LMFDB - Embedded newform 1950.2.bc.k.751.6

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			751.6
Root			$0.500000 + 1.72434i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.k.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(3.10934 + 1.79518i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(3.10934 + 1.79518i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.72163 + 2.72603i) q^{11} +1.00000 q^{12} +(0.0664404 + 3.60494i) q^{13} +3.59036 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.65519 + 6.33097i) q^{17} +1.00000i q^{18} +(-3.34713 - 1.93247i) q^{19} +3.59036i q^{21} +(-2.72603 + 4.72163i) q^{22} +(-0.929155 - 1.60934i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.86001 + 3.08875i) q^{26} -1.00000 q^{27} +(3.10934 - 1.79518i) q^{28} +(2.67578 + 4.63459i) q^{29} -2.23338i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.72163 - 2.72603i) q^{33} +7.31038i q^{34} +(0.500000 + 0.866025i) q^{36} +(-1.84713 + 1.06644i) q^{37} -3.86493 q^{38} +(-3.08875 + 1.86001i) q^{39} +(-6.33097 + 3.65519i) q^{41} +(1.79518 + 3.10934i) q^{42} +(4.10494 - 7.10996i) q^{43} +5.45207i q^{44} +(-1.60934 - 0.929155i) q^{46} +5.07700i q^{47} +(0.500000 - 0.866025i) q^{48} +(2.94535 + 5.10149i) q^{49} -7.31038 q^{51} +(3.15519 + 1.74493i) q^{52} +2.23338 q^{53} +(-0.866025 + 0.500000i) q^{54} +(1.79518 - 3.10934i) q^{56} -3.86493i q^{57} +(4.63459 + 2.67578i) q^{58} +(-0.237785 - 0.137285i) q^{59} +(2.06644 - 3.57918i) q^{61} +(-1.11669 - 1.93416i) q^{62} +(-3.10934 + 1.79518i) q^{63} -1.00000 q^{64} -5.45207 q^{66} +(12.8146 - 7.39851i) q^{67} +(3.65519 + 6.33097i) q^{68} +(0.929155 - 1.60934i) q^{69} +(12.3804 + 7.14784i) q^{71} +(0.866025 + 0.500000i) q^{72} -14.8975i q^{73} +(-1.06644 + 1.84713i) q^{74} +(-3.34713 + 1.93247i) q^{76} -19.5749 q^{77} +(-1.74493 + 3.15519i) q^{78} +2.62105 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.65519 + 6.33097i) q^{82} -7.15988i q^{83} +(3.10934 + 1.79518i) q^{84} -8.20988i q^{86} +(-2.67578 + 4.63459i) q^{87} +(2.72603 + 4.72163i) q^{88} +(8.30844 - 4.79688i) q^{89} +(-6.26493 + 11.3283i) q^{91} -1.85831 q^{92} +(1.93416 - 1.11669i) q^{93} +(2.53850 + 4.39681i) q^{94} -1.00000i q^{96} +(-1.65264 - 0.954155i) q^{97} +(5.10149 + 2.94535i) q^{98} -5.45207i 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 $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.866025	−	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
$7$	3.10934	+	1.79518i	1.17522	+	0.678514i	0.954904	−	0.296914i	$-0.0959574\pi$
$7$	3.10934	+	1.79518i	1.17522	+	0.678514i	0.220317	+	0.975428i	$0.429291\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−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	$0.640436\pi$
$12$	1.00000			0.288675
$13$	0.0664404	+	3.60494i	0.0184272	+	0.999830i
$13$	0.0664404	+	3.60494i	0.0184272	+	0.999830i
$14$	3.59036			0.959564
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.65519	+	6.33097i	−0.886514	+	1.53549i	−0.0425445	+	0.999095i	$0.513546\pi$
$17$	−3.65519	+	6.33097i	−0.886514	+	1.53549i	−0.843969	+	0.536392i	$0.819787\pi$
$18$			1.00000i			0.235702i
$19$	−3.34713	−	1.93247i	−0.767884	−	0.443338i	0.0642352	−	0.997935i	$-0.479539\pi$
$19$	−3.34713	−	1.93247i	−0.767884	−	0.443338i	−0.832119	+	0.554597i	$0.812873\pi$
$20$		0			0
$21$			3.59036i			0.783481i
$22$	−2.72603	+	4.72163i	−0.581192	+	1.00665i
$23$	−0.929155	−	1.60934i	−0.193742	−	0.335571i	0.752745	−	0.658312i	$-0.228729\pi$
$23$	−0.929155	−	1.60934i	−0.193742	−	0.335571i	−0.946487	+	0.322741i	$0.895396\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	1.86001	+	3.08875i	0.364778	+	0.605753i
$27$	−1.00000			−0.192450
$28$	3.10934	−	1.79518i	0.587611	−	0.339257i
$29$	2.67578	+	4.63459i	0.496881	+	0.860622i	0.999994	−	0.00359821i	$-0.00114535\pi$
$29$	2.67578	+	4.63459i	0.496881	+	0.860622i	−0.503113	+	0.864221i	$0.667812\pi$
$30$		0			0
$31$		−	2.23338i		−	0.401127i	−0.979681	−	0.200563i	$-0.935723\pi$
$31$		−	2.23338i		−	0.401127i	0.979681	−	0.200563i	$-0.0642773\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.72163	−	2.72603i	−0.821930	−	0.474542i
$34$			7.31038i			1.25372i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−1.84713	+	1.06644i	−0.303666	+	0.175322i	−0.644089	−	0.764951i	$-0.722763\pi$
$37$	−1.84713	+	1.06644i	−0.303666	+	0.175322i	0.340423	+	0.940273i	$0.389430\pi$
$38$	−3.86493			−0.626975
$39$	−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	$0.526717\pi$
$42$	1.79518	+	3.10934i	0.277002	+	0.479782i
$43$	4.10494	−	7.10996i	0.625997	−	1.08426i	−0.362350	−	0.932042i	$-0.618025\pi$
$43$	4.10494	−	7.10996i	0.625997	−	1.08426i	0.988347	−	0.152217i	$-0.0486413\pi$
$44$			5.45207i			0.821930i
$45$		0			0
$46$	−1.60934	−	0.929155i	−0.237285	−	0.136996i
$47$			5.07700i			0.740556i	0.928921	+	0.370278i	$0.120738\pi$
$47$			5.07700i			0.740556i	−0.928921	+	0.370278i	$0.879262\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	2.94535	+	5.10149i	0.420764	+	0.728784i
$50$		0			0
$51$	−7.31038			−1.02366
$52$	3.15519	+	1.74493i	0.437546	+	0.241978i
$53$	2.23338			0.306778			0.153389	−	0.988166i	$-0.450981\pi$
$53$	2.23338			0.306778			0.153389	+	0.988166i	$0.450981\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	1.79518	−	3.10934i	0.239891	−	0.415504i
$57$		−	3.86493i		−	0.511923i
$58$	4.63459	+	2.67578i	0.608552	+	0.351348i
$59$	−0.237785	−	0.137285i	−0.0309570	−	0.0178730i	0.484442	−	0.874824i	$-0.339023\pi$
$59$	−0.237785	−	0.137285i	−0.0309570	−	0.0178730i	−0.515399	+	0.856951i	$0.672356\pi$
$60$		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	$0.0814332\pi$
$62$	−1.11669	−	1.93416i	−0.141820	−	0.245639i
$63$	−3.10934	+	1.79518i	−0.391740	+	0.226171i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.45207			−0.671103
$67$	12.8146	−	7.39851i	1.56555	−	0.903872i	0.568874	−	0.822425i	$-0.307379\pi$
$67$	12.8146	−	7.39851i	1.56555	−	0.903872i	0.996678	−	0.0814466i	$-0.0259540\pi$
$68$	3.65519	+	6.33097i	0.443257	+	0.767743i
$69$	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	$0.344297\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	14.8975i		−	1.74362i	−0.489842	−	0.871811i	$-0.662946\pi$
$73$		−	14.8975i		−	1.74362i	0.489842	−	0.871811i	$-0.337054\pi$
$74$	−1.06644	+	1.84713i	−0.123971	+	0.214724i
$75$		0			0
$76$	−3.34713	+	1.93247i	−0.383942	+	0.221669i
$77$	−19.5749			−2.23077
$78$	−1.74493	+	3.15519i	−0.197574	+	0.357255i
$79$	2.62105			0.294891			0.147446	−	0.989070i	$-0.452895\pi$
$79$	2.62105			0.294891			0.147446	+	0.989070i	$0.452895\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.65519	+	6.33097i	−0.403648	+	0.699139i
$83$		−	7.15988i		−	0.785899i	−0.919560	−	0.392949i	$-0.871455\pi$
$83$		−	7.15988i		−	0.785899i	0.919560	−	0.392949i	$-0.128545\pi$
$84$	3.10934	+	1.79518i	0.339257	+	0.195870i
$85$		0			0
$86$		−	8.20988i		−	0.885294i
$87$	−2.67578	+	4.63459i	−0.286874	+	0.496881i
$88$	2.72603	+	4.72163i	0.290596	+	0.503327i
$89$	8.30844	−	4.79688i	0.880693	−	0.508468i	0.00980594	−	0.999952i	$-0.496879\pi$
$89$	8.30844	−	4.79688i	0.880693	−	0.508468i	0.870887	+	0.491484i	$0.163545\pi$
$90$		0			0
$91$	−6.26493	+	11.3283i	−0.656743	+	1.18753i
$92$	−1.85831			−0.193742
$93$	1.93416	−	1.11669i	0.200563	−	0.115795i
$94$	2.53850	+	4.39681i	0.261826	+	0.453496i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−1.65264	−	0.954155i	−0.167801	−	0.0968797i	0.413748	−	0.910392i	$-0.364220\pi$
$97$	−1.65264	−	0.954155i	−0.167801	−	0.0968797i	−0.581548	+	0.813512i	$0.697553\pi$
$98$	5.10149	+	2.94535i	0.515328	+	0.297525i
$99$		−	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	$0.533477\pi$
$102$	−6.33097	+	3.65519i	−0.626860	+	0.361918i
$103$	−12.9760			−1.27857			−0.639284	−	0.768971i	$-0.720769\pi$
$103$	−12.9760			−1.27857			−0.639284	+	0.768971i	$0.720769\pi$
$104$	3.60494	−	0.0664404i	0.353493	−	0.00651501i
$105$		0			0
$106$	1.93416	−	1.11669i	0.187863	−	0.108463i
$107$	4.95837	+	8.58814i	0.479343	+	0.830247i	0.999719	−	0.0236901i	$-0.00754150\pi$
$107$	4.95837	+	8.58814i	0.479343	+	0.830247i	−0.520376	+	0.853937i	$0.674208\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			7.41088i			0.709833i	0.934898	+	0.354917i	$0.115491\pi$
$109$			7.41088i			0.709833i	−0.934898	+	0.354917i	$0.884509\pi$
$110$		0			0
$111$	−1.84713	−	1.06644i	−0.175322	−	0.101222i
$112$		−	3.59036i		−	0.339257i
$113$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$	−1.93247	−	3.34713i	−0.180992	−	0.313487i
$115$		0			0
$116$	5.35157			0.496881
$117$	−3.15519	−	1.74493i	−0.291697	−	0.161319i
$118$	−0.274571			−0.0252763
$119$	−22.7305	+	13.1234i	−2.08370	+	1.20302i
$120$		0			0
$121$	9.36252	−	16.2164i	0.851138	−	1.47421i
$122$		−	4.13288i		−	0.374173i
$123$	−6.33097	−	3.65519i	−0.570845	−	0.329577i
$124$	−1.93416	−	1.11669i	−0.173693	−	0.100282i
$125$		0			0
$126$	−1.79518	+	3.10934i	−0.159927	+	0.277002i
$127$	8.99351	+	15.5772i	0.798045	+	1.38225i	0.920888	+	0.389828i	$0.127466\pi$
$127$	8.99351	+	15.5772i	0.798045	+	1.38225i	−0.122843	+	0.992426i	$0.539201\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	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	$0.151521\pi$
$132$	−4.72163	+	2.72603i	−0.410965	+	0.237271i
$133$	−6.93825	−	12.0174i	−0.601623	−	1.04204i
$134$	7.39851	−	12.8146i	0.639134	−	1.10701i
$135$		0			0
$136$	6.33097	+	3.65519i	0.542876	+	0.313430i
$137$	9.56156	+	5.52037i	0.816899	+	0.471637i	0.849346	−	0.527837i	$-0.176997\pi$
$137$	9.56156	+	5.52037i	0.816899	+	0.471637i	−0.0324469	+	0.999473i	$0.510330\pi$
$138$		−	1.85831i		−	0.158190i
$139$	−4.85096	+	8.40212i	−0.411453	+	0.712658i	−0.995049	−	0.0993864i	$-0.968312\pi$
$139$	−4.85096	+	8.40212i	−0.411453	+	0.712658i	0.583596	+	0.812044i	$0.301645\pi$
$140$		0			0
$141$	−4.39681	+	2.53850i	−0.370278	+	0.213780i
$142$	14.2957			1.19967
$143$	−10.1409	−	16.8401i	−0.848024	−	1.40824i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−7.44876	−	12.9016i	−0.616464	−	1.06775i
$147$	−2.94535	+	5.10149i	−0.242928	+	0.420764i
$148$			2.13288i			0.175322i
$149$	−4.70959	−	2.71908i	−0.385825	−	0.222756i	0.294525	−	0.955644i	$-0.404839\pi$
$149$	−4.70959	−	2.71908i	−0.385825	−	0.222756i	−0.680350	+	0.732888i	$0.738172\pi$
$150$		0			0
$151$			17.8010i			1.44862i	0.689472	+	0.724312i	$0.257843\pi$
$151$			17.8010i			1.44862i	−0.689472	+	0.724312i	$0.742157\pi$
$152$	−1.93247	+	3.34713i	−0.156744	+	0.271488i
$153$	−3.65519	−	6.33097i	−0.295505	−	0.511829i
$154$	−16.9524	+	9.78745i	−1.36606	+	0.788695i
$155$		0			0
$156$	0.0664404	+	3.60494i	0.00531949	+	0.288626i
$157$	5.93652			0.473786			0.236893	−	0.971536i	$-0.423871\pi$
$157$	5.93652			0.473786			0.236893	+	0.971536i	$0.423871\pi$
$158$	2.26990	−	1.31052i	0.180583	−	0.104260i
$159$	1.11669	+	1.93416i	0.0885593	+	0.153389i
$160$		0			0
$161$		−	6.67200i		−	0.525828i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	13.5046	+	7.79688i	1.05776	+	0.610699i	0.924812	−	0.380424i	$-0.124222\pi$
$163$	13.5046	+	7.79688i	1.05776	+	0.610699i	0.132949	+	0.991123i	$0.457555\pi$
$164$			7.31038i			0.570845i
$165$		0			0
$166$	−3.57994	−	6.20064i	−0.277857	−	0.481263i
$167$	−1.60934	+	0.929155i	−0.124535	+	0.0719002i	−0.560973	−	0.827834i	$-0.689573\pi$
$167$	−1.60934	+	0.929155i	−0.124535	+	0.0719002i	0.436439	+	0.899734i	$0.356240\pi$
$168$	3.59036			0.277002
$169$	−12.9912	+	0.479027i	−0.999321	+	0.0368482i
$170$		0			0
$171$	3.34713	−	1.93247i	0.255961	−	0.147779i
$172$	−4.10494	−	7.10996i	−0.312999	−	0.542130i
$173$	12.1687	−	21.0768i	0.925168	−	1.60244i	0.133878	−	0.990998i	$-0.457257\pi$
$173$	12.1687	−	21.0768i	0.925168	−	1.60244i	0.791290	−	0.611441i	$-0.209410\pi$
$174$			5.35157i			0.405701i
$175$		0			0
$176$	4.72163	+	2.72603i	0.355906	+	0.205483i
$177$		−	0.274571i		−	0.0206380i
$178$	4.79688	−	8.30844i	0.359541	−	0.622744i
$179$	1.53429	+	2.65746i	0.114678	+	0.198628i	0.917651	−	0.397387i	$-0.130083\pi$
$179$	1.53429	+	2.65746i	0.114678	+	0.198628i	−0.802973	+	0.596015i	$0.796750\pi$
$180$		0			0
$181$	−4.59376			−0.341451			−0.170726	−	0.985319i	$-0.554611\pi$
$181$	−4.59376			−0.341451			−0.170726	+	0.985319i	$0.554611\pi$
$182$	0.238545	+	12.9430i	0.0176821	+	0.959401i
$183$	4.13288			0.305511
$184$	−1.60934	+	0.929155i	−0.118642	+	0.0684982i
$185$		0			0
$186$	1.11669	−	1.93416i	0.0818797	−	0.141820i
$187$		−	39.8567i		−	2.91461i
$188$	4.39681	+	2.53850i	0.320670	+	0.185139i
$189$	−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	$0.996801\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−21.7276	+	12.5444i	−1.56398	+	0.902966i	−0.567136	+	0.823624i	$0.691949\pi$
$193$	−21.7276	+	12.5444i	−1.56398	+	0.902966i	−0.996847	+	0.0793424i	$0.974718\pi$
$194$	−1.90831			−0.137009
$195$		0			0
$196$	5.89069			0.420764
$197$	−7.96287	+	4.59737i	−0.567331	+	0.327549i	−0.756083	−	0.654476i	$-0.772889\pi$
$197$	−7.96287	+	4.59737i	−0.567331	+	0.327549i	0.188752	+	0.982025i	$0.439556\pi$
$198$	−2.72603	−	4.72163i	−0.193731	−	0.335552i
$199$	−11.8396	+	20.5068i	−0.839286	+	1.45369i	0.0512060	+	0.998688i	$0.483694\pi$
$199$	−11.8396	+	20.5068i	−0.839286	+	1.45369i	−0.890492	+	0.454998i	$0.849640\pi$
$200$		0			0
$201$	12.8146	+	7.39851i	0.903872	+	0.521850i
$202$	14.0779	+	8.12785i	0.990514	+	0.571874i
$203$			19.2141i			1.34856i
$204$	−3.65519	+	6.33097i	−0.255914	+	0.443257i
$205$		0			0
$206$	−11.2376	+	6.48802i	−0.782960	+	0.452042i
$207$	1.85831			0.129161
$208$	3.08875	−	1.86001i	0.214166	−	0.128968i
$209$	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	$0.721641\pi$
$212$	1.11669	−	1.93416i	0.0766946	−	0.132839i
$213$			14.2957i			0.979524i
$214$	8.58814	+	4.95837i	0.587073	+	0.338947i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	4.00932	−	6.94435i	0.272170	−	0.471413i
$218$	3.70544	+	6.41801i	0.250964	+	0.434682i
$219$	12.9016	−	7.44876i	0.871811	−	0.503340i
$220$		0			0
$221$	−23.0656	−	12.7561i	−1.55156	−	0.858068i
$222$	−2.13288			−0.143150
$223$	19.3833	−	11.1910i	1.29801	−	0.749404i	0.317946	−	0.948109i	$-0.397007\pi$
$223$	19.3833	−	11.1910i	1.29801	−	0.749404i	0.980059	+	0.198705i	$0.0636737\pi$
$224$	−1.79518	−	3.10934i	−0.119946	−	0.207752i
$225$		0			0
$226$		0			0
$227$	−11.2456	−	6.49265i	−0.746397	−	0.430933i	0.0779935	−	0.996954i	$-0.475149\pi$
$227$	−11.2456	−	6.49265i	−0.746397	−	0.430933i	−0.824391	+	0.566021i	$0.808482\pi$
$228$	−3.34713	−	1.93247i	−0.221669	−	0.127981i
$229$		−	14.4455i		−	0.954587i	−0.878744	−	0.477293i	$-0.841618\pi$
$229$		−	14.4455i		−	0.954587i	0.878744	−	0.477293i	$-0.158382\pi$
$230$		0			0
$231$	−9.78745	−	16.9524i	−0.643967	−	1.11538i
$232$	4.63459	−	2.67578i	0.304276	−	0.175674i
$233$	−12.4374			−0.814800			−0.407400	−	0.913250i	$-0.633564\pi$
$233$	−12.4374			−0.814800			−0.407400	+	0.913250i	$0.633564\pi$
$234$	−3.60494	+	0.0664404i	−0.235662	+	0.00434334i
$235$		0			0
$236$	−0.237785	+	0.137285i	−0.0154785	+	0.00893652i
$237$	1.31052	+	2.26990i	0.0851277	+	0.147446i
$238$	−13.1234	+	22.7305i	−0.850667	+	1.47340i
$239$		−	4.16983i		−	0.269724i	−0.990864	−	0.134862i	$-0.956941\pi$
$239$		−	4.16983i		−	0.269724i	0.990864	−	0.134862i	$-0.0430591\pi$
$240$		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	$0.647339\pi$
$242$		−	18.7250i		−	1.20369i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.06644	−	3.57918i	−0.132290	−	0.229134i
$245$		0			0
$246$	−7.31038			−0.466093
$247$	6.74404	−	12.1946i	0.429113	−	0.775923i
$248$	−2.23338			−0.141820
$249$	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	$0.0942150\pi$
$252$			3.59036i			0.226171i
$253$	8.77425	+	5.06582i	0.551632	+	0.318485i
$254$	15.5772	+	8.99351i	0.977401	+	0.564303i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.2489	−	17.7517i	−0.639312	−	1.10732i	−0.985584	−	0.169186i	$-0.945886\pi$
$257$	−10.2489	−	17.7517i	−0.639312	−	1.10732i	0.346272	−	0.938134i	$-0.387447\pi$
$258$	7.10996	−	4.10494i	0.442647	−	0.255562i
$259$	−7.65781			−0.475833
$260$		0			0
$261$	−5.35157			−0.331254
$262$	17.6203	−	10.1731i	1.08859	−	0.628496i
$263$	−8.85153	−	15.3313i	−0.545809	−	0.945369i	−0.998556	−	0.0537296i	$-0.982889\pi$
$263$	−8.85153	−	15.3313i	−0.545809	−	0.945369i	0.452747	−	0.891639i	$-0.350444\pi$
$264$	−2.72603	+	4.72163i	−0.167776	+	0.290596i
$265$		0			0
$266$	−12.0174	−	6.93825i	−0.736834	−	0.425411i
$267$	8.30844	+	4.79688i	0.508468	+	0.293564i
$268$		−	14.7970i		−	0.903872i
$269$	9.09319	−	15.7499i	0.554421	−	0.960286i	−0.443527	−	0.896261i	$-0.646273\pi$
$269$	9.09319	−	15.7499i	0.554421	−	0.960286i	0.997948	−	0.0640250i	$-0.0203937\pi$
$270$		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	$0.0902529\pi$
$272$	7.31038			0.443257
$273$	−12.9430	+	0.238545i	−0.783348	+	0.0144374i
$274$	11.0407			0.666995
$275$		0			0
$276$	−0.929155	−	1.60934i	−0.0559286	−	0.0968711i
$277$	8.17814	−	14.1649i	0.491377	−	0.851089i	−0.508574	−	0.861018i	$-0.669827\pi$
$277$	8.17814	−	14.1649i	0.491377	−	0.851089i	0.999951	+	0.00992898i	$0.00316055\pi$
$278$			9.70193i			0.581883i
$279$	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	$-0.0749580\pi$
$282$	−2.53850	+	4.39681i	−0.151165	+	0.261826i
$283$	−3.47266	−	6.01483i	−0.206428	−	0.357544i	0.744159	−	0.668003i	$-0.232851\pi$
$283$	−3.47266	−	6.01483i	−0.206428	−	0.357544i	−0.950587	+	0.310459i	$0.899517\pi$
$284$	12.3804	−	7.14784i	0.734643	−	0.424146i
$285$		0			0
$286$	−17.2023	−	9.51348i	−1.01719	−	0.562544i
$287$	−26.2469			−1.54931
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−18.2208	−	31.5594i	−1.07181	−	1.85643i
$290$		0			0
$291$		−	1.90831i		−	0.111867i
$292$	−12.9016	−	7.44876i	−0.755011	−	0.435906i
$293$	22.8841	+	13.2122i	1.33691	+	0.771863i	0.986347	−	0.164678i	$-0.0526586\pi$
$293$	22.8841	+	13.2122i	1.33691	+	0.771863i	0.350558	+	0.936541i	$0.385992\pi$
$294$			5.89069i			0.343552i
$295$		0			0
$296$	1.06644	+	1.84713i	0.0619856	+	0.107362i
$297$	4.72163	−	2.72603i	0.273977	−	0.158181i
$298$	−5.43817			−0.315025
$299$	5.73985	−	3.45647i	0.331944	−	0.199893i
$300$		0			0
$301$	25.5273	−	14.7382i	1.47137	−	0.849496i
$302$	8.90050	+	15.4161i	0.512166	+	0.887098i
$303$	−8.12785	+	14.0779i	−0.466933	+	0.808752i
$304$			3.86493i			0.221669i
$305$		0			0
$306$	−6.33097	−	3.65519i	−0.361918	−	0.208953i
$307$		−	7.08581i		−	0.404408i	−0.979343	−	0.202204i	$-0.935190\pi$
$307$		−	7.08581i		−	0.404408i	0.979343	−	0.202204i	$-0.0648105\pi$
$308$	−9.78745	+	16.9524i	−0.557691	+	0.965950i
$309$	−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	$0.516524\pi$
$312$	1.86001	+	3.08875i	0.105302	+	0.174866i
$313$	12.2499			0.692403			0.346201	−	0.938160i	$-0.387471\pi$
$313$	12.2499			0.692403			0.346201	+	0.938160i	$0.387471\pi$
$314$	5.14117	−	2.96826i	0.290133	−	0.167509i
$315$		0			0
$316$	1.31052	−	2.26990i	0.0737228	−	0.127692i
$317$		−	6.25100i		−	0.351091i	−0.984471	−	0.175546i	$-0.943831\pi$
$317$		−	6.25100i		−	0.351091i	0.984471	−	0.175546i	$-0.0561689\pi$
$318$	1.93416	+	1.11669i	0.108463	+	0.0626209i
$319$	−25.2681	−	14.5886i	−1.41474	−	0.816802i
$320$		0			0
$321$	−4.95837	+	8.58814i	−0.276749	+	0.479343i
$322$	−3.33600	−	5.77812i	−0.185908	−	0.322002i
$323$	24.4688	−	14.1271i	1.36148	−	0.786050i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	15.5938			0.863658
$327$	−6.41801	+	3.70544i	−0.354917	+	0.204911i
$328$	3.65519	+	6.33097i	0.201824	+	0.349570i
$329$	−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	$0.843349\pi$
$332$	−6.20064	−	3.57994i	−0.340304	−	0.196475i
$333$		−	2.13288i		−	0.116881i
$334$	−0.929155	+	1.60934i	−0.0508411	+	0.0880594i
$335$		0			0
$336$	3.10934	−	1.79518i	0.169629	−	0.0979351i
$337$	16.5450			0.901262			0.450631	−	0.892710i	$-0.351199\pi$
$337$	16.5450			0.901262			0.450631	+	0.892710i	$0.351199\pi$
$338$	−11.0112	+	6.91044i	−0.598929	+	0.375878i
$339$		0			0
$340$		0			0
$341$	6.08827	+	10.5452i	0.329698	+	0.571054i
$342$	1.93247	−	3.34713i	0.104496	−	0.180992i
$343$		−	3.98282i		−	0.215052i
$344$	−7.10996	−	4.10494i	−0.383344	−	0.221323i
$345$		0			0
$346$		−	24.3374i		−	1.30839i
$347$	2.98195	−	5.16489i	0.160079	−	0.277266i	−0.774818	−	0.632185i	$-0.782158\pi$
$347$	2.98195	−	5.16489i	0.160079	−	0.277266i	0.934897	+	0.354919i	$0.115492\pi$
$348$	2.67578	+	4.63459i	0.143437	+	0.248440i
$349$	2.76302	−	1.59523i	0.147901	−	0.0853906i	−0.424223	−	0.905558i	$-0.639453\pi$
$349$	2.76302	−	1.59523i	0.147901	−	0.0853906i	0.572124	+	0.820167i	$0.306120\pi$
$350$		0			0
$351$	−0.0664404	−	3.60494i	−0.00354632	−	0.192417i
$352$	5.45207			0.290596
$353$	−24.3395	+	14.0524i	−1.29546	+	0.747934i	−0.979616	−	0.200877i	$-0.935621\pi$
$353$	−24.3395	+	14.0524i	−1.29546	+	0.747934i	−0.315844	+	0.948811i	$0.602288\pi$
$354$	−0.137285	−	0.237785i	−0.00729663	−	0.0126381i
$355$		0			0
$356$		−	9.59376i		−	0.508468i
$357$	−22.7305	−	13.1234i	−1.20302	−	0.694566i
$358$	2.65746	+	1.53429i	0.140451	+	0.0810895i
$359$			22.7404i			1.20019i	0.799927	+	0.600097i	$0.204872\pi$
$359$			22.7404i			1.20019i	−0.799927	+	0.600097i	$0.795128\pi$
$360$		0			0
$361$	−2.03115	−	3.51806i	−0.106903	−	0.185161i
$362$	−3.97831	+	2.29688i	−0.209095	+	0.120721i
$363$	18.7250			0.982810
$364$	6.67810	+	11.0897i	0.350028	+	0.581259i
$365$		0			0
$366$	3.57918	−	2.06644i	0.187087	−	0.108015i
$367$	15.1164	+	26.1824i	0.789072	+	1.36671i	0.926536	+	0.376206i	$0.122771\pi$
$367$	15.1164	+	26.1824i	0.789072	+	1.36671i	−0.137464	+	0.990507i	$0.543895\pi$
$368$	−0.929155	+	1.60934i	−0.0484356	+	0.0838928i
$369$		−	7.31038i		−	0.380563i
$370$		0			0
$371$	6.94435	+	4.00932i	0.360533	+	0.208154i
$372$		−	2.23338i		−	0.115795i
$373$	2.33807	−	4.04965i	0.121061	−	0.209683i	−0.799126	−	0.601164i	$-0.794704\pi$
$373$	2.33807	−	4.04965i	0.121061	−	0.209683i	0.920186	+	0.391481i	$0.128037\pi$
$374$	−19.9283	−	34.5169i	−1.03047	−	1.78483i
$375$		0			0
$376$	5.07700			0.261826
$377$	−16.5296	+	9.95396i	−0.851320	+	0.512655i
$378$	−3.59036			−0.184668
$379$	18.5598	−	10.7155i	0.953353	−	0.550419i	0.0592321	−	0.998244i	$-0.481135\pi$
$379$	18.5598	−	10.7155i	0.953353	−	0.550419i	0.894121	+	0.447826i	$0.147801\pi$
$380$		0			0
$381$	−8.99351	+	15.5772i	−0.460751	+	0.798045i
$382$			14.0601i			0.719379i
$383$	−0.0443481	−	0.0256044i	−0.00226608	−	0.00130832i	0.498867	−	0.866679i	$-0.333750\pi$
$383$	−0.0443481	−	0.0256044i	−0.00226608	−	0.00130832i	−0.501133	+	0.865371i	$0.667083\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	−12.5444	+	21.7276i	−0.638494	+	1.10590i
$387$	4.10494	+	7.10996i	0.208666	+	0.361420i
$388$	−1.65264	+	0.954155i	−0.0839003	+	0.0484399i
$389$	−5.35157			−0.271335			−0.135668	−	0.990754i	$-0.543318\pi$
$389$	−5.35157			−0.271335			−0.135668	+	0.990754i	$0.543318\pi$
$390$		0			0
$391$	13.5849			0.687020
$392$	5.10149	−	2.94535i	0.257664	−	0.148762i
$393$	10.1731	+	17.6203i	0.513165	+	0.888827i
$394$	−4.59737	+	7.96287i	−0.231612	+	0.401164i
$395$		0			0
$396$	−4.72163	−	2.72603i	−0.237271	−	0.136988i
$397$	−7.36744	−	4.25359i	−0.369761	−	0.213482i	0.303593	−	0.952802i	$-0.401814\pi$
$397$	−7.36744	−	4.25359i	−0.369761	−	0.213482i	−0.673354	+	0.739320i	$0.735147\pi$
$398$			23.6792i			1.18693i
$399$	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	$0.531745\pi$
$402$	14.7970			0.738008
$403$	8.05120	−	0.148387i	0.401059	−	0.00739166i
$404$	16.2557			0.808752
$405$		0			0
$406$	9.60703	+	16.6399i	0.476789	+	0.825823i
$407$	5.81431	−	10.0707i	0.288204	−	0.499185i
$408$			7.31038i			0.361918i
$409$	−4.51511	−	2.60680i	−0.223258	−	0.128898i	0.384200	−	0.923250i	$-0.374477\pi$
$409$	−4.51511	−	2.60680i	−0.223258	−	0.128898i	−0.607458	+	0.794352i	$0.707811\pi$
$410$		0			0
$411$			11.0407i			0.544599i
$412$	−6.48802	+	11.2376i	−0.319642	+	0.553636i
$413$	−0.492904	−	0.853735i	−0.0242542	−	0.0420095i
$414$	1.60934	−	0.929155i	0.0790949	−	0.0456655i
$415$		0			0
$416$	1.74493	−	3.15519i	0.0855523	−	0.154696i
$417$	−9.70193			−0.475105
$418$	18.2488	−	10.5359i	0.892577	−	0.515329i
$419$	−9.10066	−	15.7628i	−0.444596	−	0.770064i	0.553428	−	0.832897i	$-0.313320\pi$
$419$	−9.10066	−	15.7628i	−0.444596	−	0.770064i	−0.998024	+	0.0628337i	$0.979986\pi$
$420$		0			0
$421$			25.6463i			1.24992i	0.780656	+	0.624961i	$0.214885\pi$
$421$			25.6463i			1.24992i	−0.780656	+	0.624961i	$0.785115\pi$
$422$	8.64818	+	4.99303i	0.420987	+	0.243057i
$423$	−4.39681	−	2.53850i	−0.213780	−	0.123426i
$424$		−	2.23338i		−	0.108463i
$425$		0			0
$426$	7.14784	+	12.3804i	0.346314	+	0.599834i
$427$	12.8505	−	7.41927i	0.621882	−	0.359043i
$428$	9.91673			0.479343
$429$	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	$0.349202\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	0.470915	−	0.815649i	0.0226307	−	0.0391976i	−0.854488	−	0.519471i	$-0.826129\pi$
$433$	0.470915	−	0.815649i	0.0226307	−	0.0391976i	0.877119	+	0.480273i	$0.159462\pi$
$434$		−	8.01864i		−	0.384907i
$435$		0			0
$436$	6.41801	+	3.70544i	0.307367	+	0.177458i
$437$			7.18224i			0.343573i
$438$	7.44876	−	12.9016i	0.355915	−	0.616464i
$439$	−1.80132	−	3.11997i	−0.0859722	−	0.148908i	0.819833	−	0.572603i	$-0.194066\pi$
$439$	−1.80132	−	3.11997i	−0.0859722	−	0.148908i	−0.905805	+	0.423695i	$0.860733\pi$
$440$		0			0
$441$	−5.89069			−0.280509
$442$	−26.3535	+	0.485704i	−1.25351	+	0.0231026i
$443$	5.05095			0.239978			0.119989	−	0.992775i	$-0.461714\pi$
$443$	5.05095			0.239978			0.119989	+	0.992775i	$0.461714\pi$
$444$	−1.84713	+	1.06644i	−0.0876609	+	0.0506110i
$445$		0			0
$446$	11.1910	−	19.3833i	0.529908	−	0.917828i
$447$		−	5.43817i		−	0.257217i
$448$	−3.10934	−	1.79518i	−0.146903	−	0.0848143i
$449$	−4.70017	−	2.71364i	−0.221815	−	0.128065i	0.384976	−	0.922927i	$-0.374210\pi$
$449$	−4.70017	−	2.71364i	−0.221815	−	0.128065i	−0.606790	+	0.794862i	$0.707543\pi$
$450$		0			0
$451$	19.9283	−	34.5169i	0.938389	−	1.62534i
$452$		0			0
$453$	−15.4161	+	8.90050i	−0.724312	+	0.418182i
$454$	−12.9853			−0.609431
$455$		0			0
$456$	−3.86493			−0.180992
$457$	−18.7782	+	10.8416i	−0.878405	+	0.507147i	−0.870132	−	0.492818i	$-0.835967\pi$
$457$	−18.7782	+	10.8416i	−0.878405	+	0.507147i	−0.00827291	+	0.999966i	$0.502633\pi$
$458$	−7.22276	−	12.5102i	−0.337497	−	0.584562i
$459$	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	$0.908775\pi$
$462$	−16.9524	−	9.78745i	−0.788695	−	0.455353i
$463$			28.2075i			1.31091i	0.755232	+	0.655457i	$0.227524\pi$
$463$			28.2075i			1.31091i	−0.755232	+	0.655457i	$0.772476\pi$
$464$	2.67578	−	4.63459i	0.124220	−	0.215156i
$465$		0			0
$466$	−10.7711	+	6.21869i	−0.498961	+	0.288075i
$467$	8.17371			0.378234			0.189117	−	0.981955i	$-0.439437\pi$
$467$	8.17371			0.378234			0.189117	+	0.981955i	$0.439437\pi$
$468$	−3.08875	+	1.86001i	−0.142777	+	0.0859789i
$469$	53.1266			2.45316
$470$		0			0
$471$	2.96826	+	5.14117i	0.136770	+	0.236893i
$472$	−0.137285	+	0.237785i	−0.00631907	+	0.0109450i
$473$			44.7608i			2.05810i
$474$	2.26990	+	1.31052i	0.104260	+	0.0601944i
$475$		0			0
$476$			26.2469i			1.20302i
$477$	−1.11669	+	1.93416i	−0.0511297	+	0.0885593i
$478$	−2.08491	−	3.61118i	−0.0953618	−	0.165171i
$479$	10.1231	−	5.84458i	0.462537	−	0.267046i	−0.250573	−	0.968098i	$-0.580619\pi$
$479$	10.1231	−	5.84458i	0.462537	−	0.267046i	0.713110	+	0.701052i	$0.247286\pi$
$480$		0			0
$481$	−3.96718	−	6.58793i	−0.180888	−	0.300384i
$482$	1.88407			0.0858170
$483$	5.77812	−	3.33600i	0.262914	−	0.151793i
$484$	−9.36252	−	16.2164i	−0.425569	−	0.737107i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	27.6154	+	15.9438i	1.25137	+	0.722481i	0.971382	−	0.237522i	$-0.0763351\pi$
$487$	27.6154	+	15.9438i	1.25137	+	0.722481i	0.279991	+	0.960003i	$0.409668\pi$
$488$	−3.57918	−	2.06644i	−0.162022	−	0.0935434i
$489$			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	$0.687907\pi$
$492$	−6.33097	+	3.65519i	−0.285422	+	0.164789i
$493$	−39.1220			−1.76197
$494$	−0.256787	−	13.9328i	−0.0115534	−	0.626868i
$495$		0			0
$496$	−1.93416	+	1.11669i	−0.0868465	+	0.0501409i
$497$	25.6633	+	44.4502i	1.15116	+	1.99386i
$498$	3.57994	−	6.20064i	0.160421	−	0.277857i
$499$		−	39.3428i		−	1.76123i	−0.473836	−	0.880613i	$-0.657131\pi$
$499$		−	39.3428i		−	1.76123i	0.473836	−	0.880613i	$-0.342869\pi$
$500$		0			0
$501$	−1.60934	−	0.929155i	−0.0719002	−	0.0415116i
$502$		−	7.15005i		−	0.319122i
$503$	−7.16650	+	12.4127i	−0.319538	+	0.553457i	−0.980392	−	0.197058i	$-0.936861\pi$
$503$	−7.16650	+	12.4127i	−0.319538	+	0.553457i	0.660853	+	0.750515i	$0.270194\pi$
$504$	1.79518	+	3.10934i	0.0799637	+	0.138501i
$505$		0			0
$506$	10.1316			0.450406
$507$	−6.91044	−	11.0112i	−0.306903	−	0.489023i
$508$	17.9870			0.798045
$509$	−3.23839	+	1.86968i	−0.143539	+	0.0828723i	−0.570050	−	0.821610i	$-0.693076\pi$
$509$	−3.23839	+	1.86968i	−0.143539	+	0.0828723i	0.426511	+	0.904483i	$0.359743\pi$
$510$		0			0
$511$	26.7437	−	46.3215i	1.18307	−	2.04914i
$512$			1.00000i			0.0441942i
$513$	3.34713	+	1.93247i	0.147779	+	0.0853204i
$514$	−17.7517	−	10.2489i	−0.782994	−	0.452062i
$515$		0			0
$516$	4.10494	−	7.10996i	0.180710	−	0.312999i
$517$	−13.8401	−	23.9717i	−0.608685	−	1.05427i
$518$	−6.63186	+	3.82891i	−0.291387	+	0.168232i
$519$	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	$0.843924\pi$
$522$	−4.63459	+	2.67578i	−0.202851	+	0.117116i
$523$	11.4230	+	19.7853i	0.499495	+	0.865150i	1.00000		0.000583330i	$-0.000185680\pi$
$523$	11.4230	+	19.7853i	0.499495	+	0.865150i	−0.500505	+	0.865734i	$0.666852\pi$
$524$	10.1731	−	17.6203i	0.444414	−	0.769747i
$525$		0			0
$526$	−15.3313	−	8.85153i	−0.668477	−	0.385945i
$527$	14.1395	+	8.16343i	0.615925	+	0.355605i
$528$			5.45207i			0.237271i
$529$	9.77334	−	16.9279i	0.424928	−	0.735997i
$530$		0			0
$531$	0.237785	−	0.137285i	0.0103190	−	0.00595768i
$532$	−13.8765			−0.601623
$533$	−13.5974	−	22.5799i	−0.588967	−	0.978045i
$534$	9.59376			0.415163
$535$		0			0
$536$	−7.39851	−	12.8146i	−0.319567	−	0.553506i
$537$	−1.53429	+	2.65746i	−0.0662093	+	0.114678i
$538$		−	18.1864i		−	0.784070i
$539$	−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	$0.866367\pi$
$542$	11.3847	−	19.7188i	0.489013	−	0.846996i
$543$	−2.29688	−	3.97831i	−0.0985685	−	0.170726i
$544$	6.33097	−	3.65519i	0.271438	−	0.156715i
$545$		0			0
$546$	−11.0897	+	6.67810i	−0.474596	+	0.285796i
$547$	−26.7863			−1.14530			−0.572649	−	0.819801i	$-0.694084\pi$
$547$	−26.7863			−1.14530			−0.572649	+	0.819801i	$0.694084\pi$
$548$	9.56156	−	5.52037i	0.408450	−	0.235818i
$549$	2.06644	+	3.57918i	0.0881935	+	0.152756i
$550$		0			0
$551$		−	20.6834i		−	0.881144i
$552$	−1.60934	−	0.929155i	−0.0684982	−	0.0395475i
$553$	8.14974	+	4.70526i	0.346562	+	0.200088i
$554$		−	16.3563i		−	0.694911i
$555$		0			0
$556$	4.85096	+	8.40212i	0.205727	+	0.356329i
$557$	22.7227	−	13.1189i	0.962791	−	0.555867i	0.0657599	−	0.997835i	$-0.479053\pi$
$557$	22.7227	−	13.1189i	0.962791	−	0.555867i	0.897031	+	0.441968i	$0.145720\pi$
$558$	2.23338			0.0945465
$559$	25.9037	+	14.3257i	1.09561	+	0.605911i
$560$		0			0
$561$	34.5169	−	19.9283i	1.45730	−	0.841375i
$562$	−3.91110	−	6.77423i	−0.164980	−	0.285754i
$563$	−8.10900	+	14.0452i	−0.341754	+	0.591935i	−0.984758	−	0.173927i	$-0.944354\pi$
$563$	−8.10900	+	14.0452i	−0.341754	+	0.591935i	0.643005	+	0.765862i	$0.277688\pi$
$564$			5.07700i			0.213780i
$565$		0			0
$566$	−6.01483	−	3.47266i	−0.252822	−	0.145967i
$567$		−	3.59036i		−	0.150781i
$568$	7.14784	−	12.3804i	0.299917	−	0.519471i
$569$	17.1092	+	29.6340i	0.717255	+	1.24232i	0.962083	+	0.272755i	$0.0879350\pi$
$569$	17.1092	+	29.6340i	0.717255	+	1.24232i	−0.244829	+	0.969566i	$0.578732\pi$
$570$		0			0
$571$	0.151070			0.00632206			0.00316103	−	0.999995i	$-0.498994\pi$
$571$	0.151070			0.00632206			0.00316103	+	0.999995i	$0.498994\pi$
$572$	−19.6544	+	0.362237i	−0.821791	+	0.0151459i
$573$	−14.0601			−0.587371
$574$	−22.7305	+	13.1234i	−0.948752	+	0.547762i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	33.7742i		−	1.40604i	−0.711171	−	0.703019i	$-0.751835\pi$
$577$		−	33.7742i		−	1.40604i	0.711171	−	0.703019i	$-0.248165\pi$
$578$	−31.5594	−	18.2208i	−1.31270	−	0.757886i
$579$	−21.7276	−	12.5444i	−0.902966	−	0.521328i
$580$		0			0
$581$	12.8533	−	22.2625i	0.533244	−	0.923605i
$582$	−0.954155	−	1.65264i	−0.0395510	−	0.0685043i
$583$	−10.5452	+	6.08827i	−0.436737	+	0.252150i
$584$	−14.8975			−0.616464
$585$		0			0
$586$	26.4243			1.09158
$587$	29.1037	−	16.8030i	1.20124	−	0.693535i	0.240408	−	0.970672i	$-0.422719\pi$
$587$	29.1037	−	16.8030i	1.20124	−	0.693535i	0.960831	+	0.277137i	$0.0893855\pi$
$588$	2.94535	+	5.10149i	0.121464	+	0.210382i
$589$	−4.31593	+	7.47541i	−0.177835	+	0.308019i
$590$		0			0
$591$	−7.96287	−	4.59737i	−0.327549	−	0.189110i
$592$	1.84713	+	1.06644i	0.0759165	+	0.0438304i
$593$		−	36.7529i		−	1.50926i	−0.656150	−	0.754630i	$-0.727816\pi$
$593$		−	36.7529i		−	1.50926i	0.656150	−	0.754630i	$-0.272184\pi$
$594$	2.72603	−	4.72163i	0.111851	−	0.193731i
$595$		0			0
$596$	−4.70959	+	2.71908i	−0.192912	+	0.111378i
$597$	−23.6792			−0.969124
$598$	3.24262	−	5.86332i	0.132601	−	0.239769i
$599$	−24.5241			−1.00203			−0.501015	−	0.865439i	$-0.667040\pi$
$599$	−24.5241			−1.00203			−0.501015	+	0.865439i	$0.667040\pi$
$600$		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	$0.556060\pi$
$602$	14.7382	−	25.5273i	0.600685	−	1.04042i
$603$			14.7970i			0.602581i
$604$	15.4161	+	8.90050i	0.627273	+	0.362156i
$605$		0			0
$606$			16.2557i			0.660343i
$607$	−23.2554	+	40.2796i	−0.943909	+	1.63490i	−0.185988	+	0.982552i	$0.559548\pi$
$607$	−23.2554	+	40.2796i	−0.943909	+	1.63490i	−0.757921	+	0.652346i	$0.773785\pi$
$608$	1.93247	+	3.34713i	0.0783718	+	0.135744i
$609$	−16.6399	+	9.60703i	−0.674281	+	0.389297i
$610$		0			0
$611$	−18.3023	+	0.337318i	−0.740430	+	0.0136464i
$612$	−7.31038			−0.295505
$613$	−8.91634	+	5.14785i	−0.360128	+	0.207920i	−0.669137	−	0.743139i	$-0.733336\pi$
$613$	−8.91634	+	5.14785i	−0.360128	+	0.207920i	0.309009	+	0.951059i	$0.400003\pi$
$614$	−3.54290	−	6.13649i	−0.142980	−	0.247649i
$615$		0			0
$616$			19.5749i			0.788695i
$617$	−30.9005	−	17.8404i	−1.24401	−	0.718228i	−0.274100	−	0.961701i	$-0.588380\pi$
$617$	−30.9005	−	17.8404i	−1.24401	−	0.718228i	−0.969908	+	0.243473i	$0.921713\pi$
$618$	−11.2376	−	6.48802i	−0.452042	−	0.260987i
$619$			12.9815i			0.521772i	0.965370	+	0.260886i	$0.0840146\pi$
$619$			12.9815i			0.521772i	−0.965370	+	0.260886i	$0.915985\pi$
$620$		0			0
$621$	0.929155	+	1.60934i	0.0372857	+	0.0645807i
$622$	−1.58498	+	0.915086i	−0.0635517	+	0.0366916i
$623$	34.4451			1.38001
$624$	3.15519	+	1.74493i	0.126309	+	0.0698531i
$625$		0			0
$626$	10.6087	−	6.12493i	0.424008	−	0.244801i
$627$	10.5359	+	18.2488i	0.420765	+	0.728786i
$628$	2.96826	−	5.14117i	0.118446	−	0.205155i
$629$		−	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	$0.806426\pi$
$632$		−	2.62105i		−	0.104260i
$633$	−4.99303	+	8.64818i	−0.198455	+	0.343734i
$634$	−3.12550	−	5.41352i	−0.124129	−	0.214999i
$635$		0			0
$636$	2.23338			0.0885593
$637$	−18.1949	+	10.9567i	−0.720907	+	0.434122i
$638$	−29.1771			−1.15513
$639$	−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	$0.249205\pi$
$642$			9.91673i			0.391382i
$643$	−13.6888	−	7.90323i	−0.539834	−	0.311673i	0.205178	−	0.978725i	$-0.434223\pi$
$643$	−13.6888	−	7.90323i	−0.539834	−	0.311673i	−0.745012	+	0.667052i	$0.767556\pi$
$644$	−5.77812	−	3.33600i	−0.227690	−	0.131457i
$645$		0			0
$646$	14.1271	−	24.4688i	0.555822	−	0.962711i
$647$	−11.4442	−	19.8219i	−0.449916	−	0.779277i	0.548464	−	0.836174i	$-0.315213\pi$
$647$	−11.4442	−	19.8219i	−0.449916	−	0.779277i	−0.998380	+	0.0568967i	$0.981879\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	1.49698			0.0587615
$650$		0			0
$651$	8.01864			0.314275
$652$	13.5046	−	7.79688i	0.528881	−	0.305349i
$653$	−1.08070	−	1.87183i	−0.0422911	−	0.0732504i	0.844105	−	0.536178i	$-0.180132\pi$
$653$	−1.08070	−	1.87183i	−0.0422911	−	0.0732504i	−0.886396	+	0.462927i	$0.846799\pi$
$654$	−3.70544	+	6.41801i	−0.144894	+	0.250964i
$655$		0			0
$656$	6.33097	+	3.65519i	0.247183	+	0.142711i
$657$	12.9016	+	7.44876i	0.503340	+	0.290604i
$658$			18.2283i			0.710611i
$659$	−9.79863	+	16.9717i	−0.381700	+	0.661124i	−0.991305	−	0.131581i	$-0.957995\pi$
$659$	−9.79863	+	16.9717i	−0.381700	+	0.661124i	0.609605	+	0.792705i	$0.291328\pi$
$660$		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	$0.521595\pi$
$662$	−19.1758			−0.745289
$663$	−0.485704	−	26.3535i	−0.0188632	−	1.02348i
$664$	−7.15988			−0.277857
$665$		0			0
$666$	−1.06644	−	1.84713i	−0.0413237	−	0.0715748i
$667$	4.97244	−	8.61251i	0.192534	−	0.333478i
$668$			1.85831i			0.0719002i
$669$	19.3833	+	11.1910i	0.749404	+	0.432668i
$670$		0			0
$671$			22.5327i			0.869867i
$672$	1.79518	−	3.10934i	0.0692506	−	0.119946i
$673$	25.4130	+	44.0166i	0.979599	+	1.69672i	0.663837	+	0.747878i	$0.268927\pi$
$673$	25.4130	+	44.0166i	0.979599	+	1.69672i	0.315763	+	0.948838i	$0.397740\pi$
$674$	14.3284	−	8.27248i	0.551908	−	0.318644i
$675$		0			0
$676$	−6.08074	+	11.4902i	−0.233874	+	0.441931i
$677$	−15.4058			−0.592093			−0.296046	−	0.955174i	$-0.595668\pi$
$677$	−15.4058			−0.592093			−0.296046	+	0.955174i	$0.595668\pi$
$678$		0			0
$679$	−3.42576	−	5.93359i	−0.131469	−	0.227710i
$680$		0			0
$681$		−	12.9853i		−	0.497598i
$682$	10.5452	+	6.08827i	0.403796	+	0.233132i
$683$	−19.2650	−	11.1227i	−0.737155	−	0.425597i	0.0838788	−	0.996476i	$-0.473269\pi$
$683$	−19.2650	−	11.1227i	−0.737155	−	0.425597i	−0.821034	+	0.570879i	$0.806602\pi$
$684$		−	3.86493i		−	0.147779i
$685$		0			0
$686$	−1.99141	−	3.44922i	−0.0760324	−	0.131692i
$687$	12.5102	−	7.22276i	0.477293	−	0.275565i
$688$	−8.20988			−0.312999
$689$	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	$0.296079\pi$
$692$	−12.1687	−	21.0768i	−0.462584	−	0.801219i
$693$	9.78745	−	16.9524i	0.371794	−	0.643967i
$694$		−	5.96390i		−	0.226387i
$695$		0			0
$696$	4.63459	+	2.67578i	0.175674	+	0.101425i
$697$		−	53.4416i		−	2.02425i
$698$	1.59523	−	2.76302i	0.0603803	−	0.104582i
$699$	−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	$0.655008\pi$
$702$	−1.86001	−	3.08875i	−0.0702015	−	0.116577i
$703$	8.24344			0.310907
$704$	4.72163	−	2.72603i	0.177953	−	0.102741i
$705$		0			0
$706$	−14.0524	+	24.3395i	−0.528869	+	0.916029i
$707$			58.3638i			2.19500i
$708$	−0.237785	−	0.137285i	−0.00893652	−	0.00515950i
$709$	22.3507	+	12.9042i	0.839398	+	0.484627i	0.857060	−	0.515217i	$-0.172289\pi$
$709$	22.3507	+	12.9042i	0.839398	+	0.484627i	−0.0176613	+	0.999844i	$0.505622\pi$
$710$		0			0
$711$	−1.31052	+	2.26990i	−0.0491485	+	0.0851277i
$712$	−4.79688	−	8.30844i	−0.179771	−	0.311372i
$713$	−3.59428	+	2.07516i	−0.134607	+	0.0777152i
$714$	−26.2469			−0.982265
$715$		0			0
$716$	3.06857			0.114678
$717$	3.61118	−	2.08491i	0.134862	−	0.0778625i
$718$	11.3702	+	19.6938i	0.424333	+	0.734966i
$719$	−11.7949	+	20.4293i	−0.439874	+	0.761884i	−0.997679	−	0.0680879i	$-0.978310\pi$
$719$	−11.7949	+	20.4293i	−0.439874	+	0.761884i	0.557806	+	0.829972i	$0.311643\pi$
$720$		0			0
$721$	−40.3470	−	23.2943i	−1.50260	−	0.867527i
$722$	−3.51806	−	2.03115i	−0.130929	−	0.0755917i
$723$			1.88407i			0.0700693i
$724$	−2.29688	+	3.97831i	−0.0853628	+	0.147853i
$725$		0			0
$726$	16.2164	−	9.36252i	0.601846	−	0.347476i
$727$	31.4651			1.16698			0.583489	−	0.812121i	$-0.301687\pi$
$727$	31.4651			1.16698			0.583489	+	0.812121i	$0.301687\pi$
$728$	11.3283	+	6.26493i	0.419854	+	0.232194i
$729$	1.00000			0.0370370
$730$		0			0
$731$	30.0087	+	51.9765i	1.10991	+	1.92242i
$732$	2.06644	−	3.57918i	0.0763778	−	0.132290i
$733$		−	32.2822i		−	1.19237i	−0.802847	−	0.596186i	$-0.796682\pi$
$733$		−	32.2822i		−	1.19237i	0.802847	−	0.596186i	$-0.203318\pi$
$734$	26.1824	+	15.1164i	0.966412	+	0.557958i
$735$		0			0
$736$			1.85831i			0.0684982i
$737$	−40.3372	+	69.8660i	−1.48584	+	2.57355i
$738$	−3.65519	−	6.33097i	−0.134549	−	0.233046i
$739$	−13.2643	+	7.65817i	−0.487936	+	0.281710i	−0.723718	−	0.690096i	$-0.757568\pi$
$739$	−13.2643	+	7.65817i	−0.487936	+	0.281710i	0.235782	+	0.971806i	$0.424235\pi$
$740$		0			0
$741$	13.9328	−	0.256787i	0.511836	−	0.00943332i
$742$	8.01864			0.294374
$743$	21.8518	−	12.6161i	0.801663	−	0.462841i	−0.0423891	−	0.999101i	$-0.513497\pi$
$743$	21.8518	−	12.6161i	0.801663	−	0.462841i	0.844052	+	0.536261i	$0.180164\pi$
$744$	−1.11669	−	1.93416i	−0.0409399	−	0.0709099i
$745$		0			0
$746$		−	4.67614i		−	0.171206i
$747$	6.20064	+	3.57994i	0.226869	+	0.130983i
$748$	−34.5169	−	19.9283i	−1.26206	−	0.728652i
$749$			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	$0.742742\pi$
$752$	4.39681	−	2.53850i	0.160335	−	0.0925695i
$753$	7.15005			0.260562
$754$	−9.33811	+	16.8852i	−0.340074	+	0.614923i
$755$		0			0
$756$	−3.10934	+	1.79518i	−0.113086	+	0.0652901i
$757$	18.1796	+	31.4879i	0.660747	+	1.14445i	0.980420	+	0.196920i	$0.0630938\pi$
$757$	18.1796	+	31.4879i	0.660747	+	1.14445i	−0.319673	+	0.947528i	$0.603573\pi$
$758$	10.7155	−	18.5598i	0.389205	−	0.674122i
$759$			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	$0.861109\pi$
$762$			17.9870i			0.651601i
$763$	−13.3039	+	23.0430i	−0.481632	+	0.834211i
$764$	7.03007	+	12.1764i	0.254339	+	0.440528i
$765$		0			0
$766$	−0.0512087			−0.00185025
$767$	0.479107	−	0.866322i	0.0172995	−	0.0312811i
$768$	−1.00000			−0.0360844
$769$	−10.0722	+	5.81521i	−0.363214	+	0.209702i	−0.670490	−	0.741919i	$-0.733916\pi$
$769$	−10.0722	+	5.81521i	−0.363214	+	0.209702i	0.307276	+	0.951621i	$0.400583\pi$
$770$		0			0
$771$	10.2489	−	17.7517i	0.369107	−	0.639312i
$772$			25.0888i			0.902966i
$773$	−25.2573	−	14.5823i	−0.908443	−	0.524490i	−0.0285128	−	0.999593i	$-0.509077\pi$
$773$	−25.2573	−	14.5823i	−0.908443	−	0.524490i	−0.879930	+	0.475104i	$0.842410\pi$
$774$	7.10996	+	4.10494i	0.255562	+	0.147549i
$775$		0			0
$776$	−0.954155	+	1.65264i	−0.0342522	+	0.0593265i
$777$	−3.82891	−	6.63186i	−0.137361	−	0.237917i
$778$	−4.63459	+	2.67578i	−0.166158	+	0.0959315i
$779$	28.2541			1.01231
$780$		0			0
$781$	−77.9410			−2.78895
$782$	11.7649	−	6.79247i	0.420712	−	0.242898i
$783$	−2.67578	−	4.63459i	−0.0956247	−	0.165627i
$784$	2.94535	−	5.10149i	0.105191	−	0.182196i
$785$		0			0
$786$	17.6203	+	10.1731i	0.628496	+	0.362862i
$787$	13.9155	+	8.03414i	0.496035	+	0.286386i	0.727075	−	0.686558i	$-0.240879\pi$
$787$	13.9155	+	8.03414i	0.496035	+	0.286386i	−0.231039	+	0.972944i	$0.574213\pi$
$788$			9.19473i			0.327549i
$789$	8.85153	−	15.3313i	0.315123	−	0.545809i
$790$		0			0
$791$		0			0
$792$	−5.45207			−0.193731
$793$	13.0400	+	7.21159i	0.463065	+	0.256091i
$794$	−8.50719			−0.301909
$795$		0			0
$796$	11.8396	+	20.5068i	0.419643	+	0.726843i
$797$	19.5288	−	33.8249i	0.691745	−	1.19814i	−0.279520	−	0.960140i	$-0.590175\pi$
$797$	19.5288	−	33.8249i	0.691745	−	1.19814i	0.971266	−	0.237998i	$-0.0764913\pi$
$798$		−	13.8765i		−	0.491223i
$799$	−32.1423	−	18.5574i	−1.13711	−	0.656513i
$800$		0			0
$801$			9.59376i			0.338979i
$802$	−11.6894	+	20.2467i	−0.412767	+	0.714934i
$803$	40.6111	+	70.3405i	1.43314	+	2.48226i
$804$	12.8146	−	7.39851i	0.451936	−	0.260925i
$805$		0			0
$806$	6.89835	−	4.15411i	0.242984	−	0.146322i
$807$	18.1864			0.640191
$808$	14.0779	−	8.12785i	0.495257	−	0.285937i
$809$	−7.04891	−	12.2091i	−0.247827	−	0.429248i	0.715096	−	0.699026i	$-0.246383\pi$
$809$	−7.04891	−	12.2091i	−0.247827	−	0.429248i	−0.962923	+	0.269778i	$0.913050\pi$
$810$		0			0
$811$		−	11.3869i		−	0.399846i	−0.979812	−	0.199923i	$-0.935931\pi$
$811$		−	11.3869i		−	0.399846i	0.979812	−	0.199923i	$-0.0640693\pi$
$812$	16.6399	+	9.60703i	0.583945	+	0.337141i
$813$	19.7188	+	11.3847i	0.691569	+	0.399278i
$814$		−	11.6286i		−	0.407583i
$815$		0			0
$816$	3.65519	+	6.33097i	0.127957	+	0.221628i
$817$	−27.4795	+	15.8653i	−0.961387	+	0.555057i
$818$	−5.21360			−0.182289
$819$	−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	$0.163114\pi$
$822$	5.52037	+	9.56156i	0.192545	+	0.333498i
$823$	14.1230	−	24.4617i	0.492296	−	0.852681i	−0.507665	−	0.861555i	$-0.669491\pi$
$823$	14.1230	−	24.4617i	0.492296	−	0.852681i	0.999961	+	0.00887332i	$0.00282450\pi$
$824$			12.9760i			0.452042i
$825$		0			0
$826$	−0.853735	−	0.492904i	−0.0297052	−	0.0171503i
$827$		−	37.3963i		−	1.30040i	−0.759765	−	0.650198i	$-0.774686\pi$
$827$		−	37.3963i		−	1.30040i	0.759765	−	0.650198i	$-0.225314\pi$
$828$	0.929155	−	1.60934i	0.0322904	−	0.0559286i
$829$	−0.925320	−	1.60270i	−0.0321377	−	0.0556641i	0.849509	−	0.527574i	$-0.176898\pi$
$829$	−0.925320	−	1.60270i	−0.0321377	−	0.0556641i	−0.881647	+	0.471910i	$0.843565\pi$
$830$		0			0
$831$	16.3563			0.567393
$832$	−0.0664404	−	3.60494i	−0.00230341	−	0.124979i
$833$	−43.0632			−1.49205
$834$	−8.40212	+	4.85096i	−0.290941	+	0.167975i
$835$		0			0
$836$	10.5359	−	18.2488i	0.364393	−	0.631147i
$837$			2.23338i			0.0771969i
$838$	−15.7628	−	9.10066i	−0.544517	−	0.314377i
$839$	−38.8940	−	22.4555i	−1.34277	−	0.775249i	−0.355557	−	0.934655i	$-0.615709\pi$
$839$	−38.8940	−	22.4555i	−1.34277	−	0.775249i	−0.987213	+	0.159406i	$0.949042\pi$
$840$		0			0
$841$	0.180359	−	0.312392i	0.00621929	−	0.0107721i
$842$	12.8231	+	22.2103i	0.441914	+	0.765418i
$843$	6.77423	−	3.91110i	0.233317	−	0.134706i
$844$	9.98606			0.343734
$845$		0			0
$846$	−5.07700			−0.174551
$847$	58.2226	−	33.6148i	2.00055	−	1.15502i
$848$	−1.11669	−	1.93416i	−0.0383473	−	0.0664195i
$849$	3.47266	−	6.01483i	0.119181	−	0.206428i
$850$		0			0
$851$	3.43254	+	1.98178i	0.117666	+	0.0679344i
$852$	12.3804	+	7.14784i	0.424146	+	0.244881i
$853$		−	6.75772i		−	0.231380i	−0.993285	−	0.115690i	$-0.963092\pi$
$853$		−	6.75772i		−	0.231380i	0.993285	−	0.115690i	$-0.0369079\pi$
$854$	7.41927	−	12.8505i	0.253882	−	0.439737i
$855$		0			0
$856$	8.58814	−	4.95837i	0.293537	−	0.169474i
$857$	−9.16177			−0.312960			−0.156480	−	0.987681i	$-0.550015\pi$
$857$	−9.16177			−0.312960			−0.156480	+	0.987681i	$0.550015\pi$
$858$	−0.362237	−	19.6544i	−0.0123666	−	0.670989i
$859$	11.9538			0.407857			0.203928	−	0.978986i	$-0.434629\pi$
$859$	11.9538			0.407857			0.203928	+	0.978986i	$0.434629\pi$
$860$		0			0
$861$	−13.1234	−	22.7305i	−0.447246	−	0.774653i
$862$	−1.03457	+	1.79193i	−0.0352376	+	0.0610334i
$863$		−	31.6465i		−	1.07726i	−0.842542	−	0.538630i	$-0.818942\pi$
$863$		−	31.6465i		−	1.07726i	0.842542	−	0.538630i	$-0.181058\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$		−	0.941830i		−	0.0320047i
$867$	18.2208	−	31.5594i	0.618811	−	1.07181i
$868$	−4.00932	−	6.94435i	−0.136085	−	0.235707i
$869$	−12.3756	+	7.14507i	−0.419814	+	0.242380i
$870$		0			0
$871$	27.5226	+	45.7043i	0.932567	+	1.54863i
$872$	7.41088			0.250964
$873$	1.65264	−	0.954155i	0.0559335	−	0.0322932i
$874$	3.59112	+	6.22000i	0.121471	+	0.210395i
$875$		0			0
$876$		−	14.8975i		−	0.503340i
$877$	−12.2372	−	7.06515i	−0.413221	−	0.238573i	0.278952	−	0.960305i	$-0.410013\pi$
$877$	−12.2372	−	7.06515i	−0.413221	−	0.238573i	−0.692173	+	0.721732i	$0.743346\pi$
$878$	−3.11997	−	1.80132i	−0.105294	−	0.0607915i
$879$			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	$0.937764\pi$
$882$	−5.10149	+	2.94535i	−0.171776	+	0.0991749i
$883$	7.19528			0.242140			0.121070	−	0.992644i	$-0.461367\pi$
$883$	7.19528			0.242140			0.121070	+	0.992644i	$0.461367\pi$
$884$	−22.5799	+	13.5974i	−0.759445	+	0.457329i
$885$		0			0
$886$	4.37425	−	2.52548i	0.146956	−	0.0848451i
$887$	14.4022	+	24.9453i	0.483577	+	0.837580i	0.999822	−	0.0188611i	$-0.00600402\pi$
$887$	14.4022	+	24.9453i	0.483577	+	0.837580i	−0.516245	+	0.856441i	$0.672671\pi$
$888$	−1.06644	+	1.84713i	−0.0357874	+	0.0619856i
$889$			64.5799i			2.16594i
$890$		0			0
$891$	4.72163	+	2.72603i	0.158181	+	0.0913256i
$892$		−	22.3820i		−	0.749404i
$893$	9.81112	−	16.9934i	0.328317	−	0.568661i
$894$	−2.71908	−	4.70959i	−0.0909398	−	0.157512i
$895$		0			0
$896$	−3.59036			−0.119946
$897$	5.86332	+	3.24262i	0.195771	+	0.108268i
$898$	−5.42729			−0.181111
$899$	10.3508	−	5.97604i	0.345219	−	0.199312i
$900$		0			0
$901$	−8.16343	+	14.1395i	−0.271963	+	0.471054i
$902$		−	39.8567i		−	1.32708i
$903$	25.5273	+	14.7382i	0.849496	+	0.490457i
$904$		0			0
$905$		0			0
$906$	−8.90050	+	15.4161i	−0.295699	+	0.512166i
$907$	19.5856	+	33.9233i	0.650331	+	1.12641i	0.983043	+	0.183377i	$0.0587030\pi$
$907$	19.5856	+	33.9233i	0.650331	+	1.12641i	−0.332712	+	0.943029i	$0.607964\pi$
$908$	−11.2456	+	6.49265i	−0.373199	+	0.215466i
$909$	−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	$0.356302\pi$
$912$	−3.34713	+	1.93247i	−0.110835	+	0.0639903i
$913$	19.5181	+	33.8063i	0.645954	+	1.11883i
$914$	−10.8416	+	18.7782i	−0.358607	+	0.621126i
$915$		0			0
$916$	−12.5102	−	7.22276i	−0.413348	−	0.238647i
$917$	63.2633	+	36.5251i	2.08914	+	1.20616i
$918$		−	7.31038i		−	0.241278i
$919$	−4.85456	+	8.40834i	−0.160137	+	0.277365i	−0.934918	−	0.354865i	$-0.884527\pi$
$919$	−4.85456	+	8.40834i	−0.160137	+	0.277365i	0.774781	+	0.632230i	$0.217860\pi$
$920$		0			0
$921$	6.13649	−	3.54290i	0.202204	−	0.116743i
$922$	−29.6023			−0.974901
$923$	−24.9450	+	45.1056i	−0.821074	+	1.48467i
$924$	−19.5749			−0.643967
$925$		0			0
$926$	14.1038	+	24.4284i	0.463478	+	0.802768i
$927$	6.48802	−	11.2376i	0.213095	−	0.369091i
$928$		−	5.35157i		−	0.175674i
$929$	2.68782	+	1.55181i	0.0881844	+	0.0509133i	0.543444	−	0.839446i	$-0.317120\pi$
$929$	2.68782	+	1.55181i	0.0881844	+	0.0509133i	−0.455259	+	0.890359i	$0.650453\pi$
$930$		0			0
$931$		−	22.7671i		−	0.746162i
$932$	−6.21869	+	10.7711i	−0.203700	+	0.352819i
$933$	−0.915086	−	1.58498i	−0.0299586	−	0.0518898i
$934$	7.07864	−	4.08685i	0.231620	−	0.133726i
$935$		0			0
$936$	−1.74493	+	3.15519i	−0.0570348	+	0.103131i
$937$	−53.5929			−1.75080			−0.875402	−	0.483396i	$-0.839403\pi$
$937$	−53.5929			−1.75080			−0.875402	+	0.483396i	$0.839403\pi$
$938$	46.0090	−	26.5633i	1.50225	−	0.867323i
$939$	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	$-0.247033\pi$
$942$	5.14117	+	2.96826i	0.167509	+	0.0967111i
$943$	11.7649	+	6.79247i	0.383118	+	0.221193i
$944$			0.274571i			0.00893652i
$945$		0			0
$946$	22.3804	+	38.7640i	0.727650	+	1.26033i
$947$	−9.60349	+	5.54457i	−0.312071	+	0.180174i	−0.647853	−	0.761765i	$-0.724333\pi$
$947$	−9.60349	+	5.54457i	−0.312071	+	0.180174i	0.335782	+	0.941940i	$0.391000\pi$
$948$	2.62105			0.0851277
$949$	53.7046	−	0.989796i	1.74333	−	0.0321301i
$950$		0			0
$951$	5.41352	−	3.12550i	0.175546	−	0.101351i
$952$	13.1234	+	22.7305i	0.425333	+	0.736699i
$953$	28.8278	−	49.9313i	0.933825	−	1.61743i	0.157110	−	0.987581i	$-0.449782\pi$
$953$	28.8278	−	49.9313i	0.933825	−	1.61743i	0.776715	−	0.629852i	$-0.216884\pi$
$954$			2.23338i			0.0723084i
$955$		0			0
$956$	−3.61118	−	2.08491i	−0.116794	−	0.0674309i
$957$		−	29.1771i		−	0.943162i
$958$	5.84458	−	10.1231i	0.188830	−	0.327063i
$959$	19.8201	+	34.3294i	0.640025	+	1.10856i
$960$		0			0
$961$	26.0120			0.839097
$962$	−6.72964	−	3.72173i	−0.216972	−	0.119993i
$963$	−9.91673			−0.319562
$964$	1.63165	−	0.942035i	0.0525520	−	0.0303409i
$965$		0			0
$966$	3.33600	−	5.77812i	0.107334	−	0.185908i
$967$		−	30.5218i		−	0.981516i	−0.871296	−	0.490758i	$-0.836720\pi$
$967$		−	30.5218i		−	0.981516i	0.871296	−	0.490758i	$-0.163280\pi$
$968$	−16.2164	−	9.36252i	−0.521214	−	0.300923i
$969$	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	$0.314743\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−30.1666	+	17.4167i	−0.967098	+	0.558354i
$974$	31.8875			1.02174
$975$		0			0
$976$	−4.13288			−0.132290
$977$	−1.70870	+	0.986516i	−0.0546660	+	0.0315614i	−0.527084	−	0.849813i	$-0.676715\pi$
$977$	−1.70870	+	0.986516i	−0.0546660	+	0.0315614i	0.472418	+	0.881375i	$0.343381\pi$
$978$	7.79688	+	13.5046i	0.249317	+	0.431829i
$979$	−26.1529	+	45.2982i	−0.835851	+	1.44774i
$980$		0			0
$981$	−6.41801	−	3.70544i	−0.204911	−	0.118306i
$982$	16.9309	+	9.77506i	0.540286	+	0.311935i
$983$			8.00792i			0.255413i	0.991812	+	0.127707i	$0.0407616\pi$
$983$			8.00792i			0.255413i	−0.991812	+	0.127707i	$0.959238\pi$
$984$	−3.65519	+	6.33097i	−0.116523	+	0.201824i
$985$		0			0
$986$	−33.8806	+	19.5610i	−1.07898	+	0.622949i
$987$	−18.2283			−0.580212
$988$	−7.18881	−	11.9378i	−0.228706	−	0.379792i
$989$	−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	$-0.360587\pi$
$992$	−1.11669	+	1.93416i	−0.0354550	+	0.0614098i
$993$		−	19.1758i		−	0.608526i
$994$	44.4502	+	25.6633i	1.40987	+	0.813992i
$995$		0			0
$996$		−	7.15988i		−	0.226869i
$997$	−25.5906	+	44.3242i	−0.810463	+	1.40376i	0.102078	+	0.994776i	$0.467451\pi$
$997$	−25.5906	+	44.3242i	−0.810463	+	1.40376i	−0.912541	+	0.408986i	$0.865883\pi$
$998$	−19.6714	−	34.0719i	−0.622688	−	1.07853i
$999$	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.bc.k.751.6	yes	12
5.2	odd	4		1950.2.y.n.49.4		12
5.3	odd	4		1950.2.y.m.49.3		12
5.4	even	2		1950.2.bc.h.751.1	✓	12
13.4	even	6	inner	1950.2.bc.k.901.6	yes	12
65.4	even	6		1950.2.bc.h.901.1	yes	12
65.17	odd	12		1950.2.y.m.199.3		12
65.43	odd	12		1950.2.y.n.199.4		12

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

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)

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

L-functions

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