LMFDB - Embedded newform 65.3.h.a.12.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,3,Mod(12,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("65.12");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	65.h (of order $4$, degree $2$, 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:	$1.77112171834$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.7
Character	$\chi$	$=$	65.12
Dual form			65.3.h.a.38.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456148 - 0.456148i) q^{2} +(3.37817 - 3.37817i) q^{3} +3.58386i q^{4} +(0.779969 - 4.93879i) q^{5} -3.08189i q^{6} +(-7.82065 + 7.82065i) q^{7} +(3.45936 + 3.45936i) q^{8} -13.8241i q^{9} +O(q^{10})$	\(q+(0.456148 - 0.456148i) q^{2} +(3.37817 - 3.37817i) q^{3} +3.58386i q^{4} +(0.779969 - 4.93879i) q^{5} -3.08189i q^{6} +(-7.82065 + 7.82065i) q^{7} +(3.45936 + 3.45936i) q^{8} -13.8241i q^{9} +(-1.89704 - 2.60860i) q^{10} -7.57734i q^{11} +(12.1069 + 12.1069i) q^{12} +(4.80245 + 12.0804i) q^{13} +7.13475i q^{14} +(-14.0492 - 19.3190i) q^{15} -11.1795 q^{16} +(1.84467 + 1.84467i) q^{17} +(-6.30583 - 6.30583i) q^{18} +7.21489 q^{19} +(17.6999 + 2.79530i) q^{20} +52.8390i q^{21} +(-3.45639 - 3.45639i) q^{22} +(-21.0863 + 21.0863i) q^{23} +23.3726 q^{24} +(-23.7833 - 7.70421i) q^{25} +(7.70109 + 3.31983i) q^{26} +(-16.2966 - 16.2966i) q^{27} +(-28.0281 - 28.0281i) q^{28} -22.4617i q^{29} +(-15.2208 - 2.40378i) q^{30} +5.43547i q^{31} +(-18.9369 + 18.9369i) q^{32} +(-25.5976 - 25.5976i) q^{33} +1.68288 q^{34} +(32.5247 + 44.7244i) q^{35} +49.5436 q^{36} +(11.3552 - 11.3552i) q^{37} +(3.29106 - 3.29106i) q^{38} +(57.0332 + 24.5862i) q^{39} +(19.7833 - 14.3869i) q^{40} -33.5196i q^{41} +(24.1024 + 24.1024i) q^{42} +(52.4341 - 52.4341i) q^{43} +27.1561 q^{44} +(-68.2743 - 10.7824i) q^{45} +19.2370i q^{46} +(11.2319 - 11.2319i) q^{47} +(-37.7662 + 37.7662i) q^{48} -73.3253i q^{49} +(-14.3630 + 7.33444i) q^{50} +12.4632 q^{51} +(-43.2945 + 17.2113i) q^{52} +(-0.512386 + 0.512386i) q^{53} -14.8673 q^{54} +(-37.4229 - 5.91010i) q^{55} -54.1090 q^{56} +(24.3731 - 24.3731i) q^{57} +(-10.2459 - 10.2459i) q^{58} -66.4939 q^{59} +(69.2364 - 50.3504i) q^{60} +16.2641 q^{61} +(2.47938 + 2.47938i) q^{62} +(108.113 + 108.113i) q^{63} -27.4418i q^{64} +(63.4084 - 14.2960i) q^{65} -23.3526 q^{66} +(-74.5577 + 74.5577i) q^{67} +(-6.61103 + 6.61103i) q^{68} +142.466i q^{69} +(35.2370 + 5.56489i) q^{70} -86.4528i q^{71} +(47.8225 - 47.8225i) q^{72} +(-68.6714 - 68.6714i) q^{73} -10.3593i q^{74} +(-106.370 + 54.3179i) q^{75} +25.8571i q^{76} +(59.2598 + 59.2598i) q^{77} +(37.2305 - 14.8006i) q^{78} +42.6810i q^{79} +(-8.71964 + 55.2131i) q^{80} +14.3114 q^{81} +(-15.2899 - 15.2899i) q^{82} +(94.0145 + 94.0145i) q^{83} -189.368 q^{84} +(10.5492 - 7.67164i) q^{85} -47.8354i q^{86} +(-75.8796 - 75.8796i) q^{87} +(26.2128 - 26.2128i) q^{88} +87.2716 q^{89} +(-36.0615 + 26.2248i) q^{90} +(-132.035 - 56.9184i) q^{91} +(-75.5703 - 75.5703i) q^{92} +(18.3620 + 18.3620i) q^{93} -10.2468i q^{94} +(5.62739 - 35.6328i) q^{95} +127.944i q^{96} +(24.9295 - 24.9295i) q^{97} +(-33.4472 - 33.4472i) q^{98} -104.750 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3}+O(q^{10}) $ 24 * q - 4 * q^3	$ 24 q - 4 q^{3} + 16 q^{10} + 72 q^{12} - 36 q^{13} - 104 q^{16} - 48 q^{17} + 8 q^{22} - 104 q^{23} - 88 q^{25} + 88 q^{26} + 56 q^{27} - 24 q^{30} - 64 q^{35} + 256 q^{36} + 124 q^{38} - 368 q^{40} + 216 q^{42} + 8 q^{43} + 196 q^{48} - 296 q^{51} + 16 q^{52} + 220 q^{53} + 332 q^{55} + 584 q^{56} - 8 q^{61} - 596 q^{62} + 420 q^{65} - 360 q^{66} - 640 q^{68} - 184 q^{75} + 388 q^{77} - 636 q^{78} - 224 q^{81} - 1004 q^{82} - 52 q^{87} + 780 q^{88} + 452 q^{90} - 512 q^{91} + 812 q^{92} - 136 q^{95}+O(q^{100}) $ 24 * q - 4 * q^3 + 16 * q^10 + 72 * q^12 - 36 * q^13 - 104 * q^16 - 48 * q^17 + 8 * q^22 - 104 * q^23 - 88 * q^25 + 88 * q^26 + 56 * q^27 - 24 * q^30 - 64 * q^35 + 256 * q^36 + 124 * q^38 - 368 * q^40 + 216 * q^42 + 8 * q^43 + 196 * q^48 - 296 * q^51 + 16 * q^52 + 220 * q^53 + 332 * q^55 + 584 * q^56 - 8 * q^61 - 596 * q^62 + 420 * q^65 - 360 * q^66 - 640 * q^68 - 184 * q^75 + 388 * q^77 - 636 * q^78 - 224 * q^81 - 1004 * q^82 - 52 * q^87 + 780 * q^88 + 452 * q^90 - 512 * q^91 + 812 * q^92 - 136 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.456148	−	0.456148i	0.228074	−	0.228074i	−0.583814	−	0.811888i	$-0.698440\pi$
$2$	0.456148	−	0.456148i	0.228074	−	0.228074i	0.811888	+	0.583814i	$0.198440\pi$
$3$	3.37817	−	3.37817i	1.12606	−	1.12606i	0.135245	−	0.990812i	$-0.456818\pi$
$3$	3.37817	−	3.37817i	1.12606	−	1.12606i	0.990812	−	0.135245i	$-0.0431822\pi$
$4$			3.58386i			0.895964i
$5$	0.779969	−	4.93879i	0.155994	−	0.987758i
$5$	0.779969	−	4.93879i	0.155994	−	0.987758i
$6$		−	3.08189i		−	0.513649i
$7$	−7.82065	+	7.82065i	−1.11724	+	1.11724i	−0.125091	+	0.992145i	$0.539922\pi$
$7$	−7.82065	+	7.82065i	−1.11724	+	1.11724i	−0.992145	+	0.125091i	$0.960078\pi$
$8$	3.45936	+	3.45936i	0.432420	+	0.432420i
$9$		−	13.8241i		−	1.53601i
$10$	−1.89704	−	2.60860i	−0.189704	−	0.260860i
$11$		−	7.57734i		−	0.688849i	−0.938814	−	0.344425i	$-0.888074\pi$
$11$		−	7.57734i		−	0.688849i	0.938814	−	0.344425i	$-0.111926\pi$
$12$	12.1069	+	12.1069i	1.00891	+	1.00891i
$13$	4.80245	+	12.0804i	0.369420	+	0.929263i
$13$	4.80245	+	12.0804i	0.369420	+	0.929263i
$14$			7.13475i			0.509625i
$15$	−14.0492	−	19.3190i	−0.936614	−	1.28793i
$16$	−11.1795			−0.698717
$17$	1.84467	+	1.84467i	0.108510	+	0.108510i	0.759277	−	0.650767i	$-0.225553\pi$
$17$	1.84467	+	1.84467i	0.108510	+	0.108510i	−0.650767	+	0.759277i	$0.725553\pi$
$18$	−6.30583	−	6.30583i	−0.350324	−	0.350324i
$19$	7.21489			0.379731			0.189866	−	0.981810i	$-0.439195\pi$
$19$	7.21489			0.379731			0.189866	+	0.981810i	$0.439195\pi$
$20$	17.6999	+	2.79530i	0.884996	+	0.139765i
$21$			52.8390i			2.51614i
$22$	−3.45639	−	3.45639i	−0.157109	−	0.157109i
$23$	−21.0863	+	21.0863i	−0.916796	+	0.916796i	−0.996795	−	0.0799990i	$-0.974508\pi$
$23$	−21.0863	+	21.0863i	−0.916796	+	0.916796i	0.0799990	+	0.996795i	$0.474508\pi$
$24$	23.3726			0.973860
$25$	−23.7833	−	7.70421i	−0.951332	−	0.308168i
$26$	7.70109	+	3.31983i	0.296196	+	0.127686i
$27$	−16.2966	−	16.2966i	−0.603578	−	0.603578i
$28$	−28.0281	−	28.0281i	−1.00100	−	1.00100i
$29$		−	22.4617i		−	0.774542i	−0.921966	−	0.387271i	$-0.873418\pi$
$29$		−	22.4617i		−	0.774542i	0.921966	−	0.387271i	$-0.126582\pi$
$30$	−15.2208	−	2.40378i	−0.507361	−	0.0801261i
$31$			5.43547i			0.175338i	0.996150	+	0.0876689i	$0.0279418\pi$
$31$			5.43547i			0.175338i	−0.996150	+	0.0876689i	$0.972058\pi$
$32$	−18.9369	+	18.9369i	−0.591779	+	0.591779i
$33$	−25.5976	−	25.5976i	−0.775684	−	0.775684i
$34$	1.68288			0.0494965
$35$	32.5247	+	44.7244i	0.929277	+	1.27784i
$36$	49.5436			1.37621
$37$	11.3552	−	11.3552i	0.306898	−	0.306898i	−0.536807	−	0.843705i	$-0.680370\pi$
$37$	11.3552	−	11.3552i	0.306898	−	0.306898i	0.843705	+	0.536807i	$0.180370\pi$
$38$	3.29106	−	3.29106i	0.0866068	−	0.0866068i
$39$	57.0332	+	24.5862i	1.46239	+	0.630415i
$40$	19.7833	−	14.3869i	0.494581	−	0.359672i
$41$		−	33.5196i		−	0.817551i	−0.912635	−	0.408775i	$-0.865956\pi$
$41$		−	33.5196i		−	0.817551i	0.912635	−	0.408775i	$-0.134044\pi$
$42$	24.1024	+	24.1024i	0.573867	+	0.573867i
$43$	52.4341	−	52.4341i	1.21940	−	1.21940i	0.251555	−	0.967843i	$-0.419058\pi$
$43$	52.4341	−	52.4341i	1.21940	−	1.21940i	0.967843	−	0.251555i	$-0.0809420\pi$
$44$	27.1561			0.617185
$45$	−68.2743	−	10.7824i	−1.51721	−	0.239608i
$46$			19.2370i			0.418195i
$47$	11.2319	−	11.2319i	0.238977	−	0.238977i	−0.577450	−	0.816426i	$-0.695952\pi$
$47$	11.2319	−	11.2319i	0.238977	−	0.238977i	0.816426	+	0.577450i	$0.195952\pi$
$48$	−37.7662	+	37.7662i	−0.786795	+	0.786795i
$49$		−	73.3253i		−	1.49643i
$50$	−14.3630	+	7.33444i	−0.287259	+	0.146689i
$51$	12.4632			0.244377
$52$	−43.2945	+	17.2113i	−0.832586	+	0.330987i
$53$	−0.512386	+	0.512386i	−0.00966767	+	0.00966767i	−0.711924	−	0.702256i	$-0.752176\pi$
$53$	−0.512386	+	0.512386i	−0.00966767	+	0.00966767i	0.702256	+	0.711924i	$0.252176\pi$
$54$	−14.8673			−0.275321
$55$	−37.4229	−	5.91010i	−0.680417	−	0.107456i
$56$	−54.1090			−0.966231
$57$	24.3731	−	24.3731i	0.427599	−	0.427599i
$58$	−10.2459	−	10.2459i	−0.176653	−	0.176653i
$59$	−66.4939			−1.12701			−0.563507	−	0.826111i	$-0.690548\pi$
$59$	−66.4939			−1.12701			−0.563507	+	0.826111i	$0.690548\pi$
$60$	69.2364	−	50.3504i	1.15394	−	0.839173i
$61$	16.2641			0.266625			0.133313	−	0.991074i	$-0.457439\pi$
$61$	16.2641			0.266625			0.133313	+	0.991074i	$0.457439\pi$
$62$	2.47938	+	2.47938i	0.0399900	+	0.0399900i
$63$	108.113	+	108.113i	1.71609	+	1.71609i
$64$		−	27.4418i		−	0.428778i
$65$	63.4084	−	14.2960i	0.975514	−	0.219938i
$66$	−23.3526			−0.353827
$67$	−74.5577	+	74.5577i	−1.11280	+	1.11280i	−0.120031	+	0.992770i	$0.538299\pi$
$67$	−74.5577	+	74.5577i	−1.11280	+	1.11280i	−0.992770	+	0.120031i	$0.961701\pi$
$68$	−6.61103	+	6.61103i	−0.0972210	+	0.0972210i
$69$			142.466i			2.06473i
$70$	35.2370	+	5.56489i	0.503386	+	0.0794984i
$71$		−	86.4528i		−	1.21765i	−0.793306	−	0.608823i	$-0.791642\pi$
$71$		−	86.4528i		−	1.21765i	0.793306	−	0.608823i	$-0.208358\pi$
$72$	47.8225	−	47.8225i	0.664202	−	0.664202i
$73$	−68.6714	−	68.6714i	−0.940704	−	0.940704i	0.0576338	−	0.998338i	$-0.481644\pi$
$73$	−68.6714	−	68.6714i	−0.940704	−	0.940704i	−0.998338	+	0.0576338i	$0.981644\pi$
$74$		−	10.3593i		−	0.139991i
$75$	−106.370	+	54.3179i	−1.41827	+	0.724239i
$76$			25.8571i			0.340226i
$77$	59.2598	+	59.2598i	0.769608	+	0.769608i
$78$	37.2305	−	14.8006i	0.477315	−	0.189752i
$79$			42.6810i			0.540266i	0.962823	+	0.270133i	$0.0870677\pi$
$79$			42.6810i			0.540266i	−0.962823	+	0.270133i	$0.912932\pi$
$80$	−8.71964	+	55.2131i	−0.108996	+	0.690163i
$81$	14.3114			0.176684
$82$	−15.2899	−	15.2899i	−0.186462	−	0.186462i
$83$	94.0145	+	94.0145i	1.13271	+	1.13271i	0.989726	+	0.142980i	$0.0456683\pi$
$83$	94.0145	+	94.0145i	1.13271	+	1.13271i	0.142980	+	0.989726i	$0.454332\pi$
$84$	−189.368			−2.25438
$85$	10.5492	−	7.67164i	0.124108	−	0.0902546i
$86$		−	47.8354i		−	0.556226i
$87$	−75.8796	−	75.8796i	−0.872179	−	0.872179i
$88$	26.2128	−	26.2128i	0.297872	−	0.297872i
$89$	87.2716			0.980580			0.490290	−	0.871559i	$-0.336891\pi$
$89$	87.2716			0.980580			0.490290	+	0.871559i	$0.336891\pi$
$90$	−36.0615	+	26.2248i	−0.400684	+	0.291387i
$91$	−132.035	−	56.9184i	−1.45094	−	0.625477i
$92$	−75.5703	−	75.5703i	−0.821417	−	0.821417i
$93$	18.3620	+	18.3620i	0.197440	+	0.197440i
$94$		−	10.2468i		−	0.109009i
$95$	5.62739	−	35.6328i	0.0592357	−	0.375082i
$96$			127.944i			1.33275i
$97$	24.9295	−	24.9295i	0.257005	−	0.257005i	−0.566830	−	0.823835i	$-0.691830\pi$
$97$	24.9295	−	24.9295i	0.257005	−	0.257005i	0.823835	+	0.566830i	$0.191830\pi$
$98$	−33.4472	−	33.4472i	−0.341298	−	0.341298i
$99$	−104.750			−1.05808
$100$	27.6108	−	85.2360i	0.276108	−	0.852360i
$101$	48.6932			0.482111			0.241055	−	0.970511i	$-0.422506\pi$
$101$	48.6932			0.482111			0.241055	+	0.970511i	$0.422506\pi$
$102$	5.68507	−	5.68507i	0.0557359	−	0.0557359i
$103$	−87.5857	+	87.5857i	−0.850347	+	0.850347i	−0.990176	−	0.139829i	$-0.955345\pi$
$103$	−87.5857	+	87.5857i	−0.850347	+	0.850347i	0.139829	+	0.990176i	$0.455345\pi$
$104$	−25.1771	+	58.4040i	−0.242088	+	0.561576i
$105$	260.961	+	41.2128i	2.48534	+	0.392503i
$106$			0.467448i			0.00440989i
$107$	56.0231	+	56.0231i	0.523580	+	0.523580i	0.918651	−	0.395071i	$-0.129280\pi$
$107$	56.0231	+	56.0231i	0.523580	+	0.523580i	−0.395071	+	0.918651i	$0.629280\pi$
$108$	58.4047	−	58.4047i	0.540784	−	0.540784i
$109$	32.7907			0.300832			0.150416	−	0.988623i	$-0.451939\pi$
$109$	32.7907			0.300832			0.150416	+	0.988623i	$0.451939\pi$
$110$	−19.7663	+	14.3745i	−0.179693	+	0.130677i
$111$		−	76.7198i		−	0.691170i
$112$	87.4308	−	87.4308i	0.780632	−	0.780632i
$113$	31.2390	−	31.2390i	0.276452	−	0.276452i	−0.555239	−	0.831691i	$-0.687373\pi$
$113$	31.2390	−	31.2390i	0.276452	−	0.276452i	0.831691	+	0.555239i	$0.187373\pi$
$114$		−	22.2355i		−	0.195048i
$115$	87.6942	+	120.588i	0.762558	+	1.04859i
$116$	80.4996			0.693962
$117$	167.001	−	66.3895i	1.42736	−	0.567432i
$118$	−30.3311	+	30.3311i	−0.257043	+	0.257043i
$119$	−28.8530			−0.242462
$120$	18.2299	−	115.433i	0.151916	−	0.961938i
$121$	63.5839			0.525486
$122$	7.41885	−	7.41885i	0.0608103	−	0.0608103i
$123$	−113.235	−	113.235i	−0.920609	−	0.920609i
$124$	−19.4800			−0.157096
$125$	−56.5997	+	111.452i	−0.452798	+	0.891613i
$126$	98.6314			0.782789
$127$	124.795	+	124.795i	0.982637	+	0.982637i	0.999852	−	0.0172152i	$-0.00548003\pi$
$127$	124.795	+	124.795i	0.982637	+	0.982637i	−0.0172152	+	0.999852i	$0.505480\pi$
$128$	−88.2653	−	88.2653i	−0.689572	−	0.689572i
$129$		−	354.263i		−	2.74622i
$130$	22.4025	−	35.4447i	0.172327	−	0.272651i
$131$	−192.378			−1.46853			−0.734266	−	0.678862i	$-0.762473\pi$
$131$	−192.378			−1.46853			−0.734266	+	0.678862i	$0.762473\pi$
$132$	91.7380	−	91.7380i	0.694985	−	0.694985i
$133$	−56.4252	+	56.4252i	−0.424249	+	0.424249i
$134$			68.0187i			0.507602i
$135$	−93.1963	+	67.7746i	−0.690343	+	0.502034i
$136$			12.7627i			0.0938437i
$137$	−127.457	+	127.457i	−0.930343	+	0.930343i	−0.997727	−	0.0673841i	$-0.978535\pi$
$137$	−127.457	+	127.457i	−0.930343	+	0.930343i	0.0673841	+	0.997727i	$0.478535\pi$
$138$	64.9857	+	64.9857i	0.470911	+	0.470911i
$139$			105.907i			0.761921i	0.924591	+	0.380960i	$0.124407\pi$
$139$			105.907i			0.761921i	−0.924591	+	0.380960i	$0.875593\pi$
$140$	−160.286	+	116.564i	−1.14490	+	0.832599i
$141$		−	75.8866i		−	0.538203i
$142$	−39.4353	−	39.4353i	−0.277713	−	0.277713i
$143$	91.5375	−	36.3898i	0.640122	−	0.254474i
$144$			154.546i			1.07324i
$145$	−110.934	−	17.5195i	−0.765060	−	0.120824i
$146$	−62.6486			−0.429100
$147$	−247.705	−	247.705i	−1.68507	−	1.68507i
$148$	40.6955	+	40.6955i	0.274970	+	0.274970i
$149$	147.882			0.992496			0.496248	−	0.868181i	$-0.334711\pi$
$149$	147.882			0.992496			0.496248	+	0.868181i	$0.334711\pi$
$150$	−23.7435	+	73.2976i	−0.158290	+	0.488650i
$151$			69.6030i			0.460947i	0.973079	+	0.230474i	$0.0740275\pi$
$151$			69.6030i			0.460947i	−0.973079	+	0.230474i	$0.925972\pi$
$152$	24.9589	+	24.9589i	0.164203	+	0.164203i
$153$	25.5008	−	25.5008i	0.166672	−	0.166672i
$154$	54.0625			0.351055
$155$	26.8447	+	4.23950i	0.173191	+	0.0273516i
$156$	−88.1135	+	204.399i	−0.564830	+	1.31025i
$157$	−65.3787	−	65.3787i	−0.416425	−	0.416425i	0.467545	−	0.883969i	$-0.345139\pi$
$157$	−65.3787	−	65.3787i	−0.416425	−	0.416425i	−0.883969	+	0.467545i	$0.845139\pi$
$158$	19.4689	+	19.4689i	0.123221	+	0.123221i
$159$			3.46186i			0.0217727i
$160$	78.7553	+	108.296i	0.492221	+	0.676849i
$161$		−	329.817i		−	2.04856i
$162$	6.52812	−	6.52812i	0.0402970	−	0.0402970i
$163$	80.3597	+	80.3597i	0.493004	+	0.493004i	0.909251	−	0.416247i	$-0.136655\pi$
$163$	80.3597	+	80.3597i	0.493004	+	0.493004i	−0.416247	+	0.909251i	$0.636655\pi$
$164$	120.129			0.732496
$165$	−146.386	+	106.456i	−0.887190	+	0.645186i
$166$	85.7691			0.516681
$167$	−54.8540	+	54.8540i	−0.328467	+	0.328467i	−0.852003	−	0.523536i	$-0.824612\pi$
$167$	−54.8540	+	54.8540i	−0.328467	+	0.328467i	0.523536	+	0.852003i	$0.324612\pi$
$168$	−182.789	+	182.789i	−1.08803	+	1.08803i
$169$	−122.873	+	116.031i	−0.727058	+	0.686576i
$170$	1.31260	−	8.31140i	0.00772116	−	0.0488906i
$171$		−	99.7393i		−	0.583271i
$172$	187.916	+	187.916i	1.09254	+	1.09254i
$173$	63.2129	−	63.2129i	0.365392	−	0.365392i	−0.500401	−	0.865794i	$-0.666814\pi$
$173$	63.2129	−	63.2129i	0.365392	−	0.365392i	0.865794	+	0.500401i	$0.166814\pi$
$174$	−69.2246			−0.397843
$175$	246.253	−	125.749i	1.40716	−	0.718566i
$176$			84.7107i			0.481311i
$177$	−224.628	+	224.628i	−1.26908	+	1.26908i
$178$	39.8088	−	39.8088i	0.223645	−	0.223645i
$179$		−	170.972i		−	0.955152i	−0.878590	−	0.477576i	$-0.841515\pi$
$179$		−	170.972i		−	0.955152i	0.878590	−	0.477576i	$-0.158485\pi$
$180$	38.6425	−	244.685i	0.214680	−	1.35936i
$181$	−3.68218			−0.0203436			−0.0101718	−	0.999948i	$-0.503238\pi$
$181$	−3.68218			−0.0203436			−0.0101718	+	0.999948i	$0.503238\pi$
$182$	−86.1908	+	34.2643i	−0.473576	+	0.188265i
$183$	54.9430	−	54.9430i	0.300235	−	0.300235i
$184$	−145.890			−0.792882
$185$	−47.2244	−	64.9378i	−0.255267	−	0.351015i
$186$	16.7515			0.0900621
$187$	13.9777	−	13.9777i	0.0747469	−	0.0747469i
$188$	40.2535	+	40.2535i	0.214115	+	0.214115i
$189$	254.900			1.34868
$190$	−13.6869	−	18.8208i	−0.0720364	−	0.0990567i
$191$	−171.961			−0.900322			−0.450161	−	0.892948i	$-0.648633\pi$
$191$	−171.961			−0.900322			−0.450161	+	0.892948i	$0.648633\pi$
$192$	−92.7030	−	92.7030i	−0.482828	−	0.482828i
$193$	−55.0283	−	55.0283i	−0.285121	−	0.285121i	0.550026	−	0.835147i	$-0.314618\pi$
$193$	−55.0283	−	55.0283i	−0.285121	−	0.285121i	−0.835147	+	0.550026i	$0.814618\pi$
$194$		−	22.7431i		−	0.117232i
$195$	165.910	−	262.499i	0.850822	−	1.34615i
$196$	262.787			1.34075
$197$	15.0294	−	15.0294i	0.0762915	−	0.0762915i	−0.667931	−	0.744223i	$-0.732820\pi$
$197$	15.0294	−	15.0294i	0.0762915	−	0.0762915i	0.744223	+	0.667931i	$0.232820\pi$
$198$	−47.7814	+	47.7814i	−0.241320	+	0.241320i
$199$			152.409i			0.765874i	0.923774	+	0.382937i	$0.125087\pi$
$199$			152.409i			0.765874i	−0.923774	+	0.382937i	$0.874913\pi$
$200$	−55.6234	−	108.927i	−0.278117	−	0.544633i
$201$			503.737i			2.50615i
$202$	22.2113	−	22.2113i	0.109957	−	0.109957i
$203$	175.665	+	175.665i	0.865347	+	0.865347i
$204$			44.6664i			0.218953i
$205$	−165.546	−	26.1442i	−0.807542	−	0.127533i
$206$			79.9041i			0.387884i
$207$	291.499	+	291.499i	1.40821	+	1.40821i
$208$	−53.6889	−	135.053i	−0.258120	−	0.649292i
$209$		−	54.6697i		−	0.261578i
$210$	137.836	−	100.238i	0.656362	−	0.477322i
$211$	−18.8291			−0.0892374			−0.0446187	−	0.999004i	$-0.514207\pi$
$211$	−18.8291			−0.0892374			−0.0446187	+	0.999004i	$0.514207\pi$
$212$	−1.83632	−	1.83632i	−0.00866189	−	0.00866189i
$213$	−292.052	−	292.052i	−1.37114	−	1.37114i
$214$	51.1096			0.238830
$215$	−218.064	−	299.858i	−1.01425	−	1.39469i
$216$		−	112.752i		−	0.521998i
$217$	−42.5090	−	42.5090i	−0.195894	−	0.195894i
$218$	14.9574	−	14.9574i	0.0686121	−	0.0686121i
$219$	−463.968			−2.11857
$220$	21.1809	−	134.118i	0.0962770	−	0.609629i
$221$	−13.4254	+	31.1433i	−0.0607485	+	0.140920i
$222$	−34.9956	−	34.9956i	−0.157638	−	0.157638i
$223$	−37.8603	−	37.8603i	−0.169777	−	0.169777i	0.617104	−	0.786881i	$-0.288306\pi$
$223$	−37.8603	−	37.8603i	−0.169777	−	0.169777i	−0.786881	+	0.617104i	$0.788306\pi$
$224$		−	296.199i		−	1.32231i
$225$	−106.504	+	328.782i	−0.473350	+	1.46125i
$226$		−	28.4993i		−	0.126103i
$227$	−60.9936	+	60.9936i	−0.268694	+	0.268694i	−0.828574	−	0.559880i	$-0.810847\pi$
$227$	−60.9936	+	60.9936i	−0.268694	+	0.268694i	0.559880	+	0.828574i	$0.310847\pi$
$228$	87.3499	+	87.3499i	0.383113	+	0.383113i
$229$	185.665			0.810766			0.405383	−	0.914147i	$-0.367138\pi$
$229$	185.665			0.810766			0.405383	+	0.914147i	$0.367138\pi$
$230$	95.0073	+	15.0042i	0.413075	+	0.0652358i
$231$	400.379			1.73324
$232$	77.7032	−	77.7032i	0.334928	−	0.334928i
$233$	82.8081	−	82.8081i	0.355400	−	0.355400i	−0.506714	−	0.862114i	$-0.669140\pi$
$233$	82.8081	−	82.8081i	0.355400	−	0.355400i	0.862114	+	0.506714i	$0.169140\pi$
$234$	45.8936	−	106.461i	0.196126	−	0.454959i
$235$	−46.7115	−	64.2326i	−0.198772	−	0.273330i
$236$		−	238.305i		−	1.00977i
$237$	144.184	+	144.184i	0.608370	+	0.608370i
$238$	−13.1612	+	13.1612i	−0.0552993	+	0.0552993i
$239$	189.191			0.791595			0.395797	−	0.918338i	$-0.370468\pi$
$239$	189.191			0.791595			0.395797	+	0.918338i	$0.370468\pi$
$240$	157.063	+	215.976i	0.654428	+	0.899898i
$241$		−	12.7392i		−	0.0528600i	−0.999651	−	0.0264300i	$-0.991586\pi$
$241$		−	12.7392i		−	0.0528600i	0.999651	−	0.0264300i	$-0.00841390\pi$
$242$	29.0037	−	29.0037i	0.119850	−	0.119850i
$243$	195.016	−	195.016i	0.802534	−	0.802534i
$244$			58.2883i			0.238887i
$245$	−362.138	−	57.1915i	−1.47811	−	0.233435i
$246$	−103.304			−0.419934
$247$	34.6492	+	87.1589i	0.140280	+	0.352870i
$248$	−18.8033	+	18.8033i	−0.0758196	+	0.0758196i
$249$	635.194			2.55098
$250$	25.0206	+	76.6563i	0.100082	+	0.306625i
$251$	358.566			1.42855			0.714276	−	0.699864i	$-0.246756\pi$
$251$	358.566			1.42855			0.714276	+	0.699864i	$0.246756\pi$
$252$	−387.463	+	387.463i	−1.53755	+	1.53755i
$253$	159.778	+	159.778i	0.631534	+	0.631534i
$254$	113.850			0.448228
$255$	9.72092	−	61.5532i	0.0381212	−	0.241385i
$256$	29.2431			0.114231
$257$	−245.600	−	245.600i	−0.955643	−	0.955643i	0.0434143	−	0.999057i	$-0.486176\pi$
$257$	−245.600	−	245.600i	−0.955643	−	0.955643i	−0.999057	+	0.0434143i	$0.986176\pi$
$258$	−161.596	−	161.596i	−0.626342	−	0.626342i
$259$			177.611i			0.685755i
$260$	51.2347	+	227.247i	0.197056	+	0.874026i
$261$	−310.513			−1.18970
$262$	−87.7527	+	87.7527i	−0.334934	+	0.334934i
$263$	−166.401	+	166.401i	−0.632705	+	0.632705i	−0.948746	−	0.316041i	$-0.897646\pi$
$263$	−166.401	+	166.401i	−0.632705	+	0.632705i	0.316041	+	0.948746i	$0.397646\pi$
$264$		−	177.103i		−	0.670843i
$265$	2.13092	+	2.93021i	0.00804122	+	0.0110574i
$266$			51.4765i			0.193521i
$267$	294.819	−	294.819i	1.10419	−	1.10419i
$268$	−267.204	−	267.204i	−0.997030	−	0.997030i
$269$		−	150.267i		−	0.558615i	−0.960202	−	0.279307i	$-0.909895\pi$
$269$		−	150.267i		−	0.558615i	0.960202	−	0.279307i	$-0.0901048\pi$
$270$	−11.5961	+	73.4266i	−0.0429483	+	0.271950i
$271$			320.331i			1.18203i	0.806659	+	0.591017i	$0.201273\pi$
$271$			320.331i			1.18203i	−0.806659	+	0.591017i	$0.798727\pi$
$272$	−20.6224	−	20.6224i	−0.0758176	−	0.0758176i
$273$	−638.317	+	253.757i	−2.33816	+	0.929513i
$274$			116.279i			0.424374i
$275$	−58.3775	+	180.214i	−0.212282	+	0.655324i
$276$	−510.579			−1.84992
$277$	−273.259	−	273.259i	−0.986494	−	0.986494i	0.0134156	−	0.999910i	$-0.495730\pi$
$277$	−273.259	−	273.259i	−0.986494	−	0.986494i	−0.999910	+	0.0134156i	$0.995730\pi$
$278$	48.3093	+	48.3093i	0.173774	+	0.173774i
$279$	75.1404			0.269321
$280$	−42.2033	+	267.233i	−0.150726	+	0.954403i
$281$		−	56.5121i		−	0.201111i	−0.994931	−	0.100555i	$-0.967938\pi$
$281$		−	56.5121i		−	0.201111i	0.994931	−	0.100555i	$-0.0320620\pi$
$282$	−34.6155	−	34.6155i	−0.122750	−	0.122750i
$283$	−99.9405	+	99.9405i	−0.353147	+	0.353147i	−0.861279	−	0.508132i	$-0.830336\pi$
$283$	−99.9405	+	99.9405i	−0.353147	+	0.353147i	0.508132	+	0.861279i	$0.330336\pi$
$284$	309.835			1.09097
$285$	−101.364	−	139.384i	−0.355661	−	0.489067i
$286$	25.1555	−	58.3538i	0.0879562	−	0.204034i
$287$	262.145	+	262.145i	0.913397	+	0.913397i
$288$	261.786	+	261.786i	0.908979	+	0.908979i
$289$		−	282.194i		−	0.976451i
$290$	−58.5937	+	42.6107i	−0.202047	+	0.146934i
$291$		−	168.432i		−	0.578805i
$292$	246.109	−	246.109i	0.842837	−	0.842837i
$293$	39.4381	+	39.4381i	0.134601	+	0.134601i	0.771197	−	0.636596i	$-0.219658\pi$
$293$	39.4381	+	39.4381i	0.134601	+	0.134601i	−0.636596	+	0.771197i	$0.719658\pi$
$294$	−225.981			−0.768642
$295$	−51.8632	+	328.399i	−0.175807	+	1.11322i
$296$	78.5637			0.265418
$297$	−123.485	+	123.485i	−0.415774	+	0.415774i
$298$	67.4560	−	67.4560i	0.226363	−	0.226363i
$299$	−355.997	−	153.465i	−1.19063	−	0.513262i
$300$	−194.668	−	381.216i	−0.648892	−	1.27072i
$301$			820.138i			2.72471i
$302$	31.7493	+	31.7493i	0.105130	+	0.105130i
$303$	164.494	−	164.494i	0.542884	−	0.542884i
$304$	−80.6586			−0.265324
$305$	12.6855	−	80.3251i	0.0415919	−	0.263361i
$306$		−	23.2643i		−	0.0760272i
$307$	281.174	−	281.174i	0.915876	−	0.915876i	−0.0808500	−	0.996726i	$-0.525763\pi$
$307$	281.174	−	281.174i	0.915876	−	0.915876i	0.996726	+	0.0808500i	$0.0257635\pi$
$308$	−212.379	+	212.379i	−0.689541	+	0.689541i
$309$			591.759i			1.91508i
$310$	14.1790	−	10.3113i	0.0457386	−	0.0332623i
$311$	−396.966			−1.27642			−0.638208	−	0.769864i	$-0.720324\pi$
$311$	−396.966			−1.27642			−0.638208	+	0.769864i	$0.720324\pi$
$312$	112.246	+	282.351i	0.359763	+	0.904972i
$313$	70.1940	−	70.1940i	0.224262	−	0.224262i	−0.586029	−	0.810290i	$-0.699309\pi$
$313$	70.1940	−	70.1940i	0.224262	−	0.224262i	0.810290	+	0.586029i	$0.199309\pi$
$314$	−59.6447			−0.189951
$315$	618.275	−	449.624i	1.96278	−	1.42738i
$316$	−152.963			−0.484059
$317$	196.363	−	196.363i	0.619440	−	0.619440i	−0.325948	−	0.945388i	$-0.605683\pi$
$317$	196.363	−	196.363i	0.619440	−	0.619440i	0.945388	+	0.325948i	$0.105683\pi$
$318$	1.57912	+	1.57912i	0.00496578	+	0.00496578i
$319$	−170.200			−0.533543
$320$	−135.529	−	21.4037i	−0.423529	−	0.0668867i
$321$	378.511			1.17916
$322$	−150.446	−	150.446i	−0.467222	−	0.467222i
$323$	13.3091	+	13.3091i	0.0412046	+	0.0412046i
$324$			51.2900i			0.158303i
$325$	−21.1481	−	324.311i	−0.0650711	−	0.997881i
$326$	73.3118			0.224883
$327$	110.773	−	110.773i	0.338755	−	0.338755i
$328$	115.956	−	115.956i	0.353525	−	0.353525i
$329$			175.682i			0.533987i
$330$	−18.2143	+	115.333i	−0.0551948	+	0.349495i
$331$		−	565.942i		−	1.70979i	−0.518798	−	0.854897i	$-0.673620\pi$
$331$		−	565.942i		−	1.70979i	0.518798	−	0.854897i	$-0.326380\pi$
$332$	−336.935	+	336.935i	−1.01486	+	1.01486i
$333$	−156.976	−	156.976i	−0.471398	−	0.471398i
$334$			50.0430i			0.149829i
$335$	310.072	+	426.377i	0.925588	+	1.27277i
$336$		−	590.712i		−	1.75807i
$337$	158.154	+	158.154i	0.469301	+	0.469301i	0.901688	−	0.432387i	$-0.142329\pi$
$337$	158.154	+	158.154i	0.469301	+	0.469301i	−0.432387	+	0.901688i	$0.642329\pi$
$338$	−3.12078	+	108.976i	−0.00923309	+	0.322413i
$339$		−	211.062i		−	0.622601i
$340$	27.4941	+	37.8069i	0.0808649	+	0.111197i
$341$	41.1864			0.120781
$342$	−45.4959	−	45.4959i	−0.133029	−	0.133029i
$343$	190.240	+	190.240i	0.554634	+	0.554634i
$344$	362.777			1.05458
$345$	703.611	+	111.119i	2.03945	+	0.322085i
$346$		−	57.6689i		−	0.166673i
$347$	39.0646	+	39.0646i	0.112578	+	0.112578i	0.761152	−	0.648574i	$-0.224634\pi$
$347$	39.0646	+	39.0646i	0.112578	+	0.112578i	−0.648574	+	0.761152i	$0.724634\pi$
$348$	271.942	−	271.942i	0.781441	−	0.781441i
$349$	−572.502			−1.64041			−0.820203	−	0.572073i	$-0.806140\pi$
$349$	−572.502			−1.64041			−0.820203	+	0.572073i	$0.806140\pi$
$350$	54.9676	−	169.688i	0.157050	−	0.484823i
$351$	118.606	−	275.133i	0.337909	−	0.783855i
$352$	143.492	+	143.492i	0.407647	+	0.407647i
$353$	375.338	+	375.338i	1.06328	+	1.06328i	0.997858	+	0.0654233i	$0.0208398\pi$
$353$	375.338	+	375.338i	1.06328	+	1.06328i	0.0654233	+	0.997858i	$0.479160\pi$
$354$			204.927i			0.578890i
$355$	−426.972	−	67.4306i	−1.20274	−	0.189945i
$356$			312.769i			0.878565i
$357$	−97.4704	+	97.4704i	−0.273026	+	0.273026i
$358$	−77.9887	−	77.9887i	−0.217845	−	0.217845i
$359$	−427.039			−1.18952			−0.594761	−	0.803902i	$-0.702753\pi$
$359$	−427.039			−1.18952			−0.594761	+	0.803902i	$0.702753\pi$
$360$	−198.885	−	273.485i	−0.552459	−	0.759682i
$361$	−308.945			−0.855804
$362$	−1.67962	+	1.67962i	−0.00463984	+	0.00463984i
$363$	214.797	−	214.797i	0.591728	−	0.591728i
$364$	203.988	−	473.195i	0.560405	−	1.29999i
$365$	−392.715	+	285.592i	−1.07593	+	0.782444i
$366$		−	50.1243i		−	0.136952i
$367$	−189.221	−	189.221i	−0.515590	−	0.515590i	0.400644	−	0.916234i	$-0.368786\pi$
$367$	−189.221	−	189.221i	−0.515590	−	0.515590i	−0.916234	+	0.400644i	$0.868786\pi$
$368$	235.734	−	235.734i	0.640581	−	0.640581i
$369$	−463.377			−1.25577
$370$	−51.1626	−	8.07996i	−0.138277	−	0.0218377i
$371$		−	8.01439i		−	0.0216021i
$372$	−65.8067	+	65.8067i	−0.176900	+	0.176900i
$373$	241.513	−	241.513i	0.647489	−	0.647489i	−0.304897	−	0.952385i	$-0.598622\pi$
$373$	241.513	−	241.513i	0.647489	−	0.647489i	0.952385	+	0.304897i	$0.0986220\pi$
$374$		−	12.7518i		−	0.0340957i
$375$	185.299	+	567.706i	0.494131	+	1.51388i
$376$	77.7104			0.206677
$377$	271.347	−	107.871i	0.719753	−	0.286131i
$378$	116.272	−	116.272i	0.307598	−	0.307598i
$379$	−180.595			−0.476503			−0.238252	−	0.971203i	$-0.576574\pi$
$379$	−180.595			−0.476503			−0.238252	+	0.971203i	$0.576574\pi$
$380$	127.703	+	20.1678i	0.336061	+	0.0530731i
$381$	843.157			2.21301
$382$	−78.4399	+	78.4399i	−0.205340	+	0.205340i
$383$	92.1204	+	92.1204i	0.240523	+	0.240523i	0.817067	−	0.576543i	$-0.195599\pi$
$383$	92.1204	+	92.1204i	0.240523	+	0.240523i	−0.576543	+	0.817067i	$0.695599\pi$
$384$	−596.351			−1.55300
$385$	338.892	−	246.451i	0.880240	−	0.640132i
$386$	−50.2021			−0.130057
$387$	−724.854	−	724.854i	−1.87301	−	1.87301i
$388$	89.3438	+	89.3438i	0.230268	+	0.230268i
$389$			619.506i			1.59256i	0.604928	+	0.796281i	$0.293202\pi$
$389$			619.506i			1.59256i	−0.604928	+	0.796281i	$0.706798\pi$
$390$	−44.0586	−	195.418i	−0.112971	−	0.501072i
$391$	−77.7944			−0.198963
$392$	253.659	−	253.659i	0.647088	−	0.647088i
$393$	−649.885	+	649.885i	−1.65365	+	1.65365i
$394$		−	13.7113i		−	0.0348002i
$395$	210.793	+	33.2899i	0.533652	+	0.0842782i
$396$		−	375.409i		−	0.948002i
$397$	175.381	−	175.381i	0.441765	−	0.441765i	−0.450840	−	0.892605i	$-0.648876\pi$
$397$	175.381	−	175.381i	0.441765	−	0.441765i	0.892605	+	0.450840i	$0.148876\pi$
$398$	69.5211	+	69.5211i	0.174676	+	0.174676i
$399$			381.228i			0.955458i
$400$	265.885	+	86.1290i	0.664712	+	0.215322i
$401$		−	460.626i		−	1.14869i	−0.818612	−	0.574346i	$-0.805256\pi$
$401$		−	460.626i		−	1.14869i	0.818612	−	0.574346i	$-0.194744\pi$
$402$	229.779	+	229.779i	0.571589	+	0.571589i
$403$	−65.6628	+	26.1036i	−0.162935	+	0.0647732i
$404$			174.509i			0.431954i
$405$	11.1625	−	70.6810i	0.0275616	−	0.174521i
$406$	160.259			0.394726
$407$	−86.0425	−	86.0425i	−0.211407	−	0.211407i
$408$	43.1147	+	43.1147i	0.105673	+	0.105673i
$409$	−279.847			−0.684221			−0.342111	−	0.939660i	$-0.611142\pi$
$409$	−279.847			−0.684221			−0.342111	+	0.939660i	$0.611142\pi$
$410$	−87.4392	+	63.5879i	−0.213266	+	0.155092i
$411$			861.143i			2.09524i
$412$	−313.895	−	313.895i	−0.761881	−	0.761881i
$413$	520.026	−	520.026i	1.25914	−	1.25914i
$414$	265.933			0.642351
$415$	537.646	−	390.990i	1.29553	−	0.942144i
$416$	−319.710	−	137.822i	−0.768533	−	0.331304i
$417$	357.772	+	357.772i	0.857966	+	0.857966i
$418$	−24.9375	−	24.9375i	−0.0596590	−	0.0596590i
$419$			72.0498i			0.171957i	0.996297	+	0.0859783i	$0.0274016\pi$
$419$			72.0498i			0.171957i	−0.996297	+	0.0859783i	$0.972598\pi$
$420$	−147.701	+	935.247i	−0.351669	+	2.22678i
$421$			360.709i			0.856792i	0.903591	+	0.428396i	$0.140921\pi$
$421$			360.709i			0.856792i	−0.903591	+	0.428396i	$0.859079\pi$
$422$	−8.58885	+	8.58885i	−0.0203527	+	0.0203527i
$423$	−155.271	−	155.271i	−0.367070	−	0.367070i
$424$	−3.54506			−0.00836099
$425$	−29.6606	−	58.0840i	−0.0697896	−	0.136668i
$426$	−266.438			−0.625442
$427$	−127.196	+	127.196i	−0.297883	+	0.297883i
$428$	−200.779	+	200.779i	−0.469109	+	0.469109i
$429$	186.298	−	432.160i	0.434261	−	1.00737i
$430$	−236.249	−	37.3102i	−0.549417	−	0.0867679i
$431$		−	776.318i		−	1.80120i	−0.434647	−	0.900601i	$-0.643127\pi$
$431$		−	776.318i		−	1.80120i	0.434647	−	0.900601i	$-0.356873\pi$
$432$	182.187	+	182.187i	0.421730	+	0.421730i
$433$	−489.511	+	489.511i	−1.13051	+	1.13051i	−0.140419	+	0.990092i	$0.544845\pi$
$433$	−489.511	+	489.511i	−1.13051	+	1.13051i	−0.990092	+	0.140419i	$0.955155\pi$
$434$	−38.7808			−0.0893566
$435$	−433.937	+	315.569i	−0.997556	+	0.725447i
$436$			117.517i			0.269535i
$437$	−152.135	+	152.135i	−0.348136	+	0.348136i
$438$	−211.638	+	211.638i	−0.483191	+	0.483191i
$439$			217.258i			0.494892i	0.968902	+	0.247446i	$0.0795913\pi$
$439$			217.258i			0.494892i	−0.968902	+	0.247446i	$0.920409\pi$
$440$	−109.014	−	149.905i	−0.247760	−	0.340692i
$441$	−1013.66			−2.29854
$442$	8.08197	+	20.3299i	0.0182850	+	0.0459953i
$443$	119.531	−	119.531i	0.269821	−	0.269821i	−0.559207	−	0.829028i	$-0.688894\pi$
$443$	119.531	−	119.531i	0.269821	−	0.269821i	0.829028	+	0.559207i	$0.188894\pi$
$444$	274.953			0.619263
$445$	68.0692	−	431.016i	0.152964	−	0.968576i
$446$	−34.5398			−0.0774435
$447$	499.570	−	499.570i	1.11761	−	1.11761i
$448$	214.613	+	214.613i	0.479046	+	0.479046i
$449$	457.837			1.01968			0.509841	−	0.860269i	$-0.329704\pi$
$449$	457.837			1.01968			0.509841	+	0.860269i	$0.329704\pi$
$450$	101.392	+	198.555i	0.225316	+	0.441233i
$451$	−253.989			−0.563169
$452$	111.956	+	111.956i	0.247691	+	0.247691i
$453$	235.131	+	235.131i	0.519053	+	0.519053i
$454$			55.6442i			0.122564i
$455$	−384.091	+	607.699i	−0.844157	+	1.33560i
$456$	168.631			0.369805
$457$	−611.380	+	611.380i	−1.33781	+	1.33781i	−0.439635	+	0.898177i	$0.644892\pi$
$457$	−611.380	+	611.380i	−1.33781	+	1.33781i	−0.898177	+	0.439635i	$0.855108\pi$
$458$	84.6909	−	84.6909i	0.184915	−	0.184915i
$459$		−	60.1236i		−	0.130988i
$460$	−432.169	+	314.283i	−0.939497	+	0.683225i
$461$			350.841i			0.761043i	0.924772	+	0.380522i	$0.124256\pi$
$461$			350.841i			0.761043i	−0.924772	+	0.380522i	$0.875744\pi$
$462$	182.632	−	182.632i	0.395308	−	0.395308i
$463$	−114.282	−	114.282i	−0.246829	−	0.246829i	0.572839	−	0.819668i	$-0.305842\pi$
$463$	−114.282	−	114.282i	−0.246829	−	0.246829i	−0.819668	+	0.572839i	$0.805842\pi$
$464$			251.110i			0.541186i
$465$	105.008	−	76.3641i	0.225823	−	0.164224i
$466$		−	75.5455i		−	0.162115i
$467$	−554.918	−	554.918i	−1.18826	−	1.18826i	−0.977548	−	0.210712i	$-0.932422\pi$
$467$	−554.918	−	554.918i	−1.18826	−	1.18826i	−0.210712	−	0.977548i	$-0.567578\pi$
$468$	237.931	+	598.507i	0.508399	+	1.27886i
$469$		−	1166.18i		−	2.48652i
$470$	−50.6069	−	7.99221i	−0.107674	−	0.0170047i
$471$	−441.721			−0.937836
$472$	−230.026	−	230.026i	−0.487344	−	0.487344i
$473$	−397.311	−	397.311i	−0.839982	−	0.839982i
$474$	131.538			0.277507
$475$	−171.594	−	55.5850i	−0.361250	−	0.117021i
$476$		−	103.405i		−	0.217238i
$477$	7.08327	+	7.08327i	0.0148496	+	0.0148496i
$478$	86.2992	−	86.2992i	0.180542	−	0.180542i
$479$	443.779			0.926470			0.463235	−	0.886235i	$-0.346689\pi$
$479$	443.779			0.926470			0.463235	+	0.886235i	$0.346689\pi$
$480$	631.891	+	99.7928i	1.31644	+	0.207902i
$481$	191.709	+	82.6429i	0.398563	+	0.171815i
$482$	−5.81098	−	5.81098i	−0.0120560	−	0.0120560i
$483$	−1114.18	−	1114.18i	−2.30679	−	2.30679i
$484$			227.876i			0.470817i
$485$	−103.677	−	142.566i	−0.213768	−	0.293950i
$486$		−	177.912i		−	0.366074i
$487$	96.6126	−	96.6126i	0.198383	−	0.198383i	−0.600923	−	0.799307i	$-0.705200\pi$
$487$	96.6126	−	96.6126i	0.198383	−	0.198383i	0.799307	+	0.600923i	$0.205200\pi$
$488$	56.2635	+	56.2635i	0.115294	+	0.115294i
$489$	542.937			1.11030
$490$	−191.276	+	139.101i	−0.390360	+	0.283879i
$491$	196.620			0.400449			0.200224	−	0.979750i	$-0.435833\pi$
$491$	196.620			0.400449			0.200224	+	0.979750i	$0.435833\pi$
$492$	405.818	−	405.818i	0.824833	−	0.824833i
$493$	41.4344	−	41.4344i	0.0840454	−	0.0840454i
$494$	55.5625	+	23.9522i	0.112475	+	0.0484862i
$495$	−81.7017	+	517.338i	−0.165054	+	1.04513i
$496$		−	60.7657i		−	0.122511i
$497$	676.118	+	676.118i	1.36040	+	1.36040i
$498$	289.743	−	289.743i	0.581813	−	0.581813i
$499$	340.094			0.681551			0.340776	−	0.940145i	$-0.389310\pi$
$499$	340.094			0.681551			0.340776	+	0.940145i	$0.389310\pi$
$500$	−399.427	−	202.845i	−0.798854	−	0.405691i
$501$			370.612i			0.739745i
$502$	163.559	−	163.559i	0.325816	−	0.325816i
$503$	355.465	−	355.465i	0.706691	−	0.706691i	−0.259147	−	0.965838i	$-0.583441\pi$
$503$	355.465	−	355.465i	0.706691	−	0.706691i	0.965838	+	0.259147i	$0.0834414\pi$
$504$			748.007i			1.48414i
$505$	37.9792	−	240.485i	0.0752063	−	0.476209i
$506$	145.765			0.288073
$507$	−23.1121	+	807.059i	−0.0455860	+	1.59183i
$508$	−447.247	+	447.247i	−0.880408	+	0.880408i
$509$	−691.988			−1.35950			−0.679752	−	0.733442i	$-0.737913\pi$
$509$	−691.988			−1.35950			−0.679752	+	0.733442i	$0.737913\pi$
$510$	−23.6432	−	32.5115i	−0.0463592	−	0.0637481i
$511$	1074.11			2.10198
$512$	366.400	−	366.400i	0.715626	−	0.715626i
$513$	−117.578	−	117.578i	−0.229197	−	0.229197i
$514$	−224.060			−0.435915
$515$	364.253	+	500.882i	0.707288	+	0.972586i
$516$	1269.63			2.46052
$517$	−85.1080	−	85.1080i	−0.164619	−	0.164619i
$518$	81.0168	+	81.0168i	0.156403	+	0.156403i
$519$		−	427.088i		−	0.822905i
$520$	268.808	+	169.898i	0.516938	+	0.326726i
$521$	729.272			1.39975			0.699877	−	0.714264i	$-0.253238\pi$
$521$	729.272			1.39975			0.699877	+	0.714264i	$0.253238\pi$
$522$	−141.640	+	141.640i	−0.271341	+	0.271341i
$523$	−246.362	+	246.362i	−0.471056	+	0.471056i	−0.902256	−	0.431200i	$-0.858090\pi$
$523$	−246.362	+	246.362i	−0.471056	+	0.471056i	0.431200	+	0.902256i	$0.358090\pi$
$524$		−	689.454i		−	1.31575i
$525$	407.083	−	1256.69i	0.775396	−	2.39369i
$526$			151.807i			0.288607i
$527$	−10.0266	+	10.0266i	−0.0190259	+	0.0190259i
$528$	286.167	+	286.167i	0.541983	+	0.541983i
$529$		−	360.265i		−	0.681030i
$530$	2.30863	+	0.364595i	0.00435590	+	0.000687915i
$531$			919.217i			1.73111i
$532$	−202.220	−	202.220i	−0.380112	−	0.380112i
$533$	404.930	−	160.976i	0.759719	−	0.302019i
$534$		−	268.962i		−	0.503674i
$535$	320.383	−	232.990i	0.598846	−	0.435495i
$536$	−515.844			−0.962395
$537$	−577.574	−	577.574i	−1.07556	−	1.07556i
$538$	−68.5441	−	68.5441i	−0.127405	−	0.127405i
$539$	−555.611			−1.03082
$540$	−242.895	−	334.002i	−0.449805	−	0.618523i
$541$		−	394.147i		−	0.728552i	−0.931291	−	0.364276i	$-0.881316\pi$
$541$		−	394.147i		−	0.728552i	0.931291	−	0.364276i	$-0.118684\pi$
$542$	146.118	+	146.118i	0.269591	+	0.269591i
$543$	−12.4390	+	12.4390i	−0.0229080	+	0.0229080i
$544$	−69.8647			−0.128428
$545$	25.5758	−	161.947i	0.0469280	−	0.297150i
$546$	−175.416	+	406.918i	−0.321276	+	0.745271i
$547$	224.332	+	224.332i	0.410113	+	0.410113i	0.881778	−	0.471665i	$-0.156347\pi$
$547$	224.332	+	224.332i	0.410113	+	0.410113i	−0.471665	+	0.881778i	$0.656347\pi$
$548$	−456.788	−	456.788i	−0.833554	−	0.833554i
$549$		−	224.837i		−	0.409539i
$550$	55.5756	+	108.833i	0.101047	+	0.197878i
$551$		−	162.059i		−	0.294118i
$552$	−492.843	+	492.843i	−0.892831	+	0.892831i
$553$	−333.793	−	333.793i	−0.603605	−	0.603605i
$554$	−249.293			−0.449987
$555$	−378.903	−	59.8391i	−0.682708	−	0.107818i
$556$	−379.556			−0.682654
$557$	−242.778	+	242.778i	−0.435867	+	0.435867i	−0.890618	−	0.454752i	$-0.849728\pi$
$557$	−242.778	+	242.778i	−0.435867	+	0.435867i	0.454752	+	0.890618i	$0.349728\pi$
$558$	34.2752	−	34.2752i	0.0614250	−	0.0614250i
$559$	885.238	+	381.614i	1.58361	+	0.682672i
$560$	−363.609	−	499.996i	−0.649302	−	0.892849i
$561$		−	94.4380i		−	0.168339i
$562$	−25.7779	−	25.7779i	−0.0458681	−	0.0458681i
$563$	−329.591	+	329.591i	−0.585419	+	0.585419i	−0.936387	−	0.350968i	$-0.885853\pi$
$563$	−329.591	+	329.591i	−0.585419	+	0.585419i	0.350968	+	0.936387i	$0.385853\pi$
$564$	271.967			0.482211
$565$	−129.918	−	178.649i	−0.229943	−	0.316192i
$566$			91.1753i			0.161087i
$567$	−111.925	+	111.925i	−0.197398	+	0.197398i
$568$	299.072	−	299.072i	0.526535	−	0.526535i
$569$			970.000i			1.70475i	0.522935	+	0.852373i	$0.324837\pi$
$569$			970.000i			1.70475i	−0.522935	+	0.852373i	$0.675163\pi$
$570$	−109.817	−	17.3430i	−0.192661	−	0.0304264i
$571$	45.1247			0.0790274			0.0395137	−	0.999219i	$-0.487419\pi$
$571$	45.1247			0.0790274			0.0395137	+	0.999219i	$0.487419\pi$
$572$	130.416	+	328.057i	0.228000	+	0.573527i
$573$	−580.915	+	580.915i	−1.01381	+	1.01381i
$574$	239.154			0.416644
$575$	663.955	−	339.049i	1.15470	−	0.589650i
$576$	−379.358			−0.658607
$577$	−634.253	+	634.253i	−1.09923	+	1.09923i	−0.104724	+	0.994501i	$0.533396\pi$
$577$	−634.253	+	634.253i	−1.09923	+	1.09923i	−0.994501	+	0.104724i	$0.966604\pi$
$578$	−128.722	−	128.722i	−0.222703	−	0.222703i
$579$	−371.790			−0.642125
$580$	62.7872	−	397.571i	0.108254	−	0.685467i
$581$	−1470.51			−2.53100
$582$	−76.8301	−	76.8301i	−0.132010	−	0.132010i
$583$	3.88253	+	3.88253i	0.00665957	+	0.00665957i
$584$		−	475.118i		−	0.813559i
$585$	−197.629	−	876.563i	−0.337827	−	1.49840i
$586$	35.9793			0.0613981
$587$	498.687	−	498.687i	0.849552	−	0.849552i	−0.140525	−	0.990077i	$-0.544879\pi$
$587$	498.687	−	498.687i	0.849552	−	0.849552i	0.990077	+	0.140525i	$0.0448791\pi$
$588$	887.741	−	887.741i	1.50976	−	1.50976i
$589$			39.2163i			0.0665812i
$590$	126.141	+	173.456i	0.213799	+	0.293993i
$591$		−	101.544i		−	0.171817i
$592$	−126.945	+	126.945i	−0.214435	+	0.214435i
$593$	258.679	+	258.679i	0.436221	+	0.436221i	0.890738	−	0.454517i	$-0.150188\pi$
$593$	258.679	+	258.679i	0.436221	+	0.436221i	−0.454517	+	0.890738i	$0.650188\pi$
$594$			112.655i			0.189655i
$595$	−22.5045	+	142.499i	−0.0378226	+	0.239494i
$596$			529.988i			0.889241i
$597$	514.864	+	514.864i	0.862418	+	0.862418i
$598$	−232.390	+	92.3846i	−0.388613	+	0.154489i
$599$			249.947i			0.417273i	0.977993	+	0.208637i	$0.0669026\pi$
$599$			249.947i			0.417273i	−0.977993	+	0.208637i	$0.933097\pi$
$600$	−555.878	−	180.068i	−0.926464	−	0.300113i
$601$	−195.505			−0.325300			−0.162650	−	0.986684i	$-0.552004\pi$
$601$	−195.505			−0.325300			−0.162650	+	0.986684i	$0.552004\pi$
$602$	374.104	+	374.104i	0.621436	+	0.621436i
$603$	1030.69	+	1030.69i	1.70927	+	1.70927i
$604$	−249.447			−0.412992
$605$	49.5935	−	314.027i	0.0819727	−	0.519053i
$606$		−	150.067i		−	0.247636i
$607$	518.467	+	518.467i	0.854146	+	0.854146i	0.990641	−	0.136495i	$-0.0435836\pi$
$607$	518.467	+	518.467i	0.854146	+	0.854146i	−0.136495	+	0.990641i	$0.543584\pi$
$608$	−136.628	+	136.628i	−0.224717	+	0.224717i
$609$	1186.86			1.94886
$610$	−30.8537	−	42.4266i	−0.0505798	−	0.0695518i
$611$	189.627	+	81.7454i	0.310355	+	0.133789i
$612$	91.3914	+	91.3914i	0.149332	+	0.149332i
$613$	648.228	+	648.228i	1.05747	+	1.05747i	0.998245	+	0.0592226i	$0.0188622\pi$
$613$	648.228	+	648.228i	1.05747	+	1.05747i	0.0592226	+	0.998245i	$0.481138\pi$
$614$		−	256.514i		−	0.417775i
$615$	−647.563	+	470.923i	−1.05295	+	0.765729i
$616$			410.002i			0.665588i
$617$	−277.710	+	277.710i	−0.450098	+	0.450098i	−0.895387	−	0.445289i	$-0.853101\pi$
$617$	−277.710	+	277.710i	−0.450098	+	0.450098i	0.445289	+	0.895387i	$0.353101\pi$
$618$	269.930	+	269.930i	0.436780	+	0.436780i
$619$	659.971			1.06619			0.533094	−	0.846056i	$-0.321029\pi$
$619$	659.971			1.06619			0.533094	+	0.846056i	$0.321029\pi$
$620$	−15.1938	+	96.2074i	−0.0245061	+	0.155173i
$621$	687.270			1.10671
$622$	−181.075	+	181.075i	−0.291117	+	0.291117i
$623$	−682.521	+	682.521i	−1.09554	+	1.09554i
$624$	−637.601	−	274.861i	−1.02180	−	0.440482i
$625$	506.290	+	366.463i	0.810064	+	0.586341i
$626$		−	64.0377i		−	0.102297i
$627$	−184.684	−	184.684i	−0.294551	−	0.294551i
$628$	234.308	−	234.308i	0.373102	−	0.373102i
$629$	41.8932			0.0666029
$630$	76.9295	−	487.120i	0.122110	−	0.773206i
$631$		−	1076.33i		−	1.70575i	−0.522117	−	0.852874i	$-0.674858\pi$
$631$		−	1076.33i		−	1.70575i	0.522117	−	0.852874i	$-0.325142\pi$
$632$	−147.649	+	147.649i	−0.233622	+	0.233622i
$633$	−63.6079	+	63.6079i	−0.100486	+	0.100486i
$634$		−	179.141i		−	0.282556i
$635$	713.672	−	518.999i	1.12389	−	0.817322i
$636$	−12.4068			−0.0195076
$637$	885.800	−	352.141i	1.39058	−	0.552812i
$638$	−77.6365	+	77.6365i	−0.121687	+	0.121687i
$639$	−1195.13			−1.87032
$640$	−504.768	+	367.079i	−0.788700	+	0.573562i
$641$	−176.569			−0.275458			−0.137729	−	0.990470i	$-0.543980\pi$
$641$	−176.569			−0.275458			−0.137729	+	0.990470i	$0.543980\pi$
$642$	172.657	−	172.657i	0.268936	−	0.268936i
$643$	−625.328	−	625.328i	−0.972516	−	0.972516i	0.0271167	−	0.999632i	$-0.491367\pi$
$643$	−625.328	−	625.328i	−0.972516	−	0.972516i	−0.999632	+	0.0271167i	$0.991367\pi$
$644$	1182.02			1.83543
$645$	−1749.63	−	276.314i	−2.71260	−	0.428394i
$646$	12.1418			0.0187954
$647$	−808.053	−	808.053i	−1.24892	−	1.24892i	−0.956196	−	0.292727i	$-0.905437\pi$
$647$	−808.053	−	808.053i	−1.24892	−	1.24892i	−0.292727	−	0.956196i	$-0.594563\pi$
$648$	49.5083	+	49.5083i	0.0764017	+	0.0764017i
$649$			503.847i			0.776344i
$650$	−157.581	−	138.287i	−0.242432	−	0.212750i
$651$	−287.205			−0.441175
$652$	−287.998	+	287.998i	−0.441714	+	0.441714i
$653$	−85.2121	+	85.2121i	−0.130493	+	0.130493i	−0.769337	−	0.638844i	$-0.779413\pi$
$653$	−85.2121	+	85.2121i	−0.130493	+	0.130493i	0.638844	+	0.769337i	$0.279413\pi$
$654$		−	101.058i		−	0.154522i
$655$	−150.049	+	950.113i	−0.229082	+	1.45055i
$656$			374.731i			0.571236i
$657$	−949.319	+	949.319i	−1.44493	+	1.44493i
$658$	80.1369	+	80.1369i	0.121789	+	0.121789i
$659$		−	959.837i		−	1.45651i	−0.685309	−	0.728253i	$-0.740333\pi$
$659$		−	959.837i		−	1.45651i	0.685309	−	0.728253i	$-0.259667\pi$
$660$	−381.522	−	524.628i	−0.578064	−	0.794891i
$661$			122.199i			0.184870i	0.995719	+	0.0924350i	$0.0294650\pi$
$661$			122.199i			0.184870i	−0.995719	+	0.0924350i	$0.970535\pi$
$662$	−258.153	−	258.153i	−0.389959	−	0.389959i
$663$	59.8540	+	150.561i	0.0902775	+	0.227090i
$664$			650.461i			0.979609i
$665$	234.662	+	322.682i	0.352875	+	0.485236i
$666$	−143.208			−0.215027
$667$	473.635	+	473.635i	0.710097	+	0.710097i
$668$	−196.589	−	196.589i	−0.294295	−	0.294295i
$669$	−255.797			−0.382358
$670$	335.930	+	53.0525i	0.501388	+	0.0791828i
$671$		−	123.239i		−	0.183665i
$672$	−1000.61	−	1000.61i	−1.48900	−	1.48900i
$673$	575.800	−	575.800i	0.855573	−	0.855573i	−0.135240	−	0.990813i	$-0.543181\pi$
$673$	575.800	−	575.800i	0.855573	−	0.855573i	0.990813	+	0.135240i	$0.0431806\pi$
$674$	144.284			0.214071
$675$	262.034	+	513.139i	0.388199	+	0.760206i
$676$	−415.840	−	440.359i	−0.615147	−	0.651419i
$677$	−709.123	−	709.123i	−1.04745	−	1.04745i	−0.998817	−	0.0486325i	$-0.984514\pi$
$677$	−709.123	−	709.123i	−1.04745	−	1.04745i	−0.0486325	−	0.998817i	$-0.515486\pi$
$678$	−96.2754	−	96.2754i	−0.141999	−	0.141999i
$679$			389.930i			0.574271i
$680$	63.0325	+	9.95455i	0.0926949	+	0.0146390i
$681$			412.093i			0.605130i
$682$	18.7871	−	18.7871i	0.0275471	−	0.0275471i
$683$	−452.712	−	452.712i	−0.662829	−	0.662829i	0.293217	−	0.956046i	$-0.405274\pi$
$683$	−452.712	−	452.712i	−0.662829	−	0.662829i	−0.956046	+	0.293217i	$0.905274\pi$
$684$	357.451			0.522590
$685$	530.071	+	728.896i	0.773826	+	1.06408i
$686$	173.555			0.252995
$687$	627.210	−	627.210i	0.912969	−	0.912969i
$688$	−586.186	+	586.186i	−0.852014	+	0.852014i
$689$	−8.65055	−	3.72913i	−0.0125552	−	0.00541238i
$690$	371.638	−	270.264i	0.538606	−	0.391687i
$691$			1181.67i			1.71008i	0.518562	+	0.855040i	$0.326467\pi$
$691$			1181.67i			1.71008i	−0.518562	+	0.855040i	$0.673533\pi$
$692$	226.546	+	226.546i	0.327379	+	0.327379i
$693$	819.213	−	819.213i	1.18212	−	1.18212i
$694$	35.6385			0.0513523
$695$	523.052	+	82.6042i	0.752593	+	0.118855i
$696$		−	524.990i		−	0.754296i
$697$	61.8325	−	61.8325i	0.0887123	−	0.0887123i
$698$	−261.145	+	261.145i	−0.374134	+	0.374134i
$699$		−	559.480i		−	0.800401i
$700$	450.666	+	882.535i	0.643809	+	1.26076i
$701$	953.967			1.36087			0.680433	−	0.732810i	$-0.261792\pi$
$701$	953.967			1.36087			0.680433	+	0.732810i	$0.261792\pi$
$702$	−71.3996	−	179.603i	−0.101709	−	0.255845i
$703$	81.9267	−	81.9267i	0.116539	−	0.116539i
$704$	−207.936			−0.295363
$705$	−374.788	−	59.1892i	−0.531614	−	0.0839563i
$706$	342.420			0.485014
$707$	−380.812	+	380.812i	−0.538631	+	0.538631i
$708$	−805.034	−	805.034i	−1.13705	−	1.13705i
$709$	459.338			0.647868			0.323934	−	0.946080i	$-0.394994\pi$
$709$	459.338			0.647868			0.323934	+	0.946080i	$0.394994\pi$
$710$	−225.521	+	164.004i	−0.317635	+	0.230992i
$711$	590.026			0.829854
$712$	301.904	+	301.904i	0.424023	+	0.424023i
$713$	−114.614	−	114.614i	−0.160749	−	0.160749i
$714$			88.9219i			0.124540i
$715$	−108.325	−	480.467i	−0.151504	−	0.671982i
$716$	612.740			0.855782
$717$	639.120	−	639.120i	0.891381	−	0.891381i
$718$	−194.793	+	194.793i	−0.271299	+	0.271299i
$719$			1030.14i			1.43274i	0.697721	+	0.716370i	$0.254198\pi$
$719$			1030.14i			1.43274i	−0.697721	+	0.716370i	$0.745802\pi$
$720$	763.270	+	120.541i	1.06010	+	0.167418i
$721$		−	1369.96i		−	1.90008i
$722$	−140.925	+	140.925i	−0.195187	+	0.195187i
$723$	−43.0354	−	43.0354i	−0.0595233	−	0.0595233i
$724$		−	13.1964i		−	0.0182271i
$725$	−173.050	+	534.214i	−0.238689	+	0.736847i
$726$		−	195.959i		−	0.269915i
$727$	166.903	+	166.903i	0.229577	+	0.229577i	0.812516	−	0.582939i	$-0.198097\pi$
$727$	166.903	+	166.903i	0.229577	+	0.229577i	−0.582939	+	0.812516i	$0.698097\pi$
$728$	−259.856	−	653.659i	−0.356945	−	0.897883i
$729$		−	1188.79i		−	1.63071i
$730$	−48.8640	+	309.409i	−0.0669370	+	0.423847i
$731$	193.447			0.264633
$732$	196.908	+	196.908i	0.269000	+	0.269000i
$733$	−324.969	−	324.969i	−0.443341	−	0.443341i	0.449792	−	0.893133i	$-0.351498\pi$
$733$	−324.969	−	324.969i	−0.443341	−	0.443341i	−0.893133	+	0.449792i	$0.851498\pi$
$734$	−172.626			−0.235185
$735$	−1416.57	+	1030.16i	−1.92730	+	1.40158i
$736$		−	798.620i		−	1.08508i
$737$	564.949	+	564.949i	0.766552	+	0.766552i
$738$	−211.369	+	211.369i	−0.286407	+	0.286407i
$739$	−555.480			−0.751665			−0.375832	−	0.926688i	$-0.622643\pi$
$739$	−555.480			−0.751665			−0.375832	+	0.926688i	$0.622643\pi$
$740$	232.728	−	169.245i	0.314497	−	0.228710i
$741$	411.489	+	177.387i	0.555315	+	0.239388i
$742$	−3.65575	−	3.65575i	−0.00492689	−	0.00492689i
$743$	446.623	+	446.623i	0.601108	+	0.601108i	0.940607	−	0.339499i	$-0.110257\pi$
$743$	446.623	+	446.623i	0.601108	+	0.601108i	−0.339499	+	0.940607i	$0.610257\pi$
$744$			127.041i			0.170754i
$745$	115.343	−	730.358i	0.154823	−	0.980346i
$746$		−	220.332i		−	0.295351i
$747$	1299.67	−	1299.67i	1.73985	−	1.73985i
$748$	50.0940	+	50.0940i	0.0669706	+	0.0669706i
$749$	−876.274			−1.16993
$750$	343.482	+	174.434i	0.457976	+	0.232579i
$751$	256.447			0.341474			0.170737	−	0.985317i	$-0.445385\pi$
$751$	256.447			0.341474			0.170737	+	0.985317i	$0.445385\pi$
$752$	−125.567	+	125.567i	−0.166977	+	0.166977i
$753$	1211.30	−	1211.30i	1.60863	−	1.60863i
$754$	74.5691	−	172.980i	0.0988980	−	0.229416i
$755$	343.755	+	54.2882i	0.455304	+	0.0719049i
$756$			913.526i			1.20837i
$757$	−114.764	−	114.764i	−0.151604	−	0.151604i	0.627230	−	0.778834i	$-0.284188\pi$
$757$	−114.764	−	114.764i	−0.151604	−	0.151604i	−0.778834	+	0.627230i	$0.784188\pi$
$758$	−82.3780	+	82.3780i	−0.108678	+	0.108678i
$759$	1079.52			1.42229
$760$	142.734	−	103.800i	0.187808	−	0.136579i
$761$			831.924i			1.09320i	0.837394	+	0.546599i	$0.184078\pi$
$761$			831.924i			1.09320i	−0.837394	+	0.546599i	$0.815922\pi$
$762$	384.604	−	384.604i	0.504730	−	0.504730i
$763$	−256.445	+	256.445i	−0.336101	+	0.336101i
$764$		−	616.285i		−	0.806656i
$765$	−106.053	−	145.833i	−0.138632	−	0.190632i
$766$	84.0410			0.109714
$767$	−319.334	−	803.274i	−0.416341	−	1.04729i
$768$	98.7881	−	98.7881i	0.128630	−	0.128630i
$769$	611.199			0.794798			0.397399	−	0.917646i	$-0.369913\pi$
$769$	611.199			0.794798			0.397399	+	0.917646i	$0.369913\pi$
$770$	42.1671	−	267.003i	0.0547624	−	0.346757i
$771$	−1659.36			−2.15222
$772$	197.214	−	197.214i	0.255458	−	0.255458i
$773$	−121.024	−	121.024i	−0.156565	−	0.156565i	0.624478	−	0.781042i	$-0.285312\pi$
$773$	−121.024	−	121.024i	−0.156565	−	0.156565i	−0.781042	+	0.624478i	$0.785312\pi$
$774$	−661.281			−0.854369
$775$	41.8760	−	129.273i	0.0540336	−	0.166804i
$776$	172.480			0.222269
$777$	599.999	+	599.999i	0.772200	+	0.772200i
$778$	282.587	+	282.587i	0.363222	+	0.363222i
$779$		−	241.840i		−	0.310449i
$780$	940.758	+	594.599i	1.20610	+	0.762306i
$781$	−655.083			−0.838774
$782$	−35.4858	+	35.4858i	−0.0453782	+	0.0453782i
$783$	−366.050	+	366.050i	−0.467496	+	0.467496i
$784$			819.738i			1.04558i
$785$	−373.885	+	271.898i	−0.476287	+	0.346367i
$786$			592.887i			0.754309i
$787$	110.846	−	110.846i	0.140846	−	0.140846i	−0.633168	−	0.774014i	$-0.718246\pi$
$787$	110.846	−	110.846i	0.140846	−	0.140846i	0.774014	+	0.633168i	$0.218246\pi$
$788$	53.8633	+	53.8633i	0.0683545	+	0.0683545i
$789$			1124.26i			1.42492i
$790$	111.338	−	80.9675i	0.140934	−	0.102490i
$791$			488.620i			0.617724i
$792$	−362.368	−	362.368i	−0.457535	−	0.457535i
$793$	78.1077	+	196.477i	0.0984965	+	0.247765i
$794$		−	159.999i		−	0.201510i
$795$	17.0974	+	2.70014i	0.0215061	+	0.00339641i
$796$	−546.212			−0.686196
$797$	−533.737	−	533.737i	−0.669683	−	0.669683i	0.287960	−	0.957642i	$-0.407023\pi$
$797$	−533.737	−	533.737i	−0.669683	−	0.669683i	−0.957642	+	0.287960i	$0.907023\pi$
$798$	173.896	+	173.896i	0.217915	+	0.217915i
$799$	41.4382			0.0518626
$800$	596.277	−	304.489i	0.745346	−	0.380611i
$801$		−	1206.45i		−	1.50618i
$802$	−210.114	−	210.114i	−0.261987	−	0.261987i
$803$	−520.347	+	520.347i	−0.648003	+	0.648003i
$804$	−1805.32			−2.24543
$805$	−1628.90	−	257.248i	−2.02348	−	0.319562i
$806$	−18.0448	+	41.8591i	−0.0223881	+	0.0519343i
$807$	−507.629	−	507.629i	−0.629032	−	0.629032i
$808$	168.447	+	168.447i	0.208474	+	0.208474i
$809$		−	696.426i		−	0.860848i	−0.902627	−	0.430424i	$-0.858364\pi$
$809$		−	696.426i		−	0.860848i	0.902627	−	0.430424i	$-0.141636\pi$
$810$	−27.1493	−	37.3327i	−0.0335176	−	0.0460898i
$811$			231.439i			0.285374i	0.989768	+	0.142687i	$0.0455743\pi$
$811$			231.439i			0.285374i	−0.989768	+	0.142687i	$0.954426\pi$
$812$	−629.560	+	629.560i	−0.775320	+	0.775320i
$813$	1082.13	+	1082.13i	1.33104	+	1.33104i
$814$	−78.4962			−0.0964327
$815$	459.558	−	334.201i	0.563874	−	0.410063i
$816$	−139.332			−0.170750
$817$	378.306	−	378.306i	0.463043	−	0.463043i
$818$	−127.651	+	127.651i	−0.156053	+	0.156053i
$819$	−786.845	+	1825.26i	−0.960739	+	2.22865i
$820$	93.6972	−	593.294i	0.114265	−	0.723529i
$821$		−	776.092i		−	0.945301i	−0.881250	−	0.472650i	$-0.843297\pi$
$821$		−	776.092i		−	0.945301i	0.881250	−	0.472650i	$-0.156703\pi$
$822$	392.809	+	392.809i	0.477870	+	0.477870i
$823$	407.178	−	407.178i	0.494749	−	0.494749i	−0.415050	−	0.909799i	$-0.636236\pi$
$823$	407.178	−	407.178i	0.494749	−	0.494749i	0.909799	+	0.415050i	$0.136236\pi$
$824$	−605.981			−0.735414
$825$	411.585	+	806.004i	0.498891	+	0.976974i
$826$		−	474.417i		−	0.574355i
$827$	−728.618	+	728.618i	−0.881038	+	0.881038i	−0.993640	−	0.112602i	$-0.964081\pi$
$827$	−728.618	+	728.618i	−0.881038	+	0.881038i	0.112602	+	0.993640i	$0.464081\pi$
$828$	−1044.69	+	1044.69i	−1.26170	+	1.26170i
$829$		−	580.072i		−	0.699725i	−0.936801	−	0.349862i	$-0.886228\pi$
$829$		−	580.072i		−	0.699725i	0.936801	−	0.349862i	$-0.113772\pi$
$830$	66.8973	−	423.596i	0.0805991	−	0.510356i
$831$	−1846.23			−2.22170
$832$	331.508	−	131.788i	0.398447	−	0.158399i
$833$	135.261	−	135.261i	0.162378	−	0.162378i
$834$	326.394			0.391360
$835$	228.128	+	313.697i	0.273207	+	0.375685i
$836$	195.928			0.234364
$837$	88.5797	−	88.5797i	0.105830	−	0.105830i
$838$	32.8654	+	32.8654i	0.0392188	+	0.0392188i
$839$	−1030.78			−1.22859			−0.614293	−	0.789078i	$-0.710559\pi$
$839$	−1030.78			−1.22859			−0.614293	+	0.789078i	$0.710559\pi$
$840$	760.188	+	1045.33i	0.904986	+	1.24444i
$841$	336.471			0.400084
$842$	164.537	+	164.537i	0.195412	+	0.195412i
$843$	−190.908	−	190.908i	−0.226462	−	0.226462i
$844$		−	67.4808i		−	0.0799535i
$845$	477.217	+	697.344i	0.564754	+	0.825259i
$846$	−141.653			−0.167438
$847$	−497.267	+	497.267i	−0.587093	+	0.587093i
$848$	5.72821	−	5.72821i	0.00675496	−	0.00675496i
$849$			675.232i			0.795326i
$850$	−40.0245	−	12.9653i	−0.0470876	−	0.0152533i
$851$			478.880i			0.562726i
$852$	1046.67	−	1046.67i	1.22849	−	1.22849i
$853$	506.356	+	506.356i	0.593618	+	0.593618i	0.938607	−	0.344989i	$-0.112117\pi$
$853$	506.356	+	506.356i	0.593618	+	0.593618i	−0.344989	+	0.938607i	$0.612117\pi$
$854$			116.041i			0.135879i
$855$	−492.591	−	77.7936i	−0.576130	−	0.0909866i
$856$			387.608i			0.452813i
$857$	1070.01	+	1070.01i	1.24855	+	1.24855i	0.956360	+	0.292191i	$0.0943841\pi$
$857$	1070.01	+	1070.01i	1.24855	+	1.24855i	0.292191	+	0.956360i	$0.405616\pi$
$858$	−112.150	−	282.109i	−0.130710	−	0.328798i
$859$			812.856i			0.946282i	0.880987	+	0.473141i	$0.156880\pi$
$859$			812.856i			0.946282i	−0.880987	+	0.473141i	$0.843120\pi$
$860$	1074.65	−	781.511i	1.24959	−	0.908733i
$861$	1771.14			2.05707
$862$	−354.116	−	354.116i	−0.410807	−	0.410807i
$863$	−489.451	−	489.451i	−0.567151	−	0.567151i	0.364178	−	0.931329i	$-0.381350\pi$
$863$	−489.451	−	489.451i	−0.567151	−	0.567151i	−0.931329	+	0.364178i	$0.881350\pi$
$864$	617.215			0.714370
$865$	−262.891	−	361.499i	−0.303920	−	0.417918i
$866$			446.579i			0.515680i
$867$	−953.301	−	953.301i	−1.09954	−	1.09954i
$868$	152.346	−	152.346i	0.175514	−	0.175514i
$869$	323.409			0.372162
$870$	−53.9931	+	341.886i	−0.0620610	+	0.392972i
$871$	−1258.75	−	542.628i	−1.44517	−	0.622994i
$872$	113.435	+	113.435i	0.130086	+	0.130086i
$873$	−344.628	−	344.628i	−0.394763	−	0.394763i
$874$			138.793i			0.158802i
$875$	−428.978	−	1314.27i	−0.490261	−	1.50202i
$876$		−	1662.79i		−	1.89817i
$877$	−217.170	+	217.170i	−0.247629	+	0.247629i	−0.819997	−	0.572368i	$-0.806025\pi$
$877$	−217.170	+	217.170i	−0.247629	+	0.247629i	0.572368	+	0.819997i	$0.306025\pi$
$878$	99.1017	+	99.1017i	0.112872	+	0.112872i
$879$	266.458			0.303137
$880$	418.368	+	66.0717i	0.475419	+	0.0750815i
$881$	−313.367			−0.355695			−0.177848	−	0.984058i	$-0.556913\pi$
$881$	−313.367			−0.355695			−0.177848	+	0.984058i	$0.556913\pi$
$882$	−462.377	+	462.377i	−0.524237	+	0.524237i
$883$	512.453	−	512.453i	0.580354	−	0.580354i	−0.354646	−	0.935001i	$-0.615399\pi$
$883$	512.453	−	512.453i	0.580354	−	0.580354i	0.935001	+	0.354646i	$0.115399\pi$
$884$	−111.613	−	48.1148i	−0.126259	−	0.0544285i
$885$	934.187	+	1284.59i	1.05558	+	1.45152i
$886$		−	109.047i		−	0.123078i
$887$	−577.324	−	577.324i	−0.650872	−	0.650872i	0.302331	−	0.953203i	$-0.402235\pi$
$887$	−577.324	−	577.324i	−0.650872	−	0.650872i	−0.953203	+	0.302331i	$0.902235\pi$
$888$	265.402	−	265.402i	0.298876	−	0.298876i
$889$	−1951.95			−2.19567
$890$	−165.558	−	227.657i	−0.186020	−	0.255794i
$891$		−	108.442i		−	0.121709i
$892$	135.686	−	135.686i	0.152114	−	0.152114i
$893$	81.0370	−	81.0370i	0.0907469	−	0.0907469i
$894$		−	455.756i		−	0.509794i
$895$	−844.396	−	133.353i	−0.943459	−	0.148998i
$896$	1380.58			1.54083
$897$	−1721.05	+	684.188i	−1.91868	+	0.762751i
$898$	208.841	−	208.841i	0.232563	−	0.232563i
$899$	122.090			0.135807
$900$	−1178.31	−	381.694i	−1.30923	−	0.424104i
$901$	−1.89036			−0.00209807
$902$	−115.857	+	115.857i	−0.128444	+	0.128444i
$903$	2770.57	+	2770.57i	3.06818	+	3.06818i
$904$	216.134			0.239087
$905$	−2.87199	+	18.1855i	−0.00317347	+	0.0200945i
$906$	214.509			0.236765
$907$	930.007	+	930.007i	1.02537	+	1.02537i	0.999670	+	0.0256965i	$0.00818035\pi$
$907$	930.007	+	930.007i	1.02537	+	1.02537i	0.0256965	+	0.999670i	$0.491820\pi$
$908$	−218.592	−	218.592i	−0.240740	−	0.240740i
$909$		−	673.139i		−	0.740526i
$910$	101.998	+	452.403i	0.112086	+	0.497146i
$911$	−1448.45			−1.58996			−0.794980	−	0.606635i	$-0.792519\pi$
$911$	−1448.45			−1.58996			−0.794980	+	0.606635i	$0.792519\pi$
$912$	−272.479	+	272.479i	−0.298771	+	0.298771i
$913$	712.380	−	712.380i	0.780263	−	0.780263i
$914$			557.759i			0.610240i
$915$	−228.498	−	314.206i	−0.249725	−	0.343394i
$916$			665.399i			0.726418i
$917$	1504.52	−	1504.52i	1.64070	−	1.64070i
$918$	−27.4253	−	27.4253i	−0.0298750	−	0.0298750i
$919$		−	953.528i		−	1.03757i	−0.854905	−	0.518785i	$-0.826384\pi$
$919$		−	953.528i		−	1.03757i	0.854905	−	0.518785i	$-0.173616\pi$
$920$	−113.790	+	720.522i	−0.123685	+	0.783176i
$921$		−	1899.71i		−	2.06266i
$922$	160.035	+	160.035i	0.173574	+	0.173574i
$923$	1044.39	−	415.186i	1.13151	−	0.449822i
$924$			1434.90i			1.55293i
$925$	−357.548	+	182.582i	−0.386538	+	0.197386i
$926$	−104.259			−0.112591
$927$	1210.79	+	1210.79i	1.30614	+	1.30614i
$928$	425.356	+	425.356i	0.458358	+	0.458358i
$929$	89.9259			0.0967986			0.0483993	−	0.998828i	$-0.484588\pi$
$929$	89.9259			0.0967986			0.0483993	+	0.998828i	$0.484588\pi$
$930$	13.0657	−	82.7324i	0.0140491	−	0.0889595i
$931$		−	529.034i		−	0.568243i
$932$	296.772	+	296.772i	0.318425	+	0.318425i
$933$	−1341.02	+	1341.02i	−1.43732	+	1.43732i
$934$	−506.249			−0.542023
$935$	−58.1307	−	79.9350i	−0.0621718	−	0.0854920i
$936$	807.381	+	348.050i	0.862587	+	0.371849i
$937$	−707.424	−	707.424i	−0.754988	−	0.754988i	0.220418	−	0.975406i	$-0.429258\pi$
$937$	−707.424	−	707.424i	−0.754988	−	0.754988i	−0.975406	+	0.220418i	$0.929258\pi$
$938$	−531.950	−	531.950i	−0.567111	−	0.567111i
$939$		−	474.254i		−	0.505063i
$940$	230.200	−	167.407i	0.244894	−	0.178093i
$941$			311.835i			0.331387i	0.986177	+	0.165693i	$0.0529862\pi$
$941$			311.835i			0.331387i	−0.986177	+	0.165693i	$0.947014\pi$
$942$	−201.490	+	201.490i	−0.213896	+	0.213896i
$943$	706.804	+	706.804i	0.749527	+	0.749527i
$944$	743.366			0.787464
$945$	198.814	−	1258.90i	0.210385	−	1.33217i
$946$	−362.466			−0.383156
$947$	526.366	−	526.366i	0.555825	−	0.555825i	−0.372291	−	0.928116i	$-0.621428\pi$
$947$	526.366	−	526.366i	0.555825	−	0.555825i	0.928116	+	0.372291i	$0.121428\pi$
$948$	−516.734	+	516.734i	−0.545078	+	0.545078i
$949$	499.788	−	1159.37i	0.526647	−	1.22168i
$950$	−103.627	+	52.9172i	−0.109081	+	0.0557023i
$951$		−	1326.69i		−	1.39505i
$952$	−99.8130	−	99.8130i	−0.104846	−	0.104846i
$953$	−123.996	+	123.996i	−0.130111	+	0.130111i	−0.769163	−	0.639052i	$-0.779327\pi$
$953$	−123.996	+	123.996i	−0.130111	+	0.130111i	0.639052	+	0.769163i	$0.279327\pi$
$954$	6.46204			0.00677363
$955$	−134.125	+	849.281i	−0.140445	+	0.889300i
$956$			678.034i			0.709241i
$957$	−574.966	+	574.966i	−0.600800	+	0.600800i
$958$	202.429	−	202.429i	0.211304	−	0.211304i
$959$		−	1993.59i		−	2.07883i
$960$	−530.146	+	385.535i	−0.552236	+	0.401599i
$961$	931.456			0.969257
$962$	125.145	−	49.7502i	0.130088	−	0.0517154i
$963$	774.468	−	774.468i	0.804224	−	0.804224i
$964$	45.6557			0.0473606
$965$	−314.694	+	228.853i	−0.326107	+	0.237153i
$966$	−1016.46			−1.05224
$967$	−655.305	+	655.305i	−0.677669	+	0.677669i	−0.959472	−	0.281804i	$-0.909067\pi$
$967$	−655.305	+	655.305i	−0.677669	+	0.677669i	0.281804	+	0.959472i	$0.409067\pi$
$968$	219.960	+	219.960i	0.227231	+	0.227231i
$969$	89.9207			0.0927974
$970$	−112.323	−	17.7389i	−0.115797	−	0.0182875i
$971$	166.359			0.171328			0.0856638	−	0.996324i	$-0.472699\pi$
$971$	166.359			0.171328			0.0856638	+	0.996324i	$0.472699\pi$
$972$	698.909	+	698.909i	0.719042	+	0.719042i
$973$	−828.262	−	828.262i	−0.851246	−	0.851246i
$974$		−	88.1393i		−	0.0904921i
$975$	−1167.02	−	1024.14i	−1.19694	−	1.05040i
$976$	−181.824			−0.186295
$977$	1144.68	−	1144.68i	1.17163	−	1.17163i	0.189805	−	0.981822i	$-0.439214\pi$
$977$	1144.68	−	1144.68i	1.17163	−	1.17163i	0.981822	−	0.189805i	$-0.0607856\pi$
$978$	247.660	−	247.660i	0.253231	−	0.253231i
$979$		−	661.287i		−	0.675472i
$980$	204.966	−	1297.85i	0.209149	−	1.32434i
$981$		−	453.302i		−	0.462082i
$982$	89.6880	−	89.6880i	0.0913320	−	0.0913320i
$983$	−727.296	−	727.296i	−0.739874	−	0.739874i	0.232680	−	0.972553i	$-0.425251\pi$
$983$	−727.296	−	727.296i	−0.739874	−	0.739874i	−0.972553	+	0.232680i	$0.925251\pi$
$984$		−	783.441i		−	0.796180i
$985$	−62.5047	−	85.9497i	−0.0634566	−	0.0872586i
$986$		−	37.8004i		−	0.0383372i
$987$	593.483	+	593.483i	0.601300	+	0.601300i
$988$	−312.365	+	124.178i	−0.316159	+	0.125686i
$989$			2211.28i			2.23588i
$990$	198.714	+	273.251i	0.200722	+	0.276011i
$991$	503.468			0.508040			0.254020	−	0.967199i	$-0.418247\pi$
$991$	503.468			0.508040			0.254020	+	0.967199i	$0.418247\pi$
$992$	−102.931	−	102.931i	−0.103761	−	0.103761i
$993$	−1911.85	−	1911.85i	−1.92533	−	1.92533i
$994$	616.820			0.620543
$995$	752.716	+	118.874i	0.756499	+	0.119472i
$996$			2276.45i			2.28559i
$997$	−168.172	−	168.172i	−0.168678	−	0.168678i	0.617720	−	0.786398i	$-0.288056\pi$
$997$	−168.172	−	168.172i	−0.168678	−	0.168678i	−0.786398	+	0.617720i	$0.788056\pi$
$998$	155.133	−	155.133i	0.155444	−	0.155444i
$999$	−370.103			−0.370474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.3.h.a.12.7	yes	24
5.2	odd	4		325.3.h.b.168.7		24
5.3	odd	4	inner	65.3.h.a.38.6	yes	24
5.4	even	2		325.3.h.b.207.6		24
13.12	even	2	inner	65.3.h.a.12.6	✓	24
65.12	odd	4		325.3.h.b.168.6		24
65.38	odd	4	inner	65.3.h.a.38.7	yes	24
65.64	even	2		325.3.h.b.207.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.h.a.12.6	✓	24	13.12	even	2	inner
65.3.h.a.12.7	yes	24	1.1	even	1	trivial
65.3.h.a.38.6	yes	24	5.3	odd	4	inner
65.3.h.a.38.7	yes	24	65.38	odd	4	inner
325.3.h.b.168.6		24	65.12	odd	4
325.3.h.b.168.7		24	5.2	odd	4
325.3.h.b.207.6		24	5.4	even	2
325.3.h.b.207.7		24	65.64	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	65.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.456148 - 0.456148i) q^{2} +(3.37817 - 3.37817i) q^{3} +3.58386i q^{4} +(0.779969 - 4.93879i) q^{5} -3.08189i q^{6} +(-7.82065 + 7.82065i) q^{7} +(3.45936 + 3.45936i) q^{8} -13.8241i q^{9} +O(q^{10})\)	\(q+(0.456148 - 0.456148i) q^{2} +(3.37817 - 3.37817i) q^{3} +3.58386i q^{4} +(0.779969 - 4.93879i) q^{5} -3.08189i q^{6} +(-7.82065 + 7.82065i) q^{7} +(3.45936 + 3.45936i) q^{8} -13.8241i q^{9} +(-1.89704 - 2.60860i) q^{10} -7.57734i q^{11} +(12.1069 + 12.1069i) q^{12} +(4.80245 + 12.0804i) q^{13} +7.13475i q^{14} +(-14.0492 - 19.3190i) q^{15} -11.1795 q^{16} +(1.84467 + 1.84467i) q^{17} +(-6.30583 - 6.30583i) q^{18} +7.21489 q^{19} +(17.6999 + 2.79530i) q^{20} +52.8390i q^{21} +(-3.45639 - 3.45639i) q^{22} +(-21.0863 + 21.0863i) q^{23} +23.3726 q^{24} +(-23.7833 - 7.70421i) q^{25} +(7.70109 + 3.31983i) q^{26} +(-16.2966 - 16.2966i) q^{27} +(-28.0281 - 28.0281i) q^{28} -22.4617i q^{29} +(-15.2208 - 2.40378i) q^{30} +5.43547i q^{31} +(-18.9369 + 18.9369i) q^{32} +(-25.5976 - 25.5976i) q^{33} +1.68288 q^{34} +(32.5247 + 44.7244i) q^{35} +49.5436 q^{36} +(11.3552 - 11.3552i) q^{37} +(3.29106 - 3.29106i) q^{38} +(57.0332 + 24.5862i) q^{39} +(19.7833 - 14.3869i) q^{40} -33.5196i q^{41} +(24.1024 + 24.1024i) q^{42} +(52.4341 - 52.4341i) q^{43} +27.1561 q^{44} +(-68.2743 - 10.7824i) q^{45} +19.2370i q^{46} +(11.2319 - 11.2319i) q^{47} +(-37.7662 + 37.7662i) q^{48} -73.3253i q^{49} +(-14.3630 + 7.33444i) q^{50} +12.4632 q^{51} +(-43.2945 + 17.2113i) q^{52} +(-0.512386 + 0.512386i) q^{53} -14.8673 q^{54} +(-37.4229 - 5.91010i) q^{55} -54.1090 q^{56} +(24.3731 - 24.3731i) q^{57} +(-10.2459 - 10.2459i) q^{58} -66.4939 q^{59} +(69.2364 - 50.3504i) q^{60} +16.2641 q^{61} +(2.47938 + 2.47938i) q^{62} +(108.113 + 108.113i) q^{63} -27.4418i q^{64} +(63.4084 - 14.2960i) q^{65} -23.3526 q^{66} +(-74.5577 + 74.5577i) q^{67} +(-6.61103 + 6.61103i) q^{68} +142.466i q^{69} +(35.2370 + 5.56489i) q^{70} -86.4528i q^{71} +(47.8225 - 47.8225i) q^{72} +(-68.6714 - 68.6714i) q^{73} -10.3593i q^{74} +(-106.370 + 54.3179i) q^{75} +25.8571i q^{76} +(59.2598 + 59.2598i) q^{77} +(37.2305 - 14.8006i) q^{78} +42.6810i q^{79} +(-8.71964 + 55.2131i) q^{80} +14.3114 q^{81} +(-15.2899 - 15.2899i) q^{82} +(94.0145 + 94.0145i) q^{83} -189.368 q^{84} +(10.5492 - 7.67164i) q^{85} -47.8354i q^{86} +(-75.8796 - 75.8796i) q^{87} +(26.2128 - 26.2128i) q^{88} +87.2716 q^{89} +(-36.0615 + 26.2248i) q^{90} +(-132.035 - 56.9184i) q^{91} +(-75.5703 - 75.5703i) q^{92} +(18.3620 + 18.3620i) q^{93} -10.2468i q^{94} +(5.62739 - 35.6328i) q^{95} +127.944i q^{96} +(24.9295 - 24.9295i) q^{97} +(-33.4472 - 33.4472i) q^{98} -104.750 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3}+O(q^{10}) \) 24 * q - 4 * q^3	\( 24 q - 4 q^{3} + 16 q^{10} + 72 q^{12} - 36 q^{13} - 104 q^{16} - 48 q^{17} + 8 q^{22} - 104 q^{23} - 88 q^{25} + 88 q^{26} + 56 q^{27} - 24 q^{30} - 64 q^{35} + 256 q^{36} + 124 q^{38} - 368 q^{40} + 216 q^{42} + 8 q^{43} + 196 q^{48} - 296 q^{51} + 16 q^{52} + 220 q^{53} + 332 q^{55} + 584 q^{56} - 8 q^{61} - 596 q^{62} + 420 q^{65} - 360 q^{66} - 640 q^{68} - 184 q^{75} + 388 q^{77} - 636 q^{78} - 224 q^{81} - 1004 q^{82} - 52 q^{87} + 780 q^{88} + 452 q^{90} - 512 q^{91} + 812 q^{92} - 136 q^{95}+O(q^{100}) \) 24 * q - 4 * q^3 + 16 * q^10 + 72 * q^12 - 36 * q^13 - 104 * q^16 - 48 * q^17 + 8 * q^22 - 104 * q^23 - 88 * q^25 + 88 * q^26 + 56 * q^27 - 24 * q^30 - 64 * q^35 + 256 * q^36 + 124 * q^38 - 368 * q^40 + 216 * q^42 + 8 * q^43 + 196 * q^48 - 296 * q^51 + 16 * q^52 + 220 * q^53 + 332 * q^55 + 584 * q^56 - 8 * q^61 - 596 * q^62 + 420 * q^65 - 360 * q^66 - 640 * q^68 - 184 * q^75 + 388 * q^77 - 636 * q^78 - 224 * q^81 - 1004 * q^82 - 52 * q^87 + 780 * q^88 + 452 * q^90 - 512 * q^91 + 812 * q^92 - 136 * q^95

Introduction

L-functions

Modular forms

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