LMFDB - Embedded newform 504.2.cj.c.37.1

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			37.1
Root			$1.26950 + 0.623187i$ of defining polynomial
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.c.109.1

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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	0.602664	−	0.797995i	$-0.294106\pi$
$5$	0.476087	+	0.274869i	0.212913	+	0.122925i	−0.389752	+	0.920920i	$0.627439\pi$
$6$		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	−0.154263	−	0.988030i	$-0.549300\pi$
$11$	2.07045	−	1.19538i	0.624265	−	0.360419i	0.778527	+	0.627611i	$0.215967\pi$
$12$		0			0
$13$		−	3.96641i		−	1.10008i	−0.835137	−	0.550042i	$-0.814612\pi$
$13$		−	3.96641i		−	1.10008i	0.835137	−	0.550042i	$-0.185388\pi$
$14$	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	−0.999916	−	0.0129290i	$-0.995884\pi$
$17$	−2.10755	−	3.65038i	−0.511155	−	0.885347i	0.488761	−	0.872418i	$-0.337449\pi$
$18$		0			0
$19$	5.75174	+	3.32077i	1.31954	+	0.761837i	0.983655	−	0.180066i	$-0.0576310\pi$
$19$	5.75174	+	3.32077i	1.31954	+	0.761837i	0.335886	+	0.941903i	$0.390964\pi$
$20$	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	−0.962100	−	0.272695i	$-0.912085\pi$
$23$	−1.17445	+	2.03420i	−0.244889	+	0.424160i	0.717211	+	0.696856i	$0.245418\pi$
$24$		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	$-0.723751\pi$
$29$		−	8.21720i		−	1.52590i	0.646460	−	0.762948i	$-0.276249\pi$
$30$		0			0
$31$	−0.433099	−	0.750150i	−0.0777869	−	0.134731i	0.824508	−	0.565850i	$-0.191452\pi$
$31$	−0.433099	−	0.750150i	−0.0777869	−	0.134731i	−0.902295	+	0.431120i	$0.858119\pi$
$32$	−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	0.480991	−	0.876725i	$-0.340277\pi$
$37$	−0.229805	−	0.132678i	−0.0377797	−	0.0218121i	−0.518771	+	0.854913i	$0.673610\pi$
$38$	−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	$-0.866242\pi$
$43$		−	5.35027i		−	0.815908i	0.913003	−	0.407954i	$-0.133758\pi$
$44$	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	−0.755569	−	0.655069i	$-0.772639\pi$
$47$	1.29930	−	2.25045i	0.189522	−	0.328262i	0.945091	+	0.326807i	$0.105973\pi$
$48$		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	0.308863	−	0.951107i	$-0.400052\pi$
$53$	9.36933	−	5.40939i	1.28698	−	0.743037i	0.978114	+	0.208070i	$0.0667182\pi$
$54$		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	−0.271884	−	0.962330i	$-0.587647\pi$
$59$	3.26891	−	1.88730i	0.425575	−	0.245706i	0.697460	+	0.716624i	$0.254314\pi$
$60$		0			0
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	0.0490905	−	0.998794i	$-0.484368\pi$
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	−0.840436	+	0.541911i	$0.817701\pi$
$62$	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	−0.351762	−	0.936089i	$-0.614417\pi$
$67$	2.31673	−	1.33757i	0.283034	−	0.163410i	0.634796	+	0.772680i	$0.281084\pi$
$68$	−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	0.696709	−	0.717354i	$-0.254647\pi$
$73$	−2.33159	−	4.03843i	−0.272892	−	0.472663i	−0.969601	+	0.244691i	$0.921313\pi$
$74$	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	−0.882845	−	0.469665i	$-0.844375\pi$
$79$	−0.308249	+	0.533903i	−0.0346807	+	0.0600687i	0.848164	+	0.529734i	$0.177708\pi$
$80$	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	$0.0192190\pi$
$83$			1.09948i			0.120683i	−0.998178	+	0.0603416i	$0.980781\pi$
$84$		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	−0.984238	−	0.176847i	$-0.943410\pi$
$89$	−3.19779	+	5.53873i	−0.338965	+	0.587104i	0.645273	+	0.763952i	$0.276743\pi$
$90$		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	−0.990778	−	0.135495i	$-0.956737\pi$
$101$	−13.7565	+	7.94233i	−1.36882	+	0.790291i	−0.378047	+	0.925787i	$0.623404\pi$
$102$		0			0
$103$	−9.38954	+	16.2632i	−0.925179	+	1.60246i	−0.133906	+	0.990994i	$0.542752\pi$
$103$	−9.38954	+	16.2632i	−0.925179	+	1.60246i	−0.791273	+	0.611463i	$0.790581\pi$
$104$	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	0.485746	−	0.874100i	$-0.338548\pi$
$107$	−0.293506	−	0.169456i	−0.0283743	−	0.0163819i	−0.514120	+	0.857718i	$0.671881\pi$
$108$		0			0
$109$	6.75910	−	3.90237i	0.647404	−	0.373779i	−0.140057	−	0.990143i	$-0.544729\pi$
$109$	6.75910	−	3.90237i	0.647404	−	0.373779i	0.787461	+	0.616365i	$0.211395\pi$
$110$	−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	0.829157	−	0.559015i	$-0.188821\pi$
$131$	8.69419	+	5.01959i	0.759615	+	0.438564i	−0.0695425	+	0.997579i	$0.522154\pi$
$132$		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	0.927050	−	0.374937i	$-0.122336\pi$
$137$	1.62485	+	2.81432i	0.138820	+	0.240444i	−0.788230	+	0.615381i	$0.789002\pi$
$138$		0			0
$139$			15.3349i			1.30069i	0.759639	+	0.650346i	$0.225376\pi$
$139$			15.3349i			1.30069i	−0.759639	+	0.650346i	$0.774624\pi$
$140$	−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	0.214681	−	0.976684i	$-0.431129\pi$
$149$	−6.39393	−	3.69154i	−0.523812	−	0.302423i	−0.738493	+	0.674261i	$0.764462\pi$
$150$		0			0
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	0.645259	−	0.763964i	$-0.276750\pi$
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	−0.984242	+	0.176828i	$0.943416\pi$
$152$	−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	−0.725928	−	0.687770i	$-0.758590\pi$
$157$	−6.18061	+	3.56837i	−0.493266	+	0.284787i	0.232662	+	0.972558i	$0.425256\pi$
$158$	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	0.726987	−	0.686652i	$-0.240920\pi$
$163$	6.33023	+	3.65476i	0.495822	+	0.286263i	−0.231164	+	0.972915i	$0.574254\pi$
$164$	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	0.933542	−	0.358468i	$-0.116701\pi$
$173$	14.3350	+	8.27632i	1.08987	+	0.629237i	0.156329	+	0.987705i	$0.450034\pi$
$174$		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	−0.668526	−	0.743688i	$-0.733075\pi$
$179$	−4.79957	+	2.77103i	−0.358737	+	0.207117i	0.309790	+	0.950805i	$0.399741\pi$
$180$		0			0
$181$			9.98466i			0.742154i	0.928602	+	0.371077i	$0.121011\pi$
$181$			9.98466i			0.742154i	−0.928602	+	0.371077i	$0.878989\pi$
$182$	−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	−0.862963	−	0.505267i	$-0.831394\pi$
$191$	0.0842049	−	0.145847i	0.00609285	−	0.0105531i	0.869056	+	0.494714i	$0.164727\pi$
$192$		0			0
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	0.698450	−	0.715659i	$-0.253873\pi$
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	−0.969004	+	0.247046i	$0.920540\pi$
$194$	−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	$-0.984734\pi$
$197$		−	1.34581i		−	0.0958847i	0.998850	−	0.0479424i	$-0.0152664\pi$
$198$		0			0
$199$	6.38059	+	11.0515i	0.452308	+	0.783420i	0.998529	−	0.0542208i	$-0.0172675\pi$
$199$	6.38059	+	11.0515i	0.452308	+	0.783420i	−0.546221	+	0.837641i	$0.683934\pi$
$200$	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	$-0.905903\pi$
$211$		−	8.46353i		−	0.582653i	0.956624	−	0.291327i	$-0.0940967\pi$
$212$	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	−0.790980	−	0.611843i	$-0.790429\pi$
$227$	−9.89265	+	5.71152i	−0.656598	+	0.379087i	0.134382	+	0.990930i	$0.457095\pi$
$228$		0			0
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.925164	−	0.379568i	$-0.123928\pi$
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.133866	+	0.990999i	$0.457261\pi$
$230$	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	−0.988290	−	0.152590i	$-0.951239\pi$
$233$	−5.52566	+	9.57072i	−0.361998	+	0.626999i	0.626292	+	0.779589i	$0.284572\pi$
$234$		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	0.549656	−	0.835391i	$-0.314759\pi$
$241$	−6.96479	−	12.0634i	−0.448642	−	0.777070i	−0.998298	+	0.0583207i	$0.981425\pi$
$242$	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	$0.00709323\pi$
$251$			0.706033i			0.0445644i	−0.999752	+	0.0222822i	$0.992907\pi$
$252$		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	−0.335320	−	0.942104i	$-0.608844\pi$
$257$	10.3919	−	17.9992i	0.648226	−	1.12276i	0.983546	−	0.180656i	$-0.0578222\pi$
$258$		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	−0.967654	−	0.252281i	$-0.918819\pi$
$263$	−11.3895	−	19.7273i	−0.702309	−	1.21644i	0.265345	−	0.964154i	$-0.414514\pi$
$264$		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	−0.576984	−	0.816756i	$-0.695770\pi$
$269$	−2.59376	+	1.49751i	−0.158145	+	0.0913048i	0.418839	+	0.908060i	$0.362437\pi$
$270$		0			0
$271$	12.5926	−	21.8109i	0.764943	−	1.32492i	−0.175333	−	0.984509i	$-0.556100\pi$
$271$	12.5926	−	21.8109i	0.764943	−	1.32492i	0.940277	−	0.340412i	$-0.110566\pi$
$272$	−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	−0.233724	−	0.972303i	$-0.575091\pi$
$277$	8.17940	−	4.72238i	0.491453	−	0.283740i	0.725177	+	0.688563i	$0.241758\pi$
$278$	−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	−0.127118	−	0.991888i	$-0.540573\pi$
$283$	11.2429	−	6.49111i	0.668323	−	0.385856i	0.795441	+	0.606031i	$0.207239\pi$
$284$	−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	$0.0901151\pi$
$293$			9.56300i			0.558677i	−0.960193	+	0.279338i	$0.909885\pi$
$294$		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	$0.113398\pi$
$307$			12.2217i			0.697527i	−0.937211	+	0.348763i	$0.886602\pi$
$308$	−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	0.822311	+	0.569038i	$0.192684\pi$
$311$	15.9415	+	27.6114i	0.903957	+	1.56570i	0.0816453	+	0.996661i	$0.473983\pi$
$312$		0			0
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	0.383230	+	0.923653i	$0.374811\pi$
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	−0.991522	+	0.129939i	$0.958522\pi$
$314$	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	0.942929	−	0.332995i	$-0.108059\pi$
$317$	20.0481	+	11.5747i	1.12601	+	0.650103i	0.183082	+	0.983098i	$0.441393\pi$
$318$		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	−0.410086	−	0.912047i	$-0.634501\pi$
$331$	−25.5615	−	14.7579i	−1.40499	−	0.811169i	−0.994899	+	0.100878i	$0.967835\pi$
$332$	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	0.473146	−	0.880984i	$-0.343118\pi$
$347$	27.4329	−	15.8384i	1.47267	−	0.850248i	0.999528	+	0.0307361i	$0.00978515\pi$
$348$		0			0
$349$		−	28.4807i		−	1.52454i	−0.647260	−	0.762269i	$-0.724085\pi$
$349$		−	28.4807i		−	1.52454i	0.647260	−	0.762269i	$-0.275915\pi$
$350$	−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	0.998979	+	0.0451760i	$0.0143849\pi$
$353$	10.1196	+	17.5277i	0.538613	+	0.932905i	−0.460366	+	0.887729i	$0.652282\pi$
$354$		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	−0.316889	−	0.948463i	$-0.602638\pi$
$359$	12.5611	−	21.7564i	0.662948	−	1.14826i	0.979837	−	0.199797i	$-0.0640283\pi$
$360$		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	0.924119	+	0.382104i	$0.124801\pi$
$367$	15.1912	+	26.3118i	0.792972	+	1.37347i	−0.131147	+	0.991363i	$0.541866\pi$
$368$	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	0.620593	−	0.784133i	$-0.286892\pi$
$373$	4.86327	+	2.80781i	0.251811	+	0.145383i	−0.368782	+	0.929516i	$0.620225\pi$
$374$	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	$-0.933543\pi$
$379$		−	8.07009i		−	0.414533i	0.978285	−	0.207266i	$-0.0664566\pi$
$380$	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	0.327022	+	0.945017i	$0.393955\pi$
$383$	−12.8166	+	22.1990i	−0.654898	+	1.13432i	−0.981919	+	0.189299i	$0.939378\pi$
$384$		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	0.213010	−	0.977050i	$-0.431673\pi$
$389$	22.9905	−	13.2736i	1.16566	−	0.672997i	0.952655	+	0.304053i	$0.0983401\pi$
$390$		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	0.999791	−	0.0204418i	$-0.00650729\pi$
$397$	29.5283	+	17.0482i	1.48198	+	0.855624i	0.482192	+	0.876065i	$0.339841\pi$
$398$	−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	−0.540604	−	0.841277i	$-0.681804\pi$
$401$	9.17676	−	15.8946i	0.458266	−	0.793739i	0.998869	+	0.0475379i	$0.0151375\pi$
$402$		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	0.683445	−	0.730002i	$-0.260481\pi$
$409$	−5.87455	−	10.1750i	−0.290478	−	0.503122i	−0.973923	+	0.226880i	$0.927148\pi$
$410$	−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	$0.0872709\pi$
$419$			11.0841i			0.541495i	−0.962650	+	0.270748i	$0.912729\pi$
$420$		0			0
$421$			0.137270i			0.00669012i	0.999994	+	0.00334506i	$0.00106477\pi$
$421$			0.137270i			0.00669012i	−0.999994	+	0.00334506i	$0.998935\pi$
$422$	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	0.976157	−	0.217067i	$-0.0696491\pi$
$431$	6.23008	+	10.7908i	0.300092	+	0.519775i	−0.676064	+	0.736843i	$0.736316\pi$
$432$		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	−0.793510	−	0.608557i	$-0.791749\pi$
$439$	2.72948	−	4.72760i	0.130271	−	0.225636i	0.923781	+	0.382921i	$0.125082\pi$
$440$	−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	−0.380480	−	0.924789i	$-0.624241\pi$
$443$	−28.8691	−	16.6676i	−1.37161	−	0.791900i	−0.991131	+	0.132889i	$0.957575\pi$
$444$		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	−0.998160	−	0.0606278i	$-0.980690\pi$
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	0.551585	+	0.834118i	$0.314023\pi$
$458$	−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	$-0.854786\pi$
$461$		−	18.9177i		−	0.881087i	0.897731	−	0.440543i	$-0.145214\pi$
$462$		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	0.825302	−	0.564692i	$-0.191005\pi$
$467$	16.1842	+	9.34394i	0.748914	+	0.432386i	−0.0763871	+	0.997078i	$0.524338\pi$
$468$		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	0.572577	−	0.819851i	$-0.305944\pi$
$479$	−9.27364	−	16.0624i	−0.423723	−	0.733911i	−0.996300	+	0.0859405i	$0.972610\pi$
$480$		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	0.999750	+	0.0223676i	$0.00712041\pi$
$487$	11.4588	+	19.8471i	0.519246	+	0.899360i	−0.480504	+	0.876993i	$0.659546\pi$
$488$	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	$-0.810964\pi$
$491$		−	24.7987i		−	1.11915i	0.828780	−	0.559575i	$-0.189036\pi$
$492$		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	−0.999701	−	0.0244624i	$-0.992213\pi$
$499$	−33.9707	−	19.6130i	−1.52074	−	0.877997i	−0.521035	−	0.853535i	$-0.674454\pi$
$500$	−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	0.581684	−	0.813415i	$-0.302394\pi$
$509$	3.79222	+	2.18944i	0.168087	+	0.0970451i	−0.413596	+	0.910460i	$0.635728\pi$
$510$		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	0.723828	−	0.689980i	$-0.242381\pi$
$521$	−5.37827	−	9.31544i	−0.235626	−	0.408117i	−0.959455	+	0.281863i	$0.909048\pi$
$522$		0			0
$523$	2.43561	+	1.40620i	0.106502	+	0.0614889i	0.552305	−	0.833642i	$-0.313748\pi$
$523$	2.43561	+	1.40620i	0.106502	+	0.0614889i	−0.445803	+	0.895131i	$0.647082\pi$
$524$	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	0.952218	−	0.305419i	$-0.0987966\pi$
$541$	27.0699	+	15.6288i	1.16383	+	0.671935i	0.211608	+	0.977355i	$0.432130\pi$
$542$	−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	$-0.783035\pi$
$547$		−	29.4711i		−	1.26010i	0.776556	−	0.630048i	$-0.216965\pi$
$548$	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	−0.0297941	−	0.999556i	$-0.509485\pi$
$557$	19.3751	−	11.1862i	0.820950	−	0.473976i	0.850744	+	0.525580i	$0.176152\pi$
$558$		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	0.225743	−	0.974187i	$-0.427519\pi$
$563$	28.0528	−	16.1963i	1.18229	−	0.682593i	0.956542	+	0.291594i	$0.0941856\pi$
$564$		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	0.157029	+	0.987594i	$0.449808\pi$
$569$	−18.5288	+	32.0928i	−0.776767	+	1.34540i	−0.933796	+	0.357806i	$0.883525\pi$
$570$		0			0
$571$	−19.4303	+	11.2181i	−0.813132	+	0.469462i	−0.848042	−	0.529928i	$-0.822219\pi$
$571$	−19.4303	+	11.2181i	−0.813132	+	0.469462i	0.0349102	+	0.999390i	$0.488885\pi$
$572$	−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	0.749087	−	0.662471i	$-0.230492\pi$
$577$	−4.78431	−	8.28667i	−0.199173	−	0.344978i	−0.948261	+	0.317493i	$0.897159\pi$
$578$	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	$-0.837405\pi$
$587$		−	23.6894i		−	0.977766i	0.872349	−	0.488883i	$-0.162595\pi$
$588$		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	−0.932303	−	0.361679i	$-0.882204\pi$
$593$	−3.72404	+	6.45023i	−0.152928	+	0.264879i	0.779375	+	0.626558i	$0.215537\pi$
$594$		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	0.882630	−	0.470068i	$-0.155771\pi$
$599$	0.837627	+	1.45081i	0.0342245	+	0.0592786i	−0.848406	+	0.529346i	$0.822437\pi$
$600$		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	−0.460593	−	0.887611i	$-0.652363\pi$
$607$	13.2647	−	22.9751i	0.538397	−	0.932531i	0.998991	−	0.0449200i	$-0.0143033\pi$
$608$	−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	0.167788	−	0.985823i	$-0.446338\pi$
$613$	27.3692	−	15.8016i	1.10543	−	0.638220i	0.937642	+	0.347603i	$0.113004\pi$
$614$	−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	−0.593184	−	0.805067i	$-0.702129\pi$
$619$	−4.79105	+	2.76611i	−0.192568	+	0.111179i	0.400616	+	0.916246i	$0.368796\pi$
$620$	−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	0.944229	−	0.329289i	$-0.106809\pi$
$641$	4.73300	+	8.19779i	0.186942	+	0.323793i	−0.757287	+	0.653082i	$0.773476\pi$
$642$		0			0
$643$			13.0085i			0.513007i	0.966543	+	0.256503i	$0.0825705\pi$
$643$			13.0085i			0.513007i	−0.966543	+	0.256503i	$0.917430\pi$
$644$	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	0.998847	+	0.0480078i	$0.0152872\pi$
$647$	13.7610	+	23.8347i	0.540999	+	0.937039i	−0.457848	+	0.889031i	$0.651379\pi$
$648$		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	−0.232598	−	0.972573i	$-0.574723\pi$
$653$	−30.4390	−	17.5740i	−1.19117	−	0.687723i	−0.958572	+	0.284850i	$0.908056\pi$
$654$		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	$0.0239985\pi$
$659$			3.86719i			0.150644i	−0.997159	+	0.0753222i	$0.976001\pi$
$660$		0			0
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	−0.192403	−	0.981316i	$-0.561628\pi$
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	0.753643	+	0.657284i	$0.228295\pi$
$662$	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	0.991110	−	0.133045i	$-0.0424756\pi$
$677$	35.6839	+	20.6021i	1.37144	+	0.791804i	0.380334	+	0.924849i	$0.375809\pi$
$678$		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	−0.935381	−	0.353642i	$-0.884943\pi$
$683$	−28.6643	+	16.5493i	−1.09681	+	0.633242i	−0.161427	+	0.986885i	$0.551610\pi$
$684$		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	0.724897	−	0.688857i	$-0.241887\pi$
$691$	12.9010	+	7.44840i	0.490777	+	0.283350i	−0.234120	+	0.972208i	$0.575221\pi$
$692$	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	$0.210910\pi$
$701$			32.5746i			1.23032i	−0.788401	+	0.615162i	$0.789090\pi$
$702$		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	0.675169	−	0.737663i	$-0.264071\pi$
$709$	9.95635	+	5.74830i	0.373918	+	0.215882i	−0.301251	+	0.953545i	$0.597404\pi$
$710$	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	0.496949	+	0.867780i	$0.334454\pi$
$719$	−13.4887	+	23.3632i	−0.503045	+	0.871299i	−0.999994	+	0.00351948i	$0.998880\pi$
$720$		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	0.131428	−	0.991326i	$-0.458044\pi$
$733$	−17.9059	−	10.3380i	−0.661371	−	0.381843i	−0.792799	+	0.609483i	$0.791377\pi$
$734$	−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	−0.661294	−	0.750126i	$-0.729993\pi$
$739$	−9.30563	+	5.37261i	−0.342313	+	0.197635i	0.318981	+	0.947761i	$0.396659\pi$
$740$	−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	−0.978654	−	0.205513i	$-0.934114\pi$
$751$	−8.53229	+	14.7784i	−0.311348	+	0.539270i	0.667307	+	0.744783i	$0.267447\pi$
$752$	−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	$0.318560\pi$
$757$			46.3272i			1.68379i	−0.539641	+	0.841895i	$0.681440\pi$
$758$	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	−0.967510	−	0.252832i	$-0.918638\pi$
$761$	−7.30474	+	12.6522i	−0.264796	+	0.458641i	0.702714	+	0.711473i	$0.251971\pi$
$762$		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	−0.483677	−	0.875246i	$-0.660699\pi$
$773$	0.902744	−	0.521200i	0.0324695	−	0.0187462i	0.516147	+	0.856500i	$0.327366\pi$
$774$		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	0.273847	−	0.961773i	$-0.411704\pi$
$787$	34.8899	−	20.1437i	1.24369	−	0.718045i	0.969844	+	0.243728i	$0.0783705\pi$
$788$	−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	$-0.806211\pi$
$797$		−	32.2902i		−	1.14378i	0.820331	−	0.571889i	$-0.193789\pi$
$798$		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	0.956135	+	0.292926i	$0.0946291\pi$
$809$	20.8131	+	36.0493i	0.731749	+	1.26743i	−0.224386	+	0.974500i	$0.572038\pi$
$810$		0			0
$811$			18.7227i			0.657444i	0.944427	+	0.328722i	$0.106618\pi$
$811$			18.7227i			0.657444i	−0.944427	+	0.328722i	$0.893382\pi$
$812$	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	0.755734	−	0.654878i	$-0.227280\pi$
$821$	16.2308	+	9.37088i	0.566460	+	0.327046i	−0.189274	+	0.981924i	$0.560614\pi$
$822$		0			0
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	0.987337	−	0.158636i	$-0.0507095\pi$
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	−0.631051	+	0.775741i	$0.717376\pi$
$824$	−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	$0.320659\pi$
$827$			48.6254i			1.69087i	−0.534079	+	0.845435i	$0.679341\pi$
$828$		0			0
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	−0.601559	−	0.798829i	$-0.705453\pi$
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	0.391026	+	0.920379i	$0.372120\pi$
$830$	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	$-0.823164\pi$
$853$		−	30.8071i		−	1.05482i	0.849612	−	0.527408i	$-0.176836\pi$
$854$	−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	0.958968	−	0.283514i	$-0.0915002\pi$
$857$	6.84889	+	11.8626i	0.233954	+	0.405220i	−0.725014	+	0.688734i	$0.758167\pi$
$858$		0			0
$859$	7.52869	+	4.34669i	0.256876	+	0.148307i	0.622908	−	0.782295i	$-0.285951\pi$
$859$	7.52869	+	4.34669i	0.256876	+	0.148307i	−0.366033	+	0.930602i	$0.619284\pi$
$860$	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	−0.871022	−	0.491243i	$-0.836543\pi$
$863$	−0.296174	+	0.512989i	−0.0100819	+	0.0174623i	0.860940	+	0.508706i	$0.169876\pi$
$864$		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	0.259690	−	0.965692i	$-0.416380\pi$
$877$	−13.2310	−	7.63892i	−0.446779	−	0.257948i	−0.706469	+	0.707744i	$0.749713\pi$
$878$	−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	$0.110536\pi$
$883$			20.2255i			0.680642i	−0.940309	+	0.340321i	$0.889464\pi$
$884$	−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	−0.626270	−	0.779606i	$-0.715419\pi$
$887$	10.7820	−	18.6750i	0.362024	−	0.627044i	0.988294	+	0.152563i	$0.0487525\pi$
$888$		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	0.0280482	−	0.999607i	$-0.491071\pi$
$907$	27.3384	−	15.7838i	0.907757	−	0.524094i	0.879709	+	0.475513i	$0.157737\pi$
$908$	−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	−0.965464	−	0.260535i	$-0.916101\pi$
$919$	−7.79407	+	13.4997i	−0.257103	+	0.445315i	0.708362	+	0.705849i	$0.249434\pi$
$920$	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	−0.296411	−	0.955060i	$-0.595790\pi$
$929$	20.6926	−	35.8406i	0.678901	−	1.17589i	0.975312	−	0.220830i	$-0.0708767\pi$
$930$		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	−0.932636	−	0.360818i	$-0.882498\pi$
$941$	−33.3285	+	19.2422i	−1.08648	+	0.627278i	−0.153841	+	0.988096i	$0.549164\pi$
$942$		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	0.357945	−	0.933743i	$-0.383478\pi$
$947$	−8.36198	−	4.82779i	−0.271728	−	0.156882i	−0.629673	+	0.776861i	$0.716811\pi$
$948$		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	−0.266755	−	0.963764i	$-0.585952\pi$
$971$	−38.4767	−	22.2146i	−1.23478	−	0.712899i	−0.968022	+	0.250865i	$0.919285\pi$
$972$		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	0.563858	−	0.825872i	$-0.309316\pi$
$977$	−13.5436	−	23.4581i	−0.433297	−	0.750492i	−0.997155	+	0.0753795i	$0.975983\pi$
$978$		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	0.993738	−	0.111736i	$-0.0356410\pi$
$983$	12.5444	+	21.7275i	0.400103	+	0.692999i	−0.593635	+	0.804735i	$0.702308\pi$
$984$		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	0.691258	−	0.722608i	$-0.257057\pi$
$991$	−8.81972	−	15.2762i	−0.280168	−	0.485265i	−0.971426	+	0.237343i	$0.923723\pi$
$992$	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	−0.857583	−	0.514345i	$-0.828035\pi$
$997$	−26.5529	+	15.3303i	−0.840939	+	0.485516i	0.0166442	+	0.999861i	$0.494702\pi$
$998$	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.37.1		12
3.2	odd	2		56.2.p.a.37.6	yes	12
4.3	odd	2		2016.2.cr.c.1297.4		12
7.4	even	3	inner	504.2.cj.c.109.4		12
8.3	odd	2		2016.2.cr.c.1297.3		12
8.5	even	2	inner	504.2.cj.c.37.4		12
12.11	even	2		224.2.t.a.177.5		12
21.2	odd	6		392.2.b.e.197.1		6
21.5	even	6		392.2.b.f.197.1		6
21.11	odd	6		56.2.p.a.53.3	yes	12
21.17	even	6		392.2.p.g.165.3		12
21.20	even	2		392.2.p.g.373.6		12
24.5	odd	2		56.2.p.a.37.3	✓	12
24.11	even	2		224.2.t.a.177.2		12
28.11	odd	6		2016.2.cr.c.1873.3		12
56.11	odd	6		2016.2.cr.c.1873.4		12
56.53	even	6	inner	504.2.cj.c.109.1		12
84.11	even	6		224.2.t.a.81.2		12
84.23	even	6		1568.2.b.f.785.5		6
84.47	odd	6		1568.2.b.e.785.2		6
84.59	odd	6		1568.2.t.g.753.5		12
84.83	odd	2		1568.2.t.g.177.2		12
168.5	even	6		392.2.b.f.197.2		6
168.11	even	6		224.2.t.a.81.5		12
168.53	odd	6		56.2.p.a.53.6	yes	12
168.59	odd	6		1568.2.t.g.753.2		12
168.83	odd	2		1568.2.t.g.177.5		12
168.101	even	6		392.2.p.g.165.6		12
168.107	even	6		1568.2.b.f.785.2		6
168.125	even	2		392.2.p.g.373.3		12
168.131	odd	6		1568.2.b.e.785.5		6
168.149	odd	6		392.2.b.e.197.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	24.5	odd	2
56.2.p.a.37.6	yes	12	3.2	odd	2
56.2.p.a.53.3	yes	12	21.11	odd	6
56.2.p.a.53.6	yes	12	168.53	odd	6
224.2.t.a.81.2		12	84.11	even	6
224.2.t.a.81.5		12	168.11	even	6
224.2.t.a.177.2		12	24.11	even	2
224.2.t.a.177.5		12	12.11	even	2
392.2.b.e.197.1		6	21.2	odd	6
392.2.b.e.197.2		6	168.149	odd	6
392.2.b.f.197.1		6	21.5	even	6
392.2.b.f.197.2		6	168.5	even	6
392.2.p.g.165.3		12	21.17	even	6
392.2.p.g.165.6		12	168.101	even	6
392.2.p.g.373.3		12	168.125	even	2
392.2.p.g.373.6		12	21.20	even	2
504.2.cj.c.37.1		12	1.1	even	1	trivial
504.2.cj.c.37.4		12	8.5	even	2	inner
504.2.cj.c.109.1		12	56.53	even	6	inner
504.2.cj.c.109.4		12	7.4	even	3	inner
1568.2.b.e.785.2		6	84.47	odd	6
1568.2.b.e.785.5		6	168.131	odd	6
1568.2.b.f.785.2		6	168.107	even	6
1568.2.b.f.785.5		6	84.23	even	6
1568.2.t.g.177.2		12	84.83	odd	2
1568.2.t.g.177.5		12	168.83	odd	2
1568.2.t.g.753.2		12	168.59	odd	6
1568.2.t.g.753.5		12	84.59	odd	6
2016.2.cr.c.1297.3		12	8.3	odd	2
2016.2.cr.c.1297.4		12	4.3	odd	2
2016.2.cr.c.1873.3		12	28.11	odd	6
2016.2.cr.c.1873.4		12	56.11	odd	6

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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