LMFDB - Embedded newform 300.2.e.e.251.3

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			251.3
Root			$0.273147 - 1.38758i$ of defining polynomial
Character	$\chi$	$=$	300.251
Dual form			300.2.e.e.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.273147 - 1.38758i) q^{2} +(1.55737 - 0.758030i) q^{3} +(-1.85078 + 0.758030i) q^{4} +(-1.47722 - 1.95392i) q^{6} -3.56393i q^{7} +(1.55737 + 2.36106i) q^{8} +(1.85078 - 2.36106i) q^{9} +O(q^{10})$	\(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	$-0.377767\pi$
$13$	2.70156			0.749279			0.374639	+	0.927171i	$0.377767\pi$
$14$	−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	$-0.801991\pi$
$19$		−	5.07999i		−	1.16543i	0.812677	−	0.582714i	$-0.198009\pi$
$20$		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	$-0.463662\pi$
$23$	1.09259			0.227821			0.113910	+	0.993491i	$0.463662\pi$
$24$	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	$0.172333\pi$
$29$			5.55034i			1.03067i	−0.856988	+	0.515336i	$0.827667\pi$
$30$		0			0
$31$			6.59605i			1.18468i	0.805686	+	0.592342i	$0.201797\pi$
$31$			6.59605i			1.18468i	−0.805686	+	0.592342i	$0.798203\pi$
$32$	−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	$-0.353511\pi$
$37$	5.40312			0.888268			0.444134	+	0.895960i	$0.353511\pi$
$38$	−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	$0.296308\pi$
$41$			10.2725i			1.60429i	−0.597130	+	0.802144i	$0.703692\pi$
$42$	−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	$-0.349879\pi$
$47$	6.22947			0.908661			0.454331	+	0.890833i	$0.349879\pi$
$48$	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	$-0.351174\pi$
$73$	7.70156			0.901400			0.450700	+	0.892676i	$0.351174\pi$
$74$	−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	$0.131328\pi$
$79$			7.12785i			0.801946i	−0.916090	+	0.400973i	$0.868672\pi$
$80$		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	$-0.445319\pi$
$83$	3.11473			0.341886			0.170943	+	0.985281i	$0.445319\pi$
$84$	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	$-0.919480\pi$
$89$		−	4.72212i		−	0.500544i	0.968176	−	0.250272i	$-0.0805200\pi$
$90$		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	$-0.634979\pi$
$97$	−8.10469			−0.822906			−0.411453	+	0.911431i	$0.634979\pi$
$98$	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	$0.116729\pi$
$101$			7.20677i			0.717100i	−0.933510	+	0.358550i	$0.883271\pi$
$102$	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	$-0.864857\pi$
$107$	−18.8514			−1.82244			−0.911218	+	0.411924i	$0.864857\pi$
$108$	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	$0.0204799\pi$
$139$			1.51606i			0.128591i	−0.997931	+	0.0642953i	$0.979520\pi$
$140$		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	$-0.978386\pi$
$149$		−	1.65643i		−	0.135700i	0.997696	−	0.0678501i	$-0.0216139\pi$
$150$		0			0
$151$		−	4.62754i		−	0.376583i	−0.982113	−	0.188292i	$-0.939705\pi$
$151$		−	4.62754i		−	0.376583i	0.982113	−	0.188292i	$-0.0602951\pi$
$152$	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	$-0.604830\pi$
$157$	−8.10469			−0.646824			−0.323412	+	0.946258i	$0.604830\pi$
$158$	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	$-0.540477\pi$
$167$	−3.27777			−0.253641			−0.126821	+	0.991926i	$0.540477\pi$
$168$	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	$-0.567012\pi$
$193$	−5.80625			−0.417943			−0.208971	+	0.977922i	$0.567012\pi$
$194$	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	$0.187742\pi$
$199$			15.6924i			1.11241i	−0.831047	+	0.556203i	$0.812258\pi$
$200$		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	$-0.837738\pi$
$211$		−	14.1763i		−	0.975940i	0.872860	−	0.487970i	$-0.162262\pi$
$212$	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	$-0.373157\pi$
$227$	11.6924			0.776053			0.388026	+	0.921648i	$0.373157\pi$
$228$	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	$-0.686347\pi$
$263$	−17.9219			−1.10511			−0.552555	+	0.833476i	$0.686347\pi$
$264$	−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	$-0.848882\pi$
$269$		−	14.9946i		−	0.914236i	0.889406	−	0.457118i	$-0.151118\pi$
$270$		0			0
$271$			24.4157i			1.48315i	0.670872	+	0.741573i	$0.265920\pi$
$271$			24.4157i			1.48315i	−0.670872	+	0.741573i	$0.734080\pi$
$272$	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	$-0.819997\pi$
$277$	−28.1047			−1.68865			−0.844323	+	0.535834i	$0.819997\pi$
$278$	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	$-0.931038\pi$
$281$		−	7.20677i		−	0.429920i	0.976623	−	0.214960i	$-0.0689621\pi$
$282$	−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	$-0.278278\pi$
$313$	22.7016			1.28317			0.641584	+	0.767053i	$0.278278\pi$
$314$	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	$0.308954\pi$
$331$			30.0275i			1.65046i	−0.564798	+	0.825229i	$0.691046\pi$
$332$	−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	$-0.496505\pi$
$337$	0.403124			0.0219596			0.0109798	+	0.999940i	$0.496505\pi$
$338$	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	$-0.617007\pi$
$347$	−13.3885			−0.718732			−0.359366	+	0.933197i	$0.617007\pi$
$348$	−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	$-0.647806\pi$
$373$	−17.2984			−0.895679			−0.447840	+	0.894114i	$0.647806\pi$
$374$	−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	$0.184292\pi$
$379$			21.3042i			1.09432i	−0.837027	+	0.547162i	$0.815708\pi$
$380$		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	$-0.603116\pi$
$383$	−12.4589			−0.636622			−0.318311	+	0.947986i	$0.603116\pi$
$384$	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	$0.168915\pi$
$389$			19.9639i			1.01221i	−0.862472	+	0.506104i	$0.831085\pi$
$390$		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	$-0.241609\pi$
$397$	28.9109			1.45100			0.725499	+	0.688223i	$0.241609\pi$
$398$	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	$-0.720519\pi$
$401$		−	30.8174i		−	1.53895i	0.638679	−	0.769473i	$-0.279481\pi$
$402$	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	$-0.230095\pi$
$433$	31.2094			1.49983			0.749913	+	0.661536i	$0.230095\pi$
$434$	−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	$-0.824820\pi$
$439$		−	21.9154i		−	1.04596i	0.852344	−	0.522981i	$-0.175180\pi$
$440$		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	$-0.414251\pi$
$443$	11.2033			0.532285			0.266143	+	0.963934i	$0.414251\pi$
$444$	−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	$-0.850877\pi$
$449$		−	19.1357i		−	0.903068i	0.892254	−	0.451534i	$-0.149123\pi$
$450$		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	$-0.370688\pi$
$457$	16.8953			0.790329			0.395165	+	0.918610i	$0.370688\pi$
$458$	−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	$0.0536748\pi$
$461$			7.20677i			0.335653i	−0.985817	+	0.167826i	$0.946325\pi$
$462$	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	$-0.494354\pi$
$467$	0.766519			0.0354703			0.0177351	+	0.999843i	$0.494354\pi$
$468$	−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	$0.171963\pi$
$499$			22.9790i			1.02868i	−0.857586	+	0.514340i	$0.828037\pi$
$500$		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	$-0.244713\pi$
$503$	32.2399			1.43751			0.718753	+	0.695265i	$0.244713\pi$
$504$	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	$-0.603753\pi$
$509$		−	42.7463i		−	1.89470i	0.320207	−	0.947348i	$-0.396247\pi$
$510$		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	$-0.927754\pi$
$521$		−	10.2725i		−	0.450045i	0.974354	−	0.225022i	$-0.0722455\pi$
$522$	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	$-0.718312\pi$
$563$	−30.0547			−1.26666			−0.633328	+	0.773883i	$0.718312\pi$
$564$	−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	$0.366528\pi$
$569$			43.5745i			1.82674i	−0.407133	+	0.913369i	$0.633472\pi$
$570$		0			0
$571$			32.9802i			1.38018i	0.723724	+	0.690090i	$0.242429\pi$
$571$			32.9802i			1.38018i	−0.723724	+	0.690090i	$0.757571\pi$
$572$	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	$-0.497329\pi$
$577$	0.403124			0.0167823			0.00839114	+	0.999965i	$0.497329\pi$
$578$	−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	$-0.525523\pi$
$587$	−3.88125			−0.160196			−0.0800982	+	0.996787i	$0.525523\pi$
$588$	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	$-0.638032\pi$
$613$	−20.8062			−0.840356			−0.420178	+	0.907442i	$0.638032\pi$
$614$	−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	$0.181925\pi$
$619$			26.9160i			1.08184i	−0.841073	+	0.540922i	$0.818075\pi$
$620$		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	$0.0168551\pi$
$631$			2.65903i			0.105854i	−0.998598	+	0.0529271i	$0.983145\pi$
$632$	−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	$0.301335\pi$
$641$			41.0898i			1.62295i	−0.584386	+	0.811476i	$0.698665\pi$
$642$	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	$-0.486323\pi$
$647$	2.18518			0.0859082			0.0429541	+	0.999077i	$0.486323\pi$
$648$	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	$-0.504947\pi$
$673$	−0.806248			−0.0310786			−0.0155393	+	0.999879i	$0.504947\pi$
$674$	−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	$-0.624616\pi$
$683$	−19.9440			−0.763137			−0.381568	+	0.924341i	$0.624616\pi$
$684$	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	$0.116428\pi$
$691$			18.8039i			0.715333i	−0.933849	+	0.357667i	$0.883572\pi$
$692$	−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	$0.175592\pi$
$701$			27.7517i			1.04817i	−0.851667	+	0.524083i	$0.824408\pi$
$702$	−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	$-0.625539\pi$
$733$	−20.8062			−0.768496			−0.384248	+	0.923230i	$0.625539\pi$
$734$	−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	$-0.573475\pi$
$739$		−	52.9271i		−	1.94695i	0.228785	−	0.973477i	$-0.426525\pi$
$740$		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	$-0.317204\pi$
$743$	29.6143			1.08644			0.543222	+	0.839589i	$0.317204\pi$
$744$	−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	$-0.826936\pi$
$751$		−	28.3527i		−	1.03460i	0.855803	−	0.517302i	$-0.173064\pi$
$752$	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	$-0.448226\pi$
$757$	8.91093			0.323873			0.161937	+	0.986801i	$0.448226\pi$
$758$	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	$-0.982304\pi$
$761$		−	3.06569i		−	0.111131i	0.998455	−	0.0555656i	$-0.0176962\pi$
$762$	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	$-0.996749\pi$
$809$		−	0.581045i		−	0.0204284i	0.999948	−	0.0102142i	$-0.00325134\pi$
$810$		0			0
$811$		−	15.8511i		−	0.556608i	−0.960493	−	0.278304i	$-0.910228\pi$
$811$		−	15.8511i		−	0.556608i	0.960493	−	0.278304i	$-0.0897723\pi$
$812$	−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	$0.116716\pi$
$821$			20.5449i			0.717023i	−0.933525	+	0.358511i	$0.883284\pi$
$822$	−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	$-0.582881\pi$
$827$	−14.8071			−0.514895			−0.257447	+	0.966292i	$0.582881\pi$
$828$	−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	$-0.720460\pi$
$853$	−37.2984			−1.27707			−0.638537	+	0.769591i	$0.720460\pi$
$854$	−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	$-0.815179\pi$
$859$		−	32.1547i		−	1.09710i	0.836117	−	0.548552i	$-0.184821\pi$
$860$		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	$-0.331846\pi$
$863$	29.6143			1.00808			0.504041	+	0.863680i	$0.331846\pi$
$864$	−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	$-0.190723\pi$
$877$	48.9109			1.65160			0.825802	+	0.563959i	$0.190723\pi$
$878$	−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	$0.148353\pi$
$881$			26.6763i			0.898747i	−0.893344	+	0.449374i	$0.851647\pi$
$882$	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	$-0.637384\pi$
$887$	−24.9179			−0.836660			−0.418330	+	0.908295i	$0.637384\pi$
$888$	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	$0.00279203\pi$
$919$			0.531805i			0.0175426i	−0.999962	+	0.00877132i	$0.997208\pi$
$920$		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	$-0.996966\pi$
$929$		−	0.581045i		−	0.0190635i	0.999955	−	0.00953173i	$-0.00303409\pi$
$930$		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	$-0.587471\pi$
$937$	−16.6125			−0.542707			−0.271353	+	0.962480i	$0.587471\pi$
$938$	−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	$-0.720414\pi$
$941$		−	47.2212i		−	1.53937i	0.638425	−	0.769684i	$-0.279586\pi$
$942$	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	$-0.282915\pi$
$947$	38.7955			1.26068			0.630341	+	0.776318i	$0.282915\pi$
$948$	−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	$-0.125108\pi$
$983$	57.9243			1.84750			0.923749	+	0.382998i	$0.125108\pi$
$984$	−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	$0.220883\pi$
$991$			40.2668i			1.27912i	−0.768743	+	0.639558i	$0.779117\pi$
$992$	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	$-0.684552\pi$
$997$	−34.5969			−1.09569			−0.547847	+	0.836579i	$0.684552\pi$
$998$	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.e.251.3	yes	8
3.2	odd	2	inner	300.2.e.e.251.6	yes	8
4.3	odd	2	inner	300.2.e.e.251.5	yes	8
5.2	odd	4		300.2.h.c.299.13		16
5.3	odd	4		300.2.h.c.299.4		16
5.4	even	2		300.2.e.d.251.6	yes	8
12.11	even	2	inner	300.2.e.e.251.4	yes	8
15.2	even	4		300.2.h.c.299.3		16
15.8	even	4		300.2.h.c.299.14		16
15.14	odd	2		300.2.e.d.251.3	✓	8
20.3	even	4		300.2.h.c.299.1		16
20.7	even	4		300.2.h.c.299.16		16
20.19	odd	2		300.2.e.d.251.4	yes	8
60.23	odd	4		300.2.h.c.299.15		16
60.47	odd	4		300.2.h.c.299.2		16
60.59	even	2		300.2.e.d.251.5	yes	8

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