LMFDB - Embedded newform 1300.2.bs.d.457.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(193,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("1300.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bs (of order $12$, 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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			457.2
Root			$-0.676406i$ of defining polynomial
Character	$\chi$	$=$	1300.457
Dual form			1300.2.bs.d.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834228 - 0.223531i) q^{3} +(-2.07295 - 1.19682i) q^{7} +(-1.95211 - 1.12705i) q^{9} +O(q^{10})$	\(q+(-0.834228 - 0.223531i) q^{3} +(-2.07295 - 1.19682i) q^{7} +(-1.95211 - 1.12705i) q^{9} +(0.0379829 - 0.141754i) q^{11} +(3.58903 + 0.344781i) q^{13} +(-1.33048 - 4.96543i) q^{17} +(4.18726 - 1.12197i) q^{19} +(1.46179 + 1.46179i) q^{21} +(-2.28631 + 8.53261i) q^{23} +(3.20866 + 3.20866i) q^{27} +(-5.00061 + 2.88710i) q^{29} +(-4.94351 + 4.94351i) q^{31} +(-0.0633728 + 0.109765i) q^{33} +(-3.76003 + 2.17085i) q^{37} +(-2.91700 - 1.08988i) q^{39} +(-11.6356 - 3.11775i) q^{41} +(-0.642311 + 0.172107i) q^{43} +3.88786i q^{47} +(-0.635248 - 1.10028i) q^{49} +4.43971i q^{51} +(2.38836 - 2.38836i) q^{53} -3.74392 q^{57} +(-1.94788 - 7.26959i) q^{59} +(-5.54868 + 9.61059i) q^{61} +(2.69775 + 4.67263i) q^{63} +(1.92761 + 3.33873i) q^{67} +(3.81460 - 6.60708i) q^{69} +(1.66605 + 6.21778i) q^{71} -0.839574 q^{73} +(-0.248391 + 0.248391i) q^{77} +3.64275i q^{79} +(1.42162 + 2.46232i) q^{81} +10.3431i q^{83} +(4.81701 - 1.29071i) q^{87} +(-11.7600 - 3.15109i) q^{89} +(-7.02724 - 5.01013i) q^{91} +(5.22904 - 3.01899i) q^{93} +(0.254578 - 0.440943i) q^{97} +(-0.233910 + 0.233910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9	$ 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9} - 8 q^{13} + 20 q^{19} - 12 q^{21} - 6 q^{23} + 20 q^{27} + 24 q^{29} + 8 q^{31} + 10 q^{33} + 4 q^{39} + 6 q^{41} - 38 q^{43} + 14 q^{49} - 30 q^{53} + 76 q^{57} - 24 q^{59} - 32 q^{61} + 24 q^{63} - 22 q^{67} - 16 q^{69} + 44 q^{73} + 12 q^{77} + 2 q^{81} - 38 q^{87} - 30 q^{89} - 72 q^{91} + 48 q^{93} - 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9 - 8 * q^13 + 20 * q^19 - 12 * q^21 - 6 * q^23 + 20 * q^27 + 24 * q^29 + 8 * q^31 + 10 * q^33 + 4 * q^39 + 6 * q^41 - 38 * q^43 + 14 * q^49 - 30 * q^53 + 76 * q^57 - 24 * q^59 - 32 * q^61 + 24 * q^63 - 22 * q^67 - 16 * q^69 + 44 * q^73 + 12 * q^77 + 2 * q^81 - 38 * q^87 - 30 * q^89 - 72 * q^91 + 48 * q^93 - 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.834228	−	0.223531i	−0.481642	−	0.129056i	0.00982510	−	0.999952i	$-0.496873\pi$
$3$	−0.834228	−	0.223531i	−0.481642	−	0.129056i	−0.491467	+	0.870896i	$0.663539\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.07295	−	1.19682i	−0.783502	−	0.452355i	0.0541680	−	0.998532i	$-0.482749\pi$
$7$	−2.07295	−	1.19682i	−0.783502	−	0.452355i	−0.837670	+	0.546177i	$0.816083\pi$
$8$		0			0
$9$	−1.95211	−	1.12705i	−0.650702	−	0.375683i
$10$		0			0
$11$	0.0379829	−	0.141754i	0.0114523	−	0.0427405i	−0.959963	−	0.280126i	$-0.909624\pi$
$11$	0.0379829	−	0.141754i	0.0114523	−	0.0427405i	0.971416	+	0.237385i	$0.0762904\pi$
$12$		0			0
$13$	3.58903	+	0.344781i	0.995417	+	0.0956249i
$13$	3.58903	+	0.344781i	0.995417	+	0.0956249i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.33048	−	4.96543i	−0.322689	−	1.20429i	−0.916614	−	0.399773i	$-0.869089\pi$
$17$	−1.33048	−	4.96543i	−0.322689	−	1.20429i	0.593925	−	0.804521i	$-0.297578\pi$
$18$		0			0
$19$	4.18726	−	1.12197i	0.960623	−	0.257398i	0.255759	−	0.966741i	$-0.417675\pi$
$19$	4.18726	−	1.12197i	0.960623	−	0.257398i	0.704864	+	0.709343i	$0.251008\pi$
$20$		0			0
$21$	1.46179	+	1.46179i	0.318989	+	0.318989i
$22$		0			0
$23$	−2.28631	+	8.53261i	−0.476728	+	1.77917i	0.138000	+	0.990432i	$0.455933\pi$
$23$	−2.28631	+	8.53261i	−0.476728	+	1.77917i	−0.614728	+	0.788739i	$0.710734\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.20866	+	3.20866i	0.617508	+	0.617508i
$28$		0			0
$29$	−5.00061	+	2.88710i	−0.928590	+	0.536121i	−0.886365	−	0.462987i	$-0.846778\pi$
$29$	−5.00061	+	2.88710i	−0.928590	+	0.536121i	−0.0422244	+	0.999108i	$0.513444\pi$
$30$		0			0
$31$	−4.94351	+	4.94351i	−0.887880	+	0.887880i	−0.994319	−	0.106439i	$-0.966055\pi$
$31$	−4.94351	+	4.94351i	−0.887880	+	0.887880i	0.106439	+	0.994319i	$0.466055\pi$
$32$		0			0
$33$	−0.0633728	+	0.109765i	−0.0110318	+	0.0191076i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.76003	+	2.17085i	−0.618144	+	0.356886i	−0.776146	−	0.630553i	$-0.782828\pi$
$37$	−3.76003	+	2.17085i	−0.618144	+	0.356886i	0.158002	+	0.987439i	$0.449495\pi$
$38$		0			0
$39$	−2.91700	−	1.08988i	−0.467094	−	0.174521i
$40$		0			0
$41$	−11.6356	−	3.11775i	−1.81718	−	0.486911i	−0.820744	−	0.571297i	$-0.806441\pi$
$41$	−11.6356	−	3.11775i	−1.81718	−	0.486911i	−0.996433	+	0.0843856i	$0.973107\pi$
$42$		0			0
$43$	−0.642311	+	0.172107i	−0.0979516	+	0.0262460i	−0.307462	−	0.951560i	$-0.599480\pi$
$43$	−0.642311	+	0.172107i	−0.0979516	+	0.0262460i	0.209510	+	0.977806i	$0.432813\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.88786i			0.567103i	0.958957	+	0.283552i	$0.0915127\pi$
$47$			3.88786i			0.567103i	−0.958957	+	0.283552i	$0.908487\pi$
$48$		0			0
$49$	−0.635248	−	1.10028i	−0.0907497	−	0.157183i
$50$		0			0
$51$			4.43971i			0.621683i
$52$		0			0
$53$	2.38836	−	2.38836i	0.328067	−	0.328067i	−0.523784	−	0.851851i	$-0.675480\pi$
$53$	2.38836	−	2.38836i	0.328067	−	0.328067i	0.851851	+	0.523784i	$0.175480\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.74392			−0.495895
$58$		0			0
$59$	−1.94788	−	7.26959i	−0.253592	−	0.946420i	−0.968868	−	0.247577i	$-0.920366\pi$
$59$	−1.94788	−	7.26959i	−0.253592	−	0.946420i	0.715276	−	0.698842i	$-0.246301\pi$
$60$		0			0
$61$	−5.54868	+	9.61059i	−0.710435	+	1.23051i	0.254259	+	0.967136i	$0.418168\pi$
$61$	−5.54868	+	9.61059i	−0.710435	+	1.23051i	−0.964694	+	0.263373i	$0.915165\pi$
$62$		0			0
$63$	2.69775	+	4.67263i	0.339884	+	0.588697i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.92761	+	3.33873i	0.235496	+	0.407890i	0.959417	−	0.281993i	$-0.0909953\pi$
$67$	1.92761	+	3.33873i	0.235496	+	0.407890i	−0.723921	+	0.689883i	$0.757662\pi$
$68$		0			0
$69$	3.81460	−	6.60708i	0.459224	−	0.795399i
$70$		0			0
$71$	1.66605	+	6.21778i	0.197724	+	0.737914i	0.991545	+	0.129763i	$0.0414218\pi$
$71$	1.66605	+	6.21778i	0.197724	+	0.737914i	−0.793821	+	0.608151i	$0.791912\pi$
$72$		0			0
$73$	−0.839574			−0.0982647			−0.0491323	−	0.998792i	$-0.515646\pi$
$73$	−0.839574			−0.0982647			−0.0491323	+	0.998792i	$0.515646\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.248391	+	0.248391i	−0.0283067	+	0.0283067i
$78$		0			0
$79$			3.64275i			0.409841i	0.978779	+	0.204921i	$0.0656936\pi$
$79$			3.64275i			0.409841i	−0.978779	+	0.204921i	$0.934306\pi$
$80$		0			0
$81$	1.42162	+	2.46232i	0.157958	+	0.273591i
$82$		0			0
$83$			10.3431i			1.13530i	0.823270	+	0.567651i	$0.192148\pi$
$83$			10.3431i			1.13530i	−0.823270	+	0.567651i	$0.807852\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.81701	−	1.29071i	0.516437	−	0.138379i
$88$		0			0
$89$	−11.7600	−	3.15109i	−1.24656	−	0.334015i	−0.425554	−	0.904933i	$-0.639921\pi$
$89$	−11.7600	−	3.15109i	−1.24656	−	0.334015i	−0.821007	+	0.570918i	$0.806588\pi$
$90$		0			0
$91$	−7.02724	−	5.01013i	−0.736655	−	0.525204i
$92$		0			0
$93$	5.22904	−	3.01899i	0.542226	−	0.313054i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.254578	−	0.440943i	0.0258485	−	0.0447709i	−0.852812	−	0.522218i	$-0.825105\pi$
$97$	0.254578	−	0.440943i	0.0258485	−	0.0447709i	0.878660	+	0.477447i	$0.158438\pi$
$98$		0			0
$99$	−0.233910	+	0.233910i	−0.0235089	+	0.0235089i
$100$		0			0
$101$	8.19497	−	4.73137i	0.815430	−	0.470789i	−0.0334079	−	0.999442i	$-0.510636\pi$
$101$	8.19497	−	4.73137i	0.815430	−	0.470789i	0.848838	+	0.528653i	$0.177303\pi$
$102$		0			0
$103$	−12.8189	−	12.8189i	−1.26308	−	1.26308i	−0.949590	−	0.313494i	$-0.898500\pi$
$103$	−12.8189	−	12.8189i	−1.26308	−	1.26308i	−0.313494	−	0.949590i	$-0.601500\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.14122	+	4.25910i	−0.110326	+	0.411743i	−0.998895	−	0.0470007i	$-0.985034\pi$
$107$	−1.14122	+	4.25910i	−0.110326	+	0.411743i	0.888569	+	0.458744i	$0.151700\pi$
$108$		0			0
$109$	−4.91337	−	4.91337i	−0.470615	−	0.470615i	0.431498	−	0.902114i	$-0.357985\pi$
$109$	−4.91337	−	4.91337i	−0.470615	−	0.470615i	−0.902114	+	0.431498i	$0.857985\pi$
$110$		0			0
$111$	3.62197	−	0.970505i	0.343782	−	0.0921162i
$112$		0			0
$113$	0.294624	+	1.09955i	0.0277159	+	0.103437i	0.978398	−	0.206729i	$-0.0662819\pi$
$113$	0.294624	+	1.09955i	0.0277159	+	0.103437i	−0.950682	+	0.310166i	$0.899615\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−6.61758	−	4.71806i	−0.611795	−	0.436185i
$118$		0			0
$119$	−3.18469	+	11.8854i	−0.291940	+	1.08954i
$120$		0			0
$121$	9.50763	+	5.48923i	0.864330	+	0.499021i
$122$		0			0
$123$	9.00984	+	5.20183i	0.812390	+	0.469034i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−15.6730	−	4.19958i	−1.39076	−	0.372653i	−0.515741	−	0.856744i	$-0.672483\pi$
$127$	−15.6730	−	4.19958i	−1.39076	−	0.372653i	−0.875017	+	0.484092i	$0.839150\pi$
$128$		0			0
$129$	0.574306			0.0505648
$130$		0			0
$131$	−12.0412			−1.05204			−0.526022	−	0.850471i	$-0.676317\pi$
$131$	−12.0412			−1.05204			−0.526022	+	0.850471i	$0.676317\pi$
$132$		0			0
$133$	−10.0228	−	2.68560i	−0.869085	−	0.232871i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.08519	+	0.626533i	0.0927138	+	0.0535284i	0.545640	−	0.838020i	$-0.316287\pi$
$137$	1.08519	+	0.626533i	0.0927138	+	0.0535284i	−0.452926	+	0.891548i	$0.649620\pi$
$138$		0			0
$139$	17.2116	+	9.93710i	1.45987	+	0.842854i	0.999004	−	0.0446175i	$-0.0142069\pi$
$139$	17.2116	+	9.93710i	1.45987	+	0.842854i	0.460862	+	0.887472i	$0.347540\pi$
$140$		0			0
$141$	0.869057	−	3.24337i	0.0731878	−	0.273141i
$142$		0			0
$143$	0.185196	−	0.495664i	0.0154868	−	0.0414495i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.283995	+	1.05988i	0.0234235	+	0.0874178i
$148$		0			0
$149$	−0.709453	+	0.190097i	−0.0581207	+	0.0155734i	−0.287762	−	0.957702i	$-0.592911\pi$
$149$	−0.709453	+	0.190097i	−0.0581207	+	0.0155734i	0.229642	+	0.973275i	$0.426245\pi$
$150$		0			0
$151$	13.9096	+	13.9096i	1.13195	+	1.13195i	0.989853	+	0.142093i	$0.0453834\pi$
$151$	13.9096	+	13.9096i	1.13195	+	1.13195i	0.142093	+	0.989853i	$0.454617\pi$
$152$		0			0
$153$	−2.99904	+	11.1926i	−0.242458	+	0.904865i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.54080	−	2.54080i	−0.202778	−	0.202778i	0.598411	−	0.801189i	$-0.295799\pi$
$157$	−2.54080	−	2.54080i	−0.202778	−	0.202778i	−0.801189	+	0.598411i	$0.795799\pi$
$158$		0			0
$159$	−2.52631	+	1.45857i	−0.200350	+	0.115672i
$160$		0			0
$161$	14.9514	−	14.9514i	1.17833	−	1.17833i
$162$		0			0
$163$	−4.37482	+	7.57741i	−0.342662	+	0.593509i	−0.984926	−	0.172975i	$-0.944662\pi$
$163$	−4.37482	+	7.57741i	−0.342662	+	0.593509i	0.642264	+	0.766484i	$0.277995\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.03260	−	3.48292i	0.466816	−	0.269517i	−0.248090	−	0.968737i	$-0.579803\pi$
$167$	6.03260	−	3.48292i	0.466816	−	0.269517i	0.714906	+	0.699220i	$0.246469\pi$
$168$		0			0
$169$	12.7623	+	2.47485i	0.981712	+	0.190373i
$170$		0			0
$171$	−9.43848	−	2.52903i	−0.721779	−	0.193400i
$172$		0			0
$173$	−3.10746	+	0.832640i	−0.236256	+	0.0633045i	−0.375004	−	0.927023i	$-0.622359\pi$
$173$	−3.10746	+	0.832640i	−0.236256	+	0.0633045i	0.138749	+	0.990328i	$0.455692\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			6.49991i			0.488563i
$178$		0			0
$179$	−1.04481	−	1.80967i	−0.0780930	−	0.135261i	0.824334	−	0.566104i	$-0.191550\pi$
$179$	−1.04481	−	1.80967i	−0.0780930	−	0.135261i	−0.902427	+	0.430843i	$0.858216\pi$
$180$		0			0
$181$			1.36226i			0.101256i	0.998718	+	0.0506281i	$0.0161223\pi$
$181$			1.36226i			0.101256i	−0.998718	+	0.0506281i	$0.983878\pi$
$182$		0			0
$183$	6.77713	−	6.77713i	0.500979	−	0.500979i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.754405			−0.0551676
$188$		0			0
$189$	−2.81121	−	10.4916i	−0.204486	−	0.763151i
$190$		0			0
$191$	−1.42257	+	2.46396i	−0.102933	+	0.178286i	−0.912892	−	0.408201i	$-0.866156\pi$
$191$	−1.42257	+	2.46396i	−0.102933	+	0.178286i	0.809959	+	0.586487i	$0.199489\pi$
$192$		0			0
$193$	−0.290018	−	0.502326i	−0.0208760	−	0.0361582i	0.855399	−	0.517970i	$-0.173312\pi$
$193$	−0.290018	−	0.502326i	−0.0208760	−	0.0361582i	−0.876275	+	0.481812i	$0.839979\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.636666	+	1.10274i	0.0453606	+	0.0785668i	0.887814	−	0.460202i	$-0.152223\pi$
$197$	0.636666	+	1.10274i	0.0453606	+	0.0785668i	−0.842454	+	0.538769i	$0.818890\pi$
$198$		0			0
$199$	−9.35079	+	16.1960i	−0.662860	+	1.14811i	0.317001	+	0.948425i	$0.397324\pi$
$199$	−9.35079	+	16.1960i	−0.662860	+	1.14811i	−0.979861	+	0.199682i	$0.936009\pi$
$200$		0			0
$201$	−0.861762	−	3.21614i	−0.0607840	−	0.226849i
$202$		0			0
$203$	13.8214			0.970069
$204$		0			0
$205$		0			0
$206$		0			0
$207$	14.0798	−	14.0798i	0.978612	−	0.978612i
$208$		0			0
$209$		−	0.636176i		−	0.0440052i
$210$		0			0
$211$	−9.74267	−	16.8748i	−0.670713	−	1.16171i	−0.977702	−	0.209996i	$-0.932655\pi$
$211$	−9.74267	−	16.8748i	−0.670713	−	1.16171i	0.306989	−	0.951713i	$-0.400679\pi$
$212$		0			0
$213$		−	5.55946i		−	0.380928i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	16.1641	−	4.33117i	1.09729	−	0.294019i
$218$		0			0
$219$	0.700396	+	0.187671i	0.0473284	+	0.0126816i
$220$		0			0
$221$	−3.06316	−	18.2798i	−0.206050	−	1.22963i
$222$		0			0
$223$	23.3541	−	13.4835i	1.56391	−	0.902922i	0.567050	−	0.823683i	$-0.308084\pi$
$223$	23.3541	−	13.4835i	1.56391	−	0.902922i	0.996856	−	0.0792386i	$-0.0252489\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.37425	+	4.11233i	−0.157585	+	0.272945i	−0.933997	−	0.357280i	$-0.883704\pi$
$227$	−2.37425	+	4.11233i	−0.157585	+	0.272945i	0.776412	+	0.630225i	$0.217037\pi$
$228$		0			0
$229$	18.5531	−	18.5531i	1.22603	−	1.22603i	0.260571	−	0.965455i	$-0.416089\pi$
$229$	18.5531	−	18.5531i	1.22603	−	1.22603i	0.965455	−	0.260571i	$-0.0839110\pi$
$230$		0			0
$231$	0.262737	−	0.151692i	0.0172869	−	0.00998057i
$232$		0			0
$233$	−17.8687	−	17.8687i	−1.17062	−	1.17062i	−0.982062	−	0.188558i	$-0.939619\pi$
$233$	−17.8687	−	17.8687i	−1.17062	−	1.17062i	−0.188558	−	0.982062i	$-0.560381\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.814267	−	3.03888i	0.0528923	−	0.197397i
$238$		0			0
$239$	8.92835	+	8.92835i	0.577527	+	0.577527i	0.934221	−	0.356694i	$-0.116096\pi$
$239$	8.92835	+	8.92835i	0.577527	+	0.577527i	−0.356694	+	0.934221i	$0.616096\pi$
$240$		0			0
$241$	0.894443	−	0.239665i	0.0576162	−	0.0154382i	−0.229896	−	0.973215i	$-0.573839\pi$
$241$	0.894443	−	0.239665i	0.0576162	−	0.0154382i	0.287512	+	0.957777i	$0.407172\pi$
$242$		0			0
$243$	−4.15891	−	15.5213i	−0.266794	−	0.995690i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	15.4150	−	2.58311i	0.980834	−	0.164359i
$248$		0			0
$249$	2.31200	−	8.62850i	0.146517	−	0.546809i
$250$		0			0
$251$	−5.87395	−	3.39133i	−0.370760	−	0.214059i	0.303030	−	0.952981i	$-0.402002\pi$
$251$	−5.87395	−	3.39133i	−0.370760	−	0.214059i	−0.673791	+	0.738922i	$0.735335\pi$
$252$		0			0
$253$	1.12269	+	0.648186i	0.0705830	+	0.0407511i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.41868	−	1.71988i	−0.400386	−	0.107283i	0.0530063	−	0.998594i	$-0.483120\pi$
$257$	−6.41868	−	1.71988i	−0.400386	−	0.107283i	−0.453392	+	0.891311i	$0.649786\pi$
$258$		0			0
$259$	10.3925			0.645756
$260$		0			0
$261$	13.0156			0.805647
$262$		0			0
$263$	−11.4000	−	3.05461i	−0.702952	−	0.188355i	−0.110400	−	0.993887i	$-0.535213\pi$
$263$	−11.4000	−	3.05461i	−0.702952	−	0.188355i	−0.592552	+	0.805532i	$0.701880\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	9.10619	+	5.25746i	0.557290	+	0.321752i
$268$		0			0
$269$	−14.5787	−	8.41701i	−0.888878	−	0.513194i	−0.0153026	−	0.999883i	$-0.504871\pi$
$269$	−14.5787	−	8.41701i	−0.888878	−	0.513194i	−0.873575	+	0.486689i	$0.838204\pi$
$270$		0			0
$271$	3.25919	−	12.1634i	0.197981	−	0.738877i	−0.793493	−	0.608579i	$-0.791740\pi$
$271$	3.25919	−	12.1634i	0.197981	−	0.738877i	0.991475	−	0.130298i	$-0.0415934\pi$
$272$		0			0
$273$	4.74241	+	5.75040i	0.287023	+	0.348030i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.71401	+	13.8609i	0.223153	+	0.832818i	0.983136	+	0.182876i	$0.0585405\pi$
$277$	3.71401	+	13.8609i	0.223153	+	0.832818i	−0.759983	+	0.649943i	$0.774793\pi$
$278$		0			0
$279$	15.2218	−	4.07867i	0.911307	−	0.244184i
$280$		0			0
$281$	11.1184	+	11.1184i	0.663267	+	0.663267i	0.956149	−	0.292882i	$-0.0946142\pi$
$281$	11.1184	+	11.1184i	0.663267	+	0.663267i	−0.292882	+	0.956149i	$0.594614\pi$
$282$		0			0
$283$	−4.44486	+	16.5884i	−0.264220	+	0.986081i	0.698507	+	0.715603i	$0.253848\pi$
$283$	−4.44486	+	16.5884i	−0.264220	+	0.986081i	−0.962726	+	0.270477i	$0.912819\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	20.3887	+	20.3887i	1.20350	+	1.20350i
$288$		0			0
$289$	−8.16288	+	4.71284i	−0.480169	+	0.277226i
$290$		0			0
$291$	−0.310941	+	0.310941i	−0.0182277	+	0.0182277i
$292$		0			0
$293$	12.4649	−	21.5898i	0.728205	−	1.26129i	−0.229436	−	0.973324i	$-0.573688\pi$
$293$	12.4649	−	21.5898i	0.728205	−	1.26129i	0.957641	−	0.287964i	$-0.0929785\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.576716	−	0.332967i	0.0334644	−	0.0193207i
$298$		0			0
$299$	−11.1475	+	29.8355i	−0.644676	+	1.72543i
$300$		0			0
$301$	1.53746	+	0.411961i	0.0886178	+	0.0237451i
$302$		0			0
$303$	−7.89409	+	2.11521i	−0.453503	+	0.121516i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	10.3236i		−	0.589199i	−0.955621	−	0.294599i	$-0.904814\pi$
$307$		−	10.3236i		−	0.589199i	0.955621	−	0.294599i	$-0.0951862\pi$
$308$		0			0
$309$	7.82847	+	13.5593i	0.445346	+	0.771362i
$310$		0			0
$311$		−	15.7703i		−	0.894254i	−0.894471	−	0.447127i	$-0.852447\pi$
$311$		−	15.7703i		−	0.894254i	0.894471	−	0.447127i	$-0.147553\pi$
$312$		0			0
$313$	17.7618	−	17.7618i	1.00395	−	1.00395i	0.00396212	−	0.999992i	$-0.498739\pi$
$313$	17.7618	−	17.7618i	1.00395	−	1.00395i	0.999992	−	0.00396212i	$-0.00126118\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.4146			−0.753441			−0.376721	−	0.926327i	$-0.622948\pi$
$317$	−13.4146			−0.753441			−0.376721	+	0.926327i	$0.622948\pi$
$318$		0			0
$319$	0.219321	+	0.818517i	0.0122796	+	0.0458282i
$320$		0			0
$321$	1.90408	−	3.29797i	0.106275	−	0.184074i
$322$		0			0
$323$	−11.1421	−	19.2988i	−0.619966	−	1.07381i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.00058	+	5.19716i	0.165933	+	0.287404i
$328$		0			0
$329$	4.65307	−	8.05935i	0.256532	−	0.444326i
$330$		0			0
$331$	−3.79152	−	14.1502i	−0.208401	−	0.777763i	−0.988386	−	0.151965i	$-0.951440\pi$
$331$	−3.79152	−	14.1502i	−0.208401	−	0.777763i	0.779985	−	0.625798i	$-0.215227\pi$
$332$		0			0
$333$	9.78662			0.536303
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.93205	−	7.93205i	0.432086	−	0.432086i	−0.457251	−	0.889338i	$-0.651166\pi$
$337$	7.93205	−	7.93205i	0.432086	−	0.432086i	0.889338	+	0.457251i	$0.151166\pi$
$338$		0			0
$339$		−	0.983136i		−	0.0533966i
$340$		0			0
$341$	0.512994	+	0.888531i	0.0277802	+	0.0481166i
$342$		0			0
$343$			19.7966i			1.06891i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−26.1580	+	7.00902i	−1.40424	+	0.376264i	−0.879864	−	0.475226i	$-0.842366\pi$
$347$	−26.1580	+	7.00902i	−1.40424	+	0.376264i	−0.524371	+	0.851490i	$0.675700\pi$
$348$		0			0
$349$	−7.60394	−	2.03747i	−0.407030	−	0.109063i	0.0494943	−	0.998774i	$-0.484239\pi$
$349$	−7.60394	−	2.03747i	−0.407030	−	0.109063i	−0.456524	+	0.889711i	$0.650906\pi$
$350$		0			0
$351$	10.4097	+	12.6223i	0.555629	+	0.673727i
$352$		0			0
$353$	−24.7235	+	14.2741i	−1.31590	+	0.759734i	−0.983066	−	0.183253i	$-0.941337\pi$
$353$	−24.7235	+	14.2741i	−1.31590	+	0.759734i	−0.332831	+	0.942986i	$0.608004\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.31353	−	9.20330i	0.281222	−	0.487090i
$358$		0			0
$359$	−9.94522	+	9.94522i	−0.524889	+	0.524889i	−0.919044	−	0.394155i	$-0.871037\pi$
$359$	−9.94522	+	9.94522i	−0.524889	+	0.524889i	0.394155	+	0.919044i	$0.371037\pi$
$360$		0			0
$361$	−0.180183	+	0.104029i	−0.00948333	+	0.00547520i
$362$		0			0
$363$	−6.70452	−	6.70452i	−0.351896	−	0.351896i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.83092	−	25.4933i	0.356571	−	1.33074i	−0.521925	−	0.852992i	$-0.674786\pi$
$367$	6.83092	−	25.4933i	0.356571	−	1.33074i	0.878496	−	0.477750i	$-0.158548\pi$
$368$		0			0
$369$	19.2001	+	19.2001i	0.999516	+	0.999516i
$370$		0			0
$371$	−7.80940	+	2.09252i	−0.405444	+	0.108638i
$372$		0			0
$373$	0.220619	+	0.823363i	0.0114232	+	0.0426321i	0.971402	−	0.237440i	$-0.0763083\pi$
$373$	0.220619	+	0.823363i	0.0114232	+	0.0426321i	−0.959979	+	0.280072i	$0.909642\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−18.9427	+	8.63778i	−0.975601	+	0.444868i
$378$		0			0
$379$	5.74031	−	21.4231i	0.294860	−	1.10043i	−0.646469	−	0.762940i	$-0.723755\pi$
$379$	5.74031	−	21.4231i	0.294860	−	1.10043i	0.941329	−	0.337491i	$-0.109578\pi$
$380$		0			0
$381$	12.1362	+	7.00682i	0.621755	+	0.358970i
$382$		0			0
$383$	−11.6555	−	6.72928i	−0.595566	−	0.343850i	0.171729	−	0.985144i	$-0.445065\pi$
$383$	−11.6555	−	6.72928i	−0.595566	−	0.343850i	−0.767295	+	0.641294i	$0.778398\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.44783	+	0.387945i	0.0735974	+	0.0197204i
$388$		0			0
$389$	−10.4988			−0.532310			−0.266155	−	0.963930i	$-0.585753\pi$
$389$	−10.4988			−0.532310			−0.266155	+	0.963930i	$0.585753\pi$
$390$		0			0
$391$	45.4100			2.29648
$392$		0			0
$393$	10.0451	+	2.69158i	0.506708	+	0.135772i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−20.2512	−	11.6920i	−1.01638	−	0.586805i	−0.103324	−	0.994648i	$-0.532948\pi$
$397$	−20.2512	−	11.6920i	−1.01638	−	0.586805i	−0.913052	+	0.407843i	$0.866281\pi$
$398$		0			0
$399$	7.76097	+	4.48080i	0.388535	+	0.224321i
$400$		0			0
$401$	8.35969	−	31.1988i	0.417463	−	1.55799i	−0.362388	−	0.932027i	$-0.618038\pi$
$401$	8.35969	−	31.1988i	0.417463	−	1.55799i	0.779851	−	0.625966i	$-0.215295\pi$
$402$		0			0
$403$	−19.4468	+	16.0380i	−0.968715	+	0.798908i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.164910	+	0.615454i	0.00817431	+	0.0305069i
$408$		0			0
$409$	9.26291	−	2.48199i	0.458022	−	0.122726i	−0.0224288	−	0.999748i	$-0.507140\pi$
$409$	9.26291	−	2.48199i	0.458022	−	0.122726i	0.480450	+	0.877022i	$0.340473\pi$
$410$		0			0
$411$	−0.765245	−	0.765245i	−0.0377467	−	0.0377467i
$412$		0			0
$413$	−4.66252	+	17.4008i	−0.229428	+	0.856236i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−12.1371	−	12.1371i	−0.594358	−	0.594358i
$418$		0			0
$419$	−10.4021	+	6.00568i	−0.508178	+	0.293397i	−0.732084	−	0.681214i	$-0.761452\pi$
$419$	−10.4021	+	6.00568i	−0.508178	+	0.293397i	0.223906	+	0.974611i	$0.428119\pi$
$420$		0			0
$421$	−9.06775	+	9.06775i	−0.441935	+	0.441935i	−0.892662	−	0.450727i	$-0.851165\pi$
$421$	−9.06775	+	9.06775i	−0.441935	+	0.441935i	0.450727	+	0.892662i	$0.351165\pi$
$422$		0			0
$423$	4.38181	−	7.58952i	0.213051	−	0.369015i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	23.0043	−	13.2815i	1.11325	−	0.642738i
$428$		0			0
$429$	−0.265292	+	0.372100i	−0.0128084	+	0.0179651i
$430$		0			0
$431$	6.85071	+	1.83564i	0.329987	+	0.0884197i	0.420009	−	0.907520i	$-0.362027\pi$
$431$	6.85071	+	1.83564i	0.329987	+	0.0884197i	−0.0900218	+	0.995940i	$0.528694\pi$
$432$		0			0
$433$	13.9461	−	3.73685i	0.670208	−	0.179582i	0.0923594	−	0.995726i	$-0.470559\pi$
$433$	13.9461	−	3.73685i	0.670208	−	0.179582i	0.577848	+	0.816144i	$0.303892\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			38.2934i			1.83182i
$438$		0			0
$439$	15.9695	+	27.6599i	0.762181	+	1.32014i	0.941724	+	0.336386i	$0.109205\pi$
$439$	15.9695	+	27.6599i	0.762181	+	1.32014i	−0.179543	+	0.983750i	$0.557462\pi$
$440$		0			0
$441$			2.86382i			0.136372i
$442$		0			0
$443$	1.63712	−	1.63712i	0.0777820	−	0.0777820i	−0.667145	−	0.744927i	$-0.732484\pi$
$443$	1.63712	−	1.63712i	0.0777820	−	0.0777820i	0.744927	+	0.667145i	$0.232484\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.634339			0.0300032
$448$		0			0
$449$	1.13708	+	4.24365i	0.0536622	+	0.200270i	0.987553	−	0.157289i	$-0.0502756\pi$
$449$	1.13708	+	4.24365i	0.0536622	+	0.200270i	−0.933890	+	0.357560i	$0.883609\pi$
$450$		0			0
$451$	−0.883908	+	1.53097i	−0.0416216	+	0.0720907i
$452$		0			0
$453$	−8.49456	−	14.7130i	−0.399109	−	0.691277i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.20333	−	12.4765i	−0.336957	−	0.583627i	0.646901	−	0.762574i	$-0.276065\pi$
$457$	−7.20333	−	12.4765i	−0.336957	−	0.583627i	−0.983859	+	0.178946i	$0.942731\pi$
$458$		0			0
$459$	11.6633	−	20.2015i	0.544397	−	0.942924i
$460$		0			0
$461$	4.86355	+	18.1510i	0.226518	+	0.845377i	0.981791	+	0.189966i	$0.0608379\pi$
$461$	4.86355	+	18.1510i	0.226518	+	0.845377i	−0.755272	+	0.655411i	$0.772495\pi$
$462$		0			0
$463$	32.2068			1.49678			0.748389	−	0.663260i	$-0.230828\pi$
$463$	32.2068			1.49678			0.748389	+	0.663260i	$0.230828\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.3536	+	12.3536i	−0.571656	+	0.571656i	−0.932591	−	0.360935i	$-0.882458\pi$
$467$	−12.3536	+	12.3536i	−0.571656	+	0.571656i	0.360935	+	0.932591i	$0.382458\pi$
$468$		0			0
$469$		−	9.22802i		−	0.426111i
$470$		0			0
$471$	1.55166	+	2.68756i	0.0714968	+	0.123836i
$472$		0			0
$473$			0.0975874i			0.00448707i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.35413	+	1.97053i	−0.336723	+	0.0902246i
$478$		0			0
$479$	−17.8406	−	4.78038i	−0.815158	−	0.218421i	−0.172930	−	0.984934i	$-0.555323\pi$
$479$	−17.8406	−	4.78038i	−0.815158	−	0.218421i	−0.642228	+	0.766513i	$0.721990\pi$
$480$		0			0
$481$	−14.2433	+	6.49487i	−0.649439	+	0.296140i
$482$		0			0
$483$	−15.8150	+	9.13078i	−0.719606	+	0.415465i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−17.6219	+	30.5221i	−0.798526	+	1.38309i	0.122051	+	0.992524i	$0.461053\pi$
$487$	−17.6219	+	30.5221i	−0.798526	+	1.38309i	−0.920576	+	0.390563i	$0.872280\pi$
$488$		0			0
$489$	5.34338	−	5.34338i	0.241636	−	0.241636i
$490$		0			0
$491$	−31.7390	+	18.3245i	−1.43236	+	0.826975i	−0.997301	−	0.0734250i	$-0.976607\pi$
$491$	−31.7390	+	18.3245i	−1.43236	+	0.826975i	−0.435062	+	0.900400i	$0.643274\pi$
$492$		0			0
$493$	20.9889	+	20.9889i	0.945294	+	0.945294i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.98792	−	14.8831i	0.178883	−	0.667599i
$498$		0			0
$499$	−26.6823	−	26.6823i	−1.19447	−	1.19447i	−0.975800	−	0.218666i	$-0.929829\pi$
$499$	−26.6823	−	26.6823i	−1.19447	−	1.19447i	−0.218666	−	0.975800i	$-0.570171\pi$
$500$		0			0
$501$	−5.81111	+	1.55708i	−0.259621	+	0.0695652i
$502$		0			0
$503$	−0.925275	−	3.45317i	−0.0412560	−	0.153969i	0.942225	−	0.334980i	$-0.108730\pi$
$503$	−0.925275	−	3.45317i	−0.0412560	−	0.153969i	−0.983481	+	0.181011i	$0.942063\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−10.0934	−	4.91735i	−0.448265	−	0.218387i
$508$		0			0
$509$	−7.47999	+	27.9157i	−0.331545	+	1.23734i	0.576022	+	0.817434i	$0.304604\pi$
$509$	−7.47999	+	27.9157i	−0.331545	+	1.23734i	−0.907567	+	0.419908i	$0.862062\pi$
$510$		0			0
$511$	1.74040	+	1.00482i	0.0769906	+	0.0444505i
$512$		0			0
$513$	17.0355	+	9.83547i	0.752137	+	0.434247i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.551120	+	0.147672i	0.0242382	+	0.00649462i
$518$		0			0
$519$	2.77845			0.121960
$520$		0			0
$521$	−20.7651			−0.909737			−0.454869	−	0.890559i	$-0.650314\pi$
$521$	−20.7651			−0.909737			−0.454869	+	0.890559i	$0.650314\pi$
$522$		0			0
$523$	−27.1490	−	7.27456i	−1.18714	−	0.318094i	−0.389387	−	0.921074i	$-0.627313\pi$
$523$	−27.1490	−	7.27456i	−1.18714	−	0.318094i	−0.797756	+	0.602980i	$0.793980\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	31.1239	+	17.9694i	1.35578	+	0.782759i
$528$		0			0
$529$	−47.6596	−	27.5163i	−2.07216	−	1.19636i
$530$		0			0
$531$	−4.39071	+	16.3864i	−0.190541	+	0.711107i
$532$		0			0
$533$	−40.6856	−	15.2014i	−1.76229	−	0.658447i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.467096	+	1.74323i	0.0201567	+	0.0752257i
$538$		0			0
$539$	−0.180098	+	0.0482571i	−0.00775737	+	0.00207858i
$540$		0			0
$541$	−17.0864	−	17.0864i	−0.734604	−	0.734604i	0.236924	−	0.971528i	$-0.423861\pi$
$541$	−17.0864	−	17.0864i	−0.734604	−	0.734604i	−0.971528	+	0.236924i	$0.923861\pi$
$542$		0			0
$543$	0.304508	−	1.13644i	0.0130677	−	0.0487692i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	18.9349	+	18.9349i	0.809597	+	0.809597i	0.984573	−	0.174976i	$-0.0559846\pi$
$547$	18.9349	+	18.9349i	0.809597	+	0.809597i	−0.174976	+	0.984573i	$0.555985\pi$
$548$		0			0
$549$	21.6632	−	12.5073i	0.924563	−	0.533797i
$550$		0			0
$551$	−17.6996	+	17.6996i	−0.754028	+	0.754028i
$552$		0			0
$553$	4.35971	−	7.55124i	0.185394	−	0.321111i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	23.0094	−	13.2845i	0.974940	−	0.562882i	0.0742015	−	0.997243i	$-0.476359\pi$
$557$	23.0094	−	13.2845i	0.974940	−	0.562882i	0.900739	+	0.434361i	$0.143026\pi$
$558$		0			0
$559$	−2.36461	+	0.396240i	−0.100012	+	0.0167592i
$560$		0			0
$561$	0.629346	+	0.168633i	0.0265710	+	0.00711968i
$562$		0			0
$563$	5.73354	−	1.53630i	0.241640	−	0.0647472i	−0.135967	−	0.990713i	$-0.543414\pi$
$563$	5.73354	−	1.53630i	0.241640	−	0.0647472i	0.377606	+	0.925966i	$0.376747\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	6.80570i		−	0.285812i
$568$		0			0
$569$	3.07382	+	5.32402i	0.128861	+	0.223195i	0.923236	−	0.384234i	$-0.125534\pi$
$569$	3.07382	+	5.32402i	0.128861	+	0.223195i	−0.794374	+	0.607429i	$0.792201\pi$
$570$		0			0
$571$		−	17.9884i		−	0.752792i	−0.926459	−	0.376396i	$-0.877163\pi$
$571$		−	17.9884i		−	0.752792i	0.926459	−	0.376396i	$-0.122837\pi$
$572$		0			0
$573$	1.73751	−	1.73751i	0.0725857	−	0.0725857i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	38.3328			1.59582			0.797908	−	0.602780i	$-0.205940\pi$
$577$	38.3328			1.59582			0.797908	+	0.602780i	$0.205940\pi$
$578$		0			0
$579$	0.129656	+	0.483883i	0.00538832	+	0.0201095i
$580$		0			0
$581$	12.3788	−	21.4407i	0.513559	−	0.889511i
$582$		0			0
$583$	−0.247843	−	0.429277i	−0.0102646	−	0.0177788i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.915584	−	1.58584i	−0.0377902	−	0.0654545i	0.846512	−	0.532370i	$-0.178699\pi$
$587$	−0.915584	−	1.58584i	−0.0377902	−	0.0654545i	−0.884302	+	0.466916i	$0.845365\pi$
$588$		0			0
$589$	−15.1533	+	26.2462i	−0.624379	+	1.08146i
$590$		0			0
$591$	−0.284629	−	1.06225i	−0.0117081	−	0.0436951i
$592$		0			0
$593$	47.6121			1.95519			0.977596	−	0.210488i	$-0.0675054\pi$
$593$	47.6121			1.95519			0.977596	+	0.210488i	$0.0675054\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.4210	−	11.4210i	0.467431	−	0.467431i
$598$		0			0
$599$		−	35.0349i		−	1.43149i	−0.698364	−	0.715743i	$-0.746088\pi$
$599$		−	35.0349i		−	1.43149i	0.698364	−	0.715743i	$-0.253912\pi$
$600$		0			0
$601$	5.18695	+	8.98405i	0.211580	+	0.366467i	0.952209	−	0.305447i	$-0.0988058\pi$
$601$	5.18695	+	8.98405i	0.211580	+	0.366467i	−0.740629	+	0.671914i	$0.765472\pi$
$602$		0			0
$603$		−	8.69006i		−	0.353887i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−8.57162	+	2.29676i	−0.347911	+	0.0932226i	−0.428543	−	0.903521i	$-0.640973\pi$
$607$	−8.57162	+	2.29676i	−0.347911	+	0.0932226i	0.0806315	+	0.996744i	$0.474306\pi$
$608$		0			0
$609$	−11.5302	−	3.08950i	−0.467226	−	0.125193i
$610$		0			0
$611$	−1.34046	+	13.9537i	−0.0542292	+	0.564504i
$612$		0			0
$613$	−13.8211	+	7.97961i	−0.558229	+	0.322293i	−0.752434	−	0.658667i	$-0.771120\pi$
$613$	−13.8211	+	7.97961i	−0.558229	+	0.322293i	0.194206	+	0.980961i	$0.437787\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.5171	+	23.4123i	−0.544178	+	0.942543i	0.454481	+	0.890757i	$0.349825\pi$
$617$	−13.5171	+	23.4123i	−0.544178	+	0.942543i	−0.998658	+	0.0517867i	$0.983508\pi$
$618$		0			0
$619$	23.9718	−	23.9718i	0.963509	−	0.963509i	−0.0358482	−	0.999357i	$-0.511413\pi$
$619$	23.9718	−	23.9718i	0.963509	−	0.963509i	0.999357	+	0.0358482i	$0.0114133\pi$
$620$		0			0
$621$	−34.7143	+	20.0423i	−1.39304	+	0.804269i
$622$		0			0
$623$	20.6067	+	20.6067i	0.825590	+	0.825590i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.142205	+	0.530716i	−0.00567912	+	0.0211948i
$628$		0			0
$629$	15.7819	+	15.7819i	0.629264	+	0.629264i
$630$		0			0
$631$	−18.6213	+	4.98955i	−0.741301	+	0.198631i	−0.609656	−	0.792666i	$-0.708692\pi$
$631$	−18.6213	+	4.98955i	−0.741301	+	0.198631i	−0.131645	+	0.991297i	$0.542026\pi$
$632$		0			0
$633$	4.35558	+	16.2552i	0.173119	+	0.646087i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.90057	−	4.16796i	−0.0753032	−	0.165141i
$638$		0			0
$639$	3.75543	−	14.0155i	0.148563	−	0.554443i
$640$		0			0
$641$	−18.8267	−	10.8696i	−0.743609	−	0.429323i	0.0797710	−	0.996813i	$-0.474581\pi$
$641$	−18.8267	−	10.8696i	−0.743609	−	0.429323i	−0.823380	+	0.567490i	$0.807914\pi$
$642$		0			0
$643$	34.7968	+	20.0899i	1.37225	+	0.792270i	0.991211	−	0.132289i	$-0.0422326\pi$
$643$	34.7968	+	20.0899i	1.37225	+	0.792270i	0.381040	+	0.924558i	$0.375566\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−27.5243	−	7.37512i	−1.08209	−	0.289946i	−0.326640	−	0.945149i	$-0.605916\pi$
$647$	−27.5243	−	7.37512i	−1.08209	−	0.289946i	−0.755453	+	0.655203i	$0.772583\pi$
$648$		0			0
$649$	−1.10448			−0.0433546
$650$		0			0
$651$	−14.4527			−0.566447
$652$		0			0
$653$	−3.09082	−	0.828184i	−0.120953	−	0.0324093i	0.197835	−	0.980235i	$-0.436609\pi$
$653$	−3.09082	−	0.828184i	−0.120953	−	0.0324093i	−0.318788	+	0.947826i	$0.603276\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.63894	+	0.946240i	0.0639410	+	0.0369164i
$658$		0			0
$659$	−6.29598	−	3.63499i	−0.245257	−	0.141599i	0.372334	−	0.928099i	$-0.378558\pi$
$659$	−6.29598	−	3.63499i	−0.245257	−	0.141599i	−0.617590	+	0.786500i	$0.711891\pi$
$660$		0			0
$661$	−10.9236	+	40.7674i	−0.424878	+	1.58567i	0.339311	+	0.940674i	$0.389806\pi$
$661$	−10.9236	+	40.7674i	−0.424878	+	1.58567i	−0.764189	+	0.644992i	$0.776861\pi$
$662$		0			0
$663$	−1.53072	+	15.9342i	−0.0594484	+	0.618834i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−13.2016	−	49.2690i	−0.511168	−	1.90770i
$668$		0			0
$669$	−22.4966	+	6.02795i	−0.869770	+	0.233054i
$670$		0			0
$671$	1.15159	+	1.15159i	0.0444565	+	0.0444565i
$672$		0			0
$673$	−4.70761	+	17.5690i	−0.181465	+	0.677236i	0.813895	+	0.581012i	$0.197343\pi$
$673$	−4.70761	+	17.5690i	−0.181465	+	0.677236i	−0.995360	+	0.0962240i	$0.969323\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−35.6038	−	35.6038i	−1.36836	−	1.36836i	−0.862774	−	0.505589i	$-0.831275\pi$
$677$	−35.6038	−	35.6038i	−1.36836	−	1.36836i	−0.505589	−	0.862774i	$-0.668725\pi$
$678$		0			0
$679$	−1.05546	+	0.609368i	−0.0405047	+	0.0233854i
$680$		0			0
$681$	2.89990	−	2.89990i	0.111125	−	0.111125i
$682$		0			0
$683$	−18.7730	+	32.5158i	−0.718329	+	1.24418i	0.243332	+	0.969943i	$0.421760\pi$
$683$	−18.7730	+	32.5158i	−0.718329	+	1.24418i	−0.961661	+	0.274240i	$0.911574\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−19.6248	+	11.3304i	−0.748731	+	0.432280i
$688$		0			0
$689$	9.39536	−	7.74844i	0.357935	−	0.295192i
$690$		0			0
$691$	37.6457	+	10.0871i	1.43211	+	0.383733i	0.889764	−	0.456421i	$-0.150869\pi$
$691$	37.6457	+	10.0871i	1.43211	+	0.383733i	0.542348	+	0.840154i	$0.317536\pi$
$692$		0			0
$693$	0.764833	−	0.204936i	0.0290536	−	0.00778489i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			61.9239i			2.34554i
$698$		0			0
$699$	10.9124	+	18.9008i	0.412745	+	0.714895i
$700$		0			0
$701$		−	24.5879i		−	0.928672i	−0.885659	−	0.464336i	$-0.846293\pi$
$701$		−	24.5879i		−	0.928672i	0.885659	−	0.464336i	$-0.153707\pi$
$702$		0			0
$703$	−13.3086	+	13.3086i	−0.501942	+	0.501942i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−22.6504			−0.851855
$708$		0			0
$709$	−4.35703	−	16.2607i	−0.163632	−	0.610682i	−0.998211	−	0.0597936i	$-0.980956\pi$
$709$	−4.35703	−	16.2607i	−0.163632	−	0.610682i	0.834579	−	0.550888i	$-0.185711\pi$
$710$		0			0
$711$	4.10555	−	7.11103i	0.153970	−	0.266684i
$712$		0			0
$713$	−30.8786	−	53.4834i	−1.15641	−	2.00297i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−5.45252	−	9.44404i	−0.203628	−	0.352694i
$718$		0			0
$719$	−8.79659	+	15.2361i	−0.328057	+	0.568212i	−0.982126	−	0.188223i	$-0.939727\pi$
$719$	−8.79659	+	15.2361i	−0.328057	+	0.568212i	0.654069	+	0.756435i	$0.273061\pi$
$720$		0			0
$721$	11.2311	+	41.9149i	0.418266	+	1.56099i
$722$		0			0
$723$	−0.799743			−0.0297427
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−18.0270	+	18.0270i	−0.668585	+	0.668585i	−0.957388	−	0.288803i	$-0.906743\pi$
$727$	−18.0270	+	18.0270i	−0.668585	+	0.668585i	0.288803	+	0.957388i	$0.406743\pi$
$728$		0			0
$729$			5.34819i			0.198081i
$730$		0			0
$731$	1.70917	+	2.96037i	0.0632159	+	0.109493i
$732$		0			0
$733$			24.4764i			0.904056i	0.892004	+	0.452028i	$0.149299\pi$
$733$			24.4764i			0.904056i	−0.892004	+	0.452028i	$0.850701\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.546494	−	0.146433i	0.0201304	−	0.00539392i
$738$		0			0
$739$	−12.3388	−	3.30617i	−0.453890	−	0.121619i	0.0246292	−	0.999697i	$-0.492160\pi$
$739$	−12.3388	−	3.30617i	−0.453890	−	0.121619i	−0.478519	+	0.878077i	$0.658826\pi$
$740$		0			0
$741$	−13.4371	−	1.29083i	−0.493622	−	0.0474199i
$742$		0			0
$743$	13.0449	−	7.53145i	0.478569	−	0.276302i	−0.241251	−	0.970463i	$-0.577558\pi$
$743$	13.0449	−	7.53145i	0.478569	−	0.276302i	0.719820	+	0.694161i	$0.244224\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	11.6572	−	20.1908i	0.426513	−	0.738743i
$748$		0			0
$749$	7.46308	−	7.46308i	0.272695	−	0.272695i
$750$		0			0
$751$	−0.0168245	+	0.00971361i	−0.000613933	+	0.000354455i	−0.500307	−	0.865848i	$-0.666779\pi$
$751$	−0.0168245	+	0.00971361i	−0.000613933	+	0.000354455i	0.499693	+	0.866203i	$0.333446\pi$
$752$		0			0
$753$	4.14215	+	4.14215i	0.150948	+	0.150948i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	10.4721	−	39.0825i	0.380616	−	1.42048i	−0.464347	−	0.885653i	$-0.653711\pi$
$757$	10.4721	−	39.0825i	0.380616	−	1.42048i	0.844963	−	0.534825i	$-0.179622\pi$
$758$		0			0
$759$	−0.791691	−	0.791691i	−0.0287366	−	0.0287366i
$760$		0			0
$761$	23.2860	−	6.23947i	0.844118	−	0.226181i	0.189255	−	0.981928i	$-0.439393\pi$
$761$	23.2860	−	6.23947i	0.844118	−	0.226181i	0.654863	+	0.755747i	$0.272726\pi$
$762$		0			0
$763$	4.30476	+	16.0656i	0.155843	+	0.581613i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.48459	−	26.7623i	−0.161929	−	0.966332i
$768$		0			0
$769$	2.93059	−	10.9371i	0.105680	−	0.394402i	−0.892742	−	0.450569i	$-0.851221\pi$
$769$	2.93059	−	10.9371i	0.105680	−	0.394402i	0.998421	+	0.0561669i	$0.0178879\pi$
$770$		0			0
$771$	4.97020	+	2.86954i	0.178997	+	0.103344i
$772$		0			0
$773$	23.0024	+	13.2804i	0.827338	+	0.477664i	0.852940	−	0.522008i	$-0.174817\pi$
$773$	23.0024	+	13.2804i	0.827338	+	0.477664i	−0.0256023	+	0.999672i	$0.508150\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−8.66969	−	2.32304i	−0.311023	−	0.0833385i
$778$		0			0
$779$	−52.2193			−1.87095
$780$		0			0
$781$	0.944676			0.0338032
$782$		0			0
$783$	−25.3090	−	6.78153i	−0.904470	−	0.242352i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.15890	+	0.669088i	0.0413102	+	0.0238504i	0.520513	−	0.853854i	$-0.325741\pi$
$787$	1.15890	+	0.669088i	0.0413102	+	0.0238504i	−0.479203	+	0.877704i	$0.659074\pi$
$788$		0			0
$789$	8.82737	+	5.09649i	0.314263	+	0.181440i
$790$		0			0
$791$	0.705224	−	2.63193i	0.0250749	−	0.0935807i
$792$		0			0
$793$	−23.2279	+	32.5796i	−0.824847	+	1.15694i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.7819	+	51.4349i	0.488182	+	1.82192i	0.565286	+	0.824895i	$0.308766\pi$
$797$	13.7819	+	51.4349i	0.488182	+	1.82192i	−0.0771042	+	0.997023i	$0.524567\pi$
$798$		0			0
$799$	19.3049	−	5.17274i	0.682959	−	0.182998i
$800$		0			0
$801$	19.4054	+	19.4054i	0.685656	+	0.685656i
$802$		0			0
$803$	−0.0318894	+	0.119013i	−0.00112535	+	0.00419988i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	10.2805	+	10.2805i	0.361890	+	0.361890i
$808$		0			0
$809$	−26.9017	+	15.5317i	−0.945814	+	0.546066i	−0.891778	−	0.452473i	$-0.850542\pi$
$809$	−26.9017	+	15.5317i	−0.945814	+	0.546066i	−0.0540362	+	0.998539i	$0.517209\pi$
$810$		0			0
$811$	−23.2698	+	23.2698i	−0.817114	+	0.817114i	−0.985689	−	0.168574i	$-0.946084\pi$
$811$	−23.2698	+	23.2698i	−0.817114	+	0.817114i	0.168574	+	0.985689i	$0.446084\pi$
$812$		0			0
$813$	−5.43781	+	9.41857i	−0.190712	+	0.330324i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.49642	+	1.44131i	−0.0873388	+	0.0504251i
$818$		0			0
$819$	8.07126	+	17.7003i	0.282032	+	0.618500i
$820$		0			0
$821$	33.6762	+	9.02350i	1.17531	+	0.314922i	0.793063	−	0.609139i	$-0.208485\pi$
$821$	33.6762	+	9.02350i	1.17531	+	0.314922i	0.382243	+	0.924062i	$0.375152\pi$
$822$		0			0
$823$	35.6196	−	9.54424i	1.24162	−	0.332691i	0.422527	−	0.906350i	$-0.361143\pi$
$823$	35.6196	−	9.54424i	1.24162	−	0.332691i	0.819094	+	0.573659i	$0.194476\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	30.9231i		−	1.07530i	−0.843168	−	0.537651i	$-0.819312\pi$
$827$		−	30.9231i		−	1.07530i	0.843168	−	0.537651i	$-0.180688\pi$
$828$		0			0
$829$	15.3995	+	26.6727i	0.534846	+	0.926381i	0.999171	+	0.0407156i	$0.0129638\pi$
$829$	15.3995	+	26.6727i	0.534846	+	0.926381i	−0.464325	+	0.885665i	$0.653703\pi$
$830$		0			0
$831$		−	12.3933i		−	0.429919i
$832$		0			0
$833$	−4.61819	+	4.61819i	−0.160011	+	0.160011i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−31.7241			−1.09655
$838$		0			0
$839$	−4.42837	−	16.5269i	−0.152884	−	0.570571i	−0.999277	−	0.0380128i	$-0.987897\pi$
$839$	−4.42837	−	16.5269i	−0.152884	−	0.570571i	0.846393	−	0.532559i	$-0.178769\pi$
$840$		0			0
$841$	2.17072	−	3.75980i	0.0748525	−	0.129648i
$842$		0			0
$843$	−6.78997	−	11.7606i	−0.233859	−	0.405055i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−13.1392	−	22.7578i	−0.451469	−	0.781968i
$848$		0			0
$849$	7.41606	−	12.8450i	0.254518	−	0.440839i
$850$		0			0
$851$	−9.92646	−	37.0461i	−0.340275	−	1.26992i
$852$		0			0
$853$	2.23760			0.0766141			0.0383071	−	0.999266i	$-0.487804\pi$
$853$	2.23760			0.0766141			0.0383071	+	0.999266i	$0.487804\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.2191	−	13.2191i	0.451556	−	0.451556i	−0.444315	−	0.895871i	$-0.646553\pi$
$857$	13.2191	−	13.2191i	0.451556	−	0.451556i	0.895871	+	0.444315i	$0.146553\pi$
$858$		0			0
$859$		−	26.7421i		−	0.912427i	−0.889870	−	0.456214i	$-0.849205\pi$
$859$		−	26.7421i		−	0.912427i	0.889870	−	0.456214i	$-0.150795\pi$
$860$		0			0
$861$	−12.4513	−	21.5663i	−0.424339	−	0.734978i
$862$		0			0
$863$		−	21.5085i		−	0.732157i	−0.930584	−	0.366079i	$-0.880700\pi$
$863$		−	21.5085i		−	0.732157i	0.930584	−	0.366079i	$-0.119300\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	7.86317	−	2.10693i	0.267047	−	0.0715551i
$868$		0			0
$869$	0.516374	+	0.138362i	0.0175168	+	0.00469361i
$870$		0			0
$871$	5.76714	+	12.6474i	0.195412	+	0.428540i
$872$		0			0
$873$	−0.993927	+	0.573844i	−0.0336393	+	0.0194217i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.27817	+	14.3382i	−0.279534	+	0.484167i	−0.971269	−	0.237984i	$-0.923513\pi$
$877$	−8.27817	+	14.3382i	−0.279534	+	0.484167i	0.691735	+	0.722151i	$0.256847\pi$
$878$		0			0
$879$	−15.2245	+	15.2245i	−0.513510	+	0.513510i
$880$		0			0
$881$	−41.3063	+	23.8482i	−1.39165	+	0.803467i	−0.993497	−	0.113854i	$-0.963680\pi$
$881$	−41.3063	+	23.8482i	−1.39165	+	0.803467i	−0.398148	+	0.917321i	$0.630347\pi$
$882$		0			0
$883$	−23.3722	−	23.3722i	−0.786536	−	0.786536i	0.194388	−	0.980925i	$-0.437728\pi$
$883$	−23.3722	−	23.3722i	−0.786536	−	0.786536i	−0.980925	+	0.194388i	$0.937728\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.6033	+	54.5002i	−0.490330	+	1.82994i	0.0644228	+	0.997923i	$0.479479\pi$
$887$	−14.6033	+	54.5002i	−0.490330	+	1.82994i	−0.554753	+	0.832015i	$0.687187\pi$
$888$		0			0
$889$	27.4633	+	27.4633i	0.921091	+	0.921091i
$890$		0			0
$891$	0.403041	−	0.107995i	0.0135024	−	0.00361796i
$892$		0			0
$893$	4.36207	+	16.2795i	0.145971	+	0.544772i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	15.9687	−	22.3978i	0.533180	−	0.747841i
$898$		0			0
$899$	10.4481	−	38.9930i	0.348465	−	1.30049i
$900$		0			0
$901$	−15.0369	−	8.68157i	−0.500952	−	0.289225i
$902$		0			0
$903$	−1.19051	−	0.687340i	−0.0396176	−	0.0228732i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−34.6093	−	9.27353i	−1.14918	−	0.307923i	−0.366545	−	0.930400i	$-0.619460\pi$
$907$	−34.6093	−	9.27353i	−1.14918	−	0.307923i	−0.782638	+	0.622478i	$0.786126\pi$
$908$		0			0
$909$	−21.3299			−0.707469
$910$		0			0
$911$	26.4864			0.877534			0.438767	−	0.898601i	$-0.355415\pi$
$911$	26.4864			0.877534			0.438767	+	0.898601i	$0.355415\pi$
$912$		0			0
$913$	1.46617	+	0.392860i	0.0485233	+	0.0130018i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.9608	+	14.4111i	0.824278	+	0.475897i
$918$		0			0
$919$	15.4599	+	8.92578i	0.509975	+	0.294434i	0.732823	−	0.680419i	$-0.238202\pi$
$919$	15.4599	+	8.92578i	0.509975	+	0.294434i	−0.222848	+	0.974853i	$0.571535\pi$
$920$		0			0
$921$	−2.30764	+	8.61223i	−0.0760394	+	0.283783i
$922$		0			0
$923$	3.83573	+	22.8902i	0.126254	+	0.753440i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	10.5763	+	39.4714i	0.347372	+	1.29641i
$928$		0			0
$929$	−3.69827	+	0.990949i	−0.121336	+	0.0325120i	−0.318976	−	0.947763i	$-0.603339\pi$
$929$	−3.69827	+	0.990949i	−0.121336	+	0.0325120i	0.197640	+	0.980275i	$0.436672\pi$
$930$		0			0
$931$	−3.89443	−	3.89443i	−0.127635	−	0.127635i
$932$		0			0
$933$	−3.52516	+	13.1561i	−0.115408	+	0.430710i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	19.7005	+	19.7005i	0.643586	+	0.643586i	0.951435	−	0.307849i	$-0.0996092\pi$
$937$	19.7005	+	19.7005i	0.643586	+	0.643586i	−0.307849	+	0.951435i	$0.599609\pi$
$938$		0			0
$939$	−18.7877	+	10.8471i	−0.613112	+	0.353981i
$940$		0			0
$941$	−9.21977	+	9.21977i	−0.300556	+	0.300556i	−0.841231	−	0.540675i	$-0.818169\pi$
$941$	−9.21977	+	9.21977i	−0.300556	+	0.300556i	0.540675	+	0.841231i	$0.318169\pi$
$942$		0			0
$943$	53.2051	−	92.1540i	1.73260	−	3.00095i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.2467	−	13.4215i	0.755415	−	0.436139i	−0.0722321	−	0.997388i	$-0.523012\pi$
$947$	23.2467	−	13.4215i	0.755415	−	0.436139i	0.827647	+	0.561249i	$0.189679\pi$
$948$		0			0
$949$	−3.01325	−	0.289469i	−0.0978144	−	0.00939655i
$950$		0			0
$951$	11.1909	+	2.99859i	0.362889	+	0.0972358i
$952$		0			0
$953$	−33.7931	+	9.05483i	−1.09467	+	0.293315i	−0.760590	−	0.649232i	$-0.775090\pi$
$953$	−33.7931	+	9.05483i	−1.09467	+	0.293315i	−0.334075	+	0.942547i	$0.608424\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	0.731855i		−	0.0236575i
$958$		0			0
$959$	−1.49969	−	2.59755i	−0.0484276	−	0.0838791i
$960$		0			0
$961$		−	17.8765i		−	0.576662i
$962$		0			0
$963$	7.02800	−	7.02800i	0.226474	−	0.226474i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.4047			−0.334594			−0.167297	−	0.985907i	$-0.553504\pi$
$967$	−10.4047			−0.334594			−0.167297	+	0.985907i	$0.553504\pi$
$968$		0			0
$969$	4.98123	+	18.5902i	0.160020	+	0.597203i
$970$		0			0
$971$	3.92930	−	6.80575i	0.126097	−	0.218407i	−0.796064	−	0.605212i	$-0.793088\pi$
$971$	3.92930	−	6.80575i	0.126097	−	0.218407i	0.922161	+	0.386805i	$0.126421\pi$
$972$		0			0
$973$	−23.7858	−	41.1983i	−0.762539	−	1.32076i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	26.1958	+	45.3725i	0.838078	+	1.45159i	0.891500	+	0.453021i	$0.149654\pi$
$977$	26.1958	+	45.3725i	0.838078	+	1.45159i	−0.0534218	+	0.998572i	$0.517013\pi$
$978$		0			0
$979$	−0.893361	+	1.54735i	−0.0285519	+	0.0494534i
$980$		0			0
$981$	4.05381	+	15.1290i	0.129428	+	0.483032i
$982$		0			0
$983$	38.1526			1.21688			0.608439	−	0.793600i	$-0.291796\pi$
$983$	38.1526			1.21688			0.608439	+	0.793600i	$0.291796\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.68324	+	5.68324i	−0.180899	+	0.180899i
$988$		0			0
$989$		−	5.87408i		−	0.186785i
$990$		0			0
$991$	−4.01794	−	6.95928i	−0.127634	−	0.221069i	0.795125	−	0.606445i	$-0.207405\pi$
$991$	−4.01794	−	6.95928i	−0.127634	−	0.221069i	−0.922760	+	0.385376i	$0.874072\pi$
$992$		0			0
$993$			12.6520i			0.401499i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	26.3850	−	7.06984i	0.835621	−	0.223904i	0.184456	−	0.982841i	$-0.440948\pi$
$997$	26.3850	−	7.06984i	0.835621	−	0.223904i	0.651164	+	0.758937i	$0.274281\pi$
$998$		0			0
$999$	−19.0302	−	5.09912i	−0.602089	−	0.161329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bs.d.457.2		20
5.2	odd	4		260.2.bf.c.93.2	✓	20
5.3	odd	4		1300.2.bn.d.93.4		20
5.4	even	2		260.2.bk.c.197.4	yes	20
13.7	odd	12		1300.2.bn.d.657.4		20
65.7	even	12		260.2.bk.c.33.4	yes	20
65.33	even	12	inner	1300.2.bs.d.293.2		20
65.59	odd	12		260.2.bf.c.137.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.2	✓	20	5.2	odd	4
260.2.bf.c.137.2	yes	20	65.59	odd	12
260.2.bk.c.33.4	yes	20	65.7	even	12
260.2.bk.c.197.4	yes	20	5.4	even	2
1300.2.bn.d.93.4		20	5.3	odd	4
1300.2.bn.d.657.4		20	13.7	odd	12
1300.2.bs.d.293.2		20	65.33	even	12	inner
1300.2.bs.d.457.2		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.834228 - 0.223531i) q^{3} +(-2.07295 - 1.19682i) q^{7} +(-1.95211 - 1.12705i) q^{9} +O(q^{10})\)	\(q+(-0.834228 - 0.223531i) q^{3} +(-2.07295 - 1.19682i) q^{7} +(-1.95211 - 1.12705i) q^{9} +(0.0379829 - 0.141754i) q^{11} +(3.58903 + 0.344781i) q^{13} +(-1.33048 - 4.96543i) q^{17} +(4.18726 - 1.12197i) q^{19} +(1.46179 + 1.46179i) q^{21} +(-2.28631 + 8.53261i) q^{23} +(3.20866 + 3.20866i) q^{27} +(-5.00061 + 2.88710i) q^{29} +(-4.94351 + 4.94351i) q^{31} +(-0.0633728 + 0.109765i) q^{33} +(-3.76003 + 2.17085i) q^{37} +(-2.91700 - 1.08988i) q^{39} +(-11.6356 - 3.11775i) q^{41} +(-0.642311 + 0.172107i) q^{43} +3.88786i q^{47} +(-0.635248 - 1.10028i) q^{49} +4.43971i q^{51} +(2.38836 - 2.38836i) q^{53} -3.74392 q^{57} +(-1.94788 - 7.26959i) q^{59} +(-5.54868 + 9.61059i) q^{61} +(2.69775 + 4.67263i) q^{63} +(1.92761 + 3.33873i) q^{67} +(3.81460 - 6.60708i) q^{69} +(1.66605 + 6.21778i) q^{71} -0.839574 q^{73} +(-0.248391 + 0.248391i) q^{77} +3.64275i q^{79} +(1.42162 + 2.46232i) q^{81} +10.3431i q^{83} +(4.81701 - 1.29071i) q^{87} +(-11.7600 - 3.15109i) q^{89} +(-7.02724 - 5.01013i) q^{91} +(5.22904 - 3.01899i) q^{93} +(0.254578 - 0.440943i) q^{97} +(-0.233910 + 0.233910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9	\( 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9} - 8 q^{13} + 20 q^{19} - 12 q^{21} - 6 q^{23} + 20 q^{27} + 24 q^{29} + 8 q^{31} + 10 q^{33} + 4 q^{39} + 6 q^{41} - 38 q^{43} + 14 q^{49} - 30 q^{53} + 76 q^{57} - 24 q^{59} - 32 q^{61} + 24 q^{63} - 22 q^{67} - 16 q^{69} + 44 q^{73} + 12 q^{77} + 2 q^{81} - 38 q^{87} - 30 q^{89} - 72 q^{91} + 48 q^{93} - 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9 - 8 * q^13 + 20 * q^19 - 12 * q^21 - 6 * q^23 + 20 * q^27 + 24 * q^29 + 8 * q^31 + 10 * q^33 + 4 * q^39 + 6 * q^41 - 38 * q^43 + 14 * q^49 - 30 * q^53 + 76 * q^57 - 24 * q^59 - 32 * q^61 + 24 * q^63 - 22 * q^67 - 16 * q^69 + 44 * q^73 + 12 * q^77 + 2 * q^81 - 38 * q^87 - 30 * q^89 - 72 * q^91 + 48 * q^93 - 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more