LMFDB - Embedded newform 690.2.x.a.77.18

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			77.18
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(1.00245 + 1.41248i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.92562 - 1.13666i) q^{5} +(0.530001 - 1.64897i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.990189 + 2.83188i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(1.00245 + 1.41248i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.92562 - 1.13666i) q^{5} +(0.530001 - 1.64897i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.990189 + 2.83188i) q^{9} +(0.244034 + 2.22271i) q^{10} +(-0.975922 + 0.140316i) q^{11} +(-1.63769 + 0.563902i) q^{12} +(-0.819594 + 3.76761i) q^{13} +(-3.25098 + 3.75183i) q^{14} +(-0.324824 - 3.85934i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-2.86697 + 5.25046i) q^{17} +(2.86043 - 0.904393i) q^{18} +(-1.35672 + 4.62056i) q^{19} +(1.63313 - 1.52738i) q^{20} +(5.79399 - 6.35334i) 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} +(-4.99258 + 1.44019i) q^{27} +(4.95173 + 0.354155i) q^{28} +(4.34619 - 1.27616i) q^{29} +(-2.89490 + 2.57285i) q^{30} +(-1.05620 + 2.31275i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-1.17651 - 1.23781i) q^{33} +(5.92132 - 0.851357i) q^{34} +(-3.48185 + 10.5405i) q^{35} +(-2.43820 - 1.74791i) q^{36} +(-4.04328 + 0.289181i) q^{37} +(4.51200 - 1.68289i) q^{38} +(-6.14327 + 2.61918i) q^{39} +(-2.20143 - 0.392061i) q^{40} +(3.41394 - 2.95819i) q^{41} +(-8.55832 - 0.830916i) q^{42} +(-9.84064 - 3.67037i) q^{43} +(0.140316 - 0.975922i) q^{44} +(5.12561 - 4.32760i) q^{45} +(3.80686 + 2.91682i) q^{46} +(3.34725 - 3.34725i) q^{47} +(-0.0796710 - 1.73022i) q^{48} +(-16.0505 + 7.33003i) q^{49} +(2.05655 - 4.55748i) q^{50} +(-10.2901 + 1.21379i) q^{51} +(-3.38409 - 1.84785i) q^{52} +(-2.06975 - 9.51449i) q^{53} +(4.14488 + 3.13369i) q^{54} +(2.03874 + 0.839097i) q^{55} +(-2.68395 - 4.17630i) q^{56} +(-7.88648 + 2.71554i) q^{57} +(-3.62619 - 2.71453i) q^{58} +(-5.33866 + 3.43095i) q^{59} +(3.79452 + 0.775635i) q^{60} +(-1.50002 + 3.28459i) q^{61} +(2.48440 - 0.540449i) q^{62} +(14.7821 + 1.81499i) q^{63} +(0.755750 - 0.654861i) q^{64} +(5.86073 - 6.32338i) q^{65} +(-0.285862 + 1.68363i) q^{66} +(11.9434 - 8.94072i) q^{67} +(-4.23006 - 4.23006i) q^{68} +(-6.46331 - 5.21782i) q^{69} +(10.5247 - 3.52932i) q^{70} +(-5.47868 - 0.787715i) q^{71} +(0.0618820 + 2.99936i) q^{72} +(-6.13140 + 3.34800i) q^{73} +(2.65455 + 3.06351i) q^{74} +(-3.76128 + 7.80082i) q^{75} +(-4.05116 - 2.60352i) q^{76} +(1.71051 + 4.58606i) q^{77} +(5.77829 + 3.34832i) q^{78} +(-2.63670 - 4.10278i) q^{79} +(1.00541 + 1.99729i) q^{80} +(-7.03905 - 5.60819i) q^{81} +(-4.41405 - 0.960219i) q^{82} +(10.0586 - 0.719406i) q^{83} +(4.46363 + 7.34924i) q^{84} +(11.4887 - 6.85160i) q^{85} +(2.95899 + 10.0774i) q^{86} +(6.15939 + 4.85962i) q^{87} +(-0.865354 + 0.472519i) q^{88} +(4.78829 + 10.4849i) q^{89} +(-6.53609 - 1.50983i) q^{90} +19.1413 q^{91} +(0.0536700 - 4.79553i) q^{92} +(-4.32549 + 0.826558i) q^{93} +(-4.68554 - 0.673679i) q^{94} +(7.86453 - 7.35529i) q^{95} +(-1.33737 + 1.10066i) q^{96} +(0.180812 - 2.52808i) q^{97} +(15.4867 + 8.45639i) q^{98} +(0.568988 - 2.90263i) 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
$3$	1.00245	+	1.41248i	0.578765	+	0.815495i
$3$	1.00245	+	1.41248i	0.578765	+	0.815495i
$4$	−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
$6$	0.530001	−	1.64897i	0.216372	−	0.673189i
$7$	−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
$9$	−0.990189	+	2.83188i	−0.330063	+	0.943959i
$10$	0.244034	+	2.22271i	0.0771705	+	0.702883i
$11$	−0.975922	+	0.140316i	−0.294251	+	0.0423070i	−0.287860	−	0.957673i	$-0.592944\pi$
$11$	−0.975922	+	0.140316i	−0.294251	+	0.0423070i	−0.00639178	+	0.999980i	$0.502035\pi$
$12$	−1.63769	+	0.563902i	−0.472759	+	0.162785i
$13$	−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
$15$	−0.324824	−	3.85934i	−0.0838692	−	0.996477i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	−2.86697	+	5.25046i	−0.695341	+	1.27342i	0.256415	+	0.966567i	$0.417459\pi$
$17$	−2.86697	+	5.25046i	−0.695341	+	1.27342i	−0.951756	+	0.306856i	$0.900723\pi$
$18$	2.86043	−	0.904393i	0.674210	−	0.213168i
$19$	−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
$21$	5.79399	−	6.35334i	1.26435	−	1.38641i
$22$	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
$27$	−4.99258	+	1.44019i	−0.960822	+	0.277165i
$28$	4.95173	+	0.354155i	0.935790	+	0.0669290i
$29$	4.34619	−	1.27616i	0.807068	−	0.236977i	0.147929	−	0.988998i	$-0.452739\pi$
$29$	4.34619	−	1.27616i	0.807068	−	0.236977i	0.659139	+	0.752021i	$0.270921\pi$
$30$	−2.89490	+	2.57285i	−0.528534	+	0.469736i
$31$	−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
$33$	−1.17651	−	1.23781i	−0.204803	−	0.215475i
$34$	5.92132	−	0.851357i	1.01550	−	0.146006i
$35$	−3.48185	+	10.5405i	−0.588540	+	1.78167i
$36$	−2.43820	−	1.74791i	−0.406366	−	0.291319i
$37$	−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
$39$	−6.14327	+	2.61918i	−0.983711	+	0.419405i
$40$	−2.20143	−	0.392061i	−0.348076	−	0.0619903i
$41$	3.41394	−	2.95819i	0.533168	−	0.461992i	−0.346183	−	0.938167i	$-0.612522\pi$
$41$	3.41394	−	2.95819i	0.533168	−	0.461992i	0.879351	+	0.476175i	$0.157977\pi$
$42$	−8.55832	−	0.830916i	−1.32058	−	0.128213i
$43$	−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
$45$	5.12561	−	4.32760i	0.764081	−	0.645120i
$46$	3.80686	+	2.91682i	0.561290	+	0.430062i
$47$	3.34725	−	3.34725i	0.488247	−	0.488247i	−0.419506	−	0.907753i	$-0.637797\pi$
$47$	3.34725	−	3.34725i	0.488247	−	0.488247i	0.907753	+	0.419506i	$0.137797\pi$
$48$	−0.0796710	−	1.73022i	−0.0114995	−	0.249735i
$49$	−16.0505	+	7.33003i	−2.29293	+	1.04715i
$50$	2.05655	−	4.55748i	0.290841	−	0.644524i
$51$	−10.2901	+	1.21379i	−1.44091	+	0.169965i
$52$	−3.38409	−	1.84785i	−0.469289	−	0.256251i
$53$	−2.06975	−	9.51449i	−0.284302	−	1.30692i	−0.868655	−	0.495417i	$-0.835015\pi$
$53$	−2.06975	−	9.51449i	−0.284302	−	1.30692i	0.584353	−	0.811499i	$-0.301348\pi$
$54$	4.14488	+	3.13369i	0.564046	+	0.426441i
$55$	2.03874	+	0.839097i	0.274904	+	0.113144i
$56$	−2.68395	−	4.17630i	−0.358658	−	0.558082i
$57$	−7.88648	+	2.71554i	−1.04459	+	0.359682i
$58$	−3.62619	−	2.71453i	−0.476143	−	0.356436i
$59$	−5.33866	+	3.43095i	−0.695034	+	0.446671i	−0.839872	−	0.542784i	$-0.817370\pi$
$59$	−5.33866	+	3.43095i	−0.695034	+	0.446671i	0.144838	+	0.989455i	$0.453734\pi$
$60$	3.79452	+	0.775635i	0.489871	+	0.100134i
$61$	−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
$63$	14.7821	+	1.81499i	1.86237	+	0.228667i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	5.86073	−	6.32338i	0.726934	−	0.784318i
$66$	−0.285862	+	1.68363i	−0.0351872	+	0.207241i
$67$	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
$69$	−6.46331	−	5.21782i	−0.778091	−	0.628151i
$70$	10.5247	−	3.52932i	1.25794	−	0.421835i
$71$	−5.47868	−	0.787715i	−0.650199	−	0.0934845i	−0.190680	−	0.981652i	$-0.561069\pi$
$71$	−5.47868	−	0.787715i	−0.650199	−	0.0934845i	−0.459519	+	0.888168i	$0.651978\pi$
$72$	0.0618820	+	2.99936i	0.00729287	+	0.353478i
$73$	−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
$75$	−3.76128	+	7.80082i	−0.434315	+	0.900761i
$76$	−4.05116	−	2.60352i	−0.464700	−	0.298645i
$77$	1.71051	+	4.58606i	0.194931	+	0.522630i
$78$	5.77829	+	3.34832i	0.654263	+	0.379123i
$79$	−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
$81$	−7.03905	−	5.60819i	−0.782117	−	0.623132i
$82$	−4.41405	−	0.960219i	−0.487451	−	0.106038i
$83$	10.0586	−	0.719406i	1.10408	−	0.0789650i	0.492620	−	0.870244i	$-0.336039\pi$
$83$	10.0586	−	0.719406i	1.10408	−	0.0789650i	0.611455	+	0.791279i	$0.290585\pi$
$84$	4.46363	+	7.34924i	0.487022	+	0.801867i
$85$	11.4887	−	6.85160i	1.24612	−	0.743160i
$86$	2.95899	+	10.0774i	0.319076	+	1.08667i
$87$	6.15939	+	4.85962i	0.660355	+	0.521006i
$88$	−0.865354	+	0.472519i	−0.0922470	+	0.0503707i
$89$	4.78829	+	10.4849i	0.507558	+	1.11140i	0.973938	+	0.226813i	$0.0728305\pi$
$89$	4.78829	+	10.4849i	0.507558	+	1.11140i	−0.466381	+	0.884584i	$0.654442\pi$
$90$	−6.53609	−	1.50983i	−0.688964	−	0.159150i
$91$	19.1413			2.00655
$92$	0.0536700	−	4.79553i	0.00559549	−	0.499969i
$93$	−4.32549	+	0.826558i	−0.448532	+	0.0857101i
$94$	−4.68554	−	0.673679i	−0.483277	−	0.0694847i
$95$	7.86453	−	7.35529i	0.806884	−	0.754637i
$96$	−1.33737	+	1.10066i	−0.136494	+	0.112336i
$97$	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
$99$	0.568988	−	2.90263i	0.0571855	−	0.291725i
$100$	−4.88089	+	1.08484i	−0.488089	+	0.108484i
$101$	6.25688	+	5.42162i	0.622583	+	0.539471i	0.908020	−	0.418926i	$-0.137593\pi$
$101$	6.25688	+	5.42162i	0.622583	+	0.539471i	−0.285437	+	0.958397i	$0.592139\pi$
$102$	7.13834	+	7.51029i	0.706801	+	0.743629i
$103$	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
$105$	−18.3786	+	5.64828i	−1.79357	+	0.551216i
$106$	−6.37639	+	7.35874i	−0.619330	+	0.714744i
$107$	−2.43013	−	6.51543i	−0.234930	−	0.629871i	0.764970	−	0.644066i	$-0.222754\pi$
$107$	−2.43013	−	6.51543i	−0.234930	−	0.629871i	−0.999899	+	0.0141957i	$0.995481\pi$
$108$	0.0247165	−	5.19609i	0.00237835	−	0.499994i
$109$	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
$111$	−4.46165	−	5.42115i	−0.423481	−	0.514553i
$112$	−1.73487	+	4.65138i	−0.163930	+	0.439514i
$113$	−10.6055	+	7.93914i	−0.997677	+	0.746852i	−0.967546	−	0.252694i	$-0.918683\pi$
$113$	−10.6055	+	7.93914i	−0.997677	+	0.746852i	−0.0301310	+	0.999546i	$0.509592\pi$
$114$	6.90009	+	4.68609i	0.646253	+	0.438892i
$115$	10.3666	+	2.74483i	0.966688	+	0.255957i
$116$			4.52968i			0.420570i
$117$	−9.85786	−	6.05164i	−0.911360	−	0.559474i
$118$	5.94595	+	2.21773i	0.547369	+	0.204158i
$119$	28.4950	+	8.36688i	2.61213	+	0.766991i
$120$	−1.65304	−	3.50249i	−0.150902	−	0.319732i
$121$	−9.62169	+	2.82518i	−0.874699	+	0.256835i
$122$	3.52838	−	0.767551i	0.319444	−	0.0694908i
$123$	7.60069	+	1.85667i	0.685331	+	0.167411i
$124$	−1.92150	−	1.66499i	−0.172556	−	0.149520i
$125$	0.323505	−	11.1757i	0.0289351	−	0.999581i
$126$	−7.40563	−	12.9214i	−0.659746	−	1.15113i
$127$	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
$129$	−4.68043	−	17.5790i	−0.412089	−	1.54775i
$130$	−8.57433	−	0.902294i	−0.752018	−	0.0791364i
$131$	−2.48353	+	3.86445i	−0.216987	+	0.337639i	−0.932634	−	0.360823i	$-0.882496\pi$
$131$	−2.48353	+	3.86445i	−0.216987	+	0.337639i	0.715647	+	0.698462i	$0.246132\pi$
$132$	1.51913	−	0.780119i	0.132223	−	0.0679006i
$133$	23.8457	+	1.70548i	2.06768	+	0.147884i
$134$	−14.3148	−	4.20321i	−1.23661	−	0.363102i
$135$	11.2508	+	2.90161i	0.968315	+	0.249731i
$136$	−0.851357	+	5.92132i	−0.0730032	+	0.507749i
$137$	6.34854	−	6.34854i	0.542392	−	0.542392i	−0.381837	−	0.924230i	$-0.624709\pi$
$137$	6.34854	−	6.34854i	0.542392	−	0.542392i	0.924230	+	0.381837i	$0.124709\pi$
$138$	−0.303761	+	8.30107i	−0.0258579	+	0.706634i
$139$		−	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
$141$	8.08337	+	1.37247i	0.680742	+	0.115583i
$142$	2.65265	+	4.85797i	0.222605	+	0.407671i
$143$	0.271202	−	3.79190i	0.0226790	−	0.317094i
$144$	2.36403	−	1.84699i	0.197002	−	0.153916i
$145$	−9.81966	−	2.48276i	−0.815479	−	0.206182i
$146$	6.35462	+	2.90206i	0.525912	+	0.240176i
$147$	−26.4434	−	15.3230i	−2.18101	−	1.26382i
$148$	0.861656	−	3.96097i	0.0708277	−	0.325590i
$149$	−1.26797	−	8.81890i	−0.103876	−	0.722473i	−0.973488	−	0.228738i	$-0.926540\pi$
$149$	−1.26797	−	8.81890i	−0.103876	−	0.722473i	0.869612	−	0.493735i	$-0.164369\pi$
$150$	8.49893	−	1.66380i	0.693935	−	0.135849i
$151$	−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
$153$	−12.0298	−	13.3178i	−0.972552	−	1.07668i
$154$	2.64626	−	4.11766i	0.213241	−	0.331810i
$155$	4.66264	−	3.25293i	0.374512	−	0.261281i
$156$	−0.782329	−	6.63234i	−0.0626364	−	0.531012i
$157$	−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
$159$	11.3642	−	12.4613i	0.901239	−	0.988244i
$160$	0.996394	−	2.00180i	0.0787718	−	0.158256i
$161$	11.1756	+	21.0225i	0.880757	+	1.65680i
$162$	−0.271239	+	8.99591i	−0.0213105	+	0.706786i
$163$	−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
$165$	0.858531	+	3.72083i	0.0668365	+	0.289666i
$166$	−6.60381	−	7.62121i	−0.512555	−	0.591520i
$167$	0.383777	−	0.702834i	0.0296975	−	0.0543870i	−0.862409	−	0.506212i	$-0.831045\pi$
$167$	0.383777	−	0.702834i	0.0296975	−	0.0543870i	0.892106	+	0.451825i	$0.149227\pi$
$168$	3.20842	−	7.97755i	0.247535	−	0.615481i
$169$	−1.69796	−	0.775431i	−0.130612	−	0.0596486i
$170$	−12.3699	−	5.09115i	−0.948727	−	0.390473i
$171$	−11.7414	−	8.41729i	−0.897891	−	0.643686i
$172$	6.29412	−	8.40796i	0.479922	−	0.641101i
$173$	−0.569833	+	0.761207i	−0.0433236	+	0.0578735i	−0.821680	−	0.569949i	$-0.806963\pi$
$173$	−0.569833	+	0.761207i	−0.0433236	+	0.0578735i	0.778356	+	0.627823i	$0.216054\pi$
$174$	0.199144	−	7.84310i	0.0150971	−	0.594584i
$175$	18.6857	−	16.3393i	1.41251	−	1.23513i
$176$	0.896858	+	0.409581i	0.0676032	+	0.0308734i
$177$	−10.1979	−	4.10139i	−0.766519	−	0.308279i
$178$	5.52408	−	10.1166i	0.414047	−	0.758270i
$179$	3.61968	+	4.17733i	0.270547	+	0.312228i	0.874723	−	0.484623i	$-0.161043\pi$
$179$	3.61968	+	4.17733i	0.270547	+	0.312228i	−0.604176	+	0.796851i	$0.706498\pi$
$180$	2.70825	+	6.13721i	0.201861	+	0.457441i
$181$	−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
$183$	−6.14310	+	1.17389i	−0.454111	+	0.0867762i
$184$	−3.87118	+	2.83089i	−0.285387	+	0.208696i
$185$	8.11451	+	4.03899i	0.596590	+	0.296952i
$186$	3.25386	+	2.96739i	0.238585	+	0.217580i
$187$	2.06121	−	5.52632i	0.150731	−	0.404124i
$188$	2.26863	+	4.15469i	0.165457	+	0.303012i
$189$	12.2547	+	22.6989i	0.891400	+	1.65110i
$190$	−10.6013	−	1.88802i	−0.769096	−	0.136971i
$191$	−6.94822	+	10.8116i	−0.502756	+	0.782303i	−0.996165	−	0.0874941i	$-0.972114\pi$
$191$	−6.94822	+	10.8116i	−0.502756	+	0.782303i	0.493409	+	0.869797i	$0.335750\pi$
$192$	1.68258	+	0.411015i	0.121430	+	0.0296624i
$193$	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
$195$	14.8067	+	1.93928i	1.06033	+	0.138875i
$196$	−2.51116	−	17.4655i	−0.179368	−	1.24753i
$197$	−2.09831	+	9.64578i	−0.149498	+	0.687233i	0.839988	+	0.542605i	$0.182562\pi$
$197$	−2.09831	+	9.64578i	−0.149498	+	0.687233i	−0.989486	+	0.144628i	$0.953802\pi$
$198$	−2.66466	+	1.28398i	−0.189369	+	0.0912487i
$199$	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
$201$	24.6012	+	7.90717i	1.73524	+	0.557729i
$202$	0.590620	−	8.25795i	0.0415559	−	0.581027i
$203$	−10.7769	−	19.7364i	−0.756390	−	1.38522i
$204$	1.73444	−	10.2153i	0.121435	−	0.715213i
$205$	−9.93640	+	1.81586i	−0.693989	+	0.126825i
$206$		−	4.43620i		−	0.309085i
$207$	0.890911	−	14.3599i	0.0619226	−	0.998081i
$208$	2.72641	−	2.72641i	0.189043	−	0.189043i
$209$	0.675711	−	4.69967i	0.0467399	−	0.325083i
$210$	15.5356	+	11.3279i	1.07206	+	0.781702i
$211$	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
$213$	−4.37947	−	8.52816i	−0.300076	−	0.584340i
$214$	−3.75955	+	5.84997i	−0.256998	+	0.399896i
$215$	14.7773	+	18.2532i	1.00781	+	1.24486i
$216$	−4.17450	+	3.09412i	−0.284039	+	0.210528i
$217$	12.3335	+	2.68299i	0.837254	+	0.182134i
$218$	7.73409	−	10.3315i	0.523819	−	0.699740i
$219$	−10.8754	−	5.30427i	−0.734891	−	0.358429i
$220$	−1.37949	+	1.71976i	−0.0930051	+	0.115946i
$221$	−17.4319	−	15.1049i	−1.17260	−	1.01606i
$222$	−1.66609	+	6.82051i	−0.111821	+	0.457763i
$223$	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
$225$	−14.7890	+	2.50721i	−0.985932	+	0.167147i
$226$	12.7112	+	3.73235i	0.845538	+	0.248272i
$227$	−17.1840	−	6.40932i	−1.14055	−	0.425401i	−0.292994	−	0.956114i	$-0.594651\pi$
$227$	−17.1840	−	6.40932i	−1.14055	−	0.425401i	−0.847552	+	0.530713i	$0.821924\pi$
$228$	−0.383666	−	8.33208i	−0.0254089	−	0.551805i
$229$			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	−0.973772	−	0.227528i	$-0.926936\pi$
$233$	−1.35616	+	3.63602i	−0.0888453	+	0.238203i	0.884926	+	0.465731i	$0.154209\pi$
$234$	1.06301	+	11.5182i	0.0694912	+	0.752971i
$235$	−10.2502	+	2.64083i	−0.668650	+	0.172269i
$236$	−1.78790	−	6.08901i	−0.116382	−	0.396361i
$237$	3.15193	−	7.83711i	0.204740	−	0.509075i
$238$	−10.3784	−	27.8255i	−0.672730	−	1.80366i
$239$	−2.42185	+	2.79496i	−0.156656	+	0.180791i	−0.828652	−	0.559764i	$-0.810892\pi$
$239$	−2.42185	+	2.79496i	−0.156656	+	0.180791i	0.671996	+	0.740555i	$0.265437\pi$
$240$	−1.81326	+	3.42229i	−0.117045	+	0.220908i
$241$	−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
$243$	0.865147	−	15.5644i	0.0554992	−	0.998459i
$244$	−2.72893	−	2.36463i	−0.174702	−	0.151380i
$245$	39.2389	+	4.12919i	2.50688	+	0.263805i
$246$	−3.06858	−	7.19733i	−0.195645	−	0.458885i
$247$	−16.2965	−	8.89857i	−1.03692	−	0.566203i
$248$	−0.181380	+	2.53603i	−0.0115177	+	0.161038i
$249$	11.0994	+	13.4864i	0.703395	+	0.854665i
$250$	−9.14044	+	6.43834i	−0.578092	+	0.407197i
$251$	8.69789	+	1.25057i	0.549006	+	0.0789352i	0.411236	−	0.911529i	$-0.365097\pi$
$251$	8.69789	+	1.25057i	0.549006	+	0.0789352i	0.137770	+	0.990464i	$0.456006\pi$
$252$	−5.90608	+	13.6720i	−0.372048	+	0.861256i
$253$	4.32289	−	1.91603i	0.271778	−	0.120460i
$254$	−1.56340			−0.0980964
$255$	21.1945	+	9.35912i	1.32725	+	0.586091i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−0.647538	+	0.353582i	−0.0403923	+	0.0220559i	−0.499318	−	0.866419i	$-0.666416\pi$
$257$	−0.647538	+	0.353582i	−0.0403923	+	0.0220559i	0.458926	+	0.888475i	$0.348234\pi$
$258$	−11.2679	+	14.2816i	−0.701507	+	0.889134i
$259$	5.66949	+	19.3085i	0.352285	+	1.19977i
$260$	4.41608	+	7.40483i	0.273874	+	0.459228i
$261$	−0.689633	+	13.5715i	−0.0426872	+	0.840056i
$262$	4.58198	−	0.327710i	0.283076	−	0.0202460i
$263$	−7.97301	−	1.73442i	−0.491637	−	0.106949i	−0.0400893	−	0.999196i	$-0.512764\pi$
$263$	−7.97301	−	1.73442i	−0.491637	−	0.106949i	−0.451548	+	0.892247i	$0.649128\pi$
$264$	−1.53490	−	0.748617i	−0.0944664	−	0.0460742i
$265$	−6.82921	+	20.6739i	−0.419515	+	1.26999i
$266$	−12.9249	−	20.1115i	−0.792475	−	1.23312i
$267$	−10.0097	+	17.2739i	−0.612582	+	1.05715i
$268$	5.21371	+	13.9785i	0.318478	+	0.853873i
$269$	−4.67011	−	3.00130i	−0.284742	−	0.182992i	0.390471	−	0.920615i	$-0.372312\pi$
$269$	−4.67011	−	3.00130i	−0.284742	−	0.182992i	−0.675213	+	0.737623i	$0.735948\pi$
$270$	−4.41950	−	10.7456i	−0.268962	−	0.653957i
$271$	−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
$273$	19.1882	+	27.0367i	1.16132	+	1.63633i
$274$	−8.88681	−	1.27773i	−0.536872	−	0.0771905i
$275$	−2.97207	−	3.93314i	−0.179222	−	0.237177i
$276$	6.82738	−	4.73147i	0.410960	−	0.284801i
$277$	−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
$279$	−5.50358	−	5.28107i	−0.329491	−	0.316170i
$280$	0.421209	+	11.0927i	0.0251721	+	0.662916i
$281$	−6.59924	+	5.71828i	−0.393678	+	0.341124i	−0.829098	−	0.559104i	$-0.811145\pi$
$281$	−6.59924	+	5.71828i	−0.393678	+	0.341124i	0.435420	+	0.900227i	$0.356600\pi$
$282$	−3.74546	−	7.29356i	−0.223039	−	0.434325i
$283$	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
$285$	18.2730	+	3.73517i	1.08240	+	0.221252i
$286$	−3.19810	+	2.05529i	−0.189107	+	0.121532i
$287$	−17.9526	−	13.4391i	−1.05971	−	0.793287i
$288$	−2.89530	−	0.785642i	−0.170607	−	0.0462944i
$289$	−10.1569	−	15.8044i	−0.597465	−	0.929673i
$290$	3.89715	+	9.34891i	0.228849	+	0.548987i
$291$	3.75211	−	2.27888i	0.219953	−	0.133590i
$292$	−1.48496	−	6.82627i	−0.0869010	−	0.399477i
$293$	−23.8893	−	13.0445i	−1.39563	−	0.762070i	−0.407139	−	0.913366i	$-0.633474\pi$
$293$	−23.8893	−	13.0445i	−1.39563	−	0.762070i	−0.988489	+	0.151296i	$0.951655\pi$
$294$	3.58019	+	30.3518i	0.208801	+	1.77015i
$295$	14.1800	−	0.538441i	0.825594	−	0.0313492i
$296$	−3.68729	+	1.68393i	−0.214319	+	0.0978764i
$297$	4.67028	−	2.10606i	0.270997	−	0.122206i
$298$	−6.30003	+	6.30003i	−0.364951	+	0.364951i
$299$	−1.11267	−	18.4579i	−0.0643474	−	1.06745i
$300$	−6.42516	−	5.80666i	−0.370957	−	0.335248i
$301$	−7.42031	+	51.6094i	−0.427700	+	2.97472i
$302$	22.5330	+	8.40439i	1.29663	+	0.483618i
$303$	−1.38571	+	14.2726i	−0.0796069	+	0.819940i
$304$	3.63941	−	3.15356i	0.208734	−	0.180869i
$305$	6.62193	−	4.61984i	0.379171	−	0.264531i
$306$	−3.45229	+	17.6114i	−0.197354	+	1.00678i
$307$	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
$309$	−0.195034	+	7.68124i	−0.0110951	+	0.436971i
$310$	−5.39832	−	1.78323i	−0.306604	−	0.101281i
$311$	32.2318	−	4.63424i	1.82770	−	0.262783i	0.859171	−	0.511688i	$-0.170980\pi$
$311$	32.2318	−	4.63424i	1.82770	−	0.262783i	0.968528	+	0.248905i	$0.0800706\pi$
$312$	−4.84063	+	4.60090i	−0.274047	+	0.260475i
$313$	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
$315$	−26.4017	−	20.2973i	−1.48757	−	1.14362i
$316$	4.67943	−	1.37400i	0.263239	−	0.0772938i
$317$	7.19028	+	0.514259i	0.403847	+	0.0288837i	0.271785	−	0.962358i	$-0.412386\pi$
$317$	7.19028	+	0.514259i	0.403847	+	0.0288837i	0.132061	+	0.991242i	$0.457840\pi$
$318$	−16.7861	−	1.62974i	−0.941316	−	0.0913912i
$319$	−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
$324$	7.36415	−	5.17391i	0.409119	−	0.287440i
$325$	−18.4731	+	5.51474i	−1.02470	+	0.305903i
$326$	−4.05020	+	13.7937i	−0.224320	+	0.763963i
$327$	−13.8457	+	17.5490i	−0.765672	+	0.970460i
$328$	2.16491	−	3.96473i	0.119537	−	0.218916i
$329$	−19.7695	−	12.7051i	−1.08993	−	0.700453i
$330$	2.46418	−	2.91710i	0.135649	−	0.160581i
$331$	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
$333$	3.18469	−	11.7364i	0.174520	−	0.643151i
$334$	−0.792637	+	0.113964i	−0.0433711	+	0.00623583i
$335$	−33.1610	+	3.64079i	−1.81178	+	0.198918i
$336$	−8.30909	+	2.21230i	−0.453298	+	0.120691i
$337$	−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
$339$	−21.8453	−	7.02138i	−1.18647	−	0.381349i
$340$	3.33733	+	12.9536i	0.180992	+	0.702508i
$341$	0.706248	−	2.40526i	0.0382455	−	0.130252i
$342$	0.298001	+	14.4438i	0.0161140	+	0.781031i
$343$	31.6696	+	42.3056i	1.71000	+	2.28429i
$344$	−10.5028			−0.566275
$345$	6.51496	+	17.3941i	0.350754	+	0.936468i
$346$	0.950866			0.0511189
$347$	1.65483	+	2.21059i	0.0888357	+	0.118671i	0.842757	−	0.538294i	$-0.180931\pi$
$347$	1.65483	+	2.21059i	0.0888357	+	0.118671i	−0.753921	+	0.656965i	$0.771840\pi$
$348$	−6.39807	+	4.54077i	−0.342973	+	0.243411i
$349$	−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
$351$	−1.33420	−	19.9905i	−0.0712145	−	1.06701i
$352$	−0.209580	−	0.963425i	−0.0111707	−	0.0513507i
$353$	−13.4242	+	5.00696i	−0.714496	+	0.266493i	−0.680312	−	0.732922i	$-0.738156\pi$
$353$	−13.4242	+	5.00696i	−0.714496	+	0.266493i	−0.0341839	+	0.999416i	$0.510883\pi$
$354$	2.82803	+	10.6217i	0.150308	+	0.564536i
$355$	9.65447	+	7.74424i	0.512406	+	0.411022i
$356$	−11.4092	+	1.64040i	−0.604686	+	0.0869408i
$357$	16.7467	+	48.6359i	0.886332	+	2.57409i
$358$	1.17493	−	5.40108i	0.0620972	−	0.285456i
$359$	24.2115	−	27.9416i	1.27784	−	1.47470i	0.473173	−	0.880969i	$-0.343108\pi$
$359$	24.2115	−	27.9416i	1.27784	−	1.47470i	0.804663	−	0.593732i	$-0.202346\pi$
$360$	3.29010	−	5.84596i	0.173403	−	0.308109i
$361$	−3.52506	−	2.26542i	−0.185529	−	0.119232i
$362$	−11.4990	+	21.0589i	−0.604375	+	1.10683i
$363$	−13.6358	−	10.7583i	−0.715692	−	0.564665i
$364$	−5.39273	+	18.3659i	−0.282656	+	0.962637i
$365$	15.6123	+	0.522368i	0.817183	+	0.0273420i
$366$	4.62117	+	4.21432i	0.241552	+	0.220286i
$367$	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
$372$	0.425554	−	4.38314i	0.0220639	−	0.227255i
$373$	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
$375$	16.1097	−	10.7461i	0.831900	−	0.554926i
$376$	1.96646	−	4.30595i	0.101412	−	0.222062i
$377$	1.24595	+	17.4207i	0.0641699	+	0.897212i
$378$	10.8274	−	23.4133i	0.556902	−	1.20425i
$379$	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
$381$	2.70702	+	0.0687338i	0.138685	+	0.00352134i
$382$	12.8191	−	0.916839i	0.655881	−	0.0469096i
$383$	−15.0902	+	5.62837i	−0.771075	+	0.287596i	−0.704045	−	0.710155i	$-0.748625\pi$
$383$	−15.0902	+	5.62837i	−0.771075	+	0.287596i	−0.0670294	+	0.997751i	$0.521352\pi$
$384$	−0.679297	−	1.59328i	−0.0346652	−	0.0813070i
$385$	1.91901	−	10.7753i	0.0978017	−	0.549158i
$386$	8.63070	−	7.47854i	0.439291	−	0.380648i
$387$	20.1381	−	24.2331i	1.02368	−	1.23184i
$388$	2.37474	+	0.885731i	0.120559	+	0.0449662i
$389$	−5.15316	+	35.8410i	−0.261275	+	1.81721i	0.262024	+	0.965061i	$0.415610\pi$
$389$	−5.15316	+	35.8410i	−0.261275	+	1.81721i	−0.523299	+	0.852149i	$0.675299\pi$
$390$	−7.32086	−	13.0156i	−0.370706	−	0.659068i
$391$	6.41177	−	27.9640i	0.324257	−	1.41420i
$392$	−12.4770	+	12.4770i	−0.630182	+	0.630182i
$393$	−7.94807	+	0.365984i	−0.400927	+	0.0184614i
$394$	8.97931	−	4.10072i	0.452371	−	0.206591i
$395$	0.413794	+	10.8974i	0.0208202	+	0.548308i
$396$	2.62475	+	1.36371i	0.131899	+	0.0685288i
$397$	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
$399$	21.4952	+	35.3912i	1.07610	+	1.77177i
$400$	0.334214	−	4.98882i	0.0167107	−	0.249441i
$401$	11.4790	+	17.8617i	0.573234	+	0.891970i	0.999923	−	0.0124286i	$-0.00395625\pi$
$401$	11.4790	+	17.8617i	0.573234	+	0.891970i	−0.426688	+	0.904399i	$0.640320\pi$
$402$	−8.41295	−	24.4329i	−0.419600	−	1.21860i
$403$	−7.84788	−	5.87485i	−0.390931	−	0.292647i
$404$	−6.96478	+	4.47599i	−0.346511	+	0.222689i
$405$	7.17990	+	18.8002i	0.356772	+	0.934191i
$406$	−9.34146	+	20.4549i	−0.463609	+	1.01516i
$407$	3.90535	−	0.849556i	0.193581	−	0.0421109i
$408$	−9.21717	+	4.73330i	−0.456318	+	0.234333i
$409$	−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
$411$	15.3313	+	2.60308i	0.756235	+	0.128401i
$412$	−3.55136	+	2.65851i	−0.174963	+	0.130976i
$413$	22.2769	+	22.2769i	1.09618	+	1.09618i
$414$	−12.0296	+	7.89235i	−0.591222	+	0.387888i
$415$	−20.1867	−	10.0479i	−0.990928	−	0.493234i
$416$	−3.81648	−	0.548727i	−0.187118	−	0.0269036i
$417$	11.9084	−	8.45152i	0.583158	−	0.413873i
$418$	−4.16722	+	2.27547i	−0.203825	+	0.111297i
$419$	−0.637597	−	0.735826i	−0.0311486	−	0.0359474i	0.739961	−	0.672649i	$-0.234844\pi$
$419$	−0.637597	−	0.735826i	−0.0311486	−	0.0359474i	−0.771110	+	0.636702i	$0.780298\pi$
$420$	−0.241638	−	19.2254i	−0.0117907	−	0.938106i
$421$	−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
$423$	6.16459	+	12.7934i	0.299733	+	0.622037i
$424$	−5.26423	−	8.19130i	−0.255653	−	0.397805i
$425$	−29.9107	+	0.134814i	−1.45088	+	0.00653942i
$426$	−4.20262	+	8.61668i	−0.203618	+	0.417479i
$427$	17.5162	+	3.81042i	0.847669	+	0.184399i
$428$	6.93616	−	0.496084i	0.335272	−	0.0239791i
$429$	5.62784	−	3.41812i	0.271715	−	0.165028i
$430$	5.75672	−	22.7686i	0.277613	−	1.09800i
$431$	1.78205	+	6.06911i	0.0858384	+	0.292339i	0.991213	−	0.132275i	$-0.0422282\pi$
$431$	1.78205	+	6.06911i	0.0858384	+	0.292339i	−0.905375	+	0.424614i	$0.860410\pi$
$432$	4.97865	+	1.48762i	0.239536	+	0.0715733i
$433$	−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
$435$	−6.33687	−	16.3589i	−0.303830	−	0.784349i
$436$	−12.9057			−0.618071
$437$	0.258455	−	23.0935i	0.0123636	−	1.10471i
$438$	2.27109	+	11.8849i	0.108517	+	0.567884i
$439$	−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
$441$	−4.86469	−	52.7112i	−0.231652	−	2.51006i
$442$	−1.64549	+	23.0070i	−0.0782681	+	1.09433i
$443$	5.68717	+	3.10543i	0.270205	+	0.147543i	0.608640	−	0.793447i	$-0.291715\pi$
$443$	5.68717	+	3.10543i	0.270205	+	0.147543i	−0.338434	+	0.940990i	$0.609897\pi$
$444$	6.45855	−	2.75360i	0.306509	−	0.130680i
$445$	2.69737	−	25.6326i	0.127867	−	1.21510i
$446$	−2.56866	−	2.22576i	−0.121630	−	0.105393i
$447$	11.1854	−	10.6315i	0.529053	−	0.502852i
$448$	−3.97419	−	2.97504i	−0.187763	−	0.140558i
$449$	−1.62729	−	11.3180i	−0.0767964	−	0.534131i	−0.991510	−	0.130029i	$-0.958493\pi$
$449$	−1.62729	−	11.3180i	−0.0767964	−	0.534131i	0.914714	−	0.404102i	$-0.132416\pi$
$450$	10.8698	+	10.3367i	0.512409	+	0.487275i
$451$	−2.91665	+	3.36600i	−0.137340	+	0.158499i
$452$	−4.62965	−	12.4126i	−0.217760	−	0.583838i
$453$	−38.6463	−	15.5428i	−1.81576	−	0.730264i
$454$	5.16709	+	17.5975i	0.242504	+	0.825892i
$455$	−36.8588	−	21.7572i	−1.72797	−	1.01999i
$456$	−6.44025	+	5.30037i	−0.301592	+	0.248213i
$457$	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	$-0.909882\pi$
$461$		−	11.9956i		−	0.558693i	0.960190	−	0.279346i	$-0.0901178\pi$
$462$	8.46884	−	0.389963i	0.394006	−	0.0181427i
$463$	−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
$465$	9.26875	+	3.32498i	0.429828	+	0.154192i
$466$	3.72350	−	1.09332i	0.172488	−	0.0506470i
$467$	−19.9916	+	4.34891i	−0.925102	+	0.201244i	−0.649792	−	0.760112i	$-0.725144\pi$
$467$	−19.9916	+	4.34891i	−0.925102	+	0.201244i	−0.275310	+	0.961355i	$0.588781\pi$
$468$	8.58379	−	7.75361i	0.396786	−	0.358411i
$469$	−55.9741	−	48.5019i	−2.58465	−	2.23961i
$470$	8.25681	+	6.62313i	0.380858	+	0.305502i
$471$	6.12727	−	12.5628i	0.282330	−	0.578864i
$472$	−3.80306	+	5.08029i	−0.175050	+	0.233839i
$473$	10.1187	+	2.20119i	0.465259	+	0.101211i
$474$	−8.16281	+	2.17335i	−0.374930	+	0.0998253i
$475$	−23.5046	+	5.22417i	−1.07846	+	0.239701i
$476$	−16.0559	+	24.9835i	−0.735922	+	1.14512i
$477$	28.9933	+	3.55987i	1.32751	+	0.162995i
$478$	3.68884	+	0.263831i	0.168724	+	0.0120674i
$479$	−1.49745	−	0.439691i	−0.0684202	−	0.0200900i	0.247343	−	0.968928i	$-0.420442\pi$
$479$	−1.49745	−	0.439691i	−0.0684202	−	0.0200900i	−0.315764	+	0.948838i	$0.602261\pi$
$480$	3.82633	−	0.599318i	0.174647	−	0.0273550i
$481$	2.22433	−	15.4705i	0.101421	−	0.705395i
$482$	−5.14037	+	5.14037i	−0.234138	+	0.234138i
$483$	−18.4908	+	36.8592i	−0.841362	+	1.67715i
$484$		−	10.0279i		−	0.455813i
$485$	−3.22175	+	4.66259i	−0.146292	+	0.211717i
$486$	−12.9784	+	8.63483i	−0.588714	+	0.391684i
$487$	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
$489$	7.61932	−	23.7057i	0.344558	−	1.07201i
$490$	−20.2094	−	33.8869i	−0.912969	−	1.53086i
$491$	−11.5120	−	5.25735i	−0.519529	−	0.237261i	0.138352	−	0.990383i	$-0.455820\pi$
$491$	−11.5120	−	5.25735i	−0.519529	−	0.237261i	−0.657881	+	0.753122i	$0.728547\pi$
$492$	−3.92283	+	6.76972i	−0.176855	+	0.305203i
$493$	−5.75998	+	26.4782i	−0.259416	+	1.19252i
$494$	2.64247	+	18.3787i	0.118890	+	0.826899i
$495$	−4.39496	+	4.94260i	−0.197539	+	0.222154i
$496$	2.13889	−	1.37458i	0.0960392	−	0.0617206i
$497$	1.96025	+	27.4079i	0.0879293	+	1.22941i
$498$	4.14480	−	16.9676i	0.185733	−	0.760337i
$499$	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
$501$	1.37745	−	0.162480i	0.0615401	−	0.00725907i
$502$	−4.21132	−	7.71246i	−0.187961	−	0.344224i
$503$	1.49541	−	4.00935i	0.0666770	−	0.178768i	−0.899338	−	0.437254i	$-0.855951\pi$
$503$	1.49541	−	4.00935i	0.0666770	−	0.178768i	0.966015	+	0.258486i	$0.0832237\pi$
$504$	14.4844	−	3.46528i	0.645186	−	0.154356i
$505$	−5.88581	−	17.5519i	−0.261915	−	0.781050i
$506$	−4.12447	−	2.31242i	−0.183355	−	0.102800i
$507$	−0.606837	−	3.17566i	−0.0269506	−	0.141036i
$508$	0.936911	+	1.25157i	0.0415687	+	0.0555293i
$509$	−8.75679	−	19.1747i	−0.388138	−	0.849903i	−0.998337	−	0.0576549i	$-0.981638\pi$
$509$	−8.75679	−	19.1747i	−0.388138	−	0.849903i	0.610199	−	0.792248i	$-0.291090\pi$
$510$	−5.20906	−	22.5758i	−0.230661	−	0.999674i
$511$	22.7111	+	26.2100i	1.00468	+	1.15946i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	0.119025	−	25.0224i	0.00525510	−	1.10477i
$514$	0.671112	+	0.306487i	0.0296015	+	0.0135186i
$515$	−3.81673	−	9.15597i	−0.168185	−	0.403460i
$516$	18.1856	+	0.461750i	0.800576	+	0.0203274i
$517$	−2.79698	+	3.73633i	−0.123011	+	0.164323i
$518$	12.0597	−	16.1098i	0.529871	−	0.707825i
$519$	−1.64642	−	0.0418041i	−0.0722697	−	0.00183500i
$520$	3.28141	−	7.97280i	0.143899	−	0.349630i
$521$	29.3621	+	13.4092i	1.28638	+	0.587469i	0.936940	−	0.349491i	$-0.113645\pi$
$521$	29.3621	+	13.4092i	1.28638	+	0.587469i	0.349438	+	0.936960i	$0.386373\pi$
$522$	11.2778	−	7.58103i	0.493618	−	0.331813i
$523$	−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
$525$	41.8103	+	10.0138i	1.82475	+	0.437039i
$526$	3.38957	+	7.42212i	0.147792	+	0.323620i
$527$	−9.11490	−	12.1761i	−0.397051	−	0.530398i
$528$	0.320530	+	1.67738i	0.0139493	+	0.0729985i
$529$	19.6223	−	11.9986i	0.853143	−	0.521678i
$530$	20.6429	−	6.92232i	0.896670	−	0.300687i
$531$	−4.42974	−	18.5157i	−0.192234	−	0.803513i
$532$	−8.35450	+	22.3993i	−0.362214	+	0.971132i
$533$	8.34729	+	15.2869i	0.361561	+	0.662150i
$534$	19.8271	−	2.33874i	0.858001	−	0.101207i
$535$	−2.72634	+	15.3085i	−0.117870	+	0.661843i
$536$	8.06591	−	12.5508i	0.348394	−	0.542112i
$537$	−2.27184	+	9.30028i	−0.0980373	+	0.401337i
$538$	0.396030	+	5.53723i	0.0170741	+	0.238727i
$539$	14.6355	−	9.40569i	0.630397	−	0.405132i
$540$	−5.95380	+	9.97759i	−0.256211	+	0.429367i
$541$	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
$543$	20.8363	−	35.9577i	0.894171	−	1.54309i
$544$	−5.44161	−	2.48510i	−0.233307	−	0.106548i
$545$	7.07374	−	27.9776i	0.303006	−	1.19843i
$546$	10.1449	−	31.5634i	0.434162	−	1.35079i
$547$	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
$549$	−7.81624	−	7.50024i	−0.333589	−	0.320102i
$550$	−1.36755	+	4.73631i	−0.0583124	+	0.201957i
$551$			21.8132i			0.929275i
$552$	−7.87924	−	2.63014i	−0.335363	−	0.111946i
$553$	−17.1199	+	17.1199i	−0.728012	+	0.728012i
$554$	−0.855275	+	5.94857i	−0.0363372	+	0.252730i
$555$	2.42940	+	15.5104i	0.103122	+	0.658382i
$556$	8.08936	+	2.37525i	0.343065	+	0.100733i
$557$	−13.4180	−	0.959675i	−0.568539	−	0.0406627i	−0.215889	−	0.976418i	$-0.569265\pi$
$557$	−13.4180	−	0.959675i	−0.568539	−	0.0406627i	−0.352650	+	0.935755i	$0.614719\pi$
$558$	−0.929545	+	7.57067i	−0.0393508	+	0.320492i
$559$	21.8939	−	34.0675i	0.926011	−	1.44090i
$560$	8.62774	−	6.98480i	0.364589	−	0.295162i
$561$	9.87206	−	2.62844i	0.416799	−	0.110973i
$562$	8.53250	+	1.85613i	0.359922	+	0.0782962i
$563$	−11.3972	+	15.2249i	−0.480337	+	0.641655i	−0.973610	−	0.228220i	$-0.926710\pi$
$563$	−11.3972	+	15.2249i	−0.480337	+	0.641655i	0.493273	+	0.869875i	$0.335800\pi$
$564$	−3.59422	+	7.36926i	−0.151344	+	0.310302i
$565$	29.4462	−	3.23293i	1.23881	−	0.136011i
$566$	−1.94544	−	1.68574i	−0.0817731	−	0.0708568i
$567$	−19.7769	+	40.0640i	−0.830553	+	1.68253i
$568$	−5.40852	+	1.17655i	−0.226937	+	0.0493670i
$569$	−2.03188	+	0.596614i	−0.0851808	+	0.0250113i	−0.324045	−	0.946042i	$-0.605043\pi$
$569$	−2.03188	+	0.596614i	−0.0851808	+	0.0250113i	0.238864	+	0.971053i	$0.423225\pi$
$570$	−7.96044	−	16.8667i	−0.333426	−	0.706468i
$571$	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
$573$	−22.2365	+	1.02392i	−0.928941	+	0.0427748i
$574$			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
$579$	−15.2728	+	12.5696i	−0.634715	+	0.522375i
$580$	5.14871	−	8.72242i	0.213789	−	0.362179i
$581$	−14.1042	−	48.0344i	−0.585140	−	1.99280i
$582$	−4.07290	−	1.63804i	−0.168827	−	0.0678989i
$583$	3.35495	+	8.99498i	0.138948	+	0.372534i
$584$	−4.57481	+	5.27961i	−0.189307	+	0.218472i
$585$	12.1038	+	22.8582i	0.500430	+	0.945070i
$586$	3.87363	+	26.9417i	0.160018	+	1.11295i
$587$	2.97410	+	2.22638i	0.122754	+	0.0918927i	0.658891	−	0.752239i	$-0.271026\pi$
$587$	2.97410	+	2.22638i	0.122754	+	0.0918927i	−0.536137	+	0.844131i	$0.680117\pi$
$588$	22.1523	−	21.0552i	0.913546	−	0.868303i
$589$	−9.25322	−	8.01796i	−0.381272	−	0.330374i
$590$	−8.92882	−	11.0290i	−0.367594	−	0.454058i
$591$	−15.7279	+	6.70559i	−0.646959	+	0.275831i
$592$	3.55777	+	1.94269i	0.146223	+	0.0798440i
$593$	−2.78157	+	38.8915i	−0.114225	+	1.59708i	0.540586	+	0.841289i	$0.318203\pi$
$593$	−2.78157	+	38.8915i	−0.114225	+	1.59708i	−0.654811	+	0.755792i	$0.727252\pi$
$594$	−4.48478	−	2.47664i	−0.184013	−	0.101618i
$595$	−45.3601	−	48.5006i	−1.85958	−	1.98833i
$596$	8.81890	+	1.26797i	0.361236	+	0.0519380i
$597$	4.71677	+	24.6835i	0.193045	+	1.01023i
$598$	−14.1095	+	11.9522i	−0.576981	+	0.488760i
$599$	−23.5970			−0.964148			−0.482074	−	0.876130i	$-0.660116\pi$
$599$	−23.5970			−0.964148			−0.482074	+	0.876130i	$0.660116\pi$
$600$	−0.798019	+	8.62341i	−0.0325790	+	0.352049i
$601$	−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
$603$	13.4928	+	42.6752i	0.549469	+	1.73787i
$604$	−6.77548	−	23.0752i	−0.275691	−	0.938916i
$605$	21.7390	+	5.49639i	0.883814	+	0.223460i
$606$	12.2562	−	7.44394i	0.497876	−	0.302389i
$607$	−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
$609$	17.0740	−	35.0069i	0.691871	−	1.41855i
$610$	−7.66675	−	2.53256i	−0.310418	−	0.102540i
$611$	9.86775	+	15.3545i	0.399207	+	0.621178i
$612$	16.1676	−	7.79045i	0.653535	−	0.314910i
$613$	−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
$615$	−12.5256	−	12.2147i	−0.505081	−	0.492542i
$616$	3.20533	+	3.69914i	0.129146	+	0.149043i
$617$	−6.77724	+	3.70066i	−0.272842	+	0.148983i	−0.609845	−	0.792521i	$-0.708768\pi$
$617$	−6.77724	+	3.70066i	−0.272842	+	0.148983i	0.337004	+	0.941503i	$0.390587\pi$
$618$	6.26603	−	4.44707i	0.252057	−	0.178887i
$619$	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
$621$	21.1761	−	13.1367i	0.849768	−	0.527156i
$622$	−23.0257	−	23.0257i	−0.923247	−	0.923247i
$623$	45.8086	−	34.2919i	1.83528	−	1.37388i
$624$	6.58409	+	1.11791i	0.263574	+	0.0447521i
$625$	−13.3259	+	21.1523i	−0.533036	+	0.846093i
$626$	17.0639	−	14.7860i	0.682013	−	0.590967i
$627$	7.31555	−	3.75676i	0.292155	−	0.150030i
$628$	7.88543	−	1.71537i	0.314663	−	0.0684507i
$629$	10.0736	−	22.0581i	0.401661	−	0.879515i
$630$	−0.426839	+	33.2993i	−0.0170057	+	1.32668i
$631$	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
$633$	12.2923	+	35.6994i	0.488576	+	1.41892i
$634$	−3.89729	−	6.06430i	−0.154781	−	0.240844i
$635$	−3.22674	+	1.34509i	−0.128049	+	0.0533781i
$636$	8.75485	+	14.4146i	0.347152	+	0.571576i
$637$	−14.4618	−	66.4798i	−0.572998	−	2.63403i
$638$	3.91977	+	2.14036i	0.155185	+	0.0847376i
$639$	7.65564	−	14.7349i	0.302852	−	0.582906i
$640$	1.64000	+	1.52000i	0.0648265	+	0.0600835i
$641$	0.933100	−	0.426133i	0.0368553	−	0.0168312i	−0.396902	−	0.917861i	$-0.629915\pi$
$641$	0.933100	−	0.426133i	0.0368553	−	0.0168312i	0.433757	+	0.901030i	$0.357187\pi$
$642$	−12.0317	+	0.554022i	−0.474854	+	0.0218655i
$643$	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
$645$	−10.9687	+	39.1706i	−0.431893	+	1.54234i
$646$	−4.09981	+	28.5148i	−0.161305	+	1.12190i
$647$	20.0930	+	7.49430i	0.789937	+	0.294631i	0.711865	−	0.702316i	$-0.247851\pi$
$647$	20.0930	+	7.49430i	0.789937	+	0.294631i	0.0780722	+	0.996948i	$0.475124\pi$
$648$	−8.55510	−	2.79469i	−0.336076	−	0.109786i
$649$	4.72869	−	4.09744i	0.185617	−	0.160838i
$650$	15.4853	+	11.4836i	0.607382	+	0.450423i
$651$	8.57407	+	20.1104i	0.336044	+	0.788189i
$652$	13.4696	−	5.02391i	0.527512	−	0.196752i
$653$	−0.514127	+	0.0367711i	−0.0201193	+	0.00143896i	−0.0813952	−	0.996682i	$-0.525938\pi$
$653$	−0.514127	+	0.0367711i	−0.0201193	+	0.00143896i	0.0612759	+	0.998121i	$0.480483\pi$
$654$	22.3461	+	0.567390i	0.873802	+	0.0221867i
$655$	9.17491	−	4.61852i	0.358493	−	0.180460i
$656$	−4.47131	+	0.642877i	−0.174575	+	0.0251001i
$657$	−3.40987	−	20.6785i	−0.133032	−	0.806745i
$658$	1.67647	+	23.4401i	0.0653557	+	0.913792i
$659$	−21.0612	+	46.1175i	−0.820426	+	1.79648i	−0.266710	+	0.963777i	$0.585937\pi$
$659$	−21.0612	+	46.1175i	−0.820426	+	1.79648i	−0.553716	+	0.832706i	$0.686791\pi$
$660$	−3.81199	−	0.224525i	−0.148381	−	0.00873964i
$661$	−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
$663$	3.86064	−	39.7641i	0.149935	−	1.54431i
$664$	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
$669$	4.34977	+	3.96682i	0.168172	+	0.153366i
$670$	22.7872	+	24.3649i	0.880348	+	0.941298i
$671$	1.00302	−	3.41598i	0.0387212	−	0.131872i
$672$	6.75049	+	5.32599i	0.260406	+	0.205454i
$673$	−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
$675$	−18.3666	−	18.3758i	−0.706930	−	0.707283i
$676$	1.22239	−	1.41071i	0.0470150	−	0.0542582i
$677$	1.68570	−	7.74905i	0.0647868	−	0.297820i	−0.933340	−	0.358993i	$-0.883120\pi$
$677$	1.68570	−	7.74905i	0.0647868	−	0.297820i	0.998127	+	0.0611724i	$0.0194839\pi$
$678$	7.47050	+	21.6958i	0.286903	+	0.833223i
$679$	−12.4543	+	1.79066i	−0.477954	+	0.0687194i
$680$	8.36992	−	10.4345i	0.320972	−	0.400144i
$681$	−8.17312	−	30.6971i	−0.313195	−	1.17632i
$682$	−2.34875	+	0.876038i	−0.0899383	+	0.0335452i
$683$	4.19741	+	19.2952i	0.160609	+	0.738309i	0.985037	+	0.172342i	$0.0551335\pi$
$683$	4.19741	+	19.2952i	0.160609	+	0.738309i	−0.824428	+	0.565967i	$0.808503\pi$
$684$	11.3843	−	8.89441i	0.435289	−	0.340086i
$685$	−19.4410	+	5.00871i	−0.742802	+	0.191373i
$686$	14.8885	−	50.7056i	0.568446	−	1.93595i
$687$	−17.5764	+	12.4742i	−0.670583	+	0.475919i
$688$	6.29412	+	8.40796i	0.239961	+	0.320551i
$689$	37.5433			1.43029
$690$	10.0204	−	15.6394i	0.381471	−	0.595382i
$691$	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
$693$	−14.6809	+	0.302892i	−0.557681	+	0.0115059i
$694$	0.777967	−	2.64951i	0.0295312	−	0.100574i
$695$	−9.58305	+	16.2346i	−0.363506	+	0.615814i
$696$	7.46930	+	2.40074i	0.283123	+	0.0909996i
$697$	5.74423	+	26.4058i	0.217578	+	1.00019i
$698$	0.278227	−	0.103773i	0.0105310	−	0.00392788i
$699$	−6.49528	+	1.72937i	−0.245674	+	0.0654109i
$700$	10.4131	+	22.5321i	0.393576	+	0.851633i
$701$	−45.1538	+	6.49213i	−1.70543	+	0.245204i	−0.924982	−	0.380011i	$-0.875920\pi$
$701$	−45.1538	+	6.49213i	−1.70543	+	0.245204i	−0.780453	+	0.625215i	$0.785011\pi$
$702$	−15.2036	+	13.0479i	−0.573825	+	0.492462i
$703$	4.14941	−	19.0745i	0.156498	−	0.719410i
$704$	−0.645665	+	0.745137i	−0.0243344	+	0.0280834i
$705$	−14.0054	−	11.8309i	−0.527475	−	0.445577i
$706$	12.0531	+	7.74604i	0.453624	+	0.291526i
$707$	19.6973	−	36.0729i	0.740793	−	1.35666i
$708$	6.80832	−	8.62929i	0.255872	−	0.324309i
$709$	−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
$711$	14.2294	−	3.40427i	0.533644	−	0.127670i
$712$	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
$717$	−6.37561	−	0.618999i	−0.238101	−	0.0231169i
$718$	−36.8778	−	2.63756i	−1.37627	−	0.0984327i
$719$	38.5735	−	11.3262i	1.43855	−	0.422396i	0.532811	−	0.846234i	$-0.321136\pi$
$719$	38.5735	−	11.3262i	1.43855	−	0.422396i	0.905738	+	0.423838i	$0.139318\pi$
$720$	−6.65161	+	0.869493i	−0.247891	+	0.0324041i
$721$	9.14868	−	20.0328i	0.340714	−	0.746061i
$722$	0.298929	+	4.17957i	0.0111250	+	0.155547i
$723$	9.12651	−	8.67453i	0.339419	−	0.322609i
$724$	23.7496	−	3.41468i	0.882647	−	0.126905i
$725$	16.0868	+	15.9425i	0.597451	+	0.592089i
$726$	−0.440869	+	17.3632i	−0.0163622	+	0.644409i
$727$	−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
$729$	22.8517	−	14.3806i	0.846359	−	0.532613i
$730$	−8.93790	−	12.8113i	−0.330807	−	0.474167i
$731$	47.4839	−	41.1450i	1.75625	−	1.52180i
$732$	0.604376	−	6.22499i	0.0223384	−	0.230082i
$733$	−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
$735$	33.5027	+	59.5635i	1.23576	+	2.19703i
$736$	−1.62558	−	4.51193i	−0.0599197	−	0.166312i
$737$	−10.4013	+	10.4013i	−0.383137	+	0.383137i
$738$	7.08997	−	11.5493i	0.260985	−	0.425134i
$739$	−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
$741$	−3.76740	−	31.9388i	−0.138399	−	1.17330i
$742$	42.4255	+	23.1661i	1.55749	+	0.850453i
$743$	9.84350	+	45.2498i	0.361123	+	1.66006i	0.696188	+	0.717860i	$0.254878\pi$
$743$	9.84350	+	45.2498i	0.361123	+	1.66006i	−0.335065	+	0.942195i	$0.608758\pi$
$744$	−3.76391	+	2.28605i	−0.137992	+	0.0838105i
$745$	−7.58249	+	18.4231i	−0.277801	+	0.674969i
$746$	−15.4560	−	24.0500i	−0.565885	−	0.880534i
$747$	−7.92265	+	29.1971i	−0.289875	+	1.06827i
$748$	4.72175	+	3.53466i	0.172644	+	0.129240i
$749$	−29.0415	+	18.6638i	−1.06115	+	0.681962i
$750$	−18.2569	−	6.45656i	−0.666646	−	0.235760i
$751$	−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
$753$	6.95280	+	13.5392i	0.253374	+	0.493397i
$754$	13.1993	−	11.4373i	0.480691	−	0.416521i
$755$	53.7372	−	2.04050i	1.95570	−	0.0742613i
$756$	−25.2320	+	5.36331i	−0.917678	+	0.195062i
$757$	−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
$759$	7.03983	+	4.18527i	0.255530	+	0.151916i
$760$	4.79826	−	9.63991i	0.174051	−	0.349676i
$761$	−19.7506	−	2.83971i	−0.715960	−	0.102940i	−0.225299	−	0.974290i	$-0.572336\pi$
$761$	−19.7506	−	2.83971i	−0.715960	−	0.102940i	−0.490662	+	0.871350i	$0.663245\pi$
$762$	−1.56723	−	2.20827i	−0.0567747	−	0.0799971i
$763$	56.2318	−	30.7049i	2.03573	−	1.11159i
$764$	−8.41616	−	9.71276i	−0.304486	−	0.351395i
$765$	8.02692	+	39.3189i	0.290214	+	1.42158i
$766$	13.5490	+	8.70740i	0.489544	+	0.314611i
$767$	−8.55095	−	22.9260i	−0.308757	−	0.827809i
$768$	−0.868403	+	1.49862i	−0.0313358	+	0.0540770i
$769$	−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
$771$	−1.14855	−	0.560185i	−0.0413641	−	0.0201746i
$772$	−11.1591	−	2.42751i	−0.401624	−	0.0873679i
$773$	−3.62871	+	0.259530i	−0.130515	+	0.00933465i	−0.136444	−	0.990648i	$-0.543567\pi$
$773$	−3.62871	+	0.259530i	−0.130515	+	0.00933465i	0.00592859	+	0.999982i	$0.498113\pi$
$774$	−31.4679	−	1.59903i	−1.13109	−	0.0574761i
$775$	−12.6759	+	0.964044i	−0.455333	+	0.0346295i
$776$	−0.714062	−	2.43187i	−0.0256333	−	0.0872991i
$777$	−21.5895	+	27.3638i	−0.774518	+	0.981672i
$778$	31.7804	−	17.3534i	1.13938	−	0.622149i
$779$	9.03676	+	19.7877i	0.323775	+	0.708969i
$780$	−6.03226	+	13.6606i	−0.215990	+	0.489127i
$781$	5.45729			0.195277
$782$	−26.2288	+	11.6253i	−0.937939	+	0.415720i
$783$	−19.8608	+	12.6307i	−0.709767	+	0.451384i
$784$	17.4655	+	2.51116i	0.623767	+	0.0896842i
$785$	−0.603418	+	18.0346i	−0.0215369	+	0.643684i
$786$	5.05609	+	6.14344i	0.180345	+	0.219129i
$787$	−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
$789$	−5.54271	−	13.0004i	−0.197326	−	0.462826i
$790$	8.47585	−	6.86183i	0.301557	−	0.244133i
$791$	49.7037	+	43.0685i	1.76726	+	1.53134i
$792$	−0.481251	−	2.91846i	−0.0171005	−	0.103703i
$793$	−11.1456	−	8.34353i	−0.395793	−	0.296287i
$794$	−5.29788	−	36.8475i	−0.188015	−	1.30767i
$795$	−36.0473	+	11.0784i	−1.27847	+	0.392911i
$796$	−9.50129	+	10.9651i	−0.336764	+	0.388647i
$797$	10.8367	+	29.0543i	0.383856	+	1.02916i	0.974925	+	0.222536i	$0.0714334\pi$
$797$	10.8367	+	29.0543i	0.383856	+	1.02916i	−0.591069	+	0.806621i	$0.701294\pi$
$798$	15.4505	−	38.4169i	0.546943	−	1.35994i
$799$	7.97814	+	27.1710i	0.282246	+	0.961242i
$800$	−4.19404	+	2.72213i	−0.148282	+	0.0962420i
$801$	−34.4332	+	3.17782i	−1.21664	+	0.112283i
$802$	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
$807$	−0.442283	−	9.60508i	−0.0155691	−	0.338115i
$808$	7.75705	+	2.89323i	0.272892	+	0.101783i
$809$	−30.0537	−	8.82457i	−1.05663	−	0.310255i	−0.293138	−	0.956070i	$-0.594700\pi$
$809$	−30.0537	−	8.82457i	−1.05663	−	0.310255i	−0.763494	+	0.645815i	$0.776518\pi$
$810$	10.7476	−	17.0144i	0.377633	−	0.597824i
$811$	−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
$813$	7.21165	−	29.5225i	0.252924	−	1.03540i
$814$	−3.02049	−	2.61727i	−0.105868	−	0.0917353i
$815$	3.50825	+	31.9538i	0.122889	+	1.11929i
$816$	9.31284	+	4.54217i	0.326015	+	0.159008i
$817$	30.3101	−	40.4896i	1.06042	−	1.41655i
$818$	22.3980	+	4.87239i	0.783128	+	0.170359i
$819$	−18.9535	+	54.2058i	−0.662289	+	1.89410i
$820$	1.05711	−	10.0455i	0.0369158	−	0.350804i
$821$	−0.279948	+	0.435607i	−0.00977024	+	0.0152028i	−0.846104	−	0.533017i	$-0.821058\pi$
$821$	−0.279948	+	0.435607i	−0.00977024	+	0.0152028i	0.836334	+	0.548220i	$0.184694\pi$
$822$	−7.10381	−	13.8333i	−0.247774	−	0.482491i
$823$	−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
$825$	2.57613	−	8.14076i	0.0896893	−	0.283425i
$826$	4.48353	−	31.1837i	0.156002	−	1.08502i
$827$	21.0305	−	21.0305i	0.731301	−	0.731301i	−0.239576	−	0.970878i	$-0.577009\pi$
$827$	21.0305	−	21.0305i	0.731301	−	0.731301i	0.970878	+	0.239576i	$0.0770085\pi$
$828$	13.5272	+	4.90047i	0.470103	+	0.170303i
$829$		−	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
$831$	1.74243	−	10.2623i	0.0604441	−	0.355995i
$832$	1.84785	+	3.38409i	0.0640628	+	0.117322i
$833$	7.53032	−	105.288i	0.260910	−	3.64800i
$834$	−13.9022	−	4.46837i	−0.481395	−	0.154727i
$835$	−1.53789	+	0.917165i	−0.0532209	+	0.0317398i
$836$	4.31893	+	1.97239i	0.149373	+	0.0682166i
$837$	1.94234	−	13.0677i	0.0671371	−	0.451686i
$838$	−0.206961	+	0.951386i	−0.00714936	+	0.0328651i
$839$	7.88283	+	54.8263i	0.272146	+	1.89281i	0.426005	+	0.904721i	$0.359921\pi$
$839$	7.88283	+	54.8263i	0.272146	+	1.89281i	−0.153859	+	0.988093i	$0.549170\pi$
$840$	−15.2460	+	11.7148i	−0.526035	+	0.404200i
$841$	−7.13553	+	4.58573i	−0.246053	+	0.158128i
$842$	1.47283	+	20.5929i	0.0507571	+	0.709677i
$843$	−14.6924	−	3.58900i	−0.506032	−	0.123612i
$844$	−11.7853	+	18.3382i	−0.405665	+	0.631227i
$845$	2.38821	+	3.42319i	0.0821570	+	0.117761i
$846$	6.54735	−	12.6018i	0.225103	−	0.433259i
$847$	23.8581	+	43.6928i	0.819774	+	1.50130i
$848$	−3.40274	+	9.12309i	−0.116850	+	0.313288i
$849$	3.29441	+	3.00437i	0.113064	+	0.103110i
$850$	18.0328	+	23.8640i	0.618518	+	0.818528i
$851$	18.2896	−	6.58946i	0.626959	−	0.225884i
$852$	9.41654	−	1.79941i	0.322605	−	0.0616468i
$853$	−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
$855$	13.0419	+	29.5545i	0.446024	+	1.01074i
$856$	−4.55382	−	5.25539i	−0.155646	−	0.179626i
$857$	−26.1503	+	47.8908i	−0.893279	+	1.63592i	−0.128420	+	0.991720i	$0.540990\pi$
$857$	−26.1503	+	47.8908i	−0.893279	+	1.63592i	−0.764859	+	0.644198i	$0.777191\pi$
$858$	−6.10898	−	2.45691i	−0.208557	−	0.0838777i
$859$	−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
$861$	0.985923	−	38.8297i	0.0336002	−	1.32331i
$862$	3.79063	−	5.06369i	0.129109	−	0.172470i
$863$	−5.07338	+	6.77724i	−0.172700	+	0.230700i	−0.878537	−	0.477674i	$-0.841480\pi$
$863$	−5.07338	+	6.77724i	−0.172700	+	0.230700i	0.705837	+	0.708374i	$0.250571\pi$
$864$	−1.79269	−	4.87712i	−0.0609886	−	0.165923i
$865$	1.96251	−	0.818087i	0.0667275	−	0.0278158i
$866$	8.39453	+	3.83365i	0.285258	+	0.130273i
$867$	12.1417	−	30.1896i	0.412352	−	1.02529i
$868$	−6.04907	+	11.0780i	−0.205319	+	0.376013i
$869$	3.14890	+	3.63402i	0.106819	+	0.123276i
$870$	−9.29843	+	14.8765i	−0.315246	+	0.504359i
$871$	23.8964	+	52.3259i	0.809700	+	1.77299i
$872$	7.73409	+	10.3315i	0.261909	+	0.349870i
$873$	6.98018	+	3.01532i	0.236243	+	0.102053i
$874$	−18.6422	+	13.6325i	−0.630581	+	0.461126i
$875$	−54.5537	+	10.2239i	−1.84425	+	0.345630i
$876$	8.15336	−	8.94047i	0.275476	−	0.302071i
$877$	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
$879$	−5.52269	−	46.8196i	−0.186276	−	1.57919i
$880$	−1.26145	−	1.80812i	−0.0425235	−	0.0609518i
$881$	−12.6243	+	19.6438i	−0.425323	+	0.661816i	−0.986100	−	0.166151i	$-0.946866\pi$
$881$	−12.6243	+	19.6438i	−0.425323	+	0.661816i	0.560777	+	0.827967i	$0.310502\pi$
$882$	−39.2822	+	35.4831i	−1.32270	+	1.19478i
$883$	−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
$885$	14.9753	+	19.4892i	0.503389	+	0.655123i
$886$	−0.922169	−	6.41383i	−0.0309809	−	0.215477i
$887$	9.41902	−	43.2986i	0.316260	−	1.45382i	−0.494875	−	0.868964i	$-0.664786\pi$
$887$	9.41902	−	43.2986i	0.316260	−	1.45382i	0.811135	−	0.584859i	$-0.198850\pi$
$888$	−6.07484	−	3.52016i	−0.203858	−	0.118129i
$889$	−7.05994	−	3.22417i	−0.236783	−	0.108135i
$890$	−22.1364	+	13.2017i	−0.742014	+	0.442521i
$891$	7.65648	+	4.48546i	0.256502	+	0.150268i
$892$	−0.242470	+	3.39017i	−0.00811849	+	0.113511i
$893$	10.9249	+	20.0074i	0.365587	+	0.669523i
$894$	−15.2141	−	2.58319i	−0.508836	−	0.0863949i
$895$	−2.22190	−	12.1583i	−0.0742699	−	0.406407i
$896$			4.96438i			0.165848i
$897$	24.9560	−	20.0748i	0.833257	−	0.670277i
$898$	−8.08535	+	8.08535i	−0.269812	+	0.269812i
$899$	−1.63900	+	11.3995i	−0.0546638	+	0.380195i
$900$	1.76089	−	14.8963i	0.0586962	−	0.496543i
$901$	55.8893	+	16.4106i	1.86194	+	0.546716i
$902$	4.44251	+	0.317734i	0.147919	+	0.0105794i
$903$	−80.3357	+	41.2548i	−2.67340	+	1.37287i
$904$	−7.16233	+	11.1448i	−0.238216	+	0.370671i
$905$	−5.61489	+	53.3572i	−0.186645	+	1.77365i
$906$	10.7172	+	40.2524i	0.356056	+	1.33730i
$907$	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
$909$	−21.5489	+	12.3503i	−0.714731	+	0.409633i
$910$	4.67114	+	42.5456i	0.154847	+	1.41037i
$911$	−6.54909	−	5.67482i	−0.216981	−	0.188015i	0.539587	−	0.841930i	$-0.318580\pi$
$911$	−6.54909	−	5.67482i	−0.216981	−	0.188015i	−0.756569	+	0.653914i	$0.773126\pi$
$912$	8.10266	+	1.97929i	0.268306	+	0.0655409i
$913$	−9.71547	+	2.11347i	−0.321535	+	0.0699457i
$914$	−16.1761	+	4.74973i	−0.535058	+	0.157107i
$915$	13.1636	+	4.72217i	0.435174	+	0.156110i
$916$	−11.9396	−	3.50579i	−0.394497	−	0.115835i
$917$	21.3670	+	7.96946i	0.705599	+	0.263175i
$918$	−28.3365	+	12.7783i	−0.935244	+	0.421747i
$919$		−	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
$924$	−5.38737	−	6.54596i	−0.177231	−	0.215346i
$925$	−11.0345	−	17.0010i	−0.362811	−	0.558989i
$926$	0.460509	+	1.56835i	0.0151333	+	0.0515391i
$927$	−11.0451	+	7.42458i	−0.362769	+	0.243855i
$928$	1.58296	+	4.24408i	0.0519632	+	0.139319i
$929$	20.5637	−	23.7318i	0.674674	−	0.778616i	−0.310426	−	0.950598i	$-0.600472\pi$
$929$	20.5637	−	23.7318i	0.674674	−	0.778616i	0.985100	+	0.171982i	$0.0550171\pi$
$930$	−2.89277	−	9.41260i	−0.0948576	−	0.308651i
$931$	−12.0928	−	84.1072i	−0.396325	−	2.75650i
$932$	−3.10666	−	2.32562i	−0.101762	−	0.0761781i
$933$	38.8565	+	40.8812i	1.27211	+	1.33839i
$934$	15.4620	+	13.3979i	0.505933	+	0.438393i
$935$	−10.2507	+	8.29867i	−0.335232	+	0.271395i
$936$	−11.3512	−	2.22511i	−0.371024	−	0.0727300i
$937$	−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
$939$	−30.1962	+	24.8516i	−0.985414	+	0.811003i
$940$	0.353961	−	10.5790i	0.0115449	−	0.345049i
$941$	−54.2189	−	7.79550i	−1.76748	−	0.254126i	−0.819645	−	0.572872i	$-0.805829\pi$
$941$	−54.2189	−	7.79550i	−1.76748	−	0.254126i	−0.947840	+	0.318746i	$0.896738\pi$
$942$	−13.7290	+	2.62347i	−0.447314	+	0.0854774i
$943$	−11.9157	+	18.0928i	−0.388030	+	0.589184i
$944$	6.34607			0.206547
$945$	2.20305	−	57.6388i	0.0716652	−	1.87499i
$946$	−4.30177	−	9.41956i	−0.139863	−	0.306256i
$947$	−12.2911	+	6.71144i	−0.399407	+	0.218093i	−0.666381	−	0.745611i	$-0.732158\pi$
$947$	−12.2911	+	6.71144i	−0.399407	+	0.218093i	0.266975	+	0.963704i	$0.413976\pi$
$948$	6.63165	+	5.23222i	0.215386	+	0.169935i
$949$	−7.58870	−	25.8447i	−0.246339	−	0.838955i
$950$	18.2679	+	15.6856i	0.592689	+	0.508909i
$951$	6.48152	+	10.6716i	0.210178	+	0.346052i
$952$	29.6223	−	2.11863i	0.960064	−	0.0686651i
$953$	−4.08652	−	0.888969i	−0.132375	−	0.0287965i	0.145889	−	0.989301i	$-0.453396\pi$
$953$	−4.08652	−	0.888969i	−0.132375	−	0.0287965i	−0.278265	+	0.960504i	$0.589759\pi$
$954$	−14.5252	−	25.3437i	−0.470272	−	0.820532i
$955$	25.6688	−	12.9213i	0.830623	−	0.418124i
$956$	−1.99943	−	3.11118i	−0.0646663	−	0.100623i
$957$	−6.69296	−	3.87835i	−0.216353	−	0.125369i
$958$	0.545397	+	1.46227i	0.0176210	+	0.0472437i
$959$	−37.4956	−	24.0970i	−1.21080	−	0.778132i
$960$	−2.77281	−	2.70398i	−0.0894922	−	0.0872705i
$961$	16.0674	+	18.5428i	0.518304	+	0.598155i
$962$	−13.7178	+	7.49047i	−0.442279	+	0.241503i
$963$	20.8572	−	0.430320i	0.672114	−	0.0138669i
$964$	7.19559	+	1.03457i	0.231754	+	0.0333213i
$965$	11.3789	−	22.8606i	0.366299	−	0.735910i
$966$	40.5884	−	7.28622i	1.30591	−	0.234430i
$967$	−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
$969$	8.35243	−	49.1930i	0.268319	−	1.58031i
$970$	5.66332	−	0.215046i	0.181838	−	0.00690471i
$971$	8.26099	−	7.15818i	0.265108	−	0.229717i	−0.512155	−	0.858893i	$-0.671153\pi$
$971$	8.26099	−	7.15818i	0.265108	−	0.229717i	0.777263	+	0.629176i	$0.216607\pi$
$972$	14.6902	+	5.21511i	0.471189	+	0.167275i
$973$	−40.8975	+	8.89672i	−1.31112	+	0.285216i
$974$	4.50374	−	9.86181i	0.144309	−	0.315993i
$975$	−26.3078	−	20.5645i	−0.842522	−	0.658592i
$976$	3.03768	−	1.95220i	0.0972338	−	0.0624883i
$977$	−0.456554	−	0.341772i	−0.0146064	−	0.0109342i	0.591950	−	0.805975i	$-0.298358\pi$
$977$	−0.456554	−	0.341772i	−0.0146064	−	0.0109342i	−0.606556	+	0.795041i	$0.707449\pi$
$978$	−23.5434	+	8.10669i	−0.752836	+	0.259223i
$979$	−6.14420	−	9.56056i	−0.196369	−	0.305557i
$980$	−15.0168	+	36.4862i	−0.479695	+	1.16551i
$981$	−38.6672	−	1.96486i	−1.23455	−	0.0627332i
$982$	2.69015	+	12.3664i	0.0858462	+	0.394629i
$983$	52.0815	+	28.4387i	1.66114	+	0.907053i	0.985470	+	0.169851i	$0.0543288\pi$
$983$	52.0815	+	28.4387i	1.66114	+	0.907053i	0.675673	+	0.737201i	$0.263853\pi$
$984$	7.77030	−	0.916559i	0.247708	−	0.0292188i
$985$	15.0045	−	16.1890i	0.478084	−	0.515824i
$986$	24.6487	−	11.2567i	0.784975	−	0.358486i
$987$	−1.87227	−	40.6601i	−0.0595950	−	1.29423i
$988$	13.1294	−	13.1294i	0.417701	−	0.417701i
$989$	50.1982	+	4.15537i	1.59621	+	0.132133i
$990$	6.59056	+	0.556356i	0.209462	+	0.0176821i
$991$	−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
$993$	6.21245	+	0.603158i	0.197146	+	0.0191406i
$994$	20.7664	−	17.9942i	0.658671	−	0.570742i
$995$	−18.5629	−	26.6074i	−0.588483	−	0.843513i
$996$	−16.0672	+	6.85023i	−0.509107	+	0.217058i
$997$	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
$999$	19.7699	−	7.26686i	0.625492	−	0.229913i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(1.00245 + 1.41248i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.92562 - 1.13666i) q^{5} +(0.530001 - 1.64897i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.990189 + 2.83188i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(1.00245 + 1.41248i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.92562 - 1.13666i) q^{5} +(0.530001 - 1.64897i) q^{6} +(-1.05526 - 4.85093i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.990189 + 2.83188i) q^{9} +(0.244034 + 2.22271i) q^{10} +(-0.975922 + 0.140316i) q^{11} +(-1.63769 + 0.563902i) q^{12} +(-0.819594 + 3.76761i) q^{13} +(-3.25098 + 3.75183i) q^{14} +(-0.324824 - 3.85934i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-2.86697 + 5.25046i) q^{17} +(2.86043 - 0.904393i) q^{18} +(-1.35672 + 4.62056i) q^{19} +(1.63313 - 1.52738i) q^{20} +(5.79399 - 6.35334i) 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} +(-4.99258 + 1.44019i) q^{27} +(4.95173 + 0.354155i) q^{28} +(4.34619 - 1.27616i) q^{29} +(-2.89490 + 2.57285i) q^{30} +(-1.05620 + 2.31275i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-1.17651 - 1.23781i) q^{33} +(5.92132 - 0.851357i) q^{34} +(-3.48185 + 10.5405i) q^{35} +(-2.43820 - 1.74791i) q^{36} +(-4.04328 + 0.289181i) q^{37} +(4.51200 - 1.68289i) q^{38} +(-6.14327 + 2.61918i) q^{39} +(-2.20143 - 0.392061i) q^{40} +(3.41394 - 2.95819i) q^{41} +(-8.55832 - 0.830916i) q^{42} +(-9.84064 - 3.67037i) q^{43} +(0.140316 - 0.975922i) q^{44} +(5.12561 - 4.32760i) q^{45} +(3.80686 + 2.91682i) q^{46} +(3.34725 - 3.34725i) q^{47} +(-0.0796710 - 1.73022i) q^{48} +(-16.0505 + 7.33003i) q^{49} +(2.05655 - 4.55748i) q^{50} +(-10.2901 + 1.21379i) q^{51} +(-3.38409 - 1.84785i) q^{52} +(-2.06975 - 9.51449i) q^{53} +(4.14488 + 3.13369i) q^{54} +(2.03874 + 0.839097i) q^{55} +(-2.68395 - 4.17630i) q^{56} +(-7.88648 + 2.71554i) q^{57} +(-3.62619 - 2.71453i) q^{58} +(-5.33866 + 3.43095i) q^{59} +(3.79452 + 0.775635i) q^{60} +(-1.50002 + 3.28459i) q^{61} +(2.48440 - 0.540449i) q^{62} +(14.7821 + 1.81499i) q^{63} +(0.755750 - 0.654861i) q^{64} +(5.86073 - 6.32338i) q^{65} +(-0.285862 + 1.68363i) q^{66} +(11.9434 - 8.94072i) q^{67} +(-4.23006 - 4.23006i) q^{68} +(-6.46331 - 5.21782i) q^{69} +(10.5247 - 3.52932i) q^{70} +(-5.47868 - 0.787715i) q^{71} +(0.0618820 + 2.99936i) q^{72} +(-6.13140 + 3.34800i) q^{73} +(2.65455 + 3.06351i) q^{74} +(-3.76128 + 7.80082i) q^{75} +(-4.05116 - 2.60352i) q^{76} +(1.71051 + 4.58606i) q^{77} +(5.77829 + 3.34832i) q^{78} +(-2.63670 - 4.10278i) q^{79} +(1.00541 + 1.99729i) q^{80} +(-7.03905 - 5.60819i) q^{81} +(-4.41405 - 0.960219i) q^{82} +(10.0586 - 0.719406i) q^{83} +(4.46363 + 7.34924i) q^{84} +(11.4887 - 6.85160i) q^{85} +(2.95899 + 10.0774i) q^{86} +(6.15939 + 4.85962i) q^{87} +(-0.865354 + 0.472519i) q^{88} +(4.78829 + 10.4849i) q^{89} +(-6.53609 - 1.50983i) q^{90} +19.1413 q^{91} +(0.0536700 - 4.79553i) q^{92} +(-4.32549 + 0.826558i) q^{93} +(-4.68554 - 0.673679i) q^{94} +(7.86453 - 7.35529i) q^{95} +(-1.33737 + 1.10066i) q^{96} +(0.180812 - 2.52808i) q^{97} +(15.4867 + 8.45639i) q^{98} +(0.568988 - 2.90263i) 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

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