LMFDB - Embedded newform 1950.2.y.n.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

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.y (of order $6$, degree $2$, not 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			49.4
Root			$0.500000 - 1.72434i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.n.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.79518 + 3.10934i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.79518 + 3.10934i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.72163 + 2.72603i) q^{11} +1.00000i q^{12} +(3.60494 - 0.0664404i) q^{13} -3.59036 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.33097 - 3.65519i) q^{17} +1.00000 q^{18} +(3.34713 + 1.93247i) q^{19} +3.59036i q^{21} +(-4.72163 - 2.72603i) q^{22} +(-1.60934 + 0.929155i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.86001 + 3.08875i) q^{26} -1.00000i q^{27} +(-1.79518 - 3.10934i) q^{28} +(-2.67578 - 4.63459i) q^{29} -2.23338i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.72603 + 4.72163i) q^{33} -7.31038i q^{34} +(0.500000 + 0.866025i) q^{36} +(-1.06644 - 1.84713i) q^{37} +3.86493i q^{38} +(3.08875 - 1.86001i) q^{39} +(-6.33097 + 3.65519i) q^{41} +(-3.10934 + 1.79518i) q^{42} +(-7.10996 - 4.10494i) q^{43} -5.45207i q^{44} +(-1.60934 - 0.929155i) q^{46} -5.07700 q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.94535 - 5.10149i) q^{49} -7.31038 q^{51} +(-1.74493 + 3.15519i) q^{52} -2.23338i q^{53} +(0.866025 - 0.500000i) q^{54} +(1.79518 - 3.10934i) q^{56} +3.86493 q^{57} +(2.67578 - 4.63459i) q^{58} +(0.237785 + 0.137285i) q^{59} +(2.06644 - 3.57918i) q^{61} +(1.93416 - 1.11669i) q^{62} +(1.79518 + 3.10934i) q^{63} +1.00000 q^{64} -5.45207 q^{66} +(7.39851 + 12.8146i) q^{67} +(6.33097 - 3.65519i) q^{68} +(-0.929155 + 1.60934i) q^{69} +(12.3804 + 7.14784i) q^{71} +(-0.500000 + 0.866025i) q^{72} -14.8975 q^{73} +(1.06644 - 1.84713i) q^{74} +(-3.34713 + 1.93247i) q^{76} -19.5749i q^{77} +(3.15519 + 1.74493i) q^{78} -2.62105 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.33097 - 3.65519i) q^{82} -7.15988 q^{83} +(-3.10934 - 1.79518i) q^{84} -8.20988i q^{86} +(-4.63459 - 2.67578i) q^{87} +(4.72163 - 2.72603i) q^{88} +(-8.30844 + 4.79688i) q^{89} +(-6.26493 + 11.3283i) q^{91} -1.85831i q^{92} +(-1.11669 - 1.93416i) q^{93} +(-2.53850 - 4.39681i) q^{94} -1.00000i q^{96} +(0.954155 - 1.65264i) q^{97} +(2.94535 - 5.10149i) q^{98} +5.45207i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 6 q^{16} + 12 q^{18} + 6 q^{19} - 12 q^{22} + 12 q^{23} - 4 q^{26} - 4 q^{28} + 6 q^{32} + 4 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{39} - 6 q^{42} + 12 q^{43} + 12 q^{46} + 16 q^{47} - 32 q^{49} - 8 q^{52} + 4 q^{56} + 24 q^{57} + 24 q^{61} + 4 q^{63} + 12 q^{64} + 8 q^{66} + 24 q^{67} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 40 q^{73} + 12 q^{74} - 6 q^{76} - 6 q^{78} - 52 q^{79} - 6 q^{81} + 32 q^{83} - 6 q^{84} + 12 q^{88} - 24 q^{89} - 54 q^{91} - 8 q^{93} + 8 q^{94} + 24 q^{97} + 32 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 6 * q^16 + 12 * q^18 + 6 * q^19 - 12 * q^22 + 12 * q^23 - 4 * q^26 - 4 * q^28 + 6 * q^32 + 4 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^39 - 6 * q^42 + 12 * q^43 + 12 * q^46 + 16 * q^47 - 32 * q^49 - 8 * q^52 + 4 * q^56 + 24 * q^57 + 24 * q^61 + 4 * q^63 + 12 * q^64 + 8 * q^66 + 24 * q^67 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 40 * q^73 + 12 * q^74 - 6 * q^76 - 6 * q^78 - 52 * q^79 - 6 * q^81 + 32 * q^83 - 6 * q^84 + 12 * q^88 - 24 * q^89 - 54 * q^91 - 8 * q^93 + 8 * q^94 + 24 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−1.79518	+	3.10934i	−0.678514	+	1.17522i	0.296914	+	0.954904i	$0.404043\pi$
$7$	−1.79518	+	3.10934i	−0.678514	+	1.17522i	−0.975428	+	0.220317i	$0.929291\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−4.72163	+	2.72603i	−1.42362	+	0.821930i	−0.996607	−	0.0823128i	$-0.973769\pi$
$11$	−4.72163	+	2.72603i	−1.42362	+	0.821930i	−0.427018	+	0.904243i	$0.640436\pi$
$12$			1.00000i			0.288675i
$13$	3.60494	−	0.0664404i	0.999830	−	0.0184272i
$13$	3.60494	−	0.0664404i	0.999830	−	0.0184272i
$14$	−3.59036			−0.959564
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.33097	−	3.65519i	−1.53549	−	0.886514i	−0.999095	−	0.0425445i	$-0.986454\pi$
$17$	−6.33097	−	3.65519i	−1.53549	−	0.886514i	−0.536392	−	0.843969i	$-0.680213\pi$
$18$	1.00000			0.235702
$19$	3.34713	+	1.93247i	0.767884	+	0.443338i	0.832119	−	0.554597i	$-0.187127\pi$
$19$	3.34713	+	1.93247i	0.767884	+	0.443338i	−0.0642352	+	0.997935i	$0.520461\pi$
$20$		0			0
$21$			3.59036i			0.783481i
$22$	−4.72163	−	2.72603i	−1.00665	−	0.581192i
$23$	−1.60934	+	0.929155i	−0.335571	+	0.193742i	−0.658312	−	0.752745i	$-0.728729\pi$
$23$	−1.60934	+	0.929155i	−0.335571	+	0.193742i	0.322741	+	0.946487i	$0.395396\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	1.86001	+	3.08875i	0.364778	+	0.605753i
$27$		−	1.00000i		−	0.192450i
$28$	−1.79518	−	3.10934i	−0.339257	−	0.587611i
$29$	−2.67578	−	4.63459i	−0.496881	−	0.860622i	0.503113	−	0.864221i	$-0.332188\pi$
$29$	−2.67578	−	4.63459i	−0.496881	−	0.860622i	−0.999994	+	0.00359821i	$0.998855\pi$
$30$		0			0
$31$		−	2.23338i		−	0.401127i	−0.979681	−	0.200563i	$-0.935723\pi$
$31$		−	2.23338i		−	0.401127i	0.979681	−	0.200563i	$-0.0642773\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.72603	+	4.72163i	−0.474542	+	0.821930i
$34$		−	7.31038i		−	1.25372i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−1.06644	−	1.84713i	−0.175322	−	0.303666i	0.764951	−	0.644089i	$-0.222763\pi$
$37$	−1.06644	−	1.84713i	−0.175322	−	0.303666i	−0.940273	+	0.340423i	$0.889430\pi$
$38$			3.86493i			0.626975i
$39$	3.08875	−	1.86001i	0.494596	−	0.297840i
$40$		0			0
$41$	−6.33097	+	3.65519i	−0.988732	+	0.570845i	−0.904895	−	0.425635i	$-0.860051\pi$
$41$	−6.33097	+	3.65519i	−0.988732	+	0.570845i	−0.0838369	+	0.996479i	$0.526717\pi$
$42$	−3.10934	+	1.79518i	−0.479782	+	0.277002i
$43$	−7.10996	−	4.10494i	−1.08426	−	0.625997i	−0.152217	−	0.988347i	$-0.548641\pi$
$43$	−7.10996	−	4.10494i	−1.08426	−	0.625997i	−0.932042	+	0.362350i	$0.881975\pi$
$44$		−	5.45207i		−	0.821930i
$45$		0			0
$46$	−1.60934	−	0.929155i	−0.237285	−	0.136996i
$47$	−5.07700			−0.740556			−0.370278	−	0.928921i	$-0.620738\pi$
$47$	−5.07700			−0.740556			−0.370278	+	0.928921i	$0.620738\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−2.94535	−	5.10149i	−0.420764	−	0.728784i
$50$		0			0
$51$	−7.31038			−1.02366
$52$	−1.74493	+	3.15519i	−0.241978	+	0.437546i
$53$		−	2.23338i		−	0.306778i	−0.988166	−	0.153389i	$-0.950981\pi$
$53$		−	2.23338i		−	0.306778i	0.988166	−	0.153389i	$-0.0490188\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	1.79518	−	3.10934i	0.239891	−	0.415504i
$57$	3.86493			0.511923
$58$	2.67578	−	4.63459i	0.351348	−	0.608552i
$59$	0.237785	+	0.137285i	0.0309570	+	0.0178730i	0.515399	−	0.856951i	$-0.327644\pi$
$59$	0.237785	+	0.137285i	0.0309570	+	0.0178730i	−0.484442	+	0.874824i	$0.660977\pi$
$60$		0			0
$61$	2.06644	−	3.57918i	0.264581	−	0.458267i	−0.702873	−	0.711315i	$-0.748100\pi$
$61$	2.06644	−	3.57918i	0.264581	−	0.458267i	0.967454	+	0.253048i	$0.0814332\pi$
$62$	1.93416	−	1.11669i	0.245639	−	0.141820i
$63$	1.79518	+	3.10934i	0.226171	+	0.391740i
$64$	1.00000			0.125000
$65$		0			0
$66$	−5.45207			−0.671103
$67$	7.39851	+	12.8146i	0.903872	+	1.56555i	0.822425	+	0.568874i	$0.192621\pi$
$67$	7.39851	+	12.8146i	0.903872	+	1.56555i	0.0814466	+	0.996678i	$0.474046\pi$
$68$	6.33097	−	3.65519i	0.767743	−	0.443257i
$69$	−0.929155	+	1.60934i	−0.111857	+	0.193742i
$70$		0			0
$71$	12.3804	+	7.14784i	1.46929	+	0.848293i	0.999407	−	0.0344378i	$-0.0109641\pi$
$71$	12.3804	+	7.14784i	1.46929	+	0.848293i	0.469879	+	0.882731i	$0.344297\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−14.8975			−1.74362			−0.871811	−	0.489842i	$-0.837054\pi$
$73$	−14.8975			−1.74362			−0.871811	+	0.489842i	$0.837054\pi$
$74$	1.06644	−	1.84713i	0.123971	−	0.214724i
$75$		0			0
$76$	−3.34713	+	1.93247i	−0.383942	+	0.221669i
$77$		−	19.5749i		−	2.23077i
$78$	3.15519	+	1.74493i	0.357255	+	0.197574i
$79$	−2.62105			−0.294891			−0.147446	−	0.989070i	$-0.547105\pi$
$79$	−2.62105			−0.294891			−0.147446	+	0.989070i	$0.547105\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.33097	−	3.65519i	−0.699139	−	0.403648i
$83$	−7.15988			−0.785899			−0.392949	−	0.919560i	$-0.628545\pi$
$83$	−7.15988			−0.785899			−0.392949	+	0.919560i	$0.628545\pi$
$84$	−3.10934	−	1.79518i	−0.339257	−	0.195870i
$85$		0			0
$86$		−	8.20988i		−	0.885294i
$87$	−4.63459	−	2.67578i	−0.496881	−	0.286874i
$88$	4.72163	−	2.72603i	0.503327	−	0.290596i
$89$	−8.30844	+	4.79688i	−0.880693	+	0.508468i	−0.870887	−	0.491484i	$-0.836455\pi$
$89$	−8.30844	+	4.79688i	−0.880693	+	0.508468i	−0.00980594	+	0.999952i	$0.503121\pi$
$90$		0			0
$91$	−6.26493	+	11.3283i	−0.656743	+	1.18753i
$92$		−	1.85831i		−	0.193742i
$93$	−1.11669	−	1.93416i	−0.115795	−	0.200563i
$94$	−2.53850	−	4.39681i	−0.261826	−	0.453496i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	0.954155	−	1.65264i	0.0968797	−	0.167801i	−0.813512	−	0.581548i	$-0.802447\pi$
$97$	0.954155	−	1.65264i	0.0968797	−	0.167801i	0.910392	+	0.413748i	$0.135780\pi$
$98$	2.94535	−	5.10149i	0.297525	−	0.515328i
$99$			5.45207i			0.547953i
$100$		0			0
$101$	8.12785	+	14.0779i	0.808752	+	1.40080i	0.913729	+	0.406324i	$0.133190\pi$
$101$	8.12785	+	14.0779i	0.808752	+	1.40080i	−0.104978	+	0.994475i	$0.533477\pi$
$102$	−3.65519	−	6.33097i	−0.361918	−	0.626860i
$103$			12.9760i			1.27857i	0.768971	+	0.639284i	$0.220769\pi$
$103$			12.9760i			1.27857i	−0.768971	+	0.639284i	$0.779231\pi$
$104$	−3.60494	+	0.0664404i	−0.353493	+	0.00651501i
$105$		0			0
$106$	1.93416	−	1.11669i	0.187863	−	0.108463i
$107$	−8.58814	+	4.95837i	−0.830247	+	0.479343i	−0.853937	−	0.520376i	$-0.825792\pi$
$107$	−8.58814	+	4.95837i	−0.830247	+	0.479343i	0.0236901	+	0.999719i	$0.492459\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$		−	7.41088i		−	0.709833i	−0.934898	−	0.354917i	$-0.884509\pi$
$109$		−	7.41088i		−	0.709833i	0.934898	−	0.354917i	$-0.115491\pi$
$110$		0			0
$111$	−1.84713	−	1.06644i	−0.175322	−	0.101222i
$112$	3.59036			0.339257
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$	1.93247	+	3.34713i	0.180992	+	0.313487i
$115$		0			0
$116$	5.35157			0.496881
$117$	1.74493	−	3.15519i	0.161319	−	0.291697i
$118$			0.274571i			0.0252763i
$119$	22.7305	−	13.1234i	2.08370	−	1.20302i
$120$		0			0
$121$	9.36252	−	16.2164i	0.851138	−	1.47421i
$122$	4.13288			0.374173
$123$	−3.65519	+	6.33097i	−0.329577	+	0.570845i
$124$	1.93416	+	1.11669i	0.173693	+	0.100282i
$125$		0			0
$126$	−1.79518	+	3.10934i	−0.159927	+	0.277002i
$127$	−15.5772	+	8.99351i	−1.38225	+	0.798045i	−0.992426	−	0.122843i	$-0.960799\pi$
$127$	−15.5772	+	8.99351i	−1.38225	+	0.798045i	−0.389828	+	0.920888i	$0.627466\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−8.20988			−0.722839
$130$		0			0
$131$	20.3462			1.77765			0.888827	−	0.458242i	$-0.151521\pi$
$131$	20.3462			1.77765			0.888827	+	0.458242i	$0.151521\pi$
$132$	−2.72603	−	4.72163i	−0.237271	−	0.410965i
$133$	−12.0174	+	6.93825i	−1.04204	+	0.601623i
$134$	−7.39851	+	12.8146i	−0.639134	+	1.10701i
$135$		0			0
$136$	6.33097	+	3.65519i	0.542876	+	0.313430i
$137$	−5.52037	+	9.56156i	−0.471637	+	0.816899i	−0.999473	−	0.0324469i	$-0.989670\pi$
$137$	−5.52037	+	9.56156i	−0.471637	+	0.816899i	0.527837	+	0.849346i	$0.323003\pi$
$138$	−1.85831			−0.158190
$139$	4.85096	−	8.40212i	0.411453	−	0.712658i	−0.583596	−	0.812044i	$-0.698355\pi$
$139$	4.85096	−	8.40212i	0.411453	−	0.712658i	0.995049	+	0.0993864i	$0.0316880\pi$
$140$		0			0
$141$	−4.39681	+	2.53850i	−0.370278	+	0.213780i
$142$			14.2957i			1.19967i
$143$	−16.8401	+	10.1409i	−1.40824	+	0.848024i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−7.44876	−	12.9016i	−0.616464	−	1.06775i
$147$	−5.10149	−	2.94535i	−0.420764	−	0.242928i
$148$	2.13288			0.175322
$149$	4.70959	+	2.71908i	0.385825	+	0.222756i	0.680350	−	0.732888i	$-0.261828\pi$
$149$	4.70959	+	2.71908i	0.385825	+	0.222756i	−0.294525	+	0.955644i	$0.595161\pi$
$150$		0			0
$151$			17.8010i			1.44862i	0.689472	+	0.724312i	$0.257843\pi$
$151$			17.8010i			1.44862i	−0.689472	+	0.724312i	$0.742157\pi$
$152$	−3.34713	−	1.93247i	−0.271488	−	0.156744i
$153$	−6.33097	+	3.65519i	−0.511829	+	0.295505i
$154$	16.9524	−	9.78745i	1.36606	−	0.788695i
$155$		0			0
$156$	0.0664404	+	3.60494i	0.00531949	+	0.288626i
$157$			5.93652i			0.473786i	0.971536	+	0.236893i	$0.0761290\pi$
$157$			5.93652i			0.473786i	−0.971536	+	0.236893i	$0.923871\pi$
$158$	−1.31052	−	2.26990i	−0.104260	−	0.180583i
$159$	−1.11669	−	1.93416i	−0.0885593	−	0.153389i
$160$		0			0
$161$		−	6.67200i		−	0.525828i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	7.79688	−	13.5046i	0.610699	−	1.05776i	−0.380424	−	0.924812i	$-0.624222\pi$
$163$	7.79688	−	13.5046i	0.610699	−	1.05776i	0.991123	−	0.132949i	$-0.0424447\pi$
$164$		−	7.31038i		−	0.570845i
$165$		0			0
$166$	−3.57994	−	6.20064i	−0.277857	−	0.481263i
$167$	−0.929155	−	1.60934i	−0.0719002	−	0.124535i	0.827834	−	0.560973i	$-0.189573\pi$
$167$	−0.929155	−	1.60934i	−0.0719002	−	0.124535i	−0.899734	+	0.436439i	$0.856240\pi$
$168$		−	3.59036i		−	0.277002i
$169$	12.9912	−	0.479027i	0.999321	−	0.0368482i
$170$		0			0
$171$	3.34713	−	1.93247i	0.255961	−	0.147779i
$172$	7.10996	−	4.10494i	0.542130	−	0.312999i
$173$	−21.0768	−	12.1687i	−1.60244	−	0.925168i	−0.990998	−	0.133878i	$-0.957257\pi$
$173$	−21.0768	−	12.1687i	−1.60244	−	0.925168i	−0.611441	−	0.791290i	$-0.709410\pi$
$174$		−	5.35157i		−	0.405701i
$175$		0			0
$176$	4.72163	+	2.72603i	0.355906	+	0.205483i
$177$	0.274571			0.0206380
$178$	−8.30844	−	4.79688i	−0.622744	−	0.359541i
$179$	−1.53429	−	2.65746i	−0.114678	−	0.198628i	0.802973	−	0.596015i	$-0.203250\pi$
$179$	−1.53429	−	2.65746i	−0.114678	−	0.198628i	−0.917651	+	0.397387i	$0.869917\pi$
$180$		0			0
$181$	−4.59376			−0.341451			−0.170726	−	0.985319i	$-0.554611\pi$
$181$	−4.59376			−0.341451			−0.170726	+	0.985319i	$0.554611\pi$
$182$	−12.9430	+	0.238545i	−0.959401	+	0.0176821i
$183$		−	4.13288i		−	0.305511i
$184$	1.60934	−	0.929155i	0.118642	−	0.0684982i
$185$		0			0
$186$	1.11669	−	1.93416i	0.0818797	−	0.141820i
$187$	39.8567			2.91461
$188$	2.53850	−	4.39681i	0.185139	−	0.320670i
$189$	3.10934	+	1.79518i	0.226171	+	0.130580i
$190$		0			0
$191$	−7.03007	+	12.1764i	−0.508678	+	0.881056i	0.491272	+	0.871006i	$0.336532\pi$
$191$	−7.03007	+	12.1764i	−0.508678	+	0.881056i	−0.999950	+	0.0100494i	$0.996801\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	12.5444	+	21.7276i	0.902966	+	1.56398i	0.823624	+	0.567136i	$0.191949\pi$
$193$	12.5444	+	21.7276i	0.902966	+	1.56398i	0.0793424	+	0.996847i	$0.474718\pi$
$194$	1.90831			0.137009
$195$		0			0
$196$	5.89069			0.420764
$197$	−4.59737	−	7.96287i	−0.327549	−	0.567331i	0.654476	−	0.756083i	$-0.272889\pi$
$197$	−4.59737	−	7.96287i	−0.327549	−	0.567331i	−0.982025	+	0.188752i	$0.939556\pi$
$198$	−4.72163	+	2.72603i	−0.335552	+	0.193731i
$199$	11.8396	−	20.5068i	0.839286	−	1.45369i	−0.0512060	−	0.998688i	$-0.516306\pi$
$199$	11.8396	−	20.5068i	0.839286	−	1.45369i	0.890492	−	0.454998i	$-0.150360\pi$
$200$		0			0
$201$	12.8146	+	7.39851i	0.903872	+	0.521850i
$202$	−8.12785	+	14.0779i	−0.571874	+	0.990514i
$203$	19.2141			1.34856
$204$	3.65519	−	6.33097i	0.255914	−	0.443257i
$205$		0			0
$206$	−11.2376	+	6.48802i	−0.782960	+	0.452042i
$207$			1.85831i			0.129161i
$208$	−1.86001	−	3.08875i	−0.128968	−	0.214166i
$209$	−21.0719			−1.45757
$210$		0			0
$211$	4.99303	+	8.64818i	0.343734	+	0.595366i	0.985123	−	0.171851i	$-0.0549747\pi$
$211$	4.99303	+	8.64818i	0.343734	+	0.595366i	−0.641389	+	0.767216i	$0.721641\pi$
$212$	1.93416	+	1.11669i	0.132839	+	0.0766946i
$213$	14.2957			0.979524
$214$	−8.58814	−	4.95837i	−0.587073	−	0.338947i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	6.94435	+	4.00932i	0.471413	+	0.272170i
$218$	6.41801	−	3.70544i	0.434682	−	0.250964i
$219$	−12.9016	+	7.44876i	−0.871811	+	0.503340i
$220$		0			0
$221$	−23.0656	−	12.7561i	−1.55156	−	0.858068i
$222$		−	2.13288i		−	0.143150i
$223$	−11.1910	−	19.3833i	−0.749404	−	1.29801i	−0.948109	−	0.317946i	$-0.897007\pi$
$223$	−11.1910	−	19.3833i	−0.749404	−	1.29801i	0.198705	−	0.980059i	$-0.436326\pi$
$224$	1.79518	+	3.10934i	0.119946	+	0.207752i
$225$		0			0
$226$		0			0
$227$	6.49265	−	11.2456i	0.430933	−	0.746397i	−0.566021	−	0.824391i	$-0.691518\pi$
$227$	6.49265	−	11.2456i	0.430933	−	0.746397i	0.996954	+	0.0779935i	$0.0248514\pi$
$228$	−1.93247	+	3.34713i	−0.127981	+	0.221669i
$229$			14.4455i			0.954587i	0.878744	+	0.477293i	$0.158382\pi$
$229$			14.4455i			0.954587i	−0.878744	+	0.477293i	$0.841618\pi$
$230$		0			0
$231$	−9.78745	−	16.9524i	−0.643967	−	1.11538i
$232$	2.67578	+	4.63459i	0.175674	+	0.304276i
$233$			12.4374i			0.814800i	0.913250	+	0.407400i	$0.133564\pi$
$233$			12.4374i			0.814800i	−0.913250	+	0.407400i	$0.866436\pi$
$234$	3.60494	−	0.0664404i	0.235662	−	0.00434334i
$235$		0			0
$236$	−0.237785	+	0.137285i	−0.0154785	+	0.00893652i
$237$	−2.26990	+	1.31052i	−0.147446	+	0.0851277i
$238$	22.7305	+	13.1234i	1.47340	+	0.850667i
$239$			4.16983i			0.269724i	0.990864	+	0.134862i	$0.0430591\pi$
$239$			4.16983i			0.269724i	−0.990864	+	0.134862i	$0.956941\pi$
$240$		0			0
$241$	1.63165	+	0.942035i	0.105104	+	0.0606818i	0.551631	−	0.834089i	$-0.314006\pi$
$241$	1.63165	+	0.942035i	0.105104	+	0.0606818i	−0.446527	+	0.894770i	$0.647339\pi$
$242$	18.7250			1.20369
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	2.06644	+	3.57918i	0.132290	+	0.229134i
$245$		0			0
$246$	−7.31038			−0.466093
$247$	12.1946	+	6.74404i	0.775923	+	0.429113i
$248$			2.23338i			0.141820i
$249$	−6.20064	+	3.57994i	−0.392949	+	0.226869i
$250$		0			0
$251$	3.57502	−	6.19212i	0.225653	−	0.390843i	−0.730862	−	0.682525i	$-0.760882\pi$
$251$	3.57502	−	6.19212i	0.225653	−	0.390843i	0.956515	+	0.291682i	$0.0942150\pi$
$252$	−3.59036			−0.226171
$253$	5.06582	−	8.77425i	0.318485	−	0.551632i
$254$	−15.5772	−	8.99351i	−0.977401	−	0.564303i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.7517	−	10.2489i	1.10732	−	0.639312i	0.169186	−	0.985584i	$-0.445886\pi$
$257$	17.7517	−	10.2489i	1.10732	−	0.639312i	0.938134	+	0.346272i	$0.112553\pi$
$258$	−4.10494	−	7.10996i	−0.255562	−	0.442647i
$259$	7.65781			0.475833
$260$		0			0
$261$	−5.35157			−0.331254
$262$	10.1731	+	17.6203i	0.628496	+	1.08859i
$263$	−15.3313	+	8.85153i	−0.945369	+	0.545809i	−0.891639	−	0.452747i	$-0.850444\pi$
$263$	−15.3313	+	8.85153i	−0.945369	+	0.545809i	−0.0537296	+	0.998556i	$0.517111\pi$
$264$	2.72603	−	4.72163i	0.167776	−	0.290596i
$265$		0			0
$266$	−12.0174	−	6.93825i	−0.736834	−	0.425411i
$267$	−4.79688	+	8.30844i	−0.293564	+	0.508468i
$268$	−14.7970			−0.903872
$269$	−9.09319	+	15.7499i	−0.554421	+	0.960286i	0.443527	+	0.896261i	$0.353727\pi$
$269$	−9.09319	+	15.7499i	−0.554421	+	0.960286i	−0.997948	+	0.0640250i	$0.979606\pi$
$270$		0			0
$271$	19.7188	−	11.3847i	1.19783	−	0.691569i	0.237762	−	0.971324i	$-0.423586\pi$
$271$	19.7188	−	11.3847i	1.19783	−	0.691569i	0.960072	+	0.279754i	$0.0902529\pi$
$272$			7.31038i			0.443257i
$273$	0.238545	+	12.9430i	0.0144374	+	0.783348i
$274$	−11.0407			−0.666995
$275$		0			0
$276$	−0.929155	−	1.60934i	−0.0559286	−	0.0968711i
$277$	14.1649	+	8.17814i	0.851089	+	0.491377i	0.861018	−	0.508574i	$-0.169827\pi$
$277$	14.1649	+	8.17814i	0.851089	+	0.491377i	−0.00992898	+	0.999951i	$0.503161\pi$
$278$	9.70193			0.581883
$279$	−1.93416	−	1.11669i	−0.115795	−	0.0668545i
$280$		0			0
$281$		−	7.82221i		−	0.466634i	−0.972401	−	0.233317i	$-0.925042\pi$
$281$		−	7.82221i		−	0.466634i	0.972401	−	0.233317i	$-0.0749580\pi$
$282$	−4.39681	−	2.53850i	−0.261826	−	0.151165i
$283$	−6.01483	+	3.47266i	−0.357544	+	0.206428i	−0.668003	−	0.744159i	$-0.732851\pi$
$283$	−6.01483	+	3.47266i	−0.357544	+	0.206428i	0.310459	+	0.950587i	$0.399517\pi$
$284$	−12.3804	+	7.14784i	−0.734643	+	0.424146i
$285$		0			0
$286$	−17.2023	−	9.51348i	−1.01719	−	0.562544i
$287$		−	26.2469i		−	1.54931i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	18.2208	+	31.5594i	1.07181	+	1.85643i
$290$		0			0
$291$		−	1.90831i		−	0.111867i
$292$	7.44876	−	12.9016i	0.435906	−	0.755011i
$293$	13.2122	−	22.8841i	0.771863	−	1.33691i	−0.164678	−	0.986347i	$-0.552659\pi$
$293$	13.2122	−	22.8841i	0.771863	−	1.33691i	0.936541	−	0.350558i	$-0.114008\pi$
$294$		−	5.89069i		−	0.343552i
$295$		0			0
$296$	1.06644	+	1.84713i	0.0619856	+	0.107362i
$297$	2.72603	+	4.72163i	0.158181	+	0.273977i
$298$			5.43817i			0.315025i
$299$	−5.73985	+	3.45647i	−0.331944	+	0.199893i
$300$		0			0
$301$	25.5273	−	14.7382i	1.47137	−	0.849496i
$302$	−15.4161	+	8.90050i	−0.887098	+	0.512166i
$303$	14.0779	+	8.12785i	0.808752	+	0.466933i
$304$		−	3.86493i		−	0.221669i
$305$		0			0
$306$	−6.33097	−	3.65519i	−0.361918	−	0.208953i
$307$	7.08581			0.404408			0.202204	−	0.979343i	$-0.435190\pi$
$307$	7.08581			0.404408			0.202204	+	0.979343i	$0.435190\pi$
$308$	16.9524	+	9.78745i	0.965950	+	0.557691i
$309$	6.48802	+	11.2376i	0.369091	+	0.639284i
$310$		0			0
$311$	−1.83017			−0.103780			−0.0518898	−	0.998653i	$-0.516524\pi$
$311$	−1.83017			−0.103780			−0.0518898	+	0.998653i	$0.516524\pi$
$312$	−3.08875	+	1.86001i	−0.174866	+	0.105302i
$313$		−	12.2499i		−	0.692403i	−0.938160	−	0.346201i	$-0.887471\pi$
$313$		−	12.2499i		−	0.692403i	0.938160	−	0.346201i	$-0.112529\pi$
$314$	−5.14117	+	2.96826i	−0.290133	+	0.167509i
$315$		0			0
$316$	1.31052	−	2.26990i	0.0737228	−	0.127692i
$317$	6.25100			0.351091			0.175546	−	0.984471i	$-0.443831\pi$
$317$	6.25100			0.351091			0.175546	+	0.984471i	$0.443831\pi$
$318$	1.11669	−	1.93416i	0.0626209	−	0.108463i
$319$	25.2681	+	14.5886i	1.41474	+	0.816802i
$320$		0			0
$321$	−4.95837	+	8.58814i	−0.276749	+	0.479343i
$322$	5.77812	−	3.33600i	0.322002	−	0.185908i
$323$	−14.1271	−	24.4688i	−0.786050	−	1.36148i
$324$	1.00000			0.0555556
$325$		0			0
$326$	15.5938			0.863658
$327$	−3.70544	−	6.41801i	−0.204911	−	0.354917i
$328$	6.33097	−	3.65519i	0.349570	−	0.201824i
$329$	9.11413	−	15.7861i	0.502478	−	0.870318i
$330$		0			0
$331$	−16.6067	−	9.58790i	−0.912789	−	0.526999i	−0.0314613	−	0.999505i	$-0.510016\pi$
$331$	−16.6067	−	9.58790i	−0.912789	−	0.526999i	−0.881327	+	0.472506i	$0.843349\pi$
$332$	3.57994	−	6.20064i	0.196475	−	0.340304i
$333$	−2.13288			−0.116881
$334$	0.929155	−	1.60934i	0.0508411	−	0.0880594i
$335$		0			0
$336$	3.10934	−	1.79518i	0.169629	−	0.0979351i
$337$			16.5450i			0.901262i	0.892710	+	0.450631i	$0.148801\pi$
$337$			16.5450i			0.901262i	−0.892710	+	0.450631i	$0.851199\pi$
$338$	6.91044	+	11.0112i	0.375878	+	0.598929i
$339$		0			0
$340$		0			0
$341$	6.08827	+	10.5452i	0.329698	+	0.571054i
$342$	3.34713	+	1.93247i	0.180992	+	0.104496i
$343$	−3.98282			−0.215052
$344$	7.10996	+	4.10494i	0.383344	+	0.221323i
$345$		0			0
$346$		−	24.3374i		−	1.30839i
$347$	5.16489	+	2.98195i	0.277266	+	0.160079i	0.632185	−	0.774818i	$-0.282158\pi$
$347$	5.16489	+	2.98195i	0.277266	+	0.160079i	−0.354919	+	0.934897i	$0.615492\pi$
$348$	4.63459	−	2.67578i	0.248440	−	0.143437i
$349$	−2.76302	+	1.59523i	−0.147901	+	0.0853906i	−0.572124	−	0.820167i	$-0.693880\pi$
$349$	−2.76302	+	1.59523i	−0.147901	+	0.0853906i	0.424223	+	0.905558i	$0.360547\pi$
$350$		0			0
$351$	−0.0664404	−	3.60494i	−0.00354632	−	0.192417i
$352$			5.45207i			0.290596i
$353$	14.0524	+	24.3395i	0.747934	+	1.29546i	0.948811	+	0.315844i	$0.102288\pi$
$353$	14.0524	+	24.3395i	0.747934	+	1.29546i	−0.200877	+	0.979616i	$0.564379\pi$
$354$	0.137285	+	0.237785i	0.00729663	+	0.0126381i
$355$		0			0
$356$		−	9.59376i		−	0.508468i
$357$	13.1234	−	22.7305i	0.694566	−	1.20302i
$358$	1.53429	−	2.65746i	0.0810895	−	0.140451i
$359$		−	22.7404i		−	1.20019i	−0.799927	−	0.600097i	$-0.795128\pi$
$359$		−	22.7404i		−	1.20019i	0.799927	−	0.600097i	$-0.204872\pi$
$360$		0			0
$361$	−2.03115	−	3.51806i	−0.106903	−	0.185161i
$362$	−2.29688	−	3.97831i	−0.120721	−	0.209095i
$363$		−	18.7250i		−	0.982810i
$364$	−6.67810	−	11.0897i	−0.350028	−	0.581259i
$365$		0			0
$366$	3.57918	−	2.06644i	0.187087	−	0.108015i
$367$	−26.1824	+	15.1164i	−1.36671	+	0.789072i	−0.990507	−	0.137464i	$-0.956105\pi$
$367$	−26.1824	+	15.1164i	−1.36671	+	0.789072i	−0.376206	+	0.926536i	$0.622771\pi$
$368$	1.60934	+	0.929155i	0.0838928	+	0.0484356i
$369$			7.31038i			0.380563i
$370$		0			0
$371$	6.94435	+	4.00932i	0.360533	+	0.208154i
$372$	2.23338			0.115795
$373$	−4.04965	−	2.33807i	−0.209683	−	0.121061i	0.391481	−	0.920186i	$-0.371963\pi$
$373$	−4.04965	−	2.33807i	−0.209683	−	0.121061i	−0.601164	+	0.799126i	$0.705296\pi$
$374$	19.9283	+	34.5169i	1.03047	+	1.78483i
$375$		0			0
$376$	5.07700			0.261826
$377$	−9.95396	−	16.5296i	−0.512655	−	0.851320i
$378$			3.59036i			0.184668i
$379$	−18.5598	+	10.7155i	−0.953353	+	0.550419i	−0.894121	−	0.447826i	$-0.852199\pi$
$379$	−18.5598	+	10.7155i	−0.953353	+	0.550419i	−0.0592321	+	0.998244i	$0.518865\pi$
$380$		0			0
$381$	−8.99351	+	15.5772i	−0.460751	+	0.798045i
$382$	−14.0601			−0.719379
$383$	−0.0256044	+	0.0443481i	−0.00130832	+	0.00226608i	−0.866679	−	0.498867i	$-0.833750\pi$
$383$	−0.0256044	+	0.0443481i	−0.00130832	+	0.00226608i	0.865371	+	0.501133i	$0.167083\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	−12.5444	+	21.7276i	−0.638494	+	1.10590i
$387$	−7.10996	+	4.10494i	−0.361420	+	0.208666i
$388$	0.954155	+	1.65264i	0.0484399	+	0.0839003i
$389$	5.35157			0.271335			0.135668	−	0.990754i	$-0.456682\pi$
$389$	5.35157			0.271335			0.135668	+	0.990754i	$0.456682\pi$
$390$		0			0
$391$	13.5849			0.687020
$392$	2.94535	+	5.10149i	0.148762	+	0.257664i
$393$	17.6203	−	10.1731i	0.888827	−	0.513165i
$394$	4.59737	−	7.96287i	0.231612	−	0.401164i
$395$		0			0
$396$	−4.72163	−	2.72603i	−0.237271	−	0.136988i
$397$	4.25359	−	7.36744i	0.213482	−	0.369761i	−0.739320	−	0.673354i	$-0.764853\pi$
$397$	4.25359	−	7.36744i	0.213482	−	0.369761i	0.952802	+	0.303593i	$0.0981863\pi$
$398$	23.6792			1.18693
$399$	−6.93825	+	12.0174i	−0.347347	+	0.601623i
$400$		0			0
$401$	−20.2467	+	11.6894i	−1.01107	+	0.583741i	−0.911505	−	0.411290i	$-0.865078\pi$
$401$	−20.2467	+	11.6894i	−1.01107	+	0.583741i	−0.0995649	+	0.995031i	$0.531745\pi$
$402$			14.7970i			0.738008i
$403$	−0.148387	−	8.05120i	−0.00739166	−	0.401059i
$404$	−16.2557			−0.808752
$405$		0			0
$406$	9.60703	+	16.6399i	0.476789	+	0.825823i
$407$	10.0707	+	5.81431i	0.499185	+	0.288204i
$408$	7.31038			0.361918
$409$	4.51511	+	2.60680i	0.223258	+	0.128898i	0.607458	−	0.794352i	$-0.292189\pi$
$409$	4.51511	+	2.60680i	0.223258	+	0.128898i	−0.384200	+	0.923250i	$0.625523\pi$
$410$		0			0
$411$			11.0407i			0.544599i
$412$	−11.2376	−	6.48802i	−0.553636	−	0.319642i
$413$	−0.853735	+	0.492904i	−0.0420095	+	0.0242542i
$414$	−1.60934	+	0.929155i	−0.0790949	+	0.0456655i
$415$		0			0
$416$	1.74493	−	3.15519i	0.0855523	−	0.154696i
$417$		−	9.70193i		−	0.475105i
$418$	−10.5359	−	18.2488i	−0.515329	−	0.892577i
$419$	9.10066	+	15.7628i	0.444596	+	0.770064i	0.998024	−	0.0628337i	$-0.0200138\pi$
$419$	9.10066	+	15.7628i	0.444596	+	0.770064i	−0.553428	+	0.832897i	$0.686680\pi$
$420$		0			0
$421$			25.6463i			1.24992i	0.780656	+	0.624961i	$0.214885\pi$
$421$			25.6463i			1.24992i	−0.780656	+	0.624961i	$0.785115\pi$
$422$	−4.99303	+	8.64818i	−0.243057	+	0.420987i
$423$	−2.53850	+	4.39681i	−0.123426	+	0.213780i
$424$			2.23338i			0.108463i
$425$		0			0
$426$	7.14784	+	12.3804i	0.346314	+	0.599834i
$427$	7.41927	+	12.8505i	0.359043	+	0.621882i
$428$		−	9.91673i		−	0.479343i
$429$	−9.51348	+	17.2023i	−0.459315	+	0.830535i
$430$		0			0
$431$	−1.79193	+	1.03457i	−0.0863142	+	0.0498335i	−0.542536	−	0.840033i	$-0.682536\pi$
$431$	−1.79193	+	1.03457i	−0.0863142	+	0.0498335i	0.456222	+	0.889866i	$0.349202\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−0.815649	−	0.470915i	−0.0391976	−	0.0226307i	0.480273	−	0.877119i	$-0.340538\pi$
$433$	−0.815649	−	0.470915i	−0.0391976	−	0.0226307i	−0.519471	+	0.854488i	$0.673871\pi$
$434$			8.01864i			0.384907i
$435$		0			0
$436$	6.41801	+	3.70544i	0.307367	+	0.177458i
$437$	−7.18224			−0.343573
$438$	−12.9016	−	7.44876i	−0.616464	−	0.355915i
$439$	1.80132	+	3.11997i	0.0859722	+	0.148908i	0.905805	−	0.423695i	$-0.139267\pi$
$439$	1.80132	+	3.11997i	0.0859722	+	0.148908i	−0.819833	+	0.572603i	$0.805934\pi$
$440$		0			0
$441$	−5.89069			−0.280509
$442$	−0.485704	−	26.3535i	−0.0231026	−	1.25351i
$443$		−	5.05095i		−	0.239978i	−0.992775	−	0.119989i	$-0.961714\pi$
$443$		−	5.05095i		−	0.239978i	0.992775	−	0.119989i	$-0.0382859\pi$
$444$	1.84713	−	1.06644i	0.0876609	−	0.0506110i
$445$		0			0
$446$	11.1910	−	19.3833i	0.529908	−	0.917828i
$447$	5.43817			0.257217
$448$	−1.79518	+	3.10934i	−0.0848143	+	0.146903i
$449$	4.70017	+	2.71364i	0.221815	+	0.128065i	0.606790	−	0.794862i	$-0.292457\pi$
$449$	4.70017	+	2.71364i	0.221815	+	0.128065i	−0.384976	+	0.922927i	$0.625790\pi$
$450$		0			0
$451$	19.9283	−	34.5169i	0.938389	−	1.62534i
$452$		0			0
$453$	8.90050	+	15.4161i	0.418182	+	0.724312i
$454$	12.9853			0.609431
$455$		0			0
$456$	−3.86493			−0.180992
$457$	−10.8416	−	18.7782i	−0.507147	−	0.878405i	−0.999966	−	0.00827291i	$-0.997367\pi$
$457$	−10.8416	−	18.7782i	−0.507147	−	0.878405i	0.492818	−	0.870132i	$-0.335967\pi$
$458$	−12.5102	+	7.22276i	−0.584562	+	0.337497i
$459$	−3.65519	+	6.33097i	−0.170610	+	0.295505i
$460$		0			0
$461$	−25.6364	−	14.8012i	−1.19401	−	0.689359i	−0.234793	−	0.972045i	$-0.575441\pi$
$461$	−25.6364	−	14.8012i	−1.19401	−	0.689359i	−0.959212	+	0.282686i	$0.908775\pi$
$462$	9.78745	−	16.9524i	0.455353	−	0.788695i
$463$	28.2075			1.31091			0.655457	−	0.755232i	$-0.272476\pi$
$463$	28.2075			1.31091			0.655457	+	0.755232i	$0.272476\pi$
$464$	−2.67578	+	4.63459i	−0.124220	+	0.215156i
$465$		0			0
$466$	−10.7711	+	6.21869i	−0.498961	+	0.288075i
$467$			8.17371i			0.378234i	0.981955	+	0.189117i	$0.0605626\pi$
$467$			8.17371i			0.378234i	−0.981955	+	0.189117i	$0.939437\pi$
$468$	1.86001	+	3.08875i	0.0859789	+	0.142777i
$469$	−53.1266			−2.45316
$470$		0			0
$471$	2.96826	+	5.14117i	0.136770	+	0.236893i
$472$	−0.237785	−	0.137285i	−0.0109450	−	0.00631907i
$473$	44.7608			2.05810
$474$	−2.26990	−	1.31052i	−0.104260	−	0.0601944i
$475$		0			0
$476$			26.2469i			1.20302i
$477$	−1.93416	−	1.11669i	−0.0885593	−	0.0511297i
$478$	−3.61118	+	2.08491i	−0.165171	+	0.0953618i
$479$	−10.1231	+	5.84458i	−0.462537	+	0.267046i	−0.713110	−	0.701052i	$-0.752714\pi$
$479$	−10.1231	+	5.84458i	−0.462537	+	0.267046i	0.250573	+	0.968098i	$0.419381\pi$
$480$		0			0
$481$	−3.96718	−	6.58793i	−0.180888	−	0.300384i
$482$			1.88407i			0.0858170i
$483$	−3.33600	−	5.77812i	−0.151793	−	0.262914i
$484$	9.36252	+	16.2164i	0.425569	+	0.737107i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−15.9438	+	27.6154i	−0.722481	+	1.25137i	0.237522	+	0.971382i	$0.423665\pi$
$487$	−15.9438	+	27.6154i	−0.722481	+	1.25137i	−0.960003	+	0.279991i	$0.909668\pi$
$488$	−2.06644	+	3.57918i	−0.0935434	+	0.162022i
$489$		−	15.5938i		−	0.705174i
$490$		0			0
$491$	9.77506	+	16.9309i	0.441142	+	0.764080i	0.997775	−	0.0666784i	$-0.0212402\pi$
$491$	9.77506	+	16.9309i	0.441142	+	0.764080i	−0.556632	+	0.830759i	$0.687907\pi$
$492$	−3.65519	−	6.33097i	−0.164789	−	0.285422i
$493$			39.1220i			1.76197i
$494$	0.256787	+	13.9328i	0.0115534	+	0.626868i
$495$		0			0
$496$	−1.93416	+	1.11669i	−0.0868465	+	0.0501409i
$497$	−44.4502	+	25.6633i	−1.99386	+	1.15116i
$498$	−6.20064	−	3.57994i	−0.277857	−	0.160421i
$499$			39.3428i			1.76123i	0.473836	+	0.880613i	$0.342869\pi$
$499$			39.3428i			1.76123i	−0.473836	+	0.880613i	$0.657131\pi$
$500$		0			0
$501$	−1.60934	−	0.929155i	−0.0719002	−	0.0415116i
$502$	7.15005			0.319122
$503$	12.4127	+	7.16650i	0.553457	+	0.319538i	0.750515	−	0.660853i	$-0.229806\pi$
$503$	12.4127	+	7.16650i	0.553457	+	0.319538i	−0.197058	+	0.980392i	$0.563139\pi$
$504$	−1.79518	−	3.10934i	−0.0799637	−	0.138501i
$505$		0			0
$506$	10.1316			0.450406
$507$	11.0112	−	6.91044i	0.489023	−	0.306903i
$508$		−	17.9870i		−	0.798045i
$509$	3.23839	−	1.86968i	0.143539	−	0.0828723i	−0.426511	−	0.904483i	$-0.640257\pi$
$509$	3.23839	−	1.86968i	0.143539	−	0.0828723i	0.570050	+	0.821610i	$0.306924\pi$
$510$		0			0
$511$	26.7437	−	46.3215i	1.18307	−	2.04914i
$512$	−1.00000			−0.0441942
$513$	1.93247	−	3.34713i	0.0853204	−	0.147779i
$514$	17.7517	+	10.2489i	0.782994	+	0.452062i
$515$		0			0
$516$	4.10494	−	7.10996i	0.180710	−	0.312999i
$517$	23.9717	−	13.8401i	1.05427	−	0.608685i
$518$	3.82891	+	6.63186i	0.168232	+	0.291387i
$519$	−24.3374			−1.06829
$520$		0			0
$521$	−40.2722			−1.76436			−0.882178	−	0.470915i	$-0.843924\pi$
$521$	−40.2722			−1.76436			−0.882178	+	0.470915i	$0.843924\pi$
$522$	−2.67578	−	4.63459i	−0.117116	−	0.202851i
$523$	19.7853	−	11.4230i	0.865150	−	0.499495i	−0.000583330	−	1.00000i	$-0.500186\pi$
$523$	19.7853	−	11.4230i	0.865150	−	0.499495i	0.865734	+	0.500505i	$0.166852\pi$
$524$	−10.1731	+	17.6203i	−0.444414	+	0.769747i
$525$		0			0
$526$	−15.3313	−	8.85153i	−0.668477	−	0.385945i
$527$	−8.16343	+	14.1395i	−0.355605	+	0.615925i
$528$	5.45207			0.237271
$529$	−9.77334	+	16.9279i	−0.424928	+	0.735997i
$530$		0			0
$531$	0.237785	−	0.137285i	0.0103190	−	0.00595768i
$532$		−	13.8765i		−	0.601623i
$533$	−22.5799	+	13.5974i	−0.978045	+	0.588967i
$534$	−9.59376			−0.415163
$535$		0			0
$536$	−7.39851	−	12.8146i	−0.319567	−	0.553506i
$537$	−2.65746	−	1.53429i	−0.114678	−	0.0662093i
$538$	−18.1864			−0.784070
$539$	27.8137	+	16.0582i	1.19802	+	0.691677i
$540$		0			0
$541$			18.9610i			0.815196i	0.913162	+	0.407598i	$0.133633\pi$
$541$			18.9610i			0.815196i	−0.913162	+	0.407598i	$0.866367\pi$
$542$	19.7188	+	11.3847i	0.846996	+	0.489013i
$543$	−3.97831	+	2.29688i	−0.170726	+	0.0985685i
$544$	−6.33097	+	3.65519i	−0.271438	+	0.156715i
$545$		0			0
$546$	−11.0897	+	6.67810i	−0.474596	+	0.285796i
$547$		−	26.7863i		−	1.14530i	−0.819801	−	0.572649i	$-0.805916\pi$
$547$		−	26.7863i		−	1.14530i	0.819801	−	0.572649i	$-0.194084\pi$
$548$	−5.52037	−	9.56156i	−0.235818	−	0.408450i
$549$	−2.06644	−	3.57918i	−0.0881935	−	0.152756i
$550$		0			0
$551$		−	20.6834i		−	0.881144i
$552$	0.929155	−	1.60934i	0.0395475	−	0.0684982i
$553$	4.70526	−	8.14974i	0.200088	−	0.346562i
$554$			16.3563i			0.694911i
$555$		0			0
$556$	4.85096	+	8.40212i	0.205727	+	0.356329i
$557$	13.1189	+	22.7227i	0.555867	+	0.962791i	0.997835	+	0.0657599i	$0.0209471\pi$
$557$	13.1189	+	22.7227i	0.555867	+	0.962791i	−0.441968	+	0.897031i	$0.645720\pi$
$558$		−	2.23338i		−	0.0945465i
$559$	−25.9037	−	14.3257i	−1.09561	−	0.605911i
$560$		0			0
$561$	34.5169	−	19.9283i	1.45730	−	0.841375i
$562$	6.77423	−	3.91110i	0.285754	−	0.164980i
$563$	14.0452	+	8.10900i	0.591935	+	0.341754i	0.765862	−	0.643005i	$-0.222312\pi$
$563$	14.0452	+	8.10900i	0.591935	+	0.341754i	−0.173927	+	0.984758i	$0.555646\pi$
$564$		−	5.07700i		−	0.213780i
$565$		0			0
$566$	−6.01483	−	3.47266i	−0.252822	−	0.145967i
$567$	3.59036			0.150781
$568$	−12.3804	−	7.14784i	−0.519471	−	0.299917i
$569$	−17.1092	−	29.6340i	−0.717255	−	1.24232i	−0.962083	−	0.272755i	$-0.912065\pi$
$569$	−17.1092	−	29.6340i	−0.717255	−	1.24232i	0.244829	−	0.969566i	$-0.421268\pi$
$570$		0			0
$571$	0.151070			0.00632206			0.00316103	−	0.999995i	$-0.498994\pi$
$571$	0.151070			0.00632206			0.00316103	+	0.999995i	$0.498994\pi$
$572$	−0.362237	−	19.6544i	−0.0151459	−	0.821791i
$573$			14.0601i			0.587371i
$574$	22.7305	−	13.1234i	0.948752	−	0.547762i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	33.7742			1.40604			0.703019	−	0.711171i	$-0.251835\pi$
$577$	33.7742			1.40604			0.703019	+	0.711171i	$0.251835\pi$
$578$	−18.2208	+	31.5594i	−0.757886	+	1.31270i
$579$	21.7276	+	12.5444i	0.902966	+	0.521328i
$580$		0			0
$581$	12.8533	−	22.2625i	0.533244	−	0.923605i
$582$	1.65264	−	0.954155i	0.0685043	−	0.0395510i
$583$	6.08827	+	10.5452i	0.252150	+	0.436737i
$584$	14.8975			0.616464
$585$		0			0
$586$	26.4243			1.09158
$587$	16.8030	+	29.1037i	0.693535	+	1.20124i	0.970672	+	0.240408i	$0.0772812\pi$
$587$	16.8030	+	29.1037i	0.693535	+	1.20124i	−0.277137	+	0.960831i	$0.589385\pi$
$588$	5.10149	−	2.94535i	0.210382	−	0.121464i
$589$	4.31593	−	7.47541i	0.177835	−	0.308019i
$590$		0			0
$591$	−7.96287	−	4.59737i	−0.327549	−	0.189110i
$592$	−1.06644	+	1.84713i	−0.0438304	+	0.0759165i
$593$	−36.7529			−1.50926			−0.754630	−	0.656150i	$-0.772184\pi$
$593$	−36.7529			−1.50926			−0.754630	+	0.656150i	$0.772184\pi$
$594$	−2.72603	+	4.72163i	−0.111851	+	0.193731i
$595$		0			0
$596$	−4.70959	+	2.71908i	−0.192912	+	0.111378i
$597$		−	23.6792i		−	0.969124i
$598$	−5.86332	−	3.24262i	−0.239769	−	0.132601i
$599$	24.5241			1.00203			0.501015	−	0.865439i	$-0.332960\pi$
$599$	24.5241			1.00203			0.501015	+	0.865439i	$0.332960\pi$
$600$		0			0
$601$	18.7548	+	32.4843i	0.765025	+	1.32506i	0.940233	+	0.340531i	$0.110607\pi$
$601$	18.7548	+	32.4843i	0.765025	+	1.32506i	−0.175208	+	0.984531i	$0.556060\pi$
$602$	25.5273	+	14.7382i	1.04042	+	0.600685i
$603$	14.7970			0.602581
$604$	−15.4161	−	8.90050i	−0.627273	−	0.362156i
$605$		0			0
$606$			16.2557i			0.660343i
$607$	−40.2796	−	23.2554i	−1.63490	−	0.943909i	−0.982552	−	0.185988i	$-0.940452\pi$
$607$	−40.2796	−	23.2554i	−1.63490	−	0.943909i	−0.652346	−	0.757921i	$-0.726215\pi$
$608$	3.34713	−	1.93247i	0.135744	−	0.0783718i
$609$	16.6399	−	9.60703i	0.674281	−	0.389297i
$610$		0			0
$611$	−18.3023	+	0.337318i	−0.740430	+	0.0136464i
$612$		−	7.31038i		−	0.295505i
$613$	5.14785	+	8.91634i	0.207920	+	0.360128i	0.951059	−	0.309009i	$-0.0999974\pi$
$613$	5.14785	+	8.91634i	0.207920	+	0.360128i	−0.743139	+	0.669137i	$0.766664\pi$
$614$	3.54290	+	6.13649i	0.142980	+	0.247649i
$615$		0			0
$616$			19.5749i			0.788695i
$617$	17.8404	−	30.9005i	0.718228	−	1.24401i	−0.243473	−	0.969908i	$-0.578287\pi$
$617$	17.8404	−	30.9005i	0.718228	−	1.24401i	0.961701	−	0.274100i	$-0.0883798\pi$
$618$	−6.48802	+	11.2376i	−0.260987	+	0.452042i
$619$		−	12.9815i		−	0.521772i	−0.965370	−	0.260886i	$-0.915985\pi$
$619$		−	12.9815i		−	0.521772i	0.965370	−	0.260886i	$-0.0840146\pi$
$620$		0			0
$621$	0.929155	+	1.60934i	0.0372857	+	0.0645807i
$622$	−0.915086	−	1.58498i	−0.0366916	−	0.0635517i
$623$		−	34.4451i		−	1.38001i
$624$	−3.15519	−	1.74493i	−0.126309	−	0.0698531i
$625$		0			0
$626$	10.6087	−	6.12493i	0.424008	−	0.244801i
$627$	−18.2488	+	10.5359i	−0.728786	+	0.420765i
$628$	−5.14117	−	2.96826i	−0.205155	−	0.118446i
$629$			15.5922i			0.621700i
$630$		0			0
$631$	−18.4953	−	10.6783i	−0.736287	−	0.425096i	0.0844307	−	0.996429i	$-0.473093\pi$
$631$	−18.4953	−	10.6783i	−0.736287	−	0.425096i	−0.820718	+	0.571334i	$0.806426\pi$
$632$	2.62105			0.104260
$633$	8.64818	+	4.99303i	0.343734	+	0.198455i
$634$	3.12550	+	5.41352i	0.124129	+	0.214999i
$635$		0			0
$636$	2.23338			0.0885593
$637$	−10.9567	−	18.1949i	−0.434122	−	0.720907i
$638$			29.1771i			1.15513i
$639$	12.3804	−	7.14784i	0.489762	−	0.282764i
$640$		0			0
$641$	−6.49169	+	11.2439i	−0.256407	+	0.444109i	−0.965277	−	0.261230i	$-0.915872\pi$
$641$	−6.49169	+	11.2439i	−0.256407	+	0.444109i	0.708870	+	0.705339i	$0.249205\pi$
$642$	−9.91673			−0.391382
$643$	−7.90323	+	13.6888i	−0.311673	+	0.539834i	−0.978725	−	0.205178i	$-0.934223\pi$
$643$	−7.90323	+	13.6888i	−0.311673	+	0.539834i	0.667052	+	0.745012i	$0.267556\pi$
$644$	5.77812	+	3.33600i	0.227690	+	0.131457i
$645$		0			0
$646$	14.1271	−	24.4688i	0.555822	−	0.962711i
$647$	19.8219	−	11.4442i	0.779277	−	0.449916i	−0.0568967	−	0.998380i	$-0.518121\pi$
$647$	19.8219	−	11.4442i	0.779277	−	0.449916i	0.836174	+	0.548464i	$0.184787\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−1.49698			−0.0587615
$650$		0			0
$651$	8.01864			0.314275
$652$	7.79688	+	13.5046i	0.305349	+	0.528881i
$653$	−1.87183	+	1.08070i	−0.0732504	+	0.0422911i	−0.536178	−	0.844105i	$-0.680132\pi$
$653$	−1.87183	+	1.08070i	−0.0732504	+	0.0422911i	0.462927	+	0.886396i	$0.346799\pi$
$654$	3.70544	−	6.41801i	0.144894	−	0.250964i
$655$		0			0
$656$	6.33097	+	3.65519i	0.247183	+	0.142711i
$657$	−7.44876	+	12.9016i	−0.290604	+	0.503340i
$658$	18.2283			0.710611
$659$	9.79863	−	16.9717i	0.381700	−	0.661124i	−0.609605	−	0.792705i	$-0.708672\pi$
$659$	9.79863	−	16.9717i	0.381700	−	0.661124i	0.991305	+	0.131581i	$0.0420053\pi$
$660$		0			0
$661$	−24.8286	+	14.3348i	−0.965719	+	0.557558i	−0.897929	−	0.440141i	$-0.854928\pi$
$661$	−24.8286	+	14.3348i	−0.965719	+	0.557558i	−0.0677909	+	0.997700i	$0.521595\pi$
$662$		−	19.1758i		−	0.745289i
$663$	−26.3535	+	0.485704i	−1.02348	+	0.0188632i
$664$	7.15988			0.277857
$665$		0			0
$666$	−1.06644	−	1.84713i	−0.0413237	−	0.0715748i
$667$	8.61251	+	4.97244i	0.333478	+	0.192534i
$668$	1.85831			0.0719002
$669$	−19.3833	−	11.1910i	−0.749404	−	0.432668i
$670$		0			0
$671$			22.5327i			0.869867i
$672$	3.10934	+	1.79518i	0.119946	+	0.0692506i
$673$	44.0166	−	25.4130i	1.69672	−	0.979599i	0.747878	−	0.663837i	$-0.231073\pi$
$673$	44.0166	−	25.4130i	1.69672	−	0.979599i	0.948838	−	0.315763i	$-0.102260\pi$
$674$	−14.3284	+	8.27248i	−0.551908	+	0.318644i
$675$		0			0
$676$	−6.08074	+	11.4902i	−0.233874	+	0.441931i
$677$		−	15.4058i		−	0.592093i	−0.955174	−	0.296046i	$-0.904332\pi$
$677$		−	15.4058i		−	0.592093i	0.955174	−	0.296046i	$-0.0956683\pi$
$678$		0			0
$679$	3.42576	+	5.93359i	0.131469	+	0.227710i
$680$		0			0
$681$		−	12.9853i		−	0.497598i
$682$	−6.08827	+	10.5452i	−0.233132	+	0.403796i
$683$	−11.1227	+	19.2650i	−0.425597	+	0.737155i	−0.996476	−	0.0838788i	$-0.973269\pi$
$683$	−11.1227	+	19.2650i	−0.425597	+	0.737155i	0.570879	+	0.821034i	$0.306602\pi$
$684$			3.86493i			0.147779i
$685$		0			0
$686$	−1.99141	−	3.44922i	−0.0760324	−	0.131692i
$687$	7.22276	+	12.5102i	0.275565	+	0.477293i
$688$			8.20988i			0.312999i
$689$	−0.148387	−	8.05120i	−0.00565308	−	0.306726i
$690$		0			0
$691$	5.31663	−	3.06956i	0.202254	−	0.116771i	−0.395452	−	0.918486i	$-0.629412\pi$
$691$	5.31663	−	3.06956i	0.202254	−	0.116771i	0.597706	+	0.801715i	$0.296079\pi$
$692$	21.0768	−	12.1687i	0.801219	−	0.462584i
$693$	−16.9524	−	9.78745i	−0.643967	−	0.371794i
$694$			5.96390i			0.226387i
$695$		0			0
$696$	4.63459	+	2.67578i	0.175674	+	0.101425i
$697$	53.4416			2.02425
$698$	−2.76302	−	1.59523i	−0.104582	−	0.0603803i
$699$	6.21869	+	10.7711i	0.235212	+	0.407400i
$700$		0			0
$701$	−24.7793			−0.935902			−0.467951	−	0.883754i	$-0.655008\pi$
$701$	−24.7793			−0.935902			−0.467951	+	0.883754i	$0.655008\pi$
$702$	3.08875	−	1.86001i	0.116577	−	0.0702015i
$703$		−	8.24344i		−	0.310907i
$704$	−4.72163	+	2.72603i	−0.177953	+	0.102741i
$705$		0			0
$706$	−14.0524	+	24.3395i	−0.528869	+	0.916029i
$707$	−58.3638			−2.19500
$708$	−0.137285	+	0.237785i	−0.00515950	+	0.00893652i
$709$	−22.3507	−	12.9042i	−0.839398	−	0.484627i	0.0176613	−	0.999844i	$-0.494378\pi$
$709$	−22.3507	−	12.9042i	−0.839398	−	0.484627i	−0.857060	+	0.515217i	$0.827711\pi$
$710$		0			0
$711$	−1.31052	+	2.26990i	−0.0491485	+	0.0851277i
$712$	8.30844	−	4.79688i	0.311372	−	0.179771i
$713$	2.07516	+	3.59428i	0.0777152	+	0.134607i
$714$	26.2469			0.982265
$715$		0			0
$716$	3.06857			0.114678
$717$	2.08491	+	3.61118i	0.0778625	+	0.134862i
$718$	19.6938	−	11.3702i	0.734966	−	0.424333i
$719$	11.7949	−	20.4293i	0.439874	−	0.761884i	−0.557806	−	0.829972i	$-0.688357\pi$
$719$	11.7949	−	20.4293i	0.439874	−	0.761884i	0.997679	+	0.0680879i	$0.0216898\pi$
$720$		0			0
$721$	−40.3470	−	23.2943i	−1.50260	−	0.867527i
$722$	2.03115	−	3.51806i	0.0755917	−	0.130929i
$723$	1.88407			0.0700693
$724$	2.29688	−	3.97831i	0.0853628	−	0.147853i
$725$		0			0
$726$	16.2164	−	9.36252i	0.601846	−	0.347476i
$727$			31.4651i			1.16698i	0.812121	+	0.583489i	$0.198313\pi$
$727$			31.4651i			1.16698i	−0.812121	+	0.583489i	$0.801687\pi$
$728$	6.26493	−	11.3283i	0.232194	−	0.419854i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	30.0087	+	51.9765i	1.10991	+	1.92242i
$732$	3.57918	+	2.06644i	0.132290	+	0.0763778i
$733$	−32.2822			−1.19237			−0.596186	−	0.802847i	$-0.703318\pi$
$733$	−32.2822			−1.19237			−0.596186	+	0.802847i	$0.703318\pi$
$734$	−26.1824	−	15.1164i	−0.966412	−	0.557958i
$735$		0			0
$736$			1.85831i			0.0684982i
$737$	−69.8660	−	40.3372i	−2.57355	−	1.48584i
$738$	−6.33097	+	3.65519i	−0.233046	+	0.134549i
$739$	13.2643	−	7.65817i	0.487936	−	0.281710i	−0.235782	−	0.971806i	$-0.575765\pi$
$739$	13.2643	−	7.65817i	0.487936	−	0.281710i	0.723718	+	0.690096i	$0.242432\pi$
$740$		0			0
$741$	13.9328	−	0.256787i	0.511836	−	0.00943332i
$742$			8.01864i			0.294374i
$743$	−12.6161	−	21.8518i	−0.462841	−	0.801663i	0.536261	−	0.844052i	$-0.319836\pi$
$743$	−12.6161	−	21.8518i	−0.462841	−	0.801663i	−0.999101	+	0.0423891i	$0.986503\pi$
$744$	1.11669	+	1.93416i	0.0409399	+	0.0709099i
$745$		0			0
$746$		−	4.67614i		−	0.171206i
$747$	−3.57994	+	6.20064i	−0.130983	+	0.226869i
$748$	−19.9283	+	34.5169i	−0.728652	+	1.26206i
$749$		−	35.6047i		−	1.30097i
$750$		0			0
$751$	7.69444	+	13.3272i	0.280774	+	0.486315i	0.971576	−	0.236729i	$-0.0760755\pi$
$751$	7.69444	+	13.3272i	0.280774	+	0.486315i	−0.690802	+	0.723044i	$0.742742\pi$
$752$	2.53850	+	4.39681i	0.0925695	+	0.160335i
$753$		−	7.15005i		−	0.260562i
$754$	9.33811	−	16.8852i	0.340074	−	0.614923i
$755$		0			0
$756$	−3.10934	+	1.79518i	−0.113086	+	0.0652901i
$757$	−31.4879	+	18.1796i	−1.14445	+	0.660747i	−0.947528	−	0.319673i	$-0.896427\pi$
$757$	−31.4879	+	18.1796i	−1.14445	+	0.660747i	−0.196920	+	0.980420i	$0.563094\pi$
$758$	−18.5598	−	10.7155i	−0.674122	−	0.389205i
$759$		−	10.1316i		−	0.367755i
$760$		0			0
$761$	−27.4056	−	15.8226i	−0.993453	−	0.573570i	−0.0871481	−	0.996195i	$-0.527775\pi$
$761$	−27.4056	−	15.8226i	−0.993453	−	0.573570i	−0.906305	+	0.422625i	$0.861109\pi$
$762$	−17.9870			−0.651601
$763$	23.0430	+	13.3039i	0.834211	+	0.481632i
$764$	−7.03007	−	12.1764i	−0.254339	−	0.440528i
$765$		0			0
$766$	−0.0512087			−0.00185025
$767$	0.866322	+	0.479107i	0.0312811	+	0.0172995i
$768$			1.00000i			0.0360844i
$769$	10.0722	−	5.81521i	0.363214	−	0.209702i	−0.307276	−	0.951621i	$-0.599417\pi$
$769$	10.0722	−	5.81521i	0.363214	−	0.209702i	0.670490	+	0.741919i	$0.266084\pi$
$770$		0			0
$771$	10.2489	−	17.7517i	0.369107	−	0.639312i
$772$	−25.0888			−0.902966
$773$	−14.5823	+	25.2573i	−0.524490	+	0.908443i	0.475104	+	0.879930i	$0.342410\pi$
$773$	−14.5823	+	25.2573i	−0.524490	+	0.908443i	−0.999593	+	0.0285128i	$0.990923\pi$
$774$	−7.10996	−	4.10494i	−0.255562	−	0.147549i
$775$		0			0
$776$	−0.954155	+	1.65264i	−0.0342522	+	0.0593265i
$777$	6.63186	−	3.82891i	0.237917	−	0.137361i
$778$	2.67578	+	4.63459i	0.0959315	+	0.166158i
$779$	−28.2541			−1.01231
$780$		0			0
$781$	−77.9410			−2.78895
$782$	6.79247	+	11.7649i	0.242898	+	0.420712i
$783$	−4.63459	+	2.67578i	−0.165627	+	0.0956247i
$784$	−2.94535	+	5.10149i	−0.105191	+	0.182196i
$785$		0			0
$786$	17.6203	+	10.1731i	0.628496	+	0.362862i
$787$	−8.03414	+	13.9155i	−0.286386	+	0.496035i	−0.972944	−	0.231039i	$-0.925787\pi$
$787$	−8.03414	+	13.9155i	−0.286386	+	0.496035i	0.686558	+	0.727075i	$0.259121\pi$
$788$	9.19473			0.327549
$789$	−8.85153	+	15.3313i	−0.315123	+	0.545809i
$790$		0			0
$791$		0			0
$792$		−	5.45207i		−	0.193731i
$793$	7.21159	−	13.0400i	0.256091	−	0.463065i
$794$	8.50719			0.301909
$795$		0			0
$796$	11.8396	+	20.5068i	0.419643	+	0.726843i
$797$	33.8249	+	19.5288i	1.19814	+	0.691745i	0.960140	−	0.279520i	$-0.0901754\pi$
$797$	33.8249	+	19.5288i	1.19814	+	0.691745i	0.237998	+	0.971266i	$0.423509\pi$
$798$	−13.8765			−0.491223
$799$	32.1423	+	18.5574i	1.13711	+	0.656513i
$800$		0			0
$801$			9.59376i			0.338979i
$802$	−20.2467	−	11.6894i	−0.714934	−	0.412767i
$803$	70.3405	−	40.6111i	2.48226	−	1.43314i
$804$	−12.8146	+	7.39851i	−0.451936	+	0.260925i
$805$		0			0
$806$	6.89835	−	4.15411i	0.242984	−	0.146322i
$807$			18.1864i			0.640191i
$808$	−8.12785	−	14.0779i	−0.285937	−	0.495257i
$809$	7.04891	+	12.2091i	0.247827	+	0.429248i	0.962923	−	0.269778i	$-0.0869503\pi$
$809$	7.04891	+	12.2091i	0.247827	+	0.429248i	−0.715096	+	0.699026i	$0.753617\pi$
$810$		0			0
$811$		−	11.3869i		−	0.399846i	−0.979812	−	0.199923i	$-0.935931\pi$
$811$		−	11.3869i		−	0.399846i	0.979812	−	0.199923i	$-0.0640693\pi$
$812$	−9.60703	+	16.6399i	−0.337141	+	0.583945i
$813$	11.3847	−	19.7188i	0.399278	−	0.691569i
$814$			11.6286i			0.407583i
$815$		0			0
$816$	3.65519	+	6.33097i	0.127957	+	0.221628i
$817$	−15.8653	−	27.4795i	−0.555057	−	0.961387i
$818$			5.21360i			0.182289i
$819$	6.67810	+	11.0897i	0.233352	+	0.387506i
$820$		0			0
$821$	25.2924	−	14.6026i	0.882710	−	0.509633i	0.0111593	−	0.999938i	$-0.496448\pi$
$821$	25.2924	−	14.6026i	0.882710	−	0.509633i	0.871551	+	0.490305i	$0.163114\pi$
$822$	−9.56156	+	5.52037i	−0.333498	+	0.192545i
$823$	−24.4617	−	14.1230i	−0.852681	−	0.492296i	0.00887332	−	0.999961i	$-0.497175\pi$
$823$	−24.4617	−	14.1230i	−0.852681	−	0.492296i	−0.861555	+	0.507665i	$0.830509\pi$
$824$		−	12.9760i		−	0.452042i
$825$		0			0
$826$	−0.853735	−	0.492904i	−0.0297052	−	0.0171503i
$827$	37.3963			1.30040			0.650198	−	0.759765i	$-0.274686\pi$
$827$	37.3963			1.30040			0.650198	+	0.759765i	$0.274686\pi$
$828$	−1.60934	−	0.929155i	−0.0559286	−	0.0322904i
$829$	0.925320	+	1.60270i	0.0321377	+	0.0556641i	0.881647	−	0.471910i	$-0.156435\pi$
$829$	0.925320	+	1.60270i	0.0321377	+	0.0556641i	−0.849509	+	0.527574i	$0.823102\pi$
$830$		0			0
$831$	16.3563			0.567393
$832$	3.60494	−	0.0664404i	0.124979	−	0.00230341i
$833$			43.0632i			1.49205i
$834$	8.40212	−	4.85096i	0.290941	−	0.167975i
$835$		0			0
$836$	10.5359	−	18.2488i	0.364393	−	0.631147i
$837$	−2.23338			−0.0771969
$838$	−9.10066	+	15.7628i	−0.314377	+	0.544517i
$839$	38.8940	+	22.4555i	1.34277	+	0.775249i	0.987213	−	0.159406i	$-0.0509578\pi$
$839$	38.8940	+	22.4555i	1.34277	+	0.775249i	0.355557	+	0.934655i	$0.384291\pi$
$840$		0			0
$841$	0.180359	−	0.312392i	0.00621929	−	0.0107721i
$842$	−22.2103	+	12.8231i	−0.765418	+	0.441914i
$843$	−3.91110	−	6.77423i	−0.134706	−	0.233317i
$844$	−9.98606			−0.343734
$845$		0			0
$846$	−5.07700			−0.174551
$847$	33.6148	+	58.2226i	1.15502	+	2.00055i
$848$	−1.93416	+	1.11669i	−0.0664195	+	0.0383473i
$849$	−3.47266	+	6.01483i	−0.119181	+	0.206428i
$850$		0			0
$851$	3.43254	+	1.98178i	0.117666	+	0.0679344i
$852$	−7.14784	+	12.3804i	−0.244881	+	0.424146i
$853$	−6.75772			−0.231380			−0.115690	−	0.993285i	$-0.536908\pi$
$853$	−6.75772			−0.231380			−0.115690	+	0.993285i	$0.536908\pi$
$854$	−7.41927	+	12.8505i	−0.253882	+	0.439737i
$855$		0			0
$856$	8.58814	−	4.95837i	0.293537	−	0.169474i
$857$		−	9.16177i		−	0.312960i	−0.987681	−	0.156480i	$-0.949985\pi$
$857$		−	9.16177i		−	0.312960i	0.987681	−	0.156480i	$-0.0500147\pi$
$858$	−19.6544	+	0.362237i	−0.670989	+	0.0123666i
$859$	−11.9538			−0.407857			−0.203928	−	0.978986i	$-0.565371\pi$
$859$	−11.9538			−0.407857			−0.203928	+	0.978986i	$0.565371\pi$
$860$		0			0
$861$	−13.1234	−	22.7305i	−0.447246	−	0.774653i
$862$	−1.79193	−	1.03457i	−0.0610334	−	0.0352376i
$863$	−31.6465			−1.07726			−0.538630	−	0.842542i	$-0.681058\pi$
$863$	−31.6465			−1.07726			−0.538630	+	0.842542i	$0.681058\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$		−	0.941830i		−	0.0320047i
$867$	31.5594	+	18.2208i	1.07181	+	0.618811i
$868$	−6.94435	+	4.00932i	−0.235707	+	0.136085i
$869$	12.3756	−	7.14507i	0.419814	−	0.242380i
$870$		0			0
$871$	27.5226	+	45.7043i	0.932567	+	1.54863i
$872$			7.41088i			0.250964i
$873$	−0.954155	−	1.65264i	−0.0322932	−	0.0559335i
$874$	−3.59112	−	6.22000i	−0.121471	−	0.210395i
$875$		0			0
$876$		−	14.8975i		−	0.503340i
$877$	7.06515	−	12.2372i	0.238573	−	0.413221i	−0.721732	−	0.692173i	$-0.756654\pi$
$877$	7.06515	−	12.2372i	0.238573	−	0.413221i	0.960305	+	0.278952i	$0.0899869\pi$
$878$	−1.80132	+	3.11997i	−0.0607915	+	0.105294i
$879$		−	26.4243i		−	0.891270i
$880$		0			0
$881$	−9.56417	−	16.5656i	−0.322225	−	0.558110i	0.658722	−	0.752387i	$-0.271097\pi$
$881$	−9.56417	−	16.5656i	−0.322225	−	0.558110i	−0.980947	+	0.194276i	$0.937764\pi$
$882$	−2.94535	−	5.10149i	−0.0991749	−	0.171776i
$883$		−	7.19528i		−	0.242140i	−0.992644	−	0.121070i	$-0.961367\pi$
$883$		−	7.19528i		−	0.242140i	0.992644	−	0.121070i	$-0.0386326\pi$
$884$	22.5799	−	13.5974i	0.759445	−	0.457329i
$885$		0			0
$886$	4.37425	−	2.52548i	0.146956	−	0.0848451i
$887$	−24.9453	+	14.4022i	−0.837580	+	0.483577i	−0.856441	−	0.516245i	$-0.827329\pi$
$887$	−24.9453	+	14.4022i	−0.837580	+	0.483577i	0.0188611	+	0.999822i	$0.493996\pi$
$888$	1.84713	+	1.06644i	0.0619856	+	0.0357874i
$889$		−	64.5799i		−	2.16594i
$890$		0			0
$891$	4.72163	+	2.72603i	0.158181	+	0.0913256i
$892$	22.3820			0.749404
$893$	−16.9934	−	9.81112i	−0.568661	−	0.328317i
$894$	2.71908	+	4.70959i	0.0909398	+	0.157512i
$895$		0			0
$896$	−3.59036			−0.119946
$897$	−3.24262	+	5.86332i	−0.108268	+	0.195771i
$898$			5.42729i			0.181111i
$899$	−10.3508	+	5.97604i	−0.345219	+	0.199312i
$900$		0			0
$901$	−8.16343	+	14.1395i	−0.271963	+	0.471054i
$902$	39.8567			1.32708
$903$	14.7382	−	25.5273i	0.490457	−	0.849496i
$904$		0			0
$905$		0			0
$906$	−8.90050	+	15.4161i	−0.295699	+	0.512166i
$907$	−33.9233	+	19.5856i	−1.12641	+	0.650331i	−0.943029	−	0.332712i	$-0.892036\pi$
$907$	−33.9233	+	19.5856i	−1.12641	+	0.650331i	−0.183377	+	0.983043i	$0.558703\pi$
$908$	6.49265	+	11.2456i	0.215466	+	0.373199i
$909$	16.2557			0.539168
$910$		0			0
$911$	26.3352			0.872526			0.436263	−	0.899819i	$-0.356302\pi$
$911$	26.3352			0.872526			0.436263	+	0.899819i	$0.356302\pi$
$912$	−1.93247	−	3.34713i	−0.0639903	−	0.110835i
$913$	33.8063	−	19.5181i	1.11883	−	0.645954i
$914$	10.8416	−	18.7782i	0.358607	−	0.621126i
$915$		0			0
$916$	−12.5102	−	7.22276i	−0.413348	−	0.238647i
$917$	−36.5251	+	63.2633i	−1.20616	+	2.08914i
$918$	−7.31038			−0.241278
$919$	4.85456	−	8.40834i	0.160137	−	0.277365i	−0.774781	−	0.632230i	$-0.782140\pi$
$919$	4.85456	−	8.40834i	0.160137	−	0.277365i	0.934918	+	0.354865i	$0.115473\pi$
$920$		0			0
$921$	6.13649	−	3.54290i	0.202204	−	0.116743i
$922$		−	29.6023i		−	0.974901i
$923$	45.1056	+	24.9450i	1.48467	+	0.821074i
$924$	19.5749			0.643967
$925$		0			0
$926$	14.1038	+	24.4284i	0.463478	+	0.802768i
$927$	11.2376	+	6.48802i	0.369091	+	0.213095i
$928$	−5.35157			−0.175674
$929$	−2.68782	−	1.55181i	−0.0881844	−	0.0509133i	0.455259	−	0.890359i	$-0.349547\pi$
$929$	−2.68782	−	1.55181i	−0.0881844	−	0.0509133i	−0.543444	+	0.839446i	$0.682880\pi$
$930$		0			0
$931$		−	22.7671i		−	0.746162i
$932$	−10.7711	−	6.21869i	−0.352819	−	0.203700i
$933$	−1.58498	+	0.915086i	−0.0518898	+	0.0299586i
$934$	−7.07864	+	4.08685i	−0.231620	+	0.133726i
$935$		0			0
$936$	−1.74493	+	3.15519i	−0.0570348	+	0.103131i
$937$		−	53.5929i		−	1.75080i	−0.483396	−	0.875402i	$-0.660597\pi$
$937$		−	53.5929i		−	1.75080i	0.483396	−	0.875402i	$-0.339403\pi$
$938$	−26.5633	−	46.0090i	−0.867323	−	1.50225i
$939$	−6.12493	−	10.6087i	−0.199880	−	0.346201i
$940$		0			0
$941$		−	42.9758i		−	1.40097i	−0.713667	−	0.700485i	$-0.752967\pi$
$941$		−	42.9758i		−	1.40097i	0.713667	−	0.700485i	$-0.247033\pi$
$942$	−2.96826	+	5.14117i	−0.0967111	+	0.167509i
$943$	6.79247	−	11.7649i	0.221193	−	0.383118i
$944$		−	0.274571i		−	0.00893652i
$945$		0			0
$946$	22.3804	+	38.7640i	0.727650	+	1.26033i
$947$	−5.54457	−	9.60349i	−0.180174	−	0.312071i	0.761765	−	0.647853i	$-0.224333\pi$
$947$	−5.54457	−	9.60349i	−0.180174	−	0.312071i	−0.941940	+	0.335782i	$0.891000\pi$
$948$		−	2.62105i		−	0.0851277i
$949$	−53.7046	+	0.989796i	−1.74333	+	0.0321301i
$950$		0			0
$951$	5.41352	−	3.12550i	0.175546	−	0.101351i
$952$	−22.7305	+	13.1234i	−0.736699	+	0.425333i
$953$	−49.9313	−	28.8278i	−1.61743	−	0.933825i	−0.987581	−	0.157110i	$-0.949782\pi$
$953$	−49.9313	−	28.8278i	−1.61743	−	0.933825i	−0.629852	−	0.776715i	$-0.716884\pi$
$954$		−	2.23338i		−	0.0723084i
$955$		0			0
$956$	−3.61118	−	2.08491i	−0.116794	−	0.0674309i
$957$	29.1771			0.943162
$958$	−10.1231	−	5.84458i	−0.327063	−	0.188830i
$959$	−19.8201	−	34.3294i	−0.640025	−	1.10856i
$960$		0			0
$961$	26.0120			0.839097
$962$	3.72173	−	6.72964i	0.119993	−	0.216972i
$963$			9.91673i			0.319562i
$964$	−1.63165	+	0.942035i	−0.0525520	+	0.0303409i
$965$		0			0
$966$	3.33600	−	5.77812i	0.107334	−	0.185908i
$967$	30.5218			0.981516			0.490758	−	0.871296i	$-0.336720\pi$
$967$	30.5218			0.981516			0.490758	+	0.871296i	$0.336720\pi$
$968$	−9.36252	+	16.2164i	−0.300923	+	0.521214i
$969$	−24.4688	−	14.1271i	−0.786050	−	0.453826i
$970$		0			0
$971$	−13.9787	+	24.2119i	−0.448599	+	0.776996i	−0.998295	−	0.0583686i	$-0.981410\pi$
$971$	−13.9787	+	24.2119i	−0.448599	+	0.776996i	0.549696	+	0.835365i	$0.314743\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	17.4167	+	30.1666i	0.558354	+	0.967098i
$974$	−31.8875			−1.02174
$975$		0			0
$976$	−4.13288			−0.132290
$977$	−0.986516	−	1.70870i	−0.0315614	−	0.0546660i	0.849813	−	0.527084i	$-0.176715\pi$
$977$	−0.986516	−	1.70870i	−0.0315614	−	0.0546660i	−0.881375	+	0.472418i	$0.843381\pi$
$978$	13.5046	−	7.79688i	0.431829	−	0.249317i
$979$	26.1529	−	45.2982i	0.835851	−	1.44774i
$980$		0			0
$981$	−6.41801	−	3.70544i	−0.204911	−	0.118306i
$982$	−9.77506	+	16.9309i	−0.311935	+	0.540286i
$983$	8.00792			0.255413			0.127707	−	0.991812i	$-0.459238\pi$
$983$	8.00792			0.255413			0.127707	+	0.991812i	$0.459238\pi$
$984$	3.65519	−	6.33097i	0.116523	−	0.201824i
$985$		0			0
$986$	−33.8806	+	19.5610i	−1.07898	+	0.622949i
$987$		−	18.2283i		−	0.580212i
$988$	−11.9378	+	7.18881i	−0.379792	+	0.228706i
$989$	15.2565			0.485128
$990$		0			0
$991$	−18.0138	−	31.2007i	−0.572226	−	0.991124i	−0.996337	−	0.0855139i	$-0.972747\pi$
$991$	−18.0138	−	31.2007i	−0.572226	−	0.991124i	0.424111	−	0.905610i	$-0.360587\pi$
$992$	−1.93416	−	1.11669i	−0.0614098	−	0.0354550i
$993$	−19.1758			−0.608526
$994$	−44.4502	−	25.6633i	−1.40987	−	0.813992i
$995$		0			0
$996$		−	7.15988i		−	0.226869i
$997$	−44.3242	−	25.5906i	−1.40376	−	0.810463i	−0.408986	−	0.912541i	$-0.634117\pi$
$997$	−44.3242	−	25.5906i	−1.40376	−	0.810463i	−0.994776	+	0.102078i	$0.967451\pi$
$998$	−34.0719	+	19.6714i	−1.07853	+	0.622688i
$999$	−1.84713	+	1.06644i	−0.0584406	+	0.0337407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.n.49.4		12
5.2	odd	4		1950.2.bc.h.751.1	✓	12
5.3	odd	4		1950.2.bc.k.751.6	yes	12
5.4	even	2		1950.2.y.m.49.3		12
13.4	even	6		1950.2.y.m.199.3		12
65.4	even	6	inner	1950.2.y.n.199.4		12
65.17	odd	12		1950.2.bc.h.901.1	yes	12
65.43	odd	12		1950.2.bc.k.901.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.3		12	5.4	even	2
1950.2.y.m.199.3		12	13.4	even	6
1950.2.y.n.49.4		12	1.1	even	1	trivial
1950.2.y.n.199.4		12	65.4	even	6	inner
1950.2.bc.h.751.1	✓	12	5.2	odd	4
1950.2.bc.h.901.1	yes	12	65.17	odd	12
1950.2.bc.k.751.6	yes	12	5.3	odd	4
1950.2.bc.k.901.6	yes	12	65.43	odd	12

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.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.79518 + 3.10934i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.79518 + 3.10934i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.72163 + 2.72603i) q^{11} +1.00000i q^{12} +(3.60494 - 0.0664404i) q^{13} -3.59036 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.33097 - 3.65519i) q^{17} +1.00000 q^{18} +(3.34713 + 1.93247i) q^{19} +3.59036i q^{21} +(-4.72163 - 2.72603i) q^{22} +(-1.60934 + 0.929155i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.86001 + 3.08875i) q^{26} -1.00000i q^{27} +(-1.79518 - 3.10934i) q^{28} +(-2.67578 - 4.63459i) q^{29} -2.23338i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.72603 + 4.72163i) q^{33} -7.31038i q^{34} +(0.500000 + 0.866025i) q^{36} +(-1.06644 - 1.84713i) q^{37} +3.86493i q^{38} +(3.08875 - 1.86001i) q^{39} +(-6.33097 + 3.65519i) q^{41} +(-3.10934 + 1.79518i) q^{42} +(-7.10996 - 4.10494i) q^{43} -5.45207i q^{44} +(-1.60934 - 0.929155i) q^{46} -5.07700 q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.94535 - 5.10149i) q^{49} -7.31038 q^{51} +(-1.74493 + 3.15519i) q^{52} -2.23338i q^{53} +(0.866025 - 0.500000i) q^{54} +(1.79518 - 3.10934i) q^{56} +3.86493 q^{57} +(2.67578 - 4.63459i) q^{58} +(0.237785 + 0.137285i) q^{59} +(2.06644 - 3.57918i) q^{61} +(1.93416 - 1.11669i) q^{62} +(1.79518 + 3.10934i) q^{63} +1.00000 q^{64} -5.45207 q^{66} +(7.39851 + 12.8146i) q^{67} +(6.33097 - 3.65519i) q^{68} +(-0.929155 + 1.60934i) q^{69} +(12.3804 + 7.14784i) q^{71} +(-0.500000 + 0.866025i) q^{72} -14.8975 q^{73} +(1.06644 - 1.84713i) q^{74} +(-3.34713 + 1.93247i) q^{76} -19.5749i q^{77} +(3.15519 + 1.74493i) q^{78} -2.62105 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.33097 - 3.65519i) q^{82} -7.15988 q^{83} +(-3.10934 - 1.79518i) q^{84} -8.20988i q^{86} +(-4.63459 - 2.67578i) q^{87} +(4.72163 - 2.72603i) q^{88} +(-8.30844 + 4.79688i) q^{89} +(-6.26493 + 11.3283i) q^{91} -1.85831i q^{92} +(-1.11669 - 1.93416i) q^{93} +(-2.53850 - 4.39681i) q^{94} -1.00000i q^{96} +(0.954155 - 1.65264i) q^{97} +(2.94535 - 5.10149i) q^{98} +5.45207i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 6 q^{16} + 12 q^{18} + 6 q^{19} - 12 q^{22} + 12 q^{23} - 4 q^{26} - 4 q^{28} + 6 q^{32} + 4 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{39} - 6 q^{42} + 12 q^{43} + 12 q^{46} + 16 q^{47} - 32 q^{49} - 8 q^{52} + 4 q^{56} + 24 q^{57} + 24 q^{61} + 4 q^{63} + 12 q^{64} + 8 q^{66} + 24 q^{67} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 40 q^{73} + 12 q^{74} - 6 q^{76} - 6 q^{78} - 52 q^{79} - 6 q^{81} + 32 q^{83} - 6 q^{84} + 12 q^{88} - 24 q^{89} - 54 q^{91} - 8 q^{93} + 8 q^{94} + 24 q^{97} + 32 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 6 * q^16 + 12 * q^18 + 6 * q^19 - 12 * q^22 + 12 * q^23 - 4 * q^26 - 4 * q^28 + 6 * q^32 + 4 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^39 - 6 * q^42 + 12 * q^43 + 12 * q^46 + 16 * q^47 - 32 * q^49 - 8 * q^52 + 4 * q^56 + 24 * q^57 + 24 * q^61 + 4 * q^63 + 12 * q^64 + 8 * q^66 + 24 * q^67 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 40 * q^73 + 12 * q^74 - 6 * q^76 - 6 * q^78 - 52 * q^79 - 6 * q^81 + 32 * q^83 - 6 * q^84 + 12 * q^88 - 24 * q^89 - 54 * q^91 - 8 * q^93 + 8 * q^94 + 24 * q^97 + 32 * q^98

Introduction

L-functions

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