LMFDB - Embedded newform 552.2.bb.a.445.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			445.10
Character	$\chi$	$=$	552.445
Dual form			552.2.bb.a.325.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02143 - 0.978105i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.0866214 + 1.99812i) q^{4} +(-0.620811 + 0.537936i) q^{5} +(1.33544 + 0.465400i) q^{6} +(-1.86742 - 1.20011i) q^{7} +(1.86590 - 2.12566i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-1.02143 - 0.978105i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.0866214 + 1.99812i) q^{4} +(-0.620811 + 0.537936i) q^{5} +(1.33544 + 0.465400i) q^{6} +(-1.86742 - 1.20011i) q^{7} +(1.86590 - 2.12566i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.16027 + 0.0577568i) q^{10} +(2.07838 - 0.298827i) q^{11} +(-0.908844 - 1.78157i) q^{12} +(-1.23990 - 1.92933i) q^{13} +(0.733588 + 3.05236i) q^{14} +(0.341243 - 0.747218i) q^{15} +(-3.98499 + 0.346161i) q^{16} +(3.44530 - 1.01163i) q^{17} +(-1.40809 + 0.131420i) q^{18} +(-1.51215 + 5.14991i) q^{19} +(-1.12864 - 1.19386i) q^{20} +(2.19721 + 0.315911i) q^{21} +(-2.41520 - 1.72765i) q^{22} +(0.693775 + 4.74538i) q^{23} +(-0.814249 + 2.70869i) q^{24} +(-0.615543 + 4.28119i) q^{25} +(-0.620615 + 3.18342i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(2.23622 - 3.83528i) q^{28} +(0.292928 + 0.997622i) q^{29} +(-1.07941 + 0.429456i) q^{30} +(-3.51077 + 7.68752i) q^{31} +(4.40896 + 3.54416i) q^{32} +(-1.76643 + 1.13521i) q^{33} +(-4.50860 - 2.33656i) q^{34} +(1.80490 - 0.259505i) q^{35} +(1.56681 + 1.24303i) q^{36} +(-1.54145 - 1.33567i) q^{37} +(6.58170 - 3.78121i) q^{38} +(1.92933 + 1.23990i) q^{39} +(-0.0149010 + 2.32337i) q^{40} +(7.73284 + 8.92418i) q^{41} +(-1.93529 - 2.47178i) q^{42} +(-8.42185 + 3.84613i) q^{43} +(0.777125 + 4.12698i) q^{44} +0.821451i q^{45} +(3.93284 - 5.52564i) q^{46} -1.30994 q^{47} +(3.48108 - 1.97030i) q^{48} +(-0.860942 - 1.88520i) q^{49} +(4.81619 - 3.77086i) q^{50} +(-2.71371 + 2.35144i) q^{51} +(3.74763 - 2.64460i) q^{52} +(0.123462 - 0.192111i) q^{53} +(1.22625 - 0.704487i) q^{54} +(-1.12953 + 1.30355i) q^{55} +(-6.03544 + 1.73020i) q^{56} +(-0.763849 - 5.31269i) q^{57} +(0.676575 - 1.30551i) q^{58} +(-2.43219 - 3.78456i) q^{59} +(1.52259 + 0.617121i) q^{60} +(12.3192 + 5.62598i) q^{61} +(11.1052 - 4.41833i) q^{62} +(-2.12988 + 0.625390i) q^{63} +(-1.03686 - 7.93252i) q^{64} +(1.80760 + 0.530759i) q^{65} +(2.91463 + 0.568215i) q^{66} +(8.00457 + 1.15088i) q^{67} +(2.31980 + 6.79651i) q^{68} +(-2.60238 - 4.02835i) q^{69} +(-2.09739 - 1.50031i) q^{70} +(0.139522 - 0.970394i) q^{71} +(-0.384564 - 2.80216i) q^{72} +(10.5247 + 3.09033i) q^{73} +(0.268048 + 2.87199i) q^{74} +(-1.21855 - 4.15002i) q^{75} +(-10.4211 - 2.57537i) q^{76} +(-4.23983 - 1.93627i) q^{77} +(-0.757909 - 3.15355i) q^{78} +(-9.77608 + 6.28270i) q^{79} +(2.28772 - 2.35857i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.830256 - 16.6789i) q^{82} +(2.45012 + 2.12304i) q^{83} +(-0.440903 + 4.41765i) q^{84} +(-1.59469 + 2.48138i) q^{85} +(12.3642 + 4.30892i) q^{86} +(-0.680884 - 0.785782i) q^{87} +(3.24285 - 4.97552i) q^{88} +(4.44564 + 9.73460i) q^{89} +(0.803465 - 0.839051i) q^{90} +5.09088i q^{91} +(-9.42177 + 1.79730i) q^{92} -8.45124i q^{93} +(1.33801 + 1.28126i) q^{94} +(-1.83156 - 4.01056i) q^{95} +(-5.48283 - 1.39234i) q^{96} +(-5.83731 - 6.73661i) q^{97} +(-0.964535 + 2.76768i) q^{98} +(1.13521 - 1.76643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.02143	−	0.978105i	−0.722257	−	0.691625i
$2$	−1.02143	−	0.978105i	−0.722257	−	0.691625i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	0.0866214	+	1.99812i	0.0433107	+	0.999062i
$5$	−0.620811	+	0.537936i	−0.277635	+	0.240572i	−0.782536	−	0.622605i	$-0.786074\pi$
$5$	−0.620811	+	0.537936i	−0.277635	+	0.240572i	0.504901	+	0.863177i	$0.331529\pi$
$6$	1.33544	+	0.465400i	0.545192	+	0.189999i
$7$	−1.86742	−	1.20011i	−0.705817	−	0.453601i	0.137861	−	0.990452i	$-0.455977\pi$
$7$	−1.86742	−	1.20011i	−0.705817	−	0.453601i	−0.843677	+	0.536851i	$0.819614\pi$
$8$	1.86590	−	2.12566i	0.659694	−	0.751534i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	1.16027	+	0.0577568i	0.366910	+	0.0182643i
$11$	2.07838	−	0.298827i	0.626656	−	0.0900996i	0.178332	−	0.983970i	$-0.442930\pi$
$11$	2.07838	−	0.298827i	0.626656	−	0.0900996i	0.448325	+	0.893871i	$0.352021\pi$
$12$	−0.908844	−	1.78157i	−0.262361	−	0.514296i
$13$	−1.23990	−	1.92933i	−0.343887	−	0.535099i	0.625631	−	0.780119i	$-0.284842\pi$
$13$	−1.23990	−	1.92933i	−0.343887	−	0.535099i	−0.969518	+	0.245020i	$0.921205\pi$
$14$	0.733588	+	3.05236i	0.196060	+	0.815776i
$15$	0.341243	−	0.747218i	0.0881086	−	0.192931i
$16$	−3.98499	+	0.346161i	−0.996248	+	0.0865402i
$17$	3.44530	−	1.01163i	0.835608	−	0.245357i	0.164184	−	0.986430i	$-0.447501\pi$
$17$	3.44530	−	1.01163i	0.835608	−	0.245357i	0.671424	+	0.741073i	$0.265683\pi$
$18$	−1.40809	+	0.131420i	−0.331891	+	0.0309759i
$19$	−1.51215	+	5.14991i	−0.346911	+	1.18147i	0.582626	+	0.812740i	$0.302025\pi$
$19$	−1.51215	+	5.14991i	−0.346911	+	1.18147i	−0.929537	+	0.368729i	$0.879793\pi$
$20$	−1.12864	−	1.19386i	−0.252371	−	0.266955i
$21$	2.19721	+	0.315911i	0.479470	+	0.0689373i
$22$	−2.41520	−	1.72765i	−0.514922	−	0.368336i
$23$	0.693775	+	4.74538i	0.144662	+	0.989481i
$23$	0.693775	+	4.74538i	0.144662	+	0.989481i
$24$	−0.814249	+	2.70869i	−0.166208	+	0.552909i
$25$	−0.615543	+	4.28119i	−0.123109	+	0.856239i
$26$	−0.620615	+	3.18342i	−0.121713	+	0.624320i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	2.23622	−	3.83528i	0.422606	−	0.724800i
$29$	0.292928	+	0.997622i	0.0543954	+	0.185254i	0.982209	−	0.187790i	$-0.0601324\pi$
$29$	0.292928	+	0.997622i	0.0543954	+	0.185254i	−0.927814	+	0.373044i	$0.878314\pi$
$30$	−1.07941	+	0.429456i	−0.197073	+	0.0784077i
$31$	−3.51077	+	7.68752i	−0.630553	+	1.38072i	0.277036	+	0.960860i	$0.410648\pi$
$31$	−3.51077	+	7.68752i	−0.630553	+	1.38072i	−0.907589	+	0.419860i	$0.862079\pi$
$32$	4.40896	+	3.54416i	0.779401	+	0.626526i
$33$	−1.76643	+	1.13521i	−0.307496	+	0.197615i
$34$	−4.50860	−	2.33656i	−0.773219	−	0.400716i
$35$	1.80490	−	0.259505i	0.305083	−	0.0438644i
$36$	1.56681	+	1.24303i	0.261134	+	0.207171i
$37$	−1.54145	−	1.33567i	−0.253413	−	0.219584i	0.518885	−	0.854844i	$-0.326347\pi$
$37$	−1.54145	−	1.33567i	−0.253413	−	0.219584i	−0.772298	+	0.635261i	$0.780893\pi$
$38$	6.58170	−	3.78121i	1.06769	−	0.613393i
$39$	1.92933	+	1.23990i	0.308940	+	0.198543i
$40$	−0.0149010	+	2.32337i	−0.00235605	+	0.367357i
$41$	7.73284	+	8.92418i	1.20767	+	1.39372i	0.896309	+	0.443430i	$0.146238\pi$
$41$	7.73284	+	8.92418i	1.20767	+	1.39372i	0.311358	+	0.950293i	$0.399216\pi$
$42$	−1.93529	−	2.47178i	−0.298622	−	0.381404i
$43$	−8.42185	+	3.84613i	−1.28432	+	0.586530i	−0.936380	−	0.350987i	$-0.885846\pi$
$43$	−8.42185	+	3.84613i	−1.28432	+	0.586530i	−0.347940	+	0.937517i	$0.613119\pi$
$44$	0.777125	+	4.12698i	0.117156	+	0.622166i
$45$			0.821451i			0.122455i
$46$	3.93284	−	5.52564i	0.579866	−	0.814712i
$47$	−1.30994			−0.191075			−0.0955373	−	0.995426i	$-0.530457\pi$
$47$	−1.30994			−0.191075			−0.0955373	+	0.995426i	$0.530457\pi$
$48$	3.48108	−	1.97030i	0.502450	−	0.284389i
$49$	−0.860942	−	1.88520i	−0.122992	−	0.269314i
$50$	4.81619	−	3.77086i	0.681112	−	0.533280i
$51$	−2.71371	+	2.35144i	−0.379995	+	0.329268i
$52$	3.74763	−	2.64460i	0.519703	−	0.366740i
$53$	0.123462	−	0.192111i	0.0169588	−	0.0263885i	−0.832671	−	0.553769i	$-0.813189\pi$
$53$	0.123462	−	0.192111i	0.0169588	−	0.0263885i	0.849629	+	0.527380i	$0.176826\pi$
$54$	1.22625	−	0.704487i	0.166872	−	0.0958685i
$55$	−1.12953	+	1.30355i	−0.152306	+	0.175771i
$56$	−6.03544	+	1.73020i	−0.806520	+	0.231207i
$57$	−0.763849	−	5.31269i	−0.101174	−	0.703683i
$58$	0.676575	−	1.30551i	0.0888386	−	0.171422i
$59$	−2.43219	−	3.78456i	−0.316644	−	0.492707i	0.646052	−	0.763293i	$-0.276419\pi$
$59$	−2.43219	−	3.78456i	−0.316644	−	0.492707i	−0.962696	+	0.270586i	$0.912783\pi$
$60$	1.52259	+	0.617121i	0.196566	+	0.0796699i
$61$	12.3192	+	5.62598i	1.57731	+	0.720333i	0.995656	−	0.0931047i	$-0.0296791\pi$
$61$	12.3192	+	5.62598i	1.57731	+	0.720333i	0.581652	+	0.813437i	$0.302406\pi$
$62$	11.1052	−	4.41833i	1.41036	−	0.561128i
$63$	−2.12988	+	0.625390i	−0.268340	+	0.0787917i
$64$	−1.03686	−	7.93252i	−0.129607	−	0.991565i
$65$	1.80760	+	0.530759i	0.224205	+	0.0658326i
$66$	2.91463	+	0.568215i	0.358767	+	0.0699424i
$67$	8.00457	+	1.15088i	0.977914	+	0.140603i	0.612696	−	0.790319i	$-0.290085\pi$
$67$	8.00457	+	1.15088i	0.977914	+	0.140603i	0.365219	+	0.930922i	$0.380994\pi$
$68$	2.31980	+	6.79651i	0.281317	+	0.824197i
$69$	−2.60238	−	4.02835i	−0.313290	−	0.484956i
$70$	−2.09739	−	1.50031i	−0.250686	−	0.179322i
$71$	0.139522	−	0.970394i	0.0165582	−	0.115165i	−0.979866	−	0.199656i	$-0.936017\pi$
$71$	0.139522	−	0.970394i	0.0165582	−	0.115165i	0.996424	+	0.0844915i	$0.0269266\pi$
$72$	−0.384564	−	2.80216i	−0.0453213	−	0.330238i
$73$	10.5247	+	3.09033i	1.23182	+	0.361695i	0.831937	−	0.554870i	$-0.187232\pi$
$73$	10.5247	+	3.09033i	1.23182	+	0.361695i	0.399885	+	0.916566i	$0.369050\pi$
$74$	0.268048	+	2.87199i	0.0311599	+	0.333862i
$75$	−1.21855	−	4.15002i	−0.140707	−	0.479203i
$76$	−10.4211	−	2.57537i	−1.19539	−	0.295415i
$77$	−4.23983	−	1.93627i	−0.483174	−	0.220658i
$78$	−0.757909	−	3.15355i	−0.0858163	−	0.357070i
$79$	−9.77608	+	6.28270i	−1.09989	+	0.706859i	−0.959068	−	0.283175i	$-0.908612\pi$
$79$	−9.77608	+	6.28270i	−1.09989	+	0.706859i	−0.140826	+	0.990034i	$0.544976\pi$
$80$	2.28772	−	2.35857i	0.255775	−	0.263696i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	0.830256	−	16.6789i	0.0916864	−	1.84188i
$83$	2.45012	+	2.12304i	0.268936	+	0.233034i	0.778880	−	0.627174i	$-0.215788\pi$
$83$	2.45012	+	2.12304i	0.268936	+	0.233034i	−0.509944	+	0.860208i	$0.670334\pi$
$84$	−0.440903	+	4.41765i	−0.0481065	+	0.482006i
$85$	−1.59469	+	2.48138i	−0.172968	+	0.269144i
$86$	12.3642	+	4.30892i	1.33327	+	0.464643i
$87$	−0.680884	−	0.785782i	−0.0729985	−	0.0842447i
$88$	3.24285	−	4.97552i	0.345689	−	0.530392i
$89$	4.44564	+	9.73460i	0.471237	+	1.03187i	0.984781	+	0.173802i	$0.0556052\pi$
$89$	4.44564	+	9.73460i	0.471237	+	1.03187i	−0.513544	+	0.858063i	$0.671668\pi$
$90$	0.803465	−	0.839051i	0.0846927	−	0.0884438i
$91$			5.09088i			0.533669i
$92$	−9.42177	+	1.79730i	−0.982287	+	0.187381i
$93$		−	8.45124i		−	0.876353i
$94$	1.33801	+	1.28126i	0.138005	+	0.132152i
$95$	−1.83156	−	4.01056i	−0.187914	−	0.411475i
$96$	−5.48283	−	1.39234i	−0.559589	−	0.142105i
$97$	−5.83731	−	6.73661i	−0.592689	−	0.684000i	0.377594	−	0.925971i	$-0.376751\pi$
$97$	−5.83731	−	6.73661i	−0.592689	−	0.684000i	−0.970283	+	0.241972i	$0.922206\pi$
$98$	−0.964535	+	2.76768i	−0.0974327	+	0.279578i
$99$	1.13521	−	1.76643i	0.114093	−	0.177533i
$100$	−8.60767	−	0.859087i	−0.860767	−	0.0859087i
$101$	−9.10004	−	7.88523i	−0.905488	−	0.784610i	0.0716026	−	0.997433i	$-0.477189\pi$
$101$	−9.10004	−	7.88523i	−0.905488	−	0.784610i	−0.977091	+	0.212823i	$0.931734\pi$
$102$	5.07181	+	0.252468i	0.502184	+	0.0249981i
$103$	−1.41227	−	9.82258i	−0.139155	−	0.967848i	−0.933038	−	0.359777i	$-0.882853\pi$
$103$	−1.41227	−	9.82258i	−0.139155	−	0.967848i	0.793883	−	0.608071i	$-0.208056\pi$
$104$	−6.41462	−	0.964313i	−0.629006	−	0.0945587i
$105$	−1.53399	+	0.985836i	−0.149702	+	0.0962077i
$106$	−0.314012	+	0.0754681i	−0.0304996	+	0.00733011i
$107$	1.12788	+	0.515084i	0.109036	+	0.0497950i	0.469186	−	0.883099i	$-0.344547\pi$
$107$	1.12788	+	0.515084i	0.109036	+	0.0497950i	−0.360150	+	0.932894i	$0.617275\pi$
$108$	−1.94159	−	0.479824i	−0.186830	−	0.0461711i
$109$	−0.785142	−	2.67395i	−0.0752030	−	0.256118i	0.913307	−	0.407271i	$-0.133520\pi$
$109$	−0.785142	−	2.67395i	−0.0752030	−	0.256118i	−0.988510	+	0.151153i	$0.951701\pi$
$110$	2.42875	−	0.226679i	0.231572	−	0.0216130i
$111$	1.95701	+	0.574630i	0.185751	+	0.0545415i
$112$	7.85707	+	4.13602i	0.742423	+	0.390818i
$113$	−1.11108	+	7.72776i	−0.104522	+	0.726966i	0.868405	+	0.495855i	$0.165145\pi$
$113$	−1.11108	+	7.72776i	−0.104522	+	0.726966i	−0.972927	+	0.231111i	$0.925764\pi$
$114$	−4.41615	+	6.17364i	−0.413611	+	0.578215i
$115$	−2.98342	−	2.57278i	−0.278205	−	0.239913i
$116$	−1.96800	+	0.671722i	−0.182724	+	0.0623679i
$117$	−2.27005	−	0.326384i	−0.209866	−	0.0301742i
$118$	−1.21740	+	6.24458i	−0.112070	+	0.574860i
$119$	−7.64788	−	2.24562i	−0.701080	−	0.205856i
$120$	−0.951607	−	2.11960i	−0.0868694	−	0.193492i
$121$	−6.32404	+	1.85691i	−0.574913	+	0.168810i
$122$	−7.08033	−	17.7960i	−0.641023	−	1.61117i
$123$	−10.7413	−	4.90538i	−0.968509	−	0.442303i
$124$	−15.6647	−	6.34905i	−1.40673	−	0.570162i
$125$	−4.14142	−	6.44418i	−0.370420	−	0.576385i
$126$	2.78721	+	1.44446i	0.248305	+	0.128683i
$127$	0.535830	+	3.72678i	0.0475472	+	0.330698i	0.999687	+	0.0250339i	$0.00796938\pi$
$127$	0.535830	+	3.72678i	0.0475472	+	0.330698i	−0.952139	+	0.305664i	$0.901122\pi$
$128$	−6.69977	+	9.11664i	−0.592181	+	0.805805i
$129$	6.06305	−	6.99713i	0.533822	−	0.616063i
$130$	−1.32719	−	2.31015i	−0.116402	−	0.202614i
$131$	1.84397	−	2.86928i	0.161109	−	0.250690i	−0.751309	−	0.659951i	$-0.770577\pi$
$131$	1.84397	−	2.86928i	0.161109	−	0.250690i	0.912417	+	0.409261i	$0.134213\pi$
$132$	−2.42131	−	3.43121i	−0.210748	−	0.298648i
$133$	9.00429	−	7.80226i	0.780771	−	0.676542i
$134$	−7.05039	−	9.00486i	−0.609061	−	0.777901i
$135$	−0.341243	−	0.747218i	−0.0293695	−	0.0643103i
$136$	4.27819	−	9.21113i	0.366852	−	0.789848i
$137$	8.50925			0.726995			0.363497	−	0.931595i	$-0.381583\pi$
$137$	8.50925			0.726995			0.363497	+	0.931595i	$0.381583\pi$
$138$	−1.28201	+	6.66006i	−0.109132	+	0.566942i
$139$			19.6248i			1.66455i	0.554362	+	0.832275i	$0.312962\pi$
$139$			19.6248i			1.66455i	−0.554362	+	0.832275i	$0.687038\pi$
$140$	0.674866	+	3.58393i	0.0570366	+	0.302897i
$141$	1.19156	−	0.544169i	0.100348	−	0.0458273i
$142$	−1.09166	+	0.854719i	−0.0916100	+	0.0717264i
$143$	−3.15353	−	3.63937i	−0.263711	−	0.304339i
$144$	−2.34801	+	3.23834i	−0.195667	+	0.269862i
$145$	−0.718510	−	0.461758i	−0.0596690	−	0.0383470i
$146$	−7.72752	−	13.4508i	−0.639534	−	1.11320i
$147$	1.56628	+	1.35719i	0.129185	+	0.111939i
$148$	2.53532	−	3.19571i	0.208402	−	0.262685i
$149$	−18.5403	+	2.66569i	−1.51888	+	0.218382i	−0.850713	−	0.525631i	$-0.823829\pi$
$149$	−18.5403	+	2.66569i	−1.51888	+	0.218382i	−0.668166	+	0.744012i	$0.732920\pi$
$150$	−2.81449	+	5.43081i	−0.229802	+	0.443424i
$151$	−5.33795	+	3.43049i	−0.434396	+	0.279170i	−0.739509	−	0.673147i	$-0.764942\pi$
$151$	−5.33795	+	3.43049i	−0.434396	+	0.279170i	0.305113	+	0.952316i	$0.401306\pi$
$152$	8.12544	+	12.8235i	0.659060	+	1.04012i
$153$	1.49165	−	3.26626i	0.120593	−	0.264062i
$154$	2.43680	+	6.12475i	0.196363	+	0.493547i
$155$	−1.95587	−	6.66107i	−0.157099	−	0.535030i
$156$	−2.31036	+	3.96244i	−0.184977	+	0.317249i
$157$	−0.662948	+	2.25779i	−0.0529090	+	0.180192i	−0.981708	−	0.190392i	$-0.939024\pi$
$157$	−0.662948	+	2.25779i	−0.0529090	+	0.180192i	0.928799	+	0.370584i	$0.120842\pi$
$158$	16.1307	+	3.14471i	1.28329	+	0.250180i
$159$	−0.0324994	+	0.226038i	−0.00257737	+	0.0179260i
$160$	−4.64366	+	0.171479i	−0.367114	+	0.0135566i
$161$	4.39944	−	9.69421i	0.346724	−	0.764011i
$162$	−0.822785	+	1.15023i	−0.0646441	+	0.0903704i
$163$	9.93410	+	1.42831i	0.778099	+	0.111874i	0.519910	−	0.854221i	$-0.325965\pi$
$163$	9.93410	+	1.42831i	0.778099	+	0.111874i	0.258188	+	0.966095i	$0.416874\pi$
$164$	−17.1618	+	16.2242i	−1.34011	+	1.26690i
$165$	0.485946	−	1.65498i	0.0378308	−	0.128840i
$166$	−0.426059	−	4.56501i	−0.0330686	−	0.354313i
$167$	−9.02738	+	2.65068i	−0.698560	+	0.205116i	−0.611683	−	0.791103i	$-0.709507\pi$
$167$	−9.02738	+	2.65068i	−0.698560	+	0.205116i	−0.0868773	+	0.996219i	$0.527689\pi$
$168$	4.77128	−	4.08106i	0.368112	−	0.314860i
$169$	3.21545	−	7.04086i	0.247342	−	0.541605i
$170$	4.05591	−	0.974777i	0.311074	−	0.0747620i
$171$	2.90179	+	4.51528i	0.221906	+	0.345292i
$172$	−8.41456	−	16.4947i	−0.641604	−	1.25771i
$173$	18.4590	−	2.65400i	1.40341	−	0.201780i	0.601333	−	0.798999i	$-0.294637\pi$
$173$	18.4590	−	2.65400i	1.40341	−	0.201780i	0.802078	+	0.597219i	$0.203728\pi$
$174$	−0.0731048	+	1.46859i	−0.00554206	+	0.111334i
$175$	6.28740	−	7.25604i	0.475283	−	0.548505i
$176$	−8.17891	+	1.91028i	−0.616508	+	0.143993i
$177$	3.78456	+	2.43219i	0.284465	+	0.182814i
$178$	4.98056	−	14.2915i	0.373309	−	1.07119i
$179$	−1.84948	+	1.60258i	−0.138237	+	0.119783i	−0.721235	−	0.692691i	$-0.756425\pi$
$179$	−1.84948	+	1.60258i	−0.138237	+	0.119783i	0.582998	+	0.812474i	$0.301880\pi$
$180$	−1.64136	+	0.0711553i	−0.122340	+	0.00530360i
$181$	10.0921	−	4.60893i	0.750144	−	0.342579i	−0.00338496	−	0.999994i	$-0.501077\pi$
$181$	10.0921	−	4.60893i	0.750144	−	0.342579i	0.753529	+	0.657415i	$0.228350\pi$
$182$	4.97942	−	5.19996i	0.369099	−	0.385446i
$183$	−13.5430			−1.00113
$184$	11.3816	+	7.37967i	0.839062	+	0.544036i
$185$	1.67546			0.123182
$186$	−8.26620	+	8.63232i	−0.606107	+	0.632952i
$187$	6.85835	−	3.13211i	0.501533	−	0.229042i
$188$	−0.113469	−	2.61742i	−0.00827557	−	0.190895i
$189$	1.67761	−	1.45366i	0.122028	−	0.105738i
$190$	−2.05194	+	5.88795i	−0.148864	+	0.427157i
$191$	7.54510	+	4.84894i	0.545945	+	0.350857i	0.784360	−	0.620306i	$-0.212992\pi$
$191$	7.54510	+	4.84894i	0.545945	+	0.350857i	−0.238415	+	0.971163i	$0.576628\pi$
$192$	4.23845	+	6.78495i	0.305884	+	0.489662i
$193$	−3.42066	+	3.94765i	−0.246224	+	0.284158i	−0.865386	−	0.501105i	$-0.832927\pi$
$193$	−3.42066	+	3.94765i	−0.246224	+	0.284158i	0.619162	+	0.785263i	$0.287472\pi$
$194$	−0.626737	+	12.5905i	−0.0449971	+	0.903942i
$195$	−1.86474	+	0.268109i	−0.133537	+	0.0191997i
$196$	3.69228	−	1.88357i	0.263735	−	0.134540i
$197$	−6.28117	−	9.77370i	−0.447515	−	0.696347i	0.542064	−	0.840337i	$-0.317643\pi$
$197$	−6.28117	−	9.77370i	−0.447515	−	0.696347i	−0.989579	+	0.143990i	$0.954007\pi$
$198$	−2.88729	+	0.693916i	−0.205191	+	0.0493145i
$199$	5.66574	−	12.4062i	0.401634	−	0.879455i	−0.595468	−	0.803379i	$-0.703033\pi$
$199$	5.66574	−	12.4062i	0.401634	−	0.879455i	0.997102	−	0.0760763i	$-0.0242393\pi$
$200$	7.95182	+	9.29670i	0.562279	+	0.657376i
$201$	−7.75931	+	2.27834i	−0.547300	+	0.160702i
$202$	1.58243	+	16.9550i	0.111340	+	1.19295i
$203$	0.650242	−	2.21452i	0.0456381	−	0.155429i
$204$	−4.93354	−	5.21864i	−0.345417	−	0.365378i
$205$	−9.60127	−	1.38045i	−0.670582	−	0.0964152i
$206$	−8.16498	+	11.4144i	−0.568881	+	0.795278i
$207$	4.04065	+	2.58325i	0.280844	+	0.179548i
$208$	5.60886	+	7.25915i	0.388905	+	0.503331i
$209$	−1.60390	+	11.1554i	−0.110944	+	0.771632i
$210$	2.53111	+	0.493445i	0.174663	+	0.0340510i
$211$	−2.55826	+	8.71263i	−0.176118	+	0.599802i	0.823361	+	0.567518i	$0.192096\pi$
$211$	−2.55826	+	8.71263i	−0.176118	+	0.599802i	−0.999479	+	0.0322842i	$0.989722\pi$
$212$	0.394556	+	0.230052i	0.0270982	+	0.0158000i
$213$	0.276203	+	0.940661i	0.0189251	+	0.0644530i
$214$	−0.648236	−	1.62930i	−0.0443125	−	0.111377i
$215$	3.15941	−	6.91814i	0.215470	−	0.471813i
$216$	1.51387	+	2.38918i	0.103006	+	0.162563i
$217$	15.7820	−	10.1425i	1.07135	−	0.688515i
$218$	−1.81344	+	3.49919i	−0.122822	+	0.236995i
$219$	−10.8574	+	1.56105i	−0.733672	+	0.105486i
$220$	−2.70250	−	2.14403i	−0.182203	−	0.144551i
$221$	−6.22361	−	5.39279i	−0.418645	−	0.362758i
$222$	−1.43689	−	2.50111i	−0.0964380	−	0.167863i
$223$	−19.0959	−	12.2722i	−1.27876	−	0.821806i	−0.288021	−	0.957624i	$-0.592997\pi$
$223$	−19.0959	−	12.2722i	−1.27876	−	0.821806i	−0.990734	+	0.135818i	$0.956634\pi$
$224$	−3.97995	−	11.9097i	−0.265921	−	0.795749i
$225$	2.83242	+	3.26878i	0.188828	+	0.217919i
$226$	8.69345	−	6.80657i	0.578279	−	0.452767i
$227$	19.9592	−	9.11506i	1.32474	−	0.604988i	0.377646	−	0.925950i	$-0.376734\pi$
$227$	19.9592	−	9.11506i	1.32474	−	0.604988i	0.947092	+	0.320962i	$0.104006\pi$
$228$	10.5492	−	1.98646i	0.698641	−	0.131556i
$229$			22.6562i			1.49717i	0.663041	+	0.748583i	$0.269266\pi$
$229$			22.6562i			1.49717i	−0.663041	+	0.748583i	$0.730734\pi$
$230$	0.530888	+	5.54600i	0.0350058	+	0.365692i
$231$	4.66104			0.306674
$232$	2.66718	+	1.23879i	0.175109	+	0.0813308i
$233$	−8.90883	−	19.5076i	−0.583637	−	1.27799i	−0.939212	−	0.343338i	$-0.888442\pi$
$233$	−8.90883	−	19.5076i	−0.583637	−	1.27799i	0.355575	−	0.934648i	$-0.384285\pi$
$234$	1.99945	+	2.55373i	0.130708	+	0.166942i
$235$	0.813226	−	0.704664i	0.0530490	−	0.0459672i
$236$	7.35133	−	5.18763i	0.478531	−	0.337686i
$237$	6.28270	−	9.77608i	0.408105	−	0.635024i
$238$	5.61529	+	9.77416i	0.363985	+	0.633565i
$239$	8.53699	−	9.85222i	0.552212	−	0.637287i	−0.409185	−	0.912451i	$-0.634187\pi$
$239$	8.53699	−	9.85222i	0.552212	−	0.637287i	0.961397	+	0.275165i	$0.0887324\pi$
$240$	−1.10119	+	3.09578i	−0.0710818	+	0.199832i
$241$	−1.81017	−	12.5900i	−0.116603	−	0.810995i	−0.961252	−	0.275673i	$-0.911099\pi$
$241$	−1.81017	−	12.5900i	−0.116603	−	0.810995i	0.844648	−	0.535322i	$-0.179810\pi$
$242$	8.27579	+	4.28888i	0.531988	+	0.275700i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	−10.1743	+	25.1026i	−0.651342	+	1.60703i
$245$	1.54860	+	0.707221i	0.0989364	+	0.0451827i
$246$	6.17345	+	15.5166i	0.393605	+	0.989301i
$247$	11.8108	−	3.46796i	0.751502	−	0.220661i
$248$	9.79031	+	21.8068i	0.621685	+	1.38474i
$249$	−3.11065	−	0.913370i	−0.197130	−	0.0578825i
$250$	−2.07293	+	10.6330i	−0.131103	+	0.672490i
$251$	23.1064	+	3.32221i	1.45847	+	0.209696i	0.825464	−	0.564455i	$-0.190913\pi$
$251$	23.1064	+	3.32221i	1.45847	+	0.209696i	0.633002	+	0.774150i	$0.281823\pi$
$252$	−1.43410	−	4.20160i	−0.0903398	−	0.264676i
$253$	2.85998	+	9.65541i	0.179805	+	0.607031i
$254$	3.09787	−	4.33073i	0.194378	−	0.271734i
$255$	0.419776	−	2.91960i	0.0262874	−	0.182833i
$256$	15.7603	−	2.75890i	0.985022	−	0.172431i
$257$	−9.46264	−	2.77848i	−0.590263	−	0.173317i	−0.0270579	−	0.999634i	$-0.508614\pi$
$257$	−9.46264	−	2.77848i	−0.590263	−	0.173317i	−0.563205	+	0.826317i	$0.690432\pi$
$258$	−13.0369	+	1.21675i	−0.811641	+	0.0757517i
$259$	1.27557	+	4.34418i	0.0792598	+	0.269934i
$260$	−0.903946	+	3.65778i	−0.0560603	+	0.226846i
$261$	0.945780	+	0.431923i	0.0585423	+	0.0267354i
$262$	−4.68994	+	1.12716i	−0.289745	+	0.0696359i
$263$	−3.13938	+	2.01756i	−0.193583	+	0.124408i	−0.633842	−	0.773463i	$-0.718523\pi$
$263$	−3.13938	+	2.01756i	−0.193583	+	0.124408i	0.440259	+	0.897871i	$0.354887\pi$
$264$	−0.882893	+	5.87302i	−0.0543383	+	0.361459i
$265$	0.0266967	+	0.185680i	0.00163996	+	0.0114062i
$266$	−16.8286	−	0.837709i	−1.03183	−	0.0513632i
$267$	−8.08780	−	7.00811i	−0.494965	−	0.428890i
$268$	−1.60624	+	16.0938i	−0.0981168	+	0.983086i
$269$	2.18624	−	3.40186i	0.133298	−	0.207415i	−0.768188	−	0.640224i	$-0.778841\pi$
$269$	2.18624	−	3.40186i	0.133298	−	0.207415i	0.901485	+	0.432809i	$0.142478\pi$
$270$	−0.382303	+	1.09700i	−0.0232662	+	0.0667613i
$271$	18.7314	+	21.6172i	1.13785	+	1.31315i	0.943180	+	0.332281i	$0.107818\pi$
$271$	18.7314	+	21.6172i	1.13785	+	1.31315i	0.194671	+	0.980869i	$0.437636\pi$
$272$	−13.3793	+	5.22397i	−0.811240	+	0.316750i
$273$	−2.11483	−	4.63083i	−0.127995	−	0.280270i
$274$	−8.69157	−	8.32294i	−0.525077	−	0.502807i
$275$			9.08191i			0.547659i
$276$	7.82372	−	5.54883i	0.470932	−	0.334000i
$277$			4.59959i			0.276363i	0.990407	+	0.138181i	$0.0441257\pi$
$277$			4.59959i			0.276363i	−0.990407	+	0.138181i	$0.955874\pi$
$278$	19.1951	−	20.0452i	1.15124	−	1.20223i
$279$	3.51077	+	7.68752i	0.210184	+	0.460240i
$280$	2.81613	−	4.32081i	0.168296	−	0.258218i
$281$	−0.320486	−	0.369861i	−0.0191186	−	0.0220641i	0.746110	−	0.665823i	$-0.231919\pi$
$281$	−0.320486	−	0.369861i	−0.0191186	−	0.0220641i	−0.765228	+	0.643759i	$0.777374\pi$
$282$	−1.74935	−	0.609646i	−0.104172	−	0.0363039i
$283$	4.56131	−	7.09753i	0.271141	−	0.421904i	−0.678804	−	0.734319i	$-0.737502\pi$
$283$	4.56131	−	7.09753i	0.271141	−	0.421904i	0.949946	+	0.312415i	$0.101138\pi$
$284$	1.95105	+	0.194725i	0.115774	+	0.0115548i
$285$	3.33209	+	2.88728i	0.197376	+	0.171027i
$286$	−0.338586	+	6.80183i	−0.0200210	+	0.402200i
$287$	−3.73039	−	25.9454i	−0.220198	−	1.53151i
$288$	5.56575	−	1.01113i	0.327965	−	0.0595816i
$289$	−3.45462	+	2.22015i	−0.203213	+	0.130597i
$290$	0.282257	+	1.17443i	0.0165747	+	0.0689649i
$291$	8.10829	+	3.70293i	0.475317	+	0.217070i
$292$	−5.26319	+	21.2973i	−0.308005	+	1.24633i
$293$	5.38741	+	18.3478i	0.314736	+	1.07189i	0.953225	+	0.302261i	$0.0977414\pi$
$293$	5.38741	+	18.3478i	0.314736	+	1.07189i	−0.638489	+	0.769631i	$0.720440\pi$
$294$	−0.272365	−	2.91825i	−0.0158847	−	0.170196i
$295$	3.54578	+	1.04113i	0.206443	+	0.0606172i
$296$	−5.71538	+	0.784368i	−0.332200	+	0.0455905i
$297$	−0.298827	+	2.07838i	−0.0173397	+	0.120600i
$298$	21.5448	+	15.4115i	1.24806	+	0.892766i
$299$	8.29518	−	7.22234i	0.479723	−	0.417678i
$300$	8.18669	−	2.79430i	0.472659	−	0.161329i
$301$	20.3429	+	2.92487i	1.17255	+	0.168587i
$302$	8.80770	+	1.71708i	0.506826	+	0.0988070i
$303$	11.5533	+	3.39236i	0.663722	+	0.194886i
$304$	4.24321	−	21.0458i	0.243365	−	1.20706i
$305$	−10.6743	+	3.13426i	−0.611209	+	0.179467i
$306$	−4.71836	+	1.87725i	−0.269731	+	0.107315i
$307$	−7.79944	−	3.56188i	−0.445137	−	0.203287i	0.180219	−	0.983626i	$-0.442319\pi$
$307$	−7.79944	−	3.56188i	−0.445137	−	0.203287i	−0.625357	+	0.780339i	$0.715047\pi$
$308$	3.50164	−	8.63943i	0.199524	−	0.492277i
$309$	5.36510	+	8.34825i	0.305210	+	0.474916i
$310$	−4.51745	+	8.71683i	−0.256574	+	0.495083i
$311$	−4.47361	−	31.1146i	−0.253675	−	1.76435i	−0.575741	−	0.817632i	$-0.695286\pi$
$311$	−4.47361	−	31.1146i	−0.253675	−	1.76435i	0.322066	−	0.946717i	$-0.395623\pi$
$312$	6.23554	−	1.78756i	0.353018	−	0.101201i
$313$	−12.5663	+	14.5023i	−0.710288	+	0.819716i	−0.990104	−	0.140337i	$-0.955181\pi$
$313$	−12.5663	+	14.5023i	−0.710288	+	0.819716i	0.279815	+	0.960054i	$0.409727\pi$
$314$	2.88551	−	1.65774i	0.162839	−	0.0935515i
$315$	0.985836	−	1.53399i	0.0555455	−	0.0864306i
$316$	−13.4004	−	18.9896i	−0.753833	−	1.06825i
$317$	−20.0294	+	17.3556i	−1.12497	+	0.974789i	−0.999849	−	0.0173535i	$-0.994476\pi$
$317$	−20.0294	+	17.3556i	−1.12497	+	0.974789i	−0.125117	+	0.992142i	$0.539930\pi$
$318$	0.254285	−	0.199094i	0.0142596	−	0.0111646i
$319$	0.906934	+	1.98591i	0.0507785	+	0.111189i
$320$	4.91088	+	4.36684i	0.274527	+	0.244114i
$321$	−1.23993			−0.0692059
$322$	−13.9757	+	5.59880i	−0.778833	+	0.312009i
$323$			19.2727i			1.07236i
$324$	1.96546	−	0.370102i	0.109192	−	0.0205612i
$325$	9.02304	−	4.12068i	0.500508	−	0.228574i
$326$	−8.74991	−	11.1755i	−0.484613	−	0.618954i
$327$	1.82499	+	2.10615i	0.100922	+	0.116470i
$328$	33.3985	+	0.214202i	1.84412	+	0.0118273i
$329$	2.44620	+	1.57208i	0.134864	+	0.0866715i
$330$	−2.11510	+	1.21513i	−0.116432	+	0.0668908i
$331$	−5.44329	−	4.71664i	−0.299191	−	0.259250i	0.492308	−	0.870421i	$-0.336153\pi$
$331$	−5.44329	−	4.71664i	−0.299191	−	0.259250i	−0.791499	+	0.611171i	$0.790699\pi$
$332$	−4.02987	+	5.07955i	−0.221168	+	0.278776i
$333$	−2.01887	+	0.290270i	−0.110633	+	0.0159067i
$334$	11.8134	+	6.12226i	0.646403	+	0.334995i
$335$	−5.58843	+	3.59147i	−0.305329	+	0.196223i
$336$	−8.86521	−	0.498315i	−0.483637	−	0.0271853i
$337$	0.549232	−	1.20265i	0.0299186	−	0.0655126i	−0.894083	−	0.447902i	$-0.852171\pi$
$337$	0.549232	−	1.20265i	0.0299186	−	0.0655126i	0.924001	+	0.382389i	$0.124899\pi$
$338$	−10.1710	+	4.04667i	−0.553232	+	0.220110i
$339$	−2.19955	−	7.49098i	−0.119463	−	0.406854i
$340$	−5.09624	−	2.97144i	−0.276383	−	0.161149i
$341$	−4.99950	+	17.0267i	−0.270738	+	0.922049i
$342$	1.45245	−	7.45028i	0.0785395	−	0.402865i
$343$	−2.86609	+	19.9341i	−0.154755	+	1.07634i
$344$	−7.53874	+	25.0785i	−0.406462	+	1.35214i
$345$	3.78258	+	1.10093i	0.203647	+	0.0592720i
$346$	−21.4504	−	15.3440i	−1.15318	−	0.824896i
$347$	−34.7425	−	4.99521i	−1.86507	−	0.268157i	−0.884824	−	0.465925i	$-0.845722\pi$
$347$	−34.7425	−	4.99521i	−1.86507	−	0.268157i	−0.980249	+	0.197768i	$0.936631\pi$
$348$	1.51111	−	1.42856i	0.0810040	−	0.0765787i
$349$	−3.84692	+	13.1014i	−0.205921	+	0.701302i	0.790164	+	0.612896i	$0.209996\pi$
$349$	−3.84692	+	13.1014i	−0.205921	+	0.701302i	−0.996085	+	0.0884061i	$0.971823\pi$
$350$	−13.5193	+	1.26178i	−0.722636	+	0.0674447i
$351$	2.20050	−	0.646124i	0.117454	−	0.0344876i
$352$	10.2226	+	6.04862i	0.544866	+	0.322393i
$353$	0.910897	−	1.99459i	0.0484822	−	0.106161i	−0.883841	−	0.467788i	$-0.845051\pi$
$353$	0.910897	−	1.99459i	0.0484822	−	0.106161i	0.932323	+	0.361627i	$0.117778\pi$
$354$	−1.48671	−	6.18599i	−0.0790177	−	0.328782i
$355$	0.435394	+	0.677486i	0.0231083	+	0.0359572i
$356$	−19.0658	+	9.72616i	−1.01049	+	0.515486i
$357$	7.88962	−	1.13436i	0.417563	−	0.0600365i
$358$	3.45660	+	0.172065i	0.182687	+	0.00909393i
$359$	1.15376	−	1.33151i	0.0608932	−	0.0702745i	−0.724486	−	0.689290i	$-0.757923\pi$
$359$	1.15376	−	1.33151i	0.0608932	−	0.0702745i	0.785379	+	0.619015i	$0.212468\pi$
$360$	1.74613	+	1.53274i	0.0920289	+	0.0807827i
$361$	−8.25113	−	5.30268i	−0.434270	−	0.279088i
$362$	−14.8164	−	5.16350i	−0.778733	−	0.271388i
$363$	4.98116	−	4.31620i	0.261443	−	0.226542i
$364$	−10.1722	+	0.440979i	−0.533168	+	0.0231136i
$365$	−8.19624	+	3.74310i	−0.429011	+	0.195923i
$366$	13.8332	+	13.2465i	0.723073	+	0.692406i
$367$	3.91627			0.204428			0.102214	−	0.994762i	$-0.467407\pi$
$367$	3.91627			0.204428			0.102214	+	0.994762i	$0.467407\pi$
$368$	−4.40735	−	18.6702i	−0.229749	−	0.973250i
$369$	11.8084			0.614720
$370$	−1.71136	−	1.63877i	−0.0889691	−	0.0851958i
$371$	−0.461111	+	0.210582i	−0.0239397	+	0.0109329i
$372$	16.8866	−	0.732059i	0.875531	−	0.0379555i
$373$	17.2583	−	14.9544i	0.893600	−	0.774309i	−0.0813610	−	0.996685i	$-0.525927\pi$
$373$	17.2583	−	14.9544i	0.893600	−	0.774309i	0.974961	+	0.222376i	$0.0713812\pi$
$374$	−10.0688	−	3.50898i	−0.520647	−	0.181445i
$375$	6.44418	+	4.14142i	0.332776	+	0.213862i
$376$	−2.44421	+	2.78449i	−0.126051	+	0.143599i
$377$	1.56154	−	1.80211i	0.0804232	−	0.0928134i
$378$	−3.13539	−	0.156076i	−0.161267	−	0.00802767i
$379$	−37.6774	+	5.41720i	−1.93536	+	0.278263i	−0.997613	−	0.0690551i	$-0.978002\pi$
$379$	−37.6774	+	5.41720i	−1.93536	+	0.278263i	−0.937747	+	0.347318i	$0.887092\pi$
$380$	7.85494	−	4.00709i	0.402950	−	0.205559i
$381$	−2.03557	−	3.16741i	−0.104285	−	0.162271i
$382$	−2.96399	−	12.3327i	−0.151651	−	0.630998i
$383$	1.76692	−	3.86901i	0.0902853	−	0.197697i	−0.859102	−	0.511804i	$-0.828978\pi$
$383$	1.76692	−	3.86901i	0.0902853	−	0.197697i	0.949388	+	0.314106i	$0.101705\pi$
$384$	2.30713	−	11.0760i	0.117735	−	0.565218i
$385$	3.67372	−	1.07870i	0.187230	−	0.0549758i
$386$	7.35516	−	0.686469i	0.374368	−	0.0349403i
$387$	−2.60843	+	8.88349i	−0.132594	+	0.451573i
$388$	12.9549	−	12.2472i	0.657688	−	0.621757i
$389$	13.1101	+	1.88495i	0.664708	+	0.0955706i	0.466406	−	0.884571i	$-0.345548\pi$
$389$	13.1101	+	1.88495i	0.664708	+	0.0955706i	0.198301	+	0.980141i	$0.436458\pi$
$390$	2.16693	+	1.55006i	0.109727	+	0.0784901i
$391$	7.19084	+	15.6474i	0.363657	+	0.791325i
$392$	−5.61372	−	1.68752i	−0.283536	−	0.0852326i
$393$	−0.485396	+	3.37600i	−0.0244850	+	0.170297i
$394$	−3.14395	+	16.1268i	−0.158390	+	0.812454i
$395$	2.68941	−	9.15928i	0.135319	−	0.460853i
$396$	3.62787	+	2.11529i	0.182308	+	0.106297i
$397$	−5.97708	−	20.3561i	−0.299981	−	1.02164i	−0.962203	−	0.272334i	$-0.912205\pi$
$397$	−5.97708	−	20.3561i	−0.299981	−	1.02164i	0.662222	−	0.749308i	$-0.269614\pi$
$398$	−17.9217	+	7.13037i	−0.898336	+	0.357413i
$399$	−4.94941	+	10.8377i	−0.247781	+	0.542564i
$400$	0.970953	−	17.2736i	0.0485477	−	0.863680i
$401$	10.8489	−	6.97218i	0.541769	−	0.348174i	−0.240961	−	0.970535i	$-0.577463\pi$
$401$	10.8489	−	6.97218i	0.541769	−	0.348174i	0.782731	+	0.622361i	$0.213826\pi$
$402$	10.1540	+	5.26227i	0.506436	+	0.262458i
$403$	19.1848	−	2.75835i	0.955661	−	0.137403i
$404$	14.9674	−	18.8660i	0.744656	−	0.938620i
$405$	0.620811	+	0.537936i	0.0308484	+	0.0267303i
$406$	−2.83021	+	1.62597i	−0.140461	+	0.0806953i
$407$	−3.60286	−	2.31542i	−0.178587	−	0.114771i
$408$	−0.0651355	+	10.1560i	−0.00322469	+	0.502795i
$409$	−14.1311	−	16.3082i	−0.698739	−	0.806388i	0.289843	−	0.957074i	$-0.406397\pi$
$409$	−14.1311	−	16.3082i	−0.698739	−	0.806388i	−0.988582	+	0.150687i	$0.951852\pi$
$410$	8.45676	+	10.8011i	0.417650	+	0.533428i
$411$	−7.74029	+	3.53487i	−0.381800	+	0.174362i
$412$	19.5044	−	3.67274i	0.960913	−	0.180943i
$413$			9.98624i			0.491391i
$414$	−1.60054	−	6.59077i	−0.0786621	−	0.323919i
$415$	−2.66312			−0.130728
$416$	1.37117	−	12.9007i	0.0672273	−	0.632511i
$417$	−8.15242	−	17.8513i	−0.399226	−	0.874183i
$418$	12.5494	−	9.82559i	0.613810	−	0.480585i
$419$	19.1079	−	16.5571i	0.933483	−	0.808868i	−0.0483080	−	0.998832i	$-0.515383\pi$
$419$	19.1079	−	16.5571i	0.933483	−	0.808868i	0.981791	+	0.189965i	$0.0608374\pi$
$420$	−2.10270	−	2.97971i	−0.102601	−	0.145395i
$421$	−5.92400	+	9.21792i	−0.288718	+	0.449254i	−0.955069	−	0.296385i	$-0.904219\pi$
$421$	−5.92400	+	9.21792i	−0.288718	+	0.449254i	0.666351	+	0.745638i	$0.267855\pi$
$422$	11.1349	−	6.39706i	0.542040	−	0.311404i
$423$	−0.857829	+	0.989987i	−0.0417091	+	0.0481348i
$424$	−0.177995	−	0.620898i	−0.00864419	−	0.0301535i
$425$	2.21026	+	15.3727i	0.107213	+	0.745685i
$426$	0.637944	−	1.23097i	0.0309085	−	0.0596408i
$427$	−16.2532	−	25.2905i	−0.786547	−	1.22389i
$428$	−0.931503	+	2.29825i	−0.0450259	+	0.111090i
$429$	4.38040	+	2.00046i	0.211488	+	0.0965832i
$430$	−9.99377	+	3.97613i	−0.481942	+	0.191746i
$431$	−12.0747	+	3.54544i	−0.581616	+	0.170778i	−0.559289	−	0.828973i	$-0.688926\pi$
$431$	−12.0747	+	3.54544i	−0.581616	+	0.170778i	−0.0223271	+	0.999751i	$0.507108\pi$
$432$	0.790564	−	3.92110i	0.0380360	−	0.188654i
$433$	−27.2698	−	8.00714i	−1.31050	−	0.384799i	−0.449447	−	0.893307i	$-0.648379\pi$
$433$	−27.2698	−	8.00714i	−1.31050	−	0.384799i	−0.861057	+	0.508508i	$0.830197\pi$
$434$	−26.0405	−	5.07666i	−1.24998	−	0.243687i
$435$	0.845401	+	0.121550i	0.0405339	+	0.00582789i
$436$	5.27487	−	1.80043i	0.252620	−	0.0862251i
$437$	−25.4874	−	3.60285i	−1.21923	−	0.172348i
$438$	12.6169	+	9.02514i	0.602857	+	0.431238i
$439$	−2.08457	+	14.4985i	−0.0994913	+	0.691977i	0.877637	+	0.479326i	$0.159119\pi$
$439$	−2.08457	+	14.4985i	−0.0994913	+	0.691977i	−0.977128	+	0.212651i	$0.931790\pi$
$440$	0.663314	+	4.83330i	0.0316222	+	0.230419i
$441$	−1.98854	−	0.583887i	−0.0946922	−	0.0278041i
$442$	1.08224	+	11.5957i	0.0514770	+	0.551550i
$443$	−0.625832	−	2.13139i	−0.0297342	−	0.101265i	0.943289	−	0.331973i	$-0.107714\pi$
$443$	−0.625832	−	2.13139i	−0.0297342	−	0.101265i	−0.973023	+	0.230707i	$0.925896\pi$
$444$	−0.978663	+	3.96013i	−0.0464453	+	0.187939i
$445$	−7.99650	−	3.65188i	−0.379070	−	0.173116i
$446$	7.50155	+	31.2129i	0.355209	+	1.47797i
$447$	15.7575	−	10.1267i	0.745302	−	0.478977i
$448$	−7.58370	+	16.0577i	−0.358296	+	0.758653i
$449$	−3.03012	−	21.0749i	−0.143000	−	0.994588i	−0.927330	−	0.374244i	$-0.877902\pi$
$449$	−3.03012	−	21.0749i	−0.143000	−	0.994588i	0.784330	−	0.620344i	$-0.213007\pi$
$450$	0.304109	−	6.10922i	0.0143358	−	0.287991i
$451$	18.7386	+	16.2371i	0.882366	+	0.764575i
$452$	−15.5373	−	1.55069i	−0.730811	−	0.0729385i
$453$	3.43049	−	5.33795i	0.161179	−	0.250799i
$454$	−29.3023	−	10.2118i	−1.37523	−	0.479265i
$455$	−2.73857	−	3.16048i	−0.128386	−	0.148165i
$456$	−12.7182	−	8.28925i	−0.595586	−	0.388180i
$457$	9.97180	+	21.8352i	0.466461	+	1.02141i	0.985967	+	0.166941i	$0.0533888\pi$
$457$	9.97180	+	21.8352i	0.466461	+	1.02141i	−0.519506	+	0.854467i	$0.673884\pi$
$458$	22.1602	−	23.1417i	1.03548	−	1.08134i
$459$			3.59075i			0.167602i
$460$	4.88231	−	6.18409i	0.227639	−	0.288335i
$461$			38.6093i			1.79822i	0.437726	+	0.899108i	$0.355784\pi$
$461$			38.6093i			1.79822i	−0.437726	+	0.899108i	$0.644216\pi$
$462$	−4.76091	−	4.55899i	−0.221497	−	0.212103i
$463$	−0.579644	−	1.26924i	−0.0269383	−	0.0589867i	0.895685	−	0.444690i	$-0.146686\pi$
$463$	−0.579644	−	1.26924i	−0.0269383	−	0.0589867i	−0.922623	+	0.385703i	$0.873959\pi$
$464$	−1.51265	−	3.87412i	−0.0702232	−	0.179851i
$465$	4.54623	+	5.24663i	0.210826	+	0.243307i
$466$	−9.98079	+	28.6393i	−0.462351	+	1.32669i
$467$	12.9658	−	20.1751i	0.599984	−	0.933593i	−0.399871	−	0.916571i	$-0.630945\pi$
$467$	12.9658	−	20.1751i	0.599984	−	0.933593i	0.999855	−	0.0170216i	$-0.00541839\pi$
$468$	0.455521	−	4.56412i	0.0210565	−	0.210976i
$469$	−13.5667	−	11.7556i	−0.626451	−	0.542823i
$470$	−1.51989	−	0.0756580i	−0.0701071	−	0.00348984i
$471$	−0.334883	−	2.32916i	−0.0154306	−	0.107322i
$472$	−12.5829	−	1.89159i	−0.579174	−	0.0870675i
$473$	−16.3545	+	10.5104i	−0.751982	+	0.483269i
$474$	−15.9793	+	3.84039i	−0.733955	+	0.176395i
$475$	−21.1170	−	9.64379i	−0.968912	−	0.442487i
$476$	3.82456	−	15.4759i	0.175298	−	0.709338i
$477$	−0.0643372	−	0.219113i	−0.00294580	−	0.0100325i
$478$	−18.3564	+	1.71323i	−0.839603	+	0.0783614i
$479$	33.3834	+	9.80226i	1.52533	+	0.447877i	0.933617	−	0.358274i	$-0.116635\pi$
$479$	33.3834	+	9.80226i	1.52533	+	0.447877i	0.591711	+	0.806150i	$0.298453\pi$
$480$	4.15279	−	2.08503i	0.189548	−	0.0951682i
$481$	−0.665703	+	4.63007i	−0.0303535	+	0.211113i
$482$	−10.4654	+	14.6303i	−0.476686	+	0.666393i
$483$	0.0252497	+	10.6458i	0.00114890	+	0.484399i
$484$	−4.25812	−	12.4754i	−0.193551	−	0.567062i
$485$	7.24774	+	1.04207i	0.329103	+	0.0473178i
$486$	0.270610	−	1.38808i	0.0122751	−	0.0629647i
$487$	33.3239	+	9.78477i	1.51005	+	0.443390i	0.928876	−	0.370390i	$-0.120776\pi$
$487$	33.3239	+	9.78477i	1.51005	+	0.443390i	0.581172	+	0.813781i	$0.302594\pi$
$488$	34.9452	−	15.6889i	1.58190	−	0.710202i
$489$	−9.62971	+	2.82754i	−0.435471	+	0.127866i
$490$	−0.890042	−	2.23707i	−0.0402080	−	0.101060i
$491$	−30.9369	−	14.1284i	−1.39616	−	0.637606i	−0.431746	−	0.901995i	$-0.642102\pi$
$491$	−30.9369	−	14.1284i	−1.39616	−	0.637606i	−0.964416	+	0.264389i	$0.914830\pi$
$492$	8.87113	−	21.8873i	0.399941	−	0.986756i
$493$	2.01845	+	3.14077i	0.0909065	+	0.141453i
$494$	−15.4559	−	8.00992i	−0.695392	−	0.360383i
$495$	0.245471	+	1.70729i	0.0110331	+	0.0767370i
$496$	11.3293	−	31.8500i	0.508700	−	1.43011i
$497$	−1.42513	+	1.64469i	−0.0639258	+	0.0737743i
$498$	2.28393	+	3.97549i	0.102345	+	0.178146i
$499$	−3.79588	+	5.90650i	−0.169927	+	0.264411i	−0.915764	−	0.401717i	$-0.868413\pi$
$499$	−3.79588	+	5.90650i	−0.169927	+	0.264411i	0.745837	+	0.666129i	$0.232050\pi$
$500$	12.5175	−	8.83328i	0.559801	−	0.395036i
$501$	7.11046	−	6.16125i	0.317672	−	0.275264i
$502$	−20.3521	−	25.9939i	−0.908357	−	1.16017i
$503$	−1.12172	−	2.45623i	−0.0500151	−	0.109518i	0.882975	−	0.469421i	$-0.155537\pi$
$503$	−1.12172	−	2.45623i	−0.0500151	−	0.109518i	−0.932990	+	0.359903i	$0.882810\pi$
$504$	−2.64478	+	5.69432i	−0.117808	+	0.253645i
$505$	9.89116			0.440151
$506$	6.52275	−	12.6596i	0.289972	−	0.562790i
$507$			7.74034i			0.343760i
$508$	−7.40015	+	1.39347i	−0.328328	+	0.0618254i
$509$	−8.37744	+	3.82585i	−0.371323	+	0.169578i	−0.592332	−	0.805694i	$-0.701792\pi$
$509$	−8.37744	+	3.82585i	−0.371323	+	0.169578i	0.221008	+	0.975272i	$0.429065\pi$
$510$	−3.28445	+	2.57157i	−0.145438	+	0.113871i
$511$	−15.9452	−	18.4018i	−0.705375	−	0.814046i
$512$	−18.7965	−	12.5973i	−0.830696	−	0.556726i
$513$	−4.51528	−	2.90179i	−0.199354	−	0.128117i
$514$	6.94774	+	12.0935i	0.306452	+	0.533420i
$515$	6.16068	+	5.33826i	0.271472	+	0.235232i
$516$	14.5063	+	11.5086i	0.638605	+	0.506638i
$517$	−2.72256	+	0.391445i	−0.119738	+	0.0172157i
$518$	2.94616	−	5.68489i	0.129447	−	0.249780i
$519$	−15.6884	+	10.0823i	−0.688643	+	0.442564i
$520$	4.50101	−	2.85200i	0.197382	−	0.125069i
$521$	−6.40192	+	14.0183i	−0.280473	+	0.614151i	−0.996470	−	0.0839530i	$-0.973245\pi$
$521$	−6.40192	+	14.0183i	−0.280473	+	0.614151i	0.715996	+	0.698104i	$0.245973\pi$
$522$	−0.543578	−	1.36625i	−0.0237918	−	0.0597991i
$523$	−9.89289	−	33.6921i	−0.432586	−	1.47325i	−0.831117	−	0.556098i	$-0.812298\pi$
$523$	−9.89289	−	33.6921i	−0.432586	−	1.47325i	0.398531	−	0.917155i	$-0.369520\pi$
$524$	5.89290	+	3.43595i	0.257433	+	0.150100i
$525$	−2.70495	+	9.21221i	−0.118054	+	0.402054i
$526$	5.18003	+	1.00986i	0.225860	+	0.0440319i
$527$	−4.31873	+	30.0374i	−0.188127	+	1.30845i
$528$	6.64624	−	5.13529i	0.289240	−	0.223485i
$529$	−22.0374	+	6.58446i	−0.958146	+	0.286281i
$530$	0.154345	−	0.215770i	0.00670433	−	0.00937245i
$531$	−4.45292	−	0.640233i	−0.193240	−	0.0277838i
$532$	16.3698	+	17.3158i	0.709723	+	0.750737i
$533$	7.62968	−	25.9843i	0.330478	−	1.12551i
$534$	1.40641	+	15.0690i	0.0608614	+	0.652099i
$535$	−0.977281	+	0.286955i	−0.0422515	+	0.0124062i
$536$	17.3821	−	14.8676i	0.750792	−	0.642181i
$537$	1.01661	−	2.22606i	0.0438699	−	0.0960617i
$538$	−5.56046	+	1.33637i	−0.239729	+	0.0576151i
$539$	−2.35271	−	3.66090i	−0.101339	−	0.157686i
$540$	1.46348	−	0.746571i	0.0629779	−	0.0321273i
$541$	13.8773	−	1.99526i	0.596633	−	0.0857829i	0.162619	−	0.986689i	$-0.448006\pi$
$541$	13.8773	−	1.99526i	0.596633	−	0.0857829i	0.434014	+	0.900906i	$0.357097\pi$
$542$	2.01114	−	40.4016i	0.0863859	−	1.73540i
$543$	−7.26552	+	8.38486i	−0.311793	+	0.359829i
$544$	18.7756	+	7.75047i	0.804996	+	0.332299i
$545$	1.92584	+	1.23766i	0.0824939	+	0.0530156i
$546$	−2.36930	+	6.79857i	−0.101396	+	0.290952i
$547$	9.87232	−	8.55442i	0.422110	−	0.365760i	−0.417751	−	0.908561i	$-0.637182\pi$
$547$	9.87232	−	8.55442i	0.422110	−	0.365760i	0.839861	+	0.542801i	$0.182636\pi$
$548$	0.737084	+	17.0025i	0.0314867	+	0.726312i
$549$	12.3192	−	5.62598i	0.525770	−	0.240111i
$550$	8.88306	−	9.27649i	0.378775	−	0.395551i
$551$	−5.58061			−0.237742
$552$	−13.4187	−	1.98470i	−0.571137	−	0.0844745i
$553$	25.7960			1.09696
$554$	4.49888	−	4.69814i	0.191139	−	0.199605i
$555$	−1.52405	+	0.696010i	−0.0646923	+	0.0295440i
$556$	−39.2127	+	1.69993i	−1.66299	+	0.0720929i
$557$	−14.6266	+	12.6740i	−0.619750	+	0.537016i	−0.907157	−	0.420792i	$-0.861752\pi$
$557$	−14.6266	+	12.6740i	−0.619750	+	0.537016i	0.287407	+	0.957809i	$0.407207\pi$
$558$	3.93321	−	11.2861i	0.166506	−	0.477780i
$559$	17.8627	+	11.4797i	0.755513	+	0.485539i
$560$	−7.10267	+	1.65891i	−0.300143	+	0.0701018i
$561$	−4.93746	+	5.69813i	−0.208460	+	0.240575i
$562$	−0.0344098	+	0.691255i	−0.00145149	+	0.0291588i
$563$	7.92145	−	1.13893i	0.333849	−	0.0480003i	0.0266481	−	0.999645i	$-0.491517\pi$
$563$	7.92145	−	1.13893i	0.333849	−	0.0480003i	0.307201	+	0.951645i	$0.400608\pi$
$564$	1.19053	+	2.33376i	0.0501304	+	0.0982688i
$565$	−3.46727	−	5.39517i	−0.145869	−	0.226977i
$566$	−11.6012	+	2.78816i	−0.487633	+	0.117195i
$567$	−0.922138	+	2.01920i	−0.0387262	+	0.0847985i
$568$	−1.80240	−	2.10723i	−0.0756268	−	0.0884175i
$569$	−40.4728	+	11.8839i	−1.69671	+	0.498199i	−0.979970	−	0.199143i	$-0.936184\pi$
$569$	−40.4728	+	11.8839i	−1.69671	+	0.498199i	−0.716739	+	0.697342i	$0.754366\pi$
$570$	−0.579428	−	6.20828i	−0.0242696	−	0.260036i
$571$	11.0624	−	37.6750i	0.462947	−	1.57665i	−0.315491	−	0.948929i	$-0.602169\pi$
$571$	11.0624	−	37.6750i	0.462947	−	1.57665i	0.778437	−	0.627722i	$-0.216013\pi$
$572$	6.99874	−	6.61639i	0.292632	−	0.276645i
$573$	−8.87759	−	1.27641i	−0.370867	−	0.0533226i
$574$	−21.5670	+	30.1501i	−0.900191	+	1.25844i
$575$	−20.7430	+	0.0491984i	−0.865041	+	0.00205171i
$576$	−6.67400	−	4.41109i	−0.278083	−	0.183796i
$577$	−1.88491	+	13.1099i	−0.0784700	+	0.545771i	0.912227	+	0.409685i	$0.134361\pi$
$577$	−1.88491	+	13.1099i	−0.0784700	+	0.545771i	−0.990697	+	0.136086i	$0.956548\pi$
$578$	5.70017	+	1.11126i	0.237096	+	0.0462224i
$579$	1.47163	−	5.01190i	0.0611587	−	0.208287i
$580$	0.860412	−	1.47567i	0.0357267	−	0.0612739i
$581$	−2.02750	−	6.90503i	−0.0841149	−	0.286469i
$582$	−4.66016	−	11.7130i	−0.193170	−	0.485521i
$583$	0.199194	−	0.436174i	0.00824978	−	0.0180645i
$584$	26.2070	−	16.6057i	1.08445	−	0.687148i
$585$	1.58485	−	1.01852i	0.0655254	−	0.0421106i
$586$	12.4433	−	24.0104i	0.514026	−	0.991860i
$587$	44.2308	−	6.35943i	1.82560	−	0.262482i	0.857760	−	0.514050i	$-0.171855\pi$
$587$	44.2308	−	6.35943i	1.82560	−	0.262482i	0.967840	+	0.251568i	$0.0809463\pi$
$588$	−2.57616	+	3.24718i	−0.106239	+	0.133912i
$589$	−34.2812	−	29.7048i	−1.41253	−	1.22397i
$590$	−2.60341	−	4.53159i	−0.107181	−	0.186562i
$591$	9.77370	+	6.28117i	0.402036	+	0.258373i
$592$	6.60503	+	4.78906i	0.271465	+	0.196829i
$593$	17.6114	+	20.3246i	0.723212	+	0.834631i	0.991689	−	0.128655i	$-0.0410661\pi$
$593$	17.6114	+	20.3246i	0.723212	+	0.834631i	−0.268478	+	0.963286i	$0.586521\pi$
$594$	2.33811	−	1.83063i	0.0959337	−	0.0751117i
$595$	5.95589	−	2.71996i	0.244168	−	0.111508i
$596$	−6.93236	−	36.8149i	−0.283961	−	1.50800i
$597$			13.6387i			0.558197i
$598$	−15.5371	−	0.736480i	−0.635360	−	0.0301169i
$599$	30.0051			1.22597			0.612987	−	0.790093i	$-0.289968\pi$
$599$	30.0051			1.22597			0.612987	+	0.790093i	$0.289968\pi$
$600$	−11.0952	−	5.15327i	−0.452960	−	0.210381i
$601$	3.98804	+	8.73260i	0.162676	+	0.356210i	0.973363	−	0.229269i	$-0.0736336\pi$
$601$	3.98804	+	8.73260i	0.162676	+	0.356210i	−0.810687	+	0.585479i	$0.800906\pi$
$602$	−17.9179	−	22.8850i	−0.730280	−	0.932724i
$603$	6.11166	−	5.29579i	0.248886	−	0.215661i
$604$	−7.31693	−	10.3687i	−0.297722	−	0.421898i
$605$	2.92714	−	4.55472i	0.119005	−	0.185176i
$606$	−8.48278	−	14.7654i	−0.344590	−	0.599804i
$607$	−16.5461	+	19.0952i	−0.671586	+	0.775051i	−0.984624	−	0.174689i	$-0.944108\pi$
$607$	−16.5461	+	19.0952i	−0.671586	+	0.775051i	0.313038	+	0.949741i	$0.398653\pi$
$608$	−24.9191	+	17.3464i	−1.01060	+	0.703490i
$609$	0.328465	+	2.28452i	0.0133101	+	0.0925735i
$610$	13.9686	+	7.23917i	0.565574	+	0.293106i
$611$	1.62420	+	2.52730i	0.0657081	+	0.102244i
$612$	6.65560	+	2.69758i	0.269037	+	0.109043i
$613$	16.4047	+	7.49175i	0.662578	+	0.302589i	0.718173	−	0.695864i	$-0.244979\pi$
$613$	16.4047	+	7.49175i	0.662578	+	0.302589i	−0.0555957	+	0.998453i	$0.517706\pi$
$614$	4.48265	+	11.2669i	0.180905	+	0.454694i
$615$	9.30709	−	2.73281i	0.375298	−	0.110197i
$616$	−12.0269	+	5.39957i	−0.484579	+	0.217555i
$617$	8.19481	+	2.40621i	0.329911	+	0.0968705i	0.442493	−	0.896772i	$-0.354094\pi$
$617$	8.19481	+	2.40621i	0.329911	+	0.0968705i	−0.112583	+	0.993642i	$0.535912\pi$
$618$	2.68542	−	13.7748i	0.108023	−	0.554102i
$619$	−28.4594	−	4.09185i	−1.14388	−	0.164465i	−0.455788	−	0.890088i	$-0.650643\pi$
$619$	−28.4594	−	4.09185i	−1.14388	−	0.164465i	−0.688093	+	0.725623i	$0.741552\pi$
$620$	13.1402	−	4.48506i	0.527724	−	0.180124i
$621$	−4.74862	−	0.671257i	−0.190556	−	0.0269366i
$622$	−25.8639	+	36.1569i	−1.03705	+	1.44976i
$623$	3.38078	−	23.5138i	0.135448	−	0.942061i
$624$	−8.11756	−	4.27315i	−0.324963	−	0.171063i
$625$	−14.7125	−	4.31997i	−0.588499	−	0.172799i
$626$	27.0203	−	2.52184i	1.07995	−	0.100793i
$627$	−3.17515	−	10.8136i	−0.126803	−	0.431852i
$628$	−4.56878	−	1.12908i	−0.182314	−	0.0450552i
$629$	−6.66197	−	3.04242i	−0.265630	−	0.121309i
$630$	−2.50736	+	0.602606i	−0.0998957	+	0.0240084i
$631$	39.1548	−	25.1633i	1.55873	−	1.00173i	0.575833	−	0.817567i	$-0.304678\pi$
$631$	39.1548	−	25.1633i	1.55873	−	1.00173i	0.982895	−	0.184167i	$-0.0589586\pi$
$632$	−4.88626	+	32.5035i	−0.194365	+	1.29292i
$633$	−1.29228	−	8.98803i	−0.0513637	−	0.357242i
$634$	37.4342	+	1.86343i	1.48670	+	0.0740062i
$635$	−2.33742	−	2.02538i	−0.0927576	−	0.0803749i
$636$	−0.454468	−	0.0453581i	−0.0180208	−	0.00179856i
$637$	−2.56968	+	3.99850i	−0.101814	+	0.158426i
$638$	1.01606	−	2.91553i	0.0402262	−	0.115427i
$639$	−0.642008	−	0.740917i	−0.0253974	−	0.0293102i
$640$	−0.744878	−	9.26376i	−0.0294439	−	0.366182i
$641$	13.5651	+	29.7034i	0.535789	+	1.17321i	0.963108	+	0.269114i	$0.0867307\pi$
$641$	13.5651	+	29.7034i	0.535789	+	1.17321i	−0.427319	+	0.904101i	$0.640542\pi$
$642$	1.26649	+	1.21278i	0.0499845	+	0.0478645i
$643$			17.3645i			0.684787i	0.939557	+	0.342394i	$0.111238\pi$
$643$			17.3645i			0.684787i	−0.939557	+	0.342394i	$0.888762\pi$
$644$	19.7513	+	7.95090i	0.778311	+	0.313309i
$645$			7.60543i			0.299463i
$646$	18.8507	−	19.6856i	0.741672	−	0.774521i
$647$	17.2945	+	37.8697i	0.679918	+	1.48881i	0.862730	+	0.505665i	$0.168753\pi$
$647$	17.2945	+	37.8697i	0.679918	+	1.48881i	−0.182812	+	0.983148i	$0.558520\pi$
$648$	−2.36957	−	1.54439i	−0.0930854	−	0.0606694i
$649$	−6.18594	−	7.13896i	−0.242820	−	0.280229i
$650$	−13.2468	−	4.61650i	−0.519583	−	0.181074i
$651$	−10.1425	+	15.7820i	−0.397514	+	0.618544i
$652$	−1.99343	+	19.9733i	−0.0780687	+	0.782214i
$653$	−26.8367	−	23.2541i	−1.05020	−	0.910003i	−0.0541262	−	0.998534i	$-0.517237\pi$
$653$	−26.8367	−	23.2541i	−1.05020	−	0.910003i	−0.996073	+	0.0885310i	$0.971783\pi$
$654$	0.195944	−	3.93631i	0.00766203	−	0.153922i
$655$	0.398729	+	2.77322i	0.0155796	+	0.108359i
$656$	−33.9045	−	32.8860i	−1.32375	−	1.28398i
$657$	9.22772	−	5.93029i	0.360008	−	0.231363i
$658$	−0.960957	−	3.99841i	−0.0374620	−	0.155874i
$659$	18.0152	+	8.22726i	0.701772	+	0.320489i	0.734150	−	0.678987i	$-0.237581\pi$
$659$	18.0152	+	8.22726i	0.701772	+	0.320489i	−0.0323780	+	0.999476i	$0.510308\pi$
$660$	3.34895	+	0.827623i	0.130358	+	0.0322152i
$661$	−7.18503	−	24.4700i	−0.279465	−	0.951772i	−0.972895	−	0.231247i	$-0.925719\pi$
$661$	−7.18503	−	24.4700i	−0.279465	−	0.951772i	0.693430	−	0.720524i	$-0.256099\pi$
$662$	0.946551	+	10.1418i	0.0367888	+	0.394173i
$663$	7.90144	+	2.32007i	0.306866	+	0.0901041i
$664$	9.08454	−	1.24675i	0.352549	−	0.0483831i
$665$	−1.39285	+	9.68747i	−0.0540123	+	0.375664i
$666$	2.34604	+	1.67818i	0.0909072	+	0.0650281i
$667$	−4.53088	+	2.08218i	−0.175436	+	0.0806224i
$668$	−6.07835	−	17.8082i	−0.235178	−	0.689021i
$669$	22.4683	+	3.23045i	0.868674	+	0.124896i
$670$	9.22100	+	1.79766i	0.356238	+	0.0694495i
$671$	27.2852	+	8.01165i	1.05333	+	0.309286i
$672$	8.56775	+	9.18010i	0.330508	+	0.354130i
$673$	−19.6370	+	5.76595i	−0.756952	+	0.222261i	−0.637364	−	0.770562i	$-0.719975\pi$
$673$	−19.6370	+	5.76595i	−0.756952	+	0.222261i	−0.119588	+	0.992824i	$0.538157\pi$
$674$	−1.73732	+	0.691212i	−0.0669190	+	0.0266245i
$675$	−3.93436	−	1.79676i	−0.151433	−	0.0691573i
$676$	14.3470	+	5.81498i	0.551809	+	0.223653i
$677$	9.34698	+	14.5442i	0.359234	+	0.558979i	0.973086	−	0.230442i	$-0.0740173\pi$
$677$	9.34698	+	14.5442i	0.359234	+	0.558979i	−0.613852	+	0.789421i	$0.710381\pi$
$678$	−5.08028	+	9.80287i	−0.195107	+	0.376477i
$679$	2.81597	+	19.5855i	0.108067	+	0.751622i
$680$	2.29905	+	8.01977i	0.0881646	+	0.307544i
$681$	−14.3690	+	16.5827i	−0.550621	+	0.635450i
$682$	21.7606	−	12.5015i	0.833255	−	0.478708i
$683$	7.35578	−	11.4458i	0.281461	−	0.437962i	−0.671523	−	0.740984i	$-0.734359\pi$
$683$	7.35578	−	11.4458i	0.281461	−	0.437962i	0.952983	+	0.303022i	$0.0979957\pi$
$684$	−8.77073	+	6.18926i	−0.335357	+	0.236652i
$685$	−5.28264	+	4.57743i	−0.201839	+	0.174895i
$686$	22.4252	−	17.5579i	0.856197	−	0.670363i
$687$	−9.41174	−	20.6088i	−0.359080	−	0.786277i
$688$	32.2297	−	18.2421i	1.22874	−	0.695474i
$689$	−0.523726			−0.0199524
$690$	−2.78681	−	4.82428i	−0.106092	−	0.183657i
$691$			10.3065i			0.392078i	0.980596	+	0.196039i	$0.0628079\pi$
$691$			10.3065i			0.392078i	−0.980596	+	0.196039i	$0.937192\pi$
$692$	6.90197	+	36.6534i	0.262373	+	1.39335i
$693$	−4.23983	+	1.93627i	−0.161058	+	0.0735527i
$694$	30.6010	+	39.0840i	1.16160	+	1.48361i
$695$	−10.5569	−	12.1833i	−0.400445	−	0.462138i
$696$	−2.94077	−	0.0188607i	−0.111469	−	0.000714911i
$697$	35.6699	+	22.9237i	1.35110	+	0.868296i
$698$	16.7439	−	9.61942i	0.633766	−	0.364100i
$699$	16.2075	+	14.0439i	0.613024	+	0.531189i
$700$	15.0431	+	11.9345i	0.568575	+	0.451080i
$701$	41.2573	−	5.93191i	1.55827	−	0.224045i	0.691359	−	0.722512i	$-0.257013\pi$
$701$	41.2573	−	5.93191i	1.55827	−	0.224045i	0.866909	+	0.498467i	$0.166103\pi$
$702$	−2.87962	−	1.49235i	−0.108684	−	0.0563251i
$703$	9.20950	−	5.91859i	0.347343	−	0.223224i
$704$	−4.52544	−	16.1770i	−0.170559	−	0.609693i
$705$	−0.447008	+	0.978812i	−0.0168353	+	0.0368642i
$706$	−2.88133	+	1.14637i	−0.108440	+	0.0431442i
$707$	7.53037	+	25.6461i	0.283209	+	0.964521i
$708$	−4.53199	+	7.77269i	−0.170322	+	0.292116i
$709$	−9.20183	+	31.3385i	−0.345582	+	1.17694i	0.585053	+	0.810995i	$0.301074\pi$
$709$	−9.20183	+	31.3385i	−0.345582	+	1.17694i	−0.930635	+	0.365949i	$0.880745\pi$
$710$	0.217930	−	1.11786i	0.00817876	−	0.0419526i
$711$	−1.65382	+	11.5026i	−0.0620230	+	0.431380i
$712$	28.9875	+	8.71383i	1.08635	+	0.326565i
$713$	−38.9159	−	11.3266i	−1.45741	−	0.424183i
$714$	−9.16818	−	6.55822i	−0.343111	−	0.245435i
$715$	3.91549	+	0.562963i	0.146431	+	0.0210536i
$716$	−3.36236	−	3.55667i	−0.125657	−	0.132919i
$717$	−3.67276	+	12.5083i	−0.137162	+	0.467131i
$718$	−2.48084	+	0.231541i	−0.0925841	+	0.00864102i
$719$	−16.9830	+	4.98665i	−0.633358	+	0.185971i	−0.582624	−	0.812742i	$-0.697974\pi$
$719$	−16.9830	+	4.98665i	−0.633358	+	0.185971i	−0.0507334	+	0.998712i	$0.516156\pi$
$720$	−0.284354	−	3.27348i	−0.0105972	−	0.121995i
$721$	−9.15092	+	20.0377i	−0.340798	+	0.746244i
$722$	3.24134	+	13.4868i	0.120630	+	0.501926i
$723$	6.87668	+	10.7003i	0.255746	+	0.397949i
$724$	10.0834	+	19.7661i	0.374747	+	0.734602i
$725$	−4.45132	+	0.640004i	−0.165318	+	0.0237691i
$726$	−9.30959	−	0.463420i	−0.345511	−	0.0171991i
$727$	6.39838	−	7.38413i	0.237303	−	0.273862i	−0.624590	−	0.780953i	$-0.714734\pi$
$727$	6.39838	−	7.38413i	0.237303	−	0.273862i	0.861893	+	0.507091i	$0.169279\pi$
$728$	10.8215	+	9.49906i	0.401071	+	0.352059i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	12.0330	+	4.19349i	0.445361	+	0.155208i
$731$	−25.1249	+	21.7709i	−0.929280	+	0.805225i
$732$	−1.17312	−	27.0606i	−0.0433596	−	1.00019i
$733$	−3.60469	+	1.64621i	−0.133142	+	0.0608041i	−0.480872	−	0.876791i	$-0.659680\pi$
$733$	−3.60469	+	1.64621i	−0.133142	+	0.0608041i	0.347730	+	0.937595i	$0.386953\pi$
$734$	−4.00018	−	3.83053i	−0.147649	−	0.141387i
$735$	−1.70245			−0.0627956
$736$	−13.7596	+	23.3810i	−0.507186	+	0.861837i
$737$	16.9805			0.625485
$738$	−12.0614	−	11.5498i	−0.443986	−	0.425155i
$739$	−15.7642	+	7.19929i	−0.579897	+	0.264830i	−0.683694	−	0.729768i	$-0.739628\pi$
$739$	−15.7642	+	7.19929i	−0.579897	+	0.264830i	0.103798	+	0.994598i	$0.466901\pi$
$740$	0.145131	+	3.34777i	0.00533510	+	0.123066i
$741$	−9.30282	+	8.06094i	−0.341748	+	0.296126i
$742$	0.676962	+	0.235921i	0.0248520	+	0.00866091i
$743$	−3.07864	−	1.97852i	−0.112944	−	0.0725848i	0.482949	−	0.875648i	$-0.339566\pi$
$743$	−3.07864	−	1.97852i	−0.112944	−	0.0725848i	−0.595893	+	0.803064i	$0.703202\pi$
$744$	−17.9645	−	15.7691i	−0.658609	−	0.578125i
$745$	10.0760	−	11.6284i	0.369158	−	0.426031i
$746$	−32.2550	−	1.60561i	−1.18094	−	0.0587857i
$747$	3.20898	−	0.461381i	0.117410	−	0.0168811i
$748$	6.85241	+	13.4325i	0.250549	+	0.491142i
$749$	−1.48805	−	2.31546i	−0.0543723	−	0.0846049i
$750$	−2.53151	−	10.5332i	−0.0924375	−	0.384620i
$751$	17.3147	−	37.9138i	0.631821	−	1.38349i	−0.274781	−	0.961507i	$-0.588605\pi$
$751$	17.3147	−	37.9138i	0.631821	−	1.38349i	0.906602	−	0.421988i	$-0.138667\pi$
$752$	5.22011	−	0.453450i	0.190358	−	0.0165356i
$753$	−22.3985	+	6.57678i	−0.816245	+	0.239671i
$754$	−3.35765	+	0.313374i	−0.122278	+	0.0114124i
$755$	1.46847	−	5.00117i	0.0534433	−	0.182011i
$756$	3.04991	+	3.22616i	0.110924	+	0.117334i
$757$	−6.34377	−	0.912096i	−0.230568	−	0.0331507i	0.0260622	−	0.999660i	$-0.491703\pi$
$757$	−6.34377	−	0.912096i	−0.230568	−	0.0331507i	−0.256630	+	0.966510i	$0.582612\pi$
$758$	43.7833	+	31.3192i	1.59028	+	1.13757i
$759$	−6.61253	−	7.59480i	−0.240020	−	0.275674i
$760$	−11.9426	−	3.59002i	−0.433203	−	0.130224i
$761$	0.361321	−	2.51304i	0.0130979	−	0.0910977i	−0.982224	−	0.187713i	$-0.939893\pi$
$761$	0.361321	−	2.51304i	0.0130979	−	0.0910977i	0.995322	+	0.0966152i	$0.0308016\pi$
$762$	−1.01887	+	5.22627i	−0.0369099	+	0.189328i
$763$	−1.74286	+	5.93563i	−0.0630957	+	0.214884i
$764$	−9.03522	+	15.4961i	−0.326883	+	0.560628i
$765$	0.831006	+	2.83015i	0.0300451	+	0.102324i
$766$	−5.58908	+	2.22368i	−0.201942	+	0.0803447i
$767$	−4.28597	+	9.38497i	−0.154757	+	0.338872i
$768$	−13.1900	+	9.05666i	−0.475954	+	0.326804i
$769$	16.8648	−	10.8383i	0.608159	−	0.390840i	−0.200008	−	0.979794i	$-0.564097\pi$
$769$	16.8648	−	10.8383i	0.608159	−	0.390840i	0.808166	+	0.588955i	$0.200460\pi$
$770$	−4.80752	−	2.49147i	−0.173251	−	0.0897864i
$771$	9.76174	−	1.40353i	0.351561	−	0.0505468i
$772$	−8.18419	−	6.49294i	−0.294556	−	0.233686i
$773$	27.7555	+	24.0502i	0.998294	+	0.865027i	0.990853	−	0.134945i	$-0.0430859\pi$
$773$	27.7555	+	24.0502i	0.998294	+	0.865027i	0.00744121	+	0.999972i	$0.497631\pi$
$774$	11.3533	−	6.52251i	0.408086	−	0.234447i
$775$	−30.7507	−	19.7623i	−1.10460	−	0.709883i
$776$	−25.2116	−	0.161695i	−0.905042	−	0.00580451i
$777$	−2.96493	−	3.42171i	−0.106366	−	0.122753i
$778$	−11.5473	−	14.7484i	−0.413991	−	0.528755i
$779$	−57.6519	+	26.3287i	−2.06559	+	0.943325i
$780$	−0.697240	−	3.70275i	−0.0249652	−	0.132580i
$781$		−	2.05855i		−	0.0736605i
$782$	7.95992	−	23.0161i	0.284646	−	0.823054i
$783$	−1.03974			−0.0371572
$784$	4.08343	+	7.21448i	0.145837	+	0.257660i
$785$	−0.802983	−	1.75829i	−0.0286597	−	0.0627560i
$786$	3.79788	−	2.97357i	0.135466	−	0.106064i
$787$	14.5217	−	12.5831i	0.517641	−	0.448538i	−0.356440	−	0.934318i	$-0.616010\pi$
$787$	14.5217	−	12.5831i	0.517641	−	0.448538i	0.874081	+	0.485780i	$0.161464\pi$
$788$	18.9850	−	13.3972i	0.676311	−	0.477254i
$789$	2.01756	−	3.13938i	0.0718270	−	0.111765i
$790$	−11.7058	+	6.72500i	−0.416472	+	0.239265i
$791$	11.3490	−	13.0975i	0.403526	−	0.465694i
$792$	−1.63663	−	5.70905i	−0.0581552	−	0.202862i
$793$	−4.42023	−	30.7434i	−0.156967	−	1.09173i
$794$	−13.8052	+	26.6384i	−0.489929	+	0.945362i
$795$	−0.101418	−	0.157810i	−0.00359693	−	0.00559694i
$796$	25.2800	+	10.2462i	0.896025	+	0.363167i
$797$	19.2341	+	8.78392i	0.681306	+	0.311142i	0.725838	−	0.687866i	$-0.241452\pi$
$797$	19.2341	+	8.78392i	0.681306	+	0.311142i	−0.0445315	+	0.999008i	$0.514179\pi$
$798$	15.6559	−	6.22886i	0.554212	−	0.220499i
$799$	−4.51314	+	1.32518i	−0.159663	+	0.0468814i
$800$	−17.8872	+	16.6940i	−0.632406	+	0.590222i
$801$	10.2682	+	3.01501i	0.362809	+	0.106530i
$802$	−17.9009	−	3.48982i	−0.632103	−	0.123230i
$803$	22.7978	+	3.27783i	0.804517	+	0.115672i
$804$	−5.22453	−	15.3067i	−0.184255	−	0.539826i
$805$	2.48364	+	8.38489i	0.0875370	+	0.295529i
$806$	−22.2938	−	15.9473i	−0.785264	−	0.561718i
$807$	−0.575493	+	4.00264i	−0.0202583	+	0.140900i
$808$	−33.7411	+	4.63056i	−1.18701	+	0.162903i
$809$	−12.0151	−	3.52794i	−0.422427	−	0.124036i	0.0636083	−	0.997975i	$-0.479739\pi$
$809$	−12.0151	−	3.52794i	−0.422427	−	0.124036i	−0.486035	+	0.873939i	$0.661557\pi$
$810$	−0.107955	−	1.15668i	−0.00379314	−	0.0406416i
$811$	4.98688	+	16.9837i	0.175113	+	0.596380i	0.999538	+	0.0304083i	$0.00968074\pi$
$811$	4.98688	+	16.9837i	0.175113	+	0.596380i	−0.824425	+	0.565972i	$0.808501\pi$
$812$	4.48121	+	1.10744i	0.157260	+	0.0388635i
$813$	−26.0188	−	11.8824i	−0.912518	−	0.416733i
$814$	1.41533	+	5.88900i	0.0496074	+	0.206409i
$815$	−6.93554	+	4.45720i	−0.242941	+	0.156129i
$816$	10.0001	−	10.3099i	0.350075	−	0.360917i
$817$	−7.07212	−	49.1877i	−0.247422	−	1.72086i
$818$	−1.51722	+	30.4793i	−0.0530484	+	1.06568i
$819$	3.84743	+	3.33382i	0.134440	+	0.116493i
$820$	1.92664	−	19.3041i	0.0672813	−	0.674129i
$821$	−5.77751	+	8.98998i	−0.201636	+	0.313752i	−0.927315	−	0.374281i	$-0.877889\pi$
$821$	−5.77751	+	8.98998i	−0.201636	+	0.313752i	0.725679	+	0.688034i	$0.241526\pi$
$822$	11.3636	+	3.96021i	0.396351	+	0.138128i
$823$	−35.5272	−	41.0005i	−1.23840	−	1.42919i	−0.865192	−	0.501440i	$-0.832804\pi$
$823$	−35.5272	−	41.0005i	−1.23840	−	1.42919i	−0.373206	−	0.927748i	$-0.621742\pi$
$824$	−23.5146	−	15.3259i	−0.819171	−	0.533903i
$825$	−3.77276	−	8.26119i	−0.131351	−	0.287618i
$826$	9.76759	−	10.2002i	0.339858	−	0.354911i
$827$		−	10.0489i		−	0.349436i	−0.984619	−	0.174718i	$-0.944099\pi$
$827$		−	10.0489i		−	0.349436i	0.984619	−	0.174718i	$-0.0559014\pi$
$828$	−4.81164	+	8.29748i	−0.167216	+	0.288357i
$829$		−	21.4918i		−	0.746442i	−0.927743	−	0.373221i	$-0.878253\pi$
$829$		−	21.4918i		−	0.746442i	0.927743	−	0.373221i	$-0.121747\pi$
$830$	2.72018	+	2.60482i	0.0944190	+	0.0904145i
$831$	−1.91074	−	4.18394i	−0.0662828	−	0.145139i
$832$	−14.0188	+	11.8360i	−0.486015	+	0.410339i
$833$	−4.87333	−	5.62412i	−0.168851	−	0.194864i
$834$	−9.13336	+	26.2077i	−0.316263	+	0.907499i
$835$	4.17841	−	6.50173i	0.144600	−	0.225002i
$836$	−22.4287	−	2.23849i	−0.775713	−	0.0774199i
$837$	−6.38702	−	5.53439i	−0.220768	−	0.191296i
$838$	−35.7119	−	1.77769i	−1.23365	−	0.0614094i
$839$	5.47291	+	38.0649i	0.188946	+	1.31415i	0.834744	+	0.550638i	$0.185616\pi$
$839$	5.47291	+	38.0649i	0.188946	+	1.31415i	−0.645798	+	0.763508i	$0.723475\pi$
$840$	−0.766717	+	5.10021i	−0.0264542	+	0.175974i
$841$	23.4869	−	15.0941i	0.809893	−	0.520487i
$842$	15.0670	−	3.62113i	0.519244	−	0.124792i
$843$	0.445170	+	0.203302i	0.0153325	+	0.00700211i
$844$	−17.6305	−	4.35702i	−0.606867	−	0.149975i
$845$	1.79134	+	6.10075i	0.0616241	+	0.209872i
$846$	1.84452	−	0.172152i	0.0634159	−	0.00591870i
$847$	14.0381	+	4.12196i	0.482355	+	0.141632i
$848$	−0.425495	+	0.808299i	−0.0146116	+	0.0277571i
$849$	−1.20069	+	8.35098i	−0.0412075	+	0.286605i
$850$	12.7785	−	17.8639i	0.438299	−	0.612728i
$851$	5.26887	−	8.24143i	0.180614	−	0.282513i
$852$	−1.85563	+	0.633369i	−0.0635729	+	0.0216989i
$853$	−8.72676	−	1.25472i	−0.298798	−	0.0429607i	−0.00871481	−	0.999962i	$-0.502774\pi$
$853$	−8.72676	−	1.25472i	−0.298798	−	0.0429607i	−0.290084	+	0.957001i	$0.593683\pi$
$854$	−8.13529	+	41.7297i	−0.278384	+	1.42796i
$855$	−4.23040	−	1.24216i	−0.144677	−	0.0424809i
$856$	3.19939	−	1.43639i	0.109353	−	0.0490947i
$857$	12.0541	−	3.53940i	0.411760	−	0.120904i	−0.0692905	−	0.997597i	$-0.522074\pi$
$857$	12.0541	−	3.53940i	0.411760	−	0.120904i	0.481051	+	0.876693i	$0.340255\pi$
$858$	−2.51759	−	6.32781i	−0.0859492	−	0.216028i
$859$	−29.3887	−	13.4214i	−1.00273	−	0.457931i	−0.154745	−	0.987954i	$-0.549456\pi$
$859$	−29.3887	−	13.4214i	−1.00273	−	0.457931i	−0.847983	+	0.530024i	$0.822183\pi$
$860$	14.0970	+	5.71363i	0.480703	+	0.194833i
$861$	14.1714	+	22.0511i	0.482960	+	0.751501i
$862$	15.8012	+	8.18888i	0.538190	+	0.278914i
$863$	2.22698	+	15.4890i	0.0758072	+	0.527251i	0.991973	+	0.126451i	$0.0403586\pi$
$863$	2.22698	+	15.4890i	0.0758072	+	0.527251i	−0.916166	+	0.400800i	$0.868732\pi$
$864$	−4.64275	+	3.23186i	−0.157949	+	0.109950i
$865$	−10.0319	+	11.5774i	−0.341094	+	0.393643i
$866$	20.0223	+	34.8515i	0.680385	+	1.18430i
$867$	2.22015	−	3.45462i	0.0754001	−	0.117325i
$868$	21.6329	+	30.6558i	0.734270	+	1.04053i
$869$	−18.4410	+	15.9792i	−0.625568	+	0.542058i
$870$	−0.744626	−	0.951046i	−0.0252452	−	0.0322435i
$871$	−7.70447	−	16.8704i	−0.261056	−	0.571633i
$872$	−7.14890	−	3.32037i	−0.242092	−	0.112442i
$873$	−8.91382			−0.301687
$874$	22.5095	+	28.6094i	0.761395	+	0.967727i
$875$			17.0041i			0.574845i
$876$	−4.05966	−	21.5591i	−0.137163	−	0.728415i
$877$	−27.0623	+	12.3590i	−0.913830	+	0.417332i	−0.816120	−	0.577883i	$-0.803879\pi$
$877$	−27.0623	+	12.3590i	−0.913830	+	0.417332i	−0.0977103	+	0.995215i	$0.531152\pi$
$878$	16.3103	−	12.7702i	0.550447	−	0.430975i
$879$	−12.5225	−	14.4518i	−0.422374	−	0.487446i
$880$	4.04995	−	5.58565i	0.136524	−	0.188292i
$881$	28.1632	+	18.0994i	0.948842	+	0.609784i	0.920889	−	0.389825i	$-0.127465\pi$
$881$	28.1632	+	18.0994i	0.948842	+	0.609784i	0.0279536	+	0.999609i	$0.491101\pi$
$882$	1.46004	+	2.54139i	0.0491621	+	0.0855732i
$883$	6.01514	+	5.21215i	0.202425	+	0.175403i	0.750174	−	0.661240i	$-0.229970\pi$
$883$	6.01514	+	5.21215i	0.202425	+	0.175403i	−0.547749	+	0.836643i	$0.684515\pi$
$884$	10.2364	−	12.9027i	0.344286	−	0.433964i
$885$	−3.65786	+	0.525920i	−0.122958	+	0.0176786i
$886$	−1.44548	+	2.78919i	−0.0485619	+	0.0937045i
$887$	−44.4303	+	28.5536i	−1.49182	+	0.958736i	−0.495914	+	0.868372i	$0.665167\pi$
$887$	−44.4303	+	28.5536i	−1.49182	+	0.958736i	−0.995909	+	0.0903643i	$0.971197\pi$
$888$	4.87305	−	3.08774i	0.163529	−	0.103618i
$889$	3.47195	−	7.60250i	0.116445	−	0.254980i
$890$	4.59591	+	11.5515i	0.154055	+	0.387208i
$891$	−0.591570	−	2.01470i	−0.0198183	−	0.0674950i
$892$	22.8672	−	39.2190i	0.765651	−	1.31315i
$893$	1.98083	−	6.74607i	0.0662858	−	0.225749i
$894$	−26.0001	−	5.06877i	−0.869572	−	0.169525i
$895$	0.286091	−	1.98980i	0.00956295	−	0.0665118i
$896$	23.4523	−	8.98406i	0.783485	−	0.300136i
$897$	−4.54530	+	10.0156i	−0.151763	+	0.334412i
$898$	−17.5185	+	24.4903i	−0.584599	+	0.817250i
$899$	−8.69765	−	1.25053i	−0.290083	−	0.0417076i
$900$	−6.28608	+	5.94266i	−0.209536	+	0.198089i
$901$	0.231019	−	0.786778i	0.00769636	−	0.0262114i
$902$	−3.25851	−	34.9133i	−0.108497	−	1.16249i
$903$	−19.7196	+	5.79019i	−0.656227	+	0.192686i
$904$	14.3534	+	16.7810i	0.477387	+	0.558127i
$905$	−3.78601	+	8.29021i	−0.125851	+	0.275576i
$906$	−8.72507	+	2.09694i	−0.289871	+	0.0696661i
$907$	21.5568	+	33.5430i	0.715781	+	1.11378i	0.988432	+	0.151664i	$0.0484630\pi$
$907$	21.5568	+	33.5430i	0.715781	+	1.11378i	−0.272652	+	0.962113i	$0.587901\pi$
$908$	19.9419	+	39.0914i	0.661795	+	1.29729i
$909$	−11.9185	+	1.71362i	−0.395312	+	0.0568373i
$910$	−0.294033	+	5.90680i	−0.00974710	+	0.195808i
$911$	29.2804	−	33.7914i	0.970102	−	1.11956i	−0.0226938	−	0.999742i	$-0.507224\pi$
$911$	29.2804	−	33.7914i	0.970102	−	1.11956i	0.992796	−	0.119815i	$-0.0382303\pi$
$912$	4.88298	+	20.9066i	0.161692	+	0.692287i
$913$	5.72672	+	3.68034i	0.189527	+	0.121801i
$914$	11.1717	−	32.0565i	0.369526	−	1.06034i
$915$	8.40767	−	7.28529i	0.277949	−	0.240844i
$916$	−45.2700	+	1.96252i	−1.49576	+	0.0648434i
$917$	−6.88693	+	3.14516i	−0.227426	+	0.103862i
$918$	3.51213	−	3.66769i	0.115918	−	0.121052i
$919$	−0.966399			−0.0318785			−0.0159393	−	0.999873i	$-0.505074\pi$
$919$	−0.966399			−0.0318785			−0.0159393	+	0.999873i	$0.505074\pi$
$920$	−11.0356	+	1.54118i	−0.363833	+	0.0508113i
$921$	8.57428			0.282532
$922$	37.7640	−	39.4366i	1.24369	−	1.29877i
$923$	−2.04520	+	0.934012i	−0.0673186	+	0.0307434i
$924$	0.403746	+	9.31333i	0.0132823	+	0.306386i
$925$	6.66711	−	5.77708i	0.219213	−	0.189949i
$926$	−0.649390	+	1.86339i	−0.0213403	+	0.0612348i
$927$	−8.34825	−	5.36510i	−0.274193	−	0.176213i
$928$	−2.24423	+	5.43666i	−0.0736704	+	0.178467i
$929$	29.6610	−	34.2306i	0.973146	−	1.12307i	−0.0192292	−	0.999815i	$-0.506121\pi$
$929$	29.6610	−	34.2306i	0.973146	−	1.12307i	0.992375	−	0.123255i	$-0.0393333\pi$
$930$	0.488117	−	9.80573i	0.0160060	−	0.321543i
$931$	11.0105	−	1.58307i	0.360854	−	0.0518829i
$932$	38.2069	−	19.4907i	1.25151	−	0.638440i
$933$	16.9948	+	26.4445i	0.556386	+	0.865753i
$934$	−32.9769	+	7.92551i	−1.07904	+	0.259331i
$935$	−2.57287	+	5.63380i	−0.0841419	+	0.184245i
$936$	−4.92946	+	4.21636i	−0.161125	+	0.137816i
$937$	52.6225	−	15.4514i	1.71910	−	0.504774i	0.734356	−	0.678765i	$-0.237484\pi$
$937$	52.6225	−	15.4514i	1.71910	−	0.504774i	0.984747	+	0.173991i	$0.0556663\pi$
$938$	2.35915	+	25.2771i	0.0770290	+	0.825326i
$939$	5.40623	−	18.4119i	0.176426	−	0.600851i
$940$	1.47845	+	1.56389i	0.0482217	+	0.0510084i
$941$	24.6191	+	3.53969i	0.802559	+	0.115391i	0.531375	−	0.847137i	$-0.321676\pi$
$941$	24.6191	+	3.53969i	0.802559	+	0.115391i	0.271184	+	0.962527i	$0.412585\pi$
$942$	−1.93611	+	2.70662i	−0.0630817	+	0.0881863i
$943$	−36.9838	+	42.8867i	−1.20436	+	1.39658i
$944$	11.0023	+	14.2395i	0.358095	+	0.463456i
$945$	−0.259505	+	1.80490i	−0.00844170	+	0.0587133i
$946$	26.9852	+	5.26083i	0.877365	+	0.171044i
$947$	−14.9137	+	50.7915i	−0.484631	+	1.65050i	0.247162	+	0.968974i	$0.420502\pi$
$947$	−14.9137	+	50.7915i	−0.484631	+	1.65050i	−0.731793	+	0.681527i	$0.761316\pi$
$948$	20.0780	+	11.7068i	0.652104	+	0.380219i
$949$	−7.08734	−	24.1373i	−0.230065	−	0.783529i
$950$	12.1368	+	30.5050i	0.393769	+	0.989713i
$951$	11.0096	−	24.1078i	0.357012	−	0.781748i
$952$	−19.0436	+	12.0667i	−0.617206	+	0.391084i
$953$	46.7008	−	30.0128i	1.51279	−	0.972210i	0.519763	−	0.854311i	$-0.326020\pi$
$953$	46.7008	−	30.0128i	1.51279	−	0.972210i	0.993026	−	0.117900i	$-0.0376161\pi$
$954$	−0.148599	+	0.286736i	−0.00481108	+	0.00928341i
$955$	−7.29251	+	1.04850i	−0.235980	+	0.0339288i
$956$	20.4254	+	16.2046i	0.660606	+	0.524093i
$957$	−1.64995	−	1.42969i	−0.0533354	−	0.0462154i
$958$	−24.5111	−	42.6648i	−0.791916	−	1.37844i
$959$	−15.8903	−	10.2121i	−0.513125	−	0.329765i
$960$	−6.28115	−	1.93216i	−0.202723	−	0.0623602i
$961$	−26.4718	−	30.5500i	−0.853928	−	0.985485i
$962$	5.20866	−	4.07814i	0.167934	−	0.131485i
$963$	1.12788	−	0.515084i	0.0363453	−	0.0165983i
$964$	24.9996	−	4.70751i	0.805184	−	0.151619i
$965$		−	4.29084i		−	0.138127i
$966$	10.3869	−	10.8986i	0.334192	−	0.350655i
$967$	−3.47098			−0.111619			−0.0558096	−	0.998441i	$-0.517774\pi$
$967$	−3.47098			−0.111619			−0.0558096	+	0.998441i	$0.517774\pi$
$968$	−7.85286	+	16.9075i	−0.252400	+	0.543429i
$969$	−8.00617	−	17.5311i	−0.257195	−	0.563179i
$970$	−6.38377	−	8.15344i	−0.204971	−	0.261791i
$971$	−12.8424	+	11.1280i	−0.412131	+	0.357114i	−0.836113	−	0.548557i	$-0.815177\pi$
$971$	−12.8424	+	11.1280i	−0.412131	+	0.357114i	0.423982	+	0.905671i	$0.360632\pi$
$972$	−1.63410	+	1.15314i	−0.0524137	+	0.0369869i
$973$	23.5520	−	36.6476i	0.755042	−	1.17487i
$974$	−24.4673	−	42.5886i	−0.783984	−	1.36463i
$975$	−6.49585	+	7.49661i	−0.208034	+	0.240084i
$976$	−51.0393	−	18.1551i	−1.63373	−	0.581130i
$977$	−3.75350	−	26.1061i	−0.120085	−	0.835209i	−0.957457	−	0.288576i	$-0.906818\pi$
$977$	−3.75350	−	26.1061i	−0.120085	−	0.835209i	0.837372	−	0.546633i	$-0.184091\pi$
$978$	12.6017	+	6.53075i	0.402957	+	0.208830i
$979$	12.1487	+	18.9038i	0.388274	+	0.604167i
$980$	−1.27897	+	3.15555i	−0.0408553	+	0.100800i
$981$	−2.53500	−	1.15769i	−0.0809362	−	0.0369623i
$982$	17.7807	+	44.6906i	0.567404	+	1.42614i
$983$	12.4583	−	3.65808i	0.397357	−	0.116675i	−0.0769480	−	0.997035i	$-0.524518\pi$
$983$	12.4583	−	3.65808i	0.397357	−	0.116675i	0.474305	+	0.880361i	$0.342699\pi$
$984$	−30.4693	+	13.6794i	−0.971325	+	0.436083i
$985$	9.15705	+	2.68875i	0.291768	+	0.0856708i
$986$	1.01031	−	5.18232i	0.0321747	−	0.165039i
$987$	−2.87821	−	0.413824i	−0.0916144	−	0.0131722i
$988$	7.95247	+	23.2990i	0.253002	+	0.741239i
$989$	−24.0942	−	37.2966i	−0.766153	−	1.18596i
$990$	1.41918	−	1.98397i	0.0451045	−	0.0630546i
$991$	3.95099	−	27.4797i	0.125507	−	0.872922i	−0.825643	−	0.564193i	$-0.809187\pi$
$991$	3.95099	−	27.4797i	0.125507	−	0.872922i	0.951150	−	0.308729i	$-0.0999036\pi$
$992$	−42.7247	+	21.4512i	−1.35651	+	0.681076i
$993$	6.91076	+	2.02918i	0.219306	+	0.0643941i
$994$	3.06434	−	0.286000i	0.0971950	−	0.00907136i
$995$	3.15641	+	10.7497i	0.100065	+	0.340790i
$996$	1.55558	−	6.29459i	0.0492903	−	0.199452i
$997$	25.4266	+	11.6120i	0.805269	+	0.367754i	0.775138	−	0.631792i	$-0.217680\pi$
$997$	25.4266	+	11.6120i	0.805269	+	0.367754i	0.0301312	+	0.999546i	$0.490407\pi$
$998$	9.65438	−	2.32029i	0.305604	−	0.0734474i
$999$	1.71585	−	1.10271i	0.0542870	−	0.0348881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.445.10	yes	480
8.5	even	2	inner	552.2.bb.a.445.43	yes	480
23.3	even	11	inner	552.2.bb.a.325.43	yes	480
184.141	even	22	inner	552.2.bb.a.325.10	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.325.10	✓	480	184.141	even	22	inner
552.2.bb.a.325.43	yes	480	23.3	even	11	inner
552.2.bb.a.445.10	yes	480	1.1	even	1	trivial
552.2.bb.a.445.43	yes	480	8.5	even	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02143 - 0.978105i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.0866214 + 1.99812i) q^{4} +(-0.620811 + 0.537936i) q^{5} +(1.33544 + 0.465400i) q^{6} +(-1.86742 - 1.20011i) q^{7} +(1.86590 - 2.12566i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-1.02143 - 0.978105i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.0866214 + 1.99812i) q^{4} +(-0.620811 + 0.537936i) q^{5} +(1.33544 + 0.465400i) q^{6} +(-1.86742 - 1.20011i) q^{7} +(1.86590 - 2.12566i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.16027 + 0.0577568i) q^{10} +(2.07838 - 0.298827i) q^{11} +(-0.908844 - 1.78157i) q^{12} +(-1.23990 - 1.92933i) q^{13} +(0.733588 + 3.05236i) q^{14} +(0.341243 - 0.747218i) q^{15} +(-3.98499 + 0.346161i) q^{16} +(3.44530 - 1.01163i) q^{17} +(-1.40809 + 0.131420i) q^{18} +(-1.51215 + 5.14991i) q^{19} +(-1.12864 - 1.19386i) q^{20} +(2.19721 + 0.315911i) q^{21} +(-2.41520 - 1.72765i) q^{22} +(0.693775 + 4.74538i) q^{23} +(-0.814249 + 2.70869i) q^{24} +(-0.615543 + 4.28119i) q^{25} +(-0.620615 + 3.18342i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(2.23622 - 3.83528i) q^{28} +(0.292928 + 0.997622i) q^{29} +(-1.07941 + 0.429456i) q^{30} +(-3.51077 + 7.68752i) q^{31} +(4.40896 + 3.54416i) q^{32} +(-1.76643 + 1.13521i) q^{33} +(-4.50860 - 2.33656i) q^{34} +(1.80490 - 0.259505i) q^{35} +(1.56681 + 1.24303i) q^{36} +(-1.54145 - 1.33567i) q^{37} +(6.58170 - 3.78121i) q^{38} +(1.92933 + 1.23990i) q^{39} +(-0.0149010 + 2.32337i) q^{40} +(7.73284 + 8.92418i) q^{41} +(-1.93529 - 2.47178i) q^{42} +(-8.42185 + 3.84613i) q^{43} +(0.777125 + 4.12698i) q^{44} +0.821451i q^{45} +(3.93284 - 5.52564i) q^{46} -1.30994 q^{47} +(3.48108 - 1.97030i) q^{48} +(-0.860942 - 1.88520i) q^{49} +(4.81619 - 3.77086i) q^{50} +(-2.71371 + 2.35144i) q^{51} +(3.74763 - 2.64460i) q^{52} +(0.123462 - 0.192111i) q^{53} +(1.22625 - 0.704487i) q^{54} +(-1.12953 + 1.30355i) q^{55} +(-6.03544 + 1.73020i) q^{56} +(-0.763849 - 5.31269i) q^{57} +(0.676575 - 1.30551i) q^{58} +(-2.43219 - 3.78456i) q^{59} +(1.52259 + 0.617121i) q^{60} +(12.3192 + 5.62598i) q^{61} +(11.1052 - 4.41833i) q^{62} +(-2.12988 + 0.625390i) q^{63} +(-1.03686 - 7.93252i) q^{64} +(1.80760 + 0.530759i) q^{65} +(2.91463 + 0.568215i) q^{66} +(8.00457 + 1.15088i) q^{67} +(2.31980 + 6.79651i) q^{68} +(-2.60238 - 4.02835i) q^{69} +(-2.09739 - 1.50031i) q^{70} +(0.139522 - 0.970394i) q^{71} +(-0.384564 - 2.80216i) q^{72} +(10.5247 + 3.09033i) q^{73} +(0.268048 + 2.87199i) q^{74} +(-1.21855 - 4.15002i) q^{75} +(-10.4211 - 2.57537i) q^{76} +(-4.23983 - 1.93627i) q^{77} +(-0.757909 - 3.15355i) q^{78} +(-9.77608 + 6.28270i) q^{79} +(2.28772 - 2.35857i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.830256 - 16.6789i) q^{82} +(2.45012 + 2.12304i) q^{83} +(-0.440903 + 4.41765i) q^{84} +(-1.59469 + 2.48138i) q^{85} +(12.3642 + 4.30892i) q^{86} +(-0.680884 - 0.785782i) q^{87} +(3.24285 - 4.97552i) q^{88} +(4.44564 + 9.73460i) q^{89} +(0.803465 - 0.839051i) q^{90} +5.09088i q^{91} +(-9.42177 + 1.79730i) q^{92} -8.45124i q^{93} +(1.33801 + 1.28126i) q^{94} +(-1.83156 - 4.01056i) q^{95} +(-5.48283 - 1.39234i) q^{96} +(-5.83731 - 6.73661i) q^{97} +(-0.964535 + 2.76768i) q^{98} +(1.13521 - 1.76643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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