LMFDB - Embedded newform 483.2.y.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(4,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 12]))

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

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

chi := DirichletCharacter("483.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, degree $20$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	483.121
Dual form			483.2.y.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59717 - 2.24291i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-1.82557 + 5.27464i) q^{4} +(-0.128956 - 2.70712i) q^{5} +(-1.80314 + 2.08094i) q^{6} +(2.64469 - 0.0748341i) q^{7} +(9.46243 - 2.77842i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-1.59717 - 2.24291i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-1.82557 + 5.27464i) q^{4} +(-0.128956 - 2.70712i) q^{5} +(-1.80314 + 2.08094i) q^{6} +(2.64469 - 0.0748341i) q^{7} +(9.46243 - 2.77842i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-5.86587 + 4.61297i) q^{10} +(3.33228 - 4.67953i) q^{11} +(5.55635 + 0.530567i) q^{12} +(-0.311590 - 2.16716i) q^{13} +(-4.39188 - 5.81230i) q^{14} +(-2.60041 + 0.763548i) q^{15} +(-12.5700 - 9.88514i) q^{16} +(-2.11627 - 0.407878i) q^{17} +(2.44739 + 1.26172i) q^{18} +(7.06375 - 1.36143i) q^{19} +(14.5145 + 4.26184i) q^{20} +(-0.696235 - 2.55250i) q^{21} -15.8180 q^{22} +(-2.73936 + 3.93648i) q^{23} +(-4.93095 - 8.54066i) q^{24} +(-2.33450 + 0.222917i) q^{25} +(-4.36308 + 4.16019i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-4.43335 + 14.0864i) q^{28} +(2.79880e-5 - 3.22998e-5i) q^{29} +(5.86587 + 4.61297i) q^{30} +(-1.97396 - 1.88217i) q^{31} +(-1.15661 + 24.2802i) q^{32} +(-5.33324 - 2.13511i) q^{33} +(2.46521 + 5.39807i) q^{34} +(-0.543633 - 7.14984i) q^{35} +(-0.794348 - 5.52481i) q^{36} +(-4.79844 + 2.47377i) q^{37} +(-14.3356 - 13.6690i) q^{38} +(-2.03261 + 0.813734i) q^{39} +(-8.74174 - 25.2576i) q^{40} +(2.03072 - 1.30506i) q^{41} +(-4.61303 + 5.63838i) q^{42} +(6.37560 + 1.87205i) q^{43} +(18.5995 + 26.1194i) q^{44} +(1.35509 + 2.34709i) q^{45} +(13.2044 - 0.143091i) q^{46} +(-2.33768 + 4.04899i) q^{47} +(-6.64301 + 14.5462i) q^{48} +(6.98880 - 0.395826i) q^{49} +(4.22858 + 4.88004i) q^{50} +(0.102549 + 2.15278i) q^{51} +(11.9998 + 2.31277i) q^{52} +(-4.59519 + 1.83964i) q^{53} +(0.649156 - 2.67586i) q^{54} +(-13.0978 - 8.41742i) q^{55} +(24.8173 - 8.05618i) q^{56} +(-2.98839 - 6.54367i) q^{57} +(-0.000117147 - 1.11862e-5i) q^{58} +(3.04192 - 2.39219i) q^{59} +(0.719783 - 15.1101i) q^{60} +(-2.11943 + 8.73641i) q^{61} +(-1.06879 + 7.43357i) q^{62} +(-2.31641 + 1.27838i) q^{63} +(29.4003 - 18.8944i) q^{64} +(-5.82657 + 1.12298i) q^{65} +(3.72924 + 15.3721i) q^{66} +(-10.8245 + 1.03361i) q^{67} +(6.01481 - 10.4180i) q^{68} +(4.47135 + 1.73408i) q^{69} +(-15.1682 + 12.6389i) q^{70} +(-3.52147 + 7.71095i) q^{71} +(-7.13740 + 6.80549i) q^{72} +(1.45196 - 4.19516i) q^{73} +(13.2124 + 6.81146i) q^{74} +(0.767012 + 2.21614i) q^{75} +(-5.71434 + 39.7441i) q^{76} +(8.46266 - 12.6253i) q^{77} +(5.07156 + 3.25929i) q^{78} +(-4.13206 - 1.65423i) q^{79} +(-25.1393 + 35.3032i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-6.17056 - 2.47032i) q^{82} +(2.47227 + 1.58883i) q^{83} +(14.7345 + 0.987382i) q^{84} +(-0.831268 + 5.78159i) q^{85} +(-5.98410 - 17.2899i) q^{86} +(-3.79878e-5 - 1.95841e-5i) q^{87} +(18.5297 - 53.5382i) q^{88} +(-1.13111 + 1.07852i) q^{89} +(3.10001 - 6.78807i) q^{90} +(-0.986237 - 5.70815i) q^{91} +(-15.7626 - 21.6355i) q^{92} +(-1.36373 + 2.36206i) q^{93} +(12.8152 - 1.22370i) q^{94} +(-4.59646 - 18.9469i) q^{95} +(23.8684 - 4.60027i) q^{96} +(-0.371269 + 0.238600i) q^{97} +(-12.0501 - 15.0431i) q^{98} +(-0.817562 + 5.68627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21} - 176 q^{22} - 18 q^{23} - 6 q^{24} + 8 q^{25} - 14 q^{26} + 32 q^{27} + 46 q^{28} + 34 q^{29} - 8 q^{30} + 52 q^{31} - 8 q^{32} - 5 q^{33} - 24 q^{34} - 12 q^{35} - 14 q^{36} - 30 q^{37} - 157 q^{38} + 88 q^{40} - 28 q^{41} - 45 q^{42} + 64 q^{43} - 71 q^{44} - 2 q^{45} + 4 q^{46} + 36 q^{47} + 60 q^{48} + 28 q^{49} + 210 q^{50} - 26 q^{51} - 198 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{55} + 44 q^{57} + 31 q^{58} + 10 q^{59} - 2 q^{60} - 34 q^{61} - 8 q^{62} + 2 q^{63} + 84 q^{64} + 38 q^{65} - 12 q^{67} - 22 q^{68} + 8 q^{69} - 336 q^{70} - 144 q^{71} + 6 q^{72} - 16 q^{73} - 68 q^{74} - 30 q^{75} + 8 q^{76} + 98 q^{77} + 16 q^{78} + 26 q^{79} + 225 q^{80} + 16 q^{81} - 122 q^{82} + 44 q^{84} - 240 q^{85} - 26 q^{86} - 16 q^{87} + 43 q^{88} + 68 q^{89} - 16 q^{90} + 40 q^{91} - 222 q^{92} - 8 q^{93} + 137 q^{94} - 49 q^{95} + 30 q^{96} - 8 q^{97} + 137 q^{98} - 10 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	−1.59717	−	2.24291i	−1.12937	−	1.58598i	−0.750968	−	0.660339i	$-0.770413\pi$
$2$	−1.59717	−	2.24291i	−1.12937	−	1.58598i	−0.378403	−	0.925641i	$-0.623527\pi$
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$4$	−1.82557	+	5.27464i	−0.912785	+	2.63732i
$5$	−0.128956	−	2.70712i	−0.0576708	−	1.21066i	−0.823387	−	0.567481i	$-0.807918\pi$
$5$	−0.128956	−	2.70712i	−0.0576708	−	1.21066i	0.765716	−	0.643179i	$-0.222385\pi$
$6$	−1.80314	+	2.08094i	−0.736130	+	0.849539i
$7$	2.64469	−	0.0748341i	0.999600	−	0.0282846i
$7$	2.64469	−	0.0748341i	0.999600	−	0.0282846i
$8$	9.46243	−	2.77842i	3.34547	−	0.982320i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−5.86587	+	4.61297i	−1.85495	+	1.45875i
$11$	3.33228	−	4.67953i	1.00472	−	1.41093i	0.0951102	−	0.995467i	$-0.469680\pi$
$11$	3.33228	−	4.67953i	1.00472	−	1.41093i	0.909609	−	0.415465i	$-0.136381\pi$
$12$	5.55635	+	0.530567i	1.60398	+	0.153161i
$13$	−0.311590	−	2.16716i	−0.0864196	−	0.601061i	−0.986305	−	0.164934i	$-0.947259\pi$
$13$	−0.311590	−	2.16716i	−0.0864196	−	0.601061i	0.899885	−	0.436127i	$-0.143650\pi$
$14$	−4.39188	−	5.81230i	−1.17378	−	1.55340i
$15$	−2.60041	+	0.763548i	−0.671422	+	0.197147i
$16$	−12.5700	−	9.88514i	−3.14249	−	2.47129i
$17$	−2.11627	−	0.407878i	−0.513271	−	0.0989249i	−0.0739624	−	0.997261i	$-0.523564\pi$
$17$	−2.11627	−	0.407878i	−0.513271	−	0.0989249i	−0.439309	+	0.898336i	$0.644777\pi$
$18$	2.44739	+	1.26172i	0.576854	+	0.297389i
$19$	7.06375	−	1.36143i	1.62054	−	0.312333i	0.703366	−	0.710828i	$-0.251680\pi$
$19$	7.06375	−	1.36143i	1.62054	−	0.312333i	0.917170	+	0.398495i	$0.130467\pi$
$20$	14.5145	+	4.26184i	3.24554	+	0.952976i
$21$	−0.696235	−	2.55250i	−0.151931	−	0.557001i
$22$	−15.8180			−3.37241
$23$	−2.73936	+	3.93648i	−0.571196	+	0.820814i
$23$	−2.73936	+	3.93648i	−0.571196	+	0.820814i
$24$	−4.93095	−	8.54066i	−1.00653	−	1.74335i
$25$	−2.33450	+	0.222917i	−0.466899	+	0.0445835i
$26$	−4.36308	+	4.16019i	−0.855671	+	0.815881i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−4.43335	+	14.0864i	−0.837824	+	2.66208i
$29$	2.79880e−5	0	3.22998e-5i	5.19723e−6	0	5.99793e-6i	−0.755747	−	0.654864i	$-0.772726\pi$
$29$	2.79880e−5	0	3.22998e-5i	5.19723e−6	0	5.99793e-6i	0.755752	+	0.654858i	$0.227271\pi$
$30$	5.86587	+	4.61297i	1.07096	+	0.842209i
$31$	−1.97396	−	1.88217i	−0.354534	−	0.338047i	0.491792	−	0.870713i	$-0.336342\pi$
$31$	−1.97396	−	1.88217i	−0.354534	−	0.338047i	−0.846326	+	0.532665i	$0.821190\pi$
$32$	−1.15661	+	24.2802i	−0.204461	+	4.29217i
$33$	−5.33324	−	2.13511i	−0.928397	−	0.371674i
$34$	2.46521	+	5.39807i	0.422781	+	0.925761i
$35$	−0.543633	−	7.14984i	−0.0918908	−	1.20854i
$36$	−0.794348	−	5.52481i	−0.132391	−	0.920802i
$37$	−4.79844	+	2.47377i	−0.788859	+	0.406685i	−0.805067	−	0.593184i	$-0.797871\pi$
$37$	−4.79844	+	2.47377i	−0.788859	+	0.406685i	0.0162082	+	0.999869i	$0.494841\pi$
$38$	−14.3356	−	13.6690i	−2.32554	−	2.21740i
$39$	−2.03261	+	0.813734i	−0.325478	+	0.130302i
$40$	−8.74174	−	25.2576i	−1.38219	−	3.99358i
$41$	2.03072	−	1.30506i	0.317145	−	0.203817i	−0.372377	−	0.928082i	$-0.621457\pi$
$41$	2.03072	−	1.30506i	0.317145	−	0.203817i	0.689522	+	0.724265i	$0.257821\pi$
$42$	−4.61303	+	5.63838i	−0.711806	+	0.870020i
$43$	6.37560	+	1.87205i	0.972270	+	0.285484i	0.729030	−	0.684482i	$-0.239971\pi$
$43$	6.37560	+	1.87205i	0.972270	+	0.285484i	0.243240	+	0.969966i	$0.421790\pi$
$44$	18.5995	+	26.1194i	2.80398	+	3.93764i
$45$	1.35509	+	2.34709i	0.202005	+	0.349884i
$46$	13.2044	−	0.143091i	1.94689	−	0.0210976i
$47$	−2.33768	+	4.04899i	−0.340986	+	0.590606i	−0.984616	−	0.174731i	$-0.944094\pi$
$47$	−2.33768	+	4.04899i	−0.340986	+	0.590606i	0.643630	+	0.765337i	$0.277428\pi$
$48$	−6.64301	+	14.5462i	−0.958836	+	2.09956i
$49$	6.98880	−	0.395826i	0.998400	−	0.0565466i
$50$	4.22858	+	4.88004i	0.598011	+	0.690141i
$51$	0.102549	+	2.15278i	0.0143598	+	0.301449i
$52$	11.9998	+	2.31277i	1.66407	+	0.320724i
$53$	−4.59519	+	1.83964i	−0.631198	+	0.252693i	−0.665126	−	0.746731i	$-0.731622\pi$
$53$	−4.59519	+	1.83964i	−0.631198	+	0.252693i	0.0339286	+	0.999424i	$0.489198\pi$
$54$	0.649156	−	2.67586i	0.0883390	−	0.364138i
$55$	−13.0978	−	8.41742i	−1.76610	−	1.13500i
$56$	24.8173	−	8.05618i	3.31635	−	1.07655i
$57$	−2.98839	−	6.54367i	−0.395822	−	0.866730i
$58$	−0.000117147	0	1.11862e-5i	−1.53822e−5	0	1.46882e-6i
$59$	3.04192	−	2.39219i	0.396024	−	0.311437i	−0.400212	−	0.916423i	$-0.631064\pi$
$59$	3.04192	−	2.39219i	0.396024	−	0.311437i	0.796236	+	0.604986i	$0.206821\pi$
$60$	0.719783	−	15.1101i	0.0929236	−	1.95071i
$61$	−2.11943	+	8.73641i	−0.271365	+	1.11858i	0.659057	+	0.752093i	$0.270956\pi$
$61$	−2.11943	+	8.73641i	−0.271365	+	1.11858i	−0.930422	+	0.366489i	$0.880560\pi$
$62$	−1.06879	+	7.43357i	−0.135736	+	0.944065i
$63$	−2.31641	+	1.27838i	−0.291840	+	0.161061i
$64$	29.4003	−	18.8944i	3.67503	−	2.36180i
$65$	−5.82657	+	1.12298i	−0.722697	+	0.139288i
$66$	3.72924	+	15.3721i	0.459037	+	1.89218i
$67$	−10.8245	+	1.03361i	−1.32242	+	0.126276i	−0.732269	−	0.681015i	$-0.761539\pi$
$67$	−10.8245	+	1.03361i	−1.32242	+	0.126276i	−0.590153	+	0.807291i	$0.700933\pi$
$68$	6.01481	−	10.4180i	0.729403	−	1.26336i
$69$	4.47135	+	1.73408i	0.538287	+	0.208759i
$70$	−15.1682	+	12.6389i	−1.81295	+	1.51063i
$71$	−3.52147	+	7.71095i	−0.417922	+	0.915122i	0.577212	+	0.816594i	$0.304141\pi$
$71$	−3.52147	+	7.71095i	−0.417922	+	0.915122i	−0.995134	+	0.0985277i	$0.968587\pi$
$72$	−7.13740	+	6.80549i	−0.841150	+	0.802035i
$73$	1.45196	−	4.19516i	0.169939	−	0.491006i	−0.827585	−	0.561341i	$-0.810286\pi$
$73$	1.45196	−	4.19516i	0.169939	−	0.491006i	0.997523	+	0.0703350i	$0.0224068\pi$
$74$	13.2124	+	6.81146i	1.53591	+	0.791816i
$75$	0.767012	+	2.21614i	0.0885669	+	0.255897i
$76$	−5.71434	+	39.7441i	−0.655480	+	4.55896i
$77$	8.46266	−	12.6253i	0.964410	−	1.43878i
$78$	5.07156	+	3.25929i	0.574241	+	0.369042i
$79$	−4.13206	−	1.65423i	−0.464893	−	0.186115i	0.127377	−	0.991854i	$-0.459344\pi$
$79$	−4.13206	−	1.65423i	−0.464893	−	0.186115i	−0.592271	+	0.805739i	$0.701768\pi$
$80$	−25.1393	+	35.3032i	−2.81066	+	3.94701i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	−6.17056	−	2.47032i	−0.681424	−	0.272801i
$83$	2.47227	+	1.58883i	0.271366	+	0.174397i	0.669246	−	0.743041i	$-0.266617\pi$
$83$	2.47227	+	1.58883i	0.271366	+	0.174397i	−0.397879	+	0.917438i	$0.630254\pi$
$84$	14.7345	+	0.987382i	1.60767	+	0.107732i
$85$	−0.831268	+	5.78159i	−0.0901636	+	0.627102i
$86$	−5.98410	−	17.2899i	−0.645282	−	1.86442i
$87$	−3.79878e−5	0	1.95841e-5i	−4.07272e−6	0	2.09963e-6i
$88$	18.5297	−	53.5382i	1.97528	−	5.70719i
$89$	−1.13111	+	1.07852i	−0.119898	+	0.114322i	−0.747656	−	0.664086i	$-0.768821\pi$
$89$	−1.13111	+	1.07852i	−0.119898	+	0.114322i	0.627759	+	0.778408i	$0.283973\pi$
$90$	3.10001	−	6.78807i	0.326769	−	0.715525i
$91$	−0.986237	−	5.70815i	−0.103386	−	0.598376i
$92$	−15.7626	−	21.6355i	−1.64337	−	2.25565i
$93$	−1.36373	+	2.36206i	−0.141413	+	0.244934i
$94$	12.8152	−	1.22370i	1.32179	−	0.126216i
$95$	−4.59646	−	18.9469i	−0.471586	−	1.94391i
$96$	23.8684	−	4.60027i	2.43606	−	0.469513i
$97$	−0.371269	+	0.238600i	−0.0376966	+	0.0242262i	−0.559353	−	0.828929i	$-0.688951\pi$
$97$	−0.371269	+	0.238600i	−0.0376966	+	0.0242262i	0.521657	+	0.853155i	$0.325314\pi$
$98$	−12.0501	−	15.0431i	−1.21725	−	1.51958i
$99$	−0.817562	+	5.68627i	−0.0821681	+	0.571492i
$100$	3.08598	−	12.7206i	0.308598	−	1.27206i
$101$	0.524544	−	11.0115i	0.0521941	−	1.09569i	−0.809129	−	0.587631i	$-0.800061\pi$
$101$	0.524544	−	11.0115i	0.0521941	−	1.09569i	0.861323	−	0.508058i	$-0.169636\pi$
$102$	4.66471	−	3.66837i	0.461875	−	0.363222i
$103$	−4.53273	−	0.432823i	−0.446623	−	0.0426473i	−0.130678	−	0.991425i	$-0.541715\pi$
$103$	−4.53273	−	0.432823i	−0.446623	−	0.0426473i	−0.315945	+	0.948778i	$0.602321\pi$
$104$	−8.96967	−	19.6408i	−0.879549	−	1.92594i
$105$	−6.82013	+	2.21395i	−0.665577	+	0.216059i
$106$	11.4655	+	7.36840i	1.11362	+	0.715682i
$107$	0.507228	−	2.09082i	0.0490356	−	0.202128i	−0.942024	−	0.335544i	$-0.891080\pi$
$107$	0.507228	−	2.09082i	0.0490356	−	0.202128i	0.991060	+	0.133417i	$0.0425949\pi$
$108$	−5.18180	+	2.07448i	−0.498619	+	0.199617i
$109$	12.6921	+	2.44620i	1.21568	+	0.234304i	0.756474	−	0.654024i	$-0.226920\pi$
$109$	12.6921	+	2.44620i	1.21568	+	0.234304i	0.459210	+	0.888328i	$0.348133\pi$
$110$	2.03982	+	42.8212i	0.194490	+	4.08284i
$111$	3.53531	+	4.07997i	0.335557	+	0.387253i
$112$	−33.9835	−	25.2025i	−3.21114	−	2.38141i
$113$	−5.38597	+	11.7936i	−0.506669	+	1.10945i	0.467574	+	0.883954i	$0.345128\pi$
$113$	−5.38597	+	11.7936i	−0.506669	+	1.10945i	−0.974244	+	0.225498i	$0.927599\pi$
$114$	−9.90391	+	17.1541i	−0.927586	+	1.60663i
$115$	11.0098	+	6.90814i	1.02667	+	0.644187i
$116$	0.000119276	0	0.000206592i	1.10745e−5	0	1.91816e-5i
$117$	1.27000	+	1.78347i	0.117412	+	0.164882i
$118$	−10.2240	−	3.00202i	−0.941191	−	0.276359i
$119$	−5.62741	−	0.920342i	−0.515864	−	0.0843676i
$120$	−22.4847	+	14.4500i	−2.05256	+	1.31910i
$121$	−7.19617	−	20.7920i	−0.654198	−	1.89018i
$122$	22.9801	−	9.19985i	2.08052	−	0.832915i
$123$	−1.74704	−	1.66580i	−0.157525	−	0.150200i
$124$	13.5314	−	6.97590i	1.21515	−	0.626454i
$125$	−1.02399	−	7.12200i	−0.0915883	−	0.637011i
$126$	6.56700	+	3.15370i	0.585035	+	0.280954i
$127$	−3.22370	−	7.05891i	−0.286057	−	0.626377i	0.710988	−	0.703205i	$-0.248248\pi$
$127$	−3.22370	−	7.05891i	−0.286057	−	0.626377i	−0.997044	+	0.0768276i	$0.975521\pi$
$128$	−44.2028	−	17.6961i	−3.90701	−	1.56413i
$129$	0.316171	−	6.63724i	0.0278373	−	0.584376i
$130$	11.8248	+	11.2749i	1.03710	+	0.988874i
$131$	−10.3373	−	8.12935i	−0.903175	−	0.710265i	0.0543786	−	0.998520i	$-0.482682\pi$
$131$	−10.3373	−	8.12935i	−0.903175	−	0.710265i	−0.957553	+	0.288256i	$0.906925\pi$
$132$	20.9981	−	24.2331i	1.82765	−	2.10922i
$133$	18.5796	−	4.12917i	1.61105	−	0.358044i
$134$	19.6069	+	22.6276i	1.69378	+	1.95472i
$135$	1.96145	−	1.87024i	0.168815	−	0.160965i
$136$	−21.1583	+	2.02037i	−1.81431	+	0.173246i
$137$	0.604038	+	1.04622i	0.0516065	+	0.0893850i	0.890675	−	0.454641i	$-0.150233\pi$
$137$	0.604038	+	1.04622i	0.0516065	+	0.0893850i	−0.839068	+	0.544026i	$0.816899\pi$
$138$	−3.25212	−	12.7985i	−0.276839	−	1.08948i
$139$	12.4295			1.05426			0.527129	−	0.849785i	$-0.323268\pi$
$139$	12.4295			1.05426			0.527129	+	0.849785i	$0.323268\pi$
$140$	38.7053	+	10.1851i	3.27119	+	0.860795i
$141$	4.48598	+	1.31720i	0.377788	+	0.110929i
$142$	22.9194	−	4.41735i	1.92335	−	0.370696i
$143$	−11.1796	−	5.76347i	−0.934883	−	0.481966i
$144$	15.7023	+	3.02637i	1.30852	+	0.252197i
$145$	−9.10486e−5	0	7.16014e-5i	−7.56118e−6	0	5.94618e-6i
$146$	−11.7284	+	3.44377i	−0.970650	+	0.285008i
$147$	−2.03234	−	6.69848i	−0.167625	−	0.552481i
$148$	−4.28834	−	29.8261i	−0.352500	−	2.45169i
$149$	13.7313	+	1.31118i	1.12491	+	0.107416i	0.640885	−	0.767637i	$-0.278567\pi$
$149$	13.7313	+	1.31118i	1.12491	+	0.107416i	0.484028	+	0.875053i	$0.339173\pi$
$150$	3.74555	−	5.25989i	0.305823	−	0.429468i
$151$	−5.01210	+	3.94156i	−0.407879	+	0.320760i	−0.800931	−	0.598757i	$-0.795662\pi$
$151$	−5.01210	+	3.94156i	−0.407879	+	0.320760i	0.393052	+	0.919516i	$0.371419\pi$
$152$	63.0577	−	32.5085i	5.11465	−	2.63679i
$153$	2.06792	−	0.607195i	0.167181	−	0.0490888i
$154$	−41.8338	+	1.18373i	−3.37106	+	0.0953874i
$155$	−4.84070	+	5.58646i	−0.388814	+	0.448715i
$156$	−0.581481	−	12.2068i	−0.0465558	−	0.977326i
$157$	−4.28340	+	12.3761i	−0.341853	+	0.987718i	0.634760	+	0.772710i	$0.281099\pi$
$157$	−4.28340	+	12.3761i	−0.341853	+	0.987718i	−0.976612	+	0.215009i	$0.931022\pi$
$158$	2.88932	+	11.9099i	0.229862	+	0.947505i
$159$	2.87114	+	4.03195i	0.227696	+	0.319754i
$160$	65.8785			5.20815
$161$	−6.95018	+	10.6158i	−0.547751	+	0.836641i
$162$	−2.75347			−0.216333
$163$	−3.78238	−	5.31161i	−0.296259	−	0.416038i	0.639438	−	0.768843i	$-0.279167\pi$
$163$	−3.78238	−	5.31161i	−0.296259	−	0.416038i	−0.935697	+	0.352805i	$0.885228\pi$
$164$	3.17652	+	13.0938i	0.248045	+	1.02245i
$165$	−5.09223	+	14.7130i	−0.396429	+	1.14541i
$166$	−0.385027	−	8.08271i	−0.0298839	−	0.627340i
$167$	8.30396	−	9.58328i	0.642580	−	0.741577i	−0.337249	−	0.941416i	$-0.609496\pi$
$167$	8.30396	−	9.58328i	0.642580	−	0.741577i	0.979829	+	0.199839i	$0.0640419\pi$
$168$	−13.6800	−	22.2184i	−1.05543	−	1.71419i
$169$	7.87393	−	2.31199i	0.605687	−	0.177846i
$170$	14.2953	−	7.36974i	1.09640	−	0.565233i
$171$	−5.65467	+	4.44688i	−0.432424	+	0.340062i
$172$	−21.5135	+	30.2114i	−1.64039	+	2.30360i
$173$	21.4533	+	2.04854i	1.63106	+	0.155748i	0.870041	−	0.492979i	$-0.164092\pi$
$173$	21.4533	+	2.04854i	1.63106	+	0.155748i	0.761021	+	0.648727i	$0.224698\pi$
$174$	1.67476e−5	0	0.000116482i	1.26964e−6	0	8.83051e-6i
$175$	−6.15734	+	0.764248i	−0.465451	+	0.0577717i
$176$	−88.1445	+	25.8816i	−6.64414	+	1.95090i
$177$	−3.04192	−	2.39219i	−0.228645	−	0.179808i
$178$	4.22560	+	0.814418i	0.316722	+	0.0610432i
$179$	−2.15470	−	1.11083i	−0.161050	−	0.0830270i	0.375817	−	0.926694i	$-0.377362\pi$
$179$	−2.15470	−	1.11083i	−0.161050	−	0.0830270i	−0.536867	+	0.843667i	$0.680392\pi$
$180$	−14.8539	+	2.86285i	−1.10714	+	0.213384i
$181$	3.58313	+	1.05210i	0.266332	+	0.0782020i	0.412172	−	0.911106i	$-0.364770\pi$
$181$	3.58313	+	1.05210i	0.266332	+	0.0782020i	−0.145840	+	0.989308i	$0.546589\pi$
$182$	−11.2277	+	11.3289i	−0.832252	+	0.839757i
$183$	8.98982			0.664546
$184$	−14.9838	+	44.8598i	−1.10462	+	3.30711i
$185$	7.31557	+	12.6709i	0.537851	+	0.931586i
$186$	7.47601	−	0.713872i	0.548167	−	0.0523436i
$187$	−8.96068	+	8.54399i	−0.655270	+	0.624798i
$188$	−17.0893	−	19.7221i	−1.24637	−	1.43839i
$189$	1.78846	+	1.94972i	0.130091	+	0.141821i
$190$	−35.1548	+	40.5708i	−2.55040	+	2.94332i
$191$	−4.55925	−	3.58543i	−0.329896	−	0.259433i	0.439448	−	0.898268i	$-0.355174\pi$
$191$	−4.55925	−	3.58543i	−0.329896	−	0.259433i	−0.769344	+	0.638835i	$0.779417\pi$
$192$	−25.2932	−	24.1170i	−1.82538	−	1.74049i
$193$	−0.782745	+	16.4318i	−0.0563432	+	1.18279i	0.776805	+	0.629741i	$0.216839\pi$
$193$	−0.782745	+	16.4318i	−0.0563432	+	1.18279i	−0.833149	+	0.553049i	$0.813464\pi$
$194$	1.12814	+	0.451639i	0.0809957	+	0.0324258i
$195$	2.46499	+	5.39757i	0.176522	+	0.386528i
$196$	−10.6707	+	37.5860i	−0.762193	+	2.68471i
$197$	3.10088	+	21.5671i	0.220929	+	1.53659i	0.734537	+	0.678569i	$0.237400\pi$
$197$	3.10088	+	21.5671i	0.220929	+	1.53659i	−0.513608	+	0.858025i	$0.671691\pi$
$198$	14.0596	−	7.24823i	0.999172	−	0.515109i
$199$	19.1689	+	18.2775i	1.35885	+	1.29566i	0.917176	+	0.398482i	$0.130463\pi$
$199$	19.1689	+	18.2775i	1.35885	+	1.29566i	0.441672	+	0.897177i	$0.354385\pi$
$200$	−21.4706	+	8.59555i	−1.51820	+	0.607797i
$201$	3.55645	+	10.2757i	0.250853	+	0.724791i
$202$	−25.5357	+	16.4108i	−1.79669	+	1.15466i
$203$	7.16024e−5	0	8.75176e-5i	5.02551e−6	0	6.14253e-6i
$204$	−11.5423	−	3.38913i	−0.808125	−	0.237287i
$205$	−3.79484	−	5.32910i	−0.265043	−	0.372201i
$206$	6.26876	+	10.8578i	0.436765	+	0.756499i
$207$	0.631039	−	4.75413i	0.0438603	−	0.330435i
$208$	−17.5060	+	30.3212i	−1.21382	+	2.10240i
$209$	17.1676	−	37.5917i	1.18750	−	2.60027i
$210$	15.8586	+	11.7609i	1.09435	+	0.811581i
$211$	4.36954	+	5.04272i	0.300812	+	0.347155i	0.885952	−	0.463777i	$-0.153506\pi$
$211$	4.36954	+	5.04272i	0.300812	+	0.347155i	−0.585140	+	0.810932i	$0.698961\pi$
$212$	−1.31458	−	27.5963i	−0.0902854	−	1.89532i
$213$	8.32381	+	1.60428i	0.570338	+	0.109924i
$214$	−5.49967	+	2.20174i	−0.375950	+	0.150508i
$215$	4.24568	−	17.5009i	0.289553	−	1.19355i
$216$	8.29636	+	5.33175i	0.564496	+	0.362780i
$217$	−5.36137	−	4.83004i	−0.363954	−	0.327884i
$218$	−14.7849	−	32.3743i	−1.00136	−	2.19267i
$219$	−4.41921	−	0.421984i	−0.298623	−	0.0285150i
$220$	68.3097	−	53.7193i	4.60544	−	3.62176i
$221$	−0.224526	+	4.71338i	−0.0151033	+	0.317056i
$222$	3.50452	−	14.4458i	0.235208	−	0.969540i
$223$	−2.14837	+	14.9423i	−0.143866	+	1.00061i	0.782141	+	0.623101i	$0.214127\pi$
$223$	−2.14837	+	14.9423i	−0.143866	+	1.00061i	−0.926007	+	0.377506i	$0.876782\pi$
$224$	−1.24189	+	64.3002i	−0.0829770	+	4.29624i
$225$	1.97284	−	1.26786i	0.131522	−	0.0845243i
$226$	35.0544	−	6.75619i	2.33179	−	0.449415i
$227$	−0.0983441	−	0.405380i	−0.00652733	−	0.0269060i	0.968455	−	0.249189i	$-0.0801642\pi$
$227$	−0.0983441	−	0.405380i	−0.00652733	−	0.0269060i	−0.974982	+	0.222283i	$0.928649\pi$
$228$	39.9710	−	3.81677i	2.64714	−	0.252772i
$229$	6.34892	−	10.9966i	0.419548	−	0.726679i	−0.576346	−	0.817206i	$-0.695522\pi$
$229$	6.34892	−	10.9966i	0.419548	−	0.726679i	0.995894	+	0.0905272i	$0.0288552\pi$
$230$	−2.09015	−	35.7275i	−0.137821	−	2.35580i
$231$	−14.2645	−	5.24759i	−0.938538	−	0.345266i
$232$	0.000175092	0	0.000383397i	1.14953e−5	0	2.51713e-5i
$233$	−6.84544	+	6.52712i	−0.448460	+	0.427606i	−0.880353	−	0.474319i	$-0.842694\pi$
$233$	−6.84544	+	6.52712i	−0.448460	+	0.427606i	0.431893	+	0.901925i	$0.357846\pi$
$234$	1.97175	−	5.69701i	0.128898	−	0.372425i
$235$	11.2625	+	5.80625i	0.734687	+	0.378758i
$236$	7.06471	+	20.4121i	0.459874	+	1.32872i
$237$	−0.633427	+	4.40558i	−0.0411455	+	0.286173i
$238$	6.92369	+	14.0917i	0.448796	+	0.913432i
$239$	−9.42020	−	6.05400i	−0.609342	−	0.391600i	0.199268	−	0.979945i	$-0.436144\pi$
$239$	−9.42020	−	6.05400i	−0.609342	−	0.391600i	−0.808610	+	0.588345i	$0.799780\pi$
$240$	40.2348	+	16.1076i	2.59715	+	1.03974i
$241$	16.4810	−	23.1443i	1.06163	−	1.49086i	0.202379	−	0.979307i	$-0.435133\pi$
$241$	16.4810	−	23.1443i	1.06163	−	1.49086i	0.859255	−	0.511548i	$-0.170928\pi$
$242$	−35.1411	+	49.3488i	−2.25896	+	3.17226i
$243$	−0.928368	−	0.371662i	−0.0595548	−	0.0238422i
$244$	−42.2122	−	27.1281i	−2.70236	−	1.73670i
$245$	−1.97280	−	18.8685i	−0.126037	−	1.20546i
$246$	−0.945920	+	6.57902i	−0.0603097	+	0.419463i
$247$	−5.15142	−	14.8841i	−0.327777	−	0.947050i
$248$	−23.9079	−	12.3254i	−1.51815	−	0.782663i
$249$	0.961183	−	2.77716i	0.0609125	−	0.175995i
$250$	−14.3385	+	13.6718i	−0.906849	+	0.864679i
$251$	−5.44450	+	11.9218i	−0.343654	+	0.752497i	−0.999998	−	0.00196443i	$-0.999375\pi$
$251$	−5.44450	+	11.9218i	−0.343654	+	0.752497i	0.656344	+	0.754462i	$0.272102\pi$
$252$	−2.51425	−	14.5520i	−0.158383	−	0.916688i
$253$	9.29258	+	25.9364i	0.584220	+	1.63061i
$254$	−10.6837	+	18.5048i	−0.670357	+	1.16109i
$255$	5.81460	−	0.555227i	0.364124	−	0.0347696i
$256$	14.4299	+	59.4807i	0.901867	+	3.71755i
$257$	26.1530	−	5.04057i	1.63138	−	0.314422i	0.710329	−	0.703870i	$-0.248546\pi$
$257$	26.1530	−	5.04057i	1.63138	−	0.314422i	0.921049	+	0.389448i	$0.127334\pi$
$258$	−15.3917	+	9.89167i	−0.958247	+	0.615828i
$259$	−12.5053	+	6.90145i	−0.777040	+	0.428835i
$260$	4.71350	−	32.7831i	0.292319	−	2.03312i
$261$	−1.00761e−5	0	4.15341e-5i	−6.23692e−7	0	2.57089e-6i
$262$	−1.72297	+	36.1697i	−0.106446	+	2.23457i
$263$	18.7636	−	14.7558i	1.15701	−	0.909883i	0.159998	−	0.987117i	$-0.448851\pi$
$263$	18.7636	−	14.7558i	1.15701	−	0.909883i	0.997013	+	0.0772341i	$0.0246089\pi$
$264$	−56.3976	−	5.38532i	−3.47103	−	0.331443i
$265$	5.57269	+	12.2025i	0.342328	+	0.749593i
$266$	−38.9361	−	35.0774i	−2.38733	−	2.15073i
$267$	1.31478	+	0.844961i	0.0804635	+	0.0517108i
$268$	14.3089	−	58.9822i	0.874057	−	3.60291i
$269$	13.2806	−	5.31674i	0.809730	−	0.324167i	0.0704075	−	0.997518i	$-0.477570\pi$
$269$	13.2806	−	5.31674i	0.809730	−	0.324167i	0.739323	+	0.673351i	$0.235146\pi$
$270$	−7.32758	−	1.41227i	−0.445942	−	0.0859483i
$271$	0.784409	+	16.4668i	0.0476494	+	1.00029i	0.888460	+	0.458955i	$0.151776\pi$
$271$	0.784409	+	16.4668i	0.0476494	+	1.00029i	−0.840810	+	0.541330i	$0.817921\pi$
$272$	22.5696	+	26.0467i	1.36848	+	1.57931i
$273$	−5.31473	+	2.30418i	−0.321662	+	0.139456i
$274$	1.38184	−	3.02581i	0.0834800	−	0.182796i
$275$	−6.73604	+	11.6672i	−0.406199	+	0.703557i
$276$	−17.3094	+	20.4191i	−1.04190	+	1.22908i
$277$	−6.01269	−	10.4143i	−0.361267	−	0.625734i	0.626902	−	0.779098i	$-0.284323\pi$
$277$	−6.01269	−	10.4143i	−0.361267	−	0.625734i	−0.988170	+	0.153364i	$0.950989\pi$
$278$	−19.8521	−	27.8784i	−1.19065	−	1.67203i
$279$	2.61699	+	0.768416i	0.156675	+	0.0460039i
$280$	−25.0094	−	66.1444i	−1.49460	−	3.95289i
$281$	2.07384	−	1.33278i	0.123715	−	0.0795069i	−0.477320	−	0.878730i	$-0.658392\pi$
$281$	2.07384	−	1.33278i	0.123715	−	0.0795069i	0.601035	+	0.799223i	$0.294755\pi$
$282$	−4.21051	−	12.1655i	−0.250732	−	0.724444i
$283$	5.59762	−	2.24095i	0.332744	−	0.133211i	−0.199274	−	0.979944i	$-0.563858\pi$
$283$	5.59762	−	2.24095i	0.332744	−	0.133211i	0.532018	+	0.846733i	$0.321434\pi$
$284$	−34.2438	−	32.6514i	−2.03200	−	1.93750i
$285$	−17.3291	+	8.93378i	−1.02649	+	0.529191i
$286$	4.92873	+	34.2801i	0.291442	+	2.02702i
$287$	5.27297	−	3.60346i	0.311253	−	0.212706i
$288$	−10.0978	−	22.1111i	−0.595018	−	1.30291i
$289$	−11.4700	−	4.59190i	−0.674707	−	0.270112i
$290$	−1.51756e−5	0	0.000318574i	−8.91139e−7	0	1.87073e-5i
$291$	0.319404	+	0.304551i	0.0187238	+	0.0178531i
$292$	19.4773	+	15.3171i	1.13982	+	0.896366i
$293$	−6.70190	+	7.73440i	−0.391529	+	0.451849i	−0.916955	−	0.398991i	$-0.869361\pi$
$293$	−6.70190	+	7.73440i	−0.391529	+	0.451849i	0.525426	+	0.850839i	$0.323906\pi$
$294$	−11.7781	+	15.2570i	−0.686913	+	0.889805i
$295$	−6.86822	−	7.92635i	−0.399883	−	0.461490i
$296$	−38.5317	+	36.7399i	−2.23961	+	2.13547i
$297$	5.71873	−	0.546073i	0.331834	−	0.0316863i
$298$	−18.9904	−	32.8923i	−1.10008	−	1.90540i
$299$	9.38454	+	4.71005i	0.542722	+	0.272389i
$300$	−13.0895			−0.755725
$301$	17.0016	+	4.47387i	0.979956	+	0.257870i
$302$	16.8458	+	4.94636i	0.969365	+	0.284631i
$303$	−10.8248	+	2.08631i	−0.621869	+	0.119855i
$304$	−102.249	−	52.7131i	−5.86439	−	3.02330i
$305$	23.9238	+	4.61093i	1.36987	+	0.264021i
$306$	−4.66471	−	3.66837i	−0.266663	−	0.209706i
$307$	2.53834	−	0.745324i	0.144871	−	0.0425379i	−0.208493	−	0.978024i	$-0.566856\pi$
$307$	2.53834	−	0.745324i	0.144871	−	0.0425379i	0.353364	+	0.935486i	$0.385038\pi$
$308$	51.1446	+	67.6858i	2.91424	+	3.85676i
$309$	0.648008	+	4.50700i	0.0368639	+	0.256394i
$310$	20.2614	+	1.93473i	1.15077	+	0.109885i
$311$	−4.66810	+	6.55543i	−0.264704	+	0.371724i	−0.925440	−	0.378894i	$-0.876305\pi$
$311$	−4.66810	+	6.55543i	−0.264704	+	0.371724i	0.660737	+	0.750618i	$0.270244\pi$
$312$	−16.9725	+	13.3473i	−0.960879	+	0.755644i
$313$	21.4641	−	11.0655i	1.21322	−	0.625461i	0.271693	−	0.962384i	$-0.412417\pi$
$313$	21.4641	−	11.0655i	1.21322	−	0.625461i	0.941532	+	0.336923i	$0.109386\pi$
$314$	34.5998	−	10.1594i	1.95258	−	0.573329i
$315$	3.75945	+	6.10593i	0.211821	+	0.344030i
$316$	16.2688	−	18.7752i	0.915193	−	1.05619i
$317$	0.183654	+	3.85537i	0.0103150	+	0.216539i	0.998140	+	0.0609679i	$0.0194187\pi$
$317$	0.183654	+	3.85537i	0.0103150	+	0.216539i	−0.987825	+	0.155571i	$0.950278\pi$
$318$	4.45761	−	12.8794i	0.249971	−	0.722242i
$319$	−5.78843e−5	0	0.000238603i	−3.24090e−6	0	1.33592e-5i
$320$	−54.9407	−	77.1534i	−3.07128	−	4.31301i
$321$	−2.15147			−0.120083
$322$	34.9109	−	1.36657i	1.94551	−	0.0761562i
$323$	−15.5041			−0.862672
$324$	3.23766	+	4.54666i	0.179870	+	0.252592i
$325$	1.21050	+	4.98976i	0.0671466	+	0.276782i
$326$	−5.87238	+	16.9671i	−0.325241	+	0.939722i
$327$	−0.615029	−	12.9111i	−0.0340112	−	0.713983i
$328$	15.5895	−	17.9913i	0.860788	−	0.993402i
$329$	−5.87946	+	10.8833i	−0.324145	+	0.600014i
$330$	41.1332	−	12.0778i	2.26431	−	0.664861i
$331$	−23.9471	+	12.3456i	−1.31625	+	0.678576i	−0.966113	−	0.258121i	$-0.916897\pi$
$331$	−23.9471	+	12.3456i	−1.31625	+	0.678576i	−0.350141	+	0.936697i	$0.613866\pi$
$332$	−12.8938	+	10.1398i	−0.707638	+	0.556493i
$333$	3.13148	−	4.39755i	0.171604	−	0.240984i
$334$	−34.7573	−	3.31892i	−1.90184	−	0.181603i
$335$	4.19400	+	29.1699i	0.229143	+	1.59372i
$336$	−16.4802	+	38.9673i	−0.899067	+	2.12584i
$337$	−7.09741	+	2.08399i	−0.386621	+	0.113522i	−0.469266	−	0.883057i	$-0.655481\pi$
$337$	−7.09741	+	2.08399i	−0.386621	+	0.113522i	0.0826452	+	0.996579i	$0.473663\pi$
$338$	−17.7616	−	13.9679i	−0.966105	−	0.759753i
$339$	12.7310	+	2.45369i	0.691452	+	0.133266i
$340$	−28.9783	−	14.9393i	−1.57157	−	0.810199i
$341$	−15.3854	+	2.96530i	−0.833169	+	0.160580i
$342$	19.0055	+	5.58051i	1.02770	+	0.301759i
$343$	18.4536	−	1.56984i	0.996401	−	0.0847634i
$344$	65.5300			3.53314
$345$	4.11775	−	12.3281i	0.221692	−	0.663722i
$346$	−29.6699	−	51.3897i	−1.59506	−	2.76273i
$347$	−5.15292	+	0.492044i	−0.276623	+	0.0264143i	−0.232446	−	0.972609i	$-0.574673\pi$
$347$	−5.15292	+	0.492044i	−0.276623	+	0.0264143i	−0.0441775	+	0.999024i	$0.514067\pi$
$348$	0.000172648	0	0.000164620i	9.25491e−6	0	8.82454e-6i
$349$	−0.692868	−	0.799613i	−0.0370884	−	0.0428023i	0.736902	−	0.675999i	$-0.236288\pi$
$349$	−0.692868	−	0.799613i	−0.0370884	−	0.0428023i	−0.773991	+	0.633197i	$0.781742\pi$
$350$	11.5485	+	12.5898i	0.617292	+	0.672951i
$351$	1.43378	−	1.65467i	0.0765295	−	0.0883198i
$352$	109.766	+	86.3207i	5.85053	+	4.60091i
$353$	−8.23303	−	7.85018i	−0.438200	−	0.417823i	0.438597	−	0.898684i	$-0.355476\pi$
$353$	−8.23303	−	7.85018i	−0.438200	−	0.417823i	−0.876797	+	0.480861i	$0.840324\pi$
$354$	−0.507013	+	10.6435i	−0.0269474	+	0.565696i
$355$	21.3286	+	8.53867i	1.13200	+	0.453186i
$356$	−3.62385	−	7.93513i	−0.192064	−	0.420561i
$357$	0.432313	+	5.68576i	0.0228804	+	0.300922i
$358$	0.949942	+	6.60699i	0.0502060	+	0.349190i
$359$	−19.4399	+	10.0219i	−1.02600	+	0.528938i	−0.887201	−	0.461383i	$-0.847354\pi$
$359$	−19.4399	+	10.0219i	−1.02600	+	0.528938i	−0.138796	+	0.990321i	$0.544323\pi$
$360$	19.3437	+	18.4442i	1.01950	+	0.972093i
$361$	30.4042	−	12.1720i	1.60022	−	0.640631i
$362$	−3.36310	−	9.71703i	−0.176760	−	0.510716i
$363$	−18.5093	+	11.8952i	−0.971488	+	0.624337i
$364$	31.9088	+	5.21858i	1.67248	+	0.273528i
$365$	−11.5440	−	3.38963i	−0.604242	−	0.177421i
$366$	−14.3583	−	20.1634i	−0.750519	−	1.05396i
$367$	−1.04010	−	1.80151i	−0.0542930	−	0.0940383i	0.837602	−	0.546282i	$-0.183957\pi$
$367$	−1.04010	−	1.80151i	−0.0542930	−	0.0940383i	−0.891895	+	0.452243i	$0.850624\pi$
$368$	73.3464	−	22.4026i	3.82345	−	1.16781i
$369$	−1.20696	+	2.09052i	−0.0628319	+	0.108828i
$370$	16.7356	−	36.6459i	0.870043	−	1.90513i
$371$	−12.0152	+	5.20915i	−0.623798	+	0.270446i
$372$	−9.96940	−	11.5053i	−0.516889	−	0.596522i
$373$	−0.262910	−	5.51916i	−0.0136130	−	0.285771i	−0.995401	−	0.0957930i	$-0.969461\pi$
$373$	−0.262910	−	5.51916i	−0.0136130	−	0.285771i	0.981788	−	0.189978i	$-0.0608417\pi$
$374$	33.4752	+	6.45181i	1.73096	+	0.333615i
$375$	−6.67983	+	2.67420i	−0.344945	+	0.138095i
$376$	−10.8704	+	44.8083i	−0.560597	+	2.31081i
$377$	−7.87196e−5	0	5.05900e-5i	−4.05426e−6	0	2.60552e-6i
$378$	1.51657	−	7.12540i	0.0780041	−	0.366491i
$379$	−7.87656	−	17.2473i	−0.404592	−	0.885932i	−0.996784	−	0.0801354i	$-0.974465\pi$
$379$	−7.87656	−	17.2473i	−0.404592	−	0.885932i	0.592192	−	0.805797i	$-0.298263\pi$
$380$	108.329	+	10.3442i	5.55716	+	0.530644i
$381$	−6.09991	+	4.79703i	−0.312508	+	0.245759i
$382$	−0.759914	+	15.9526i	−0.0388806	+	0.816204i
$383$	−7.91414	+	32.6225i	−0.404394	+	1.66693i	0.297553	+	0.954705i	$0.403829\pi$
$383$	−7.91414	+	32.6225i	−0.404394	+	1.66693i	−0.701947	+	0.712229i	$0.747686\pi$
$384$	−6.77610	+	47.1288i	−0.345791	+	2.40503i
$385$	−35.2694	−	21.2813i	−1.79750	−	1.08460i
$386$	38.1054	−	24.4888i	1.93951	−	1.24645i
$387$	−6.52468	+	1.25753i	−0.331668	+	0.0639238i
$388$	−0.580751	−	2.39389i	−0.0294832	−	0.121531i
$389$	−4.91824	+	0.469635i	−0.249365	+	0.0238115i	−0.218990	−	0.975727i	$-0.570276\pi$
$389$	−4.91824	+	0.469635i	−0.249365	+	0.0238115i	−0.0303749	+	0.999539i	$0.509670\pi$
$390$	8.16928	−	14.1496i	0.413668	−	0.716493i
$391$	7.40283	−	7.21334i	0.374377	−	0.364794i
$392$	65.0312	−	23.1633i	3.28457	−	1.16992i
$393$	−5.46308	+	11.9625i	−0.275576	+	0.603427i
$394$	43.4206	−	41.4014i	2.18750	−	2.08577i
$395$	−3.94534	+	11.3993i	−0.198511	+	0.573561i
$396$	−28.5005	−	14.6930i	−1.43220	−	0.738352i
$397$	−3.59474	−	10.3863i	−0.180415	−	0.521275i	0.818140	−	0.575020i	$-0.195006\pi$
$397$	−3.59474	−	10.3863i	−0.180415	−	0.521275i	−0.998555	+	0.0537445i	$0.982884\pi$
$398$	10.3789	−	72.1866i	0.520245	−	3.61839i
$399$	−8.39307	−	17.0824i	−0.420179	−	0.855188i
$400$	31.5481	+	20.2748i	1.57741	+	1.01374i
$401$	−4.64981	−	1.86150i	−0.232200	−	0.0929590i	0.252645	−	0.967559i	$-0.418700\pi$
$401$	−4.64981	−	1.86150i	−0.232200	−	0.0929590i	−0.484845	+	0.874600i	$0.661124\pi$
$402$	17.3672	−	24.3888i	0.866198	−	1.21641i
$403$	−3.46389	+	4.86435i	−0.172549	+	0.242310i
$404$	57.1243	+	22.8691i	2.84204	+	1.13778i
$405$	−2.27995	−	1.46524i	−0.113292	−	0.0728083i
$406$	−0.000310656	0	2.08175e-5i	−1.54176e−5	0	1.03315e-6i
$407$	−4.41367	+	30.6977i	−0.218777	+	1.52163i
$408$	6.95169	+	20.0856i	0.344160	+	0.994384i
$409$	16.2114	+	8.35753i	0.801600	+	0.413254i	0.809795	−	0.586713i	$-0.199578\pi$
$409$	16.2114	+	8.35753i	0.801600	+	0.413254i	−0.00819505	+	0.999966i	$0.502609\pi$
$410$	−5.89171	+	17.0230i	−0.290971	+	0.840705i
$411$	0.874326	−	0.833668i	0.0431273	−	0.0411218i
$412$	10.5578	−	23.1183i	0.520145	−	1.13896i
$413$	7.86593	−	6.55426i	0.387057	−	0.322514i
$414$	−11.6710	+	6.17780i	−0.573598	+	0.303622i
$415$	3.98233	−	6.89760i	0.195485	−	0.338590i
$416$	52.9794	−	5.05892i	2.59753	−	0.248034i
$417$	−2.93037	−	12.0792i	−0.143501	−	0.591519i
$418$	−111.735	+	21.5351i	−5.46511	+	1.05331i
$419$	−21.5015	+	13.8182i	−1.05042	+	0.675062i	−0.947542	−	0.319632i	$-0.896441\pi$
$419$	−21.5015	+	13.8182i	−1.05042	+	0.675062i	−0.102876	+	0.994694i	$0.532804\pi$
$420$	0.772854	−	40.0155i	0.0377114	−	1.95255i
$421$	1.97879	−	13.7628i	0.0964403	−	0.670757i	−0.883052	−	0.469275i	$-0.844515\pi$
$421$	1.97879	−	13.7628i	0.0964403	−	0.670757i	0.979492	−	0.201482i	$-0.0645757\pi$
$422$	4.33148	−	17.8546i	0.210853	−	0.869148i
$423$	0.222463	−	4.67007i	0.0108165	−	0.227067i
$424$	−38.3704	+	30.1748i	−1.86343	+	1.46542i
$425$	5.03135	+	0.480436i	0.244056	+	0.0233046i
$426$	−9.69629	−	21.2319i	−0.469787	−	1.02869i
$427$	−4.95146	+	23.2637i	−0.239618	+	1.12581i
$428$	10.1024	+	6.49239i	0.488316	+	0.313822i
$429$	−2.96532	+	12.2232i	−0.143167	+	0.590143i
$430$	−46.0341	+	18.4293i	−2.21996	+	0.888739i
$431$	−29.6030	−	5.70552i	−1.42593	−	0.274825i	−0.582834	−	0.812591i	$-0.698056\pi$
$431$	−29.6030	−	5.70552i	−1.42593	−	0.274825i	−0.843094	+	0.537766i	$0.819268\pi$
$432$	−0.760895	−	15.9731i	−0.0366086	−	0.768508i
$433$	−16.7621	−	19.3445i	−0.805536	−	0.929638i	0.193135	−	0.981172i	$-0.438134\pi$
$433$	−16.7621	−	19.3445i	−0.805536	−	0.929638i	−0.998671	+	0.0515340i	$0.983589\pi$
$434$	−2.27033	+	19.7395i	−0.108979	+	0.947526i
$435$	−4.81176e−5	0	0.000105363i	−2.30706e−6	0	5.05176e-6i
$436$	−36.0732	+	62.4806i	−1.72759	+	2.99228i
$437$	−13.9909	+	31.5358i	−0.669277	+	1.50856i
$438$	6.11177	+	10.5859i	0.292032	+	0.505814i
$439$	−2.70834	−	3.80333i	−0.129262	−	0.181523i	0.744873	−	0.667207i	$-0.232510\pi$
$439$	−2.70834	−	3.80333i	−0.129262	−	0.181523i	−0.874135	+	0.485683i	$0.838571\pi$
$440$	−147.324	−	43.2581i	−7.02338	−	2.06225i
$441$	−6.03051	+	3.55428i	−0.287167	+	0.169251i
$442$	10.9303	−	7.02449i	0.519902	−	0.334121i
$443$	−5.38000	−	15.5445i	−0.255612	−	0.738541i	−0.997671	−	0.0682074i	$-0.978272\pi$
$443$	−5.38000	−	15.5445i	−0.255612	−	0.738541i	0.742060	−	0.670334i	$-0.233849\pi$
$444$	−27.9743	+	11.1992i	−1.32760	+	0.531492i
$445$	3.06553	+	2.92298i	0.145320	+	0.138563i
$446$	36.9455	−	19.0467i	1.74942	−	0.901889i
$447$	−1.96306	−	13.6534i	−0.0928495	−	0.645782i
$448$	76.3407	−	52.1700i	3.60676	−	2.46480i
$449$	0.122964	+	0.269254i	0.00580305	+	0.0127069i	0.912511	−	0.409051i	$-0.134140\pi$
$449$	0.122964	+	0.269254i	0.00580305	+	0.0127069i	−0.906708	+	0.421758i	$0.861413\pi$
$450$	−5.99467	−	2.39990i	−0.282591	−	0.113133i
$451$	0.659836	−	13.8517i	0.0310704	−	0.652249i
$452$	−52.3747	−	49.9391i	−2.46350	−	2.34894i
$453$	5.01210	+	3.94156i	0.235489	+	0.185191i
$454$	−0.752160	+	0.868039i	−0.0353006	+	0.0407391i
$455$	−15.3254	+	3.40596i	−0.718468	+	0.159674i
$456$	−46.4585	−	53.6160i	−2.17562	−	2.51080i
$457$	1.09773	−	1.04669i	0.0513497	−	0.0489619i	−0.663970	−	0.747759i	$-0.731130\pi$
$457$	1.09773	−	1.04669i	0.0513497	−	0.0489619i	0.715320	+	0.698798i	$0.246281\pi$
$458$	−34.8048	+	3.32346i	−1.62632	+	0.155295i
$459$	−1.07761	−	1.86647i	−0.0502985	−	0.0871195i
$460$	−56.5370	+	45.4613i	−2.63605	+	2.11964i
$461$	24.3194			1.13267			0.566333	−	0.824177i	$-0.308362\pi$
$461$	24.3194			1.13267			0.566333	+	0.824177i	$0.308362\pi$
$462$	11.0130	+	40.3755i	0.512373	+	1.87844i
$463$	25.4654	+	7.47733i	1.18348	+	0.347501i	0.813514	−	0.581545i	$-0.197552\pi$
$463$	25.4654	+	7.47733i	1.18348	+	0.347501i	0.369965	+	0.929046i	$0.379370\pi$
$464$	−0.000671096	0	0.000129343i	−3.11549e−5	0	6.00461e-6i
$465$	6.57023	+	3.38719i	0.304687	+	0.157077i
$466$	25.5731	+	4.92881i	1.18465	+	0.228323i
$467$	−20.0825	−	15.7930i	−0.929305	−	0.730814i	0.0339437	−	0.999424i	$-0.489193\pi$
$467$	−20.0825	−	15.7930i	−0.929305	−	0.730814i	−0.963249	+	0.268610i	$0.913436\pi$
$468$	−11.7256	+	3.44295i	−0.542017	+	0.159151i
$469$	−28.5501	+	3.54363i	−1.31832	+	0.163630i
$470$	−4.96531	−	34.5345i	−0.229033	−	1.59296i
$471$	13.0371	+	1.24489i	0.600716	+	0.0573614i
$472$	22.1374	−	31.0877i	1.01896	−	1.43093i
$473$	30.0056	−	23.5966i	1.37966	−	1.08498i
$474$	10.8930	−	5.61575i	0.500334	−	0.257940i
$475$	−16.1868	+	4.75288i	−0.742702	+	0.218077i
$476$	15.1277	−	28.0024i	0.693377	−	1.28349i
$477$	3.24140	−	3.74077i	0.148413	−	0.171278i
$478$	1.46709	+	30.7980i	0.0671031	+	1.40867i
$479$	9.37332	−	27.0824i	0.428278	−	1.23743i	−0.500157	−	0.865934i	$-0.666725\pi$
$479$	9.37332	−	27.0824i	0.428278	−	1.23743i	0.928435	−	0.371494i	$-0.121154\pi$
$480$	−15.5314	−	64.0215i	−0.708910	−	2.92217i
$481$	6.85619	+	9.62818i	0.312615	+	0.439007i
$482$	−78.2336			−3.56345
$483$	11.9551	+	4.25150i	0.543976	+	0.193450i
$484$	122.807			5.58215
$485$	0.693796	+	0.974300i	0.0315036	+	0.0442407i
$486$	0.649156	+	2.67586i	0.0294463	+	0.121379i
$487$	13.1878	−	38.1037i	0.597597	−	1.72664i	−0.0855236	−	0.996336i	$-0.527256\pi$
$487$	13.1878	−	38.1037i	0.597597	−	1.72664i	0.683120	−	0.730306i	$-0.260622\pi$
$488$	4.21846	+	88.5563i	0.190961	+	4.00876i
$489$	−4.27016	+	4.92802i	−0.193103	+	0.222853i
$490$	−39.1694	+	34.5610i	−1.76949	+	1.56131i
$491$	11.3298	−	3.32672i	0.511305	−	0.150133i	−0.0158956	−	0.999874i	$-0.505060\pi$
$491$	11.3298	−	3.32672i	0.511305	−	0.150133i	0.527200	+	0.849741i	$0.323242\pi$
$492$	11.9758	−	6.17396i	0.539911	−	0.278344i
$493$	−7.24045e−5	0	5.69395e-5i	−3.26093e−6	0	2.56443e-6i
$494$	−25.1560	+	35.3266i	−1.13182	+	1.58942i
$495$	15.4988	+	1.47996i	0.696621	+	0.0665192i
$496$	6.20715	+	43.1717i	0.278709	+	1.93847i
$497$	−8.73618	+	20.6566i	−0.391871	+	0.926577i
$498$	−7.76410	+	2.27974i	−0.347918	+	0.102158i
$499$	19.2432	+	15.1330i	0.861442	+	0.677445i	0.947816	−	0.318817i	$-0.103286\pi$
$499$	19.2432	+	15.1330i	0.861442	+	0.677445i	−0.0863742	+	0.996263i	$0.527528\pi$
$500$	39.4353	+	7.60054i	1.76360	+	0.339906i
$501$	−11.2709	−	5.81054i	−0.503546	−	0.259596i
$502$	35.4354	−	6.82961i	1.58156	−	0.304820i
$503$	0.582741	+	0.171108i	0.0259831	+	0.00762933i	0.294698	−	0.955590i	$-0.404781\pi$
$503$	0.582741	+	0.171108i	0.0259831	+	0.00762933i	−0.268715	+	0.963220i	$0.586599\pi$
$504$	−18.3669	+	18.5326i	−0.818128	+	0.825506i
$505$	−29.8772			−1.32952
$506$	43.3312	−	62.2673i	1.92631	−	2.76812i
$507$	−4.10317	−	7.10690i	−0.182228	−	0.315629i
$508$	43.1183	−	4.11730i	1.91306	−	0.182675i
$509$	−28.2460	+	26.9325i	−1.25198	+	1.19376i	−0.279665	+	0.960098i	$0.590223\pi$
$509$	−28.2460	+	26.9325i	−1.25198	+	1.19376i	−0.972317	+	0.233665i	$0.924928\pi$
$510$	−10.5322	−	12.1548i	−0.466375	−	0.538226i
$511$	3.52604	−	11.2036i	0.155983	−	0.495616i
$512$	48.0029	−	55.3983i	2.12145	−	2.44828i
$513$	5.65467	+	4.44688i	0.249660	+	0.196335i
$514$	−53.0764	−	50.6082i	−2.34110	−	2.23223i
$515$	−0.587181	+	12.3264i	−0.0258743	+	0.543168i
$516$	34.4318	+	13.7844i	1.51578	+	0.606825i
$517$	11.1575	+	24.4316i	0.490708	+	1.07450i
$518$	35.4524	+	17.0255i	1.55769	+	0.748057i
$519$	−3.06701	−	21.3315i	−0.134627	−	0.936349i
$520$	−52.0134	+	26.8148i	−2.28094	+	1.17590i
$521$	3.43153	+	3.27196i	0.150338	+	0.143347i	0.761516	−	0.648146i	$-0.224455\pi$
$521$	3.43153	+	3.27196i	0.150338	+	0.143347i	−0.611178	+	0.791493i	$0.709304\pi$
$522$	0.000109251	0	4.37373e-5i	4.78177e−6	0	1.91433e-6i
$523$	−7.58962	−	21.9288i	−0.331871	−	0.958878i	−0.980285	−	0.197590i	$-0.936689\pi$
$523$	−7.58962	−	21.9288i	−0.331871	−	0.958878i	0.648414	−	0.761288i	$-0.275433\pi$
$524$	61.7508	−	39.6849i	2.69760	−	1.73364i
$525$	2.19435	+	5.80360i	0.0957694	+	0.253290i
$526$	−63.0647	−	18.5175i	−2.74975	−	0.807400i
$527$	3.40974	+	4.78831i	0.148531	+	0.208582i
$528$	45.9328	+	79.5580i	1.99897	+	3.46232i
$529$	−7.99181	−	21.5669i	−0.347470	−	0.937691i
$530$	18.4686	−	31.9885i	0.802224	−	1.38949i
$531$	−1.60760	+	3.52016i	−0.0697639	+	0.152762i
$532$	−12.1385	+	105.539i	−0.526269	+	4.57568i
$533$	−3.46103	−	3.99424i	−0.149914	−	0.173010i
$534$	−0.204763	−	4.29850i	−0.00886094	−	0.186014i
$535$	−5.72552	−	1.10350i	−0.247536	−	0.0477086i
$536$	−99.5542	+	39.8555i	−4.30009	+	1.72149i
$537$	−0.571523	+	2.35585i	−0.0246630	+	0.101662i
$538$	−33.1363	−	21.2954i	−1.42861	−	0.918111i
$539$	21.4363	−	34.0233i	0.923329	−	1.46549i
$540$	6.28408	+	13.7602i	0.270424	+	0.592146i
$541$	29.3248	+	2.80018i	1.26077	+	0.120389i	0.703954	−	0.710246i	$-0.251416\pi$
$541$	29.3248	+	2.80018i	1.26077	+	0.120389i	0.556818	+	0.830635i	$0.312022\pi$
$542$	35.6807	−	28.0596i	1.53262	−	1.20526i
$543$	0.177690	−	3.73016i	0.00762539	−	0.160077i
$544$	12.3510	−	50.9117i	0.529547	−	2.18282i
$545$	4.98544	−	34.6745i	0.213553	−	1.48529i
$546$	13.6566	+	8.24030i	0.584449	+	0.352652i
$547$	−32.8182	+	21.0909i	−1.40320	+	0.901784i	−0.999912	−	0.0132879i	$-0.995770\pi$
$547$	−32.8182	+	21.0909i	−1.40320	+	0.901784i	−0.403291	+	0.915072i	$0.632134\pi$
$548$	−6.62117	+	1.27613i	−0.282842	+	0.0545134i
$549$	−2.11943	−	8.73641i	−0.0904550	−	0.372861i
$550$	36.9271	−	3.52611i	1.57458	−	0.150354i
$551$	0.000153726	0	0.000266262i	6.54896e−6	0	1.13431e-5i
$552$	47.1278	+	3.98533i	2.00589	+	0.169627i
$553$	−11.0518	−	4.06571i	−0.469972	−	0.172891i
$554$	−13.7550	+	30.1193i	−0.584396	+	1.27965i
$555$	10.5891	−	10.0966i	0.449480	−	0.428579i
$556$	−22.6910	+	65.5612i	−0.962311	+	2.78042i
$557$	22.4083	+	11.5523i	0.949471	+	0.489487i	0.862127	−	0.506692i	$-0.169132\pi$
$557$	22.4083	+	11.5523i	0.949471	+	0.489487i	0.0873441	+	0.996178i	$0.472162\pi$
$558$	−2.45628	−	7.09697i	−0.103983	−	0.300439i
$559$	2.07044	−	14.4002i	0.0875704	−	0.609065i
$560$	−63.8438	+	95.2473i	−2.69789	+	4.02493i
$561$	10.4157	+	6.69377i	0.439752	+	0.282611i
$562$	−6.30159	−	2.52278i	−0.265817	−	0.106417i
$563$	−3.37904	+	4.74520i	−0.142410	+	0.199986i	−0.879620	−	0.475677i	$-0.842203\pi$
$563$	−3.37904	+	4.74520i	−0.142410	+	0.199986i	0.737210	+	0.675663i	$0.236143\pi$
$564$	−15.1372	+	21.2573i	−0.637393	+	0.895093i
$565$	32.6213	+	13.0596i	1.37239	+	0.549421i
$566$	−13.9666	−	8.97580i	−0.587061	−	0.377281i
$567$	1.47311	−	2.19771i	0.0618650	−	0.0922952i
$568$	−11.8974	+	82.7485i	−0.499205	+	3.47205i
$569$	4.98074	+	14.3909i	0.208803	+	0.603297i	0.999965	−	0.00830894i	$-0.00264485\pi$
$569$	4.98074	+	14.3909i	0.208803	+	0.603297i	−0.791162	+	0.611606i	$0.790524\pi$
$570$	47.7153	+	24.5989i	1.99857	+	1.03034i
$571$	−10.6301	+	30.7136i	−0.444856	+	1.28533i	0.470400	+	0.882453i	$0.344110\pi$
$571$	−10.6301	+	30.7136i	−0.444856	+	1.28533i	−0.915256	+	0.402873i	$0.868012\pi$
$572$	50.8093	−	48.4466i	2.12445	−	2.02565i
$573$	−2.40948	+	5.27603i	−0.100658	+	0.220409i
$574$	−16.5041	−	6.07147i	−0.688868	−	0.253418i
$575$	5.51752	−	9.80036i	0.230096	−	0.408703i
$576$	−17.4741	+	30.2660i	−0.728087	+	1.26108i
$577$	−36.7884	+	3.51286i	−1.53152	+	0.146242i	−0.826496	−	0.562942i	$-0.809669\pi$
$577$	−36.7884	+	3.51286i	−1.53152	+	0.146242i	−0.705023	+	0.709184i	$0.749063\pi$
$578$	8.02035	+	33.0603i	0.333602	+	1.37513i
$579$	16.1532	−	3.11327i	0.671304	−	0.129383i
$580$	0.000543887	0	0.000349535i	2.25837e−5	0	1.45137e-5i
$581$	6.65728	+	4.01695i	0.276191	+	0.166651i
$582$	0.172939	−	1.20282i	0.00716855	−	0.0498584i
$583$	−6.70382	+	27.6335i	−0.277644	+	1.14446i
$584$	2.08314	−	43.7305i	0.0862010	−	1.80958i
$585$	4.66428	−	3.66803i	0.192844	−	0.151654i
$586$	28.0517	+	2.67861i	1.15880	+	0.110652i
$587$	−1.38201	−	3.02618i	−0.0570416	−	0.124904i	0.878965	−	0.476887i	$-0.158235\pi$
$587$	−1.38201	−	3.02618i	−0.0570416	−	0.124904i	−0.936006	+	0.351983i	$0.885507\pi$
$588$	39.0422	+	1.50868i	1.61007	+	0.0622168i
$589$	−16.5060	−	10.6078i	−0.680118	−	0.437086i
$590$	−6.80839	+	28.0646i	−0.280297	+	1.15540i
$591$	20.2281	−	8.09812i	0.832074	−	0.333112i
$592$	84.7699	+	16.3381i	3.48402	+	0.671490i
$593$	0.991699	+	20.8183i	0.0407242	+	0.854906i	0.923147	+	0.384448i	$0.125608\pi$
$593$	0.991699	+	20.8183i	0.0407242	+	0.854906i	−0.882422	+	0.470458i	$0.844089\pi$
$594$	−10.3586	−	11.9544i	−0.425018	−	0.490497i
$595$	−1.76579	+	15.3527i	−0.0723902	+	0.629401i
$596$	−31.9835	+	70.0340i	−1.31009	+	2.86871i
$597$	13.2431	−	22.9377i	0.542002	−	0.938776i
$598$	−4.42447	−	28.5715i	−0.180930	−	1.16837i
$599$	13.0844	+	22.6628i	0.534614	+	0.925978i	0.999182	+	0.0404406i	$0.0128762\pi$
$599$	13.0844	+	22.6628i	0.534614	+	0.925978i	−0.464568	+	0.885537i	$0.653791\pi$
$600$	13.4152	+	18.8389i	0.547671	+	0.769097i
$601$	16.1741	+	4.74914i	0.659755	+	0.193722i	0.594436	−	0.804143i	$-0.297375\pi$
$601$	16.1741	+	4.74914i	0.659755	+	0.193722i	0.0653190	+	0.997864i	$0.479194\pi$
$602$	−17.1200	−	45.2787i	−0.697758	−	1.84542i
$603$	9.14756	−	5.87878i	0.372518	−	0.239403i
$604$	−11.6404	−	33.6326i	−0.473639	−	1.36849i
$605$	−55.3583	+	22.1621i	−2.25064	+	0.901019i
$606$	21.9685	+	20.9469i	0.892409	+	0.850910i
$607$	−10.6034	+	5.46645i	−0.430380	+	0.221876i	−0.659784	−	0.751455i	$-0.729352\pi$
$607$	−10.6034	+	5.46645i	−0.430380	+	0.221876i	0.229405	+	0.973331i	$0.426322\pi$
$608$	24.8857	+	173.084i	1.00925	+	7.01948i
$609$	−0.000101932	0	4.89510e-5i	−4.13047e−6	0	1.98360e-6i
$610$	−27.8685	−	61.0235i	−1.12836	−	2.47077i
$611$	9.50319	+	3.80450i	0.384458	+	0.153914i
$612$	−0.572392	+	12.0160i	−0.0231376	+	0.485718i
$613$	−26.5314	−	25.2976i	−1.07159	−	1.02176i	−0.999704	−	0.0243489i	$-0.992249\pi$
$613$	−26.5314	−	25.2976i	−1.07159	−	1.02176i	−0.0718891	−	0.997413i	$-0.522903\pi$
$614$	−5.72587	−	4.50287i	−0.231077	−	0.181721i
$615$	−4.28422	+	4.94425i	−0.172756	+	0.199371i
$616$	44.9990	−	142.979i	1.81306	−	5.76078i
$617$	23.4026	+	27.0080i	0.942152	+	1.08730i	0.996053	+	0.0887553i	$0.0282889\pi$
$617$	23.4026	+	27.0080i	0.942152	+	1.08730i	−0.0539013	+	0.998546i	$0.517166\pi$
$618$	9.07383	−	8.65188i	0.365003	−	0.348030i
$619$	43.4723	−	4.15111i	1.74730	−	0.166847i	0.828085	−	0.560602i	$-0.189430\pi$
$619$	43.4723	−	4.15111i	1.74730	−	0.166847i	0.919215	+	0.393755i	$0.128824\pi$
$620$	−20.6295	−	35.7314i	−0.828502	−	1.43501i
$621$	−4.76890	+	0.507578i	−0.191369	+	0.0203684i
$622$	22.1590			0.888495
$623$	−2.91074	+	2.93699i	−0.116616	+	0.117668i
$624$	33.5937	+	9.86400i	1.34482	+	0.394876i
$625$	−30.6617	+	5.90956i	−1.22647	+	0.236382i
$626$	−59.1010	−	30.4687i	−2.36215	−	1.21777i
$627$	−40.5795	−	7.82105i	−1.62059	−	0.312343i
$628$	−57.4597	−	45.1868i	−2.29289	−	1.80315i
$629$	11.1638	−	3.27799i	0.445130	−	0.130702i
$630$	7.69058	−	18.1843i	0.306400	−	0.724481i
$631$	−2.16788	−	15.0779i	−0.0863018	−	0.600242i	−0.986376	−	0.164506i	$-0.947397\pi$
$631$	−2.16788	−	15.0779i	−0.0863018	−	0.600242i	0.900074	−	0.435737i	$-0.143512\pi$
$632$	−43.6955	−	4.17241i	−1.73811	−	0.165970i
$633$	3.87041	−	5.43524i	0.153835	−	0.216031i
$634$	8.35393	−	6.56960i	0.331777	−	0.260912i
$635$	−18.6936	+	9.63721i	−0.741832	+	0.382441i
$636$	−26.5085	+	7.78360i	−1.05113	+	0.308640i
$637$	−3.03546	−	15.0225i	−0.120269	−	0.595213i
$638$	−0.000442714	0	0.000510919i	−1.75272e−5	0	2.02275e-5i
$639$	−0.403352	−	8.46740i	−0.0159564	−	0.334965i
$640$	−42.2053	+	121.944i	−1.66831	+	4.82027i
$641$	4.23221	+	17.4454i	0.167162	+	0.689052i	0.992272	+	0.124080i	$0.0395979\pi$
$641$	4.23221	+	17.4454i	0.167162	+	0.689052i	−0.825110	+	0.564972i	$0.808887\pi$
$642$	3.43627	+	4.82556i	0.135619	+	0.190450i
$643$	30.9538			1.22070			0.610350	−	0.792132i	$-0.291029\pi$
$643$	30.9538			1.22070			0.610350	+	0.792132i	$0.291029\pi$
$644$	−43.3064	−	56.0396i	−1.70651	−	2.20827i
$645$	−18.0086			−0.709086
$646$	24.7627	+	34.7744i	0.974277	+	1.36818i
$647$	−9.80610	−	40.4213i	−0.385517	−	1.58912i	−0.752302	−	0.658819i	$-0.771057\pi$
$647$	−9.80610	−	40.4213i	−0.385517	−	1.58912i	0.366784	−	0.930306i	$-0.380459\pi$
$648$	3.22551	−	9.31951i	0.126710	−	0.366105i
$649$	−1.05781	−	22.2062i	−0.0415228	−	0.871670i
$650$	9.25822	−	10.6846i	0.363137	−	0.419083i
$651$	−3.42989	+	6.34897i	−0.134428	+	0.248836i
$652$	34.9218	−	10.2540i	1.36765	−	0.401577i
$653$	−24.7880	+	12.7791i	−0.970028	+	0.500084i	−0.869007	−	0.494800i	$-0.835241\pi$
$653$	−24.7880	+	12.7791i	−0.970028	+	0.500084i	−0.101021	+	0.994884i	$0.532211\pi$
$654$	−27.9761	+	22.0006i	−1.09395	+	0.860293i
$655$	−20.6740	+	29.0326i	−0.807802	+	1.13440i
$656$	−38.4269	−	3.66932i	−1.50032	−	0.143263i
$657$	0.631781	+	4.39413i	0.0246481	+	0.171431i
$658$	33.8007	−	4.19534i	1.31769	−	0.163551i
$659$	−30.7508	+	9.02925i	−1.19788	+	0.351730i	−0.819042	−	0.573733i	$-0.805495\pi$
$659$	−30.7508	+	9.02925i	−1.19788	+	0.351730i	−0.378839	+	0.925463i	$0.623677\pi$
$660$	−68.3097	−	53.7193i	−2.65895	−	2.09102i
$661$	11.1920	+	2.15709i	0.435320	+	0.0839011i	0.402203	−	0.915550i	$-0.368245\pi$
$661$	11.1920	+	2.15709i	0.435320	+	0.0839011i	0.0331169	+	0.999451i	$0.489457\pi$
$662$	65.9378	+	33.9933i	2.56275	+	1.32119i
$663$	4.63345	−	0.893025i	0.179948	−	0.0346822i
$664$	27.8081	+	8.16518i	1.07916	+	0.316871i
$665$	−13.5741	−	49.7646i	−0.526380	−	1.92979i
$666$	−14.8648			−0.576000
$667$	5.04786e−5	0	0.000198655i	1.95454e−6	0	7.69195e-6i
$668$	35.3889	+	61.2953i	1.36924	+	2.37159i
$669$	15.0276	−	1.43496i	0.580999	−	0.0554786i
$670$	58.7270	−	55.9961i	2.26882	−	2.16332i
$671$	33.8197	+	39.0301i	1.30560	+	1.50674i
$672$	62.7804	−	13.9525i	2.42181	−	0.538228i
$673$	−1.96321	+	2.26566i	−0.0756761	+	0.0873349i	−0.792325	−	0.610099i	$-0.791130\pi$
$673$	−1.96321	+	2.26566i	−0.0756761	+	0.0873349i	0.716649	+	0.697434i	$0.245675\pi$
$674$	16.0100	+	12.5904i	0.616682	+	0.484964i
$675$	−1.69724	−	1.61831i	−0.0653268	−	0.0622890i
$676$	−2.17948	+	45.7528i	−0.0838260	+	1.75972i
$677$	−12.5180	−	5.01143i	−0.481104	−	0.192605i	0.118417	−	0.992964i	$-0.462218\pi$
$677$	−12.5180	−	5.01143i	−0.481104	−	0.192605i	−0.599521	+	0.800359i	$0.704642\pi$
$678$	−14.8301	−	32.4735i	−0.569548	−	1.24714i
$679$	−0.964037	+	0.658807i	−0.0369963	+	0.0252827i
$680$	8.19788	+	57.0175i	0.314374	+	2.18652i
$681$	−0.370768	+	0.191144i	−0.0142078	+	0.00732465i
$682$	31.2241	+	29.7721i	1.19563	+	1.14003i
$683$	42.0009	−	16.8146i	1.60712	−	0.643394i	0.617430	−	0.786626i	$-0.288174\pi$
$683$	42.0009	−	16.8146i	1.60712	−	0.643394i	0.989689	+	0.143232i	$0.0457495\pi$
$684$	−13.1327	−	37.9445i	−0.502141	−	1.45084i
$685$	2.75436	−	1.77012i	0.105239	−	0.0676328i
$686$	−32.9946	−	38.8826i	−1.25974	−	1.48454i
$687$	−12.1835	−	3.57739i	−0.464829	−	0.136486i
$688$	−61.6358	−	86.5553i	−2.34984	−	3.29989i
$689$	5.41860	+	9.38528i	0.206432	+	0.357551i
$690$	−34.2276	+	10.4543i	−1.30302	+	0.397989i
$691$	18.4990	−	32.0412i	0.703735	−	1.21890i	−0.263411	−	0.964684i	$-0.584848\pi$
$691$	18.4990	−	32.0412i	0.703735	−	1.21890i	0.967146	−	0.254221i	$-0.0818190\pi$
$692$	−49.9698	+	109.419i	−1.89957	+	4.15947i
$693$	−1.73667	+	15.0996i	−0.0659708	+	0.573587i
$694$	9.33371	+	10.7717i	0.354303	+	0.408887i
$695$	−1.60286	−	33.6482i	−0.0608000	−	1.27635i
$696$	−0.000413869	0	7.97667e-5i	−1.56877e−5	0	3.02355e-6i
$697$	−4.82986	+	1.93358i	−0.182944	+	0.0732397i
$698$	−0.686833	+	2.83116i	−0.0259970	+	0.107161i
$699$	7.95700	+	5.11365i	0.300961	+	0.193416i
$700$	7.20953	−	33.8729i	0.272495	−	1.28028i
$701$	8.17144	+	17.8929i	0.308631	+	0.675807i	0.998858	−	0.0477858i	$-0.0152165\pi$
$701$	8.17144	+	17.8929i	0.308631	+	0.675807i	−0.690227	+	0.723593i	$0.742489\pi$
$702$	−6.00128	−	0.573052i	−0.226504	−	0.0216285i
$703$	−30.5272	+	24.0068i	−1.15135	+	0.905435i
$704$	9.55294	−	200.541i	0.360040	−	7.55817i
$705$	2.98733	−	12.3139i	0.112509	−	0.463770i
$706$	−4.45771	+	31.0041i	−0.167768	+	1.16685i
$707$	0.563220	−	29.1614i	0.0211821	−	1.09673i
$708$	18.1712	−	11.6779i	0.682915	−	0.438883i
$709$	−8.78834	+	1.69381i	−0.330053	+	0.0636125i	−0.351586	−	0.936156i	$-0.614357\pi$
$709$	−8.78834	+	1.69381i	−0.330053	+	0.0636125i	0.0215328	+	0.999768i	$0.493145\pi$
$710$	−14.9139	−	61.4759i	−0.559708	−	2.30715i
$711$	4.43073	−	0.423084i	0.166166	−	0.0158669i
$712$	−7.70652	+	13.3481i	−0.288814	+	0.500241i
$713$	12.8165	−	2.61453i	0.479982	−	0.0979149i
$714$	12.0622	−	10.0508i	0.451416	−	0.376141i
$715$	−14.1607	+	31.0077i	−0.529581	+	1.15962i
$716$	9.79276	−	9.33738i	0.365973	−	0.348954i
$717$	−3.66245	+	10.5819i	−0.136777	+	0.395190i
$718$	53.5272	+	27.5952i	1.99762	+	1.02984i
$719$	12.3128	+	35.5756i	0.459191	+	1.32674i	0.902621	+	0.430436i	$0.141640\pi$
$719$	12.3128	+	35.5756i	0.459191	+	1.32674i	−0.443431	+	0.896309i	$0.646239\pi$
$720$	6.16783	−	42.8982i	0.229861	−	1.59872i
$721$	−12.0201	−	0.805481i	−0.447650	−	0.0299977i
$722$	−75.8614	−	48.7532i	−2.82327	−	1.81440i
$723$	−26.3774	−	10.5599i	−0.980988	−	0.392728i
$724$	−12.0907	+	16.9790i	−0.449347	+	0.631020i
$725$	−5.81376e−5	0	8.16428e-5i	−2.15918e−6	0	3.03214e-6i
$726$	56.2425	+	22.5161i	2.08736	+	0.835651i
$727$	−38.0730	−	24.4681i	−1.41205	−	0.907470i	−0.412058	−	0.911158i	$-0.635190\pi$
$727$	−38.0730	−	24.4681i	−1.41205	−	0.907470i	−0.999993	+	0.00368748i	$0.998826\pi$
$728$	−25.1918	−	51.2727i	−0.933671	−	1.90029i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	10.8351	+	31.3061i	0.401026	+	1.15869i
$731$	−12.7289	−	6.56222i	−0.470797	−	0.242713i
$732$	−16.4115	+	47.4180i	−0.606588	+	1.75262i
$733$	−12.6164	+	12.0297i	−0.465996	+	0.444326i	−0.886338	−	0.463040i	$-0.846759\pi$
$733$	−12.6164	+	12.0297i	−0.465996	+	0.444326i	0.420341	+	0.907366i	$0.361910\pi$
$734$	−2.37942	+	5.21019i	−0.0878258	+	0.192312i
$735$	−17.8715	+	6.36559i	−0.659200	+	0.234798i
$736$	−92.4102	−	71.0651i	−3.40628	−	2.61950i
$737$	−31.2334	+	54.0978i	−1.15050	+	1.99272i
$738$	6.61658	−	0.631806i	0.243560	−	0.0232571i
$739$	−9.04818	−	37.2971i	−0.332843	−	1.37200i	−0.854770	−	0.519006i	$-0.826302\pi$
$739$	−9.04818	−	37.2971i	−0.332843	−	1.37200i	0.521928	−	0.852990i	$-0.325213\pi$
$740$	−80.1897	+	15.4553i	−2.94783	+	0.568148i
$741$	−13.2500	+	8.51526i	−0.486751	+	0.312816i
$742$	30.8740	+	18.6291i	1.13342	+	0.683898i
$743$	4.54567	−	31.6158i	0.166764	−	1.15987i	−0.718753	−	0.695266i	$-0.755287\pi$
$743$	4.54567	−	31.6158i	0.166764	−	1.15987i	0.885517	−	0.464607i	$-0.153804\pi$
$744$	−6.34145	+	26.1398i	−0.232489	+	0.958332i
$745$	1.77879	−	37.3414i	0.0651698	−	1.36808i
$746$	−11.9591	+	9.40473i	−0.437853	+	0.344331i
$747$	−2.92548	−	0.279350i	−0.107038	−	0.0102209i
$748$	−28.7081	−	62.8620i	−1.04967	−	2.29846i
$749$	1.18500	−	5.56755i	0.0432989	−	0.203434i
$750$	16.6668	+	10.7111i	0.608587	+	0.391115i
$751$	0.0534818	−	0.220455i	0.00195158	−	0.00804451i	−0.970827	−	0.239779i	$-0.922925\pi$
$751$	0.0534818	−	0.220455i	0.00195158	−	0.00804451i	0.972779	+	0.231735i	$0.0744401\pi$
$752$	69.4095	−	27.7874i	2.53110	−	1.01330i
$753$	12.8693	+	2.48036i	0.468985	+	0.0903894i
$754$	1.22597e−5	0	0.000257362i	4.46471e−7	0	9.37258e-6i
$755$	11.3166	+	13.0601i	0.411853	+	0.475304i
$756$	−13.5490	+	5.87414i	−0.492773	+	0.213640i
$757$	18.6474	−	40.8321i	0.677751	−	1.48407i	−0.187257	−	0.982311i	$-0.559960\pi$
$757$	18.6474	−	40.8321i	0.677751	−	1.48407i	0.865008	−	0.501757i	$-0.167313\pi$
$758$	−26.1039	+	45.2133i	−0.948136	+	1.64222i
$759$	23.0145	−	15.1454i	0.835372	−	0.549742i
$760$	−96.1359	−	166.512i	−3.48722	−	6.04004i
$761$	30.5563	+	42.9104i	1.10767	+	1.55550i	0.795988	+	0.605312i	$0.206952\pi$
$761$	30.5563	+	42.9104i	1.10767	+	1.55550i	0.311678	+	0.950188i	$0.399109\pi$
$762$	20.5019	+	6.01991i	0.742707	+	0.218078i
$763$	33.7498	+	5.51965i	1.22182	+	0.199825i
$764$	27.2351	−	17.5029i	0.985331	−	0.633234i
$765$	−1.91042	−	5.51979i	−0.0690713	−	0.199569i
$766$	85.8098	−	34.3531i	3.10043	−	1.24123i
$767$	−6.13209	−	5.84694i	−0.221417	−	0.211121i
$768$	54.4021	−	28.0462i	1.96307	−	1.01203i
$769$	3.03833	+	21.1320i	0.109565	+	0.762041i	0.968330	+	0.249672i	$0.0803228\pi$
$769$	3.03833	+	21.1320i	0.109565	+	0.762041i	−0.858766	+	0.512369i	$0.828768\pi$
$770$	8.59920	+	113.096i	0.309894	+	4.07571i
$771$	−11.0643	−	24.2274i	−0.398470	−	0.872528i
$772$	−85.2431	−	34.1262i	−3.06796	−	1.22823i
$773$	−0.659889	+	13.8528i	−0.0237346	+	0.498250i	0.955435	+	0.295203i	$0.0953873\pi$
$773$	−0.659889	+	13.8528i	−0.0237346	+	0.498250i	−0.979169	+	0.203047i	$0.934916\pi$
$774$	13.2416	+	12.6258i	0.475959	+	0.453826i
$775$	5.02777	+	3.95388i	0.180603	+	0.142028i
$776$	−2.85017	+	3.28928i	−0.102315	+	0.118078i
$777$	9.65514	+	10.5257i	0.346376	+	0.377607i
$778$	8.90863	+	10.2811i	0.319390	+	0.368596i
$779$	12.5678	−	11.9833i	0.450287	−	0.429348i
$780$	−32.9702	+	3.14828i	−1.18052	+	0.112726i
$781$	24.3491	+	42.1739i	0.871280	+	1.50910i
$782$	−28.0025	−	5.08297i	−1.00137	−	0.181767i
$783$	4.27388e−5	0		1.52736e−6	0
$784$	−91.7619	−	64.1097i	−3.27721	−	2.28963i
$785$	34.0559	+	9.99970i	1.21551	+	0.356905i
$786$	35.5563	−	6.85292i	1.26825	−	0.244435i
$787$	4.92433	+	2.53867i	0.175533	+	0.0904937i	0.543754	−	0.839245i	$-0.317003\pi$
$787$	4.92433	+	2.53867i	0.175533	+	0.0904937i	−0.368220	+	0.929739i	$0.620033\pi$
$788$	−119.420	−	23.0163i	−4.25415	−	0.819920i
$789$	−18.7636	−	14.7558i	−0.668000	−	0.525321i
$790$	31.8690	−	9.35759i	1.13385	−	0.332928i
$791$	−13.3617	+	31.5936i	−0.475086	+	1.12334i
$792$	8.06272	+	56.0775i	0.286496	+	1.99263i
$793$	19.5936	+	1.87096i	0.695788	+	0.0664397i
$794$	−17.5542	+	24.6515i	−0.622976	+	0.874847i
$795$	10.5447	−	8.29245i	0.373982	−	0.294103i
$796$	−131.401	+	67.7422i	−4.65740	+	2.40106i
$797$	−3.36903	+	0.989238i	−0.119337	+	0.0350406i	−0.340856	−	0.940116i	$-0.610717\pi$
$797$	−3.36903	+	0.989238i	−0.119337	+	0.0350406i	0.221519	+	0.975156i	$0.428899\pi$
$798$	−24.9091	+	46.1084i	−0.881772	+	1.63222i
$799$	6.59867	−	7.61527i	0.233444	−	0.269409i
$800$	−2.71238	−	56.9398i	−0.0958970	−	2.01313i
$801$	0.511170	−	1.47693i	0.0180613	−	0.0521847i
$802$	3.25135	+	13.4023i	0.114809	+	0.473250i
$803$	−14.7930	−	20.7739i	−0.522035	−	0.733095i
$804$	−60.6931			−2.14048
$805$	29.6345	+	17.4460i	1.04448	+	0.614891i
$806$	16.4427			0.579171
$807$	−8.29788	−	11.6527i	−0.292099	−	0.410196i
$808$	−25.6312	−	105.653i	−0.901703	−	3.71687i
$809$	3.62001	−	10.4593i	0.127273	−	0.367730i	−0.863305	−	0.504683i	$-0.831609\pi$
$809$	3.62001	−	10.4593i	0.127273	−	0.367730i	0.990578	+	0.136952i	$0.0437307\pi$
$810$	0.355077	+	7.45398i	0.0124761	+	0.261906i
$811$	−0.712820	+	0.822639i	−0.0250305	+	0.0288867i	−0.768127	−	0.640298i	$-0.778811\pi$
$811$	−0.712820	+	0.822639i	−0.0250305	+	0.0288867i	0.743096	+	0.669185i	$0.233356\pi$
$812$	0.000330908	0	0.000537446i	1.16126e−5	0	1.88607e-5i
$813$	15.8177	−	4.64449i	0.554750	−	0.162889i
$814$	75.9018	−	39.1301i	2.66036	−	1.37151i
$815$	−13.8914	+	10.9243i	−0.486595	+	0.382662i
$816$	19.9915	−	28.0741i	0.699841	−	0.982789i
$817$	47.5844	+	4.54376i	1.66477	+	0.158966i
$818$	−7.14709	−	49.7091i	−0.249892	−	1.73804i
$819$	3.49223	+	4.62168i	0.122028	+	0.161495i
$820$	35.0368	−	10.2877i	1.22354	−	0.359263i
$821$	13.7607	+	10.8215i	0.480252	+	0.377675i	0.828736	−	0.559640i	$-0.189061\pi$
$821$	13.7607	+	10.8215i	0.480252	+	0.377675i	−0.348483	+	0.937315i	$0.613303\pi$
$822$	−3.26630	−	0.629527i	−0.113925	−	0.0219573i
$823$	8.72635	+	4.49874i	0.304181	+	0.156816i	0.603559	−	0.797318i	$-0.293749\pi$
$823$	8.72635	+	4.49874i	0.304181	+	0.156816i	−0.299378	+	0.954135i	$0.596779\pi$
$824$	−44.0932	+	8.49826i	−1.53606	+	0.296051i
$825$	12.9264	+	3.79552i	0.450038	+	0.132143i
$826$	−27.2639	−	7.17433i	−0.948632	−	0.249627i
$827$	−0.784101			−0.0272659			−0.0136329	−	0.999907i	$-0.504340\pi$
$827$	−0.784101			−0.0272659			−0.0136329	+	0.999907i	$0.504340\pi$
$828$	23.9243	+	12.0075i	0.831428	+	0.417290i
$829$	26.8576	+	46.5187i	0.932803	+	1.61566i	0.778505	+	0.627638i	$0.215978\pi$
$829$	26.8576	+	46.5187i	0.932803	+	1.61566i	0.154298	+	0.988024i	$0.450689\pi$
$830$	−21.8312	+	2.08463i	−0.757772	+	0.0723584i
$831$	−8.70317	+	8.29846i	−0.301910	+	0.287870i
$832$	−50.1080	−	57.8277i	−1.73718	−	2.00481i
$833$	−14.9516	−	2.01290i	−0.518044	−	0.0697429i
$834$	−22.4122	+	25.8651i	−0.776071	+	0.895634i
$835$	−27.0139	−	21.2440i	−0.934855	−	0.735178i
$836$	166.942	+	159.179i	5.77381	+	5.50532i
$837$	0.129778	−	2.72438i	0.00448579	−	0.0941683i
$838$	65.3346	+	26.1560i	2.25695	+	0.903545i
$839$	2.31665	+	5.07276i	0.0799797	+	0.175131i	0.945397	−	0.325920i	$-0.105674\pi$
$839$	2.31665	+	5.07276i	0.0799797	+	0.175131i	−0.865418	+	0.501051i	$0.832947\pi$
$840$	−58.3838	+	39.8985i	−2.01443	+	1.37663i
$841$	4.12713	+	28.7048i	0.142315	+	0.989821i
$842$	−34.0292	+	17.5433i	−1.17272	+	0.604581i
$843$	−1.78414	−	1.70117i	−0.0614489	−	0.0585914i
$844$	−34.5754	+	13.8419i	−1.19014	+	0.476458i
$845$	−7.27423	−	21.0175i	−0.250241	−	0.723024i
$846$	−10.8299	+	6.95994i	−0.372339	+	0.239288i
$847$	−20.5876	−	54.4499i	−0.707399	−	1.87092i
$848$	75.9465	+	22.2999i	2.60801	+	0.765782i
$849$	−3.49747	−	4.91151i	−0.120033	−	0.168563i
$850$	−6.95835	−	12.0522i	−0.238670	−	0.413388i
$851$	3.40671	−	25.6655i	0.116781	−	0.879803i
$852$	−23.6577	+	40.9764i	−0.810500	+	1.40383i
$853$	5.20592	−	11.3994i	0.178247	−	0.390307i	−0.799328	−	0.600896i	$-0.794811\pi$
$853$	5.20592	−	11.3994i	0.178247	−	0.390307i	0.977575	+	0.210589i	$0.0675380\pi$
$854$	60.0869	−	26.0505i	2.05613	−	0.891428i
$855$	12.7674	+	14.7344i	0.436637	+	0.503906i
$856$	−1.00957	−	21.1936i	−0.0345065	−	0.724381i
$857$	−40.0358	−	7.71627i	−1.36760	−	0.263583i	−0.547979	−	0.836492i	$-0.684603\pi$
$857$	−40.0358	−	7.71627i	−1.36760	−	0.263583i	−0.819619	+	0.572909i	$0.805815\pi$
$858$	32.1518	−	12.8716i	1.09764	−	0.439431i
$859$	5.27555	−	21.7461i	0.179999	−	0.741968i	−0.808214	−	0.588888i	$-0.799566\pi$
$859$	5.27555	−	21.7461i	0.179999	−	0.741968i	0.988214	−	0.153080i	$-0.0489191\pi$
$860$	84.5602	+	54.3436i	2.88348	+	1.85310i
$861$	−4.74504	−	4.27478i	−0.161710	−	0.145684i
$862$	34.4842	+	75.5098i	1.17454	+	2.57187i
$863$	51.8515	+	4.95122i	1.76504	+	0.168541i	0.926501	−	0.376293i	$-0.122801\pi$
$863$	51.8515	+	4.95122i	1.76504	+	0.168541i	0.838544	+	0.544834i	$0.183407\pi$
$864$	−19.1072	+	15.0260i	−0.650039	+	0.511196i
$865$	2.77911	−	58.3407i	0.0944926	−	1.98364i
$866$	−16.6161	+	68.4925i	−0.564638	+	2.32747i
$867$	−1.75830	+	12.2293i	−0.0597152	+	0.415328i
$868$	35.2642	−	19.4617i	1.19695	−	0.660574i
$869$	−21.5102	+	13.8238i	−0.729683	+	0.468939i
$870$	0.000313172	0	6.03589e-5i	1.06175e−5	0	2.04636e-6i
$871$	5.61281	+	23.1363i	0.190183	+	0.783944i
$872$	126.895	−	12.1170i	4.29720	−	0.410333i
$873$	0.220664	−	0.382201i	0.00746835	−	0.0129356i
$874$	93.0780	−	18.9876i	3.14841	−	0.642266i
$875$	−3.24110	−	18.7589i	−0.109569	−	0.634165i
$876$	10.2934	−	22.5394i	0.347782	−	0.761536i
$877$	−25.4474	+	24.2640i	−0.859297	+	0.819338i	−0.984968	−	0.172734i	$-0.944740\pi$
$877$	−25.4474	+	24.2640i	−0.859297	+	0.819338i	0.125672	+	0.992072i	$0.459891\pi$
$878$	−4.20486	+	12.1492i	−0.141907	+	0.410014i
$879$	9.09641	+	4.68953i	0.306814	+	0.158174i
$880$	81.4312	+	235.280i	2.74504	+	7.93128i
$881$	4.66394	−	32.4384i	0.157132	−	1.09288i	−0.746752	−	0.665102i	$-0.768388\pi$
$881$	4.66394	−	32.4384i	0.157132	−	1.09288i	0.903885	−	0.427776i	$-0.140703\pi$
$882$	17.6037	+	7.84913i	0.592748	+	0.264294i
$883$	29.1135	+	18.7101i	0.979746	+	0.629645i	0.929395	−	0.369087i	$-0.120330\pi$
$883$	29.1135	+	18.7101i	0.979746	+	0.629645i	0.0503514	+	0.998732i	$0.483966\pi$
$884$	−24.4515	−	9.78890i	−0.822393	−	0.329236i
$885$	−6.08367	+	8.54333i	−0.204500	+	0.287181i
$886$	−26.2722	+	36.8941i	−0.882631	+	1.23948i
$887$	−36.2776	−	14.5234i	−1.21808	−	0.487647i	−0.328536	−	0.944491i	$-0.606555\pi$
$887$	−36.2776	−	14.5234i	−1.21808	−	0.487647i	−0.889546	+	0.456845i	$0.848980\pi$
$888$	44.7885	+	28.7838i	1.50300	+	0.965922i
$889$	−9.05393	−	18.4274i	−0.303659	−	0.618035i
$890$	1.65981	−	11.5442i	0.0556369	−	0.386963i
$891$	−1.87892	−	5.42879i	−0.0629462	−	0.181871i
$892$	−74.8930	−	38.6100i	−2.50760	−	1.29276i
$893$	−11.0004	+	31.7836i	−0.368115	+	1.06360i
$894$	−27.4880	+	26.2097i	−0.919336	+	0.876585i
$895$	−2.72927	+	5.97628i	−0.0912296	+	0.199765i
$896$	−118.227	−	43.4929i	−3.94969	−	1.45300i
$897$	2.36480	−	10.2304i	0.0789583	−	0.341584i
$898$	0.407519	−	0.705844i	0.0135991	−	0.0235543i
$899$	−0.000116041	0	1.10806e-5i	−3.87018e−6	0	3.69557e-7i
$900$	3.08598	+	12.7206i	0.102866	+	0.424019i
$901$	10.4750	−	2.01889i	0.348973	−	0.0672591i
$902$	−32.1219	+	20.6435i	−1.06954	+	0.687354i
$903$	0.339482	−	17.5771i	0.0112973	−	0.584930i
$904$	−18.1967	+	126.561i	−0.605213	+	4.20935i
$905$	2.38609	−	9.83562i	0.0793165	−	0.326947i
$906$	0.835393	−	17.5371i	0.0277541	−	0.582630i
$907$	−21.7035	+	17.0678i	−0.720652	+	0.566727i	−0.909713	−	0.415239i	$-0.863698\pi$
$907$	−21.7035	+	17.0678i	−0.720652	+	0.566727i	0.189061	+	0.981965i	$0.439456\pi$
$908$	2.31777	+	0.221320i	0.0769178	+	0.00734476i
$909$	4.57955	+	10.0278i	0.151894	+	0.332601i
$910$	32.1166	+	28.9337i	1.06466	+	0.959144i
$911$	26.2486	+	16.8690i	0.869656	+	0.558894i	0.897648	−	0.440714i	$-0.145275\pi$
$911$	26.2486	+	16.8690i	0.869656	+	0.558894i	−0.0279913	+	0.999608i	$0.508911\pi$
$912$	−27.1210	+	111.794i	−0.898068	+	3.70189i
$913$	15.6732	−	6.27462i	0.518709	−	0.207660i
$914$	−4.10089	−	0.790382i	−0.135645	−	0.0261435i
$915$	−1.15929	−	24.3365i	−0.0383249	−	0.804540i
$916$	46.4129	+	53.5634i	1.53353	+	1.76978i
$917$	−27.9474	−	20.7260i	−0.922903	−	0.684434i
$918$	−2.46521	+	5.39807i	−0.0813642	+	0.178163i
$919$	−10.4800	+	18.1519i	−0.345704	+	0.598776i	−0.985481	−	0.169784i	$-0.945693\pi$
$919$	−10.4800	+	18.1519i	−0.345704	+	0.598776i	0.639778	+	0.768560i	$0.279026\pi$
$920$	123.373	+	34.7780i	4.06749	+	1.14660i
$921$	−1.32275	−	2.29107i	−0.0435861	−	0.0754934i
$922$	−38.8422	−	54.5462i	−1.27920	−	1.79638i
$923$	17.8081	+	5.22893i	0.586161	+	0.172112i
$924$	53.7201	−	65.6605i	1.76726	−	2.16007i
$925$	10.6505	−	6.84466i	0.350186	−	0.225051i
$926$	−23.9017	−	69.0594i	−0.785458	−	2.26943i
$927$	4.22718	−	1.69231i	0.138839	−	0.0555827i
$928$	0.000751875	0	0.000716911i	2.46815e−5	0	2.35338e-5i
$929$	2.50023	−	1.28896i	0.0820299	−	0.0422893i	−0.416723	−	0.909033i	$-0.636822\pi$
$929$	2.50023	−	1.28896i	0.0820299	−	0.0422893i	0.498753	+	0.866744i	$0.333791\pi$
$930$	−2.89661	−	20.1464i	−0.0949836	−	0.660626i
$931$	48.8283	−	12.3108i	1.60028	−	0.403469i
$932$	−21.9313	−	48.0229i	−0.718385	−	1.57304i
$933$	7.47118	+	2.99101i	0.244596	+	0.0979213i
$934$	−3.34725	+	70.2674i	−0.109525	+	2.29922i
$935$	24.2851	+	23.1558i	0.794208	+	0.757276i
$936$	16.9725	+	13.3473i	0.554764	+	0.436271i
$937$	28.5547	−	32.9538i	0.932840	−	1.07655i	−0.0640655	−	0.997946i	$-0.520407\pi$
$937$	28.5547	−	32.9538i	0.932840	−	1.07655i	0.996906	−	0.0786091i	$-0.0250479\pi$
$938$	53.5475	+	58.3757i	1.74839	+	1.90603i
$939$	−15.8140	−	18.2503i	−0.516070	−	0.595576i
$940$	−51.1864	+	48.8061i	−1.66952	+	1.59188i
$941$	−24.1721	+	2.30815i	−0.787987	+	0.0752436i	−0.481288	−	0.876563i	$-0.659831\pi$
$941$	−24.1721	+	2.30815i	−0.787987	+	0.0752436i	−0.306699	+	0.951806i	$0.599225\pi$
$942$	−18.0303	−	31.2293i	−0.587457	−	1.01751i
$943$	−0.425509	+	11.5689i	−0.0138565	+	0.376737i
$944$	−61.8841			−2.01415
$945$	5.04749	−	5.09300i	0.164195	−	0.165675i
$946$	−100.849	−	29.6120i	−3.27889	−	0.962770i
$947$	−12.9451	+	2.49497i	−0.420660	+	0.0810756i	−0.395189	−	0.918600i	$-0.629321\pi$
$947$	−12.9451	+	2.49497i	−0.420660	+	0.0810756i	−0.0254713	+	0.999676i	$0.508109\pi$
$948$	−22.0815	−	11.3838i	−0.717174	−	0.369729i
$949$	−9.54398	−	1.83945i	−0.309811	−	0.0597111i
$950$	36.5134	+	28.7145i	1.18465	+	0.931621i
$951$	3.70339	−	1.08741i	0.120091	−	0.0352618i
$952$	−55.8061	+	6.92663i	−1.80868	+	0.224493i
$953$	6.89137	+	47.9305i	0.223233	+	1.55262i	0.725692	+	0.688020i	$0.241520\pi$
$953$	6.89137	+	47.9305i	0.223233	+	1.55262i	−0.502459	+	0.864601i	$0.667571\pi$
$954$	−13.5673	−	1.29552i	−0.439258	−	0.0419440i
$955$	−9.11825	+	12.8048i	−0.295060	+	0.414353i
$956$	49.1299	−	38.6362i	1.58897	−	1.24958i
$957$	−0.000218230	0	0.000112505i	−7.05437e−6	0	3.63678e-6i
$958$	−75.7144	+	22.2318i	−2.44622	+	0.718275i
$959$	1.67579	+	2.72174i	0.0541140	+	0.0878896i
$960$	−62.0258	+	71.5816i	−2.00187	+	2.31029i
$961$	−1.12107	−	23.5342i	−0.0361637	−	0.759169i
$962$	10.6447	−	30.7557i	0.343197	−	0.991604i
$963$	0.507228	+	2.09082i	0.0163452	+	0.0673759i
$964$	91.9906	+	129.183i	2.96282	+	4.16070i
$965$	44.5839			1.43521
$966$	−9.55862	−	33.6047i	−0.307543	−	1.08121i
$967$	18.4334			0.592777			0.296389	−	0.955067i	$-0.404218\pi$
$967$	18.4334			0.592777			0.296389	+	0.955067i	$0.404218\pi$
$968$	−125.862	−	176.749i	−4.04536	−	5.68092i
$969$	3.65523	+	15.0671i	0.117423	+	0.484024i
$970$	1.07716	−	3.11225i	0.0345855	−	0.0999283i
$971$	−2.35783	−	49.4970i	−0.0756665	−	1.58843i	−0.643601	−	0.765361i	$-0.722560\pi$
$971$	−2.35783	−	49.4970i	−0.0756665	−	1.58843i	0.567935	−	0.823074i	$-0.307743\pi$
$972$	3.65519	−	4.21831i	0.117240	−	0.135302i
$973$	32.8723	−	0.930152i	1.05384	−	0.0298193i
$974$	−106.526	+	31.2790i	−3.41333	+	1.00224i
$975$	4.56372	−	2.35276i	0.146156	−	0.0753487i
$976$	113.002	−	88.8656i	3.61710	−	2.84452i
$977$	21.0010	−	29.4918i	0.671882	−	0.943527i	−0.328117	−	0.944637i	$-0.606414\pi$
$977$	21.0010	−	29.4918i	0.671882	−	0.943527i	0.999999	+	0.00111023i	$0.000353398\pi$
$978$	17.8733	+	1.70669i	0.571526	+	0.0545741i
$979$	1.27776	+	8.88700i	0.0408373	+	0.284030i
$980$	103.126	+	24.0399i	3.29423	+	0.767927i
$981$	−12.4021	+	3.64159i	−0.395969	+	0.116267i
$982$	−25.5571	−	20.0983i	−0.815560	−	0.641363i
$983$	−2.79291	−	0.538290i	−0.0890801	−	0.0171688i	0.144516	−	0.989502i	$-0.453837\pi$
$983$	−2.79291	−	0.538290i	−0.0890801	−	0.0171688i	−0.233596	+	0.972334i	$0.575049\pi$
$984$	−21.1595	−	10.9085i	−0.674540	−	0.347750i
$985$	57.9849	−	11.1757i	1.84755	−	0.356086i
$986$	0.000243353	0	7.14549e-5i	7.74993e−6	0	2.27559e-6i
$987$	11.9626	+	3.14789i	0.380774	+	0.100199i
$988$	87.9123			2.79686
$989$	−24.8344	+	19.9693i	−0.789687	+	0.634985i
$990$	−21.4349	−	37.1263i	−0.681245	−	1.17995i
$991$	−44.5298	+	4.25208i	−1.41454	+	0.135072i	−0.774161	−	0.632989i	$-0.781828\pi$
$991$	−44.5298	+	4.25208i	−1.41454	+	0.135072i	−0.640376	+	0.768061i	$0.721222\pi$
$992$	47.9825	−	45.7512i	1.52345	−	1.45260i
$993$	17.6433	+	20.3615i	0.559895	+	0.646153i
$994$	60.2842	−	13.3977i	1.91210	−	0.424949i
$995$	47.0074	−	54.2495i	1.49024	−	1.71982i
$996$	12.8938	+	10.1398i	0.408555	+	0.321291i
$997$	−21.5934	−	20.5893i	−0.683870	−	0.652068i	0.266268	−	0.963899i	$-0.414209\pi$
$997$	−21.5934	−	20.5893i	−0.683870	−	0.652068i	−0.950138	+	0.311831i	$0.899058\pi$
$998$	3.20736	−	67.3307i	0.101527	−	2.13132i
$999$	−5.01186	−	2.00645i	−0.158568	−	0.0634812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.a.121.1	yes	320
7.4	even	3	inner	483.2.y.a.466.16	yes	320
23.4	even	11	inner	483.2.y.a.142.16	yes	320
161.4	even	33	inner	483.2.y.a.4.1	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.a.4.1	✓	320	161.4	even	33	inner
483.2.y.a.121.1	yes	320	1.1	even	1	trivial
483.2.y.a.142.16	yes	320	23.4	even	11	inner
483.2.y.a.466.16	yes	320	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59717 - 2.24291i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-1.82557 + 5.27464i) q^{4} +(-0.128956 - 2.70712i) q^{5} +(-1.80314 + 2.08094i) q^{6} +(2.64469 - 0.0748341i) q^{7} +(9.46243 - 2.77842i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-1.59717 - 2.24291i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-1.82557 + 5.27464i) q^{4} +(-0.128956 - 2.70712i) q^{5} +(-1.80314 + 2.08094i) q^{6} +(2.64469 - 0.0748341i) q^{7} +(9.46243 - 2.77842i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-5.86587 + 4.61297i) q^{10} +(3.33228 - 4.67953i) q^{11} +(5.55635 + 0.530567i) q^{12} +(-0.311590 - 2.16716i) q^{13} +(-4.39188 - 5.81230i) q^{14} +(-2.60041 + 0.763548i) q^{15} +(-12.5700 - 9.88514i) q^{16} +(-2.11627 - 0.407878i) q^{17} +(2.44739 + 1.26172i) q^{18} +(7.06375 - 1.36143i) q^{19} +(14.5145 + 4.26184i) q^{20} +(-0.696235 - 2.55250i) q^{21} -15.8180 q^{22} +(-2.73936 + 3.93648i) q^{23} +(-4.93095 - 8.54066i) q^{24} +(-2.33450 + 0.222917i) q^{25} +(-4.36308 + 4.16019i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-4.43335 + 14.0864i) q^{28} +(2.79880e-5 - 3.22998e-5i) q^{29} +(5.86587 + 4.61297i) q^{30} +(-1.97396 - 1.88217i) q^{31} +(-1.15661 + 24.2802i) q^{32} +(-5.33324 - 2.13511i) q^{33} +(2.46521 + 5.39807i) q^{34} +(-0.543633 - 7.14984i) q^{35} +(-0.794348 - 5.52481i) q^{36} +(-4.79844 + 2.47377i) q^{37} +(-14.3356 - 13.6690i) q^{38} +(-2.03261 + 0.813734i) q^{39} +(-8.74174 - 25.2576i) q^{40} +(2.03072 - 1.30506i) q^{41} +(-4.61303 + 5.63838i) q^{42} +(6.37560 + 1.87205i) q^{43} +(18.5995 + 26.1194i) q^{44} +(1.35509 + 2.34709i) q^{45} +(13.2044 - 0.143091i) q^{46} +(-2.33768 + 4.04899i) q^{47} +(-6.64301 + 14.5462i) q^{48} +(6.98880 - 0.395826i) q^{49} +(4.22858 + 4.88004i) q^{50} +(0.102549 + 2.15278i) q^{51} +(11.9998 + 2.31277i) q^{52} +(-4.59519 + 1.83964i) q^{53} +(0.649156 - 2.67586i) q^{54} +(-13.0978 - 8.41742i) q^{55} +(24.8173 - 8.05618i) q^{56} +(-2.98839 - 6.54367i) q^{57} +(-0.000117147 - 1.11862e-5i) q^{58} +(3.04192 - 2.39219i) q^{59} +(0.719783 - 15.1101i) q^{60} +(-2.11943 + 8.73641i) q^{61} +(-1.06879 + 7.43357i) q^{62} +(-2.31641 + 1.27838i) q^{63} +(29.4003 - 18.8944i) q^{64} +(-5.82657 + 1.12298i) q^{65} +(3.72924 + 15.3721i) q^{66} +(-10.8245 + 1.03361i) q^{67} +(6.01481 - 10.4180i) q^{68} +(4.47135 + 1.73408i) q^{69} +(-15.1682 + 12.6389i) q^{70} +(-3.52147 + 7.71095i) q^{71} +(-7.13740 + 6.80549i) q^{72} +(1.45196 - 4.19516i) q^{73} +(13.2124 + 6.81146i) q^{74} +(0.767012 + 2.21614i) q^{75} +(-5.71434 + 39.7441i) q^{76} +(8.46266 - 12.6253i) q^{77} +(5.07156 + 3.25929i) q^{78} +(-4.13206 - 1.65423i) q^{79} +(-25.1393 + 35.3032i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-6.17056 - 2.47032i) q^{82} +(2.47227 + 1.58883i) q^{83} +(14.7345 + 0.987382i) q^{84} +(-0.831268 + 5.78159i) q^{85} +(-5.98410 - 17.2899i) q^{86} +(-3.79878e-5 - 1.95841e-5i) q^{87} +(18.5297 - 53.5382i) q^{88} +(-1.13111 + 1.07852i) q^{89} +(3.10001 - 6.78807i) q^{90} +(-0.986237 - 5.70815i) q^{91} +(-15.7626 - 21.6355i) q^{92} +(-1.36373 + 2.36206i) q^{93} +(12.8152 - 1.22370i) q^{94} +(-4.59646 - 18.9469i) q^{95} +(23.8684 - 4.60027i) q^{96} +(-0.371269 + 0.238600i) q^{97} +(-12.0501 - 15.0431i) q^{98} +(-0.817562 + 5.68627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21} - 176 q^{22} - 18 q^{23} - 6 q^{24} + 8 q^{25} - 14 q^{26} + 32 q^{27} + 46 q^{28} + 34 q^{29} - 8 q^{30} + 52 q^{31} - 8 q^{32} - 5 q^{33} - 24 q^{34} - 12 q^{35} - 14 q^{36} - 30 q^{37} - 157 q^{38} + 88 q^{40} - 28 q^{41} - 45 q^{42} + 64 q^{43} - 71 q^{44} - 2 q^{45} + 4 q^{46} + 36 q^{47} + 60 q^{48} + 28 q^{49} + 210 q^{50} - 26 q^{51} - 198 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{55} + 44 q^{57} + 31 q^{58} + 10 q^{59} - 2 q^{60} - 34 q^{61} - 8 q^{62} + 2 q^{63} + 84 q^{64} + 38 q^{65} - 12 q^{67} - 22 q^{68} + 8 q^{69} - 336 q^{70} - 144 q^{71} + 6 q^{72} - 16 q^{73} - 68 q^{74} - 30 q^{75} + 8 q^{76} + 98 q^{77} + 16 q^{78} + 26 q^{79} + 225 q^{80} + 16 q^{81} - 122 q^{82} + 44 q^{84} - 240 q^{85} - 26 q^{86} - 16 q^{87} + 43 q^{88} + 68 q^{89} - 16 q^{90} + 40 q^{91} - 222 q^{92} - 8 q^{93} + 137 q^{94} - 49 q^{95} + 30 q^{96} - 8 q^{97} + 137 q^{98} - 10 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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