LMFDB - Embedded newform 1480.2.q.b.1321.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1480,2,Mod(121,1480)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1480.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1480, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1480 = 2^{3} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1480.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,2,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.8178594991$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 18 x^{16} - 22 x^{15} + 194 x^{14} - 224 x^{13} + 1053 x^{12} - 770 x^{11} + \cdots + 441 $ x^18 - 2x^17 + 18x^16 - 22x^15 + 194x^14 - 224x^13 + 1053x^12 - 770x^11 + 3419x^10 - 2128x^9 + 7324x^8 - 2915x^7 + 9758x^6 - 3440x^5 + 7942x^4 - 786x^3 + 2419x^2 - 483*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1321.4
Root			$-0.306255 + 0.530449i$ of defining polynomial
Character	$\chi$	$=$	1480.1321
Dual form			1480.2.q.b.121.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.306255 + 0.530449i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.678169 + 1.17462i) q^{7} +(1.31242 + 2.27317i) q^{9} -2.73037 q^{11} +(3.10944 - 5.38571i) q^{13} +(0.306255 + 0.530449i) q^{15} +(2.91361 + 5.04652i) q^{17} +(-2.51249 + 4.35176i) q^{19} +(-0.415385 - 0.719468i) q^{21} -0.514732 q^{23} +(-0.500000 - 0.866025i) q^{25} -3.44526 q^{27} +1.82540 q^{29} +6.69702 q^{31} +(0.836188 - 1.44832i) q^{33} +(0.678169 + 1.17462i) q^{35} +(-5.61559 + 2.33778i) q^{37} +(1.90456 + 3.29880i) q^{39} +(-1.20673 + 2.09012i) q^{41} -6.52538 q^{43} +2.62483 q^{45} +13.2834 q^{47} +(2.58017 + 4.46899i) q^{49} -3.56923 q^{51} +(6.71541 + 11.6314i) q^{53} +(-1.36518 + 2.36457i) q^{55} +(-1.53892 - 2.66550i) q^{57} +(-2.57006 - 4.45148i) q^{59} +(-1.70164 + 2.94732i) q^{61} -3.56016 q^{63} +(-3.10944 - 5.38571i) q^{65} +(-7.05205 + 12.2145i) q^{67} +(0.157639 - 0.273039i) q^{69} +(-0.706064 + 1.22294i) q^{71} +5.23092 q^{73} +0.612510 q^{75} +(1.85165 - 3.20715i) q^{77} +(-2.48939 + 4.31175i) q^{79} +(-2.88212 + 4.99198i) q^{81} +(3.93127 + 6.80917i) q^{83} +5.82722 q^{85} +(-0.559038 + 0.968282i) q^{87} +(-6.89387 - 11.9405i) q^{89} +(4.21746 + 7.30485i) q^{91} +(-2.05099 + 3.55243i) q^{93} +(2.51249 + 4.35176i) q^{95} +16.6114 q^{97} +(-3.58338 - 6.20659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{3} + 9 q^{5} - 5 q^{9} - 6 q^{11} + 2 q^{13} - 2 q^{15} + q^{17} - 5 q^{21} + 12 q^{23} - 9 q^{25} - 10 q^{27} - 20 q^{29} + 28 q^{31} + 11 q^{33} - 5 q^{39} - 5 q^{41} + 2 q^{43} - 10 q^{45}+ \cdots + 30 q^{99}+O(q^{100}) $ 18 * q + 2 * q^3 + 9 * q^5 - 5 * q^9 - 6 * q^11 + 2 * q^13 - 2 * q^15 + q^17 - 5 * q^21 + 12 * q^23 - 9 * q^25 - 10 * q^27 - 20 * q^29 + 28 * q^31 + 11 * q^33 - 5 * q^39 - 5 * q^41 + 2 * q^43 - 10 * q^45 - 36 * q^47 + 7 * q^49 - 2 * q^51 - 10 * q^53 - 3 * q^55 + 22 * q^57 - 10 * q^59 + 16 * q^61 + 42 * q^63 - 2 * q^65 - 4 * q^67 - 13 * q^69 + 17 * q^71 + 56 * q^73 - 4 * q^75 + 43 * q^77 - 23 * q^79 - 17 * q^81 + 29 * q^83 + 2 * q^85 - q^87 - 16 * q^89 - 4 * q^91 + 5 * q^93 + 26 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1480\mathbb{Z}\right)^\times$.

$n$	$297$	$741$	$1001$	$1111$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.306255	+	0.530449i	−0.176816	+	0.306255i	−0.940788	−	0.338995i	$-0.889913\pi$
$3$	−0.306255	+	0.530449i	−0.176816	+	0.306255i	0.763972	+	0.645249i	$0.223247\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−0.678169	+	1.17462i	−0.256324	+	0.443966i	−0.965254	−	0.261313i	$-0.915845\pi$
$7$	−0.678169	+	1.17462i	−0.256324	+	0.443966i	0.708930	+	0.705278i	$0.249178\pi$
$8$		0			0
$9$	1.31242	+	2.27317i	0.437472	+	0.757724i
$10$		0			0
$11$	−2.73037			−0.823237			−0.411618	−	0.911356i	$-0.635036\pi$
$11$	−2.73037			−0.823237			−0.411618	+	0.911356i	$0.635036\pi$
$12$		0			0
$13$	3.10944	−	5.38571i	0.862405	−	1.49373i	−0.00719691	−	0.999974i	$-0.502291\pi$
$13$	3.10944	−	5.38571i	0.862405	−	1.49373i	0.869601	−	0.493754i	$-0.164376\pi$
$14$		0			0
$15$	0.306255	+	0.530449i	0.0790746	+	0.136961i
$16$		0			0
$17$	2.91361	+	5.04652i	0.706655	+	1.22396i	0.966091	+	0.258202i	$0.0831299\pi$
$17$	2.91361	+	5.04652i	0.706655	+	1.22396i	−0.259436	+	0.965760i	$0.583537\pi$
$18$		0			0
$19$	−2.51249	+	4.35176i	−0.576405	+	0.998362i	0.419483	+	0.907763i	$0.362212\pi$
$19$	−2.51249	+	4.35176i	−0.576405	+	0.998362i	−0.995887	+	0.0905991i	$0.971122\pi$
$20$		0			0
$21$	−0.415385	−	0.719468i	−0.0906444	−	0.157001i
$22$		0			0
$23$	−0.514732			−0.107329			−0.0536645	−	0.998559i	$-0.517090\pi$
$23$	−0.514732			−0.107329			−0.0536645	+	0.998559i	$0.517090\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−3.44526			−0.663041
$28$		0			0
$29$	1.82540			0.338969			0.169484	−	0.985533i	$-0.445790\pi$
$29$	1.82540			0.338969			0.169484	+	0.985533i	$0.445790\pi$
$30$		0			0
$31$	6.69702			1.20282			0.601410	−	0.798940i	$-0.294606\pi$
$31$	6.69702			1.20282			0.601410	+	0.798940i	$0.294606\pi$
$32$		0			0
$33$	0.836188	−	1.44832i	0.145562	−	0.252120i
$34$		0			0
$35$	0.678169	+	1.17462i	0.114631	+	0.198548i
$36$		0			0
$37$	−5.61559	+	2.33778i	−0.923197	+	0.384328i
$37$	−5.61559	+	2.33778i	−0.923197	+	0.384328i
$38$		0			0
$39$	1.90456	+	3.29880i	0.304974	+	0.528231i
$40$		0			0
$41$	−1.20673	+	2.09012i	−0.188460	+	0.326422i	−0.944737	−	0.327830i	$-0.893683\pi$
$41$	−1.20673	+	2.09012i	−0.188460	+	0.326422i	0.756277	+	0.654251i	$0.227016\pi$
$42$		0			0
$43$	−6.52538			−0.995112			−0.497556	−	0.867432i	$-0.665769\pi$
$43$	−6.52538			−0.995112			−0.497556	+	0.867432i	$0.665769\pi$
$44$		0			0
$45$	2.62483			0.391287
$46$		0			0
$47$	13.2834			1.93758			0.968791	−	0.247878i	$-0.0797332\pi$
$47$	13.2834			1.93758			0.968791	+	0.247878i	$0.0797332\pi$
$48$		0			0
$49$	2.58017	+	4.46899i	0.368596	+	0.638427i
$50$		0			0
$51$	−3.56923			−0.499792
$52$		0			0
$53$	6.71541	+	11.6314i	0.922433	+	1.59770i	0.795638	+	0.605772i	$0.207136\pi$
$53$	6.71541	+	11.6314i	0.922433	+	1.59770i	0.126795	+	0.991929i	$0.459531\pi$
$54$		0			0
$55$	−1.36518	+	2.36457i	−0.184081	+	0.318838i
$56$		0			0
$57$	−1.53892	−	2.66550i	−0.203836	−	0.353053i
$58$		0			0
$59$	−2.57006	−	4.45148i	−0.334594	−	0.579533i	0.648813	−	0.760948i	$-0.275266\pi$
$59$	−2.57006	−	4.45148i	−0.334594	−	0.579533i	−0.983407	+	0.181415i	$0.941932\pi$
$60$		0			0
$61$	−1.70164	+	2.94732i	−0.217872	+	0.377366i	−0.954157	−	0.299306i	$-0.903245\pi$
$61$	−1.70164	+	2.94732i	−0.217872	+	0.377366i	0.736285	+	0.676672i	$0.236578\pi$
$62$		0			0
$63$	−3.56016			−0.448538
$64$		0			0
$65$	−3.10944	−	5.38571i	−0.385679	−	0.668016i
$66$		0			0
$67$	−7.05205	+	12.2145i	−0.861545	+	1.49224i	0.00889193	+	0.999960i	$0.497170\pi$
$67$	−7.05205	+	12.2145i	−0.861545	+	1.49224i	−0.870437	+	0.492280i	$0.836164\pi$
$68$		0			0
$69$	0.157639	−	0.273039i	0.0189775	−	0.0328700i
$70$		0			0
$71$	−0.706064	+	1.22294i	−0.0837943	+	0.145136i	−0.904877	−	0.425674i	$-0.860037\pi$
$71$	−0.706064	+	1.22294i	−0.0837943	+	0.145136i	0.821082	+	0.570810i	$0.193371\pi$
$72$		0			0
$73$	5.23092			0.612233			0.306116	−	0.951994i	$-0.400970\pi$
$73$	5.23092			0.612233			0.306116	+	0.951994i	$0.400970\pi$
$74$		0			0
$75$	0.612510			0.0707265
$76$		0			0
$77$	1.85165	−	3.20715i	0.211015	−	0.365489i
$78$		0			0
$79$	−2.48939	+	4.31175i	−0.280079	+	0.485110i	−0.971404	−	0.237433i	$-0.923694\pi$
$79$	−2.48939	+	4.31175i	−0.280079	+	0.485110i	0.691325	+	0.722544i	$0.257027\pi$
$80$		0			0
$81$	−2.88212	+	4.99198i	−0.320236	+	0.554664i
$82$		0			0
$83$	3.93127	+	6.80917i	0.431513	+	0.747403i	0.997004	−	0.0773516i	$-0.0246464\pi$
$83$	3.93127	+	6.80917i	0.431513	+	0.747403i	−0.565490	+	0.824755i	$0.691313\pi$
$84$		0			0
$85$	5.82722			0.632051
$86$		0			0
$87$	−0.559038	+	0.968282i	−0.0599352	+	0.103811i
$88$		0			0
$89$	−6.89387	−	11.9405i	−0.730749	−	1.26569i	−0.956564	−	0.291524i	$-0.905838\pi$
$89$	−6.89387	−	11.9405i	−0.730749	−	1.26569i	0.225815	−	0.974170i	$-0.427496\pi$
$90$		0			0
$91$	4.21746	+	7.30485i	0.442110	+	0.765756i
$92$		0			0
$93$	−2.05099	+	3.55243i	−0.212678	+	0.368370i
$94$		0			0
$95$	2.51249	+	4.35176i	0.257776	+	0.446481i
$96$		0			0
$97$	16.6114			1.68663			0.843314	−	0.537421i	$-0.180602\pi$
$97$	16.6114			1.68663			0.843314	+	0.537421i	$0.180602\pi$
$98$		0			0
$99$	−3.58338	−	6.20659i	−0.360143	−	0.623786i
$100$		0			0
$101$	1.58871			0.158082			0.0790412	−	0.996871i	$-0.474814\pi$
$101$	1.58871			0.158082			0.0790412	+	0.996871i	$0.474814\pi$
$102$		0			0
$103$	−2.72413			−0.268417			−0.134208	−	0.990953i	$-0.542849\pi$
$103$	−2.72413			−0.268417			−0.134208	+	0.990953i	$0.542849\pi$
$104$		0			0
$105$	−0.830770			−0.0810749
$106$		0			0
$107$	5.48744	−	9.50452i	0.530491	−	0.918837i	−0.468876	−	0.883264i	$-0.655341\pi$
$107$	5.48744	−	9.50452i	0.530491	−	0.918837i	0.999367	−	0.0355731i	$-0.0113257\pi$
$108$		0			0
$109$	−6.56474	−	11.3705i	−0.628788	−	1.08909i	−0.987795	−	0.155758i	$-0.950218\pi$
$109$	−6.56474	−	11.3705i	−0.628788	−	1.08909i	0.359008	−	0.933335i	$-0.383115\pi$
$110$		0			0
$111$	0.479728	−	3.69474i	0.0455338	−	0.350689i
$112$		0			0
$113$	6.04864	+	10.4766i	0.569009	+	0.985552i	0.996664	+	0.0816100i	$0.0260062\pi$
$113$	6.04864	+	10.4766i	0.569009	+	0.985552i	−0.427656	+	0.903942i	$0.640660\pi$
$114$		0			0
$115$	−0.257366	+	0.445771i	−0.0239995	+	0.0415684i
$116$		0			0
$117$	16.3235			1.50911
$118$		0			0
$119$	−7.90369			−0.724530
$120$		0			0
$121$	−3.54509			−0.322281
$122$		0			0
$123$	−0.739134	−	1.28022i	−0.0666455	−	0.115433i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.02114	+	12.1610i	0.623025	+	1.07911i	0.988919	+	0.148454i	$0.0474299\pi$
$127$	7.02114	+	12.1610i	0.623025	+	1.07911i	−0.365894	+	0.930656i	$0.619237\pi$
$128$		0			0
$129$	1.99843	−	3.46138i	0.175952	−	0.304758i
$130$		0			0
$131$	−2.05596	−	3.56103i	−0.179630	−	0.311129i	0.762124	−	0.647431i	$-0.224157\pi$
$131$	−2.05596	−	3.56103i	−0.179630	−	0.311129i	−0.941754	+	0.336303i	$0.890823\pi$
$132$		0			0
$133$	−3.40779	−	5.90246i	−0.295493	−	0.511808i
$134$		0			0
$135$	−1.72263	+	2.98369i	−0.148261	+	0.256795i
$136$		0			0
$137$	16.3643			1.39810			0.699049	−	0.715074i	$-0.253607\pi$
$137$	16.3643			1.39810			0.699049	+	0.715074i	$0.253607\pi$
$138$		0			0
$139$	9.93668	+	17.2108i	0.842818	+	1.45980i	0.887503	+	0.460802i	$0.152438\pi$
$139$	9.93668	+	17.2108i	0.842818	+	1.45980i	−0.0446850	+	0.999001i	$0.514228\pi$
$140$		0			0
$141$	−4.06810	+	7.04616i	−0.342596	+	0.593394i
$142$		0			0
$143$	−8.48992	+	14.7050i	−0.709963	+	1.22969i
$144$		0			0
$145$	0.912701	−	1.58084i	0.0757957	−	0.131282i
$146$		0			0
$147$	−3.16076			−0.260695
$148$		0			0
$149$	−16.9239			−1.38646			−0.693231	−	0.720715i	$-0.743814\pi$
$149$	−16.9239			−1.38646			−0.693231	+	0.720715i	$0.743814\pi$
$150$		0			0
$151$	−1.57163	+	2.72215i	−0.127898	+	0.221525i	−0.922862	−	0.385131i	$-0.874156\pi$
$151$	−1.57163	+	2.72215i	−0.127898	+	0.221525i	0.794964	+	0.606656i	$0.207490\pi$
$152$		0			0
$153$	−7.64774	+	13.2463i	−0.618283	+	1.07090i
$154$		0			0
$155$	3.34851	−	5.79979i	0.268959	−	0.465850i
$156$		0			0
$157$	7.61633	+	13.1919i	0.607849	+	1.05283i	0.991594	+	0.129387i	$0.0413008\pi$
$157$	7.61633	+	13.1919i	0.607849	+	1.05283i	−0.383745	+	0.923439i	$0.625366\pi$
$158$		0			0
$159$	−8.22651			−0.652405
$160$		0			0
$161$	0.349075	−	0.604616i	0.0275110	−	0.0476504i
$162$		0			0
$163$	−0.329069	−	0.569965i	−0.0257747	−	0.0446431i	0.852850	−	0.522155i	$-0.174872\pi$
$163$	−0.329069	−	0.569965i	−0.0257747	−	0.0446431i	−0.878625	+	0.477512i	$0.841539\pi$
$164$		0			0
$165$	−0.836188	−	1.44832i	−0.0650971	−	0.112752i
$166$		0			0
$167$	−7.13516	+	12.3585i	−0.552136	+	0.956327i	0.445985	+	0.895041i	$0.352854\pi$
$167$	−7.13516	+	12.3585i	−0.552136	+	0.956327i	−0.998120	+	0.0612862i	$0.980480\pi$
$168$		0			0
$169$	−12.8373	−	22.2348i	−0.987483	−	1.71037i
$170$		0			0
$171$	−13.1897			−1.00864
$172$		0			0
$173$	−11.6384	−	20.1582i	−0.884849	−	1.53260i	−0.845887	−	0.533362i	$-0.820928\pi$
$173$	−11.6384	−	20.1582i	−0.884849	−	1.53260i	−0.0389615	−	0.999241i	$-0.512405\pi$
$174$		0			0
$175$	1.35634			0.102530
$176$		0			0
$177$	3.14838			0.236646
$178$		0			0
$179$	−7.53264			−0.563016			−0.281508	−	0.959559i	$-0.590835\pi$
$179$	−7.53264			−0.563016			−0.281508	+	0.959559i	$0.590835\pi$
$180$		0			0
$181$	1.96924	−	3.41082i	0.146372	−	0.253524i	−0.783512	−	0.621377i	$-0.786574\pi$
$181$	1.96924	−	3.41082i	0.146372	−	0.253524i	0.929884	+	0.367853i	$0.119907\pi$
$182$		0			0
$183$	−1.04227	−	1.80526i	−0.0770468	−	0.133449i
$184$		0			0
$185$	−0.783218	+	6.03213i	−0.0575833	+	0.443491i
$186$		0			0
$187$	−7.95523	−	13.7789i	−0.581744	−	1.00761i
$188$		0			0
$189$	2.33647	−	4.04689i	0.169953	−	0.294368i
$190$		0			0
$191$	−0.518016			−0.0374823			−0.0187411	−	0.999824i	$-0.505966\pi$
$191$	−0.518016			−0.0374823			−0.0187411	+	0.999824i	$0.505966\pi$
$192$		0			0
$193$	−14.7767			−1.06365			−0.531825	−	0.846855i	$-0.678493\pi$
$193$	−14.7767			−1.06365			−0.531825	+	0.846855i	$0.678493\pi$
$194$		0			0
$195$	3.80913			0.272777
$196$		0			0
$197$	−5.37374	−	9.30759i	−0.382863	−	0.663138i	0.608607	−	0.793472i	$-0.291729\pi$
$197$	−5.37374	−	9.30759i	−0.382863	−	0.663138i	−0.991470	+	0.130334i	$0.958395\pi$
$198$		0			0
$199$	0.397018			0.0281438			0.0140719	−	0.999901i	$-0.495521\pi$
$199$	0.397018			0.0281438			0.0140719	+	0.999901i	$0.495521\pi$
$200$		0			0
$201$	−4.31945	−	7.48150i	−0.304670	−	0.527705i
$202$		0			0
$203$	−1.23793	+	2.14416i	−0.0868857	+	0.150490i
$204$		0			0
$205$	1.20673	+	2.09012i	0.0842817	+	0.145980i
$206$		0			0
$207$	−0.675543	−	1.17007i	−0.0469535	−	0.0813258i
$208$		0			0
$209$	6.86002	−	11.8819i	0.474518	−	0.821889i
$210$		0			0
$211$	26.6079			1.83176			0.915882	−	0.401447i	$-0.131492\pi$
$211$	26.6079			1.83176			0.915882	+	0.401447i	$0.131492\pi$
$212$		0			0
$213$	−0.432471	−	0.749061i	−0.0296324	−	0.0513248i
$214$		0			0
$215$	−3.26269	+	5.65115i	−0.222514	+	0.385405i
$216$		0			0
$217$	−4.54171	+	7.86648i	−0.308312	+	0.534011i
$218$		0			0
$219$	−1.60199	+	2.77473i	−0.108253	+	0.187499i
$220$		0			0
$221$	36.2389			2.43769
$222$		0			0
$223$	−9.47163			−0.634267			−0.317134	−	0.948381i	$-0.602720\pi$
$223$	−9.47163			−0.634267			−0.317134	+	0.948381i	$0.602720\pi$
$224$		0			0
$225$	1.31242	−	2.27317i	0.0874944	−	0.151545i
$226$		0			0
$227$	12.2462	−	21.2110i	0.812806	−	1.40782i	−0.0980871	−	0.995178i	$-0.531272\pi$
$227$	12.2462	−	21.2110i	0.812806	−	1.40782i	0.910893	−	0.412643i	$-0.135394\pi$
$228$		0			0
$229$	−5.07983	+	8.79852i	−0.335684	+	0.581422i	−0.983616	−	0.180276i	$-0.942301\pi$
$229$	−5.07983	+	8.79852i	−0.335684	+	0.581422i	0.647932	+	0.761698i	$0.275634\pi$
$230$		0			0
$231$	1.13415	+	1.96441i	0.0746218	+	0.129249i
$232$		0			0
$233$	12.2345			0.801510			0.400755	−	0.916185i	$-0.368748\pi$
$233$	12.2345			0.801510			0.400755	+	0.916185i	$0.368748\pi$
$234$		0			0
$235$	6.64170	−	11.5038i	0.433257	−	0.750422i
$236$		0			0
$237$	−1.52478	−	2.64099i	−0.0990449	−	0.171551i
$238$		0			0
$239$	−7.40511	−	12.8260i	−0.478997	−	0.829647i	0.520713	−	0.853732i	$-0.325666\pi$
$239$	−7.40511	−	12.8260i	−0.478997	−	0.829647i	−0.999710	+	0.0240848i	$0.992333\pi$
$240$		0			0
$241$	0.920953	−	1.59514i	0.0593238	−	0.102752i	−0.834838	−	0.550495i	$-0.814439\pi$
$241$	0.920953	−	1.59514i	0.0593238	−	0.102752i	0.894162	+	0.447743i	$0.147772\pi$
$242$		0			0
$243$	−6.93322	−	12.0087i	−0.444766	−	0.770358i
$244$		0			0
$245$	5.16035			0.329682
$246$		0			0
$247$	15.6249	+	27.0631i	0.994188	+	1.72198i
$248$		0			0
$249$	−4.81589			−0.305194
$250$		0			0
$251$	0.899505			0.0567762			0.0283881	−	0.999597i	$-0.490963\pi$
$251$	0.899505			0.0567762			0.0283881	+	0.999597i	$0.490963\pi$
$252$		0			0
$253$	1.40541			0.0883572
$254$		0			0
$255$	−1.78462	+	3.09104i	−0.111757	+	0.193569i
$256$		0			0
$257$	−13.3337	−	23.0946i	−0.831732	−	1.44060i	−0.896664	−	0.442713i	$-0.854016\pi$
$257$	−13.3337	−	23.0946i	−0.831732	−	1.44060i	0.0649314	−	0.997890i	$-0.479317\pi$
$258$		0			0
$259$	1.06231	−	8.18161i	0.0660086	−	0.508380i
$260$		0			0
$261$	2.39569	+	4.14945i	0.148289	+	0.256845i
$262$		0			0
$263$	14.9665	−	25.9227i	0.922872	−	1.59846i	0.127923	−	0.991784i	$-0.459169\pi$
$263$	14.9665	−	25.9227i	0.922872	−	1.59846i	0.794948	−	0.606677i	$-0.207498\pi$
$264$		0			0
$265$	13.4308			0.825049
$266$		0			0
$267$	8.44512			0.516833
$268$		0			0
$269$	4.46816			0.272428			0.136214	−	0.990679i	$-0.456506\pi$
$269$	4.46816			0.272428			0.136214	+	0.990679i	$0.456506\pi$
$270$		0			0
$271$	−2.61844	−	4.53527i	−0.159059	−	0.275498i	0.775471	−	0.631384i	$-0.217513\pi$
$271$	−2.61844	−	4.53527i	−0.159059	−	0.275498i	−0.934530	+	0.355886i	$0.884179\pi$
$272$		0			0
$273$	−5.16647			−0.312689
$274$		0			0
$275$	1.36518	+	2.36457i	0.0823237	+	0.142589i
$276$		0			0
$277$	7.09495	−	12.2888i	0.426294	−	0.738363i	−0.570246	−	0.821474i	$-0.693152\pi$
$277$	7.09495	−	12.2888i	0.426294	−	0.738363i	0.996540	+	0.0831109i	$0.0264856\pi$
$278$		0			0
$279$	8.78928	+	15.2235i	0.526200	+	0.911406i
$280$		0			0
$281$	−11.4250	−	19.7887i	−0.681560	−	1.18050i	−0.974505	−	0.224367i	$-0.927968\pi$
$281$	−11.4250	−	19.7887i	−0.681560	−	1.18050i	0.292945	−	0.956129i	$-0.405365\pi$
$282$		0			0
$283$	11.8382	−	20.5044i	0.703710	−	1.21886i	−0.263446	−	0.964674i	$-0.584859\pi$
$283$	11.8382	−	20.5044i	0.703710	−	1.21886i	0.967155	−	0.254186i	$-0.0818077\pi$
$284$		0			0
$285$	−3.07785			−0.182316
$286$		0			0
$287$	−1.63673	−	2.83491i	−0.0966134	−	0.167339i
$288$		0			0
$289$	−8.47827	+	14.6848i	−0.498722	+	0.863811i
$290$		0			0
$291$	−5.08731	+	8.81147i	−0.298223	+	0.516538i
$292$		0			0
$293$	8.24410	−	14.2792i	0.481625	−	0.834199i	−0.518152	−	0.855288i	$-0.673380\pi$
$293$	8.24410	−	14.2792i	0.481625	−	0.834199i	0.999778	+	0.0210889i	$0.00671332\pi$
$294$		0			0
$295$	−5.14013			−0.299270
$296$		0			0
$297$	9.40683			0.545840
$298$		0			0
$299$	−1.60053	+	2.77220i	−0.0925611	+	0.160320i
$300$		0			0
$301$	4.42531	−	7.66487i	0.255071	−	0.441796i
$302$		0			0
$303$	−0.486550	+	0.842729i	−0.0279516	+	0.0484135i
$304$		0			0
$305$	1.70164	+	2.94732i	0.0974355	+	0.168763i
$306$		0			0
$307$	−12.1002			−0.690597			−0.345299	−	0.938493i	$-0.612222\pi$
$307$	−12.1002			−0.690597			−0.345299	+	0.938493i	$0.612222\pi$
$308$		0			0
$309$	0.834278	−	1.44501i	0.0474604	−	0.0822039i
$310$		0			0
$311$	−14.8212	−	25.6710i	−0.840431	−	1.45567i	−0.889531	−	0.456875i	$-0.848969\pi$
$311$	−14.8212	−	25.6710i	−0.840431	−	1.45567i	0.0491004	−	0.998794i	$-0.484365\pi$
$312$		0			0
$313$	1.39331	+	2.41328i	0.0787543	+	0.136406i	0.902713	−	0.430244i	$-0.141572\pi$
$313$	1.39331	+	2.41328i	0.0787543	+	0.136406i	−0.823958	+	0.566650i	$0.808239\pi$
$314$		0			0
$315$	−1.78008	+	3.08319i	−0.100296	+	0.173718i
$316$		0			0
$317$	9.11267	+	15.7836i	0.511818	+	0.886495i	0.999906	+	0.0137008i	$0.00436123\pi$
$317$	9.11267	+	15.7836i	0.511818	+	0.886495i	−0.488088	+	0.872795i	$0.662305\pi$
$318$		0			0
$319$	−4.98402			−0.279051
$320$		0			0
$321$	3.36111	+	5.82161i	0.187599	+	0.324931i
$322$		0			0
$323$	−29.2817			−1.62928
$324$		0			0
$325$	−6.21889			−0.344962
$326$		0			0
$327$	8.04193			0.444720
$328$		0			0
$329$	−9.00839	+	15.6030i	−0.496649	+	0.860220i
$330$		0			0
$331$	−16.4084	−	28.4202i	−0.901887	−	1.56211i	−0.825043	−	0.565070i	$-0.808849\pi$
$331$	−16.4084	−	28.4202i	−0.901887	−	1.56211i	−0.0768438	−	0.997043i	$-0.524484\pi$
$332$		0			0
$333$	−12.6842	−	9.69705i	−0.695087	−	0.531395i
$334$		0			0
$335$	7.05205	+	12.2145i	0.385295	+	0.667350i
$336$		0			0
$337$	−1.62221	+	2.80975i	−0.0883675	+	0.153057i	−0.906821	−	0.421515i	$-0.861498\pi$
$337$	−1.62221	+	2.80975i	−0.0883675	+	0.153057i	0.818454	+	0.574572i	$0.194832\pi$
$338$		0			0
$339$	−7.40970			−0.402440
$340$		0			0
$341$	−18.2853			−0.990206
$342$		0			0
$343$	−16.4935			−0.890568
$344$		0			0
$345$	−0.157639	−	0.273039i	−0.00848701	−	0.0146999i
$346$		0			0
$347$	23.5901			1.26638			0.633190	−	0.773996i	$-0.281745\pi$
$347$	23.5901			1.26638			0.633190	+	0.773996i	$0.281745\pi$
$348$		0			0
$349$	−1.36694	−	2.36762i	−0.0731709	−	0.126736i	0.827119	−	0.562028i	$-0.189979\pi$
$349$	−1.36694	−	2.36762i	−0.0731709	−	0.126736i	−0.900289	+	0.435292i	$0.856645\pi$
$350$		0			0
$351$	−10.7129	+	18.5552i	−0.571810	+	0.990404i
$352$		0			0
$353$	5.93272	+	10.2758i	0.315767	+	0.546924i	0.979600	−	0.200956i	$-0.0644049\pi$
$353$	5.93272	+	10.2758i	0.315767	+	0.546924i	−0.663833	+	0.747881i	$0.731072\pi$
$354$		0			0
$355$	0.706064	+	1.22294i	0.0374740	+	0.0649068i
$356$		0			0
$357$	2.42054	−	4.19250i	0.128109	−	0.221891i
$358$		0			0
$359$	−6.17772			−0.326048			−0.163024	−	0.986622i	$-0.552125\pi$
$359$	−6.17772			−0.326048			−0.163024	+	0.986622i	$0.552125\pi$
$360$		0			0
$361$	−3.12522	−	5.41303i	−0.164485	−	0.284897i
$362$		0			0
$363$	1.08570	−	1.88049i	0.0569846	−	0.0987002i
$364$		0			0
$365$	2.61546	−	4.53011i	0.136899	−	0.237117i
$366$		0			0
$367$	5.38025	−	9.31886i	0.280847	−	0.486441i	−0.690747	−	0.723097i	$-0.742718\pi$
$367$	5.38025	−	9.31886i	0.280847	−	0.486441i	0.971594	+	0.236656i	$0.0760514\pi$
$368$		0			0
$369$	−6.33493			−0.329783
$370$		0			0
$371$	−18.2167			−0.945766
$372$		0			0
$373$	−11.8085	+	20.4529i	−0.611419	+	1.05901i	0.379582	+	0.925158i	$0.376068\pi$
$373$	−11.8085	+	20.4529i	−0.611419	+	1.05901i	−0.991001	+	0.133851i	$0.957266\pi$
$374$		0			0
$375$	0.306255	−	0.530449i	0.0158149	−	0.0273923i
$376$		0			0
$377$	5.67598	−	9.83109i	0.292328	−	0.506327i
$378$		0			0
$379$	−15.3305	−	26.5533i	−0.787477	−	1.36395i	−0.927508	−	0.373803i	$-0.878054\pi$
$379$	−15.3305	−	26.5533i	−0.787477	−	1.36395i	0.140031	−	0.990147i	$-0.455280\pi$
$380$		0			0
$381$	−8.60102			−0.440644
$382$		0			0
$383$	9.04640	−	15.6688i	0.462250	−	0.800640i	−0.536823	−	0.843695i	$-0.680376\pi$
$383$	9.04640	−	15.6688i	0.462250	−	0.800640i	0.999073	+	0.0430550i	$0.0137091\pi$
$384$		0			0
$385$	−1.85165	−	3.20715i	−0.0943689	−	0.163452i
$386$		0			0
$387$	−8.56402	−	14.8333i	−0.435334	−	0.754020i
$388$		0			0
$389$	16.1718	−	28.0103i	0.819941	−	1.42018i	−0.0857843	−	0.996314i	$-0.527340\pi$
$389$	16.1718	−	28.0103i	0.819941	−	1.42018i	0.905725	−	0.423865i	$-0.139327\pi$
$390$		0			0
$391$	−1.49973	−	2.59761i	−0.0758446	−	0.131367i
$392$		0			0
$393$	2.51859			0.127046
$394$		0			0
$395$	2.48939	+	4.31175i	0.125255	+	0.216948i
$396$		0			0
$397$	6.73163			0.337851			0.168925	−	0.985629i	$-0.445970\pi$
$397$	6.73163			0.337851			0.168925	+	0.985629i	$0.445970\pi$
$398$		0			0
$399$	4.17460			0.208992
$400$		0			0
$401$	8.91980			0.445434			0.222717	−	0.974883i	$-0.428507\pi$
$401$	8.91980			0.445434			0.222717	+	0.974883i	$0.428507\pi$
$402$		0			0
$403$	20.8240	−	36.0682i	1.03732	−	1.79669i
$404$		0			0
$405$	2.88212	+	4.99198i	0.143214	+	0.248053i
$406$		0			0
$407$	15.3326	−	6.38299i	0.760009	−	0.316393i
$408$		0			0
$409$	−6.78629	−	11.7542i	−0.335561	−	0.581208i	0.648032	−	0.761613i	$-0.275592\pi$
$409$	−6.78629	−	11.7542i	−0.335561	−	0.581208i	−0.983592	+	0.180405i	$0.942259\pi$
$410$		0			0
$411$	−5.01165	+	8.68043i	−0.247206	+	0.428174i
$412$		0			0
$413$	6.97175			0.343057
$414$		0			0
$415$	7.86255			0.385957
$416$		0			0
$417$	−12.1726			−0.596096
$418$		0			0
$419$	18.1984	+	31.5206i	0.889051	+	1.53988i	0.840999	+	0.541037i	$0.181968\pi$
$419$	18.1984	+	31.5206i	0.889051	+	1.53988i	0.0480525	+	0.998845i	$0.484699\pi$
$420$		0			0
$421$	2.00978			0.0979505			0.0489753	−	0.998800i	$-0.484404\pi$
$421$	2.00978			0.0979505			0.0489753	+	0.998800i	$0.484404\pi$
$422$		0			0
$423$	17.4333	+	30.1954i	0.847638	+	1.46815i
$424$		0			0
$425$	2.91361	−	5.04652i	0.141331	−	0.244792i
$426$		0			0
$427$	−2.30800	−	3.99757i	−0.111692	−	0.193456i
$428$		0			0
$429$	−5.20016	−	9.00694i	−0.251066	−	0.434859i
$430$		0			0
$431$	2.86903	−	4.96931i	0.138196	−	0.239363i	−0.788618	−	0.614884i	$-0.789203\pi$
$431$	2.86903	−	4.96931i	0.138196	−	0.239363i	0.926814	+	0.375521i	$0.122536\pi$
$432$		0			0
$433$	−16.7097			−0.803018			−0.401509	−	0.915855i	$-0.631514\pi$
$433$	−16.7097			−0.803018			−0.401509	+	0.915855i	$0.631514\pi$
$434$		0			0
$435$	0.559038	+	0.968282i	0.0268038	+	0.0464256i
$436$		0			0
$437$	1.29326	−	2.23999i	0.0618650	−	0.107153i
$438$		0			0
$439$	−8.10459	+	14.0376i	−0.386811	+	0.669977i	−0.992019	−	0.126091i	$-0.959757\pi$
$439$	−8.10459	+	14.0376i	−0.386811	+	0.669977i	0.605207	+	0.796068i	$0.293090\pi$
$440$		0			0
$441$	−6.77252	+	11.7304i	−0.322501	+	0.558588i
$442$		0			0
$443$	−39.2925			−1.86684			−0.933422	−	0.358780i	$-0.883193\pi$
$443$	−39.2925			−1.86684			−0.933422	+	0.358780i	$0.883193\pi$
$444$		0			0
$445$	−13.7877			−0.653602
$446$		0			0
$447$	5.18303	−	8.97728i	0.245149	−	0.424611i
$448$		0			0
$449$	7.17341	−	12.4247i	0.338534	−	0.586359i	−0.645623	−	0.763656i	$-0.723402\pi$
$449$	7.17341	−	12.4247i	0.338534	−	0.586359i	0.984157	+	0.177298i	$0.0567355\pi$
$450$		0			0
$451$	3.29482	−	5.70679i	0.155147	−	0.268722i
$452$		0			0
$453$	−0.962640	−	1.66734i	−0.0452288	−	0.0783385i
$454$		0			0
$455$	8.43491			0.395435
$456$		0			0
$457$	−14.4454	+	25.0201i	−0.675725	+	1.17039i	0.300531	+	0.953772i	$0.402836\pi$
$457$	−14.4454	+	25.0201i	−0.675725	+	1.17039i	−0.976256	+	0.216618i	$0.930497\pi$
$458$		0			0
$459$	−10.0382	−	17.3866i	−0.468541	−	0.811537i
$460$		0			0
$461$	11.8683	+	20.5564i	0.552760	+	0.957409i	0.998074	+	0.0620343i	$0.0197588\pi$
$461$	11.8683	+	20.5564i	0.552760	+	0.957409i	−0.445314	+	0.895375i	$0.646908\pi$
$462$		0			0
$463$	6.29313	−	10.9000i	0.292467	−	0.506567i	−0.681926	−	0.731421i	$-0.738857\pi$
$463$	6.29313	−	10.9000i	0.292467	−	0.506567i	0.974392	+	0.224854i	$0.0721906\pi$
$464$		0			0
$465$	2.05099	+	3.55243i	0.0951126	+	0.164740i
$466$		0			0
$467$	−4.78804			−0.221564			−0.110782	−	0.993845i	$-0.535336\pi$
$467$	−4.78804			−0.221564			−0.110782	+	0.993845i	$0.535336\pi$
$468$		0			0
$469$	−9.56497	−	16.5670i	−0.441669	−	0.764993i
$470$		0			0
$471$	−9.33015			−0.429910
$472$		0			0
$473$	17.8167			0.819213
$474$		0			0
$475$	5.02498			0.230562
$476$		0			0
$477$	−17.6268	+	30.5306i	−0.807077	+	1.39790i
$478$		0			0
$479$	12.5778	+	21.7853i	0.574693	+	0.995397i	0.996075	+	0.0885141i	$0.0282118\pi$
$479$	12.5778	+	21.7853i	0.574693	+	0.995397i	−0.421382	+	0.906883i	$0.638455\pi$
$480$		0			0
$481$	−4.87074	+	37.5131i	−0.222087	+	1.71045i
$482$		0			0
$483$	0.213812	+	0.370333i	0.00972878	+	0.0168507i
$484$		0			0
$485$	8.30568	−	14.3859i	0.377141	−	0.653228i
$486$		0			0
$487$	38.3971			1.73994			0.869970	−	0.493104i	$-0.164138\pi$
$487$	38.3971			1.73994			0.869970	+	0.493104i	$0.164138\pi$
$488$		0			0
$489$	0.403116			0.0182295
$490$		0			0
$491$	19.4434			0.877469			0.438735	−	0.898617i	$-0.355427\pi$
$491$	19.4434			0.877469			0.438735	+	0.898617i	$0.355427\pi$
$492$		0			0
$493$	5.31851	+	9.21193i	0.239534	+	0.414885i
$494$		0			0
$495$	−7.16676			−0.322122
$496$		0			0
$497$	−0.957661	−	1.65872i	−0.0429570	−	0.0744036i
$498$		0			0
$499$	−12.7614	+	22.1034i	−0.571279	+	0.989484i	0.425156	+	0.905120i	$0.360219\pi$
$499$	−12.7614	+	22.1034i	−0.571279	+	0.989484i	−0.996435	+	0.0843641i	$0.973114\pi$
$500$		0			0
$501$	−4.37036	−	7.56968i	−0.195253	−	0.338188i
$502$		0			0
$503$	1.86071	+	3.22285i	0.0829651	+	0.143700i	0.904522	−	0.426426i	$-0.140228\pi$
$503$	1.86071	+	3.22285i	0.0829651	+	0.143700i	−0.821557	+	0.570126i	$0.806894\pi$
$504$		0			0
$505$	0.794355	−	1.37586i	0.0353483	−	0.0612251i
$506$		0			0
$507$	15.7259			0.698412
$508$		0			0
$509$	−12.8873	−	22.3215i	−0.571221	−	0.989383i	−0.996441	−	0.0842932i	$-0.973137\pi$
$509$	−12.8873	−	22.3215i	−0.571221	−	0.989383i	0.425220	−	0.905090i	$-0.360197\pi$
$510$		0			0
$511$	−3.54745	+	6.14436i	−0.156930	+	0.271810i
$512$		0			0
$513$	8.65619	−	14.9930i	0.382180	−	0.661955i
$514$		0			0
$515$	−1.36207	+	2.35917i	−0.0600198	+	0.103957i
$516$		0			0
$517$	−36.2686			−1.59509
$518$		0			0
$519$	14.2572			0.625822
$520$		0			0
$521$	−1.24309	+	2.15310i	−0.0544609	+	0.0943290i	−0.891971	−	0.452093i	$-0.850677\pi$
$521$	−1.24309	+	2.15310i	−0.0544609	+	0.0943290i	0.837510	+	0.546422i	$0.184011\pi$
$522$		0			0
$523$	−10.7289	+	18.5830i	−0.469142	+	0.812577i	−0.999378	−	0.0352727i	$-0.988770\pi$
$523$	−10.7289	+	18.5830i	−0.469142	+	0.812577i	0.530236	+	0.847850i	$0.322103\pi$
$524$		0			0
$525$	−0.415385	+	0.719468i	−0.0181289	+	0.0314002i
$526$		0			0
$527$	19.5125	+	33.7967i	0.849979	+	1.47221i
$528$		0			0
$529$	−22.7351			−0.988480
$530$		0			0
$531$	6.74599	−	11.6844i	0.292751	−	0.507059i
$532$		0			0
$533$	7.50452	+	12.9982i	0.325057	+	0.563015i
$534$		0			0
$535$	−5.48744	−	9.50452i	−0.237243	−	0.410916i
$536$		0			0
$537$	2.30691	−	3.99568i	0.0995504	−	0.172426i
$538$		0			0
$539$	−7.04482	−	12.2020i	−0.303442	−	0.525577i
$540$		0			0
$541$	−10.4218			−0.448069			−0.224035	−	0.974581i	$-0.571923\pi$
$541$	−10.4218			−0.448069			−0.224035	+	0.974581i	$0.571923\pi$
$542$		0			0
$543$	1.20618	+	2.08916i	0.0517620	+	0.0896544i
$544$		0			0
$545$	−13.1295			−0.562405
$546$		0			0
$547$	−13.8476			−0.592082			−0.296041	−	0.955175i	$-0.595666\pi$
$547$	−13.8476			−0.592082			−0.296041	+	0.955175i	$0.595666\pi$
$548$		0			0
$549$	−8.93303			−0.381252
$550$		0			0
$551$	−4.58630	+	7.94371i	−0.195383	+	0.338413i
$552$		0			0
$553$	−3.37646	−	5.84820i	−0.143582	−	0.248691i
$554$		0			0
$555$	−2.95987	−	2.26282i	−0.125640	−	0.0960516i
$556$		0			0
$557$	16.9417	+	29.3439i	0.717842	+	1.24334i	0.961853	+	0.273567i	$0.0882034\pi$
$557$	16.9417	+	29.3439i	0.717842	+	1.24334i	−0.244011	+	0.969772i	$0.578463\pi$
$558$		0			0
$559$	−20.2903	+	35.1439i	−0.858189	+	1.48643i
$560$		0			0
$561$	9.74531			0.411447
$562$		0			0
$563$	25.9013			1.09161			0.545805	−	0.837912i	$-0.316224\pi$
$563$	25.9013			1.09161			0.545805	+	0.837912i	$0.316224\pi$
$564$		0			0
$565$	12.0973			0.508937
$566$		0			0
$567$	−3.90913	−	6.77081i	−0.164168	−	0.284347i
$568$		0			0
$569$	−8.45724			−0.354546			−0.177273	−	0.984162i	$-0.556728\pi$
$569$	−8.45724			−0.354546			−0.177273	+	0.984162i	$0.556728\pi$
$570$		0			0
$571$	6.92323	+	11.9914i	0.289728	+	0.501824i	0.973745	−	0.227642i	$-0.0731018\pi$
$571$	6.92323	+	11.9914i	0.289728	+	0.501824i	−0.684017	+	0.729466i	$0.739768\pi$
$572$		0			0
$573$	0.158645	−	0.274781i	0.00662748	−	0.0114791i
$574$		0			0
$575$	0.257366	+	0.445771i	0.0107329	+	0.0185899i
$576$		0			0
$577$	7.14576	+	12.3768i	0.297482	+	0.515254i	0.975559	−	0.219737i	$-0.0705198\pi$
$577$	7.14576	+	12.3768i	0.297482	+	0.515254i	−0.678077	+	0.734991i	$0.737187\pi$
$578$		0			0
$579$	4.52543	−	7.83828i	0.188070	−	0.325748i
$580$		0			0
$581$	−10.6643			−0.442429
$582$		0			0
$583$	−18.3355	−	31.7581i	−0.759381	−	1.31529i
$584$		0			0
$585$	8.16177	−	14.1366i	0.337448	−	0.584476i
$586$		0			0
$587$	14.4511	−	25.0300i	0.596461	−	1.03310i	−0.396878	−	0.917871i	$-0.629907\pi$
$587$	14.4511	−	25.0300i	0.596461	−	1.03310i	0.993339	−	0.115229i	$-0.0367602\pi$
$588$		0			0
$589$	−16.8262	+	29.1438i	−0.693312	+	1.20085i
$590$		0			0
$591$	6.58293			0.270786
$592$		0			0
$593$	8.27506			0.339816			0.169908	−	0.985460i	$-0.445653\pi$
$593$	8.27506			0.339816			0.169908	+	0.985460i	$0.445653\pi$
$594$		0			0
$595$	−3.95184	+	6.84479i	−0.162010	+	0.280609i
$596$		0			0
$597$	−0.121589	+	0.210598i	−0.00497629	+	0.00861919i
$598$		0			0
$599$	−3.63294	+	6.29244i	−0.148438	+	0.257102i	−0.930650	−	0.365910i	$-0.880758\pi$
$599$	−3.63294	+	6.29244i	−0.148438	+	0.257102i	0.782212	+	0.623012i	$0.214091\pi$
$600$		0			0
$601$	−11.7975	−	20.4338i	−0.481229	−	0.833513i	0.518539	−	0.855054i	$-0.326476\pi$
$601$	−11.7975	−	20.4338i	−0.481229	−	0.833513i	−0.999768	+	0.0215412i	$0.993143\pi$
$602$		0			0
$603$	−37.0209			−1.50761
$604$		0			0
$605$	−1.77255	+	3.07014i	−0.0720643	+	0.124819i
$606$		0			0
$607$	8.85148	+	15.3312i	0.359271	+	0.622275i	0.987839	−	0.155479i	$-0.0496922\pi$
$607$	8.85148	+	15.3312i	0.359271	+	0.622275i	−0.628569	+	0.777754i	$0.716359\pi$
$608$		0			0
$609$	−0.758244	−	1.31332i	−0.0307256	−	0.0532183i
$610$		0			0
$611$	41.3040	−	71.5406i	1.67098	−	2.89422i
$612$		0			0
$613$	7.17698	+	12.4309i	0.289875	+	0.502079i	0.973780	−	0.227493i	$-0.0730528\pi$
$613$	7.17698	+	12.4309i	0.289875	+	0.502079i	−0.683904	+	0.729572i	$0.739719\pi$
$614$		0			0
$615$	−1.47827			−0.0596095
$616$		0			0
$617$	12.9750	+	22.4733i	0.522352	+	0.904740i	0.999662	+	0.0260053i	$0.00827866\pi$
$617$	12.9750	+	22.4733i	0.522352	+	0.904740i	−0.477310	+	0.878735i	$0.658388\pi$
$618$		0			0
$619$	40.6118			1.63232			0.816162	−	0.577823i	$-0.196098\pi$
$619$	40.6118			1.63232			0.816162	+	0.577823i	$0.196098\pi$
$620$		0			0
$621$	1.77339			0.0711636
$622$		0			0
$623$	18.7008			0.749233
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	4.20183	+	7.27778i	0.167805	+	0.290647i
$628$		0			0
$629$	−28.1593	−	21.5278i	−1.12278	−	0.858370i
$630$		0			0
$631$	−13.7563	−	23.8266i	−0.547631	−	0.948524i	−0.998436	−	0.0559019i	$-0.982197\pi$
$631$	−13.7563	−	23.8266i	−0.547631	−	0.948524i	0.450806	−	0.892622i	$-0.351137\pi$
$632$		0			0
$633$	−8.14880	+	14.1141i	−0.323886	+	0.560987i
$634$		0			0
$635$	14.0423			0.557250
$636$		0			0
$637$	32.0916			1.27152
$638$		0			0
$639$	−3.70660			−0.146631
$640$		0			0
$641$	9.49302	+	16.4424i	0.374952	+	0.649435i	0.990320	−	0.138804i	$-0.0443259\pi$
$641$	9.49302	+	16.4424i	0.374952	+	0.649435i	−0.615368	+	0.788240i	$0.710993\pi$
$642$		0			0
$643$	−25.1997			−0.993779			−0.496889	−	0.867814i	$-0.665525\pi$
$643$	−25.1997			−0.993779			−0.496889	+	0.867814i	$0.665525\pi$
$644$		0			0
$645$	−1.99843	−	3.46138i	−0.0786881	−	0.136292i
$646$		0			0
$647$	5.18443	−	8.97970i	0.203821	−	0.353028i	−0.745935	−	0.666018i	$-0.767997\pi$
$647$	5.18443	−	8.97970i	0.203821	−	0.353028i	0.949756	+	0.312990i	$0.101331\pi$
$648$		0			0
$649$	7.01722	+	12.1542i	0.275450	+	0.477093i
$650$		0			0
$651$	−2.78184	−	4.81829i	−0.109029	−	0.188844i
$652$		0			0
$653$	−9.07725	+	15.7222i	−0.355220	+	0.615259i	−0.987156	−	0.159762i	$-0.948927\pi$
$653$	−9.07725	+	15.7222i	−0.355220	+	0.615259i	0.631936	+	0.775021i	$0.282261\pi$
$654$		0			0
$655$	−4.11192			−0.160666
$656$		0			0
$657$	6.86514	+	11.8908i	0.267835	+	0.463903i
$658$		0			0
$659$	21.0929	−	36.5339i	0.821661	−	1.42316i	−0.0827834	−	0.996568i	$-0.526381\pi$
$659$	21.0929	−	36.5339i	0.821661	−	1.42316i	0.904445	−	0.426591i	$-0.140286\pi$
$660$		0			0
$661$	−15.5426	+	26.9205i	−0.604536	+	1.04709i	0.387589	+	0.921832i	$0.373308\pi$
$661$	−15.5426	+	26.9205i	−0.604536	+	1.04709i	−0.992125	+	0.125255i	$0.960025\pi$
$662$		0			0
$663$	−11.0983	+	19.2229i	−0.431023	+	0.746554i
$664$		0			0
$665$	−6.81557			−0.264297
$666$		0			0
$667$	−0.939593			−0.0363812
$668$		0			0
$669$	2.90073	−	5.02422i	0.112149	−	0.194247i
$670$		0			0
$671$	4.64610	−	8.04727i	0.179361	−	0.310662i
$672$		0			0
$673$	−14.3198	+	24.8026i	−0.551987	+	0.956070i	0.446144	+	0.894961i	$0.352797\pi$
$673$	−14.3198	+	24.8026i	−0.551987	+	0.956070i	−0.998131	+	0.0611085i	$0.980536\pi$
$674$		0			0
$675$	1.72263	+	2.98369i	0.0663041	+	0.114842i
$676$		0			0
$677$	4.45376			0.171172			0.0855860	−	0.996331i	$-0.472724\pi$
$677$	4.45376			0.171172			0.0855860	+	0.996331i	$0.472724\pi$
$678$		0			0
$679$	−11.2653	+	19.5121i	−0.432323	+	0.748805i
$680$		0			0
$681$	7.50089	+	12.9919i	0.287435	+	0.497851i
$682$		0			0
$683$	−12.8708	−	22.2928i	−0.492487	−	0.853012i	0.507476	−	0.861666i	$-0.330579\pi$
$683$	−12.8708	−	22.2928i	−0.492487	−	0.853012i	−0.999963	+	0.00865405i	$0.997245\pi$
$684$		0			0
$685$	8.18216	−	14.1719i	0.312624	−	0.541481i
$686$		0			0
$687$	−3.11144	−	5.38918i	−0.118709	−	0.205610i
$688$		0			0
$689$	83.5248			3.18204
$690$		0			0
$691$	24.8233	+	42.9951i	0.944321	+	1.63561i	0.757105	+	0.653293i	$0.226613\pi$
$691$	24.8233	+	42.9951i	0.944321	+	1.63561i	0.187216	+	0.982319i	$0.440054\pi$
$692$		0			0
$693$	9.72054			0.369253
$694$		0			0
$695$	19.8734			0.753839
$696$		0			0
$697$	−14.0638			−0.532704
$698$		0			0
$699$	−3.74688	+	6.48979i	−0.141720	+	0.245466i
$700$		0			0
$701$	13.3414	+	23.1079i	0.503897	+	0.872775i	0.999990	+	0.00450565i	$0.00143420\pi$
$701$	13.3414	+	23.1079i	0.503897	+	0.872775i	−0.496093	+	0.868269i	$0.665232\pi$
$702$		0			0
$703$	3.93565	−	30.3113i	0.148436	−	1.14321i
$704$		0			0
$705$	4.06810	+	7.04616i	0.153214	+	0.265374i
$706$		0			0
$707$	−1.07741	+	1.86613i	−0.0405203	+	0.0701832i
$708$		0			0
$709$	−12.8591			−0.482934			−0.241467	−	0.970409i	$-0.577629\pi$
$709$	−12.8591			−0.482934			−0.241467	+	0.970409i	$0.577629\pi$
$710$		0			0
$711$	−13.0685			−0.490106
$712$		0			0
$713$	−3.44717			−0.129098
$714$		0			0
$715$	8.48992	+	14.7050i	0.317505	+	0.549935i
$716$		0			0
$717$	9.07140			0.338778
$718$		0			0
$719$	−4.28143	−	7.41566i	−0.159670	−	0.276557i	0.775079	−	0.631864i	$-0.217710\pi$
$719$	−4.28143	−	7.41566i	−0.159670	−	0.276557i	−0.934750	+	0.355307i	$0.884376\pi$
$720$		0			0
$721$	1.84742	−	3.19983i	0.0688016	−	0.119168i
$722$		0			0
$723$	0.564093	+	0.977037i	0.0209788	+	0.0363364i
$724$		0			0
$725$	−0.912701	−	1.58084i	−0.0338969	−	0.0587111i
$726$		0			0
$727$	−0.194055	+	0.336112i	−0.00719709	+	0.0124657i	−0.869602	−	0.493754i	$-0.835624\pi$
$727$	−0.194055	+	0.336112i	−0.00719709	+	0.0124657i	0.862404	+	0.506220i	$0.168958\pi$
$728$		0			0
$729$	−8.79939			−0.325903
$730$		0			0
$731$	−19.0124	−	32.9305i	−0.703200	−	1.21798i
$732$		0			0
$733$	0.330452	−	0.572360i	0.0122055	−	0.0211406i	−0.859858	−	0.510533i	$-0.829448\pi$
$733$	0.330452	−	0.572360i	0.0122055	−	0.0211406i	0.872064	+	0.489392i	$0.162781\pi$
$734$		0			0
$735$	−1.58038	+	2.73730i	−0.0582932	+	0.100967i
$736$		0			0
$737$	19.2547	−	33.3501i	0.709256	−	1.22847i
$738$		0			0
$739$	−25.3973			−0.934256			−0.467128	−	0.884190i	$-0.654711\pi$
$739$	−25.3973			−0.934256			−0.467128	+	0.884190i	$0.654711\pi$
$740$		0			0
$741$	−19.1408			−0.703155
$742$		0			0
$743$	10.2557	−	17.7633i	0.376243	−	0.651673i	−0.614269	−	0.789097i	$-0.710549\pi$
$743$	10.2557	−	17.7633i	0.376243	−	0.651673i	0.990512	+	0.137424i	$0.0438823\pi$
$744$		0			0
$745$	−8.46197	+	14.6566i	−0.310022	+	0.536975i
$746$		0			0
$747$	−10.3189	+	17.8729i	−0.377550	+	0.653936i
$748$		0			0
$749$	7.44282	+	12.8913i	0.271955	+	0.471040i
$750$		0			0
$751$	37.8461			1.38102			0.690512	−	0.723321i	$-0.257385\pi$
$751$	37.8461			1.38102			0.690512	+	0.723321i	$0.257385\pi$
$752$		0			0
$753$	−0.275478	+	0.477141i	−0.0100390	+	0.0173880i
$754$		0			0
$755$	1.57163	+	2.72215i	0.0571976	+	0.0990691i
$756$		0			0
$757$	−7.48595	−	12.9660i	−0.272081	−	0.471259i	0.697313	−	0.716766i	$-0.254379\pi$
$757$	−7.48595	−	12.9660i	−0.272081	−	0.471259i	−0.969395	+	0.245508i	$0.921045\pi$
$758$		0			0
$759$	−0.430413	+	0.745497i	−0.0156230	+	0.0270598i
$760$		0			0
$761$	−2.17862	−	3.77348i	−0.0789749	−	0.136789i	0.823833	−	0.566833i	$-0.191831\pi$
$761$	−2.17862	−	3.77348i	−0.0789749	−	0.136789i	−0.902808	+	0.430044i	$0.858498\pi$
$762$		0			0
$763$	17.8080			0.644693
$764$		0			0
$765$	7.64774	+	13.2463i	0.276505	+	0.478920i
$766$		0			0
$767$	−31.9659			−1.15422
$768$		0			0
$769$	−41.7694			−1.50624			−0.753121	−	0.657882i	$-0.771453\pi$
$769$	−41.7694			−1.50624			−0.753121	+	0.657882i	$0.771453\pi$
$770$		0			0
$771$	16.3340			0.588255
$772$		0			0
$773$	−5.35537	+	9.27577i	−0.192619	+	0.333626i	−0.946117	−	0.323824i	$-0.895032\pi$
$773$	−5.35537	+	9.27577i	−0.192619	+	0.333626i	0.753498	+	0.657450i	$0.228365\pi$
$774$		0			0
$775$	−3.34851	−	5.79979i	−0.120282	−	0.208335i
$776$		0			0
$777$	4.01459	+	3.06916i	0.144022	+	0.110105i
$778$		0			0
$779$	−6.06380	−	10.5028i	−0.217258	−	0.376302i
$780$		0			0
$781$	1.92781	−	3.33907i	0.0689826	−	0.119481i
$782$		0			0
$783$	−6.28899			−0.224750
$784$		0			0
$785$	15.2327			0.543677
$786$		0			0
$787$	−21.4240			−0.763682			−0.381841	−	0.924228i	$-0.624710\pi$
$787$	−21.4240			−0.763682			−0.381841	+	0.924228i	$0.624710\pi$
$788$		0			0
$789$	9.16710	+	15.8779i	0.326358	+	0.565268i
$790$		0			0
$791$	−16.4080			−0.583402
$792$		0			0
$793$	10.5823	+	18.3291i	0.375788	+	0.650884i
$794$		0			0
$795$	−4.11325	+	7.12437i	−0.145882	+	0.252675i
$796$		0			0
$797$	25.8006	+	44.6879i	0.913903	+	1.58293i	0.808500	+	0.588496i	$0.200280\pi$
$797$	25.8006	+	44.6879i	0.913903	+	1.58293i	0.105403	+	0.994430i	$0.466387\pi$
$798$		0			0
$799$	38.7027	+	67.0350i	1.36920	+	2.37153i
$800$		0			0
$801$	18.0953	−	31.3419i	0.639364	−	1.10741i
$802$		0			0
$803$	−14.2823			−0.504012
$804$		0			0
$805$	−0.349075	−	0.604616i	−0.0123033	−	0.0213099i
$806$		0			0
$807$	−1.36839	+	2.37013i	−0.0481698	+	0.0834325i
$808$		0			0
$809$	−14.7928	+	25.6219i	−0.520088	+	0.900819i	0.479639	+	0.877466i	$0.340768\pi$
$809$	−14.7928	+	25.6219i	−0.520088	+	0.900819i	−0.999727	+	0.0233533i	$0.992566\pi$
$810$		0			0
$811$	12.0977	−	20.9539i	0.424808	−	0.735790i	−0.571594	−	0.820537i	$-0.693675\pi$
$811$	12.0977	−	20.9539i	0.424808	−	0.735790i	0.996403	+	0.0847468i	$0.0270081\pi$
$812$		0			0
$813$	3.20764			0.112497
$814$		0			0
$815$	−0.658138			−0.0230536
$816$		0			0
$817$	16.3950	−	28.3969i	0.573587	−	0.993482i
$818$		0			0
$819$	−11.0701	+	19.1740i	−0.386821	+	0.669994i
$820$		0			0
$821$	8.61632	−	14.9239i	0.300712	−	0.520848i	−0.675586	−	0.737282i	$-0.736109\pi$
$821$	8.61632	−	14.9239i	0.300712	−	0.520848i	0.976297	+	0.216434i	$0.0694425\pi$
$822$		0			0
$823$	18.5884	+	32.1960i	0.647950	+	1.12228i	0.983612	+	0.180300i	$0.0577067\pi$
$823$	18.5884	+	32.1960i	0.647950	+	1.12228i	−0.335662	+	0.941983i	$0.608960\pi$
$824$		0			0
$825$	−1.67238			−0.0582247
$826$		0			0
$827$	−15.8955	+	27.5319i	−0.552742	+	0.957376i	0.445334	+	0.895365i	$0.353085\pi$
$827$	−15.8955	+	27.5319i	−0.552742	+	0.957376i	−0.998075	+	0.0620119i	$0.980248\pi$
$828$		0			0
$829$	−10.5312	−	18.2405i	−0.365763	−	0.633520i	0.623136	−	0.782114i	$-0.285858\pi$
$829$	−10.5312	−	18.2405i	−0.365763	−	0.633520i	−0.988898	+	0.148594i	$0.952525\pi$
$830$		0			0
$831$	4.34572	+	7.52701i	0.150751	+	0.261109i
$832$		0			0
$833$	−15.0352	+	26.0418i	−0.520940	+	0.902295i
$834$		0			0
$835$	7.13516	+	12.3585i	0.246923	+	0.427682i
$836$		0			0
$837$	−23.0730			−0.797520
$838$		0			0
$839$	19.9494	+	34.5533i	0.688729	+	1.19291i	0.972249	+	0.233947i	$0.0751643\pi$
$839$	19.9494	+	34.5533i	0.688729	+	1.19291i	−0.283520	+	0.958966i	$0.591502\pi$
$840$		0			0
$841$	−25.6679			−0.885100
$842$		0			0
$843$	13.9959			0.482044
$844$		0			0
$845$	−25.6746			−0.883232
$846$		0			0
$847$	2.40417	−	4.16415i	0.0826084	−	0.143082i
$848$		0			0
$849$	7.25103	+	12.5591i	0.248855	+	0.431029i
$850$		0			0
$851$	2.89052	−	1.20333i	0.0990858	−	0.0412496i
$852$		0			0
$853$	−7.33687	−	12.7078i	−0.251210	−	0.435108i	0.712649	−	0.701520i	$-0.247495\pi$
$853$	−7.33687	−	12.7078i	−0.251210	−	0.435108i	−0.963859	+	0.266412i	$0.914162\pi$
$854$		0			0
$855$	−6.59487	+	11.4226i	−0.225540	+	0.390646i
$856$		0			0
$857$	−16.2439			−0.554880			−0.277440	−	0.960743i	$-0.589486\pi$
$857$	−16.2439			−0.554880			−0.277440	+	0.960743i	$0.589486\pi$
$858$		0			0
$859$	0.608441			0.0207597			0.0103799	−	0.999946i	$-0.496696\pi$
$859$	0.608441			0.0207597			0.0103799	+	0.999946i	$0.496696\pi$
$860$		0			0
$861$	2.00503			0.0683313
$862$		0			0
$863$	7.09010	+	12.2804i	0.241350	+	0.418030i	0.961099	−	0.276204i	$-0.0890766\pi$
$863$	7.09010	+	12.2804i	0.241350	+	0.418030i	−0.719749	+	0.694234i	$0.755743\pi$
$864$		0			0
$865$	−23.2767			−0.791433
$866$		0			0
$867$	−5.19302	−	8.99458i	−0.176364	−	0.305472i
$868$		0			0
$869$	6.79696	−	11.7727i	0.230571	−	0.399361i
$870$		0			0
$871$	43.8559	+	75.9607i	1.48600	+	2.57383i
$872$		0			0
$873$	21.8010	+	37.7605i	0.737852	+	1.27800i
$874$		0			0
$875$	0.678169	−	1.17462i	0.0229263	−	0.0397095i
$876$		0			0
$877$	28.5790			0.965044			0.482522	−	0.875884i	$-0.339721\pi$
$877$	28.5790			0.965044			0.482522	+	0.875884i	$0.339721\pi$
$878$		0			0
$879$	5.04959	+	8.74614i	0.170318	+	0.295000i
$880$		0			0
$881$	−2.54077	+	4.40074i	−0.0856006	+	0.148265i	−0.905647	−	0.424033i	$-0.860614\pi$
$881$	−2.54077	+	4.40074i	−0.0856006	+	0.148265i	0.820046	+	0.572297i	$0.193948\pi$
$882$		0			0
$883$	24.2768	−	42.0487i	0.816980	−	1.41505i	−0.0909177	−	0.995858i	$-0.528980\pi$
$883$	24.2768	−	42.0487i	0.816980	−	1.41505i	0.907898	−	0.419192i	$-0.137687\pi$
$884$		0			0
$885$	1.57419	−	2.72657i	0.0529158	−	0.0916528i
$886$		0			0
$887$	8.99351			0.301973			0.150986	−	0.988536i	$-0.451755\pi$
$887$	8.99351			0.301973			0.150986	+	0.988536i	$0.451755\pi$
$888$		0			0
$889$	−19.0461			−0.638785
$890$		0			0
$891$	7.86925	−	13.6299i	0.263630	−	0.456620i
$892$		0			0
$893$	−33.3744	+	57.8062i	−1.11683	+	1.93441i
$894$		0			0
$895$	−3.76632	+	6.52346i	−0.125894	+	0.218055i
$896$		0			0
$897$	−0.980340	−	1.69800i	−0.0327326	−	0.0566945i
$898$		0			0
$899$	12.2248			0.407718
$900$		0			0
$901$	−39.1322	+	67.7790i	−1.30368	+	2.25805i
$902$		0			0
$903$	2.71055	+	4.69480i	0.0902013	+	0.156233i
$904$		0			0
$905$	−1.96924	−	3.41082i	−0.0654597	−	0.113380i
$906$		0			0
$907$	13.0674	−	22.6334i	0.433896	−	0.751529i	−0.563309	−	0.826246i	$-0.690472\pi$
$907$	13.0674	−	22.6334i	0.433896	−	0.751529i	0.997205	+	0.0747170i	$0.0238053\pi$
$908$		0			0
$909$	2.08505	+	3.61141i	0.0691567	+	0.119783i
$910$		0			0
$911$	−36.3860			−1.20552			−0.602760	−	0.797922i	$-0.705933\pi$
$911$	−36.3860			−1.20552			−0.602760	+	0.797922i	$0.705933\pi$
$912$		0			0
$913$	−10.7338	−	18.5915i	−0.355238	−	0.615290i
$914$		0			0
$915$	−2.08454			−0.0689127
$916$		0			0
$917$	5.57716			0.184174
$918$		0			0
$919$	53.2591			1.75686			0.878429	−	0.477874i	$-0.158592\pi$
$919$	53.2591			1.75686			0.878429	+	0.477874i	$0.158592\pi$
$920$		0			0
$921$	3.70576	−	6.41856i	0.122109	−	0.211499i
$922$		0			0
$923$	4.39093	+	7.60531i	0.144529	+	0.250332i
$924$		0			0
$925$	4.83237	+	3.69435i	0.158887	+	0.121469i
$926$		0			0
$927$	−3.57519	−	6.19242i	−0.117425	−	0.203386i
$928$		0			0
$929$	9.31870	−	16.1405i	0.305736	−	0.529551i	−0.671689	−	0.740834i	$-0.734431\pi$
$929$	9.31870	−	16.1405i	0.305736	−	0.529551i	0.977425	+	0.211283i	$0.0677640\pi$
$930$		0			0
$931$	−25.9306			−0.849843
$932$		0			0
$933$	18.1562			0.594407
$934$		0			0
$935$	−15.9105			−0.520328
$936$		0			0
$937$	−4.14033	−	7.17126i	−0.135259	−	0.234275i	0.790438	−	0.612543i	$-0.209853\pi$
$937$	−4.14033	−	7.17126i	−0.135259	−	0.234275i	−0.925696	+	0.378268i	$0.876520\pi$
$938$		0			0
$939$	−1.70683			−0.0557002
$940$		0			0
$941$	−16.8458	−	29.1778i	−0.549157	−	0.951168i	−0.998333	−	0.0577242i	$-0.981616\pi$
$941$	−16.8458	−	29.1778i	−0.549157	−	0.951168i	0.449176	−	0.893443i	$-0.351718\pi$
$942$		0			0
$943$	0.621143	−	1.07585i	0.0202272	−	0.0350345i
$944$		0			0
$945$	−2.33647	−	4.04689i	−0.0760054	−	0.131645i
$946$		0			0
$947$	−17.1443	−	29.6948i	−0.557115	−	0.964951i	−0.997736	−	0.0672579i	$-0.978575\pi$
$947$	−17.1443	−	29.6948i	−0.557115	−	0.964951i	0.440621	−	0.897693i	$-0.354758\pi$
$948$		0			0
$949$	16.2652	−	28.1722i	0.527992	−	0.914509i
$950$		0			0
$951$	−11.1632			−0.361991
$952$		0			0
$953$	−20.5729	−	35.6333i	−0.666422	−	1.15428i	−0.978898	−	0.204351i	$-0.934492\pi$
$953$	−20.5729	−	35.6333i	−0.666422	−	1.15428i	0.312476	−	0.949926i	$-0.398842\pi$
$954$		0			0
$955$	−0.259008	+	0.448615i	−0.00838130	+	0.0145168i
$956$		0			0
$957$	1.52638	−	2.64377i	0.0493408	−	0.0854608i
$958$		0			0
$959$	−11.0978	+	19.2219i	−0.358366	+	0.620708i
$960$		0			0
$961$	13.8501			0.446777
$962$		0			0
$963$	28.8072			0.928299
$964$		0			0
$965$	−7.38834	+	12.7970i	−0.237839	+	0.411950i
$966$		0			0
$967$	6.83966	−	11.8466i	0.219949	−	0.380962i	−0.734843	−	0.678237i	$-0.762744\pi$
$967$	6.83966	−	11.8466i	0.219949	−	0.380962i	0.954792	+	0.297275i	$0.0960777\pi$
$968$		0			0
$969$	8.96766	−	15.5324i	0.288083	−	0.498974i
$970$		0			0
$971$	10.6780	+	18.4949i	0.342674	+	0.593529i	0.984928	−	0.172963i	$-0.0553341\pi$
$971$	10.6780	+	18.4949i	0.342674	+	0.593529i	−0.642254	+	0.766491i	$0.722001\pi$
$972$		0			0
$973$	−26.9550			−0.864137
$974$		0			0
$975$	1.90456	−	3.29880i	0.0609949	−	0.105646i
$976$		0			0
$977$	−23.5224	−	40.7419i	−0.752547	−	1.30345i	−0.946585	−	0.322455i	$-0.895492\pi$
$977$	−23.5224	−	40.7419i	−0.752547	−	1.30345i	0.194038	−	0.980994i	$-0.437842\pi$
$978$		0			0
$979$	18.8228	+	32.6020i	0.601579	+	1.04197i
$980$		0			0
$981$	17.2313	−	29.8455i	0.550154	−	0.952895i
$982$		0			0
$983$	−3.44977	−	5.97518i	−0.110031	−	0.190579i	0.805752	−	0.592253i	$-0.201762\pi$
$983$	−3.44977	−	5.97518i	−0.110031	−	0.190579i	−0.915782	+	0.401675i	$0.868428\pi$
$984$		0			0
$985$	−10.7475			−0.342443
$986$		0			0
$987$	−5.51772	−	9.55698i	−0.175631	−	0.304202i
$988$		0			0
$989$	3.35883			0.106804
$990$		0			0
$991$	−44.9203			−1.42694			−0.713470	−	0.700686i	$-0.752877\pi$
$991$	−44.9203			−1.42694			−0.713470	+	0.700686i	$0.752877\pi$
$992$		0			0
$993$	20.1006			0.637873
$994$		0			0
$995$	0.198509	−	0.343828i	0.00629316	−	0.0109001i
$996$		0			0
$997$	−1.80908	−	3.13341i	−0.0572941	−	0.0992362i	0.835956	−	0.548797i	$-0.184914\pi$
$997$	−1.80908	−	3.13341i	−0.0572941	−	0.0992362i	−0.893250	+	0.449561i	$0.851581\pi$
$998$		0			0
$999$	19.3472	−	8.05426i	0.612117	−	0.254825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1480.2.q.b.1321.4	yes	18
37.10	even	3	inner	1480.2.q.b.121.4	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1480.2.q.b.121.4	✓	18	37.10	even	3	inner
1480.2.q.b.1321.4	yes	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1480 = 2^{3} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1480.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.306255 + 0.530449i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.678169 + 1.17462i) q^{7} +(1.31242 + 2.27317i) q^{9} -2.73037 q^{11} +(3.10944 - 5.38571i) q^{13} +(0.306255 + 0.530449i) q^{15} +(2.91361 + 5.04652i) q^{17} +(-2.51249 + 4.35176i) q^{19} +(-0.415385 - 0.719468i) q^{21} -0.514732 q^{23} +(-0.500000 - 0.866025i) q^{25} -3.44526 q^{27} +1.82540 q^{29} +6.69702 q^{31} +(0.836188 - 1.44832i) q^{33} +(0.678169 + 1.17462i) q^{35} +(-5.61559 + 2.33778i) q^{37} +(1.90456 + 3.29880i) q^{39} +(-1.20673 + 2.09012i) q^{41} -6.52538 q^{43} +2.62483 q^{45} +13.2834 q^{47} +(2.58017 + 4.46899i) q^{49} -3.56923 q^{51} +(6.71541 + 11.6314i) q^{53} +(-1.36518 + 2.36457i) q^{55} +(-1.53892 - 2.66550i) q^{57} +(-2.57006 - 4.45148i) q^{59} +(-1.70164 + 2.94732i) q^{61} -3.56016 q^{63} +(-3.10944 - 5.38571i) q^{65} +(-7.05205 + 12.2145i) q^{67} +(0.157639 - 0.273039i) q^{69} +(-0.706064 + 1.22294i) q^{71} +5.23092 q^{73} +0.612510 q^{75} +(1.85165 - 3.20715i) q^{77} +(-2.48939 + 4.31175i) q^{79} +(-2.88212 + 4.99198i) q^{81} +(3.93127 + 6.80917i) q^{83} +5.82722 q^{85} +(-0.559038 + 0.968282i) q^{87} +(-6.89387 - 11.9405i) q^{89} +(4.21746 + 7.30485i) q^{91} +(-2.05099 + 3.55243i) q^{93} +(2.51249 + 4.35176i) q^{95} +16.6114 q^{97} +(-3.58338 - 6.20659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{3} + 9 q^{5} - 5 q^{9} - 6 q^{11} + 2 q^{13} - 2 q^{15} + q^{17} - 5 q^{21} + 12 q^{23} - 9 q^{25} - 10 q^{27} - 20 q^{29} + 28 q^{31} + 11 q^{33} - 5 q^{39} - 5 q^{41} + 2 q^{43} - 10 q^{45}+ \cdots + 30 q^{99}+O(q^{100}) \) 18 * q + 2 * q^3 + 9 * q^5 - 5 * q^9 - 6 * q^11 + 2 * q^13 - 2 * q^15 + q^17 - 5 * q^21 + 12 * q^23 - 9 * q^25 - 10 * q^27 - 20 * q^29 + 28 * q^31 + 11 * q^33 - 5 * q^39 - 5 * q^41 + 2 * q^43 - 10 * q^45 - 36 * q^47 + 7 * q^49 - 2 * q^51 - 10 * q^53 - 3 * q^55 + 22 * q^57 - 10 * q^59 + 16 * q^61 + 42 * q^63 - 2 * q^65 - 4 * q^67 - 13 * q^69 + 17 * q^71 + 56 * q^73 - 4 * q^75 + 43 * q^77 - 23 * q^79 - 17 * q^81 + 29 * q^83 + 2 * q^85 - q^87 - 16 * q^89 - 4 * q^91 + 5 * q^93 + 26 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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