LMFDB - Embedded newform 690.2.x.a.77.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.48
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599278 + 0.800541i) q^{2} +(1.68258 - 0.411015i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.92562 + 1.13666i) q^{5} +(1.33737 + 1.10066i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(-0.936950 + 0.349464i) q^{8} +(2.66213 - 1.38313i) q^{9} +O(q^{10})$	\(q+(0.599278 + 0.800541i) q^{2} +(1.68258 - 0.411015i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.92562 + 1.13666i) q^{5} +(1.33737 + 1.10066i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(-0.936950 + 0.349464i) q^{8} +(2.66213 - 1.38313i) q^{9} +(0.244034 + 2.22271i) q^{10} +(0.975922 - 0.140316i) q^{11} +(-0.0796710 + 1.73022i) q^{12} +(-0.819594 + 3.76761i) q^{13} +(3.25098 - 3.75183i) q^{14} +(3.70718 + 1.12106i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(2.86697 - 5.25046i) q^{17} +(2.70261 + 1.30227i) q^{18} +(-1.35672 + 4.62056i) q^{19} +(-1.63313 + 1.52738i) q^{20} +(-3.76935 - 7.72834i) q^{21} +(0.697177 + 0.697177i) q^{22} +(4.61640 - 1.29956i) q^{23} +(-1.43286 + 0.973101i) q^{24} +(2.41600 + 4.37755i) q^{25} +(-3.50729 + 1.60173i) q^{26} +(3.91076 - 3.42140i) q^{27} +(4.95173 + 0.354155i) q^{28} +(-4.34619 + 1.27616i) q^{29} +(1.32417 + 3.63958i) q^{30} +(-1.05620 + 2.31275i) q^{31} +(-0.0713392 - 0.997452i) q^{32} +(1.58439 - 0.637211i) q^{33} +(5.92132 - 0.851357i) q^{34} +(3.48185 - 10.5405i) q^{35} +(0.577092 + 2.94397i) q^{36} +(-4.04328 + 0.289181i) q^{37} +(-4.51200 + 1.68289i) q^{38} +(0.169514 + 6.67617i) q^{39} +(-2.20143 - 0.392061i) q^{40} +(-3.41394 + 2.95819i) q^{41} +(3.92797 - 7.64894i) q^{42} +(-9.84064 - 3.67037i) q^{43} +(-0.140316 + 0.975922i) q^{44} +(6.69840 + 0.362570i) q^{45} +(3.80686 + 2.91682i) q^{46} +(-3.34725 + 3.34725i) q^{47} +(-1.63769 - 0.563902i) q^{48} +(-16.0505 + 7.33003i) q^{49} +(-2.05655 + 4.55748i) q^{50} +(2.66588 - 10.0127i) q^{51} +(-3.38409 - 1.84785i) q^{52} +(2.06975 + 9.51449i) q^{53} +(5.08260 + 1.08036i) q^{54} +(2.03874 + 0.839097i) q^{55} +(2.68395 + 4.17630i) q^{56} +(-0.383666 + 8.33208i) q^{57} +(-3.62619 - 2.71453i) q^{58} +(5.33866 - 3.43095i) q^{59} +(-2.12009 + 3.24118i) q^{60} +(-1.50002 + 3.28459i) q^{61} +(-2.48440 + 0.540449i) q^{62} +(-9.51869 - 11.4543i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-5.86073 + 6.32338i) q^{65} +(1.45960 + 0.886504i) q^{66} +(11.9434 - 8.94072i) q^{67} +(4.23006 + 4.23006i) q^{68} +(7.23331 - 4.08402i) q^{69} +(10.5247 - 3.52932i) q^{70} +(5.47868 + 0.787715i) q^{71} +(-2.01093 + 2.22624i) q^{72} +(-6.13140 + 3.34800i) q^{73} +(-2.65455 - 3.06351i) q^{74} +(5.86434 + 6.37256i) q^{75} +(-4.05116 - 2.60352i) q^{76} +(-1.71051 - 4.58606i) q^{77} +(-5.24296 + 4.13658i) q^{78} +(-2.63670 - 4.10278i) q^{79} +(-1.00541 - 1.99729i) q^{80} +(5.17391 - 7.36415i) q^{81} +(-4.41405 - 0.960219i) q^{82} +(-10.0586 + 0.719406i) q^{83} +(8.47724 - 1.43934i) q^{84} +(11.4887 - 6.85160i) q^{85} +(-2.95899 - 10.0774i) q^{86} +(-6.78829 + 3.93358i) q^{87} +(-0.865354 + 0.472519i) q^{88} +(-4.78829 - 10.4849i) q^{89} +(3.72395 + 5.57962i) q^{90} +19.1413 q^{91} +(-0.0536700 + 4.79553i) q^{92} +(-0.826558 + 4.32549i) q^{93} +(-4.68554 - 0.673679i) q^{94} +(-7.86453 + 7.35529i) q^{95} +(-0.530001 - 1.64897i) q^{96} +(0.180812 - 2.52808i) q^{97} +(-15.4867 - 8.45639i) q^{98} +(2.40396 - 1.72337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.599278	+	0.800541i	0.423753	+	0.566068i
$2$	0.599278	+	0.800541i	0.423753	+	0.566068i
$3$	1.68258	−	0.411015i	0.971437	−	0.237300i
$3$	1.68258	−	0.411015i	0.971437	−	0.237300i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	1.92562	+	1.13666i	0.861162	+	0.508331i
$5$	1.92562	+	1.13666i	0.861162	+	0.508331i
$6$	1.33737	+	1.10066i	0.545977	+	0.449343i
$7$	−1.05526	−	4.85093i	−0.398849	−	1.83348i	−0.537662	−	0.843160i	$-0.680692\pi$
$7$	−1.05526	−	4.85093i	−0.398849	−	1.83348i	0.138813	−	0.990319i	$-0.455671\pi$
$8$	−0.936950	+	0.349464i	−0.331262	+	0.123554i
$9$	2.66213	−	1.38313i	0.887378	−	0.461043i
$10$	0.244034	+	2.22271i	0.0771705	+	0.702883i
$11$	0.975922	−	0.140316i	0.294251	−	0.0423070i	0.00639178	−	0.999980i	$-0.497965\pi$
$11$	0.975922	−	0.140316i	0.294251	−	0.0423070i	0.287860	+	0.957673i	$0.407056\pi$
$12$	−0.0796710	+	1.73022i	−0.0229990	+	0.499471i
$13$	−0.819594	+	3.76761i	−0.227314	+	1.04495i	0.712077	+	0.702101i	$0.247755\pi$
$13$	−0.819594	+	3.76761i	−0.227314	+	1.04495i	−0.939391	+	0.342846i	$0.888609\pi$
$14$	3.25098	−	3.75183i	0.868861	−	1.00272i
$15$	3.70718	+	1.12106i	0.957191	+	0.289458i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	2.86697	−	5.25046i	0.695341	−	1.27342i	−0.256415	−	0.966567i	$-0.582541\pi$
$17$	2.86697	−	5.25046i	0.695341	−	1.27342i	0.951756	−	0.306856i	$-0.0992769\pi$
$18$	2.70261	+	1.30227i	0.637011	+	0.306948i
$19$	−1.35672	+	4.62056i	−0.311253	+	1.06003i	0.644193	+	0.764863i	$0.277193\pi$
$19$	−1.35672	+	4.62056i	−0.311253	+	1.06003i	−0.955446	+	0.295166i	$0.904625\pi$
$20$	−1.63313	+	1.52738i	−0.365179	+	0.341533i
$21$	−3.76935	−	7.72834i	−0.822540	−	1.68646i
$22$	0.697177	+	0.697177i	0.148639	+	0.148639i
$23$	4.61640	−	1.29956i	0.962586	−	0.270977i
$23$	4.61640	−	1.29956i	0.962586	−	0.270977i
$24$	−1.43286	+	0.973101i	−0.292480	+	0.198633i
$25$	2.41600	+	4.37755i	0.483200	+	0.875510i
$26$	−3.50729	+	1.60173i	−0.687837	+	0.314125i
$27$	3.91076	−	3.42140i	0.752626	−	0.658448i
$28$	4.95173	+	0.354155i	0.935790	+	0.0669290i
$29$	−4.34619	+	1.27616i	−0.807068	+	0.236977i	−0.659139	−	0.752021i	$-0.729079\pi$
$29$	−4.34619	+	1.27616i	−0.807068	+	0.236977i	−0.147929	+	0.988998i	$0.547261\pi$
$30$	1.32417	+	3.63958i	0.241760	+	0.664494i
$31$	−1.05620	+	2.31275i	−0.189698	+	0.415381i	−0.980453	−	0.196751i	$-0.936961\pi$
$31$	−1.05620	+	2.31275i	−0.189698	+	0.415381i	0.790755	+	0.612133i	$0.209688\pi$
$32$	−0.0713392	−	0.997452i	−0.0126111	−	0.176326i
$33$	1.58439	−	0.637211i	0.275807	−	0.110924i
$34$	5.92132	−	0.851357i	1.01550	−	0.146006i
$35$	3.48185	−	10.5405i	0.588540	−	1.78167i
$36$	0.577092	+	2.94397i	0.0961821	+	0.490662i
$37$	−4.04328	+	0.289181i	−0.664711	+	0.0475411i	−0.399618	−	0.916682i	$-0.630857\pi$
$37$	−4.04328	+	0.289181i	−0.664711	+	0.0475411i	−0.265093	+	0.964223i	$0.585403\pi$
$38$	−4.51200	+	1.68289i	−0.731943	+	0.273001i
$39$	0.169514	+	6.67617i	0.0271440	+	1.06904i
$40$	−2.20143	−	0.392061i	−0.348076	−	0.0619903i
$41$	−3.41394	+	2.95819i	−0.533168	+	0.461992i	−0.879351	−	0.476175i	$-0.842023\pi$
$41$	−3.41394	+	2.95819i	−0.533168	+	0.461992i	0.346183	+	0.938167i	$0.387478\pi$
$42$	3.92797	−	7.64894i	0.606098	−	1.18026i
$43$	−9.84064	−	3.67037i	−1.50068	−	0.559726i	−0.541052	−	0.840989i	$-0.681974\pi$
$43$	−9.84064	−	3.67037i	−1.50068	−	0.559726i	−0.959631	+	0.281263i	$0.909247\pi$
$44$	−0.140316	+	0.975922i	−0.0211535	+	0.147126i
$45$	6.69840	+	0.362570i	0.998538	+	0.0540488i
$46$	3.80686	+	2.91682i	0.561290	+	0.430062i
$47$	−3.34725	+	3.34725i	−0.488247	+	0.488247i	−0.907753	−	0.419506i	$-0.862203\pi$
$47$	−3.34725	+	3.34725i	−0.488247	+	0.488247i	0.419506	+	0.907753i	$0.362203\pi$
$48$	−1.63769	−	0.563902i	−0.236380	−	0.0813923i
$49$	−16.0505	+	7.33003i	−2.29293	+	1.04715i
$50$	−2.05655	+	4.55748i	−0.290841	+	0.644524i
$51$	2.66588	−	10.0127i	0.373297	−	1.40205i
$52$	−3.38409	−	1.84785i	−0.469289	−	0.256251i
$53$	2.06975	+	9.51449i	0.284302	+	1.30692i	0.868655	+	0.495417i	$0.164985\pi$
$53$	2.06975	+	9.51449i	0.284302	+	1.30692i	−0.584353	+	0.811499i	$0.698652\pi$
$54$	5.08260	+	1.08036i	0.691654	+	0.147018i
$55$	2.03874	+	0.839097i	0.274904	+	0.113144i
$56$	2.68395	+	4.17630i	0.358658	+	0.558082i
$57$	−0.383666	+	8.33208i	−0.0508178	+	1.10361i
$58$	−3.62619	−	2.71453i	−0.476143	−	0.356436i
$59$	5.33866	−	3.43095i	0.695034	−	0.446671i	−0.144838	−	0.989455i	$-0.546266\pi$
$59$	5.33866	−	3.43095i	0.695034	−	0.446671i	0.839872	+	0.542784i	$0.182630\pi$
$60$	−2.12009	+	3.24118i	−0.273702	+	0.418434i
$61$	−1.50002	+	3.28459i	−0.192058	+	0.420548i	−0.981023	−	0.193889i	$-0.937890\pi$
$61$	−1.50002	+	3.28459i	−0.192058	+	0.420548i	0.788965	+	0.614438i	$0.210617\pi$
$62$	−2.48440	+	0.540449i	−0.315520	+	0.0686371i
$63$	−9.51869	−	11.4543i	−1.19924	−	1.44310i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	−5.86073	+	6.32338i	−0.726934	+	0.784318i
$66$	1.45960	+	0.886504i	0.179665	+	0.109121i
$67$	11.9434	−	8.94072i	1.45912	−	1.09228i	0.482854	−	0.875701i	$-0.339600\pi$
$67$	11.9434	−	8.94072i	1.45912	−	1.09228i	0.976264	−	0.216582i	$-0.0694909\pi$
$68$	4.23006	+	4.23006i	0.512970	+	0.512970i
$69$	7.23331	−	4.08402i	0.870788	−	0.491658i
$70$	10.5247	−	3.52932i	1.25794	−	0.421835i
$71$	5.47868	+	0.787715i	0.650199	+	0.0934845i	0.459519	−	0.888168i	$-0.348022\pi$
$71$	5.47868	+	0.787715i	0.650199	+	0.0934845i	0.190680	+	0.981652i	$0.438931\pi$
$72$	−2.01093	+	2.22624i	−0.236991	+	0.262365i
$73$	−6.13140	+	3.34800i	−0.717626	+	0.391853i	−0.796183	−	0.605056i	$-0.793151\pi$
$73$	−6.13140	+	3.34800i	−0.717626	+	0.391853i	0.0785570	+	0.996910i	$0.474969\pi$
$74$	−2.65455	−	3.06351i	−0.308585	−	0.356126i
$75$	5.86434	+	6.37256i	0.677156	+	0.735839i
$76$	−4.05116	−	2.60352i	−0.464700	−	0.298645i
$77$	−1.71051	−	4.58606i	−0.194931	−	0.522630i
$78$	−5.24296	+	4.13658i	−0.593648	+	0.468375i
$79$	−2.63670	−	4.10278i	−0.296651	−	0.461599i	0.660648	−	0.750695i	$-0.270281\pi$
$79$	−2.63670	−	4.10278i	−0.296651	−	0.461599i	−0.957300	+	0.289097i	$0.906645\pi$
$80$	−1.00541	−	1.99729i	−0.112408	−	0.223304i
$81$	5.17391	−	7.36415i	0.574879	−	0.818238i
$82$	−4.41405	−	0.960219i	−0.487451	−	0.106038i
$83$	−10.0586	+	0.719406i	−1.10408	+	0.0789650i	−0.611455	−	0.791279i	$-0.709415\pi$
$83$	−10.0586	+	0.719406i	−1.10408	+	0.0789650i	−0.492620	+	0.870244i	$0.663961\pi$
$84$	8.47724	−	1.43934i	0.924942	−	0.157045i
$85$	11.4887	−	6.85160i	1.24612	−	0.743160i
$86$	−2.95899	−	10.0774i	−0.319076	−	1.08667i
$87$	−6.78829	+	3.93358i	−0.727781	+	0.421724i
$88$	−0.865354	+	0.472519i	−0.0922470	+	0.0503707i
$89$	−4.78829	−	10.4849i	−0.507558	−	1.11140i	−0.973938	−	0.226813i	$-0.927170\pi$
$89$	−4.78829	−	10.4849i	−0.507558	−	1.11140i	0.466381	−	0.884584i	$-0.345558\pi$
$90$	3.72395	+	5.57962i	0.392539	+	0.588144i
$91$	19.1413			2.00655
$92$	−0.0536700	+	4.79553i	−0.00559549	+	0.499969i
$93$	−0.826558	+	4.32549i	−0.0857101	+	0.448532i
$94$	−4.68554	−	0.673679i	−0.483277	−	0.0694847i
$95$	−7.86453	+	7.35529i	−0.806884	+	0.754637i
$96$	−0.530001	−	1.64897i	−0.0540930	−	0.168297i
$97$	0.180812	−	2.52808i	0.0183587	−	0.256688i	−0.979981	−	0.199090i	$-0.936201\pi$
$97$	0.180812	−	2.52808i	0.0183587	−	0.256688i	0.998340	−	0.0575977i	$-0.0183441\pi$
$98$	−15.4867	−	8.45639i	−1.56439	−	0.854224i
$99$	2.40396	−	1.72337i	0.241607	−	0.173205i
$100$	−4.88089	+	1.08484i	−0.488089	+	0.108484i
$101$	−6.25688	−	5.42162i	−0.622583	−	0.539471i	0.285437	−	0.958397i	$-0.407861\pi$
$101$	−6.25688	−	5.42162i	−0.622583	−	0.539471i	−0.908020	+	0.418926i	$0.862407\pi$
$102$	9.61315	−	3.86622i	0.951844	−	0.382813i
$103$	3.55136	+	2.65851i	0.349926	+	0.261951i	0.759753	−	0.650212i	$-0.225320\pi$
$103$	3.55136	+	2.65851i	0.349926	+	0.261951i	−0.409827	+	0.912163i	$0.634411\pi$
$104$	−0.548727	−	3.81648i	−0.0538071	−	0.374237i
$105$	1.52618	−	19.1663i	0.148940	−	1.87044i
$106$	−6.37639	+	7.35874i	−0.619330	+	0.714744i
$107$	2.43013	+	6.51543i	0.234930	+	0.629871i	0.999899	−	0.0141957i	$-0.00451877\pi$
$107$	2.43013	+	6.51543i	0.234930	+	0.629871i	−0.764970	+	0.644066i	$0.777246\pi$
$108$	2.18102	+	4.71627i	0.209869	+	0.453823i
$109$	3.63595	+	12.3829i	0.348261	+	1.18607i	0.928410	+	0.371558i	$0.121176\pi$
$109$	3.63595	+	12.3829i	0.348261	+	1.18607i	−0.580148	+	0.814511i	$0.697005\pi$
$110$	0.550041	+	2.13495i	0.0524444	+	0.203560i
$111$	−6.68427	+	2.14842i	−0.634443	+	0.203919i
$112$	−1.73487	+	4.65138i	−0.163930	+	0.439514i
$113$	10.6055	−	7.93914i	0.997677	−	0.746852i	0.0301310	−	0.999546i	$-0.490408\pi$
$113$	10.6055	−	7.93914i	0.997677	−	0.746852i	0.967546	+	0.252694i	$0.0813167\pi$
$114$	−6.90009	+	4.68609i	−0.646253	+	0.438892i
$115$	10.3666	+	2.74483i	0.966688	+	0.255957i
$116$		−	4.52968i		−	0.420570i
$117$	3.02922	+	11.1635i	0.280052	+	1.03207i
$118$	5.94595	+	2.21773i	0.547369	+	0.204158i
$119$	−28.4950	−	8.36688i	−2.61213	−	0.766991i
$120$	−3.86522	+	0.245147i	−0.352844	+	0.0223788i
$121$	−9.62169	+	2.82518i	−0.874699	+	0.256835i
$122$	−3.52838	+	0.767551i	−0.319444	+	0.0694908i
$123$	−4.52835	+	6.38057i	−0.408308	+	0.575317i
$124$	−1.92150	−	1.66499i	−0.172556	−	0.149520i
$125$	−0.323505	+	11.1757i	−0.0289351	+	0.999581i
$126$	3.46528	−	14.4844i	0.308711	−	1.29037i
$127$	0.936911	−	1.25157i	0.0831374	−	0.111059i	−0.757044	−	0.653363i	$-0.773357\pi$
$127$	0.936911	−	1.25157i	0.0831374	−	0.111059i	0.840182	+	0.542305i	$0.182448\pi$
$128$	0.977147	+	0.212565i	0.0863684	+	0.0187883i
$129$	−18.0662	−	2.13103i	−1.59064	−	0.187627i
$130$	−8.57433	−	0.902294i	−0.752018	−	0.0791364i
$131$	2.48353	−	3.86445i	0.216987	−	0.337639i	−0.715647	−	0.698462i	$-0.753868\pi$
$131$	2.48353	−	3.86445i	0.216987	−	0.337639i	0.932634	+	0.360823i	$0.117504\pi$
$132$	0.165025	+	1.69974i	0.0143636	+	0.147943i
$133$	23.8457	+	1.70548i	2.06768	+	0.147884i
$134$	14.3148	+	4.20321i	1.23661	+	0.363102i
$135$	11.4196	−	2.14309i	0.982842	−	0.184448i
$136$	−0.851357	+	5.92132i	−0.0730032	+	0.507749i
$137$	−6.34854	+	6.34854i	−0.542392	+	0.542392i	−0.924230	−	0.381837i	$-0.875291\pi$
$137$	−6.34854	+	6.34854i	−0.542392	+	0.542392i	0.381837	+	0.924230i	$0.375291\pi$
$138$	7.60419	+	3.34310i	0.647311	+	0.284584i
$139$		−	8.43087i		−	0.715097i	−0.933895	−	0.357548i	$-0.883613\pi$
$139$		−	8.43087i		−	0.715097i	0.933895	−	0.357548i	$-0.116387\pi$
$140$	9.13259	+	6.31041i	0.771844	+	0.533327i
$141$	−4.25624	+	7.00778i	−0.358440	+	0.590161i
$142$	2.65265	+	4.85797i	0.222605	+	0.407671i
$143$	−0.271202	+	3.79190i	−0.0226790	+	0.317094i
$144$	−2.98731	−	0.275696i	−0.248942	−	0.0229747i
$145$	−9.81966	−	2.48276i	−0.815479	−	0.206182i
$146$	−6.35462	−	2.90206i	−0.525912	−	0.240176i
$147$	−23.9935	+	18.9304i	−1.97895	+	1.56135i
$148$	0.861656	−	3.96097i	0.0708277	−	0.325590i
$149$	1.26797	+	8.81890i	0.103876	+	0.722473i	0.973488	+	0.228738i	$0.0734597\pi$
$149$	1.26797	+	8.81890i	0.103876	+	0.722473i	−0.869612	+	0.493735i	$0.835631\pi$
$150$	−1.58712	+	8.51358i	−0.129588	+	0.695131i
$151$	−20.2316	+	13.0021i	−1.64642	+	1.05809i	−0.711845	+	0.702336i	$0.752140\pi$
$151$	−20.2316	+	13.0021i	−1.64642	+	1.05809i	−0.934579	+	0.355756i	$0.884223\pi$
$152$	−0.343543	−	4.80336i	−0.0278650	−	0.389604i
$153$	0.370191	−	17.9428i	0.0299282	−	1.45059i
$154$	2.64626	−	4.11766i	0.213241	−	0.331810i
$155$	−4.66264	+	3.25293i	−0.374512	+	0.261281i
$156$	−6.45349	−	1.71825i	−0.516693	−	0.137570i
$157$	−3.86747	−	7.08274i	−0.308658	−	0.565264i	0.676598	−	0.736353i	$-0.263453\pi$
$157$	−3.86747	−	7.08274i	−0.308658	−	0.565264i	−0.985256	+	0.171088i	$0.945272\pi$
$158$	1.70433	−	4.56949i	0.135589	−	0.363529i
$159$	7.39311	+	15.1582i	0.586312	+	1.20212i
$160$	0.996394	−	2.00180i	0.0787718	−	0.158256i
$161$	−11.1756	−	21.0225i	−0.880757	−	1.65680i
$162$	8.99591	−	0.271239i	0.706786	−	0.0213105i
$163$	−8.61524	−	11.5086i	−0.674798	−	0.901425i	0.324209	−	0.945986i	$-0.394902\pi$
$163$	−8.61524	−	11.5086i	−0.674798	−	0.901425i	−0.999007	+	0.0445611i	$0.985811\pi$
$164$	−1.87655	−	4.10907i	−0.146534	−	0.320864i
$165$	3.77523	+	0.573893i	0.293901	+	0.0446775i
$166$	−6.60381	−	7.62121i	−0.512555	−	0.591520i
$167$	−0.383777	+	0.702834i	−0.0296975	+	0.0543870i	−0.892106	−	0.451825i	$-0.850773\pi$
$167$	−0.383777	+	0.702834i	−0.0296975	+	0.0543870i	0.862409	+	0.506212i	$0.168955\pi$
$168$	6.23247	+	5.92381i	0.480846	+	0.457032i
$169$	−1.69796	−	0.775431i	−0.130612	−	0.0596486i
$170$	12.3699	+	5.09115i	0.948727	+	0.390473i
$171$	2.77906	+	14.1771i	0.212520	+	1.08415i
$172$	6.29412	−	8.40796i	0.479922	−	0.641101i
$173$	0.569833	−	0.761207i	0.0433236	−	0.0578735i	−0.778356	−	0.627823i	$-0.783946\pi$
$173$	0.569833	−	0.761207i	0.0433236	−	0.0578735i	0.821680	+	0.569949i	$0.193037\pi$
$174$	−7.21707	−	3.07700i	−0.547124	−	0.233266i
$175$	18.6857	−	16.3393i	1.41251	−	1.23513i
$176$	−0.896858	−	0.409581i	−0.0676032	−	0.0308734i
$177$	7.57253	−	7.96710i	0.569187	−	0.598844i
$178$	5.52408	−	10.1166i	0.414047	−	0.758270i
$179$	−3.61968	−	4.17733i	−0.270547	−	0.312228i	0.604176	−	0.796851i	$-0.293502\pi$
$179$	−3.61968	−	4.17733i	−0.270547	−	0.312228i	−0.874723	+	0.484623i	$0.838957\pi$
$180$	−2.23504	+	6.32492i	−0.166590	+	0.471432i
$181$	−9.96739	−	21.8255i	−0.740871	−	1.62228i	−0.782117	−	0.623131i	$-0.785860\pi$
$181$	−9.96739	−	21.8255i	−0.740871	−	1.62228i	0.0412467	−	0.999149i	$-0.486867\pi$
$182$	11.4710	+	15.3234i	0.850284	+	1.13585i
$183$	−1.17389	+	6.14310i	−0.0867762	+	0.454111i
$184$	−3.87118	+	2.83089i	−0.285387	+	0.208696i
$185$	−8.11451	−	4.03899i	−0.596590	−	0.296952i
$186$	−3.95807	+	1.93047i	−0.290220	+	0.141549i
$187$	2.06121	−	5.52632i	0.150731	−	0.404124i
$188$	−2.26863	−	4.15469i	−0.165457	−	0.303012i
$189$	−20.7238	−	15.3604i	−1.50744	−	1.11730i
$190$	−10.6013	−	1.88802i	−0.769096	−	0.136971i
$191$	6.94822	−	10.8116i	0.502756	−	0.782303i	−0.493409	−	0.869797i	$-0.664250\pi$
$191$	6.94822	−	10.8116i	0.502756	−	0.782303i	0.996165	+	0.0874941i	$0.0278859\pi$
$192$	1.00245	−	1.41248i	0.0723456	−	0.101937i
$193$	0.814697	+	11.3910i	0.0586432	+	0.819939i	0.938627	+	0.344935i	$0.112099\pi$
$193$	0.814697	+	11.3910i	0.0586432	+	0.819939i	−0.879984	+	0.475004i	$0.842447\pi$
$194$	2.13219	−	1.37028i	0.153082	−	0.0983800i
$195$	−7.26212	+	13.0484i	−0.520051	+	0.934417i
$196$	−2.51116	−	17.4655i	−0.179368	−	1.24753i
$197$	2.09831	−	9.64578i	0.149498	−	0.687233i	−0.839988	−	0.542605i	$-0.817438\pi$
$197$	2.09831	−	9.64578i	0.149498	−	0.687233i	0.989486	−	0.144628i	$-0.0461985\pi$
$198$	2.82026	+	0.891693i	0.200427	+	0.0633699i
$199$	13.1977	+	6.02720i	0.935562	+	0.427257i	0.824057	−	0.566507i	$-0.191706\pi$
$199$	13.1977	+	6.02720i	0.935562	+	0.427257i	0.111505	+	0.993764i	$0.464433\pi$
$200$	−3.79347	−	3.25724i	−0.268239	−	0.230322i
$201$	16.4209	−	19.9524i	1.15824	−	1.40733i
$202$	0.590620	−	8.25795i	0.0415559	−	0.581027i
$203$	10.7769	+	19.7364i	0.756390	+	1.38522i
$204$	8.85602	+	5.37878i	0.620045	+	0.376590i
$205$	−9.93640	+	1.81586i	−0.693989	+	0.126825i
$206$			4.43620i			0.309085i
$207$	10.4920	−	9.84468i	0.729245	−	0.684252i
$208$	2.72641	−	2.72641i	0.189043	−	0.189043i
$209$	−0.675711	+	4.69967i	−0.0467399	+	0.325083i
$210$	16.2580	−	10.2642i	1.12191	−	0.708295i
$211$	20.9157	+	6.14140i	1.43989	+	0.422791i	0.906187	−	0.422878i	$-0.138980\pi$
$211$	20.9157	+	6.14140i	1.43989	+	0.422791i	0.533708	+	0.845669i	$0.320798\pi$
$212$	−9.71221	−	0.694631i	−0.667037	−	0.0477074i
$213$	9.54206	−	0.926426i	0.653811	−	0.0634777i
$214$	−3.75955	+	5.84997i	−0.256998	+	0.399896i
$215$	−14.7773	−	18.2532i	−1.00781	−	1.24486i
$216$	−2.46853	+	4.57235i	−0.167962	+	0.311109i
$217$	12.3335	+	2.68299i	0.837254	+	0.182134i
$218$	−7.73409	+	10.3315i	−0.523819	+	0.699740i
$219$	−8.94047	+	8.15336i	−0.604141	+	0.550953i
$220$	−1.37949	+	1.71976i	−0.0930051	+	0.115946i
$221$	17.4319	+	15.1049i	1.17260	+	1.01606i
$222$	−5.72563	−	4.06354i	−0.384279	−	0.272727i
$223$	3.32116	−	0.722473i	0.222401	−	0.0483804i	−0.0999839	−	0.994989i	$-0.531879\pi$
$223$	3.32116	−	0.722473i	0.222401	−	0.0483804i	0.322385	+	0.946609i	$0.395515\pi$
$224$	−4.76329	+	1.39863i	−0.318261	+	0.0934498i
$225$	12.4864	+	8.31199i	0.832429	+	0.554132i
$226$	12.7112	+	3.73235i	0.845538	+	0.248272i
$227$	17.1840	+	6.40932i	1.14055	+	0.425401i	0.847552	−	0.530713i	$-0.178076\pi$
$227$	17.1840	+	6.40932i	1.14055	+	0.425401i	0.292994	+	0.956114i	$0.405349\pi$
$228$	−7.88648	−	2.71554i	−0.522295	−	0.179841i
$229$			12.4437i			0.822302i	0.911567	+	0.411151i	$0.134873\pi$
$229$			12.4437i			0.822302i	−0.911567	+	0.411151i	$0.865127\pi$
$230$	4.01511	+	9.94379i	0.264749	+	0.655674i
$231$	−4.76301	−	7.01335i	−0.313383	−	0.461445i
$232$	3.62619	−	2.71453i	0.238071	−	0.178218i
$233$	1.35616	−	3.63602i	0.0888453	−	0.238203i	−0.884926	−	0.465731i	$-0.845791\pi$
$233$	1.35616	−	3.63602i	0.0888453	−	0.238203i	0.973772	+	0.227528i	$0.0730642\pi$
$234$	−7.12149	+	9.11505i	−0.465546	+	0.595870i
$235$	−10.2502	+	2.64083i	−0.668650	+	0.172269i
$236$	1.78790	+	6.08901i	0.116382	+	0.396361i
$237$	−6.12275	−	5.81952i	−0.397715	−	0.378019i
$238$	−10.3784	−	27.8255i	−0.672730	−	1.80366i
$239$	2.42185	−	2.79496i	0.156656	−	0.180791i	−0.671996	−	0.740555i	$-0.734563\pi$
$239$	2.42185	−	2.79496i	0.156656	−	0.180791i	0.828652	+	0.559764i	$0.189108\pi$
$240$	−2.51259	−	2.94735i	−0.162187	−	0.190251i
$241$	−1.03457	−	7.19559i	−0.0666425	−	0.463509i	−0.995629	−	0.0933955i	$-0.970228\pi$
$241$	−1.03457	−	7.19559i	−0.0666425	−	0.463509i	0.928987	−	0.370113i	$-0.120681\pi$
$242$	−8.02774	−	6.00949i	−0.516043	−	0.386305i
$243$	5.67873	−	14.5173i	0.364291	−	0.931285i
$244$	−2.72893	−	2.36463i	−0.174702	−	0.151380i
$245$	−39.2389	−	4.12919i	−2.50688	−	0.263805i
$246$	−7.82165	+	0.198599i	−0.498690	+	0.0126622i
$247$	−16.2965	−	8.89857i	−1.03692	−	0.566203i
$248$	0.181380	−	2.53603i	0.0115177	−	0.161038i
$249$	−16.6287	+	5.34469i	−1.05380	+	0.338706i
$250$	−9.14044	+	6.43834i	−0.578092	+	0.407197i
$251$	−8.69789	−	1.25057i	−0.549006	−	0.0789352i	−0.137770	−	0.990464i	$-0.543994\pi$
$251$	−8.69789	−	1.25057i	−0.549006	−	0.0789352i	−0.411236	+	0.911529i	$0.634903\pi$
$252$	13.6720	−	5.90608i	0.861256	−	0.372048i
$253$	4.32289	−	1.91603i	0.271778	−	0.120460i
$254$	1.56340			0.0980964
$255$	16.5145	−	16.2504i	1.03418	−	1.01764i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	0.647538	−	0.353582i	0.0403923	−	0.0220559i	−0.458926	−	0.888475i	$-0.651766\pi$
$257$	0.647538	−	0.353582i	0.0403923	−	0.0220559i	0.499318	+	0.866419i	$0.333584\pi$
$258$	−9.12070	−	15.7398i	−0.567830	−	0.979919i
$259$	5.66949	+	19.3085i	0.352285	+	1.19977i
$260$	−4.41608	−	7.40483i	−0.273874	−	0.459228i
$261$	−9.80506	+	9.40865i	−0.606918	+	0.582381i
$262$	4.58198	−	0.327710i	0.283076	−	0.0202460i
$263$	7.97301	+	1.73442i	0.491637	+	0.106949i	0.451548	−	0.892247i	$-0.350872\pi$
$263$	7.97301	+	1.73442i	0.491637	+	0.106949i	0.0400893	+	0.999196i	$0.487236\pi$
$264$	−1.26181	+	1.15072i	−0.0776592	+	0.0708221i
$265$	−6.82921	+	20.6739i	−0.419515	+	1.26999i
$266$	12.9249	+	20.1115i	0.792475	+	1.23312i
$267$	−12.3661	−	15.6736i	−0.756794	−	0.959208i
$268$	5.21371	+	13.9785i	0.318478	+	0.853873i
$269$	4.67011	+	3.00130i	0.284742	+	0.182992i	0.675213	−	0.737623i	$-0.264052\pi$
$269$	4.67011	+	3.00130i	0.284742	+	0.182992i	−0.390471	+	0.920615i	$0.627688\pi$
$270$	8.55914	+	7.85755i	0.520893	+	0.478195i
$271$	−11.4902	−	13.2604i	−0.697978	−	0.805510i	0.290500	−	0.956875i	$-0.406178\pi$
$271$	−11.4902	−	13.2604i	−0.697978	−	0.805510i	−0.988478	+	0.151366i	$0.951633\pi$
$272$	−5.25046	+	2.86697i	−0.318356	+	0.173835i
$273$	32.2067	−	7.86736i	1.94924	−	0.476154i
$274$	−8.88681	−	1.27773i	−0.536872	−	0.0771905i
$275$	2.97207	+	3.93314i	0.179222	+	0.237177i
$276$	1.88073	+	8.09091i	0.113207	+	0.487016i
$277$	−4.24953	−	4.24953i	−0.255329	−	0.255329i	0.567822	−	0.823151i	$-0.307786\pi$
$277$	−4.24953	−	4.24953i	−0.255329	−	0.255329i	−0.823151	+	0.567822i	$0.807786\pi$
$278$	6.74926	−	5.05243i	0.404794	−	0.303025i
$279$	0.387091	+	7.61769i	0.0231745	+	0.456059i
$280$	0.421209	+	11.0927i	0.0251721	+	0.662916i
$281$	6.59924	−	5.71828i	0.393678	−	0.341124i	−0.435420	−	0.900227i	$-0.643400\pi$
$281$	6.59924	−	5.71828i	0.393678	−	0.341124i	0.829098	+	0.559104i	$0.188855\pi$
$282$	−8.16068	+	0.792310i	−0.485961	+	0.0471814i
$283$	2.51536	−	0.547184i	0.149523	−	0.0325267i	−0.137181	−	0.990546i	$-0.543804\pi$
$283$	2.51536	−	0.547184i	0.149523	−	0.0325267i	0.286704	+	0.958019i	$0.407440\pi$
$284$	−2.29933	+	5.03483i	−0.136440	+	0.298762i
$285$	−10.2095	+	15.6083i	−0.604761	+	0.924555i
$286$	−3.19810	+	2.05529i	−0.189107	+	0.121532i
$287$	17.9526	+	13.4391i	1.05971	+	0.793287i
$288$	−1.56952	−	2.55668i	−0.0924848	−	0.150654i
$289$	−10.1569	−	15.8044i	−0.597465	−	0.929673i
$290$	−3.89715	−	9.34891i	−0.228849	−	0.548987i
$291$	−0.734849	−	4.32801i	−0.0430776	−	0.253712i
$292$	−1.48496	−	6.82627i	−0.0869010	−	0.399477i
$293$	23.8893	+	13.0445i	1.39563	+	0.762070i	0.988489	−	0.151296i	$-0.0483447\pi$
$293$	23.8893	+	13.0445i	1.39563	+	0.762070i	0.407139	+	0.913366i	$0.366526\pi$
$294$	−29.5333	−	7.86326i	−1.72242	−	0.458594i
$295$	14.1800	−	0.538441i	0.825594	−	0.0313492i
$296$	3.68729	−	1.68393i	0.214319	−	0.0978764i
$297$	3.33652	−	3.88776i	0.193604	−	0.225591i
$298$	−6.30003	+	6.30003i	−0.364951	+	0.364951i
$299$	1.11267	+	18.4579i	0.0643474	+	1.06745i
$300$	−7.76660	+	3.83144i	−0.448405	+	0.221208i
$301$	−7.42031	+	51.6094i	−0.427700	+	2.97472i
$302$	−22.5330	−	8.40439i	−1.29663	−	0.483618i
$303$	−12.7561	−	6.55063i	−0.732816	−	0.376324i
$304$	3.63941	−	3.15356i	0.208734	−	0.180869i
$305$	−6.62193	+	4.61984i	−0.379171	+	0.264531i
$306$	14.5858	−	10.4564i	0.833815	−	0.597751i
$307$	20.0767	−	7.48823i	1.14584	−	0.427376i	0.296401	−	0.955064i	$-0.404214\pi$
$307$	20.0767	−	7.48823i	1.14584	−	0.427376i	0.849438	+	0.527688i	$0.176941\pi$
$308$	4.88220	−	0.349182i	0.278189	−	0.0198965i
$309$	7.06813	+	3.01349i	0.402092	+	0.171432i
$310$	−5.39832	−	1.78323i	−0.306604	−	0.101281i
$311$	−32.2318	+	4.63424i	−1.82770	+	0.262783i	−0.968528	−	0.248905i	$-0.919929\pi$
$311$	−32.2318	+	4.63424i	−1.82770	+	0.262783i	−0.859171	+	0.511688i	$0.829020\pi$
$312$	−2.49191	−	6.19599i	−0.141076	−	0.350779i
$313$	1.61076	+	22.5213i	0.0910453	+	1.27298i	0.813501	+	0.581563i	$0.197559\pi$
$313$	1.61076	+	22.5213i	0.0910453	+	1.27298i	−0.722456	+	0.691417i	$0.756987\pi$
$314$	3.35234	−	7.34060i	0.189183	−	0.414254i
$315$	−5.30972	−	32.8761i	−0.299169	−	1.85236i
$316$	4.67943	−	1.37400i	0.263239	−	0.0772938i
$317$	−7.19028	−	0.514259i	−0.403847	−	0.0288837i	−0.132061	−	0.991242i	$-0.542160\pi$
$317$	−7.19028	−	0.514259i	−0.403847	−	0.0288837i	−0.271785	+	0.962358i	$0.587614\pi$
$318$	−7.70421	+	15.0024i	−0.432031	+	0.841295i
$319$	−4.06248	+	1.85527i	−0.227455	+	0.103875i
$320$	2.19964	−	0.401979i	0.122964	−	0.0224713i
$321$	6.76682	+	9.96390i	0.377687	+	0.556131i
$322$	10.1321	−	21.5448i	0.564639	−	1.20064i
$323$	20.3704	+	20.3704i	1.13344	+	1.13344i
$324$	5.60819	+	7.03905i	0.311566	+	0.391058i
$325$	−18.4731	+	5.51474i	−1.02470	+	0.305903i
$326$	4.05020	−	13.7937i	0.224320	−	0.763963i
$327$	11.2073	+	19.3408i	0.619767	+	1.06955i
$328$	2.16491	−	3.96473i	0.119537	−	0.218916i
$329$	19.7695	+	12.7051i	1.08993	+	0.700453i
$330$	1.80298	+	3.36614i	0.0992510	+	0.185300i
$331$	2.35987	−	2.72344i	0.129710	−	0.149694i	−0.687179	−	0.726488i	$-0.741151\pi$
$331$	2.35987	−	2.72344i	0.129710	−	0.149694i	0.816889	+	0.576795i	$0.195697\pi$
$332$	2.14357	−	9.85384i	0.117644	−	0.540800i
$333$	−10.3638	+	6.36221i	−0.567931	+	0.348647i
$334$	−0.792637	+	0.113964i	−0.0433711	+	0.00623583i
$335$	33.1610	−	3.64079i	1.81178	−	0.198918i
$336$	−1.00727	+	8.53936i	−0.0549513	+	0.465860i
$337$	−17.3444	+	6.46914i	−0.944812	+	0.352397i	−0.774200	−	0.632942i	$-0.781847\pi$
$337$	−17.3444	+	6.46914i	−0.944812	+	0.352397i	−0.170612	+	0.985338i	$0.554575\pi$
$338$	−0.396783	−	1.82398i	−0.0215822	−	0.0992116i
$339$	14.5814	−	17.7172i	0.791952	−	0.962267i
$340$	3.33733	+	12.9536i	0.180992	+	0.702508i
$341$	−0.706248	+	2.40526i	−0.0382455	+	0.130252i
$342$	−9.68389	+	10.7207i	−0.523645	+	0.579712i
$343$	31.6696	+	42.3056i	1.71000	+	2.28429i
$344$	10.5028			0.566275
$345$	18.5707	+	0.357568i	0.999815	+	0.0192508i
$346$	0.950866			0.0511189
$347$	−1.65483	−	2.21059i	−0.0888357	−	0.118671i	0.753921	−	0.656965i	$-0.228160\pi$
$347$	−1.65483	−	2.21059i	−0.0888357	−	0.118671i	−0.842757	+	0.538294i	$0.819069\pi$
$348$	−1.86176	−	7.62153i	−0.0998011	−	0.408557i
$349$	−0.0836604	+	0.284921i	−0.00447824	+	0.0152515i	−0.961702	−	0.274098i	$-0.911621\pi$
$349$	−0.0836604	+	0.284921i	−0.00447824	+	0.0152515i	0.957224	+	0.289349i	$0.0934389\pi$
$350$	24.2782	+	5.16690i	1.29772	+	0.276183i
$351$	9.68527	+	17.5384i	0.516961	+	0.936130i
$352$	−0.209580	−	0.963425i	−0.0111707	−	0.0513507i
$353$	13.4242	−	5.00696i	0.714496	−	0.266493i	0.0341839	−	0.999416i	$-0.489117\pi$
$353$	13.4242	−	5.00696i	0.714496	−	0.266493i	0.680312	+	0.732922i	$0.261844\pi$
$354$	10.9160	+	1.28762i	0.580181	+	0.0684363i
$355$	9.65447	+	7.74424i	0.512406	+	0.411022i
$356$	11.4092	−	1.64040i	0.604686	−	0.0869408i
$357$	−51.3839	−	2.36607i	−2.71952	−	0.125225i
$358$	1.17493	−	5.40108i	0.0620972	−	0.285456i
$359$	−24.2115	+	27.9416i	−1.27784	+	1.47470i	−0.473173	+	0.880969i	$0.656892\pi$
$359$	−24.2115	+	27.9416i	−1.27784	+	1.47470i	−0.804663	+	0.593732i	$0.797654\pi$
$360$	−6.40277	+	2.00114i	−0.337456	+	0.105469i
$361$	−3.52506	−	2.26542i	−0.185529	−	0.119232i
$362$	11.4990	−	21.0589i	0.604375	−	1.10683i
$363$	−15.0280	+	8.70824i	−0.788768	+	0.457064i
$364$	−5.39273	+	18.3659i	−0.282656	+	0.962637i
$365$	−15.6123	−	0.522368i	−0.817183	−	0.0273420i
$366$	−5.62129	+	2.74168i	−0.293830	+	0.143310i
$367$	17.1571	+	17.1571i	0.895593	+	0.895593i	0.995043	−	0.0994495i	$-0.0317082\pi$
$367$	17.1571	+	17.1571i	0.895593	+	0.895593i	−0.0994495	+	0.995043i	$0.531708\pi$
$368$	−4.58616	−	1.40255i	−0.239070	−	0.0731131i
$369$	−4.99680	+	12.5970i	−0.260123	+	0.655775i
$370$	−1.62947	−	8.91647i	−0.0847119	−	0.463545i
$371$	43.9700	−	20.0804i	2.28281	−	1.04252i
$372$	−3.91741	−	2.01171i	−0.203108	−	0.104302i
$373$	28.5155	+	2.03947i	1.47648	+	0.105600i	0.786212	−	0.617957i	$-0.212040\pi$
$373$	28.5155	+	2.03947i	1.47648	+	0.105600i	0.690264	+	0.723557i	$0.257494\pi$
$374$	5.65928	−	1.66171i	0.292634	−	0.0859252i
$375$	4.04904	+	18.9369i	0.209092	+	0.977896i
$376$	1.96646	−	4.30595i	0.101412	−	0.222062i
$377$	−1.24595	−	17.4207i	−0.0641699	−	0.897212i
$378$	−0.122702	−	25.7954i	−0.00631112	−	1.32677i
$379$	23.1653	−	3.33067i	1.18992	−	0.171085i	0.481224	−	0.876598i	$-0.340192\pi$
$379$	23.1653	−	3.33067i	1.18992	−	0.171085i	0.708697	+	0.705513i	$0.249283\pi$
$380$	−4.84166	−	9.61819i	−0.248372	−	0.493403i
$381$	1.06201	−	2.49094i	0.0544086	−	0.127615i
$382$	12.8191	−	0.916839i	0.655881	−	0.0469096i
$383$	15.0902	−	5.62837i	0.771075	−	0.287596i	0.0670294	−	0.997751i	$-0.478648\pi$
$383$	15.0902	−	5.62837i	0.771075	−	0.287596i	0.704045	+	0.710155i	$0.251375\pi$
$384$	1.73149	−	0.0439643i	0.0883599	−	0.00224354i
$385$	1.91901	−	10.7753i	0.0978017	−	0.549158i
$386$	−8.63070	+	7.47854i	−0.439291	+	0.380648i
$387$	−31.2737	+	3.83986i	−1.58973	+	0.195191i
$388$	2.37474	+	0.885731i	0.120559	+	0.0449662i
$389$	5.15316	−	35.8410i	0.261275	−	1.81721i	−0.262024	−	0.965061i	$-0.584390\pi$
$389$	5.15316	−	35.8410i	0.261275	−	1.81721i	0.523299	−	0.852149i	$-0.324701\pi$
$390$	−14.7978	+	2.00600i	−0.749317	+	0.101578i
$391$	6.41177	−	27.9640i	0.324257	−	1.41420i
$392$	12.4770	−	12.4770i	0.630182	−	0.630182i
$393$	2.59039	−	7.52301i	0.130668	−	0.379486i
$394$	8.97931	−	4.10072i	0.452371	−	0.206591i
$395$	−0.413794	−	10.8974i	−0.0208202	−	0.548308i
$396$	0.976284	+	2.79211i	0.0490601	+	0.140309i
$397$	32.6729	+	17.8407i	1.63980	+	0.895401i	0.990911	+	0.134522i	$0.0429499\pi$
$397$	32.6729	+	17.8407i	1.63980	+	0.895401i	0.648894	+	0.760879i	$0.275232\pi$
$398$	3.08408	+	14.1773i	0.154591	+	0.710644i
$399$	40.8232	−	6.93133i	2.04372	−	0.347001i
$400$	0.334214	−	4.98882i	0.0167107	−	0.249441i
$401$	−11.4790	−	17.8617i	−0.573234	−	0.891970i	0.426688	−	0.904399i	$-0.359680\pi$
$401$	−11.4790	−	17.8617i	−0.573234	−	0.891970i	−0.999923	+	0.0124286i	$0.996044\pi$
$402$	25.8134	+	1.18862i	1.28745	+	0.0592832i
$403$	−7.84788	−	5.87485i	−0.390931	−	0.292647i
$404$	6.96478	−	4.47599i	0.346511	−	0.222689i
$405$	18.3335	−	8.29954i	0.911000	−	0.412407i
$406$	−9.34146	+	20.4549i	−0.463609	+	1.01516i
$407$	−3.90535	+	0.849556i	−0.193581	+	0.0421109i
$408$	1.00127	+	10.3130i	0.0495705	+	0.510569i
$409$	−17.3232	+	15.0106i	−0.856576	+	0.742227i	−0.967841	−	0.251564i	$-0.919055\pi$
$409$	−17.3232	+	15.0106i	−0.856576	+	0.742227i	0.111265	+	0.993791i	$0.464510\pi$
$410$	−7.40833	−	6.86630i	−0.365871	−	0.339102i
$411$	−8.07257	+	13.2913i	−0.398190	+	0.655609i
$412$	−3.55136	+	2.65851i	−0.174963	+	0.130976i
$413$	−22.2769	−	22.2769i	−1.09618	−	1.09618i
$414$	14.1687	+	2.49959i	0.696354	+	0.122848i
$415$	−20.1867	−	10.0479i	−0.990928	−	0.493234i
$416$	3.81648	+	0.548727i	0.187118	+	0.0269036i
$417$	−3.46521	−	14.1856i	−0.169692	−	0.694671i
$418$	−4.16722	+	2.27547i	−0.203825	+	0.111297i
$419$	0.637597	+	0.735826i	0.0311486	+	0.0359474i	0.771110	−	0.636702i	$-0.219702\pi$
$419$	0.637597	+	0.735826i	0.0311486	+	0.0359474i	−0.739961	+	0.672649i	$0.765156\pi$
$420$	17.9600	+	6.86413i	0.876356	+	0.334935i
$421$	−17.3681	−	11.1618i	−0.846469	−	0.543992i	0.0440029	−	0.999031i	$-0.485989\pi$
$421$	−17.3681	−	11.1618i	−0.846469	−	0.543992i	−0.890471	+	0.455039i	$0.849625\pi$
$422$	7.61786	+	20.4243i	0.370831	+	0.994238i
$423$	−4.28115	+	13.5405i	−0.208157	+	0.658362i
$424$	−5.26423	−	8.19130i	−0.255653	−	0.397805i
$425$	29.9107	−	0.134814i	1.45088	−	0.00653942i
$426$	6.45999	+	7.08363i	0.312987	+	0.343203i
$427$	17.5162	+	3.81042i	0.847669	+	0.184399i
$428$	−6.93616	+	0.496084i	−0.335272	+	0.0239791i
$429$	1.10221	+	6.49163i	0.0532151	+	0.313419i
$430$	5.75672	−	22.7686i	0.277613	−	1.09800i
$431$	−1.78205	−	6.06911i	−0.0858384	−	0.292339i	0.905375	−	0.424614i	$-0.139590\pi$
$431$	−1.78205	−	6.06911i	−0.0858384	−	0.292339i	−0.991213	+	0.132275i	$0.957772\pi$
$432$	−5.13969	+	0.763946i	−0.247283	+	0.0367554i
$433$	−8.09965	+	4.42274i	−0.389244	+	0.212544i	−0.661940	−	0.749557i	$-0.730267\pi$
$433$	−8.09965	+	4.42274i	−0.389244	+	0.212544i	0.272696	+	0.962100i	$0.412085\pi$
$434$	5.24336	+	11.4814i	0.251689	+	0.551123i
$435$	−17.5428	−	0.141412i	−0.841113	−	0.00678020i
$436$	−12.9057			−0.618071
$437$	−0.258455	+	23.0935i	−0.0123636	+	1.10471i
$438$	−11.8849	−	2.27109i	−0.567884	−	0.108517i
$439$	−4.07701	−	0.586186i	−0.194585	−	0.0279771i	0.0443331	−	0.999017i	$-0.485884\pi$
$439$	−4.07701	−	0.586186i	−0.194585	−	0.0279771i	−0.238918	+	0.971040i	$0.576793\pi$
$440$	−2.20343	−	0.0737243i	−0.105045	−	0.00351467i
$441$	−32.5903	+	41.7135i	−1.55192	+	1.98636i
$442$	−1.64549	+	23.0070i	−0.0782681	+	1.09433i
$443$	−5.68717	−	3.10543i	−0.270205	−	0.147543i	0.338434	−	0.940990i	$-0.390103\pi$
$443$	−5.68717	−	3.10543i	−0.270205	−	0.147543i	−0.608640	+	0.793447i	$0.708285\pi$
$444$	−0.178214	−	7.01879i	−0.00845766	−	0.333097i
$445$	2.69737	−	25.6326i	0.127867	−	1.21510i
$446$	2.56866	+	2.22576i	0.121630	+	0.105393i
$447$	5.75815	+	14.3173i	0.272351	+	0.677187i
$448$	−3.97419	−	2.97504i	−0.187763	−	0.140558i
$449$	1.62729	+	11.3180i	0.0767964	+	0.534131i	0.991510	+	0.130029i	$0.0415069\pi$
$449$	1.62729	+	11.3180i	0.0767964	+	0.534131i	−0.914714	+	0.404102i	$0.867584\pi$
$450$	0.828751	+	14.9771i	0.0390677	+	0.706027i
$451$	−2.91665	+	3.36600i	−0.137340	+	0.158499i
$452$	4.62965	+	12.4126i	0.217760	+	0.583838i
$453$	−28.6972	+	30.1925i	−1.34831	+	1.41857i
$454$	5.16709	+	17.5975i	0.242504	+	0.825892i
$455$	36.8588	+	21.7572i	1.72797	+	1.01999i
$456$	−2.55229	−	7.94082i	−0.119522	−	0.371863i
$457$	5.89162	−	15.7960i	0.275598	−	0.738907i	−0.723234	−	0.690603i	$-0.757345\pi$
$457$	5.89162	−	15.7960i	0.275598	−	0.738907i	0.998833	−	0.0483047i	$-0.0153819\pi$
$458$	−9.96169	+	7.45723i	−0.465479	+	0.348453i
$459$	−6.75188	−	30.3423i	−0.315151	−	1.41626i
$460$	−5.55425	+	9.17335i	−0.258968	+	0.427710i
$461$			11.9956i			0.558693i	0.960190	+	0.279346i	$0.0901178\pi$
$461$			11.9956i			0.558693i	−0.960190	+	0.279346i	$0.909882\pi$
$462$	2.76011	−	8.01593i	0.128412	−	0.372935i
$463$	−1.53150	−	0.571220i	−0.0711748	−	0.0265468i	0.313625	−	0.949547i	$-0.398457\pi$
$463$	−1.53150	−	0.571220i	−0.0711748	−	0.0265468i	−0.384799	+	0.923000i	$0.625729\pi$
$464$	4.34619	+	1.27616i	0.201767	+	0.0592441i
$465$	−6.50825	+	7.38971i	−0.301813	+	0.342690i
$466$	3.72350	−	1.09332i	0.172488	−	0.0506470i
$467$	19.9916	−	4.34891i	0.925102	−	0.201244i	0.275310	−	0.961355i	$-0.411219\pi$
$467$	19.9916	−	4.34891i	0.925102	−	0.201244i	0.649792	+	0.760112i	$0.274856\pi$
$468$	−11.5647	−	0.238600i	−0.534580	−	0.0110293i
$469$	−55.9741	−	48.5019i	−2.58465	−	2.23961i
$470$	−8.25681	−	6.62313i	−0.380858	−	0.305502i
$471$	−9.41843	−	10.3277i	−0.433978	−	0.475874i
$472$	−3.80306	+	5.08029i	−0.175050	+	0.233839i
$473$	−10.1187	−	2.20119i	−0.465259	−	0.101211i
$474$	0.989541	−	8.38902i	0.0454511	−	0.385321i
$475$	−23.5046	+	5.22417i	−1.07846	+	0.239701i
$476$	16.0559	−	24.9835i	0.735922	−	1.14512i
$477$	18.6697	+	22.4661i	0.854828	+	1.02865i
$478$	3.68884	+	0.263831i	0.168724	+	0.0120674i
$479$	1.49745	+	0.439691i	0.0684202	+	0.0200900i	0.315764	−	0.948838i	$-0.397739\pi$
$479$	1.49745	+	0.439691i	0.0684202	+	0.0200900i	−0.247343	+	0.968928i	$0.579558\pi$
$480$	0.853741	−	3.77771i	0.0389678	−	0.172428i
$481$	2.22433	−	15.4705i	0.101421	−	0.705395i
$482$	5.14037	−	5.14037i	0.234138	−	0.234138i
$483$	−27.4443	−	30.7786i	−1.24876	−	1.40047i
$484$		−	10.0279i		−	0.455813i
$485$	3.22175	−	4.66259i	0.146292	−	0.211717i
$486$	15.0248	−	4.15383i	0.681540	−	0.188422i
$487$	5.19580	+	9.51539i	0.235444	+	0.431184i	0.968510	−	0.248974i	$-0.0800933\pi$
$487$	5.19580	+	9.51539i	0.235444	+	0.431184i	−0.733066	+	0.680157i	$0.761911\pi$
$488$	0.257598	−	3.60170i	0.0116609	−	0.163041i
$489$	−19.2260	−	15.8231i	−0.869431	−	0.715547i
$490$	−20.2094	−	33.8869i	−0.912969	−	1.53086i
$491$	11.5120	+	5.25735i	0.519529	+	0.237261i	0.657881	−	0.753122i	$-0.271453\pi$
$491$	11.5120	+	5.25735i	0.519529	+	0.237261i	−0.138352	+	0.990383i	$0.544180\pi$
$492$	−4.84633	−	6.14254i	−0.218489	−	0.276927i
$493$	−5.75998	+	26.4782i	−0.259416	+	1.19252i
$494$	−2.64247	−	18.3787i	−0.118890	−	0.826899i
$495$	6.58799	−	0.586055i	0.296108	−	0.0263412i
$496$	2.13889	−	1.37458i	0.0960392	−	0.0617206i
$497$	−1.96025	−	27.4079i	−0.0879293	−	1.22941i
$498$	−14.2439	−	10.1090i	−0.638282	−	0.452995i
$499$	7.53762	−	11.7288i	0.337430	−	0.525052i	−0.630527	−	0.776167i	$-0.717161\pi$
$499$	7.53762	−	11.7288i	0.337430	−	0.525052i	0.967957	+	0.251116i	$0.0807975\pi$
$500$	−10.6318	−	3.45895i	−0.475470	−	0.154689i
$501$	−0.356858	+	1.34031i	−0.0159433	+	0.0598807i
$502$	−4.21132	−	7.71246i	−0.187961	−	0.344224i
$503$	−1.49541	+	4.00935i	−0.0666770	+	0.178768i	−0.966015	−	0.258486i	$-0.916776\pi$
$503$	−1.49541	+	4.00935i	−0.0666770	+	0.178768i	0.899338	+	0.437254i	$0.144049\pi$
$504$	12.9214	+	7.40563i	0.575564	+	0.329873i
$505$	−5.88581	−	17.5519i	−0.261915	−	0.781050i
$506$	4.12447	+	2.31242i	0.183355	+	0.102800i
$507$	−3.17566	−	0.606837i	−0.141036	−	0.0269506i
$508$	0.936911	+	1.25157i	0.0415687	+	0.0555293i
$509$	8.75679	+	19.1747i	0.388138	+	0.849903i	0.998337	+	0.0576549i	$0.0183623\pi$
$509$	8.75679	+	19.1747i	0.388138	+	0.849903i	−0.610199	+	0.792248i	$0.708910\pi$
$510$	22.9058	+	3.48204i	1.01429	+	0.154187i
$511$	22.7111	+	26.2100i	1.00468	+	1.15946i
$512$	−0.479249	+	0.877679i	−0.0211800	+	0.0387883i
$513$	10.5030	+	22.7118i	0.463717	+	1.00275i
$514$	0.671112	+	0.306487i	0.0296015	+	0.0135186i
$515$	3.81673	+	9.15597i	0.168185	+	0.403460i
$516$	7.13455	−	16.7340i	0.314081	−	0.736674i
$517$	−2.79698	+	3.73633i	−0.123011	+	0.164323i
$518$	−12.0597	+	16.1098i	−0.529871	+	0.707825i
$519$	0.645920	−	1.51500i	0.0283527	−	0.0665011i
$520$	3.28141	−	7.97280i	0.143899	−	0.349630i
$521$	−29.3621	−	13.4092i	−1.28638	−	0.587469i	−0.349438	−	0.936960i	$-0.613627\pi$
$521$	−29.3621	−	13.4092i	−1.28638	−	0.587469i	−0.936940	+	0.349491i	$0.886355\pi$
$522$	−13.4080	−	2.21096i	−0.586851	−	0.0967712i
$523$	−5.17159	+	9.47106i	−0.226138	+	0.414141i	−0.965971	−	0.258650i	$-0.916723\pi$
$523$	−5.17159	+	9.47106i	−0.226138	+	0.414141i	0.739833	+	0.672790i	$0.234904\pi$
$524$	3.00822	+	3.47168i	0.131415	+	0.151661i
$525$	24.7244	−	35.1722i	1.07906	−	1.53504i
$526$	3.38957	+	7.42212i	0.147792	+	0.323620i
$527$	9.11490	+	12.1761i	0.397051	+	0.530398i
$528$	−1.67738	−	0.320530i	−0.0729985	−	0.0139493i
$529$	19.6223	−	11.9986i	0.853143	−	0.521678i
$530$	−20.6429	+	6.92232i	−0.896670	+	0.300687i
$531$	9.46678	−	16.5177i	0.410823	−	0.716807i
$532$	−8.35450	+	22.3993i	−0.362214	+	0.971132i
$533$	−8.34729	−	15.2869i	−0.361561	−	0.662150i
$534$	5.13662	−	19.2924i	0.222283	−	0.834865i
$535$	−2.72634	+	15.3085i	−0.117870	+	0.661843i
$536$	−8.06591	+	12.5508i	−0.348394	+	0.542112i
$537$	−7.80733	−	5.54094i	−0.336911	−	0.239109i
$538$	0.396030	+	5.53723i	0.0170741	+	0.238727i
$539$	−14.6355	+	9.40569i	−0.630397	+	0.405132i
$540$	−1.16099	+	11.5608i	−0.0499612	+	0.497498i
$541$	5.99991	+	41.7303i	0.257956	+	1.79413i	0.547337	+	0.836912i	$0.315642\pi$
$541$	5.99991	+	41.7303i	0.257956	+	1.79413i	−0.289381	+	0.957214i	$0.593449\pi$
$542$	3.72966	−	17.1450i	0.160203	−	0.736440i
$543$	−25.7415	−	32.6264i	−1.10468	−	1.40013i
$544$	−5.44161	−	2.48510i	−0.233307	−	0.106548i
$545$	−7.07374	+	27.9776i	−0.303006	+	1.19843i
$546$	25.5989	+	21.0681i	1.09553	+	0.901631i
$547$	0.899835	−	12.5813i	0.0384742	−	0.537939i	−0.941266	−	0.337666i	$-0.890363\pi$
$547$	0.899835	−	12.5813i	0.0384742	−	0.537939i	0.979740	−	0.200273i	$-0.0641829\pi$
$548$	−4.30279	−	7.87997i	−0.183806	−	0.336616i
$549$	0.549751	+	10.8187i	0.0234628	+	0.461732i
$550$	−1.36755	+	4.73631i	−0.0583124	+	0.201957i
$551$		−	21.8132i		−	0.929275i
$552$	−5.35003	+	6.35430i	−0.227712	+	0.270457i
$553$	−17.1199	+	17.1199i	−0.728012	+	0.728012i
$554$	0.855275	−	5.94857i	0.0363372	−	0.252730i
$555$	−15.3134	−	3.46073i	−0.650016	−	0.146900i
$556$	8.08936	+	2.37525i	0.343065	+	0.100733i
$557$	13.4180	+	0.959675i	0.568539	+	0.0406627i	0.352650	−	0.935755i	$-0.385281\pi$
$557$	13.4180	+	0.959675i	0.568539	+	0.0406627i	0.215889	+	0.976418i	$0.430735\pi$
$558$	−5.86630	+	4.87500i	−0.248340	+	0.206375i
$559$	21.8939	−	34.0675i	0.926011	−	1.44090i
$560$	−8.62774	+	6.98480i	−0.364589	+	0.295162i
$561$	1.19675	−	10.1456i	0.0505267	−	0.428349i
$562$	8.53250	+	1.85613i	0.359922	+	0.0782962i
$563$	11.3972	−	15.2249i	0.480337	−	0.641655i	−0.493273	−	0.869875i	$-0.664200\pi$
$563$	11.3972	−	15.2249i	0.480337	−	0.641655i	0.973610	+	0.228220i	$0.0732905\pi$
$564$	−5.52479	−	6.05815i	−0.232636	−	0.255094i
$565$	29.4462	−	3.23293i	1.23881	−	0.136011i
$566$	1.94544	+	1.68574i	0.0817731	+	0.0708568i
$567$	−41.1828	−	17.3272i	−1.72951	−	0.727675i
$568$	−5.40852	+	1.17655i	−0.226937	+	0.0493670i
$569$	2.03188	−	0.596614i	0.0851808	−	0.0250113i	−0.238864	−	0.971053i	$-0.576775\pi$
$569$	2.03188	−	0.596614i	0.0851808	−	0.0250113i	0.324045	+	0.946042i	$0.394957\pi$
$570$	−18.6134	+	1.18054i	−0.779631	+	0.0494472i
$571$	3.02093	+	0.887024i	0.126422	+	0.0371208i	0.344331	−	0.938848i	$-0.388106\pi$
$571$	3.02093	+	0.887024i	0.126422	+	0.0371208i	−0.217910	+	0.975969i	$0.569924\pi$
$572$	−3.56189	−	1.32852i	−0.148930	−	0.0555481i
$573$	7.24718	−	21.0473i	0.302755	−	0.879262i
$574$			22.4255i			0.936024i
$575$	16.8421	+	17.0688i	0.702365	+	0.711817i
$576$	1.10615	−	2.78863i	0.0460896	−	0.116193i
$577$	8.71688	−	6.52538i	0.362889	−	0.271655i	−0.402238	−	0.915535i	$-0.631767\pi$
$577$	8.71688	−	6.52538i	0.362889	−	0.271655i	0.765126	+	0.643880i	$0.222677\pi$
$578$	6.56531	−	17.6023i	0.273081	−	0.732158i
$579$	6.05264	+	18.8313i	0.251539	+	0.782603i
$580$	5.14871	−	8.72242i	0.213789	−	0.362179i
$581$	14.1042	+	48.0344i	0.585140	+	1.99280i
$582$	3.02437	−	3.18196i	0.125364	−	0.131896i
$583$	3.35495	+	8.99498i	0.138948	+	0.372534i
$584$	4.57481	−	5.27961i	0.189307	−	0.218472i
$585$	−6.85599	+	24.9398i	−0.283460	+	1.03113i
$586$	3.87363	+	26.9417i	0.160018	+	1.11295i
$587$	−2.97410	−	2.22638i	−0.122754	−	0.0918927i	0.536137	−	0.844131i	$-0.319883\pi$
$587$	−2.97410	−	2.22638i	−0.122754	−	0.0918927i	−0.658891	+	0.752239i	$0.728974\pi$
$588$	−11.4038	−	28.3549i	−0.470284	−	1.16934i
$589$	−9.25322	−	8.01796i	−0.381272	−	0.330374i
$590$	8.92882	+	11.0290i	0.367594	+	0.454058i
$591$	−0.433988	−	17.0922i	−0.0178519	−	0.703079i
$592$	3.55777	+	1.94269i	0.146223	+	0.0798440i
$593$	2.78157	−	38.8915i	0.114225	−	1.59708i	−0.540586	−	0.841289i	$-0.681797\pi$
$593$	2.78157	−	38.8915i	0.114225	−	1.59708i	0.654811	−	0.755792i	$-0.272748\pi$
$594$	5.11181	+	0.341172i	0.209740	+	0.0139985i
$595$	−45.3601	−	48.5006i	−1.85958	−	1.98833i
$596$	−8.81890	−	1.26797i	−0.361236	−	0.0519380i
$597$	24.6835	+	4.71677i	1.01023	+	0.193045i
$598$	−14.1095	+	11.9522i	−0.576981	+	0.488760i
$599$	23.5970			0.964148			0.482074	−	0.876130i	$-0.339884\pi$
$599$	23.5970			0.964148			0.482074	+	0.876130i	$0.339884\pi$
$600$	−7.72158	−	3.92139i	−0.315232	−	0.160090i
$601$	−4.42104	−	9.68072i	−0.180338	−	0.394885i	0.797776	−	0.602953i	$-0.206010\pi$
$601$	−4.42104	−	9.68072i	−0.180338	−	0.394885i	−0.978114	+	0.208069i	$0.933282\pi$
$602$	−45.7623	+	24.9881i	−1.86513	+	1.01844i
$603$	19.4288	−	40.3206i	0.791201	−	1.64198i
$604$	−6.77548	−	23.0752i	−0.275691	−	0.938916i
$605$	−21.7390	−	5.49639i	−0.883814	−	0.223460i
$606$	−2.40038	−	14.1374i	−0.0975086	−	0.574292i
$607$	−35.3810	+	2.53050i	−1.43607	+	0.102710i	−0.767552	−	0.640986i	$-0.778526\pi$
$607$	−35.3810	+	2.53050i	−1.43607	+	0.102710i	−0.668518	+	0.743696i	$0.733071\pi$
$608$	4.70557	+	1.02363i	0.190836	+	0.0415139i
$609$	26.2449	+	28.7786i	1.06350	+	1.16617i
$610$	−7.66675	−	2.53256i	−0.310418	−	0.102540i
$611$	−9.86775	−	15.3545i	−0.399207	−	0.621178i
$612$	17.1117	+	5.41027i	0.691699	+	0.218697i
$613$	−8.67823	−	23.2672i	−0.350511	−	0.939755i	−0.985866	−	0.167535i	$-0.946419\pi$
$613$	−8.67823	−	23.2672i	−0.350511	−	0.939755i	0.635356	−	0.772220i	$-0.280854\pi$
$614$	18.0262	+	11.5847i	0.727477	+	0.467521i
$615$	−15.9724	+	7.13933i	−0.644070	+	0.287885i
$616$	3.20533	+	3.69914i	0.129146	+	0.149043i
$617$	6.77724	−	3.70066i	0.272842	−	0.148983i	−0.337004	−	0.941503i	$-0.609413\pi$
$617$	6.77724	−	3.70066i	0.272842	−	0.148983i	0.609845	+	0.792521i	$0.291232\pi$
$618$	1.82334	+	7.46425i	0.0733456	+	0.300256i
$619$	10.3349	+	1.48593i	0.415393	+	0.0597245i	0.346843	−	0.937923i	$-0.387254\pi$
$619$	10.3349	+	1.48593i	0.415393	+	0.0597245i	0.0685499	+	0.997648i	$0.478163\pi$
$620$	−1.80754	−	5.39022i	−0.0725926	−	0.216477i
$621$	13.6073	−	20.8768i	0.546043	−	0.837757i
$622$	−23.0257	−	23.0257i	−0.923247	−	0.923247i
$623$	−45.8086	+	34.2919i	−1.83528	+	1.37388i
$624$	3.46680	−	5.70799i	0.138783	−	0.228503i
$625$	−13.3259	+	21.1523i	−0.533036	+	0.846093i
$626$	−17.0639	+	14.7860i	−0.682013	+	0.590967i
$627$	0.794699	+	8.18529i	0.0317372	+	0.326889i
$628$	7.88543	−	1.71537i	0.314663	−	0.0684507i
$629$	−10.0736	+	22.0581i	−0.401661	+	0.879515i
$630$	23.1367	−	23.9525i	0.921786	−	0.954292i
$631$	13.8135	−	8.87741i	0.549907	−	0.353404i	−0.235995	−	0.971754i	$-0.575835\pi$
$631$	13.8135	−	8.87741i	0.549907	−	0.353404i	0.785903	+	0.618350i	$0.212199\pi$
$632$	3.90423	+	2.92267i	0.155302	+	0.116257i
$633$	37.7164	+	1.73672i	1.49909	+	0.0690285i
$634$	−3.89729	−	6.06430i	−0.154781	−	0.240844i
$635$	3.22674	−	1.34509i	0.128049	−	0.0533781i
$636$	−16.6270	+	2.82309i	−0.659305	+	0.111943i
$637$	−14.4618	−	66.4798i	−0.572998	−	2.63403i
$638$	−3.91977	−	2.14036i	−0.155185	−	0.0847376i
$639$	15.6745	−	5.48071i	0.620073	−	0.216814i
$640$	1.64000	+	1.52000i	0.0648265	+	0.0600835i
$641$	−0.933100	+	0.426133i	−0.0368553	+	0.0168312i	−0.433757	−	0.901030i	$-0.642813\pi$
$641$	−0.933100	+	0.426133i	−0.0368553	+	0.0168312i	0.396902	+	0.917861i	$0.370085\pi$
$642$	−3.92131	+	11.3883i	−0.154762	+	0.449459i
$643$	11.2827	−	11.2827i	0.444948	−	0.444948i	−0.448723	−	0.893671i	$-0.648121\pi$
$643$	11.2827	−	11.2827i	0.444948	−	0.444948i	0.893671	+	0.448723i	$0.148121\pi$
$644$	23.3194	−	4.80016i	0.918914	−	0.189153i
$645$	−32.3663	−	24.6387i	−1.27442	−	0.970149i
$646$	−4.09981	+	28.5148i	−0.161305	+	1.12190i
$647$	−20.0930	−	7.49430i	−0.789937	−	0.294631i	−0.0780722	−	0.996948i	$-0.524876\pi$
$647$	−20.0930	−	7.49430i	−0.789937	−	0.294631i	−0.711865	+	0.702316i	$0.752149\pi$
$648$	−2.27419	+	8.70793i	−0.0893386	+	0.342080i
$649$	4.72869	−	4.09744i	0.185617	−	0.160838i
$650$	−15.4853	−	11.4836i	−0.607382	−	0.450423i
$651$	21.8549	−	0.554916i	0.856560	−	0.0217489i
$652$	13.4696	−	5.02391i	0.527512	−	0.196752i
$653$	0.514127	−	0.0367711i	0.0201193	−	0.00143896i	−0.0612759	−	0.998121i	$-0.519517\pi$
$653$	0.514127	−	0.0367711i	0.0201193	−	0.00143896i	0.0813952	+	0.996682i	$0.474062\pi$
$654$	−8.76680	+	20.5624i	−0.342809	+	0.804055i
$655$	9.17491	−	4.61852i	0.358493	−	0.180460i
$656$	4.47131	−	0.642877i	0.174575	−	0.0251001i
$657$	−11.6919	+	17.3933i	−0.456144	+	0.678578i
$658$	1.67647	+	23.4401i	0.0653557	+	0.913792i
$659$	21.0612	−	46.1175i	0.820426	−	1.79648i	0.266710	−	0.963777i	$-0.414063\pi$
$659$	21.0612	−	46.1175i	0.820426	−	1.79648i	0.553716	−	0.832706i	$-0.313209\pi$
$660$	−1.61425	+	3.46062i	−0.0628346	+	0.134704i
$661$	−28.3006	+	8.30981i	−1.10077	+	0.323214i	−0.781156	−	0.624335i	$-0.785370\pi$
$661$	−28.3006	+	8.30981i	−1.10077	+	0.323214i	−0.319610	+	0.947549i	$0.603552\pi$
$662$	3.59444	+	0.257079i	0.139702	+	0.00999168i
$663$	35.5389	+	18.2503i	1.38022	+	0.708783i
$664$	9.17300	−	4.18917i	0.355982	−	0.162571i
$665$	43.9791	+	30.3886i	1.70544	+	1.17842i
$666$	−11.3040	−	4.48390i	−0.438021	−	0.173747i
$667$	−18.4053	+	11.5394i	−0.712657	+	0.446807i
$668$	−0.566242	−	0.566242i	−0.0219086	−	0.0219086i
$669$	5.29115	−	2.58066i	0.204568	−	0.0997741i
$670$	22.7872	+	24.3649i	0.880348	+	0.941298i
$671$	−1.00302	+	3.41598i	−0.0387212	+	0.131872i
$672$	−7.43975	+	4.31108i	−0.286994	+	0.166304i
$673$	−4.25813	+	7.79819i	−0.164139	+	0.300598i	−0.946784	−	0.321871i	$-0.895688\pi$
$673$	−4.25813	+	7.79819i	−0.164139	+	0.300598i	0.782645	+	0.622469i	$0.213870\pi$
$674$	−15.5729	−	10.0081i	−0.599848	−	0.385499i
$675$	24.4257	+	8.85345i	0.940147	+	0.340770i
$676$	1.22239	−	1.41071i	0.0470150	−	0.0542582i
$677$	−1.68570	+	7.74905i	−0.0647868	+	0.297820i	−0.998127	−	0.0611724i	$-0.980516\pi$
$677$	−1.68570	+	7.74905i	−0.0647868	+	0.297820i	0.933340	+	0.358993i	$0.116880\pi$
$678$	22.9217	+	1.05547i	0.880301	+	0.0405351i
$679$	−12.4543	+	1.79066i	−0.477954	+	0.0687194i
$680$	−8.36992	+	10.4345i	−0.320972	+	0.400144i
$681$	31.5478	+	3.72128i	1.20891	+	0.142600i
$682$	−2.34875	+	0.876038i	−0.0899383	+	0.0335452i
$683$	−4.19741	−	19.2952i	−0.160609	−	0.738309i	−0.985037	−	0.172342i	$-0.944867\pi$
$683$	−4.19741	−	19.2952i	−0.160609	−	0.738309i	0.824428	−	0.565967i	$-0.191497\pi$
$684$	−14.3857	−	1.32765i	−0.550053	−	0.0507640i
$685$	−19.4410	+	5.00871i	−0.742802	+	0.191373i
$686$	−14.8885	+	50.7056i	−0.568446	+	1.93595i
$687$	5.11454	+	20.9375i	0.195132	+	0.798814i
$688$	6.29412	+	8.40796i	0.239961	+	0.320551i
$689$	−37.5433			−1.43029
$690$	10.8428	+	15.0809i	0.412777	+	0.574121i
$691$	37.1311			1.41253			0.706267	−	0.707946i	$-0.250378\pi$
$691$	37.1311			1.41253			0.706267	+	0.707946i	$0.250378\pi$
$692$	0.569833	+	0.761207i	0.0216618	+	0.0289368i
$693$	−10.8967	−	9.84284i	−0.413932	−	0.373899i
$694$	0.777967	−	2.64951i	0.0295312	−	0.100574i
$695$	9.58305	−	16.2346i	0.363506	−	0.615814i
$696$	4.98564	−	6.05783i	0.188980	−	0.229622i
$697$	5.74423	+	26.4058i	0.217578	+	1.00019i
$698$	−0.278227	+	0.103773i	−0.0105310	+	0.00392788i
$699$	0.787395	−	6.67529i	0.0297820	−	0.252483i
$700$	10.4131	+	22.5321i	0.393576	+	0.851633i
$701$	45.1538	−	6.49213i	1.70543	−	0.245204i	0.780453	−	0.625215i	$-0.214989\pi$
$701$	45.1538	−	6.49213i	1.70543	−	0.245204i	0.924982	+	0.380011i	$0.124080\pi$
$702$	−8.23604	+	18.2638i	−0.310849	+	0.689323i
$703$	4.14941	−	19.0745i	0.156498	−	0.719410i
$704$	0.645665	−	0.745137i	0.0243344	−	0.0280834i
$705$	−16.1614	+	8.65639i	−0.608672	+	0.326018i
$706$	12.0531	+	7.74604i	0.453624	+	0.291526i
$707$	−19.6973	+	36.0729i	−0.740793	+	1.35666i
$708$	5.51095	+	9.51039i	0.207114	+	0.357422i
$709$	−6.72808	+	22.9138i	−0.252679	+	0.860544i	0.731269	+	0.682089i	$0.238928\pi$
$709$	−6.72808	+	22.9138i	−0.252679	+	0.860544i	−0.983948	+	0.178455i	$0.942890\pi$
$710$	−0.413877	+	12.3697i	−0.0155325	+	0.464228i
$711$	−12.6939	−	7.27526i	−0.476059	−	0.272843i
$712$	8.15048	+	8.15048i	0.305452	+	0.305452i
$713$	−1.87027	+	12.0492i	−0.0700420	+	0.451244i
$714$	−28.8991	−	42.5529i	−1.08152	−	1.59250i
$715$	−4.83234	+	6.99348i	−0.180719	+	0.261541i
$716$	5.02790	−	2.29617i	0.187901	−	0.0858117i
$717$	2.92618	−	5.69816i	0.109280	−	0.212802i
$718$	−36.8778	−	2.63756i	−1.37627	−	0.0984327i
$719$	−38.5735	+	11.3262i	−1.43855	+	0.422396i	−0.905738	−	0.423838i	$-0.860682\pi$
$719$	−38.5735	+	11.3262i	−1.43855	+	0.422396i	−0.532811	+	0.846234i	$0.678864\pi$
$720$	−5.43903	−	3.92644i	−0.202701	−	0.146330i
$721$	9.14868	−	20.0328i	0.340714	−	0.746061i
$722$	−0.298929	−	4.17957i	−0.0111250	−	0.155547i
$723$	−4.69824	−	11.6819i	−0.174729	−	0.434455i
$724$	23.7496	−	3.41468i	0.882647	−	0.126905i
$725$	−16.0868	−	15.9425i	−0.597451	−	0.592089i
$726$	−15.9773	−	6.81191i	−0.592972	−	0.252814i
$727$	−39.3816	+	2.81662i	−1.46058	+	0.104463i	−0.778882	−	0.627170i	$-0.784213\pi$
$727$	−39.3816	+	2.81662i	−1.46058	+	0.104463i	−0.681699	+	0.731633i	$0.738759\pi$
$728$	−17.9344	+	6.68920i	−0.664695	+	0.247918i
$729$	3.58808	−	26.7605i	0.132892	−	0.991131i
$730$	−8.93790	−	12.8113i	−0.330807	−	0.474167i
$731$	−47.4839	+	41.1450i	−1.75625	+	1.52180i
$732$	−5.56354	−	2.85705i	−0.205634	−	0.105600i
$733$	−8.35365	−	3.11575i	−0.308549	−	0.115083i	0.190420	−	0.981703i	$-0.439015\pi$
$733$	−8.35365	−	3.11575i	−0.308549	−	0.115083i	−0.498969	+	0.866620i	$0.666288\pi$
$734$	−3.45310	+	24.0168i	−0.127456	+	0.886477i
$735$	−67.7197	+	9.18010i	−2.49788	+	0.338613i
$736$	−1.62558	−	4.51193i	−0.0599197	−	0.166312i
$737$	10.4013	−	10.4013i	0.383137	−	0.383137i
$738$	−13.0789	+	3.54897i	−0.481441	+	0.130640i
$739$	−41.9768	+	19.1702i	−1.54414	+	0.705185i	−0.991725	−	0.128383i	$-0.959021\pi$
$739$	−41.9768	+	19.1702i	−1.54414	+	0.705185i	−0.552416	+	0.833569i	$0.686294\pi$
$740$	6.16150	−	6.64790i	0.226501	−	0.244382i
$741$	−31.0776	−	8.27443i	−1.14166	−	0.303969i
$742$	42.4255	+	23.1661i	1.55749	+	0.850453i
$743$	−9.84350	−	45.2498i	−0.361123	−	1.66006i	−0.696188	−	0.717860i	$-0.745122\pi$
$743$	−9.84350	−	45.2498i	−0.361123	−	1.66006i	0.335065	−	0.942195i	$-0.391242\pi$
$744$	−0.737159	−	4.34162i	−0.0270256	−	0.159171i
$745$	−7.58249	+	18.4231i	−0.277801	+	0.674969i
$746$	15.4560	+	24.0500i	0.565885	+	0.880534i
$747$	−25.7823	+	15.8275i	−0.943326	+	0.579098i
$748$	4.72175	+	3.53466i	0.172644	+	0.129240i
$749$	29.0415	−	18.6638i	1.06115	−	0.681962i
$750$	−12.7333	+	14.5899i	−0.464953	+	0.532747i
$751$	−10.9310	+	23.9355i	−0.398877	+	0.873418i	0.598506	+	0.801118i	$0.295761\pi$
$751$	−10.9310	+	23.9355i	−0.398877	+	0.873418i	−0.997383	+	0.0722998i	$0.976966\pi$
$752$	4.62555	−	1.00623i	0.168676	−	0.0366933i
$753$	−15.1489	+	1.47079i	−0.552056	+	0.0535984i
$754$	13.1993	−	11.4373i	0.480691	−	0.416521i
$755$	−53.7372	+	2.04050i	−1.95570	+	0.0742613i
$756$	20.5767	−	15.5568i	0.748369	−	0.565796i
$757$	−20.9599	+	15.6904i	−0.761800	+	0.570276i	−0.907996	−	0.418979i	$-0.862388\pi$
$757$	−20.9599	+	15.6904i	−0.761800	+	0.570276i	0.146196	+	0.989256i	$0.453297\pi$
$758$	16.5488	+	16.5488i	0.601079	+	0.601079i
$759$	6.48609	−	5.00064i	0.235430	−	0.181512i
$760$	4.79826	−	9.63991i	0.174051	−	0.349676i
$761$	19.7506	+	2.83971i	0.715960	+	0.102940i	0.490662	−	0.871350i	$-0.336755\pi$
$761$	19.7506	+	2.83971i	0.715960	+	0.102940i	0.225299	+	0.974290i	$0.427664\pi$
$762$	2.63054	−	0.642581i	0.0952945	−	0.0232782i
$763$	56.2318	−	30.7049i	2.03573	−	1.11159i
$764$	8.41616	+	9.71276i	0.304486	+	0.351395i
$765$	21.1077	−	34.1302i	0.763152	−	1.23398i
$766$	13.5490	+	8.70740i	0.489544	+	0.314611i
$767$	8.55095	+	22.9260i	0.308757	+	0.827809i
$768$	1.07284	+	1.35978i	0.0387128	+	0.0490670i
$769$	−7.74992	−	12.0591i	−0.279469	−	0.434863i	0.672934	−	0.739702i	$-0.265034\pi$
$769$	−7.74992	−	12.0591i	−0.279469	−	0.434863i	−0.952404	+	0.304839i	$0.901397\pi$
$770$	9.77606	−	4.92113i	0.352305	−	0.177345i
$771$	0.944205	−	0.861078i	0.0340047	−	0.0310109i
$772$	−11.1591	−	2.42751i	−0.401624	−	0.0873679i
$773$	3.62871	−	0.259530i	0.130515	−	0.00933465i	−0.00592859	−	0.999982i	$-0.501887\pi$
$773$	3.62871	−	0.259530i	0.130515	−	0.00933465i	0.136444	+	0.990648i	$0.456433\pi$
$774$	−21.8156	−	22.7347i	−0.784145	−	0.817183i
$775$	−12.6759	+	0.964044i	−0.455333	+	0.0346295i
$776$	0.714062	+	2.43187i	0.0256333	+	0.0872991i
$777$	17.4754	+	30.1578i	0.626928	+	1.08191i
$778$	31.7804	−	17.3534i	1.13938	−	0.622149i
$779$	−9.03676	−	19.7877i	−0.323775	−	0.708969i
$780$	−10.4739	−	10.6441i	−0.375025	−	0.381121i
$781$	5.45729			0.195277
$782$	26.2288	−	11.6253i	0.937939	−	0.415720i
$783$	−12.6307	+	19.8608i	−0.451384	+	0.709767i
$784$	17.4655	+	2.51116i	0.623767	+	0.0896842i
$785$	0.603418	−	18.0346i	0.0215369	−	0.643684i
$786$	7.57484	−	2.43466i	0.270186	−	0.0868414i
$787$	−1.59011	+	22.2327i	−0.0566813	+	0.792509i	0.887024	+	0.461722i	$0.152768\pi$
$787$	−1.59011	+	22.2327i	−0.0566813	+	0.792509i	−0.943706	+	0.330786i	$0.892686\pi$
$788$	8.66389	+	4.73084i	0.308638	+	0.168529i
$789$	14.1281	−	0.358726i	0.502973	−	0.0127710i
$790$	8.47585	−	6.86183i	0.301557	−	0.244133i
$791$	−49.7037	−	43.0685i	−1.76726	−	1.53134i
$792$	−1.65013	+	2.45480i	−0.0586349	+	0.0872277i
$793$	−11.1456	−	8.34353i	−0.395793	−	0.296287i
$794$	5.29788	+	36.8475i	0.188015	+	1.30767i
$795$	−2.99341	+	37.5923i	−0.106165	+	1.33326i
$796$	−9.50129	+	10.9651i	−0.336764	+	0.388647i
$797$	−10.8367	−	29.0543i	−0.383856	−	1.02916i	−0.974925	−	0.222536i	$-0.928567\pi$
$797$	−10.8367	−	29.0543i	−0.383856	−	1.02916i	0.591069	−	0.806621i	$-0.298706\pi$
$798$	30.0132	+	28.5269i	1.06246	+	1.00984i
$799$	7.97814	+	27.1710i	0.282246	+	0.961242i
$800$	4.19404	−	2.72213i	0.148282	−	0.0962420i
$801$	−27.2490	−	21.2894i	−0.962797	−	0.752223i
$802$	7.41990	−	19.8935i	0.262006	−	0.702465i
$803$	−5.51398	+	4.12772i	−0.194584	+	0.145664i
$804$	14.5178	+	21.3770i	0.512005	+	0.753909i
$805$	2.37558	−	53.1840i	0.0837283	−	1.87449i
$806$		−	9.80322i		−	0.345304i
$807$	9.09140	+	3.13043i	0.320032	+	0.110196i
$808$	7.75705	+	2.89323i	0.272892	+	0.101783i
$809$	30.0537	+	8.82457i	1.05663	+	0.310255i	0.763494	−	0.645815i	$-0.223482\pi$
$809$	30.0537	+	8.82457i	1.05663	+	0.310255i	0.293138	+	0.956070i	$0.405300\pi$
$810$	17.6310	+	9.70301i	0.619490	+	0.340929i
$811$	−8.30711	+	2.43919i	−0.291702	+	0.0856515i	−0.424310	−	0.905517i	$-0.639483\pi$
$811$	−8.30711	+	2.43919i	−0.291702	+	0.0856515i	0.132608	+	0.991169i	$0.457665\pi$
$812$	−21.9731	+	4.77997i	−0.771106	+	0.167744i
$813$	−24.7833	−	17.5890i	−0.869188	−	0.616872i
$814$	−3.02049	−	2.61727i	−0.105868	−	0.0917353i
$815$	−3.50825	−	31.9538i	−0.122889	−	1.11929i
$816$	−7.65593	+	6.98191i	−0.268011	+	0.244416i
$817$	30.3101	−	40.4896i	1.06042	−	1.41655i
$818$	−22.3980	−	4.87239i	−0.783128	−	0.170359i
$819$	50.9567	−	26.4749i	1.78057	−	0.925107i
$820$	1.05711	−	10.0455i	0.0369158	−	0.350804i
$821$	0.279948	−	0.435607i	0.00977024	−	0.0152028i	−0.836334	−	0.548220i	$-0.815306\pi$
$821$	0.279948	−	0.435607i	0.00977024	−	0.0152028i	0.846104	+	0.533017i	$0.178942\pi$
$822$	−15.4779	+	1.50273i	−0.539854	+	0.0524137i
$823$	−21.3889	−	1.52976i	−0.745570	−	0.0533242i	−0.306615	−	0.951833i	$-0.599197\pi$
$823$	−21.3889	−	1.52976i	−0.745570	−	0.0533242i	−0.438955	+	0.898509i	$0.644651\pi$
$824$	−4.25650	−	1.24982i	−0.148282	−	0.0435396i
$825$	6.61731	+	5.39625i	0.230385	+	0.187873i
$826$	4.48353	−	31.1837i	0.156002	−	1.08502i
$827$	−21.0305	+	21.0305i	−0.731301	+	0.731301i	−0.970878	−	0.239576i	$-0.922991\pi$
$827$	−21.0305	+	21.0305i	−0.731301	+	0.731301i	0.239576	+	0.970878i	$0.422991\pi$
$828$	6.48996	+	12.8406i	0.225542	+	0.446241i
$829$		−	5.42934i		−	0.188569i	−0.995545	−	0.0942844i	$-0.969944\pi$
$829$		−	5.42934i		−	0.188569i	0.995545	−	0.0942844i	$-0.0300563\pi$
$830$	−4.05368	−	22.1818i	−0.140705	−	0.769942i
$831$	−8.89678	−	5.40354i	−0.308626	−	0.187447i
$832$	1.84785	+	3.38409i	0.0640628	+	0.117322i
$833$	−7.53032	+	105.288i	−0.260910	+	3.64800i
$834$	9.27952	−	11.2752i	0.321324	−	0.390427i
$835$	−1.53789	+	0.917165i	−0.0532209	+	0.0317398i
$836$	−4.31893	−	1.97239i	−0.149373	−	0.0682166i
$837$	3.78230	+	12.6583i	0.130735	+	0.437533i
$838$	−0.206961	+	0.951386i	−0.00714936	+	0.0328651i
$839$	−7.88283	−	54.8263i	−0.272146	−	1.89281i	−0.426005	−	0.904721i	$-0.640079\pi$
$839$	−7.88283	−	54.8263i	−0.272146	−	1.89281i	0.153859	−	0.988093i	$-0.450830\pi$
$840$	5.26798	+	18.4912i	0.181763	+	0.638007i
$841$	−7.13553	+	4.58573i	−0.246053	+	0.158128i
$842$	−1.47283	−	20.5929i	−0.0507571	−	0.709677i
$843$	8.75344	−	12.3338i	0.301485	−	0.424800i
$844$	−11.7853	+	18.3382i	−0.405665	+	0.631227i
$845$	−2.38821	−	3.42319i	−0.0821570	−	0.117761i
$846$	−13.4053	+	4.68728i	−0.460885	+	0.161152i
$847$	23.8581	+	43.6928i	0.819774	+	1.50130i
$848$	3.40274	−	9.12309i	0.116850	−	0.313288i
$849$	4.00739	−	1.95453i	0.137533	−	0.0670793i
$850$	18.0328	+	23.8640i	0.618518	+	0.818528i
$851$	−18.2896	+	6.58946i	−0.626959	+	0.225884i
$852$	−1.79941	+	9.41654i	−0.0616468	+	0.322605i
$853$	−19.9798	−	26.6899i	−0.684096	−	0.913846i	0.315286	−	0.948997i	$-0.397900\pi$
$853$	−19.9798	−	26.6899i	−0.684096	−	0.913846i	−0.999382	+	0.0351510i	$0.988809\pi$
$854$	7.44667	+	16.3059i	0.254820	+	0.557978i
$855$	−10.7631	+	30.4584i	−0.368091	+	1.04166i
$856$	−4.55382	−	5.25539i	−0.155646	−	0.179626i
$857$	26.1503	−	47.8908i	0.893279	−	1.63592i	0.128420	−	0.991720i	$-0.459010\pi$
$857$	26.1503	−	47.8908i	0.893279	−	1.63592i	0.764859	−	0.644198i	$-0.222809\pi$
$858$	−4.53629	+	4.77265i	−0.154866	+	0.162936i
$859$	−1.95134	−	0.891149i	−0.0665790	−	0.0304056i	0.381847	−	0.924225i	$-0.375288\pi$
$859$	−1.95134	−	0.891149i	−0.0665790	−	0.0304056i	−0.448426	+	0.893820i	$0.648015\pi$
$860$	21.6771	−	9.03622i	0.739182	−	0.308133i
$861$	35.7303	+	15.2336i	1.21768	+	0.519160i
$862$	3.79063	−	5.06369i	0.129109	−	0.172470i
$863$	5.07338	−	6.77724i	0.172700	−	0.230700i	−0.705837	−	0.708374i	$-0.749429\pi$
$863$	5.07338	−	6.77724i	0.172700	−	0.230700i	0.878537	+	0.477674i	$0.158520\pi$
$864$	−3.69167	−	3.65672i	−0.125593	−	0.124404i
$865$	1.96251	−	0.818087i	0.0667275	−	0.0278158i
$866$	−8.39453	−	3.83365i	−0.285258	−	0.130273i
$867$	−23.5856	−	22.4176i	−0.801010	−	0.761341i
$868$	−6.04907	+	11.0780i	−0.205319	+	0.376013i
$869$	−3.14890	−	3.63402i	−0.106819	−	0.123276i
$870$	−10.3998	−	14.1285i	−0.352586	−	0.479000i
$871$	23.8964	+	52.3259i	0.809700	+	1.77299i
$872$	−7.73409	−	10.3315i	−0.261909	−	0.349870i
$873$	−3.01532	−	6.98018i	−0.102053	−	0.236243i
$874$	−18.6422	+	13.6325i	−0.630581	+	0.461126i
$875$	54.5537	−	10.2239i	1.84425	−	0.345630i
$876$	−5.30427	−	10.8754i	−0.179215	−	0.367445i
$877$	8.41515	−	22.5619i	0.284160	−	0.761861i	−0.713938	−	0.700209i	$-0.753090\pi$
$877$	8.41515	−	22.5619i	0.284160	−	0.761861i	0.998098	−	0.0616524i	$-0.0196370\pi$
$878$	−1.97400	−	3.61510i	−0.0666191	−	0.122004i
$879$	45.5571	+	12.1296i	1.53660	+	0.409121i
$880$	−1.26145	−	1.80812i	−0.0425235	−	0.0609518i
$881$	12.6243	−	19.6438i	0.425323	−	0.661816i	−0.560777	−	0.827967i	$-0.689498\pi$
$881$	12.6243	−	19.6438i	0.425323	−	0.661816i	0.986100	+	0.166151i	$0.0531339\pi$
$882$	−52.9240	−	1.09191i	−1.78204	−	0.0367666i
$883$	−3.49487	−	48.8647i	−0.117612	−	1.64443i	−0.623496	−	0.781826i	$-0.714288\pi$
$883$	−3.49487	−	48.8647i	−0.117612	−	1.64443i	0.505885	−	0.862601i	$-0.331166\pi$
$884$	−19.4042	+	12.4703i	−0.652632	+	0.419421i
$885$	23.6377	−	6.73417i	0.794573	−	0.226367i
$886$	−0.922169	−	6.41383i	−0.0309809	−	0.215477i
$887$	−9.41902	+	43.2986i	−0.316260	+	1.45382i	0.494875	+	0.868964i	$0.335214\pi$
$887$	−9.41902	+	43.2986i	−0.316260	+	1.45382i	−0.811135	+	0.584859i	$0.801150\pi$
$888$	5.51203	−	4.34887i	0.184972	−	0.145939i
$889$	−7.05994	−	3.22417i	−0.236783	−	0.108135i
$890$	22.1364	−	13.2017i	0.742014	−	0.442521i
$891$	4.01602	−	7.91281i	0.134542	−	0.265089i
$892$	−0.242470	+	3.39017i	−0.00811849	+	0.113511i
$893$	−10.9249	−	20.0074i	−0.365587	−	0.669523i
$894$	−8.01089	+	13.1897i	−0.267924	+	0.441130i
$895$	−2.22190	−	12.1583i	−0.0742699	−	0.406407i
$896$		−	4.96438i		−	0.165848i
$897$	9.45863	+	30.5996i	0.315815	+	1.02169i
$898$	−8.08535	+	8.08535i	−0.269812	+	0.269812i
$899$	1.63900	−	11.3995i	0.0546638	−	0.380195i
$900$	−11.4931	+	9.63888i	−0.383104	+	0.321296i
$901$	55.8893	+	16.4106i	1.86194	+	0.546716i
$902$	−4.44251	−	0.317734i	−0.147919	−	0.0105794i
$903$	8.72698	+	89.8867i	0.290416	+	2.99124i
$904$	−7.16233	+	11.1448i	−0.238216	+	0.370671i
$905$	5.61489	−	53.3572i	0.186645	−	1.77365i
$906$	−41.3679	−	4.87962i	−1.37436	−	0.162115i
$907$	13.1827	+	2.86773i	0.437726	+	0.0952214i	0.426028	−	0.904710i	$-0.359913\pi$
$907$	13.1827	+	2.86773i	0.437726	+	0.0952214i	0.0116982	+	0.999932i	$0.496276\pi$
$908$	−10.9910	+	14.6823i	−0.364749	+	0.487248i
$909$	−24.1555	−	5.77900i	−0.801186	−	0.191677i
$910$	4.67114	+	42.5456i	0.154847	+	1.41037i
$911$	6.54909	+	5.67482i	0.216981	+	0.188015i	0.756569	−	0.653914i	$-0.226874\pi$
$911$	6.54909	+	5.67482i	0.216981	+	0.188015i	−0.539587	+	0.841930i	$0.681420\pi$
$912$	4.82742	−	6.80197i	0.159852	−	0.225236i
$913$	−9.71547	+	2.11347i	−0.321535	+	0.0699457i
$914$	16.1761	−	4.74973i	0.535058	−	0.157107i
$915$	−9.24309	+	10.4949i	−0.305567	+	0.346952i
$916$	−11.9396	−	3.50579i	−0.394497	−	0.115835i
$917$	−21.3670	−	7.96946i	−0.705599	−	0.263175i
$918$	20.2440	−	23.5886i	0.668152	−	0.778541i
$919$		−	33.5567i		−	1.10693i	−0.832871	−	0.553467i	$-0.813304\pi$
$919$		−	33.5567i		−	1.10693i	0.832871	−	0.553467i	$-0.186696\pi$
$920$	−10.6722	+	1.05098i	−0.351851	+	0.0346498i
$921$	30.7029	−	20.8514i	1.01169	−	0.687076i
$922$	−9.60301	+	7.18872i	−0.316258	+	0.236748i
$923$	−7.45809	+	19.9959i	−0.245486	+	0.658174i
$924$	8.07116	−	2.59418i	0.265522	−	0.0853423i
$925$	−11.0345	−	17.0010i	−0.362811	−	0.558989i
$926$	−0.460509	−	1.56835i	−0.0151333	−	0.0515391i
$927$	13.1313	+	2.16533i	0.431287	+	0.0711189i
$928$	1.58296	+	4.24408i	0.0519632	+	0.139319i
$929$	−20.5637	+	23.7318i	−0.674674	+	0.778616i	−0.985100	−	0.171982i	$-0.944983\pi$
$929$	−20.5637	+	23.7318i	−0.674674	+	0.778616i	0.310426	+	0.950598i	$0.399528\pi$
$930$	−9.81602	−	0.781633i	−0.321880	−	0.0256308i
$931$	−12.0928	−	84.1072i	−0.396325	−	2.75650i
$932$	3.10666	+	2.32562i	0.101762	+	0.0761781i
$933$	−52.3278	+	21.0452i	−1.71314	+	0.688990i
$934$	15.4620	+	13.3979i	0.505933	+	0.438393i
$935$	10.2507	−	8.29867i	0.335232	−	0.271395i
$936$	−6.73947	−	9.40103i	−0.220287	−	0.307282i
$937$	−28.1409	−	15.3661i	−0.919322	−	0.501988i	−0.0513942	−	0.998678i	$-0.516366\pi$
$937$	−28.1409	−	15.3661i	−0.919322	−	0.501988i	−0.867928	+	0.496691i	$0.834548\pi$
$938$	5.28369	−	73.8757i	0.172519	−	2.41213i
$939$	11.9668	+	37.2318i	0.390522	+	1.21501i
$940$	0.353961	−	10.5790i	0.0115449	−	0.345049i
$941$	54.2189	+	7.79550i	1.76748	+	0.254126i	0.947840	−	0.318746i	$-0.103262\pi$
$941$	54.2189	+	7.79550i	1.76748	+	0.254126i	0.819645	+	0.572872i	$0.194171\pi$
$942$	2.62347	−	13.7290i	0.0854774	−	0.447314i
$943$	−11.9157	+	18.0928i	−0.388030	+	0.589184i
$944$	−6.34607			−0.206547
$945$	−22.4466	−	53.1342i	−0.730187	−	1.72845i
$946$	−4.30177	−	9.41956i	−0.139863	−	0.306256i
$947$	12.2911	−	6.71144i	0.399407	−	0.218093i	−0.266975	−	0.963704i	$-0.586024\pi$
$947$	12.2911	−	6.71144i	0.399407	−	0.218093i	0.666381	+	0.745611i	$0.267842\pi$
$948$	7.30877	−	4.23519i	0.237378	−	0.137552i
$949$	−7.58870	−	25.8447i	−0.246339	−	0.838955i
$950$	−18.2679	−	15.6856i	−0.592689	−	0.508909i
$951$	−12.3096	+	2.09003i	−0.399165	+	0.0677739i
$952$	29.6223	−	2.11863i	0.960064	−	0.0686651i
$953$	4.08652	+	0.888969i	0.132375	+	0.0287965i	0.278265	−	0.960504i	$-0.410241\pi$
$953$	4.08652	+	0.888969i	0.132375	+	0.0287965i	−0.145889	+	0.989301i	$0.546604\pi$
$954$	−6.79671	+	28.4093i	−0.220052	+	0.919786i
$955$	25.6688	−	12.9213i	0.830623	−	0.418124i
$956$	1.99943	+	3.11118i	0.0646663	+	0.100623i
$957$	−6.07289	+	4.79138i	−0.196309	+	0.154883i
$958$	0.545397	+	1.46227i	0.0176210	+	0.0472437i
$959$	37.4956	+	24.0970i	1.21080	+	0.778132i
$960$	3.53584	−	1.58045i	0.114119	−	0.0510087i
$961$	16.0674	+	18.5428i	0.518304	+	0.598155i
$962$	13.7178	−	7.49047i	0.442279	−	0.241503i
$963$	15.4810	+	13.9838i	0.498869	+	0.450621i
$964$	7.19559	+	1.03457i	0.231754	+	0.0333213i
$965$	−11.3789	+	22.8606i	−0.366299	+	0.735910i
$966$	8.19279	−	40.4152i	0.263599	−	1.30034i
$967$	−11.0722	−	11.0722i	−0.356057	−	0.356057i	0.506300	−	0.862357i	$-0.331013\pi$
$967$	−11.0722	−	11.0722i	−0.356057	−	0.356057i	−0.862357	+	0.506300i	$0.831013\pi$
$968$	8.02774	−	6.00949i	0.258021	−	0.193152i
$969$	42.6473	+	25.9022i	1.37003	+	0.832099i
$970$	5.66332	−	0.215046i	0.181838	−	0.00690471i
$971$	−8.26099	+	7.15818i	−0.265108	+	0.229717i	−0.777263	−	0.629176i	$-0.783393\pi$
$971$	−8.26099	+	7.15818i	−0.265108	+	0.229717i	0.512155	+	0.858893i	$0.328847\pi$
$972$	12.3294	+	9.53870i	0.395465	+	0.305954i
$973$	−40.8975	+	8.89672i	−1.31112	+	0.285216i
$974$	−4.50374	+	9.86181i	−0.144309	+	0.315993i
$975$	−28.8157	+	16.8717i	−0.922841	+	0.540326i
$976$	3.03768	−	1.95220i	0.0972338	−	0.0624883i
$977$	0.456554	+	0.341772i	0.0146064	+	0.0109342i	0.606556	−	0.795041i	$-0.292551\pi$
$977$	0.456554	+	0.341772i	0.0146064	+	0.0109342i	−0.591950	+	0.805975i	$0.701642\pi$
$978$	1.14535	−	24.8737i	0.0366244	−	0.795373i
$979$	−6.14420	−	9.56056i	−0.196369	−	0.305557i
$980$	15.0168	−	36.4862i	0.479695	−	1.16551i
$981$	26.8066	+	27.9360i	0.855868	+	0.891928i
$982$	2.69015	+	12.3664i	0.0858462	+	0.394629i
$983$	−52.0815	−	28.4387i	−1.66114	−	0.907053i	−0.985470	−	0.169851i	$-0.945671\pi$
$983$	−52.0815	−	28.4387i	−1.66114	−	0.907053i	−0.675673	−	0.737201i	$-0.736147\pi$
$984$	2.01306	−	7.56077i	0.0641740	−	0.241029i
$985$	15.0045	−	16.1890i	0.478084	−	0.515824i
$986$	−24.6487	+	11.2567i	−0.784975	+	0.358486i
$987$	38.4856	+	13.2517i	1.22501	+	0.421807i
$988$	13.1294	−	13.1294i	0.417701	−	0.417701i
$989$	−50.1982	−	4.15537i	−1.59621	−	0.132133i
$990$	4.41719	+	4.92275i	0.140388	+	0.156455i
$991$	−2.44854	+	17.0300i	−0.0777805	+	0.540975i	0.913256	+	0.407386i	$0.133559\pi$
$991$	−2.44854	+	17.0300i	−0.0777805	+	0.540975i	−0.991037	+	0.133590i	$0.957350\pi$
$992$	2.38220	+	0.888515i	0.0756350	+	0.0282104i
$993$	2.85129	−	5.55233i	0.0904830	−	0.176198i
$994$	20.7664	−	17.9942i	0.658671	−	0.570742i
$995$	18.5629	+	26.6074i	0.588483	+	0.843513i
$996$	−0.443349	−	17.4609i	−0.0140481	−	0.553270i
$997$	3.07284	−	1.14611i	0.0973178	−	0.0362977i	−0.300334	−	0.953834i	$-0.597098\pi$
$997$	3.07284	−	1.14611i	0.0973178	−	0.0362977i	0.397652	+	0.917537i	$0.369825\pi$
$998$	13.9065	−	0.994612i	0.440202	−	0.0314839i
$999$	−14.8229	+	14.9646i	−0.468975	+	0.473458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.48	yes	960
3.2	odd	2	inner	690.2.x.a.77.18	✓	960
5.3	odd	4	inner	690.2.x.a.353.38	yes	960
15.8	even	4	inner	690.2.x.a.353.6	yes	960
23.3	even	11	inner	690.2.x.a.647.6	yes	960
69.26	odd	22	inner	690.2.x.a.647.38	yes	960
115.3	odd	44	inner	690.2.x.a.233.18	yes	960
345.233	even	44	inner	690.2.x.a.233.48	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.18	✓	960	3.2	odd	2	inner
690.2.x.a.77.48	yes	960	1.1	even	1	trivial
690.2.x.a.233.18	yes	960	115.3	odd	44	inner
690.2.x.a.233.48	yes	960	345.233	even	44	inner
690.2.x.a.353.6	yes	960	15.8	even	4	inner
690.2.x.a.353.38	yes	960	5.3	odd	4	inner
690.2.x.a.647.6	yes	960	23.3	even	11	inner
690.2.x.a.647.38	yes	960	69.26	odd	22	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599278 + 0.800541i) q^{2} +(1.68258 - 0.411015i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.92562 + 1.13666i) q^{5} +(1.33737 + 1.10066i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(-0.936950 + 0.349464i) q^{8} +(2.66213 - 1.38313i) q^{9} +O(q^{10})\)	\(q+(0.599278 + 0.800541i) q^{2} +(1.68258 - 0.411015i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(1.92562 + 1.13666i) q^{5} +(1.33737 + 1.10066i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(-0.936950 + 0.349464i) q^{8} +(2.66213 - 1.38313i) q^{9} +(0.244034 + 2.22271i) q^{10} +(0.975922 - 0.140316i) q^{11} +(-0.0796710 + 1.73022i) q^{12} +(-0.819594 + 3.76761i) q^{13} +(3.25098 - 3.75183i) q^{14} +(3.70718 + 1.12106i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(2.86697 - 5.25046i) q^{17} +(2.70261 + 1.30227i) q^{18} +(-1.35672 + 4.62056i) q^{19} +(-1.63313 + 1.52738i) q^{20} +(-3.76935 - 7.72834i) q^{21} +(0.697177 + 0.697177i) q^{22} +(4.61640 - 1.29956i) q^{23} +(-1.43286 + 0.973101i) q^{24} +(2.41600 + 4.37755i) q^{25} +(-3.50729 + 1.60173i) q^{26} +(3.91076 - 3.42140i) q^{27} +(4.95173 + 0.354155i) q^{28} +(-4.34619 + 1.27616i) q^{29} +(1.32417 + 3.63958i) q^{30} +(-1.05620 + 2.31275i) q^{31} +(-0.0713392 - 0.997452i) q^{32} +(1.58439 - 0.637211i) q^{33} +(5.92132 - 0.851357i) q^{34} +(3.48185 - 10.5405i) q^{35} +(0.577092 + 2.94397i) q^{36} +(-4.04328 + 0.289181i) q^{37} +(-4.51200 + 1.68289i) q^{38} +(0.169514 + 6.67617i) q^{39} +(-2.20143 - 0.392061i) q^{40} +(-3.41394 + 2.95819i) q^{41} +(3.92797 - 7.64894i) q^{42} +(-9.84064 - 3.67037i) q^{43} +(-0.140316 + 0.975922i) q^{44} +(6.69840 + 0.362570i) q^{45} +(3.80686 + 2.91682i) q^{46} +(-3.34725 + 3.34725i) q^{47} +(-1.63769 - 0.563902i) q^{48} +(-16.0505 + 7.33003i) q^{49} +(-2.05655 + 4.55748i) q^{50} +(2.66588 - 10.0127i) q^{51} +(-3.38409 - 1.84785i) q^{52} +(2.06975 + 9.51449i) q^{53} +(5.08260 + 1.08036i) q^{54} +(2.03874 + 0.839097i) q^{55} +(2.68395 + 4.17630i) q^{56} +(-0.383666 + 8.33208i) q^{57} +(-3.62619 - 2.71453i) q^{58} +(5.33866 - 3.43095i) q^{59} +(-2.12009 + 3.24118i) q^{60} +(-1.50002 + 3.28459i) q^{61} +(-2.48440 + 0.540449i) q^{62} +(-9.51869 - 11.4543i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-5.86073 + 6.32338i) q^{65} +(1.45960 + 0.886504i) q^{66} +(11.9434 - 8.94072i) q^{67} +(4.23006 + 4.23006i) q^{68} +(7.23331 - 4.08402i) q^{69} +(10.5247 - 3.52932i) q^{70} +(5.47868 + 0.787715i) q^{71} +(-2.01093 + 2.22624i) q^{72} +(-6.13140 + 3.34800i) q^{73} +(-2.65455 - 3.06351i) q^{74} +(5.86434 + 6.37256i) q^{75} +(-4.05116 - 2.60352i) q^{76} +(-1.71051 - 4.58606i) q^{77} +(-5.24296 + 4.13658i) q^{78} +(-2.63670 - 4.10278i) q^{79} +(-1.00541 - 1.99729i) q^{80} +(5.17391 - 7.36415i) q^{81} +(-4.41405 - 0.960219i) q^{82} +(-10.0586 + 0.719406i) q^{83} +(8.47724 - 1.43934i) q^{84} +(11.4887 - 6.85160i) q^{85} +(-2.95899 - 10.0774i) q^{86} +(-6.78829 + 3.93358i) q^{87} +(-0.865354 + 0.472519i) q^{88} +(-4.78829 - 10.4849i) q^{89} +(3.72395 + 5.57962i) q^{90} +19.1413 q^{91} +(-0.0536700 + 4.79553i) q^{92} +(-0.826558 + 4.32549i) q^{93} +(-4.68554 - 0.673679i) q^{94} +(-7.86453 + 7.35529i) q^{95} +(-0.530001 - 1.64897i) q^{96} +(0.180812 - 2.52808i) q^{97} +(-15.4867 - 8.45639i) q^{98} +(2.40396 - 1.72337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

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