LMFDB - Embedded newform 864.2.bk.a.37.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(37,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("864.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bk (of order $24$, degree $8$, not 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.19
Character	$\chi$	$=$	864.37
Dual form			864.2.bk.a.397.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.532138 + 1.31028i) q^{2} +(-1.43366 - 1.39450i) q^{4} +(-0.794880 + 0.609933i) q^{5} +(0.0316510 - 0.118123i) q^{7} +(2.59008 - 1.13642i) q^{8} +O(q^{10})$	\(q+(-0.532138 + 1.31028i) q^{2} +(-1.43366 - 1.39450i) q^{4} +(-0.794880 + 0.609933i) q^{5} +(0.0316510 - 0.118123i) q^{7} +(2.59008 - 1.13642i) q^{8} +(-0.376196 - 1.36608i) q^{10} +(-1.26719 + 0.166829i) q^{11} +(0.202906 - 1.54122i) q^{13} +(0.137931 + 0.104329i) q^{14} +(0.110749 + 3.99847i) q^{16} -3.85821i q^{17} +(5.06862 - 2.09949i) q^{19} +(1.99014 + 0.234024i) q^{20} +(0.455730 - 1.74915i) q^{22} +(0.861873 + 3.21656i) q^{23} +(-1.03428 + 3.85998i) q^{25} +(1.91146 + 1.08601i) q^{26} +(-0.210099 + 0.125211i) q^{28} +(2.86265 - 3.73067i) q^{29} +(4.33882 - 7.51506i) q^{31} +(-5.29804 - 1.98262i) q^{32} +(5.05533 + 2.05310i) q^{34} +(0.0468884 + 0.113199i) q^{35} +(0.853436 + 0.353505i) q^{37} +(0.0537109 + 7.75852i) q^{38} +(-1.36566 + 2.48310i) q^{40} +(1.62055 + 6.04799i) q^{41} +(8.05657 - 1.06067i) q^{43} +(2.04937 + 1.52792i) q^{44} +(-4.67322 - 0.582358i) q^{46} +(0.450951 - 0.260357i) q^{47} +(6.04923 + 3.49252i) q^{49} +(-4.50727 - 3.40924i) q^{50} +(-2.44013 + 1.92664i) q^{52} +(0.213988 - 0.516614i) q^{53} +(0.905513 - 0.905513i) q^{55} +(-0.0522592 - 0.341918i) q^{56} +(3.36490 + 5.73610i) q^{58} +(4.19411 - 3.21826i) q^{59} +(0.0436465 - 0.0568812i) q^{61} +(7.53797 + 9.68411i) q^{62} +(5.41708 - 5.88687i) q^{64} +(0.778757 + 1.34885i) q^{65} +(13.2432 + 1.74350i) q^{67} +(-5.38027 + 5.53136i) q^{68} +(-0.173273 + 0.00119954i) q^{70} +(5.82525 + 5.82525i) q^{71} +(-0.0446149 + 0.0446149i) q^{73} +(-0.917335 + 0.930125i) q^{74} +(-10.1944 - 4.05823i) q^{76} +(-0.0204015 + 0.154965i) q^{77} +(-10.5100 + 6.06793i) q^{79} +(-2.52683 - 3.11075i) q^{80} +(-8.78691 - 1.09499i) q^{82} +(-4.44119 - 3.40785i) q^{83} +(2.35325 + 3.06682i) q^{85} +(-2.89744 + 11.1208i) q^{86} +(-3.09255 + 1.87217i) q^{88} +(1.12858 + 1.12858i) q^{89} +(-0.175632 - 0.0727491i) q^{91} +(3.24985 - 5.81332i) q^{92} +(0.101171 + 0.729417i) q^{94} +(-2.74840 + 4.76036i) q^{95} +(-2.01243 - 3.48563i) q^{97} +(-7.79520 + 6.06766i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.532138	+	1.31028i	−0.376279	+	0.926507i
$2$	−0.532138	+	1.31028i	−0.376279	+	0.926507i
$3$		0			0
$3$		0			0
$4$	−1.43366	−	1.39450i	−0.716829	−	0.697249i
$5$	−0.794880	+	0.609933i	−0.355481	+	0.272770i	−0.771028	−	0.636802i	$-0.780257\pi$
$5$	−0.794880	+	0.609933i	−0.355481	+	0.272770i	0.415546	+	0.909572i	$0.363590\pi$
$6$		0			0
$7$	0.0316510	−	0.118123i	0.0119629	−	0.0446463i	−0.959686	−	0.281073i	$-0.909310\pi$
$7$	0.0316510	−	0.118123i	0.0119629	−	0.0446463i	0.971649	+	0.236427i	$0.0759763\pi$
$8$	2.59008	−	1.13642i	0.915733	−	0.401787i
$9$		0			0
$10$	−0.376196	−	1.36608i	−0.118964	−	0.431993i
$11$	−1.26719	+	0.166829i	−0.382073	+	0.0503009i	−0.319117	−	0.947715i	$-0.603386\pi$
$11$	−1.26719	+	0.166829i	−0.382073	+	0.0503009i	−0.0629564	+	0.998016i	$0.520053\pi$
$12$		0			0
$13$	0.202906	−	1.54122i	0.0562760	−	0.427458i	−0.939996	−	0.341186i	$-0.889171\pi$
$13$	0.202906	−	1.54122i	0.0562760	−	0.427458i	0.996272	−	0.0862720i	$-0.0274954\pi$
$14$	0.137931	+	0.104329i	0.0368637	+	0.0278832i
$15$		0			0
$16$	0.110749	+	3.99847i	0.0276873	+	0.999617i
$17$		−	3.85821i		−	0.935754i	−0.883794	−	0.467877i	$-0.845019\pi$
$17$		−	3.85821i		−	0.935754i	0.883794	−	0.467877i	$-0.154981\pi$
$18$		0			0
$19$	5.06862	−	2.09949i	1.16282	−	0.481656i	0.284008	−	0.958822i	$-0.408336\pi$
$19$	5.06862	−	2.09949i	1.16282	−	0.481656i	0.878813	+	0.477166i	$0.158336\pi$
$20$	1.99014	+	0.234024i	0.445008	+	0.0523293i
$21$		0			0
$22$	0.455730	−	1.74915i	0.0971619	−	0.372921i
$23$	0.861873	+	3.21656i	0.179713	+	0.670698i	0.995701	+	0.0926288i	$0.0295270\pi$
$23$	0.861873	+	3.21656i	0.179713	+	0.670698i	−0.815988	+	0.578069i	$0.803806\pi$
$24$		0			0
$25$	−1.03428	+	3.85998i	−0.206856	+	0.771996i
$26$	1.91146	+	1.08601i	0.374868	+	0.212984i
$27$		0			0
$28$	−0.210099	+	0.125211i	−0.0397050	+	0.0236626i
$29$	2.86265	−	3.73067i	0.531580	−	0.692769i	−0.447952	−	0.894058i	$-0.647846\pi$
$29$	2.86265	−	3.73067i	0.531580	−	0.692769i	0.979532	+	0.201289i	$0.0645131\pi$
$30$		0			0
$31$	4.33882	−	7.51506i	0.779275	−	1.34974i	−0.153084	−	0.988213i	$-0.548921\pi$
$31$	4.33882	−	7.51506i	0.779275	−	1.34974i	0.932360	−	0.361532i	$-0.117746\pi$
$32$	−5.29804	−	1.98262i	−0.936570	−	0.350482i
$33$		0			0
$34$	5.05533	+	2.05310i	0.866982	+	0.352104i
$35$	0.0468884	+	0.113199i	0.00792559	+	0.0191341i
$36$		0			0
$37$	0.853436	+	0.353505i	0.140304	+	0.0581158i	0.451731	−	0.892154i	$-0.350807\pi$
$37$	0.853436	+	0.353505i	0.140304	+	0.0581158i	−0.311427	+	0.950270i	$0.600807\pi$
$38$	0.0537109	+	7.75852i	0.00871306	+	1.25860i
$39$		0			0
$40$	−1.36566	+	2.48310i	−0.215930	+	0.392613i
$41$	1.62055	+	6.04799i	0.253088	+	0.944538i	0.969144	+	0.246495i	$0.0792788\pi$
$41$	1.62055	+	6.04799i	0.253088	+	0.944538i	−0.716056	+	0.698043i	$0.754055\pi$
$42$		0			0
$43$	8.05657	−	1.06067i	1.22862	−	0.161750i	0.511857	−	0.859071i	$-0.328958\pi$
$43$	8.05657	−	1.06067i	1.22862	−	0.161750i	0.716759	+	0.697321i	$0.245625\pi$
$44$	2.04937	+	1.52792i	0.308953	+	0.230343i
$45$		0			0
$46$	−4.67322	−	0.582358i	−0.689028	−	0.0858640i
$47$	0.450951	−	0.260357i	0.0657779	−	0.0379769i	−0.466750	−	0.884389i	$-0.654575\pi$
$47$	0.450951	−	0.260357i	0.0657779	−	0.0379769i	0.532528	+	0.846412i	$0.321242\pi$
$48$		0			0
$49$	6.04923	+	3.49252i	0.864175	+	0.498932i
$50$	−4.50727	−	3.40924i	−0.637424	−	0.482139i
$51$		0			0
$52$	−2.44013	+	1.92664i	−0.338385	+	0.267176i
$53$	0.213988	−	0.516614i	0.0293936	−	0.0709623i	−0.908501	−	0.417882i	$-0.862772\pi$
$53$	0.213988	−	0.516614i	0.0293936	−	0.0709623i	0.937895	+	0.346920i	$0.112772\pi$
$54$		0			0
$55$	0.905513	−	0.905513i	0.122099	−	0.122099i
$56$	−0.0522592	−	0.341918i	−0.00698343	−	0.0456907i
$57$		0			0
$58$	3.36490	+	5.73610i	0.441832	+	0.753186i
$59$	4.19411	−	3.21826i	0.546027	−	0.418981i	−0.298567	−	0.954389i	$-0.596509\pi$
$59$	4.19411	−	3.21826i	0.546027	−	0.418981i	0.844594	+	0.535408i	$0.179842\pi$
$60$		0			0
$61$	0.0436465	−	0.0568812i	0.00558836	−	0.00728289i	−0.790551	−	0.612396i	$-0.790206\pi$
$61$	0.0436465	−	0.0568812i	0.00558836	−	0.00728289i	0.796139	+	0.605114i	$0.206872\pi$
$62$	7.53797	+	9.68411i	0.957323	+	1.22988i
$63$		0			0
$64$	5.41708	−	5.88687i	0.677135	−	0.735859i
$65$	0.778757	+	1.34885i	0.0965930	+	0.167304i
$66$		0			0
$67$	13.2432	+	1.74350i	1.61792	+	0.213003i	0.884421	−	0.466690i	$-0.154554\pi$
$67$	13.2432	+	1.74350i	1.61792	+	0.213003i	0.733497	+	0.679693i	$0.237887\pi$
$68$	−5.38027	+	5.53136i	−0.652454	+	0.670776i
$69$		0			0
$70$	−0.173273	+	0.00119954i	−0.0207101	+	0.000143372i
$71$	5.82525	+	5.82525i	0.691331	+	0.691331i	0.962525	−	0.271194i	$-0.0874185\pi$
$71$	5.82525	+	5.82525i	0.691331	+	0.691331i	−0.271194	+	0.962525i	$0.587419\pi$
$72$		0			0
$73$	−0.0446149	+	0.0446149i	−0.00522177	+	0.00522177i	−0.709713	−	0.704491i	$-0.751175\pi$
$73$	−0.0446149	+	0.0446149i	−0.00522177	+	0.00522177i	0.704491	+	0.709713i	$0.251175\pi$
$74$	−0.917335	+	0.930125i	−0.106638	+	0.108125i
$75$		0			0
$76$	−10.1944	−	4.05823i	−1.16938	−	0.465511i
$77$	−0.0204015	+	0.154965i	−0.00232497	+	0.0176599i
$78$		0			0
$79$	−10.5100	+	6.06793i	−1.18246	+	0.682695i	−0.956583	−	0.291460i	$-0.905859\pi$
$79$	−10.5100	+	6.06793i	−1.18246	+	0.682695i	−0.225879	+	0.974155i	$0.572526\pi$
$80$	−2.52683	−	3.11075i	−0.282508	−	0.347793i
$81$		0			0
$82$	−8.78691	−	1.09499i	−0.970352	−	0.120921i
$83$	−4.44119	−	3.40785i	−0.487484	−	0.374060i	0.335577	−	0.942013i	$-0.391069\pi$
$83$	−4.44119	−	3.40785i	−0.487484	−	0.374060i	−0.823061	+	0.567953i	$0.807735\pi$
$84$		0			0
$85$	2.35325	+	3.06682i	0.255246	+	0.332643i
$86$	−2.89744	+	11.1208i	−0.312439	+	1.19918i
$87$		0			0
$88$	−3.09255	+	1.87217i	−0.329667	+	0.199574i
$89$	1.12858	+	1.12858i	0.119629	+	0.119629i	0.764387	−	0.644758i	$-0.223042\pi$
$89$	1.12858	+	1.12858i	0.119629	+	0.119629i	−0.644758	+	0.764387i	$0.723042\pi$
$90$		0			0
$91$	−0.175632	−	0.0727491i	−0.0184112	−	0.00762618i
$92$	3.24985	−	5.81332i	0.338820	−	0.606081i
$93$		0			0
$94$	0.101171	+	0.729417i	0.0104350	+	0.0752336i
$95$	−2.74840	+	4.76036i	−0.281980	+	0.488403i
$96$		0			0
$97$	−2.01243	−	3.48563i	−0.204331	−	0.353912i	0.745588	−	0.666407i	$-0.232169\pi$
$97$	−2.01243	−	3.48563i	−0.204331	−	0.353912i	−0.949919	+	0.312495i	$0.898835\pi$
$98$	−7.79520	+	6.06766i	−0.787434	+	0.612927i
$99$		0			0
$100$	6.86554	−	4.09159i	0.686554	−	0.409159i
$101$	−2.24156	−	17.0263i	−0.223044	−	1.69418i	−0.626689	−	0.779269i	$-0.715590\pi$
$101$	−2.24156	−	17.0263i	−0.223044	−	1.69418i	0.403646	−	0.914915i	$-0.367743\pi$
$102$		0			0
$103$	7.04432	−	1.88752i	0.694098	−	0.185983i	0.105512	−	0.994418i	$-0.466352\pi$
$103$	7.04432	−	1.88752i	0.694098	−	0.185983i	0.588585	+	0.808435i	$0.299685\pi$
$104$	−1.22594	−	4.22249i	−0.120213	−	0.414049i
$105$		0			0
$106$	0.563036	+	0.555294i	0.0546869	+	0.0539349i
$107$	6.13203	−	14.8040i	0.592806	−	1.43116i	−0.287976	−	0.957638i	$-0.592982\pi$
$107$	6.13203	−	14.8040i	0.592806	−	1.43116i	0.880782	−	0.473522i	$-0.157018\pi$
$108$		0			0
$109$	−16.8802	+	6.99200i	−1.61683	+	0.669712i	−0.993665	−	0.112381i	$-0.964152\pi$
$109$	−16.8802	+	6.99200i	−1.61683	+	0.669712i	−0.623162	+	0.782093i	$0.714152\pi$
$110$	0.704616	+	1.66833i	0.0671825	+	0.159069i
$111$		0			0
$112$	0.475816	+	0.113473i	0.0449604	+	0.0107222i
$113$	−5.21429	−	3.01047i	−0.490520	−	0.283202i	0.234270	−	0.972171i	$-0.424730\pi$
$113$	−5.21429	−	3.01047i	−0.490520	−	0.283202i	−0.724790	+	0.688970i	$0.758063\pi$
$114$		0			0
$115$	−2.64697	−	2.03109i	−0.246831	−	0.189400i
$116$	−9.30647	+	1.35655i	−0.864084	+	0.125953i
$117$		0			0
$118$	1.98496	+	7.20801i	0.182731	+	0.663551i
$119$	−0.455744	−	0.122116i	−0.0417780	−	0.0111944i
$120$		0			0
$121$	−9.04724	+	2.42420i	−0.822476	+	0.220382i
$122$	0.0513043	+	0.0874577i	0.00464487	+	0.00791805i
$123$		0			0
$124$	−16.7001	+	4.72355i	−1.49972	+	0.424187i
$125$	−3.44930	−	8.32735i	−0.308515	−	0.744821i
$126$		0			0
$127$	7.69512			0.682832			0.341416	−	0.939912i	$-0.389094\pi$
$127$	7.69512			0.682832			0.341416	+	0.939912i	$0.389094\pi$
$128$	4.83081	+	10.2305i	0.426987	+	0.904258i
$129$		0			0
$130$	−2.18177	+	0.302616i	−0.191354	+	0.0265411i
$131$	6.06164	+	0.798030i	0.529608	+	0.0697242i	0.390588	−	0.920565i	$-0.372272\pi$
$131$	6.06164	+	0.798030i	0.529608	+	0.0697242i	0.139019	+	0.990290i	$0.455605\pi$
$132$		0			0
$133$	−0.0875715	−	0.665172i	−0.00759341	−	0.0576777i
$134$	−9.33171	+	16.4245i	−0.806137	+	1.41886i
$135$		0			0
$136$	−4.38457	−	9.99310i	−0.375974	−	0.856901i
$137$	−0.962610	−	0.257931i	−0.0822413	−	0.0220365i	0.217464	−	0.976068i	$-0.430222\pi$
$137$	−0.962610	−	0.257931i	−0.0822413	−	0.0220365i	−0.299705	+	0.954032i	$0.596888\pi$
$138$		0			0
$139$	9.87188	+	12.8653i	0.837322	+	1.09122i	0.994612	+	0.103666i	$0.0330575\pi$
$139$	9.87188	+	12.8653i	0.837322	+	1.09122i	−0.157290	+	0.987552i	$0.550276\pi$
$140$	0.0906334	−	0.227674i	0.00765992	−	0.0192420i
$141$		0			0
$142$	−10.7325	+	4.53286i	−0.900655	+	0.380389i
$143$			1.98688i			0.166151i
$144$		0			0
$145$			4.71146i			0.391266i
$146$	−0.0347166	−	0.0821992i	−0.00287317	−	0.00680285i
$147$		0			0
$148$	−0.730573	−	1.69692i	−0.0600527	−	0.139486i
$149$	10.8432	+	14.1311i	0.888310	+	1.15767i	0.986705	+	0.162521i	$0.0519626\pi$
$149$	10.8432	+	14.1311i	0.888310	+	1.15767i	−0.0983946	+	0.995147i	$0.531371\pi$
$150$		0			0
$151$	−15.2442	−	4.08468i	−1.24056	−	0.332407i	−0.421877	−	0.906653i	$-0.638629\pi$
$151$	−15.2442	−	4.08468i	−1.24056	−	0.332407i	−0.818683	+	0.574246i	$0.805295\pi$
$152$	10.7422	−	11.1980i	0.871311	−	0.908275i
$153$		0			0
$154$	−0.192191	−	0.109195i	−0.0154872	−	0.00879915i
$155$	1.13484	+	8.61996i	0.0911525	+	0.692372i
$156$		0			0
$157$	−13.5505	−	1.78395i	−1.08145	−	0.142375i	−0.431318	−	0.902200i	$-0.641951\pi$
$157$	−13.5505	−	1.78395i	−1.08145	−	0.142375i	−0.650128	+	0.759825i	$0.725285\pi$
$158$	−2.35792	−	16.9999i	−0.187586	−	1.35244i
$159$		0			0
$160$	5.42057	−	1.65550i	0.428534	−	0.130879i
$161$	0.407228			0.0320941
$162$		0			0
$163$	−4.10244	−	9.90416i	−0.321328	−	0.775753i	−0.999177	−	0.0405530i	$-0.987088\pi$
$163$	−4.10244	−	9.90416i	−0.321328	−	0.775753i	0.677850	−	0.735200i	$-0.262912\pi$
$164$	6.11059	−	10.9306i	0.477157	−	0.853537i
$165$		0			0
$166$	6.82855	−	4.00575i	0.529999	−	0.310907i
$167$	23.7864	−	6.37356i	1.84065	−	0.493201i	0.841741	−	0.539882i	$-0.181531\pi$
$167$	23.7864	−	6.37356i	1.84065	−	0.493201i	0.998910	+	0.0466813i	$0.0148645\pi$
$168$		0			0
$169$	10.2228	+	2.73920i	0.786372	+	0.210708i
$170$	−5.27064	+	1.45144i	−0.404240	+	0.111321i
$171$		0			0
$172$	−13.0295	−	9.71424i	−0.993488	−	0.740704i
$173$	−15.9881	−	12.2681i	−1.21555	−	0.932726i	−0.216501	−	0.976282i	$-0.569465\pi$
$173$	−15.9881	−	12.2681i	−1.21555	−	0.932726i	−0.999051	+	0.0435561i	$0.986131\pi$
$174$		0			0
$175$	0.423217	+	0.244344i	0.0319922	+	0.0184707i
$176$	−0.807402	−	5.04836i	−0.0608602	−	0.380534i
$177$		0			0
$178$	−2.07931	+	0.878189i	−0.155851	+	0.0658231i
$179$	21.1693	−	8.76861i	1.58227	−	0.655397i	0.593497	−	0.804836i	$-0.297747\pi$
$179$	21.1693	−	8.76861i	1.58227	−	0.655397i	0.988771	+	0.149440i	$0.0477469\pi$
$180$		0			0
$181$	2.65204	−	6.40259i	0.197124	−	0.475900i	−0.794149	−	0.607723i	$-0.792083\pi$
$181$	2.65204	−	6.40259i	0.197124	−	0.475900i	0.991273	+	0.131823i	$0.0420830\pi$
$182$	0.188782	−	0.191414i	0.0139934	−	0.0141885i
$183$		0			0
$184$	5.88770	+	7.35170i	0.434047	+	0.541974i
$185$	−0.893993	+	0.239545i	−0.0657277	+	0.0176117i
$186$		0			0
$187$	0.643663	+	4.88910i	0.0470693	+	0.357527i
$188$	−1.00958	−	0.255588i	−0.0736309	−	0.0186407i
$189$		0			0
$190$	−4.77487	−	6.13434i	−0.346406	−	0.445031i
$191$	−0.100299	−	0.173723i	−0.00725737	−	0.0125701i	0.862374	−	0.506272i	$-0.168977\pi$
$191$	−0.100299	−	0.173723i	−0.00725737	−	0.0125701i	−0.869631	+	0.493702i	$0.835643\pi$
$192$		0			0
$193$	−6.63653	+	11.4948i	−0.477708	+	0.827414i	−0.999673	−	0.0255525i	$-0.991865\pi$
$193$	−6.63653	+	11.4948i	−0.477708	+	0.827414i	0.521966	+	0.852966i	$0.325199\pi$
$194$	5.63803	−	0.782005i	0.404787	−	0.0561447i
$195$		0			0
$196$	−3.80220	−	13.4427i	−0.271586	−	0.960194i
$197$	−23.1886	−	9.60502i	−1.65212	−	0.684329i	−0.654682	−	0.755904i	$-0.727197\pi$
$197$	−23.1886	−	9.60502i	−1.65212	−	0.684329i	−0.997435	+	0.0715750i	$0.977197\pi$
$198$		0			0
$199$	−12.0736	−	12.0736i	−0.855875	−	0.855875i	0.134974	−	0.990849i	$-0.456905\pi$
$199$	−12.0736	−	12.0736i	−0.855875	−	0.855875i	−0.990849	+	0.134974i	$0.956905\pi$
$200$	1.70771	+	11.1731i	0.120753	+	0.790055i
$201$		0			0
$202$	23.5021	+	6.12330i	1.65360	+	0.430834i
$203$	−0.350073	−	0.456224i	−0.0245703	−	0.0320206i
$204$		0			0
$205$	−4.97702	−	3.81900i	−0.347610	−	0.266730i
$206$	−1.27538	+	10.2344i	−0.0888597	+	0.713067i
$207$		0			0
$208$	6.18500	+	0.640623i	0.428853	+	0.0444192i
$209$	−6.07267	+	3.50606i	−0.420055	+	0.242519i
$210$		0			0
$211$	1.87066	−	14.2090i	0.128781	−	0.978191i	−0.798018	−	0.602634i	$-0.794118\pi$
$211$	1.87066	−	14.2090i	0.128781	−	0.978191i	0.926799	−	0.375557i	$-0.122549\pi$
$212$	−1.02720	+	0.442241i	−0.0705486	+	0.0303732i
$213$		0			0
$214$	16.1343	+	15.9125i	1.10292	+	1.08775i
$215$	−5.75707	+	5.75707i	−0.392629	+	0.392629i
$216$		0			0
$217$	−0.750374	−	0.750374i	−0.0509387	−	0.0509387i
$218$	−0.178875	−	25.8384i	−0.0121150	−	1.75000i
$219$		0			0
$220$	−2.56093	+	0.0354595i	−0.172658	+	0.00239068i
$221$	−5.94637	−	0.782854i	−0.399996	−	0.0526605i
$222$		0			0
$223$	−2.24595	−	3.89010i	−0.150400	−	0.260501i	0.780975	−	0.624563i	$-0.214723\pi$
$223$	−2.24595	−	3.89010i	−0.150400	−	0.260501i	−0.931375	+	0.364062i	$0.881390\pi$
$224$	−0.401882	+	0.563068i	−0.0268518	+	0.0376216i
$225$		0			0
$226$	6.71928	−	5.23019i	0.446960	−	0.347907i
$227$	−2.47119	+	3.22052i	−0.164019	+	0.213754i	−0.868131	−	0.496335i	$-0.834679\pi$
$227$	−2.47119	+	3.22052i	−0.164019	+	0.213754i	0.704112	+	0.710089i	$0.251345\pi$
$228$		0			0
$229$	3.37639	−	2.59079i	0.223118	−	0.171204i	−0.491154	−	0.871073i	$-0.663425\pi$
$229$	3.37639	−	2.59079i	0.223118	−	0.171204i	0.714272	+	0.699868i	$0.246758\pi$
$230$	4.06985	−	2.38745i	0.268358	−	0.157423i
$231$		0			0
$232$	3.17487	−	12.9159i	0.208440	−	0.847973i
$233$	−8.36462	+	8.36462i	−0.547985	+	0.547985i	−0.925858	−	0.377873i	$-0.876656\pi$
$233$	−8.36462	+	8.36462i	−0.547985	+	0.547985i	0.377873	+	0.925858i	$0.376656\pi$
$234$		0			0
$235$	−0.199652	+	0.482002i	−0.0130238	+	0.0314424i
$236$	−10.5008	−	1.23480i	−0.683542	−	0.0803790i
$237$		0			0
$238$	0.402525	−	0.532169i	0.0260918	−	0.0344954i
$239$	−17.7190	−	10.2301i	−1.14615	−	0.661728i	−0.198201	−	0.980161i	$-0.563510\pi$
$239$	−17.7190	−	10.2301i	−1.14615	−	0.661728i	−0.947945	+	0.318433i	$0.896843\pi$
$240$		0			0
$241$	10.5833	−	6.11029i	0.681732	−	0.393598i	−0.118775	−	0.992921i	$-0.537897\pi$
$241$	10.5833	−	6.11029i	0.681732	−	0.393598i	0.800507	+	0.599323i	$0.204563\pi$
$242$	1.63800	−	13.1444i	0.105295	−	0.844954i
$243$		0			0
$244$	−0.141895	+	0.0206832i	−0.00908389	+	0.00132411i
$245$	−6.93862	+	0.913486i	−0.443292	+	0.0583605i
$246$		0			0
$247$	−2.20733	−	8.23787i	−0.140449	−	0.524163i
$248$	2.69762	−	24.3954i	0.171299	−	1.54911i
$249$		0			0
$250$	12.7467	−	0.0882429i	0.806169	−	0.00558097i
$251$	−3.66903	−	1.51976i	−0.231587	−	0.0959265i	0.263872	−	0.964558i	$-0.415000\pi$
$251$	−3.66903	−	1.51976i	−0.231587	−	0.0959265i	−0.495459	+	0.868631i	$0.665000\pi$
$252$		0			0
$253$	−1.62878	−	3.93221i	−0.102400	−	0.247216i
$254$	−4.09487	+	10.0827i	−0.256935	+	0.632648i
$255$		0			0
$256$	−15.9755	+	0.885655i	−0.998467	+	0.0553535i
$257$	12.4007	−	21.4787i	0.773537	−	1.33981i	−0.162076	−	0.986778i	$-0.551819\pi$
$257$	12.4007	−	21.4787i	0.773537	−	1.33981i	0.935613	−	0.353027i	$-0.114848\pi$
$258$		0			0
$259$	0.0687691	−	0.0896216i	0.00427310	−	0.00556882i
$260$	0.764494	−	3.01976i	0.0474119	−	0.187278i
$261$		0			0
$262$	−4.27127	+	7.51777i	−0.263880	+	0.464449i
$263$	−2.48915	+	9.28963i	−0.153487	+	0.572823i	0.845743	+	0.533591i	$0.179158\pi$
$263$	−2.48915	+	9.28963i	−0.153487	+	0.572823i	−0.999230	+	0.0392320i	$0.987509\pi$
$264$		0			0
$265$	0.145005	+	0.541165i	0.00890756	+	0.0332435i
$266$	0.918160	+	0.239220i	0.0562960	+	0.0146675i
$267$		0			0
$268$	−16.5549	−	20.9673i	−1.01125	−	1.28078i
$269$	8.30063	−	3.43823i	0.506099	−	0.209633i	−0.115000	−	0.993366i	$-0.536687\pi$
$269$	8.30063	−	3.43823i	0.506099	−	0.209633i	0.621098	+	0.783733i	$0.286687\pi$
$270$		0			0
$271$			14.5560i			0.884215i	0.896962	+	0.442108i	$0.145769\pi$
$271$			14.5560i			0.884215i	−0.896962	+	0.442108i	$0.854231\pi$
$272$	15.4269	−	0.427295i	0.935396	−	0.0259085i
$273$		0			0
$274$	0.850202	−	1.12403i	0.0513626	−	0.0679053i
$275$	0.666674	−	5.06389i	0.0402020	−	0.305364i
$276$		0			0
$277$	21.9893	−	2.89495i	1.32121	−	0.173940i	0.563274	−	0.826270i	$-0.309542\pi$
$277$	21.9893	−	2.89495i	1.32121	−	0.173940i	0.757935	+	0.652330i	$0.226208\pi$
$278$	−22.1103	+	6.08880i	−1.32609	+	0.365182i
$279$		0			0
$280$	0.250087	+	0.239909i	0.0149455	+	0.0143373i
$281$	−5.07033	+	18.9227i	−0.302471	+	1.12884i	0.632630	+	0.774454i	$0.281975\pi$
$281$	−5.07033	+	18.9227i	−0.302471	+	1.12884i	−0.935101	+	0.354382i	$0.884691\pi$
$282$		0			0
$283$	0.0461480	−	0.0354106i	0.00274322	−	0.00210494i	−0.607389	−	0.794405i	$-0.707783\pi$
$283$	0.0461480	−	0.0354106i	0.00274322	−	0.00210494i	0.610132	+	0.792300i	$0.291116\pi$
$284$	−0.228114	−	16.4747i	−0.0135361	−	0.977595i
$285$		0			0
$286$	−2.60336	−	1.05729i	−0.153940	−	0.0625191i
$287$	0.765699			0.0451978
$288$		0			0
$289$	2.11419			0.124364
$290$	−6.17332	−	2.50715i	−0.362510	−	0.147225i
$291$		0			0
$292$	0.126178	−	0.00174710i	0.00738400	−	0.000102241i
$293$	−19.2172	+	14.7459i	−1.12268	+	0.861465i	−0.991528	−	0.129896i	$-0.958536\pi$
$293$	−19.2172	+	14.7459i	−1.12268	+	0.861465i	−0.131156	+	0.991362i	$0.541869\pi$
$294$		0			0
$295$	−1.37090	+	5.11626i	−0.0798167	+	0.297880i
$296$	2.61220	−	0.0542584i	0.151831	−	0.00315371i
$297$		0			0
$298$	−24.2858	+	6.68790i	−1.40684	+	0.387420i
$299$	5.13231	−	0.675681i	0.296809	−	0.0390757i
$300$		0			0
$301$	0.129709	−	0.985238i	0.00747630	−	0.0567882i
$302$	13.4641	−	17.8006i	0.774773	−	1.02431i
$303$		0			0
$304$	8.95609	+	20.0342i	0.513667	+	1.14904i
$305$			0.0718352i			0.00411327i
$306$		0			0
$307$	3.72383	−	1.54246i	0.212530	−	0.0880329i	−0.273878	−	0.961764i	$-0.588307\pi$
$307$	3.72383	−	1.54246i	0.212530	−	0.0880329i	0.486409	+	0.873731i	$0.338307\pi$
$308$	0.245347	−	0.193717i	0.0139800	−	0.0110380i
$309$		0			0
$310$	−11.8984	−	3.10006i	−0.675786	−	0.176071i
$311$	5.93415	+	22.1465i	0.336495	+	1.25581i	0.902240	+	0.431235i	$0.141922\pi$
$311$	5.93415	+	22.1465i	0.336495	+	1.25581i	−0.565745	+	0.824580i	$0.691411\pi$
$312$		0			0
$313$	−8.07338	+	30.1303i	−0.456334	+	1.70306i	0.227800	+	0.973708i	$0.426847\pi$
$313$	−8.07338	+	30.1303i	−0.456334	+	1.70306i	−0.684135	+	0.729356i	$0.739820\pi$
$314$	9.54820	−	16.8056i	0.538836	−	0.948394i
$315$		0			0
$316$	23.5294	+	5.95679i	1.32363	+	0.335095i
$317$	−4.89002	+	6.37280i	−0.274651	+	0.357932i	−0.910230	−	0.414104i	$-0.864095\pi$
$317$	−4.89002	+	6.37280i	−0.274651	+	0.357932i	0.635579	+	0.772036i	$0.280762\pi$
$318$		0			0
$319$	−3.00514	+	5.20506i	−0.168256	+	0.291427i
$320$	−0.715330	+	7.98341i	−0.0399882	+	0.446286i
$321$		0			0
$322$	−0.216702	+	0.533582i	−0.0120763	+	0.0297354i
$323$	−8.10028	−	19.5558i	−0.450712	−	1.08811i
$324$		0			0
$325$	5.73923	+	2.37727i	0.318355	+	0.131867i
$326$	15.1603	−	0.104952i	0.839649	−	0.00581275i
$327$		0			0
$328$	11.0705	+	13.8232i	0.611264	+	0.763257i
$329$	−0.0164811	−	0.0615082i	−0.000908631	−	0.00339106i
$330$		0			0
$331$	11.7820	−	1.55114i	0.647600	−	0.0852581i	0.200431	−	0.979708i	$-0.435766\pi$
$331$	11.7820	−	1.55114i	0.647600	−	0.0852581i	0.447169	+	0.894450i	$0.352432\pi$
$332$	1.61491	+	11.0789i	0.0886299	+	0.608035i
$333$		0			0
$334$	−4.30654	+	34.5585i	−0.235644	+	1.89096i
$335$	−11.5902	+	6.69161i	−0.633240	+	0.365602i
$336$		0			0
$337$	−22.3125	−	12.8821i	−1.21544	−	0.701733i	−0.251499	−	0.967858i	$-0.580923\pi$
$337$	−22.3125	−	12.8821i	−1.21544	−	0.701733i	−0.963939	+	0.266124i	$0.914257\pi$
$338$	−9.02908	+	11.9371i	−0.491117	+	0.649294i
$339$		0			0
$340$	0.902914	−	7.67837i	0.0489674	−	0.416418i
$341$	−4.24440	+	10.2469i	−0.229847	+	0.554900i
$342$		0			0
$343$	1.20932	−	1.20932i	0.0652969	−	0.0652969i
$344$	19.6618	−	11.9029i	1.06010	−	0.641762i
$345$		0			0
$346$	24.5825	−	14.4205i	1.32156	−	0.775252i
$347$	−15.9952	+	12.2736i	−0.858670	+	0.658881i	−0.941252	−	0.337704i	$-0.890350\pi$
$347$	−15.9952	+	12.2736i	−0.858670	+	0.658881i	0.0825826	+	0.996584i	$0.473683\pi$
$348$		0			0
$349$	5.66695	−	7.38531i	0.303345	−	0.395326i	−0.616663	−	0.787227i	$-0.711516\pi$
$349$	5.66695	−	7.38531i	0.303345	−	0.395326i	0.920007	+	0.391901i	$0.128182\pi$
$350$	−0.545369	+	0.424507i	−0.0291512	+	0.0226908i
$351$		0			0
$352$	7.04440	+	1.62850i	0.375468	+	0.0867994i
$353$	2.48420	+	4.30276i	0.132221	+	0.229013i	0.924532	−	0.381104i	$-0.124456\pi$
$353$	2.48420	+	4.30276i	0.132221	+	0.229013i	−0.792312	+	0.610117i	$0.791123\pi$
$354$		0			0
$355$	−8.18340	−	1.07736i	−0.434330	−	0.0571806i
$356$	−0.0441945	−	3.19179i	−0.00234230	−	0.169164i
$357$		0			0
$358$	0.224326	+	32.4038i	0.0118560	+	1.71259i
$359$	18.5138	+	18.5138i	0.977119	+	0.977119i	0.999744	−	0.0226253i	$-0.00720246\pi$
$359$	18.5138	+	18.5138i	0.977119	+	0.977119i	−0.0226253	+	0.999744i	$0.507202\pi$
$360$		0			0
$361$	7.84801	−	7.84801i	0.413053	−	0.413053i
$362$	6.97792	+	6.88197i	0.366751	+	0.361708i
$363$		0			0
$364$	0.150347	+	0.349216i	0.00788035	+	0.0183039i
$365$	0.00825139	−	0.0626756i	0.000431898	−	0.00328059i
$366$		0			0
$367$	−30.8631	+	17.8188i	−1.61104	+	0.930135i	−0.621911	+	0.783088i	$0.713643\pi$
$367$	−30.8631	+	17.8188i	−1.61104	+	0.930135i	−0.989130	+	0.147046i	$0.953023\pi$
$368$	−12.7658	+	3.80240i	−0.665465	+	0.198214i
$369$		0			0
$370$	0.161858	−	1.29885i	0.00841458	−	0.0675240i
$371$	−0.0542510	−	0.0416283i	−0.00281657	−	0.00216123i
$372$		0			0
$373$	−4.46303	−	5.81633i	−0.231087	−	0.301158i	0.663389	−	0.748275i	$-0.269118\pi$
$373$	−4.46303	−	5.81633i	−0.231087	−	0.301158i	−0.894476	+	0.447117i	$0.852451\pi$
$374$	−6.74860	−	1.75830i	−0.348962	−	0.0909196i
$375$		0			0
$376$	0.872125	−	1.18682i	0.0449764	−	0.0612054i
$377$	−5.16895	−	5.16895i	−0.266215	−	0.266215i
$378$		0			0
$379$	−0.351452	−	0.145576i	−0.0180529	−	0.00747774i	0.373639	−	0.927574i	$-0.378110\pi$
$379$	−0.351452	−	0.145576i	−0.0180529	−	0.00747774i	−0.391692	+	0.920097i	$0.628110\pi$
$380$	10.5786	−	2.99210i	0.542670	−	0.153491i
$381$		0			0
$382$	0.280998	−	0.0389749i	0.0143771	−	0.00199413i
$383$	−6.85529	+	11.8737i	−0.350289	+	0.606718i	−0.986300	−	0.164962i	$-0.947250\pi$
$383$	−6.85529	+	11.8737i	−0.350289	+	0.606718i	0.636011	+	0.771680i	$0.280583\pi$
$384$		0			0
$385$	−0.0783015	−	0.135622i	−0.00399062	−	0.00691195i
$386$	−11.5298	−	14.8125i	−0.586853	−	0.753937i
$387$		0			0
$388$	−1.97557	+	7.80353i	−0.100294	+	0.396164i
$389$	3.59621	+	27.3159i	0.182335	+	1.38497i	0.800693	+	0.599075i	$0.204465\pi$
$389$	3.59621	+	27.3159i	0.182335	+	1.38497i	−0.618358	+	0.785897i	$0.712202\pi$
$390$		0			0
$391$	12.4102	−	3.32529i	0.627609	−	0.168167i
$392$	19.6370	+	2.17144i	0.991818	+	0.109674i
$393$		0			0
$394$	24.9248	−	25.2723i	1.25569	−	1.27320i
$395$	4.65313	−	11.2336i	0.234124	−	0.565226i
$396$		0			0
$397$	−9.13622	+	3.78435i	−0.458534	+	0.189931i	−0.599980	−	0.800015i	$-0.704825\pi$
$397$	−9.13622	+	3.78435i	−0.458534	+	0.189931i	0.141446	+	0.989946i	$0.454825\pi$
$398$	22.2446	−	9.39495i	1.11502	−	0.470926i
$399$		0			0
$400$	−15.5486	−	3.70804i	−0.777428	−	0.185402i
$401$	30.7045	+	17.7273i	1.53331	+	0.885258i	0.999206	+	0.0398402i	$0.0126849\pi$
$401$	30.7045	+	17.7273i	1.53331	+	0.885258i	0.534106	+	0.845418i	$0.320648\pi$
$402$		0			0
$403$	−10.7020	−	8.21194i	−0.533105	−	0.409066i
$404$	−20.5296	+	27.5358i	−1.02138	+	1.36996i
$405$		0			0
$406$	0.784067	−	0.215919i	0.0389126	−	0.0107159i
$407$	−1.14044	−	0.305581i	−0.0565297	−	0.0151471i
$408$		0			0
$409$	−31.7462	+	8.50637i	−1.56975	+	0.420613i	−0.935734	−	0.352707i	$-0.885261\pi$
$409$	−31.7462	+	8.50637i	−1.56975	+	0.420613i	−0.634016	+	0.773320i	$0.718595\pi$
$410$	7.65241	−	4.48904i	0.377926	−	0.221698i
$411$		0			0
$412$	−12.7313	−	7.11724i	−0.627226	−	0.350641i
$413$	−0.247402	−	0.597282i	−0.0121739	−	0.0293903i
$414$		0			0
$415$	5.60877			0.275324
$416$	−4.13067	+	7.76317i	−0.202523	+	0.380621i
$417$		0			0
$418$	−1.36241	−	9.82259i	−0.0666377	−	0.480439i
$419$	8.94362	+	1.17745i	0.436924	+	0.0575222i	0.345780	−	0.938316i	$-0.387614\pi$
$419$	8.94362	+	1.17745i	0.436924	+	0.0575222i	0.0911440	+	0.995838i	$0.470948\pi$
$420$		0			0
$421$	−3.88453	−	29.5059i	−0.189320	−	1.43803i	−0.777287	−	0.629146i	$-0.783405\pi$
$421$	−3.88453	−	29.5059i	−0.189320	−	1.43803i	0.587967	−	0.808885i	$-0.299928\pi$
$422$	17.6224	+	10.0123i	0.857843	+	0.487389i
$423$		0			0
$424$	−0.0328445	−	1.58125i	−0.00159507	−	0.0767925i
$425$	14.8926	+	3.99047i	0.722399	+	0.193566i
$426$		0			0
$427$	−0.00533753	−	0.00695600i	−0.000258301	−	0.000336625i
$428$	−29.4354	+	12.6728i	−1.42282	+	0.612563i
$429$		0			0
$430$	−4.47981	−	10.6069i	−0.216036	−	0.511511i
$431$			6.70544i			0.322990i	0.986874	+	0.161495i	$0.0516315\pi$
$431$			6.70544i			0.322990i	−0.986874	+	0.161495i	$0.948368\pi$
$432$		0			0
$433$			28.5862i			1.37376i	0.726769	+	0.686882i	$0.241021\pi$
$433$			28.5862i			1.37376i	−0.726769	+	0.686882i	$0.758979\pi$
$434$	1.38250	−	0.583896i	0.0663622	−	0.0280279i
$435$		0			0
$436$	33.9507	+	13.5152i	1.62594	+	0.647263i
$437$	11.1216	+	14.4940i	0.532020	+	0.693342i
$438$		0			0
$439$	19.4283	+	5.20581i	0.927264	+	0.248460i	0.690687	−	0.723153i	$-0.257308\pi$
$439$	19.4283	+	5.20581i	0.927264	+	0.248460i	0.236576	+	0.971613i	$0.423975\pi$
$440$	1.31631	−	3.37440i	0.0627525	−	0.160868i
$441$		0			0
$442$	4.19005	−	7.37481i	0.199300	−	0.350784i
$443$	2.39980	+	18.2283i	0.114018	+	0.866052i	0.948890	+	0.315608i	$0.102208\pi$
$443$	2.39980	+	18.2283i	0.114018	+	0.866052i	−0.834872	+	0.550444i	$0.814458\pi$
$444$		0			0
$445$	−1.58544	−	0.208727i	−0.0751569	−	0.00989460i
$446$	6.29227	−	0.872749i	0.297948	−	0.0413259i
$447$		0			0
$448$	−0.523919	−	0.826207i	−0.0247529	−	0.0390346i
$449$	37.0532			1.74865			0.874324	−	0.485342i	$-0.161305\pi$
$449$	37.0532			1.74865			0.874324	+	0.485342i	$0.161305\pi$
$450$		0			0
$451$	−3.06254	−	7.39362i	−0.144209	−	0.348152i
$452$	3.27741	+	11.5873i	0.154157	+	0.545021i
$453$		0			0
$454$	−2.90476	−	4.95171i	−0.136327	−	0.232395i
$455$	0.183978	−	0.0492968i	0.00862504	−	0.00231107i
$456$		0			0
$457$	12.7504	+	3.41645i	0.596436	+	0.159815i	0.544393	−	0.838830i	$-0.316760\pi$
$457$	12.7504	+	3.41645i	0.596436	+	0.159815i	0.0520433	+	0.998645i	$0.483427\pi$
$458$	1.59795	+	5.80266i	0.0746675	+	0.271141i
$459$		0			0
$460$	0.962495	+	6.60308i	0.0448766	+	0.307870i
$461$	−11.3120	−	8.68002i	−0.526853	−	0.404269i	0.310796	−	0.950477i	$-0.399404\pi$
$461$	−11.3120	−	8.68002i	−0.526853	−	0.404269i	−0.837650	+	0.546208i	$0.816071\pi$
$462$		0			0
$463$	−7.81897	−	4.51428i	−0.363378	−	0.209797i	0.307183	−	0.951650i	$-0.400614\pi$
$463$	−7.81897	−	4.51428i	−0.363378	−	0.209797i	−0.670562	+	0.741854i	$0.733947\pi$
$464$	15.2340	+	11.0330i	0.707221	+	0.512195i
$465$		0			0
$466$	−6.50885	−	15.4111i	−0.301517	−	0.713906i
$467$	0.957228	−	0.396497i	0.0442952	−	0.0183477i	−0.360426	−	0.932788i	$-0.617369\pi$
$467$	0.957228	−	0.396497i	0.0442952	−	0.0183477i	0.404721	+	0.914440i	$0.367369\pi$
$468$		0			0
$469$	0.625109	−	1.50915i	0.0288649	−	0.0696859i
$470$	−0.525315	−	0.518091i	−0.0242310	−	0.0238978i
$471$		0			0
$472$	7.20580	−	13.1018i	0.331674	−	0.603061i
$473$	−10.0323	+	2.68814i	−0.461285	+	0.123601i
$474$		0			0
$475$	2.86163	+	21.7362i	0.131301	+	0.997327i
$476$	0.483090	+	0.810607i	0.0221424	+	0.0371541i
$477$		0			0
$478$	22.8332	−	17.7730i	1.04437	−	0.812918i
$479$	−3.17922	−	5.50658i	−0.145262	−	0.251602i	0.784208	−	0.620498i	$-0.213069\pi$
$479$	−3.17922	−	5.50658i	−0.145262	−	0.251602i	−0.929471	+	0.368896i	$0.879736\pi$
$480$		0			0
$481$	0.717997	−	1.24361i	0.0327378	−	0.0567036i
$482$	2.37438	+	17.1186i	0.108150	+	0.779732i
$483$		0			0
$484$	16.3512	+	9.14088i	0.743236	+	0.415495i
$485$	3.72564	+	1.54321i	0.169173	+	0.0700736i
$486$		0			0
$487$	−21.2038	−	21.2038i	−0.960837	−	0.960837i	0.0384245	−	0.999262i	$-0.487766\pi$
$487$	−21.2038	−	21.2038i	−0.960837	−	0.960837i	−0.999262	+	0.0384245i	$0.987766\pi$
$488$	0.0484069	−	0.196928i	0.00219128	−	0.00891452i
$489$		0			0
$490$	2.49538	−	9.57762i	0.112730	−	0.432673i
$491$	17.2914	+	22.5346i	0.780350	+	1.01697i	0.999151	+	0.0412026i	$0.0131189\pi$
$491$	17.2914	+	22.5346i	0.780350	+	1.01697i	−0.218801	+	0.975770i	$0.570214\pi$
$492$		0			0
$493$	−14.3937	−	11.0447i	−0.648261	−	0.497428i
$494$	11.9685	+	1.49147i	0.538489	+	0.0671044i
$495$		0			0
$496$	30.5292	+	16.5163i	1.37080	+	0.741606i
$497$	0.872472	−	0.503722i	0.0391357	−	0.0225950i
$498$		0			0
$499$	−2.43360	+	18.4850i	−0.108943	+	0.827502i	0.846513	+	0.532368i	$0.178698\pi$
$499$	−2.43360	+	18.4850i	−0.108943	+	0.827502i	−0.955456	+	0.295134i	$0.904636\pi$
$500$	−6.66736	+	16.7486i	−0.298173	+	0.749021i
$501$		0			0
$502$	3.94374	−	3.99873i	0.176018	−	0.178472i
$503$	−18.9876	+	18.9876i	−0.846617	+	0.846617i	−0.989709	−	0.143092i	$-0.954295\pi$
$503$	−18.9876	+	18.9876i	−0.846617	+	0.846617i	0.143092	+	0.989709i	$0.454295\pi$
$504$		0			0
$505$	12.1667	+	12.1667i	0.541411	+	0.541411i
$506$	6.01903	−	0.0416687i	0.267578	−	0.00185240i
$507$		0			0
$508$	−11.0322	−	10.7308i	−0.489473	−	0.476104i
$509$	−38.5505	−	5.07527i	−1.70872	−	0.224958i	−0.788137	−	0.615500i	$-0.788954\pi$
$509$	−38.5505	−	5.07527i	−1.70872	−	0.224958i	−0.920585	+	0.390542i	$0.872288\pi$
$510$		0			0
$511$	0.00385794	+	0.00668215i	0.000170665	+	0.000295601i
$512$	7.34070	−	21.4036i	0.324416	−	0.945914i
$513$		0			0
$514$	21.5442	+	27.6781i	0.950273	+	1.22083i
$515$	−4.44813	+	5.79692i	−0.196008	+	0.255443i
$516$		0			0
$517$	−0.528007	+	0.405154i	−0.0232217	+	0.0178187i
$518$	0.0808346	+	0.137798i	0.00355167	+	0.00605449i
$519$		0			0
$520$	3.54991	+	2.60863i	0.155674	+	0.114396i
$521$	6.04746	−	6.04746i	0.264944	−	0.264944i	−0.562115	−	0.827059i	$-0.690012\pi$
$521$	6.04746	−	6.04746i	0.264944	−	0.264944i	0.827059	+	0.562115i	$0.190012\pi$
$522$		0			0
$523$	7.13800	−	17.2326i	0.312123	−	0.753531i	−0.687503	−	0.726181i	$-0.741293\pi$
$523$	7.13800	−	17.2326i	0.312123	−	0.753531i	0.999626	−	0.0273497i	$-0.00870677\pi$
$524$	−7.57746	−	9.59705i	−0.331023	−	0.419249i
$525$		0			0
$526$	−10.8474	−	8.20484i	−0.472970	−	0.357748i
$527$	−28.9947	−	16.7401i	−1.26303	−	0.729210i
$528$		0			0
$529$	10.3152	−	5.95547i	0.448486	−	0.258934i
$530$	−0.786239	−	0.0979780i	−0.0341520	−	0.00425589i
$531$		0			0
$532$	−0.802033	+	1.07575i	−0.0347725	+	0.0466395i
$533$	9.65013	−	1.27046i	0.417993	−	0.0550299i
$534$		0			0
$535$	4.15524	+	15.5076i	0.179647	+	0.670450i
$536$	36.2825	−	10.5341i	1.56716	−	0.455004i
$537$		0			0
$538$	0.0879598	+	12.7058i	0.00379222	+	0.547784i
$539$	−8.24820	−	3.41652i	−0.355275	−	0.147160i
$540$		0			0
$541$	13.0357	+	31.4709i	0.560447	+	1.35304i	0.909410	+	0.415901i	$0.136534\pi$
$541$	13.0357	+	31.4709i	0.560447	+	1.35304i	−0.348963	+	0.937136i	$0.613466\pi$
$542$	−19.0724	−	7.74582i	−0.819231	−	0.332711i
$543$		0			0
$544$	−7.64939	+	20.4410i	−0.327965	+	0.876399i
$545$	9.15307	−	15.8536i	0.392074	−	0.679093i
$546$		0			0
$547$	−2.27292	+	2.96213i	−0.0971830	+	0.126651i	−0.839413	−	0.543493i	$-0.817101\pi$
$547$	−2.27292	+	2.96213i	−0.0971830	+	0.126651i	0.742230	+	0.670145i	$0.233768\pi$
$548$	1.02037	+	1.71214i	0.0435880	+	0.0731391i
$549$		0			0
$550$	6.28035	+	3.56822i	0.267795	+	0.152149i
$551$	6.67715	−	24.9195i	0.284456	−	1.06160i
$552$		0			0
$553$	0.384111	+	1.43352i	0.0163341	+	0.0609596i
$554$	−7.90816	+	30.3526i	−0.335986	+	1.28956i
$555$		0			0
$556$	3.78772	−	32.2107i	0.160635	−	1.36604i
$557$	36.0622	−	14.9375i	1.52801	−	0.632921i	0.548830	−	0.835934i	$-0.315073\pi$
$557$	36.0622	−	14.9375i	1.52801	−	0.632921i	0.979176	+	0.203013i	$0.0650733\pi$
$558$		0			0
$559$		−	12.6322i		−	0.534285i
$560$	−0.447428	+	0.200018i	−0.0189073	+	0.00845232i
$561$		0			0
$562$	−22.0959	−	16.7131i	−0.932061	−	0.704998i
$563$	2.04496	−	15.5330i	0.0861849	−	0.654640i	−0.892763	−	0.450527i	$-0.851236\pi$
$563$	2.04496	−	15.5330i	0.0861849	−	0.654640i	0.978948	−	0.204112i	$-0.0654307\pi$
$564$		0			0
$565$	5.98093	−	0.787404i	0.251620	−	0.0331263i
$566$	0.0218406	+	0.0793101i	0.000918031	+	0.00333365i
$567$		0			0
$568$	21.7079	+	8.46794i	0.910842	+	0.355307i
$569$	−5.53337	+	20.6508i	−0.231971	+	0.865728i	0.747520	+	0.664240i	$0.231245\pi$
$569$	−5.53337	+	20.6508i	−0.231971	+	0.865728i	−0.979491	+	0.201488i	$0.935422\pi$
$570$		0			0
$571$	−16.9369	+	12.9961i	−0.708787	+	0.543871i	−0.899042	−	0.437863i	$-0.855735\pi$
$571$	−16.9369	+	12.9961i	−0.708787	+	0.543871i	0.190254	+	0.981735i	$0.439069\pi$
$572$	2.77070	−	2.84851i	0.115849	−	0.119102i
$573$		0			0
$574$	−0.407458	+	1.00328i	−0.0170070	+	0.0418761i
$575$	−13.3073			−0.554951
$576$		0			0
$577$	−2.60840			−0.108589			−0.0542945	−	0.998525i	$-0.517291\pi$
$577$	−2.60840			−0.108589			−0.0542945	+	0.998525i	$0.517291\pi$
$578$	−1.12504	+	2.77017i	−0.0467955	+	0.115224i
$579$		0			0
$580$	6.57012	−	6.75462i	0.272810	−	0.280470i
$581$	−0.543113	+	0.416745i	−0.0225321	+	0.0172895i
$582$		0			0
$583$	−0.184978	+	0.690349i	−0.00766103	+	0.0285913i
$584$	−0.0648548	+	0.166258i	−0.00268371	+	0.00687979i
$585$		0			0
$586$	−9.09501	−	33.0268i	−0.375712	−	1.36432i
$587$	0.709211	−	0.0933694i	0.0292723	−	0.00385377i	−0.115876	−	0.993264i	$-0.536967\pi$
$587$	0.709211	−	0.0933694i	0.0292723	−	0.00385377i	0.145148	+	0.989410i	$0.453634\pi$
$588$		0			0
$589$	6.21404	−	47.2003i	0.256045	−	1.94485i
$590$	−5.97421	−	4.51881i	−0.245954	−	0.186037i
$591$		0			0
$592$	−1.31896	+	3.45158i	−0.0542089	+	0.141859i
$593$		−	1.07763i		−	0.0442532i	−0.999755	−	0.0221266i	$-0.992956\pi$
$593$		−	1.07763i		−	0.0442532i	0.999755	−	0.0221266i	$-0.00704368\pi$
$594$		0			0
$595$	0.436744	−	0.180905i	0.0179048	−	0.00741640i
$596$	4.16041	−	35.3801i	0.170417	−	1.44922i
$597$		0			0
$598$	−1.84577	+	7.08431i	−0.0754790	+	0.289699i
$599$	−10.2864	−	38.3894i	−0.420291	−	1.56855i	−0.773995	−	0.633191i	$-0.781745\pi$
$599$	−10.2864	−	38.3894i	−0.420291	−	1.56855i	0.353704	−	0.935357i	$-0.384922\pi$
$600$		0			0
$601$	−4.95162	+	18.4797i	−0.201981	+	0.753803i	0.788368	+	0.615204i	$0.210926\pi$
$601$	−4.95162	+	18.4797i	−0.201981	+	0.753803i	−0.990349	+	0.138598i	$0.955740\pi$
$602$	1.22191	+	0.694238i	0.0498014	+	0.0282950i
$603$		0			0
$604$	16.1590	+	27.1141i	0.657498	+	1.10326i
$605$	5.71287	−	7.44516i	0.232261	−	0.302689i
$606$		0			0
$607$	−19.9918	+	34.6268i	−0.811441	+	1.40546i	0.100414	+	0.994946i	$0.467983\pi$
$607$	−19.9918	+	34.6268i	−0.811441	+	1.40546i	−0.911855	+	0.410512i	$0.865350\pi$
$608$	−31.0162	+	1.07401i	−1.25787	+	0.0435570i
$609$		0			0
$610$	−0.0941241	−	0.0382263i	−0.00381097	−	0.00154774i
$611$	−0.309767	−	0.747844i	−0.0125318	−	0.0302545i
$612$		0			0
$613$	5.44549	+	2.25559i	0.219941	+	0.0911026i	0.489933	−	0.871760i	$-0.337021\pi$
$613$	5.44549	+	2.25559i	0.219941	+	0.0911026i	−0.269992	+	0.962863i	$0.587021\pi$
$614$	0.0394605	+	5.70006i	0.00159250	+	0.230036i
$615$		0			0
$616$	0.123264	+	0.424557i	0.00496646	+	0.0171059i
$617$	−7.39757	−	27.6081i	−0.297815	−	1.11146i	−0.938956	−	0.344037i	$-0.888205\pi$
$617$	−7.39757	−	27.6081i	−0.297815	−	1.11146i	0.641141	−	0.767423i	$-0.278461\pi$
$618$		0			0
$619$	27.7342	−	3.65127i	1.11473	−	0.146757i	0.449418	−	0.893322i	$-0.351632\pi$
$619$	27.7342	−	3.65127i	1.11473	−	0.146757i	0.665313	+	0.746565i	$0.268298\pi$
$620$	10.3936	−	13.9406i	0.417415	−	0.559868i
$621$		0			0
$622$	−32.1759	−	4.00964i	−1.29014	−	0.160772i
$623$	0.169031	−	0.0975902i	0.00677209	−	0.00390987i
$624$		0			0
$625$	−9.48291	−	5.47496i	−0.379317	−	0.218999i
$626$	−35.1829	−	26.6118i	−1.40619	−	1.06362i
$627$		0			0
$628$	16.9390	+	21.4537i	0.675941	+	0.856095i
$629$	1.36390	−	3.29274i	0.0543821	−	0.131290i
$630$		0			0
$631$	−4.10168	+	4.10168i	−0.163285	+	0.163285i	−0.784020	−	0.620735i	$-0.786834\pi$
$631$	−4.10168	+	4.10168i	−0.163285	+	0.163285i	0.620735	+	0.784020i	$0.286834\pi$
$632$	−20.3259	+	27.6602i	−0.808522	+	1.10026i
$633$		0			0
$634$	−5.74797	−	9.79850i	−0.228281	−	0.389148i
$635$	−6.11670	+	4.69351i	−0.242734	+	0.186256i
$636$		0			0
$637$	6.61018	−	8.61456i	0.261905	−	0.341321i
$638$	−5.22092	−	6.70738i	−0.206698	−	0.265548i
$639$		0			0
$640$	−10.0798	−	5.18556i	−0.398441	−	0.204977i
$641$	−1.10724	−	1.91779i	−0.0437333	−	0.0757483i	0.843330	−	0.537396i	$-0.180592\pi$
$641$	−1.10724	−	1.91779i	−0.0437333	−	0.0757483i	−0.887063	+	0.461647i	$0.847259\pi$
$642$		0			0
$643$	24.7870	+	3.26327i	0.977504	+	0.128691i	0.602316	−	0.798258i	$-0.294245\pi$
$643$	24.7870	+	3.26327i	0.977504	+	0.128691i	0.375188	+	0.926949i	$0.377578\pi$
$644$	−0.583826	−	0.567879i	−0.0230060	−	0.0223776i
$645$		0			0
$646$	29.9340	−	0.207228i	1.17774	−	0.00815329i
$647$	1.12972	+	1.12972i	0.0444140	+	0.0444140i	0.728965	−	0.684551i	$-0.240002\pi$
$647$	1.12972	+	1.12972i	0.0444140	+	0.0444140i	−0.684551	+	0.728965i	$0.740002\pi$
$648$		0			0
$649$	−4.77785	+	4.77785i	−0.187547	+	0.187547i
$650$	−6.16895	+	6.25496i	−0.241966	+	0.245340i
$651$		0			0
$652$	−7.92984	+	19.9200i	−0.310556	+	0.780128i
$653$	−0.633187	+	4.80953i	−0.0247785	+	0.188212i	−0.999358	−	0.0358311i	$-0.988592\pi$
$653$	−0.633187	+	4.80953i	−0.0247785	+	0.188212i	0.974579	+	0.224043i	$0.0719255\pi$
$654$		0			0
$655$	−5.30502	+	3.06286i	−0.207284	+	0.119676i
$656$	−24.0032	+	7.14954i	−0.937168	+	0.279143i
$657$		0			0
$658$	0.0893631	+	0.0111361i	0.00348374	+	0.000434130i
$659$	−6.06228	−	4.65175i	−0.236153	−	0.181206i	0.483905	−	0.875121i	$-0.339218\pi$
$659$	−6.06228	−	4.65175i	−0.236153	−	0.181206i	−0.720058	+	0.693914i	$0.755885\pi$
$660$		0			0
$661$	27.1734	+	35.4131i	1.05692	+	1.37741i	0.922284	+	0.386514i	$0.126321\pi$
$661$	27.1734	+	35.4131i	1.05692	+	1.37741i	0.134639	+	0.990895i	$0.457012\pi$
$662$	−4.23726	+	16.2632i	−0.164686	+	0.632086i
$663$		0			0
$664$	−15.3758	−	3.77953i	−0.596698	−	0.146674i
$665$	0.475319	+	0.475319i	0.0184321	+	0.0184321i
$666$		0			0
$667$	14.4672	+	5.99249i	0.560170	+	0.232030i
$668$	−42.9895	−	24.0327i	−1.66332	−	0.929851i
$669$		0			0
$670$	−2.60028	−	18.7473i	−0.100457	−	0.724269i
$671$	−0.0458191	+	0.0793610i	−0.00176883	+	0.00306370i
$672$		0			0
$673$	−13.3956	−	23.2019i	−0.516364	−	0.894368i	−0.999819	−	0.0189996i	$-0.993952\pi$
$673$	−13.3956	−	23.2019i	−0.516364	−	0.894368i	0.483456	−	0.875369i	$-0.339381\pi$
$674$	28.7525	−	22.3805i	1.10750	−	0.862064i
$675$		0			0
$676$	−10.8362	−	18.1828i	−0.416778	−	0.699339i
$677$	−4.42179	−	33.5869i	−0.169943	−	1.29085i	−0.837561	−	0.546344i	$-0.816019\pi$
$677$	−4.42179	−	33.5869i	−0.169943	−	1.29085i	0.667618	−	0.744504i	$-0.267314\pi$
$678$		0			0
$679$	−0.475428	+	0.127391i	−0.0182453	+	0.00488880i
$680$	9.58033	+	5.26902i	0.367389	+	0.202058i
$681$		0			0
$682$	−11.1677	−	11.0141i	−0.427632	−	0.421752i
$683$	−5.72343	+	13.8176i	−0.219001	+	0.528715i	−0.994751	−	0.102325i	$-0.967372\pi$
$683$	−5.72343	+	13.8176i	−0.219001	+	0.528715i	0.775750	+	0.631040i	$0.217372\pi$
$684$		0			0
$685$	0.922480	−	0.382104i	0.0352461	−	0.0145994i
$686$	0.941017	+	2.22806i	0.0359282	+	0.0850678i
$687$		0			0
$688$	5.13331	+	32.0965i	0.195705	+	1.22367i
$689$	−0.752798	−	0.434628i	−0.0286793	−	0.0165580i
$690$		0			0
$691$	−30.5463	−	23.4390i	−1.16203	−	0.891660i	−0.166498	−	0.986042i	$-0.553246\pi$
$691$	−30.5463	−	23.4390i	−1.16203	−	0.891660i	−0.995536	+	0.0943812i	$0.969913\pi$
$692$	5.81362	+	39.8836i	0.221001	+	1.51615i
$693$		0			0
$694$	−7.57013	−	27.4895i	−0.287358	−	1.04349i
$695$	−15.6939	−	4.20517i	−0.595304	−	0.159511i
$696$		0			0
$697$	23.3344	−	6.25245i	0.883855	−	0.236828i
$698$	6.66121	+	11.3553i	0.252130	+	0.429804i
$699$		0			0
$700$	−0.266010	−	0.940481i	−0.0100542	−	0.0355468i
$701$	−2.58206	−	6.23365i	−0.0975232	−	0.235442i	0.867587	−	0.497285i	$-0.165670\pi$
$701$	−2.58206	−	6.23365i	−0.0975232	−	0.235442i	−0.965110	+	0.261843i	$0.915670\pi$
$702$		0			0
$703$	5.06792			0.191140
$704$	−5.88238	+	8.36354i	−0.221701	+	0.315213i
$705$		0			0
$706$	−6.95975	+	0.965330i	−0.261934	+	0.0363307i
$707$	−2.08215	−	0.274120i	−0.0783073	−	0.0103094i
$708$		0			0
$709$	−2.68098	−	20.3641i	−0.100686	−	0.764788i	−0.965077	−	0.261967i	$-0.915629\pi$
$709$	−2.68098	−	20.3641i	−0.100686	−	0.764788i	0.864391	−	0.502821i	$-0.167705\pi$
$710$	5.76634	−	10.1492i	0.216407	−	0.380893i
$711$		0			0
$712$	4.20565	+	1.64056i	0.157613	+	0.0614828i
$713$	27.9121	+	7.47903i	1.04532	+	0.280092i
$714$		0			0
$715$	−1.21186	−	1.57933i	−0.0453211	−	0.0590636i
$716$	−42.5773	−	16.9494i	−1.59119	−	0.633427i
$717$		0			0
$718$	−34.1101	+	14.4063i	−1.27298	+	0.537638i
$719$			12.2840i			0.458118i	0.973413	+	0.229059i	$0.0735648\pi$
$719$			12.2840i			0.458118i	−0.973413	+	0.229059i	$0.926435\pi$
$720$		0			0
$721$		−	0.891838i		−	0.0332138i
$722$	6.10685	+	14.4593i	0.227274	+	0.538120i
$723$		0			0
$724$	−12.7305	+	5.48086i	−0.473126	+	0.203694i
$725$	11.4396	+	14.9083i	0.424854	+	0.553681i
$726$		0			0
$727$	33.5764	+	8.99678i	1.24528	+	0.333672i	0.820512	−	0.571629i	$-0.193688\pi$
$727$	33.5764	+	8.99678i	1.24528	+	0.333672i	0.424769	+	0.905302i	$0.360355\pi$
$728$	−0.537575	+	0.0111661i	−0.0199239	+	0.000413841i
$729$		0			0
$730$	0.0777315	+	0.0441637i	0.00287697	+	0.00163457i
$731$	−4.09228	−	31.0840i	−0.151359	−	1.14968i
$732$		0			0
$733$	−29.4446	−	3.87646i	−1.08756	−	0.143180i	−0.434639	−	0.900605i	$-0.643124\pi$
$733$	−29.4446	−	3.87646i	−1.08756	−	0.143180i	−0.652923	+	0.757424i	$0.726457\pi$
$734$	−6.92417	−	49.9213i	−0.255576	−	1.84263i
$735$		0			0
$736$	1.81098	−	18.7502i	0.0667537	−	0.691142i
$737$	−17.0726			−0.628878
$738$		0			0
$739$	−16.7632	−	40.4700i	−0.616646	−	1.48871i	−0.855576	−	0.517678i	$-0.826797\pi$
$739$	−16.7632	−	40.4700i	−0.616646	−	1.48871i	0.238930	−	0.971037i	$-0.423203\pi$
$740$	1.61573	+	0.903247i	0.0593952	+	0.0332040i
$741$		0			0
$742$	0.0834137	−	0.0489319i	0.00306221	−	0.00179635i
$743$	−20.8879	+	5.59691i	−0.766304	+	0.205331i	−0.620738	−	0.784018i	$-0.713167\pi$
$743$	−20.8879	+	5.59691i	−0.766304	+	0.205331i	−0.145566	+	0.989349i	$0.546500\pi$
$744$		0			0
$745$	−17.2381	−	4.61894i	−0.631555	−	0.169225i
$746$	9.99596	−	2.75272i	0.365978	−	0.100784i
$747$		0			0
$748$	5.89506	−	7.90689i	0.215545	−	0.289105i
$749$	−1.55461	−	1.19290i	−0.0568043	−	0.0435875i
$750$		0			0
$751$	−2.44194	−	1.40985i	−0.0891076	−	0.0514463i	0.454784	−	0.890602i	$-0.349716\pi$
$751$	−2.44194	−	1.40985i	−0.0891076	−	0.0514463i	−0.543892	+	0.839155i	$0.683050\pi$
$752$	1.09097	+	1.77428i	0.0397836	+	0.0647012i
$753$		0			0
$754$	9.52336	−	4.02217i	0.346820	−	0.146479i
$755$	14.6087	−	6.05114i	0.531666	−	0.220223i
$756$		0			0
$757$	3.64303	−	8.79505i	0.132408	−	0.319662i	−0.843745	−	0.536744i	$-0.819654\pi$
$757$	3.64303	−	8.79505i	0.132408	−	0.319662i	0.976153	+	0.217082i	$0.0696541\pi$
$758$	0.377766	−	0.383033i	0.0137211	−	0.0139124i
$759$		0			0
$760$	−1.70879	+	15.4531i	−0.0619842	+	0.560542i
$761$	17.7816	−	4.76458i	0.644584	−	0.172716i	0.0783050	−	0.996929i	$-0.475049\pi$
$761$	17.7816	−	4.76458i	0.644584	−	0.172716i	0.566279	+	0.824214i	$0.308383\pi$
$762$		0			0
$763$	0.291642	+	2.21524i	0.0105581	+	0.0801971i
$764$	−0.0984617	+	0.388925i	−0.00356222	+	0.0140708i
$765$		0			0
$766$	−11.9099	−	15.3008i	−0.430322	−	0.552840i
$767$	−4.10904	−	7.11707i	−0.148369	−	0.256982i
$768$		0			0
$769$	17.1838	−	29.7632i	0.619664	−	1.07329i	−0.369883	−	0.929078i	$-0.620602\pi$
$769$	17.1838	−	29.7632i	0.619664	−	1.07329i	0.989547	−	0.144212i	$-0.0460646\pi$
$770$	0.219370	−	0.0304270i	0.00790555	−	0.00109651i
$771$		0			0
$772$	25.5440	−	7.22499i	0.919348	−	0.260033i
$773$	45.9170	+	19.0194i	1.65152	+	0.684081i	0.997383	−	0.0722964i	$-0.0230328\pi$
$773$	45.9170	+	19.0194i	1.65152	+	0.684081i	0.654135	+	0.756378i	$0.273033\pi$
$774$		0			0
$775$	24.5204	+	24.5204i	0.880800	+	0.880800i
$776$	−9.17352	−	6.74110i	−0.329310	−	0.241991i
$777$		0			0
$778$	−37.7051	−	9.82381i	−1.35179	−	0.352201i
$779$	20.9117	+	27.2526i	0.749239	+	0.976427i
$780$		0			0
$781$	−8.35355	−	6.40990i	−0.298914	−	0.229364i
$782$	−2.24686	+	18.0303i	−0.0803476	+	0.644761i
$783$		0			0
$784$	−13.2948	+	24.5744i	−0.474814	+	0.877658i
$785$	11.8591	−	6.84685i	0.423269	−	0.244375i
$786$		0			0
$787$	1.86348	−	14.1545i	0.0664258	−	0.504554i	−0.925598	−	0.378507i	$-0.876438\pi$
$787$	1.86348	−	14.1545i	0.0664258	−	0.504554i	0.992024	−	0.126047i	$-0.0402291\pi$
$788$	19.8503	+	46.1067i	0.707137	+	1.64248i
$789$		0			0
$790$	12.2431	+	12.0747i	0.435590	+	0.429600i
$791$	−0.520644	+	0.520644i	−0.0185120	+	0.0185120i
$792$		0			0
$793$	−0.0788105	−	0.0788105i	−0.00279864	−	0.00279864i
$794$	−0.0968143	−	13.9848i	−0.00343581	−	0.496301i
$795$		0			0
$796$	0.472797	+	34.1460i	0.0167578	+	1.21027i
$797$	5.19086	+	0.683390i	0.183870	+	0.0242069i	0.221899	−	0.975070i	$-0.428775\pi$
$797$	5.19086	+	0.683390i	0.183870	+	0.0242069i	−0.0380290	+	0.999277i	$0.512108\pi$
$798$		0			0
$799$	−1.00451	−	1.73986i	−0.0355371	−	0.0615520i
$800$	13.1325	−	18.3997i	0.464305	−	0.650529i
$801$		0			0
$802$	−39.5667	+	30.7981i	−1.39715	+	1.08752i
$803$	0.0490926	−	0.0639787i	0.00173244	−	0.00225776i
$804$		0			0
$805$	−0.323698	+	0.248382i	−0.0114088	+	0.00875432i
$806$	16.4549	−	9.65273i	0.579599	−	0.340003i
$807$		0			0
$808$	−25.1550	−	41.5523i	−0.884950	−	1.46181i
$809$	−19.0956	+	19.0956i	−0.671364	+	0.671364i	−0.958031	−	0.286666i	$-0.907453\pi$
$809$	−19.0956	+	19.0956i	−0.671364	+	0.671364i	0.286666	+	0.958031i	$0.407453\pi$
$810$		0			0
$811$	−8.43381	+	20.3610i	−0.296151	+	0.714972i	0.703838	+	0.710360i	$0.251468\pi$
$811$	−8.43381	+	20.3610i	−0.296151	+	0.714972i	−0.999989	+	0.00461198i	$0.998532\pi$
$812$	−0.134319	+	1.14224i	−0.00471366	+	0.0400849i
$813$		0			0
$814$	1.00727	−	1.33169i	0.0353048	−	0.0466756i
$815$	9.30182	+	5.37041i	0.325828	+	0.188117i
$816$		0			0
$817$	38.6088	−	22.2908i	1.35075	−	0.779857i
$818$	5.74766	−	46.1229i	0.200962	−	1.61265i
$819$		0			0
$820$	1.80975	+	12.4156i	0.0631993	+	0.433571i
$821$	−1.13787	+	0.149803i	−0.0397119	+	0.00522817i	−0.150356	−	0.988632i	$-0.548042\pi$
$821$	−1.13787	+	0.149803i	−0.0397119	+	0.00522817i	0.110644	+	0.993860i	$0.464709\pi$
$822$		0			0
$823$	−4.50146	−	16.7997i	−0.156911	−	0.585600i	−0.998934	−	0.0461585i	$-0.985302\pi$
$823$	−4.50146	−	16.7997i	−0.156911	−	0.585600i	0.842023	−	0.539441i	$-0.181365\pi$
$824$	16.1004	−	12.8942i	0.560883	−	0.449190i
$825$		0			0
$826$	0.914258	−	0.00632925i	0.0318111	−	0.000220223i
$827$	−46.9089	−	19.4303i	−1.63118	−	0.675657i	−0.635818	−	0.771839i	$-0.719337\pi$
$827$	−46.9089	−	19.4303i	−1.63118	−	0.675657i	−0.995364	+	0.0961819i	$0.969337\pi$
$828$		0			0
$829$	13.6084	+	32.8535i	0.472638	+	1.14105i	0.962993	+	0.269527i	$0.0868673\pi$
$829$	13.6084	+	32.8535i	0.472638	+	1.14105i	−0.490354	+	0.871523i	$0.663133\pi$
$830$	−2.98464	+	7.34905i	−0.103598	+	0.255089i
$831$		0			0
$832$	−7.97383	−	9.54341i	−0.276443	−	0.330858i
$833$	13.4749	−	23.3392i	0.466878	−	0.808656i
$834$		0			0
$835$	−15.0199	+	19.5744i	−0.519786	+	0.677399i
$836$	13.5953	+	3.44184i	0.470204	+	0.119038i
$837$		0			0
$838$	−6.30203	+	11.0921i	−0.217700	+	0.383169i
$839$	13.4038	−	50.0237i	0.462751	−	1.72701i	−0.201489	−	0.979491i	$-0.564578\pi$
$839$	13.4038	−	50.0237i	0.462751	−	1.72701i	0.664240	−	0.747519i	$-0.268755\pi$
$840$		0			0
$841$	1.78257	+	6.65266i	0.0614681	+	0.229402i
$842$	40.7281	+	10.6114i	1.40358	+	0.365693i
$843$		0			0
$844$	−22.4964	+	17.7623i	−0.774357	+	0.611403i
$845$	−9.79666	+	4.05791i	−0.337015	+	0.139596i
$846$		0			0
$847$			1.14542i			0.0393569i
$848$	2.08936	+	0.798411i	0.0717490	+	0.0274175i
$849$		0			0
$850$	−13.1536	+	17.3900i	−0.451164	+	0.596472i
$851$	−0.401514	+	3.04980i	−0.0137637	+	0.104546i
$852$		0			0
$853$	0.00721128		0.000949383i	0.000246910		3.25063e-5i	−0.130403	−	0.991461i	$-0.541627\pi$
$853$	0.00721128		0.000949383i	0.000246910		3.25063e-5i	0.130650	+	0.991429i	$0.458294\pi$
$854$	0.0119546	−	0.00329209i	0.000409078	−	0.000112653i
$855$		0			0
$856$	−0.941188	−	45.3123i	−0.0321691	−	1.54874i
$857$	2.92592	−	10.9197i	0.0999475	−	0.373009i	−0.897776	−	0.440453i	$-0.854818\pi$
$857$	2.92592	−	10.9197i	0.0999475	−	0.373009i	0.997723	+	0.0674441i	$0.0214844\pi$
$858$		0			0
$859$	−10.7008	+	8.21102i	−0.365107	+	0.280156i	−0.774979	−	0.631986i	$-0.782240\pi$
$859$	−10.7008	+	8.21102i	−0.365107	+	0.280156i	0.409873	+	0.912143i	$0.365573\pi$
$860$	16.2819	−	0.225445i	0.555208	−	0.00768759i
$861$		0			0
$862$	−8.78599	−	3.56822i	−0.299252	−	0.121534i
$863$	−28.8650			−0.982577			−0.491288	−	0.870997i	$-0.663474\pi$
$863$	−28.8650			−0.982577			−0.491288	+	0.870997i	$0.663474\pi$
$864$		0			0
$865$	20.1913			0.686526
$866$	−37.4558	−	15.2118i	−1.27280	−	0.516918i
$867$		0			0
$868$	0.0293843	+	2.12217i	0.000997368	+	0.0720313i
$869$	12.3058	−	9.44261i	0.417447	−	0.320318i
$870$		0			0
$871$	5.37426	−	20.0570i	0.182100	−	0.679606i
$872$	−35.7752	+	37.2929i	−1.21150	+	1.26290i
$873$		0			0
$874$	−24.9094	+	6.85963i	−0.842574	+	0.232030i
$875$	−1.09283	+	0.143873i	−0.0369443	+	0.00486380i
$876$		0			0
$877$	4.93850	−	37.5116i	0.166761	−	1.26668i	−0.679407	−	0.733762i	$-0.737763\pi$
$877$	4.93850	−	37.5116i	0.166761	−	1.26668i	0.846168	−	0.532916i	$-0.178904\pi$
$878$	−17.1596	+	22.6863i	−0.579109	+	0.765626i
$879$		0			0
$880$	3.72095	+	3.52038i	0.125433	+	0.118672i
$881$			48.2365i			1.62513i	0.582872	+	0.812564i	$0.301929\pi$
$881$			48.2365i			1.62513i	−0.582872	+	0.812564i	$0.698071\pi$
$882$		0			0
$883$	−34.8410	+	14.4316i	−1.17249	+	0.485662i	−0.882016	−	0.471220i	$-0.843814\pi$
$883$	−34.8410	+	14.4316i	−1.17249	+	0.485662i	−0.290477	+	0.956882i	$0.593814\pi$
$884$	7.43337	+	9.41455i	0.250011	+	0.316645i
$885$		0			0
$886$	−25.1612	−	6.55556i	−0.845305	−	0.220238i
$887$	2.93262	+	10.9447i	0.0984678	+	0.367487i	0.997522	−	0.0703496i	$-0.0224115\pi$
$887$	2.93262	+	10.9447i	0.0984678	+	0.367487i	−0.899055	+	0.437837i	$0.855745\pi$
$888$		0			0
$889$	0.243558	−	0.908971i	0.00816867	−	0.0304859i
$890$	1.11716	−	1.96629i	0.0374474	−	0.0659103i
$891$		0			0
$892$	−2.20481	+	8.70905i	−0.0738227	+	0.291601i
$893$	1.73908	−	2.26642i	0.0581962	−	0.0758427i
$894$		0			0
$895$	−11.4788	+	19.8819i	−0.383694	+	0.664577i
$896$	1.36136	−	0.246824i	0.0454798	−	0.00824581i
$897$		0			0
$898$	−19.7174	+	48.5500i	−0.657979	+	1.62013i
$899$	−15.6157	−	37.6997i	−0.520813	−	1.25735i
$900$		0			0
$901$	−1.99321	−	0.825613i	−0.0664033	−	0.0275052i
$902$	11.3174	−	0.0783484i	0.376828	−	0.00260872i
$903$		0			0
$904$	−16.9266	−	1.87173i	−0.562972	−	0.0622528i
$905$	1.79710	+	6.70685i	0.0597375	+	0.222943i
$906$		0			0
$907$	1.67790	−	0.220900i	0.0557138	−	0.00733486i	−0.102618	−	0.994721i	$-0.532722\pi$
$907$	1.67790	−	0.220900i	0.0557138	−	0.00733486i	0.158332	+	0.987386i	$0.449389\pi$
$908$	8.03386	−	1.17105i	0.266613	−	0.0388627i
$909$		0			0
$910$	−0.0333093	+	0.267296i	−0.00110419	+	0.00886076i
$911$	35.3404	−	20.4038i	1.17088	−	0.676007i	0.216992	−	0.976173i	$-0.430375\pi$
$911$	35.3404	−	20.4038i	1.17088	−	0.676007i	0.953887	+	0.300166i	$0.0970421\pi$
$912$		0			0
$913$	6.19638	+	3.57748i	0.205070	+	0.118397i
$914$	−11.2614	+	14.8885i	−0.372496	+	0.492468i
$915$		0			0
$916$	−8.45343	−	0.994055i	−0.279309	−	0.0328445i
$917$	0.286122	−	0.690761i	0.00944859	−	0.0228109i
$918$		0			0
$919$	−23.0870	+	23.0870i	−0.761569	+	0.761569i	−0.976606	−	0.215037i	$-0.931013\pi$
$919$	−23.0870	+	23.0870i	−0.761569	+	0.761569i	0.215037	+	0.976606i	$0.431013\pi$
$920$	−9.16406	−	2.25262i	−0.302130	−	0.0742666i
$921$		0			0
$922$	17.3928	−	10.2029i	0.572801	−	0.336015i
$923$	10.1600	−	7.79604i	0.334420	−	0.256610i
$924$		0			0
$925$	−2.24721	+	2.92862i	−0.0738879	+	0.0962925i
$926$	10.0757	−	7.84280i	0.331109	−	0.257730i
$927$		0			0
$928$	−22.5629	+	14.0897i	−0.740664	+	0.462517i
$929$	11.7699	+	20.3860i	0.386157	+	0.668843i	0.991929	−	0.126795i	$-0.0404690\pi$
$929$	11.7699	+	20.3860i	0.386157	+	0.668843i	−0.605772	+	0.795638i	$0.707136\pi$
$930$		0			0
$931$	37.9937	+	5.00197i	1.24519	+	0.163933i
$932$	23.6565	−	0.327555i	0.774893	−	0.0107294i
$933$		0			0
$934$	0.0101435	+	1.46523i	0.000331906	+	0.0479437i
$935$	−3.49366	−	3.49366i	−0.114255	−	0.114255i
$936$		0			0
$937$	−1.65091	+	1.65091i	−0.0539329	+	0.0539329i	−0.733559	−	0.679626i	$-0.762142\pi$
$937$	−1.65091	+	1.65091i	−0.0539329	+	0.0539329i	0.679626	+	0.733559i	$0.262142\pi$
$938$	1.64476	+	1.62214i	0.0537032	+	0.0529648i
$939$		0			0
$940$	0.958384	−	0.412612i	0.0312590	−	0.0134579i
$941$	2.24388	−	17.0439i	0.0731483	−	0.555616i	−0.915154	−	0.403105i	$-0.867931\pi$
$941$	2.24388	−	17.0439i	0.0731483	−	0.555616i	0.988302	−	0.152511i	$-0.0487359\pi$
$942$		0			0
$943$	−18.0570	+	10.4252i	−0.588016	+	0.339491i
$944$	13.3326	+	16.4136i	0.433939	+	0.534217i
$945$		0			0
$946$	1.81635	−	14.5756i	0.0590546	−	0.473892i
$947$	−30.2056	−	23.1776i	−0.981549	−	0.753169i	−0.0124709	−	0.999922i	$-0.503970\pi$
$947$	−30.2056	−	23.1776i	−0.981549	−	0.753169i	−0.969078	+	0.246753i	$0.920636\pi$
$948$		0			0
$949$	0.0597089	+	0.0778141i	0.00193823	+	0.00252595i
$950$	−30.0033	−	7.81715i	−0.973436	−	0.253622i
$951$		0			0
$952$	−1.31919	+	0.201627i	−0.0427552	+	0.00653478i
$953$	−38.1383	−	38.1383i	−1.23542	−	1.23542i	−0.961853	−	0.273567i	$-0.911797\pi$
$953$	−38.1383	−	38.1383i	−1.23542	−	1.23542i	−0.273567	−	0.961853i	$-0.588203\pi$
$954$		0			0
$955$	0.185685	+	0.0769131i	0.00600862	+	0.00248885i
$956$	11.1372	+	39.3755i	0.360202	+	1.27350i
$957$		0			0
$958$	8.90693	−	1.23541i	0.287770	−	0.0399142i
$959$	−0.0609351	+	0.105543i	−0.00196770	+	0.00340815i
$960$		0			0
$961$	−22.1508	−	38.3662i	−0.714540	−	1.23762i
$962$	1.24740	+	1.60255i	0.0402177	+	0.0516682i
$963$		0			0
$964$	−23.6937	−	5.99837i	−0.763121	−	0.193195i
$965$	−1.73582	−	13.1848i	−0.0558779	−	0.424435i
$966$		0			0
$967$	59.0589	−	15.8248i	1.89921	−	0.508891i	0.902222	−	0.431271i	$-0.141935\pi$
$967$	59.0589	−	15.8248i	1.89921	−	0.508891i	0.996983	−	0.0776194i	$-0.0247319\pi$
$968$	−20.6782	+	16.5604i	−0.664622	+	0.532271i
$969$		0			0
$970$	−4.00459	+	4.06042i	−0.128580	+	0.130372i
$971$	−10.2748	+	24.8055i	−0.329734	+	0.796048i	0.668878	+	0.743372i	$0.266775\pi$
$971$	−10.2748	+	24.8055i	−0.329734	+	0.796048i	−0.998612	+	0.0526753i	$0.983225\pi$
$972$		0			0
$973$	1.83214	−	0.758897i	0.0587357	−	0.0243291i
$974$	39.0663	−	16.4995i	1.25176	−	0.528679i
$975$		0			0
$976$	0.232271	+	0.168219i	0.00743483	+	0.00538457i
$977$	−0.627058	−	0.362032i	−0.0200614	−	0.0115824i	0.489936	−	0.871759i	$-0.337020\pi$
$977$	−0.627058	−	0.362032i	−0.0200614	−	0.0115824i	−0.509997	+	0.860176i	$0.670354\pi$
$978$		0			0
$979$	−1.61840	−	1.24184i	−0.0517244	−	0.0396895i
$980$	11.2215	+	8.36626i	0.358456	+	0.267250i
$981$		0			0
$982$	−38.7280	+	10.6650i	−1.23586	+	0.340335i
$983$	52.2698	+	14.0057i	1.66715	+	0.446711i	0.964340	−	0.264667i	$-0.0852622\pi$
$983$	52.2698	+	14.0057i	1.66715	+	0.446711i	0.702809	+	0.711379i	$0.251929\pi$
$984$		0			0
$985$	24.2906	−	6.50864i	0.773961	−	0.207382i
$986$	22.1311	−	12.9825i	0.704797	−	0.413447i
$987$		0			0
$988$	−8.32314	+	14.8884i	−0.264794	+	0.473664i
$989$	10.3554	+	25.0002i	0.329284	+	0.794962i
$990$		0			0
$991$	−4.02605			−0.127892			−0.0639458	−	0.997953i	$-0.520368\pi$
$991$	−4.02605			−0.127892			−0.0639458	+	0.997953i	$0.520368\pi$
$992$	−37.8868	+	31.2128i	−1.20291	+	0.991008i
$993$		0			0
$994$	0.195740	+	1.41123i	0.00620850	+	0.0447615i
$995$	16.9612	+	2.23298i	0.537705	+	0.0707902i
$996$		0			0
$997$	3.15203	+	23.9421i	0.0998259	+	0.758253i	0.966006	+	0.258521i	$0.0832350\pi$
$997$	3.15203	+	23.9421i	0.0998259	+	0.758253i	−0.866180	+	0.499732i	$0.833432\pi$
$998$	−22.9255	−	13.0253i	−0.725693	−	0.412307i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.37.19		368
3.2	odd	2		288.2.bc.a.229.28	yes	368
9.2	odd	6		288.2.bc.a.133.2	yes	368
9.7	even	3	inner	864.2.bk.a.613.45		368
32.13	even	8	inner	864.2.bk.a.685.45		368
96.77	odd	8		288.2.bc.a.13.2	✓	368
288.173	odd	24		288.2.bc.a.205.28	yes	368
288.205	even	24	inner	864.2.bk.a.397.19		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.2	✓	368	96.77	odd	8
288.2.bc.a.133.2	yes	368	9.2	odd	6
288.2.bc.a.205.28	yes	368	288.173	odd	24
288.2.bc.a.229.28	yes	368	3.2	odd	2
864.2.bk.a.37.19		368	1.1	even	1	trivial
864.2.bk.a.397.19		368	288.205	even	24	inner
864.2.bk.a.613.45		368	9.7	even	3	inner
864.2.bk.a.685.45		368	32.13	even	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bk (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.532138 + 1.31028i) q^{2} +(-1.43366 - 1.39450i) q^{4} +(-0.794880 + 0.609933i) q^{5} +(0.0316510 - 0.118123i) q^{7} +(2.59008 - 1.13642i) q^{8} +O(q^{10})\)	\(q+(-0.532138 + 1.31028i) q^{2} +(-1.43366 - 1.39450i) q^{4} +(-0.794880 + 0.609933i) q^{5} +(0.0316510 - 0.118123i) q^{7} +(2.59008 - 1.13642i) q^{8} +(-0.376196 - 1.36608i) q^{10} +(-1.26719 + 0.166829i) q^{11} +(0.202906 - 1.54122i) q^{13} +(0.137931 + 0.104329i) q^{14} +(0.110749 + 3.99847i) q^{16} -3.85821i q^{17} +(5.06862 - 2.09949i) q^{19} +(1.99014 + 0.234024i) q^{20} +(0.455730 - 1.74915i) q^{22} +(0.861873 + 3.21656i) q^{23} +(-1.03428 + 3.85998i) q^{25} +(1.91146 + 1.08601i) q^{26} +(-0.210099 + 0.125211i) q^{28} +(2.86265 - 3.73067i) q^{29} +(4.33882 - 7.51506i) q^{31} +(-5.29804 - 1.98262i) q^{32} +(5.05533 + 2.05310i) q^{34} +(0.0468884 + 0.113199i) q^{35} +(0.853436 + 0.353505i) q^{37} +(0.0537109 + 7.75852i) q^{38} +(-1.36566 + 2.48310i) q^{40} +(1.62055 + 6.04799i) q^{41} +(8.05657 - 1.06067i) q^{43} +(2.04937 + 1.52792i) q^{44} +(-4.67322 - 0.582358i) q^{46} +(0.450951 - 0.260357i) q^{47} +(6.04923 + 3.49252i) q^{49} +(-4.50727 - 3.40924i) q^{50} +(-2.44013 + 1.92664i) q^{52} +(0.213988 - 0.516614i) q^{53} +(0.905513 - 0.905513i) q^{55} +(-0.0522592 - 0.341918i) q^{56} +(3.36490 + 5.73610i) q^{58} +(4.19411 - 3.21826i) q^{59} +(0.0436465 - 0.0568812i) q^{61} +(7.53797 + 9.68411i) q^{62} +(5.41708 - 5.88687i) q^{64} +(0.778757 + 1.34885i) q^{65} +(13.2432 + 1.74350i) q^{67} +(-5.38027 + 5.53136i) q^{68} +(-0.173273 + 0.00119954i) q^{70} +(5.82525 + 5.82525i) q^{71} +(-0.0446149 + 0.0446149i) q^{73} +(-0.917335 + 0.930125i) q^{74} +(-10.1944 - 4.05823i) q^{76} +(-0.0204015 + 0.154965i) q^{77} +(-10.5100 + 6.06793i) q^{79} +(-2.52683 - 3.11075i) q^{80} +(-8.78691 - 1.09499i) q^{82} +(-4.44119 - 3.40785i) q^{83} +(2.35325 + 3.06682i) q^{85} +(-2.89744 + 11.1208i) q^{86} +(-3.09255 + 1.87217i) q^{88} +(1.12858 + 1.12858i) q^{89} +(-0.175632 - 0.0727491i) q^{91} +(3.24985 - 5.81332i) q^{92} +(0.101171 + 0.729417i) q^{94} +(-2.74840 + 4.76036i) q^{95} +(-2.01243 - 3.48563i) q^{97} +(-7.79520 + 6.06766i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Introduction

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