LMFDB - Embedded newform 300.2.o.a.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(109,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("300.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.o (of order $10$, degree $4$, 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	300.289
Dual form			300.2.o.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{3} +(-2.10592 - 0.751722i) q^{5} -0.595901i q^{7} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{3} +(-2.10592 - 0.751722i) q^{5} -0.595901i q^{7} +(0.809017 + 0.587785i) q^{9} +(-2.71474 + 1.97238i) q^{11} +(-2.80319 + 3.85825i) q^{13} +(1.77056 + 1.36570i) q^{15} +(-7.11384 + 2.31143i) q^{17} +(-1.91242 - 5.88583i) q^{19} +(-0.184143 + 0.566735i) q^{21} +(-2.59154 - 3.56694i) q^{23} +(3.86983 + 3.16614i) q^{25} +(-0.587785 - 0.809017i) q^{27} +(0.853035 - 2.62537i) q^{29} +(1.38708 + 4.26899i) q^{31} +(3.19137 - 1.03694i) q^{33} +(-0.447952 + 1.25492i) q^{35} +(-0.764512 + 1.05226i) q^{37} +(3.85825 - 2.80319i) q^{39} +(7.61184 + 5.53032i) q^{41} -7.59854i q^{43} +(-1.26188 - 1.84599i) q^{45} +(-4.18645 - 1.36026i) q^{47} +6.64490 q^{49} +7.47993 q^{51} +(-7.80561 - 2.53620i) q^{53} +(7.19972 - 2.11294i) q^{55} +6.18873i q^{57} +(-1.80309 - 1.31002i) q^{59} +(-10.2014 + 7.41175i) q^{61} +(0.350262 - 0.482094i) q^{63} +(8.80363 - 6.01797i) q^{65} +(7.94930 - 2.58288i) q^{67} +(1.36245 + 4.19319i) q^{69} +(2.09986 - 6.46271i) q^{71} +(4.29801 + 5.91570i) q^{73} +(-2.70203 - 4.20702i) q^{75} +(1.17534 + 1.61772i) q^{77} +(3.26546 - 10.0500i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-3.97694 + 1.29219i) q^{83} +(16.7188 + 0.479942i) q^{85} +(-1.62257 + 2.23328i) q^{87} +(3.43862 - 2.49830i) q^{89} +(2.29914 + 1.67042i) q^{91} -4.48868i q^{93} +(-0.397094 + 13.8327i) q^{95} +(-11.6744 - 3.79326i) q^{97} -3.35561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^5 + 6 * q^9	$ 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$		0			0
$5$	−2.10592	−	0.751722i	−0.941798	−	0.336180i
$5$	−2.10592	−	0.751722i	−0.941798	−	0.336180i
$6$		0			0
$7$		−	0.595901i		−	0.225229i	−0.993639	−	0.112615i	$-0.964077\pi$
$7$		−	0.595901i		−	0.225229i	0.993639	−	0.112615i	$-0.0359225\pi$
$8$		0			0
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	−2.71474	+	1.97238i	−0.818526	+	0.594694i	−0.916290	−	0.400515i	$-0.868831\pi$
$11$	−2.71474	+	1.97238i	−0.818526	+	0.594694i	0.0977636	+	0.995210i	$0.468831\pi$
$12$		0			0
$13$	−2.80319	+	3.85825i	−0.777464	+	1.07009i	0.218094	+	0.975928i	$0.430016\pi$
$13$	−2.80319	+	3.85825i	−0.777464	+	1.07009i	−0.995557	+	0.0941591i	$0.969984\pi$
$14$		0			0
$15$	1.77056	+	1.36570i	0.457156	+	0.352621i
$16$		0			0
$17$	−7.11384	+	2.31143i	−1.72536	+	0.560603i	−0.992766	−	0.120064i	$-0.961690\pi$
$17$	−7.11384	+	2.31143i	−1.72536	+	0.560603i	−0.732593	+	0.680667i	$0.761690\pi$
$18$		0			0
$19$	−1.91242	−	5.88583i	−0.438740	−	1.35030i	−0.889205	−	0.457508i	$-0.848742\pi$
$19$	−1.91242	−	5.88583i	−0.438740	−	1.35030i	0.450466	−	0.892794i	$-0.351258\pi$
$20$		0			0
$21$	−0.184143	+	0.566735i	−0.0401834	+	0.123672i
$22$		0			0
$23$	−2.59154	−	3.56694i	−0.540373	−	0.743759i	0.448294	−	0.893886i	$-0.352032\pi$
$23$	−2.59154	−	3.56694i	−0.540373	−	0.743759i	−0.988667	+	0.150127i	$0.952032\pi$
$24$		0			0
$25$	3.86983	+	3.16614i	0.773966	+	0.633228i
$26$		0			0
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$		0			0
$29$	0.853035	−	2.62537i	0.158405	−	0.487519i	−0.840085	−	0.542454i	$-0.817495\pi$
$29$	0.853035	−	2.62537i	0.158405	−	0.487519i	0.998490	+	0.0549349i	$0.0174951\pi$
$30$		0			0
$31$	1.38708	+	4.26899i	0.249127	+	0.766734i	0.994930	+	0.100567i	$0.0320658\pi$
$31$	1.38708	+	4.26899i	0.249127	+	0.766734i	−0.745803	+	0.666166i	$0.767934\pi$
$32$		0			0
$33$	3.19137	−	1.03694i	0.555547	−	0.180508i
$34$		0			0
$35$	−0.447952	+	1.25492i	−0.0757176	+	0.212120i
$36$		0			0
$37$	−0.764512	+	1.05226i	−0.125685	+	0.172991i	−0.867222	−	0.497921i	$-0.834097\pi$
$37$	−0.764512	+	1.05226i	−0.125685	+	0.172991i	0.741537	+	0.670912i	$0.234097\pi$
$38$		0			0
$39$	3.85825	−	2.80319i	0.617815	−	0.448869i
$40$		0			0
$41$	7.61184	+	5.53032i	1.18877	+	0.863691i	0.993134	−	0.116985i	$-0.0373230\pi$
$41$	7.61184	+	5.53032i	1.18877	+	0.863691i	0.195636	+	0.980677i	$0.437323\pi$
$42$		0			0
$43$		−	7.59854i		−	1.15877i	−0.815055	−	0.579383i	$-0.803294\pi$
$43$		−	7.59854i		−	1.15877i	0.815055	−	0.579383i	$-0.196706\pi$
$44$		0			0
$45$	−1.26188	−	1.84599i	−0.188109	−	0.275183i
$46$		0			0
$47$	−4.18645	−	1.36026i	−0.610656	−	0.198414i	−0.0126688	−	0.999920i	$-0.504033\pi$
$47$	−4.18645	−	1.36026i	−0.610656	−	0.198414i	−0.597987	+	0.801506i	$0.704033\pi$
$48$		0			0
$49$	6.64490			0.949272
$50$		0			0
$51$	7.47993			1.04740
$52$		0			0
$53$	−7.80561	−	2.53620i	−1.07218	−	0.348373i	−0.280846	−	0.959753i	$-0.590615\pi$
$53$	−7.80561	−	2.53620i	−1.07218	−	0.348373i	−0.791338	+	0.611379i	$0.790615\pi$
$54$		0			0
$55$	7.19972	−	2.11294i	0.970811	−	0.284909i
$56$		0			0
$57$			6.18873i			0.819717i
$58$		0			0
$59$	−1.80309	−	1.31002i	−0.234743	−	0.170550i	0.464195	−	0.885733i	$-0.346344\pi$
$59$	−1.80309	−	1.31002i	−0.234743	−	0.170550i	−0.698938	+	0.715182i	$0.746344\pi$
$60$		0			0
$61$	−10.2014	+	7.41175i	−1.30615	+	0.948977i	−0.999995	−	0.00300353i	$-0.999044\pi$
$61$	−10.2014	+	7.41175i	−1.30615	+	0.948977i	−0.306159	+	0.951980i	$0.599044\pi$
$62$		0			0
$63$	0.350262	−	0.482094i	0.0441288	−	0.0607381i
$64$		0			0
$65$	8.80363	−	6.01797i	1.09196	−	0.746437i
$66$		0			0
$67$	7.94930	−	2.58288i	0.971161	−	0.315549i	0.219877	−	0.975528i	$-0.429435\pi$
$67$	7.94930	−	2.58288i	0.971161	−	0.315549i	0.751285	+	0.659978i	$0.229435\pi$
$68$		0			0
$69$	1.36245	+	4.19319i	0.164020	+	0.504801i
$70$		0			0
$71$	2.09986	−	6.46271i	0.249208	−	0.766983i	−0.745708	−	0.666273i	$-0.767889\pi$
$71$	2.09986	−	6.46271i	0.249208	−	0.766983i	0.994916	−	0.100710i	$-0.0321114\pi$
$72$		0			0
$73$	4.29801	+	5.91570i	0.503044	+	0.692381i	0.982727	−	0.185061i	$-0.0592483\pi$
$73$	4.29801	+	5.91570i	0.503044	+	0.692381i	−0.479683	+	0.877442i	$0.659248\pi$
$74$		0			0
$75$	−2.70203	−	4.20702i	−0.312004	−	0.485785i
$76$		0			0
$77$	1.17534	+	1.61772i	0.133943	+	0.184356i
$78$		0			0
$79$	3.26546	−	10.0500i	0.367393	−	1.13072i	−0.581076	−	0.813849i	$-0.697368\pi$
$79$	3.26546	−	10.0500i	0.367393	−	1.13072i	0.948469	−	0.316870i	$-0.102632\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−3.97694	+	1.29219i	−0.436526	+	0.141836i	−0.519032	−	0.854755i	$-0.673708\pi$
$83$	−3.97694	+	1.29219i	−0.436526	+	0.141836i	0.0825062	+	0.996591i	$0.473708\pi$
$84$		0			0
$85$	16.7188	+	0.479942i	1.81340	+	0.0520571i
$86$		0			0
$87$	−1.62257	+	2.23328i	−0.173958	+	0.239432i
$88$		0			0
$89$	3.43862	−	2.49830i	0.364493	−	0.264819i	−0.390431	−	0.920632i	$-0.627674\pi$
$89$	3.43862	−	2.49830i	0.364493	−	0.264819i	0.754924	+	0.655813i	$0.227674\pi$
$90$		0			0
$91$	2.29914	+	1.67042i	0.241015	+	0.175108i
$92$		0			0
$93$		−	4.48868i		−	0.465455i
$94$		0			0
$95$	−0.397094	+	13.8327i	−0.0407409	+	1.41921i
$96$		0			0
$97$	−11.6744	−	3.79326i	−1.18536	−	0.385147i	−0.351004	−	0.936374i	$-0.614160\pi$
$97$	−11.6744	−	3.79326i	−1.18536	−	0.385147i	−0.834355	+	0.551227i	$0.814160\pi$
$98$		0			0
$99$	−3.35561			−0.337251
$100$		0			0
$101$	−8.00835			−0.796860			−0.398430	−	0.917199i	$-0.630445\pi$
$101$	−8.00835			−0.796860			−0.398430	+	0.917199i	$0.630445\pi$
$102$		0			0
$103$	−5.34989	−	1.73829i	−0.527141	−	0.171278i	0.0333428	−	0.999444i	$-0.489385\pi$
$103$	−5.34989	−	1.73829i	−0.527141	−	0.171278i	−0.560484	+	0.828166i	$0.689385\pi$
$104$		0			0
$105$	0.813819	−	1.05508i	0.0794206	−	0.102965i
$106$		0			0
$107$			13.7701i			1.33120i	0.746308	+	0.665601i	$0.231825\pi$
$107$			13.7701i			1.33120i	−0.746308	+	0.665601i	$0.768175\pi$
$108$		0			0
$109$	−10.3566	−	7.52450i	−0.991981	−	0.720716i	−0.0316266	−	0.999500i	$-0.510069\pi$
$109$	−10.3566	−	7.52450i	−0.991981	−	0.720716i	−0.960354	+	0.278784i	$0.910069\pi$
$110$		0			0
$111$	1.05226	−	0.764512i	0.0998761	−	0.0725643i
$112$		0			0
$113$	6.84147	−	9.41647i	0.643591	−	0.885827i	−0.355210	−	0.934787i	$-0.615591\pi$
$113$	6.84147	−	9.41647i	0.643591	−	0.885827i	0.998801	+	0.0489597i	$0.0155906\pi$
$114$		0			0
$115$	2.77623	+	9.45983i	0.258885	+	0.882133i
$116$		0			0
$117$	−4.53565	+	1.47372i	−0.419321	+	0.136246i
$118$		0			0
$119$	1.37738	+	4.23914i	0.126264	+	0.388601i
$120$		0			0
$121$	0.0803793	−	0.247382i	0.00730721	−	0.0224893i
$122$		0			0
$123$	−5.53032	−	7.61184i	−0.498652	−	0.686336i
$124$		0			0
$125$	−5.76951	−	9.57668i	−0.516040	−	0.856564i
$126$		0			0
$127$	1.56452	+	2.15338i	0.138829	+	0.191081i	0.872770	−	0.488132i	$-0.162321\pi$
$127$	1.56452	+	2.15338i	0.138829	+	0.191081i	−0.733941	+	0.679213i	$0.762321\pi$
$128$		0			0
$129$	−2.34808	+	7.22664i	−0.206737	+	0.636270i
$130$		0			0
$131$	3.00070	+	9.23520i	0.262172	+	0.806883i	0.992331	+	0.123606i	$0.0394458\pi$
$131$	3.00070	+	9.23520i	0.262172	+	0.806883i	−0.730159	+	0.683277i	$0.760554\pi$
$132$		0			0
$133$	−3.50737	+	1.13961i	−0.304128	+	0.0988170i
$134$		0			0
$135$	0.629675	+	2.14558i	0.0541938	+	0.184662i
$136$		0			0
$137$	−2.25823	+	3.10819i	−0.192934	+	0.265551i	−0.894514	−	0.447040i	$-0.852478\pi$
$137$	−2.25823	+	3.10819i	−0.192934	+	0.265551i	0.701580	+	0.712591i	$0.252478\pi$
$138$		0			0
$139$	−3.98655	+	2.89640i	−0.338135	+	0.245670i	−0.743875	−	0.668319i	$-0.767014\pi$
$139$	−3.98655	+	2.89640i	−0.338135	+	0.245670i	0.405740	+	0.913989i	$0.367014\pi$
$140$		0			0
$141$	3.56121	+	2.58737i	0.299908	+	0.217896i
$142$		0			0
$143$		−	16.0031i		−	1.33825i
$144$		0			0
$145$	−3.76998	+	4.88759i	−0.313080	+	0.405892i
$146$		0			0
$147$	−6.31968	−	2.05339i	−0.521238	−	0.169361i
$148$		0			0
$149$	6.59040			0.539907			0.269953	−	0.962873i	$-0.412992\pi$
$149$	6.59040			0.539907			0.269953	+	0.962873i	$0.412992\pi$
$150$		0			0
$151$	−19.5433			−1.59041			−0.795207	−	0.606338i	$-0.792638\pi$
$151$	−19.5433			−1.59041			−0.795207	+	0.606338i	$0.792638\pi$
$152$		0			0
$153$	−7.11384	−	2.31143i	−0.575120	−	0.186868i
$154$		0			0
$155$	0.288012	−	10.0329i	0.0231337	−	0.805859i
$156$		0			0
$157$			0.341995i			0.0272942i	0.999907	+	0.0136471i	$0.00434414\pi$
$157$			0.341995i			0.0272942i	−0.999907	+	0.0136471i	$0.995656\pi$
$158$		0			0
$159$	6.63985	+	4.82413i	0.526574	+	0.382579i
$160$		0			0
$161$	−2.12554	+	1.54430i	−0.167516	+	0.121708i
$162$		0			0
$163$	−13.2347	+	18.2161i	−1.03663	+	1.42679i	−0.136770	+	0.990603i	$0.543672\pi$
$163$	−13.2347	+	18.2161i	−1.03663	+	1.42679i	−0.899855	+	0.436190i	$0.856328\pi$
$164$		0			0
$165$	−7.50028	−	0.215309i	−0.583896	−	0.0167618i
$166$		0			0
$167$	4.10375	−	1.33339i	0.317557	−	0.103181i	−0.145901	−	0.989299i	$-0.546608\pi$
$167$	4.10375	−	1.33339i	0.317557	−	0.103181i	0.463459	+	0.886118i	$0.346608\pi$
$168$		0			0
$169$	−3.01105	−	9.26706i	−0.231619	−	0.712851i
$170$		0			0
$171$	1.91242	−	5.88583i	0.146247	−	0.450101i
$172$		0			0
$173$	10.0916	+	13.8898i	0.767247	+	1.05602i	0.996577	+	0.0826755i	$0.0263465\pi$
$173$	10.0916	+	13.8898i	0.767247	+	1.05602i	−0.229330	+	0.973349i	$0.573653\pi$
$174$		0			0
$175$	1.88670	−	2.30603i	0.142621	−	0.174320i
$176$		0			0
$177$	1.31002	+	1.80309i	0.0984674	+	0.135529i
$178$		0			0
$179$	−0.328670	+	1.01154i	−0.0245659	+	0.0756062i	−0.962588	−	0.270970i	$-0.912656\pi$
$179$	−0.328670	+	1.01154i	−0.0245659	+	0.0756062i	0.938022	+	0.346576i	$0.112656\pi$
$180$		0			0
$181$	−3.71645	−	11.4380i	−0.276241	−	0.850183i	−0.988888	−	0.148660i	$-0.952504\pi$
$181$	−3.71645	−	11.4380i	−0.276241	−	0.850183i	0.712647	−	0.701523i	$-0.247496\pi$
$182$		0			0
$183$	11.9925	−	3.89659i	0.886508	−	0.288044i
$184$		0			0
$185$	2.40101	−	1.64128i	0.176526	−	0.120669i
$186$		0			0
$187$	14.7533	−	20.3061i	1.07886	−	1.48493i
$188$		0			0
$189$	−0.482094	+	0.350262i	−0.0350672	+	0.0254778i
$190$		0			0
$191$	17.7737	+	12.9134i	1.28606	+	0.934379i	0.999718	−	0.0237480i	$-0.00755992\pi$
$191$	17.7737	+	12.9134i	1.28606	+	0.934379i	0.286344	+	0.958127i	$0.407560\pi$
$192$		0			0
$193$			20.4002i			1.46844i	0.678912	+	0.734220i	$0.262452\pi$
$193$			20.4002i			1.46844i	−0.678912	+	0.734220i	$0.737548\pi$
$194$		0			0
$195$	−10.2324	+	3.00296i	−0.732758	+	0.215046i
$196$		0			0
$197$	−3.90410	−	1.26852i	−0.278155	−	0.0903781i	0.166617	−	0.986022i	$-0.446716\pi$
$197$	−3.90410	−	1.26852i	−0.278155	−	0.0903781i	−0.444773	+	0.895644i	$0.646716\pi$
$198$		0			0
$199$	−25.5940			−1.81431			−0.907156	−	0.420795i	$-0.861751\pi$
$199$	−25.5940			−1.81431			−0.907156	+	0.420795i	$0.861751\pi$
$200$		0			0
$201$	−8.35839			−0.589555
$202$		0			0
$203$	−1.56446	−	0.508324i	−0.109804	−	0.0356774i
$204$		0			0
$205$	−11.8727	−	17.3684i	−0.829224	−	1.21306i
$206$		0			0
$207$		−	4.40898i		−	0.306446i
$208$		0			0
$209$	16.8008	+	12.2065i	1.16214	+	0.844342i
$210$		0			0
$211$	−15.7826	+	11.4667i	−1.08652	+	0.789402i	−0.978808	−	0.204781i	$-0.934352\pi$
$211$	−15.7826	+	11.4667i	−1.08652	+	0.789402i	−0.107710	+	0.994182i	$0.534352\pi$
$212$		0			0
$213$	−3.99418	+	5.49751i	−0.273676	+	0.376683i
$214$		0			0
$215$	−5.71199	+	16.0019i	−0.389554	+	1.09132i
$216$		0			0
$217$	2.54389	−	0.826561i	0.172691	−	0.0561106i
$218$		0			0
$219$	−2.25960	−	6.95433i	−0.152689	−	0.469930i
$220$		0			0
$221$	11.0233	−	33.9263i	0.741510	−	2.28213i
$222$		0			0
$223$	1.30975	+	1.80271i	0.0877071	+	0.120718i	0.850616	−	0.525788i	$-0.176229\pi$
$223$	1.30975	+	1.80271i	0.0877071	+	0.120718i	−0.762909	+	0.646506i	$0.776229\pi$
$224$		0			0
$225$	1.26975	+	4.83609i	0.0846498	+	0.322406i
$226$		0			0
$227$	−2.67322	−	3.67938i	−0.177428	−	0.244209i	0.711035	−	0.703156i	$-0.248227\pi$
$227$	−2.67322	−	3.67938i	−0.177428	−	0.244209i	−0.888463	+	0.458947i	$0.848227\pi$
$228$		0			0
$229$	−1.05533	+	3.24796i	−0.0697380	+	0.214631i	−0.979851	−	0.199728i	$-0.935994\pi$
$229$	−1.05533	+	3.24796i	−0.0697380	+	0.214631i	0.910113	+	0.414359i	$0.135994\pi$
$230$		0			0
$231$	−0.617913	−	1.90174i	−0.0406557	−	0.125125i
$232$		0			0
$233$	15.9202	−	5.17279i	1.04297	−	0.338881i	0.263063	−	0.964779i	$-0.415267\pi$
$233$	15.9202	−	5.17279i	1.04297	−	0.338881i	0.779905	+	0.625898i	$0.215267\pi$
$234$		0			0
$235$	7.79380	+	6.01165i	0.508412	+	0.392157i
$236$		0			0
$237$	−6.21127	+	8.54908i	−0.403465	+	0.555323i
$238$		0			0
$239$	−18.0931	+	13.1454i	−1.17035	+	0.850306i	−0.991050	−	0.133490i	$-0.957382\pi$
$239$	−18.0931	+	13.1454i	−1.17035	+	0.850306i	−0.179295	+	0.983795i	$0.557382\pi$
$240$		0			0
$241$	−0.214678	−	0.155973i	−0.0138286	−	0.0100471i	0.580849	−	0.814011i	$-0.302720\pi$
$241$	−0.214678	−	0.155973i	−0.0138286	−	0.0100471i	−0.594678	+	0.803964i	$0.702720\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$	−13.9937	−	4.99512i	−0.894022	−	0.319126i
$246$		0			0
$247$	28.0699	+	9.12046i	1.78604	+	0.580321i
$248$		0			0
$249$	4.18160			0.264998
$250$		0			0
$251$	29.0694			1.83484			0.917422	−	0.397915i	$-0.130266\pi$
$251$	29.0694			1.83484			0.917422	+	0.397915i	$0.130266\pi$
$252$		0			0
$253$	14.0707	+	4.57185i	0.884619	+	0.287430i
$254$		0			0
$255$	−15.7522	−	5.62283i	−0.986439	−	0.352115i
$256$		0			0
$257$		−	7.05952i		−	0.440361i	−0.975459	−	0.220180i	$-0.929335\pi$
$257$		−	7.05952i		−	0.440361i	0.975459	−	0.220180i	$-0.0706646\pi$
$258$		0			0
$259$	0.627043	+	0.455573i	0.0389625	+	0.0283079i
$260$		0			0
$261$	2.23328	−	1.62257i	0.138236	−	0.100435i
$262$		0			0
$263$	−0.814961	+	1.12170i	−0.0502527	+	0.0691669i	−0.833404	−	0.552665i	$-0.813611\pi$
$263$	−0.814961	+	1.12170i	−0.0502527	+	0.0691669i	0.783151	+	0.621831i	$0.213611\pi$
$264$		0			0
$265$	14.5315	+	11.2087i	0.892663	+	0.688544i
$266$		0			0
$267$	−4.04234	+	1.31343i	−0.247387	+	0.0803809i
$268$		0			0
$269$	4.38039	+	13.4815i	0.267077	+	0.821979i	0.991208	+	0.132316i	$0.0422414\pi$
$269$	4.38039	+	13.4815i	0.267077	+	0.821979i	−0.724130	+	0.689663i	$0.757759\pi$
$270$		0			0
$271$	4.64795	−	14.3049i	0.282343	−	0.868963i	−0.704839	−	0.709367i	$-0.748981\pi$
$271$	4.64795	−	14.3049i	0.282343	−	0.868963i	0.987182	−	0.159596i	$-0.0510191\pi$
$272$		0			0
$273$	−1.67042	−	2.29914i	−0.101098	−	0.139150i
$274$		0			0
$275$	−16.7504	−	0.962496i	−1.01009	−	0.0580407i
$276$		0			0
$277$	−7.51973	−	10.3500i	−0.451817	−	0.621873i	0.520970	−	0.853575i	$-0.325570\pi$
$277$	−7.51973	−	10.3500i	−0.451817	−	0.621873i	−0.972787	+	0.231703i	$0.925570\pi$
$278$		0			0
$279$	−1.38708	+	4.26899i	−0.0830423	+	0.255578i
$280$		0			0
$281$	−4.72976	−	14.5567i	−0.282154	−	0.868380i	−0.987237	−	0.159256i	$-0.949091\pi$
$281$	−4.72976	−	14.5567i	−0.282154	−	0.868380i	0.705084	−	0.709124i	$-0.250909\pi$
$282$		0			0
$283$	22.2073	−	7.21559i	1.32009	−	0.428923i	0.437563	−	0.899188i	$-0.355842\pi$
$283$	22.2073	−	7.21559i	1.32009	−	0.428923i	0.882525	+	0.470265i	$0.155842\pi$
$284$		0			0
$285$	4.65220	−	13.0330i	0.275573	−	0.772008i
$286$		0			0
$287$	3.29552	−	4.53590i	0.194529	−	0.267746i
$288$		0			0
$289$	31.5107	−	22.8939i	1.85357	−	1.34670i
$290$		0			0
$291$	9.93087	+	7.21520i	0.582158	+	0.422963i
$292$		0			0
$293$		−	6.36651i		−	0.371936i	−0.982556	−	0.185968i	$-0.940458\pi$
$293$		−	6.36651i		−	0.371936i	0.982556	−	0.185968i	$-0.0595420\pi$
$294$		0			0
$295$	2.81240	+	4.11423i	0.163744	+	0.239540i
$296$		0			0
$297$	3.19137	+	1.03694i	0.185182	+	0.0601694i
$298$		0			0
$299$	21.0267			1.21601
$300$		0			0
$301$	−4.52797			−0.260988
$302$		0			0
$303$	7.61639	+	2.47472i	0.437550	+	0.142169i
$304$		0			0
$305$	27.0549	−	7.93996i	1.54916	−	0.454641i
$306$		0			0
$307$		−	27.2317i		−	1.55419i	−0.629382	−	0.777096i	$-0.716692\pi$
$307$		−	27.2317i		−	1.55419i	0.629382	−	0.777096i	$-0.283308\pi$
$308$		0			0
$309$	4.55089	+	3.30642i	0.258891	+	0.188095i
$310$		0			0
$311$	−13.8814	+	10.0854i	−0.787142	+	0.571892i	−0.907114	−	0.420885i	$-0.861719\pi$
$311$	−13.8814	+	10.0854i	−0.787142	+	0.571892i	0.119972	+	0.992777i	$0.461719\pi$
$312$		0			0
$313$	−11.9120	+	16.3955i	−0.673307	+	0.926728i	−0.999830	−	0.0184618i	$-0.994123\pi$
$313$	−11.9120	+	16.3955i	−0.673307	+	0.926728i	0.326523	+	0.945189i	$0.394123\pi$
$314$		0			0
$315$	−1.10002	+	0.751953i	−0.0619794	+	0.0423678i
$316$		0			0
$317$	19.9868	−	6.49409i	1.12257	−	0.364745i	0.311821	−	0.950141i	$-0.399061\pi$
$317$	19.9868	−	6.49409i	1.12257	−	0.364745i	0.810747	+	0.585396i	$0.199061\pi$
$318$		0			0
$319$	2.86245	+	8.80972i	0.160267	+	0.493250i
$320$		0			0
$321$	4.25518	−	13.0961i	0.237501	−	0.730953i
$322$		0			0
$323$	27.2093	+	37.4504i	1.51397	+	2.08380i
$324$		0			0
$325$	−23.0636	+	6.05550i	−1.27934	+	0.335899i
$326$		0			0
$327$	7.52450	+	10.3566i	0.416106	+	0.572720i
$328$		0			0
$329$	−0.810579	+	2.49471i	−0.0446887	+	0.137538i
$330$		0			0
$331$	−3.93765	−	12.1188i	−0.216433	−	0.666111i	−0.999049	−	0.0436066i	$-0.986115\pi$
$331$	−3.93765	−	12.1188i	−0.216433	−	0.666111i	0.782616	−	0.622505i	$-0.213885\pi$
$332$		0			0
$333$	−1.23701	+	0.401928i	−0.0677875	+	0.0220255i
$334$		0			0
$335$	−18.6822	−	0.536308i	−1.02072	−	0.0293016i
$336$		0			0
$337$	7.25720	−	9.98868i	0.395325	−	0.544118i	−0.564238	−	0.825612i	$-0.690830\pi$
$337$	7.25720	−	9.98868i	0.395325	−	0.544118i	0.959563	+	0.281494i	$0.0908300\pi$
$338$		0			0
$339$	−9.41647	+	6.84147i	−0.511432	+	0.371577i
$340$		0			0
$341$	−12.1856	−	8.85338i	−0.659889	−	0.479437i
$342$		0			0
$343$		−	8.13100i		−	0.439033i
$344$		0			0
$345$	0.282898	−	9.85473i	0.0152307	−	0.530561i
$346$		0			0
$347$	12.5175	+	4.06718i	0.671974	+	0.218337i	0.625078	−	0.780562i	$-0.285067\pi$
$347$	12.5175	+	4.06718i	0.671974	+	0.218337i	0.0468956	+	0.998900i	$0.485067\pi$
$348$		0			0
$349$	−20.8060			−1.11372			−0.556861	−	0.830606i	$-0.687994\pi$
$349$	−20.8060			−1.11372			−0.556861	+	0.830606i	$0.687994\pi$
$350$		0			0
$351$	4.76906			0.254554
$352$		0			0
$353$	−27.3852	−	8.89800i	−1.45757	−	0.473593i	−0.530242	−	0.847846i	$-0.677899\pi$
$353$	−27.3852	−	8.89800i	−1.45757	−	0.473593i	−0.927326	+	0.374254i	$0.877899\pi$
$354$		0			0
$355$	−9.28031	+	12.0315i	−0.492548	+	0.638564i
$356$		0			0
$357$		−	4.45730i		−	0.235905i
$358$		0			0
$359$	−26.9627	−	19.5896i	−1.42304	−	1.03390i	−0.991260	−	0.131919i	$-0.957886\pi$
$359$	−26.9627	−	19.5896i	−1.42304	−	1.03390i	−0.431779	−	0.901979i	$-0.642114\pi$
$360$		0			0
$361$	−15.6143	+	11.3445i	−0.821806	+	0.597077i
$362$		0			0
$363$	−0.152891	+	0.210436i	−0.00802468	+	0.0110450i
$364$		0			0
$365$	−4.60432	−	15.6889i	−0.241001	−	0.821196i
$366$		0			0
$367$	1.80441	−	0.586288i	0.0941894	−	0.0306040i	−0.261543	−	0.965192i	$-0.584231\pi$
$367$	1.80441	−	0.586288i	0.0941894	−	0.0306040i	0.355733	+	0.934588i	$0.384231\pi$
$368$		0			0
$369$	2.90746	+	8.94825i	0.151356	+	0.465827i
$370$		0			0
$371$	−1.51132	+	4.65137i	−0.0784639	+	0.241487i
$372$		0			0
$373$	18.1572	+	24.9912i	0.940143	+	1.29400i	0.955769	+	0.294118i	$0.0950258\pi$
$373$	18.1572	+	24.9912i	0.940143	+	1.29400i	−0.0156262	+	0.999878i	$0.504974\pi$
$374$		0			0
$375$	2.52777	+	10.8908i	0.130533	+	0.562401i
$376$		0			0
$377$	7.73814	+	10.6506i	0.398534	+	0.548535i
$378$		0			0
$379$	−6.96979	+	21.4508i	−0.358014	+	1.10185i	0.596227	+	0.802816i	$0.296666\pi$
$379$	−6.96979	+	21.4508i	−0.358014	+	1.10185i	−0.954241	+	0.299038i	$0.903334\pi$
$380$		0			0
$381$	−0.822516	−	2.53145i	−0.0421388	−	0.129690i
$382$		0			0
$383$	−4.13113	+	1.34229i	−0.211091	+	0.0685877i	−0.412654	−	0.910888i	$-0.635398\pi$
$383$	−4.13113	+	1.34229i	−0.211091	+	0.0685877i	0.201563	+	0.979476i	$0.435398\pi$
$384$		0			0
$385$	−1.25910	−	4.29032i	−0.0641699	−	0.218655i
$386$		0			0
$387$	4.46631	−	6.14735i	0.227035	−	0.312487i
$388$		0			0
$389$	−15.0039	+	10.9010i	−0.760729	+	0.552702i	−0.899134	−	0.437674i	$-0.855802\pi$
$389$	−15.0039	+	10.9010i	−0.760729	+	0.552702i	0.138405	+	0.990376i	$0.455802\pi$
$390$		0			0
$391$	26.6805	+	19.3845i	1.34929	+	0.980317i
$392$		0			0
$393$		−	9.71046i		−	0.489828i
$394$		0			0
$395$	−14.4317	+	18.7099i	−0.726135	+	0.941398i
$396$		0			0
$397$	0.672391	+	0.218473i	0.0337463	+	0.0109648i	0.325842	−	0.945424i	$-0.394352\pi$
$397$	0.672391	+	0.218473i	0.0337463	+	0.0109648i	−0.292095	+	0.956389i	$0.594352\pi$
$398$		0			0
$399$	3.68787			0.184624
$400$		0			0
$401$	−24.8304			−1.23997			−0.619986	−	0.784613i	$-0.712862\pi$
$401$	−24.8304			−1.23997			−0.619986	+	0.784613i	$0.712862\pi$
$402$		0			0
$403$	−20.3591	−	6.61507i	−1.01416	−	0.329520i
$404$		0			0
$405$	0.0641640	−	2.23515i	0.00318833	−	0.111065i
$406$		0			0
$407$		−	4.36453i		−	0.216341i
$408$		0			0
$409$	−0.590588	−	0.429087i	−0.0292027	−	0.0212170i	0.573088	−	0.819494i	$-0.305745\pi$
$409$	−0.590588	−	0.429087i	−0.0292027	−	0.0212170i	−0.602291	+	0.798277i	$0.705745\pi$
$410$		0			0
$411$	3.10819	−	2.25823i	0.153316	−	0.111390i
$412$		0			0
$413$	−0.780643	+	1.07446i	−0.0384130	+	0.0528709i
$414$		0			0
$415$	9.34650	+	0.268308i	0.458802	+	0.0131707i
$416$		0			0
$417$	4.68647	−	1.52273i	0.229498	−	0.0745683i
$418$		0			0
$419$	3.98923	+	12.2776i	0.194887	+	0.599799i	0.999978	+	0.00664830i	$0.00211623\pi$
$419$	3.98923	+	12.2776i	0.194887	+	0.599799i	−0.805091	+	0.593151i	$0.797884\pi$
$420$		0			0
$421$	11.7828	−	36.2639i	0.574261	−	1.76739i	−0.0644219	−	0.997923i	$-0.520520\pi$
$421$	11.7828	−	36.2639i	0.574261	−	1.76739i	0.638683	−	0.769470i	$-0.279480\pi$
$422$		0			0
$423$	−2.58737	−	3.56121i	−0.125802	−	0.173152i
$424$		0			0
$425$	−34.8476	−	13.5786i	−1.69036	−	0.658658i
$426$		0			0
$427$	4.41666	+	6.07902i	0.213737	+	0.294184i
$428$		0			0
$429$	−4.94523	+	15.2199i	−0.238758	+	0.734822i
$430$		0			0
$431$	−11.1829	−	34.4175i	−0.538663	−	1.65783i	−0.735599	−	0.677418i	$-0.763099\pi$
$431$	−11.1829	−	34.4175i	−0.538663	−	1.65783i	0.196936	−	0.980416i	$-0.436901\pi$
$432$		0			0
$433$	20.6842	−	6.72071i	0.994021	−	0.322977i	0.233547	−	0.972346i	$-0.424967\pi$
$433$	20.6842	−	6.72071i	0.994021	−	0.322977i	0.760474	+	0.649369i	$0.224967\pi$
$434$		0			0
$435$	5.09581	−	3.48339i	0.244325	−	0.167016i
$436$		0			0
$437$	−16.0383	+	22.0748i	−0.767217	+	1.05598i
$438$		0			0
$439$	−31.8418	+	23.1344i	−1.51973	+	1.10415i	−0.558103	+	0.829772i	$0.688471\pi$
$439$	−31.8418	+	23.1344i	−1.51973	+	1.10415i	−0.961623	+	0.274374i	$0.911529\pi$
$440$		0			0
$441$	5.37584	+	3.90578i	0.255992	+	0.185989i
$442$		0			0
$443$		−	27.4919i		−	1.30618i	−0.757281	−	0.653089i	$-0.773473\pi$
$443$		−	27.4919i		−	1.30618i	0.757281	−	0.653089i	$-0.226527\pi$
$444$		0			0
$445$	−9.11949	+	2.67635i	−0.432305	+	0.126871i
$446$		0			0
$447$	−6.26784	−	2.03655i	−0.296459	−	0.0963253i
$448$		0			0
$449$	−3.51087			−0.165688			−0.0828441	−	0.996563i	$-0.526400\pi$
$449$	−3.51087			−0.165688			−0.0828441	+	0.996563i	$0.526400\pi$
$450$		0			0
$451$	−31.5721			−1.48667
$452$		0			0
$453$	18.5868	+	6.03923i	0.873285	+	0.283748i
$454$		0			0
$455$	−3.58611	−	5.24609i	−0.168120	−	0.245940i
$456$		0			0
$457$			10.1677i			0.475624i	0.971311	+	0.237812i	$0.0764302\pi$
$457$			10.1677i			0.475624i	−0.971311	+	0.237812i	$0.923570\pi$
$458$		0			0
$459$	6.05139	+	4.39659i	0.282455	+	0.205215i
$460$		0			0
$461$	−0.755758	+	0.549090i	−0.0351992	+	0.0255737i	−0.605246	−	0.796039i	$-0.706925\pi$
$461$	−0.755758	+	0.549090i	−0.0351992	+	0.0255737i	0.570047	+	0.821612i	$0.306925\pi$
$462$		0			0
$463$	2.87183	−	3.95274i	0.133465	−	0.183699i	−0.737053	−	0.675835i	$-0.763783\pi$
$463$	2.87183	−	3.95274i	0.133465	−	0.183699i	0.870519	+	0.492135i	$0.163783\pi$
$464$		0			0
$465$	−3.37424	+	9.45282i	−0.156477	+	0.438364i
$466$		0			0
$467$	−24.5416	+	7.97406i	−1.13565	+	0.368996i	−0.815721	−	0.578445i	$-0.803660\pi$
$467$	−24.5416	+	7.97406i	−1.13565	+	0.368996i	−0.319931	+	0.947441i	$0.603660\pi$
$468$		0			0
$469$	−1.53914	−	4.73699i	−0.0710710	−	0.218734i
$470$		0			0
$471$	0.105682	−	0.325257i	0.00486958	−	0.0149870i
$472$		0			0
$473$	14.9872	+	20.6281i	0.689111	+	0.948480i
$474$		0			0
$475$	11.2346	−	28.8321i	0.515479	−	1.32291i
$476$		0			0
$477$	−4.82413	−	6.63985i	−0.220882	−	0.304018i
$478$		0			0
$479$	5.22721	−	16.0877i	0.238837	−	0.735065i	−0.757752	−	0.652543i	$-0.773702\pi$
$479$	5.22721	−	16.0877i	0.238837	−	0.735065i	0.996589	−	0.0825225i	$-0.0262976\pi$
$480$		0			0
$481$	−1.91682	−	5.89936i	−0.0873994	−	0.268988i
$482$		0			0
$483$	2.49873	−	0.811885i	0.113696	−	0.0369421i
$484$		0			0
$485$	21.7340	+	16.7642i	0.986890	+	0.761225i
$486$		0			0
$487$	−9.63237	+	13.2578i	−0.436484	+	0.600769i	−0.969426	−	0.245383i	$-0.921086\pi$
$487$	−9.63237	+	13.2578i	−0.436484	+	0.600769i	0.532942	+	0.846152i	$0.321086\pi$
$488$		0			0
$489$	18.2161	−	13.2347i	0.823759	−	0.598496i
$490$		0			0
$491$	8.30972	+	6.03737i	0.375013	+	0.272463i	0.759286	−	0.650757i	$-0.225548\pi$
$491$	8.30972	+	6.03737i	0.375013	+	0.272463i	−0.384274	+	0.923219i	$0.625548\pi$
$492$		0			0
$493$			20.6482i			0.929948i
$494$		0			0
$495$	7.06666	+	2.52249i	0.317623	+	0.113377i
$496$		0			0
$497$	−3.85113	−	1.25131i	−0.172747	−	0.0561289i
$498$		0			0
$499$	16.5015			0.738707			0.369354	−	0.929289i	$-0.379579\pi$
$499$	16.5015			0.738707			0.369354	+	0.929289i	$0.379579\pi$
$500$		0			0
$501$	−4.31493			−0.192777
$502$		0			0
$503$	−7.22834	−	2.34863i	−0.322296	−	0.104720i	0.143401	−	0.989665i	$-0.454196\pi$
$503$	−7.22834	−	2.34863i	−0.322296	−	0.104720i	−0.465697	+	0.884944i	$0.654196\pi$
$504$		0			0
$505$	16.8650	+	6.02005i	0.750481	+	0.267889i
$506$		0			0
$507$			9.74397i			0.432745i
$508$		0			0
$509$	−17.7590	−	12.9027i	−0.787154	−	0.571901i	0.119963	−	0.992778i	$-0.461722\pi$
$509$	−17.7590	−	12.9027i	−0.787154	−	0.571901i	−0.907118	+	0.420877i	$0.861722\pi$
$510$		0			0
$511$	3.52517	−	2.56119i	0.155944	−	0.113300i
$512$		0			0
$513$	−3.63764	+	5.00679i	−0.160606	+	0.221055i
$514$		0			0
$515$	9.95976	+	7.68233i	0.438879	+	0.338524i
$516$		0			0
$517$	14.0481	−	4.56450i	0.617834	−	0.200746i
$518$		0			0
$519$	−5.30544	−	16.3285i	−0.232883	−	0.716741i
$520$		0			0
$521$	−11.3835	+	35.0349i	−0.498722	+	1.53491i	0.312353	+	0.949966i	$0.398883\pi$
$521$	−11.3835	+	35.0349i	−0.498722	+	1.53491i	−0.811075	+	0.584942i	$0.801117\pi$
$522$		0			0
$523$	−24.4517	−	33.6548i	−1.06920	−	1.47162i	−0.870887	−	0.491484i	$-0.836455\pi$
$523$	−24.4517	−	33.6548i	−1.06920	−	1.47162i	−0.198310	−	0.980139i	$-0.563545\pi$
$524$		0			0
$525$	−2.50696	+	1.61014i	−0.109413	+	0.0702724i
$526$		0			0
$527$	−19.7349	−	27.1628i	−0.859667	−	1.18323i
$528$		0			0
$529$	1.10036	−	3.38657i	0.0478419	−	0.147242i
$530$		0			0
$531$	−0.688720	−	2.11966i	−0.0298879	−	0.0919855i
$532$		0			0
$533$	−42.6748	+	13.8659i	−1.84845	+	0.600598i
$534$		0			0
$535$	10.3513	−	28.9987i	0.447524	−	1.25372i
$536$		0			0
$537$	0.625167	−	0.860469i	0.0269779	−	0.0371320i
$538$		0			0
$539$	−18.0392	+	13.1063i	−0.777004	+	0.564526i
$540$		0			0
$541$	12.5570	+	9.12319i	0.539867	+	0.392237i	0.824036	−	0.566538i	$-0.191717\pi$
$541$	12.5570	+	9.12319i	0.539867	+	0.392237i	−0.284168	+	0.958774i	$0.591717\pi$
$542$		0			0
$543$			12.0267i			0.516114i
$544$		0			0
$545$	16.1538	+	23.6313i	0.691954	+	1.01225i
$546$		0			0
$547$	22.1633	+	7.20130i	0.947636	+	0.307906i	0.741755	−	0.670671i	$-0.233994\pi$
$547$	22.1633	+	7.20130i	0.947636	+	0.307906i	0.205881	+	0.978577i	$0.433994\pi$
$548$		0			0
$549$	−12.6096			−0.538165
$550$		0			0
$551$	−17.0839			−0.727797
$552$		0			0
$553$	−5.98883	−	1.94589i	−0.254671	−	0.0827476i
$554$		0			0
$555$	−2.79068	+	0.818996i	−0.118458	+	0.0347645i
$556$		0			0
$557$		−	11.0914i		−	0.469959i	−0.972000	−	0.234979i	$-0.924498\pi$
$557$		−	11.0914i		−	0.469959i	0.972000	−	0.234979i	$-0.0755023\pi$
$558$		0			0
$559$	29.3171	+	21.3001i	1.23998	+	0.900898i
$560$		0			0
$561$	−20.3061	+	14.7533i	−0.857325	+	0.622883i
$562$		0			0
$563$	8.40836	−	11.5731i	0.354370	−	0.487749i	−0.594199	−	0.804318i	$-0.702531\pi$
$563$	8.40836	−	11.5731i	0.354370	−	0.487749i	0.948569	+	0.316569i	$0.102531\pi$
$564$		0			0
$565$	−21.4862	+	14.6875i	−0.903930	+	0.617907i
$566$		0			0
$567$	0.566735	−	0.184143i	0.0238006	−	0.00773330i
$568$		0			0
$569$	8.89176	+	27.3660i	0.372762	+	1.14724i	0.944976	+	0.327139i	$0.106085\pi$
$569$	8.89176	+	27.3660i	0.372762	+	1.14724i	−0.572214	+	0.820104i	$0.693915\pi$
$570$		0			0
$571$	−4.02941	+	12.4012i	−0.168625	+	0.518976i	−0.999285	−	0.0378048i	$-0.987963\pi$
$571$	−4.02941	+	12.4012i	−0.168625	+	0.518976i	0.830660	+	0.556780i	$0.187963\pi$
$572$		0			0
$573$	−12.9134	−	17.7737i	−0.539464	−	0.742508i
$574$		0			0
$575$	1.26464	−	22.0086i	0.0527390	−	0.917823i
$576$		0			0
$577$	1.05786	+	1.45601i	0.0440391	+	0.0606147i	0.830469	−	0.557065i	$-0.188073\pi$
$577$	1.05786	+	1.45601i	0.0440391	+	0.0606147i	−0.786430	+	0.617680i	$0.788073\pi$
$578$		0			0
$579$	6.30401	−	19.4018i	0.261986	−	0.806309i
$580$		0			0
$581$	0.770015	+	2.36986i	0.0319456	+	0.0983184i
$582$		0			0
$583$	26.1926	−	8.51049i	1.08479	−	0.352468i
$584$		0			0
$585$	10.6596	+	0.306002i	0.440719	+	0.0126516i
$586$		0			0
$587$	23.8620	−	32.8432i	0.984889	−	1.35558i	0.0507360	−	0.998712i	$-0.483843\pi$
$587$	23.8620	−	32.8432i	0.984889	−	1.35558i	0.934153	−	0.356872i	$-0.116157\pi$
$588$		0			0
$589$	22.4739	−	16.3282i	0.926020	−	0.672793i
$590$		0			0
$591$	3.32102	+	2.41286i	0.136609	+	0.0992519i
$592$		0			0
$593$		−	29.4991i		−	1.21138i	−0.795700	−	0.605690i	$-0.792897\pi$
$593$		−	29.4991i		−	1.21138i	0.795700	−	0.605690i	$-0.207103\pi$
$594$		0			0
$595$	0.285998	−	9.96271i	0.0117248	−	0.408431i
$596$		0			0
$597$	24.3413	+	7.90898i	0.996225	+	0.323693i
$598$		0			0
$599$	8.91418			0.364224			0.182112	−	0.983278i	$-0.441707\pi$
$599$	8.91418			0.364224			0.182112	+	0.983278i	$0.441707\pi$
$600$		0			0
$601$	16.6757			0.680217			0.340109	−	0.940386i	$-0.389536\pi$
$601$	16.6757			0.680217			0.340109	+	0.940386i	$0.389536\pi$
$602$		0			0
$603$	7.94930	+	2.58288i	0.323720	+	0.105183i
$604$		0			0
$605$	−0.355235	+	0.460545i	−0.0144424	+	0.0187238i
$606$		0			0
$607$			26.9626i			1.09438i	0.837008	+	0.547190i	$0.184302\pi$
$607$			26.9626i			1.09438i	−0.837008	+	0.547190i	$0.815698\pi$
$608$		0			0
$609$	1.33081	+	0.966890i	0.0539271	+	0.0391804i
$610$		0			0
$611$	16.9836	−	12.3393i	0.687083	−	0.499195i
$612$		0			0
$613$	−9.71195	+	13.3673i	−0.392262	+	0.539902i	−0.958781	−	0.284147i	$-0.908290\pi$
$613$	−9.71195	+	13.3673i	−0.392262	+	0.539902i	0.566519	+	0.824049i	$0.308290\pi$
$614$		0			0
$615$	5.92445	+	20.1872i	0.238897	+	0.814027i
$616$		0			0
$617$	−21.8628	+	7.10364i	−0.880161	+	0.285982i	−0.714024	−	0.700121i	$-0.753129\pi$
$617$	−21.8628	+	7.10364i	−0.880161	+	0.285982i	−0.166137	+	0.986103i	$0.553129\pi$
$618$		0			0
$619$	−15.2396	−	46.9028i	−0.612533	−	1.88518i	−0.432875	−	0.901454i	$-0.642501\pi$
$619$	−15.2396	−	46.9028i	−0.612533	−	1.88518i	−0.179658	−	0.983729i	$-0.557499\pi$
$620$		0			0
$621$	−1.36245	+	4.19319i	−0.0546733	+	0.168267i
$622$		0			0
$623$	−1.48874	−	2.04907i	−0.0596451	−	0.0820944i
$624$		0			0
$625$	4.95114	+	24.5048i	0.198045	+	0.980193i
$626$		0			0
$627$	−12.2065	−	16.8008i	−0.487481	−	0.670960i
$628$		0			0
$629$	3.00639	−	9.25273i	0.119873	−	0.368930i
$630$		0			0
$631$	7.47148	+	22.9948i	0.297435	+	0.915410i	0.982393	+	0.186828i	$0.0598206\pi$
$631$	7.47148	+	22.9948i	0.297435	+	0.915410i	−0.684958	+	0.728583i	$0.740179\pi$
$632$		0			0
$633$	18.5535	−	6.02841i	0.737437	−	0.239608i
$634$		0			0
$635$	−1.67602	−	5.71093i	−0.0665107	−	0.226631i
$636$		0			0
$637$	−18.6269	+	25.6377i	−0.738024	+	1.01580i
$638$		0			0
$639$	5.49751	−	3.99418i	0.217478	−	0.158007i
$640$		0			0
$641$	39.9382	+	29.0168i	1.57746	+	1.14610i	0.919530	+	0.393020i	$0.128570\pi$
$641$	39.9382	+	29.0168i	1.57746	+	1.14610i	0.657935	+	0.753075i	$0.271430\pi$
$642$		0			0
$643$		−	3.97743i		−	0.156854i	−0.996920	−	0.0784272i	$-0.975010\pi$
$643$		−	3.97743i		−	0.156854i	0.996920	−	0.0784272i	$-0.0249898\pi$
$644$		0			0
$645$	10.3773	−	13.4536i	0.408606	−	0.529737i
$646$		0			0
$647$	0.964765	+	0.313471i	0.0379288	+	0.0123238i	0.327920	−	0.944706i	$-0.393652\pi$
$647$	0.964765	+	0.313471i	0.0379288	+	0.0123238i	−0.289991	+	0.957029i	$0.593652\pi$
$648$		0			0
$649$	7.47879			0.293568
$650$		0			0
$651$	−2.67481			−0.104834
$652$		0			0
$653$	7.77161	+	2.52515i	0.304127	+	0.0988167i	0.457105	−	0.889413i	$-0.348886\pi$
$653$	7.77161	+	2.52515i	0.304127	+	0.0988167i	−0.152978	+	0.988230i	$0.548886\pi$
$654$		0			0
$655$	0.623062	−	21.7043i	0.0243450	−	0.848057i
$656$		0			0
$657$			7.31221i			0.285277i
$658$		0			0
$659$	6.22020	+	4.51924i	0.242305	+	0.176045i	0.702309	−	0.711872i	$-0.252152\pi$
$659$	6.22020	+	4.51924i	0.242305	+	0.176045i	−0.460005	+	0.887916i	$0.652152\pi$
$660$		0			0
$661$	29.2864	−	21.2778i	1.13911	−	0.827611i	0.152114	−	0.988363i	$-0.451392\pi$
$661$	29.2864	−	21.2778i	1.13911	−	0.827611i	0.986995	+	0.160752i	$0.0513919\pi$
$662$		0			0
$663$	−20.9676	+	28.8595i	−0.814316	+	1.12081i
$664$		0			0
$665$	8.24292	+	0.236628i	0.319647	+	0.00917605i
$666$		0			0
$667$	−11.5752	+	3.76102i	−0.448195	+	0.145627i
$668$		0			0
$669$	−0.688574	−	2.11921i	−0.0266218	−	0.0819335i
$670$		0			0
$671$	13.0754	−	40.2420i	0.504771	−	1.55353i
$672$		0			0
$673$	−17.7405	−	24.4177i	−0.683845	−	0.941233i	0.316127	−	0.948717i	$-0.397618\pi$
$673$	−17.7405	−	24.4177i	−0.683845	−	0.941233i	−0.999972	+	0.00748451i	$0.997618\pi$
$674$		0			0
$675$	0.286832	−	4.99177i	0.0110402	−	0.192133i
$676$		0			0
$677$	27.6349	+	38.0362i	1.06210	+	1.46185i	0.877829	+	0.478975i	$0.158991\pi$
$677$	27.6349	+	38.0362i	1.06210	+	1.46185i	0.184268	+	0.982876i	$0.441009\pi$
$678$		0			0
$679$	−2.26040	+	6.95680i	−0.0867463	+	0.266978i
$680$		0			0
$681$	1.40540	+	4.32537i	0.0538549	+	0.165748i
$682$		0			0
$683$	2.08476	−	0.677379i	0.0797710	−	0.0259192i	−0.268860	−	0.963179i	$-0.586647\pi$
$683$	2.08476	−	0.677379i	0.0797710	−	0.0259192i	0.348631	+	0.937260i	$0.386647\pi$
$684$		0			0
$685$	7.09217	−	4.84805i	0.270978	−	0.185235i
$686$		0			0
$687$	2.00735	−	2.76288i	0.0765852	−	0.105411i
$688$		0			0
$689$	31.6659	−	23.0066i	1.20637	−	0.876482i
$690$		0			0
$691$	−1.44427	−	1.04932i	−0.0549425	−	0.0399181i	0.559975	−	0.828509i	$-0.310811\pi$
$691$	−1.44427	−	1.04932i	−0.0549425	−	0.0399181i	−0.614918	+	0.788591i	$0.710811\pi$
$692$		0			0
$693$			1.99961i			0.0759589i
$694$		0			0
$695$	10.5727	−	3.10282i	0.401044	−	0.117697i
$696$		0			0
$697$	−66.9323	−	21.7476i	−2.53524	−	0.823750i
$698$		0			0
$699$	−16.7395			−0.633146
$700$		0			0
$701$	−11.0728			−0.418215			−0.209107	−	0.977893i	$-0.567056\pi$
$701$	−11.0728			−0.418215			−0.209107	+	0.977893i	$0.567056\pi$
$702$		0			0
$703$	7.65550	+	2.48742i	0.288733	+	0.0938149i
$704$		0			0
$705$	−5.55464	−	8.12583i	−0.209200	−	0.306037i
$706$		0			0
$707$			4.77218i			0.179476i
$708$		0			0
$709$	16.1099	+	11.7045i	0.605020	+	0.439573i	0.847657	−	0.530544i	$-0.178012\pi$
$709$	16.1099	+	11.7045i	0.605020	+	0.439573i	−0.242637	+	0.970117i	$0.578012\pi$
$710$		0			0
$711$	8.54908	−	6.21127i	0.320616	−	0.232941i
$712$		0			0
$713$	11.6326	−	16.0109i	0.435644	−	0.599612i
$714$		0			0
$715$	−12.0299	+	33.7013i	−0.449892	+	1.26036i
$716$		0			0
$717$	21.2697	−	6.91095i	0.794332	−	0.258094i
$718$		0			0
$719$	−10.7477	−	33.0782i	−0.400823	−	1.23361i	−0.924333	−	0.381587i	$-0.875377\pi$
$719$	−10.7477	−	33.0782i	−0.400823	−	1.23361i	0.523509	−	0.852020i	$-0.324623\pi$
$720$		0			0
$721$	−1.03585	+	3.18801i	−0.0385769	+	0.118728i
$722$		0			0
$723$	0.155973	+	0.214678i	0.00580068	+	0.00798395i
$724$		0			0
$725$	11.6134	−	7.45891i	0.431311	−	0.277017i
$726$		0			0
$727$	−9.38558	−	12.9181i	−0.348092	−	0.479107i	0.598691	−	0.800980i	$-0.295688\pi$
$727$	−9.38558	−	12.9181i	−0.348092	−	0.479107i	−0.946783	+	0.321873i	$0.895688\pi$
$728$		0			0
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	17.5635	+	54.0548i	0.649608	+	1.99929i
$732$		0			0
$733$	9.64606	−	3.13420i	0.356286	−	0.115764i	−0.125405	−	0.992106i	$-0.540023\pi$
$733$	9.64606	−	3.13420i	0.356286	−	0.115764i	0.481690	+	0.876341i	$0.340023\pi$
$734$		0			0
$735$	11.7652	+	9.07492i	0.433965	+	0.334733i
$736$		0			0
$737$	−16.4859	+	22.6909i	−0.607266	+	0.835830i
$738$		0			0
$739$	2.65234	−	1.92704i	0.0975681	−	0.0708873i	−0.537932	−	0.842988i	$-0.680794\pi$
$739$	2.65234	−	1.92704i	0.0975681	−	0.0708873i	0.635500	+	0.772101i	$0.280794\pi$
$740$		0			0
$741$	−23.8777	−	17.3482i	−0.877169	−	0.637300i
$742$		0			0
$743$			38.7278i			1.42078i	0.703806	+	0.710392i	$0.251482\pi$
$743$			38.7278i			1.42078i	−0.703806	+	0.710392i	$0.748518\pi$
$744$		0			0
$745$	−13.8789	−	4.95415i	−0.508483	−	0.181506i
$746$		0			0
$747$	−3.97694	−	1.29219i	−0.145509	−	0.0472786i
$748$		0			0
$749$	8.20559			0.299826
$750$		0			0
$751$	13.0211			0.475146			0.237573	−	0.971370i	$-0.423648\pi$
$751$	13.0211			0.475146			0.237573	+	0.971370i	$0.423648\pi$
$752$		0			0
$753$	−27.6466	−	8.98294i	−1.00750	−	0.327357i
$754$		0			0
$755$	41.1568	+	14.6912i	1.49785	+	0.534666i
$756$		0			0
$757$		−	33.4057i		−	1.21415i	−0.794645	−	0.607075i	$-0.792343\pi$
$757$		−	33.4057i		−	1.21415i	0.794645	−	0.607075i	$-0.207657\pi$
$758$		0			0
$759$	−11.9693	−	8.69618i	−0.434457	−	0.315651i
$760$		0			0
$761$	−24.0536	+	17.4760i	−0.871943	+	0.633504i	−0.931108	−	0.364745i	$-0.881156\pi$
$761$	−24.0536	+	17.4760i	−0.871943	+	0.633504i	0.0591647	+	0.998248i	$0.481156\pi$
$762$		0			0
$763$	−4.48385	+	6.17149i	−0.162326	+	0.223423i
$764$		0			0
$765$	13.2437	+	10.2153i	0.478825	+	0.369336i
$766$		0			0
$767$	10.1088	−	3.28455i	0.365008	−	0.118598i
$768$		0			0
$769$	1.68546	+	5.18732i	0.0607794	+	0.187060i	0.976836	−	0.213989i	$-0.0686458\pi$
$769$	1.68546	+	5.18732i	0.0607794	+	0.187060i	−0.916057	+	0.401049i	$0.868646\pi$
$770$		0			0
$771$	−2.18151	+	6.71400i	−0.0785652	+	0.241799i
$772$		0			0
$773$	17.0953	+	23.5297i	0.614875	+	0.846303i	0.996967	−	0.0778211i	$-0.0247963\pi$
$773$	17.0953	+	23.5297i	0.614875	+	0.846303i	−0.382092	+	0.924124i	$0.624796\pi$
$774$		0			0
$775$	−8.14846	+	20.9119i	−0.292701	+	0.751179i
$776$		0			0
$777$	−0.455573	−	0.627043i	−0.0163436	−	0.0224950i
$778$		0			0
$779$	17.9935	−	55.3783i	0.644684	−	1.98413i
$780$		0			0
$781$	7.04632	+	21.6863i	0.252137	+	0.775998i
$782$		0			0
$783$	−2.62537	+	0.853035i	−0.0938232	+	0.0304850i
$784$		0			0
$785$	0.257085	−	0.720216i	0.00917577	−	0.0257056i
$786$		0			0
$787$	−20.0518	+	27.5989i	−0.714768	+	0.983794i	0.284913	+	0.958553i	$0.408035\pi$
$787$	−20.0518	+	27.5989i	−0.714768	+	0.983794i	−0.999681	+	0.0252406i	$0.991965\pi$
$788$		0			0
$789$	1.12170	−	0.814961i	0.0399335	−	0.0290134i
$790$		0			0
$791$	−5.61128	−	4.07683i	−0.199514	−	0.144955i
$792$		0			0
$793$		−	60.1361i		−	2.13549i
$794$		0			0
$795$	−10.3566	−	15.1506i	−0.367311	−	0.537336i
$796$		0			0
$797$	23.2590	+	7.55732i	0.823877	+	0.267694i	0.690464	−	0.723367i	$-0.257406\pi$
$797$	23.2590	+	7.55732i	0.823877	+	0.267694i	0.133413	+	0.991061i	$0.457406\pi$
$798$		0			0
$799$	32.9259			1.16483
$800$		0			0
$801$	4.25036			0.150179
$802$		0			0
$803$	−23.3360	−	7.58233i	−0.823510	−	0.267574i
$804$		0			0
$805$	5.63712	−	1.65436i	0.198682	−	0.0583084i
$806$		0			0
$807$		−	14.1752i		−	0.498992i
$808$		0			0
$809$	−42.2701	−	30.7110i	−1.48614	−	1.07974i	−0.975514	−	0.219937i	$-0.929415\pi$
$809$	−42.2701	−	30.7110i	−1.48614	−	1.07974i	−0.510623	−	0.859805i	$-0.670585\pi$
$810$		0			0
$811$	−14.2781	+	10.3736i	−0.501371	+	0.364267i	−0.809540	−	0.587064i	$-0.800284\pi$
$811$	−14.2781	+	10.3736i	−0.501371	+	0.364267i	0.308170	+	0.951331i	$0.400284\pi$
$812$		0			0
$813$	−8.84093	+	12.1685i	−0.310065	+	0.426768i
$814$		0			0
$815$	41.5648	−	28.4128i	1.45595	−	0.995257i
$816$		0			0
$817$	−44.7237	+	14.5316i	−1.56468	+	0.508397i
$818$		0			0
$819$	0.878192	+	2.70280i	0.0306865	+	0.0944433i
$820$		0			0
$821$	−10.5469	+	32.4602i	−0.368091	+	1.13287i	0.579932	+	0.814665i	$0.303079\pi$
$821$	−10.5469	+	32.4602i	−0.368091	+	1.13287i	−0.948023	+	0.318202i	$0.896921\pi$
$822$		0			0
$823$	−26.7608	−	36.8331i	−0.932823	−	1.28392i	−0.958748	−	0.284257i	$-0.908253\pi$
$823$	−26.7608	−	36.8331i	−0.932823	−	1.28392i	0.0259255	−	0.999664i	$-0.491747\pi$
$824$		0			0
$825$	15.6332	+	6.09155i	0.544277	+	0.212081i
$826$		0			0
$827$	−11.2248	−	15.4496i	−0.390323	−	0.537234i	0.567959	−	0.823057i	$-0.307733\pi$
$827$	−11.2248	−	15.4496i	−0.390323	−	0.537234i	−0.958282	+	0.285823i	$0.907733\pi$
$828$		0			0
$829$	−3.51719	+	10.8248i	−0.122157	+	0.375961i	−0.993372	−	0.114940i	$-0.963332\pi$
$829$	−3.51719	+	10.8248i	−0.122157	+	0.375961i	0.871215	+	0.490901i	$0.163332\pi$
$830$		0			0
$831$	3.95336	+	12.1672i	0.137140	+	0.422075i
$832$		0			0
$833$	−47.2708	+	15.3592i	−1.63783	+	0.532165i
$834$		0			0
$835$	−9.64451	−	0.276863i	−0.333762	−	0.00958125i
$836$		0			0
$837$	2.63838	−	3.63142i	0.0911958	−	0.125520i
$838$		0			0
$839$	20.8665	−	15.1604i	0.720391	−	0.523395i	−0.166118	−	0.986106i	$-0.553123\pi$
$839$	20.8665	−	15.1604i	0.720391	−	0.523395i	0.886509	+	0.462711i	$0.153123\pi$
$840$		0			0
$841$	17.2966	+	12.5667i	0.596434	+	0.433335i
$842$		0			0
$843$			15.3058i			0.527160i
$844$		0			0
$845$	−0.625212	+	21.7792i	−0.0215079	+	0.749227i
$846$		0			0
$847$	−0.147415	−	0.0478981i	−0.00506525	−	0.00164580i
$848$		0			0
$849$	−23.3502			−0.801375
$850$		0			0
$851$	5.73461			0.196580
$852$		0			0
$853$	−14.9706	−	4.86423i	−0.512582	−	0.166548i	0.0412941	−	0.999147i	$-0.486852\pi$
$853$	−14.9706	−	4.86423i	−0.512582	−	0.166548i	−0.553876	+	0.832599i	$0.686852\pi$
$854$		0			0
$855$	−8.45192	+	10.9575i	−0.289050	+	0.374739i
$856$		0			0
$857$		−	46.4948i		−	1.58823i	−0.607767	−	0.794116i	$-0.707934\pi$
$857$		−	46.4948i		−	1.58823i	0.607767	−	0.794116i	$-0.292066\pi$
$858$		0			0
$859$	9.86663	+	7.16852i	0.336645	+	0.244587i	0.743245	−	0.669019i	$-0.233286\pi$
$859$	9.86663	+	7.16852i	0.336645	+	0.244587i	−0.406600	+	0.913606i	$0.633286\pi$
$860$		0			0
$861$	−4.53590	+	3.29552i	−0.154583	+	0.112311i
$862$		0			0
$863$	26.6811	−	36.7234i	0.908235	−	1.25008i	−0.0595307	−	0.998226i	$-0.518960\pi$
$863$	26.6811	−	36.7234i	0.908235	−	1.25008i	0.967766	−	0.251852i	$-0.0810396\pi$
$864$		0			0
$865$	−10.8107	−	36.8370i	−0.367576	−	1.25249i
$866$		0			0
$867$	−37.0431	+	12.0360i	−1.25805	+	0.408765i
$868$		0			0
$869$	10.9576	+	33.7240i	0.371711	+	1.14401i
$870$		0			0
$871$	−12.3179	+	37.9107i	−0.417377	+	1.28456i
$872$		0			0
$873$	−7.21520	−	9.93087i	−0.244198	−	0.336109i
$874$		0			0
$875$	−5.70675	+	3.43805i	−0.192923	+	0.116227i
$876$		0			0
$877$	11.1859	+	15.3960i	0.377720	+	0.519887i	0.954979	−	0.296675i	$-0.0958777\pi$
$877$	11.1859	+	15.3960i	0.377720	+	0.519887i	−0.577259	+	0.816561i	$0.695878\pi$
$878$		0			0
$879$	−1.96736	+	6.05491i	−0.0663574	+	0.204227i
$880$		0			0
$881$	−4.70004	−	14.4652i	−0.158348	−	0.487346i	0.840136	−	0.542375i	$-0.182475\pi$
$881$	−4.70004	−	14.4652i	−0.158348	−	0.487346i	−0.998485	+	0.0550289i	$0.982475\pi$
$882$		0			0
$883$	−45.9532	+	14.9311i	−1.54645	+	0.502472i	−0.953147	−	0.302507i	$-0.902176\pi$
$883$	−45.9532	+	14.9311i	−1.54645	+	0.502472i	−0.593303	+	0.804979i	$0.702176\pi$
$884$		0			0
$885$	−1.40338	−	4.78195i	−0.0471742	−	0.160743i
$886$		0			0
$887$	−19.0449	+	26.2130i	−0.639464	+	0.880146i	−0.998587	−	0.0531439i	$-0.983076\pi$
$887$	−19.0449	+	26.2130i	−0.639464	+	0.880146i	0.359123	+	0.933290i	$0.383076\pi$
$888$		0			0
$889$	1.28320	−	0.932298i	0.0430371	−	0.0312683i
$890$		0			0
$891$	−2.71474	−	1.97238i	−0.0909474	−	0.0660771i
$892$		0			0
$893$			27.2421i			0.911622i
$894$		0			0
$895$	1.45255	−	1.88316i	0.0485534	−	0.0629471i
$896$		0			0
$897$	−19.9976	−	6.49762i	−0.667701	−	0.216949i
$898$		0			0
$899$	12.3909			0.413260
$900$		0			0
$901$	61.3901			2.04520
$902$		0			0
$903$	4.30636	+	1.39922i	0.143307	+	0.0465631i
$904$		0			0
$905$	−0.771680	+	26.8814i	−0.0256515	+	0.893568i
$906$		0			0
$907$			30.8525i			1.02444i	0.858854	+	0.512220i	$0.171177\pi$
$907$			30.8525i			1.02444i	−0.858854	+	0.512220i	$0.828823\pi$
$908$		0			0
$909$	−6.47889	−	4.70719i	−0.214891	−	0.156128i
$910$		0			0
$911$	−29.3011	+	21.2885i	−0.970787	+	0.705318i	−0.955631	−	0.294567i	$-0.904825\pi$
$911$	−29.3011	+	21.2885i	−0.970787	+	0.705318i	−0.0151564	+	0.999885i	$0.504825\pi$
$912$		0			0
$913$	8.24770	−	11.3520i	0.272959	−	0.375696i
$914$		0			0
$915$	−28.1843	−	0.809083i	−0.931746	−	0.0267475i
$916$		0			0
$917$	5.50326	−	1.78812i	0.181734	−	0.0590488i
$918$		0			0
$919$	11.7420	+	36.1380i	0.387331	+	1.19208i	0.934775	+	0.355240i	$0.115601\pi$
$919$	11.7420	+	36.1380i	0.387331	+	1.19208i	−0.547444	+	0.836842i	$0.684399\pi$
$920$		0			0
$921$	−8.41505	+	25.8988i	−0.277285	+	0.853396i
$922$		0			0
$923$	19.0485	+	26.2180i	0.626988	+	0.862975i
$924$		0			0
$925$	−6.29013	+	1.65152i	−0.206818	+	0.0543015i
$926$		0			0
$927$	−3.30642	−	4.55089i	−0.108597	−	0.149471i
$928$		0			0
$929$	3.23230	−	9.94801i	0.106048	−	0.326384i	−0.883927	−	0.467626i	$-0.845110\pi$
$929$	3.23230	−	9.94801i	0.106048	−	0.326384i	0.989975	+	0.141242i	$0.0451096\pi$
$930$		0			0
$931$	−12.7079	−	39.1108i	−0.416483	−	1.28180i
$932$		0			0
$933$	16.3186	−	5.30222i	0.534246	−	0.173587i
$934$		0			0
$935$	−46.3338	+	31.6728i	−1.51528	+	1.03581i
$936$		0			0
$937$	−19.8458	+	27.3155i	−0.648335	+	0.892357i	−0.999026	−	0.0441344i	$-0.985947\pi$
$937$	−19.8458	+	27.3155i	−0.648335	+	0.892357i	0.350690	+	0.936492i	$0.385947\pi$
$938$		0			0
$939$	16.3955	−	11.9120i	0.535046	−	0.388734i
$940$		0			0
$941$	−1.80449	−	1.31104i	−0.0588247	−	0.0427386i	0.557984	−	0.829851i	$-0.311575\pi$
$941$	−1.80449	−	1.31104i	−0.0588247	−	0.0427386i	−0.616809	+	0.787113i	$0.711575\pi$
$942$		0			0
$943$		−	41.4830i		−	1.35087i
$944$		0			0
$945$	1.27855	−	0.375224i	0.0415913	−	0.0122060i
$946$		0			0
$947$	−7.27701	−	2.36444i	−0.236471	−	0.0768341i	0.188384	−	0.982095i	$-0.439675\pi$
$947$	−7.27701	−	2.36444i	−0.236471	−	0.0768341i	−0.424855	+	0.905261i	$0.639675\pi$
$948$		0			0
$949$	−34.8724			−1.13201
$950$		0			0
$951$	−21.0153			−0.681469
$952$		0			0
$953$	−11.0823	−	3.60086i	−0.358991	−	0.116643i	0.123968	−	0.992286i	$-0.460438\pi$
$953$	−11.0823	−	3.60086i	−0.358991	−	0.116643i	−0.482959	+	0.875643i	$0.660438\pi$
$954$		0			0
$955$	−27.7229	−	40.5555i	−0.897091	−	1.31234i
$956$		0			0
$957$		−	9.26309i		−	0.299433i
$958$		0			0
$959$	1.85217	+	1.34568i	0.0598098	+	0.0434544i
$960$		0			0
$961$	8.77922	−	6.37848i	0.283201	−	0.205757i
$962$		0			0
$963$	−8.09384	+	11.1402i	−0.260820	+	0.358988i
$964$		0			0
$965$	15.3353	−	42.9613i	0.493660	−	1.38297i
$966$		0			0
$967$	−32.1250	+	10.4380i	−1.03307	+	0.335665i	−0.776004	−	0.630729i	$-0.782756\pi$
$967$	−32.1250	+	10.4380i	−1.03307	+	0.335665i	−0.257067	+	0.966394i	$0.582756\pi$
$968$		0			0
$969$	−14.3048	−	44.0256i	−0.459536	−	1.41431i
$970$		0			0
$971$	10.4403	−	32.1319i	0.335045	−	1.03116i	−0.631655	−	0.775250i	$-0.717624\pi$
$971$	10.4403	−	32.1319i	0.335045	−	1.03116i	0.966700	−	0.255913i	$-0.0823760\pi$
$972$		0			0
$973$	1.72597	+	2.37559i	0.0553320	+	0.0761579i
$974$		0			0
$975$	23.8060	+	1.36792i	0.762404	+	0.0438085i
$976$		0			0
$977$	−2.21653	−	3.05079i	−0.0709131	−	0.0976035i	0.772087	−	0.635517i	$-0.219213\pi$
$977$	−2.21653	−	3.05079i	−0.0709131	−	0.0976035i	−0.843000	+	0.537913i	$0.819213\pi$
$978$		0			0
$979$	−4.40737	+	13.5645i	−0.140860	+	0.433523i
$980$		0			0
$981$	−3.95586	−	12.1749i	−0.126301	−	0.388714i
$982$		0			0
$983$	−40.2335	+	13.0727i	−1.28325	+	0.416953i	−0.869723	−	0.493539i	$-0.835703\pi$
$983$	−40.2335	+	13.0727i	−1.28325	+	0.416953i	−0.413526	+	0.910492i	$0.635703\pi$
$984$		0			0
$985$	7.26815	+	5.60620i	0.231583	+	0.178628i
$986$		0			0
$987$	1.54181	−	2.12212i	0.0490765	−	0.0675480i
$988$		0			0
$989$	−27.1036	+	19.6919i	−0.861843	+	0.626165i
$990$		0			0
$991$	−25.8789	−	18.8021i	−0.822071	−	0.597269i	0.0952341	−	0.995455i	$-0.469640\pi$
$991$	−25.8789	−	18.8021i	−0.822071	−	0.597269i	−0.917305	+	0.398186i	$0.869640\pi$
$992$		0			0
$993$			12.7425i			0.404371i
$994$		0			0
$995$	53.8990	+	19.2396i	1.70871	+	0.609936i
$996$		0			0
$997$	15.8900	+	5.16296i	0.503240	+	0.163513i	0.549626	−	0.835411i	$-0.314770\pi$
$997$	15.8900	+	5.16296i	0.503240	+	0.163513i	−0.0463858	+	0.998924i	$0.514770\pi$
$998$		0			0
$999$	1.30067			0.0411512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.o.a.289.1	yes	24
3.2	odd	2		900.2.w.c.289.6		24
5.2	odd	4		1500.2.m.d.301.4		24
5.3	odd	4		1500.2.m.c.301.3		24
5.4	even	2		1500.2.o.c.949.5		24
25.3	odd	20		7500.2.a.n.1.6		12
25.4	even	10		7500.2.d.g.1249.19		24
25.9	even	10	inner	300.2.o.a.109.1	✓	24
25.12	odd	20		1500.2.m.d.1201.4		24
25.13	odd	20		1500.2.m.c.1201.3		24
25.16	even	5		1500.2.o.c.49.5		24
25.21	even	5		7500.2.d.g.1249.6		24
25.22	odd	20		7500.2.a.m.1.7		12
75.59	odd	10		900.2.w.c.109.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.1	✓	24	25.9	even	10	inner
300.2.o.a.289.1	yes	24	1.1	even	1	trivial
900.2.w.c.109.6		24	75.59	odd	10
900.2.w.c.289.6		24	3.2	odd	2
1500.2.m.c.301.3		24	5.3	odd	4
1500.2.m.c.1201.3		24	25.13	odd	20
1500.2.m.d.301.4		24	5.2	odd	4
1500.2.m.d.1201.4		24	25.12	odd	20
1500.2.o.c.49.5		24	25.16	even	5
1500.2.o.c.949.5		24	5.4	even	2
7500.2.a.m.1.7		12	25.22	odd	20
7500.2.a.n.1.6		12	25.3	odd	20
7500.2.d.g.1249.6		24	25.21	even	5
7500.2.d.g.1249.19		24	25.4	even	10

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.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{3} +(-2.10592 - 0.751722i) q^{5} -0.595901i q^{7} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{3} +(-2.10592 - 0.751722i) q^{5} -0.595901i q^{7} +(0.809017 + 0.587785i) q^{9} +(-2.71474 + 1.97238i) q^{11} +(-2.80319 + 3.85825i) q^{13} +(1.77056 + 1.36570i) q^{15} +(-7.11384 + 2.31143i) q^{17} +(-1.91242 - 5.88583i) q^{19} +(-0.184143 + 0.566735i) q^{21} +(-2.59154 - 3.56694i) q^{23} +(3.86983 + 3.16614i) q^{25} +(-0.587785 - 0.809017i) q^{27} +(0.853035 - 2.62537i) q^{29} +(1.38708 + 4.26899i) q^{31} +(3.19137 - 1.03694i) q^{33} +(-0.447952 + 1.25492i) q^{35} +(-0.764512 + 1.05226i) q^{37} +(3.85825 - 2.80319i) q^{39} +(7.61184 + 5.53032i) q^{41} -7.59854i q^{43} +(-1.26188 - 1.84599i) q^{45} +(-4.18645 - 1.36026i) q^{47} +6.64490 q^{49} +7.47993 q^{51} +(-7.80561 - 2.53620i) q^{53} +(7.19972 - 2.11294i) q^{55} +6.18873i q^{57} +(-1.80309 - 1.31002i) q^{59} +(-10.2014 + 7.41175i) q^{61} +(0.350262 - 0.482094i) q^{63} +(8.80363 - 6.01797i) q^{65} +(7.94930 - 2.58288i) q^{67} +(1.36245 + 4.19319i) q^{69} +(2.09986 - 6.46271i) q^{71} +(4.29801 + 5.91570i) q^{73} +(-2.70203 - 4.20702i) q^{75} +(1.17534 + 1.61772i) q^{77} +(3.26546 - 10.0500i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-3.97694 + 1.29219i) q^{83} +(16.7188 + 0.479942i) q^{85} +(-1.62257 + 2.23328i) q^{87} +(3.43862 - 2.49830i) q^{89} +(2.29914 + 1.67042i) q^{91} -4.48868i q^{93} +(-0.397094 + 13.8327i) q^{95} +(-11.6744 - 3.79326i) q^{97} -3.35561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^5 + 6 * q^9	\( 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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