LMFDB - Embedded newform 123.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [123,2,Mod(1,123)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(123, 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("123.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 123 = 3 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	123.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:	$0.982159944862$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	123.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +1.00000 q^{3} +3.41421 q^{5} -1.41421 q^{6} -3.41421 q^{7} +2.82843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +1.00000 q^{3} +3.41421 q^{5} -1.41421 q^{6} -3.41421 q^{7} +2.82843 q^{8} +1.00000 q^{9} -4.82843 q^{10} +2.41421 q^{11} +6.24264 q^{13} +4.82843 q^{14} +3.41421 q^{15} -4.00000 q^{16} -0.414214 q^{17} -1.41421 q^{18} -5.41421 q^{19} -3.41421 q^{21} -3.41421 q^{22} -1.41421 q^{23} +2.82843 q^{24} +6.65685 q^{25} -8.82843 q^{26} +1.00000 q^{27} -6.07107 q^{29} -4.82843 q^{30} -3.00000 q^{31} +2.41421 q^{33} +0.585786 q^{34} -11.6569 q^{35} -9.48528 q^{37} +7.65685 q^{38} +6.24264 q^{39} +9.65685 q^{40} -1.00000 q^{41} +4.82843 q^{42} -5.00000 q^{43} +3.41421 q^{45} +2.00000 q^{46} +10.4142 q^{47} -4.00000 q^{48} +4.65685 q^{49} -9.41421 q^{50} -0.414214 q^{51} +6.82843 q^{53} -1.41421 q^{54} +8.24264 q^{55} -9.65685 q^{56} -5.41421 q^{57} +8.58579 q^{58} -8.48528 q^{59} -4.65685 q^{61} +4.24264 q^{62} -3.41421 q^{63} +8.00000 q^{64} +21.3137 q^{65} -3.41421 q^{66} +10.4853 q^{67} -1.41421 q^{69} +16.4853 q^{70} +10.0711 q^{71} +2.82843 q^{72} -10.3137 q^{73} +13.4142 q^{74} +6.65685 q^{75} -8.24264 q^{77} -8.82843 q^{78} -7.65685 q^{79} -13.6569 q^{80} +1.00000 q^{81} +1.41421 q^{82} +1.07107 q^{83} -1.41421 q^{85} +7.07107 q^{86} -6.07107 q^{87} +6.82843 q^{88} -11.6569 q^{89} -4.82843 q^{90} -21.3137 q^{91} -3.00000 q^{93} -14.7279 q^{94} -18.4853 q^{95} +7.75736 q^{97} -6.58579 q^{98} +2.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9} - 4 q^{10} + 2 q^{11} + 4 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} + 2 q^{17} - 8 q^{19} - 4 q^{21} - 4 q^{22} + 2 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{29} - 4 q^{30} - 6 q^{31} + 2 q^{33} + 4 q^{34} - 12 q^{35} - 2 q^{37} + 4 q^{38} + 4 q^{39} + 8 q^{40} - 2 q^{41} + 4 q^{42} - 10 q^{43} + 4 q^{45} + 4 q^{46} + 18 q^{47} - 8 q^{48} - 2 q^{49} - 16 q^{50} + 2 q^{51} + 8 q^{53} + 8 q^{55} - 8 q^{56} - 8 q^{57} + 20 q^{58} + 2 q^{61} - 4 q^{63} + 16 q^{64} + 20 q^{65} - 4 q^{66} + 4 q^{67} + 16 q^{70} + 6 q^{71} + 2 q^{73} + 24 q^{74} + 2 q^{75} - 8 q^{77} - 12 q^{78} - 4 q^{79} - 16 q^{80} + 2 q^{81} - 12 q^{83} + 2 q^{87} + 8 q^{88} - 12 q^{89} - 4 q^{90} - 20 q^{91} - 6 q^{93} - 4 q^{94} - 20 q^{95} + 24 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9 - 4 * q^10 + 2 * q^11 + 4 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 + 2 * q^17 - 8 * q^19 - 4 * q^21 - 4 * q^22 + 2 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^29 - 4 * q^30 - 6 * q^31 + 2 * q^33 + 4 * q^34 - 12 * q^35 - 2 * q^37 + 4 * q^38 + 4 * q^39 + 8 * q^40 - 2 * q^41 + 4 * q^42 - 10 * q^43 + 4 * q^45 + 4 * q^46 + 18 * q^47 - 8 * q^48 - 2 * q^49 - 16 * q^50 + 2 * q^51 + 8 * q^53 + 8 * q^55 - 8 * q^56 - 8 * q^57 + 20 * q^58 + 2 * q^61 - 4 * q^63 + 16 * q^64 + 20 * q^65 - 4 * q^66 + 4 * q^67 + 16 * q^70 + 6 * q^71 + 2 * q^73 + 24 * q^74 + 2 * q^75 - 8 * q^77 - 12 * q^78 - 4 * q^79 - 16 * q^80 + 2 * q^81 - 12 * q^83 + 2 * q^87 + 8 * q^88 - 12 * q^89 - 4 * q^90 - 20 * q^91 - 6 * q^93 - 4 * q^94 - 20 * q^95 + 24 * q^97 - 16 * q^98 + 2 * 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 $

$2$	−1.41421	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−1.41421	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0	0
$5$	3.41421	1.52688	0.763441	−	0.645877i	$-0.223508\pi$
$5$	3.41421	1.52688	0.763441	+	0.645877i	$0.223508\pi$
$6$	−1.41421	−0.577350
$7$	−3.41421	−1.29045	−0.645226	−	0.763992i	$-0.723237\pi$
$7$	−3.41421	−1.29045	−0.645226	+	0.763992i	$0.723237\pi$
$8$	2.82843	1.00000
$9$	1.00000	0.333333
$10$	−4.82843	−1.52688
$11$	2.41421	0.727913	0.363956	−	0.931416i	$-0.381426\pi$
$11$	2.41421	0.727913	0.363956	+	0.931416i	$0.381426\pi$
$12$	0	0
$13$	6.24264	1.73140	0.865699	−	0.500566i	$-0.166875\pi$
$13$	6.24264	1.73140	0.865699	+	0.500566i	$0.166875\pi$
$14$	4.82843	1.29045
$15$	3.41421	0.881546
$16$	−4.00000	−1.00000
$17$	−0.414214	−0.100462	−0.0502308	−	0.998738i	$-0.515996\pi$
$17$	−0.414214	−0.100462	−0.0502308	+	0.998738i	$0.515996\pi$
$18$	−1.41421	−0.333333
$19$	−5.41421	−1.24211	−0.621053	−	0.783769i	$-0.713295\pi$
$19$	−5.41421	−1.24211	−0.621053	+	0.783769i	$0.713295\pi$
$20$	0	0
$21$	−3.41421	−0.745042
$22$	−3.41421	−0.727913
$23$	−1.41421	−0.294884	−0.147442	−	0.989071i	$-0.547104\pi$
$23$	−1.41421	−0.294884	−0.147442	+	0.989071i	$0.547104\pi$
$24$	2.82843	0.577350
$25$	6.65685	1.33137
$26$	−8.82843	−1.73140
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.07107	−1.12737	−0.563684	−	0.825990i	$-0.690617\pi$
$29$	−6.07107	−1.12737	−0.563684	+	0.825990i	$0.690617\pi$
$30$	−4.82843	−0.881546
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	0	0
$33$	2.41421	0.420261
$34$	0.585786	0.100462
$35$	−11.6569	−1.97037
$36$	0	0
$37$	−9.48528	−1.55937	−0.779685	−	0.626172i	$-0.784621\pi$
$37$	−9.48528	−1.55937	−0.779685	+	0.626172i	$0.784621\pi$
$38$	7.65685	1.24211
$39$	6.24264	0.999623
$40$	9.65685	1.52688
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	4.82843	0.745042
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	0	0
$45$	3.41421	0.508961
$46$	2.00000	0.294884
$47$	10.4142	1.51907	0.759535	−	0.650467i	$-0.225427\pi$
$47$	10.4142	1.51907	0.759535	+	0.650467i	$0.225427\pi$
$48$	−4.00000	−0.577350
$49$	4.65685	0.665265
$50$	−9.41421	−1.33137
$51$	−0.414214	−0.0580015
$52$	0	0
$53$	6.82843	0.937957	0.468978	−	0.883210i	$-0.344622\pi$
$53$	6.82843	0.937957	0.468978	+	0.883210i	$0.344622\pi$
$54$	−1.41421	−0.192450
$55$	8.24264	1.11144
$56$	−9.65685	−1.29045
$57$	−5.41421	−0.717130
$58$	8.58579	1.12737
$59$	−8.48528	−1.10469	−0.552345	−	0.833616i	$-0.686267\pi$
$59$	−8.48528	−1.10469	−0.552345	+	0.833616i	$0.686267\pi$
$60$	0	0
$61$	−4.65685	−0.596249	−0.298125	−	0.954527i	$-0.596361\pi$
$61$	−4.65685	−0.596249	−0.298125	+	0.954527i	$0.596361\pi$
$62$	4.24264	0.538816
$63$	−3.41421	−0.430150
$64$	8.00000	1.00000
$65$	21.3137	2.64364
$66$	−3.41421	−0.420261
$67$	10.4853	1.28098	0.640490	−	0.767966i	$-0.278731\pi$
$67$	10.4853	1.28098	0.640490	+	0.767966i	$0.278731\pi$
$68$	0	0
$69$	−1.41421	−0.170251
$70$	16.4853	1.97037
$71$	10.0711	1.19522	0.597608	−	0.801788i	$-0.296118\pi$
$71$	10.0711	1.19522	0.597608	+	0.801788i	$0.296118\pi$
$72$	2.82843	0.333333
$73$	−10.3137	−1.20713	−0.603564	−	0.797314i	$-0.706253\pi$
$73$	−10.3137	−1.20713	−0.603564	+	0.797314i	$0.706253\pi$
$74$	13.4142	1.55937
$75$	6.65685	0.768667
$76$	0	0
$77$	−8.24264	−0.939336
$78$	−8.82843	−0.999623
$79$	−7.65685	−0.861463	−0.430732	−	0.902480i	$-0.641744\pi$
$79$	−7.65685	−0.861463	−0.430732	+	0.902480i	$0.641744\pi$
$80$	−13.6569	−1.52688
$81$	1.00000	0.111111
$82$	1.41421	0.156174
$83$	1.07107	0.117565	0.0587825	−	0.998271i	$-0.481278\pi$
$83$	1.07107	0.117565	0.0587825	+	0.998271i	$0.481278\pi$
$84$	0	0
$85$	−1.41421	−0.153393
$86$	7.07107	0.762493
$87$	−6.07107	−0.650887
$88$	6.82843	0.727913
$89$	−11.6569	−1.23562	−0.617812	−	0.786326i	$-0.711981\pi$
$89$	−11.6569	−1.23562	−0.617812	+	0.786326i	$0.711981\pi$
$90$	−4.82843	−0.508961
$91$	−21.3137	−2.23428
$92$	0	0
$93$	−3.00000	−0.311086
$94$	−14.7279	−1.51907
$95$	−18.4853	−1.89655
$96$	0	0
$97$	7.75736	0.787641	0.393820	−	0.919187i	$-0.371153\pi$
$97$	7.75736	0.787641	0.393820	+	0.919187i	$0.371153\pi$
$98$	−6.58579	−0.665265
$99$	2.41421	0.242638
$100$	0	0
$101$	−0.414214	−0.0412158	−0.0206079	−	0.999788i	$-0.506560\pi$
$101$	−0.414214	−0.0412158	−0.0206079	+	0.999788i	$0.506560\pi$
$102$	0.585786	0.0580015
$103$	6.31371	0.622108	0.311054	−	0.950392i	$-0.399318\pi$
$103$	6.31371	0.622108	0.311054	+	0.950392i	$0.399318\pi$
$104$	17.6569	1.73140
$105$	−11.6569	−1.13759
$106$	−9.65685	−0.937957
$107$	−0.343146	−0.0331732	−0.0165866	−	0.999862i	$-0.505280\pi$
$107$	−0.343146	−0.0331732	−0.0165866	+	0.999862i	$0.505280\pi$
$108$	0	0
$109$	7.89949	0.756634	0.378317	−	0.925676i	$-0.376503\pi$
$109$	7.89949	0.756634	0.378317	+	0.925676i	$0.376503\pi$
$110$	−11.6569	−1.11144
$111$	−9.48528	−0.900303
$112$	13.6569	1.29045
$113$	6.72792	0.632910	0.316455	−	0.948608i	$-0.397507\pi$
$113$	6.72792	0.632910	0.316455	+	0.948608i	$0.397507\pi$
$114$	7.65685	0.717130
$115$	−4.82843	−0.450253
$116$	0	0
$117$	6.24264	0.577132
$118$	12.0000	1.10469
$119$	1.41421	0.129641
$120$	9.65685	0.881546
$121$	−5.17157	−0.470143
$122$	6.58579	0.596249
$123$	−1.00000	−0.0901670
$124$	0	0
$125$	5.65685	0.505964
$126$	4.82843	0.430150
$127$	9.31371	0.826458	0.413229	−	0.910627i	$-0.364401\pi$
$127$	9.31371	0.826458	0.413229	+	0.910627i	$0.364401\pi$
$128$	−11.3137	−1.00000
$129$	−5.00000	−0.440225
$130$	−30.1421	−2.64364
$131$	−10.5858	−0.924884	−0.462442	−	0.886649i	$-0.653027\pi$
$131$	−10.5858	−0.924884	−0.462442	+	0.886649i	$0.653027\pi$
$132$	0	0
$133$	18.4853	1.60288
$134$	−14.8284	−1.28098
$135$	3.41421	0.293849
$136$	−1.17157	−0.100462
$137$	3.92893	0.335671	0.167836	−	0.985815i	$-0.446322\pi$
$137$	3.92893	0.335671	0.167836	+	0.985815i	$0.446322\pi$
$138$	2.00000	0.170251
$139$	3.65685	0.310170	0.155085	−	0.987901i	$-0.450435\pi$
$139$	3.65685	0.310170	0.155085	+	0.987901i	$0.450435\pi$
$140$	0	0
$141$	10.4142	0.877035
$142$	−14.2426	−1.19522
$143$	15.0711	1.26031
$144$	−4.00000	−0.333333
$145$	−20.7279	−1.72136
$146$	14.5858	1.20713
$147$	4.65685	0.384091
$148$	0	0
$149$	17.3137	1.41839	0.709197	−	0.705010i	$-0.249058\pi$
$149$	17.3137	1.41839	0.709197	+	0.705010i	$0.249058\pi$
$150$	−9.41421	−0.768667
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	−15.3137	−1.24211
$153$	−0.414214	−0.0334872
$154$	11.6569	0.939336
$155$	−10.2426	−0.822709
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	10.8284	0.861463
$159$	6.82843	0.541529
$160$	0	0
$161$	4.82843	0.380533
$162$	−1.41421	−0.111111
$163$	−9.48528	−0.742945	−0.371472	−	0.928444i	$-0.621147\pi$
$163$	−9.48528	−0.742945	−0.371472	+	0.928444i	$0.621147\pi$
$164$	0	0
$165$	8.24264	0.641689
$166$	−1.51472	−0.117565
$167$	−3.65685	−0.282976	−0.141488	−	0.989940i	$-0.545189\pi$
$167$	−3.65685	−0.282976	−0.141488	+	0.989940i	$0.545189\pi$
$168$	−9.65685	−0.745042
$169$	25.9706	1.99774
$170$	2.00000	0.153393
$171$	−5.41421	−0.414035
$172$	0	0
$173$	−9.07107	−0.689661	−0.344830	−	0.938665i	$-0.612064\pi$
$173$	−9.07107	−0.689661	−0.344830	+	0.938665i	$0.612064\pi$
$174$	8.58579	0.650887
$175$	−22.7279	−1.71807
$176$	−9.65685	−0.727913
$177$	−8.48528	−0.637793
$178$	16.4853	1.23562
$179$	−4.89949	−0.366205	−0.183103	−	0.983094i	$-0.558614\pi$
$179$	−4.89949	−0.366205	−0.183103	+	0.983094i	$0.558614\pi$
$180$	0	0
$181$	−7.31371	−0.543624	−0.271812	−	0.962350i	$-0.587623\pi$
$181$	−7.31371	−0.543624	−0.271812	+	0.962350i	$0.587623\pi$
$182$	30.1421	2.23428
$183$	−4.65685	−0.344245
$184$	−4.00000	−0.294884
$185$	−32.3848	−2.38098
$186$	4.24264	0.311086
$187$	−1.00000	−0.0731272
$188$	0	0
$189$	−3.41421	−0.248347
$190$	26.1421	1.89655
$191$	18.8284	1.36238	0.681189	−	0.732108i	$-0.261463\pi$
$191$	18.8284	1.36238	0.681189	+	0.732108i	$0.261463\pi$
$192$	8.00000	0.577350
$193$	0.585786	0.0421658	0.0210829	−	0.999778i	$-0.493289\pi$
$193$	0.585786	0.0421658	0.0210829	+	0.999778i	$0.493289\pi$
$194$	−10.9706	−0.787641
$195$	21.3137	1.52631
$196$	0	0
$197$	22.2426	1.58472	0.792361	−	0.610052i	$-0.208852\pi$
$197$	22.2426	1.58472	0.792361	+	0.610052i	$0.208852\pi$
$198$	−3.41421	−0.242638
$199$	−16.2426	−1.15141	−0.575705	−	0.817657i	$-0.695272\pi$
$199$	−16.2426	−1.15141	−0.575705	+	0.817657i	$0.695272\pi$
$200$	18.8284	1.33137
$201$	10.4853	0.739575
$202$	0.585786	0.0412158
$203$	20.7279	1.45481
$204$	0	0
$205$	−3.41421	−0.238459
$206$	−8.92893	−0.622108
$207$	−1.41421	−0.0982946
$208$	−24.9706	−1.73140
$209$	−13.0711	−0.904145
$210$	16.4853	1.13759
$211$	−24.4853	−1.68564	−0.842818	−	0.538198i	$-0.819105\pi$
$211$	−24.4853	−1.68564	−0.842818	+	0.538198i	$0.819105\pi$
$212$	0	0
$213$	10.0711	0.690058
$214$	0.485281	0.0331732
$215$	−17.0711	−1.16424
$216$	2.82843	0.192450
$217$	10.2426	0.695316
$218$	−11.1716	−0.756634
$219$	−10.3137	−0.696936
$220$	0	0
$221$	−2.58579	−0.173939
$222$	13.4142	0.900303
$223$	10.3431	0.692628	0.346314	−	0.938119i	$-0.387433\pi$
$223$	10.3431	0.692628	0.346314	+	0.938119i	$0.387433\pi$
$224$	0	0
$225$	6.65685	0.443790
$226$	−9.51472	−0.632910
$227$	1.10051	0.0730431	0.0365215	−	0.999333i	$-0.488372\pi$
$227$	1.10051	0.0730431	0.0365215	+	0.999333i	$0.488372\pi$
$228$	0	0
$229$	−0.242641	−0.0160341	−0.00801707	−	0.999968i	$-0.502552\pi$
$229$	−0.242641	−0.0160341	−0.00801707	+	0.999968i	$0.502552\pi$
$230$	6.82843	0.450253
$231$	−8.24264	−0.542326
$232$	−17.1716	−1.12737
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	−8.82843	−0.577132
$235$	35.5563	2.31944
$236$	0	0
$237$	−7.65685	−0.497366
$238$	−2.00000	−0.129641
$239$	18.1421	1.17352	0.586759	−	0.809762i	$-0.300404\pi$
$239$	18.1421	1.17352	0.586759	+	0.809762i	$0.300404\pi$
$240$	−13.6569	−0.881546
$241$	9.48528	0.611001	0.305500	−	0.952192i	$-0.401176\pi$
$241$	9.48528	0.611001	0.305500	+	0.952192i	$0.401176\pi$
$242$	7.31371	0.470143
$243$	1.00000	0.0641500
$244$	0	0
$245$	15.8995	1.01578
$246$	1.41421	0.0901670
$247$	−33.7990	−2.15058
$248$	−8.48528	−0.538816
$249$	1.07107	0.0678762
$250$	−8.00000	−0.505964
$251$	8.82843	0.557245	0.278623	−	0.960401i	$-0.410122\pi$
$251$	8.82843	0.557245	0.278623	+	0.960401i	$0.410122\pi$
$252$	0	0
$253$	−3.41421	−0.214650
$254$	−13.1716	−0.826458
$255$	−1.41421	−0.0885615
$256$	0	0
$257$	−5.10051	−0.318161	−0.159080	−	0.987266i	$-0.550853\pi$
$257$	−5.10051	−0.318161	−0.159080	+	0.987266i	$0.550853\pi$
$258$	7.07107	0.440225
$259$	32.3848	2.01229
$260$	0	0
$261$	−6.07107	−0.375790
$262$	14.9706	0.924884
$263$	2.41421	0.148867	0.0744334	−	0.997226i	$-0.476285\pi$
$263$	2.41421	0.148867	0.0744334	+	0.997226i	$0.476285\pi$
$264$	6.82843	0.420261
$265$	23.3137	1.43215
$266$	−26.1421	−1.60288
$267$	−11.6569	−0.713388
$268$	0	0
$269$	−8.48528	−0.517357	−0.258678	−	0.965964i	$-0.583287\pi$
$269$	−8.48528	−0.517357	−0.258678	+	0.965964i	$0.583287\pi$
$270$	−4.82843	−0.293849
$271$	18.7990	1.14196	0.570979	−	0.820965i	$-0.306564\pi$
$271$	18.7990	1.14196	0.570979	+	0.820965i	$0.306564\pi$
$272$	1.65685	0.100462
$273$	−21.3137	−1.28996
$274$	−5.55635	−0.335671
$275$	16.0711	0.969122
$276$	0	0
$277$	−27.2843	−1.63935	−0.819676	−	0.572827i	$-0.805847\pi$
$277$	−27.2843	−1.63935	−0.819676	+	0.572827i	$0.805847\pi$
$278$	−5.17157	−0.310170
$279$	−3.00000	−0.179605
$280$	−32.9706	−1.97037
$281$	17.3848	1.03709	0.518544	−	0.855051i	$-0.326474\pi$
$281$	17.3848	1.03709	0.518544	+	0.855051i	$0.326474\pi$
$282$	−14.7279	−0.877035
$283$	16.1716	0.961300	0.480650	−	0.876912i	$-0.340401\pi$
$283$	16.1716	0.961300	0.480650	+	0.876912i	$0.340401\pi$
$284$	0	0
$285$	−18.4853	−1.09497
$286$	−21.3137	−1.26031
$287$	3.41421	0.201535
$288$	0	0
$289$	−16.8284	−0.989907
$290$	29.3137	1.72136
$291$	7.75736	0.454744
$292$	0	0
$293$	9.58579	0.560008	0.280004	−	0.959999i	$-0.409664\pi$
$293$	9.58579	0.560008	0.280004	+	0.959999i	$0.409664\pi$
$294$	−6.58579	−0.384091
$295$	−28.9706	−1.68673
$296$	−26.8284	−1.55937
$297$	2.41421	0.140087
$298$	−24.4853	−1.41839
$299$	−8.82843	−0.510561
$300$	0	0
$301$	17.0711	0.983960
$302$	22.6274	1.30206
$303$	−0.414214	−0.0237959
$304$	21.6569	1.24211
$305$	−15.8995	−0.910402
$306$	0.585786	0.0334872
$307$	−0.313708	−0.0179043	−0.00895214	−	0.999960i	$-0.502850\pi$
$307$	−0.313708	−0.0179043	−0.00895214	+	0.999960i	$0.502850\pi$
$308$	0	0
$309$	6.31371	0.359174
$310$	14.4853	0.822709
$311$	26.8284	1.52130	0.760650	−	0.649162i	$-0.224880\pi$
$311$	26.8284	1.52130	0.760650	+	0.649162i	$0.224880\pi$
$312$	17.6569	0.999623
$313$	−28.8701	−1.63183	−0.815916	−	0.578170i	$-0.803767\pi$
$313$	−28.8701	−1.63183	−0.815916	+	0.578170i	$0.803767\pi$
$314$	−25.4558	−1.43656
$315$	−11.6569	−0.656789
$316$	0	0
$317$	−12.0711	−0.677979	−0.338989	−	0.940790i	$-0.610085\pi$
$317$	−12.0711	−0.677979	−0.338989	+	0.940790i	$0.610085\pi$
$318$	−9.65685	−0.541529
$319$	−14.6569	−0.820626
$320$	27.3137	1.52688
$321$	−0.343146	−0.0191525
$322$	−6.82843	−0.380533
$323$	2.24264	0.124784
$324$	0	0
$325$	41.5563	2.30513
$326$	13.4142	0.742945
$327$	7.89949	0.436843
$328$	−2.82843	−0.156174
$329$	−35.5563	−1.96028
$330$	−11.6569	−0.641689
$331$	16.2426	0.892776	0.446388	−	0.894839i	$-0.352710\pi$
$331$	16.2426	0.892776	0.446388	+	0.894839i	$0.352710\pi$
$332$	0	0
$333$	−9.48528	−0.519790
$334$	5.17157	0.282976
$335$	35.7990	1.95591
$336$	13.6569	0.745042
$337$	19.9706	1.08787	0.543933	−	0.839129i	$-0.316935\pi$
$337$	19.9706	1.08787	0.543933	+	0.839129i	$0.316935\pi$
$338$	−36.7279	−1.99774
$339$	6.72792	0.365411
$340$	0	0
$341$	−7.24264	−0.392211
$342$	7.65685	0.414035
$343$	8.00000	0.431959
$344$	−14.1421	−0.762493
$345$	−4.82843	−0.259954
$346$	12.8284	0.689661
$347$	0.899495	0.0482874	0.0241437	−	0.999708i	$-0.492314\pi$
$347$	0.899495	0.0482874	0.0241437	+	0.999708i	$0.492314\pi$
$348$	0	0
$349$	9.14214	0.489367	0.244684	−	0.969603i	$-0.421316\pi$
$349$	9.14214	0.489367	0.244684	+	0.969603i	$0.421316\pi$
$350$	32.1421	1.71807
$351$	6.24264	0.333208
$352$	0	0
$353$	−34.9706	−1.86130	−0.930648	−	0.365917i	$-0.880756\pi$
$353$	−34.9706	−1.86130	−0.930648	+	0.365917i	$0.880756\pi$
$354$	12.0000	0.637793
$355$	34.3848	1.82495
$356$	0	0
$357$	1.41421	0.0748481
$358$	6.92893	0.366205
$359$	16.2426	0.857254	0.428627	−	0.903482i	$-0.358997\pi$
$359$	16.2426	0.857254	0.428627	+	0.903482i	$0.358997\pi$
$360$	9.65685	0.508961
$361$	10.3137	0.542827
$362$	10.3431	0.543624
$363$	−5.17157	−0.271437
$364$	0	0
$365$	−35.2132	−1.84314
$366$	6.58579	0.344245
$367$	−6.65685	−0.347485	−0.173742	−	0.984791i	$-0.555586\pi$
$367$	−6.65685	−0.347485	−0.173742	+	0.984791i	$0.555586\pi$
$368$	5.65685	0.294884
$369$	−1.00000	−0.0520579
$370$	45.7990	2.38098
$371$	−23.3137	−1.21039
$372$	0	0
$373$	33.1421	1.71603	0.858017	−	0.513621i	$-0.171696\pi$
$373$	33.1421	1.71603	0.858017	+	0.513621i	$0.171696\pi$
$374$	1.41421	0.0731272
$375$	5.65685	0.292119
$376$	29.4558	1.51907
$377$	−37.8995	−1.95192
$378$	4.82843	0.248347
$379$	26.9706	1.38538	0.692692	−	0.721233i	$-0.256424\pi$
$379$	26.9706	1.38538	0.692692	+	0.721233i	$0.256424\pi$
$380$	0	0
$381$	9.31371	0.477156
$382$	−26.6274	−1.36238
$383$	17.1005	0.873795	0.436897	−	0.899511i	$-0.356077\pi$
$383$	17.1005	0.873795	0.436897	+	0.899511i	$0.356077\pi$
$384$	−11.3137	−0.577350
$385$	−28.1421	−1.43426
$386$	−0.828427	−0.0421658
$387$	−5.00000	−0.254164
$388$	0	0
$389$	−22.2426	−1.12775	−0.563873	−	0.825861i	$-0.690689\pi$
$389$	−22.2426	−1.12775	−0.563873	+	0.825861i	$0.690689\pi$
$390$	−30.1421	−1.52631
$391$	0.585786	0.0296245
$392$	13.1716	0.665265
$393$	−10.5858	−0.533982
$394$	−31.4558	−1.58472
$395$	−26.1421	−1.31535
$396$	0	0
$397$	30.5269	1.53210	0.766051	−	0.642780i	$-0.222219\pi$
$397$	30.5269	1.53210	0.766051	+	0.642780i	$0.222219\pi$
$398$	22.9706	1.15141
$399$	18.4853	0.925422
$400$	−26.6274	−1.33137
$401$	10.6274	0.530708	0.265354	−	0.964151i	$-0.414511\pi$
$401$	10.6274	0.530708	0.265354	+	0.964151i	$0.414511\pi$
$402$	−14.8284	−0.739575
$403$	−18.7279	−0.932904
$404$	0	0
$405$	3.41421	0.169654
$406$	−29.3137	−1.45481
$407$	−22.8995	−1.13509
$408$	−1.17157	−0.0580015
$409$	16.1716	0.799633	0.399816	−	0.916595i	$-0.369074\pi$
$409$	16.1716	0.799633	0.399816	+	0.916595i	$0.369074\pi$
$410$	4.82843	0.238459
$411$	3.92893	0.193800
$412$	0	0
$413$	28.9706	1.42555
$414$	2.00000	0.0982946
$415$	3.65685	0.179508
$416$	0	0
$417$	3.65685	0.179077
$418$	18.4853	0.904145
$419$	15.0711	0.736270	0.368135	−	0.929772i	$-0.379996\pi$
$419$	15.0711	0.736270	0.368135	+	0.929772i	$0.379996\pi$
$420$	0	0
$421$	−8.97056	−0.437198	−0.218599	−	0.975815i	$-0.570149\pi$
$421$	−8.97056	−0.437198	−0.218599	+	0.975815i	$0.570149\pi$
$422$	34.6274	1.68564
$423$	10.4142	0.506356
$424$	19.3137	0.937957
$425$	−2.75736	−0.133752
$426$	−14.2426	−0.690058
$427$	15.8995	0.769430
$428$	0	0
$429$	15.0711	0.727638
$430$	24.1421	1.16424
$431$	24.9289	1.20078	0.600392	−	0.799706i	$-0.295011\pi$
$431$	24.9289	1.20078	0.600392	+	0.799706i	$0.295011\pi$
$432$	−4.00000	−0.192450
$433$	5.48528	0.263606	0.131803	−	0.991276i	$-0.457923\pi$
$433$	5.48528	0.263606	0.131803	+	0.991276i	$0.457923\pi$
$434$	−14.4853	−0.695316
$435$	−20.7279	−0.993828
$436$	0	0
$437$	7.65685	0.366277
$438$	14.5858	0.696936
$439$	2.97056	0.141777	0.0708886	−	0.997484i	$-0.477417\pi$
$439$	2.97056	0.141777	0.0708886	+	0.997484i	$0.477417\pi$
$440$	23.3137	1.11144
$441$	4.65685	0.221755
$442$	3.65685	0.173939
$443$	−36.2843	−1.72392	−0.861959	−	0.506978i	$-0.830762\pi$
$443$	−36.2843	−1.72392	−0.861959	+	0.506978i	$0.830762\pi$
$444$	0	0
$445$	−39.7990	−1.88665
$446$	−14.6274	−0.692628
$447$	17.3137	0.818910
$448$	−27.3137	−1.29045
$449$	3.51472	0.165870	0.0829349	−	0.996555i	$-0.473571\pi$
$449$	3.51472	0.165870	0.0829349	+	0.996555i	$0.473571\pi$
$450$	−9.41421	−0.443790
$451$	−2.41421	−0.113681
$452$	0	0
$453$	−16.0000	−0.751746
$454$	−1.55635	−0.0730431
$455$	−72.7696	−3.41149
$456$	−15.3137	−0.717130
$457$	−4.00000	−0.187112	−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000	−0.187112	−0.0935561	+	0.995614i	$0.529823\pi$
$458$	0.343146	0.0160341
$459$	−0.414214	−0.0193338
$460$	0	0
$461$	28.6274	1.33331	0.666656	−	0.745366i	$-0.267725\pi$
$461$	28.6274	1.33331	0.666656	+	0.745366i	$0.267725\pi$
$462$	11.6569	0.542326
$463$	−25.5563	−1.18770	−0.593852	−	0.804574i	$-0.702394\pi$
$463$	−25.5563	−1.18770	−0.593852	+	0.804574i	$0.702394\pi$
$464$	24.2843	1.12737
$465$	−10.2426	−0.474991
$466$	25.4558	1.17922
$467$	−1.31371	−0.0607912	−0.0303956	−	0.999538i	$-0.509677\pi$
$467$	−1.31371	−0.0607912	−0.0303956	+	0.999538i	$0.509677\pi$
$468$	0	0
$469$	−35.7990	−1.65304
$470$	−50.2843	−2.31944
$471$	18.0000	0.829396
$472$	−24.0000	−1.10469
$473$	−12.0711	−0.555028
$474$	10.8284	0.497366
$475$	−36.0416	−1.65370
$476$	0	0
$477$	6.82843	0.312652
$478$	−25.6569	−1.17352
$479$	6.89949	0.315246	0.157623	−	0.987499i	$-0.449617\pi$
$479$	6.89949	0.315246	0.157623	+	0.987499i	$0.449617\pi$
$480$	0	0
$481$	−59.2132	−2.69989
$482$	−13.4142	−0.611001
$483$	4.82843	0.219701
$484$	0	0
$485$	26.4853	1.20263
$486$	−1.41421	−0.0641500
$487$	1.97056	0.0892947	0.0446474	−	0.999003i	$-0.485784\pi$
$487$	1.97056	0.0892947	0.0446474	+	0.999003i	$0.485784\pi$
$488$	−13.1716	−0.596249
$489$	−9.48528	−0.428939
$490$	−22.4853	−1.01578
$491$	−13.0711	−0.589889	−0.294945	−	0.955514i	$-0.595301\pi$
$491$	−13.0711	−0.589889	−0.294945	+	0.955514i	$0.595301\pi$
$492$	0	0
$493$	2.51472	0.113257
$494$	47.7990	2.15058
$495$	8.24264	0.370479
$496$	12.0000	0.538816
$497$	−34.3848	−1.54237
$498$	−1.51472	−0.0678762
$499$	−19.5147	−0.873599	−0.436799	−	0.899559i	$-0.643888\pi$
$499$	−19.5147	−0.873599	−0.436799	+	0.899559i	$0.643888\pi$
$500$	0	0
$501$	−3.65685	−0.163376
$502$	−12.4853	−0.557245
$503$	1.38478	0.0617441	0.0308721	−	0.999523i	$-0.490172\pi$
$503$	1.38478	0.0617441	0.0308721	+	0.999523i	$0.490172\pi$
$504$	−9.65685	−0.430150
$505$	−1.41421	−0.0629317
$506$	4.82843	0.214650
$507$	25.9706	1.15339
$508$	0	0
$509$	19.8701	0.880725	0.440362	−	0.897820i	$-0.354850\pi$
$509$	19.8701	0.880725	0.440362	+	0.897820i	$0.354850\pi$
$510$	2.00000	0.0885615
$511$	35.2132	1.55774
$512$	22.6274	1.00000
$513$	−5.41421	−0.239043
$514$	7.21320	0.318161
$515$	21.5563	0.949886
$516$	0	0
$517$	25.1421	1.10575
$518$	−45.7990	−2.01229
$519$	−9.07107	−0.398176
$520$	60.2843	2.64364
$521$	31.2426	1.36876	0.684382	−	0.729123i	$-0.260072\pi$
$521$	31.2426	1.36876	0.684382	+	0.729123i	$0.260072\pi$
$522$	8.58579	0.375790
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	0	0
$525$	−22.7279	−0.991928
$526$	−3.41421	−0.148867
$527$	1.24264	0.0541303
$528$	−9.65685	−0.420261
$529$	−21.0000	−0.913043
$530$	−32.9706	−1.43215
$531$	−8.48528	−0.368230
$532$	0	0
$533$	−6.24264	−0.270399
$534$	16.4853	0.713388
$535$	−1.17157	−0.0506515
$536$	29.6569	1.28098
$537$	−4.89949	−0.211429
$538$	12.0000	0.517357
$539$	11.2426	0.484255
$540$	0	0
$541$	−14.9706	−0.643635	−0.321817	−	0.946802i	$-0.604294\pi$
$541$	−14.9706	−0.643635	−0.321817	+	0.946802i	$0.604294\pi$
$542$	−26.5858	−1.14196
$543$	−7.31371	−0.313861
$544$	0	0
$545$	26.9706	1.15529
$546$	30.1421	1.28996
$547$	−24.4853	−1.04692	−0.523458	−	0.852052i	$-0.675358\pi$
$547$	−24.4853	−1.04692	−0.523458	+	0.852052i	$0.675358\pi$
$548$	0	0
$549$	−4.65685	−0.198750
$550$	−22.7279	−0.969122
$551$	32.8701	1.40031
$552$	−4.00000	−0.170251
$553$	26.1421	1.11168
$554$	38.5858	1.63935
$555$	−32.3848	−1.37466
$556$	0	0
$557$	14.2721	0.604727	0.302364	−	0.953193i	$-0.402224\pi$
$557$	14.2721	0.604727	0.302364	+	0.953193i	$0.402224\pi$
$558$	4.24264	0.179605
$559$	−31.2132	−1.32018
$560$	46.6274	1.97037
$561$	−1.00000	−0.0422200
$562$	−24.5858	−1.03709
$563$	6.89949	0.290779	0.145390	−	0.989374i	$-0.453556\pi$
$563$	6.89949	0.290779	0.145390	+	0.989374i	$0.453556\pi$
$564$	0	0
$565$	22.9706	0.966379
$566$	−22.8701	−0.961300
$567$	−3.41421	−0.143383
$568$	28.4853	1.19522
$569$	−4.44365	−0.186288	−0.0931438	−	0.995653i	$-0.529692\pi$
$569$	−4.44365	−0.186288	−0.0931438	+	0.995653i	$0.529692\pi$
$570$	26.1421	1.09497
$571$	−2.62742	−0.109954	−0.0549770	−	0.998488i	$-0.517509\pi$
$571$	−2.62742	−0.109954	−0.0549770	+	0.998488i	$0.517509\pi$
$572$	0	0
$573$	18.8284	0.786569
$574$	−4.82843	−0.201535
$575$	−9.41421	−0.392600
$576$	8.00000	0.333333
$577$	−36.4853	−1.51890	−0.759451	−	0.650564i	$-0.774532\pi$
$577$	−36.4853	−1.51890	−0.759451	+	0.650564i	$0.774532\pi$
$578$	23.7990	0.989907
$579$	0.585786	0.0243445
$580$	0	0
$581$	−3.65685	−0.151712
$582$	−10.9706	−0.454744
$583$	16.4853	0.682751
$584$	−29.1716	−1.20713
$585$	21.3137	0.881213
$586$	−13.5563	−0.560008
$587$	−29.3848	−1.21284	−0.606420	−	0.795145i	$-0.707395\pi$
$587$	−29.3848	−1.21284	−0.606420	+	0.795145i	$0.707395\pi$
$588$	0	0
$589$	16.2426	0.669266
$590$	40.9706	1.68673
$591$	22.2426	0.914940
$592$	37.9411	1.55937
$593$	1.58579	0.0651204	0.0325602	−	0.999470i	$-0.489634\pi$
$593$	1.58579	0.0651204	0.0325602	+	0.999470i	$0.489634\pi$
$594$	−3.41421	−0.140087
$595$	4.82843	0.197946
$596$	0	0
$597$	−16.2426	−0.664767
$598$	12.4853	0.510561
$599$	−35.3553	−1.44458	−0.722290	−	0.691590i	$-0.756910\pi$
$599$	−35.3553	−1.44458	−0.722290	+	0.691590i	$0.756910\pi$
$600$	18.8284	0.768667
$601$	−26.4853	−1.08036	−0.540179	−	0.841550i	$-0.681643\pi$
$601$	−26.4853	−1.08036	−0.540179	+	0.841550i	$0.681643\pi$
$602$	−24.1421	−0.983960
$603$	10.4853	0.426994
$604$	0	0
$605$	−17.6569	−0.717853
$606$	0.585786	0.0237959
$607$	−34.4853	−1.39971	−0.699857	−	0.714283i	$-0.746753\pi$
$607$	−34.4853	−1.39971	−0.699857	+	0.714283i	$0.746753\pi$
$608$	0	0
$609$	20.7279	0.839938
$610$	22.4853	0.910402
$611$	65.0122	2.63011
$612$	0	0
$613$	19.3137	0.780073	0.390037	−	0.920799i	$-0.372462\pi$
$613$	19.3137	0.780073	0.390037	+	0.920799i	$0.372462\pi$
$614$	0.443651	0.0179043
$615$	−3.41421	−0.137674
$616$	−23.3137	−0.939336
$617$	−15.2132	−0.612461	−0.306230	−	0.951957i	$-0.599068\pi$
$617$	−15.2132	−0.612461	−0.306230	+	0.951957i	$0.599068\pi$
$618$	−8.92893	−0.359174
$619$	−10.3137	−0.414543	−0.207271	−	0.978283i	$-0.566458\pi$
$619$	−10.3137	−0.414543	−0.207271	+	0.978283i	$0.566458\pi$
$620$	0	0
$621$	−1.41421	−0.0567504
$622$	−37.9411	−1.52130
$623$	39.7990	1.59451
$624$	−24.9706	−0.999623
$625$	−13.9706	−0.558823
$626$	40.8284	1.63183
$627$	−13.0711	−0.522008
$628$	0	0
$629$	3.92893	0.156657
$630$	16.4853	0.656789
$631$	−28.4558	−1.13281	−0.566405	−	0.824127i	$-0.691666\pi$
$631$	−28.4558	−1.13281	−0.566405	+	0.824127i	$0.691666\pi$
$632$	−21.6569	−0.861463
$633$	−24.4853	−0.973203
$634$	17.0711	0.677979
$635$	31.7990	1.26190
$636$	0	0
$637$	29.0711	1.15184
$638$	20.7279	0.820626
$639$	10.0711	0.398405
$640$	−38.6274	−1.52688
$641$	−8.55635	−0.337955	−0.168978	−	0.985620i	$-0.554047\pi$
$641$	−8.55635	−0.337955	−0.168978	+	0.985620i	$0.554047\pi$
$642$	0.485281	0.0191525
$643$	37.4558	1.47711	0.738557	−	0.674191i	$-0.235507\pi$
$643$	37.4558	1.47711	0.738557	+	0.674191i	$0.235507\pi$
$644$	0	0
$645$	−17.0711	−0.672173
$646$	−3.17157	−0.124784
$647$	−23.5563	−0.926096	−0.463048	−	0.886333i	$-0.653244\pi$
$647$	−23.5563	−0.926096	−0.463048	+	0.886333i	$0.653244\pi$
$648$	2.82843	0.111111
$649$	−20.4853	−0.804118
$650$	−58.7696	−2.30513
$651$	10.2426	0.401441
$652$	0	0
$653$	−6.89949	−0.269998	−0.134999	−	0.990846i	$-0.543103\pi$
$653$	−6.89949	−0.269998	−0.134999	+	0.990846i	$0.543103\pi$
$654$	−11.1716	−0.436843
$655$	−36.1421	−1.41219
$656$	4.00000	0.156174
$657$	−10.3137	−0.402376
$658$	50.2843	1.96028
$659$	−34.8284	−1.35672	−0.678361	−	0.734728i	$-0.737310\pi$
$659$	−34.8284	−1.35672	−0.678361	+	0.734728i	$0.737310\pi$
$660$	0	0
$661$	13.4558	0.523372	0.261686	−	0.965153i	$-0.415722\pi$
$661$	13.4558	0.523372	0.261686	+	0.965153i	$0.415722\pi$
$662$	−22.9706	−0.892776
$663$	−2.58579	−0.100424
$664$	3.02944	0.117565
$665$	63.1127	2.44741
$666$	13.4142	0.519790
$667$	8.58579	0.332443
$668$	0	0
$669$	10.3431	0.399889
$670$	−50.6274	−1.95591
$671$	−11.2426	−0.434017
$672$	0	0
$673$	21.7990	0.840289	0.420145	−	0.907457i	$-0.361979\pi$
$673$	21.7990	0.840289	0.420145	+	0.907457i	$0.361979\pi$
$674$	−28.2426	−1.08787
$675$	6.65685	0.256222
$676$	0	0
$677$	33.5563	1.28968	0.644838	−	0.764320i	$-0.276925\pi$
$677$	33.5563	1.28968	0.644838	+	0.764320i	$0.276925\pi$
$678$	−9.51472	−0.365411
$679$	−26.4853	−1.01641
$680$	−4.00000	−0.153393
$681$	1.10051	0.0421714
$682$	10.2426	0.392211
$683$	−6.28427	−0.240461	−0.120230	−	0.992746i	$-0.538363\pi$
$683$	−6.28427	−0.240461	−0.120230	+	0.992746i	$0.538363\pi$
$684$	0	0
$685$	13.4142	0.512531
$686$	−11.3137	−0.431959
$687$	−0.242641	−0.00925732
$688$	20.0000	0.762493
$689$	42.6274	1.62398
$690$	6.82843	0.259954
$691$	10.7279	0.408109	0.204055	−	0.978959i	$-0.434588\pi$
$691$	10.7279	0.408109	0.204055	+	0.978959i	$0.434588\pi$
$692$	0	0
$693$	−8.24264	−0.313112
$694$	−1.27208	−0.0482874
$695$	12.4853	0.473594
$696$	−17.1716	−0.650887
$697$	0.414214	0.0156895
$698$	−12.9289	−0.489367
$699$	−18.0000	−0.680823
$700$	0	0
$701$	−45.7990	−1.72980	−0.864902	−	0.501941i	$-0.832620\pi$
$701$	−45.7990	−1.72980	−0.864902	+	0.501941i	$0.832620\pi$
$702$	−8.82843	−0.333208
$703$	51.3553	1.93690
$704$	19.3137	0.727913
$705$	35.5563	1.33913
$706$	49.4558	1.86130
$707$	1.41421	0.0531870
$708$	0	0
$709$	−30.4853	−1.14490	−0.572449	−	0.819940i	$-0.694007\pi$
$709$	−30.4853	−1.14490	−0.572449	+	0.819940i	$0.694007\pi$
$710$	−48.6274	−1.82495
$711$	−7.65685	−0.287154
$712$	−32.9706	−1.23562
$713$	4.24264	0.158888
$714$	−2.00000	−0.0748481
$715$	51.4558	1.92434
$716$	0	0
$717$	18.1421	0.677530
$718$	−22.9706	−0.857254
$719$	40.5563	1.51250	0.756248	−	0.654285i	$-0.227030\pi$
$719$	40.5563	1.51250	0.756248	+	0.654285i	$0.227030\pi$
$720$	−13.6569	−0.508961
$721$	−21.5563	−0.802800
$722$	−14.5858	−0.542827
$723$	9.48528	0.352761
$724$	0	0
$725$	−40.4142	−1.50095
$726$	7.31371	0.271437
$727$	−32.7279	−1.21381	−0.606906	−	0.794774i	$-0.707589\pi$
$727$	−32.7279	−1.21381	−0.606906	+	0.794774i	$0.707589\pi$
$728$	−60.2843	−2.23428
$729$	1.00000	0.0370370
$730$	49.7990	1.84314
$731$	2.07107	0.0766012
$732$	0	0
$733$	−31.1421	−1.15026	−0.575131	−	0.818062i	$-0.695049\pi$
$733$	−31.1421	−1.15026	−0.575131	+	0.818062i	$0.695049\pi$
$734$	9.41421	0.347485
$735$	15.8995	0.586462
$736$	0	0
$737$	25.3137	0.932442
$738$	1.41421	0.0520579
$739$	22.6569	0.833446	0.416723	−	0.909034i	$-0.363179\pi$
$739$	22.6569	0.833446	0.416723	+	0.909034i	$0.363179\pi$
$740$	0	0
$741$	−33.7990	−1.24164
$742$	32.9706	1.21039
$743$	16.6274	0.610001	0.305000	−	0.952352i	$-0.401343\pi$
$743$	16.6274	0.610001	0.305000	+	0.952352i	$0.401343\pi$
$744$	−8.48528	−0.311086
$745$	59.1127	2.16572
$746$	−46.8701	−1.71603
$747$	1.07107	0.0391883
$748$	0	0
$749$	1.17157	0.0428083
$750$	−8.00000	−0.292119
$751$	34.9706	1.27609	0.638047	−	0.769997i	$-0.279743\pi$
$751$	34.9706	1.27609	0.638047	+	0.769997i	$0.279743\pi$
$752$	−41.6569	−1.51907
$753$	8.82843	0.321726
$754$	53.5980	1.95192
$755$	−54.6274	−1.98810
$756$	0	0
$757$	8.24264	0.299584	0.149792	−	0.988718i	$-0.452140\pi$
$757$	8.24264	0.299584	0.149792	+	0.988718i	$0.452140\pi$
$758$	−38.1421	−1.38538
$759$	−3.41421	−0.123928
$760$	−52.2843	−1.89655
$761$	14.8284	0.537530	0.268765	−	0.963206i	$-0.413384\pi$
$761$	14.8284	0.537530	0.268765	+	0.963206i	$0.413384\pi$
$762$	−13.1716	−0.477156
$763$	−26.9706	−0.976400
$764$	0	0
$765$	−1.41421	−0.0511310
$766$	−24.1838	−0.873795
$767$	−52.9706	−1.91266
$768$	0	0
$769$	−33.4853	−1.20751	−0.603755	−	0.797170i	$-0.706330\pi$
$769$	−33.4853	−1.20751	−0.603755	+	0.797170i	$0.706330\pi$
$770$	39.7990	1.43426
$771$	−5.10051	−0.183690
$772$	0	0
$773$	50.4142	1.81327	0.906637	−	0.421912i	$-0.138641\pi$
$773$	50.4142	1.81327	0.906637	+	0.421912i	$0.138641\pi$
$774$	7.07107	0.254164
$775$	−19.9706	−0.717364
$776$	21.9411	0.787641
$777$	32.3848	1.16180
$778$	31.4558	1.12775
$779$	5.41421	0.193984
$780$	0	0
$781$	24.3137	0.870013
$782$	−0.828427	−0.0296245
$783$	−6.07107	−0.216962
$784$	−18.6274	−0.665265
$785$	61.4558	2.19345
$786$	14.9706	0.533982
$787$	−13.9706	−0.497997	−0.248998	−	0.968504i	$-0.580101\pi$
$787$	−13.9706	−0.497997	−0.248998	+	0.968504i	$0.580101\pi$
$788$	0	0
$789$	2.41421	0.0859483
$790$	36.9706	1.31535
$791$	−22.9706	−0.816739
$792$	6.82843	0.242638
$793$	−29.0711	−1.03234
$794$	−43.1716	−1.53210
$795$	23.3137	0.826852
$796$	0	0
$797$	−44.1421	−1.56359	−0.781797	−	0.623533i	$-0.785697\pi$
$797$	−44.1421	−1.56359	−0.781797	+	0.623533i	$0.785697\pi$
$798$	−26.1421	−0.925422
$799$	−4.31371	−0.152608
$800$	0	0
$801$	−11.6569	−0.411875
$802$	−15.0294	−0.530708
$803$	−24.8995	−0.878684
$804$	0	0
$805$	16.4853	0.581030
$806$	26.4853	0.932904
$807$	−8.48528	−0.298696
$808$	−1.17157	−0.0412158
$809$	25.1127	0.882915	0.441458	−	0.897282i	$-0.354462\pi$
$809$	25.1127	0.882915	0.441458	+	0.897282i	$0.354462\pi$
$810$	−4.82843	−0.169654
$811$	−17.9706	−0.631032	−0.315516	−	0.948920i	$-0.602178\pi$
$811$	−17.9706	−0.631032	−0.315516	+	0.948920i	$0.602178\pi$
$812$	0	0
$813$	18.7990	0.659309
$814$	32.3848	1.13509
$815$	−32.3848	−1.13439
$816$	1.65685	0.0580015
$817$	27.0711	0.947097
$818$	−22.8701	−0.799633
$819$	−21.3137	−0.744761
$820$	0	0
$821$	−38.8701	−1.35657	−0.678287	−	0.734797i	$-0.737277\pi$
$821$	−38.8701	−1.35657	−0.678287	+	0.734797i	$0.737277\pi$
$822$	−5.55635	−0.193800
$823$	32.4264	1.13031	0.565157	−	0.824984i	$-0.308816\pi$
$823$	32.4264	1.13031	0.565157	+	0.824984i	$0.308816\pi$
$824$	17.8579	0.622108
$825$	16.0711	0.559523
$826$	−40.9706	−1.42555
$827$	7.92893	0.275716	0.137858	−	0.990452i	$-0.455978\pi$
$827$	7.92893	0.275716	0.137858	+	0.990452i	$0.455978\pi$
$828$	0	0
$829$	−24.9411	−0.866241	−0.433121	−	0.901336i	$-0.642588\pi$
$829$	−24.9411	−0.866241	−0.433121	+	0.901336i	$0.642588\pi$
$830$	−5.17157	−0.179508
$831$	−27.2843	−0.946481
$832$	49.9411	1.73140
$833$	−1.92893	−0.0668335
$834$	−5.17157	−0.179077
$835$	−12.4853	−0.432071
$836$	0	0
$837$	−3.00000	−0.103695
$838$	−21.3137	−0.736270
$839$	−22.8284	−0.788125	−0.394062	−	0.919084i	$-0.628931\pi$
$839$	−22.8284	−0.788125	−0.394062	+	0.919084i	$0.628931\pi$
$840$	−32.9706	−1.13759
$841$	7.85786	0.270961
$842$	12.6863	0.437198
$843$	17.3848	0.598764
$844$	0	0
$845$	88.6690	3.05031
$846$	−14.7279	−0.506356
$847$	17.6569	0.606697
$848$	−27.3137	−0.937957
$849$	16.1716	0.555007
$850$	3.89949	0.133752
$851$	13.4142	0.459833
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	−22.4853	−0.769430
$855$	−18.4853	−0.632183
$856$	−0.970563	−0.0331732
$857$	51.7990	1.76942	0.884710	−	0.466142i	$-0.154356\pi$
$857$	51.7990	1.76942	0.884710	+	0.466142i	$0.154356\pi$
$858$	−21.3137	−0.727638
$859$	16.6569	0.568325	0.284162	−	0.958776i	$-0.408285\pi$
$859$	16.6569	0.568325	0.284162	+	0.958776i	$0.408285\pi$
$860$	0	0
$861$	3.41421	0.116356
$862$	−35.2548	−1.20078
$863$	25.0711	0.853429	0.426715	−	0.904386i	$-0.359671\pi$
$863$	25.0711	0.853429	0.426715	+	0.904386i	$0.359671\pi$
$864$	0	0
$865$	−30.9706	−1.05303
$866$	−7.75736	−0.263606
$867$	−16.8284	−0.571523
$868$	0	0
$869$	−18.4853	−0.627070
$870$	29.3137	0.993828
$871$	65.4558	2.21789
$872$	22.3431	0.756634
$873$	7.75736	0.262547
$874$	−10.8284	−0.366277
$875$	−19.3137	−0.652923
$876$	0	0
$877$	−27.1421	−0.916525	−0.458262	−	0.888817i	$-0.651528\pi$
$877$	−27.1421	−0.916525	−0.458262	+	0.888817i	$0.651528\pi$
$878$	−4.20101	−0.141777
$879$	9.58579	0.323321
$880$	−32.9706	−1.11144
$881$	−42.6274	−1.43615	−0.718077	−	0.695964i	$-0.754977\pi$
$881$	−42.6274	−1.43615	−0.718077	+	0.695964i	$0.754977\pi$
$882$	−6.58579	−0.221755
$883$	−9.41421	−0.316814	−0.158407	−	0.987374i	$-0.550636\pi$
$883$	−9.41421	−0.316814	−0.158407	+	0.987374i	$0.550636\pi$
$884$	0	0
$885$	−28.9706	−0.973835
$886$	51.3137	1.72392
$887$	36.0122	1.20917	0.604586	−	0.796540i	$-0.293339\pi$
$887$	36.0122	1.20917	0.604586	+	0.796540i	$0.293339\pi$
$888$	−26.8284	−0.900303
$889$	−31.7990	−1.06650
$890$	56.2843	1.88665
$891$	2.41421	0.0808792
$892$	0	0
$893$	−56.3848	−1.88684
$894$	−24.4853	−0.818910
$895$	−16.7279	−0.559153
$896$	38.6274	1.29045
$897$	−8.82843	−0.294773
$898$	−4.97056	−0.165870
$899$	18.2132	0.607444
$900$	0	0
$901$	−2.82843	−0.0942286
$902$	3.41421	0.113681
$903$	17.0711	0.568090
$904$	19.0294	0.632910
$905$	−24.9706	−0.830050
$906$	22.6274	0.751746
$907$	15.6569	0.519877	0.259939	−	0.965625i	$-0.416298\pi$
$907$	15.6569	0.519877	0.259939	+	0.965625i	$0.416298\pi$
$908$	0	0
$909$	−0.414214	−0.0137386
$910$	102.912	3.41149
$911$	34.1005	1.12980	0.564900	−	0.825159i	$-0.308915\pi$
$911$	34.1005	1.12980	0.564900	+	0.825159i	$0.308915\pi$
$912$	21.6569	0.717130
$913$	2.58579	0.0855770
$914$	5.65685	0.187112
$915$	−15.8995	−0.525621
$916$	0	0
$917$	36.1421	1.19352
$918$	0.585786	0.0193338
$919$	−15.4142	−0.508468	−0.254234	−	0.967143i	$-0.581823\pi$
$919$	−15.4142	−0.508468	−0.254234	+	0.967143i	$0.581823\pi$
$920$	−13.6569	−0.450253
$921$	−0.313708	−0.0103370
$922$	−40.4853	−1.33331
$923$	62.8701	2.06939
$924$	0	0
$925$	−63.1421	−2.07610
$926$	36.1421	1.18770
$927$	6.31371	0.207369
$928$	0	0
$929$	−7.87006	−0.258208	−0.129104	−	0.991631i	$-0.541210\pi$
$929$	−7.87006	−0.258208	−0.129104	+	0.991631i	$0.541210\pi$
$930$	14.4853	0.474991
$931$	−25.2132	−0.826329
$932$	0	0
$933$	26.8284	0.878323
$934$	1.85786	0.0607912
$935$	−3.41421	−0.111657
$936$	17.6569	0.577132
$937$	52.9706	1.73047	0.865236	−	0.501364i	$-0.167168\pi$
$937$	52.9706	1.73047	0.865236	+	0.501364i	$0.167168\pi$
$938$	50.6274	1.65304
$939$	−28.8701	−0.942139
$940$	0	0
$941$	−52.6274	−1.71560	−0.857802	−	0.513980i	$-0.828171\pi$
$941$	−52.6274	−1.71560	−0.857802	+	0.513980i	$0.828171\pi$
$942$	−25.4558	−0.829396
$943$	1.41421	0.0460531
$944$	33.9411	1.10469
$945$	−11.6569	−0.379197
$946$	17.0711	0.555028
$947$	21.5980	0.701840	0.350920	−	0.936405i	$-0.385869\pi$
$947$	21.5980	0.701840	0.350920	+	0.936405i	$0.385869\pi$
$948$	0	0
$949$	−64.3848	−2.09002
$950$	50.9706	1.65370
$951$	−12.0711	−0.391431
$952$	4.00000	0.129641
$953$	−41.6985	−1.35075	−0.675373	−	0.737476i	$-0.736017\pi$
$953$	−41.6985	−1.35075	−0.675373	+	0.737476i	$0.736017\pi$
$954$	−9.65685	−0.312652
$955$	64.2843	2.08019
$956$	0	0
$957$	−14.6569	−0.473789
$958$	−9.75736	−0.315246
$959$	−13.4142	−0.433168
$960$	27.3137	0.881546
$961$	−22.0000	−0.709677
$962$	83.7401	2.69989
$963$	−0.343146	−0.0110577
$964$	0	0
$965$	2.00000	0.0643823
$966$	−6.82843	−0.219701
$967$	−1.02944	−0.0331045	−0.0165522	−	0.999863i	$-0.505269\pi$
$967$	−1.02944	−0.0331045	−0.0165522	+	0.999863i	$0.505269\pi$
$968$	−14.6274	−0.470143
$969$	2.24264	0.0720440
$970$	−37.4558	−1.20263
$971$	40.5563	1.30152	0.650758	−	0.759286i	$-0.274451\pi$
$971$	40.5563	1.30152	0.650758	+	0.759286i	$0.274451\pi$
$972$	0	0
$973$	−12.4853	−0.400260
$974$	−2.78680	−0.0892947
$975$	41.5563	1.33087
$976$	18.6274	0.596249
$977$	7.58579	0.242691	0.121345	−	0.992610i	$-0.461279\pi$
$977$	7.58579	0.242691	0.121345	+	0.992610i	$0.461279\pi$
$978$	13.4142	0.428939
$979$	−28.1421	−0.899427
$980$	0	0
$981$	7.89949	0.252211
$982$	18.4853	0.589889
$983$	−22.9289	−0.731319	−0.365660	−	0.930749i	$-0.619157\pi$
$983$	−22.9289	−0.731319	−0.365660	+	0.930749i	$0.619157\pi$
$984$	−2.82843	−0.0901670
$985$	75.9411	2.41969
$986$	−3.55635	−0.113257
$987$	−35.5563	−1.13177
$988$	0	0
$989$	7.07107	0.224847
$990$	−11.6569	−0.370479
$991$	−28.4853	−0.904865	−0.452432	−	0.891799i	$-0.649444\pi$
$991$	−28.4853	−0.904865	−0.452432	+	0.891799i	$0.649444\pi$
$992$	0	0
$993$	16.2426	0.515445
$994$	48.6274	1.54237
$995$	−55.4558	−1.75807
$996$	0	0
$997$	15.4142	0.488173	0.244087	−	0.969753i	$-0.421512\pi$
$997$	15.4142	0.488173	0.244087	+	0.969753i	$0.421512\pi$
$998$	27.5980	0.873599
$999$	−9.48528	−0.300101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	123.2.a.c.1.1	✓	2
3.2	odd	2		369.2.a.c.1.2		2
4.3	odd	2		1968.2.a.r.1.2		2
5.4	even	2		3075.2.a.p.1.2		2
7.6	odd	2		6027.2.a.m.1.1		2
8.3	odd	2		7872.2.a.bo.1.1		2
8.5	even	2		7872.2.a.bk.1.1		2
12.11	even	2		5904.2.a.w.1.1		2
15.14	odd	2		9225.2.a.bm.1.1		2
41.40	even	2		5043.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
123.2.a.c.1.1	✓	2	1.1	even	1	trivial
369.2.a.c.1.2		2	3.2	odd	2
1968.2.a.r.1.2		2	4.3	odd	2
3075.2.a.p.1.2		2	5.4	even	2
5043.2.a.e.1.1		2	41.40	even	2
5904.2.a.w.1.1		2	12.11	even	2
6027.2.a.m.1.1		2	7.6	odd	2
7872.2.a.bk.1.1		2	8.5	even	2
7872.2.a.bo.1.1		2	8.3	odd	2
9225.2.a.bm.1.1		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	123.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +1.00000 q^{3} +3.41421 q^{5} -1.41421 q^{6} -3.41421 q^{7} +2.82843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +1.00000 q^{3} +3.41421 q^{5} -1.41421 q^{6} -3.41421 q^{7} +2.82843 q^{8} +1.00000 q^{9} -4.82843 q^{10} +2.41421 q^{11} +6.24264 q^{13} +4.82843 q^{14} +3.41421 q^{15} -4.00000 q^{16} -0.414214 q^{17} -1.41421 q^{18} -5.41421 q^{19} -3.41421 q^{21} -3.41421 q^{22} -1.41421 q^{23} +2.82843 q^{24} +6.65685 q^{25} -8.82843 q^{26} +1.00000 q^{27} -6.07107 q^{29} -4.82843 q^{30} -3.00000 q^{31} +2.41421 q^{33} +0.585786 q^{34} -11.6569 q^{35} -9.48528 q^{37} +7.65685 q^{38} +6.24264 q^{39} +9.65685 q^{40} -1.00000 q^{41} +4.82843 q^{42} -5.00000 q^{43} +3.41421 q^{45} +2.00000 q^{46} +10.4142 q^{47} -4.00000 q^{48} +4.65685 q^{49} -9.41421 q^{50} -0.414214 q^{51} +6.82843 q^{53} -1.41421 q^{54} +8.24264 q^{55} -9.65685 q^{56} -5.41421 q^{57} +8.58579 q^{58} -8.48528 q^{59} -4.65685 q^{61} +4.24264 q^{62} -3.41421 q^{63} +8.00000 q^{64} +21.3137 q^{65} -3.41421 q^{66} +10.4853 q^{67} -1.41421 q^{69} +16.4853 q^{70} +10.0711 q^{71} +2.82843 q^{72} -10.3137 q^{73} +13.4142 q^{74} +6.65685 q^{75} -8.24264 q^{77} -8.82843 q^{78} -7.65685 q^{79} -13.6569 q^{80} +1.00000 q^{81} +1.41421 q^{82} +1.07107 q^{83} -1.41421 q^{85} +7.07107 q^{86} -6.07107 q^{87} +6.82843 q^{88} -11.6569 q^{89} -4.82843 q^{90} -21.3137 q^{91} -3.00000 q^{93} -14.7279 q^{94} -18.4853 q^{95} +7.75736 q^{97} -6.58579 q^{98} +2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9} - 4 q^{10} + 2 q^{11} + 4 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} + 2 q^{17} - 8 q^{19} - 4 q^{21} - 4 q^{22} + 2 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{29} - 4 q^{30} - 6 q^{31} + 2 q^{33} + 4 q^{34} - 12 q^{35} - 2 q^{37} + 4 q^{38} + 4 q^{39} + 8 q^{40} - 2 q^{41} + 4 q^{42} - 10 q^{43} + 4 q^{45} + 4 q^{46} + 18 q^{47} - 8 q^{48} - 2 q^{49} - 16 q^{50} + 2 q^{51} + 8 q^{53} + 8 q^{55} - 8 q^{56} - 8 q^{57} + 20 q^{58} + 2 q^{61} - 4 q^{63} + 16 q^{64} + 20 q^{65} - 4 q^{66} + 4 q^{67} + 16 q^{70} + 6 q^{71} + 2 q^{73} + 24 q^{74} + 2 q^{75} - 8 q^{77} - 12 q^{78} - 4 q^{79} - 16 q^{80} + 2 q^{81} - 12 q^{83} + 2 q^{87} + 8 q^{88} - 12 q^{89} - 4 q^{90} - 20 q^{91} - 6 q^{93} - 4 q^{94} - 20 q^{95} + 24 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9 - 4 * q^10 + 2 * q^11 + 4 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 + 2 * q^17 - 8 * q^19 - 4 * q^21 - 4 * q^22 + 2 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^29 - 4 * q^30 - 6 * q^31 + 2 * q^33 + 4 * q^34 - 12 * q^35 - 2 * q^37 + 4 * q^38 + 4 * q^39 + 8 * q^40 - 2 * q^41 + 4 * q^42 - 10 * q^43 + 4 * q^45 + 4 * q^46 + 18 * q^47 - 8 * q^48 - 2 * q^49 - 16 * q^50 + 2 * q^51 + 8 * q^53 + 8 * q^55 - 8 * q^56 - 8 * q^57 + 20 * q^58 + 2 * q^61 - 4 * q^63 + 16 * q^64 + 20 * q^65 - 4 * q^66 + 4 * q^67 + 16 * q^70 + 6 * q^71 + 2 * q^73 + 24 * q^74 + 2 * q^75 - 8 * q^77 - 12 * q^78 - 4 * q^79 - 16 * q^80 + 2 * q^81 - 12 * q^83 + 2 * q^87 + 8 * q^88 - 12 * q^89 - 4 * q^90 - 20 * q^91 - 6 * q^93 - 4 * q^94 - 20 * q^95 + 24 * q^97 - 16 * q^98 + 2 * q^99

Introduction

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