LMFDB - Embedded newform 1470.2.m.c.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 $ x^16 - 32x^13 + 2x^12 + 352x^10 - 288x^9 + 2x^8 - 1440x^7 + 8800x^6 + 1250x^4 - 100000*x^3 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.7
Root			$2.21573 + 0.300921i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.c.1273.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.569907 - 2.16222i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.569907 - 2.16222i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.12594 - 1.93191i) q^{10} -2.01606 q^{11} +(-0.707107 + 0.707107i) q^{12} +(3.44007 + 3.44007i) q^{13} +(1.12594 - 1.93191i) q^{15} -1.00000 q^{16} +(3.40102 - 3.40102i) q^{17} +(-0.707107 + 0.707107i) q^{18} +6.72400 q^{19} +(2.16222 - 0.569907i) q^{20} +(-1.42557 - 1.42557i) q^{22} +(4.65016 - 4.65016i) q^{23} -1.00000 q^{24} +(-4.35041 + 2.46453i) q^{25} +4.86500i q^{26} +(-0.707107 + 0.707107i) q^{27} +1.60303i q^{29} +(2.16222 - 0.569907i) q^{30} +6.25097i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.42557 - 1.42557i) q^{33} +4.80977 q^{34} -1.00000 q^{36} +(3.63458 + 3.63458i) q^{37} +(4.75459 + 4.75459i) q^{38} +4.86500i q^{39} +(1.93191 + 1.12594i) q^{40} +4.94376i q^{41} +(-4.68143 + 4.68143i) q^{43} -2.01606i q^{44} +(2.16222 - 0.569907i) q^{45} +6.57632 q^{46} +(-1.07805 + 1.07805i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-4.81889 - 1.33352i) q^{50} +4.80977 q^{51} +(-3.44007 + 3.44007i) q^{52} +(1.42923 - 1.42923i) q^{53} -1.00000 q^{54} +(1.14896 + 4.35916i) q^{55} +(4.75459 + 4.75459i) q^{57} +(-1.13351 + 1.13351i) q^{58} +12.8185 q^{59} +(1.93191 + 1.12594i) q^{60} -9.00341i q^{61} +(-4.42010 + 4.42010i) q^{62} -1.00000i q^{64} +(5.47768 - 9.39873i) q^{65} -2.01606i q^{66} +(-1.19011 - 1.19011i) q^{67} +(3.40102 + 3.40102i) q^{68} +6.57632 q^{69} -3.49027 q^{71} +(-0.707107 - 0.707107i) q^{72} +(5.97245 + 5.97245i) q^{73} +5.14007i q^{74} +(-4.81889 - 1.33352i) q^{75} +6.72400i q^{76} +(-3.44007 + 3.44007i) q^{78} -13.9865i q^{79} +(0.569907 + 2.16222i) q^{80} -1.00000 q^{81} +(-3.49577 + 3.49577i) q^{82} +(-8.59652 - 8.59652i) q^{83} +(-9.29202 - 5.41549i) q^{85} -6.62055 q^{86} +(-1.13351 + 1.13351i) q^{87} +(1.42557 - 1.42557i) q^{88} +2.40171 q^{89} +(1.93191 + 1.12594i) q^{90} +(4.65016 + 4.65016i) q^{92} +(-4.42010 + 4.42010i) q^{93} -1.52460 q^{94} +(-3.83206 - 14.5388i) q^{95} -1.00000i q^{96} +(13.1830 - 13.1830i) q^{97} -2.01606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5}+O(q^{10}) $ 16 * q - 8 * q^5	$ 16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57} + 24 q^{58} - 48 q^{59} + 8 q^{62} + 72 q^{65} - 48 q^{67} + 8 q^{68} - 16 q^{73} + 8 q^{78} + 8 q^{80} - 16 q^{81} + 16 q^{82} - 72 q^{85} + 24 q^{87} + 8 q^{88} + 64 q^{89} - 8 q^{92} + 8 q^{93} - 64 q^{94} + 48 q^{95} + 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 - 8 * q^13 - 16 * q^16 + 8 * q^17 + 48 * q^19 - 8 * q^22 - 8 * q^23 - 16 * q^24 + 8 * q^25 - 8 * q^33 - 16 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^47 + 8 * q^52 + 8 * q^53 - 16 * q^54 + 8 * q^57 + 24 * q^58 - 48 * q^59 + 8 * q^62 + 72 * q^65 - 48 * q^67 + 8 * q^68 - 16 * q^73 + 8 * q^78 + 8 * q^80 - 16 * q^81 + 16 * q^82 - 72 * q^85 + 24 * q^87 + 8 * q^88 + 64 * q^89 - 8 * q^92 + 8 * q^93 - 64 * q^94 + 48 * q^95 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	−0.569907	−	2.16222i	−0.254870	−	0.966975i
$5$	−0.569907	−	2.16222i	−0.254870	−	0.966975i
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	1.12594	−	1.93191i	0.356053	−	0.610923i
$11$	−2.01606			−0.607864			−0.303932	−	0.952694i	$-0.598300\pi$
$11$	−2.01606			−0.607864			−0.303932	+	0.952694i	$0.598300\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	3.44007	+	3.44007i	0.954105	+	0.954105i	0.998992	−	0.0448871i	$-0.0142928\pi$
$13$	3.44007	+	3.44007i	0.954105	+	0.954105i	−0.0448871	+	0.998992i	$0.514293\pi$
$14$		0			0
$15$	1.12594	−	1.93191i	0.290716	−	0.498816i
$16$	−1.00000			−0.250000
$17$	3.40102	−	3.40102i	0.824868	−	0.824868i	−0.161933	−	0.986802i	$-0.551773\pi$
$17$	3.40102	−	3.40102i	0.824868	−	0.824868i	0.986802	+	0.161933i	$0.0517730\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	6.72400			1.54259			0.771296	−	0.636477i	$-0.219609\pi$
$19$	6.72400			1.54259			0.771296	+	0.636477i	$0.219609\pi$
$20$	2.16222	−	0.569907i	0.483488	−	0.127435i
$21$		0			0
$22$	−1.42557	−	1.42557i	−0.303932	−	0.303932i
$23$	4.65016	−	4.65016i	0.969625	−	0.969625i	−0.0299268	−	0.999552i	$-0.509527\pi$
$23$	4.65016	−	4.65016i	0.969625	−	0.969625i	0.999552	+	0.0299268i	$0.00952742\pi$
$24$	−1.00000			−0.204124
$25$	−4.35041	+	2.46453i	−0.870082	+	0.492906i
$26$			4.86500i			0.954105i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			1.60303i			0.297675i	0.988862	+	0.148837i	$0.0475531\pi$
$29$			1.60303i			0.297675i	−0.988862	+	0.148837i	$0.952447\pi$
$30$	2.16222	−	0.569907i	0.394766	−	0.104050i
$31$			6.25097i			1.12271i	0.827576	+	0.561353i	$0.189719\pi$
$31$			6.25097i			1.12271i	−0.827576	+	0.561353i	$0.810281\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.42557	−	1.42557i	−0.248159	−	0.248159i
$34$	4.80977			0.824868
$35$		0			0
$36$	−1.00000			−0.166667
$37$	3.63458	+	3.63458i	0.597521	+	0.597521i	0.939652	−	0.342131i	$-0.111149\pi$
$37$	3.63458	+	3.63458i	0.597521	+	0.597521i	−0.342131	+	0.939652i	$0.611149\pi$
$38$	4.75459	+	4.75459i	0.771296	+	0.771296i
$39$			4.86500i			0.779023i
$40$	1.93191	+	1.12594i	0.305461	+	0.178026i
$41$			4.94376i			0.772086i	0.922481	+	0.386043i	$0.126158\pi$
$41$			4.94376i			0.772086i	−0.922481	+	0.386043i	$0.873842\pi$
$42$		0			0
$43$	−4.68143	+	4.68143i	−0.713912	+	0.713912i	−0.967351	−	0.253439i	$-0.918438\pi$
$43$	−4.68143	+	4.68143i	−0.713912	+	0.713912i	0.253439	+	0.967351i	$0.418438\pi$
$44$		−	2.01606i		−	0.303932i
$45$	2.16222	−	0.569907i	0.322325	−	0.0849568i
$46$	6.57632			0.969625
$47$	−1.07805	+	1.07805i	−0.157250	+	0.157250i	−0.781347	−	0.624097i	$-0.785467\pi$
$47$	−1.07805	+	1.07805i	−0.157250	+	0.157250i	0.624097	+	0.781347i	$0.285467\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		0			0
$50$	−4.81889	−	1.33352i	−0.681494	−	0.188588i
$51$	4.80977			0.673502
$52$	−3.44007	+	3.44007i	−0.477052	+	0.477052i
$53$	1.42923	−	1.42923i	0.196320	−	0.196320i	−0.602100	−	0.798421i	$-0.705669\pi$
$53$	1.42923	−	1.42923i	0.196320	−	0.196320i	0.798421	+	0.602100i	$0.205669\pi$
$54$	−1.00000			−0.136083
$55$	1.14896	+	4.35916i	0.154926	+	0.587789i
$56$		0			0
$57$	4.75459	+	4.75459i	0.629760	+	0.629760i
$58$	−1.13351	+	1.13351i	−0.148837	+	0.148837i
$59$	12.8185			1.66883			0.834413	−	0.551140i	$-0.185807\pi$
$59$	12.8185			1.66883			0.834413	+	0.551140i	$0.185807\pi$
$60$	1.93191	+	1.12594i	0.249408	+	0.145358i
$61$		−	9.00341i		−	1.15277i	−0.817179	−	0.576384i	$-0.804463\pi$
$61$		−	9.00341i		−	1.15277i	0.817179	−	0.576384i	$-0.195537\pi$
$62$	−4.42010	+	4.42010i	−0.561353	+	0.561353i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	5.47768	−	9.39873i	0.679423	−	1.16577i
$66$		−	2.01606i		−	0.248159i
$67$	−1.19011	−	1.19011i	−0.145395	−	0.145395i	0.630662	−	0.776057i	$-0.282783\pi$
$67$	−1.19011	−	1.19011i	−0.145395	−	0.145395i	−0.776057	+	0.630662i	$0.782783\pi$
$68$	3.40102	+	3.40102i	0.412434	+	0.412434i
$69$	6.57632			0.791696
$70$		0			0
$71$	−3.49027			−0.414219			−0.207110	−	0.978318i	$-0.566406\pi$
$71$	−3.49027			−0.414219			−0.207110	+	0.978318i	$0.566406\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	5.97245	+	5.97245i	0.699023	+	0.699023i	0.964200	−	0.265177i	$-0.0854304\pi$
$73$	5.97245	+	5.97245i	0.699023	+	0.699023i	−0.265177	+	0.964200i	$0.585430\pi$
$74$			5.14007i			0.597521i
$75$	−4.81889	−	1.33352i	−0.556438	−	0.153981i
$76$			6.72400i			0.771296i
$77$		0			0
$78$	−3.44007	+	3.44007i	−0.389512	+	0.389512i
$79$		−	13.9865i		−	1.57361i	−0.617203	−	0.786804i	$-0.711734\pi$
$79$		−	13.9865i		−	1.57361i	0.617203	−	0.786804i	$-0.288266\pi$
$80$	0.569907	+	2.16222i	0.0637176	+	0.241744i
$81$	−1.00000			−0.111111
$82$	−3.49577	+	3.49577i	−0.386043	+	0.386043i
$83$	−8.59652	−	8.59652i	−0.943590	−	0.943590i	0.0549015	−	0.998492i	$-0.482516\pi$
$83$	−8.59652	−	8.59652i	−0.943590	−	0.943590i	−0.998492	+	0.0549015i	$0.982516\pi$
$84$		0			0
$85$	−9.29202	−	5.41549i	−1.00786	−	0.587393i
$86$	−6.62055			−0.713912
$87$	−1.13351	+	1.13351i	−0.121525	+	0.121525i
$88$	1.42557	−	1.42557i	0.151966	−	0.151966i
$89$	2.40171			0.254581			0.127290	−	0.991865i	$-0.459372\pi$
$89$	2.40171			0.254581			0.127290	+	0.991865i	$0.459372\pi$
$90$	1.93191	+	1.12594i	0.203641	+	0.118684i
$91$		0			0
$92$	4.65016	+	4.65016i	0.484813	+	0.484813i
$93$	−4.42010	+	4.42010i	−0.458343	+	0.458343i
$94$	−1.52460			−0.157250
$95$	−3.83206	−	14.5388i	−0.393161	−	1.49165i
$96$		−	1.00000i		−	0.102062i
$97$	13.1830	−	13.1830i	1.33854	−	1.33854i	0.441055	−	0.897480i	$-0.354604\pi$
$97$	13.1830	−	13.1830i	1.33854	−	1.33854i	0.897480	−	0.441055i	$-0.145396\pi$
$98$		0			0
$99$		−	2.01606i		−	0.202621i
$100$	−2.46453	−	4.35041i	−0.246453	−	0.435041i
$101$			13.9054i			1.38364i	0.722069	+	0.691821i	$0.243191\pi$
$101$			13.9054i			1.38364i	−0.722069	+	0.691821i	$0.756809\pi$
$102$	3.40102	+	3.40102i	0.336751	+	0.336751i
$103$	−1.68753	−	1.68753i	−0.166278	−	0.166278i	0.619063	−	0.785341i	$-0.287512\pi$
$103$	−1.68753	−	1.68753i	−0.166278	−	0.166278i	−0.785341	+	0.619063i	$0.787512\pi$
$104$	−4.86500			−0.477052
$105$		0			0
$106$	2.02124			0.196320
$107$	8.03115	+	8.03115i	0.776400	+	0.776400i	0.979217	−	0.202816i	$-0.0650094\pi$
$107$	8.03115	+	8.03115i	0.776400	+	0.776400i	−0.202816	+	0.979217i	$0.565009\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			15.8201i			1.51529i	0.652664	+	0.757647i	$0.273651\pi$
$109$			15.8201i			1.51529i	−0.652664	+	0.757647i	$0.726349\pi$
$110$	−2.26995	+	3.89483i	−0.216431	+	0.371358i
$111$			5.14007i			0.487874i
$112$		0			0
$113$	−10.9390	+	10.9390i	−1.02905	+	1.02905i	−0.0294854	+	0.999565i	$0.509387\pi$
$113$	−10.9390	+	10.9390i	−1.02905	+	1.02905i	−0.999565	+	0.0294854i	$0.990613\pi$
$114$			6.72400i			0.629760i
$115$	−12.7048	−	7.40452i	−1.18473	−	0.690475i
$116$	−1.60303			−0.148837
$117$	−3.44007	+	3.44007i	−0.318035	+	0.318035i
$118$	9.06404	+	9.06404i	0.834413	+	0.834413i
$119$		0			0
$120$	0.569907	+	2.16222i	0.0520252	+	0.197383i
$121$	−6.93552			−0.630502
$122$	6.36637	−	6.36637i	0.576384	−	0.576384i
$123$	−3.49577	+	3.49577i	−0.315203	+	0.315203i
$124$	−6.25097			−0.561353
$125$	7.80820	+	8.00200i	0.698386	+	0.715721i
$126$		0			0
$127$	−0.559216	−	0.559216i	−0.0496224	−	0.0496224i	0.681860	−	0.731483i	$-0.261171\pi$
$127$	−0.559216	−	0.559216i	−0.0496224	−	0.0496224i	−0.731483	+	0.681860i	$0.761171\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−6.62055			−0.582907
$130$	10.5192	−	2.77260i	0.922596	−	0.243173i
$131$		−	15.7930i		−	1.37984i	−0.723885	−	0.689920i	$-0.757646\pi$
$131$		−	15.7930i		−	1.37984i	0.723885	−	0.689920i	$-0.242354\pi$
$132$	1.42557	−	1.42557i	0.124080	−	0.124080i
$133$		0			0
$134$		−	1.68307i		−	0.145395i
$135$	1.93191	+	1.12594i	0.166272	+	0.0969052i
$136$			4.80977i			0.412434i
$137$	−9.99143	−	9.99143i	−0.853625	−	0.853625i	0.136952	−	0.990578i	$-0.456269\pi$
$137$	−9.99143	−	9.99143i	−0.853625	−	0.853625i	−0.990578	+	0.136952i	$0.956269\pi$
$138$	4.65016	+	4.65016i	0.395848	+	0.395848i
$139$	−4.06459			−0.344754			−0.172377	−	0.985031i	$-0.555145\pi$
$139$	−4.06459			−0.344754			−0.172377	+	0.985031i	$0.555145\pi$
$140$		0			0
$141$	−1.52460			−0.128394
$142$	−2.46800	−	2.46800i	−0.207110	−	0.207110i
$143$	−6.93538	−	6.93538i	−0.579966	−	0.579966i
$144$		−	1.00000i		−	0.0833333i
$145$	3.46610	−	0.913577i	0.287844	−	0.0758684i
$146$			8.44633i			0.699023i
$147$		0			0
$148$	−3.63458	+	3.63458i	−0.298760	+	0.298760i
$149$		−	10.4743i		−	0.858092i	−0.903283	−	0.429046i	$-0.858850\pi$
$149$		−	10.4743i		−	0.858092i	0.903283	−	0.429046i	$-0.141150\pi$
$150$	−2.46453	−	4.35041i	−0.201228	−	0.355210i
$151$	−10.5250			−0.856516			−0.428258	−	0.903656i	$-0.640873\pi$
$151$	−10.5250			−0.856516			−0.428258	+	0.903656i	$0.640873\pi$
$152$	−4.75459	+	4.75459i	−0.385648	+	0.385648i
$153$	3.40102	+	3.40102i	0.274956	+	0.274956i
$154$		0			0
$155$	13.5160	−	3.56247i	1.08563	−	0.286145i
$156$	−4.86500			−0.389512
$157$	−5.51100	+	5.51100i	−0.439826	+	0.439826i	−0.891953	−	0.452128i	$-0.850665\pi$
$157$	−5.51100	+	5.51100i	−0.439826	+	0.439826i	0.452128	+	0.891953i	$0.350665\pi$
$158$	9.88997	−	9.88997i	0.786804	−	0.786804i
$159$	2.02124			0.160295
$160$	−1.12594	+	1.93191i	−0.0890131	+	0.152731i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−3.18264	+	3.18264i	−0.249283	+	0.249283i	−0.820676	−	0.571393i	$-0.806403\pi$
$163$	−3.18264	+	3.18264i	−0.249283	+	0.249283i	0.571393	+	0.820676i	$0.306403\pi$
$164$	−4.94376			−0.386043
$165$	−2.26995	+	3.89483i	−0.176715	+	0.303212i
$166$		−	12.1573i		−	0.943590i
$167$	−3.06894	+	3.06894i	−0.237482	+	0.237482i	−0.815806	−	0.578325i	$-0.803707\pi$
$167$	−3.06894	+	3.06894i	−0.237482	+	0.237482i	0.578325	+	0.815806i	$0.303707\pi$
$168$		0			0
$169$			10.6682i			0.820632i
$170$	−2.74112	−	10.3998i	−0.210234	−	0.797627i
$171$			6.72400i			0.514197i
$172$	−4.68143	−	4.68143i	−0.356956	−	0.356956i
$173$	−12.4162	−	12.4162i	−0.943986	−	0.943986i	0.0545259	−	0.998512i	$-0.482635\pi$
$173$	−12.4162	−	12.4162i	−0.943986	−	0.943986i	−0.998512	+	0.0545259i	$0.982635\pi$
$174$	−1.60303			−0.121525
$175$		0			0
$176$	2.01606			0.151966
$177$	9.06404	+	9.06404i	0.681295	+	0.681295i
$178$	1.69827	+	1.69827i	0.127290	+	0.127290i
$179$		−	21.3788i		−	1.59792i	−0.601382	−	0.798961i	$-0.705383\pi$
$179$		−	21.3788i		−	1.59792i	0.601382	−	0.798961i	$-0.294617\pi$
$180$	0.569907	+	2.16222i	0.0424784	+	0.161163i
$181$		−	17.6702i		−	1.31341i	−0.754146	−	0.656707i	$-0.771949\pi$
$181$		−	17.6702i		−	1.31341i	0.754146	−	0.656707i	$-0.228051\pi$
$182$		0			0
$183$	6.36637	−	6.36637i	0.470616	−	0.470616i
$184$			6.57632i			0.484813i
$185$	5.78739	−	9.93014i	0.425498	−	0.730078i
$186$	−6.25097			−0.458343
$187$	−6.85664	+	6.85664i	−0.501407	+	0.501407i
$188$	−1.07805	−	1.07805i	−0.0786251	−	0.0786251i
$189$		0			0
$190$	7.57080	−	12.9901i	0.549244	−	0.942404i
$191$	−3.33512			−0.241321			−0.120660	−	0.992694i	$-0.538501\pi$
$191$	−3.33512			−0.241321			−0.120660	+	0.992694i	$0.538501\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−14.8727	+	14.8727i	−1.07056	+	1.07056i	−0.0732463	+	0.997314i	$0.523336\pi$
$193$	−14.8727	+	14.8727i	−1.07056	+	1.07056i	−0.997314	+	0.0732463i	$0.976664\pi$
$194$	18.6436			1.33854
$195$	10.5192	−	2.77260i	0.753296	−	0.198550i
$196$		0			0
$197$	6.84201	+	6.84201i	0.487473	+	0.487473i	0.907508	−	0.420035i	$-0.137982\pi$
$197$	6.84201	+	6.84201i	0.487473	+	0.487473i	−0.420035	+	0.907508i	$0.637982\pi$
$198$	1.42557	−	1.42557i	0.101311	−	0.101311i
$199$	−17.8747			−1.26710			−0.633551	−	0.773701i	$-0.718403\pi$
$199$	−17.8747			−1.26710			−0.633551	+	0.773701i	$0.718403\pi$
$200$	1.33352	−	4.81889i	0.0942940	−	0.340747i
$201$		−	1.68307i		−	0.118715i
$202$	−9.83263	+	9.83263i	−0.691821	+	0.691821i
$203$		0			0
$204$			4.80977i			0.336751i
$205$	10.6895	−	2.81749i	0.746588	−	0.196782i
$206$		−	2.38653i		−	0.166278i
$207$	4.65016	+	4.65016i	0.323208	+	0.323208i
$208$	−3.44007	−	3.44007i	−0.238526	−	0.238526i
$209$	−13.5560			−0.937685
$210$		0			0
$211$	8.70108			0.599007			0.299504	−	0.954095i	$-0.403179\pi$
$211$	8.70108			0.599007			0.299504	+	0.954095i	$0.403179\pi$
$212$	1.42923	+	1.42923i	0.0981602	+	0.0981602i
$213$	−2.46800	−	2.46800i	−0.169104	−	0.169104i
$214$			11.3578i			0.776400i
$215$	12.7903	+	7.45432i	0.872290	+	0.508380i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	−11.1865	+	11.1865i	−0.757647	+	0.757647i
$219$			8.44633i			0.570750i
$220$	−4.35916	+	1.14896i	−0.293895	+	0.0774632i
$221$	23.3995			1.57402
$222$	−3.63458	+	3.63458i	−0.243937	+	0.243937i
$223$	−17.0152	−	17.0152i	−1.13942	−	1.13942i	−0.988554	−	0.150867i	$-0.951793\pi$
$223$	−17.0152	−	17.0152i	−1.13942	−	1.13942i	−0.150867	−	0.988554i	$-0.548207\pi$
$224$		0			0
$225$	−2.46453	−	4.35041i	−0.164302	−	0.290027i
$226$	−15.4700			−1.02905
$227$	5.71327	−	5.71327i	0.379203	−	0.379203i	−0.491611	−	0.870815i	$-0.663592\pi$
$227$	5.71327	−	5.71327i	0.379203	−	0.379203i	0.870815	+	0.491611i	$0.163592\pi$
$228$	−4.75459	+	4.75459i	−0.314880	+	0.314880i
$229$	−6.23842			−0.412246			−0.206123	−	0.978526i	$-0.566085\pi$
$229$	−6.23842			−0.412246			−0.206123	+	0.978526i	$0.566085\pi$
$230$	−3.74789	−	14.2195i	−0.247129	−	0.937604i
$231$		0			0
$232$	−1.13351	−	1.13351i	−0.0744187	−	0.0744187i
$233$	−6.88051	+	6.88051i	−0.450757	+	0.450757i	−0.895606	−	0.444849i	$-0.853257\pi$
$233$	−6.88051	+	6.88051i	−0.450757	+	0.450757i	0.444849	+	0.895606i	$0.353257\pi$
$234$	−4.86500			−0.318035
$235$	2.94538	+	1.71660i	0.192135	+	0.111979i
$236$			12.8185i			0.834413i
$237$	9.88997	−	9.88997i	0.642423	−	0.642423i
$238$		0			0
$239$		−	10.6330i		−	0.687792i	−0.939008	−	0.343896i	$-0.888253\pi$
$239$		−	10.6330i		−	0.687792i	0.939008	−	0.343896i	$-0.111747\pi$
$240$	−1.12594	+	1.93191i	−0.0726789	+	0.124704i
$241$		−	8.44540i		−	0.544016i	−0.962295	−	0.272008i	$-0.912312\pi$
$241$		−	8.44540i		−	0.544016i	0.962295	−	0.272008i	$-0.0876878\pi$
$242$	−4.90415	−	4.90415i	−0.315251	−	0.315251i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	9.00341			0.576384
$245$		0			0
$246$	−4.94376			−0.315203
$247$	23.1311	+	23.1311i	1.47179	+	1.47179i
$248$	−4.42010	−	4.42010i	−0.280677	−	0.280677i
$249$		−	12.1573i		−	0.770438i
$250$	−0.137040	+	11.1795i	−0.00866720	+	0.707054i
$251$		−	11.8182i		−	0.745957i	−0.927840	−	0.372979i	$-0.878337\pi$
$251$		−	11.8182i		−	0.745957i	0.927840	−	0.372979i	$-0.121663\pi$
$252$		0			0
$253$	−9.37498	+	9.37498i	−0.589400	+	0.589400i
$254$		−	0.790851i		−	0.0496224i
$255$	−2.74112	−	10.3998i	−0.171656	−	0.651260i
$256$	1.00000			0.0625000
$257$	−10.7015	+	10.7015i	−0.667540	+	0.667540i	−0.957146	−	0.289606i	$-0.906476\pi$
$257$	−10.7015	+	10.7015i	−0.667540	+	0.667540i	0.289606	+	0.957146i	$0.406476\pi$
$258$	−4.68143	−	4.68143i	−0.291453	−	0.291453i
$259$		0			0
$260$	9.39873	+	5.47768i	0.582884	+	0.339711i
$261$	−1.60303			−0.0992249
$262$	11.1673	−	11.1673i	0.689920	−	0.689920i
$263$	12.5956	−	12.5956i	0.776679	−	0.776679i	−0.202586	−	0.979265i	$-0.564934\pi$
$263$	12.5956	−	12.5956i	0.776679	−	0.776679i	0.979265	+	0.202586i	$0.0649345\pi$
$264$	2.01606			0.124080
$265$	−3.90485	−	2.27579i	−0.239873	−	0.139801i
$266$		0			0
$267$	1.69827	+	1.69827i	0.103932	+	0.103932i
$268$	1.19011	−	1.19011i	0.0726976	−	0.0726976i
$269$	18.8098			1.14685			0.573426	−	0.819257i	$-0.305614\pi$
$269$	18.8098			1.14685			0.573426	+	0.819257i	$0.305614\pi$
$270$	0.569907	+	2.16222i	0.0346834	+	0.131589i
$271$		−	5.82286i		−	0.353713i	−0.984237	−	0.176857i	$-0.943407\pi$
$271$		−	5.82286i		−	0.353713i	0.984237	−	0.176857i	$-0.0565929\pi$
$272$	−3.40102	+	3.40102i	−0.206217	+	0.206217i
$273$		0			0
$274$		−	14.1300i		−	0.853625i
$275$	8.77067	−	4.96863i	0.528891	−	0.299620i
$276$			6.57632i			0.395848i
$277$	5.08820	+	5.08820i	0.305720	+	0.305720i	0.843247	−	0.537527i	$-0.180641\pi$
$277$	5.08820	+	5.08820i	0.305720	+	0.305720i	−0.537527	+	0.843247i	$0.680641\pi$
$278$	−2.87410	−	2.87410i	−0.172377	−	0.172377i
$279$	−6.25097			−0.374236
$280$		0			0
$281$	22.5943			1.34786			0.673930	−	0.738795i	$-0.264605\pi$
$281$	22.5943			1.34786			0.673930	+	0.738795i	$0.264605\pi$
$282$	−1.07805	−	1.07805i	−0.0641971	−	0.0641971i
$283$	−5.22535	−	5.22535i	−0.310615	−	0.310615i	0.534533	−	0.845148i	$-0.320488\pi$
$283$	−5.22535	−	5.22535i	−0.310615	−	0.310615i	−0.845148	+	0.534533i	$0.820488\pi$
$284$		−	3.49027i		−	0.207110i
$285$	7.57080	−	12.9901i	0.448455	−	0.769470i
$286$		−	9.80811i		−	0.579966i
$287$		0			0
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$		−	6.13386i		−	0.360815i
$290$	3.09690	+	1.80491i	0.181856	+	0.105988i
$291$	18.6436			1.09291
$292$	−5.97245	+	5.97245i	−0.349511	+	0.349511i
$293$	−16.8432	−	16.8432i	−0.983990	−	0.983990i	0.0158834	−	0.999874i	$-0.494944\pi$
$293$	−16.8432	−	16.8432i	−0.983990	−	0.983990i	−0.999874	+	0.0158834i	$0.994944\pi$
$294$		0			0
$295$	−7.30535	−	27.7164i	−0.425334	−	1.61371i
$296$	−5.14007			−0.298760
$297$	1.42557	−	1.42557i	0.0827198	−	0.0827198i
$298$	7.40648	−	7.40648i	0.429046	−	0.429046i
$299$	31.9938			1.85025
$300$	1.33352	−	4.81889i	0.0769907	−	0.278219i
$301$		0			0
$302$	−7.44233	−	7.44233i	−0.428258	−	0.428258i
$303$	−9.83263	+	9.83263i	−0.564870	+	0.564870i
$304$	−6.72400			−0.385648
$305$	−19.4674	+	5.13111i	−1.11470	+	0.293806i
$306$			4.80977i			0.274956i
$307$	−20.0279	+	20.0279i	−1.14305	+	1.14305i	−0.155164	+	0.987889i	$0.549591\pi$
$307$	−20.0279	+	20.0279i	−1.14305	+	1.14305i	−0.987889	+	0.155164i	$0.950409\pi$
$308$		0			0
$309$		−	2.38653i		−	0.135765i
$310$	12.0763	+	7.03819i	0.685887	+	0.399743i
$311$			22.8400i			1.29514i	0.762007	+	0.647568i	$0.224214\pi$
$311$			22.8400i			1.29514i	−0.762007	+	0.647568i	$0.775786\pi$
$312$	−3.44007	−	3.44007i	−0.194756	−	0.194756i
$313$	15.2546	+	15.2546i	0.862244	+	0.862244i	0.991598	−	0.129355i	$-0.0412906\pi$
$313$	15.2546	+	15.2546i	0.862244	+	0.862244i	−0.129355	+	0.991598i	$0.541291\pi$
$314$	−7.79373			−0.439826
$315$		0			0
$316$	13.9865			0.786804
$317$	−16.9641	−	16.9641i	−0.952798	−	0.952798i	0.0461374	−	0.998935i	$-0.485309\pi$
$317$	−16.9641	−	16.9641i	−0.952798	−	0.952798i	−0.998935	+	0.0461374i	$0.985309\pi$
$318$	1.42923	+	1.42923i	0.0801475	+	0.0801475i
$319$		−	3.23179i		−	0.180946i
$320$	−2.16222	+	0.569907i	−0.120872	+	0.0318588i
$321$			11.3578i			0.633928i
$322$		0			0
$323$	22.8685	−	22.8685i	1.27243	−	1.27243i
$324$		−	1.00000i		−	0.0555556i
$325$	−23.4439	−	6.48756i	−1.30043	−	0.359865i
$326$	−4.50093			−0.249283
$327$	−11.1865	+	11.1865i	−0.618617	+	0.618617i
$328$	−3.49577	−	3.49577i	−0.193022	−	0.193022i
$329$		0			0
$330$	−4.35916	+	1.14896i	−0.239964	+	0.0632484i
$331$	−21.9108			−1.20432			−0.602162	−	0.798374i	$-0.705694\pi$
$331$	−21.9108			−1.20432			−0.602162	+	0.798374i	$0.705694\pi$
$332$	8.59652	−	8.59652i	0.471795	−	0.471795i
$333$	−3.63458	+	3.63458i	−0.199174	+	0.199174i
$334$	−4.34013			−0.237482
$335$	−1.89503	+	3.25154i	−0.103537	+	0.177651i
$336$		0			0
$337$	21.6311	+	21.6311i	1.17832	+	1.17832i	0.980172	+	0.198147i	$0.0634922\pi$
$337$	21.6311	+	21.6311i	1.17832	+	1.17832i	0.198147	+	0.980172i	$0.436508\pi$
$338$	−7.54357	+	7.54357i	−0.410316	+	0.410316i
$339$	−15.4700			−0.840216
$340$	5.41549	−	9.29202i	0.293696	−	0.503931i
$341$		−	12.6023i		−	0.682453i
$342$	−4.75459	+	4.75459i	−0.257099	+	0.257099i
$343$		0			0
$344$		−	6.62055i		−	0.356956i
$345$	−3.74789	−	14.2195i	−0.201780	−	0.765550i
$346$		−	17.5592i		−	0.943986i
$347$	18.8604	+	18.8604i	1.01248	+	1.01248i	0.999921	+	0.0125582i	$0.00399750\pi$
$347$	18.8604	+	18.8604i	1.01248	+	1.01248i	0.0125582	+	0.999921i	$0.496003\pi$
$348$	−1.13351	−	1.13351i	−0.0607626	−	0.0607626i
$349$	17.0176			0.910933			0.455467	−	0.890253i	$-0.349472\pi$
$349$	17.0176			0.910933			0.455467	+	0.890253i	$0.349472\pi$
$350$		0			0
$351$	−4.86500			−0.259674
$352$	1.42557	+	1.42557i	0.0759830	+	0.0759830i
$353$	9.74603	+	9.74603i	0.518729	+	0.518729i	0.917187	−	0.398458i	$-0.130455\pi$
$353$	9.74603	+	9.74603i	0.518729	+	0.518729i	−0.398458	+	0.917187i	$0.630455\pi$
$354$			12.8185i			0.681295i
$355$	1.98913	+	7.54675i	0.105572	+	0.400540i
$356$			2.40171i			0.127290i
$357$		0			0
$358$	15.1171	−	15.1171i	0.798961	−	0.798961i
$359$			1.60107i			0.0845013i	0.999107	+	0.0422507i	$0.0134528\pi$
$359$			1.60107i			0.0845013i	−0.999107	+	0.0422507i	$0.986547\pi$
$360$	−1.12594	+	1.93191i	−0.0593421	+	0.101820i
$361$	26.2122			1.37959
$362$	12.4947	−	12.4947i	0.656707	−	0.656707i
$363$	−4.90415	−	4.90415i	−0.257401	−	0.257401i
$364$		0			0
$365$	9.51003	−	16.3175i	0.497778	−	0.854098i
$366$	9.00341			0.470616
$367$	17.6900	−	17.6900i	0.923411	−	0.923411i	−0.0738577	−	0.997269i	$-0.523531\pi$
$367$	17.6900	−	17.6900i	0.923411	−	0.923411i	0.997269	+	0.0738577i	$0.0235310\pi$
$368$	−4.65016	+	4.65016i	−0.242406	+	0.242406i
$369$	−4.94376			−0.257362
$370$	11.1140	−	2.92936i	0.577788	−	0.152290i
$371$		0			0
$372$	−4.42010	−	4.42010i	−0.229172	−	0.229172i
$373$	−19.8270	+	19.8270i	−1.02660	+	1.02660i	−0.0269674	+	0.999636i	$0.508585\pi$
$373$	−19.8270	+	19.8270i	−1.02660	+	1.02660i	−0.999636	+	0.0269674i	$0.991415\pi$
$374$	−9.69676			−0.501407
$375$	−0.137040	+	11.1795i	−0.00707674	+	0.577307i
$376$		−	1.52460i		−	0.0786251i
$377$	−5.51453	+	5.51453i	−0.284013	+	0.284013i
$378$		0			0
$379$			3.69997i			0.190055i	0.995475	+	0.0950275i	$0.0302939\pi$
$379$			3.69997i			0.190055i	−0.995475	+	0.0950275i	$0.969706\pi$
$380$	14.5388	−	3.83206i	0.745824	−	0.196580i
$381$		−	0.790851i		−	0.0405165i
$382$	−2.35828	−	2.35828i	−0.120660	−	0.120660i
$383$	−9.22741	−	9.22741i	−0.471499	−	0.471499i	0.430901	−	0.902399i	$-0.358196\pi$
$383$	−9.22741	−	9.22741i	−0.471499	−	0.471499i	−0.902399	+	0.430901i	$0.858196\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−21.0332			−1.07056
$387$	−4.68143	−	4.68143i	−0.237971	−	0.237971i
$388$	13.1830	+	13.1830i	0.669268	+	0.669268i
$389$		−	13.5526i		−	0.687147i	−0.939126	−	0.343573i	$-0.888363\pi$
$389$		−	13.5526i		−	0.687147i	0.939126	−	0.343573i	$-0.111637\pi$
$390$	9.39873	+	5.47768i	0.475923	+	0.277373i
$391$		−	31.6306i		−	1.59963i
$392$		0			0
$393$	11.1673	−	11.1673i	0.563318	−	0.563318i
$394$			9.67606i			0.487473i
$395$	−30.2420	+	7.97102i	−1.52164	+	0.401066i
$396$	2.01606			0.101311
$397$	1.18143	−	1.18143i	0.0592943	−	0.0592943i	−0.676838	−	0.736132i	$-0.736650\pi$
$397$	1.18143	−	1.18143i	0.0592943	−	0.0592943i	0.736132	+	0.676838i	$0.236650\pi$
$398$	−12.6393	−	12.6393i	−0.633551	−	0.633551i
$399$		0			0
$400$	4.35041	−	2.46453i	0.217521	−	0.123227i
$401$	5.26427			0.262885			0.131443	−	0.991324i	$-0.458039\pi$
$401$	5.26427			0.262885			0.131443	+	0.991324i	$0.458039\pi$
$402$	1.19011	−	1.19011i	0.0593574	−	0.0593574i
$403$	−21.5038	+	21.5038i	−1.07118	+	1.07118i
$404$	−13.9054			−0.691821
$405$	0.569907	+	2.16222i	0.0283189	+	0.107442i
$406$		0			0
$407$	−7.32751	−	7.32751i	−0.363211	−	0.363211i
$408$	−3.40102	+	3.40102i	−0.168376	+	0.168376i
$409$	30.8758			1.52671			0.763355	−	0.645979i	$-0.223551\pi$
$409$	30.8758			1.52671			0.763355	+	0.645979i	$0.223551\pi$
$410$	9.55089	+	5.56636i	0.471685	+	0.274903i
$411$		−	14.1300i		−	0.696982i
$412$	1.68753	−	1.68753i	0.0831388	−	0.0831388i
$413$		0			0
$414$			6.57632i			0.323208i
$415$	−13.6884	+	23.4868i	−0.671935	+	1.15292i
$416$		−	4.86500i		−	0.238526i
$417$	−2.87410	−	2.87410i	−0.140745	−	0.140745i
$418$	−9.58551	−	9.58551i	−0.468843	−	0.468843i
$419$	−27.7914			−1.35770			−0.678850	−	0.734277i	$-0.737521\pi$
$419$	−27.7914			−1.35770			−0.678850	+	0.734277i	$0.737521\pi$
$420$		0			0
$421$	−38.3633			−1.86971			−0.934855	−	0.355029i	$-0.884471\pi$
$421$	−38.3633			−1.86971			−0.934855	+	0.355029i	$0.884471\pi$
$422$	6.15259	+	6.15259i	0.299504	+	0.299504i
$423$	−1.07805	−	1.07805i	−0.0524167	−	0.0524167i
$424$			2.02124i			0.0981602i
$425$	−6.41391	+	23.1778i	−0.311120	+	1.12429i
$426$		−	3.49027i		−	0.169104i
$427$		0			0
$428$	−8.03115	+	8.03115i	−0.388200	+	0.388200i
$429$		−	9.80811i		−	0.473540i
$430$	3.77310	+	14.3151i	0.181955	+	0.690335i
$431$	−28.2654			−1.36150			−0.680748	−	0.732518i	$-0.738345\pi$
$431$	−28.2654			−1.36150			−0.680748	+	0.732518i	$0.738345\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	20.1385	+	20.1385i	0.967796	+	0.967796i	0.999497	−	0.0317009i	$-0.0100924\pi$
$433$	20.1385	+	20.1385i	0.967796	+	0.967796i	−0.0317009	+	0.999497i	$0.510092\pi$
$434$		0			0
$435$	3.09690	+	1.80491i	0.148485	+	0.0865387i
$436$	−15.8201			−0.757647
$437$	31.2677	−	31.2677i	1.49574	−	1.49574i
$438$	−5.97245	+	5.97245i	−0.285375	+	0.285375i
$439$	4.59353			0.219237			0.109619	−	0.993974i	$-0.465037\pi$
$439$	4.59353			0.219237			0.109619	+	0.993974i	$0.465037\pi$
$440$	−3.89483	−	2.26995i	−0.185679	−	0.108216i
$441$		0			0
$442$	16.5460	+	16.5460i	0.787011	+	0.787011i
$443$	−26.3918	+	26.3918i	−1.25391	+	1.25391i	−0.299957	+	0.953953i	$0.596972\pi$
$443$	−26.3918	+	26.3918i	−1.25391	+	1.25391i	−0.953953	+	0.299957i	$0.903028\pi$
$444$	−5.14007			−0.243937
$445$	−1.36875	−	5.19304i	−0.0648851	−	0.246173i
$446$		−	24.0631i		−	1.13942i
$447$	7.40648	−	7.40648i	0.350314	−	0.350314i
$448$		0			0
$449$		−	17.5778i		−	0.829549i	−0.909924	−	0.414775i	$-0.863860\pi$
$449$		−	17.5778i		−	0.829549i	0.909924	−	0.414775i	$-0.136140\pi$
$450$	1.33352	−	4.81889i	0.0628626	−	0.227165i
$451$		−	9.96690i		−	0.469323i
$452$	−10.9390	−	10.9390i	−0.514525	−	0.514525i
$453$	−7.44233	−	7.44233i	−0.349671	−	0.349671i
$454$	8.07979			0.379203
$455$		0			0
$456$	−6.72400			−0.314880
$457$	22.3868	+	22.3868i	1.04721	+	1.04721i	0.998829	+	0.0483833i	$0.0154069\pi$
$457$	22.3868	+	22.3868i	1.04721	+	1.04721i	0.0483833	+	0.998829i	$0.484593\pi$
$458$	−4.41123	−	4.41123i	−0.206123	−	0.206123i
$459$			4.80977i			0.224501i
$460$	7.40452	−	12.7048i	0.345238	−	0.592366i
$461$			7.25807i			0.338042i	0.985612	+	0.169021i	$0.0540606\pi$
$461$			7.25807i			0.338042i	−0.985612	+	0.169021i	$0.945939\pi$
$462$		0			0
$463$	−14.8885	+	14.8885i	−0.691926	+	0.691926i	−0.962655	−	0.270730i	$-0.912735\pi$
$463$	−14.8885	+	14.8885i	−0.691926	+	0.691926i	0.270730	+	0.962655i	$0.412735\pi$
$464$		−	1.60303i		−	0.0744187i
$465$	12.0763	+	7.03819i	0.560024	+	0.326388i
$466$	−9.73051			−0.450757
$467$	−7.66720	+	7.66720i	−0.354796	+	0.354796i	−0.861890	−	0.507095i	$-0.830719\pi$
$467$	−7.66720	+	7.66720i	−0.354796	+	0.354796i	0.507095	+	0.861890i	$0.330719\pi$
$468$	−3.44007	−	3.44007i	−0.159017	−	0.159017i
$469$		0			0
$470$	0.868879	+	3.29652i	0.0400784	+	0.152057i
$471$	−7.79373			−0.359116
$472$	−9.06404	+	9.06404i	−0.417206	+	0.417206i
$473$	9.43803	−	9.43803i	0.433961	−	0.433961i
$474$	13.9865			0.642423
$475$	−29.2522	+	16.5715i	−1.34218	+	0.760353i
$476$		0			0
$477$	1.42923	+	1.42923i	0.0654402	+	0.0654402i
$478$	7.51867	−	7.51867i	0.343896	−	0.343896i
$479$	−26.8377			−1.22625			−0.613123	−	0.789987i	$-0.710087\pi$
$479$	−26.8377			−1.22625			−0.613123	+	0.789987i	$0.710087\pi$
$480$	−2.16222	+	0.569907i	−0.0986915	+	0.0260126i
$481$			25.0064i			1.14020i
$482$	5.97180	−	5.97180i	0.272008	−	0.272008i
$483$		0			0
$484$		−	6.93552i		−	0.315251i
$485$	−36.0178	−	20.9916i	−1.63548	−	0.953178i
$486$		−	1.00000i		−	0.0453609i
$487$	−12.3064	−	12.3064i	−0.557658	−	0.557658i	0.370982	−	0.928640i	$-0.379021\pi$
$487$	−12.3064	−	12.3064i	−0.557658	−	0.557658i	−0.928640	+	0.370982i	$0.879021\pi$
$488$	6.36637	+	6.36637i	0.288192	+	0.288192i
$489$	−4.50093			−0.203539
$490$		0			0
$491$	−27.9347			−1.26067			−0.630337	−	0.776322i	$-0.717083\pi$
$491$	−27.9347			−1.26067			−0.630337	+	0.776322i	$0.717083\pi$
$492$	−3.49577	−	3.49577i	−0.157601	−	0.157601i
$493$	5.45192	+	5.45192i	0.245542	+	0.245542i
$494$			32.7123i			1.47179i
$495$	−4.35916	+	1.14896i	−0.195930	+	0.0516421i
$496$		−	6.25097i		−	0.280677i
$497$		0			0
$498$	8.59652	−	8.59652i	0.385219	−	0.385219i
$499$		−	29.2011i		−	1.30722i	−0.756831	−	0.653610i	$-0.773254\pi$
$499$		−	29.2011i		−	1.30722i	0.756831	−	0.653610i	$-0.226746\pi$
$500$	−8.00200	+	7.80820i	−0.357860	+	0.349193i
$501$	−4.34013			−0.193903
$502$	8.35672	−	8.35672i	0.372979	−	0.372979i
$503$	17.8373	+	17.8373i	0.795326	+	0.795326i	0.982354	−	0.187028i	$-0.0598857\pi$
$503$	17.8373	+	17.8373i	0.795326	+	0.795326i	−0.187028	+	0.982354i	$0.559886\pi$
$504$		0			0
$505$	30.0666	−	7.92481i	1.33795	−	0.352649i
$506$	−13.2582			−0.589400
$507$	−7.54357	+	7.54357i	−0.335022	+	0.335022i
$508$	0.559216	−	0.559216i	0.0248112	−	0.0248112i
$509$	21.1693			0.938312			0.469156	−	0.883115i	$-0.344558\pi$
$509$	21.1693			0.938312			0.469156	+	0.883115i	$0.344558\pi$
$510$	5.41549	−	9.29202i	0.239802	−	0.411458i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.75459	+	4.75459i	−0.209920	+	0.209920i
$514$	−15.1342			−0.667540
$515$	−2.68709	+	4.61056i	−0.118407	+	0.203166i
$516$		−	6.62055i		−	0.291453i
$517$	2.17341	−	2.17341i	0.0955867	−	0.0955867i
$518$		0			0
$519$		−	17.5592i		−	0.770762i
$520$	2.77260	+	10.5192i	0.121586	+	0.461298i
$521$			12.3957i			0.543066i	0.962429	+	0.271533i	$0.0875306\pi$
$521$			12.3957i			0.543066i	−0.962429	+	0.271533i	$0.912469\pi$
$522$	−1.13351	−	1.13351i	−0.0496124	−	0.0496124i
$523$	6.44681	+	6.44681i	0.281899	+	0.281899i	0.833866	−	0.551967i	$-0.186122\pi$
$523$	6.44681	+	6.44681i	0.281899	+	0.281899i	−0.551967	+	0.833866i	$0.686122\pi$
$524$	15.7930			0.689920
$525$		0			0
$526$	17.8129			0.776679
$527$	21.2597	+	21.2597i	0.926085	+	0.926085i
$528$	1.42557	+	1.42557i	0.0620398	+	0.0620398i
$529$		−	20.2480i		−	0.880346i
$530$	−1.15192	−	4.37038i	−0.0500362	−	0.189837i
$531$			12.8185i			0.556275i
$532$		0			0
$533$	−17.0069	+	17.0069i	−0.736651	+	0.736651i
$534$			2.40171i			0.103932i
$535$	12.7881	−	21.9421i	0.552879	−	0.948641i
$536$	1.68307			0.0726976
$537$	15.1171	−	15.1171i	0.652349	−	0.652349i
$538$	13.3005	+	13.3005i	0.573426	+	0.573426i
$539$		0			0
$540$	−1.12594	+	1.93191i	−0.0484526	+	0.0831361i
$541$	15.8888			0.683112			0.341556	−	0.939861i	$-0.389046\pi$
$541$	15.8888			0.683112			0.341556	+	0.939861i	$0.389046\pi$
$542$	4.11738	−	4.11738i	0.176857	−	0.176857i
$543$	12.4947	−	12.4947i	0.536199	−	0.536199i
$544$	−4.80977			−0.206217
$545$	34.2067	−	9.01601i	1.46525	−	0.386204i
$546$		0			0
$547$	−8.25721	−	8.25721i	−0.353053	−	0.353053i	0.508191	−	0.861244i	$-0.330314\pi$
$547$	−8.25721	−	8.25721i	−0.353053	−	0.353053i	−0.861244	+	0.508191i	$0.830314\pi$
$548$	9.99143	−	9.99143i	0.426813	−	0.426813i
$549$	9.00341			0.384256
$550$	9.71516	+	2.68845i	0.414256	+	0.114636i
$551$			10.7788i			0.459190i
$552$	−4.65016	+	4.65016i	−0.197924	+	0.197924i
$553$		0			0
$554$			7.19579i			0.305720i
$555$	11.1140	−	2.92936i	0.471762	−	0.124345i
$556$		−	4.06459i		−	0.172377i
$557$	20.3695	+	20.3695i	0.863082	+	0.863082i	0.991695	−	0.128613i	$-0.0410524\pi$
$557$	20.3695	+	20.3695i	0.863082	+	0.863082i	−0.128613	+	0.991695i	$0.541052\pi$
$558$	−4.42010	−	4.42010i	−0.187118	−	0.187118i
$559$	−32.2090			−1.36229
$560$		0			0
$561$	−9.69676			−0.409397
$562$	15.9766	+	15.9766i	0.673930	+	0.673930i
$563$	−13.6409	−	13.6409i	−0.574895	−	0.574895i	0.358598	−	0.933492i	$-0.383255\pi$
$563$	−13.6409	−	13.6409i	−0.574895	−	0.574895i	−0.933492	+	0.358598i	$0.883255\pi$
$564$		−	1.52460i		−	0.0641971i
$565$	29.8867	+	17.4183i	1.25734	+	0.732792i
$566$		−	7.38976i		−	0.310615i
$567$		0			0
$568$	2.46800	−	2.46800i	0.103555	−	0.103555i
$569$		−	23.8046i		−	0.997941i	−0.866619	−	0.498971i	$-0.833712\pi$
$569$		−	23.8046i		−	0.997941i	0.866619	−	0.498971i	$-0.166288\pi$
$570$	14.5388	−	3.83206i	0.608963	−	0.160507i
$571$	27.8052			1.16361			0.581805	−	0.813329i	$-0.302347\pi$
$571$	27.8052			1.16361			0.581805	+	0.813329i	$0.302347\pi$
$572$	6.93538	−	6.93538i	0.289983	−	0.289983i
$573$	−2.35828	−	2.35828i	−0.0985187	−	0.0985187i
$574$		0			0
$575$	−8.76964	+	31.6906i	−0.365719	+	1.32159i
$576$	1.00000			0.0416667
$577$	−23.1463	+	23.1463i	−0.963593	+	0.963593i	−0.999360	−	0.0357671i	$-0.988613\pi$
$577$	−23.1463	+	23.1463i	−0.963593	+	0.963593i	0.0357671	+	0.999360i	$0.488613\pi$
$578$	4.33729	−	4.33729i	0.180408	−	0.180408i
$579$	−21.0332			−0.874109
$580$	0.913577	+	3.46610i	0.0379342	+	0.143922i
$581$		0			0
$582$	13.1830	+	13.1830i	0.546455	+	0.546455i
$583$	−2.88142	+	2.88142i	−0.119336	+	0.119336i
$584$	−8.44633			−0.349511
$585$	9.39873	+	5.47768i	0.388590	+	0.226474i
$586$		−	23.8199i		−	0.983990i
$587$	10.2376	−	10.2376i	0.422551	−	0.422551i	−0.463530	−	0.886081i	$-0.653417\pi$
$587$	10.2376	−	10.2376i	0.422551	−	0.422551i	0.886081	+	0.463530i	$0.153417\pi$
$588$		0			0
$589$			42.0315i			1.73188i
$590$	14.4328	−	24.7641i	0.594189	−	1.01952i
$591$			9.67606i			0.398020i
$592$	−3.63458	−	3.63458i	−0.149380	−	0.149380i
$593$	−13.4975	−	13.4975i	−0.554278	−	0.554278i	0.373395	−	0.927673i	$-0.378194\pi$
$593$	−13.4975	−	13.4975i	−0.554278	−	0.554278i	−0.927673	+	0.373395i	$0.878194\pi$
$594$	2.01606			0.0827198
$595$		0			0
$596$	10.4743			0.429046
$597$	−12.6393	−	12.6393i	−0.517293	−	0.517293i
$598$	22.6230	+	22.6230i	0.925124	+	0.925124i
$599$		−	14.4212i		−	0.589233i	−0.955616	−	0.294616i	$-0.904808\pi$
$599$		−	14.4212i		−	0.589233i	0.955616	−	0.294616i	$-0.0951919\pi$
$600$	4.35041	−	2.46453i	0.177605	−	0.100614i
$601$		−	33.8262i		−	1.37980i	−0.723906	−	0.689899i	$-0.757655\pi$
$601$		−	33.8262i		−	1.37980i	0.723906	−	0.689899i	$-0.242345\pi$
$602$		0			0
$603$	1.19011	−	1.19011i	0.0484651	−	0.0484651i
$604$		−	10.5250i		−	0.428258i
$605$	3.95260	+	14.9961i	0.160696	+	0.609680i
$606$	−13.9054			−0.564870
$607$	−2.25227	+	2.25227i	−0.0914168	+	0.0914168i	−0.751336	−	0.659919i	$-0.770590\pi$
$607$	−2.25227	+	2.25227i	−0.0914168	+	0.0914168i	0.659919	+	0.751336i	$0.270590\pi$
$608$	−4.75459	−	4.75459i	−0.192824	−	0.192824i
$609$		0			0
$610$	−17.3938	−	10.1373i	−0.704252	−	0.410446i
$611$	−7.41716			−0.300066
$612$	−3.40102	+	3.40102i	−0.137478	+	0.137478i
$613$	12.7193	−	12.7193i	0.513726	−	0.513726i	−0.401940	−	0.915666i	$-0.631664\pi$
$613$	12.7193	−	12.7193i	0.513726	−	0.513726i	0.915666	+	0.401940i	$0.131664\pi$
$614$	−28.3237			−1.14305
$615$	9.55089	+	5.56636i	0.385129	+	0.224457i
$616$		0			0
$617$	1.92028	+	1.92028i	0.0773075	+	0.0773075i	0.744703	−	0.667396i	$-0.232591\pi$
$617$	1.92028	+	1.92028i	0.0773075	+	0.0773075i	−0.667396	+	0.744703i	$0.732591\pi$
$618$	1.68753	−	1.68753i	0.0678826	−	0.0678826i
$619$	−2.09236			−0.0840992			−0.0420496	−	0.999116i	$-0.513389\pi$
$619$	−2.09236			−0.0840992			−0.0420496	+	0.999116i	$0.513389\pi$
$620$	3.56247	+	13.5160i	0.143072	+	0.542815i
$621$			6.57632i			0.263899i
$622$	−16.1503	+	16.1503i	−0.647568	+	0.647568i
$623$		0			0
$624$		−	4.86500i		−	0.194756i
$625$	12.8522	−	21.4435i	0.514086	−	0.857738i
$626$			21.5733i			0.862244i
$627$	−9.58551	−	9.58551i	−0.382808	−	0.382808i
$628$	−5.51100	−	5.51100i	−0.219913	−	0.219913i
$629$	24.7225			0.985752
$630$		0			0
$631$	19.9051			0.792410			0.396205	−	0.918162i	$-0.370327\pi$
$631$	19.9051			0.792410			0.396205	+	0.918162i	$0.370327\pi$
$632$	9.88997	+	9.88997i	0.393402	+	0.393402i
$633$	6.15259	+	6.15259i	0.244544	+	0.244544i
$634$		−	23.9908i		−	0.952798i
$635$	−0.890448	+	1.52785i	−0.0353364	+	0.0606309i
$636$			2.02124i			0.0801475i
$637$		0			0
$638$	2.28522	−	2.28522i	0.0904728	−	0.0904728i
$639$		−	3.49027i		−	0.138073i
$640$	−1.93191	−	1.12594i	−0.0763653	−	0.0445066i
$641$	−17.5462			−0.693032			−0.346516	−	0.938044i	$-0.612635\pi$
$641$	−17.5462			−0.693032			−0.346516	+	0.938044i	$0.612635\pi$
$642$	−8.03115	+	8.03115i	−0.316964	+	0.316964i
$643$	24.0108	+	24.0108i	0.946895	+	0.946895i	0.998659	−	0.0517644i	$-0.0164845\pi$
$643$	24.0108	+	24.0108i	0.946895	+	0.946895i	−0.0517644	+	0.998659i	$0.516484\pi$
$644$		0			0
$645$	3.77310	+	14.3151i	0.148566	+	0.563656i
$646$	32.3409			1.27243
$647$	1.70120	−	1.70120i	0.0668810	−	0.0668810i	−0.672875	−	0.739756i	$-0.734941\pi$
$647$	1.70120	−	1.70120i	0.0668810	−	0.0668810i	0.739756	+	0.672875i	$0.234941\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−25.8428			−1.01442
$650$	−11.9899	−	21.1648i	−0.470284	−	0.830150i
$651$		0			0
$652$	−3.18264	−	3.18264i	−0.124642	−	0.124642i
$653$	22.7164	−	22.7164i	0.888962	−	0.888962i	−0.105462	−	0.994423i	$-0.533632\pi$
$653$	22.7164	−	22.7164i	0.888962	−	0.888962i	0.994423	+	0.105462i	$0.0336320\pi$
$654$	−15.8201			−0.618617
$655$	−34.1480	+	9.00054i	−1.33427	+	0.351680i
$656$		−	4.94376i		−	0.193022i
$657$	−5.97245	+	5.97245i	−0.233008	+	0.233008i
$658$		0			0
$659$		−	20.3970i		−	0.794552i	−0.917699	−	0.397276i	$-0.869955\pi$
$659$		−	20.3970i		−	0.794552i	0.917699	−	0.397276i	$-0.130045\pi$
$660$	−3.89483	−	2.26995i	−0.151606	−	0.0883577i
$661$		−	18.4521i		−	0.717702i	−0.933395	−	0.358851i	$-0.883169\pi$
$661$		−	18.4521i		−	0.717702i	0.933395	−	0.358851i	$-0.116831\pi$
$662$	−15.4933	−	15.4933i	−0.602162	−	0.602162i
$663$	16.5460	+	16.5460i	0.642592	+	0.642592i
$664$	12.1573			0.471795
$665$		0			0
$666$	−5.14007			−0.199174
$667$	7.45433	+	7.45433i	0.288633	+	0.288633i
$668$	−3.06894	−	3.06894i	−0.118741	−	0.118741i
$669$		−	24.0631i		−	0.930333i
$670$	−3.63918	+	0.959195i	−0.140594	+	0.0370569i
$671$			18.1514i			0.700726i
$672$		0			0
$673$	−31.5335	+	31.5335i	−1.21553	+	1.21553i	−0.246344	+	0.969182i	$0.579229\pi$
$673$	−31.5335	+	31.5335i	−1.21553	+	1.21553i	−0.969182	+	0.246344i	$0.920771\pi$
$674$			30.5909i			1.17832i
$675$	1.33352	−	4.81889i	0.0513271	−	0.185479i
$676$	−10.6682			−0.410316
$677$	−9.14781	+	9.14781i	−0.351579	+	0.351579i	−0.860697	−	0.509118i	$-0.829972\pi$
$677$	−9.14781	+	9.14781i	−0.351579	+	0.351579i	0.509118	+	0.860697i	$0.329972\pi$
$678$	−10.9390	−	10.9390i	−0.420108	−	0.420108i
$679$		0			0
$680$	10.3998	−	2.74112i	0.398814	−	0.105117i
$681$	8.07979			0.309618
$682$	8.91117	−	8.91117i	0.341226	−	0.341226i
$683$	−13.1956	+	13.1956i	−0.504916	+	0.504916i	−0.912962	−	0.408046i	$-0.866210\pi$
$683$	−13.1956	+	13.1956i	−0.504916	+	0.504916i	0.408046	+	0.912962i	$0.366210\pi$
$684$	−6.72400			−0.257099
$685$	−15.9095	+	27.2979i	−0.607871	+	1.04300i
$686$		0			0
$687$	−4.41123	−	4.41123i	−0.168299	−	0.168299i
$688$	4.68143	−	4.68143i	0.178478	−	0.178478i
$689$	9.83335			0.374621
$690$	7.40452	−	12.7048i	0.281885	−	0.483665i
$691$			41.3069i			1.57139i	0.618615	+	0.785694i	$0.287694\pi$
$691$			41.3069i			1.57139i	−0.618615	+	0.785694i	$0.712306\pi$
$692$	12.4162	−	12.4162i	0.471993	−	0.471993i
$693$		0			0
$694$			26.6726i			1.01248i
$695$	2.31644	+	8.78854i	0.0878675	+	0.333368i
$696$		−	1.60303i		−	0.0607626i
$697$	16.8138	+	16.8138i	0.636869	+	0.636869i
$698$	12.0333	+	12.0333i	0.455467	+	0.455467i
$699$	−9.73051			−0.368042
$700$		0			0
$701$	−38.7798			−1.46469			−0.732347	−	0.680931i	$-0.761575\pi$
$701$	−38.7798			−1.46469			−0.732347	+	0.680931i	$0.761575\pi$
$702$	−3.44007	−	3.44007i	−0.129837	−	0.129837i
$703$	24.4389	+	24.4389i	0.921731	+	0.921731i
$704$			2.01606i			0.0759830i
$705$	0.868879	+	3.29652i	0.0327239	+	0.124154i
$706$			13.7830i			0.518729i
$707$		0			0
$708$	−9.06404	+	9.06404i	−0.340647	+	0.340647i
$709$		−	38.8263i		−	1.45815i	−0.684432	−	0.729077i	$-0.739950\pi$
$709$		−	38.8263i		−	1.45815i	0.684432	−	0.729077i	$-0.260050\pi$
$710$	−3.92983	+	6.74289i	−0.147484	+	0.253056i
$711$	13.9865			0.524536
$712$	−1.69827	+	1.69827i	−0.0636452	+	0.0636452i
$713$	29.0680	+	29.0680i	1.08860	+	1.08860i
$714$		0			0
$715$	−11.0433	+	18.9484i	−0.412996	+	0.708629i
$716$	21.3788			0.798961
$717$	7.51867	−	7.51867i	0.280790	−	0.280790i
$718$	−1.13213	+	1.13213i	−0.0422507	+	0.0422507i
$719$	−35.2226			−1.31358			−0.656791	−	0.754073i	$-0.728087\pi$
$719$	−35.2226			−1.31358			−0.656791	+	0.754073i	$0.728087\pi$
$720$	−2.16222	+	0.569907i	−0.0805813	+	0.0212392i
$721$		0			0
$722$	18.5348	+	18.5348i	0.689794	+	0.689794i
$723$	5.97180	−	5.97180i	0.222094	−	0.222094i
$724$	17.6702			0.656707
$725$	−3.95071	−	6.97383i	−0.146726	−	0.259001i
$726$		−	6.93552i		−	0.257401i
$727$	−5.41810	+	5.41810i	−0.200946	+	0.200946i	−0.800405	−	0.599459i	$-0.795382\pi$
$727$	−5.41810	+	5.41810i	−0.200946	+	0.200946i	0.599459	+	0.800405i	$0.295382\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	18.2628	−	4.81362i	0.675938	−	0.178160i
$731$			31.8433i			1.17777i
$732$	6.36637	+	6.36637i	0.235308	+	0.235308i
$733$	−21.5955	−	21.5955i	−0.797647	−	0.797647i	0.185077	−	0.982724i	$-0.440747\pi$
$733$	−21.5955	−	21.5955i	−0.797647	−	0.797647i	−0.982724	+	0.185077i	$0.940747\pi$
$734$	25.0175			0.923411
$735$		0			0
$736$	−6.57632			−0.242406
$737$	2.39933	+	2.39933i	0.0883805	+	0.0883805i
$738$	−3.49577	−	3.49577i	−0.128681	−	0.128681i
$739$		−	25.0262i		−	0.920603i	−0.887763	−	0.460302i	$-0.847741\pi$
$739$		−	25.0262i		−	0.920603i	0.887763	−	0.460302i	$-0.152259\pi$
$740$	9.93014	+	5.78739i	0.365039	+	0.212749i
$741$			32.7123i			1.20171i
$742$		0			0
$743$	12.3224	−	12.3224i	0.452064	−	0.452064i	−0.443975	−	0.896039i	$-0.646432\pi$
$743$	12.3224	−	12.3224i	0.452064	−	0.452064i	0.896039	+	0.443975i	$0.146432\pi$
$744$		−	6.25097i		−	0.229172i
$745$	−22.6479	+	5.96940i	−0.829753	+	0.218702i
$746$	−28.0396			−1.02660
$747$	8.59652	−	8.59652i	0.314530	−	0.314530i
$748$	−6.85664	−	6.85664i	−0.250704	−	0.250704i
$749$		0			0
$750$	−8.00200	+	7.80820i	−0.292192	+	0.285115i
$751$	−51.8620			−1.89247			−0.946235	−	0.323479i	$-0.895147\pi$
$751$	−51.8620			−1.89247			−0.946235	+	0.323479i	$0.895147\pi$
$752$	1.07805	−	1.07805i	0.0393125	−	0.0393125i
$753$	8.35672	−	8.35672i	0.304536	−	0.304536i
$754$	−7.79873			−0.284013
$755$	5.99830	+	22.7575i	0.218301	+	0.828230i
$756$		0			0
$757$	−15.0109	−	15.0109i	−0.545581	−	0.545581i	0.379578	−	0.925160i	$-0.376069\pi$
$757$	−15.0109	−	15.0109i	−0.545581	−	0.545581i	−0.925160	+	0.379578i	$0.876069\pi$
$758$	−2.61628	+	2.61628i	−0.0950275	+	0.0950275i
$759$	−13.2582			−0.481243
$760$	12.9901	+	7.57080i	0.471202	+	0.274622i
$761$			31.8137i			1.15325i	0.817010	+	0.576623i	$0.195630\pi$
$761$			31.8137i			1.15325i	−0.817010	+	0.576623i	$0.804370\pi$
$762$	0.559216	−	0.559216i	0.0202583	−	0.0202583i
$763$		0			0
$764$		−	3.33512i		−	0.120660i
$765$	5.41549	−	9.29202i	0.195798	−	0.335954i
$766$		−	13.0495i		−	0.471499i
$767$	44.0966	+	44.0966i	1.59223	+	1.59223i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	40.6705			1.46662			0.733308	−	0.679896i	$-0.237975\pi$
$769$	40.6705			1.46662			0.733308	+	0.679896i	$0.237975\pi$
$770$		0			0
$771$	−15.1342			−0.545044
$772$	−14.8727	−	14.8727i	−0.535280	−	0.535280i
$773$	−25.2031	−	25.2031i	−0.906493	−	0.906493i	0.0894947	−	0.995987i	$-0.471475\pi$
$773$	−25.2031	−	25.2031i	−0.906493	−	0.906493i	−0.995987	+	0.0894947i	$0.971475\pi$
$774$		−	6.62055i		−	0.237971i
$775$	−15.4057	−	27.1943i	−0.553389	−	0.976847i
$776$			18.6436i			0.669268i
$777$		0			0
$778$	9.58317	−	9.58317i	0.343573	−	0.343573i
$779$			33.2419i			1.19101i
$780$	2.77260	+	10.5192i	0.0992749	+	0.376648i
$781$	7.03659			0.251789
$782$	22.3662	−	22.3662i	0.799813	−	0.799813i
$783$	−1.13351	−	1.13351i	−0.0405084	−	0.0405084i
$784$		0			0
$785$	15.0568	+	8.77525i	0.537399	+	0.313202i
$786$	15.7930			0.563318
$787$	−5.04970	+	5.04970i	−0.180003	+	0.180003i	−0.791357	−	0.611354i	$-0.790625\pi$
$787$	−5.04970	+	5.04970i	−0.180003	+	0.180003i	0.611354	+	0.791357i	$0.290625\pi$
$788$	−6.84201	+	6.84201i	−0.243736	+	0.243736i
$789$	17.8129			0.634156
$790$	−27.0207	−	15.7479i	−0.961353	−	0.560287i
$791$		0			0
$792$	1.42557	+	1.42557i	0.0506553	+	0.0506553i
$793$	30.9724	−	30.9724i	1.09986	−	1.09986i
$794$	1.67080			0.0592943
$795$	−1.15192	−	4.37038i	−0.0408544	−	0.155001i
$796$		−	17.8747i		−	0.633551i
$797$	−6.34127	+	6.34127i	−0.224619	+	0.224619i	−0.810440	−	0.585821i	$-0.800772\pi$
$797$	−6.34127	+	6.34127i	−0.224619	+	0.224619i	0.585821	+	0.810440i	$0.300772\pi$
$798$		0			0
$799$			7.33295i			0.259421i
$800$	4.81889	+	1.33352i	0.170374	+	0.0471470i
$801$			2.40171i			0.0848603i
$802$	3.72240	+	3.72240i	0.131443	+	0.131443i
$803$	−12.0408	−	12.0408i	−0.424911	−	0.424911i
$804$	1.68307			0.0593574
$805$		0			0
$806$	−30.4110			−1.07118
$807$	13.3005	+	13.3005i	0.468201	+	0.468201i
$808$	−9.83263	−	9.83263i	−0.345911	−	0.345911i
$809$			35.0348i			1.23176i	0.787840	+	0.615880i	$0.211199\pi$
$809$			35.0348i			1.23176i	−0.787840	+	0.615880i	$0.788801\pi$
$810$	−1.12594	+	1.93191i	−0.0395614	+	0.0678803i
$811$			11.8588i			0.416417i	0.978084	+	0.208209i	$0.0667633\pi$
$811$			11.8588i			0.416417i	−0.978084	+	0.208209i	$0.933237\pi$
$812$		0			0
$813$	4.11738	−	4.11738i	0.144403	−	0.144403i
$814$		−	10.3627i		−	0.363211i
$815$	8.69538	+	5.06776i	0.304586	+	0.177516i
$816$	−4.80977			−0.168376
$817$	−31.4780	+	31.4780i	−1.10127	+	1.10127i
$818$	21.8325	+	21.8325i	0.763355	+	0.763355i
$819$		0			0
$820$	2.81749	+	10.6895i	0.0983909	+	0.373294i
$821$	40.9820			1.43028			0.715141	−	0.698980i	$-0.246362\pi$
$821$	40.9820			1.43028			0.715141	+	0.698980i	$0.246362\pi$
$822$	9.99143	−	9.99143i	0.348491	−	0.348491i
$823$	4.17227	−	4.17227i	0.145436	−	0.145436i	−0.630640	−	0.776076i	$-0.717207\pi$
$823$	4.17227	−	4.17227i	0.145436	−	0.145436i	0.776076	+	0.630640i	$0.217207\pi$
$824$	2.38653			0.0831388
$825$	9.71516	+	2.68845i	0.338238	+	0.0935997i
$826$		0			0
$827$	23.5494	+	23.5494i	0.818893	+	0.818893i	0.985948	−	0.167054i	$-0.0534255\pi$
$827$	23.5494	+	23.5494i	0.818893	+	0.818893i	−0.167054	+	0.985948i	$0.553426\pi$
$828$	−4.65016	+	4.65016i	−0.161604	+	0.161604i
$829$	38.6065			1.34086			0.670430	−	0.741973i	$-0.266110\pi$
$829$	38.6065			1.34086			0.670430	+	0.741973i	$0.266110\pi$
$830$	−26.2868	+	6.92854i	−0.912428	+	0.240493i
$831$			7.19579i			0.249619i
$832$	3.44007	−	3.44007i	0.119263	−	0.119263i
$833$		0			0
$834$		−	4.06459i		−	0.140745i
$835$	8.38474	+	4.88672i	0.290166	+	0.169112i
$836$		−	13.5560i		−	0.468843i
$837$	−4.42010	−	4.42010i	−0.152781	−	0.152781i
$838$	−19.6515	−	19.6515i	−0.678850	−	0.678850i
$839$	30.3854			1.04902			0.524510	−	0.851404i	$-0.324248\pi$
$839$	30.3854			1.04902			0.524510	+	0.851404i	$0.324248\pi$
$840$		0			0
$841$	26.4303			0.911390
$842$	−27.1269	−	27.1269i	−0.934855	−	0.934855i
$843$	15.9766	+	15.9766i	0.550262	+	0.550262i
$844$			8.70108i			0.299504i
$845$	23.0671	−	6.07990i	0.793531	−	0.209155i
$846$		−	1.52460i		−	0.0524167i
$847$		0			0
$848$	−1.42923	+	1.42923i	−0.0490801	+	0.0490801i
$849$		−	7.38976i		−	0.253616i
$850$	−20.9245	+	11.8538i	−0.717703	+	0.406583i
$851$	33.8027			1.15874
$852$	2.46800	−	2.46800i	0.0845522	−	0.0845522i
$853$	16.1195	+	16.1195i	0.551920	+	0.551920i	0.926995	−	0.375074i	$-0.122383\pi$
$853$	16.1195	+	16.1195i	0.551920	+	0.551920i	−0.375074	+	0.926995i	$0.622383\pi$
$854$		0			0
$855$	14.5388	−	3.83206i	0.497216	−	0.131054i
$856$	−11.3578			−0.388200
$857$	−30.9961	+	30.9961i	−1.05881	+	1.05881i	−0.0606487	+	0.998159i	$0.519317\pi$
$857$	−30.9961	+	30.9961i	−1.05881	+	1.05881i	−0.998159	+	0.0606487i	$0.980683\pi$
$858$	6.93538	−	6.93538i	0.236770	−	0.236770i
$859$	21.2260			0.724221			0.362110	−	0.932135i	$-0.382056\pi$
$859$	21.2260			0.724221			0.362110	+	0.932135i	$0.382056\pi$
$860$	−7.45432	+	12.7903i	−0.254190	+	0.436145i
$861$		0			0
$862$	−19.9866	−	19.9866i	−0.680748	−	0.680748i
$863$	−9.89635	+	9.89635i	−0.336876	+	0.336876i	−0.855190	−	0.518315i	$-0.826560\pi$
$863$	−9.89635	+	9.89635i	−0.336876	+	0.336876i	0.518315	+	0.855190i	$0.326560\pi$
$864$	1.00000			0.0340207
$865$	−19.7705	+	33.9227i	−0.672217	+	1.15341i
$866$			28.4802i			0.967796i
$867$	4.33729	−	4.33729i	0.147302	−	0.147302i
$868$		0			0
$869$			28.1976i			0.956539i
$870$	0.913577	+	3.46610i	0.0309732	+	0.117512i
$871$		−	8.18814i		−	0.277445i
$872$	−11.1865	−	11.1865i	−0.378824	−	0.378824i
$873$	13.1830	+	13.1830i	0.446178	+	0.446178i
$874$	44.2192			1.49574
$875$		0			0
$876$	−8.44633			−0.285375
$877$	−18.4262	−	18.4262i	−0.622208	−	0.622208i	0.323888	−	0.946096i	$-0.395010\pi$
$877$	−18.4262	−	18.4262i	−0.622208	−	0.622208i	−0.946096	+	0.323888i	$0.895010\pi$
$878$	3.24812	+	3.24812i	0.109619	+	0.109619i
$879$		−	23.8199i		−	0.803425i
$880$	−1.14896	−	4.35916i	−0.0387316	−	0.146947i
$881$			21.4410i			0.722367i	0.932495	+	0.361184i	$0.117627\pi$
$881$			21.4410i			0.722367i	−0.932495	+	0.361184i	$0.882373\pi$
$882$		0			0
$883$	28.4356	−	28.4356i	0.956934	−	0.956934i	−0.0421764	−	0.999110i	$-0.513429\pi$
$883$	28.4356	−	28.4356i	0.956934	−	0.956934i	0.999110	+	0.0421764i	$0.0134292\pi$
$884$			23.3995i			0.787011i
$885$	14.4328	−	24.7641i	0.485154	−	0.832437i
$886$	−37.3236			−1.25391
$887$	−14.4859	+	14.4859i	−0.486388	+	0.486388i	−0.907164	−	0.420776i	$-0.861758\pi$
$887$	−14.4859	+	14.4859i	−0.486388	+	0.486388i	0.420776	+	0.907164i	$0.361758\pi$
$888$	−3.63458	−	3.63458i	−0.121968	−	0.121968i
$889$		0			0
$890$	2.70418	−	4.63988i	0.0906442	−	0.155529i
$891$	2.01606			0.0675404
$892$	17.0152	−	17.0152i	0.569711	−	0.569711i
$893$	−7.24883	+	7.24883i	−0.242573	+	0.242573i
$894$	10.4743			0.350314
$895$	−46.2256	+	12.1839i	−1.54515	+	0.407263i
$896$		0			0
$897$	22.6230	+	22.6230i	0.755361	+	0.755361i
$898$	12.4294	−	12.4294i	0.414775	−	0.414775i
$899$	−10.0205			−0.334201
$900$	4.35041	−	2.46453i	0.145014	−	0.0821511i
$901$		−	9.72171i		−	0.323877i
$902$	7.04766	−	7.04766i	0.234662	−	0.234662i
$903$		0			0
$904$		−	15.4700i		−	0.514525i
$905$	−38.2069	+	10.0704i	−1.27004	+	0.334750i
$906$		−	10.5250i		−	0.349671i
$907$	−30.4690	−	30.4690i	−1.01170	−	1.01170i	−0.999931	−	0.0117742i	$-0.996252\pi$
$907$	−30.4690	−	30.4690i	−1.01170	−	1.01170i	−0.0117742	−	0.999931i	$-0.503748\pi$
$908$	5.71327	+	5.71327i	0.189602	+	0.189602i
$909$	−13.9054			−0.461214
$910$		0			0
$911$	−34.8475			−1.15455			−0.577275	−	0.816550i	$-0.695884\pi$
$911$	−34.8475			−1.15455			−0.577275	+	0.816550i	$0.695884\pi$
$912$	−4.75459	−	4.75459i	−0.157440	−	0.157440i
$913$	17.3311	+	17.3311i	0.573574	+	0.573574i
$914$			31.6598i			1.04721i
$915$	−17.3938	−	10.1373i	−0.575020	−	0.335128i
$916$		−	6.23842i		−	0.206123i
$917$		0			0
$918$	−3.40102	+	3.40102i	−0.112250	+	0.112250i
$919$		−	4.08697i		−	0.134817i	−0.997725	−	0.0674084i	$-0.978527\pi$
$919$		−	4.08697i		−	0.134817i	0.997725	−	0.0674084i	$-0.0214731\pi$
$920$	14.2195	−	3.74789i	0.468802	−	0.123564i
$921$	−28.3237			−0.933299
$922$	−5.13223	+	5.13223i	−0.169021	+	0.169021i
$923$	−12.0068	−	12.0068i	−0.395209	−	0.395209i
$924$		0			0
$925$	−24.7694	−	6.85437i	−0.814414	−	0.225370i
$926$	−21.0555			−0.691926
$927$	1.68753	−	1.68753i	0.0554259	−	0.0554259i
$928$	1.13351	−	1.13351i	0.0372093	−	0.0372093i
$929$	10.8143			0.354805			0.177403	−	0.984138i	$-0.443231\pi$
$929$	10.8143			0.354805			0.177403	+	0.984138i	$0.443231\pi$
$930$	3.56247	+	13.5160i	0.116818	+	0.443206i
$931$		0			0
$932$	−6.88051	−	6.88051i	−0.225379	−	0.225379i
$933$	−16.1503	+	16.1503i	−0.528737	+	0.528737i
$934$	−10.8431			−0.354796
$935$	18.7332	+	10.9179i	0.612642	+	0.357055i
$936$		−	4.86500i		−	0.159017i
$937$	−5.40732	+	5.40732i	−0.176649	+	0.176649i	−0.789894	−	0.613244i	$-0.789864\pi$
$937$	−5.40732	+	5.40732i	−0.176649	+	0.176649i	0.613244	+	0.789894i	$0.289864\pi$
$938$		0			0
$939$			21.5733i			0.704019i
$940$	−1.71660	+	2.94538i	−0.0559893	+	0.0960677i
$941$		−	45.9833i		−	1.49901i	−0.661997	−	0.749507i	$-0.730291\pi$
$941$		−	45.9833i		−	1.49901i	0.661997	−	0.749507i	$-0.269709\pi$
$942$	−5.51100	−	5.51100i	−0.179558	−	0.179558i
$943$	22.9893	+	22.9893i	0.748634	+	0.748634i
$944$	−12.8185			−0.417206
$945$		0			0
$946$	13.3474			0.433961
$947$	1.91345	+	1.91345i	0.0621786	+	0.0621786i	0.737512	−	0.675334i	$-0.236000\pi$
$947$	1.91345	+	1.91345i	0.0621786	+	0.0621786i	−0.675334	+	0.737512i	$0.736000\pi$
$948$	9.88997	+	9.88997i	0.321211	+	0.321211i
$949$			41.0914i			1.33388i
$950$	−32.4022	−	8.96658i	−1.05127	−	0.290914i
$951$		−	23.9908i		−	0.777956i
$952$		0			0
$953$	−8.34628	+	8.34628i	−0.270363	+	0.270363i	−0.829246	−	0.558884i	$-0.811230\pi$
$953$	−8.34628	+	8.34628i	−0.270363	+	0.270363i	0.558884	+	0.829246i	$0.311230\pi$
$954$			2.02124i			0.0654402i
$955$	1.90071	+	7.21126i	0.0615054	+	0.233351i
$956$	10.6330			0.343896
$957$	2.28522	−	2.28522i	0.0738707	−	0.0738707i
$958$	−18.9771	−	18.9771i	−0.613123	−	0.613123i
$959$		0			0
$960$	−1.93191	−	1.12594i	−0.0623520	−	0.0363395i
$961$	−8.07459			−0.260471
$962$	−17.6822	+	17.6822i	−0.570098	+	0.570098i
$963$	−8.03115	+	8.03115i	−0.258800	+	0.258800i
$964$	8.44540			0.272008
$965$	40.6341	+	23.6820i	1.30806	+	0.762351i
$966$		0			0
$967$	−15.8242	−	15.8242i	−0.508871	−	0.508871i	0.405309	−	0.914180i	$-0.367164\pi$
$967$	−15.8242	−	15.8242i	−0.508871	−	0.508871i	−0.914180	+	0.405309i	$0.867164\pi$
$968$	4.90415	−	4.90415i	0.157625	−	0.157625i
$969$	32.3409			1.03894
$970$	−10.6251	−	40.3117i	−0.341153	−	1.29433i
$971$		−	29.2160i		−	0.937587i	−0.883308	−	0.468793i	$-0.844689\pi$
$971$		−	29.2160i		−	0.937587i	0.883308	−	0.468793i	$-0.155311\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$		0			0
$974$		−	17.4039i		−	0.557658i
$975$	−11.9899	−	21.1648i	−0.383986	−	0.677814i
$976$			9.00341i			0.288192i
$977$	3.83196	+	3.83196i	0.122595	+	0.122595i	0.765742	−	0.643147i	$-0.222372\pi$
$977$	3.83196	+	3.83196i	0.122595	+	0.122595i	−0.643147	+	0.765742i	$0.722372\pi$
$978$	−3.18264	−	3.18264i	−0.101770	−	0.101770i
$979$	−4.84198			−0.154751
$980$		0			0
$981$	−15.8201			−0.505098
$982$	−19.7528	−	19.7528i	−0.630337	−	0.630337i
$983$	−15.3737	−	15.3737i	−0.490344	−	0.490344i	0.418071	−	0.908415i	$-0.362706\pi$
$983$	−15.3737	−	15.3737i	−0.490344	−	0.490344i	−0.908415	+	0.418071i	$0.862706\pi$
$984$		−	4.94376i		−	0.157601i
$985$	10.8946	−	18.6932i	0.347132	−	0.595616i
$986$			7.71019i			0.245542i
$987$		0			0
$988$	−23.1311	+	23.1311i	−0.735897	+	0.735897i
$989$			43.5388i			1.38445i
$990$	−3.89483	−	2.26995i	−0.123786	−	0.0721438i
$991$	14.6567			0.465585			0.232792	−	0.972526i	$-0.425214\pi$
$991$	14.6567			0.465585			0.232792	+	0.972526i	$0.425214\pi$
$992$	4.42010	−	4.42010i	0.140338	−	0.140338i
$993$	−15.4933	−	15.4933i	−0.491663	−	0.491663i
$994$		0			0
$995$	10.1869	+	38.6490i	0.322947	+	1.22526i
$996$	12.1573			0.385219
$997$	−18.4510	+	18.4510i	−0.584350	+	0.584350i	−0.936096	−	0.351745i	$-0.885588\pi$
$997$	−18.4510	+	18.4510i	−0.584350	+	0.584350i	0.351745	+	0.936096i	$0.385588\pi$
$998$	20.6483	−	20.6483i	0.653610	−	0.653610i
$999$	−5.14007			−0.162625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.c.97.7	✓	16
5.3	odd	4		1470.2.m.f.1273.6	yes	16
7.6	odd	2		1470.2.m.f.97.6	yes	16
35.13	even	4	inner	1470.2.m.c.1273.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.7	✓	16	1.1	even	1	trivial
1470.2.m.c.1273.7	yes	16	35.13	even	4	inner
1470.2.m.f.97.6	yes	16	7.6	odd	2
1470.2.m.f.1273.6	yes	16	5.3	odd	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.569907 - 2.16222i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.569907 - 2.16222i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.12594 - 1.93191i) q^{10} -2.01606 q^{11} +(-0.707107 + 0.707107i) q^{12} +(3.44007 + 3.44007i) q^{13} +(1.12594 - 1.93191i) q^{15} -1.00000 q^{16} +(3.40102 - 3.40102i) q^{17} +(-0.707107 + 0.707107i) q^{18} +6.72400 q^{19} +(2.16222 - 0.569907i) q^{20} +(-1.42557 - 1.42557i) q^{22} +(4.65016 - 4.65016i) q^{23} -1.00000 q^{24} +(-4.35041 + 2.46453i) q^{25} +4.86500i q^{26} +(-0.707107 + 0.707107i) q^{27} +1.60303i q^{29} +(2.16222 - 0.569907i) q^{30} +6.25097i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.42557 - 1.42557i) q^{33} +4.80977 q^{34} -1.00000 q^{36} +(3.63458 + 3.63458i) q^{37} +(4.75459 + 4.75459i) q^{38} +4.86500i q^{39} +(1.93191 + 1.12594i) q^{40} +4.94376i q^{41} +(-4.68143 + 4.68143i) q^{43} -2.01606i q^{44} +(2.16222 - 0.569907i) q^{45} +6.57632 q^{46} +(-1.07805 + 1.07805i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-4.81889 - 1.33352i) q^{50} +4.80977 q^{51} +(-3.44007 + 3.44007i) q^{52} +(1.42923 - 1.42923i) q^{53} -1.00000 q^{54} +(1.14896 + 4.35916i) q^{55} +(4.75459 + 4.75459i) q^{57} +(-1.13351 + 1.13351i) q^{58} +12.8185 q^{59} +(1.93191 + 1.12594i) q^{60} -9.00341i q^{61} +(-4.42010 + 4.42010i) q^{62} -1.00000i q^{64} +(5.47768 - 9.39873i) q^{65} -2.01606i q^{66} +(-1.19011 - 1.19011i) q^{67} +(3.40102 + 3.40102i) q^{68} +6.57632 q^{69} -3.49027 q^{71} +(-0.707107 - 0.707107i) q^{72} +(5.97245 + 5.97245i) q^{73} +5.14007i q^{74} +(-4.81889 - 1.33352i) q^{75} +6.72400i q^{76} +(-3.44007 + 3.44007i) q^{78} -13.9865i q^{79} +(0.569907 + 2.16222i) q^{80} -1.00000 q^{81} +(-3.49577 + 3.49577i) q^{82} +(-8.59652 - 8.59652i) q^{83} +(-9.29202 - 5.41549i) q^{85} -6.62055 q^{86} +(-1.13351 + 1.13351i) q^{87} +(1.42557 - 1.42557i) q^{88} +2.40171 q^{89} +(1.93191 + 1.12594i) q^{90} +(4.65016 + 4.65016i) q^{92} +(-4.42010 + 4.42010i) q^{93} -1.52460 q^{94} +(-3.83206 - 14.5388i) q^{95} -1.00000i q^{96} +(13.1830 - 13.1830i) q^{97} -2.01606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5}+O(q^{10}) \) 16 * q - 8 * q^5	\( 16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57} + 24 q^{58} - 48 q^{59} + 8 q^{62} + 72 q^{65} - 48 q^{67} + 8 q^{68} - 16 q^{73} + 8 q^{78} + 8 q^{80} - 16 q^{81} + 16 q^{82} - 72 q^{85} + 24 q^{87} + 8 q^{88} + 64 q^{89} - 8 q^{92} + 8 q^{93} - 64 q^{94} + 48 q^{95} + 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 - 8 * q^13 - 16 * q^16 + 8 * q^17 + 48 * q^19 - 8 * q^22 - 8 * q^23 - 16 * q^24 + 8 * q^25 - 8 * q^33 - 16 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^47 + 8 * q^52 + 8 * q^53 - 16 * q^54 + 8 * q^57 + 24 * q^58 - 48 * q^59 + 8 * q^62 + 72 * q^65 - 48 * q^67 + 8 * q^68 - 16 * q^73 + 8 * q^78 + 8 * q^80 - 16 * q^81 + 16 * q^82 - 72 * q^85 + 24 * q^87 + 8 * q^88 + 64 * q^89 - 8 * q^92 + 8 * q^93 - 64 * q^94 + 48 * q^95 + 64 * q^97

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