LMFDB - Embedded newform 300.2.h.c.299.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(299,300)]

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, 1]))

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

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

chi := DirichletCharacter("300.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.h (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 10 x^{13} - 42 x^{11} + 134 x^{10} + 110 x^{9} + 92 x^{8} + 142 x^{7} + \cdots + 100 $ x^16 - 2x^15 + 2x^14 + 10x^13 - 42x^11 + 134x^10 + 110x^9 + 92x^8 + 142x^7 + 1514x^6 + 1102x^5 + 249x^4 - 1056x^3 + 392x^2 - 280x + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.16
Root			$-0.0108430 + 0.474040i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.c.299.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 + 0.758030i) q^{4} +(0.626440 + 2.36803i) q^{6} -3.56393 q^{7} +(2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} +O(q^{10})$	\(q+(1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 + 0.758030i) q^{4} +(0.626440 + 2.36803i) q^{6} -3.56393 q^{7} +(2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} +4.20732 q^{11} +(0.222417 + 3.45695i) q^{12} -2.70156i q^{13} +(-4.94525 - 0.973477i) q^{14} +(2.85078 + 2.80590i) q^{16} -0.828216 q^{17} +(-3.21303 + 2.77064i) q^{18} -5.07999i q^{19} +(-2.70156 - 5.55034i) q^{21} +(5.83802 + 1.14922i) q^{22} +1.09259i q^{23} +(-0.635635 + 4.85757i) q^{24} +(0.737925 - 3.74865i) q^{26} +(-5.07999 - 1.09259i) q^{27} +(-6.59605 - 2.70156i) q^{28} -5.55034i q^{29} -6.59605i q^{31} +(3.18928 + 4.67210i) q^{32} +(3.18928 + 6.55234i) q^{33} +(-1.14922 - 0.226225i) q^{34} +(-5.21515 + 2.96686i) q^{36} +5.40312i q^{37} +(1.38758 - 7.04891i) q^{38} +(4.20732 - 2.04787i) q^{39} +10.2725i q^{41} +(-2.23259 - 8.43949i) q^{42} +0.531805 q^{43} +(7.78683 + 3.18928i) q^{44} +(-0.298438 + 1.51606i) q^{46} -6.22947i q^{47} +(-2.20883 + 6.56666i) q^{48} +5.70156 q^{49} +(-0.627812 - 1.28984i) q^{51} +(2.04787 - 5.00000i) q^{52} -5.55034 q^{53} +(-6.75047 - 2.90364i) q^{54} +(-8.41464 - 5.55034i) q^{56} +(7.91140 - 3.85078i) q^{57} +(1.51606 - 7.70156i) q^{58} +0.701562 q^{61} +(1.80169 - 9.15257i) q^{62} +(6.59605 - 8.41464i) q^{63} +(3.14922 + 7.35408i) q^{64} +(2.63564 + 9.96307i) q^{66} +2.04787 q^{67} +(-1.53285 - 0.627812i) q^{68} +(-1.70156 + 0.828216i) q^{69} -11.3663 q^{71} +(-8.04684 + 2.69226i) q^{72} -7.70156i q^{73} +(-1.47585 + 7.49729i) q^{74} +(3.85078 - 9.40194i) q^{76} -14.9946 q^{77} +(6.39738 - 1.69237i) q^{78} +7.12785i q^{79} +(-2.14922 - 8.73961i) q^{81} +(-2.80590 + 14.2539i) q^{82} +3.11473i q^{83} +(-0.792678 - 12.3203i) q^{84} +(0.737925 + 0.145261i) q^{86} +(8.64391 - 4.20732i) q^{87} +(9.93375 + 6.55234i) q^{88} +4.72212i q^{89} +9.62817i q^{91} +(-0.828216 + 2.02214i) q^{92} +(10.2725 - 5.00000i) q^{93} +(1.70156 - 8.64391i) q^{94} +(-4.85860 + 8.50846i) q^{96} -8.10469i q^{97} +(7.91140 + 1.55737i) q^{98} +(-7.78683 + 9.93375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	$ 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9} + 20 q^{16} + 8 q^{21} - 26 q^{24} - 44 q^{34} - 42 q^{36} - 56 q^{46} + 40 q^{49} + 56 q^{54} - 40 q^{61} + 76 q^{64} + 58 q^{66} + 24 q^{69} + 36 q^{76} - 60 q^{81} - 80 q^{84} - 24 q^{94} - 78 q^{96}+O(q^{100}) $ 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 + 20 * q^16 + 8 * q^21 - 26 * q^24 - 44 * q^34 - 42 * q^36 - 56 * q^46 + 40 * q^49 + 56 * q^54 - 40 * q^61 + 76 * q^64 + 58 * q^66 + 24 * q^69 + 36 * q^76 - 60 * q^81 - 80 * q^84 - 24 * q^94 - 78 * q^96

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 $

$2$	1.38758	+	0.273147i	0.981170	+	0.193144i
$2$	1.38758	+	0.273147i	0.981170	+	0.193144i
$3$	0.758030	+	1.55737i	0.437649	+	0.899146i
$3$	0.758030	+	1.55737i	0.437649	+	0.899146i
$4$	1.85078	+	0.758030i	0.925391	+	0.379015i
$5$		0			0
$5$		0			0
$6$	0.626440	+	2.36803i	0.255743	+	0.966745i
$7$	−3.56393			−1.34704			−0.673519	−	0.739170i	$-0.735218\pi$
$7$	−3.56393			−1.34704			−0.673519	+	0.739170i	$0.735218\pi$
$8$	2.36106	+	1.55737i	0.834761	+	0.550612i
$9$	−1.85078	+	2.36106i	−0.616927	+	0.787020i
$10$		0			0
$11$	4.20732			1.26856			0.634278	−	0.773105i	$-0.281298\pi$
$11$	4.20732			1.26856			0.634278	+	0.773105i	$0.281298\pi$
$12$	0.222417	+	3.45695i	0.0642063	+	0.997937i
$13$		−	2.70156i		−	0.749279i	−0.927171	−	0.374639i	$-0.877767\pi$
$13$		−	2.70156i		−	0.749279i	0.927171	−	0.374639i	$-0.122233\pi$
$14$	−4.94525	−	0.973477i	−1.32167	−	0.260173i
$15$		0			0
$16$	2.85078	+	2.80590i	0.712695	+	0.701474i
$17$	−0.828216			−0.200872			−0.100436	−	0.994944i	$-0.532024\pi$
$17$	−0.828216			−0.200872			−0.100436	+	0.994944i	$0.532024\pi$
$18$	−3.21303	+	2.77064i	−0.757319	+	0.653045i
$19$		−	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
$22$	5.83802	+	1.14922i	1.24467	+	0.245014i
$23$			1.09259i			0.227821i	0.993491	+	0.113910i	$0.0363377\pi$
$23$			1.09259i			0.227821i	−0.993491	+	0.113910i	$0.963662\pi$
$24$	−0.635635	+	4.85757i	−0.129749	+	0.991547i
$25$		0			0
$26$	0.737925	−	3.74865i	0.144719	−	0.735170i
$27$	−5.07999	−	1.09259i	−0.977644	−	0.210269i
$28$	−6.59605	−	2.70156i	−1.24654	−	0.510547i
$29$		−	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	$-0.201797\pi$
$32$	3.18928	+	4.67210i	0.563790	+	0.825918i
$33$	3.18928	+	6.55234i	0.555182	+	1.14062i
$34$	−1.14922	−	0.226225i	−0.197089	−	0.0387972i
$35$		0			0
$36$	−5.21515	+	2.96686i	−0.869191	+	0.494477i
$37$			5.40312i			0.888268i	0.895960	+	0.444134i	$0.146489\pi$
$37$			5.40312i			0.888268i	−0.895960	+	0.444134i	$0.853511\pi$
$38$	1.38758	−	7.04891i	0.225096	−	1.14348i
$39$	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	$0.703692\pi$
$42$	−2.23259	−	8.43949i	−0.344495	−	1.30224i
$43$	0.531805			0.0810995			0.0405498	−	0.999178i	$-0.487089\pi$
$43$	0.531805			0.0810995			0.0405498	+	0.999178i	$0.487089\pi$
$44$	7.78683	+	3.18928i	1.17391	+	0.480802i
$45$		0			0
$46$	−0.298438	+	1.51606i	−0.0440023	+	0.223531i
$47$		−	6.22947i		−	0.908661i	−0.890833	−	0.454331i	$-0.849879\pi$
$47$		−	6.22947i		−	0.908661i	0.890833	−	0.454331i	$-0.150121\pi$
$48$	−2.20883	+	6.56666i	−0.318817	+	0.947816i
$49$	5.70156			0.814509
$50$		0			0
$51$	−0.627812	−	1.28984i	−0.0879113	−	0.180613i
$52$	2.04787	−	5.00000i	0.283988	−	0.693375i
$53$	−5.55034			−0.762398			−0.381199	−	0.924493i	$-0.624489\pi$
$53$	−5.55034			−0.762398			−0.381199	+	0.924493i	$0.624489\pi$
$54$	−6.75047	−	2.90364i	−0.918623	−	0.395136i
$55$		0			0
$56$	−8.41464	−	5.55034i	−1.12445	−	0.741695i
$57$	7.91140	−	3.85078i	1.04789	−	0.510048i
$58$	1.51606	−	7.70156i	0.199068	−	1.01126i
$59$		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	$0.485699\pi$
$62$	1.80169	−	9.15257i	0.228815	−	1.16238i
$63$	6.59605	−	8.41464i	0.831024	−	1.06015i
$64$	3.14922	+	7.35408i	0.393652	+	0.919259i
$65$		0			0
$66$	2.63564	+	9.96307i	0.324424	+	1.22637i
$67$	2.04787			0.250187			0.125093	−	0.992145i	$-0.460077\pi$
$67$	2.04787			0.250187			0.125093	+	0.992145i	$0.460077\pi$
$68$	−1.53285	−	0.627812i	−0.185885	−	0.0761334i
$69$	−1.70156	+	0.828216i	−0.204844	+	0.0997054i
$70$		0			0
$71$	−11.3663			−1.34894			−0.674468	−	0.738304i	$-0.735627\pi$
$71$	−11.3663			−1.34894			−0.674468	+	0.738304i	$0.735627\pi$
$72$	−8.04684	+	2.69226i	−0.948330	+	0.317286i
$73$		−	7.70156i		−	0.901400i	−0.892676	−	0.450700i	$-0.851174\pi$
$73$		−	7.70156i		−	0.901400i	0.892676	−	0.450700i	$-0.148826\pi$
$74$	−1.47585	+	7.49729i	−0.171564	+	0.871542i
$75$		0			0
$76$	3.85078	−	9.40194i	0.441715	−	1.07848i
$77$	−14.9946			−1.70879
$78$	6.39738	−	1.69237i	0.724361	−	0.191623i
$79$			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
$82$	−2.80590	+	14.2539i	−0.309859	+	1.57408i
$83$			3.11473i			0.341886i	0.985281	+	0.170943i	$0.0546815\pi$
$83$			3.11473i			0.341886i	−0.985281	+	0.170943i	$0.945319\pi$
$84$	−0.792678	−	12.3203i	−0.0864882	−	1.34426i
$85$		0			0
$86$	0.737925	+	0.145261i	0.0795724	+	0.0156639i
$87$	8.64391	−	4.20732i	0.926724	−	0.451072i
$88$	9.93375	+	6.55234i	1.05894	+	0.698482i
$89$			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
$92$	−0.828216	+	2.02214i	−0.0863474	+	0.210823i
$93$	10.2725	−	5.00000i	1.06520	−	0.518476i
$94$	1.70156	−	8.64391i	0.175503	−	0.891551i
$95$		0			0
$96$	−4.85860	+	8.50846i	−0.495879	+	0.868392i
$97$		−	8.10469i		−	0.822906i	−0.911431	−	0.411453i	$-0.865021\pi$
$97$		−	8.10469i		−	0.822906i	0.911431	−	0.411453i	$-0.134979\pi$
$98$	7.91140	+	1.55737i	0.799172	+	0.157318i
$99$	−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	$0.883271\pi$
$102$	−0.518827	−	1.96124i	−0.0513716	−	0.194192i
$103$	−4.09573			−0.403564			−0.201782	−	0.979430i	$-0.564673\pi$
$103$	−4.09573			−0.403564			−0.201782	+	0.979430i	$0.564673\pi$
$104$	4.20732	−	6.37855i	0.412562	−	0.625469i
$105$		0			0
$106$	−7.70156	−	1.51606i	−0.748042	−	0.147253i
$107$			18.8514i			1.82244i	0.411924	+	0.911218i	$0.364857\pi$
$107$			18.8514i			1.82244i	−0.411924	+	0.911218i	$0.635143\pi$
$108$	−8.57372	−	5.87292i	−0.825007	−	0.565122i
$109$	−8.70156			−0.833458			−0.416729	−	0.909031i	$-0.636824\pi$
$109$	−8.70156			−0.833458			−0.416729	+	0.909031i	$0.636824\pi$
$110$		0			0
$111$	−8.41464	+	4.09573i	−0.798683	+	0.388750i
$112$	−10.1600	−	10.0000i	−0.960027	−	0.944911i
$113$	−15.8228			−1.48848			−0.744242	−	0.667910i	$-0.767189\pi$
$113$	−15.8228			−1.48848			−0.744242	+	0.667910i	$0.767189\pi$
$114$	12.0296	−	3.18231i	1.12667	−	0.298050i
$115$		0			0
$116$	4.20732	−	10.2725i	0.390640	−	0.953774i
$117$	6.37855	+	5.00000i	0.589697	+	0.462250i
$118$		0			0
$119$	2.95170			0.270582
$120$		0			0
$121$	6.70156			0.609233
$122$	0.973477	+	0.191630i	0.0881344	+	0.0173493i
$123$	−15.9980	+	7.78683i	−1.44249	+	0.702115i
$124$	5.00000	−	12.2078i	0.449013	−	1.09630i
$125$		0			0
$126$	11.4510	−	9.87434i	1.02014	−	0.879676i
$127$	16.2242			1.43967			0.719833	−	0.694147i	$-0.244218\pi$
$127$	16.2242			1.43967			0.719833	+	0.694147i	$0.244218\pi$
$128$	2.36106	+	11.0646i	0.208690	+	0.977982i
$129$	0.403124	+	0.828216i	0.0354931	+	0.0729203i
$130$		0			0
$131$	19.7810			1.72827			0.864136	−	0.503258i	$-0.167865\pi$
$131$	19.7810			1.72827			0.864136	+	0.503258i	$0.167865\pi$
$132$	0.935780	+	14.5445i	0.0814492	+	1.26594i
$133$			18.1047i			1.56988i
$134$	2.84159	+	0.559369i	0.245476	+	0.0483221i
$135$		0			0
$136$	−1.95547	−	1.28984i	−0.167680	−	0.110602i
$137$	6.37855			0.544957			0.272478	−	0.962162i	$-0.412157\pi$
$137$	6.37855			0.544957			0.272478	+	0.962162i	$0.412157\pi$
$138$	−2.58729	+	0.684442i	−0.220244	+	0.0582636i
$139$			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
$142$	−15.7718	−	3.10469i	−1.32354	−	0.260539i
$143$		−	11.3663i		−	0.950501i
$144$	−11.9011	+	1.53777i	−0.991755	+	0.128148i
$145$		0			0
$146$	2.10366	−	10.6866i	0.174100	−	0.884427i
$147$	4.32196	+	8.87942i	0.356469	+	0.732362i
$148$	−4.09573	+	10.0000i	−0.336667	+	0.821995i
$149$			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	$0.939705\pi$
$152$	7.91140	−	11.9942i	0.641699	−	0.972854i
$153$	1.53285	−	1.95547i	0.123923	−	0.158090i
$154$	−20.8062	−	4.09573i	−1.67662	−	0.330043i
$155$		0			0
$156$	9.33918	−	0.600873i	0.747732	−	0.0481084i
$157$		−	8.10469i		−	0.646824i	−0.946258	−	0.323412i	$-0.895170\pi$
$157$		−	8.10469i		−	0.646824i	0.946258	−	0.323412i	$-0.104830\pi$
$158$	−1.94695	+	9.89049i	−0.154891	+	0.786845i
$159$	−4.20732	−	8.64391i	−0.333662	−	0.685507i
$160$		0			0
$161$		−	3.89391i		−	0.306883i
$162$	−0.595020	−	12.7140i	−0.0467492	−	0.998907i
$163$	−5.07999			−0.397895			−0.198948	−	0.980010i	$-0.563752\pi$
$163$	−5.07999			−0.397895			−0.198948	+	0.980010i	$0.563752\pi$
$164$	−7.78683	+	19.0121i	−0.608049	+	1.48459i
$165$		0			0
$166$	−0.850781	+	4.32196i	−0.0660334	+	0.335449i
$167$			3.27777i			0.253641i	0.991926	+	0.126821i	$0.0404773\pi$
$167$			3.27777i			0.253641i	−0.991926	+	0.126821i	$0.959523\pi$
$168$	2.26536	−	17.3120i	0.174776	−	1.33565i
$169$	5.70156			0.438582
$170$		0			0
$171$	11.9942	+	9.40194i	0.917216	+	0.718984i
$172$	0.984255	+	0.403124i	0.0750487	+	0.0307379i
$173$	14.9946			1.14002			0.570008	−	0.821639i	$-0.306940\pi$
$173$	14.9946			1.14002			0.570008	+	0.821639i	$0.306940\pi$
$174$	13.1434	−	3.47695i	0.996397	−	0.263587i
$175$		0			0
$176$	11.9942	+	11.8053i	0.904093	+	0.889858i
$177$		0			0
$178$	−1.28984	+	6.55234i	−0.0966772	+	0.491119i
$179$	−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	$0.794813\pi$
$182$	−2.62991	+	13.3599i	−0.194942	+	0.990301i
$183$	0.531805	+	1.09259i	0.0393122	+	0.0807665i
$184$	−1.70156	+	2.57967i	−0.125441	+	0.190176i
$185$		0			0
$186$	15.6196	−	4.13203i	1.14529	−	0.302975i
$187$	−3.48457			−0.254817
$188$	4.72212	−	11.5294i	0.344396	−	0.840866i
$189$	18.1047	+	3.89391i	1.31692	+	0.283240i
$190$		0			0
$191$	−11.3663			−0.822440			−0.411220	−	0.911536i	$-0.634897\pi$
$191$	−11.3663			−0.822440			−0.411220	+	0.911536i	$0.634897\pi$
$192$	−9.06579	+	10.4791i	−0.654267	+	0.756264i
$193$			5.80625i			0.417943i	0.977922	+	0.208971i	$0.0670116\pi$
$193$			5.80625i			0.417943i	−0.977922	+	0.208971i	$0.932988\pi$
$194$	2.21377	−	11.2459i	0.158940	−	0.807411i
$195$		0			0
$196$	10.5523	+	4.32196i	0.753739	+	0.308711i
$197$	9.44424			0.672875			0.336437	−	0.941706i	$-0.390778\pi$
$197$	9.44424			0.672875			0.336437	+	0.941706i	$0.390778\pi$
$198$	−13.5183	+	11.6570i	−0.960701	+	0.828424i
$199$			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
$202$	−1.96851	+	10.0000i	−0.138504	+	0.703598i
$203$			19.7810i			1.38835i
$204$	−0.184209	−	2.86310i	−0.0128972	−	0.200457i
$205$		0			0
$206$	−5.68317	−	1.11874i	−0.395965	−	0.0779462i
$207$	−2.57967	−	2.02214i	−0.179299	−	0.140549i
$208$	7.58030	−	7.70156i	0.525599	−	0.534007i
$209$		−	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	$0.837738\pi$
$212$	−10.2725	−	4.20732i	−0.705515	−	0.288960i
$213$	−8.61603	−	17.7016i	−0.590361	−	1.21289i
$214$	−5.14922	+	26.1580i	−0.351993	+	1.78812i
$215$		0			0
$216$	−10.2926	−	10.4911i	−0.700322	−	0.713827i
$217$			23.5078i			1.59581i
$218$	−12.0742	−	2.37681i	−0.817765	−	0.160978i
$219$	11.9942	−	5.83802i	0.810490	−	0.394497i
$220$		0			0
$221$			2.23748i			0.150509i
$222$	−12.7948	+	3.38473i	−0.858729	+	0.227168i
$223$	15.6924			1.05084			0.525421	−	0.850843i	$-0.323908\pi$
$223$	15.6924			1.05084			0.525421	+	0.850843i	$0.323908\pi$
$224$	−11.3663	−	16.6510i	−0.759446	−	1.11254i
$225$		0			0
$226$	−21.9555	−	4.32196i	−1.46046	−	0.287492i
$227$		−	11.6924i		−	0.776053i	−0.921648	−	0.388026i	$-0.873157\pi$
$227$		−	11.6924i		−	0.776053i	0.921648	−	0.388026i	$-0.126843\pi$
$228$	17.5613	−	1.12988i	1.16302	−	0.0748278i
$229$	−8.70156			−0.575015			−0.287508	−	0.957778i	$-0.592827\pi$
$229$	−8.70156			−0.575015			−0.287508	+	0.957778i	$0.592827\pi$
$230$		0			0
$231$	−11.3663	−	23.3521i	−0.747850	−	1.53645i
$232$	8.64391	−	13.1047i	0.567501	−	0.860365i
$233$	14.9946			0.982328			0.491164	−	0.871067i	$-0.336572\pi$
$233$	14.9946			0.982328			0.491164	+	0.871067i	$0.336572\pi$
$234$	7.48504	+	8.68021i	0.489313	+	0.567443i
$235$		0			0
$236$		0			0
$237$	−11.1007	+	5.40312i	−0.721066	+	0.350971i
$238$	4.09573	+	0.806248i	0.265487	+	0.0522613i
$239$	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	$0.427613\pi$
$242$	9.29898	+	1.83051i	0.597761	+	0.117670i
$243$	11.9816	−	9.97201i	0.768621	−	0.639705i
$244$	1.29844	+	0.531805i	0.0831240	+	0.0340453i
$245$		0			0
$246$	−24.3255	+	6.43508i	−1.55094	+	0.410286i
$247$	−13.7239			−0.873231
$248$	10.2725	−	15.5737i	0.652302	−	0.988929i
$249$	−4.85078	+	2.36106i	−0.307406	+	0.149626i
$250$		0			0
$251$	−1.25562			−0.0792543			−0.0396272	−	0.999215i	$-0.512617\pi$
$251$	−1.25562			−0.0792543			−0.0396272	+	0.999215i	$0.512617\pi$
$252$	18.5864	−	10.5737i	1.17083	−	0.666078i
$253$			4.59688i			0.289003i
$254$	22.5125	+	4.43160i	1.41256	+	0.278063i
$255$		0			0
$256$	0.253905	+	15.9980i	0.0158691	+	0.999874i
$257$	−11.1007			−0.692441			−0.346221	−	0.938153i	$-0.612535\pi$
$257$	−11.1007			−0.692441			−0.346221	+	0.938153i	$0.612535\pi$
$258$	0.333144	+	1.25933i	0.0207406	+	0.0784025i
$259$		−	19.2563i		−	1.19653i
$260$		0			0
$261$	13.1047	+	10.2725i	0.811160	+	0.635849i
$262$	27.4478	+	5.40312i	1.69573	+	0.333806i
$263$		−	17.9219i		−	1.10511i	−0.833476	−	0.552555i	$-0.813653\pi$
$263$		−	17.9219i		−	1.10511i	0.833476	−	0.552555i	$-0.186347\pi$
$264$	−2.67432	+	20.4374i	−0.164593	+	1.25783i
$265$		0			0
$266$	−4.94525	+	25.1218i	−0.303213	+	1.54032i
$267$	−7.35408	+	3.57951i	−0.450062	+	0.219062i
$268$	3.79015	+	1.55234i	0.231520	+	0.0948245i
$269$			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	$-0.265920\pi$
$272$	−2.36106	−	2.32389i	−0.143160	−	0.140906i
$273$	−14.9946	+	7.29844i	−0.907513	+	0.441722i
$274$	8.85078	+	1.74228i	0.534695	+	0.105255i
$275$		0			0
$276$	−3.77703	+	0.243010i	−0.227351	+	0.0146275i
$277$		−	28.1047i		−	1.68865i	−0.535834	−	0.844323i	$-0.680003\pi$
$277$		−	28.1047i		−	1.68865i	0.535834	−	0.844323i	$-0.319997\pi$
$278$	−0.414108	+	2.10366i	−0.0248365	+	0.126169i
$279$	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	$-0.0689621\pi$
$282$	14.7516	−	3.90239i	0.878443	−	0.232384i
$283$	6.14360			0.365199			0.182599	−	0.983187i	$-0.441549\pi$
$283$	6.14360			0.365199			0.182599	+	0.983187i	$0.441549\pi$
$284$	−21.0366	−	8.61603i	−1.24829	−	0.511267i
$285$		0			0
$286$	3.10469	−	15.7718i	0.183584	−	0.932604i
$287$		−	36.6103i		−	2.16104i
$288$	−16.9338	−	1.11696i	−0.997832	−	0.0658173i
$289$	−16.3141			−0.959651
$290$		0			0
$291$	12.6220	−	6.14360i	0.739913	−	0.360144i
$292$	5.83802	−	14.2539i	0.341644	−	0.834147i
$293$	−18.8885			−1.10348			−0.551739	−	0.834017i	$-0.686035\pi$
$293$	−18.8885			−1.10348			−0.551739	+	0.834017i	$0.686035\pi$
$294$	3.57169	+	13.5015i	0.208305	+	0.787422i
$295$		0			0
$296$	−8.41464	+	12.7571i	−0.489091	+	0.741492i
$297$	−21.3731	−	4.59688i	−1.24020	−	0.266738i
$298$	−0.452450	+	2.29844i	−0.0262097	+	0.133145i
$299$	2.95170			0.170701
$300$		0			0
$301$	−1.89531			−0.109244
$302$	−1.26400	+	6.42110i	−0.0727350	+	0.369493i
$303$	−11.2236	+	5.46295i	−0.644778	+	0.313838i
$304$	14.2539	−	14.4819i	0.817518	−	0.830595i
$305$		0			0
$306$	2.66108	−	2.29468i	0.152124	−	0.131178i
$307$	−20.3993			−1.16425			−0.582125	−	0.813100i	$-0.697778\pi$
$307$	−20.3993			−1.16425			−0.582125	+	0.813100i	$0.697778\pi$
$308$	−27.7517	−	11.3663i	−1.58130	−	0.647657i
$309$	−3.10469	−	6.37855i	−0.176619	−	0.362863i
$310$		0			0
$311$	−16.8293			−0.954301			−0.477151	−	0.878821i	$-0.658330\pi$
$311$	−16.8293			−0.954301			−0.477151	+	0.878821i	$0.658330\pi$
$312$	13.1230	+	1.71721i	0.742945	+	0.0972178i
$313$		−	22.7016i		−	1.28317i	−0.767053	−	0.641584i	$-0.778278\pi$
$313$		−	22.7016i		−	1.28317i	0.767053	−	0.641584i	$-0.221722\pi$
$314$	2.21377	−	11.2459i	0.124930	−	0.634645i
$315$		0			0
$316$	−5.40312	+	13.1921i	−0.303949	+	0.742113i
$317$	29.9892			1.68436			0.842180	−	0.539197i	$-0.181272\pi$
$317$	29.9892			1.68436			0.842180	+	0.539197i	$0.181272\pi$
$318$	−3.47695	−	13.1434i	−0.194978	−	0.737044i
$319$		−	23.3521i		−	1.30746i
$320$		0			0
$321$	−29.3586	+	14.2900i	−1.63864	+	0.797587i
$322$	1.06361	−	5.40312i	0.0592727	−	0.301104i
$323$			4.20732i			0.234102i
$324$	2.64716	−	17.8043i	0.147064	−	0.989127i
$325$		0			0
$326$	−7.04891	−	1.38758i	−0.390403	−	0.0768512i
$327$	−6.59605	−	13.5515i	−0.364762	−	0.749401i
$328$	−15.9980	+	24.2539i	−0.883341	+	1.33920i
$329$			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	$-0.308954\pi$
$332$	−2.36106	+	5.76469i	−0.129580	+	0.316378i
$333$	−12.7571	−	10.0000i	−0.699085	−	0.547997i
$334$	−0.895314	+	4.54818i	−0.0489894	+	0.248865i
$335$		0			0
$336$	7.87210	−	23.4031i	0.429458	−	1.27674i
$337$			0.403124i			0.0219596i	0.999940	+	0.0109798i	$0.00349505\pi$
$337$			0.403124i			0.0219596i	−0.999940	+	0.0109798i	$0.996505\pi$
$338$	7.91140	+	1.55737i	0.430323	+	0.0847096i
$339$	−11.9942	−	24.6419i	−0.651433	−	1.33836i
$340$		0			0
$341$		−	27.7517i		−	1.50284i
$342$	14.0748	+	16.3222i	0.761077	+	0.882601i
$343$	4.62754			0.249863
$344$	1.25562	+	0.828216i	0.0676987	+	0.0446544i
$345$		0			0
$346$	20.8062	+	4.09573i	1.11855	+	0.220188i
$347$			13.3885i			0.718732i	0.933197	+	0.359366i	$0.117007\pi$
$347$			13.3885i			0.718732i	−0.933197	+	0.359366i	$0.882993\pi$
$348$	19.1873	−	1.23449i	1.02855	−	0.0661756i
$349$	12.2094			0.653553			0.326776	−	0.945102i	$-0.394038\pi$
$349$	12.2094			0.653553			0.326776	+	0.945102i	$0.394038\pi$
$350$		0			0
$351$	−2.95170	+	13.7239i	−0.157550	+	0.732527i
$352$	13.4183	+	19.6570i	0.715199	+	1.04772i
$353$	29.4081			1.56524			0.782618	−	0.622502i	$-0.213884\pi$
$353$	29.4081			1.56524			0.782618	+	0.622502i	$0.213884\pi$
$354$		0			0
$355$		0			0
$356$	−3.57951	+	8.73961i	−0.189714	+	0.463199i
$357$	2.23748	+	4.59688i	0.118420	+	0.243292i
$358$	−21.6098	−	4.25391i	−1.14211	−	0.224826i
$359$	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
$362$	−29.8439	−	5.87480i	−1.56856	−	0.308773i
$363$	5.07999	+	10.4368i	0.266630	+	0.547789i
$364$	−7.29844	+	17.8196i	−0.382542	+	0.934002i
$365$		0			0
$366$	0.439487	+	1.66132i	0.0229723	+	0.0868386i
$367$	−3.56393			−0.186035			−0.0930177	−	0.995664i	$-0.529651\pi$
$367$	−3.56393			−0.186035			−0.0930177	+	0.995664i	$0.529651\pi$
$368$	−3.06569	+	3.11473i	−0.159810	+	0.162367i
$369$	−24.2539	−	19.0121i	−1.26261	−	0.989729i
$370$		0			0
$371$	19.7810			1.02698
$372$	22.8022	−	1.46707i	1.18224	−	0.0760642i
$373$			17.2984i			0.895679i	0.894114	+	0.447840i	$0.147806\pi$
$373$			17.2984i			0.895679i	−0.894114	+	0.447840i	$0.852194\pi$
$374$	−4.83513	−	0.951801i	−0.250019	−	0.0492165i
$375$		0			0
$376$	9.70156	−	14.7082i	0.500320	−	0.758515i
$377$	−14.9946			−0.772260
$378$	24.0582	+	10.3484i	1.23742	+	0.532263i
$379$			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
$382$	−15.7718	−	3.10469i	−0.806953	−	0.158850i
$383$		−	12.4589i		−	0.636622i	−0.947986	−	0.318311i	$-0.896884\pi$
$383$		−	12.4589i		−	0.636622i	0.947986	−	0.318311i	$-0.103116\pi$
$384$	−15.4419	+	12.0643i	−0.788015	+	0.615656i
$385$		0			0
$386$	−1.58596	+	8.05666i	−0.0807233	+	0.410073i
$387$	−0.984255	+	1.25562i	−0.0500325	+	0.0638270i
$388$	6.14360	−	15.0000i	0.311894	−	0.761510i
$389$		−	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
$392$	13.4617	+	8.87942i	0.679920	+	0.448479i
$393$	14.9946	+	30.8062i	0.756377	+	1.55397i
$394$	13.1047	+	2.57967i	0.660205	+	0.129962i
$395$		0			0
$396$	−21.9418	+	12.4825i	−1.10262	+	0.627271i
$397$			28.9109i			1.45100i	0.688223	+	0.725499i	$0.258391\pi$
$397$			28.9109i			1.45100i	−0.688223	+	0.725499i	$0.741609\pi$
$398$	−4.28634	+	21.7745i	−0.214855	+	1.09146i
$399$	−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	$-0.279481\pi$
$402$	1.28286	+	4.84941i	0.0639835	+	0.241867i
$403$	−17.8196			−0.887659
$404$	−5.46295	+	13.3382i	−0.271792	+	0.663598i
$405$		0			0
$406$	−5.40312	+	27.4478i	−0.268153	+	1.36221i
$407$			22.7327i			1.12682i
$408$	0.526443	−	4.02311i	0.0260628	−	0.199174i
$409$	27.2094			1.34542			0.672708	−	0.739908i	$-0.265131\pi$
$409$	27.2094			1.34542			0.672708	+	0.739908i	$0.265131\pi$
$410$		0			0
$411$	4.83513	+	9.93375i	0.238500	+	0.489996i
$412$	−7.58030	−	3.10469i	−0.373455	−	0.152957i
$413$		0			0
$414$	−3.02717	−	3.51053i	−0.148777	−	0.172533i
$415$		0			0
$416$	12.6220	−	8.61603i	0.618843	−	0.422436i
$417$	−2.36106	+	1.14922i	−0.115622	+	0.0562775i
$418$	5.83802	−	29.6570i	0.285547	−	1.45057i
$419$	−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	$0.299149\pi$
$422$	−3.87223	+	19.6709i	−0.188497	+	0.957563i
$423$	14.7082	+	11.5294i	0.715135	+	0.560578i
$424$	−13.1047	−	8.64391i	−0.636420	−	0.419785i
$425$		0			0
$426$	−7.12033	−	26.9159i	−0.344981	−	1.30408i
$427$	−2.50031			−0.120999
$428$	−14.2900	+	34.8899i	−0.690731	+	1.68647i
$429$	17.7016	−	8.61603i	0.854639	−	0.415986i
$430$		0			0
$431$	19.7810			0.952817			0.476408	−	0.879224i	$-0.341938\pi$
$431$	19.7810			0.952817			0.476408	+	0.879224i	$0.341938\pi$
$432$	−11.4162	−	17.3686i	−0.549264	−	0.835649i
$433$		−	31.2094i		−	1.49983i	−0.661536	−	0.749913i	$-0.730095\pi$
$433$		−	31.2094i		−	1.49983i	0.661536	−	0.749913i	$-0.269905\pi$
$434$	−6.42110	+	32.6191i	−0.308222	+	1.56577i
$435$		0			0
$436$	−16.1047	−	6.59605i	−0.771275	−	0.315893i
$437$	5.55034			0.265509
$438$	18.2375	−	4.82457i	0.871423	−	0.230527i
$439$		−	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
$442$	−0.611161	+	3.10469i	−0.0290699	+	0.147675i
$443$			11.2033i			0.532285i	0.963934	+	0.266143i	$0.0857492\pi$
$443$			11.2033i			0.532285i	−0.963934	+	0.266143i	$0.914251\pi$
$444$	−18.6784	+	1.20175i	−0.886435	+	0.0570324i
$445$		0			0
$446$	21.7745	+	4.28634i	1.03105	+	0.202964i
$447$	−2.57967	+	1.25562i	−0.122014	+	0.0593890i
$448$	−11.2236	−	26.2094i	−0.530264	−	1.23828i
$449$			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
$452$	−29.2845	−	11.9942i	−1.37743	−	0.564158i
$453$	−7.20677	+	3.50781i	−0.338604	+	0.164811i
$454$	3.19375	−	16.2242i	0.149890	−	0.761440i
$455$		0			0
$456$	24.6764	+	3.22902i	1.15558	+	0.151213i
$457$			16.8953i			0.790329i	0.918610	+	0.395165i	$0.129312\pi$
$457$			16.8953i			0.790329i	−0.918610	+	0.395165i	$0.870688\pi$
$458$	−12.0742	−	2.37681i	−0.564188	−	0.111061i
$459$	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	$0.946325\pi$
$462$	−9.39321	−	35.5076i	−0.437012	−	1.65196i
$463$	7.12785			0.331259			0.165630	−	0.986188i	$-0.447034\pi$
$463$	7.12785			0.331259			0.165630	+	0.986188i	$0.447034\pi$
$464$	15.5737	−	15.8228i	0.722989	−	0.734555i
$465$		0			0
$466$	20.8062	+	4.09573i	0.963831	+	0.189731i
$467$		−	0.766519i		−	0.0354703i	−0.999843	−	0.0177351i	$-0.994354\pi$
$467$		−	0.766519i		−	0.0354703i	0.999843	−	0.0177351i	$-0.00564557\pi$
$468$	8.01516	+	14.0890i	0.370501	+	0.651266i
$469$	−7.29844			−0.337011
$470$		0			0
$471$	12.6220	−	6.14360i	0.581590	−	0.283082i
$472$		0			0
$473$	2.23748			0.102879
$474$	−16.8790	+	4.46517i	−0.775277	+	0.205092i
$475$		0			0
$476$	5.46295	+	2.23748i	0.250394	+	0.102555i
$477$	10.2725	−	13.1047i	0.470344	−	0.600022i
$478$	7.58030	+	1.49219i	0.346715	+	0.0682512i
$479$	−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
$482$	9.71309	+	1.91203i	0.442419	+	0.0870906i
$483$	6.06424	−	2.95170i	0.275932	−	0.134307i
$484$	12.4031	+	5.07999i	0.563778	+	0.230908i
$485$		0			0
$486$	19.3493	−	10.5643i	0.877703	−	0.479205i
$487$	34.0438			1.54267			0.771337	−	0.636427i	$-0.219588\pi$
$487$	34.0438			1.54267			0.771337	+	0.636427i	$0.219588\pi$
$488$	1.65643	+	1.09259i	0.0749831	+	0.0494592i
$489$	−3.85078	−	7.91140i	−0.174138	−	0.357766i
$490$		0			0
$491$	−16.8293			−0.759495			−0.379748	−	0.925090i	$-0.623989\pi$
$491$	−16.8293			−0.759495			−0.379748	+	0.925090i	$0.623989\pi$
$492$	−35.5114	+	2.28477i	−1.60098	+	0.103005i
$493$			4.59688i			0.207033i
$494$	−19.0431	−	3.74865i	−0.856788	−	0.168660i
$495$		0			0
$496$	18.5078	−	18.8039i	0.831025	−	0.844319i
$497$	40.5088			1.81707
$498$	−7.37579	+	1.95119i	−0.330517	+	0.0874351i
$499$			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
$502$	−1.74228	−	0.342970i	−0.0777620	−	0.0153075i
$503$			32.2399i			1.43751i	0.695265	+	0.718753i	$0.255287\pi$
$503$			32.2399i			1.43751i	−0.695265	+	0.718753i	$0.744713\pi$
$504$	28.6784	−	9.59503i	1.27744	−	0.427397i
$505$		0			0
$506$	−1.25562	+	6.37855i	−0.0558193	+	0.283561i
$507$	4.32196	+	8.87942i	0.191945	+	0.394349i
$508$	30.0275	+	12.2984i	1.33225	+	0.545655i
$509$			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
$512$	−4.01749	+	22.2679i	−0.177550	+	0.984112i
$513$	−5.55034	+	25.8062i	−0.245053	+	1.13937i
$514$	−15.4031	−	3.03212i	−0.679403	−	0.133741i
$515$		0			0
$516$	0.118283	+	1.83843i	0.00520710	+	0.0809322i
$517$		−	26.2094i		−	1.15269i
$518$	5.25982	−	26.7198i	0.231103	−	1.17400i
$519$	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	$-0.0722455\pi$
$522$	15.3780	+	17.8334i	0.673075	+	0.780547i
$523$	−31.4642			−1.37583			−0.687916	−	0.725790i	$-0.741474\pi$
$523$	−31.4642			−1.37583			−0.687916	+	0.725790i	$0.741474\pi$
$524$	36.6103	+	14.9946i	1.59933	+	0.655041i
$525$		0			0
$526$	4.89531	−	24.8681i	0.213446	−	1.08430i
$527$			5.46295i			0.237970i
$528$	−9.29326	+	27.6281i	−0.404437	+	1.20236i
$529$	21.8062			0.948098
$530$		0			0
$531$		0			0
$532$	−13.7239	+	33.5078i	−0.595006	+	1.45275i
$533$	27.7517			1.20206
$534$	−11.1821	+	2.95813i	−0.483898	+	0.128011i
$535$		0			0
$536$	4.83513	+	3.18928i	0.208846	+	0.137756i
$537$	−11.8053	−	24.2539i	−0.509437	−	1.04663i
$538$	−4.09573	+	20.8062i	−0.176579	+	0.897021i
$539$	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	$0.636167\pi$
$542$	6.66908	−	33.8788i	0.286461	−	1.45522i
$543$	−16.3036	−	33.4955i	−0.699653	−	1.43743i
$544$	−2.64141	−	3.86951i	−0.113249	−	0.165904i
$545$		0			0
$546$	−22.7998	+	6.03147i	−0.975741	+	0.258123i
$547$	21.8360			0.933640			0.466820	−	0.884352i	$-0.345400\pi$
$547$	21.8360			0.933640			0.466820	+	0.884352i	$0.345400\pi$
$548$	11.8053	+	4.83513i	0.504298	+	0.206547i
$549$	−1.29844	+	1.65643i	−0.0554160	+	0.0706948i
$550$		0			0
$551$	−28.1956			−1.20117
$552$	−5.30733	−	0.694488i	−0.225895	−	0.0295594i
$553$		−	25.4031i		−	1.08025i
$554$	7.67672	−	38.9976i	0.326153	−	1.65685i
$555$		0			0
$556$	−1.14922	+	2.80590i	−0.0487377	+	0.118996i
$557$	−17.2321			−0.730146			−0.365073	−	0.930979i	$-0.618956\pi$
$557$	−17.2321			−0.730146			−0.365073	+	0.930979i	$0.618956\pi$
$558$	18.2752	+	21.1933i	0.773653	+	0.897184i
$559$		−	1.43670i		−	0.0607661i
$560$		0			0
$561$	−2.64141	−	5.42675i	−0.111520	−	0.229118i
$562$	1.96851	−	10.0000i	0.0830366	−	0.421825i
$563$		−	30.0547i		−	1.26666i	−0.773883	−	0.633328i	$-0.781688\pi$
$563$		−	30.0547i		−	1.26666i	0.773883	−	0.633328i	$-0.218312\pi$
$564$	21.5350	−	1.38554i	0.906786	−	0.0583417i
$565$		0			0
$566$	8.52476	+	1.67811i	0.358322	+	0.0705361i
$567$	7.65966	+	31.1473i	0.321675	+	1.30806i
$568$	−26.8366	−	17.7016i	−1.12604	−	0.742741i
$569$		−	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	$-0.242429\pi$
$572$	8.61603	−	21.0366i	0.360254	−	0.879585i
$573$	−8.61603	−	17.7016i	−0.359940	−	0.739493i
$574$	10.0000	−	50.7999i	0.417392	−	2.12034i
$575$		0			0
$576$	−23.1919	−	6.17528i	−0.966331	−	0.257304i
$577$			0.403124i			0.0167823i	0.999965	+	0.00839114i	$0.00267101\pi$
$577$			0.403124i			0.0167823i	−0.999965	+	0.00839114i	$0.997329\pi$
$578$	−22.6371	−	4.45614i	−0.941581	−	0.185351i
$579$	−9.04246	+	4.40131i	−0.375792	+	0.182912i
$580$		0			0
$581$		−	11.1007i		−	0.460534i
$582$	19.1922	−	5.07710i	0.795540	−	0.210453i
$583$	−23.3521			−0.967144
$584$	11.9942	−	18.1839i	0.496322	−	0.752453i
$585$		0			0
$586$	−26.2094	−	5.15934i	−1.08270	−	0.213130i
$587$			3.88125i			0.160196i	0.996787	+	0.0800982i	$0.0255234\pi$
$587$			3.88125i			0.160196i	−0.996787	+	0.0800982i	$0.974477\pi$
$588$	1.26812	+	19.7100i	0.0522966	+	0.812828i
$589$	−33.5078			−1.38067
$590$		0			0
$591$	7.15902	+	14.7082i	0.294483	+	0.605012i
$592$	−15.1606	+	15.4031i	−0.623097	+	0.633065i
$593$	−43.5745			−1.78939			−0.894695	−	0.446678i	$-0.852607\pi$
$593$	−43.5745			−1.78939			−0.894695	+	0.446678i	$0.852607\pi$
$594$	−28.4014	−	12.2166i	−1.16532	−	0.501252i
$595$		0			0
$596$	−1.25562	+	3.06569i	−0.0514324	+	0.125576i
$597$	−24.4388	+	11.8953i	−1.00021	+	0.486843i
$598$	4.09573	+	0.806248i	0.167487	+	0.0329700i
$599$		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	$0.337067\pi$
$602$	−2.62991	−	0.517700i	−0.107187	−	0.0210999i
$603$	−3.79015	+	4.83513i	−0.154347	+	0.196902i
$604$	−3.50781	+	8.56455i	−0.142731	+	0.348487i
$605$		0			0
$606$	−17.0659	+	4.51461i	−0.693253	+	0.183393i
$607$	27.4478			1.11407			0.557036	−	0.830489i	$-0.311939\pi$
$607$	27.4478			1.11407			0.557036	+	0.830489i	$0.311939\pi$
$608$	23.7342	−	16.2015i	0.962549	−	0.657057i
$609$	−30.8062	+	14.9946i	−1.24833	+	0.607611i
$610$		0			0
$611$	−16.8293			−0.680840
$612$	4.31926	−	2.45720i	0.174596	−	0.0993264i
$613$			20.8062i			0.840356i	0.907442	+	0.420178i	$0.138032\pi$
$613$			20.8062i			0.840356i	−0.907442	+	0.420178i	$0.861968\pi$
$614$	−28.3057	−	5.57201i	−1.14233	−	0.224868i
$615$		0			0
$616$	−35.4031	−	23.3521i	−1.42643	−	0.940881i
$617$	−18.3074			−0.737030			−0.368515	−	0.929622i	$-0.620134\pi$
$617$	−18.3074			−0.737030			−0.368515	+	0.929622i	$0.620134\pi$
$618$	−2.56573	−	9.69882i	−0.103209	−	0.390144i
$619$			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
$622$	−23.3521	−	4.59688i	−0.936332	−	0.184318i
$623$		−	16.8293i		−	0.674251i
$624$	17.7402	+	5.96729i	0.710178	+	0.238883i
$625$		0			0
$626$	6.20087	−	31.5003i	0.247837	−	1.25901i
$627$	33.2858	−	16.2015i	1.32931	−	0.647025i
$628$	6.14360	−	15.0000i	0.245156	−	0.598565i
$629$		−	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	$-0.0168551\pi$
$632$	−11.1007	+	16.8293i	−0.441561	+	0.669433i
$633$	−22.0778	+	10.7461i	−0.877512	+	0.427119i
$634$	41.6125	+	8.19146i	1.65264	+	0.325324i
$635$		0			0
$636$	−1.23449	−	19.1873i	−0.0489507	−	0.760824i
$637$		−	15.4031i		−	0.610294i
$638$	6.37855	−	32.4030i	0.252529	−	1.28285i
$639$	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	$0.698665\pi$
$642$	−44.6408	+	11.8093i	−1.76183	+	0.466076i
$643$	22.2885			0.878971			0.439485	−	0.898250i	$-0.355161\pi$
$643$	22.2885			0.878971			0.439485	+	0.898250i	$0.355161\pi$
$644$	2.95170	−	7.20677i	0.116313	−	0.283986i
$645$		0			0
$646$	−1.14922	+	5.83802i	−0.0452154	+	0.229694i
$647$		−	2.18518i		−	0.0859082i	−0.999077	−	0.0429541i	$-0.986323\pi$
$647$		−	2.18518i		−	0.0859082i	0.999077	−	0.0429541i	$-0.0136769\pi$
$648$	8.53635	−	23.9819i	0.335339	−	0.942097i
$649$		0			0
$650$		0			0
$651$	−36.6103	+	17.8196i	−1.43487	+	0.698406i
$652$	−9.40194	−	3.85078i	−0.368208	−	0.150808i
$653$	7.78781			0.304761			0.152380	−	0.988322i	$-0.451306\pi$
$653$	7.78781			0.304761			0.152380	+	0.988322i	$0.451306\pi$
$654$	−5.45101	−	20.6056i	−0.213151	−	0.805742i
$655$		0			0
$656$	−28.8234	+	29.2845i	−1.12537	+	1.14337i
$657$	18.1839	+	14.2539i	0.709420	+	0.556098i
$658$	−6.06424	+	30.8062i	−0.236409	+	1.20095i
$659$	−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	$0.613839\pi$
$662$	8.20192	−	41.6656i	0.318777	−	1.61938i
$663$	−3.48457	+	1.69607i	−0.135329	+	0.0658700i
$664$	−4.85078	+	7.35408i	−0.188247	+	0.285393i
$665$		0			0
$666$	−14.9701	−	17.3604i	−0.580079	−	0.672702i
$667$	6.06424			0.234808
$668$	−2.48465	+	6.06643i	−0.0961339	+	0.234717i
$669$	11.8953	+	24.4388i	0.459899	+	0.944860i
$670$		0			0
$671$	2.95170			0.113949
$672$	17.3157	−	30.3235i	0.667968	−	1.16976i
$673$			0.806248i			0.0310786i	0.999879	+	0.0155393i	$0.00494651\pi$
$673$			0.806248i			0.0310786i	−0.999879	+	0.0155393i	$0.995053\pi$
$674$	−0.110112	+	0.559369i	−0.00424137	+	0.0215461i
$675$		0			0
$676$	10.5523	+	4.32196i	0.405859	+	0.166229i
$677$	−3.89391			−0.149655			−0.0748275	−	0.997196i	$-0.523841\pi$
$677$	−3.89391			−0.149655			−0.0748275	+	0.997196i	$0.523841\pi$
$678$	−9.91203	−	37.4689i	−0.380669	−	1.43898i
$679$			28.8845i			1.10849i
$680$		0			0
$681$	18.2094	−	8.86320i	0.697785	−	0.339639i
$682$	7.58030	−	38.5078i	0.290265	−	1.47454i
$683$		−	19.9440i		−	0.763137i	−0.924341	−	0.381568i	$-0.875384\pi$
$683$		−	19.9440i		−	0.763137i	0.924341	−	0.381568i	$-0.124616\pi$
$684$	15.0716	+	26.4929i	0.576277	+	1.01298i
$685$		0			0
$686$	6.42110	+	1.26400i	0.245159	+	0.0482597i
$687$	−6.59605	−	13.5515i	−0.251655	−	0.517023i
$688$	1.51606	+	1.49219i	0.0577992	+	0.0568892i
$689$			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	$-0.116428\pi$
$692$	27.7517	+	11.3663i	1.05496	+	0.432084i
$693$	27.7517	−	35.4031i	1.05420	−	1.34485i
$694$	−3.65703	+	18.5777i	−0.138819	+	0.705198i
$695$		0			0
$696$	26.9611	+	3.52799i	1.02196	+	0.133728i
$697$		−	8.50781i		−	0.322256i
$698$	16.9415	+	3.33496i	0.641247	+	0.126230i
$699$	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	$0.824408\pi$
$702$	−7.84438	+	18.2368i	−0.296067	+	0.688304i
$703$	27.4478			1.03521
$704$	13.2498	+	30.9410i	0.499370	+	1.16613i
$705$		0			0
$706$	40.8062	+	8.03275i	1.53576	+	0.302317i
$707$		−	25.6844i		−	0.965961i
$708$		0			0
$709$	11.2984			0.424322			0.212161	−	0.977235i	$-0.431950\pi$
$709$	11.2984			0.424322			0.212161	+	0.977235i	$0.431950\pi$
$710$		0			0
$711$	−16.8293	−	13.1921i	−0.631148	−	0.494742i
$712$	−7.35408	+	11.1492i	−0.275606	+	0.417835i
$713$	7.20677			0.269896
$714$	1.84906	+	6.98971i	0.0691994	+	0.261583i
$715$		0			0
$716$	−28.8234	−	11.8053i	−1.07718	−	0.441185i
$717$	4.14108	+	8.50781i	0.154651	+	0.317730i
$718$	50.7999	+	10.0000i	1.89583	+	0.373197i
$719$	−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
$722$	−9.44424	−	1.85911i	−0.351478	−	0.0691889i
$723$	5.30621	+	10.9016i	0.197340	+	0.405434i
$724$	−39.8062	−	16.3036i	−1.47939	−	0.605917i
$725$		0			0
$726$	4.19813	+	15.8695i	0.155807	+	0.588973i
$727$	−45.1087			−1.67299			−0.836495	−	0.547975i	$-0.815399\pi$
$727$	−45.1087			−1.67299			−0.836495	+	0.547975i	$0.815399\pi$
$728$	−14.9946	+	22.7327i	−0.555736	+	0.842529i
$729$	24.6125	+	11.1007i	0.911574	+	0.411136i
$730$		0			0
$731$	−0.440449			−0.0162906
$732$	0.156039	+	2.42527i	0.00576738	+	0.0896405i
$733$			20.8062i			0.768496i	0.923230	+	0.384248i	$0.125539\pi$
$733$			20.8062i			0.768496i	−0.923230	+	0.384248i	$0.874461\pi$
$734$	−4.94525	−	0.973477i	−0.182532	−	0.0359317i
$735$		0			0
$736$	−5.10469	+	3.48457i	−0.188161	+	0.128443i
$737$	8.61603			0.317376
$738$	−28.4612	−	33.0057i	−1.04767	−	1.21496i
$739$		−	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
$742$	27.4478	+	5.40312i	1.00764	+	0.198355i
$743$			29.6143i			1.08644i	0.839589	+	0.543222i	$0.182796\pi$
$743$			29.6143i			1.08644i	−0.839589	+	0.543222i	$0.817204\pi$
$744$	32.0407	+	4.19268i	1.17467	+	0.153711i
$745$		0			0
$746$	−4.72502	+	24.0030i	−0.172995	+	0.878814i
$747$	−7.35408	−	5.76469i	−0.269072	−	0.210919i
$748$	−6.44918	−	2.64141i	−0.235805	−	0.0965795i
$749$		−	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	$0.826936\pi$
$752$	17.4792	−	17.7588i	0.637402	−	0.647598i
$753$	−0.951801	−	1.95547i	−0.0346856	−	0.0712612i
$754$	−20.8062	−	4.09573i	−0.757719	−	0.149158i
$755$		0			0
$756$	30.5561	+	20.9307i	1.11132	+	0.761241i
$757$			8.91093i			0.323873i	0.986801	+	0.161937i	$0.0517740\pi$
$757$			8.91093i			0.323873i	−0.986801	+	0.161937i	$0.948226\pi$
$758$	−5.81918	+	29.5614i	−0.211362	+	1.07372i
$759$	−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	$-0.0176962\pi$
$762$	10.1635	+	38.4194i	0.368185	+	1.39179i
$763$	31.0117			1.12270
$764$	−21.0366	−	8.61603i	−0.761078	−	0.311717i
$765$		0			0
$766$	3.40312	−	17.2878i	0.122960	−	0.624634i
$767$		0			0
$768$	−24.7223	+	12.5224i	−0.892088	+	0.451862i
$769$	39.8062			1.43545			0.717725	−	0.696327i	$-0.245183\pi$
$769$	39.8062			1.43545			0.717725	+	0.696327i	$0.245183\pi$
$770$		0			0
$771$	−8.41464	−	17.2878i	−0.303046	−	0.622606i
$772$	−4.40131	+	10.7461i	−0.158407	+	0.386760i
$773$	−5.55034			−0.199632			−0.0998159	−	0.995006i	$-0.531825\pi$
$773$	−5.55034			−0.199632			−0.0998159	+	0.995006i	$0.531825\pi$
$774$	−1.70871	+	1.47344i	−0.0614182	+	0.0529616i
$775$		0			0
$776$	12.6220	−	19.1357i	0.453102	−	0.686930i
$777$	29.9892	−	14.5969i	1.07586	−	0.523660i
$778$	5.45308	−	27.7016i	0.195502	−	0.993149i
$779$	52.1839			1.86968
$780$		0			0
$781$	−47.8219			−1.71120
$782$	0.247171	−	1.25562i	0.00883881	−	0.0449010i
$783$	−6.06424	+	28.1956i	−0.216718	+	1.00763i
$784$	16.2539	+	15.9980i	0.580497	+	0.571357i
$785$		0			0
$786$	12.3916	+	46.8420i	0.441994	+	1.67080i
$787$	−14.7875			−0.527118			−0.263559	−	0.964643i	$-0.584896\pi$
$787$	−14.7875			−0.527118			−0.263559	+	0.964643i	$0.584896\pi$
$788$	17.4792	+	7.15902i	0.622672	+	0.255030i
$789$	27.9109	−	13.5853i	0.993656	−	0.483650i
$790$		0			0
$791$	56.3913			2.00504
$792$	−33.8557	+	11.3272i	−1.20301	+	0.402495i
$793$		−	1.89531i		−	0.0673046i
$794$	−7.89694	+	40.1164i	−0.280252	+	1.42368i
$795$		0			0
$796$	−11.8953	+	29.0432i	−0.421618	+	1.02941i
$797$	−4.96929			−0.176021			−0.0880107	−	0.996120i	$-0.528051\pi$
$797$	−4.96929			−0.176021			−0.0880107	+	0.996120i	$0.528051\pi$
$798$	−42.8725	+	11.3415i	−1.51767	+	0.401485i
$799$			5.15934i			0.182524i
$800$		0			0
$801$	−11.1492	−	8.73961i	−0.393938	−	0.308799i
$802$	8.41769	−	42.7617i	0.297239	−	1.50997i
$803$		−	32.4030i		−	1.14348i
$804$	0.455480	+	7.07938i	0.0160635	+	0.249670i
$805$		0			0
$806$	−24.7262	−	4.86738i	−0.870944	−	0.171446i
$807$	−23.3521	+	11.3663i	−0.822031	+	0.400114i
$808$	−11.2236	+	17.0156i	−0.394844	+	0.598607i
$809$			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	$0.910228\pi$
$812$	−14.9946	+	36.6103i	−0.526207	+	1.28477i
$813$	38.0241	−	18.5078i	1.33357	−	0.649097i
$814$	−6.20937	+	31.5435i	−0.217638	+	1.10560i
$815$		0			0
$816$	1.82939	−	5.43861i	0.0640414	−	0.190390i
$817$		−	2.70156i		−	0.0945157i
$818$	37.7553	+	7.43217i	1.32008	+	0.259860i
$819$	−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	$0.883284\pi$
$822$	3.99578	+	15.1046i	0.139369	+	0.526834i
$823$	−37.0760			−1.29239			−0.646193	−	0.763174i	$-0.723640\pi$
$823$	−37.0760			−1.29239			−0.646193	+	0.763174i	$0.723640\pi$
$824$	−9.67027	−	6.37855i	−0.336880	−	0.222207i
$825$		0			0
$826$		0			0
$827$			14.8071i			0.514895i	0.966292	+	0.257447i	$0.0828814\pi$
$827$			14.8071i			0.514895i	−0.966292	+	0.257447i	$0.917119\pi$
$828$	−3.24156	−	5.69801i	−0.112652	−	0.198020i
$829$	−44.8062			−1.55619			−0.778093	−	0.628150i	$-0.783813\pi$
$829$	−44.8062			−1.55619			−0.778093	+	0.628150i	$0.783813\pi$
$830$		0			0
$831$	43.7693	−	21.3042i	1.51834	−	0.739034i
$832$	19.8675	−	8.50781i	0.688781	−	0.294955i
$833$	−4.72212			−0.163612
$834$	−3.59008	+	0.949721i	−0.124314	+	0.0328861i
$835$		0			0
$836$	16.2015	−	39.5570i	0.560340	−	1.36811i
$837$	−7.20677	+	33.5078i	−0.249102	+	1.15820i
$838$	−14.0295	−	2.76172i	−0.484640	−	0.0954019i
$839$	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
$842$	33.5925	+	6.61273i	1.15768	+	0.227890i
$843$	11.2236	−	5.46295i	0.386561	−	0.188154i
$844$	−10.7461	+	26.2373i	−0.369896	+	0.903125i
$845$		0			0
$846$	17.2596	+	20.0155i	0.593397	+	0.688146i
$847$	−23.8839			−0.820659
$848$	−15.8228	−	15.5737i	−0.543357	−	0.534802i
$849$	4.65703	+	9.56783i	0.159829	+	0.328367i
$850$		0			0
$851$	−5.90340			−0.202366
$852$	−2.52807	−	39.2929i	−0.0866102	−	1.34615i
$853$			37.2984i			1.27707i	0.769591	+	0.638537i	$0.220460\pi$
$853$			37.2984i			1.27707i	−0.769591	+	0.638537i	$0.779540\pi$
$854$	−3.46940	−	0.682954i	−0.118720	−	0.0233702i
$855$		0			0
$856$	−29.3586	+	44.5094i	−1.00346	+	1.52130i
$857$	12.5099			0.427331			0.213666	−	0.976907i	$-0.431460\pi$
$857$	12.5099			0.427331			0.213666	+	0.976907i	$0.431460\pi$
$858$	26.9159	−	7.12033i	0.918892	−	0.243084i
$859$		−	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
$862$	27.4478	+	5.40312i	0.934875	+	0.184031i
$863$			29.6143i			1.00808i	0.863680	+	0.504041i	$0.168154\pi$
$863$			29.6143i			1.00808i	−0.863680	+	0.504041i	$0.831846\pi$
$864$	−11.0968	−	27.2188i	−0.377521	−	0.926001i
$865$		0			0
$866$	8.52476	−	43.3056i	0.289683	−	1.47159i
$867$	−12.3665	−	25.4070i	−0.419990	−	0.862866i
$868$	−17.8196	+	43.5078i	−0.604838	+	1.47675i
$869$			29.9892i			1.01731i
$870$		0			0
$871$		−	5.53243i		−	0.187459i
$872$	−20.5449	−	13.5515i	−0.695739	−	0.458912i
$873$	19.1357	+	15.0000i	0.647644	+	0.507673i
$874$	7.70156	+	1.51606i	0.260509	+	0.0512815i
$875$		0			0
$876$	26.6239	−	1.71296i	0.899540	−	0.0578755i
$877$			48.9109i			1.65160i	0.563959	+	0.825802i	$0.309277\pi$
$877$			48.9109i			1.65160i	−0.563959	+	0.825802i	$0.690723\pi$
$878$	5.98612	−	30.4094i	0.202022	−	1.02627i
$879$	−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	$0.851647\pi$
$882$	−18.3193	+	15.7970i	−0.616843	+	0.531911i
$883$	25.2412			0.849435			0.424717	−	0.905326i	$-0.360374\pi$
$883$	25.2412			0.849435			0.424717	+	0.905326i	$0.360374\pi$
$884$	−1.69607	+	4.14108i	−0.0570451	+	0.139280i
$885$		0			0
$886$	−3.06015	+	15.5455i	−0.102808	+	0.522262i
$887$			24.9179i			0.836660i	0.908295	+	0.418330i	$0.137384\pi$
$887$			24.9179i			0.836660i	−0.908295	+	0.418330i	$0.862616\pi$
$888$	−26.2460	−	3.43442i	−0.880760	−	0.115251i
$889$	−57.8219			−1.93928
$890$		0			0
$891$	−9.04246	−	36.7704i	−0.302934	−	1.23185i
$892$	29.0432	+	11.8953i	0.972438	+	0.398285i
$893$	−31.6456			−1.05898
$894$	−3.92248	+	1.03765i	−0.131187	+	0.0347044i
$895$		0			0
$896$	−8.41464	−	39.4334i	−0.281114	−	1.31738i
$897$	2.23748	+	4.59688i	0.0747071	+	0.153485i
$898$	−5.22685	+	26.5523i	−0.174422	+	0.886063i
$899$	−36.6103			−1.22102
$900$		0			0
$901$	4.59688			0.153144
$902$	−11.8053	+	59.9708i	−0.393074	+	1.99681i
$903$	−1.43670	−	2.95170i	−0.0478105	−	0.0982264i
$904$	−37.3586	−	24.6419i	−1.24253	−	0.819577i
$905$		0			0
$906$	−10.9581	+	2.89887i	−0.364060	+	0.0963086i
$907$	−10.1600			−0.337356			−0.168678	−	0.985671i	$-0.553950\pi$
$907$	−10.1600			−0.337356			−0.168678	+	0.985671i	$0.553950\pi$
$908$	8.86320	−	21.6401i	0.294136	−	0.718152i
$909$	−17.0156	−	13.3382i	−0.564373	−	0.442399i
$910$		0			0
$911$	56.3913			1.86833			0.934163	−	0.356847i	$-0.116148\pi$
$911$	56.3913			1.86833			0.934163	+	0.356847i	$0.116148\pi$
$912$	33.3586	+	11.2208i	1.10461	+	0.371559i
$913$			13.1047i			0.433702i
$914$	−4.61491	+	23.4437i	−0.152648	+	0.775448i
$915$		0			0
$916$	−16.1047	−	6.59605i	−0.532114	−	0.217939i
$917$	−70.4980			−2.32805
$918$	5.59084	+	2.40484i	0.184525	+	0.0793717i
$919$			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
$922$	−1.96851	+	10.0000i	−0.0648294	+	0.329332i
$923$			30.7069i			1.01073i
$924$	−3.33505	−	51.8356i	−0.109715	−	1.70527i
$925$		0			0
$926$	9.89049	+	1.94695i	0.325022	+	0.0639809i
$927$	7.58030	−	9.67027i	0.248970	−	0.317613i
$928$	25.9317	−	17.7016i	0.851251	−	0.581082i
$929$			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
$932$	27.7517	+	11.3663i	0.909037	+	0.372317i
$933$	−12.7571	−	26.2094i	−0.417649	−	0.858056i
$934$	0.209373	−	1.06361i	0.00685088	−	0.0348024i
$935$		0			0
$936$	7.27332	+	21.7391i	0.237736	+	0.710563i
$937$		−	16.6125i		−	0.542707i	−0.962480	−	0.271353i	$-0.912529\pi$
$937$		−	16.6125i		−	0.542707i	0.962480	−	0.271353i	$-0.0874712\pi$
$938$	−10.1272	−	1.99355i	−0.330665	−	0.0650917i
$939$	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	$-0.279586\pi$
$942$	19.1922	−	5.07710i	0.625314	−	0.165421i
$943$	−11.2236			−0.365490
$944$		0			0
$945$		0			0
$946$	3.10469	+	0.611161i	0.100942	+	0.0198705i
$947$		−	38.7955i		−	1.26068i	−0.776318	−	0.630341i	$-0.782915\pi$
$947$		−	38.7955i		−	1.26068i	0.776318	−	0.630341i	$-0.217085\pi$
$948$	−24.6406	+	1.58536i	−0.800291	+	0.0514899i
$949$	−20.8062			−0.675399
$950$		0			0
$951$	22.7327	+	46.7041i	0.737158	+	1.51448i
$952$	6.96914	+	4.59688i	0.225871	+	0.148986i
$953$	−21.9542			−0.711166			−0.355583	−	0.934645i	$-0.615718\pi$
$953$	−21.9542			−0.711166			−0.355583	+	0.934645i	$0.615718\pi$
$954$	17.8334	−	15.3780i	0.577378	−	0.497880i
$955$		0			0
$956$	10.1107	+	4.14108i	0.327004	+	0.133932i
$957$	36.3677	−	17.7016i	1.17560	−	0.572210i
$958$	−58.3802	−	11.4922i	−1.88618	−	0.371296i
$959$	−22.7327			−0.734077
$960$		0			0
$961$	−12.5078			−0.403478
$962$	20.2544	+	3.98710i	0.653028	+	0.128549i
$963$	−44.5094	−	34.8899i	−1.43429	−	1.12431i
$964$	12.9555	+	5.30621i	0.417268	+	0.170902i
$965$		0			0
$966$	9.22089	−	2.43930i	0.296677	−	0.0784832i
$967$	−47.7677			−1.53611			−0.768053	−	0.640386i	$-0.778774\pi$
$967$	−47.7677			−1.53611			−0.768053	+	0.640386i	$0.778774\pi$
$968$	15.8228	+	10.4368i	0.508564	+	0.335451i
$969$	−6.55234	+	3.18928i	−0.210492	+	0.102454i
$970$		0			0
$971$	−21.4771			−0.689232			−0.344616	−	0.938744i	$-0.611991\pi$
$971$	−21.4771			−0.689232			−0.344616	+	0.938744i	$0.611991\pi$
$972$	29.7344	−	9.37359i	0.953732	−	0.300658i
$973$		−	5.40312i		−	0.173216i
$974$	47.2387	+	9.29898i	1.51363	+	0.297959i
$975$		0			0
$976$	2.00000	+	1.96851i	0.0640184	+	0.0630105i
$977$	−28.5799			−0.914352			−0.457176	−	0.889376i	$-0.651139\pi$
$977$	−28.5799			−0.914352			−0.457176	+	0.889376i	$0.651139\pi$
$978$	−3.18231	−	12.0296i	−0.101759	−	0.384663i
$979$			19.8675i			0.634968i
$980$		0			0
$981$	16.1047	−	20.5449i	0.514183	−	0.655949i
$982$	−23.3521	−	4.59688i	−0.745194	−	0.146692i
$983$			57.9243i			1.84750i	0.382998	+	0.923749i	$0.374892\pi$
$983$			57.9243i			1.84750i	−0.382998	+	0.923749i	$0.625108\pi$
$984$	−49.8992	−	6.52954i	−1.59073	−	0.208154i
$985$		0			0
$986$	−1.25562	+	6.37855i	−0.0399872	+	0.203135i
$987$	−34.5756	+	16.8293i	−1.10055	+	0.535682i
$988$	−25.3999	−	10.4031i	−0.808079	−	0.330967i
$989$			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	$-0.220883\pi$
$992$	30.8174	−	21.0366i	0.978453	−	0.667913i
$993$	46.7638	−	22.7617i	1.48400	−	0.722321i
$994$	56.2094	+	11.0649i	1.78285	+	0.350956i
$995$		0			0
$996$	−10.7675	+	0.692770i	−0.341181	+	0.0219512i
$997$		−	34.5969i		−	1.09569i	−0.836579	−	0.547847i	$-0.815448\pi$
$997$		−	34.5969i		−	1.09569i	0.836579	−	0.547847i	$-0.184552\pi$
$998$	−6.27664	+	31.8853i	−0.198684	+	1.00931i
$999$	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.h.c.299.16		16
3.2	odd	2	inner	300.2.h.c.299.2		16
4.3	odd	2	inner	300.2.h.c.299.13		16
5.2	odd	4		300.2.e.d.251.4	yes	8
5.3	odd	4		300.2.e.e.251.5	yes	8
5.4	even	2	inner	300.2.h.c.299.1		16
12.11	even	2	inner	300.2.h.c.299.3		16
15.2	even	4		300.2.e.d.251.5	yes	8
15.8	even	4		300.2.e.e.251.4	yes	8
15.14	odd	2	inner	300.2.h.c.299.15		16
20.3	even	4		300.2.e.e.251.3	yes	8
20.7	even	4		300.2.e.d.251.6	yes	8
20.19	odd	2	inner	300.2.h.c.299.4		16
60.23	odd	4		300.2.e.e.251.6	yes	8
60.47	odd	4		300.2.e.d.251.3	✓	8
60.59	even	2	inner	300.2.h.c.299.14		16

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

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.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 + 0.758030i) q^{4} +(0.626440 + 2.36803i) q^{6} -3.56393 q^{7} +(2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} +O(q^{10})\)	\(q+(1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 + 0.758030i) q^{4} +(0.626440 + 2.36803i) q^{6} -3.56393 q^{7} +(2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} +4.20732 q^{11} +(0.222417 + 3.45695i) q^{12} -2.70156i q^{13} +(-4.94525 - 0.973477i) q^{14} +(2.85078 + 2.80590i) q^{16} -0.828216 q^{17} +(-3.21303 + 2.77064i) q^{18} -5.07999i q^{19} +(-2.70156 - 5.55034i) q^{21} +(5.83802 + 1.14922i) q^{22} +1.09259i q^{23} +(-0.635635 + 4.85757i) q^{24} +(0.737925 - 3.74865i) q^{26} +(-5.07999 - 1.09259i) q^{27} +(-6.59605 - 2.70156i) q^{28} -5.55034i q^{29} -6.59605i q^{31} +(3.18928 + 4.67210i) q^{32} +(3.18928 + 6.55234i) q^{33} +(-1.14922 - 0.226225i) q^{34} +(-5.21515 + 2.96686i) q^{36} +5.40312i q^{37} +(1.38758 - 7.04891i) q^{38} +(4.20732 - 2.04787i) q^{39} +10.2725i q^{41} +(-2.23259 - 8.43949i) q^{42} +0.531805 q^{43} +(7.78683 + 3.18928i) q^{44} +(-0.298438 + 1.51606i) q^{46} -6.22947i q^{47} +(-2.20883 + 6.56666i) q^{48} +5.70156 q^{49} +(-0.627812 - 1.28984i) q^{51} +(2.04787 - 5.00000i) q^{52} -5.55034 q^{53} +(-6.75047 - 2.90364i) q^{54} +(-8.41464 - 5.55034i) q^{56} +(7.91140 - 3.85078i) q^{57} +(1.51606 - 7.70156i) q^{58} +0.701562 q^{61} +(1.80169 - 9.15257i) q^{62} +(6.59605 - 8.41464i) q^{63} +(3.14922 + 7.35408i) q^{64} +(2.63564 + 9.96307i) q^{66} +2.04787 q^{67} +(-1.53285 - 0.627812i) q^{68} +(-1.70156 + 0.828216i) q^{69} -11.3663 q^{71} +(-8.04684 + 2.69226i) q^{72} -7.70156i q^{73} +(-1.47585 + 7.49729i) q^{74} +(3.85078 - 9.40194i) q^{76} -14.9946 q^{77} +(6.39738 - 1.69237i) q^{78} +7.12785i q^{79} +(-2.14922 - 8.73961i) q^{81} +(-2.80590 + 14.2539i) q^{82} +3.11473i q^{83} +(-0.792678 - 12.3203i) q^{84} +(0.737925 + 0.145261i) q^{86} +(8.64391 - 4.20732i) q^{87} +(9.93375 + 6.55234i) q^{88} +4.72212i q^{89} +9.62817i q^{91} +(-0.828216 + 2.02214i) q^{92} +(10.2725 - 5.00000i) q^{93} +(1.70156 - 8.64391i) q^{94} +(-4.85860 + 8.50846i) q^{96} -8.10469i q^{97} +(7.91140 + 1.55737i) q^{98} +(-7.78683 + 9.93375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	\( 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9} + 20 q^{16} + 8 q^{21} - 26 q^{24} - 44 q^{34} - 42 q^{36} - 56 q^{46} + 40 q^{49} + 56 q^{54} - 40 q^{61} + 76 q^{64} + 58 q^{66} + 24 q^{69} + 36 q^{76} - 60 q^{81} - 80 q^{84} - 24 q^{94} - 78 q^{96}+O(q^{100}) \) 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 + 20 * q^16 + 8 * q^21 - 26 * q^24 - 44 * q^34 - 42 * q^36 - 56 * q^46 + 40 * q^49 + 56 * q^54 - 40 * q^61 + 76 * q^64 + 58 * q^66 + 24 * q^69 + 36 * q^76 - 60 * q^81 - 80 * q^84 - 24 * q^94 - 78 * q^96

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