
$895$	0	0
$896$	−4.27844	−0.142933
$897$	−1.47389	−0.0492118
$898$	11.7183	0.391045
$899$	7.47252	0.249223
$900$	0	0
$901$	0.0408561	0.00136111
$902$	25.3101	0.842735
$903$	−9.04755	−0.301084
$904$	−8.91842	−0.296622
$905$	0	0
$906$	8.76311	0.291135
$907$	21.5247	0.714715	0.357358	−	0.933968i	$-0.383678\pi$
$907$	21.5247	0.714715	0.357358	+	0.933968i	$0.383678\pi$
$908$	19.2501	0.638837
$909$	−42.6049	−1.41312
$910$	0	0
$911$	48.7212	1.61421	0.807103	−	0.590410i	$-0.201034\pi$
$911$	48.7212	1.61421	0.807103	+	0.590410i	$0.201034\pi$
$912$	−0.985065	−0.0326188
$913$	−1.55841	−0.0515758
$914$	−19.6698	−0.650620
$915$	0	0
$916$	−23.1807	−0.765911
$917$	−37.3107	−1.23211
$918$	0.429425	0.0141731
$919$	−25.3406	−0.835910	−0.417955	−	0.908468i	$-0.637253\pi$
$919$	−25.3406	−0.835910	−0.417955	+	0.908468i	$0.637253\pi$
$920$	0	0
$921$	6.24625	0.205821
$922$	−34.0577	−1.12163
$923$	−36.5476	−1.20298
$924$	−4.45621	−0.146599
$925$	0	0
$926$	−16.0140	−0.526253
$927$	−37.3480	−1.22667
$928$	7.47252	0.245298
$929$	42.3414	1.38918	0.694588	−	0.719408i	$-0.255587\pi$
$929$	42.3414	1.38918	0.694588	+	0.719408i	$0.255587\pi$
$930$	0	0
$931$	30.0714	0.985551
$932$	−7.04155	−0.230654
$933$	3.01027	0.0985517
$934$	31.6506	1.03564
$935$	0	0
$936$	12.9804	0.424279
$937$	−17.1119	−0.559022	−0.279511	−	0.960142i	$-0.590172\pi$
$937$	−17.1119	−0.559022	−0.279511	+	0.960142i	$0.590172\pi$
$938$	24.4115	0.797064
$939$	3.16022	0.103130
$940$	0	0
$941$	10.0045	0.326137	0.163069	−	0.986615i	$-0.447861\pi$
$941$	10.0045	0.326137	0.163069	+	0.986615i	$0.447861\pi$
$942$	−5.25751	−0.171299
$943$	−7.89933	−0.257238
$944$	4.55688	0.148314
$945$	0	0
$946$	−16.0604	−0.522170
$947$	41.7436	1.35648	0.678242	−	0.734839i	$-0.262742\pi$
$947$	41.7436	1.35648	0.678242	+	0.734839i	$0.262742\pi$
$948$	−0.732335	−0.0237851
$949$	−67.1403	−2.17946
$950$	0	0
$951$	−8.16895	−0.264896
$952$	0.846211	0.0274259
$953$	−16.7473	−0.542497	−0.271248	−	0.962509i	$-0.587436\pi$
$953$	−16.7473	−0.542497	−0.271248	+	0.962509i	$0.587436\pi$
$954$	−0.591376	−0.0191465
$955$	0	0
$956$	−19.9908	−0.646547
$957$	7.78301	0.251589
$958$	−3.25751	−0.105245
$959$	−39.0288	−1.26031
$960$	0	0
$961$	1.00000	0.0322581
$962$	−26.6336	−0.858702
$963$	−0.295201	−0.00951271
$964$	−22.7788	−0.733657
$965$	0	0
$966$	1.39079	0.0447480
$967$	2.16792	0.0697155	0.0348577	−	0.999392i	$-0.488902\pi$
$967$	2.16792	0.0697155	0.0348577	+	0.999392i	$0.488902\pi$
$968$	3.08971	0.0993069
$969$	0.194831	0.00625888
$970$	0	0
$971$	−28.7397	−0.922301	−0.461151	−	0.887322i	$-0.652563\pi$
$971$	−28.7397	−0.922301	−0.461151	+	0.887322i	$0.652563\pi$
$972$	−9.39632	−0.301387
$973$	70.7684	2.26873
$974$	40.0906	1.28459
$975$	0	0
$976$	−5.96876	−0.191055
$977$	2.81612	0.0900956	0.0450478	−	0.998985i	$-0.485656\pi$
$977$	2.81612	0.0900956	0.0450478	+	0.998985i	$0.485656\pi$
$978$	0.678169	0.0216855
$979$	33.9000	1.08345
$980$	0	0
$981$	−29.0331	−0.926956
$982$	28.6488	0.914219
$983$	8.69493	0.277325	0.138663	−	0.990340i	$-0.455720\pi$
$983$	8.69493	0.277325	0.138663	+	0.990340i	$0.455720\pi$
$984$	−3.33259	−0.106239
$985$	0	0
$986$	−1.47795	−0.0470676
$987$	−15.9824	−0.508726
$988$	12.0606	0.383700
$989$	5.01249	0.159388
$990$	0	0
$991$	−57.3615	−1.82215	−0.911073	−	0.412244i	$-0.864745\pi$
$991$	−57.3615	−1.82215	−0.911073	+	0.412244i	$0.864745\pi$
$992$	1.00000	0.0317500
$993$	13.1133	0.416137
$994$	34.4870	1.09386
$995$	0	0
$996$	0.205196	0.00650189
$997$	−43.3782	−1.37380	−0.686901	−	0.726751i	$-0.741029\pi$
$997$	−43.3782	−1.37380	−0.686901	+	0.726751i	$0.741029\pi$
$998$	18.5438	0.586994
$999$	12.7536	0.403507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1550.2.a.o.1.2		4
5.2	odd	4		310.2.b.a.249.3	✓	8
5.3	odd	4		310.2.b.a.249.6	yes	8
5.4	even	2		1550.2.a.p.1.3		4
15.2	even	4		2790.2.d.m.559.6		8
15.8	even	4		2790.2.d.m.559.2		8
20.3	even	4		2480.2.d.d.1489.5		8
20.7	even	4		2480.2.d.d.1489.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.a.249.3	✓	8	5.2	odd	4
310.2.b.a.249.6	yes	8	5.3	odd	4
1550.2.a.o.1.2		4	1.1	even	1	trivial
1550.2.a.p.1.3		4	5.4	even	2
2480.2.d.d.1489.4		8	20.7	even	4
2480.2.d.d.1489.5		8	20.3	even	4
2790.2.d.m.559.2		8	15.8	even	4
2790.2.d.m.559.6		8	15.2	even	4

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:	\( N \)	\(=\)	\( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1550.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.370326 q^{3} +1.00000 q^{4} +0.370326 q^{6} +4.27844 q^{7} -1.00000 q^{8} -2.86286 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.370326 q^{3} +1.00000 q^{4} +0.370326 q^{6} +4.27844 q^{7} -1.00000 q^{8} -2.86286 q^{9} +2.81252 q^{11} -0.370326 q^{12} +4.53408 q^{13} -4.27844 q^{14} +1.00000 q^{16} -0.197785 q^{17} +2.86286 q^{18} +2.66000 q^{19} -1.58442 q^{21} -2.81252 q^{22} +0.877793 q^{23} +0.370326 q^{24} -4.53408 q^{26} +2.17117 q^{27} +4.27844 q^{28} -7.47252 q^{29} -1.00000 q^{31} -1.00000 q^{32} -1.04155 q^{33} +0.197785 q^{34} -2.86286 q^{36} +5.87409 q^{37} -2.66000 q^{38} -1.67909 q^{39} -8.99908 q^{41} +1.58442 q^{42} +5.71033 q^{43} +2.81252 q^{44} -0.877793 q^{46} +10.0873 q^{47} -0.370326 q^{48} +11.3051 q^{49} +0.0732449 q^{51} +4.53408 q^{52} -0.206568 q^{53} -2.17117 q^{54} -4.27844 q^{56} -0.985065 q^{57} +7.47252 q^{58} +4.55688 q^{59} -5.96876 q^{61} +1.00000 q^{62} -12.2486 q^{63} +1.00000 q^{64} +1.04155 q^{66} -5.70571 q^{67} -0.197785 q^{68} -0.325070 q^{69} -8.06064 q^{71} +2.86286 q^{72} -14.8079 q^{73} -5.87409 q^{74} +2.66000 q^{76} +12.0332 q^{77} +1.67909 q^{78} +1.97754 q^{79} +7.78454 q^{81} +8.99908 q^{82} -0.554096 q^{83} -1.58442 q^{84} -5.71033 q^{86} +2.76727 q^{87} -2.81252 q^{88} +12.0532 q^{89} +19.3988 q^{91} +0.877793 q^{92} +0.370326 q^{93} -10.0873 q^{94} +0.370326 q^{96} +1.88287 q^{97} -11.3051 q^{98} -8.05186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{11} + 4 q^{12} + 10 q^{13} - 6 q^{14} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{21} + 8 q^{22} + 8 q^{23} - 4 q^{24} - 10 q^{26} + 22 q^{27} + 6 q^{28} - 6 q^{29} - 4 q^{31} - 4 q^{32} - 6 q^{33} - 4 q^{34} + 4 q^{36} + 20 q^{37} - 6 q^{38} + 20 q^{39} + 2 q^{42} + 22 q^{43} - 8 q^{44} - 8 q^{46} + 2 q^{47} + 4 q^{48} + 16 q^{49} - 22 q^{51} + 10 q^{52} + 2 q^{53} - 22 q^{54} - 6 q^{56} + 16 q^{57} + 6 q^{58} - 4 q^{59} + 2 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 6 q^{66} + 22 q^{67} + 4 q^{68} + 14 q^{69} - 12 q^{71} - 4 q^{72} + 4 q^{73} - 20 q^{74} + 6 q^{76} - 2 q^{77} - 20 q^{78} - 16 q^{79} + 44 q^{81} - 8 q^{83} - 2 q^{84} - 22 q^{86} - 18 q^{87} + 8 q^{88} + 12 q^{89} - 10 q^{91} + 8 q^{92} - 4 q^{93} - 2 q^{94} - 4 q^{96} + 6 q^{97} - 16 q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^11 + 4 * q^12 + 10 * q^13 - 6 * q^14 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 6 * q^19 - 2 * q^21 + 8 * q^22 + 8 * q^23 - 4 * q^24 - 10 * q^26 + 22 * q^27 + 6 * q^28 - 6 * q^29 - 4 * q^31 - 4 * q^32 - 6 * q^33 - 4 * q^34 + 4 * q^36 + 20 * q^37 - 6 * q^38 + 20 * q^39 + 2 * q^42 + 22 * q^43 - 8 * q^44 - 8 * q^46 + 2 * q^47 + 4 * q^48 + 16 * q^49 - 22 * q^51 + 10 * q^52 + 2 * q^53 - 22 * q^54 - 6 * q^56 + 16 * q^57 + 6 * q^58 - 4 * q^59 + 2 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 + 6 * q^66 + 22 * q^67 + 4 * q^68 + 14 * q^69 - 12 * q^71 - 4 * q^72 + 4 * q^73 - 20 * q^74 + 6 * q^76 - 2 * q^77 - 20 * q^78 - 16 * q^79 + 44 * q^81 - 8 * q^83 - 2 * q^84 - 22 * q^86 - 18 * q^87 + 8 * q^88 + 12 * q^89 - 10 * q^91 + 8 * q^92 - 4 * q^93 - 2 * q^94 - 4 * q^96 + 6 * q^97 - 16 * q^98 - 10 * q^99

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