LMFDB - Embedded newform 1500.2.o.a.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, 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("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.3
Root			$0.207912 + 0.978148i$ of defining polynomial
Character	$\chi$	$=$	1500.49
Dual form			1500.2.o.a.949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{3} -4.78339i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{3} -4.78339i q^{7} +(0.809017 - 0.587785i) q^{9} +(-1.58268 - 1.14988i) q^{11} +(0.634721 + 0.873619i) q^{13} +(-3.61946 - 1.17603i) q^{17} +(-1.31359 + 4.04280i) q^{19} +(-1.47815 - 4.54927i) q^{21} +(3.44633 - 4.74346i) q^{23} +(0.587785 - 0.809017i) q^{27} +(-3.26015 - 10.0337i) q^{29} +(-1.33369 + 4.10468i) q^{31} +(-1.86055 - 0.604528i) q^{33} +(-3.32676 - 4.57890i) q^{37} +(0.873619 + 0.634721i) q^{39} +(-0.694596 + 0.504654i) q^{41} +10.8764i q^{43} +(-2.85467 + 0.927539i) q^{47} -15.8808 q^{49} -3.80573 q^{51} +(4.01711 - 1.30524i) q^{53} +4.25085i q^{57} +(-3.85916 + 2.80384i) q^{59} +(-2.93822 - 2.13474i) q^{61} +(-2.81160 - 3.86984i) q^{63} +(6.59126 + 2.14163i) q^{67} +(1.81184 - 5.57627i) q^{69} +(-3.70731 - 11.4099i) q^{71} +(9.96647 - 13.7177i) q^{73} +(-5.50033 + 7.57055i) q^{77} +(2.04587 + 6.29656i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.45552 + 0.797847i) q^{83} +(-6.20118 - 8.53519i) q^{87} +(-0.673699 - 0.489471i) q^{89} +(4.17886 - 3.03612i) q^{91} +4.31592i q^{93} +(8.67076 - 2.81730i) q^{97} -1.95630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^9	$ 16 q + 4 q^{9} - 4 q^{11} - 10 q^{19} - 6 q^{21} - 54 q^{29} - 6 q^{31} + 40 q^{41} + 16 q^{49} - 16 q^{51} - 4 q^{59} - 28 q^{61} - 4 q^{69} - 30 q^{71} - 48 q^{79} - 4 q^{81} + 10 q^{91} + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^9 - 4 * q^11 - 10 * q^19 - 6 * q^21 - 54 * q^29 - 6 * q^31 + 40 * q^41 + 16 * q^49 - 16 * q^51 - 4 * q^59 - 28 * q^61 - 4 * q^69 - 30 * q^71 - 48 * q^79 - 4 * q^81 + 10 * q^91 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

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

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

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

$2$		0			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
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	4.78339i		−	1.80795i	−0.427585	−	0.903975i	$-0.640636\pi$
$7$		−	4.78339i		−	1.80795i	0.427585	−	0.903975i	$-0.359364\pi$
$8$		0			0
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−1.58268	−	1.14988i	−0.477195	−	0.346702i	0.323044	−	0.946384i	$-0.395294\pi$
$11$	−1.58268	−	1.14988i	−0.477195	−	0.346702i	−0.800239	+	0.599682i	$0.795294\pi$
$12$		0			0
$13$	0.634721	+	0.873619i	0.176040	+	0.242298i	0.887915	−	0.460008i	$-0.152154\pi$
$13$	0.634721	+	0.873619i	0.176040	+	0.242298i	−0.711875	+	0.702307i	$0.752154\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.61946	−	1.17603i	−0.877848	−	0.285230i	−0.164785	−	0.986330i	$-0.552693\pi$
$17$	−3.61946	−	1.17603i	−0.877848	−	0.285230i	−0.713064	+	0.701099i	$0.752693\pi$
$18$		0			0
$19$	−1.31359	+	4.04280i	−0.301357	+	0.927482i	0.679654	+	0.733533i	$0.262130\pi$
$19$	−1.31359	+	4.04280i	−0.301357	+	0.927482i	−0.981012	+	0.193949i	$0.937870\pi$
$20$		0			0
$21$	−1.47815	−	4.54927i	−0.322558	−	0.992732i
$22$		0			0
$23$	3.44633	−	4.74346i	0.718608	−	0.989080i	−0.280960	−	0.959719i	$-0.590653\pi$
$23$	3.44633	−	4.74346i	0.718608	−	0.989080i	0.999569	−	0.0293604i	$-0.00934704\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$		0			0
$29$	−3.26015	−	10.0337i	−0.605395	−	1.86322i	−0.494050	−	0.869433i	$-0.664484\pi$
$29$	−3.26015	−	10.0337i	−0.605395	−	1.86322i	−0.111345	−	0.993782i	$-0.535516\pi$
$30$		0			0
$31$	−1.33369	+	4.10468i	−0.239538	+	0.737223i	0.756949	+	0.653474i	$0.226689\pi$
$31$	−1.33369	+	4.10468i	−0.239538	+	0.737223i	−0.996487	+	0.0837487i	$0.973311\pi$
$32$		0			0
$33$	−1.86055	−	0.604528i	−0.323880	−	0.105235i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.32676	−	4.57890i	−0.546917	−	0.752766i	0.442673	−	0.896683i	$-0.354030\pi$
$37$	−3.32676	−	4.57890i	−0.546917	−	0.752766i	−0.989590	+	0.143917i	$0.954030\pi$
$38$		0			0
$39$	0.873619	+	0.634721i	0.139891	+	0.101637i
$40$		0			0
$41$	−0.694596	+	0.504654i	−0.108478	+	0.0788137i	−0.640702	−	0.767790i	$-0.721356\pi$
$41$	−0.694596	+	0.504654i	−0.108478	+	0.0788137i	0.532224	+	0.846604i	$0.321356\pi$
$42$		0			0
$43$			10.8764i			1.65864i	0.558773	+	0.829321i	$0.311272\pi$
$43$			10.8764i			1.65864i	−0.558773	+	0.829321i	$0.688728\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.85467	+	0.927539i	−0.416397	+	0.135295i	−0.509720	−	0.860340i	$-0.670251\pi$
$47$	−2.85467	+	0.927539i	−0.416397	+	0.135295i	0.0933233	+	0.995636i	$0.470251\pi$
$48$		0			0
$49$	−15.8808			−2.26868
$50$		0			0
$51$	−3.80573			−0.532908
$52$		0			0
$53$	4.01711	−	1.30524i	0.551793	−	0.179288i	−0.0198323	−	0.999803i	$-0.506313\pi$
$53$	4.01711	−	1.30524i	0.551793	−	0.179288i	0.571625	+	0.820515i	$0.306313\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			4.25085i			0.563039i
$58$		0			0
$59$	−3.85916	+	2.80384i	−0.502420	+	0.365029i	−0.809940	−	0.586512i	$-0.800501\pi$
$59$	−3.85916	+	2.80384i	−0.502420	+	0.365029i	0.307521	+	0.951541i	$0.400501\pi$
$60$		0			0
$61$	−2.93822	−	2.13474i	−0.376201	−	0.273326i	0.383577	−	0.923509i	$-0.374692\pi$
$61$	−2.93822	−	2.13474i	−0.376201	−	0.273326i	−0.759777	+	0.650183i	$0.774692\pi$
$62$		0			0
$63$	−2.81160	−	3.86984i	−0.354229	−	0.487554i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.59126	+	2.14163i	0.805251	+	0.261642i	0.682585	−	0.730806i	$-0.260856\pi$
$67$	6.59126	+	2.14163i	0.805251	+	0.261642i	0.122666	+	0.992448i	$0.460856\pi$
$68$		0			0
$69$	1.81184	−	5.57627i	0.218120	−	0.671304i
$70$		0			0
$71$	−3.70731	−	11.4099i	−0.439977	−	1.35411i	−0.887899	−	0.460038i	$-0.847836\pi$
$71$	−3.70731	−	11.4099i	−0.439977	−	1.35411i	0.447922	−	0.894072i	$-0.352164\pi$
$72$		0			0
$73$	9.96647	−	13.7177i	1.16649	−	1.60553i	0.482864	−	0.875695i	$-0.339596\pi$
$73$	9.96647	−	13.7177i	1.16649	−	1.60553i	0.683622	−	0.729836i	$-0.260404\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.50033	+	7.57055i	−0.626820	+	0.862744i
$78$		0			0
$79$	2.04587	+	6.29656i	0.230179	+	0.708418i	0.997724	+	0.0674234i	$0.0214778\pi$
$79$	2.04587	+	6.29656i	0.230179	+	0.708418i	−0.767546	+	0.640994i	$0.778522\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	2.45552	+	0.797847i	0.269528	+	0.0875751i	0.440663	−	0.897673i	$-0.354743\pi$
$83$	2.45552	+	0.797847i	0.269528	+	0.0875751i	−0.171135	+	0.985248i	$0.554743\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.20118	−	8.53519i	−0.664836	−	0.915069i
$88$		0			0
$89$	−0.673699	−	0.489471i	−0.0714120	−	0.0518838i	0.551507	−	0.834171i	$-0.314053\pi$
$89$	−0.673699	−	0.489471i	−0.0714120	−	0.0518838i	−0.622918	+	0.782287i	$0.714053\pi$
$90$		0			0
$91$	4.17886	−	3.03612i	0.438063	−	0.318272i
$92$		0			0
$93$			4.31592i			0.447540i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.67076	−	2.81730i	0.880382	−	0.286054i	0.166266	−	0.986081i	$-0.446829\pi$
$97$	8.67076	−	2.81730i	0.880382	−	0.286054i	0.714116	+	0.700027i	$0.246829\pi$
$98$		0			0
$99$	−1.95630			−0.196615
$100$		0			0
$101$	1.49541			0.148799			0.0743994	−	0.997229i	$-0.476296\pi$
$101$	1.49541			0.148799			0.0743994	+	0.997229i	$0.476296\pi$
$102$		0			0
$103$	10.3307	−	3.35664i	1.01791	−	0.330739i	0.247911	−	0.968783i	$-0.420256\pi$
$103$	10.3307	−	3.35664i	1.01791	−	0.330739i	0.770000	+	0.638044i	$0.220256\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	19.8390i		−	1.91791i	−0.283563	−	0.958954i	$-0.591516\pi$
$107$		−	19.8390i		−	1.91791i	0.283563	−	0.958954i	$-0.408484\pi$
$108$		0			0
$109$	−1.89626	+	1.37771i	−0.181629	+	0.131961i	−0.674885	−	0.737923i	$-0.735807\pi$
$109$	−1.89626	+	1.37771i	−0.181629	+	0.131961i	0.493256	+	0.869884i	$0.335807\pi$
$110$		0			0
$111$	−4.57890	−	3.32676i	−0.434610	−	0.315762i
$112$		0			0
$113$	−1.89767	−	2.61192i	−0.178518	−	0.245709i	0.710376	−	0.703823i	$-0.248525\pi$
$113$	−1.89767	−	2.61192i	−0.178518	−	0.245709i	−0.888893	+	0.458114i	$0.848525\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.02700	+	0.333693i	0.0949463	+	0.0308499i
$118$		0			0
$119$	−5.62543	+	17.3133i	−0.515682	+	1.58711i
$120$		0			0
$121$	−2.21655	−	6.82184i	−0.201505	−	0.620167i
$122$		0			0
$123$	−0.504654	+	0.694596i	−0.0455031	+	0.0626296i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	4.34156	−	5.97565i	0.385251	−	0.530253i	−0.571715	−	0.820452i	$-0.693722\pi$
$127$	4.34156	−	5.97565i	0.385251	−	0.530253i	0.956966	+	0.290199i	$0.0937216\pi$
$128$		0			0
$129$	3.36101	+	10.3441i	0.295920	+	0.910748i
$130$		0			0
$131$	−5.21740	+	16.0575i	−0.455847	+	1.40295i	0.414292	+	0.910144i	$0.364029\pi$
$131$	−5.21740	+	16.0575i	−0.455847	+	1.40295i	−0.870138	+	0.492808i	$0.835971\pi$
$132$		0			0
$133$	19.3383	+	6.28339i	1.67684	+	0.544839i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.493339	−	0.679023i	−0.0421488	−	0.0580128i	0.787422	−	0.616414i	$-0.211415\pi$
$137$	−0.493339	−	0.679023i	−0.0421488	−	0.0580128i	−0.829571	+	0.558401i	$0.811415\pi$
$138$		0			0
$139$	−9.02701	−	6.55851i	−0.765661	−	0.556285i	0.134980	−	0.990848i	$-0.456903\pi$
$139$	−9.02701	−	6.55851i	−0.765661	−	0.556285i	−0.900641	+	0.434563i	$0.856903\pi$
$140$		0			0
$141$	−2.42833	+	1.76428i	−0.204502	+	0.148580i
$142$		0			0
$143$		−	2.11251i		−	0.176657i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−15.1035	+	4.90743i	−1.24572	+	0.404758i
$148$		0			0
$149$	22.0277			1.80458			0.902288	−	0.431134i	$-0.141886\pi$
$149$	22.0277			1.80458			0.902288	+	0.431134i	$0.141886\pi$
$150$		0			0
$151$	11.7890			0.959378			0.479689	−	0.877439i	$-0.340750\pi$
$151$	11.7890			0.959378			0.479689	+	0.877439i	$0.340750\pi$
$152$		0			0
$153$	−3.61946	+	1.17603i	−0.292616	+	0.0950767i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			11.2769i			0.899994i	0.893030	+	0.449997i	$0.148575\pi$
$157$			11.2769i			0.899994i	−0.893030	+	0.449997i	$0.851425\pi$
$158$		0			0
$159$	3.41716	−	2.48271i	0.270998	−	0.196892i
$160$		0			0
$161$	−22.6898	−	16.4851i	−1.78821	−	1.29921i
$162$		0			0
$163$	5.81690	+	8.00627i	0.455615	+	0.627100i	0.973592	−	0.228295i	$-0.0733149\pi$
$163$	5.81690	+	8.00627i	0.455615	+	0.627100i	−0.517978	+	0.855394i	$0.673315\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.14780	−	2.32246i	−0.553113	−	0.179717i	0.0191070	−	0.999817i	$-0.493918\pi$
$167$	−7.14780	−	2.32246i	−0.553113	−	0.179717i	−0.572220	+	0.820100i	$0.693918\pi$
$168$		0			0
$169$	3.65688	−	11.2547i	0.281299	−	0.865748i
$170$		0			0
$171$	1.31359	+	4.04280i	0.100452	+	0.309161i
$172$		0			0
$173$	−7.21698	+	9.93332i	−0.548697	+	0.755217i	−0.989835	−	0.142223i	$-0.954575\pi$
$173$	−7.21698	+	9.93332i	−0.548697	+	0.755217i	0.441138	+	0.897439i	$0.354575\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.80384	+	3.85916i	−0.210750	+	0.290072i
$178$		0			0
$179$	−4.69982	−	14.4646i	−0.351281	−	1.08113i	−0.958135	−	0.286318i	$-0.907569\pi$
$179$	−4.69982	−	14.4646i	−0.351281	−	1.08113i	0.606854	−	0.794813i	$-0.292431\pi$
$180$		0			0
$181$	−6.45087	+	19.8537i	−0.479490	+	1.47572i	0.360316	+	0.932830i	$0.382669\pi$
$181$	−6.45087	+	19.8537i	−0.479490	+	1.47572i	−0.839806	+	0.542887i	$0.817331\pi$
$182$		0			0
$183$	−3.45409	−	1.12230i	−0.255333	−	0.0829629i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.37613	+	6.02323i	0.320015	+	0.440462i
$188$		0			0
$189$	−3.86984	−	2.81160i	−0.281489	−	0.204514i
$190$		0			0
$191$	4.24803	−	3.08637i	0.307377	−	0.223322i	−0.423393	−	0.905946i	$-0.639161\pi$
$191$	4.24803	−	3.08637i	0.307377	−	0.223322i	0.730770	+	0.682624i	$0.239161\pi$
$192$		0			0
$193$		−	7.94565i		−	0.571940i	−0.958239	−	0.285970i	$-0.907684\pi$
$193$		−	7.94565i		−	0.571940i	0.958239	−	0.285970i	$-0.0923158\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.3694	−	4.01905i	0.881281	−	0.286345i	0.166792	−	0.985992i	$-0.446659\pi$
$197$	12.3694	−	4.01905i	0.881281	−	0.286345i	0.714489	+	0.699647i	$0.246659\pi$
$198$		0			0
$199$	−1.06434			−0.0754490			−0.0377245	−	0.999288i	$-0.512011\pi$
$199$	−1.06434			−0.0754490			−0.0377245	+	0.999288i	$0.512011\pi$
$200$		0			0
$201$	6.93046			0.488837
$202$		0			0
$203$	−47.9952	+	15.5946i	−3.36860	+	1.09452i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	5.86324i		−	0.407523i
$208$		0			0
$209$	6.72772	−	4.88798i	0.465366	−	0.338108i
$210$		0			0
$211$	16.5791	+	12.0454i	1.14135	+	0.829239i	0.987307	−	0.158825i	$-0.0507707\pi$
$211$	16.5791	+	12.0454i	1.14135	+	0.829239i	0.154043	+	0.988064i	$0.450771\pi$
$212$		0			0
$213$	−7.05173	−	9.70587i	−0.483176	−	0.665035i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	19.6343	+	6.37957i	1.33286	+	0.433073i
$218$		0			0
$219$	5.23968	−	16.1261i	0.354065	−	1.08970i
$220$		0			0
$221$	−1.26994	−	3.90848i	−0.0854257	−	0.262913i
$222$		0			0
$223$	−6.06130	+	8.34266i	−0.405895	+	0.558666i	−0.962211	−	0.272304i	$-0.912214\pi$
$223$	−6.06130	+	8.34266i	−0.405895	+	0.558666i	0.556316	+	0.830971i	$0.312214\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.6630	+	14.6763i	−0.707725	+	0.974100i	0.292118	+	0.956382i	$0.405640\pi$
$227$	−10.6630	+	14.6763i	−0.707725	+	0.974100i	−0.999843	+	0.0177176i	$0.994360\pi$
$228$		0			0
$229$	3.00311	+	9.24263i	0.198451	+	0.610770i	0.999919	+	0.0127320i	$0.00405284\pi$
$229$	3.00311	+	9.24263i	0.198451	+	0.610770i	−0.801468	+	0.598038i	$0.795947\pi$
$230$		0			0
$231$	−2.89169	+	8.89972i	−0.190259	+	0.585558i
$232$		0			0
$233$	21.1310	+	6.86586i	1.38433	+	0.449798i	0.904092	−	0.427338i	$-0.140549\pi$
$233$	21.1310	+	6.86586i	1.38433	+	0.449798i	0.480243	+	0.877136i	$0.340549\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.89149	+	5.35617i	0.252779	+	0.347921i
$238$		0			0
$239$	12.8871	+	9.36300i	0.833595	+	0.605642i	0.920574	−	0.390568i	$-0.127721\pi$
$239$	12.8871	+	9.36300i	0.833595	+	0.605642i	−0.0869793	+	0.996210i	$0.527721\pi$
$240$		0			0
$241$	3.98964	−	2.89864i	0.256995	−	0.186718i	−0.451826	−	0.892106i	$-0.649227\pi$
$241$	3.98964	−	2.89864i	0.256995	−	0.186718i	0.708821	+	0.705388i	$0.249227\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.36563	+	1.41848i	−0.277778	+	0.0902556i
$248$		0			0
$249$	2.58189			0.163620
$250$		0			0
$251$	15.4351			0.974252			0.487126	−	0.873332i	$-0.338045\pi$
$251$	15.4351			0.974252			0.487126	+	0.873332i	$0.338045\pi$
$252$		0			0
$253$	−10.9088	+	3.54449i	−0.685832	+	0.222840i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			21.1828i			1.32134i	0.750674	+	0.660672i	$0.229729\pi$
$257$			21.1828i			1.32134i	−0.750674	+	0.660672i	$0.770271\pi$
$258$		0			0
$259$	−21.9026	+	15.9132i	−1.36096	+	0.988798i
$260$		0			0
$261$	−8.53519	−	6.20118i	−0.528315	−	0.383843i
$262$		0			0
$263$	−12.3002	−	16.9298i	−0.758465	−	1.04394i	−0.997340	−	0.0728867i	$-0.976779\pi$
$263$	−12.3002	−	16.9298i	−0.758465	−	1.04394i	0.238876	−	0.971050i	$-0.423221\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.791981	−	0.257330i	−0.0484684	−	0.0157483i
$268$		0			0
$269$	4.25938	−	13.1090i	0.259699	−	0.799272i	−0.733168	−	0.680048i	$-0.761959\pi$
$269$	4.25938	−	13.1090i	0.259699	−	0.799272i	0.992867	−	0.119225i	$-0.0380409\pi$
$270$		0			0
$271$	3.25998	+	10.0332i	0.198029	+	0.609472i	0.999928	+	0.0120115i	$0.00382346\pi$
$271$	3.25998	+	10.0332i	0.198029	+	0.609472i	−0.801898	+	0.597460i	$0.796177\pi$
$272$		0			0
$273$	3.03612	−	4.17886i	0.183754	−	0.252916i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.5579	−	14.5317i	0.634364	−	0.873127i	−0.363935	−	0.931424i	$-0.618567\pi$
$277$	10.5579	−	14.5317i	0.634364	−	0.873127i	0.998299	+	0.0582969i	$0.0185670\pi$
$278$		0			0
$279$	1.33369	+	4.10468i	0.0798461	+	0.245741i
$280$		0			0
$281$	−0.286375	+	0.881371i	−0.0170837	+	0.0525782i	−0.959235	−	0.282610i	$-0.908800\pi$
$281$	−0.286375	+	0.881371i	−0.0170837	+	0.0525782i	0.942151	+	0.335188i	$0.108800\pi$
$282$		0			0
$283$	6.25556	+	2.03256i	0.371855	+	0.120823i	0.488982	−	0.872294i	$-0.337368\pi$
$283$	6.25556	+	2.03256i	0.371855	+	0.120823i	−0.117127	+	0.993117i	$0.537368\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.41395	+	3.32252i	0.142491	+	0.196122i
$288$		0			0
$289$	−2.03585	−	1.47913i	−0.119756	−	0.0870076i
$290$		0			0
$291$	7.37579	−	5.35882i	0.432376	−	0.314140i
$292$		0			0
$293$		−	25.6208i		−	1.49678i	−0.663257	−	0.748391i	$-0.730827\pi$
$293$		−	25.6208i		−	1.49678i	0.663257	−	0.748391i	$-0.269173\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.86055	+	0.604528i	−0.107960	+	0.0350783i
$298$		0			0
$299$	6.33143			0.366156
$300$		0			0
$301$	52.0262			2.99874
$302$		0			0
$303$	1.42222	−	0.462107i	0.0817044	−	0.0265474i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	6.18420i		−	0.352951i	−0.984305	−	0.176476i	$-0.943530\pi$
$307$		−	6.18420i		−	0.352951i	0.984305	−	0.176476i	$-0.0564697\pi$
$308$		0			0
$309$	8.78779	−	6.38470i	0.499920	−	0.363213i
$310$		0			0
$311$	19.6091	+	14.2468i	1.11193	+	0.807864i	0.982966	−	0.183785i	$-0.0588351\pi$
$311$	19.6091	+	14.2468i	1.11193	+	0.807864i	0.128963	+	0.991649i	$0.458835\pi$
$312$		0			0
$313$	−17.6108	−	24.2392i	−0.995420	−	1.37008i	−0.928094	−	0.372347i	$-0.878553\pi$
$313$	−17.6108	−	24.2392i	−0.995420	−	1.37008i	−0.0673262	−	0.997731i	$-0.521447\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.34214	+	0.761007i	0.131548	+	0.0427424i	0.374051	−	0.927408i	$-0.377969\pi$
$317$	2.34214	+	0.761007i	0.131548	+	0.0427424i	−0.242503	+	0.970151i	$0.577969\pi$
$318$		0			0
$319$	−6.37782	+	19.6289i	−0.357090	+	1.09901i
$320$		0			0
$321$	−6.13058	−	18.8680i	−0.342176	−	1.05311i
$322$		0			0
$323$	9.50894	−	13.0879i	0.529092	−	0.728232i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.37771	+	1.89626i	−0.0761878	+	0.104863i
$328$		0			0
$329$	4.43678	+	13.6550i	0.244607	+	0.752824i
$330$		0			0
$331$	−8.27755	+	25.4757i	−0.454975	+	1.40027i	0.416189	+	0.909278i	$0.363366\pi$
$331$	−8.27755	+	25.4757i	−0.454975	+	1.40027i	−0.871164	+	0.490992i	$0.836634\pi$
$332$		0			0
$333$	−5.38282	−	1.74898i	−0.294977	−	0.0958437i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.43219	−	1.97124i	−0.0780165	−	0.107381i	0.768225	−	0.640180i	$-0.221140\pi$
$337$	−1.43219	−	1.97124i	−0.0780165	−	0.107381i	−0.846242	+	0.532799i	$0.821140\pi$
$338$		0			0
$339$	−2.61192	−	1.89767i	−0.141860	−	0.103067i
$340$		0			0
$341$	6.83070	−	4.96280i	0.369903	−	0.268751i
$342$		0			0
$343$			42.4802i			2.29372i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.26368	−	2.36011i	0.389935	−	0.126698i	−0.107487	−	0.994207i	$-0.534280\pi$
$347$	7.26368	−	2.36011i	0.389935	−	0.126698i	0.497421	+	0.867509i	$0.334280\pi$
$348$		0			0
$349$	20.2283			1.08280			0.541398	−	0.840766i	$-0.317895\pi$
$349$	20.2283			1.08280			0.541398	+	0.840766i	$0.317895\pi$
$350$		0			0
$351$	1.07985			0.0576383
$352$		0			0
$353$	−26.9075	+	8.74279i	−1.43214	+	0.465331i	−0.919439	−	0.393234i	$-0.871356\pi$
$353$	−26.9075	+	8.74279i	−1.43214	+	0.465331i	−0.512705	+	0.858565i	$0.671356\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			18.2043i			0.963472i
$358$		0			0
$359$	18.4713	−	13.4202i	0.974880	−	0.708292i	0.0183215	−	0.999832i	$-0.494168\pi$
$359$	18.4713	−	13.4202i	0.974880	−	0.708292i	0.956559	+	0.291540i	$0.0941678\pi$
$360$		0			0
$361$	0.752597	+	0.546793i	0.0396103	+	0.0287786i
$362$		0			0
$363$	−4.21613	−	5.80301i	−0.221289	−	0.304579i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.39472	−	0.778091i	−0.125003	−	0.0406160i	0.245847	−	0.969309i	$-0.420934\pi$
$367$	−2.39472	−	0.778091i	−0.125003	−	0.0406160i	−0.370851	+	0.928693i	$0.620934\pi$
$368$		0			0
$369$	−0.265312	+	0.816547i	−0.0138116	+	0.0425077i
$370$		0			0
$371$	−6.24346	−	19.2154i	−0.324144	−	0.997614i
$372$		0			0
$373$	−3.32332	+	4.57416i	−0.172075	+	0.236841i	−0.886341	−	0.463034i	$-0.846761\pi$
$373$	−3.32332	+	4.57416i	−0.172075	+	0.236841i	0.714265	+	0.699875i	$0.246761\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.69636	−	9.21675i	0.344880	−	0.474687i
$378$		0			0
$379$	4.44729	+	13.6874i	0.228442	+	0.703073i	0.997924	+	0.0644039i	$0.0205146\pi$
$379$	4.44729	+	13.6874i	0.228442	+	0.703073i	−0.769482	+	0.638669i	$0.779485\pi$
$380$		0			0
$381$	2.28249	−	7.02479i	0.116936	−	0.359891i
$382$		0			0
$383$	7.79859	+	2.53391i	0.398489	+	0.129477i	0.501404	−	0.865213i	$-0.332817\pi$
$383$	7.79859	+	2.53391i	0.398489	+	0.129477i	−0.102915	+	0.994690i	$0.532817\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.39301	+	8.79923i	0.324975	+	0.447290i
$388$		0			0
$389$	3.82719	+	2.78062i	0.194046	+	0.140983i	0.680566	−	0.732687i	$-0.261734\pi$
$389$	3.82719	+	2.78062i	0.194046	+	0.140983i	−0.486520	+	0.873670i	$0.661734\pi$
$390$		0			0
$391$	−18.0523	+	13.1158i	−0.912945	+	0.663293i
$392$		0			0
$393$			16.8839i			0.851679i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	7.21211	−	2.34336i	0.361965	−	0.117610i	−0.122387	−	0.992482i	$-0.539055\pi$
$397$	7.21211	−	2.34336i	0.361965	−	0.117610i	0.484353	+	0.874873i	$0.339055\pi$
$398$		0			0
$399$	20.3335			1.01795
$400$		0			0
$401$	10.1128			0.505011			0.252506	−	0.967595i	$-0.418745\pi$
$401$	10.1128			0.505011			0.252506	+	0.967595i	$0.418745\pi$
$402$		0			0
$403$	−4.43245	+	1.44019i	−0.220796	+	0.0717411i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			11.0723i			0.548833i
$408$		0			0
$409$	3.21927	−	2.33894i	0.159183	−	0.115653i	−0.505342	−	0.862919i	$-0.668634\pi$
$409$	3.21927	−	2.33894i	0.159183	−	0.115653i	0.664525	+	0.747266i	$0.268634\pi$
$410$		0			0
$411$	−0.679023	−	0.493339i	−0.0334937	−	0.0243346i
$412$		0			0
$413$	13.4119	+	18.4598i	0.659955	+	0.908350i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−10.6119	−	3.44801i	−0.519666	−	0.168850i
$418$		0			0
$419$	−0.555164	+	1.70862i	−0.0271215	+	0.0834714i	−0.963701	−	0.266984i	$-0.913973\pi$
$419$	−0.555164	+	1.70862i	−0.0271215	+	0.0834714i	0.936580	+	0.350455i	$0.113973\pi$
$420$		0			0
$421$	4.84234	+	14.9032i	0.236001	+	0.726337i	0.996987	+	0.0775686i	$0.0247157\pi$
$421$	4.84234	+	14.9032i	0.236001	+	0.726337i	−0.760986	+	0.648769i	$0.775284\pi$
$422$		0			0
$423$	−1.76428	+	2.42833i	−0.0857824	+	0.118069i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.2113	+	14.0546i	−0.494159	+	0.680152i
$428$		0			0
$429$	−0.652802	−	2.00912i	−0.0315176	−	0.0970011i
$430$		0			0
$431$	−11.9206	+	36.6880i	−0.574197	+	1.76720i	0.0646985	+	0.997905i	$0.479391\pi$
$431$	−11.9206	+	36.6880i	−0.574197	+	1.76720i	−0.638896	+	0.769293i	$0.720609\pi$
$432$		0			0
$433$	−8.72070	−	2.83353i	−0.419090	−	0.136171i	0.0918780	−	0.995770i	$-0.470713\pi$
$433$	−8.72070	−	2.83353i	−0.419090	−	0.136171i	−0.510968	+	0.859600i	$0.670713\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.6498	+	20.1637i	0.700796	+	0.964563i
$438$		0			0
$439$	14.3101	+	10.3969i	0.682982	+	0.496216i	0.874346	−	0.485304i	$-0.161291\pi$
$439$	14.3101	+	10.3969i	0.682982	+	0.496216i	−0.191363	+	0.981519i	$0.561291\pi$
$440$		0			0
$441$	−12.8478	+	9.33449i	−0.611801	+	0.444500i
$442$		0			0
$443$			18.6673i			0.886912i	0.896296	+	0.443456i	$0.146248\pi$
$443$			18.6673i			0.886912i	−0.896296	+	0.443456i	$0.853752\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	20.9495	−	6.80692i	0.990880	−	0.321956i
$448$		0			0
$449$	−41.2111			−1.94487			−0.972436	−	0.233171i	$-0.925090\pi$
$449$	−41.2111			−1.94487			−0.972436	+	0.233171i	$0.925090\pi$
$450$		0			0
$451$	1.67961			0.0790899
$452$		0			0
$453$	11.2120	−	3.64301i	0.526787	−	0.171164i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	5.56092i		−	0.260129i	−0.991506	−	0.130064i	$-0.958482\pi$
$457$		−	5.56092i		−	0.260129i	0.991506	−	0.130064i	$-0.0415184\pi$
$458$		0			0
$459$	−3.07890	+	2.23695i	−0.143711	+	0.104412i
$460$		0			0
$461$	−17.1210	−	12.4391i	−0.797404	−	0.579348i	0.112747	−	0.993624i	$-0.464035\pi$
$461$	−17.1210	−	12.4391i	−0.797404	−	0.579348i	−0.910151	+	0.414276i	$0.864035\pi$
$462$		0			0
$463$	−4.55278	−	6.26637i	−0.211586	−	0.291223i	0.690012	−	0.723798i	$-0.257605\pi$
$463$	−4.55278	−	6.26637i	−0.211586	−	0.291223i	−0.901598	+	0.432575i	$0.857605\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.31301	−	0.751544i	−0.107034	−	0.0347773i	0.255011	−	0.966938i	$-0.417921\pi$
$467$	−2.31301	−	0.751544i	−0.107034	−	0.0347773i	−0.362044	+	0.932161i	$0.617921\pi$
$468$		0			0
$469$	10.2442	−	31.5286i	0.473036	−	1.45585i
$470$		0			0
$471$	3.48475	+	10.7250i	0.160569	+	0.494180i
$472$		0			0
$473$	12.5066	−	17.2139i	0.575055	−	0.791495i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.48271	−	3.41716i	0.113676	−	0.156461i
$478$		0			0
$479$	−10.5465	−	32.4587i	−0.481880	−	1.48308i	−0.836449	−	0.548045i	$-0.815372\pi$
$479$	−10.5465	−	32.4587i	−0.481880	−	1.48308i	0.354569	−	0.935030i	$-0.384628\pi$
$480$		0			0
$481$	1.88864	−	5.81265i	0.0861148	−	0.265034i
$482$		0			0
$483$	−26.6735	−	8.66673i	−1.21368	−	0.394350i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	18.8302	+	25.9175i	0.853277	+	1.17443i	0.983131	+	0.182902i	$0.0585491\pi$
$487$	18.8302	+	25.9175i	0.853277	+	1.17443i	−0.129854	+	0.991533i	$0.541451\pi$
$488$		0			0
$489$	8.00627	+	5.81690i	0.362056	+	0.263049i
$490$		0			0
$491$	−23.7860	+	17.2815i	−1.07345	+	0.779904i	−0.976529	−	0.215388i	$-0.930898\pi$
$491$	−23.7860	+	17.2815i	−1.07345	+	0.779904i	−0.0969178	+	0.995292i	$0.530898\pi$
$492$		0			0
$493$			40.1507i			1.80830i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−54.5781	+	17.7335i	−2.44816	+	0.795456i
$498$		0			0
$499$	9.04298			0.404819			0.202410	−	0.979301i	$-0.435123\pi$
$499$	9.04298			0.404819			0.202410	+	0.979301i	$0.435123\pi$
$500$		0			0
$501$	−7.51564			−0.335774
$502$		0			0
$503$	2.92641	−	0.950848i	0.130482	−	0.0423962i	−0.243048	−	0.970014i	$-0.578147\pi$
$503$	2.92641	−	0.950848i	0.130482	−	0.0423962i	0.373530	+	0.927618i	$0.378147\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	11.8339i		−	0.525563i
$508$		0			0
$509$	21.2410	−	15.4325i	0.941491	−	0.684033i	−0.00728833	−	0.999973i	$-0.502320\pi$
$509$	21.2410	−	15.4325i	0.941491	−	0.684033i	0.948779	+	0.315940i	$0.102320\pi$
$510$		0			0
$511$	−65.6169	−	47.6735i	−2.90272	−	2.10895i
$512$		0			0
$513$	2.49859	+	3.43901i	0.110315	+	0.151836i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.58458	+	1.81454i	0.245610	+	0.0798034i
$518$		0			0
$519$	−3.79419	+	11.6773i	−0.166547	+	0.512578i
$520$		0			0
$521$	6.41127	+	19.7319i	0.280883	+	0.864469i	0.987603	+	0.156975i	$0.0501742\pi$
$521$	6.41127	+	19.7319i	0.280883	+	0.864469i	−0.706720	+	0.707494i	$0.749826\pi$
$522$		0			0
$523$	13.1957	−	18.1623i	0.577007	−	0.794182i	−0.416356	−	0.909202i	$-0.636693\pi$
$523$	13.1957	−	18.1623i	0.577007	−	0.794182i	0.993363	+	0.115020i	$0.0366931\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.65450	−	13.2883i	0.420557	−	0.578846i
$528$		0			0
$529$	−3.51586	−	10.8207i	−0.152864	−	0.470466i
$530$		0			0
$531$	−1.47407	+	4.53671i	−0.0639691	+	0.196877i
$532$		0			0
$533$	−0.881750	−	0.286498i	−0.0381928	−	0.0124096i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.93959	−	12.3043i	−0.385772	−	0.530969i
$538$		0			0
$539$	25.1341	+	18.2610i	1.08260	+	0.786558i
$540$		0			0
$541$	20.4954	−	14.8908i	0.881166	−	0.640205i	−0.0523936	−	0.998627i	$-0.516685\pi$
$541$	20.4954	−	14.8908i	0.881166	−	0.640205i	0.933560	+	0.358422i	$0.116685\pi$
$542$		0			0
$543$			20.8755i			0.895852i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.2294	−	3.64866i	0.480135	−	0.156005i	−0.0589426	−	0.998261i	$-0.518773\pi$
$547$	11.2294	−	3.64866i	0.480135	−	0.156005i	0.539078	+	0.842256i	$0.318773\pi$
$548$		0			0
$549$	−3.63184			−0.155003
$550$		0			0
$551$	44.8468			1.91054
$552$		0			0
$553$	30.1189	−	9.78621i	1.28078	−	0.416152i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			5.93356i			0.251413i	0.992067	+	0.125706i	$0.0401197\pi$
$557$			5.93356i			0.251413i	−0.992067	+	0.125706i	$0.959880\pi$
$558$		0			0
$559$	−9.50187	+	6.90351i	−0.401886	+	0.291987i
$560$		0			0
$561$	6.02323	+	4.37613i	0.254301	+	0.184761i
$562$		0			0
$563$	8.07772	+	11.1180i	0.340435	+	0.468569i	0.944569	−	0.328314i	$-0.106480\pi$
$563$	8.07772	+	11.1180i	0.340435	+	0.468569i	−0.604133	+	0.796883i	$0.706480\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−4.54927	−	1.47815i	−0.191051	−	0.0620764i
$568$		0			0
$569$	−10.2309	+	31.4874i	−0.428900	+	1.32002i	0.470309	+	0.882502i	$0.344142\pi$
$569$	−10.2309	+	31.4874i	−0.428900	+	1.32002i	−0.899210	+	0.437518i	$0.855858\pi$
$570$		0			0
$571$	−7.91367	−	24.3558i	−0.331177	−	1.01926i	−0.968575	−	0.248722i	$-0.919989\pi$
$571$	−7.91367	−	24.3558i	−0.331177	−	1.01926i	0.637398	−	0.770535i	$-0.280011\pi$
$572$		0			0
$573$	3.08637	−	4.24803i	0.128935	−	0.177464i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.04995	−	2.82151i	0.0853405	−	0.117461i	−0.764212	−	0.644965i	$-0.776872\pi$
$577$	2.04995	−	2.82151i	0.0853405	−	0.117461i	0.849553	+	0.527504i	$0.176872\pi$
$578$		0			0
$579$	−2.45534	−	7.55676i	−0.102040	−	0.314048i
$580$		0			0
$581$	3.81641	−	11.7457i	0.158331	−	0.487294i
$582$		0			0
$583$	−7.85866	−	2.55343i	−0.325472	−	0.105752i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.2480	−	27.8690i	−0.835724	−	1.15028i	−0.986831	−	0.161758i	$-0.948284\pi$
$587$	−20.2480	−	27.8690i	−0.835724	−	1.15028i	0.151107	−	0.988517i	$-0.451716\pi$
$588$		0			0
$589$	−14.8425	−	10.7837i	−0.611575	−	0.444335i
$590$		0			0
$591$	10.5220	−	7.64469i	0.432818	−	0.314460i
$592$		0			0
$593$		−	35.7248i		−	1.46704i	−0.679666	−	0.733522i	$-0.737875\pi$
$593$		−	35.7248i		−	1.46704i	0.679666	−	0.733522i	$-0.262125\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.01225	+	0.328899i	−0.0414285	+	0.0134609i
$598$		0			0
$599$	−39.7697			−1.62495			−0.812473	−	0.582998i	$-0.801879\pi$
$599$	−39.7697			−1.62495			−0.812473	+	0.582998i	$0.801879\pi$
$600$		0			0
$601$	−15.5134			−0.632805			−0.316402	−	0.948625i	$-0.602475\pi$
$601$	−15.5134			−0.632805			−0.316402	+	0.948625i	$0.602475\pi$
$602$		0			0
$603$	6.59126	−	2.14163i	0.268417	−	0.0872140i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			15.1855i			0.616358i	0.951328	+	0.308179i	$0.0997197\pi$
$607$			15.1855i			0.616358i	−0.951328	+	0.308179i	$0.900280\pi$
$608$		0			0
$609$	−40.8271	+	29.6626i	−1.65440	+	1.20199i
$610$		0			0
$611$	−2.62224	−	1.90517i	−0.106084	−	0.0770748i
$612$		0			0
$613$	−18.8882	−	25.9974i	−0.762887	−	1.05002i	−0.996968	−	0.0778070i	$-0.975208\pi$
$613$	−18.8882	−	25.9974i	−0.762887	−	1.05002i	0.234081	−	0.972217i	$-0.424792\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.11082	+	1.33569i	0.165495	+	0.0537727i	0.390593	−	0.920564i	$-0.372270\pi$
$617$	4.11082	+	1.33569i	0.165495	+	0.0537727i	−0.225097	+	0.974336i	$0.572270\pi$
$618$		0			0
$619$	−10.3201	+	31.7621i	−0.414801	+	1.27663i	0.497627	+	0.867391i	$0.334205\pi$
$619$	−10.3201	+	31.7621i	−0.414801	+	1.27663i	−0.912428	+	0.409236i	$0.865795\pi$
$620$		0			0
$621$	−1.81184	−	5.57627i	−0.0727067	−	0.223768i
$622$		0			0
$623$	−2.34133	+	3.22256i	−0.0938034	+	0.129109i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	4.88798	−	6.72772i	0.195207	−	0.268679i
$628$		0			0
$629$	6.65615	+	20.4855i	0.265398	+	0.816812i
$630$		0			0
$631$	3.39726	−	10.4557i	0.135243	−	0.416234i	−0.860385	−	0.509645i	$-0.829777\pi$
$631$	3.39726	−	10.4557i	0.135243	−	0.416234i	0.995628	+	0.0934106i	$0.0297769\pi$
$632$		0			0
$633$	19.4898	+	6.33264i	0.774652	+	0.251700i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−10.0799	−	13.8738i	−0.399379	−	0.549698i
$638$		0			0
$639$	−9.70587	−	7.05173i	−0.383958	−	0.278962i
$640$		0			0
$641$	5.55031	−	4.03253i	0.219224	−	0.159276i	−0.472753	−	0.881195i	$-0.656740\pi$
$641$	5.55031	−	4.03253i	0.219224	−	0.159276i	0.691977	+	0.721919i	$0.256740\pi$
$642$		0			0
$643$		−	23.1923i		−	0.914615i	−0.889309	−	0.457308i	$-0.848814\pi$
$643$		−	23.1923i		−	0.914615i	0.889309	−	0.457308i	$-0.151186\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	29.2779	−	9.51298i	1.15103	−	0.373994i	0.329502	−	0.944155i	$-0.393119\pi$
$647$	29.2779	−	9.51298i	1.15103	−	0.373994i	0.821533	+	0.570161i	$0.193119\pi$
$648$		0			0
$649$	9.33188			0.366309
$650$		0			0
$651$	20.6447			0.809130
$652$		0			0
$653$	−7.42477	+	2.41245i	−0.290554	+	0.0944066i	−0.450667	−	0.892692i	$-0.648814\pi$
$653$	−7.42477	+	2.41245i	−0.290554	+	0.0944066i	0.160114	+	0.987099i	$0.448814\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	16.9560i		−	0.661515i
$658$		0			0
$659$	4.26388	−	3.09789i	0.166097	−	0.120677i	−0.501632	−	0.865081i	$-0.667267\pi$
$659$	4.26388	−	3.09789i	0.166097	−	0.120677i	0.667729	+	0.744405i	$0.267267\pi$
$660$		0			0
$661$	29.8490	+	21.6865i	1.16099	+	0.843509i	0.989903	−	0.141747i	$-0.0452719\pi$
$661$	29.8490	+	21.6865i	1.16099	+	0.843509i	0.171088	+	0.985256i	$0.445272\pi$
$662$		0			0
$663$	−2.41558	−	3.32476i	−0.0938132	−	0.129123i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−58.8301	−	19.1151i	−2.27791	−	0.740138i
$668$		0			0
$669$	−3.18661	+	9.80739i	−0.123202	+	0.379176i
$670$		0			0
$671$	2.19555	+	6.75721i	0.0847583	+	0.260859i
$672$		0			0
$673$	26.4626	−	36.4227i	1.02006	−	1.40399i	0.107897	−	0.994162i	$-0.465588\pi$
$673$	26.4626	−	36.4227i	1.02006	−	1.40399i	0.912162	−	0.409829i	$-0.134412\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.5385	−	25.5161i	0.712493	−	0.980662i	−0.287247	−	0.957856i	$-0.592740\pi$
$677$	18.5385	−	25.5161i	0.712493	−	0.980662i	0.999740	−	0.0228056i	$-0.00725988\pi$
$678$		0			0
$679$	−13.4762	−	41.4756i	−0.517171	−	1.59169i
$680$		0			0
$681$	−5.60585	+	17.2530i	−0.214816	+	0.661137i
$682$		0			0
$683$	19.6762	+	6.39320i	0.752891	+	0.244629i	0.660225	−	0.751068i	$-0.270461\pi$
$683$	19.6762	+	6.39320i	0.752891	+	0.244629i	0.0926660	+	0.995697i	$0.470461\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.71226	+	7.86225i	0.217936	+	0.299964i
$688$		0			0
$689$	3.69003	+	2.68096i	0.140579	+	0.102137i
$690$		0			0
$691$	27.6523	−	20.0906i	1.05194	−	0.764282i	0.0793624	−	0.996846i	$-0.474712\pi$
$691$	27.6523	−	20.0906i	1.05194	−	0.764282i	0.972581	+	0.232564i	$0.0747116\pi$
$692$		0			0
$693$			9.35772i			0.355470i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.10755	−	1.00971i	0.117707	−	0.0382453i
$698$		0			0
$699$	22.2184			0.840377
$700$		0			0
$701$	−16.6859			−0.630216			−0.315108	−	0.949056i	$-0.602041\pi$
$701$	−16.6859			−0.630216			−0.315108	+	0.949056i	$0.602041\pi$
$702$		0			0
$703$	22.8816	−	7.43467i	0.862994	−	0.280404i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	7.15312i		−	0.269021i
$708$		0			0
$709$	38.2796	−	27.8118i	1.43762	−	1.04449i	0.449089	−	0.893487i	$-0.351749\pi$
$709$	38.2796	−	27.8118i	1.43762	−	1.04449i	0.988533	−	0.151007i	$-0.0482515\pi$
$710$		0			0
$711$	5.35617	+	3.89149i	0.200872	+	0.145942i
$712$		0			0
$713$	14.8741	+	20.4724i	0.557038	+	0.766697i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	15.1496	+	4.92242i	0.565774	+	0.183831i
$718$		0			0
$719$	−1.73431	+	5.33767i	−0.0646790	+	0.199062i	−0.978174	−	0.207789i	$-0.933373\pi$
$719$	−1.73431	+	5.33767i	−0.0646790	+	0.199062i	0.913495	+	0.406851i	$0.133373\pi$
$720$		0			0
$721$	−16.0561	−	49.4156i	−0.597960	−	1.84033i
$722$		0			0
$723$	2.89864	−	3.98964i	0.107802	−	0.148376i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.60317	+	11.8412i	−0.319074	+	0.439167i	−0.938184	−	0.346137i	$-0.887493\pi$
$727$	−8.60317	+	11.8412i	−0.319074	+	0.439167i	0.619110	+	0.785304i	$0.287493\pi$
$728$		0			0
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	12.7911	−	39.3669i	0.473095	−	1.45604i
$732$		0			0
$733$	−30.6789	−	9.96818i	−1.13315	−	0.368183i	−0.318378	−	0.947964i	$-0.603138\pi$
$733$	−30.6789	−	9.96818i	−1.13315	−	0.368183i	−0.814773	+	0.579781i	$0.803138\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.96921	−	10.9687i	−0.293550	−	0.404037i
$738$		0			0
$739$	−19.2956	−	14.0191i	−0.709800	−	0.515700i	0.173309	−	0.984867i	$-0.444554\pi$
$739$	−19.2956	−	14.0191i	−0.709800	−	0.515700i	−0.883109	+	0.469168i	$0.844554\pi$
$740$		0			0
$741$	−3.71363	+	2.69811i	−0.136423	+	0.0991174i
$742$		0			0
$743$		−	7.48188i		−	0.274483i	−0.990538	−	0.137242i	$-0.956176\pi$
$743$		−	7.48188i		−	0.274483i	0.990538	−	0.137242i	$-0.0438237\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.45552	−	0.797847i	0.0898428	−	0.0291917i
$748$		0			0
$749$	−94.8975			−3.46748
$750$		0			0
$751$	−32.3687			−1.18115			−0.590576	−	0.806982i	$-0.701099\pi$
$751$	−32.3687			−1.18115			−0.590576	+	0.806982i	$0.701099\pi$
$752$		0			0
$753$	14.6796	−	4.76969i	0.534955	−	0.173817i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	10.2847i		−	0.373804i	−0.982379	−	0.186902i	$-0.940155\pi$
$757$		−	10.2847i		−	0.373804i	0.982379	−	0.186902i	$-0.0598447\pi$
$758$		0			0
$759$	−9.27961	+	6.74203i	−0.336828	+	0.244720i
$760$		0			0
$761$	−23.3033	−	16.9308i	−0.844743	−	0.613742i	0.0789487	−	0.996879i	$-0.474844\pi$
$761$	−23.3033	−	16.9308i	−0.844743	−	0.613742i	−0.923691	+	0.383137i	$0.874844\pi$
$762$		0			0
$763$	6.59014	+	9.07055i	0.238579	+	0.328376i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.89898	−	1.59178i	−0.176892	−	0.0574757i
$768$		0			0
$769$	12.1673	−	37.4472i	0.438765	−	1.35038i	−0.450414	−	0.892820i	$-0.648724\pi$
$769$	12.1673	−	37.4472i	0.438765	−	1.35038i	0.889179	−	0.457560i	$-0.151276\pi$
$770$		0			0
$771$	6.54584	+	20.1460i	0.235743	+	0.725541i
$772$		0			0
$773$	−2.97658	+	4.09692i	−0.107060	+	0.147356i	−0.859185	−	0.511665i	$-0.829029\pi$
$773$	−2.97658	+	4.09692i	−0.107060	+	0.147356i	0.752125	+	0.659021i	$0.229029\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−15.9132	+	21.9026i	−0.570883	+	0.785753i
$778$		0			0
$779$	−1.12780	−	3.47102i	−0.0404077	−	0.124362i
$780$		0			0
$781$	−7.25260	+	22.3212i	−0.259518	+	0.798715i
$782$		0			0
$783$	−10.0337	−	3.26015i	−0.358576	−	0.116508i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.13378	−	4.31328i	−0.111707	−	0.153752i	0.749503	−	0.662001i	$-0.230293\pi$
$787$	−3.13378	−	4.31328i	−0.111707	−	0.153752i	−0.861210	+	0.508250i	$0.830293\pi$
$788$		0			0
$789$	−16.9298	−	12.3002i	−0.602717	−	0.437900i
$790$		0			0
$791$	−12.4938	+	9.07729i	−0.444229	+	0.322751i
$792$		0			0
$793$		−	3.92185i		−	0.139269i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21.3277	+	6.92980i	−0.755467	+	0.245466i	−0.661332	−	0.750093i	$-0.730009\pi$
$797$	−21.3277	+	6.92980i	−0.755467	+	0.245466i	−0.0941349	+	0.995559i	$0.530009\pi$
$798$		0			0
$799$	11.4232			0.404124
$800$		0			0
$801$	−0.832738			−0.0294233
$802$		0			0
$803$	−31.5474	+	10.2504i	−1.11328	+	0.361727i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	13.7837i		−	0.485208i
$808$		0			0
$809$	9.76605	−	7.09545i	0.343356	−	0.249463i	−0.402721	−	0.915323i	$-0.631935\pi$
$809$	9.76605	−	7.09545i	0.343356	−	0.249463i	0.746076	+	0.665860i	$0.231935\pi$
$810$		0			0
$811$	−21.4731	−	15.6011i	−0.754023	−	0.547830i	0.143048	−	0.989716i	$-0.454310\pi$
$811$	−21.4731	−	15.6011i	−0.754023	−	0.547830i	−0.897071	+	0.441886i	$0.854310\pi$
$812$		0			0
$813$	6.20084	+	8.53473i	0.217473	+	0.299326i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−43.9713	−	14.2871i	−1.53836	−	0.499844i
$818$		0			0
$819$	1.59618	−	4.91254i	0.0557751	−	0.171658i
$820$		0			0
$821$	−0.554306	−	1.70598i	−0.0193454	−	0.0595391i	0.940918	−	0.338635i	$-0.109965\pi$
$821$	−0.554306	−	1.70598i	−0.0193454	−	0.0595391i	−0.960263	+	0.279096i	$0.909965\pi$
$822$		0			0
$823$	−20.9181	+	28.7913i	−0.729160	+	1.00360i	0.270009	+	0.962858i	$0.412973\pi$
$823$	−20.9181	+	28.7913i	−0.729160	+	1.00360i	−0.999170	+	0.0407453i	$0.987027\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.1302	−	22.2013i	0.560902	−	0.772016i	−0.430539	−	0.902572i	$-0.641676\pi$
$827$	16.1302	−	22.2013i	0.560902	−	0.772016i	0.991441	+	0.130556i	$0.0416764\pi$
$828$		0			0
$829$	11.7501	+	36.1631i	0.408098	+	1.25600i	0.918281	+	0.395930i	$0.129578\pi$
$829$	11.7501	+	36.1631i	0.408098	+	1.25600i	−0.510183	+	0.860066i	$0.670422\pi$
$830$		0			0
$831$	5.55063	−	17.0831i	0.192549	−	0.592606i
$832$		0			0
$833$	57.4799	+	18.6763i	1.99156	+	0.647097i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.53683	+	3.49165i	0.0876858	+	0.120689i
$838$		0			0
$839$	−29.2065	−	21.2197i	−1.00832	−	0.732586i	−0.0444629	−	0.999011i	$-0.514158\pi$
$839$	−29.2065	−	21.2197i	−1.00832	−	0.732586i	−0.963856	+	0.266425i	$0.914158\pi$
$840$		0			0
$841$	−66.5855	+	48.3772i	−2.29605	+	1.66818i
$842$		0			0
$843$			0.926728i			0.0319182i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−32.6315	+	10.6026i	−1.12123	+	0.364310i
$848$		0			0
$849$	6.57749			0.225739
$850$		0			0
$851$	−33.1849			−1.13756
$852$		0			0
$853$	−31.3363	+	10.1818i	−1.07293	+	0.348617i	−0.791630	−	0.611001i	$-0.790767\pi$
$853$	−31.3363	+	10.1818i	−1.07293	+	0.348617i	−0.281304	+	0.959619i	$0.590767\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	13.9514i		−	0.476572i	−0.971195	−	0.238286i	$-0.923414\pi$
$857$		−	13.9514i		−	0.476572i	0.971195	−	0.238286i	$-0.0765855\pi$
$858$		0			0
$859$	−31.2696	+	22.7187i	−1.06691	+	0.775152i	−0.975354	−	0.220648i	$-0.929183\pi$
$859$	−31.2696	+	22.7187i	−1.06691	+	0.775152i	−0.0915521	+	0.995800i	$0.529183\pi$
$860$		0			0
$861$	3.32252	+	2.41395i	0.113231	+	0.0822673i
$862$		0			0
$863$	−2.10177	−	2.89284i	−0.0715451	−	0.0984734i	0.771745	−	0.635932i	$-0.219384\pi$
$863$	−2.10177	−	2.89284i	−0.0715451	−	0.0984734i	−0.843290	+	0.537459i	$0.819384\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.39328	−	0.777624i	−0.0812801	−	0.0264095i
$868$		0			0
$869$	4.00234	−	12.3179i	0.135770	−	0.417857i
$870$		0			0
$871$	2.31265	+	7.11759i	0.0783610	+	0.241170i
$872$		0			0
$873$	5.35882	−	7.37579i	0.181369	−	0.249633i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.42095	+	6.08491i	−0.149285	+	0.205473i	−0.877110	−	0.480290i	$-0.840531\pi$
$877$	−4.42095	+	6.08491i	−0.149285	+	0.205473i	0.727825	+	0.685763i	$0.240531\pi$
$878$		0			0
$879$	−7.91726	−	24.3668i	−0.267043	−	0.821873i
$880$		0			0
$881$	−8.14735	+	25.0750i	−0.274491	+	0.844797i	0.714862	+	0.699265i	$0.246489\pi$
$881$	−8.14735	+	25.0750i	−0.274491	+	0.844797i	−0.989354	+	0.145532i	$0.953511\pi$
$882$		0			0
$883$	0.391511	+	0.127210i	0.0131754	+	0.00428095i	0.315597	−	0.948893i	$-0.397795\pi$
$883$	0.391511	+	0.127210i	0.0131754	+	0.00428095i	−0.302422	+	0.953174i	$0.597795\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.9290	−	23.3008i	−0.568420	−	0.782363i	0.423946	−	0.905687i	$-0.360645\pi$
$887$	−16.9290	−	23.3008i	−0.568420	−	0.782363i	−0.992366	+	0.123324i	$0.960645\pi$
$888$		0			0
$889$	−28.5838	−	20.7674i	−0.958671	−	0.696515i
$890$		0			0
$891$	−1.58268	+	1.14988i	−0.0530216	+	0.0385225i
$892$		0			0
$893$		−	12.7593i		−	0.426973i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.02155	−	1.95652i	0.201054	−	0.0653263i
$898$		0			0
$899$	45.5333			1.51862
$900$		0			0
$901$	−16.0748			−0.535529
$902$		0			0
$903$	49.4799	−	16.0770i	1.64659	−	0.535009i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	1.80122i		−	0.0598085i	−0.999553	−	0.0299042i	$-0.990480\pi$
$907$		−	1.80122i		−	0.0598085i	0.999553	−	0.0299042i	$-0.00952023\pi$
$908$		0			0
$909$	1.20981	−	0.878980i	0.0401269	−	0.0291539i
$910$		0			0
$911$	−3.50521	−	2.54669i	−0.116133	−	0.0843755i	0.528203	−	0.849118i	$-0.322866\pi$
$911$	−3.50521	−	2.54669i	−0.116133	−	0.0843755i	−0.644336	+	0.764743i	$0.722866\pi$
$912$		0			0
$913$	−2.96886	−	4.08629i	−0.0982550	−	0.135236i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	76.8093	+	24.9569i	2.53647	+	0.824148i
$918$		0			0
$919$	2.40845	−	7.41244i	0.0794473	−	0.244514i	−0.903442	−	0.428710i	$-0.858968\pi$
$919$	2.40845	−	7.41244i	0.0794473	−	0.244514i	0.982889	+	0.184196i	$0.0589682\pi$
$920$		0			0
$921$	−1.91102	−	5.88153i	−0.0629704	−	0.193803i
$922$		0			0
$923$	7.61483	−	10.4809i	0.250645	−	0.344983i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.38470	−	8.78779i	0.209701	−	0.288629i
$928$		0			0
$929$	10.3076	+	31.7234i	0.338180	+	1.04081i	0.965134	+	0.261756i	$0.0843015\pi$
$929$	10.3076	+	31.7234i	0.338180	+	1.04081i	−0.626954	+	0.779056i	$0.715699\pi$
$930$		0			0
$931$	20.8608	−	64.2028i	0.683684	−	2.10416i
$932$		0			0
$933$	23.0519	+	7.49001i	0.754684	+	0.245212i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.4033	−	26.7063i	−0.633878	−	0.872458i	0.364393	−	0.931245i	$-0.381277\pi$
$937$	−19.4033	−	26.7063i	−0.633878	−	0.872458i	−0.998271	+	0.0587876i	$0.981277\pi$
$938$		0			0
$939$	−24.2392	−	17.6108i	−0.791015	−	0.574706i
$940$		0			0
$941$	41.4034	−	30.0813i	1.34971	−	0.980624i	0.350687	−	0.936493i	$-0.385948\pi$
$941$	41.4034	−	30.0813i	1.34971	−	0.980624i	0.999026	−	0.0441311i	$-0.0140519\pi$
$942$		0			0
$943$			5.03399i			0.163929i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.81485	−	2.21428i	0.221453	−	0.0719544i	−0.196189	−	0.980566i	$-0.562857\pi$
$947$	6.81485	−	2.21428i	0.221453	−	0.0719544i	0.417642	+	0.908612i	$0.362857\pi$
$948$		0			0
$949$	18.3099			0.594366
$950$		0			0
$951$	2.46267			0.0798575
$952$		0			0
$953$	−12.7472	+	4.14180i	−0.412921	+	0.134166i	−0.508108	−	0.861293i	$-0.669655\pi$
$953$	−12.7472	+	4.14180i	−0.412921	+	0.134166i	0.0951872	+	0.995459i	$0.469655\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			20.6391i			0.667166i
$958$		0			0
$959$	−3.24803	+	2.35983i	−0.104884	+	0.0762029i
$960$		0			0
$961$	10.0098	+	7.27257i	0.322898	+	0.234599i
$962$		0			0
$963$	−11.6611	−	16.0501i	−0.375773	−	0.517207i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.0286	−	3.58341i	−0.354656	−	0.115235i	0.126270	−	0.991996i	$-0.459699\pi$
$967$	−11.0286	−	3.58341i	−0.354656	−	0.115235i	−0.480926	+	0.876761i	$0.659699\pi$
$968$		0			0
$969$	4.99915	−	15.3858i	0.160596	−	0.494263i
$970$		0			0
$971$	−2.35477	−	7.24723i	−0.0755681	−	0.232575i	0.906136	−	0.422986i	$-0.139018\pi$
$971$	−2.35477	−	7.24723i	−0.0755681	−	0.232575i	−0.981704	+	0.190411i	$0.939018\pi$
$972$		0			0
$973$	−31.3719	+	43.1797i	−1.00574	+	1.38428i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.5159	−	35.1197i	0.816327	−	1.12358i	−0.173989	−	0.984748i	$-0.555666\pi$
$977$	25.5159	−	35.1197i	0.816327	−	1.12358i	0.990316	−	0.138830i	$-0.0443343\pi$
$978$		0			0
$979$	0.503414	+	1.54935i	0.0160892	+	0.0495174i
$980$		0			0
$981$	−0.724307	+	2.22919i	−0.0231254	+	0.0711725i
$982$		0			0
$983$	52.1172	+	16.9339i	1.66228	+	0.540107i	0.981348	−	0.192240i	$-0.0615753\pi$
$983$	52.1172	+	16.9339i	1.66228	+	0.540107i	0.680931	+	0.732348i	$0.261575\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	8.43925	+	11.6156i	0.268624	+	0.369730i
$988$		0			0
$989$	51.5920	+	37.4838i	1.64053	+	1.19191i
$990$		0			0
$991$	−17.7531	+	12.8984i	−0.563945	+	0.409730i	−0.832901	−	0.553422i	$-0.813322\pi$
$991$	−17.7531	+	12.8984i	−0.563945	+	0.409730i	0.268956	+	0.963153i	$0.413322\pi$
$992$		0			0
$993$			26.7867i			0.850051i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−37.1725	+	12.0781i	−1.17726	+	0.382516i	−0.831350	−	0.555750i	$-0.812431\pi$
$997$	−37.1725	+	12.0781i	−1.17726	+	0.382516i	−0.345914	+	0.938266i	$0.612431\pi$
$998$		0			0
$999$	−5.65983			−0.179069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.a.49.3		16
5.2	odd	4		1500.2.m.b.1201.2		8
5.3	odd	4		300.2.m.a.241.1	yes	8
5.4	even	2	inner	1500.2.o.a.49.2		16
15.8	even	4		900.2.n.a.541.2		8
25.2	odd	20		1500.2.m.b.301.2		8
25.6	even	5		7500.2.d.d.1249.1		8
25.8	odd	20		7500.2.a.g.1.1		4
25.11	even	5	inner	1500.2.o.a.949.1		16
25.14	even	10	inner	1500.2.o.a.949.4		16
25.17	odd	20		7500.2.a.d.1.4		4
25.19	even	10		7500.2.d.d.1249.8		8
25.23	odd	20		300.2.m.a.61.1	✓	8
75.23	even	20		900.2.n.a.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.61.1	✓	8	25.23	odd	20
300.2.m.a.241.1	yes	8	5.3	odd	4
900.2.n.a.361.2		8	75.23	even	20
900.2.n.a.541.2		8	15.8	even	4
1500.2.m.b.301.2		8	25.2	odd	20
1500.2.m.b.1201.2		8	5.2	odd	4
1500.2.o.a.49.2		16	5.4	even	2	inner
1500.2.o.a.49.3		16	1.1	even	1	trivial
1500.2.o.a.949.1		16	25.11	even	5	inner
1500.2.o.a.949.4		16	25.14	even	10	inner
7500.2.a.d.1.4		4	25.17	odd	20
7500.2.a.g.1.1		4	25.8	odd	20
7500.2.d.d.1249.1		8	25.6	even	5
7500.2.d.d.1249.8		8	25.19	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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{3} -4.78339i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{3} -4.78339i q^{7} +(0.809017 - 0.587785i) q^{9} +(-1.58268 - 1.14988i) q^{11} +(0.634721 + 0.873619i) q^{13} +(-3.61946 - 1.17603i) q^{17} +(-1.31359 + 4.04280i) q^{19} +(-1.47815 - 4.54927i) q^{21} +(3.44633 - 4.74346i) q^{23} +(0.587785 - 0.809017i) q^{27} +(-3.26015 - 10.0337i) q^{29} +(-1.33369 + 4.10468i) q^{31} +(-1.86055 - 0.604528i) q^{33} +(-3.32676 - 4.57890i) q^{37} +(0.873619 + 0.634721i) q^{39} +(-0.694596 + 0.504654i) q^{41} +10.8764i q^{43} +(-2.85467 + 0.927539i) q^{47} -15.8808 q^{49} -3.80573 q^{51} +(4.01711 - 1.30524i) q^{53} +4.25085i q^{57} +(-3.85916 + 2.80384i) q^{59} +(-2.93822 - 2.13474i) q^{61} +(-2.81160 - 3.86984i) q^{63} +(6.59126 + 2.14163i) q^{67} +(1.81184 - 5.57627i) q^{69} +(-3.70731 - 11.4099i) q^{71} +(9.96647 - 13.7177i) q^{73} +(-5.50033 + 7.57055i) q^{77} +(2.04587 + 6.29656i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.45552 + 0.797847i) q^{83} +(-6.20118 - 8.53519i) q^{87} +(-0.673699 - 0.489471i) q^{89} +(4.17886 - 3.03612i) q^{91} +4.31592i q^{93} +(8.67076 - 2.81730i) q^{97} -1.95630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^9	\( 16 q + 4 q^{9} - 4 q^{11} - 10 q^{19} - 6 q^{21} - 54 q^{29} - 6 q^{31} + 40 q^{41} + 16 q^{49} - 16 q^{51} - 4 q^{59} - 28 q^{61} - 4 q^{69} - 30 q^{71} - 48 q^{79} - 4 q^{81} + 10 q^{91} + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^9 - 4 * q^11 - 10 * q^19 - 6 * q^21 - 54 * q^29 - 6 * q^31 + 40 * q^41 + 16 * q^49 - 16 * q^51 - 4 * q^59 - 28 * q^61 - 4 * q^69 - 30 * q^71 - 48 * q^79 - 4 * q^81 + 10 * q^91 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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