LMFDB - Embedded newform 300.2.e.d.251.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(251,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("300.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.e (of order $2$, degree $1$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4521217600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} - 2x^{4} + 4x^{2} + 16 $ x^8 + x^6 - 2x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.5
Root			$-0.273147 - 1.38758i$ of defining polynomial
Character	$\chi$	$=$	300.251
Dual form			300.2.e.d.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.273147 - 1.38758i) q^{2} +(-1.55737 - 0.758030i) q^{3} +(-1.85078 - 0.758030i) q^{4} +(-1.47722 + 1.95392i) q^{6} -3.56393i q^{7} +(-1.55737 + 2.36106i) q^{8} +(1.85078 + 2.36106i) q^{9} +O(q^{10})$	\(q+(0.273147 - 1.38758i) q^{2} +(-1.55737 - 0.758030i) q^{3} +(-1.85078 - 0.758030i) q^{4} +(-1.47722 + 1.95392i) q^{6} -3.56393i q^{7} +(-1.55737 + 2.36106i) q^{8} +(1.85078 + 2.36106i) q^{9} -4.20732 q^{11} +(2.30774 + 2.58348i) q^{12} -2.70156 q^{13} +(-4.94525 - 0.973477i) q^{14} +(2.85078 + 2.80590i) q^{16} +0.828216i q^{17} +(3.78171 - 1.92320i) q^{18} +5.07999i q^{19} +(-2.70156 + 5.55034i) q^{21} +(-1.14922 + 5.83802i) q^{22} -1.09259 q^{23} +(4.21515 - 2.49651i) q^{24} +(-0.737925 + 3.74865i) q^{26} +(-1.09259 - 5.07999i) q^{27} +(-2.70156 + 6.59605i) q^{28} -5.55034i q^{29} -6.59605i q^{31} +(4.67210 - 3.18928i) q^{32} +(6.55234 + 3.18928i) q^{33} +(1.14922 + 0.226225i) q^{34} +(-1.63564 - 5.77275i) q^{36} -5.40312 q^{37} +(7.04891 + 1.38758i) q^{38} +(4.20732 + 2.04787i) q^{39} -10.2725i q^{41} +(6.96364 + 5.26471i) q^{42} -0.531805i q^{43} +(7.78683 + 3.18928i) q^{44} +(-0.298438 + 1.51606i) q^{46} -6.22947 q^{47} +(-2.31276 - 6.53078i) q^{48} -5.70156 q^{49} +(0.627812 - 1.28984i) q^{51} +(5.00000 + 2.04787i) q^{52} -5.55034i q^{53} +(-7.34735 + 0.128476i) q^{54} +(8.41464 + 5.55034i) q^{56} +(3.85078 - 7.91140i) q^{57} +(-7.70156 - 1.51606i) q^{58} +0.701562 q^{61} +(-9.15257 - 1.80169i) q^{62} +(8.41464 - 6.59605i) q^{63} +(-3.14922 - 7.35408i) q^{64} +(6.21515 - 8.22079i) q^{66} +2.04787i q^{67} +(0.627812 - 1.53285i) q^{68} +(1.70156 + 0.828216i) q^{69} +11.3663 q^{71} +(-8.45695 + 0.692770i) q^{72} -7.70156 q^{73} +(-1.47585 + 7.49729i) q^{74} +(3.85078 - 9.40194i) q^{76} +14.9946i q^{77} +(3.99080 - 5.27865i) q^{78} -7.12785i q^{79} +(-2.14922 + 8.73961i) q^{81} +(-14.2539 - 2.80590i) q^{82} -3.11473 q^{83} +(9.20732 - 8.22459i) q^{84} +(-0.737925 - 0.145261i) q^{86} +(-4.20732 + 8.64391i) q^{87} +(6.55234 - 9.93375i) q^{88} +4.72212i q^{89} +9.62817i q^{91} +(2.02214 + 0.828216i) q^{92} +(-5.00000 + 10.2725i) q^{93} +(-1.70156 + 8.64391i) q^{94} +(-9.69374 + 1.42528i) q^{96} +8.10469 q^{97} +(-1.55737 + 7.91140i) q^{98} +(-7.78683 - 9.93375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9	$ 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9} - 11 q^{12} + 4 q^{13} + 10 q^{16} + 7 q^{18} + 4 q^{21} - 22 q^{22} + 13 q^{24} + 4 q^{28} + 14 q^{33} + 22 q^{34} - 21 q^{36} + 8 q^{37} + 36 q^{42} - 28 q^{46} - 15 q^{48} - 20 q^{49} + 40 q^{52} - 28 q^{54} + 18 q^{57} - 36 q^{58} - 20 q^{61} - 38 q^{64} + 29 q^{66} - 12 q^{69} - 51 q^{72} - 36 q^{73} + 18 q^{76} + 22 q^{78} - 30 q^{81} - 50 q^{82} + 40 q^{84} + 14 q^{88} - 40 q^{93} + 12 q^{94} - 39 q^{96} - 12 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9 - 11 * q^12 + 4 * q^13 + 10 * q^16 + 7 * q^18 + 4 * q^21 - 22 * q^22 + 13 * q^24 + 4 * q^28 + 14 * q^33 + 22 * q^34 - 21 * q^36 + 8 * q^37 + 36 * q^42 - 28 * q^46 - 15 * q^48 - 20 * q^49 + 40 * q^52 - 28 * q^54 + 18 * q^57 - 36 * q^58 - 20 * q^61 - 38 * q^64 + 29 * q^66 - 12 * q^69 - 51 * q^72 - 36 * q^73 + 18 * q^76 + 22 * q^78 - 30 * q^81 - 50 * q^82 + 40 * q^84 + 14 * q^88 - 40 * q^93 + 12 * q^94 - 39 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.273147	−	1.38758i	0.193144	−	0.981170i
$2$	0.273147	−	1.38758i	0.193144	−	0.981170i
$3$	−1.55737	−	0.758030i	−0.899146	−	0.437649i
$3$	−1.55737	−	0.758030i	−0.899146	−	0.437649i
$4$	−1.85078	−	0.758030i	−0.925391	−	0.379015i
$5$		0			0
$5$		0			0
$6$	−1.47722	+	1.95392i	−0.603073	+	0.797686i
$7$		−	3.56393i		−	1.34704i	−0.739170	−	0.673519i	$-0.764782\pi$
$7$		−	3.56393i		−	1.34704i	0.739170	−	0.673519i	$-0.235218\pi$
$8$	−1.55737	+	2.36106i	−0.550612	+	0.834761i
$9$	1.85078	+	2.36106i	0.616927	+	0.787020i
$10$		0			0
$11$	−4.20732			−1.26856			−0.634278	−	0.773105i	$-0.718702\pi$
$11$	−4.20732			−1.26856			−0.634278	+	0.773105i	$0.718702\pi$
$12$	2.30774	+	2.58348i	0.666186	+	0.745786i
$13$	−2.70156			−0.749279			−0.374639	−	0.927171i	$-0.622233\pi$
$13$	−2.70156			−0.749279			−0.374639	+	0.927171i	$0.622233\pi$
$14$	−4.94525	−	0.973477i	−1.32167	−	0.260173i
$15$		0			0
$16$	2.85078	+	2.80590i	0.712695	+	0.701474i
$17$			0.828216i			0.200872i	0.994944	+	0.100436i	$0.0320237\pi$
$17$			0.828216i			0.200872i	−0.994944	+	0.100436i	$0.967976\pi$
$18$	3.78171	−	1.92320i	0.891357	−	0.453302i
$19$			5.07999i			1.16543i	0.812677	+	0.582714i	$0.198009\pi$
$19$			5.07999i			1.16543i	−0.812677	+	0.582714i	$0.801991\pi$
$20$		0			0
$21$	−2.70156	+	5.55034i	−0.589529	+	1.21118i
$22$	−1.14922	+	5.83802i	−0.245014	+	1.24467i
$23$	−1.09259			−0.227821			−0.113910	−	0.993491i	$-0.536338\pi$
$23$	−1.09259			−0.227821			−0.113910	+	0.993491i	$0.536338\pi$
$24$	4.21515	−	2.49651i	0.860413	−	0.509597i
$25$		0			0
$26$	−0.737925	+	3.74865i	−0.144719	+	0.735170i
$27$	−1.09259	−	5.07999i	−0.210269	−	0.977644i
$28$	−2.70156	+	6.59605i	−0.510547	+	1.24654i
$29$		−	5.55034i		−	1.03067i	−0.856988	−	0.515336i	$-0.827667\pi$
$29$		−	5.55034i		−	1.03067i	0.856988	−	0.515336i	$-0.172333\pi$
$30$		0			0
$31$		−	6.59605i		−	1.18468i	−0.805686	−	0.592342i	$-0.798203\pi$
$31$		−	6.59605i		−	1.18468i	0.805686	−	0.592342i	$-0.201797\pi$
$32$	4.67210	−	3.18928i	0.825918	−	0.563790i
$33$	6.55234	+	3.18928i	1.14062	+	0.555182i
$34$	1.14922	+	0.226225i	0.197089	+	0.0387972i
$35$		0			0
$36$	−1.63564	−	5.77275i	−0.272606	−	0.962126i
$37$	−5.40312			−0.888268			−0.444134	−	0.895960i	$-0.646489\pi$
$37$	−5.40312			−0.888268			−0.444134	+	0.895960i	$0.646489\pi$
$38$	7.04891	+	1.38758i	1.14348	+	0.225096i
$39$	4.20732	+	2.04787i	0.673711	+	0.327921i
$40$		0			0
$41$		−	10.2725i		−	1.60429i	−0.597130	−	0.802144i	$-0.703692\pi$
$41$		−	10.2725i		−	1.60429i	0.597130	−	0.802144i	$-0.296308\pi$
$42$	6.96364	+	5.26471i	1.07451	+	0.812362i
$43$		−	0.531805i		−	0.0810995i	−0.999178	−	0.0405498i	$-0.987089\pi$
$43$		−	0.531805i		−	0.0810995i	0.999178	−	0.0405498i	$-0.0129109\pi$
$44$	7.78683	+	3.18928i	1.17391	+	0.480802i
$45$		0			0
$46$	−0.298438	+	1.51606i	−0.0440023	+	0.223531i
$47$	−6.22947			−0.908661			−0.454331	−	0.890833i	$-0.650121\pi$
$47$	−6.22947			−0.908661			−0.454331	+	0.890833i	$0.650121\pi$
$48$	−2.31276	−	6.53078i	−0.333818	−	0.942638i
$49$	−5.70156			−0.814509
$50$		0			0
$51$	0.627812	−	1.28984i	0.0879113	−	0.180613i
$52$	5.00000	+	2.04787i	0.693375	+	0.283988i
$53$		−	5.55034i		−	0.762398i	−0.924493	−	0.381199i	$-0.875511\pi$
$53$		−	5.55034i		−	0.762398i	0.924493	−	0.381199i	$-0.124489\pi$
$54$	−7.34735	+	0.128476i	−0.999847	+	0.0174833i
$55$		0			0
$56$	8.41464	+	5.55034i	1.12445	+	0.741695i
$57$	3.85078	−	7.91140i	0.510048	−	1.04789i
$58$	−7.70156	−	1.51606i	−1.01126	−	0.199068i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	0.701562			0.0898258			0.0449129	−	0.998991i	$-0.485699\pi$
$61$	0.701562			0.0898258			0.0449129	+	0.998991i	$0.485699\pi$
$62$	−9.15257	−	1.80169i	−1.16238	−	0.228815i
$63$	8.41464	−	6.59605i	1.06015	−	0.831024i
$64$	−3.14922	−	7.35408i	−0.393652	−	0.919259i
$65$		0			0
$66$	6.21515	−	8.22079i	0.765032	−	1.01191i
$67$			2.04787i			0.250187i	0.992145	+	0.125093i	$0.0399230\pi$
$67$			2.04787i			0.250187i	−0.992145	+	0.125093i	$0.960077\pi$
$68$	0.627812	−	1.53285i	0.0761334	−	0.185885i
$69$	1.70156	+	0.828216i	0.204844	+	0.0997054i
$70$		0			0
$71$	11.3663			1.34894			0.674468	−	0.738304i	$-0.264373\pi$
$71$	11.3663			1.34894			0.674468	+	0.738304i	$0.264373\pi$
$72$	−8.45695	+	0.692770i	−0.996662	+	0.0816437i
$73$	−7.70156			−0.901400			−0.450700	−	0.892676i	$-0.648826\pi$
$73$	−7.70156			−0.901400			−0.450700	+	0.892676i	$0.648826\pi$
$74$	−1.47585	+	7.49729i	−0.171564	+	0.871542i
$75$		0			0
$76$	3.85078	−	9.40194i	0.441715	−	1.07848i
$77$			14.9946i			1.70879i
$78$	3.99080	−	5.27865i	0.451870	−	0.597689i
$79$		−	7.12785i		−	0.801946i	−0.916090	−	0.400973i	$-0.868672\pi$
$79$		−	7.12785i		−	0.801946i	0.916090	−	0.400973i	$-0.131328\pi$
$80$		0			0
$81$	−2.14922	+	8.73961i	−0.238802	+	0.971068i
$82$	−14.2539	−	2.80590i	−1.57408	−	0.309859i
$83$	−3.11473			−0.341886			−0.170943	−	0.985281i	$-0.554681\pi$
$83$	−3.11473			−0.341886			−0.170943	+	0.985281i	$0.554681\pi$
$84$	9.20732	−	8.22459i	1.00460	−	0.897377i
$85$		0			0
$86$	−0.737925	−	0.145261i	−0.0795724	−	0.0156639i
$87$	−4.20732	+	8.64391i	−0.451072	+	0.926724i
$88$	6.55234	−	9.93375i	0.698482	−	1.05894i
$89$			4.72212i			0.500544i	0.968176	+	0.250272i	$0.0805200\pi$
$89$			4.72212i			0.500544i	−0.968176	+	0.250272i	$0.919480\pi$
$90$		0			0
$91$			9.62817i			1.00931i
$92$	2.02214	+	0.828216i	0.210823	+	0.0863474i
$93$	−5.00000	+	10.2725i	−0.518476	+	1.06520i
$94$	−1.70156	+	8.64391i	−0.175503	+	0.891551i
$95$		0			0
$96$	−9.69374	+	1.42528i	−0.989363	+	0.145467i
$97$	8.10469			0.822906			0.411453	−	0.911431i	$-0.365021\pi$
$97$	8.10469			0.822906			0.411453	+	0.911431i	$0.365021\pi$
$98$	−1.55737	+	7.91140i	−0.157318	+	0.799172i
$99$	−7.78683	−	9.93375i	−0.782606	−	0.998379i
$100$		0			0
$101$		−	7.20677i		−	0.717100i	−0.933510	−	0.358550i	$-0.883271\pi$
$101$		−	7.20677i		−	0.717100i	0.933510	−	0.358550i	$-0.116729\pi$
$102$	−1.61827	−	1.22346i	−0.160233	−	0.121140i
$103$			4.09573i			0.403564i	0.979430	+	0.201782i	$0.0646733\pi$
$103$			4.09573i			0.403564i	−0.979430	+	0.201782i	$0.935327\pi$
$104$	4.20732	−	6.37855i	0.412562	−	0.625469i
$105$		0			0
$106$	−7.70156	−	1.51606i	−0.748042	−	0.147253i
$107$	18.8514			1.82244			0.911218	−	0.411924i	$-0.135143\pi$
$107$	18.8514			1.82244			0.911218	+	0.411924i	$0.135143\pi$
$108$	−1.82864	+	10.2302i	−0.175961	+	0.984397i
$109$	8.70156			0.833458			0.416729	−	0.909031i	$-0.363176\pi$
$109$	8.70156			0.833458			0.416729	+	0.909031i	$0.363176\pi$
$110$		0			0
$111$	8.41464	+	4.09573i	0.798683	+	0.388750i
$112$	10.0000	−	10.1600i	0.944911	−	0.960027i
$113$		−	15.8228i		−	1.48848i	−0.667910	−	0.744242i	$-0.732811\pi$
$113$		−	15.8228i		−	1.48848i	0.667910	−	0.744242i	$-0.267189\pi$
$114$	−9.92590	−	7.50426i	−0.929646	−	0.702838i
$115$		0			0
$116$	−4.20732	+	10.2725i	−0.390640	+	0.953774i
$117$	−5.00000	−	6.37855i	−0.462250	−	0.589697i
$118$		0			0
$119$	2.95170			0.270582
$120$		0			0
$121$	6.70156			0.609233
$122$	0.191630	−	0.973477i	0.0173493	−	0.0881344i
$123$	−7.78683	+	15.9980i	−0.702115	+	1.44249i
$124$	−5.00000	+	12.2078i	−0.449013	+	1.09630i
$125$		0			0
$126$	−6.85413	−	13.4777i	−0.610615	−	1.20069i
$127$			16.2242i			1.43967i	0.694147	+	0.719833i	$0.255782\pi$
$127$			16.2242i			1.43967i	−0.694147	+	0.719833i	$0.744218\pi$
$128$	−11.0646	+	2.36106i	−0.977982	+	0.208690i
$129$	−0.403124	+	0.828216i	−0.0354931	+	0.0729203i
$130$		0			0
$131$	−19.7810			−1.72827			−0.864136	−	0.503258i	$-0.832135\pi$
$131$	−19.7810			−1.72827			−0.864136	+	0.503258i	$0.832135\pi$
$132$	−9.70939	−	10.8695i	−0.845094	−	0.946071i
$133$	18.1047			1.56988
$134$	2.84159	+	0.559369i	0.245476	+	0.0483221i
$135$		0			0
$136$	−1.95547	−	1.28984i	−0.167680	−	0.110602i
$137$		−	6.37855i		−	0.544957i	−0.962162	−	0.272478i	$-0.912157\pi$
$137$		−	6.37855i		−	0.544957i	0.962162	−	0.272478i	$-0.0878433\pi$
$138$	1.61400	−	2.13484i	0.137392	−	0.181729i
$139$		−	1.51606i		−	0.128591i	−0.997931	−	0.0642953i	$-0.979520\pi$
$139$		−	1.51606i		−	0.128591i	0.997931	−	0.0642953i	$-0.0204799\pi$
$140$		0			0
$141$	9.70156	+	4.72212i	0.817019	+	0.397674i
$142$	3.10469	−	15.7718i	0.260539	−	1.32354i
$143$	11.3663			0.950501
$144$	−1.34872	+	11.9240i	−0.112393	+	0.993664i
$145$		0			0
$146$	−2.10366	+	10.6866i	−0.174100	+	0.884427i
$147$	8.87942	+	4.32196i	0.732362	+	0.356469i
$148$	10.0000	+	4.09573i	0.821995	+	0.336667i
$149$			1.65643i			0.135700i	0.997696	+	0.0678501i	$0.0216139\pi$
$149$			1.65643i			0.135700i	−0.997696	+	0.0678501i	$0.978386\pi$
$150$		0			0
$151$			4.62754i			0.376583i	0.982113	+	0.188292i	$0.0602951\pi$
$151$			4.62754i			0.376583i	−0.982113	+	0.188292i	$0.939705\pi$
$152$	−11.9942	−	7.91140i	−0.972854	−	0.641699i
$153$	−1.95547	+	1.53285i	−0.158090	+	0.123923i
$154$	20.8062	+	4.09573i	1.67662	+	0.330043i
$155$		0			0
$156$	−6.23449	−	6.97943i	−0.499159	−	0.558801i
$157$	8.10469			0.646824			0.323412	−	0.946258i	$-0.395170\pi$
$157$	8.10469			0.646824			0.323412	+	0.946258i	$0.395170\pi$
$158$	−9.89049	−	1.94695i	−0.786845	−	0.154891i
$159$	−4.20732	+	8.64391i	−0.333662	+	0.685507i
$160$		0			0
$161$			3.89391i			0.306883i
$162$	11.5399	+	5.36943i	0.906660	+	0.421862i
$163$			5.07999i			0.397895i	0.980010	+	0.198948i	$0.0637523\pi$
$163$			5.07999i			0.397895i	−0.980010	+	0.198948i	$0.936248\pi$
$164$	−7.78683	+	19.0121i	−0.608049	+	1.48459i
$165$		0			0
$166$	−0.850781	+	4.32196i	−0.0660334	+	0.335449i
$167$	3.27777			0.253641			0.126821	−	0.991926i	$-0.459523\pi$
$167$	3.27777			0.253641			0.126821	+	0.991926i	$0.459523\pi$
$168$	−8.89736	−	15.0225i	−0.686447	−	1.15901i
$169$	−5.70156			−0.438582
$170$		0			0
$171$	−11.9942	+	9.40194i	−0.917216	+	0.718984i
$172$	−0.403124	+	0.984255i	−0.0307379	+	0.0750487i
$173$			14.9946i			1.14002i	0.821639	+	0.570008i	$0.193060\pi$
$173$			14.9946i			1.14002i	−0.821639	+	0.570008i	$0.806940\pi$
$174$	10.8449	+	8.19908i	0.822152	+	0.621570i
$175$		0			0
$176$	−11.9942	−	11.8053i	−0.904093	−	0.889858i
$177$		0			0
$178$	6.55234	+	1.28984i	0.491119	+	0.0966772i
$179$	−15.5737			−1.16403			−0.582015	−	0.813178i	$-0.697736\pi$
$179$	−15.5737			−1.16403			−0.582015	+	0.813178i	$0.697736\pi$
$180$		0			0
$181$	−21.5078			−1.59866			−0.799331	−	0.600890i	$-0.794813\pi$
$181$	−21.5078			−1.59866			−0.799331	+	0.600890i	$0.794813\pi$
$182$	13.3599	+	2.62991i	0.990301	+	0.194942i
$183$	−1.09259	−	0.531805i	−0.0807665	−	0.0393122i
$184$	1.70156	−	2.57967i	0.125441	−	0.190176i
$185$		0			0
$186$	12.8882	+	9.74382i	0.945006	+	0.714451i
$187$		−	3.48457i		−	0.254817i
$188$	11.5294	+	4.72212i	0.840866	+	0.344396i
$189$	−18.1047	+	3.89391i	−1.31692	+	0.283240i
$190$		0			0
$191$	11.3663			0.822440			0.411220	−	0.911536i	$-0.365103\pi$
$191$	11.3663			0.822440			0.411220	+	0.911536i	$0.365103\pi$
$192$	−0.670121	+	13.8402i	−0.0483618	+	0.998830i
$193$	5.80625			0.417943			0.208971	−	0.977922i	$-0.432988\pi$
$193$	5.80625			0.417943			0.208971	+	0.977922i	$0.432988\pi$
$194$	2.21377	−	11.2459i	0.158940	−	0.807411i
$195$		0			0
$196$	10.5523	+	4.32196i	0.753739	+	0.308711i
$197$		−	9.44424i		−	0.672875i	−0.941706	−	0.336437i	$-0.890778\pi$
$197$		−	9.44424i		−	0.672875i	0.941706	−	0.336437i	$-0.109222\pi$
$198$	−15.9109	+	8.09151i	−1.13074	+	0.575039i
$199$		−	15.6924i		−	1.11241i	−0.831047	−	0.556203i	$-0.812258\pi$
$199$		−	15.6924i		−	1.11241i	0.831047	−	0.556203i	$-0.187742\pi$
$200$		0			0
$201$	1.55234	−	3.18928i	0.109494	−	0.224954i
$202$	−10.0000	−	1.96851i	−0.703598	−	0.138504i
$203$	−19.7810			−1.38835
$204$	−2.13968	+	1.91130i	−0.149807	+	0.133818i
$205$		0			0
$206$	5.68317	+	1.11874i	0.395965	+	0.0779462i
$207$	−2.02214	−	2.57967i	−0.140549	−	0.179299i
$208$	−7.70156	−	7.58030i	−0.534007	−	0.525599i
$209$		−	21.3731i		−	1.47841i
$210$		0			0
$211$			14.1763i			0.975940i	0.872860	+	0.487970i	$0.162262\pi$
$211$			14.1763i			0.975940i	−0.872860	+	0.487970i	$0.837738\pi$
$212$	−4.20732	+	10.2725i	−0.288960	+	0.705515i
$213$	−17.7016	−	8.61603i	−1.21289	−	0.590361i
$214$	5.14922	−	26.1580i	0.351993	−	1.78812i
$215$		0			0
$216$	13.6957	+	5.33173i	0.931876	+	0.362778i
$217$	−23.5078			−1.59581
$218$	2.37681	−	12.0742i	0.160978	−	0.817765i
$219$	11.9942	+	5.83802i	0.810490	+	0.394497i
$220$		0			0
$221$		−	2.23748i		−	0.150509i
$222$	7.98161	−	10.5573i	0.535691	−	0.708559i
$223$		−	15.6924i		−	1.05084i	−0.850843	−	0.525421i	$-0.823908\pi$
$223$		−	15.6924i		−	1.05084i	0.850843	−	0.525421i	$-0.176092\pi$
$224$	−11.3663	−	16.6510i	−0.759446	−	1.11254i
$225$		0			0
$226$	−21.9555	−	4.32196i	−1.46046	−	0.287492i
$227$	−11.6924			−0.776053			−0.388026	−	0.921648i	$-0.626843\pi$
$227$	−11.6924			−0.776053			−0.388026	+	0.921648i	$0.626843\pi$
$228$	−13.1240	+	11.7233i	−0.869160	+	0.776392i
$229$	8.70156			0.575015			0.287508	−	0.957778i	$-0.407173\pi$
$229$	8.70156			0.575015			0.287508	+	0.957778i	$0.407173\pi$
$230$		0			0
$231$	11.3663	−	23.3521i	0.747850	−	1.53645i
$232$	13.1047	+	8.64391i	0.860365	+	0.567501i
$233$			14.9946i			0.982328i	0.871067	+	0.491164i	$0.163428\pi$
$233$			14.9946i			0.982328i	−0.871067	+	0.491164i	$0.836572\pi$
$234$	−10.2165	+	5.19564i	−0.667875	+	0.339649i
$235$		0			0
$236$		0			0
$237$	−5.40312	+	11.1007i	−0.350971	+	0.721066i
$238$	0.806248	−	4.09573i	0.0522613	−	0.265487i
$239$	5.46295			0.353369			0.176684	−	0.984268i	$-0.443463\pi$
$239$	5.46295			0.353369			0.176684	+	0.984268i	$0.443463\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$	1.83051	−	9.29898i	0.117670	−	0.597761i
$243$	9.97201	−	11.9816i	0.639705	−	0.768621i
$244$	−1.29844	−	0.531805i	−0.0831240	−	0.0340453i
$245$		0			0
$246$	20.0716	+	15.1747i	1.27972	+	0.967503i
$247$		−	13.7239i		−	0.873231i
$248$	15.5737	+	10.2725i	0.988929	+	0.652302i
$249$	4.85078	+	2.36106i	0.307406	+	0.149626i
$250$		0			0
$251$	1.25562			0.0792543			0.0396272	−	0.999215i	$-0.487383\pi$
$251$	1.25562			0.0792543			0.0396272	+	0.999215i	$0.487383\pi$
$252$	−20.5737	+	5.82928i	−1.29602	+	0.367210i
$253$	4.59688			0.289003
$254$	22.5125	+	4.43160i	1.41256	+	0.278063i
$255$		0			0
$256$	0.253905	+	15.9980i	0.0158691	+	0.999874i
$257$			11.1007i			0.692441i	0.938153	+	0.346221i	$0.112535\pi$
$257$			11.1007i			0.692441i	−0.938153	+	0.346221i	$0.887465\pi$
$258$	1.03911	+	0.785594i	0.0646920	+	0.0489089i
$259$			19.2563i			1.19653i
$260$		0			0
$261$	13.1047	−	10.2725i	0.811160	−	0.635849i
$262$	−5.40312	+	27.4478i	−0.333806	+	1.69573i
$263$	17.9219			1.10511			0.552555	−	0.833476i	$-0.313653\pi$
$263$	17.9219			1.10511			0.552555	+	0.833476i	$0.313653\pi$
$264$	−17.7345	+	10.5036i	−1.09148	+	0.646452i
$265$		0			0
$266$	4.94525	−	25.1218i	0.303213	−	1.54032i
$267$	3.57951	−	7.35408i	0.219062	−	0.450062i
$268$	1.55234	−	3.79015i	0.0948245	−	0.231520i
$269$			14.9946i			0.914236i	0.889406	+	0.457118i	$0.151118\pi$
$269$			14.9946i			0.914236i	−0.889406	+	0.457118i	$0.848882\pi$
$270$		0			0
$271$		−	24.4157i		−	1.48315i	−0.670872	−	0.741573i	$-0.734080\pi$
$271$		−	24.4157i		−	1.48315i	0.670872	−	0.741573i	$-0.265920\pi$
$272$	−2.32389	+	2.36106i	−0.140906	+	0.143160i
$273$	7.29844	−	14.9946i	0.441722	−	0.907513i
$274$	−8.85078	−	1.74228i	−0.534695	−	0.105255i
$275$		0			0
$276$	−2.52141	−	2.82268i	−0.151771	−	0.169905i
$277$	28.1047			1.68865			0.844323	−	0.535834i	$-0.180003\pi$
$277$	28.1047			1.68865			0.844323	+	0.535834i	$0.180003\pi$
$278$	−2.10366	−	0.414108i	−0.126169	−	0.0248365i
$279$	15.5737	−	12.2078i	0.932371	−	0.730864i
$280$		0			0
$281$			7.20677i			0.429920i	0.976623	+	0.214960i	$0.0689621\pi$
$281$			7.20677i			0.429920i	−0.976623	+	0.214960i	$0.931038\pi$
$282$	9.20230	−	12.1719i	0.547989	−	0.724826i
$283$		−	6.14360i		−	0.365199i	−0.983187	−	0.182599i	$-0.941549\pi$
$283$		−	6.14360i		−	0.365199i	0.983187	−	0.182599i	$-0.0584511\pi$
$284$	−21.0366	−	8.61603i	−1.24829	−	0.511267i
$285$		0			0
$286$	3.10469	−	15.7718i	0.183584	−	0.932604i
$287$	−36.6103			−2.16104
$288$	16.1771	+	5.12846i	0.953245	+	0.302197i
$289$	16.3141			0.959651
$290$		0			0
$291$	−12.6220	−	6.14360i	−0.739913	−	0.360144i
$292$	14.2539	+	5.83802i	0.834147	+	0.341644i
$293$		−	18.8885i		−	1.10348i	−0.834017	−	0.551739i	$-0.813965\pi$
$293$		−	18.8885i		−	1.10348i	0.834017	−	0.551739i	$-0.186035\pi$
$294$	8.42247	−	11.1404i	0.491208	−	0.649722i
$295$		0			0
$296$	8.41464	−	12.7571i	0.489091	−	0.741492i
$297$	4.59688	+	21.3731i	0.266738	+	1.24020i
$298$	2.29844	+	0.452450i	0.133145	+	0.0262097i
$299$	2.95170			0.170701
$300$		0			0
$301$	−1.89531			−0.109244
$302$	6.42110	+	1.26400i	0.369493	+	0.0727350i
$303$	−5.46295	+	11.2236i	−0.313838	+	0.644778i
$304$	−14.2539	+	14.4819i	−0.817518	+	0.830595i
$305$		0			0
$306$	1.59282	+	3.13207i	0.0910556	+	0.179048i
$307$		−	20.3993i		−	1.16425i	−0.813100	−	0.582125i	$-0.802222\pi$
$307$		−	20.3993i		−	1.16425i	0.813100	−	0.582125i	$-0.197778\pi$
$308$	11.3663	−	27.7517i	0.647657	−	1.58130i
$309$	3.10469	−	6.37855i	0.176619	−	0.362863i
$310$		0			0
$311$	16.8293			0.954301			0.477151	−	0.878821i	$-0.341670\pi$
$311$	16.8293			0.954301			0.477151	+	0.878821i	$0.341670\pi$
$312$	−11.3875	+	6.74447i	−0.644689	+	0.381830i
$313$	−22.7016			−1.28317			−0.641584	−	0.767053i	$-0.721722\pi$
$313$	−22.7016			−1.28317			−0.641584	+	0.767053i	$0.721722\pi$
$314$	2.21377	−	11.2459i	0.124930	−	0.634645i
$315$		0			0
$316$	−5.40312	+	13.1921i	−0.303949	+	0.742113i
$317$		−	29.9892i		−	1.68436i	−0.539197	−	0.842180i	$-0.681272\pi$
$317$		−	29.9892i		−	1.68436i	0.539197	−	0.842180i	$-0.318728\pi$
$318$	10.8449	+	8.19908i	0.608154	+	0.459781i
$319$			23.3521i			1.30746i
$320$		0			0
$321$	−29.3586	−	14.2900i	−1.63864	−	0.797587i
$322$	5.40312	+	1.06361i	0.301104	+	0.0592727i
$323$	−4.20732			−0.234102
$324$	10.6026	−	14.5459i	0.589035	−	0.808108i
$325$		0			0
$326$	7.04891	+	1.38758i	0.390403	+	0.0768512i
$327$	−13.5515	−	6.59605i	−0.749401	−	0.364762i
$328$	24.2539	+	15.9980i	1.33920	+	0.883341i
$329$			22.2014i			1.22400i
$330$		0			0
$331$		−	30.0275i		−	1.65046i	−0.564798	−	0.825229i	$-0.691046\pi$
$331$		−	30.0275i		−	1.65046i	0.564798	−	0.825229i	$-0.308954\pi$
$332$	5.76469	+	2.36106i	0.316378	+	0.129580i
$333$	−10.0000	−	12.7571i	−0.547997	−	0.699085i
$334$	0.895314	−	4.54818i	0.0489894	−	0.248865i
$335$		0			0
$336$	−23.2752	+	8.24250i	−1.26977	+	0.449665i
$337$	−0.403124			−0.0219596			−0.0109798	−	0.999940i	$-0.503495\pi$
$337$	−0.403124			−0.0219596			−0.0109798	+	0.999940i	$0.503495\pi$
$338$	−1.55737	+	7.91140i	−0.0847096	+	0.430323i
$339$	−11.9942	+	24.6419i	−0.651433	+	1.33836i
$340$		0			0
$341$			27.7517i			1.50284i
$342$	9.76981	+	19.2110i	0.528291	+	1.03881i
$343$		−	4.62754i		−	0.249863i
$344$	1.25562	+	0.828216i	0.0676987	+	0.0446544i
$345$		0			0
$346$	20.8062	+	4.09573i	1.11855	+	0.220188i
$347$	13.3885			0.718732			0.359366	−	0.933197i	$-0.382993\pi$
$347$	13.3885			0.718732			0.359366	+	0.933197i	$0.382993\pi$
$348$	14.3392	−	12.8087i	0.768661	−	0.686619i
$349$	−12.2094			−0.653553			−0.326776	−	0.945102i	$-0.605962\pi$
$349$	−12.2094			−0.653553			−0.326776	+	0.945102i	$0.605962\pi$
$350$		0			0
$351$	2.95170	+	13.7239i	0.157550	+	0.732527i
$352$	−19.6570	+	13.4183i	−1.04772	+	0.715199i
$353$			29.4081i			1.56524i	0.622502	+	0.782618i	$0.286116\pi$
$353$			29.4081i			1.56524i	−0.622502	+	0.782618i	$0.713884\pi$
$354$		0			0
$355$		0			0
$356$	3.57951	−	8.73961i	0.189714	−	0.463199i
$357$	−4.59688	−	2.23748i	−0.243292	−	0.118420i
$358$	−4.25391	+	21.6098i	−0.224826	+	1.14211i
$359$	36.6103			1.93222			0.966108	−	0.258137i	$-0.0831087\pi$
$359$	36.6103			1.93222			0.966108	+	0.258137i	$0.0831087\pi$
$360$		0			0
$361$	−6.80625			−0.358224
$362$	−5.87480	+	29.8439i	−0.308773	+	1.56856i
$363$	−10.4368	−	5.07999i	−0.547789	−	0.266630i
$364$	7.29844	−	17.8196i	0.382542	−	0.934002i
$365$		0			0
$366$	−1.03636	+	1.37080i	−0.0541715	+	0.0716528i
$367$		−	3.56393i		−	0.186035i	−0.995664	−	0.0930177i	$-0.970349\pi$
$367$		−	3.56393i		−	0.186035i	0.995664	−	0.0930177i	$-0.0296513\pi$
$368$	−3.11473	−	3.06569i	−0.162367	−	0.159810i
$369$	24.2539	−	19.0121i	1.26261	−	0.989729i
$370$		0			0
$371$	−19.7810			−1.02698
$372$	17.0407	−	15.2219i	0.883521	−	0.789220i
$373$	17.2984			0.895679			0.447840	−	0.894114i	$-0.352194\pi$
$373$	17.2984			0.895679			0.447840	+	0.894114i	$0.352194\pi$
$374$	−4.83513	−	0.951801i	−0.250019	−	0.0492165i
$375$		0			0
$376$	9.70156	−	14.7082i	0.500320	−	0.758515i
$377$			14.9946i			0.772260i
$378$	0.457877	+	26.1854i	0.0235507	+	1.34683i
$379$		−	21.3042i		−	1.09432i	−0.837027	−	0.547162i	$-0.815708\pi$
$379$		−	21.3042i		−	1.09432i	0.837027	−	0.547162i	$-0.184292\pi$
$380$		0			0
$381$	12.2984	−	25.2670i	0.630068	−	1.29447i
$382$	3.10469	−	15.7718i	0.158850	−	0.806953i
$383$	12.4589			0.636622			0.318311	−	0.947986i	$-0.396884\pi$
$383$	12.4589			0.636622			0.318311	+	0.947986i	$0.396884\pi$
$384$	19.0214	+	4.71026i	0.970681	+	0.240370i
$385$		0			0
$386$	1.58596	−	8.05666i	0.0807233	−	0.410073i
$387$	1.25562	−	0.984255i	0.0638270	−	0.0500325i
$388$	−15.0000	−	6.14360i	−0.761510	−	0.311894i
$389$		−	19.9639i		−	1.01221i	−0.862472	−	0.506104i	$-0.831085\pi$
$389$		−	19.9639i		−	1.01221i	0.862472	−	0.506104i	$-0.168915\pi$
$390$		0			0
$391$		−	0.904899i		−	0.0457627i
$392$	8.87942	−	13.4617i	0.448479	−	0.679920i
$393$	30.8062	+	14.9946i	1.55397	+	0.756377i
$394$	−13.1047	−	2.57967i	−0.660205	−	0.129962i
$395$		0			0
$396$	6.88165	+	24.2878i	0.345816	+	1.22051i
$397$	−28.9109			−1.45100			−0.725499	−	0.688223i	$-0.758391\pi$
$397$	−28.9109			−1.45100			−0.725499	+	0.688223i	$0.758391\pi$
$398$	−21.7745	−	4.28634i	−1.09146	−	0.214855i
$399$	−28.1956	−	13.7239i	−1.41155	−	0.687054i
$400$		0			0
$401$			30.8174i			1.53895i	0.638679	+	0.769473i	$0.279481\pi$
$401$			30.8174i			1.53895i	−0.638679	+	0.769473i	$0.720519\pi$
$402$	−4.00137	−	3.02515i	−0.199570	−	0.150881i
$403$			17.8196i			0.887659i
$404$	−5.46295	+	13.3382i	−0.271792	+	0.663598i
$405$		0			0
$406$	−5.40312	+	27.4478i	−0.268153	+	1.36221i
$407$	22.7327			1.12682
$408$	2.06765	+	3.49105i	0.102364	+	0.172833i
$409$	−27.2094			−1.34542			−0.672708	−	0.739908i	$-0.734869\pi$
$409$	−27.2094			−1.34542			−0.672708	+	0.739908i	$0.734869\pi$
$410$		0			0
$411$	−4.83513	+	9.93375i	−0.238500	+	0.489996i
$412$	3.10469	−	7.58030i	0.152957	−	0.373455i
$413$		0			0
$414$	−4.13185	+	2.10127i	−0.203070	+	0.103272i
$415$		0			0
$416$	−12.6220	+	8.61603i	−0.618843	+	0.422436i
$417$	−1.14922	+	2.36106i	−0.0562775	+	0.115622i
$418$	−29.6570	−	5.83802i	−1.45057	−	0.285547i
$419$	−10.1107			−0.493941			−0.246970	−	0.969023i	$-0.579435\pi$
$419$	−10.1107			−0.493941			−0.246970	+	0.969023i	$0.579435\pi$
$420$		0			0
$421$	24.2094			1.17989			0.589946	−	0.807442i	$-0.299149\pi$
$421$	24.2094			1.17989			0.589946	+	0.807442i	$0.299149\pi$
$422$	19.6709	+	3.87223i	0.957563	+	0.188497i
$423$	−11.5294	−	14.7082i	−0.560578	−	0.715135i
$424$	13.1047	+	8.64391i	0.636420	+	0.419785i
$425$		0			0
$426$	−16.7906	+	22.2090i	−0.813507	+	1.07603i
$427$		−	2.50031i		−	0.120999i
$428$	−34.8899	−	14.2900i	−1.68647	−	0.690731i
$429$	−17.7016	−	8.61603i	−0.854639	−	0.415986i
$430$		0			0
$431$	−19.7810			−0.952817			−0.476408	−	0.879224i	$-0.658062\pi$
$431$	−19.7810			−0.952817			−0.476408	+	0.879224i	$0.658062\pi$
$432$	11.1392	−	17.5476i	0.535934	−	0.844260i
$433$	−31.2094			−1.49983			−0.749913	−	0.661536i	$-0.769905\pi$
$433$	−31.2094			−1.49983			−0.749913	+	0.661536i	$0.769905\pi$
$434$	−6.42110	+	32.6191i	−0.308222	+	1.56577i
$435$		0			0
$436$	−16.1047	−	6.59605i	−0.771275	−	0.315893i
$437$		−	5.55034i		−	0.265509i
$438$	11.3769	−	15.0483i	0.543610	−	0.719034i
$439$			21.9154i			1.04596i	0.852344	+	0.522981i	$0.175180\pi$
$439$			21.9154i			1.04596i	−0.852344	+	0.522981i	$0.824820\pi$
$440$		0			0
$441$	−10.5523	−	13.4617i	−0.502493	−	0.641035i
$442$	−3.10469	−	0.611161i	−0.147675	−	0.0290699i
$443$	−11.2033			−0.532285			−0.266143	−	0.963934i	$-0.585749\pi$
$443$	−11.2033			−0.532285			−0.266143	+	0.963934i	$0.585749\pi$
$444$	−12.4690	−	13.9589i	−0.591752	−	0.662458i
$445$		0			0
$446$	−21.7745	−	4.28634i	−1.03105	−	0.202964i
$447$	1.25562	−	2.57967i	0.0593890	−	0.122014i
$448$	−26.2094	+	11.2236i	−1.23828	+	0.530264i
$449$			19.1357i			0.903068i	0.892254	+	0.451534i	$0.149123\pi$
$449$			19.1357i			0.903068i	−0.892254	+	0.451534i	$0.850877\pi$
$450$		0			0
$451$			43.2196i			2.03513i
$452$	−11.9942	+	29.2845i	−0.564158	+	1.37743i
$453$	3.50781	−	7.20677i	0.164811	−	0.338604i
$454$	−3.19375	+	16.2242i	−0.149890	+	0.761440i
$455$		0			0
$456$	12.6822	+	21.4129i	0.593899	+	1.00275i
$457$	−16.8953			−0.790329			−0.395165	−	0.918610i	$-0.629312\pi$
$457$	−16.8953			−0.790329			−0.395165	+	0.918610i	$0.629312\pi$
$458$	2.37681	−	12.0742i	0.111061	−	0.564188i
$459$	4.20732	−	0.904899i	0.196381	−	0.0422371i
$460$		0			0
$461$		−	7.20677i		−	0.335653i	−0.985817	−	0.167826i	$-0.946325\pi$
$461$		−	7.20677i		−	0.335653i	0.985817	−	0.167826i	$-0.0536748\pi$
$462$	−29.2983	−	22.1503i	−1.36308	−	1.03053i
$463$		−	7.12785i		−	0.331259i	−0.986188	−	0.165630i	$-0.947034\pi$
$463$		−	7.12785i		−	0.331259i	0.986188	−	0.165630i	$-0.0529656\pi$
$464$	15.5737	−	15.8228i	0.722989	−	0.734555i
$465$		0			0
$466$	20.8062	+	4.09573i	0.963831	+	0.189731i
$467$	−0.766519			−0.0354703			−0.0177351	−	0.999843i	$-0.505646\pi$
$467$	−0.766519			−0.0354703			−0.0177351	+	0.999843i	$0.505646\pi$
$468$	4.41877	+	15.5955i	0.204258	+	0.720900i
$469$	7.29844			0.337011
$470$		0			0
$471$	−12.6220	−	6.14360i	−0.581590	−	0.283082i
$472$		0			0
$473$			2.23748i			0.102879i
$474$	13.9273	+	10.5294i	0.639701	+	0.483632i
$475$		0			0
$476$	−5.46295	−	2.23748i	−0.250394	−	0.102555i
$477$	13.1047	−	10.2725i	0.600022	−	0.470344i
$478$	1.49219	−	7.58030i	0.0682512	−	0.346715i
$479$	−42.0732			−1.92237			−0.961187	−	0.275897i	$-0.911025\pi$
$479$	−42.0732			−1.92237			−0.961187	+	0.275897i	$0.911025\pi$
$480$		0			0
$481$	14.5969			0.665560
$482$	1.91203	−	9.71309i	0.0870906	−	0.442419i
$483$	2.95170	−	6.06424i	0.134307	−	0.275932i
$484$	−12.4031	−	5.07999i	−0.563778	−	0.230908i
$485$		0			0
$486$	−13.9017	−	17.1098i	−0.630592	−	0.776114i
$487$			34.0438i			1.54267i	0.636427	+	0.771337i	$0.280412\pi$
$487$			34.0438i			1.54267i	−0.636427	+	0.771337i	$0.719588\pi$
$488$	−1.09259	+	1.65643i	−0.0494592	+	0.0749831i
$489$	3.85078	−	7.91140i	0.174138	−	0.357766i
$490$		0			0
$491$	16.8293			0.759495			0.379748	−	0.925090i	$-0.376011\pi$
$491$	16.8293			0.759495			0.379748	+	0.925090i	$0.376011\pi$
$492$	26.5387	−	23.7061i	1.19646	−	1.06875i
$493$	4.59688			0.207033
$494$	−19.0431	−	3.74865i	−0.856788	−	0.168660i
$495$		0			0
$496$	18.5078	−	18.8039i	0.831025	−	0.844319i
$497$		−	40.5088i		−	1.81707i
$498$	4.60115	−	6.08595i	0.206182	−	0.272718i
$499$		−	22.9790i		−	1.02868i	−0.857586	−	0.514340i	$-0.828037\pi$
$499$		−	22.9790i		−	1.02868i	0.857586	−	0.514340i	$-0.171963\pi$
$500$		0			0
$501$	−5.10469	−	2.48465i	−0.228061	−	0.111006i
$502$	0.342970	−	1.74228i	0.0153075	−	0.0777620i
$503$	−32.2399			−1.43751			−0.718753	−	0.695265i	$-0.755287\pi$
$503$	−32.2399			−1.43751			−0.718753	+	0.695265i	$0.755287\pi$
$504$	2.46898	+	30.1400i	0.109977	+	1.34254i
$505$		0			0
$506$	1.25562	−	6.37855i	0.0558193	−	0.283561i
$507$	8.87942	+	4.32196i	0.394349	+	0.191945i
$508$	12.2984	−	30.0275i	0.545655	−	1.33225i
$509$			42.7463i			1.89470i	0.320207	+	0.947348i	$0.396247\pi$
$509$			42.7463i			1.89470i	−0.320207	+	0.947348i	$0.603753\pi$
$510$		0			0
$511$			27.4478i			1.21422i
$512$	22.2679	+	4.01749i	0.984112	+	0.177550i
$513$	25.8062	−	5.55034i	1.13937	−	0.245053i
$514$	15.4031	+	3.03212i	0.679403	+	0.133741i
$515$		0			0
$516$	1.37391	−	1.22727i	0.0604829	−	0.0540273i
$517$	26.2094			1.15269
$518$	26.7198	+	5.25982i	1.17400	+	0.231103i
$519$	11.3663	−	23.3521i	0.498927	−	1.02504i
$520$		0			0
$521$			10.2725i			0.450045i	0.974354	+	0.225022i	$0.0722455\pi$
$521$			10.2725i			0.450045i	−0.974354	+	0.225022i	$0.927754\pi$
$522$	−10.6744	−	20.9898i	−0.467206	−	0.918697i
$523$			31.4642i			1.37583i	0.725790	+	0.687916i	$0.241474\pi$
$523$			31.4642i			1.37583i	−0.725790	+	0.687916i	$0.758526\pi$
$524$	36.6103	+	14.9946i	1.59933	+	0.655041i
$525$		0			0
$526$	4.89531	−	24.8681i	0.213446	−	1.08430i
$527$	5.46295			0.237970
$528$	9.73052	+	27.4771i	0.423467	+	1.19579i
$529$	−21.8062			−0.948098
$530$		0			0
$531$		0			0
$532$	−33.5078	−	13.7239i	−1.45275	−	0.595006i
$533$			27.7517i			1.20206i
$534$	−9.22667	−	6.97562i	−0.399277	−	0.301865i
$535$		0			0
$536$	−4.83513	−	3.18928i	−0.208846	−	0.137756i
$537$	24.2539	+	11.8053i	1.04663	+	0.509437i
$538$	20.8062	+	4.09573i	0.897021	+	0.176579i
$539$	23.9883			1.03325
$540$		0			0
$541$	−19.2984			−0.829705			−0.414852	−	0.909889i	$-0.636167\pi$
$541$	−19.2984			−0.829705			−0.414852	+	0.909889i	$0.636167\pi$
$542$	−33.8788	−	6.66908i	−1.45522	−	0.286461i
$543$	33.4955	+	16.3036i	1.43743	+	0.699653i
$544$	2.64141	+	3.86951i	0.113249	+	0.165904i
$545$		0			0
$546$	−18.8127	−	14.2229i	−0.805109	−	0.608685i
$547$			21.8360i			0.933640i	0.884352	+	0.466820i	$0.154600\pi$
$547$			21.8360i			0.933640i	−0.884352	+	0.466820i	$0.845400\pi$
$548$	−4.83513	+	11.8053i	−0.206547	+	0.504298i
$549$	1.29844	+	1.65643i	0.0554160	+	0.0706948i
$550$		0			0
$551$	28.1956			1.20117
$552$	−4.60542	+	2.72766i	−0.196020	+	0.116097i
$553$	−25.4031			−1.08025
$554$	7.67672	−	38.9976i	0.326153	−	1.65685i
$555$		0			0
$556$	−1.14922	+	2.80590i	−0.0487377	+	0.118996i
$557$			17.2321i			0.730146i	0.930979	+	0.365073i	$0.118956\pi$
$557$			17.2321i			0.730146i	−0.930979	+	0.365073i	$0.881044\pi$
$558$	−12.6855	−	24.9443i	−0.537020	−	1.05598i
$559$			1.43670i			0.0607661i
$560$		0			0
$561$	−2.64141	+	5.42675i	−0.111520	+	0.229118i
$562$	10.0000	+	1.96851i	0.421825	+	0.0830366i
$563$	30.0547			1.26666			0.633328	−	0.773883i	$-0.281688\pi$
$563$	30.0547			1.26666			0.633328	+	0.773883i	$0.281688\pi$
$564$	−14.3760	−	16.0937i	−0.605337	−	0.677667i
$565$		0			0
$566$	−8.52476	−	1.67811i	−0.358322	−	0.0705361i
$567$	31.1473	+	7.65966i	1.30806	+	0.321675i
$568$	−17.7016	+	26.8366i	−0.742741	+	1.12604i
$569$		−	43.5745i		−	1.82674i	−0.407133	−	0.913369i	$-0.633472\pi$
$569$		−	43.5745i		−	1.82674i	0.407133	−	0.913369i	$-0.366528\pi$
$570$		0			0
$571$		−	32.9802i		−	1.38018i	−0.723724	−	0.690090i	$-0.757571\pi$
$571$		−	32.9802i		−	1.38018i	0.723724	−	0.690090i	$-0.242429\pi$
$572$	−21.0366	−	8.61603i	−0.879585	−	0.360254i
$573$	−17.7016	−	8.61603i	−0.739493	−	0.359940i
$574$	−10.0000	+	50.7999i	−0.417392	+	2.12034i
$575$		0			0
$576$	11.5349	−	21.0463i	0.480621	−	0.876928i
$577$	−0.403124			−0.0167823			−0.00839114	−	0.999965i	$-0.502671\pi$
$577$	−0.403124			−0.0167823			−0.00839114	+	0.999965i	$0.502671\pi$
$578$	4.45614	−	22.6371i	0.185351	−	0.941581i
$579$	−9.04246	−	4.40131i	−0.375792	−	0.182912i
$580$		0			0
$581$			11.1007i			0.460534i
$582$	−11.9724	+	15.8359i	−0.496273	+	0.656421i
$583$			23.3521i			0.967144i
$584$	11.9942	−	18.1839i	0.496322	−	0.752453i
$585$		0			0
$586$	−26.2094	−	5.15934i	−1.08270	−	0.213130i
$587$	3.88125			0.160196			0.0800982	−	0.996787i	$-0.474477\pi$
$587$	3.88125			0.160196			0.0800982	+	0.996787i	$0.474477\pi$
$588$	−13.1577	−	14.7299i	−0.542614	−	0.607449i
$589$	33.5078			1.38067
$590$		0			0
$591$	−7.15902	+	14.7082i	−0.294483	+	0.605012i
$592$	−15.4031	−	15.1606i	−0.633065	−	0.623097i
$593$		−	43.5745i		−	1.78939i	−0.446678	−	0.894695i	$-0.647393\pi$
$593$		−	43.5745i		−	1.78939i	0.446678	−	0.894695i	$-0.352607\pi$
$594$	30.9127	−	0.540538i	1.26836	−	0.0221785i
$595$		0			0
$596$	1.25562	−	3.06569i	0.0514324	−	0.125576i
$597$	−11.8953	+	24.4388i	−0.486843	+	1.00021i
$598$	0.806248	−	4.09573i	0.0329700	−	0.167487i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	24.0156			0.979618			0.489809	−	0.871830i	$-0.337067\pi$
$601$	24.0156			0.979618			0.489809	+	0.871830i	$0.337067\pi$
$602$	−0.517700	+	2.62991i	−0.0210999	+	0.107187i
$603$	−4.83513	+	3.79015i	−0.196902	+	0.154347i
$604$	3.50781	−	8.56455i	0.142731	−	0.348487i
$605$		0			0
$606$	14.0815	+	10.6460i	0.572021	+	0.432464i
$607$			27.4478i			1.11407i	0.830489	+	0.557036i	$0.188061\pi$
$607$			27.4478i			1.11407i	−0.830489	+	0.557036i	$0.811939\pi$
$608$	16.2015	+	23.7342i	0.657057	+	0.962549i
$609$	30.8062	+	14.9946i	1.24833	+	0.607611i
$610$		0			0
$611$	16.8293			0.680840
$612$	4.78108	−	1.35466i	0.193264	−	0.0547588i
$613$	20.8062			0.840356			0.420178	−	0.907442i	$-0.361968\pi$
$613$	20.8062			0.840356			0.420178	+	0.907442i	$0.361968\pi$
$614$	−28.3057	−	5.57201i	−1.14233	−	0.224868i
$615$		0			0
$616$	−35.4031	−	23.3521i	−1.42643	−	0.940881i
$617$			18.3074i			0.737030i	0.929622	+	0.368515i	$0.120134\pi$
$617$			18.3074i			0.737030i	−0.929622	+	0.368515i	$0.879866\pi$
$618$	−8.00274	−	6.05030i	−0.321918	−	0.243379i
$619$		−	26.9160i		−	1.08184i	−0.841073	−	0.540922i	$-0.818075\pi$
$619$		−	26.9160i		−	1.08184i	0.841073	−	0.540922i	$-0.181925\pi$
$620$		0			0
$621$	1.19375	+	5.55034i	0.0479036	+	0.222727i
$622$	4.59688	−	23.3521i	0.184318	−	0.936332i
$623$	16.8293			0.674251
$624$	6.24806	+	17.6433i	0.250123	+	0.706298i
$625$		0			0
$626$	−6.20087	+	31.5003i	−0.247837	+	1.25901i
$627$	−16.2015	+	33.2858i	−0.647025	+	1.32931i
$628$	−15.0000	−	6.14360i	−0.598565	−	0.245156i
$629$		−	4.47495i		−	0.178428i
$630$		0			0
$631$		−	2.65903i		−	0.105854i	−0.998598	−	0.0529271i	$-0.983145\pi$
$631$		−	2.65903i		−	0.105854i	0.998598	−	0.0529271i	$-0.0168551\pi$
$632$	16.8293	+	11.1007i	0.669433	+	0.441561i
$633$	10.7461	−	22.0778i	0.427119	−	0.877512i
$634$	−41.6125	−	8.19146i	−1.65264	−	0.325324i
$635$		0			0
$636$	14.3392	−	12.8087i	0.568585	−	0.507898i
$637$	15.4031			0.610294
$638$	32.4030	+	6.37855i	1.28285	+	0.252529i
$639$	21.0366	+	26.8366i	0.832196	+	1.06164i
$640$		0			0
$641$		−	41.0898i		−	1.62295i	−0.584386	−	0.811476i	$-0.698665\pi$
$641$		−	41.0898i		−	1.62295i	0.584386	−	0.811476i	$-0.301335\pi$
$642$	−27.8477	+	36.8343i	−1.09906	+	1.45373i
$643$		−	22.2885i		−	0.878971i	−0.898250	−	0.439485i	$-0.855161\pi$
$643$		−	22.2885i		−	0.878971i	0.898250	−	0.439485i	$-0.144839\pi$
$644$	2.95170	−	7.20677i	0.116313	−	0.283986i
$645$		0			0
$646$	−1.14922	+	5.83802i	−0.0452154	+	0.229694i
$647$	−2.18518			−0.0859082			−0.0429541	−	0.999077i	$-0.513677\pi$
$647$	−2.18518			−0.0859082			−0.0429541	+	0.999077i	$0.513677\pi$
$648$	−17.2876	−	18.6852i	−0.679123	−	0.734025i
$649$		0			0
$650$		0			0
$651$	36.6103	+	17.8196i	1.43487	+	0.698406i
$652$	3.85078	−	9.40194i	0.150808	−	0.368208i
$653$			7.78781i			0.304761i	0.988322	+	0.152380i	$0.0486939\pi$
$653$			7.78781i			0.304761i	−0.988322	+	0.152380i	$0.951306\pi$
$654$	−12.8541	+	17.0022i	−0.502636	+	0.664838i
$655$		0			0
$656$	28.8234	−	29.2845i	1.12537	−	1.14337i
$657$	−14.2539	−	18.1839i	−0.556098	−	0.709420i
$658$	30.8062	+	6.06424i	1.20095	+	0.236409i
$659$	−21.0366			−0.819470			−0.409735	−	0.912205i	$-0.634379\pi$
$659$	−21.0366			−0.819470			−0.409735	+	0.912205i	$0.634379\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$	−41.6656	−	8.20192i	−1.61938	−	0.318777i
$663$	−1.69607	+	3.48457i	−0.0658700	+	0.135329i
$664$	4.85078	−	7.35408i	0.188247	−	0.285393i
$665$		0			0
$666$	−20.4330	+	10.3913i	−0.791764	+	0.402654i
$667$			6.06424i			0.234808i
$668$	−6.06643	−	2.48465i	−0.234717	−	0.0961339i
$669$	−11.8953	+	24.4388i	−0.459899	+	0.944860i
$670$		0			0
$671$	−2.95170			−0.113949
$672$	5.07959	+	34.5478i	0.195950	+	1.33271i
$673$	0.806248			0.0310786			0.0155393	−	0.999879i	$-0.495053\pi$
$673$	0.806248			0.0310786			0.0155393	+	0.999879i	$0.495053\pi$
$674$	−0.110112	+	0.559369i	−0.00424137	+	0.0215461i
$675$		0			0
$676$	10.5523	+	4.32196i	0.405859	+	0.166229i
$677$			3.89391i			0.149655i	0.997196	+	0.0748275i	$0.0238406\pi$
$677$			3.89391i			0.149655i	−0.997196	+	0.0748275i	$0.976159\pi$
$678$	30.9165	+	23.3738i	1.18734	+	0.897664i
$679$		−	28.8845i		−	1.10849i
$680$		0			0
$681$	18.2094	+	8.86320i	0.697785	+	0.339639i
$682$	38.5078	+	7.58030i	1.47454	+	0.290265i
$683$	19.9440			0.763137			0.381568	−	0.924341i	$-0.375384\pi$
$683$	19.9440			0.763137			0.381568	+	0.924341i	$0.375384\pi$
$684$	29.3255	−	8.30900i	1.12129	−	0.317703i
$685$		0			0
$686$	−6.42110	−	1.26400i	−0.245159	−	0.0482597i
$687$	−13.5515	−	6.59605i	−0.517023	−	0.251655i
$688$	1.49219	−	1.51606i	0.0568892	−	0.0577992i
$689$			14.9946i			0.571248i
$690$		0			0
$691$		−	18.8039i		−	0.715333i	−0.933849	−	0.357667i	$-0.883572\pi$
$691$		−	18.8039i		−	0.715333i	0.933849	−	0.357667i	$-0.116428\pi$
$692$	11.3663	−	27.7517i	0.432084	−	1.05496i
$693$	−35.4031	+	27.7517i	−1.34485	+	1.05420i
$694$	3.65703	−	18.5777i	0.138819	−	0.705198i
$695$		0			0
$696$	−13.8565	−	23.3955i	−0.525228	−	0.886803i
$697$	8.50781			0.322256
$698$	−3.33496	+	16.9415i	−0.126230	+	0.641247i
$699$	11.3663	−	23.3521i	0.429915	−	0.883256i
$700$		0			0
$701$		−	27.7517i		−	1.04817i	−0.851667	−	0.524083i	$-0.824408\pi$
$701$		−	27.7517i		−	1.04817i	0.851667	−	0.524083i	$-0.175592\pi$
$702$	19.8493	−	0.347085i	0.749164	−	0.0130999i
$703$		−	27.4478i		−	1.03521i
$704$	13.2498	+	30.9410i	0.499370	+	1.16613i
$705$		0			0
$706$	40.8062	+	8.03275i	1.53576	+	0.302317i
$707$	−25.6844			−0.965961
$708$		0			0
$709$	−11.2984			−0.424322			−0.212161	−	0.977235i	$-0.568050\pi$
$709$	−11.2984			−0.424322			−0.212161	+	0.977235i	$0.568050\pi$
$710$		0			0
$711$	16.8293	−	13.1921i	0.631148	−	0.494742i
$712$	−11.1492	−	7.35408i	−0.417835	−	0.275606i
$713$			7.20677i			0.269896i
$714$	−4.36031	+	5.76739i	−0.163181	+	0.215839i
$715$		0			0
$716$	28.8234	+	11.8053i	1.07718	+	0.441185i
$717$	−8.50781	−	4.14108i	−0.317730	−	0.154651i
$718$	10.0000	−	50.7999i	0.373197	−	1.89583i
$719$	−25.6844			−0.957866			−0.478933	−	0.877851i	$-0.658976\pi$
$719$	−25.6844			−0.957866			−0.478933	+	0.877851i	$0.658976\pi$
$720$		0			0
$721$	14.5969			0.543616
$722$	−1.85911	+	9.44424i	−0.0691889	+	0.351478i
$723$	−10.9016	−	5.30621i	−0.405434	−	0.197340i
$724$	39.8062	+	16.3036i	1.47939	+	0.605917i
$725$		0			0
$726$	−9.89969	+	13.0943i	−0.367412	+	0.485977i
$727$		−	45.1087i		−	1.67299i	−0.547975	−	0.836495i	$-0.684601\pi$
$727$		−	45.1087i		−	1.67299i	0.547975	−	0.836495i	$-0.315399\pi$
$728$	−22.7327	−	14.9946i	−0.842529	−	0.555736i
$729$	−24.6125	+	11.1007i	−0.911574	+	0.411136i
$730$		0			0
$731$	0.440449			0.0162906
$732$	1.61902	+	1.81247i	0.0598407	+	0.0669908i
$733$	20.8062			0.768496			0.384248	−	0.923230i	$-0.374461\pi$
$733$	20.8062			0.768496			0.384248	+	0.923230i	$0.374461\pi$
$734$	−4.94525	−	0.973477i	−0.182532	−	0.0359317i
$735$		0			0
$736$	−5.10469	+	3.48457i	−0.188161	+	0.128443i
$737$		−	8.61603i		−	0.317376i
$738$	−19.7560	−	38.8474i	−0.727227	−	1.42999i
$739$			52.9271i			1.94695i	0.228785	+	0.973477i	$0.426525\pi$
$739$			52.9271i			1.94695i	−0.228785	+	0.973477i	$0.573475\pi$
$740$		0			0
$741$	−10.4031	+	21.3731i	−0.382168	+	0.785162i
$742$	−5.40312	+	27.4478i	−0.198355	+	1.00764i
$743$	−29.6143			−1.08644			−0.543222	−	0.839589i	$-0.682796\pi$
$743$	−29.6143			−1.08644			−0.543222	+	0.839589i	$0.682796\pi$
$744$	−16.4671	−	27.8033i	−0.603712	−	1.01932i
$745$		0			0
$746$	4.72502	−	24.0030i	0.172995	−	0.878814i
$747$	−5.76469	−	7.35408i	−0.210919	−	0.269072i
$748$	−2.64141	+	6.44918i	−0.0965795	+	0.235805i
$749$		−	67.1851i		−	2.45489i
$750$		0			0
$751$			28.3527i			1.03460i	0.855803	+	0.517302i	$0.173064\pi$
$751$			28.3527i			1.03460i	−0.855803	+	0.517302i	$0.826936\pi$
$752$	−17.7588	−	17.4792i	−0.647598	−	0.637402i
$753$	−1.95547	−	0.951801i	−0.0712612	−	0.0346856i
$754$	20.8062	+	4.09573i	0.757719	+	0.149158i
$755$		0			0
$756$	36.4595	+	6.51713i	1.32602	+	0.237026i
$757$	−8.91093			−0.323873			−0.161937	−	0.986801i	$-0.551774\pi$
$757$	−8.91093			−0.323873			−0.161937	+	0.986801i	$0.551774\pi$
$758$	−29.5614	−	5.81918i	−1.07372	−	0.211362i
$759$	−7.15902	−	3.48457i	−0.259856	−	0.126482i
$760$		0			0
$761$			3.06569i			0.111131i	0.998455	+	0.0555656i	$0.0176962\pi$
$761$			3.06569i			0.111131i	−0.998455	+	0.0555656i	$0.982304\pi$
$762$	−31.7009	−	23.9667i	−1.14840	−	0.868224i
$763$		−	31.0117i		−	1.12270i
$764$	−21.0366	−	8.61603i	−0.761078	−	0.311717i
$765$		0			0
$766$	3.40312	−	17.2878i	0.122960	−	0.624634i
$767$		0			0
$768$	11.7315	−	25.1072i	0.423325	−	0.905978i
$769$	−39.8062			−1.43545			−0.717725	−	0.696327i	$-0.754817\pi$
$769$	−39.8062			−1.43545			−0.717725	+	0.696327i	$0.754817\pi$
$770$		0			0
$771$	8.41464	−	17.2878i	0.303046	−	0.622606i
$772$	−10.7461	−	4.40131i	−0.386760	−	0.158407i
$773$		−	5.55034i		−	0.199632i	−0.995006	−	0.0998159i	$-0.968175\pi$
$773$		−	5.55034i		−	0.199632i	0.995006	−	0.0998159i	$-0.0318254\pi$
$774$	−1.02277	−	2.01113i	−0.0367626	−	0.0722886i
$775$		0			0
$776$	−12.6220	+	19.1357i	−0.453102	+	0.686930i
$777$	14.5969	−	29.9892i	0.523660	−	1.07586i
$778$	−27.7016	−	5.45308i	−0.993149	−	0.195502i
$779$	52.1839			1.86968
$780$		0			0
$781$	−47.8219			−1.71120
$782$	−1.25562	−	0.247171i	−0.0449010	−	0.00883881i
$783$	−28.1956	+	6.06424i	−1.00763	+	0.216718i
$784$	−16.2539	−	15.9980i	−0.580497	−	0.571357i
$785$		0			0
$786$	29.2209	−	38.6505i	1.04227	−	1.37862i
$787$		−	14.7875i		−	0.527118i	−0.964643	−	0.263559i	$-0.915104\pi$
$787$		−	14.7875i		−	0.527118i	0.964643	−	0.263559i	$-0.0848963\pi$
$788$	−7.15902	+	17.4792i	−0.255030	+	0.622672i
$789$	−27.9109	−	13.5853i	−0.993656	−	0.483650i
$790$		0			0
$791$	−56.3913			−2.00504
$792$	35.5811	−	2.91471i	1.26432	−	0.103570i
$793$	−1.89531			−0.0673046
$794$	−7.89694	+	40.1164i	−0.280252	+	1.42368i
$795$		0			0
$796$	−11.8953	+	29.0432i	−0.421618	+	1.02941i
$797$			4.96929i			0.176021i	0.996120	+	0.0880107i	$0.0280510\pi$
$797$			4.96929i			0.176021i	−0.996120	+	0.0880107i	$0.971949\pi$
$798$	−26.7446	+	35.3752i	−0.946749	+	1.25227i
$799$		−	5.15934i		−	0.182524i
$800$		0			0
$801$	−11.1492	+	8.73961i	−0.393938	+	0.308799i
$802$	42.7617	+	8.41769i	1.50997	+	0.297239i
$803$	32.4030			1.14348
$804$	−5.29061	+	4.72593i	−0.186586	+	0.166671i
$805$		0			0
$806$	24.7262	+	4.86738i	0.870944	+	0.171446i
$807$	11.3663	−	23.3521i	0.400114	−	0.822031i
$808$	17.0156	+	11.2236i	0.598607	+	0.394844i
$809$			0.581045i			0.0204284i	0.999948	+	0.0102142i	$0.00325134\pi$
$809$			0.581045i			0.0204284i	−0.999948	+	0.0102142i	$0.996749\pi$
$810$		0			0
$811$			15.8511i			0.556608i	0.960493	+	0.278304i	$0.0897723\pi$
$811$			15.8511i			0.556608i	−0.960493	+	0.278304i	$0.910228\pi$
$812$	36.6103	+	14.9946i	1.28477	+	0.526207i
$813$	−18.5078	+	38.0241i	−0.649097	+	1.33357i
$814$	6.20937	−	31.5435i	0.217638	−	1.10560i
$815$		0			0
$816$	5.40890	−	1.91546i	0.189349	−	0.0670546i
$817$	2.70156			0.0945157
$818$	−7.43217	+	37.7553i	−0.259860	+	1.32008i
$819$	−22.7327	+	17.8196i	−0.794344	+	0.622668i
$820$		0			0
$821$		−	20.5449i		−	0.717023i	−0.933525	−	0.358511i	$-0.883284\pi$
$821$		−	20.5449i		−	0.717023i	0.933525	−	0.358511i	$-0.116716\pi$
$822$	12.4632	+	9.42253i	0.434704	+	0.328649i
$823$			37.0760i			1.29239i	0.763174	+	0.646193i	$0.223640\pi$
$823$			37.0760i			1.29239i	−0.763174	+	0.646193i	$0.776360\pi$
$824$	−9.67027	−	6.37855i	−0.336880	−	0.222207i
$825$		0			0
$826$		0			0
$827$	14.8071			0.514895			0.257447	−	0.966292i	$-0.417119\pi$
$827$	14.8071			0.514895			0.257447	+	0.966292i	$0.417119\pi$
$828$	1.78708	+	6.30725i	0.0621052	+	0.219192i
$829$	44.8062			1.55619			0.778093	−	0.628150i	$-0.216187\pi$
$829$	44.8062			1.55619			0.778093	+	0.628150i	$0.216187\pi$
$830$		0			0
$831$	−43.7693	−	21.3042i	−1.51834	−	0.739034i
$832$	8.50781	+	19.8675i	0.294955	+	0.688781i
$833$		−	4.72212i		−	0.163612i
$834$	2.96227	+	2.23956i	0.102575	+	0.0775495i
$835$		0			0
$836$	−16.2015	+	39.5570i	−0.560340	+	1.36811i
$837$	−33.5078	+	7.20677i	−1.15820	+	0.249102i
$838$	−2.76172	+	14.0295i	−0.0954019	+	0.484640i
$839$	25.6844			0.886723			0.443362	−	0.896343i	$-0.353786\pi$
$839$	25.6844			0.886723			0.443362	+	0.896343i	$0.353786\pi$
$840$		0			0
$841$	−1.80625			−0.0622844
$842$	6.61273	−	33.5925i	0.227890	−	1.15768i
$843$	5.46295	−	11.2236i	0.188154	−	0.386561i
$844$	10.7461	−	26.2373i	0.369896	−	0.903125i
$845$		0			0
$846$	−23.5580	+	11.9805i	−0.809941	+	0.411898i
$847$		−	23.8839i		−	0.820659i
$848$	15.5737	−	15.8228i	0.534802	−	0.543357i
$849$	−4.65703	+	9.56783i	−0.159829	+	0.328367i
$850$		0			0
$851$	5.90340			0.202366
$852$	26.2305	+	29.3647i	0.898642	+	1.00602i
$853$	37.2984			1.27707			0.638537	−	0.769591i	$-0.279540\pi$
$853$	37.2984			1.27707			0.638537	+	0.769591i	$0.279540\pi$
$854$	−3.46940	−	0.682954i	−0.118720	−	0.0233702i
$855$		0			0
$856$	−29.3586	+	44.5094i	−1.00346	+	1.52130i
$857$		−	12.5099i		−	0.427331i	−0.976907	−	0.213666i	$-0.931460\pi$
$857$		−	12.5099i		−	0.427331i	0.976907	−	0.213666i	$-0.0685403\pi$
$858$	−16.7906	+	22.2090i	−0.573222	+	0.758202i
$859$			32.1547i			1.09710i	0.836117	+	0.548552i	$0.184821\pi$
$859$			32.1547i			1.09710i	−0.836117	+	0.548552i	$0.815179\pi$
$860$		0			0
$861$	57.0156	+	27.7517i	1.94309	+	0.945775i
$862$	−5.40312	+	27.4478i	−0.184031	+	0.934875i
$863$	−29.6143			−1.00808			−0.504041	−	0.863680i	$-0.668154\pi$
$863$	−29.6143			−1.00808			−0.504041	+	0.863680i	$0.668154\pi$
$864$	−21.3062	−	20.2496i	−0.724850	−	0.688906i
$865$		0			0
$866$	−8.52476	+	43.3056i	−0.289683	+	1.47159i
$867$	−25.4070	−	12.3665i	−0.862866	−	0.419990i
$868$	43.5078	+	17.8196i	1.47675	+	0.604838i
$869$			29.9892i			1.01731i
$870$		0			0
$871$		−	5.53243i		−	0.187459i
$872$	−13.5515	+	20.5449i	−0.458912	+	0.695739i
$873$	15.0000	+	19.1357i	0.507673	+	0.647644i
$874$	−7.70156	−	1.51606i	−0.260509	−	0.0512815i
$875$		0			0
$876$	−17.7732	−	19.8968i	−0.600500	−	0.672251i
$877$	−48.9109			−1.65160			−0.825802	−	0.563959i	$-0.809277\pi$
$877$	−48.9109			−1.65160			−0.825802	+	0.563959i	$0.809277\pi$
$878$	30.4094	+	5.98612i	1.02627	+	0.202022i
$879$	−14.3180	+	29.4163i	−0.482936	+	0.992187i
$880$		0			0
$881$		−	26.6763i		−	0.898747i	−0.893344	−	0.449374i	$-0.851647\pi$
$881$		−	26.6763i		−	0.898747i	0.893344	−	0.449374i	$-0.148353\pi$
$882$	−21.5616	+	10.9652i	−0.726018	+	0.369218i
$883$		−	25.2412i		−	0.849435i	−0.905326	−	0.424717i	$-0.860374\pi$
$883$		−	25.2412i		−	0.849435i	0.905326	−	0.424717i	$-0.139626\pi$
$884$	−1.69607	+	4.14108i	−0.0570451	+	0.139280i
$885$		0			0
$886$	−3.06015	+	15.5455i	−0.102808	+	0.522262i
$887$	24.9179			0.836660			0.418330	−	0.908295i	$-0.362616\pi$
$887$	24.9179			0.836660			0.418330	+	0.908295i	$0.362616\pi$
$888$	−22.7750	+	13.4889i	−0.764277	+	0.452659i
$889$	57.8219			1.93928
$890$		0			0
$891$	9.04246	−	36.7704i	0.302934	−	1.23185i
$892$	−11.8953	+	29.0432i	−0.398285	+	0.972438i
$893$		−	31.6456i		−	1.05898i
$894$	−3.23654	−	2.44691i	−0.108246	−	0.0818371i
$895$		0			0
$896$	8.41464	+	39.4334i	0.281114	+	1.31738i
$897$	−4.59688	−	2.23748i	−0.153485	−	0.0747071i
$898$	26.5523	+	5.22685i	0.886063	+	0.174422i
$899$	−36.6103			−1.22102
$900$		0			0
$901$	4.59688			0.153144
$902$	59.9708	+	11.8053i	1.99681	+	0.393074i
$903$	2.95170	+	1.43670i	0.0982264	+	0.0478105i
$904$	37.3586	+	24.6419i	1.24253	+	0.819577i
$905$		0			0
$906$	−9.04185	−	6.83589i	−0.300395	−	0.227107i
$907$		−	10.1600i		−	0.337356i	−0.985671	−	0.168678i	$-0.946050\pi$
$907$		−	10.1600i		−	0.337356i	0.985671	−	0.168678i	$-0.0539498\pi$
$908$	21.6401	+	8.86320i	0.718152	+	0.294136i
$909$	17.0156	−	13.3382i	0.564373	−	0.442399i
$910$		0			0
$911$	−56.3913			−1.86833			−0.934163	−	0.356847i	$-0.883852\pi$
$911$	−56.3913			−1.86833			−0.934163	+	0.356847i	$0.883852\pi$
$912$	33.1763	−	11.7488i	1.09858	−	0.389041i
$913$	13.1047			0.433702
$914$	−4.61491	+	23.4437i	−0.152648	+	0.775448i
$915$		0			0
$916$	−16.1047	−	6.59605i	−0.532114	−	0.217939i
$917$			70.4980i			2.32805i
$918$	−0.106405	−	6.08519i	−0.00351190	−	0.200841i
$919$		−	0.531805i		−	0.0175426i	−0.999962	−	0.00877132i	$-0.997208\pi$
$919$		−	0.531805i		−	0.0175426i	0.999962	−	0.00877132i	$-0.00279203\pi$
$920$		0			0
$921$	−15.4633	+	31.7692i	−0.509532	+	1.04683i
$922$	−10.0000	−	1.96851i	−0.329332	−	0.0648294i
$923$	−30.7069			−1.01073
$924$	−38.7382	+	34.6035i	−1.27439	+	1.13837i
$925$		0			0
$926$	−9.89049	−	1.94695i	−0.325022	−	0.0639809i
$927$	−9.67027	+	7.58030i	−0.317613	+	0.248970i
$928$	−17.7016	−	25.9317i	−0.581082	−	0.851251i
$929$			0.581045i			0.0190635i	0.999955	+	0.00953173i	$0.00303409\pi$
$929$			0.581045i			0.0190635i	−0.999955	+	0.00953173i	$0.996966\pi$
$930$		0			0
$931$		−	28.9639i		−	0.949252i
$932$	11.3663	−	27.7517i	0.372317	−	0.909037i
$933$	−26.2094	−	12.7571i	−0.858056	−	0.417649i
$934$	−0.209373	+	1.06361i	−0.00685088	+	0.0348024i
$935$		0			0
$936$	22.8470	−	1.87156i	0.746777	−	0.0611739i
$937$	16.6125			0.542707			0.271353	−	0.962480i	$-0.412529\pi$
$937$	16.6125			0.542707			0.271353	+	0.962480i	$0.412529\pi$
$938$	1.99355	−	10.1272i	0.0650917	−	0.330665i
$939$	35.3547	+	17.2085i	1.15376	+	0.561577i
$940$		0			0
$941$			47.2212i			1.53937i	0.638425	+	0.769684i	$0.279586\pi$
$941$			47.2212i			1.53937i	−0.638425	+	0.769684i	$0.720414\pi$
$942$	−11.9724	+	15.8359i	−0.390082	+	0.515963i
$943$			11.2236i			0.365490i
$944$		0			0
$945$		0			0
$946$	3.10469	+	0.611161i	0.100942	+	0.0198705i
$947$	−38.7955			−1.26068			−0.630341	−	0.776318i	$-0.717085\pi$
$947$	−38.7955			−1.26068			−0.630341	+	0.776318i	$0.717085\pi$
$948$	18.4146	−	16.4492i	0.598080	−	0.534245i
$949$	20.8062			0.675399
$950$		0			0
$951$	−22.7327	+	46.7041i	−0.737158	+	1.51448i
$952$	−4.59688	+	6.96914i	−0.148986	+	0.225871i
$953$		−	21.9542i		−	0.711166i	−0.934645	−	0.355583i	$-0.884282\pi$
$953$		−	21.9542i		−	0.711166i	0.934645	−	0.355583i	$-0.115718\pi$
$954$	−10.6744	−	20.9898i	−0.345596	−	0.679568i
$955$		0			0
$956$	−10.1107	−	4.14108i	−0.327004	−	0.133932i
$957$	17.7016	−	36.3677i	0.572210	−	1.17560i
$958$	−11.4922	+	58.3802i	−0.371296	+	1.88618i
$959$	−22.7327			−0.734077
$960$		0			0
$961$	−12.5078			−0.403478
$962$	3.98710	−	20.2544i	0.128549	−	0.653028i
$963$	34.8899	+	44.5094i	1.12431	+	1.43429i
$964$	−12.9555	−	5.30621i	−0.417268	−	0.170902i
$965$		0			0
$966$	−7.60840	−	5.75216i	−0.244796	−	0.185073i
$967$		−	47.7677i		−	1.53611i	−0.640386	−	0.768053i	$-0.721226\pi$
$967$		−	47.7677i		−	1.53611i	0.640386	−	0.768053i	$-0.278774\pi$
$968$	−10.4368	+	15.8228i	−0.335451	+	0.508564i
$969$	6.55234	+	3.18928i	0.210492	+	0.102454i
$970$		0			0
$971$	21.4771			0.689232			0.344616	−	0.938744i	$-0.388009\pi$
$971$	21.4771			0.689232			0.344616	+	0.938744i	$0.388009\pi$
$972$	−27.5384	+	14.6163i	−0.883296	+	0.468817i
$973$	−5.40312			−0.173216
$974$	47.2387	+	9.29898i	1.51363	+	0.297959i
$975$		0			0
$976$	2.00000	+	1.96851i	0.0640184	+	0.0630105i
$977$			28.5799i			0.914352i	0.889376	+	0.457176i	$0.151139\pi$
$977$			28.5799i			0.914352i	−0.889376	+	0.457176i	$0.848861\pi$
$978$	−9.92590	−	7.50426i	−0.317395	−	0.239960i
$979$		−	19.8675i		−	0.634968i
$980$		0			0
$981$	16.1047	+	20.5449i	0.514183	+	0.655949i
$982$	4.59688	−	23.3521i	0.146692	−	0.745194i
$983$	−57.9243			−1.84750			−0.923749	−	0.382998i	$-0.874892\pi$
$983$	−57.9243			−1.84750			−0.923749	+	0.382998i	$0.874892\pi$
$984$	−25.6453	−	43.2999i	−0.817541	−	1.38035i
$985$		0			0
$986$	1.25562	−	6.37855i	0.0399872	−	0.203135i
$987$	16.8293	−	34.5756i	0.535682	−	1.10055i
$988$	−10.4031	+	25.3999i	−0.330967	+	0.808079i
$989$			0.581045i			0.0184761i
$990$		0			0
$991$		−	40.2668i		−	1.27912i	−0.768743	−	0.639558i	$-0.779117\pi$
$991$		−	40.2668i		−	1.27912i	0.768743	−	0.639558i	$-0.220883\pi$
$992$	−21.0366	−	30.8174i	−0.667913	−	0.978453i
$993$	−22.7617	+	46.7638i	−0.722321	+	1.48400i
$994$	−56.2094	−	11.0649i	−1.78285	−	0.350956i
$995$		0			0
$996$	−7.18798	−	8.04684i	−0.227760	−	0.254974i
$997$	34.5969			1.09569			0.547847	−	0.836579i	$-0.315448\pi$
$997$	34.5969			1.09569			0.547847	+	0.836579i	$0.315448\pi$
$998$	−31.8853	−	6.27664i	−1.00931	−	0.198684i
$999$	5.90340	+	27.4478i	0.186775	+	0.868410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.e.d.251.5	yes	8
3.2	odd	2	inner	300.2.e.d.251.4	yes	8
4.3	odd	2	inner	300.2.e.d.251.3	✓	8
5.2	odd	4		300.2.h.c.299.15		16
5.3	odd	4		300.2.h.c.299.2		16
5.4	even	2		300.2.e.e.251.4	yes	8
12.11	even	2	inner	300.2.e.d.251.6	yes	8
15.2	even	4		300.2.h.c.299.1		16
15.8	even	4		300.2.h.c.299.16		16
15.14	odd	2		300.2.e.e.251.5	yes	8
20.3	even	4		300.2.h.c.299.3		16
20.7	even	4		300.2.h.c.299.14		16
20.19	odd	2		300.2.e.e.251.6	yes	8
60.23	odd	4		300.2.h.c.299.13		16
60.47	odd	4		300.2.h.c.299.4		16
60.59	even	2		300.2.e.e.251.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.e.d.251.3	✓	8	4.3	odd	2	inner
300.2.e.d.251.4	yes	8	3.2	odd	2	inner
300.2.e.d.251.5	yes	8	1.1	even	1	trivial
300.2.e.d.251.6	yes	8	12.11	even	2	inner
300.2.e.e.251.3	yes	8	60.59	even	2
300.2.e.e.251.4	yes	8	5.4	even	2
300.2.e.e.251.5	yes	8	15.14	odd	2
300.2.e.e.251.6	yes	8	20.19	odd	2
300.2.h.c.299.1		16	15.2	even	4
300.2.h.c.299.2		16	5.3	odd	4
300.2.h.c.299.3		16	20.3	even	4
300.2.h.c.299.4		16	60.47	odd	4
300.2.h.c.299.13		16	60.23	odd	4
300.2.h.c.299.14		16	20.7	even	4
300.2.h.c.299.15		16	5.2	odd	4
300.2.h.c.299.16		16	15.8	even	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273147 - 1.38758i) q^{2} +(-1.55737 - 0.758030i) q^{3} +(-1.85078 - 0.758030i) q^{4} +(-1.47722 + 1.95392i) q^{6} -3.56393i q^{7} +(-1.55737 + 2.36106i) q^{8} +(1.85078 + 2.36106i) q^{9} +O(q^{10})\)	\(q+(0.273147 - 1.38758i) q^{2} +(-1.55737 - 0.758030i) q^{3} +(-1.85078 - 0.758030i) q^{4} +(-1.47722 + 1.95392i) q^{6} -3.56393i q^{7} +(-1.55737 + 2.36106i) q^{8} +(1.85078 + 2.36106i) q^{9} -4.20732 q^{11} +(2.30774 + 2.58348i) q^{12} -2.70156 q^{13} +(-4.94525 - 0.973477i) q^{14} +(2.85078 + 2.80590i) q^{16} +0.828216i q^{17} +(3.78171 - 1.92320i) q^{18} +5.07999i q^{19} +(-2.70156 + 5.55034i) q^{21} +(-1.14922 + 5.83802i) q^{22} -1.09259 q^{23} +(4.21515 - 2.49651i) q^{24} +(-0.737925 + 3.74865i) q^{26} +(-1.09259 - 5.07999i) q^{27} +(-2.70156 + 6.59605i) q^{28} -5.55034i q^{29} -6.59605i q^{31} +(4.67210 - 3.18928i) q^{32} +(6.55234 + 3.18928i) q^{33} +(1.14922 + 0.226225i) q^{34} +(-1.63564 - 5.77275i) q^{36} -5.40312 q^{37} +(7.04891 + 1.38758i) q^{38} +(4.20732 + 2.04787i) q^{39} -10.2725i q^{41} +(6.96364 + 5.26471i) q^{42} -0.531805i q^{43} +(7.78683 + 3.18928i) q^{44} +(-0.298438 + 1.51606i) q^{46} -6.22947 q^{47} +(-2.31276 - 6.53078i) q^{48} -5.70156 q^{49} +(0.627812 - 1.28984i) q^{51} +(5.00000 + 2.04787i) q^{52} -5.55034i q^{53} +(-7.34735 + 0.128476i) q^{54} +(8.41464 + 5.55034i) q^{56} +(3.85078 - 7.91140i) q^{57} +(-7.70156 - 1.51606i) q^{58} +0.701562 q^{61} +(-9.15257 - 1.80169i) q^{62} +(8.41464 - 6.59605i) q^{63} +(-3.14922 - 7.35408i) q^{64} +(6.21515 - 8.22079i) q^{66} +2.04787i q^{67} +(0.627812 - 1.53285i) q^{68} +(1.70156 + 0.828216i) q^{69} +11.3663 q^{71} +(-8.45695 + 0.692770i) q^{72} -7.70156 q^{73} +(-1.47585 + 7.49729i) q^{74} +(3.85078 - 9.40194i) q^{76} +14.9946i q^{77} +(3.99080 - 5.27865i) q^{78} -7.12785i q^{79} +(-2.14922 + 8.73961i) q^{81} +(-14.2539 - 2.80590i) q^{82} -3.11473 q^{83} +(9.20732 - 8.22459i) q^{84} +(-0.737925 - 0.145261i) q^{86} +(-4.20732 + 8.64391i) q^{87} +(6.55234 - 9.93375i) q^{88} +4.72212i q^{89} +9.62817i q^{91} +(2.02214 + 0.828216i) q^{92} +(-5.00000 + 10.2725i) q^{93} +(-1.70156 + 8.64391i) q^{94} +(-9.69374 + 1.42528i) q^{96} +8.10469 q^{97} +(-1.55737 + 7.91140i) q^{98} +(-7.78683 - 9.93375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9	\( 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9} - 11 q^{12} + 4 q^{13} + 10 q^{16} + 7 q^{18} + 4 q^{21} - 22 q^{22} + 13 q^{24} + 4 q^{28} + 14 q^{33} + 22 q^{34} - 21 q^{36} + 8 q^{37} + 36 q^{42} - 28 q^{46} - 15 q^{48} - 20 q^{49} + 40 q^{52} - 28 q^{54} + 18 q^{57} - 36 q^{58} - 20 q^{61} - 38 q^{64} + 29 q^{66} - 12 q^{69} - 51 q^{72} - 36 q^{73} + 18 q^{76} + 22 q^{78} - 30 q^{81} - 50 q^{82} + 40 q^{84} + 14 q^{88} - 40 q^{93} + 12 q^{94} - 39 q^{96} - 12 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9 - 11 * q^12 + 4 * q^13 + 10 * q^16 + 7 * q^18 + 4 * q^21 - 22 * q^22 + 13 * q^24 + 4 * q^28 + 14 * q^33 + 22 * q^34 - 21 * q^36 + 8 * q^37 + 36 * q^42 - 28 * q^46 - 15 * q^48 - 20 * q^49 + 40 * q^52 - 28 * q^54 + 18 * q^57 - 36 * q^58 - 20 * q^61 - 38 * q^64 + 29 * q^66 - 12 * q^69 - 51 * q^72 - 36 * q^73 + 18 * q^76 + 22 * q^78 - 30 * q^81 - 50 * q^82 + 40 * q^84 + 14 * q^88 - 40 * q^93 + 12 * q^94 - 39 * q^96 - 12 * q^97

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