LMFDB - Embedded newform 552.2.bb.a.469.13

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			469.13
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.960856 + 1.03767i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-0.153511 - 1.99410i) q^{4} +(0.708272 - 0.101834i) q^{5} +(0.0466382 - 1.41344i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(2.21672 + 1.75675i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.960856 + 1.03767i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-0.153511 - 1.99410i) q^{4} +(0.708272 - 0.101834i) q^{5} +(0.0466382 - 1.41344i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(2.21672 + 1.75675i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-0.574878 + 0.832800i) q^{10} +(-0.408449 + 1.39105i) q^{11} +(1.42187 + 1.40651i) q^{12} +(5.37158 - 2.45312i) q^{13} +(-2.08279 - 4.98993i) q^{14} +(-0.468589 + 0.540781i) q^{15} +(-3.95287 + 0.612234i) q^{16} +(-2.62931 - 1.68976i) q^{17} +(0.890362 + 1.09875i) q^{18} +(4.06828 + 6.33036i) q^{19} +(-0.311795 - 1.39673i) q^{20} +(-1.07719 - 3.66856i) q^{21} +(-1.05099 - 1.76043i) q^{22} +(-4.77745 - 0.419530i) q^{23} +(-2.82571 + 0.123979i) q^{24} +(-4.30619 + 1.26441i) q^{25} +(-2.61579 + 7.93102i) q^{26} +(0.540641 + 0.841254i) q^{27} +(7.17915 + 2.63336i) q^{28} +(-4.55518 + 7.08801i) q^{29} +(-0.110904 - 1.00585i) q^{30} +(0.311933 - 0.359990i) q^{31} +(3.16284 - 4.69004i) q^{32} +(-0.602259 - 1.31876i) q^{33} +(4.27980 - 1.10474i) q^{34} +(-0.770788 + 2.62506i) q^{35} +(-1.99565 - 0.131841i) q^{36} +(-5.60156 - 0.805383i) q^{37} +(-10.4778 - 1.86104i) q^{38} +(-2.45312 + 5.37158i) q^{39} +(1.74894 + 1.01852i) q^{40} +(1.28520 + 8.93879i) q^{41} +(4.84178 + 2.40720i) q^{42} +(2.10648 - 1.82527i) q^{43} +(2.83660 + 0.600947i) q^{44} -0.715556i q^{45} +(5.02577 - 4.55430i) q^{46} -9.11704 q^{47} +(2.58645 - 3.05127i) q^{48} +(-4.98919 - 5.75783i) q^{49} +(2.82559 - 5.68331i) q^{50} +(3.09366 - 0.444801i) q^{51} +(-5.71636 - 10.3349i) q^{52} +(-4.16104 - 1.90028i) q^{53} +(-1.39242 - 0.247318i) q^{54} +(-0.147637 + 1.02684i) q^{55} +(-9.63068 + 4.91930i) q^{56} +(-7.22010 - 2.12001i) q^{57} +(-2.97812 - 11.5373i) q^{58} +(1.26601 - 0.578167i) q^{59} +(1.15030 + 0.851398i) q^{60} +(3.93018 + 3.40552i) q^{61} +(0.0738275 + 0.669582i) q^{62} +(3.21648 + 2.06711i) q^{63} +(1.82767 + 7.78843i) q^{64} +(3.55473 - 2.28449i) q^{65} +(1.94712 + 0.642197i) q^{66} +(-3.26376 - 11.1154i) q^{67} +(-2.96591 + 5.50251i) q^{68} +(3.88529 - 2.81150i) q^{69} +(-1.98333 - 3.32213i) q^{70} +(-13.1999 + 3.87584i) q^{71} +(2.05434 - 1.94414i) q^{72} +(7.18235 - 4.61582i) q^{73} +(6.21802 - 5.03871i) q^{74} +(2.42639 - 3.77553i) q^{75} +(11.9988 - 9.08433i) q^{76} +(-4.18922 - 3.62998i) q^{77} +(-3.21683 - 7.70684i) q^{78} +(5.49995 + 12.0432i) q^{79} +(-2.73736 + 0.836166i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-10.5104 - 7.25528i) q^{82} +(11.5494 + 1.66055i) q^{83} +(-7.15012 + 2.71119i) q^{84} +(-2.03434 - 0.929053i) q^{85} +(-0.129993 + 3.93965i) q^{86} +(-1.19908 - 8.33977i) q^{87} +(-3.34914 + 2.36602i) q^{88} +(-3.74534 - 4.32235i) q^{89} +(0.742509 + 0.687546i) q^{90} +22.5783i q^{91} +(-0.103191 + 9.59111i) q^{92} +0.476335i q^{93} +(8.76016 - 9.46046i) q^{94} +(3.52609 + 4.06933i) q^{95} +(0.681004 + 5.61571i) q^{96} +(1.61798 + 11.2533i) q^{97} +(10.7686 + 0.355323i) q^{98} +(1.31876 + 0.602259i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.960856	+	1.03767i	−0.679428	+	0.733742i
$2$	−0.960856	+	1.03767i	−0.679428	+	0.733742i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	−0.153511	−	1.99410i	−0.0767557	−	0.997050i
$5$	0.708272	−	0.101834i	0.316749	−	0.0455416i	0.0178932	−	0.999840i	$-0.494304\pi$
$5$	0.708272	−	0.101834i	0.316749	−	0.0455416i	0.298856	+	0.954298i	$0.403395\pi$
$6$	0.0466382	−	1.41344i	0.0190400	−	0.577036i
$7$	−1.58831	+	3.47792i	−0.600327	+	1.31453i	0.328671	+	0.944445i	$0.393399\pi$
$7$	−1.58831	+	3.47792i	−0.600327	+	1.31453i	−0.928997	+	0.370087i	$0.879328\pi$
$8$	2.21672	+	1.75675i	0.783728	+	0.621105i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−0.574878	+	0.832800i	−0.181792	+	0.263354i
$11$	−0.408449	+	1.39105i	−0.123152	+	0.419418i	−0.997871	−	0.0652123i	$-0.979228\pi$
$11$	−0.408449	+	1.39105i	−0.123152	+	0.419418i	0.874719	+	0.484630i	$0.161046\pi$
$12$	1.42187	+	1.40651i	0.410460	+	0.406025i
$13$	5.37158	−	2.45312i	1.48981	−	0.680373i	0.506487	−	0.862248i	$-0.330944\pi$
$13$	5.37158	−	2.45312i	1.48981	−	0.680373i	0.983322	+	0.181875i	$0.0582165\pi$
$14$	−2.08279	−	4.98993i	−0.556649	−	1.33361i
$15$	−0.468589	+	0.540781i	−0.120989	+	0.139629i
$16$	−3.95287	+	0.612234i	−0.988217	+	0.153059i
$17$	−2.62931	−	1.68976i	−0.637702	−	0.409826i	0.181452	−	0.983400i	$-0.441920\pi$
$17$	−2.62931	−	1.68976i	−0.637702	−	0.409826i	−0.819154	+	0.573574i	$0.805557\pi$
$18$	0.890362	+	1.09875i	0.209860	+	0.258978i
$19$	4.06828	+	6.33036i	0.933326	+	1.45228i	0.891428	+	0.453162i	$0.149704\pi$
$19$	4.06828	+	6.33036i	0.933326	+	1.45228i	0.0418984	+	0.999122i	$0.486659\pi$
$20$	−0.311795	−	1.39673i	−0.0697196	−	0.312319i
$21$	−1.07719	−	3.66856i	−0.235062	−	0.800546i
$22$	−1.05099	−	1.76043i	−0.224072	−	0.375326i
$23$	−4.77745	−	0.419530i	−0.996166	−	0.0874780i
$23$	−4.77745	−	0.419530i	−0.996166	−	0.0874780i
$24$	−2.82571	+	0.123979i	−0.576795	+	0.0253070i
$25$	−4.30619	+	1.26441i	−0.861237	+	0.252882i
$26$	−2.61579	+	7.93102i	−0.512999	+	1.55540i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	7.17915	+	2.63336i	1.35673	+	0.497658i
$29$	−4.55518	+	7.08801i	−0.845877	+	1.31621i	0.101090	+	0.994877i	$0.467767\pi$
$29$	−4.55518	+	7.08801i	−0.845877	+	1.31621i	−0.946966	+	0.321332i	$0.895869\pi$
$30$	−0.110904	−	1.00585i	−0.0202483	−	0.183643i
$31$	0.311933	−	0.359990i	0.0560249	−	0.0646562i	−0.727045	−	0.686589i	$-0.759107\pi$
$31$	0.311933	−	0.359990i	0.0560249	−	0.0646562i	0.783070	+	0.621933i	$0.213652\pi$
$32$	3.16284	−	4.69004i	0.559117	−	0.829089i
$33$	−0.602259	−	1.31876i	−0.104840	−	0.229567i
$34$	4.27980	−	1.10474i	0.733979	−	0.189462i
$35$	−0.770788	+	2.62506i	−0.130287	+	0.443716i
$36$	−1.99565	−	0.131841i	−0.332608	−	0.0219735i
$37$	−5.60156	−	0.805383i	−0.920891	−	0.132404i	−0.334466	−	0.942408i	$-0.608556\pi$
$37$	−5.60156	−	0.805383i	−0.920891	−	0.132404i	−0.586425	+	0.810003i	$0.699465\pi$
$38$	−10.4778	−	1.86104i	−1.69973	−	0.301901i
$39$	−2.45312	+	5.37158i	−0.392813	+	0.860142i
$40$	1.74894	+	1.01852i	0.276531	+	0.161042i
$41$	1.28520	+	8.93879i	0.200715	+	1.39601i	0.802169	+	0.597097i	$0.203679\pi$
$41$	1.28520	+	8.93879i	0.200715	+	1.39601i	−0.601454	+	0.798908i	$0.705412\pi$
$42$	4.84178	+	2.40720i	0.747102	+	0.371439i
$43$	2.10648	−	1.82527i	0.321235	−	0.278351i	−0.479283	−	0.877660i	$-0.659103\pi$
$43$	2.10648	−	1.82527i	0.321235	−	0.278351i	0.800518	+	0.599309i	$0.204558\pi$
$44$	2.83660	+	0.600947i	0.427633	+	0.0905961i
$45$		−	0.715556i		−	0.106669i
$46$	5.02577	−	4.55430i	0.741009	−	0.671495i
$47$	−9.11704			−1.32986			−0.664928	−	0.746907i	$-0.731538\pi$
$47$	−9.11704			−1.32986			−0.664928	+	0.746907i	$0.731538\pi$
$48$	2.58645	−	3.05127i	0.373322	−	0.440413i
$49$	−4.98919	−	5.75783i	−0.712741	−	0.822547i
$50$	2.82559	−	5.68331i	0.399598	−	0.803741i
$51$	3.09366	−	0.444801i	0.433198	−	0.0622845i
$52$	−5.71636	−	10.3349i	−0.792717	−	1.43319i
$53$	−4.16104	−	1.90028i	−0.571563	−	0.261024i	0.108599	−	0.994086i	$-0.465363\pi$
$53$	−4.16104	−	1.90028i	−0.571563	−	0.261024i	−0.680162	+	0.733062i	$0.738091\pi$
$54$	−1.39242	−	0.247318i	−0.189484	−	0.0336557i
$55$	−0.147637	+	1.02684i	−0.0199074	+	0.138459i
$56$	−9.63068	+	4.91930i	−1.28695	+	0.657369i
$57$	−7.22010	−	2.12001i	−0.956326	−	0.280803i
$58$	−2.97812	−	11.5373i	−0.391047	−	1.51492i
$59$	1.26601	−	0.578167i	0.164820	−	0.0752709i	−0.331296	−	0.943527i	$-0.607486\pi$
$59$	1.26601	−	0.578167i	0.164820	−	0.0752709i	0.496117	+	0.868256i	$0.334759\pi$
$60$	1.15030	+	0.851398i	0.148504	+	0.109915i
$61$	3.93018	+	3.40552i	0.503209	+	0.436033i	0.869108	−	0.494622i	$-0.164693\pi$
$61$	3.93018	+	3.40552i	0.503209	+	0.436033i	−0.365900	+	0.930654i	$0.619239\pi$
$62$	0.0738275	+	0.669582i	0.00937610	+	0.0850370i
$63$	3.21648	+	2.06711i	0.405239	+	0.260431i
$64$	1.82767	+	7.78843i	0.228458	+	0.973554i
$65$	3.55473	−	2.28449i	0.440910	−	0.283356i
$66$	1.94712	+	0.642197i	0.239674	+	0.0790489i
$67$	−3.26376	−	11.1154i	−0.398732	−	1.35796i	−0.877315	−	0.479914i	$-0.840668\pi$
$67$	−3.26376	−	11.1154i	−0.398732	−	1.35796i	0.478584	−	0.878042i	$-0.341150\pi$
$68$	−2.96591	+	5.50251i	−0.359670	+	0.667277i
$69$	3.88529	−	2.81150i	0.467734	−	0.338465i
$70$	−1.98333	−	3.32213i	−0.237053	−	0.397070i
$71$	−13.1999	+	3.87584i	−1.56654	+	0.459978i	−0.945992	−	0.324189i	$-0.894909\pi$
$71$	−13.1999	+	3.87584i	−1.56654	+	0.459978i	−0.620549	+	0.784167i	$0.713090\pi$
$72$	2.05434	−	1.94414i	0.242106	−	0.229119i
$73$	7.18235	−	4.61582i	0.840630	−	0.540240i	−0.0480090	−	0.998847i	$-0.515288\pi$
$73$	7.18235	−	4.61582i	0.840630	−	0.540240i	0.888639	+	0.458607i	$0.151651\pi$
$74$	6.21802	−	5.03871i	0.722830	−	0.585738i
$75$	2.42639	−	3.77553i	0.280175	−	0.435961i
$76$	11.9988	−	9.08433i	1.37636	−	1.04204i
$77$	−4.18922	−	3.62998i	−0.477406	−	0.413675i
$78$	−3.21683	−	7.70684i	−0.364234	−	0.872628i
$79$	5.49995	+	12.0432i	0.618793	+	1.35497i	0.916394	+	0.400277i	$0.131086\pi$
$79$	5.49995	+	12.0432i	0.618793	+	1.35497i	−0.297601	+	0.954690i	$0.596187\pi$
$80$	−2.73736	+	0.836166i	−0.306046	+	0.0934862i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−10.5104	−	7.25528i	−1.16068	−	0.801211i
$83$	11.5494	+	1.66055i	1.26771	+	0.182269i	0.743161	−	0.669113i	$-0.233326\pi$
$83$	11.5494	+	1.66055i	1.26771	+	0.182269i	0.524546	+	0.851382i	$0.324235\pi$
$84$	−7.15012	+	2.71119i	−0.780142	+	0.295815i
$85$	−2.03434	−	0.929053i	−0.220655	−	0.100770i
$86$	−0.129993	+	3.93965i	−0.0140175	+	0.424823i
$87$	−1.19908	−	8.33977i	−0.128555	−	0.894117i
$88$	−3.34914	+	2.36602i	−0.357020	+	0.252219i
$89$	−3.74534	−	4.32235i	−0.397005	−	0.458168i	0.521690	−	0.853135i	$-0.325302\pi$
$89$	−3.74534	−	4.32235i	−0.397005	−	0.458168i	−0.918696	+	0.394966i	$0.870756\pi$
$90$	0.742509	+	0.687546i	0.0782674	+	0.0724737i
$91$			22.5783i			2.36685i
$92$	−0.103191	+	9.59111i	−0.0107584	+	0.999942i
$93$			0.476335i			0.0493937i
$94$	8.76016	−	9.46046i	0.903542	−	0.975772i
$95$	3.52609	+	4.06933i	0.361770	+	0.417504i
$96$	0.681004	+	5.61571i	0.0695047	+	0.573151i
$97$	1.61798	+	11.2533i	0.164281	+	1.14260i	0.890449	+	0.455083i	$0.150391\pi$
$97$	1.61798	+	11.2533i	0.164281	+	1.14260i	−0.726168	+	0.687518i	$0.758700\pi$
$98$	10.7686	+	0.355323i	1.08779	+	0.0358930i
$99$	1.31876	+	0.602259i	0.132541	+	0.0605293i
$100$	3.18241	+	8.39286i	0.318241	+	0.839286i
$101$	0.132610	+	0.0190665i	0.0131952	+	0.00189719i	0.148909	−	0.988851i	$-0.452424\pi$
$101$	0.132610	+	0.0190665i	0.0131952	+	0.00189719i	−0.135714	+	0.990748i	$0.543333\pi$
$102$	−2.51100	+	3.63758i	−0.248626	+	0.360174i
$103$	14.5733	+	4.27911i	1.43595	+	0.421634i	0.904871	−	0.425687i	$-0.139967\pi$
$103$	14.5733	+	4.27911i	1.43595	+	0.421634i	0.531082	+	0.847321i	$0.321786\pi$
$104$	16.2168	+	3.99865i	1.59019	+	0.392100i
$105$	−1.13653	−	2.48865i	−0.110914	−	0.242867i
$106$	5.97002	−	2.49188i	0.579860	−	0.242033i
$107$	1.72355	+	1.49346i	0.166622	+	0.144378i	0.734180	−	0.678954i	$-0.237567\pi$
$107$	1.72355	+	1.49346i	0.166622	+	0.144378i	−0.567559	+	0.823333i	$0.692112\pi$
$108$	1.59455	−	1.20723i	0.153436	−	0.116166i
$109$	0.459352	−	0.714766i	0.0439980	−	0.0684622i	−0.818558	−	0.574424i	$-0.805226\pi$
$109$	0.459352	−	0.714766i	0.0439980	−	0.0684622i	0.862556	+	0.505962i	$0.168862\pi$
$110$	−0.923658	−	1.13984i	−0.0880674	−	0.108680i
$111$	4.76079	−	3.05958i	0.451875	−	0.290402i
$112$	4.14909	−	14.7202i	0.392053	−	1.39093i
$113$	9.29057	−	2.72796i	0.873984	−	0.256625i	0.186175	−	0.982517i	$-0.440391\pi$
$113$	9.29057	−	2.72796i	0.873984	−	0.256625i	0.687809	+	0.725892i	$0.258573\pi$
$114$	9.13735	−	5.45504i	0.855791	−	0.510912i
$115$	−3.42646	+	0.189366i	−0.319519	+	0.0176585i
$116$	14.8335	+	7.99540i	1.37725	+	0.742355i
$117$	−1.66369	−	5.66602i	−0.153809	−	0.523824i
$118$	−0.616507	+	1.86923i	−0.0567541	+	0.172077i
$119$	10.0530	−	6.46068i	0.921558	−	0.592250i
$120$	−1.98875	+	0.375564i	−0.181547	+	0.0342842i
$121$	7.48560	+	4.81070i	0.680509	+	0.437336i
$122$	−7.31015	+	0.806010i	−0.661830	+	0.0729727i
$123$	−6.82496	−	5.91386i	−0.615386	−	0.533235i
$124$	−0.765742	−	0.566764i	−0.0687656	−	0.0508969i
$125$	−6.17565	+	2.82033i	−0.552367	+	0.252258i
$126$	−5.23555	+	1.35145i	−0.466420	+	0.120397i
$127$	−16.1877	−	4.75314i	−1.43643	−	0.421773i	−0.531397	−	0.847123i	$-0.678333\pi$
$127$	−16.1877	−	4.75314i	−1.43643	−	0.421773i	−0.905029	+	0.425350i	$0.860151\pi$
$128$	−9.83793	−	5.58705i	−0.869559	−	0.493830i
$129$	−0.396670	+	2.75890i	−0.0349248	+	0.242907i
$130$	−1.04504	+	5.88370i	−0.0916565	+	0.516034i
$131$	4.95676	+	2.26368i	0.433074	+	0.197778i	0.620010	−	0.784594i	$-0.287128\pi$
$131$	4.95676	+	2.26368i	0.433074	+	0.197778i	−0.186936	+	0.982372i	$0.559856\pi$
$132$	−2.53729	+	1.40341i	−0.220843	+	0.122151i
$133$	−28.4782	+	4.09455i	−2.46937	+	0.355042i
$134$	14.6701	+	7.29355i	1.26730	+	0.630067i
$135$	0.468589	+	0.540781i	0.0403297	+	0.0465430i
$136$	−2.85996	−	8.36475i	−0.245240	−	0.717271i
$137$	22.2078			1.89734			0.948671	−	0.316265i	$-0.102429\pi$
$137$	22.2078			1.89734			0.948671	+	0.316265i	$0.102429\pi$
$138$	−0.815793	+	6.73309i	−0.0694449	+	0.573159i
$139$			19.7869i			1.67831i	0.543895	+	0.839153i	$0.316949\pi$
$139$			19.7869i			1.67831i	−0.543895	+	0.839153i	$0.683051\pi$
$140$	5.35296	+	1.13405i	0.452408	+	0.0958448i
$141$	6.89020	−	5.97039i	0.580259	−	0.502798i
$142$	8.66138	−	17.4213i	0.726846	−	1.46196i
$143$	1.21839	+	8.47412i	0.101887	+	0.708641i
$144$	0.0434508	+	3.99976i	0.00362090	+	0.333314i
$145$	−2.50451	+	5.48411i	−0.207988	+	0.455431i
$146$	−2.11152	+	11.8880i	−0.174750	+	0.983861i
$147$	7.54115	+	1.08425i	0.621984	+	0.0894278i
$148$	−0.746111	+	11.2937i	−0.0613299	+	0.928338i
$149$	2.82573	−	9.62354i	0.231492	−	0.788391i	−0.759032	−	0.651053i	$-0.774327\pi$
$149$	2.82573	−	9.62354i	0.231492	−	0.788391i	0.990524	−	0.137337i	$-0.0438545\pi$
$150$	1.58634	+	6.14552i	0.129524	+	0.501780i
$151$	−3.44502	−	7.54354i	−0.280352	−	0.613884i	0.716105	−	0.697993i	$-0.245923\pi$
$151$	−3.44502	−	7.54354i	−0.280352	−	0.613884i	−0.996457	+	0.0841081i	$0.973196\pi$
$152$	−2.10264	+	21.1796i	−0.170546	+	1.71789i
$153$	−2.04675	+	2.36207i	−0.165470	+	0.190962i
$154$	7.79196	−	0.859134i	0.627894	−	0.0692310i
$155$	0.184274	−	0.286737i	0.0148013	−	0.0230312i
$156$	11.0881	+	4.06717i	0.887755	+	0.325634i
$157$	0.664966	+	1.03471i	0.0530700	+	0.0825786i	0.866775	−	0.498700i	$-0.166189\pi$
$157$	0.664966	+	1.03471i	0.0530700	+	0.0825786i	−0.813705	+	0.581279i	$0.802553\pi$
$158$	−17.7815	−	5.86467i	−1.41462	−	0.466568i
$159$	4.38913	−	1.28876i	0.348080	−	0.102206i
$160$	1.76255	−	3.64391i	0.139342	−	0.288076i
$161$	9.04718	−	15.9493i	0.713018	−	1.25698i
$162$	1.21428	−	0.724931i	0.0954028	−	0.0569560i
$163$	1.47331	+	5.01765i	0.115399	+	0.393012i	0.996854	−	0.0792546i	$-0.0252540\pi$
$163$	1.47331	+	5.01765i	0.115399	+	0.393012i	−0.881456	+	0.472267i	$0.843436\pi$
$164$	17.6276	−	3.93503i	1.37648	−	0.307274i
$165$	−0.560859	−	0.872713i	−0.0436628	−	0.0679406i
$166$	−12.8204	+	10.3889i	−0.995054	+	0.806332i
$167$	−14.8745	−	9.55923i	−1.15102	−	0.739715i	−0.181178	−	0.983450i	$-0.557991\pi$
$167$	−14.8745	−	9.55923i	−1.15102	−	0.739715i	−0.969842	+	0.243735i	$0.921627\pi$
$168$	4.05693	−	10.0245i	0.312999	−	0.773408i
$169$	14.3229	−	16.5295i	1.10176	−	1.27150i
$170$	2.91876	−	1.21829i	0.223859	−	0.0934384i
$171$	6.84490	−	3.12596i	0.523443	−	0.239048i
$172$	−3.96314	−	3.92032i	−0.302187	−	0.298922i
$173$	−2.40566	+	8.19292i	−0.182899	+	0.622897i	0.816089	+	0.577926i	$0.196138\pi$
$173$	−2.40566	+	8.19292i	−0.182899	+	0.622897i	−0.998988	+	0.0449708i	$0.985681\pi$
$174$	9.80606	+	6.76907i	0.743395	+	0.513162i
$175$	2.44206	−	16.9849i	0.184602	−	1.28394i
$176$	0.762898	−	5.74871i	0.0575056	−	0.433325i
$177$	−0.578167	+	1.26601i	−0.0434577	+	0.0951591i
$178$	8.08390	+	0.266738i	0.605914	+	0.0199928i
$179$	0.201507	−	0.0289723i	0.0150613	−	0.00216549i	−0.134780	−	0.990876i	$-0.543033\pi$
$179$	0.201507	−	0.0289723i	0.0150613	−	0.00216549i	0.149841	+	0.988710i	$0.452124\pi$
$180$	−1.42689	+	0.109846i	−0.106354	+	0.00818744i
$181$	5.75664	−	4.98816i	0.427888	−	0.370767i	−0.414129	−	0.910218i	$-0.635914\pi$
$181$	5.75664	−	4.98816i	0.427888	−	0.370767i	0.842017	+	0.539451i	$0.181368\pi$
$182$	−23.4288	−	21.6945i	−1.73666	−	1.60810i
$183$	−5.20038			−0.384423
$184$	−9.85324	−	9.32275i	−0.726390	−	0.687282i
$185$	−4.04945			−0.297721
$186$	−0.494278	−	0.457690i	−0.0362422	−	0.0335594i
$187$	3.42448	−	2.96733i	0.250423	−	0.216992i
$188$	1.39957	+	18.1803i	0.102074	+	1.32593i
$189$	−3.78452	+	0.544132i	−0.275284	+	0.0395798i
$190$	−7.61068	−	0.251123i	−0.552137	−	0.0182184i
$191$	0.862579	−	1.88878i	0.0624140	−	0.136668i	−0.875855	−	0.482575i	$-0.839702\pi$
$191$	0.862579	−	1.88878i	0.0624140	−	0.136668i	0.938269	+	0.345907i	$0.112429\pi$
$192$	−6.48160	−	4.68923i	−0.467769	−	0.338416i
$193$	−0.687034	+	4.77842i	−0.0494538	+	0.343959i	0.950040	+	0.312130i	$0.101042\pi$
$193$	−0.687034	+	4.77842i	−0.0494538	+	0.343959i	−0.999493	+	0.0318290i	$0.989867\pi$
$194$	−13.2319	−	9.13389i	−0.949992	−	0.655775i
$195$	−1.19047	+	4.05435i	−0.0852510	+	0.290338i
$196$	−10.7158	+	10.8328i	−0.765413	+	0.773774i
$197$	19.8941	−	9.08532i	1.41739	−	0.647302i	0.448275	−	0.893896i	$-0.352039\pi$
$197$	19.8941	−	9.08532i	1.41739	−	0.647302i	0.969119	+	0.246594i	$0.0793114\pi$
$198$	−1.89209	+	0.789755i	−0.134465	+	0.0561254i
$199$	6.64117	−	7.66431i	0.470780	−	0.543309i	−0.469849	−	0.882747i	$-0.655691\pi$
$199$	6.64117	−	7.66431i	0.470780	−	0.543309i	0.940628	+	0.339438i	$0.110237\pi$
$200$	−11.7668	−	4.76205i	−0.832042	−	0.336728i
$201$	9.74559	+	6.26311i	0.687401	+	0.441766i
$202$	−0.147204	+	0.119285i	−0.0103572	+	0.00839289i
$203$	−17.4165	−	27.1006i	−1.22240	−	1.90209i
$204$	−1.36189	−	6.10078i	−0.0953512	−	0.427140i
$205$	1.82055	+	6.20022i	0.127153	+	0.433042i
$206$	−18.4432	+	11.0107i	−1.28500	+	0.767149i
$207$	−1.09516	+	4.66911i	−0.0761189	+	0.324526i
$208$	−19.7313	+	12.9855i	−1.36812	+	0.900384i
$209$	−10.4675	+	3.07355i	−0.724055	+	0.212602i
$210$	3.67443	+	1.21189i	0.253560	+	0.0836286i
$211$	5.74585	+	8.94071i	0.395560	+	0.615504i	0.980721	−	0.195413i	$-0.0626049\pi$
$211$	5.74585	+	8.94071i	0.395560	+	0.615504i	−0.585161	+	0.810917i	$0.698968\pi$
$212$	−3.15059	+	8.58925i	−0.216383	+	0.589912i
$213$	7.43769	−	11.5733i	0.509622	−	0.792988i
$214$	−3.20580	+	0.353468i	−0.219144	+	0.0241626i
$215$	1.30608	−	1.50730i	0.0890742	−	0.102797i
$216$	−0.279424	+	2.81459i	−0.0190124	+	0.191509i
$217$	0.756570	+	1.65666i	0.0513593	+	0.112461i
$218$	0.300319	+	1.16344i	0.0203402	+	0.0787983i
$219$	−2.40534	+	8.19184i	−0.162538	+	0.553553i
$220$	2.07028	+	0.136771i	0.139578	+	0.00922113i
$221$	−18.2687	−	2.62665i	−1.22889	−	0.176687i
$222$	−1.39961	+	7.87994i	−0.0939358	+	0.528867i
$223$	2.97243	−	6.50872i	0.199049	−	0.435856i	−0.783616	−	0.621245i	$-0.786627\pi$
$223$	2.97243	−	6.50872i	0.199049	−	0.435856i	0.982665	+	0.185389i	$0.0593545\pi$
$224$	11.2880	+	18.4494i	0.754211	+	1.23270i
$225$	0.638706	+	4.44230i	0.0425804	+	0.296153i
$226$	−6.09619	+	12.2617i	−0.405512	+	0.815637i
$227$	9.07896	−	7.86697i	0.602592	−	0.522149i	−0.299273	−	0.954168i	$-0.596744\pi$
$227$	9.07896	−	7.86697i	0.602592	−	0.522149i	0.901865	+	0.432019i	$0.142199\pi$
$228$	−3.11915	+	14.7230i	−0.206571	+	0.975058i
$229$		−	16.1553i		−	1.06757i	−0.845619	−	0.533787i	$-0.820769\pi$
$229$		−	16.1553i		−	1.06757i	0.845619	−	0.533787i	$-0.179231\pi$
$230$	3.09583	−	3.73748i	0.204133	−	0.246442i
$231$	5.54314			0.364712
$232$	−22.5494	+	7.70979i	−1.48044	+	0.506172i
$233$	−1.26783	−	1.46316i	−0.0830586	−	0.0958547i	0.712699	−	0.701470i	$-0.247473\pi$
$233$	−1.26783	−	1.46316i	−0.0830586	−	0.0958547i	−0.795758	+	0.605615i	$0.792927\pi$
$234$	7.47802	+	3.71787i	0.488854	+	0.243045i
$235$	−6.45735	+	0.928426i	−0.421231	+	0.0605638i
$236$	−1.34727	−	2.43579i	−0.0876998	−	0.158557i
$237$	−12.0432	−	5.49995i	−0.782291	−	0.357260i
$238$	−2.95546	+	16.6395i	−0.191574	+	1.07858i
$239$	−1.51652	+	10.5476i	−0.0980956	+	0.682270i	0.880131	+	0.474731i	$0.157455\pi$
$239$	−1.51652	+	10.5476i	−0.0980956	+	0.682270i	−0.978227	+	0.207539i	$0.933455\pi$
$240$	1.52119	−	2.42452i	0.0981922	−	0.156502i
$241$	−20.6858	−	6.07391i	−1.33249	−	0.391255i	−0.463507	−	0.886093i	$-0.653409\pi$
$241$	−20.6858	−	6.07391i	−1.33249	−	0.391255i	−0.868985	+	0.494838i	$0.835227\pi$
$242$	−12.1845	+	3.14518i	−0.783249	+	0.202180i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	6.18763	−	8.35997i	0.396122	−	0.535192i
$245$	−4.12005	−	3.57004i	−0.263220	−	0.228082i
$246$	12.6944	−	1.39968i	0.809367	−	0.0892401i
$247$	37.3822	+	24.0241i	2.37857	+	1.52862i
$248$	1.32388	−	0.250008i	0.0840665	−	0.0158755i
$249$	−9.81585	+	6.30826i	−0.622054	+	0.399770i
$250$	3.00735	−	9.11821i	0.190201	−	0.576686i
$251$	−2.28812	−	7.79262i	−0.144425	−	0.491866i	0.855227	−	0.518254i	$-0.173418\pi$
$251$	−2.28812	−	7.79262i	−0.144425	−	0.491866i	−0.999652	+	0.0263880i	$0.991599\pi$
$252$	3.62825	−	6.73131i	0.228558	−	0.424033i
$253$	2.53493	−	6.47431i	0.159370	−	0.407037i
$254$	20.4862	−	12.2304i	1.28542	−	0.767402i
$255$	2.14585	−	0.630080i	0.134379	−	0.0394571i
$256$	15.2503	−	4.84016i	0.953146	−	0.302510i
$257$	6.62270	−	4.25615i	0.413113	−	0.265492i	−0.317534	−	0.948247i	$-0.602855\pi$
$257$	6.62270	−	4.25615i	0.413113	−	0.265492i	0.730647	+	0.682755i	$0.239218\pi$
$258$	−2.48168	−	3.06251i	−0.154503	−	0.190664i
$259$	11.6981	−	18.2026i	0.726885	−	1.13106i
$260$	−5.10119	−	6.73779i	−0.316362	−	0.417860i
$261$	6.36759	+	5.51755i	0.394144	+	0.341528i
$262$	−7.11168	+	2.96841i	−0.439361	+	0.183389i
$263$	4.70803	+	10.3091i	0.290309	+	0.635689i	0.997449	−	0.0713854i	$-0.0227420\pi$
$263$	4.70803	+	10.3091i	0.290309	+	0.635689i	−0.707140	+	0.707074i	$0.750015\pi$
$264$	0.981699	−	3.98134i	0.0604194	−	0.245035i
$265$	−3.14066	−	0.922182i	−0.192929	−	0.0566492i
$266$	23.1147	−	33.4852i	1.41725	−	2.05311i
$267$	5.66108	+	0.813940i	0.346452	+	0.0498123i
$268$	−21.6641	+	8.21460i	−1.32335	+	0.501787i
$269$	21.9914	+	10.0431i	1.34084	+	0.612341i	0.951185	−	0.308621i	$-0.0998674\pi$
$269$	21.9914	+	10.0431i	1.34084	+	0.612341i	0.389654	+	0.920961i	$0.372595\pi$
$270$	−1.01140	−	0.0333722i	−0.0615517	−	0.00203097i
$271$	1.05589	+	7.34389i	0.0641409	+	0.446110i	0.996432	+	0.0844005i	$0.0268975\pi$
$271$	1.05589	+	7.34389i	0.0641409	+	0.446110i	−0.932291	+	0.361709i	$0.882193\pi$
$272$	11.4278	+	5.06963i	0.692915	+	0.307391i
$273$	−14.7856	−	17.0635i	−0.894867	−	1.03273i
$274$	−21.3385	+	23.0444i	−1.28911	+	1.39216i
$275$		−	6.50657i		−	0.392361i
$276$	−6.20285	−	7.31605i	−0.373368	−	0.440375i
$277$			16.7084i			1.00391i	0.864893	+	0.501957i	$0.167386\pi$
$277$			16.7084i			1.00391i	−0.864893	+	0.501957i	$0.832614\pi$
$278$	−20.5323	−	19.0124i	−1.23144	−	1.14029i
$279$	−0.311933	−	0.359990i	−0.0186750	−	0.0215521i
$280$	−6.32019	+	4.46494i	−0.377704	+	0.266831i
$281$	1.07110	+	7.44965i	0.0638964	+	0.444409i	0.996506	+	0.0835220i	$0.0266169\pi$
$281$	1.07110	+	7.44965i	0.0638964	+	0.444409i	−0.932610	+	0.360887i	$0.882474\pi$
$282$	−0.425203	+	12.8864i	−0.0253204	+	0.767376i
$283$	−8.69836	−	3.97241i	−0.517064	−	0.236135i	0.139751	−	0.990187i	$-0.455370\pi$
$283$	−8.69836	−	3.97241i	−0.517064	−	0.236135i	−0.656815	+	0.754051i	$0.728097\pi$
$284$	9.75516	+	25.7270i	0.578862	+	1.52661i
$285$	−5.32969	−	0.766293i	−0.315703	−	0.0453913i
$286$	−9.96403	−	6.87812i	−0.589185	−	0.406712i
$287$	−33.1298	−	9.72777i	−1.95559	−	0.574212i
$288$	−4.19218	−	3.79811i	−0.247026	−	0.223806i
$289$	−3.00405	−	6.57796i	−0.176709	−	0.386939i
$290$	−3.28422	−	7.86829i	−0.192856	−	0.462042i
$291$	−8.59214	−	7.44513i	−0.503680	−	0.436442i
$292$	−10.3070	−	13.6137i	−0.603170	−	0.796684i
$293$	−5.52159	+	8.59176i	−0.322575	+	0.501936i	−0.964233	−	0.265054i	$-0.914610\pi$
$293$	−5.52159	+	8.59176i	−0.322575	+	0.501936i	0.641659	+	0.766990i	$0.278246\pi$
$294$	−8.37106	+	6.78340i	−0.488210	+	0.395616i
$295$	0.837802	−	0.538423i	0.0487787	−	0.0313482i
$296$	−11.0022	−	11.6258i	−0.639491	−	0.675739i
$297$	−1.39105	+	0.408449i	−0.0807170	+	0.0237006i
$298$	7.27092	+	12.1790i	0.421193	+	0.705510i
$299$	−26.6916	+	9.46611i	−1.54362	+	0.547439i
$300$	−7.90126	−	4.25887i	−0.456179	−	0.245886i
$301$	3.00241	+	10.2253i	0.173056	+	0.589375i
$302$	11.1379	+	3.67347i	0.640912	+	0.211384i
$303$	−0.112706	+	0.0724318i	−0.00647480	+	0.00416110i
$304$	−19.9570	−	22.5323i	−1.14461	−	1.29232i
$305$	3.13044	+	2.01181i	0.179248	+	0.115196i
$306$	−0.484418	−	4.39345i	−0.0276923	−	0.251157i
$307$	17.5689	+	15.2236i	1.00271	+	0.868855i	0.991372	−	0.131081i	$-0.0418447\pi$
$307$	17.5689	+	15.2236i	1.00271	+	0.868855i	0.0113403	+	0.999936i	$0.496390\pi$
$308$	−6.59545	+	8.91097i	−0.375811	+	0.507750i
$309$	−13.8160	+	6.30956i	−0.785965	+	0.358938i
$310$	0.120476	+	0.466728i	0.00684259	+	0.0265084i
$311$	−1.47956	−	0.434439i	−0.0838983	−	0.0246348i	0.239514	−	0.970893i	$-0.423012\pi$
$311$	−1.47956	−	0.434439i	−0.0838983	−	0.0246348i	−0.323412	+	0.946258i	$0.604830\pi$
$312$	−14.8744	+	7.59776i	−0.842097	+	0.430139i
$313$	2.42168	−	16.8432i	0.136881	−	0.952032i	−0.799405	−	0.600793i	$-0.794852\pi$
$313$	2.42168	−	16.8432i	0.136881	−	0.952032i	0.936286	−	0.351239i	$-0.114239\pi$
$314$	−1.71262	−	0.304190i	−0.0966487	−	0.0171665i
$315$	2.48865	+	1.13653i	0.140219	+	0.0640361i
$316$	23.1711	−	12.8162i	1.30347	−	0.720969i
$317$	29.2576	−	4.20661i	1.64327	−	0.236267i	0.742275	−	0.670095i	$-0.233747\pi$
$317$	29.2576	−	4.20661i	1.64327	−	0.236267i	0.900996	+	0.433828i	$0.142838\pi$
$318$	−2.88001	+	5.79277i	−0.161503	+	0.324843i
$319$	−7.99922	−	9.23159i	−0.447870	−	0.516870i
$320$	2.08761	+	5.33021i	0.116701	+	0.297968i
$321$	−2.28058			−0.127290
$322$	7.85700	+	24.7129i	0.437853	+	1.37720i
$323$		−	23.5189i		−	1.30863i
$324$	−0.414510	+	1.95657i	−0.0230283	+	0.108699i
$325$	−20.0293	+	17.3555i	−1.11102	+	0.962708i
$326$	−6.62230	−	3.29242i	−0.366775	−	0.182351i
$327$	0.120917	+	0.840996i	0.00668672	+	0.0465072i
$328$	−12.8543	+	22.0726i	−0.709759	+	1.21875i
$329$	14.4807	−	31.7084i	0.798348	−	1.74814i
$330$	1.44449	+	0.256566i	0.0795166	+	0.0141235i
$331$	−27.6918	−	3.98148i	−1.52208	−	0.218842i	−0.670043	−	0.742323i	$-0.733724\pi$
$331$	−27.6918	−	3.98148i	−1.52208	−	0.218842i	−0.852038	+	0.523481i	$0.824633\pi$
$332$	1.53834	−	23.2855i	0.0844273	−	1.27796i
$333$	−1.59437	+	5.42993i	−0.0873710	+	0.297558i
$334$	24.2115	−	6.24970i	1.32480	−	0.341969i
$335$	−3.44355	−	7.54033i	−0.188141	−	0.411972i
$336$	6.50400	+	13.8419i	0.354822	+	0.755135i
$337$	−3.56218	+	4.11097i	−0.194044	+	0.223939i	−0.844431	−	0.535664i	$-0.820061\pi$
$337$	−3.56218	+	4.11097i	−0.194044	+	0.223939i	0.650387	+	0.759603i	$0.274607\pi$
$338$	3.38991	+	30.7449i	0.184387	+	1.67230i
$339$	−5.23491	+	8.14569i	−0.284322	+	0.442413i
$340$	−1.54033	+	4.19930i	−0.0835361	+	0.227739i
$341$	0.373356	+	0.580953i	0.0202183	+	0.0314604i
$342$	−3.33325	+	10.1063i	−0.180242	+	0.546488i
$343$	2.26974	−	0.666455i	0.122554	−	0.0359852i
$344$	7.87601	−	0.345562i	0.424646	−	0.0186314i
$345$	2.46553	−	2.38696i	0.132740	−	0.128510i
$346$	−6.19005	−	10.3685i	−0.332779	−	0.557414i
$347$	−3.14945	−	10.7260i	−0.169071	−	0.575804i	−0.999817	−	0.0191514i	$-0.993904\pi$
$347$	−3.14945	−	10.7260i	−0.169071	−	0.575804i	0.830745	−	0.556653i	$-0.187915\pi$
$348$	−16.4463	+	3.67133i	−0.881612	+	0.196804i
$349$	−9.84647	−	15.3214i	−0.527069	−	0.820136i	0.471007	−	0.882129i	$-0.343891\pi$
$349$	−9.84647	−	15.3214i	−0.527069	−	0.820136i	−0.998077	+	0.0619936i	$0.980254\pi$
$350$	15.2782	+	18.8541i	0.816654	+	1.00779i
$351$	4.96779	+	3.19261i	0.265161	+	0.170409i
$352$	5.23222	+	6.31532i	0.278878	+	0.336607i
$353$	−7.13423	+	8.23334i	−0.379717	+	0.438216i	−0.913149	−	0.407627i	$-0.866357\pi$
$353$	−7.13423	+	8.23334i	−0.379717	+	0.438216i	0.533432	+	0.845843i	$0.320902\pi$
$354$	−0.758163	−	1.81640i	−0.0402959	−	0.0965405i
$355$	−8.95444	+	4.08936i	−0.475252	+	0.217040i
$356$	−8.04425	+	8.13211i	−0.426344	+	0.431001i
$357$	−3.36672	+	11.4660i	−0.178186	+	0.606844i
$358$	−0.163555	+	0.236935i	−0.00864416	+	0.0125224i
$359$	−0.185539	+	1.29046i	−0.00979240	+	0.0681076i	−0.994132	−	0.108177i	$-0.965499\pi$
$359$	−0.185539	+	1.29046i	−0.00979240	+	0.0681076i	0.984339	+	0.176284i	$0.0564078\pi$
$360$	1.25705	−	1.58618i	0.0662524	−	0.0835992i
$361$	−15.6297	+	34.2243i	−0.822616	+	1.80128i
$362$	−0.355249	+	10.7664i	−0.0186715	+	0.565869i
$363$	−8.80758	+	1.26634i	−0.462278	+	0.0664655i
$364$	45.0233	−	3.46602i	2.35986	−	0.181669i
$365$	4.61701	−	4.00066i	0.241665	−	0.209404i
$366$	4.99682	−	5.39627i	0.261188	−	0.282068i
$367$	−26.5583			−1.38633			−0.693167	−	0.720777i	$-0.743785\pi$
$367$	−26.5583			−1.38633			−0.693167	+	0.720777i	$0.743785\pi$
$368$	19.1415	−	1.26657i	0.997818	−	0.0660246i
$369$	9.03071			0.470120
$370$	3.89094	−	4.20198i	0.202280	−	0.218451i
$371$	13.2181	−	11.4535i	0.686249	−	0.594638i
$372$	0.949860	−	0.0731229i	0.0492480	−	0.00379125i
$373$	5.67492	−	0.815931i	0.293836	−	0.0422473i	0.00617973	−	0.999981i	$-0.498033\pi$
$373$	5.67492	−	0.815931i	0.293836	−	0.0422473i	0.287657	+	0.957734i	$0.407124\pi$
$374$	−0.211329	+	6.40465i	−0.0109275	+	0.331176i
$375$	2.82033	−	6.17565i	0.145641	−	0.318909i
$376$	−20.2099	−	16.0163i	−1.04225	−	0.825980i
$377$	−7.08082	+	49.2482i	−0.364681	+	2.53641i
$378$	3.07175	−	4.44991i	0.157994	−	0.228879i
$379$	5.30399	−	18.0637i	0.272448	−	0.927872i	−0.703651	−	0.710546i	$-0.748448\pi$
$379$	5.30399	−	18.0637i	0.272448	−	0.927872i	0.976099	−	0.217327i	$-0.0697337\pi$
$380$	7.57335	−	7.65607i	0.388505	−	0.392748i
$381$	15.3465	−	7.00851i	0.786224	−	0.359057i
$382$	1.13112	+	2.70992i	0.0578730	+	0.138652i
$383$	7.31662	−	8.44382i	0.373862	−	0.431459i	−0.537374	−	0.843344i	$-0.680584\pi$
$383$	7.31662	−	8.44382i	0.373862	−	0.431459i	0.911236	+	0.411884i	$0.135129\pi$
$384$	11.0938	−	2.22007i	0.566126	−	0.113292i
$385$	−3.33677	−	2.14441i	−0.170057	−	0.109289i
$386$	−4.29828	−	5.30429i	−0.218777	−	0.269981i
$387$	−1.50691	−	2.34480i	−0.0766006	−	0.119193i
$388$	22.1919	−	4.95393i	1.12662	−	0.251498i
$389$	7.90748	+	26.9304i	0.400925	+	1.36543i	0.874651	+	0.484753i	$0.161091\pi$
$389$	7.90748	+	26.9304i	0.400925	+	1.36543i	−0.473726	+	0.880672i	$0.657091\pi$
$390$	−3.06321	−	5.13096i	−0.155112	−	0.259816i
$391$	11.8525	+	9.17579i	0.599406	+	0.464040i
$392$	−0.944556	−	21.5282i	−0.0477073	−	1.08734i
$393$	−5.22846	+	1.53522i	−0.263741	+	0.0774414i
$394$	−9.68779	+	29.3731i	−0.488064	+	1.47980i
$395$	5.12187	+	7.96979i	0.257709	+	0.401004i
$396$	0.998520	−	2.72220i	0.0501775	−	0.136796i
$397$	−1.12288	+	1.74724i	−0.0563558	+	0.0876914i	−0.868288	−	0.496060i	$-0.834779\pi$
$397$	−1.12288	+	1.74724i	−0.0563558	+	0.0876914i	0.811932	+	0.583752i	$0.198416\pi$
$398$	1.57181	+	14.2556i	0.0787878	+	0.714570i
$399$	18.8410	−	21.7437i	0.943232	−	1.08855i
$400$	16.2477	−	7.63444i	0.812383	−	0.381722i
$401$	10.0368	+	21.9776i	0.501215	+	1.09751i	0.976072	+	0.217446i	$0.0697725\pi$
$401$	10.0368	+	21.9776i	0.501215	+	1.09751i	−0.474857	+	0.880063i	$0.657500\pi$
$402$	−15.8631	+	4.09474i	−0.791182	+	0.204227i
$403$	0.792476	−	2.69893i	0.0394761	−	0.134443i
$404$	0.0176633	−	0.267365i	0.000878781	−	0.0133019i
$405$	−0.708272	−	0.101834i	−0.0351943	−	0.00506018i
$406$	44.8561	+	7.96722i	2.22617	+	0.395406i
$407$	3.40828	−	7.46310i	0.168942	−	0.369932i
$408$	7.63916	+	4.44878i	0.378195	+	0.220247i
$409$	−1.74400	−	12.1298i	−0.0862354	−	0.599780i	−0.986416	−	0.164264i	$-0.947475\pi$
$409$	−1.74400	−	12.1298i	−0.0862354	−	0.599780i	0.900181	−	0.435516i	$-0.143434\pi$
$410$	−8.18306	−	4.06839i	−0.404133	−	0.200924i
$411$	−16.7835	+	14.5430i	−0.827871	+	0.717355i
$412$	6.29581	−	29.7176i	0.310172	−	1.46408i
$413$			5.32140i			0.261849i
$414$	−3.79270	−	5.62276i	−0.186401	−	0.276344i
$415$	8.34919			0.409846
$416$	5.48424	−	32.9517i	0.268887	−	1.61559i
$417$	−12.9577	−	14.9540i	−0.634541	−	0.732299i
$418$	6.86847	−	13.8151i	0.335948	−	0.675717i
$419$	−1.15065	+	0.165438i	−0.0562129	+	0.00808220i	−0.170364	−	0.985381i	$-0.554494\pi$
$419$	−1.15065	+	0.165438i	−0.0562129	+	0.00808220i	0.114151	+	0.993463i	$0.463585\pi$
$420$	−4.78814	+	2.64839i	−0.233637	+	0.129228i
$421$	17.2221	+	7.86506i	0.839353	+	0.383320i	0.788236	−	0.615373i	$-0.210995\pi$
$421$	17.2221	+	7.86506i	0.839353	+	0.383320i	0.0511170	+	0.998693i	$0.483722\pi$
$422$	−14.7984	−	2.62845i	−0.720376	−	0.127951i
$423$	−1.29749	+	9.02424i	−0.0630861	+	0.438774i
$424$	−5.88553	−	11.5223i	−0.285826	−	0.559572i
$425$	13.4588	+	3.95187i	0.652850	+	0.191694i
$426$	4.86267	+	18.8381i	0.235597	+	0.912709i
$427$	−18.0865	+	8.25984i	−0.875268	+	0.399722i
$428$	2.71353	−	3.66619i	0.131163	−	0.177212i
$429$	−6.47017	−	5.60643i	−0.312383	−	0.270681i
$430$	0.309120	+	2.80358i	0.0149071	+	0.135201i
$431$	−2.81702	−	1.81039i	−0.135691	−	0.0872033i	0.471034	−	0.882115i	$-0.343881\pi$
$431$	−2.81702	−	1.81039i	−0.135691	−	0.0872033i	−0.606725	+	0.794912i	$0.707517\pi$
$432$	−2.65213	−	2.99437i	−0.127600	−	0.144066i
$433$	21.7134	−	13.9544i	1.04348	−	0.670604i	0.0976346	−	0.995222i	$-0.468872\pi$
$433$	21.7134	−	13.9544i	1.04348	−	0.670604i	0.945845	+	0.324619i	$0.105236\pi$
$434$	−2.44602	−	0.806741i	−0.117413	−	0.0387248i
$435$	−1.69855	−	5.78472i	−0.0814391	−	0.277356i
$436$	−1.49583	−	0.806270i	−0.0716373	−	0.0386133i
$437$	−16.7802	−	31.9497i	−0.802706	−	1.52836i
$438$	−6.18923	−	10.3671i	−0.295733	−	0.495360i
$439$	0.381882	−	0.112131i	0.0182262	−	0.00535170i	−0.272607	−	0.962126i	$-0.587886\pi$
$439$	0.381882	−	0.112131i	0.0182262	−	0.00535170i	0.290833	+	0.956774i	$0.406068\pi$
$440$	−2.13116	+	2.01685i	−0.101599	+	0.0961493i
$441$	−6.40926	+	4.11898i	−0.305203	+	0.196142i
$442$	20.2792	−	16.4331i	0.964584	−	0.781641i
$443$	−4.32278	+	6.72637i	−0.205381	+	0.319579i	−0.928629	−	0.371009i	$-0.879012\pi$
$443$	−4.32278	+	6.72637i	−0.205381	+	0.319579i	0.723248	+	0.690588i	$0.242648\pi$
$444$	−6.83194	−	9.02382i	−0.324229	−	0.428251i
$445$	−3.09288	−	2.68000i	−0.146617	−	0.127044i
$446$	3.89781	+	9.33834i	0.184567	+	0.442183i
$447$	4.16654	+	9.12344i	0.197070	+	0.431524i
$448$	−29.9905	−	6.01399i	−1.41692	−	0.284134i
$449$	2.86601	+	0.841537i	0.135255	+	0.0397146i	0.348660	−	0.937249i	$-0.386637\pi$
$449$	2.86601	+	0.841537i	0.135255	+	0.0397146i	−0.213404	+	0.976964i	$0.568455\pi$
$450$	−5.22334	−	3.60564i	−0.246231	−	0.169972i
$451$	−12.9593	−	1.86326i	−0.610228	−	0.0877375i
$452$	−6.86603	−	18.1076i	−0.322951	−	0.851708i
$453$	7.54354	+	3.44502i	0.354426	+	0.161861i
$454$	−0.560274	+	16.9800i	−0.0262950	+	0.796910i
$455$	2.29924	+	15.9916i	0.107790	+	0.749696i
$456$	−12.2806	−	17.3834i	−0.575091	−	0.814051i
$457$	16.7543	+	19.3355i	0.783735	+	0.904478i	0.997373	−	0.0724348i	$-0.0230769\pi$
$457$	16.7543	+	19.3355i	0.783735	+	0.904478i	−0.213638	+	0.976913i	$0.568531\pi$
$458$	16.7639	+	15.5229i	0.783324	+	0.725339i
$459$		−	3.12547i		−	0.145884i
$460$	0.903615	+	6.80362i	0.0421313	+	0.317221i
$461$		−	13.5694i		−	0.631988i	−0.948761	−	0.315994i	$-0.897662\pi$
$461$		−	13.5694i		−	0.631988i	0.948761	−	0.315994i	$-0.102338\pi$
$462$	−5.32616	+	5.75194i	−0.247795	+	0.267604i
$463$	−0.789187	−	0.910771i	−0.0366766	−	0.0423271i	0.737115	−	0.675767i	$-0.236188\pi$
$463$	−0.789187	−	0.910771i	−0.0366766	−	0.0423271i	−0.773792	+	0.633440i	$0.781642\pi$
$464$	13.6665	−	30.8068i	0.634453	−	1.43017i
$465$	0.0485072	+	0.337375i	0.00224947	+	0.0156454i
$466$	2.73648	+	0.0902933i	0.126765	+	0.00418276i
$467$	32.8795	+	15.0156i	1.52148	+	0.694837i	0.988490	−	0.151284i	$-0.0483407\pi$
$467$	32.8795	+	15.0156i	1.52148	+	0.694837i	0.532991	+	0.846121i	$0.321068\pi$
$468$	−11.0432	+	4.18737i	−0.510473	+	0.193561i
$469$	43.8422	+	6.30356i	2.02445	+	0.291071i
$470$	5.24118	−	7.59267i	0.241758	−	0.350224i
$471$	−1.18014	−	0.346519i	−0.0543778	−	0.0159668i
$472$	3.82208	+	0.942428i	0.175925	+	0.0433788i
$473$	1.67866	+	3.67575i	0.0771848	+	0.169011i
$474$	17.2789	−	7.21220i	0.793647	−	0.331267i
$475$	−25.5229	−	22.1157i	−1.17107	−	1.01474i
$476$	−14.4265	−	19.0549i	−0.661237	−	0.873381i
$477$	−2.47312	+	3.84825i	−0.113236	+	0.176199i
$478$	−9.48779	−	11.7084i	−0.433961	−	0.535530i
$479$	18.2903	−	11.7545i	0.835707	−	0.537076i	−0.0513798	−	0.998679i	$-0.516362\pi$
$479$	18.2903	−	11.7545i	0.835707	−	0.537076i	0.887087	+	0.461603i	$0.152726\pi$
$480$	1.05421	+	3.90810i	0.0481178	+	0.178380i
$481$	−32.0650	+	9.41512i	−1.46204	+	0.429293i
$482$	26.1788	−	15.6289i	1.19241	−	0.711877i
$483$	3.60714	+	17.9783i	0.164130	+	0.818040i
$484$	8.44389	−	15.6655i	0.383813	−	0.712069i
$485$	2.29194	+	7.80564i	0.104072	+	0.354436i
$486$	−0.442962	+	1.34305i	−0.0200932	+	0.0609220i
$487$	14.7498	−	9.47915i	0.668379	−	0.429541i	−0.161962	−	0.986797i	$-0.551782\pi$
$487$	14.7498	−	9.47915i	0.668379	−	0.429541i	0.830341	+	0.557256i	$0.188146\pi$
$488$	2.72946	+	14.4534i	0.123557	+	0.654276i
$489$	−4.39932	−	2.82727i	−0.198944	−	0.127854i
$490$	7.66329	−	0.844947i	0.346192	−	0.0381708i
$491$	−12.0227	−	10.4177i	−0.542575	−	0.470144i	0.339928	−	0.940452i	$-0.389597\pi$
$491$	−12.0227	−	10.4177i	−0.542575	−	0.470144i	−0.882502	+	0.470308i	$0.844143\pi$
$492$	−10.7451	+	14.5175i	−0.484427	+	0.654499i
$493$	23.9540	−	10.9394i	1.07883	−	0.492687i
$494$	−60.8479	+	15.7066i	−2.73768	+	0.706675i
$495$	0.995374	+	0.292268i	0.0447387	+	0.0131365i
$496$	−1.01263	+	1.61397i	−0.0454686	+	0.0724694i
$497$	7.48572	−	52.0644i	0.335781	−	2.33541i
$498$	2.88573	−	16.2469i	0.129313	−	0.728042i
$499$	23.0525	+	10.5277i	1.03197	+	0.471285i	0.858099	−	0.513484i	$-0.171645\pi$
$499$	23.0525	+	10.5277i	1.03197	+	0.471285i	0.173870	+	0.984769i	$0.444373\pi$
$500$	6.57205	+	11.8819i	0.293911	+	0.531375i
$501$	17.5013	−	2.51631i	0.781901	−	0.112420i
$502$	10.2847	+	5.11327i	0.459029	+	0.228217i
$503$	−4.31600	−	4.98093i	−0.192441	−	0.222089i	0.651326	−	0.758798i	$-0.274213\pi$
$503$	−4.31600	−	4.98093i	−0.192441	−	0.222089i	−0.843768	+	0.536709i	$0.819667\pi$
$504$	3.49864	+	10.2327i	0.155842	+	0.455803i
$505$	0.0958658			0.00426597
$506$	4.28249	+	8.85130i	0.190380	+	0.393488i
$507$			21.8717i			0.971356i
$508$	−6.99323	+	33.0095i	−0.310275	+	1.46456i
$509$	−18.3485	+	15.8990i	−0.813281	+	0.704712i	−0.958626	−	0.284669i	$-0.908116\pi$
$509$	−18.3485	+	15.8990i	−0.813281	+	0.704712i	0.145345	+	0.989381i	$0.453571\pi$
$510$	−1.40804	+	2.83210i	−0.0623492	+	0.125408i
$511$	4.64563	+	32.3110i	0.205510	+	1.42936i
$512$	−9.63089	+	20.4755i	−0.425629	+	0.904898i
$513$	−3.12596	+	6.84490i	−0.138015	+	0.302210i
$514$	−1.94699	+	10.9617i	−0.0858780	+	0.483501i
$515$	10.7576	+	1.54672i	0.474038	+	0.0681564i
$516$	5.56241	+	0.367476i	0.244871	+	0.0161772i
$517$	3.72385	−	12.6823i	0.163775	−	0.557765i
$518$	7.64808	+	29.6288i	0.336037	+	1.30182i
$519$	−3.54715	−	7.76717i	−0.155703	−	0.340941i
$520$	11.8931	+	1.18071i	0.521547	+	0.0517775i
$521$	12.2136	−	14.0953i	0.535089	−	0.617526i	−0.422255	−	0.906477i	$-0.638761\pi$
$521$	12.2136	−	14.0953i	0.535089	−	0.617526i	0.957344	+	0.288952i	$0.0933067\pi$
$522$	−11.8437	+	1.30588i	−0.518386	+	0.0571567i
$523$	−1.58325	+	2.46358i	−0.0692307	+	0.107725i	−0.874143	−	0.485669i	$-0.838576\pi$
$523$	−1.58325	+	2.46358i	−0.0692307	+	0.107725i	0.804912	+	0.593394i	$0.202212\pi$
$524$	3.75308	−	10.2318i	0.163954	−	0.446977i
$525$	9.27714	+	14.4355i	0.404888	+	0.630017i
$526$	−15.2212	−	5.02023i	−0.663676	−	0.218892i
$527$	−1.42847	+	0.419435i	−0.0622249	+	0.0182709i
$528$	3.18804	+	4.84418i	0.138742	+	0.210816i
$529$	22.6480	+	4.00856i	0.984695	+	0.174285i
$530$	3.97464	−	2.37288i	0.172648	−	0.103071i
$531$	−0.392110	−	1.33541i	−0.0170161	−	0.0579516i
$532$	12.5367	+	56.1598i	0.543534	+	2.43484i
$533$	28.8315	+	44.8627i	1.24883	+	1.94322i
$534$	−6.28408	+	5.09224i	−0.271939	+	0.220363i
$535$	1.37283	+	0.882262i	0.0593524	+	0.0381435i
$536$	12.2920	−	30.3732i	0.530935	−	1.31192i
$537$	−0.133316	+	0.153854i	−0.00575300	+	0.00663931i
$538$	−31.5520	+	13.1698i	−1.36030	+	0.567789i
$539$	10.0473	−	4.58843i	0.432766	−	0.197638i
$540$	1.00644	−	1.01743i	0.0433102	−	0.0437832i
$541$	2.88361	−	9.82067i	0.123976	−	0.422224i	−0.873992	−	0.485940i	$-0.838477\pi$
$541$	2.88361	−	9.82067i	0.123976	−	0.422224i	0.997968	+	0.0637167i	$0.0202954\pi$
$542$	−8.63508	−	5.96075i	−0.370909	−	0.256036i
$543$	−1.08403	+	7.53960i	−0.0465202	+	0.323555i
$544$	−16.2411	+	6.98713i	−0.696332	+	0.299571i
$545$	0.252559	−	0.553027i	0.0108184	−	0.0236891i
$546$	31.9131	+	1.05301i	1.36576	+	0.0450647i
$547$	−2.07438	+	0.298250i	−0.0886940	+	0.0127523i	−0.186519	−	0.982451i	$-0.559721\pi$
$547$	−2.07438	+	0.298250i	−0.0886940	+	0.0127523i	0.0978249	+	0.995204i	$0.468811\pi$
$548$	−3.40915	−	44.2846i	−0.145632	−	1.89174i
$549$	3.93018	−	3.40552i	0.167736	−	0.145344i
$550$	6.75166	+	6.25188i	0.287892	+	0.266581i
$551$	−63.4014			−2.70099
$552$	13.5517	+	0.593167i	0.576798	+	0.0252469i
$553$	−50.6210			−2.15262
$554$	−17.3378	−	16.0544i	−0.736614	−	0.682087i
$555$	3.06037	−	2.65182i	0.129905	−	0.112564i
$556$	39.4571	−	3.03752i	1.67336	−	0.128820i
$557$	−17.7144	+	2.54695i	−0.750583	+	0.107918i	−0.506981	−	0.861957i	$-0.669238\pi$
$557$	−17.7144	+	2.54695i	−0.750583	+	0.107918i	−0.243603	+	0.969875i	$0.578329\pi$
$558$	0.673273	+	0.0222154i	0.0285019	+	0.000940454i
$559$	6.83750	−	14.9720i	0.289195	−	0.633250i
$560$	1.43967	−	10.8484i	0.0608371	−	0.458430i
$561$	−0.644862	+	4.48511i	−0.0272261	+	0.189362i
$562$	−8.75944	−	6.04660i	−0.369495	−	0.255060i
$563$	8.45934	−	28.8099i	0.356519	−	1.21419i	−0.564749	−	0.825263i	$-0.691027\pi$
$563$	8.45934	−	28.8099i	0.356519	−	1.21419i	0.921268	−	0.388929i	$-0.127155\pi$
$564$	−12.9633	−	12.8232i	−0.545853	−	0.539955i
$565$	6.30246	−	2.87824i	0.265146	−	0.121088i
$566$	12.4799	−	5.20910i	0.524570	−	0.218955i
$567$	2.50382	−	2.88956i	0.105151	−	0.121350i
$568$	−36.0694	−	14.5973i	−1.51344	−	0.612488i
$569$	8.61612	+	5.53724i	0.361207	+	0.232133i	0.708638	−	0.705572i	$-0.249310\pi$
$569$	8.61612	+	5.53724i	0.361207	+	0.232133i	−0.347432	+	0.937705i	$0.612946\pi$
$570$	5.91622	−	4.79415i	0.247803	−	0.200805i
$571$	8.89724	+	13.8444i	0.372338	+	0.579369i	0.975973	−	0.217892i	$-0.0699180\pi$
$571$	8.89724	+	13.8444i	0.372338	+	0.579369i	−0.603635	+	0.797261i	$0.706282\pi$
$572$	16.7112	−	3.73047i	0.698731	−	0.155979i
$573$	0.584997	+	1.99232i	0.0244386	+	0.0832302i
$574$	41.9271	−	25.0307i	1.75000	−	1.04476i
$575$	21.1030	−	4.23408i	0.880057	−	0.176573i
$576$	7.96926	−	0.700655i	0.332052	−	0.0291939i
$577$	−33.8648	+	9.94361i	−1.40981	+	0.413958i	−0.896041	−	0.443970i	$-0.853570\pi$
$577$	−33.8648	+	9.94361i	−1.40981	+	0.413958i	−0.513770	+	0.857928i	$0.671751\pi$
$578$	9.71220	+	3.20326i	0.403974	+	0.133238i
$579$	−2.60998	−	4.06120i	−0.108467	−	0.168778i
$580$	11.3203	+	4.15237i	0.470051	+	0.172418i
$581$	−24.1193	+	37.5303i	−1.00064	+	1.55702i
$582$	15.9814	−	1.76209i	0.662450	−	0.0730411i
$583$	4.34297	−	5.01205i	0.179867	−	0.207578i
$584$	24.0301	+	2.38563i	0.994371	+	0.0987180i
$585$	−1.75534	−	3.84367i	−0.0725745	−	0.158916i
$586$	−3.60994	−	13.9850i	−0.149125	−	0.577716i
$587$	2.43599	−	8.29623i	0.100544	−	0.342422i	−0.893822	−	0.448422i	$-0.851986\pi$
$587$	2.43599	−	8.29623i	0.100544	−	0.342422i	0.994366	+	0.106000i	$0.0338044\pi$
$588$	1.00446	−	15.2043i	0.0414231	−	0.627013i
$589$	3.54790	+	0.510111i	0.146189	+	0.0210187i
$590$	−0.246303	+	1.38671i	−0.0101401	+	0.0570898i
$591$	−9.08532	+	19.8941i	−0.373720	+	0.818332i
$592$	22.6353	−	0.245895i	0.930306	−	0.0101062i
$593$	5.73637	+	39.8973i	0.235564	+	1.63839i	0.673362	+	0.739313i	$0.264850\pi$
$593$	5.73637	+	39.8973i	0.235564	+	1.63839i	−0.437797	+	0.899074i	$0.644241\pi$
$594$	0.912765	−	1.83591i	0.0374512	−	0.0753283i
$595$	6.46235	−	5.59966i	0.264931	−	0.229564i
$596$	−19.6241	−	4.15746i	−0.803833	−	0.170296i
$597$			10.1413i			0.415057i
$598$	15.8241	−	36.7926i	0.647096	−	1.50456i
$599$	−13.7874			−0.563338			−0.281669	−	0.959512i	$-0.590888\pi$
$599$	−13.7874			−0.563338			−0.281669	+	0.959512i	$0.590888\pi$
$600$	12.0113	−	4.10673i	0.490358	−	0.167657i
$601$	9.63910	+	11.1241i	0.393187	+	0.453762i	0.917484	−	0.397774i	$-0.130217\pi$
$601$	9.63910	+	11.1241i	0.393187	+	0.453762i	−0.524296	+	0.851536i	$0.675672\pi$
$602$	−13.4953	−	6.70951i	−0.550028	−	0.273459i
$603$	−11.4667	+	1.64866i	−0.466960	+	0.0671387i
$604$	−14.5137	+	8.02773i	−0.590555	+	0.326644i
$605$	5.79173	+	2.64500i	0.235467	+	0.107534i
$606$	0.0331341	−	0.186548i	0.00134598	−	0.00757800i
$607$	0.0211358	−	0.147003i	0.000857877	−	0.00596667i	−0.989388	−	0.145298i	$-0.953586\pi$
$607$	0.0211358	−	0.147003i	0.000857877	−	0.00596667i	0.990246	+	0.139331i	$0.0444952\pi$
$608$	42.5569	+	0.941567i	1.72591	+	0.0381856i
$609$	30.9096	+	9.07588i	1.25252	+	0.367773i
$610$	−5.09549	+	1.31530i	−0.206311	+	0.0532548i
$611$	−48.9729	+	22.3652i	−1.98123	+	0.904799i
$612$	5.02441	+	3.71881i	0.203100	+	0.150324i
$613$	18.2342	+	15.8000i	0.736471	+	0.638156i	0.940103	−	0.340892i	$-0.110729\pi$
$613$	18.2342	+	15.8000i	0.736471	+	0.638156i	−0.203631	+	0.979048i	$0.565274\pi$
$614$	−32.6782	+	3.60307i	−1.31879	+	0.145408i
$615$	−5.43616	−	3.49361i	−0.219207	−	0.140876i
$616$	−2.90935	−	15.4061i	−0.117221	−	0.620728i
$617$	−38.5389	+	24.7674i	−1.55152	+	0.997100i	−0.566616	+	0.823982i	$0.691748\pi$
$617$	−38.5389	+	24.7674i	−1.55152	+	0.997100i	−0.984901	+	0.173118i	$0.944616\pi$
$618$	6.72796	−	20.3990i	0.270638	−	0.820569i
$619$	−9.95818	−	33.9145i	−0.400253	−	1.36314i	−0.875472	−	0.483269i	$-0.839449\pi$
$619$	−9.95818	−	33.9145i	−0.400253	−	1.36314i	0.475218	−	0.879868i	$-0.342369\pi$
$620$	−0.600070	−	0.323444i	−0.0240994	−	0.0129898i
$621$	−2.22995	−	4.24586i	−0.0894849	−	0.170380i
$622$	1.87245	−	1.11786i	0.0750784	−	0.0448222i
$623$	20.9816	−	6.16075i	0.840610	−	0.246825i
$624$	6.40819	−	22.7350i	0.256533	−	0.910130i
$625$	14.7908	−	9.50548i	0.591632	−	0.380219i
$626$	15.1507	+	18.6968i	0.605545	+	0.747273i
$627$	5.89809	−	9.17761i	0.235547	−	0.366518i
$628$	1.96123	−	1.48485i	0.0782615	−	0.0592518i
$629$	13.3674	+	11.5829i	0.532991	+	0.461840i
$630$	−3.57057	+	1.49035i	−0.142255	+	0.0593770i
$631$	−9.35822	−	20.4916i	−0.372545	−	0.815759i	−0.999331	−	0.0365682i	$-0.988357\pi$
$631$	−9.35822	−	20.4916i	−0.372545	−	0.815759i	0.626786	−	0.779191i	$-0.284370\pi$
$632$	−8.96507	+	36.3584i	−0.356611	+	1.44626i
$633$	−10.1973	−	2.99421i	−0.405308	−	0.119009i
$634$	−23.7473	+	34.4016i	−0.943125	+	1.36626i
$635$	−11.9493	−	1.71805i	−0.474195	−	0.0681789i
$636$	−3.24370	−	8.55451i	−0.128621	−	0.339209i
$637$	−40.9245	−	18.6896i	−1.62149	−	0.740508i
$638$	17.2654	+	0.569692i	0.683545	+	0.0225543i
$639$	1.95785	+	13.6171i	0.0774514	+	0.538686i
$640$	−7.53689	−	2.95531i	−0.297922	−	0.116819i
$641$	−3.94380	−	4.55139i	−0.155771	−	0.179769i	0.672500	−	0.740097i	$-0.265221\pi$
$641$	−3.94380	−	4.55139i	−0.155771	−	0.179769i	−0.828271	+	0.560328i	$0.810675\pi$
$642$	2.19131	−	2.36649i	0.0864841	−	0.0933977i
$643$			11.1761i			0.440743i	0.975416	+	0.220372i	$0.0707270\pi$
$643$			11.1761i			0.440743i	−0.975416	+	0.220372i	$0.929273\pi$
$644$	−33.1932	−	15.5926i	−1.30800	−	0.614434i
$645$			1.99444i			0.0785312i
$646$	24.4048	+	22.5983i	0.960194	+	0.889117i
$647$	−21.9453	−	25.3262i	−0.862757	−	0.995675i	−0.999987	−	0.00513556i	$-0.998365\pi$
$647$	−21.9453	−	25.3262i	−0.862757	−	0.995675i	0.137230	−	0.990539i	$-0.456180\pi$
$648$	−1.63199	−	2.31011i	−0.0641107	−	0.0907497i
$649$	0.287159	+	1.99724i	0.0112720	+	0.0783984i
$650$	1.23603	−	37.4599i	0.0484811	−	1.46930i
$651$	−1.65666	−	0.756570i	−0.0649295	−	0.0296523i
$652$	9.77952	−	3.70820i	0.382996	−	0.145224i
$653$	−4.12173	−	0.592615i	−0.161296	−	0.0231908i	0.0611938	−	0.998126i	$-0.480509\pi$
$653$	−4.12173	−	0.592615i	−0.161296	−	0.0231908i	−0.222490	+	0.974935i	$0.571418\pi$
$654$	−0.988859	−	0.682604i	−0.0386674	−	0.0266919i
$655$	3.74126	+	1.09853i	0.146183	+	0.0429232i
$656$	−10.5529	−	34.5470i	−0.412021	−	1.34883i
$657$	−3.54668	−	7.76614i	−0.138369	−	0.302986i
$658$	18.9889	+	45.4934i	0.740264	+	1.77352i
$659$	3.63113	+	3.14640i	0.141449	+	0.122566i	0.722711	−	0.691150i	$-0.242896\pi$
$659$	3.63113	+	3.14640i	0.141449	+	0.122566i	−0.581262	+	0.813716i	$0.697441\pi$
$660$	−1.65418	+	1.25238i	−0.0643888	+	0.0487488i
$661$	−1.69224	+	2.63318i	−0.0658205	+	0.102419i	−0.872604	−	0.488429i	$-0.837570\pi$
$661$	−1.69224	+	2.63318i	−0.0658205	+	0.102419i	0.806783	+	0.590848i	$0.201207\pi$
$662$	30.7393	−	24.9093i	1.19472	−	0.968127i
$663$	15.5267	−	9.97839i	0.603006	−	0.387529i
$664$	22.6845	+	23.9703i	0.880329	+	0.930228i
$665$	−19.7534	+	5.80011i	−0.766003	+	0.224919i
$666$	−4.10251	−	6.87181i	−0.158969	−	0.266277i
$667$	24.7358	−	31.9515i	0.957773	−	1.23717i
$668$	−16.7787	+	31.1286i	−0.649186	+	1.20440i
$669$	2.01589	+	6.86549i	0.0779388	+	0.265435i
$670$	11.1331	+	3.67191i	0.430110	+	0.141858i
$671$	−6.34254	+	4.07610i	−0.244851	+	0.157356i
$672$	−20.6127	−	6.55104i	−0.795151	−	0.252712i
$673$	−40.0916	−	25.7653i	−1.54542	−	0.993181i	−0.986463	−	0.163983i	$-0.947566\pi$
$673$	−40.0916	−	25.7653i	−1.54542	−	0.993181i	−0.558956	−	0.829197i	$-0.688798\pi$
$674$	−0.843086	−	7.64641i	−0.0324745	−	0.294529i
$675$	−3.39179	−	2.93900i	−0.130550	−	0.113122i
$676$	−35.1602	−	26.0238i	−1.35232	−	1.00092i
$677$	7.16768	−	3.27337i	0.275476	−	0.125806i	−0.272887	−	0.962046i	$-0.587978\pi$
$677$	7.16768	−	3.27337i	0.275476	−	0.125806i	0.548363	+	0.836240i	$0.315251\pi$
$678$	−3.42252	−	13.2589i	−0.131441	−	0.509206i
$679$	−41.7080	−	12.2466i	−1.60061	−	0.469981i
$680$	−2.87745	−	5.63328i	−0.110345	−	0.216026i
$681$	−1.70966	+	11.8909i	−0.0655141	+	0.455661i
$682$	−0.961578	−	0.170793i	−0.0368207	−	0.00653999i
$683$	9.29577	+	4.24524i	0.355693	+	0.162439i	0.585244	−	0.810857i	$-0.300999\pi$
$683$	9.29577	+	4.24524i	0.355693	+	0.162439i	−0.229551	+	0.973297i	$0.573726\pi$
$684$	−7.28425	−	13.1695i	−0.278520	−	0.503550i
$685$	15.7292	−	2.26151i	0.600981	−	0.0864080i
$686$	−1.48933	+	2.99560i	−0.0568630	+	0.114373i
$687$	10.5795	+	12.2094i	0.403632	+	0.465817i
$688$	−7.20913	+	8.50472i	−0.274845	+	0.324239i
$689$	−27.0130			−1.02911
$690$	0.107855	+	4.85194i	0.00410596	+	0.184710i
$691$			11.3134i			0.430382i	0.976572	+	0.215191i	$0.0690375\pi$
$691$			11.3134i			0.430382i	−0.976572	+	0.215191i	$0.930963\pi$
$692$	16.7068	+	3.53942i	0.635097	+	0.134548i
$693$	−4.18922	+	3.62998i	−0.159135	+	0.137892i
$694$	14.1562	+	7.03810i	0.537364	+	0.267163i
$695$	2.01499	+	14.0145i	0.0764328	+	0.531602i
$696$	11.9929	−	20.5934i	0.454588	−	0.780590i
$697$	11.7252	−	25.6746i	0.444123	−	0.972493i
$698$	25.3596	+	4.50429i	0.959874	+	0.170490i
$699$	1.91633	+	0.275527i	0.0724822	+	0.0104214i
$700$	−34.2444	−	2.26233i	−1.29432	−	0.0855081i
$701$	−3.99746	+	13.6141i	−0.150982	+	0.514197i	−0.999897	−	0.0143318i	$-0.995438\pi$
$701$	−3.99746	+	13.6141i	−0.150982	+	0.514197i	0.848915	+	0.528529i	$0.177256\pi$
$702$	−8.08620	+	2.08729i	−0.305194	+	0.0787795i
$703$	−17.6903	−	38.7364i	−0.667204	−	1.46097i
$704$	−11.5806	−	0.638802i	−0.436461	−	0.0240757i
$705$	4.27215	−	4.93032i	0.160898	−	0.185687i
$706$	−1.68851	−	15.3140i	−0.0635479	−	0.576351i
$707$	−0.276939	+	0.430925i	−0.0104154	+	0.0162066i
$708$	2.61330	+	0.958576i	0.0982140	+	0.0360255i
$709$	−11.4675	−	17.8438i	−0.430671	−	0.670137i	0.556310	−	0.830975i	$-0.312217\pi$
$709$	−11.4675	−	17.8438i	−0.430671	−	0.670137i	−0.986981	+	0.160838i	$0.948580\pi$
$710$	4.36053	−	13.2210i	0.163648	−	0.496176i
$711$	12.7034	−	3.73004i	0.476413	−	0.139887i
$712$	−0.709070	−	16.1611i	−0.0265735	−	0.605661i
$713$	−1.64127	+	1.58897i	−0.0614661	+	0.0595073i
$714$	−8.66296	−	14.5107i	−0.324203	−	0.543049i
$715$	1.72591	+	5.87791i	0.0645454	+	0.219821i
$716$	−0.0887071	−	0.397377i	−0.00331514	−	0.0148507i
$717$	−5.76112	−	8.96448i	−0.215153	−	0.334785i
$718$	−1.16079	−	1.43247i	−0.0433202	−	0.0534593i
$719$	37.1006	+	23.8431i	1.38362	+	0.889199i	0.999420	−	0.0340509i	$-0.0108408\pi$
$719$	37.1006	+	23.8431i	1.38362	+	0.889199i	0.384200	+	0.923250i	$0.374477\pi$
$720$	0.438088	+	2.82850i	0.0163266	+	0.105412i
$721$	−38.0295	+	43.8883i	−1.41629	+	1.63449i
$722$	−20.4956	−	49.1031i	−0.762766	−	1.82743i
$723$	19.6109	−	8.95599i	0.729337	−	0.333077i
$724$	−10.8306	−	10.7136i	−0.402516	−	0.398167i
$725$	10.6533	−	36.2819i	0.395655	−	1.34748i
$726$	7.14877	−	10.3561i	0.265316	−	0.384351i
$727$	−3.22664	+	22.4418i	−0.119669	+	0.832319i	0.838251	+	0.545285i	$0.183578\pi$
$727$	−3.22664	+	22.4418i	−0.119669	+	0.832319i	−0.957920	+	0.287034i	$0.907331\pi$
$728$	−39.6644	+	50.0497i	−1.47006	+	1.85496i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−0.284921	+	8.63499i	−0.0105454	+	0.319595i
$731$	−8.62285	+	1.23978i	−0.318927	+	0.0458549i
$732$	0.798318	+	10.3701i	0.0295067	+	0.383289i
$733$	−5.35278	+	4.63821i	−0.197709	+	0.171316i	−0.748089	−	0.663598i	$-0.769028\pi$
$733$	−5.35278	+	4.63821i	−0.197709	+	0.171316i	0.550380	+	0.834914i	$0.314483\pi$
$734$	25.5187	−	27.5588i	0.941914	−	1.01721i
$735$	5.45160			0.201085
$736$	−17.0779	+	21.0795i	−0.629500	+	0.777000i
$737$	16.7951			0.618655
$738$	−8.67722	+	9.37089i	−0.319413	+	0.344947i
$739$	33.0204	−	28.6123i	1.21467	−	1.05252i	0.217603	−	0.976037i	$-0.430176\pi$
$739$	33.0204	−	28.6123i	1.21467	−	1.05252i	0.997071	−	0.0764839i	$-0.0243694\pi$
$740$	0.621637	+	8.07500i	0.0228518	+	0.296843i
$741$	−43.9840	+	6.32395i	−1.61579	+	0.232316i
$742$	−0.815704	+	24.7212i	−0.0299454	+	0.907543i
$743$	17.3858	−	38.0696i	0.637824	−	1.39664i	−0.263995	−	0.964524i	$-0.585040\pi$
$743$	17.3858	−	38.0696i	0.637824	−	1.39664i	0.901818	−	0.432115i	$-0.142233\pi$
$744$	−0.836802	+	1.05590i	−0.0306786	+	0.0387112i
$745$	1.02138	−	7.10384i	0.0374204	−	0.260265i
$746$	−4.60612	+	6.67268i	−0.168642	+	0.244304i
$747$	3.28729	−	11.1955i	0.120276	−	0.409621i
$748$	−6.44284	−	6.37323i	−0.235574	−	0.233028i
$749$	−7.93168	+	3.62228i	−0.289817	+	0.132355i
$750$	3.69835	+	8.86048i	0.135045	+	0.323539i
$751$	−12.1120	+	13.9780i	−0.441973	+	0.510064i	−0.932405	−	0.361415i	$-0.882294\pi$
$751$	−12.1120	+	13.9780i	−0.441973	+	0.510064i	0.490432	+	0.871480i	$0.336839\pi$
$752$	36.0385	−	5.58176i	1.31419	−	0.203546i
$753$	6.83232	+	4.39087i	0.248984	+	0.160012i
$754$	−44.2997	−	54.6680i	−1.61330	−	1.99089i
$755$	−3.20820	−	4.99206i	−0.116758	−	0.181680i
$756$	1.66602	+	7.46319i	0.0605926	+	0.271434i
$757$	2.35614	+	8.02429i	0.0856355	+	0.291648i	0.991165	−	0.132636i	$-0.0423441\pi$
$757$	2.35614	+	8.02429i	0.0856355	+	0.291648i	−0.905529	+	0.424284i	$0.860526\pi$
$758$	13.6478	+	22.8604i	0.495711	+	0.830329i
$759$	2.32400	+	6.55299i	0.0843559	+	0.237858i
$760$	0.667562	+	15.2150i	0.0242150	+	0.551906i
$761$	6.64698	−	1.95173i	0.240953	−	0.0707502i	−0.159026	−	0.987274i	$-0.550835\pi$
$761$	6.64698	−	1.95173i	0.240953	−	0.0707502i	0.399979	+	0.916524i	$0.369017\pi$
$762$	−7.47326	+	22.6587i	−0.270728	+	0.820839i
$763$	1.75631	+	2.73287i	0.0635826	+	0.0989364i
$764$	−3.89884	−	1.43012i	−0.141055	−	0.0517399i
$765$	−1.20911	+	1.88142i	−0.0437156	+	0.0680228i
$766$	1.73168	+	15.7055i	0.0625680	+	0.567464i
$767$	5.38216	−	6.21134i	0.194339	−	0.224279i
$768$	−8.35580	+	13.6448i	−0.301514	+	0.492364i
$769$	10.2955	+	22.5440i	0.371266	+	0.812958i	0.999393	+	0.0348474i	$0.0110945\pi$
$769$	10.2955	+	22.5440i	0.371266	+	0.812958i	−0.628127	+	0.778111i	$0.716178\pi$
$770$	5.43134	−	1.40199i	0.195732	−	0.0505242i
$771$	−2.21792	+	7.55353i	−0.0798764	+	0.272034i
$772$	9.63412	+	0.636471i	0.346740	+	0.0229071i
$773$	−7.26933	−	1.04517i	−0.261460	−	0.0375922i	0.0103384	−	0.999947i	$-0.496709\pi$
$773$	−7.26933	−	1.04517i	−0.261460	−	0.0375922i	−0.271798	+	0.962354i	$0.587618\pi$
$774$	3.88105	+	0.689340i	0.139501	+	0.0247778i
$775$	−0.888067	+	1.94460i	−0.0319003	+	0.0698520i
$776$	−16.1826	+	27.7878i	−0.580923	+	0.997524i
$777$	3.07934	+	21.4172i	0.110471	+	0.768340i
$778$	−35.5428	−	17.6709i	−1.27427	−	0.633532i
$779$	−51.3572	+	44.5013i	−1.84006	+	1.59442i
$780$	8.26754	+	1.75152i	0.296025	+	0.0627144i
$781$		−	19.9448i		−	0.713682i
$782$	−20.9100	+	3.48234i	−0.747739	+	0.124528i
$783$	−8.42553			−0.301104
$784$	23.2467	+	19.7054i	0.830241	+	0.703764i
$785$	0.576345	+	0.665138i	0.0205706	+	0.0237398i
$786$	3.43076	−	6.90053i	0.122371	−	0.246134i
$787$	29.7909	−	4.28328i	1.06193	−	0.152683i	0.410859	−	0.911699i	$-0.365229\pi$
$787$	29.7909	−	4.28328i	1.06193	−	0.152683i	0.651072	+	0.759016i	$0.274320\pi$
$788$	−21.1710	−	38.2761i	−0.754185	−	1.36353i
$789$	−10.3091	−	4.70803i	−0.367015	−	0.167610i
$790$	−13.1914	−	2.34301i	−0.469328	−	0.0833607i
$791$	−5.26872	+	36.6448i	−0.187334	+	1.30294i
$792$	1.86531	+	3.65177i	0.0662808	+	0.129760i
$793$	29.4655	+	8.65184i	1.04635	+	0.307236i
$794$	−0.734126	−	2.84402i	−0.0260532	−	0.100931i
$795$	2.97746	−	1.35976i	0.105599	−	0.0482257i
$796$	−16.3029	−	12.0666i	−0.577841	−	0.427689i
$797$	23.0252	+	19.9515i	0.815596	+	0.706718i	0.959142	−	0.282926i	$-0.0913050\pi$
$797$	23.0252	+	19.9515i	0.815596	+	0.706718i	−0.143546	+	0.989644i	$0.545850\pi$
$798$	4.45924	+	40.4433i	0.157856	+	1.43168i
$799$	23.9715	+	15.4056i	0.848052	+	0.545010i
$800$	−7.68965	+	24.1953i	−0.271870	+	0.855433i
$801$	−4.81138	+	3.09208i	−0.170002	+	0.109253i
$802$	−32.4494	−	10.7024i	−1.14583	−	0.377915i
$803$	3.48721	+	11.8763i	0.123061	+	0.419107i
$804$	10.9932	−	20.3951i	0.387701	−	0.719281i
$805$	4.78369	−	12.2177i	0.168603	−	0.430618i
$806$	2.03914	+	3.41561i	0.0718255	+	0.120310i
$807$	−23.1968	+	6.81121i	−0.816567	+	0.239766i
$808$	0.260465	+	0.275228i	0.00916311	+	0.00968249i
$809$	31.3598	−	20.1537i	1.10255	−	0.708568i	0.142895	−	0.989738i	$-0.454359\pi$
$809$	31.3598	−	20.1537i	1.10255	−	0.708568i	0.959658	+	0.281170i	$0.0907225\pi$
$810$	0.786218	−	0.637104i	0.0276249	−	0.0223855i
$811$	−8.27577	+	12.8773i	−0.290601	+	0.452185i	−0.955603	−	0.294657i	$-0.904794\pi$
$811$	−8.27577	+	12.8773i	−0.290601	+	0.452185i	0.665002	+	0.746842i	$0.268431\pi$
$812$	−51.3676	+	38.8904i	−1.80265	+	1.36479i
$813$	−5.60721	−	4.85868i	−0.196654	−	0.170401i
$814$	4.46936	+	10.7076i	0.156651	+	0.375302i
$815$	1.55448	+	3.40383i	0.0544509	+	0.119231i
$816$	−11.9565	+	3.65228i	−0.418561	+	0.127855i
$817$	20.1244	+	5.90904i	0.704062	+	0.206731i
$818$	14.2624	+	9.84530i	0.498675	+	0.344233i
$819$	22.3485	+	3.21322i	0.780919	+	0.112279i
$820$	12.0844	−	4.58216i	0.422005	−	0.160016i
$821$	12.2929	+	5.61400i	0.429026	+	0.195930i	0.618212	−	0.786012i	$-0.287857\pi$
$821$	12.2929	+	5.61400i	0.429026	+	0.195930i	−0.189185	+	0.981941i	$0.560585\pi$
$822$	1.03573	−	31.3895i	0.0361253	−	1.09484i
$823$	3.34264	+	23.2486i	0.116517	+	0.810395i	0.961343	+	0.275354i	$0.0887950\pi$
$823$	3.34264	+	23.2486i	0.116517	+	0.810395i	−0.844826	+	0.535042i	$0.820296\pi$
$824$	24.7876	+	35.0873i	0.863517	+	1.22232i
$825$	4.26090	+	4.91734i	0.148345	+	0.171200i
$826$	−5.52184	−	5.11310i	−0.192130	−	0.177907i
$827$			48.8451i			1.69851i	0.527982	+	0.849256i	$0.322949\pi$
$827$			48.8451i			1.69851i	−0.527982	+	0.849256i	$0.677051\pi$
$828$	9.47880	+	1.46710i	0.329411	+	0.0509852i
$829$			33.7473i			1.17209i	0.810278	+	0.586046i	$0.199316\pi$
$829$			33.7473i			1.17209i	−0.810278	+	0.586046i	$0.800684\pi$
$830$	−8.02237	+	8.66369i	−0.278461	+	0.300721i
$831$	−10.9417	−	12.6274i	−0.379564	−	0.438040i
$832$	28.9234	+	37.3527i	1.00274	+	1.29497i
$833$	3.38880	+	23.5696i	0.117415	+	0.816639i
$834$	27.9677	+	0.922828i	0.968444	+	0.0319549i
$835$	−11.5086	−	5.25581i	−0.398272	−	0.181885i
$836$	7.73585	+	20.4015i	0.267550	+	0.705600i
$837$	0.471487	+	0.0677896i	0.0162970	+	0.00234315i
$838$	0.933938	−	1.35296i	0.0322624	−	0.0467371i
$839$	33.6798	+	9.88928i	1.16276	+	0.341416i	0.805503	−	0.592592i	$-0.201895\pi$
$839$	33.6798	+	9.88928i	1.16276	+	0.341416i	0.357253	+	0.934008i	$0.383713\pi$
$840$	1.85257	−	7.51322i	0.0639197	−	0.259231i
$841$	−17.4431	−	38.1950i	−0.601486	−	1.31707i
$842$	−24.7093	+	10.3136i	−0.851538	+	0.355431i
$843$	−5.68797	−	4.92865i	−0.195904	−	0.169752i
$844$	16.9466	−	12.8303i	0.583327	−	0.441637i
$845$	8.46125	−	13.1660i	0.291076	−	0.452923i
$846$	−8.11747	−	10.0174i	−0.279084	−	0.344404i
$847$	−28.6207	+	18.3934i	−0.983420	+	0.632006i
$848$	17.6115	+	4.96404i	0.604780	+	0.170466i
$849$	9.17516	−	2.69407i	0.314891	−	0.0924603i
$850$	−17.0327	+	10.1686i	−0.584218	+	0.348781i
$851$	26.4233	+	6.19770i	0.905779	+	0.212454i
$852$	−24.2200	−	13.0549i	−0.829765	−	0.447252i
$853$	−3.34683	−	11.3983i	−0.114593	−	0.390269i	0.882144	−	0.470979i	$-0.156099\pi$
$853$	−3.34683	−	11.3983i	−0.114593	−	0.390269i	−0.996738	+	0.0807104i	$0.974281\pi$
$854$	8.80757	−	26.7043i	0.301389	−	0.913803i
$855$	4.52972	−	2.91108i	0.154913	−	0.0995567i
$856$	1.19698	+	6.33842i	0.0409119	+	0.216643i
$857$	−17.9645	−	11.5451i	−0.613656	−	0.394373i	0.196571	−	0.980490i	$-0.437019\pi$
$857$	−17.9645	−	11.5451i	−0.613656	−	0.394373i	−0.810226	+	0.586117i	$0.800656\pi$
$858$	12.0345	−	1.32691i	0.410852	−	0.0453001i
$859$	−30.8322	−	26.7162i	−1.05198	−	0.911547i	−0.0557636	−	0.998444i	$-0.517759\pi$
$859$	−30.8322	−	26.7162i	−1.05198	−	0.911547i	−0.996217	+	0.0868974i	$0.972305\pi$
$860$	−3.20621	−	2.37307i	−0.109331	−	0.0809211i
$861$	31.4081	−	14.3436i	1.07039	−	0.488829i
$862$	4.58533	−	1.18361i	0.156177	−	0.0403139i
$863$	2.90071	+	0.851725i	0.0987413	+	0.0289931i	0.330730	−	0.943725i	$-0.392705\pi$
$863$	2.90071	+	0.851725i	0.0987413	+	0.0289931i	−0.231989	+	0.972718i	$0.574523\pi$
$864$	5.65547	+	0.125127i	0.192403	+	0.00425689i
$865$	−0.869542	+	6.04780i	−0.0295653	+	0.205631i
$866$	−6.38346	+	35.9394i	−0.216919	+	1.22127i
$867$	6.57796	+	3.00405i	0.223399	+	0.102023i
$868$	3.18740	−	1.76299i	0.108187	−	0.0598399i
$869$	−18.9992	+	2.73167i	−0.644503	+	0.0926655i
$870$	7.63468	+	3.79575i	0.258840	+	0.128688i
$871$	−44.7988	−	51.7006i	−1.51795	−	1.75181i
$872$	2.27392	−	0.777468i	0.0770046	−	0.0263284i
$873$	11.3690			0.384784
$874$	49.2766	+	13.2868i	1.66680	+	0.449433i
$875$		−	25.9580i		−	0.877541i
$876$	16.7046	+	3.53895i	0.564396	+	0.119570i
$877$	−25.4976	+	22.0938i	−0.860993	+	0.746055i	−0.968728	−	0.248125i	$-0.920186\pi$
$877$	−25.4976	+	22.0938i	−0.860993	+	0.746055i	0.107735	+	0.994180i	$0.465640\pi$
$878$	−0.250579	+	0.504008i	−0.00845663	+	0.0170095i
$879$	−1.45347	−	10.1091i	−0.0490242	−	0.340971i
$880$	−0.0450757	−	4.14934i	−0.00151950	−	0.139874i
$881$	−1.55258	+	3.39969i	−0.0523079	+	0.114538i	−0.933981	−	0.357322i	$-0.883690\pi$
$881$	−1.55258	+	3.39969i	−0.0523079	+	0.114538i	0.881673	+	0.471860i	$0.156417\pi$
$882$	1.88424	−	10.6084i	0.0634456	−	0.357204i
$883$	6.13076	+	0.881470i	0.206316	+	0.0296638i	0.244698	−	0.969599i	$-0.421311\pi$
$883$	6.13076	+	0.881470i	0.206316	+	0.0296638i	−0.0383816	+	0.999263i	$0.512220\pi$
$884$	−2.43334	+	36.8329i	−0.0818420	+	1.23882i
$885$	−0.280577	+	0.955557i	−0.00943148	+	0.0321207i
$886$	−2.82618	−	10.9487i	−0.0949473	−	0.367828i
$887$	17.3746	+	38.0450i	0.583381	+	1.27743i	0.939360	+	0.342933i	$0.111420\pi$
$887$	17.3746	+	38.0450i	0.583381	+	1.27743i	−0.355979	+	0.934494i	$0.615852\pi$
$888$	15.9282	+	1.58130i	0.534517	+	0.0530651i
$889$	42.2422	−	48.7501i	1.41676	−	1.63503i
$890$	5.75277	−	0.634295i	0.192833	−	0.0212616i
$891$	0.783809	−	1.21963i	0.0262586	−	0.0408591i
$892$	−13.4353	−	4.92817i	−0.449848	−	0.165007i
$893$	−37.0906	−	57.7141i	−1.24119	−	1.93133i
$894$	−13.4705	−	4.44283i	−0.450522	−	0.148590i
$895$	0.139771	−	0.0410405i	0.00467203	−	0.00137183i
$896$	35.0571	−	25.3416i	1.17117	−	0.846603i
$897$	13.9732	−	24.6333i	0.466551	−	0.822482i
$898$	−3.62706	+	2.16537i	−0.121037	+	0.0722595i
$899$	1.13070	+	3.85081i	0.0377109	+	0.128432i
$900$	8.76034	−	1.95559i	0.292011	−	0.0651863i
$901$	7.72966	+	12.0276i	0.257512	+	0.400697i
$902$	14.3854	−	11.6571i	0.478982	−	0.388139i
$903$	−8.96520	−	5.76158i	−0.298343	−	0.191733i
$904$	25.3869	+	10.2741i	0.844356	+	0.341711i
$905$	3.56931	−	4.11920i	0.118648	−	0.136927i
$906$	−10.8230	+	4.51752i	−0.359571	+	0.150085i
$907$	−39.1812	+	17.8935i	−1.30099	+	0.594143i	−0.940872	−	0.338763i	$-0.889992\pi$
$907$	−39.1812	+	17.8935i	−1.30099	+	0.594143i	−0.360120	+	0.932906i	$0.617264\pi$
$908$	−17.0812	−	16.8967i	−0.566861	−	0.560736i
$909$	0.0377448	−	0.128547i	0.00125192	−	0.00426364i
$910$	−18.8032	−	12.9797i	−0.623320	−	0.430274i
$911$	1.32850	−	9.23989i	0.0440150	−	0.306131i	−0.955907	−	0.293669i	$-0.905124\pi$
$911$	1.32850	−	9.23989i	0.0440150	−	0.306131i	0.999922	−	0.0124628i	$-0.00396712\pi$
$912$	29.8381	+	3.95974i	0.988037	+	0.131120i
$913$	−7.02724	+	15.3875i	−0.232568	+	0.509252i
$914$	−36.1624	−	1.19322i	−1.19614	−	0.0394682i
$915$	−3.68328	+	0.529576i	−0.121766	+	0.0175073i
$916$	−32.2153	+	2.48003i	−1.06442	+	0.0819424i
$917$	−15.7458	+	13.6438i	−0.519972	+	0.450558i
$918$	3.24320	+	3.00313i	0.107042	+	0.0991179i
$919$	9.85595			0.325118			0.162559	−	0.986699i	$-0.448025\pi$
$919$	9.85595			0.325118			0.162559	+	0.986699i	$0.448025\pi$
$920$	−7.92815	−	5.59965i	−0.261383	−	0.184615i
$921$	−23.2470			−0.766016
$922$	14.0805	+	13.0382i	0.463716	+	0.429390i
$923$	−61.3965	+	53.2004i	−2.02089	+	1.75111i
$924$	−0.850935	−	11.0536i	−0.0279937	−	0.363636i
$925$	25.1397	−	3.61454i	0.826589	−	0.118845i
$926$	1.70337	+	0.0562048i	0.0559763	+	0.00184700i
$927$	6.30956	−	13.8160i	0.207233	−	0.453777i
$928$	18.8357	+	43.7822i	0.618311	+	1.43722i
$929$	−0.0902499	+	0.627702i	−0.00296100	+	0.0205942i	−0.991248	−	0.132010i	$-0.957857\pi$
$929$	−0.0902499	+	0.627702i	−0.00296100	+	0.0205942i	0.988287	+	0.152604i	$0.0487660\pi$
$930$	−0.396692	−	0.273834i	−0.0130080	−	0.00897939i
$931$	16.1517	−	55.0078i	0.529352	−	1.80281i
$932$	−2.72306	+	2.75280i	−0.0891967	+	0.0901709i
$933$	1.40268	−	0.640580i	0.0459215	−	0.0209717i
$934$	−47.1736	+	19.6902i	−1.54357	+	0.644284i
$935$	2.12329	−	2.45040i	0.0694389	−	0.0801368i
$936$	6.26584	−	15.4827i	0.204805	−	0.506067i
$937$	−42.7108	−	27.4486i	−1.39530	−	0.896705i	−0.395537	−	0.918450i	$-0.629442\pi$
$937$	−42.7108	−	27.4486i	−1.39530	−	0.896705i	−0.999764	+	0.0217447i	$0.993078\pi$
$938$	−48.6671	+	39.4369i	−1.58904	+	1.28766i
$939$	9.19974	+	14.3151i	0.300222	+	0.467155i
$940$	2.84265	+	12.7341i	0.0927171	+	0.415340i
$941$	3.45367	+	11.7621i	0.112586	+	0.383434i	0.996438	−	0.0843341i	$-0.0268763\pi$
$941$	3.45367	+	11.7621i	0.112586	+	0.383434i	−0.883851	+	0.467768i	$0.845058\pi$
$942$	1.49351	−	0.891635i	0.0486613	−	0.0290510i
$943$	−2.38991	−	43.2438i	−0.0778261	−	1.40821i
$944$	−4.65040	+	3.06051i	−0.151357	+	0.0996112i
$945$	−2.62506	+	0.770788i	−0.0853933	+	0.0250737i
$946$	−5.42716	−	1.78997i	−0.176452	−	0.0581971i
$947$	−10.2553	−	15.9576i	−0.333253	−	0.518552i	0.633676	−	0.773599i	$-0.281545\pi$
$947$	−10.2553	−	15.9576i	−0.333253	−	0.518552i	−0.966929	+	0.255047i	$0.917909\pi$
$948$	−9.11868	+	24.8597i	−0.296161	+	0.807405i
$949$	27.2574	−	42.4134i	0.884814	−	1.37680i
$950$	47.4727	−	5.23429i	1.54022	−	0.169823i
$951$	−19.3567	+	22.3388i	−0.627683	+	0.724385i
$952$	33.6345	+	3.33912i	1.09010	+	0.108222i
$953$	−16.0552	−	35.1560i	−0.520078	−	1.13881i	−0.969410	−	0.245448i	$-0.921065\pi$
$953$	−16.0552	−	35.1560i	−0.520078	−	1.13881i	0.449331	−	0.893365i	$-0.351662\pi$
$954$	−1.61689	−	6.26389i	−0.0523489	−	0.202801i
$955$	0.418598	−	1.42561i	0.0135455	−	0.0461318i
$956$	21.2658	+	1.40491i	0.687787	+	0.0454381i
$957$	12.0908	+	1.73840i	0.390840	+	0.0561943i
$958$	−5.37712	+	30.2737i	−0.173727	+	0.978098i
$959$	−35.2730	+	77.2371i	−1.13902	+	2.49412i
$960$	−5.06826	−	2.66121i	−0.163577	−	0.0858901i
$961$	4.37947	+	30.4599i	0.141273	+	0.982577i
$962$	21.0400	−	42.3194i	0.678358	−	1.36443i
$963$	1.72355	−	1.49346i	0.0555405	−	0.0481261i
$964$	−8.93647	+	42.1821i	−0.287824	+	1.35859i
$965$			3.45439i			0.111201i
$966$	−22.1214	−	13.5315i	−0.711745	−	0.435370i
$967$	−12.8613			−0.413592			−0.206796	−	0.978384i	$-0.566304\pi$
$967$	−12.8613			−0.413592			−0.206796	+	0.978384i	$0.566304\pi$
$968$	8.14226	+	23.8143i	0.261702	+	0.765420i
$969$	15.4016	+	17.7744i	0.494770	+	0.570995i
$970$	−10.3019	−	5.12182i	−0.330774	−	0.164452i
$971$	35.4895	−	5.10262i	1.13891	−	0.163751i	0.453052	−	0.891484i	$-0.350335\pi$
$971$	35.4895	−	5.10262i	1.13891	−	0.163751i	0.685860	+	0.727733i	$0.259426\pi$
$972$	−0.968018	−	1.75013i	−0.0310492	−	0.0561353i
$973$	−68.8175	−	31.4279i	−2.20619	−	1.00753i
$974$	−4.33626	+	24.4135i	−0.138943	+	0.782260i
$975$	3.77170	−	26.2328i	0.120791	−	0.840121i
$976$	−17.6205	−	11.0554i	−0.564018	−	0.353875i
$977$	4.82289	+	1.41613i	0.154298	+	0.0453060i	0.357969	−	0.933733i	$-0.383469\pi$
$977$	4.82289	+	1.41613i	0.154298	+	0.0453060i	−0.203671	+	0.979039i	$0.565287\pi$
$978$	7.16088	−	1.84843i	0.228980	−	0.0591064i
$979$	7.54240	−	3.44450i	0.241056	−	0.110087i
$980$	−6.48654	+	8.76383i	−0.207205	+	0.279950i
$981$	−0.642118	−	0.556399i	−0.0205013	−	0.0177644i
$982$	22.3621	−	2.46563i	0.713605	−	0.0786814i
$983$	−23.3362	−	14.9972i	−0.744308	−	0.478338i	0.112707	−	0.993628i	$-0.464048\pi$
$983$	−23.3362	−	14.9972i	−0.744308	−	0.478338i	−0.857016	+	0.515290i	$0.827684\pi$
$984$	−4.73983	−	25.0991i	−0.151100	−	0.800130i
$985$	13.1652	−	8.46077i	0.419479	−	0.269583i
$986$	−11.6648	+	35.3675i	−0.371484	+	1.12633i
$987$	9.82076	+	33.4464i	0.312598	+	1.06461i
$988$	42.1678	−	78.2318i	1.34154	−	2.48889i
$989$	−10.8293	+	7.83641i	−0.344353	+	0.249183i
$990$	−1.25969	+	0.752041i	−0.0400355	+	0.0239014i
$991$	41.5334	−	12.1953i	1.31935	−	0.387397i	0.455093	−	0.890444i	$-0.349606\pi$
$991$	41.5334	−	12.1953i	1.31935	−	0.387397i	0.864259	+	0.503047i	$0.167788\pi$
$992$	−0.701771	−	2.60157i	−0.0222813	−	0.0825999i
$993$	23.5354	−	15.1253i	0.746873	−	0.479986i
$994$	46.8328	+	57.7941i	1.48545	+	1.83312i
$995$	3.92326	−	6.10472i	0.124376	−	0.193533i
$996$	14.0862	+	18.6054i	0.446337	+	0.589535i
$997$	−28.9973	−	25.1263i	−0.918354	−	0.795758i	0.0609525	−	0.998141i	$-0.480586\pi$
$997$	−28.9973	−	25.1263i	−0.918354	−	0.795758i	−0.979307	+	0.202382i	$0.935132\pi$
$998$	−33.0744	+	13.8052i	−1.04695	+	0.436996i
$999$	−2.35090	−	5.14776i	−0.0743793	−	0.162868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.13	yes	480
8.5	even	2	inner	552.2.bb.a.469.5	yes	480
23.18	even	11	inner	552.2.bb.a.133.5	✓	480
184.133	even	22	inner	552.2.bb.a.133.13	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.5	✓	480	23.18	even	11	inner
552.2.bb.a.133.13	yes	480	184.133	even	22	inner
552.2.bb.a.469.5	yes	480	8.5	even	2	inner
552.2.bb.a.469.13	yes	480	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.960856 + 1.03767i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-0.153511 - 1.99410i) q^{4} +(0.708272 - 0.101834i) q^{5} +(0.0466382 - 1.41344i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(2.21672 + 1.75675i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.960856 + 1.03767i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-0.153511 - 1.99410i) q^{4} +(0.708272 - 0.101834i) q^{5} +(0.0466382 - 1.41344i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(2.21672 + 1.75675i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-0.574878 + 0.832800i) q^{10} +(-0.408449 + 1.39105i) q^{11} +(1.42187 + 1.40651i) q^{12} +(5.37158 - 2.45312i) q^{13} +(-2.08279 - 4.98993i) q^{14} +(-0.468589 + 0.540781i) q^{15} +(-3.95287 + 0.612234i) q^{16} +(-2.62931 - 1.68976i) q^{17} +(0.890362 + 1.09875i) q^{18} +(4.06828 + 6.33036i) q^{19} +(-0.311795 - 1.39673i) q^{20} +(-1.07719 - 3.66856i) q^{21} +(-1.05099 - 1.76043i) q^{22} +(-4.77745 - 0.419530i) q^{23} +(-2.82571 + 0.123979i) q^{24} +(-4.30619 + 1.26441i) q^{25} +(-2.61579 + 7.93102i) q^{26} +(0.540641 + 0.841254i) q^{27} +(7.17915 + 2.63336i) q^{28} +(-4.55518 + 7.08801i) q^{29} +(-0.110904 - 1.00585i) q^{30} +(0.311933 - 0.359990i) q^{31} +(3.16284 - 4.69004i) q^{32} +(-0.602259 - 1.31876i) q^{33} +(4.27980 - 1.10474i) q^{34} +(-0.770788 + 2.62506i) q^{35} +(-1.99565 - 0.131841i) q^{36} +(-5.60156 - 0.805383i) q^{37} +(-10.4778 - 1.86104i) q^{38} +(-2.45312 + 5.37158i) q^{39} +(1.74894 + 1.01852i) q^{40} +(1.28520 + 8.93879i) q^{41} +(4.84178 + 2.40720i) q^{42} +(2.10648 - 1.82527i) q^{43} +(2.83660 + 0.600947i) q^{44} -0.715556i q^{45} +(5.02577 - 4.55430i) q^{46} -9.11704 q^{47} +(2.58645 - 3.05127i) q^{48} +(-4.98919 - 5.75783i) q^{49} +(2.82559 - 5.68331i) q^{50} +(3.09366 - 0.444801i) q^{51} +(-5.71636 - 10.3349i) q^{52} +(-4.16104 - 1.90028i) q^{53} +(-1.39242 - 0.247318i) q^{54} +(-0.147637 + 1.02684i) q^{55} +(-9.63068 + 4.91930i) q^{56} +(-7.22010 - 2.12001i) q^{57} +(-2.97812 - 11.5373i) q^{58} +(1.26601 - 0.578167i) q^{59} +(1.15030 + 0.851398i) q^{60} +(3.93018 + 3.40552i) q^{61} +(0.0738275 + 0.669582i) q^{62} +(3.21648 + 2.06711i) q^{63} +(1.82767 + 7.78843i) q^{64} +(3.55473 - 2.28449i) q^{65} +(1.94712 + 0.642197i) q^{66} +(-3.26376 - 11.1154i) q^{67} +(-2.96591 + 5.50251i) q^{68} +(3.88529 - 2.81150i) q^{69} +(-1.98333 - 3.32213i) q^{70} +(-13.1999 + 3.87584i) q^{71} +(2.05434 - 1.94414i) q^{72} +(7.18235 - 4.61582i) q^{73} +(6.21802 - 5.03871i) q^{74} +(2.42639 - 3.77553i) q^{75} +(11.9988 - 9.08433i) q^{76} +(-4.18922 - 3.62998i) q^{77} +(-3.21683 - 7.70684i) q^{78} +(5.49995 + 12.0432i) q^{79} +(-2.73736 + 0.836166i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-10.5104 - 7.25528i) q^{82} +(11.5494 + 1.66055i) q^{83} +(-7.15012 + 2.71119i) q^{84} +(-2.03434 - 0.929053i) q^{85} +(-0.129993 + 3.93965i) q^{86} +(-1.19908 - 8.33977i) q^{87} +(-3.34914 + 2.36602i) q^{88} +(-3.74534 - 4.32235i) q^{89} +(0.742509 + 0.687546i) q^{90} +22.5783i q^{91} +(-0.103191 + 9.59111i) q^{92} +0.476335i q^{93} +(8.76016 - 9.46046i) q^{94} +(3.52609 + 4.06933i) q^{95} +(0.681004 + 5.61571i) q^{96} +(1.61798 + 11.2533i) q^{97} +(10.7686 + 0.355323i) q^{98} +(1.31876 + 0.602259i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more