LMFDB - Embedded newform 504.2.cj.c.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.1
Root			$1.26950 - 0.623187i$ of defining polynomial
Character	$\chi$	$=$	504.109
Dual form			504.2.cj.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38687 - 0.276739i) q^{2} +(1.84683 + 0.767603i) q^{4} +(0.476087 - 0.274869i) q^{5} +(-2.60755 + 0.447998i) q^{7} +(-2.34889 - 1.57566i) q^{8} +O(q^{10})$	\(q+(-1.38687 - 0.276739i) q^{2} +(1.84683 + 0.767603i) q^{4} +(0.476087 - 0.274869i) q^{5} +(-2.60755 + 0.447998i) q^{7} +(-2.34889 - 1.57566i) q^{8} +(-0.736339 + 0.249456i) q^{10} +(2.07045 + 1.19538i) q^{11} +3.96641i q^{13} +(3.74031 + 0.100292i) q^{14} +(2.82157 + 2.83527i) q^{16} +(-2.10755 + 3.65038i) q^{17} +(5.75174 - 3.32077i) q^{19} +(1.09024 - 0.142191i) q^{20} +(-2.54065 - 2.23081i) q^{22} +(-1.17445 - 2.03420i) q^{23} +(-2.34889 + 4.06840i) q^{25} +(1.09766 - 5.50090i) q^{26} +(-5.15958 - 1.17418i) q^{28} +8.21720i q^{29} +(-0.433099 + 0.750150i) q^{31} +(-3.12853 - 4.71299i) q^{32} +(3.93310 - 4.47937i) q^{34} +(-1.11828 + 0.930019i) q^{35} +(-0.229805 + 0.132678i) q^{37} +(-8.89592 + 3.01376i) q^{38} +(-1.55138 - 0.104512i) q^{40} +6.24970 q^{41} +5.35027i q^{43} +(2.90620 + 3.79694i) q^{44} +(1.06587 + 3.14619i) q^{46} +(1.29930 + 2.25045i) q^{47} +(6.59859 - 2.33635i) q^{49} +(4.38350 - 4.99233i) q^{50} +(-3.04463 + 7.32529i) q^{52} +(9.36933 + 5.40939i) q^{53} +1.31429 q^{55} +(6.83074 + 3.05630i) q^{56} +(2.27402 - 11.3962i) q^{58} +(3.26891 + 1.88730i) q^{59} +(-6.18061 + 3.56837i) q^{61} +(0.808249 - 0.920507i) q^{62} +(3.03461 + 7.40210i) q^{64} +(1.09024 + 1.88835i) q^{65} +(2.31673 + 1.33757i) q^{67} +(-6.69432 + 5.12387i) q^{68} +(1.80828 - 0.980348i) q^{70} -8.76700 q^{71} +(-2.33159 + 4.03843i) q^{73} +(0.355428 - 0.120412i) q^{74} +(13.1715 - 1.71785i) q^{76} +(-5.93432 - 2.18944i) q^{77} +(-0.308249 - 0.533903i) q^{79} +(2.12264 + 0.574271i) q^{80} +(-8.66754 - 1.72953i) q^{82} -1.09948i q^{83} +2.31720i q^{85} +(1.48063 - 7.42014i) q^{86} +(-2.97977 - 6.07013i) q^{88} +(-3.19779 - 5.53873i) q^{89} +(-1.77694 - 10.3426i) q^{91} +(-0.607546 - 4.65834i) q^{92} +(-1.17917 - 3.48065i) q^{94} +(1.82555 - 3.16195i) q^{95} +12.9475 q^{97} +(-9.79797 + 1.41414i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40} + 8 q^{41} + 30 q^{44} - 4 q^{46} - 30 q^{47} - 12 q^{49} + 16 q^{50} - 32 q^{52} + 4 q^{55} + 40 q^{56} - 22 q^{58} + 28 q^{62} + 24 q^{64} - 8 q^{65} - 4 q^{68} - 48 q^{70} - 32 q^{71} - 10 q^{73} - 18 q^{74} + 52 q^{76} - 22 q^{79} - 36 q^{80} - 26 q^{82} - 40 q^{86} - 14 q^{88} + 10 q^{89} + 20 q^{92} + 42 q^{94} + 34 q^{95} + 40 q^{97} - 52 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.38687	−	0.276739i	−0.980667	−	0.195684i
$2$	−1.38687	−	0.276739i	−0.980667	−	0.195684i
$3$		0			0
$3$		0			0
$4$	1.84683	+	0.767603i	0.923416	+	0.383801i
$5$	0.476087	−	0.274869i	0.212913	−	0.122925i	−0.389752	−	0.920920i	$-0.627439\pi$
$5$	0.476087	−	0.274869i	0.212913	−	0.122925i	0.602664	+	0.797995i	$0.294106\pi$
$6$		0			0
$7$	−2.60755	+	0.447998i	−0.985560	+	0.169327i
$7$	−2.60755	+	0.447998i	−0.985560	+	0.169327i
$8$	−2.34889	−	1.57566i	−0.830460	−	0.557079i
$9$		0			0
$10$	−0.736339	+	0.249456i	−0.232851	+	0.0788850i
$11$	2.07045	+	1.19538i	0.624265	+	0.360419i	0.778527	−	0.627611i	$-0.215967\pi$
$11$	2.07045	+	1.19538i	0.624265	+	0.360419i	−0.154263	+	0.988030i	$0.549300\pi$
$12$		0			0
$13$			3.96641i			1.10008i	0.835137	+	0.550042i	$0.185388\pi$
$13$			3.96641i			1.10008i	−0.835137	+	0.550042i	$0.814612\pi$
$14$	3.74031	+	0.100292i	0.999641	+	0.0268043i
$15$		0			0
$16$	2.82157	+	2.83527i	0.705393	+	0.708817i
$17$	−2.10755	+	3.65038i	−0.511155	+	0.885347i	0.488761	+	0.872418i	$0.337449\pi$
$17$	−2.10755	+	3.65038i	−0.511155	+	0.885347i	−0.999916	+	0.0129290i	$0.995884\pi$
$18$		0			0
$19$	5.75174	−	3.32077i	1.31954	−	0.761837i	0.335886	−	0.941903i	$-0.390964\pi$
$19$	5.75174	−	3.32077i	1.31954	−	0.761837i	0.983655	+	0.180066i	$0.0576310\pi$
$20$	1.09024	−	0.142191i	0.243786	−	0.0317948i
$21$		0			0
$22$	−2.54065	−	2.23081i	−0.541667	−	0.475610i
$23$	−1.17445	−	2.03420i	−0.244889	−	0.424160i	0.717211	−	0.696856i	$-0.245418\pi$
$23$	−1.17445	−	2.03420i	−0.244889	−	0.424160i	−0.962100	+	0.272695i	$0.912085\pi$
$24$		0			0
$25$	−2.34889	+	4.06840i	−0.469779	+	0.813681i
$26$	1.09766	−	5.50090i	0.215269	−	1.07882i
$27$		0			0
$28$	−5.15958	−	1.17418i	−0.975070	−	0.221900i
$29$			8.21720i			1.52590i	0.646460	+	0.762948i	$0.276249\pi$
$29$			8.21720i			1.52590i	−0.646460	+	0.762948i	$0.723751\pi$
$30$		0			0
$31$	−0.433099	+	0.750150i	−0.0777869	+	0.134731i	−0.902295	−	0.431120i	$-0.858119\pi$
$31$	−0.433099	+	0.750150i	−0.0777869	+	0.134731i	0.824508	+	0.565850i	$0.191452\pi$
$32$	−3.12853	−	4.71299i	−0.553052	−	0.833147i
$33$		0			0
$34$	3.93310	−	4.47937i	0.674521	−	0.768205i
$35$	−1.11828	+	0.930019i	−0.189023	+	0.157202i
$36$		0			0
$37$	−0.229805	+	0.132678i	−0.0377797	+	0.0218121i	−0.518771	−	0.854913i	$-0.673610\pi$
$37$	−0.229805	+	0.132678i	−0.0377797	+	0.0218121i	0.480991	+	0.876725i	$0.340277\pi$
$38$	−8.89592	+	3.01376i	−1.44311	+	0.488896i
$39$		0			0
$40$	−1.55138	−	0.104512i	−0.245294	−	0.0165248i
$41$	6.24970			0.976039			0.488020	−	0.872833i	$-0.337719\pi$
$41$	6.24970			0.976039			0.488020	+	0.872833i	$0.337719\pi$
$42$		0			0
$43$			5.35027i			0.815908i	0.913003	+	0.407954i	$0.133758\pi$
$43$			5.35027i			0.815908i	−0.913003	+	0.407954i	$0.866242\pi$
$44$	2.90620	+	3.79694i	0.438126	+	0.572410i
$45$		0			0
$46$	1.06587	+	3.14619i	0.157153	+	0.463881i
$47$	1.29930	+	2.25045i	0.189522	+	0.328262i	0.945091	−	0.326807i	$-0.105973\pi$
$47$	1.29930	+	2.25045i	0.189522	+	0.328262i	−0.755569	+	0.655069i	$0.772639\pi$
$48$		0			0
$49$	6.59859	−	2.33635i	0.942656	−	0.333765i
$50$	4.38350	−	4.99233i	0.619921	−	0.706022i
$51$		0			0
$52$	−3.04463	+	7.32529i	−0.422214	+	1.01583i
$53$	9.36933	+	5.40939i	1.28698	+	0.743037i	0.978114	−	0.208070i	$-0.0667182\pi$
$53$	9.36933	+	5.40939i	1.28698	+	0.743037i	0.308863	+	0.951107i	$0.400052\pi$
$54$		0			0
$55$	1.31429			0.177218
$56$	6.83074	+	3.05630i	0.912796	+	0.408415i
$57$		0			0
$58$	2.27402	−	11.3962i	0.298593	−	1.49640i
$59$	3.26891	+	1.88730i	0.425575	+	0.245706i	0.697460	−	0.716624i	$-0.254314\pi$
$59$	3.26891	+	1.88730i	0.425575	+	0.245706i	−0.271884	+	0.962330i	$0.587647\pi$
$60$		0			0
$61$	−6.18061	+	3.56837i	−0.791345	+	0.456884i	−0.840436	−	0.541911i	$-0.817701\pi$
$61$	−6.18061	+	3.56837i	−0.791345	+	0.456884i	0.0490905	+	0.998794i	$0.484368\pi$
$62$	0.808249	−	0.920507i	0.102648	−	0.116904i
$63$		0			0
$64$	3.03461	+	7.40210i	0.379326	+	0.925263i
$65$	1.09024	+	1.88835i	0.135228	+	0.234222i
$66$		0			0
$67$	2.31673	+	1.33757i	0.283034	+	0.163410i	0.634796	−	0.772680i	$-0.281084\pi$
$67$	2.31673	+	1.33757i	0.283034	+	0.163410i	−0.351762	+	0.936089i	$0.614417\pi$
$68$	−6.69432	+	5.12387i	−0.811806	+	0.621361i
$69$		0			0
$70$	1.80828	−	0.980348i	0.216131	−	0.117174i
$71$	−8.76700			−1.04045			−0.520226	−	0.854029i	$-0.674152\pi$
$71$	−8.76700			−1.04045			−0.520226	+	0.854029i	$0.674152\pi$
$72$		0			0
$73$	−2.33159	+	4.03843i	−0.272892	+	0.472663i	−0.969601	−	0.244691i	$-0.921313\pi$
$73$	−2.33159	+	4.03843i	−0.272892	+	0.472663i	0.696709	+	0.717354i	$0.254647\pi$
$74$	0.355428	−	0.120412i	0.0413176	−	0.0139976i
$75$		0			0
$76$	13.1715	−	1.71785i	1.51088	−	0.197051i
$77$	−5.93432	−	2.18944i	−0.676279	−	0.249510i
$78$		0			0
$79$	−0.308249	−	0.533903i	−0.0346807	−	0.0600687i	0.848164	−	0.529734i	$-0.177708\pi$
$79$	−0.308249	−	0.533903i	−0.0346807	−	0.0600687i	−0.882845	+	0.469665i	$0.844375\pi$
$80$	2.12264	+	0.574271i	0.237318	+	0.0642054i
$81$		0			0
$82$	−8.66754	−	1.72953i	−0.957170	−	0.190995i
$83$		−	1.09948i		−	0.120683i	−0.998178	−	0.0603416i	$-0.980781\pi$
$83$		−	1.09948i		−	0.120683i	0.998178	−	0.0603416i	$-0.0192190\pi$
$84$		0			0
$85$			2.31720i			0.251335i
$86$	1.48063	−	7.42014i	0.159660	−	0.800134i
$87$		0			0
$88$	−2.97977	−	6.07013i	−0.317644	−	0.647078i
$89$	−3.19779	−	5.53873i	−0.338965	−	0.587104i	0.645273	−	0.763952i	$-0.276743\pi$
$89$	−3.19779	−	5.53873i	−0.338965	−	0.587104i	−0.984238	+	0.176847i	$0.943410\pi$
$90$		0			0
$91$	−1.77694	−	10.3426i	−0.186274	−	1.08420i
$92$	−0.607546	−	4.65834i	−0.0633411	−	0.485665i
$93$		0			0
$94$	−1.17917	−	3.48065i	−0.121622	−	0.359002i
$95$	1.82555	−	3.16195i	0.187298	−	0.324409i
$96$		0			0
$97$	12.9475			1.31462			0.657309	−	0.753621i	$-0.271695\pi$
$97$	12.9475			1.31462			0.657309	+	0.753621i	$0.271695\pi$
$98$	−9.79797	+	1.41414i	−0.989744	+	0.142849i
$99$		0			0
$100$	−7.46093	+	5.71064i	−0.746093	+	0.571064i
$101$	−13.7565	−	7.94233i	−1.36882	−	0.790291i	−0.378047	−	0.925787i	$-0.623404\pi$
$101$	−13.7565	−	7.94233i	−1.36882	−	0.790291i	−0.990778	+	0.135495i	$0.956737\pi$
$102$		0			0
$103$	−9.38954	−	16.2632i	−0.925179	−	1.60246i	−0.791273	−	0.611463i	$-0.790581\pi$
$103$	−9.38954	−	16.2632i	−0.925179	−	1.60246i	−0.133906	−	0.990994i	$-0.542752\pi$
$104$	6.24970	−	9.31667i	0.612834	−	0.913575i
$105$		0			0
$106$	−11.4971	−	10.0950i	−1.11670	−	0.980512i
$107$	−0.293506	+	0.169456i	−0.0283743	+	0.0163819i	−0.514120	−	0.857718i	$-0.671881\pi$
$107$	−0.293506	+	0.169456i	−0.0283743	+	0.0163819i	0.485746	+	0.874100i	$0.338548\pi$
$108$		0			0
$109$	6.75910	+	3.90237i	0.647404	+	0.373779i	0.787461	−	0.616365i	$-0.211395\pi$
$109$	6.75910	+	3.90237i	0.647404	+	0.373779i	−0.140057	+	0.990143i	$0.544729\pi$
$110$	−1.82275	−	0.363714i	−0.173792	−	0.0346788i
$111$		0			0
$112$	−8.62757	−	6.12903i	−0.815229	−	0.579139i
$113$	−2.51730			−0.236808			−0.118404	−	0.992966i	$-0.537778\pi$
$113$	−2.51730			−0.236808			−0.118404	+	0.992966i	$0.537778\pi$
$114$		0			0
$115$	−1.11828	−	0.645638i	−0.104280	−	0.0602060i
$116$	−6.30755	+	15.1758i	−0.585641	+	1.40904i
$117$		0			0
$118$	−4.01127	−	3.52208i	−0.369267	−	0.324234i
$119$	3.86016	−	10.4627i	0.353860	−	0.959115i
$120$		0			0
$121$	−2.64215	−	4.57635i	−0.240196	−	0.416031i
$122$	9.55922	−	3.23847i	0.865451	−	0.293197i
$123$		0			0
$124$	−1.37568	+	1.05295i	−0.123540	+	0.0945579i
$125$			5.33124i			0.476841i
$126$		0			0
$127$	−5.30221			−0.470495			−0.235248	−	0.971935i	$-0.575590\pi$
$127$	−5.30221			−0.470495			−0.235248	+	0.971935i	$0.575590\pi$
$128$	−2.16017	−	11.1056i	−0.190933	−	0.981603i
$129$		0			0
$130$	−0.989446	−	2.92062i	−0.0867802	−	0.256155i
$131$	8.69419	−	5.01959i	0.759615	−	0.438564i	−0.0695425	−	0.997579i	$-0.522154\pi$
$131$	8.69419	−	5.01959i	0.759615	−	0.438564i	0.829157	+	0.559015i	$0.188821\pi$
$132$		0			0
$133$	−13.5102	+	11.2358i	−1.17149	+	0.974270i
$134$	−2.84286	−	2.49616i	−0.245585	−	0.215636i
$135$		0			0
$136$	10.7021	−	5.25358i	0.917702	−	0.450491i
$137$	1.62485	−	2.81432i	0.138820	−	0.240444i	−0.788230	−	0.615381i	$-0.789002\pi$
$137$	1.62485	−	2.81432i	0.138820	−	0.240444i	0.927050	+	0.374937i	$0.122336\pi$
$138$		0			0
$139$		−	15.3349i		−	1.30069i	−0.759639	−	0.650346i	$-0.774624\pi$
$139$		−	15.3349i		−	1.30069i	0.759639	−	0.650346i	$-0.225376\pi$
$140$	−2.77916	+	0.859196i	−0.234882	+	0.0726153i
$141$		0			0
$142$	12.1587	+	2.42617i	1.02034	+	0.203600i
$143$	−4.74135	+	8.21226i	−0.396491	+	0.686743i
$144$		0			0
$145$	2.25865	+	3.91210i	0.187571	+	0.324882i
$146$	4.35121	−	4.95555i	0.360109	−	0.410124i
$147$		0			0
$148$	−0.526255	+	0.0686349i	−0.0432579	+	0.00564175i
$149$	−6.39393	+	3.69154i	−0.523812	+	0.302423i	−0.738493	−	0.674261i	$-0.764462\pi$
$149$	−6.39393	+	3.69154i	−0.523812	+	0.302423i	0.214681	+	0.976684i	$0.431129\pi$
$150$		0			0
$151$	−4.16550	+	7.21485i	−0.338983	+	0.587136i	−0.984242	−	0.176828i	$-0.943416\pi$
$151$	−4.16550	+	7.21485i	−0.338983	+	0.587136i	0.645259	+	0.763964i	$0.276750\pi$
$152$	−18.7426	−	1.26264i	−1.52023	−	0.102413i
$153$		0			0
$154$	7.62425	+	4.67873i	0.614379	+	0.377023i
$155$			0.476182i			0.0382478i
$156$		0			0
$157$	−6.18061	−	3.56837i	−0.493266	−	0.284787i	0.232662	−	0.972558i	$-0.425256\pi$
$157$	−6.18061	−	3.56837i	−0.493266	−	0.284787i	−0.725928	+	0.687770i	$0.758590\pi$
$158$	0.279750	+	0.825759i	0.0222557	+	0.0656939i
$159$		0			0
$160$	−2.78491	−	1.38386i	−0.220166	−	0.109404i
$161$	3.97374	+	4.77813i	0.313175	+	0.376569i
$162$		0			0
$163$	6.33023	−	3.65476i	0.495822	−	0.286263i	−0.231164	−	0.972915i	$-0.574254\pi$
$163$	6.33023	−	3.65476i	0.495822	−	0.286263i	0.726987	+	0.686652i	$0.240920\pi$
$164$	11.5421	+	4.79729i	0.901290	+	0.374605i
$165$		0			0
$166$	−0.304268	+	1.52483i	−0.0236157	+	0.118350i
$167$	−1.88873			−0.146154			−0.0730772	−	0.997326i	$-0.523282\pi$
$167$	−1.88873			−0.146154			−0.0730772	+	0.997326i	$0.523282\pi$
$168$		0			0
$169$	−2.73240			−0.210184
$170$	0.641258	−	3.21365i	0.0491822	−	0.246476i
$171$		0			0
$172$	−4.10688	+	9.88104i	−0.313147	+	0.753422i
$173$	14.3350	−	8.27632i	1.08987	−	0.629237i	0.156329	−	0.987705i	$-0.450034\pi$
$173$	14.3350	−	8.27632i	1.08987	−	0.629237i	0.933542	+	0.358468i	$0.116701\pi$
$174$		0			0
$175$	4.30221	−	11.6609i	0.325217	−	0.881478i
$176$	2.45272	+	9.24312i	0.184881	+	0.696726i
$177$		0			0
$178$	2.90214	+	8.56647i	0.217525	+	0.642084i
$179$	−4.79957	−	2.77103i	−0.358737	−	0.207117i	0.309790	−	0.950805i	$-0.399741\pi$
$179$	−4.79957	−	2.77103i	−0.358737	−	0.207117i	−0.668526	+	0.743688i	$0.733075\pi$
$180$		0			0
$181$		−	9.98466i		−	0.742154i	−0.928602	−	0.371077i	$-0.878989\pi$
$181$		−	9.98466i		−	0.742154i	0.928602	−	0.371077i	$-0.121011\pi$
$182$	−0.397801	+	14.8356i	−0.0294870	+	1.09969i
$183$		0			0
$184$	−0.446553	+	6.62865i	−0.0329203	+	0.488671i
$185$	−0.0729381	+	0.126333i	−0.00536252	+	0.00928816i
$186$		0			0
$187$	−8.72714	+	5.03862i	−0.638192	+	0.368460i
$188$	0.672132	+	5.15354i	0.0490202	+	0.375861i
$189$		0			0
$190$	−3.40684	+	3.88002i	−0.247158	+	0.281486i
$191$	0.0842049	+	0.145847i	0.00609285	+	0.0105531i	0.869056	−	0.494714i	$-0.164727\pi$
$191$	0.0842049	+	0.145847i	0.00609285	+	0.0105531i	−0.862963	+	0.505267i	$0.831394\pi$
$192$		0			0
$193$	−3.75865	+	6.51018i	−0.270554	+	0.468613i	−0.969004	−	0.247046i	$-0.920540\pi$
$193$	−3.75865	+	6.51018i	−0.270554	+	0.468613i	0.698450	+	0.715659i	$0.253873\pi$
$194$	−17.9565	−	3.58307i	−1.28920	−	0.257250i
$195$		0			0
$196$	13.9799	+	0.750250i	0.998563	+	0.0535893i
$197$			1.34581i			0.0958847i	0.998850	+	0.0479424i	$0.0152664\pi$
$197$			1.34581i			0.0958847i	−0.998850	+	0.0479424i	$0.984734\pi$
$198$		0			0
$199$	6.38059	−	11.0515i	0.452308	−	0.783420i	−0.546221	−	0.837641i	$-0.683934\pi$
$199$	6.38059	−	11.0515i	0.452308	−	0.783420i	0.998529	+	0.0542208i	$0.0172675\pi$
$200$	11.9277	−	5.85520i	0.843417	−	0.414025i
$201$		0			0
$202$	16.8806	+	14.8220i	1.18771	+	1.04287i
$203$	−3.68129	−	21.4267i	−0.258376	−	1.50386i
$204$		0			0
$205$	2.97540	−	1.71785i	0.207811	−	0.119980i
$206$	8.52145	+	25.1534i	0.593717	+	1.75252i
$207$		0			0
$208$	−11.2458	+	11.1915i	−0.779758	+	0.775991i
$209$	15.8783			1.09832
$210$		0			0
$211$			8.46353i			0.582653i	0.956624	+	0.291327i	$0.0940967\pi$
$211$			8.46353i			0.582653i	−0.956624	+	0.291327i	$0.905903\pi$
$212$	13.1513	+	17.1822i	0.903236	+	1.18008i
$213$		0			0
$214$	0.453951	−	0.153789i	0.0310315	−	0.0105128i
$215$	1.47062	+	2.54719i	0.100296	+	0.173717i
$216$		0			0
$217$	0.793260	−	2.15008i	0.0538500	−	0.145957i
$218$	−8.29407	−	7.28259i	−0.561745	−	0.493239i
$219$		0			0
$220$	2.42726	+	1.00885i	0.163646	+	0.0680166i
$221$	−14.4789	−	8.35939i	−0.973955	−	0.562313i
$222$		0			0
$223$	−5.80161			−0.388505			−0.194252	−	0.980952i	$-0.562228\pi$
$223$	−5.80161			−0.388505			−0.194252	+	0.980952i	$0.562228\pi$
$224$	10.2692	+	10.8878i	0.686140	+	0.727469i
$225$		0			0
$226$	3.49118	+	0.696636i	0.232230	+	0.0463395i
$227$	−9.89265	−	5.71152i	−0.656598	−	0.379087i	0.134382	−	0.990930i	$-0.457095\pi$
$227$	−9.89265	−	5.71152i	−0.656598	−	0.379087i	−0.790980	+	0.611843i	$0.790429\pi$
$228$		0			0
$229$	16.0260	−	9.25263i	1.05903	−	0.611431i	0.133866	−	0.990999i	$-0.457261\pi$
$229$	16.0260	−	9.25263i	1.05903	−	0.611431i	0.925164	+	0.379568i	$0.123928\pi$
$230$	1.37224	+	1.20489i	0.0904825	+	0.0794480i
$231$		0			0
$232$	12.9475	−	19.3013i	0.850044	−	1.26719i
$233$	−5.52566	−	9.57072i	−0.361998	−	0.626999i	0.626292	−	0.779589i	$-0.284572\pi$
$233$	−5.52566	−	9.57072i	−0.361998	−	0.626999i	−0.988290	+	0.152590i	$0.951239\pi$
$234$		0			0
$235$	1.23716	+	0.714273i	0.0807032	+	0.0465940i
$236$	4.58842	+	5.99475i	0.298681	+	0.390225i
$237$		0			0
$238$	−8.24899	+	13.4422i	−0.534702	+	0.871327i
$239$	22.6107			1.46256			0.731281	−	0.682076i	$-0.238923\pi$
$239$	22.6107			1.46256			0.731281	+	0.682076i	$0.238923\pi$
$240$		0			0
$241$	−6.96479	+	12.0634i	−0.448642	+	0.777070i	−0.998298	−	0.0583207i	$-0.981425\pi$
$241$	−6.96479	+	12.0634i	−0.448642	+	0.777070i	0.549656	+	0.835391i	$0.314759\pi$
$242$	2.39788	+	7.07799i	0.154142	+	0.454991i
$243$		0			0
$244$	−14.1536	+	1.84593i	−0.906093	+	0.118174i
$245$	2.49931	−	2.92606i	0.159675	−	0.186939i
$246$		0			0
$247$	13.1715	+	22.8138i	0.838085	+	1.45161i
$248$	2.19928	−	1.07961i	0.139655	−	0.0685551i
$249$		0			0
$250$	1.47536	−	7.39375i	0.0933100	−	0.467622i
$251$		−	0.706033i		−	0.0445644i	−0.999752	−	0.0222822i	$-0.992907\pi$
$251$		−	0.706033i		−	0.0445644i	0.999752	−	0.0222822i	$-0.00709323\pi$
$252$		0			0
$253$		−	5.61562i		−	0.353051i
$254$	7.35349	+	1.46733i	0.461399	+	0.0920683i
$255$		0			0
$256$	−0.0774679	+	15.9998i	−0.00484175	+	0.999988i
$257$	10.3919	+	17.9992i	0.648226	+	1.12276i	0.983546	+	0.180656i	$0.0578222\pi$
$257$	10.3919	+	17.9992i	0.648226	+	1.12276i	−0.335320	+	0.942104i	$0.608844\pi$
$258$		0			0
$259$	0.539788	−	0.448917i	0.0335408	−	0.0278943i
$260$	0.563987	+	4.32435i	0.0349770	+	0.268185i
$261$		0			0
$262$	−13.4469	+	4.55552i	−0.830749	+	0.281441i
$263$	−11.3895	+	19.7273i	−0.702309	+	1.21644i	0.265345	+	0.964154i	$0.414514\pi$
$263$	−11.3895	+	19.7273i	−0.702309	+	1.21644i	−0.967654	+	0.252281i	$0.918819\pi$
$264$		0			0
$265$	5.94749			0.365351
$266$	21.8464	−	11.8439i	1.33949	−	0.726194i
$267$		0			0
$268$	3.25189	+	4.24859i	0.198641	+	0.259524i
$269$	−2.59376	−	1.49751i	−0.158145	−	0.0913048i	0.418839	−	0.908060i	$-0.362437\pi$
$269$	−2.59376	−	1.49751i	−0.158145	−	0.0913048i	−0.576984	+	0.816756i	$0.695770\pi$
$270$		0			0
$271$	12.5926	+	21.8109i	0.764943	+	1.32492i	0.940277	+	0.340412i	$0.110566\pi$
$271$	12.5926	+	21.8109i	0.764943	+	1.32492i	−0.175333	+	0.984509i	$0.556100\pi$
$272$	−16.2964	+	4.32435i	−0.988113	+	0.262202i
$273$		0			0
$274$	−3.03229	+	3.45345i	−0.183188	+	0.208630i
$275$	−9.72654	+	5.61562i	−0.586533	+	0.338635i
$276$		0			0
$277$	8.17940	+	4.72238i	0.491453	+	0.283740i	0.725177	−	0.688563i	$-0.241758\pi$
$277$	8.17940	+	4.72238i	0.491453	+	0.283740i	−0.233724	+	0.972303i	$0.575091\pi$
$278$	−4.24377	+	21.2676i	−0.254524	+	1.27554i
$279$		0			0
$280$	4.09211	−	0.422495i	0.244550	−	0.0252489i
$281$	−26.8425			−1.60129			−0.800644	−	0.599141i	$-0.795509\pi$
$281$	−26.8425			−1.60129			−0.800644	+	0.599141i	$0.795509\pi$
$282$		0			0
$283$	11.2429	+	6.49111i	0.668323	+	0.385856i	0.795441	−	0.606031i	$-0.207239\pi$
$283$	11.2429	+	6.49111i	0.668323	+	0.385856i	−0.127118	+	0.991888i	$0.540573\pi$
$284$	−16.1912	−	6.72958i	−0.960770	−	0.399327i
$285$		0			0
$286$	8.84830	−	10.0772i	0.523211	−	0.595880i
$287$	−16.2964	+	2.79986i	−0.961945	+	0.165270i
$288$		0			0
$289$	−0.383502	−	0.664245i	−0.0225590	−	0.0390733i
$290$	−2.04983	−	6.05064i	−0.120370	−	0.355306i
$291$		0			0
$292$	−7.40597	+	5.66857i	−0.433401	+	0.331728i
$293$		−	9.56300i		−	0.558677i	−0.960193	−	0.279338i	$-0.909885\pi$
$293$		−	9.56300i		−	0.558677i	0.960193	−	0.279338i	$-0.0901151\pi$
$294$		0			0
$295$	2.07504			0.120814
$296$	0.748843	+	0.0504474i	0.0435256	+	0.00293220i
$297$		0			0
$298$	9.88916	−	3.35025i	0.572864	−	0.194075i
$299$	8.06848	−	4.65834i	0.466612	−	0.269399i
$300$		0			0
$301$	−2.39691	−	13.9511i	−0.138156	−	0.804126i
$302$	7.77364	−	8.85332i	0.447323	−	0.509452i
$303$		0			0
$304$	25.6442	+	6.93793i	1.47080	+	0.397918i
$305$	−1.96167	+	3.39771i	−0.112325	+	0.194552i
$306$		0			0
$307$		−	12.2217i		−	0.697527i	−0.937211	−	0.348763i	$-0.886602\pi$
$307$		−	12.2217i		−	0.697527i	0.937211	−	0.348763i	$-0.113398\pi$
$308$	−9.27908	−	8.59873i	−0.528724	−	0.489958i
$309$		0			0
$310$	0.131778	−	0.660404i	0.00748449	−	0.0375084i
$311$	15.9415	−	27.6114i	0.903957	−	1.56570i	0.0816453	−	0.996661i	$-0.473983\pi$
$311$	15.9415	−	27.6114i	0.903957	−	1.56570i	0.822311	−	0.569038i	$-0.192684\pi$
$312$		0			0
$313$	−10.7618	−	18.6399i	−0.608291	−	1.05359i	−0.991522	−	0.129939i	$-0.958522\pi$
$313$	−10.7618	−	18.6399i	−0.608291	−	1.05359i	0.383230	−	0.923653i	$-0.374811\pi$
$314$	7.58420	+	6.65929i	0.428001	+	0.375806i
$315$		0			0
$316$	−0.159458	−	1.22264i	−0.00897023	−	0.0687789i
$317$	20.0481	−	11.5747i	1.12601	−	0.650103i	0.183082	−	0.983098i	$-0.441393\pi$
$317$	20.0481	−	11.5747i	1.12601	−	0.650103i	0.942929	+	0.332995i	$0.108059\pi$
$318$		0			0
$319$	−9.82264	+	17.0133i	−0.549962	+	0.952562i
$320$	3.47935	+	2.68993i	0.194501	+	0.150371i
$321$		0			0
$322$	−4.18878	−	7.72634i	−0.233432	−	0.430572i
$323$			27.9947i			1.55767i
$324$		0			0
$325$	−16.1370	−	9.31667i	−0.895117	−	0.516796i
$326$	−9.79064	+	3.31687i	−0.542253	+	0.183704i
$327$		0			0
$328$	−14.6799	−	9.84739i	−0.810561	−	0.543731i
$329$	−4.39618	−	5.28607i	−0.242369	−	0.291430i
$330$		0			0
$331$	−25.5615	+	14.7579i	−1.40499	+	0.811169i	−0.994899	−	0.100878i	$-0.967835\pi$
$331$	−25.5615	+	14.7579i	−1.40499	+	0.811169i	−0.410086	+	0.912047i	$0.634501\pi$
$332$	0.843961	−	2.03055i	0.0463184	−	0.111441i
$333$		0			0
$334$	2.61943	+	0.522685i	0.143329	+	0.0286001i
$335$	1.47062			0.0803486
$336$		0			0
$337$	−3.28431			−0.178908			−0.0894538	−	0.995991i	$-0.528512\pi$
$337$	−3.28431			−0.178908			−0.0894538	+	0.995991i	$0.528512\pi$
$338$	3.78949	+	0.756160i	0.206121	+	0.0411297i
$339$		0			0
$340$	−1.77869	+	4.27947i	−0.0964628	+	0.232087i
$341$	−1.79342	+	1.03543i	−0.0971192	+	0.0560718i
$342$		0			0
$343$	−16.1595	+	9.04831i	−0.872529	+	0.488563i
$344$	8.43018	−	12.5672i	0.454525	−	0.677578i
$345$		0			0
$346$	−22.1712	+	7.51115i	−1.19193	+	0.403802i
$347$	27.4329	+	15.8384i	1.47267	+	0.850248i	0.999528	−	0.0307361i	$-0.00978515\pi$
$347$	27.4329	+	15.8384i	1.47267	+	0.850248i	0.473146	+	0.880984i	$0.343118\pi$
$348$		0			0
$349$			28.4807i			1.52454i	0.647260	+	0.762269i	$0.275915\pi$
$349$			28.4807i			1.52454i	−0.647260	+	0.762269i	$0.724085\pi$
$350$	−9.19363	+	14.9815i	−0.491420	+	0.800796i
$351$		0			0
$352$	−0.843679	−	13.4978i	−0.0449682	−	0.719435i
$353$	10.1196	−	17.5277i	0.538613	−	0.932905i	−0.460366	−	0.887729i	$-0.652282\pi$
$353$	10.1196	−	17.5277i	0.538613	−	0.932905i	0.998979	−	0.0451760i	$-0.0143849\pi$
$354$		0			0
$355$	−4.17386	+	2.40978i	−0.221525	+	0.127898i
$356$	−1.65423	−	12.6837i	−0.0876740	−	0.672237i
$357$		0			0
$358$	5.88954	+	5.17130i	0.311272	+	0.273312i
$359$	12.5611	+	21.7564i	0.662948	+	1.14826i	0.979837	+	0.199797i	$0.0640283\pi$
$359$	12.5611	+	21.7564i	0.662948	+	1.14826i	−0.316889	+	0.948463i	$0.602638\pi$
$360$		0			0
$361$	12.5550	−	21.7460i	0.660791	−	1.14452i
$362$	−2.76314	+	13.8474i	−0.145228	+	0.727806i
$363$		0			0
$364$	4.65729	−	20.4650i	0.244108	−	1.07266i
$365$			2.56353i			0.134181i
$366$		0			0
$367$	15.1912	−	26.3118i	0.792972	−	1.37347i	−0.131147	−	0.991363i	$-0.541866\pi$
$367$	15.1912	−	26.3118i	0.792972	−	1.37347i	0.924119	−	0.382104i	$-0.124801\pi$
$368$	2.45372	−	9.06952i	0.127909	−	0.472781i
$369$		0			0
$370$	0.136117	−	0.155022i	0.00707639	−	0.00805923i
$371$	−26.8544	−	9.90778i	−1.39421	−	0.514386i
$372$		0			0
$373$	4.86327	−	2.80781i	0.251811	−	0.145383i	−0.368782	−	0.929516i	$-0.620225\pi$
$373$	4.86327	−	2.80781i	0.251811	−	0.145383i	0.620593	+	0.784133i	$0.286892\pi$
$374$	13.4978	−	4.57278i	0.697956	−	0.236453i
$375$		0			0
$376$	0.494024	−	7.33331i	0.0254774	−	0.378187i
$377$	−32.5928			−1.67861
$378$		0			0
$379$			8.07009i			0.414533i	0.978285	+	0.207266i	$0.0664566\pi$
$379$			8.07009i			0.414533i	−0.978285	+	0.207266i	$0.933543\pi$
$380$	5.79861	−	4.43829i	0.297462	−	0.227679i
$381$		0			0
$382$	−0.0764199	−	0.225574i	−0.00390998	−	0.0115414i
$383$	−12.8166	−	22.1990i	−0.654898	−	1.13432i	−0.981919	−	0.189299i	$-0.939378\pi$
$383$	−12.8166	−	22.1990i	−0.654898	−	1.13432i	0.327022	−	0.945017i	$-0.393955\pi$
$384$		0			0
$385$	−3.42706	+	0.588798i	−0.174659	+	0.0300079i
$386$	7.01439	−	7.98862i	0.357023	−	0.406610i
$387$		0			0
$388$	23.9118	+	9.93853i	1.21394	+	0.504552i
$389$	22.9905	+	13.2736i	1.16566	+	0.672997i	0.952655	−	0.304053i	$-0.0983401\pi$
$389$	22.9905	+	13.2736i	1.16566	+	0.672997i	0.213010	+	0.977050i	$0.431673\pi$
$390$		0			0
$391$	9.90081			0.500705
$392$	−19.1807	−	4.90928i	−0.968771	−	0.247956i
$393$		0			0
$394$	0.372437	−	1.86646i	0.0187631	−	0.0940310i
$395$	−0.293506	−	0.169456i	−0.0147679	−	0.00852626i
$396$		0			0
$397$	29.5283	−	17.0482i	1.48198	−	0.855624i	0.482192	−	0.876065i	$-0.339841\pi$
$397$	29.5283	−	17.0482i	1.48198	−	0.855624i	0.999791	+	0.0204418i	$0.00650729\pi$
$398$	−11.9074	+	13.5613i	−0.596866	+	0.679765i
$399$		0			0
$400$	−18.1626	+	4.81955i	−0.908129	+	0.240978i
$401$	9.17676	+	15.8946i	0.458266	+	0.793739i	0.998869	−	0.0475379i	$-0.0151375\pi$
$401$	9.17676	+	15.8946i	0.458266	+	0.793739i	−0.540604	+	0.841277i	$0.681804\pi$
$402$		0			0
$403$	−2.97540	−	1.71785i	−0.148215	−	0.0855721i
$404$	−19.3094	−	25.2277i	−0.960679	−	1.25512i
$405$		0			0
$406$	−0.824123	+	30.7349i	−0.0409005	+	1.52535i
$407$	−0.634401			−0.0314461
$408$		0			0
$409$	−5.87455	+	10.1750i	−0.290478	+	0.503122i	−0.973923	−	0.226880i	$-0.927148\pi$
$409$	−5.87455	+	10.1750i	−0.290478	+	0.503122i	0.683445	+	0.730002i	$0.260481\pi$
$410$	−4.60190	+	1.55903i	−0.227271	+	0.0769949i
$411$		0			0
$412$	−4.85725	−	37.2427i	−0.239299	−	1.83482i
$413$	−9.36933	−	3.45677i	−0.461035	−	0.170096i
$414$		0			0
$415$	−0.302212	−	0.523446i	−0.0148350	−	0.0256949i
$416$	18.6936	−	12.4090i	0.916532	−	0.608403i
$417$		0			0
$418$	−22.0211	−	4.39413i	−1.07709	−	0.214924i
$419$		−	11.0841i		−	0.541495i	−0.962650	−	0.270748i	$-0.912729\pi$
$419$		−	11.0841i		−	0.541495i	0.962650	−	0.270748i	$-0.0872709\pi$
$420$		0			0
$421$		−	0.137270i		−	0.00669012i	−0.999994	−	0.00334506i	$-0.998935\pi$
$421$		−	0.137270i		−	0.00669012i	0.999994	−	0.00334506i	$-0.00106477\pi$
$422$	2.34219	−	11.7378i	0.114016	−	0.571389i
$423$		0			0
$424$	−13.4842	−	27.4689i	−0.654852	−	1.33401i
$425$	−9.90081	−	17.1487i	−0.480260	−	0.831834i
$426$		0			0
$427$	14.5176	−	12.0736i	0.702555	−	0.584283i
$428$	−0.672132	+	0.0876603i	−0.0324887	+	0.00423722i
$429$		0			0
$430$	−1.33466	−	3.93961i	−0.0643629	−	0.189985i
$431$	6.23008	−	10.7908i	0.300092	−	0.519775i	−0.676064	−	0.736843i	$-0.736316\pi$
$431$	6.23008	−	10.7908i	0.300092	−	0.519775i	0.976157	+	0.217067i	$0.0696491\pi$
$432$		0			0
$433$	−14.1563			−0.680310			−0.340155	−	0.940369i	$-0.610480\pi$
$433$	−14.1563			−0.680310			−0.340155	+	0.940369i	$0.610480\pi$
$434$	−1.69516	+	2.76236i	−0.0813703	+	0.132597i
$435$		0			0
$436$	9.48744	+	12.3953i	0.454366	+	0.593628i
$437$	−13.5102	−	7.80014i	−0.646282	−	0.373131i
$438$		0			0
$439$	2.72948	+	4.72760i	0.130271	+	0.225636i	0.923781	−	0.382921i	$-0.125082\pi$
$439$	2.72948	+	4.72760i	0.130271	+	0.225636i	−0.793510	+	0.608557i	$0.791749\pi$
$440$	−3.08712	−	2.07086i	−0.147173	−	0.0987246i
$441$		0			0
$442$	17.7670	+	15.6003i	0.845090	+	0.742030i
$443$	−28.8691	+	16.6676i	−1.37161	+	0.791900i	−0.991131	−	0.132889i	$-0.957575\pi$
$443$	−28.8691	+	16.6676i	−1.37161	+	0.791900i	−0.380480	+	0.924789i	$0.624241\pi$
$444$		0			0
$445$	−3.04485	−	1.75794i	−0.144340	−	0.0833346i
$446$	8.04610	+	1.60553i	0.380994	+	0.0760241i
$447$		0			0
$448$	−11.2290	−	17.9418i	−0.530521	−	0.847672i
$449$	26.9716			1.27287			0.636435	−	0.771330i	$-0.280408\pi$
$449$	26.9716			1.27287			0.636435	+	0.771330i	$0.280408\pi$
$450$		0			0
$451$	12.9397	+	7.47074i	0.609307	+	0.351783i
$452$	−4.64904	−	1.93229i	−0.218672	−	0.0908873i
$453$		0			0
$454$	12.1392	+	10.6588i	0.569723	+	0.500244i
$455$	−3.68884	−	4.43555i	−0.172935	−	0.207942i
$456$		0			0
$457$	−9.54668	−	16.5353i	−0.446575	−	0.773491i	0.551585	−	0.834118i	$-0.314023\pi$
$457$	−9.54668	−	16.5353i	−0.446575	−	0.773491i	−0.998160	+	0.0606278i	$0.980690\pi$
$458$	−24.7866	+	8.39720i	−1.15820	+	0.392375i
$459$		0			0
$460$	−1.56968	−	2.05078i	−0.0731865	−	0.0956180i
$461$			18.9177i			0.881087i	0.897731	+	0.440543i	$0.145214\pi$
$461$			18.9177i			0.881087i	−0.897731	+	0.440543i	$0.854786\pi$
$462$		0			0
$463$	0.860370			0.0399848			0.0199924	−	0.999800i	$-0.493636\pi$
$463$	0.860370			0.0399848			0.0199924	+	0.999800i	$0.493636\pi$
$464$	−23.2979	+	23.1854i	−1.08158	+	1.07636i
$465$		0			0
$466$	5.01479	+	14.8025i	0.232306	+	0.685714i
$467$	16.1842	−	9.34394i	0.748914	−	0.432386i	−0.0763871	−	0.997078i	$-0.524338\pi$
$467$	16.1842	−	9.34394i	0.748914	−	0.432386i	0.825302	+	0.564692i	$0.191005\pi$
$468$		0			0
$469$	−6.64022	−	2.44987i	−0.306617	−	0.113125i
$470$	−1.51811	−	1.33297i	−0.0700253	−	0.0614855i
$471$		0			0
$472$	−4.70457	−	9.58375i	−0.216545	−	0.441128i
$473$	−6.39558	+	11.0775i	−0.294069	+	0.509342i
$474$		0			0
$475$			31.2006i			1.43158i
$476$	15.1603	−	16.3598i	0.694870	−	0.749849i
$477$		0			0
$478$	−31.3581	−	6.25725i	−1.43429	−	0.286200i
$479$	−9.27364	+	16.0624i	−0.423723	+	0.733911i	−0.996300	−	0.0859405i	$-0.972610\pi$
$479$	−9.27364	+	16.0624i	−0.423723	+	0.733911i	0.572577	+	0.819851i	$0.305944\pi$
$480$		0			0
$481$	−0.526255	−	0.911501i	−0.0239952	−	0.0415609i
$482$	12.9977	−	14.8029i	0.592028	−	0.674255i
$483$		0			0
$484$	−1.36680	−	10.4799i	−0.0621271	−	0.476357i
$485$	6.16413	−	3.55886i	0.279899	−	0.161600i
$486$		0			0
$487$	11.4588	−	19.8471i	0.519246	−	0.899360i	−0.480504	−	0.876993i	$-0.659546\pi$
$487$	11.4588	−	19.8471i	0.519246	−	0.899360i	0.999750	−	0.0223676i	$-0.00712041\pi$
$488$	20.1401	+	1.35678i	0.911701	+	0.0614187i
$489$		0			0
$490$	−4.27598	+	3.36641i	−0.193169	+	0.152079i
$491$			24.7987i			1.11915i	0.828780	+	0.559575i	$0.189036\pi$
$491$			24.7987i			1.11915i	−0.828780	+	0.559575i	$0.810964\pi$
$492$		0			0
$493$	−29.9959	−	17.3181i	−1.35095	−	0.779969i
$494$	−11.9538	−	35.2849i	−0.537826	−	1.58754i
$495$		0			0
$496$	−3.34889	+	0.888650i	−0.150370	+	0.0399016i
$497$	22.8604	−	3.92760i	1.02543	−	0.176177i
$498$		0			0
$499$	−33.9707	+	19.6130i	−1.52074	+	0.877997i	−0.521035	+	0.853535i	$0.674454\pi$
$499$	−33.9707	+	19.6130i	−1.52074	+	0.877997i	−0.999701	+	0.0244624i	$0.992213\pi$
$500$	−4.09228	+	9.84590i	−0.183012	+	0.440322i
$501$		0			0
$502$	−0.195387	+	0.979178i	−0.00872054	+	0.0437028i
$503$	−7.59396			−0.338598			−0.169299	−	0.985565i	$-0.554150\pi$
$503$	−7.59396			−0.338598			−0.169299	+	0.985565i	$0.554150\pi$
$504$		0			0
$505$	−8.73240			−0.388587
$506$	−1.55406	+	7.78815i	−0.0690864	+	0.346226i
$507$		0			0
$508$	−9.79229	−	4.06999i	−0.434463	−	0.180577i
$509$	3.79222	−	2.18944i	0.168087	−	0.0970451i	−0.413596	−	0.910460i	$-0.635728\pi$
$509$	3.79222	−	2.18944i	0.168087	−	0.0970451i	0.581684	+	0.813415i	$0.302394\pi$
$510$		0			0
$511$	4.27052	−	11.5749i	0.188917	−	0.512046i
$512$	4.53521	−	22.1683i	0.200430	−	0.979708i
$513$		0			0
$514$	−9.43110	−	27.8385i	−0.415988	−	1.22790i
$515$	−8.94047	−	5.16178i	−0.393964	−	0.227455i
$516$		0			0
$517$			6.21259i			0.273230i
$518$	−0.872850	+	0.473210i	−0.0383508	+	0.0207916i
$519$		0			0
$520$	0.414537	−	6.15339i	0.0181786	−	0.269844i
$521$	−5.37827	+	9.31544i	−0.235626	+	0.408117i	−0.959455	−	0.281863i	$-0.909048\pi$
$521$	−5.37827	+	9.31544i	−0.235626	+	0.408117i	0.723828	+	0.689980i	$0.242381\pi$
$522$		0			0
$523$	2.43561	−	1.40620i	0.106502	−	0.0614889i	−0.445803	−	0.895131i	$-0.647082\pi$
$523$	2.43561	−	1.40620i	0.106502	−	0.0614889i	0.552305	+	0.833642i	$0.313748\pi$
$524$	19.9098	−	2.59666i	0.869762	−	0.113435i
$525$		0			0
$526$	21.2551	−	24.2073i	0.926768	−	1.05549i
$527$	−1.82555	−	3.16195i	−0.0795223	−	0.137737i
$528$		0			0
$529$	8.74135	−	15.1405i	0.380059	−	0.658281i
$530$	−8.24841	−	1.64590i	−0.358288	−	0.0714934i
$531$		0			0
$532$	−33.5758	+	10.3802i	−1.45570	+	0.450039i
$533$			24.7889i			1.07372i
$534$		0			0
$535$	−0.0931564	+	0.161352i	−0.00402750	+	0.00697584i
$536$	−3.33421	−	6.79218i	−0.144016	−	0.293377i
$537$		0			0
$538$	3.18280	+	2.79465i	0.137220	+	0.120486i
$539$	16.4549	+	3.05049i	0.708762	+	0.131394i
$540$		0			0
$541$	27.0699	−	15.6288i	1.16383	−	0.671935i	0.211608	−	0.977355i	$-0.432130\pi$
$541$	27.0699	−	15.6288i	1.16383	−	0.671935i	0.952218	+	0.305419i	$0.0987966\pi$
$542$	−11.4283	−	33.7339i	−0.490889	−	1.44899i
$543$		0			0
$544$	23.7977	−	1.48748i	1.02032	−	0.0637750i
$545$	4.29055			0.183787
$546$		0			0
$547$			29.4711i			1.26010i	0.776556	+	0.630048i	$0.216965\pi$
$547$			29.4711i			1.26010i	−0.776556	+	0.630048i	$0.783035\pi$
$548$	5.16111	−	3.95034i	0.220472	−	0.168750i
$549$		0			0
$550$	15.0435	−	5.09644i	0.641458	−	0.217313i
$551$	27.2874	+	47.2632i	1.16248	+	2.01348i
$552$		0			0
$553$	1.04296	+	1.25408i	0.0443512	+	0.0533289i
$554$	−10.0369	−	8.81290i	−0.426428	−	0.374424i
$555$		0			0
$556$	11.7711	−	28.3210i	0.499207	−	1.20108i
$557$	19.3751	+	11.1862i	0.820950	+	0.473976i	0.850744	−	0.525580i	$-0.176152\pi$
$557$	19.3751	+	11.1862i	0.820950	+	0.473976i	−0.0297941	+	0.999556i	$0.509485\pi$
$558$		0			0
$559$	−21.2213			−0.897567
$560$	−5.79215	−	0.546498i	−0.244763	−	0.0230938i
$561$		0			0
$562$	37.2271	+	7.42835i	1.57033	+	0.313346i
$563$	28.0528	+	16.1963i	1.18229	+	0.682593i	0.956542	−	0.291594i	$-0.0941856\pi$
$563$	28.0528	+	16.1963i	1.18229	+	0.682593i	0.225743	+	0.974187i	$0.427519\pi$
$564$		0			0
$565$	−1.19846	+	0.691928i	−0.0504194	+	0.0291097i
$566$	−13.7962	−	12.1137i	−0.579896	−	0.509177i
$567$		0			0
$568$	20.5928	+	13.8138i	0.864053	+	0.579614i
$569$	−18.5288	−	32.0928i	−0.776767	−	1.34540i	−0.933796	−	0.357806i	$-0.883525\pi$
$569$	−18.5288	−	32.0928i	−0.776767	−	1.34540i	0.157029	−	0.987594i	$-0.449808\pi$
$570$		0			0
$571$	−19.4303	−	11.2181i	−0.813132	−	0.469462i	0.0349102	−	0.999390i	$-0.488885\pi$
$571$	−19.4303	−	11.2181i	−0.813132	−	0.469462i	−0.848042	+	0.529928i	$0.822219\pi$
$572$	−15.0602	+	11.5272i	−0.629699	+	0.481976i
$573$		0			0
$574$	23.3758	+	0.626798i	0.975689	+	0.0261620i
$575$	11.0346			0.460175
$576$		0			0
$577$	−4.78431	+	8.28667i	−0.199173	+	0.344978i	−0.948261	−	0.317493i	$-0.897159\pi$
$577$	−4.78431	+	8.28667i	−0.199173	+	0.344978i	0.749087	+	0.662471i	$0.230492\pi$
$578$	0.348046	+	1.02735i	0.0144768	+	0.0427323i
$579$		0			0
$580$	1.16841	+	8.95874i	0.0485156	+	0.371991i
$581$	0.492563	+	2.86693i	0.0204350	+	0.118940i
$582$		0			0
$583$	12.9325	+	22.3997i	0.535609	+	0.927703i
$584$	11.8398	−	5.81206i	0.489936	−	0.240505i
$585$		0			0
$586$	−2.64645	+	13.2627i	−0.109324	+	0.547876i
$587$			23.6894i			0.977766i	0.872349	+	0.488883i	$0.162595\pi$
$587$			23.6894i			0.977766i	−0.872349	+	0.488883i	$0.837405\pi$
$588$		0			0
$589$			5.75289i			0.237044i
$590$	−2.87782	−	0.574245i	−0.118478	−	0.0236413i
$591$		0			0
$592$	−1.02459	−	0.277198i	−0.0421104	−	0.0113928i
$593$	−3.72404	−	6.45023i	−0.152928	−	0.264879i	0.779375	−	0.626558i	$-0.215537\pi$
$593$	−3.72404	−	6.45023i	−0.152928	−	0.264879i	−0.932303	+	0.361679i	$0.882204\pi$
$594$		0			0
$595$	−1.03810	−	6.04219i	−0.0425579	−	0.247706i
$596$	−14.6422	+	1.90965i	−0.599766	+	0.0782222i
$597$		0			0
$598$	−12.4791	+	4.22766i	−0.510308	+	0.172882i
$599$	0.837627	−	1.45081i	0.0342245	−	0.0592786i	−0.848406	−	0.529346i	$-0.822437\pi$
$599$	0.837627	−	1.45081i	0.0342245	−	0.0592786i	0.882630	+	0.470068i	$0.155771\pi$
$600$		0			0
$601$	−8.27385			−0.337497			−0.168749	−	0.985659i	$-0.553973\pi$
$601$	−8.27385			−0.337497			−0.168749	+	0.985659i	$0.553973\pi$
$602$	−0.536591	+	20.0117i	−0.0218698	+	0.815615i
$603$		0			0
$604$	−13.2311	+	10.1272i	−0.538366	+	0.412068i
$605$	−2.51579	−	1.45249i	−0.102281	−	0.0590522i
$606$		0			0
$607$	13.2647	+	22.9751i	0.538397	+	0.932531i	0.998991	+	0.0449200i	$0.0143033\pi$
$607$	13.2647	+	22.9751i	0.538397	+	0.932531i	−0.460593	+	0.887611i	$0.652363\pi$
$608$	−33.6453	−	16.7188i	−1.36450	−	0.678036i
$609$		0			0
$610$	3.66087	−	4.16932i	0.148224	−	0.168811i
$611$	−8.92620	+	5.15354i	−0.361115	+	0.208490i
$612$		0			0
$613$	27.3692	+	15.8016i	1.10543	+	0.638220i	0.937642	−	0.347603i	$-0.113004\pi$
$613$	27.3692	+	15.8016i	1.10543	+	0.638220i	0.167788	+	0.985823i	$0.446338\pi$
$614$	−3.38221	+	16.9499i	−0.136495	+	0.684042i
$615$		0			0
$616$	10.4893	+	14.4932i	0.422626	+	0.583948i
$617$	−10.1113			−0.407064			−0.203532	−	0.979068i	$-0.565242\pi$
$617$	−10.1113			−0.407064			−0.203532	+	0.979068i	$0.565242\pi$
$618$		0			0
$619$	−4.79105	−	2.76611i	−0.192568	−	0.111179i	0.400616	−	0.916246i	$-0.368796\pi$
$619$	−4.79105	−	2.76611i	−0.192568	−	0.111179i	−0.593184	+	0.805067i	$0.702129\pi$
$620$	−0.365519	+	0.879428i	−0.0146796	+	0.0353187i
$621$		0			0
$622$	−29.7499	+	33.8819i	−1.19286	+	1.35854i
$623$	10.8197	+	13.0099i	0.433483	+	0.521230i
$624$		0			0
$625$	−10.2791	−	17.8039i	−0.411163	−	0.712155i
$626$	9.76682	+	28.8294i	0.390360	+	1.15226i
$627$		0			0
$628$	−8.67544	−	11.3344i	−0.346188	−	0.452293i
$629$		−	1.11850i		−	0.0445975i
$630$		0			0
$631$	35.5582			1.41555			0.707774	−	0.706439i	$-0.249700\pi$
$631$	35.5582			1.41555			0.707774	+	0.706439i	$0.249700\pi$
$632$	−0.117204	+	1.73978i	−0.00466211	+	0.0692046i
$633$		0			0
$634$	−31.0073	+	10.5046i	−1.23146	+	0.417192i
$635$	−2.52431	+	1.45741i	−0.100174	+	0.0578357i
$636$		0			0
$637$	9.26693	+	26.1727i	0.367169	+	1.03700i
$638$	18.3310	−	20.8770i	0.725731	−	0.826528i
$639$		0			0
$640$	−4.08100	−	4.69345i	−0.161316	−	0.185525i
$641$	4.73300	−	8.19779i	0.186942	−	0.323793i	−0.757287	−	0.653082i	$-0.773476\pi$
$641$	4.73300	−	8.19779i	0.186942	−	0.323793i	0.944229	+	0.329289i	$0.106809\pi$
$642$		0			0
$643$		−	13.0085i		−	0.513007i	−0.966543	−	0.256503i	$-0.917430\pi$
$643$		−	13.0085i		−	0.513007i	0.966543	−	0.256503i	$-0.0825705\pi$
$644$	3.67113	+	11.8746i	0.144663	+	0.467927i
$645$		0			0
$646$	7.74722	−	38.8251i	0.304810	−	1.52755i
$647$	13.7610	−	23.8347i	0.540999	−	0.937039i	−0.457848	−	0.889031i	$-0.651379\pi$
$647$	13.7610	−	23.8347i	0.540999	−	0.937039i	0.998847	−	0.0480078i	$-0.0152872\pi$
$648$		0			0
$649$	4.51207	+	7.81514i	0.177114	+	0.306771i
$650$	19.8016	+	17.3868i	0.776683	+	0.681965i
$651$		0			0
$652$	14.4963	−	1.89062i	0.567718	−	0.0740425i
$653$	−30.4390	+	17.5740i	−1.19117	+	0.687723i	−0.958572	−	0.284850i	$-0.908056\pi$
$653$	−30.4390	+	17.5740i	−1.19117	+	0.687723i	−0.232598	+	0.972573i	$0.574723\pi$
$654$		0			0
$655$	2.75946	−	4.77952i	0.107821	−	0.186751i
$656$	17.6340	+	17.7196i	0.688491	+	0.691833i
$657$		0			0
$658$	4.63408	+	8.54769i	0.180655	+	0.333224i
$659$		−	3.86719i		−	0.150644i	−0.997159	−	0.0753222i	$-0.976001\pi$
$659$		−	3.86719i		−	0.150644i	0.997159	−	0.0753222i	$-0.0239985\pi$
$660$		0			0
$661$	14.4295	+	8.33085i	0.561241	+	0.324033i	0.753643	−	0.657284i	$-0.228295\pi$
$661$	14.4295	+	8.33085i	0.561241	+	0.324033i	−0.192403	+	0.981316i	$0.561628\pi$
$662$	39.5346	−	13.3935i	1.53656	−	0.520553i
$663$		0			0
$664$	−1.73240	+	2.58255i	−0.0672300	+	0.100222i
$665$	−3.34366	+	9.06278i	−0.129662	+	0.351439i
$666$		0			0
$667$	16.7154	−	9.65067i	0.647225	−	0.373675i
$668$	−3.48817	−	1.44980i	−0.134961	−	0.0560943i
$669$		0			0
$670$	−2.03956	−	0.406978i	−0.0787953	−	0.0157229i
$671$	−17.0622			−0.658679
$672$		0			0
$673$	−3.95795			−0.152568			−0.0762838	−	0.997086i	$-0.524306\pi$
$673$	−3.95795			−0.152568			−0.0762838	+	0.997086i	$0.524306\pi$
$674$	4.55492	+	0.908896i	0.175449	+	0.0350094i
$675$		0			0
$676$	−5.04628	−	2.09740i	−0.194088	−	0.0806691i
$677$	35.6839	−	20.6021i	1.37144	−	0.791804i	0.380334	−	0.924849i	$-0.375809\pi$
$677$	35.6839	−	20.6021i	1.37144	−	0.791804i	0.991110	+	0.133045i	$0.0424756\pi$
$678$		0			0
$679$	−33.7612	+	5.80045i	−1.29564	+	0.222601i
$680$	3.65111	−	5.44285i	0.140014	−	0.208724i
$681$		0			0
$682$	2.77379	−	0.939703i	0.106214	−	0.0359831i
$683$	−28.6643	−	16.5493i	−1.09681	−	0.633242i	−0.161427	−	0.986885i	$-0.551610\pi$
$683$	−28.6643	−	16.5493i	−1.09681	−	0.633242i	−0.935381	+	0.353642i	$0.884943\pi$
$684$		0			0
$685$		−	1.78648i		−	0.0682580i
$686$	24.9151	−	8.07690i	0.951264	−	0.308378i
$687$		0			0
$688$	−15.1694	+	15.0962i	−0.578329	+	0.575536i
$689$	−21.4558	+	37.1626i	−0.817402	+	1.41578i
$690$		0			0
$691$	12.9010	−	7.44840i	0.490777	−	0.283350i	−0.234120	−	0.972208i	$-0.575221\pi$
$691$	12.9010	−	7.44840i	0.490777	−	0.283350i	0.724897	+	0.688857i	$0.241887\pi$
$692$	32.8273	−	4.28137i	1.24791	−	0.162753i
$693$		0			0
$694$	−33.6628	−	29.5575i	−1.27782	−	1.12199i
$695$	−4.21509	−	7.30075i	−0.159888	−	0.276933i
$696$		0			0
$697$	−13.1715	+	22.8138i	−0.498907	+	0.864133i
$698$	7.88172	−	39.4992i	0.298328	−	1.49506i
$699$		0			0
$700$	16.8964	−	18.2332i	0.638623	−	0.689152i
$701$		−	32.5746i		−	1.23032i	−0.788401	−	0.615162i	$-0.789090\pi$
$701$		−	32.5746i		−	1.23032i	0.788401	−	0.615162i	$-0.210910\pi$
$702$		0			0
$703$	−0.881187	+	1.52626i	−0.0332346	+	0.0575640i
$704$	−2.56529	+	18.9532i	−0.0966829	+	0.714325i
$705$		0			0
$706$	−18.8852	+	21.5082i	−0.710755	+	0.809471i
$707$	39.4289	+	14.5471i	1.48288	+	0.547100i
$708$		0			0
$709$	9.95635	−	5.74830i	0.373918	−	0.215882i	−0.301251	−	0.953545i	$-0.597404\pi$
$709$	9.95635	−	5.74830i	0.373918	−	0.215882i	0.675169	+	0.737663i	$0.264071\pi$
$710$	6.45548	−	2.18699i	0.242270	−	0.0820761i
$711$		0			0
$712$	−1.21588	+	18.0485i	−0.0455669	+	0.676397i
$713$	2.03461			0.0761967
$714$		0			0
$715$			5.21300i			0.194955i
$716$	−6.73694	−	8.80179i	−0.251771	−	0.328938i
$717$		0			0
$718$	−11.3998	−	33.6495i	−0.425435	−	1.25579i
$719$	−13.4887	−	23.3632i	−0.503045	−	0.871299i	−0.999994	−	0.00351948i	$-0.998880\pi$
$719$	−13.4887	−	23.3632i	−0.503045	−	0.871299i	0.496949	−	0.867780i	$-0.334454\pi$
$720$		0			0
$721$	31.7695	+	38.2004i	1.18316	+	1.42266i
$722$	−23.4302	+	26.6844i	−0.871981	+	0.993091i
$723$		0			0
$724$	7.66425	−	18.4400i	0.284840	−	0.685316i
$725$	−33.4309	−	19.3013i	−1.24159	−	0.716833i
$726$		0			0
$727$	−27.0230			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$727$	−27.0230			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$728$	−12.1225	+	27.0935i	−0.449291	+	1.00415i
$729$		0			0
$730$	0.709427	−	3.55528i	0.0262571	−	0.131587i
$731$	−19.5305	−	11.2759i	−0.722361	−	0.417055i
$732$		0			0
$733$	−17.9059	+	10.3380i	−0.661371	+	0.381843i	−0.792799	−	0.609483i	$-0.791377\pi$
$733$	−17.9059	+	10.3380i	−0.661371	+	0.381843i	0.131428	+	0.991326i	$0.458044\pi$
$734$	−28.3497	+	32.2872i	−1.04641	+	1.19174i
$735$		0			0
$736$	−5.91288	+	11.8992i	−0.217952	+	0.438611i
$737$	3.19779	+	5.53873i	0.117792	+	0.204022i
$738$		0			0
$739$	−9.30563	−	5.37261i	−0.342313	−	0.197635i	0.318981	−	0.947761i	$-0.396659\pi$
$739$	−9.30563	−	5.37261i	−0.342313	−	0.197635i	−0.661294	+	0.750126i	$0.729993\pi$
$740$	−0.231678	+	0.177327i	−0.00851664	+	0.00651869i
$741$		0			0
$742$	34.5017	+	21.1725i	1.26660	+	0.777266i
$743$	−11.8708			−0.435498			−0.217749	−	0.976005i	$-0.569871\pi$
$743$	−11.8708			−0.435498			−0.217749	+	0.976005i	$0.569871\pi$
$744$		0			0
$745$	−2.02938	+	3.51499i	−0.0743507	+	0.128779i
$746$	−7.52177	+	2.54822i	−0.275391	+	0.0932970i
$747$		0			0
$748$	−19.9852	+	2.60650i	−0.730732	+	0.0953030i
$749$	0.689416	−	0.573355i	0.0251907	−	0.0209499i
$750$		0			0
$751$	−8.53229	−	14.7784i	−0.311348	−	0.539270i	0.667307	−	0.744783i	$-0.267447\pi$
$751$	−8.53229	−	14.7784i	−0.311348	−	0.539270i	−0.978654	+	0.205513i	$0.934114\pi$
$752$	−2.71456	+	10.0337i	−0.0989899	+	0.365890i
$753$		0			0
$754$	45.2020	+	9.01968i	1.64616	+	0.328477i
$755$			4.57986i			0.166678i
$756$		0			0
$757$		−	46.3272i		−	1.68379i	−0.539641	−	0.841895i	$-0.681440\pi$
$757$		−	46.3272i		−	1.68379i	0.539641	−	0.841895i	$-0.318560\pi$
$758$	2.23331	−	11.1922i	0.0811173	−	0.406518i
$759$		0			0
$760$	−9.27018	+	4.55064i	−0.336265	+	0.165069i
$761$	−7.30474	−	12.6522i	−0.264796	−	0.458641i	0.702714	−	0.711473i	$-0.251971\pi$
$761$	−7.30474	−	12.6522i	−0.264796	−	0.458641i	−0.967510	+	0.252832i	$0.918638\pi$
$762$		0			0
$763$	−19.3729	−	7.14753i	−0.701346	−	0.258758i
$764$	0.0435595	+	0.333991i	0.00157593	+	0.0120834i
$765$		0			0
$766$	11.6317	+	34.3340i	0.420269	+	1.24054i
$767$	−7.48582	+	12.9658i	−0.270297	+	0.468169i
$768$		0			0
$769$	49.3177			1.77844			0.889221	−	0.457477i	$-0.151247\pi$
$769$	49.3177			1.77844			0.889221	+	0.457477i	$0.151247\pi$
$770$	4.91584	+	0.131813i	0.177155	+	0.00475021i
$771$		0			0
$772$	−11.9388	+	9.13804i	−0.429688	+	0.328885i
$773$	0.902744	+	0.521200i	0.0324695	+	0.0187462i	0.516147	−	0.856500i	$-0.327366\pi$
$773$	0.902744	+	0.521200i	0.0324695	+	0.0187462i	−0.483677	+	0.875246i	$0.660699\pi$
$774$		0			0
$775$	−2.03461	−	3.52404i	−0.0730853	−	0.126587i
$776$	−30.4123	−	20.4008i	−1.09174	−	0.732346i
$777$		0			0
$778$	−28.2116	−	24.7711i	−1.01143	−	0.888087i
$779$	35.9467	−	20.7538i	1.28792	−	0.743583i
$780$		0			0
$781$	−18.1517	−	10.4799i	−0.649517	−	0.374999i
$782$	−13.7312	−	2.73994i	−0.491025	−	0.0979800i
$783$		0			0
$784$	25.2426	+	12.1166i	0.901521	+	0.432735i
$785$	−3.92334			−0.140030
$786$		0			0
$787$	34.8899	+	20.1437i	1.24369	+	0.718045i	0.969844	−	0.243728i	$-0.0783705\pi$
$787$	34.8899	+	20.1437i	1.24369	+	0.718045i	0.273847	+	0.961773i	$0.411704\pi$
$788$	−1.03304	+	2.48548i	−0.0368007	+	0.0885415i
$789$		0			0
$790$	0.360161	+	0.316239i	0.0128140	+	0.0112513i
$791$	6.56399	−	1.12775i	0.233388	−	0.0400981i
$792$		0			0
$793$	−14.1536	−	24.5148i	−0.502610	−	0.870546i
$794$	−45.6699	+	15.4720i	−1.62076	+	0.549082i
$795$		0			0
$796$	20.2670	−	15.5125i	0.718346	−	0.549826i
$797$			32.2902i			1.14378i	0.820331	+	0.571889i	$0.193789\pi$
$797$			32.2902i			1.14378i	−0.820331	+	0.571889i	$0.806211\pi$
$798$		0			0
$799$	−10.9533			−0.387501
$800$	26.5229	−	1.65782i	0.937728	−	0.0586126i
$801$		0			0
$802$	−8.32834	−	24.5834i	−0.294084	−	0.868069i
$803$	−9.65489	+	5.57425i	−0.340714	+	0.196711i
$804$		0			0
$805$	3.20521	+	1.18254i	0.112969	+	0.0416792i
$806$	3.65111	+	3.20585i	0.128605	+	0.112921i
$807$		0			0
$808$	19.7982	+	40.3313i	0.696499	+	1.41885i
$809$	20.8131	−	36.0493i	0.731749	−	1.26743i	−0.224386	−	0.974500i	$-0.572038\pi$
$809$	20.8131	−	36.0493i	0.731749	−	1.26743i	0.956135	−	0.292926i	$-0.0946291\pi$
$810$		0			0
$811$		−	18.7227i		−	0.657444i	−0.944427	−	0.328722i	$-0.893382\pi$
$811$		−	18.7227i		−	0.657444i	0.944427	−	0.328722i	$-0.106618\pi$
$812$	9.64849	−	42.3973i	0.338596	−	1.48785i
$813$		0			0
$814$	0.879833	+	0.175563i	0.0308381	+	0.00615349i
$815$	2.00916	−	3.47997i	0.0703778	−	0.121898i
$816$		0			0
$817$	17.7670	+	30.7734i	0.621589	+	1.07662i
$818$	10.9631	−	12.4857i	0.383315	−	0.436554i
$819$		0			0
$820$	6.81369	−	0.888650i	0.237944	−	0.0310330i
$821$	16.2308	−	9.37088i	0.566460	−	0.327046i	−0.189274	−	0.981924i	$-0.560614\pi$
$821$	16.2308	−	9.37088i	0.566460	−	0.327046i	0.755734	+	0.654878i	$0.227280\pi$
$822$		0			0
$823$	10.2211	−	17.7035i	0.356286	−	0.617106i	−0.631051	−	0.775741i	$-0.717376\pi$
$823$	10.2211	−	17.7035i	0.356286	−	0.617106i	0.987337	+	0.158636i	$0.0507095\pi$
$824$	−3.57013	+	52.9951i	−0.124371	+	1.84617i
$825$		0			0
$826$	12.0375	+	7.38695i	0.418837	+	0.257025i
$827$		−	48.6254i		−	1.69087i	−0.534079	−	0.845435i	$-0.679341\pi$
$827$		−	48.6254i		−	1.69087i	0.534079	−	0.845435i	$-0.320659\pi$
$828$		0			0
$829$	−6.06173	−	3.49974i	−0.210532	−	0.121551i	0.391026	−	0.920379i	$-0.372120\pi$
$829$	−6.06173	−	3.49974i	−0.210532	−	0.121551i	−0.601559	+	0.798829i	$0.705453\pi$
$830$	0.274271	+	0.809586i	0.00952009	+	0.0281012i
$831$		0			0
$832$	−29.3598	+	12.0365i	−1.01787	+	0.417290i
$833$	−5.37827	+	29.0113i	−0.186346	+	1.00518i
$834$		0			0
$835$	−0.899200	+	0.519154i	−0.0311181	+	0.0179660i
$836$	29.3245	+	12.1882i	1.01421	+	0.421538i
$837$		0			0
$838$	−3.06741	+	15.3723i	−0.105962	+	0.531027i
$839$	−40.1867			−1.38740			−0.693700	−	0.720264i	$-0.744021\pi$
$839$	−40.1867			−1.38740			−0.693700	+	0.720264i	$0.744021\pi$
$840$		0			0
$841$	−38.5224			−1.32836
$842$	−0.0379879	+	0.190376i	−0.00130915	+	0.00656078i
$843$		0			0
$844$	−6.49663	+	15.6307i	−0.223623	+	0.538031i
$845$	−1.30086	+	0.751051i	−0.0447509	+	0.0258369i
$846$		0			0
$847$	8.93974	+	10.7494i	0.307173	+	0.369352i
$848$	11.0992	+	41.8275i	0.381148	+	1.43636i
$849$		0			0
$850$	8.98545	+	26.5230i	0.308198	+	0.909731i
$851$	0.539788	+	0.311647i	0.0185037	+	0.0106831i
$852$		0			0
$853$			30.8071i			1.05482i	0.849612	+	0.527408i	$0.176836\pi$
$853$			30.8071i			1.05482i	−0.849612	+	0.527408i	$0.823164\pi$
$854$	−23.4753	+	12.7270i	−0.803308	+	0.435508i
$855$		0			0
$856$	0.956420	+	0.0644313i	0.0326898	+	0.00220222i
$857$	6.84889	−	11.8626i	0.233954	−	0.405220i	−0.725014	−	0.688734i	$-0.758167\pi$
$857$	6.84889	−	11.8626i	0.233954	−	0.405220i	0.958968	+	0.283514i	$0.0915002\pi$
$858$		0			0
$859$	7.52869	−	4.34669i	0.256876	−	0.148307i	−0.366033	−	0.930602i	$-0.619284\pi$
$859$	7.52869	−	4.34669i	0.256876	−	0.148307i	0.622908	+	0.782295i	$0.285951\pi$
$860$	0.760758	+	5.83309i	0.0259416	+	0.198907i
$861$		0			0
$862$	−11.6266	+	13.2414i	−0.396002	+	0.451003i
$863$	−0.296174	−	0.512989i	−0.0100819	−	0.0174623i	0.860940	−	0.508706i	$-0.169876\pi$
$863$	−0.296174	−	0.512989i	−0.0100819	−	0.0174623i	−0.871022	+	0.491243i	$0.836543\pi$
$864$		0			0
$865$	4.54981	−	7.88049i	0.154698	−	0.267945i
$866$	19.6330	+	3.91761i	0.667158	+	0.133126i
$867$		0			0
$868$	3.11542	−	3.36192i	0.105744	−	0.114111i
$869$		−	1.47389i		−	0.0499984i
$870$		0			0
$871$	−5.30533	+	9.18911i	−0.179764	+	0.311361i
$872$	−9.72761	−	19.8163i	−0.329418	−	0.671063i
$873$		0			0
$874$	16.5784	+	14.5566i	0.560772	+	0.492385i
$875$	−2.38839	−	13.9015i	−0.0807422	−	0.469955i
$876$		0			0
$877$	−13.2310	+	7.63892i	−0.446779	+	0.257948i	−0.706469	−	0.707744i	$-0.749713\pi$
$877$	−13.2310	+	7.63892i	−0.446779	+	0.257948i	0.259690	+	0.965692i	$0.416380\pi$
$878$	−2.47713	−	7.31194i	−0.0835992	−	0.246766i
$879$		0			0
$880$	3.70835	+	3.72635i	0.125009	+	0.125615i
$881$	43.1280			1.45302			0.726509	−	0.687157i	$-0.241141\pi$
$881$	43.1280			1.45302			0.726509	+	0.687157i	$0.241141\pi$
$882$		0			0
$883$		−	20.2255i		−	0.680642i	−0.940309	−	0.340321i	$-0.889464\pi$
$883$		−	20.2255i		−	0.680642i	0.940309	−	0.340321i	$-0.110536\pi$
$884$	−20.3234	−	26.5524i	−0.683549	−	0.893054i
$885$		0			0
$886$	44.6503	−	15.1266i	1.50006	−	0.508188i
$887$	10.7820	+	18.6750i	0.362024	+	0.627044i	0.988294	−	0.152563i	$-0.0487525\pi$
$887$	10.7820	+	18.6750i	0.362024	+	0.627044i	−0.626270	+	0.779606i	$0.715419\pi$
$888$		0			0
$889$	13.8258	−	2.37538i	0.463701	−	0.0796678i
$890$	3.73633	+	3.28067i	0.125242	+	0.109968i
$891$		0			0
$892$	−10.7146	−	4.45333i	−0.358751	−	0.149109i
$893$	14.9465	+	8.62934i	0.500164	+	0.288770i
$894$		0			0
$895$	−3.04668			−0.101839
$896$	10.6080	+	27.9905i	0.354389	+	0.935098i
$897$		0			0
$898$	−37.4062	−	7.46410i	−1.24826	−	0.249080i
$899$	−6.16413	−	3.55886i	−0.205585	−	0.118695i
$900$		0			0
$901$	−39.4926	+	22.8011i	−1.31569	+	0.759614i
$902$	−15.8783	−	13.9419i	−0.528689	−	0.464214i
$903$		0			0
$904$	5.91288	+	3.96641i	0.196659	+	0.131921i
$905$	−2.74447	−	4.75356i	−0.0912293	−	0.158014i
$906$		0			0
$907$	27.3384	+	15.7838i	0.907757	+	0.524094i	0.879709	−	0.475513i	$-0.157737\pi$
$907$	27.3384	+	15.7838i	0.907757	+	0.524094i	0.0280482	+	0.999607i	$0.491071\pi$
$908$	−13.8859	−	18.1418i	−0.460819	−	0.602058i
$909$		0			0
$910$	3.88846	+	7.17238i	0.128901	+	0.237762i
$911$	−15.6873			−0.519744			−0.259872	−	0.965643i	$-0.583680\pi$
$911$	−15.6873			−0.519744			−0.259872	+	0.965643i	$0.583680\pi$
$912$		0			0
$913$	1.31429	−	2.27641i	0.0434965	−	0.0753382i
$914$	8.66406	+	25.5743i	0.286582	+	0.845924i
$915$		0			0
$916$	36.6997	−	4.78642i	1.21259	−	0.158148i
$917$	−20.4217	+	16.9838i	−0.674385	+	0.560855i
$918$		0			0
$919$	−7.79407	−	13.4997i	−0.257103	−	0.445315i	0.708362	−	0.705849i	$-0.249434\pi$
$919$	−7.79407	−	13.4997i	−0.257103	−	0.445315i	−0.965464	+	0.260535i	$0.916101\pi$
$920$	1.60941	+	3.27856i	0.0530607	+	0.108091i
$921$		0			0
$922$	5.23527	−	26.2365i	0.172414	−	0.864052i
$923$		−	34.7735i		−	1.14458i
$924$		0			0
$925$		−	1.24659i		−	0.0409875i
$926$	−1.19322	−	0.238098i	−0.0392118	−	0.00782438i
$927$		0			0
$928$	38.7276	−	25.7078i	1.27130	−	0.843899i
$929$	20.6926	+	35.8406i	0.678901	+	1.17589i	0.975312	+	0.220830i	$0.0708767\pi$
$929$	20.6926	+	35.8406i	0.678901	+	1.17589i	−0.296411	+	0.955060i	$0.595790\pi$
$930$		0			0
$931$	30.1949	−	35.3505i	0.989599	−	1.15857i
$932$	−2.85844	−	21.9170i	−0.0936315	−	0.717916i
$933$		0			0
$934$	−25.0312	+	8.48006i	−0.819047	+	0.277476i
$935$	−2.76992	+	4.79764i	−0.0905860	+	0.156900i
$936$		0			0
$937$	−23.9308			−0.781785			−0.390892	−	0.920436i	$-0.627834\pi$
$937$	−23.9308			−0.781785			−0.390892	+	0.920436i	$0.627834\pi$
$938$	8.53116	+	5.23527i	0.278552	+	0.170938i
$939$		0			0
$940$	1.73654	+	2.26879i	0.0566398	+	0.0739997i
$941$	−33.3285	−	19.2422i	−1.08648	−	0.627278i	−0.153841	−	0.988096i	$-0.549164\pi$
$941$	−33.3285	−	19.2422i	−1.08648	−	0.627278i	−0.932636	+	0.360818i	$0.882498\pi$
$942$		0			0
$943$	−7.33994	−	12.7132i	−0.239021	−	0.413997i
$944$	3.87244	+	14.5934i	0.126037	+	0.474974i
$945$		0			0
$946$	11.9354	−	13.5931i	0.388054	−	0.441951i
$947$	−8.36198	+	4.82779i	−0.271728	+	0.156882i	−0.629673	−	0.776861i	$-0.716811\pi$
$947$	−8.36198	+	4.82779i	−0.271728	+	0.156882i	0.357945	+	0.933743i	$0.383478\pi$
$948$		0			0
$949$	−16.0181	−	9.24804i	−0.519969	−	0.300204i
$950$	8.63440	−	43.2712i	0.280137	−	1.40390i
$951$		0			0
$952$	−25.5527	+	18.4935i	−0.828169	+	0.599378i
$953$	19.3777			0.627704			0.313852	−	0.949472i	$-0.398380\pi$
$953$	19.3777			0.627704			0.313852	+	0.949472i	$0.398380\pi$
$954$		0			0
$955$	0.0801777	+	0.0462906i	0.00259449	+	0.00149793i
$956$	41.7581	+	17.3560i	1.35055	+	0.561334i
$957$		0			0
$958$	17.3065	−	19.7101i	0.559146	−	0.636806i
$959$	−2.97606	+	8.06641i	−0.0961020	+	0.260478i
$960$		0			0
$961$	15.1249	+	26.1970i	0.487898	+	0.845065i
$962$	0.477602	+	1.40977i	0.0153985	+	0.0454529i
$963$		0			0
$964$	−22.1227	+	16.9328i	−0.712524	+	0.545370i
$965$			4.13255i			0.133031i
$966$		0			0
$967$	34.8845			1.12181			0.560905	−	0.827880i	$-0.310453\pi$
$967$	34.8845			1.12181			0.560905	+	0.827880i	$0.310453\pi$
$968$	−1.00461	+	14.9125i	−0.0322894	+	0.479305i
$969$		0			0
$970$	−9.53374	+	3.22983i	−0.306110	+	0.103704i
$971$	−38.4767	+	22.2146i	−1.23478	+	0.712899i	−0.968022	−	0.250865i	$-0.919285\pi$
$971$	−38.4767	+	22.2146i	−1.23478	+	0.712899i	−0.266755	+	0.963764i	$0.585952\pi$
$972$		0			0
$973$	6.87002	+	39.9865i	0.220243	+	1.28191i
$974$	−21.3843	+	24.3544i	−0.685197	+	0.780365i
$975$		0			0
$976$	−27.5563	−	7.45524i	−0.882056	−	0.238636i
$977$	−13.5436	+	23.4581i	−0.433297	+	0.750492i	−0.997155	−	0.0753795i	$-0.975983\pi$
$977$	−13.5436	+	23.4581i	−0.433297	+	0.750492i	0.563858	+	0.825872i	$0.309316\pi$
$978$		0			0
$979$		−	15.2902i		−	0.488678i
$980$	6.86186	−	3.48545i	0.219194	−	0.111339i
$981$		0			0
$982$	6.86276	−	34.3926i	0.219000	−	1.09751i
$983$	12.5444	−	21.7275i	0.400103	−	0.692999i	−0.593635	−	0.804735i	$-0.702308\pi$
$983$	12.5444	−	21.7275i	0.400103	−	0.692999i	0.993738	+	0.111736i	$0.0356410\pi$
$984$		0			0
$985$	0.369920	+	0.640721i	0.0117866	+	0.0204151i
$986$	36.8079	+	32.3191i	1.17220	+	1.02925i
$987$		0			0
$988$	6.81369	+	52.2437i	0.216772	+	1.66209i
$989$	10.8835	−	6.28360i	0.346076	−	0.199807i
$990$		0			0
$991$	−8.81972	+	15.2762i	−0.280168	+	0.485265i	−0.971426	−	0.237343i	$-0.923723\pi$
$991$	−8.81972	+	15.2762i	−0.280168	+	0.485265i	0.691258	+	0.722608i	$0.257057\pi$
$992$	4.89041	−	0.305675i	0.155271	−	0.00970519i
$993$		0			0
$994$	−32.7913	−	0.879264i	−1.04008	−	0.0278886i
$995$		−	7.01530i		−	0.222400i
$996$		0			0
$997$	−26.5529	−	15.3303i	−0.840939	−	0.485516i	0.0166442	−	0.999861i	$-0.494702\pi$
$997$	−26.5529	−	15.3303i	−0.840939	−	0.485516i	−0.857583	+	0.514345i	$0.828035\pi$
$998$	52.5407	−	17.7997i	1.66315	−	0.563440i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.c.109.1		12
3.2	odd	2		56.2.p.a.53.6	yes	12
4.3	odd	2		2016.2.cr.c.1873.4		12
7.2	even	3	inner	504.2.cj.c.37.4		12
8.3	odd	2		2016.2.cr.c.1873.3		12
8.5	even	2	inner	504.2.cj.c.109.4		12
12.11	even	2		224.2.t.a.81.5		12
21.2	odd	6		56.2.p.a.37.3	✓	12
21.5	even	6		392.2.p.g.373.3		12
21.11	odd	6		392.2.b.e.197.2		6
21.17	even	6		392.2.b.f.197.2		6
21.20	even	2		392.2.p.g.165.6		12
24.5	odd	2		56.2.p.a.53.3	yes	12
24.11	even	2		224.2.t.a.81.2		12
28.23	odd	6		2016.2.cr.c.1297.3		12
56.37	even	6	inner	504.2.cj.c.37.1		12
56.51	odd	6		2016.2.cr.c.1297.4		12
84.11	even	6		1568.2.b.f.785.2		6
84.23	even	6		224.2.t.a.177.2		12
84.47	odd	6		1568.2.t.g.177.5		12
84.59	odd	6		1568.2.b.e.785.5		6
84.83	odd	2		1568.2.t.g.753.2		12
168.5	even	6		392.2.p.g.373.6		12
168.11	even	6		1568.2.b.f.785.5		6
168.53	odd	6		392.2.b.e.197.1		6
168.59	odd	6		1568.2.b.e.785.2		6
168.83	odd	2		1568.2.t.g.753.5		12
168.101	even	6		392.2.b.f.197.1		6
168.107	even	6		224.2.t.a.177.5		12
168.125	even	2		392.2.p.g.165.3		12
168.131	odd	6		1568.2.t.g.177.2		12
168.149	odd	6		56.2.p.a.37.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	21.2	odd	6
56.2.p.a.37.6	yes	12	168.149	odd	6
56.2.p.a.53.3	yes	12	24.5	odd	2
56.2.p.a.53.6	yes	12	3.2	odd	2
224.2.t.a.81.2		12	24.11	even	2
224.2.t.a.81.5		12	12.11	even	2
224.2.t.a.177.2		12	84.23	even	6
224.2.t.a.177.5		12	168.107	even	6
392.2.b.e.197.1		6	168.53	odd	6
392.2.b.e.197.2		6	21.11	odd	6
392.2.b.f.197.1		6	168.101	even	6
392.2.b.f.197.2		6	21.17	even	6
392.2.p.g.165.3		12	168.125	even	2
392.2.p.g.165.6		12	21.20	even	2
392.2.p.g.373.3		12	21.5	even	6
392.2.p.g.373.6		12	168.5	even	6
504.2.cj.c.37.1		12	56.37	even	6	inner
504.2.cj.c.37.4		12	7.2	even	3	inner
504.2.cj.c.109.1		12	1.1	even	1	trivial
504.2.cj.c.109.4		12	8.5	even	2	inner
1568.2.b.e.785.2		6	168.59	odd	6
1568.2.b.e.785.5		6	84.59	odd	6
1568.2.b.f.785.2		6	84.11	even	6
1568.2.b.f.785.5		6	168.11	even	6
1568.2.t.g.177.2		12	168.131	odd	6
1568.2.t.g.177.5		12	84.47	odd	6
1568.2.t.g.753.2		12	84.83	odd	2
1568.2.t.g.753.5		12	168.83	odd	2
2016.2.cr.c.1297.3		12	28.23	odd	6
2016.2.cr.c.1297.4		12	56.51	odd	6
2016.2.cr.c.1873.3		12	8.3	odd	2
2016.2.cr.c.1873.4		12	4.3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38687 - 0.276739i) q^{2} +(1.84683 + 0.767603i) q^{4} +(0.476087 - 0.274869i) q^{5} +(-2.60755 + 0.447998i) q^{7} +(-2.34889 - 1.57566i) q^{8} +O(q^{10})\)	\(q+(-1.38687 - 0.276739i) q^{2} +(1.84683 + 0.767603i) q^{4} +(0.476087 - 0.274869i) q^{5} +(-2.60755 + 0.447998i) q^{7} +(-2.34889 - 1.57566i) q^{8} +(-0.736339 + 0.249456i) q^{10} +(2.07045 + 1.19538i) q^{11} +3.96641i q^{13} +(3.74031 + 0.100292i) q^{14} +(2.82157 + 2.83527i) q^{16} +(-2.10755 + 3.65038i) q^{17} +(5.75174 - 3.32077i) q^{19} +(1.09024 - 0.142191i) q^{20} +(-2.54065 - 2.23081i) q^{22} +(-1.17445 - 2.03420i) q^{23} +(-2.34889 + 4.06840i) q^{25} +(1.09766 - 5.50090i) q^{26} +(-5.15958 - 1.17418i) q^{28} +8.21720i q^{29} +(-0.433099 + 0.750150i) q^{31} +(-3.12853 - 4.71299i) q^{32} +(3.93310 - 4.47937i) q^{34} +(-1.11828 + 0.930019i) q^{35} +(-0.229805 + 0.132678i) q^{37} +(-8.89592 + 3.01376i) q^{38} +(-1.55138 - 0.104512i) q^{40} +6.24970 q^{41} +5.35027i q^{43} +(2.90620 + 3.79694i) q^{44} +(1.06587 + 3.14619i) q^{46} +(1.29930 + 2.25045i) q^{47} +(6.59859 - 2.33635i) q^{49} +(4.38350 - 4.99233i) q^{50} +(-3.04463 + 7.32529i) q^{52} +(9.36933 + 5.40939i) q^{53} +1.31429 q^{55} +(6.83074 + 3.05630i) q^{56} +(2.27402 - 11.3962i) q^{58} +(3.26891 + 1.88730i) q^{59} +(-6.18061 + 3.56837i) q^{61} +(0.808249 - 0.920507i) q^{62} +(3.03461 + 7.40210i) q^{64} +(1.09024 + 1.88835i) q^{65} +(2.31673 + 1.33757i) q^{67} +(-6.69432 + 5.12387i) q^{68} +(1.80828 - 0.980348i) q^{70} -8.76700 q^{71} +(-2.33159 + 4.03843i) q^{73} +(0.355428 - 0.120412i) q^{74} +(13.1715 - 1.71785i) q^{76} +(-5.93432 - 2.18944i) q^{77} +(-0.308249 - 0.533903i) q^{79} +(2.12264 + 0.574271i) q^{80} +(-8.66754 - 1.72953i) q^{82} -1.09948i q^{83} +2.31720i q^{85} +(1.48063 - 7.42014i) q^{86} +(-2.97977 - 6.07013i) q^{88} +(-3.19779 - 5.53873i) q^{89} +(-1.77694 - 10.3426i) q^{91} +(-0.607546 - 4.65834i) q^{92} +(-1.17917 - 3.48065i) q^{94} +(1.82555 - 3.16195i) q^{95} +12.9475 q^{97} +(-9.79797 + 1.41414i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40} + 8 q^{41} + 30 q^{44} - 4 q^{46} - 30 q^{47} - 12 q^{49} + 16 q^{50} - 32 q^{52} + 4 q^{55} + 40 q^{56} - 22 q^{58} + 28 q^{62} + 24 q^{64} - 8 q^{65} - 4 q^{68} - 48 q^{70} - 32 q^{71} - 10 q^{73} - 18 q^{74} + 52 q^{76} - 22 q^{79} - 36 q^{80} - 26 q^{82} - 40 q^{86} - 14 q^{88} + 10 q^{89} + 20 q^{92} + 42 q^{94} + 34 q^{95} + 40 q^{97} - 52 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

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