LMFDB - Embedded newform 1950.2.bc.h.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 $ x^12 - 6x^11 + 87x^10 - 380x^9 + 2556x^8 - 8010x^7 + 29687x^6 - 62556x^5 + 115386x^4 - 135130x^3 + 113253x^2 - 54888*x + 14089
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.3
Root			$0.500000 + 4.41310i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.h.751.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.20583 - 1.27354i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.20583 - 1.27354i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.15713 - 0.668069i) q^{11} -1.00000 q^{12} +(-1.62862 - 3.21677i) q^{13} -2.54707 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.47149 - 2.54870i) q^{17} +1.00000i q^{18} +(-6.05291 + 3.49465i) q^{19} +2.54707i q^{21} +(0.668069 + 1.15713i) q^{22} +(-2.13956 + 3.70583i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.197956 + 3.60011i) q^{26} +1.00000 q^{27} +(2.20583 + 1.27354i) q^{28} +(-1.07721 + 1.86578i) q^{29} +8.74779i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.15713 - 0.668069i) q^{33} +2.94298i q^{34} +(0.500000 - 0.866025i) q^{36} +(4.55291 + 2.62862i) q^{37} +6.98929 q^{38} +(3.60011 + 0.197956i) q^{39} +(2.54870 + 1.47149i) q^{41} +(1.27354 - 2.20583i) q^{42} +(2.71677 + 4.70558i) q^{43} -1.33614i q^{44} +(3.70583 - 2.13956i) q^{46} -11.6908i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.256215 + 0.443778i) q^{49} +2.94298 q^{51} +(1.97149 - 3.01881i) q^{52} -8.74779 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.27354 - 2.20583i) q^{56} -6.98929i q^{57} +(1.86578 - 1.07721i) q^{58} +(-8.25873 + 4.76818i) q^{59} +(3.62862 + 6.28496i) q^{61} +(4.37390 - 7.57581i) q^{62} +(-2.20583 - 1.27354i) q^{63} -1.00000 q^{64} -1.33614 q^{66} +(5.27123 + 3.04334i) q^{67} +(1.47149 - 2.54870i) q^{68} +(-2.13956 - 3.70583i) q^{69} +(-11.3470 + 6.55122i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.59614i q^{73} +(-2.62862 - 4.55291i) q^{74} +(-6.05291 - 3.49465i) q^{76} -3.40324 q^{77} +(-3.01881 - 1.97149i) q^{78} +13.9773 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.47149 - 2.54870i) q^{82} +12.2440i q^{83} +(-2.20583 + 1.27354i) q^{84} -5.43353i q^{86} +(-1.07721 - 1.86578i) q^{87} +(-0.668069 + 1.15713i) q^{88} +(10.0591 + 5.80763i) q^{89} +(-7.68913 - 5.02153i) q^{91} -4.27912 q^{92} +(-7.57581 - 4.37390i) q^{93} +(-5.84539 + 10.1245i) q^{94} +1.00000i q^{96} +(1.32617 - 0.765663i) q^{97} +(0.443778 - 0.256215i) q^{98} +1.33614i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9} - 12 q^{11} - 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{26} + 12 q^{27} - 6 q^{28} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 24 q^{38} + 6 q^{39} - 4 q^{42} - 10 q^{43} + 12 q^{46} - 6 q^{48} + 32 q^{49} + 6 q^{52} - 16 q^{53} + 4 q^{56} + 24 q^{61} + 8 q^{62} + 6 q^{63} - 12 q^{64} + 8 q^{66} + 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} - 48 q^{77} + 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} + 4 q^{88} + 24 q^{89} - 54 q^{91} + 8 q^{92} - 8 q^{94} + 12 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9 - 12 * q^11 - 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^26 + 12 * q^27 - 6 * q^28 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 24 * q^38 + 6 * q^39 - 4 * q^42 - 10 * q^43 + 12 * q^46 - 6 * q^48 + 32 * q^49 + 6 * q^52 - 16 * q^53 + 4 * q^56 + 24 * q^61 + 8 * q^62 + 6 * q^63 - 12 * q^64 + 8 * q^66 + 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 - 48 * q^77 + 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 + 4 * q^88 + 24 * q^89 - 54 * q^91 + 8 * q^92 - 8 * q^94 + 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	2.20583	−	1.27354i	0.833725	−	0.481351i	−0.0214016	−	0.999771i	$-0.506813\pi$
$7$	2.20583	−	1.27354i	0.833725	−	0.481351i	0.855126	+	0.518420i	$0.173480\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.15713	−	0.668069i	−0.348888	−	0.201430i	0.315307	−	0.948990i	$-0.397892\pi$
$11$	−1.15713	−	0.668069i	−0.348888	−	0.201430i	−0.664195	+	0.747559i	$0.731226\pi$
$12$	−1.00000			−0.288675
$13$	−1.62862	−	3.21677i	−0.451698	−	0.892171i
$13$	−1.62862	−	3.21677i	−0.451698	−	0.892171i
$14$	−2.54707			−0.680733
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.47149	−	2.54870i	−0.356889	−	0.618150i	0.630550	−	0.776148i	$-0.282829\pi$
$17$	−1.47149	−	2.54870i	−0.356889	−	0.618150i	−0.987439	+	0.157998i	$0.949496\pi$
$18$			1.00000i			0.235702i
$19$	−6.05291	+	3.49465i	−1.38863	+	0.801727i	−0.993161	−	0.116752i	$-0.962752\pi$
$19$	−6.05291	+	3.49465i	−1.38863	+	0.801727i	−0.395471	+	0.918479i	$0.629419\pi$
$20$		0			0
$21$			2.54707i			0.555816i
$22$	0.668069	+	1.15713i	0.142433	+	0.246701i
$23$	−2.13956	+	3.70583i	−0.446129	+	0.772719i	−0.998130	−	0.0611250i	$-0.980531\pi$
$23$	−2.13956	+	3.70583i	−0.446129	+	0.772719i	0.552001	+	0.833844i	$0.313865\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−0.197956	+	3.60011i	−0.0388224	+	0.706040i
$27$	1.00000			0.192450
$28$	2.20583	+	1.27354i	0.416862	+	0.240676i
$29$	−1.07721	+	1.86578i	−0.200032	+	0.346466i	−0.948539	−	0.316662i	$-0.897438\pi$
$29$	−1.07721	+	1.86578i	−0.200032	+	0.346466i	0.748506	+	0.663128i	$0.230771\pi$
$30$		0			0
$31$			8.74779i			1.57115i	0.618766	+	0.785575i	$0.287633\pi$
$31$			8.74779i			1.57115i	−0.618766	+	0.785575i	$0.712367\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.15713	−	0.668069i	0.201430	−	0.116296i
$34$			2.94298i			0.504717i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	4.55291	+	2.62862i	0.748493	+	0.432143i	0.825149	−	0.564915i	$-0.191091\pi$
$37$	4.55291	+	2.62862i	0.748493	+	0.432143i	−0.0766560	+	0.997058i	$0.524424\pi$
$38$	6.98929			1.13381
$39$	3.60011	+	0.197956i	0.576479	+	0.0316983i
$40$		0			0
$41$	2.54870	+	1.47149i	0.398040	+	0.229808i	0.685638	−	0.727943i	$-0.259523\pi$
$41$	2.54870	+	1.47149i	0.398040	+	0.229808i	−0.287598	+	0.957751i	$0.592857\pi$
$42$	1.27354	−	2.20583i	0.196511	−	0.340367i
$43$	2.71677	+	4.70558i	0.414303	+	0.717594i	0.995355	−	0.0962724i	$-0.0306920\pi$
$43$	2.71677	+	4.70558i	0.414303	+	0.717594i	−0.581052	+	0.813867i	$0.697359\pi$
$44$		−	1.33614i		−	0.201430i
$45$		0			0
$46$	3.70583	−	2.13956i	0.546395	−	0.315461i
$47$		−	11.6908i		−	1.70528i	−0.522503	−	0.852638i	$-0.675002\pi$
$47$		−	11.6908i		−	1.70528i	0.522503	−	0.852638i	$-0.324998\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.256215	+	0.443778i	−0.0366022	+	0.0633968i
$50$		0			0
$51$	2.94298			0.412100
$52$	1.97149	−	3.01881i	0.273397	−	0.418634i
$53$	−8.74779			−1.20160			−0.600801	−	0.799399i	$-0.705152\pi$
$53$	−8.74779			−1.20160			−0.600801	+	0.799399i	$0.705152\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−1.27354	−	2.20583i	−0.170183	−	0.294766i
$57$		−	6.98929i		−	0.925755i
$58$	1.86578	−	1.07721i	0.244988	−	0.141444i
$59$	−8.25873	+	4.76818i	−1.07520	+	0.620764i	−0.929596	−	0.368579i	$-0.879844\pi$
$59$	−8.25873	+	4.76818i	−1.07520	+	0.620764i	−0.145599	+	0.989344i	$0.546511\pi$
$60$		0			0
$61$	3.62862	+	6.28496i	0.464597	+	0.804706i	0.999183	−	0.0404079i	$-0.0128657\pi$
$61$	3.62862	+	6.28496i	0.464597	+	0.804706i	−0.534586	+	0.845114i	$0.679532\pi$
$62$	4.37390	−	7.57581i	0.555486	−	0.962129i
$63$	−2.20583	−	1.27354i	−0.277908	−	0.160450i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.33614			−0.164467
$67$	5.27123	+	3.04334i	0.643983	+	0.371804i	0.786147	−	0.618039i	$-0.212073\pi$
$67$	5.27123	+	3.04334i	0.643983	+	0.371804i	−0.142164	+	0.989843i	$0.545406\pi$
$68$	1.47149	−	2.54870i	0.178445	−	0.309075i
$69$	−2.13956	−	3.70583i	−0.257573	−	0.446129i
$70$		0			0
$71$	−11.3470	+	6.55122i	−1.34665	+	0.777486i	−0.987773	−	0.155900i	$-0.950172\pi$
$71$	−11.3470	+	6.55122i	−1.34665	+	0.777486i	−0.358873	+	0.933386i	$0.616839\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			2.59614i			0.303855i	0.988392	+	0.151927i	$0.0485480\pi$
$73$			2.59614i			0.303855i	−0.988392	+	0.151927i	$0.951452\pi$
$74$	−2.62862	−	4.55291i	−0.305571	−	0.529265i
$75$		0			0
$76$	−6.05291	−	3.49465i	−0.694316	−	0.400863i
$77$	−3.40324			−0.387835
$78$	−3.01881	−	1.97149i	−0.341813	−	0.223227i
$79$	13.9773			1.57257			0.786283	−	0.617867i	$-0.212003\pi$
$79$	13.9773			1.57257			0.786283	+	0.617867i	$0.212003\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.47149	−	2.54870i	−0.162499	−	0.281457i
$83$			12.2440i			1.34395i	0.740573	+	0.671976i	$0.234554\pi$
$83$			12.2440i			1.34395i	−0.740573	+	0.671976i	$0.765446\pi$
$84$	−2.20583	+	1.27354i	−0.240676	+	0.138954i
$85$		0			0
$86$		−	5.43353i		−	0.585913i
$87$	−1.07721	−	1.86578i	−0.115489	−	0.200032i
$88$	−0.668069	+	1.15713i	−0.0712164	+	0.123350i
$89$	10.0591	+	5.80763i	1.06626	+	0.615608i	0.927158	−	0.374670i	$-0.122244\pi$
$89$	10.0591	+	5.80763i	1.06626	+	0.615608i	0.139105	+	0.990278i	$0.455577\pi$
$90$		0			0
$91$	−7.68913	−	5.02153i	−0.806039	−	0.526399i
$92$	−4.27912			−0.446129
$93$	−7.57581	−	4.37390i	−0.785575	−	0.453552i
$94$	−5.84539	+	10.1245i	−0.602906	+	1.04426i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	1.32617	−	0.765663i	0.134652	−	0.0777413i	−0.431161	−	0.902275i	$-0.641896\pi$
$97$	1.32617	−	0.765663i	0.134652	−	0.0777413i	0.565813	+	0.824534i	$0.308563\pi$
$98$	0.443778	−	0.256215i	0.0448283	−	0.0258816i
$99$			1.33614i			0.134287i
$100$		0			0
$101$	0.258932	−	0.448484i	0.0257647	−	0.0446258i	−0.852856	−	0.522147i	$-0.825131\pi$
$101$	0.258932	−	0.448484i	0.0257647	−	0.0446258i	0.878620	+	0.477521i	$0.158465\pi$
$102$	−2.54870	−	1.47149i	−0.252359	−	0.145699i
$103$	−2.42318			−0.238763			−0.119382	−	0.992848i	$-0.538091\pi$
$103$	−2.42318			−0.238763			−0.119382	+	0.992848i	$0.538091\pi$
$104$	−3.21677	+	1.62862i	−0.315430	+	0.159699i
$105$		0			0
$106$	7.57581	+	4.37390i	0.735828	+	0.424830i
$107$	3.06258	−	5.30455i	0.296071	−	0.512810i	−0.679163	−	0.733988i	$-0.737657\pi$
$107$	3.06258	−	5.30455i	0.296071	−	0.512810i	0.975233	+	0.221178i	$0.0709902\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$		−	0.547569i		−	0.0524476i	−0.999656	−	0.0262238i	$-0.991652\pi$
$109$		−	0.547569i		−	0.0524476i	0.999656	−	0.0262238i	$-0.00834825\pi$
$110$		0			0
$111$	−4.55291	+	2.62862i	−0.432143	+	0.249498i
$112$			2.54707i			0.240676i
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$	−3.49465	+	6.05291i	−0.327304	+	0.566907i
$115$		0			0
$116$	−2.15441			−0.200032
$117$	−1.97149	+	3.01881i	−0.182264	+	0.279089i
$118$	9.53636			0.877894
$119$	−6.49171	−	3.74799i	−0.595094	−	0.343578i
$120$		0			0
$121$	−4.60737	−	7.98019i	−0.418852	−	0.725472i
$122$		−	7.25724i		−	0.657040i
$123$	−2.54870	+	1.47149i	−0.229808	+	0.132680i
$124$	−7.57581	+	4.37390i	−0.680328	+	0.392788i
$125$		0			0
$126$	1.27354	+	2.20583i	0.113456	+	0.196511i
$127$	−3.55954	+	6.16530i	−0.315858	+	0.547082i	−0.979619	−	0.200862i	$-0.935626\pi$
$127$	−3.55954	+	6.16530i	−0.315858	+	0.547082i	0.663762	+	0.747944i	$0.268959\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−5.43353			−0.478396
$130$		0			0
$131$	−9.42233			−0.823233			−0.411616	−	0.911357i	$-0.635036\pi$
$131$	−9.42233			−0.823233			−0.411616	+	0.911357i	$0.635036\pi$
$132$	1.15713	+	0.668069i	0.100715	+	0.0581480i
$133$	−8.90111	+	15.4172i	−0.771824	+	1.33684i
$134$	−3.04334	−	5.27123i	−0.262905	−	0.455365i
$135$		0			0
$136$	−2.54870	+	1.47149i	−0.218549	+	0.126179i
$137$	−16.0619	+	9.27336i	−1.37226	+	0.792277i	−0.991213	−	0.132278i	$-0.957771\pi$
$137$	−16.0619	+	9.27336i	−1.37226	+	0.792277i	−0.381050	+	0.924554i	$0.624438\pi$
$138$			4.27912i			0.364263i
$139$	9.85885	+	17.0760i	0.836216	+	1.44837i	0.893036	+	0.449985i	$0.148571\pi$
$139$	9.85885	+	17.0760i	0.836216	+	1.44837i	−0.0568196	+	0.998384i	$0.518096\pi$
$140$		0			0
$141$	10.1245	+	5.84539i	0.852638	+	0.492271i
$142$	13.1024			1.09953
$143$	−0.264497	+	4.81025i	−0.0221183	+	0.402253i
$144$	1.00000			0.0833333
$145$		0			0
$146$	1.29807	−	2.24832i	0.107429	−	0.186072i
$147$	−0.256215	−	0.443778i	−0.0211323	−	0.0366022i
$148$			5.25724i			0.432143i
$149$	−6.84990	+	3.95479i	−0.561165	+	0.323989i	−0.753613	−	0.657318i	$-0.771691\pi$
$149$	−6.84990	+	3.95479i	−0.561165	+	0.323989i	0.192448	+	0.981307i	$0.438357\pi$
$150$		0			0
$151$		−	17.1864i		−	1.39861i	−0.714823	−	0.699305i	$-0.753493\pi$
$151$		−	17.1864i		−	1.39861i	0.714823	−	0.699305i	$-0.246507\pi$
$152$	3.49465	+	6.05291i	0.283453	+	0.490956i
$153$	−1.47149	+	2.54870i	−0.118963	+	0.206050i
$154$	2.94729	+	1.70162i	0.237500	+	0.137120i
$155$		0			0
$156$	1.62862	+	3.21677i	0.130394	+	0.257548i
$157$	2.56103			0.204393			0.102196	−	0.994764i	$-0.467413\pi$
$157$	2.56103			0.204393			0.102196	+	0.994764i	$0.467413\pi$
$158$	−12.1047	−	6.98864i	−0.962996	−	0.555986i
$159$	4.37390	−	7.57581i	0.346873	−	0.600801i
$160$		0			0
$161$			10.8992i			0.858979i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−15.2553	+	8.80763i	−1.19488	+	0.689867i	−0.959410	−	0.282014i	$-0.908998\pi$
$163$	−15.2553	+	8.80763i	−1.19488	+	0.689867i	−0.235474	+	0.971881i	$0.575664\pi$
$164$			2.94298i			0.229808i
$165$		0			0
$166$	6.12199	−	10.6036i	0.475159	−	0.822999i
$167$	−3.70583	−	2.13956i	−0.286766	−	0.165564i	0.349717	−	0.936855i	$-0.386278\pi$
$167$	−3.70583	−	2.13956i	−0.286766	−	0.165564i	−0.636482	+	0.771291i	$0.719611\pi$
$168$	2.54707			0.196511
$169$	−7.69518	+	10.4778i	−0.591937	+	0.805984i
$170$		0			0
$171$	6.05291	+	3.49465i	0.462877	+	0.267242i
$172$	−2.71677	+	4.70558i	−0.207152	+	0.358797i
$173$	4.22210	+	7.31290i	0.321001	+	0.555989i	0.980695	−	0.195545i	$-0.0626475\pi$
$173$	4.22210	+	7.31290i	0.321001	+	0.555989i	−0.659694	+	0.751534i	$0.729314\pi$
$174$			2.15441i			0.163326i
$175$		0			0
$176$	1.15713	−	0.668069i	0.0872220	−	0.0503576i
$177$		−	9.53636i		−	0.716797i
$178$	−5.80763	−	10.0591i	−0.435300	−	0.753962i
$179$	0.982856	−	1.70236i	0.0734621	−	0.127240i	−0.826954	−	0.562269i	$-0.809929\pi$
$179$	0.982856	−	1.70236i	0.0734621	−	0.127240i	0.900416	+	0.435029i	$0.143262\pi$
$180$		0			0
$181$	−6.61526			−0.491708			−0.245854	−	0.969307i	$-0.579068\pi$
$181$	−6.61526			−0.491708			−0.245854	+	0.969307i	$0.579068\pi$
$182$	4.14821	+	8.19333i	0.307486	+	0.607330i
$183$	−7.25724			−0.536471
$184$	3.70583	+	2.13956i	0.273197	+	0.157731i
$185$		0			0
$186$	4.37390	+	7.57581i	0.320710	+	0.555486i
$187$			3.93223i			0.287553i
$188$	10.1245	−	5.84539i	0.738406	−	0.426319i
$189$	2.20583	−	1.27354i	0.160450	−	0.0926361i
$190$		0			0
$191$	−5.21624	−	9.03479i	−0.377434	−	0.653735i	0.613254	−	0.789886i	$-0.289860\pi$
$191$	−5.21624	−	9.03479i	−0.377434	−	0.653735i	−0.990688	+	0.136151i	$0.956527\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	0.705866	+	0.407532i	0.0508093	+	0.0293348i	0.525189	−	0.850985i	$-0.323994\pi$
$193$	0.705866	+	0.407532i	0.0508093	+	0.0293348i	−0.474380	+	0.880320i	$0.657328\pi$
$194$	−1.53133			−0.109943
$195$		0			0
$196$	−0.512430			−0.0366022
$197$	−14.5794	−	8.41742i	−1.03874	−	0.599716i	−0.119263	−	0.992863i	$-0.538053\pi$
$197$	−14.5794	−	8.41742i	−1.03874	−	0.599716i	−0.919476	+	0.393146i	$0.871387\pi$
$198$	0.668069	−	1.15713i	0.0474776	−	0.0822337i
$199$	3.36600	+	5.83009i	0.238610	+	0.413284i	0.960316	−	0.278916i	$-0.0899750\pi$
$199$	3.36600	+	5.83009i	0.238610	+	0.413284i	−0.721706	+	0.692200i	$0.756642\pi$
$200$		0			0
$201$	−5.27123	+	3.04334i	−0.371804	+	0.214661i
$202$	−0.448484	+	0.258932i	−0.0315552	+	0.0182184i
$203$			5.48744i			0.385143i
$204$	1.47149	+	2.54870i	0.103025	+	0.178445i
$205$		0			0
$206$	2.09854	+	1.21159i	0.146212	+	0.0844155i
$207$	4.27912			0.297420
$208$	3.60011	+	0.197956i	0.249623	+	0.0137258i
$209$	9.33867			0.645969
$210$		0			0
$211$	6.00378	−	10.3989i	0.413317	−	0.715887i	−0.581933	−	0.813237i	$-0.697703\pi$
$211$	6.00378	−	10.3989i	0.413317	−	0.715887i	0.995250	+	0.0973501i	$0.0310367\pi$
$212$	−4.37390	−	7.57581i	−0.300401	−	0.520309i
$213$		−	13.1024i		−	0.897764i
$214$	−5.30455	+	3.06258i	−0.362611	+	0.209354i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	11.1406	+	19.2961i	0.756275	+	1.30991i
$218$	−0.273784	+	0.474209i	−0.0185430	+	0.0321175i
$219$	−2.24832	−	1.29807i	−0.151927	−	0.0877154i
$220$		0			0
$221$	−5.80207	+	8.88431i	−0.390289	+	0.597623i
$222$	5.25724			0.352843
$223$	−0.438808	−	0.253346i	−0.0293848	−	0.0169653i	0.485236	−	0.874383i	$-0.338734\pi$
$223$	−0.438808	−	0.253346i	−0.0293848	−	0.0169653i	−0.514620	+	0.857418i	$0.672067\pi$
$224$	1.27354	−	2.20583i	0.0850917	−	0.147383i
$225$		0			0
$226$		0			0
$227$	−3.60219	+	2.07973i	−0.239086	+	0.138036i	−0.614756	−	0.788717i	$-0.710746\pi$
$227$	−3.60219	+	2.07973i	−0.239086	+	0.138036i	0.375671	+	0.926753i	$0.377412\pi$
$228$	6.05291	−	3.49465i	0.400863	−	0.231439i
$229$		−	22.3688i		−	1.47817i	−0.673611	−	0.739086i	$-0.735258\pi$
$229$		−	22.3688i		−	1.47817i	0.673611	−	0.739086i	$-0.264742\pi$
$230$		0			0
$231$	1.70162	−	2.94729i	0.111958	−	0.193918i
$232$	1.86578	+	1.07721i	0.122494	+	0.0707221i
$233$	−8.82331			−0.578034			−0.289017	−	0.957324i	$-0.593328\pi$
$233$	−8.82331			−0.578034			−0.289017	+	0.957324i	$0.593328\pi$
$234$	3.21677	−	1.62862i	0.210287	−	0.106466i
$235$		0			0
$236$	−8.25873	−	4.76818i	−0.537598	−	0.310382i
$237$	−6.98864	+	12.1047i	−0.453961	+	0.786283i
$238$	3.74799	+	6.49171i	0.242946	+	0.420795i
$239$			25.6233i			1.65743i	0.559669	+	0.828716i	$0.310928\pi$
$239$			25.6233i			1.65743i	−0.559669	+	0.828716i	$0.689072\pi$
$240$		0			0
$241$	−11.9346	+	6.89042i	−0.768773	+	0.443851i	−0.832437	−	0.554120i	$-0.813055\pi$
$241$	−11.9346	+	6.89042i	−0.768773	+	0.443851i	0.0636639	+	0.997971i	$0.479721\pi$
$242$			9.21473i			0.592345i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.62862	+	6.28496i	−0.232299	+	0.402353i
$245$		0			0
$246$	2.94298			0.187638
$247$	21.0994	+	13.7793i	1.34252	+	0.876758i
$248$	8.74779			0.555486
$249$	−10.6036	−	6.12199i	−0.671976	−	0.387965i
$250$		0			0
$251$	10.5296	+	18.2378i	0.664621	+	1.15116i	0.979388	+	0.201988i	$0.0647402\pi$
$251$	10.5296	+	18.2378i	0.664621	+	1.15116i	−0.314767	+	0.949169i	$0.601926\pi$
$252$		−	2.54707i		−	0.160450i
$253$	4.95150	−	2.85875i	0.311298	−	0.179728i
$254$	6.16530	−	3.55954i	0.386845	−	0.223345i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.14377	−	12.3734i	0.445616	−	0.771830i	−0.552479	−	0.833527i	$-0.686318\pi$
$257$	7.14377	−	12.3734i	0.445616	−	0.771830i	0.998095	+	0.0616973i	$0.0196513\pi$
$258$	4.70558	+	2.71677i	0.292957	+	0.169139i
$259$	13.3906			0.832050
$260$		0			0
$261$	2.15441			0.133355
$262$	8.15998	+	4.71117i	0.504125	+	0.291057i
$263$	13.0638	−	22.6272i	0.805551	−	1.39526i	−0.110367	−	0.993891i	$-0.535203\pi$
$263$	13.0638	−	22.6272i	0.805551	−	1.39526i	0.915918	−	0.401365i	$-0.131464\pi$
$264$	−0.668069	−	1.15713i	−0.0411168	−	0.0712164i
$265$		0			0
$266$	15.4172	−	8.90111i	0.945288	−	0.545762i
$267$	−10.0591	+	5.80763i	−0.615608	+	0.355421i
$268$			6.08669i			0.371804i
$269$	−7.80743	−	13.5229i	−0.476028	−	0.824504i	0.523595	−	0.851967i	$-0.324590\pi$
$269$	−7.80743	−	13.5229i	−0.476028	−	0.824504i	−0.999623	+	0.0274633i	$0.991257\pi$
$270$		0			0
$271$	−22.6267	−	13.0635i	−1.37447	−	0.793553i	−0.382987	−	0.923754i	$-0.625105\pi$
$271$	−22.6267	−	13.0635i	−1.37447	−	0.793553i	−0.991488	+	0.130201i	$0.958438\pi$
$272$	2.94298			0.178445
$273$	8.19333	−	4.14821i	0.495883	−	0.251061i
$274$	18.5467			1.12045
$275$		0			0
$276$	2.13956	−	3.70583i	0.128786	−	0.223065i
$277$	9.71405	+	16.8252i	0.583661	+	1.01093i	0.995041	+	0.0994662i	$0.0317135\pi$
$277$	9.71405	+	16.8252i	0.583661	+	1.01093i	−0.411380	+	0.911464i	$0.634953\pi$
$278$		−	19.7177i		−	1.18259i
$279$	7.57581	−	4.37390i	0.453552	−	0.261858i
$280$		0			0
$281$		−	10.6630i		−	0.636102i	−0.948074	−	0.318051i	$-0.896972\pi$
$281$		−	10.6630i		−	0.636102i	0.948074	−	0.318051i	$-0.103028\pi$
$282$	−5.84539	−	10.1245i	−0.348088	−	0.602906i
$283$	0.730424	−	1.26513i	0.0434192	−	0.0752042i	−0.843499	−	0.537131i	$-0.819508\pi$
$283$	0.730424	−	1.26513i	0.0434192	−	0.0752042i	0.886918	+	0.461926i	$0.152842\pi$
$284$	−11.3470	−	6.55122i	−0.673323	−	0.388743i
$285$		0			0
$286$	2.63419	−	4.03355i	0.155763	−	0.238509i
$287$	7.49599			0.442474
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	4.16943	−	7.22166i	0.245260	−	0.424803i
$290$		0			0
$291$			1.53133i			0.0897680i
$292$	−2.24832	+	1.29807i	−0.131573	+	0.0759637i
$293$	−15.3566	+	8.86614i	−0.897142	+	0.517965i	−0.876272	−	0.481817i	$-0.839977\pi$
$293$	−15.3566	+	8.86614i	−0.897142	+	0.517965i	−0.0208703	+	0.999782i	$0.506644\pi$
$294$			0.512430i			0.0298855i
$295$		0			0
$296$	2.62862	−	4.55291i	0.152786	−	0.264632i
$297$	−1.15713	−	0.668069i	−0.0671435	−	0.0387653i
$298$	7.90958			0.458190
$299$	15.4053	+	0.847078i	0.890913	+	0.0489878i
$300$		0			0
$301$	11.9854	+	6.91980i	0.690829	+	0.398851i
$302$	−8.59321	+	14.8839i	−0.494483	+	0.856470i
$303$	0.258932	+	0.448484i	0.0148753	+	0.0257647i
$304$		−	6.98929i		−	0.400863i
$305$		0			0
$306$	2.54870	−	1.47149i	0.145699	−	0.0841196i
$307$			6.66890i			0.380614i	0.981725	+	0.190307i	$0.0609484\pi$
$307$			6.66890i			0.380614i	−0.981725	+	0.190307i	$0.939052\pi$
$308$	−1.70162	−	2.94729i	−0.0969588	−	0.167938i
$309$	1.21159	−	2.09854i	0.0689250	−	0.119382i
$310$		0			0
$311$	19.6233			1.11273			0.556367	−	0.830937i	$-0.312195\pi$
$311$	19.6233			1.11273			0.556367	+	0.830937i	$0.312195\pi$
$312$	0.197956	−	3.60011i	0.0112071	−	0.203816i
$313$	13.0538			0.737846			0.368923	−	0.929460i	$-0.379727\pi$
$313$	13.0538			0.737846			0.368923	+	0.929460i	$0.379727\pi$
$314$	−2.21792	−	1.28052i	−0.125164	−	0.0722637i
$315$		0			0
$316$	6.98864	+	12.1047i	0.393141	+	0.680941i
$317$		−	18.7916i		−	1.05544i	−0.849419	−	0.527719i	$-0.823047\pi$
$317$		−	18.7916i		−	1.05544i	0.849419	−	0.527719i	$-0.176953\pi$
$318$	−7.57581	+	4.37390i	−0.424830	+	0.245276i
$319$	2.49294	−	1.43930i	0.139578	−	0.0805852i
$320$		0			0
$321$	3.06258	+	5.30455i	0.170937	+	0.296071i
$322$	5.44961	−	9.43901i	0.303695	−	0.526015i
$323$	17.8136	+	10.2847i	0.991175	+	0.572255i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	17.6153			0.975619
$327$	0.474209	+	0.273784i	0.0262238	+	0.0151403i
$328$	1.47149	−	2.54870i	0.0812495	−	0.140728i
$329$	−14.8886	−	25.7878i	−0.820836	−	1.42173i
$330$		0			0
$331$	−20.4013	+	11.7787i	−1.12136	+	0.647417i	−0.941747	−	0.336321i	$-0.890817\pi$
$331$	−20.4013	+	11.7787i	−1.12136	+	0.647417i	−0.179611	+	0.983738i	$0.557484\pi$
$332$	−10.6036	+	6.12199i	−0.581948	+	0.335988i
$333$		−	5.25724i		−	0.288095i
$334$	2.13956	+	3.70583i	0.117072	+	0.202774i
$335$		0			0
$336$	−2.20583	−	1.27354i	−0.120338	−	0.0694771i
$337$	−27.2137			−1.48242			−0.741212	−	0.671271i	$-0.765749\pi$
$337$	−27.2137			−1.48242			−0.741212	+	0.671271i	$0.765749\pi$
$338$	11.9031	−	5.22644i	0.647444	−	0.284281i
$339$		0			0
$340$		0			0
$341$	5.84413	−	10.1223i	0.316478	−	0.548155i
$342$	−3.49465	−	6.05291i	−0.188969	−	0.327304i
$343$			19.1347i			1.03318i
$344$	4.70558	−	2.71677i	0.253708	−	0.146478i
$345$		0			0
$346$		−	8.44421i		−	0.453963i
$347$	3.19194	+	5.52861i	0.171353	+	0.296791i	0.938893	−	0.344209i	$-0.111853\pi$
$347$	3.19194	+	5.52861i	0.171353	+	0.296791i	−0.767540	+	0.641001i	$0.778520\pi$
$348$	1.07721	−	1.86578i	0.0577443	−	0.100016i
$349$	7.31585	+	4.22381i	0.391608	+	0.226095i	0.682857	−	0.730552i	$-0.260737\pi$
$349$	7.31585	+	4.22381i	0.391608	+	0.226095i	−0.291248	+	0.956647i	$0.594071\pi$
$350$		0			0
$351$	−1.62862	−	3.21677i	−0.0869294	−	0.171698i
$352$	−1.33614			−0.0712164
$353$	−13.3901	−	7.73075i	−0.712681	−	0.411466i	0.0993721	−	0.995050i	$-0.468317\pi$
$353$	−13.3901	−	7.73075i	−0.712681	−	0.411466i	−0.812053	+	0.583584i	$0.801650\pi$
$354$	−4.76818	+	8.25873i	−0.253426	+	0.438947i
$355$		0			0
$356$			11.6153i			0.615608i
$357$	6.49171	−	3.74799i	0.343578	−	0.198365i
$358$	−1.70236	+	0.982856i	−0.0899724	+	0.0519456i
$359$		−	34.4839i		−	1.81999i	−0.414617	−	0.909996i	$-0.636084\pi$
$359$		−	34.4839i		−	1.81999i	0.414617	−	0.909996i	$-0.363916\pi$
$360$		0			0
$361$	14.9251	−	25.8511i	0.785532	−	1.36058i
$362$	5.72898	+	3.30763i	0.301109	+	0.173845i
$363$	9.21473			0.483648
$364$	0.504208	−	9.16974i	0.0264277	−	0.480625i
$365$		0			0
$366$	6.28496	+	3.62862i	0.328520	+	0.189671i
$367$	−18.4700	+	31.9910i	−0.964128	+	1.66992i	−0.252188	+	0.967678i	$0.581150\pi$
$367$	−18.4700	+	31.9910i	−0.964128	+	1.66992i	−0.711940	+	0.702240i	$0.752183\pi$
$368$	−2.13956	−	3.70583i	−0.111532	−	0.193180i
$369$		−	2.94298i		−	0.153206i
$370$		0			0
$371$	−19.2961	+	11.1406i	−1.00181	+	0.578393i
$372$		−	8.74779i		−	0.453552i
$373$	−6.09620	−	10.5589i	−0.315649	−	0.546721i	0.663926	−	0.747798i	$-0.268889\pi$
$373$	−6.09620	−	10.5589i	−0.315649	−	0.546721i	−0.979575	+	0.201078i	$0.935556\pi$
$374$	1.96612	−	3.40541i	0.101665	−	0.176090i
$375$		0			0
$376$	−11.6908			−0.602906
$377$	7.75613	+	0.426479i	0.399461	+	0.0219648i
$378$	−2.54707			−0.131007
$379$	−1.24346	−	0.717912i	−0.0638723	−	0.0368767i	0.467724	−	0.883875i	$-0.345074\pi$
$379$	−1.24346	−	0.717912i	−0.0638723	−	0.0368767i	−0.531596	+	0.846998i	$0.678408\pi$
$380$		0			0
$381$	−3.55954	−	6.16530i	−0.182361	−	0.315858i
$382$			10.4325i			0.533772i
$383$	17.5104	−	10.1097i	0.894742	−	0.516579i	0.0192512	−	0.999815i	$-0.493872\pi$
$383$	17.5104	−	10.1097i	0.894742	−	0.516579i	0.875491	+	0.483235i	$0.160538\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−0.407532	−	0.705866i	−0.0207428	−	0.0359276i
$387$	2.71677	−	4.70558i	0.138101	−	0.239198i
$388$	1.32617	+	0.765663i	0.0673260	+	0.0388707i
$389$	2.15441			0.109233			0.0546165	−	0.998507i	$-0.482606\pi$
$389$	2.15441			0.109233			0.0546165	+	0.998507i	$0.482606\pi$
$390$		0			0
$391$	12.5934			0.636875
$392$	0.443778	+	0.256215i	0.0224142	+	0.0129408i
$393$	4.71117	−	8.15998i	0.237647	−	0.411616i
$394$	8.41742	+	14.5794i	0.424063	+	0.734499i
$395$		0			0
$396$	−1.15713	+	0.668069i	−0.0581480	+	0.0335717i
$397$	−23.2589	+	13.4286i	−1.16733	+	0.673960i	−0.953050	−	0.302812i	$-0.902075\pi$
$397$	−23.2589	+	13.4286i	−1.16733	+	0.673960i	−0.214282	+	0.976772i	$0.568741\pi$
$398$		−	6.73201i		−	0.337445i
$399$	−8.90111	−	15.4172i	−0.445613	−	0.771824i
$400$		0			0
$401$	−17.8763	−	10.3209i	−0.892698	−	0.515399i	−0.0178737	−	0.999840i	$-0.505690\pi$
$401$	−17.8763	−	10.3209i	−0.892698	−	0.515399i	−0.874824	+	0.484441i	$0.839023\pi$
$402$	6.08669			0.303576
$403$	28.1396	−	14.2468i	1.40173	−	0.709686i
$404$	0.517864			0.0257647
$405$		0			0
$406$	2.74372	−	4.75226i	0.136169	−	0.235851i
$407$	−3.51220	−	6.08331i	−0.174093	−	0.301539i
$408$		−	2.94298i		−	0.145699i
$409$	−3.62316	+	2.09183i	−0.179154	+	0.103434i	−0.586895	−	0.809663i	$-0.699650\pi$
$409$	−3.62316	+	2.09183i	−0.179154	+	0.103434i	0.407741	+	0.913097i	$0.366317\pi$
$410$		0			0
$411$		−	18.5467i		−	0.914842i
$412$	−1.21159	−	2.09854i	−0.0596908	−	0.103387i
$413$	−12.1449	+	21.0356i	−0.597611	+	1.03509i
$414$	−3.70583	−	2.13956i	−0.182132	−	0.105154i
$415$		0			0
$416$	−3.01881	−	1.97149i	−0.148009	−	0.0966603i
$417$	−19.7177			−0.965580
$418$	−8.08752	−	4.66933i	−0.395574	−	0.228385i
$419$	−14.4210	+	24.9779i	−0.704511	+	1.22025i	0.262357	+	0.964971i	$0.415500\pi$
$419$	−14.4210	+	24.9779i	−0.704511	+	1.22025i	−0.966868	+	0.255277i	$0.917833\pi$
$420$		0			0
$421$		−	11.3986i		−	0.555532i	−0.960649	−	0.277766i	$-0.910406\pi$
$421$		−	11.3986i		−	0.555532i	0.960649	−	0.277766i	$-0.0895939\pi$
$422$	−10.3989	+	6.00378i	−0.506208	+	0.292260i
$423$	−10.1245	+	5.84539i	−0.492271	+	0.284213i
$424$			8.74779i			0.424830i
$425$		0			0
$426$	−6.55122	+	11.3470i	−0.317407	+	0.549766i
$427$	16.0082	+	9.24236i	0.774693	+	0.447269i
$428$	6.12516			0.296071
$429$	−4.03355	−	2.63419i	−0.194742	−	0.127180i
$430$		0			0
$431$	26.5014	+	15.3006i	1.27653	+	0.737003i	0.976208	−	0.216836i	$-0.0695738\pi$
$431$	26.5014	+	15.3006i	1.27653	+	0.737003i	0.300318	+	0.953839i	$0.402907\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−19.0717	−	33.0332i	−0.916527	−	1.58747i	−0.804649	−	0.593750i	$-0.797647\pi$
$433$	−19.0717	−	33.0332i	−0.916527	−	1.58747i	−0.111878	−	0.993722i	$-0.535687\pi$
$434$		−	22.2813i		−	1.06953i
$435$		0			0
$436$	0.474209	−	0.273784i	0.0227105	−	0.0131119i
$437$		−	29.9080i		−	1.43070i
$438$	1.29807	+	2.24832i	0.0620241	+	0.107429i
$439$	7.39969	−	12.8166i	0.353168	−	0.611705i	−0.633635	−	0.773632i	$-0.718438\pi$
$439$	7.39969	−	12.8166i	0.353168	−	0.611705i	0.986803	+	0.161928i	$0.0517711\pi$
$440$		0			0
$441$	0.512430			0.0244014
$442$	9.46689	−	4.79301i	0.450294	−	0.227980i
$443$	2.07804			0.0987309			0.0493654	−	0.998781i	$-0.484280\pi$
$443$	2.07804			0.0987309			0.0493654	+	0.998781i	$0.484280\pi$
$444$	−4.55291	−	2.62862i	−0.216071	−	0.124749i
$445$		0			0
$446$	0.253346	+	0.438808i	0.0119963	+	0.0207782i
$447$		−	7.90958i		−	0.374110i
$448$	−2.20583	+	1.27354i	−0.104216	+	0.0601689i
$449$	8.50224	−	4.90877i	0.401246	−	0.231659i	−0.285776	−	0.958297i	$-0.592251\pi$
$449$	8.50224	−	4.90877i	0.401246	−	0.231659i	0.687021	+	0.726637i	$0.258918\pi$
$450$		0			0
$451$	−1.96612	−	3.40541i	−0.0925808	−	0.160355i
$452$		0			0
$453$	14.8839	+	8.59321i	0.699305	+	0.403744i
$454$	4.15945			0.195213
$455$		0			0
$456$	−6.98929			−0.327304
$457$	−27.8311	−	16.0683i	−1.30188	−	0.751642i	−0.321155	−	0.947027i	$-0.604071\pi$
$457$	−27.8311	−	16.0683i	−1.30188	−	0.751642i	−0.980727	+	0.195385i	$0.937404\pi$
$458$	−11.1844	+	19.3719i	−0.522613	+	0.905191i
$459$	−1.47149	−	2.54870i	−0.0686833	−	0.118963i
$460$		0			0
$461$	17.8943	−	10.3313i	0.833423	−	0.481177i	−0.0216003	−	0.999767i	$-0.506876\pi$
$461$	17.8943	−	10.3313i	0.833423	−	0.481177i	0.855023	+	0.518590i	$0.173543\pi$
$462$	−2.94729	+	1.70162i	−0.137120	+	0.0791665i
$463$		−	18.2175i		−	0.846639i	−0.905981	−	0.423319i	$-0.860865\pi$
$463$		−	18.2175i		−	0.846639i	0.905981	−	0.423319i	$-0.139135\pi$
$464$	−1.07721	−	1.86578i	−0.0500081	−	0.0866165i
$465$		0			0
$466$	7.64121	+	4.41166i	0.353972	+	0.204366i
$467$	−5.61909			−0.260021			−0.130010	−	0.991513i	$-0.541501\pi$
$467$	−5.61909			−0.260021			−0.130010	+	0.991513i	$0.541501\pi$
$468$	−3.60011	−	0.197956i	−0.166415	−	0.00915052i
$469$	15.5032			0.715873
$470$		0			0
$471$	−1.28052	+	2.21792i	−0.0590030	+	0.102196i
$472$	4.76818	+	8.25873i	0.219473	+	0.380139i
$473$		−	7.25996i		−	0.333813i
$474$	12.1047	−	6.98864i	0.555986	−	0.320999i
$475$		0			0
$476$		−	7.49599i		−	0.343578i
$477$	4.37390	+	7.57581i	0.200267	+	0.346873i
$478$	12.8116	−	22.1904i	0.585991	−	1.01497i
$479$	23.1239	+	13.3506i	1.05656	+	0.610003i	0.924478	−	0.381236i	$-0.124502\pi$
$479$	23.1239	+	13.3506i	1.05656	+	0.610003i	0.132078	+	0.991239i	$0.457835\pi$
$480$		0			0
$481$	1.04070	−	18.9267i	0.0474520	−	0.862982i
$482$	13.7808			0.627700
$483$	−9.43901	−	5.44961i	−0.429490	−	0.247966i
$484$	4.60737	−	7.98019i	0.209426	−	0.362736i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	26.8721	−	15.5146i	1.21769	−	0.703035i	0.253269	−	0.967396i	$-0.418494\pi$
$487$	26.8721	−	15.5146i	1.21769	−	0.703035i	0.964424	+	0.264361i	$0.0851609\pi$
$488$	6.28496	−	3.62862i	0.284507	−	0.164260i
$489$		−	17.6153i		−	0.796590i
$490$		0			0
$491$	−7.27846	+	12.6067i	−0.328472	+	0.568931i	−0.982209	−	0.187791i	$-0.939867\pi$
$491$	−7.27846	+	12.6067i	−0.328472	+	0.568931i	0.653737	+	0.756722i	$0.273200\pi$
$492$	−2.54870	−	1.47149i	−0.114904	−	0.0663400i
$493$	6.34040			0.285557
$494$	−11.3829	−	22.4829i	−0.512142	−	1.01155i
$495$		0			0
$496$	−7.57581	−	4.37390i	−0.340164	−	0.196394i
$497$	−16.6864	+	28.9017i	−0.748488	+	1.29642i
$498$	6.12199	+	10.6036i	0.274333	+	0.475159i
$499$		−	26.5871i		−	1.19020i	−0.803652	−	0.595100i	$-0.797112\pi$
$499$		−	26.5871i		−	1.19020i	0.803652	−	0.595100i	$-0.202888\pi$
$500$		0			0
$501$	3.70583	−	2.13956i	0.165564	−	0.0955885i
$502$		−	21.0591i		−	0.939916i
$503$	6.84516	+	11.8562i	0.305211	+	0.528640i	0.977308	−	0.211822i	$-0.0679398\pi$
$503$	6.84516	+	11.8562i	0.305211	+	0.528640i	−0.672098	+	0.740463i	$0.734606\pi$
$504$	−1.27354	+	2.20583i	−0.0567278	+	0.0982554i
$505$		0			0
$506$	−5.71750			−0.254174
$507$	−5.22644	−	11.9031i	−0.232114	−	0.528636i
$508$	−7.11907			−0.315858
$509$	6.53323	+	3.77196i	0.289581	+	0.167189i	0.637753	−	0.770241i	$-0.279864\pi$
$509$	6.53323	+	3.77196i	0.289581	+	0.167189i	−0.348172	+	0.937431i	$0.613198\pi$
$510$		0			0
$511$	3.30627	+	5.72663i	0.146261	+	0.253331i
$512$			1.00000i			0.0441942i
$513$	−6.05291	+	3.49465i	−0.267242	+	0.154292i
$514$	−12.3734	+	7.14377i	−0.545766	+	0.315098i
$515$		0			0
$516$	−2.71677	−	4.70558i	−0.119599	−	0.207152i
$517$	−7.81025	+	13.5278i	−0.343494	+	0.594950i
$518$	−11.5966	−	6.69529i	−0.509524	−	0.294174i
$519$	−8.44421			−0.370660
$520$		0			0
$521$	15.2218			0.666881			0.333440	−	0.942771i	$-0.391790\pi$
$521$	15.2218			0.666881			0.333440	+	0.942771i	$0.391790\pi$
$522$	−1.86578	−	1.07721i	−0.0816628	−	0.0471480i
$523$	−12.5035	+	21.6567i	−0.546739	+	0.946980i	0.451756	+	0.892141i	$0.350798\pi$
$523$	−12.5035	+	21.6567i	−0.546739	+	0.946980i	−0.998495	+	0.0548385i	$0.982536\pi$
$524$	−4.71117	−	8.15998i	−0.205808	−	0.356470i
$525$		0			0
$526$	−22.6272	+	13.0638i	−0.986595	+	0.569611i
$527$	22.2955	−	12.8723i	0.971207	−	0.560726i
$528$			1.33614i			0.0581480i
$529$	2.34456	+	4.06090i	0.101937	+	0.176561i
$530$		0			0
$531$	8.25873	+	4.76818i	0.358399	+	0.206921i
$532$	−17.8022			−0.771824
$533$	0.582581	−	10.5951i	0.0252344	−	0.458923i
$534$	11.6153			0.502641
$535$		0			0
$536$	3.04334	−	5.27123i	0.131452	−	0.227682i
$537$	0.982856	+	1.70236i	0.0424134	+	0.0734621i
$538$			15.6149i			0.673205i
$539$	0.592949	−	0.342339i	0.0255401	−	0.0147456i
$540$		0			0
$541$			32.2610i			1.38701i	0.720452	+	0.693504i	$0.243934\pi$
$541$			32.2610i			1.38701i	−0.720452	+	0.693504i	$0.756066\pi$
$542$	13.0635	+	22.6267i	0.561127	+	0.971900i
$543$	3.30763	−	5.72898i	0.141944	−	0.245854i
$544$	−2.54870	−	1.47149i	−0.109275	−	0.0630897i
$545$		0			0
$546$	−9.16974	−	0.504208i	−0.392429	−	0.0215781i
$547$	36.4353			1.55786			0.778931	−	0.627110i	$-0.215762\pi$
$547$	36.4353			1.55786			0.778931	+	0.627110i	$0.215762\pi$
$548$	−16.0619	−	9.27336i	−0.686132	−	0.396138i
$549$	3.62862	−	6.28496i	0.154866	−	0.268235i
$550$		0			0
$551$		−	15.0578i		−	0.641485i
$552$	−3.70583	+	2.13956i	−0.157731	+	0.0910658i
$553$	30.8315	−	17.8005i	1.31109	−	0.756956i
$554$		−	19.4281i		−	0.825421i
$555$		0			0
$556$	−9.85885	+	17.0760i	−0.418108	+	0.724185i
$557$	−31.6356	−	18.2648i	−1.34044	−	0.773905i	−0.353570	−	0.935408i	$-0.615032\pi$
$557$	−31.6356	−	18.2648i	−1.34044	−	0.773905i	−0.986872	+	0.161503i	$0.948366\pi$
$558$	−8.74779			−0.370324
$559$	10.7122	−	16.4028i	0.453076	−	0.693765i
$560$		0			0
$561$	−3.40541	−	1.96612i	−0.143777	−	0.0830095i
$562$	−5.33151	+	9.23444i	−0.224896	+	0.389531i
$563$	−22.4766	−	38.9307i	−0.947277	−	1.64073i	−0.751127	−	0.660158i	$-0.770489\pi$
$563$	−22.4766	−	38.9307i	−0.947277	−	1.64073i	−0.196150	−	0.980574i	$-0.562844\pi$
$564$			11.6908i			0.492271i
$565$		0			0
$566$	−1.26513	+	0.730424i	−0.0531774	+	0.0307020i
$567$			2.54707i			0.106967i
$568$	6.55122	+	11.3470i	0.274883	+	0.476111i
$569$	−4.13745	+	7.16627i	−0.173451	+	0.300426i	−0.939624	−	0.342209i	$-0.888825\pi$
$569$	−4.13745	+	7.16627i	−0.173451	+	0.300426i	0.766173	+	0.642634i	$0.222158\pi$
$570$		0			0
$571$	−22.2659			−0.931797			−0.465899	−	0.884838i	$-0.654269\pi$
$571$	−22.2659			−0.931797			−0.465899	+	0.884838i	$0.654269\pi$
$572$	−4.29805	+	2.17606i	−0.179710	+	0.0909858i
$573$	10.4325			0.435823
$574$	−6.49171	−	3.74799i	−0.270959	−	0.156438i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	35.3355i		−	1.47104i	−0.677505	−	0.735518i	$-0.736939\pi$
$577$		−	35.3355i		−	1.47104i	0.677505	−	0.735518i	$-0.263061\pi$
$578$	−7.22166	+	4.16943i	−0.300381	+	0.173425i
$579$	−0.705866	+	0.407532i	−0.0293348	+	0.0169364i
$580$		0			0
$581$	15.5931	+	27.0081i	0.646913	+	1.12049i
$582$	0.765663	−	1.32617i	0.0317378	−	0.0549714i
$583$	10.1223	+	5.84413i	0.419224	+	0.242039i
$584$	2.59614			0.107429
$585$		0			0
$586$	17.7323			0.732514
$587$	3.50343	+	2.02271i	0.144602	+	0.0834861i	0.570556	−	0.821259i	$-0.306728\pi$
$587$	3.50343	+	2.02271i	0.144602	+	0.0834861i	−0.425953	+	0.904745i	$0.640061\pi$
$588$	0.256215	−	0.443778i	0.0105661	−	0.0183011i
$589$	−30.5705	−	52.9496i	−1.25963	−	2.18175i
$590$		0			0
$591$	14.5794	−	8.41742i	0.599716	−	0.346246i
$592$	−4.55291	+	2.62862i	−0.187123	+	0.108036i
$593$			7.73381i			0.317590i	0.987312	+	0.158795i	$0.0507608\pi$
$593$			7.73381i			0.317590i	−0.987312	+	0.158795i	$0.949239\pi$
$594$	0.668069	+	1.15713i	0.0274112	+	0.0474776i
$595$		0			0
$596$	−6.84990	−	3.95479i	−0.280583	−	0.161994i
$597$	−6.73201			−0.275523
$598$	−12.9179	−	8.43625i	−0.528251	−	0.344984i
$599$	23.3807			0.955310			0.477655	−	0.878548i	$-0.341487\pi$
$599$	23.3807			0.955310			0.477655	+	0.878548i	$0.341487\pi$
$600$		0			0
$601$	4.78494	−	8.28776i	0.195182	−	0.338065i	−0.751778	−	0.659416i	$-0.770804\pi$
$601$	4.78494	−	8.28776i	0.195182	−	0.338065i	0.946960	+	0.321351i	$0.104137\pi$
$602$	−6.91980	−	11.9854i	−0.282030	−	0.488490i
$603$		−	6.08669i		−	0.247869i
$604$	14.8839	−	8.59321i	0.605616	−	0.349653i
$605$		0			0
$606$		−	0.517864i		−	0.0210368i
$607$	16.4894	+	28.5604i	0.669283	+	1.15923i	0.978105	+	0.208112i	$0.0667319\pi$
$607$	16.4894	+	28.5604i	0.669283	+	1.15923i	−0.308822	+	0.951120i	$0.599935\pi$
$608$	−3.49465	+	6.05291i	−0.141727	+	0.245478i
$609$	−4.75226	−	2.74372i	−0.192571	−	0.111181i
$610$		0			0
$611$	−37.6065	+	19.0399i	−1.52140	+	0.770270i
$612$	−2.94298			−0.118963
$613$	6.00479	+	3.46687i	0.242531	+	0.140026i	0.616340	−	0.787480i	$-0.288615\pi$
$613$	6.00479	+	3.46687i	0.242531	+	0.140026i	−0.373808	+	0.927506i	$0.621948\pi$
$614$	3.33445	−	5.77544i	0.134567	−	0.233078i
$615$		0			0
$616$			3.40324i			0.137120i
$617$	30.2962	−	17.4915i	1.21968	−	0.704182i	0.254830	−	0.966986i	$-0.417981\pi$
$617$	30.2962	−	17.4915i	1.21968	−	0.704182i	0.964849	+	0.262804i	$0.0846473\pi$
$618$	−2.09854	+	1.21159i	−0.0844155	+	0.0487373i
$619$			31.0002i			1.24600i	0.782221	+	0.623001i	$0.214087\pi$
$619$			31.0002i			1.24600i	−0.782221	+	0.623001i	$0.785913\pi$
$620$		0			0
$621$	−2.13956	+	3.70583i	−0.0858576	+	0.148710i
$622$	−16.9943	−	9.81164i	−0.681408	−	0.393411i
$623$	29.5849			1.18529
$624$	−1.97149	+	3.01881i	−0.0789228	+	0.120849i
$625$		0			0
$626$	−11.3050	−	6.52692i	−0.451837	−	0.260868i
$627$	−4.66933	+	8.08752i	−0.186475	+	0.322985i
$628$	1.28052	+	2.21792i	0.0510981	+	0.0885046i
$629$		−	15.4720i		−	0.616908i
$630$		0			0
$631$	12.5912	−	7.26955i	0.501249	−	0.289396i	−0.227980	−	0.973666i	$-0.573212\pi$
$631$	12.5912	−	7.26955i	0.501249	−	0.289396i	0.729229	+	0.684269i	$0.239879\pi$
$632$		−	13.9773i		−	0.555986i
$633$	6.00378	+	10.3989i	0.238629	+	0.413317i
$634$	−9.39578	+	16.2740i	−0.373154	+	0.646322i
$635$		0			0
$636$	8.74779			0.346873
$637$	1.84481	+	0.101439i	0.0730939	+	0.00401915i
$638$	−2.87859			−0.113965
$639$	11.3470	+	6.55122i	0.448882	+	0.259162i
$640$		0			0
$641$	20.5538	+	35.6002i	0.811825	+	1.40612i	0.911585	+	0.411111i	$0.134859\pi$
$641$	20.5538	+	35.6002i	0.811825	+	1.40612i	−0.0997605	+	0.995011i	$0.531808\pi$
$642$		−	6.12516i		−	0.241741i
$643$	21.0180	−	12.1347i	0.828868	−	0.478547i	−0.0245971	−	0.999697i	$-0.507830\pi$
$643$	21.0180	−	12.1347i	0.828868	−	0.478547i	0.853465	+	0.521150i	$0.174497\pi$
$644$	−9.43901	+	5.44961i	−0.371949	+	0.214745i
$645$		0			0
$646$	−10.2847	−	17.8136i	−0.404646	−	0.700867i
$647$	−20.1663	+	34.9290i	−0.792818	+	1.37320i	0.131397	+	0.991330i	$0.458054\pi$
$647$	−20.1663	+	34.9290i	−0.792818	+	1.37320i	−0.924215	+	0.381872i	$0.875280\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	12.7419			0.500164
$650$		0			0
$651$	−22.2813			−0.873271
$652$	−15.2553	−	8.80763i	−0.597442	−	0.344933i
$653$	19.6399	−	34.0173i	0.768568	−	1.33120i	−0.169771	−	0.985483i	$-0.554303\pi$
$653$	19.6399	−	34.0173i	0.768568	−	1.33120i	0.938339	−	0.345716i	$-0.112364\pi$
$654$	−0.273784	−	0.474209i	−0.0107058	−	0.0185430i
$655$		0			0
$656$	−2.54870	+	1.47149i	−0.0995099	+	0.0574521i
$657$	2.24832	−	1.29807i	0.0877154	−	0.0506425i
$658$			29.7772i			1.16084i
$659$	10.5336	+	18.2448i	0.410333	+	0.710717i	0.994926	−	0.100609i	$-0.0320793\pi$
$659$	10.5336	+	18.2448i	0.410333	+	0.710717i	−0.584593	+	0.811326i	$0.698746\pi$
$660$		0			0
$661$	−20.3964	−	11.7759i	−0.793330	−	0.458029i	0.0478037	−	0.998857i	$-0.484778\pi$
$661$	−20.3964	−	11.7759i	−0.793330	−	0.458029i	−0.841133	+	0.540828i	$0.818111\pi$
$662$	23.5574			0.915585
$663$	−4.79301	−	9.46689i	−0.186145	−	0.367664i
$664$	12.2440			0.475159
$665$		0			0
$666$	−2.62862	+	4.55291i	−0.101857	+	0.176422i
$667$	−4.60950	−	7.98388i	−0.178480	−	0.309137i
$668$		−	4.27912i		−	0.165564i
$669$	0.438808	−	0.253346i	0.0169653	−	0.00979492i
$670$		0			0
$671$		−	9.69668i		−	0.374336i
$672$	1.27354	+	2.20583i	0.0491277	+	0.0850917i
$673$	−6.78980	+	11.7603i	−0.261728	+	0.453325i	−0.966701	−	0.255908i	$-0.917626\pi$
$673$	−6.78980	+	11.7603i	−0.261728	+	0.453325i	0.704974	+	0.709234i	$0.250959\pi$
$674$	23.5677	+	13.6068i	0.907795	+	0.524116i
$675$		0			0
$676$	−12.9216	−	1.42533i	−0.496986	−	0.0548203i
$677$	18.1429			0.697288			0.348644	−	0.937255i	$-0.386642\pi$
$677$	18.1429			0.697288			0.348644	+	0.937255i	$0.386642\pi$
$678$		0			0
$679$	1.95020	−	3.37784i	0.0748418	−	0.129630i
$680$		0			0
$681$		−	4.15945i		−	0.159391i
$682$	−10.1223	+	5.84413i	−0.387604	+	0.223783i
$683$	−16.7486	+	9.66980i	−0.640867	+	0.370005i	−0.784948	−	0.619561i	$-0.787311\pi$
$683$	−16.7486	+	9.66980i	−0.640867	+	0.370005i	0.144082	+	0.989566i	$0.453977\pi$
$684$			6.98929i			0.267242i
$685$		0			0
$686$	9.56735	−	16.5711i	0.365283	−	0.632689i
$687$	19.3719	+	11.1844i	0.739086	+	0.426711i
$688$	−5.43353			−0.207152
$689$	14.2468	+	28.1396i	0.542762	+	1.07203i
$690$		0			0
$691$	16.8778	+	9.74437i	0.642060	+	0.370693i	0.785408	−	0.618979i	$-0.212453\pi$
$691$	16.8778	+	9.74437i	0.642060	+	0.370693i	−0.143348	+	0.989672i	$0.545787\pi$
$692$	−4.22210	+	7.31290i	−0.160500	+	0.277995i
$693$	1.70162	+	2.94729i	0.0646392	+	0.111958i
$694$		−	6.38389i		−	0.242329i
$695$		0			0
$696$	−1.86578	+	1.07721i	−0.0707221	+	0.0408314i
$697$		−	8.66115i		−	0.328064i
$698$	−4.22381	−	7.31585i	−0.159873	−	0.276909i
$699$	4.41166	−	7.64121i	0.166864	−	0.289017i
$700$		0			0
$701$	10.6682			0.402931			0.201466	−	0.979496i	$-0.435430\pi$
$701$	10.6682			0.402931			0.201466	+	0.979496i	$0.435430\pi$
$702$	−0.197956	+	3.60011i	−0.00747137	+	0.135878i
$703$	−36.7444			−1.38584
$704$	1.15713	+	0.668069i	0.0436110	+	0.0251788i
$705$		0			0
$706$	7.73075	+	13.3901i	0.290951	+	0.503941i
$707$		−	1.31904i		−	0.0496075i
$708$	8.25873	−	4.76818i	0.310382	−	0.179199i
$709$	−35.9403	+	20.7502i	−1.34977	+	0.779289i	−0.988216	−	0.153063i	$-0.951086\pi$
$709$	−35.9403	+	20.7502i	−1.34977	+	0.779289i	−0.361551	+	0.932352i	$0.617753\pi$
$710$		0			0
$711$	−6.98864	−	12.1047i	−0.262094	−	0.453961i
$712$	5.80763	−	10.0591i	0.217650	−	0.376981i
$713$	−32.4178	−	18.7164i	−1.21406	−	0.700936i
$714$	−7.49599			−0.280530
$715$		0			0
$716$	1.96571			0.0734621
$717$	−22.1904	−	12.8116i	−0.828716	−	0.478459i
$718$	−17.2420	+	29.8640i	−0.643464	+	1.11451i
$719$	20.4278	+	35.3820i	0.761828	+	1.31953i	0.941907	+	0.335873i	$0.109031\pi$
$719$	20.4278	+	35.3820i	0.761828	+	1.31953i	−0.180079	+	0.983652i	$0.557635\pi$
$720$		0			0
$721$	−5.34512	+	3.08601i	−0.199063	+	0.114929i
$722$	−25.8511	+	14.9251i	−0.962077	+	0.555455i
$723$		−	13.7808i		−	0.512515i
$724$	−3.30763	−	5.72898i	−0.122927	−	0.212916i
$725$		0			0
$726$	−7.98019	−	4.60737i	−0.296173	−	0.170995i
$727$	−6.84248			−0.253773			−0.126887	−	0.991917i	$-0.540498\pi$
$727$	−6.84248			−0.253773			−0.126887	+	0.991917i	$0.540498\pi$
$728$	−5.02153	+	7.68913i	−0.186110	+	0.284978i
$729$	1.00000			0.0370370
$730$		0			0
$731$	7.99540	−	13.8484i	0.295721	−	0.512203i
$732$	−3.62862	−	6.28496i	−0.134118	−	0.232299i
$733$			25.2614i			0.933051i	0.884508	+	0.466525i	$0.154494\pi$
$733$			25.2614i			0.933051i	−0.884508	+	0.466525i	$0.845506\pi$
$734$	31.9910	−	18.4700i	1.18081	−	0.681741i
$735$		0			0
$736$			4.27912i			0.157731i
$737$	−4.06633	−	7.04309i	−0.149785	−	0.259436i
$738$	−1.47149	+	2.54870i	−0.0541663	+	0.0938189i
$739$	3.67362	+	2.12096i	0.135136	+	0.0780209i	0.566044	−	0.824375i	$-0.308473\pi$
$739$	3.67362	+	2.12096i	0.135136	+	0.0780209i	−0.430908	+	0.902396i	$0.641807\pi$
$740$		0			0
$741$	−22.4829	+	11.3829i	−0.825931	+	0.418162i
$742$	22.2813			0.817971
$743$	5.28067	+	3.04879i	0.193729	+	0.111849i	0.593727	−	0.804667i	$-0.297656\pi$
$743$	5.28067	+	3.04879i	0.193729	+	0.111849i	−0.399998	+	0.916516i	$0.630989\pi$
$744$	−4.37390	+	7.57581i	−0.160355	+	0.277743i
$745$		0			0
$746$			12.1924i			0.446395i
$747$	10.6036	−	6.12199i	0.387965	−	0.223992i
$748$	−3.40541	+	1.96612i	−0.124514	+	0.0718883i
$749$		−	15.6012i		−	0.570056i
$750$		0			0
$751$	17.3192	−	29.9977i	0.631986	−	1.09463i	−0.355160	−	0.934806i	$-0.615574\pi$
$751$	17.3192	−	29.9977i	0.631986	−	1.09463i	0.987145	−	0.159825i	$-0.0510931\pi$
$752$	10.1245	+	5.84539i	0.369203	+	0.213159i
$753$	−21.0591			−0.767438
$754$	−6.50377	−	4.24741i	−0.236853	−	0.154681i
$755$		0			0
$756$	2.20583	+	1.27354i	0.0802252	+	0.0463180i
$757$	−1.32054	+	2.28724i	−0.0479957	+	0.0831310i	−0.889025	−	0.457858i	$-0.848617\pi$
$757$	−1.32054	+	2.28724i	−0.0479957	+	0.0831310i	0.841029	+	0.540989i	$0.181950\pi$
$758$	0.717912	+	1.24346i	0.0260757	+	0.0451645i
$759$			5.71750i			0.207532i
$760$		0			0
$761$	47.6508	−	27.5112i	1.72734	−	0.997281i	0.826826	−	0.562458i	$-0.190144\pi$
$761$	47.6508	−	27.5112i	1.72734	−	0.997281i	0.900516	−	0.434823i	$-0.143189\pi$
$762$			7.11907i			0.257897i
$763$	−0.697348	−	1.20784i	−0.0252457	−	0.0437268i
$764$	5.21624	−	9.03479i	0.188717	−	0.326867i
$765$		0			0
$766$	−20.2193			−0.730554
$767$	28.7885	+	18.8009i	1.03949	+	0.678860i
$768$	1.00000			0.0360844
$769$	−27.7928	−	16.0462i	−1.00223	−	0.578639i	−0.0933243	−	0.995636i	$-0.529749\pi$
$769$	−27.7928	−	16.0462i	−1.00223	−	0.578639i	−0.908908	+	0.416997i	$0.863083\pi$
$770$		0			0
$771$	7.14377	+	12.3734i	0.257277	+	0.445616i
$772$			0.815063i			0.0293348i
$773$	−46.4995	+	26.8465i	−1.67247	+	0.965601i	−0.706220	+	0.707993i	$0.749601\pi$
$773$	−46.4995	+	26.8465i	−1.67247	+	0.965601i	−0.966250	+	0.257608i	$0.917066\pi$
$774$	−4.70558	+	2.71677i	−0.169139	+	0.0976522i
$775$		0			0
$776$	−0.765663	−	1.32617i	−0.0274857	−	0.0476067i
$777$	−6.69529	+	11.5966i	−0.240192	+	0.416025i
$778$	−1.86578	−	1.07721i	−0.0668913	−	0.0386197i
$779$	−20.5694			−0.736974
$780$		0			0
$781$	17.5067			0.626438
$782$	−10.9062	−	6.29669i	−0.390005	−	0.225169i
$783$	−1.07721	+	1.86578i	−0.0384962	+	0.0666774i
$784$	−0.256215	−	0.443778i	−0.00915054	−	0.0158492i
$785$		0			0
$786$	−8.15998	+	4.71117i	−0.291057	+	0.168042i
$787$	14.6337	−	8.44876i	0.521635	−	0.301166i	−0.215969	−	0.976400i	$-0.569291\pi$
$787$	14.6337	−	8.44876i	0.521635	−	0.301166i	0.737603	+	0.675234i	$0.235958\pi$
$788$		−	16.8348i		−	0.599716i
$789$	13.0638	+	22.6272i	0.465085	+	0.805551i
$790$		0			0
$791$		0			0
$792$	1.33614			0.0474776
$793$	14.3076	−	21.9082i	0.508078	−	0.777985i
$794$	26.8571			0.953123
$795$		0			0
$796$	−3.36600	+	5.83009i	−0.119305	+	0.206642i
$797$	−7.61687	−	13.1928i	−0.269803	−	0.467313i	0.699008	−	0.715114i	$-0.253625\pi$
$797$	−7.61687	−	13.1928i	−0.269803	−	0.467313i	−0.968811	+	0.247801i	$0.920292\pi$
$798$			17.8022i			0.630192i
$799$	−29.7963	+	17.2029i	−1.05412	+	0.608594i
$800$		0			0
$801$		−	11.6153i		−	0.410405i
$802$	10.3209	+	17.8763i	0.364442	+	0.631233i
$803$	1.73440	−	3.00407i	0.0612057	−	0.106011i
$804$	−5.27123	−	3.04334i	−0.185902	−	0.107330i
$805$		0			0
$806$	−31.4930	−	1.73168i	−1.10930	−	0.0609958i
$807$	15.6149			0.549669
$808$	−0.448484	−	0.258932i	−0.0157776	−	0.00910920i
$809$	−27.9518	+	48.4139i	−0.982733	+	1.70214i	−0.331127	+	0.943586i	$0.607429\pi$
$809$	−27.9518	+	48.4139i	−0.982733	+	1.70214i	−0.651606	+	0.758557i	$0.725905\pi$
$810$		0			0
$811$			0.263496i			0.00925261i	0.999989	+	0.00462630i	$0.00147260\pi$
$811$			0.263496i			0.00925261i	−0.999989	+	0.00462630i	$0.998527\pi$
$812$	−4.75226	+	2.74372i	−0.166772	+	0.0962857i
$813$	22.6267	−	13.0635i	0.793553	−	0.458158i
$814$			7.02441i			0.246205i
$815$		0			0
$816$	−1.47149	+	2.54870i	−0.0515125	+	0.0892223i
$817$	−32.8887	−	18.9883i	−1.15063	−	0.664316i
$818$	4.18366			0.146278
$819$	−0.504208	+	9.16974i	−0.0176185	+	0.320417i
$820$		0			0
$821$	34.0125	+	19.6371i	1.18705	+	0.685341i	0.957634	−	0.287989i	$-0.0929866\pi$
$821$	34.0125	+	19.6371i	1.18705	+	0.685341i	0.229411	+	0.973330i	$0.426320\pi$
$822$	−9.27336	+	16.0619i	−0.323446	+	0.560224i
$823$	−11.1922	−	19.3855i	−0.390137	−	0.675737i	0.602330	−	0.798247i	$-0.294239\pi$
$823$	−11.1922	−	19.3855i	−0.390137	−	0.675737i	−0.992467	+	0.122510i	$0.960906\pi$
$824$			2.42318i			0.0844155i
$825$		0			0
$826$	21.0356	−	12.1449i	0.731921	−	0.422575i
$827$			10.0484i			0.349417i	0.984620	+	0.174709i	$0.0558983\pi$
$827$			10.0484i			0.349417i	−0.984620	+	0.174709i	$0.944102\pi$
$828$	2.13956	+	3.70583i	0.0743549	+	0.128786i
$829$	−15.2722	+	26.4522i	−0.530425	+	0.918723i	0.468945	+	0.883228i	$0.344634\pi$
$829$	−15.2722	+	26.4522i	−0.530425	+	0.918723i	−0.999370	+	0.0354958i	$0.988699\pi$
$830$		0			0
$831$	−19.4281			−0.673953
$832$	1.62862	+	3.21677i	0.0564623	+	0.111521i
$833$	1.50807			0.0522517
$834$	17.0760	+	9.85885i	0.591294	+	0.341384i
$835$		0			0
$836$	4.66933	+	8.08752i	0.161492	+	0.279713i
$837$			8.74779i			0.302368i
$838$	24.9779	−	14.4210i	0.862846	−	0.498164i
$839$	−28.8867	+	16.6777i	−0.997279	+	0.575780i	−0.907442	−	0.420177i	$-0.861968\pi$
$839$	−28.8867	+	16.6777i	−0.997279	+	0.575780i	−0.0898372	+	0.995956i	$0.528635\pi$
$840$		0			0
$841$	12.1793	+	21.0951i	0.419974	+	0.727417i
$842$	−5.69928	+	9.87144i	−0.196410	+	0.340192i
$843$	9.23444	+	5.33151i	0.318051	+	0.183627i
$844$	12.0076			0.413317
$845$		0			0
$846$	11.6908			0.401937
$847$	−20.3261	−	11.7353i	−0.698414	−	0.403229i
$848$	4.37390	−	7.57581i	0.150200	−	0.260154i
$849$	0.730424	+	1.26513i	0.0250681	+	0.0434192i
$850$		0			0
$851$	−19.4824	+	11.2482i	−0.667849	+	0.385583i
$852$	11.3470	−	6.55122i	0.388743	−	0.224441i
$853$		−	10.4152i		−	0.356609i	−0.983975	−	0.178305i	$-0.942939\pi$
$853$		−	10.4152i		−	0.356609i	0.983975	−	0.178305i	$-0.0570613\pi$
$854$	−9.24236	−	16.0082i	−0.316267	−	0.547790i
$855$		0			0
$856$	−5.30455	−	3.06258i	−0.181306	−	0.104677i
$857$	46.7684			1.59758			0.798789	−	0.601611i	$-0.205474\pi$
$857$	46.7684			1.59758			0.798789	+	0.601611i	$0.205474\pi$
$858$	2.17606	+	4.29805i	0.0742896	+	0.146733i
$859$	−9.19564			−0.313751			−0.156876	−	0.987618i	$-0.550142\pi$
$859$	−9.19564			−0.313751			−0.156876	+	0.987618i	$0.550142\pi$
$860$		0			0
$861$	−3.74799	+	6.49171i	−0.127731	+	0.221237i
$862$	−15.3006	−	26.5014i	−0.521140	−	0.902640i
$863$			25.7961i			0.878108i	0.898461	+	0.439054i	$0.144686\pi$
$863$			25.7961i			0.878108i	−0.898461	+	0.439054i	$0.855314\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$			38.1434i			1.29617i
$867$	4.16943	+	7.22166i	0.141601	+	0.245260i
$868$	−11.1406	+	19.2961i	−0.378137	+	0.654953i
$869$	−16.1735	−	9.33779i	−0.548649	−	0.316763i
$870$		0			0
$871$	1.20490	−	21.9128i	0.0408264	−	0.742486i
$872$	−0.547569			−0.0185430
$873$	−1.32617	−	0.765663i	−0.0448840	−	0.0259138i
$874$	−14.9540	+	25.9011i	−0.505827	+	0.876118i
$875$		0			0
$876$		−	2.59614i		−	0.0877154i
$877$	4.17893	−	2.41271i	0.141112	−	0.0814713i	−0.427782	−	0.903882i	$-0.640705\pi$
$877$	4.17893	−	2.41271i	0.141112	−	0.0814713i	0.568894	+	0.822411i	$0.307371\pi$
$878$	−12.8166	+	7.39969i	−0.432541	+	0.249727i
$879$		−	17.7323i		−	0.598095i
$880$		0			0
$881$	−2.98574	+	5.17145i	−0.100592	+	0.174231i	−0.911929	−	0.410349i	$-0.865407\pi$
$881$	−2.98574	+	5.17145i	−0.100592	+	0.174231i	0.811337	+	0.584579i	$0.198740\pi$
$882$	−0.443778	−	0.256215i	−0.0149428	−	0.00862721i
$883$	36.7779			1.23767			0.618837	−	0.785520i	$-0.287604\pi$
$883$	36.7779			1.23767			0.618837	+	0.785520i	$0.287604\pi$
$884$	−10.5951	−	0.582581i	−0.356351	−	0.0195943i
$885$		0			0
$886$	−1.79964	−	1.03902i	−0.0604601	−	0.0349066i
$887$	−24.7668	+	42.8974i	−0.831588	+	1.44035i	0.0651906	+	0.997873i	$0.479234\pi$
$887$	−24.7668	+	42.8974i	−0.831588	+	1.44035i	−0.896779	+	0.442480i	$0.854099\pi$
$888$	2.62862	+	4.55291i	0.0882108	+	0.152786i
$889$			18.1328i			0.608154i
$890$		0			0
$891$	1.15713	−	0.668069i	0.0387653	−	0.0223812i
$892$		−	0.506692i		−	0.0169653i
$893$	40.8551	+	70.7632i	1.36717	+	2.36800i
$894$	−3.95479	+	6.84990i	−0.132268	+	0.229095i
$895$		0			0
$896$	2.54707			0.0850917
$897$	−8.43625	+	12.9179i	−0.281678	+	0.431315i
$898$	−9.81754			−0.327616
$899$	−16.3214	−	9.42318i	−0.544350	−	0.314281i
$900$		0			0
$901$	12.8723	+	22.2955i	0.428839	+	0.742770i
$902$			3.93223i			0.130929i
$903$	−11.9854	+	6.91980i	−0.398851	+	0.230276i
$904$		0			0
$905$		0			0
$906$	−8.59321	−	14.8839i	−0.285490	−	0.494483i
$907$	15.2263	−	26.3728i	0.505582	−	0.875694i	−0.494397	−	0.869236i	$-0.664611\pi$
$907$	15.2263	−	26.3728i	0.505582	−	0.875694i	0.999979	−	0.00645802i	$-0.00205566\pi$
$908$	−3.60219	−	2.07973i	−0.119543	−	0.0690181i
$909$	−0.517864			−0.0171765
$910$		0			0
$911$	14.0258			0.464696			0.232348	−	0.972633i	$-0.425359\pi$
$911$	14.0258			0.464696			0.232348	+	0.972633i	$0.425359\pi$
$912$	6.05291	+	3.49465i	0.200432	+	0.115719i
$913$	8.17983	−	14.1679i	0.270713	−	0.468888i
$914$	16.0683	+	27.8311i	0.531491	+	0.920570i
$915$		0			0
$916$	19.3719	−	11.1844i	0.640067	−	0.369543i
$917$	−20.7840	+	11.9997i	−0.686349	+	0.396264i
$918$			2.94298i			0.0971329i
$919$	2.17806	+	3.77251i	0.0718476	+	0.124444i	0.899711	−	0.436486i	$-0.143777\pi$
$919$	2.17806	+	3.77251i	0.0718476	+	0.124444i	−0.827863	+	0.560930i	$0.810444\pi$
$920$		0			0
$921$	−5.77544	−	3.33445i	−0.190307	−	0.109874i
$922$	−20.6626			−0.680487
$923$	39.5538	+	25.8313i	1.30193	+	0.850249i
$924$	3.40324			0.111958
$925$		0			0
$926$	−9.10874	+	15.7768i	−0.299332	+	0.518458i
$927$	1.21159	+	2.09854i	0.0397939	+	0.0689250i
$928$			2.15441i			0.0707221i
$929$	−31.7664	+	18.3403i	−1.04222	+	0.601727i	−0.920462	−	0.390833i	$-0.872187\pi$
$929$	−31.7664	+	18.3403i	−1.04222	+	0.601727i	−0.121759	+	0.992560i	$0.538854\pi$
$930$		0			0
$931$		−	3.58153i		−	0.117380i
$932$	−4.41166	−	7.64121i	−0.144509	−	0.250296i
$933$	−9.81164	+	16.9943i	−0.321219	+	0.556367i
$934$	4.86628	+	2.80955i	0.159229	+	0.0919312i
$935$		0			0
$936$	3.01881	+	1.97149i	0.0986729	+	0.0644402i
$937$	37.1292			1.21296			0.606478	−	0.795100i	$-0.292582\pi$
$937$	37.1292			1.21296			0.606478	+	0.795100i	$0.292582\pi$
$938$	−13.4262	−	7.75161i	−0.438381	−	0.253099i
$939$	−6.52692	+	11.3050i	−0.212998	+	0.368923i
$940$		0			0
$941$		−	4.28642i		−	0.139733i	−0.997556	−	0.0698666i	$-0.977743\pi$
$941$		−	4.28642i		−	0.139733i	0.997556	−	0.0698666i	$-0.0222574\pi$
$942$	2.21792	−	1.28052i	0.0722637	−	0.0417215i
$943$	−10.9062	+	6.29669i	−0.355154	+	0.205048i
$944$		−	9.53636i		−	0.310382i
$945$		0			0
$946$	−3.62998	+	6.28731i	−0.118021	+	0.204418i
$947$	35.7346	+	20.6314i	1.16122	+	0.670429i	0.951596	−	0.307353i	$-0.0994433\pi$
$947$	35.7346	+	20.6314i	1.16122	+	0.670429i	0.209622	+	0.977782i	$0.432777\pi$
$948$	−13.9773			−0.453961
$949$	8.35117	−	4.22813i	0.271091	−	0.137251i
$950$		0			0
$951$	16.2740	+	9.39578i	0.527719	+	0.304679i
$952$	−3.74799	+	6.49171i	−0.121473	+	0.210398i
$953$	−3.54333	−	6.13723i	−0.114780	−	0.198804i	0.802912	−	0.596098i	$-0.203283\pi$
$953$	−3.54333	−	6.13723i	−0.114780	−	0.198804i	−0.917692	+	0.397293i	$0.869950\pi$
$954$		−	8.74779i		−	0.283220i
$955$		0			0
$956$	−22.1904	+	12.8116i	−0.717689	+	0.414358i
$957$			2.87859i			0.0930517i
$958$	−13.3506	−	23.1239i	−0.431337	−	0.747098i
$959$	−23.6199	+	40.9109i	−0.762726	+	1.32108i
$960$		0			0
$961$	−45.5239			−1.46851
$962$	−10.3646	+	15.8706i	−0.334168	+	0.511689i
$963$	−6.12516			−0.197381
$964$	−11.9346	−	6.89042i	−0.384386	−	0.221926i
$965$		0			0
$966$	5.44961	+	9.43901i	0.175338	+	0.303695i
$967$		−	29.4591i		−	0.947340i	−0.880702	−	0.473670i	$-0.842929\pi$
$967$		−	29.4591i		−	0.947340i	0.880702	−	0.473670i	$-0.157071\pi$
$968$	−7.98019	+	4.60737i	−0.256493	+	0.148086i
$969$	−17.8136	+	10.2847i	−0.572255	+	0.330392i
$970$		0			0
$971$	−25.6123	−	44.3618i	−0.821938	−	1.42364i	−0.904237	−	0.427031i	$-0.859559\pi$
$971$	−25.6123	−	44.3618i	−0.821938	−	1.42364i	0.0822983	−	0.996608i	$-0.473774\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	43.4938	+	25.1112i	1.39435	+	0.805028i
$974$	−31.0293			−0.994242
$975$		0			0
$976$	−7.25724			−0.232299
$977$	−3.03210	−	1.75058i	−0.0970054	−	0.0560061i	0.450713	−	0.892669i	$-0.351170\pi$
$977$	−3.03210	−	1.75058i	−0.0970054	−	0.0560061i	−0.547718	+	0.836663i	$0.684503\pi$
$978$	−8.80763	+	15.2553i	−0.281637	+	0.487810i
$979$	−7.75980	−	13.4404i	−0.248004	−	0.429556i
$980$		0			0
$981$	−0.474209	+	0.273784i	−0.0151403	+	0.00874126i
$982$	12.6067	−	7.27846i	0.402295	−	0.232265i
$983$			0.473855i			0.0151136i	0.999971	+	0.00755682i	$0.00240543\pi$
$983$			0.473855i			0.0151136i	−0.999971	+	0.00755682i	$0.997595\pi$
$984$	1.47149	+	2.54870i	0.0469094	+	0.0812495i
$985$		0			0
$986$	−5.49095	−	3.17020i	−0.174867	−	0.100960i
$987$	29.7772			0.947820
$988$	−1.38357	+	25.1622i	−0.0440173	+	0.800518i
$989$	−23.2508			−0.739331
$990$		0			0
$991$	4.50506	−	7.80299i	0.143108	−	0.247870i	−0.785558	−	0.618789i	$-0.787624\pi$
$991$	4.50506	−	7.80299i	0.143108	−	0.247870i	0.928665	+	0.370918i	$0.120957\pi$
$992$	4.37390	+	7.57581i	0.138871	+	0.240532i
$993$		−	23.5574i		−	0.747572i
$994$	28.9017	−	16.6864i	0.916707	−	0.529261i
$995$		0			0
$996$		−	12.2440i		−	0.387965i
$997$	16.1136	+	27.9096i	0.510324	+	0.883906i	0.999928	+	0.0119620i	$0.00380771\pi$
$997$	16.1136	+	27.9096i	0.510324	+	0.883906i	−0.489605	+	0.871944i	$0.662859\pi$
$998$	−13.2935	+	23.0251i	−0.420799	+	0.728846i
$999$	4.55291	+	2.62862i	0.144048	+	0.0831659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.h.901.3	yes	12
5.2	odd	4		1950.2.y.n.199.6		12
5.3	odd	4		1950.2.y.m.199.1		12
5.4	even	2		1950.2.bc.k.901.4	yes	12
13.10	even	6	inner	1950.2.bc.h.751.3	✓	12
65.23	odd	12		1950.2.y.n.49.6		12
65.49	even	6		1950.2.bc.k.751.4	yes	12
65.62	odd	12		1950.2.y.m.49.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.1		12	65.62	odd	12
1950.2.y.m.199.1		12	5.3	odd	4
1950.2.y.n.49.6		12	65.23	odd	12
1950.2.y.n.199.6		12	5.2	odd	4
1950.2.bc.h.751.3	✓	12	13.10	even	6	inner
1950.2.bc.h.901.3	yes	12	1.1	even	1	trivial
1950.2.bc.k.751.4	yes	12	65.49	even	6
1950.2.bc.k.901.4	yes	12	5.4	even	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.20583 - 1.27354i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.20583 - 1.27354i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.15713 - 0.668069i) q^{11} -1.00000 q^{12} +(-1.62862 - 3.21677i) q^{13} -2.54707 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.47149 - 2.54870i) q^{17} +1.00000i q^{18} +(-6.05291 + 3.49465i) q^{19} +2.54707i q^{21} +(0.668069 + 1.15713i) q^{22} +(-2.13956 + 3.70583i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.197956 + 3.60011i) q^{26} +1.00000 q^{27} +(2.20583 + 1.27354i) q^{28} +(-1.07721 + 1.86578i) q^{29} +8.74779i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.15713 - 0.668069i) q^{33} +2.94298i q^{34} +(0.500000 - 0.866025i) q^{36} +(4.55291 + 2.62862i) q^{37} +6.98929 q^{38} +(3.60011 + 0.197956i) q^{39} +(2.54870 + 1.47149i) q^{41} +(1.27354 - 2.20583i) q^{42} +(2.71677 + 4.70558i) q^{43} -1.33614i q^{44} +(3.70583 - 2.13956i) q^{46} -11.6908i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.256215 + 0.443778i) q^{49} +2.94298 q^{51} +(1.97149 - 3.01881i) q^{52} -8.74779 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.27354 - 2.20583i) q^{56} -6.98929i q^{57} +(1.86578 - 1.07721i) q^{58} +(-8.25873 + 4.76818i) q^{59} +(3.62862 + 6.28496i) q^{61} +(4.37390 - 7.57581i) q^{62} +(-2.20583 - 1.27354i) q^{63} -1.00000 q^{64} -1.33614 q^{66} +(5.27123 + 3.04334i) q^{67} +(1.47149 - 2.54870i) q^{68} +(-2.13956 - 3.70583i) q^{69} +(-11.3470 + 6.55122i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.59614i q^{73} +(-2.62862 - 4.55291i) q^{74} +(-6.05291 - 3.49465i) q^{76} -3.40324 q^{77} +(-3.01881 - 1.97149i) q^{78} +13.9773 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.47149 - 2.54870i) q^{82} +12.2440i q^{83} +(-2.20583 + 1.27354i) q^{84} -5.43353i q^{86} +(-1.07721 - 1.86578i) q^{87} +(-0.668069 + 1.15713i) q^{88} +(10.0591 + 5.80763i) q^{89} +(-7.68913 - 5.02153i) q^{91} -4.27912 q^{92} +(-7.57581 - 4.37390i) q^{93} +(-5.84539 + 10.1245i) q^{94} +1.00000i q^{96} +(1.32617 - 0.765663i) q^{97} +(0.443778 - 0.256215i) q^{98} +1.33614i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9} - 12 q^{11} - 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{26} + 12 q^{27} - 6 q^{28} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 24 q^{38} + 6 q^{39} - 4 q^{42} - 10 q^{43} + 12 q^{46} - 6 q^{48} + 32 q^{49} + 6 q^{52} - 16 q^{53} + 4 q^{56} + 24 q^{61} + 8 q^{62} + 6 q^{63} - 12 q^{64} + 8 q^{66} + 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} - 48 q^{77} + 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} + 4 q^{88} + 24 q^{89} - 54 q^{91} + 8 q^{92} - 8 q^{94} + 12 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9 - 12 * q^11 - 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^26 + 12 * q^27 - 6 * q^28 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 24 * q^38 + 6 * q^39 - 4 * q^42 - 10 * q^43 + 12 * q^46 - 6 * q^48 + 32 * q^49 + 6 * q^52 - 16 * q^53 + 4 * q^56 + 24 * q^61 + 8 * q^62 + 6 * q^63 - 12 * q^64 + 8 * q^66 + 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 - 48 * q^77 + 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 + 4 * q^88 + 24 * q^89 - 54 * q^91 + 8 * q^92 - 8 * q^94 + 12 * q^97 + 36 * q^98

Introduction

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