LMFDB - Embedded newform 896.2.bh.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.53727 + 1.94692i) q^{3} +(0.157528 - 0.205294i) q^{5} +(-0.893273 - 2.49039i) q^{7} +(1.87081 - 6.98194i) q^{9} +O(q^{10})$	\(q+(-2.53727 + 1.94692i) q^{3} +(0.157528 - 0.205294i) q^{5} +(-0.893273 - 2.49039i) q^{7} +(1.87081 - 6.98194i) q^{9} +(-0.343245 + 2.60720i) q^{11} +(-0.457727 + 1.10505i) q^{13} +0.827582i q^{15} +(1.42851 + 0.824752i) q^{17} +(6.88548 - 0.906491i) q^{19} +(7.11507 + 4.57968i) q^{21} +(1.36736 - 5.10304i) q^{23} +(1.27676 + 4.76495i) q^{25} +(5.17487 + 12.4933i) q^{27} +(-5.37418 - 2.22606i) q^{29} +(-3.39941 + 5.88794i) q^{31} +(-4.20510 - 7.28345i) q^{33} +(-0.651980 - 0.208923i) q^{35} +(-0.889991 + 1.15986i) q^{37} +(-0.990065 - 3.69497i) q^{39} +(5.66876 + 5.66876i) q^{41} +(2.80536 - 1.16202i) q^{43} +(-1.13865 - 1.48392i) q^{45} +(-4.74574 + 2.73995i) q^{47} +(-5.40413 + 4.44921i) q^{49} +(-5.23025 + 0.688575i) q^{51} +(0.197981 - 1.50382i) q^{53} +(0.481173 + 0.481173i) q^{55} +(-15.7055 + 15.7055i) q^{57} +(5.18904 + 0.683150i) q^{59} +(1.97579 + 15.0076i) q^{61} +(-19.0589 + 1.57774i) q^{63} +(0.154756 + 0.268045i) q^{65} +(-9.66430 + 7.41568i) q^{67} +(6.46584 + 15.6099i) q^{69} +(1.84933 - 1.84933i) q^{71} +(1.83947 - 0.492885i) q^{73} +(-12.5165 - 9.60422i) q^{75} +(6.79957 - 1.47413i) q^{77} +(6.40914 - 3.70032i) q^{79} +(-18.6739 - 10.7814i) q^{81} +(-4.84186 + 11.6893i) q^{83} +(0.394348 - 0.163344i) q^{85} +(17.9697 - 4.81497i) q^{87} +(5.99190 + 1.60553i) q^{89} +(3.16089 + 0.152808i) q^{91} +(-2.83812 - 21.5577i) q^{93} +(0.898559 - 1.55635i) q^{95} +2.19537 q^{97} +(17.5612 + 7.27408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.53727	+	1.94692i	−1.46489	+	1.12405i	−0.498532	+	0.866871i	$0.666127\pi$
$3$	−2.53727	+	1.94692i	−1.46489	+	1.12405i	−0.966363	+	0.257182i	$0.917206\pi$
$4$		0			0
$5$	0.157528	−	0.205294i	0.0704486	−	0.0918105i	−0.756800	−	0.653647i	$-0.773238\pi$
$5$	0.157528	−	0.205294i	0.0704486	−	0.0918105i	0.827248	+	0.561836i	$0.189905\pi$
$6$		0			0
$7$	−0.893273	−	2.49039i	−0.337626	−	0.941280i
$7$	−0.893273	−	2.49039i	−0.337626	−	0.941280i
$8$		0			0
$9$	1.87081	−	6.98194i	0.623602	−	2.32731i
$10$		0			0
$11$	−0.343245	+	2.60720i	−0.103492	+	0.786101i	0.858460	+	0.512881i	$0.171422\pi$
$11$	−0.343245	+	2.60720i	−0.103492	+	0.786101i	−0.961952	+	0.273220i	$0.911911\pi$
$12$		0			0
$13$	−0.457727	+	1.10505i	−0.126951	+	0.306486i	−0.974557	−	0.224139i	$-0.928043\pi$
$13$	−0.457727	+	1.10505i	−0.126951	+	0.306486i	0.847606	+	0.530625i	$0.178043\pi$
$14$		0			0
$15$			0.827582i			0.213681i
$16$		0			0
$17$	1.42851	+	0.824752i	0.346465	+	0.200032i	0.663127	−	0.748507i	$-0.269229\pi$
$17$	1.42851	+	0.824752i	0.346465	+	0.200032i	−0.316662	+	0.948538i	$0.602562\pi$
$18$		0			0
$19$	6.88548	−	0.906491i	1.57964	−	0.207963i	0.710921	−	0.703272i	$-0.248278\pi$
$19$	6.88548	−	0.906491i	1.57964	−	0.207963i	0.868717	+	0.495308i	$0.164945\pi$
$20$		0			0
$21$	7.11507	+	4.57968i	1.55264	+	0.999368i
$22$		0			0
$23$	1.36736	−	5.10304i	0.285113	−	1.06406i	−0.663643	−	0.748049i	$-0.730991\pi$
$23$	1.36736	−	5.10304i	0.285113	−	1.06406i	0.948757	−	0.316008i	$-0.102343\pi$
$24$		0			0
$25$	1.27676	+	4.76495i	0.255353	+	0.952990i
$26$		0			0
$27$	5.17487	+	12.4933i	0.995905	+	2.40433i
$28$		0			0
$29$	−5.37418	−	2.22606i	−0.997960	−	0.413368i	−0.176911	−	0.984227i	$-0.556611\pi$
$29$	−5.37418	−	2.22606i	−0.997960	−	0.413368i	−0.821049	+	0.570858i	$0.806611\pi$
$30$		0			0
$31$	−3.39941	+	5.88794i	−0.610551	+	1.05751i	0.380596	+	0.924741i	$0.375719\pi$
$31$	−3.39941	+	5.88794i	−0.610551	+	1.05751i	−0.991148	+	0.132765i	$0.957615\pi$
$32$		0			0
$33$	−4.20510	−	7.28345i	−0.732014	−	1.26789i
$34$		0			0
$35$	−0.651980	−	0.208923i	−0.110205	−	0.0353144i
$36$		0			0
$37$	−0.889991	+	1.15986i	−0.146314	+	0.190680i	−0.860761	−	0.509010i	$-0.830012\pi$
$37$	−0.889991	+	1.15986i	−0.146314	+	0.190680i	0.714447	+	0.699689i	$0.246678\pi$
$38$		0			0
$39$	−0.990065	−	3.69497i	−0.158537	−	0.591669i
$40$		0			0
$41$	5.66876	+	5.66876i	0.885312	+	0.885312i	0.994068	−	0.108756i	$-0.0346868\pi$
$41$	5.66876	+	5.66876i	0.885312	+	0.885312i	−0.108756	+	0.994068i	$0.534687\pi$
$42$		0			0
$43$	2.80536	−	1.16202i	0.427814	−	0.177206i	−0.158378	−	0.987379i	$-0.550626\pi$
$43$	2.80536	−	1.16202i	0.427814	−	0.177206i	0.586192	+	0.810172i	$0.300626\pi$
$44$		0			0
$45$	−1.13865	−	1.48392i	−0.169740	−	0.221209i
$46$		0			0
$47$	−4.74574	+	2.73995i	−0.692237	+	0.399663i	−0.804450	−	0.594021i	$-0.797540\pi$
$47$	−4.74574	+	2.73995i	−0.692237	+	0.399663i	0.112212	+	0.993684i	$0.464206\pi$
$48$		0			0
$49$	−5.40413	+	4.44921i	−0.772018	+	0.635601i
$50$		0			0
$51$	−5.23025	+	0.688575i	−0.732381	+	0.0964198i
$52$		0			0
$53$	0.197981	−	1.50382i	0.0271948	−	0.206565i	−0.972453	−	0.233099i	$-0.925113\pi$
$53$	0.197981	−	1.50382i	0.0271948	−	0.206565i	0.999648	+	0.0265334i	$0.00844683\pi$
$54$		0			0
$55$	0.481173	+	0.481173i	0.0648814	+	0.0648814i
$56$		0			0
$57$	−15.7055	+	15.7055i	−2.08024	+	2.08024i
$58$		0			0
$59$	5.18904	+	0.683150i	0.675555	+	0.0889385i	0.460495	−	0.887662i	$-0.347672\pi$
$59$	5.18904	+	0.683150i	0.675555	+	0.0889385i	0.215060	+	0.976601i	$0.431005\pi$
$60$		0			0
$61$	1.97579	+	15.0076i	0.252974	+	1.92153i	0.371217	+	0.928546i	$0.378941\pi$
$61$	1.97579	+	15.0076i	0.252974	+	1.92153i	−0.118242	+	0.992985i	$0.537726\pi$
$62$		0			0
$63$	−19.0589	+	1.57774i	−2.40120	+	0.198777i
$64$		0			0
$65$	0.154756	+	0.268045i	0.0191951	+	0.0332469i
$66$		0			0
$67$	−9.66430	+	7.41568i	−1.18068	+	0.905969i	−0.997029	−	0.0770222i	$-0.975459\pi$
$67$	−9.66430	+	7.41568i	−1.18068	+	0.905969i	−0.183652	+	0.982991i	$0.558792\pi$
$68$		0			0
$69$	6.46584	+	15.6099i	0.778396	+	1.87921i
$70$		0			0
$71$	1.84933	−	1.84933i	0.219475	−	0.219475i	−0.588802	−	0.808277i	$-0.700400\pi$
$71$	1.84933	−	1.84933i	0.219475	−	0.219475i	0.808277	+	0.588802i	$0.200400\pi$
$72$		0			0
$73$	1.83947	−	0.492885i	0.215294	−	0.0576878i	−0.149560	−	0.988753i	$-0.547786\pi$
$73$	1.83947	−	0.492885i	0.215294	−	0.0576878i	0.364854	+	0.931065i	$0.381119\pi$
$74$		0			0
$75$	−12.5165	−	9.60422i	−1.44528	−	1.10900i
$76$		0			0
$77$	6.79957	−	1.47413i	0.774883	−	0.167993i
$78$		0			0
$79$	6.40914	−	3.70032i	0.721085	−	0.416319i	−0.0940669	−	0.995566i	$-0.529987\pi$
$79$	6.40914	−	3.70032i	0.721085	−	0.416319i	0.815152	+	0.579247i	$0.196653\pi$
$80$		0			0
$81$	−18.6739	−	10.7814i	−2.07488	−	1.19793i
$82$		0			0
$83$	−4.84186	+	11.6893i	−0.531463	+	1.28307i	0.399091	+	0.916911i	$0.369326\pi$
$83$	−4.84186	+	11.6893i	−0.531463	+	1.28307i	−0.930554	+	0.366154i	$0.880674\pi$
$84$		0			0
$85$	0.394348	−	0.163344i	0.0427730	−	0.0177172i
$86$		0			0
$87$	17.9697	−	4.81497i	1.92655	−	0.516219i
$88$		0			0
$89$	5.99190	+	1.60553i	0.635140	+	0.170185i	0.562001	−	0.827136i	$-0.310032\pi$
$89$	5.99190	+	1.60553i	0.635140	+	0.170185i	0.0731392	+	0.997322i	$0.476698\pi$
$90$		0			0
$91$	3.16089	+	0.152808i	0.331351	+	0.0160186i
$92$		0			0
$93$	−2.83812	−	21.5577i	−0.294300	−	2.23543i
$94$		0			0
$95$	0.898559	−	1.55635i	0.0921902	−	0.159678i
$96$		0			0
$97$	2.19537			0.222906			0.111453	−	0.993770i	$-0.464449\pi$
$97$	2.19537			0.222906			0.111453	+	0.993770i	$0.464449\pi$
$98$		0			0
$99$	17.5612	+	7.27408i	1.76497	+	0.731073i
$100$		0			0
$101$	2.71500	+	0.357437i	0.270153	+	0.0355663i	0.264385	−	0.964417i	$-0.414831\pi$
$101$	2.71500	+	0.357437i	0.270153	+	0.0355663i	0.00576725	+	0.999983i	$0.498164\pi$
$102$		0			0
$103$	13.7803	+	3.69243i	1.35782	+	0.363826i	0.863014	−	0.505180i	$-0.168574\pi$
$103$	13.7803	+	3.69243i	1.35782	+	0.363826i	0.494802	+	0.869006i	$0.335241\pi$
$104$		0			0
$105$	2.06100	−	0.739257i	0.201133	−	0.0721441i
$106$		0			0
$107$	4.01874	+	3.08369i	0.388506	+	0.298111i	0.784484	−	0.620149i	$-0.212928\pi$
$107$	4.01874	+	3.08369i	0.388506	+	0.298111i	−0.395978	+	0.918260i	$0.629594\pi$
$108$		0			0
$109$	0.395773	+	0.515781i	0.0379082	+	0.0494029i	0.811923	−	0.583765i	$-0.198421\pi$
$109$	0.395773	+	0.515781i	0.0379082	+	0.0494029i	−0.774015	+	0.633168i	$0.781754\pi$
$110$		0			0
$111$		−	4.67562i		−	0.443790i
$112$		0			0
$113$		−	10.3106i		−	0.969940i	−0.874531	−	0.484970i	$-0.838830\pi$
$113$		−	10.3106i		−	0.969940i	0.874531	−	0.484970i	$-0.161170\pi$
$114$		0			0
$115$	−0.832229	−	1.08458i	−0.0776057	−	0.101138i
$116$		0			0
$117$	6.85909	+	5.26316i	0.634123	+	0.486579i
$118$		0			0
$119$	0.777905	−	4.29429i	0.0713105	−	0.393657i
$120$		0			0
$121$	3.94550	+	1.05719i	0.358682	+	0.0961085i
$122$		0			0
$123$	−25.4198	−	3.34658i	−2.29203	−	0.301751i
$124$		0			0
$125$	2.37470	+	0.983631i	0.212399	+	0.0879787i
$126$		0			0
$127$	14.7023			1.30462			0.652310	−	0.757952i	$-0.273800\pi$
$127$	14.7023			1.30462			0.652310	+	0.757952i	$0.273800\pi$
$128$		0			0
$129$	−4.85561	+	8.41017i	−0.427513	+	0.740474i
$130$		0			0
$131$	−0.755002	−	5.73481i	−0.0659649	−	0.501053i	−0.992253	−	0.124236i	$-0.960352\pi$
$131$	−0.755002	−	5.73481i	−0.0659649	−	0.501053i	0.926288	−	0.376817i	$-0.122981\pi$
$132$		0			0
$133$	−8.40814	−	16.3378i	−0.729078	−	1.41667i
$134$		0			0
$135$	3.37998	+	0.905663i	0.290903	+	0.0779471i
$136$		0			0
$137$	−16.1344	+	4.32319i	−1.37845	+	0.369355i	−0.870558	−	0.492066i	$-0.836242\pi$
$137$	−16.1344	+	4.32319i	−1.37845	+	0.369355i	−0.507893	+	0.861420i	$0.669575\pi$
$138$		0			0
$139$	−2.03886	+	0.844522i	−0.172934	+	0.0716315i	−0.467471	−	0.884009i	$-0.654835\pi$
$139$	−2.03886	+	0.844522i	−0.172934	+	0.0716315i	0.294537	+	0.955640i	$0.404835\pi$
$140$		0			0
$141$	6.70677	−	16.1916i	0.564812	−	1.36358i
$142$		0			0
$143$	−2.72398	−	1.57269i	−0.227791	−	0.131515i
$144$		0			0
$145$	−1.30358	+	0.752622i	−0.108256	+	0.0625019i
$146$		0			0
$147$	5.04950	−	21.8102i	0.416476	−	1.79888i
$148$		0			0
$149$	4.75700	+	3.65017i	0.389709	+	0.299034i	0.784969	−	0.619535i	$-0.212679\pi$
$149$	4.75700	+	3.65017i	0.389709	+	0.299034i	−0.395260	+	0.918569i	$0.629346\pi$
$150$		0			0
$151$	8.38036	−	2.24551i	0.681984	−	0.182737i	0.0988369	−	0.995104i	$-0.468488\pi$
$151$	8.38036	−	2.24551i	0.681984	−	0.182737i	0.583147	+	0.812367i	$0.301821\pi$
$152$		0			0
$153$	8.43084	−	8.43084i	0.681593	−	0.681593i
$154$		0			0
$155$	0.673261	+	1.62539i	0.0540776	+	0.130555i
$156$		0			0
$157$	4.38579	−	3.36534i	0.350024	−	0.268583i	−0.418752	−	0.908100i	$-0.637532\pi$
$157$	4.38579	−	3.36534i	0.350024	−	0.268583i	0.768777	+	0.639517i	$0.220866\pi$
$158$		0			0
$159$	2.42548	+	4.20105i	0.192353	+	0.333165i
$160$		0			0
$161$	−13.9300	+	1.15316i	−1.09784	+	0.0908814i
$162$		0			0
$163$	−0.108800	−	0.826419i	−0.00852188	−	0.0647301i	0.986656	−	0.162822i	$-0.0520595\pi$
$163$	−0.108800	−	0.826419i	−0.00852188	−	0.0647301i	−0.995177	+	0.0980916i	$0.968726\pi$
$164$		0			0
$165$	−2.15767	−	0.284063i	−0.167975	−	0.0221143i
$166$		0			0
$167$	−6.88779	+	6.88779i	−0.532993	+	0.532993i	−0.921462	−	0.388469i	$-0.873004\pi$
$167$	−6.88779	+	6.88779i	−0.532993	+	0.532993i	0.388469	+	0.921462i	$0.373004\pi$
$168$		0			0
$169$	8.18076	+	8.18076i	0.629290	+	0.629290i
$170$		0			0
$171$	6.55234	−	49.7699i	0.501070	−	3.80600i
$172$		0			0
$173$	−15.6579	+	2.06140i	−1.19045	+	0.156725i	−0.699610	−	0.714525i	$-0.746643\pi$
$173$	−15.6579	+	2.06140i	−1.19045	+	0.156725i	−0.490838	+	0.871251i	$0.663309\pi$
$174$		0			0
$175$	10.7261	−	7.43605i	0.810817	−	0.562113i
$176$		0			0
$177$	−14.4960	+	8.36929i	−1.08959	+	0.629074i
$178$		0			0
$179$	13.8430	+	18.0406i	1.03468	+	1.34842i	0.935492	+	0.353348i	$0.114957\pi$
$179$	13.8430	+	18.0406i	1.03468	+	1.34842i	0.0991851	+	0.995069i	$0.468376\pi$
$180$		0			0
$181$	10.5303	−	4.36180i	0.782713	−	0.324210i	0.0447030	−	0.999000i	$-0.485766\pi$
$181$	10.5303	−	4.36180i	0.782713	−	0.324210i	0.738010	+	0.674790i	$0.235766\pi$
$182$		0			0
$183$	−34.2318	−	34.2318i	−2.53048	−	2.53048i
$184$		0			0
$185$	0.0979141	+	0.365420i	0.00719879	+	0.0268662i
$186$		0			0
$187$	−2.64062	+	3.44133i	−0.193102	+	0.251655i
$188$		0			0
$189$	26.4905	−	24.0474i	1.92690	−	1.74919i
$190$		0			0
$191$	10.1959	+	17.6598i	0.737747	+	1.27782i	0.953508	+	0.301369i	$0.0974435\pi$
$191$	10.1959	+	17.6598i	0.737747	+	1.27782i	−0.215761	+	0.976446i	$0.569223\pi$
$192$		0			0
$193$	0.820576	−	1.42128i	0.0590664	−	0.102306i	−0.834980	−	0.550280i	$-0.814521\pi$
$193$	0.820576	−	1.42128i	0.0590664	−	0.102306i	0.894047	+	0.447974i	$0.147854\pi$
$194$		0			0
$195$	−0.914520	−	0.378807i	−0.0654901	−	0.0271269i
$196$		0			0
$197$	−9.42293	−	22.7490i	−0.671356	−	1.62080i	−0.779309	−	0.626640i	$-0.784430\pi$
$197$	−9.42293	−	22.7490i	−0.671356	−	1.62080i	0.107953	−	0.994156i	$-0.465570\pi$
$198$		0			0
$199$	0.322739	+	1.20448i	0.0228784	+	0.0853832i	0.976421	−	0.215875i	$-0.0692602\pi$
$199$	0.322739	+	1.20448i	0.0228784	+	0.0853832i	−0.953543	+	0.301258i	$0.902594\pi$
$200$		0			0
$201$	10.0832	−	37.6312i	0.711217	−	2.65430i
$202$		0			0
$203$	−0.743150	+	15.3723i	−0.0521589	+	1.07892i
$204$		0			0
$205$	2.05675	−	0.270777i	0.143650	−	0.0189119i
$206$		0			0
$207$	−33.0711	−	19.0936i	−2.29860	−	1.32710i
$208$		0			0
$209$			18.2630i			1.26328i
$210$		0			0
$211$	−0.658436	+	1.58961i	−0.0453286	+	0.109433i	−0.944922	−	0.327295i	$-0.893863\pi$
$211$	−0.658436	+	1.58961i	−0.0453286	+	0.109433i	0.899594	+	0.436728i	$0.143863\pi$
$212$		0			0
$213$	−1.09176	+	8.29273i	−0.0748060	+	0.568208i
$214$		0			0
$215$	0.203367	−	0.758976i	0.0138695	−	0.0517617i
$216$		0			0
$217$	17.6999	+	3.20632i	1.20155	+	0.217659i
$218$		0			0
$219$	−3.70763	+	4.83188i	−0.250539	+	0.326508i
$220$		0			0
$221$	−1.56526	+	1.20107i	−0.105291	+	0.0807926i
$222$		0			0
$223$	11.0072			0.737098			0.368549	−	0.929608i	$-0.379855\pi$
$223$	11.0072			0.737098			0.368549	+	0.929608i	$0.379855\pi$
$224$		0			0
$225$	35.6572			2.37715
$226$		0			0
$227$	−2.93532	+	2.25235i	−0.194824	+	0.149494i	−0.701567	−	0.712603i	$-0.747516\pi$
$227$	−2.93532	+	2.25235i	−0.194824	+	0.149494i	0.506743	+	0.862097i	$0.330849\pi$
$228$		0			0
$229$	4.09927	−	5.34227i	0.270887	−	0.353027i	−0.638024	−	0.770016i	$-0.720248\pi$
$229$	4.09927	−	5.34227i	0.270887	−	0.353027i	0.908912	+	0.416989i	$0.136915\pi$
$230$		0			0
$231$	−14.3824	+	16.9785i	−0.946290	+	1.11710i
$232$		0			0
$233$	2.52858	−	9.43681i	0.165653	−	0.618226i	−0.832303	−	0.554321i	$-0.812978\pi$
$233$	2.52858	−	9.43681i	0.165653	−	0.618226i	0.997956	−	0.0639047i	$-0.0203554\pi$
$234$		0			0
$235$	−0.185089	+	1.40589i	−0.0120739	+	0.0917103i
$236$		0			0
$237$	−9.05752	+	21.8668i	−0.588349	+	1.42040i
$238$		0			0
$239$			19.4188i			1.25610i	0.778173	+	0.628050i	$0.216147\pi$
$239$			19.4188i			1.25610i	−0.778173	+	0.628050i	$0.783853\pi$
$240$		0			0
$241$	16.5879	+	9.57701i	1.06852	+	0.616909i	0.927776	−	0.373137i	$-0.121718\pi$
$241$	16.5879	+	9.57701i	1.06852	+	0.616909i	0.140742	+	0.990046i	$0.455051\pi$
$242$		0			0
$243$	28.1504	−	3.70607i	1.80585	−	0.237745i
$244$		0			0
$245$	0.0620964	+	1.81031i	0.00396719	+	0.115657i
$246$		0			0
$247$	−2.14995	+	8.02374i	−0.136798	+	0.510538i
$248$		0			0
$249$	−10.4730	−	39.0856i	−0.663696	−	2.47695i
$250$		0			0
$251$	−10.5124	−	25.3793i	−0.663539	−	1.60193i	−0.792217	−	0.610239i	$-0.791073\pi$
$251$	−10.5124	−	25.3793i	−0.663539	−	1.60193i	0.128678	−	0.991686i	$-0.458927\pi$
$252$		0			0
$253$	12.8353	+	5.31656i	0.806949	+	0.334249i
$254$		0			0
$255$	−0.682550	+	1.18221i	−0.0427429	+	0.0740329i
$256$		0			0
$257$	−0.339437	−	0.587922i	−0.0211735	−	0.0366736i	0.855245	−	0.518225i	$-0.173407\pi$
$257$	−0.339437	−	0.587922i	−0.0211735	−	0.0366736i	−0.876418	+	0.481551i	$0.840074\pi$
$258$		0			0
$259$	3.68351	+	1.18036i	0.228882	+	0.0733438i
$260$		0			0
$261$	−25.5963	+	33.3577i	−1.58437	+	2.06479i
$262$		0			0
$263$	−5.56573	−	20.7716i	−0.343197	−	1.28083i	−0.894704	−	0.446660i	$-0.852613\pi$
$263$	−5.56573	−	20.7716i	−0.343197	−	1.28083i	0.551506	−	0.834171i	$-0.314053\pi$
$264$		0			0
$265$	−0.277538	−	0.277538i	−0.0170490	−	0.0170490i
$266$		0			0
$267$	−18.3289	+	7.59209i	−1.12171	+	0.464628i
$268$		0			0
$269$	−10.1825	−	13.2701i	−0.620837	−	0.809090i	0.372042	−	0.928216i	$-0.378658\pi$
$269$	−10.1825	−	13.2701i	−0.620837	−	0.809090i	−0.992879	+	0.119125i	$0.961991\pi$
$270$		0			0
$271$	−19.3264	+	11.1581i	−1.17400	+	0.677807i	−0.954618	−	0.297833i	$-0.903736\pi$
$271$	−19.3264	+	11.1581i	−1.17400	+	0.677807i	−0.219378	+	0.975640i	$0.570403\pi$
$272$		0			0
$273$	−8.31754	+	5.76627i	−0.503400	+	0.348991i
$274$		0			0
$275$	−12.8614	+	1.69324i	−0.775573	+	0.102106i
$276$		0			0
$277$	−3.65561	+	27.7671i	−0.219644	+	1.66836i	0.425999	+	0.904724i	$0.359923\pi$
$277$	−3.65561	+	27.7671i	−0.219644	+	1.66836i	−0.645643	+	0.763639i	$0.723411\pi$
$278$		0			0
$279$	34.7497	+	34.7497i	2.08041	+	2.08041i
$280$		0			0
$281$	3.27274	−	3.27274i	0.195235	−	0.195235i	−0.602719	−	0.797954i	$-0.705916\pi$
$281$	3.27274	−	3.27274i	0.195235	−	0.195235i	0.797954	+	0.602719i	$0.205916\pi$
$282$		0			0
$283$	−16.1054	−	2.12032i	−0.957369	−	0.126040i	−0.364380	−	0.931250i	$-0.618719\pi$
$283$	−16.1054	−	2.12032i	−0.957369	−	0.126040i	−0.592989	+	0.805210i	$0.702052\pi$
$284$		0			0
$285$	0.750196	+	5.69830i	0.0444378	+	0.337538i
$286$		0			0
$287$	9.05370	−	19.1812i	0.534423	−	1.13223i
$288$		0			0
$289$	−7.13957	−	12.3661i	−0.419975	−	0.727417i
$290$		0			0
$291$	−5.57026	+	4.27421i	−0.326534	+	0.250559i
$292$		0			0
$293$	−2.93669	−	7.08979i	−0.171563	−	0.414190i	0.814588	−	0.580040i	$-0.196963\pi$
$293$	−2.93669	−	7.08979i	−0.171563	−	0.414190i	−0.986151	+	0.165850i	$0.946963\pi$
$294$		0			0
$295$	0.957665	−	0.957665i	0.0557574	−	0.0557574i
$296$		0			0
$297$	−34.3487	+	9.20370i	−1.99311	+	0.534053i
$298$		0			0
$299$	5.01324	+	3.84680i	0.289923	+	0.222466i
$300$		0			0
$301$	−5.39984	−	5.94846i	−0.311242	−	0.342863i
$302$		0			0
$303$	−7.58460	+	4.37897i	−0.435724	+	0.251565i
$304$		0			0
$305$	3.39223	+	1.95850i	0.194238	+	0.112144i
$306$		0			0
$307$	−3.62493	+	8.75135i	−0.206886	+	0.499466i	−0.992930	−	0.118705i	$-0.962126\pi$
$307$	−3.62493	+	8.75135i	−0.206886	+	0.499466i	0.786044	+	0.618170i	$0.212126\pi$
$308$		0			0
$309$	−42.1533	+	17.4605i	−2.39802	+	0.993291i
$310$		0			0
$311$	−14.1832	+	3.80038i	−0.804256	+	0.215500i	−0.637452	−	0.770490i	$-0.720012\pi$
$311$	−14.1832	+	3.80038i	−0.804256	+	0.215500i	−0.166804	+	0.985990i	$0.553345\pi$
$312$		0			0
$313$	11.9963	+	3.21439i	0.678069	+	0.181688i	0.581387	−	0.813627i	$-0.302510\pi$
$313$	11.9963	+	3.21439i	0.678069	+	0.181688i	0.0966824	+	0.995315i	$0.469177\pi$
$314$		0			0
$315$	−2.67841	+	4.16123i	−0.150912	+	0.234459i
$316$		0			0
$317$	−1.99120	−	15.1247i	−0.111837	−	0.849486i	−0.951774	−	0.306802i	$-0.900741\pi$
$317$	−1.99120	−	15.1247i	−0.111837	−	0.849486i	0.839937	−	0.542685i	$-0.182592\pi$
$318$		0			0
$319$	7.64844	−	13.2475i	0.428230	−	0.741717i
$320$		0			0
$321$	−16.2003			−0.904214
$322$		0			0
$323$	10.5836	+	4.38388i	0.588889	+	0.243926i
$324$		0			0
$325$	−5.84992	−	0.770157i	−0.324495	−	0.0427206i
$326$		0			0
$327$	−2.00837	−	0.538140i	−0.111063	−	0.0297592i
$328$		0			0
$329$	11.0628	+	9.37123i	0.609912	+	0.516653i
$330$		0			0
$331$	14.4788	+	11.1100i	0.795827	+	0.610660i	0.924567	−	0.381019i	$-0.124427\pi$
$331$	14.4788	+	11.1100i	0.795827	+	0.610660i	−0.128740	+	0.991678i	$0.541093\pi$
$332$		0			0
$333$	6.43307	+	8.38374i	0.352530	+	0.459426i
$334$		0			0
$335$			3.15220i			0.172223i
$336$		0			0
$337$		−	5.70487i		−	0.310764i	−0.987854	−	0.155382i	$-0.950339\pi$
$337$		−	5.70487i		−	0.310764i	0.987854	−	0.155382i	$-0.0496609\pi$
$338$		0			0
$339$	20.0739	+	26.1608i	1.09026	+	1.42086i
$340$		0			0
$341$	−14.1842	−	10.8839i	−0.768119	−	0.589399i
$342$		0			0
$343$	15.9076	+	9.48404i	0.858932	+	0.512090i
$344$		0			0
$345$	4.22318	+	1.13160i	0.227368	+	0.0609232i
$346$		0			0
$347$	32.7717	+	4.31448i	1.75928	+	0.231613i	0.939854	−	0.341576i	$-0.110961\pi$
$347$	32.7717	+	4.31448i	1.75928	+	0.231613i	0.819423	+	0.573189i	$0.194294\pi$
$348$		0			0
$349$	16.4221	+	6.80227i	0.879056	+	0.364117i	0.776131	−	0.630572i	$-0.217180\pi$
$349$	16.4221	+	6.80227i	0.879056	+	0.364117i	0.102926	+	0.994689i	$0.467180\pi$
$350$		0			0
$351$	−16.1744			−0.863323
$352$		0			0
$353$	−6.08282	+	10.5357i	−0.323756	+	0.560761i	−0.981260	−	0.192690i	$-0.938279\pi$
$353$	−6.08282	+	10.5357i	−0.323756	+	0.560761i	0.657504	+	0.753451i	$0.271612\pi$
$354$		0			0
$355$	−0.0883357	−	0.670977i	−0.00468837	−	0.0356117i
$356$		0			0
$357$	6.38687	+	12.4103i	0.338029	+	0.656823i
$358$		0			0
$359$	−18.3436	−	4.91515i	−0.968137	−	0.259412i	−0.260096	−	0.965583i	$-0.583754\pi$
$359$	−18.3436	−	4.91515i	−0.968137	−	0.259412i	−0.708041	+	0.706171i	$0.750421\pi$
$360$		0			0
$361$	28.2356	−	7.56570i	1.48608	−	0.398195i
$362$		0			0
$363$	−12.0691	+	4.99918i	−0.633462	+	0.262389i
$364$		0			0
$365$	0.188582	−	0.455276i	0.00987081	−	0.0238302i
$366$		0			0
$367$	−24.1791	−	13.9598i	−1.26214	−	0.728696i	−0.288651	−	0.957435i	$-0.593207\pi$
$367$	−24.1791	−	13.9598i	−1.26214	−	0.728696i	−0.973488	+	0.228739i	$0.926540\pi$
$368$		0			0
$369$	50.1842	−	28.9738i	2.61248	−	1.50832i
$370$		0			0
$371$	−3.92195	+	0.850269i	−0.203618	+	0.0441438i
$372$		0			0
$373$	−5.32574	−	4.08658i	−0.275756	−	0.211595i	0.461619	−	0.887078i	$-0.347269\pi$
$373$	−5.32574	−	4.08658i	−0.275756	−	0.211595i	−0.737376	+	0.675483i	$0.763935\pi$
$374$		0			0
$375$	−7.94030	+	2.12760i	−0.410035	+	0.109869i
$376$		0			0
$377$	4.91981	−	4.91981i	0.253383	−	0.253383i
$378$		0			0
$379$	−10.9562	−	26.4506i	−0.562781	−	1.35867i	−0.907533	−	0.419980i	$-0.862037\pi$
$379$	−10.9562	−	26.4506i	−0.562781	−	1.35867i	0.344752	−	0.938694i	$-0.387963\pi$
$380$		0			0
$381$	−37.3038	+	28.6242i	−1.91113	+	1.46646i
$382$		0			0
$383$	1.24195	+	2.15112i	0.0634606	+	0.109917i	0.896010	−	0.444034i	$-0.146453\pi$
$383$	1.24195	+	2.15112i	0.0634606	+	0.109917i	−0.832549	+	0.553951i	$0.813120\pi$
$384$		0			0
$385$	0.768492	−	1.62813i	0.0391660	−	0.0829772i
$386$		0			0
$387$	−2.86486	−	21.7608i	−0.145629	−	1.10616i
$388$		0			0
$389$	9.81868	+	1.29265i	0.497827	+	0.0655402i	0.375259	−	0.926920i	$-0.377554\pi$
$389$	9.81868	+	1.29265i	0.497827	+	0.0655402i	0.122568	+	0.992460i	$0.460887\pi$
$390$		0			0
$391$	6.16203	−	6.16203i	0.311627	−	0.311627i
$392$		0			0
$393$	13.0809	+	13.0809i	0.659842	+	0.659842i
$394$		0			0
$395$	0.249964	−	1.89867i	0.0125771	−	0.0955322i
$396$		0			0
$397$	4.96510	−	0.653667i	0.249191	−	0.0328066i	−0.00489583	−	0.999988i	$-0.501558\pi$
$397$	4.96510	−	0.653667i	0.249191	−	0.0328066i	0.254087	+	0.967181i	$0.418225\pi$
$398$		0			0
$399$	53.1421	+	25.0836i	2.66043	+	1.25575i
$400$		0			0
$401$	−15.4675	+	8.93017i	−0.772410	+	0.445951i	−0.833734	−	0.552167i	$-0.813801\pi$
$401$	−15.4675	+	8.93017i	−0.772410	+	0.445951i	0.0613236	+	0.998118i	$0.480468\pi$
$402$		0			0
$403$	−4.95048	−	6.45159i	−0.246601	−	0.321377i
$404$		0			0
$405$	−5.15501	+	2.13528i	−0.256155	+	0.106103i
$406$		0			0
$407$	−2.71850	−	2.71850i	−0.134751	−	0.134751i
$408$		0			0
$409$	0.133054	+	0.496564i	0.00657910	+	0.0245535i	0.969137	−	0.246521i	$-0.0792876\pi$
$409$	0.133054	+	0.496564i	0.00657910	+	0.0245535i	−0.962558	+	0.271075i	$0.912621\pi$
$410$		0			0
$411$	32.5204	−	42.3814i	1.60411	−	2.09052i
$412$		0			0
$413$	−2.93392	−	13.5330i	−0.144369	−	0.665915i
$414$		0			0
$415$	1.63702	+	2.83539i	0.0803580	+	0.139184i
$416$		0			0
$417$	3.52892	−	6.11227i	0.172812	−	0.299319i
$418$		0			0
$419$	−11.7803	−	4.87958i	−0.575508	−	0.238383i	0.0758944	−	0.997116i	$-0.475819\pi$
$419$	−11.7803	−	4.87958i	−0.575508	−	0.238383i	−0.651402	+	0.758733i	$0.725819\pi$
$420$		0			0
$421$	−9.44068	−	22.7918i	−0.460110	−	1.11080i	−0.968352	−	0.249590i	$-0.919704\pi$
$421$	−9.44068	−	22.7918i	−0.460110	−	1.11080i	0.508241	−	0.861215i	$-0.330296\pi$
$422$		0			0
$423$	10.2518	+	38.2604i	0.498462	+	1.86028i
$424$		0			0
$425$	−2.10603	+	7.85980i	−0.102157	+	0.381257i
$426$		0			0
$427$	35.6100	−	18.3264i	1.72329	−	0.886878i
$428$		0			0
$429$	9.97337	−	1.31302i	0.481519	−	0.0633932i
$430$		0			0
$431$	3.29192	+	1.90059i	0.158566	+	0.0915484i	0.577184	−	0.816614i	$-0.304152\pi$
$431$	3.29192	+	1.90059i	0.158566	+	0.0915484i	−0.418617	+	0.908163i	$0.637485\pi$
$432$		0			0
$433$		−	2.83491i		−	0.136237i	−0.997677	−	0.0681185i	$-0.978300\pi$
$433$		−	2.83491i		−	0.136237i	0.997677	−	0.0681185i	$-0.0216996\pi$
$434$		0			0
$435$	1.84224	−	4.44757i	0.0883289	−	0.213245i
$436$		0			0
$437$	4.78904	−	36.3764i	0.229091	−	1.74012i
$438$		0			0
$439$	5.23250	−	19.5279i	0.249733	−	0.932018i	−0.721212	−	0.692715i	$-0.756414\pi$
$439$	5.23250	−	19.5279i	0.249733	−	0.932018i	0.970945	−	0.239303i	$-0.0769189\pi$
$440$		0			0
$441$	20.9540	+	46.0549i	0.997811	+	2.19309i
$442$		0			0
$443$	1.19168	−	1.55303i	0.0566187	−	0.0737869i	−0.764186	−	0.644996i	$-0.776859\pi$
$443$	1.19168	−	1.55303i	0.0566187	−	0.0737869i	0.820804	+	0.571209i	$0.193526\pi$
$444$		0			0
$445$	1.27350	−	0.977189i	0.0603696	−	0.0463232i
$446$		0			0
$447$	−19.1764			−0.907012
$448$		0			0
$449$	−3.60976			−0.170355			−0.0851776	−	0.996366i	$-0.527146\pi$
$449$	−3.60976			−0.170355			−0.0851776	+	0.996366i	$0.527146\pi$
$450$		0			0
$451$	−16.7254	+	12.8338i	−0.787568	+	0.604322i
$452$		0			0
$453$	−16.8914	+	22.0133i	−0.793629	+	1.03428i
$454$		0			0
$455$	0.529299	−	0.624841i	0.0248139	−	0.0292930i
$456$		0			0
$457$	−6.23430	+	23.2667i	−0.291628	+	1.08837i	0.652230	+	0.758021i	$0.273834\pi$
$457$	−6.23430	+	23.2667i	−0.291628	+	1.08837i	−0.943858	+	0.330351i	$0.892833\pi$
$458$		0			0
$459$	−2.91146	+	22.1148i	−0.135895	+	1.03223i
$460$		0			0
$461$	−3.24808	+	7.84157i	−0.151278	+	0.365218i	−0.981292	−	0.192525i	$-0.938332\pi$
$461$	−3.24808	+	7.84157i	−0.151278	+	0.365218i	0.830014	+	0.557743i	$0.188332\pi$
$462$		0			0
$463$		−	10.8011i		−	0.501971i	−0.967991	−	0.250985i	$-0.919245\pi$
$463$		−	10.8011i		−	0.501971i	0.967991	−	0.250985i	$-0.0807546\pi$
$464$		0			0
$465$	−4.87276	−	2.81329i	−0.225969	−	0.130463i
$466$		0			0
$467$	1.65471	−	0.217847i	0.0765710	−	0.0100808i	−0.0921434	−	0.995746i	$-0.529372\pi$
$467$	1.65471	−	0.217847i	0.0765710	−	0.0100808i	0.168714	+	0.985665i	$0.446038\pi$
$468$		0			0
$469$	27.1008	+	17.4437i	1.25140	+	0.805474i
$470$		0			0
$471$	−4.57592	+	17.0776i	−0.210847	+	0.786892i
$472$		0			0
$473$	2.06669	+	7.71300i	0.0950267	+	0.354644i
$474$		0			0
$475$	13.1105	+	31.6516i	0.601552	+	1.45228i
$476$		0			0
$477$	−10.1292	−	4.19565i	−0.463784	−	0.192105i
$478$		0			0
$479$	5.35009	−	9.26663i	0.244452	−	0.423403i	−0.717525	−	0.696532i	$-0.754725\pi$
$479$	5.35009	−	9.26663i	0.244452	−	0.423403i	0.961977	+	0.273129i	$0.0880586\pi$
$480$		0			0
$481$	−0.874330	−	1.51438i	−0.0398660	−	0.0690500i
$482$		0			0
$483$	33.0991	−	30.0464i	1.50606	−	1.36716i
$484$		0			0
$485$	0.345833	−	0.450698i	0.0157035	−	0.0204651i
$486$		0			0
$487$	9.55793	+	35.6707i	0.433111	+	1.61639i	0.745546	+	0.666454i	$0.232189\pi$
$487$	9.55793	+	35.6707i	0.433111	+	1.61639i	−0.312435	+	0.949939i	$0.601145\pi$
$488$		0			0
$489$	1.88503	+	1.88503i	0.0852438	+	0.0852438i
$490$		0			0
$491$	−25.0392	+	10.3716i	−1.13000	+	0.468062i	−0.867781	−	0.496946i	$-0.834455\pi$
$491$	−25.0392	+	10.3716i	−1.13000	+	0.468062i	−0.262220	+	0.965008i	$0.584455\pi$
$492$		0			0
$493$	−5.84113	−	7.61231i	−0.263071	−	0.342841i
$494$		0			0
$495$	4.25971	−	2.45934i	0.191460	−	0.110539i
$496$		0			0
$497$	−6.25750	−	2.95360i	−0.280687	−	0.132487i
$498$		0			0
$499$	−29.3888	+	3.86911i	−1.31562	+	0.173205i	−0.755470	−	0.655183i	$-0.772592\pi$
$499$	−29.3888	+	3.86911i	−1.31562	+	0.173205i	−0.560155	+	0.828388i	$0.689258\pi$
$500$		0			0
$501$	4.06624	−	30.8862i	0.181666	−	1.37989i
$502$		0			0
$503$	−11.3156	−	11.3156i	−0.504540	−	0.504540i	0.408306	−	0.912845i	$-0.366120\pi$
$503$	−11.3156	−	11.3156i	−0.504540	−	0.504540i	−0.912845	+	0.408306i	$0.866120\pi$
$504$		0			0
$505$	0.501068	−	0.501068i	0.0222972	−	0.0222972i
$506$		0			0
$507$	−36.6841	−	4.82955i	−1.62920	−	0.214488i
$508$		0			0
$509$	−1.51106	−	11.4776i	−0.0669764	−	0.508736i	−0.991747	−	0.128211i	$-0.959077\pi$
$509$	−1.51106	−	11.4776i	−0.0669764	−	0.508736i	0.924771	−	0.380525i	$-0.124257\pi$
$510$		0			0
$511$	−2.87063	−	4.14073i	−0.126989	−	0.183175i
$512$		0			0
$513$	46.9565	+	81.3311i	2.07318	+	3.59086i
$514$		0			0
$515$	2.92882	−	2.24736i	0.129059	−	0.0990307i
$516$		0			0
$517$	−5.51466	−	13.3136i	−0.242535	−	0.585530i
$518$		0			0
$519$	35.7150	−	35.7150i	1.56771	−	1.56771i
$520$		0			0
$521$	−21.6326	+	5.79644i	−0.947741	+	0.253947i	−0.699404	−	0.714727i	$-0.746551\pi$
$521$	−21.6326	+	5.79644i	−0.947741	+	0.253947i	−0.248338	+	0.968674i	$0.579884\pi$
$522$		0			0
$523$	−4.24996	−	3.26111i	−0.185838	−	0.142598i	0.511653	−	0.859192i	$-0.329033\pi$
$523$	−4.24996	−	3.26111i	−0.185838	−	0.142598i	−0.697490	+	0.716594i	$0.745700\pi$
$524$		0			0
$525$	−12.7377	+	39.7501i	−0.555917	+	1.73484i
$526$		0			0
$527$	−9.71219	+	5.60733i	−0.423070	+	0.244259i
$528$		0			0
$529$	−4.25276	−	2.45533i	−0.184903	−	0.106754i
$530$		0			0
$531$	14.4774	−	34.9515i	0.628265	−	1.51677i
$532$		0			0
$533$	−8.85902	+	3.66953i	−0.383727	+	0.158945i
$534$		0			0
$535$	1.26613	−	0.339258i	0.0547395	−	0.0146674i
$536$		0			0
$537$	−70.2471	−	18.8227i	−3.03139	−	0.812257i
$538$		0			0
$539$	−9.74504	−	15.6168i	−0.419749	−	0.672664i
$540$		0			0
$541$	3.22285	+	24.4800i	0.138561	+	1.05248i	0.909540	+	0.415616i	$0.136434\pi$
$541$	3.22285	+	24.4800i	0.138561	+	1.05248i	−0.770979	+	0.636860i	$0.780233\pi$
$542$		0			0
$543$	−18.2262	+	31.5688i	−0.782162	+	1.35474i
$544$		0			0
$545$	0.168232			0.00720628
$546$		0			0
$547$	−28.2776	−	11.7130i	−1.20906	−	0.500811i	−0.315147	−	0.949043i	$-0.602054\pi$
$547$	−28.2776	−	11.7130i	−1.20906	−	0.500811i	−0.893917	+	0.448232i	$0.852054\pi$
$548$		0			0
$549$	108.479	+	14.2815i	4.62976	+	0.609520i
$550$		0			0
$551$	−39.0217	−	10.4558i	−1.66238	−	0.445434i
$552$		0			0
$553$	−14.9404	−	12.6559i	−0.635329	−	0.538183i
$554$		0			0
$555$	−0.959878	−	0.736540i	−0.0407445	−	0.0312644i
$556$		0			0
$557$	−3.53265	−	4.60385i	−0.149683	−	0.195071i	0.712493	−	0.701679i	$-0.247566\pi$
$557$	−3.53265	−	4.60385i	−0.149683	−	0.195071i	−0.862177	+	0.506608i	$0.830899\pi$
$558$		0			0
$559$			3.63196i			0.153615i
$560$		0			0
$561$		−	13.8727i		−	0.585704i
$562$		0			0
$563$	0.275993	+	0.359681i	0.0116317	+	0.0151587i	0.799133	−	0.601154i	$-0.205292\pi$
$563$	0.275993	+	0.359681i	0.0116317	+	0.0151587i	−0.787501	+	0.616313i	$0.788626\pi$
$564$		0			0
$565$	−2.11671	−	1.62421i	−0.0890507	−	0.0683310i
$566$		0			0
$567$	−10.1690	+	56.1360i	−0.427057	+	2.35749i
$568$		0			0
$569$	23.0507	+	6.17642i	0.966336	+	0.258929i	0.707280	−	0.706934i	$-0.249922\pi$
$569$	23.0507	+	6.17642i	0.966336	+	0.258929i	0.259056	+	0.965862i	$0.416589\pi$
$570$		0			0
$571$	25.0250	+	3.29461i	1.04727	+	0.137875i	0.634469	−	0.772948i	$-0.281219\pi$
$571$	25.0250	+	3.29461i	1.04727	+	0.137875i	0.412796	+	0.910823i	$0.364552\pi$
$572$		0			0
$573$	−60.2518	−	24.9571i	−2.51705	−	1.04260i
$574$		0			0
$575$	26.0615			1.08684
$576$		0			0
$577$	19.2126	−	33.2772i	0.799832	−	1.38535i	−0.119893	−	0.992787i	$-0.538255\pi$
$577$	19.2126	−	33.2772i	0.799832	−	1.38535i	0.919725	−	0.392563i	$-0.128411\pi$
$578$		0			0
$579$	0.685089	+	5.20377i	0.0284713	+	0.216261i
$580$		0			0
$581$	33.4360	+	1.61641i	1.38716	+	0.0670601i
$582$		0			0
$583$	3.85280	+	1.03235i	0.159567	+	0.0427558i
$584$		0			0
$585$	2.16100	−	0.579037i	0.0893462	−	0.0239402i
$586$		0			0
$587$	−13.0929	+	5.42328i	−0.540404	+	0.223843i	−0.636153	−	0.771563i	$-0.719475\pi$
$587$	−13.0929	+	5.42328i	−0.540404	+	0.223843i	0.0957493	+	0.995405i	$0.469475\pi$
$588$		0			0
$589$	−18.0692	+	43.6229i	−0.744528	+	1.79745i
$590$		0			0
$591$	68.1989	+	39.3746i	2.80533	+	1.61966i
$592$		0			0
$593$	−6.61865	+	3.82128i	−0.271796	+	0.156921i	−0.629703	−	0.776836i	$-0.716824\pi$
$593$	−6.61865	+	3.82128i	−0.271796	+	0.156921i	0.357908	+	0.933757i	$0.383490\pi$
$594$		0			0
$595$	−0.759052	−	0.836170i	−0.0311181	−	0.0342796i
$596$		0			0
$597$	−3.16390	−	2.42774i	−0.129490	−	0.0993609i
$598$		0			0
$599$	24.6150	−	6.59556i	1.00574	−	0.269487i	0.281892	−	0.959446i	$-0.409038\pi$
$599$	24.6150	−	6.59556i	1.00574	−	0.269487i	0.723849	+	0.689959i	$0.242371\pi$
$600$		0			0
$601$	−8.02087	+	8.02087i	−0.327178	+	0.327178i	−0.851512	−	0.524334i	$-0.824314\pi$
$601$	−8.02087	+	8.02087i	−0.327178	+	0.327178i	0.524334	+	0.851512i	$0.324314\pi$
$602$		0			0
$603$	33.6958	+	81.3489i	1.37220	+	3.31278i
$604$		0			0
$605$	0.838563	−	0.643452i	0.0340924	−	0.0261600i
$606$		0			0
$607$	22.3948	+	38.7889i	0.908977	+	1.57439i	0.815488	+	0.578774i	$0.196469\pi$
$607$	22.3948	+	38.7889i	0.908977	+	1.57439i	0.0934892	+	0.995620i	$0.470198\pi$
$608$		0			0
$609$	−28.0430	−	40.4506i	−1.13636	−	1.63914i
$610$		0			0
$611$	−0.855535	−	6.49843i	−0.0346112	−	0.262899i
$612$		0			0
$613$	−13.6845	−	1.80160i	−0.552713	−	0.0727660i	−0.151003	−	0.988533i	$-0.548250\pi$
$613$	−13.6845	−	1.80160i	−0.552713	−	0.0727660i	−0.401709	+	0.915767i	$0.631584\pi$
$614$		0			0
$615$	−4.69137	+	4.69137i	−0.189174	+	0.189174i
$616$		0			0
$617$	−11.8237	−	11.8237i	−0.476003	−	0.476003i	0.427848	−	0.903851i	$-0.359272\pi$
$617$	−11.8237	−	11.8237i	−0.476003	−	0.476003i	−0.903851	+	0.427848i	$0.859272\pi$
$618$		0			0
$619$	4.47255	−	33.9724i	0.179767	−	1.36547i	−0.629031	−	0.777380i	$-0.716548\pi$
$619$	4.47255	−	33.9724i	0.179767	−	1.36547i	0.808798	−	0.588087i	$-0.200119\pi$
$620$		0			0
$621$	70.8294	−	9.32487i	2.84229	−	0.374194i
$622$		0			0
$623$	−1.35402	−	16.3564i	−0.0542475	−	0.655304i
$624$		0			0
$625$	−20.7847	+	12.0000i	−0.831387	+	0.480001i
$626$		0			0
$627$	−35.5565	−	46.3382i	−1.41999	−	1.85057i
$628$		0			0
$629$	−2.22796	+	0.922851i	−0.0888345	+	0.0367965i
$630$		0			0
$631$	1.76797	+	1.76797i	0.0703818	+	0.0703818i	0.741421	−	0.671040i	$-0.234152\pi$
$631$	1.76797	+	1.76797i	0.0703818	+	0.0703818i	−0.671040	+	0.741421i	$0.734152\pi$
$632$		0			0
$633$	−1.42420	−	5.31519i	−0.0566069	−	0.211260i
$634$		0			0
$635$	2.31603	−	3.01830i	0.0919087	−	0.119778i
$636$		0			0
$637$	−2.44298	−	8.00836i	−0.0967946	−	0.317303i
$638$		0			0
$639$	−9.45216	−	16.3716i	−0.373921	−	0.647651i
$640$		0			0
$641$	−18.7908	+	32.5466i	−0.742192	+	1.28551i	0.209303	+	0.977851i	$0.432880\pi$
$641$	−18.7908	+	32.5466i	−0.742192	+	1.28551i	−0.951495	+	0.307663i	$0.900453\pi$
$642$		0			0
$643$	8.44646	+	3.49864i	0.333096	+	0.137973i	0.542962	−	0.839757i	$-0.317303\pi$
$643$	8.44646	+	3.49864i	0.333096	+	0.137973i	−0.209866	+	0.977730i	$0.567303\pi$
$644$		0			0
$645$	0.961666	+	2.32167i	0.0378656	+	0.0914156i
$646$		0			0
$647$	1.04917	+	3.91557i	0.0412473	+	0.153937i	0.983478	−	0.181028i	$-0.0579423\pi$
$647$	1.04917	+	3.91557i	0.0412473	+	0.153937i	−0.942231	+	0.334965i	$0.891276\pi$
$648$		0			0
$649$	−3.56222	+	13.2944i	−0.139829	+	0.521850i
$650$		0			0
$651$	−51.1519	+	26.3249i	−2.00480	+	1.03176i
$652$		0			0
$653$	−10.4782	+	1.37948i	−0.410043	+	0.0539831i	−0.332726	−	0.943023i	$-0.607969\pi$
$653$	−10.4782	+	1.37948i	−0.410043	+	0.0539831i	−0.0773164	+	0.997007i	$0.524635\pi$
$654$		0			0
$655$	−1.29626	−	0.748395i	−0.0506490	−	0.0292422i
$656$		0			0
$657$		−	13.7652i		−	0.537031i
$658$		0			0
$659$	9.75327	−	23.5465i	0.379934	−	0.917241i	−0.612044	−	0.790824i	$-0.709652\pi$
$659$	9.75327	−	23.5465i	0.379934	−	0.917241i	0.991977	−	0.126417i	$-0.0403477\pi$
$660$		0			0
$661$	3.73252	−	28.3513i	0.145178	−	1.10274i	−0.751398	−	0.659849i	$-0.770620\pi$
$661$	3.73252	−	28.3513i	0.145178	−	1.10274i	0.896576	−	0.442889i	$-0.146047\pi$
$662$		0			0
$663$	1.63312	−	6.09487i	0.0634250	−	0.236705i
$664$		0			0
$665$	−4.67858	−	0.847520i	−0.181428	−	0.0328654i
$666$		0			0
$667$	−18.7081	+	24.3808i	−0.724379	+	0.944029i
$668$		0			0
$669$	−27.9283	+	21.4302i	−1.07977	+	0.828538i
$670$		0			0
$671$	−39.8061			−1.53670
$672$		0			0
$673$	31.3939			1.21015			0.605074	−	0.796169i	$-0.293144\pi$
$673$	31.3939			1.21015			0.605074	+	0.796169i	$0.293144\pi$
$674$		0			0
$675$	−52.9226	+	40.6090i	−2.03699	+	1.56304i
$676$		0			0
$677$	−4.09639	+	5.33852i	−0.157437	+	0.205176i	−0.865411	−	0.501062i	$-0.832943\pi$
$677$	−4.09639	+	5.33852i	−0.157437	+	0.205176i	0.707974	+	0.706238i	$0.249609\pi$
$678$		0			0
$679$	−1.96107	−	5.46734i	−0.0752589	−	0.209817i
$680$		0			0
$681$	3.06257	−	11.4297i	0.117358	−	0.437986i
$682$		0			0
$683$	1.33222	−	10.1192i	0.0509759	−	0.387200i	−0.946871	−	0.321614i	$-0.895775\pi$
$683$	1.33222	−	10.1192i	0.0509759	−	0.387200i	0.997847	−	0.0655867i	$-0.0208919\pi$
$684$		0			0
$685$	−1.65409	+	3.99331i	−0.0631993	+	0.152577i
$686$		0			0
$687$			21.5357i			0.821640i
$688$		0			0
$689$	1.57117	+	0.907118i	0.0598570	+	0.0345584i
$690$		0			0
$691$	−12.2826	+	1.61704i	−0.467253	+	0.0615150i	−0.360477	−	0.932768i	$-0.617386\pi$
$691$	−12.2826	+	1.61704i	−0.467253	+	0.0615150i	−0.106776	+	0.994283i	$0.534053\pi$
$692$		0			0
$693$	2.42839	−	50.2320i	0.0922469	−	1.90816i
$694$		0			0
$695$	−0.147801	+	0.551602i	−0.00560642	+	0.0209235i
$696$		0			0
$697$	3.42258	+	12.7732i	0.129639	+	0.483820i
$698$		0			0
$699$	11.9570	+	28.8667i	0.452254	+	1.09184i
$700$		0			0
$701$	29.9756	+	12.4163i	1.13216	+	0.468958i	0.868516	−	0.495661i	$-0.165074\pi$
$701$	29.9756	+	12.4163i	1.13216	+	0.468958i	0.263648	+	0.964619i	$0.415074\pi$
$702$		0			0
$703$	−5.07662	+	8.79296i	−0.191468	+	0.331633i
$704$		0			0
$705$	−2.26754	−	3.92749i	−0.0854003	−	0.147918i
$706$		0			0
$707$	−1.53508	−	7.08071i	−0.0577326	−	0.266298i
$708$		0			0
$709$	−5.93322	+	7.73232i	−0.222827	+	0.290393i	−0.891367	−	0.453283i	$-0.850253\pi$
$709$	−5.93322	+	7.73232i	−0.222827	+	0.290393i	0.668540	+	0.743676i	$0.266920\pi$
$710$		0			0
$711$	−13.8452	−	51.6709i	−0.519234	−	1.93781i
$712$		0			0
$713$	25.3982	+	25.3982i	0.951170	+	0.951170i
$714$		0			0
$715$	−0.751967	+	0.311475i	−0.0281220	+	0.0116485i
$716$		0			0
$717$	−37.8069	−	49.2709i	−1.41192	−	1.84005i
$718$		0			0
$719$	−42.6269	+	24.6106i	−1.58971	+	0.917822i	−0.596361	+	0.802717i	$0.703387\pi$
$719$	−42.6269	+	24.6106i	−1.58971	+	0.917822i	−0.993353	+	0.115105i	$0.963279\pi$
$720$		0			0
$721$	−3.11400	−	37.6168i	−0.115971	−	1.40092i
$722$		0			0
$723$	−60.7336	+	7.99573i	−2.25871	+	0.297364i
$724$		0			0
$725$	3.74549	−	28.4498i	0.139104	−	1.05660i
$726$		0			0
$727$	−11.4373	−	11.4373i	−0.424184	−	0.424184i	0.462457	−	0.886642i	$-0.346968\pi$
$727$	−11.4373	−	11.4373i	−0.424184	−	0.424184i	−0.886642	+	0.462457i	$0.846968\pi$
$728$		0			0
$729$	−18.4684	+	18.4684i	−0.684015	+	0.684015i
$730$		0			0
$731$	4.96587	+	0.653770i	0.183669	+	0.0241805i
$732$		0			0
$733$	3.09198	+	23.4859i	0.114205	+	0.867471i	0.948638	+	0.316363i	$0.102462\pi$
$733$	3.09198	+	23.4859i	0.114205	+	0.867471i	−0.834434	+	0.551109i	$0.814205\pi$
$734$		0			0
$735$	−3.68208	−	4.47236i	−0.135816	−	0.164965i
$736$		0			0
$737$	−16.0169	−	27.7422i	−0.589992	−	1.02190i
$738$		0			0
$739$	15.9372	−	12.2290i	0.586258	−	0.449852i	−0.272555	−	0.962140i	$-0.587869\pi$
$739$	15.9372	−	12.2290i	0.586258	−	0.449852i	0.858813	+	0.512289i	$0.171202\pi$
$740$		0			0
$741$	−10.1665	−	24.5442i	−0.373477	−	0.901653i
$742$		0			0
$743$	19.0259	−	19.0259i	0.697991	−	0.697991i	−0.265986	−	0.963977i	$-0.585697\pi$
$743$	19.0259	−	19.0259i	0.697991	−	0.697991i	0.963977	+	0.265986i	$0.0856974\pi$
$744$		0			0
$745$	1.49872	−	0.401581i	0.0549089	−	0.0147128i
$746$		0			0
$747$	72.5557	+	55.6740i	2.65467	+	2.03700i
$748$		0			0
$749$	4.08976	−	12.7628i	0.149437	−	0.466343i
$750$		0			0
$751$	22.6315	−	13.0663i	0.825837	−	0.476797i	−0.0265884	−	0.999646i	$-0.508464\pi$
$751$	22.6315	−	13.0663i	0.825837	−	0.476797i	0.852425	+	0.522849i	$0.175131\pi$
$752$		0			0
$753$	76.0843	+	43.9273i	2.77267	+	1.60080i
$754$		0			0
$755$	0.859150	−	2.07417i	0.0312677	−	0.0754868i
$756$		0			0
$757$	−3.71862	+	1.54030i	−0.135155	+	0.0559832i	−0.449236	−	0.893413i	$-0.648304\pi$
$757$	−3.71862	+	1.54030i	−0.135155	+	0.0559832i	0.314081	+	0.949396i	$0.398304\pi$
$758$		0			0
$759$	−42.9176	+	11.4997i	−1.55781	+	0.417414i
$760$		0			0
$761$	−36.5270	−	9.78737i	−1.32410	−	0.354792i	−0.473589	−	0.880746i	$-0.657042\pi$
$761$	−36.5270	−	9.78737i	−1.32410	−	0.354792i	−0.850513	+	0.525954i	$0.823708\pi$
$762$		0			0
$763$	0.930965	−	1.44636i	0.0337032	−	0.0523619i
$764$		0			0
$765$	−0.402712	−	3.05890i	−0.0145601	−	0.110595i
$766$		0			0
$767$	−3.13008	+	5.42145i	−0.113021	+	0.195757i
$768$		0			0
$769$	−3.99453			−0.144046			−0.0720232	−	0.997403i	$-0.522946\pi$
$769$	−3.99453			−0.144046			−0.0720232	+	0.997403i	$0.522946\pi$
$770$		0			0
$771$	2.00588	+	0.830863i	0.0722400	+	0.0299228i
$772$		0			0
$773$	27.7395	+	3.65198i	0.997722	+	0.131353i	0.611660	−	0.791120i	$-0.290502\pi$
$773$	27.7395	+	3.65198i	0.997722	+	0.131353i	0.386061	+	0.922473i	$0.373835\pi$
$774$		0			0
$775$	−32.3960	−	8.68048i	−1.16370	−	0.311812i
$776$		0			0
$777$	−11.6441	+	4.17660i	−0.417731	+	0.149835i
$778$		0			0
$779$	44.1709	+	33.8935i	1.58259	+	1.21436i
$780$		0			0
$781$	4.18679	+	5.45633i	0.149815	+	0.195243i
$782$		0			0
$783$		−	78.6605i		−	2.81110i
$784$		0			0
$785$		−	1.43051i		−	0.0510572i
$786$		0			0
$787$	4.49639	+	5.85981i	0.160279	+	0.208880i	0.866588	−	0.499024i	$-0.166308\pi$
$787$	4.49639	+	5.85981i	0.160279	+	0.208880i	−0.706309	+	0.707903i	$0.749641\pi$
$788$		0			0
$789$	54.5623	+	41.8671i	1.94247	+	1.49051i
$790$		0			0
$791$	−25.6775	+	9.21019i	−0.912986	+	0.327477i
$792$		0			0
$793$	−17.4886	−	4.68605i	−0.621038	−	0.166407i
$794$		0			0
$795$	1.24453	+	0.163846i	0.0441390	+	0.00581101i
$796$		0			0
$797$	21.3606	+	8.84786i	0.756632	+	0.313407i	0.727444	−	0.686167i	$-0.240708\pi$
$797$	21.3606	+	8.84786i	0.756632	+	0.313407i	0.0291879	+	0.999574i	$0.490708\pi$
$798$		0			0
$799$	−9.03913			−0.319781
$800$		0			0
$801$	22.4194	−	38.8315i	0.792150	−	1.37204i
$802$		0			0
$803$	0.653661	+	4.96505i	0.0230672	+	0.175213i
$804$		0			0
$805$	−1.95763	+	3.04141i	−0.0689973	+	0.107195i
$806$		0			0
$807$	51.6715	+	13.8453i	1.81892	+	0.487379i
$808$		0			0
$809$	−6.85906	+	1.83788i	−0.241152	+	0.0646164i	−0.377370	−	0.926062i	$-0.623172\pi$
$809$	−6.85906	+	1.83788i	−0.241152	+	0.0646164i	0.136219	+	0.990679i	$0.456505\pi$
$810$		0			0
$811$	33.7524	−	13.9807i	1.18521	−	0.490928i	0.299015	−	0.954248i	$-0.403342\pi$
$811$	33.7524	−	13.9807i	1.18521	−	0.490928i	0.886191	+	0.463320i	$0.153342\pi$
$812$		0			0
$813$	27.3125	−	65.9381i	0.957890	−	2.31255i
$814$		0			0
$815$	−0.186798	−	0.107848i	−0.00654326	−	0.00377775i
$816$		0			0
$817$	18.2629	−	10.5441i	0.638939	−	0.368891i
$818$		0			0
$819$	6.98031	−	21.7833i	0.243912	−	0.761169i
$820$		0			0
$821$	−9.04920	−	6.94369i	−0.315819	−	0.242337i	0.438671	−	0.898648i	$-0.355449\pi$
$821$	−9.04920	−	6.94369i	−0.315819	−	0.242337i	−0.754490	+	0.656311i	$0.772116\pi$
$822$		0			0
$823$	10.4144	−	2.79052i	0.363022	−	0.0972715i	−0.0726972	−	0.997354i	$-0.523161\pi$
$823$	10.4144	−	2.79052i	0.363022	−	0.0972715i	0.435719	+	0.900083i	$0.356494\pi$
$824$		0			0
$825$	29.3364	−	29.3364i	1.02136	−	1.02136i
$826$		0			0
$827$	−13.9833	−	33.7587i	−0.486247	−	1.17390i	−0.956594	−	0.291422i	$-0.905871\pi$
$827$	−13.9833	−	33.7587i	−0.486247	−	1.17390i	0.470348	−	0.882481i	$-0.344129\pi$
$828$		0			0
$829$	−1.60583	+	1.23220i	−0.0557729	+	0.0427961i	−0.636272	−	0.771465i	$-0.719524\pi$
$829$	−1.60583	+	1.23220i	−0.0557729	+	0.0427961i	0.580499	+	0.814261i	$0.302858\pi$
$830$		0			0
$831$	−44.7850	−	77.5699i	−1.55357	−	2.69087i
$832$		0			0
$833$	−11.3894	+	1.89868i	−0.394618	+	0.0657854i
$834$		0			0
$835$	0.329005	+	2.49904i	0.0113857	+	0.0864830i
$836$		0			0
$837$	−91.1511	−	12.0003i	−3.15064	−	0.414790i
$838$		0			0
$839$	33.5412	−	33.5412i	1.15797	−	1.15797i	0.173060	−	0.984911i	$-0.444635\pi$
$839$	33.5412	−	33.5412i	1.15797	−	1.15797i	0.984911	−	0.173060i	$-0.0553654\pi$
$840$		0			0
$841$	3.42035	+	3.42035i	0.117943	+	0.117943i
$842$		0			0
$843$	−1.93208	+	14.6756i	−0.0665443	+	0.505454i
$844$		0			0
$845$	2.96816	−	0.390766i	0.102108	−	0.0134428i
$846$		0			0
$847$	−0.891582	−	10.7702i	−0.0306351	−	0.370069i
$848$		0			0
$849$	44.9920	−	25.9761i	1.54412	−	0.891499i
$850$		0			0
$851$	4.70187	+	6.12760i	0.161178	+	0.210051i
$852$		0			0
$853$	−19.5339	+	8.09121i	−0.668829	+	0.277038i	−0.691148	−	0.722713i	$-0.742895\pi$
$853$	−19.5339	+	8.09121i	−0.668829	+	0.277038i	0.0223196	+	0.999751i	$0.492895\pi$
$854$		0			0
$855$	−9.18531	−	9.18531i	−0.314131	−	0.314131i
$856$		0			0
$857$	4.49757	+	16.7852i	0.153634	+	0.573371i	0.999218	+	0.0395287i	$0.0125857\pi$
$857$	4.49757	+	16.7852i	0.153634	+	0.573371i	−0.845584	+	0.533842i	$0.820748\pi$
$858$		0			0
$859$	31.0389	−	40.4506i	1.05903	−	1.38016i	0.138108	−	0.990417i	$-0.455898\pi$
$859$	31.0389	−	40.4506i	1.05903	−	1.38016i	0.920924	−	0.389741i	$-0.127436\pi$
$860$		0			0
$861$	14.3725	+	66.2948i	0.489815	+	2.25932i
$862$		0			0
$863$	−27.4516	−	47.5476i	−0.934464	−	1.61854i	−0.775586	−	0.631242i	$-0.782546\pi$
$863$	−27.4516	−	47.5476i	−0.934464	−	1.61854i	−0.158878	−	0.987298i	$-0.550788\pi$
$864$		0			0
$865$	−2.04336	+	3.53921i	−0.0694764	+	0.120337i
$866$		0			0
$867$	42.1908	+	17.4760i	1.43287	+	0.593516i
$868$		0			0
$869$	7.44758	+	17.9800i	0.252642	+	0.609931i
$870$		0			0
$871$	−3.77109	−	14.0739i	−0.127778	−	0.476876i
$872$		0			0
$873$	4.10712	−	15.3280i	0.139005	−	0.518773i
$874$		0			0
$875$	0.328377	−	6.79258i	0.0111012	−	0.229631i
$876$		0			0
$877$	30.5122	−	4.01701i	1.03032	−	0.135645i	0.403640	−	0.914918i	$-0.367745\pi$
$877$	30.5122	−	4.01701i	1.03032	−	0.135645i	0.626684	+	0.779273i	$0.284412\pi$
$878$		0			0
$879$	21.2544	+	12.2712i	0.716894	+	0.413899i
$880$		0			0
$881$			37.0879i			1.24952i	0.780816	+	0.624761i	$0.214804\pi$
$881$			37.0879i			1.24952i	−0.780816	+	0.624761i	$0.785196\pi$
$882$		0			0
$883$	−10.9392	+	26.4095i	−0.368133	+	0.888751i	0.625924	+	0.779884i	$0.284722\pi$
$883$	−10.9392	+	26.4095i	−0.368133	+	0.888751i	−0.994056	+	0.108867i	$0.965278\pi$
$884$		0			0
$885$	−0.565362	+	4.29435i	−0.0190044	+	0.144353i
$886$		0			0
$887$	−1.69875	+	6.33983i	−0.0570385	+	0.212871i	−0.988563	−	0.150808i	$-0.951813\pi$
$887$	−1.69875	+	6.33983i	−0.0570385	+	0.212871i	0.931525	+	0.363678i	$0.118479\pi$
$888$		0			0
$889$	−13.1332	−	36.6146i	−0.440473	−	1.22801i
$890$		0			0
$891$	34.5189	−	44.9859i	1.15643	−	1.50709i
$892$		0			0
$893$	−30.1930	+	23.1679i	−1.01037	+	0.775283i
$894$		0			0
$895$	5.88430			0.196690
$896$		0			0
$897$	−20.2094			−0.674771
$898$		0			0
$899$	31.3759	−	24.0756i	1.04645	−	0.802966i
$900$		0			0
$901$	1.52310	−	1.98494i	0.0507417	−	0.0661278i
$902$		0			0
$903$	25.2820	+	4.57981i	0.841333	+	0.152407i
$904$		0			0
$905$	0.763366	−	2.84892i	0.0253752	−	0.0947014i
$906$		0			0
$907$	2.90435	−	22.0607i	0.0964374	−	0.732514i	−0.873095	−	0.487550i	$-0.837891\pi$
$907$	2.90435	−	22.0607i	0.0964374	−	0.732514i	0.969532	−	0.244964i	$-0.0787761\pi$
$908$		0			0
$909$	7.57484	−	18.2873i	0.251242	−	0.606551i
$910$		0			0
$911$		−	12.7706i		−	0.423108i	−0.977366	−	0.211554i	$-0.932148\pi$
$911$		−	12.7706i		−	0.423108i	0.977366	−	0.211554i	$-0.0678525\pi$
$912$		0			0
$913$	−28.8144	−	16.6360i	−0.953616	−	0.550571i
$914$		0			0
$915$	−12.4200	+	1.63513i	−0.410594	+	0.0540557i
$916$		0			0
$917$	−13.6075	+	7.00301i	−0.449360	+	0.231260i
$918$		0			0
$919$	11.6857	−	43.6117i	0.385476	−	1.43862i	−0.451939	−	0.892049i	$-0.649268\pi$
$919$	11.6857	−	43.6117i	0.385476	−	1.43862i	0.837415	−	0.546567i	$-0.184066\pi$
$920$		0			0
$921$	−7.84073	−	29.2620i	−0.258361	−	0.964215i
$922$		0			0
$923$	1.19711	+	2.89008i	0.0394034	+	0.0951283i
$924$		0			0
$925$	−6.66298	−	2.75990i	−0.219077	−	0.0907448i
$926$		0			0
$927$	51.5606	−	89.3056i	1.69347	−	2.93318i
$928$		0			0
$929$	2.59982	+	4.50302i	0.0852974	+	0.147739i	0.905518	−	0.424308i	$-0.139483\pi$
$929$	2.59982	+	4.50302i	0.0852974	+	0.147739i	−0.820221	+	0.572047i	$0.806149\pi$
$930$		0			0
$931$	−33.1768	+	35.5337i	−1.08733	+	1.16457i
$932$		0			0
$933$	28.5877	−	37.2562i	0.935918	−	1.21971i
$934$		0			0
$935$	0.290513	+	1.08421i	0.00950080	+	0.0354575i
$936$		0			0
$937$	−16.7827	−	16.7827i	−0.548266	−	0.548266i	0.377673	−	0.925939i	$-0.376724\pi$
$937$	−16.7827	−	16.7827i	−0.548266	−	0.548266i	−0.925939	+	0.377673i	$0.876724\pi$
$938$		0			0
$939$	−36.6960	+	15.2000i	−1.19753	+	0.496032i
$940$		0			0
$941$	23.1839	+	30.2138i	0.755772	+	0.984942i	0.999885	+	0.0151948i	$0.00483685\pi$
$941$	23.1839	+	30.2138i	0.755772	+	0.984942i	−0.244112	+	0.969747i	$0.578496\pi$
$942$		0			0
$943$	36.6791	−	21.1767i	1.19444	−	0.689609i
$944$		0			0
$945$	−0.763789	−	9.22649i	−0.0248461	−	0.300138i
$946$		0			0
$947$	31.2971	−	4.12034i	1.01702	−	0.133893i	0.396459	−	0.918053i	$-0.370239\pi$
$947$	31.2971	−	4.12034i	1.01702	−	0.133893i	0.620559	+	0.784160i	$0.286906\pi$
$948$		0			0
$949$	−0.297313	+	2.25832i	−0.00965118	+	0.0733080i
$950$		0			0
$951$	34.4987	+	34.4987i	1.11870	+	1.11870i
$952$		0			0
$953$	35.3705	−	35.3705i	1.14576	−	1.14576i	0.158386	−	0.987377i	$-0.449371\pi$
$953$	35.3705	−	35.3705i	1.14576	−	1.14576i	0.987377	−	0.158386i	$-0.0506291\pi$
$954$		0			0
$955$	5.23158	+	0.688751i	0.169290	+	0.0222875i
$956$		0			0
$957$	6.38559	+	48.5033i	0.206417	+	1.56789i
$958$		0			0
$959$	25.1788	+	36.3191i	0.813067	+	1.17281i
$960$		0			0
$961$	−7.61192	−	13.1842i	−0.245546	−	0.425298i
$962$		0			0
$963$	29.0484	−	22.2896i	0.936072	−	0.718273i
$964$		0			0
$965$	−0.162517	−	0.392351i	−0.00523161	−	0.0126302i
$966$		0			0
$967$	−20.1833	+	20.1833i	−0.649051	+	0.649051i	−0.952764	−	0.303713i	$-0.901774\pi$
$967$	−20.1833	+	20.1833i	−0.649051	+	0.649051i	0.303713	+	0.952764i	$0.401774\pi$
$968$		0			0
$969$	−35.3886	+	9.48235i	−1.13685	+	0.304617i
$970$		0			0
$971$	−5.49245	−	4.21451i	−0.176261	−	0.135250i	0.516863	−	0.856068i	$-0.327100\pi$
$971$	−5.49245	−	4.21451i	−0.176261	−	0.135250i	−0.693124	+	0.720818i	$0.743766\pi$
$972$		0			0
$973$	3.92445	+	4.32317i	0.125812	+	0.138594i
$974$		0			0
$975$	16.3423	−	9.43522i	0.523372	−	0.302169i
$976$		0			0
$977$	24.1636	+	13.9508i	0.773061	+	0.446327i	0.833966	−	0.551816i	$-0.186065\pi$
$977$	24.1636	+	13.9508i	0.773061	+	0.446327i	−0.0609043	+	0.998144i	$0.519398\pi$
$978$		0			0
$979$	−6.24262	+	15.0710i	−0.199515	+	0.481672i
$980$		0			0
$981$	4.34157	−	1.79834i	0.138616	−	0.0574165i
$982$		0			0
$983$	−37.9275	+	10.1626i	−1.20970	+	0.324138i	−0.806644	−	0.591038i	$-0.798718\pi$
$983$	−37.9275	+	10.1626i	−1.20970	+	0.324138i	−0.403055	+	0.915176i	$0.632052\pi$
$984$		0			0
$985$	−6.15461	−	1.64912i	−0.196102	−	0.0525454i
$986$		0			0
$987$	−46.3144	−	2.23900i	−1.47420	−	0.0712680i
$988$		0			0
$989$	−2.09390	−	15.9048i	−0.0665822	−	0.505742i
$990$		0			0
$991$	−5.33256	+	9.23626i	−0.169394	+	0.293400i	−0.938207	−	0.346074i	$-0.887514\pi$
$991$	−5.33256	+	9.23626i	−0.169394	+	0.293400i	0.768813	+	0.639474i	$0.220848\pi$
$992$		0			0
$993$	−58.3669			−1.85222
$994$		0			0
$995$	0.298113	+	0.123482i	0.00945082	+	0.00391466i
$996$		0			0
$997$	−27.8533	−	3.66695i	−0.882122	−	0.116134i	−0.324162	−	0.946002i	$-0.605082\pi$
$997$	−27.8533	−	3.66695i	−0.882122	−	0.116134i	−0.557960	+	0.829868i	$0.688416\pi$
$998$		0			0
$999$	−19.0960	−	5.11676i	−0.604171	−	0.161887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.1		240
4.3	odd	2		224.2.bd.a.221.9	yes	240
7.2	even	3	inner	896.2.bh.a.849.1		240
28.23	odd	6		224.2.bd.a.93.12	yes	240
32.11	odd	8		224.2.bd.a.53.12	✓	240
32.21	even	8	inner	896.2.bh.a.305.1		240
224.107	odd	24		224.2.bd.a.149.9	yes	240
224.149	even	24	inner	896.2.bh.a.177.1		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.12	✓	240	32.11	odd	8
224.2.bd.a.93.12	yes	240	28.23	odd	6
224.2.bd.a.149.9	yes	240	224.107	odd	24
224.2.bd.a.221.9	yes	240	4.3	odd	2
896.2.bh.a.81.1		240	1.1	even	1	trivial
896.2.bh.a.177.1		240	224.149	even	24	inner
896.2.bh.a.305.1		240	32.21	even	8	inner
896.2.bh.a.849.1		240	7.2	even	3	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.53727 + 1.94692i) q^{3} +(0.157528 - 0.205294i) q^{5} +(-0.893273 - 2.49039i) q^{7} +(1.87081 - 6.98194i) q^{9} +O(q^{10})\)	\(q+(-2.53727 + 1.94692i) q^{3} +(0.157528 - 0.205294i) q^{5} +(-0.893273 - 2.49039i) q^{7} +(1.87081 - 6.98194i) q^{9} +(-0.343245 + 2.60720i) q^{11} +(-0.457727 + 1.10505i) q^{13} +0.827582i q^{15} +(1.42851 + 0.824752i) q^{17} +(6.88548 - 0.906491i) q^{19} +(7.11507 + 4.57968i) q^{21} +(1.36736 - 5.10304i) q^{23} +(1.27676 + 4.76495i) q^{25} +(5.17487 + 12.4933i) q^{27} +(-5.37418 - 2.22606i) q^{29} +(-3.39941 + 5.88794i) q^{31} +(-4.20510 - 7.28345i) q^{33} +(-0.651980 - 0.208923i) q^{35} +(-0.889991 + 1.15986i) q^{37} +(-0.990065 - 3.69497i) q^{39} +(5.66876 + 5.66876i) q^{41} +(2.80536 - 1.16202i) q^{43} +(-1.13865 - 1.48392i) q^{45} +(-4.74574 + 2.73995i) q^{47} +(-5.40413 + 4.44921i) q^{49} +(-5.23025 + 0.688575i) q^{51} +(0.197981 - 1.50382i) q^{53} +(0.481173 + 0.481173i) q^{55} +(-15.7055 + 15.7055i) q^{57} +(5.18904 + 0.683150i) q^{59} +(1.97579 + 15.0076i) q^{61} +(-19.0589 + 1.57774i) q^{63} +(0.154756 + 0.268045i) q^{65} +(-9.66430 + 7.41568i) q^{67} +(6.46584 + 15.6099i) q^{69} +(1.84933 - 1.84933i) q^{71} +(1.83947 - 0.492885i) q^{73} +(-12.5165 - 9.60422i) q^{75} +(6.79957 - 1.47413i) q^{77} +(6.40914 - 3.70032i) q^{79} +(-18.6739 - 10.7814i) q^{81} +(-4.84186 + 11.6893i) q^{83} +(0.394348 - 0.163344i) q^{85} +(17.9697 - 4.81497i) q^{87} +(5.99190 + 1.60553i) q^{89} +(3.16089 + 0.152808i) q^{91} +(-2.83812 - 21.5577i) q^{93} +(0.898559 - 1.55635i) q^{95} +2.19537 q^{97} +(17.5612 + 7.27408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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