LMFDB - Embedded newform 600.2.k.e.301.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(301,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.8
Root			$1.41216 - 0.0762223i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.e.301.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29150 + 0.576222i) q^{2} -1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} +1.97676 q^{7} +(0.867721 + 2.69204i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.29150 + 0.576222i) q^{2} -1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} +1.97676 q^{7} +(0.867721 + 2.69204i) q^{8} -1.00000 q^{9} -1.43055i q^{11} +(1.48838 - 1.33594i) q^{12} -0.241319i q^{13} +(2.55298 + 1.13905i) q^{14} +(-0.430552 + 3.97676i) q^{16} +7.38407 q^{17} +(-1.29150 - 0.576222i) q^{18} +3.04033i q^{19} -1.97676i q^{21} +(0.824316 - 1.84756i) q^{22} -0.874337 q^{23} +(2.69204 - 0.867721i) q^{24} +(0.139054 - 0.311664i) q^{26} +1.00000i q^{27} +(2.64082 + 2.94217i) q^{28} -9.07918i q^{29} -7.44764 q^{31} +(-2.84756 + 4.88789i) q^{32} -1.43055 q^{33} +(9.53652 + 4.25487i) q^{34} +(-1.33594 - 1.48838i) q^{36} +8.81463i q^{37} +(-1.75191 + 3.92658i) q^{38} -0.241319 q^{39} -1.91319 q^{41} +(1.13905 - 2.55298i) q^{42} -11.2452i q^{43} +(2.12921 - 1.91113i) q^{44} +(-1.12921 - 0.503813i) q^{46} +3.34374 q^{47} +(3.97676 + 0.430552i) q^{48} -3.09242 q^{49} -7.38407i q^{51} +(0.359175 - 0.322387i) q^{52} +9.20632i q^{53} +(-0.576222 + 1.29150i) q^{54} +(1.71528 + 5.32151i) q^{56} +3.04033 q^{57} +(5.23163 - 11.7258i) q^{58} -6.43616i q^{59} +4.57331i q^{61} +(-9.61862 - 4.29150i) q^{62} -1.97676 q^{63} +(-6.49412 + 4.67187i) q^{64} +(-1.84756 - 0.824316i) q^{66} +4.86671i q^{67} +(9.86465 + 10.9903i) q^{68} +0.874337i q^{69} -8.21808 q^{71} +(-0.867721 - 2.69204i) q^{72} +4.12714 q^{73} +(-5.07918 + 11.3841i) q^{74} +(-4.52517 + 4.06169i) q^{76} -2.82786i q^{77} +(-0.311664 - 0.139054i) q^{78} -13.6757 q^{79} +1.00000 q^{81} +(-2.47088 - 1.10242i) q^{82} -12.3320i q^{83} +(2.94217 - 2.64082i) q^{84} +(6.47972 - 14.5231i) q^{86} -9.07918 q^{87} +(3.85110 - 1.24132i) q^{88} -8.08066 q^{89} -0.477031i q^{91} +(-1.16806 - 1.30135i) q^{92} +7.44764i q^{93} +(4.31844 + 1.92674i) q^{94} +(4.88789 + 2.84756i) q^{96} -10.6757 q^{97} +(-3.99385 - 1.78192i) q^{98} +1.43055i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9	$ 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} - 2 q^{18} - 12 q^{22} - 8 q^{23} - 8 q^{24} - 2 q^{26} + 4 q^{28} + 8 q^{31} - 28 q^{32} + 12 q^{34} - 4 q^{36} - 30 q^{38} + 6 q^{42} - 12 q^{44} + 20 q^{46} + 8 q^{48} + 20 q^{52} - 2 q^{54} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 30 q^{62} + 8 q^{63} - 32 q^{64} - 20 q^{66} + 28 q^{68} - 40 q^{71} + 4 q^{72} + 16 q^{73} + 8 q^{74} - 20 q^{76} + 22 q^{78} - 16 q^{79} + 8 q^{81} + 24 q^{82} + 24 q^{84} - 18 q^{86} - 24 q^{87} + 8 q^{88} + 36 q^{92} - 4 q^{94} + 12 q^{96} + 8 q^{97} + 48 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 - 2 * q^18 - 12 * q^22 - 8 * q^23 - 8 * q^24 - 2 * q^26 + 4 * q^28 + 8 * q^31 - 28 * q^32 + 12 * q^34 - 4 * q^36 - 30 * q^38 + 6 * q^42 - 12 * q^44 + 20 * q^46 + 8 * q^48 + 20 * q^52 - 2 * q^54 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 30 * q^62 + 8 * q^63 - 32 * q^64 - 20 * q^66 + 28 * q^68 - 40 * q^71 + 4 * q^72 + 16 * q^73 + 8 * q^74 - 20 * q^76 + 22 * q^78 - 16 * q^79 + 8 * q^81 + 24 * q^82 + 24 * q^84 - 18 * q^86 - 24 * q^87 + 8 * q^88 + 36 * q^92 - 4 * q^94 + 12 * q^96 + 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	1.29150	+	0.576222i	0.913227	+	0.407451i
$2$	1.29150	+	0.576222i	0.913227	+	0.407451i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.33594	+	1.48838i	0.667968	+	0.744190i
$5$		0			0
$5$		0			0
$6$	0.576222	−	1.29150i	0.235242	−	0.527252i
$7$	1.97676			0.747145			0.373573	−	0.927601i	$-0.378133\pi$
$7$	1.97676			0.747145			0.373573	+	0.927601i	$0.378133\pi$
$8$	0.867721	+	2.69204i	0.306786	+	0.951779i
$9$	−1.00000			−0.333333
$10$		0			0
$11$		−	1.43055i		−	0.431328i	−0.976468	−	0.215664i	$-0.930808\pi$
$11$		−	1.43055i		−	0.431328i	0.976468	−	0.215664i	$-0.0691915\pi$
$12$	1.48838	−	1.33594i	0.429658	−	0.385651i
$13$		−	0.241319i		−	0.0669300i	−0.999440	−	0.0334650i	$-0.989346\pi$
$13$		−	0.241319i		−	0.0669300i	0.999440	−	0.0334650i	$-0.0106542\pi$
$14$	2.55298	+	1.13905i	0.682313	+	0.304425i
$15$		0			0
$16$	−0.430552	+	3.97676i	−0.107638	+	0.994190i
$17$	7.38407			1.79090			0.895450	−	0.445161i	$-0.146854\pi$
$17$	7.38407			1.79090			0.895450	+	0.445161i	$0.146854\pi$
$18$	−1.29150	−	0.576222i	−0.304409	−	0.135817i
$19$			3.04033i			0.697500i	0.937216	+	0.348750i	$0.113394\pi$
$19$			3.04033i			0.697500i	−0.937216	+	0.348750i	$0.886606\pi$
$20$		0			0
$21$		−	1.97676i		−	0.431365i
$22$	0.824316	−	1.84756i	0.175745	−	0.393900i
$23$	−0.874337			−0.182312			−0.0911560	−	0.995837i	$-0.529056\pi$
$23$	−0.874337			−0.182312			−0.0911560	+	0.995837i	$0.529056\pi$
$24$	2.69204	−	0.867721i	0.549510	−	0.177123i
$25$		0			0
$26$	0.139054	−	0.311664i	0.0272707	−	0.0611223i
$27$			1.00000i			0.192450i
$28$	2.64082	+	2.94217i	0.499069	+	0.556018i
$29$		−	9.07918i		−	1.68596i	−0.537943	−	0.842981i	$-0.680799\pi$
$29$		−	9.07918i		−	1.68596i	0.537943	−	0.842981i	$-0.319201\pi$
$30$		0			0
$31$	−7.44764			−1.33764			−0.668818	−	0.743426i	$-0.733200\pi$
$31$	−7.44764			−1.33764			−0.668818	+	0.743426i	$0.733200\pi$
$32$	−2.84756	+	4.88789i	−0.503381	+	0.864064i
$33$	−1.43055			−0.249027
$34$	9.53652	+	4.25487i	1.63550	+	0.729704i
$35$		0			0
$36$	−1.33594	−	1.48838i	−0.222656	−	0.248063i
$37$			8.81463i			1.44912i	0.689214	+	0.724558i	$0.257956\pi$
$37$			8.81463i			1.44912i	−0.689214	+	0.724558i	$0.742044\pi$
$38$	−1.75191	+	3.92658i	−0.284197	+	0.636976i
$39$	−0.241319			−0.0386420
$40$		0			0
$41$	−1.91319			−0.298790			−0.149395	−	0.988778i	$-0.547733\pi$
$41$	−1.91319			−0.298790			−0.149395	+	0.988778i	$0.547733\pi$
$42$	1.13905	−	2.55298i	0.175760	−	0.393934i
$43$		−	11.2452i		−	1.71487i	−0.514589	−	0.857437i	$-0.672056\pi$
$43$		−	11.2452i		−	1.71487i	0.514589	−	0.857437i	$-0.327944\pi$
$44$	2.12921	−	1.91113i	0.320990	−	0.288113i
$45$		0			0
$46$	−1.12921	−	0.503813i	−0.166492	−	0.0742831i
$47$	3.34374			0.487735			0.243867	−	0.969809i	$-0.421584\pi$
$47$	3.34374			0.487735			0.243867	+	0.969809i	$0.421584\pi$
$48$	3.97676	+	0.430552i	0.573996	+	0.0621448i
$49$	−3.09242			−0.441774
$50$		0			0
$51$		−	7.38407i		−	1.03398i
$52$	0.359175	−	0.322387i	0.0498086	−	0.0447071i
$53$			9.20632i			1.26459i	0.774729	+	0.632293i	$0.217886\pi$
$53$			9.20632i			1.26459i	−0.774729	+	0.632293i	$0.782114\pi$
$54$	−0.576222	+	1.29150i	−0.0784139	+	0.175751i
$55$		0			0
$56$	1.71528	+	5.32151i	0.229213	+	0.711117i
$57$	3.04033			0.402702
$58$	5.23163	−	11.7258i	0.686946	−	1.53967i
$59$		−	6.43616i		−	0.837917i	−0.908005	−	0.418958i	$-0.862395\pi$
$59$		−	6.43616i		−	0.837917i	0.908005	−	0.418958i	$-0.137605\pi$
$60$		0			0
$61$			4.57331i			0.585552i	0.956181	+	0.292776i	$0.0945790\pi$
$61$			4.57331i			0.585552i	−0.956181	+	0.292776i	$0.905421\pi$
$62$	−9.61862	−	4.29150i	−1.22157	−	0.545021i
$63$	−1.97676			−0.249048
$64$	−6.49412	+	4.67187i	−0.811765	+	0.583984i
$65$		0			0
$66$	−1.84756	−	0.824316i	−0.227418	−	0.101466i
$67$			4.86671i			0.594563i	0.954790	+	0.297282i	$0.0960801\pi$
$67$			4.86671i			0.594563i	−0.954790	+	0.297282i	$0.903920\pi$
$68$	9.86465	+	10.9903i	1.19626	+	1.33277i
$69$			0.874337i			0.105258i
$70$		0			0
$71$	−8.21808			−0.975307			−0.487653	−	0.873037i	$-0.662147\pi$
$71$	−8.21808			−0.975307			−0.487653	+	0.873037i	$0.662147\pi$
$72$	−0.867721	−	2.69204i	−0.102262	−	0.317260i
$73$	4.12714			0.483045			0.241523	−	0.970395i	$-0.422353\pi$
$73$	4.12714			0.483045			0.241523	+	0.970395i	$0.422353\pi$
$74$	−5.07918	+	11.3841i	−0.590443	+	1.32337i
$75$		0			0
$76$	−4.52517	+	4.06169i	−0.519072	+	0.465907i
$77$		−	2.82786i		−	0.322264i
$78$	−0.311664	−	0.139054i	−0.0352890	−	0.0157447i
$79$	−13.6757			−1.53864			−0.769320	−	0.638864i	$-0.779405\pi$
$79$	−13.6757			−1.53864			−0.769320	+	0.638864i	$0.779405\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−2.47088	−	1.10242i	−0.272863	−	0.121742i
$83$		−	12.3320i		−	1.35361i	−0.736162	−	0.676806i	$-0.763364\pi$
$83$		−	12.3320i		−	1.35361i	0.736162	−	0.676806i	$-0.236636\pi$
$84$	2.94217	−	2.64082i	0.321017	−	0.288138i
$85$		0			0
$86$	6.47972	−	14.5231i	0.698726	−	1.56607i
$87$	−9.07918			−0.973391
$88$	3.85110	−	1.24132i	0.410528	−	0.132325i
$89$	−8.08066			−0.856548			−0.428274	−	0.903649i	$-0.640878\pi$
$89$	−8.08066			−0.856548			−0.428274	+	0.903649i	$0.640878\pi$
$90$		0			0
$91$		−	0.477031i		−	0.0500064i
$92$	−1.16806	−	1.30135i	−0.121779	−	0.135675i
$93$			7.44764i			0.772285i
$94$	4.31844	+	1.92674i	0.445413	+	0.198728i
$95$		0			0
$96$	4.88789	+	2.84756i	0.498868	+	0.290627i
$97$	−10.6757			−1.08396			−0.541978	−	0.840393i	$-0.682324\pi$
$97$	−10.6757			−1.08396			−0.541978	+	0.840393i	$0.682324\pi$
$98$	−3.99385	−	1.78192i	−0.403440	−	0.180001i
$99$			1.43055i			0.143776i
$100$		0			0
$101$			13.2063i			1.31408i	0.753856	+	0.657039i	$0.228191\pi$
$101$			13.2063i			1.31408i	−0.753856	+	0.657039i	$0.771809\pi$
$102$	4.25487	−	9.53652i	0.421295	−	0.944256i
$103$	−19.4244			−1.91394			−0.956972	−	0.290181i	$-0.906284\pi$
$103$	−19.4244			−1.91394			−0.956972	+	0.290181i	$0.906284\pi$
$104$	0.649641	−	0.209398i	0.0637025	−	0.0205331i
$105$		0			0
$106$	−5.30489	+	11.8900i	−0.515256	+	1.15485i
$107$		−	14.8085i		−	1.43159i	−0.698311	−	0.715795i	$-0.746065\pi$
$107$		−	14.8085i		−	1.43159i	0.698311	−	0.715795i	$-0.253935\pi$
$108$	−1.48838	+	1.33594i	−0.143219	+	0.128550i
$109$		−	15.2296i		−	1.45873i	−0.684126	−	0.729364i	$-0.739816\pi$
$109$		−	15.2296i		−	1.45873i	0.684126	−	0.729364i	$-0.260184\pi$
$110$		0			0
$111$	8.81463			0.836647
$112$	−0.851098	+	7.86110i	−0.0804212	+	0.742804i
$113$	1.13890			0.107138			0.0535692	−	0.998564i	$-0.482940\pi$
$113$	1.13890			0.107138			0.0535692	+	0.998564i	$0.482940\pi$
$114$	3.92658	+	1.75191i	0.367758	+	0.164081i
$115$		0			0
$116$	13.5133	−	12.1292i	1.25468	−	1.12617i
$117$			0.241319i			0.0223100i
$118$	3.70866	−	8.31229i	0.341410	−	0.765208i
$119$	14.5965			1.33806
$120$		0			0
$121$	8.95352			0.813956
$122$	−2.63524	+	5.90642i	−0.238583	+	0.534742i
$123$			1.91319i			0.172507i
$124$	−9.94957	−	11.0849i	−0.893498	−	0.995456i
$125$		0			0
$126$	−2.55298	−	1.13905i	−0.227438	−	0.101475i
$127$	−2.43616			−0.216174			−0.108087	−	0.994141i	$-0.534473\pi$
$127$	−2.43616			−0.216174			−0.108087	+	0.994141i	$0.534473\pi$
$128$	−11.0792	+	2.29166i	−0.979271	+	0.202556i
$129$	−11.2452			−0.990083
$130$		0			0
$131$		−	6.90143i		−	0.602981i	−0.953469	−	0.301491i	$-0.902516\pi$
$131$		−	6.90143i		−	0.602981i	0.953469	−	0.301491i	$-0.0974842\pi$
$132$	−1.91113	−	2.12921i	−0.166342	−	0.185324i
$133$			6.01001i			0.521134i
$134$	−2.80431	+	6.28535i	−0.242255	+	0.542972i
$135$		0			0
$136$	6.40731	+	19.8782i	0.549423	+	1.70454i
$137$	5.39022			0.460518			0.230259	−	0.973129i	$-0.426043\pi$
$137$	5.39022			0.460518			0.230259	+	0.973129i	$0.426043\pi$
$138$	−0.503813	+	1.12921i	−0.0428874	+	0.0961243i
$139$			17.4244i			1.47792i	0.673750	+	0.738959i	$0.264682\pi$
$139$			17.4244i			1.47792i	−0.673750	+	0.738959i	$0.735318\pi$
$140$		0			0
$141$		−	3.34374i		−	0.281594i
$142$	−10.6136	−	4.73544i	−0.890677	−	0.397389i
$143$	−0.345220			−0.0288687
$144$	0.430552	−	3.97676i	0.0358793	−	0.331397i
$145$		0			0
$146$	5.33019	+	2.37815i	0.441130	+	0.196817i
$147$			3.09242i			0.255058i
$148$	−13.1195	+	11.7758i	−1.07842	+	0.967962i
$149$		−	2.28551i		−	0.187236i	−0.995608	−	0.0936180i	$-0.970157\pi$
$149$		−	2.28551i		−	0.187236i	0.995608	−	0.0936180i	$-0.0298432\pi$
$150$		0			0
$151$	6.66425			0.542329			0.271164	−	0.962533i	$-0.412591\pi$
$151$	6.66425			0.542329			0.271164	+	0.962533i	$0.412591\pi$
$152$	−8.18468	+	2.63816i	−0.663865	+	0.213983i
$153$	−7.38407			−0.596967
$154$	1.62948	−	3.65217i	0.131307	−	0.294301i
$155$		0			0
$156$	−0.322387	−	0.359175i	−0.0258116	−	0.0287570i
$157$			17.4144i			1.38982i	0.719097	+	0.694910i	$0.244556\pi$
$157$			17.4144i			1.38982i	−0.719097	+	0.694910i	$0.755444\pi$
$158$	−17.6622	−	7.88026i	−1.40513	−	0.626920i
$159$	9.20632			0.730109
$160$		0			0
$161$	−1.72836			−0.136214
$162$	1.29150	+	0.576222i	0.101470	+	0.0452723i
$163$			4.66187i			0.365145i	0.983192	+	0.182573i	$0.0584425\pi$
$163$			4.66187i			0.365145i	−0.983192	+	0.182573i	$0.941557\pi$
$164$	−2.55590	−	2.84756i	−0.199582	−	0.222357i
$165$		0			0
$166$	7.10597	−	15.9267i	0.551530	−	1.23615i
$167$	0.137419			0.0106338			0.00531690	−	0.999986i	$-0.498308\pi$
$167$	0.137419			0.0106338			0.00531690	+	0.999986i	$0.498308\pi$
$168$	5.32151	−	1.71528i	0.410564	−	0.132336i
$169$	12.9418			0.995520
$170$		0			0
$171$		−	3.04033i		−	0.232500i
$172$	16.7371	−	15.0228i	1.27619	−	1.14548i
$173$		−	3.96675i		−	0.301587i	−0.988565	−	0.150793i	$-0.951817\pi$
$173$		−	3.96675i		−	0.301587i	0.988565	−	0.150793i	$-0.0481828\pi$
$174$	−11.7258	−	5.23163i	−0.888927	−	0.396609i
$175$		0			0
$176$	5.68896	+	0.615927i	0.428822	+	0.0464272i
$177$	−6.43616			−0.483771
$178$	−10.4362	−	4.65626i	−0.782223	−	0.349001i
$179$			4.68749i			0.350359i	0.984537	+	0.175180i	$0.0560506\pi$
$179$			4.68749i			0.350359i	−0.984537	+	0.175180i	$0.943949\pi$
$180$		0			0
$181$			9.10242i			0.676578i	0.941042	+	0.338289i	$0.109848\pi$
$181$			9.10242i			0.676578i	−0.941042	+	0.338289i	$0.890152\pi$
$182$	0.274876	−	0.616084i	0.0203751	−	0.0456672i
$183$	4.57331			0.338068
$184$	−0.758681	−	2.35375i	−0.0559307	−	0.173521i
$185$		0			0
$186$	−4.29150	+	9.61862i	−0.314668	+	0.705271i
$187$		−	10.5633i		−	0.772465i
$188$	4.46702	+	4.97676i	0.325791	+	0.362968i
$189$			1.97676i			0.143788i
$190$		0			0
$191$	15.2063			1.10029			0.550145	−	0.835069i	$-0.314572\pi$
$191$	15.2063			1.10029			0.550145	+	0.835069i	$0.314572\pi$
$192$	4.67187	+	6.49412i	0.337163	+	0.468673i
$193$	20.7564			1.49408			0.747039	−	0.664780i	$-0.231475\pi$
$193$	20.7564			1.49408			0.747039	+	0.664780i	$0.231475\pi$
$194$	−13.7877	−	6.15159i	−0.989898	−	0.441659i
$195$		0			0
$196$	−4.13127	−	4.60269i	−0.295091	−	0.328764i
$197$		−	23.2508i		−	1.65655i	−0.560322	−	0.828275i	$-0.689323\pi$
$197$		−	23.2508i		−	1.65655i	0.560322	−	0.828275i	$-0.310677\pi$
$198$	−0.824316	+	1.84756i	−0.0585816	+	0.131300i
$199$	−7.21633			−0.511552			−0.255776	−	0.966736i	$-0.582331\pi$
$199$	−7.21633			−0.511552			−0.255776	+	0.966736i	$0.582331\pi$
$200$		0			0
$201$	4.86671			0.343271
$202$	−7.60978	+	17.0559i	−0.535422	+	1.20005i
$203$		−	17.9474i		−	1.25966i
$204$	10.9903	−	9.86465i	0.769476	−	0.690663i
$205$		0			0
$206$	−25.0866	−	11.1928i	−1.74787	−	0.779838i
$207$	0.874337			0.0607707
$208$	0.959669	+	0.103901i	0.0665411	+	0.00720420i
$209$	4.34935			0.300851
$210$		0			0
$211$		−	4.38407i		−	0.301812i	−0.988548	−	0.150906i	$-0.951781\pi$
$211$		−	4.38407i		−	0.301812i	0.988548	−	0.150906i	$-0.0482191\pi$
$212$	−13.7025	+	12.2991i	−0.941092	+	0.844703i
$213$			8.21808i			0.563094i
$214$	8.53298	−	19.1251i	0.583302	−	1.30737i
$215$		0			0
$216$	−2.69204	+	0.867721i	−0.183170	+	0.0590409i
$217$	−14.7222			−0.999409
$218$	8.77561	−	19.6690i	0.594360	−	1.33215i
$219$		−	4.12714i		−	0.278886i
$220$		0			0
$221$		−	1.78192i		−	0.119865i
$222$	11.3841	+	5.07918i	0.764049	+	0.340892i
$223$	4.98852			0.334056			0.167028	−	0.985952i	$-0.446583\pi$
$223$	4.98852			0.334056			0.167028	+	0.985952i	$0.446583\pi$
$224$	−5.62894	+	9.66218i	−0.376099	+	0.645582i
$225$		0			0
$226$	1.47088	+	0.656257i	0.0978416	+	0.0436536i
$227$		−	11.2569i		−	0.747149i	−0.927600	−	0.373574i	$-0.878132\pi$
$227$		−	11.2569i		−	0.747149i	0.927600	−	0.373574i	$-0.121868\pi$
$228$	4.06169	+	4.52517i	0.268992	+	0.299687i
$229$			15.8364i			1.04650i	0.852180	+	0.523249i	$0.175280\pi$
$229$			15.8364i			1.04650i	−0.852180	+	0.523249i	$0.824720\pi$
$230$		0			0
$231$	−2.82786			−0.186059
$232$	24.4415	−	7.87820i	1.60466	−	0.517229i
$233$	10.9591			0.717956			0.358978	−	0.933346i	$-0.383125\pi$
$233$	10.9591			0.717956			0.358978	+	0.933346i	$0.383125\pi$
$234$	−0.139054	+	0.311664i	−0.00909022	+	0.0203741i
$235$		0			0
$236$	9.57945	−	8.59830i	0.623569	−	0.559701i
$237$			13.6757i			0.888334i
$238$	18.8514	+	8.41086i	1.22196	+	0.545195i
$239$	17.3182			1.12022			0.560111	−	0.828418i	$-0.310758\pi$
$239$	17.3182			1.12022			0.560111	+	0.828418i	$0.310758\pi$
$240$		0			0
$241$	4.76869			0.307178			0.153589	−	0.988135i	$-0.450917\pi$
$241$	4.76869			0.307178			0.153589	+	0.988135i	$0.450917\pi$
$242$	11.5635	+	5.15922i	0.743327	+	0.331647i
$243$		−	1.00000i		−	0.0641500i
$244$	−6.80682	+	6.10964i	−0.435762	+	0.391130i
$245$		0			0
$246$	−1.10242	+	2.47088i	−0.0702879	+	0.157538i
$247$	0.733691			0.0466836
$248$	−6.46247	−	20.0493i	−0.410367	−	1.27313i
$249$	−12.3320			−0.781508
$250$		0			0
$251$			6.15837i			0.388713i	0.980931	+	0.194356i	$0.0622618\pi$
$251$			6.15837i			0.388713i	−0.980931	+	0.194356i	$0.937738\pi$
$252$	−2.64082	−	2.94217i	−0.166356	−	0.185339i
$253$			1.25079i			0.0786362i
$254$	−3.14630	−	1.40377i	−0.197416	−	0.0880804i
$255$		0			0
$256$	−15.6293	−	3.42440i	−0.976828	−	0.214025i
$257$	14.1584			0.883175			0.441587	−	0.897218i	$-0.354416\pi$
$257$	14.1584			0.883175			0.441587	+	0.897218i	$0.354416\pi$
$258$	−14.5231	−	6.47972i	−0.904170	−	0.403410i
$259$			17.4244i			1.08270i
$260$		0			0
$261$			9.07918i			0.561987i
$262$	3.97676	−	8.91319i	0.245685	−	0.550659i
$263$	15.5960			0.961691			0.480845	−	0.876805i	$-0.340330\pi$
$263$	15.5960			0.961691			0.480845	+	0.876805i	$0.340330\pi$
$264$	−1.24132	−	3.85110i	−0.0763979	−	0.237019i
$265$		0			0
$266$	−3.46310	+	7.76191i	−0.212336	+	0.475913i
$267$			8.08066i			0.494528i
$268$	−7.24352	+	6.50161i	−0.442468	+	0.397149i
$269$			11.3182i			0.690084i	0.938587	+	0.345042i	$0.112135\pi$
$269$			11.3182i			0.690084i	−0.938587	+	0.345042i	$0.887865\pi$
$270$		0			0
$271$	−6.20485			−0.376918			−0.188459	−	0.982081i	$-0.560349\pi$
$271$	−6.20485			−0.376918			−0.188459	+	0.982081i	$0.560349\pi$
$272$	−3.17923	+	29.3647i	−0.192769	+	1.78050i
$273$	−0.477031			−0.0288712
$274$	6.96146	+	3.10597i	0.420557	+	0.187638i
$275$		0			0
$276$	−1.30135	+	1.16806i	−0.0783319	+	0.0703089i
$277$		−	18.9288i		−	1.13732i	−0.822572	−	0.568661i	$-0.807462\pi$
$277$		−	18.9288i		−	1.13732i	0.822572	−	0.568661i	$-0.192538\pi$
$278$	−10.0403	+	22.5036i	−0.602179	+	1.34968i
$279$	7.44764			0.445879
$280$		0			0
$281$	−21.6231			−1.28993			−0.644963	−	0.764214i	$-0.723127\pi$
$281$	−21.6231			−1.28993			−0.644963	+	0.764214i	$0.723127\pi$
$282$	1.92674	−	4.31844i	0.114736	−	0.257159i
$283$			29.1522i			1.73292i	0.499247	+	0.866460i	$0.333610\pi$
$283$			29.1522i			1.73292i	−0.499247	+	0.866460i	$0.666390\pi$
$284$	−10.9788	−	12.2316i	−0.651473	−	0.725814i
$285$		0			0
$286$	−0.445851	−	0.198923i	−0.0263637	−	0.0117626i
$287$	−3.78192			−0.223240
$288$	2.84756	−	4.88789i	0.167794	−	0.288021i
$289$	37.5245			2.20733
$290$		0			0
$291$			10.6757i			0.625822i
$292$	5.51359	+	6.14275i	0.322659	+	0.359477i
$293$			2.32427i			0.135785i	0.997693	+	0.0678927i	$0.0216275\pi$
$293$			2.32427i			0.135785i	−0.997693	+	0.0678927i	$0.978372\pi$
$294$	−1.78192	+	3.99385i	−0.103924	+	0.232926i
$295$		0			0
$296$	−23.7293	+	7.64863i	−1.37924	+	0.444568i
$297$	1.43055			0.0830090
$298$	1.31696	−	2.95173i	0.0762895	−	0.170989i
$299$			0.210995i			0.0122021i
$300$		0			0
$301$		−	22.2290i		−	1.28126i
$302$	8.60686	+	3.84009i	0.495269	+	0.220972i
$303$	13.2063			0.758683
$304$	−12.0907	−	1.30902i	−0.693447	−	0.0750775i
$305$		0			0
$306$	−9.53652	−	4.25487i	−0.545166	−	0.243235i
$307$		−	3.52297i		−	0.201066i	−0.994934	−	0.100533i	$-0.967945\pi$
$307$		−	3.52297i		−	0.201066i	0.994934	−	0.100533i	$-0.0320549\pi$
$308$	4.20893	−	3.77784i	0.239826	−	0.215262i
$309$			19.4244i			1.10502i
$310$		0			0
$311$	−21.6757			−1.22912			−0.614559	−	0.788871i	$-0.710666\pi$
$311$	−21.6757			−1.22912			−0.614559	+	0.788871i	$0.710666\pi$
$312$	−0.209398	−	0.649641i	−0.0118548	−	0.0367787i
$313$	12.5486			0.709288			0.354644	−	0.935001i	$-0.384602\pi$
$313$	12.5486			0.709288			0.354644	+	0.935001i	$0.384602\pi$
$314$	−10.0346	+	22.4907i	−0.566283	+	1.26922i
$315$		0			0
$316$	−18.2699	−	20.3547i	−1.02776	−	1.14504i
$317$			10.8611i			0.610020i	0.952349	+	0.305010i	$0.0986599\pi$
$317$			10.8611i			0.610020i	−0.952349	+	0.305010i	$0.901340\pi$
$318$	11.8900	+	5.30489i	0.666755	+	0.297483i
$319$	−12.9882			−0.727202
$320$		0			0
$321$	−14.8085			−0.826529
$322$	−2.23217	−	0.995917i	−0.124394	−	0.0555003i
$323$			22.4500i			1.24915i
$324$	1.33594	+	1.48838i	0.0742186	+	0.0826878i
$325$		0			0
$326$	−2.68627	+	6.02079i	−0.148779	+	0.333461i
$327$	−15.2296			−0.842197
$328$	−1.66011	−	5.15038i	−0.0916645	−	0.284382i
$329$	6.60978			0.364409
$330$		0			0
$331$			1.23185i			0.0677088i	0.999427	+	0.0338544i	$0.0107783\pi$
$331$			1.23185i			0.0677088i	−0.999427	+	0.0338544i	$0.989222\pi$
$332$	18.3547	−	16.4747i	1.00734	−	0.904169i
$333$		−	8.81463i		−	0.483038i
$334$	0.177476	+	0.0791838i	0.00971107	+	0.00433275i
$335$		0			0
$336$	7.86110	+	0.851098i	0.428858	+	0.0464312i
$337$	−4.13890			−0.225460			−0.112730	−	0.993626i	$-0.535960\pi$
$337$	−4.13890			−0.225460			−0.112730	+	0.993626i	$0.535960\pi$
$338$	16.7143	+	7.45733i	0.909136	+	0.405625i
$339$		−	1.13890i		−	0.0618564i
$340$		0			0
$341$			10.6542i			0.576959i
$342$	1.75191	−	3.92658i	0.0947322	−	0.212325i
$343$	−19.9503			−1.07721
$344$	30.2724	−	9.75767i	1.63218	−	0.526098i
$345$		0			0
$346$	2.28573	−	5.12306i	0.122882	−	0.275417i
$347$			17.4586i			0.937226i	0.883404	+	0.468613i	$0.155246\pi$
$347$			17.4586i			0.937226i	−0.883404	+	0.468613i	$0.844754\pi$
$348$	−12.1292	−	13.5133i	−0.650194	−	0.724388i
$349$		−	21.2196i		−	1.13586i	−0.823078	−	0.567928i	$-0.807745\pi$
$349$		−	21.2196i		−	1.13586i	0.823078	−	0.567928i	$-0.192255\pi$
$350$		0			0
$351$	0.241319			0.0128807
$352$	6.99237	+	4.07358i	0.372695	+	0.217122i
$353$	−21.0398			−1.11984			−0.559918	−	0.828548i	$-0.689167\pi$
$353$	−21.0398			−1.11984			−0.559918	+	0.828548i	$0.689167\pi$
$354$	−8.31229	−	3.70866i	−0.441793	−	0.197113i
$355$		0			0
$356$	−10.7952	−	12.0271i	−0.572147	−	0.637435i
$357$		−	14.5965i		−	0.772531i
$358$	−2.70103	+	6.05388i	−0.142754	+	0.319957i
$359$	23.5153			1.24109			0.620546	−	0.784170i	$-0.286911\pi$
$359$	23.5153			1.24109			0.620546	+	0.784170i	$0.286911\pi$
$360$		0			0
$361$	9.75639			0.513494
$362$	−5.24502	+	11.7558i	−0.275672	+	0.617869i
$363$		−	8.95352i		−	0.469938i
$364$	0.710003	−	0.637282i	0.0372143	−	0.0334027i
$365$		0			0
$366$	5.90642	+	2.63524i	0.308733	+	0.137746i
$367$	25.4012			1.32593			0.662965	−	0.748650i	$-0.269298\pi$
$367$	25.4012			1.32593			0.662965	+	0.748650i	$0.269298\pi$
$368$	0.376448	−	3.47703i	0.0196237	−	0.181253i
$369$	1.91319			0.0995967
$370$		0			0
$371$			18.1987i			0.944829i
$372$	−11.0849	+	9.94957i	−0.574727	+	0.515861i
$373$			10.0677i			0.521286i	0.965435	+	0.260643i	$0.0839345\pi$
$373$			10.0677i			0.521286i	−0.965435	+	0.260643i	$0.916065\pi$
$374$	6.08681	−	13.6425i	0.314741	−	0.705436i
$375$		0			0
$376$	2.90143	+	9.00148i	0.149630	+	0.464216i
$377$	−2.19098			−0.112841
$378$	−1.13905	+	2.55298i	−0.0585866	+	0.131311i
$379$		−	18.9674i		−	0.974289i	−0.873321	−	0.487145i	$-0.838038\pi$
$379$		−	18.9674i		−	0.974289i	0.873321	−	0.487145i	$-0.161962\pi$
$380$		0			0
$381$			2.43616i			0.124808i
$382$	19.6389	+	8.76222i	1.00482	+	0.448314i
$383$	28.7446			1.46878			0.734391	−	0.678727i	$-0.237468\pi$
$383$	28.7446			1.46878			0.734391	+	0.678727i	$0.237468\pi$
$384$	2.29166	+	11.0792i	0.116946	+	0.565382i
$385$		0			0
$386$	26.8068	+	11.9603i	1.36443	+	0.608763i
$387$			11.2452i			0.571624i
$388$	−14.2621	−	15.8895i	−0.724048	−	0.806669i
$389$			29.8161i			1.51174i	0.654724	+	0.755868i	$0.272785\pi$
$389$			29.8161i			1.51174i	−0.654724	+	0.755868i	$0.727215\pi$
$390$		0			0
$391$	−6.45617			−0.326503
$392$	−2.68335	−	8.32490i	−0.135530	−	0.420471i
$393$	−6.90143			−0.348131
$394$	13.3976	−	30.0283i	0.674962	−	1.51281i
$395$		0			0
$396$	−2.12921	+	1.91113i	−0.106997	+	0.0960377i
$397$		−	2.73167i		−	0.137099i	−0.997648	−	0.0685494i	$-0.978163\pi$
$397$		−	2.73167i		−	0.137099i	0.997648	−	0.0685494i	$-0.0218371\pi$
$398$	−9.31988	−	4.15821i	−0.467163	−	0.208432i
$399$	6.01001			0.300877
$400$		0			0
$401$	25.8744			1.29211			0.646054	−	0.763292i	$-0.276418\pi$
$401$	25.8744			1.29211			0.646054	+	0.763292i	$0.276418\pi$
$402$	6.28535	+	2.80431i	0.313485	+	0.139866i
$403$			1.79726i			0.0895279i
$404$	−19.6560	+	17.6428i	−0.977924	+	0.877762i
$405$		0			0
$406$	10.3417	−	23.1790i	0.513249	−	1.15035i
$407$	12.6098			0.625044
$408$	19.8782	−	6.40731i	0.984117	−	0.317209i
$409$	22.4786			1.11150			0.555748	−	0.831351i	$-0.312432\pi$
$409$	22.4786			1.11150			0.555748	+	0.831351i	$0.312432\pi$
$410$		0			0
$411$		−	5.39022i		−	0.265880i
$412$	−25.9498	−	28.9109i	−1.27845	−	1.42434i
$413$		−	12.7227i		−	0.626045i
$414$	1.12921	+	0.503813i	0.0554974	+	0.0247610i
$415$		0			0
$416$	1.17954	+	0.687170i	0.0578318	+	0.0336913i
$417$	17.4244			0.853277
$418$	5.61718	+	2.50619i	0.274745	+	0.122582i
$419$		−	24.5307i		−	1.19840i	−0.800598	−	0.599201i	$-0.795485\pi$
$419$		−	24.5307i		−	1.19840i	0.800598	−	0.599201i	$-0.204515\pi$
$420$		0			0
$421$		−	33.3856i		−	1.62712i	−0.581483	−	0.813558i	$-0.697527\pi$
$421$		−	33.3856i		−	1.62712i	0.581483	−	0.813558i	$-0.302473\pi$
$422$	2.52620	−	5.66202i	0.122974	−	0.275623i
$423$	−3.34374			−0.162578
$424$	−24.7838	+	7.98852i	−1.20361	+	0.387957i
$425$		0			0
$426$	−4.73544	+	10.6136i	−0.229433	+	0.514232i
$427$			9.04033i			0.437492i
$428$	22.0406	−	19.7832i	1.06537	−	0.956256i
$429$			0.345220i			0.0166674i
$430$		0			0
$431$	11.6548			0.561391			0.280696	−	0.959797i	$-0.409435\pi$
$431$	11.6548			0.561391			0.280696	+	0.959797i	$0.409435\pi$
$432$	−3.97676	−	0.430552i	−0.191332	−	0.0207149i
$433$	−19.7681			−0.949996			−0.474998	−	0.879987i	$-0.657551\pi$
$433$	−19.7681			−0.949996			−0.474998	+	0.879987i	$0.657551\pi$
$434$	−19.0137	−	8.48326i	−0.912687	−	0.407210i
$435$		0			0
$436$	22.6674	−	20.3457i	1.08557	−	0.974383i
$437$		−	2.65827i		−	0.127163i
$438$	2.37815	−	5.33019i	0.113632	−	0.254687i
$439$	−25.1699			−1.20129			−0.600646	−	0.799515i	$-0.705090\pi$
$439$	−25.1699			−1.20129			−0.600646	+	0.799515i	$0.705090\pi$
$440$		0			0
$441$	3.09242			0.147258
$442$	1.02678	−	2.30135i	0.0488390	−	0.109464i
$443$			19.5515i			0.928922i	0.885594	+	0.464461i	$0.153752\pi$
$443$			19.5515i			0.928922i	−0.885594	+	0.464461i	$0.846248\pi$
$444$	11.7758	+	13.1195i	0.558853	+	0.622625i
$445$		0			0
$446$	6.44266	+	2.87449i	0.305069	+	0.136111i
$447$	−2.28551			−0.108101
$448$	−12.8373	+	9.23517i	−0.606507	+	0.436321i
$449$	−19.9612			−0.942029			−0.471014	−	0.882125i	$-0.656112\pi$
$449$	−19.9612			−0.942029			−0.471014	+	0.882125i	$0.656112\pi$
$450$		0			0
$451$			2.73692i			0.128876i
$452$	1.52149	+	1.69511i	0.0715650	+	0.0797313i
$453$		−	6.66425i		−	0.313114i
$454$	6.48650	−	14.5383i	0.304426	−	0.682317i
$455$		0			0
$456$	2.63816	+	8.18468i	0.123543	+	0.383283i
$457$	5.01176			0.234440			0.117220	−	0.993106i	$-0.462602\pi$
$457$	5.01176			0.234440			0.117220	+	0.993106i	$0.462602\pi$
$458$	−9.12528	+	20.4527i	−0.426396	+	0.955690i
$459$			7.38407i			0.344659i
$460$		0			0
$461$		−	5.12566i		−	0.238726i	−0.992851	−	0.119363i	$-0.961915\pi$
$461$		−	5.12566i		−	0.238726i	0.992851	−	0.119363i	$-0.0380852\pi$
$462$	−3.65217	−	1.62948i	−0.169915	−	0.0758101i
$463$	5.79515			0.269324			0.134662	−	0.990892i	$-0.457005\pi$
$463$	5.79515			0.269324			0.134662	+	0.990892i	$0.457005\pi$
$464$	36.1057	+	3.90906i	1.67617	+	0.181474i
$465$		0			0
$466$	14.1537	+	6.31490i	0.655657	+	0.292532i
$467$			16.8208i			0.778373i	0.921159	+	0.389186i	$0.127244\pi$
$467$			16.8208i			0.778373i	−0.921159	+	0.389186i	$0.872756\pi$
$468$	−0.359175	+	0.322387i	−0.0166029	+	0.0149024i
$469$			9.62032i			0.444225i
$470$		0			0
$471$	17.4144			0.802413
$472$	17.3264	−	5.58479i	0.797511	−	0.257061i
$473$	−16.0868			−0.739672
$474$	−7.88026	+	17.6622i	−0.361952	+	0.811251i
$475$		0			0
$476$	19.5000	+	21.7252i	0.893783	+	0.995773i
$477$		−	9.20632i		−	0.421529i
$478$	22.3664	+	9.97914i	1.02302	+	0.456435i
$479$	−36.9065			−1.68630			−0.843151	−	0.537678i	$-0.819302\pi$
$479$	−36.9065			−1.68630			−0.843151	+	0.537678i	$0.819302\pi$
$480$		0			0
$481$	2.12714			0.0969892
$482$	6.15875	+	2.74782i	0.280523	+	0.125160i
$483$			1.72836i			0.0786429i
$484$	11.9613	+	13.3262i	0.543697	+	0.605738i
$485$		0			0
$486$	0.576222	−	1.29150i	0.0261380	−	0.0585836i
$487$	5.14984			0.233361			0.116681	−	0.993169i	$-0.462775\pi$
$487$	5.14984			0.233361			0.116681	+	0.993169i	$0.462775\pi$
$488$	−12.3115	+	3.96835i	−0.557316	+	0.179639i
$489$	4.66187			0.210817
$490$		0			0
$491$			23.1154i			1.04318i	0.853195	+	0.521591i	$0.174661\pi$
$491$			23.1154i			1.04318i	−0.853195	+	0.521591i	$0.825339\pi$
$492$	−2.84756	+	2.55590i	−0.128378	+	0.115229i
$493$		−	67.0414i		−	3.01939i
$494$	0.947560	+	0.422769i	0.0426328	+	0.0190213i
$495$		0			0
$496$	3.20660	−	29.6175i	0.143980	−	1.32986i
$497$	−16.2452			−0.728696
$498$	−15.9267	−	7.10597i	−0.713694	−	0.318426i
$499$		−	14.3111i		−	0.640654i	−0.947307	−	0.320327i	$-0.896207\pi$
$499$		−	14.3111i		−	0.640654i	0.947307	−	0.320327i	$-0.103793\pi$
$500$		0			0
$501$		−	0.137419i		−	0.00613942i
$502$	−3.54859	+	7.95352i	−0.158381	+	0.354983i
$503$	−15.4224			−0.687650			−0.343825	−	0.939034i	$-0.611723\pi$
$503$	−15.4224			−0.687650			−0.343825	+	0.939034i	$0.611723\pi$
$504$	−1.71528	−	5.32151i	−0.0764045	−	0.237039i
$505$		0			0
$506$	−0.720730	+	1.61539i	−0.0320404	+	0.0718127i
$507$		−	12.9418i		−	0.574764i
$508$	−3.25455	−	3.62593i	−0.144397	−	0.160875i
$509$		−	43.1578i		−	1.91294i	−0.291835	−	0.956469i	$-0.594266\pi$
$509$		−	43.1578i		−	1.91294i	0.291835	−	0.956469i	$-0.405734\pi$
$510$		0			0
$511$	8.15837			0.360905
$512$	−18.2119	−	13.4285i	−0.804861	−	0.593463i
$513$	−3.04033			−0.134234
$514$	18.2855	+	8.15837i	0.806539	+	0.359850i
$515$		0			0
$516$	−15.0228	−	16.7371i	−0.661343	−	0.736810i
$517$		−	4.78340i		−	0.210374i
$518$	−10.0403	+	22.5036i	−0.441147	+	0.988751i
$519$	−3.96675			−0.174121
$520$		0			0
$521$	−17.8232			−0.780848			−0.390424	−	0.920635i	$-0.627672\pi$
$521$	−17.8232			−0.780848			−0.390424	+	0.920635i	$0.627672\pi$
$522$	−5.23163	+	11.7258i	−0.228982	+	0.513222i
$523$			24.7502i			1.08225i	0.840941	+	0.541126i	$0.182002\pi$
$523$			24.7502i			1.08225i	−0.840941	+	0.541126i	$0.817998\pi$
$524$	10.2720	−	9.21987i	0.448733	−	0.402772i
$525$		0			0
$526$	20.1422	+	8.98677i	0.878242	+	0.391842i
$527$	−54.9939			−2.39557
$528$	0.615927	−	5.68896i	0.0268048	−	0.247580i
$529$	−22.2355			−0.966762
$530$		0			0
$531$			6.43616i			0.279306i
$532$	−8.94517	+	8.02898i	−0.387822	+	0.348100i
$533$			0.461690i			0.0199980i
$534$	−4.65626	+	10.4362i	−0.201496	+	0.451617i
$535$		0			0
$536$	−13.1014	+	4.22295i	−0.565893	+	0.182403i
$537$	4.68749			0.202280
$538$	−6.52181	+	14.6175i	−0.281175	+	0.630203i
$539$			4.42386i			0.190549i
$540$		0			0
$541$		−	16.9982i		−	0.730812i	−0.930848	−	0.365406i	$-0.880930\pi$
$541$		−	16.9982i		−	0.730812i	0.930848	−	0.365406i	$-0.119070\pi$
$542$	−8.01355	−	3.57537i	−0.344211	−	0.153575i
$543$	9.10242			0.390622
$544$	−21.0266	+	36.0925i	−0.901506	+	1.54745i
$545$		0			0
$546$	−0.616084	−	0.274876i	−0.0263660	−	0.0117636i
$547$		−	37.2385i		−	1.59220i	−0.605163	−	0.796101i	$-0.706892\pi$
$547$		−	37.2385i		−	1.59220i	0.605163	−	0.796101i	$-0.293108\pi$
$548$	7.20099	+	8.02270i	0.307611	+	0.342713i
$549$		−	4.57331i		−	0.195184i
$550$		0			0
$551$	27.6037			1.17596
$552$	−2.35375	+	0.758681i	−0.100182	+	0.0322916i
$553$	−27.0336			−1.14959
$554$	10.9072	−	24.4465i	0.463403	−	1.03863i
$555$		0			0
$556$	−25.9341	+	23.2779i	−1.09985	+	0.987202i
$557$			14.7604i			0.625420i	0.949849	+	0.312710i	$0.101237\pi$
$557$			14.7604i			0.625420i	−0.949849	+	0.312710i	$0.898763\pi$
$558$	9.61862	+	4.29150i	0.407189	+	0.181674i
$559$	−2.71368			−0.114776
$560$		0			0
$561$	−10.5633			−0.445983
$562$	−27.9262	−	12.4597i	−1.17800	−	0.525581i
$563$		−	3.00561i		−	0.126671i	−0.997992	−	0.0633356i	$-0.979826\pi$
$563$		−	3.00561i		−	0.126671i	0.997992	−	0.0633356i	$-0.0201739\pi$
$564$	4.97676	−	4.46702i	0.209559	−	0.188096i
$565$		0			0
$566$	−16.7982	+	37.6500i	−0.706079	+	1.58255i
$567$	1.97676			0.0830161
$568$	−7.13100	−	22.1234i	−0.299210	−	0.928276i
$569$	−23.1840			−0.971923			−0.485962	−	0.873980i	$-0.661531\pi$
$569$	−23.1840			−0.971923			−0.485962	+	0.873980i	$0.661531\pi$
$570$		0			0
$571$		−	0.202739i		−	0.00848438i	−0.999991	−	0.00424219i	$-0.998650\pi$
$571$		−	0.202739i		−	0.00848438i	0.999991	−	0.00424219i	$-0.00135033\pi$
$572$	−0.461192	−	0.513819i	−0.0192834	−	0.0214838i
$573$		−	15.2063i		−	0.635253i
$574$	−4.88434	−	2.17923i	−0.203869	−	0.0909592i
$575$		0			0
$576$	6.49412	−	4.67187i	0.270588	−	0.194661i
$577$	−21.8023			−0.907643			−0.453821	−	0.891093i	$-0.649940\pi$
$577$	−21.8023			−0.907643			−0.453821	+	0.891093i	$0.649940\pi$
$578$	48.4629	+	21.6225i	2.01579	+	0.899376i
$579$		−	20.7564i		−	0.862606i
$580$		0			0
$581$		−	24.3774i		−	1.01134i
$582$	−6.15159	+	13.7877i	−0.254992	+	0.571518i
$583$	13.1701			0.545451
$584$	3.58120	+	11.1104i	0.148191	+	0.459752i
$585$		0			0
$586$	−1.33930	+	3.00179i	−0.0553258	+	0.124003i
$587$			36.7126i			1.51529i	0.652667	+	0.757645i	$0.273650\pi$
$587$			36.7126i			1.51529i	−0.652667	+	0.757645i	$0.726350\pi$
$588$	−4.60269	+	4.13127i	−0.189812	+	0.170371i
$589$		−	22.6433i		−	0.933001i
$590$		0			0
$591$	−23.2508			−0.956409
$592$	−35.0537	−	3.79515i	−1.44070	−	0.155980i
$593$	−10.6036			−0.435439			−0.217719	−	0.976011i	$-0.569862\pi$
$593$	−10.6036			−0.435439			−0.217719	+	0.976011i	$0.569862\pi$
$594$	1.84756	+	0.824316i	0.0758061	+	0.0338221i
$595$		0			0
$596$	3.40170	−	3.05329i	0.139339	−	0.125068i
$597$			7.21633i			0.295345i
$598$	−0.121580	+	0.272499i	−0.00497177	+	0.0111433i
$599$	−25.7988			−1.05411			−0.527056	−	0.849831i	$-0.676704\pi$
$599$	−25.7988			−1.05411			−0.527056	+	0.849831i	$0.676704\pi$
$600$		0			0
$601$	18.5021			0.754717			0.377358	−	0.926067i	$-0.376832\pi$
$601$	18.5021			0.754717			0.377358	+	0.926067i	$0.376832\pi$
$602$	12.8089	−	28.7087i	0.522050	−	1.17008i
$603$		−	4.86671i		−	0.198188i
$604$	8.90300	+	9.91893i	0.362258	+	0.403596i
$605$		0			0
$606$	17.0559	+	7.60978i	0.692850	+	0.309126i
$607$	37.5828			1.52544			0.762719	−	0.646730i	$-0.223864\pi$
$607$	37.5828			1.52544			0.762719	+	0.646730i	$0.223864\pi$
$608$	−14.8608	−	8.65751i	−0.602685	−	0.351108i
$609$	−17.9474			−0.727264
$610$		0			0
$611$		−	0.806910i		−	0.0326441i
$612$	−9.86465	−	10.9903i	−0.398755	−	0.444257i
$613$			4.93405i			0.199284i	0.995023	+	0.0996422i	$0.0317698\pi$
$613$			4.93405i			0.199284i	−0.995023	+	0.0996422i	$0.968230\pi$
$614$	2.03001	−	4.54991i	0.0819247	−	0.183619i
$615$		0			0
$616$	7.61270	−	2.45379i	0.306724	−	0.0988661i
$617$	6.26043			0.252035			0.126018	−	0.992028i	$-0.459780\pi$
$617$	6.26043			0.252035			0.126018	+	0.992028i	$0.459780\pi$
$618$	−11.1928	+	25.0866i	−0.450239	+	1.00913i
$619$		−	8.02562i		−	0.322577i	−0.986907	−	0.161288i	$-0.948435\pi$
$619$		−	8.02562i		−	0.322577i	0.986907	−	0.161288i	$-0.0515649\pi$
$620$		0			0
$621$		−	0.874337i		−	0.0350860i
$622$	−27.9942	−	12.4900i	−1.12246	−	0.500805i
$623$	−15.9735			−0.639966
$624$	0.103901	−	0.959669i	0.00415935	−	0.0384175i
$625$		0			0
$626$	16.2065	+	7.23078i	0.647741	+	0.289000i
$627$		−	4.34935i		−	0.173696i
$628$	−25.9192	+	23.2645i	−1.03429	+	0.928355i
$629$			65.0878i			2.59522i
$630$		0			0
$631$	−26.5248			−1.05594			−0.527968	−	0.849264i	$-0.677046\pi$
$631$	−26.5248			−1.05594			−0.527968	+	0.849264i	$0.677046\pi$
$632$	−11.8667	−	36.8156i	−0.472032	−	1.46444i
$633$	−4.38407			−0.174251
$634$	−6.25841	+	14.0271i	−0.248553	+	0.557087i
$635$		0			0
$636$	12.2991	+	13.7025i	0.487689	+	0.543340i
$637$			0.746260i			0.0295679i
$638$	−16.7743	−	7.48412i	−0.664101	−	0.296299i
$639$	8.21808			0.325102
$640$		0			0
$641$	−26.5863			−1.05009			−0.525047	−	0.851073i	$-0.675952\pi$
$641$	−26.5863			−1.05009			−0.525047	+	0.851073i	$0.675952\pi$
$642$	−19.1251	−	8.53298i	−0.754808	−	0.336770i
$643$		−	2.89233i		−	0.114062i	−0.998372	−	0.0570312i	$-0.981837\pi$
$643$		−	2.89233i		−	0.114062i	0.998372	−	0.0570312i	$-0.0181635\pi$
$644$	−2.30897	−	2.57245i	−0.0909862	−	0.101369i
$645$		0			0
$646$	−12.9362	+	28.9942i	−0.508968	+	1.14076i
$647$	12.3472			0.485420			0.242710	−	0.970099i	$-0.421964\pi$
$647$	12.3472			0.485420			0.242710	+	0.970099i	$0.421964\pi$
$648$	0.867721	+	2.69204i	0.0340873	+	0.105753i
$649$	−9.20726			−0.361417
$650$		0			0
$651$			14.7222i			0.577009i
$652$	−6.93863	+	6.22795i	−0.271738	+	0.243905i
$653$		−	39.0507i		−	1.52817i	−0.645114	−	0.764086i	$-0.723190\pi$
$653$		−	39.0507i		−	1.52817i	0.645114	−	0.764086i	$-0.276810\pi$
$654$	−19.6690	−	8.77561i	−0.769117	−	0.343154i
$655$		0			0
$656$	0.823728	−	7.60830i	0.0321612	−	0.297054i
$657$	−4.12714			−0.161015
$658$	8.53652	+	3.80870i	0.332788	+	0.148479i
$659$		−	23.7738i		−	0.926094i	−0.886334	−	0.463047i	$-0.846756\pi$
$659$		−	23.7738i		−	0.926094i	0.886334	−	0.463047i	$-0.153244\pi$
$660$		0			0
$661$			21.5051i			0.836450i	0.908343	+	0.418225i	$0.137348\pi$
$661$			21.5051i			0.836450i	−0.908343	+	0.418225i	$0.862652\pi$
$662$	−0.709822	+	1.59094i	−0.0275880	+	0.0618335i
$663$	−1.78192			−0.0692040
$664$	33.1982	−	10.7007i	1.28834	−	0.415268i
$665$		0			0
$666$	5.07918	−	11.3841i	0.196814	−	0.441124i
$667$			7.93827i			0.307371i
$668$	0.183583	+	0.204532i	0.00710303	+	0.00791356i
$669$		−	4.98852i		−	0.192867i
$670$		0			0
$671$	6.54235			0.252565
$672$	9.66218	+	5.62894i	0.372727	+	0.217141i
$673$	36.1896			1.39501			0.697503	−	0.716582i	$-0.254294\pi$
$673$	36.1896			1.39501			0.697503	+	0.716582i	$0.254294\pi$
$674$	−5.34538	−	2.38492i	−0.205896	−	0.0918639i
$675$		0			0
$676$	17.2894	+	19.2623i	0.664976	+	0.740856i
$677$		−	9.17214i		−	0.352514i	−0.984344	−	0.176257i	$-0.943601\pi$
$677$		−	9.17214i		−	0.352514i	0.984344	−	0.176257i	$-0.0563990\pi$
$678$	0.656257	−	1.47088i	0.0252034	−	0.0564889i
$679$	−21.1034			−0.809873
$680$		0			0
$681$	−11.2569			−0.431367
$682$	−6.13921	+	13.7599i	−0.235083	+	0.526895i
$683$			16.3974i			0.627429i	0.949517	+	0.313714i	$0.101573\pi$
$683$			16.3974i			0.627429i	−0.949517	+	0.313714i	$0.898427\pi$
$684$	4.52517	−	4.06169i	0.173024	−	0.155302i
$685$		0			0
$686$	−25.7658	−	11.4958i	−0.983742	−	0.438912i
$687$	15.8364			0.604196
$688$	44.7194	+	4.84163i	1.70491	+	0.184586i
$689$	2.22166			0.0846387
$690$		0			0
$691$			24.4904i			0.931657i	0.884875	+	0.465828i	$0.154244\pi$
$691$			24.4904i			0.931657i	−0.884875	+	0.465828i	$0.845756\pi$
$692$	5.90404	−	5.29933i	0.224438	−	0.201450i
$693$			2.82786i			0.107421i
$694$	−10.0600	+	22.5477i	−0.381873	+	0.855900i
$695$		0			0
$696$	−7.87820	−	24.4415i	−0.298622	−	0.926452i
$697$	−14.1271			−0.535104
$698$	12.2272	−	27.4050i	0.462806	−	1.03730i
$699$		−	10.9591i		−	0.414512i
$700$		0			0
$701$		−	12.3887i		−	0.467916i	−0.972247	−	0.233958i	$-0.924832\pi$
$701$		−	12.3887i		−	0.467916i	0.972247	−	0.233958i	$-0.0751679\pi$
$702$	0.311664	+	0.139054i	0.0117630	+	0.00524824i
$703$	−26.7994			−1.01076
$704$	6.68335	+	9.29018i	0.251888	+	0.350137i
$705$		0			0
$706$	−27.1729	−	12.1236i	−1.02266	−	0.456278i
$707$			26.1057i			0.981807i
$708$	−8.59830	−	9.57945i	−0.323144	−	0.360018i
$709$			33.4144i			1.25490i	0.778655	+	0.627452i	$0.215902\pi$
$709$			33.4144i			1.25490i	−0.778655	+	0.627452i	$0.784098\pi$
$710$		0			0
$711$	13.6757			0.512880
$712$	−7.01176	−	21.7534i	−0.262777	−	0.815244i
$713$	6.51175			0.243867
$714$	8.41086	−	18.8514i	0.314768	−	0.705496i
$715$		0			0
$716$	−6.97676	+	6.26218i	−0.260734	+	0.234029i
$717$		−	17.3182i		−	0.646761i
$718$	30.3700	+	13.5501i	1.13340	+	0.505684i
$719$	−33.8938			−1.26403			−0.632013	−	0.774958i	$-0.717771\pi$
$719$	−33.8938			−1.26403			−0.632013	+	0.774958i	$0.717771\pi$
$720$		0			0
$721$	−38.3974			−1.42999
$722$	12.6004	+	5.62185i	0.468937	+	0.209224i
$723$		−	4.76869i		−	0.177349i
$724$	−13.5479	+	12.1603i	−0.503503	+	0.451932i
$725$		0			0
$726$	5.15922	−	11.5635i	0.191477	−	0.429160i
$727$	−14.1846			−0.526076			−0.263038	−	0.964785i	$-0.584725\pi$
$727$	−14.1846			−0.526076			−0.263038	+	0.964785i	$0.584725\pi$
$728$	1.28418	−	0.413929i	0.0475950	−	0.0153412i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		−	83.0352i		−	3.07117i
$732$	6.10964	+	6.80682i	0.225819	+	0.251587i
$733$		−	8.09296i		−	0.298920i	−0.988768	−	0.149460i	$-0.952246\pi$
$733$		−	8.09296i		−	0.298920i	0.988768	−	0.149460i	$-0.0477536\pi$
$734$	32.8056	+	14.6367i	1.21088	+	0.540251i
$735$		0			0
$736$	2.48972	−	4.27366i	0.0917725	−	0.157529i
$737$	6.96208			0.256452
$738$	2.47088	+	1.10242i	0.0909544	+	0.0405808i
$739$		−	22.0919i		−	0.812663i	−0.913726	−	0.406331i	$-0.866808\pi$
$739$		−	22.0919i		−	0.812663i	0.913726	−	0.406331i	$-0.133192\pi$
$740$		0			0
$741$		−	0.733691i		−	0.0269528i
$742$	−10.4865	+	23.5036i	−0.384971	+	0.862844i
$743$	8.78340			0.322232			0.161116	−	0.986936i	$-0.448491\pi$
$743$	8.78340			0.322232			0.161116	+	0.986936i	$0.448491\pi$
$744$	−20.0493	+	6.46247i	−0.735044	+	0.236926i
$745$		0			0
$746$	−5.80123	+	13.0024i	−0.212398	+	0.476052i
$747$			12.3320i			0.451204i
$748$	15.7222	−	14.1119i	0.574861	−	0.515982i
$749$		−	29.2728i		−	1.06961i
$750$		0			0
$751$	13.3779			0.488167			0.244084	−	0.969754i	$-0.421513\pi$
$751$	13.3779			0.488167			0.244084	+	0.969754i	$0.421513\pi$
$752$	−1.43965	+	13.2973i	−0.0524988	+	0.484901i
$753$	6.15837			0.224423
$754$	−2.82965	−	1.26249i	−0.103050	−	0.0459773i
$755$		0			0
$756$	−2.94217	+	2.64082i	−0.107006	+	0.0960459i
$757$		−	9.72450i		−	0.353443i	−0.984261	−	0.176721i	$-0.943451\pi$
$757$		−	9.72450i		−	0.353443i	0.984261	−	0.176721i	$-0.0565492\pi$
$758$	10.9294	−	24.4963i	0.396975	−	0.889747i
$759$	1.25079			0.0454006
$760$		0			0
$761$	33.8835			1.22828			0.614138	−	0.789198i	$-0.289504\pi$
$761$	33.8835			1.22828			0.614138	+	0.789198i	$0.289504\pi$
$762$	−1.40377	+	3.14630i	−0.0508532	+	0.113978i
$763$		−	30.1052i		−	1.08988i
$764$	20.3147	+	22.6328i	0.734959	+	0.818826i
$765$		0			0
$766$	37.1236	+	16.5633i	1.34133	+	0.598456i
$767$	−1.55317			−0.0560817
$768$	−3.42440	+	15.6293i	−0.123568	+	0.563972i
$769$	18.7334			0.675545			0.337772	−	0.941228i	$-0.390327\pi$
$769$	18.7334			0.675545			0.337772	+	0.941228i	$0.390327\pi$
$770$		0			0
$771$		−	14.1584i		−	0.509901i
$772$	27.7292	+	30.8934i	0.997996	+	1.11188i
$773$			22.5006i			0.809292i	0.914474	+	0.404646i	$0.132605\pi$
$773$			22.5006i			0.809292i	−0.914474	+	0.404646i	$0.867395\pi$
$774$	−6.47972	+	14.5231i	−0.232909	+	0.522023i
$775$		0			0
$776$	−9.26355	−	28.7395i	−0.332542	−	1.03169i
$777$	17.4244			0.625097
$778$	−17.1807	+	38.5074i	−0.615958	+	1.38056i
$779$		−	5.81673i		−	0.208406i
$780$		0			0
$781$			11.7564i			0.420677i
$782$	−8.33813	−	3.72019i	−0.298171	−	0.133034i
$783$	9.07918			0.324464
$784$	1.33145	−	12.2978i	0.0475517	−	0.439207i
$785$		0			0
$786$	−8.91319	−	3.97676i	−0.317923	−	0.141846i
$787$			28.1063i			1.00188i	0.865482	+	0.500940i	$0.167012\pi$
$787$			28.1063i			1.00188i	−0.865482	+	0.500940i	$0.832988\pi$
$788$	34.6060	−	31.0616i	1.23279	−	1.10652i
$789$		−	15.5960i		−	0.555232i
$790$		0			0
$791$	2.25133			0.0800479
$792$	−3.85110	+	1.24132i	−0.136843	+	0.0441084i
$793$	1.10363			0.0391910
$794$	1.57405	−	3.52795i	0.0558610	−	0.125202i
$795$		0			0
$796$	−9.64055	−	10.7406i	−0.341700	−	0.380692i
$797$			38.1461i			1.35120i	0.737267	+	0.675602i	$0.236116\pi$
$797$			38.1461i			1.35120i	−0.737267	+	0.675602i	$0.763884\pi$
$798$	7.76191	+	3.46310i	0.274769	+	0.122592i
$799$	24.6904			0.873485
$800$		0			0
$801$	8.08066			0.285516
$802$	33.4168	+	14.9094i	1.17999	+	0.526470i
$803$		−	5.90409i		−	0.208351i
$804$	6.50161	+	7.24352i	0.229294	+	0.255459i
$805$		0			0
$806$	−1.03562	+	2.32116i	−0.0364782	+	0.0817593i
$807$	11.3182			0.398420
$808$	−35.5519	+	11.4594i	−1.25071	+	0.403140i
$809$	−10.0745			−0.354201			−0.177101	−	0.984193i	$-0.556672\pi$
$809$	−10.0745			−0.354201			−0.177101	+	0.984193i	$0.556672\pi$
$810$		0			0
$811$			40.6001i			1.42566i	0.701335	+	0.712832i	$0.252588\pi$
$811$			40.6001i			1.42566i	−0.701335	+	0.712832i	$0.747412\pi$
$812$	26.7125	−	23.9765i	0.937426	−	0.841411i
$813$			6.20485i			0.217613i
$814$	16.2855	+	7.26604i	0.570807	+	0.254674i
$815$		0			0
$816$	29.3647	+	3.17923i	1.02797	+	0.111295i
$817$	34.1891			1.19612
$818$	29.0311	+	12.9527i	1.01505	+	0.452879i
$819$			0.477031i			0.0166688i
$820$		0			0
$821$		−	10.3397i		−	0.360858i	−0.983588	−	0.180429i	$-0.942251\pi$
$821$		−	10.3397i		−	0.360858i	0.983588	−	0.180429i	$-0.0577486\pi$
$822$	3.10597	−	6.96146i	0.108333	−	0.242809i
$823$	28.5013			0.993493			0.496746	−	0.867896i	$-0.334528\pi$
$823$	28.5013			0.993493			0.496746	+	0.867896i	$0.334528\pi$
$824$	−16.8550	−	52.2912i	−0.587170	−	1.82165i
$825$		0			0
$826$	7.33113	−	16.4314i	0.255083	−	0.571722i
$827$		−	32.1957i		−	1.11956i	−0.828643	−	0.559778i	$-0.810886\pi$
$827$		−	32.1957i		−	1.11956i	0.828643	−	0.559778i	$-0.189114\pi$
$828$	1.16806	+	1.30135i	0.0405928	+	0.0452249i
$829$		−	31.5286i		−	1.09503i	−0.836795	−	0.547516i	$-0.815573\pi$
$829$		−	31.5286i		−	1.09503i	0.836795	−	0.547516i	$-0.184427\pi$
$830$		0			0
$831$	−18.9288			−0.656633
$832$	1.12741	+	1.56716i	0.0390860	+	0.0543314i
$833$	−22.8346			−0.791173
$834$	22.5036	+	10.0403i	0.779236	+	0.347668i
$835$		0			0
$836$	5.81045	+	6.47349i	0.200959	+	0.223890i
$837$		−	7.44764i		−	0.257428i
$838$	14.1351	−	31.6813i	0.488290	−	1.09441i
$839$	54.9816			1.89818			0.949089	−	0.315009i	$-0.102008\pi$
$839$	54.9816			1.89818			0.949089	+	0.315009i	$0.102008\pi$
$840$		0			0
$841$	−53.4316			−1.84247
$842$	19.2376	−	43.1175i	0.662970	−	1.48593i
$843$			21.6231i			0.744739i
$844$	6.52517	−	5.85684i	0.224606	−	0.201601i
$845$		0			0
$846$	−4.31844	−	1.92674i	−0.148471	−	0.0662427i
$847$	17.6990			0.608144
$848$	−36.6113	−	3.96380i	−1.25724	−	0.136117i
$849$	29.1522			1.00050
$850$		0			0
$851$		−	7.70696i		−	0.264191i
$852$	−12.2316	+	10.9788i	−0.419049	+	0.376128i
$853$		−	4.22607i		−	0.144698i	−0.997379	−	0.0723489i	$-0.976950\pi$
$853$		−	4.22607i		−	0.144698i	0.997379	−	0.0723489i	$-0.0230495\pi$
$854$	−5.20924	+	11.6756i	−0.178257	+	0.399530i
$855$		0			0
$856$	39.8650	−	12.8496i	1.36256	−	0.439191i
$857$	−54.8223			−1.87270			−0.936348	−	0.351074i	$-0.885817\pi$
$857$	−54.8223			−1.87270			−0.936348	+	0.351074i	$0.885817\pi$
$858$	−0.198923	+	0.445851i	−0.00679113	+	0.0152211i
$859$			14.2126i			0.484926i	0.970161	+	0.242463i	$0.0779554\pi$
$859$			14.2126i			0.484926i	−0.970161	+	0.242463i	$0.922045\pi$
$860$		0			0
$861$			3.78192i			0.128887i
$862$	15.0521	+	6.71574i	0.512678	+	0.228739i
$863$	−40.7446			−1.38696			−0.693482	−	0.720474i	$-0.743924\pi$
$863$	−40.7446			−1.38696			−0.693482	+	0.720474i	$0.743924\pi$
$864$	−4.88789	−	2.84756i	−0.166289	−	0.0968758i
$865$		0			0
$866$	−25.5305	−	11.3908i	−0.867563	−	0.387077i
$867$		−	37.5245i		−	1.27440i
$868$	−19.6679	−	21.9122i	−0.667573	−	0.743750i
$869$			19.5638i			0.663658i
$870$		0			0
$871$	1.17443			0.0397941
$872$	40.9985	−	13.2150i	1.38839	−	0.447517i
$873$	10.6757			0.361319
$874$	1.53176	−	3.43316i	0.0518125	−	0.116128i
$875$		0			0
$876$	6.14275	−	5.51359i	0.207544	−	0.186287i
$877$			34.4568i			1.16352i	0.813359	+	0.581762i	$0.197637\pi$
$877$			34.4568i			1.16352i	−0.813359	+	0.581762i	$0.802363\pi$
$878$	−32.5068	−	14.5034i	−1.09705	−	0.489467i
$879$	2.32427			0.0783957
$880$		0			0
$881$	23.8528			0.803623			0.401811	−	0.915722i	$-0.368381\pi$
$881$	23.8528			0.803623			0.401811	+	0.915722i	$0.368381\pi$
$882$	3.99385	+	1.78192i	0.134480	+	0.0600004i
$883$			24.2417i			0.815798i	0.913027	+	0.407899i	$0.133738\pi$
$883$			24.2417i			0.815798i	−0.913027	+	0.407899i	$0.866262\pi$
$884$	2.65217	−	2.38053i	0.0892023	−	0.0800659i
$885$		0			0
$886$	−11.2660	+	25.2508i	−0.378490	+	0.848317i
$887$	39.1843			1.31568			0.657840	−	0.753158i	$-0.271470\pi$
$887$	39.1843			1.31568			0.657840	+	0.753158i	$0.271470\pi$
$888$	7.64863	+	23.7293i	0.256671	+	0.796303i
$889$	−4.81571			−0.161514
$890$		0			0
$891$		−	1.43055i		−	0.0479253i
$892$	6.66434	+	7.42481i	0.223139	+	0.248601i
$893$			10.1661i			0.340195i
$894$	−2.95173	−	1.31696i	−0.0987206	−	0.0440457i
$895$		0			0
$896$	−21.9009	+	4.53005i	−0.731658	+	0.151339i
$897$	0.210995			0.00704490
$898$	−25.7799	−	11.5021i	−0.860286	−	0.383830i
$899$			67.6185i			2.25520i
$900$		0			0
$901$			67.9802i			2.26475i
$902$	−1.57707	+	3.53473i	−0.0525108	+	0.117693i
$903$	−22.2290			−0.739736
$904$	0.988244	+	3.06595i	0.0328685	+	0.101972i
$905$		0			0
$906$	3.84009	−	8.60686i	0.127578	−	0.285944i
$907$			18.9418i			0.628951i	0.949266	+	0.314475i	$0.101829\pi$
$907$			18.9418i			0.628951i	−0.949266	+	0.314475i	$0.898171\pi$
$908$	16.7546	−	15.0385i	0.556021	−	0.499071i
$909$		−	13.2063i		−	0.438026i
$910$		0			0
$911$	17.8493			0.591375			0.295688	−	0.955285i	$-0.404451\pi$
$911$	17.8493			0.591375			0.295688	+	0.955285i	$0.404451\pi$
$912$	−1.30902	+	12.0907i	−0.0433460	+	0.400362i
$913$	−17.6415			−0.583850
$914$	6.47267	+	2.88789i	0.214097	+	0.0955228i
$915$		0			0
$916$	−23.5706	+	21.1564i	−0.778793	+	0.699027i
$917$		−	13.6425i		−	0.450515i
$918$	−4.25487	+	9.53652i	−0.140432	+	0.314752i
$919$	24.4983			0.808126			0.404063	−	0.914731i	$-0.367598\pi$
$919$	24.4983			0.808126			0.404063	+	0.914731i	$0.367598\pi$
$920$		0			0
$921$	−3.52297			−0.116086
$922$	2.95352	−	6.61978i	0.0972690	−	0.218011i
$923$			1.98318i			0.0652772i
$924$	−3.77784	−	4.20893i	−0.124282	−	0.138464i
$925$		0			0
$926$	7.48443	+	3.33930i	0.245954	+	0.109736i
$927$	19.4244			0.637981
$928$	44.3780	+	25.8535i	1.45678	+	0.848682i
$929$	11.5577			0.379196			0.189598	−	0.981862i	$-0.439282\pi$
$929$	11.5577			0.379196			0.189598	+	0.981862i	$0.439282\pi$
$930$		0			0
$931$		−	9.40197i		−	0.308137i
$932$	14.6407	+	16.3114i	0.479572	+	0.534296i
$933$			21.6757i			0.709632i
$934$	−9.69251	+	21.7240i	−0.317148	+	0.710831i
$935$		0			0
$936$	−0.649641	+	0.209398i	−0.0212342	+	0.00684438i
$937$	59.5587			1.94570			0.972849	−	0.231440i	$-0.0743436\pi$
$937$	59.5587			1.94570			0.972849	+	0.231440i	$0.0743436\pi$
$938$	−5.54345	+	12.4246i	−0.181000	+	0.405679i
$939$		−	12.5486i		−	0.409508i
$940$		0			0
$941$		−	55.9289i		−	1.82323i	−0.411044	−	0.911615i	$-0.634836\pi$
$941$		−	55.9289i		−	1.82323i	0.411044	−	0.911615i	$-0.365164\pi$
$942$	22.4907	+	10.0346i	0.732785	+	0.326944i
$943$	1.67277			0.0544730
$944$	25.5951	+	2.77110i	0.833048	+	0.0901917i
$945$		0			0
$946$	−20.7761	−	9.26958i	−0.675489	−	0.301380i
$947$		−	30.0945i		−	0.977941i	−0.872300	−	0.488970i	$-0.837373\pi$
$947$		−	30.0945i		−	0.977941i	0.872300	−	0.488970i	$-0.162627\pi$
$948$	−20.3547	+	18.2699i	−0.661089	+	0.593379i
$949$		−	0.995959i		−	0.0323302i
$950$		0			0
$951$	10.8611			0.352195
$952$	12.6657	+	39.2944i	0.410498	+	1.27354i
$953$	−12.4097			−0.401989			−0.200995	−	0.979592i	$-0.564417\pi$
$953$	−12.4097			−0.401989			−0.200995	+	0.979592i	$0.564417\pi$
$954$	5.30489	−	11.8900i	0.171752	−	0.384951i
$955$		0			0
$956$	23.1360	+	25.7761i	0.748272	+	0.833658i
$957$			12.9882i			0.419850i
$958$	−47.6647	−	21.2664i	−1.53998	−	0.687085i
$959$	10.6552			0.344074
$960$		0			0
$961$	24.4674			0.789271
$962$	2.74720	+	1.22571i	0.0885732	+	0.0395183i
$963$			14.8085i			0.477196i
$964$	6.37066	+	7.09762i	0.205185	+	0.228599i
$965$		0			0
$966$	−0.995917	+	2.23217i	−0.0320431	+	0.0718188i
$967$	−41.8371			−1.34539			−0.672694	−	0.739920i	$-0.734863\pi$
$967$	−41.8371			−1.34539			−0.672694	+	0.739920i	$0.734863\pi$
$968$	7.76916	+	24.1032i	0.249710	+	0.774706i
$969$	22.4500			0.721199
$970$		0			0
$971$			40.6875i			1.30572i	0.757477	+	0.652862i	$0.226432\pi$
$971$			40.6875i			1.30572i	−0.757477	+	0.652862i	$0.773568\pi$
$972$	1.48838	−	1.33594i	0.0477398	−	0.0428502i
$973$			34.4439i			1.10422i
$974$	6.65101	+	2.96745i	0.213112	+	0.0950833i
$975$		0			0
$976$	−18.1869	−	1.96905i	−0.582150	−	0.0630276i
$977$	−1.67923			−0.0537233			−0.0268617	−	0.999639i	$-0.508551\pi$
$977$	−1.67923			−0.0537233			−0.0268617	+	0.999639i	$0.508551\pi$
$978$	6.02079	+	2.68627i	0.192524	+	0.0858975i
$979$			11.5598i			0.369453i
$980$		0			0
$981$			15.2296i			0.486243i
$982$	−13.3196	+	29.8535i	−0.425046	+	0.952663i
$983$	13.4944			0.430404			0.215202	−	0.976570i	$-0.430959\pi$
$983$	13.4944			0.430404			0.215202	+	0.976570i	$0.430959\pi$
$984$	−5.15038	+	1.66011i	−0.164188	+	0.0529225i
$985$		0			0
$986$	38.6307	−	86.5838i	1.23025	−	2.75739i
$987$		−	6.60978i		−	0.210392i
$988$	0.980164	+	1.09201i	0.0311832	+	0.0347415i
$989$			9.83208i			0.312642i
$990$		0			0
$991$	−10.8502			−0.344667			−0.172333	−	0.985039i	$-0.555131\pi$
$991$	−10.8502			−0.344667			−0.172333	+	0.985039i	$0.555131\pi$
$992$	21.2076	−	36.4032i	0.673341	−	1.15580i
$993$	1.23185			0.0390917
$994$	−20.9806	−	9.36083i	−0.665465	−	0.296908i
$995$		0			0
$996$	−16.4747	−	18.3547i	−0.522022	−	0.581590i
$997$		−	39.0972i		−	1.23822i	−0.785304	−	0.619110i	$-0.787493\pi$
$997$		−	39.0972i		−	1.23822i	0.785304	−	0.619110i	$-0.212507\pi$
$998$	8.24639	−	18.4828i	0.261035	−	0.585063i
$999$	−8.81463			−0.278882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.k.e.301.8	yes	8
3.2	odd	2		1800.2.k.q.901.1		8
4.3	odd	2		2400.2.k.e.1201.5		8
5.2	odd	4		600.2.d.g.349.4		8
5.3	odd	4		600.2.d.h.349.5		8
5.4	even	2		600.2.k.d.301.1	✓	8
8.3	odd	2		2400.2.k.e.1201.1		8
8.5	even	2	inner	600.2.k.e.301.7	yes	8
12.11	even	2		7200.2.k.s.3601.1		8
15.2	even	4		1800.2.d.t.1549.5		8
15.8	even	4		1800.2.d.s.1549.4		8
15.14	odd	2		1800.2.k.t.901.8		8
20.3	even	4		2400.2.d.g.49.7		8
20.7	even	4		2400.2.d.h.49.2		8
20.19	odd	2		2400.2.k.d.1201.4		8
24.5	odd	2		1800.2.k.q.901.2		8
24.11	even	2		7200.2.k.s.3601.2		8
40.3	even	4		2400.2.d.h.49.7		8
40.13	odd	4		600.2.d.g.349.3		8
40.19	odd	2		2400.2.k.d.1201.8		8
40.27	even	4		2400.2.d.g.49.2		8
40.29	even	2		600.2.k.d.301.2	yes	8
40.37	odd	4		600.2.d.h.349.6		8
60.23	odd	4		7200.2.d.s.2449.7		8
60.47	odd	4		7200.2.d.t.2449.2		8
60.59	even	2		7200.2.k.r.3601.7		8
120.29	odd	2		1800.2.k.t.901.7		8
120.53	even	4		1800.2.d.t.1549.6		8
120.59	even	2		7200.2.k.r.3601.8		8
120.77	even	4		1800.2.d.s.1549.3		8
120.83	odd	4		7200.2.d.t.2449.7		8
120.107	odd	4		7200.2.d.s.2449.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.d.g.349.3		8	40.13	odd	4
600.2.d.g.349.4		8	5.2	odd	4
600.2.d.h.349.5		8	5.3	odd	4
600.2.d.h.349.6		8	40.37	odd	4
600.2.k.d.301.1	✓	8	5.4	even	2
600.2.k.d.301.2	yes	8	40.29	even	2
600.2.k.e.301.7	yes	8	8.5	even	2	inner
600.2.k.e.301.8	yes	8	1.1	even	1	trivial
1800.2.d.s.1549.3		8	120.77	even	4
1800.2.d.s.1549.4		8	15.8	even	4
1800.2.d.t.1549.5		8	15.2	even	4
1800.2.d.t.1549.6		8	120.53	even	4
1800.2.k.q.901.1		8	3.2	odd	2
1800.2.k.q.901.2		8	24.5	odd	2
1800.2.k.t.901.7		8	120.29	odd	2
1800.2.k.t.901.8		8	15.14	odd	2
2400.2.d.g.49.2		8	40.27	even	4
2400.2.d.g.49.7		8	20.3	even	4
2400.2.d.h.49.2		8	20.7	even	4
2400.2.d.h.49.7		8	40.3	even	4
2400.2.k.d.1201.4		8	20.19	odd	2
2400.2.k.d.1201.8		8	40.19	odd	2
2400.2.k.e.1201.1		8	8.3	odd	2
2400.2.k.e.1201.5		8	4.3	odd	2
7200.2.d.s.2449.2		8	120.107	odd	4
7200.2.d.s.2449.7		8	60.23	odd	4
7200.2.d.t.2449.2		8	60.47	odd	4
7200.2.d.t.2449.7		8	120.83	odd	4
7200.2.k.r.3601.7		8	60.59	even	2
7200.2.k.r.3601.8		8	120.59	even	2
7200.2.k.s.3601.1		8	12.11	even	2
7200.2.k.s.3601.2		8	24.11	even	2

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29150 + 0.576222i) q^{2} -1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} +1.97676 q^{7} +(0.867721 + 2.69204i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.29150 + 0.576222i) q^{2} -1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} +1.97676 q^{7} +(0.867721 + 2.69204i) q^{8} -1.00000 q^{9} -1.43055i q^{11} +(1.48838 - 1.33594i) q^{12} -0.241319i q^{13} +(2.55298 + 1.13905i) q^{14} +(-0.430552 + 3.97676i) q^{16} +7.38407 q^{17} +(-1.29150 - 0.576222i) q^{18} +3.04033i q^{19} -1.97676i q^{21} +(0.824316 - 1.84756i) q^{22} -0.874337 q^{23} +(2.69204 - 0.867721i) q^{24} +(0.139054 - 0.311664i) q^{26} +1.00000i q^{27} +(2.64082 + 2.94217i) q^{28} -9.07918i q^{29} -7.44764 q^{31} +(-2.84756 + 4.88789i) q^{32} -1.43055 q^{33} +(9.53652 + 4.25487i) q^{34} +(-1.33594 - 1.48838i) q^{36} +8.81463i q^{37} +(-1.75191 + 3.92658i) q^{38} -0.241319 q^{39} -1.91319 q^{41} +(1.13905 - 2.55298i) q^{42} -11.2452i q^{43} +(2.12921 - 1.91113i) q^{44} +(-1.12921 - 0.503813i) q^{46} +3.34374 q^{47} +(3.97676 + 0.430552i) q^{48} -3.09242 q^{49} -7.38407i q^{51} +(0.359175 - 0.322387i) q^{52} +9.20632i q^{53} +(-0.576222 + 1.29150i) q^{54} +(1.71528 + 5.32151i) q^{56} +3.04033 q^{57} +(5.23163 - 11.7258i) q^{58} -6.43616i q^{59} +4.57331i q^{61} +(-9.61862 - 4.29150i) q^{62} -1.97676 q^{63} +(-6.49412 + 4.67187i) q^{64} +(-1.84756 - 0.824316i) q^{66} +4.86671i q^{67} +(9.86465 + 10.9903i) q^{68} +0.874337i q^{69} -8.21808 q^{71} +(-0.867721 - 2.69204i) q^{72} +4.12714 q^{73} +(-5.07918 + 11.3841i) q^{74} +(-4.52517 + 4.06169i) q^{76} -2.82786i q^{77} +(-0.311664 - 0.139054i) q^{78} -13.6757 q^{79} +1.00000 q^{81} +(-2.47088 - 1.10242i) q^{82} -12.3320i q^{83} +(2.94217 - 2.64082i) q^{84} +(6.47972 - 14.5231i) q^{86} -9.07918 q^{87} +(3.85110 - 1.24132i) q^{88} -8.08066 q^{89} -0.477031i q^{91} +(-1.16806 - 1.30135i) q^{92} +7.44764i q^{93} +(4.31844 + 1.92674i) q^{94} +(4.88789 + 2.84756i) q^{96} -10.6757 q^{97} +(-3.99385 - 1.78192i) q^{98} +1.43055i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9	\( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} - 2 q^{18} - 12 q^{22} - 8 q^{23} - 8 q^{24} - 2 q^{26} + 4 q^{28} + 8 q^{31} - 28 q^{32} + 12 q^{34} - 4 q^{36} - 30 q^{38} + 6 q^{42} - 12 q^{44} + 20 q^{46} + 8 q^{48} + 20 q^{52} - 2 q^{54} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 30 q^{62} + 8 q^{63} - 32 q^{64} - 20 q^{66} + 28 q^{68} - 40 q^{71} + 4 q^{72} + 16 q^{73} + 8 q^{74} - 20 q^{76} + 22 q^{78} - 16 q^{79} + 8 q^{81} + 24 q^{82} + 24 q^{84} - 18 q^{86} - 24 q^{87} + 8 q^{88} + 36 q^{92} - 4 q^{94} + 12 q^{96} + 8 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 - 2 * q^18 - 12 * q^22 - 8 * q^23 - 8 * q^24 - 2 * q^26 + 4 * q^28 + 8 * q^31 - 28 * q^32 + 12 * q^34 - 4 * q^36 - 30 * q^38 + 6 * q^42 - 12 * q^44 + 20 * q^46 + 8 * q^48 + 20 * q^52 - 2 * q^54 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 30 * q^62 + 8 * q^63 - 32 * q^64 - 20 * q^66 + 28 * q^68 - 40 * q^71 + 4 * q^72 + 16 * q^73 + 8 * q^74 - 20 * q^76 + 22 * q^78 - 16 * q^79 + 8 * q^81 + 24 * q^82 + 24 * q^84 - 18 * q^86 - 24 * q^87 + 8 * q^88 + 36 * q^92 - 4 * q^94 + 12 * q^96 + 8 * q^97 + 48 * q^98

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